Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(559,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.559");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
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 | 559.1 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.559 |
Dual form | 930.2.d.d.559.2 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 2.00000 | + | 1.00000i | 0.894427 | + | 0.447214i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.00000 | − | 2.00000i | 0.316228 | − | 0.632456i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 1.00000i | 0.288675i | ||||||||
\(13\) | 2.00000i | 0.554700i | 0.960769 | + | 0.277350i | \(0.0894562\pi\) | ||||
−0.960769 | + | 0.277350i | \(0.910544\pi\) | |||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 1.00000 | − | 2.00000i | 0.258199 | − | 0.516398i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | −2.00000 | − | 1.00000i | −0.447214 | − | 0.223607i | ||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 3.00000 | + | 4.00000i | 0.600000 | + | 0.800000i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 2.00000i | − | 0.377964i | ||||||
\(29\) | 10.0000 | 1.85695 | 0.928477 | − | 0.371391i | \(-0.121119\pi\) | ||||
0.928477 | + | 0.371391i | \(0.121119\pi\) | |||||||
\(30\) | −2.00000 | − | 1.00000i | −0.365148 | − | 0.182574i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | − | 1.00000i | − | 0.176777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 4.00000i | −0.338062 | + | 0.676123i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − | 4.00000i | − | 0.648886i | ||||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | −1.00000 | + | 2.00000i | −0.158114 | + | 0.316228i | ||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | − | 2.00000i | − | 0.308607i | ||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.00000 | − | 1.00000i | −0.298142 | − | 0.149071i | ||||
\(46\) | 2.00000 | 0.294884 | ||||||||
\(47\) | − | 4.00000i | − | 0.583460i | −0.956501 | − | 0.291730i | \(-0.905769\pi\) | ||
0.956501 | − | 0.291730i | \(-0.0942309\pi\) | |||||||
\(48\) | − | 1.00000i | − | 0.144338i | ||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.00000i | − | 0.277350i | ||||||
\(53\) | 2.00000i | 0.274721i | 0.990521 | + | 0.137361i | \(0.0438619\pi\) | ||||
−0.990521 | + | 0.137361i | \(0.956138\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | − | 4.00000i | − | 0.529813i | ||||||
\(58\) | − | 10.0000i | − | 1.31306i | ||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | −1.00000 | + | 2.00000i | −0.129099 | + | 0.258199i | ||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 1.00000i | 0.127000i | ||||||||
\(63\) | − | 2.00000i | − | 0.251976i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.00000 | + | 4.00000i | −0.248069 | + | 0.496139i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.00000 | 0.240772 | ||||||||
\(70\) | 4.00000 | + | 2.00000i | 0.478091 | + | 0.239046i | ||||
\(71\) | −8.00000 | −0.949425 | −0.474713 | − | 0.880141i | \(-0.657448\pi\) | ||||
−0.474713 | + | 0.880141i | \(0.657448\pi\) | |||||||
\(72\) | − | 1.00000i | − | 0.117851i | ||||||
\(73\) | − | 10.0000i | − | 1.17041i | −0.810885 | − | 0.585206i | \(-0.801014\pi\) | ||
0.810885 | − | 0.585206i | \(-0.198986\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 4.00000 | − | 3.00000i | 0.461880 | − | 0.346410i | ||||
\(76\) | −4.00000 | −0.458831 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − | 2.00000i | − | 0.226455i | ||||||
\(79\) | −12.0000 | −1.35011 | −0.675053 | − | 0.737769i | \(-0.735879\pi\) | ||||
−0.675053 | + | 0.737769i | \(0.735879\pi\) | |||||||
\(80\) | 2.00000 | + | 1.00000i | 0.223607 | + | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 2.00000i | − | 0.220863i | ||||||
\(83\) | 4.00000i | 0.439057i | 0.975606 | + | 0.219529i | \(0.0704519\pi\) | ||||
−0.975606 | + | 0.219529i | \(0.929548\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | − | 10.0000i | − | 1.07211i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.0000 | 1.48400 | 0.741999 | − | 0.670402i | \(-0.233878\pi\) | ||||
0.741999 | + | 0.670402i | \(0.233878\pi\) | |||||||
\(90\) | −1.00000 | + | 2.00000i | −0.105409 | + | 0.210819i | ||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | − | 2.00000i | − | 0.208514i | ||||||
\(93\) | 1.00000i | 0.103695i | ||||||||
\(94\) | −4.00000 | −0.412568 | ||||||||
\(95\) | 8.00000 | + | 4.00000i | 0.820783 | + | 0.410391i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 4.00000i | 0.406138i | 0.979164 | + | 0.203069i | \(0.0650917\pi\) | ||||
−0.979164 | + | 0.203069i | \(0.934908\pi\) | |||||||
\(98\) | − | 3.00000i | − | 0.303046i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | − | 4.00000i | −0.300000 | − | 0.400000i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 18.0000i | − | 1.77359i | −0.462160 | − | 0.886796i | \(-0.652926\pi\) | ||
0.462160 | − | 0.886796i | \(-0.347074\pi\) | |||||||
\(104\) | −2.00000 | −0.196116 | ||||||||
\(105\) | 4.00000 | + | 2.00000i | 0.390360 | + | 0.195180i | ||||
\(106\) | 2.00000 | 0.194257 | ||||||||
\(107\) | − | 4.00000i | − | 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | − | 1.00000i | − | 0.0962250i | ||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | 2.00000i | 0.188982i | ||||||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | −4.00000 | −0.374634 | ||||||||
\(115\) | −2.00000 | + | 4.00000i | −0.186501 | + | 0.373002i | ||||
\(116\) | −10.0000 | −0.928477 | ||||||||
\(117\) | − | 2.00000i | − | 0.184900i | ||||||
\(118\) | − | 6.00000i | − | 0.552345i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 2.00000 | + | 1.00000i | 0.182574 | + | 0.0912871i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | 8.00000i | 0.724286i | ||||||||
\(123\) | − | 2.00000i | − | 0.180334i | ||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | − | 8.00000i | − | 0.709885i | −0.934888 | − | 0.354943i | \(-0.884500\pi\) | ||
0.934888 | − | 0.354943i | \(-0.115500\pi\) | |||||||
\(128\) | 1.00000i | 0.0883883i | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 4.00000 | + | 2.00000i | 0.350823 | + | 0.175412i | ||||
\(131\) | −2.00000 | −0.174741 | −0.0873704 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873704 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.00000i | 0.693688i | ||||||||
\(134\) | −8.00000 | −0.691095 | ||||||||
\(135\) | −1.00000 | + | 2.00000i | −0.0860663 | + | 0.172133i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.0000i | 1.36697i | 0.729964 | + | 0.683486i | \(0.239537\pi\) | ||||
−0.729964 | + | 0.683486i | \(0.760463\pi\) | |||||||
\(138\) | − | 2.00000i | − | 0.170251i | ||||||
\(139\) | −10.0000 | −0.848189 | −0.424094 | − | 0.905618i | \(-0.639408\pi\) | ||||
