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 | 497.1 | ||
Root | \(0.692297i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.497 |
Dual form | 930.2.j.f.683.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 | ||||
\(3\) | 1.70711 | + | 0.292893i | 0.985599 | + | 0.169102i | ||||
\(4\) | − | 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 | 0.874935 | + | 0.484239i | \(0.160904\pi\) |
0.484239 | + | 0.874935i | \(0.339096\pi\) | |||||||
\(8\) | 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 | \(0.918923\pi\) | |||||||
\(12\) | 0.292893 | − | 1.70711i | 0.0845510 | − | 0.492799i | ||||
\(13\) | −0.721916 | + | 0.721916i | −0.200224 | + | 0.200224i | −0.800096 | − | 0.599872i | \(-0.795218\pi\) |
0.599872 | + | 0.800096i | \(0.295218\pi\) | |||||||
\(14\) | −5.08557 | −1.35917 | ||||||||
\(15\) | −2.59604 | + | 2.87412i | −0.670294 | + | 0.742095i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −5.06462 | + | 5.06462i | −1.22835 | + | 1.22835i | −0.263764 | + | 0.964587i | \(0.584964\pi\) |
−0.964587 | + | 0.263764i | \(0.915036\pi\) | |||||||
\(18\) | −2.70711 | + | 1.29289i | −0.638071 | + | 0.304738i | ||||
\(19\) | − | 7.32821i | − | 1.68121i | −0.541652 | − | 0.840603i | \(-0.682201\pi\) | ||
0.541652 | − | 0.840603i | \(-0.317799\pi\) | |||||||
\(20\) | 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 | \(-0.396383\pi\) |
−0.947484 | + | 0.319803i | \(0.896383\pi\) | |||||||
\(24\) | 1.00000 | + | 1.41421i | 0.204124 | + | 0.288675i | ||||
\(25\) | −2.13613 | − | 4.52072i | −0.427226 | − | 0.904145i | ||||
\(26\) | − | 1.02094i | − | 0.200224i | ||||||
\(27\) | 4.53553 | + | 2.53553i | 0.872864 | + | 0.487964i | ||||
\(28\) | 3.59604 | − | 3.59604i | 0.679587 | − | 0.679587i | ||||
\(29\) | 10.0205 | 1.86076 | 0.930381 | − | 0.366595i | \(-0.119477\pi\) | ||||
0.930381 | + | 0.366595i | \(0.119477\pi\) | |||||||
\(30\) | −0.196635 | − | 3.86799i | −0.0359005 | − | 0.706195i | ||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −0.489528 | + | 2.85318i | −0.0852159 | + | 0.496675i | ||||
\(34\) | − | 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 | 0.523331 | − | 0.852129i | \(-0.324689\pi\) |
−0.852129 | + | 0.523331i | \(0.824689\pi\) | |||||||
\(38\) | 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 | \(-0.311960\pi\) | |||||||
\(42\) | −8.68161 | − | 1.48953i | −1.33960 | − | 0.229839i | ||||
\(43\) | −5.28834 | + | 5.28834i | −0.806464 | + | 0.806464i | −0.984097 | − | 0.177633i | \(-0.943156\pi\) |
0.177633 | + | 0.984097i | \(0.443156\pi\) | |||||||
\(44\) | 1.67135 | 0.251966 | ||||||||
\(45\) | −5.27353 | + | 4.14607i | −0.786131 | + | 0.618060i | ||||
\(46\) | 4.25714 | 0.627681 | ||||||||
\(47\) | −1.86387 | + | 1.86387i | −0.271873 | + | 0.271873i | −0.829854 | − | 0.557981i | \(-0.811576\pi\) |
0.557981 | + | 0.829854i | \(0.311576\pi\) | |||||||
\(48\) | −1.70711 | − | 0.292893i | −0.246400 | − | 0.0422755i | ||||
\(49\) | 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 | \(-0.255890\pi\) |
−0.720069 | + | 0.693902i | \(0.755890\pi\) | |||||||
\(54\) | −5.00000 | + | 1.41421i | −0.680414 | + | 0.192450i | ||||
\(55\) | −3.15707 | − | 2.00000i | −0.425700 | − | 0.269680i | ||||
\(56\) | 5.08557i | 0.679587i | ||||||||
\(57\) | 2.14638 | − | 12.5100i | 0.284295 | − | 1.65699i | ||||
\(58\) | −7.08557 | + | 7.08557i | −0.930381 | + | 0.930381i | ||||
\(59\) | −3.00868 | −0.391696 | −0.195848 | − | 0.980634i | \(-0.562746\pi\) | ||||
−0.195848 | + | 0.980634i | \(0.562746\pi\) | |||||||
\(60\) | 2.87412 | + | 2.59604i | 0.371048 | + | 0.335147i | ||||
\(61\) | 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 | ||||
\(63\) | 6.57510 | + | 13.7672i | 0.828384 | + | 1.73450i | ||||
\(64\) | 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 | 0.785948 | − | 0.618292i | \(-0.212175\pi\) |
−0.618292 | + | 0.785948i | \(0.712175\pi\) | |||||||
\(68\) | 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 | \(0.974886\pi\) | |||||||
\(72\) | 1.29289 | + | 2.70711i | 0.152369 | + | 0.319036i | ||||
\(73\) | −0.424905 | + | 0.424905i | −0.0497313 | + | 0.0497313i | −0.731535 | − | 0.681804i | \(-0.761196\pi\) |
0.681804 | + | 0.731535i | \(0.261196\pi\) | |||||||
\(74\) | 2.82843 | 0.328798 | ||||||||
\(75\) | −2.32251 | − | 8.34302i | −0.268181 | − | 0.963369i | ||||
\(76\) | −7.32821 | −0.840603 | ||||||||
\(77\) | −6.01025 | + | 6.01025i | −0.684932 | + | 0.684932i | ||||
\(78\) | 0.299028 | − | 1.74286i | 0.0338582 | − | 0.197340i | ||||
\(79\) | − | 1.39909i | − | 0.157410i | −0.996898 | − | 0.0787052i | \(-0.974921\pi\) | ||
0.996898 | − | 0.0787052i | \(-0.0250786\pi\) | |||||||
\(80\) | 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 | \(-0.0561560\pi\) |
−0.175505 | + | 0.984478i | \(0.556156\pi\) | |||||||
\(84\) | 7.19208 | − | 5.08557i | 0.784720 | − | 0.554881i | ||||
\(85\) | −3.50623 | − | 15.6272i | −0.380304 | − | 1.69501i | ||||
\(86\) | − | 7.47884i | − | 0.806464i | ||||||
\(87\) | 17.1061 | + | 2.93494i | 1.83396 | + | 0.314658i | ||||
\(88\) | −1.18183 | + | 1.18183i | −0.125983 | + | 0.125983i | ||||
\(89\) | −3.30770 | −0.350616 | −0.175308 | − | 0.984514i | \(-0.556092\pi\) | ||||
−0.175308 | + | 0.984514i | \(0.556092\pi\) | |||||||
\(90\) | 0.797231 | − | 6.66066i | 0.0840355 | − | 0.702095i | ||||
\(91\) | −5.19208 | −0.544278 | ||||||||
\(92\) | −3.01025 | + | 3.01025i | −0.313841 | + | 0.313841i | ||||
\(93\) | 1.70711 | + | 0.292893i | 0.177019 | + | 0.0303716i | ||||
\(94\) | − | 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 | 0.941795 | − | 0.336186i | \(-0.109137\pi\) |
−0.336186 | + | 0.941795i | \(0.609137\pi\) | |||||||
\(98\) | −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 | \(-0.156156\pi\) | |||||||
\(102\) | 2.09784 | − | 12.2271i | 0.207717 | − | 1.21066i | ||||
\(103\) | 1.93494 | − | 1.93494i | 0.190655 | − | 0.190655i | −0.605324 | − | 0.795979i | \(-0.706956\pi\) |
0.795979 | + | 0.605324i | \(0.206956\pi\) | |||||||
\(104\) | −1.02094 | −0.100112 | ||||||||
\(105\) | −19.6709 | + | 1.00000i | −1.91968 | + | 0.0975900i | ||||
\(106\) | 0.269409 | 0.0261673 | ||||||||
\(107\) | −0.0543708 | + | 0.0543708i | −0.00525622 | + | 0.00525622i | −0.709730 | − | 0.704474i | \(-0.751183\pi\) |
0.704474 | + | 0.709730i | \(0.251183\pi\) | |||||||
\(108\) | 2.53553 | − | 4.53553i | 0.243982 | − | 0.436432i | ||||
