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 | 559.2 | ||
Root | \(1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.559 |
Dual form | 930.2.d.a.559.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | −1.00000 | + | 2.00000i | −0.447214 | + | 0.894427i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000i | 0.377964i | 0.981981 | + | 0.188982i | \(0.0605189\pi\) | ||||
−0.981981 | + | 0.188982i | \(0.939481\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −2.00000 | − | 1.00000i | −0.632456 | − | 0.316228i | ||||
\(11\) | −3.00000 | −0.904534 | −0.452267 | − | 0.891883i | \(-0.649385\pi\) | ||||
−0.452267 | + | 0.891883i | \(0.649385\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 4.00000i | 1.10940i | 0.832050 | + | 0.554700i | \(0.187167\pi\) | ||||
−0.832050 | + | 0.554700i | \(0.812833\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −2.00000 | − | 1.00000i | −0.516398 | − | 0.258199i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | 1.00000 | 0.229416 | 0.114708 | − | 0.993399i | \(-0.463407\pi\) | ||||
0.114708 | + | 0.993399i | \(0.463407\pi\) | |||||||
\(20\) | 1.00000 | − | 2.00000i | 0.223607 | − | 0.447214i | ||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − | 3.00000i | − | 0.639602i | ||||||
\(23\) | − | 5.00000i | − | 1.04257i | −0.853382 | − | 0.521286i | \(-0.825452\pi\) | ||
0.853382 | − | 0.521286i | \(-0.174548\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | −3.00000 | − | 4.00000i | −0.600000 | − | 0.800000i | ||||
\(26\) | −4.00000 | −0.784465 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | − | 1.00000i | − | 0.188982i | ||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 1.00000 | − | 2.00000i | 0.182574 | − | 0.365148i | ||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 3.00000i | − | 0.522233i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 1.00000i | −0.338062 | − | 0.169031i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 4.00000i | 0.657596i | 0.944400 | + | 0.328798i | \(0.106644\pi\) | ||||
−0.944400 | + | 0.328798i | \(0.893356\pi\) | |||||||
\(38\) | 1.00000i | 0.162221i | ||||||||
\(39\) | −4.00000 | −0.640513 | ||||||||
\(40\) | 2.00000 | + | 1.00000i | 0.316228 | + | 0.158114i | ||||
\(41\) | −10.0000 | −1.56174 | −0.780869 | − | 0.624695i | \(-0.785223\pi\) | ||||
−0.780869 | + | 0.624695i | \(0.785223\pi\) | |||||||
\(42\) | − | 1.00000i | − | 0.154303i | ||||||
\(43\) | 5.00000i | 0.762493i | 0.924473 | + | 0.381246i | \(0.124505\pi\) | ||||
−0.924473 | + | 0.381246i | \(0.875495\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 1.00000 | − | 2.00000i | 0.149071 | − | 0.298142i | ||||
\(46\) | 5.00000 | 0.737210 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 6.00000 | 0.857143 | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.00000i | − | 0.554700i | ||||||
\(53\) | − | 5.00000i | − | 0.686803i | −0.939189 | − | 0.343401i | \(-0.888421\pi\) | ||
0.939189 | − | 0.343401i | \(-0.111579\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 3.00000 | − | 6.00000i | 0.404520 | − | 0.809040i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | − | 2.00000i | − | 0.262613i | ||||||
\(59\) | 6.00000 | 0.781133 | 0.390567 | − | 0.920575i | \(-0.372279\pi\) | ||||
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 2.00000 | + | 1.00000i | 0.258199 | + | 0.129099i | ||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | − | 1.00000i | − | 0.127000i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −8.00000 | − | 4.00000i | −0.992278 | − | 0.496139i | ||||
\(66\) | 3.00000 | 0.369274 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.00000 | 0.601929 | ||||||||
\(70\) | 1.00000 | − | 2.00000i | 0.119523 | − | 0.239046i | ||||
\(71\) | −5.00000 | −0.593391 | −0.296695 | − | 0.954972i | \(-0.595885\pi\) | ||||
−0.296695 | + | 0.954972i | \(0.595885\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | 7.00000i | 0.819288i | 0.912245 | + | 0.409644i | \(0.134347\pi\) | ||||
−0.912245 | + | 0.409644i | \(0.865653\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | 4.00000 | − | 3.00000i | 0.461880 | − | 0.346410i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | − | 3.00000i | − | 0.341882i | ||||||
\(78\) | − | 4.00000i | − | 0.452911i | ||||||
\(79\) | −3.00000 | −0.337526 | −0.168763 | − | 0.985657i | \(-0.553977\pi\) | ||||
−0.168763 | + | 0.985657i | \(0.553977\pi\) | |||||||
\(80\) | −1.00000 | + | 2.00000i | −0.111803 | + | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 10.0000i | − | 1.10432i | ||||||
\(83\) | 2.00000i | 0.219529i | 0.993958 | + | 0.109764i | \(0.0350096\pi\) | ||||
−0.993958 | + | 0.109764i | \(0.964990\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.00000 | −0.539164 | ||||||||
\(87\) | − | 2.00000i | − | 0.214423i | ||||||
\(88\) | 3.00000i | 0.319801i | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 2.00000 | + | 1.00000i | 0.210819 | + | 0.105409i | ||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 5.00000i | 0.521286i | ||||||||
\(93\) | − | 1.00000i | − | 0.103695i | ||||||
\(94\) | 8.00000 | 0.825137 | ||||||||
\(95\) | −1.00000 | + | 2.00000i | −0.102598 | + | 0.205196i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 10.0000i | − | 1.01535i | −0.861550 | − | 0.507673i | \(-0.830506\pi\) | ||
0.861550 | − | 0.507673i | \(-0.169494\pi\) | |||||||
\(98\) | 6.00000i | 0.606092i | ||||||||
\(99\) | 3.00000 | 0.301511 | ||||||||
\(100\) | 3.00000 | + | 4.00000i | 0.300000 | + | 0.400000i | ||||
\(101\) | −15.0000 | −1.49256 | −0.746278 | − | 0.665635i | \(-0.768161\pi\) | ||||
−0.746278 | + | 0.665635i | \(0.768161\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 4.00000 | 0.392232 | ||||||||
\(105\) | 1.00000 | − | 2.00000i | 0.0975900 | − | 0.195180i | ||||
\(106\) | 5.00000 | 0.485643 | ||||||||
\(107\) | 19.0000i | 1.83680i | 0.395654 | + | 0.918400i | \(0.370518\pi\) | ||||
−0.395654 | + | 0.918400i | \(0.629482\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | −2.00000 | −0.191565 | −0.0957826 | − | 0.995402i | \(-0.530535\pi\) | ||||
−0.0957826 | + | 0.995402i | \(0.530535\pi\) | |||||||
\(110\) | 6.00000 | + | 3.00000i | 0.572078 | + | 0.286039i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | 15.0000i | 1.41108i | 0.708669 | + | 0.705541i | \(0.249296\pi\) | ||||
−0.708669 | + | 0.705541i | \(0.750704\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 10.0000 | + | 5.00000i | 0.932505 | + | 0.466252i | ||||
\(116\) | 2.00000 | 0.185695 | ||||||||
\(117\) | − | 4.00000i | − | 0.369800i | ||||||
\(118\) | 6.00000i | 0.552345i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.00000 | + | 2.00000i | −0.0912871 | + | 0.182574i | ||||
\(121\) | −2.00000 | −0.181818 | ||||||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | − | 10.0000i | − | 0.901670i | ||||||
\(124\) | 1.00000 | 0.0898027 | ||||||||
\(125\) | 11.0000 | − | 2.00000i | 0.983870 | − | 0.178885i | ||||
\(126\) | 1.00000 | 0.0890871 | ||||||||
\(127\) | 8.00000i | 0.709885i | 0.934888 | + | 0.354943i | \(0.115500\pi\) | ||||
−0.934888 | + | 0.354943i | \(0.884500\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −5.00000 | −0.440225 | ||||||||
\(130\) | 4.00000 | − | 8.00000i | 0.350823 | − | 0.701646i | ||||
\(131\) | −2.00000 | −0.174741 | −0.0873704 | − | 0.996176i | \(-0.527846\pi\) | ||||
−0.0873704 | + | 0.996176i | \(0.527846\pi\) | |||||||
\(132\) | 3.00000i | 0.261116i | ||||||||
\(133\) | 1.00000i | 0.0867110i | ||||||||
