Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,2,Mod(121,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.121");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.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: | \(1.67685844245\) |
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: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.121 |
Dual form | 210.2.i.a.151.1 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −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 | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 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 | ||||
\(10\) | −0.500000 | − | 0.866025i | −0.158114 | − | 0.273861i | ||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 7.00000 | 1.94145 | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) | ||||
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | −2.50000 | + | 0.866025i | −0.668153 | + | 0.231455i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −0.500000 | + | 0.866025i | −0.114708 | + | 0.198680i | −0.917663 | − | 0.397360i | \(-0.869927\pi\) |
0.802955 | + | 0.596040i | \(0.203260\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.500000 | − | 2.59808i | 0.109109 | − | 0.566947i | ||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | −0.913434 | − | 0.406986i | \(-0.866580\pi\) |
0.809177 | + | 0.587565i | \(0.199913\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | −3.50000 | + | 6.06218i | −0.686406 | + | 1.18889i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.500000 | − | 2.59808i | 0.0944911 | − | 0.490990i | ||||
\(29\) | −8.00000 | −1.48556 | −0.742781 | − | 0.669534i | \(-0.766494\pi\) | ||||
−0.742781 | + | 0.669534i | \(0.766494\pi\) | |||||||
\(30\) | −0.500000 | + | 0.866025i | −0.0912871 | + | 0.158114i | ||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.500000 | − | 0.866025i | 0.0870388 | − | 0.150756i | ||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | −2.50000 | + | 0.866025i | −0.422577 | + | 0.146385i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.50000 | − | 2.59808i | 0.246598 | − | 0.427121i | −0.715981 | − | 0.698119i | \(-0.754020\pi\) |
0.962580 | + | 0.270998i | \(0.0873538\pi\) | |||||||
\(38\) | −0.500000 | − | 0.866025i | −0.0811107 | − | 0.140488i | ||||
\(39\) | −3.50000 | − | 6.06218i | −0.560449 | − | 0.970725i | ||||
\(40\) | −0.500000 | + | 0.866025i | −0.0790569 | + | 0.136931i | ||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 2.00000 | + | 1.73205i | 0.308607 | + | 0.267261i | ||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 1.00000 | + | 6.92820i | 0.142857 | + | 0.989743i | ||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | −3.50000 | − | 6.06218i | −0.485363 | − | 0.840673i | ||||
\(53\) | 0.500000 | + | 0.866025i | 0.0686803 | + | 0.118958i | 0.898321 | − | 0.439340i | \(-0.144788\pi\) |
−0.829640 | + | 0.558298i | \(0.811454\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | 4.00000 | − | 6.92820i | 0.525226 | − | 0.909718i | ||||
\(59\) | −6.00000 | − | 10.3923i | −0.781133 | − | 1.35296i | −0.931282 | − | 0.364299i | \(-0.881308\pi\) |
0.150148 | − | 0.988663i | \(-0.452025\pi\) | |||||||
\(60\) | −0.500000 | − | 0.866025i | −0.0645497 | − | 0.111803i | ||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | −2.50000 | + | 0.866025i | −0.314970 | + | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −3.50000 | + | 6.06218i | −0.434122 | + | 0.751921i | ||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | −6.00000 | − | 10.3923i | −0.733017 | − | 1.26962i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.222571 | − | 0.974916i | \(-0.428555\pi\) | |||||||
\(68\) | 2.00000 | − | 3.46410i | 0.242536 | − | 0.420084i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0.500000 | − | 2.59808i | 0.0597614 | − | 0.310530i | ||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 7.00000 | + | 12.1244i | 0.819288 | + | 1.41905i | 0.906208 | + | 0.422833i | \(0.138964\pi\) |
−0.0869195 | + | 0.996215i | \(0.527702\pi\) | |||||||
\(74\) | 1.50000 | + | 2.59808i | 0.174371 | + | 0.302020i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | −0.500000 | + | 2.59808i | −0.0569803 | + | 0.296078i | ||||
\(78\) | 7.00000 | 0.792594 | ||||||||
\(79\) | −2.00000 | + | 3.46410i | −0.225018 | + | 0.389742i | −0.956325 | − | 0.292306i | \(-0.905577\pi\) |
0.731307 | + | 0.682048i | \(0.238911\pi\) | |||||||
\(80\) | −0.500000 | − | 0.866025i | −0.0559017 | − | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.50000 | + | 7.79423i | −0.496942 | + | 0.860729i | ||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | −2.50000 | + | 0.866025i | −0.272772 | + | 0.0944911i | ||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 2.00000 | − | 3.46410i | 0.215666 | − | 0.373544i | ||||
\(87\) | 4.00000 | + | 6.92820i | 0.428845 | + | 0.742781i | ||||
\(88\) | 0.500000 | + | 0.866025i | 0.0533002 | + | 0.0923186i | ||||
\(89\) | 1.00000 | − | 1.73205i | 0.106000 | − | 0.183597i | −0.808146 | − | 0.588982i | \(-0.799529\pi\) |
0.914146 | + | 0.405385i | \(0.132862\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 14.0000 | + | 12.1244i | 1.46760 | + | 1.27098i | ||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −3.00000 | + | 5.19615i | −0.311086 | + | 0.538816i | ||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | −0.500000 | − | 0.866025i | −0.0512989 | − | 0.0888523i | ||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −16.0000 | −1.62455 | −0.812277 | − | 0.583272i | \(-0.801772\pi\) | ||||
−0.812277 | + | 0.583272i | \(0.801772\pi\) | |||||||
\(98\) | −6.50000 | − | 2.59808i | −0.656599 | − | 0.262445i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | −0.500000 | + | 0.866025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 2.00000 | + | 3.46410i | 0.198030 | + | 0.342997i | ||||
\(103\) | −8.00000 | + | 13.8564i | −0.788263 | + | 1.36531i | 0.138767 | + | 0.990325i | \(0.455686\pi\) |
−0.927030 | + | 0.374987i | \(0.877647\pi\) | |||||||
\(104\) | 7.00000 | 0.686406 | ||||||||
\(105\) | 2.00000 | + | 1.73205i | 0.195180 | + | 0.169031i | ||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 9.00000 | − | 15.5885i | 0.870063 | − | 1.50699i | 0.00813215 | − | 0.999967i | \(-0.497411\pi\) |
0.861931 | − | 0.507026i | \(-0.169255\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | 5.00000 | + | 8.66025i | 0.478913 | + | 0.829502i | 0.999708 | − | 0.0241802i | \(-0.00769755\pi\) |
−0.520794 | + | 0.853682i | \(0.674364\pi\) | |||||||
\(110\) | 0.500000 | − | 0.866025i | 0.0476731 | − | 0.0825723i | ||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | −2.50000 | + | 0.866025i | −0.236228 | + | 0.0818317i | ||||
\(113\) | −6.00000 | −0.564433 | −0.282216 | − | 0.959351i | \(-0.591070\pi\) | ||||
−0.282216 | + | 0.959351i | \(0.591070\pi\) | |||||||
\(114\) | −0.500000 | + | 0.866025i | −0.0468293 | + | 0.0811107i | ||||
\(115\) | −0.500000 | − | 0.866025i | −0.0466252 | − | 0.0807573i | ||||
\(116\) | 4.00000 | + | 6.92820i | 0.371391 | + | 0.643268i | ||||
\(117\) | −3.50000 | + | 6.06218i | −0.323575 | + | 0.560449i | ||||
\(118\) | 12.0000 | 1.10469 | ||||||||
\(119\) | −2.00000 | + | 10.3923i | −0.183340 | + | 0.952661i | ||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 2.00000 | + | 3.46410i | 0.181071 | + | 0.313625i | ||||
\(123\) | −4.50000 | − | 7.79423i | −0.405751 | − | 0.702782i | ||||
\(124\) | −3.00000 | + | 5.19615i | −0.269408 | + | 0.466628i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 2.00000 | + | 3.46410i | 0.176090 | + | 0.304997i | ||||
\(130\) | −3.50000 | − | 6.06218i | −0.306970 | − | 0.531688i | ||||
\(131\) | 6.50000 | − | 11.2583i | 0.567908 | − | 0.983645i | −0.428865 | − | 0.903369i | \(-0.641086\pi\) |
0.996773 | − | 0.0802763i | \(-0.0255803\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | −2.50000 | + | 0.866025i | −0.216777 | + | 0.0750939i | ||||
\(134\) | 12.0000 | 1.03664 | ||||||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | −0.500000 | + | 0.866025i | −0.0425628 | + | 0.0737210i | ||||
\(139\) | −4.00000 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(140\) | 2.00000 | + | 1.73205i | 0.169031 | + | 0.146385i | ||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | 7.00000 | − | 12.1244i | 0.587427 | − | 1.01745i | ||||
\(143\) | 3.50000 | + | 6.06218i | 0.292685 | + | 0.506945i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 4.00000 | − | 6.92820i | 0.332182 | − | 0.575356i | ||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | 5.50000 | − | 4.33013i | 0.453632 | − | 0.357143i | ||||
\(148\) | −3.00000 | −0.246598 | ||||||||
\(149\) | 2.00000 | − | 3.46410i | 0.163846 | − | 0.283790i | −0.772399 | − | 0.635138i | \(-0.780943\pi\) |
