Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3900,2,Mod(1357,3900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3900.1357");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3900.r (of order \(4\), 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: | \(31.1416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 780) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3193.14 | ||
Character | \(\chi\) | \(=\) | 3900.3193 |
Dual form | 3900.2.r.b.1357.14 |
$q$-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 \(\left(\mathbb{Z}/3900\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(1301\) | \(1951\) | \(3277\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.16665i | − | 1.57485i | −0.616413 | − | 0.787423i | \(-0.711415\pi\) | ||
0.616413 | − | 0.787423i | \(-0.288585\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.15147 | + | 3.15147i | −0.950205 | + | 0.950205i | −0.998818 | − | 0.0486129i | \(-0.984520\pi\) |
0.0486129 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82867 | − | 3.10741i | −0.507182 | − | 0.861839i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.18610 | + | 4.18610i | 1.01528 | + | 1.01528i | 0.999881 | + | 0.0153976i | \(0.00490140\pi\) |
0.0153976 | + | 0.999881i | \(0.495099\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.37727 | + | 4.37727i | −1.00422 | + | 1.00422i | −0.00422428 | + | 0.999991i | \(0.501345\pi\) |
−0.999991 | + | 0.00422428i | \(0.998655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.94627 | − | 2.94627i | 0.642928 | − | 0.642928i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.31199 | − | 1.31199i | 0.273569 | − | 0.273569i | −0.556966 | − | 0.830535i | \(-0.688035\pi\) |
0.830535 | + | 0.556966i | \(0.188035\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.93181i | 0.730119i | 0.930984 | + | 0.365060i | \(0.118951\pi\) | ||||
−0.930984 | + | 0.365060i | \(0.881049\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84918 | + | 3.84918i | 0.691334 | + | 0.691334i | 0.962525 | − | 0.271192i | \(-0.0874177\pi\) |
−0.271192 | + | 0.962525i | \(0.587418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.45686 | −0.775839 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 8.44004i | − | 1.38753i | −0.720200 | − | 0.693767i | \(-0.755950\pi\) | ||
0.720200 | − | 0.693767i | \(-0.244050\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.904203 | − | 3.49033i | 0.144788 | − | 0.558900i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.55464 | + | 1.55464i | 0.242794 | + | 0.242794i | 0.818005 | − | 0.575211i | \(-0.195080\pi\) |
−0.575211 | + | 0.818005i | \(0.695080\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.11673 | + | 8.11673i | −1.23779 | + | 1.23779i | −0.276887 | + | 0.960903i | \(0.589303\pi\) |
−0.960903 | + | 0.276887i | \(0.910697\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 1.02013i | − | 0.148801i | −0.997228 | − | 0.0744003i | \(-0.976296\pi\) | ||
0.997228 | − | 0.0744003i | \(-0.0237043\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.3610 | −1.48014 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.92004i | 0.828972i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.36494 | + | 1.36494i | 0.187489 | + | 0.187489i | 0.794610 | − | 0.607121i | \(-0.207676\pi\) |
−0.607121 | + | 0.794610i | \(0.707676\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.19040 | −0.819938 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.43740 | − | 1.43740i | −0.187134 | − | 0.187134i | 0.607322 | − | 0.794456i | \(-0.292244\pi\) |
−0.794456 | + | 0.607322i | \(0.792244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.293533 | 0.0375831 | 0.0187915 | − | 0.999823i | \(-0.494018\pi\) | ||||
0.0187915 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.16665 | 0.524949 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.8746 | 1.45071 | 0.725357 | − | 0.688373i | \(-0.241675\pi\) | ||||
0.725357 | + | 0.688373i | \(0.241675\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.85543 | 0.223368 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.3963 | + | 11.3963i | 1.35249 | + | 1.35249i | 0.882866 | + | 0.469625i | \(0.155611\pi\) |
0.469625 | + | 0.882866i | \(0.344389\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.46158 | −0.756271 | −0.378135 | − | 0.925750i | \(-0.623435\pi\) | ||||
−0.378135 | + | 0.925750i | \(0.623435\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 13.1311 | + | 13.1311i | 1.49643 | + | 1.49643i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.32607i | 0.936756i | 0.883528 | + | 0.468378i | \(0.155162\pi\) | ||||
−0.883528 | + | 0.468378i | \(0.844838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.1492i | 1.66285i | 0.555640 | + | 0.831423i | \(0.312473\pi\) | ||||
−0.555640 | + | 0.831423i | \(0.687527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.78021 | + | 2.78021i | −0.298070 | + | 0.298070i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.44206 | + | 6.44206i | 0.682857 | + | 0.682857i | 0.960643 | − | 0.277786i | \(-0.0896005\pi\) |
−0.277786 | + | 0.960643i | \(0.589601\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.9475 | + | 7.61943i | −1.35726 | + | 0.798733i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.44357i | 0.564472i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.9521 | 1.11201 | 0.556007 | − | 0.831178i | \(-0.312333\pi\) | ||||
0.556007 | + | 0.831178i | \(0.312333\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.15147 | − | 3.15147i | −0.316735 | − | 0.316735i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 8.05908i | − | 0.801908i | −0.916098 | − | 0.400954i | \(-0.868679\pi\) | ||
0.916098 | − | 0.400954i | \(-0.131321\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.15942 | + | 4.15942i | −0.409840 | + | 0.409840i | −0.881683 | − | 0.471843i | \(-0.843589\pi\) |
0.471843 | + | 0.881683i | \(0.343589\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.88527 | + | 1.88527i | −0.182256 | + | 0.182256i | −0.792338 | − | 0.610082i | \(-0.791137\pi\) |
0.610082 | + | 0.792338i | \(0.291137\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.25319 | + | 3.25319i | −0.311599 | + | 0.311599i | −0.845529 | − | 0.533930i | \(-0.820715\pi\) |
0.533930 | + | 0.845529i | \(0.320715\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.96801 | − | 5.96801i | 0.566458 | − | 0.566458i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.79437 | − | 7.79437i | −0.733233 | − | 0.733233i | 0.238026 | − | 0.971259i | \(-0.423500\pi\) |
