Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(211,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.211");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.j (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: | \(5.03057532734\) |
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 | 421.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.421 |
Dual form | 630.2.j.d.211.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −0.500000 | − | 0.866025i | −0.223607 | − | 0.387298i | ||||
\(6\) | 1.50000 | + | 0.866025i | 0.612372 | + | 0.353553i | ||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | −1.50000 | + | 2.59808i | −0.452267 | + | 0.783349i | −0.998526 | − | 0.0542666i | \(-0.982718\pi\) |
0.546259 | + | 0.837616i | \(0.316051\pi\) | |||||||
\(12\) | 1.50000 | − | 0.866025i | 0.433013 | − | 0.250000i | ||||
\(13\) | 3.50000 | + | 6.06218i | 0.970725 | + | 1.68135i | 0.693375 | + | 0.720577i | \(0.256123\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0.500000 | + | 0.866025i | 0.133631 | + | 0.231455i | ||||
\(15\) | 1.50000 | − | 0.866025i | 0.387298 | − | 0.223607i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.00000 | −0.727607 | −0.363803 | − | 0.931476i | \(-0.618522\pi\) | ||||
−0.363803 | + | 0.931476i | \(0.618522\pi\) | |||||||
\(18\) | −1.50000 | + | 2.59808i | −0.353553 | + | 0.612372i | ||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | −0.500000 | + | 0.866025i | −0.111803 | + | 0.193649i | ||||
\(21\) | −1.50000 | − | 0.866025i | −0.327327 | − | 0.188982i | ||||
\(22\) | 1.50000 | + | 2.59808i | 0.319801 | + | 0.553912i | ||||
\(23\) | 3.00000 | + | 5.19615i | 0.625543 | + | 1.08347i | 0.988436 | + | 0.151642i | \(0.0484560\pi\) |
−0.362892 | + | 0.931831i | \(0.618211\pi\) | |||||||
\(24\) | − | 1.73205i | − | 0.353553i | ||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 7.00000 | 1.37281 | ||||||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −3.00000 | + | 5.19615i | −0.557086 | + | 0.964901i | 0.440652 | + | 0.897678i | \(0.354747\pi\) |
−0.997738 | + | 0.0672232i | \(0.978586\pi\) | |||||||
\(30\) | − | 1.73205i | − | 0.316228i | ||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | −4.50000 | − | 2.59808i | −0.783349 | − | 0.452267i | ||||
\(34\) | −1.50000 | + | 2.59808i | −0.257248 | + | 0.445566i | ||||
\(35\) | 1.00000 | 0.169031 | ||||||||
\(36\) | 1.50000 | + | 2.59808i | 0.250000 | + | 0.433013i | ||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | 1.00000 | − | 1.73205i | 0.162221 | − | 0.280976i | ||||
\(39\) | −10.5000 | + | 6.06218i | −1.68135 | + | 0.970725i | ||||
\(40\) | 0.500000 | + | 0.866025i | 0.0790569 | + | 0.136931i | ||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | −1.50000 | + | 0.866025i | −0.231455 | + | 0.133631i | ||||
\(43\) | −1.00000 | + | 1.73205i | −0.152499 | + | 0.264135i | −0.932145 | − | 0.362084i | \(-0.882065\pi\) |
0.779647 | + | 0.626219i | \(0.215399\pi\) | |||||||
\(44\) | 3.00000 | 0.452267 | ||||||||
\(45\) | 1.50000 | + | 2.59808i | 0.223607 | + | 0.387298i | ||||
\(46\) | 6.00000 | 0.884652 | ||||||||
\(47\) | 4.50000 | − | 7.79423i | 0.656392 | − | 1.13691i | −0.325150 | − | 0.945662i | \(-0.605415\pi\) |
0.981543 | − | 0.191243i | \(-0.0612518\pi\) | |||||||
\(48\) | −1.50000 | − | 0.866025i | −0.216506 | − | 0.125000i | ||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0.500000 | + | 0.866025i | 0.0707107 | + | 0.122474i | ||||
\(51\) | − | 5.19615i | − | 0.727607i | ||||||
\(52\) | 3.50000 | − | 6.06218i | 0.485363 | − | 0.840673i | ||||
\(53\) | −12.0000 | −1.64833 | −0.824163 | − | 0.566352i | \(-0.808354\pi\) | ||||
−0.824163 | + | 0.566352i | \(0.808354\pi\) | |||||||
\(54\) | −4.50000 | − | 2.59808i | −0.612372 | − | 0.353553i | ||||
\(55\) | 3.00000 | 0.404520 | ||||||||
\(56\) | 0.500000 | − | 0.866025i | 0.0668153 | − | 0.115728i | ||||
\(57\) | 3.46410i | 0.458831i | ||||||||
\(58\) | 3.00000 | + | 5.19615i | 0.393919 | + | 0.682288i | ||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | −1.50000 | − | 0.866025i | −0.193649 | − | 0.111803i | ||||
\(61\) | −7.00000 | + | 12.1244i | −0.896258 | + | 1.55236i | −0.0640184 | + | 0.997949i | \(0.520392\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −2.00000 | −0.254000 | ||||||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.50000 | − | 6.06218i | 0.434122 | − | 0.751921i | ||||
\(66\) | −4.50000 | + | 2.59808i | −0.553912 | + | 0.319801i | ||||
\(67\) | 5.00000 | + | 8.66025i | 0.610847 | + | 1.05802i | 0.991098 | + | 0.133135i | \(0.0425044\pi\) |
−0.380251 | + | 0.924883i | \(0.624162\pi\) | |||||||
\(68\) | 1.50000 | + | 2.59808i | 0.181902 | + | 0.315063i | ||||
\(69\) | −9.00000 | + | 5.19615i | −1.08347 | + | 0.625543i | ||||
\(70\) | 0.500000 | − | 0.866025i | 0.0597614 | − | 0.103510i | ||||
\(71\) | 3.00000 | 0.356034 | 0.178017 | − | 0.984027i | \(-0.443032\pi\) | ||||
0.178017 | + | 0.984027i | \(0.443032\pi\) | |||||||
\(72\) | 3.00000 | 0.353553 | ||||||||
\(73\) | 11.0000 | 1.28745 | 0.643726 | − | 0.765256i | \(-0.277388\pi\) | ||||
0.643726 | + | 0.765256i | \(0.277388\pi\) | |||||||
\(74\) | 1.00000 | − | 1.73205i | 0.116248 | − | 0.201347i | ||||
\(75\) | −1.50000 | − | 0.866025i | −0.173205 | − | 0.100000i | ||||
\(76\) | −1.00000 | − | 1.73205i | −0.114708 | − | 0.198680i | ||||
\(77\) | −1.50000 | − | 2.59808i | −0.170941 | − | 0.296078i | ||||
\(78\) | 12.1244i | 1.37281i | ||||||||
\(79\) | 6.50000 | − | 11.2583i | 0.731307 | − | 1.26666i | −0.225018 | − | 0.974355i | \(-0.572244\pi\) |
0.956325 | − | 0.292306i | \(-0.0944227\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.50000 | − | 12.9904i | 0.823232 | − | 1.42588i | −0.0800311 | − | 0.996792i | \(-0.525502\pi\) |
0.903263 | − | 0.429087i | \(-0.141165\pi\) | |||||||
\(84\) | 1.73205i | 0.188982i | ||||||||
\(85\) | 1.50000 | + | 2.59808i | 0.162698 | + | 0.281801i | ||||
\(86\) | 1.00000 | + | 1.73205i | 0.107833 | + | 0.186772i | ||||
\(87\) | −9.00000 | − | 5.19615i | −0.964901 | − | 0.557086i | ||||
\(88\) | 1.50000 | − | 2.59808i | 0.159901 | − | 0.276956i | ||||
\(89\) | −18.0000 | −1.90800 | −0.953998 | − | 0.299813i | \(-0.903076\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 3.00000 | 0.316228 | ||||||||
\(91\) | −7.00000 | −0.733799 | ||||||||
\(92\) | 3.00000 | − | 5.19615i | 0.312772 | − | 0.541736i | ||||
\(93\) | 3.00000 | − | 1.73205i | 0.311086 | − | 0.179605i | ||||
\(94\) | −4.50000 | − | 7.79423i | −0.464140 | − | 0.803913i | ||||
\(95\) | −1.00000 | − | 1.73205i | −0.102598 | − | 0.177705i | ||||
\(96\) | −1.50000 | + | 0.866025i | −0.153093 | + | 0.0883883i | ||||
\(97\) | 3.50000 | − | 6.06218i | 0.355371 | − | 0.615521i | −0.631810 | − | 0.775123i | \(-0.717688\pi\) |
0.987181 | + | 0.159602i | \(0.0510211\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 4.50000 | − | 7.79423i | 0.452267 | − | 0.783349i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 9.00000 | − | 15.5885i | 0.895533 | − | 1.55111i | 0.0623905 | − | 0.998052i | \(-0.480128\pi\) |
0.833143 | − | 0.553058i | \(-0.186539\pi\) | |||||||
\(102\) | −4.50000 | − | 2.59808i | −0.445566 | − | 0.257248i | ||||
\(103\) | −4.00000 | − | 6.92820i | −0.394132 | − | 0.682656i | 0.598858 | − | 0.800855i | \(-0.295621\pi\) |
−0.992990 | + | 0.118199i | \(0.962288\pi\) | |||||||
\(104\) | −3.50000 | − | 6.06218i | −0.343203 | − | 0.594445i | ||||
\(105\) | 1.73205i | 0.169031i | ||||||||
\(106\) | −6.00000 | + | 10.3923i | −0.582772 | + | 1.00939i | ||||
\(107\) | 6.00000 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(108\) | −4.50000 | + | 2.59808i | −0.433013 | + | 0.250000i | ||||
\(109\) | −1.00000 | −0.0957826 | −0.0478913 | − | 0.998853i | \(-0.515250\pi\) | ||||
−0.0478913 | + | 0.998853i | \(0.515250\pi\) | |||||||
\(110\) | 1.50000 | − | 2.59808i | 0.143019 | − | 0.247717i | ||||
\(111\) | 3.46410i | 0.328798i | ||||||||
\(112\) | −0.500000 | − | 0.866025i | −0.0472456 | − | 0.0818317i | ||||
\(113\) | −3.00000 | − | 5.19615i | −0.282216 | − | 0.488813i | 0.689714 | − | 0.724082i | \(-0.257736\pi\) |
−0.971930 | + | 0.235269i | \(0.924403\pi\) | |||||||
\(114\) | 3.00000 | + | 1.73205i | 0.280976 | + | 0.162221i | ||||
\(115\) | 3.00000 | − | 5.19615i | 0.279751 | − | 0.484544i | ||||
\(116\) | 6.00000 | 0.557086 | ||||||||
\(117\) | −10.5000 | − | 18.1865i | −0.970725 | − | 1.68135i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.50000 | − | 2.59808i | 0.137505 | − | 0.238165i | ||||
\(120\) | −1.50000 | + | 0.866025i | −0.136931 | + | 0.0790569i | ||||
\(121\) | 1.00000 | + | 1.73205i | 0.0909091 | + | 0.157459i | ||||