0.936245 | + | 0.351348i | \(0.114277\pi\) | |||||||
\(150\) | −0.500000 | − | 0.866025i | −0.0408248 | − | 0.0707107i | ||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | −0.500000 | + | 0.866025i | −0.0405554 | + | 0.0702439i | ||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | −2.00000 | − | 1.73205i | −0.161165 | − | 0.139573i | ||||
\(155\) | 6.00000 | 0.481932 | ||||||||
\(156\) | −3.50000 | + | 6.06218i | −0.280224 | + | 0.485363i | ||||
\(157\) | −7.50000 | − | 12.9904i | −0.598565 | − | 1.03675i | −0.993033 | − | 0.117836i | \(-0.962404\pi\) |
0.394468 | − | 0.918910i | \(-0.370929\pi\) | |||||||
\(158\) | −2.00000 | − | 3.46410i | −0.159111 | − | 0.275589i | ||||
\(159\) | 0.500000 | − | 0.866025i | 0.0396526 | − | 0.0686803i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −2.50000 | + | 0.866025i | −0.197028 | + | 0.0682524i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −4.00000 | + | 6.92820i | −0.313304 | + | 0.542659i | −0.979076 | − | 0.203497i | \(-0.934769\pi\) |
0.665771 | + | 0.746156i | \(0.268103\pi\) | |||||||
\(164\) | −4.50000 | − | 7.79423i | −0.351391 | − | 0.608627i | ||||
\(165\) | 0.500000 | + | 0.866025i | 0.0389249 | + | 0.0674200i | ||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | −5.00000 | −0.386912 | −0.193456 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(168\) | 0.500000 | − | 2.59808i | 0.0385758 | − | 0.200446i | ||||
\(169\) | 36.0000 | 2.76923 | ||||||||
\(170\) | 2.00000 | − | 3.46410i | 0.153393 | − | 0.265684i | ||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 10.5000 | − | 18.1865i | 0.798300 | − | 1.38270i | −0.122422 | − | 0.992478i | \(-0.539066\pi\) |
0.920722 | − | 0.390218i | \(-0.127601\pi\) | |||||||
\(174\) | −8.00000 | −0.606478 | ||||||||
\(175\) | 0.500000 | − | 2.59808i | 0.0377964 | − | 0.196396i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −6.00000 | + | 10.3923i | −0.450988 | + | 0.781133i | ||||
\(178\) | 1.00000 | + | 1.73205i | 0.0749532 | + | 0.129823i | ||||
\(179\) | −6.50000 | − | 11.2583i | −0.485833 | − | 0.841487i | 0.514035 | − | 0.857769i | \(-0.328150\pi\) |
−0.999867 | + | 0.0162823i | \(0.994817\pi\) | |||||||
\(180\) | −0.500000 | + | 0.866025i | −0.0372678 | + | 0.0645497i | ||||
\(181\) | −12.0000 | −0.891953 | −0.445976 | − | 0.895045i | \(-0.647144\pi\) | ||||
−0.445976 | + | 0.895045i | \(0.647144\pi\) | |||||||
\(182\) | −17.5000 | + | 6.06218i | −1.29719 | + | 0.449359i | ||||
\(183\) | −4.00000 | −0.295689 | ||||||||
\(184\) | −0.500000 | + | 0.866025i | −0.0368605 | + | 0.0638442i | ||||
\(185\) | 1.50000 | + | 2.59808i | 0.110282 | + | 0.191014i | ||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | −2.00000 | + | 3.46410i | −0.146254 | + | 0.253320i | ||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | 2.00000 | + | 1.73205i | 0.145479 | + | 0.125988i | ||||
\(190\) | 1.00000 | 0.0725476 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −13.0000 | − | 22.5167i | −0.935760 | − | 1.62078i | −0.773272 | − | 0.634074i | \(-0.781381\pi\) |
−0.162488 | − | 0.986710i | \(-0.551952\pi\) | |||||||
\(194\) | 8.00000 | − | 13.8564i | 0.574367 | − | 0.994832i | ||||
\(195\) | 7.00000 | 0.501280 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | −3.00000 | −0.213741 | −0.106871 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106871 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(198\) | 0.500000 | − | 0.866025i | 0.0355335 | − | 0.0615457i | ||||
\(199\) | 6.00000 | + | 10.3923i | 0.425329 | + | 0.736691i | 0.996451 | − | 0.0841740i | \(-0.0268252\pi\) |
−0.571122 | + | 0.820865i | \(0.693492\pi\) | |||||||
\(200\) | −0.500000 | − | 0.866025i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −16.0000 | − | 13.8564i | −1.12298 | − | 0.972529i | ||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | −4.50000 | + | 7.79423i | −0.314294 | + | 0.544373i | ||||
\(206\) | −8.00000 | − | 13.8564i | −0.557386 | − | 0.965422i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | −3.50000 | + | 6.06218i | −0.242681 | + | 0.420336i | ||||
\(209\) | −1.00000 | −0.0691714 | ||||||||
\(210\) | −2.50000 | + | 0.866025i | −0.172516 | + | 0.0597614i | ||||
\(211\) | −15.0000 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(212\) | 0.500000 | − | 0.866025i | 0.0343401 | − | 0.0594789i | ||||
\(213\) | 7.00000 | + | 12.1244i | 0.479632 | + | 0.830747i | ||||
\(214\) | 9.00000 | + | 15.5885i | 0.615227 | + | 1.06561i | ||||
\(215\) | 2.00000 | − | 3.46410i | 0.136399 | − | 0.236250i | ||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.00000 | − | 15.5885i | 0.203653 | − | 1.05821i | ||||
\(218\) | −10.0000 | −0.677285 | ||||||||
\(219\) | 7.00000 | − | 12.1244i | 0.473016 | − | 0.819288i | ||||
\(220\) | 0.500000 | + | 0.866025i | 0.0337100 | + | 0.0583874i | ||||
\(221\) | 14.0000 | + | 24.2487i | 0.941742 | + | 1.63114i | ||||
\(222\) | 1.50000 | − | 2.59808i | 0.100673 | − | 0.174371i | ||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0.500000 | − | 2.59808i | 0.0334077 | − | 0.173591i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 10.0000 | + | 17.3205i | 0.663723 | + | 1.14960i | 0.979630 | + | 0.200812i | \(0.0643581\pi\) |
−0.315906 | + | 0.948790i | \(0.602309\pi\) | |||||||
\(228\) | −0.500000 | − | 0.866025i | −0.0331133 | − | 0.0573539i | ||||
\(229\) | 11.0000 | − | 19.0526i | 0.726900 | − | 1.25903i | −0.231287 | − | 0.972886i | \(-0.574293\pi\) |
0.958187 | − | 0.286143i | \(-0.0923732\pi\) | |||||||
\(230\) | 1.00000 | 0.0659380 | ||||||||
\(231\) | 2.50000 | − | 0.866025i | 0.164488 | − | 0.0569803i | ||||
\(232\) | −8.00000 | −0.525226 | ||||||||
\(233\) | −13.0000 | + | 22.5167i | −0.851658 | + | 1.47512i | 0.0280525 | + | 0.999606i | \(0.491069\pi\) |
−0.879711 | + | 0.475509i | \(0.842264\pi\) | |||||||
\(234\) | −3.50000 | − | 6.06218i | −0.228802 | − | 0.396297i | ||||
\(235\) | 1.50000 | + | 2.59808i | 0.0978492 | + | 0.169480i | ||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | 4.00000 | 0.259828 | ||||||||
\(238\) | −8.00000 | − | 6.92820i | −0.518563 | − | 0.449089i | ||||
\(239\) | −6.00000 | −0.388108 | −0.194054 | − | 0.980991i | \(-0.562164\pi\) | ||||
−0.194054 | + | 0.980991i | \(0.562164\pi\) | |||||||
\(240\) | −0.500000 | + | 0.866025i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | 5.00000 | + | 8.66025i | 0.321412 | + | 0.556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −4.00000 | −0.256074 | ||||||||
\(245\) | −6.50000 | − | 2.59808i | −0.415270 | − | 0.165985i | ||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | −3.50000 | + | 6.06218i | −0.222700 | + | 0.385727i | ||||
\(248\) | −3.00000 | − | 5.19615i | −0.190500 | − | 0.329956i | ||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | −0.500000 | + | 0.866025i | −0.0316228 | + | 0.0547723i | ||||
\(251\) | −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 | ||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | −2.50000 | + | 4.33013i | −0.156864 | + | 0.271696i | ||||
\(255\) | 2.00000 | + | 3.46410i | 0.125245 | + | 0.216930i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 4.00000 | − | 6.92820i | 0.249513 | − | 0.432169i | −0.713878 | − | 0.700270i | \(-0.753063\pi\) |
0.963391 | + | 0.268101i | \(0.0863961\pi\) | |||||||
\(258\) | −4.00000 | −0.249029 | ||||||||
\(259\) | 7.50000 | − | 2.59808i | 0.466027 | − | 0.161437i | ||||
\(260\) | 7.00000 | 0.434122 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 6.50000 | + | 11.2583i | 0.401571 | + | 0.695542i | ||||
\(263\) | 8.00000 | + | 13.8564i | 0.493301 | + | 0.854423i | 0.999970 | − | 0.00771799i | \(-0.00245674\pi\) |
−0.506669 | + | 0.862141i | \(0.669123\pi\) | |||||||
\(264\) | 0.500000 | − | 0.866025i | 0.0307729 | − | 0.0533002i | ||||
\(265\) | −1.00000 | −0.0614295 | ||||||||
\(266\) | 0.500000 | − | 2.59808i | 0.0306570 | − | 0.159298i | ||||
\(267\) | −2.00000 | −0.122398 | ||||||||
\(268\) | −6.00000 | + | 10.3923i | −0.366508 | + | 0.634811i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | −0.500000 | − | 0.866025i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 3.50000 | − | 18.1865i | 0.211830 | − | 1.10070i | ||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 0.500000 | − | 0.866025i | 0.0301511 | − | 0.0522233i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | 1.00000 | + | 1.73205i | 0.0600842 | + | 0.104069i | 0.894503 | − | 0.447062i | \(-0.147530\pi\) |
−0.834419 | + | 0.551131i | \(0.814196\pi\) | |||||||
\(278\) | 2.00000 | − | 3.46410i | 0.119952 | − | 0.207763i | ||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | −2.50000 | + | 0.866025i | −0.149404 | + | 0.0517549i | ||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | 1.50000 | − | 2.59808i | 0.0893237 | − | 0.154713i | ||||
