Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(229,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.229");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 229.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.229 |
Dual form | 570.2.d.a.229.2 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | ||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 2.00000 | + | 1.00000i | 0.632456 | + | 0.316228i | ||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | + | 1.00000i | 0.516398 | + | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.00000i | 1.45521i | 0.685994 | + | 0.727607i | \(0.259367\pi\) | ||||
−0.685994 | + | 0.727607i | \(0.740633\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.00000 | 0.371391 | 0.185695 | − | 0.982607i | \(-0.440546\pi\) | ||||
0.185695 | + | 0.982607i | \(0.440546\pi\) | |||||||
\(30\) | 1.00000 | − | 2.00000i | 0.182574 | − | 0.365148i | ||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 4.00000i | 0.696311i | ||||||||
\(34\) | 6.00000 | 1.02899 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 10.0000i | 1.64399i | 0.569495 | + | 0.821995i | \(0.307139\pi\) | ||||
−0.569495 | + | 0.821995i | \(0.692861\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | −2.00000 | − | 1.00000i | −0.316228 | − | 0.158114i | ||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 6.00000i | − | 0.914991i | −0.889212 | − | 0.457496i | \(-0.848747\pi\) | ||
0.889212 | − | 0.457496i | \(-0.151253\pi\) | |||||||
\(44\) | 4.00000 | 0.603023 | ||||||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | − | 6.00000i | − | 0.875190i | −0.899172 | − | 0.437595i | \(-0.855830\pi\) | ||
0.899172 | − | 0.437595i | \(-0.144170\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −4.00000 | + | 3.00000i | −0.565685 | + | 0.424264i | ||||
\(51\) | 6.00000 | 0.840168 | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 10.0000i | 1.37361i | 0.726844 | + | 0.686803i | \(0.240986\pi\) | ||||
−0.726844 | + | 0.686803i | \(0.759014\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 4.00000 | − | 8.00000i | 0.539360 | − | 1.07872i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | −2.00000 | −0.260378 | −0.130189 | − | 0.991489i | \(-0.541558\pi\) | ||||
−0.130189 | + | 0.991489i | \(0.541558\pi\) | |||||||
\(60\) | −2.00000 | − | 1.00000i | −0.258199 | − | 0.129099i | ||||
\(61\) | −6.00000 | −0.768221 | −0.384111 | − | 0.923287i | \(-0.625492\pi\) | ||||
−0.384111 | + | 0.923287i | \(0.625492\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.00000 | − | 2.00000i | −0.496139 | − | 0.248069i | ||||
\(66\) | 4.00000 | 0.492366 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | − | 6.00000i | − | 0.727607i | ||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.0000 | −1.42414 | −0.712069 | − | 0.702109i | \(-0.752242\pi\) | ||||
−0.712069 | + | 0.702109i | \(0.752242\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 16.0000i | − | 1.87266i | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||
0.351123 | − | 0.936329i | \(-0.385800\pi\) | |||||||
\(74\) | 10.0000 | 1.16248 | ||||||||
\(75\) | −4.00000 | + | 3.00000i | −0.461880 | + | 0.346410i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | 14.0000 | 1.57512 | 0.787562 | − | 0.616236i | \(-0.211343\pi\) | ||||
0.787562 | + | 0.616236i | \(0.211343\pi\) | |||||||
\(80\) | −1.00000 | + | 2.00000i | −0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.0000 | − | 6.00000i | −1.30158 | − | 0.650791i | ||||
\(86\) | −6.00000 | −0.646997 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | − | 4.00000i | − | 0.426401i | ||||||
\(89\) | −4.00000 | −0.423999 | −0.212000 | − | 0.977270i | \(-0.567998\pi\) | ||||
−0.212000 | + | 0.977270i | \(0.567998\pi\) | |||||||
\(90\) | −2.00000 | − | 1.00000i | −0.210819 | − | 0.105409i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | −6.00000 | −0.618853 | ||||||||
\(95\) | −1.00000 | + | 2.00000i | −0.102598 | + | 0.205196i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 10.0000i | 1.01535i | 0.861550 | + | 0.507673i | \(0.169494\pi\) | ||||
−0.861550 | + | 0.507673i | \(0.830506\pi\) | |||||||
\(98\) | − | 7.00000i | − | 0.707107i | ||||||
\(99\) | 4.00000 | 0.402015 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | −18.0000 | −1.79107 | −0.895533 | − | 0.444994i | \(-0.853206\pi\) | ||||
−0.895533 | + | 0.444994i | \(0.853206\pi\) | |||||||
\(102\) | − | 6.00000i | − | 0.594089i | ||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.0000 | 0.971286 | ||||||||
\(107\) | 4.00000i | 0.386695i | 0.981130 | + | 0.193347i | \(0.0619344\pi\) | ||||
−0.981130 | + | 0.193347i | \(0.938066\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −4.00000 | −0.383131 | −0.191565 | − | 0.981480i | \(-0.561356\pi\) | ||||
−0.191565 | + | 0.981480i | \(0.561356\pi\) | |||||||
\(110\) | −8.00000 | − | 4.00000i | −0.762770 | − | 0.381385i | ||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000i | 0.188144i | 0.995565 | + | 0.0940721i | \(0.0299884\pi\) | ||||
−0.995565 | + | 0.0940721i | \(0.970012\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −12.0000 | − | 6.00000i | −1.11901 | − | 0.559503i | ||||
\(116\) | −2.00000 | −0.185695 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | 2.00000i | 0.184115i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 2.00000i | −0.0912871 | + | 0.182574i | ||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 6.00000i | 0.543214i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | −6.00000 | −0.528271 | ||||||||
\(130\) | −2.00000 | + | 4.00000i | −0.175412 | + | 0.350823i | ||||
\(131\) | −8.00000 | −0.698963 | −0.349482 | − | 0.936943i | \(-0.613642\pi\) | ||||
−0.349482 | + | 0.936943i | \(0.613642\pi\) | |||||||
\(132\) | − | 4.00000i | − | 0.348155i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −2.00000 | − | 1.00000i | −0.172133 | − | 0.0860663i | ||||
\(136\) | −6.00000 | −0.514496 | ||||||||
\(137\) | − | 6.00000i | − | 0.512615i | −0.966595 | − | 0.256307i | \(-0.917494\pi\) | ||
0.966595 | − | 0.256307i | \(-0.0825059\pi\) | |||||||
\(138\) | − | 6.00000i | − | 0.510754i | ||||||
\(139\) | −12.0000 | −1.01783 | −0.508913 | − | 0.860818i | \(-0.669953\pi\) | ||||
−0.508913 | + | 0.860818i | \(0.669953\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 12.0000i | 1.00702i | ||||||||
\(143\) | − | 8.00000i | − | 0.668994i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −2.00000 | + | 4.00000i | −0.166091 | + | 0.332182i | ||||
\(146\) | −16.0000 | −1.32417 | ||||||||
\(147\) | − | 7.00000i | − | 0.577350i | ||||||