\(122\) | 7.00000 | + | 12.1244i | 0.633750 | + | 1.09769i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.00000 | + | 1.73205i | −0.0898027 | + | 0.155543i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.50000 | − | 2.59808i | −0.133631 | − | 0.231455i | ||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −3.00000 | − | 1.73205i | −0.264135 | − | 0.152499i | ||||
\(130\) | −3.50000 | − | 6.06218i | −0.306970 | − | 0.531688i | ||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 5.19615i | 0.452267i | ||||||||
\(133\) | −1.00000 | + | 1.73205i | −0.0867110 | + | 0.150188i | ||||
\(134\) | 10.0000 | 0.863868 | ||||||||
\(135\) | −4.50000 | + | 2.59808i | −0.387298 | + | 0.223607i | ||||
\(136\) | 3.00000 | 0.257248 | ||||||||
\(137\) | −3.00000 | + | 5.19615i | −0.256307 | + | 0.443937i | −0.965250 | − | 0.261329i | \(-0.915839\pi\) |
0.708942 | + | 0.705266i | \(0.249173\pi\) | |||||||
\(138\) | 10.3923i | 0.884652i | ||||||||
\(139\) | 11.0000 | + | 19.0526i | 0.933008 | + | 1.61602i | 0.778148 | + | 0.628080i | \(0.216159\pi\) |
0.154859 | + | 0.987937i | \(0.450508\pi\) | |||||||
\(140\) | −0.500000 | − | 0.866025i | −0.0422577 | − | 0.0731925i | ||||
\(141\) | 13.5000 | + | 7.79423i | 1.13691 | + | 0.656392i | ||||
\(142\) | 1.50000 | − | 2.59808i | 0.125877 | − | 0.218026i | ||||
\(143\) | −21.0000 | −1.75611 | ||||||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 5.50000 | − | 9.52628i | 0.455183 | − | 0.788400i | ||||
\(147\) | 1.50000 | − | 0.866025i | 0.123718 | − | 0.0714286i | ||||
\(148\) | −1.00000 | − | 1.73205i | −0.0821995 | − | 0.142374i | ||||
\(149\) | 7.50000 | + | 12.9904i | 0.614424 | + | 1.06421i | 0.990485 | + | 0.137619i | \(0.0439449\pi\) |
−0.376061 | + | 0.926595i | \(0.622722\pi\) | |||||||
\(150\) | −1.50000 | + | 0.866025i | −0.122474 | + | 0.0707107i | ||||
\(151\) | −2.50000 | + | 4.33013i | −0.203447 | + | 0.352381i | −0.949637 | − | 0.313353i | \(-0.898548\pi\) |
0.746190 | + | 0.665733i | \(0.231881\pi\) | |||||||
\(152\) | −2.00000 | −0.162221 | ||||||||
\(153\) | 9.00000 | 0.727607 | ||||||||
\(154\) | −3.00000 | −0.241747 | ||||||||
\(155\) | −1.00000 | + | 1.73205i | −0.0803219 | + | 0.139122i | ||||
\(156\) | 10.5000 | + | 6.06218i | 0.840673 | + | 0.485363i | ||||
\(157\) | −2.50000 | − | 4.33013i | −0.199522 | − | 0.345582i | 0.748852 | − | 0.662738i | \(-0.230606\pi\) |
−0.948373 | + | 0.317156i | \(0.897272\pi\) | |||||||
\(158\) | −6.50000 | − | 11.2583i | −0.517112 | − | 0.895665i | ||||
\(159\) | − | 20.7846i | − | 1.64833i | ||||||
\(160\) | 0.500000 | − | 0.866025i | 0.0395285 | − | 0.0684653i | ||||
\(161\) | −6.00000 | −0.472866 | ||||||||
\(162\) | 4.50000 | − | 7.79423i | 0.353553 | − | 0.612372i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.19615i | 0.404520i | ||||||||
\(166\) | −7.50000 | − | 12.9904i | −0.582113 | − | 1.00825i | ||||
\(167\) | −4.50000 | − | 7.79423i | −0.348220 | − | 0.603136i | 0.637713 | − | 0.770274i | \(-0.279881\pi\) |
−0.985933 | + | 0.167139i | \(0.946547\pi\) | |||||||
\(168\) | 1.50000 | + | 0.866025i | 0.115728 | + | 0.0668153i | ||||
\(169\) | −18.0000 | + | 31.1769i | −1.38462 | + | 2.39822i | ||||
\(170\) | 3.00000 | 0.230089 | ||||||||
\(171\) | −6.00000 | −0.458831 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | −9.00000 | + | 5.19615i | −0.682288 | + | 0.393919i | ||||
\(175\) | −0.500000 | − | 0.866025i | −0.0377964 | − | 0.0654654i | ||||
\(176\) | −1.50000 | − | 2.59808i | −0.113067 | − | 0.195837i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.00000 | + | 15.5885i | −0.674579 | + | 1.16840i | ||||
\(179\) | −9.00000 | −0.672692 | −0.336346 | − | 0.941739i | \(-0.609191\pi\) | ||||
−0.336346 | + | 0.941739i | \(0.609191\pi\) | |||||||
\(180\) | 1.50000 | − | 2.59808i | 0.111803 | − | 0.193649i | ||||
\(181\) | 2.00000 | 0.148659 | 0.0743294 | − | 0.997234i | \(-0.476318\pi\) | ||||
0.0743294 | + | 0.997234i | \(0.476318\pi\) | |||||||
\(182\) | −3.50000 | + | 6.06218i | −0.259437 | + | 0.449359i | ||||
\(183\) | −21.0000 | − | 12.1244i | −1.55236 | − | 0.896258i | ||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | −1.00000 | − | 1.73205i | −0.0735215 | − | 0.127343i | ||||
\(186\) | − | 3.46410i | − | 0.254000i | ||||||
\(187\) | 4.50000 | − | 7.79423i | 0.329073 | − | 0.569970i | ||||
\(188\) | −9.00000 | −0.656392 | ||||||||
\(189\) | 4.50000 | + | 2.59808i | 0.327327 | + | 0.188982i | ||||
\(190\) | −2.00000 | −0.145095 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 1.73205i | 0.125000i | ||||||||
\(193\) | 5.00000 | + | 8.66025i | 0.359908 | + | 0.623379i | 0.987945 | − | 0.154805i | \(-0.0494748\pi\) |
−0.628037 | + | 0.778183i | \(0.716141\pi\) | |||||||
\(194\) | −3.50000 | − | 6.06218i | −0.251285 | − | 0.435239i | ||||
\(195\) | 10.5000 | + | 6.06218i | 0.751921 | + | 0.434122i | ||||
\(196\) | −0.500000 | + | 0.866025i | −0.0357143 | + | 0.0618590i | ||||
\(197\) | 18.0000 | 1.28245 | 0.641223 | − | 0.767354i | \(-0.278427\pi\) | ||||
0.641223 | + | 0.767354i | \(0.278427\pi\) | |||||||
\(198\) | −4.50000 | − | 7.79423i | −0.319801 | − | 0.553912i | ||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | −15.0000 | + | 8.66025i | −1.05802 | + | 0.610847i | ||||
\(202\) | −9.00000 | − | 15.5885i | −0.633238 | − | 1.09680i | ||||
\(203\) | −3.00000 | − | 5.19615i | −0.210559 | − | 0.364698i | ||||
\(204\) | −4.50000 | + | 2.59808i | −0.315063 | + | 0.181902i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | −0.557386 | ||||||||
\(207\) | −9.00000 | − | 15.5885i | −0.625543 | − | 1.08347i | ||||
\(208\) | −7.00000 | −0.485363 | ||||||||
\(209\) | −3.00000 | + | 5.19615i | −0.207514 | + | 0.359425i | ||||
\(210\) | 1.50000 | + | 0.866025i | 0.103510 | + | 0.0597614i | ||||
\(211\) | −8.50000 | − | 14.7224i | −0.585164 | − | 1.01353i | −0.994855 | − | 0.101310i | \(-0.967697\pi\) |
0.409691 | − | 0.912224i | \(-0.365637\pi\) | |||||||
\(212\) | 6.00000 | + | 10.3923i | 0.412082 | + | 0.713746i | ||||
\(213\) | 5.19615i | 0.356034i | ||||||||
\(214\) | 3.00000 | − | 5.19615i | 0.205076 | − | 0.355202i | ||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 5.19615i | 0.353553i | ||||||||
\(217\) | 2.00000 | 0.135769 | ||||||||
\(218\) | −0.500000 | + | 0.866025i | −0.0338643 | + | 0.0586546i | ||||
\(219\) | 19.0526i | 1.28745i | ||||||||
\(220\) | −1.50000 | − | 2.59808i | −0.101130 | − | 0.175162i | ||||
\(221\) | −10.5000 | − | 18.1865i | −0.706306 | − | 1.22336i | ||||
\(222\) | 3.00000 | + | 1.73205i | 0.201347 | + | 0.116248i | ||||
\(223\) | 9.50000 | − | 16.4545i | 0.636167 | − | 1.10187i | −0.350100 | − | 0.936713i | \(-0.613852\pi\) |
0.986267 | − | 0.165161i | \(-0.0528144\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 1.50000 | − | 2.59808i | 0.100000 | − | 0.173205i | ||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | −1.50000 | + | 2.59808i | −0.0995585 | + | 0.172440i | −0.911502 | − | 0.411296i | \(-0.865076\pi\) |
0.811943 | + | 0.583736i | \(0.198410\pi\) | |||||||
\(228\) | 3.00000 | − | 1.73205i | 0.198680 | − | 0.114708i | ||||
\(229\) | 5.00000 | + | 8.66025i | 0.330409 | + | 0.572286i | 0.982592 | − | 0.185776i | \(-0.0594799\pi\) |
−0.652183 | + | 0.758062i | \(0.726147\pi\) | |||||||
\(230\) | −3.00000 | − | 5.19615i | −0.197814 | − | 0.342624i | ||||
\(231\) | 4.50000 | − | 2.59808i | 0.296078 | − | 0.170941i | ||||
\(232\) | 3.00000 | − | 5.19615i | 0.196960 | − | 0.341144i | ||||
\(233\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(234\) | −21.0000 | −1.37281 | ||||||||
\(235\) | −9.00000 | −0.587095 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 19.5000 | + | 11.2583i | 1.26666 | + | 0.731307i | ||||
\(238\) | −1.50000 | − | 2.59808i | −0.0972306 | − | 0.168408i | ||||
\(239\) | 12.0000 | + | 20.7846i | 0.776215 | + | 1.34444i | 0.934109 | + | 0.356988i | \(0.116196\pi\) |
−0.157893 | + | 0.987456i | \(0.550470\pi\) | |||||||
\(240\) | 1.73205i | 0.111803i | ||||||||
\(241\) | −4.00000 | + | 6.92820i | −0.257663 | + | 0.446285i | −0.965615 | − | 0.259975i | \(-0.916286\pi\) |
0.707953 | + | 0.706260i | \(0.249619\pi\) | |||||||
\(242\) | 2.00000 | 0.128565 | ||||||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | 14.0000 | 0.896258 | ||||||||
\(245\) | −0.500000 | + | 0.866025i | −0.0319438 | + | 0.0553283i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.00000 | + | 12.1244i | 0.445399 | + | 0.771454i | ||||
\(248\) | 1.00000 | + | 1.73205i | 0.0635001 | + | 0.109985i | ||||
\(249\) | 22.5000 | + | 12.9904i | 1.42588 | + | 0.823232i | ||||
\(250\) | 0.500000 | − | 0.866025i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −6.00000 | −0.378717 | −0.189358 | − | 0.981908i | \(-0.560641\pi\) | ||||
−0.189358 | + | 0.981908i | \(0.560641\pi\) | |||||||
\(252\) | −3.00000 | −0.188982 | ||||||||
\(253\) | −18.0000 | −1.13165 | ||||||||
\(254\) | 4.00000 | − | 6.92820i | 0.250982 | − | 0.434714i | ||||