−0.424094 | + | 0.905618i | \(0.639408\pi\) | |||||||
\(140\) | 2.00000 | − | 4.00000i | 0.169031 | − | 0.338062i | ||||
\(141\) | −4.00000 | −0.336861 | ||||||||
\(142\) | 8.00000i | 0.671345i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 20.0000 | + | 10.0000i | 1.66091 | + | 0.830455i | ||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | − | 3.00000i | − | 0.247436i | ||||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | 12.0000 | 0.983078 | 0.491539 | − | 0.870855i | \(-0.336434\pi\) | ||||
0.491539 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(150\) | −3.00000 | − | 4.00000i | −0.244949 | − | 0.326599i | ||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | 4.00000i | 0.324443i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | − | 1.00000i | −0.160644 | − | 0.0803219i | ||||
\(156\) | −2.00000 | −0.160128 | ||||||||
\(157\) | 18.0000i | 1.43656i | 0.695756 | + | 0.718278i | \(0.255069\pi\) | ||||
−0.695756 | + | 0.718278i | \(0.744931\pi\) | |||||||
\(158\) | 12.0000i | 0.954669i | ||||||||
\(159\) | 2.00000 | 0.158610 | ||||||||
\(160\) | 1.00000 | − | 2.00000i | 0.0790569 | − | 0.158114i | ||||
\(161\) | −4.00000 | −0.315244 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 4.00000i | − | 0.313304i | −0.987654 | − | 0.156652i | \(-0.949930\pi\) | ||
0.987654 | − | 0.156652i | \(-0.0500701\pi\) | |||||||
\(164\) | −2.00000 | −0.156174 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.00000 | 0.310460 | ||||||||
\(167\) | 18.0000i | 1.39288i | 0.717614 | + | 0.696441i | \(0.245234\pi\) | ||||
−0.717614 | + | 0.696441i | \(0.754766\pi\) | |||||||
\(168\) | 2.00000i | 0.154303i | ||||||||
\(169\) | 9.00000 | 0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | − | 4.00000i | − | 0.304997i | ||||||
\(173\) | − | 2.00000i | − | 0.152057i | −0.997106 | − | 0.0760286i | \(-0.975776\pi\) | ||
0.997106 | − | 0.0760286i | \(-0.0242240\pi\) | |||||||
\(174\) | −10.0000 | −0.758098 | ||||||||
\(175\) | −8.00000 | + | 6.00000i | −0.604743 | + | 0.453557i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.00000i | − | 0.450988i | ||||||
\(178\) | − | 14.0000i | − | 1.04934i | ||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 2.00000 | + | 1.00000i | 0.149071 | + | 0.0745356i | ||||
\(181\) | −20.0000 | −1.48659 | −0.743294 | − | 0.668965i | \(-0.766738\pi\) | ||||
−0.743294 | + | 0.668965i | \(0.766738\pi\) | |||||||
\(182\) | 4.00000i | 0.296500i | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | −2.00000 | −0.147442 | ||||||||
\(185\) | −2.00000 | + | 4.00000i | −0.147043 | + | 0.294086i | ||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.00000i | 0.291730i | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 4.00000 | − | 8.00000i | 0.290191 | − | 0.580381i | ||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 1.00000i | 0.0721688i | ||||||||
\(193\) | − | 16.0000i | − | 1.15171i | −0.817554 | − | 0.575853i | \(-0.804670\pi\) | ||
0.817554 | − | 0.575853i | \(-0.195330\pi\) | |||||||
\(194\) | 4.00000 | 0.287183 | ||||||||
\(195\) | 4.00000 | + | 2.00000i | 0.286446 | + | 0.143223i | ||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | − | 6.00000i | − | 0.427482i | −0.976890 | − | 0.213741i | \(-0.931435\pi\) | ||
0.976890 | − | 0.213741i | \(-0.0685649\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −24.0000 | −1.70131 | −0.850657 | − | 0.525720i | \(-0.823796\pi\) | ||||
−0.850657 | + | 0.525720i | \(0.823796\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | −8.00000 | −0.564276 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.0000i | 1.40372i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.00000 | + | 2.00000i | 0.279372 | + | 0.139686i | ||||
\(206\) | −18.0000 | −1.25412 | ||||||||
\(207\) | − | 2.00000i | − | 0.139010i | ||||||
\(208\) | 2.00000i | 0.138675i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 2.00000 | − | 4.00000i | 0.138013 | − | 0.276026i | ||||
\(211\) | 4.00000 | 0.275371 | 0.137686 | − | 0.990476i | \(-0.456034\pi\) | ||||
0.137686 | + | 0.990476i | \(0.456034\pi\) | |||||||
\(212\) | − | 2.00000i | − | 0.137361i | ||||||
\(213\) | 8.00000i | 0.548151i | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | −4.00000 | + | 8.00000i | −0.272798 | + | 0.545595i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − | 2.00000i | − | 0.135769i | ||||||
\(218\) | 2.00000i | 0.135457i | ||||||||
\(219\) | −10.0000 | −0.675737 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 2.00000i | − | 0.134231i | ||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | −3.00000 | − | 4.00000i | −0.200000 | − | 0.266667i | ||||
\(226\) | 6.00000 | 0.399114 | ||||||||
\(227\) | − | 12.0000i | − | 0.796468i | −0.917284 | − | 0.398234i | \(-0.869623\pi\) | ||
0.917284 | − | 0.398234i | \(-0.130377\pi\) | |||||||
\(228\) | 4.00000i | 0.264906i | ||||||||
\(229\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(230\) | 4.00000 | + | 2.00000i | 0.263752 | + | 0.131876i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 10.0000i | 0.656532i | ||||||||
\(233\) | − | 6.00000i | − | 0.393073i | −0.980497 | − | 0.196537i | \(-0.937031\pi\) | ||
0.980497 | − | 0.196537i | \(-0.0629694\pi\) | |||||||
\(234\) | −2.00000 | −0.130744 | ||||||||
\(235\) | 4.00000 | − | 8.00000i | 0.260931 | − | 0.521862i | ||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | 12.0000i | 0.779484i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 1.00000 | − | 2.00000i | 0.0645497 | − | 0.129099i | ||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 11.0000i | 0.707107i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 8.00000 | 0.512148 | ||||||||
\(245\) | 6.00000 | + | 3.00000i | 0.383326 | + | 0.191663i | ||||
\(246\) | −2.00000 | −0.127515 | ||||||||
\(247\) | 8.00000i | 0.509028i | ||||||||
\(248\) | − | 1.00000i | − | 0.0635001i | ||||||
\(249\) | 4.00000 | 0.253490 | ||||||||
\(250\) | 11.0000 | − | 2.00000i | 0.695701 | − | 0.126491i | ||||
\(251\) | −12.0000 | −0.757433 | −0.378717 | − | 0.925513i | \(-0.623635\pi\) | ||||
−0.378717 | + | 0.925513i | \(0.623635\pi\) | |||||||
\(252\) | 2.00000i | 0.125988i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 14.0000i | − | 0.873296i | −0.899632 | − | 0.436648i | \(-0.856166\pi\) | ||
0.899632 | − | 0.436648i | \(-0.143834\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 2.00000 | − | 4.00000i | 0.124035 | − | 0.248069i | ||||
\(261\) | −10.0000 | −0.618984 | ||||||||
\(262\) | 2.00000i | 0.123560i | ||||||||
\(263\) | − | 6.00000i | − | 0.369976i | −0.982741 | − | 0.184988i | \(-0.940775\pi\) | ||
0.982741 | − | 0.184988i | \(-0.0592246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | + | 4.00000i | −0.122859 | + | 0.245718i | ||||
\(266\) | 8.00000 | 0.490511 | ||||||||