\(283\) | 1.00000 | + | 1.73205i | 0.0594438 | + | 0.102960i | 0.894216 | − | 0.447636i | \(-0.147734\pi\) |
−0.834772 | + | 0.550596i | \(0.814401\pi\) | |||||||
\(284\) | 7.00000 | + | 12.1244i | 0.415374 | + | 0.719448i | ||||
\(285\) | −0.500000 | + | 0.866025i | −0.0296174 | + | 0.0512989i | ||||
\(286\) | −7.00000 | −0.413919 | ||||||||
\(287\) | 18.0000 | + | 15.5885i | 1.06251 | + | 0.920158i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | 4.00000 | + | 6.92820i | 0.234888 | + | 0.406838i | ||||
\(291\) | 8.00000 | + | 13.8564i | 0.468968 | + | 0.812277i | ||||
\(292\) | 7.00000 | − | 12.1244i | 0.409644 | − | 0.709524i | ||||
\(293\) | 9.00000 | 0.525786 | 0.262893 | − | 0.964825i | \(-0.415323\pi\) | ||||
0.262893 | + | 0.964825i | \(0.415323\pi\) | |||||||
\(294\) | 1.00000 | + | 6.92820i | 0.0583212 | + | 0.404061i | ||||
\(295\) | 12.0000 | 0.698667 | ||||||||
\(296\) | 1.50000 | − | 2.59808i | 0.0871857 | − | 0.151010i | ||||
\(297\) | 0.500000 | + | 0.866025i | 0.0290129 | + | 0.0502519i | ||||
\(298\) | 2.00000 | + | 3.46410i | 0.115857 | + | 0.200670i | ||||
\(299\) | −3.50000 | + | 6.06218i | −0.202410 | + | 0.350585i | ||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | −8.00000 | − | 6.92820i | −0.461112 | − | 0.399335i | ||||
\(302\) | −2.00000 | −0.115087 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.500000 | − | 0.866025i | −0.0286770 | − | 0.0496700i | ||||
\(305\) | 2.00000 | + | 3.46410i | 0.114520 | + | 0.198354i | ||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | 8.00000 | 0.456584 | 0.228292 | − | 0.973593i | \(-0.426686\pi\) | ||||
0.228292 | + | 0.973593i | \(0.426686\pi\) | |||||||
\(308\) | 2.50000 | − | 0.866025i | 0.142451 | − | 0.0493464i | ||||
\(309\) | 16.0000 | 0.910208 | ||||||||
\(310\) | −3.00000 | + | 5.19615i | −0.170389 | + | 0.295122i | ||||
\(311\) | −8.00000 | − | 13.8564i | −0.453638 | − | 0.785725i | 0.544970 | − | 0.838455i | \(-0.316541\pi\) |
−0.998609 | + | 0.0527306i | \(0.983208\pi\) | |||||||
\(312\) | −3.50000 | − | 6.06218i | −0.198148 | − | 0.343203i | ||||
\(313\) | 12.0000 | − | 20.7846i | 0.678280 | − | 1.17482i | −0.297218 | − | 0.954810i | \(-0.596059\pi\) |
0.975499 | − | 0.220006i | \(-0.0706077\pi\) | |||||||
\(314\) | 15.0000 | 0.846499 | ||||||||
\(315\) | 0.500000 | − | 2.59808i | 0.0281718 | − | 0.146385i | ||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | −5.00000 | + | 8.66025i | −0.280828 | + | 0.486408i | −0.971589 | − | 0.236675i | \(-0.923942\pi\) |
0.690761 | + | 0.723083i | \(0.257276\pi\) | |||||||
\(318\) | 0.500000 | + | 0.866025i | 0.0280386 | + | 0.0485643i | ||||
\(319\) | −4.00000 | − | 6.92820i | −0.223957 | − | 0.387905i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | 0.500000 | − | 2.59808i | 0.0278639 | − | 0.144785i | ||||
\(323\) | −4.00000 | −0.222566 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −3.50000 | − | 6.06218i | −0.194145 | − | 0.336269i | ||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | 5.00000 | − | 8.66025i | 0.276501 | − | 0.478913i | ||||
\(328\) | 9.00000 | 0.496942 | ||||||||
\(329\) | 7.50000 | − | 2.59808i | 0.413488 | − | 0.143237i | ||||
\(330\) | −1.00000 | −0.0550482 | ||||||||
\(331\) | 4.50000 | − | 7.79423i | 0.247342 | − | 0.428410i | −0.715445 | − | 0.698669i | \(-0.753776\pi\) |
0.962788 | + | 0.270259i | \(0.0871094\pi\) | |||||||
\(332\) | −6.00000 | − | 10.3923i | −0.329293 | − | 0.570352i | ||||
\(333\) | 1.50000 | + | 2.59808i | 0.0821995 | + | 0.142374i | ||||
\(334\) | 2.50000 | − | 4.33013i | 0.136794 | − | 0.236934i | ||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 2.00000 | + | 1.73205i | 0.109109 | + | 0.0944911i | ||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | −18.0000 | + | 31.1769i | −0.979071 | + | 1.69580i | ||||
\(339\) | 3.00000 | + | 5.19615i | 0.162938 | + | 0.282216i | ||||
\(340\) | 2.00000 | + | 3.46410i | 0.108465 | + | 0.187867i | ||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −4.00000 | −0.215666 | ||||||||
\(345\) | −0.500000 | + | 0.866025i | −0.0269191 | + | 0.0466252i | ||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | 17.0000 | + | 29.4449i | 0.912608 | + | 1.58068i | 0.810366 | + | 0.585923i | \(0.199268\pi\) |
0.102241 | + | 0.994760i | \(0.467399\pi\) | |||||||
\(348\) | 4.00000 | − | 6.92820i | 0.214423 | − | 0.371391i | ||||
\(349\) | −28.0000 | −1.49881 | −0.749403 | − | 0.662114i | \(-0.769659\pi\) | ||||
−0.749403 | + | 0.662114i | \(0.769659\pi\) | |||||||
\(350\) | 2.00000 | + | 1.73205i | 0.106904 | + | 0.0925820i | ||||
\(351\) | 7.00000 | 0.373632 | ||||||||
\(352\) | 0.500000 | − | 0.866025i | 0.0266501 | − | 0.0461593i | ||||
\(353\) | 4.00000 | + | 6.92820i | 0.212899 | + | 0.368751i | 0.952620 | − | 0.304162i | \(-0.0983763\pi\) |
−0.739722 | + | 0.672913i | \(0.765043\pi\) | |||||||
\(354\) | −6.00000 | − | 10.3923i | −0.318896 | − | 0.552345i | ||||
\(355\) | 7.00000 | − | 12.1244i | 0.371521 | − | 0.643494i | ||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | 10.0000 | − | 3.46410i | 0.529256 | − | 0.183340i | ||||
\(358\) | 13.0000 | 0.687071 | ||||||||
\(359\) | −18.0000 | + | 31.1769i | −0.950004 | + | 1.64545i | −0.204595 | + | 0.978847i | \(0.565588\pi\) |
−0.745409 | + | 0.666608i | \(0.767746\pi\) | |||||||
\(360\) | −0.500000 | − | 0.866025i | −0.0263523 | − | 0.0456435i | ||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | 6.00000 | − | 10.3923i | 0.315353 | − | 0.546207i | ||||
\(363\) | −10.0000 | −0.524864 | ||||||||
\(364\) | 3.50000 | − | 18.1865i | 0.183450 | − | 0.953233i | ||||
\(365\) | −14.0000 | −0.732793 | ||||||||
\(366\) | 2.00000 | − | 3.46410i | 0.104542 | − | 0.181071i | ||||
\(367\) | −9.50000 | − | 16.4545i | −0.495896 | − | 0.858917i | 0.504093 | − | 0.863649i | \(-0.331827\pi\) |
−0.999989 | + | 0.00473247i | \(0.998494\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | −4.50000 | + | 7.79423i | −0.234261 | + | 0.405751i | ||||
\(370\) | −3.00000 | −0.155963 | ||||||||
\(371\) | −0.500000 | + | 2.59808i | −0.0259587 | + | 0.134885i | ||||
\(372\) | 6.00000 | 0.311086 | ||||||||
\(373\) | −13.0000 | + | 22.5167i | −0.673114 | + | 1.16587i | 0.303902 | + | 0.952703i | \(0.401711\pi\) |
−0.977016 | + | 0.213165i | \(0.931623\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | −56.0000 | −2.88415 | ||||||||
\(378\) | −2.50000 | + | 0.866025i | −0.128586 | + | 0.0445435i | ||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | −0.500000 | + | 0.866025i | −0.0256495 | + | 0.0444262i | ||||
\(381\) | −2.50000 | − | 4.33013i | −0.128079 | − | 0.221839i | ||||
\(382\) | 5.00000 | + | 8.66025i | 0.255822 | + | 0.443097i | ||||
\(383\) | −6.50000 | + | 11.2583i | −0.332134 | + | 0.575274i | −0.982930 | − | 0.183979i | \(-0.941102\pi\) |
0.650796 | + | 0.759253i | \(0.274435\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −2.00000 | − | 1.73205i | −0.101929 | − | 0.0882735i | ||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | 2.00000 | − | 3.46410i | 0.101666 | − | 0.176090i | ||||
\(388\) | 8.00000 | + | 13.8564i | 0.406138 | + | 0.703452i | ||||
\(389\) | 7.00000 | + | 12.1244i | 0.354914 | + | 0.614729i | 0.987103 | − | 0.160085i | \(-0.0511768\pi\) |
−0.632189 | + | 0.774814i | \(0.717843\pi\) | |||||||
\(390\) | −3.50000 | + | 6.06218i | −0.177229 | + | 0.306970i | ||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 1.00000 | + | 6.92820i | 0.0505076 | + | 0.349927i | ||||
\(393\) | −13.0000 | −0.655763 | ||||||||
\(394\) | 1.50000 | − | 2.59808i | 0.0755689 | − | 0.130889i | ||||
\(395\) | −2.00000 | − | 3.46410i | −0.100631 | − | 0.174298i | ||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | −9.00000 | + | 15.5885i | −0.451697 | + | 0.782362i | −0.998492 | − | 0.0549046i | \(-0.982515\pi\) |
0.546795 | + | 0.837267i | \(0.315848\pi\) | |||||||
\(398\) | −12.0000 | −0.601506 | ||||||||
\(399\) | 2.00000 | + | 1.73205i | 0.100125 | + | 0.0867110i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 8.50000 | − | 14.7224i | 0.424470 | − | 0.735203i | −0.571901 | − | 0.820323i | \(-0.693794\pi\) |
0.996371 | + | 0.0851195i | \(0.0271272\pi\) | |||||||
\(402\) | −6.00000 | − | 10.3923i | −0.299253 | − | 0.518321i | ||||
\(403\) | −21.0000 | − | 36.3731i | −1.04608 | − | 1.81187i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 20.0000 | − | 6.92820i | 0.992583 | − | 0.343841i | ||||
\(407\) | 3.00000 | 0.148704 | ||||||||
\(408\) | 2.00000 | − | 3.46410i | 0.0990148 | − | 0.171499i | ||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | −4.50000 | − | 7.79423i | −0.222239 | − | 0.384930i | ||||
