Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(49,1900)]
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, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.s (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 9x^{10} + 59x^{8} - 180x^{6} + 403x^{4} - 198x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 380) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.6 | ||
Root | \(0.617942 + 0.356769i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.349 |
Dual form | 1900.2.s.c.49.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 2.77509 | − | 1.60220i | 1.60220 | − | 0.925031i | 0.611155 | − | 0.791511i | \(-0.290705\pi\) |
0.991046 | − | 0.133520i | \(-0.0426280\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.20440i | − | 0.833185i | −0.909093 | − | 0.416593i | \(-0.863224\pi\) | ||
0.909093 | − | 0.416593i | \(-0.136776\pi\) | |||||||
\(8\) | 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 | ||||||||
\(13\) | −0.866025 | − | 0.500000i | −0.240192 | − | 0.138675i | 0.375073 | − | 0.926995i | \(-0.377618\pi\) |
−0.615265 | + | 0.788320i | \(0.710951\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.85383 | + | 1.07031i | −0.449619 | + | 0.259588i | −0.707669 | − | 0.706544i | \(-0.750253\pi\) |
0.258050 | + | 0.966131i | \(0.416920\pi\) | |||||||
\(18\) | 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 | ||||||||
\(23\) | −8.02649 | − | 4.63409i | −1.67364 | − | 0.966276i | −0.965574 | − | 0.260127i | \(-0.916235\pi\) |
−0.708064 | − | 0.706148i | \(-0.750431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 13.6770i | − | 2.63214i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.16599 | − | 7.21570i | 0.773605 | − | 1.33992i | −0.161971 | − | 0.986796i | \(-0.551785\pi\) |
0.935575 | − | 0.353127i | \(-0.114882\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.26819 | 1.48501 | 0.742505 | − | 0.669840i | \(-0.233637\pi\) | ||||
0.742505 | + | 0.669840i | \(0.233637\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.34233 | + | 1.92969i | −0.581824 | + | 0.335916i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.20440i | − | 0.362401i | −0.983446 | − | 0.181201i | \(-0.942002\pi\) | ||
0.983446 | − | 0.181201i | \(-0.0579984\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.20440 | −0.513115 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.30660 | + | 5.72720i | 0.516405 | + | 0.894439i | 0.999819 | + | 0.0190471i | \(0.00606323\pi\) |
−0.483414 | + | 0.875392i | \(0.660603\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.03084 | + | 1.17251i | −0.309701 | + | 0.178806i | −0.646793 | − | 0.762666i | \(-0.723890\pi\) |
0.337092 | + | 0.941472i | \(0.390557\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.21570 | + | 4.16599i | 1.05252 | + | 0.607672i | 0.923353 | − | 0.383951i | \(-0.125437\pi\) |
0.129165 | + | 0.991623i | \(0.458770\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.14061 | 0.305802 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.42969 | + | 5.94040i | −0.480253 | + | 0.831823i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.232259 | + | 0.134095i | 0.0319032 | + | 0.0184193i | 0.515867 | − | 0.856669i | \(-0.327470\pi\) |
−0.483964 | + | 0.875088i | \(0.660803\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −10.8726 | + | 8.76819i | −1.44012 | + | 1.16138i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.16599 | − | 7.21570i | −0.542366 | − | 0.939405i | −0.998768 | − | 0.0496310i | \(-0.984195\pi\) |
0.456402 | − | 0.889774i | \(-0.349138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.70440 | − | 2.95211i | 0.218226 | − | 0.377979i | −0.736040 | − | 0.676939i | \(-0.763306\pi\) |
0.954266 | + | 0.298960i | \(0.0966396\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −13.8755 | − | 8.01100i | −1.74814 | − | 1.00929i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.84253 | + | 1.06379i | 0.225101 | + | 0.129962i | 0.608310 | − | 0.793699i | \(-0.291848\pi\) |
−0.383209 | + | 0.923662i | \(0.625181\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −29.6990 | −3.57534 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.23630 | + | 9.06953i | 0.621434 | + | 1.07636i | 0.989219 | + | 0.146444i | \(0.0467829\pi\) |
−0.367785 | + | 0.929911i | \(0.619884\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.20835 | − | 2.42969i | 0.492550 | − | 0.284374i | −0.233082 | − | 0.972457i | \(-0.574881\pi\) |
0.725632 | + | 0.688083i | \(0.241548\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.65498i | 0.302564i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.20440 | + | 14.2104i | 0.923067 | + | 1.59880i | 0.794640 | + | 0.607080i | \(0.207659\pi\) |
0.128427 | + | 0.991719i | \(0.459007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0110 | − | 19.0716i | −1.22344 | − | 2.11907i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.73181i | 0.629148i | 0.949233 | + | 0.314574i | \(0.101862\pi\) | ||||
−0.949233 | + | 0.314574i | \(0.898138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 26.6990i | − | 2.86243i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.40880 | + | 9.36832i | −0.573332 | + | 0.993040i | 0.422889 | + | 0.906182i | \(0.361016\pi\) |
−0.996221 | + | 0.0868585i | \(0.972317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.10220 | + | 1.90907i | −0.115542 | + | 0.200125i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.9450 | − | 13.2473i | 2.37929 | − | 1.37368i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.6319 | − | 7.87039i | 1.38411 | − | 0.799117i | 0.391468 | − | 0.920192i | \(-0.371967\pi\) |
0.992643 | + | 0.121075i | \(0.0386341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.37691 | + | 7.58103i | −0.439896 | + | 0.761922i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.27471 | − | 9.13606i | 0.524853 | − | 0.909072i | −0.474728 | − | 0.880133i | \(-0.657454\pi\) |
0.999581 | − | 0.0289397i | \(-0.00921308\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.731811i | 0.0721075i | 0.999350 | + | 0.0360537i | \(0.0114787\pi\) | ||||
−0.999350 | + | 0.0360537i | \(0.988521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13.3958i | − | 1.29502i | −0.762058 | − | 0.647509i | \(-0.775811\pi\) | ||
