Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(201,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.1783323.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 5x^{4} - 2x^{3} + 19x^{2} - 12x + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 201.1 | ||
Root | \(0.356769 + 0.617942i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.201 |
Dual form | 1900.2.i.c.501.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.60220 | + | 2.77509i | −0.925031 | + | 1.60220i | −0.133520 | + | 0.991046i | \(0.542628\pi\) |
−0.791511 | + | 0.611155i | \(0.790705\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.20440 | 0.833185 | 0.416593 | − | 0.909093i | \(-0.363224\pi\) | ||||
0.416593 | + | 0.909093i | \(0.363224\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.63409 | − | 6.29444i | −1.21136 | − | 2.09815i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20440 | −0.363141 | −0.181570 | − | 0.983378i | \(-0.558118\pi\) | ||||
−0.181570 | + | 0.983378i | \(0.558118\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.07031 | + | 1.85383i | −0.259588 | + | 0.449619i | −0.966131 | − | 0.258050i | \(-0.916920\pi\) |
0.706544 | + | 0.707669i | \(0.250253\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.30660 | + | 0.673184i | 0.988002 | + | 0.154439i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.53189 | + | 6.11742i | −0.770722 | + | 1.33493i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.63409 | − | 8.02649i | −0.966276 | − | 1.67364i | −0.706148 | − | 0.708064i | \(-0.749569\pi\) |
−0.260127 | − | 0.965574i | \(-0.583765\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 13.6770 | 2.63214 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.16599 | − | 7.21570i | −0.773605 | − | 1.33992i | −0.935575 | − | 0.353127i | \(-0.885118\pi\) |
0.161971 | − | 0.986796i | \(-0.448215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26819 | 1.48501 | 0.742505 | − | 0.669840i | \(-0.233637\pi\) | ||||
0.742505 | + | 0.669840i | \(0.233637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.92969 | − | 3.34233i | 0.335916 | − | 0.581824i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.20440 | 0.362401 | 0.181201 | − | 0.983446i | \(-0.442002\pi\) | ||||
0.181201 | + | 0.983446i | \(0.442002\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.20440 | 0.513115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.30660 | − | 5.72720i | 0.516405 | − | 0.894439i | −0.483414 | − | 0.875392i | \(-0.660603\pi\) |
0.999819 | − | 0.0190471i | \(-0.00606323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17251 | − | 2.03084i | 0.178806 | − | 0.309701i | −0.762666 | − | 0.646793i | \(-0.776110\pi\) |
0.941472 | + | 0.337092i | \(0.109443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.16599 | − | 7.21570i | −0.607672 | − | 1.05252i | −0.991623 | − | 0.129165i | \(-0.958770\pi\) |
0.383951 | − | 0.923353i | \(-0.374563\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.14061 | −0.305802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.42969 | − | 5.94040i | −0.480253 | − | 0.831823i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.134095 | + | 0.232259i | 0.0184193 | + | 0.0319032i | 0.875088 | − | 0.483964i | \(-0.160803\pi\) |
−0.856669 | + | 0.515867i | \(0.827470\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.76819 | + | 10.8726i | −1.16138 | + | 1.44012i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.16599 | − | 7.21570i | 0.542366 | − | 0.939405i | −0.456402 | − | 0.889774i | \(-0.650862\pi\) |
0.998768 | − | 0.0496310i | \(-0.0158045\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70440 | + | 2.95211i | 0.218226 | + | 0.377979i | 0.954266 | − | 0.298960i | \(-0.0966396\pi\) |
−0.736040 | + | 0.676939i | \(0.763306\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8.01100 | − | 13.8755i | −1.00929 | − | 1.74814i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.06379 | − | 1.84253i | −0.129962 | − | 0.225101i | 0.793699 | − | 0.608310i | \(-0.208152\pi\) |
−0.923662 | + | 0.383209i | \(0.874819\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 29.6990 | 3.57534 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.23630 | − | 9.06953i | 0.621434 | − | 1.07636i | −0.367785 | − | 0.929911i | \(-0.619884\pi\) |
0.989219 | − | 0.146444i | \(-0.0467829\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.42969 | + | 4.20835i | −0.284374 | + | 0.492550i | −0.972457 | − | 0.233082i | \(-0.925119\pi\) |
0.688083 | + | 0.725632i | \(0.258452\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.65498 | −0.302564 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.20440 | + | 14.2104i | −0.923067 | + | 1.59880i | −0.128427 | + | 0.991719i | \(0.540993\pi\) |
−0.794640 | + | 0.607080i | \(0.792341\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0110 | + | 19.0716i | −1.22344 | + | 2.11907i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.73181 | 0.629148 | 0.314574 | − | 0.949233i | \(-0.398138\pi\) | ||||
0.314574 | + | 0.949233i | \(0.398138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 26.6990 | 2.86243 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.40880 | + | 9.36832i | 0.573332 | + | 0.993040i | 0.996221 | + | 0.0868585i | \(0.0276828\pi\) |
−0.422889 | + | 0.906182i | \(0.638984\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10220 | − | 1.90907i | −0.115542 | − | 0.200125i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.2473 | + | 22.9450i | −1.37368 | + | 2.37929i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.87039 | − | 13.6319i | 0.799117 | − | 1.38411i | −0.121075 | − | 0.992643i | \(-0.538634\pi\) |
0.920192 | − | 0.391468i | \(-0.128033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.37691 | + | 7.58103i | 0.439896 | + | 0.761922i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.27471 | + | 9.13606i | 0.524853 | + | 0.909072i | 0.999581 | + | 0.0289397i | \(0.00921308\pi\) |
−0.474728 | + | 0.880133i | \(0.657454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.731811 | 0.0721075 | 0.0360537 | − | 0.999350i | \(-0.488521\pi\) | ||||
0.0360537 | + | 0.999350i | \(0.488521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3958 | 1.29502 | 0.647509 | − | 0.762058i | \(-0.275811\pi\) | ||||
0.647509 | + | 0.762058i | \(0.275811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.96811 | + | 5.14091i | −0.284293 | + | 0.492410i | −0.972437 | − | 0.233164i | \(-0.925092\pi\) |
