Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [280,2,Mod(81,280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(280, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("280.81");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 280 = 2^{3} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 280.q (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.23581125660\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 280.121 |
Dual form | 280.2.q.a.81.1 |
$q$-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 \(\left(\mathbb{Z}/280\mathbb{Z}\right)^\times\).
\(n\) | \(57\) | \(71\) | \(141\) | \(241\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | 0.684819 | − | 0.728714i | \(-0.259881\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 1.73205i | 0.333333 | − | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | − | 1.73205i | −0.301511 | − | 0.522233i | 0.674967 | − | 0.737848i | \(-0.264158\pi\) |
−0.976478 | + | 0.215615i | \(0.930824\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | − | 3.46410i | −0.485071 | − | 0.840168i | 0.514782 | − | 0.857321i | \(-0.327873\pi\) |
−0.999853 | + | 0.0171533i | \(0.994540\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | − | 1.73205i | 0.229416 | − | 0.397360i | −0.728219 | − | 0.685344i | \(-0.759652\pi\) |
0.957635 | + | 0.287984i | \(0.0929851\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.59808i | 0.109109 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.00000 | 1.67126 | 0.835629 | − | 0.549294i | \(-0.185103\pi\) | ||||
0.835629 | + | 0.549294i | \(0.185103\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.00000 | − | 3.46410i | −0.359211 | − | 0.622171i | 0.628619 | − | 0.777714i | \(-0.283621\pi\) |
−0.987829 | + | 0.155543i | \(0.950287\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.00000 | + | 1.73205i | −0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | + | 1.73205i | −0.338062 | + | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.00000 | + | 3.46410i | −0.328798 | + | 0.569495i | −0.982274 | − | 0.187453i | \(-0.939977\pi\) |
0.653476 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.00000 | 0.156174 | 0.0780869 | − | 0.996947i | \(-0.475119\pi\) | ||||
0.0780869 | + | 0.996947i | \(0.475119\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.00000 | 1.37249 | 0.686244 | − | 0.727372i | \(-0.259258\pi\) | ||||
0.686244 | + | 0.727372i | \(0.259258\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | − | 1.73205i | −0.149071 | − | 0.258199i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | + | 3.46410i | −0.280056 | + | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.00000 | + | 8.66025i | 0.686803 | + | 1.18958i | 0.972867 | + | 0.231367i | \(0.0743197\pi\) |
−0.286064 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.00000 | −0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | + | 8.66025i | 0.650945 | + | 1.12747i | 0.982894 | + | 0.184172i | \(0.0589603\pi\) |
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.50000 | + | 7.79423i | −0.576166 | + | 0.997949i | 0.419748 | + | 0.907641i | \(0.362118\pi\) |
−0.995914 | + | 0.0903080i | \(0.971215\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.00000 | + | 3.46410i | −0.503953 | + | 0.436436i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.50000 | − | 4.33013i | −0.305424 | − | 0.529009i | 0.671932 | − | 0.740613i | \(-0.265465\pi\) |
−0.977356 | + | 0.211604i | \(0.932131\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000 | 1.66149 | 0.830747 | − | 0.556650i | \(-0.187914\pi\) | ||||
0.830747 | + | 0.556650i | \(0.187914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | − | 10.3923i | −0.702247 | − | 1.21633i | −0.967676 | − | 0.252197i | \(-0.918847\pi\) |
0.265429 | − | 0.964130i | \(-0.414486\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000 | + | 5.19615i | 0.113961 | + | 0.592157i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.0000 | 1.20741 | 0.603703 | − | 0.797209i | \(-0.293691\pi\) | ||||
0.603703 | + | 0.797209i | \(0.293691\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.50000 | − | 7.79423i | −0.482451 | − | 0.835629i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | − | 12.9904i | 0.794998 | − | 1.37698i | −0.127842 | − | 0.991795i | \(-0.540805\pi\) |
0.922840 | − | 0.385183i | \(-0.125862\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 3.46410i | −0.207390 | + | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −18.0000 | −1.82762 | −0.913812 | − | 0.406138i | \(-0.866875\pi\) | ||||
−0.913812 | + | 0.406138i | \(0.866875\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.00000 | −0.402015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.50000 | − | 2.59808i | −0.149256 | − | 0.258518i | 0.781697 | − | 0.623658i | \(-0.214354\pi\) |
−0.930953 | + | 0.365140i | \(0.881021\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.50000 | − | 11.2583i | 0.640464 | − | 1.10932i | −0.344865 | − | 0.938652i | \(-0.612075\pi\) |
0.985329 | − | 0.170664i | \(-0.0545913\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.50000 | + | 0.866025i | 0.243975 | + | 0.0845154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.50000 | + | 7.79423i | −0.435031 | + | 0.753497i | −0.997298 | − | 0.0734594i | \(-0.976596\pi\) |
0.562267 | + | 0.826956i | \(0.309929\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.500000 | + | 0.866025i | 0.0478913 | + | 0.0829502i | 0.888977 | − | 0.457951i | \(-0.151417\pi\) |
−0.841086 | + | 0.540901i | \(0.818083\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.00000 | 0.379663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.500000 | + | 0.866025i | 0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | + | 10.3923i | 0.183340 | + | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | − | 6.06218i | 0.318182 | − | 0.551107i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.500000 | − | 0.866025i | −0.0450835 | − | 0.0780869i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.50000 | − | 7.79423i | −0.396203 | − | 0.686244i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.00000 | − | 6.92820i | 0.349482 | − | 0.605320i | −0.636676 | − | 0.771132i | \(-0.719691\pi\) |
0.986157 | + | 0.165812i | \(0.0530244\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00000 | + | 3.46410i | −0.346844 | + | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.50000 | + | 4.33013i | −0.215166 | + | 0.372678i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.00000 | − | 10.3923i | −0.512615 | − | 0.887875i | −0.999893 | − | 0.0146279i | \(-0.995344\pi\) |
