Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(401,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.401");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 401.4 | ||
Root | \(-1.58114 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 804.401 |
Dual form | 804.2.g.b.401.3 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.58114 | + | 0.707107i | 0.912871 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.16228 | −1.41421 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.41421i | − | 0.534522i | −0.963624 | − | 0.267261i | \(-0.913881\pi\) | ||
0.963624 | − | 0.267261i | \(-0.0861187\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | + | 2.23607i | 0.666667 | + | 0.745356i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.16228 | −0.953463 | −0.476731 | − | 0.879049i | \(-0.658179\pi\) | ||||
−0.476731 | + | 0.879049i | \(0.658179\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264i | 1.17670i | 0.808608 | + | 0.588348i | \(0.200222\pi\) | ||||
−0.808608 | + | 0.588348i | \(0.799778\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.00000 | − | 2.23607i | −1.29099 | − | 0.577350i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.70820i | 1.62698i | 0.581580 | + | 0.813489i | \(0.302435\pi\) | ||||
−0.581580 | + | 0.813489i | \(0.697565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.00000 | −0.688247 | −0.344124 | − | 0.938924i | \(-0.611824\pi\) | ||||
−0.344124 | + | 0.938924i | \(0.611824\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000 | − | 2.23607i | 0.218218 | − | 0.487950i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.70820i | 1.39876i | 0.714751 | + | 0.699379i | \(0.246540\pi\) | ||||
−0.714751 | + | 0.699379i | \(0.753460\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58114 | + | 4.94975i | 0.304290 | + | 0.952579i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.23607i | − | 0.415227i | −0.978211 | − | 0.207614i | \(-0.933430\pi\) | ||
0.978211 | − | 0.207614i | \(-0.0665697\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 4.24264i | − | 0.762001i | −0.924575 | − | 0.381000i | \(-0.875580\pi\) | ||
0.924575 | − | 0.381000i | \(-0.124420\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.00000 | − | 2.23607i | −0.870388 | − | 0.389249i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.47214i | 0.755929i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.00000 | + | 6.70820i | −0.480384 | + | 1.07417i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −12.6491 | −1.97546 | −0.987730 | − | 0.156174i | \(-0.950084\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.3137i | 1.72532i | 0.505781 | + | 0.862662i | \(0.331205\pi\) | ||||
−0.505781 | + | 0.862662i | \(0.668795\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.32456 | − | 7.07107i | −0.942809 | − | 1.05409i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.23607i | − | 0.326164i | −0.986613 | − | 0.163082i | \(-0.947856\pi\) | ||
0.986613 | − | 0.163082i | \(-0.0521435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000 | 0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.74342 | + | 10.6066i | −0.664211 | + | 1.48522i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.0000 | 1.34840 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.74342 | − | 2.12132i | −0.628281 | − | 0.280976i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 2.23607i | − | 0.291111i | −0.989350 | − | 0.145556i | \(-0.953503\pi\) | ||
0.989350 | − | 0.145556i | \(-0.0464970\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.82843i | − | 0.362143i | −0.983470 | − | 0.181071i | \(-0.942043\pi\) | ||
0.983470 | − | 0.181071i | \(-0.0579565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.16228 | − | 2.82843i | 0.398410 | − | 0.356348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 13.4164i | − | 1.66410i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 4.24264i | −0.855186 | − | 0.518321i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.74342 | + | 10.6066i | −0.571040 | + | 1.27688i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.4164i | − | 1.59223i | −0.605142 | − | 0.796117i | \(-0.706884\pi\) | ||
0.605142 | − | 0.796117i | \(-0.293116\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.00000 | 0.585206 | 0.292603 | − | 0.956234i | \(-0.405479\pi\) | ||||
0.292603 | + | 0.956234i | \(0.405479\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.90569 | + | 3.53553i | 0.912871 | + | 0.408248i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.47214i | 0.509647i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.1421i | − | 1.59111i | −0.605878 | − | 0.795557i | \(-0.707178\pi\) | ||
0.605878 | − | 0.795557i | \(-0.292822\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | + | 8.94427i | −0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.47214i | 0.490881i | 0.969412 | + | 0.245440i | \(0.0789325\pi\) | ||||
−0.969412 | + | 0.245440i | \(0.921067\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 21.2132i | − | 2.30089i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.58114 | − | 3.53553i | 0.169516 | − | 0.379049i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.23607i | 0.237023i | 0.992953 | + | 0.118511i | \(0.0378122\pi\) | ||||
−0.992953 | + | 0.118511i | \(0.962188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.00000 | 0.628971 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.00000 | − | 6.70820i | 0.311086 | − | 0.695608i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.48683 | 0.973329 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.48528i | 0.861550i | 0.902459 | + | 0.430775i | \(0.141760\pi\) | ||||
−0.902459 | + | 0.430775i | \(0.858240\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.32456 | − | 7.07107i | −0.635642 | − | 0.710669i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.16228 | −0.314658 | −0.157329 | − | 0.987546i | \(-0.550288\pi\) | ||||
−0.157329 | + | 0.987546i | \(0.550288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.0000 | 0.985329 | 0.492665 | − | 0.870219i | \(-0.336023\pi\) | ||||
0.492665 | + | 0.870219i | \(0.336023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.16228 | + | 7.07107i | −0.308607 | + | 0.690066i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.1803i | 1.08084i | 0.841394 | + | 0.540422i | \(0.181735\pi\) | ||||
−0.841394 | + | 0.540422i | \(0.818265\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.7279i | 1.21911i | 0.792742 | + | 0.609557i | \(0.208653\pi\) | ||||
−0.792742 | + | 0.609557i | \(0.791347\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.90569 | + | 3.53553i | 0.750375 | + | 0.335578i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.48683 | 0.892446 | 0.446223 | − | 0.894922i | \(-0.352769\pi\) | ||||