0.762058 | − | 0.647509i | \(-0.224189\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.96811 | + | 5.14091i | 0.284293 | + | 0.492410i | 0.972437 | − | 0.233164i | \(-0.0749078\pi\) |
−0.688144 | + | 0.725574i | \(0.741574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.53189 | − | 6.11742i | −0.335233 | − | 0.580640i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 15.6132i | − | 1.46877i | −0.678735 | − | 0.734383i | \(-0.737471\pi\) | ||
0.678735 | − | 0.734383i | \(-0.262529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.29444 | + | 3.63409i | −0.581921 | + | 0.335972i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.35939 | + | 4.08658i | 0.216285 | + | 0.374616i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.54942 | −0.868129 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 18.3523 | + | 10.5957i | 1.65477 | + | 0.955380i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.2969 | + | 7.67699i | 1.17991 | + | 0.681223i | 0.955994 | − | 0.293385i | \(-0.0947818\pi\) |
0.223918 | + | 0.974608i | \(0.428115\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.75719 | + | 6.50764i | −0.330802 | + | 0.572965i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.89780 | + | 6.75119i | 0.340552 | + | 0.589854i | 0.984535 | − | 0.175186i | \(-0.0560526\pi\) |
−0.643983 | + | 0.765040i | \(0.722719\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.48397 | + | 9.49348i | 0.128676 | + | 0.823189i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.2657 | − | 8.23630i | −1.21880 | − | 0.703674i | −0.254138 | − | 0.967168i | \(-0.581792\pi\) |
−0.964661 | + | 0.263494i | \(0.915125\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.76819 | + | 16.9190i | −0.828527 | + | 1.43505i | 0.0706667 | + | 0.997500i | \(0.477487\pi\) |
−0.899194 | + | 0.437551i | \(0.855846\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.6990 | 2.24846 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.04304 | + | 0.602201i | 0.0872236 | + | 0.0503586i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.94040 | − | 3.42969i | 0.489956 | − | 0.282876i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.83850 | − | 4.91642i | −0.232539 | − | 0.402769i | 0.726016 | − | 0.687678i | \(-0.241370\pi\) |
−0.958555 | + | 0.284909i | \(0.908037\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.2264 | −1.15773 | −0.578864 | − | 0.815424i | \(-0.696504\pi\) | ||||
−0.578864 | + | 0.815424i | \(0.696504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 15.5584i | 1.25782i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.567233 | + | 0.327492i | −0.0452701 | + | 0.0261367i | −0.522464 | − | 0.852661i | \(-0.674987\pi\) |
0.477194 | + | 0.878798i | \(0.341654\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.859386 | 0.0681538 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.2154 | + | 17.6936i | −0.805087 | + | 1.39445i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.6770i | 0.992939i | 0.868054 | + | 0.496469i | \(0.165370\pi\) | ||||
−0.868054 | + | 0.496469i | \(0.834630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.75119 | + | 3.89780i | 0.522422 | + | 0.301621i | 0.737925 | − | 0.674882i | \(-0.235806\pi\) |
−0.215503 | + | 0.976503i | \(0.569139\pi\) | |||||||
\(168\) | 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 | ||||||||
\(173\) | 9.30179 | − | 5.37039i | 0.707202 | − | 0.408303i | −0.102822 | − | 0.994700i | \(-0.532787\pi\) |
0.810024 | + | 0.586397i | \(0.199454\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −23.1220 | − | 13.3495i | −1.73796 | − | 1.00341i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.54942 | 0.115809 | 0.0579044 | − | 0.998322i | \(-0.481558\pi\) | ||||
0.0579044 | + | 0.998322i | \(0.481558\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.11320 | − | 7.12428i | 0.305732 | − | 0.529544i | −0.671692 | − | 0.740831i | \(-0.734432\pi\) |
0.977424 | + | 0.211287i | \(0.0677655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 10.9232i | − | 0.807464i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.23275 | − | 1.28908i | 0.163275 | − | 0.0942668i | ||||
\(188\) | 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 | ||||||||
\(193\) | −14.9072 | + | 8.60669i | −1.07304 | + | 0.619523i | −0.929012 | − | 0.370050i | \(-0.879341\pi\) |
−0.144033 | + | 0.989573i | \(0.546007\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 10.2044i | − | 0.727034i | −0.931588 | − | 0.363517i | \(-0.881576\pi\) | ||
0.931588 | − | 0.363517i | \(-0.118424\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.03189 | − | 8.71550i | 0.356701 | − | 0.617825i | −0.630706 | − | 0.776022i | \(-0.717235\pi\) |
0.987408 | + | 0.158197i | \(0.0505680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.81761 | 0.480877 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.9063 | − | 9.18351i | −1.11640 | − | 0.644556i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −58.3380 | + | 33.6815i | −4.05477 | + | 2.34102i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.18688 | − | 0.810784i | 0.358784 | − | 0.0560831i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.12758 | + | 10.6133i | 0.421840 | + | 0.730648i | 0.996119 | − | 0.0880113i | \(-0.0280512\pi\) |
−0.574280 | + | 0.818659i | \(0.694718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.0624 | + | 16.7792i | 1.99132 | + | 1.14969i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 18.2264i | − | 1.23729i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.78571 | − | 13.4852i | 0.526110 | − | 0.911249i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.14061 | 0.143993 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.4501 | − | 10.0748i | 1.16854 | − | 0.674658i | 0.215206 | − | 0.976569i | \(-0.430958\pi\) |
0.953336 | + | 0.301911i | \(0.0976245\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 8.25515i | − | 0.547914i | −0.961742 | − | 0.273957i | \(-0.911667\pi\) | ||
0.961742 | − | 0.273957i | \(-0.0883325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.6860 | 1.76346 | 0.881729 | − | 0.471756i | \(-0.156380\pi\) | ||||