0.487278 | − | 0.873247i | \(-0.337990\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.00000 | −0.169638 | −0.0848189 | − | 0.996396i | \(-0.527031\pi\) | ||||
−0.0848189 | + | 0.996396i | \(0.527031\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.50000 | − | 7.79423i | 0.373705 | − | 0.647275i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | − | 6.92820i | 0.0824786 | − | 0.571429i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.50000 | − | 4.33013i | 0.204808 | − | 0.354738i | −0.745264 | − | 0.666770i | \(-0.767676\pi\) |
0.950072 | + | 0.312032i | \(0.101010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | − | 6.92820i | −0.325515 | − | 0.563809i | 0.656101 | − | 0.754673i | \(-0.272204\pi\) |
−0.981617 | + | 0.190864i | \(0.938871\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.00000 | −0.646762 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.00000 | − | 1.73205i | −0.0798087 | − | 0.138233i | 0.823359 | − | 0.567521i | \(-0.192098\pi\) |
−0.903167 | + | 0.429289i | \(0.858764\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.00000 | − | 8.66025i | 0.396526 | − | 0.686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | − | 1.73205i | 0.157622 | − | 0.136505i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.00000 | + | 1.73205i | 0.0778499 | + | 0.134840i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.0000 | 1.31550 | 0.657750 | − | 0.753237i | \(-0.271508\pi\) | ||||
0.657750 | + | 0.753237i | \(0.271508\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.00000 | − | 3.46410i | −0.152944 | − | 0.264906i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.00000 | + | 13.8564i | −0.608229 | + | 1.05348i | 0.383304 | + | 0.923622i | \(0.374786\pi\) |
−0.991532 | + | 0.129861i | \(0.958547\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.00000 | − | 8.66025i | 0.375823 | − | 0.650945i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.00000 | − | 10.3923i | −0.448461 | − | 0.776757i | 0.549825 | − | 0.835280i | \(-0.314694\pi\) |
−0.998286 | + | 0.0585225i | \(0.981361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −25.0000 | −1.85824 | −0.929118 | − | 0.369784i | \(-0.879432\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.00000 | 0.665299 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.00000 | + | 3.46410i | 0.147043 | + | 0.254686i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.00000 | + | 6.92820i | −0.292509 | + | 0.506640i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.5000 | + | 4.33013i | 0.909241 | + | 0.314970i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.00000 | + | 15.5885i | −0.651217 | + | 1.12794i | 0.331611 | + | 0.943416i | \(0.392408\pi\) |
−0.982828 | + | 0.184525i | \(0.940925\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.00000 | + | 12.1244i | 0.503871 | + | 0.872730i | 0.999990 | + | 0.00447566i | \(0.00142465\pi\) |
−0.496119 | + | 0.868255i | \(0.665242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000 | + | 3.46410i | 0.141776 | + | 0.245564i | 0.928166 | − | 0.372168i | \(-0.121385\pi\) |
−0.786389 | + | 0.617731i | \(0.788052\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.50000 | + | 4.33013i | −0.176336 | + | 0.305424i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −22.5000 | − | 7.79423i | −1.57919 | − | 0.547048i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.500000 | − | 0.866025i | 0.0349215 | − | 0.0604858i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | + | 1.73205i | 0.0695048 | + | 0.120386i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.00000 | − | 12.1244i | −0.479632 | − | 0.830747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.50000 | − | 7.79423i | 0.306897 | − | 0.531562i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.00000 | + | 10.3923i | 0.135769 | + | 0.705476i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | + | 10.3923i | −0.405442 | + | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.00000 | −0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.00000 | − | 8.66025i | 0.330409 | − | 0.572286i | −0.652183 | − | 0.758062i | \(-0.726147\pi\) |
0.982592 | + | 0.185776i | \(0.0594799\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | − | 3.46410i | 0.263181 | − | 0.227921i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.00000 | + | 6.92820i | −0.262049 | + | 0.453882i | −0.966786 | − | 0.255586i | \(-0.917731\pi\) |
0.704737 | + | 0.709468i | \(0.251065\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.0000 | + | 19.0526i | 0.708572 | + | 1.22728i | 0.965387 | + | 0.260822i | \(0.0839937\pi\) |
−0.256814 | + | 0.966461i | \(0.582673\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | + | 13.8564i | −0.513200 | + | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.50000 | − | 2.59808i | 0.415270 | − | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.50000 | − | 9.52628i | −0.348548 | − | 0.603703i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.00000 | 0.504956 | 0.252478 | − | 0.967603i | \(-0.418755\pi\) | ||||
0.252478 | + | 0.967603i | \(0.418755\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | 0.125739 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.00000 | − | 6.92820i | 0.497096 | − | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.00000 | − | 15.5885i | 0.557086 | − | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.500000 | + | 0.866025i | 0.0308313 | + | 0.0534014i | 0.881029 | − | 0.473062i | \(-0.156851\pi\) |
−0.850198 | + | 0.526463i | \(0.823518\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.0000 | 0.614295 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −15.0000 | −0.917985 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.5000 | + | 18.1865i | 0.640196 | + | 1.10885i | 0.985389 | + | 0.170321i | \(0.0544803\pi\) |
−0.345192 | + | 0.938532i | \(0.612186\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.0000 | + | 19.0526i | −0.668202 | + | 1.15736i | 0.310204 | + | 0.950670i | \(0.399603\pi\) |
−0.978406 | + | 0.206691i | \(0.933731\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.00000 | + | 1.73205i | −0.0603023 | + | 0.104447i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.0000 | + | 24.2487i | 0.841178 | + | 1.45696i | 0.888899 | + | 0.458103i | \(0.151471\pi\) |