−0.971259 | + | 0.238026i | \(0.923500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.10741 | − | 1.82867i | 0.287280 | − | 0.169061i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 17.4420 | − | 17.4420i | 1.59891 | − | 1.59891i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 8.86356i | − | 0.805778i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.19859i | 0.198240i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.51457 | + | 4.51457i | 0.400604 | + | 0.400604i | 0.878446 | − | 0.477842i | \(-0.158581\pi\) |
−0.477842 | + | 0.878446i | \(0.658581\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.4788 | −1.01065 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.47998 | 0.566158 | 0.283079 | − | 0.959097i | \(-0.408644\pi\) | ||||
0.283079 | + | 0.959097i | \(0.408644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.2386 | + | 18.2386i | 1.58148 | + | 1.58148i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 14.7302i | 1.25848i | 0.777209 | + | 0.629242i | \(0.216635\pi\) | ||||
−0.777209 | + | 0.629242i | \(0.783365\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.19379i | 0.610169i | 0.952325 | + | 0.305085i | \(0.0986848\pi\) | ||||
−0.952325 | + | 0.305085i | \(0.901315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.721338 | − | 0.721338i | 0.0607476 | − | 0.0607476i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 15.5559 | + | 4.02990i | 1.30085 | + | 0.336997i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.32632 | − | 7.32632i | −0.604265 | − | 0.604265i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.19801 | − | 7.19801i | 0.589684 | − | 0.589684i | −0.347862 | − | 0.937546i | \(-0.613092\pi\) |
0.937546 | + | 0.347862i | \(0.113092\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.77767 | − | 6.77767i | 0.551559 | − | 0.551559i | −0.375332 | − | 0.926891i | \(-0.622471\pi\) |
0.926891 | + | 0.375332i | \(0.122471\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.18610 | + | 4.18610i | −0.338426 | + | 0.338426i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4226 | + | 11.4226i | −0.911626 | + | 0.911626i | −0.996400 | − | 0.0847741i | \(-0.972983\pi\) |
0.0847741 | + | 0.996400i | \(0.472983\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.93032i | 0.153084i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.46661 | − | 5.46661i | −0.430829 | − | 0.430829i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.5052 | 1.21446 | 0.607230 | − | 0.794526i | \(-0.292281\pi\) | ||||
0.607230 | + | 0.794526i | \(0.292281\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 10.8047i | − | 0.836092i | −0.908426 | − | 0.418046i | \(-0.862715\pi\) | ||
0.908426 | − | 0.418046i | \(-0.137285\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.31194 | + | 11.3648i | −0.485534 | + | 0.874218i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.37727 | − | 4.37727i | −0.334738 | − | 0.334738i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.61397 | + | 7.61397i | −0.578879 | + | 0.578879i | −0.934594 | − | 0.355715i | \(-0.884237\pi\) |
0.355715 | + | 0.934594i | \(0.384237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.03280i | − | 0.152794i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.2476 | −0.990175 | −0.495087 | − | 0.868843i | \(-0.664864\pi\) | ||||
−0.495087 | + | 0.868843i | \(0.664864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5363i | 1.00614i | 0.864245 | + | 0.503072i | \(0.167797\pi\) | ||||
−0.864245 | + | 0.503072i | \(0.832203\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.207559 | + | 0.207559i | 0.0153432 | + | 0.0153432i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.3848 | −1.92945 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.94627 | + | 2.94627i | 0.214309 | + | 0.214309i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.5256 | −1.70226 | −0.851128 | − | 0.524959i | \(-0.824081\pi\) | ||||
−0.851128 | + | 0.524959i | \(0.824081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.6069 | −0.907466 | −0.453733 | − | 0.891138i | \(-0.649908\pi\) | ||||
−0.453733 | + | 0.891138i | \(0.649908\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.4136 | 0.955681 | 0.477841 | − | 0.878447i | \(-0.341420\pi\) | ||||
0.477841 | + | 0.878447i | \(0.341420\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.5835 | 1.60091 | 0.800453 | − | 0.599396i | \(-0.204592\pi\) | ||||
0.800453 | + | 0.599396i | \(0.204592\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.39661 | + | 8.39661i | 0.592251 | + | 0.592251i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.3825 | 1.14983 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.31199 | + | 1.31199i | 0.0911896 | + | 0.0911896i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 27.5897i | − | 1.90842i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.0590 | −0.830175 | −0.415088 | − | 0.909781i | \(-0.636249\pi\) | ||||
−0.415088 | + | 0.909781i | \(0.636249\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.1168i | 1.10430i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.0382 | − | 16.0382i | 1.08874 | − | 1.08874i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −4.56903 | − | 4.56903i | −0.308746 | − | 0.308746i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.35292 | − | 20.6629i | 0.360076 | − | 1.38994i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 9.25360i | − | 0.619667i | −0.950791 | − | 0.309834i | \(-0.899727\pi\) | ||
0.950791 | − | 0.309834i | \(-0.100273\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 16.0754 | 1.06696 | 0.533481 | − | 0.845812i | \(-0.320884\pi\) | ||||
0.533481 | + | 0.845812i | \(0.320884\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.43244 | − | 5.43244i | −0.358986 | − | 0.358986i | 0.504453 | − | 0.863439i | \(-0.331694\pi\) |
−0.863439 | + | 0.504453i | \(0.831694\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.5702i | 1.22183i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.12524 | − | 1.12524i | 0.0737170 | − | 0.0737170i | −0.669287 | − | 0.743004i | \(-0.733400\pi\) |
0.743004 | + | 0.669287i | \(0.233400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.88742 | + | 5.88742i | −0.382429 | + | 0.382429i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.4781 | + | 12.4781i | −0.807144 | + | 0.807144i | −0.984201 | − | 0.177057i | \(-0.943342\pi\) |