0.446223 | + | 0.894922i | \(0.352769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 21.2132i | − | 1.97814i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.48683 | + | 8.48528i | −0.877058 | + | 0.784465i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.48683 | 0.869657 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −20.0000 | − | 8.94427i | −1.80334 | − | 0.806478i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.00000 | −0.443678 | −0.221839 | − | 0.975083i | \(-0.571206\pi\) | ||||
−0.221839 | + | 0.975083i | \(0.571206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.00000 | + | 17.8885i | −0.704361 | + | 1.57500i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.94427i | − | 0.781465i | −0.920504 | − | 0.390732i | \(-0.872222\pi\) | ||
0.920504 | − | 0.390732i | \(-0.127778\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.24264i | 0.367884i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.00000 | − | 15.6525i | −0.430331 | − | 1.34715i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 22.1359 | 1.89120 | 0.945601 | − | 0.325330i | \(-0.105475\pi\) | ||||
0.945601 | + | 0.325330i | \(0.105475\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.1421i | 1.19952i | 0.800180 | + | 0.599760i | \(0.204737\pi\) | ||||
−0.800180 | + | 0.599760i | \(0.795263\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.58114 | − | 3.53553i | 0.133156 | − | 0.297746i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 13.4164i | − | 1.12194i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.07107i | 0.587220i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.90569 | + | 3.53553i | 0.652051 | + | 0.291606i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.6525i | 1.28230i | 0.767415 | + | 0.641150i | \(0.221543\pi\) | ||||
−0.767415 | + | 0.641150i | \(0.778457\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | 0.895167 | 0.447584 | − | 0.894242i | \(-0.352285\pi\) | ||||
0.447584 | + | 0.894242i | \(0.352285\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.0000 | + | 13.4164i | −1.21268 | + | 1.08465i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4164i | 1.07763i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.0000 | −1.67598 | −0.837991 | − | 0.545684i | \(-0.816270\pi\) | ||||
−0.837991 | + | 0.545684i | \(0.816270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.48683 | 0.747667 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.00000 | 0.234978 | 0.117489 | − | 0.993074i | \(-0.462515\pi\) | ||||
0.117489 | + | 0.993074i | \(0.462515\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 15.8114 | + | 7.07107i | 1.23091 | + | 0.550482i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.47214i | − | 0.346064i | −0.984916 | − | 0.173032i | \(-0.944644\pi\) | ||
0.984916 | − | 0.173032i | \(-0.0553564\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.00000 | − | 6.70820i | −0.458831 | − | 0.512989i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 15.6525i | − | 1.19004i | −0.803712 | − | 0.595018i | \(-0.797145\pi\) | ||
0.803712 | − | 0.595018i | \(-0.202855\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 7.07107i | − | 0.534522i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.58114 | − | 3.53553i | 0.118846 | − | 0.265747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.48683 | 0.709079 | 0.354540 | − | 0.935041i | \(-0.384638\pi\) | ||||
0.354540 | + | 0.935041i | \(0.384638\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0000 | −1.41226 | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.00000 | − | 4.47214i | 0.147844 | − | 0.330590i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.8114 | −1.16248 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 21.2132i | − | 1.55126i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.00000 | − | 2.23607i | 0.509175 | − | 0.162650i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 9.48683 | 0.686443 | 0.343222 | − | 0.939254i | \(-0.388482\pi\) | ||||
0.343222 | + | 0.939254i | \(0.388482\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −23.0000 | −1.65558 | −0.827788 | − | 0.561041i | \(-0.810401\pi\) | ||||
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.48683 | − | 21.2132i | 0.679366 | − | 1.51911i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.0000 | 0.921546 | 0.460773 | − | 0.887518i | \(-0.347572\pi\) | ||||
0.460773 | + | 0.887518i | \(0.347572\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.06797 | − | 11.6580i | −0.569071 | − | 0.822288i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.16228 | −0.221948 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.0000 | 2.79372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.0000 | + | 13.4164i | −1.04257 | + | 0.932505i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 9.48683 | 0.656218 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000 | 1.78991 | 0.894957 | − | 0.446153i | \(-0.147206\pi\) | ||||
0.894957 | + | 0.446153i | \(0.147206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.48683 | − | 21.2132i | 0.650027 | − | 1.45350i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 35.7771i | − | 2.43998i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | −0.407307 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.90569 | + | 3.53553i | 0.534217 | + | 0.238909i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −28.4605 | −1.91446 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00000 | −0.200895 | −0.100447 | − | 0.994942i | \(-0.532027\pi\) | ||||
−0.100447 | + | 0.994942i | \(0.532027\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 10.0000 | + | 11.1803i | 0.666667 | + | 0.745356i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 2.23607i | − | 0.148413i | −0.997243 | − | 0.0742065i | \(-0.976358\pi\) | ||
0.997243 | − | 0.0742065i | \(-0.0236424\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7279i | 0.841085i | 0.907273 | + | 0.420542i | \(0.138160\pi\) | ||||
−0.907273 | + | 0.420542i | \(0.861840\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.16228 | + | 7.07107i | −0.208063 | + | 0.465242i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.48683 | 0.621503 | 0.310752 | − | 0.950491i | \(-0.399419\pi\) | ||||
0.310752 | + | 0.950491i | \(0.399419\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.07107i | 0.461266i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.0000 | − | 22.3607i | 0.649570 | − | 1.45248i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.6491 | 0.818203 | 0.409101 | − | 0.912489i | \(-0.365842\pi\) | ||||
0.409101 | + | 0.912489i | \(0.365842\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.0000 | 1.22390 | 0.611949 | − | 0.790897i | \(-0.290386\pi\) | ||||