−0.0477206 | + | 0.998861i | \(0.515196\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.00000 | −0.478947 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.00000 | + | 3.46410i | 0.118888 | + | 0.205919i | 0.919327 | − | 0.393494i | \(-0.128734\pi\) |
−0.800439 | + | 0.599414i | \(0.795400\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.00000 | + | 1.73205i | −0.0592349 | + | 0.102598i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.50000 | − | 0.866025i | −0.147570 | − | 0.0511199i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.00000 | + | 15.5885i | 0.527589 | + | 0.913812i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.0000 | 0.701047 | 0.350524 | − | 0.936554i | \(-0.386004\pi\) | ||||
0.350524 | + | 0.936554i | \(0.386004\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000 | 0.582223 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.00000 | + | 8.66025i | 0.290129 | + | 0.502519i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −22.5000 | − | 7.79423i | −1.29688 | − | 0.449252i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.50000 | + | 2.59808i | −0.0861727 | + | 0.149256i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.50000 | + | 7.79423i | 0.257669 | + | 0.446296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.0000 | 1.19853 | 0.599267 | − | 0.800549i | \(-0.295459\pi\) | ||||
0.599267 | + | 0.800549i | \(0.295459\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −13.0000 | −0.739544 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.0000 | − | 22.5167i | −0.737162 | − | 1.27680i | −0.953768 | − | 0.300544i | \(-0.902832\pi\) |
0.216606 | − | 0.976259i | \(-0.430501\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.00000 | + | 13.8564i | −0.452187 | + | 0.783210i | −0.998522 | − | 0.0543564i | \(-0.982689\pi\) |
0.546335 | + | 0.837567i | \(0.316023\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.00000 | + | 5.19615i | 0.0563436 | + | 0.292770i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 8.00000 | − | 13.8564i | 0.449325 | − | 0.778253i | −0.549017 | − | 0.835811i | \(-0.684998\pi\) |
0.998342 | + | 0.0575576i | \(0.0183313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.00000 | − | 15.5885i | −0.503903 | − | 0.872786i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.00000 | 0.502331 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.00000 | −0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0.500000 | − | 0.866025i | 0.0276501 | − | 0.0478913i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.00000 | + | 6.92820i | 0.219199 | + | 0.379663i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.00000 | −0.273179 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.00000 | − | 1.73205i | −0.0543125 | − | 0.0940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.00000 | + | 6.92820i | −0.216612 | + | 0.375183i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.500000 | − | 0.866025i | 0.0269191 | − | 0.0466252i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.50000 | + | 6.06218i | 0.187890 | + | 0.325435i | 0.944547 | − | 0.328378i | \(-0.106502\pi\) |
−0.756657 | + | 0.653812i | \(0.773169\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −19.0000 | −1.01705 | −0.508523 | − | 0.861048i | \(-0.669808\pi\) | ||||
−0.508523 | + | 0.861048i | \(0.669808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.00000 | − | 12.1244i | −0.372572 | − | 0.645314i | 0.617388 | − | 0.786659i | \(-0.288191\pi\) |
−0.989960 | + | 0.141344i | \(0.954858\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.00000 | − | 12.1244i | 0.371521 | − | 0.643494i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.00000 | − | 6.92820i | 0.423405 | − | 0.366679i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | + | 10.3923i | −0.316668 | + | 0.548485i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.50000 | + | 12.9904i | 0.394737 | + | 0.683704i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −12.0000 | −0.628109 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.50000 | − | 6.06218i | −0.182699 | − | 0.316443i | 0.760100 | − | 0.649806i | \(-0.225150\pi\) |
−0.942799 | + | 0.333363i | \(0.891817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.00000 | − | 1.73205i | 0.0520579 | − | 0.0901670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.00000 | − | 25.9808i | −0.259587 | − | 1.34885i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.0000 | − | 24.2487i | 0.724893 | − | 1.25555i | −0.234126 | − | 0.972206i | \(-0.575223\pi\) |
0.959018 | − | 0.283344i | \(-0.0914439\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.500000 | + | 0.866025i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.0000 | −1.54100 | −0.770498 | − | 0.637442i | \(-0.779993\pi\) | ||||
−0.770498 | + | 0.637442i | \(0.779993\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.00000 | − | 6.92820i | −0.204926 | − | 0.354943i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.5000 | + | 18.1865i | −0.536525 | + | 0.929288i | 0.462563 | + | 0.886586i | \(0.346930\pi\) |
−0.999088 | + | 0.0427020i | \(0.986403\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.00000 | + | 1.73205i | 0.254824 | + | 0.0882735i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.00000 | − | 15.5885i | 0.457496 | − | 0.792406i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.0000 | − | 22.5167i | −0.659126 | − | 1.14164i | −0.980842 | − | 0.194804i | \(-0.937593\pi\) |
0.321716 | − | 0.946836i | \(-0.395740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | 0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.00000 | −0.403547 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.00000 | + | 12.1244i | 0.352208 | + | 0.610043i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.00000 | + | 5.19615i | −0.150566 | + | 0.260787i | −0.931436 | − | 0.363906i | \(-0.881443\pi\) |
0.780870 | + | 0.624694i | \(0.214776\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.00000 | + | 1.73205i | 0.250313 | + | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.50000 | − | 14.7224i | 0.424470 | − | 0.735203i | −0.571901 | − | 0.820323i | \(-0.693794\pi\) |
0.996371 | + | 0.0851195i | \(0.0271272\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.00000 | 0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.5000 | + | 18.1865i | 0.519192 | + | 0.899266i | 0.999751 | + | 0.0223042i | \(0.00710022\pi\) |
