Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,2,Mod(316,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.316");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.j (of order \(6\), degree \(2\), not 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: | \(4.04841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.17213603549184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 316.5 | ||
Root | \(1.07992 - 0.623490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.316 |
Dual form | 507.2.j.i.361.5 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.04113 | + | 1.17845i | 1.44330 | + | 0.833289i | 0.998068 | − | 0.0621278i | \(-0.0197886\pi\) |
0.445230 | + | 0.895416i | \(0.353122\pi\) | |||||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | 1.77748 | + | 3.07868i | 0.888740 | + | 1.53934i | ||||
\(5\) | − | 3.69202i | − | 1.65112i | −0.564313 | − | 0.825561i | \(-0.690859\pi\) | ||
0.564313 | − | 0.825561i | \(-0.309141\pi\) | |||||||
\(6\) | 2.04113 | − | 1.17845i | 0.833289 | − | 0.481099i | ||||
\(7\) | −0.694498 | + | 0.400969i | −0.262496 | + | 0.151552i | −0.625473 | − | 0.780246i | \(-0.715094\pi\) |
0.362977 | + | 0.931798i | \(0.381760\pi\) | |||||||
\(8\) | 3.66487i | 1.29573i | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 4.35086 | − | 7.53590i | 1.37586 | − | 2.38306i | ||||
\(11\) | 2.46891 | + | 1.42543i | 0.744405 | + | 0.429783i | 0.823669 | − | 0.567071i | \(-0.191924\pi\) |
−0.0792636 | + | 0.996854i | \(0.525257\pi\) | |||||||
\(12\) | 3.55496 | 1.02623 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.89008 | −0.505146 | ||||||||
\(15\) | −3.19738 | − | 1.84601i | −0.825561 | − | 0.476638i | ||||
\(16\) | −0.763906 | + | 1.32312i | −0.190976 | + | 0.330781i | ||||
\(17\) | 1.46950 | + | 2.54525i | 0.356406 | + | 0.617314i | 0.987358 | − | 0.158509i | \(-0.0506686\pi\) |
−0.630951 | + | 0.775822i | \(0.717335\pi\) | |||||||
\(18\) | − | 2.35690i | − | 0.555526i | ||||||
\(19\) | 2.11747 | − | 1.22252i | 0.485781 | − | 0.280466i | −0.237042 | − | 0.971499i | \(-0.576178\pi\) |
0.722822 | + | 0.691034i | \(0.242844\pi\) | |||||||
\(20\) | 11.3666 | − | 6.56249i | 2.54164 | − | 1.46742i | ||||
\(21\) | 0.801938i | 0.174997i | ||||||||
\(22\) | 3.35958 | + | 5.81897i | 0.716266 | + | 1.24061i | ||||
\(23\) | −3.89493 | + | 6.74621i | −0.812149 | + | 1.40668i | 0.0992087 | + | 0.995067i | \(0.468369\pi\) |
−0.911357 | + | 0.411616i | \(0.864964\pi\) | |||||||
\(24\) | 3.17387 | + | 1.83244i | 0.647864 | + | 0.374045i | ||||
\(25\) | −8.63102 | −1.72620 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.46891 | − | 1.42543i | −0.466581 | − | 0.269380i | ||||
\(29\) | −1.92543 | + | 3.33494i | −0.357543 | + | 0.619282i | −0.987550 | − | 0.157307i | \(-0.949719\pi\) |
0.630007 | + | 0.776590i | \(0.283052\pi\) | |||||||
\(30\) | −4.35086 | − | 7.53590i | −0.794354 | − | 1.37586i | ||||
\(31\) | − | 2.34481i | − | 0.421141i | −0.977579 | − | 0.210571i | \(-0.932468\pi\) | ||
0.977579 | − | 0.210571i | \(-0.0675322\pi\) | |||||||
\(32\) | 3.22929 | − | 1.86443i | 0.570862 | − | 0.329588i | ||||
\(33\) | 2.46891 | − | 1.42543i | 0.429783 | − | 0.248135i | ||||
\(34\) | 6.92692i | 1.18796i | ||||||||
\(35\) | 1.48039 | + | 2.56410i | 0.250231 | + | 0.433413i | ||||
\(36\) | 1.77748 | − | 3.07868i | 0.296247 | − | 0.513114i | ||||
\(37\) | −6.44760 | − | 3.72252i | −1.05998 | − | 0.611979i | −0.134552 | − | 0.990907i | \(-0.542960\pi\) |
−0.925426 | + | 0.378928i | \(0.876293\pi\) | |||||||
\(38\) | 5.76271 | 0.934835 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 13.5308 | 2.13941 | ||||||||
\(41\) | −0.736862 | − | 0.425428i | −0.115079 | − | 0.0664406i | 0.441356 | − | 0.897332i | \(-0.354498\pi\) |
−0.556434 | + | 0.830892i | \(0.687831\pi\) | |||||||
\(42\) | −0.945042 | + | 1.63686i | −0.145823 | + | 0.252573i | ||||
\(43\) | −0.807979 | − | 1.39946i | −0.123216 | − | 0.213416i | 0.797818 | − | 0.602898i | \(-0.205987\pi\) |
−0.921034 | + | 0.389482i | \(0.872654\pi\) | |||||||
\(44\) | 10.1347i | 1.52786i | ||||||||
\(45\) | −3.19738 | + | 1.84601i | −0.476638 | + | 0.275187i | ||||
\(46\) | −15.9001 | + | 9.17994i | −2.34435 | + | 1.35351i | ||||
\(47\) | 2.44504i | 0.356646i | 0.983972 | + | 0.178323i | \(0.0570672\pi\) | ||||
−0.983972 | + | 0.178323i | \(0.942933\pi\) | |||||||
\(48\) | 0.763906 | + | 1.32312i | 0.110260 | + | 0.190976i | ||||