\(411\) | 1.00000 | − | 1.73205i | 0.0493264 | − | 0.0854358i | ||||
\(412\) | 16.0000 | 0.788263 | ||||||||
\(413\) | 6.00000 | − | 31.1769i | 0.295241 | − | 1.53412i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −6.00000 | + | 10.3923i | −0.294528 | + | 0.510138i | ||||
\(416\) | −3.50000 | − | 6.06218i | −0.171602 | − | 0.297223i | ||||
\(417\) | 2.00000 | + | 3.46410i | 0.0979404 | + | 0.169638i | ||||
\(418\) | 0.500000 | − | 0.866025i | 0.0244558 | − | 0.0423587i | ||||
\(419\) | 11.0000 | 0.537385 | 0.268693 | − | 0.963226i | \(-0.413408\pi\) | ||||
0.268693 | + | 0.963226i | \(0.413408\pi\) | |||||||
\(420\) | 0.500000 | − | 2.59808i | 0.0243975 | − | 0.126773i | ||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | 7.50000 | − | 12.9904i | 0.365094 | − | 0.632362i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | 0.500000 | + | 0.866025i | 0.0242821 | + | 0.0420579i | ||||
\(425\) | 2.00000 | − | 3.46410i | 0.0970143 | − | 0.168034i | ||||
\(426\) | −14.0000 | −0.678302 | ||||||||
\(427\) | 10.0000 | − | 3.46410i | 0.483934 | − | 0.167640i | ||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 3.50000 | − | 6.06218i | 0.168982 | − | 0.292685i | ||||
\(430\) | 2.00000 | + | 3.46410i | 0.0964486 | + | 0.167054i | ||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 40.0000 | 1.92228 | 0.961139 | − | 0.276066i | \(-0.0890309\pi\) | ||||
0.961139 | + | 0.276066i | \(0.0890309\pi\) | |||||||
\(434\) | 12.0000 | + | 10.3923i | 0.576018 | + | 0.498847i | ||||
\(435\) | −8.00000 | −0.383571 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −0.500000 | − | 0.866025i | −0.0239182 | − | 0.0414276i | ||||
\(438\) | 7.00000 | + | 12.1244i | 0.334473 | + | 0.579324i | ||||
\(439\) | −8.00000 | + | 13.8564i | −0.381819 | + | 0.661330i | −0.991322 | − | 0.131453i | \(-0.958036\pi\) |
0.609503 | + | 0.792784i | \(0.291369\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | −28.0000 | −1.33182 | ||||||||
\(443\) | 18.0000 | − | 31.1769i | 0.855206 | − | 1.48126i | −0.0212481 | − | 0.999774i | \(-0.506764\pi\) |
0.876454 | − | 0.481486i | \(-0.159903\pi\) | |||||||
\(444\) | 1.50000 | + | 2.59808i | 0.0711868 | + | 0.123299i | ||||
\(445\) | 1.00000 | + | 1.73205i | 0.0474045 | + | 0.0821071i | ||||
\(446\) | 2.00000 | − | 3.46410i | 0.0947027 | − | 0.164030i | ||||
\(447\) | −4.00000 | −0.189194 | ||||||||
\(448\) | 2.00000 | + | 1.73205i | 0.0944911 | + | 0.0818317i | ||||
\(449\) | −25.0000 | −1.17982 | −0.589911 | − | 0.807468i | \(-0.700837\pi\) | ||||
−0.589911 | + | 0.807468i | \(0.700837\pi\) | |||||||
\(450\) | −0.500000 | + | 0.866025i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | 4.50000 | + | 7.79423i | 0.211897 | + | 0.367016i | ||||
\(452\) | 3.00000 | + | 5.19615i | 0.141108 | + | 0.244406i | ||||
\(453\) | 1.00000 | − | 1.73205i | 0.0469841 | − | 0.0813788i | ||||
\(454\) | −20.0000 | −0.938647 | ||||||||
\(455\) | −17.5000 | + | 6.06218i | −0.820413 | + | 0.284199i | ||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | −5.00000 | + | 8.66025i | −0.233890 | + | 0.405110i | −0.958950 | − | 0.283577i | \(-0.908479\pi\) |
0.725059 | + | 0.688686i | \(0.241812\pi\) | |||||||
\(458\) | 11.0000 | + | 19.0526i | 0.513996 | + | 0.890268i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | −0.500000 | + | 0.866025i | −0.0233126 | + | 0.0403786i | ||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | −0.500000 | + | 2.59808i | −0.0232621 | + | 0.120873i | ||||
\(463\) | 33.0000 | 1.53364 | 0.766820 | − | 0.641862i | \(-0.221838\pi\) | ||||
0.766820 | + | 0.641862i | \(0.221838\pi\) | |||||||
\(464\) | 4.00000 | − | 6.92820i | 0.185695 | − | 0.321634i | ||||
\(465\) | −3.00000 | − | 5.19615i | −0.139122 | − | 0.240966i | ||||
\(466\) | −13.0000 | − | 22.5167i | −0.602213 | − | 1.04306i | ||||
\(467\) | −6.00000 | + | 10.3923i | −0.277647 | + | 0.480899i | −0.970799 | − | 0.239892i | \(-0.922888\pi\) |
0.693153 | + | 0.720791i | \(0.256221\pi\) | |||||||
\(468\) | 7.00000 | 0.323575 | ||||||||
\(469\) | 6.00000 | − | 31.1769i | 0.277054 | − | 1.43962i | ||||
\(470\) | −3.00000 | −0.138380 | ||||||||
\(471\) | −7.50000 | + | 12.9904i | −0.345582 | + | 0.598565i | ||||
\(472\) | −6.00000 | − | 10.3923i | −0.276172 | − | 0.478345i | ||||
\(473\) | −2.00000 | − | 3.46410i | −0.0919601 | − | 0.159280i | ||||
\(474\) | −2.00000 | + | 3.46410i | −0.0918630 | + | 0.159111i | ||||
\(475\) | 1.00000 | 0.0458831 | ||||||||
\(476\) | 10.0000 | − | 3.46410i | 0.458349 | − | 0.158777i | ||||
\(477\) | −1.00000 | −0.0457869 | ||||||||
\(478\) | 3.00000 | − | 5.19615i | 0.137217 | − | 0.237666i | ||||
\(479\) | −13.0000 | − | 22.5167i | −0.593985 | − | 1.02881i | −0.993689 | − | 0.112168i | \(-0.964220\pi\) |
0.399704 | − | 0.916644i | \(-0.369113\pi\) | |||||||
\(480\) | −0.500000 | − | 0.866025i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | 10.5000 | − | 18.1865i | 0.478759 | − | 0.829235i | ||||
\(482\) | 7.00000 | 0.318841 | ||||||||
\(483\) | 2.00000 | + | 1.73205i | 0.0910032 | + | 0.0788110i | ||||
\(484\) | −10.0000 | −0.454545 | ||||||||
\(485\) | 8.00000 | − | 13.8564i | 0.363261 | − | 0.629187i | ||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 4.00000 | + | 6.92820i | 0.181257 | + | 0.313947i | 0.942309 | − | 0.334744i | \(-0.108650\pi\) |
−0.761052 | + | 0.648691i | \(0.775317\pi\) | |||||||
\(488\) | 2.00000 | − | 3.46410i | 0.0905357 | − | 0.156813i | ||||
\(489\) | 8.00000 | 0.361773 | ||||||||
\(490\) | 5.50000 | − | 4.33013i | 0.248465 | − | 0.195615i | ||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | −4.50000 | + | 7.79423i | −0.202876 | + | 0.351391i | ||||
\(493\) | −16.0000 | − | 27.7128i | −0.720604 | − | 1.24812i | ||||
\(494\) | −3.50000 | − | 6.06218i | −0.157472 | − | 0.272750i | ||||
\(495\) | 0.500000 | − | 0.866025i | 0.0224733 | − | 0.0389249i | ||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −28.0000 | − | 24.2487i | −1.25597 | − | 1.08770i | ||||
\(498\) | 12.0000 | 0.537733 | ||||||||
\(499\) | −12.0000 | + | 20.7846i | −0.537194 | + | 0.930447i | 0.461860 | + | 0.886953i | \(0.347182\pi\) |
−0.999054 | + | 0.0434940i | \(0.986151\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 2.50000 | + | 4.33013i | 0.111692 | + | 0.193456i | ||||
\(502\) | 1.50000 | − | 2.59808i | 0.0669483 | − | 0.115958i | ||||
\(503\) | 28.0000 | 1.24846 | 0.624229 | − | 0.781241i | \(-0.285413\pi\) | ||||
0.624229 | + | 0.781241i | \(0.285413\pi\) | |||||||
\(504\) | −2.50000 | + | 0.866025i | −0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.500000 | − | 0.866025i | 0.0222277 | − | 0.0384995i | ||||
\(507\) | −18.0000 | − | 31.1769i | −0.799408 | − | 1.38462i | ||||
\(508\) | −2.50000 | − | 4.33013i | −0.110920 | − | 0.192118i | ||||
\(509\) | −15.0000 | + | 25.9808i | −0.664863 | + | 1.15158i | 0.314459 | + | 0.949271i | \(0.398177\pi\) |
−0.979322 | + | 0.202306i | \(0.935156\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | −7.00000 | + | 36.3731i | −0.309662 | + | 1.60905i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.500000 | + | 0.866025i | −0.0220755 | + | 0.0382360i | ||||
\(514\) | 4.00000 | + | 6.92820i | 0.176432 | + | 0.305590i | ||||
\(515\) | −8.00000 | − | 13.8564i | −0.352522 | − | 0.610586i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | 3.00000 | 0.131940 | ||||||||
\(518\) | −1.50000 | + | 7.79423i | −0.0659062 | + | 0.342459i | ||||
\(519\) | −21.0000 | −0.921798 | ||||||||
\(520\) | −3.50000 | + | 6.06218i | −0.153485 | + | 0.265844i | ||||
\(521\) | 10.5000 | + | 18.1865i | 0.460013 | + | 0.796766i | 0.998961 | − | 0.0455727i | \(-0.0145113\pi\) |
−0.538948 | + | 0.842339i | \(0.681178\pi\) | |||||||
\(522\) | 4.00000 | + | 6.92820i | 0.175075 | + | 0.303239i | ||||
\(523\) | 7.00000 | − | 12.1244i | 0.306089 | − | 0.530161i | −0.671414 | − | 0.741082i | \(-0.734313\pi\) |
0.977503 | + | 0.210921i | \(0.0676463\pi\) | |||||||
\(524\) | −13.0000 | −0.567908 | ||||||||
\(525\) | −2.50000 | + | 0.866025i | −0.109109 | + | 0.0377964i | ||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | 12.0000 | − | 20.7846i | 0.522728 | − | 0.905392i | ||||
\(528\) | 0.500000 | + | 0.866025i | 0.0217597 | + | 0.0376889i | ||||
\(529\) | 11.0000 | + | 19.0526i | 0.478261 | + | 0.828372i | ||||
\(530\) | 0.500000 | − | 0.866025i | 0.0217186 | − | 0.0376177i | ||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 2.00000 | + | 1.73205i | 0.0867110 | + | 0.0750939i | ||||
\(533\) | 63.0000 | 2.72883 | ||||||||
\(534\) | 1.00000 | − | 1.73205i | 0.0432742 | − | 0.0749532i | ||||
