Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(151,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([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("1050.151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.i (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: | \(8.38429221223\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 151.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.151 |
Dual form | 1050.2.i.f.751.1 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.00000 | + | 1.73205i | −0.755929 | + | 0.654654i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | − | 4.33013i | 0.753778 | − | 1.30558i | −0.192201 | − | 0.981356i | \(-0.561563\pi\) |
0.945979 | − | 0.324227i | \(-0.105104\pi\) | |||||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.00000 | + | 1.73205i | −0.242536 | + | 0.420084i | −0.961436 | − | 0.275029i | \(-0.911312\pi\) |
0.718900 | + | 0.695113i | \(0.244646\pi\) | |||||||
\(18\) | −0.500000 | + | 0.866025i | −0.117851 | + | 0.204124i | ||||
\(19\) | −3.50000 | − | 6.06218i | −0.802955 | − | 1.39076i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.114708 | − | 0.993399i | \(-0.463407\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | + | 2.59808i | 0.109109 | + | 0.566947i | ||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | 1.50000 | + | 2.59808i | 0.312772 | + | 0.541736i | 0.978961 | − | 0.204046i | \(-0.0654092\pi\) |
−0.666190 | + | 0.745782i | \(0.732076\pi\) | |||||||
\(24\) | 0.500000 | − | 0.866025i | 0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.500000 | + | 0.866025i | 0.0980581 | + | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.500000 | − | 2.59808i | −0.0944911 | − | 0.490990i | ||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | − | 5.19615i | 0.538816 | − | 0.933257i | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −2.50000 | − | 4.33013i | −0.435194 | − | 0.753778i | ||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.50000 | − | 4.33013i | −0.410997 | − | 0.711868i | 0.584002 | − | 0.811752i | \(-0.301486\pi\) |
−0.994999 | + | 0.0998840i | \(0.968153\pi\) | |||||||
\(38\) | −3.50000 | + | 6.06218i | −0.567775 | + | 0.983415i | ||||
\(39\) | −0.500000 | + | 0.866025i | −0.0800641 | + | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.00000 | −1.40556 | −0.702782 | − | 0.711405i | \(-0.748059\pi\) | ||||
−0.702782 | + | 0.711405i | \(0.748059\pi\) | |||||||
\(42\) | 2.00000 | − | 1.73205i | 0.308607 | − | 0.267261i | ||||
\(43\) | −10.0000 | −1.52499 | −0.762493 | − | 0.646997i | \(-0.776025\pi\) | ||||
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | 2.50000 | + | 4.33013i | 0.376889 | + | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.50000 | − | 2.59808i | 0.221163 | − | 0.383065i | ||||
\(47\) | −6.50000 | − | 11.2583i | −0.948122 | − | 1.64220i | −0.749375 | − | 0.662145i | \(-0.769646\pi\) |
−0.198747 | − | 0.980051i | \(-0.563687\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.00000 | + | 1.73205i | 0.140028 | + | 0.242536i | ||||
\(52\) | 0.500000 | − | 0.866025i | 0.0693375 | − | 0.120096i | ||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.00000 | + | 3.46410i | −0.260378 | + | 0.450988i | −0.966342 | − | 0.257260i | \(-0.917180\pi\) |
0.705965 | + | 0.708247i | \(0.250514\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.00000 | + | 1.73205i | 0.128037 | + | 0.221766i | 0.922916 | − | 0.385002i | \(-0.125799\pi\) |
−0.794879 | + | 0.606768i | \(0.792466\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 2.50000 | + | 0.866025i | 0.314970 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.50000 | + | 4.33013i | −0.307729 | + | 0.533002i | ||||
\(67\) | 3.00000 | − | 5.19615i | 0.366508 | − | 0.634811i | −0.622509 | − | 0.782613i | \(-0.713886\pi\) |
0.989017 | + | 0.147802i | \(0.0472198\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 3.00000 | 0.361158 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | −0.500000 | − | 0.866025i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 2.00000 | − | 3.46410i | 0.234082 | − | 0.405442i | −0.724923 | − | 0.688830i | \(-0.758125\pi\) |
0.959006 | + | 0.283387i | \(0.0914581\pi\) | |||||||
\(74\) | −2.50000 | + | 4.33013i | −0.290619 | + | 0.503367i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | 2.50000 | + | 12.9904i | 0.284901 | + | 1.48039i | ||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 4.50000 | + | 7.79423i | 0.496942 | + | 0.860729i | ||||
\(83\) | 10.0000 | 1.09764 | 0.548821 | − | 0.835940i | \(-0.315077\pi\) | ||||
0.548821 | + | 0.835940i | \(0.315077\pi\) | |||||||
\(84\) | −2.50000 | − | 0.866025i | −0.272772 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.00000 | + | 8.66025i | 0.539164 | + | 0.933859i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.50000 | − | 4.33013i | 0.266501 | − | 0.461593i | ||||
\(89\) | −5.00000 | − | 8.66025i | −0.529999 | − | 0.917985i | −0.999388 | − | 0.0349934i | \(-0.988859\pi\) |
0.469389 | − | 0.882992i | \(-0.344474\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.00000 | − | 1.73205i | 0.209657 | − | 0.181568i | ||||
\(92\) | −3.00000 | −0.312772 | ||||||||
\(93\) | −3.00000 | − | 5.19615i | −0.311086 | − | 0.538816i | ||||
\(94\) | −6.50000 | + | 11.2583i | −0.670424 | + | 1.16121i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −8.00000 | −0.812277 | −0.406138 | − | 0.913812i | \(-0.633125\pi\) | ||||
−0.406138 | + | 0.913812i | \(0.633125\pi\) | |||||||
\(98\) | −6.50000 | + | 2.59808i | −0.656599 | + | 0.262445i | ||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.00000 | + | 6.92820i | −0.398015 | + | 0.689382i | −0.993481 | − | 0.113998i | \(-0.963634\pi\) |
0.595466 | + | 0.803380i | \(0.296967\pi\) | |||||||
\(102\) | 1.00000 | − | 1.73205i | 0.0990148 | − | 0.171499i | ||||
\(103\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 6.00000 | + | 10.3923i | 0.580042 | + | 1.00466i | 0.995474 | + | 0.0950377i | \(0.0302972\pi\) |
−0.415432 | + | 0.909624i | \(0.636370\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 9.00000 | − | 15.5885i | 0.862044 | − | 1.49310i | −0.00790932 | − | 0.999969i | \(-0.502518\pi\) |
0.869953 | − | 0.493135i | \(-0.164149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.00000 | −0.474579 | ||||||||
\(112\) | 2.50000 | + | 0.866025i | 0.236228 | + | 0.0818317i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | 3.50000 | + | 6.06218i | 0.327805 | + | 0.567775i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.500000 | + | 0.866025i | 0.0462250 | + | 0.0800641i | ||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | −1.00000 | − | 5.19615i | −0.0916698 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | − | 12.1244i | −0.636364 | − | 1.10221i | ||||
\(122\) | 1.00000 | − | 1.73205i | 0.0905357 | − | 0.156813i | ||||
\(123\) | −4.50000 | + | 7.79423i | −0.405751 | + | 0.702782i | ||||
\(124\) | 3.00000 | + | 5.19615i | 0.269408 | + | 0.466628i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.500000 | − | 2.59808i | −0.0445435 | − | 0.231455i | ||||
\(127\) | −9.00000 | −0.798621 | −0.399310 | − | 0.916816i | \(-0.630750\pi\) | ||||
−0.399310 | + | 0.916816i | \(0.630750\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −5.00000 | + | 8.66025i | −0.440225 | + | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.50000 | + | 14.7224i | 0.742648 | + | 1.28630i | 0.951285 | + | 0.308312i | \(0.0997640\pi\) |
−0.208637 | + | 0.977993i | \(0.566903\pi\) | |||||||
\(132\) | 5.00000 | 0.435194 | ||||||||
\(133\) | 17.5000 | + | 6.06218i | 1.51744 | + | 0.525657i | ||||
\(134\) | −6.00000 | −0.518321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.00000 | + | 1.73205i | −0.0857493 | + | 0.148522i | ||||
\(137\) | −2.00000 | + | 3.46410i | −0.170872 | + | 0.295958i | −0.938725 | − | 0.344668i | \(-0.887992\pi\) |
0.767853 | + | 0.640626i | \(0.221325\pi\) | |||||||
\(138\) | −1.50000 | − | 2.59808i | −0.127688 | − | 0.221163i | ||||