\(255\) | −4.50000 | + | 2.59808i | −0.281801 | + | 0.162698i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | −3.00000 | + | 1.73205i | −0.186772 | + | 0.107833i | ||||
\(259\) | −1.00000 | + | 1.73205i | −0.0621370 | + | 0.107624i | ||||
\(260\) | −7.00000 | −0.434122 | ||||||||
\(261\) | 9.00000 | − | 15.5885i | 0.557086 | − | 0.964901i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 6.00000 | − | 10.3923i | 0.369976 | − | 0.640817i | −0.619586 | − | 0.784929i | \(-0.712699\pi\) |
0.989561 | + | 0.144112i | \(0.0460326\pi\) | |||||||
\(264\) | 4.50000 | + | 2.59808i | 0.276956 | + | 0.159901i | ||||
\(265\) | 6.00000 | + | 10.3923i | 0.368577 | + | 0.638394i | ||||
\(266\) | 1.00000 | + | 1.73205i | 0.0613139 | + | 0.106199i | ||||
\(267\) | − | 31.1769i | − | 1.90800i | ||||||
\(268\) | 5.00000 | − | 8.66025i | 0.305424 | − | 0.529009i | ||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | 5.19615i | 0.316228i | ||||||||
\(271\) | −28.0000 | −1.70088 | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||||
−0.850439 | + | 0.526073i | \(0.823664\pi\) | |||||||
\(272\) | 1.50000 | − | 2.59808i | 0.0909509 | − | 0.157532i | ||||
\(273\) | − | 12.1244i | − | 0.733799i | ||||||
\(274\) | 3.00000 | + | 5.19615i | 0.181237 | + | 0.313911i | ||||
\(275\) | −1.50000 | − | 2.59808i | −0.0904534 | − | 0.156670i | ||||
\(276\) | 9.00000 | + | 5.19615i | 0.541736 | + | 0.312772i | ||||
\(277\) | −1.00000 | + | 1.73205i | −0.0600842 | + | 0.104069i | −0.894503 | − | 0.447062i | \(-0.852470\pi\) |
0.834419 | + | 0.551131i | \(0.185804\pi\) | |||||||
\(278\) | 22.0000 | 1.31947 | ||||||||
\(279\) | 3.00000 | + | 5.19615i | 0.179605 | + | 0.311086i | ||||
\(280\) | −1.00000 | −0.0597614 | ||||||||
\(281\) | 4.50000 | − | 7.79423i | 0.268447 | − | 0.464965i | −0.700014 | − | 0.714130i | \(-0.746823\pi\) |
0.968461 | + | 0.249165i | \(0.0801561\pi\) | |||||||
\(282\) | 13.5000 | − | 7.79423i | 0.803913 | − | 0.464140i | ||||
\(283\) | 0.500000 | + | 0.866025i | 0.0297219 | + | 0.0514799i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525519i | \(0.823871\pi\) | |||||||
\(284\) | −1.50000 | − | 2.59808i | −0.0890086 | − | 0.154167i | ||||
\(285\) | 3.00000 | − | 1.73205i | 0.177705 | − | 0.102598i | ||||
\(286\) | −10.5000 | + | 18.1865i | −0.620878 | + | 1.07539i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1.50000 | − | 2.59808i | −0.0883883 | − | 0.153093i | ||||
\(289\) | −8.00000 | −0.470588 | ||||||||
\(290\) | 3.00000 | − | 5.19615i | 0.176166 | − | 0.305129i | ||||
\(291\) | 10.5000 | + | 6.06218i | 0.615521 | + | 0.355371i | ||||
\(292\) | −5.50000 | − | 9.52628i | −0.321863 | − | 0.557483i | ||||
\(293\) | −3.00000 | − | 5.19615i | −0.175262 | − | 0.303562i | 0.764990 | − | 0.644042i | \(-0.222744\pi\) |
−0.940252 | + | 0.340480i | \(0.889411\pi\) | |||||||
\(294\) | − | 1.73205i | − | 0.101015i | ||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | −0.116248 | ||||||||
\(297\) | 13.5000 | + | 7.79423i | 0.783349 | + | 0.452267i | ||||
\(298\) | 15.0000 | 0.868927 | ||||||||
\(299\) | −21.0000 | + | 36.3731i | −1.21446 | + | 2.10351i | ||||
\(300\) | 1.73205i | 0.100000i | ||||||||
\(301\) | −1.00000 | − | 1.73205i | −0.0576390 | − | 0.0998337i | ||||
\(302\) | 2.50000 | + | 4.33013i | 0.143859 | + | 0.249171i | ||||
\(303\) | 27.0000 | + | 15.5885i | 1.55111 | + | 0.895533i | ||||
\(304\) | −1.00000 | + | 1.73205i | −0.0573539 | + | 0.0993399i | ||||
\(305\) | 14.0000 | 0.801638 | ||||||||
\(306\) | 4.50000 | − | 7.79423i | 0.257248 | − | 0.445566i | ||||
\(307\) | 29.0000 | 1.65512 | 0.827559 | − | 0.561379i | \(-0.189729\pi\) | ||||
0.827559 | + | 0.561379i | \(0.189729\pi\) | |||||||
\(308\) | −1.50000 | + | 2.59808i | −0.0854704 | + | 0.148039i | ||||
\(309\) | 12.0000 | − | 6.92820i | 0.682656 | − | 0.394132i | ||||
\(310\) | 1.00000 | + | 1.73205i | 0.0567962 | + | 0.0983739i | ||||
\(311\) | 12.0000 | + | 20.7846i | 0.680458 | + | 1.17859i | 0.974841 | + | 0.222900i | \(0.0715523\pi\) |
−0.294384 | + | 0.955687i | \(0.595114\pi\) | |||||||
\(312\) | 10.5000 | − | 6.06218i | 0.594445 | − | 0.343203i | ||||
\(313\) | 5.00000 | − | 8.66025i | 0.282617 | − | 0.489506i | −0.689412 | − | 0.724370i | \(-0.742131\pi\) |
0.972028 | + | 0.234863i | \(0.0754642\pi\) | |||||||
\(314\) | −5.00000 | −0.282166 | ||||||||
\(315\) | −3.00000 | −0.169031 | ||||||||
\(316\) | −13.0000 | −0.731307 | ||||||||
\(317\) | −9.00000 | + | 15.5885i | −0.505490 | + | 0.875535i | 0.494489 | + | 0.869184i | \(0.335355\pi\) |
−0.999980 | + | 0.00635137i | \(0.997978\pi\) | |||||||
\(318\) | −18.0000 | − | 10.3923i | −1.00939 | − | 0.582772i | ||||
\(319\) | −9.00000 | − | 15.5885i | −0.503903 | − | 0.872786i | ||||
\(320\) | −0.500000 | − | 0.866025i | −0.0279508 | − | 0.0484123i | ||||
\(321\) | 10.3923i | 0.580042i | ||||||||
\(322\) | −3.00000 | + | 5.19615i | −0.167183 | + | 0.289570i | ||||
\(323\) | −6.00000 | −0.333849 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | −7.00000 | −0.388290 | ||||||||
\(326\) | 1.00000 | − | 1.73205i | 0.0553849 | − | 0.0959294i | ||||
\(327\) | − | 1.73205i | − | 0.0957826i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | + | 7.79423i | 0.248093 | + | 0.429710i | ||||
\(330\) | 4.50000 | + | 2.59808i | 0.247717 | + | 0.143019i | ||||
\(331\) | −8.50000 | + | 14.7224i | −0.467202 | + | 0.809218i | −0.999298 | − | 0.0374662i | \(-0.988071\pi\) |
0.532096 | + | 0.846684i | \(0.321405\pi\) | |||||||
\(332\) | −15.0000 | −0.823232 | ||||||||
\(333\) | −6.00000 | −0.328798 | ||||||||
\(334\) | −9.00000 | −0.492458 | ||||||||
\(335\) | 5.00000 | − | 8.66025i | 0.273179 | − | 0.473160i | ||||
\(336\) | 1.50000 | − | 0.866025i | 0.0818317 | − | 0.0472456i | ||||
\(337\) | 11.0000 | + | 19.0526i | 0.599208 | + | 1.03786i | 0.992938 | + | 0.118633i | \(0.0378512\pi\) |
−0.393730 | + | 0.919226i | \(0.628816\pi\) | |||||||
\(338\) | 18.0000 | + | 31.1769i | 0.979071 | + | 1.69580i | ||||
\(339\) | 9.00000 | − | 5.19615i | 0.488813 | − | 0.282216i | ||||
\(340\) | 1.50000 | − | 2.59808i | 0.0813489 | − | 0.140900i | ||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | −3.00000 | + | 5.19615i | −0.162221 | + | 0.280976i | ||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 1.00000 | − | 1.73205i | 0.0539164 | − | 0.0933859i | ||||
\(345\) | 9.00000 | + | 5.19615i | 0.484544 | + | 0.279751i | ||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | −6.00000 | − | 10.3923i | −0.322097 | − | 0.557888i | 0.658824 | − | 0.752297i | \(-0.271054\pi\) |
−0.980921 | + | 0.194409i | \(0.937721\pi\) | |||||||
\(348\) | 10.3923i | 0.557086i | ||||||||
\(349\) | 14.0000 | − | 24.2487i | 0.749403 | − | 1.29800i | −0.198706 | − | 0.980059i | \(-0.563674\pi\) |
0.948109 | − | 0.317945i | \(-0.102993\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 31.5000 | − | 18.1865i | 1.68135 | − | 0.970725i | ||||
\(352\) | −3.00000 | −0.159901 | ||||||||
\(353\) | −9.00000 | + | 15.5885i | −0.479022 | + | 0.829690i | −0.999711 | − | 0.0240566i | \(-0.992342\pi\) |
0.520689 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.50000 | − | 2.59808i | −0.0796117 | − | 0.137892i | ||||
\(356\) | 9.00000 | + | 15.5885i | 0.476999 | + | 0.826187i | ||||
\(357\) | 4.50000 | + | 2.59808i | 0.238165 | + | 0.137505i | ||||
\(358\) | −4.50000 | + | 7.79423i | −0.237832 | + | 0.411938i | ||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | −1.50000 | − | 2.59808i | −0.0790569 | − | 0.136931i | ||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | 1.00000 | − | 1.73205i | 0.0525588 | − | 0.0910346i | ||||
\(363\) | −3.00000 | + | 1.73205i | −0.157459 | + | 0.0909091i | ||||
\(364\) | 3.50000 | + | 6.06218i | 0.183450 | + | 0.317744i | ||||
\(365\) | −5.50000 | − | 9.52628i | −0.287883 | − | 0.498628i | ||||
\(366\) | −21.0000 | + | 12.1244i | −1.09769 | + | 0.633750i | ||||
\(367\) | 9.50000 | − | 16.4545i | 0.495896 | − | 0.858917i | −0.504093 | − | 0.863649i | \(-0.668173\pi\) |
0.999989 | + | 0.00473247i | \(0.00150640\pi\) | |||||||
\(368\) | −6.00000 | −0.312772 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.00000 | −0.103975 | ||||||||
\(371\) | 6.00000 | − | 10.3923i | 0.311504 | − | 0.539542i | ||||
\(372\) | −3.00000 | − | 1.73205i | −0.155543 | − | 0.0898027i | ||||
\(373\) | 2.00000 | + | 3.46410i | 0.103556 | + | 0.179364i | 0.913147 | − | 0.407630i | \(-0.133645\pi\) |
−0.809591 | + | 0.586994i | \(0.800311\pi\) | |||||||
\(374\) | −4.50000 | − | 7.79423i | −0.232689 | − | 0.403030i | ||||
\(375\) | 1.73205i | 0.0894427i | ||||||||
\(376\) | −4.50000 | + | 7.79423i | −0.232070 | + | 0.401957i | ||||
\(377\) | −42.0000 | −2.16311 | ||||||||
\(378\) | 4.50000 | − | 2.59808i | 0.231455 | − | 0.133631i | ||||
\(379\) | 29.0000 | 1.48963 | 0.744815 | − | 0.667271i | \(-0.232538\pi\) | ||||
0.744815 | + | 0.667271i | \(0.232538\pi\) | |||||||