0.177057 | + | 0.984201i | \(0.443342\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.27702 | − | 1.27702i | 0.0822603 | − | 0.0822603i | −0.664779 | − | 0.747040i | \(-0.731474\pi\) |
0.747040 | + | 0.664779i | \(0.231474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.6065 | + | 5.59738i | 1.37479 | + | 0.356153i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −10.7121 | + | 10.7121i | −0.678854 | + | 0.678854i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.6566i | 1.24072i | 0.784319 | + | 0.620358i | \(0.213013\pi\) | ||||
−0.784319 | + | 0.620358i | \(0.786987\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.26940i | 0.519893i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.8698 | − | 20.8698i | −1.30182 | − | 1.30182i | −0.927162 | − | 0.374662i | \(-0.877759\pi\) |
−0.374662 | − | 0.927162i | \(-0.622241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −35.1667 | −2.18515 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.93181 | −0.243373 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.80349 | − | 3.80349i | −0.234533 | − | 0.234533i | 0.580049 | − | 0.814582i | \(-0.303034\pi\) |
−0.814582 | + | 0.580049i | \(0.803034\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.11045i | 0.557551i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 3.31848i | − | 0.202332i | −0.994870 | − | 0.101166i | \(-0.967743\pi\) | ||
0.994870 | − | 0.101166i | \(-0.0322572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.56659 | − | 5.56659i | 0.338146 | − | 0.338146i | −0.517523 | − | 0.855669i | \(-0.673146\pi\) |
0.855669 | + | 0.517523i | \(0.173146\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.5430 | − | 3.76750i | −0.880182 | − | 0.228019i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.00278 | + | 3.00278i | 0.180419 | + | 0.180419i | 0.791539 | − | 0.611119i | \(-0.209280\pi\) |
−0.611119 | + | 0.791539i | \(0.709280\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.84918 | + | 3.84918i | −0.230445 | + | 0.230445i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.34615 | − | 2.34615i | 0.139960 | − | 0.139960i | −0.633656 | − | 0.773615i | \(-0.718446\pi\) |
0.773615 | + | 0.633656i | \(0.218446\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.7918 | + | 16.7918i | −0.998167 | + | 0.998167i | −0.999998 | − | 0.00183106i | \(-0.999417\pi\) |
0.00183106 | + | 0.999998i | \(0.499417\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.47764 | − | 6.47764i | 0.382363 | − | 0.382363i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.0469i | 1.06158i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.74428 | + | 7.74428i | 0.453978 | + | 0.453978i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −10.6729 | −0.623516 | −0.311758 | − | 0.950162i | \(-0.600918\pi\) | ||||
−0.311758 | + | 0.950162i | \(0.600918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 4.45686i | − | 0.258613i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.47608 | − | 1.67769i | −0.374522 | − | 0.0970233i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.8196 | + | 33.8196i | 1.94933 | + | 1.94933i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.69863 | − | 5.69863i | 0.327378 | − | 0.327378i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.95047i | 0.567903i | 0.958839 | + | 0.283952i | \(0.0916455\pi\) | ||||
−0.958839 | + | 0.283952i | \(0.908355\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.88231 | −0.334633 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 5.16651i | − | 0.292966i | −0.989213 | − | 0.146483i | \(-0.953205\pi\) | ||
0.989213 | − | 0.146483i | \(-0.0467954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.76718 | − | 2.76718i | −0.156410 | − | 0.156410i | 0.624564 | − | 0.780974i | \(-0.285277\pi\) |
−0.780974 | + | 0.624564i | \(0.785277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −29.1994 | −1.64000 | −0.820000 | − | 0.572363i | \(-0.806027\pi\) | ||||
−0.820000 | + | 0.572363i | \(0.806027\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.3910 | − | 12.3910i | −0.693763 | − | 0.693763i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.66618 | −0.148812 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −36.6474 | −2.03912 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4.60071 | −0.254420 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.25051 | −0.234338 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.69091 | − | 8.69091i | −0.477696 | − | 0.477696i | 0.426698 | − | 0.904394i | \(-0.359677\pi\) |
−0.904394 | + | 0.426698i | \(0.859677\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 8.44004 | 0.462511 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.49283 | + | 7.49283i | 0.408161 | + | 0.408161i | 0.881097 | − | 0.472936i | \(-0.156806\pi\) |
−0.472936 | + | 0.881097i | \(0.656806\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 11.0229i | − | 0.598682i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −24.2612 | −1.31382 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.0040i | 0.756147i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.92612 | − | 9.92612i | 0.532862 | − | 0.532862i | −0.388561 | − | 0.921423i | \(-0.627028\pi\) |
0.921423 | + | 0.388561i | \(0.127028\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.52765 | + | 7.52765i | 0.402946 | + | 0.402946i | 0.879270 | − | 0.476324i | \(-0.158031\pi\) |
−0.476324 | + | 0.879270i | \(0.658031\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.49033 | + | 0.904203i | 0.186300 | + | 0.0482628i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.33990i | 0.390664i | 0.980737 | + | 0.195332i | \(0.0625784\pi\) | ||||
−0.980737 | + | 0.195332i | \(0.937422\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 24.6668 | 1.30550 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.1816 | + | 24.1816i | 1.27626 | + | 1.27626i | 0.942747 | + | 0.333509i | \(0.108233\pi\) |
0.333509 | + | 0.942747i | \(0.391767\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 19.3210i | − | 1.01690i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.26749 | − | 6.26749i | 0.328958 | − | 0.328958i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −17.7690 | + | 17.7690i | −0.927537 | + | 0.927537i | −0.997546 | − | 0.0700097i | \(-0.977697\pi\) |