0.881729 | + | 0.471756i | \(0.156380\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.25382 | + | 7.36783i | 0.279881 | + | 0.484768i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1321 | + | 7.00448i | −0.794802 | + | 0.458879i | −0.841650 | − | 0.540023i | \(-0.818416\pi\) |
0.0468485 | + | 0.998902i | \(0.485082\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 45.5360 | + | 26.2902i | 2.95788 | + | 1.70773i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 12.2682 | 0.793563 | 0.396782 | − | 0.917913i | \(-0.370127\pi\) | ||||
0.396782 | + | 0.917913i | \(0.370127\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.93621 | + | 8.54977i | −0.317969 | + | 0.550739i | −0.980064 | − | 0.198681i | \(-0.936334\pi\) |
0.662095 | + | 0.749420i | \(0.269668\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −25.5793 | − | 14.7682i | −1.64091 | − | 0.947380i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.06622 | + | 1.57031i | 0.258727 | + | 0.0999162i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.18351 | + | 15.9063i | 0.581981 | + | 1.00802i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.4198 | + | 24.9758i | −0.910170 | + | 1.57646i | −0.0963474 | + | 0.995348i | \(0.530716\pi\) |
−0.813823 | + | 0.581113i | \(0.802617\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.66711 | + | 5.58131i | 0.607766 | + | 0.350894i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.15311 | + | 2.39780i | 0.259064 | + | 0.149571i | 0.623907 | − | 0.781498i | \(-0.285544\pi\) |
−0.364844 | + | 0.931069i | \(0.618878\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.85939 | −0.301948 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.2792 | − | 52.4451i | −1.87424 | − | 3.24627i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −17.6745 | + | 10.2044i | −1.08986 | + | 0.629230i | −0.933539 | − | 0.358476i | \(-0.883296\pi\) |
−0.156320 | + | 0.987706i | \(0.549963\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 34.6640i | 2.12140i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.563788 | + | 0.976509i | 0.0343747 | + | 0.0595388i | 0.882701 | − | 0.469935i | \(-0.155723\pi\) |
−0.848326 | + | 0.529474i | \(0.822389\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.83850 | − | 17.0408i | −0.597646 | − | 1.03515i | −0.993168 | − | 0.116697i | \(-0.962769\pi\) |
0.395522 | − | 0.918457i | \(-0.370564\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.06379i | 0.427520i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.35398i | 0.441858i | 0.975290 | + | 0.220929i | \(0.0709089\pi\) | ||||
−0.975290 | + | 0.220929i | \(0.929091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 30.0474 | − | 52.0436i | 1.79889 | − | 3.11577i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.73630 | + | 11.6676i | −0.401854 | + | 0.696031i | −0.993950 | − | 0.109836i | \(-0.964967\pi\) |
0.592096 | + | 0.805867i | \(0.298301\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.4627 | + | 10.6595i | −1.09750 | + | 0.633640i | −0.935562 | − | 0.353162i | \(-0.885106\pi\) |
−0.161934 | + | 0.986802i | \(0.551773\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.6251 | − | 7.28908i | 0.745233 | − | 0.430261i | ||||
\(288\) | 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 | ||||||||
\(293\) | − | 8.08580i | − | 0.472377i | −0.971707 | − | 0.236189i | \(-0.924102\pi\) | ||
0.971707 | − | 0.236189i | \(-0.0758983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 16.4726i | 0.955837i | ||||||||
\(298\) | 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 | ||||||||
\(303\) | − | 33.8046i | − | 1.94202i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.7549 | − | 14.2922i | 1.41284 | − | 0.815701i | 0.417180 | − | 0.908824i | \(-0.363018\pi\) |
0.995655 | + | 0.0931229i | \(0.0296850\pi\) | |||||||
\(308\) | 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 | ||||||||
\(313\) | 9.89160 | + | 5.71092i | 0.559107 | + | 0.322800i | 0.752787 | − | 0.658264i | \(-0.228709\pi\) |
−0.193680 | + | 0.981065i | \(0.562042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.81128 | − | 1.62309i | −0.157897 | − | 0.0911619i | 0.418970 | − | 0.908000i | \(-0.362391\pi\) |
−0.576867 | + | 0.816838i | \(0.695725\pi\) | |||||||
\(318\) | 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 | ||||||||
\(323\) | 7.26318 | − | 5.85735i | 0.404134 | − | 0.325912i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.4735 | + | 9.51100i | 0.910989 | + | 0.525960i | ||||
\(328\) | 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 | ||||||||
\(333\) | −13.8755 | − | 8.01100i | −0.760371 | − | 0.439000i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.7459 | − | 7.93621i | 0.748788 | − | 0.432313i | −0.0764677 | − | 0.997072i | \(-0.524364\pi\) |
0.825256 | + | 0.564759i | \(0.191031\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.0155 | − | 43.3281i | −1.35865 | − | 2.35326i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.95822 | −0.539268 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 20.1496i | − | 1.08798i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −28.2707 | + | 16.3221i | −1.51765 | + | 0.876216i | −0.517866 | + | 0.855462i | \(0.673273\pi\) |
−0.999785 | + | 0.0207537i | \(0.993393\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.7538 | 1.16446 | 0.582228 | − | 0.813026i | \(-0.302181\pi\) | ||||
0.582228 | + | 0.813026i | \(0.302181\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −6.83850 | + | 11.8446i | −0.365012 | + | 0.632219i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 8.67699i | − | 0.461830i | −0.972974 | − | 0.230915i | \(-0.925828\pi\) | ||
0.972974 | − | 0.230915i | \(-0.0741719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 13.0950 | + | 7.56042i | 0.693063 | + | 0.400140i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.81109 | + | 10.0651i | 0.306697 | + | 0.531216i | 0.977638 | − | 0.210296i | \(-0.0674427\pi\) |