\(380\) | −1.00000 | + | 1.73205i | −0.0512989 | + | 0.0888523i | ||||
\(381\) | 13.8564i | 0.709885i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 13.5000 | + | 23.3827i | 0.689818 | + | 1.19480i | 0.971897 | + | 0.235408i | \(0.0756427\pi\) |
−0.282079 | + | 0.959391i | \(0.591024\pi\) | |||||||
\(384\) | 1.50000 | + | 0.866025i | 0.0765466 | + | 0.0441942i | ||||
\(385\) | −1.50000 | + | 2.59808i | −0.0764471 | + | 0.132410i | ||||
\(386\) | 10.0000 | 0.508987 | ||||||||
\(387\) | 3.00000 | − | 5.19615i | 0.152499 | − | 0.264135i | ||||
\(388\) | −7.00000 | −0.355371 | ||||||||
\(389\) | −7.50000 | + | 12.9904i | −0.380265 | + | 0.658638i | −0.991100 | − | 0.133120i | \(-0.957501\pi\) |
0.610835 | + | 0.791758i | \(0.290834\pi\) | |||||||
\(390\) | 10.5000 | − | 6.06218i | 0.531688 | − | 0.306970i | ||||
\(391\) | −9.00000 | − | 15.5885i | −0.455150 | − | 0.788342i | ||||
\(392\) | 0.500000 | + | 0.866025i | 0.0252538 | + | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.00000 | − | 15.5885i | 0.453413 | − | 0.785335i | ||||
\(395\) | −13.0000 | −0.654101 | ||||||||
\(396\) | −9.00000 | −0.452267 | ||||||||
\(397\) | 26.0000 | 1.30490 | 0.652451 | − | 0.757831i | \(-0.273741\pi\) | ||||
0.652451 | + | 0.757831i | \(0.273741\pi\) | |||||||
\(398\) | −2.00000 | + | 3.46410i | −0.100251 | + | 0.173640i | ||||
\(399\) | −3.00000 | − | 1.73205i | −0.150188 | − | 0.0867110i | ||||
\(400\) | −0.500000 | − | 0.866025i | −0.0250000 | − | 0.0433013i | ||||
\(401\) | 3.00000 | + | 5.19615i | 0.149813 | + | 0.259483i | 0.931158 | − | 0.364615i | \(-0.118800\pi\) |
−0.781345 | + | 0.624099i | \(0.785466\pi\) | |||||||
\(402\) | 17.3205i | 0.863868i | ||||||||
\(403\) | 7.00000 | − | 12.1244i | 0.348695 | − | 0.603957i | ||||
\(404\) | −18.0000 | −0.895533 | ||||||||
\(405\) | −4.50000 | − | 7.79423i | −0.223607 | − | 0.387298i | ||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | −3.00000 | + | 5.19615i | −0.148704 | + | 0.257564i | ||||
\(408\) | 5.19615i | 0.257248i | ||||||||
\(409\) | −16.0000 | − | 27.7128i | −0.791149 | − | 1.37031i | −0.925256 | − | 0.379344i | \(-0.876150\pi\) |
0.134107 | − | 0.990967i | \(-0.457183\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.00000 | − | 5.19615i | −0.443937 | − | 0.256307i | ||||
\(412\) | −4.00000 | + | 6.92820i | −0.197066 | + | 0.341328i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −18.0000 | −0.884652 | ||||||||
\(415\) | −15.0000 | −0.736321 | ||||||||
\(416\) | −3.50000 | + | 6.06218i | −0.171602 | + | 0.297223i | ||||
\(417\) | −33.0000 | + | 19.0526i | −1.61602 | + | 0.933008i | ||||
\(418\) | 3.00000 | + | 5.19615i | 0.146735 | + | 0.254152i | ||||
\(419\) | 6.00000 | + | 10.3923i | 0.293119 | + | 0.507697i | 0.974546 | − | 0.224189i | \(-0.0719734\pi\) |
−0.681426 | + | 0.731887i | \(0.738640\pi\) | |||||||
\(420\) | 1.50000 | − | 0.866025i | 0.0731925 | − | 0.0422577i | ||||
\(421\) | 18.5000 | − | 32.0429i | 0.901635 | − | 1.56168i | 0.0762630 | − | 0.997088i | \(-0.475701\pi\) |
0.825372 | − | 0.564590i | \(-0.190966\pi\) | |||||||
\(422\) | −17.0000 | −0.827547 | ||||||||
\(423\) | −13.5000 | + | 23.3827i | −0.656392 | + | 1.13691i | ||||
\(424\) | 12.0000 | 0.582772 | ||||||||
\(425\) | 1.50000 | − | 2.59808i | 0.0727607 | − | 0.126025i | ||||
\(426\) | 4.50000 | + | 2.59808i | 0.218026 | + | 0.125877i | ||||
\(427\) | −7.00000 | − | 12.1244i | −0.338754 | − | 0.586739i | ||||
\(428\) | −3.00000 | − | 5.19615i | −0.145010 | − | 0.251166i | ||||
\(429\) | − | 36.3731i | − | 1.75611i | ||||||
\(430\) | 1.00000 | − | 1.73205i | 0.0482243 | − | 0.0835269i | ||||
\(431\) | −33.0000 | −1.58955 | −0.794777 | − | 0.606902i | \(-0.792412\pi\) | ||||
−0.794777 | + | 0.606902i | \(0.792412\pi\) | |||||||
\(432\) | 4.50000 | + | 2.59808i | 0.216506 | + | 0.125000i | ||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 1.00000 | − | 1.73205i | 0.0480015 | − | 0.0831411i | ||||
\(435\) | 10.3923i | 0.498273i | ||||||||
\(436\) | 0.500000 | + | 0.866025i | 0.0239457 | + | 0.0414751i | ||||
\(437\) | 6.00000 | + | 10.3923i | 0.287019 | + | 0.497131i | ||||
\(438\) | 16.5000 | + | 9.52628i | 0.788400 | + | 0.455183i | ||||
\(439\) | −4.00000 | + | 6.92820i | −0.190910 | + | 0.330665i | −0.945552 | − | 0.325471i | \(-0.894477\pi\) |
0.754642 | + | 0.656136i | \(0.227810\pi\) | |||||||
\(440\) | −3.00000 | −0.143019 | ||||||||
\(441\) | 1.50000 | + | 2.59808i | 0.0714286 | + | 0.123718i | ||||
\(442\) | −21.0000 | −0.998868 | ||||||||
\(443\) | −9.00000 | + | 15.5885i | −0.427603 | + | 0.740630i | −0.996660 | − | 0.0816684i | \(-0.973975\pi\) |
0.569057 | + | 0.822298i | \(0.307309\pi\) | |||||||
\(444\) | 3.00000 | − | 1.73205i | 0.142374 | − | 0.0821995i | ||||
\(445\) | 9.00000 | + | 15.5885i | 0.426641 | + | 0.738964i | ||||
\(446\) | −9.50000 | − | 16.4545i | −0.449838 | − | 0.779142i | ||||
\(447\) | −22.5000 | + | 12.9904i | −1.06421 | + | 0.614424i | ||||
\(448\) | −0.500000 | + | 0.866025i | −0.0236228 | + | 0.0409159i | ||||
\(449\) | −30.0000 | −1.41579 | −0.707894 | − | 0.706319i | \(-0.750354\pi\) | ||||
−0.707894 | + | 0.706319i | \(0.750354\pi\) | |||||||
\(450\) | −1.50000 | − | 2.59808i | −0.0707107 | − | 0.122474i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −3.00000 | + | 5.19615i | −0.141108 | + | 0.244406i | ||||
\(453\) | −7.50000 | − | 4.33013i | −0.352381 | − | 0.203447i | ||||
\(454\) | 1.50000 | + | 2.59808i | 0.0703985 | + | 0.121934i | ||||
\(455\) | 3.50000 | + | 6.06218i | 0.164083 | + | 0.284199i | ||||
\(456\) | − | 3.46410i | − | 0.162221i | ||||||
\(457\) | −19.0000 | + | 32.9090i | −0.888783 | + | 1.53942i | −0.0474665 | + | 0.998873i | \(0.515115\pi\) |
−0.841316 | + | 0.540544i | \(0.818219\pi\) | |||||||
\(458\) | 10.0000 | 0.467269 | ||||||||
\(459\) | 15.5885i | 0.727607i | ||||||||
\(460\) | −6.00000 | −0.279751 | ||||||||
\(461\) | 21.0000 | − | 36.3731i | 0.978068 | − | 1.69406i | 0.308651 | − | 0.951175i | \(-0.400123\pi\) |
0.669417 | − | 0.742887i | \(-0.266544\pi\) | |||||||
\(462\) | − | 5.19615i | − | 0.241747i | ||||||
\(463\) | −16.0000 | − | 27.7128i | −0.743583 | − | 1.28792i | −0.950854 | − | 0.309640i | \(-0.899791\pi\) |
0.207271 | − | 0.978284i | \(-0.433542\pi\) | |||||||
\(464\) | −3.00000 | − | 5.19615i | −0.139272 | − | 0.241225i | ||||
\(465\) | −3.00000 | − | 1.73205i | −0.139122 | − | 0.0803219i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.00000 | 0.138823 | 0.0694117 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694117 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(468\) | −10.5000 | + | 18.1865i | −0.485363 | + | 0.840673i | ||||
\(469\) | −10.0000 | −0.461757 | ||||||||
\(470\) | −4.50000 | + | 7.79423i | −0.207570 | + | 0.359521i | ||||
\(471\) | 7.50000 | − | 4.33013i | 0.345582 | − | 0.199522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.00000 | − | 5.19615i | −0.137940 | − | 0.238919i | ||||
\(474\) | 19.5000 | − | 11.2583i | 0.895665 | − | 0.517112i | ||||
\(475\) | −1.00000 | + | 1.73205i | −0.0458831 | + | 0.0794719i | ||||
\(476\) | −3.00000 | −0.137505 | ||||||||
\(477\) | 36.0000 | 1.64833 | ||||||||
\(478\) | 24.0000 | 1.09773 | ||||||||
\(479\) | 3.00000 | − | 5.19615i | 0.137073 | − | 0.237418i | −0.789314 | − | 0.613990i | \(-0.789564\pi\) |
0.926388 | + | 0.376571i | \(0.122897\pi\) | |||||||
\(480\) | 1.50000 | + | 0.866025i | 0.0684653 | + | 0.0395285i | ||||
\(481\) | 7.00000 | + | 12.1244i | 0.319173 | + | 0.552823i | ||||
\(482\) | 4.00000 | + | 6.92820i | 0.182195 | + | 0.315571i | ||||
\(483\) | − | 10.3923i | − | 0.472866i | ||||||
\(484\) | 1.00000 | − | 1.73205i | 0.0454545 | − | 0.0787296i | ||||
\(485\) | −7.00000 | −0.317854 | ||||||||
\(486\) | 13.5000 | + | 7.79423i | 0.612372 | + | 0.353553i | ||||
\(487\) | 2.00000 | 0.0906287 | 0.0453143 | − | 0.998973i | \(-0.485571\pi\) | ||||
0.0453143 | + | 0.998973i | \(0.485571\pi\) | |||||||
\(488\) | 7.00000 | − | 12.1244i | 0.316875 | − | 0.548844i | ||||
\(489\) | 3.46410i | 0.156652i | ||||||||
\(490\) | 0.500000 | + | 0.866025i | 0.0225877 | + | 0.0391230i | ||||
\(491\) | 4.50000 | + | 7.79423i | 0.203082 | + | 0.351749i | 0.949520 | − | 0.313707i | \(-0.101571\pi\) |
−0.746438 | + | 0.665455i | \(0.768237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.00000 | − | 15.5885i | 0.405340 | − | 0.702069i | ||||
\(494\) | 14.0000 | 0.629890 | ||||||||
\(495\) | −9.00000 | −0.404520 | ||||||||
\(496\) | 2.00000 | 0.0898027 | ||||||||
\(497\) | −1.50000 | + | 2.59808i | −0.0672842 | + | 0.116540i | ||||
\(498\) | 22.5000 | − | 12.9904i | 1.00825 | − | 0.582113i | ||||
\(499\) | −2.50000 | − | 4.33013i | −0.111915 | − | 0.193843i | 0.804627 | − | 0.593780i | \(-0.202365\pi\) |
−0.916542 | + | 0.399937i | \(0.869032\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 13.5000 | − | 7.79423i | 0.603136 | − | 0.348220i | ||||
