Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(211,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 211.1 | ||
Root | \(-1.32288 - 2.29129i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.211 |
Dual form | 930.2.i.j.811.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0.500000 | + | 0.866025i | 0.204124 | + | 0.353553i | ||||
\(7\) | −0.500000 | − | 0.866025i | −0.188982 | − | 0.327327i | 0.755929 | − | 0.654654i | \(-0.227186\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | −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 | −0.780750 | − | 0.624844i | \(-0.785163\pi\) |
0.931505 | + | 0.363727i | \(0.118496\pi\) | |||||||
\(12\) | −0.500000 | − | 0.866025i | −0.144338 | − | 0.250000i | ||||
\(13\) | −1.00000 | + | 1.73205i | −0.277350 | + | 0.480384i | −0.970725 | − | 0.240192i | \(-0.922790\pi\) |
0.693375 | + | 0.720577i | \(0.256123\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.64575 | − | 2.85052i | −0.399153 | − | 0.691354i | 0.594468 | − | 0.804119i | \(-0.297363\pi\) |
−0.993622 | + | 0.112765i | \(0.964029\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 1.64575 | + | 2.85052i | 0.377561 | + | 0.653955i | 0.990707 | − | 0.136015i | \(-0.0434294\pi\) |
−0.613146 | + | 0.789970i | \(0.710096\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −0.500000 | + | 0.866025i | −0.109109 | + | 0.188982i | ||||
\(22\) | −0.500000 | + | 0.866025i | −0.106600 | + | 0.184637i | ||||
\(23\) | −3.29150 | −0.686326 | −0.343163 | − | 0.939276i | \(-0.611498\pi\) | ||||
−0.343163 | + | 0.939276i | \(0.611498\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.00000 | − | 1.73205i | 0.196116 | − | 0.339683i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.500000 | − | 0.866025i | −0.0944911 | − | 0.163663i | ||||
\(29\) | −6.29150 | −1.16830 | −0.584151 | − | 0.811645i | \(-0.698573\pi\) | ||||
−0.584151 | + | 0.811645i | \(0.698573\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.14575 | + | 5.44860i | 0.205783 | + | 0.978598i | ||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −1.00000 | −0.174078 | ||||||||
\(34\) | 1.64575 | + | 2.85052i | 0.282244 | + | 0.488861i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | −0.500000 | + | 0.866025i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −0.645751 | − | 1.11847i | −0.106161 | − | 0.183876i | 0.808051 | − | 0.589112i | \(-0.200523\pi\) |
−0.914212 | + | 0.405236i | \(0.867189\pi\) | |||||||
\(38\) | −1.64575 | − | 2.85052i | −0.266976 | − | 0.462416i | ||||
\(39\) | 2.00000 | 0.320256 | ||||||||
\(40\) | 0.500000 | − | 0.866025i | 0.0790569 | − | 0.136931i | ||||
\(41\) | −2.64575 | + | 4.58258i | −0.413197 | + | 0.715678i | −0.995237 | − | 0.0974818i | \(-0.968921\pi\) |
0.582040 | + | 0.813160i | \(0.302255\pi\) | |||||||
\(42\) | 0.500000 | − | 0.866025i | 0.0771517 | − | 0.133631i | ||||
\(43\) | 2.00000 | + | 3.46410i | 0.304997 | + | 0.528271i | 0.977261 | − | 0.212041i | \(-0.0680112\pi\) |
−0.672264 | + | 0.740312i | \(0.734678\pi\) | |||||||
\(44\) | 0.500000 | − | 0.866025i | 0.0753778 | − | 0.130558i | ||||
\(45\) | −0.500000 | − | 0.866025i | −0.0745356 | − | 0.129099i | ||||
\(46\) | 3.29150 | 0.485306 | ||||||||
\(47\) | −11.2915 | −1.64703 | −0.823517 | − | 0.567291i | \(-0.807992\pi\) | ||||
−0.823517 | + | 0.567291i | \(0.807992\pi\) | |||||||
\(48\) | −0.500000 | − | 0.866025i | −0.0721688 | − | 0.125000i | ||||
\(49\) | 3.00000 | − | 5.19615i | 0.428571 | − | 0.742307i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | −1.64575 | + | 2.85052i | −0.230451 | + | 0.399153i | ||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −1.50000 | + | 2.59808i | −0.206041 | + | 0.356873i | −0.950464 | − | 0.310835i | \(-0.899391\pi\) |
0.744423 | + | 0.667708i | \(0.232725\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.500000 | + | 0.866025i | 0.0674200 | + | 0.116775i | ||||
\(56\) | 0.500000 | + | 0.866025i | 0.0668153 | + | 0.115728i | ||||
\(57\) | 1.64575 | − | 2.85052i | 0.217985 | − | 0.377561i | ||||
\(58\) | 6.29150 | 0.826115 | ||||||||
\(59\) | 3.50000 | + | 6.06218i | 0.455661 | + | 0.789228i | 0.998726 | − | 0.0504625i | \(-0.0160695\pi\) |
−0.543065 | + | 0.839691i | \(0.682736\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −3.29150 | −0.421434 | −0.210717 | − | 0.977547i | \(-0.567580\pi\) | ||||
−0.210717 | + | 0.977547i | \(0.567580\pi\) | |||||||
\(62\) | −1.14575 | − | 5.44860i | −0.145511 | − | 0.691973i | ||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | − | 1.73205i | −0.124035 | − | 0.214834i | ||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | −0.645751 | + | 1.11847i | −0.0788911 | + | 0.136643i | −0.902772 | − | 0.430120i | \(-0.858471\pi\) |
0.823881 | + | 0.566763i | \(0.191805\pi\) | |||||||
\(68\) | −1.64575 | − | 2.85052i | −0.199577 | − | 0.345677i | ||||
\(69\) | 1.64575 | + | 2.85052i | 0.198125 | + | 0.343163i | ||||
\(70\) | −1.00000 | −0.119523 | ||||||||
\(71\) | −7.29150 | + | 12.6293i | −0.865342 | + | 1.49882i | 0.00136488 | + | 0.999999i | \(0.499566\pi\) |
−0.866707 | + | 0.498818i | \(0.833768\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −2.29150 | + | 3.96900i | −0.268200 | + | 0.464536i | −0.968397 | − | 0.249414i | \(-0.919762\pi\) |
0.700197 | + | 0.713950i | \(0.253096\pi\) | |||||||
\(74\) | 0.645751 | + | 1.11847i | 0.0750671 | + | 0.130020i | ||||
\(75\) | −0.500000 | + | 0.866025i | −0.0577350 | + | 0.100000i | ||||
\(76\) | 1.64575 | + | 2.85052i | 0.188781 | + | 0.326978i | ||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | −2.00000 | −0.226455 | ||||||||
\(79\) | 4.00000 | + | 6.92820i | 0.450035 | + | 0.779484i | 0.998388 | − | 0.0567635i | \(-0.0180781\pi\) |
−0.548352 | + | 0.836247i | \(0.684745\pi\) | |||||||
\(80\) | −0.500000 | + | 0.866025i | −0.0559017 | + | 0.0968246i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 2.64575 | − | 4.58258i | 0.292174 | − | 0.506061i | ||||
\(83\) | −4.14575 | + | 7.18065i | −0.455055 | + | 0.788179i | −0.998691 | − | 0.0511421i | \(-0.983714\pi\) |
0.543636 | + | 0.839321i | \(0.317047\pi\) | |||||||
\(84\) | −0.500000 | + | 0.866025i | −0.0545545 | + | 0.0944911i | ||||
\(85\) | 3.29150 | 0.357014 | ||||||||
\(86\) | −2.00000 | − | 3.46410i | −0.215666 | − | 0.373544i | ||||
\(87\) | 3.14575 | + | 5.44860i | 0.337260 | + | 0.584151i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0.500000 | + | 0.866025i | 0.0527046 | + | 0.0912871i | ||||
\(91\) | 2.00000 | 0.209657 | ||||||||
\(92\) | −3.29150 | −0.343163 | ||||||||
\(93\) | 4.14575 | − | 3.71655i | 0.429894 | − | 0.385388i | ||||
\(94\) | 11.2915 | 1.16463 | ||||||||
\(95\) | −3.29150 | −0.337701 | ||||||||
\(96\) | 0.500000 | + | 0.866025i | 0.0510310 | + | 0.0883883i | ||||
\(97\) | −10.2915 | −1.04494 | −0.522472 | − | 0.852657i | \(-0.674990\pi\) | ||||
−0.522472 | + | 0.852657i | \(0.674990\pi\) | |||||||
\(98\) | −3.00000 | + | 5.19615i | −0.303046 | + | 0.524891i | ||||
\(99\) | 0.500000 | + | 0.866025i | 0.0502519 | + | 0.0870388i | ||||
\(100\) | −0.500000 | − | 0.866025i | −0.0500000 | − | 0.0866025i | ||||
\(101\) | 1.70850 | 0.170002 | 0.0850009 | − | 0.996381i | \(-0.472911\pi\) | ||||
0.0850009 | + | 0.996381i | \(0.472911\pi\) | |||||||
\(102\) | 1.64575 | − | 2.85052i | 0.162954 | − | 0.282244i | ||||
\(103\) | −1.79150 | + | 3.10297i | −0.176522 | + | 0.305745i | −0.940687 | − | 0.339276i | \(-0.889818\pi\) |
0.764165 | + | 0.645021i | \(0.223151\pi\) | |||||||
\(104\) | 1.00000 | − | 1.73205i | 0.0980581 | − | 0.169842i | ||||
\(105\) | −0.500000 | − | 0.866025i | −0.0487950 | − | 0.0845154i | ||||
\(106\) | 1.50000 | − | 2.59808i | 0.145693 | − | 0.252347i | ||||
\(107\) | −0.145751 | − | 0.252449i | −0.0140903 | − | 0.0244051i | 0.858894 | − | 0.512153i | \(-0.171152\pi\) |
−0.872985 | + | 0.487748i | \(0.837819\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −4.70850 | −0.450992 | −0.225496 | − | 0.974244i | \(-0.572400\pi\) | ||||
−0.225496 | + | 0.974244i | \(0.572400\pi\) | |||||||
\(110\) | −0.500000 | − | 0.866025i | −0.0476731 | − | 0.0825723i | ||||
\(111\) | −0.645751 | + | 1.11847i | −0.0612920 | + | 0.106161i | ||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | −4.29150 | + | 7.43310i | −0.403711 | + | 0.699247i | −0.994170 | − | 0.107820i | \(-0.965613\pi\) |
0.590460 | + | 0.807067i | \(0.298946\pi\) | |||||||
\(114\) | −1.64575 | + | 2.85052i | −0.154139 | + | 0.266976i | ||||
\(115\) | 1.64575 | − | 2.85052i | 0.153467 | − | 0.265813i | ||||
\(116\) | −6.29150 | −0.584151 | ||||||||
\(117\) | −1.00000 | − | 1.73205i | −0.0924500 | − | 0.160128i | ||||
\(118\) | −3.50000 | − | 6.06218i | −0.322201 | − | 0.558069i | ||||
\(119\) | −1.64575 | + | 2.85052i | −0.150866 | + | 0.261307i | ||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 5.00000 | + | 8.66025i | 0.454545 | + | 0.787296i | ||||
\(122\) | 3.29150 | 0.297999 | ||||||||
\(123\) | 5.29150 | 0.477119 | ||||||||
\(124\) | 1.14575 | + | 5.44860i | 0.102892 | + | 0.489299i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | −4.79150 | − | 8.29913i | −0.425177 | − | 0.736428i | 0.571260 | − | 0.820769i | \(-0.306455\pi\) |
−0.996437 | + | 0.0843409i | \(0.973122\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 2.00000 | − | 3.46410i | 0.176090 | − | 0.304997i | ||||