−0.480560 | + | 0.876962i | \(0.659566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 10.3923i | −0.295958 | + | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.00000 | − | 25.9808i | −0.246034 | − | 1.27843i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.50000 | − | 9.52628i | 0.269984 | − | 0.467627i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.00000 | + | 1.73205i | 0.0489702 | + | 0.0848189i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.0000 | 0.781651 | 0.390826 | − | 0.920465i | \(-0.372190\pi\) | ||||
0.390826 | + | 0.920465i | \(0.372190\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0000 | −1.31590 | −0.657950 | − | 0.753062i | \(-0.728576\pi\) | ||||
−0.657950 | + | 0.753062i | \(0.728576\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.00000 | + | 3.46410i | −0.0970143 | + | 0.168034i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 18.0000 | − | 15.5885i | 0.871081 | − | 0.754378i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.00000 | − | 12.1244i | −0.337178 | − | 0.584010i | 0.646723 | − | 0.762725i | \(-0.276139\pi\) |
−0.983901 | + | 0.178716i | \(0.942806\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 30.0000 | 1.44171 | 0.720854 | − | 0.693087i | \(-0.243750\pi\) | ||||
0.720854 | + | 0.693087i | \(0.243750\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −9.00000 | −0.431517 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.00000 | + | 1.73205i | 0.0478365 | + | 0.0828552i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.0000 | − | 24.2487i | 0.668184 | − | 1.15733i | −0.310228 | − | 0.950662i | \(-0.600405\pi\) |
0.978412 | − | 0.206666i | \(-0.0662612\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 13.0000 | − | 5.19615i | 0.619048 | − | 0.247436i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.50000 | − | 9.52628i | 0.261313 | − | 0.452607i | −0.705278 | − | 0.708931i | \(-0.749178\pi\) |
0.966591 | + | 0.256323i | \(0.0825112\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.50000 | − | 12.9904i | −0.355534 | − | 0.615803i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.00000 | −0.236492 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −41.0000 | −1.93491 | −0.967455 | − | 0.253044i | \(-0.918568\pi\) | ||||
−0.967455 | + | 0.253044i | \(0.918568\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00000 | − | 1.73205i | −0.0470882 | − | 0.0815591i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.00000 | + | 6.92820i | −0.187936 | + | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.00000 | + | 6.92820i | −0.187112 | + | 0.324088i | −0.944286 | − | 0.329125i | \(-0.893246\pi\) |
0.757174 | + | 0.653213i | \(0.226579\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.0000 | + | 17.3205i | 0.466760 | + | 0.808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.00000 | 0.0931493 | 0.0465746 | − | 0.998915i | \(-0.485169\pi\) | ||||
0.0465746 | + | 0.998915i | \(0.485169\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 39.0000 | 1.81248 | 0.906242 | − | 0.422760i | \(-0.138939\pi\) | ||||
0.906242 | + | 0.422760i | \(0.138939\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.00000 | + | 3.46410i | 0.0927478 | + | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.50000 | − | 6.06218i | 0.161961 | − | 0.280524i | −0.773611 | − | 0.633661i | \(-0.781552\pi\) |
0.935572 | + | 0.353137i | \(0.114885\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.50000 | + | 12.9904i | 0.115439 | + | 0.599840i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.00000 | + | 1.73205i | −0.0460776 | + | 0.0798087i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00000 | − | 15.5885i | −0.413820 | − | 0.716758i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.00000 | −0.0917663 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 20.0000 | 0.915737 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.00000 | + | 13.8564i | 0.365529 | + | 0.633115i | 0.988861 | − | 0.148842i | \(-0.0475547\pi\) |
−0.623332 | + | 0.781958i | \(0.714221\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.50000 | − | 0.866025i | −0.113754 | − | 0.0394055i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.00000 | + | 15.5885i | −0.408669 | + | 0.707835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.00000 | + | 6.92820i | 0.181257 | + | 0.313947i | 0.942309 | − | 0.334744i | \(-0.108650\pi\) |
−0.761052 | + | 0.648691i | \(0.775317\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.0000 | −0.902587 | −0.451294 | − | 0.892375i | \(-0.649037\pi\) | ||||
−0.451294 | + | 0.892375i | \(0.649037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.0000 | − | 31.1769i | −0.810679 | − | 1.40414i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.00000 | + | 3.46410i | −0.0898933 | + | 0.155700i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −35.0000 | − | 12.1244i | −1.56996 | − | 0.543852i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.0000 | − | 32.9090i | 0.850557 | − | 1.47321i | −0.0301498 | − | 0.999545i | \(-0.509598\pi\) |
0.880707 | − | 0.473662i | \(-0.157068\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.50000 | − | 14.7224i | −0.379752 | − | 0.657750i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.0000 | −1.02552 | −0.512760 | − | 0.858532i | \(-0.671377\pi\) | ||||
−0.512760 | + | 0.858532i | \(0.671377\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00000 | −0.133498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.50000 | + | 11.2583i | 0.288675 | + | 0.500000i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.50000 | − | 12.9904i | 0.332432 | − | 0.575789i | −0.650556 | − | 0.759458i | \(-0.725464\pi\) |
0.982988 | + | 0.183669i | \(0.0587976\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 31.1769i | 0.265424 | + | 1.37919i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | + | 8.66025i | −0.220755 | + | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.50000 | − | 11.2583i | −0.286424 | − | 0.496101i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0000 | 0.702322 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21.0000 | + | 36.3731i | 0.920027 | + | 1.59353i | 0.799370 | + | 0.600839i | \(0.205167\pi\) |
0.120656 | + | 0.992694i | \(0.461500\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.0000 | + | 24.2487i | −0.612177 | + | 1.06032i | 0.378695 | + | 0.925521i | \(0.376373\pi\) |