\(148\) | − | 10.0000i | − | 0.821995i | ||||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 3.00000 | + | 4.00000i | 0.244949 | + | 0.326599i | ||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | − | 6.00000i | − | 0.485071i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000 | − | 12.0000i | 0.481932 | − | 0.963863i | ||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 18.0000i | 1.43656i | 0.695756 | + | 0.718278i | \(0.255069\pi\) | ||||
−0.695756 | + | 0.718278i | \(0.744931\pi\) | |||||||
\(158\) | − | 14.0000i | − | 1.11378i | ||||||
\(159\) | 10.0000 | 0.793052 | ||||||||
\(160\) | 2.00000 | + | 1.00000i | 0.158114 | + | 0.0790569i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 10.0000i | − | 0.783260i | −0.920123 | − | 0.391630i | \(-0.871911\pi\) | ||
0.920123 | − | 0.391630i | \(-0.128089\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.00000 | − | 4.00000i | −0.622799 | − | 0.311400i | ||||
\(166\) | 12.0000 | 0.931381 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | −6.00000 | + | 12.0000i | −0.460179 | + | 0.920358i | ||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 6.00000i | 0.457496i | ||||||||
\(173\) | − | 14.0000i | − | 1.06440i | −0.846619 | − | 0.532200i | \(-0.821365\pi\) | ||
0.846619 | − | 0.532200i | \(-0.178635\pi\) | |||||||
\(174\) | −2.00000 | −0.151620 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | 2.00000i | 0.150329i | ||||||||
\(178\) | 4.00000i | 0.299813i | ||||||||
\(179\) | 18.0000 | 1.34538 | 0.672692 | − | 0.739923i | \(-0.265138\pi\) | ||||
0.672692 | + | 0.739923i | \(0.265138\pi\) | |||||||
\(180\) | −1.00000 | + | 2.00000i | −0.0745356 | + | 0.149071i | ||||
\(181\) | −4.00000 | −0.297318 | −0.148659 | − | 0.988889i | \(-0.547496\pi\) | ||||
−0.148659 | + | 0.988889i | \(0.547496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.00000i | 0.443533i | ||||||||
\(184\) | −6.00000 | −0.442326 | ||||||||
\(185\) | −20.0000 | − | 10.0000i | −1.47043 | − | 0.735215i | ||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | − | 24.0000i | − | 1.75505i | ||||||
\(188\) | 6.00000i | 0.437595i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.00000 | + | 1.00000i | 0.145095 | + | 0.0725476i | ||||
\(191\) | 24.0000 | 1.73658 | 0.868290 | − | 0.496058i | \(-0.165220\pi\) | ||||
0.868290 | + | 0.496058i | \(0.165220\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | 14.0000i | 1.00774i | 0.863779 | + | 0.503871i | \(0.168091\pi\) | ||||
−0.863779 | + | 0.503871i | \(0.831909\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | −2.00000 | + | 4.00000i | −0.143223 | + | 0.286446i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | − | 8.00000i | − | 0.569976i | −0.958531 | − | 0.284988i | \(-0.908010\pi\) | ||
0.958531 | − | 0.284988i | \(-0.0919897\pi\) | |||||||
\(198\) | − | 4.00000i | − | 0.284268i | ||||||
\(199\) | 16.0000 | 1.13421 | 0.567105 | − | 0.823646i | \(-0.308063\pi\) | ||||
0.567105 | + | 0.823646i | \(0.308063\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 18.0000i | 1.26648i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | − | 6.00000i | − | 0.417029i | ||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | − | 10.0000i | − | 0.686803i | ||||||
\(213\) | 12.0000i | 0.822226i | ||||||||
\(214\) | 4.00000 | 0.273434 | ||||||||
\(215\) | 12.0000 | + | 6.00000i | 0.818393 | + | 0.409197i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 4.00000i | 0.270914i | ||||||||
\(219\) | −16.0000 | −1.08118 | ||||||||
\(220\) | −4.00000 | + | 8.00000i | −0.269680 | + | 0.539360i | ||||
\(221\) | −12.0000 | −0.807207 | ||||||||
\(222\) | − | 10.0000i | − | 0.671156i | ||||||
\(223\) | − | 8.00000i | − | 0.535720i | −0.963458 | − | 0.267860i | \(-0.913684\pi\) | ||
0.963458 | − | 0.267860i | \(-0.0863164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | 2.00000 | 0.133038 | ||||||||
\(227\) | 12.0000i | 0.796468i | 0.917284 | + | 0.398234i | \(0.130377\pi\) | ||||
−0.917284 | + | 0.398234i | \(0.869623\pi\) | |||||||
\(228\) | 1.00000i | 0.0662266i | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | −6.00000 | + | 12.0000i | −0.395628 | + | 0.791257i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | 14.0000i | 0.917170i | 0.888650 | + | 0.458585i | \(0.151644\pi\) | ||||
−0.888650 | + | 0.458585i | \(0.848356\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 12.0000 | + | 6.00000i | 0.782794 | + | 0.391397i | ||||
\(236\) | 2.00000 | 0.130189 | ||||||||
\(237\) | − | 14.0000i | − | 0.909398i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 2.00000 | + | 1.00000i | 0.129099 | + | 0.0645497i | ||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | − | 5.00000i | − | 0.321412i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | −7.00000 | + | 14.0000i | −0.447214 | + | 0.894427i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000i | 0.127257i | ||||||||
\(248\) | − | 6.00000i | − | 0.381000i | ||||||
\(249\) | 12.0000 | 0.760469 | ||||||||
\(250\) | −2.00000 | − | 11.0000i | −0.126491 | − | 0.695701i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 24.0000i | − | 1.50887i | ||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | −6.00000 | + | 12.0000i | −0.375735 | + | 0.751469i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 22.0000i | − | 1.37232i | −0.727450 | − | 0.686161i | \(-0.759294\pi\) | ||
0.727450 | − | 0.686161i | \(-0.240706\pi\) | |||||||
\(258\) | 6.00000i | 0.373544i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.00000 | + | 2.00000i | 0.248069 | + | 0.124035i | ||||
\(261\) | −2.00000 | −0.123797 | ||||||||
\(262\) | 8.00000i | 0.494242i | ||||||||
\(263\) | − | 2.00000i | − | 0.123325i | −0.998097 | − | 0.0616626i | \(-0.980360\pi\) | ||
0.998097 | − | 0.0616626i | \(-0.0196403\pi\) | |||||||
\(264\) | −4.00000 | −0.246183 | ||||||||
\(265\) | −20.0000 | − | 10.0000i | −1.22859 | − | 0.614295i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.00000i | 0.244796i | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | −1.00000 | + | 2.00000i | −0.0608581 | + | 0.121716i | ||||
\(271\) | 32.0000 | 1.94386 | 0.971931 | − | 0.235267i | \(-0.0755965\pi\) | ||||
0.971931 | + | 0.235267i | \(0.0755965\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 12.0000 | + | 16.0000i | 0.723627 | + | 0.964836i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 26.0000i | 1.56219i | 0.624413 | + | 0.781094i | \(0.285338\pi\) | ||||
−0.624413 | + | 0.781094i | \(0.714662\pi\) | |||||||
\(278\) | 12.0000i | 0.719712i | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 6.00000i | 0.357295i | ||||||||