\(130\) | 1.00000 | + | 1.73205i | 0.0877058 | + | 0.151911i | ||||
\(131\) | 4.00000 | + | 6.92820i | 0.349482 | + | 0.605320i | 0.986157 | − | 0.165812i | \(-0.0530244\pi\) |
−0.636676 | + | 0.771132i | \(0.719691\pi\) | |||||||
\(132\) | −1.00000 | −0.0870388 | ||||||||
\(133\) | 1.64575 | − | 2.85052i | 0.142705 | − | 0.247172i | ||||
\(134\) | 0.645751 | − | 1.11847i | 0.0557844 | − | 0.0966214i | ||||
\(135\) | −0.500000 | + | 0.866025i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | 1.64575 | + | 2.85052i | 0.141122 | + | 0.244430i | ||||
\(137\) | 7.93725 | − | 13.7477i | 0.678125 | − | 1.17455i | −0.297419 | − | 0.954747i | \(-0.596126\pi\) |
0.975545 | − | 0.219801i | \(-0.0705407\pi\) | |||||||
\(138\) | −1.64575 | − | 2.85052i | −0.140096 | − | 0.242653i | ||||
\(139\) | −9.29150 | −0.788095 | −0.394047 | − | 0.919090i | \(-0.628925\pi\) | ||||
−0.394047 | + | 0.919090i | \(0.628925\pi\) | |||||||
\(140\) | 1.00000 | 0.0845154 | ||||||||
\(141\) | 5.64575 | + | 9.77873i | 0.475458 | + | 0.823517i | ||||
\(142\) | 7.29150 | − | 12.6293i | 0.611889 | − | 1.05982i | ||||
\(143\) | 1.00000 | + | 1.73205i | 0.0836242 | + | 0.144841i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 3.14575 | − | 5.44860i | 0.261240 | − | 0.452482i | ||||
\(146\) | 2.29150 | − | 3.96900i | 0.189646 | − | 0.328477i | ||||
\(147\) | −6.00000 | −0.494872 | ||||||||
\(148\) | −0.645751 | − | 1.11847i | −0.0530804 | − | 0.0919380i | ||||
\(149\) | −5.14575 | − | 8.91270i | −0.421556 | − | 0.730157i | 0.574536 | − | 0.818480i | \(-0.305183\pi\) |
−0.996092 | + | 0.0883226i | \(0.971849\pi\) | |||||||
\(150\) | 0.500000 | − | 0.866025i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | −8.29150 | −0.674753 | −0.337376 | − | 0.941370i | \(-0.609540\pi\) | ||||
−0.337376 | + | 0.941370i | \(0.609540\pi\) | |||||||
\(152\) | −1.64575 | − | 2.85052i | −0.133488 | − | 0.231208i | ||||
\(153\) | 3.29150 | 0.266102 | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | −5.29150 | − | 1.73205i | −0.425024 | − | 0.139122i | ||||
\(156\) | 2.00000 | 0.160128 | ||||||||
\(157\) | −8.70850 | −0.695014 | −0.347507 | − | 0.937677i | \(-0.612972\pi\) | ||||
−0.347507 | + | 0.937677i | \(0.612972\pi\) | |||||||
\(158\) | −4.00000 | − | 6.92820i | −0.318223 | − | 0.551178i | ||||
\(159\) | 3.00000 | 0.237915 | ||||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | 1.64575 | + | 2.85052i | 0.129703 | + | 0.224653i | ||||
\(162\) | 0.500000 | + | 0.866025i | 0.0392837 | + | 0.0680414i | ||||
\(163\) | 9.87451 | 0.773431 | 0.386716 | − | 0.922199i | \(-0.373610\pi\) | ||||
0.386716 | + | 0.922199i | \(0.373610\pi\) | |||||||
\(164\) | −2.64575 | + | 4.58258i | −0.206598 | + | 0.357839i | ||||
\(165\) | 0.500000 | − | 0.866025i | 0.0389249 | − | 0.0674200i | ||||
\(166\) | 4.14575 | − | 7.18065i | 0.321773 | − | 0.557327i | ||||
\(167\) | −8.64575 | − | 14.9749i | −0.669028 | − | 1.15879i | −0.978176 | − | 0.207777i | \(-0.933377\pi\) |
0.309148 | − | 0.951014i | \(-0.399956\pi\) | |||||||
\(168\) | 0.500000 | − | 0.866025i | 0.0385758 | − | 0.0668153i | ||||
\(169\) | 4.50000 | + | 7.79423i | 0.346154 | + | 0.599556i | ||||
\(170\) | −3.29150 | −0.252447 | ||||||||
\(171\) | −3.29150 | −0.251707 | ||||||||
\(172\) | 2.00000 | + | 3.46410i | 0.152499 | + | 0.264135i | ||||
\(173\) | 5.50000 | − | 9.52628i | 0.418157 | − | 0.724270i | −0.577597 | − | 0.816322i | \(-0.696009\pi\) |
0.995754 | + | 0.0920525i | \(0.0293428\pi\) | |||||||
\(174\) | −3.14575 | − | 5.44860i | −0.238479 | − | 0.413057i | ||||
\(175\) | −0.500000 | + | 0.866025i | −0.0377964 | + | 0.0654654i | ||||
\(176\) | 0.500000 | − | 0.866025i | 0.0376889 | − | 0.0652791i | ||||
\(177\) | 3.50000 | − | 6.06218i | 0.263076 | − | 0.455661i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.500000 | − | 0.866025i | −0.0373718 | − | 0.0647298i | 0.846735 | − | 0.532016i | \(-0.178565\pi\) |
−0.884106 | + | 0.467286i | \(0.845232\pi\) | |||||||
\(180\) | −0.500000 | − | 0.866025i | −0.0372678 | − | 0.0645497i | ||||
\(181\) | 7.29150 | − | 12.6293i | 0.541973 | − | 0.938725i | −0.456818 | − | 0.889560i | \(-0.651011\pi\) |
0.998791 | − | 0.0491646i | \(-0.0156559\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | 1.64575 | + | 2.85052i | 0.121657 | + | 0.210717i | ||||
\(184\) | 3.29150 | 0.242653 | ||||||||
\(185\) | 1.29150 | 0.0949532 | ||||||||
\(186\) | −4.14575 | + | 3.71655i | −0.303981 | + | 0.272511i | ||||
\(187\) | −3.29150 | −0.240699 | ||||||||
\(188\) | −11.2915 | −0.823517 | ||||||||
\(189\) | −0.500000 | − | 0.866025i | −0.0363696 | − | 0.0629941i | ||||
\(190\) | 3.29150 | 0.238791 | ||||||||
\(191\) | 7.93725 | − | 13.7477i | 0.574320 | − | 0.994751i | −0.421796 | − | 0.906691i | \(-0.638600\pi\) |
0.996115 | − | 0.0880597i | \(-0.0280666\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −1.14575 | − | 1.98450i | −0.0824730 | − | 0.142847i | 0.821839 | − | 0.569720i | \(-0.192948\pi\) |
−0.904312 | + | 0.426873i | \(0.859615\pi\) | |||||||
\(194\) | 10.2915 | 0.738887 | ||||||||
\(195\) | −1.00000 | + | 1.73205i | −0.0716115 | + | 0.124035i | ||||
\(196\) | 3.00000 | − | 5.19615i | 0.214286 | − | 0.371154i | ||||
\(197\) | 9.58301 | − | 16.5983i | 0.682761 | − | 1.18258i | −0.291374 | − | 0.956609i | \(-0.594112\pi\) |
0.974135 | − | 0.225967i | \(-0.0725542\pi\) | |||||||
\(198\) | −0.500000 | − | 0.866025i | −0.0355335 | − | 0.0615457i | ||||
\(199\) | 4.85425 | − | 8.40781i | 0.344109 | − | 0.596014i | −0.641083 | − | 0.767472i | \(-0.721515\pi\) |
0.985191 | + | 0.171458i | \(0.0548478\pi\) | |||||||
\(200\) | 0.500000 | + | 0.866025i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 1.29150 | 0.0910956 | ||||||||
\(202\) | −1.70850 | −0.120209 | ||||||||
\(203\) | 3.14575 | + | 5.44860i | 0.220788 | + | 0.382417i | ||||
\(204\) | −1.64575 | + | 2.85052i | −0.115226 | + | 0.199577i | ||||
\(205\) | −2.64575 | − | 4.58258i | −0.184787 | − | 0.320061i | ||||
\(206\) | 1.79150 | − | 3.10297i | 0.124820 | − | 0.216194i | ||||
\(207\) | 1.64575 | − | 2.85052i | 0.114388 | − | 0.198125i | ||||
\(208\) | −1.00000 | + | 1.73205i | −0.0693375 | + | 0.120096i | ||||
\(209\) | 3.29150 | 0.227678 | ||||||||
\(210\) | 0.500000 | + | 0.866025i | 0.0345033 | + | 0.0597614i | ||||
\(211\) | −2.35425 | − | 4.07768i | −0.162073 | − | 0.280719i | 0.773539 | − | 0.633749i | \(-0.218485\pi\) |
−0.935612 | + | 0.353030i | \(0.885151\pi\) | |||||||
\(212\) | −1.50000 | + | 2.59808i | −0.103020 | + | 0.178437i | ||||
\(213\) | 14.5830 | 0.999211 | ||||||||
\(214\) | 0.145751 | + | 0.252449i | 0.00996335 | + | 0.0172570i | ||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 4.14575 | − | 3.71655i | 0.281432 | − | 0.252296i | ||||
\(218\) | 4.70850 | 0.318900 | ||||||||
\(219\) | 4.58301 | 0.309691 | ||||||||
\(220\) | 0.500000 | + | 0.866025i | 0.0337100 | + | 0.0583874i | ||||
\(221\) | 6.58301 | 0.442821 | ||||||||
\(222\) | 0.645751 | − | 1.11847i | 0.0433400 | − | 0.0750671i | ||||
\(223\) | 12.7915 | + | 22.1555i | 0.856582 | + | 1.48364i | 0.875169 | + | 0.483817i | \(0.160750\pi\) |
−0.0185869 | + | 0.999827i | \(0.505917\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.29150 | − | 7.43310i | 0.285467 | − | 0.494442i | ||||
\(227\) | 4.43725 | − | 7.68555i | 0.294511 | − | 0.510108i | −0.680360 | − | 0.732878i | \(-0.738177\pi\) |
0.974871 | + | 0.222770i | \(0.0715099\pi\) | |||||||
\(228\) | 1.64575 | − | 2.85052i | 0.108993 | − | 0.188781i | ||||
\(229\) | −3.93725 | − | 6.81952i | −0.260181 | − | 0.450647i | 0.706109 | − | 0.708103i | \(-0.250449\pi\) |
−0.966290 | + | 0.257457i | \(0.917116\pi\) | |||||||
\(230\) | −1.64575 | + | 2.85052i | −0.108518 | + | 0.187958i | ||||
\(231\) | 0.500000 | + | 0.866025i | 0.0328976 | + | 0.0569803i | ||||
\(232\) | 6.29150 | 0.413057 | ||||||||
\(233\) | 11.8745 | 0.777925 | 0.388962 | − | 0.921254i | \(-0.372834\pi\) | ||||
0.388962 | + | 0.921254i | \(0.372834\pi\) | |||||||
\(234\) | 1.00000 | + | 1.73205i | 0.0653720 | + | 0.113228i | ||||
\(235\) | 5.64575 | − | 9.77873i | 0.368288 | − | 0.637894i | ||||
\(236\) | 3.50000 | + | 6.06218i | 0.227831 | + | 0.394614i | ||||
\(237\) | 4.00000 | − | 6.92820i | 0.259828 | − | 0.450035i | ||||
\(238\) | 1.64575 | − | 2.85052i | 0.106678 | − | 0.184772i | ||||
\(239\) | −8.29150 | + | 14.3613i | −0.536333 | + | 0.928956i | 0.462765 | + | 0.886481i | \(0.346857\pi\) |
−0.999098 | + | 0.0424744i | \(0.986476\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −2.20850 | − | 3.82523i | −0.142262 | − | 0.246405i | 0.786086 | − | 0.618117i | \(-0.212104\pi\) |
−0.928348 | + | 0.371712i | \(0.878771\pi\) | |||||||
\(242\) | −5.00000 | − | 8.66025i | −0.321412 | − | 0.556702i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −3.29150 | −0.210717 | ||||||||
\(245\) | 3.00000 | + | 5.19615i | 0.191663 | + | 0.331970i | ||||
\(246\) | −5.29150 | −0.337374 | ||||||||
\(247\) | −6.58301 | −0.418867 | ||||||||
\(248\) | −1.14575 | − | 5.44860i | −0.0727553 | − | 0.345987i | ||||
\(249\) | 8.29150 | 0.525453 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −10.0000 | − | 17.3205i | −0.631194 | − | 1.09326i | −0.987308 | − | 0.158818i | \(-0.949232\pi\) |
