Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(497,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("930.497");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.j (of order \(4\), 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: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 683.4 | ||
Root | \(-0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.683 |
Dual form | 930.2.j.c.497.4 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.292893 | + | 1.70711i | −0.169102 | + | 0.985599i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.19663 | + | 1.88893i | 0.535151 | + | 0.844756i | ||||
\(6\) | −1.41421 | + | 1.00000i | −0.577350 | + | 0.408248i | ||||
\(7\) | 3.59604 | − | 3.59604i | 1.35917 | − | 1.35917i | 0.484239 | − | 0.874935i | \(-0.339096\pi\) |
0.874935 | − | 0.484239i | \(-0.160904\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | −2.82843 | − | 1.00000i | −0.942809 | − | 0.333333i | ||||
\(10\) | −0.489528 | + | 2.18183i | −0.154802 | + | 0.689954i | ||||
\(11\) | 1.67135i | 0.503932i | 0.967736 | + | 0.251966i | \(0.0810771\pi\) | ||||
−0.967736 | + | 0.251966i | \(0.918923\pi\) | |||||||
\(12\) | −1.70711 | − | 0.292893i | −0.492799 | − | 0.0845510i | ||||
\(13\) | −0.721916 | − | 0.721916i | −0.200224 | − | 0.200224i | 0.599872 | − | 0.800096i | \(-0.295218\pi\) |
−0.800096 | + | 0.599872i | \(0.795218\pi\) | |||||||
\(14\) | 5.08557 | 1.35917 | ||||||||
\(15\) | −3.57510 | + | 1.48953i | −0.923086 | + | 0.384595i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.06462 | + | 5.06462i | 1.22835 | + | 1.22835i | 0.964587 | + | 0.263764i | \(0.0849642\pi\) |
0.263764 | + | 0.964587i | \(0.415036\pi\) | |||||||
\(18\) | −1.29289 | − | 2.70711i | −0.304738 | − | 0.638071i | ||||
\(19\) | 7.32821i | 1.68121i | 0.541652 | + | 0.840603i | \(0.317799\pi\) | ||||
−0.541652 | + | 0.840603i | \(0.682201\pi\) | |||||||
\(20\) | −1.88893 | + | 1.19663i | −0.422378 | + | 0.267576i | ||||
\(21\) | 5.08557 | + | 7.19208i | 1.10976 | + | 1.56944i | ||||
\(22\) | −1.18183 | + | 1.18183i | −0.251966 | + | 0.251966i | ||||
\(23\) | 3.01025 | − | 3.01025i | 0.627681 | − | 0.627681i | −0.319803 | − | 0.947484i | \(-0.603617\pi\) |
0.947484 | + | 0.319803i | \(0.103617\pi\) | |||||||
\(24\) | −1.00000 | − | 1.41421i | −0.204124 | − | 0.288675i | ||||
\(25\) | −2.13613 | + | 4.52072i | −0.427226 | + | 0.904145i | ||||
\(26\) | − | 1.02094i | − | 0.200224i | ||||||
\(27\) | 2.53553 | − | 4.53553i | 0.487964 | − | 0.872864i | ||||
\(28\) | 3.59604 | + | 3.59604i | 0.679587 | + | 0.679587i | ||||
\(29\) | −10.0205 | −1.86076 | −0.930381 | − | 0.366595i | \(-0.880523\pi\) | ||||
−0.930381 | + | 0.366595i | \(0.880523\pi\) | |||||||
\(30\) | −3.58123 | − | 1.47472i | −0.653840 | − | 0.269246i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.85318 | − | 0.489528i | −0.496675 | − | 0.0852159i | ||||
\(34\) | 7.16246i | 1.22835i | ||||||||
\(35\) | 11.0958 | + | 2.48953i | 1.87554 | + | 0.420807i | ||||
\(36\) | 1.00000 | − | 2.82843i | 0.166667 | − | 0.471405i | ||||
\(37\) | −2.00000 | + | 2.00000i | −0.328798 | + | 0.328798i | −0.852129 | − | 0.523331i | \(-0.824689\pi\) |
0.523331 | + | 0.852129i | \(0.324689\pi\) | |||||||
\(38\) | −5.18183 | + | 5.18183i | −0.840603 | + | 0.840603i | ||||
\(39\) | 1.44383 | − | 1.02094i | 0.231198 | − | 0.163482i | ||||
\(40\) | −2.18183 | − | 0.489528i | −0.344977 | − | 0.0774012i | ||||
\(41\) | − | 10.6359i | − | 1.66105i | −0.556981 | − | 0.830525i | \(-0.688040\pi\) | ||
0.556981 | − | 0.830525i | \(-0.311960\pi\) | |||||||
\(42\) | −1.48953 | + | 8.68161i | −0.229839 | + | 1.33960i | ||||
\(43\) | −5.28834 | − | 5.28834i | −0.806464 | − | 0.806464i | 0.177633 | − | 0.984097i | \(-0.443156\pi\) |
−0.984097 | + | 0.177633i | \(0.943156\pi\) | |||||||
\(44\) | −1.67135 | −0.251966 | ||||||||
\(45\) | −1.49566 | − | 6.53934i | −0.222960 | − | 0.974828i | ||||
\(46\) | 4.25714 | 0.627681 | ||||||||
\(47\) | 1.86387 | + | 1.86387i | 0.271873 | + | 0.271873i | 0.829854 | − | 0.557981i | \(-0.188424\pi\) |
−0.557981 | + | 0.829854i | \(0.688424\pi\) | |||||||
\(48\) | 0.292893 | − | 1.70711i | 0.0422755 | − | 0.246400i | ||||
\(49\) | − | 18.8630i | − | 2.69471i | ||||||
\(50\) | −4.70711 | + | 1.68616i | −0.665685 | + | 0.238459i | ||||
\(51\) | −10.1292 | + | 7.16246i | −1.41838 | + | 1.00294i | ||||
\(52\) | 0.721916 | − | 0.721916i | 0.100112 | − | 0.100112i | ||||
\(53\) | 0.190501 | − | 0.190501i | 0.0261673 | − | 0.0261673i | −0.693902 | − | 0.720069i | \(-0.744110\pi\) |
0.720069 | + | 0.693902i | \(0.244110\pi\) | |||||||
\(54\) | 5.00000 | − | 1.41421i | 0.680414 | − | 0.192450i | ||||
\(55\) | −3.15707 | + | 2.00000i | −0.425700 | + | 0.269680i | ||||
\(56\) | 5.08557i | 0.679587i | ||||||||
\(57\) | −12.5100 | − | 2.14638i | −1.65699 | − | 0.284295i | ||||
\(58\) | −7.08557 | − | 7.08557i | −0.930381 | − | 0.930381i | ||||
\(59\) | 3.00868 | 0.391696 | 0.195848 | − | 0.980634i | \(-0.437254\pi\) | ||||
0.195848 | + | 0.980634i | \(0.437254\pi\) | |||||||
\(60\) | −1.48953 | − | 3.57510i | −0.192297 | − | 0.461543i | ||||
\(61\) | 9.83710 | 1.25951 | 0.629756 | − | 0.776793i | \(-0.283155\pi\) | ||||
0.629756 | + | 0.776793i | \(0.283155\pi\) | |||||||
\(62\) | 0.707107 | + | 0.707107i | 0.0898027 | + | 0.0898027i | ||||
\(63\) | −13.7672 | + | 6.57510i | −1.73450 | + | 0.828384i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 0.499781 | − | 2.22752i | 0.0619902 | − | 0.276290i | ||||
\(66\) | −1.67135 | − | 2.36365i | −0.205729 | − | 0.290945i | ||||
\(67\) | 1.37233 | − | 1.37233i | 0.167656 | − | 0.167656i | −0.618292 | − | 0.785948i | \(-0.712175\pi\) |
0.785948 | + | 0.618292i | \(0.212175\pi\) | |||||||
\(68\) | −5.06462 | + | 5.06462i | −0.614176 | + | 0.614176i | ||||
\(69\) | 4.25714 | + | 6.02051i | 0.512499 | + | 0.724784i | ||||
\(70\) | 6.08557 | + | 9.60629i | 0.727364 | + | 1.14817i | ||||
\(71\) | 1.32821i | 0.157629i | 0.996889 | + | 0.0788146i | \(0.0251135\pi\) | ||||
−0.996889 | + | 0.0788146i | \(0.974886\pi\) | |||||||
\(72\) | 2.70711 | − | 1.29289i | 0.319036 | − | 0.152369i | ||||
\(73\) | −0.424905 | − | 0.424905i | −0.0497313 | − | 0.0497313i | 0.681804 | − | 0.731535i | \(-0.261196\pi\) |
−0.731535 | + | 0.681804i | \(0.761196\pi\) | |||||||
\(74\) | −2.82843 | −0.328798 | ||||||||
\(75\) | −7.09170 | − | 4.97069i | −0.818879 | − | 0.573966i | ||||
\(76\) | −7.32821 | −0.840603 | ||||||||
\(77\) | 6.01025 | + | 6.01025i | 0.684932 | + | 0.684932i | ||||
\(78\) | 1.74286 | + | 0.299028i | 0.197340 | + | 0.0338582i | ||||
\(79\) | 1.39909i | 0.157410i | 0.996898 | + | 0.0787052i | \(0.0250786\pi\) | ||||
−0.996898 | + | 0.0787052i | \(0.974921\pi\) | |||||||
\(80\) | −1.19663 | − | 1.88893i | −0.133788 | − | 0.211189i | ||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 7.52072 | − | 7.52072i | 0.830525 | − | 0.830525i | ||||
\(83\) | −7.37010 | + | 7.37010i | −0.808973 | + | 0.808973i | −0.984478 | − | 0.175505i | \(-0.943844\pi\) |
0.175505 | + | 0.984478i | \(0.443844\pi\) | |||||||
\(84\) | −7.19208 | + | 5.08557i | −0.784720 | + | 0.554881i | ||||
\(85\) | −3.50623 | + | 15.6272i | −0.380304 | + | 1.69501i | ||||
\(86\) | − | 7.47884i | − | 0.806464i | ||||||
\(87\) | 2.93494 | − | 17.1061i | 0.314658 | − | 1.83396i | ||||
\(88\) | −1.18183 | − | 1.18183i | −0.125983 | − | 0.125983i | ||||
\(89\) | 3.30770 | 0.350616 | 0.175308 | − | 0.984514i | \(-0.443908\pi\) | ||||
0.175308 | + | 0.984514i | \(0.443908\pi\) | |||||||
\(90\) | 3.56642 | − | 5.68161i | 0.375934 | − | 0.598894i | ||||
\(91\) | −5.19208 | −0.544278 | ||||||||
\(92\) | 3.01025 | + | 3.01025i | 0.313841 | + | 0.313841i | ||||
\(93\) | −0.292893 | + | 1.70711i | −0.0303716 | + | 0.177019i | ||||
\(94\) | 2.63591i | 0.271873i | ||||||||
\(95\) | −13.8425 | + | 8.76919i | −1.42021 | + | 0.899700i | ||||
\(96\) | 1.41421 | − | 1.00000i | 0.144338 | − | 0.102062i | ||||
\(97\) | 5.96456 | − | 5.96456i | 0.605609 | − | 0.605609i | −0.336186 | − | 0.941795i | \(-0.609137\pi\) |
0.941795 | + | 0.336186i | \(0.109137\pi\) | |||||||
\(98\) | 13.3382 | − | 13.3382i | 1.34736 | − | 1.34736i | ||||
\(99\) | 1.67135 | − | 4.72730i | 0.167977 | − | 0.475112i | ||||
\(100\) | −4.52072 | − | 2.13613i | −0.452072 | − | 0.213613i | ||||
\(101\) | − | 9.46972i | − | 0.942273i | −0.882060 | − | 0.471136i | \(-0.843844\pi\) | ||
0.882060 | − | 0.471136i | \(-0.156156\pi\) | |||||||
\(102\) | −12.2271 | − | 2.09784i | −1.21066 | − | 0.207717i | ||||
\(103\) | 1.93494 | + | 1.93494i | 0.190655 | + | 0.190655i | 0.795979 | − | 0.605324i | \(-0.206956\pi\) |
−0.605324 | + | 0.795979i | \(0.706956\pi\) | |||||||
\(104\) | 1.02094 | 0.100112 | ||||||||
\(105\) | −7.49978 | + | 18.2126i | −0.731904 | + | 1.77737i | ||||
\(106\) | 0.269409 | 0.0261673 | ||||||||
\(107\) | 0.0543708 | + | 0.0543708i | 0.00525622 | + | 0.00525622i | 0.709730 | − | 0.704474i | \(-0.248817\pi\) |
−0.704474 | + | 0.709730i | \(0.748817\pi\) | |||||||
\(108\) | 4.53553 | + | 2.53553i | 0.436432 | + | 0.243982i | ||||
\(109\) | − | 6.07974i | − | 0.582334i | −0.956672 | − | 0.291167i | \(-0.905957\pi\) | ||
0.956672 | − | 0.291167i | \(-0.0940435\pi\) | |||||||
\(110\) | −3.64660 | − | 0.818175i | −0.347690 | − | 0.0780099i | ||||
\(111\) | −2.82843 | − | 4.00000i | −0.268462 | − | 0.379663i | ||||
\(112\) | −3.59604 | + | 3.59604i | −0.339794 | + | 0.339794i | ||||
\(113\) | −2.23239 | + | 2.23239i | −0.210005 | + | 0.210005i | −0.804270 | − | 0.594264i | \(-0.797443\pi\) |
0.594264 | + | 0.804270i | \(0.297443\pi\) | |||||||
\(114\) | −7.32821 | − | 10.3637i | −0.686350 | − | 0.970645i | ||||
\(115\) | 9.28834 | + | 2.08399i | 0.866142 | + | 0.194333i | ||||
\(116\) | − | 10.0205i | − | 0.930381i | ||||||