\(139\) | −8.00000 | −0.678551 | −0.339276 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339276 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −13.0000 | −1.09480 | ||||||||
\(142\) | 1.00000 | + | 1.73205i | 0.0839181 | + | 0.145350i | ||||
\(143\) | −2.50000 | + | 4.33013i | −0.209061 | + | 0.362103i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | −5.50000 | − | 4.33013i | −0.453632 | − | 0.357143i | ||||
\(148\) | 5.00000 | 0.410997 | ||||||||
\(149\) | 3.00000 | + | 5.19615i | 0.245770 | + | 0.425685i | 0.962348 | − | 0.271821i | \(-0.0876260\pi\) |
−0.716578 | + | 0.697507i | \(0.754293\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.0000 | − | 19.0526i | 0.895167 | − | 1.55048i | 0.0615699 | − | 0.998103i | \(-0.480389\pi\) |
0.833597 | − | 0.552372i | \(-0.186277\pi\) | |||||||
\(152\) | −3.50000 | − | 6.06218i | −0.283887 | − | 0.491708i | ||||
\(153\) | 2.00000 | 0.161690 | ||||||||
\(154\) | 10.0000 | − | 8.66025i | 0.805823 | − | 0.697863i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.500000 | − | 0.866025i | −0.0400320 | − | 0.0693375i | ||||
\(157\) | 6.50000 | − | 11.2583i | 0.518756 | − | 0.898513i | −0.481006 | − | 0.876717i | \(-0.659728\pi\) |
0.999762 | − | 0.0217953i | \(-0.00693820\pi\) | |||||||
\(158\) | 7.00000 | − | 12.1244i | 0.556890 | − | 0.964562i | ||||
\(159\) | 0.500000 | + | 0.866025i | 0.0396526 | + | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.50000 | − | 2.59808i | −0.591083 | − | 0.204757i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.00000 | − | 10.3923i | −0.469956 | − | 0.813988i | 0.529454 | − | 0.848339i | \(-0.322397\pi\) |
−0.999410 | + | 0.0343508i | \(0.989064\pi\) | |||||||
\(164\) | 4.50000 | − | 7.79423i | 0.351391 | − | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.00000 | − | 8.66025i | −0.388075 | − | 0.672166i | ||||
\(167\) | 19.0000 | 1.47026 | 0.735132 | − | 0.677924i | \(-0.237120\pi\) | ||||
0.735132 | + | 0.677924i | \(0.237120\pi\) | |||||||
\(168\) | 0.500000 | + | 2.59808i | 0.0385758 | + | 0.200446i | ||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50000 | + | 6.06218i | −0.267652 | + | 0.463586i | ||||
\(172\) | 5.00000 | − | 8.66025i | 0.381246 | − | 0.660338i | ||||
\(173\) | 3.50000 | + | 6.06218i | 0.266100 | + | 0.460899i | 0.967851 | − | 0.251523i | \(-0.0809315\pi\) |
−0.701751 | + | 0.712422i | \(0.747598\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 2.00000 | + | 3.46410i | 0.150329 | + | 0.260378i | ||||
\(178\) | −5.00000 | + | 8.66025i | −0.374766 | + | 0.649113i | ||||
\(179\) | 5.50000 | − | 9.52628i | 0.411089 | − | 0.712028i | −0.583920 | − | 0.811811i | \(-0.698482\pi\) |
0.995009 | + | 0.0997838i | \(0.0318151\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | −2.50000 | − | 0.866025i | −0.185312 | − | 0.0641941i | ||||
\(183\) | 2.00000 | 0.147844 | ||||||||
\(184\) | 1.50000 | + | 2.59808i | 0.110581 | + | 0.191533i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | 5.00000 | + | 8.66025i | 0.365636 | + | 0.633300i | ||||
\(188\) | 13.0000 | 0.948122 | ||||||||
\(189\) | 2.00000 | − | 1.73205i | 0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | + | 13.8564i | 0.578860 | + | 1.00261i | 0.995610 | + | 0.0935936i | \(0.0298354\pi\) |
−0.416751 | + | 0.909021i | \(0.636831\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −9.00000 | + | 15.5885i | −0.647834 | + | 1.12208i | 0.335805 | + | 0.941932i | \(0.390992\pi\) |
−0.983639 | + | 0.180150i | \(0.942342\pi\) | |||||||
\(194\) | 4.00000 | + | 6.92820i | 0.287183 | + | 0.497416i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 27.0000 | 1.92367 | 0.961835 | − | 0.273629i | \(-0.0882242\pi\) | ||||
0.961835 | + | 0.273629i | \(0.0882242\pi\) | |||||||
\(198\) | 2.50000 | + | 4.33013i | 0.177667 | + | 0.307729i | ||||
\(199\) | 7.00000 | − | 12.1244i | 0.496217 | − | 0.859473i | −0.503774 | − | 0.863836i | \(-0.668055\pi\) |
0.999990 | + | 0.00436292i | \(0.00138876\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | − | 5.19615i | −0.211604 | − | 0.366508i | ||||
\(202\) | 8.00000 | 0.562878 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −2.00000 | −0.140028 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.50000 | − | 2.59808i | 0.104257 | − | 0.180579i | ||||
\(208\) | 0.500000 | + | 0.866025i | 0.0346688 | + | 0.0600481i | ||||
\(209\) | −35.0000 | −2.42100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.0000 | 1.30801 | 0.654007 | − | 0.756489i | \(-0.273087\pi\) | ||||
0.654007 | + | 0.756489i | \(0.273087\pi\) | |||||||
\(212\) | −0.500000 | − | 0.866025i | −0.0343401 | − | 0.0594789i | ||||
\(213\) | −1.00000 | + | 1.73205i | −0.0685189 | + | 0.118678i | ||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.00000 | + | 15.5885i | 0.203653 | + | 1.05821i | ||||
\(218\) | −18.0000 | −1.21911 | ||||||||
\(219\) | −2.00000 | − | 3.46410i | −0.135147 | − | 0.234082i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.00000 | − | 1.73205i | 0.0672673 | − | 0.116510i | ||||
\(222\) | 2.50000 | + | 4.33013i | 0.167789 | + | 0.290619i | ||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | + | 5.19615i | 0.199557 | + | 0.345643i | ||||
\(227\) | 7.00000 | − | 12.1244i | 0.464606 | − | 0.804722i | −0.534577 | − | 0.845120i | \(-0.679529\pi\) |
0.999184 | + | 0.0403978i | \(0.0128625\pi\) | |||||||
\(228\) | 3.50000 | − | 6.06218i | 0.231793 | − | 0.401478i | ||||
\(229\) | 2.00000 | + | 3.46410i | 0.132164 | + | 0.228914i | 0.924510 | − | 0.381157i | \(-0.124474\pi\) |
−0.792347 | + | 0.610071i | \(0.791141\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.5000 | + | 4.33013i | 0.822440 | + | 0.284901i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(234\) | 0.500000 | − | 0.866025i | 0.0326860 | − | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.00000 | − | 3.46410i | −0.130189 | − | 0.225494i | ||||
\(237\) | 14.0000 | 0.909398 | ||||||||
\(238\) | −4.00000 | + | 3.46410i | −0.259281 | + | 0.224544i | ||||
\(239\) | 20.0000 | 1.29369 | 0.646846 | − | 0.762620i | \(-0.276088\pi\) | ||||
0.646846 | + | 0.762620i | \(0.276088\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.500000 | − | 0.866025i | 0.0322078 | − | 0.0557856i | −0.849472 | − | 0.527633i | \(-0.823079\pi\) |
0.881680 | + | 0.471848i | \(0.156413\pi\) | |||||||
\(242\) | −7.00000 | + | 12.1244i | −0.449977 | + | 0.779383i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 3.50000 | + | 6.06218i | 0.222700 | + | 0.385727i | ||||
\(248\) | 3.00000 | − | 5.19615i | 0.190500 | − | 0.329956i | ||||
\(249\) | 5.00000 | − | 8.66025i | 0.316862 | − | 0.548821i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | −2.00000 | + | 1.73205i | −0.125988 | + | 0.109109i | ||||
\(253\) | 15.0000 | 0.943042 | ||||||||
\(254\) | 4.50000 | + | 7.79423i | 0.282355 | + | 0.489053i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −5.00000 | − | 8.66025i | −0.311891 | − | 0.540212i | 0.666880 | − | 0.745165i | \(-0.267629\pi\) |
−0.978772 | + | 0.204953i | \(0.934296\pi\) | |||||||
\(258\) | 10.0000 | 0.622573 | ||||||||
\(259\) | 12.5000 | + | 4.33013i | 0.776712 | + | 0.269061i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.50000 | − | 14.7224i | 0.525132 | − | 0.909555i | ||||
\(263\) | 12.0000 | − | 20.7846i | 0.739952 | − | 1.28163i | −0.212565 | − | 0.977147i | \(-0.568182\pi\) |
0.952517 | − | 0.304487i | \(-0.0984850\pi\) | |||||||
\(264\) | −2.50000 | − | 4.33013i | −0.153864 | − | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −3.50000 | − | 18.1865i | −0.214599 | − | 1.11509i | ||||
\(267\) | −10.0000 | −0.611990 | ||||||||
\(268\) | 3.00000 | + | 5.19615i | 0.183254 | + | 0.317406i | ||||
\(269\) | −7.00000 | + | 12.1244i | −0.426798 | + | 0.739235i | −0.996586 | − | 0.0825561i | \(-0.973692\pi\) |
0.569789 | + | 0.821791i | \(0.307025\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | − | 6.92820i | −0.242983 | − | 0.420858i | 0.718580 | − | 0.695444i | \(-0.244792\pi\) |
−0.961563 | + | 0.274586i | \(0.911459\pi\) | |||||||