−0.670940 | + | 0.741511i | \(0.734109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.0936 | − | 5.79827i | 0.952297 | − | 0.305172i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −26.5005 | + | 15.3001i | −1.39092 | + | 0.803046i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −26.5083 | − | 15.3046i | −1.38372 | − | 0.798892i | −0.391123 | − | 0.920338i | \(-0.627913\pi\) |
−0.992598 | + | 0.121446i | \(0.961247\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 48.0660 | 2.50222 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.295598 | − | 0.511992i | 0.0153467 | − | 0.0265813i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 4.70980i | − | 0.243864i | −0.992538 | − | 0.121932i | \(-0.961091\pi\) | ||
0.992538 | − | 0.121932i | \(-0.0389090\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.21570 | + | 4.16599i | −0.371628 | + | 0.214559i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.0638 | −0.516942 | −0.258471 | − | 0.966019i | \(-0.583219\pi\) | ||||
−0.258471 | + | 0.966019i | \(0.583219\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 49.2003 | 2.52061 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.7671 | + | 13.7219i | −1.21444 | + | 0.701158i | −0.963723 | − | 0.266903i | \(-0.914000\pi\) |
−0.250717 | + | 0.968060i | \(0.580666\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.0440i | 0.866396i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.257185 | − | 0.445458i | 0.0130398 | − | 0.0225856i | −0.859432 | − | 0.511250i | \(-0.829183\pi\) |
0.872472 | + | 0.488665i | \(0.162516\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 19.8396 | 1.00333 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.6335 | + | 12.4901i | 1.09127 | + | 0.630043i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.68950 | − | 1.55278i | 0.134982 | − | 0.0779320i | −0.430988 | − | 0.902358i | \(-0.641835\pi\) |
0.565970 | + | 0.824426i | \(0.308502\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 19.3286 | + | 23.9677i | 0.967641 | + | 1.19988i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.51752 | + | 11.2887i | 0.325470 | + | 0.563730i | 0.981607 | − | 0.190911i | \(-0.0611443\pi\) |
−0.656138 | + | 0.754641i | \(0.727811\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.16046 | − | 4.13409i | −0.356688 | − | 0.205934i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.65498i | 0.131603i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.7747 | − | 23.8585i | 0.681115 | − | 1.17973i | −0.293525 | − | 0.955951i | \(-0.594828\pi\) |
0.974641 | − | 0.223775i | \(-0.0718382\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −52.7848 | −2.60368 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −15.9063 | + | 9.18351i | −0.782698 | + | 0.451891i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 62.6024i | 3.06565i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.5494 | −0.808492 | −0.404246 | − | 0.914650i | \(-0.632466\pi\) | ||||
−0.404246 | + | 0.914650i | \(0.632466\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.93418 | + | 13.7424i | 0.386688 | + | 0.669764i | 0.992002 | − | 0.126223i | \(-0.0402856\pi\) |
−0.605314 | + | 0.795987i | \(0.706952\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 52.4451 | − | 30.2792i | 2.54997 | − | 1.47222i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.50764 | − | 3.75719i | −0.314927 | − | 0.181823i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.85939 | 0.186333 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.4472 | + | 19.8272i | −0.551393 | + | 0.955041i | 0.446781 | + | 0.894643i | \(0.352570\pi\) |
−0.998174 | + | 0.0603975i | \(0.980763\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4740 | − | 10.6660i | −0.887805 | − | 0.512575i | −0.0145814 | − | 0.999894i | \(-0.504642\pi\) |
−0.873224 | + | 0.487319i | \(0.837975\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.6865 | + | 14.5539i | 1.80279 | + | 0.696208i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.08783 | − | 8.81238i | −0.242829 | − | 0.420592i | 0.718690 | − | 0.695331i | \(-0.244742\pi\) |
−0.961519 | + | 0.274739i | \(0.911409\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.77919 | − | 13.4740i | 0.370438 | − | 0.641617i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.72720 | − | 3.30660i | −0.272108 | − | 0.157101i | 0.357737 | − | 0.933822i | \(-0.383548\pi\) |
−0.629845 | + | 0.776721i | \(0.716882\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.7542 | − | 9.09568i | −0.745147 | − | 0.430211i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9870 | −0.518507 | −0.259253 | − | 0.965809i | \(-0.583476\pi\) | ||||
−0.259253 | + | 0.965809i | \(0.583476\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.98248 | − | 6.89785i | −0.187528 | − | 0.324807i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −39.4796 | + | 22.7936i | −1.85491 | + | 1.07094i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 12.5494i | 0.587037i | 0.955953 | + | 0.293518i | \(0.0948262\pi\) | ||||
−0.955953 | + | 0.293518i | \(0.905174\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.6386 | + | 25.3548i | 0.683270 | + | 1.18346i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.6386 | + | 20.1586i | 0.542063 | + | 0.938880i | 0.998785 | + | 0.0492710i | \(0.0156898\pi\) |
−0.456723 | + | 0.889609i | \(0.650977\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 23.3958i | 1.08729i | 0.839314 | + | 0.543647i | \(0.182957\pi\) | ||||
−0.839314 | + | 0.543647i | \(0.817043\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 12.6352i | − | 0.584688i | −0.956313 | − | 0.292344i | \(-0.905565\pi\) | ||
0.956313 | − | 0.292344i | \(-0.0944352\pi\) | |||||||
\(468\) | 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 | ||||||||
\(473\) | 2.44595 | − | 1.41217i | 0.112465 | − | 0.0649316i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.68810 | − | 0.974625i | 0.0772928 | − | 0.0446250i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.01752 | − | 3.49445i | 0.0921830 | − | 0.159666i | −0.816246 | − | 0.577704i | \(-0.803949\pi\) |
0.908429 | + | 0.418038i | \(0.137282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.10220 | + | 1.90907i | −0.0502560 | + | 0.0870460i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 65.4685i | 2.97892i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.54942i | 0.296782i | 0.988929 | + | 0.148391i | \(0.0474095\pi\) | ||||