\(117\) | 1.31997 | + | 2.76380i | 0.122031 | + | 0.255514i | ||||
\(118\) | 2.12745 | + | 2.12745i | 0.195848 | + | 0.195848i | ||||
\(119\) | 36.4252 | 3.33909 | ||||||||
\(120\) | 1.47472 | − | 3.58123i | 0.134623 | − | 0.326920i | ||||
\(121\) | 8.20658 | 0.746052 | ||||||||
\(122\) | 6.95588 | + | 6.95588i | 0.629756 | + | 0.629756i | ||||
\(123\) | 18.1566 | + | 3.11519i | 1.63713 | + | 0.280887i | ||||
\(124\) | 1.00000i | 0.0898027i | ||||||||
\(125\) | −11.0955 | + | 1.37465i | −0.992413 | + | 0.122953i | ||||
\(126\) | −14.3842 | − | 5.08557i | −1.28144 | − | 0.453058i | ||||
\(127\) | −9.51384 | + | 9.51384i | −0.844217 | + | 0.844217i | −0.989404 | − | 0.145187i | \(-0.953622\pi\) |
0.145187 | + | 0.989404i | \(0.453622\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 10.5767 | − | 7.47884i | 0.931224 | − | 0.658475i | ||||
\(130\) | 1.92849 | − | 1.22170i | 0.169140 | − | 0.107150i | ||||
\(131\) | − | 4.47704i | − | 0.391161i | −0.980688 | − | 0.195581i | \(-0.937341\pi\) | ||
0.980688 | − | 0.195581i | \(-0.0626591\pi\) | |||||||
\(132\) | 0.489528 | − | 2.85318i | 0.0426080 | − | 0.248337i | ||||
\(133\) | 26.3525 | + | 26.3525i | 2.28505 | + | 2.28505i | ||||
\(134\) | 1.94076 | 0.167656 | ||||||||
\(135\) | 11.6014 | − | 0.637927i | 0.998492 | − | 0.0549040i | ||||
\(136\) | −7.16246 | −0.614176 | ||||||||
\(137\) | −4.29859 | − | 4.29859i | −0.367253 | − | 0.367253i | 0.499221 | − | 0.866475i | \(-0.333619\pi\) |
−0.866475 | + | 0.499221i | \(0.833619\pi\) | |||||||
\(138\) | −1.24689 | + | 7.26739i | −0.106142 | + | 0.618642i | ||||
\(139\) | − | 8.18340i | − | 0.694107i | −0.937845 | − | 0.347054i | \(-0.887182\pi\) | ||
0.937845 | − | 0.347054i | \(-0.112818\pi\) | |||||||
\(140\) | −2.48953 | + | 11.0958i | −0.210404 | + | 0.937768i | ||||
\(141\) | −3.72774 | + | 2.63591i | −0.313932 | + | 0.221984i | ||||
\(142\) | −0.939185 | + | 0.939185i | −0.0788146 | + | 0.0788146i | ||||
\(143\) | 1.20658 | − | 1.20658i | 0.100899 | − | 0.100899i | ||||
\(144\) | 2.82843 | + | 1.00000i | 0.235702 | + | 0.0833333i | ||||
\(145\) | −11.9909 | − | 18.9281i | −0.995789 | − | 1.57189i | ||||
\(146\) | − | 0.600906i | − | 0.0497313i | ||||||
\(147\) | 32.2011 | + | 5.52484i | 2.65591 | + | 0.455681i | ||||
\(148\) | −2.00000 | − | 2.00000i | −0.164399 | − | 0.164399i | ||||
\(149\) | 15.9667 | 1.30804 | 0.654020 | − | 0.756478i | \(-0.273081\pi\) | ||||
0.654020 | + | 0.756478i | \(0.273081\pi\) | |||||||
\(150\) | −1.49978 | − | 8.52940i | −0.122457 | − | 0.696423i | ||||
\(151\) | 10.3004 | 0.838233 | 0.419117 | − | 0.907932i | \(-0.362340\pi\) | ||||
0.419117 | + | 0.907932i | \(0.362340\pi\) | |||||||
\(152\) | −5.18183 | − | 5.18183i | −0.420302 | − | 0.420302i | ||||
\(153\) | −9.26029 | − | 19.3895i | −0.748650 | − | 1.56755i | ||||
\(154\) | 8.49978i | 0.684932i | ||||||||
\(155\) | 1.19663 | + | 1.88893i | 0.0961160 | + | 0.151723i | ||||
\(156\) | 1.02094 | + | 1.44383i | 0.0817409 | + | 0.115599i | ||||
\(157\) | 4.58377 | − | 4.58377i | 0.365825 | − | 0.365825i | −0.500127 | − | 0.865952i | \(-0.666713\pi\) |
0.865952 | + | 0.500127i | \(0.166713\pi\) | |||||||
\(158\) | −0.989309 | + | 0.989309i | −0.0787052 | + | 0.0787052i | ||||
\(159\) | 0.269409 | + | 0.381001i | 0.0213655 | + | 0.0302154i | ||||
\(160\) | 0.489528 | − | 2.18183i | 0.0387006 | − | 0.172488i | ||||
\(161\) | − | 21.6500i | − | 1.70626i | ||||||
\(162\) | 0.949747 | + | 8.94975i | 0.0746192 | + | 0.703159i | ||||
\(163\) | 3.08557 | + | 3.08557i | 0.241680 | + | 0.241680i | 0.817545 | − | 0.575865i | \(-0.195335\pi\) |
−0.575865 | + | 0.817545i | \(0.695335\pi\) | |||||||
\(164\) | 10.6359 | 0.830525 | ||||||||
\(165\) | −2.48953 | − | 5.97525i | −0.193810 | − | 0.465172i | ||||
\(166\) | −10.4229 | −0.808973 | ||||||||
\(167\) | −10.8177 | − | 10.8177i | −0.837102 | − | 0.837102i | 0.151375 | − | 0.988476i | \(-0.451630\pi\) |
−0.988476 | + | 0.151375i | \(0.951630\pi\) | |||||||
\(168\) | −8.68161 | − | 1.48953i | −0.669800 | − | 0.114920i | ||||
\(169\) | − | 11.9577i | − | 0.919821i | ||||||
\(170\) | −13.5294 | + | 8.57085i | −1.03766 | + | 0.657354i | ||||
\(171\) | 7.32821 | − | 20.7273i | 0.560402 | − | 1.58506i | ||||
\(172\) | 5.28834 | − | 5.28834i | 0.403232 | − | 0.403232i | ||||
\(173\) | −6.45251 | + | 6.45251i | −0.490575 | + | 0.490575i | −0.908487 | − | 0.417912i | \(-0.862762\pi\) |
0.417912 | + | 0.908487i | \(0.362762\pi\) | |||||||
\(174\) | 14.1711 | − | 10.0205i | 1.07431 | − | 0.759653i | ||||
\(175\) | 8.57510 | + | 23.9383i | 0.648216 | + | 1.80957i | ||||
\(176\) | − | 1.67135i | − | 0.125983i | ||||||
\(177\) | −0.881221 | + | 5.13613i | −0.0662366 | + | 0.386055i | ||||
\(178\) | 2.33890 | + | 2.33890i | 0.175308 | + | 0.175308i | ||||
\(179\) | −16.5843 | −1.23957 | −0.619784 | − | 0.784772i | \(-0.712780\pi\) | ||||
−0.619784 | + | 0.784772i | \(0.712780\pi\) | |||||||
\(180\) | 6.53934 | − | 1.49566i | 0.487414 | − | 0.111480i | ||||
\(181\) | 1.87211 | 0.139153 | 0.0695763 | − | 0.997577i | \(-0.477835\pi\) | ||||
0.0695763 | + | 0.997577i | \(0.477835\pi\) | |||||||
\(182\) | −3.67135 | − | 3.67135i | −0.272139 | − | 0.272139i | ||||
\(183\) | −2.88122 | + | 16.7930i | −0.212986 | + | 1.24137i | ||||
\(184\) | 4.25714i | 0.313841i | ||||||||
\(185\) | −6.17113 | − | 1.38459i | −0.453711 | − | 0.101797i | ||||
\(186\) | −1.41421 | + | 1.00000i | −0.103695 | + | 0.0733236i | ||||
\(187\) | −8.46478 | + | 8.46478i | −0.619006 | + | 0.619006i | ||||
\(188\) | −1.86387 | + | 1.86387i | −0.135937 | + | 0.135937i | ||||
\(189\) | −7.19208 | − | 25.4278i | −0.523147 | − | 1.84960i | ||||
\(190\) | −15.9889 | − | 3.58736i | −1.15995 | − | 0.260255i | ||||
\(191\) | − | 17.4430i | − | 1.26213i | −0.775731 | − | 0.631064i | \(-0.782619\pi\) | ||
0.775731 | − | 0.631064i | \(-0.217381\pi\) | |||||||
\(192\) | 1.70711 | + | 0.292893i | 0.123200 | + | 0.0211377i | ||||
\(193\) | −1.90216 | − | 1.90216i | −0.136921 | − | 0.136921i | 0.635325 | − | 0.772245i | \(-0.280866\pi\) |
−0.772245 | + | 0.635325i | \(0.780866\pi\) | |||||||
\(194\) | 8.43516 | 0.605609 | ||||||||
\(195\) | 3.65623 | + | 1.50560i | 0.261828 | + | 0.107819i | ||||
\(196\) | 18.8630 | 1.34736 | ||||||||
\(197\) | 2.69768 | + | 2.69768i | 0.192202 | + | 0.192202i | 0.796647 | − | 0.604445i | \(-0.206605\pi\) |
−0.604445 | + | 0.796647i | \(0.706605\pi\) | |||||||
\(198\) | 4.52453 | − | 2.16088i | 0.321545 | − | 0.153567i | ||||
\(199\) | 24.1848i | 1.71441i | 0.514974 | + | 0.857206i | \(0.327802\pi\) | ||||
−0.514974 | + | 0.857206i | \(0.672198\pi\) | |||||||
\(200\) | −1.68616 | − | 4.70711i | −0.119230 | − | 0.332843i | ||||
\(201\) | 1.94076 | + | 2.74465i | 0.136891 | + | 0.193593i | ||||
\(202\) | 6.69611 | − | 6.69611i | 0.471136 | − | 0.471136i | ||||
\(203\) | −36.0341 | + | 36.0341i | −2.52910 | + | 2.52910i | ||||
\(204\) | −7.16246 | − | 10.1292i | −0.501472 | − | 0.709189i | ||||
\(205\) | 20.0905 | − | 12.7273i | 1.40318 | − | 0.888913i | ||||
\(206\) | 2.73642i | 0.190655i | ||||||||
\(207\) | −11.5245 | + | 5.50403i | −0.801010 | + | 0.382556i | ||||
\(208\) | 0.721916 | + | 0.721916i | 0.0500559 | + | 0.0500559i | ||||
\(209\) | −12.2480 | −0.847214 | ||||||||
\(210\) | −18.1814 | + | 7.57510i | −1.25463 | + | 0.522731i | ||||
\(211\) | −14.6009 | −1.00517 | −0.502584 | − | 0.864528i | \(-0.667617\pi\) | ||||
−0.502584 | + | 0.864528i | \(0.667617\pi\) | |||||||
\(212\) | 0.190501 | + | 0.190501i | 0.0130836 | + | 0.0130836i | ||||
\(213\) | −2.26739 | − | 0.389023i | −0.155359 | − | 0.0266554i | ||||
\(214\) | 0.0768919i | 0.00525622i | ||||||||
\(215\) | 3.66110 | − | 16.3175i | 0.249685 | − | 1.11285i | ||||
\(216\) | 1.41421 | + | 5.00000i | 0.0962250 | + | 0.340207i | ||||
\(217\) | 3.59604 | − | 3.59604i | 0.244115 | − | 0.244115i | ||||
\(218\) | 4.29903 | − | 4.29903i | 0.291167 | − | 0.291167i | ||||
\(219\) | 0.849810 | − | 0.600906i | 0.0574248 | − | 0.0406055i | ||||
\(220\) | −2.00000 | − | 3.15707i | −0.134840 | − | 0.212850i | ||||
\(221\) | − | 7.31247i | − | 0.491890i | ||||||
\(222\) | 0.828427 | − | 4.82843i | 0.0556004 | − | 0.324063i | ||||
\(223\) | 12.2654 | + | 12.2654i | 0.821350 | + | 0.821350i | 0.986302 | − | 0.164951i | \(-0.0527467\pi\) |
−0.164951 | + | 0.986302i | \(0.552747\pi\) | |||||||
\(224\) | −5.08557 | −0.339794 | ||||||||
\(225\) | 10.5626 | − | 10.6504i | 0.704174 | − | 0.710027i | ||||
\(226\) | −3.15707 | −0.210005 | ||||||||
\(227\) | 4.98392 | + | 4.98392i | 0.330795 | + | 0.330795i | 0.852888 | − | 0.522094i | \(-0.174849\pi\) |
−0.522094 | + | 0.852888i | \(0.674849\pi\) | |||||||
\(228\) | 2.14638 | − | 12.5100i | 0.142148 | − | 0.828497i | ||||
\(229\) | − | 12.3993i | − | 0.819367i | −0.912228 | − | 0.409684i | \(-0.865639\pi\) | ||
0.912228 | − | 0.409684i | \(-0.134361\pi\) | |||||||
\(230\) | 5.09424 | + | 8.04145i | 0.335904 | + | 0.530237i | ||||
\(231\) | −12.0205 | + | 8.49978i | −0.790891 | + | 0.559245i | ||||
\(232\) | 7.08557 | − | 7.08557i | 0.465190 | − | 0.465190i | ||||
\(233\) | 19.3438 | − | 19.3438i | 1.26726 | − | 1.26726i | 0.319758 | − | 0.947499i | \(-0.396398\pi\) |
0.947499 | − | 0.319758i | \(-0.103602\pi\) | |||||||
\(234\) | −1.02094 | + | 2.88767i | −0.0667412 | + | 0.188773i | ||||
\(235\) | −1.29035 | + | 5.75110i | −0.0841733 | + | 0.375160i | ||||
\(236\) | 3.00868i | 0.195848i | ||||||||
\(237\) | −2.38840 | − | 0.409785i | −0.155143 | − | 0.0266184i | ||||
\(238\) | 25.7565 | + | 25.7565i | 1.66954 | + | 1.66954i | ||||
\(239\) | 8.86716 | 0.573569 | 0.286784 | − | 0.957995i | \(-0.407414\pi\) | ||||
0.286784 | + | 0.957995i | \(0.407414\pi\) | |||||||
\(240\) | 3.57510 | − | 1.48953i | 0.230771 | − | 0.0961486i | ||||