\(109\) | 6.07974i | 0.582334i | 0.956672 | + | 0.291167i | \(0.0940435\pi\) | ||||
−0.956672 | + | 0.291167i | \(0.905957\pi\) | |||||||
\(110\) | 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 | \(-0.202557\pi\) |
−0.594264 | + | 0.804270i | \(0.702557\pi\) | |||||||
\(114\) | 7.32821 | + | 10.3637i | 0.686350 | + | 0.970645i | ||||
\(115\) | 9.28834 | − | 2.08399i | 0.866142 | − | 0.194333i | ||||
\(116\) | − | 10.0205i | − | 0.930381i | ||||||
\(117\) | −2.76380 | + | 1.31997i | −0.255514 | + | 0.122031i | ||||
\(118\) | 2.12745 | − | 2.12745i | 0.195848 | − | 0.195848i | ||||
\(119\) | −36.4252 | −3.33909 | ||||||||
\(120\) | −3.86799 | + | 0.196635i | −0.353097 | + | 0.0179502i | ||||
\(121\) | 8.20658 | 0.746052 | ||||||||
\(122\) | −6.95588 | + | 6.95588i | −0.629756 | + | 0.629756i | ||||
\(123\) | 3.11519 | − | 18.1566i | 0.280887 | − | 1.63713i | ||||
\(124\) | − | 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 | 0.145187 | − | 0.989404i | \(-0.453622\pi\) |
−0.989404 | + | 0.145187i | \(0.953622\pi\) | |||||||
\(128\) | −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 | \(-0.0626591\pi\) | |||||||
\(132\) | 2.85318 | + | 0.489528i | 0.248337 | + | 0.0426080i | ||||
\(133\) | 26.3525 | − | 26.3525i | 2.28505 | − | 2.28505i | ||||
\(134\) | −1.94076 | −0.167656 | ||||||||
\(135\) | −10.2168 | + | 5.53321i | −0.879325 | + | 0.476223i | ||||
\(136\) | −7.16246 | −0.614176 | ||||||||
\(137\) | 4.29859 | − | 4.29859i | 0.367253 | − | 0.367253i | −0.499221 | − | 0.866475i | \(-0.666381\pi\) |
0.866475 | + | 0.499221i | \(0.166381\pi\) | |||||||
\(138\) | 7.26739 | + | 1.24689i | 0.618642 | + | 0.106142i | ||||
\(139\) | 8.18340i | 0.694107i | 0.937845 | + | 0.347054i | \(0.112818\pi\) | ||||
−0.937845 | + | 0.347054i | \(0.887182\pi\) | |||||||
\(140\) | 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 | ||||||
\(147\) | −5.52484 | + | 32.2011i | −0.455681 | + | 2.65591i | ||||
\(148\) | −2.00000 | + | 2.00000i | −0.164399 | + | 0.164399i | ||||
\(149\) | −15.9667 | −1.30804 | −0.654020 | − | 0.756478i | \(-0.726919\pi\) | ||||
−0.654020 | + | 0.756478i | \(0.726919\pi\) | |||||||
\(150\) | 7.54167 | + | 4.25714i | 0.615775 | + | 0.347594i | ||||
\(151\) | 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 | ||||
\(153\) | −19.3895 | + | 9.26029i | −1.56755 | + | 0.748650i | ||||
\(154\) | − | 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 | 0.865952 | − | 0.500127i | \(-0.166713\pi\) |
−0.500127 | + | 0.865952i | \(0.666713\pi\) | |||||||
\(158\) | 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 | ||||||
\(162\) | −8.94975 | + | 0.949747i | −0.703159 | + | 0.0746192i | ||||
\(163\) | 3.08557 | − | 3.08557i | 0.241680 | − | 0.241680i | −0.575865 | − | 0.817545i | \(-0.695335\pi\) |
0.817545 | + | 0.575865i | \(0.195335\pi\) | |||||||
\(164\) | −10.6359 | −0.830525 | ||||||||
\(165\) | −4.80368 | − | 4.33890i | −0.373966 | − | 0.337783i | ||||
\(166\) | −10.4229 | −0.808973 | ||||||||
\(167\) | 10.8177 | − | 10.8177i | 0.837102 | − | 0.837102i | −0.151375 | − | 0.988476i | \(-0.548370\pi\) |
0.988476 | + | 0.151375i | \(0.0483701\pi\) | |||||||
\(168\) | −1.48953 | + | 8.68161i | −0.114920 | + | 0.669800i | ||||
\(169\) | 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 | \(-0.137238\pi\) |
−0.417912 | + | 0.908487i | \(0.637238\pi\) | |||||||
\(174\) | −14.1711 | + | 10.0205i | −1.07431 | + | 0.759653i | ||||
\(175\) | 8.57510 | − | 23.9383i | 0.648216 | − | 1.80957i | ||||
\(176\) | − | 1.67135i | − | 0.125983i | ||||||
\(177\) | −5.13613 | − | 0.881221i | −0.386055 | − | 0.0662366i | ||||
\(178\) | 2.33890 | − | 2.33890i | 0.175308 | − | 0.175308i | ||||
\(179\) | 16.5843 | 1.23957 | 0.619784 | − | 0.784772i | \(-0.287220\pi\) | ||||
0.619784 | + | 0.784772i | \(0.287220\pi\) | |||||||
\(180\) | 4.14607 | + | 5.27353i | 0.309030 | + | 0.393065i | ||||
\(181\) | 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 | ||||
\(183\) | 16.7930 | + | 2.88122i | 1.24137 | + | 0.212986i | ||||
\(184\) | − | 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 | \(-0.217381\pi\) | |||||||
\(192\) | −0.292893 | + | 1.70711i | −0.0211377 | + | 0.123200i | ||||
\(193\) | −1.90216 | + | 1.90216i | −0.136921 | + | 0.136921i | −0.772245 | − | 0.635325i | \(-0.780866\pi\) |
0.635325 | + | 0.772245i | \(0.280866\pi\) | |||||||
\(194\) | −8.43516 | −0.605609 | ||||||||
\(195\) | −0.200753 | − | 3.94900i | −0.0143762 | − | 0.282794i | ||||
\(196\) | 18.8630 | 1.34736 | ||||||||
\(197\) | −2.69768 | + | 2.69768i | −0.192202 | + | 0.192202i | −0.796647 | − | 0.604445i | \(-0.793395\pi\) |
0.604445 | + | 0.796647i | \(0.293395\pi\) | |||||||
\(198\) | −2.16088 | − | 4.52453i | −0.153567 | − | 0.321545i | ||||
\(199\) | − | 24.1848i | − | 1.71441i | −0.514974 | − | 0.857206i | \(-0.672198\pi\) | ||
0.514974 | − | 0.857206i | \(-0.327802\pi\) | |||||||
\(200\) | 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 | ||||||||
\(207\) | −5.50403 | − | 11.5245i | −0.382556 | − | 0.801010i | ||||
\(208\) | 0.721916 | − | 0.721916i | 0.0500559 | − | 0.0500559i | ||||
\(209\) | 12.2480 | 0.847214 | ||||||||
\(210\) | 13.2023 | − | 14.6165i | 0.911047 | − | 1.00864i | ||||
\(211\) | −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 | ||||
\(213\) | −0.389023 | + | 2.26739i | −0.0266554 | + | 0.155359i | ||||
\(214\) | − | 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 | ||||||
\(222\) | 4.82843 | + | 0.828427i | 0.324063 | + | 0.0556004i | ||||
\(223\) | 12.2654 | − | 12.2654i | 0.821350 | − | 0.821350i | −0.164951 | − | 0.986302i | \(-0.552747\pi\) |
0.986302 | + | 0.164951i | \(0.0527467\pi\) | |||||||
\(224\) | 5.08557 | 0.339794 | ||||||||
\(225\) | −1.52116 | − | 14.9227i | −0.101411 | − | 0.994845i | ||||
\(226\) | −3.15707 | −0.210005 | ||||||||
\(227\) | −4.98392 | + | 4.98392i | −0.330795 | + | 0.330795i | −0.852888 | − | 0.522094i | \(-0.825151\pi\) |
0.522094 | + | 0.852888i | \(0.325151\pi\) | |||||||
\(228\) | −12.5100 | − | 2.14638i | −0.828497 | − | 0.142148i | ||||
\(229\) | 12.3993i | 0.819367i | 0.912228 | + | 0.409684i | \(0.134361\pi\) | ||||
−0.912228 | + | 0.409684i | \(0.865639\pi\) | |||||||
\(230\) | −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 | −0.947499 | − | 0.319758i | \(-0.896398\pi\) |
−0.319758 | − | 0.947499i | \(-0.603602\pi\) | |||||||
\(234\) | 1.02094 | − | 2.88767i | 0.0667412 | − | 0.188773i | ||||