\(49\) | −3.17845 | + | 5.50523i | −0.454064 | + | 0.786462i | ||||
\(50\) | −17.6171 | − | 10.1712i | −2.49143 | − | 1.43843i | ||||
\(51\) | 2.93900 | 0.411542 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.96077 | −1.36822 | −0.684109 | − | 0.729380i | \(-0.739809\pi\) | ||||
−0.684109 | + | 0.729380i | \(0.739809\pi\) | |||||||
\(54\) | −2.04113 | − | 1.17845i | −0.277763 | − | 0.160366i | ||||
\(55\) | 5.26271 | − | 9.11528i | 0.709624 | − | 1.22910i | ||||
\(56\) | −1.46950 | − | 2.54525i | −0.196370 | − | 0.340123i | ||||
\(57\) | − | 2.44504i | − | 0.323854i | ||||||
\(58\) | −7.86010 | + | 4.53803i | −1.03208 | + | 0.595873i | ||||
\(59\) | −4.66272 | + | 2.69202i | −0.607034 | + | 0.350471i | −0.771804 | − | 0.635861i | \(-0.780645\pi\) |
0.164770 | + | 0.986332i | \(0.447312\pi\) | |||||||
\(60\) | − | 13.1250i | − | 1.69443i | ||||||
\(61\) | 6.62833 | + | 11.4806i | 0.848671 | + | 1.46994i | 0.882394 | + | 0.470510i | \(0.155930\pi\) |
−0.0337232 | + | 0.999431i | \(0.510736\pi\) | |||||||
\(62\) | 2.76324 | − | 4.78607i | 0.350932 | − | 0.607832i | ||||
\(63\) | 0.694498 | + | 0.400969i | 0.0874986 | + | 0.0505173i | ||||
\(64\) | 11.8442 | 1.48052 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 6.71917 | 0.827072 | ||||||||
\(67\) | 12.4653 | + | 7.19687i | 1.52288 | + | 0.879237i | 0.999634 | + | 0.0270575i | \(0.00861373\pi\) |
0.523249 | + | 0.852180i | \(0.324720\pi\) | |||||||
\(68\) | −5.22401 | + | 9.04826i | −0.633505 | + | 1.09726i | ||||
\(69\) | 3.89493 | + | 6.74621i | 0.468894 | + | 0.812149i | ||||
\(70\) | 6.97823i | 0.834058i | ||||||||
\(71\) | −7.03644 | + | 4.06249i | −0.835072 | + | 0.482129i | −0.855586 | − | 0.517661i | \(-0.826803\pi\) |
0.0205142 | + | 0.999790i | \(0.493470\pi\) | |||||||
\(72\) | 3.17387 | − | 1.83244i | 0.374045 | − | 0.215955i | ||||
\(73\) | − | 11.8877i | − | 1.39135i | −0.718357 | − | 0.695674i | \(-0.755106\pi\) | ||
0.718357 | − | 0.695674i | \(-0.244894\pi\) | |||||||
\(74\) | −8.77359 | − | 15.1963i | −1.01991 | − | 1.76654i | ||||
\(75\) | −4.31551 | + | 7.47468i | −0.498312 | + | 0.863102i | ||||
\(76\) | 7.52751 | + | 4.34601i | 0.863465 | + | 0.498522i | ||||
\(77\) | −2.28621 | −0.260538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.40581 | 0.608202 | 0.304101 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304101 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(80\) | 4.88500 | + | 2.82036i | 0.546160 | + | 0.315325i | ||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −1.00269 | − | 1.73671i | −0.110728 | − | 0.191787i | ||||
\(83\) | − | 7.04892i | − | 0.773719i | −0.922139 | − | 0.386860i | \(-0.873560\pi\) | ||
0.922139 | − | 0.386860i | \(-0.126440\pi\) | |||||||
\(84\) | −2.46891 | + | 1.42543i | −0.269380 | + | 0.155527i | ||||
\(85\) | 9.39712 | − | 5.42543i | 1.01926 | − | 0.588470i | ||||
\(86\) | − | 3.80864i | − | 0.410696i | ||||||
\(87\) | 1.92543 | + | 3.33494i | 0.206427 | + | 0.357543i | ||||
\(88\) | −5.22401 | + | 9.04826i | −0.556882 | + | 0.964547i | ||||
\(89\) | −0.980069 | − | 0.565843i | −0.103887 | − | 0.0599793i | 0.447156 | − | 0.894456i | \(-0.352437\pi\) |
−0.551043 | + | 0.834477i | \(0.685770\pi\) | |||||||
\(90\) | −8.70171 | −0.917241 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −27.6926 | −2.88715 | ||||||||
\(93\) | −2.03067 | − | 1.17241i | −0.210571 | − | 0.121573i | ||||
\(94\) | −2.88135 | + | 4.99065i | −0.297189 | + | 0.514746i | ||||
\(95\) | −4.51357 | − | 7.81774i | −0.463083 | − | 0.802083i | ||||
\(96\) | − | 3.72886i | − | 0.380575i | ||||||
\(97\) | 5.14798 | − | 2.97219i | 0.522698 | − | 0.301780i | −0.215340 | − | 0.976539i | \(-0.569086\pi\) |
0.738038 | + | 0.674759i | \(0.235753\pi\) | |||||||
\(98\) | −12.9753 | + | 7.49127i | −1.31070 | + | 0.756733i | ||||
\(99\) | − | 2.85086i | − | 0.286522i | ||||||
\(100\) | −15.3415 | − | 26.5722i | −1.53415 | − | 2.65722i | ||||
\(101\) | 2.31282 | − | 4.00593i | 0.230134 | − | 0.398605i | −0.727713 | − | 0.685882i | \(-0.759417\pi\) |
0.957848 | + | 0.287277i | \(0.0927501\pi\) | |||||||
\(102\) | 5.99889 | + | 3.46346i | 0.593978 | + | 0.342934i | ||||
\(103\) | −1.20775 | −0.119003 | −0.0595016 | − | 0.998228i | \(-0.518951\pi\) | ||||
−0.0595016 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.96077 | 0.288942 | ||||||||