0.0700097 | + | 0.997546i | \(0.477697\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.55464 | + | 1.55464i | −0.0809313 | + | 0.0809313i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.68722 | − | 5.68722i | 0.295266 | − | 0.295266i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.42778 | + | 3.42778i | 0.177484 | + | 0.177484i | 0.790258 | − | 0.612774i | \(-0.209946\pi\) |
−0.612774 | + | 0.790258i | \(0.709946\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.2177 | − | 7.18999i | 0.629245 | − | 0.370303i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.32325 | − | 6.32325i | 0.324804 | − | 0.324804i | −0.525803 | − | 0.850606i | \(-0.676235\pi\) |
0.850606 | + | 0.525803i | \(0.176235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.38457i | 0.327092i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 24.6950i | − | 1.26186i | −0.775841 | − | 0.630928i | \(-0.782674\pi\) | ||
0.775841 | − | 0.630928i | \(-0.217326\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −8.11673 | − | 8.11673i | −0.412596 | − | 0.412596i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.4062 | −1.38955 | −0.694775 | − | 0.719228i | \(-0.744496\pi\) | ||||
−0.694775 | + | 0.719228i | \(0.744496\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.9843 | 0.555498 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.58204 | + | 4.58204i | 0.231133 | + | 0.231133i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 39.1875i | − | 1.96676i | −0.181554 | − | 0.983381i | \(-0.558113\pi\) | ||
0.181554 | − | 0.983381i | \(-0.441887\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.7932i | 1.29128i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.9890 | − | 21.9890i | 1.09808 | − | 1.09808i | 0.103441 | − | 0.994636i | \(-0.467015\pi\) |
0.994636 | − | 0.103441i | \(-0.0329854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.92209 | − | 18.9999i | 0.245187 | − | 0.946450i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 26.5985 | + | 26.5985i | 1.31844 | + | 1.31844i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.71373 | + | 2.71373i | −0.134185 | + | 0.134185i | −0.771009 | − | 0.636824i | \(-0.780248\pi\) |
0.636824 | + | 0.771009i | \(0.280248\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −10.4158 | + | 10.4158i | −0.513774 | + | 0.513774i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.98916 | + | 5.98916i | −0.294707 | + | 0.294707i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.08678 | + | 5.08678i | −0.249101 | + | 0.249101i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 34.1751i | 1.66956i | 0.550583 | + | 0.834780i | \(0.314405\pi\) | ||||
−0.550583 | + | 0.834780i | \(0.685595\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.5333 | + | 15.5333i | 0.757049 | + | 0.757049i | 0.975784 | − | 0.218736i | \(-0.0701932\pi\) |
−0.218736 | + | 0.975784i | \(0.570193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.02013 | 0.0496002 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.22305i | − | 0.0591875i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.15012 | + | 13.8493i | 0.393491 | + | 0.668648i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.4717 | − | 26.4717i | −1.27510 | − | 1.27510i | −0.943377 | − | 0.331722i | \(-0.892371\pi\) |
−0.331722 | − | 0.943377i | \(-0.607629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0961 | − | 26.0961i | 1.25410 | − | 1.25410i | 0.300232 | − | 0.953866i | \(-0.402936\pi\) |
0.953866 | − | 0.300232i | \(-0.0970641\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.4859i | 0.549444i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.5133 | −0.597226 | −0.298613 | − | 0.954374i | \(-0.596524\pi\) | ||||
−0.298613 | + | 0.954374i | \(0.596524\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 10.3610i | − | 0.493380i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.48719 | + | 1.48719i | 0.0706585 | + | 0.0706585i | 0.741553 | − | 0.670894i | \(-0.234090\pi\) |
−0.670894 | + | 0.741553i | \(0.734090\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.1795 | 0.481475 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 11.5904 | + | 11.5904i | 0.546986 | + | 0.546986i | 0.925568 | − | 0.378582i | \(-0.123588\pi\) |
−0.378582 | + | 0.925568i | \(0.623588\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.79880 | −0.461408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.58507 | 0.450346 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.6269 | −1.61978 | −0.809888 | − | 0.586584i | \(-0.800472\pi\) | ||||
−0.809888 | + | 0.586584i | \(0.800472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.92004 | −0.276324 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −18.8332 | − | 18.8332i | −0.877149 | − | 0.877149i | 0.116090 | − | 0.993239i | \(-0.462964\pi\) |
−0.993239 | + | 0.116090i | \(0.962964\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −13.5047 | −0.627615 | −0.313808 | − | 0.949487i | \(-0.601605\pi\) | ||||
−0.313808 | + | 0.949487i | \(0.601605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.20739 | + | 7.20739i | 0.333518 | + | 0.333518i | 0.853921 | − | 0.520403i | \(-0.174218\pi\) |
−0.520403 | + | 0.853921i | \(0.674218\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 49.4773i | − | 2.28465i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −16.1541 | −0.744340 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 51.1593i | − | 2.35231i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.36494 | + | 1.36494i | −0.0624963 | + | 0.0624963i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.3993 | + | 12.3993i | 0.566537 | + | 0.566537i | 0.931157 | − | 0.364620i | \(-0.118801\pi\) |
−0.364620 | + | 0.931157i | \(0.618801\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −26.2266 | + | 15.4340i | −1.19583 | + | 0.703731i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7.73095i | − | 0.351770i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −32.1455 | −1.45665 | −0.728326 | − | 0.685230i | \(-0.759702\pi\) | ||||
−0.728326 | + | 0.685230i | \(0.759702\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.9638 | + | 10.9638i | 0.495801 | + | 0.495801i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.73137i | 0.168395i | 0.996449 | + | 0.0841973i | \(0.0268326\pi\) | ||||
−0.996449 | + | 0.0841973i | \(0.973167\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.4590 | + | 16.4590i | −0.741275 | + | 0.741275i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 47.4844 | − | 47.4844i | 2.12997 | − | 2.12997i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.85645 | − | 5.85645i | 0.262171 | − | 0.262171i | −0.563765 | − | 0.825936i | \(-0.690647\pi\) |