\(502\) | −3.00000 | + | 5.19615i | −0.133897 | + | 0.231916i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | −1.50000 | + | 2.59808i | −0.0668153 | + | 0.115728i | ||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | −9.00000 | + | 15.5885i | −0.400099 | + | 0.692991i | ||||
\(507\) | −54.0000 | − | 31.1769i | −2.39822 | − | 1.38462i | ||||
\(508\) | −4.00000 | − | 6.92820i | −0.177471 | − | 0.307389i | ||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 5.19615i | 0.230089i | ||||||||
\(511\) | −5.50000 | + | 9.52628i | −0.243306 | + | 0.421418i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | − | 10.3923i | − | 0.458831i | ||||||
\(514\) | 27.0000 | 1.19092 | ||||||||
\(515\) | −4.00000 | + | 6.92820i | −0.176261 | + | 0.305293i | ||||
\(516\) | 3.46410i | 0.152499i | ||||||||
\(517\) | 13.5000 | + | 23.3827i | 0.593729 | + | 1.02837i | ||||
\(518\) | 1.00000 | + | 1.73205i | 0.0439375 | + | 0.0761019i | ||||
\(519\) | 9.00000 | + | 5.19615i | 0.395056 | + | 0.228086i | ||||
\(520\) | −3.50000 | + | 6.06218i | −0.153485 | + | 0.265844i | ||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | −9.00000 | − | 15.5885i | −0.393919 | − | 0.682288i | ||||
\(523\) | −13.0000 | −0.568450 | −0.284225 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284225 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.50000 | − | 0.866025i | 0.0654654 | − | 0.0377964i | ||||
\(526\) | −6.00000 | − | 10.3923i | −0.261612 | − | 0.453126i | ||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | 4.50000 | − | 2.59808i | 0.195837 | − | 0.113067i | ||||
\(529\) | −6.50000 | + | 11.2583i | −0.282609 | + | 0.489493i | ||||
\(530\) | 12.0000 | 0.521247 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.00000 | 0.0867110 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −27.0000 | − | 15.5885i | −1.16840 | − | 0.674579i | ||||
\(535\) | −3.00000 | − | 5.19615i | −0.129701 | − | 0.224649i | ||||
\(536\) | −5.00000 | − | 8.66025i | −0.215967 | − | 0.374066i | ||||
\(537\) | − | 15.5885i | − | 0.672692i | ||||||
\(538\) | 9.00000 | − | 15.5885i | 0.388018 | − | 0.672066i | ||||
\(539\) | 3.00000 | 0.129219 | ||||||||
\(540\) | 4.50000 | + | 2.59808i | 0.193649 | + | 0.111803i | ||||
\(541\) | −43.0000 | −1.84871 | −0.924357 | − | 0.381528i | \(-0.875398\pi\) | ||||
−0.924357 | + | 0.381528i | \(0.875398\pi\) | |||||||
\(542\) | −14.0000 | + | 24.2487i | −0.601351 | + | 1.04157i | ||||
\(543\) | 3.46410i | 0.148659i | ||||||||
\(544\) | −1.50000 | − | 2.59808i | −0.0643120 | − | 0.111392i | ||||
\(545\) | 0.500000 | + | 0.866025i | 0.0214176 | + | 0.0370965i | ||||
\(546\) | −10.5000 | − | 6.06218i | −0.449359 | − | 0.259437i | ||||
\(547\) | 11.0000 | − | 19.0526i | 0.470326 | − | 0.814629i | −0.529098 | − | 0.848561i | \(-0.677470\pi\) |
0.999424 | + | 0.0339321i | \(0.0108030\pi\) | |||||||
\(548\) | 6.00000 | 0.256307 | ||||||||
\(549\) | 21.0000 | − | 36.3731i | 0.896258 | − | 1.55236i | ||||
\(550\) | −3.00000 | −0.127920 | ||||||||
\(551\) | −6.00000 | + | 10.3923i | −0.255609 | + | 0.442727i | ||||
\(552\) | 9.00000 | − | 5.19615i | 0.383065 | − | 0.221163i | ||||
\(553\) | 6.50000 | + | 11.2583i | 0.276408 | + | 0.478753i | ||||
\(554\) | 1.00000 | + | 1.73205i | 0.0424859 | + | 0.0735878i | ||||
\(555\) | 3.00000 | − | 1.73205i | 0.127343 | − | 0.0735215i | ||||
\(556\) | 11.0000 | − | 19.0526i | 0.466504 | − | 0.808008i | ||||
\(557\) | −6.00000 | −0.254228 | −0.127114 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127114 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(558\) | 6.00000 | 0.254000 | ||||||||
\(559\) | −14.0000 | −0.592137 | ||||||||
\(560\) | −0.500000 | + | 0.866025i | −0.0211289 | + | 0.0365963i | ||||
\(561\) | 13.5000 | + | 7.79423i | 0.569970 | + | 0.329073i | ||||
\(562\) | −4.50000 | − | 7.79423i | −0.189821 | − | 0.328780i | ||||
\(563\) | 7.50000 | + | 12.9904i | 0.316087 | + | 0.547479i | 0.979668 | − | 0.200625i | \(-0.0642974\pi\) |
−0.663581 | + | 0.748105i | \(0.730964\pi\) | |||||||
\(564\) | − | 15.5885i | − | 0.656392i | ||||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | 1.00000 | 0.0420331 | ||||||||
\(567\) | −4.50000 | + | 7.79423i | −0.188982 | + | 0.327327i | ||||
\(568\) | −3.00000 | −0.125877 | ||||||||
\(569\) | −4.50000 | + | 7.79423i | −0.188650 | + | 0.326751i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) |
0.756151 | + | 0.654398i | \(0.227078\pi\) | |||||||
\(570\) | − | 3.46410i | − | 0.145095i | ||||||
\(571\) | −2.50000 | − | 4.33013i | −0.104622 | − | 0.181210i | 0.808962 | − | 0.587861i | \(-0.200030\pi\) |
−0.913584 | + | 0.406651i | \(0.866697\pi\) | |||||||
\(572\) | 10.5000 | + | 18.1865i | 0.439027 | + | 0.760417i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | −3.00000 | −0.125000 | ||||||||
\(577\) | 23.0000 | 0.957503 | 0.478751 | − | 0.877951i | \(-0.341090\pi\) | ||||
0.478751 | + | 0.877951i | \(0.341090\pi\) | |||||||
\(578\) | −4.00000 | + | 6.92820i | −0.166378 | + | 0.288175i | ||||
\(579\) | −15.0000 | + | 8.66025i | −0.623379 | + | 0.359908i | ||||
\(580\) | −3.00000 | − | 5.19615i | −0.124568 | − | 0.215758i | ||||
\(581\) | 7.50000 | + | 12.9904i | 0.311152 | + | 0.538932i | ||||
\(582\) | 10.5000 | − | 6.06218i | 0.435239 | − | 0.251285i | ||||
\(583\) | 18.0000 | − | 31.1769i | 0.745484 | − | 1.29122i | ||||
\(584\) | −11.0000 | −0.455183 | ||||||||
\(585\) | −10.5000 | + | 18.1865i | −0.434122 | + | 0.751921i | ||||
\(586\) | −6.00000 | −0.247858 | ||||||||
\(587\) | 6.00000 | − | 10.3923i | 0.247647 | − | 0.428936i | −0.715226 | − | 0.698893i | \(-0.753676\pi\) |
0.962872 | + | 0.269957i | \(0.0870095\pi\) | |||||||
\(588\) | −1.50000 | − | 0.866025i | −0.0618590 | − | 0.0357143i | ||||
\(589\) | −2.00000 | − | 3.46410i | −0.0824086 | − | 0.142736i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 31.1769i | 1.28245i | ||||||||
\(592\) | −1.00000 | + | 1.73205i | −0.0410997 | + | 0.0711868i | ||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 13.5000 | − | 7.79423i | 0.553912 | − | 0.319801i | ||||
\(595\) | −3.00000 | −0.122988 | ||||||||
\(596\) | 7.50000 | − | 12.9904i | 0.307212 | − | 0.532107i | ||||
\(597\) | − | 6.92820i | − | 0.283552i | ||||||
\(598\) | 21.0000 | + | 36.3731i | 0.858754 | + | 1.48741i | ||||
\(599\) | −19.5000 | − | 33.7750i | −0.796748 | − | 1.38001i | −0.921723 | − | 0.387849i | \(-0.873218\pi\) |
0.124975 | − | 0.992160i | \(-0.460115\pi\) | |||||||
\(600\) | 1.50000 | + | 0.866025i | 0.0612372 | + | 0.0353553i | ||||
\(601\) | 2.00000 | − | 3.46410i | 0.0815817 | − | 0.141304i | −0.822348 | − | 0.568985i | \(-0.807336\pi\) |
0.903929 | + | 0.427682i | \(0.140670\pi\) | |||||||
\(602\) | −2.00000 | −0.0815139 | ||||||||
\(603\) | −15.0000 | − | 25.9808i | −0.610847 | − | 1.05802i | ||||
\(604\) | 5.00000 | 0.203447 | ||||||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 27.0000 | − | 15.5885i | 1.09680 | − | 0.633238i | ||||
\(607\) | −16.0000 | − | 27.7128i | −0.649420 | − | 1.12483i | −0.983262 | − | 0.182199i | \(-0.941678\pi\) |
0.333842 | − | 0.942629i | \(-0.391655\pi\) | |||||||
\(608\) | 1.00000 | + | 1.73205i | 0.0405554 | + | 0.0702439i | ||||
\(609\) | 9.00000 | − | 5.19615i | 0.364698 | − | 0.210559i | ||||
\(610\) | 7.00000 | − | 12.1244i | 0.283422 | − | 0.490901i | ||||
\(611\) | 63.0000 | 2.54871 | ||||||||
\(612\) | −4.50000 | − | 7.79423i | −0.181902 | − | 0.315063i | ||||
\(613\) | −46.0000 | −1.85792 | −0.928961 | − | 0.370177i | \(-0.879297\pi\) | ||||
−0.928961 | + | 0.370177i | \(0.879297\pi\) | |||||||
\(614\) | 14.5000 | − | 25.1147i | 0.585172 | − | 1.01355i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.50000 | + | 2.59808i | 0.0604367 | + | 0.104679i | ||||
\(617\) | 6.00000 | + | 10.3923i | 0.241551 | + | 0.418378i | 0.961156 | − | 0.276005i | \(-0.0890106\pi\) |
−0.719605 | + | 0.694383i | \(0.755677\pi\) | |||||||
\(618\) | − | 13.8564i | − | 0.557386i | ||||||
\(619\) | 17.0000 | − | 29.4449i | 0.683288 | − | 1.18349i | −0.290684 | − | 0.956819i | \(-0.593883\pi\) |
0.973972 | − | 0.226670i | \(-0.0727838\pi\) | |||||||
\(620\) | 2.00000 | 0.0803219 | ||||||||
\(621\) | 27.0000 | − | 15.5885i | 1.08347 | − | 0.625543i | ||||
\(622\) | 24.0000 | 0.962312 | ||||||||
\(623\) | 9.00000 | − | 15.5885i | 0.360577 | − | 0.624538i | ||||
\(624\) | − | 12.1244i | − | 0.485363i | ||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −5.00000 | − | 8.66025i | −0.199840 | − | 0.346133i | ||||
\(627\) | −9.00000 | − | 5.19615i | −0.359425 | − | 0.207514i | ||||
\(628\) | −2.50000 | + | 4.33013i | −0.0997609 | + | 0.172791i | ||||
\(629\) | −6.00000 | −0.239236 | ||||||||
\(630\) | −1.50000 | + | 2.59808i | −0.0597614 | + | 0.103510i | ||||
\(631\) | −7.00000 | −0.278666 | −0.139333 | − | 0.990246i | \(-0.544496\pi\) | ||||