\(106\) | −20.3312 | − | 11.7383i | −1.97475 | − | 1.14012i | ||||
\(107\) | 4.76055 | − | 8.24552i | 0.460220 | − | 0.797124i | −0.538752 | − | 0.842465i | \(-0.681104\pi\) |
0.998972 | + | 0.0453402i | \(0.0144372\pi\) | |||||||
\(108\) | −1.77748 | − | 3.07868i | −0.171038 | − | 0.296247i | ||||
\(109\) | 1.78448i | 0.170922i | 0.996342 | + | 0.0854611i | \(0.0272363\pi\) | ||||
−0.996342 | + | 0.0854611i | \(0.972764\pi\) | |||||||
\(110\) | 21.4838 | − | 12.4037i | 2.04840 | − | 1.18264i | ||||
\(111\) | −6.44760 | + | 3.72252i | −0.611979 | + | 0.353326i | ||||
\(112\) | − | 1.22521i | − | 0.115771i | ||||||
\(113\) | −2.47554 | − | 4.28776i | −0.232879 | − | 0.403359i | 0.725775 | − | 0.687932i | \(-0.241481\pi\) |
−0.958654 | + | 0.284573i | \(0.908148\pi\) | |||||||
\(114\) | 2.88135 | − | 4.99065i | 0.269864 | − | 0.467417i | ||||
\(115\) | 24.9072 | + | 14.3802i | 2.32261 | + | 1.34096i | ||||
\(116\) | −13.6896 | −1.27105 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −12.6896 | −1.16817 | ||||||||
\(119\) | −2.04113 | − | 1.17845i | −0.187110 | − | 0.108028i | ||||
\(120\) | 6.76540 | − | 11.7180i | 0.617593 | − | 1.06970i | ||||
\(121\) | −1.43631 | − | 2.48777i | −0.130574 | − | 0.226161i | ||||
\(122\) | 31.2446i | 2.82875i | ||||||||
\(123\) | −0.736862 | + | 0.425428i | −0.0664406 | + | 0.0383595i | ||||
\(124\) | 7.21894 | − | 4.16786i | 0.648280 | − | 0.374285i | ||||
\(125\) | 13.4058i | 1.19905i | ||||||||
\(126\) | 0.945042 | + | 1.63686i | 0.0841910 | + | 0.145823i | ||||
\(127\) | 2.83513 | − | 4.91058i | 0.251577 | − | 0.435744i | −0.712383 | − | 0.701791i | \(-0.752384\pi\) |
0.963960 | + | 0.266047i | \(0.0857176\pi\) | |||||||
\(128\) | 17.7169 | + | 10.2289i | 1.56597 | + | 0.904112i | ||||
\(129\) | −1.61596 | −0.142277 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.2228 | 1.59213 | 0.796067 | − | 0.605208i | \(-0.206910\pi\) | ||||
0.796067 | + | 0.605208i | \(0.206910\pi\) | |||||||
\(132\) | 8.77688 | + | 5.06734i | 0.763930 | + | 0.441055i | ||||
\(133\) | −0.980386 | + | 1.69808i | −0.0850102 | + | 0.147242i | ||||
\(134\) | 16.9623 | + | 29.3795i | 1.46532 | + | 2.53800i | ||||
\(135\) | 3.69202i | 0.317759i | ||||||||
\(136\) | −9.32802 | + | 5.38553i | −0.799871 | + | 0.461806i | ||||
\(137\) | 8.18430 | − | 4.72521i | 0.699232 | − | 0.403702i | −0.107829 | − | 0.994169i | \(-0.534390\pi\) |
0.807061 | + | 0.590468i | \(0.201057\pi\) | |||||||
\(138\) | 18.3599i | 1.56290i | ||||||||
\(139\) | −2.00753 | − | 3.47715i | −0.170277 | − | 0.294928i | 0.768240 | − | 0.640162i | \(-0.221133\pi\) |
−0.938517 | + | 0.345234i | \(0.887799\pi\) | |||||||
\(140\) | −5.26271 | + | 9.11528i | −0.444780 | + | 0.770382i | ||||
\(141\) | 2.11747 | + | 1.22252i | 0.178323 | + | 0.102955i | ||||
\(142\) | −19.1497 | −1.60701 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.52781 | 0.127318 | ||||||||
\(145\) | 12.3127 | + | 7.10872i | 1.02251 | + | 0.590347i | ||||
\(146\) | 14.0090 | − | 24.2643i | 1.15940 | − | 2.00813i | ||||
\(147\) | 3.17845 | + | 5.50523i | 0.262154 | + | 0.454064i | ||||
\(148\) | − | 26.4668i | − | 2.17556i | ||||||
\(149\) | −16.8059 | + | 9.70291i | −1.37680 | + | 0.794893i | −0.991772 | − | 0.128014i | \(-0.959140\pi\) |
−0.385023 | + | 0.922907i | \(0.625806\pi\) | |||||||
\(150\) | −17.6171 | + | 10.1712i | −1.43843 | + | 0.830476i | ||||
\(151\) | − | 12.3623i | − | 1.00603i | −0.864278 | − | 0.503014i | \(-0.832225\pi\) | ||
0.864278 | − | 0.503014i | \(-0.167775\pi\) | |||||||
\(152\) | 4.48039 | + | 7.76026i | 0.363407 | + | 0.629440i | ||||
\(153\) | 1.46950 | − | 2.54525i | 0.118802 | − | 0.205771i | ||||
\(154\) | −4.66645 | − | 2.69418i | −0.376033 | − | 0.217103i | ||||
\(155\) | −8.65710 | −0.695355 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.6775 | −1.49063 | −0.745315 | − | 0.666712i | \(-0.767701\pi\) | ||||
−0.745315 | + | 0.666712i | \(0.767701\pi\) | |||||||
\(158\) | 11.0340 | + | 6.37047i | 0.877816 | + | 0.506807i | ||||
\(159\) | −4.98039 | + | 8.62628i | −0.394970 | + | 0.684109i | ||||
\(160\) | −6.88351 | − | 11.9226i | −0.544189 | − | 0.942563i | ||||
\(161\) | − | 6.24698i | − | 0.492331i | ||||||
\(162\) | −2.04113 | + | 1.17845i | −0.160366 | + | 0.0925876i | ||||
\(163\) | 10.6863 | − | 6.16972i | 0.837013 | − | 0.483250i | −0.0192348 | − | 0.999815i | \(-0.506123\pi\) |
0.856248 | + | 0.516565i | \(0.172790\pi\) | |||||||