0.611949 | + | 0.790897i | \(0.290386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.90569 | + | 13.4350i | −0.507151 | + | 0.861858i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.8114 | −1.01015 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 12.7279i | − | 0.809858i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.16228 | + | 7.07107i | −0.200401 | + | 0.448111i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.2132i | − | 1.33366i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.0000 | − | 33.5410i | 0.939336 | − | 2.10042i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 15.6525i | 0.976375i | 0.872739 | + | 0.488187i | \(0.162342\pi\) | ||||
−0.872739 | + | 0.488187i | \(0.837658\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.07107i | − | 0.439375i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.00000 | − | 4.47214i | 0.309492 | − | 0.276818i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.47214i | 0.275764i | 0.990449 | + | 0.137882i | \(0.0440294\pi\) | ||||
−0.990449 | + | 0.137882i | \(0.955971\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.58114 | + | 3.53553i | −0.0967641 | + | 0.216371i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 17.8885i | − | 1.09068i | −0.838214 | − | 0.545342i | \(-0.816400\pi\) | ||
0.838214 | − | 0.545342i | \(-0.183600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.07107i | − | 0.429537i | −0.976665 | − | 0.214768i | \(-0.931100\pi\) | ||
0.976665 | − | 0.214768i | \(-0.0688997\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.48683 | + | 4.24264i | 0.574169 | + | 0.256776i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.8114 | −0.953463 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.00000 | 0.240337 | 0.120168 | − | 0.992754i | \(-0.461657\pi\) | ||||
0.120168 | + | 0.992754i | \(0.461657\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.48683 | − | 8.48528i | 0.567962 | − | 0.508001i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.32456 | 0.377291 | 0.188646 | − | 0.982045i | \(-0.439590\pi\) | ||||
0.188646 | + | 0.982045i | \(0.439590\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.0000 | −0.772770 | −0.386385 | − | 0.922338i | \(-0.626276\pi\) | ||||
−0.386385 | + | 0.922338i | \(0.626276\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 15.0000 | + | 6.70820i | 0.888523 | + | 0.397360i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 17.8885i | 1.05593i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −28.0000 | −1.64706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | + | 13.4164i | −0.351726 | + | 0.786484i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 26.8328i | 1.56759i | 0.621020 | + | 0.783795i | \(0.286719\pi\) | ||||
−0.621020 | + | 0.783795i | \(0.713281\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.07107i | 0.411693i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.00000 | − | 15.6525i | −0.290129 | − | 0.908249i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.4605 | −1.64591 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | 0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.00000 | − | 2.23607i | −0.287242 | − | 0.128459i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.94427i | 0.512148i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.0000 | −0.627803 | −0.313902 | − | 0.949456i | \(-0.601636\pi\) | ||||
−0.313902 | + | 0.949456i | \(0.601636\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.8114 | + | 7.07107i | 0.899478 | + | 0.402259i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.9737 | −1.07590 | −0.537949 | − | 0.842977i | \(-0.680801\pi\) | ||||
−0.537949 | + | 0.842977i | \(0.680801\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.0416i | − | 1.35891i | −0.733716 | − | 0.679457i | \(-0.762216\pi\) | ||
0.733716 | − | 0.679457i | \(-0.237784\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −10.0000 | + | 8.94427i | −0.563436 | + | 0.503953i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.47214i | 0.251180i | 0.992082 | + | 0.125590i | \(0.0400824\pi\) | ||||
−0.992082 | + | 0.125590i | \(0.959918\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.07107i | 0.395904i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.90569 | + | 17.6777i | −0.441253 | + | 0.986671i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 20.1246i | − | 1.11976i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 21.2132i | 1.17670i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.00000 | + | 20.1246i | −0.497701 | + | 1.11289i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.16228 | −0.174342 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 7.07107i | − | 0.388661i | −0.980936 | − | 0.194331i | \(-0.937747\pi\) | ||
0.980936 | − | 0.194331i | \(-0.0622534\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0000 | + | 11.1803i | 0.547997 | + | 0.612679i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.1359 | + | 13.4164i | 1.20942 | + | 0.733017i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.6274i | 1.23259i | 0.787514 | + | 0.616297i | \(0.211368\pi\) | ||||
−0.787514 | + | 0.616297i | \(0.788632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | + | 6.70820i | 0.814688 | + | 0.364340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4164i | 0.726539i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.0000 | − | 33.5410i | 0.807573 | − | 1.80579i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.32456 | −0.339520 | −0.169760 | − | 0.985485i | \(-0.554299\pi\) | ||||
−0.169760 | + | 0.985485i | \(0.554299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | −1.28469 | −0.642345 | − | 0.766415i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766415i | \(0.722038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −21.0000 | + | 6.70820i | −1.12090 | + | 0.358057i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.32456 | −0.336622 | −0.168311 | − | 0.985734i | \(-0.553831\pi\) | ||||
−0.168311 | + | 0.985734i | \(0.553831\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 42.4264i | 2.25176i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 15.0000 | + | 6.70820i | 0.793884 | + | 0.355036i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 20.1246i | − | 1.06214i | −0.847329 | − | 0.531068i | \(-0.821791\pi\) | ||
0.847329 | − | 0.531068i | \(-0.178209\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.0000 | −0.526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.58114 | − | 0.707107i | −0.0829883 | − | 0.0371135i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.8114 | −0.827606 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 33.9411i | 1.77171i | 0.463960 | + | 0.885856i | \(0.346428\pi\) | ||||