\(272\) | 2.00000 | 0.121268 | ||||||||
\(273\) | −0.500000 | − | 2.59808i | −0.0302614 | − | 0.157243i | ||||
\(274\) | 4.00000 | 0.241649 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.50000 | + | 2.59808i | −0.0902894 | + | 0.156386i | ||||
\(277\) | 1.00000 | − | 1.73205i | 0.0600842 | − | 0.104069i | −0.834419 | − | 0.551131i | \(-0.814196\pi\) |
0.894503 | + | 0.447062i | \(0.147530\pi\) | |||||||
\(278\) | 4.00000 | + | 6.92820i | 0.239904 | + | 0.415526i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.0000 | −0.656205 | −0.328102 | − | 0.944642i | \(-0.606409\pi\) | ||||
−0.328102 | + | 0.944642i | \(0.606409\pi\) | |||||||
\(282\) | 6.50000 | + | 11.2583i | 0.387069 | + | 0.670424i | ||||
\(283\) | 13.0000 | − | 22.5167i | 0.772770 | − | 1.33848i | −0.163270 | − | 0.986581i | \(-0.552204\pi\) |
0.936039 | − | 0.351895i | \(-0.114463\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | 18.0000 | − | 15.5885i | 1.06251 | − | 0.920158i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.00000 | + | 6.92820i | −0.234484 | + | 0.406138i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | −1.00000 | −0.0584206 | −0.0292103 | − | 0.999573i | \(-0.509299\pi\) | ||||
−0.0292103 | + | 0.999573i | \(0.509299\pi\) | |||||||
\(294\) | −1.00000 | + | 6.92820i | −0.0583212 | + | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.50000 | − | 4.33013i | −0.145310 | − | 0.251684i | ||||
\(297\) | −2.50000 | + | 4.33013i | −0.145065 | + | 0.251259i | ||||
\(298\) | 3.00000 | − | 5.19615i | 0.173785 | − | 0.301005i | ||||
\(299\) | −1.50000 | − | 2.59808i | −0.0867472 | − | 0.150251i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.0000 | − | 17.3205i | 1.15278 | − | 0.998337i | ||||
\(302\) | −22.0000 | −1.26596 | ||||||||
\(303\) | 4.00000 | + | 6.92820i | 0.229794 | + | 0.398015i | ||||
\(304\) | −3.50000 | + | 6.06218i | −0.200739 | + | 0.347690i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −1.00000 | − | 1.73205i | −0.0571662 | − | 0.0990148i | ||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | −12.5000 | − | 4.33013i | −0.712254 | − | 0.246732i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.0000 | − | 22.5167i | 0.737162 | − | 1.27680i | −0.216606 | − | 0.976259i | \(-0.569499\pi\) |
0.953768 | − | 0.300544i | \(-0.0971681\pi\) | |||||||
\(312\) | −0.500000 | + | 0.866025i | −0.0283069 | + | 0.0490290i | ||||
\(313\) | −5.00000 | − | 8.66025i | −0.282617 | − | 0.489506i | 0.689412 | − | 0.724370i | \(-0.257869\pi\) |
−0.972028 | + | 0.234863i | \(0.924536\pi\) | |||||||
\(314\) | −13.0000 | −0.733632 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.0000 | −0.787562 | ||||||||
\(317\) | 1.00000 | + | 1.73205i | 0.0561656 | + | 0.0972817i | 0.892741 | − | 0.450570i | \(-0.148779\pi\) |
−0.836576 | + | 0.547852i | \(0.815446\pi\) | |||||||
\(318\) | 0.500000 | − | 0.866025i | 0.0280386 | − | 0.0485643i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | 0.669775 | ||||||||
\(322\) | 1.50000 | + | 7.79423i | 0.0835917 | + | 0.434355i | ||||
\(323\) | 14.0000 | 0.778981 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.00000 | + | 10.3923i | −0.332309 | + | 0.575577i | ||||
\(327\) | −9.00000 | − | 15.5885i | −0.497701 | − | 0.862044i | ||||
\(328\) | −9.00000 | −0.496942 | ||||||||
\(329\) | 32.5000 | + | 11.2583i | 1.79178 | + | 0.620692i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.50000 | + | 12.9904i | 0.412237 | + | 0.714016i | 0.995134 | − | 0.0985303i | \(-0.0314141\pi\) |
−0.582897 | + | 0.812546i | \(0.698081\pi\) | |||||||
\(332\) | −5.00000 | + | 8.66025i | −0.274411 | + | 0.475293i | ||||
\(333\) | −2.50000 | + | 4.33013i | −0.136999 | + | 0.237289i | ||||
\(334\) | −9.50000 | − | 16.4545i | −0.519817 | − | 0.900349i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | − | 1.73205i | 0.109109 | − | 0.0944911i | ||||
\(337\) | 14.0000 | 0.762629 | 0.381314 | − | 0.924445i | \(-0.375472\pi\) | ||||
0.381314 | + | 0.924445i | \(0.375472\pi\) | |||||||
\(338\) | 6.00000 | + | 10.3923i | 0.326357 | + | 0.565267i | ||||
\(339\) | −3.00000 | + | 5.19615i | −0.162938 | + | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.0000 | − | 25.9808i | −0.812296 | − | 1.40694i | ||||
\(342\) | 7.00000 | 0.378517 | ||||||||
\(343\) | 10.0000 | + | 15.5885i | 0.539949 | + | 0.841698i | ||||
\(344\) | −10.0000 | −0.539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.50000 | − | 6.06218i | 0.188161 | − | 0.325905i | ||||
\(347\) | −8.00000 | + | 13.8564i | −0.429463 | + | 0.743851i | −0.996826 | − | 0.0796169i | \(-0.974630\pi\) |
0.567363 | + | 0.823468i | \(0.307964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −24.0000 | −1.28469 | −0.642345 | − | 0.766415i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766415i | \(0.722038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.50000 | + | 4.33013i | 0.133250 | + | 0.230797i | ||||
\(353\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(354\) | 2.00000 | − | 3.46410i | 0.106299 | − | 0.184115i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | −5.00000 | − | 1.73205i | −0.264628 | − | 0.0916698i | ||||
\(358\) | −11.0000 | −0.581368 | ||||||||
\(359\) | 14.0000 | + | 24.2487i | 0.738892 | + | 1.27980i | 0.952995 | + | 0.302987i | \(0.0979839\pi\) |
−0.214103 | + | 0.976811i | \(0.568683\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | + | 25.9808i | −0.789474 | + | 1.36741i | ||||
\(362\) | 1.00000 | + | 1.73205i | 0.0525588 | + | 0.0910346i | ||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | 0.500000 | + | 2.59808i | 0.0262071 | + | 0.136176i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.00000 | − | 1.73205i | −0.0522708 | − | 0.0905357i | ||||
\(367\) | −18.5000 | + | 32.0429i | −0.965692 | + | 1.67263i | −0.257948 | + | 0.966159i | \(0.583046\pi\) |
−0.707744 | + | 0.706469i | \(0.750287\pi\) | |||||||
\(368\) | 1.50000 | − | 2.59808i | 0.0781929 | − | 0.135434i | ||||
\(369\) | 4.50000 | + | 7.79423i | 0.234261 | + | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.500000 | − | 2.59808i | −0.0259587 | − | 0.134885i | ||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | 3.00000 | + | 5.19615i | 0.155334 | + | 0.269047i | 0.933181 | − | 0.359408i | \(-0.117021\pi\) |
−0.777847 | + | 0.628454i | \(0.783688\pi\) | |||||||
\(374\) | 5.00000 | − | 8.66025i | 0.258544 | − | 0.447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.50000 | − | 11.2583i | −0.335212 | − | 0.580604i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.50000 | − | 0.866025i | −0.128586 | − | 0.0445435i | ||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.50000 | + | 7.79423i | −0.230542 | + | 0.399310i | ||||
\(382\) | 8.00000 | − | 13.8564i | 0.409316 | − | 0.708955i | ||||
\(383\) | −4.50000 | − | 7.79423i | −0.229939 | − | 0.398266i | 0.727851 | − | 0.685736i | \(-0.240519\pi\) |
−0.957790 | + | 0.287469i | \(0.907186\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.0000 | 0.916176 | ||||||||
\(387\) | 5.00000 | + | 8.66025i | 0.254164 | + | 0.440225i | ||||
\(388\) | 4.00000 | − | 6.92820i | 0.203069 | − | 0.351726i | ||||
\(389\) | −3.00000 | + | 5.19615i | −0.152106 | + | 0.263455i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) |
0.779895 | + | 0.625910i | \(0.215272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.00000 | −0.303433 | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 17.0000 | 0.857537 | ||||||||
\(394\) | −13.5000 | − | 23.3827i | −0.680120 | − | 1.17800i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | − | 4.33013i | 0.125630 | − | 0.217597i | ||||
\(397\) | −1.00000 | − | 1.73205i | −0.0501886 | − | 0.0869291i | 0.839840 | − | 0.542834i | \(-0.182649\pi\) |
−0.890028 | + | 0.455905i | \(0.849316\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 14.0000 | − | 12.1244i | 0.700877 | − | 0.606977i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | + | 23.3827i | 0.674158 | + | 1.16768i | 0.976714 | + | 0.214544i | \(0.0688266\pi\) |