\(164\) | − | 3.02475i | − | 0.236194i | ||||||
\(165\) | −5.26271 | − | 9.11528i | −0.409701 | − | 0.709624i | ||||
\(166\) | 8.30678 | − | 14.3878i | 0.644731 | − | 1.11671i | ||||
\(167\) | −9.95406 | − | 5.74698i | −0.770268 | − | 0.444715i | 0.0627020 | − | 0.998032i | \(-0.480028\pi\) |
−0.832970 | + | 0.553318i | \(0.813362\pi\) | |||||||
\(168\) | −2.93900 | −0.226749 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 25.5743 | 1.96146 | ||||||||
\(171\) | −2.11747 | − | 1.22252i | −0.161927 | − | 0.0934885i | ||||
\(172\) | 2.87233 | − | 4.97502i | 0.219013 | − | 0.379342i | ||||
\(173\) | 6.05711 | + | 10.4912i | 0.460514 | + | 0.797633i | 0.998987 | − | 0.0450096i | \(-0.0143318\pi\) |
−0.538473 | + | 0.842643i | \(0.680998\pi\) | |||||||
\(174\) | 9.07606i | 0.688055i | ||||||||
\(175\) | 5.99423 | − | 3.46077i | 0.453121 | − | 0.261610i | ||||
\(176\) | −3.77203 | + | 2.17778i | −0.284328 | + | 0.164157i | ||||
\(177\) | 5.38404i | 0.404689i | ||||||||
\(178\) | −1.33363 | − | 2.30992i | −0.0999601 | − | 0.173136i | ||||
\(179\) | −0.269282 | + | 0.466411i | −0.0201271 | + | 0.0348612i | −0.875914 | − | 0.482468i | \(-0.839740\pi\) |
0.855786 | + | 0.517329i | \(0.173074\pi\) | |||||||
\(180\) | −11.3666 | − | 6.56249i | −0.847214 | − | 0.489139i | ||||
\(181\) | 23.2838 | 1.73067 | 0.865336 | − | 0.501192i | \(-0.167105\pi\) | ||||
0.865336 | + | 0.501192i | \(0.167105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.2567 | 0.979961 | ||||||||
\(184\) | −24.7240 | − | 14.2744i | −1.82268 | − | 1.05232i | ||||
\(185\) | −13.7436 | + | 23.8047i | −1.01045 | + | 1.75015i | ||||
\(186\) | −2.76324 | − | 4.78607i | −0.202611 | − | 0.350932i | ||||
\(187\) | 8.37867i | 0.612709i | ||||||||
\(188\) | −7.52751 | + | 4.34601i | −0.549000 | + | 0.316965i | ||||
\(189\) | 0.694498 | − | 0.400969i | 0.0505173 | − | 0.0291662i | ||||
\(190\) | − | 21.2760i | − | 1.54353i | ||||||
\(191\) | −8.38285 | − | 14.5195i | −0.606561 | − | 1.05060i | −0.991803 | − | 0.127779i | \(-0.959215\pi\) |
0.385241 | − | 0.922816i | \(-0.374118\pi\) | |||||||
\(192\) | 5.92208 | − | 10.2573i | 0.427389 | − | 0.740259i | ||||
\(193\) | −22.2949 | − | 12.8720i | −1.60482 | − | 0.926544i | −0.990504 | − | 0.137485i | \(-0.956098\pi\) |
−0.614318 | − | 0.789059i | \(-0.710569\pi\) | |||||||
\(194\) | 14.0103 | 1.00588 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −22.5985 | −1.61418 | ||||||||
\(197\) | 18.5510 | + | 10.7104i | 1.32171 | + | 0.763087i | 0.984001 | − | 0.178165i | \(-0.0570160\pi\) |
0.337705 | + | 0.941252i | \(0.390349\pi\) | |||||||
\(198\) | 3.35958 | − | 5.81897i | 0.238755 | − | 0.413536i | ||||
\(199\) | 1.76391 | + | 3.05517i | 0.125040 | + | 0.216576i | 0.921749 | − | 0.387788i | \(-0.126761\pi\) |
−0.796709 | + | 0.604364i | \(0.793427\pi\) | |||||||
\(200\) | − | 31.6316i | − | 2.23669i | ||||||
\(201\) | 12.4653 | − | 7.19687i | 0.879237 | − | 0.507628i | ||||
\(202\) | 9.44155 | − | 5.45108i | 0.664305 | − | 0.383537i | ||||
\(203\) | − | 3.08815i | − | 0.216745i | ||||||
\(204\) | 5.22401 | + | 9.04826i | 0.365754 | + | 0.633505i | ||||
\(205\) | −1.57069 | + | 2.72051i | −0.109702 | + | 0.190009i | ||||
\(206\) | −2.46518 | − | 1.42327i | −0.171757 | − | 0.0991640i | ||||
\(207\) | 7.78986 | 0.541432 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.97046 | 0.482157 | ||||||||
\(210\) | 6.04332 | + | 3.48911i | 0.417029 | + | 0.240772i | ||||
\(211\) | −0.607760 | + | 1.05267i | −0.0418399 | + | 0.0724689i | −0.886187 | − | 0.463328i | \(-0.846655\pi\) |
0.844347 | + | 0.535797i | \(0.179989\pi\) | |||||||
\(212\) | −17.7051 | − | 30.6661i | −1.21599 | − | 2.10615i | ||||
\(213\) | 8.12498i | 0.556715i | ||||||||
\(214\) | 19.4338 | − | 11.2201i | 1.32847 | − | 0.766992i | ||||
\(215\) | −5.16684 | + | 2.98307i | −0.352375 | + | 0.203444i | ||||
\(216\) | − | 3.66487i | − | 0.249363i | ||||||
\(217\) | 0.940198 | + | 1.62847i | 0.0638248 | + | 0.110548i | ||||
\(218\) | −2.10292 | + | 3.64236i | −0.142427 | + | 0.246692i | ||||
\(219\) | −10.2950 | − | 5.94385i | −0.695674 | − | 0.401648i | ||||
\(220\) | 37.4174 | 2.52268 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −17.5472 | −1.17769 | ||||||||
\(223\) | −15.0588 | − | 8.69418i | −1.00841 | − | 0.582205i | −0.0976835 | − | 0.995218i | \(-0.531143\pi\) |
−0.910725 | + | 0.413012i | \(0.864477\pi\) | |||||||