\(267\) | − | 14.0000i | − | 0.856786i | ||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | −14.0000 | −0.853595 | −0.426798 | − | 0.904347i | \(-0.640358\pi\) | ||||
−0.426798 | + | 0.904347i | \(0.640358\pi\) | |||||||
\(270\) | 2.00000 | + | 1.00000i | 0.121716 | + | 0.0608581i | ||||
\(271\) | −12.0000 | −0.728948 | −0.364474 | − | 0.931214i | \(-0.618751\pi\) | ||||
−0.364474 | + | 0.931214i | \(0.618751\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000i | 0.242091i | ||||||||
\(274\) | 16.0000 | 0.966595 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −2.00000 | −0.120386 | ||||||||
\(277\) | 22.0000i | 1.32185i | 0.750451 | + | 0.660926i | \(0.229836\pi\) | ||||
−0.750451 | + | 0.660926i | \(0.770164\pi\) | |||||||
\(278\) | 10.0000i | 0.599760i | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −4.00000 | − | 2.00000i | −0.239046 | − | 0.119523i | ||||
\(281\) | −2.00000 | −0.119310 | −0.0596550 | − | 0.998219i | \(-0.519000\pi\) | ||||
−0.0596550 | + | 0.998219i | \(0.519000\pi\) | |||||||
\(282\) | 4.00000i | 0.238197i | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 4.00000 | − | 8.00000i | 0.236940 | − | 0.473879i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.00000i | 0.236113i | ||||||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 10.0000 | − | 20.0000i | 0.587220 | − | 1.17444i | ||||
\(291\) | 4.00000 | 0.234484 | ||||||||
\(292\) | 10.0000i | 0.585206i | ||||||||
\(293\) | 6.00000i | 0.350524i | 0.984522 | + | 0.175262i | \(0.0560772\pi\) | ||||
−0.984522 | + | 0.175262i | \(0.943923\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 12.0000 | + | 6.00000i | 0.698667 | + | 0.349334i | ||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 12.0000i | − | 0.695141i | ||||||
\(299\) | −4.00000 | −0.231326 | ||||||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | −8.00000 | −0.461112 | ||||||||
\(302\) | 16.0000i | 0.920697i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −16.0000 | − | 8.00000i | −0.916157 | − | 0.458079i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000i | 0.228292i | 0.993464 | + | 0.114146i | \(0.0364132\pi\) | ||||
−0.993464 | + | 0.114146i | \(0.963587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.0000 | −1.02398 | ||||||||
\(310\) | −1.00000 | + | 2.00000i | −0.0567962 | + | 0.113592i | ||||
\(311\) | −20.0000 | −1.13410 | −0.567048 | − | 0.823685i | \(-0.691915\pi\) | ||||
−0.567048 | + | 0.823685i | \(0.691915\pi\) | |||||||
\(312\) | 2.00000i | 0.113228i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | 18.0000 | 1.01580 | ||||||||
\(315\) | 2.00000 | − | 4.00000i | 0.112687 | − | 0.225374i | ||||
\(316\) | 12.0000 | 0.675053 | ||||||||
\(317\) | − | 30.0000i | − | 1.68497i | −0.538721 | − | 0.842484i | \(-0.681092\pi\) | ||
0.538721 | − | 0.842484i | \(-0.318908\pi\) | |||||||
\(318\) | − | 2.00000i | − | 0.112154i | ||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −2.00000 | − | 1.00000i | −0.111803 | − | 0.0559017i | ||||
\(321\) | −4.00000 | −0.223258 | ||||||||
\(322\) | 4.00000i | 0.222911i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −8.00000 | + | 6.00000i | −0.443760 | + | 0.332820i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | 2.00000i | 0.110600i | ||||||||
\(328\) | 2.00000i | 0.110432i | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.0000 | 0.769510 | 0.384755 | − | 0.923019i | \(-0.374286\pi\) | ||||
0.384755 | + | 0.923019i | \(0.374286\pi\) | |||||||
\(332\) | − | 4.00000i | − | 0.219529i | ||||||
\(333\) | − | 2.00000i | − | 0.109599i | ||||||
\(334\) | 18.0000 | 0.984916 | ||||||||
\(335\) | 8.00000 | − | 16.0000i | 0.437087 | − | 0.874173i | ||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | − | 2.00000i | − | 0.108947i | −0.998515 | − | 0.0544735i | \(-0.982652\pi\) | ||
0.998515 | − | 0.0544735i | \(-0.0173480\pi\) | |||||||
\(338\) | − | 9.00000i | − | 0.489535i | ||||||
\(339\) | 6.00000 | 0.325875 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 4.00000i | 0.216295i | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | 4.00000 | + | 2.00000i | 0.215353 | + | 0.107676i | ||||
\(346\) | −2.00000 | −0.107521 | ||||||||
\(347\) | − | 32.0000i | − | 1.71785i | −0.512101 | − | 0.858925i | \(-0.671133\pi\) | ||
0.512101 | − | 0.858925i | \(-0.328867\pi\) | |||||||
\(348\) | 10.0000i | 0.536056i | ||||||||
\(349\) | 10.0000 | 0.535288 | 0.267644 | − | 0.963518i | \(-0.413755\pi\) | ||||
0.267644 | + | 0.963518i | \(0.413755\pi\) | |||||||
\(350\) | 6.00000 | + | 8.00000i | 0.320713 | + | 0.427618i | ||||
\(351\) | −2.00000 | −0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0000i | 0.638696i | 0.947638 | + | 0.319348i | \(0.103464\pi\) | ||||
−0.947638 | + | 0.319348i | \(0.896536\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | −16.0000 | − | 8.00000i | −0.849192 | − | 0.424596i | ||||
\(356\) | −14.0000 | −0.741999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | −24.0000 | −1.26667 | −0.633336 | − | 0.773877i | \(-0.718315\pi\) | ||||
−0.633336 | + | 0.773877i | \(0.718315\pi\) | |||||||
\(360\) | 1.00000 | − | 2.00000i | 0.0527046 | − | 0.105409i | ||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 20.0000i | 1.05118i | ||||||||
\(363\) | 11.0000i | 0.577350i | ||||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | 10.0000 | − | 20.0000i | 0.523424 | − | 1.04685i | ||||
\(366\) | 8.00000 | 0.418167 | ||||||||
\(367\) | − | 32.0000i | − | 1.67039i | −0.549957 | − | 0.835193i | \(-0.685356\pi\) | ||
0.549957 | − | 0.835193i | \(-0.314644\pi\) | |||||||
\(368\) | 2.00000i | 0.104257i | ||||||||
\(369\) | −2.00000 | −0.104116 | ||||||||
\(370\) | 4.00000 | + | 2.00000i | 0.207950 | + | 0.103975i | ||||
\(371\) | −4.00000 | −0.207670 | ||||||||
\(372\) | − | 1.00000i | − | 0.0518476i | ||||||
\(373\) | − | 26.0000i | − | 1.34623i | −0.739538 | − | 0.673114i | \(-0.764956\pi\) | ||
0.739538 | − | 0.673114i | \(-0.235044\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.0000 | − | 2.00000i | 0.568038 | − | 0.103280i | ||||
\(376\) | 4.00000 | 0.206284 | ||||||||
\(377\) | 20.0000i | 1.03005i | ||||||||
\(378\) | 2.00000i | 0.102869i | ||||||||
\(379\) | −24.0000 | −1.23280 | −0.616399 | − | 0.787434i | \(-0.711409\pi\) | ||||
−0.616399 | + | 0.787434i | \(0.711409\pi\) | |||||||
\(380\) | −8.00000 | − | 4.00000i | −0.410391 | − | 0.205196i | ||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | − | 8.00000i | − | 0.409316i | ||||||
\(383\) | − | 38.0000i | − | 1.94171i | −0.239669 | − | 0.970855i | \(-0.577039\pi\) | ||
0.239669 | − | 0.970855i | \(-0.422961\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −16.0000 | −0.814379 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | − | 4.00000i | − | 0.203069i | ||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 2.00000 | − | 4.00000i | 0.101274 | − | 0.202548i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 2.00000i | 0.100887i | ||||||||