\(134\) | −2.00000 | −0.172774 | ||||||||
\(135\) | 2.00000 | + | 1.00000i | 0.172133 | + | 0.0860663i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.00000i | 0.170872i | 0.996344 | + | 0.0854358i | \(0.0272282\pi\) | ||||
−0.996344 | + | 0.0854358i | \(0.972772\pi\) | |||||||
\(138\) | 5.00000i | 0.425628i | ||||||||
\(139\) | 20.0000 | 1.69638 | 0.848189 | − | 0.529694i | \(-0.177693\pi\) | ||||
0.848189 | + | 0.529694i | \(0.177693\pi\) | |||||||
\(140\) | 2.00000 | + | 1.00000i | 0.169031 | + | 0.0845154i | ||||
\(141\) | 8.00000 | 0.673722 | ||||||||
\(142\) | − | 5.00000i | − | 0.419591i | ||||||
\(143\) | − | 12.0000i | − | 1.00349i | ||||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 2.00000 | − | 4.00000i | 0.166091 | − | 0.332182i | ||||
\(146\) | −7.00000 | −0.579324 | ||||||||
\(147\) | 6.00000i | 0.494872i | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −15.0000 | −1.22885 | −0.614424 | − | 0.788976i | \(-0.710612\pi\) | ||||
−0.614424 | + | 0.788976i | \(0.710612\pi\) | |||||||
\(150\) | 3.00000 | + | 4.00000i | 0.244949 | + | 0.326599i | ||||
\(151\) | −16.0000 | −1.30206 | −0.651031 | − | 0.759051i | \(-0.725663\pi\) | ||||
−0.651031 | + | 0.759051i | \(0.725663\pi\) | |||||||
\(152\) | − | 1.00000i | − | 0.0811107i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | 0.241747 | ||||||||
\(155\) | 1.00000 | − | 2.00000i | 0.0803219 | − | 0.160644i | ||||
\(156\) | 4.00000 | 0.320256 | ||||||||
\(157\) | 9.00000i | 0.718278i | 0.933284 | + | 0.359139i | \(0.116930\pi\) | ||||
−0.933284 | + | 0.359139i | \(0.883070\pi\) | |||||||
\(158\) | − | 3.00000i | − | 0.238667i | ||||||
\(159\) | 5.00000 | 0.396526 | ||||||||
\(160\) | −2.00000 | − | 1.00000i | −0.158114 | − | 0.0790569i | ||||
\(161\) | 5.00000 | 0.394055 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 4.00000i | 0.313304i | 0.987654 | + | 0.156652i | \(0.0500701\pi\) | ||||
−0.987654 | + | 0.156652i | \(0.949930\pi\) | |||||||
\(164\) | 10.0000 | 0.780869 | ||||||||
\(165\) | 6.00000 | + | 3.00000i | 0.467099 | + | 0.233550i | ||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 21.0000i | 1.62503i | 0.582941 | + | 0.812514i | \(0.301902\pi\) | ||||
−0.582941 | + | 0.812514i | \(0.698098\pi\) | |||||||
\(168\) | 1.00000i | 0.0771517i | ||||||||
\(169\) | −3.00000 | −0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | − | 5.00000i | − | 0.381246i | ||||||
\(173\) | 2.00000i | 0.152057i | 0.997106 | + | 0.0760286i | \(0.0242240\pi\) | ||||
−0.997106 | + | 0.0760286i | \(0.975776\pi\) | |||||||
\(174\) | 2.00000 | 0.151620 | ||||||||
\(175\) | 4.00000 | − | 3.00000i | 0.302372 | − | 0.226779i | ||||
\(176\) | −3.00000 | −0.226134 | ||||||||
\(177\) | 6.00000i | 0.450988i | ||||||||
\(178\) | − | 1.00000i | − | 0.0749532i | ||||||
\(179\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(180\) | −1.00000 | + | 2.00000i | −0.0745356 | + | 0.149071i | ||||
\(181\) | −5.00000 | −0.371647 | −0.185824 | − | 0.982583i | \(-0.559495\pi\) | ||||
−0.185824 | + | 0.982583i | \(0.559495\pi\) | |||||||
\(182\) | − | 4.00000i | − | 0.296500i | ||||||
\(183\) | − | 2.00000i | − | 0.147844i | ||||||
\(184\) | −5.00000 | −0.368605 | ||||||||
\(185\) | −8.00000 | − | 4.00000i | −0.588172 | − | 0.294086i | ||||
\(186\) | 1.00000 | 0.0733236 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 8.00000i | 0.583460i | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −2.00000 | − | 1.00000i | −0.145095 | − | 0.0725476i | ||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | 10.0000i | 0.719816i | 0.932988 | + | 0.359908i | \(0.117192\pi\) | ||||
−0.932988 | + | 0.359908i | \(0.882808\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 4.00000 | − | 8.00000i | 0.286446 | − | 0.572892i | ||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 3.00000i | 0.213201i | ||||||||
\(199\) | 21.0000 | 1.48865 | 0.744325 | − | 0.667817i | \(-0.232771\pi\) | ||||
0.744325 | + | 0.667817i | \(0.232771\pi\) | |||||||
\(200\) | −4.00000 | + | 3.00000i | −0.282843 | + | 0.212132i | ||||
\(201\) | −2.00000 | −0.141069 | ||||||||
\(202\) | − | 15.0000i | − | 1.05540i | ||||||
\(203\) | − | 2.00000i | − | 0.140372i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | − | 20.0000i | 0.698430 | − | 1.39686i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.00000i | 0.347524i | ||||||||
\(208\) | 4.00000i | 0.277350i | ||||||||
\(209\) | −3.00000 | −0.207514 | ||||||||
\(210\) | 2.00000 | + | 1.00000i | 0.138013 | + | 0.0690066i | ||||
\(211\) | 7.00000 | 0.481900 | 0.240950 | − | 0.970538i | \(-0.422541\pi\) | ||||
0.240950 | + | 0.970538i | \(0.422541\pi\) | |||||||
\(212\) | 5.00000i | 0.343401i | ||||||||
\(213\) | − | 5.00000i | − | 0.342594i | ||||||
\(214\) | −19.0000 | −1.29881 | ||||||||
\(215\) | −10.0000 | − | 5.00000i | −0.681994 | − | 0.340997i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | − | 1.00000i | − | 0.0678844i | ||||||
\(218\) | − | 2.00000i | − | 0.135457i | ||||||
\(219\) | −7.00000 | −0.473016 | ||||||||
\(220\) | −3.00000 | + | 6.00000i | −0.202260 | + | 0.404520i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | − | 4.00000i | − | 0.268462i | ||||||
\(223\) | 20.0000i | 1.33930i | 0.742677 | + | 0.669650i | \(0.233556\pi\) | ||||
−0.742677 | + | 0.669650i | \(0.766444\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 3.00000 | + | 4.00000i | 0.200000 | + | 0.266667i | ||||
\(226\) | −15.0000 | −0.997785 | ||||||||
\(227\) | − | 9.00000i | − | 0.597351i | −0.954355 | − | 0.298675i | \(-0.903455\pi\) | ||
0.954355 | − | 0.298675i | \(-0.0965448\pi\) | |||||||
\(228\) | − | 1.00000i | − | 0.0662266i | ||||||
\(229\) | −15.0000 | −0.991228 | −0.495614 | − | 0.868543i | \(-0.665057\pi\) | ||||
−0.495614 | + | 0.868543i | \(0.665057\pi\) | |||||||
\(230\) | −5.00000 | + | 10.0000i | −0.329690 | + | 0.659380i | ||||
\(231\) | 3.00000 | 0.197386 | ||||||||
\(232\) | 2.00000i | 0.131306i | ||||||||
\(233\) | 21.0000i | 1.37576i | 0.725826 | + | 0.687878i | \(0.241458\pi\) | ||||
−0.725826 | + | 0.687878i | \(0.758542\pi\) | |||||||
\(234\) | 4.00000 | 0.261488 | ||||||||
\(235\) | 16.0000 | + | 8.00000i | 1.04372 | + | 0.521862i | ||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | − | 3.00000i | − | 0.194871i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.0000 | 0.905585 | 0.452792 | − | 0.891616i | \(-0.350428\pi\) | ||||
0.452792 | + | 0.891616i | \(0.350428\pi\) | |||||||
\(240\) | −2.00000 | − | 1.00000i | −0.129099 | − | 0.0645497i | ||||
\(241\) | −12.0000 | −0.772988 | −0.386494 | − | 0.922292i | \(-0.626314\pi\) | ||||
−0.386494 | + | 0.922292i | \(0.626314\pi\) | |||||||
\(242\) | − | 2.00000i | − | 0.128565i | ||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | −6.00000 | + | 12.0000i | −0.383326 | + | 0.766652i | ||||
\(246\) | 10.0000 | 0.637577 | ||||||||
\(247\) | 4.00000i | 0.254514i | ||||||||
\(248\) | 1.00000i | 0.0635001i | ||||||||
\(249\) | −2.00000 | −0.126745 | ||||||||
\(250\) | 2.00000 | + | 11.0000i | 0.126491 | + | 0.695701i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | 1.00000i | 0.0629941i | ||||||||
\(253\) | 15.0000i | 0.943042i | ||||||||
\(254\) | −8.00000 | −0.501965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.00000i | 0.311891i | 0.987766 | + | 0.155946i | \(0.0498425\pi\) | ||||
−0.987766 | + | 0.155946i | \(0.950158\pi\) | |||||||
\(258\) | − | 5.00000i | − | 0.311286i | ||||||
\(259\) | −4.00000 | −0.248548 | ||||||||
\(260\) | 8.00000 | + | 4.00000i | 0.496139 | + | 0.248069i | ||||