−0.463960 | + | 0.885856i | \(0.653572\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −25.2982 | − | 28.2843i | −1.31697 | − | 1.47242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.3137i | 0.585802i | 0.956143 | + | 0.292901i | \(0.0946206\pi\) | ||||
−0.956143 | + | 0.292901i | \(0.905379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.48683 | 0.488597 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.65685i | 0.290573i | 0.989390 | + | 0.145287i | \(0.0464104\pi\) | ||||
−0.989390 | + | 0.145287i | \(0.953590\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.90569 | − | 3.53553i | −0.405021 | − | 0.181131i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 31.6228 | 1.61585 | 0.807924 | − | 0.589286i | \(-0.200591\pi\) | ||||
0.807924 | + | 0.589286i | \(0.200591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 14.1421i | − | 0.720750i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −25.2982 | + | 22.6274i | −1.28598 | + | 1.15022i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 8.94427i | − | 0.453493i | −0.973954 | − | 0.226746i | \(-0.927191\pi\) | ||
0.973954 | − | 0.226746i | \(-0.0728088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −45.0000 | −2.27575 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.32456 | − | 14.1421i | 0.319032 | − | 0.713376i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 44.7214i | 2.25018i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −21.0000 | −1.05396 | −0.526980 | − | 0.849878i | \(-0.676676\pi\) | ||||
−0.526980 | + | 0.849878i | \(0.676676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.00000 | + | 6.70820i | −0.150188 | + | 0.335830i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.8114 | −0.789583 | −0.394792 | − | 0.918771i | \(-0.629183\pi\) | ||||
−0.394792 | + | 0.918771i | \(0.629183\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.0000 | 0.896644 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.16228 | − | 28.2843i | 0.157135 | − | 1.40546i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.8114 | −0.783741 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.9411i | 1.67828i | 0.543915 | + | 0.839140i | \(0.316941\pi\) | ||||
−0.543915 | + | 0.839140i | \(0.683059\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 35.0000 | + | 15.6525i | 1.72642 | + | 0.772080i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.16228 | −0.155606 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14.1421i | − | 0.694210i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | + | 22.3607i | −0.489702 | + | 1.09501i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 11.1803i | − | 0.546195i | −0.961986 | − | 0.273098i | \(-0.911952\pi\) | ||
0.961986 | − | 0.273098i | \(-0.0880482\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.00000 | − | 4.47214i | 0.243108 | − | 0.217443i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 33.5410i | 1.62698i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.00000 | −0.193574 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.48683 | − | 21.2132i | 0.458029 | − | 1.02418i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.6525i | 0.753953i | 0.926223 | + | 0.376977i | \(0.123036\pi\) | ||||
−0.926223 | + | 0.376977i | \(0.876964\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.24264i | − | 0.203888i | −0.994790 | − | 0.101944i | \(-0.967494\pi\) | ||
0.994790 | − | 0.101944i | \(-0.0325063\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.00000 | + | 11.1803i | −0.239732 | + | 0.536056i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 20.1246i | − | 0.962691i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0000 | 0.620456 | 0.310228 | − | 0.950662i | \(-0.399595\pi\) | ||||
0.310228 | + | 0.950662i | \(0.399595\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.0000 | + | 11.1803i | 0.476190 | + | 0.532397i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.4605 | 1.35220 | 0.676100 | − | 0.736810i | \(-0.263669\pi\) | ||||
0.676100 | + | 0.736810i | \(0.263669\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7.07107i | − | 0.335201i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11.0680 | + | 24.7487i | −0.523497 | + | 1.17058i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.70820i | 0.316580i | 0.987393 | + | 0.158290i | \(0.0505980\pi\) | ||||
−0.987393 | + | 0.158290i | \(0.949402\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 40.0000 | 1.88353 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 17.3925 | + | 7.77817i | 0.817172 | + | 0.365451i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18.9737 | −0.889499 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 35.0000 | 1.63723 | 0.818615 | − | 0.574342i | \(-0.194742\pi\) | ||||
0.818615 | + | 0.574342i | \(0.194742\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −33.2039 | + | 10.6066i | −1.54983 | + | 0.495074i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.5967i | 1.14558i | 0.819700 | + | 0.572792i | \(0.194140\pi\) | ||||
−0.819700 | + | 0.572792i | \(0.805860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.48528i | 0.394344i | 0.980369 | + | 0.197172i | \(0.0631758\pi\) | ||||
−0.980369 | + | 0.197172i | \(0.936824\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.48683 | + | 21.2132i | −0.439941 | + | 0.983739i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 26.8328i | − | 1.24167i | −0.783939 | − | 0.620837i | \(-0.786793\pi\) | ||
0.783939 | − | 0.620837i | \(-0.213207\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.00000 | + | 9.89949i | −0.277054 | + | 0.457116i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −33.2039 | − | 14.8492i | −1.52996 | − | 0.684217i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 35.7771i | − | 1.64503i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −15.0000 | −0.688247 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 15.6525i | 0.715180i | 0.933879 | + | 0.357590i | \(0.116401\pi\) | ||||
−0.933879 | + | 0.357590i | \(0.883599\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.2132i | 0.967239i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | + | 6.70820i | 0.682524 | + | 0.305234i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 26.8328i | − | 1.21842i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.8406i | 1.98661i | 0.115529 | + | 0.993304i | \(0.463144\pi\) | ||||
−0.115529 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.74342 | + | 2.12132i | 0.214505 | + | 0.0959294i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.23607i | − | 0.100912i | −0.998726 | − | 0.0504562i | \(-0.983932\pi\) | ||