\(235\) | −1.29035 | − | 5.75110i | −0.0841733 | − | 0.375160i | ||||
\(236\) | 3.00868i | 0.195848i | ||||||||
\(237\) | 0.409785 | − | 2.38840i | 0.0266184 | − | 0.155143i | ||||
\(238\) | 25.7565 | − | 25.7565i | 1.66954 | − | 1.66954i | ||||
\(239\) | −8.86716 | −0.573569 | −0.286784 | − | 0.957995i | \(-0.592586\pi\) | ||||
−0.286784 | + | 0.957995i | \(0.592586\pi\) | |||||||
\(240\) | 2.59604 | − | 2.87412i | 0.167574 | − | 0.185524i | ||||
\(241\) | −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 | ||||
\(243\) | 10.2929 | + | 11.7071i | 0.660289 | + | 0.751011i | ||||
\(244\) | − | 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 | \(0.818619\pi\) | |||||||
\(252\) | 13.7672 | − | 6.57510i | 0.867250 | − | 0.414192i | ||||
\(253\) | 5.03120 | − | 5.03120i | 0.316309 | − | 0.316309i | ||||
\(254\) | 13.4546 | 0.844217 | ||||||||
\(255\) | −1.40839 | − | 27.7043i | −0.0881968 | − | 1.73491i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.3020 | − | 17.3020i | 1.07927 | − | 1.07927i | 0.0826913 | − | 0.996575i | \(-0.473648\pi\) |
0.996575 | − | 0.0826913i | \(-0.0263515\pi\) | |||||||
\(258\) | 2.19050 | − | 12.7672i | 0.136375 | − | 0.794849i | ||||
\(259\) | − | 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 | \(-0.267045\pi\) |
−0.743939 | + | 0.668247i | \(0.767045\pi\) | |||||||
\(264\) | −2.36365 | + | 1.67135i | −0.145473 | + | 0.102865i | ||||
\(265\) | 0.587802 | − | 0.131883i | 0.0361084 | − | 0.00810151i | ||||
\(266\) | 37.2681i | 2.28505i | ||||||||
\(267\) | −5.64660 | − | 0.968804i | −0.345566 | − | 0.0592898i | ||||
\(268\) | 1.37233 | − | 1.37233i | 0.0838282 | − | 0.0838282i | ||||
\(269\) | 0.283908 | 0.0173102 | 0.00865508 | − | 0.999963i | \(-0.497245\pi\) | ||||
0.00865508 | + | 0.999963i | \(0.497245\pi\) | |||||||
\(270\) | 3.31182 | − | 11.1370i | 0.201551 | − | 0.677774i | ||||
\(271\) | 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 | ||||
\(273\) | −8.86343 | − | 1.52072i | −0.536439 | − | 0.0920384i | ||||
\(274\) | 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 | 0.278574 | − | 0.960415i | \(-0.410138\pi\) |
−0.960415 | + | 0.278574i | \(0.910138\pi\) | |||||||
\(278\) | −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 | \(-0.170691\pi\) | |||||||
\(282\) | 0.772040 | − | 4.49978i | 0.0459743 | − | 0.267958i | ||||
\(283\) | 19.5708 | − | 19.5708i | 1.16337 | − | 1.16337i | 0.179632 | − | 0.983734i | \(-0.442509\pi\) |
0.983734 | − | 0.179632i | \(-0.0574908\pi\) | |||||||
\(284\) | 1.32821 | 0.0788146 | ||||||||
\(285\) | 21.0622 | + | 19.0243i | 1.24762 | + | 1.12690i | ||||
\(286\) | 1.70636 | 0.100899 | ||||||||
\(287\) | 38.2471 | − | 38.2471i | 2.25766 | − | 2.25766i | ||||
\(288\) | 2.70711 | − | 1.29289i | 0.159518 | − | 0.0761845i | ||||
\(289\) | − | 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 | \(-0.347822\pi\) |
−0.887880 | + | 0.460076i | \(0.847822\pi\) | |||||||
\(294\) | −18.8630 | − | 26.6763i | −1.10011 | − | 1.55579i | ||||
\(295\) | 3.60029 | − | 5.68318i | 0.209617 | − | 0.330888i | ||||
\(296\) | − | 2.82843i | − | 0.164399i | ||||||
\(297\) | −4.23777 | + | 7.58048i | −0.245901 | + | 0.439864i | ||||
\(298\) | 11.2901 | − | 11.2901i | 0.654020 | − | 0.654020i | ||||
\(299\) | 4.34630 | 0.251353 | ||||||||
\(300\) | −8.34302 | + | 2.32251i | −0.481684 | + | 0.134090i | ||||
\(301\) | −38.0341 | −2.19225 | ||||||||
\(302\) | −7.28347 | + | 7.28347i | −0.419117 | + | 0.419117i | ||||
\(303\) | 2.77362 | − | 16.1658i | 0.159340 | − | 0.928703i | ||||
\(304\) | 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 | 0.997413 | + | 0.0718804i | \(0.0229000\pi\) |
0.0718804 | + | 0.997413i | \(0.477100\pi\) | |||||||
\(308\) | 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 | \(0.970926\pi\) | |||||||
\(312\) | −1.74286 | − | 0.299028i | −0.0986700 | − | 0.0169291i | ||||
\(313\) | −11.4423 | + | 11.4423i | −0.646759 | + | 0.646759i | −0.952208 | − | 0.305449i | \(-0.901193\pi\) |
0.305449 | + | 0.952208i | \(0.401193\pi\) | |||||||
\(314\) | −6.48243 | −0.365825 | ||||||||
\(315\) | −33.8732 | − | 4.05437i | −1.90854 | − | 0.228438i | ||||
\(316\) | −1.39909 | −0.0787052 | ||||||||
\(317\) | −5.94299 | + | 5.94299i | −0.333792 | + | 0.333792i | −0.854025 | − | 0.520233i | \(-0.825845\pi\) |
0.520233 | + | 0.854025i | \(0.325845\pi\) | |||||||
\(318\) | 0.459909 | + | 0.0789079i | 0.0257904 | + | 0.00442494i | ||||
\(319\) | 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 | ||||||||
\(327\) | −1.78072 | + | 10.3788i | −0.0984738 | + | 0.573947i | ||||
\(328\) | 7.52072 | − | 7.52072i | 0.415263 | − | 0.415263i | ||||
\(329\) | −13.4051 | −0.739047 | ||||||||
\(330\) | 6.46478 | − | 0.328646i | 0.355874 | − | 0.0180914i | ||||
\(331\) | −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 | ||||
\(333\) | −3.65685 | − | 7.65685i | −0.200394 | − | 0.419593i | ||||
\(334\) | 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 | 0.916906 | − | 0.399103i | \(-0.130678\pi\) |
−0.399103 | + | 0.916906i | \(0.630678\pi\) | |||||||
\(338\) | −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 | ||||||||
\(342\) | 9.47459 | + | 19.8382i | 0.512327 | + | 1.07273i | ||||
\(343\) | −42.6598 | + | 42.6598i | −2.30341 | + | 2.30341i | ||||
\(344\) | −7.47884 | −0.403232 | ||||||||
\(345\) | 16.4666 | − | 0.837102i | 0.886530 | − | 0.0450681i | ||||
\(346\) | −9.12522 | −0.490575 | ||||||||
\(347\) | −4.39104 | + | 4.39104i | −0.235723 | + | 0.235723i | −0.815077 | − | 0.579353i | \(-0.803305\pi\) |
0.579353 | + | 0.815077i | \(0.303305\pi\) | |||||||
\(348\) | 2.93494 | − | 17.1061i | 0.157329 | − | 0.916982i | ||||
\(349\) | − | 15.3708i | − | 0.822782i | −0.911459 | − | 0.411391i | \(-0.865043\pi\) | ||
0.911459 | − | 0.411391i | \(-0.134957\pi\) | |||||||
\(350\) | 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 | \(-0.202511\pi\) |
−0.594148 | + | 0.804356i | \(0.702511\pi\) | |||||||
\(354\) | 4.25491 | − | 3.00868i | 0.226146 | − | 0.159909i | ||||
\(355\) | −2.50889 | − | 1.58938i | −0.133158 | − | 0.0843555i | ||||
\(356\) | 3.30770i | 0.175308i | ||||||||
\(357\) | −62.1816 | − | 10.6687i | −3.29100 | − | 0.564647i | ||||
\(358\) | −11.7269 | + | 11.7269i | −0.619784 | + | 0.619784i | ||||
\(359\) | −7.94361 | −0.419248 | −0.209624 | − | 0.977782i | \(-0.567224\pi\) | ||||
−0.209624 | + | 0.977782i | \(0.567224\pi\) | |||||||