0.688144 | + | 0.725574i | \(0.258426\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.53189 | + | 6.11742i | −0.335233 | + | 0.580640i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6132 | −1.46877 | −0.734383 | − | 0.678735i | \(-0.762529\pi\) | ||||
−0.734383 | + | 0.678735i | \(0.762529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.63409 | + | 6.29444i | −0.335972 | + | 0.581921i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.35939 | + | 4.08658i | −0.216285 | + | 0.374616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54942 | −0.868129 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.5957 | + | 18.3523i | 0.955380 | + | 1.65477i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.67699 | − | 13.2969i | −0.681223 | − | 1.17991i | −0.974608 | − | 0.223918i | \(-0.928115\pi\) |
0.293385 | − | 0.955994i | \(-0.405218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.75719 | + | 6.50764i | 0.330802 | + | 0.572965i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89780 | − | 6.75119i | 0.340552 | − | 0.589854i | −0.643983 | − | 0.765040i | \(-0.722719\pi\) |
0.984535 | + | 0.175186i | \(0.0560526\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.49348 | + | 1.48397i | 0.823189 | + | 0.128676i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.23630 | + | 14.2657i | 0.703674 | + | 1.21880i | 0.967168 | + | 0.254138i | \(0.0817919\pi\) |
−0.263494 | + | 0.964661i | \(0.584875\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.76819 | + | 16.9190i | 0.828527 | + | 1.43505i | 0.899194 | + | 0.437551i | \(0.144154\pi\) |
−0.0706667 | + | 0.997500i | \(0.522513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.6990 | 2.24846 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.602201 | + | 1.04304i | 0.0503586 | + | 0.0872236i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.42969 | − | 5.94040i | 0.282876 | − | 0.489956i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.83850 | − | 4.91642i | 0.232539 | − | 0.402769i | −0.726016 | − | 0.687678i | \(-0.758630\pi\) |
0.958555 | + | 0.284909i | \(0.0919634\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2264 | −1.15773 | −0.578864 | − | 0.815424i | \(-0.696504\pi\) | ||||
−0.578864 | + | 0.815424i | \(0.696504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.5584 | 1.25782 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.327492 | + | 0.567233i | −0.0261367 | + | 0.0452701i | −0.878798 | − | 0.477194i | \(-0.841654\pi\) |
0.852661 | + | 0.522464i | \(0.174987\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.859386 | −0.0681538 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2154 | − | 17.6936i | −0.805087 | − | 1.39445i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6770 | 0.992939 | 0.496469 | − | 0.868054i | \(-0.334630\pi\) | ||||
0.496469 | + | 0.868054i | \(0.334630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −3.89780 | − | 6.75119i | −0.301621 | − | 0.522422i | 0.674882 | − | 0.737925i | \(-0.264194\pi\) |
−0.976503 | + | 0.215503i | \(0.930861\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11.4133 | − | 29.5540i | −0.872796 | − | 2.26005i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.37039 | + | 9.30179i | −0.408303 | + | 0.707202i | −0.994700 | − | 0.102822i | \(-0.967213\pi\) |
0.586397 | + | 0.810024i | \(0.300546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.3495 | + | 23.1220i | 1.00341 | + | 1.73796i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.54942 | −0.115809 | −0.0579044 | − | 0.998322i | \(-0.518442\pi\) | ||||
−0.0579044 | + | 0.998322i | \(0.518442\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.11320 | + | 7.12428i | 0.305732 | + | 0.529544i | 0.977424 | − | 0.211287i | \(-0.0677655\pi\) |
−0.671692 | + | 0.740831i | \(0.734432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10.9232 | −0.807464 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.28908 | − | 2.23275i | 0.0942668 | − | 0.163275i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 30.1496 | 2.19306 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.2812 | 1.17807 | 0.589034 | − | 0.808108i | \(-0.299508\pi\) | ||||
0.589034 | + | 0.808108i | \(0.299508\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.60669 | − | 14.9072i | 0.619523 | − | 1.07304i | −0.370050 | − | 0.929012i | \(-0.620659\pi\) |
0.989573 | − | 0.144033i | \(-0.0460072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.2044 | 0.727034 | 0.363517 | − | 0.931588i | \(-0.381576\pi\) | ||||
0.363517 | + | 0.931588i | \(0.381576\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.03189 | − | 8.71550i | −0.356701 | − | 0.617825i | 0.630706 | − | 0.776022i | \(-0.282765\pi\) |
−0.987408 | + | 0.158197i | \(0.949432\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.81761 | 0.480877 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.18351 | − | 15.9063i | −0.644556 | − | 1.11640i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −33.6815 | + | 58.3380i | −2.34102 | + | 4.05477i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.18688 | − | 0.810784i | −0.358784 | − | 0.0560831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.12758 | − | 10.6133i | 0.421840 | − | 0.730648i | −0.574280 | − | 0.818659i | \(-0.694718\pi\) |
0.996119 | + | 0.0880113i | \(0.0280512\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.7792 | + | 29.0624i | 1.14969 | + | 1.99132i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.2264 | 1.23729 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −7.78571 | − | 13.4852i | −0.526110 | − | 0.911249i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.14061 | 0.143993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.0748 | + | 17.4501i | −0.674658 | + | 1.16854i | 0.301911 | + | 0.953336i | \(0.402376\pi\) |
−0.976569 | + | 0.215206i | \(0.930958\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.25515 | 0.547914 | 0.273957 | − | 0.961742i | \(-0.411667\pi\) | ||||
0.273957 | + | 0.961742i | \(0.411667\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.6860 | −1.76346 | −0.881729 | − | 0.471756i | \(-0.843620\pi\) | ||||
−0.881729 | + | 0.471756i | \(0.843620\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.25382 | − | 7.36783i | 0.279881 | − | 0.484768i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.00448 | − | 12.1321i | 0.458879 | − | 0.794802i | −0.540023 | − | 0.841650i | \(-0.681584\pi\) |
0.998902 | + | 0.0468485i | \(0.0149178\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.2902 | − | 45.5360i | −1.70773 | − | 2.95788i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2682 | −0.793563 | −0.396782 | − | 0.917913i | \(-0.629873\pi\) | ||||