0.998726 | − | 0.0504562i | \(-0.0160675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.0000 | 0.675566 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.0000 | + | 22.3607i | 0.898933 | + | 1.00504i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −18.9737 | −0.851085 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 26.8701i | − | 1.20287i | −0.798922 | − | 0.601434i | \(-0.794596\pi\) | ||
0.798922 | − | 0.601434i | \(-0.205404\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.16228 | − | 7.07107i | 0.141280 | − | 0.315912i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.7851 | 1.55099 | 0.775494 | − | 0.631354i | \(-0.217501\pi\) | ||||
0.775494 | + | 0.631354i | \(0.217501\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.90569 | − | 3.53553i | −0.351104 | − | 0.157019i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.0689i | 1.28846i | 0.764834 | + | 0.644228i | \(0.222821\pi\) | ||||
−0.764834 | + | 0.644228i | \(0.777179\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 7.07107i | − | 0.312806i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.74342 | − | 14.8492i | −0.209427 | − | 0.655610i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.6228 | −1.39347 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.07107i | 0.310985i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 11.0680 | − | 24.7487i | 0.485830 | − | 1.08635i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.48683 | 0.415626 | 0.207813 | − | 0.978169i | \(-0.433365\pi\) | ||||
0.207813 | + | 0.978169i | \(0.433365\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.0000 | 1.61790 | 0.808949 | − | 0.587879i | \(-0.200037\pi\) | ||||
0.808949 | + | 0.587879i | \(0.200037\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.00000 | − | 11.1803i | 0.218218 | − | 0.487950i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 28.4605 | 1.23976 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.00000 | − | 4.47214i | 0.216982 | − | 0.194074i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 53.6656i | − | 2.32452i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 35.3553i | − | 1.52854i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0000 | + | 6.70820i | 0.647298 | + | 0.289480i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −15.8114 | −0.681045 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 24.0416i | − | 1.03363i | −0.856097 | − | 0.516815i | \(-0.827117\pi\) | ||
0.856097 | − | 0.516815i | \(-0.172883\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −30.0416 | − | 13.4350i | −1.28921 | − | 0.576552i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 40.2492i | − | 1.72409i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 16.9706i | − | 0.725609i | −0.931865 | − | 0.362804i | \(-0.881819\pi\) | ||
0.931865 | − | 0.362804i | \(-0.118181\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.32456 | − | 5.65685i | 0.269925 | − | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.70820i | 0.285779i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.0000 | −0.850487 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −25.0000 | − | 11.1803i | −1.06119 | − | 0.474579i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.8885i | 0.757962i | 0.925404 | + | 0.378981i | \(0.123725\pi\) | ||||
−0.925404 | + | 0.378981i | \(0.876275\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −48.0000 | −2.03018 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.0000 | − | 33.5410i | 0.633300 | − | 1.41610i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.32456 | −0.266548 | −0.133274 | − | 0.991079i | \(-0.542549\pi\) | ||||
−0.133274 | + | 0.991079i | \(0.542549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −30.0000 | −1.26211 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 12.6491 | + | 1.41421i | 0.531213 | + | 0.0593914i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 38.0132i | − | 1.59359i | −0.604247 | − | 0.796797i | \(-0.706526\pi\) | ||
0.604247 | − | 0.796797i | \(-0.293474\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.0000 | −1.29731 | −0.648655 | − | 0.761083i | \(-0.724668\pi\) | ||||
−0.648655 | + | 0.761083i | \(0.724668\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.0000 | + | 6.70820i | 0.626634 | + | 0.280239i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.5410i | 1.39876i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.48528i | 0.353247i | 0.984278 | + | 0.176623i | \(0.0565175\pi\) | ||||
−0.984278 | + | 0.176623i | \(0.943483\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −36.3662 | − | 16.2635i | −1.51133 | − | 0.675886i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.32456 | 0.262387 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 30.0000 | − | 26.8328i | 1.24035 | − | 1.10940i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.6228 | −1.30521 | −0.652606 | − | 0.757698i | \(-0.726324\pi\) | ||||
−0.652606 | + | 0.757698i | \(0.726324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.7279i | 0.524445i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −18.9737 | −0.779155 | −0.389578 | − | 0.920994i | \(-0.627379\pi\) | ||||
−0.389578 | + | 0.920994i | \(0.627379\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.0000 | −1.22988 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 20.5548 | + | 9.19239i | 0.841252 | + | 0.376219i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.4605 | 1.16286 | 0.581432 | − | 0.813595i | \(-0.302493\pi\) | ||||
0.581432 | + | 0.813595i | \(0.302493\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.0000 | 1.18293 | 0.591467 | − | 0.806329i | \(-0.298549\pi\) | ||||
0.591467 | + | 0.806329i | \(0.298549\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.51317 | − | 24.1378i | −0.183790 | − | 0.982965i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.16228 | 0.128565 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.0000 | 0.811775 | 0.405887 | − | 0.913923i | \(-0.366962\pi\) | ||||
0.405887 | + | 0.913923i | \(0.366962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.00000 | − | 2.23607i | −0.202610 | − | 0.0906100i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.48683 | 0.383796 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.0000 | −0.605844 | −0.302922 | − | 0.953015i | \(-0.597962\pi\) | ||||
−0.302922 | + | 0.953015i | \(0.597962\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 63.2456 | + | 28.2843i | 2.55031 | + | 1.14053i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.0132i | 1.53035i | 0.643821 | + | 0.765176i | \(0.277348\pi\) | ||||
−0.643821 | + | 0.765176i | \(0.722652\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.0000 | 0.884255 | 0.442127 | − | 0.896952i | \(-0.354224\pi\) | ||||