\(283\) | 22.0000i | 1.30776i | 0.756596 | + | 0.653882i | \(0.226861\pi\) | ||||
−0.756596 | + | 0.653882i | \(0.773139\pi\) | |||||||
\(284\) | 12.0000 | 0.712069 | ||||||||
\(285\) | 2.00000 | + | 1.00000i | 0.118470 | + | 0.0592349i | ||||
\(286\) | −8.00000 | −0.473050 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 4.00000 | + | 2.00000i | 0.234888 | + | 0.117444i | ||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | 16.0000i | 0.936329i | ||||||||
\(293\) | 2.00000i | 0.116841i | 0.998292 | + | 0.0584206i | \(0.0186065\pi\) | ||||
−0.998292 | + | 0.0584206i | \(0.981394\pi\) | |||||||
\(294\) | −7.00000 | −0.408248 | ||||||||
\(295\) | 2.00000 | − | 4.00000i | 0.116445 | − | 0.232889i | ||||
\(296\) | −10.0000 | −0.581238 | ||||||||
\(297\) | − | 4.00000i | − | 0.232104i | ||||||
\(298\) | − | 6.00000i | − | 0.347571i | ||||||
\(299\) | −12.0000 | −0.693978 | ||||||||
\(300\) | 4.00000 | − | 3.00000i | 0.230940 | − | 0.173205i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 10.0000i | − | 0.575435i | ||||||
\(303\) | 18.0000i | 1.03407i | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 6.00000 | − | 12.0000i | 0.343559 | − | 0.687118i | ||||
\(306\) | −6.00000 | −0.342997 | ||||||||
\(307\) | 12.0000i | 0.684876i | 0.939540 | + | 0.342438i | \(0.111253\pi\) | ||||
−0.939540 | + | 0.342438i | \(0.888747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −12.0000 | − | 6.00000i | −0.681554 | − | 0.340777i | ||||
\(311\) | 24.0000 | 1.36092 | 0.680458 | − | 0.732787i | \(-0.261781\pi\) | ||||
0.680458 | + | 0.732787i | \(0.261781\pi\) | |||||||
\(312\) | 2.00000i | 0.113228i | ||||||||
\(313\) | 28.0000i | 1.58265i | 0.611393 | + | 0.791327i | \(0.290609\pi\) | ||||
−0.611393 | + | 0.791327i | \(0.709391\pi\) | |||||||
\(314\) | 18.0000 | 1.01580 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | − | 6.00000i | − | 0.336994i | −0.985702 | − | 0.168497i | \(-0.946109\pi\) | ||
0.985702 | − | 0.168497i | \(-0.0538913\pi\) | |||||||
\(318\) | − | 10.0000i | − | 0.560772i | ||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | 1.00000 | − | 2.00000i | 0.0559017 | − | 0.111803i | ||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.00000i | 0.333849i | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 8.00000 | − | 6.00000i | 0.443760 | − | 0.332820i | ||||
\(326\) | −10.0000 | −0.553849 | ||||||||
\(327\) | 4.00000i | 0.221201i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −4.00000 | + | 8.00000i | −0.220193 | + | 0.440386i | ||||
\(331\) | −4.00000 | −0.219860 | −0.109930 | − | 0.993939i | \(-0.535063\pi\) | ||||
−0.109930 | + | 0.993939i | \(0.535063\pi\) | |||||||
\(332\) | − | 12.0000i | − | 0.658586i | ||||||
\(333\) | − | 10.0000i | − | 0.547997i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.0000 | + | 8.00000i | 0.874173 | + | 0.437087i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.00000i | − | 0.326841i | −0.986557 | − | 0.163420i | \(-0.947747\pi\) | ||
0.986557 | − | 0.163420i | \(-0.0522527\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 2.00000 | 0.108625 | ||||||||
\(340\) | 12.0000 | + | 6.00000i | 0.650791 | + | 0.325396i | ||||
\(341\) | 24.0000 | 1.29967 | ||||||||
\(342\) | 1.00000i | 0.0540738i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6.00000 | 0.323498 | ||||||||
\(345\) | −6.00000 | + | 12.0000i | −0.323029 | + | 0.646058i | ||||
\(346\) | −14.0000 | −0.752645 | ||||||||
\(347\) | − | 20.0000i | − | 1.07366i | −0.843692 | − | 0.536828i | \(-0.819622\pi\) | ||
0.843692 | − | 0.536828i | \(-0.180378\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | 26.0000 | 1.39175 | 0.695874 | − | 0.718164i | \(-0.255017\pi\) | ||||
0.695874 | + | 0.718164i | \(0.255017\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 4.00000i | 0.213201i | ||||||||
\(353\) | − | 2.00000i | − | 0.106449i | −0.998583 | − | 0.0532246i | \(-0.983050\pi\) | ||
0.998583 | − | 0.0532246i | \(-0.0169499\pi\) | |||||||
\(354\) | 2.00000 | 0.106299 | ||||||||
\(355\) | 12.0000 | − | 24.0000i | 0.636894 | − | 1.27379i | ||||
\(356\) | 4.00000 | 0.212000 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 18.0000i | − | 0.951330i | ||||||
\(359\) | 8.00000 | 0.422224 | 0.211112 | − | 0.977462i | \(-0.432292\pi\) | ||||
0.211112 | + | 0.977462i | \(0.432292\pi\) | |||||||
\(360\) | 2.00000 | + | 1.00000i | 0.105409 | + | 0.0527046i | ||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 4.00000i | 0.210235i | ||||||||
\(363\) | − | 5.00000i | − | 0.262432i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0000 | + | 16.0000i | 1.67496 | + | 0.837478i | ||||
\(366\) | 6.00000 | 0.313625 | ||||||||
\(367\) | − | 12.0000i | − | 0.626395i | −0.949688 | − | 0.313197i | \(-0.898600\pi\) | ||
0.949688 | − | 0.313197i | \(-0.101400\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.0000 | + | 20.0000i | −0.519875 | + | 1.03975i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | − | 6.00000i | − | 0.311086i | ||||||
\(373\) | 6.00000i | 0.310668i | 0.987862 | + | 0.155334i | \(0.0496454\pi\) | ||||
−0.987862 | + | 0.155334i | \(0.950355\pi\) | |||||||
\(374\) | −24.0000 | −1.24101 | ||||||||
\(375\) | −2.00000 | − | 11.0000i | −0.103280 | − | 0.568038i | ||||
\(376\) | 6.00000 | 0.309426 | ||||||||
\(377\) | 4.00000i | 0.206010i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | 1.00000 | − | 2.00000i | 0.0512989 | − | 0.102598i | ||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | − | 24.0000i | − | 1.22795i | ||||||
\(383\) | 36.0000i | 1.83951i | 0.392488 | + | 0.919757i | \(0.371614\pi\) | ||||
−0.392488 | + | 0.919757i | \(0.628386\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 14.0000 | 0.712581 | ||||||||
\(387\) | 6.00000i | 0.304997i | ||||||||
\(388\) | − | 10.0000i | − | 0.507673i | ||||||
\(389\) | −38.0000 | −1.92668 | −0.963338 | − | 0.268290i | \(-0.913542\pi\) | ||||
−0.963338 | + | 0.268290i | \(0.913542\pi\) | |||||||
\(390\) | 4.00000 | + | 2.00000i | 0.202548 | + | 0.101274i | ||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 7.00000i | 0.353553i | ||||||||
\(393\) | 8.00000i | 0.403547i | ||||||||
\(394\) | −8.00000 | −0.403034 | ||||||||
\(395\) | −14.0000 | + | 28.0000i | −0.704416 | + | 1.40883i | ||||
\(396\) | −4.00000 | −0.201008 | ||||||||
\(397\) | 30.0000i | 1.50566i | 0.658217 | + | 0.752828i | \(0.271311\pi\) | ||||
−0.658217 | + | 0.752828i | \(0.728689\pi\) | |||||||
\(398\) | − | 16.0000i | − | 0.802008i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | 16.0000 | 0.799002 | 0.399501 | − | 0.916733i | \(-0.369183\pi\) | ||||