−0.396782 | + | 0.917913i | \(0.629873\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.93621 | − | 8.54977i | −0.317969 | − | 0.550739i | 0.662095 | − | 0.749420i | \(-0.269668\pi\) |
−0.980064 | + | 0.198681i | \(0.936334\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.7682 | − | 25.5793i | −0.947380 | − | 1.64091i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.57031 | − | 4.06622i | −0.0999162 | − | 0.258727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.18351 | + | 15.9063i | −0.581981 | + | 1.00802i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.4198 | − | 24.9758i | −0.910170 | − | 1.57646i | −0.813823 | − | 0.581113i | \(-0.802617\pi\) |
−0.0963474 | − | 0.995348i | \(-0.530716\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.58131 | + | 9.66711i | 0.350894 | + | 0.607766i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.39780 | − | 4.15311i | −0.149571 | − | 0.259064i | 0.781498 | − | 0.623907i | \(-0.214456\pi\) |
−0.931069 | + | 0.364844i | \(0.881122\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.85939 | 0.301948 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.2792 | + | 52.4451i | −1.87424 | + | 3.24627i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 10.2044 | − | 17.6745i | 0.629230 | − | 1.08986i | −0.358476 | − | 0.933539i | \(-0.616704\pi\) |
0.987706 | − | 0.156320i | \(-0.0499631\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −34.6640 | −2.12140 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.563788 | + | 0.976509i | −0.0343747 | + | 0.0595388i | −0.882701 | − | 0.469935i | \(-0.844277\pi\) |
0.848326 | + | 0.529474i | \(0.177611\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.83850 | + | 17.0408i | −0.597646 | + | 1.03515i | 0.395522 | + | 0.918457i | \(0.370564\pi\) |
−0.993168 | + | 0.116697i | \(0.962769\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.06379 | 0.427520 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.35398 | −0.441858 | −0.220929 | − | 0.975290i | \(-0.570909\pi\) | ||||
−0.220929 | + | 0.975290i | \(0.570909\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.0474 | − | 52.0436i | −1.79889 | − | 3.11577i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.73630 | − | 11.6676i | −0.401854 | − | 0.696031i | 0.592096 | − | 0.805867i | \(-0.298301\pi\) |
−0.993950 | + | 0.109836i | \(0.964967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.6595 | − | 18.4627i | 0.633640 | − | 1.09750i | −0.353162 | − | 0.935562i | \(-0.614894\pi\) |
0.986802 | − | 0.161934i | \(-0.0517731\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.28908 | − | 12.6251i | 0.430261 | − | 0.745233i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.20889 | + | 10.7541i | 0.365229 | + | 0.632594i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.2199 | + | 43.6821i | 1.47842 | + | 2.56069i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.08580 | −0.472377 | −0.236189 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236189 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −16.4726 | −0.955837 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.63409 | + | 8.02649i | −0.267997 | + | 0.464184i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.58468 | − | 4.47679i | 0.148978 | − | 0.258038i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −33.8046 | −1.94202 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.2922 | − | 24.7549i | 0.815701 | − | 1.41284i | −0.0931229 | − | 0.995655i | \(-0.529685\pi\) |
0.908824 | − | 0.417180i | \(-0.136982\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.17251 | + | 2.03084i | −0.0667016 | + | 0.115531i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.7408 | −0.609054 | −0.304527 | − | 0.952504i | \(-0.598498\pi\) | ||||
−0.304527 | + | 0.952504i | \(0.598498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.71092 | + | 9.89160i | 0.322800 | + | 0.559107i | 0.981065 | − | 0.193680i | \(-0.0620424\pi\) |
−0.658264 | + | 0.752787i | \(0.728709\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.62309 | + | 2.81128i | 0.0911619 | + | 0.157897i | 0.908000 | − | 0.418970i | \(-0.137609\pi\) |
−0.816838 | + | 0.576867i | \(0.804275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.01752 | + | 8.69060i | 0.280927 | + | 0.486580i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.4627 | + | 37.1745i | −1.19793 | + | 2.07488i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.85735 | + | 7.26318i | −0.325912 | + | 0.404134i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.51100 | − | 16.4735i | −0.525960 | − | 0.910989i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.18351 | − | 15.9063i | −0.506303 | − | 0.876943i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 35.1208 | 1.93042 | 0.965208 | − | 0.261483i | \(-0.0842116\pi\) | ||||
0.965208 | + | 0.261483i | \(0.0842116\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.01100 | − | 13.8755i | −0.439000 | − | 0.760371i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.93621 | − | 13.7459i | 0.432313 | − | 0.748788i | −0.564759 | − | 0.825256i | \(-0.691031\pi\) |
0.997072 | + | 0.0764677i | \(0.0243642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 25.0155 | − | 43.3281i | 1.35865 | − | 2.35326i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.95822 | −0.539268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1496 | −1.08798 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.3221 | + | 28.2707i | −0.876216 | + | 1.51765i | −0.0207537 | + | 0.999785i | \(0.506607\pi\) |
−0.855462 | + | 0.517866i | \(0.826727\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.7538 | −1.16446 | −0.582228 | − | 0.813026i | \(-0.697819\pi\) | ||||
−0.582228 | + | 0.813026i | \(0.697819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.83850 | − | 11.8446i | −0.365012 | − | 0.632219i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.67699 | −0.461830 | −0.230915 | − | 0.972974i | \(-0.574172\pi\) | ||||
−0.230915 | + | 0.972974i | \(0.574172\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7.56042 | − | 13.0950i | −0.400140 | − | 0.693063i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.81109 | + | 10.0651i | −0.306697 | + | 0.531216i | −0.977638 | − | 0.210296i | \(-0.932557\pi\) |
0.670940 | + | 0.741511i | \(0.265891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0936 | + | 5.79827i | 0.952297 | + | 0.305172i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.3001 | − | 26.5005i | 0.803046 | − | 1.39092i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.3046 | + | 26.5083i | 0.798892 | + | 1.38372i | 0.920338 | + | 0.391123i | \(0.127913\pi\) |