0.442127 | + | 0.896952i | \(0.354224\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −33.2039 | + | 10.6066i | −1.33243 | + | 0.425628i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.16228 | 0.126694 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −25.0000 | −1.00000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 15.0000 | + | 6.70820i | 0.599042 | + | 0.267900i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 33.5410i | 1.33737i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 16.9706i | 0.675587i | 0.941220 | + | 0.337794i | \(0.109681\pi\) | ||||
−0.941220 | + | 0.337794i | \(0.890319\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 41.1096 | + | 18.3848i | 1.63396 | + | 0.730729i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.8114 | 0.627456 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 21.2132i | 0.840498i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.0000 | − | 26.8328i | 1.18678 | − | 1.06149i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.0000 | −0.394362 | −0.197181 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197181 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.2982 | − | 56.5685i | 0.996116 | − | 2.22738i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.2719 | −1.74051 | −0.870254 | − | 0.492604i | \(-0.836045\pi\) | ||||
−0.870254 | + | 0.492604i | \(0.836045\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.07107i | 0.277564i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.48683 | − | 4.24264i | −0.371818 | − | 0.166282i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 25.2982 | 0.989996 | 0.494998 | − | 0.868894i | \(-0.335169\pi\) | ||||
0.494998 | + | 0.868894i | \(0.335169\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 28.2843i | 1.10516i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 10.0000 | + | 11.1803i | 0.390137 | + | 0.436187i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.0689i | 1.13236i | 0.824281 | + | 0.566181i | \(0.191580\pi\) | ||||
−0.824281 | + | 0.566181i | \(0.808420\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.4975i | 1.92523i | 0.270876 | + | 0.962614i | \(0.412687\pi\) | ||||
−0.270876 | + | 0.962614i | \(0.587313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −45.0000 | − | 20.1246i | −1.74766 | − | 0.781575i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 13.4164i | − | 0.520266i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 15.0000 | 0.580802 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −4.74342 | − | 2.12132i | −0.183391 | − | 0.0820150i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.94427i | 0.345290i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.41421i | − | 0.0545139i | −0.999628 | − | 0.0272570i | \(-0.991323\pi\) | ||
0.999628 | − | 0.0272570i | \(-0.00867724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.90569 | + | 24.7487i | 0.304290 | + | 0.952579i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 15.8114 | 0.607681 | 0.303841 | − | 0.952723i | \(-0.401731\pi\) | ||||
0.303841 | + | 0.952723i | \(0.401731\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.58114 | − | 3.53553i | 0.0605894 | − | 0.135482i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.32456 | 0.242002 | 0.121001 | − | 0.992652i | \(-0.461390\pi\) | ||||
0.121001 | + | 0.992652i | \(0.461390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −70.0000 | −2.67456 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −9.00000 | + | 20.1246i | −0.343371 | + | 0.767802i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.0000 | 1.78796 | 0.893982 | − | 0.448103i | \(-0.147900\pi\) | ||||
0.893982 | + | 0.448103i | \(0.147900\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10.0000 | + | 8.94427i | −0.379869 | + | 0.339765i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 44.7214i | − | 1.69638i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 84.8528i | − | 3.21403i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 15.0000 | + | 6.70820i | 0.567352 | + | 0.253728i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.48683 | −0.358313 | −0.179156 | − | 0.983821i | \(-0.557337\pi\) | ||||
−0.179156 | + | 0.983821i | \(0.557337\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −15.0000 | −0.565736 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.00000 | + | 11.1803i | −0.188311 | + | 0.421076i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 4.47214i | 0.168192i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.00000 | 0.0751116 | 0.0375558 | − | 0.999295i | \(-0.488043\pi\) | ||||
0.0375558 | + | 0.999295i | \(0.488043\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.6228 | − | 28.2843i | 1.18595 | − | 1.06074i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 28.4605 | 1.06585 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.4264i | 1.58666i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.0000 | + | 8.94427i | 0.746914 | + | 0.334030i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 42.4853i | − | 1.58443i | −0.610239 | − | 0.792217i | \(-0.708927\pi\) | ||
0.610239 | − | 0.792217i | \(-0.291073\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 14.1421i | − | 0.526681i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 30.0416 | + | 13.4350i | 1.11726 | + | 0.499654i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 11.1803i | − | 0.415227i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 8.48528i | − | 0.314702i | −0.987543 | − | 0.157351i | \(-0.949705\pi\) | ||
0.987543 | − | 0.157351i | \(-0.0502953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.0000 | + | 15.6525i | −0.814815 | + | 0.579721i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −75.8947 | −2.80707 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1.41421i | − | 0.0522352i | −0.999659 | − | 0.0261176i | \(-0.991686\pi\) | ||
0.999659 | − | 0.0261176i | \(-0.00831443\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −25.0000 | − | 11.1803i | −0.922139 | − | 0.412393i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 22.1359 | + | 13.4164i | 0.815388 | + | 0.494200i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 28.2843i | − | 1.04045i | −0.854028 | − | 0.520227i | \(-0.825847\pi\) | ||
0.854028 | − | 0.520227i | \(-0.174153\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.00000 | − | 20.1246i | 0.330623 | − | 0.739296i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 31.3050i | 1.14847i | 0.818691 | + | 0.574234i | \(0.194700\pi\) | ||||
−0.818691 | + | 0.574234i | \(0.805300\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 49.4975i | − | 1.81345i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.0000 | + | 8.94427i | −0.365881 | + | 0.327254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.8114 | 0.577736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.0000 | −0.620339 | −0.310169 | − | 0.950681i | \(-0.600386\pi\) | ||||