−0.990873 | + | 0.134801i | \(0.956961\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000 | − | 1.73205i | 0.0872872 | − | 0.0755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.00000 | + | 13.8564i | −0.348485 | + | 0.603595i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | 0.867926 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.50000 | + | 7.79423i | 0.194552 | + | 0.336974i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.00000 | − | 13.8564i | 0.0861461 | − | 0.596838i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.50000 | − | 11.2583i | 0.279457 | − | 0.484033i | −0.691793 | − | 0.722096i | \(-0.743179\pi\) |
0.971250 | + | 0.238062i | \(0.0765123\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 12.5000 | + | 21.6506i | 0.536426 | + | 0.929118i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.00000 | 0.0428353 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −35.0000 | −1.49649 | −0.748246 | − | 0.663421i | \(-0.769104\pi\) | ||||
−0.748246 | + | 0.663421i | \(0.769104\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.00000 | + | 15.5885i | 0.384111 | + | 0.665299i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.00000 | − | 15.5885i | 0.383413 | − | 0.664091i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | − | 24.2487i | 1.19068 | − | 1.03116i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.00000 | − | 3.46410i | 0.0848953 | − | 0.147043i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −15.0000 | − | 25.9808i | −0.635570 | − | 1.10084i | −0.986394 | − | 0.164399i | \(-0.947432\pi\) |
0.350824 | − | 0.936442i | \(-0.385902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.5000 | + | 38.9711i | 0.948262 | + | 1.64244i | 0.749085 | + | 0.662474i | \(0.230494\pi\) |
0.199177 | + | 0.979963i | \(0.436173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.00000 | − | 1.73205i | 0.0420703 | − | 0.0728679i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.500000 | + | 2.59808i | 0.0209980 | + | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −23.0000 | + | 39.8372i | −0.964210 | + | 1.67006i | −0.252488 | + | 0.967600i | \(0.581249\pi\) |
−0.711722 | + | 0.702461i | \(0.752085\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.0000 | + | 22.5167i | 0.544033 | + | 0.942293i | 0.998667 | + | 0.0516146i | \(0.0164367\pi\) |
−0.454634 | + | 0.890678i | \(0.650230\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.0000 | 0.751961 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.00000 | − | 1.73205i | −0.0416305 | − | 0.0721062i | 0.844459 | − | 0.535620i | \(-0.179922\pi\) |
−0.886090 | + | 0.463513i | \(0.846589\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.00000 | − | 12.1244i | 0.290910 | − | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −27.5000 | − | 9.52628i | −1.14089 | − | 0.395217i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0000 | − | 17.3205i | 0.414158 | − | 0.717342i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.0000 | −0.495293 | −0.247647 | − | 0.968850i | \(-0.579657\pi\) | ||||
−0.247647 | + | 0.968850i | \(0.579657\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.00000 | −0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.00000 | − | 15.5885i | −0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.00000 | + | 15.5885i | −0.369586 | + | 0.640141i | −0.989501 | − | 0.144528i | \(-0.953834\pi\) |
0.619915 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | + | 3.46410i | 0.409960 | + | 0.142014i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.00000 | − | 3.46410i | 0.0818546 | − | 0.141776i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.00000 | − | 3.46410i | −0.0817178 | − | 0.141539i | 0.822270 | − | 0.569097i | \(-0.192707\pi\) |
−0.903988 | + | 0.427558i | \(0.859374\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −10.0000 | −0.407231 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.50000 | − | 6.06218i | −0.142295 | − | 0.246463i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −13.5000 | + | 23.3827i | −0.547948 | + | 0.949074i | 0.450467 | + | 0.892793i | \(0.351258\pi\) |
−0.998415 | + | 0.0562808i | \(0.982076\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.50000 | + | 23.3827i | 0.182349 | + | 0.947514i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | + | 17.3205i | 0.403896 | + | 0.699569i | 0.994192 | − | 0.107618i | \(-0.0343224\pi\) |
−0.590296 | + | 0.807187i | \(0.700989\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.00000 | −0.0403239 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0000 | −0.483102 | −0.241551 | − | 0.970388i | \(-0.577656\pi\) | ||||
−0.241551 | + | 0.970388i | \(0.577656\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.0000 | + | 29.4449i | 0.683288 | + | 1.18349i | 0.973972 | + | 0.226670i | \(0.0727838\pi\) |
−0.290684 | + | 0.956819i | \(0.593883\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.50000 | − | 4.33013i | 0.100322 | − | 0.173762i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −30.0000 | + | 25.9808i | −1.20192 | + | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.00000 | + | 3.46410i | 0.0798723 | + | 0.138343i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0000 | 0.637962 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.00000 | −0.0796187 | −0.0398094 | − | 0.999207i | \(-0.512675\pi\) | ||||
−0.0398094 | + | 0.999207i | \(0.512675\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.00000 | − | 1.73205i | −0.0397464 | − | 0.0688428i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00000 | − | 6.92820i | 0.158735 | − | 0.274937i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 14.0000 | − | 24.2487i | 0.553831 | − | 0.959264i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.50000 | + | 16.4545i | 0.375227 | + | 0.649913i | 0.990361 | − | 0.138510i | \(-0.0442313\pi\) |
−0.615134 | + | 0.788423i | \(0.710898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.00000 | −0.157745 | −0.0788723 | − | 0.996885i | \(-0.525132\pi\) | ||||
−0.0788723 | + | 0.996885i | \(0.525132\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −9.00000 | −0.354375 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.5000 | − | 19.9186i | −0.452112 | − | 0.783080i | 0.546405 | − | 0.837521i | \(-0.315996\pi\) |