\(224\) | −1.49516 | + | 2.58969i | −0.0998993 | + | 0.173031i | ||||
\(225\) | 4.31551 | + | 7.47468i | 0.287701 | + | 0.498312i | ||||
\(226\) | − | 11.6692i | − | 0.776223i | ||||||
\(227\) | −15.0823 | + | 8.70775i | −1.00105 | + | 0.577954i | −0.908557 | − | 0.417760i | \(-0.862815\pi\) |
−0.0924878 | + | 0.995714i | \(0.529482\pi\) | |||||||
\(228\) | 7.52751 | − | 4.34601i | 0.498522 | − | 0.287822i | ||||
\(229\) | 18.7603i | 1.23972i | 0.784714 | + | 0.619858i | \(0.212810\pi\) | ||||
−0.784714 | + | 0.619858i | \(0.787190\pi\) | |||||||
\(230\) | 33.8925 | + | 58.7036i | 2.23481 | + | 3.87080i | ||||
\(231\) | −1.14310 | + | 1.97991i | −0.0752107 | + | 0.130269i | ||||
\(232\) | −12.2221 | − | 7.05645i | −0.802422 | − | 0.463279i | ||||
\(233\) | −3.95108 | −0.258844 | −0.129422 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129422 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.02715 | 0.588866 | ||||||||
\(236\) | −16.5758 | − | 9.57002i | −1.07899 | − | 0.622955i | ||||
\(237\) | 2.70291 | − | 4.68157i | 0.175573 | − | 0.304101i | ||||
\(238\) | −2.77748 | − | 4.81073i | −0.180037 | − | 0.311834i | ||||
\(239\) | − | 0.818331i | − | 0.0529334i | −0.999650 | − | 0.0264667i | \(-0.991574\pi\) | ||
0.999650 | − | 0.0264667i | \(-0.00842560\pi\) | |||||||
\(240\) | 4.88500 | − | 2.82036i | 0.315325 | − | 0.182053i | ||||
\(241\) | 5.22432 | − | 3.01626i | 0.336528 | − | 0.194295i | −0.322208 | − | 0.946669i | \(-0.604425\pi\) |
0.658736 | + | 0.752375i | \(0.271092\pi\) | |||||||
\(242\) | − | 6.77048i | − | 0.435223i | ||||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | −23.5635 | + | 40.8131i | −1.50850 | + | 2.61279i | ||||
\(245\) | 20.3254 | + | 11.7349i | 1.29854 | + | 0.749715i | ||||
\(246\) | −2.00538 | −0.127858 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 8.59345 | 0.545685 | ||||||||
\(249\) | −6.10454 | − | 3.52446i | −0.386860 | − | 0.223353i | ||||
\(250\) | −15.7981 | + | 27.3630i | −0.999157 | + | 1.73059i | ||||
\(251\) | −13.4400 | − | 23.2787i | −0.848323 | − | 1.46934i | −0.882704 | − | 0.469929i | \(-0.844279\pi\) |
0.0343812 | − | 0.999409i | \(-0.489054\pi\) | |||||||
\(252\) | 2.85086i | 0.179587i | ||||||||
\(253\) | −19.2325 | + | 11.1039i | −1.20914 | + | 0.698095i | ||||
\(254\) | 11.5737 | − | 6.68210i | 0.726200 | − | 0.419272i | ||||
\(255\) | − | 10.8509i | − | 0.679507i | ||||||
\(256\) | 12.2642 | + | 21.2422i | 0.766513 | + | 1.32764i | ||||
\(257\) | −4.52661 | + | 7.84033i | −0.282362 | + | 0.489066i | −0.971966 | − | 0.235121i | \(-0.924451\pi\) |
0.689604 | + | 0.724187i | \(0.257785\pi\) | |||||||
\(258\) | −3.29838 | − | 1.90432i | −0.205348 | − | 0.118558i | ||||
\(259\) | 5.97046 | 0.370986 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.85086 | 0.238362 | ||||||||
\(262\) | 37.1952 | + | 21.4746i | 2.29793 | + | 1.32671i | ||||
\(263\) | −11.5755 | + | 20.0494i | −0.713778 | + | 1.23630i | 0.249651 | + | 0.968336i | \(0.419684\pi\) |
−0.963429 | + | 0.267964i | \(0.913649\pi\) | |||||||
\(264\) | 5.22401 | + | 9.04826i | 0.321516 | + | 0.556882i | ||||
\(265\) | 36.7754i | 2.25909i | ||||||||
\(266\) | −4.00219 | + | 2.31067i | −0.245390 | + | 0.141676i | ||||
\(267\) | −0.980069 | + | 0.565843i | −0.0599793 | + | 0.0346290i | ||||
\(268\) | 51.1691i | 3.12565i | ||||||||
\(269\) | 1.21044 | + | 2.09654i | 0.0738018 | + | 0.127828i | 0.900565 | − | 0.434722i | \(-0.143153\pi\) |
−0.826763 | + | 0.562551i | \(0.809820\pi\) | |||||||
\(270\) | −4.35086 | + | 7.53590i | −0.264785 | + | 0.458620i | ||||
\(271\) | 18.5720 | + | 10.7225i | 1.12817 | + | 0.651347i | 0.943473 | − | 0.331450i | \(-0.107538\pi\) |
0.184693 | + | 0.982796i | \(0.440871\pi\) | |||||||
\(272\) | −4.49024 | −0.272261 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 22.2737 | 1.34560 | ||||||||
\(275\) | −21.3092 | − | 12.3029i | −1.28500 | − | 0.741893i | ||||
\(276\) | −13.8463 | + | 23.9825i | −0.833450 | + | 1.44358i | ||||
\(277\) | −7.40366 | − | 12.8235i | −0.444843 | − | 0.770490i | 0.553199 | − | 0.833049i | \(-0.313407\pi\) |
−0.998041 | + | 0.0625593i | \(0.980074\pi\) | |||||||
\(278\) | − | 9.46309i | − | 0.567558i | ||||||
\(279\) | −2.03067 | + | 1.17241i | −0.121573 | + | 0.0701902i | ||||
\(280\) | −9.39712 | + | 5.42543i | −0.561585 | + | 0.324231i | ||||
\(281\) | 14.5036i | 0.865215i | 0.901582 | + | 0.432608i | \(0.142406\pi\) | ||||