\(360\) | −6.66066 | − | 0.797231i | −0.351048 | − | 0.0420178i | ||||
\(361\) | −34.7026 | −1.82645 | ||||||||
\(362\) | −1.32378 | + | 1.32378i | −0.0695763 | + | 0.0695763i | ||||
\(363\) | 14.0095 | + | 2.40365i | 0.735308 | + | 0.126159i | ||||
\(364\) | 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 | 0.679403 | − | 0.733766i | \(-0.262239\pi\) |
−0.733766 | + | 0.679403i | \(0.762239\pi\) | |||||||
\(368\) | 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 | ||||||
\(372\) | 0.292893 | − | 1.70711i | 0.0151858 | − | 0.0885094i | ||||
\(373\) | −4.50403 | + | 4.50403i | −0.233210 | + | 0.233210i | −0.814031 | − | 0.580821i | \(-0.802731\pi\) |
0.580821 | + | 0.814031i | \(0.302731\pi\) | |||||||
\(374\) | 11.9710 | 0.619006 | ||||||||
\(375\) | 18.5386 | + | 5.59648i | 0.957329 | + | 0.289001i | ||||
\(376\) | −2.63591 | −0.135937 | ||||||||
\(377\) | −7.23397 | + | 7.23397i | −0.372568 | + | 0.372568i | ||||
\(378\) | −23.0658 | − | 12.8946i | −1.18637 | − | 0.663228i | ||||
\(379\) | 25.4703i | 1.30832i | 0.756355 | + | 0.654162i | \(0.226978\pi\) | ||||
−0.756355 | + | 0.654162i | \(0.773022\pi\) | |||||||
\(380\) | 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 | \(-0.219950\pi\) |
−0.637302 | + | 0.770614i | \(0.719950\pi\) | |||||||
\(384\) | −1.00000 | − | 1.41421i | −0.0510310 | − | 0.0721688i | ||||
\(385\) | −4.16088 | − | 18.5450i | −0.212058 | − | 0.945143i | ||||
\(386\) | − | 2.69007i | − | 0.136921i | ||||||
\(387\) | −20.2460 | + | 9.66934i | −1.02916 | + | 0.491520i | ||||
\(388\) | 5.96456 | − | 5.96456i | 0.302805 | − | 0.302805i | ||||
\(389\) | −7.76113 | −0.393505 | −0.196753 | − | 0.980453i | \(-0.563040\pi\) | ||||
−0.196753 | + | 0.980453i | \(0.563040\pi\) | |||||||
\(390\) | 2.93432 | + | 2.65041i | 0.148585 | + | 0.134209i | ||||
\(391\) | 30.4916 | 1.54203 | ||||||||
\(392\) | −13.3382 | + | 13.3382i | −0.673678 | + | 0.673678i | ||||
\(393\) | 1.31130 | − | 7.64279i | 0.0661461 | − | 0.385528i | ||||
\(394\) | − | 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 | 0.855282 | − | 0.518163i | \(-0.173384\pi\) |
−0.518163 | + | 0.855282i | \(0.673384\pi\) | |||||||
\(398\) | 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 | \(-0.338303\pi\) | |||||||
\(402\) | −3.31309 | − | 0.568436i | −0.165242 | − | 0.0283510i | ||||
\(403\) | −0.721916 | + | 0.721916i | −0.0359612 | + | 0.0359612i | ||||
\(404\) | −9.46972 | −0.471136 | ||||||||
\(405\) | −19.0619 | + | 6.45334i | −0.947191 | + | 0.320669i | ||||
\(406\) | −50.9600 | −2.52910 | ||||||||
\(407\) | 3.34271 | − | 3.34271i | 0.165692 | − | 0.165692i | ||||
\(408\) | −12.2271 | − | 2.09784i | −0.605331 | − | 0.103858i | ||||
\(409\) | 32.7857i | 1.62115i | 0.585637 | + | 0.810573i | \(0.300844\pi\) | ||||
−0.585637 | + | 0.810573i | \(0.699156\pi\) | |||||||
\(410\) | −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 | ||||||||
\(417\) | −2.39686 | + | 13.9699i | −0.117375 | + | 0.684111i | ||||
\(418\) | −8.66066 | + | 8.66066i | −0.423607 | + | 0.423607i | ||||
\(419\) | 7.13118 | 0.348381 | 0.174191 | − | 0.984712i | \(-0.444269\pi\) | ||||
0.174191 | + | 0.984712i | \(0.444269\pi\) | |||||||
\(420\) | 1.00000 | + | 19.6709i | 0.0487950 | + | 0.959842i | ||||
\(421\) | −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 | ||||
\(423\) | −7.13569 | + | 3.40795i | −0.346949 | + | 0.165700i | ||||
\(424\) | − | 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 | \(0.838167\pi\) | |||||||
\(432\) | −4.53553 | − | 2.53553i | −0.218216 | − | 0.121991i | ||||
\(433\) | −23.9174 | + | 23.9174i | −1.14940 | + | 1.14940i | −0.162723 | + | 0.986672i | \(0.552028\pi\) |
−0.986672 | + | 0.162723i | \(0.947972\pi\) | |||||||
\(434\) | −5.08557 | −0.244115 | ||||||||
\(435\) | −26.0136 | + | 28.8002i | −1.24726 | + | 1.38086i | ||||
\(436\) | 6.07974 | 0.291167 | ||||||||
\(437\) | −22.0598 | + | 22.0598i | −1.05526 | + | 1.05526i | ||||
\(438\) | 0.176001 | − | 1.02581i | 0.00840967 | − | 0.0490151i | ||||
\(439\) | − | 12.5477i | − | 0.598868i | −0.954117 | − | 0.299434i | \(-0.903202\pi\) | ||
0.954117 | − | 0.299434i | \(-0.0967978\pi\) | |||||||
\(440\) | −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 | \(-0.406987\pi\) |
−0.957610 | + | 0.288068i | \(0.906987\pi\) | |||||||
\(444\) | −4.00000 | + | 2.82843i | −0.189832 | + | 0.134231i | ||||
\(445\) | 3.95811 | − | 6.24803i | 0.187633 | − | 0.296185i | ||||
\(446\) | 17.3459i | 0.821350i | ||||||||
\(447\) | −27.2568 | − | 4.67652i | −1.28920 | − | 0.221192i | ||||
\(448\) | −3.59604 | + | 3.59604i | −0.169897 | + | 0.169897i | ||||
\(449\) | 10.0174 | 0.472748 | 0.236374 | − | 0.971662i | \(-0.424041\pi\) | ||||
0.236374 | + | 0.971662i | \(0.424041\pi\) | |||||||
\(450\) | 11.6275 | + | 9.47630i | 0.548128 | + | 0.446717i | ||||
\(451\) | 17.7764 | 0.837056 | ||||||||
\(452\) | 2.23239 | − | 2.23239i | 0.105003 | − | 0.105003i | ||||
\(453\) | 17.5839 | + | 3.01691i | 0.826161 | + | 0.141747i | ||||
\(454\) | − | 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 | 0.00386099 | − | 0.999993i | \(-0.498771\pi\) |
−0.999993 | + | 0.00386099i | \(0.998771\pi\) | |||||||
\(458\) | −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 | \(0.806613\pi\) | |||||||
\(462\) | 2.48953 | − | 14.5100i | 0.115823 | − | 0.675068i | ||||
\(463\) | 8.63306 | − | 8.63306i | 0.401212 | − | 0.401212i | −0.477448 | − | 0.878660i | \(-0.658438\pi\) |
0.878660 | + | 0.477448i | \(0.158438\pi\) | |||||||
\(464\) | −10.0205 | −0.465190 | ||||||||
\(465\) | −2.59604 | + | 2.87412i | −0.120388 | + | 0.133284i | ||||
\(466\) | 27.3563 | 1.26726 | ||||||||
\(467\) | 21.3541 | − | 21.3541i | 0.988150 | − | 0.988150i | −0.0117808 | − | 0.999931i | \(-0.503750\pi\) |
0.999931 | + | 0.0117808i | \(0.00375002\pi\) | |||||||
\(468\) | 1.31997 | + | 2.76380i | 0.0610157 | + | 0.127757i | ||||
\(469\) | 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 | ||||||||
\(477\) | −0.348317 | − | 0.729318i | −0.0159483 | − | 0.0333932i | ||||
\(478\) | 6.27003 | − | 6.27003i | 0.286784 | − | 0.286784i | ||||
\(479\) | 7.69589 | 0.351634 | 0.175817 | − | 0.984423i | \(-0.443743\pi\) | ||||
0.175817 | + | 0.984423i | \(0.443743\pi\) | |||||||
\(480\) | 0.196635 | + | 3.86799i | 0.00897511 | + | 0.176549i | ||||
\(481\) | 2.88767 | 0.131666 | ||||||||
\(482\) | 4.93494 | − | 4.93494i | 0.224780 | − | 0.224780i | ||||