−0.302556 | + | 0.953131i | \(0.597840\pi\) | |||||||
\(402\) | −3.00000 | + | 5.19615i | −0.149626 | + | 0.259161i | ||||
\(403\) | −3.00000 | + | 5.19615i | −0.149441 | + | 0.258839i | ||||
\(404\) | −4.00000 | − | 6.92820i | −0.199007 | − | 0.344691i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −25.0000 | −1.23920 | ||||||||
\(408\) | 1.00000 | + | 1.73205i | 0.0495074 | + | 0.0857493i | ||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.00000 | + | 3.46410i | 0.0986527 | + | 0.170872i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.00000 | − | 10.3923i | −0.0984136 | − | 0.511372i | ||||
\(414\) | −3.00000 | −0.147442 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | − | 0.866025i | 0.0245145 | − | 0.0424604i | ||||
\(417\) | −4.00000 | + | 6.92820i | −0.195881 | + | 0.339276i | ||||
\(418\) | 17.5000 | + | 30.3109i | 0.855953 | + | 1.48255i | ||||
\(419\) | 3.00000 | 0.146560 | 0.0732798 | − | 0.997311i | \(-0.476653\pi\) | ||||
0.0732798 | + | 0.997311i | \(0.476653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | −9.50000 | − | 16.4545i | −0.462453 | − | 0.800992i | ||||
\(423\) | −6.50000 | + | 11.2583i | −0.316041 | + | 0.547399i | ||||
\(424\) | −0.500000 | + | 0.866025i | −0.0242821 | + | 0.0420579i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.00000 | 0.0969003 | ||||||||
\(427\) | −5.00000 | − | 1.73205i | −0.241967 | − | 0.0838198i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 2.50000 | + | 4.33013i | 0.120701 | + | 0.209061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.00000 | + | 15.5885i | −0.433515 | + | 0.750870i | −0.997173 | − | 0.0751385i | \(-0.976060\pi\) |
0.563658 | + | 0.826008i | \(0.309393\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −4.00000 | −0.192228 | −0.0961139 | − | 0.995370i | \(-0.530641\pi\) | ||||
−0.0961139 | + | 0.995370i | \(0.530641\pi\) | |||||||
\(434\) | 12.0000 | − | 10.3923i | 0.576018 | − | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 15.5885i | 0.431022 | + | 0.746552i | ||||
\(437\) | 10.5000 | − | 18.1865i | 0.502283 | − | 0.869980i | ||||
\(438\) | −2.00000 | + | 3.46410i | −0.0955637 | + | 0.165521i | ||||
\(439\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | −2.00000 | −0.0951303 | ||||||||
\(443\) | −3.00000 | − | 5.19615i | −0.142534 | − | 0.246877i | 0.785916 | − | 0.618333i | \(-0.212192\pi\) |
−0.928450 | + | 0.371457i | \(0.878858\pi\) | |||||||
\(444\) | 2.50000 | − | 4.33013i | 0.118645 | − | 0.205499i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | 6.00000 | 0.283790 | ||||||||
\(448\) | −2.00000 | + | 1.73205i | −0.0944911 | + | 0.0818317i | ||||
\(449\) | 9.00000 | 0.424736 | 0.212368 | − | 0.977190i | \(-0.431882\pi\) | ||||
0.212368 | + | 0.977190i | \(0.431882\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.5000 | + | 38.9711i | −1.05948 | + | 1.83508i | ||||
\(452\) | 3.00000 | − | 5.19615i | 0.141108 | − | 0.244406i | ||||
\(453\) | −11.0000 | − | 19.0526i | −0.516825 | − | 0.895167i | ||||
\(454\) | −14.0000 | −0.657053 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | −19.0000 | − | 32.9090i | −0.888783 | − | 1.53942i | −0.841316 | − | 0.540544i | \(-0.818219\pi\) |
−0.0474665 | − | 0.998873i | \(-0.515115\pi\) | |||||||
\(458\) | 2.00000 | − | 3.46410i | 0.0934539 | − | 0.161867i | ||||
\(459\) | 1.00000 | − | 1.73205i | 0.0466760 | − | 0.0808452i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | −2.50000 | − | 12.9904i | −0.116311 | − | 0.604367i | ||||
\(463\) | 15.0000 | 0.697109 | 0.348555 | − | 0.937288i | \(-0.386673\pi\) | ||||
0.348555 | + | 0.937288i | \(0.386673\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.00000 | + | 1.73205i | 0.0462745 | + | 0.0801498i | 0.888235 | − | 0.459390i | \(-0.151932\pi\) |
−0.841960 | + | 0.539539i | \(0.818598\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 3.00000 | + | 15.5885i | 0.138527 | + | 0.719808i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.50000 | − | 11.2583i | −0.299504 | − | 0.518756i | ||||
\(472\) | −2.00000 | + | 3.46410i | −0.0920575 | + | 0.159448i | ||||
\(473\) | −25.0000 | + | 43.3013i | −1.14950 | + | 1.99099i | ||||
\(474\) | −7.00000 | − | 12.1244i | −0.321521 | − | 0.556890i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.00000 | + | 1.73205i | 0.229175 | + | 0.0793884i | ||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | −10.0000 | − | 17.3205i | −0.457389 | − | 0.792222i | ||||
\(479\) | −4.00000 | + | 6.92820i | −0.182765 | + | 0.316558i | −0.942821 | − | 0.333300i | \(-0.891838\pi\) |
0.760056 | + | 0.649857i | \(0.225171\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.50000 | + | 4.33013i | 0.113990 | + | 0.197437i | ||||
\(482\) | −1.00000 | −0.0455488 | ||||||||
\(483\) | −6.00000 | + | 5.19615i | −0.273009 | + | 0.236433i | ||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | 12.0000 | − | 20.7846i | 0.543772 | − | 0.941841i | −0.454911 | − | 0.890537i | \(-0.650329\pi\) |
0.998683 | − | 0.0513038i | \(-0.0163377\pi\) | |||||||
\(488\) | 1.00000 | + | 1.73205i | 0.0452679 | + | 0.0784063i | ||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 24.0000 | 1.08310 | 0.541552 | − | 0.840667i | \(-0.317837\pi\) | ||||
0.541552 | + | 0.840667i | \(0.317837\pi\) | |||||||
\(492\) | −4.50000 | − | 7.79423i | −0.202876 | − | 0.351391i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 3.50000 | − | 6.06218i | 0.157472 | − | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 4.00000 | − | 3.46410i | 0.179425 | − | 0.155386i | ||||
\(498\) | −10.0000 | −0.448111 | ||||||||
\(499\) | 14.0000 | + | 24.2487i | 0.626726 | + | 1.08552i | 0.988204 | + | 0.153141i | \(0.0489388\pi\) |
−0.361478 | + | 0.932381i | \(0.617728\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.50000 | − | 16.4545i | 0.424429 | − | 0.735132i | ||||
\(502\) | 1.50000 | + | 2.59808i | 0.0669483 | + | 0.115958i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 2.50000 | + | 0.866025i | 0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −7.50000 | − | 12.9904i | −0.333416 | − | 0.577493i | ||||
\(507\) | −6.00000 | + | 10.3923i | −0.266469 | + | 0.461538i | ||||
\(508\) | 4.50000 | − | 7.79423i | 0.199655 | − | 0.345813i | ||||
\(509\) | −7.00000 | − | 12.1244i | −0.310270 | − | 0.537403i | 0.668151 | − | 0.744026i | \(-0.267086\pi\) |
−0.978421 | + | 0.206623i | \(0.933753\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.00000 | + | 10.3923i | 0.0884748 | + | 0.459728i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.50000 | + | 6.06218i | 0.154529 | + | 0.267652i | ||||
\(514\) | −5.00000 | + | 8.66025i | −0.220541 | + | 0.381987i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −5.00000 | − | 8.66025i | −0.220113 | − | 0.381246i | ||||
\(517\) | −65.0000 | −2.85870 | ||||||||
\(518\) | −2.50000 | − | 12.9904i | −0.109844 | − | 0.570765i | ||||
\(519\) | 7.00000 | 0.307266 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.50000 | − | 12.9904i | 0.328581 | − | 0.569119i | −0.653650 | − | 0.756797i | \(-0.726763\pi\) |
0.982231 | + | 0.187678i | \(0.0600963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.00000 | + | 10.3923i | 0.262362 | + | 0.454424i | 0.966869 | − | 0.255273i | \(-0.0821653\pi\) |
−0.704507 | + | 0.709697i | \(0.748832\pi\) | |||||||
\(524\) | −17.0000 | −0.742648 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | −1.04645 | ||||||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | −2.50000 | + | 4.33013i | −0.108799 | + | 0.188445i | ||||
\(529\) | 7.00000 | − | 12.1244i | 0.304348 | − | 0.527146i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.00000 | 0.173585 | ||||||||
\(532\) | −14.0000 | + | 12.1244i | −0.606977 | + | 0.525657i | ||||
\(533\) | 9.00000 | 0.389833 | ||||||||
\(534\) | 5.00000 | + | 8.66025i | 0.216371 | + | 0.374766i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.00000 | − | 5.19615i | 0.129580 | − | 0.224440i | ||||