\(394\) | −6.00000 | −0.302276 | ||||||||
\(395\) | −24.0000 | − | 12.0000i | −1.20757 | − | 0.603786i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 26.0000i | − | 1.30490i | −0.757831 | − | 0.652451i | \(-0.773741\pi\) | ||
0.757831 | − | 0.652451i | \(-0.226259\pi\) | |||||||
\(398\) | 24.0000i | 1.20301i | ||||||||
\(399\) | 8.00000 | 0.400501 | ||||||||
\(400\) | 3.00000 | + | 4.00000i | 0.150000 | + | 0.200000i | ||||
\(401\) | 2.00000 | 0.0998752 | 0.0499376 | − | 0.998752i | \(-0.484098\pi\) | ||||
0.0499376 | + | 0.998752i | \(0.484098\pi\) | |||||||
\(402\) | 8.00000i | 0.399004i | ||||||||
\(403\) | − | 2.00000i | − | 0.0996271i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | + | 1.00000i | 0.0993808 | + | 0.0496904i | ||||
\(406\) | 20.0000 | 0.992583 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.00000 | 0.0988936 | 0.0494468 | − | 0.998777i | \(-0.484254\pi\) | ||||
0.0494468 | + | 0.998777i | \(0.484254\pi\) | |||||||
\(410\) | 2.00000 | − | 4.00000i | 0.0987730 | − | 0.197546i | ||||
\(411\) | 16.0000 | 0.789222 | ||||||||
\(412\) | 18.0000i | 0.886796i | ||||||||
\(413\) | 12.0000i | 0.590481i | ||||||||
\(414\) | −2.00000 | −0.0982946 | ||||||||
\(415\) | −4.00000 | + | 8.00000i | −0.196352 | + | 0.392705i | ||||
\(416\) | 2.00000 | 0.0980581 | ||||||||
\(417\) | 10.0000i | 0.489702i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | −4.00000 | − | 2.00000i | −0.195180 | − | 0.0975900i | ||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | − | 4.00000i | − | 0.194717i | ||||||
\(423\) | 4.00000i | 0.194487i | ||||||||
\(424\) | −2.00000 | −0.0971286 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 8.00000 | 0.387601 | ||||||||
\(427\) | − | 16.0000i | − | 0.774294i | ||||||
\(428\) | 4.00000i | 0.193347i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.00000 | + | 4.00000i | 0.385794 | + | 0.192897i | ||||
\(431\) | 24.0000 | 1.15604 | 0.578020 | − | 0.816023i | \(-0.303826\pi\) | ||||
0.578020 | + | 0.816023i | \(0.303826\pi\) | |||||||
\(432\) | 1.00000i | 0.0481125i | ||||||||
\(433\) | − | 2.00000i | − | 0.0961139i | −0.998845 | − | 0.0480569i | \(-0.984697\pi\) | ||
0.998845 | − | 0.0480569i | \(-0.0153029\pi\) | |||||||
\(434\) | −2.00000 | −0.0960031 | ||||||||
\(435\) | 10.0000 | − | 20.0000i | 0.479463 | − | 0.958927i | ||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | 8.00000i | 0.382692i | ||||||||
\(438\) | 10.0000i | 0.477818i | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.0000i | 0.950229i | 0.879924 | + | 0.475114i | \(0.157593\pi\) | ||||
−0.879924 | + | 0.475114i | \(0.842407\pi\) | |||||||
\(444\) | −2.00000 | −0.0949158 | ||||||||
\(445\) | 28.0000 | + | 14.0000i | 1.32733 | + | 0.663664i | ||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | − | 12.0000i | − | 0.567581i | ||||||
\(448\) | − | 2.00000i | − | 0.0944911i | ||||||
\(449\) | −2.00000 | −0.0943858 | −0.0471929 | − | 0.998886i | \(-0.515028\pi\) | ||||
−0.0471929 | + | 0.998886i | \(0.515028\pi\) | |||||||
\(450\) | −4.00000 | + | 3.00000i | −0.188562 | + | 0.141421i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 16.0000i | 0.751746i | ||||||||
\(454\) | −12.0000 | −0.563188 | ||||||||
\(455\) | −8.00000 | − | 4.00000i | −0.375046 | − | 0.187523i | ||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 18.0000i | 0.842004i | 0.907060 | + | 0.421002i | \(0.138322\pi\) | ||||
−0.907060 | + | 0.421002i | \(0.861678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.00000 | − | 4.00000i | 0.0932505 | − | 0.186501i | ||||
\(461\) | 10.0000 | 0.465746 | 0.232873 | − | 0.972507i | \(-0.425187\pi\) | ||||
0.232873 | + | 0.972507i | \(0.425187\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 8.00000i | − | 0.371792i | −0.982569 | − | 0.185896i | \(-0.940481\pi\) | ||
0.982569 | − | 0.185896i | \(-0.0595187\pi\) | |||||||
\(464\) | 10.0000 | 0.464238 | ||||||||
\(465\) | −1.00000 | + | 2.00000i | −0.0463739 | + | 0.0927478i | ||||
\(466\) | −6.00000 | −0.277945 | ||||||||
\(467\) | − | 4.00000i | − | 0.185098i | −0.995708 | − | 0.0925490i | \(-0.970499\pi\) | ||
0.995708 | − | 0.0925490i | \(-0.0295015\pi\) | |||||||
\(468\) | 2.00000i | 0.0924500i | ||||||||
\(469\) | 16.0000 | 0.738811 | ||||||||
\(470\) | −8.00000 | − | 4.00000i | −0.369012 | − | 0.184506i | ||||
\(471\) | 18.0000 | 0.829396 | ||||||||
\(472\) | 6.00000i | 0.276172i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 12.0000 | 0.551178 | ||||||||
\(475\) | 12.0000 | + | 16.0000i | 0.550598 | + | 0.734130i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 2.00000i | − | 0.0915737i | ||||||
\(478\) | − | 8.00000i | − | 0.365911i | ||||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | −2.00000 | − | 1.00000i | −0.0912871 | − | 0.0456435i | ||||
\(481\) | −4.00000 | −0.182384 | ||||||||
\(482\) | − | 18.0000i | − | 0.819878i | ||||||
\(483\) | 4.00000i | 0.182006i | ||||||||
\(484\) | 11.0000 | 0.500000 | ||||||||
\(485\) | −4.00000 | + | 8.00000i | −0.181631 | + | 0.363261i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | − | 8.00000i | − | 0.362143i | ||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | 3.00000 | − | 6.00000i | 0.135526 | − | 0.271052i | ||||
\(491\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(492\) | 2.00000i | 0.0901670i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 8.00000 | 0.359937 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | − | 16.0000i | − | 0.717698i | ||||||
\(498\) | − | 4.00000i | − | 0.179244i | ||||||
\(499\) | 14.0000 | 0.626726 | 0.313363 | − | 0.949633i | \(-0.398544\pi\) | ||||
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | −2.00000 | − | 11.0000i | −0.0894427 | − | 0.491935i | ||||
\(501\) | 18.0000 | 0.804181 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | − | 16.0000i | − | 0.713405i | −0.934218 | − | 0.356702i | \(-0.883901\pi\) | ||
0.934218 | − | 0.356702i | \(-0.116099\pi\) | |||||||
\(504\) | 2.00000 | 0.0890871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.00000i | − | 0.399704i | ||||||
\(508\) | 8.00000i | 0.354943i | ||||||||
\(509\) | −26.0000 | −1.15243 | −0.576215 | − | 0.817298i | \(-0.695471\pi\) | ||||
−0.576215 | + | 0.817298i | \(0.695471\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 20.0000 | 0.884748 | ||||||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 4.00000i | 0.176604i | ||||||||
\(514\) | −14.0000 | −0.617514 | ||||||||
\(515\) | 18.0000 | − | 36.0000i | 0.793175 | − | 1.58635i | ||||
\(516\) | −4.00000 | −0.176090 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 4.00000i | 0.175750i | ||||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | −4.00000 | − | 2.00000i | −0.175412 | − | 0.0877058i | ||||