0.356113 | − | 0.934443i | \(-0.384102\pi\) | |||||||
\(252\) | 1.00000 | 0.0629941 | ||||||||
\(253\) | −1.64575 | + | 2.85052i | −0.103467 | + | 0.179211i | ||||
\(254\) | 4.79150 | + | 8.29913i | 0.300646 | + | 0.520733i | ||||
\(255\) | −1.64575 | − | 2.85052i | −0.103061 | − | 0.178507i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.93725 | − | 8.55157i | 0.307977 | − | 0.533433i | −0.669942 | − | 0.742413i | \(-0.733681\pi\) |
0.977920 | + | 0.208981i | \(0.0670145\pi\) | |||||||
\(258\) | −2.00000 | + | 3.46410i | −0.124515 | + | 0.215666i | ||||
\(259\) | −0.645751 | + | 1.11847i | −0.0401250 | + | 0.0694986i | ||||
\(260\) | −1.00000 | − | 1.73205i | −0.0620174 | − | 0.107417i | ||||
\(261\) | 3.14575 | − | 5.44860i | 0.194717 | − | 0.337260i | ||||
\(262\) | −4.00000 | − | 6.92820i | −0.247121 | − | 0.428026i | ||||
\(263\) | −8.58301 | −0.529251 | −0.264625 | − | 0.964351i | \(-0.585248\pi\) | ||||
−0.264625 | + | 0.964351i | \(0.585248\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −1.50000 | − | 2.59808i | −0.0921443 | − | 0.159599i | ||||
\(266\) | −1.64575 | + | 2.85052i | −0.100907 | + | 0.174777i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.645751 | + | 1.11847i | −0.0394455 | + | 0.0683217i | ||||
\(269\) | 3.00000 | − | 5.19615i | 0.182913 | − | 0.316815i | −0.759958 | − | 0.649972i | \(-0.774781\pi\) |
0.942871 | + | 0.333157i | \(0.108114\pi\) | |||||||
\(270\) | 0.500000 | − | 0.866025i | 0.0304290 | − | 0.0527046i | ||||
\(271\) | −5.70850 | −0.346767 | −0.173383 | − | 0.984854i | \(-0.555470\pi\) | ||||
−0.173383 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(272\) | −1.64575 | − | 2.85052i | −0.0997883 | − | 0.172838i | ||||
\(273\) | −1.00000 | − | 1.73205i | −0.0605228 | − | 0.104828i | ||||
\(274\) | −7.93725 | + | 13.7477i | −0.479507 | + | 0.830531i | ||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 1.64575 | + | 2.85052i | 0.0990626 | + | 0.171581i | ||||
\(277\) | 0.708497 | 0.0425695 | 0.0212847 | − | 0.999773i | \(-0.493224\pi\) | ||||
0.0212847 | + | 0.999773i | \(0.493224\pi\) | |||||||
\(278\) | 9.29150 | 0.557267 | ||||||||
\(279\) | −5.29150 | − | 1.73205i | −0.316794 | − | 0.103695i | ||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | −12.0000 | −0.715860 | −0.357930 | − | 0.933748i | \(-0.616517\pi\) | ||||
−0.357930 | + | 0.933748i | \(0.616517\pi\) | |||||||
\(282\) | −5.64575 | − | 9.77873i | −0.336200 | − | 0.582315i | ||||
\(283\) | 14.0000 | 0.832214 | 0.416107 | − | 0.909316i | \(-0.363394\pi\) | ||||
0.416107 | + | 0.909316i | \(0.363394\pi\) | |||||||
\(284\) | −7.29150 | + | 12.6293i | −0.432671 | + | 0.749408i | ||||
\(285\) | 1.64575 | + | 2.85052i | 0.0974859 | + | 0.168851i | ||||
\(286\) | −1.00000 | − | 1.73205i | −0.0591312 | − | 0.102418i | ||||
\(287\) | 5.29150 | 0.312348 | ||||||||
\(288\) | 0.500000 | − | 0.866025i | 0.0294628 | − | 0.0510310i | ||||
\(289\) | 3.08301 | − | 5.33992i | 0.181353 | − | 0.314113i | ||||
\(290\) | −3.14575 | + | 5.44860i | −0.184725 | + | 0.319953i | ||||
\(291\) | 5.14575 | + | 8.91270i | 0.301649 | + | 0.522472i | ||||
\(292\) | −2.29150 | + | 3.96900i | −0.134100 | + | 0.232268i | ||||
\(293\) | 11.7915 | + | 20.4235i | 0.688867 | + | 1.19315i | 0.972205 | + | 0.234132i | \(0.0752249\pi\) |
−0.283338 | + | 0.959020i | \(0.591442\pi\) | |||||||
\(294\) | 6.00000 | 0.349927 | ||||||||
\(295\) | −7.00000 | −0.407556 | ||||||||
\(296\) | 0.645751 | + | 1.11847i | 0.0375335 | + | 0.0650100i | ||||
\(297\) | 0.500000 | − | 0.866025i | 0.0290129 | − | 0.0502519i | ||||
\(298\) | 5.14575 | + | 8.91270i | 0.298085 | + | 0.516299i | ||||
\(299\) | 3.29150 | − | 5.70105i | 0.190353 | − | 0.329700i | ||||
\(300\) | −0.500000 | + | 0.866025i | −0.0288675 | + | 0.0500000i | ||||
\(301\) | 2.00000 | − | 3.46410i | 0.115278 | − | 0.199667i | ||||
\(302\) | 8.29150 | 0.477122 | ||||||||
\(303\) | −0.854249 | − | 1.47960i | −0.0490753 | − | 0.0850009i | ||||
\(304\) | 1.64575 | + | 2.85052i | 0.0943903 | + | 0.163489i | ||||
\(305\) | 1.64575 | − | 2.85052i | 0.0942354 | − | 0.163221i | ||||
\(306\) | −3.29150 | −0.188163 | ||||||||
\(307\) | 9.35425 | + | 16.2020i | 0.533875 | + | 0.924699i | 0.999217 | + | 0.0395678i | \(0.0125981\pi\) |
−0.465342 | + | 0.885131i | \(0.654069\pi\) | |||||||
\(308\) | −1.00000 | −0.0569803 | ||||||||
\(309\) | 3.58301 | 0.203830 | ||||||||
\(310\) | 5.29150 | + | 1.73205i | 0.300537 | + | 0.0983739i | ||||
\(311\) | 18.0000 | 1.02069 | 0.510343 | − | 0.859971i | \(-0.329518\pi\) | ||||
0.510343 | + | 0.859971i | \(0.329518\pi\) | |||||||
\(312\) | −2.00000 | −0.113228 | ||||||||
\(313\) | −7.85425 | − | 13.6040i | −0.443948 | − | 0.768941i | 0.554030 | − | 0.832497i | \(-0.313089\pi\) |
−0.997978 | + | 0.0635556i | \(0.979756\pi\) | |||||||
\(314\) | 8.70850 | 0.491449 | ||||||||
\(315\) | −0.500000 | + | 0.866025i | −0.0281718 | + | 0.0487950i | ||||
\(316\) | 4.00000 | + | 6.92820i | 0.225018 | + | 0.389742i | ||||
\(317\) | −4.20850 | − | 7.28933i | −0.236373 | − | 0.409410i | 0.723298 | − | 0.690536i | \(-0.242625\pi\) |
−0.959671 | + | 0.281126i | \(0.909292\pi\) | |||||||
\(318\) | −3.00000 | −0.168232 | ||||||||
\(319\) | −3.14575 | + | 5.44860i | −0.176128 | + | 0.305063i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | −0.145751 | + | 0.252449i | −0.00813504 | + | 0.0140903i | ||||
\(322\) | −1.64575 | − | 2.85052i | −0.0917141 | − | 0.158854i | ||||
\(323\) | 5.41699 | − | 9.38251i | 0.301410 | − | 0.522057i | ||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | −9.87451 | −0.546898 | ||||||||
\(327\) | 2.35425 | + | 4.07768i | 0.130190 | + | 0.225496i | ||||
\(328\) | 2.64575 | − | 4.58258i | 0.146087 | − | 0.253030i | ||||
\(329\) | 5.64575 | + | 9.77873i | 0.311260 | + | 0.539119i | ||||
\(330\) | −0.500000 | + | 0.866025i | −0.0275241 | + | 0.0476731i | ||||
\(331\) | 4.93725 | − | 8.55157i | 0.271376 | − | 0.470037i | −0.697838 | − | 0.716255i | \(-0.745855\pi\) |
0.969214 | + | 0.246218i | \(0.0791880\pi\) | |||||||
\(332\) | −4.14575 | + | 7.18065i | −0.227528 | + | 0.394089i | ||||
\(333\) | 1.29150 | 0.0707739 | ||||||||
\(334\) | 8.64575 | + | 14.9749i | 0.473074 | + | 0.819389i | ||||
\(335\) | −0.645751 | − | 1.11847i | −0.0352812 | − | 0.0611088i | ||||
\(336\) | −0.500000 | + | 0.866025i | −0.0272772 | + | 0.0472456i | ||||
\(337\) | −14.8745 | −0.810266 | −0.405133 | − | 0.914258i | \(-0.632775\pi\) | ||||
−0.405133 | + | 0.914258i | \(0.632775\pi\) | |||||||
\(338\) | −4.50000 | − | 7.79423i | −0.244768 | − | 0.423950i | ||||
\(339\) | 8.58301 | 0.466165 | ||||||||
\(340\) | 3.29150 | 0.178507 | ||||||||
\(341\) | 5.29150 | + | 1.73205i | 0.286551 | + | 0.0937958i | ||||
\(342\) | 3.29150 | 0.177984 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −2.00000 | − | 3.46410i | −0.107833 | − | 0.186772i | ||||
\(345\) | −3.29150 | −0.177209 | ||||||||
\(346\) | −5.50000 | + | 9.52628i | −0.295682 | + | 0.512136i | ||||
\(347\) | −3.14575 | − | 5.44860i | −0.168873 | − | 0.292496i | 0.769151 | − | 0.639067i | \(-0.220679\pi\) |
−0.938024 | + | 0.346571i | \(0.887346\pi\) | |||||||
\(348\) | 3.14575 | + | 5.44860i | 0.168630 | + | 0.292076i | ||||
\(349\) | −24.4575 | −1.30918 | −0.654590 | − | 0.755984i | \(-0.727159\pi\) | ||||
−0.654590 | + | 0.755984i | \(0.727159\pi\) | |||||||
\(350\) | 0.500000 | − | 0.866025i | 0.0267261 | − | 0.0462910i | ||||
\(351\) | −1.00000 | + | 1.73205i | −0.0533761 | + | 0.0924500i | ||||
\(352\) | −0.500000 | + | 0.866025i | −0.0266501 | + | 0.0461593i | ||||
\(353\) | 15.5830 | + | 26.9906i | 0.829400 | + | 1.43656i | 0.898510 | + | 0.438953i | \(0.144651\pi\) |
−0.0691102 | + | 0.997609i | \(0.522016\pi\) | |||||||
\(354\) | −3.50000 | + | 6.06218i | −0.186023 | + | 0.322201i | ||||
\(355\) | −7.29150 | − | 12.6293i | −0.386993 | − | 0.670291i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.29150 | 0.174205 | ||||||||
\(358\) | 0.500000 | + | 0.866025i | 0.0264258 | + | 0.0457709i | ||||
\(359\) | 7.64575 | − | 13.2428i | 0.403527 | − | 0.698930i | −0.590622 | − | 0.806949i | \(-0.701117\pi\) |
0.994149 | + | 0.108019i | \(0.0344507\pi\) | |||||||
\(360\) | 0.500000 | + | 0.866025i | 0.0263523 | + | 0.0456435i | ||||
\(361\) | 4.08301 | − | 7.07197i | 0.214895 | − | 0.372209i | ||||
\(362\) | −7.29150 | + | 12.6293i | −0.383233 | + | 0.663779i | ||||
\(363\) | 5.00000 | − | 8.66025i | 0.262432 | − | 0.454545i | ||||
\(364\) | 2.00000 | 0.104828 | ||||||||
\(365\) | −2.29150 | − | 3.96900i | −0.119943 | − | 0.207747i | ||||
\(366\) | −1.64575 | − | 2.85052i | −0.0860248 | − | 0.148999i | ||||
\(367\) | −16.5830 | + | 28.7226i | −0.865626 | + | 1.49931i | 0.000798600 | 1.00000i | \(0.499746\pi\) | |
−0.866424 | + | 0.499308i | \(0.833588\pi\) | |||||||
\(368\) | −3.29150 | −0.171581 | ||||||||
\(369\) | −2.64575 | − | 4.58258i | −0.137732 | − | 0.238559i | ||||
\(370\) | −1.29150 | −0.0671420 | ||||||||
\(371\) | 3.00000 | 0.155752 | ||||||||
\(372\) | 4.14575 | − | 3.71655i | 0.214947 | − | 0.192694i | ||||
\(373\) | −27.2915 | −1.41310 | −0.706550 | − | 0.707663i | \(-0.749750\pi\) | ||||
−0.706550 | + | 0.707663i | \(0.749750\pi\) | |||||||