−0.121446 | + | 0.992598i | \(0.538753\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −48.0660 | −2.50222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.295598 | + | 0.511992i | 0.0153467 | + | 0.0265813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.70980 | −0.243864 | −0.121932 | − | 0.992538i | \(-0.538909\pi\) | ||||
−0.121932 | + | 0.992538i | \(0.538909\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.16599 | + | 7.21570i | −0.214559 | + | 0.371628i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.0638 | 0.516942 | 0.258471 | − | 0.966019i | \(-0.416781\pi\) | ||||
0.258471 | + | 0.966019i | \(0.416781\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.2003 | 2.52061 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.7219 | − | 23.7671i | 0.701158 | − | 1.21444i | −0.266903 | − | 0.963723i | \(-0.586000\pi\) |
0.968060 | − | 0.250717i | \(-0.0806664\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.0440 | −0.866396 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.257185 | − | 0.445458i | −0.0130398 | − | 0.0225856i | 0.859432 | − | 0.511250i | \(-0.170817\pi\) |
−0.872472 | + | 0.488665i | \(0.837484\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8396 | 1.00333 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4901 | + | 21.6335i | 0.630043 | + | 1.09127i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.55278 | − | 2.68950i | 0.0779320 | − | 0.134982i | −0.824426 | − | 0.565970i | \(-0.808502\pi\) |
0.902358 | + | 0.430988i | \(0.141835\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.3286 | + | 23.9677i | −0.967641 | + | 1.19988i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.51752 | − | 11.2887i | 0.325470 | − | 0.563730i | −0.656138 | − | 0.754641i | \(-0.727811\pi\) |
0.981607 | + | 0.190911i | \(0.0611443\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.13409 | − | 7.16046i | −0.205934 | − | 0.356688i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.65498 | −0.131603 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.7747 | − | 23.8585i | −0.681115 | − | 1.17973i | −0.974641 | − | 0.223775i | \(-0.928162\pi\) |
0.293525 | − | 0.955951i | \(-0.405172\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −52.7848 | −2.60368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.18351 | − | 15.9063i | 0.451891 | − | 0.782698i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −62.6024 | −3.06565 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.5494 | 0.808492 | 0.404246 | − | 0.914650i | \(-0.367534\pi\) | ||||
0.404246 | + | 0.914650i | \(0.367534\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.93418 | − | 13.7424i | 0.386688 | − | 0.669764i | −0.605314 | − | 0.795987i | \(-0.706952\pi\) |
0.992002 | + | 0.126223i | \(0.0402856\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −30.2792 | + | 52.4451i | −1.47222 | + | 2.54997i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.75719 | + | 6.50764i | 0.181823 | + | 0.314927i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.85939 | −0.186333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.4472 | − | 19.8272i | −0.551393 | − | 0.955041i | −0.998174 | − | 0.0603975i | \(-0.980763\pi\) |
0.446781 | − | 0.894643i | \(-0.352570\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.6660 | − | 18.4740i | −0.512575 | − | 0.887805i | −0.999894 | − | 0.0145814i | \(-0.995358\pi\) |
0.487319 | − | 0.873224i | \(-0.337975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.5539 | − | 37.6865i | −0.696208 | − | 1.80279i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.08783 | − | 8.81238i | 0.242829 | − | 0.420592i | −0.718690 | − | 0.695331i | \(-0.755258\pi\) |
0.961519 | + | 0.274739i | \(0.0885913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.77919 | + | 13.4740i | 0.370438 | + | 0.641617i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.30660 | − | 5.72720i | −0.157101 | − | 0.272108i | 0.776721 | − | 0.629845i | \(-0.216882\pi\) |
−0.933822 | + | 0.357737i | \(0.883548\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.09568 | + | 15.7542i | 0.430211 | + | 0.745147i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.9870 | 0.518507 | 0.259253 | − | 0.965809i | \(-0.416524\pi\) | ||||
0.259253 | + | 0.965809i | \(0.416524\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.98248 | + | 6.89785i | −0.187528 | + | 0.324807i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.7936 | − | 39.4796i | 1.07094 | − | 1.85491i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.5494 | −0.587037 | −0.293518 | − | 0.955953i | \(-0.594826\pi\) | ||||
−0.293518 | + | 0.955953i | \(0.594826\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.6386 | + | 25.3548i | −0.683270 | + | 1.18346i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6386 | − | 20.1586i | 0.542063 | − | 0.938880i | −0.456723 | − | 0.889609i | \(-0.650977\pi\) |
0.998785 | − | 0.0492710i | \(-0.0156898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3958 | 1.08729 | 0.543647 | − | 0.839314i | \(-0.317043\pi\) | ||||
0.543647 | + | 0.839314i | \(0.317043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 12.6352 | 0.584688 | 0.292344 | − | 0.956313i | \(-0.405565\pi\) | ||||
0.292344 | + | 0.956313i | \(0.405565\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.34502 | − | 4.06169i | −0.108283 | − | 0.187551i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.04942 | − | 1.81764i | −0.0483546 | − | 0.0837526i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.41217 | + | 2.44595i | −0.0649316 | + | 0.112465i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.974625 | − | 1.68810i | 0.0446250 | − | 0.0772928i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.01752 | − | 3.49445i | −0.0921830 | − | 0.159666i | 0.816246 | − | 0.577704i | \(-0.196051\pi\) |
−0.908429 | + | 0.418038i | \(0.862718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.10220 | − | 1.90907i | −0.0502560 | − | 0.0870460i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 65.4685 | 2.97892 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.54942 | −0.296782 | −0.148391 | − | 0.988929i | \(-0.547409\pi\) | ||||
−0.148391 | + | 0.988929i | \(0.547409\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.3111 | + | 35.1798i | −0.918499 | + | 1.59089i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04290 | + | 1.80635i | −0.0470653 | + | 0.0815195i | −0.888598 | − | 0.458686i | \(-0.848320\pi\) |