\(261\) | 2.00000 | 0.123797 | ||||||||
\(262\) | − | 2.00000i | − | 0.123560i | ||||||
\(263\) | − | 24.0000i | − | 1.47990i | −0.672660 | − | 0.739952i | \(-0.734848\pi\) | ||
0.672660 | − | 0.739952i | \(-0.265152\pi\) | |||||||
\(264\) | −3.00000 | −0.184637 | ||||||||
\(265\) | 10.0000 | + | 5.00000i | 0.614295 | + | 0.307148i | ||||
\(266\) | −1.00000 | −0.0613139 | ||||||||
\(267\) | − | 1.00000i | − | 0.0611990i | ||||||
\(268\) | − | 2.00000i | − | 0.122169i | ||||||
\(269\) | −2.00000 | −0.121942 | −0.0609711 | − | 0.998140i | \(-0.519420\pi\) | ||||
−0.0609711 | + | 0.998140i | \(0.519420\pi\) | |||||||
\(270\) | −1.00000 | + | 2.00000i | −0.0608581 | + | 0.121716i | ||||
\(271\) | 9.00000 | 0.546711 | 0.273356 | − | 0.961913i | \(-0.411866\pi\) | ||||
0.273356 | + | 0.961913i | \(0.411866\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 4.00000i | − | 0.242091i | ||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 9.00000 | + | 12.0000i | 0.542720 | + | 0.723627i | ||||
\(276\) | −5.00000 | −0.300965 | ||||||||
\(277\) | 2.00000i | 0.120168i | 0.998193 | + | 0.0600842i | \(0.0191369\pi\) | ||||
−0.998193 | + | 0.0600842i | \(0.980863\pi\) | |||||||
\(278\) | 20.0000i | 1.19952i | ||||||||
\(279\) | 1.00000 | 0.0598684 | ||||||||
\(280\) | −1.00000 | + | 2.00000i | −0.0597614 | + | 0.119523i | ||||
\(281\) | −32.0000 | −1.90896 | −0.954480 | − | 0.298275i | \(-0.903589\pi\) | ||||
−0.954480 | + | 0.298275i | \(0.903589\pi\) | |||||||
\(282\) | 8.00000i | 0.476393i | ||||||||
\(283\) | − | 14.0000i | − | 0.832214i | −0.909316 | − | 0.416107i | \(-0.863394\pi\) | ||
0.909316 | − | 0.416107i | \(-0.136606\pi\) | |||||||
\(284\) | 5.00000 | 0.296695 | ||||||||
\(285\) | −2.00000 | − | 1.00000i | −0.118470 | − | 0.0592349i | ||||
\(286\) | 12.0000 | 0.709575 | ||||||||
\(287\) | − | 10.0000i | − | 0.590281i | ||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 4.00000 | + | 2.00000i | 0.234888 | + | 0.117444i | ||||
\(291\) | 10.0000 | 0.586210 | ||||||||
\(292\) | − | 7.00000i | − | 0.409644i | ||||||
\(293\) | 18.0000i | 1.05157i | 0.850617 | + | 0.525786i | \(0.176229\pi\) | ||||
−0.850617 | + | 0.525786i | \(0.823771\pi\) | |||||||
\(294\) | −6.00000 | −0.349927 | ||||||||
\(295\) | −6.00000 | + | 12.0000i | −0.349334 | + | 0.698667i | ||||
\(296\) | 4.00000 | 0.232495 | ||||||||
\(297\) | 3.00000i | 0.174078i | ||||||||
\(298\) | − | 15.0000i | − | 0.868927i | ||||||
\(299\) | 20.0000 | 1.15663 | ||||||||
\(300\) | −4.00000 | + | 3.00000i | −0.230940 | + | 0.173205i | ||||
\(301\) | −5.00000 | −0.288195 | ||||||||
\(302\) | − | 16.0000i | − | 0.920697i | ||||||
\(303\) | − | 15.0000i | − | 0.861727i | ||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | 2.00000 | − | 4.00000i | 0.114520 | − | 0.229039i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.00000i | − | 0.228292i | −0.993464 | − | 0.114146i | \(-0.963587\pi\) | ||
0.993464 | − | 0.114146i | \(-0.0364132\pi\) | |||||||
\(308\) | 3.00000i | 0.170941i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.00000 | + | 1.00000i | 0.113592 | + | 0.0567962i | ||||
\(311\) | 16.0000 | 0.907277 | 0.453638 | − | 0.891186i | \(-0.350126\pi\) | ||||
0.453638 | + | 0.891186i | \(0.350126\pi\) | |||||||
\(312\) | 4.00000i | 0.226455i | ||||||||
\(313\) | 6.00000i | 0.339140i | 0.985518 | + | 0.169570i | \(0.0542379\pi\) | ||||
−0.985518 | + | 0.169570i | \(0.945762\pi\) | |||||||
\(314\) | −9.00000 | −0.507899 | ||||||||
\(315\) | 2.00000 | + | 1.00000i | 0.112687 | + | 0.0563436i | ||||
\(316\) | 3.00000 | 0.168763 | ||||||||
\(317\) | 18.0000i | 1.01098i | 0.862832 | + | 0.505490i | \(0.168688\pi\) | ||||
−0.862832 | + | 0.505490i | \(0.831312\pi\) | |||||||
\(318\) | 5.00000i | 0.280386i | ||||||||
\(319\) | 6.00000 | 0.335936 | ||||||||
\(320\) | 1.00000 | − | 2.00000i | 0.0559017 | − | 0.111803i | ||||
\(321\) | −19.0000 | −1.06048 | ||||||||
\(322\) | 5.00000i | 0.278639i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 16.0000 | − | 12.0000i | 0.887520 | − | 0.665640i | ||||
\(326\) | −4.00000 | −0.221540 | ||||||||
\(327\) | − | 2.00000i | − | 0.110600i | ||||||
\(328\) | 10.0000i | 0.552158i | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | −3.00000 | + | 6.00000i | −0.165145 | + | 0.330289i | ||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | − | 2.00000i | − | 0.109764i | ||||||
\(333\) | − | 4.00000i | − | 0.219199i | ||||||
\(334\) | −21.0000 | −1.14907 | ||||||||
\(335\) | −4.00000 | − | 2.00000i | −0.218543 | − | 0.109272i | ||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | − | 34.0000i | − | 1.85210i | −0.377403 | − | 0.926049i | \(-0.623183\pi\) | ||
0.377403 | − | 0.926049i | \(-0.376817\pi\) | |||||||
\(338\) | − | 3.00000i | − | 0.163178i | ||||||
\(339\) | −15.0000 | −0.814688 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | 0.162459 | ||||||||
\(342\) | − | 1.00000i | − | 0.0540738i | ||||||
\(343\) | 13.0000i | 0.701934i | ||||||||
\(344\) | 5.00000 | 0.269582 | ||||||||
\(345\) | −5.00000 | + | 10.0000i | −0.269191 | + | 0.538382i | ||||
\(346\) | −2.00000 | −0.107521 | ||||||||
\(347\) | − | 22.0000i | − | 1.18102i | −0.807030 | − | 0.590511i | \(-0.798926\pi\) | ||
0.807030 | − | 0.590511i | \(-0.201074\pi\) | |||||||
\(348\) | 2.00000i | 0.107211i | ||||||||
\(349\) | −20.0000 | −1.07058 | −0.535288 | − | 0.844670i | \(-0.679797\pi\) | ||||
−0.535288 | + | 0.844670i | \(0.679797\pi\) | |||||||
\(350\) | 3.00000 | + | 4.00000i | 0.160357 | + | 0.213809i | ||||
\(351\) | 4.00000 | 0.213504 | ||||||||
\(352\) | − | 3.00000i | − | 0.159901i | ||||||
\(353\) | − | 24.0000i | − | 1.27739i | −0.769460 | − | 0.638696i | \(-0.779474\pi\) | ||
0.769460 | − | 0.638696i | \(-0.220526\pi\) | |||||||
\(354\) | −6.00000 | −0.318896 | ||||||||
\(355\) | 5.00000 | − | 10.0000i | 0.265372 | − | 0.530745i | ||||
\(356\) | 1.00000 | 0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.00000 | −0.158334 | −0.0791670 | − | 0.996861i | \(-0.525226\pi\) | ||||
−0.0791670 | + | 0.996861i | \(0.525226\pi\) | |||||||
\(360\) | −2.00000 | − | 1.00000i | −0.105409 | − | 0.0527046i | ||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | − | 5.00000i | − | 0.262794i | ||||||
\(363\) | − | 2.00000i | − | 0.104973i | ||||||
\(364\) | 4.00000 | 0.209657 | ||||||||
\(365\) | −14.0000 | − | 7.00000i | −0.732793 | − | 0.366397i | ||||
\(366\) | 2.00000 | 0.104542 | ||||||||
\(367\) | 14.0000i | 0.730794i | 0.930852 | + | 0.365397i | \(0.119067\pi\) | ||||
−0.930852 | + | 0.365397i | \(0.880933\pi\) | |||||||
\(368\) | − | 5.00000i | − | 0.260643i | ||||||
\(369\) | 10.0000 | 0.520579 | ||||||||
\(370\) | 4.00000 | − | 8.00000i | 0.207950 | − | 0.415900i | ||||
\(371\) | 5.00000 | 0.259587 | ||||||||
\(372\) | 1.00000i | 0.0518476i | ||||||||
\(373\) | 11.0000i | 0.569558i | 0.958593 | + | 0.284779i | \(0.0919203\pi\) | ||||
−0.958593 | + | 0.284779i | \(0.908080\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.00000 | + | 11.0000i | 0.103280 | + | 0.568038i | ||||
\(376\) | −8.00000 | −0.412568 | ||||||||
\(377\) | − | 8.00000i | − | 0.412021i | ||||||
\(378\) | 1.00000i | 0.0514344i | ||||||||
\(379\) | 15.0000 | 0.770498 | 0.385249 | − | 0.922813i | \(-0.374116\pi\) | ||||
0.385249 | + | 0.922813i | \(0.374116\pi\) | |||||||
\(380\) | 1.00000 | − | 2.00000i | 0.0512989 | − | 0.102598i | ||||
\(381\) | −8.00000 | −0.409852 | ||||||||
\(382\) | − | 16.0000i | − | 0.818631i | ||||||