0.399501 | + | 0.916733i | \(0.369183\pi\) | |||||||
\(402\) | 8.00000i | 0.399004i | ||||||||
\(403\) | − | 12.0000i | − | 0.597763i | ||||||
\(404\) | 18.0000 | 0.895533 | ||||||||
\(405\) | −1.00000 | + | 2.00000i | −0.0496904 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 40.0000i | − | 1.98273i | ||||||
\(408\) | 6.00000i | 0.297044i | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | −0.295958 | ||||||||
\(412\) | − | 8.00000i | − | 0.394132i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −6.00000 | −0.294884 | ||||||||
\(415\) | −24.0000 | − | 12.0000i | −1.17811 | − | 0.589057i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 12.0000i | 0.587643i | ||||||||
\(418\) | 4.00000i | 0.195646i | ||||||||
\(419\) | −8.00000 | −0.390826 | −0.195413 | − | 0.980721i | \(-0.562605\pi\) | ||||
−0.195413 | + | 0.980721i | \(0.562605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.0000 | 0.779792 | 0.389896 | − | 0.920859i | \(-0.372511\pi\) | ||||
0.389896 | + | 0.920859i | \(0.372511\pi\) | |||||||
\(422\) | 8.00000i | 0.389434i | ||||||||
\(423\) | 6.00000i | 0.291730i | ||||||||
\(424\) | −10.0000 | −0.485643 | ||||||||
\(425\) | 24.0000 | − | 18.0000i | 1.16417 | − | 0.873128i | ||||
\(426\) | 12.0000 | 0.581402 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 4.00000i | − | 0.193347i | ||||||
\(429\) | −8.00000 | −0.386244 | ||||||||
\(430\) | 6.00000 | − | 12.0000i | 0.289346 | − | 0.578691i | ||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | 6.00000i | 0.288342i | 0.989553 | + | 0.144171i | \(0.0460515\pi\) | ||||
−0.989553 | + | 0.144171i | \(0.953949\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.00000 | + | 2.00000i | 0.191785 | + | 0.0958927i | ||||
\(436\) | 4.00000 | 0.191565 | ||||||||
\(437\) | 6.00000i | 0.287019i | ||||||||
\(438\) | 16.0000i | 0.764510i | ||||||||
\(439\) | 14.0000 | 0.668184 | 0.334092 | − | 0.942541i | \(-0.391570\pi\) | ||||
0.334092 | + | 0.942541i | \(0.391570\pi\) | |||||||
\(440\) | 8.00000 | + | 4.00000i | 0.381385 | + | 0.190693i | ||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 12.0000i | 0.570782i | ||||||||
\(443\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(444\) | −10.0000 | −0.474579 | ||||||||
\(445\) | 4.00000 | − | 8.00000i | 0.189618 | − | 0.379236i | ||||
\(446\) | −8.00000 | −0.378811 | ||||||||
\(447\) | − | 6.00000i | − | 0.283790i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.00000 | −0.188772 | −0.0943858 | − | 0.995536i | \(-0.530089\pi\) | ||||
−0.0943858 | + | 0.995536i | \(0.530089\pi\) | |||||||
\(450\) | 4.00000 | − | 3.00000i | 0.188562 | − | 0.141421i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 2.00000i | − | 0.0940721i | ||||||
\(453\) | − | 10.0000i | − | 0.469841i | ||||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | − | 16.0000i | − | 0.748448i | −0.927338 | − | 0.374224i | \(-0.877909\pi\) | ||
0.927338 | − | 0.374224i | \(-0.122091\pi\) | |||||||
\(458\) | − | 10.0000i | − | 0.467269i | ||||||
\(459\) | −6.00000 | −0.280056 | ||||||||
\(460\) | 12.0000 | + | 6.00000i | 0.559503 | + | 0.279751i | ||||
\(461\) | −18.0000 | −0.838344 | −0.419172 | − | 0.907907i | \(-0.637680\pi\) | ||||
−0.419172 | + | 0.907907i | \(0.637680\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | 2.00000 | 0.0928477 | ||||||||
\(465\) | −12.0000 | − | 6.00000i | −0.556487 | − | 0.278243i | ||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 6.00000 | − | 12.0000i | 0.276759 | − | 0.553519i | ||||
\(471\) | 18.0000 | 0.829396 | ||||||||
\(472\) | − | 2.00000i | − | 0.0920575i | ||||||
\(473\) | 24.0000i | 1.10352i | ||||||||
\(474\) | −14.0000 | −0.643041 | ||||||||
\(475\) | −3.00000 | − | 4.00000i | −0.137649 | − | 0.183533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 10.0000i | − | 0.457869i | ||||||
\(478\) | − | 8.00000i | − | 0.365911i | ||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 1.00000 | − | 2.00000i | 0.0456435 | − | 0.0912871i | ||||
\(481\) | −20.0000 | −0.911922 | ||||||||
\(482\) | 10.0000i | 0.455488i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.00000 | −0.227273 | ||||||||
\(485\) | −20.0000 | − | 10.0000i | −0.908153 | − | 0.454077i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − | 24.0000i | − | 1.08754i | −0.839233 | − | 0.543772i | \(-0.816996\pi\) | ||
0.839233 | − | 0.543772i | \(-0.183004\pi\) | |||||||
\(488\) | − | 6.00000i | − | 0.271607i | ||||||
\(489\) | −10.0000 | −0.452216 | ||||||||
\(490\) | 14.0000 | + | 7.00000i | 0.632456 | + | 0.316228i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0000i | 0.540453i | ||||||||
\(494\) | 2.00000 | 0.0899843 | ||||||||
\(495\) | −4.00000 | + | 8.00000i | −0.179787 | + | 0.359573i | ||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − | 12.0000i | − | 0.537733i | ||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 12.0000i | − | 0.535586i | ||||||
\(503\) | − | 14.0000i | − | 0.624229i | −0.950044 | − | 0.312115i | \(-0.898963\pi\) | ||
0.950044 | − | 0.312115i | \(-0.101037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | − | 36.0000i | 0.800989 | − | 1.60198i | ||||
\(506\) | −24.0000 | −1.06693 | ||||||||
\(507\) | − | 9.00000i | − | 0.399704i | ||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | −6.00000 | −0.265945 | −0.132973 | − | 0.991120i | \(-0.542452\pi\) | ||||
−0.132973 | + | 0.991120i | \(0.542452\pi\) | |||||||
\(510\) | 12.0000 | + | 6.00000i | 0.531369 | + | 0.265684i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 1.00000i | 0.0441511i | ||||||||
\(514\) | −22.0000 | −0.970378 | ||||||||
\(515\) | −16.0000 | − | 8.00000i | −0.705044 | − | 0.352522i | ||||
\(516\) | 6.00000 | 0.264135 | ||||||||
\(517\) | 24.0000i | 1.05552i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.0000 | −0.614532 | ||||||||
\(520\) | 2.00000 | − | 4.00000i | 0.0877058 | − | 0.175412i | ||||
\(521\) | −24.0000 | −1.05146 | −0.525730 | − | 0.850652i | \(-0.676208\pi\) | ||||
−0.525730 | + | 0.850652i | \(0.676208\pi\) | |||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | 36.0000i | 1.57417i | 0.616844 | + | 0.787085i | \(0.288411\pi\) | ||||
−0.616844 | + | 0.787085i | \(0.711589\pi\) | |||||||
\(524\) | 8.00000 | 0.349482 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.00000 | −0.0872041 | ||||||||
\(527\) | − | 36.0000i | − | 1.56818i | ||||||
\(528\) | 4.00000i | 0.174078i | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −10.0000 | + | 20.0000i | −0.434372 | + | 0.868744i | ||||
\(531\) | 2.00000 | 0.0867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4.00000 | 0.173097 | ||||||||