\(241\) | −6.97906 | −0.449561 | −0.224780 | − | 0.974409i | \(-0.572166\pi\) | ||||
−0.224780 | + | 0.974409i | \(0.572166\pi\) | |||||||
\(242\) | 5.80293 | + | 5.80293i | 0.373026 | + | 0.373026i | ||||
\(243\) | −11.7071 | + | 10.2929i | −0.751011 | + | 0.660289i | ||||
\(244\) | 9.83710i | 0.629756i | ||||||||
\(245\) | 35.6309 | − | 22.5721i | 2.27638 | − | 1.44208i | ||||
\(246\) | 10.6359 | + | 15.0414i | 0.678121 | + | 0.959008i | ||||
\(247\) | 5.29035 | − | 5.29035i | 0.336617 | − | 0.336617i | ||||
\(248\) | −0.707107 | + | 0.707107i | −0.0449013 | + | 0.0449013i | ||||
\(249\) | −10.4229 | − | 14.7402i | −0.660524 | − | 0.934122i | ||||
\(250\) | −8.81774 | − | 6.87368i | −0.557683 | − | 0.434730i | ||||
\(251\) | 17.0941i | 1.07897i | 0.841995 | + | 0.539485i | \(0.181381\pi\) | ||||
−0.841995 | + | 0.539485i | \(0.818619\pi\) | |||||||
\(252\) | −6.57510 | − | 13.7672i | −0.414192 | − | 0.867250i | ||||
\(253\) | 5.03120 | + | 5.03120i | 0.316309 | + | 0.316309i | ||||
\(254\) | −13.4546 | −0.844217 | ||||||||
\(255\) | −25.6504 | − | 10.5626i | −1.60629 | − | 0.661456i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.3020 | − | 17.3020i | −1.07927 | − | 1.07927i | −0.996575 | − | 0.0826913i | \(-0.973648\pi\) |
−0.0826913 | − | 0.996575i | \(-0.526352\pi\) | |||||||
\(258\) | 12.7672 | + | 2.19050i | 0.794849 | + | 0.136375i | ||||
\(259\) | 14.3842i | 0.893788i | ||||||||
\(260\) | 2.22752 | + | 0.499781i | 0.138145 | + | 0.0309951i | ||||
\(261\) | 28.3423 | + | 10.0205i | 1.75434 | + | 0.620254i | ||||
\(262\) | 3.16575 | − | 3.16575i | 0.195581 | − | 0.195581i | ||||
\(263\) | 1.22752 | − | 1.22752i | 0.0756922 | − | 0.0756922i | −0.668247 | − | 0.743939i | \(-0.732955\pi\) |
0.743939 | + | 0.668247i | \(0.232955\pi\) | |||||||
\(264\) | 2.36365 | − | 1.67135i | 0.145473 | − | 0.102865i | ||||
\(265\) | 0.587802 | + | 0.131883i | 0.0361084 | + | 0.00810151i | ||||
\(266\) | 37.2681i | 2.28505i | ||||||||
\(267\) | −0.968804 | + | 5.64660i | −0.0592898 | + | 0.345566i | ||||
\(268\) | 1.37233 | + | 1.37233i | 0.0838282 | + | 0.0838282i | ||||
\(269\) | −0.283908 | −0.0173102 | −0.00865508 | − | 0.999963i | \(-0.502755\pi\) | ||||
−0.00865508 | + | 0.999963i | \(0.502755\pi\) | |||||||
\(270\) | 8.65453 | + | 7.75236i | 0.526698 | + | 0.471794i | ||||
\(271\) | 21.0688 | 1.27984 | 0.639920 | − | 0.768441i | \(-0.278967\pi\) | ||||
0.639920 | + | 0.768441i | \(0.278967\pi\) | |||||||
\(272\) | −5.06462 | − | 5.06462i | −0.307088 | − | 0.307088i | ||||
\(273\) | 1.52072 | − | 8.86343i | 0.0920384 | − | 0.536439i | ||||
\(274\) | − | 6.07912i | − | 0.367253i | ||||||
\(275\) | −7.55573 | − | 3.57023i | −0.455628 | − | 0.215293i | ||||
\(276\) | −6.02051 | + | 4.25714i | −0.362392 | + | 0.256250i | ||||
\(277\) | −11.3481 | + | 11.3481i | −0.681841 | + | 0.681841i | −0.960415 | − | 0.278574i | \(-0.910138\pi\) |
0.278574 | + | 0.960415i | \(0.410138\pi\) | |||||||
\(278\) | 5.78654 | − | 5.78654i | 0.347054 | − | 0.347054i | ||||
\(279\) | −2.82843 | − | 1.00000i | −0.169334 | − | 0.0598684i | ||||
\(280\) | −9.60629 | + | 6.08557i | −0.574086 | + | 0.363682i | ||||
\(281\) | − | 17.1288i | − | 1.02182i | −0.859634 | − | 0.510910i | \(-0.829309\pi\) | ||
0.859634 | − | 0.510910i | \(-0.170691\pi\) | |||||||
\(282\) | −4.49978 | − | 0.772040i | −0.267958 | − | 0.0459743i | ||||
\(283\) | 19.5708 | + | 19.5708i | 1.16337 | + | 1.16337i | 0.983734 | + | 0.179632i | \(0.0574908\pi\) |
0.179632 | + | 0.983734i | \(0.442509\pi\) | |||||||
\(284\) | −1.32821 | −0.0788146 | ||||||||
\(285\) | −10.9156 | − | 26.1990i | −0.646583 | − | 1.55190i | ||||
\(286\) | 1.70636 | 0.100899 | ||||||||
\(287\) | −38.2471 | − | 38.2471i | −2.25766 | − | 2.25766i | ||||
\(288\) | 1.29289 | + | 2.70711i | 0.0761845 | + | 0.159518i | ||||
\(289\) | 34.3008i | 2.01770i | ||||||||
\(290\) | 4.90532 | − | 21.8630i | 0.288050 | − | 1.28384i | ||||
\(291\) | 8.43516 | + | 11.9291i | 0.494478 | + | 0.699297i | ||||
\(292\) | 0.424905 | − | 0.424905i | 0.0248657 | − | 0.0248657i | ||||
\(293\) | 7.32282 | − | 7.32282i | 0.427804 | − | 0.427804i | −0.460076 | − | 0.887880i | \(-0.652178\pi\) |
0.887880 | + | 0.460076i | \(0.152178\pi\) | |||||||
\(294\) | 18.8630 | + | 26.6763i | 1.10011 | + | 1.55579i | ||||
\(295\) | 3.60029 | + | 5.68318i | 0.209617 | + | 0.330888i | ||||
\(296\) | − | 2.82843i | − | 0.164399i | ||||||
\(297\) | 7.58048 | + | 4.23777i | 0.439864 | + | 0.245901i | ||||
\(298\) | 11.2901 | + | 11.2901i | 0.654020 | + | 0.654020i | ||||
\(299\) | −4.34630 | −0.251353 | ||||||||
\(300\) | 4.97069 | − | 7.09170i | 0.286983 | − | 0.409440i | ||||
\(301\) | −38.0341 | −2.19225 | ||||||||
\(302\) | 7.28347 | + | 7.28347i | 0.419117 | + | 0.419117i | ||||
\(303\) | 16.1658 | + | 2.77362i | 0.928703 | + | 0.159340i | ||||
\(304\) | − | 7.32821i | − | 0.420302i | ||||||
\(305\) | 11.7714 | + | 18.5816i | 0.674030 | + | 1.06398i | ||||
\(306\) | 7.16246 | − | 20.2585i | 0.409451 | − | 1.15810i | ||||
\(307\) | 18.7355 | − | 18.7355i | 1.06929 | − | 1.06929i | 0.0718804 | − | 0.997413i | \(-0.477100\pi\) |
0.997413 | − | 0.0718804i | \(-0.0229000\pi\) | |||||||
\(308\) | −6.01025 | + | 6.01025i | −0.342466 | + | 0.342466i | ||||
\(309\) | −3.86988 | + | 2.73642i | −0.220150 | + | 0.155669i | ||||
\(310\) | −0.489528 | + | 2.18183i | −0.0278033 | + | 0.123919i | ||||
\(311\) | 3.21704i | 0.182422i | 0.995832 | + | 0.0912109i | \(0.0290737\pi\) | ||||
−0.995832 | + | 0.0912109i | \(0.970926\pi\) | |||||||
\(312\) | −0.299028 | + | 1.74286i | −0.0169291 | + | 0.0986700i | ||||
\(313\) | −11.4423 | − | 11.4423i | −0.646759 | − | 0.646759i | 0.305449 | − | 0.952208i | \(-0.401193\pi\) |
−0.952208 | + | 0.305449i | \(0.901193\pi\) | |||||||
\(314\) | 6.48243 | 0.365825 | ||||||||
\(315\) | −28.8942 | − | 18.1373i | −1.62800 | − | 1.02192i | ||||
\(316\) | −1.39909 | −0.0787052 | ||||||||
\(317\) | 5.94299 | + | 5.94299i | 0.333792 | + | 0.333792i | 0.854025 | − | 0.520233i | \(-0.174155\pi\) |
−0.520233 | + | 0.854025i | \(0.674155\pi\) | |||||||
\(318\) | −0.0789079 | + | 0.459909i | −0.00442494 | + | 0.0257904i | ||||
\(319\) | − | 16.7478i | − | 0.937697i | ||||||
\(320\) | 1.88893 | − | 1.19663i | 0.105595 | − | 0.0668939i | ||||
\(321\) | −0.108742 | + | 0.0768919i | −0.00606936 | + | 0.00429169i | ||||
\(322\) | 15.3088 | − | 15.3088i | 0.853128 | − | 0.853128i | ||||
\(323\) | −37.1146 | + | 37.1146i | −2.06511 | + | 2.06511i | ||||
\(324\) | −5.65685 | + | 7.00000i | −0.314270 | + | 0.388889i | ||||
\(325\) | 4.80569 | − | 1.72148i | 0.266572 | − | 0.0954904i | ||||
\(326\) | 4.36365i | 0.241680i | ||||||||
\(327\) | 10.3788 | + | 1.78072i | 0.573947 | + | 0.0984738i | ||||
\(328\) | 7.52072 | + | 7.52072i | 0.415263 | + | 0.415263i | ||||
\(329\) | 13.4051 | 0.739047 | ||||||||
\(330\) | 2.46478 | − | 5.98550i | 0.135681 | − | 0.329491i | ||||
\(331\) | −11.5358 | −0.634067 | −0.317034 | − | 0.948414i | \(-0.602687\pi\) | ||||
−0.317034 | + | 0.948414i | \(0.602687\pi\) | |||||||
\(332\) | −7.37010 | − | 7.37010i | −0.404487 | − | 0.404487i | ||||
\(333\) | 7.65685 | − | 3.65685i | 0.419593 | − | 0.200394i | ||||
\(334\) | − | 15.2986i | − | 0.837102i | ||||||
\(335\) | 4.23440 | + | 0.950058i | 0.231350 | + | 0.0519072i | ||||
\(336\) | −5.08557 | − | 7.19208i | −0.277440 | − | 0.392360i | ||||
\(337\) | 9.50560 | − | 9.50560i | 0.517803 | − | 0.517803i | −0.399103 | − | 0.916906i | \(-0.630678\pi\) |
0.916906 | + | 0.399103i | \(0.130678\pi\) | |||||||
\(338\) | 8.45535 | − | 8.45535i | 0.459911 | − | 0.459911i | ||||
\(339\) | −3.15707 | − | 4.46478i | −0.171469 | − | 0.242493i | ||||
\(340\) | −15.6272 | − | 3.50623i | −0.847506 | − | 0.190152i | ||||
\(341\) | 1.67135i | 0.0905089i | ||||||||
\(342\) | 19.8382 | − | 9.47459i | 1.07273 | − | 0.512327i | ||||
\(343\) | −42.6598 | − | 42.6598i | −2.30341 | − | 2.30341i | ||||
\(344\) | 7.47884 | 0.403232 | ||||||||
\(345\) | −6.27808 | + | 15.2458i | −0.338001 | + | 0.820806i | ||||
\(346\) | −9.12522 | −0.490575 | ||||||||
\(347\) | 4.39104 | + | 4.39104i | 0.235723 | + | 0.235723i | 0.815077 | − | 0.579353i | \(-0.196695\pi\) |
−0.579353 | + | 0.815077i | \(0.696695\pi\) | |||||||
\(348\) | 17.1061 | + | 2.93494i | 0.916982 | + | 0.157329i | ||||
\(349\) | 15.3708i | 0.822782i | 0.911459 | + | 0.411391i | \(0.134957\pi\) | ||||
−0.911459 | + | 0.411391i | \(0.865043\pi\) | |||||||
\(350\) | −10.8634 | + | 22.9904i | −0.580675 | + | 1.22889i | ||||
\(351\) | −5.10472 | + | 1.44383i | −0.272470 | + | 0.0770661i | ||||
\(352\) | 1.18183 | − | 1.18183i | 0.0629915 | − | 0.0629915i | ||||
\(353\) | −3.94944 | + | 3.94944i | −0.210207 | + | 0.210207i | −0.804356 | − | 0.594148i | \(-0.797489\pi\) |
0.594148 | + | 0.804356i | \(0.297489\pi\) | |||||||
\(354\) | −4.25491 | + | 3.00868i | −0.226146 | + | 0.159909i | ||||
\(355\) | −2.50889 | + | 1.58938i | −0.133158 | + | 0.0843555i | ||||
\(356\) | 3.30770i | 0.175308i | ||||||||
\(357\) | −10.6687 | + | 62.1816i | −0.564647 | + | 3.29100i | ||||
\(358\) | −11.7269 | − | 11.7269i | −0.619784 | − | 0.619784i | ||||
\(359\) | 7.94361 | 0.419248 | 0.209624 | − | 0.977782i | \(-0.432776\pi\) | ||||
0.209624 | + | 0.977782i | \(0.432776\pi\) | |||||||
\(360\) | 5.68161 | + | 3.56642i | 0.299447 | + | 0.187967i | ||||
\(361\) | −34.7026 | −1.82645 | ||||||||
\(362\) | 1.32378 | + | 1.32378i | 0.0695763 | + | 0.0695763i | ||||
\(363\) | −2.40365 | + | 14.0095i | −0.126159 | + | 0.735308i | ||||
\(364\) | − | 5.19208i | − | 0.272139i | ||||||
\(365\) | 0.294160 | − | 1.31107i | 0.0153971 | − | 0.0686247i | ||||
\(366\) | −13.9118 | + | 9.83710i | −0.727180 | + | 0.514194i | ||||
\(367\) | −1.04145 | + | 1.04145i | −0.0543632 | + | 0.0543632i | −0.733766 | − | 0.679403i | \(-0.762239\pi\) |