\(537\) | −5.50000 | − | 9.52628i | −0.237343 | − | 0.411089i | ||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | −27.5000 | − | 21.6506i | −1.18451 | − | 0.932559i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.00000 | − | 3.46410i | −0.0859867 | − | 0.148933i | 0.819825 | − | 0.572615i | \(-0.194071\pi\) |
−0.905811 | + | 0.423681i | \(0.860738\pi\) | |||||||
\(542\) | −4.00000 | + | 6.92820i | −0.171815 | + | 0.297592i | ||||
\(543\) | −1.00000 | + | 1.73205i | −0.0429141 | + | 0.0743294i | ||||
\(544\) | −1.00000 | − | 1.73205i | −0.0428746 | − | 0.0742611i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | + | 1.73205i | −0.0855921 | + | 0.0741249i | ||||
\(547\) | 14.0000 | 0.598597 | 0.299298 | − | 0.954160i | \(-0.403247\pi\) | ||||
0.299298 | + | 0.954160i | \(0.403247\pi\) | |||||||
\(548\) | −2.00000 | − | 3.46410i | −0.0854358 | − | 0.147979i | ||||
\(549\) | 1.00000 | − | 1.73205i | 0.0426790 | − | 0.0739221i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.00000 | 0.127688 | ||||||||
\(553\) | −35.0000 | − | 12.1244i | −1.48835 | − | 0.515580i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.00000 | − | 6.92820i | 0.169638 | − | 0.293821i | ||||
\(557\) | −19.5000 | + | 33.7750i | −0.826242 | + | 1.43109i | 0.0747252 | + | 0.997204i | \(0.476192\pi\) |
−0.900967 | + | 0.433888i | \(0.857141\pi\) | |||||||
\(558\) | 3.00000 | + | 5.19615i | 0.127000 | + | 0.219971i | ||||
\(559\) | 10.0000 | 0.422955 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.0000 | 0.422200 | ||||||||
\(562\) | 5.50000 | + | 9.52628i | 0.232003 | + | 0.401842i | ||||
\(563\) | 15.0000 | − | 25.9808i | 0.632175 | − | 1.09496i | −0.354932 | − | 0.934892i | \(-0.615496\pi\) |
0.987106 | − | 0.160066i | \(-0.0511708\pi\) | |||||||
\(564\) | 6.50000 | − | 11.2583i | 0.273699 | − | 0.474061i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.0000 | −1.09286 | ||||||||
\(567\) | −0.500000 | − | 2.59808i | −0.0209980 | − | 0.109109i | ||||
\(568\) | −2.00000 | −0.0839181 | ||||||||
\(569\) | 1.50000 | + | 2.59808i | 0.0628833 | + | 0.108917i | 0.895753 | − | 0.444552i | \(-0.146637\pi\) |
−0.832870 | + | 0.553469i | \(0.813304\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | − | 6.92820i | 0.167395 | − | 0.289936i | −0.770108 | − | 0.637913i | \(-0.779798\pi\) |
0.937503 | + | 0.347977i | \(0.113131\pi\) | |||||||
\(572\) | −2.50000 | − | 4.33013i | −0.104530 | − | 0.181052i | ||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | −22.5000 | − | 7.79423i | −0.939132 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 12.0000 | − | 20.7846i | 0.499567 | − | 0.865275i | −0.500433 | − | 0.865775i | \(-0.666826\pi\) |
1.00000 | 0.000500448i | \(0.000159298\pi\) | ||||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | 9.00000 | + | 15.5885i | 0.374027 | + | 0.647834i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.0000 | + | 17.3205i | −0.829740 | + | 0.718576i | ||||
\(582\) | 8.00000 | 0.331611 | ||||||||
\(583\) | 2.50000 | + | 4.33013i | 0.103539 | + | 0.179336i | ||||
\(584\) | 2.00000 | − | 3.46410i | 0.0827606 | − | 0.143346i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.500000 | + | 0.866025i | 0.0206548 | + | 0.0357752i | ||||
\(587\) | −2.00000 | −0.0825488 | −0.0412744 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412744 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(588\) | 6.50000 | − | 2.59808i | 0.268055 | − | 0.107143i | ||||
\(589\) | −42.0000 | −1.73058 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5000 | − | 23.3827i | 0.555316 | − | 0.961835i | ||||
\(592\) | −2.50000 | + | 4.33013i | −0.102749 | + | 0.177967i | ||||
\(593\) | −17.0000 | − | 29.4449i | −0.698106 | − | 1.20916i | −0.969122 | − | 0.246581i | \(-0.920693\pi\) |
0.271016 | − | 0.962575i | \(-0.412640\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.00000 | −0.245770 | ||||||||
\(597\) | −7.00000 | − | 12.1244i | −0.286491 | − | 0.496217i | ||||
\(598\) | −1.50000 | + | 2.59808i | −0.0613396 | + | 0.106243i | ||||
\(599\) | 14.0000 | − | 24.2487i | 0.572024 | − | 0.990775i | −0.424333 | − | 0.905506i | \(-0.639492\pi\) |
0.996358 | − | 0.0852695i | \(-0.0271751\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −30.0000 | −1.22373 | −0.611863 | − | 0.790964i | \(-0.709580\pi\) | ||||
−0.611863 | + | 0.790964i | \(0.709580\pi\) | |||||||
\(602\) | −25.0000 | − | 8.66025i | −1.01892 | − | 0.352966i | ||||
\(603\) | −6.00000 | −0.244339 | ||||||||
\(604\) | 11.0000 | + | 19.0526i | 0.447584 | + | 0.775238i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.00000 | − | 6.92820i | 0.162489 | − | 0.281439i | ||||
\(607\) | 6.50000 | + | 11.2583i | 0.263827 | + | 0.456962i | 0.967256 | − | 0.253804i | \(-0.0816819\pi\) |
−0.703429 | + | 0.710766i | \(0.748349\pi\) | |||||||
\(608\) | 7.00000 | 0.283887 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.50000 | + | 11.2583i | 0.262962 | + | 0.455463i | ||||
\(612\) | −1.00000 | + | 1.73205i | −0.0404226 | + | 0.0700140i | ||||
\(613\) | 9.50000 | − | 16.4545i | 0.383701 | − | 0.664590i | −0.607887 | − | 0.794024i | \(-0.707983\pi\) |
0.991588 | + | 0.129433i | \(0.0413159\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.50000 | + | 12.9904i | 0.100728 | + | 0.523397i | ||||
\(617\) | −30.0000 | −1.20775 | −0.603877 | − | 0.797077i | \(-0.706378\pi\) | ||||
−0.603877 | + | 0.797077i | \(0.706378\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.50000 | + | 12.9904i | −0.301450 | + | 0.522127i | −0.976465 | − | 0.215677i | \(-0.930804\pi\) |
0.675014 | + | 0.737805i | \(0.264137\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.50000 | − | 2.59808i | −0.0601929 | − | 0.104257i | ||||
\(622\) | −26.0000 | −1.04251 | ||||||||
\(623\) | 25.0000 | + | 8.66025i | 1.00160 | + | 0.346966i | ||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −5.00000 | + | 8.66025i | −0.199840 | + | 0.346133i | ||||
\(627\) | −17.5000 | + | 30.3109i | −0.698883 | + | 1.21050i | ||||
\(628\) | 6.50000 | + | 11.2583i | 0.259378 | + | 0.449256i | ||||
\(629\) | 10.0000 | 0.398726 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.0000 | 0.716569 | 0.358284 | − | 0.933613i | \(-0.383362\pi\) | ||||
0.358284 | + | 0.933613i | \(0.383362\pi\) | |||||||
\(632\) | 7.00000 | + | 12.1244i | 0.278445 | + | 0.482281i | ||||
\(633\) | 9.50000 | − | 16.4545i | 0.377591 | − | 0.654007i | ||||
\(634\) | 1.00000 | − | 1.73205i | 0.0397151 | − | 0.0687885i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −1.00000 | + | 6.92820i | −0.0396214 | + | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.00000 | + | 1.73205i | 0.0395594 | + | 0.0685189i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5000 | − | 28.5788i | 0.651711 | − | 1.12880i | −0.330997 | − | 0.943632i | \(-0.607385\pi\) |
0.982708 | − | 0.185164i | \(-0.0592817\pi\) | |||||||
\(642\) | −6.00000 | − | 10.3923i | −0.236801 | − | 0.410152i | ||||
\(643\) | −38.0000 | −1.49857 | −0.749287 | − | 0.662246i | \(-0.769604\pi\) | ||||
−0.749287 | + | 0.662246i | \(0.769604\pi\) | |||||||
\(644\) | 6.00000 | − | 5.19615i | 0.236433 | − | 0.204757i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.00000 | − | 12.1244i | −0.275411 | − | 0.477026i | ||||
\(647\) | −0.500000 | + | 0.866025i | −0.0196570 | + | 0.0340470i | −0.875687 | − | 0.482880i | \(-0.839591\pi\) |
0.856030 | + | 0.516927i | \(0.172924\pi\) | |||||||
\(648\) | −0.500000 | + | 0.866025i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 10.0000 | + | 17.3205i | 0.392534 | + | 0.679889i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | + | 5.19615i | 0.587896 | + | 0.203653i | ||||
\(652\) | 12.0000 | 0.469956 | ||||||||
\(653\) | 2.50000 | + | 4.33013i | 0.0978326 | + | 0.169451i | 0.910787 | − | 0.412876i | \(-0.135476\pi\) |
−0.812955 | + | 0.582327i | \(0.802142\pi\) | |||||||
\(654\) | −9.00000 | + | 15.5885i | −0.351928 | + | 0.609557i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.50000 | + | 7.79423i | 0.175695 | + | 0.304314i | ||||
\(657\) | −4.00000 | −0.156055 | ||||||||