−0.998517 | + | 0.0544405i | \(0.982662\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.0000 | − | 17.3205i | 0.392534 | − | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.00000 | − | 6.92820i | 0.313545 | − | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | + | 31.1769i | −0.704394 | + | 1.22005i | 0.262515 | + | 0.964928i | \(0.415448\pi\) |
−0.966910 | + | 0.255119i | \(0.917885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | − | 6.92820i | −0.156293 | − | 0.270707i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −24.0000 | −0.936329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.00000 | 0.0779089 | 0.0389545 | − | 0.999241i | \(-0.487597\pi\) | ||||
0.0389545 | + | 0.999241i | \(0.487597\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.50000 | + | 2.59808i | 0.0583432 | + | 0.101053i | 0.893722 | − | 0.448622i | \(-0.148085\pi\) |
−0.835379 | + | 0.549675i | \(0.814752\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.00000 | + | 5.19615i | 0.0387783 | + | 0.201498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.50000 | + | 7.79423i | −0.174241 | + | 0.301794i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.00000 | + | 3.46410i | 0.0773245 | + | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.0000 | 0.694882 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.50000 | + | 4.33013i | 0.0962250 | + | 0.166667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.0000 | − | 20.7846i | 0.461197 | − | 0.798817i | −0.537823 | − | 0.843057i | \(-0.680753\pi\) |
0.999021 | + | 0.0442400i | \(0.0140866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 45.0000 | + | 15.5885i | 1.72694 | + | 0.598230i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | − | 17.3205i | 0.383201 | − | 0.663723i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.50000 | − | 7.79423i | −0.172188 | − | 0.298238i | 0.766997 | − | 0.641651i | \(-0.221750\pi\) |
−0.939184 | + | 0.343413i | \(0.888417\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10.0000 | −0.381524 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0000 | + | 43.3013i | −0.951045 | + | 1.64726i | −0.207875 | + | 0.978155i | \(0.566655\pi\) |
−0.743170 | + | 0.669102i | \(0.766679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.0000 | + | 3.46410i | 0.379869 | + | 0.131590i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.00000 | + | 1.73205i | −0.0379322 | + | 0.0657004i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.00000 | − | 3.46410i | −0.0757554 | − | 0.131212i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8.00000 | 0.302588 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | + | 6.92820i | 0.150863 | + | 0.261302i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.50000 | + | 7.79423i | 0.0564133 | + | 0.293132i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.5000 | + | 18.1865i | −0.394336 | + | 0.683010i | −0.993016 | − | 0.117978i | \(-0.962359\pi\) |
0.598680 | + | 0.800988i | \(0.295692\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.0000 | + | 24.2487i | 0.525041 | + | 0.909398i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.00000 | 0.149801 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | + | 20.7846i | 0.448148 | + | 0.776215i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 21.0000 | − | 36.3731i | 0.783168 | − | 1.35649i | −0.146920 | − | 0.989148i | \(-0.546936\pi\) |
0.930087 | − | 0.367338i | \(-0.119731\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26.0000 | + | 22.5167i | −0.968291 | + | 0.838564i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.0000 | − | 19.0526i | 0.409094 | − | 0.708572i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.50000 | − | 7.79423i | −0.167126 | − | 0.289470i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.0000 | −1.14973 | −0.574863 | − | 0.818250i | \(-0.694945\pi\) | ||||
−0.574863 | + | 0.818250i | \(0.694945\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −18.0000 | − | 31.1769i | −0.665754 | − | 1.15312i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.0000 | − | 22.5167i | 0.480166 | − | 0.831672i | −0.519575 | − | 0.854425i | \(-0.673910\pi\) |
0.999741 | + | 0.0227529i | \(0.00724310\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.50000 | − | 4.33013i | −0.202871 | − | 0.159719i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.00000 | − | 8.66025i | −0.183928 | − | 0.318573i | 0.759287 | − | 0.650756i | \(-0.225548\pi\) |
−0.943215 | + | 0.332184i | \(0.892215\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0000 | 0.990534 | 0.495267 | − | 0.868741i | \(-0.335070\pi\) | ||||
0.495267 | + | 0.868741i | \(0.335070\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.50000 | − | 4.33013i | −0.0915929 | − | 0.158644i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 11.0000 | − | 19.0526i | 0.402469 | − | 0.697097i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | − | 15.5885i | 0.657706 | − | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.00000 | + | 10.3923i | −0.218943 | + | 0.379221i | −0.954485 | − | 0.298259i | \(-0.903594\pi\) |
0.735542 | + | 0.677479i | \(0.236928\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.00000 | − | 6.92820i | −0.145768 | − | 0.252478i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −24.0000 | −0.872295 | −0.436147 | − | 0.899875i | \(-0.643657\pi\) | ||||
−0.436147 | + | 0.899875i | \(0.643657\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.00000 | − | 1.73205i | −0.0362977 | − | 0.0628695i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.00000 | − | 5.19615i | 0.108750 | − | 0.188360i | −0.806514 | − | 0.591215i | \(-0.798649\pi\) |
0.915264 | + | 0.402854i | \(0.131982\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.500000 | − | 2.59808i | −0.0181012 | − | 0.0940567i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.00000 | + | 6.92820i | −0.144620 | + | 0.250490i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.0000 | 1.22607 | 0.613036 | − | 0.790055i | \(-0.289948\pi\) | ||||
0.613036 | + | 0.790055i | \(0.289948\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.00000 | + | 3.46410i | −0.0718421 | + | 0.124434i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.0000 | − | 3.46410i | −0.358748 | − | 0.124274i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.00000 | − | 1.73205i | 0.0358287 | − | 0.0620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.0000 | − | 24.2487i | −0.500959 | − | 0.867687i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.0000 | −1.60817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −22.5000 | − | 38.9711i | −0.802038 | − | 1.38917i | −0.918272 | − | 0.395949i | \(-0.870416\pi\) |