0.679403 | + | 0.733766i | \(0.262239\pi\) | |||||||
\(368\) | −3.01025 | + | 3.01025i | −0.156920 | + | 0.156920i | ||||
\(369\) | −10.6359 | + | 30.0829i | −0.553683 | + | 1.56605i | ||||
\(370\) | −3.38459 | − | 5.34271i | −0.175957 | − | 0.277754i | ||||
\(371\) | − | 1.37010i | − | 0.0711318i | ||||||
\(372\) | −1.70711 | − | 0.292893i | −0.0885094 | − | 0.0151858i | ||||
\(373\) | −4.50403 | − | 4.50403i | −0.233210 | − | 0.233210i | 0.580821 | − | 0.814031i | \(-0.302731\pi\) |
−0.814031 | + | 0.580821i | \(0.802731\pi\) | |||||||
\(374\) | −11.9710 | −0.619006 | ||||||||
\(375\) | 0.903121 | − | 19.3438i | 0.0466370 | − | 0.998912i | ||||
\(376\) | −2.63591 | −0.135937 | ||||||||
\(377\) | 7.23397 | + | 7.23397i | 0.372568 | + | 0.372568i | ||||
\(378\) | 12.8946 | − | 23.0658i | 0.663228 | − | 1.18637i | ||||
\(379\) | − | 25.4703i | − | 1.30832i | −0.756355 | − | 0.654162i | \(-0.773022\pi\) | ||
0.756355 | − | 0.654162i | \(-0.226978\pi\) | |||||||
\(380\) | −8.76919 | − | 13.8425i | −0.449850 | − | 0.710105i | ||||
\(381\) | −13.4546 | − | 19.0277i | −0.689300 | − | 0.974818i | ||||
\(382\) | 12.3340 | − | 12.3340i | 0.631064 | − | 0.631064i | ||||
\(383\) | −2.60896 | + | 2.60896i | −0.133312 | + | 0.133312i | −0.770614 | − | 0.637302i | \(-0.780050\pi\) |
0.637302 | + | 0.770614i | \(0.280050\pi\) | |||||||
\(384\) | 1.00000 | + | 1.41421i | 0.0510310 | + | 0.0721688i | ||||
\(385\) | −4.16088 | + | 18.5450i | −0.212058 | + | 0.945143i | ||||
\(386\) | − | 2.69007i | − | 0.136921i | ||||||
\(387\) | 9.66934 | + | 20.2460i | 0.491520 | + | 1.02916i | ||||
\(388\) | 5.96456 | + | 5.96456i | 0.302805 | + | 0.302805i | ||||
\(389\) | 7.76113 | 0.393505 | 0.196753 | − | 0.980453i | \(-0.436960\pi\) | ||||
0.196753 | + | 0.980453i | \(0.436960\pi\) | |||||||
\(390\) | 1.52072 | + | 3.64997i | 0.0770049 | + | 0.184823i | ||||
\(391\) | 30.4916 | 1.54203 | ||||||||
\(392\) | 13.3382 | + | 13.3382i | 0.673678 | + | 0.673678i | ||||
\(393\) | 7.64279 | + | 1.31130i | 0.385528 | + | 0.0661461i | ||||
\(394\) | 3.81510i | 0.192202i | ||||||||
\(395\) | −2.64279 | + | 1.67420i | −0.132973 | + | 0.0842384i | ||||
\(396\) | 4.72730 | + | 1.67135i | 0.237556 | + | 0.0839887i | ||||
\(397\) | 6.71705 | − | 6.71705i | 0.337119 | − | 0.337119i | −0.518163 | − | 0.855282i | \(-0.673384\pi\) |
0.855282 | + | 0.518163i | \(0.173384\pi\) | |||||||
\(398\) | −17.1012 | + | 17.1012i | −0.857206 | + | 0.857206i | ||||
\(399\) | −52.7050 | + | 37.2681i | −2.63855 | + | 1.86574i | ||||
\(400\) | 2.13613 | − | 4.52072i | 0.106806 | − | 0.226036i | ||||
\(401\) | − | 34.9927i | − | 1.74745i | −0.486419 | − | 0.873725i | \(-0.661697\pi\) | ||
0.486419 | − | 0.873725i | \(-0.338303\pi\) | |||||||
\(402\) | −0.568436 | + | 3.31309i | −0.0283510 | + | 0.165242i | ||||
\(403\) | −0.721916 | − | 0.721916i | −0.0359612 | − | 0.0359612i | ||||
\(404\) | 9.46972 | 0.471136 | ||||||||
\(405\) | −2.30897 | + | 19.9917i | −0.114734 | + | 0.993396i | ||||
\(406\) | −50.9600 | −2.52910 | ||||||||
\(407\) | −3.34271 | − | 3.34271i | −0.165692 | − | 0.165692i | ||||
\(408\) | 2.09784 | − | 12.2271i | 0.103858 | − | 0.605331i | ||||
\(409\) | − | 32.7857i | − | 1.62115i | −0.585637 | − | 0.810573i | \(-0.699156\pi\) | ||
0.585637 | − | 0.810573i | \(-0.300844\pi\) | |||||||
\(410\) | 23.2057 | + | 5.20658i | 1.14605 | + | 0.257135i | ||||
\(411\) | 8.59718 | − | 6.07912i | 0.424068 | − | 0.299861i | ||||
\(412\) | −1.93494 | + | 1.93494i | −0.0953276 | + | 0.0953276i | ||||
\(413\) | 10.8193 | − | 10.8193i | 0.532384 | − | 0.532384i | ||||
\(414\) | −12.0410 | − | 4.25714i | −0.591783 | − | 0.209227i | ||||
\(415\) | −22.7409 | − | 5.10230i | −1.11631 | − | 0.250462i | ||||
\(416\) | 1.02094i | 0.0500559i | ||||||||
\(417\) | 13.9699 | + | 2.39686i | 0.684111 | + | 0.117375i | ||||
\(418\) | −8.66066 | − | 8.66066i | −0.423607 | − | 0.423607i | ||||
\(419\) | −7.13118 | −0.348381 | −0.174191 | − | 0.984712i | \(-0.555731\pi\) | ||||
−0.174191 | + | 0.984712i | \(0.555731\pi\) | |||||||
\(420\) | −18.2126 | − | 7.49978i | −0.888683 | − | 0.365952i | ||||
\(421\) | −4.65642 | −0.226940 | −0.113470 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113470 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(422\) | −10.3244 | − | 10.3244i | −0.502584 | − | 0.502584i | ||||
\(423\) | −3.40795 | − | 7.13569i | −0.165700 | − | 0.346949i | ||||
\(424\) | 0.269409i | 0.0130836i | ||||||||
\(425\) | −33.7145 | + | 12.0771i | −1.63539 | + | 0.585824i | ||||
\(426\) | −1.32821 | − | 1.87837i | −0.0643519 | − | 0.0910073i | ||||
\(427\) | 35.3746 | − | 35.3746i | 1.71190 | − | 1.71190i | ||||
\(428\) | −0.0543708 | + | 0.0543708i | −0.00262811 | + | 0.00262811i | ||||
\(429\) | 1.70636 | + | 2.41315i | 0.0823837 | + | 0.116508i | ||||
\(430\) | 14.1270 | − | 8.94944i | 0.681265 | − | 0.431580i | ||||
\(431\) | 20.2121i | 0.973585i | 0.873518 | + | 0.486792i | \(0.161833\pi\) | ||||
−0.873518 | + | 0.486792i | \(0.838167\pi\) | |||||||
\(432\) | −2.53553 | + | 4.53553i | −0.121991 | + | 0.218216i | ||||
\(433\) | −23.9174 | − | 23.9174i | −1.14940 | − | 1.14940i | −0.986672 | − | 0.162723i | \(-0.947972\pi\) |
−0.162723 | − | 0.986672i | \(-0.552028\pi\) | |||||||
\(434\) | 5.08557 | 0.244115 | ||||||||
\(435\) | 35.8243 | − | 14.9258i | 1.71764 | − | 0.715638i | ||||
\(436\) | 6.07974 | 0.291167 | ||||||||
\(437\) | 22.0598 | + | 22.0598i | 1.05526 | + | 1.05526i | ||||
\(438\) | 1.02581 | + | 0.176001i | 0.0490151 | + | 0.00840967i | ||||
\(439\) | 12.5477i | 0.598868i | 0.954117 | + | 0.299434i | \(0.0967978\pi\) | ||||
−0.954117 | + | 0.299434i | \(0.903202\pi\) | |||||||
\(440\) | 0.818175 | − | 3.64660i | 0.0390049 | − | 0.173845i | ||||
\(441\) | −18.8630 | + | 53.3526i | −0.898238 | + | 2.54060i | ||||
\(442\) | 5.17070 | − | 5.17070i | 0.245945 | − | 0.245945i | ||||
\(443\) | 14.0922 | − | 14.0922i | 0.669542 | − | 0.669542i | −0.288068 | − | 0.957610i | \(-0.593013\pi\) |
0.957610 | + | 0.288068i | \(0.0930129\pi\) | |||||||
\(444\) | 4.00000 | − | 2.82843i | 0.189832 | − | 0.134231i | ||||
\(445\) | 3.95811 | + | 6.24803i | 0.187633 | + | 0.296185i | ||||
\(446\) | 17.3459i | 0.821350i | ||||||||
\(447\) | −4.67652 | + | 27.2568i | −0.221192 | + | 1.28920i | ||||
\(448\) | −3.59604 | − | 3.59604i | −0.169897 | − | 0.169897i | ||||
\(449\) | −10.0174 | −0.472748 | −0.236374 | − | 0.971662i | \(-0.575959\pi\) | ||||
−0.236374 | + | 0.971662i | \(0.575959\pi\) | |||||||
\(450\) | 14.9999 | − | 0.0620825i | 0.707101 | − | 0.00292660i | ||||
\(451\) | 17.7764 | 0.837056 | ||||||||
\(452\) | −2.23239 | − | 2.23239i | −0.105003 | − | 0.105003i | ||||
\(453\) | −3.01691 | + | 17.5839i | −0.141747 | + | 0.826161i | ||||
\(454\) | 7.04833i | 0.330795i | ||||||||
\(455\) | −6.21302 | − | 9.80748i | −0.291271 | − | 0.459782i | ||||
\(456\) | 10.3637 | − | 7.32821i | 0.485322 | − | 0.343175i | ||||
\(457\) | −21.2949 | + | 21.2949i | −0.996132 | + | 0.996132i | −0.999993 | − | 0.00386099i | \(-0.998771\pi\) |
0.00386099 | + | 0.999993i | \(0.498771\pi\) | |||||||
\(458\) | 8.76761 | − | 8.76761i | 0.409684 | − | 0.409684i | ||||
\(459\) | 35.8123 | − | 10.1292i | 1.67157 | − | 0.472793i | ||||
\(460\) | −2.08399 | + | 9.28834i | −0.0971665 | + | 0.433071i | ||||
\(461\) | 24.5134i | 1.14170i | 0.821053 | + | 0.570851i | \(0.193387\pi\) | ||||
−0.821053 | + | 0.570851i | \(0.806613\pi\) | |||||||
\(462\) | −14.5100 | − | 2.48953i | −0.675068 | − | 0.115823i | ||||
\(463\) | 8.63306 | + | 8.63306i | 0.401212 | + | 0.401212i | 0.878660 | − | 0.477448i | \(-0.158438\pi\) |
−0.477448 | + | 0.878660i | \(0.658438\pi\) | |||||||
\(464\) | 10.0205 | 0.465190 | ||||||||
\(465\) | −3.57510 | + | 1.48953i | −0.165791 | + | 0.0690752i | ||||
\(466\) | 27.3563 | 1.26726 | ||||||||
\(467\) | −21.3541 | − | 21.3541i | −0.988150 | − | 0.988150i | 0.0117808 | − | 0.999931i | \(-0.496250\pi\) |
−0.999931 | + | 0.0117808i | \(0.996250\pi\) | |||||||
\(468\) | −2.76380 | + | 1.31997i | −0.127757 | + | 0.0610157i | ||||
\(469\) | − | 9.86988i | − | 0.455749i | ||||||
\(470\) | −4.97906 | + | 3.15422i | −0.229667 | + | 0.145493i | ||||
\(471\) | 6.48243 | + | 9.16754i | 0.298695 | + | 0.422418i | ||||
\(472\) | −2.12745 | + | 2.12745i | −0.0979240 | + | 0.0979240i | ||||
\(473\) | 8.83868 | − | 8.83868i | 0.406403 | − | 0.406403i | ||||
\(474\) | −1.39909 | − | 1.97862i | −0.0642625 | − | 0.0908809i | ||||
\(475\) | −33.1288 | − | 15.6540i | −1.52005 | − | 0.718255i | ||||
\(476\) | 36.4252i | 1.66954i | ||||||||
\(477\) | −0.729318 | + | 0.348317i | −0.0333932 | + | 0.0159483i | ||||
\(478\) | 6.27003 | + | 6.27003i | 0.286784 | + | 0.286784i | ||||
\(479\) | −7.69589 | −0.351634 | −0.175817 | − | 0.984423i | \(-0.556257\pi\) | ||||
−0.175817 | + | 0.984423i | \(0.556257\pi\) | |||||||
\(480\) | 3.58123 | + | 1.47472i | 0.163460 | + | 0.0673114i | ||||
\(481\) | 2.88767 | 0.131666 | ||||||||
\(482\) | −4.93494 | − | 4.93494i | −0.224780 | − | 0.224780i | ||||
\(483\) | 36.9588 | + | 6.34113i | 1.68168 | + | 0.288531i | ||||
\(484\) | 8.20658i | 0.373026i | ||||||||
\(485\) | 18.4040 | + | 4.12925i | 0.835684 | + | 0.187499i | ||||
\(486\) | −15.5563 | − | 1.00000i | −0.705650 | − | 0.0453609i | ||||
\(487\) | −10.0281 | + | 10.0281i | −0.454418 | + | 0.454418i | −0.896818 | − | 0.442400i | \(-0.854127\pi\) |
0.442400 | + | 0.896818i | \(0.354127\pi\) | |||||||
\(488\) | −6.95588 | + | 6.95588i | −0.314878 | + | 0.314878i | ||||
\(489\) | −6.17113 | + | 4.36365i | −0.279068 | + | 0.197331i | ||||
\(490\) | 41.1558 | + | 9.23397i | 1.85923 | + | 0.417148i | ||||
\(491\) | − | 12.1695i | − | 0.549203i | −0.961558 | − | 0.274601i | \(-0.911454\pi\) | ||