−0.310169 | + | 0.950681i | \(0.600386\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −34.7851 | −1.26596 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 15.5563i | − | 0.565405i | −0.959208 | − | 0.282703i | \(-0.908769\pi\) | ||
0.959208 | − | 0.282703i | \(-0.0912309\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0000 | − | 33.5410i | 0.544466 | − | 1.21746i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.4853i | − | 1.54009i | −0.637989 | − | 0.770045i | \(-0.720234\pi\) | ||
0.637989 | − | 0.770045i | \(-0.279766\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000 | 0.651644 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 47.4342 | − | 42.4264i | 1.71499 | − | 1.53393i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 9.48683 | 0.342550 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 36.7696i | − | 1.32594i | −0.748644 | − | 0.662972i | \(-0.769295\pi\) | ||
0.748644 | − | 0.662972i | \(-0.230705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −11.0680 | + | 24.7487i | −0.398603 | + | 0.891304i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 29.0689i | − | 1.04554i | −0.852475 | − | 0.522768i | \(-0.824900\pi\) | ||
0.852475 | − | 0.522768i | \(-0.175100\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 21.2132i | − | 0.762001i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.00000 | − | 11.1803i | 0.179374 | − | 0.401092i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37.9473 | 1.35960 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 42.4264i | 1.51814i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.0680 | − | 3.53553i | 0.395537 | − | 0.126350i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 66.4078 | 2.37020 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.7990i | 0.705758i | 0.935669 | + | 0.352879i | \(0.114797\pi\) | ||||
−0.935669 | + | 0.352879i | \(0.885203\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.16228 | + | 7.07107i | −0.112580 | + | 0.251737i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 13.4164i | − | 0.477033i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.0000 | 0.426132 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 26.8328i | − | 0.950467i | −0.879860 | − | 0.475234i | \(-0.842364\pi\) | ||
0.879860 | − | 0.475234i | \(-0.157636\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0000 | 0.530662 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | + | 4.47214i | −0.176666 | + | 0.158015i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −15.8114 | −0.557972 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −30.0000 | −1.05736 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 12.6491 | − | 28.2843i | 0.445270 | − | 0.995654i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 28.4605 | 1.00062 | 0.500309 | − | 0.865847i | \(-0.333220\pi\) | ||||
0.500309 | + | 0.865847i | \(0.333220\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 25.4558i | 0.893876i | 0.894565 | + | 0.446938i | \(0.147485\pi\) | ||||
−0.894565 | + | 0.446938i | \(0.852515\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.00000 | − | 11.1803i | 0.175358 | − | 0.392112i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.48683 | −0.332309 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 33.9411i | − | 1.18745i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | + | 13.4164i | 0.419314 | + | 0.468807i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1803i | 0.390197i | 0.980784 | + | 0.195098i | \(0.0625026\pi\) | ||||
−0.980784 | + | 0.195098i | \(0.937497\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.0000 | −0.453152 | −0.226576 | − | 0.973994i | \(-0.572753\pi\) | ||||
−0.226576 | + | 0.973994i | \(0.572753\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −25.0000 | − | 11.1803i | −0.870388 | − | 0.389249i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 29.0689i | 1.01082i | 0.862878 | + | 0.505412i | \(0.168659\pi\) | ||||
−0.862878 | + | 0.505412i | \(0.831341\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0000 | −0.659897 | −0.329949 | − | 0.943999i | \(-0.607031\pi\) | ||||
−0.329949 | + | 0.943999i | \(0.607031\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.32456 | + | 2.82843i | 0.219396 | + | 0.0981170i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.5410i | 1.16213i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.1421i | 0.489409i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.0000 | − | 6.70820i | 0.725866 | − | 0.231869i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 20.1246i | 0.694779i | 0.937721 | + | 0.347389i | \(0.112932\pi\) | ||||
−0.937721 | + | 0.347389i | \(0.887068\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.0000 | 0.827586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.0000 | + | 4.47214i | 0.344418 | + | 0.154029i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.8114 | 0.543928 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.41421i | 0.0485930i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −20.5548 | − | 9.19239i | −0.705439 | − | 0.315482i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.5410i | 1.14977i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 27.0000 | 0.924462 | 0.462231 | − | 0.886759i | \(-0.347049\pi\) | ||||
0.462231 | + | 0.886759i | \(0.347049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.9737 | + | 21.2132i | 0.648886 | + | 0.725476i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.4605 | −0.972192 | −0.486096 | − | 0.873905i | \(-0.661579\pi\) | ||||
−0.486096 | + | 0.873905i | \(0.661579\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.0000 | −0.477674 | −0.238837 | − | 0.971060i | \(-0.576766\pi\) | ||||
−0.238837 | + | 0.971060i | \(0.576766\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.6491 | + | 28.2843i | −0.431081 | + | 0.963925i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 11.1803i | − | 0.380583i | −0.981728 | − | 0.190292i | \(-0.939057\pi\) | ||
0.981728 | − | 0.190292i | \(-0.0609433\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.4975i | 1.68296i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −44.2719 | − | 19.7990i | −1.50355 | − | 0.672409i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 44.7214i | 1.51707i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.0000 | − | 29.6985i | 0.609907 | − | 1.00629i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.9737 | + | 16.9706i | −0.642161 | + | 0.574367i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.0000 | −0.709120 | −0.354560 | − | 0.935033i | \(-0.615369\pi\) | ||||
−0.354560 | + | 0.935033i | \(0.615369\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −18.9737 | + | 42.4264i | −0.639966 | + | 1.43101i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.6525i | − | 0.527345i | −0.964612 | − | 0.263673i | \(-0.915066\pi\) | ||