\(535\) | 9.00000 | + | 15.5885i | 0.389104 | + | 0.673948i | ||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | −6.50000 | + | 11.2583i | −0.280496 | + | 0.485833i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.50000 | + | 4.33013i | −0.236902 | + | 0.186512i | ||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −1.00000 | + | 1.73205i | −0.0429934 | + | 0.0744667i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(542\) | −8.00000 | − | 13.8564i | −0.343629 | − | 0.595184i | ||||
\(543\) | 6.00000 | + | 10.3923i | 0.257485 | + | 0.445976i | ||||
\(544\) | 2.00000 | − | 3.46410i | 0.0857493 | − | 0.148522i | ||||
\(545\) | −10.0000 | −0.428353 | ||||||||
\(546\) | 14.0000 | + | 12.1244i | 0.599145 | + | 0.518875i | ||||
\(547\) | 36.0000 | 1.53925 | 0.769624 | − | 0.638497i | \(-0.220443\pi\) | ||||
0.769624 | + | 0.638497i | \(0.220443\pi\) | |||||||
\(548\) | 1.00000 | − | 1.73205i | 0.0427179 | − | 0.0739895i | ||||
\(549\) | 2.00000 | + | 3.46410i | 0.0853579 | + | 0.147844i | ||||
\(550\) | 0.500000 | + | 0.866025i | 0.0213201 | + | 0.0369274i | ||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −10.0000 | + | 3.46410i | −0.425243 | + | 0.147309i | ||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 1.50000 | − | 2.59808i | 0.0636715 | − | 0.110282i | ||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −22.5000 | − | 38.9711i | −0.953356 | − | 1.65126i | −0.738087 | − | 0.674705i | \(-0.764271\pi\) |
−0.215268 | − | 0.976555i | \(-0.569063\pi\) | |||||||
\(558\) | −3.00000 | + | 5.19615i | −0.127000 | + | 0.219971i | ||||
\(559\) | −28.0000 | −1.18427 | ||||||||
\(560\) | 0.500000 | − | 2.59808i | 0.0211289 | − | 0.109789i | ||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | −1.50000 | + | 2.59808i | −0.0632737 | + | 0.109593i | ||||
\(563\) | −7.00000 | − | 12.1244i | −0.295015 | − | 0.510981i | 0.679974 | − | 0.733237i | \(-0.261991\pi\) |
−0.974988 | + | 0.222256i | \(0.928658\pi\) | |||||||
\(564\) | 1.50000 | + | 2.59808i | 0.0631614 | + | 0.109399i | ||||
\(565\) | 3.00000 | − | 5.19615i | 0.126211 | − | 0.218604i | ||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 0.500000 | − | 2.59808i | 0.0209980 | − | 0.109109i | ||||
\(568\) | −14.0000 | −0.587427 | ||||||||
\(569\) | 18.5000 | − | 32.0429i | 0.775560 | − | 1.34331i | −0.158919 | − | 0.987292i | \(-0.550801\pi\) |
0.934479 | − | 0.356018i | \(-0.115866\pi\) | |||||||
\(570\) | −0.500000 | − | 0.866025i | −0.0209427 | − | 0.0362738i | ||||
\(571\) | 4.00000 | + | 6.92820i | 0.167395 | + | 0.289936i | 0.937503 | − | 0.347977i | \(-0.113131\pi\) |
−0.770108 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(572\) | 3.50000 | − | 6.06218i | 0.146342 | − | 0.253472i | ||||
\(573\) | −10.0000 | −0.417756 | ||||||||
\(574\) | −22.5000 | + | 7.79423i | −0.939132 | + | 0.325325i | ||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 7.00000 | + | 12.1244i | 0.291414 | + | 0.504744i | 0.974144 | − | 0.225927i | \(-0.0725410\pi\) |
−0.682730 | + | 0.730670i | \(0.739208\pi\) | |||||||
\(578\) | 0.500000 | + | 0.866025i | 0.0207973 | + | 0.0360219i | ||||
\(579\) | −13.0000 | + | 22.5167i | −0.540262 | + | 0.935760i | ||||
\(580\) | −8.00000 | −0.332182 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | −16.0000 | −0.663221 | ||||||||
\(583\) | −0.500000 | + | 0.866025i | −0.0207079 | + | 0.0358671i | ||||
\(584\) | 7.00000 | + | 12.1244i | 0.289662 | + | 0.501709i | ||||
\(585\) | −3.50000 | − | 6.06218i | −0.144707 | − | 0.250640i | ||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | 42.0000 | 1.73353 | 0.866763 | − | 0.498721i | \(-0.166197\pi\) | ||||
0.866763 | + | 0.498721i | \(0.166197\pi\) | |||||||
\(588\) | −6.50000 | − | 2.59808i | −0.268055 | − | 0.107143i | ||||
\(589\) | 6.00000 | 0.247226 | ||||||||
\(590\) | −6.00000 | + | 10.3923i | −0.247016 | + | 0.427844i | ||||
\(591\) | 1.50000 | + | 2.59808i | 0.0617018 | + | 0.106871i | ||||
\(592\) | 1.50000 | + | 2.59808i | 0.0616496 | + | 0.106780i | ||||
\(593\) | −6.00000 | + | 10.3923i | −0.246390 | + | 0.426761i | −0.962522 | − | 0.271205i | \(-0.912578\pi\) |
0.716131 | + | 0.697966i | \(0.245911\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | −8.00000 | − | 6.92820i | −0.327968 | − | 0.284029i | ||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | 6.00000 | − | 10.3923i | 0.245564 | − | 0.425329i | ||||
\(598\) | −3.50000 | − | 6.06218i | −0.143126 | − | 0.247901i | ||||
\(599\) | −3.00000 | − | 5.19615i | −0.122577 | − | 0.212309i | 0.798206 | − | 0.602384i | \(-0.205782\pi\) |
−0.920783 | + | 0.390075i | \(0.872449\pi\) | |||||||
\(600\) | −0.500000 | + | 0.866025i | −0.0204124 | + | 0.0353553i | ||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 10.0000 | − | 3.46410i | 0.407570 | − | 0.141186i | ||||
\(603\) | 12.0000 | 0.488678 | ||||||||
\(604\) | 1.00000 | − | 1.73205i | 0.0406894 | − | 0.0704761i | ||||
\(605\) | 5.00000 | + | 8.66025i | 0.203279 | + | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.5000 | + | 21.6506i | −0.507359 | + | 0.878772i | 0.492604 | + | 0.870253i | \(0.336045\pi\) |
−0.999964 | + | 0.00851879i | \(0.997288\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | −4.00000 | + | 20.7846i | −0.162088 | + | 0.842235i | ||||
\(610\) | −4.00000 | −0.161955 | ||||||||
\(611\) | 10.5000 | − | 18.1865i | 0.424785 | − | 0.735748i | ||||
\(612\) | 2.00000 | + | 3.46410i | 0.0808452 | + | 0.140028i | ||||
\(613\) | 7.50000 | + | 12.9904i | 0.302922 | + | 0.524677i | 0.976797 | − | 0.214169i | \(-0.0687045\pi\) |
−0.673874 | + | 0.738846i | \(0.735371\pi\) | |||||||
\(614\) | −4.00000 | + | 6.92820i | −0.161427 | + | 0.279600i | ||||
\(615\) | 9.00000 | 0.362915 | ||||||||
\(616\) | −0.500000 | + | 2.59808i | −0.0201456 | + | 0.104679i | ||||
\(617\) | 8.00000 | 0.322068 | 0.161034 | − | 0.986949i | \(-0.448517\pi\) | ||||
0.161034 | + | 0.986949i | \(0.448517\pi\) | |||||||
\(618\) | −8.00000 | + | 13.8564i | −0.321807 | + | 0.557386i | ||||
\(619\) | 3.50000 | + | 6.06218i | 0.140677 | + | 0.243659i | 0.927752 | − | 0.373198i | \(-0.121739\pi\) |
−0.787075 | + | 0.616858i | \(0.788405\pi\) | |||||||
\(620\) | −3.00000 | − | 5.19615i | −0.120483 | − | 0.208683i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | 16.0000 | 0.641542 | ||||||||
\(623\) | 5.00000 | − | 1.73205i | 0.200321 | − | 0.0693932i | ||||
\(624\) | 7.00000 | 0.280224 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 12.0000 | + | 20.7846i | 0.479616 | + | 0.830720i | ||||
\(627\) | 0.500000 | + | 0.866025i | 0.0199681 | + | 0.0345857i | ||||
\(628\) | −7.50000 | + | 12.9904i | −0.299283 | + | 0.518373i | ||||
\(629\) | 12.0000 | 0.478471 | ||||||||
\(630\) | 2.00000 | + | 1.73205i | 0.0796819 | + | 0.0690066i | ||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | −2.00000 | + | 3.46410i | −0.0795557 | + | 0.137795i | ||||
\(633\) | 7.50000 | + | 12.9904i | 0.298098 | + | 0.516321i | ||||
\(634\) | −5.00000 | − | 8.66025i | −0.198575 | − | 0.343943i | ||||
\(635\) | −2.50000 | + | 4.33013i | −0.0992095 | + | 0.171836i | ||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 7.00000 | + | 48.4974i | 0.277350 | + | 1.92154i | ||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | 7.00000 | − | 12.1244i | 0.276916 | − | 0.479632i | ||||
\(640\) | −0.500000 | − | 0.866025i | −0.0197642 | − | 0.0342327i | ||||
\(641\) | 11.5000 | + | 19.9186i | 0.454223 | + | 0.786737i | 0.998643 | − | 0.0520757i | \(-0.0165837\pi\) |
−0.544420 | + | 0.838812i | \(0.683250\pi\) | |||||||
\(642\) | 9.00000 | − | 15.5885i | 0.355202 | − | 0.615227i | ||||
\(643\) | 26.0000 | 1.02534 | 0.512670 | − | 0.858586i | \(-0.328656\pi\) | ||||
0.512670 | + | 0.858586i | \(0.328656\pi\) | |||||||
\(644\) | 2.00000 | + | 1.73205i | 0.0788110 | + | 0.0682524i | ||||
\(645\) | −4.00000 | −0.157500 | ||||||||
\(646\) | 2.00000 | − | 3.46410i | 0.0786889 | − | 0.136293i | ||||
\(647\) | 7.50000 | + | 12.9904i | 0.294855 | + | 0.510705i | 0.974951 | − | 0.222419i | \(-0.0713952\pi\) |
−0.680096 | + | 0.733123i | \(0.738062\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 6.00000 | − | 10.3923i | 0.235521 | − | 0.407934i | ||||
\(650\) | 7.00000 | 0.274563 | ||||||||
\(651\) | −15.0000 | + | 5.19615i | −0.587896 | + | 0.203653i | ||||
\(652\) | 8.00000 | 0.313304 | ||||||||
\(653\) | −14.5000 | + | 25.1147i | −0.567429 | + | 0.982816i | 0.429390 | + | 0.903119i | \(0.358728\pi\) |
−0.996819 | + | 0.0796966i | \(0.974605\pi\) | |||||||
\(654\) | 5.00000 | + | 8.66025i | 0.195515 | + | 0.338643i | ||||
\(655\) | 6.50000 | + | 11.2583i | 0.253976 | + | 0.439899i | ||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | −1.50000 | + | 7.79423i | −0.0584761 | + | 0.303851i | ||||
\(659\) | −12.0000 | −0.467454 | −0.233727 | − | 0.972302i | \(-0.575092\pi\) | ||||
−0.233727 | + | 0.972302i | \(0.575092\pi\) | |||||||