\(521\) | 30.0000 | 1.31432 | 0.657162 | − | 0.753749i | \(-0.271757\pi\) | ||||
0.657162 | + | 0.753749i | \(0.271757\pi\) | |||||||
\(522\) | 10.0000i | 0.437688i | ||||||||
\(523\) | − | 20.0000i | − | 0.874539i | −0.899331 | − | 0.437269i | \(-0.855946\pi\) | ||
0.899331 | − | 0.437269i | \(-0.144054\pi\) | |||||||
\(524\) | 2.00000 | 0.0873704 | ||||||||
\(525\) | 6.00000 | + | 8.00000i | 0.261861 | + | 0.349149i | ||||
\(526\) | −6.00000 | −0.261612 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 4.00000 | + | 2.00000i | 0.173749 | + | 0.0868744i | ||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | − | 8.00000i | − | 0.346844i | ||||||
\(533\) | 4.00000i | 0.173259i | ||||||||
\(534\) | −14.0000 | −0.605839 | ||||||||
\(535\) | 4.00000 | − | 8.00000i | 0.172935 | − | 0.345870i | ||||
\(536\) | 8.00000 | 0.345547 | ||||||||
\(537\) | − | 12.0000i | − | 0.517838i | ||||||
\(538\) | 14.0000i | 0.603583i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 1.00000 | − | 2.00000i | 0.0430331 | − | 0.0860663i | ||||
\(541\) | −30.0000 | −1.28980 | −0.644900 | − | 0.764267i | \(-0.723101\pi\) | ||||
−0.644900 | + | 0.764267i | \(0.723101\pi\) | |||||||
\(542\) | 12.0000i | 0.515444i | ||||||||
\(543\) | 20.0000i | 0.858282i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.00000 | − | 2.00000i | −0.171341 | − | 0.0856706i | ||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | 8.00000i | 0.342055i | 0.985266 | + | 0.171028i | \(0.0547087\pi\) | ||||
−0.985266 | + | 0.171028i | \(0.945291\pi\) | |||||||
\(548\) | − | 16.0000i | − | 0.683486i | ||||||
\(549\) | 8.00000 | 0.341432 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.0000 | 1.70406 | ||||||||
\(552\) | 2.00000i | 0.0851257i | ||||||||
\(553\) | − | 24.0000i | − | 1.02058i | ||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | 4.00000 | + | 2.00000i | 0.169791 | + | 0.0848953i | ||||
\(556\) | 10.0000 | 0.424094 | ||||||||
\(557\) | − | 30.0000i | − | 1.27114i | −0.772043 | − | 0.635570i | \(-0.780765\pi\) | ||
0.772043 | − | 0.635570i | \(-0.219235\pi\) | |||||||
\(558\) | − | 1.00000i | − | 0.0423334i | ||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | −2.00000 | + | 4.00000i | −0.0845154 | + | 0.169031i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.00000i | 0.0843649i | ||||||||
\(563\) | − | 12.0000i | − | 0.505740i | −0.967500 | − | 0.252870i | \(-0.918626\pi\) | ||
0.967500 | − | 0.252870i | \(-0.0813744\pi\) | |||||||
\(564\) | 4.00000 | 0.168430 | ||||||||
\(565\) | −6.00000 | + | 12.0000i | −0.252422 | + | 0.504844i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 2.00000i | 0.0839921i | ||||||||
\(568\) | − | 8.00000i | − | 0.335673i | ||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | −8.00000 | − | 4.00000i | −0.335083 | − | 0.167542i | ||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 8.00000i | − | 0.334205i | ||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | −8.00000 | + | 6.00000i | −0.333623 | + | 0.250217i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 32.0000i | − | 1.33218i | −0.745873 | − | 0.666089i | \(-0.767967\pi\) | ||
0.745873 | − | 0.666089i | \(-0.232033\pi\) | |||||||
\(578\) | − | 17.0000i | − | 0.707107i | ||||||
\(579\) | −16.0000 | −0.664937 | ||||||||
\(580\) | −20.0000 | − | 10.0000i | −0.830455 | − | 0.415227i | ||||
\(581\) | −8.00000 | −0.331896 | ||||||||
\(582\) | − | 4.00000i | − | 0.165805i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 10.0000 | 0.413803 | ||||||||
\(585\) | 2.00000 | − | 4.00000i | 0.0826898 | − | 0.165380i | ||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | − | 12.0000i | − | 0.495293i | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||
0.968850 | − | 0.247647i | \(-0.0796572\pi\) | |||||||
\(588\) | 3.00000i | 0.123718i | ||||||||
\(589\) | −4.00000 | −0.164817 | ||||||||
\(590\) | 6.00000 | − | 12.0000i | 0.247016 | − | 0.494032i | ||||
\(591\) | −6.00000 | −0.246807 | ||||||||
\(592\) | 2.00000i | 0.0821995i | ||||||||
\(593\) | 18.0000i | 0.739171i | 0.929197 | + | 0.369586i | \(0.120500\pi\) | ||||
−0.929197 | + | 0.369586i | \(0.879500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.0000 | −0.491539 | ||||||||
\(597\) | 24.0000i | 0.982255i | ||||||||
\(598\) | 4.00000i | 0.163572i | ||||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | 3.00000 | + | 4.00000i | 0.122474 | + | 0.163299i | ||||
\(601\) | −2.00000 | −0.0815817 | −0.0407909 | − | 0.999168i | \(-0.512988\pi\) | ||||
−0.0407909 | + | 0.999168i | \(0.512988\pi\) | |||||||
\(602\) | 8.00000i | 0.326056i | ||||||||
\(603\) | 8.00000i | 0.325785i | ||||||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | −22.0000 | − | 11.0000i | −0.894427 | − | 0.447214i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 6.00000i | − | 0.243532i | −0.992559 | − | 0.121766i | \(-0.961144\pi\) | ||
0.992559 | − | 0.121766i | \(-0.0388558\pi\) | |||||||
\(608\) | − | 4.00000i | − | 0.162221i | ||||||
\(609\) | 20.0000 | 0.810441 | ||||||||
\(610\) | −8.00000 | + | 16.0000i | −0.323911 | + | 0.647821i | ||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 6.00000i | − | 0.242338i | −0.992632 | − | 0.121169i | \(-0.961336\pi\) | ||
0.992632 | − | 0.121169i | \(-0.0386643\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | 2.00000 | − | 4.00000i | 0.0806478 | − | 0.161296i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 38.0000i | − | 1.52982i | −0.644136 | − | 0.764911i | \(-0.722783\pi\) | ||
0.644136 | − | 0.764911i | \(-0.277217\pi\) | |||||||
\(618\) | 18.0000i | 0.724066i | ||||||||
\(619\) | 30.0000 | 1.20580 | 0.602901 | − | 0.797816i | \(-0.294011\pi\) | ||||
0.602901 | + | 0.797816i | \(0.294011\pi\) | |||||||
\(620\) | 2.00000 | + | 1.00000i | 0.0803219 | + | 0.0401610i | ||||
\(621\) | −2.00000 | −0.0802572 | ||||||||
\(622\) | 20.0000i | 0.801927i | ||||||||
\(623\) | 28.0000i | 1.12180i | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | 6.00000 | 0.239808 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 18.0000i | − | 0.718278i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −4.00000 | − | 2.00000i | −0.159364 | − | 0.0796819i | ||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | − | 12.0000i | − | 0.477334i | ||||||
\(633\) | − | 4.00000i | − | 0.158986i | ||||||
\(634\) | −30.0000 | −1.19145 | ||||||||
\(635\) | 8.00000 | − | 16.0000i | 0.317470 | − | 0.634941i | ||||
\(636\) | −2.00000 | −0.0793052 | ||||||||
\(637\) | 6.00000i | 0.237729i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | −1.00000 | + | 2.00000i | −0.0395285 | + | 0.0790569i | ||||
\(641\) | −10.0000 | −0.394976 | −0.197488 | − | 0.980305i | \(-0.563278\pi\) | ||||
−0.197488 | + | 0.980305i | \(0.563278\pi\) | |||||||