−0.901582 | + | 0.432608i | \(0.857594\pi\) | |||||||
\(282\) | 2.88135 | + | 4.99065i | 0.171582 | + | 0.297189i | ||||
\(283\) | 12.8361 | − | 22.2328i | 0.763026 | − | 1.32160i | −0.178258 | − | 0.983984i | \(-0.557046\pi\) |
0.941284 | − | 0.337616i | \(-0.109621\pi\) | |||||||
\(284\) | −25.0143 | − | 14.4420i | −1.48432 | − | 0.856974i | ||||
\(285\) | −9.02715 | −0.534722 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.682333 | 0.0402768 | ||||||||
\(288\) | −3.22929 | − | 1.86443i | −0.190287 | − | 0.109863i | ||||
\(289\) | 4.18114 | − | 7.24194i | 0.245949 | − | 0.425997i | ||||
\(290\) | 16.7545 | + | 29.0197i | 0.983859 | + | 1.70409i | ||||
\(291\) | − | 5.94438i | − | 0.348466i | ||||||
\(292\) | 36.5984 | − | 21.1301i | 2.14176 | − | 1.23655i | ||||
\(293\) | −22.9696 | + | 13.2615i | −1.34190 | + | 0.774746i | −0.987086 | − | 0.160191i | \(-0.948789\pi\) |
−0.354813 | + | 0.934937i | \(0.615456\pi\) | |||||||
\(294\) | 14.9825i | 0.873800i | ||||||||
\(295\) | 9.93900 | + | 17.2149i | 0.578671 | + | 1.00229i | ||||
\(296\) | 13.6426 | − | 23.6296i | 0.792958 | − | 1.37344i | ||||
\(297\) | −2.46891 | − | 1.42543i | −0.143261 | − | 0.0827117i | ||||
\(298\) | −45.7375 | −2.64950 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −30.6829 | −1.77148 | ||||||||
\(301\) | 1.12228 | + | 0.647948i | 0.0646871 | + | 0.0373471i | ||||
\(302\) | 14.5683 | − | 25.2330i | 0.838311 | − | 1.45200i | ||||
\(303\) | −2.31282 | − | 4.00593i | −0.132868 | − | 0.230134i | ||||
\(304\) | 3.73556i | 0.214249i | ||||||||
\(305\) | 42.3867 | − | 24.4720i | 2.42705 | − | 1.40126i | ||||
\(306\) | 5.99889 | − | 3.46346i | 0.342934 | − | 0.197993i | ||||
\(307\) | − | 8.24698i | − | 0.470680i | −0.971913 | − | 0.235340i | \(-0.924380\pi\) | ||
0.971913 | − | 0.235340i | \(-0.0756204\pi\) | |||||||
\(308\) | −4.06369 | − | 7.03851i | −0.231550 | − | 0.401056i | ||||
\(309\) | −0.603875 | + | 1.04594i | −0.0343533 | + | 0.0595016i | ||||
\(310\) | −17.6703 | − | 10.2019i | −1.00361 | − | 0.579432i | ||||
\(311\) | 14.4179 | 0.817564 | 0.408782 | − | 0.912632i | \(-0.365954\pi\) | ||||
0.408782 | + | 0.912632i | \(0.365954\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.2338 | 0.804544 | 0.402272 | − | 0.915520i | \(-0.368221\pi\) | ||||
0.402272 | + | 0.915520i | \(0.368221\pi\) | |||||||
\(314\) | −38.1233 | − | 22.0105i | −2.15142 | − | 1.24213i | ||||
\(315\) | 1.48039 | − | 2.56410i | 0.0834103 | − | 0.144471i | ||||
\(316\) | 9.60872 | + | 16.6428i | 0.540533 | + | 0.936230i | ||||
\(317\) | 6.84415i | 0.384406i | 0.981355 | + | 0.192203i | \(0.0615632\pi\) | ||||
−0.981355 | + | 0.192203i | \(0.938437\pi\) | |||||||
\(318\) | −20.3312 | + | 11.7383i | −1.14012 | + | 0.658248i | ||||
\(319\) | −9.50743 | + | 5.48911i | −0.532314 | + | 0.307331i | ||||
\(320\) | − | 43.7289i | − | 2.44452i | ||||||
\(321\) | −4.76055 | − | 8.24552i | −0.265708 | − | 0.460220i | ||||
\(322\) | 7.36174 | − | 12.7509i | 0.410254 | − | 0.710580i | ||||
\(323\) | 6.22324 | + | 3.59299i | 0.346270 | + | 0.199919i | ||||
\(324\) | −3.55496 | −0.197498 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 29.0828 | 1.61075 | ||||||||
\(327\) | 1.54540 | + | 0.892240i | 0.0854611 | + | 0.0493410i | ||||
\(328\) | 1.55914 | − | 2.70051i | 0.0860890 | − | 0.149111i | ||||
\(329\) | −0.980386 | − | 1.69808i | −0.0540504 | − | 0.0936181i | ||||
\(330\) | − | 24.8073i | − | 1.36560i | ||||||
\(331\) | −8.17757 | + | 4.72132i | −0.449480 | + | 0.259507i | −0.707611 | − | 0.706603i | \(-0.750227\pi\) |
0.258130 | + | 0.966110i | \(0.416894\pi\) | |||||||
\(332\) | 21.7014 | − | 12.5293i | 1.19102 | − | 0.687635i | ||||
\(333\) | 7.44504i | 0.407986i | ||||||||
\(334\) | −13.5450 | − | 23.4607i | −0.741151 | − | 1.28371i | ||||
\(335\) | 26.5710 | − | 46.0223i | 1.45173 | − | 2.51447i | ||||
\(336\) | −1.06106 | − | 0.612605i | −0.0578857 | − | 0.0334203i | ||||
\(337\) | −2.64310 | −0.143979 | −0.0719895 | − | 0.997405i | \(-0.522935\pi\) | ||||
−0.0719895 | + | 0.997405i | \(0.522935\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.95108 | −0.268906 | ||||||||
\(340\) | 33.4064 | + | 19.2872i | 1.81171 | + | 1.04599i | ||||
\(341\) | 3.34236 | − | 5.78914i | 0.180999 | − | 0.313500i | ||||
\(342\) | −2.88135 | − | 4.99065i | −0.155806 | − | 0.269864i | ||||