0.841533 | + | 0.540206i | \(0.181654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8355 | 0.803273 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.5429 | − | 19.9929i | 0.517770 | − | 0.896803i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0539 | − | 20.8780i | 0.539607 | − | 0.934626i | −0.459318 | − | 0.888272i | \(-0.651906\pi\) |
0.998925 | − | 0.0463546i | \(-0.0147604\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.9802 | 1.11603 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.13858 | − | 7.16823i | −0.184530 | − | 0.319616i | 0.758888 | − | 0.651221i | \(-0.225743\pi\) |
−0.943418 | + | 0.331606i | \(0.892410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.2264 | + | 33.3011i | 0.853875 | + | 1.47895i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.86591 | + | 4.96389i | 0.127029 | + | 0.220021i | 0.922524 | − | 0.385939i | \(-0.126123\pi\) |
−0.795495 | + | 0.605960i | \(0.792789\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.35602 | + | 9.27690i | −0.236936 | + | 0.410386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 58.9014 | + | 9.20713i | 2.60056 | + | 0.406505i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.01752 | + | 8.69060i | 0.220670 | + | 0.382212i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −17.2089 | − | 29.8067i | −0.755386 | − | 1.30837i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 14.8086 | 0.648778 | 0.324389 | − | 0.945924i | \(-0.394841\pi\) | ||||
0.324389 | + | 0.945924i | \(0.394841\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.79356 | + | 13.4988i | 0.340789 | + | 0.590263i | 0.984579 | − | 0.174938i | \(-0.0559726\pi\) |
−0.643791 | + | 0.765202i | \(0.722639\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.84950 | + | 15.3278i | −0.385490 | + | 0.667689i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −31.4497 | + | 54.4724i | −1.36738 | + | 2.36837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −60.5584 | −2.62801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.61320 | −0.286450 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.48248 | − | 4.29978i | 0.107127 | − | 0.185549i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.57816 | 0.111049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0539 | − | 24.3421i | −0.604224 | − | 1.04655i | −0.992174 | − | 0.124867i | \(-0.960150\pi\) |
0.387949 | − | 0.921681i | \(-0.373184\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.3607 | −1.13125 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.6835 | − | 37.5569i | −0.927120 | − | 1.60582i | −0.788116 | − | 0.615527i | \(-0.788943\pi\) |
−0.139004 | − | 0.990292i | \(-0.544390\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 12.3879 | − | 21.4565i | 0.528703 | − | 0.915741i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.0838 | − | 33.8796i | −0.557387 | − | 1.44332i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.0858 | + | 31.3255i | −0.769086 | + | 1.33210i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.65814 | + | 14.9963i | 0.366857 | + | 0.635415i | 0.989072 | − | 0.147431i | \(-0.0471005\pi\) |
−0.622215 | + | 0.782846i | \(0.713767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.34502 | −0.0991836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13073 | + | 7.15463i | 0.174399 | + | 0.302069i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.35398 | −0.352078 | −0.176039 | − | 0.984383i | \(-0.556329\pi\) | ||||
−0.176039 | + | 0.984383i | \(0.556329\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.2727 | + | 42.0415i | −1.01936 | + | 1.76558i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.6640 | −0.447056 | −0.223528 | − | 0.974697i | \(-0.571757\pi\) | ||||
−0.223528 | + | 0.974697i | \(0.571757\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.56512 | −0.107347 | −0.0536735 | − | 0.998559i | \(-0.517093\pi\) | ||||
−0.0536735 | + | 0.998559i | \(0.517093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −26.0858 | + | 45.1819i | −1.08975 | + | 1.88750i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.4218 | −0.850172 | −0.425086 | − | 0.905153i | \(-0.639756\pi\) | ||||
−0.425086 | + | 0.905153i | \(0.639756\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 27.5793 | + | 47.7687i | 1.14616 | + | 1.98520i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6352 | 0.524197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.161504 | − | 0.279733i | −0.00668880 | − | 0.0115853i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.40432 | + | 7.62850i | −0.181786 | + | 0.314862i | −0.942489 | − | 0.334238i | \(-0.891521\pi\) |
0.760703 | + | 0.649100i | \(0.224854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.6078 | + | 5.56601i | 1.46719 | + | 0.229343i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −16.3495 | + | 28.3182i | −0.672529 | + | 1.16485i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.4726 | + | 28.5314i | 0.676448 | + | 1.17164i | 0.976043 | + | 0.217576i | \(0.0698151\pi\) |
−0.299595 | + | 0.954066i | \(0.596852\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 32.2484 | 1.31984 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.56379 | + | 16.5650i | 0.390766 | + | 0.676826i | 0.992551 | − | 0.121832i | \(-0.0388769\pi\) |
−0.601785 | + | 0.798658i | \(0.705544\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3100 | 0.787670 | 0.393835 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.73181 | + | 13.3919i | −0.314864 | + | 0.545360i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −36.8773 | −1.49680 | −0.748402 | − | 0.663245i | \(-0.769179\pi\) | ||||
−0.748402 | + | 0.663245i | \(0.769179\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 58.8553 | 2.38494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.16599 | + | 7.21570i | −0.168538 | + | 0.291916i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.2603 | + | 24.6996i | −0.575970 | + | 0.997609i | 0.419966 | + | 0.907540i | \(0.362042\pi\) |
−0.995936 | + | 0.0900688i | \(0.971291\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.64713 | − | 9.78112i | −0.227345 | − | 0.393773i | 0.729675 | − | 0.683794i | \(-0.239671\pi\) |
−0.957020 | + | 0.290021i | \(0.906338\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 27.2044 | 1.09344 | 0.546719 | − | 0.837316i | \(-0.315877\pi\) | ||||