0.825936 | + | 0.563765i | \(0.190647\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.64007 | − | 7.64007i | 0.341333 | − | 0.341333i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 21.0951 | + | 21.0951i | 0.940586 | + | 0.940586i | 0.998331 | − | 0.0577458i | \(-0.0183913\pi\) |
−0.0577458 | + | 0.998331i | \(0.518391\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.4994 | + | 3.57294i | −0.555116 | + | 0.158680i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 23.2392 | − | 23.2392i | 1.03006 | − | 1.03006i | 0.0305246 | − | 0.999534i | \(-0.490282\pi\) |
0.999534 | − | 0.0305246i | \(-0.00971780\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 26.9231i | 1.19101i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 6.19040i | − | 0.273313i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.21490 | + | 3.21490i | 0.141391 | + | 0.141391i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.7678 | −0.472653 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.5024 | 0.942038 | 0.471019 | − | 0.882123i | \(-0.343886\pi\) | ||||
0.471019 | + | 0.882123i | \(0.343886\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0736 | − | 14.0736i | −0.615395 | − | 0.615395i | 0.328952 | − | 0.944347i | \(-0.393305\pi\) |
−0.944347 | + | 0.328952i | \(0.893305\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.2262i | 1.40379i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.5574i | 0.850320i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.43740 | − | 1.43740i | 0.0623780 | − | 0.0623780i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.98797 | − | 7.67381i | 0.0861087 | − | 0.332390i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −9.36749 | − | 9.36749i | −0.404237 | − | 0.404237i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.6523 | − | 32.6523i | 1.40644 | − | 1.40644i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.4516 | − | 11.4516i | 0.492344 | − | 0.492344i | −0.416700 | − | 0.909044i | \(-0.636813\pi\) |
0.909044 | + | 0.416700i | \(0.136813\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −9.57160 | + | 9.57160i | −0.410756 | + | 0.410756i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.7429 | + | 16.7429i | −0.715874 | + | 0.715874i | −0.967757 | − | 0.251884i | \(-0.918950\pi\) |
0.251884 | + | 0.967757i | \(0.418950\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.293533i | 0.0125277i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −17.2106 | − | 17.2106i | −0.733197 | − | 0.733197i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34.6918 | 1.47525 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 38.6119i | − | 1.63604i | −0.575189 | − | 0.818020i | \(-0.695072\pi\) | ||
0.575189 | − | 0.818020i | \(-0.304928\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 40.0648 | + | 10.3792i | 1.69456 | + | 0.438991i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −18.6569 | − | 18.6569i | −0.787693 | − | 0.787693i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.62289 | + | 9.62289i | −0.405556 | + | 0.405556i | −0.880186 | − | 0.474629i | \(-0.842582\pi\) |
0.474629 | + | 0.880186i | \(0.342582\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.16665i | 0.174983i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.7899 | 0.997326 | 0.498663 | − | 0.866796i | \(-0.333825\pi\) | ||||
0.498663 | + | 0.866796i | \(0.333825\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.2205i | 0.469562i | 0.972048 | + | 0.234781i | \(0.0754373\pi\) | ||||
−0.972048 | + | 0.234781i | \(0.924563\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.6351 | − | 16.6351i | −0.694943 | − | 0.694943i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −40.0865 | −1.66882 | −0.834411 | − | 0.551143i | \(-0.814192\pi\) | ||||
−0.834411 | + | 0.551143i | \(0.814192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.91444 | − | 8.91444i | −0.370471 | − | 0.370471i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 63.1216 | 2.61873 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.60314 | −0.356305 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.7208 | −0.483770 | −0.241885 | − | 0.970305i | \(-0.577766\pi\) | ||||
−0.241885 | + | 0.970305i | \(0.577766\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −33.6979 | −1.38850 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.48487 | + | 9.48487i | 0.390155 | + | 0.390155i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.4834 | 0.635826 | 0.317913 | − | 0.948120i | \(-0.397018\pi\) | ||||
0.317913 | + | 0.948120i | \(0.397018\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.9690 | + | 15.9690i | 0.653567 | + | 0.653567i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.5127i | − | 0.552115i | −0.961141 | − | 0.276058i | \(-0.910972\pi\) | ||
0.961141 | − | 0.276058i | \(-0.0890280\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 27.4625 | 1.12022 | 0.560108 | − | 0.828419i | \(-0.310759\pi\) | ||||
0.560108 | + | 0.828419i | \(0.310759\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.8746i | 0.483571i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.34983 | + | 9.34983i | −0.379498 | + | 0.379498i | −0.870921 | − | 0.491423i | \(-0.836477\pi\) |
0.491423 | + | 0.870921i | \(0.336477\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.5842 | + | 11.5842i | 0.469414 | + | 0.469414i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.16994 | + | 1.86547i | −0.128242 | + | 0.0754689i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 16.7293i | − | 0.675690i | −0.941202 | − | 0.337845i | \(-0.890302\pi\) | ||
0.941202 | − | 0.337845i | \(-0.109698\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.3846 | 1.34401 | 0.672007 | − | 0.740544i | \(-0.265432\pi\) | ||||
0.672007 | + | 0.740544i | \(0.265432\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.9465 | + | 12.9465i | 0.520365 | + | 0.520365i | 0.917682 | − | 0.397316i | \(-0.130058\pi\) |
−0.397316 | + | 0.917682i | \(0.630058\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.85543i | 0.0744560i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.8418 | − | 26.8418i | 1.07540 | − | 1.07540i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.5089 | − | 19.5089i | 0.779109 | − | 0.779109i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35.3309 | − | 35.3309i | 1.40873 | − | 1.40873i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.0903 | − | 29.0903i | 1.15807 | − | 1.15807i | 0.173174 | − | 0.984891i | \(-0.444598\pi\) |