−0.988929 | + | 0.148391i | \(0.952591\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.3111 | + | 35.1798i | 0.918499 | + | 1.59089i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.04290 | − | 1.80635i | −0.0470653 | − | 0.0815195i | 0.841533 | − | 0.540206i | \(-0.181654\pi\) |
−0.888598 | + | 0.458686i | \(0.848320\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8355i | 0.803273i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 19.9929 | − | 11.5429i | 0.896803 | − | 0.517770i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.0539 | − | 20.8780i | −0.539607 | − | 0.934626i | −0.998925 | − | 0.0463546i | \(-0.985240\pi\) |
0.459318 | − | 0.888272i | \(-0.348094\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 24.9802 | 1.11603 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.16823 | − | 4.13858i | −0.319616 | − | 0.184530i | 0.331606 | − | 0.943418i | \(-0.392410\pi\) |
−0.651221 | + | 0.758888i | \(0.725743\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.3011 | − | 19.2264i | −1.47895 | − | 0.853875i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.86591 | + | 4.96389i | −0.127029 | + | 0.220021i | −0.922524 | − | 0.385939i | \(-0.873877\pi\) |
0.795495 | + | 0.605960i | \(0.207211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.35602 | − | 9.27690i | −0.236936 | − | 0.410386i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.20713 | + | 58.9014i | 0.406505 | + | 2.60056i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.69060 | − | 5.01752i | −0.382212 | − | 0.220670i | ||||
\(518\) | 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 | ||||||||
\(523\) | 13.4988 | + | 7.79356i | 0.590263 | + | 0.340789i | 0.765202 | − | 0.643791i | \(-0.222639\pi\) |
−0.174938 | + | 0.984579i | \(0.555973\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −15.3278 | + | 8.84950i | −0.667689 | + | 0.385490i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 31.4497 | + | 54.4724i | 1.36738 | + | 2.36837i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −60.5584 | −2.62801 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 6.61320i | − | 0.286450i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.29978 | − | 2.48248i | 0.185549 | − | 0.107127i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.57816 | −0.111049 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.0539 | + | 24.3421i | −0.604224 | + | 1.04655i | 0.387949 | + | 0.921681i | \(0.373184\pi\) |
−0.992174 | + | 0.124867i | \(0.960150\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 26.3607i | − | 1.13125i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 37.5569 | + | 21.6835i | 1.60582 | + | 0.927120i | 0.990292 | + | 0.139004i | \(0.0443902\pi\) |
0.615527 | + | 0.788116i | \(0.288943\pi\) | |||||||
\(548\) | 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 | ||||||||
\(553\) | 31.3255 | − | 18.0858i | 1.33210 | − | 0.769086i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.9963 | − | 8.65814i | −0.635415 | − | 0.366857i | 0.147431 | − | 0.989072i | \(-0.452900\pi\) |
−0.782846 | + | 0.622215i | \(0.786233\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.34502 | 0.0991836 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.13073 | − | 7.15463i | 0.174399 | − | 0.302069i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 8.35398i | − | 0.352078i | −0.984383 | − | 0.176039i | \(-0.943671\pi\) | ||
0.984383 | − | 0.176039i | \(-0.0563286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −42.0415 | + | 24.2727i | −1.76558 | + | 1.01936i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.6640 | 0.447056 | 0.223528 | − | 0.974697i | \(-0.428243\pi\) | ||||
0.223528 | + | 0.974697i | \(0.428243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.56512 | −0.107347 | −0.0536735 | − | 0.998559i | \(-0.517093\pi\) | ||||
−0.0536735 | + | 0.998559i | \(0.517093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 45.1819 | − | 26.0858i | 1.88750 | − | 1.08975i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20.4218i | 0.850172i | 0.905153 | + | 0.425086i | \(0.139756\pi\) | ||||
−0.905153 | + | 0.425086i | \(0.860244\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −27.5793 | + | 47.7687i | −1.14616 | + | 1.98520i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.6352 | 0.524197 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.279733 | − | 0.161504i | −0.0115853 | − | 0.00668880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.62850 | + | 4.40432i | −0.314862 | + | 0.181786i | −0.649100 | − | 0.760703i | \(-0.724854\pi\) |
0.334238 | + | 0.942489i | \(0.391521\pi\) | |||||||
\(588\) | 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 | ||||||||
\(593\) | 28.5314 | + | 16.4726i | 1.17164 | + | 0.676448i | 0.954066 | − | 0.299595i | \(-0.0968516\pi\) |
0.217576 | + | 0.976043i | \(0.430185\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 32.2484i | − | 1.31984i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.56379 | + | 16.5650i | −0.390766 | + | 0.676826i | −0.992551 | − | 0.121832i | \(-0.961123\pi\) |
0.601785 | + | 0.798658i | \(0.294456\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.3100 | 0.787670 | 0.393835 | − | 0.919181i | \(-0.371148\pi\) | ||||
0.393835 | + | 0.919181i | \(0.371148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 13.3919 | − | 7.73181i | 0.545360 | − | 0.314864i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 36.8773i | 1.49680i | 0.663245 | + | 0.748402i | \(0.269179\pi\) | ||||
−0.663245 | + | 0.748402i | \(0.730821\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −58.8553 | −2.38494 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.16599 | − | 7.21570i | −0.168538 | − | 0.291916i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 24.6996 | − | 14.2603i | 0.997609 | − | 0.575970i | 0.0900688 | − | 0.995936i | \(-0.471291\pi\) |
0.907540 | + | 0.419966i | \(0.137958\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.78112 | + | 5.64713i | 0.393773 | + | 0.227345i | 0.683794 | − | 0.729675i | \(-0.260329\pi\) |