\(383\) | − | 28.0000i | − | 1.43073i | −0.698749 | − | 0.715367i | \(-0.746260\pi\) | ||
0.698749 | − | 0.715367i | \(-0.253740\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 6.00000 | + | 3.00000i | 0.305788 | + | 0.152894i | ||||
\(386\) | −10.0000 | −0.508987 | ||||||||
\(387\) | − | 5.00000i | − | 0.254164i | ||||||
\(388\) | 10.0000i | 0.507673i | ||||||||
\(389\) | 28.0000 | 1.41966 | 0.709828 | − | 0.704375i | \(-0.248773\pi\) | ||||
0.709828 | + | 0.704375i | \(0.248773\pi\) | |||||||
\(390\) | 8.00000 | + | 4.00000i | 0.405096 | + | 0.202548i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | − | 6.00000i | − | 0.303046i | ||||||
\(393\) | − | 2.00000i | − | 0.100887i | ||||||
\(394\) | −18.0000 | −0.906827 | ||||||||
\(395\) | 3.00000 | − | 6.00000i | 0.150946 | − | 0.301893i | ||||
\(396\) | −3.00000 | −0.150756 | ||||||||
\(397\) | − | 31.0000i | − | 1.55585i | −0.628360 | − | 0.777923i | \(-0.716273\pi\) | ||
0.628360 | − | 0.777923i | \(-0.283727\pi\) | |||||||
\(398\) | 21.0000i | 1.05263i | ||||||||
\(399\) | −1.00000 | −0.0500626 | ||||||||
\(400\) | −3.00000 | − | 4.00000i | −0.150000 | − | 0.200000i | ||||
\(401\) | 5.00000 | 0.249688 | 0.124844 | − | 0.992176i | \(-0.460157\pi\) | ||||
0.124844 | + | 0.992176i | \(0.460157\pi\) | |||||||
\(402\) | − | 2.00000i | − | 0.0997509i | ||||||
\(403\) | − | 4.00000i | − | 0.199254i | ||||||
\(404\) | 15.0000 | 0.746278 | ||||||||
\(405\) | −1.00000 | + | 2.00000i | −0.0496904 | + | 0.0993808i | ||||
\(406\) | 2.00000 | 0.0992583 | ||||||||
\(407\) | − | 12.0000i | − | 0.594818i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.00000 | −0.197787 | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 20.0000 | + | 10.0000i | 0.987730 | + | 0.493865i | ||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.00000i | 0.295241i | ||||||||
\(414\) | −5.00000 | −0.245737 | ||||||||
\(415\) | −4.00000 | − | 2.00000i | −0.196352 | − | 0.0981761i | ||||
\(416\) | −4.00000 | −0.196116 | ||||||||
\(417\) | 20.0000i | 0.979404i | ||||||||
\(418\) | − | 3.00000i | − | 0.146735i | ||||||
\(419\) | 18.0000 | 0.879358 | 0.439679 | − | 0.898155i | \(-0.355092\pi\) | ||||
0.439679 | + | 0.898155i | \(0.355092\pi\) | |||||||
\(420\) | −1.00000 | + | 2.00000i | −0.0487950 | + | 0.0975900i | ||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | 7.00000i | 0.340755i | ||||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | −5.00000 | −0.242821 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.00000 | 0.242251 | ||||||||
\(427\) | − | 2.00000i | − | 0.0967868i | ||||||
\(428\) | − | 19.0000i | − | 0.918400i | ||||||
\(429\) | 12.0000 | 0.579365 | ||||||||
\(430\) | 5.00000 | − | 10.0000i | 0.241121 | − | 0.482243i | ||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 19.0000i | − | 0.913082i | −0.889702 | − | 0.456541i | \(-0.849088\pi\) | ||
0.889702 | − | 0.456541i | \(-0.150912\pi\) | |||||||
\(434\) | 1.00000 | 0.0480015 | ||||||||
\(435\) | 4.00000 | + | 2.00000i | 0.191785 | + | 0.0958927i | ||||
\(436\) | 2.00000 | 0.0957826 | ||||||||
\(437\) | − | 5.00000i | − | 0.239182i | ||||||
\(438\) | − | 7.00000i | − | 0.334473i | ||||||
\(439\) | −20.0000 | −0.954548 | −0.477274 | − | 0.878755i | \(-0.658375\pi\) | ||||
−0.477274 | + | 0.878755i | \(0.658375\pi\) | |||||||
\(440\) | −6.00000 | − | 3.00000i | −0.286039 | − | 0.143019i | ||||
\(441\) | −6.00000 | −0.285714 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 29.0000i | − | 1.37783i | −0.724841 | − | 0.688916i | \(-0.758087\pi\) | ||
0.724841 | − | 0.688916i | \(-0.241913\pi\) | |||||||
\(444\) | 4.00000 | 0.189832 | ||||||||
\(445\) | 1.00000 | − | 2.00000i | 0.0474045 | − | 0.0948091i | ||||
\(446\) | −20.0000 | −0.947027 | ||||||||
\(447\) | − | 15.0000i | − | 0.709476i | ||||||
\(448\) | − | 1.00000i | − | 0.0472456i | ||||||
\(449\) | −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 | ||||
\(451\) | 30.0000 | 1.41264 | ||||||||
\(452\) | − | 15.0000i | − | 0.705541i | ||||||
\(453\) | − | 16.0000i | − | 0.751746i | ||||||
\(454\) | 9.00000 | 0.422391 | ||||||||
\(455\) | 4.00000 | − | 8.00000i | 0.187523 | − | 0.375046i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 30.0000i | 1.40334i | 0.712502 | + | 0.701670i | \(0.247562\pi\) | ||||
−0.712502 | + | 0.701670i | \(0.752438\pi\) | |||||||
\(458\) | − | 15.0000i | − | 0.700904i | ||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0000 | − | 5.00000i | −0.466252 | − | 0.233126i | ||||
\(461\) | 16.0000 | 0.745194 | 0.372597 | − | 0.927993i | \(-0.378467\pi\) | ||||
0.372597 | + | 0.927993i | \(0.378467\pi\) | |||||||
\(462\) | 3.00000i | 0.139573i | ||||||||
\(463\) | 14.0000i | 0.650635i | 0.945605 | + | 0.325318i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325318i | \(0.894529\pi\) | |||||||
\(464\) | −2.00000 | −0.0928477 | ||||||||
\(465\) | 2.00000 | + | 1.00000i | 0.0927478 | + | 0.0463739i | ||||
\(466\) | −21.0000 | −0.972806 | ||||||||
\(467\) | 28.0000i | 1.29569i | 0.761774 | + | 0.647843i | \(0.224329\pi\) | ||||
−0.761774 | + | 0.647843i | \(0.775671\pi\) | |||||||
\(468\) | 4.00000i | 0.184900i | ||||||||
\(469\) | −2.00000 | −0.0923514 | ||||||||
\(470\) | −8.00000 | + | 16.0000i | −0.369012 | + | 0.738025i | ||||
\(471\) | −9.00000 | −0.414698 | ||||||||
\(472\) | − | 6.00000i | − | 0.276172i | ||||||
\(473\) | − | 15.0000i | − | 0.689701i | ||||||
\(474\) | 3.00000 | 0.137795 | ||||||||
\(475\) | −3.00000 | − | 4.00000i | −0.137649 | − | 0.183533i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.00000i | 0.228934i | ||||||||
\(478\) | 14.0000i | 0.640345i | ||||||||
\(479\) | 25.0000 | 1.14228 | 0.571140 | − | 0.820853i | \(-0.306501\pi\) | ||||
0.571140 | + | 0.820853i | \(0.306501\pi\) | |||||||
\(480\) | 1.00000 | − | 2.00000i | 0.0456435 | − | 0.0912871i | ||||
\(481\) | −16.0000 | −0.729537 | ||||||||
\(482\) | − | 12.0000i | − | 0.546585i | ||||||
\(483\) | 5.00000i | 0.227508i | ||||||||
\(484\) | 2.00000 | 0.0909091 | ||||||||
\(485\) | 20.0000 | + | 10.0000i | 0.908153 | + | 0.454077i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | − | 4.00000i | − | 0.181257i | −0.995885 | − | 0.0906287i | \(-0.971112\pi\) | ||
0.995885 | − | 0.0906287i | \(-0.0288876\pi\) | |||||||
\(488\) | 2.00000i | 0.0905357i | ||||||||
\(489\) | −4.00000 | −0.180886 | ||||||||
\(490\) | −12.0000 | − | 6.00000i | −0.542105 | − | 0.271052i | ||||
\(491\) | 33.0000 | 1.48927 | 0.744635 | − | 0.667472i | \(-0.232624\pi\) | ||||
0.744635 | + | 0.667472i | \(0.232624\pi\) | |||||||
\(492\) | 10.0000i | 0.450835i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −4.00000 | −0.179969 | ||||||||
\(495\) | −3.00000 | + | 6.00000i | −0.134840 | + | 0.269680i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | − | 5.00000i | − | 0.224281i | ||||||
\(498\) | − | 2.00000i | − | 0.0896221i | ||||||
\(499\) | −22.0000 | −0.984855 | −0.492428 | − | 0.870353i | \(-0.663890\pi\) | ||||
−0.492428 | + | 0.870353i | \(0.663890\pi\) | |||||||
\(500\) | −11.0000 | + | 2.00000i | −0.491935 | + | 0.0894427i | ||||
\(501\) | −21.0000 | −0.938211 | ||||||||
\(502\) | 12.0000i | 0.535586i | ||||||||
\(503\) | − | 14.0000i | − | 0.624229i | −0.950044 | − | 0.312115i | \(-0.898963\pi\) | ||
0.950044 | − | 0.312115i | \(-0.101037\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | 15.0000 | − | 30.0000i | 0.667491 | − | 1.33498i | ||||
\(506\) | −15.0000 | −0.666831 | ||||||||
\(507\) | − | 3.00000i | − | 0.133235i | ||||||
\(508\) | − | 8.00000i | − | 0.354943i | ||||||