\(374\) | 3.29150 | 0.170200 | ||||||||
\(375\) | −0.500000 | − | 0.866025i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | 11.2915 | 0.582315 | ||||||||
\(377\) | 6.29150 | − | 10.8972i | 0.324029 | − | 0.561234i | ||||
\(378\) | 0.500000 | + | 0.866025i | 0.0257172 | + | 0.0445435i | ||||
\(379\) | −6.70850 | − | 11.6195i | −0.344592 | − | 0.596851i | 0.640687 | − | 0.767802i | \(-0.278650\pi\) |
−0.985280 | + | 0.170950i | \(0.945316\pi\) | |||||||
\(380\) | −3.29150 | −0.168851 | ||||||||
\(381\) | −4.79150 | + | 8.29913i | −0.245476 | + | 0.425177i | ||||
\(382\) | −7.93725 | + | 13.7477i | −0.406105 | + | 0.703395i | ||||
\(383\) | −16.6458 | + | 28.8313i | −0.850558 | + | 1.47321i | 0.0301472 | + | 0.999545i | \(0.490402\pi\) |
−0.880705 | + | 0.473664i | \(0.842931\pi\) | |||||||
\(384\) | 0.500000 | + | 0.866025i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 0.500000 | − | 0.866025i | 0.0254824 | − | 0.0441367i | ||||
\(386\) | 1.14575 | + | 1.98450i | 0.0583172 | + | 0.101008i | ||||
\(387\) | −4.00000 | −0.203331 | ||||||||
\(388\) | −10.2915 | −0.522472 | ||||||||
\(389\) | −1.00000 | − | 1.73205i | −0.0507020 | − | 0.0878185i | 0.839561 | − | 0.543266i | \(-0.182813\pi\) |
−0.890263 | + | 0.455448i | \(0.849479\pi\) | |||||||
\(390\) | 1.00000 | − | 1.73205i | 0.0506370 | − | 0.0877058i | ||||
\(391\) | 5.41699 | + | 9.38251i | 0.273949 | + | 0.474494i | ||||
\(392\) | −3.00000 | + | 5.19615i | −0.151523 | + | 0.262445i | ||||
\(393\) | 4.00000 | − | 6.92820i | 0.201773 | − | 0.349482i | ||||
\(394\) | −9.58301 | + | 16.5983i | −0.482785 | + | 0.836208i | ||||
\(395\) | −8.00000 | −0.402524 | ||||||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | −6.58301 | − | 11.4021i | −0.330392 | − | 0.572255i | 0.652197 | − | 0.758049i | \(-0.273847\pi\) |
−0.982589 | + | 0.185794i | \(0.940514\pi\) | |||||||
\(398\) | −4.85425 | + | 8.40781i | −0.243322 | + | 0.421445i | ||||
\(399\) | −3.29150 | −0.164781 | ||||||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | −7.16601 | −0.357853 | −0.178927 | − | 0.983862i | \(-0.557263\pi\) | ||||
−0.178927 | + | 0.983862i | \(0.557263\pi\) | |||||||
\(402\) | −1.29150 | −0.0644143 | ||||||||
\(403\) | −10.5830 | − | 3.46410i | −0.527177 | − | 0.172559i | ||||
\(404\) | 1.70850 | 0.0850009 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | −3.14575 | − | 5.44860i | −0.156121 | − | 0.270410i | ||||
\(407\) | −1.29150 | −0.0640174 | ||||||||
\(408\) | 1.64575 | − | 2.85052i | 0.0814768 | − | 0.141122i | ||||
\(409\) | 4.50000 | + | 7.79423i | 0.222511 | + | 0.385400i | 0.955570 | − | 0.294765i | \(-0.0952414\pi\) |
−0.733059 | + | 0.680165i | \(0.761908\pi\) | |||||||
\(410\) | 2.64575 | + | 4.58258i | 0.130664 | + | 0.226317i | ||||
\(411\) | −15.8745 | −0.783032 | ||||||||
\(412\) | −1.79150 | + | 3.10297i | −0.0882610 | + | 0.152873i | ||||
\(413\) | 3.50000 | − | 6.06218i | 0.172224 | − | 0.298300i | ||||
\(414\) | −1.64575 | + | 2.85052i | −0.0808843 | + | 0.140096i | ||||
\(415\) | −4.14575 | − | 7.18065i | −0.203507 | − | 0.352484i | ||||
\(416\) | 1.00000 | − | 1.73205i | 0.0490290 | − | 0.0849208i | ||||
\(417\) | 4.64575 | + | 8.04668i | 0.227503 | + | 0.394047i | ||||
\(418\) | −3.29150 | −0.160993 | ||||||||
\(419\) | −15.5830 | −0.761280 | −0.380640 | − | 0.924723i | \(-0.624296\pi\) | ||||
−0.380640 | + | 0.924723i | \(0.624296\pi\) | |||||||
\(420\) | −0.500000 | − | 0.866025i | −0.0243975 | − | 0.0422577i | ||||
\(421\) | 10.3542 | − | 17.9341i | 0.504635 | − | 0.874054i | −0.495350 | − | 0.868693i | \(-0.664960\pi\) |
0.999986 | − | 0.00536057i | \(-0.00170633\pi\) | |||||||
\(422\) | 2.35425 | + | 4.07768i | 0.114603 | + | 0.198498i | ||||
\(423\) | 5.64575 | − | 9.77873i | 0.274506 | − | 0.475458i | ||||
\(424\) | 1.50000 | − | 2.59808i | 0.0728464 | − | 0.126174i | ||||
\(425\) | −1.64575 | + | 2.85052i | −0.0798307 | + | 0.138271i | ||||
\(426\) | −14.5830 | −0.706549 | ||||||||
\(427\) | 1.64575 | + | 2.85052i | 0.0796435 | + | 0.137947i | ||||
\(428\) | −0.145751 | − | 0.252449i | −0.00704516 | − | 0.0122026i | ||||
\(429\) | 1.00000 | − | 1.73205i | 0.0482805 | − | 0.0836242i | ||||
\(430\) | 4.00000 | 0.192897 | ||||||||
\(431\) | −0.645751 | − | 1.11847i | −0.0311047 | − | 0.0538750i | 0.850054 | − | 0.526696i | \(-0.176569\pi\) |
−0.881159 | + | 0.472821i | \(0.843236\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 22.0000 | 1.05725 | 0.528626 | − | 0.848855i | \(-0.322707\pi\) | ||||
0.528626 | + | 0.848855i | \(0.322707\pi\) | |||||||
\(434\) | −4.14575 | + | 3.71655i | −0.199002 | + | 0.178400i | ||||
\(435\) | −6.29150 | −0.301654 | ||||||||
\(436\) | −4.70850 | −0.225496 | ||||||||
\(437\) | −5.41699 | − | 9.38251i | −0.259130 | − | 0.448826i | ||||
\(438\) | −4.58301 | −0.218984 | ||||||||
\(439\) | −3.14575 | + | 5.44860i | −0.150139 | + | 0.260048i | −0.931278 | − | 0.364309i | \(-0.881305\pi\) |
0.781140 | + | 0.624356i | \(0.214639\pi\) | |||||||
\(440\) | −0.500000 | − | 0.866025i | −0.0238366 | − | 0.0412861i | ||||
\(441\) | 3.00000 | + | 5.19615i | 0.142857 | + | 0.247436i | ||||
\(442\) | −6.58301 | −0.313122 | ||||||||
\(443\) | −15.2915 | + | 26.4857i | −0.726521 | + | 1.25837i | 0.231824 | + | 0.972758i | \(0.425531\pi\) |
−0.958345 | + | 0.285614i | \(0.907803\pi\) | |||||||
\(444\) | −0.645751 | + | 1.11847i | −0.0306460 | + | 0.0530804i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −12.7915 | − | 22.1555i | −0.605695 | − | 1.04909i | ||||
\(447\) | −5.14575 | + | 8.91270i | −0.243386 | + | 0.421556i | ||||
\(448\) | −0.500000 | − | 0.866025i | −0.0236228 | − | 0.0409159i | ||||
\(449\) | −5.41699 | −0.255644 | −0.127822 | − | 0.991797i | \(-0.540799\pi\) | ||||
−0.127822 | + | 0.991797i | \(0.540799\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | 2.64575 | + | 4.58258i | 0.124584 | + | 0.215785i | ||||
\(452\) | −4.29150 | + | 7.43310i | −0.201855 | + | 0.349624i | ||||
\(453\) | 4.14575 | + | 7.18065i | 0.194784 | + | 0.337376i | ||||
\(454\) | −4.43725 | + | 7.68555i | −0.208251 | + | 0.360701i | ||||
\(455\) | −1.00000 | + | 1.73205i | −0.0468807 | + | 0.0811998i | ||||
\(456\) | −1.64575 | + | 2.85052i | −0.0770694 | + | 0.133488i | ||||
\(457\) | −35.1660 | −1.64500 | −0.822498 | − | 0.568768i | \(-0.807420\pi\) | ||||
−0.822498 | + | 0.568768i | \(0.807420\pi\) | |||||||
\(458\) | 3.93725 | + | 6.81952i | 0.183976 | + | 0.318655i | ||||
\(459\) | −1.64575 | − | 2.85052i | −0.0768171 | − | 0.133051i | ||||
\(460\) | 1.64575 | − | 2.85052i | 0.0767336 | − | 0.132906i | ||||
\(461\) | 6.29150 | 0.293024 | 0.146512 | − | 0.989209i | \(-0.453195\pi\) | ||||
0.146512 | + | 0.989209i | \(0.453195\pi\) | |||||||
\(462\) | −0.500000 | − | 0.866025i | −0.0232621 | − | 0.0402911i | ||||
\(463\) | 15.0000 | 0.697109 | 0.348555 | − | 0.937288i | \(-0.386673\pi\) | ||||
0.348555 | + | 0.937288i | \(0.386673\pi\) | |||||||
\(464\) | −6.29150 | −0.292076 | ||||||||
\(465\) | 1.14575 | + | 5.44860i | 0.0531329 | + | 0.252673i | ||||
\(466\) | −11.8745 | −0.550076 | ||||||||
\(467\) | 4.29150 | 0.198587 | 0.0992935 | − | 0.995058i | \(-0.468342\pi\) | ||||
0.0992935 | + | 0.995058i | \(0.468342\pi\) | |||||||
\(468\) | −1.00000 | − | 1.73205i | −0.0462250 | − | 0.0800641i | ||||
\(469\) | 1.29150 | 0.0596361 | ||||||||
\(470\) | −5.64575 | + | 9.77873i | −0.260419 | + | 0.451059i | ||||
\(471\) | 4.35425 | + | 7.54178i | 0.200633 | + | 0.347507i | ||||
\(472\) | −3.50000 | − | 6.06218i | −0.161101 | − | 0.279034i | ||||
\(473\) | 4.00000 | 0.183920 | ||||||||
\(474\) | −4.00000 | + | 6.92820i | −0.183726 | + | 0.318223i | ||||
\(475\) | 1.64575 | − | 2.85052i | 0.0755122 | − | 0.130791i | ||||
\(476\) | −1.64575 | + | 2.85052i | −0.0754329 | + | 0.130654i | ||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | 8.29150 | − | 14.3613i | 0.379245 | − | 0.656871i | ||||
\(479\) | 17.6458 | + | 30.5633i | 0.806255 | + | 1.39647i | 0.915441 | + | 0.402453i | \(0.131842\pi\) |
−0.109186 | + | 0.994021i | \(0.534824\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 2.58301 | 0.117775 | ||||||||
\(482\) | 2.20850 | + | 3.82523i | 0.100594 | + | 0.174234i | ||||
\(483\) | 1.64575 | − | 2.85052i | 0.0748843 | − | 0.129703i | ||||
\(484\) | 5.00000 | + | 8.66025i | 0.227273 | + | 0.393648i | ||||
\(485\) | 5.14575 | − | 8.91270i | 0.233657 | − | 0.404705i | ||||
\(486\) | 0.500000 | − | 0.866025i | 0.0226805 | − | 0.0392837i | ||||
\(487\) | −13.0830 | + | 22.6604i | −0.592848 | + | 1.02684i | 0.400999 | + | 0.916078i | \(0.368663\pi\) |
−0.993847 | + | 0.110764i | \(0.964670\pi\) | |||||||
\(488\) | 3.29150 | 0.148999 | ||||||||
\(489\) | −4.93725 | − | 8.55157i | −0.223270 | − | 0.386716i | ||||
\(490\) | −3.00000 | − | 5.19615i | −0.135526 | − | 0.234738i | ||||
\(491\) | −16.7915 | + | 29.0837i | −0.757790 | + | 1.31253i | 0.186185 | + | 0.982515i | \(0.440387\pi\) |
−0.943975 | + | 0.330016i | \(0.892946\pi\) | |||||||
\(492\) | 5.29150 | 0.238559 | ||||||||
\(493\) | 10.3542 | + | 17.9341i | 0.466332 | + | 0.807711i | ||||
\(494\) | 6.58301 | 0.296183 | ||||||||
\(495\) | −1.00000 | −0.0449467 | ||||||||
\(496\) | 1.14575 | + | 5.44860i | 0.0514458 | + | 0.244649i | ||||
\(497\) | 14.5830 | 0.654137 | ||||||||