\(642\) | 4.00000i | 0.157867i | ||||||||
\(643\) | 44.0000i | 1.73519i | 0.497271 | + | 0.867595i | \(0.334335\pi\) | ||||
−0.497271 | + | 0.867595i | \(0.665665\pi\) | |||||||
\(644\) | 4.00000 | 0.157622 | ||||||||
\(645\) | 8.00000 | + | 4.00000i | 0.315000 | + | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 34.0000i | − | 1.33668i | −0.743857 | − | 0.668339i | \(-0.767006\pi\) | ||
0.743857 | − | 0.668339i | \(-0.232994\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.00000 | + | 8.00000i | 0.235339 | + | 0.313786i | ||||
\(651\) | −2.00000 | −0.0783862 | ||||||||
\(652\) | 4.00000i | 0.156652i | ||||||||
\(653\) | 42.0000i | 1.64359i | 0.569785 | + | 0.821794i | \(0.307026\pi\) | ||||
−0.569785 | + | 0.821794i | \(0.692974\pi\) | |||||||
\(654\) | 2.00000 | 0.0782062 | ||||||||
\(655\) | −4.00000 | − | 2.00000i | −0.156293 | − | 0.0781465i | ||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 10.0000i | 0.390137i | ||||||||
\(658\) | − | 8.00000i | − | 0.311872i | ||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 42.0000 | 1.63361 | 0.816805 | − | 0.576913i | \(-0.195743\pi\) | ||||
0.816805 | + | 0.576913i | \(0.195743\pi\) | |||||||
\(662\) | − | 14.0000i | − | 0.544125i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | −0.155230 | ||||||||
\(665\) | −8.00000 | + | 16.0000i | −0.310227 | + | 0.620453i | ||||
\(666\) | −2.00000 | −0.0774984 | ||||||||
\(667\) | 20.0000i | 0.774403i | ||||||||
\(668\) | − | 18.0000i | − | 0.696441i | ||||||
\(669\) | 4.00000 | 0.154649 | ||||||||
\(670\) | −16.0000 | − | 8.00000i | −0.618134 | − | 0.309067i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | − | 2.00000i | − | 0.0771517i | ||||||
\(673\) | − | 6.00000i | − | 0.231283i | −0.993291 | − | 0.115642i | \(-0.963108\pi\) | ||
0.993291 | − | 0.115642i | \(-0.0368924\pi\) | |||||||
\(674\) | −2.00000 | −0.0770371 | ||||||||
\(675\) | −4.00000 | + | 3.00000i | −0.153960 | + | 0.115470i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | 26.0000i | 0.999261i | 0.866239 | + | 0.499631i | \(0.166531\pi\) | ||||
−0.866239 | + | 0.499631i | \(0.833469\pi\) | |||||||
\(678\) | − | 6.00000i | − | 0.230429i | ||||||
\(679\) | −8.00000 | −0.307012 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.0000 | −0.459841 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 28.0000i | − | 1.07139i | −0.844411 | − | 0.535695i | \(-0.820050\pi\) | ||
0.844411 | − | 0.535695i | \(-0.179950\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −16.0000 | + | 32.0000i | −0.611329 | + | 1.22266i | ||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.00000i | 0.152499i | ||||||||
\(689\) | −4.00000 | −0.152388 | ||||||||
\(690\) | 2.00000 | − | 4.00000i | 0.0761387 | − | 0.152277i | ||||
\(691\) | −8.00000 | −0.304334 | −0.152167 | − | 0.988355i | \(-0.548625\pi\) | ||||
−0.152167 | + | 0.988355i | \(0.548625\pi\) | |||||||
\(692\) | 2.00000i | 0.0760286i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −32.0000 | −1.21470 | ||||||||
\(695\) | −20.0000 | − | 10.0000i | −0.758643 | − | 0.379322i | ||||
\(696\) | 10.0000 | 0.379049 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 10.0000i | − | 0.378506i | ||||||
\(699\) | −6.00000 | −0.226941 | ||||||||
\(700\) | 8.00000 | − | 6.00000i | 0.302372 | − | 0.226779i | ||||
\(701\) | −20.0000 | −0.755390 | −0.377695 | − | 0.925930i | \(-0.623283\pi\) | ||||
−0.377695 | + | 0.925930i | \(0.623283\pi\) | |||||||
\(702\) | 2.00000i | 0.0754851i | ||||||||
\(703\) | 8.00000i | 0.301726i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.00000 | − | 4.00000i | −0.301297 | − | 0.150649i | ||||
\(706\) | 12.0000 | 0.451626 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.00000i | 0.225494i | ||||||||
\(709\) | −20.0000 | −0.751116 | −0.375558 | − | 0.926799i | \(-0.622549\pi\) | ||||
−0.375558 | + | 0.926799i | \(0.622549\pi\) | |||||||
\(710\) | −8.00000 | + | 16.0000i | −0.300235 | + | 0.600469i | ||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 14.0000i | 0.524672i | ||||||||
\(713\) | − | 2.00000i | − | 0.0749006i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | − | 8.00000i | − | 0.298765i | ||||||
\(718\) | 24.0000i | 0.895672i | ||||||||
\(719\) | 8.00000 | 0.298350 | 0.149175 | − | 0.988811i | \(-0.452338\pi\) | ||||
0.149175 | + | 0.988811i | \(0.452338\pi\) | |||||||
\(720\) | −2.00000 | − | 1.00000i | −0.0745356 | − | 0.0372678i | ||||
\(721\) | 36.0000 | 1.34071 | ||||||||
\(722\) | 3.00000i | 0.111648i | ||||||||
\(723\) | − | 18.0000i | − | 0.669427i | ||||||
\(724\) | 20.0000 | 0.743294 | ||||||||
\(725\) | 30.0000 | + | 40.0000i | 1.11417 | + | 1.48556i | ||||
\(726\) | 11.0000 | 0.408248 | ||||||||
\(727\) | 26.0000i | 0.964287i | 0.876092 | + | 0.482143i | \(0.160142\pi\) | ||||
−0.876092 | + | 0.482143i | \(0.839858\pi\) | |||||||
\(728\) | − | 4.00000i | − | 0.148250i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −20.0000 | − | 10.0000i | −0.740233 | − | 0.370117i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | − | 8.00000i | − | 0.295689i | ||||||
\(733\) | − | 22.0000i | − | 0.812589i | −0.913742 | − | 0.406294i | \(-0.866821\pi\) | ||
0.913742 | − | 0.406294i | \(-0.133179\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 3.00000 | − | 6.00000i | 0.110657 | − | 0.221313i | ||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 2.00000i | 0.0736210i | ||||||||
\(739\) | −54.0000 | −1.98642 | −0.993211 | − | 0.116326i | \(-0.962888\pi\) | ||||
−0.993211 | + | 0.116326i | \(0.962888\pi\) | |||||||
\(740\) | 2.00000 | − | 4.00000i | 0.0735215 | − | 0.147043i | ||||
\(741\) | 8.00000 | 0.293887 | ||||||||
\(742\) | 4.00000i | 0.146845i | ||||||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 24.0000 | + | 12.0000i | 0.879292 | + | 0.439646i | ||||
\(746\) | −26.0000 | −0.951928 | ||||||||
\(747\) | − | 4.00000i | − | 0.146352i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | −2.00000 | − | 11.0000i | −0.0730297 | − | 0.401663i | ||||
\(751\) | −32.0000 | −1.16770 | −0.583848 | − | 0.811863i | \(-0.698454\pi\) | ||||
−0.583848 | + | 0.811863i | \(0.698454\pi\) | |||||||
\(752\) | − | 4.00000i | − | 0.145865i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 20.0000 | 0.728357 | ||||||||
\(755\) | −32.0000 | − | 16.0000i | −1.16460 | − | 0.582300i | ||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | 22.0000i | 0.799604i | 0.916602 | + | 0.399802i | \(0.130921\pi\) | ||||
−0.916602 | + | 0.399802i | \(0.869079\pi\) | |||||||
\(758\) | 24.0000i | 0.871719i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.00000 | + | 8.00000i | −0.145095 | + | 0.290191i | ||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 8.00000i | 0.289809i | ||||||||
\(763\) | − | 4.00000i | − | 0.144810i | ||||||