\(535\) | −8.00000 | − | 4.00000i | −0.345870 | − | 0.172935i | ||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | − | 18.0000i | − | 0.776757i | ||||||
\(538\) | − | 14.0000i | − | 0.603583i | ||||||
\(539\) | −28.0000 | −1.20605 | ||||||||
\(540\) | 2.00000 | + | 1.00000i | 0.0860663 | + | 0.0430331i | ||||
\(541\) | 38.0000 | 1.63375 | 0.816874 | − | 0.576816i | \(-0.195705\pi\) | ||||
0.816874 | + | 0.576816i | \(0.195705\pi\) | |||||||
\(542\) | − | 32.0000i | − | 1.37452i | ||||||
\(543\) | 4.00000i | 0.171656i | ||||||||
\(544\) | 6.00000 | 0.257248 | ||||||||
\(545\) | 4.00000 | − | 8.00000i | 0.171341 | − | 0.342682i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.0000i | 1.53925i | 0.638497 | + | 0.769624i | \(0.279557\pi\) | ||||
−0.638497 | + | 0.769624i | \(0.720443\pi\) | |||||||
\(548\) | 6.00000i | 0.256307i | ||||||||
\(549\) | 6.00000 | 0.256074 | ||||||||
\(550\) | 16.0000 | − | 12.0000i | 0.682242 | − | 0.511682i | ||||
\(551\) | 2.00000 | 0.0852029 | ||||||||
\(552\) | 6.00000i | 0.255377i | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 26.0000 | 1.10463 | ||||||||
\(555\) | −10.0000 | + | 20.0000i | −0.424476 | + | 0.848953i | ||||
\(556\) | 12.0000 | 0.508913 | ||||||||
\(557\) | − | 24.0000i | − | 1.01691i | −0.861088 | − | 0.508456i | \(-0.830216\pi\) | ||
0.861088 | − | 0.508456i | \(-0.169784\pi\) | |||||||
\(558\) | − | 6.00000i | − | 0.254000i | ||||||
\(559\) | 12.0000 | 0.507546 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | −1.01328 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 12.0000i | − | 0.505740i | −0.967500 | − | 0.252870i | \(-0.918626\pi\) | ||
0.967500 | − | 0.252870i | \(-0.0813744\pi\) | |||||||
\(564\) | 6.00000 | 0.252646 | ||||||||
\(565\) | −4.00000 | − | 2.00000i | −0.168281 | − | 0.0841406i | ||||
\(566\) | 22.0000 | 0.924729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 12.0000i | − | 0.503509i | ||||||
\(569\) | 28.0000 | 1.17382 | 0.586911 | − | 0.809652i | \(-0.300344\pi\) | ||||
0.586911 | + | 0.809652i | \(0.300344\pi\) | |||||||
\(570\) | 1.00000 | − | 2.00000i | 0.0418854 | − | 0.0837708i | ||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 8.00000i | 0.334497i | ||||||||
\(573\) | − | 24.0000i | − | 1.00261i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 24.0000 | − | 18.0000i | 1.00087 | − | 0.750652i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 8.00000i | 0.333044i | 0.986038 | + | 0.166522i | \(0.0532537\pi\) | ||||
−0.986038 | + | 0.166522i | \(0.946746\pi\) | |||||||
\(578\) | 19.0000i | 0.790296i | ||||||||
\(579\) | 14.0000 | 0.581820 | ||||||||
\(580\) | 2.00000 | − | 4.00000i | 0.0830455 | − | 0.166091i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | − | 10.0000i | − | 0.414513i | ||||||
\(583\) | − | 40.0000i | − | 1.65663i | ||||||
\(584\) | 16.0000 | 0.662085 | ||||||||
\(585\) | 4.00000 | + | 2.00000i | 0.165380 | + | 0.0826898i | ||||
\(586\) | 2.00000 | 0.0826192 | ||||||||
\(587\) | 28.0000i | 1.15568i | 0.816149 | + | 0.577842i | \(0.196105\pi\) | ||||
−0.816149 | + | 0.577842i | \(0.803895\pi\) | |||||||
\(588\) | 7.00000i | 0.288675i | ||||||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | −4.00000 | − | 2.00000i | −0.164677 | − | 0.0823387i | ||||
\(591\) | −8.00000 | −0.329076 | ||||||||
\(592\) | 10.0000i | 0.410997i | ||||||||
\(593\) | − | 46.0000i | − | 1.88899i | −0.328521 | − | 0.944497i | \(-0.606550\pi\) | ||
0.328521 | − | 0.944497i | \(-0.393450\pi\) | |||||||
\(594\) | −4.00000 | −0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | − | 16.0000i | − | 0.654836i | ||||||
\(598\) | 12.0000i | 0.490716i | ||||||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | −3.00000 | − | 4.00000i | −0.122474 | − | 0.163299i | ||||
\(601\) | 30.0000 | 1.22373 | 0.611863 | − | 0.790964i | \(-0.290420\pi\) | ||||
0.611863 | + | 0.790964i | \(0.290420\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | −5.00000 | + | 10.0000i | −0.203279 | + | 0.406558i | ||||
\(606\) | 18.0000 | 0.731200 | ||||||||
\(607\) | 24.0000i | 0.974130i | 0.873366 | + | 0.487065i | \(0.161933\pi\) | ||||
−0.873366 | + | 0.487065i | \(0.838067\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.0000 | − | 6.00000i | −0.485866 | − | 0.242933i | ||||
\(611\) | 12.0000 | 0.485468 | ||||||||
\(612\) | 6.00000i | 0.242536i | ||||||||
\(613\) | − | 22.0000i | − | 0.888572i | −0.895885 | − | 0.444286i | \(-0.853457\pi\) | ||
0.895885 | − | 0.444286i | \(-0.146543\pi\) | |||||||
\(614\) | 12.0000 | 0.484281 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | − | 8.00000i | − | 0.321807i | ||||||
\(619\) | −44.0000 | −1.76851 | −0.884255 | − | 0.467005i | \(-0.845333\pi\) | ||||
−0.884255 | + | 0.467005i | \(0.845333\pi\) | |||||||
\(620\) | −6.00000 | + | 12.0000i | −0.240966 | + | 0.481932i | ||||
\(621\) | −6.00000 | −0.240772 | ||||||||
\(622\) | − | 24.0000i | − | 0.962312i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 28.0000 | 1.11911 | ||||||||
\(627\) | 4.00000i | 0.159745i | ||||||||
\(628\) | − | 18.0000i | − | 0.718278i | ||||||
\(629\) | −60.0000 | −2.39236 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.0000 | −0.796187 | −0.398094 | − | 0.917345i | \(-0.630328\pi\) | ||||
−0.398094 | + | 0.917345i | \(0.630328\pi\) | |||||||
\(632\) | 14.0000i | 0.556890i | ||||||||
\(633\) | 8.00000i | 0.317971i | ||||||||
\(634\) | −6.00000 | −0.238290 | ||||||||
\(635\) | 16.0000 | + | 8.00000i | 0.634941 | + | 0.317470i | ||||
\(636\) | −10.0000 | −0.396526 | ||||||||
\(637\) | 14.0000i | 0.554700i | ||||||||
\(638\) | 8.00000i | 0.316723i | ||||||||
\(639\) | 12.0000 | 0.474713 | ||||||||
\(640\) | −2.00000 | − | 1.00000i | −0.0790569 | − | 0.0395285i | ||||
\(641\) | 48.0000 | 1.89589 | 0.947943 | − | 0.318440i | \(-0.103159\pi\) | ||||
0.947943 | + | 0.318440i | \(0.103159\pi\) | |||||||
\(642\) | − | 4.00000i | − | 0.157867i | ||||||
\(643\) | − | 26.0000i | − | 1.02534i | −0.858586 | − | 0.512670i | \(-0.828656\pi\) | ||
0.858586 | − | 0.512670i | \(-0.171344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | − | 12.0000i | 0.236250 | − | 0.472500i | ||||
\(646\) | 6.00000 | 0.236067 | ||||||||
\(647\) | − | 6.00000i | − | 0.235884i | −0.993020 | − | 0.117942i | \(-0.962370\pi\) | ||
0.993020 | − | 0.117942i | \(-0.0376297\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | −6.00000 | − | 8.00000i | −0.235339 | − | 0.313786i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000i | 0.391630i | ||||||||
\(653\) | 48.0000i | 1.87839i | 0.343391 | + | 0.939193i | \(0.388424\pi\) | ||||
−0.343391 | + | 0.939193i | \(0.611576\pi\) | |||||||