\(483\) | 6.34113 | − | 36.9588i | 0.288531 | − | 1.68168i | ||||
\(484\) | − | 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 | 0.442400 | − | 0.896818i | \(-0.354127\pi\) |
−0.896818 | + | 0.442400i | \(0.854127\pi\) | |||||||
\(488\) | 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 | \(-0.0885459\pi\) | |||||||
\(492\) | −18.1566 | − | 3.11519i | −0.818564 | − | 0.140443i | ||||
\(493\) | −50.7501 | + | 50.7501i | −2.28567 | + | 2.28567i | ||||
\(494\) | −7.48169 | −0.336617 | ||||||||
\(495\) | −6.92955 | − | 8.81393i | −0.311460 | − | 0.396157i | ||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −4.77629 | + | 4.77629i | −0.214246 | + | 0.214246i | ||||
\(498\) | −17.7930 | − | 3.05279i | −0.797323 | − | 0.136799i | ||||
\(499\) | − | 29.7110i | − | 1.33005i | −0.746822 | − | 0.665024i | \(-0.768421\pi\) | ||
0.746822 | − | 0.665024i | \(-0.231579\pi\) | |||||||
\(500\) | 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 | \(-0.221646\pi\) |
−0.641400 | + | 0.767207i | \(0.721646\pi\) | |||||||
\(504\) | −5.08557 | + | 14.3842i | −0.226529 | + | 0.640721i | ||||
\(505\) | 17.8877 | + | 11.3318i | 0.795991 | + | 0.504259i | ||||
\(506\) | 7.11519i | 0.316309i | ||||||||
\(507\) | −3.50232 | + | 20.4130i | −0.155544 | + | 0.906574i | ||||
\(508\) | −9.51384 | + | 9.51384i | −0.422108 | + | 0.422108i | ||||
\(509\) | −10.2585 | −0.454700 | −0.227350 | − | 0.973813i | \(-0.573006\pi\) | ||||
−0.227350 | + | 0.973813i | \(0.573006\pi\) | |||||||
\(510\) | 20.5858 | + | 18.5940i | 0.911554 | + | 0.823357i | ||||
\(511\) | −3.05595 | −0.135187 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 18.5809 | − | 33.2373i | 0.820368 | − | 1.46746i | ||||
\(514\) | 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 | \(-0.126649\pi\) | |||||||
\(522\) | −27.1266 | + | 12.9554i | −1.18730 | + | 0.567044i | ||||
\(523\) | 8.57689 | − | 8.57689i | 0.375041 | − | 0.375041i | −0.494268 | − | 0.869309i | \(-0.664564\pi\) |
0.869309 | + | 0.494268i | \(0.164564\pi\) | |||||||
\(524\) | −4.47704 | −0.195581 | ||||||||
\(525\) | 21.6500 | − | 38.3537i | 0.944882 | − | 1.67389i | ||||
\(526\) | 1.73598 | 0.0756922 | ||||||||
\(527\) | −5.06462 | + | 5.06462i | −0.220618 | + | 0.220618i | ||||
\(528\) | 0.489528 | − | 2.85318i | 0.0213040 | − | 0.124169i | ||||
\(529\) | − | 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 | ||||||||
\(537\) | 28.3112 | + | 4.85743i | 1.22172 | + | 0.209613i | ||||
\(538\) | −0.200753 | + | 0.200753i | −0.00865508 | + | 0.00865508i | ||||
\(539\) | −31.5267 | −1.35795 | ||||||||
\(540\) | 5.53321 | + | 10.2168i | 0.238111 | + | 0.439662i | ||||
\(541\) | −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 | ||||
\(543\) | 3.19589 | + | 0.548327i | 0.137149 | + | 0.0235310i | ||||
\(544\) | 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 | 0.384669 | − | 0.923055i | \(-0.374316\pi\) |
−0.923055 | + | 0.384669i | \(0.874316\pi\) | |||||||
\(548\) | −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 | ||||||
\(552\) | 1.24689 | − | 7.26739i | 0.0530711 | − | 0.309321i | ||||
\(553\) | 5.03120 | − | 5.03120i | 0.213948 | − | 0.213948i | ||||
\(554\) | 16.0486 | 0.681841 | ||||||||
\(555\) | 10.9403 | − | 0.556167i | 0.464391 | − | 0.0236080i | ||||
\(556\) | 8.18340 | 0.347054 | ||||||||
\(557\) | 12.0399 | − | 12.0399i | 0.510146 | − | 0.510146i | −0.404425 | − | 0.914571i | \(-0.632528\pi\) |
0.914571 | + | 0.404425i | \(0.132528\pi\) | |||||||
\(558\) | −2.70711 | + | 1.29289i | −0.114601 | + | 0.0547325i | ||||
\(559\) | − | 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 | \(-0.0285693\pi\) |
−0.0896326 | + | 0.995975i | \(0.528569\pi\) | |||||||
\(564\) | 2.63591 | + | 3.72774i | 0.110992 | + | 0.156966i | ||||
\(565\) | −6.88818 | + | 1.54548i | −0.289788 | + | 0.0650187i | ||||
\(566\) | 27.6774i | 1.16337i | ||||||||
\(567\) | 4.83000 | + | 45.5145i | 0.202841 | + | 1.91143i | ||||
\(568\) | −0.939185 | + | 0.939185i | −0.0394073 | + | 0.0394073i | ||||
\(569\) | −1.35317 | −0.0567280 | −0.0283640 | − | 0.999598i | \(-0.509030\pi\) | ||||
−0.0283640 | + | 0.999598i | \(0.509030\pi\) | |||||||
\(570\) | −28.3454 | + | 1.44098i | −1.18726 | + | 0.0603561i | ||||
\(571\) | −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 | ||||
\(573\) | 5.10892 | − | 29.7770i | 0.213428 | − | 1.24395i | ||||
\(574\) | 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 | −0.990014 | − | 0.140967i | \(-0.954979\pi\) |
−0.140967 | − | 0.990014i | \(-0.545021\pi\) | |||||||
\(578\) | 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 | ||||||||
\(582\) | −14.3997 | − | 2.47060i | −0.596887 | − | 0.102410i | ||||
\(583\) | 0.318394 | − | 0.318394i | 0.0131865 | − | 0.0131865i | ||||
\(584\) | −0.600906 | −0.0248657 | ||||||||
\(585\) | 0.813928 | − | 6.80016i | 0.0336518 | − | 0.281152i | ||||
\(586\) | 10.3560 | 0.427804 | ||||||||
\(587\) | −31.6919 | + | 31.6919i | −1.30806 | + | 1.30806i | −0.385251 | + | 0.922812i | \(0.625885\pi\) |
−0.922812 | + | 0.385251i | \(0.874115\pi\) | |||||||
\(588\) | 32.2011 | + | 5.52484i | 1.32795 | + | 0.227841i | ||||
\(589\) | − | 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 | \(-0.222065\pi\) |
−0.642410 | + | 0.766361i | \(0.722065\pi\) | |||||||
\(594\) | −2.36365 | − | 8.35677i | −0.0969818 | − | 0.342882i | ||||
\(595\) | 43.5876 | − | 68.8047i | 1.78692 | − | 2.82072i | ||||
\(596\) | 15.9667i | 0.654020i | ||||||||
\(597\) | 7.08355 | − | 41.2860i | 0.289910 | − | 1.68972i | ||||
\(598\) | −3.07330 | + | 3.07330i | −0.125677 | + | 0.125677i | ||||
\(599\) | 45.0422 | 1.84037 | 0.920187 | − | 0.391479i | \(-0.128037\pi\) | ||||
0.920187 | + | 0.391479i | \(0.128037\pi\) | |||||||
\(600\) | 4.25714 | − | 7.54167i | 0.173797 | − | 0.307887i | ||||
\(601\) | −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 | ||||
\(603\) | 2.50920 | + | 5.25385i | 0.102182 | + | 0.213953i | ||||
\(604\) | − | 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 | −0.905126 | − | 0.425144i | \(-0.860223\pi\) |
−0.425144 | − | 0.905126i | \(-0.639777\pi\) | |||||||
\(608\) | −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 | ||||||
\(612\) | 9.26029 | + | 19.3895i | 0.374325 | + | 0.783776i | ||||
\(613\) | 6.91802 | − | 6.91802i | 0.279416 | − | 0.279416i | −0.553460 | − | 0.832876i | \(-0.686693\pi\) |
0.832876 | + | 0.553460i | \(0.186693\pi\) | |||||||