\(764\) | −8.00000 | −0.289430 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −38.0000 | −1.37300 | ||||||||
\(767\) | 12.0000i | 0.433295i | ||||||||
\(768\) | − | 1.00000i | − | 0.0360844i | ||||||
\(769\) | −6.00000 | −0.216366 | −0.108183 | − | 0.994131i | \(-0.534503\pi\) | ||||
−0.108183 | + | 0.994131i | \(0.534503\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | 16.0000i | 0.575853i | ||||||||
\(773\) | − | 14.0000i | − | 0.503545i | −0.967786 | − | 0.251773i | \(-0.918987\pi\) | ||
0.967786 | − | 0.251773i | \(-0.0810135\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | −3.00000 | − | 4.00000i | −0.107763 | − | 0.143684i | ||||
\(776\) | −4.00000 | −0.143592 | ||||||||
\(777\) | 4.00000i | 0.143499i | ||||||||
\(778\) | 14.0000i | 0.501924i | ||||||||
\(779\) | 8.00000 | 0.286630 | ||||||||
\(780\) | −4.00000 | − | 2.00000i | −0.143223 | − | 0.0716115i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.0000i | 0.357371i | ||||||||
\(784\) | 3.00000 | 0.107143 | ||||||||
\(785\) | −18.0000 | + | 36.0000i | −0.642448 | + | 1.28490i | ||||
\(786\) | 2.00000 | 0.0713376 | ||||||||
\(787\) | − | 12.0000i | − | 0.427754i | −0.976861 | − | 0.213877i | \(-0.931391\pi\) | ||
0.976861 | − | 0.213877i | \(-0.0686091\pi\) | |||||||
\(788\) | 6.00000i | 0.213741i | ||||||||
\(789\) | −6.00000 | −0.213606 | ||||||||
\(790\) | −12.0000 | + | 24.0000i | −0.426941 | + | 0.853882i | ||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 16.0000i | − | 0.568177i | ||||||
\(794\) | −26.0000 | −0.922705 | ||||||||
\(795\) | 4.00000 | + | 2.00000i | 0.141865 | + | 0.0709327i | ||||
\(796\) | 24.0000 | 0.850657 | ||||||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | − | 8.00000i | − | 0.283197i | ||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | −14.0000 | −0.494666 | ||||||||
\(802\) | − | 2.00000i | − | 0.0706225i | ||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 8.00000 | 0.282138 | ||||||||
\(805\) | −8.00000 | − | 4.00000i | −0.281963 | − | 0.140981i | ||||
\(806\) | −2.00000 | −0.0704470 | ||||||||
\(807\) | 14.0000i | 0.492823i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −42.0000 | −1.47664 | −0.738321 | − | 0.674450i | \(-0.764381\pi\) | ||||
−0.738321 | + | 0.674450i | \(0.764381\pi\) | |||||||
\(810\) | 1.00000 | − | 2.00000i | 0.0351364 | − | 0.0702728i | ||||
\(811\) | −40.0000 | −1.40459 | −0.702295 | − | 0.711886i | \(-0.747841\pi\) | ||||
−0.702295 | + | 0.711886i | \(0.747841\pi\) | |||||||
\(812\) | − | 20.0000i | − | 0.701862i | ||||||
\(813\) | 12.0000i | 0.420858i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.00000 | − | 8.00000i | 0.140114 | − | 0.280228i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.0000i | 0.559769i | ||||||||
\(818\) | − | 2.00000i | − | 0.0699284i | ||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | −4.00000 | − | 2.00000i | −0.139686 | − | 0.0698430i | ||||
\(821\) | 30.0000 | 1.04701 | 0.523504 | − | 0.852023i | \(-0.324625\pi\) | ||||
0.523504 | + | 0.852023i | \(0.324625\pi\) | |||||||
\(822\) | − | 16.0000i | − | 0.558064i | ||||||
\(823\) | 36.0000i | 1.25488i | 0.778664 | + | 0.627441i | \(0.215897\pi\) | ||||
−0.778664 | + | 0.627441i | \(0.784103\pi\) | |||||||
\(824\) | 18.0000 | 0.627060 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.0000 | 0.417533 | ||||||||
\(827\) | − | 32.0000i | − | 1.11275i | −0.830932 | − | 0.556375i | \(-0.812192\pi\) | ||
0.830932 | − | 0.556375i | \(-0.187808\pi\) | |||||||
\(828\) | 2.00000i | 0.0695048i | ||||||||
\(829\) | 4.00000 | 0.138926 | 0.0694629 | − | 0.997585i | \(-0.477871\pi\) | ||||
0.0694629 | + | 0.997585i | \(0.477871\pi\) | |||||||
\(830\) | 8.00000 | + | 4.00000i | 0.277684 | + | 0.138842i | ||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | − | 2.00000i | − | 0.0693375i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.0000 | 0.346272 | ||||||||
\(835\) | −18.0000 | + | 36.0000i | −0.622916 | + | 1.24583i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 1.00000i | − | 0.0345651i | ||||||
\(838\) | − | 18.0000i | − | 0.621800i | ||||||
\(839\) | −24.0000 | −0.828572 | −0.414286 | − | 0.910147i | \(-0.635969\pi\) | ||||
−0.414286 | + | 0.910147i | \(0.635969\pi\) | |||||||
\(840\) | −2.00000 | + | 4.00000i | −0.0690066 | + | 0.138013i | ||||
\(841\) | 71.0000 | 2.44828 | ||||||||
\(842\) | 14.0000i | 0.482472i | ||||||||
\(843\) | 2.00000i | 0.0688837i | ||||||||
\(844\) | −4.00000 | −0.137686 | ||||||||
\(845\) | 18.0000 | + | 9.00000i | 0.619219 | + | 0.309609i | ||||
\(846\) | 4.00000 | 0.137523 | ||||||||
\(847\) | − | 22.0000i | − | 0.755929i | ||||||
\(848\) | 2.00000i | 0.0686803i | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.00000 | −0.137118 | ||||||||
\(852\) | − | 8.00000i | − | 0.274075i | ||||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | −16.0000 | −0.547509 | ||||||||
\(855\) | −8.00000 | − | 4.00000i | −0.273594 | − | 0.136797i | ||||
\(856\) | 4.00000 | 0.136717 | ||||||||
\(857\) | 22.0000i | 0.751506i | 0.926720 | + | 0.375753i | \(0.122616\pi\) | ||||
−0.926720 | + | 0.375753i | \(0.877384\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −22.0000 | −0.750630 | −0.375315 | − | 0.926897i | \(-0.622466\pi\) | ||||
−0.375315 | + | 0.926897i | \(0.622466\pi\) | |||||||
\(860\) | 4.00000 | − | 8.00000i | 0.136399 | − | 0.272798i | ||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | − | 24.0000i | − | 0.817443i | ||||||
\(863\) | 46.0000i | 1.56586i | 0.622111 | + | 0.782929i | \(0.286275\pi\) | ||||
−0.622111 | + | 0.782929i | \(0.713725\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 2.00000 | − | 4.00000i | 0.0680020 | − | 0.136004i | ||||
\(866\) | −2.00000 | −0.0679628 | ||||||||
\(867\) | − | 17.0000i | − | 0.577350i | ||||||
\(868\) | 2.00000i | 0.0678844i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −20.0000 | − | 10.0000i | −0.678064 | − | 0.339032i | ||||
\(871\) | 16.0000 | 0.542139 | ||||||||
\(872\) | − | 2.00000i | − | 0.0677285i | ||||||
\(873\) | − | 4.00000i | − | 0.135379i | ||||||
\(874\) | 8.00000 | 0.270604 | ||||||||
\(875\) | −22.0000 | + | 4.00000i | −0.743736 | + | 0.135225i | ||||
\(876\) | 10.0000 | 0.337869 | ||||||||
\(877\) | − | 54.0000i | − | 1.82345i | −0.410801 | − | 0.911725i | \(-0.634751\pi\) | ||
0.410801 | − | 0.911725i | \(-0.365249\pi\) | |||||||
\(878\) | − | 16.0000i | − | 0.539974i | ||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 3.00000i | 0.101015i | ||||||||
\(883\) | − | 44.0000i | − | 1.48072i | −0.672212 | − | 0.740359i | \(-0.734656\pi\) | ||
0.672212 | − | 0.740359i | \(-0.265344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000 | − | 12.0000i | 0.201688 | − | 0.403376i | ||||
\(886\) | 20.0000 | 0.671913 | ||||||||