−0.139333 | + | 0.990246i | \(0.544496\pi\) | |||||||
\(632\) | −6.50000 | + | 11.2583i | −0.258556 | + | 0.447832i | ||||
\(633\) | 25.5000 | − | 14.7224i | 1.01353 | − | 0.585164i | ||||
\(634\) | 9.00000 | + | 15.5885i | 0.357436 | + | 0.619097i | ||||
\(635\) | −4.00000 | − | 6.92820i | −0.158735 | − | 0.274937i | ||||
\(636\) | −18.0000 | + | 10.3923i | −0.713746 | + | 0.412082i | ||||
\(637\) | 3.50000 | − | 6.06218i | 0.138675 | − | 0.240192i | ||||
\(638\) | −18.0000 | −0.712627 | ||||||||
\(639\) | −9.00000 | −0.356034 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 9.00000 | − | 15.5885i | 0.355479 | − | 0.615707i | −0.631721 | − | 0.775196i | \(-0.717651\pi\) |
0.987200 | + | 0.159489i | \(0.0509845\pi\) | |||||||
\(642\) | 9.00000 | + | 5.19615i | 0.355202 | + | 0.205076i | ||||
\(643\) | 15.5000 | + | 26.8468i | 0.611260 | + | 1.05873i | 0.991028 | + | 0.133652i | \(0.0426705\pi\) |
−0.379768 | + | 0.925082i | \(0.623996\pi\) | |||||||
\(644\) | 3.00000 | + | 5.19615i | 0.118217 | + | 0.204757i | ||||
\(645\) | 3.46410i | 0.136399i | ||||||||
\(646\) | −3.00000 | + | 5.19615i | −0.118033 | + | 0.204440i | ||||
\(647\) | 36.0000 | 1.41531 | 0.707653 | − | 0.706560i | \(-0.249754\pi\) | ||||
0.707653 | + | 0.706560i | \(0.249754\pi\) | |||||||
\(648\) | −9.00000 | −0.353553 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −3.50000 | + | 6.06218i | −0.137281 | + | 0.237778i | ||||
\(651\) | 3.46410i | 0.135769i | ||||||||
\(652\) | −1.00000 | − | 1.73205i | −0.0391630 | − | 0.0678323i | ||||
\(653\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(654\) | −1.50000 | − | 0.866025i | −0.0586546 | − | 0.0338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −33.0000 | −1.28745 | ||||||||
\(658\) | 9.00000 | 0.350857 | ||||||||
\(659\) | 1.50000 | − | 2.59808i | 0.0584317 | − | 0.101207i | −0.835330 | − | 0.549749i | \(-0.814723\pi\) |
0.893762 | + | 0.448542i | \(0.148057\pi\) | |||||||
\(660\) | 4.50000 | − | 2.59808i | 0.175162 | − | 0.101130i | ||||
\(661\) | −7.00000 | − | 12.1244i | −0.272268 | − | 0.471583i | 0.697174 | − | 0.716902i | \(-0.254441\pi\) |
−0.969442 | + | 0.245319i | \(0.921107\pi\) | |||||||
\(662\) | 8.50000 | + | 14.7224i | 0.330362 | + | 0.572204i | ||||
\(663\) | 31.5000 | − | 18.1865i | 1.22336 | − | 0.706306i | ||||
\(664\) | −7.50000 | + | 12.9904i | −0.291056 | + | 0.504125i | ||||
\(665\) | 2.00000 | 0.0775567 | ||||||||
\(666\) | −3.00000 | + | 5.19615i | −0.116248 | + | 0.201347i | ||||
\(667\) | −36.0000 | −1.39393 | ||||||||
\(668\) | −4.50000 | + | 7.79423i | −0.174110 | + | 0.301568i | ||||
\(669\) | 28.5000 | + | 16.4545i | 1.10187 | + | 0.636167i | ||||
\(670\) | −5.00000 | − | 8.66025i | −0.193167 | − | 0.334575i | ||||
\(671\) | −21.0000 | − | 36.3731i | −0.810696 | − | 1.40417i | ||||
\(672\) | − | 1.73205i | − | 0.0668153i | ||||||
\(673\) | −4.00000 | + | 6.92820i | −0.154189 | + | 0.267063i | −0.932763 | − | 0.360489i | \(-0.882610\pi\) |
0.778575 | + | 0.627552i | \(0.215943\pi\) | |||||||
\(674\) | 22.0000 | 0.847408 | ||||||||
\(675\) | 4.50000 | + | 2.59808i | 0.173205 | + | 0.100000i | ||||
\(676\) | 36.0000 | 1.38462 | ||||||||
\(677\) | −16.5000 | + | 28.5788i | −0.634147 | + | 1.09837i | 0.352549 | + | 0.935793i | \(0.385315\pi\) |
−0.986695 | + | 0.162581i | \(0.948018\pi\) | |||||||
\(678\) | − | 10.3923i | − | 0.399114i | ||||||
\(679\) | 3.50000 | + | 6.06218i | 0.134318 | + | 0.232645i | ||||
\(680\) | −1.50000 | − | 2.59808i | −0.0575224 | − | 0.0996317i | ||||
\(681\) | −4.50000 | − | 2.59808i | −0.172440 | − | 0.0995585i | ||||
\(682\) | 3.00000 | − | 5.19615i | 0.114876 | − | 0.198971i | ||||
\(683\) | 48.0000 | 1.83667 | 0.918334 | − | 0.395805i | \(-0.129534\pi\) | ||||
0.918334 | + | 0.395805i | \(0.129534\pi\) | |||||||
\(684\) | 3.00000 | + | 5.19615i | 0.114708 | + | 0.198680i | ||||
\(685\) | 6.00000 | 0.229248 | ||||||||
\(686\) | 0.500000 | − | 0.866025i | 0.0190901 | − | 0.0330650i | ||||
\(687\) | −15.0000 | + | 8.66025i | −0.572286 | + | 0.330409i | ||||
\(688\) | −1.00000 | − | 1.73205i | −0.0381246 | − | 0.0660338i | ||||
\(689\) | −42.0000 | − | 72.7461i | −1.60007 | − | 2.77141i | ||||
\(690\) | 9.00000 | − | 5.19615i | 0.342624 | − | 0.197814i | ||||
\(691\) | −1.00000 | + | 1.73205i | −0.0380418 | + | 0.0658903i | −0.884419 | − | 0.466693i | \(-0.845445\pi\) |
0.846378 | + | 0.532583i | \(0.178779\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | 4.50000 | + | 7.79423i | 0.170941 | + | 0.296078i | ||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | 11.0000 | − | 19.0526i | 0.417254 | − | 0.722705i | ||||
\(696\) | 9.00000 | + | 5.19615i | 0.341144 | + | 0.196960i | ||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14.0000 | − | 24.2487i | −0.529908 | − | 0.917827i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.500000 | + | 0.866025i | −0.0188982 | + | 0.0327327i | ||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | − | 36.3731i | − | 1.37281i | ||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | −1.50000 | + | 2.59808i | −0.0565334 | + | 0.0979187i | ||||
\(705\) | − | 15.5885i | − | 0.587095i | ||||||
\(706\) | 9.00000 | + | 15.5885i | 0.338719 | + | 0.586679i | ||||
\(707\) | 9.00000 | + | 15.5885i | 0.338480 | + | 0.586264i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.0000 | − | 29.4449i | 0.638448 | − | 1.10583i | −0.347325 | − | 0.937745i | \(-0.612910\pi\) |
0.985773 | − | 0.168080i | \(-0.0537568\pi\) | |||||||
\(710\) | −3.00000 | −0.112588 | ||||||||
\(711\) | −19.5000 | + | 33.7750i | −0.731307 | + | 1.26666i | ||||
\(712\) | 18.0000 | 0.674579 | ||||||||
\(713\) | 6.00000 | − | 10.3923i | 0.224702 | − | 0.389195i | ||||
\(714\) | 4.50000 | − | 2.59808i | 0.168408 | − | 0.0972306i | ||||
\(715\) | 10.5000 | + | 18.1865i | 0.392678 | + | 0.680138i | ||||
\(716\) | 4.50000 | + | 7.79423i | 0.168173 | + | 0.291284i | ||||
\(717\) | −36.0000 | + | 20.7846i | −1.34444 | + | 0.776215i | ||||
\(718\) | 12.0000 | − | 20.7846i | 0.447836 | − | 0.775675i | ||||
\(719\) | 18.0000 | 0.671287 | 0.335643 | − | 0.941989i | \(-0.391046\pi\) | ||||
0.335643 | + | 0.941989i | \(0.391046\pi\) | |||||||
\(720\) | −3.00000 | −0.111803 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | −7.50000 | + | 12.9904i | −0.279121 | + | 0.483452i | ||||
\(723\) | −12.0000 | − | 6.92820i | −0.446285 | − | 0.257663i | ||||
\(724\) | −1.00000 | − | 1.73205i | −0.0371647 | − | 0.0643712i | ||||
\(725\) | −3.00000 | − | 5.19615i | −0.111417 | − | 0.192980i | ||||
\(726\) | 3.46410i | 0.128565i | ||||||||
\(727\) | 9.50000 | − | 16.4545i | 0.352335 | − | 0.610263i | −0.634323 | − | 0.773068i | \(-0.718721\pi\) |
0.986658 | + | 0.162805i | \(0.0520543\pi\) | |||||||
\(728\) | 7.00000 | 0.259437 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −11.0000 | −0.407128 | ||||||||
\(731\) | 3.00000 | − | 5.19615i | 0.110959 | − | 0.192187i | ||||
\(732\) | 24.2487i | 0.896258i | ||||||||
\(733\) | 17.0000 | + | 29.4449i | 0.627909 | + | 1.08757i | 0.987971 | + | 0.154642i | \(0.0494225\pi\) |
−0.360061 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(734\) | −9.50000 | − | 16.4545i | −0.350651 | − | 0.607346i | ||||
\(735\) | −1.50000 | − | 0.866025i | −0.0553283 | − | 0.0319438i | ||||
\(736\) | −3.00000 | + | 5.19615i | −0.110581 | + | 0.191533i | ||||
\(737\) | −30.0000 | −1.10506 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 44.0000 | 1.61857 | 0.809283 | − | 0.587419i | \(-0.199856\pi\) | ||||
0.809283 | + | 0.587419i | \(0.199856\pi\) | |||||||
\(740\) | −1.00000 | + | 1.73205i | −0.0367607 | + | 0.0636715i | ||||
\(741\) | −21.0000 | + | 12.1244i | −0.771454 | + | 0.445399i | ||||
\(742\) | −6.00000 | − | 10.3923i | −0.220267 | − | 0.381514i | ||||
\(743\) | 18.0000 | + | 31.1769i | 0.660356 | + | 1.14377i | 0.980522 | + | 0.196409i | \(0.0629279\pi\) |
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(744\) | −3.00000 | + | 1.73205i | −0.109985 | + | 0.0635001i | ||||
\(745\) | 7.50000 | − | 12.9904i | 0.274779 | − | 0.475931i | ||||
\(746\) | 4.00000 | 0.146450 | ||||||||
\(747\) | −22.5000 | + | 38.9711i | −0.823232 | + | 1.42588i | ||||
\(748\) | −9.00000 | −0.329073 | ||||||||
\(749\) | −3.00000 | + | 5.19615i | −0.109618 | + | 0.189863i | ||||
\(750\) | 1.50000 | + | 0.866025i | 0.0547723 | + | 0.0316228i | ||||
\(751\) | 2.00000 | + | 3.46410i | 0.0729810 | + | 0.126407i | 0.900207 | − | 0.435463i | \(-0.143415\pi\) |
−0.827225 | + | 0.561870i | \(0.810082\pi\) | |||||||
\(752\) | 4.50000 | + | 7.79423i | 0.164098 | + | 0.284226i | ||||
\(753\) | − | 10.3923i | − | 0.378717i | ||||||
\(754\) | −21.0000 | + | 36.3731i | −0.764775 | + | 1.32463i | ||||
\(755\) | 5.00000 | 0.181969 | ||||||||
\(756\) | − | 5.19615i | − | 0.188982i | ||||||