0.546719 | + | 0.837316i | \(0.315877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −63.3805 | − | 109.778i | −2.54337 | − | 4.40525i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.9232 | + | 20.6515i | 0.477692 | + | 0.827387i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.5604 | − | 13.0950i | 0.421743 | − | 0.522965i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.35939 | + | 4.08658i | −0.0940749 | + | 0.162942i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19136 | − | 7.25965i | −0.166856 | − | 0.289002i | 0.770457 | − | 0.637492i | \(-0.220028\pi\) |
−0.937313 | + | 0.348490i | \(0.886695\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 19.6352 | + | 34.0092i | 0.780430 | + | 1.35174i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.07031 | + | 1.85383i | 0.0424071 | + | 0.0734513i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −76.1168 | −3.01113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.55594 | + | 16.5514i | −0.377437 | + | 0.653740i | −0.990689 | − | 0.136148i | \(-0.956528\pi\) |
0.613252 | + | 0.789888i | \(0.289861\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.1112 | + | 41.7618i | −0.950852 | + | 1.64692i | −0.207264 | + | 0.978285i | \(0.566456\pi\) |
−0.743588 | + | 0.668638i | \(0.766877\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.0817 | 1.18263 | 0.591317 | − | 0.806439i | \(-0.298608\pi\) | ||||
0.591317 | + | 0.806439i | \(0.298608\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.01752 | + | 8.69060i | −0.196955 | + | 0.341136i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −29.2024 | + | 50.5800i | −1.14453 | + | 1.98239i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −41.9124 | −1.64016 | −0.820079 | − | 0.572250i | \(-0.806071\pi\) | ||||
−0.820079 | + | 0.572250i | \(0.806071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 35.3189 | 1.37792 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0936 | + | 34.8032i | 0.782737 | + | 1.35574i | 0.930341 | + | 0.366694i | \(0.119511\pi\) |
−0.147604 | + | 0.989047i | \(0.547156\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.757185 | + | 1.31148i | 0.0294511 | + | 0.0510108i | 0.880375 | − | 0.474278i | \(-0.157291\pi\) |
−0.850924 | + | 0.525289i | \(0.823957\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.42969 | + | 5.94040i | −0.133198 | + | 0.230706i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −38.6112 | + | 66.8765i | −1.49503 | + | 2.58947i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.2837 | − | 55.9170i | −1.24816 | − | 2.16187i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.05278 | − | 3.55553i | −0.0792468 | − | 0.137260i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.76686 | 0.299390 | 0.149695 | − | 0.988732i | \(-0.452171\pi\) | ||||
0.149695 | + | 0.988732i | \(0.452171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.19136 | −0.237953 | −0.118977 | − | 0.992897i | \(-0.537961\pi\) | ||||
−0.118977 | + | 0.992897i | \(0.537961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.3495 | − | 30.0502i | 0.665813 | − | 1.15322i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −13.2264 | + | 22.9088i | −0.506837 | + | 0.877868i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.92317 | −0.111852 | −0.0559261 | − | 0.998435i | \(-0.517811\pi\) | ||||
−0.0559261 | + | 0.998435i | \(0.517811\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 42.7563 | − | 74.0560i | 1.63125 | − | 2.82541i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.134095 | − | 0.232259i | 0.00510860 | − | 0.00884835i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.35805 | −0.0897046 | −0.0448523 | − | 0.998994i | \(-0.514282\pi\) | ||||
−0.0448523 | + | 0.998994i | \(0.514282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.64847 | + | 16.7116i | 0.366515 | + | 0.634822i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.07816 | + | 12.2597i | 0.268104 | + | 0.464370i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 22.4452 | + | 38.8762i | 0.848955 | + | 1.47043i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.2792 | + | 21.2682i | −0.463779 | + | 0.803288i | −0.999145 | − | 0.0413314i | \(-0.986840\pi\) |
0.535367 | + | 0.844620i | \(0.320173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.49348 | + | 1.48397i | 0.358053 | + | 0.0559689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.6276 | + | 20.1396i | 0.437300 | + | 0.757426i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.63858 | − | 6.30220i | −0.136650 | − | 0.236684i | 0.789577 | − | 0.613652i | \(-0.210300\pi\) |
−0.926226 | + | 0.376968i | \(0.876967\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 119.262 | 4.47269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −38.3156 | − | 66.3645i | −1.43493 | − | 2.48537i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19.6561 | − | 34.0454i | 0.734071 | − | 1.27145i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −16.4452 | + | 28.4839i | −0.613302 | + | 1.06227i | 0.377378 | + | 0.926059i | \(0.376826\pi\) |
−0.990680 | + | 0.136211i | \(0.956508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.61320 | 0.0600789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.6352 | 1.17653 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.9551 | − | 24.1709i | 0.517565 | − | 0.896449i | −0.482227 | − | 0.876046i | \(-0.660172\pi\) |
0.999792 | − | 0.0204023i | \(-0.00649470\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 28.5804 | 1.05853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50989 | + | 4.34725i | 0.0928315 | + | 0.160789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.89710 | 0.180878 | 0.0904392 | − | 0.995902i | \(-0.471173\pi\) | ||||
0.0904392 | + | 0.995902i | \(0.471173\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.28123 | + | 2.21915i | 0.0471946 | + | 0.0817435i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5936 | − | 20.0808i | 0.426479 | − | 0.738684i | −0.570078 | − | 0.821591i | \(-0.693087\pi\) |
0.996557 | + | 0.0829069i | \(0.0264204\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8001 | + | 2.15715i | 0.506959 | + | 0.0792449i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19.9901 | − | 34.6239i | 0.733366 | − | 1.27023i | −0.222070 | − | 0.975031i | \(-0.571281\pi\) |
0.955436 | − | 0.295197i | \(-0.0953852\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −20.8299 | − | 36.0785i | −0.762128 | − | 1.32004i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.5296 | 1.07899 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2936 | + | 17.8290i | 0.375617 | + | 0.650589i | 0.990419 | − | 0.138093i | \(-0.0440973\pi\) |
−0.614802 | + | 0.788682i | \(0.710764\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 92.4137 | 3.36774 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3176 | + | 29.9950i | −0.629419 | + | 1.09019i | 0.358249 | + | 0.933626i | \(0.383374\pi\) |