\(614\) | −26.4961 | −1.06929 | ||||||||
\(615\) | 30.5689 | + | 27.6112i | 1.23266 | + | 1.11339i | ||||
\(616\) | −8.49978 | −0.342466 | ||||||||
\(617\) | −24.9415 | + | 24.9415i | −1.00411 | + | 1.00411i | −0.00411392 | + | 0.999992i | \(0.501310\pi\) |
−0.999992 | + | 0.00411392i | \(0.998690\pi\) | |||||||
\(618\) | −0.801478 | + | 4.67135i | −0.0322402 | + | 0.187909i | ||||
\(619\) | 25.7810i | 1.03623i | 0.855312 | + | 0.518113i | \(0.173365\pi\) | ||||
−0.855312 | + | 0.518113i | \(0.826635\pi\) | |||||||
\(620\) | 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 | ||||||
\(627\) | 20.9087 | + | 3.58736i | 0.835013 | + | 0.143266i | ||||
\(628\) | 4.58377 | − | 4.58377i | 0.182912 | − | 0.182912i | ||||
\(629\) | 20.2585 | 0.807759 | ||||||||
\(630\) | 26.8189 | − | 21.0851i | 1.06849 | − | 0.840052i | ||||
\(631\) | 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 | ||||
\(633\) | −24.9253 | − | 4.27651i | −0.990692 | − | 0.169976i | ||||
\(634\) | − | 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 | \(0.789385\pi\) | |||||||
\(642\) | 0.0225211 | − | 0.131263i | 0.000888838 | − | 0.00518053i | ||||
\(643\) | −6.93380 | + | 6.93380i | −0.273442 | + | 0.273442i | −0.830484 | − | 0.557042i | \(-0.811936\pi\) |
0.557042 | + | 0.830484i | \(0.311936\pi\) | |||||||
\(644\) | −21.6500 | −0.853128 | ||||||||
\(645\) | −1.47060 | − | 28.9281i | −0.0579048 | − | 1.13904i | ||||
\(646\) | −52.4880 | −2.06511 | ||||||||
\(647\) | 16.5241 | − | 16.5241i | 0.649629 | − | 0.649629i | −0.303274 | − | 0.952903i | \(-0.598080\pi\) |
0.952903 | + | 0.303274i | \(0.0980798\pi\) | |||||||
\(648\) | 0.949747 | + | 8.94975i | 0.0373096 | + | 0.351579i | ||||
\(649\) | − | 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 | \(-0.255488\pi\) |
−0.719192 | + | 0.694811i | \(0.755488\pi\) | |||||||
\(654\) | −6.07974 | − | 8.59806i | −0.237737 | − | 0.336211i | ||||
\(655\) | 8.45683 | + | 5.35739i | 0.330436 | + | 0.209330i | ||||
\(656\) | 10.6359i | 0.415263i | ||||||||
\(657\) | −1.62672 | + | 0.776907i | −0.0634643 | + | 0.0303100i | ||||
\(658\) | 9.47884 | − | 9.47884i | 0.369524 | − | 0.369524i | ||||
\(659\) | 3.37145 | 0.131333 | 0.0656665 | − | 0.997842i | \(-0.479083\pi\) | ||||
0.0656665 | + | 0.997842i | \(0.479083\pi\) | |||||||
\(660\) | −4.33890 | + | 4.80368i | −0.168891 | + | 0.186983i | ||||
\(661\) | −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 | ||||
\(663\) | 2.14177 | − | 12.4832i | 0.0831795 | − | 0.484806i | ||||
\(664\) | 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 | ||||||||
\(672\) | 8.68161 | + | 1.48953i | 0.334900 | + | 0.0574598i | ||||
\(673\) | 29.1402 | − | 29.1402i | 1.12327 | − | 1.12327i | 0.132026 | − | 0.991246i | \(-0.457852\pi\) |
0.991246 | − | 0.132026i | \(-0.0421482\pi\) | |||||||
\(674\) | −13.4430 | −0.517803 | ||||||||
\(675\) | 1.77396 | − | 25.9201i | 0.0682798 | − | 0.997666i | ||||
\(676\) | 11.9577 | 0.459911 | ||||||||
\(677\) | 19.7632 | − | 19.7632i | 0.759560 | − | 0.759560i | −0.216683 | − | 0.976242i | \(-0.569524\pi\) |
0.976242 | + | 0.216683i | \(0.0695237\pi\) | |||||||
\(678\) | −5.38946 | − | 0.924685i | −0.206981 | − | 0.0355123i | ||||
\(679\) | 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 | \(-0.444422\pi\) |
−0.984796 | + | 0.173717i | \(0.944422\pi\) | |||||||
\(684\) | −20.7273 | − | 7.32821i | −0.792528 | − | 0.280201i | ||||
\(685\) | 2.97590 | + | 13.2636i | 0.113703 | + | 0.506776i | ||||
\(686\) | − | 60.3300i | − | 2.30341i | ||||||
\(687\) | −3.63166 | + | 21.1669i | −0.138557 | + | 0.807567i | ||||
\(688\) | 5.28834 | − | 5.28834i | 0.201616 | − | 0.201616i | ||||
\(689\) | 0.275051 | 0.0104786 | ||||||||
\(690\) | −11.0517 | + | 12.2355i | −0.420731 | + | 0.465799i | ||||
\(691\) | −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 | ||||
\(693\) | −23.0098 | + | 10.9893i | −0.874071 | + | 0.417449i | ||||
\(694\) | − | 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 | \(-0.156572\pi\) | |||||||
\(702\) | 2.58864 | − | 4.63053i | 0.0977018 | − | 0.174768i | ||||
\(703\) | −14.6564 | + | 14.6564i | −0.552777 | + | 0.552777i | ||||
\(704\) | −1.67135 | −0.0629915 | ||||||||
\(705\) | −0.518312 | − | 10.1957i | −0.0195208 | − | 0.383991i | ||||
\(706\) | −5.58535 | −0.210207 | ||||||||
\(707\) | 34.0535 | − | 34.0535i | 1.28071 | − | 1.28071i | ||||
\(708\) | −0.881221 | + | 5.13613i | −0.0331183 | + | 0.193028i | ||||
\(709\) | − | 45.1020i | − | 1.69384i | −0.531718 | − | 0.846921i | \(-0.678453\pi\) | ||
0.531718 | − | 0.846921i | \(-0.321547\pi\) | |||||||
\(710\) | 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 | ||||||
\(717\) | −15.1372 | − | 2.59713i | −0.565309 | − | 0.0969916i | ||||
\(718\) | 5.61698 | − | 5.61698i | 0.209624 | − | 0.209624i | ||||
\(719\) | 21.5174 | 0.802465 | 0.401232 | − | 0.915976i | \(-0.368582\pi\) | ||||
0.401232 | + | 0.915976i | \(0.368582\pi\) | |||||||
\(720\) | 5.27353 | − | 4.14607i | 0.196533 | − | 0.154515i | ||||
\(721\) | 13.9162 | 0.518267 | ||||||||
\(722\) | 24.5385 | − | 24.5385i | 0.913227 | − | 0.913227i | ||||
\(723\) | −11.9140 | − | 2.04412i | −0.443086 | − | 0.0760216i | ||||
\(724\) | − | 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 | 0.209458 | − | 0.977818i | \(-0.432830\pi\) |
−0.977818 | + | 0.209458i | \(0.932830\pi\) | |||||||
\(728\) | −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 | ||||||
\(732\) | 2.88122 | − | 16.7930i | 0.106493 | − | 0.620687i | ||||
\(733\) | −10.2304 | + | 10.2304i | −0.377867 | + | 0.377867i | −0.870332 | − | 0.492465i | \(-0.836096\pi\) |
0.492465 | + | 0.870332i | \(0.336096\pi\) | |||||||
\(734\) | 1.47283 | 0.0543632 | ||||||||
\(735\) | −54.2146 | − | 48.9691i | −1.99973 | − | 1.80625i | ||||
\(736\) | −4.25714 | −0.156920 | ||||||||
\(737\) | −2.29364 | + | 2.29364i | −0.0844874 | + | 0.0844874i | ||||
\(738\) | 13.7511 | + | 28.7925i | 0.506185 | + | 1.05987i | ||||
\(739\) | 32.5957i | 1.19905i | 0.800355 | + | 0.599526i | \(0.204644\pi\) | ||||
−0.800355 | + | 0.599526i | \(0.795356\pi\) | |||||||
\(740\) | −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 | \(-0.0479407\pi\) |
−0.150041 | + | 0.988680i | \(0.547941\pi\) | |||||||
\(744\) | 1.00000 | + | 1.41421i | 0.0366618 | + | 0.0518476i | ||||
\(745\) | 19.1063 | − | 30.1599i | 0.699999 | − | 1.10497i | ||||
\(746\) | − | 6.36966i | − | 0.233210i | ||||||