−0.290021 | + | 0.957020i | \(0.593662\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.2044 | −1.09344 | −0.546719 | − | 0.837316i | \(-0.684123\pi\) | ||||
−0.546719 | + | 0.837316i | \(0.684123\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −63.3805 | + | 109.778i | −2.54337 | + | 4.40525i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 20.6515 | + | 11.9232i | 0.827387 | + | 0.477692i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 13.0950 | − | 10.5604i | 0.522965 | − | 0.421743i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.35939 | + | 4.08658i | 0.0940749 | + | 0.162942i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19136 | + | 7.25965i | −0.166856 | + | 0.289002i | −0.937313 | − | 0.348490i | \(-0.886695\pi\) |
0.770457 | + | 0.637492i | \(0.220028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 34.0092 | + | 19.6352i | 1.35174 | + | 0.780430i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85383 | − | 1.07031i | −0.0734513 | − | 0.0424071i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 76.1168 | 3.01113 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.55594 | − | 16.5514i | −0.377437 | − | 0.653740i | 0.613252 | − | 0.789888i | \(-0.289861\pi\) |
−0.990689 | + | 0.136148i | \(0.956528\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 41.7618 | − | 24.1112i | 1.64692 | − | 0.950852i | 0.668638 | − | 0.743588i | \(-0.266877\pi\) |
0.978285 | − | 0.207264i | \(-0.0664559\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 30.0817i | − | 1.18263i | −0.806439 | − | 0.591317i | \(-0.798608\pi\) | ||
0.806439 | − | 0.591317i | \(-0.201392\pi\) | |||||||
\(648\) | 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 | ||||||||
\(653\) | − | 41.9124i | − | 1.64016i | −0.572250 | − | 0.820079i | \(-0.693929\pi\) | ||
0.572250 | − | 0.820079i | \(-0.306071\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 35.3189i | − | 1.37792i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.0936 | + | 34.8032i | −0.782737 | + | 1.35574i | 0.147604 | + | 0.989047i | \(0.452844\pi\) |
−0.930341 | + | 0.366694i | \(0.880489\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.757185 | − | 1.31148i | 0.0294511 | − | 0.0510108i | −0.850924 | − | 0.525289i | \(-0.823957\pi\) |
0.880375 | + | 0.474278i | \(0.157291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.94040 | − | 3.42969i | 0.230706 | − | 0.133198i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −66.8765 | + | 38.6112i | −2.58947 | + | 1.49503i | ||||
\(668\) | 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 | ||||||||
\(673\) | 7.76686i | 0.299390i | 0.988732 | + | 0.149695i | \(0.0478292\pi\) | ||||
−0.988732 | + | 0.149695i | \(0.952171\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.19136i | 0.237953i | 0.992897 | + | 0.118977i | \(0.0379614\pi\) | ||||
−0.992897 | + | 0.118977i | \(0.962039\pi\) | |||||||
\(678\) | 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 | ||||||||
\(683\) | − | 2.92317i | − | 0.111852i | −0.998435 | − | 0.0559261i | \(-0.982189\pi\) | ||
0.998435 | − | 0.0559261i | \(-0.0178111\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 74.0560 | − | 42.7563i | 2.82541 | − | 1.63125i | ||||
\(688\) | 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 | ||||||||
\(693\) | 16.7116 | + | 9.64847i | 0.634822 | + | 0.366515i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −12.2597 | − | 7.07816i | −0.464370 | − | 0.268104i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −22.4452 | + | 38.8762i | −0.848955 | + | 1.47043i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.2792 | − | 21.2682i | −0.463779 | − | 0.803288i | 0.535367 | − | 0.844620i | \(-0.320173\pi\) |
−0.999145 | + | 0.0413314i | \(0.986840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.48397 | + | 9.49348i | 0.0559689 | + | 0.358053i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −20.1396 | − | 11.6276i | −0.757426 | − | 0.437300i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.63858 | − | 6.30220i | 0.136650 | − | 0.236684i | −0.789577 | − | 0.613652i | \(-0.789700\pi\) |
0.926226 | + | 0.376968i | \(0.123033\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 119.262 | 4.47269 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −66.3645 | − | 38.3156i | −2.48537 | − | 1.43493i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 34.0454 | − | 19.6561i | 1.27145 | − | 0.734071i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 16.4452 | + | 28.4839i | 0.613302 | + | 1.06227i | 0.990680 | + | 0.136211i | \(0.0434924\pi\) |
−0.377378 | + | 0.926059i | \(0.623174\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.61320 | 0.0600789 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 31.6352i | 1.17653i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.1709 | − | 13.9551i | 0.896449 | − | 0.517565i | 0.0204023 | − | 0.999792i | \(-0.493505\pi\) |
0.876046 | + | 0.482227i | \(0.160172\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −28.5804 | −1.05853 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.50989 | − | 4.34725i | 0.0928315 | − | 0.160789i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.89710i | 0.180878i | 0.995902 | + | 0.0904392i | \(0.0288271\pi\) | ||||
−0.995902 | + | 0.0904392i | \(0.971173\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.21915 | − | 1.28123i | −0.0817435 | − | 0.0471946i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −11.5936 | − | 20.0808i | −0.426479 | − | 0.738684i | 0.570078 | − | 0.821591i | \(-0.306913\pi\) |
−0.996557 | + | 0.0829069i | \(0.973580\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.8001 | − | 2.15715i | 0.506959 | − | 0.0792449i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −34.6239 | + | 19.9901i | −1.27023 | + | 0.733366i | −0.975031 | − | 0.222070i | \(-0.928719\pi\) |
−0.295197 | + | 0.955436i | \(0.595385\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 36.0785 | + | 20.8299i | 1.32004 | + | 0.762128i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.5296 | −1.07899 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.2936 | − | 17.8290i | 0.375617 | − | 0.650589i | −0.614802 | − | 0.788682i | \(-0.710764\pi\) |