−0.987668 | + | 0.156560i | \(0.949960\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −35.7695 | −1.29835 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.3890 | 0.884102 | 0.442051 | − | 0.896990i | \(-0.354251\pi\) | ||||
0.442051 | + | 0.896990i | \(0.354251\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.54290 | + | 11.3326i | −0.236869 | + | 0.410269i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.33198 | −0.300850 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.27471 | − | 5.67196i | −0.118089 | − | 0.204536i | 0.800921 | − | 0.598770i | \(-0.204343\pi\) |
−0.919010 | + | 0.394233i | \(0.871010\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.3670 | 0.553430 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.7363 | − | 32.4522i | −0.673898 | − | 1.16723i | −0.976790 | − | 0.214200i | \(-0.931286\pi\) |
0.302892 | − | 0.953025i | \(-0.402048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.78571 | + | 13.4852i | −0.279311 | + | 0.483781i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.0957 | − | 22.4388i | 0.648345 | − | 0.803955i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.30660 | + | 10.9234i | −0.225668 | + | 0.390868i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −56.9782 | − | 98.6891i | −2.03623 | − | 3.52686i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.8306 | 0.457363 | 0.228682 | − | 0.973501i | \(-0.426559\pi\) | ||||
0.228682 | + | 0.973501i | \(0.426559\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 32.6990 | + | 56.6363i | 1.16412 | + | 2.01631i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.4178 | −1.22376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.70440 | − | 2.95211i | 0.0605251 | − | 0.104833i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.3032 | 1.00255 | 0.501276 | − | 0.865287i | \(-0.332864\pi\) | ||||
0.501276 | + | 0.865287i | \(0.332864\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 17.8355 | 0.630976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.3122 | − | 68.0907i | 1.38903 | − | 2.40587i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.92633 | − | 5.06855i | 0.103268 | − | 0.178865i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.80660 | − | 3.12913i | −0.0635954 | − | 0.110150i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −55.4946 | −1.95109 | −0.975543 | − | 0.219808i | \(-0.929457\pi\) | ||||
−0.975543 | + | 0.219808i | \(0.929457\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8540 | + | 20.5317i | 0.416250 | + | 0.720966i | 0.995559 | − | 0.0941424i | \(-0.0300109\pi\) |
−0.579309 | + | 0.815108i | \(0.696678\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −31.5265 | − | 54.6055i | −1.10568 | − | 1.91510i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.41665 | − | 7.95672i | 0.224490 | − | 0.278370i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −8.01100 | + | 13.8755i | −0.279927 | + | 0.484848i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.3625 | − | 19.6805i | −0.396555 | − | 0.686854i | 0.596743 | − | 0.802432i | \(-0.296461\pi\) |
−0.993298 | + | 0.115578i | \(0.963128\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9.94722 | + | 17.2291i | 0.345899 | + | 0.599114i | 0.985517 | − | 0.169579i | \(-0.0542408\pi\) |
−0.639618 | + | 0.768693i | \(0.720907\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.37109 | 0.151814 | 0.0759071 | − | 0.997115i | \(-0.475815\pi\) | ||||
0.0759071 | + | 0.997115i | \(0.475815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.7826 | − | 20.4080i | 0.408732 | − | 0.707945i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.29111 | − | 3.96833i | 0.0793824 | − | 0.137494i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 113.084 | 3.90875 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.22396 | + | 2.11996i | −0.0422558 | + | 0.0731891i | −0.886380 | − | 0.462959i | \(-0.846788\pi\) |
0.844124 | + | 0.536148i | \(0.180121\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2109 | + | 35.0063i | −0.696928 | + | 1.20712i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.1716 | 1.48691 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0507 | −0.723312 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 34.1572 | + | 59.1620i | 1.17227 | + | 2.03044i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.2154 | − | 17.6936i | −0.350180 | − | 0.606529i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.96607 | + | 15.5297i | −0.306992 | + | 0.531727i | −0.977703 | − | 0.209993i | \(-0.932656\pi\) |
0.670711 | + | 0.741719i | \(0.265989\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29.0474 | + | 50.3115i | −0.992240 | + | 1.71861i | −0.388438 | + | 0.921475i | \(0.626985\pi\) |
−0.603801 | + | 0.797135i | \(0.706348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10.0409 | − | 17.3913i | −0.342590 | − | 0.593383i | 0.642323 | − | 0.766434i | \(-0.277971\pi\) |
−0.984913 | + | 0.173051i | \(0.944637\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.3571 | + | 40.4557i | 0.796009 | + | 1.37873i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6262 | 0.974449 | 0.487224 | − | 0.873277i | \(-0.338009\pi\) | ||||
0.487224 | + | 0.873277i | \(0.338009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −39.7915 | −1.35139 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.88139 | − | 17.1151i | 0.335203 | − | 0.580589i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.06379 | + | 1.84253i | −0.0360451 | + | 0.0624319i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −114.407 | −3.87209 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.5200 | − | 44.2019i | 0.861748 | − | 1.49259i | −0.00849182 | − | 0.999964i | \(-0.502703\pi\) |
0.870240 | − | 0.492628i | \(-0.163964\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.9551 | − | 22.4388i | 0.436964 | − | 0.756843i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.2992 | −0.481751 | −0.240876 | − | 0.970556i | \(-0.577435\pi\) | ||||
−0.240876 | + | 0.970556i | \(0.577435\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.6999 | + | 25.4610i | 0.494692 | + | 0.856831i | 0.999981 | − | 0.00611882i | \(-0.00194769\pi\) |
−0.505290 | + | 0.862950i | \(0.668614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.46811 | + | 11.2031i | 0.217178 | + | 0.376163i | 0.953944 | − | 0.299985i | \(-0.0969815\pi\) |