0.984891 | − | 0.173174i | \(-0.0554024\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.52700 | − | 8.52700i | −0.338918 | − | 0.338918i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.9468 | + | 32.1958i | 0.750700 | + | 1.27564i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.3963 | + | 11.3963i | −0.450830 | + | 0.450830i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.5037i | 1.08633i | 0.839626 | + | 0.543165i | \(0.182774\pi\) | ||||
−0.839626 | + | 0.543165i | \(0.817226\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.97198i | − | 0.156640i | −0.996928 | − | 0.0783198i | \(-0.975044\pi\) | ||
0.996928 | − | 0.0783198i | \(-0.0249555\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.2989 | + | 24.2989i | 0.955290 | + | 0.955290i | 0.999042 | − | 0.0437527i | \(-0.0139314\pi\) |
−0.0437527 | + | 0.999042i | \(0.513931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.05987 | 0.355631 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 22.6814 | 0.888956 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.39282 | + | 6.39282i | 0.250170 | + | 0.250170i | 0.821040 | − | 0.570870i | \(-0.193394\pi\) |
−0.570870 | + | 0.821040i | \(0.693394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 6.46158i | − | 0.252090i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11.4763i | − | 0.447052i | −0.974698 | − | 0.223526i | \(-0.928243\pi\) | ||
0.974698 | − | 0.223526i | \(-0.0717567\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.3374 | + | 19.3374i | −0.752139 | + | 0.752139i | −0.974878 | − | 0.222739i | \(-0.928500\pi\) |
0.222739 | + | 0.974878i | \(0.428500\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 18.3960 | − | 10.8258i | 0.714440 | − | 0.420439i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.15850 | + | 5.15850i | 0.199738 | + | 0.199738i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.54329 | − | 6.54329i | 0.252978 | − | 0.252978i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.925062 | + | 0.925062i | −0.0357116 | + | 0.0357116i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.06351 | + | 6.06351i | −0.233731 | + | 0.233731i | −0.814248 | − | 0.580517i | \(-0.802850\pi\) |
0.580517 | + | 0.814248i | \(0.302850\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.6902 | − | 10.6902i | 0.410859 | − | 0.410859i | −0.471179 | − | 0.882038i | \(-0.656171\pi\) |
0.882038 | + | 0.471179i | \(0.156171\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 45.6334i | − | 1.75125i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.3670 | + | 11.3670i | 0.435585 | + | 0.435585i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.96421 | 0.0751586 | 0.0375793 | − | 0.999294i | \(-0.488035\pi\) | ||||
0.0375793 | + | 0.999294i | \(0.488035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 7.68263i | − | 0.293111i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.74540 | − | 6.73744i | 0.0664943 | − | 0.256676i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.0749 | − | 29.0749i | −1.10606 | − | 1.10606i | −0.993663 | − | 0.112400i | \(-0.964146\pi\) |
−0.112400 | − | 0.993663i | \(-0.535854\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −13.1311 | + | 13.1311i | −0.498809 | + | 0.498809i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.0158i | 0.493007i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.59133 | 0.0601897 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31.8458i | − | 1.20280i | −0.798949 | − | 0.601399i | \(-0.794610\pi\) | ||
0.798949 | − | 0.601399i | \(-0.205390\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 36.9443 | + | 36.9443i | 1.39338 | + | 1.39338i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.5794 | −1.26288 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4104 | − | 20.4104i | −0.766528 | − | 0.766528i | 0.210966 | − | 0.977493i | \(-0.432339\pi\) |
−0.977493 | + | 0.210966i | \(0.932339\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.32607 | −0.312252 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 10.1002 | 0.378255 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.6468 | −0.659030 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.3675 | 1.16981 | 0.584905 | − | 0.811102i | \(-0.301132\pi\) | ||||
0.584905 | + | 0.811102i | \(0.301132\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 17.3309 | + | 17.3309i | 0.645435 | + | 0.645435i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.80598 | 0.0671652 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.3838 | − | 13.3838i | −0.496379 | − | 0.496379i | 0.413930 | − | 0.910309i | \(-0.364156\pi\) |
−0.910309 | + | 0.413930i | \(0.864156\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −67.9549 | −2.51340 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.1954i | 0.856740i | 0.903603 | + | 0.428370i | \(0.140912\pi\) | ||||
−0.903603 | + | 0.428370i | \(0.859088\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −37.4225 | + | 37.4225i | −1.37847 | + | 1.37847i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.46527 | − | 3.46527i | −0.127472 | − | 0.127472i | 0.640492 | − | 0.767965i | \(-0.278730\pi\) |
−0.767965 | + | 0.640492i | \(0.778730\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 11.3202 | + | 19.2361i | 0.415858 | + | 0.706655i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.29558i | 0.0475301i | 0.999718 | + | 0.0237650i | \(0.00756536\pi\) | ||||
−0.999718 | + | 0.0237650i | \(0.992435\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −15.1492 | −0.554282 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.85528 | + | 7.85528i | 0.287026 | + | 0.287026i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.38749i | 0.0506301i | 0.999680 | + | 0.0253150i | \(0.00805889\pi\) | ||||
−0.999680 | + | 0.0253150i | \(0.991941\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.8993 | + | 13.8993i | −0.506520 | + | 0.506520i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.11127 | − | 9.11127i | 0.331155 | − | 0.331155i | −0.521870 | − | 0.853025i | \(-0.674765\pi\) |