\(498\) | −8.29150 | −0.371551 | ||||||||
\(499\) | −0.645751 | − | 1.11847i | −0.0289078 | − | 0.0500698i | 0.851210 | − | 0.524826i | \(-0.175870\pi\) |
−0.880117 | + | 0.474756i | \(0.842536\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −8.64575 | + | 14.9749i | −0.386264 | + | 0.669028i | ||||
\(502\) | 10.0000 | + | 17.3205i | 0.446322 | + | 0.773052i | ||||
\(503\) | 5.35425 | + | 9.27383i | 0.238734 | + | 0.413500i | 0.960351 | − | 0.278793i | \(-0.0899342\pi\) |
−0.721617 | + | 0.692292i | \(0.756601\pi\) | |||||||
\(504\) | −1.00000 | −0.0445435 | ||||||||
\(505\) | −0.854249 | + | 1.47960i | −0.0380136 | + | 0.0658414i | ||||
\(506\) | 1.64575 | − | 2.85052i | 0.0731626 | − | 0.126721i | ||||
\(507\) | 4.50000 | − | 7.79423i | 0.199852 | − | 0.346154i | ||||
\(508\) | −4.79150 | − | 8.29913i | −0.212589 | − | 0.368214i | ||||
\(509\) | 13.8542 | − | 23.9963i | 0.614079 | − | 1.06362i | −0.376467 | − | 0.926430i | \(-0.622861\pi\) |
0.990545 | − | 0.137185i | \(-0.0438056\pi\) | |||||||
\(510\) | 1.64575 | + | 2.85052i | 0.0728751 | + | 0.126223i | ||||
\(511\) | 4.58301 | 0.202740 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.64575 | + | 2.85052i | 0.0726617 | + | 0.125854i | ||||
\(514\) | −4.93725 | + | 8.55157i | −0.217773 | + | 0.377194i | ||||
\(515\) | −1.79150 | − | 3.10297i | −0.0789430 | − | 0.136733i | ||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | −5.64575 | + | 9.77873i | −0.248300 | + | 0.430068i | ||||
\(518\) | 0.645751 | − | 1.11847i | 0.0283727 | − | 0.0491429i | ||||
\(519\) | −11.0000 | −0.482846 | ||||||||
\(520\) | 1.00000 | + | 1.73205i | 0.0438529 | + | 0.0759555i | ||||
\(521\) | 12.8745 | + | 22.2993i | 0.564042 | + | 0.976950i | 0.997138 | + | 0.0756022i | \(0.0240879\pi\) |
−0.433096 | + | 0.901348i | \(0.642579\pi\) | |||||||
\(522\) | −3.14575 | + | 5.44860i | −0.137686 | + | 0.238479i | ||||
\(523\) | 5.16601 | 0.225894 | 0.112947 | − | 0.993601i | \(-0.463971\pi\) | ||||
0.112947 | + | 0.993601i | \(0.463971\pi\) | |||||||
\(524\) | 4.00000 | + | 6.92820i | 0.174741 | + | 0.302660i | ||||
\(525\) | 1.00000 | 0.0436436 | ||||||||
\(526\) | 8.58301 | 0.374237 | ||||||||
\(527\) | 13.6458 | − | 12.2330i | 0.594418 | − | 0.532879i | ||||
\(528\) | −1.00000 | −0.0435194 | ||||||||
\(529\) | −12.1660 | −0.528957 | ||||||||
\(530\) | 1.50000 | + | 2.59808i | 0.0651558 | + | 0.112853i | ||||
\(531\) | −7.00000 | −0.303774 | ||||||||
\(532\) | 1.64575 | − | 2.85052i | 0.0713524 | − | 0.123586i | ||||
\(533\) | −5.29150 | − | 9.16515i | −0.229200 | − | 0.396987i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.291503 | 0.0126028 | ||||||||
\(536\) | 0.645751 | − | 1.11847i | 0.0278922 | − | 0.0483107i | ||||
\(537\) | −0.500000 | + | 0.866025i | −0.0215766 | + | 0.0373718i | ||||
\(538\) | −3.00000 | + | 5.19615i | −0.129339 | + | 0.224022i | ||||
\(539\) | −3.00000 | − | 5.19615i | −0.129219 | − | 0.223814i | ||||
\(540\) | −0.500000 | + | 0.866025i | −0.0215166 | + | 0.0372678i | ||||
\(541\) | −13.6458 | − | 23.6351i | −0.586677 | − | 1.01615i | −0.994664 | − | 0.103166i | \(-0.967103\pi\) |
0.407987 | − | 0.912988i | \(-0.366231\pi\) | |||||||
\(542\) | 5.70850 | 0.245201 | ||||||||
\(543\) | −14.5830 | −0.625817 | ||||||||
\(544\) | 1.64575 | + | 2.85052i | 0.0705610 | + | 0.122215i | ||||
\(545\) | 2.35425 | − | 4.07768i | 0.100845 | − | 0.174669i | ||||
\(546\) | 1.00000 | + | 1.73205i | 0.0427960 | + | 0.0741249i | ||||
\(547\) | −6.58301 | + | 11.4021i | −0.281469 | + | 0.487519i | −0.971747 | − | 0.236026i | \(-0.924155\pi\) |
0.690278 | + | 0.723544i | \(0.257488\pi\) | |||||||
\(548\) | 7.93725 | − | 13.7477i | 0.339063 | − | 0.587274i | ||||
\(549\) | 1.64575 | − | 2.85052i | 0.0702390 | − | 0.121657i | ||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | −10.3542 | − | 17.9341i | −0.441106 | − | 0.764018i | ||||
\(552\) | −1.64575 | − | 2.85052i | −0.0700478 | − | 0.121326i | ||||
\(553\) | 4.00000 | − | 6.92820i | 0.170097 | − | 0.294617i | ||||
\(554\) | −0.708497 | −0.0301012 | ||||||||
\(555\) | −0.645751 | − | 1.11847i | −0.0274106 | − | 0.0474766i | ||||
\(556\) | −9.29150 | −0.394047 | ||||||||
\(557\) | 40.7490 | 1.72659 | 0.863296 | − | 0.504699i | \(-0.168396\pi\) | ||||
0.863296 | + | 0.504699i | \(0.168396\pi\) | |||||||
\(558\) | 5.29150 | + | 1.73205i | 0.224007 | + | 0.0733236i | ||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 1.00000 | 0.0422577 | ||||||||
\(561\) | 1.64575 | + | 2.85052i | 0.0694837 | + | 0.120349i | ||||
\(562\) | 12.0000 | 0.506189 | ||||||||
\(563\) | 5.56275 | − | 9.63496i | 0.234442 | − | 0.406065i | −0.724669 | − | 0.689098i | \(-0.758007\pi\) |
0.959110 | + | 0.283033i | \(0.0913404\pi\) | |||||||
\(564\) | 5.64575 | + | 9.77873i | 0.237729 | + | 0.411759i | ||||
\(565\) | −4.29150 | − | 7.43310i | −0.180545 | − | 0.312713i | ||||
\(566\) | −14.0000 | −0.588464 | ||||||||
\(567\) | −0.500000 | + | 0.866025i | −0.0209980 | + | 0.0363696i | ||||
\(568\) | 7.29150 | − | 12.6293i | 0.305945 | − | 0.529912i | ||||
\(569\) | 12.2915 | − | 21.2895i | 0.515287 | − | 0.892503i | −0.484556 | − | 0.874760i | \(-0.661019\pi\) |
0.999843 | − | 0.0177423i | \(-0.00564785\pi\) | |||||||
\(570\) | −1.64575 | − | 2.85052i | −0.0689329 | − | 0.119395i | ||||
\(571\) | 19.2915 | − | 33.4139i | 0.807324 | − | 1.39833i | −0.107386 | − | 0.994217i | \(-0.534248\pi\) |
0.914711 | − | 0.404109i | \(-0.132418\pi\) | |||||||
\(572\) | 1.00000 | + | 1.73205i | 0.0418121 | + | 0.0724207i | ||||
\(573\) | −15.8745 | −0.663167 | ||||||||
\(574\) | −5.29150 | −0.220863 | ||||||||
\(575\) | 1.64575 | + | 2.85052i | 0.0686326 | + | 0.118875i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 12.8745 | + | 22.2993i | 0.535973 | + | 0.928332i | 0.999116 | + | 0.0420484i | \(0.0133884\pi\) |
−0.463143 | + | 0.886284i | \(0.653278\pi\) | |||||||
\(578\) | −3.08301 | + | 5.33992i | −0.128236 | + | 0.222111i | ||||
\(579\) | −1.14575 | + | 1.98450i | −0.0476158 | + | 0.0824730i | ||||
\(580\) | 3.14575 | − | 5.44860i | 0.130620 | − | 0.226241i | ||||
\(581\) | 8.29150 | 0.343989 | ||||||||
\(582\) | −5.14575 | − | 8.91270i | −0.213298 | − | 0.369443i | ||||
\(583\) | 1.50000 | + | 2.59808i | 0.0621237 | + | 0.107601i | ||||
\(584\) | 2.29150 | − | 3.96900i | 0.0948231 | − | 0.164238i | ||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | −11.7915 | − | 20.4235i | −0.487102 | − | 0.843686i | ||||
\(587\) | 43.4575 | 1.79368 | 0.896842 | − | 0.442352i | \(-0.145856\pi\) | ||||
0.896842 | + | 0.442352i | \(0.145856\pi\) | |||||||
\(588\) | −6.00000 | −0.247436 | ||||||||
\(589\) | −13.6458 | + | 12.2330i | −0.562263 | + | 0.504053i | ||||
\(590\) | 7.00000 | 0.288185 | ||||||||
\(591\) | −19.1660 | −0.788384 | ||||||||
\(592\) | −0.645751 | − | 1.11847i | −0.0265402 | − | 0.0459690i | ||||
\(593\) | −1.29150 | −0.0530357 | −0.0265178 | − | 0.999648i | \(-0.508442\pi\) | ||||
−0.0265178 | + | 0.999648i | \(0.508442\pi\) | |||||||
\(594\) | −0.500000 | + | 0.866025i | −0.0205152 | + | 0.0355335i | ||||
\(595\) | −1.64575 | − | 2.85052i | −0.0674692 | − | 0.116860i | ||||
\(596\) | −5.14575 | − | 8.91270i | −0.210778 | − | 0.365079i | ||||
\(597\) | −9.70850 | −0.397342 | ||||||||
\(598\) | −3.29150 | + | 5.70105i | −0.134600 | + | 0.233133i | ||||
\(599\) | −15.8745 | + | 27.4955i | −0.648615 | + | 1.12343i | 0.334839 | + | 0.942275i | \(0.391318\pi\) |
−0.983454 | + | 0.181158i | \(0.942015\pi\) | |||||||
\(600\) | 0.500000 | − | 0.866025i | 0.0204124 | − | 0.0353553i | ||||
\(601\) | 8.29150 | + | 14.3613i | 0.338217 | + | 0.585810i | 0.984098 | − | 0.177629i | \(-0.0568427\pi\) |
−0.645880 | + | 0.763439i | \(0.723509\pi\) | |||||||
\(602\) | −2.00000 | + | 3.46410i | −0.0815139 | + | 0.141186i | ||||
\(603\) | −0.645751 | − | 1.11847i | −0.0262970 | − | 0.0455478i | ||||
\(604\) | −8.29150 | −0.337376 | ||||||||
\(605\) | −10.0000 | −0.406558 | ||||||||
\(606\) | 0.854249 | + | 1.47960i | 0.0347015 | + | 0.0601047i | ||||
\(607\) | −10.5830 | + | 18.3303i | −0.429551 | + | 0.744004i | −0.996833 | − | 0.0795193i | \(-0.974661\pi\) |
0.567282 | + | 0.823523i | \(0.307995\pi\) | |||||||
\(608\) | −1.64575 | − | 2.85052i | −0.0667440 | − | 0.115604i | ||||
\(609\) | 3.14575 | − | 5.44860i | 0.127472 | − | 0.220788i | ||||
\(610\) | −1.64575 | + | 2.85052i | −0.0666345 | + | 0.115414i | ||||
\(611\) | 11.2915 | − | 19.5575i | 0.456805 | − | 0.791210i | ||||
\(612\) | 3.29150 | 0.133051 | ||||||||
\(613\) | −12.5830 | − | 21.7944i | −0.508223 | − | 0.880268i | −0.999955 | − | 0.00952103i | \(-0.996969\pi\) |
0.491732 | − | 0.870747i | \(-0.336364\pi\) | |||||||
\(614\) | −9.35425 | − | 16.2020i | −0.377507 | − | 0.653861i | ||||
\(615\) | −2.64575 | + | 4.58258i | −0.106687 | + | 0.184787i | ||||
\(616\) | 1.00000 | 0.0402911 | ||||||||
\(617\) | 22.9373 | + | 39.7285i | 0.923419 | + | 1.59941i | 0.794084 | + | 0.607808i | \(0.207951\pi\) |
0.129335 | + | 0.991601i | \(0.458716\pi\) | |||||||
\(618\) | −3.58301 | −0.144130 | ||||||||
\(619\) | 16.0000 | 0.643094 | 0.321547 | − | 0.946894i | \(-0.395797\pi\) | ||||
0.321547 | + | 0.946894i | \(0.395797\pi\) | |||||||
\(620\) | −5.29150 | − | 1.73205i | −0.212512 | − | 0.0695608i | ||||