\(654\) | 4.00000 | 0.156412 | ||||||||
\(655\) | 8.00000 | − | 16.0000i | 0.312586 | − | 0.625172i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.0000i | 0.624219i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.0000 | −1.79191 | −0.895953 | − | 0.444149i | \(-0.853506\pi\) | ||||
−0.895953 | + | 0.444149i | \(0.853506\pi\) | |||||||
\(660\) | 8.00000 | + | 4.00000i | 0.311400 | + | 0.155700i | ||||
\(661\) | −8.00000 | −0.311164 | −0.155582 | − | 0.987823i | \(-0.549725\pi\) | ||||
−0.155582 | + | 0.987823i | \(0.549725\pi\) | |||||||
\(662\) | 4.00000i | 0.155464i | ||||||||
\(663\) | 12.0000i | 0.466041i | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10.0000 | −0.387492 | ||||||||
\(667\) | 12.0000i | 0.464642i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −8.00000 | −0.309298 | ||||||||
\(670\) | 8.00000 | − | 16.0000i | 0.309067 | − | 0.618134i | ||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000i | 1.00223i | 0.865382 | + | 0.501113i | \(0.167076\pi\) | ||||
−0.865382 | + | 0.501113i | \(0.832924\pi\) | |||||||
\(674\) | −6.00000 | −0.231111 | ||||||||
\(675\) | 4.00000 | − | 3.00000i | 0.153960 | − | 0.115470i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 6.00000i | 0.230599i | 0.993331 | + | 0.115299i | \(0.0367827\pi\) | ||||
−0.993331 | + | 0.115299i | \(0.963217\pi\) | |||||||
\(678\) | − | 2.00000i | − | 0.0768095i | ||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 6.00000 | − | 12.0000i | 0.230089 | − | 0.460179i | ||||
\(681\) | 12.0000 | 0.459841 | ||||||||
\(682\) | − | 24.0000i | − | 0.919007i | ||||||
\(683\) | − | 36.0000i | − | 1.37750i | −0.724998 | − | 0.688751i | \(-0.758159\pi\) | ||
0.724998 | − | 0.688751i | \(-0.241841\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | 12.0000 | + | 6.00000i | 0.458496 | + | 0.229248i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 10.0000i | − | 0.381524i | ||||||
\(688\) | − | 6.00000i | − | 0.228748i | ||||||
\(689\) | −20.0000 | −0.761939 | ||||||||
\(690\) | 12.0000 | + | 6.00000i | 0.456832 | + | 0.228416i | ||||
\(691\) | 44.0000 | 1.67384 | 0.836919 | − | 0.547326i | \(-0.184354\pi\) | ||||
0.836919 | + | 0.547326i | \(0.184354\pi\) | |||||||
\(692\) | 14.0000i | 0.532200i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −20.0000 | −0.759190 | ||||||||
\(695\) | 12.0000 | − | 24.0000i | 0.455186 | − | 0.910372i | ||||
\(696\) | 2.00000 | 0.0758098 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 26.0000i | − | 0.984115i | ||||||
\(699\) | 14.0000 | 0.529529 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0000 | −0.830929 | −0.415464 | − | 0.909610i | \(-0.636381\pi\) | ||||
−0.415464 | + | 0.909610i | \(0.636381\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | 10.0000i | 0.377157i | ||||||||
\(704\) | 4.00000 | 0.150756 | ||||||||
\(705\) | 6.00000 | − | 12.0000i | 0.225973 | − | 0.451946i | ||||
\(706\) | −2.00000 | −0.0752710 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | − | 2.00000i | − | 0.0751646i | ||||||
\(709\) | 2.00000 | 0.0751116 | 0.0375558 | − | 0.999295i | \(-0.488043\pi\) | ||||
0.0375558 | + | 0.999295i | \(0.488043\pi\) | |||||||
\(710\) | −24.0000 | − | 12.0000i | −0.900704 | − | 0.450352i | ||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | − | 4.00000i | − | 0.149906i | ||||||
\(713\) | − | 36.0000i | − | 1.34821i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000 | + | 8.00000i | 0.598366 | + | 0.299183i | ||||
\(716\) | −18.0000 | −0.672692 | ||||||||
\(717\) | − | 8.00000i | − | 0.298765i | ||||||
\(718\) | − | 8.00000i | − | 0.298557i | ||||||
\(719\) | −48.0000 | −1.79010 | −0.895049 | − | 0.445968i | \(-0.852860\pi\) | ||||
−0.895049 | + | 0.445968i | \(0.852860\pi\) | |||||||
\(720\) | 1.00000 | − | 2.00000i | 0.0372678 | − | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 1.00000i | − | 0.0372161i | ||||||
\(723\) | 10.0000i | 0.371904i | ||||||||
\(724\) | 4.00000 | 0.148659 | ||||||||
\(725\) | −6.00000 | − | 8.00000i | −0.222834 | − | 0.297113i | ||||
\(726\) | −5.00000 | −0.185567 | ||||||||
\(727\) | 28.0000i | 1.03846i | 0.854634 | + | 0.519231i | \(0.173782\pi\) | ||||
−0.854634 | + | 0.519231i | \(0.826218\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 16.0000 | − | 32.0000i | 0.592187 | − | 1.18437i | ||||
\(731\) | 36.0000 | 1.33151 | ||||||||
\(732\) | − | 6.00000i | − | 0.221766i | ||||||
\(733\) | 46.0000i | 1.69905i | 0.527549 | + | 0.849524i | \(0.323111\pi\) | ||||
−0.527549 | + | 0.849524i | \(0.676889\pi\) | |||||||
\(734\) | −12.0000 | −0.442928 | ||||||||
\(735\) | 14.0000 | + | 7.00000i | 0.516398 | + | 0.258199i | ||||
\(736\) | 6.00000 | 0.221163 | ||||||||
\(737\) | 32.0000i | 1.17874i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −20.0000 | −0.735712 | −0.367856 | − | 0.929883i | \(-0.619908\pi\) | ||||
−0.367856 | + | 0.929883i | \(0.619908\pi\) | |||||||
\(740\) | 20.0000 | + | 10.0000i | 0.735215 | + | 0.367607i | ||||
\(741\) | 2.00000 | 0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.00000i | − | 0.293492i | −0.989174 | − | 0.146746i | \(-0.953120\pi\) | ||
0.989174 | − | 0.146746i | \(-0.0468799\pi\) | |||||||
\(744\) | −6.00000 | −0.219971 | ||||||||
\(745\) | −6.00000 | + | 12.0000i | −0.219823 | + | 0.439646i | ||||
\(746\) | 6.00000 | 0.219676 | ||||||||
\(747\) | − | 12.0000i | − | 0.439057i | ||||||
\(748\) | 24.0000i | 0.877527i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −11.0000 | + | 2.00000i | −0.401663 | + | 0.0730297i | ||||
\(751\) | −26.0000 | −0.948753 | −0.474377 | − | 0.880322i | \(-0.657327\pi\) | ||||
−0.474377 | + | 0.880322i | \(0.657327\pi\) | |||||||
\(752\) | − | 6.00000i | − | 0.218797i | ||||||
\(753\) | − | 12.0000i | − | 0.437304i | ||||||
\(754\) | 4.00000 | 0.145671 | ||||||||
\(755\) | −10.0000 | + | 20.0000i | −0.363937 | + | 0.727875i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | 24.0000i | 0.871719i | ||||||||
\(759\) | −24.0000 | −0.871145 | ||||||||
\(760\) | −2.00000 | − | 1.00000i | −0.0725476 | − | 0.0362738i | ||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 8.00000i | 0.289809i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 12.0000 | + | 6.00000i | 0.433861 | + | 0.216930i | ||||
\(766\) | 36.0000 | 1.30073 | ||||||||
\(767\) | − | 4.00000i | − | 0.144432i | ||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.0000 | −0.792311 | ||||||||
\(772\) | − | 14.0000i | − | 0.503871i | ||||||
\(773\) | − | 50.0000i | − | 1.79838i | −0.437564 | − | 0.899188i | \(-0.644158\pi\) | ||
0.437564 | − | 0.899188i | \(-0.355842\pi\) | |||||||