0.853025 | + | 0.521870i | \(0.174765\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.84735 | + | 5.84735i | −0.212245 | + | 0.212245i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.8539 | + | 19.8539i | −0.719703 | + | 0.719703i | −0.968544 | − | 0.248841i | \(-0.919950\pi\) |
0.248841 | + | 0.968544i | \(0.419950\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.5549 | + | 13.5549i | 0.490721 | + | 0.490721i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.83806 | + | 7.09513i | −0.0663685 | + | 0.256190i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 22.6182 | − | 22.6182i | 0.815634 | − | 0.815634i | −0.169838 | − | 0.985472i | \(-0.554324\pi\) |
0.985472 | + | 0.169838i | \(0.0543243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 29.5144i | − | 1.06293i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 20.5557i | 0.739336i | 0.929164 | + | 0.369668i | \(0.120529\pi\) | ||||
−0.929164 | + | 0.369668i | \(0.879471\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −24.8666 | − | 24.8666i | −0.892084 | − | 0.892084i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −13.6102 | −0.487634 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.8302 | −2.57029 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.78021 | − | 2.78021i | −0.0993567 | − | 0.0993567i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 13.3191i | − | 0.474774i | −0.971415 | − | 0.237387i | \(-0.923709\pi\) | ||
0.971415 | − | 0.237387i | \(-0.0762909\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 5.37895i | − | 0.191496i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.4764 | + | 32.4764i | −1.15473 | + | 1.15473i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.536775 | − | 0.912126i | −0.0190614 | − | 0.0323906i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.3474 | − | 20.3474i | −0.720743 | − | 0.720743i | 0.248014 | − | 0.968757i | \(-0.420222\pi\) |
−0.968757 | + | 0.248014i | \(0.920222\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.27035 | − | 4.27035i | 0.151074 | − | 0.151074i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.44206 | + | 6.44206i | −0.227619 | + | 0.227619i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.3635 | − | 20.3635i | 0.718612 | − | 0.718612i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.34652 | − | 2.34652i | 0.0826015 | − | 0.0826015i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 42.5767i | − | 1.49692i | −0.663182 | − | 0.748458i | \(-0.730795\pi\) | ||
0.663182 | − | 0.748458i | \(-0.269205\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.7142 | + | 22.7142i | 0.797603 | + | 0.797603i | 0.982717 | − | 0.185114i | \(-0.0592655\pi\) |
−0.185114 | + | 0.982717i | \(0.559265\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.87235 | 0.276095 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 71.0583i | − | 2.48601i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.61943 | − | 12.9475i | −0.266244 | − | 0.452421i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.60013 | + | 7.60013i | 0.265246 | + | 0.265246i | 0.827181 | − | 0.561935i | \(-0.189943\pi\) |
−0.561935 | + | 0.827181i | \(0.689943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −25.4074 | + | 25.4074i | −0.885648 | + | 0.885648i | −0.994101 | − | 0.108454i | \(-0.965410\pi\) |
0.108454 | + | 0.994101i | \(0.465410\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.7770i | 1.31363i | 0.754050 | + | 0.656817i | \(0.228098\pi\) | ||||
−0.754050 | + | 0.656817i | \(0.771902\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −32.0493 | −1.11312 | −0.556559 | − | 0.830808i | \(-0.687878\pi\) | ||||
−0.556559 | + | 0.830808i | \(0.687878\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.24657i | 0.147312i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −43.3721 | − | 43.3721i | −1.50276 | − | 1.50276i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.44357 | −0.188157 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.17521 | − | 9.17521i | −0.316763 | − | 0.316763i | 0.530759 | − | 0.847523i | \(-0.321907\pi\) |
−0.847523 | + | 0.530759i | \(0.821907\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.5408 | 0.466926 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.31796 | 0.114277 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −36.9314 | −1.26898 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.7472 | −0.815000 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.0732 | − | 11.0732i | −0.379586 | − | 0.379586i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.1821 | −0.862220 | −0.431110 | − | 0.902299i | \(-0.641878\pi\) | ||||
−0.431110 | + | 0.902299i | \(0.641878\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.17990 | + | 7.17990i | 0.245261 | + | 0.245261i | 0.819022 | − | 0.573762i | \(-0.194516\pi\) |
−0.573762 | + | 0.819022i | \(0.694516\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 44.4341i | 1.51607i | 0.652213 | + | 0.758036i | \(0.273841\pi\) | ||||
−0.652213 | + | 0.758036i | \(0.726159\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.16076 | 0.312198 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 21.1546i | − | 0.720111i | −0.932931 | − | 0.360055i | \(-0.882758\pi\) | ||
0.932931 | − | 0.360055i | \(-0.117242\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −12.7611 | + | 12.7611i | −0.433389 | + | 0.433389i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −26.2394 | − | 26.2394i | −0.890111 | − | 0.890111i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −21.7147 | − | 36.8992i | −0.735775 | − | 1.25028i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.9521i | 0.370671i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.6352 | −1.30462 | −0.652309 | − | 0.757953i | \(-0.726200\pi\) | ||||
−0.652309 | + | 0.757953i | \(0.726200\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −7.54686 | − | 7.54686i | −0.254549 | − | 0.254549i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4550i | 0.588072i | 0.955794 | + | 0.294036i | \(0.0949986\pi\) | ||||
−0.955794 | + | 0.294036i | \(0.905001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 22.8569 | − | 22.8569i | 0.769196 | − | 0.769196i | −0.208769 | − | 0.977965i | \(-0.566946\pi\) |
0.977965 | + | 0.208769i | \(0.0669457\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −12.6394 | + | 12.6394i | −0.424390 | + | 0.424390i | −0.886712 | − | 0.462322i | \(-0.847016\pi\) |