0.961558 | − | 0.274601i | \(-0.0885459\pi\) | |||||||
\(492\) | −3.11519 | + | 18.1566i | −0.140443 | + | 0.818564i | ||||
\(493\) | −50.7501 | − | 50.7501i | −2.28567 | − | 2.28567i | ||||
\(494\) | 7.48169 | 0.336617 | ||||||||
\(495\) | 10.9296 | − | 2.49978i | 0.491247 | − | 0.112357i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | 4.77629 | + | 4.77629i | 0.214246 | + | 0.214246i | ||||
\(498\) | 3.05279 | − | 17.7930i | 0.136799 | − | 0.797323i | ||||
\(499\) | 29.7110i | 1.33005i | 0.746822 | + | 0.665024i | \(0.231579\pi\) | ||||
−0.746822 | + | 0.665024i | \(0.768421\pi\) | |||||||
\(500\) | −1.37465 | − | 11.0955i | −0.0614763 | − | 0.496206i | ||||
\(501\) | 21.6355 | − | 15.2986i | 0.966602 | − | 0.683491i | ||||
\(502\) | −12.0874 | + | 12.0874i | −0.539485 | + | 0.539485i | ||||
\(503\) | −2.82154 | + | 2.82154i | −0.125806 | + | 0.125806i | −0.767207 | − | 0.641400i | \(-0.778354\pi\) |
0.641400 | + | 0.767207i | \(0.278354\pi\) | |||||||
\(504\) | 5.08557 | − | 14.3842i | 0.226529 | − | 0.640721i | ||||
\(505\) | 17.8877 | − | 11.3318i | 0.795991 | − | 0.504259i | ||||
\(506\) | 7.11519i | 0.316309i | ||||||||
\(507\) | 20.4130 | + | 3.50232i | 0.906574 | + | 0.155544i | ||||
\(508\) | −9.51384 | − | 9.51384i | −0.422108 | − | 0.422108i | ||||
\(509\) | 10.2585 | 0.454700 | 0.227350 | − | 0.973813i | \(-0.426994\pi\) | ||||
0.227350 | + | 0.973813i | \(0.426994\pi\) | |||||||
\(510\) | −10.6687 | − | 25.6065i | −0.472417 | − | 1.13387i | ||||
\(511\) | −3.05595 | −0.135187 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 33.2373 | + | 18.5809i | 1.46746 | + | 0.820368i | ||||
\(514\) | − | 24.4687i | − | 1.07927i | ||||||
\(515\) | −1.33955 | + | 5.97038i | −0.0590277 | + | 0.263086i | ||||
\(516\) | 7.47884 | + | 10.5767i | 0.329237 | + | 0.465612i | ||||
\(517\) | −3.11519 | + | 3.11519i | −0.137006 | + | 0.137006i | ||||
\(518\) | −10.1711 | + | 10.1711i | −0.446894 | + | 0.446894i | ||||
\(519\) | −9.12522 | − | 12.9050i | −0.400553 | − | 0.566467i | ||||
\(520\) | 1.22170 | + | 1.92849i | 0.0535750 | + | 0.0845700i | ||||
\(521\) | − | 17.6881i | − | 0.774931i | −0.921884 | − | 0.387466i | \(-0.873351\pi\) | ||
0.921884 | − | 0.387466i | \(-0.126649\pi\) | |||||||
\(522\) | 12.9554 | + | 27.1266i | 0.567044 | + | 1.18730i | ||||
\(523\) | 8.57689 | + | 8.57689i | 0.375041 | + | 0.375041i | 0.869309 | − | 0.494268i | \(-0.164564\pi\) |
−0.494268 | + | 0.869309i | \(0.664564\pi\) | |||||||
\(524\) | 4.47704 | 0.195581 | ||||||||
\(525\) | −43.3768 | + | 7.62724i | −1.89312 | + | 0.332880i | ||||
\(526\) | 1.73598 | 0.0756922 | ||||||||
\(527\) | 5.06462 | + | 5.06462i | 0.220618 | + | 0.220618i | ||||
\(528\) | 2.85318 | + | 0.489528i | 0.124169 | + | 0.0213040i | ||||
\(529\) | 4.87676i | 0.212033i | ||||||||
\(530\) | 0.322384 | + | 0.508895i | 0.0140035 | + | 0.0221050i | ||||
\(531\) | −8.50982 | − | 3.00868i | −0.369295 | − | 0.130565i | ||||
\(532\) | −26.3525 | + | 26.3525i | −1.14253 | + | 1.14253i | ||||
\(533\) | −7.67824 | + | 7.67824i | −0.332581 | + | 0.332581i | ||||
\(534\) | −4.67780 | + | 3.30770i | −0.202428 | + | 0.143138i | ||||
\(535\) | −0.0376408 | + | 0.167765i | −0.00162735 | + | 0.00725310i | ||||
\(536\) | 1.94076i | 0.0838282i | ||||||||
\(537\) | 4.85743 | − | 28.3112i | 0.209613 | − | 1.22172i | ||||
\(538\) | −0.200753 | − | 0.200753i | −0.00865508 | − | 0.00865508i | ||||
\(539\) | 31.5267 | 1.35795 | ||||||||
\(540\) | 0.637927 | + | 11.6014i | 0.0274520 | + | 0.499246i | ||||
\(541\) | −32.1779 | −1.38343 | −0.691717 | − | 0.722168i | \(-0.743146\pi\) | ||||
−0.691717 | + | 0.722168i | \(0.743146\pi\) | |||||||
\(542\) | 14.8979 | + | 14.8979i | 0.639920 | + | 0.639920i | ||||
\(543\) | −0.548327 | + | 3.19589i | −0.0235310 | + | 0.137149i | ||||
\(544\) | − | 7.16246i | − | 0.307088i | ||||||
\(545\) | 11.4842 | − | 7.27523i | 0.491930 | − | 0.311637i | ||||
\(546\) | 7.34271 | − | 5.19208i | 0.314239 | − | 0.222200i | ||||
\(547\) | −12.5918 | + | 12.5918i | −0.538386 | + | 0.538386i | −0.923055 | − | 0.384669i | \(-0.874316\pi\) |
0.384669 | + | 0.923055i | \(0.374316\pi\) | |||||||
\(548\) | 4.29859 | − | 4.29859i | 0.183627 | − | 0.183627i | ||||
\(549\) | −27.8235 | − | 9.83710i | −1.18748 | − | 0.419837i | ||||
\(550\) | −2.81817 | − | 7.86724i | −0.120167 | − | 0.335460i | ||||
\(551\) | − | 73.4323i | − | 3.12832i | ||||||
\(552\) | −7.26739 | − | 1.24689i | −0.309321 | − | 0.0530711i | ||||
\(553\) | 5.03120 | + | 5.03120i | 0.213948 | + | 0.213948i | ||||
\(554\) | −16.0486 | −0.681841 | ||||||||
\(555\) | 4.17113 | − | 10.1292i | 0.177055 | − | 0.429963i | ||||
\(556\) | 8.18340 | 0.347054 | ||||||||
\(557\) | −12.0399 | − | 12.0399i | −0.510146 | − | 0.510146i | 0.404425 | − | 0.914571i | \(-0.367472\pi\) |
−0.914571 | + | 0.404425i | \(0.867472\pi\) | |||||||
\(558\) | −1.29289 | − | 2.70711i | −0.0547325 | − | 0.114601i | ||||
\(559\) | 7.63547i | 0.322946i | ||||||||
\(560\) | −11.0958 | − | 2.48953i | −0.468884 | − | 0.105202i | ||||
\(561\) | −11.9710 | − | 16.9296i | −0.505416 | − | 0.714766i | ||||
\(562\) | 12.1119 | − | 12.1119i | 0.510910 | − | 0.510910i | ||||
\(563\) | −21.5053 | + | 21.5053i | −0.906342 | + | 0.906342i | −0.995975 | − | 0.0896326i | \(-0.971431\pi\) |
0.0896326 | + | 0.995975i | \(0.471431\pi\) | |||||||
\(564\) | −2.63591 | − | 3.72774i | −0.110992 | − | 0.156966i | ||||
\(565\) | −6.88818 | − | 1.54548i | −0.289788 | − | 0.0650187i | ||||
\(566\) | 27.6774i | 1.16337i | ||||||||
\(567\) | 45.5145 | − | 4.83000i | 1.91143 | − | 0.202841i | ||||
\(568\) | −0.939185 | − | 0.939185i | −0.0394073 | − | 0.0394073i | ||||
\(569\) | 1.35317 | 0.0567280 | 0.0283640 | − | 0.999598i | \(-0.490970\pi\) | ||||
0.0283640 | + | 0.999598i | \(0.490970\pi\) | |||||||
\(570\) | 10.8070 | − | 26.2440i | 0.452657 | − | 1.09924i | ||||
\(571\) | −15.6166 | −0.653535 | −0.326768 | − | 0.945105i | \(-0.605959\pi\) | ||||
−0.326768 | + | 0.945105i | \(0.605959\pi\) | |||||||
\(572\) | 1.20658 | + | 1.20658i | 0.0504495 | + | 0.0504495i | ||||
\(573\) | 29.7770 | + | 5.10892i | 1.24395 | + | 0.213428i | ||||
\(574\) | − | 54.0896i | − | 2.25766i | ||||||
\(575\) | 7.17823 | + | 20.0388i | 0.299353 | + | 0.835676i | ||||
\(576\) | −1.00000 | + | 2.82843i | −0.0416667 | + | 0.117851i | ||||
\(577\) | −27.1671 | + | 27.1671i | −1.13098 | + | 1.13098i | −0.140967 | + | 0.990014i | \(0.545021\pi\) |
−0.990014 | + | 0.140967i | \(0.954979\pi\) | |||||||
\(578\) | −24.2543 | + | 24.2543i | −1.00885 | + | 1.00885i | ||||
\(579\) | 3.80433 | − | 2.69007i | 0.158103 | − | 0.111795i | ||||
\(580\) | 18.9281 | − | 11.9909i | 0.785945 | − | 0.497894i | ||||
\(581\) | 53.0063i | 2.19907i | ||||||||
\(582\) | −2.47060 | + | 14.3997i | −0.102410 | + | 0.596887i | ||||
\(583\) | 0.318394 | + | 0.318394i | 0.0131865 | + | 0.0131865i | ||||
\(584\) | 0.600906 | 0.0248657 | ||||||||
\(585\) | −3.64111 | + | 5.80060i | −0.150542 | + | 0.239825i | ||||
\(586\) | 10.3560 | 0.427804 | ||||||||
\(587\) | 31.6919 | + | 31.6919i | 1.30806 | + | 1.30806i | 0.922812 | + | 0.385251i | \(0.125885\pi\) |
0.385251 | + | 0.922812i | \(0.374115\pi\) | |||||||
\(588\) | −5.52484 | + | 32.2011i | −0.227841 | + | 1.32795i | ||||
\(589\) | 7.32821i | 0.301954i | ||||||||
\(590\) | −1.47283 | + | 6.56440i | −0.0606355 | + | 0.270252i | ||||
\(591\) | −5.39537 | + | 3.81510i | −0.221936 | + | 0.156932i | ||||
\(592\) | 2.00000 | − | 2.00000i | 0.0821995 | − | 0.0821995i | ||||
\(593\) | −3.01841 | + | 3.01841i | −0.123951 | + | 0.123951i | −0.766361 | − | 0.642410i | \(-0.777935\pi\) |
0.642410 | + | 0.766361i | \(0.277935\pi\) | |||||||
\(594\) | 2.36365 | + | 8.35677i | 0.0969818 | + | 0.342882i | ||||
\(595\) | 43.5876 | + | 68.8047i | 1.78692 | + | 2.82072i | ||||
\(596\) | 15.9667i | 0.654020i | ||||||||
\(597\) | −41.2860 | − | 7.08355i | −1.68972 | − | 0.289910i | ||||
\(598\) | −3.07330 | − | 3.07330i | −0.125677 | − | 0.125677i | ||||
\(599\) | −45.0422 | −1.84037 | −0.920187 | − | 0.391479i | \(-0.871963\pi\) | ||||
−0.920187 | + | 0.391479i | \(0.871963\pi\) | |||||||
\(600\) | 8.52940 | − | 1.49978i | 0.348211 | − | 0.0612283i | ||||
\(601\) | −19.9056 | −0.811967 | −0.405983 | − | 0.913880i | \(-0.633071\pi\) | ||||
−0.405983 | + | 0.913880i | \(0.633071\pi\) | |||||||
\(602\) | −26.8942 | − | 26.8942i | −1.09613 | − | 1.09613i | ||||
\(603\) | −5.25385 | + | 2.50920i | −0.213953 | + | 0.102182i | ||||
\(604\) | 10.3004i | 0.419117i | ||||||||
\(605\) | 9.82028 | + | 15.5017i | 0.399251 | + | 0.630232i | ||||
\(606\) | 9.46972 | + | 13.3922i | 0.384681 | + | 0.544021i | ||||
\(607\) | −32.7744 | + | 32.7744i | −1.33027 | + | 1.33027i | −0.425144 | + | 0.905126i | \(0.639777\pi\) |
−0.905126 | + | 0.425144i | \(0.860223\pi\) | |||||||
\(608\) | 5.18183 | − | 5.18183i | 0.210151 | − | 0.210151i | ||||
\(609\) | −50.9600 | − | 72.0683i | −2.06500 | − | 2.92035i | ||||
\(610\) | −4.81554 | + | 21.4628i | −0.194975 | + | 0.869005i | ||||
\(611\) | − | 2.69112i | − | 0.108871i | ||||||
\(612\) | 19.3895 | − | 9.26029i | 0.783776 | − | 0.374325i | ||||
\(613\) | 6.91802 | + | 6.91802i | 0.279416 | + | 0.279416i | 0.832876 | − | 0.553460i | \(-0.186693\pi\) |
−0.553460 | + | 0.832876i | \(0.686693\pi\) | |||||||
\(614\) | 26.4961 | 1.06929 | ||||||||
\(615\) | 15.8425 | + | 38.0244i | 0.638831 | + | 1.53329i | ||||
\(616\) | −8.49978 | −0.342466 | ||||||||
\(617\) | 24.9415 | + | 24.9415i | 1.00411 | + | 1.00411i | 0.999992 | + | 0.00411392i | \(0.00130951\pi\) |
0.00411392 | + | 0.999992i | \(0.498690\pi\) | |||||||
\(618\) | −4.67135 | − | 0.801478i | −0.187909 | − | 0.0322402i | ||||
\(619\) | − | 25.7810i | − | 1.03623i | −0.855312 | − | 0.518113i | \(-0.826635\pi\) | ||