\(509\) | −32.0000 | −1.41838 | −0.709188 | − | 0.705020i | \(-0.750938\pi\) | ||||
−0.709188 | + | 0.705020i | \(0.750938\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | −0.309662 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − | 1.00000i | − | 0.0441511i | ||||||
\(514\) | −5.00000 | −0.220541 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 5.00000 | 0.220113 | ||||||||
\(517\) | 24.0000i | 1.05552i | ||||||||
\(518\) | − | 4.00000i | − | 0.175750i | ||||||
\(519\) | −2.00000 | −0.0877903 | ||||||||
\(520\) | −4.00000 | + | 8.00000i | −0.175412 | + | 0.350823i | ||||
\(521\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(522\) | 2.00000i | 0.0875376i | ||||||||
\(523\) | − | 19.0000i | − | 0.830812i | −0.909636 | − | 0.415406i | \(-0.863640\pi\) | ||
0.909636 | − | 0.415406i | \(-0.136360\pi\) | |||||||
\(524\) | 2.00000 | 0.0873704 | ||||||||
\(525\) | 3.00000 | + | 4.00000i | 0.130931 | + | 0.174574i | ||||
\(526\) | 24.0000 | 1.04645 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | − | 3.00000i | − | 0.130558i | ||||||
\(529\) | −2.00000 | −0.0869565 | ||||||||
\(530\) | −5.00000 | + | 10.0000i | −0.217186 | + | 0.434372i | ||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | − | 1.00000i | − | 0.0433555i | ||||||
\(533\) | − | 40.0000i | − | 1.73259i | ||||||
\(534\) | 1.00000 | 0.0432742 | ||||||||
\(535\) | −38.0000 | − | 19.0000i | −1.64288 | − | 0.821442i | ||||
\(536\) | 2.00000 | 0.0863868 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 2.00000i | − | 0.0862261i | ||||||
\(539\) | −18.0000 | −0.775315 | ||||||||
\(540\) | −2.00000 | − | 1.00000i | −0.0860663 | − | 0.0430331i | ||||
\(541\) | 24.0000 | 1.03184 | 0.515920 | − | 0.856637i | \(-0.327450\pi\) | ||||
0.515920 | + | 0.856637i | \(0.327450\pi\) | |||||||
\(542\) | 9.00000i | 0.386583i | ||||||||
\(543\) | − | 5.00000i | − | 0.214571i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.00000 | − | 4.00000i | 0.0856706 | − | 0.171341i | ||||
\(546\) | 4.00000 | 0.171184 | ||||||||
\(547\) | 28.0000i | 1.19719i | 0.801050 | + | 0.598597i | \(0.204275\pi\) | ||||
−0.801050 | + | 0.598597i | \(0.795725\pi\) | |||||||
\(548\) | − | 2.00000i | − | 0.0854358i | ||||||
\(549\) | 2.00000 | 0.0853579 | ||||||||
\(550\) | −12.0000 | + | 9.00000i | −0.511682 | + | 0.383761i | ||||
\(551\) | −2.00000 | −0.0852029 | ||||||||
\(552\) | − | 5.00000i | − | 0.212814i | ||||||
\(553\) | − | 3.00000i | − | 0.127573i | ||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 4.00000 | − | 8.00000i | 0.169791 | − | 0.339581i | ||||
\(556\) | −20.0000 | −0.848189 | ||||||||
\(557\) | 9.00000i | 0.381342i | 0.981654 | + | 0.190671i | \(0.0610664\pi\) | ||||
−0.981654 | + | 0.190671i | \(0.938934\pi\) | |||||||
\(558\) | 1.00000i | 0.0423334i | ||||||||
\(559\) | −20.0000 | −0.845910 | ||||||||
\(560\) | −2.00000 | − | 1.00000i | −0.0845154 | − | 0.0422577i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 32.0000i | − | 1.34984i | ||||||
\(563\) | − | 36.0000i | − | 1.51722i | −0.651546 | − | 0.758610i | \(-0.725879\pi\) | ||
0.651546 | − | 0.758610i | \(-0.274121\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | −30.0000 | − | 15.0000i | −1.26211 | − | 0.631055i | ||||
\(566\) | 14.0000 | 0.588464 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 5.00000i | 0.209795i | ||||||||
\(569\) | 39.0000 | 1.63497 | 0.817483 | − | 0.575953i | \(-0.195369\pi\) | ||||
0.817483 | + | 0.575953i | \(0.195369\pi\) | |||||||
\(570\) | 1.00000 | − | 2.00000i | 0.0418854 | − | 0.0837708i | ||||
\(571\) | 26.0000 | 1.08807 | 0.544033 | − | 0.839064i | \(-0.316897\pi\) | ||||
0.544033 | + | 0.839064i | \(0.316897\pi\) | |||||||
\(572\) | 12.0000i | 0.501745i | ||||||||
\(573\) | − | 16.0000i | − | 0.668410i | ||||||
\(574\) | 10.0000 | 0.417392 | ||||||||
\(575\) | −20.0000 | + | 15.0000i | −0.834058 | + | 0.625543i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | − | 34.0000i | − | 1.41544i | −0.706494 | − | 0.707719i | \(-0.749724\pi\) | ||
0.706494 | − | 0.707719i | \(-0.250276\pi\) | |||||||
\(578\) | 17.0000i | 0.707107i | ||||||||
\(579\) | −10.0000 | −0.415586 | ||||||||
\(580\) | −2.00000 | + | 4.00000i | −0.0830455 | + | 0.166091i | ||||
\(581\) | −2.00000 | −0.0829740 | ||||||||
\(582\) | 10.0000i | 0.414513i | ||||||||
\(583\) | 15.0000i | 0.621237i | ||||||||
\(584\) | 7.00000 | 0.289662 | ||||||||
\(585\) | 8.00000 | + | 4.00000i | 0.330759 | + | 0.165380i | ||||
\(586\) | −18.0000 | −0.743573 | ||||||||
\(587\) | 6.00000i | 0.247647i | 0.992304 | + | 0.123823i | \(0.0395156\pi\) | ||||
−0.992304 | + | 0.123823i | \(0.960484\pi\) | |||||||
\(588\) | − | 6.00000i | − | 0.247436i | ||||||
\(589\) | −1.00000 | −0.0412043 | ||||||||
\(590\) | −12.0000 | − | 6.00000i | −0.494032 | − | 0.247016i | ||||
\(591\) | −18.0000 | −0.740421 | ||||||||
\(592\) | 4.00000i | 0.164399i | ||||||||
\(593\) | − | 6.00000i | − | 0.246390i | −0.992382 | − | 0.123195i | \(-0.960686\pi\) | ||
0.992382 | − | 0.123195i | \(-0.0393141\pi\) | |||||||
\(594\) | −3.00000 | −0.123091 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 15.0000 | 0.614424 | ||||||||
\(597\) | 21.0000i | 0.859473i | ||||||||
\(598\) | 20.0000i | 0.817861i | ||||||||
\(599\) | −13.0000 | −0.531166 | −0.265583 | − | 0.964088i | \(-0.585564\pi\) | ||||
−0.265583 | + | 0.964088i | \(0.585564\pi\) | |||||||
\(600\) | −3.00000 | − | 4.00000i | −0.122474 | − | 0.163299i | ||||
\(601\) | −44.0000 | −1.79480 | −0.897399 | − | 0.441221i | \(-0.854546\pi\) | ||||
−0.897399 | + | 0.441221i | \(0.854546\pi\) | |||||||
\(602\) | − | 5.00000i | − | 0.203785i | ||||||
\(603\) | − | 2.00000i | − | 0.0814463i | ||||||
\(604\) | 16.0000 | 0.651031 | ||||||||
\(605\) | 2.00000 | − | 4.00000i | 0.0813116 | − | 0.162623i | ||||
\(606\) | 15.0000 | 0.609333 | ||||||||
\(607\) | − | 27.0000i | − | 1.09590i | −0.836512 | − | 0.547948i | \(-0.815409\pi\) | ||
0.836512 | − | 0.547948i | \(-0.184591\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | 2.00000 | 0.0810441 | ||||||||
\(610\) | 4.00000 | + | 2.00000i | 0.161955 | + | 0.0809776i | ||||
\(611\) | 32.0000 | 1.29458 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.0000i | − | 0.969351i | −0.874694 | − | 0.484675i | \(-0.838938\pi\) | ||
0.874694 | − | 0.484675i | \(-0.161062\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | 20.0000 | + | 10.0000i | 0.806478 | + | 0.403239i | ||||
\(616\) | −3.00000 | −0.120873 | ||||||||
\(617\) | 5.00000i | 0.201292i | 0.994922 | + | 0.100646i | \(0.0320910\pi\) | ||||
−0.994922 | + | 0.100646i | \(0.967909\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.0000 | 0.482321 | 0.241160 | − | 0.970485i | \(-0.422472\pi\) | ||||
0.241160 | + | 0.970485i | \(0.422472\pi\) | |||||||
\(620\) | −1.00000 | + | 2.00000i | −0.0401610 | + | 0.0803219i | ||||
\(621\) | −5.00000 | −0.200643 | ||||||||
\(622\) | 16.0000i | 0.641542i | ||||||||
\(623\) | − | 1.00000i | − | 0.0400642i | ||||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −7.00000 | + | 24.0000i | −0.280000 | + | 0.960000i | ||||
\(626\) | −6.00000 | −0.239808 | ||||||||
\(627\) | − | 3.00000i | − | 0.119808i | ||||||
\(628\) | − | 9.00000i | − | 0.359139i | ||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −1.00000 | + | 2.00000i | −0.0398410 | + | 0.0796819i | ||||
\(631\) | 25.0000 | 0.995234 | 0.497617 | − | 0.867397i | \(-0.334208\pi\) | ||||
0.497617 | + | 0.867397i | \(0.334208\pi\) | |||||||
\(632\) | 3.00000i | 0.119334i | ||||||||