−0.736766 | + | 0.676147i | \(0.763648\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.9232 | − | 29.3118i | −0.567585 | − | 0.983086i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.2617 | − | 22.9699i | 0.444283 | − | 0.769520i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.0838 | − | 33.8796i | −0.437831 | − | 1.13374i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.8495 | − | 25.7201i | −0.495810 | − | 0.858769i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.4452 | − | 59.6608i | −1.14881 | − | 1.98980i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.574090 | −0.0191257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.28235 | + | 14.3454i | 0.275619 | + | 0.477386i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.00000 | + | 8.66025i | −0.166022 | + | 0.287559i | −0.937018 | − | 0.349281i | \(-0.886426\pi\) |
0.770996 | + | 0.636841i | \(0.219759\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.3376 | − | 66.4026i | 1.27158 | − | 2.20244i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.10964 | −0.103027 | −0.0515134 | − | 0.998672i | \(-0.516404\pi\) | ||||
−0.0515134 | + | 0.998672i | \(0.516404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.90340 | −0.228469 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.59231 | − | 14.8823i | 0.283743 | − | 0.491458i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 23.4987 | 0.775150 | 0.387575 | − | 0.921838i | \(-0.373313\pi\) | ||||
0.387575 | + | 0.921838i | \(0.373313\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.7980 | + | 79.3245i | 1.50910 | + | 2.61383i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.4726 | −0.344710 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.65947 | − | 4.60634i | −0.0873484 | − | 0.151292i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 22.3221 | − | 38.6630i | 0.732364 | − | 1.26849i | −0.223506 | − | 0.974703i | \(-0.571750\pi\) |
0.955870 | − | 0.293789i | \(-0.0949164\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.21877 | − | 1.44103i | −0.302133 | − | 0.0472277i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.2089 | − | 29.8067i | 0.563394 | − | 0.975826i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.7363 | − | 20.3279i | −0.383408 | − | 0.664082i | 0.608139 | − | 0.793831i | \(-0.291916\pi\) |
−0.991547 | + | 0.129748i | \(0.958583\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −36.6002 | −1.19440 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0858 | − | 34.7896i | −0.654778 | − | 1.13411i | −0.981949 | − | 0.189144i | \(-0.939429\pi\) |
0.327171 | − | 0.944965i | \(-0.393905\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.2924 | −1.99596 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.68148 | − | 16.7688i | 0.314606 | − | 0.544913i | −0.664748 | − | 0.747068i | \(-0.731461\pi\) |
0.979354 | + | 0.202155i | \(0.0647944\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.85939 | 0.157742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.4021 | −0.337310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.41981 | − | 4.19123i | 0.0783852 | − | 0.135767i | −0.824168 | − | 0.566345i | \(-0.808357\pi\) |
0.902553 | + | 0.430578i | \(0.141690\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −32.1563 | −1.03947 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.1561 | + | 31.4473i | 0.586291 | + | 1.01549i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.3630 | 1.20526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −48.6815 | − | 84.3188i | −1.56874 | − | 2.71714i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.5364 | − | 23.4457i | 0.435301 | − | 0.753963i | −0.562020 | − | 0.827124i | \(-0.689975\pi\) |
0.997320 | + | 0.0731612i | \(0.0233088\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.7713 | − | 27.8918i | −0.346025 | − | 0.896013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.61769 | + | 2.80192i | −0.0519141 | + | 0.0899179i | −0.890815 | − | 0.454367i | \(-0.849866\pi\) |
0.838901 | + | 0.544285i | \(0.183199\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.5330 | + | 37.2963i | 0.690317 | + | 1.19566i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.93214 | 0.0618147 | 0.0309074 | − | 0.999522i | \(-0.490160\pi\) | ||||
0.0309074 | + | 0.999522i | \(0.490160\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.51437 | − | 11.2832i | −0.208200 | − | 0.360613i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.1455 | 1.37753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.18555 | + | 12.4457i | −0.229183 | + | 0.396957i | −0.957566 | − | 0.288213i | \(-0.906939\pi\) |
0.728383 | + | 0.685170i | \(0.240272\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 58.8553 | 1.87339 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.7340 | −0.691102 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7956 | + | 30.8229i | −0.565296 | + | 0.979121i | 0.431726 | + | 0.902005i | \(0.357905\pi\) |
−0.997022 | + | 0.0771164i | \(0.975429\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −56.2706 | + | 97.4636i | −1.78569 | + | 3.09291i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.7902 | + | 41.2058i | 0.753443 | + | 1.30500i | 0.946145 | + | 0.323744i | \(0.104942\pi\) |
−0.192702 | + | 0.981257i | \(0.561725\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 30.1496 | 0.953891 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1900.2.i.c.201.1 | 6 | ||
5.2 | odd | 4 | 1900.2.s.c.49.6 | 12 | |||
5.3 | odd | 4 | 1900.2.s.c.49.1 | 12 | |||
5.4 | even | 2 | 380.2.i.b.201.3 | yes | 6 | ||
15.14 | odd | 2 | 3420.2.t.v.3241.1 | 6 | |||
19.7 | even | 3 | inner | 1900.2.i.c.501.1 | 6 | ||
20.19 | odd | 2 | 1520.2.q.i.961.1 | 6 | |||
95.7 | odd | 12 | 1900.2.s.c.349.1 | 12 | |||
95.49 | even | 6 | 7220.2.a.n.1.1 | 3 | |||
95.64 | even | 6 | 380.2.i.b.121.3 | ✓ | 6 | ||
95.83 | odd | 12 | 1900.2.s.c.349.6 | 12 | |||
95.84 | odd | 6 | 7220.2.a.o.1.3 | 3 | |||
285.254 | odd | 6 | 3420.2.t.v.1261.1 | 6 | |||
380.159 | odd | 6 | 1520.2.q.i.881.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.3 | ✓ | 6 | 95.64 | even | 6 | ||
380.2.i.b.201.3 | yes | 6 | 5.4 | even | 2 | ||
1520.2.q.i.881.1 | 6 | 380.159 | odd | 6 | |||
1520.2.q.i.961.1 | 6 | 20.19 | odd | 2 | |||
1900.2.i.c.201.1 | 6 | 1.1 | even | 1 | trivial | ||
1900.2.i.c.501.1 | 6 | 19.7 | even | 3 | inner | ||
1900.2.s.c.49.1 | 12 | 5.3 | odd | 4 | |||
1900.2.s.c.49.6 | 12 | 5.2 | odd | 4 | |||
1900.2.s.c.349.1 | 12 | 95.7 | odd | 12 | |||
1900.2.s.c.349.6 | 12 | 95.83 | odd | 12 | |||
3420.2.t.v.1261.1 | 6 | 285.254 | odd | 6 | |||
3420.2.t.v.3241.1 | 6 | 15.14 | odd | 2 | |||
7220.2.a.n.1.1 | 3 | 95.49 | even | 6 | |||
7220.2.a.o.1.3 | 3 | 95.84 | odd | 6 |