\(621\) | −3.29150 | −0.132083 | ||||||||
\(622\) | −18.0000 | −0.721734 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 2.00000 | 0.0800641 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 7.85425 | + | 13.6040i | 0.313919 | + | 0.543724i | ||||
\(627\) | −1.64575 | − | 2.85052i | −0.0657250 | − | 0.113839i | ||||
\(628\) | −8.70850 | −0.347507 | ||||||||
\(629\) | −2.12549 | + | 3.68146i | −0.0847489 | + | 0.146789i | ||||
\(630\) | 0.500000 | − | 0.866025i | 0.0199205 | − | 0.0345033i | ||||
\(631\) | 11.4373 | − | 19.8099i | 0.455310 | − | 0.788620i | −0.543396 | − | 0.839476i | \(-0.682862\pi\) |
0.998706 | + | 0.0508566i | \(0.0161951\pi\) | |||||||
\(632\) | −4.00000 | − | 6.92820i | −0.159111 | − | 0.275589i | ||||
\(633\) | −2.35425 | + | 4.07768i | −0.0935730 | + | 0.162073i | ||||
\(634\) | 4.20850 | + | 7.28933i | 0.167141 | + | 0.289496i | ||||
\(635\) | 9.58301 | 0.380290 | ||||||||
\(636\) | 3.00000 | 0.118958 | ||||||||
\(637\) | 6.00000 | + | 10.3923i | 0.237729 | + | 0.411758i | ||||
\(638\) | 3.14575 | − | 5.44860i | 0.124541 | − | 0.215712i | ||||
\(639\) | −7.29150 | − | 12.6293i | −0.288447 | − | 0.499606i | ||||
\(640\) | 0.500000 | − | 0.866025i | 0.0197642 | − | 0.0342327i | ||||
\(641\) | −16.2288 | + | 28.1090i | −0.640997 | + | 1.11024i | 0.344213 | + | 0.938892i | \(0.388146\pi\) |
−0.985210 | + | 0.171348i | \(0.945188\pi\) | |||||||
\(642\) | 0.145751 | − | 0.252449i | 0.00575235 | − | 0.00996335i | ||||
\(643\) | −24.7085 | −0.974408 | −0.487204 | − | 0.873288i | \(-0.661983\pi\) | ||||
−0.487204 | + | 0.873288i | \(0.661983\pi\) | |||||||
\(644\) | 1.64575 | + | 2.85052i | 0.0648517 | + | 0.112326i | ||||
\(645\) | 2.00000 | + | 3.46410i | 0.0787499 | + | 0.136399i | ||||
\(646\) | −5.41699 | + | 9.38251i | −0.213129 | + | 0.369150i | ||||
\(647\) | −8.70850 | −0.342366 | −0.171183 | − | 0.985239i | \(-0.554759\pi\) | ||||
−0.171183 | + | 0.985239i | \(0.554759\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | 7.00000 | 0.274774 | ||||||||
\(650\) | −2.00000 | −0.0784465 | ||||||||
\(651\) | −5.29150 | − | 1.73205i | −0.207390 | − | 0.0678844i | ||||
\(652\) | 9.87451 | 0.386716 | ||||||||
\(653\) | −15.0000 | −0.586995 | −0.293498 | − | 0.955960i | \(-0.594819\pi\) | ||||
−0.293498 | + | 0.955960i | \(0.594819\pi\) | |||||||
\(654\) | −2.35425 | − | 4.07768i | −0.0920584 | − | 0.159450i | ||||
\(655\) | −8.00000 | −0.312586 | ||||||||
\(656\) | −2.64575 | + | 4.58258i | −0.103299 | + | 0.178920i | ||||
\(657\) | −2.29150 | − | 3.96900i | −0.0894000 | − | 0.154845i | ||||
\(658\) | −5.64575 | − | 9.77873i | −0.220094 | − | 0.381215i | ||||
\(659\) | 18.1660 | 0.707647 | 0.353824 | − | 0.935312i | \(-0.384881\pi\) | ||||
0.353824 | + | 0.935312i | \(0.384881\pi\) | |||||||
\(660\) | 0.500000 | − | 0.866025i | 0.0194625 | − | 0.0337100i | ||||
\(661\) | −5.64575 | + | 9.77873i | −0.219594 | + | 0.380348i | −0.954684 | − | 0.297621i | \(-0.903807\pi\) |
0.735090 | + | 0.677970i | \(0.237140\pi\) | |||||||
\(662\) | −4.93725 | + | 8.55157i | −0.191892 | + | 0.332366i | ||||
\(663\) | −3.29150 | − | 5.70105i | −0.127831 | − | 0.221410i | ||||
\(664\) | 4.14575 | − | 7.18065i | 0.160886 | − | 0.278663i | ||||
\(665\) | 1.64575 | + | 2.85052i | 0.0638195 | + | 0.110539i | ||||
\(666\) | −1.29150 | −0.0500447 | ||||||||
\(667\) | 20.7085 | 0.801836 | ||||||||
\(668\) | −8.64575 | − | 14.9749i | −0.334514 | − | 0.579396i | ||||
\(669\) | 12.7915 | − | 22.1555i | 0.494548 | − | 0.856582i | ||||
\(670\) | 0.645751 | + | 1.11847i | 0.0249475 | + | 0.0432104i | ||||
\(671\) | −1.64575 | + | 2.85052i | −0.0635335 | + | 0.110043i | ||||
\(672\) | 0.500000 | − | 0.866025i | 0.0192879 | − | 0.0334077i | ||||
\(673\) | 5.43725 | − | 9.41760i | 0.209591 | − | 0.363022i | −0.741995 | − | 0.670406i | \(-0.766120\pi\) |
0.951586 | + | 0.307384i | \(0.0994535\pi\) | |||||||
\(674\) | 14.8745 | 0.572945 | ||||||||
\(675\) | −0.500000 | − | 0.866025i | −0.0192450 | − | 0.0333333i | ||||
\(676\) | 4.50000 | + | 7.79423i | 0.173077 | + | 0.299778i | ||||
\(677\) | −4.50000 | + | 7.79423i | −0.172949 | + | 0.299557i | −0.939450 | − | 0.342687i | \(-0.888663\pi\) |
0.766501 | + | 0.642244i | \(0.221996\pi\) | |||||||
\(678\) | −8.58301 | −0.329628 | ||||||||
\(679\) | 5.14575 | + | 8.91270i | 0.197476 | + | 0.342038i | ||||
\(680\) | −3.29150 | −0.126223 | ||||||||
\(681\) | −8.87451 | −0.340072 | ||||||||
\(682\) | −5.29150 | − | 1.73205i | −0.202622 | − | 0.0663237i | ||||
\(683\) | 16.8745 | 0.645685 | 0.322843 | − | 0.946453i | \(-0.395362\pi\) | ||||
0.322843 | + | 0.946453i | \(0.395362\pi\) | |||||||
\(684\) | −3.29150 | −0.125854 | ||||||||
\(685\) | 7.93725 | + | 13.7477i | 0.303267 | + | 0.525274i | ||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | −3.93725 | + | 6.81952i | −0.150216 | + | 0.260181i | ||||
\(688\) | 2.00000 | + | 3.46410i | 0.0762493 | + | 0.132068i | ||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 3.29150 | 0.125305 | ||||||||
\(691\) | −8.64575 | + | 14.9749i | −0.328900 | + | 0.569671i | −0.982294 | − | 0.187347i | \(-0.940011\pi\) |
0.653394 | + | 0.757018i | \(0.273345\pi\) | |||||||
\(692\) | 5.50000 | − | 9.52628i | 0.209079 | − | 0.362135i | ||||
\(693\) | 0.500000 | − | 0.866025i | 0.0189934 | − | 0.0328976i | ||||
\(694\) | 3.14575 | + | 5.44860i | 0.119411 | + | 0.206826i | ||||
\(695\) | 4.64575 | − | 8.04668i | 0.176223 | − | 0.305228i | ||||
\(696\) | −3.14575 | − | 5.44860i | −0.119239 | − | 0.206529i | ||||
\(697\) | 17.4170 | 0.659716 | ||||||||
\(698\) | 24.4575 | 0.925731 | ||||||||
\(699\) | −5.93725 | − | 10.2836i | −0.224568 | − | 0.388962i | ||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | 19.1458 | + | 33.1614i | 0.723125 | + | 1.25249i | 0.959741 | + | 0.280886i | \(0.0906283\pi\) |
−0.236616 | + | 0.971603i | \(0.576038\pi\) | |||||||
\(702\) | 1.00000 | − | 1.73205i | 0.0377426 | − | 0.0653720i | ||||
\(703\) | 2.12549 | − | 3.68146i | 0.0801645 | − | 0.138849i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | −11.2915 | −0.425263 | ||||||||
\(706\) | −15.5830 | − | 26.9906i | −0.586474 | − | 1.01580i | ||||
\(707\) | −0.854249 | − | 1.47960i | −0.0321273 | − | 0.0556462i | ||||
\(708\) | 3.50000 | − | 6.06218i | 0.131538 | − | 0.227831i | ||||
\(709\) | 1.29150 | 0.0485034 | 0.0242517 | − | 0.999706i | \(-0.492280\pi\) | ||||
0.0242517 | + | 0.999706i | \(0.492280\pi\) | |||||||
\(710\) | 7.29150 | + | 12.6293i | 0.273645 | + | 0.473967i | ||||
\(711\) | −8.00000 | −0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.77124 | − | 17.9341i | −0.141234 | − | 0.671637i | ||||
\(714\) | −3.29150 | −0.123181 | ||||||||
\(715\) | −2.00000 | −0.0747958 | ||||||||
\(716\) | −0.500000 | − | 0.866025i | −0.0186859 | − | 0.0323649i | ||||
\(717\) | 16.5830 | 0.619304 | ||||||||
\(718\) | −7.64575 | + | 13.2428i | −0.285337 | + | 0.494218i | ||||
\(719\) | −1.93725 | − | 3.35542i | −0.0722474 | − | 0.125136i | 0.827639 | − | 0.561261i | \(-0.189684\pi\) |
−0.899886 | + | 0.436125i | \(0.856350\pi\) | |||||||
\(720\) | −0.500000 | − | 0.866025i | −0.0186339 | − | 0.0322749i | ||||
\(721\) | 3.58301 | 0.133438 | ||||||||
\(722\) | −4.08301 | + | 7.07197i | −0.151954 | + | 0.263192i | ||||
\(723\) | −2.20850 | + | 3.82523i | −0.0821349 | + | 0.142262i | ||||
\(724\) | 7.29150 | − | 12.6293i | 0.270987 | − | 0.469362i | ||||
\(725\) | 3.14575 | + | 5.44860i | 0.116830 | + | 0.202356i | ||||
\(726\) | −5.00000 | + | 8.66025i | −0.185567 | + | 0.321412i | ||||
\(727\) | 11.0830 | + | 19.1963i | 0.411046 | + | 0.711952i | 0.995004 | − | 0.0998311i | \(-0.0318303\pi\) |
−0.583958 | + | 0.811784i | \(0.698497\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.29150 | + | 3.96900i | 0.0848123 | + | 0.146899i | ||||
\(731\) | 6.58301 | − | 11.4021i | 0.243481 | − | 0.421722i | ||||
\(732\) | 1.64575 | + | 2.85052i | 0.0608287 | + | 0.105358i | ||||
\(733\) | −1.70850 | + | 2.95920i | −0.0631048 | + | 0.109301i | −0.895852 | − | 0.444353i | \(-0.853434\pi\) |
0.832747 | + | 0.553654i | \(0.186767\pi\) | |||||||
\(734\) | 16.5830 | − | 28.7226i | 0.612090 | − | 1.06017i | ||||
\(735\) | 3.00000 | − | 5.19615i | 0.110657 | − | 0.191663i | ||||
\(736\) | 3.29150 | 0.121326 | ||||||||
\(737\) | 0.645751 | + | 1.11847i | 0.0237866 | + | 0.0411995i | ||||
\(738\) | 2.64575 | + | 4.58258i | 0.0973915 | + | 0.168687i | ||||
\(739\) | 9.93725 | − | 17.2118i | 0.365548 | − | 0.633147i | −0.623316 | − | 0.781970i | \(-0.714215\pi\) |
0.988864 | + | 0.148823i | \(0.0475483\pi\) | |||||||
\(740\) | 1.29150 | 0.0474766 | ||||||||
\(741\) | 3.29150 | + | 5.70105i | 0.120916 | + | 0.209433i | ||||
\(742\) | −3.00000 | −0.110133 | ||||||||
\(743\) | −23.7490 | −0.871267 | −0.435633 | − | 0.900124i | \(-0.643476\pi\) | ||||
−0.435633 | + | 0.900124i | \(0.643476\pi\) | |||||||
\(744\) | −4.14575 | + | 3.71655i | −0.151991 | + | 0.136255i | ||||
\(745\) | 10.2915 | 0.377051 | ||||||||
\(746\) | 27.2915 | 0.999213 | ||||||||
\(747\) | −4.14575 | − | 7.18065i | −0.151685 | − | 0.262726i | ||||
\(748\) | −3.29150 | −0.120349 | ||||||||
\(749\) | −0.145751 | + | 0.252449i | −0.00532564 | + | 0.00922427i | ||||
\(750\) | 0.500000 | + | 0.866025i | 0.0182574 | + | 0.0316228i | ||||