0.990419 | + | 0.138093i | \(0.0440973\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 92.4137i | 3.36774i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.9950 | + | 17.3176i | −1.09019 | + | 0.629419i | −0.933626 | − | 0.358249i | \(-0.883374\pi\) |
−0.156560 | + | 0.987668i | \(0.550040\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 11.3326 | − | 6.54290i | 0.410269 | − | 0.236869i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.33198i | 0.300850i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.27471 | − | 5.67196i | 0.118089 | − | 0.204536i | −0.800921 | − | 0.598770i | \(-0.795657\pi\) |
0.919010 | + | 0.394233i | \(0.128990\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.3670 | 0.553430 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.4522 | − | 18.7363i | −1.16723 | − | 0.673898i | −0.214200 | − | 0.976790i | \(-0.568714\pi\) |
−0.953025 | + | 0.302892i | \(0.902048\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.4852 | + | 7.78571i | −0.483781 | + | 0.279311i | ||||
\(778\) | 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 | ||||||||
\(783\) | −98.6891 | − | 56.9782i | −3.52686 | − | 2.03623i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 12.8306i | − | 0.457363i | −0.973501 | − | 0.228682i | \(-0.926559\pi\) | ||
0.973501 | − | 0.228682i | \(-0.0734415\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −32.6990 | + | 56.6363i | −1.16412 | + | 2.01631i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.4178 | −1.22376 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.95211 | + | 1.70440i | −0.104833 | + | 0.0605251i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 28.3032i | − | 1.00255i | −0.865287 | − | 0.501276i | \(-0.832864\pi\) | ||
0.865287 | − | 0.501276i | \(-0.167136\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.8355 | −0.630976 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 39.3122 | + | 68.0907i | 1.38903 | + | 2.40587i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.06855 | + | 2.92633i | −0.178865 | + | 0.103268i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.12913 | + | 1.80660i | 0.110150 | + | 0.0635954i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 55.4946 | 1.95109 | 0.975543 | − | 0.219808i | \(-0.0705432\pi\) | ||||
0.975543 | + | 0.219808i | \(0.0705432\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.8540 | − | 20.5317i | 0.416250 | − | 0.720966i | −0.579309 | − | 0.815108i | \(-0.696678\pi\) |
0.995559 | + | 0.0941424i | \(0.0300109\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −54.6055 | − | 31.5265i | −1.91510 | − | 1.10568i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.95672 | − | 6.41665i | 0.278370 | − | 0.224490i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 8.01100 | + | 13.8755i | 0.279927 | + | 0.484848i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.3625 | + | 19.6805i | −0.396555 | + | 0.686854i | −0.993298 | − | 0.115578i | \(-0.963128\pi\) |
0.596743 | + | 0.802432i | \(0.296461\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −13.8564 | − | 8.00000i | −0.483004 | − | 0.278862i | 0.238664 | − | 0.971102i | \(-0.423291\pi\) |
−0.721668 | + | 0.692240i | \(0.756624\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.2291 | − | 9.94722i | −0.599114 | − | 0.345899i | 0.169579 | − | 0.985517i | \(-0.445759\pi\) |
−0.768693 | + | 0.639618i | \(0.779093\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.37109 | −0.151814 | −0.0759071 | − | 0.997115i | \(-0.524185\pi\) | ||||
−0.0759071 | + | 0.997115i | \(0.524185\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.7826 | + | 20.4080i | 0.408732 | + | 0.707945i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.96833 | + | 2.29111i | −0.137494 | + | 0.0793824i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 113.084i | − | 3.90875i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.22396 | + | 2.11996i | 0.0422558 | + | 0.0731891i | 0.886380 | − | 0.462959i | \(-0.153212\pi\) |
−0.844124 | + | 0.536148i | \(0.819879\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.2109 | − | 35.0063i | −0.696928 | − | 1.20712i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 43.1716i | 1.48691i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.0507i | 0.723312i | ||||||||
\(848\) | 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 | ||||||||
\(853\) | 15.5297 | − | 8.96607i | 0.531727 | − | 0.306992i | −0.209993 | − | 0.977703i | \(-0.567344\pi\) |
0.741719 | + | 0.670711i | \(0.234011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.3115 | + | 29.0474i | −1.71861 | + | 0.992240i | −0.797135 | + | 0.603801i | \(0.793652\pi\) |
−0.921475 | + | 0.388438i | \(0.873015\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0409 | − | 17.3913i | 0.342590 | − | 0.593383i | −0.642323 | − | 0.766434i | \(-0.722029\pi\) |
0.984913 | + | 0.173051i | \(0.0553626\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 23.3571 | − | 40.4557i | 0.796009 | − | 1.37873i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.6262i | 0.974449i | 0.873277 | + | 0.487224i | \(0.161991\pi\) | ||||
−0.873277 | + | 0.487224i | \(0.838009\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 39.7915i | 1.35139i | ||||||||
\(868\) | 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 | ||||||||
\(873\) | − | 114.407i | − | 3.87209i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.2019 | − | 25.5200i | 1.49259 | − | 0.861748i | 0.492628 | − | 0.870240i | \(-0.336036\pi\) |
0.999964 | + | 0.00849182i | \(0.00270306\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | 25.4610 | + | 14.6999i | 0.856831 | + | 0.494692i | 0.862950 | − | 0.505290i | \(-0.168614\pi\) |
−0.00611882 | + | 0.999981i | \(0.501948\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.2031 | − | 6.46811i | −0.376163 | − | 0.217178i | 0.299985 | − | 0.953944i | \(-0.403018\pi\) |
−0.676147 | + | 0.736766i | \(0.736352\pi\) | |||||||
\(888\) | 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 | ||||||||