\(633\) | 7.00000i | 0.278225i | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | −16.0000 | − | 8.00000i | −0.634941 | − | 0.317470i | ||||
\(636\) | −5.00000 | −0.198263 | ||||||||
\(637\) | 24.0000i | 0.950915i | ||||||||
\(638\) | 6.00000i | 0.237542i | ||||||||
\(639\) | 5.00000 | 0.197797 | ||||||||
\(640\) | 2.00000 | + | 1.00000i | 0.0790569 | + | 0.0395285i | ||||
\(641\) | 50.0000 | 1.97488 | 0.987441 | − | 0.157991i | \(-0.0505015\pi\) | ||||
0.987441 | + | 0.157991i | \(0.0505015\pi\) | |||||||
\(642\) | − | 19.0000i | − | 0.749870i | ||||||
\(643\) | 7.00000i | 0.276053i | 0.990429 | + | 0.138027i | \(0.0440759\pi\) | ||||
−0.990429 | + | 0.138027i | \(0.955924\pi\) | |||||||
\(644\) | −5.00000 | −0.197028 | ||||||||
\(645\) | 5.00000 | − | 10.0000i | 0.196875 | − | 0.393750i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.00000i | 0.275198i | 0.990488 | + | 0.137599i | \(0.0439386\pi\) | ||||
−0.990488 | + | 0.137599i | \(0.956061\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | −18.0000 | −0.706562 | ||||||||
\(650\) | 12.0000 | + | 16.0000i | 0.470679 | + | 0.627572i | ||||
\(651\) | 1.00000 | 0.0391931 | ||||||||
\(652\) | − | 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 | ||||||||
\(655\) | 2.00000 | − | 4.00000i | 0.0781465 | − | 0.156293i | ||||
\(656\) | −10.0000 | −0.390434 | ||||||||
\(657\) | − | 7.00000i | − | 0.273096i | ||||||
\(658\) | 8.00000i | 0.311872i | ||||||||
\(659\) | −6.00000 | −0.233727 | −0.116863 | − | 0.993148i | \(-0.537284\pi\) | ||||
−0.116863 | + | 0.993148i | \(0.537284\pi\) | |||||||
\(660\) | −6.00000 | − | 3.00000i | −0.233550 | − | 0.116775i | ||||
\(661\) | 36.0000 | 1.40024 | 0.700119 | − | 0.714026i | \(-0.253130\pi\) | ||||
0.700119 | + | 0.714026i | \(0.253130\pi\) | |||||||
\(662\) | 8.00000i | 0.310929i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.00000 | 0.0776151 | ||||||||
\(665\) | −2.00000 | − | 1.00000i | −0.0775567 | − | 0.0387783i | ||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 10.0000i | 0.387202i | ||||||||
\(668\) | − | 21.0000i | − | 0.812514i | ||||||
\(669\) | −20.0000 | −0.773245 | ||||||||
\(670\) | 2.00000 | − | 4.00000i | 0.0772667 | − | 0.154533i | ||||
\(671\) | 6.00000 | 0.231627 | ||||||||
\(672\) | − | 1.00000i | − | 0.0385758i | ||||||
\(673\) | 30.0000i | 1.15642i | 0.815890 | + | 0.578208i | \(0.196248\pi\) | ||||
−0.815890 | + | 0.578208i | \(0.803752\pi\) | |||||||
\(674\) | 34.0000 | 1.30963 | ||||||||
\(675\) | −4.00000 | + | 3.00000i | −0.153960 | + | 0.115470i | ||||
\(676\) | 3.00000 | 0.115385 | ||||||||
\(677\) | 13.0000i | 0.499631i | 0.968294 | + | 0.249815i | \(0.0803699\pi\) | ||||
−0.968294 | + | 0.249815i | \(0.919630\pi\) | |||||||
\(678\) | − | 15.0000i | − | 0.576072i | ||||||
\(679\) | 10.0000 | 0.383765 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.00000 | 0.344881 | ||||||||
\(682\) | 3.00000i | 0.114876i | ||||||||
\(683\) | − | 35.0000i | − | 1.33924i | −0.742705 | − | 0.669619i | \(-0.766457\pi\) | ||
0.742705 | − | 0.669619i | \(-0.233543\pi\) | |||||||
\(684\) | 1.00000 | 0.0382360 | ||||||||
\(685\) | −4.00000 | − | 2.00000i | −0.152832 | − | 0.0764161i | ||||
\(686\) | −13.0000 | −0.496342 | ||||||||
\(687\) | − | 15.0000i | − | 0.572286i | ||||||
\(688\) | 5.00000i | 0.190623i | ||||||||
\(689\) | 20.0000 | 0.761939 | ||||||||
\(690\) | −10.0000 | − | 5.00000i | −0.380693 | − | 0.190347i | ||||
\(691\) | −41.0000 | −1.55971 | −0.779857 | − | 0.625958i | \(-0.784708\pi\) | ||||
−0.779857 | + | 0.625958i | \(0.784708\pi\) | |||||||
\(692\) | − | 2.00000i | − | 0.0760286i | ||||||
\(693\) | 3.00000i | 0.113961i | ||||||||
\(694\) | 22.0000 | 0.835109 | ||||||||
\(695\) | −20.0000 | + | 40.0000i | −0.758643 | + | 1.51729i | ||||
\(696\) | −2.00000 | −0.0758098 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | − | 20.0000i | − | 0.757011i | ||||||
\(699\) | −21.0000 | −0.794293 | ||||||||
\(700\) | −4.00000 | + | 3.00000i | −0.151186 | + | 0.113389i | ||||
\(701\) | −35.0000 | −1.32193 | −0.660966 | − | 0.750416i | \(-0.729853\pi\) | ||||
−0.660966 | + | 0.750416i | \(0.729853\pi\) | |||||||
\(702\) | 4.00000i | 0.150970i | ||||||||
\(703\) | 4.00000i | 0.150863i | ||||||||
\(704\) | 3.00000 | 0.113067 | ||||||||
\(705\) | −8.00000 | + | 16.0000i | −0.301297 | + | 0.602595i | ||||
\(706\) | 24.0000 | 0.903252 | ||||||||
\(707\) | − | 15.0000i | − | 0.564133i | ||||||
\(708\) | − | 6.00000i | − | 0.225494i | ||||||
\(709\) | −5.00000 | −0.187779 | −0.0938895 | − | 0.995583i | \(-0.529930\pi\) | ||||
−0.0938895 | + | 0.995583i | \(0.529930\pi\) | |||||||
\(710\) | 10.0000 | + | 5.00000i | 0.375293 | + | 0.187647i | ||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 1.00000i | 0.0374766i | ||||||||
\(713\) | 5.00000i | 0.187251i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.0000 | + | 12.0000i | 0.897549 | + | 0.448775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 14.0000i | 0.522840i | ||||||||
\(718\) | − | 3.00000i | − | 0.111959i | ||||||
\(719\) | −10.0000 | −0.372937 | −0.186469 | − | 0.982461i | \(-0.559704\pi\) | ||||
−0.186469 | + | 0.982461i | \(0.559704\pi\) | |||||||
\(720\) | 1.00000 | − | 2.00000i | 0.0372678 | − | 0.0745356i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.0000i | − | 0.669891i | ||||||
\(723\) | − | 12.0000i | − | 0.446285i | ||||||
\(724\) | 5.00000 | 0.185824 | ||||||||
\(725\) | 6.00000 | + | 8.00000i | 0.222834 | + | 0.297113i | ||||
\(726\) | 2.00000 | 0.0742270 | ||||||||
\(727\) | 49.0000i | 1.81731i | 0.417548 | + | 0.908655i | \(0.362889\pi\) | ||||
−0.417548 | + | 0.908655i | \(0.637111\pi\) | |||||||
\(728\) | 4.00000i | 0.148250i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 7.00000 | − | 14.0000i | 0.259082 | − | 0.518163i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 2.00000i | 0.0739221i | ||||||||
\(733\) | 22.0000i | 0.812589i | 0.913742 | + | 0.406294i | \(0.133179\pi\) | ||||
−0.913742 | + | 0.406294i | \(0.866821\pi\) | |||||||
\(734\) | −14.0000 | −0.516749 | ||||||||
\(735\) | −12.0000 | − | 6.00000i | −0.442627 | − | 0.221313i | ||||
\(736\) | 5.00000 | 0.184302 | ||||||||
\(737\) | − | 6.00000i | − | 0.221013i | ||||||
\(738\) | 10.0000i | 0.368105i | ||||||||
\(739\) | 18.0000 | 0.662141 | 0.331070 | − | 0.943606i | \(-0.392590\pi\) | ||||
0.331070 | + | 0.943606i | \(0.392590\pi\) | |||||||
\(740\) | 8.00000 | + | 4.00000i | 0.294086 | + | 0.147043i | ||||
\(741\) | −4.00000 | −0.146944 | ||||||||
\(742\) | 5.00000i | 0.183556i | ||||||||
\(743\) | − | 15.0000i | − | 0.550297i | −0.961402 | − | 0.275148i | \(-0.911273\pi\) | ||
0.961402 | − | 0.275148i | \(-0.0887270\pi\) | |||||||
\(744\) | −1.00000 | −0.0366618 | ||||||||
\(745\) | 15.0000 | − | 30.0000i | 0.549557 | − | 1.09911i | ||||
\(746\) | −11.0000 | −0.402739 | ||||||||
\(747\) | − | 2.00000i | − | 0.0731762i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.0000 | −0.694245 | ||||||||
\(750\) | −11.0000 | + | 2.00000i | −0.401663 | + | 0.0730297i | ||||
\(751\) | 22.0000 | 0.802791 | 0.401396 | − | 0.915905i | \(-0.368525\pi\) | ||||
0.401396 | + | 0.915905i | \(0.368525\pi\) | |||||||
\(752\) | − | 8.00000i | − | 0.291730i | ||||||
\(753\) | 12.0000i | 0.437304i | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 16.0000 | − | 32.0000i | 0.582300 | − | 1.16460i | ||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | 20.0000i | 0.726912i | 0.931611 | + | 0.363456i | \(0.118403\pi\) | ||||