\(660\) | 0.500000 | − | 0.866025i | 0.0194625 | − | 0.0337100i | ||||
\(661\) | −4.00000 | − | 6.92820i | −0.155582 | − | 0.269476i | 0.777689 | − | 0.628649i | \(-0.216392\pi\) |
−0.933271 | + | 0.359174i | \(0.883059\pi\) | |||||||
\(662\) | 4.50000 | + | 7.79423i | 0.174897 | + | 0.302931i | ||||
\(663\) | 14.0000 | − | 24.2487i | 0.543715 | − | 0.941742i | ||||
\(664\) | 12.0000 | 0.465690 | ||||||||
\(665\) | 0.500000 | − | 2.59808i | 0.0193892 | − | 0.100749i | ||||
\(666\) | −3.00000 | −0.116248 | ||||||||
\(667\) | 4.00000 | − | 6.92820i | 0.154881 | − | 0.268261i | ||||
\(668\) | 2.50000 | + | 4.33013i | 0.0967279 | + | 0.167538i | ||||
\(669\) | 2.00000 | + | 3.46410i | 0.0773245 | + | 0.133930i | ||||
\(670\) | −6.00000 | + | 10.3923i | −0.231800 | + | 0.401490i | ||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | −2.50000 | + | 0.866025i | −0.0964396 | + | 0.0334077i | ||||
\(673\) | −12.0000 | −0.462566 | −0.231283 | − | 0.972887i | \(-0.574292\pi\) | ||||
−0.231283 | + | 0.972887i | \(0.574292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | −18.0000 | − | 31.1769i | −0.692308 | − | 1.19911i | ||||
\(677\) | −0.500000 | + | 0.866025i | −0.0192166 | + | 0.0332841i | −0.875474 | − | 0.483266i | \(-0.839451\pi\) |
0.856257 | + | 0.516550i | \(0.172784\pi\) | |||||||
\(678\) | −6.00000 | −0.230429 | ||||||||
\(679\) | −32.0000 | − | 27.7128i | −1.22805 | − | 1.06352i | ||||
\(680\) | −4.00000 | −0.153393 | ||||||||
\(681\) | 10.0000 | − | 17.3205i | 0.383201 | − | 0.663723i | ||||
\(682\) | 3.00000 | + | 5.19615i | 0.114876 | + | 0.198971i | ||||
\(683\) | −6.00000 | − | 10.3923i | −0.229584 | − | 0.397650i | 0.728101 | − | 0.685470i | \(-0.240403\pi\) |
−0.957685 | + | 0.287819i | \(0.907070\pi\) | |||||||
\(684\) | −0.500000 | + | 0.866025i | −0.0191180 | + | 0.0331133i | ||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −22.0000 | −0.839352 | ||||||||
\(688\) | 2.00000 | − | 3.46410i | 0.0762493 | − | 0.132068i | ||||
\(689\) | 3.50000 | + | 6.06218i | 0.133339 | + | 0.230951i | ||||
\(690\) | −0.500000 | − | 0.866025i | −0.0190347 | − | 0.0329690i | ||||
\(691\) | −6.00000 | + | 10.3923i | −0.228251 | + | 0.395342i | −0.957290 | − | 0.289130i | \(-0.906634\pi\) |
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(692\) | −21.0000 | −0.798300 | ||||||||
\(693\) | −2.00000 | − | 1.73205i | −0.0759737 | − | 0.0657952i | ||||
\(694\) | −34.0000 | −1.29062 | ||||||||
\(695\) | 2.00000 | − | 3.46410i | 0.0758643 | − | 0.131401i | ||||
\(696\) | 4.00000 | + | 6.92820i | 0.151620 | + | 0.262613i | ||||
\(697\) | 18.0000 | + | 31.1769i | 0.681799 | + | 1.18091i | ||||
\(698\) | 14.0000 | − | 24.2487i | 0.529908 | − | 0.917827i | ||||
\(699\) | 26.0000 | 0.983410 | ||||||||
\(700\) | −2.50000 | + | 0.866025i | −0.0944911 | + | 0.0327327i | ||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | −3.50000 | + | 6.06218i | −0.132099 | + | 0.228802i | ||||
\(703\) | 1.50000 | + | 2.59808i | 0.0565736 | + | 0.0979883i | ||||
\(704\) | 0.500000 | + | 0.866025i | 0.0188445 | + | 0.0326396i | ||||
\(705\) | 1.50000 | − | 2.59808i | 0.0564933 | − | 0.0978492i | ||||
\(706\) | −8.00000 | −0.301084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000 | 0.450988 | ||||||||
\(709\) | −2.00000 | + | 3.46410i | −0.0751116 | + | 0.130097i | −0.901135 | − | 0.433539i | \(-0.857265\pi\) |
0.826023 | + | 0.563636i | \(0.190598\pi\) | |||||||
\(710\) | 7.00000 | + | 12.1244i | 0.262705 | + | 0.455019i | ||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | 1.00000 | − | 1.73205i | 0.0374766 | − | 0.0649113i | ||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −2.00000 | + | 10.3923i | −0.0748481 | + | 0.388922i | ||||
\(715\) | −7.00000 | −0.261785 | ||||||||
\(716\) | −6.50000 | + | 11.2583i | −0.242916 | + | 0.420744i | ||||
\(717\) | 3.00000 | + | 5.19615i | 0.112037 | + | 0.194054i | ||||
\(718\) | −18.0000 | − | 31.1769i | −0.671754 | − | 1.16351i | ||||
\(719\) | −13.0000 | + | 22.5167i | −0.484818 | + | 0.839730i | −0.999848 | − | 0.0174426i | \(-0.994448\pi\) |
0.515030 | + | 0.857172i | \(0.327781\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −40.0000 | + | 13.8564i | −1.48968 | + | 0.516040i | ||||
\(722\) | −18.0000 | −0.669891 | ||||||||
\(723\) | −3.50000 | + | 6.06218i | −0.130166 | + | 0.225455i | ||||
\(724\) | 6.00000 | + | 10.3923i | 0.222988 | + | 0.386227i | ||||
\(725\) | 4.00000 | + | 6.92820i | 0.148556 | + | 0.257307i | ||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | 17.0000 | 0.630495 | 0.315248 | − | 0.949009i | \(-0.397912\pi\) | ||||
0.315248 | + | 0.949009i | \(0.397912\pi\) | |||||||
\(728\) | 14.0000 | + | 12.1244i | 0.518875 | + | 0.449359i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 7.00000 | − | 12.1244i | 0.259082 | − | 0.448743i | ||||
\(731\) | −8.00000 | − | 13.8564i | −0.295891 | − | 0.512498i | ||||
\(732\) | 2.00000 | + | 3.46410i | 0.0739221 | + | 0.128037i | ||||
\(733\) | −18.5000 | + | 32.0429i | −0.683313 | + | 1.18353i | 0.290651 | + | 0.956829i | \(0.406128\pi\) |
−0.973964 | + | 0.226704i | \(0.927205\pi\) | |||||||
\(734\) | 19.0000 | 0.701303 | ||||||||
\(735\) | 1.00000 | + | 6.92820i | 0.0368856 | + | 0.255551i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 6.00000 | − | 10.3923i | 0.221013 | − | 0.382805i | ||||
\(738\) | −4.50000 | − | 7.79423i | −0.165647 | − | 0.286910i | ||||
\(739\) | −20.5000 | − | 35.5070i | −0.754105 | − | 1.30615i | −0.945818 | − | 0.324697i | \(-0.894738\pi\) |
0.191714 | − | 0.981451i | \(-0.438596\pi\) | |||||||
\(740\) | 1.50000 | − | 2.59808i | 0.0551411 | − | 0.0955072i | ||||
\(741\) | 7.00000 | 0.257151 | ||||||||
\(742\) | −2.00000 | − | 1.73205i | −0.0734223 | − | 0.0635856i | ||||
\(743\) | −9.00000 | −0.330178 | −0.165089 | − | 0.986279i | \(-0.552791\pi\) | ||||
−0.165089 | + | 0.986279i | \(0.552791\pi\) | |||||||
\(744\) | −3.00000 | + | 5.19615i | −0.109985 | + | 0.190500i | ||||
\(745\) | 2.00000 | + | 3.46410i | 0.0732743 | + | 0.126915i | ||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | −6.00000 | + | 10.3923i | −0.219529 | + | 0.380235i | ||||
\(748\) | 4.00000 | 0.146254 | ||||||||
\(749\) | 45.0000 | − | 15.5885i | 1.64426 | − | 0.569590i | ||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | 13.0000 | − | 22.5167i | 0.474377 | − | 0.821645i | −0.525193 | − | 0.850983i | \(-0.676007\pi\) |
0.999570 | + | 0.0293387i | \(0.00934013\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 1.50000 | + | 2.59808i | 0.0546630 | + | 0.0946792i | ||||
\(754\) | 28.0000 | − | 48.4974i | 1.01970 | − | 1.76617i | ||||
\(755\) | −2.00000 | −0.0727875 | ||||||||
\(756\) | 0.500000 | − | 2.59808i | 0.0181848 | − | 0.0944911i | ||||
\(757\) | −2.00000 | −0.0726912 | −0.0363456 | − | 0.999339i | \(-0.511572\pi\) | ||||
−0.0363456 | + | 0.999339i | \(0.511572\pi\) | |||||||
\(758\) | −0.500000 | + | 0.866025i | −0.0181608 | + | 0.0314555i | ||||
\(759\) | 0.500000 | + | 0.866025i | 0.0181489 | + | 0.0314347i | ||||
\(760\) | −0.500000 | − | 0.866025i | −0.0181369 | − | 0.0314140i | ||||
\(761\) | 8.50000 | − | 14.7224i | 0.308125 | − | 0.533688i | −0.669827 | − | 0.742517i | \(-0.733632\pi\) |
0.977952 | + | 0.208829i | \(0.0669652\pi\) | |||||||
\(762\) | 5.00000 | 0.181131 | ||||||||
\(763\) | −5.00000 | + | 25.9808i | −0.181012 | + | 0.940567i | ||||
\(764\) | −10.0000 | −0.361787 | ||||||||
\(765\) | 2.00000 | − | 3.46410i | 0.0723102 | − | 0.125245i | ||||
\(766\) | −6.50000 | − | 11.2583i | −0.234855 | − | 0.406780i | ||||
\(767\) | −42.0000 | − | 72.7461i | −1.51653 | − | 2.62671i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −29.0000 | −1.04577 | −0.522883 | − | 0.852404i | \(-0.675144\pi\) | ||||
−0.522883 | + | 0.852404i | \(0.675144\pi\) | |||||||
\(770\) | 2.50000 | − | 0.866025i | 0.0900937 | − | 0.0312094i | ||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | −13.0000 | + | 22.5167i | −0.467880 | + | 0.810392i | ||||
\(773\) | −21.5000 | − | 37.2391i | −0.773301 | − | 1.33940i | −0.935744 | − | 0.352679i | \(-0.885271\pi\) |
0.162443 | − | 0.986718i | \(-0.448063\pi\) | |||||||
\(774\) | 2.00000 | + | 3.46410i | 0.0718885 | + | 0.124515i | ||||
\(775\) | −3.00000 | + | 5.19615i | −0.107763 | + | 0.186651i | ||||
\(776\) | −16.0000 | −0.574367 | ||||||||
\(777\) | −6.00000 | − | 5.19615i | −0.215249 | − | 0.186411i | ||||
\(778\) | −14.0000 | −0.501924 | ||||||||
\(779\) | −4.50000 | + | 7.79423i | −0.161229 | + | 0.279257i | ||||
\(780\) | −3.50000 | − | 6.06218i | −0.125320 | − | 0.217061i | ||||
\(781\) | −7.00000 | − | 12.1244i | −0.250480 | − | 0.433844i | ||||
\(782\) | 2.00000 | − | 3.46410i | 0.0715199 | − | 0.123876i | ||||
\(783\) | −8.00000 | −0.285897 | ||||||||