\(757\) | −46.0000 | −1.67190 | −0.835949 | − | 0.548807i | \(-0.815082\pi\) | ||||
−0.835949 | + | 0.548807i | \(0.815082\pi\) | |||||||
\(758\) | 14.5000 | − | 25.1147i | 0.526664 | − | 0.912208i | ||||
\(759\) | − | 31.1769i | − | 1.13165i | ||||||
\(760\) | 1.00000 | + | 1.73205i | 0.0362738 | + | 0.0628281i | ||||
\(761\) | 3.00000 | + | 5.19615i | 0.108750 | + | 0.188360i | 0.915264 | − | 0.402854i | \(-0.131982\pi\) |
−0.806514 | + | 0.591215i | \(0.798649\pi\) | |||||||
\(762\) | 12.0000 | + | 6.92820i | 0.434714 | + | 0.250982i | ||||
\(763\) | 0.500000 | − | 0.866025i | 0.0181012 | − | 0.0313522i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.50000 | − | 7.79423i | −0.162698 | − | 0.281801i | ||||
\(766\) | 27.0000 | 0.975550 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.50000 | − | 0.866025i | 0.0541266 | − | 0.0312500i | ||||
\(769\) | −7.00000 | − | 12.1244i | −0.252426 | − | 0.437215i | 0.711767 | − | 0.702416i | \(-0.247895\pi\) |
−0.964193 | + | 0.265200i | \(0.914562\pi\) | |||||||
\(770\) | 1.50000 | + | 2.59808i | 0.0540562 | + | 0.0936282i | ||||
\(771\) | −40.5000 | + | 23.3827i | −1.45857 | + | 0.842107i | ||||
\(772\) | 5.00000 | − | 8.66025i | 0.179954 | − | 0.311689i | ||||
\(773\) | 21.0000 | 0.755318 | 0.377659 | − | 0.925945i | \(-0.376729\pi\) | ||||
0.377659 | + | 0.925945i | \(0.376729\pi\) | |||||||
\(774\) | −3.00000 | − | 5.19615i | −0.107833 | − | 0.186772i | ||||
\(775\) | 2.00000 | 0.0718421 | ||||||||
\(776\) | −3.50000 | + | 6.06218i | −0.125643 | + | 0.217620i | ||||
\(777\) | −3.00000 | − | 1.73205i | −0.107624 | − | 0.0621370i | ||||
\(778\) | 7.50000 | + | 12.9904i | 0.268888 | + | 0.465728i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | − | 12.1244i | − | 0.434122i | ||||||
\(781\) | −4.50000 | + | 7.79423i | −0.161023 | + | 0.278899i | ||||
\(782\) | −18.0000 | −0.643679 | ||||||||
\(783\) | 27.0000 | + | 15.5885i | 0.964901 | + | 0.557086i | ||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −2.50000 | + | 4.33013i | −0.0892288 | + | 0.154549i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.5000 | + | 21.6506i | 0.445577 | + | 0.771762i | 0.998092 | − | 0.0617409i | \(-0.0196653\pi\) |
−0.552515 | + | 0.833503i | \(0.686332\pi\) | |||||||
\(788\) | −9.00000 | − | 15.5885i | −0.320612 | − | 0.555316i | ||||
\(789\) | 18.0000 | + | 10.3923i | 0.640817 | + | 0.369976i | ||||
\(790\) | −6.50000 | + | 11.2583i | −0.231260 | + | 0.400553i | ||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | −4.50000 | + | 7.79423i | −0.159901 | + | 0.276956i | ||||
\(793\) | −98.0000 | −3.48008 | ||||||||
\(794\) | 13.0000 | − | 22.5167i | 0.461353 | − | 0.799086i | ||||
\(795\) | −18.0000 | + | 10.3923i | −0.638394 | + | 0.368577i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −19.5000 | − | 33.7750i | −0.690725 | − | 1.19637i | −0.971601 | − | 0.236627i | \(-0.923958\pi\) |
0.280875 | − | 0.959744i | \(-0.409375\pi\) | |||||||
\(798\) | −3.00000 | + | 1.73205i | −0.106199 | + | 0.0613139i | ||||
\(799\) | −13.5000 | + | 23.3827i | −0.477596 | + | 0.827220i | ||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 54.0000 | 1.90800 | ||||||||
\(802\) | 6.00000 | 0.211867 | ||||||||
\(803\) | −16.5000 | + | 28.5788i | −0.582272 | + | 1.00853i | ||||
\(804\) | 15.0000 | + | 8.66025i | 0.529009 | + | 0.305424i | ||||
\(805\) | 3.00000 | + | 5.19615i | 0.105736 | + | 0.183140i | ||||
\(806\) | −7.00000 | − | 12.1244i | −0.246564 | − | 0.427062i | ||||
\(807\) | 31.1769i | 1.09748i | ||||||||
\(808\) | −9.00000 | + | 15.5885i | −0.316619 | + | 0.548400i | ||||
\(809\) | 33.0000 | 1.16022 | 0.580109 | − | 0.814539i | \(-0.303010\pi\) | ||||
0.580109 | + | 0.814539i | \(0.303010\pi\) | |||||||
\(810\) | −9.00000 | −0.316228 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −3.00000 | + | 5.19615i | −0.105279 | + | 0.182349i | ||||
\(813\) | − | 48.4974i | − | 1.70088i | ||||||
\(814\) | 3.00000 | + | 5.19615i | 0.105150 | + | 0.182125i | ||||
\(815\) | −1.00000 | − | 1.73205i | −0.0350285 | − | 0.0606711i | ||||
\(816\) | 4.50000 | + | 2.59808i | 0.157532 | + | 0.0909509i | ||||
\(817\) | −2.00000 | + | 3.46410i | −0.0699711 | + | 0.121194i | ||||
\(818\) | −32.0000 | −1.11885 | ||||||||
\(819\) | 21.0000 | 0.733799 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.5000 | − | 28.5788i | 0.575854 | − | 0.997408i | −0.420094 | − | 0.907480i | \(-0.638003\pi\) |
0.995948 | − | 0.0899279i | \(-0.0286637\pi\) | |||||||
\(822\) | −9.00000 | + | 5.19615i | −0.313911 | + | 0.181237i | ||||
\(823\) | −22.0000 | − | 38.1051i | −0.766872 | − | 1.32826i | −0.939251 | − | 0.343230i | \(-0.888479\pi\) |
0.172379 | − | 0.985031i | \(-0.444854\pi\) | |||||||
\(824\) | 4.00000 | + | 6.92820i | 0.139347 | + | 0.241355i | ||||
\(825\) | 4.50000 | − | 2.59808i | 0.156670 | − | 0.0904534i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0000 | 0.625921 | 0.312961 | − | 0.949766i | \(-0.398679\pi\) | ||||
0.312961 | + | 0.949766i | \(0.398679\pi\) | |||||||
\(828\) | −9.00000 | + | 15.5885i | −0.312772 | + | 0.541736i | ||||
\(829\) | −16.0000 | −0.555703 | −0.277851 | − | 0.960624i | \(-0.589622\pi\) | ||||
−0.277851 | + | 0.960624i | \(0.589622\pi\) | |||||||
\(830\) | −7.50000 | + | 12.9904i | −0.260329 | + | 0.450903i | ||||
\(831\) | −3.00000 | − | 1.73205i | −0.104069 | − | 0.0600842i | ||||
\(832\) | 3.50000 | + | 6.06218i | 0.121341 | + | 0.210168i | ||||
\(833\) | 1.50000 | + | 2.59808i | 0.0519719 | + | 0.0900180i | ||||
\(834\) | 38.1051i | 1.31947i | ||||||||
\(835\) | −4.50000 | + | 7.79423i | −0.155729 | + | 0.269730i | ||||
\(836\) | 6.00000 | 0.207514 | ||||||||
\(837\) | −9.00000 | + | 5.19615i | −0.311086 | + | 0.179605i | ||||
\(838\) | 12.0000 | 0.414533 | ||||||||
\(839\) | −18.0000 | + | 31.1769i | −0.621429 | + | 1.07635i | 0.367791 | + | 0.929909i | \(0.380114\pi\) |
−0.989220 | + | 0.146438i | \(0.953219\pi\) | |||||||
\(840\) | − | 1.73205i | − | 0.0597614i | ||||||
\(841\) | −3.50000 | − | 6.06218i | −0.120690 | − | 0.209041i | ||||
\(842\) | −18.5000 | − | 32.0429i | −0.637552 | − | 1.10427i | ||||
\(843\) | 13.5000 | + | 7.79423i | 0.464965 | + | 0.268447i | ||||
\(844\) | −8.50000 | + | 14.7224i | −0.292582 | + | 0.506767i | ||||
\(845\) | 36.0000 | 1.23844 | ||||||||
\(846\) | 13.5000 | + | 23.3827i | 0.464140 | + | 0.803913i | ||||
\(847\) | −2.00000 | −0.0687208 | ||||||||
\(848\) | 6.00000 | − | 10.3923i | 0.206041 | − | 0.356873i | ||||
\(849\) | −1.50000 | + | 0.866025i | −0.0514799 | + | 0.0297219i | ||||
\(850\) | −1.50000 | − | 2.59808i | −0.0514496 | − | 0.0891133i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | 4.50000 | − | 2.59808i | 0.154167 | − | 0.0890086i | ||||
\(853\) | 23.0000 | − | 39.8372i | 0.787505 | − | 1.36400i | −0.139986 | − | 0.990153i | \(-0.544706\pi\) |
0.927491 | − | 0.373845i | \(-0.121961\pi\) | |||||||
\(854\) | −14.0000 | −0.479070 | ||||||||
\(855\) | 3.00000 | + | 5.19615i | 0.102598 | + | 0.177705i | ||||
\(856\) | −6.00000 | −0.205076 | ||||||||
\(857\) | 22.5000 | − | 38.9711i | 0.768585 | − | 1.33123i | −0.169745 | − | 0.985488i | \(-0.554294\pi\) |
0.938330 | − | 0.345741i | \(-0.112372\pi\) | |||||||
\(858\) | −31.5000 | − | 18.1865i | −1.07539 | − | 0.620878i | ||||
\(859\) | −25.0000 | − | 43.3013i | −0.852989 | − | 1.47742i | −0.878498 | − | 0.477746i | \(-0.841454\pi\) |
0.0255092 | − | 0.999675i | \(-0.491879\pi\) | |||||||
\(860\) | −1.00000 | − | 1.73205i | −0.0340997 | − | 0.0590624i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.5000 | + | 28.5788i | −0.561992 | + | 0.973399i | ||||
\(863\) | 18.0000 | 0.612727 | 0.306364 | − | 0.951915i | \(-0.400888\pi\) | ||||
0.306364 | + | 0.951915i | \(0.400888\pi\) | |||||||
\(864\) | 4.50000 | − | 2.59808i | 0.153093 | − | 0.0883883i | ||||
\(865\) | −6.00000 | −0.204006 | ||||||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | − | 13.8564i | − | 0.470588i | ||||||
\(868\) | −1.00000 | − | 1.73205i | −0.0339422 | − | 0.0587896i | ||||
\(869\) | 19.5000 | + | 33.7750i | 0.661492 | + | 1.14574i | ||||
\(870\) | 9.00000 | + | 5.19615i | 0.305129 | + | 0.176166i | ||||
\(871\) | −35.0000 | + | 60.6218i | −1.18593 | + | 2.05409i | ||||
\(872\) | 1.00000 | 0.0338643 | ||||||||
\(873\) | −10.5000 | + | 18.1865i | −0.355371 | + | 0.615521i | ||||
\(874\) | 12.0000 | 0.405906 | ||||||||
\(875\) | −0.500000 | + | 0.866025i | −0.0169031 | + | 0.0292770i | ||||
\(876\) | 16.5000 | − | 9.52628i | 0.557483 | − | 0.321863i | ||||
\(877\) | 11.0000 | + | 19.0526i | 0.371444 | + | 0.643359i | 0.989788 | − | 0.142548i | \(-0.0455296\pi\) |
−0.618344 | + | 0.785907i | \(0.712196\pi\) | |||||||
\(878\) | 4.00000 | + | 6.92820i | 0.134993 | + | 0.233816i | ||||
\(879\) | 9.00000 | − | 5.19615i | 0.303562 | − | 0.175262i | ||||
\(880\) | −1.50000 | + | 2.59808i | −0.0505650 | + | 0.0875811i | ||||