\(747\) | 13.4757 | + | 28.2159i | 0.493049 | + | 1.03236i | ||||
\(748\) | −8.46478 | + | 8.46478i | −0.309503 | + | 0.309503i | ||||
\(749\) | −0.391039 | −0.0142883 | ||||||||
\(750\) | −17.0661 | + | 9.15146i | −0.623165 | + | 0.334164i | ||||
\(751\) | 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 | ||||
\(753\) | −5.00675 | + | 29.1815i | −0.182456 | + | 1.06343i | ||||
\(754\) | − | 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 | 0.870510 | − | 0.492151i | \(-0.163789\pi\) |
−0.492151 | + | 0.870510i | \(0.663789\pi\) | |||||||
\(758\) | −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 | \(0.921343\pi\) | |||||||
\(762\) | 22.9684 | + | 3.94076i | 0.832059 | + | 0.142759i | ||||
\(763\) | −21.8630 | + | 21.8630i | −0.791493 | + | 0.791493i | ||||
\(764\) | −17.4430 | −0.631064 | ||||||||
\(765\) | 5.71013 | − | 47.7067i | 0.206450 | − | 1.72484i | ||||
\(766\) | −3.68963 | −0.133312 | ||||||||
\(767\) | 2.17201 | − | 2.17201i | 0.0784268 | − | 0.0784268i | ||||
\(768\) | 1.70711 | + | 0.292893i | 0.0615999 | + | 0.0105689i | ||||
\(769\) | 37.0453i | 1.33589i | 0.744211 | + | 0.667945i | \(0.232826\pi\) | ||||
−0.744211 | + | 0.667945i | \(0.767174\pi\) | |||||||
\(770\) | 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 | \(-0.191198\pi\) |
−0.565193 | + | 0.824958i | \(0.691198\pi\) | |||||||
\(774\) | 7.47884 | − | 21.1533i | 0.268821 | − | 0.760341i | ||||
\(775\) | −2.13613 | − | 4.52072i | −0.0767320 | − | 0.162389i | ||||
\(776\) | 8.43516i | 0.302805i | ||||||||
\(777\) | 4.21302 | − | 24.5553i | 0.151141 | − | 0.880916i | ||||
\(778\) | 5.48795 | − | 5.48795i | 0.196753 | − | 0.196753i | ||||
\(779\) | −77.9422 | −2.79257 | ||||||||
\(780\) | −3.94900 | + | 0.200753i | −0.141397 | + | 0.00718812i | ||||
\(781\) | −2.21990 | −0.0794344 | ||||||||
\(782\) | −21.5608 | + | 21.5608i | −0.771013 | + | 0.771013i | ||||
\(783\) | 45.4483 | + | 25.4073i | 1.62419 | + | 0.907984i | ||||
\(784\) | − | 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 | 0.803511 | − | 0.595290i | \(-0.202963\pi\) |
−0.595290 | + | 0.803511i | \(0.702963\pi\) | |||||||
\(788\) | 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 | ||||||||
\(792\) | −4.52453 | + | 2.16088i | −0.160772 | + | 0.0767836i | ||||
\(793\) | −7.10156 | + | 7.10156i | −0.252184 | + | 0.252184i | ||||
\(794\) | −9.49934 | −0.337119 | ||||||||
\(795\) | 1.04207 | − | 0.0529751i | 0.0369584 | − | 0.00187883i | ||||
\(796\) | −24.1848 | −0.857206 | ||||||||
\(797\) | −0.330877 | + | 0.330877i | −0.0117203 | + | 0.0117203i | −0.712943 | − | 0.701222i | \(-0.752638\pi\) |
0.701222 | + | 0.712943i | \(0.252638\pi\) | |||||||
\(798\) | −10.9156 | + | 63.6206i | −0.386407 | + | 2.25215i | ||||
\(799\) | − | 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 | ||||||
\(807\) | 0.484661 | + | 0.0831547i | 0.0170609 | + | 0.00292718i | ||||
\(808\) | 6.69611 | − | 6.69611i | 0.235568 | − | 0.235568i | ||||
\(809\) | −18.3644 | −0.645657 | −0.322829 | − | 0.946457i | \(-0.604634\pi\) | ||||
−0.322829 | + | 0.946457i | \(0.604634\pi\) | |||||||
\(810\) | 8.91557 | − | 18.0420i | 0.313261 | − | 0.633930i | ||||
\(811\) | 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 | ||||
\(813\) | 35.9668 | + | 6.17092i | 1.26141 | + | 0.216424i | ||||
\(814\) | 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 | \(0.964177\pi\) | |||||||
\(822\) | −1.78053 | + | 10.3777i | −0.0621032 | + | 0.361964i | ||||
\(823\) | 1.00359 | − | 1.00359i | 0.0349831 | − | 0.0349831i | −0.689399 | − | 0.724382i | \(-0.742125\pi\) |
0.724382 | + | 0.689399i | \(0.242125\pi\) | |||||||
\(824\) | 2.73642 | 0.0953276 | ||||||||
\(825\) | 13.9441 | − | 3.88174i | 0.485472 | − | 0.135145i | ||||
\(826\) | 15.3008 | 0.532384 | ||||||||
\(827\) | −17.7824 | + | 17.7824i | −0.618354 | + | 0.618354i | −0.945109 | − | 0.326755i | \(-0.894045\pi\) |
0.326755 | + | 0.945109i | \(0.394045\pi\) | |||||||
\(828\) | −11.5245 | + | 5.50403i | −0.400505 | + | 0.191278i | ||||
\(829\) | − | 18.3026i | − | 0.635676i | −0.948145 | − | 0.317838i | \(-0.897043\pi\) | ||
0.948145 | − | 0.317838i | \(-0.102957\pi\) | |||||||
\(830\) | 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 | ||||||
\(837\) | 4.53553 | + | 2.53553i | 0.156771 | + | 0.0876409i | ||||
\(838\) | −5.04251 | + | 5.04251i | −0.174191 | + | 0.174191i | ||||
\(839\) | −30.9423 | −1.06825 | −0.534123 | − | 0.845407i | \(-0.679358\pi\) | ||||
−0.534123 | + | 0.845407i | \(0.679358\pi\) | |||||||
\(840\) | −14.6165 | − | 13.2023i | −0.504319 | − | 0.455524i | ||||
\(841\) | 71.4105 | 2.46243 | ||||||||
\(842\) | 3.29258 | − | 3.29258i | 0.113470 | − | 0.113470i | ||||
\(843\) | 5.01691 | − | 29.2407i | 0.172792 | − | 1.00710i | ||||
\(844\) | 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 | ||||||||
\(852\) | 2.26739 | + | 0.389023i | 0.0776796 | + | 0.0133277i | ||||
\(853\) | −39.7674 | + | 39.7674i | −1.36161 | + | 1.36161i | −0.489739 | + | 0.871869i | \(0.662908\pi\) |
−0.871869 | + | 0.489739i | \(0.837092\pi\) | |||||||
\(854\) | −50.0272 | −1.71190 | ||||||||
\(855\) | 30.3833 | + | 38.6455i | 1.03909 | + | 1.32165i | ||||
\(856\) | −0.0768919 | −0.00262811 | ||||||||
\(857\) | −13.3607 | + | 13.3607i | −0.456392 | + | 0.456392i | −0.897469 | − | 0.441077i | \(-0.854597\pi\) |
0.441077 | + | 0.897469i | \(0.354597\pi\) | |||||||
\(858\) | 2.91294 | + | 0.499781i | 0.0994460 | + | 0.0170622i | ||||
\(859\) | 53.6202i | 1.82950i | 0.404023 | + | 0.914749i | \(0.367612\pi\) | ||||
−0.404023 | + | 0.914749i | \(0.632388\pi\) | |||||||
\(860\) | −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 | \(-0.117933\pi\) |
−0.362078 | + | 0.932148i | \(0.617933\pi\) | |||||||
\(864\) | 5.00000 | − | 1.41421i | 0.170103 | − | 0.0481125i | ||||
\(865\) | −19.9096 | + | 4.46705i | −0.676948 | + | 0.151884i | ||||
\(866\) | − | 33.8243i | − | 1.14940i | ||||||
\(867\) | 10.0465 | − | 58.5552i | 0.341196 | − | 1.98864i | ||||
\(868\) | 3.59604 | − | 3.59604i | 0.122058 | − | 0.122058i | ||||
\(869\) | 2.33838 | 0.0793241 | ||||||||
\(870\) | −1.97038 | − | 38.7592i | −0.0668022 | − | 1.31406i | ||||
\(871\) | −1.98141 | −0.0671375 | ||||||||
\(872\) | −4.29903 | + | 4.29903i | −0.145583 | + | 0.145583i | ||||
\(873\) | 10.9058 | + | 22.8349i | 0.369104 | + | 0.772843i | ||||
\(874\) | − | 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 | 0.00858855 | − | 0.999963i | \(-0.497266\pi\) |