\(784\) | −6.50000 | − | 2.59808i | −0.232143 | − | 0.0927884i | ||||
\(785\) | 15.0000 | 0.535373 | ||||||||
\(786\) | 6.50000 | − | 11.2583i | 0.231847 | − | 0.401571i | ||||
\(787\) | 11.0000 | + | 19.0526i | 0.392108 | + | 0.679150i | 0.992727 | − | 0.120384i | \(-0.0384127\pi\) |
−0.600620 | + | 0.799535i | \(0.705079\pi\) | |||||||
\(788\) | 1.50000 | + | 2.59808i | 0.0534353 | + | 0.0925526i | ||||
\(789\) | 8.00000 | − | 13.8564i | 0.284808 | − | 0.493301i | ||||
\(790\) | 4.00000 | 0.142314 | ||||||||
\(791\) | −12.0000 | − | 10.3923i | −0.426671 | − | 0.369508i | ||||
\(792\) | −1.00000 | −0.0355335 | ||||||||
\(793\) | 14.0000 | − | 24.2487i | 0.497155 | − | 0.861097i | ||||
\(794\) | −9.00000 | − | 15.5885i | −0.319398 | − | 0.553214i | ||||
\(795\) | 0.500000 | + | 0.866025i | 0.0177332 | + | 0.0307148i | ||||
\(796\) | 6.00000 | − | 10.3923i | 0.212664 | − | 0.368345i | ||||
\(797\) | −6.00000 | −0.212531 | −0.106265 | − | 0.994338i | \(-0.533889\pi\) | ||||
−0.106265 | + | 0.994338i | \(0.533889\pi\) | |||||||
\(798\) | −2.50000 | + | 0.866025i | −0.0884990 | + | 0.0306570i | ||||
\(799\) | 12.0000 | 0.424529 | ||||||||
\(800\) | −0.500000 | + | 0.866025i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | 1.00000 | + | 1.73205i | 0.0353333 | + | 0.0611990i | ||||
\(802\) | 8.50000 | + | 14.7224i | 0.300145 | + | 0.519867i | ||||
\(803\) | −7.00000 | + | 12.1244i | −0.247025 | + | 0.427859i | ||||
\(804\) | 12.0000 | 0.423207 | ||||||||
\(805\) | 0.500000 | − | 2.59808i | 0.0176227 | − | 0.0915702i | ||||
\(806\) | 42.0000 | 1.47939 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −26.5000 | − | 45.8993i | −0.931690 | − | 1.61374i | −0.780432 | − | 0.625241i | \(-0.785001\pi\) |
−0.151259 | − | 0.988494i | \(-0.548333\pi\) | |||||||
\(810\) | −0.500000 | + | 0.866025i | −0.0175682 | + | 0.0304290i | ||||
\(811\) | 37.0000 | 1.29925 | 0.649623 | − | 0.760257i | \(-0.274927\pi\) | ||||
0.649623 | + | 0.760257i | \(0.274927\pi\) | |||||||
\(812\) | −4.00000 | + | 20.7846i | −0.140372 | + | 0.729397i | ||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | −1.50000 | + | 2.59808i | −0.0525750 | + | 0.0910625i | ||||
\(815\) | −4.00000 | − | 6.92820i | −0.140114 | − | 0.242684i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 2.00000 | − | 3.46410i | 0.0699711 | − | 0.121194i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −17.5000 | + | 6.06218i | −0.611499 | + | 0.211830i | ||||
\(820\) | 9.00000 | 0.314294 | ||||||||
\(821\) | −17.0000 | + | 29.4449i | −0.593304 | + | 1.02763i | 0.400480 | + | 0.916306i | \(0.368843\pi\) |
−0.993784 | + | 0.111327i | \(0.964490\pi\) | |||||||
\(822\) | 1.00000 | + | 1.73205i | 0.0348790 | + | 0.0604122i | ||||
\(823\) | −24.0000 | − | 41.5692i | −0.836587 | − | 1.44901i | −0.892731 | − | 0.450589i | \(-0.851214\pi\) |
0.0561440 | − | 0.998423i | \(-0.482119\pi\) | |||||||
\(824\) | −8.00000 | + | 13.8564i | −0.278693 | + | 0.482711i | ||||
\(825\) | −1.00000 | −0.0348155 | ||||||||
\(826\) | 24.0000 | + | 20.7846i | 0.835067 | + | 0.723189i | ||||
\(827\) | 10.0000 | 0.347734 | 0.173867 | − | 0.984769i | \(-0.444374\pi\) | ||||
0.173867 | + | 0.984769i | \(0.444374\pi\) | |||||||
\(828\) | −0.500000 | + | 0.866025i | −0.0173762 | + | 0.0300965i | ||||
\(829\) | −6.00000 | − | 10.3923i | −0.208389 | − | 0.360940i | 0.742818 | − | 0.669493i | \(-0.233489\pi\) |
−0.951207 | + | 0.308553i | \(0.900155\pi\) | |||||||
\(830\) | −6.00000 | − | 10.3923i | −0.208263 | − | 0.360722i | ||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | 7.00000 | 0.242681 | ||||||||
\(833\) | −22.0000 | + | 17.3205i | −0.762255 | + | 0.600120i | ||||
\(834\) | −4.00000 | −0.138509 | ||||||||
\(835\) | 2.50000 | − | 4.33013i | 0.0865161 | − | 0.149850i | ||||
\(836\) | 0.500000 | + | 0.866025i | 0.0172929 | + | 0.0299521i | ||||
\(837\) | −3.00000 | − | 5.19615i | −0.103695 | − | 0.179605i | ||||
\(838\) | −5.50000 | + | 9.52628i | −0.189994 | + | 0.329080i | ||||
\(839\) | 44.0000 | 1.51905 | 0.759524 | − | 0.650479i | \(-0.225432\pi\) | ||||
0.759524 | + | 0.650479i | \(0.225432\pi\) | |||||||
\(840\) | 2.00000 | + | 1.73205i | 0.0690066 | + | 0.0597614i | ||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | 7.00000 | − | 12.1244i | 0.241236 | − | 0.417833i | ||||
\(843\) | −1.50000 | − | 2.59808i | −0.0516627 | − | 0.0894825i | ||||
\(844\) | 7.50000 | + | 12.9904i | 0.258161 | + | 0.447147i | ||||
\(845\) | −18.0000 | + | 31.1769i | −0.619219 | + | 1.07252i | ||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 25.0000 | − | 8.66025i | 0.859010 | − | 0.297570i | ||||
\(848\) | −1.00000 | −0.0343401 | ||||||||
\(849\) | 1.00000 | − | 1.73205i | 0.0343199 | − | 0.0594438i | ||||
\(850\) | 2.00000 | + | 3.46410i | 0.0685994 | + | 0.118818i | ||||
\(851\) | 1.50000 | + | 2.59808i | 0.0514193 | + | 0.0890609i | ||||
\(852\) | 7.00000 | − | 12.1244i | 0.239816 | − | 0.415374i | ||||
\(853\) | 1.00000 | 0.0342393 | 0.0171197 | − | 0.999853i | \(-0.494550\pi\) | ||||
0.0171197 | + | 0.999853i | \(0.494550\pi\) | |||||||
\(854\) | −2.00000 | + | 10.3923i | −0.0684386 | + | 0.355617i | ||||
\(855\) | 1.00000 | 0.0341993 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | 11.0000 | + | 19.0526i | 0.375753 | + | 0.650823i | 0.990439 | − | 0.137948i | \(-0.0440508\pi\) |
−0.614687 | + | 0.788771i | \(0.710717\pi\) | |||||||
\(858\) | 3.50000 | + | 6.06218i | 0.119488 | + | 0.206959i | ||||
\(859\) | 10.0000 | − | 17.3205i | 0.341196 | − | 0.590968i | −0.643459 | − | 0.765480i | \(-0.722501\pi\) |
0.984655 | + | 0.174512i | \(0.0558348\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | 4.50000 | − | 23.3827i | 0.153360 | − | 0.796880i | ||||
\(862\) | −12.0000 | −0.408722 | ||||||||
\(863\) | −14.5000 | + | 25.1147i | −0.493586 | + | 0.854916i | −0.999973 | − | 0.00739078i | \(-0.997647\pi\) |
0.506387 | + | 0.862306i | \(0.330981\pi\) | |||||||
\(864\) | −0.500000 | − | 0.866025i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | 10.5000 | + | 18.1865i | 0.357011 | + | 0.618361i | ||||
\(866\) | −20.0000 | + | 34.6410i | −0.679628 | + | 1.17715i | ||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −15.0000 | + | 5.19615i | −0.509133 | + | 0.176369i | ||||
\(869\) | −4.00000 | −0.135691 | ||||||||
\(870\) | 4.00000 | − | 6.92820i | 0.135613 | − | 0.234888i | ||||
\(871\) | −42.0000 | − | 72.7461i | −1.42312 | − | 2.46491i | ||||
\(872\) | 5.00000 | + | 8.66025i | 0.169321 | + | 0.293273i | ||||
\(873\) | 8.00000 | − | 13.8564i | 0.270759 | − | 0.468968i | ||||
\(874\) | 1.00000 | 0.0338255 | ||||||||
\(875\) | 2.00000 | + | 1.73205i | 0.0676123 | + | 0.0585540i | ||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | −11.5000 | + | 19.9186i | −0.388327 | + | 0.672603i | −0.992225 | − | 0.124459i | \(-0.960280\pi\) |
0.603897 | + | 0.797062i | \(0.293614\pi\) | |||||||
\(878\) | −8.00000 | − | 13.8564i | −0.269987 | − | 0.467631i | ||||
\(879\) | −4.50000 | − | 7.79423i | −0.151781 | − | 0.262893i | ||||
\(880\) | 0.500000 | − | 0.866025i | 0.0168550 | − | 0.0291937i | ||||
\(881\) | −25.0000 | −0.842271 | −0.421136 | − | 0.906998i | \(-0.638368\pi\) | ||||
−0.421136 | + | 0.906998i | \(0.638368\pi\) | |||||||
\(882\) | 5.50000 | − | 4.33013i | 0.185195 | − | 0.145803i | ||||
\(883\) | −58.0000 | −1.95186 | −0.975928 | − | 0.218094i | \(-0.930016\pi\) | ||||
−0.975928 | + | 0.218094i | \(0.930016\pi\) | |||||||
\(884\) | 14.0000 | − | 24.2487i | 0.470871 | − | 0.815572i | ||||
\(885\) | −6.00000 | − | 10.3923i | −0.201688 | − | 0.349334i | ||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | −10.0000 | + | 17.3205i | −0.335767 | + | 0.581566i | −0.983632 | − | 0.180190i | \(-0.942329\pi\) |
0.647865 | + | 0.761755i | \(0.275662\pi\) | |||||||
\(888\) | −3.00000 | −0.100673 | ||||||||
\(889\) | 10.0000 | + | 8.66025i | 0.335389 | + | 0.290456i | ||||
\(890\) | −2.00000 | −0.0670402 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 2.00000 | + | 3.46410i | 0.0669650 | + | 0.115987i | ||||
\(893\) | 1.50000 | + | 2.59808i | 0.0501956 | + | 0.0869413i | ||||
\(894\) | 2.00000 | − | 3.46410i | 0.0668900 | − | 0.115857i | ||||
\(895\) | 13.0000 | 0.434542 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | 7.00000 | 0.233723 | ||||||||
\(898\) | 12.5000 | − | 21.6506i | 0.417130 | − | 0.722491i | ||||
\(899\) | 24.0000 | + | 41.5692i | 0.800445 | + | 1.38641i | ||||
\(900\) | −0.500000 | − | 0.866025i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −2.00000 | + | 3.46410i | −0.0666297 | + | 0.115406i | ||||
\(902\) | −9.00000 | −0.299667 | ||||||||
\(903\) | −2.00000 | + | 10.3923i | −0.0665558 | + | 0.345834i | ||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | 6.00000 | − | 10.3923i | 0.199447 | − | 0.345452i | ||||