\(658\) | −6.50000 | − | 33.7750i | −0.253396 | − | 1.31669i | ||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | + | 34.6410i | −0.777910 | + | 1.34738i | 0.155235 | + | 0.987878i | \(0.450387\pi\) |
−0.933144 | + | 0.359502i | \(0.882947\pi\) | |||||||
\(662\) | 7.50000 | − | 12.9904i | 0.291496 | − | 0.504885i | ||||
\(663\) | −1.00000 | − | 1.73205i | −0.0388368 | − | 0.0672673i | ||||
\(664\) | 10.0000 | 0.388075 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 5.00000 | 0.193746 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | −9.50000 | + | 16.4545i | −0.367566 | + | 0.636643i | ||||
\(669\) | −8.00000 | + | 13.8564i | −0.309298 | + | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | −2.50000 | − | 0.866025i | −0.0964396 | − | 0.0334077i | ||||
\(673\) | −36.0000 | −1.38770 | −0.693849 | − | 0.720121i | \(-0.744086\pi\) | ||||
−0.693849 | + | 0.720121i | \(0.744086\pi\) | |||||||
\(674\) | −7.00000 | − | 12.1244i | −0.269630 | − | 0.467013i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.00000 | − | 10.3923i | 0.230769 | − | 0.399704i | ||||
\(677\) | 16.5000 | + | 28.5788i | 0.634147 | + | 1.09837i | 0.986695 | + | 0.162581i | \(0.0519817\pi\) |
−0.352549 | + | 0.935793i | \(0.614685\pi\) | |||||||
\(678\) | 6.00000 | 0.230429 | ||||||||
\(679\) | 16.0000 | − | 13.8564i | 0.614024 | − | 0.531760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | − | 12.1244i | −0.268241 | − | 0.464606i | ||||
\(682\) | −15.0000 | + | 25.9808i | −0.574380 | + | 0.994855i | ||||
\(683\) | −2.00000 | + | 3.46410i | −0.0765279 | + | 0.132550i | −0.901750 | − | 0.432259i | \(-0.857717\pi\) |
0.825222 | + | 0.564809i | \(0.191050\pi\) | |||||||
\(684\) | −3.50000 | − | 6.06218i | −0.133826 | − | 0.231793i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 4.00000 | 0.152610 | ||||||||
\(688\) | 5.00000 | + | 8.66025i | 0.190623 | + | 0.330169i | ||||
\(689\) | 0.500000 | − | 0.866025i | 0.0190485 | − | 0.0329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.0000 | + | 17.3205i | 0.380418 | + | 0.658903i | 0.991122 | − | 0.132956i | \(-0.0424468\pi\) |
−0.610704 | + | 0.791859i | \(0.709113\pi\) | |||||||
\(692\) | −7.00000 | −0.266100 | ||||||||
\(693\) | 10.0000 | − | 8.66025i | 0.379869 | − | 0.328976i | ||||
\(694\) | 16.0000 | 0.607352 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.00000 | − | 15.5885i | 0.340899 | − | 0.590455i | ||||
\(698\) | 12.0000 | + | 20.7846i | 0.454207 | + | 0.786709i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.0000 | 0.679851 | 0.339925 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339925 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(702\) | −0.500000 | − | 0.866025i | −0.0188713 | − | 0.0326860i | ||||
\(703\) | −17.5000 | + | 30.3109i | −0.660025 | + | 1.14320i | ||||
\(704\) | 2.50000 | − | 4.33013i | 0.0942223 | − | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.00000 | − | 20.7846i | −0.150435 | − | 0.781686i | ||||
\(708\) | −4.00000 | −0.150329 | ||||||||
\(709\) | −8.00000 | − | 13.8564i | −0.300446 | − | 0.520388i | 0.675791 | − | 0.737093i | \(-0.263802\pi\) |
−0.976237 | + | 0.216705i | \(0.930469\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.00000 | − | 12.1244i | 0.262521 | − | 0.454699i | ||||
\(712\) | −5.00000 | − | 8.66025i | −0.187383 | − | 0.324557i | ||||
\(713\) | 18.0000 | 0.674105 | ||||||||
\(714\) | 1.00000 | + | 5.19615i | 0.0374241 | + | 0.194461i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.50000 | + | 9.52628i | 0.205545 | + | 0.356014i | ||||
\(717\) | 10.0000 | − | 17.3205i | 0.373457 | − | 0.646846i | ||||
\(718\) | 14.0000 | − | 24.2487i | 0.522475 | − | 0.904954i | ||||
\(719\) | 1.00000 | + | 1.73205i | 0.0372937 | + | 0.0645946i | 0.884070 | − | 0.467355i | \(-0.154793\pi\) |
−0.846776 | + | 0.531949i | \(0.821460\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | −0.500000 | − | 0.866025i | −0.0185952 | − | 0.0322078i | ||||
\(724\) | 1.00000 | − | 1.73205i | 0.0371647 | − | 0.0643712i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | + | 12.1244i | 0.259794 | + | 0.449977i | ||||
\(727\) | −53.0000 | −1.96566 | −0.982831 | − | 0.184510i | \(-0.940930\pi\) | ||||
−0.982831 | + | 0.184510i | \(0.940930\pi\) | |||||||
\(728\) | 2.00000 | − | 1.73205i | 0.0741249 | − | 0.0641941i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000 | − | 17.3205i | 0.369863 | − | 0.640622i | ||||
\(732\) | −1.00000 | + | 1.73205i | −0.0369611 | + | 0.0640184i | ||||
\(733\) | −10.5000 | − | 18.1865i | −0.387826 | − | 0.671735i | 0.604331 | − | 0.796734i | \(-0.293441\pi\) |
−0.992157 | + | 0.124999i | \(0.960107\pi\) | |||||||
\(734\) | 37.0000 | 1.36569 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.00000 | −0.110581 | ||||||||
\(737\) | −15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | ||||
\(738\) | 4.50000 | − | 7.79423i | 0.165647 | − | 0.286910i | ||||
\(739\) | −23.5000 | + | 40.7032i | −0.864461 | + | 1.49729i | 0.00311943 | + | 0.999995i | \(0.499007\pi\) |
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.00000 | 0.257151 | ||||||||
\(742\) | −2.00000 | + | 1.73205i | −0.0734223 | + | 0.0635856i | ||||
\(743\) | 31.0000 | 1.13728 | 0.568640 | − | 0.822587i | \(-0.307470\pi\) | ||||
0.568640 | + | 0.822587i | \(0.307470\pi\) | |||||||
\(744\) | −3.00000 | − | 5.19615i | −0.109985 | − | 0.190500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.00000 | − | 5.19615i | 0.109838 | − | 0.190245i | ||||
\(747\) | −5.00000 | − | 8.66025i | −0.182940 | − | 0.316862i | ||||
\(748\) | −10.0000 | −0.365636 | ||||||||
\(749\) | −30.0000 | − | 10.3923i | −1.09618 | − | 0.379727i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.00000 | − | 3.46410i | −0.0729810 | − | 0.126407i | 0.827225 | − | 0.561870i | \(-0.189918\pi\) |
−0.900207 | + | 0.435463i | \(0.856585\pi\) | |||||||
\(752\) | −6.50000 | + | 11.2583i | −0.237031 | + | 0.410549i | ||||
\(753\) | −1.50000 | + | 2.59808i | −0.0546630 | + | 0.0946792i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | + | 2.59808i | 0.0181848 | + | 0.0944911i | ||||
\(757\) | 26.0000 | 0.944986 | 0.472493 | − | 0.881334i | \(-0.343354\pi\) | ||||
0.472493 | + | 0.881334i | \(0.343354\pi\) | |||||||
\(758\) | 0.500000 | + | 0.866025i | 0.0181608 | + | 0.0314555i | ||||
\(759\) | 7.50000 | − | 12.9904i | 0.272233 | − | 0.471521i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.50000 | + | 2.59808i | 0.0543750 | + | 0.0941802i | 0.891932 | − | 0.452170i | \(-0.149350\pi\) |
−0.837557 | + | 0.546350i | \(0.816017\pi\) | |||||||
\(762\) | 9.00000 | 0.326036 | ||||||||
\(763\) | 9.00000 | + | 46.7654i | 0.325822 | + | 1.69302i | ||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.50000 | + | 7.79423i | −0.162592 | + | 0.281617i | ||||
\(767\) | 2.00000 | − | 3.46410i | 0.0722158 | − | 0.125081i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | 51.0000 | 1.83911 | 0.919554 | − | 0.392965i | \(-0.128551\pi\) | ||||
0.919554 | + | 0.392965i | \(0.128551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.0000 | −0.360141 | ||||||||
\(772\) | −9.00000 | − | 15.5885i | −0.323917 | − | 0.561041i | ||||
\(773\) | −18.5000 | + | 32.0429i | −0.665399 | + | 1.15250i | 0.313778 | + | 0.949496i | \(0.398405\pi\) |
−0.979177 | + | 0.203008i | \(0.934928\pi\) | |||||||
\(774\) | 5.00000 | − | 8.66025i | 0.179721 | − | 0.311286i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.00000 | −0.287183 | ||||||||
\(777\) | 10.0000 | − | 8.66025i | 0.358748 | − | 0.310685i | ||||
\(778\) | 6.00000 | 0.215110 | ||||||||
\(779\) | 31.5000 | + | 54.5596i | 1.12860 | + | 1.95480i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.00000 | + | 8.66025i | −0.178914 | + | 0.309888i | ||||
\(782\) | 3.00000 | + | 5.19615i | 0.107280 | + | 0.185814i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −8.50000 | − | 14.7224i | −0.303185 | − | 0.525132i | ||||
\(787\) | 19.0000 | − | 32.9090i | 0.677277 | − | 1.17308i | −0.298521 | − | 0.954403i | \(-0.596493\pi\) |