\(751\) | −20.4373 | − | 35.3984i | −0.745766 | − | 1.29170i | −0.949836 | − | 0.312748i | \(-0.898750\pi\) |
0.204070 | − | 0.978956i | \(-0.434583\pi\) | |||||||
\(752\) | −11.2915 | −0.411759 | ||||||||
\(753\) | −10.0000 | + | 17.3205i | −0.364420 | + | 0.631194i | ||||
\(754\) | −6.29150 | + | 10.8972i | −0.229123 | + | 0.396853i | ||||
\(755\) | 4.14575 | − | 7.18065i | 0.150879 | − | 0.261331i | ||||
\(756\) | −0.500000 | − | 0.866025i | −0.0181848 | − | 0.0314970i | ||||
\(757\) | 12.0000 | − | 20.7846i | 0.436147 | − | 0.755429i | −0.561241 | − | 0.827652i | \(-0.689676\pi\) |
0.997389 | + | 0.0722229i | \(0.0230093\pi\) | |||||||
\(758\) | 6.70850 | + | 11.6195i | 0.243664 | + | 0.422038i | ||||
\(759\) | 3.29150 | 0.119474 | ||||||||
\(760\) | 3.29150 | 0.119395 | ||||||||
\(761\) | −9.93725 | − | 17.2118i | −0.360225 | − | 0.623928i | 0.627773 | − | 0.778397i | \(-0.283967\pi\) |
−0.987998 | + | 0.154469i | \(0.950633\pi\) | |||||||
\(762\) | 4.79150 | − | 8.29913i | 0.173578 | − | 0.300646i | ||||
\(763\) | 2.35425 | + | 4.07768i | 0.0852295 | + | 0.147622i | ||||
\(764\) | 7.93725 | − | 13.7477i | 0.287160 | − | 0.497375i | ||||
\(765\) | −1.64575 | + | 2.85052i | −0.0595023 | + | 0.103061i | ||||
\(766\) | 16.6458 | − | 28.8313i | 0.601435 | − | 1.04172i | ||||
\(767\) | −14.0000 | −0.505511 | ||||||||
\(768\) | −0.500000 | − | 0.866025i | −0.0180422 | − | 0.0312500i | ||||
\(769\) | −20.5000 | − | 35.5070i | −0.739249 | − | 1.28042i | −0.952834 | − | 0.303492i | \(-0.901847\pi\) |
0.213585 | − | 0.976924i | \(-0.431486\pi\) | |||||||
\(770\) | −0.500000 | + | 0.866025i | −0.0180187 | + | 0.0312094i | ||||
\(771\) | −9.87451 | −0.355622 | ||||||||
\(772\) | −1.14575 | − | 1.98450i | −0.0412365 | − | 0.0714237i | ||||
\(773\) | 16.5830 | 0.596449 | 0.298225 | − | 0.954496i | \(-0.403606\pi\) | ||||
0.298225 | + | 0.954496i | \(0.403606\pi\) | |||||||
\(774\) | 4.00000 | 0.143777 | ||||||||
\(775\) | 4.14575 | − | 3.71655i | 0.148920 | − | 0.133502i | ||||
\(776\) | 10.2915 | 0.369443 | ||||||||
\(777\) | 1.29150 | 0.0463324 | ||||||||
\(778\) | 1.00000 | + | 1.73205i | 0.0358517 | + | 0.0620970i | ||||
\(779\) | −17.4170 | −0.624029 | ||||||||
\(780\) | −1.00000 | + | 1.73205i | −0.0358057 | + | 0.0620174i | ||||
\(781\) | 7.29150 | + | 12.6293i | 0.260910 | + | 0.451910i | ||||
\(782\) | −5.41699 | − | 9.38251i | −0.193711 | − | 0.335518i | ||||
\(783\) | −6.29150 | −0.224840 | ||||||||
\(784\) | 3.00000 | − | 5.19615i | 0.107143 | − | 0.185577i | ||||
\(785\) | 4.35425 | − | 7.54178i | 0.155410 | − | 0.269178i | ||||
\(786\) | −4.00000 | + | 6.92820i | −0.142675 | + | 0.247121i | ||||
\(787\) | 16.2288 | + | 28.1090i | 0.578493 | + | 1.00198i | 0.995652 | + | 0.0931456i | \(0.0296922\pi\) |
−0.417160 | + | 0.908833i | \(0.636974\pi\) | |||||||
\(788\) | 9.58301 | − | 16.5983i | 0.341380 | − | 0.591288i | ||||
\(789\) | 4.29150 | + | 7.43310i | 0.152782 | + | 0.264625i | ||||
\(790\) | 8.00000 | 0.284627 | ||||||||
\(791\) | 8.58301 | 0.305177 | ||||||||
\(792\) | −0.500000 | − | 0.866025i | −0.0177667 | − | 0.0307729i | ||||
\(793\) | 3.29150 | − | 5.70105i | 0.116885 | − | 0.202450i | ||||
\(794\) | 6.58301 | + | 11.4021i | 0.233622 | + | 0.404645i | ||||
\(795\) | −1.50000 | + | 2.59808i | −0.0531995 | + | 0.0921443i | ||||
\(796\) | 4.85425 | − | 8.40781i | 0.172054 | − | 0.298007i | ||||
\(797\) | 10.0830 | − | 17.4643i | 0.357158 | − | 0.618616i | −0.630327 | − | 0.776330i | \(-0.717079\pi\) |
0.987485 | + | 0.157714i | \(0.0504123\pi\) | |||||||
\(798\) | 3.29150 | 0.116518 | ||||||||
\(799\) | 18.5830 | + | 32.1867i | 0.657419 | + | 1.13868i | ||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.16601 | 0.253041 | ||||||||
\(803\) | 2.29150 | + | 3.96900i | 0.0808654 | + | 0.140063i | ||||
\(804\) | 1.29150 | 0.0455478 | ||||||||
\(805\) | −3.29150 | −0.116010 | ||||||||
\(806\) | 10.5830 | + | 3.46410i | 0.372770 | + | 0.122018i | ||||
\(807\) | −6.00000 | −0.211210 | ||||||||
\(808\) | −1.70850 | −0.0601047 | ||||||||
\(809\) | −20.2288 | − | 35.0372i | −0.711205 | − | 1.23184i | −0.964405 | − | 0.264430i | \(-0.914816\pi\) |
0.253200 | − | 0.967414i | \(-0.418517\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 14.8745 | − | 25.7634i | 0.522315 | − | 0.904675i | −0.477348 | − | 0.878714i | \(-0.658402\pi\) |
0.999663 | − | 0.0259613i | \(-0.00826467\pi\) | |||||||
\(812\) | 3.14575 | + | 5.44860i | 0.110394 | + | 0.191208i | ||||
\(813\) | 2.85425 | + | 4.94370i | 0.100103 | + | 0.173383i | ||||
\(814\) | 1.29150 | 0.0452671 | ||||||||
\(815\) | −4.93725 | + | 8.55157i | −0.172944 | + | 0.299549i | ||||
\(816\) | −1.64575 | + | 2.85052i | −0.0576128 | + | 0.0997883i | ||||
\(817\) | −6.58301 | + | 11.4021i | −0.230310 | + | 0.398909i | ||||
\(818\) | −4.50000 | − | 7.79423i | −0.157339 | − | 0.272519i | ||||
\(819\) | −1.00000 | + | 1.73205i | −0.0349428 | + | 0.0605228i | ||||
\(820\) | −2.64575 | − | 4.58258i | −0.0923936 | − | 0.160030i | ||||
\(821\) | 0.291503 | 0.0101735 | 0.00508676 | − | 0.999987i | \(-0.498381\pi\) | ||||
0.00508676 | + | 0.999987i | \(0.498381\pi\) | |||||||
\(822\) | 15.8745 | 0.553687 | ||||||||
\(823\) | −4.79150 | − | 8.29913i | −0.167021 | − | 0.289289i | 0.770350 | − | 0.637621i | \(-0.220082\pi\) |
−0.937371 | + | 0.348332i | \(0.886748\pi\) | |||||||
\(824\) | 1.79150 | − | 3.10297i | 0.0624100 | − | 0.108097i | ||||
\(825\) | 0.500000 | + | 0.866025i | 0.0174078 | + | 0.0301511i | ||||
\(826\) | −3.50000 | + | 6.06218i | −0.121781 | + | 0.210930i | ||||
\(827\) | 1.29150 | − | 2.23695i | 0.0449099 | − | 0.0777863i | −0.842697 | − | 0.538389i | \(-0.819033\pi\) |
0.887607 | + | 0.460602i | \(0.152367\pi\) | |||||||
\(828\) | 1.64575 | − | 2.85052i | 0.0571938 | − | 0.0990626i | ||||
\(829\) | −35.2915 | −1.22572 | −0.612862 | − | 0.790190i | \(-0.709982\pi\) | ||||
−0.612862 | + | 0.790190i | \(0.709982\pi\) | |||||||
\(830\) | 4.14575 | + | 7.18065i | 0.143901 | + | 0.249244i | ||||
\(831\) | −0.354249 | − | 0.613577i | −0.0122888 | − | 0.0212847i | ||||
\(832\) | −1.00000 | + | 1.73205i | −0.0346688 | + | 0.0600481i | ||||
\(833\) | −19.7490 | −0.684263 | ||||||||
\(834\) | −4.64575 | − | 8.04668i | −0.160869 | − | 0.278634i | ||||
\(835\) | 17.2915 | 0.598397 | ||||||||
\(836\) | 3.29150 | 0.113839 | ||||||||
\(837\) | 1.14575 | + | 5.44860i | 0.0396030 | + | 0.188331i | ||||
\(838\) | 15.5830 | 0.538306 | ||||||||
\(839\) | 19.2915 | 0.666017 | 0.333008 | − | 0.942924i | \(-0.391936\pi\) | ||||
0.333008 | + | 0.942924i | \(0.391936\pi\) | |||||||
\(840\) | 0.500000 | + | 0.866025i | 0.0172516 | + | 0.0298807i | ||||
\(841\) | 10.5830 | 0.364931 | ||||||||
\(842\) | −10.3542 | + | 17.9341i | −0.356831 | + | 0.618049i | ||||
\(843\) | 6.00000 | + | 10.3923i | 0.206651 | + | 0.357930i | ||||
\(844\) | −2.35425 | − | 4.07768i | −0.0810366 | − | 0.140359i | ||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | −5.64575 | + | 9.77873i | −0.194105 | + | 0.336200i | ||||
\(847\) | 5.00000 | − | 8.66025i | 0.171802 | − | 0.297570i | ||||
\(848\) | −1.50000 | + | 2.59808i | −0.0515102 | + | 0.0892183i | ||||
\(849\) | −7.00000 | − | 12.1244i | −0.240239 | − | 0.416107i | ||||
\(850\) | 1.64575 | − | 2.85052i | 0.0564488 | − | 0.0977722i | ||||
\(851\) | 2.12549 | + | 3.68146i | 0.0728609 | + | 0.126199i | ||||
\(852\) | 14.5830 | 0.499606 | ||||||||
\(853\) | −38.3320 | −1.31246 | −0.656232 | − | 0.754559i | \(-0.727851\pi\) | ||||
−0.656232 | + | 0.754559i | \(0.727851\pi\) | |||||||
\(854\) | −1.64575 | − | 2.85052i | −0.0563165 | − | 0.0975430i | ||||
\(855\) | 1.64575 | − | 2.85052i | 0.0562835 | − | 0.0974859i | ||||
\(856\) | 0.145751 | + | 0.252449i | 0.00498168 | + | 0.00862852i | ||||
\(857\) | 5.29150 | − | 9.16515i | 0.180754 | − | 0.313076i | −0.761383 | − | 0.648302i | \(-0.775479\pi\) |
0.942138 | + | 0.335226i | \(0.108813\pi\) | |||||||
\(858\) | −1.00000 | + | 1.73205i | −0.0341394 | + | 0.0591312i | ||||
\(859\) | 27.8118 | − | 48.1714i | 0.948925 | − | 1.64359i | 0.201230 | − | 0.979544i | \(-0.435506\pi\) |
0.747695 | − | 0.664042i | \(-0.231161\pi\) | |||||||
\(860\) | −4.00000 | −0.136399 | ||||||||
\(861\) | −2.64575 | − | 4.58258i | −0.0901670 | − | 0.156174i | ||||
\(862\) | 0.645751 | + | 1.11847i | 0.0219944 | + | 0.0380954i | ||||
\(863\) | −5.41699 | + | 9.38251i | −0.184397 | + | 0.319384i | −0.943373 | − | 0.331734i | \(-0.892366\pi\) |
0.758976 | + | 0.651118i | \(0.225700\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 5.50000 | + | 9.52628i | 0.187006 | + | 0.323903i | ||||
\(866\) | −22.0000 | −0.747590 | ||||||||
\(867\) | −6.16601 | −0.209409 | ||||||||
\(868\) | 4.14575 | − | 3.71655i | 0.140716 | − | 0.126148i | ||||
\(869\) | 8.00000 | 0.271381 | ||||||||
\(870\) | 6.29150 | 0.213302 | ||||||||
\(871\) | −1.29150 | − | 2.23695i | −0.0437609 | − | 0.0757961i | ||||
\(872\) | 4.70850 | 0.159450 | ||||||||
\(873\) | 5.14575 | − | 8.91270i | 0.174157 | − | 0.301649i | ||||
\(874\) | 5.41699 | + | 9.38251i | 0.183233 | + | 0.317368i | ||||
\(875\) | −0.500000 | − | 0.866025i | −0.0169031 | − | 0.0292770i | ||||
\(876\) | 4.58301 | 0.154845 | ||||||||