0.462322 | + | 0.886712i | \(0.347016\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.8107 | − | 18.8107i | 0.630889 | − | 0.630889i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.15147 | − | 3.15147i | 0.105578 | − | 0.105578i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.46537 | + | 4.46537i | 0.149428 | + | 0.149428i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.39298 | − | 5.76559i | −0.113288 | − | 0.192507i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −15.1343 | + | 15.1343i | −0.504756 | + | 0.504756i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.4275i | 0.380707i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 47.8281i | 1.59162i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.4274 | + | 16.4274i | 0.545462 | + | 0.545462i | 0.925125 | − | 0.379663i | \(-0.123960\pi\) |
−0.379663 | + | 0.925125i | \(0.623960\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 8.05908 | 0.267303 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.40393 | −0.0796456 | −0.0398228 | − | 0.999207i | \(-0.512679\pi\) | ||||
−0.0398228 | + | 0.999207i | \(0.512679\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −47.7424 | − | 47.7424i | −1.58004 | − | 1.58004i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 26.9998i | − | 0.891612i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.76783i | − | 0.256237i | −0.991759 | − | 0.128118i | \(-0.959106\pi\) | ||
0.991759 | − | 0.128118i | \(-0.0408938\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.03604 | + | 7.03604i | −0.231845 | + | 0.231845i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.5729 | − | 56.2530i | 0.479671 | − | 1.85159i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.15942 | − | 4.15942i | −0.136613 | − | 0.136613i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.0133 | − | 17.0133i | 0.558189 | − | 0.558189i | −0.370602 | − | 0.928792i | \(-0.620849\pi\) |
0.928792 | + | 0.370602i | \(0.120849\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 45.3528 | − | 45.3528i | 1.48638 | − | 1.48638i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.65328 | − | 3.65328i | 0.119603 | − | 0.119603i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.62978 | + | 6.62978i | −0.216586 | + | 0.216586i | −0.807058 | − | 0.590472i | \(-0.798941\pi\) |
0.590472 | + | 0.807058i | \(0.298941\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.91338i | − | 0.127708i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.5888 | − | 23.5888i | −0.768973 | − | 0.768973i | 0.208953 | − | 0.977926i | \(-0.432994\pi\) |
−0.977926 | + | 0.208953i | \(0.932994\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.07934 | 0.132842 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.31026i | 0.205056i | 0.994730 | + | 0.102528i | \(0.0326931\pi\) | ||||
−0.994730 | + | 0.102528i | \(0.967307\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 11.8161 | + | 20.0787i | 0.383567 | + | 0.651784i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20.6471 | − | 20.6471i | −0.669527 | − | 0.669527i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.37109 | − | 4.37109i | 0.141594 | − | 0.141594i | −0.632757 | − | 0.774350i | \(-0.718077\pi\) |
0.774350 | + | 0.632757i | \(0.218077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.5235i | − | 0.566455i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 61.3755 | 1.98192 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 1.36757i | − | 0.0441152i | ||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.88527 | − | 1.88527i | −0.0607521 | − | 0.0607521i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.7361 | 1.27783 | 0.638914 | − | 0.769278i | \(-0.279384\pi\) | ||||
0.638914 | + | 0.769278i | \(0.279384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −25.9136 | − | 25.9136i | −0.832466 | − | 0.832466i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.5420 | 1.01223 | 0.506115 | − | 0.862466i | \(-0.331081\pi\) | ||||
0.506115 | + | 0.862466i | \(0.331081\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.9740 | 0.960923 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.9665 | 1.27864 | 0.639322 | − | 0.768940i | \(-0.279215\pi\) | ||||
0.639322 | + | 0.768940i | \(0.279215\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.6040 | −1.29771 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.25319 | − | 3.25319i | −0.103866 | − | 0.103866i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23.4700 | 0.748577 | 0.374289 | − | 0.927312i | \(-0.377887\pi\) | ||||
0.374289 | + | 0.927312i | \(0.377887\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.00556 | − | 3.00556i | −0.0956681 | − | 0.0956681i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.2981i | 0.677241i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33.6588 | 1.06921 | 0.534604 | − | 0.845103i | \(-0.320461\pi\) | ||||
0.534604 | + | 0.845103i | \(0.320461\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 12.2908i | − | 0.390037i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.7331 | − | 16.7331i | 0.529943 | − | 0.529943i | −0.390613 | − | 0.920555i | \(-0.627737\pi\) |
0.920555 | + | 0.390613i | \(0.127737\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.96801 | + | 5.96801i | 0.188819 | + | 0.188819i |
(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 | 3900.2.r.b.3193.14 | 28 | ||
5.2 | odd | 4 | 3900.2.bm.b.2257.14 | 28 | |||
5.3 | odd | 4 | 780.2.bm.a.697.2 | yes | 28 | ||
5.4 | even | 2 | 780.2.r.a.73.5 | ✓ | 28 | ||
13.5 | odd | 4 | 3900.2.bm.b.2293.14 | 28 | |||
15.8 | even | 4 | 2340.2.bp.i.1477.13 | 28 | |||
15.14 | odd | 2 | 2340.2.u.i.73.6 | 28 | |||
65.18 | even | 4 | 780.2.r.a.577.5 | yes | 28 | ||
65.44 | odd | 4 | 780.2.bm.a.733.2 | yes | 28 | ||
65.57 | even | 4 | inner | 3900.2.r.b.1357.14 | 28 | ||
195.44 | even | 4 | 2340.2.bp.i.1513.13 | 28 | |||
195.83 | odd | 4 | 2340.2.u.i.577.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
780.2.r.a.73.5 | ✓ | 28 | 5.4 | even | 2 | ||
780.2.r.a.577.5 | yes | 28 | 65.18 | even | 4 | ||
780.2.bm.a.697.2 | yes | 28 | 5.3 | odd | 4 | ||
780.2.bm.a.733.2 | yes | 28 | 65.44 | odd | 4 | ||
2340.2.u.i.73.6 | 28 | 15.14 | odd | 2 | |||
2340.2.u.i.577.6 | 28 | 195.83 | odd | 4 | |||
2340.2.bp.i.1477.13 | 28 | 15.8 | even | 4 | |||
2340.2.bp.i.1513.13 | 28 | 195.44 | even | 4 | |||
3900.2.r.b.1357.14 | 28 | 65.57 | even | 4 | inner | ||
3900.2.r.b.3193.14 | 28 | 1.1 | even | 1 | trivial | ||
3900.2.bm.b.2257.14 | 28 | 5.2 | odd | 4 | |||
3900.2.bm.b.2293.14 | 28 | 13.5 | odd | 4 |