0.855312 | − | 0.518113i | \(-0.173365\pi\) | |||||||
\(620\) | −1.88893 | + | 1.19663i | −0.0758613 | + | 0.0480580i | ||||
\(621\) | −6.02051 | − | 21.2857i | −0.241595 | − | 0.854166i | ||||
\(622\) | −2.27479 | + | 2.27479i | −0.0912109 | + | 0.0912109i | ||||
\(623\) | 11.8946 | − | 11.8946i | 0.476548 | − | 0.476548i | ||||
\(624\) | −1.44383 | + | 1.02094i | −0.0577996 | + | 0.0408705i | ||||
\(625\) | −15.8739 | − | 19.3137i | −0.634956 | − | 0.772548i | ||||
\(626\) | − | 16.1819i | − | 0.646759i | ||||||
\(627\) | 3.58736 | − | 20.9087i | 0.143266 | − | 0.835013i | ||||
\(628\) | 4.58377 | + | 4.58377i | 0.182912 | + | 0.182912i | ||||
\(629\) | −20.2585 | −0.807759 | ||||||||
\(630\) | −7.60629 | − | 33.2563i | −0.303042 | − | 1.32496i | ||||
\(631\) | 3.45745 | 0.137639 | 0.0688195 | − | 0.997629i | \(-0.478077\pi\) | ||||
0.0688195 | + | 0.997629i | \(0.478077\pi\) | |||||||
\(632\) | −0.989309 | − | 0.989309i | −0.0393526 | − | 0.0393526i | ||||
\(633\) | 4.27651 | − | 24.9253i | 0.169976 | − | 0.990692i | ||||
\(634\) | 8.40466i | 0.333792i | ||||||||
\(635\) | −29.3556 | − | 6.58641i | −1.16494 | − | 0.261374i | ||||
\(636\) | −0.381001 | + | 0.269409i | −0.0151077 | + | 0.0106827i | ||||
\(637\) | −13.6175 | + | 13.6175i | −0.539545 | + | 0.539545i | ||||
\(638\) | 11.8425 | − | 11.8425i | 0.468849 | − | 0.468849i | ||||
\(639\) | 1.32821 | − | 3.75674i | 0.0525431 | − | 0.148614i | ||||
\(640\) | 2.18183 | + | 0.489528i | 0.0862442 | + | 0.0193503i | ||||
\(641\) | 31.1123i | 1.22886i | 0.788970 | + | 0.614432i | \(0.210615\pi\) | ||||
−0.788970 | + | 0.614432i | \(0.789385\pi\) | |||||||
\(642\) | −0.131263 | − | 0.0225211i | −0.00518053 | − | 0.000888838i | ||||
\(643\) | −6.93380 | − | 6.93380i | −0.273442 | − | 0.273442i | 0.557042 | − | 0.830484i | \(-0.311936\pi\) |
−0.830484 | + | 0.557042i | \(0.811936\pi\) | |||||||
\(644\) | 21.6500 | 0.853128 | ||||||||
\(645\) | 26.7834 | + | 11.0292i | 1.05460 | + | 0.434274i | ||||
\(646\) | −52.4880 | −2.06511 | ||||||||
\(647\) | −16.5241 | − | 16.5241i | −0.649629 | − | 0.649629i | 0.303274 | − | 0.952903i | \(-0.401920\pi\) |
−0.952903 | + | 0.303274i | \(0.901920\pi\) | |||||||
\(648\) | −8.94975 | + | 0.949747i | −0.351579 | + | 0.0373096i | ||||
\(649\) | 5.02856i | 0.197388i | ||||||||
\(650\) | 4.61541 | + | 2.18087i | 0.181031 | + | 0.0855407i | ||||
\(651\) | 5.08557 | + | 7.19208i | 0.199319 | + | 0.281880i | ||||
\(652\) | −3.08557 | + | 3.08557i | −0.120840 | + | 0.120840i | ||||
\(653\) | 0.623022 | − | 0.623022i | 0.0243807 | − | 0.0243807i | −0.694811 | − | 0.719192i | \(-0.744512\pi\) |
0.719192 | + | 0.694811i | \(0.244512\pi\) | |||||||
\(654\) | 6.07974 | + | 8.59806i | 0.237737 | + | 0.336211i | ||||
\(655\) | 8.45683 | − | 5.35739i | 0.330436 | − | 0.209330i | ||||
\(656\) | 10.6359i | 0.415263i | ||||||||
\(657\) | 0.776907 | + | 1.62672i | 0.0303100 | + | 0.0634643i | ||||
\(658\) | 9.47884 | + | 9.47884i | 0.369524 | + | 0.369524i | ||||
\(659\) | −3.37145 | −0.131333 | −0.0656665 | − | 0.997842i | \(-0.520917\pi\) | ||||
−0.0656665 | + | 0.997842i | \(0.520917\pi\) | |||||||
\(660\) | 5.97525 | − | 2.48953i | 0.232586 | − | 0.0969048i | ||||
\(661\) | −2.09797 | −0.0816016 | −0.0408008 | − | 0.999167i | \(-0.512991\pi\) | ||||
−0.0408008 | + | 0.999167i | \(0.512991\pi\) | |||||||
\(662\) | −8.15707 | − | 8.15707i | −0.317034 | − | 0.317034i | ||||
\(663\) | 12.4832 | + | 2.14177i | 0.484806 | + | 0.0831795i | ||||
\(664\) | − | 10.4229i | − | 0.404487i | ||||||
\(665\) | −18.2438 | + | 81.3125i | −0.707463 | + | 3.15316i | ||||
\(666\) | 8.00000 | + | 2.82843i | 0.309994 | + | 0.109599i | ||||
\(667\) | −30.1643 | + | 30.1643i | −1.16796 | + | 1.16796i | ||||
\(668\) | 10.8177 | − | 10.8177i | 0.418551 | − | 0.418551i | ||||
\(669\) | −24.5308 | + | 17.3459i | −0.948414 | + | 0.670630i | ||||
\(670\) | 2.32238 | + | 3.66597i | 0.0897215 | + | 0.141629i | ||||
\(671\) | 16.4413i | 0.634708i | ||||||||
\(672\) | 1.48953 | − | 8.68161i | 0.0574598 | − | 0.334900i | ||||
\(673\) | 29.1402 | + | 29.1402i | 1.12327 | + | 1.12327i | 0.991246 | + | 0.132026i | \(0.0421482\pi\) |
0.132026 | + | 0.991246i | \(0.457852\pi\) | |||||||
\(674\) | 13.4430 | 0.517803 | ||||||||
\(675\) | 15.0877 | + | 21.1509i | 0.580725 | + | 0.814100i | ||||
\(676\) | 11.9577 | 0.459911 | ||||||||
\(677\) | −19.7632 | − | 19.7632i | −0.759560 | − | 0.759560i | 0.216683 | − | 0.976242i | \(-0.430476\pi\) |
−0.976242 | + | 0.216683i | \(0.930476\pi\) | |||||||
\(678\) | 0.924685 | − | 5.38946i | 0.0355123 | − | 0.206981i | ||||
\(679\) | − | 42.8976i | − | 1.64626i | ||||||
\(680\) | −8.57085 | − | 13.5294i | −0.328677 | − | 0.518829i | ||||
\(681\) | −9.96785 | + | 7.04833i | −0.381969 | + | 0.270093i | ||||
\(682\) | −1.18183 | + | 1.18183i | −0.0452544 | + | 0.0452544i | ||||
\(683\) | 21.1969 | − | 21.1969i | 0.811079 | − | 0.811079i | −0.173717 | − | 0.984796i | \(-0.555578\pi\) |
0.984796 | + | 0.173717i | \(0.0555778\pi\) | |||||||
\(684\) | 20.7273 | + | 7.32821i | 0.792528 | + | 0.280201i | ||||
\(685\) | 2.97590 | − | 13.2636i | 0.113703 | − | 0.506776i | ||||
\(686\) | − | 60.3300i | − | 2.30341i | ||||||
\(687\) | 21.1669 | + | 3.63166i | 0.807567 | + | 0.138557i | ||||
\(688\) | 5.28834 | + | 5.28834i | 0.201616 | + | 0.201616i | ||||
\(689\) | −0.275051 | −0.0104786 | ||||||||
\(690\) | −15.2197 | + | 6.34113i | −0.579403 | + | 0.241403i | ||||
\(691\) | −25.9726 | −0.988045 | −0.494022 | − | 0.869449i | \(-0.664474\pi\) | ||||
−0.494022 | + | 0.869449i | \(0.664474\pi\) | |||||||
\(692\) | −6.45251 | − | 6.45251i | −0.245288 | − | 0.245288i | ||||
\(693\) | −10.9893 | − | 23.0098i | −0.417449 | − | 0.874071i | ||||
\(694\) | 6.20987i | 0.235723i | ||||||||
\(695\) | 15.4579 | − | 9.79255i | 0.586351 | − | 0.371452i | ||||
\(696\) | 10.0205 | + | 14.1711i | 0.379826 | + | 0.537155i | ||||
\(697\) | 53.8669 | − | 53.8669i | 2.04035 | − | 2.04035i | ||||
\(698\) | −10.8688 | + | 10.8688i | −0.411391 | + | 0.411391i | ||||
\(699\) | 27.3563 | + | 38.6877i | 1.03471 | + | 1.46330i | ||||
\(700\) | −23.9383 | + | 8.57510i | −0.904783 | + | 0.324108i | ||||
\(701\) | − | 25.0090i | − | 0.944576i | −0.881444 | − | 0.472288i | \(-0.843428\pi\) | ||
0.881444 | − | 0.472288i | \(-0.156572\pi\) | |||||||
\(702\) | −4.63053 | − | 2.58864i | −0.174768 | − | 0.0977018i | ||||
\(703\) | −14.6564 | − | 14.6564i | −0.552777 | − | 0.552777i | ||||
\(704\) | 1.67135 | 0.0629915 | ||||||||
\(705\) | −9.43980 | − | 3.88723i | −0.355523 | − | 0.146401i | ||||
\(706\) | −5.58535 | −0.210207 | ||||||||
\(707\) | −34.0535 | − | 34.0535i | −1.28071 | − | 1.28071i | ||||
\(708\) | −5.13613 | − | 0.881221i | −0.193028 | − | 0.0331183i | ||||
\(709\) | 45.1020i | 1.69384i | 0.531718 | + | 0.846921i | \(0.321547\pi\) | ||||
−0.531718 | + | 0.846921i | \(0.678453\pi\) | |||||||
\(710\) | −2.89792 | − | 0.650195i | −0.108757 | − | 0.0244014i | ||||
\(711\) | 1.39909 | − | 3.95724i | 0.0524701 | − | 0.148408i | ||||
\(712\) | −2.33890 | + | 2.33890i | −0.0876539 | + | 0.0876539i | ||||
\(713\) | 3.01025 | − | 3.01025i | 0.112735 | − | 0.112735i | ||||
\(714\) | −51.5130 | + | 36.4252i | −1.92782 | + | 1.36318i | ||||
\(715\) | 3.72298 | + | 0.835310i | 0.139231 | + | 0.0312388i | ||||
\(716\) | − | 16.5843i | − | 0.619784i | ||||||
\(717\) | −2.59713 | + | 15.1372i | −0.0969916 | + | 0.565309i | ||||
\(718\) | 5.61698 | + | 5.61698i | 0.209624 | + | 0.209624i | ||||
\(719\) | −21.5174 | −0.802465 | −0.401232 | − | 0.915976i | \(-0.631418\pi\) | ||||
−0.401232 | + | 0.915976i | \(0.631418\pi\) | |||||||
\(720\) | 1.49566 | + | 6.53934i | 0.0557400 | + | 0.243707i | ||||
\(721\) | 13.9162 | 0.518267 | ||||||||
\(722\) | −24.5385 | − | 24.5385i | −0.913227 | − | 0.913227i | ||||
\(723\) | 2.04412 | − | 11.9140i | 0.0760216 | − | 0.443086i | ||||
\(724\) | 1.87211i | 0.0695763i | ||||||||
\(725\) | 21.4051 | − | 45.2999i | 0.794965 | − | 1.68240i | ||||
\(726\) | −11.6059 | + | 8.20658i | −0.430734 | + | 0.304575i | ||||
\(727\) | −20.7172 | + | 20.7172i | −0.768360 | + | 0.768360i | −0.977818 | − | 0.209458i | \(-0.932830\pi\) |
0.209458 | + | 0.977818i | \(0.432830\pi\) | |||||||
\(728\) | 3.67135 | − | 3.67135i | 0.136069 | − | 0.136069i | ||||
\(729\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(730\) | 1.13507 | − | 0.719065i | 0.0420109 | − | 0.0266138i | ||||
\(731\) | − | 53.5669i | − | 1.98124i | ||||||
\(732\) | −16.7930 | − | 2.88122i | −0.620687 | − | 0.106493i | ||||
\(733\) | −10.2304 | − | 10.2304i | −0.377867 | − | 0.377867i | 0.492465 | − | 0.870332i | \(-0.336096\pi\) |
−0.870332 | + | 0.492465i | \(0.836096\pi\) | |||||||
\(734\) | −1.47283 | −0.0543632 | ||||||||
\(735\) | 28.0970 | + | 67.4370i | 1.03637 | + | 2.48745i | ||||
\(736\) | −4.25714 | −0.156920 | ||||||||
\(737\) | 2.29364 | + | 2.29364i | 0.0844874 | + | 0.0844874i | ||||
\(738\) | −28.7925 | + | 13.7511i | −1.05987 | + | 0.506185i | ||||
\(739\) | − | 32.5957i | − | 1.19905i | −0.800355 | − | 0.599526i | \(-0.795356\pi\) | ||
0.800355 | − | 0.599526i | \(-0.204644\pi\) | |||||||
\(740\) | 1.38459 | − | 6.17113i | 0.0508987 | − | 0.226855i | ||||
\(741\) | 7.48169 | + | 10.5807i | 0.274847 | + | 0.388692i | ||||
\(742\) | 0.968804 | − | 0.968804i | 0.0355659 | − | 0.0355659i | ||||
\(743\) | −22.8596 | + | 22.8596i | −0.838638 | + | 0.838638i | −0.988680 | − | 0.150041i | \(-0.952059\pi\) |
0.150041 | + | 0.988680i | \(0.452059\pi\) | |||||||
\(744\) | −1.00000 | − | 1.41421i | −0.0366618 | − | 0.0518476i | ||||
\(745\) | 19.1063 | + | 30.1599i | 0.699999 | + | 1.10497i | ||||
\(746\) | − | 6.36966i | − | 0.233210i | ||||||
\(747\) | 28.2159 | − | 13.4757i | 1.03236 | − | 0.493049i | ||||