−0.931611 | + | 0.363456i | \(0.881597\pi\) | |||||||
\(758\) | 15.0000i | 0.544825i | ||||||||
\(759\) | −15.0000 | −0.544466 | ||||||||
\(760\) | 2.00000 | + | 1.00000i | 0.0725476 | + | 0.0362738i | ||||
\(761\) | 21.0000 | 0.761249 | 0.380625 | − | 0.924730i | \(-0.375709\pi\) | ||||
0.380625 | + | 0.924730i | \(0.375709\pi\) | |||||||
\(762\) | − | 8.00000i | − | 0.289809i | ||||||
\(763\) | − | 2.00000i | − | 0.0724049i | ||||||
\(764\) | 16.0000 | 0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 28.0000 | 1.01168 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −45.0000 | −1.62274 | −0.811371 | − | 0.584532i | \(-0.801278\pi\) | ||||
−0.811371 | + | 0.584532i | \(0.801278\pi\) | |||||||
\(770\) | −3.00000 | + | 6.00000i | −0.108112 | + | 0.216225i | ||||
\(771\) | −5.00000 | −0.180071 | ||||||||
\(772\) | − | 10.0000i | − | 0.359908i | ||||||
\(773\) | 29.0000i | 1.04306i | 0.853234 | + | 0.521529i | \(0.174638\pi\) | ||||
−0.853234 | + | 0.521529i | \(0.825362\pi\) | |||||||
\(774\) | 5.00000 | 0.179721 | ||||||||
\(775\) | 3.00000 | + | 4.00000i | 0.107763 | + | 0.143684i | ||||
\(776\) | −10.0000 | −0.358979 | ||||||||
\(777\) | − | 4.00000i | − | 0.143499i | ||||||
\(778\) | 28.0000i | 1.00385i | ||||||||
\(779\) | −10.0000 | −0.358287 | ||||||||
\(780\) | −4.00000 | + | 8.00000i | −0.143223 | + | 0.286446i | ||||
\(781\) | 15.0000 | 0.536742 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000i | 0.0714742i | ||||||||
\(784\) | 6.00000 | 0.214286 | ||||||||
\(785\) | −18.0000 | − | 9.00000i | −0.642448 | − | 0.321224i | ||||
\(786\) | 2.00000 | 0.0713376 | ||||||||
\(787\) | 27.0000i | 0.962446i | 0.876598 | + | 0.481223i | \(0.159807\pi\) | ||||
−0.876598 | + | 0.481223i | \(0.840193\pi\) | |||||||
\(788\) | − | 18.0000i | − | 0.641223i | ||||||
\(789\) | 24.0000 | 0.854423 | ||||||||
\(790\) | 6.00000 | + | 3.00000i | 0.213470 | + | 0.106735i | ||||
\(791\) | −15.0000 | −0.533339 | ||||||||
\(792\) | − | 3.00000i | − | 0.106600i | ||||||
\(793\) | − | 8.00000i | − | 0.284088i | ||||||
\(794\) | 31.0000 | 1.10015 | ||||||||
\(795\) | −5.00000 | + | 10.0000i | −0.177332 | + | 0.354663i | ||||
\(796\) | −21.0000 | −0.744325 | ||||||||
\(797\) | − | 22.0000i | − | 0.779280i | −0.920967 | − | 0.389640i | \(-0.872599\pi\) | ||
0.920967 | − | 0.389640i | \(-0.127401\pi\) | |||||||
\(798\) | − | 1.00000i | − | 0.0353996i | ||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | 1.00000 | 0.0353333 | ||||||||
\(802\) | 5.00000i | 0.176556i | ||||||||
\(803\) | − | 21.0000i | − | 0.741074i | ||||||
\(804\) | 2.00000 | 0.0705346 | ||||||||
\(805\) | −5.00000 | + | 10.0000i | −0.176227 | + | 0.352454i | ||||
\(806\) | 4.00000 | 0.140894 | ||||||||
\(807\) | − | 2.00000i | − | 0.0704033i | ||||||
\(808\) | 15.0000i | 0.527698i | ||||||||
\(809\) | −9.00000 | −0.316423 | −0.158212 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158212 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(810\) | −2.00000 | − | 1.00000i | −0.0702728 | − | 0.0351364i | ||||
\(811\) | 35.0000 | 1.22902 | 0.614508 | − | 0.788911i | \(-0.289355\pi\) | ||||
0.614508 | + | 0.788911i | \(0.289355\pi\) | |||||||
\(812\) | 2.00000i | 0.0701862i | ||||||||
\(813\) | 9.00000i | 0.315644i | ||||||||
\(814\) | 12.0000 | 0.420600 | ||||||||
\(815\) | −8.00000 | − | 4.00000i | −0.280228 | − | 0.140114i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.00000i | 0.174928i | ||||||||
\(818\) | − | 4.00000i | − | 0.139857i | ||||||
\(819\) | 4.00000 | 0.139771 | ||||||||
\(820\) | −10.0000 | + | 20.0000i | −0.349215 | + | 0.698430i | ||||
\(821\) | 18.0000 | 0.628204 | 0.314102 | − | 0.949389i | \(-0.398297\pi\) | ||||
0.314102 | + | 0.949389i | \(0.398297\pi\) | |||||||
\(822\) | − | 2.00000i | − | 0.0697580i | ||||||
\(823\) | 6.00000i | 0.209147i | 0.994517 | + | 0.104573i | \(0.0333477\pi\) | ||||
−0.994517 | + | 0.104573i | \(0.966652\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.0000 | + | 9.00000i | −0.417786 | + | 0.313340i | ||||
\(826\) | −6.00000 | −0.208767 | ||||||||
\(827\) | 14.0000i | 0.486828i | 0.969923 | + | 0.243414i | \(0.0782673\pi\) | ||||
−0.969923 | + | 0.243414i | \(0.921733\pi\) | |||||||
\(828\) | − | 5.00000i | − | 0.173762i | ||||||
\(829\) | 25.0000 | 0.868286 | 0.434143 | − | 0.900844i | \(-0.357051\pi\) | ||||
0.434143 | + | 0.900844i | \(0.357051\pi\) | |||||||
\(830\) | 2.00000 | − | 4.00000i | 0.0694210 | − | 0.138842i | ||||
\(831\) | −2.00000 | −0.0693792 | ||||||||
\(832\) | − | 4.00000i | − | 0.138675i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −20.0000 | −0.692543 | ||||||||
\(835\) | −42.0000 | − | 21.0000i | −1.45347 | − | 0.726735i | ||||
\(836\) | 3.00000 | 0.103757 | ||||||||
\(837\) | 1.00000i | 0.0345651i | ||||||||
\(838\) | 18.0000i | 0.621800i | ||||||||
\(839\) | −39.0000 | −1.34643 | −0.673215 | − | 0.739447i | \(-0.735087\pi\) | ||||
−0.673215 | + | 0.739447i | \(0.735087\pi\) | |||||||
\(840\) | −2.00000 | − | 1.00000i | −0.0690066 | − | 0.0345033i | ||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | − | 14.0000i | − | 0.482472i | ||||||
\(843\) | − | 32.0000i | − | 1.10214i | ||||||
\(844\) | −7.00000 | −0.240950 | ||||||||
\(845\) | 3.00000 | − | 6.00000i | 0.103203 | − | 0.206406i | ||||
\(846\) | −8.00000 | −0.275046 | ||||||||
\(847\) | − | 2.00000i | − | 0.0687208i | ||||||
\(848\) | − | 5.00000i | − | 0.171701i | ||||||
\(849\) | 14.0000 | 0.480479 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20.0000 | 0.685591 | ||||||||
\(852\) | 5.00000i | 0.171297i | ||||||||
\(853\) | 55.0000i | 1.88316i | 0.336784 | + | 0.941582i | \(0.390661\pi\) | ||||
−0.336784 | + | 0.941582i | \(0.609339\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 1.00000 | − | 2.00000i | 0.0341993 | − | 0.0683986i | ||||
\(856\) | 19.0000 | 0.649407 | ||||||||
\(857\) | − | 22.0000i | − | 0.751506i | −0.926720 | − | 0.375753i | \(-0.877384\pi\) | ||
0.926720 | − | 0.375753i | \(-0.122616\pi\) | |||||||
\(858\) | 12.0000i | 0.409673i | ||||||||
\(859\) | 32.0000 | 1.09183 | 0.545913 | − | 0.837842i | \(-0.316183\pi\) | ||||
0.545913 | + | 0.837842i | \(0.316183\pi\) | |||||||
\(860\) | 10.0000 | + | 5.00000i | 0.340997 | + | 0.170499i | ||||
\(861\) | 10.0000 | 0.340799 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.0000i | 0.987171i | 0.869697 | + | 0.493586i | \(0.164314\pi\) | ||||
−0.869697 | + | 0.493586i | \(0.835686\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −4.00000 | − | 2.00000i | −0.136004 | − | 0.0680020i | ||||
\(866\) | 19.0000 | 0.645646 | ||||||||
\(867\) | 17.0000i | 0.577350i | ||||||||
\(868\) | 1.00000i | 0.0339422i | ||||||||
\(869\) | 9.00000 | 0.305304 | ||||||||
\(870\) | −2.00000 | + | 4.00000i | −0.0678064 | + | 0.135613i | ||||
\(871\) | −8.00000 | −0.271070 | ||||||||
\(872\) | 2.00000i | 0.0677285i | ||||||||
\(873\) | 10.0000i | 0.338449i | ||||||||
\(874\) | 5.00000 | 0.169128 | ||||||||
\(875\) | 2.00000 | + | 11.0000i | 0.0676123 | + | 0.371868i | ||||
\(876\) | 7.00000 | 0.236508 | ||||||||
\(877\) | 42.0000i | 1.41824i | 0.705088 | + | 0.709120i | \(0.250907\pi\) | ||||
−0.705088 | + | 0.709120i | \(0.749093\pi\) | |||||||
\(878\) | − | 20.0000i | − | 0.674967i | ||||||
\(879\) | −18.0000 | −0.607125 | ||||||||
\(880\) | 3.00000 | − | 6.00000i | 0.101130 | − | 0.202260i | ||||
\(881\) | 42.0000 | 1.41502 | 0.707508 | − | 0.706705i | \(-0.249819\pi\) | ||||
0.707508 | + | 0.706705i | \(0.249819\pi\) | |||||||
\(882\) | − | 6.00000i | − | 0.202031i | ||||||