0.116234 | − | 0.993222i | \(-0.462918\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.500000 | − | 0.866025i | 0.0178005 | − | 0.0308313i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.00000 | − | 1.73205i | −0.177780 | − | 0.0615846i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.00000 | − | 8.66025i | −0.177332 | − | 0.307148i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8.00000 | 0.283375 | 0.141687 | − | 0.989911i | \(-0.454747\pi\) | ||||
0.141687 | + | 0.989911i | \(0.454747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.0000 | − | 25.9808i | −0.529999 | − | 0.917985i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | + | 20.7846i | −0.423471 | + | 0.733473i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.500000 | − | 2.59808i | −0.0176227 | − | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.5000 | − | 18.1865i | 0.369618 | − | 0.640196i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.50000 | − | 11.2583i | −0.228528 | − | 0.395822i | 0.728844 | − | 0.684680i | \(-0.240058\pi\) |
−0.957372 | + | 0.288858i | \(0.906725\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −44.0000 | −1.54505 | −0.772524 | − | 0.634985i | \(-0.781006\pi\) | ||||
−0.772524 | + | 0.634985i | \(0.781006\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 22.0000 | 0.771574 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.0000 | − | 17.3205i | −0.350285 | − | 0.606711i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.00000 | − | 15.5885i | 0.314870 | − | 0.545371i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −15.0000 | + | 25.9808i | −0.523504 | + | 0.906735i | 0.476122 | + | 0.879379i | \(0.342042\pi\) |
−0.999626 | + | 0.0273557i | \(0.991291\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5000 | − | 42.4352i | −0.854016 | − | 1.47920i | −0.877555 | − | 0.479477i | \(-0.840826\pi\) |
0.0235383 | − | 0.999723i | \(-0.492507\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.00000 | 0.0696311 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.0000 | −0.591148 | −0.295574 | − | 0.955320i | \(-0.595511\pi\) | ||||
−0.295574 | + | 0.955320i | \(0.595511\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.00000 | − | 1.73205i | −0.0347314 | − | 0.0601566i | 0.848137 | − | 0.529777i | \(-0.177724\pi\) |
−0.882869 | + | 0.469620i | \(0.844391\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.0000 | − | 24.2487i | 0.485655 | − | 0.841178i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.00000 | − | 27.7128i | 0.138592 | − | 0.960192i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.50000 | − | 14.7224i | 0.294155 | − | 0.509491i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | + | 17.3205i | 0.345651 | + | 0.598684i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.0000 | 0.345238 | 0.172619 | − | 0.984989i | \(-0.444777\pi\) | ||||
0.172619 | + | 0.984989i | \(0.444777\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −9.00000 | − | 15.5885i | −0.309976 | − | 0.536895i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.50000 | + | 11.2583i | −0.223607 | + | 0.387298i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −14.0000 | + | 12.1244i | −0.481046 | + | 0.416598i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.00000 | − | 3.46410i | 0.0686398 | − | 0.118888i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | − | 3.46410i | −0.0685591 | − | 0.118748i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.0000 | 1.30110 | 0.650548 | − | 0.759465i | \(-0.274539\pi\) | ||||
0.650548 | + | 0.759465i | \(0.274539\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.00000 | −0.136797 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.0000 | − | 25.9808i | −0.512390 | − | 0.887486i | −0.999897 | − | 0.0143666i | \(-0.995427\pi\) |
0.487507 | − | 0.873119i | \(-0.337907\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.0000 | + | 34.6410i | −0.682391 | + | 1.18194i | 0.291858 | + | 0.956462i | \(0.405727\pi\) |
−0.974249 | + | 0.225475i | \(0.927607\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.500000 | + | 2.59808i | 0.0170400 | + | 0.0885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.500000 | − | 0.866025i | 0.0170202 | − | 0.0294798i | −0.857390 | − | 0.514667i | \(-0.827915\pi\) |
0.874410 | + | 0.485188i | \(0.161249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.00000 | + | 13.8564i | 0.272008 | + | 0.471132i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 28.0000 | 0.949835 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.0000 | + | 31.1769i | −0.609208 | + | 1.05518i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.50000 | + | 0.866025i | 0.0845154 | + | 0.0292770i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.00000 | + | 5.19615i | −0.101303 | + | 0.175462i | −0.912222 | − | 0.409697i | \(-0.865634\pi\) |
0.810919 | + | 0.585159i | \(0.198968\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.00000 | − | 10.3923i | −0.202375 | − | 0.350524i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.0000 | 0.572745 | 0.286372 | − | 0.958118i | \(-0.407551\pi\) | ||||
0.286372 | + | 0.958118i | \(0.407551\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0000 | 0.673054 | 0.336527 | − | 0.941674i | \(-0.390748\pi\) | ||||
0.336527 | + | 0.941674i | \(0.390748\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −5.00000 | − | 8.66025i | −0.168073 | − | 0.291111i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.50000 | + | 12.9904i | −0.251825 | + | 0.436174i | −0.964028 | − | 0.265799i | \(-0.914364\pi\) |
0.712203 | + | 0.701974i | \(0.247698\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | − | 6.92820i | −0.670778 | − | 0.232364i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | + | 1.73205i | −0.0335013 | + | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.0000 | −0.401116 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −18.0000 | − | 31.1769i | −0.600334 | − | 1.03981i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.0000 | − | 34.6410i | 0.666297 | − | 1.15406i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.50000 | + | 23.3827i | 0.149751 | + | 0.778127i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −12.5000 | + | 21.6506i | −0.415514 | + | 0.719691i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50000 | − | 6.06218i | −0.116216 | − | 0.201291i | 0.802049 | − | 0.597258i | \(-0.203743\pi\) |