\(881\) | −36.0000 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | 2.00000 | 0.0673054 | 0.0336527 | − | 0.999434i | \(-0.489286\pi\) | ||||
0.0336527 | + | 0.999434i | \(0.489286\pi\) | |||||||
\(884\) | −10.5000 | + | 18.1865i | −0.353153 | + | 0.611679i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.00000 | + | 15.5885i | 0.302361 | + | 0.523704i | ||||
\(887\) | −12.0000 | − | 20.7846i | −0.402921 | − | 0.697879i | 0.591156 | − | 0.806557i | \(-0.298672\pi\) |
−0.994077 | + | 0.108678i | \(0.965338\pi\) | |||||||
\(888\) | − | 3.46410i | − | 0.116248i | ||||||
\(889\) | −4.00000 | + | 6.92820i | −0.134156 | + | 0.232364i | ||||
\(890\) | 18.0000 | 0.603361 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | −19.0000 | −0.636167 | ||||||||
\(893\) | 9.00000 | − | 15.5885i | 0.301174 | − | 0.521648i | ||||
\(894\) | 25.9808i | 0.868927i | ||||||||
\(895\) | 4.50000 | + | 7.79423i | 0.150418 | + | 0.260532i | ||||
\(896\) | 0.500000 | + | 0.866025i | 0.0167038 | + | 0.0289319i | ||||
\(897\) | −63.0000 | − | 36.3731i | −2.10351 | − | 1.21446i | ||||
\(898\) | −15.0000 | + | 25.9808i | −0.500556 | + | 0.866989i | ||||
\(899\) | 12.0000 | 0.400222 | ||||||||
\(900\) | −3.00000 | −0.100000 | ||||||||
\(901\) | 36.0000 | 1.19933 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.00000 | − | 1.73205i | 0.0998337 | − | 0.0576390i | ||||
\(904\) | 3.00000 | + | 5.19615i | 0.0997785 | + | 0.172821i | ||||
\(905\) | −1.00000 | − | 1.73205i | −0.0332411 | − | 0.0575753i | ||||
\(906\) | −7.50000 | + | 4.33013i | −0.249171 | + | 0.143859i | ||||
\(907\) | −7.00000 | + | 12.1244i | −0.232431 | + | 0.402583i | −0.958523 | − | 0.285015i | \(-0.908001\pi\) |
0.726092 | + | 0.687598i | \(0.241335\pi\) | |||||||
\(908\) | 3.00000 | 0.0995585 | ||||||||
\(909\) | −27.0000 | + | 46.7654i | −0.895533 | + | 1.55111i | ||||
\(910\) | 7.00000 | 0.232048 | ||||||||
\(911\) | 1.50000 | − | 2.59808i | 0.0496972 | − | 0.0860781i | −0.840107 | − | 0.542421i | \(-0.817508\pi\) |
0.889804 | + | 0.456343i | \(0.150841\pi\) | |||||||
\(912\) | −3.00000 | − | 1.73205i | −0.0993399 | − | 0.0573539i | ||||
\(913\) | 22.5000 | + | 38.9711i | 0.744641 | + | 1.28976i | ||||
\(914\) | 19.0000 | + | 32.9090i | 0.628464 | + | 1.08853i | ||||
\(915\) | 24.2487i | 0.801638i | ||||||||
\(916\) | 5.00000 | − | 8.66025i | 0.165205 | − | 0.286143i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.5000 | + | 7.79423i | 0.445566 | + | 0.257248i | ||||
\(919\) | −16.0000 | −0.527791 | −0.263896 | − | 0.964551i | \(-0.585007\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585007\pi\) | |||||||
\(920\) | −3.00000 | + | 5.19615i | −0.0989071 | + | 0.171312i | ||||
\(921\) | 50.2295i | 1.65512i | ||||||||
\(922\) | −21.0000 | − | 36.3731i | −0.691598 | − | 1.19788i | ||||
\(923\) | 10.5000 | + | 18.1865i | 0.345612 | + | 0.598617i | ||||
\(924\) | −4.50000 | − | 2.59808i | −0.148039 | − | 0.0854704i | ||||
\(925\) | −1.00000 | + | 1.73205i | −0.0328798 | + | 0.0569495i | ||||
\(926\) | −32.0000 | −1.05159 | ||||||||
\(927\) | 12.0000 | + | 20.7846i | 0.394132 | + | 0.682656i | ||||
\(928\) | −6.00000 | −0.196960 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | −3.00000 | + | 1.73205i | −0.0983739 | + | 0.0567962i | ||||
\(931\) | −1.00000 | − | 1.73205i | −0.0327737 | − | 0.0567657i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −36.0000 | + | 20.7846i | −1.17859 | + | 0.680458i | ||||
\(934\) | 1.50000 | − | 2.59808i | 0.0490815 | − | 0.0850117i | ||||
\(935\) | −9.00000 | −0.294331 | ||||||||
\(936\) | 10.5000 | + | 18.1865i | 0.343203 | + | 0.594445i | ||||
\(937\) | −43.0000 | −1.40475 | −0.702374 | − | 0.711808i | \(-0.747877\pi\) | ||||
−0.702374 | + | 0.711808i | \(0.747877\pi\) | |||||||
\(938\) | −5.00000 | + | 8.66025i | −0.163256 | + | 0.282767i | ||||
\(939\) | 15.0000 | + | 8.66025i | 0.489506 | + | 0.282617i | ||||
\(940\) | 4.50000 | + | 7.79423i | 0.146774 | + | 0.254220i | ||||
\(941\) | −6.00000 | − | 10.3923i | −0.195594 | − | 0.338779i | 0.751501 | − | 0.659732i | \(-0.229330\pi\) |
−0.947095 | + | 0.320953i | \(0.895997\pi\) | |||||||
\(942\) | − | 8.66025i | − | 0.282166i | ||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 5.19615i | − | 0.169031i | ||||||
\(946\) | −6.00000 | −0.195077 | ||||||||
\(947\) | −6.00000 | + | 10.3923i | −0.194974 | + | 0.337705i | −0.946892 | − | 0.321552i | \(-0.895796\pi\) |
0.751918 | + | 0.659256i | \(0.229129\pi\) | |||||||
\(948\) | − | 22.5167i | − | 0.731307i | ||||||
\(949\) | 38.5000 | + | 66.6840i | 1.24976 | + | 2.16465i | ||||
\(950\) | 1.00000 | + | 1.73205i | 0.0324443 | + | 0.0561951i | ||||
\(951\) | −27.0000 | − | 15.5885i | −0.875535 | − | 0.505490i | ||||
\(952\) | −1.50000 | + | 2.59808i | −0.0486153 | + | 0.0842041i | ||||
\(953\) | 6.00000 | 0.194359 | 0.0971795 | − | 0.995267i | \(-0.469018\pi\) | ||||
0.0971795 | + | 0.995267i | \(0.469018\pi\) | |||||||
\(954\) | 18.0000 | − | 31.1769i | 0.582772 | − | 1.00939i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.0000 | − | 20.7846i | 0.388108 | − | 0.672222i | ||||
\(957\) | 27.0000 | − | 15.5885i | 0.872786 | − | 0.503903i | ||||
\(958\) | −3.00000 | − | 5.19615i | −0.0969256 | − | 0.167880i | ||||
\(959\) | −3.00000 | − | 5.19615i | −0.0968751 | − | 0.167793i | ||||
\(960\) | 1.50000 | − | 0.866025i | 0.0484123 | − | 0.0279508i | ||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 14.0000 | 0.451378 | ||||||||
\(963\) | −18.0000 | −0.580042 | ||||||||
\(964\) | 8.00000 | 0.257663 | ||||||||
\(965\) | 5.00000 | − | 8.66025i | 0.160956 | − | 0.278783i | ||||
\(966\) | −9.00000 | − | 5.19615i | −0.289570 | − | 0.167183i | ||||
\(967\) | 23.0000 | + | 39.8372i | 0.739630 | + | 1.28108i | 0.952662 | + | 0.304032i | \(0.0983329\pi\) |
−0.213032 | + | 0.977045i | \(0.568334\pi\) | |||||||
\(968\) | −1.00000 | − | 1.73205i | −0.0321412 | − | 0.0556702i | ||||
\(969\) | − | 10.3923i | − | 0.333849i | ||||||
\(970\) | −3.50000 | + | 6.06218i | −0.112378 | + | 0.194645i | ||||
\(971\) | 30.0000 | 0.962746 | 0.481373 | − | 0.876516i | \(-0.340138\pi\) | ||||
0.481373 | + | 0.876516i | \(0.340138\pi\) | |||||||
\(972\) | 13.5000 | − | 7.79423i | 0.433013 | − | 0.250000i | ||||
\(973\) | −22.0000 | −0.705288 | ||||||||
\(974\) | 1.00000 | − | 1.73205i | 0.0320421 | − | 0.0554985i | ||||
\(975\) | − | 12.1244i | − | 0.388290i | ||||||
\(976\) | −7.00000 | − | 12.1244i | −0.224065 | − | 0.388091i | ||||
\(977\) | −12.0000 | − | 20.7846i | −0.383914 | − | 0.664959i | 0.607704 | − | 0.794164i | \(-0.292091\pi\) |
−0.991618 | + | 0.129205i | \(0.958757\pi\) | |||||||
\(978\) | 3.00000 | + | 1.73205i | 0.0959294 | + | 0.0553849i | ||||
\(979\) | 27.0000 | − | 46.7654i | 0.862924 | − | 1.49463i | ||||
\(980\) | 1.00000 | 0.0319438 | ||||||||
\(981\) | 3.00000 | 0.0957826 | ||||||||
\(982\) | 9.00000 | 0.287202 | ||||||||
\(983\) | 13.5000 | − | 23.3827i | 0.430583 | − | 0.745792i | −0.566340 | − | 0.824171i | \(-0.691641\pi\) |
0.996924 | + | 0.0783795i | \(0.0249746\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00000 | − | 15.5885i | −0.286764 | − | 0.496690i | ||||
\(986\) | −9.00000 | − | 15.5885i | −0.286618 | − | 0.496438i | ||||
\(987\) | −13.5000 | + | 7.79423i | −0.429710 | + | 0.248093i | ||||
\(988\) | 7.00000 | − | 12.1244i | 0.222700 | − | 0.385727i | ||||
\(989\) | −12.0000 | −0.381578 | ||||||||
\(990\) | −4.50000 | + | 7.79423i | −0.143019 | + | 0.247717i | ||||
\(991\) | 41.0000 | 1.30241 | 0.651204 | − | 0.758903i | \(-0.274264\pi\) | ||||
0.651204 | + | 0.758903i | \(0.274264\pi\) | |||||||
\(992\) | 1.00000 | − | 1.73205i | 0.0317500 | − | 0.0549927i | ||||
\(993\) | −25.5000 | − | 14.7224i | −0.809218 | − | 0.467202i | ||||
\(994\) | 1.50000 | + | 2.59808i | 0.0475771 | + | 0.0824060i | ||||
\(995\) | 2.00000 | + | 3.46410i | 0.0634043 | + | 0.109819i | ||||
\(996\) | − | 25.9808i | − | 0.823232i | ||||||
\(997\) | −13.0000 | + | 22.5167i | −0.411714 | + | 0.713110i | −0.995077 | − | 0.0991016i | \(-0.968403\pi\) |
0.583363 | + | 0.812211i | \(0.301736\pi\) | |||||||
\(998\) | −5.00000 | −0.158272 | ||||||||
\(999\) | − | 10.3923i | − | 0.328798i |
(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 | 630.2.j.d.421.1 | yes | 2 | |
3.2 | odd | 2 | 1890.2.j.d.1261.1 | 2 | |||
9.2 | odd | 6 | 5670.2.a.j.1.1 | 1 | |||
9.4 | even | 3 | inner | 630.2.j.d.211.1 | ✓ | 2 | |
9.5 | odd | 6 | 1890.2.j.d.631.1 | 2 | |||
9.7 | even | 3 | 5670.2.a.i.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.j.d.211.1 | ✓ | 2 | 9.4 | even | 3 | inner | |
630.2.j.d.421.1 | yes | 2 | 1.1 | even | 1 | trivial | |
1890.2.j.d.631.1 | 2 | 9.5 | odd | 6 | |||
1890.2.j.d.1261.1 | 2 | 3.2 | odd | 2 | |||
5670.2.a.i.1.1 | 1 | 9.7 | even | 3 | |||
5670.2.a.j.1.1 | 1 | 9.2 | odd | 6 |