\(887\) | 48.0000i | 1.61168i | 0.592132 | + | 0.805841i | \(0.298286\pi\) | ||||
−0.592132 | + | 0.805841i | \(0.701714\pi\) | |||||||
\(888\) | 2.00000i | 0.0671156i | ||||||||
\(889\) | 16.0000 | 0.536623 | ||||||||
\(890\) | 14.0000 | − | 28.0000i | 0.469281 | − | 0.938562i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | − | 16.0000i | − | 0.535420i | ||||||
\(894\) | −12.0000 | −0.401340 | ||||||||
\(895\) | 24.0000 | + | 12.0000i | 0.802232 | + | 0.401116i | ||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 4.00000i | 0.133556i | ||||||||
\(898\) | 2.00000i | 0.0667409i | ||||||||
\(899\) | −10.0000 | −0.333519 | ||||||||
\(900\) | 3.00000 | + | 4.00000i | 0.100000 | + | 0.133333i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.00000i | 0.266223i | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | −40.0000 | − | 20.0000i | −1.32964 | − | 0.664822i | ||||
\(906\) | 16.0000 | 0.531564 | ||||||||
\(907\) | 12.0000i | 0.398453i | 0.979953 | + | 0.199227i | \(0.0638430\pi\) | ||||
−0.979953 | + | 0.199227i | \(0.936157\pi\) | |||||||
\(908\) | 12.0000i | 0.398234i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.00000 | + | 8.00000i | −0.132599 | + | 0.265197i | ||||
\(911\) | 32.0000 | 1.06021 | 0.530104 | − | 0.847933i | \(-0.322153\pi\) | ||||
0.530104 | + | 0.847933i | \(0.322153\pi\) | |||||||
\(912\) | − | 4.00000i | − | 0.132453i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 18.0000 | 0.595387 | ||||||||
\(915\) | −8.00000 | + | 16.0000i | −0.264472 | + | 0.528944i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.00000i | − | 0.132092i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | −4.00000 | − | 2.00000i | −0.131876 | − | 0.0659380i | ||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | − | 10.0000i | − | 0.329332i | ||||||
\(923\) | − | 16.0000i | − | 0.526646i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.00000 | + | 6.00000i | −0.263038 | + | 0.197279i | ||||
\(926\) | −8.00000 | −0.262896 | ||||||||
\(927\) | 18.0000i | 0.591198i | ||||||||
\(928\) | − | 10.0000i | − | 0.328266i | ||||||
\(929\) | 34.0000 | 1.11550 | 0.557752 | − | 0.830008i | \(-0.311664\pi\) | ||||
0.557752 | + | 0.830008i | \(0.311664\pi\) | |||||||
\(930\) | 2.00000 | + | 1.00000i | 0.0655826 | + | 0.0327913i | ||||
\(931\) | 12.0000 | 0.393284 | ||||||||
\(932\) | 6.00000i | 0.196537i | ||||||||
\(933\) | 20.0000i | 0.654771i | ||||||||
\(934\) | −4.00000 | −0.130884 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | 0.0653720 | ||||||||
\(937\) | 20.0000i | 0.653372i | 0.945133 | + | 0.326686i | \(0.105932\pi\) | ||||
−0.945133 | + | 0.326686i | \(0.894068\pi\) | |||||||
\(938\) | − | 16.0000i | − | 0.522419i | ||||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | −4.00000 | + | 8.00000i | −0.130466 | + | 0.260931i | ||||
\(941\) | −50.0000 | −1.62995 | −0.814977 | − | 0.579494i | \(-0.803250\pi\) | ||||
−0.814977 | + | 0.579494i | \(0.803250\pi\) | |||||||
\(942\) | − | 18.0000i | − | 0.586472i | ||||||
\(943\) | 4.00000i | 0.130258i | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | −4.00000 | − | 2.00000i | −0.130120 | − | 0.0650600i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 52.0000i | − | 1.68977i | −0.534946 | − | 0.844886i | \(-0.679668\pi\) | ||
0.534946 | − | 0.844886i | \(-0.320332\pi\) | |||||||
\(948\) | − | 12.0000i | − | 0.389742i | ||||||
\(949\) | 20.0000 | 0.649227 | ||||||||
\(950\) | 16.0000 | − | 12.0000i | 0.519109 | − | 0.389331i | ||||
\(951\) | −30.0000 | −0.972817 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 8.00000i | 0.259145i | 0.991570 | + | 0.129573i | \(0.0413606\pi\) | ||||
−0.991570 | + | 0.129573i | \(0.958639\pi\) | |||||||
\(954\) | −2.00000 | −0.0647524 | ||||||||
\(955\) | 16.0000 | + | 8.00000i | 0.517748 | + | 0.258874i | ||||
\(956\) | −8.00000 | −0.258738 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 4.00000i | − | 0.129234i | ||||||
\(959\) | −32.0000 | −1.03333 | ||||||||
\(960\) | −1.00000 | + | 2.00000i | −0.0322749 | + | 0.0645497i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 4.00000i | 0.128965i | ||||||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | −18.0000 | −0.579741 | ||||||||
\(965\) | 16.0000 | − | 32.0000i | 0.515058 | − | 1.03012i | ||||
\(966\) | 4.00000 | 0.128698 | ||||||||
\(967\) | 32.0000i | 1.02905i | 0.857475 | + | 0.514525i | \(0.172032\pi\) | ||||
−0.857475 | + | 0.514525i | \(0.827968\pi\) | |||||||
\(968\) | − | 11.0000i | − | 0.353553i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.00000 | + | 4.00000i | 0.256865 | + | 0.128432i | ||||
\(971\) | 18.0000 | 0.577647 | 0.288824 | − | 0.957382i | \(-0.406736\pi\) | ||||
0.288824 | + | 0.957382i | \(0.406736\pi\) | |||||||
\(972\) | 1.00000i | 0.0320750i | ||||||||
\(973\) | − | 20.0000i | − | 0.641171i | ||||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 6.00000 | + | 8.00000i | 0.192154 | + | 0.256205i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 42.0000i | 1.34370i | 0.740688 | + | 0.671850i | \(0.234500\pi\) | ||||
−0.740688 | + | 0.671850i | \(0.765500\pi\) | |||||||
\(978\) | 4.00000i | 0.127906i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | − | 3.00000i | −0.191663 | − | 0.0958315i | ||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.00000i | 0.191370i | 0.995412 | + | 0.0956851i | \(0.0305042\pi\) | ||||
−0.995412 | + | 0.0956851i | \(0.969496\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | 6.00000 | − | 12.0000i | 0.191176 | − | 0.382352i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 8.00000i | − | 0.254643i | ||||||
\(988\) | − | 8.00000i | − | 0.254514i | ||||||
\(989\) | −8.00000 | −0.254385 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 1.00000i | 0.0317500i | ||||||||
\(993\) | − | 14.0000i | − | 0.444277i | ||||||
\(994\) | −16.0000 | −0.507489 | ||||||||
\(995\) | −48.0000 | − | 24.0000i | −1.52170 | − | 0.760851i | ||||
\(996\) | −4.00000 | −0.126745 | ||||||||
\(997\) | 42.0000i | 1.33015i | 0.746775 | + | 0.665077i | \(0.231601\pi\) | ||||
−0.746775 | + | 0.665077i | \(0.768399\pi\) | |||||||
\(998\) | − | 14.0000i | − | 0.443162i | ||||||
\(999\) | −2.00000 | −0.0632772 |
(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 | 930.2.d.d.559.1 | ✓ | 2 | |
3.2 | odd | 2 | 2790.2.d.d.559.2 | 2 | |||
5.2 | odd | 4 | 4650.2.a.z.1.1 | 1 | |||
5.3 | odd | 4 | 4650.2.a.u.1.1 | 1 | |||
5.4 | even | 2 | inner | 930.2.d.d.559.2 | yes | 2 | |
15.14 | odd | 2 | 2790.2.d.d.559.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.d.d.559.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
930.2.d.d.559.2 | yes | 2 | 5.4 | even | 2 | inner | |
2790.2.d.d.559.1 | 2 | 15.14 | odd | 2 | |||
2790.2.d.d.559.2 | 2 | 3.2 | odd | 2 | |||
4650.2.a.u.1.1 | 1 | 5.3 | odd | 4 | |||
4650.2.a.z.1.1 | 1 | 5.2 | odd | 4 |