\(877\) | −4.35425 | + | 7.54178i | −0.147033 | + | 0.254668i | −0.930129 | − | 0.367232i | \(-0.880306\pi\) |
0.783097 | + | 0.621900i | \(0.213639\pi\) | |||||||
\(878\) | 3.14575 | − | 5.44860i | 0.106164 | − | 0.183881i | ||||
\(879\) | 11.7915 | − | 20.4235i | 0.397718 | − | 0.688867i | ||||
\(880\) | 0.500000 | + | 0.866025i | 0.0168550 | + | 0.0291937i | ||||
\(881\) | 11.3542 | − | 19.6661i | 0.382534 | − | 0.662569i | −0.608889 | − | 0.793255i | \(-0.708385\pi\) |
0.991424 | + | 0.130686i | \(0.0417180\pi\) | |||||||
\(882\) | −3.00000 | − | 5.19615i | −0.101015 | − | 0.174964i | ||||
\(883\) | 29.0405 | 0.977291 | 0.488646 | − | 0.872482i | \(-0.337491\pi\) | ||||
0.488646 | + | 0.872482i | \(0.337491\pi\) | |||||||
\(884\) | 6.58301 | 0.221410 | ||||||||
\(885\) | 3.50000 | + | 6.06218i | 0.117651 | + | 0.203778i | ||||
\(886\) | 15.2915 | − | 26.4857i | 0.513728 | − | 0.889803i | ||||
\(887\) | 11.2915 | + | 19.5575i | 0.379132 | + | 0.656675i | 0.990936 | − | 0.134334i | \(-0.0428894\pi\) |
−0.611805 | + | 0.791009i | \(0.709556\pi\) | |||||||
\(888\) | 0.645751 | − | 1.11847i | 0.0216700 | − | 0.0375335i | ||||
\(889\) | −4.79150 | + | 8.29913i | −0.160702 | + | 0.278344i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 12.7915 | + | 22.1555i | 0.428291 | + | 0.741822i | ||||
\(893\) | −18.5830 | − | 32.1867i | −0.621857 | − | 1.07709i | ||||
\(894\) | 5.14575 | − | 8.91270i | 0.172100 | − | 0.298085i | ||||
\(895\) | 1.00000 | 0.0334263 | ||||||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −6.58301 | −0.219800 | ||||||||
\(898\) | 5.41699 | 0.180767 | ||||||||
\(899\) | −7.20850 | − | 34.2799i | −0.240417 | − | 1.14330i | ||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 9.87451 | 0.328968 | ||||||||
\(902\) | −2.64575 | − | 4.58258i | −0.0880939 | − | 0.152583i | ||||
\(903\) | −4.00000 | −0.133112 | ||||||||
\(904\) | 4.29150 | − | 7.43310i | 0.142733 | − | 0.247221i | ||||
\(905\) | 7.29150 | + | 12.6293i | 0.242378 | + | 0.419811i | ||||
\(906\) | −4.14575 | − | 7.18065i | −0.137733 | − | 0.238561i | ||||
\(907\) | −19.4170 | −0.644731 | −0.322365 | − | 0.946615i | \(-0.604478\pi\) | ||||
−0.322365 | + | 0.946615i | \(0.604478\pi\) | |||||||
\(908\) | 4.43725 | − | 7.68555i | 0.147255 | − | 0.255054i | ||||
\(909\) | −0.854249 | + | 1.47960i | −0.0283336 | + | 0.0490753i | ||||
\(910\) | 1.00000 | − | 1.73205i | 0.0331497 | − | 0.0574169i | ||||
\(911\) | −21.2288 | − | 36.7693i | −0.703340 | − | 1.21822i | −0.967287 | − | 0.253684i | \(-0.918358\pi\) |
0.263947 | − | 0.964537i | \(-0.414976\pi\) | |||||||
\(912\) | 1.64575 | − | 2.85052i | 0.0544963 | − | 0.0943903i | ||||
\(913\) | 4.14575 | + | 7.18065i | 0.137204 | + | 0.237645i | ||||
\(914\) | 35.1660 | 1.16319 | ||||||||
\(915\) | −3.29150 | −0.108814 | ||||||||
\(916\) | −3.93725 | − | 6.81952i | −0.130091 | − | 0.225323i | ||||
\(917\) | 4.00000 | − | 6.92820i | 0.132092 | − | 0.228789i | ||||
\(918\) | 1.64575 | + | 2.85052i | 0.0543179 | + | 0.0940813i | ||||
\(919\) | −17.4373 | + | 30.2022i | −0.575202 | + | 0.996279i | 0.420818 | + | 0.907145i | \(0.361743\pi\) |
−0.996020 | + | 0.0891338i | \(0.971590\pi\) | |||||||
\(920\) | −1.64575 | + | 2.85052i | −0.0542588 | + | 0.0939790i | ||||
\(921\) | 9.35425 | − | 16.2020i | 0.308233 | − | 0.533875i | ||||
\(922\) | −6.29150 | −0.207200 | ||||||||
\(923\) | −14.5830 | − | 25.2585i | −0.480005 | − | 0.831394i | ||||
\(924\) | 0.500000 | + | 0.866025i | 0.0164488 | + | 0.0284901i | ||||
\(925\) | −0.645751 | + | 1.11847i | −0.0212322 | + | 0.0367752i | ||||
\(926\) | −15.0000 | −0.492931 | ||||||||
\(927\) | −1.79150 | − | 3.10297i | −0.0588407 | − | 0.101915i | ||||
\(928\) | 6.29150 | 0.206529 | ||||||||
\(929\) | −4.45751 | −0.146246 | −0.0731231 | − | 0.997323i | \(-0.523297\pi\) | ||||
−0.0731231 | + | 0.997323i | \(0.523297\pi\) | |||||||
\(930\) | −1.14575 | − | 5.44860i | −0.0375707 | − | 0.178667i | ||||
\(931\) | 19.7490 | 0.647248 | ||||||||
\(932\) | 11.8745 | 0.388962 | ||||||||
\(933\) | −9.00000 | − | 15.5885i | −0.294647 | − | 0.510343i | ||||
\(934\) | −4.29150 | −0.140422 | ||||||||
\(935\) | 1.64575 | − | 2.85052i | 0.0538218 | − | 0.0932221i | ||||
\(936\) | 1.00000 | + | 1.73205i | 0.0326860 | + | 0.0566139i | ||||
\(937\) | −12.2915 | − | 21.2895i | −0.401546 | − | 0.695498i | 0.592367 | − | 0.805668i | \(-0.298194\pi\) |
−0.993913 | + | 0.110171i | \(0.964860\pi\) | |||||||
\(938\) | −1.29150 | −0.0421691 | ||||||||
\(939\) | −7.85425 | + | 13.6040i | −0.256314 | + | 0.443948i | ||||
\(940\) | 5.64575 | − | 9.77873i | 0.184144 | − | 0.318947i | ||||
\(941\) | −21.0203 | + | 36.4082i | −0.685241 | + | 1.18687i | 0.288120 | + | 0.957594i | \(0.406970\pi\) |
−0.973361 | + | 0.229278i | \(0.926364\pi\) | |||||||
\(942\) | −4.35425 | − | 7.54178i | −0.141869 | − | 0.245724i | ||||
\(943\) | 8.70850 | − | 15.0836i | 0.283588 | − | 0.491188i | ||||
\(944\) | 3.50000 | + | 6.06218i | 0.113915 | + | 0.197307i | ||||
\(945\) | 1.00000 | 0.0325300 | ||||||||
\(946\) | −4.00000 | −0.130051 | ||||||||
\(947\) | 12.5830 | + | 21.7944i | 0.408893 | + | 0.708223i | 0.994766 | − | 0.102180i | \(-0.0325817\pi\) |
−0.585873 | + | 0.810403i | \(0.699248\pi\) | |||||||
\(948\) | 4.00000 | − | 6.92820i | 0.129914 | − | 0.225018i | ||||
\(949\) | −4.58301 | − | 7.93800i | −0.148771 | − | 0.257678i | ||||
\(950\) | −1.64575 | + | 2.85052i | −0.0533952 | + | 0.0924832i | ||||
\(951\) | −4.20850 | + | 7.28933i | −0.136470 | + | 0.236373i | ||||
\(952\) | 1.64575 | − | 2.85052i | 0.0533391 | − | 0.0923860i | ||||
\(953\) | −15.2915 | −0.495340 | −0.247670 | − | 0.968844i | \(-0.579665\pi\) | ||||
−0.247670 | + | 0.968844i | \(0.579665\pi\) | |||||||
\(954\) | 1.50000 | + | 2.59808i | 0.0485643 | + | 0.0841158i | ||||
\(955\) | 7.93725 | + | 13.7477i | 0.256844 | + | 0.444866i | ||||
\(956\) | −8.29150 | + | 14.3613i | −0.268166 | + | 0.464478i | ||||
\(957\) | 6.29150 | 0.203375 | ||||||||
\(958\) | −17.6458 | − | 30.5633i | −0.570108 | − | 0.987457i | ||||
\(959\) | −15.8745 | −0.512615 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −28.3745 | + | 12.4855i | −0.915307 | + | 0.402758i | ||||
\(962\) | −2.58301 | −0.0832794 | ||||||||
\(963\) | 0.291503 | 0.00939354 | ||||||||
\(964\) | −2.20850 | − | 3.82523i | −0.0711309 | − | 0.123202i | ||||
\(965\) | 2.29150 | 0.0737661 | ||||||||
\(966\) | −1.64575 | + | 2.85052i | −0.0529512 | + | 0.0917141i | ||||
\(967\) | 14.5830 | + | 25.2585i | 0.468958 | + | 0.812259i | 0.999370 | − | 0.0354809i | \(-0.0112963\pi\) |
−0.530413 | + | 0.847740i | \(0.677963\pi\) | |||||||
\(968\) | −5.00000 | − | 8.66025i | −0.160706 | − | 0.278351i | ||||
\(969\) | −10.8340 | −0.348038 | ||||||||
\(970\) | −5.14575 | + | 8.91270i | −0.165220 | + | 0.286170i | ||||
\(971\) | −13.7915 | + | 23.8876i | −0.442590 | + | 0.766589i | −0.997881 | − | 0.0650674i | \(-0.979274\pi\) |
0.555290 | + | 0.831656i | \(0.312607\pi\) | |||||||
\(972\) | −0.500000 | + | 0.866025i | −0.0160375 | + | 0.0277778i | ||||
\(973\) | 4.64575 | + | 8.04668i | 0.148936 | + | 0.257965i | ||||
\(974\) | 13.0830 | − | 22.6604i | 0.419207 | − | 0.726087i | ||||
\(975\) | −1.00000 | − | 1.73205i | −0.0320256 | − | 0.0554700i | ||||
\(976\) | −3.29150 | −0.105358 | ||||||||
\(977\) | −6.58301 | −0.210609 | −0.105304 | − | 0.994440i | \(-0.533582\pi\) | ||||
−0.105304 | + | 0.994440i | \(0.533582\pi\) | |||||||
\(978\) | 4.93725 | + | 8.55157i | 0.157876 | + | 0.273449i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.00000 | + | 5.19615i | 0.0958315 | + | 0.165985i | ||||
\(981\) | 2.35425 | − | 4.07768i | 0.0751654 | − | 0.130190i | ||||
\(982\) | 16.7915 | − | 29.0837i | 0.535838 | − | 0.928099i | ||||
\(983\) | 3.41699 | − | 5.91841i | 0.108985 | − | 0.188768i | −0.806374 | − | 0.591406i | \(-0.798573\pi\) |
0.915359 | + | 0.402638i | \(0.131907\pi\) | |||||||
\(984\) | −5.29150 | −0.168687 | ||||||||
\(985\) | 9.58301 | + | 16.5983i | 0.305340 | + | 0.528864i | ||||
\(986\) | −10.3542 | − | 17.9341i | −0.329746 | − | 0.571138i | ||||
\(987\) | 5.64575 | − | 9.77873i | 0.179706 | − | 0.311260i | ||||
\(988\) | −6.58301 | −0.209433 | ||||||||
\(989\) | −6.58301 | − | 11.4021i | −0.209327 | − | 0.362566i | ||||
\(990\) | 1.00000 | 0.0317821 | ||||||||
\(991\) | 35.7490 | 1.13560 | 0.567802 | − | 0.823165i | \(-0.307794\pi\) | ||||
0.567802 | + | 0.823165i | \(0.307794\pi\) | |||||||
\(992\) | −1.14575 | − | 5.44860i | −0.0363776 | − | 0.172993i | ||||
\(993\) | −9.87451 | −0.313358 | ||||||||
\(994\) | −14.5830 | −0.462545 | ||||||||
\(995\) | 4.85425 | + | 8.40781i | 0.153890 | + | 0.266545i | ||||
\(996\) | 8.29150 | 0.262726 | ||||||||
\(997\) | −1.93725 | + | 3.35542i | −0.0613534 | + | 0.106267i | −0.895071 | − | 0.445924i | \(-0.852875\pi\) |
0.833717 | + | 0.552192i | \(0.186208\pi\) | |||||||
\(998\) | 0.645751 | + | 1.11847i | 0.0204409 | + | 0.0354047i | ||||
\(999\) | −0.645751 | − | 1.11847i | −0.0204307 | − | 0.0353870i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 930.2.i.j.211.1 | ✓ | 4 | |
31.5 | even | 3 | inner | 930.2.i.j.811.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.i.j.211.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
930.2.i.j.811.1 | yes | 4 | 31.5 | even | 3 | inner |