\(343\) | − | 10.7114i | − | 0.578361i | ||||||
\(344\) | 5.12884 | − | 2.96114i | 0.276529 | − | 0.159654i | ||||
\(345\) | 24.9072 | − | 14.3802i | 1.34096 | − | 0.774202i | ||||
\(346\) | 28.5520i | 1.53496i | ||||||||
\(347\) | 5.07942 | + | 8.79781i | 0.272677 | + | 0.472291i | 0.969547 | − | 0.244907i | \(-0.0787575\pi\) |
−0.696869 | + | 0.717198i | \(0.745424\pi\) | |||||||
\(348\) | −6.84481 | + | 11.8556i | −0.366921 | + | 0.635525i | ||||
\(349\) | −9.04102 | − | 5.21983i | −0.483954 | − | 0.279411i | 0.238109 | − | 0.971239i | \(-0.423473\pi\) |
−0.722063 | + | 0.691827i | \(0.756806\pi\) | |||||||
\(350\) | 16.3134 | 0.871986 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 10.6304 | 0.566604 | ||||||||
\(353\) | 15.8406 | + | 9.14556i | 0.843108 | + | 0.486769i | 0.858320 | − | 0.513115i | \(-0.171509\pi\) |
−0.0152113 | + | 0.999884i | \(0.504842\pi\) | |||||||
\(354\) | −6.34481 | + | 10.9895i | −0.337223 | + | 0.584087i | ||||
\(355\) | 14.9988 | + | 25.9787i | 0.796054 | + | 1.37881i | ||||
\(356\) | − | 4.02310i | − | 0.213224i | ||||||
\(357\) | −2.04113 | + | 1.17845i | −0.108028 | + | 0.0623701i | ||||
\(358\) | −1.09928 | + | 0.634670i | −0.0580988 | + | 0.0335434i | ||||
\(359\) | − | 15.2731i | − | 0.806081i | −0.915182 | − | 0.403041i | \(-0.867953\pi\) | ||
0.915182 | − | 0.403041i | \(-0.132047\pi\) | |||||||
\(360\) | −6.76540 | − | 11.7180i | −0.356568 | − | 0.617593i | ||||
\(361\) | −6.51089 | + | 11.2772i | −0.342678 | + | 0.593536i | ||||
\(362\) | 47.5253 | + | 27.4388i | 2.49788 | + | 1.44215i | ||||
\(363\) | −2.87263 | −0.150774 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −43.8896 | −2.29729 | ||||||||
\(366\) | 27.0586 | + | 15.6223i | 1.41438 | + | 0.816590i | ||||
\(367\) | 11.1359 | − | 19.2879i | 0.581288 | − | 1.00682i | −0.414040 | − | 0.910259i | \(-0.635882\pi\) |
0.995327 | − | 0.0965606i | \(-0.0307842\pi\) | |||||||
\(368\) | −5.95071 | − | 10.3069i | −0.310202 | − | 0.537286i | ||||
\(369\) | 0.850855i | 0.0442937i | ||||||||
\(370\) | −56.1051 | + | 32.3923i | −2.91677 | + | 1.68400i | ||||
\(371\) | 6.91774 | − | 3.99396i | 0.359151 | − | 0.207356i | ||||
\(372\) | − | 8.33572i | − | 0.432187i | ||||||
\(373\) | −2.06315 | − | 3.57349i | −0.106826 | − | 0.185028i | 0.807657 | − | 0.589653i | \(-0.200735\pi\) |
−0.914483 | + | 0.404625i | \(0.867402\pi\) | |||||||
\(374\) | −9.87382 | + | 17.1020i | −0.510563 | + | 0.884321i | ||||
\(375\) | 11.6098 | + | 6.70291i | 0.599526 | + | 0.346137i | ||||
\(376\) | −8.96077 | −0.462116 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.89008 | 0.0972154 | ||||||||
\(379\) | −9.27261 | − | 5.35354i | −0.476302 | − | 0.274993i | 0.242572 | − | 0.970133i | \(-0.422009\pi\) |
−0.718874 | + | 0.695140i | \(0.755342\pi\) | |||||||
\(380\) | 16.0456 | − | 27.7917i | 0.823120 | − | 1.42569i | ||||
\(381\) | −2.83513 | − | 4.91058i | −0.145248 | − | 0.251577i | ||||
\(382\) | − | 39.5150i | − | 2.02176i | ||||||
\(383\) | −5.65210 | + | 3.26324i | −0.288809 | + | 0.166744i | −0.637405 | − | 0.770529i | \(-0.719992\pi\) |
0.348596 | + | 0.937273i | \(0.386659\pi\) | |||||||
\(384\) | 17.7169 | − | 10.2289i | 0.904112 | − | 0.521989i | ||||
\(385\) | 8.44073i | 0.430179i | ||||||||
\(386\) | −30.3379 | − | 52.5467i | −1.54416 | − | 2.67456i | ||||
\(387\) | −0.807979 | + | 1.39946i | −0.0410719 | + | 0.0711385i | ||||
\(388\) | 18.3009 | + | 10.5660i | 0.929085 | + | 0.536408i | ||||
\(389\) | 11.7922 | 0.597891 | 0.298945 | − | 0.954270i | \(-0.403365\pi\) | ||||
0.298945 | + | 0.954270i | \(0.403365\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −22.8944 | −1.15782 | ||||||||
\(392\) | −20.1760 | − | 11.6486i | −1.01904 | − | 0.588344i | ||||
\(393\) | 9.11141 | − | 15.7814i | 0.459610 | − | 0.796067i | ||||
\(394\) | 25.2434 | + | 43.7228i | 1.27174 | + | 2.20272i | ||||
\(395\) | − | 19.9584i | − | 1.00422i | ||||||
\(396\) | 8.77688 | − | 5.06734i | 0.441055 | − | 0.254643i | ||||
\(397\) | −10.8624 | + | 6.27144i | −0.545171 | + | 0.314754i | −0.747172 | − | 0.664631i | \(-0.768589\pi\) |
0.202001 | + | 0.979385i | \(0.435256\pi\) | |||||||
\(398\) | 8.31468i | 0.416777i | ||||||||
\(399\) | 0.980386 | + | 1.69808i | 0.0490807 | + | 0.0850102i | ||||
\(400\) | 6.59329 | − | 11.4199i | 0.329664 | − | 0.570995i | ||||
\(401\) | −15.4761 | − | 8.93512i | −0.772838 | − | 0.446198i | 0.0610479 | − | 0.998135i | \(-0.480556\pi\) |