\(883\) | 35.0000i | 1.17784i | 0.808190 | + | 0.588922i | \(0.200447\pi\) | ||||
−0.808190 | + | 0.588922i | \(0.799553\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.0000 | − | 6.00000i | −0.403376 | − | 0.201688i | ||||
\(886\) | 29.0000 | 0.974274 | ||||||||
\(887\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(888\) | 4.00000i | 0.134231i | ||||||||
\(889\) | −8.00000 | −0.268311 | ||||||||
\(890\) | 2.00000 | + | 1.00000i | 0.0670402 | + | 0.0335201i | ||||
\(891\) | −3.00000 | −0.100504 | ||||||||
\(892\) | − | 20.0000i | − | 0.669650i | ||||||
\(893\) | − | 8.00000i | − | 0.267710i | ||||||
\(894\) | 15.0000 | 0.501675 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 20.0000i | 0.667781i | ||||||||
\(898\) | − | 2.00000i | − | 0.0667409i | ||||||
\(899\) | 2.00000 | 0.0667037 | ||||||||
\(900\) | −3.00000 | − | 4.00000i | −0.100000 | − | 0.133333i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 30.0000i | 0.998891i | ||||||||
\(903\) | − | 5.00000i | − | 0.166390i | ||||||
\(904\) | 15.0000 | 0.498893 | ||||||||
\(905\) | 5.00000 | − | 10.0000i | 0.166206 | − | 0.332411i | ||||
\(906\) | 16.0000 | 0.531564 | ||||||||
\(907\) | − | 36.0000i | − | 1.19536i | −0.801735 | − | 0.597680i | \(-0.796089\pi\) | ||
0.801735 | − | 0.597680i | \(-0.203911\pi\) | |||||||
\(908\) | 9.00000i | 0.298675i | ||||||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | 8.00000 | + | 4.00000i | 0.265197 | + | 0.132599i | ||||
\(911\) | −46.0000 | −1.52405 | −0.762024 | − | 0.647549i | \(-0.775794\pi\) | ||||
−0.762024 | + | 0.647549i | \(0.775794\pi\) | |||||||
\(912\) | 1.00000i | 0.0331133i | ||||||||
\(913\) | − | 6.00000i | − | 0.198571i | ||||||
\(914\) | −30.0000 | −0.992312 | ||||||||
\(915\) | 4.00000 | + | 2.00000i | 0.132236 | + | 0.0661180i | ||||
\(916\) | 15.0000 | 0.495614 | ||||||||
\(917\) | − | 2.00000i | − | 0.0660458i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.0000 | −0.659739 | −0.329870 | − | 0.944027i | \(-0.607005\pi\) | ||||
−0.329870 | + | 0.944027i | \(0.607005\pi\) | |||||||
\(920\) | 5.00000 | − | 10.0000i | 0.164845 | − | 0.329690i | ||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | 16.0000i | 0.526932i | ||||||||
\(923\) | − | 20.0000i | − | 0.658308i | ||||||
\(924\) | −3.00000 | −0.0986928 | ||||||||
\(925\) | 16.0000 | − | 12.0000i | 0.526077 | − | 0.394558i | ||||
\(926\) | −14.0000 | −0.460069 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 2.00000i | − | 0.0656532i | ||||||
\(929\) | 1.00000 | 0.0328089 | 0.0164045 | − | 0.999865i | \(-0.494778\pi\) | ||||
0.0164045 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(930\) | −1.00000 | + | 2.00000i | −0.0327913 | + | 0.0655826i | ||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | − | 21.0000i | − | 0.687878i | ||||||
\(933\) | 16.0000i | 0.523816i | ||||||||
\(934\) | −28.0000 | −0.916188 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −4.00000 | −0.130744 | ||||||||
\(937\) | − | 2.00000i | − | 0.0653372i | −0.999466 | − | 0.0326686i | \(-0.989599\pi\) | ||
0.999466 | − | 0.0326686i | \(-0.0104006\pi\) | |||||||
\(938\) | − | 2.00000i | − | 0.0653023i | ||||||
\(939\) | −6.00000 | −0.195803 | ||||||||
\(940\) | −16.0000 | − | 8.00000i | −0.521862 | − | 0.260931i | ||||
\(941\) | 16.0000 | 0.521585 | 0.260793 | − | 0.965395i | \(-0.416016\pi\) | ||||
0.260793 | + | 0.965395i | \(0.416016\pi\) | |||||||
\(942\) | − | 9.00000i | − | 0.293236i | ||||||
\(943\) | 50.0000i | 1.62822i | ||||||||
\(944\) | 6.00000 | 0.195283 | ||||||||
\(945\) | −1.00000 | + | 2.00000i | −0.0325300 | + | 0.0650600i | ||||
\(946\) | 15.0000 | 0.487692 | ||||||||
\(947\) | 46.0000i | 1.49480i | 0.664375 | + | 0.747400i | \(0.268698\pi\) | ||||
−0.664375 | + | 0.747400i | \(0.731302\pi\) | |||||||
\(948\) | 3.00000i | 0.0974355i | ||||||||
\(949\) | −28.0000 | −0.908918 | ||||||||
\(950\) | 4.00000 | − | 3.00000i | 0.129777 | − | 0.0973329i | ||||
\(951\) | −18.0000 | −0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000i | 0.907009i | 0.891254 | + | 0.453504i | \(0.149826\pi\) | ||||
−0.891254 | + | 0.453504i | \(0.850174\pi\) | |||||||
\(954\) | −5.00000 | −0.161881 | ||||||||
\(955\) | 16.0000 | − | 32.0000i | 0.517748 | − | 1.03550i | ||||
\(956\) | −14.0000 | −0.452792 | ||||||||
\(957\) | 6.00000i | 0.193952i | ||||||||
\(958\) | 25.0000i | 0.807713i | ||||||||
\(959\) | −2.00000 | −0.0645834 | ||||||||
\(960\) | 2.00000 | + | 1.00000i | 0.0645497 | + | 0.0322749i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | − | 16.0000i | − | 0.515861i | ||||||
\(963\) | − | 19.0000i | − | 0.612266i | ||||||
\(964\) | 12.0000 | 0.386494 | ||||||||
\(965\) | −20.0000 | − | 10.0000i | −0.643823 | − | 0.321911i | ||||
\(966\) | −5.00000 | −0.160872 | ||||||||
\(967\) | − | 8.00000i | − | 0.257263i | −0.991692 | − | 0.128631i | \(-0.958942\pi\) | ||
0.991692 | − | 0.128631i | \(-0.0410584\pi\) | |||||||
\(968\) | 2.00000i | 0.0642824i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −10.0000 | + | 20.0000i | −0.321081 | + | 0.642161i | ||||
\(971\) | −18.0000 | −0.577647 | −0.288824 | − | 0.957382i | \(-0.593264\pi\) | ||||
−0.288824 | + | 0.957382i | \(0.593264\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 20.0000i | 0.641171i | ||||||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 12.0000 | + | 16.0000i | 0.384308 | + | 0.512410i | ||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | 6.00000i | 0.191957i | 0.995383 | + | 0.0959785i | \(0.0305980\pi\) | ||||
−0.995383 | + | 0.0959785i | \(0.969402\pi\) | |||||||
\(978\) | − | 4.00000i | − | 0.127906i | ||||||
\(979\) | 3.00000 | 0.0958804 | ||||||||
\(980\) | 6.00000 | − | 12.0000i | 0.191663 | − | 0.383326i | ||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 33.0000i | 1.05307i | ||||||||
\(983\) | 36.0000i | 1.14822i | 0.818778 | + | 0.574111i | \(0.194652\pi\) | ||||
−0.818778 | + | 0.574111i | \(0.805348\pi\) | |||||||
\(984\) | −10.0000 | −0.318788 | ||||||||
\(985\) | −36.0000 | − | 18.0000i | −1.14706 | − | 0.573528i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.00000i | 0.254643i | ||||||||
\(988\) | − | 4.00000i | − | 0.127257i | ||||||
\(989\) | 25.0000 | 0.794954 | ||||||||
\(990\) | −6.00000 | − | 3.00000i | −0.190693 | − | 0.0953463i | ||||
\(991\) | −53.0000 | −1.68360 | −0.841800 | − | 0.539789i | \(-0.818504\pi\) | ||||
−0.841800 | + | 0.539789i | \(0.818504\pi\) | |||||||
\(992\) | − | 1.00000i | − | 0.0317500i | ||||||
\(993\) | 8.00000i | 0.253872i | ||||||||
\(994\) | 5.00000 | 0.158590 | ||||||||
\(995\) | −21.0000 | + | 42.0000i | −0.665745 | + | 1.33149i | ||||
\(996\) | 2.00000 | 0.0633724 | ||||||||
\(997\) | 6.00000i | 0.190022i | 0.995476 | + | 0.0950110i | \(0.0302886\pi\) | ||||
−0.995476 | + | 0.0950110i | \(0.969711\pi\) | |||||||
\(998\) | − | 22.0000i | − | 0.696398i | ||||||
\(999\) | 4.00000 | 0.126554 |
(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.a.559.2 | yes | 2 | |
3.2 | odd | 2 | 2790.2.d.f.559.1 | 2 | |||
5.2 | odd | 4 | 4650.2.a.p.1.1 | 1 | |||
5.3 | odd | 4 | 4650.2.a.bc.1.1 | 1 | |||
5.4 | even | 2 | inner | 930.2.d.a.559.1 | ✓ | 2 | |
15.14 | odd | 2 | 2790.2.d.f.559.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.d.a.559.1 | ✓ | 2 | 5.4 | even | 2 | inner | |
930.2.d.a.559.2 | yes | 2 | 1.1 | even | 1 | trivial | |
2790.2.d.f.559.1 | 2 | 3.2 | odd | 2 | |||
2790.2.d.f.559.2 | 2 | 15.14 | odd | 2 | |||
4650.2.a.p.1.1 | 1 | 5.2 | odd | 4 | |||
4650.2.a.bc.1.1 | 1 | 5.3 | odd | 4 |