\(906\) | 1.00000 | + | 1.73205i | 0.0332228 | + | 0.0575435i | ||||
\(907\) | −23.0000 | − | 39.8372i | −0.763702 | − | 1.32277i | −0.940930 | − | 0.338602i | \(-0.890046\pi\) |
0.177227 | − | 0.984170i | \(-0.443287\pi\) | |||||||
\(908\) | 10.0000 | − | 17.3205i | 0.331862 | − | 0.574801i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.50000 | − | 18.1865i | 0.116024 | − | 0.602878i | ||||
\(911\) | −58.0000 | −1.92163 | −0.960813 | − | 0.277198i | \(-0.910594\pi\) | ||||
−0.960813 | + | 0.277198i | \(0.910594\pi\) | |||||||
\(912\) | −0.500000 | + | 0.866025i | −0.0165567 | + | 0.0286770i | ||||
\(913\) | 6.00000 | + | 10.3923i | 0.198571 | + | 0.343935i | ||||
\(914\) | −5.00000 | − | 8.66025i | −0.165385 | − | 0.286456i | ||||
\(915\) | 2.00000 | − | 3.46410i | 0.0661180 | − | 0.114520i | ||||
\(916\) | −22.0000 | −0.726900 | ||||||||
\(917\) | 32.5000 | − | 11.2583i | 1.07324 | − | 0.371783i | ||||
\(918\) | −4.00000 | −0.132020 | ||||||||
\(919\) | 22.0000 | − | 38.1051i | 0.725713 | − | 1.25697i | −0.232967 | − | 0.972485i | \(-0.574843\pi\) |
0.958680 | − | 0.284487i | \(-0.0918233\pi\) | |||||||
\(920\) | −0.500000 | − | 0.866025i | −0.0164845 | − | 0.0285520i | ||||
\(921\) | −4.00000 | − | 6.92820i | −0.131804 | − | 0.228292i | ||||
\(922\) | 14.0000 | − | 24.2487i | 0.461065 | − | 0.798589i | ||||
\(923\) | −98.0000 | −3.22571 | ||||||||
\(924\) | −2.00000 | − | 1.73205i | −0.0657952 | − | 0.0569803i | ||||
\(925\) | −3.00000 | −0.0986394 | ||||||||
\(926\) | −16.5000 | + | 28.5788i | −0.542224 | + | 0.939159i | ||||
\(927\) | −8.00000 | − | 13.8564i | −0.262754 | − | 0.455104i | ||||
\(928\) | 4.00000 | + | 6.92820i | 0.131306 | + | 0.227429i | ||||
\(929\) | −15.5000 | + | 26.8468i | −0.508539 | + | 0.880815i | 0.491413 | + | 0.870927i | \(0.336481\pi\) |
−0.999951 | + | 0.00988764i | \(0.996853\pi\) | |||||||
\(930\) | 6.00000 | 0.196748 | ||||||||
\(931\) | −6.50000 | − | 2.59808i | −0.213029 | − | 0.0851485i | ||||
\(932\) | 26.0000 | 0.851658 | ||||||||
\(933\) | −8.00000 | + | 13.8564i | −0.261908 | + | 0.453638i | ||||
\(934\) | −6.00000 | − | 10.3923i | −0.196326 | − | 0.340047i | ||||
\(935\) | −2.00000 | − | 3.46410i | −0.0654070 | − | 0.113288i | ||||
\(936\) | −3.50000 | + | 6.06218i | −0.114401 | + | 0.198148i | ||||
\(937\) | 16.0000 | 0.522697 | 0.261349 | − | 0.965244i | \(-0.415833\pi\) | ||||
0.261349 | + | 0.965244i | \(0.415833\pi\) | |||||||
\(938\) | 24.0000 | + | 20.7846i | 0.783628 | + | 0.678642i | ||||
\(939\) | −24.0000 | −0.783210 | ||||||||
\(940\) | 1.50000 | − | 2.59808i | 0.0489246 | − | 0.0847399i | ||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | −7.50000 | − | 12.9904i | −0.244363 | − | 0.423249i | ||||
\(943\) | −4.50000 | + | 7.79423i | −0.146540 | + | 0.253815i | ||||
\(944\) | 12.0000 | 0.390567 | ||||||||
\(945\) | −2.50000 | + | 0.866025i | −0.0813250 | + | 0.0281718i | ||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | −23.0000 | + | 39.8372i | −0.747400 | + | 1.29453i | 0.201666 | + | 0.979454i | \(0.435365\pi\) |
−0.949065 | + | 0.315080i | \(0.897969\pi\) | |||||||
\(948\) | −2.00000 | − | 3.46410i | −0.0649570 | − | 0.112509i | ||||
\(949\) | 49.0000 | + | 84.8705i | 1.59061 | + | 2.75501i | ||||
\(950\) | −0.500000 | + | 0.866025i | −0.0162221 | + | 0.0280976i | ||||
\(951\) | 10.0000 | 0.324272 | ||||||||
\(952\) | −2.00000 | + | 10.3923i | −0.0648204 | + | 0.336817i | ||||
\(953\) | 44.0000 | 1.42530 | 0.712650 | − | 0.701520i | \(-0.247495\pi\) | ||||
0.712650 | + | 0.701520i | \(0.247495\pi\) | |||||||
\(954\) | 0.500000 | − | 0.866025i | 0.0161881 | − | 0.0280386i | ||||
\(955\) | 5.00000 | + | 8.66025i | 0.161796 | + | 0.280239i | ||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | −4.00000 | + | 6.92820i | −0.129302 | + | 0.223957i | ||||
\(958\) | 26.0000 | 0.840022 | ||||||||
\(959\) | −1.00000 | + | 5.19615i | −0.0322917 | + | 0.167793i | ||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 10.5000 | + | 18.1865i | 0.338534 | + | 0.586357i | ||||
\(963\) | 9.00000 | + | 15.5885i | 0.290021 | + | 0.502331i | ||||
\(964\) | −3.50000 | + | 6.06218i | −0.112727 | + | 0.195250i | ||||
\(965\) | 26.0000 | 0.836970 | ||||||||
\(966\) | −2.50000 | + | 0.866025i | −0.0804362 | + | 0.0278639i | ||||
\(967\) | −20.0000 | −0.643157 | −0.321578 | − | 0.946883i | \(-0.604213\pi\) | ||||
−0.321578 | + | 0.946883i | \(0.604213\pi\) | |||||||
\(968\) | 5.00000 | − | 8.66025i | 0.160706 | − | 0.278351i | ||||
\(969\) | 2.00000 | + | 3.46410i | 0.0642493 | + | 0.111283i | ||||
\(970\) | 8.00000 | + | 13.8564i | 0.256865 | + | 0.444902i | ||||
\(971\) | −21.5000 | + | 37.2391i | −0.689968 | + | 1.19506i | 0.281880 | + | 0.959450i | \(0.409042\pi\) |
−0.971848 | + | 0.235610i | \(0.924291\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −8.00000 | − | 6.92820i | −0.256468 | − | 0.222108i | ||||
\(974\) | −8.00000 | −0.256337 | ||||||||
\(975\) | −3.50000 | + | 6.06218i | −0.112090 | + | 0.194145i | ||||
\(976\) | 2.00000 | + | 3.46410i | 0.0640184 | + | 0.110883i | ||||
\(977\) | −9.00000 | − | 15.5885i | −0.287936 | − | 0.498719i | 0.685381 | − | 0.728184i | \(-0.259636\pi\) |
−0.973317 | + | 0.229465i | \(0.926302\pi\) | |||||||
\(978\) | −4.00000 | + | 6.92820i | −0.127906 | + | 0.221540i | ||||
\(979\) | 2.00000 | 0.0639203 | ||||||||
\(980\) | 1.00000 | + | 6.92820i | 0.0319438 | + | 0.221313i | ||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | 6.00000 | − | 10.3923i | 0.191468 | − | 0.331632i | ||||
\(983\) | 16.5000 | + | 28.5788i | 0.526268 | + | 0.911523i | 0.999532 | + | 0.0306024i | \(0.00974257\pi\) |
−0.473263 | + | 0.880921i | \(0.656924\pi\) | |||||||
\(984\) | −4.50000 | − | 7.79423i | −0.143455 | − | 0.248471i | ||||
\(985\) | 1.50000 | − | 2.59808i | 0.0477940 | − | 0.0827816i | ||||
\(986\) | 32.0000 | 1.01909 | ||||||||
\(987\) | −6.00000 | − | 5.19615i | −0.190982 | − | 0.165395i | ||||
\(988\) | 7.00000 | 0.222700 | ||||||||
\(989\) | 2.00000 | − | 3.46410i | 0.0635963 | − | 0.110152i | ||||
\(990\) | 0.500000 | + | 0.866025i | 0.0158910 | + | 0.0275241i | ||||
\(991\) | −5.00000 | − | 8.66025i | −0.158830 | − | 0.275102i | 0.775617 | − | 0.631204i | \(-0.217439\pi\) |
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(992\) | −3.00000 | + | 5.19615i | −0.0952501 | + | 0.164978i | ||||
\(993\) | −9.00000 | −0.285606 | ||||||||
\(994\) | 35.0000 | − | 12.1244i | 1.11013 | − | 0.384561i | ||||
\(995\) | −12.0000 | −0.380426 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | −5.00000 | − | 8.66025i | −0.158352 | − | 0.274273i | 0.775923 | − | 0.630828i | \(-0.217285\pi\) |
−0.934274 | + | 0.356555i | \(0.883951\pi\) | |||||||
\(998\) | −12.0000 | − | 20.7846i | −0.379853 | − | 0.657925i | ||||
\(999\) | 1.50000 | − | 2.59808i | 0.0474579 | − | 0.0821995i |
(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 | 210.2.i.a.121.1 | ✓ | 2 | |
3.2 | odd | 2 | 630.2.k.h.541.1 | 2 | |||
4.3 | odd | 2 | 1680.2.bg.k.961.1 | 2 | |||
5.2 | odd | 4 | 1050.2.o.j.499.1 | 4 | |||
5.3 | odd | 4 | 1050.2.o.j.499.2 | 4 | |||
5.4 | even | 2 | 1050.2.i.s.751.1 | 2 | |||
7.2 | even | 3 | 1470.2.a.r.1.1 | 1 | |||
7.3 | odd | 6 | 1470.2.i.i.361.1 | 2 | |||
7.4 | even | 3 | inner | 210.2.i.a.151.1 | yes | 2 | |
7.5 | odd | 6 | 1470.2.a.k.1.1 | 1 | |||
7.6 | odd | 2 | 1470.2.i.i.961.1 | 2 | |||
21.2 | odd | 6 | 4410.2.a.g.1.1 | 1 | |||
21.5 | even | 6 | 4410.2.a.q.1.1 | 1 | |||
21.11 | odd | 6 | 630.2.k.h.361.1 | 2 | |||
28.11 | odd | 6 | 1680.2.bg.k.1201.1 | 2 | |||
35.4 | even | 6 | 1050.2.i.s.151.1 | 2 | |||
35.9 | even | 6 | 7350.2.a.j.1.1 | 1 | |||
35.18 | odd | 12 | 1050.2.o.j.949.1 | 4 | |||
35.19 | odd | 6 | 7350.2.a.ba.1.1 | 1 | |||
35.32 | odd | 12 | 1050.2.o.j.949.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.a.121.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
210.2.i.a.151.1 | yes | 2 | 7.4 | even | 3 | inner | |
630.2.k.h.361.1 | 2 | 21.11 | odd | 6 | |||
630.2.k.h.541.1 | 2 | 3.2 | odd | 2 | |||
1050.2.i.s.151.1 | 2 | 35.4 | even | 6 | |||
1050.2.i.s.751.1 | 2 | 5.4 | even | 2 | |||
1050.2.o.j.499.1 | 4 | 5.2 | odd | 4 | |||
1050.2.o.j.499.2 | 4 | 5.3 | odd | 4 | |||
1050.2.o.j.949.1 | 4 | 35.18 | odd | 12 | |||
1050.2.o.j.949.2 | 4 | 35.32 | odd | 12 | |||
1470.2.a.k.1.1 | 1 | 7.5 | odd | 6 | |||
1470.2.a.r.1.1 | 1 | 7.2 | even | 3 | |||
1470.2.i.i.361.1 | 2 | 7.3 | odd | 6 | |||
1470.2.i.i.961.1 | 2 | 7.6 | odd | 2 | |||
1680.2.bg.k.961.1 | 2 | 4.3 | odd | 2 | |||
1680.2.bg.k.1201.1 | 2 | 28.11 | odd | 6 | |||
4410.2.a.g.1.1 | 1 | 21.2 | odd | 6 | |||
4410.2.a.q.1.1 | 1 | 21.5 | even | 6 | |||
7350.2.a.j.1.1 | 1 | 35.9 | even | 6 | |||
7350.2.a.ba.1.1 | 1 | 35.19 | odd | 6 |