\(893\) | −33.8796 | − | 13.0838i | −1.13374 | − | 0.437831i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 25.7201 | + | 14.8495i | 0.858769 | + | 0.495810i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 34.4452 | − | 59.6608i | 1.14881 | − | 1.98980i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.574090 | −0.0191257 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 14.3454 | + | 8.28235i | 0.477386 | + | 0.275619i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.66025 | + | 5.00000i | −0.287559 | + | 0.166022i | −0.636841 | − | 0.770996i | \(-0.719759\pi\) |
0.349281 | + | 0.937018i | \(0.386426\pi\) | |||||||
\(908\) | 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 | ||||||||
\(913\) | − | 6.90340i | − | 0.228469i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8823 | − | 8.59231i | 0.491458 | − | 0.283743i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −23.4987 | −0.775150 | −0.387575 | − | 0.921838i | \(-0.626687\pi\) | ||||
−0.387575 | + | 0.921838i | \(0.626687\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 45.7980 | − | 79.3245i | 1.50910 | − | 2.61383i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 10.4726i | − | 0.344710i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.60634 | + | 2.65947i | 0.151292 | + | 0.0873484i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −22.3221 | − | 38.6630i | −0.732364 | − | 1.26849i | −0.955870 | − | 0.293789i | \(-0.905084\pi\) |
0.223506 | − | 0.974703i | \(-0.428250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.21877 | + | 1.44103i | −0.302133 | + | 0.0472277i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.8067 | + | 17.2089i | −0.975826 | + | 0.563394i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.3279 | + | 11.7363i | 0.664082 | + | 0.383408i | 0.793831 | − | 0.608139i | \(-0.208084\pi\) |
−0.129748 | + | 0.991547i | \(0.541417\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 36.6002 | 1.19440 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0858 | + | 34.7896i | −0.654778 | + | 1.13411i | 0.327171 | + | 0.944965i | \(0.393905\pi\) |
−0.981949 | + | 0.189144i | \(0.939429\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 61.2924i | − | 1.99596i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.7688 | − | 9.68148i | 0.544913 | − | 0.314606i | −0.202155 | − | 0.979354i | \(-0.564794\pi\) |
0.747068 | + | 0.664748i | \(0.231461\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.85939 | −0.157742 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.4021 | −0.337310 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.19123 | + | 2.41981i | −0.135767 | + | 0.0783852i | −0.566345 | − | 0.824168i | \(-0.691643\pi\) |
0.430578 | + | 0.902553i | \(0.358310\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 32.1563i | 1.03947i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −18.1561 | + | 31.4473i | −0.586291 | + | 1.01549i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 37.3630 | 1.20526 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −84.3188 | − | 48.6815i | −2.71714 | − | 1.56874i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 23.4457 | − | 13.5364i | 0.753963 | − | 0.435301i | −0.0731612 | − | 0.997320i | \(-0.523309\pi\) |
0.827124 | + | 0.562020i | \(0.189975\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.7713 | − | 27.8918i | 0.346025 | − | 0.896013i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.61769 | − | 2.80192i | −0.0519141 | − | 0.0899179i | 0.838901 | − | 0.544285i | \(-0.183199\pi\) |
−0.890815 | + | 0.454367i | \(0.849866\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 37.2963 | + | 21.5330i | 1.19566 | + | 0.690317i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.93214i | − | 0.0618147i | −0.999522 | − | 0.0309074i | \(-0.990160\pi\) | ||
0.999522 | − | 0.0309074i | \(-0.00983969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.51437 | − | 11.2832i | 0.208200 | − | 0.360613i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 43.1455 | 1.37753 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.4457 | − | 7.18555i | 0.396957 | − | 0.229183i | −0.288213 | − | 0.957566i | \(-0.593061\pi\) |
0.685170 | + | 0.728383i | \(0.259728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 58.8553i | − | 1.87339i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.7340 | 0.691102 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.7956 | − | 30.8229i | −0.565296 | − | 0.979121i | −0.997022 | − | 0.0771164i | \(-0.975429\pi\) |
0.431726 | − | 0.902005i | \(-0.357905\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 97.4636 | − | 56.2706i | 3.09291 | − | 1.78569i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −41.2058 | − | 23.7902i | −1.30500 | − | 0.753443i | −0.323744 | − | 0.946145i | \(-0.604942\pi\) |
−0.981257 | + | 0.192702i | \(0.938275\pi\) | |||||||
\(998\) | 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.s.c.349.6 | 12 | ||
5.2 | odd | 4 | 1900.2.i.c.501.1 | 6 | |||
5.3 | odd | 4 | 380.2.i.b.121.3 | ✓ | 6 | ||
5.4 | even | 2 | inner | 1900.2.s.c.349.1 | 12 | ||
15.8 | even | 4 | 3420.2.t.v.1261.1 | 6 | |||
19.11 | even | 3 | inner | 1900.2.s.c.49.1 | 12 | ||
20.3 | even | 4 | 1520.2.q.i.881.1 | 6 | |||
95.49 | even | 6 | inner | 1900.2.s.c.49.6 | 12 | ||
95.68 | odd | 12 | 380.2.i.b.201.3 | yes | 6 | ||
95.83 | odd | 12 | 7220.2.a.n.1.1 | 3 | |||
95.87 | odd | 12 | 1900.2.i.c.201.1 | 6 | |||
95.88 | even | 12 | 7220.2.a.o.1.3 | 3 | |||
285.68 | even | 12 | 3420.2.t.v.3241.1 | 6 | |||
380.163 | even | 12 | 1520.2.q.i.961.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
380.2.i.b.121.3 | ✓ | 6 | 5.3 | odd | 4 | ||
380.2.i.b.201.3 | yes | 6 | 95.68 | odd | 12 | ||
1520.2.q.i.881.1 | 6 | 20.3 | even | 4 | |||
1520.2.q.i.961.1 | 6 | 380.163 | even | 12 | |||
1900.2.i.c.201.1 | 6 | 95.87 | odd | 12 | |||
1900.2.i.c.501.1 | 6 | 5.2 | odd | 4 | |||
1900.2.s.c.49.1 | 12 | 19.11 | even | 3 | inner | ||
1900.2.s.c.49.6 | 12 | 95.49 | even | 6 | inner | ||
1900.2.s.c.349.1 | 12 | 5.4 | even | 2 | inner | ||
1900.2.s.c.349.6 | 12 | 1.1 | even | 1 | trivial | ||
3420.2.t.v.1261.1 | 6 | 15.8 | even | 4 | |||
3420.2.t.v.3241.1 | 6 | 285.68 | even | 12 | |||
7220.2.a.n.1.1 | 3 | 95.83 | odd | 12 | |||
7220.2.a.o.1.3 | 3 | 95.88 | even | 12 |