\(774\) | 6.00000 | 0.215666 | ||||||||
\(775\) | 18.0000 | + | 24.0000i | 0.646579 | + | 0.862105i | ||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 38.0000i | 1.36237i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 2.00000 | − | 4.00000i | 0.0716115 | − | 0.143223i | ||||
\(781\) | 48.0000 | 1.71758 | ||||||||
\(782\) | 36.0000i | 1.28736i | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 7.00000 | 0.250000 | ||||||||
\(785\) | −36.0000 | − | 18.0000i | −1.28490 | − | 0.642448i | ||||
\(786\) | 8.00000 | 0.285351 | ||||||||
\(787\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(788\) | 8.00000i | 0.284988i | ||||||||
\(789\) | −2.00000 | −0.0712019 | ||||||||
\(790\) | 28.0000 | + | 14.0000i | 0.996195 | + | 0.498098i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.00000i | 0.142134i | ||||||||
\(793\) | − | 12.0000i | − | 0.426132i | ||||||
\(794\) | 30.0000 | 1.06466 | ||||||||
\(795\) | −10.0000 | + | 20.0000i | −0.354663 | + | 0.709327i | ||||
\(796\) | −16.0000 | −0.567105 | ||||||||
\(797\) | 54.0000i | 1.91278i | 0.292096 | + | 0.956389i | \(0.405647\pi\) | ||||
−0.292096 | + | 0.956389i | \(0.594353\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0000 | 1.27359 | ||||||||
\(800\) | −4.00000 | + | 3.00000i | −0.141421 | + | 0.106066i | ||||
\(801\) | 4.00000 | 0.141333 | ||||||||
\(802\) | − | 16.0000i | − | 0.564980i | ||||||
\(803\) | 64.0000i | 2.25851i | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −12.0000 | −0.422682 | ||||||||
\(807\) | − | 14.0000i | − | 0.492823i | ||||||
\(808\) | − | 18.0000i | − | 0.633238i | ||||||
\(809\) | 10.0000 | 0.351581 | 0.175791 | − | 0.984428i | \(-0.443752\pi\) | ||||
0.175791 | + | 0.984428i | \(0.443752\pi\) | |||||||
\(810\) | 2.00000 | + | 1.00000i | 0.0702728 | + | 0.0351364i | ||||
\(811\) | −28.0000 | −0.983213 | −0.491606 | − | 0.870817i | \(-0.663590\pi\) | ||||
−0.491606 | + | 0.870817i | \(0.663590\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 32.0000i | − | 1.12229i | ||||||
\(814\) | −40.0000 | −1.40200 | ||||||||
\(815\) | 20.0000 | + | 10.0000i | 0.700569 | + | 0.350285i | ||||
\(816\) | 6.00000 | 0.210042 | ||||||||
\(817\) | − | 6.00000i | − | 0.209913i | ||||||
\(818\) | 26.0000i | 0.909069i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 50.0000 | 1.74501 | 0.872506 | − | 0.488603i | \(-0.162493\pi\) | ||||
0.872506 | + | 0.488603i | \(0.162493\pi\) | |||||||
\(822\) | 6.00000i | 0.209274i | ||||||||
\(823\) | − | 12.0000i | − | 0.418294i | −0.977884 | − | 0.209147i | \(-0.932931\pi\) | ||
0.977884 | − | 0.209147i | \(-0.0670687\pi\) | |||||||
\(824\) | −8.00000 | −0.278693 | ||||||||
\(825\) | 16.0000 | − | 12.0000i | 0.557048 | − | 0.417786i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | 28.0000 | 0.972480 | 0.486240 | − | 0.873825i | \(-0.338368\pi\) | ||||
0.486240 | + | 0.873825i | \(0.338368\pi\) | |||||||
\(830\) | −12.0000 | + | 24.0000i | −0.416526 | + | 0.833052i | ||||
\(831\) | 26.0000 | 0.901930 | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | 42.0000i | 1.45521i | ||||||||
\(834\) | 12.0000 | 0.415526 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | − | 6.00000i | − | 0.207390i | ||||||
\(838\) | 8.00000i | 0.276355i | ||||||||
\(839\) | −44.0000 | −1.51905 | −0.759524 | − | 0.650479i | \(-0.774568\pi\) | ||||
−0.759524 | + | 0.650479i | \(0.774568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 16.0000i | − | 0.551396i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.00000 | 0.275371 | ||||||||
\(845\) | −9.00000 | + | 18.0000i | −0.309609 | + | 0.619219i | ||||
\(846\) | 6.00000 | 0.206284 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.0000i | 0.343401i | ||||||||
\(849\) | 22.0000 | 0.755038 | ||||||||
\(850\) | −18.0000 | − | 24.0000i | −0.617395 | − | 0.823193i | ||||
\(851\) | −60.0000 | −2.05677 | ||||||||
\(852\) | − | 12.0000i | − | 0.411113i | ||||||
\(853\) | − | 14.0000i | − | 0.479351i | −0.970853 | − | 0.239675i | \(-0.922959\pi\) | ||
0.970853 | − | 0.239675i | \(-0.0770410\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.00000 | − | 2.00000i | 0.0341993 | − | 0.0683986i | ||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | 18.0000i | 0.614868i | 0.951569 | + | 0.307434i | \(0.0994704\pi\) | ||||
−0.951569 | + | 0.307434i | \(0.900530\pi\) | |||||||
\(858\) | 8.00000i | 0.273115i | ||||||||
\(859\) | 28.0000 | 0.955348 | 0.477674 | − | 0.878537i | \(-0.341480\pi\) | ||||
0.477674 | + | 0.878537i | \(0.341480\pi\) | |||||||
\(860\) | −12.0000 | − | 6.00000i | −0.409197 | − | 0.204598i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.0000i | 0.817443i | ||||||||
\(863\) | 36.0000i | 1.22545i | 0.790295 | + | 0.612727i | \(0.209928\pi\) | ||||
−0.790295 | + | 0.612727i | \(0.790072\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 28.0000 | + | 14.0000i | 0.952029 | + | 0.476014i | ||||
\(866\) | 6.00000 | 0.203888 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −56.0000 | −1.89967 | ||||||||
\(870\) | 2.00000 | − | 4.00000i | 0.0678064 | − | 0.135613i | ||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | − | 4.00000i | − | 0.135457i | ||||||
\(873\) | − | 10.0000i | − | 0.338449i | ||||||
\(874\) | 6.00000 | 0.202953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 16.0000 | 0.540590 | ||||||||
\(877\) | 46.0000i | 1.55331i | 0.629926 | + | 0.776655i | \(0.283085\pi\) | ||||
−0.629926 | + | 0.776655i | \(0.716915\pi\) | |||||||
\(878\) | − | 14.0000i | − | 0.472477i | ||||||
\(879\) | 2.00000 | 0.0674583 | ||||||||
\(880\) | 4.00000 | − | 8.00000i | 0.134840 | − | 0.269680i | ||||
\(881\) | 18.0000 | 0.606435 | 0.303218 | − | 0.952921i | \(-0.401939\pi\) | ||||
0.303218 | + | 0.952921i | \(0.401939\pi\) | |||||||
\(882\) | 7.00000i | 0.235702i | ||||||||
\(883\) | 10.0000i | 0.336527i | 0.985742 | + | 0.168263i | \(0.0538159\pi\) | ||||
−0.985742 | + | 0.168263i | \(0.946184\pi\) | |||||||
\(884\) | 12.0000 | 0.403604 | ||||||||
\(885\) | −4.00000 | − | 2.00000i | −0.134459 | − | 0.0672293i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000i | 0.402921i | 0.979497 | + | 0.201460i | \(0.0645687\pi\) | ||||
−0.979497 | + | 0.201460i | \(0.935431\pi\) | |||||||
\(888\) | 10.0000i | 0.335578i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8.00000 | − | 4.00000i | −0.268161 | − | 0.134080i | ||||
\(891\) | −4.00000 | −0.134005 | ||||||||
\(892\) | 8.00000i | 0.267860i | ||||||||
\(893\) | − | 6.00000i | − | 0.200782i | ||||||
\(894\) | −6.00000 | −0.200670 | ||||||||