0.975798 | − | 0.218675i | \(-0.0701734\pi\) | |||||||
\(788\) | −13.5000 | + | 23.3827i | −0.480918 | + | 0.832974i | ||||
\(789\) | −12.0000 | − | 20.7846i | −0.427211 | − | 0.739952i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | − | 10.3923i | 0.426671 | − | 0.369508i | ||||
\(792\) | −5.00000 | −0.177667 | ||||||||
\(793\) | −1.00000 | − | 1.73205i | −0.0355110 | − | 0.0615069i | ||||
\(794\) | −1.00000 | + | 1.73205i | −0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.00000 | + | 12.1244i | 0.248108 | + | 0.429736i | ||||
\(797\) | 30.0000 | 1.06265 | 0.531327 | − | 0.847167i | \(-0.321693\pi\) | ||||
0.531327 | + | 0.847167i | \(0.321693\pi\) | |||||||
\(798\) | −17.5000 | − | 6.06218i | −0.619493 | − | 0.214599i | ||||
\(799\) | 26.0000 | 0.919814 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.00000 | + | 8.66025i | −0.176666 | + | 0.305995i | ||||
\(802\) | 13.5000 | − | 23.3827i | 0.476702 | − | 0.825671i | ||||
\(803\) | −10.0000 | − | 17.3205i | −0.352892 | − | 0.611227i | ||||
\(804\) | 6.00000 | 0.211604 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6.00000 | 0.211341 | ||||||||
\(807\) | 7.00000 | + | 12.1244i | 0.246412 | + | 0.426798i | ||||
\(808\) | −4.00000 | + | 6.92820i | −0.140720 | + | 0.243733i | ||||
\(809\) | 4.50000 | − | 7.79423i | 0.158212 | − | 0.274030i | −0.776012 | − | 0.630718i | \(-0.782761\pi\) |
0.934224 | + | 0.356687i | \(0.116094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0000 | 0.386262 | 0.193131 | − | 0.981173i | \(-0.438136\pi\) | ||||
0.193131 | + | 0.981173i | \(0.438136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.00000 | −0.280572 | ||||||||
\(814\) | 12.5000 | + | 21.6506i | 0.438125 | + | 0.758854i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.00000 | − | 1.73205i | 0.0350070 | − | 0.0606339i | ||||
\(817\) | 35.0000 | + | 60.6218i | 1.22449 | + | 2.12089i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −2.50000 | − | 0.866025i | −0.0873571 | − | 0.0302614i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.00000 | − | 5.19615i | −0.104701 | − | 0.181347i | 0.808915 | − | 0.587925i | \(-0.200055\pi\) |
−0.913616 | + | 0.406578i | \(0.866722\pi\) | |||||||
\(822\) | 2.00000 | − | 3.46410i | 0.0697580 | − | 0.120824i | ||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.00000 | + | 6.92820i | −0.278356 | + | 0.241063i | ||||
\(827\) | 42.0000 | 1.46048 | 0.730242 | − | 0.683189i | \(-0.239408\pi\) | ||||
0.730242 | + | 0.683189i | \(0.239408\pi\) | |||||||
\(828\) | 1.50000 | + | 2.59808i | 0.0521286 | + | 0.0902894i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.00000 | − | 1.73205i | −0.0346896 | − | 0.0600842i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | 11.0000 | + | 8.66025i | 0.381127 | + | 0.300060i | ||||
\(834\) | 8.00000 | 0.277017 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.5000 | − | 30.3109i | 0.605250 | − | 1.04832i | ||||
\(837\) | −3.00000 | + | 5.19615i | −0.103695 | + | 0.179605i | ||||
\(838\) | −1.50000 | − | 2.59808i | −0.0518166 | − | 0.0897491i | ||||
\(839\) | 2.00000 | 0.0690477 | 0.0345238 | − | 0.999404i | \(-0.489009\pi\) | ||||
0.0345238 | + | 0.999404i | \(0.489009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 10.0000 | + | 17.3205i | 0.344623 | + | 0.596904i | ||||
\(843\) | −5.50000 | + | 9.52628i | −0.189430 | + | 0.328102i | ||||
\(844\) | −9.50000 | + | 16.4545i | −0.327003 | + | 0.566387i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.0000 | 0.446949 | ||||||||
\(847\) | 35.0000 | + | 12.1244i | 1.20261 | + | 0.416598i | ||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −13.0000 | − | 22.5167i | −0.446159 | − | 0.772770i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.50000 | − | 12.9904i | 0.257097 | − | 0.445305i | ||||
\(852\) | −1.00000 | − | 1.73205i | −0.0342594 | − | 0.0593391i | ||||
\(853\) | 49.0000 | 1.67773 | 0.838864 | − | 0.544341i | \(-0.183220\pi\) | ||||
0.838864 | + | 0.544341i | \(0.183220\pi\) | |||||||
\(854\) | 1.00000 | + | 5.19615i | 0.0342193 | + | 0.177809i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.00000 | + | 10.3923i | 0.205076 | + | 0.355202i | ||||
\(857\) | −28.0000 | + | 48.4974i | −0.956462 | + | 1.65664i | −0.225475 | + | 0.974249i | \(0.572393\pi\) |
−0.730987 | + | 0.682391i | \(0.760940\pi\) | |||||||
\(858\) | 2.50000 | − | 4.33013i | 0.0853486 | − | 0.147828i | ||||
\(859\) | −18.0000 | − | 31.1769i | −0.614152 | − | 1.06374i | −0.990533 | − | 0.137277i | \(-0.956165\pi\) |
0.376381 | − | 0.926465i | \(-0.377169\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.50000 | − | 23.3827i | −0.153360 | − | 0.796880i | ||||
\(862\) | 18.0000 | 0.613082 | ||||||||
\(863\) | 7.50000 | + | 12.9904i | 0.255303 | + | 0.442198i | 0.964978 | − | 0.262332i | \(-0.0844915\pi\) |
−0.709675 | + | 0.704529i | \(0.751158\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.00000 | + | 3.46410i | 0.0679628 | + | 0.117715i | ||||
\(867\) | 13.0000 | 0.441503 | ||||||||
\(868\) | −15.0000 | − | 5.19615i | −0.509133 | − | 0.176369i | ||||
\(869\) | 70.0000 | 2.37459 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00000 | + | 5.19615i | −0.101651 | + | 0.176065i | ||||
\(872\) | 9.00000 | − | 15.5885i | 0.304778 | − | 0.527892i | ||||
\(873\) | 4.00000 | + | 6.92820i | 0.135379 | + | 0.234484i | ||||
\(874\) | −21.0000 | −0.710336 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 4.00000 | 0.135147 | ||||||||
\(877\) | −13.5000 | − | 23.3827i | −0.455863 | − | 0.789577i | 0.542875 | − | 0.839814i | \(-0.317336\pi\) |
−0.998737 | + | 0.0502365i | \(0.984002\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.500000 | + | 0.866025i | −0.0168646 | + | 0.0292103i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.00000 | −0.101073 | −0.0505363 | − | 0.998722i | \(-0.516093\pi\) | ||||
−0.0505363 | + | 0.998722i | \(0.516093\pi\) | |||||||
\(882\) | 5.50000 | + | 4.33013i | 0.185195 | + | 0.145803i | ||||
\(883\) | 52.0000 | 1.74994 | 0.874970 | − | 0.484178i | \(-0.160881\pi\) | ||||
0.874970 | + | 0.484178i | \(0.160881\pi\) | |||||||
\(884\) | 1.00000 | + | 1.73205i | 0.0336336 | + | 0.0582552i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.00000 | + | 5.19615i | −0.100787 | + | 0.174568i | ||||
\(887\) | −6.00000 | − | 10.3923i | −0.201460 | − | 0.348939i | 0.747539 | − | 0.664218i | \(-0.231235\pi\) |
−0.948999 | + | 0.315279i | \(0.897902\pi\) | |||||||
\(888\) | −5.00000 | −0.167789 | ||||||||
\(889\) | 18.0000 | − | 15.5885i | 0.603701 | − | 0.522820i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | + | 4.33013i | 0.0837532 | + | 0.145065i | ||||
\(892\) | 8.00000 | − | 13.8564i | 0.267860 | − | 0.463947i | ||||
\(893\) | −45.5000 | + | 78.8083i | −1.52260 | + | 2.63722i | ||||
\(894\) | −3.00000 | − | 5.19615i | −0.100335 | − | 0.173785i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.50000 | + | 0.866025i | 0.0835191 | + | 0.0289319i | ||||
\(897\) | −3.00000 | −0.100167 | ||||||||
\(898\) | −4.50000 | − | 7.79423i | −0.150167 | − | 0.260097i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.00000 | − | 1.73205i | −0.0333148 | − | 0.0577030i | ||||
\(902\) | 45.0000 | 1.49834 | ||||||||
\(903\) | −5.00000 | − | 25.9808i | −0.166390 | − | 0.864586i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.0000 | + | 19.0526i | −0.365451 | + | 0.632979i | ||||
\(907\) | −8.00000 | + | 13.8564i | −0.265636 | + | 0.460094i | −0.967730 | − | 0.251990i | \(-0.918915\pi\) |
0.702094 | + | 0.712084i | \(0.252248\pi\) | |||||||
\(908\) | 7.00000 | + | 12.1244i | 0.232303 | + | 0.402361i | ||||
\(909\) | 8.00000 | 0.265343 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.00000 | −0.198789 | −0.0993944 | − | 0.995048i | \(-0.531691\pi\) | ||||
−0.0993944 | + | 0.995048i | \(0.531691\pi\) | |||||||
\(912\) | 3.50000 | + | 6.06218i | 0.115897 | + | 0.200739i | ||||
\(913\) | 25.0000 | − | 43.3013i | 0.827379 | − | 1.43306i | ||||