0.964612 | − | 0.263673i | \(-0.0849339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 16.9706i | − | 0.571105i | −0.958363 | − | 0.285552i | \(-0.907823\pi\) | ||
0.958363 | − | 0.285552i | \(-0.0921771\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | + | 11.1803i | −0.168073 | + | 0.375823i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 42.4853i | − | 1.42652i | −0.700901 | − | 0.713258i | \(-0.747219\pi\) | ||
0.700901 | − | 0.713258i | \(-0.252781\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.07107i | 0.237156i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.16228 | − | 28.2843i | 0.105940 | − | 0.947559i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.70820i | 0.224481i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.0000 | −1.00279 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −45.0000 | − | 20.1246i | −1.50251 | − | 0.671941i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.48683 | −0.316404 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.2982 | + | 11.3137i | 0.841872 | + | 0.376497i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 60.0833 | 1.99724 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 15.0000 | 0.498067 | 0.249033 | − | 0.968495i | \(-0.419887\pi\) | ||||
0.249033 | + | 0.968495i | \(0.419887\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.32456 | − | 7.07107i | −0.209772 | − | 0.234533i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 38.0132i | − | 1.25943i | −0.776825 | − | 0.629716i | \(-0.783171\pi\) | ||
0.776825 | − | 0.629716i | \(-0.216829\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.1421i | − | 0.468036i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.32456 | + | 14.1421i | −0.209083 | + | 0.467525i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −12.6491 | −0.417710 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.7279i | 0.419855i | 0.977717 | + | 0.209928i | \(0.0673229\pi\) | ||||
−0.977717 | + | 0.209928i | \(0.932677\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.3925 | − | 7.77817i | −0.573103 | − | 0.256300i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 56.9210 | 1.87358 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.0000 | 0.821995 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 20.0000 | + | 22.3607i | 0.656886 | + | 0.734421i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.48683 | 0.311253 | 0.155626 | − | 0.987816i | \(-0.450260\pi\) | ||||
0.155626 | + | 0.987816i | \(0.450260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.0000 | −0.491605 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −30.0000 | − | 13.4164i | −0.982156 | − | 0.439233i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 67.0820i | 2.19382i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 43.8406i | 1.43221i | 0.697992 | + | 0.716105i | \(0.254077\pi\) | ||||
−0.697992 | + | 0.716105i | \(0.745923\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 17.0000 | − | 38.0132i | 0.554774 | − | 1.24051i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.48683 | 0.309262 | 0.154631 | − | 0.987972i | \(-0.450581\pi\) | ||||
0.154631 | + | 0.987972i | \(0.450581\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 84.8528i | − | 2.76319i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −22.1359 | + | 7.07107i | −0.720082 | + | 0.230022i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 42.4853i | − | 1.38059i | −0.723530 | − | 0.690293i | \(-0.757482\pi\) | ||
0.723530 | − | 0.690293i | \(-0.242518\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.2132i | 0.688610i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.16228 | + | 7.07107i | −0.102544 | + | 0.229295i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24.5967i | − | 0.796767i | −0.917219 | − | 0.398383i | \(-0.869571\pi\) | ||
0.917219 | − | 0.398383i | \(-0.130429\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −30.0000 | −0.970777 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.00000 | + | 11.1803i | −0.161627 | + | 0.361409i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 31.3050i | − | 1.01089i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.0000 | 0.419355 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −25.0000 | + | 22.3607i | −0.805614 | + | 0.720563i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 72.7324 | 2.34134 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.0000 | −0.643157 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 14.2302 | − | 31.8198i | 0.457141 | − | 1.02220i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 60.3738i | 1.93749i | 0.248061 | + | 0.968744i | \(0.420206\pi\) | ||||
−0.248061 | + | 0.968744i | \(0.579794\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −15.0000 | + | 33.5410i | −0.480384 | + | 1.07417i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 38.0132i | − | 1.21615i | −0.793880 | − | 0.608074i | \(-0.791942\pi\) | ||
0.793880 | − | 0.608074i | \(-0.208058\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 7.07107i | − | 0.225992i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −28.4605 | + | 25.4558i | −0.908674 | + | 0.812743i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9737 | −0.605166 | −0.302583 | − | 0.953123i | \(-0.597849\pi\) | ||||
−0.302583 | + | 0.953123i | \(0.597849\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.00000 | − | 2.23607i | −0.159152 | − | 0.0711748i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −75.8947 | −2.41331 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.24264i | − | 0.134772i | −0.997727 | − | 0.0673860i | \(-0.978534\pi\) | ||
0.997727 | − | 0.0673860i | \(-0.0214659\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.00000 | − | 11.1803i | 0.158670 | − | 0.354797i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −41.1096 | −1.30326 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.0000 | −0.950110 | −0.475055 | − | 0.879956i | \(-0.657572\pi\) | ||||
−0.475055 | + | 0.879956i | \(0.657572\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.90569 | + | 24.7487i | 0.250125 | + | 0.783015i |
(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 | 804.2.g.b.401.4 | yes | 4 | |
3.2 | odd | 2 | inner | 804.2.g.b.401.2 | yes | 4 | |
67.66 | odd | 2 | inner | 804.2.g.b.401.1 | ✓ | 4 | |
201.200 | even | 2 | inner | 804.2.g.b.401.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.g.b.401.1 | ✓ | 4 | 67.66 | odd | 2 | inner | |
804.2.g.b.401.2 | yes | 4 | 3.2 | odd | 2 | inner | |
804.2.g.b.401.3 | yes | 4 | 201.200 | even | 2 | inner | |
804.2.g.b.401.4 | yes | 4 | 1.1 | even | 1 | trivial |