−0.999963 | + | 0.00858855i | \(0.997266\pi\) | |||||||
\(878\) | 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 | \(0.846183\pi\) | |||||||
\(882\) | −24.3878 | − | 51.0641i | −0.821181 | − | 1.71942i | ||||
\(883\) | −13.0070 | + | 13.0070i | −0.437719 | + | 0.437719i | −0.891244 | − | 0.453525i | \(-0.850166\pi\) |
0.453525 | + | 0.891244i | \(0.350166\pi\) | |||||||
\(884\) | −7.31247 | −0.245945 | ||||||||
\(885\) | 7.81064 | − | 8.64730i | 0.262552 | − | 0.290676i | ||||
\(886\) | 19.9294 | 0.669542 | ||||||||
\(887\) | −22.1276 | + | 22.1276i | −0.742973 | + | 0.742973i | −0.973149 | − | 0.230176i | \(-0.926070\pi\) |
0.230176 | + | 0.973149i | \(0.426070\pi\) | |||||||
\(888\) | 0.828427 | − | 4.82843i | 0.0278002 | − | 0.162031i | ||||
\(889\) | − | 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 | ||||||
\(897\) | 7.41960 | + | 1.27300i | 0.247733 | + | 0.0425043i | ||||
\(898\) | −7.08334 | + | 7.08334i | −0.236374 | + | 0.236374i | ||||
\(899\) | 10.0205 | 0.334203 | ||||||||
\(900\) | −14.9227 | + | 1.52116i | −0.497422 | + | 0.0507054i | ||||
\(901\) | 1.92963 | 0.0642852 | ||||||||
\(902\) | −12.5698 | + | 12.5698i | −0.418528 | + | 0.418528i | ||||
\(903\) | −64.9283 | − | 11.1399i | −2.16068 | − | 0.370714i | ||||
\(904\) | 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 | 0.704644 | − | 0.709561i | \(-0.251107\pi\) |
−0.709561 | + | 0.704644i | \(0.751107\pi\) | |||||||
\(908\) | 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 | \(-0.0968857\pi\) | |||||||
\(912\) | −2.14638 | + | 12.5100i | −0.0710738 | + | 0.414249i | ||||
\(913\) | −12.3180 | + | 12.3180i | −0.407667 | + | 0.407667i | ||||
\(914\) | 30.1155 | 0.996132 | ||||||||
\(915\) | −25.5375 | + | 28.2730i | −0.844244 | + | 0.934678i | ||||
\(916\) | 12.3993 | 0.409684 | ||||||||
\(917\) | 16.0996 | − | 16.0996i | 0.531657 | − | 0.531657i | ||||
\(918\) | 18.1607 | − | 32.4856i | 0.599391 | − | 1.07218i | ||||
\(919\) | − | 48.1668i | − | 1.58888i | −0.607344 | − | 0.794439i | \(-0.707765\pi\) | ||
0.607344 | − | 0.794439i | \(-0.292235\pi\) | |||||||
\(920\) | 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 | ||||||||
\(927\) | 7.40777 | − | 3.53789i | 0.243303 | − | 0.116200i | ||||
\(928\) | 7.08557 | − | 7.08557i | 0.232595 | − | 0.232595i | ||||
\(929\) | 44.8497 | 1.47147 | 0.735735 | − | 0.677270i | \(-0.236837\pi\) | ||||
0.735735 | + | 0.677270i | \(0.236837\pi\) | |||||||
\(930\) | −0.196635 | − | 3.86799i | −0.00644791 | − | 0.126836i | ||||
\(931\) | 138.232 | 4.53037 | ||||||||
\(932\) | −19.3438 | + | 19.3438i | −0.633629 | + | 0.633629i | ||||
\(933\) | −0.942251 | + | 5.49184i | −0.0308479 | + | 0.179795i | ||||
\(934\) | 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 | 0.0142928 | − | 0.999898i | \(-0.495450\pi\) |
−0.999898 | + | 0.0142928i | \(0.995450\pi\) | |||||||
\(938\) | −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 | \(0.678070\pi\) | |||||||
\(942\) | −11.0662 | − | 1.89866i | −0.360556 | − | 0.0618617i | ||||
\(943\) | −32.0168 | + | 32.0168i | −1.04261 | + | 1.04261i | ||||
\(944\) | 3.00868 | 0.0979240 | ||||||||
\(945\) | −56.6377 | − | 16.8425i | −1.84243 | − | 0.547886i | ||||
\(946\) | 12.4998 | 0.406403 | ||||||||
\(947\) | 5.52445 | − | 5.52445i | 0.179521 | − | 0.179521i | −0.611626 | − | 0.791147i | \(-0.709484\pi\) |
0.791147 | + | 0.611626i | \(0.209484\pi\) | |||||||
\(948\) | −2.38840 | − | 0.409785i | −0.0775717 | − | 0.0133092i | ||||
\(949\) | − | 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 | \(-0.195266\pi\) |
−0.575688 | + | 0.817670i | \(0.695266\pi\) | |||||||
\(954\) | 0.762002 | + | 0.269409i | 0.0246707 | + | 0.00872242i | ||||
\(955\) | 32.9486 | + | 20.8728i | 1.06619 | + | 0.675430i | ||||
\(956\) | 8.86716i | 0.286784i | ||||||||
\(957\) | −4.90532 | + | 28.5903i | −0.158566 | + | 0.924193i | ||||
\(958\) | −5.44182 | + | 5.44182i | −0.175817 | + | 0.175817i | ||||
\(959\) | 30.9158 | 0.998323 | ||||||||
\(960\) | −2.87412 | − | 2.59604i | −0.0927619 | − | 0.0837868i | ||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | −2.04189 | + | 2.04189i | −0.0658331 | + | 0.0658331i | ||||
\(963\) | −0.208155 | + | 0.0994131i | −0.00670769 | + | 0.00320354i | ||||
\(964\) | 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 | 0.739921 | − | 0.672694i | \(-0.234863\pi\) |
−0.672694 | + | 0.739921i | \(0.734863\pi\) | |||||||
\(968\) | 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 | \(0.954576\pi\) | |||||||
\(972\) | 11.7071 | − | 10.2929i | 0.375506 | − | 0.330145i | ||||
\(973\) | −29.4278 | + | 29.4278i | −0.943413 | + | 0.943413i | ||||
\(974\) | 14.1819 | 0.454418 | ||||||||
\(975\) | 7.69962 | + | 4.34630i | 0.246585 | + | 0.139193i | ||||
\(976\) | −9.83710 | −0.314878 | ||||||||
\(977\) | 34.8184 | − | 34.8184i | 1.11394 | − | 1.11394i | 0.121328 | − | 0.992612i | \(-0.461285\pi\) |
0.992612 | − | 0.121328i | \(-0.0387153\pi\) | |||||||
\(978\) | −1.27808 | + | 7.44922i | −0.0408686 | + | 0.238200i | ||||
\(979\) | − | 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 | \(-0.217987\pi\) |
−0.632539 | + | 0.774528i | \(0.717987\pi\) | |||||||
\(984\) | 15.0414 | − | 10.6359i | 0.479504 | − | 0.339060i | ||||
\(985\) | −1.86760 | − | 8.32388i | −0.0595066 | − | 0.265221i | ||||
\(986\) | − | 71.7715i | − | 2.28567i | ||||||
\(987\) | −22.8839 | − | 3.92626i | −0.728404 | − | 0.124974i | ||||
\(988\) | 5.29035 | − | 5.29035i | 0.168309 | − | 0.168309i | ||||
\(989\) | 31.8385 | 1.01240 | ||||||||
\(990\) | 11.1323 | + | 1.33245i | 0.353808 | + | 0.0423482i | ||||
\(991\) | −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 | ||||
\(993\) | −19.6929 | − | 3.37877i | −0.624936 | − | 0.107222i | ||||
\(994\) | − | 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 | 0.747787 | − | 0.663938i | \(-0.231116\pi\) |
−0.663938 | + | 0.747787i | \(0.731116\pi\) | |||||||
\(998\) | 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.f.497.1 | yes | 8 | |
3.2 | odd | 2 | 930.2.j.c.497.4 | ✓ | 8 | ||
5.3 | odd | 4 | 930.2.j.c.683.4 | yes | 8 | ||
15.8 | even | 4 | inner | 930.2.j.f.683.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.j.c.497.4 | ✓ | 8 | 3.2 | odd | 2 | ||
930.2.j.c.683.4 | yes | 8 | 5.3 | odd | 4 | ||
930.2.j.f.497.1 | yes | 8 | 1.1 | even | 1 | trivial | |
930.2.j.f.683.1 | yes | 8 | 15.8 | even | 4 | inner |