\(914\) | −19.0000 | + | 32.9090i | −0.628464 | + | 1.08853i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.00000 | −0.132164 | ||||||||
\(917\) | −42.5000 | − | 14.7224i | −1.40347 | − | 0.486178i | ||||
\(918\) | −2.00000 | −0.0660098 | ||||||||
\(919\) | −28.0000 | − | 48.4974i | −0.923635 | − | 1.59978i | −0.793742 | − | 0.608254i | \(-0.791870\pi\) |
−0.129893 | − | 0.991528i | \(-0.541463\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.00000 | + | 1.73205i | −0.0329511 | + | 0.0570730i | ||||
\(922\) | 6.00000 | + | 10.3923i | 0.197599 | + | 0.342252i | ||||
\(923\) | 2.00000 | 0.0658308 | ||||||||
\(924\) | −10.0000 | + | 8.66025i | −0.328976 | + | 0.284901i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −7.50000 | − | 12.9904i | −0.246465 | − | 0.426890i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.5000 | − | 28.5788i | −0.541347 | − | 0.937641i | −0.998827 | − | 0.0484211i | \(-0.984581\pi\) |
0.457480 | − | 0.889220i | \(-0.348752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.5000 | + | 18.1865i | −1.49120 | + | 0.596040i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.0000 | − | 22.5167i | −0.425601 | − | 0.737162i | ||||
\(934\) | 1.00000 | − | 1.73205i | 0.0327210 | − | 0.0566744i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | + | 0.866025i | 0.0163430 | + | 0.0283069i | ||||
\(937\) | 34.0000 | 1.11073 | 0.555366 | − | 0.831606i | \(-0.312578\pi\) | ||||
0.555366 | + | 0.831606i | \(0.312578\pi\) | |||||||
\(938\) | 12.0000 | − | 10.3923i | 0.391814 | − | 0.339321i | ||||
\(939\) | −10.0000 | −0.326338 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(942\) | −6.50000 | + | 11.2583i | −0.211781 | + | 0.366816i | ||||
\(943\) | −13.5000 | − | 23.3827i | −0.439620 | − | 0.761445i | ||||
\(944\) | 4.00000 | 0.130189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50.0000 | 1.62564 | ||||||||
\(947\) | 6.00000 | + | 10.3923i | 0.194974 | + | 0.337705i | 0.946892 | − | 0.321552i | \(-0.104204\pi\) |
−0.751918 | + | 0.659256i | \(0.770871\pi\) | |||||||
\(948\) | −7.00000 | + | 12.1244i | −0.227349 | + | 0.393781i | ||||
\(949\) | −2.00000 | + | 3.46410i | −0.0649227 | + | 0.112449i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.00000 | 0.0648544 | ||||||||
\(952\) | −1.00000 | − | 5.19615i | −0.0324102 | − | 0.168408i | ||||
\(953\) | 24.0000 | 0.777436 | 0.388718 | − | 0.921357i | \(-0.372918\pi\) | ||||
0.388718 | + | 0.921357i | \(0.372918\pi\) | |||||||
\(954\) | −0.500000 | − | 0.866025i | −0.0161881 | − | 0.0280386i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10.0000 | + | 17.3205i | −0.323423 | + | 0.560185i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000 | 0.258468 | ||||||||
\(959\) | −2.00000 | − | 10.3923i | −0.0645834 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | 2.50000 | − | 4.33013i | 0.0806032 | − | 0.139609i | ||||
\(963\) | 6.00000 | − | 10.3923i | 0.193347 | − | 0.334887i | ||||
\(964\) | 0.500000 | + | 0.866025i | 0.0161039 | + | 0.0278928i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 7.50000 | + | 2.59808i | 0.241309 | + | 0.0835917i | ||||
\(967\) | 24.0000 | 0.771788 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(968\) | −7.00000 | − | 12.1244i | −0.224989 | − | 0.389692i | ||||
\(969\) | 7.00000 | − | 12.1244i | 0.224872 | − | 0.389490i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5000 | − | 33.7750i | −0.625785 | − | 1.08389i | −0.988389 | − | 0.151948i | \(-0.951445\pi\) |
0.362604 | − | 0.931943i | \(-0.381888\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 16.0000 | − | 13.8564i | 0.512936 | − | 0.444216i | ||||
\(974\) | −24.0000 | −0.769010 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00000 | − | 1.73205i | 0.0320092 | − | 0.0554416i | ||||
\(977\) | 21.0000 | − | 36.3731i | 0.671850 | − | 1.16368i | −0.305530 | − | 0.952183i | \(-0.598833\pi\) |
0.977379 | − | 0.211495i | \(-0.0678332\pi\) | |||||||
\(978\) | 6.00000 | + | 10.3923i | 0.191859 | + | 0.332309i | ||||
\(979\) | −50.0000 | −1.59801 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | −12.0000 | − | 20.7846i | −0.382935 | − | 0.663264i | ||||
\(983\) | 16.5000 | − | 28.5788i | 0.526268 | − | 0.911523i | −0.473263 | − | 0.880921i | \(-0.656924\pi\) |
0.999532 | − | 0.0306024i | \(-0.00974257\pi\) | |||||||
\(984\) | −4.50000 | + | 7.79423i | −0.143455 | + | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 26.0000 | − | 22.5167i | 0.827589 | − | 0.716713i | ||||
\(988\) | −7.00000 | −0.222700 | ||||||||
\(989\) | −15.0000 | − | 25.9808i | −0.476972 | − | 0.826140i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000 | − | 31.1769i | 0.571789 | − | 0.990367i | −0.424594 | − | 0.905384i | \(-0.639583\pi\) |
0.996382 | − | 0.0849833i | \(-0.0270837\pi\) | |||||||
\(992\) | 3.00000 | + | 5.19615i | 0.0952501 | + | 0.164978i | ||||
\(993\) | 15.0000 | 0.476011 | ||||||||
\(994\) | −5.00000 | − | 1.73205i | −0.158590 | − | 0.0549373i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 5.00000 | + | 8.66025i | 0.158431 | + | 0.274411i | ||||
\(997\) | −5.00000 | + | 8.66025i | −0.158352 | + | 0.274273i | −0.934274 | − | 0.356555i | \(-0.883951\pi\) |
0.775923 | + | 0.630828i | \(0.217285\pi\) | |||||||
\(998\) | 14.0000 | − | 24.2487i | 0.443162 | − | 0.767580i | ||||
\(999\) | 2.50000 | + | 4.33013i | 0.0790965 | + | 0.136999i |
(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 | 1050.2.i.f.151.1 | 2 | ||
5.2 | odd | 4 | 210.2.n.a.109.2 | yes | 4 | ||
5.3 | odd | 4 | 210.2.n.a.109.1 | yes | 4 | ||
5.4 | even | 2 | 1050.2.i.o.151.1 | 2 | |||
7.2 | even | 3 | inner | 1050.2.i.f.751.1 | 2 | ||
7.3 | odd | 6 | 7350.2.a.ch.1.1 | 1 | |||
7.4 | even | 3 | 7350.2.a.bn.1.1 | 1 | |||
15.2 | even | 4 | 630.2.u.c.109.1 | 4 | |||
15.8 | even | 4 | 630.2.u.c.109.2 | 4 | |||
20.3 | even | 4 | 1680.2.di.a.529.1 | 4 | |||
20.7 | even | 4 | 1680.2.di.a.529.2 | 4 | |||
35.2 | odd | 12 | 210.2.n.a.79.1 | ✓ | 4 | ||
35.3 | even | 12 | 1470.2.g.a.589.1 | 2 | |||
35.4 | even | 6 | 7350.2.a.t.1.1 | 1 | |||
35.9 | even | 6 | 1050.2.i.o.751.1 | 2 | |||
35.12 | even | 12 | 1470.2.n.i.79.1 | 4 | |||
35.13 | even | 4 | 1470.2.n.i.949.1 | 4 | |||
35.17 | even | 12 | 1470.2.g.a.589.2 | 2 | |||
35.18 | odd | 12 | 1470.2.g.f.589.1 | 2 | |||
35.23 | odd | 12 | 210.2.n.a.79.2 | yes | 4 | ||
35.24 | odd | 6 | 7350.2.a.b.1.1 | 1 | |||
35.27 | even | 4 | 1470.2.n.i.949.2 | 4 | |||
35.32 | odd | 12 | 1470.2.g.f.589.2 | 2 | |||
35.33 | even | 12 | 1470.2.n.i.79.2 | 4 | |||
105.2 | even | 12 | 630.2.u.c.289.2 | 4 | |||
105.23 | even | 12 | 630.2.u.c.289.1 | 4 | |||
140.23 | even | 12 | 1680.2.di.a.289.2 | 4 | |||
140.107 | even | 12 | 1680.2.di.a.289.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.n.a.79.1 | ✓ | 4 | 35.2 | odd | 12 | ||
210.2.n.a.79.2 | yes | 4 | 35.23 | odd | 12 | ||
210.2.n.a.109.1 | yes | 4 | 5.3 | odd | 4 | ||
210.2.n.a.109.2 | yes | 4 | 5.2 | odd | 4 | ||
630.2.u.c.109.1 | 4 | 15.2 | even | 4 | |||
630.2.u.c.109.2 | 4 | 15.8 | even | 4 | |||
630.2.u.c.289.1 | 4 | 105.23 | even | 12 | |||
630.2.u.c.289.2 | 4 | 105.2 | even | 12 | |||
1050.2.i.f.151.1 | 2 | 1.1 | even | 1 | trivial | ||
1050.2.i.f.751.1 | 2 | 7.2 | even | 3 | inner | ||
1050.2.i.o.151.1 | 2 | 5.4 | even | 2 | |||
1050.2.i.o.751.1 | 2 | 35.9 | even | 6 | |||
1470.2.g.a.589.1 | 2 | 35.3 | even | 12 | |||
1470.2.g.a.589.2 | 2 | 35.17 | even | 12 | |||
1470.2.g.f.589.1 | 2 | 35.18 | odd | 12 | |||
1470.2.g.f.589.2 | 2 | 35.32 | odd | 12 | |||
1470.2.n.i.79.1 | 4 | 35.12 | even | 12 | |||
1470.2.n.i.79.2 | 4 | 35.33 | even | 12 | |||
1470.2.n.i.949.1 | 4 | 35.13 | even | 4 | |||
1470.2.n.i.949.2 | 4 | 35.27 | even | 4 | |||
1680.2.di.a.289.1 | 4 | 140.107 | even | 12 | |||
1680.2.di.a.289.2 | 4 | 140.23 | even | 12 | |||
1680.2.di.a.529.1 | 4 | 20.3 | even | 4 | |||
1680.2.di.a.529.2 | 4 | 20.7 | even | 4 | |||
7350.2.a.b.1.1 | 1 | 35.24 | odd | 6 | |||
7350.2.a.t.1.1 | 1 | 35.4 | even | 6 | |||
7350.2.a.bn.1.1 | 1 | 7.4 | even | 3 | |||
7350.2.a.ch.1.1 | 1 | 7.3 | odd | 6 |