\(748\) | −8.46478 | − | 8.46478i | −0.309503 | − | 0.309503i | ||||
\(749\) | 0.391039 | 0.0142883 | ||||||||
\(750\) | 14.3168 | − | 13.0396i | 0.522774 | − | 0.476137i | ||||
\(751\) | 48.8210 | 1.78150 | 0.890751 | − | 0.454491i | \(-0.150179\pi\) | ||||
0.890751 | + | 0.454491i | \(0.150179\pi\) | |||||||
\(752\) | −1.86387 | − | 1.86387i | −0.0679684 | − | 0.0679684i | ||||
\(753\) | −29.1815 | − | 5.00675i | −1.06343 | − | 0.182456i | ||||
\(754\) | 10.2304i | 0.372568i | ||||||||
\(755\) | 12.3258 | + | 19.4567i | 0.448582 | + | 0.708103i | ||||
\(756\) | 25.4278 | − | 7.19208i | 0.924801 | − | 0.261573i | ||||
\(757\) | 10.4100 | − | 10.4100i | 0.378360 | − | 0.378360i | −0.492151 | − | 0.870510i | \(-0.663789\pi\) |
0.870510 | + | 0.492151i | \(0.163789\pi\) | |||||||
\(758\) | 18.0103 | − | 18.0103i | 0.654162 | − | 0.654162i | ||||
\(759\) | −10.0624 | + | 7.11519i | −0.365242 | + | 0.258265i | ||||
\(760\) | 3.58736 | − | 15.9889i | 0.130127 | − | 0.579977i | ||||
\(761\) | 13.4953i | 0.489205i | 0.969623 | + | 0.244602i | \(0.0786574\pi\) | ||||
−0.969623 | + | 0.244602i | \(0.921343\pi\) | |||||||
\(762\) | 3.94076 | − | 22.9684i | 0.142759 | − | 0.832059i | ||||
\(763\) | −21.8630 | − | 21.8630i | −0.791493 | − | 0.791493i | ||||
\(764\) | 17.4430 | 0.631064 | ||||||||
\(765\) | 25.5443 | − | 40.6943i | 0.923557 | − | 1.47130i | ||||
\(766\) | −3.68963 | −0.133312 | ||||||||
\(767\) | −2.17201 | − | 2.17201i | −0.0784268 | − | 0.0784268i | ||||
\(768\) | −0.292893 | + | 1.70711i | −0.0105689 | + | 0.0615999i | ||||
\(769\) | − | 37.0453i | − | 1.33589i | −0.744211 | − | 0.667945i | \(-0.767174\pi\) | ||
0.744211 | − | 0.667945i | \(-0.232826\pi\) | |||||||
\(770\) | −16.0555 | + | 10.1711i | −0.578600 | + | 0.366542i | ||||
\(771\) | 34.6039 | − | 24.4687i | 1.24623 | − | 0.881217i | ||||
\(772\) | 1.90216 | − | 1.90216i | 0.0684604 | − | 0.0684604i | ||||
\(773\) | −7.22222 | + | 7.22222i | −0.259765 | + | 0.259765i | −0.824958 | − | 0.565193i | \(-0.808802\pi\) |
0.565193 | + | 0.824958i | \(0.308802\pi\) | |||||||
\(774\) | −7.47884 | + | 21.1533i | −0.268821 | + | 0.760341i | ||||
\(775\) | −2.13613 | + | 4.52072i | −0.0767320 | + | 0.162389i | ||||
\(776\) | 8.43516i | 0.302805i | ||||||||
\(777\) | −24.5553 | − | 4.21302i | −0.880916 | − | 0.151141i | ||||
\(778\) | 5.48795 | + | 5.48795i | 0.196753 | + | 0.196753i | ||||
\(779\) | 77.9422 | 2.79257 | ||||||||
\(780\) | −1.50560 | + | 3.65623i | −0.0539093 | + | 0.130914i | ||||
\(781\) | −2.21990 | −0.0794344 | ||||||||
\(782\) | 21.5608 | + | 21.5608i | 0.771013 | + | 0.771013i | ||||
\(783\) | −25.4073 | + | 45.4483i | −0.907984 | + | 1.62419i | ||||
\(784\) | 18.8630i | 0.673678i | ||||||||
\(785\) | 14.1435 | + | 3.17333i | 0.504804 | + | 0.113261i | ||||
\(786\) | 4.47704 | + | 6.33150i | 0.159691 | + | 0.225837i | ||||
\(787\) | 5.84135 | − | 5.84135i | 0.208222 | − | 0.208222i | −0.595290 | − | 0.803511i | \(-0.702963\pi\) |
0.803511 | + | 0.595290i | \(0.202963\pi\) | |||||||
\(788\) | −2.69768 | + | 2.69768i | −0.0961010 | + | 0.0961010i | ||||
\(789\) | 1.73598 | + | 2.45504i | 0.0618024 | + | 0.0874018i | ||||
\(790\) | −3.05258 | − | 0.684896i | −0.108606 | − | 0.0243675i | ||||
\(791\) | 16.0555i | 0.570868i | ||||||||
\(792\) | 2.16088 | + | 4.52453i | 0.0767836 | + | 0.160772i | ||||
\(793\) | −7.10156 | − | 7.10156i | −0.252184 | − | 0.252184i | ||||
\(794\) | 9.49934 | 0.337119 | ||||||||
\(795\) | −0.397302 | + | 0.964814i | −0.0140908 | + | 0.0342184i | ||||
\(796\) | −24.1848 | −0.857206 | ||||||||
\(797\) | 0.330877 | + | 0.330877i | 0.0117203 | + | 0.0117203i | 0.712943 | − | 0.701222i | \(-0.247362\pi\) |
−0.701222 | + | 0.712943i | \(0.747362\pi\) | |||||||
\(798\) | −63.6206 | − | 10.9156i | −2.25215 | − | 0.386407i | ||||
\(799\) | 18.8796i | 0.667912i | ||||||||
\(800\) | 4.70711 | − | 1.68616i | 0.166421 | − | 0.0596149i | ||||
\(801\) | −9.35560 | − | 3.30770i | −0.330564 | − | 0.116872i | ||||
\(802\) | 24.7436 | − | 24.7436i | 0.873725 | − | 0.873725i | ||||
\(803\) | 0.710166 | − | 0.710166i | 0.0250612 | − | 0.0250612i | ||||
\(804\) | −2.74465 | + | 1.94076i | −0.0967964 | + | 0.0684454i | ||||
\(805\) | 40.8953 | − | 25.9071i | 1.44137 | − | 0.913106i | ||||
\(806\) | − | 1.02094i | − | 0.0359612i | ||||||
\(807\) | 0.0831547 | − | 0.484661i | 0.00292718 | − | 0.0170609i | ||||
\(808\) | 6.69611 | + | 6.69611i | 0.235568 | + | 0.235568i | ||||
\(809\) | 18.3644 | 0.645657 | 0.322829 | − | 0.946457i | \(-0.395366\pi\) | ||||
0.322829 | + | 0.946457i | \(0.395366\pi\) | |||||||
\(810\) | −15.7690 | + | 12.5036i | −0.554065 | + | 0.439331i | ||||
\(811\) | 29.4003 | 1.03239 | 0.516193 | − | 0.856472i | \(-0.327349\pi\) | ||||
0.516193 | + | 0.856472i | \(0.327349\pi\) | |||||||
\(812\) | −36.0341 | − | 36.0341i | −1.26455 | − | 1.26455i | ||||
\(813\) | −6.17092 | + | 35.9668i | −0.216424 | + | 1.26141i | ||||
\(814\) | − | 4.72730i | − | 0.165692i | ||||||
\(815\) | −2.13613 | + | 9.52072i | −0.0748254 | + | 0.333496i | ||||
\(816\) | 10.1292 | − | 7.16246i | 0.354595 | − | 0.250736i | ||||
\(817\) | 38.7540 | − | 38.7540i | 1.35583 | − | 1.35583i | ||||
\(818\) | 23.1830 | − | 23.1830i | 0.810573 | − | 0.810573i | ||||
\(819\) | 14.6854 | + | 5.19208i | 0.513150 | + | 0.181426i | ||||
\(820\) | 12.7273 | + | 20.0905i | 0.444457 | + | 0.701591i | ||||
\(821\) | 6.43578i | 0.224610i | 0.993674 | + | 0.112305i | \(0.0358234\pi\) | ||||
−0.993674 | + | 0.112305i | \(0.964177\pi\) | |||||||
\(822\) | 10.3777 | + | 1.78053i | 0.361964 | + | 0.0621032i | ||||
\(823\) | 1.00359 | + | 1.00359i | 0.0349831 | + | 0.0349831i | 0.724382 | − | 0.689399i | \(-0.242125\pi\) |
−0.689399 | + | 0.724382i | \(0.742125\pi\) | |||||||
\(824\) | −2.73642 | −0.0953276 | ||||||||
\(825\) | 8.30778 | − | 11.8527i | 0.289240 | − | 0.412659i | ||||
\(826\) | 15.3008 | 0.532384 | ||||||||
\(827\) | 17.7824 | + | 17.7824i | 0.618354 | + | 0.618354i | 0.945109 | − | 0.326755i | \(-0.105955\pi\) |
−0.326755 | + | 0.945109i | \(0.605955\pi\) | |||||||
\(828\) | −5.50403 | − | 11.5245i | −0.191278 | − | 0.400505i | ||||
\(829\) | 18.3026i | 0.635676i | 0.948145 | + | 0.317838i | \(0.102957\pi\) | ||||
−0.948145 | + | 0.317838i | \(0.897043\pi\) | |||||||
\(830\) | −12.4724 | − | 19.6881i | −0.432923 | − | 0.683385i | ||||
\(831\) | −16.0486 | − | 22.6962i | −0.556721 | − | 0.787322i | ||||
\(832\) | −0.721916 | + | 0.721916i | −0.0250279 | + | 0.0250279i | ||||
\(833\) | 95.5340 | − | 95.5340i | 3.31006 | − | 3.31006i | ||||
\(834\) | 8.18340 | + | 11.5731i | 0.283368 | + | 0.400743i | ||||
\(835\) | 7.48909 | − | 33.3789i | 0.259171 | − | 1.15512i | ||||
\(836\) | − | 12.2480i | − | 0.423607i | ||||||
\(837\) | 2.53553 | − | 4.53553i | 0.0876409 | − | 0.156771i | ||||
\(838\) | −5.04251 | − | 5.04251i | −0.174191 | − | 0.174191i | ||||
\(839\) | 30.9423 | 1.06825 | 0.534123 | − | 0.845407i | \(-0.320642\pi\) | ||||
0.534123 | + | 0.845407i | \(0.320642\pi\) | |||||||
\(840\) | −7.57510 | − | 18.1814i | −0.261366 | − | 0.627317i | ||||
\(841\) | 71.4105 | 2.46243 | ||||||||
\(842\) | −3.29258 | − | 3.29258i | −0.113470 | − | 0.113470i | ||||
\(843\) | 29.2407 | + | 5.01691i | 1.00710 | + | 0.172792i | ||||
\(844\) | − | 14.6009i | − | 0.502584i | ||||||
\(845\) | 22.5872 | − | 14.3090i | 0.777025 | − | 0.492244i | ||||
\(846\) | 2.63591 | − | 7.45548i | 0.0906245 | − | 0.256325i | ||||
\(847\) | 29.5112 | − | 29.5112i | 1.01402 | − | 1.01402i | ||||
\(848\) | −0.190501 | + | 0.190501i | −0.00654182 | + | 0.00654182i | ||||
\(849\) | −39.1417 | + | 27.6774i | −1.34334 | + | 0.949885i | ||||
\(850\) | −32.3795 | − | 15.2999i | −1.11061 | − | 0.524784i | ||||
\(851\) | 12.0410i | 0.412761i | ||||||||
\(852\) | 0.389023 | − | 2.26739i | 0.0133277 | − | 0.0776796i | ||||
\(853\) | −39.7674 | − | 39.7674i | −1.36161 | − | 1.36161i | −0.871869 | − | 0.489739i | \(-0.837092\pi\) |
−0.489739 | − | 0.871869i | \(-0.662908\pi\) | |||||||
\(854\) | 50.0272 | 1.71190 | ||||||||
\(855\) | 47.9217 | − | 10.9605i | 1.63889 | − | 0.374842i | ||||
\(856\) | −0.0768919 | −0.00262811 | ||||||||
\(857\) | 13.3607 | + | 13.3607i | 0.456392 | + | 0.456392i | 0.897469 | − | 0.441077i | \(-0.145403\pi\) |
−0.441077 | + | 0.897469i | \(0.645403\pi\) | |||||||
\(858\) | −0.499781 | + | 2.91294i | −0.0170622 | + | 0.0994460i | ||||
\(859\) | − | 53.6202i | − | 1.82950i | −0.404023 | − | 0.914749i | \(-0.632388\pi\) | ||
0.404023 | − | 0.914749i | \(-0.367612\pi\) | |||||||
\(860\) | 16.3175 | + | 3.66110i | 0.556423 | + | 0.124843i | ||||
\(861\) | 76.4943 | − | 54.0896i | 2.60692 | − | 1.84337i | ||||
\(862\) | −14.2921 | + | 14.2921i | −0.486792 | + | 0.486792i | ||||
\(863\) | −16.7468 | + | 16.7468i | −0.570069 | + | 0.570069i | −0.932148 | − | 0.362078i | \(-0.882067\pi\) |
0.362078 | + | 0.932148i | \(0.382067\pi\) | |||||||
\(864\) | −5.00000 | + | 1.41421i | −0.170103 | + | 0.0481125i | ||||
\(865\) | −19.9096 | − | 4.46705i | −0.676948 | − | 0.151884i | ||||
\(866\) | − | 33.8243i | − | 1.14940i | ||||||
\(867\) | −58.5552 | − | 10.0465i | −1.98864 | − | 0.341196i | ||||
\(868\) | 3.59604 | + | 3.59604i | 0.122058 | + | 0.122058i | ||||
\(869\) | −2.33838 | −0.0793241 | ||||||||
\(870\) | 35.8857 | + | 14.7774i | 1.21664 | + | 0.501002i | ||||
\(871\) | −1.98141 | −0.0671375 | ||||||||
\(872\) | 4.29903 | + | 4.29903i | 0.145583 | + | 0.145583i | ||||
\(873\) | −22.8349 | + | 10.9058i | −0.772843 | + | 0.369104i | ||||
\(874\) | 31.1972i | 1.05526i | ||||||||
\(875\) | −34.9566 | + | 44.8432i | −1.18175 | + | 1.51598i | ||||
\(876\) | 0.600906 | + | 0.849810i | 0.0203027 | + | 0.0287124i | ||||
\(877\) | −29.3588 | + | 29.3588i | −0.991375 | + | 0.991375i | −0.999963 | − | 0.00858855i | \(-0.997266\pi\) |