−0.918265 | + | 0.395966i | \(0.870410\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −11.0000 | − | 19.0526i | −0.364047 | − | 0.630548i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.50000 | − | 7.79423i | 0.148765 | − | 0.257669i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.0000 | + | 13.8564i | −0.528367 | + | 0.457579i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.0000 | + | 36.3731i | −0.692726 | + | 1.19984i | 0.278215 | + | 0.960519i | \(0.410257\pi\) |
−0.970941 | + | 0.239318i | \(0.923076\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.5000 | − | 18.1865i | −0.345987 | − | 0.599267i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.00000 | 0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −13.0000 | − | 22.5167i | −0.426976 | − | 0.739544i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.50000 | − | 11.2583i | 0.213258 | − | 0.369374i | −0.739474 | − | 0.673185i | \(-0.764926\pi\) |
0.952732 | + | 0.303811i | \(0.0982592\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.0000 | − | 5.19615i | 0.426058 | − | 0.170297i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.0000 | + | 22.5167i | −0.425601 | + | 0.737162i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.00000 | + | 6.92820i | 0.130814 | + | 0.226576i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.00000 | 0.130674 | 0.0653372 | − | 0.997863i | \(-0.479188\pi\) | ||||
0.0653372 | + | 0.997863i | \(0.479188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 16.0000 | 0.522140 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.500000 | + | 0.866025i | −0.0162822 | + | 0.0282017i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | − | 8.66025i | 0.325300 | − | 0.281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.50000 | + | 4.33013i | −0.0812391 | + | 0.140710i | −0.903782 | − | 0.427992i | \(-0.859221\pi\) |
0.822543 | + | 0.568702i | \(0.192554\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −16.0000 | −0.518836 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.0000 | 0.907009 | 0.453504 | − | 0.891254i | \(-0.350174\pi\) | ||||
0.453504 | + | 0.891254i | \(0.350174\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.00000 | + | 15.5885i | 0.291233 | + | 0.504431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −9.00000 | + | 15.5885i | −0.290929 | + | 0.503903i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.00000 | + | 31.1769i | 0.193750 | + | 1.00676i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50000 | − | 12.9904i | 0.241935 | − | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.00000 | + | 15.5885i | 0.290021 | + | 0.502331i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 14.0000 | 0.450676 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 55.0000 | 1.76868 | 0.884340 | − | 0.466843i | \(-0.154609\pi\) | ||||
0.884340 | + | 0.466843i | \(0.154609\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.00000 | + | 6.92820i | 0.128499 | + | 0.222566i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.00000 | − | 6.92820i | 0.128366 | − | 0.222337i | −0.794678 | − | 0.607032i | \(-0.792360\pi\) |
0.923044 | + | 0.384695i | \(0.125693\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.00000 | + | 1.73205i | 0.160293 | + | 0.0555270i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −21.0000 | − | 36.3731i | −0.671850 | − | 1.16368i | −0.977379 | − | 0.211495i | \(-0.932167\pi\) |
0.305530 | − | 0.952183i | \(-0.401167\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.0000 | −0.958804 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.00000 | 0.0638551 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | − | 2.59808i | −0.0478426 | − | 0.0828658i | 0.841112 | − | 0.540860i | \(-0.181901\pi\) |
−0.888955 | + | 0.457995i | \(0.848568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.00000 | − | 15.5885i | 0.286764 | − | 0.496690i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50000 | + | 7.79423i | −0.143092 | + | 0.247842i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | + | 34.6410i | 0.635321 | + | 1.10041i | 0.986447 | + | 0.164080i | \(0.0524655\pi\) |
−0.351126 | + | 0.936328i | \(0.614201\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.00000 | 0.126809 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.00000 | − | 8.66025i | −0.158352 | − | 0.274273i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.0000 | − | 17.3205i | 0.316386 | − | 0.547997i |
(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 | 280.2.q.a.121.1 | yes | 2 | |
3.2 | odd | 2 | 2520.2.bi.a.1801.1 | 2 | |||
4.3 | odd | 2 | 560.2.q.h.401.1 | 2 | |||
5.2 | odd | 4 | 1400.2.bh.b.849.1 | 4 | |||
5.3 | odd | 4 | 1400.2.bh.b.849.2 | 4 | |||
5.4 | even | 2 | 1400.2.q.e.401.1 | 2 | |||
7.2 | even | 3 | 1960.2.a.i.1.1 | 1 | |||
7.3 | odd | 6 | 1960.2.q.k.361.1 | 2 | |||
7.4 | even | 3 | inner | 280.2.q.a.81.1 | ✓ | 2 | |
7.5 | odd | 6 | 1960.2.a.e.1.1 | 1 | |||
7.6 | odd | 2 | 1960.2.q.k.961.1 | 2 | |||
21.11 | odd | 6 | 2520.2.bi.a.361.1 | 2 | |||
28.11 | odd | 6 | 560.2.q.h.81.1 | 2 | |||
28.19 | even | 6 | 3920.2.a.y.1.1 | 1 | |||
28.23 | odd | 6 | 3920.2.a.m.1.1 | 1 | |||
35.4 | even | 6 | 1400.2.q.e.1201.1 | 2 | |||
35.9 | even | 6 | 9800.2.a.r.1.1 | 1 | |||
35.18 | odd | 12 | 1400.2.bh.b.249.1 | 4 | |||
35.19 | odd | 6 | 9800.2.a.bc.1.1 | 1 | |||
35.32 | odd | 12 | 1400.2.bh.b.249.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
280.2.q.a.81.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
280.2.q.a.121.1 | yes | 2 | 1.1 | even | 1 | trivial | |
560.2.q.h.81.1 | 2 | 28.11 | odd | 6 | |||
560.2.q.h.401.1 | 2 | 4.3 | odd | 2 | |||
1400.2.q.e.401.1 | 2 | 5.4 | even | 2 | |||
1400.2.q.e.1201.1 | 2 | 35.4 | even | 6 | |||
1400.2.bh.b.249.1 | 4 | 35.18 | odd | 12 | |||
1400.2.bh.b.249.2 | 4 | 35.32 | odd | 12 | |||
1400.2.bh.b.849.1 | 4 | 5.2 | odd | 4 | |||
1400.2.bh.b.849.2 | 4 | 5.3 | odd | 4 | |||
1960.2.a.e.1.1 | 1 | 7.5 | odd | 6 | |||
1960.2.a.i.1.1 | 1 | 7.2 | even | 3 | |||
1960.2.q.k.361.1 | 2 | 7.3 | odd | 6 | |||
1960.2.q.k.961.1 | 2 | 7.6 | odd | 2 | |||
2520.2.bi.a.361.1 | 2 | 21.11 | odd | 6 | |||
2520.2.bi.a.1801.1 | 2 | 3.2 | odd | 2 | |||
3920.2.a.m.1.1 | 1 | 28.23 | odd | 6 | |||
3920.2.a.y.1.1 | 1 | 28.19 | even | 6 | |||
9800.2.a.r.1.1 | 1 | 35.9 | even | 6 | |||
9800.2.a.bc.1.1 | 1 | 35.19 | odd | 6 |