\(895\) | −18.0000 | + | 36.0000i | −0.601674 | + | 1.20335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | 4.00000i | 0.133482i | ||||||||
\(899\) | −12.0000 | −0.400222 | ||||||||
\(900\) | −3.00000 | − | 4.00000i | −0.100000 | − | 0.133333i | ||||
\(901\) | −60.0000 | −1.99889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.00000 | −0.0665190 | ||||||||
\(905\) | 4.00000 | − | 8.00000i | 0.132964 | − | 0.265929i | ||||
\(906\) | −10.0000 | −0.332228 | ||||||||
\(907\) | − | 24.0000i | − | 0.796907i | −0.917189 | − | 0.398453i | \(-0.869547\pi\) | ||
0.917189 | − | 0.398453i | \(-0.130453\pi\) | |||||||
\(908\) | − | 12.0000i | − | 0.398234i | ||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.0000 | −1.19273 | −0.596367 | − | 0.802712i | \(-0.703390\pi\) | ||||
−0.596367 | + | 0.802712i | \(0.703390\pi\) | |||||||
\(912\) | − | 1.00000i | − | 0.0331133i | ||||||
\(913\) | − | 48.0000i | − | 1.58857i | ||||||
\(914\) | −16.0000 | −0.529233 | ||||||||
\(915\) | −12.0000 | − | 6.00000i | −0.396708 | − | 0.198354i | ||||
\(916\) | −10.0000 | −0.330409 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 6.00000i | 0.198030i | ||||||||
\(919\) | −28.0000 | −0.923635 | −0.461817 | − | 0.886975i | \(-0.652802\pi\) | ||||
−0.461817 | + | 0.886975i | \(0.652802\pi\) | |||||||
\(920\) | 6.00000 | − | 12.0000i | 0.197814 | − | 0.395628i | ||||
\(921\) | 12.0000 | 0.395413 | ||||||||
\(922\) | 18.0000i | 0.592798i | ||||||||
\(923\) | − | 24.0000i | − | 0.789970i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 40.0000 | − | 30.0000i | 1.31519 | − | 0.986394i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | − | 8.00000i | − | 0.262754i | ||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | −18.0000 | −0.590561 | −0.295280 | − | 0.955411i | \(-0.595413\pi\) | ||||
−0.295280 | + | 0.955411i | \(0.595413\pi\) | |||||||
\(930\) | −6.00000 | + | 12.0000i | −0.196748 | + | 0.393496i | ||||
\(931\) | 7.00000 | 0.229416 | ||||||||
\(932\) | − | 14.0000i | − | 0.458585i | ||||||
\(933\) | − | 24.0000i | − | 0.785725i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 48.0000 | + | 24.0000i | 1.56977 | + | 0.784884i | ||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 44.0000i | 1.43742i | 0.695311 | + | 0.718709i | \(0.255266\pi\) | ||||
−0.695311 | + | 0.718709i | \(0.744734\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 28.0000 | 0.913745 | ||||||||
\(940\) | −12.0000 | − | 6.00000i | −0.391397 | − | 0.195698i | ||||
\(941\) | 22.0000 | 0.717180 | 0.358590 | − | 0.933495i | \(-0.383258\pi\) | ||||
0.358590 | + | 0.933495i | \(0.383258\pi\) | |||||||
\(942\) | − | 18.0000i | − | 0.586472i | ||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24.0000 | 0.780307 | ||||||||
\(947\) | 8.00000i | 0.259965i | 0.991516 | + | 0.129983i | \(0.0414921\pi\) | ||||
−0.991516 | + | 0.129983i | \(0.958508\pi\) | |||||||
\(948\) | 14.0000i | 0.454699i | ||||||||
\(949\) | 32.0000 | 1.03876 | ||||||||
\(950\) | −4.00000 | + | 3.00000i | −0.129777 | + | 0.0973329i | ||||
\(951\) | −6.00000 | −0.194563 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 42.0000i | − | 1.36051i | −0.732974 | − | 0.680257i | \(-0.761868\pi\) | ||
0.732974 | − | 0.680257i | \(-0.238132\pi\) | |||||||
\(954\) | −10.0000 | −0.323762 | ||||||||
\(955\) | −24.0000 | + | 48.0000i | −0.776622 | + | 1.55324i | ||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 8.00000i | 0.258603i | ||||||||
\(958\) | − | 16.0000i | − | 0.516937i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −2.00000 | − | 1.00000i | −0.0645497 | − | 0.0322749i | ||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 20.0000i | 0.644826i | ||||||||
\(963\) | − | 4.00000i | − | 0.128898i | ||||||
\(964\) | 10.0000 | 0.322078 | ||||||||
\(965\) | −28.0000 | − | 14.0000i | −0.901352 | − | 0.450676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 28.0000i | − | 0.900419i | −0.892923 | − | 0.450210i | \(-0.851349\pi\) | ||
0.892923 | − | 0.450210i | \(-0.148651\pi\) | |||||||
\(968\) | 5.00000i | 0.160706i | ||||||||
\(969\) | 6.00000 | 0.192748 | ||||||||
\(970\) | −10.0000 | + | 20.0000i | −0.321081 | + | 0.642161i | ||||
\(971\) | −58.0000 | −1.86131 | −0.930654 | − | 0.365900i | \(-0.880761\pi\) | ||||
−0.930654 | + | 0.365900i | \(0.880761\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | −6.00000 | − | 8.00000i | −0.192154 | − | 0.256205i | ||||
\(976\) | −6.00000 | −0.192055 | ||||||||
\(977\) | 26.0000i | 0.831814i | 0.909407 | + | 0.415907i | \(0.136536\pi\) | ||||
−0.909407 | + | 0.415907i | \(0.863464\pi\) | |||||||
\(978\) | 10.0000i | 0.319765i | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 7.00000 | − | 14.0000i | 0.223607 | − | 0.447214i | ||||
\(981\) | 4.00000 | 0.127710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 56.0000i | 1.78612i | 0.449935 | + | 0.893061i | \(0.351447\pi\) | ||||
−0.449935 | + | 0.893061i | \(0.648553\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 16.0000 | + | 8.00000i | 0.509802 | + | 0.254901i | ||||
\(986\) | 12.0000 | 0.382158 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 2.00000i | − | 0.0636285i | ||||||
\(989\) | 36.0000 | 1.14473 | ||||||||
\(990\) | 8.00000 | + | 4.00000i | 0.254257 | + | 0.127128i | ||||
\(991\) | −6.00000 | −0.190596 | −0.0952981 | − | 0.995449i | \(-0.530380\pi\) | ||||
−0.0952981 | + | 0.995449i | \(0.530380\pi\) | |||||||
\(992\) | 6.00000i | 0.190500i | ||||||||
\(993\) | 4.00000i | 0.126936i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −16.0000 | + | 32.0000i | −0.507234 | + | 1.01447i | ||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | 2.00000i | 0.0633406i | 0.999498 | + | 0.0316703i | \(0.0100827\pi\) | ||||
−0.999498 | + | 0.0316703i | \(0.989917\pi\) | |||||||
\(998\) | 20.0000i | 0.633089i | ||||||||
\(999\) | −10.0000 | −0.316386 |
(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 | 570.2.d.a.229.1 | ✓ | 2 | |
3.2 | odd | 2 | 1710.2.d.b.1369.2 | 2 | |||
5.2 | odd | 4 | 2850.2.a.t.1.1 | 1 | |||
5.3 | odd | 4 | 2850.2.a.i.1.1 | 1 | |||
5.4 | even | 2 | inner | 570.2.d.a.229.2 | yes | 2 | |
15.2 | even | 4 | 8550.2.a.k.1.1 | 1 | |||
15.8 | even | 4 | 8550.2.a.bb.1.1 | 1 | |||
15.14 | odd | 2 | 1710.2.d.b.1369.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.d.a.229.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
570.2.d.a.229.2 | yes | 2 | 5.4 | even | 2 | inner | |
1710.2.d.b.1369.1 | 2 | 15.14 | odd | 2 | |||
1710.2.d.b.1369.2 | 2 | 3.2 | odd | 2 | |||
2850.2.a.i.1.1 | 1 | 5.3 | odd | 4 | |||
2850.2.a.t.1.1 | 1 | 5.2 | odd | 4 | |||
8550.2.a.k.1.1 | 1 | 15.2 | even | 4 | |||
8550.2.a.bb.1.1 | 1 | 15.8 | even | 4 |