0.00858855 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(878\) | −8.87255 | + | 8.87255i | −0.299434 | + | 0.299434i | ||||
\(879\) | 10.3560 | + | 14.6456i | 0.349300 | + | 0.493985i | ||||
\(880\) | 3.15707 | − | 2.00000i | 0.106425 | − | 0.0674200i | ||||
\(881\) | 27.5826i | 0.929282i | 0.885499 | + | 0.464641i | \(0.153817\pi\) | ||||
−0.885499 | + | 0.464641i | \(0.846183\pi\) | |||||||
\(882\) | −51.0641 | + | 24.3878i | −1.71942 | + | 0.821181i | ||||
\(883\) | −13.0070 | − | 13.0070i | −0.437719 | − | 0.437719i | 0.453525 | − | 0.891244i | \(-0.350166\pi\) |
−0.891244 | + | 0.453525i | \(0.850166\pi\) | |||||||
\(884\) | 7.31247 | 0.245945 | ||||||||
\(885\) | −10.7563 | + | 4.48151i | −0.361569 | + | 0.150644i | ||||
\(886\) | 19.9294 | 0.669542 | ||||||||
\(887\) | 22.1276 | + | 22.1276i | 0.742973 | + | 0.742973i | 0.973149 | − | 0.230176i | \(-0.0739301\pi\) |
−0.230176 | + | 0.973149i | \(0.573930\pi\) | |||||||
\(888\) | 4.82843 | + | 0.828427i | 0.162031 | + | 0.0278002i | ||||
\(889\) | 68.4243i | 2.29488i | ||||||||
\(890\) | −1.61921 | + | 7.21683i | −0.0542762 | + | 0.241909i | ||||
\(891\) | −9.45460 | + | 11.6995i | −0.316741 | + | 0.391947i | ||||
\(892\) | −12.2654 | + | 12.2654i | −0.410675 | + | 0.410675i | ||||
\(893\) | −13.6588 | + | 13.6588i | −0.457075 | + | 0.457075i | ||||
\(894\) | −22.5803 | + | 15.9667i | −0.755197 | + | 0.534005i | ||||
\(895\) | −19.8453 | − | 31.3266i | −0.663357 | − | 1.04713i | ||||
\(896\) | − | 5.08557i | − | 0.169897i | ||||||
\(897\) | 1.27300 | − | 7.41960i | 0.0425043 | − | 0.247733i | ||||
\(898\) | −7.08334 | − | 7.08334i | −0.236374 | − | 0.236374i | ||||
\(899\) | −10.0205 | −0.334203 | ||||||||
\(900\) | 10.6504 | + | 10.5626i | 0.355014 | + | 0.352087i | ||||
\(901\) | 1.92963 | 0.0642852 | ||||||||
\(902\) | 12.5698 | + | 12.5698i | 0.418528 | + | 0.418528i | ||||
\(903\) | 11.1399 | − | 64.9283i | 0.370714 | − | 2.16068i | ||||
\(904\) | − | 3.15707i | − | 0.105003i | ||||||
\(905\) | 2.24023 | + | 3.53628i | 0.0744677 | + | 0.117550i | ||||
\(906\) | −14.5669 | + | 10.3004i | −0.483954 | + | 0.342207i | ||||
\(907\) | −0.148095 | + | 0.148095i | −0.00491740 | + | 0.00491740i | −0.709561 | − | 0.704644i | \(-0.751107\pi\) |
0.704644 | + | 0.709561i | \(0.251107\pi\) | |||||||
\(908\) | −4.98392 | + | 4.98392i | −0.165397 | + | 0.165397i | ||||
\(909\) | −9.46972 | + | 26.7844i | −0.314091 | + | 0.888383i | ||||
\(910\) | 2.54167 | − | 11.3282i | 0.0842555 | − | 0.375526i | ||||
\(911\) | − | 18.0914i | − | 0.599395i | −0.954034 | − | 0.299697i | \(-0.903114\pi\) | ||
0.954034 | − | 0.299697i | \(-0.0968857\pi\) | |||||||
\(912\) | 12.5100 | + | 2.14638i | 0.414249 | + | 0.0710738i | ||||
\(913\) | −12.3180 | − | 12.3180i | −0.407667 | − | 0.407667i | ||||
\(914\) | −30.1155 | −0.996132 | ||||||||
\(915\) | −35.1686 | + | 14.6526i | −1.16264 | + | 0.484401i | ||||
\(916\) | 12.3993 | 0.409684 | ||||||||
\(917\) | −16.0996 | − | 16.0996i | −0.531657 | − | 0.531657i | ||||
\(918\) | 32.4856 | + | 18.1607i | 1.07218 | + | 0.599391i | ||||
\(919\) | 48.1668i | 1.58888i | 0.607344 | + | 0.794439i | \(0.292235\pi\) | ||||
−0.607344 | + | 0.794439i | \(0.707765\pi\) | |||||||
\(920\) | −8.04145 | + | 5.09424i | −0.265119 | + | 0.167952i | ||||
\(921\) | 26.4961 | + | 37.4711i | 0.873075 | + | 1.23471i | ||||
\(922\) | −17.3336 | + | 17.3336i | −0.570851 | + | 0.570851i | ||||
\(923\) | 0.958855 | − | 0.958855i | 0.0315611 | − | 0.0315611i | ||||
\(924\) | −8.49978 | − | 12.0205i | −0.279622 | − | 0.395446i | ||||
\(925\) | −4.76919 | − | 13.3137i | −0.156810 | − | 0.437752i | ||||
\(926\) | 12.2090i | 0.401212i | ||||||||
\(927\) | −3.53789 | − | 7.40777i | −0.116200 | − | 0.243303i | ||||
\(928\) | 7.08557 | + | 7.08557i | 0.232595 | + | 0.232595i | ||||
\(929\) | −44.8497 | −1.47147 | −0.735735 | − | 0.677270i | \(-0.763163\pi\) | ||||
−0.735735 | + | 0.677270i | \(0.763163\pi\) | |||||||
\(930\) | −3.58123 | − | 1.47472i | −0.117433 | − | 0.0483579i | ||||
\(931\) | 138.232 | 4.53037 | ||||||||
\(932\) | 19.3438 | + | 19.3438i | 0.633629 | + | 0.633629i | ||||
\(933\) | −5.49184 | − | 0.942251i | −0.179795 | − | 0.0308479i | ||||
\(934\) | − | 30.1993i | − | 0.988150i | ||||||
\(935\) | −26.1186 | − | 5.86014i | −0.854171 | − | 0.191647i | ||||
\(936\) | −2.88767 | − | 1.02094i | −0.0943863 | − | 0.0333706i | ||||
\(937\) | −30.1698 | + | 30.1698i | −0.985605 | + | 0.985605i | −0.999898 | − | 0.0142928i | \(-0.995450\pi\) |
0.0142928 | + | 0.999898i | \(0.495450\pi\) | |||||||
\(938\) | 6.97906 | − | 6.97906i | 0.227874 | − | 0.227874i | ||||
\(939\) | 22.8847 | − | 16.1819i | 0.746813 | − | 0.528077i | ||||
\(940\) | −5.75110 | − | 1.29035i | −0.187580 | − | 0.0420867i | ||||
\(941\) | 51.9991i | 1.69512i | 0.530697 | + | 0.847561i | \(0.321930\pi\) | ||||
−0.530697 | + | 0.847561i | \(0.678070\pi\) | |||||||
\(942\) | −1.89866 | + | 11.0662i | −0.0618617 | + | 0.360556i | ||||
\(943\) | −32.0168 | − | 32.0168i | −1.04261 | − | 1.04261i | ||||
\(944\) | −3.00868 | −0.0979240 | ||||||||
\(945\) | 39.4252 | − | 44.0132i | 1.28250 | − | 1.43175i | ||||
\(946\) | 12.4998 | 0.406403 | ||||||||
\(947\) | −5.52445 | − | 5.52445i | −0.179521 | − | 0.179521i | 0.611626 | − | 0.791147i | \(-0.290516\pi\) |
−0.791147 | + | 0.611626i | \(0.790516\pi\) | |||||||
\(948\) | 0.409785 | − | 2.38840i | 0.0133092 | − | 0.0775717i | ||||
\(949\) | 0.613491i | 0.0199148i | ||||||||
\(950\) | −12.3566 | − | 34.4947i | −0.400900 | − | 1.11915i | ||||
\(951\) | −11.8860 | + | 8.40466i | −0.385429 | + | 0.272540i | ||||
\(952\) | −25.7565 | + | 25.7565i | −0.834772 | + | 0.834772i | ||||
\(953\) | −7.47016 | + | 7.47016i | −0.241982 | + | 0.241982i | −0.817670 | − | 0.575688i | \(-0.804734\pi\) |
0.575688 | + | 0.817670i | \(0.304734\pi\) | |||||||
\(954\) | −0.762002 | − | 0.269409i | −0.0246707 | − | 0.00872242i | ||||
\(955\) | 32.9486 | − | 20.8728i | 1.06619 | − | 0.675430i | ||||
\(956\) | 8.86716i | 0.286784i | ||||||||
\(957\) | 28.5903 | + | 4.90532i | 0.924193 | + | 0.158566i | ||||
\(958\) | −5.44182 | − | 5.44182i | −0.175817 | − | 0.175817i | ||||
\(959\) | −30.9158 | −0.998323 | ||||||||
\(960\) | 1.48953 | + | 3.57510i | 0.0480743 | + | 0.115386i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 2.04189 | + | 2.04189i | 0.0658331 | + | 0.0658331i | ||||
\(963\) | −0.0994131 | − | 0.208155i | −0.00320354 | − | 0.00670769i | ||||
\(964\) | − | 6.97906i | − | 0.224780i | ||||||
\(965\) | 1.31686 | − | 5.86926i | 0.0423913 | − | 0.188938i | ||||
\(966\) | 21.6500 | + | 30.6177i | 0.696576 | + | 0.985108i | ||||
\(967\) | 2.09051 | − | 2.09051i | 0.0672264 | − | 0.0672264i | −0.672694 | − | 0.739921i | \(-0.734863\pi\) |
0.739921 | + | 0.672694i | \(0.234863\pi\) | |||||||
\(968\) | −5.80293 | + | 5.80293i | −0.186513 | + | 0.186513i | ||||
\(969\) | −52.4880 | − | 74.2292i | −1.68616 | − | 2.38459i | ||||
\(970\) | 10.0938 | + | 15.9334i | 0.324093 | + | 0.511592i | ||||
\(971\) | 8.86332i | 0.284437i | 0.989835 | + | 0.142219i | \(0.0454236\pi\) | ||||
−0.989835 | + | 0.142219i | \(0.954576\pi\) | |||||||
\(972\) | −10.2929 | − | 11.7071i | −0.330145 | − | 0.375506i | ||||
\(973\) | −29.4278 | − | 29.4278i | −0.943413 | − | 0.943413i | ||||
\(974\) | −14.1819 | −0.454418 | ||||||||
\(975\) | 1.53119 | + | 8.70804i | 0.0490374 | + | 0.278880i | ||||
\(976\) | −9.83710 | −0.314878 | ||||||||
\(977\) | −34.8184 | − | 34.8184i | −1.11394 | − | 1.11394i | −0.992612 | − | 0.121328i | \(-0.961285\pi\) |
−0.121328 | − | 0.992612i | \(-0.538715\pi\) | |||||||
\(978\) | −7.44922 | − | 1.27808i | −0.238200 | − | 0.0408686i | ||||
\(979\) | 5.52834i | 0.176687i | ||||||||
\(980\) | 22.5721 | + | 35.6309i | 0.721040 | + | 1.13819i | ||||
\(981\) | −6.07974 | + | 17.1961i | −0.194111 | + | 0.549030i | ||||
\(982\) | 8.60515 | − | 8.60515i | 0.274601 | − | 0.274601i | ||||
\(983\) | −4.45175 | + | 4.45175i | −0.141989 | + | 0.141989i | −0.774528 | − | 0.632539i | \(-0.782013\pi\) |
0.632539 | + | 0.774528i | \(0.282013\pi\) | |||||||
\(984\) | −15.0414 | + | 10.6359i | −0.479504 | + | 0.339060i | ||||
\(985\) | −1.86760 | + | 8.32388i | −0.0595066 | + | 0.265221i | ||||
\(986\) | − | 71.7715i | − | 2.28567i | ||||||
\(987\) | −3.92626 | + | 22.8839i | −0.124974 | + | 0.728404i | ||||
\(988\) | 5.29035 | + | 5.29035i | 0.168309 | + | 0.168309i | ||||
\(989\) | −31.8385 | −1.01240 | ||||||||
\(990\) | 9.49597 | + | 5.96075i | 0.301802 | + | 0.189445i | ||||
\(991\) | −7.97049 | −0.253191 | −0.126596 | − | 0.991954i | \(-0.540405\pi\) | ||||
−0.126596 | + | 0.991954i | \(0.540405\pi\) | |||||||
\(992\) | −0.707107 | − | 0.707107i | −0.0224507 | − | 0.0224507i | ||||
\(993\) | 3.37877 | − | 19.6929i | 0.107222 | − | 0.624936i | ||||
\(994\) | 6.75469i | 0.214246i | ||||||||
\(995\) | −45.6834 | + | 28.9403i | −1.44826 | + | 0.917470i | ||||
\(996\) | 14.7402 | − | 10.4229i | 0.467061 | − | 0.330262i | ||||
\(997\) | 2.64756 | − | 2.64756i | 0.0838490 | − | 0.0838490i | −0.663938 | − | 0.747787i | \(-0.731116\pi\) |
0.747787 | + | 0.663938i | \(0.231116\pi\) | |||||||
\(998\) | −21.0089 | + | 21.0089i | −0.665024 | + | 0.665024i | ||||
\(999\) | 4.00000 | + | 14.1421i | 0.126554 | + | 0.447437i |
(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.j.c.683.4 | yes | 8 | |
3.2 | odd | 2 | 930.2.j.f.683.1 | yes | 8 | ||
5.2 | odd | 4 | 930.2.j.f.497.1 | yes | 8 | ||
15.2 | even | 4 | inner | 930.2.j.c.497.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.c.497.4 | ✓ | 8 | 15.2 | even | 4 | inner | |
930.2.j.c.683.4 | yes | 8 | 1.1 | even | 1 | trivial | |
930.2.j.f.497.1 | yes | 8 | 5.2 | odd | 4 | ||
930.2.j.f.683.1 | yes | 8 | 3.2 | odd | 2 |