−0.833886 | + | 0.551936i | \(0.813889\pi\) | |||||||
\(402\) | 33.9245 | 1.69200 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.4440 | 0.818118 | ||||||||
\(405\) | 3.19738 | + | 1.84601i | 0.158879 | + | 0.0917290i | ||||
\(406\) | 3.63922 | − | 6.30331i | 0.180611 | − | 0.312828i | ||||
\(407\) | −10.6124 | − | 18.3812i | −0.526036 | − | 0.911120i | ||||
\(408\) | 10.7711i | 0.533247i | ||||||||
\(409\) | 24.1724 | − | 13.9559i | 1.19525 | − | 0.690076i | 0.235755 | − | 0.971812i | \(-0.424244\pi\) |
0.959492 | + | 0.281736i | \(0.0909103\pi\) | |||||||
\(410\) | −6.41196 | + | 3.70195i | −0.316664 | + | 0.182826i | ||||
\(411\) | − | 9.45042i | − | 0.466155i | ||||||
\(412\) | −2.14675 | − | 3.71828i | −0.105763 | − | 0.183187i | ||||
\(413\) | 2.15883 | − | 3.73921i | 0.106229 | − | 0.183994i | ||||
\(414\) | 15.9001 | + | 9.17994i | 0.781448 | + | 0.451169i | ||||
\(415\) | −26.0248 | −1.27750 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.01507 | −0.196619 | ||||||||
\(418\) | 14.2276 | + | 8.21432i | 0.695896 | + | 0.401776i | ||||
\(419\) | 8.20171 | − | 14.2058i | 0.400680 | − | 0.693998i | −0.593128 | − | 0.805108i | \(-0.702107\pi\) |
0.993808 | + | 0.111110i | \(0.0354407\pi\) | |||||||
\(420\) | 5.26271 | + | 9.11528i | 0.256794 | + | 0.444780i | ||||
\(421\) | 3.03684i | 0.148006i | 0.997258 | + | 0.0740032i | \(0.0235775\pi\) | ||||
−0.997258 | + | 0.0740032i | \(0.976423\pi\) | |||||||
\(422\) | −2.48104 | + | 1.43243i | −0.120775 | + | 0.0697295i | ||||
\(423\) | 2.11747 | − | 1.22252i | 0.102955 | − | 0.0594410i | ||||
\(424\) | − | 36.5050i | − | 1.77284i | ||||||
\(425\) | −12.6833 | − | 21.9681i | −0.615230 | − | 1.06561i | ||||
\(426\) | −9.57487 | + | 16.5842i | −0.463904 | + | 0.803505i | ||||
\(427\) | −9.20674 | − | 5.31551i | −0.445545 | − | 0.257236i | ||||
\(428\) | 33.8471 | 1.63606 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.0616 | −0.678110 | ||||||||
\(431\) | −2.89089 | − | 1.66905i | −0.139249 | − | 0.0803955i | 0.428757 | − | 0.903420i | \(-0.358952\pi\) |
−0.568006 | + | 0.823024i | \(0.692285\pi\) | |||||||
\(432\) | 0.763906 | − | 1.32312i | 0.0367534 | − | 0.0636588i | ||||
\(433\) | 5.95138 | + | 10.3081i | 0.286005 | + | 0.495375i | 0.972852 | − | 0.231426i | \(-0.0743393\pi\) |
−0.686847 | + | 0.726802i | \(0.741006\pi\) | |||||||
\(434\) | 4.43190i | 0.212738i | ||||||||
\(435\) | 12.3127 | − | 7.10872i | 0.590347 | − | 0.340837i | ||||
\(436\) | −5.49385 | + | 3.17187i | −0.263108 | + | 0.151905i | ||||
\(437\) | 19.0465i | 0.911119i | ||||||||
\(438\) | −14.0090 | − | 24.2643i | −0.669377 | − | 1.15940i | ||||
\(439\) | 1.85905 | − | 3.21997i | 0.0887277 | − | 0.153681i | −0.818246 | − | 0.574868i | \(-0.805053\pi\) |
0.906974 | + | 0.421188i | \(0.138387\pi\) | |||||||
\(440\) | 33.4064 | + | 19.2872i | 1.59259 | + | 0.919480i | ||||
\(441\) | 6.35690 | 0.302709 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.45712 | 0.0692300 | 0.0346150 | − | 0.999401i | \(-0.488979\pi\) | ||||
0.0346150 | + | 0.999401i | \(0.488979\pi\) | |||||||
\(444\) | −22.9209 | − | 13.2334i | −1.08778 | − | 0.628030i | ||||
\(445\) | −2.08911 | + | 3.61844i | −0.0990331 | + | 0.171530i | ||||
\(446\) | −20.4913 | − | 35.4919i | −0.970290 | − | 1.68059i | ||||
\(447\) | 19.4058i | 0.917863i | ||||||||
\(448\) | −8.22574 | + | 4.74914i | −0.388630 | + | 0.224376i | ||||
\(449\) | −10.5026 | + | 6.06369i | −0.495649 | + | 0.286163i | −0.726915 | − | 0.686727i | \(-0.759047\pi\) |
0.231266 | + | 0.972891i | \(0.425713\pi\) | |||||||
\(450\) | 20.3424i | 0.958951i | ||||||||
\(451\) | −1.21283 | − | 2.10069i | −0.0571100 | − | 0.0989175i | ||||
\(452\) | 8.80045 | − | 15.2428i | 0.413938 | − | 0.716962i | ||||
\(453\) | −10.7060 | − | 6.18114i | −0.503014 | − | 0.290415i | ||||
\(454\) | −41.0465 | −1.92641 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.96077 | 0.419627 | ||||||||
\(457\) | −2.98608 | − | 1.72401i | −0.139683 | − | 0.0806459i | 0.428530 | − | 0.903528i | \(-0.359032\pi\) |
−0.568213 | + | 0.822882i | \(0.692365\pi\) | |||||||
\(458\) | −22.1081 | + | 38.2923i | −1.03304 | + | 1.78928i | ||||
\(459\) | −1.46950 | − | 2.54525i | −0.0685904 | − | 0.118802i | ||||
\(460\) | 102.242i | 4.76704i | ||||||||
\(461\) | 5.85087 | − | 3.37800i | 0.272502 | − | 0.157329i | −0.357522 | − | 0.933905i | \(-0.616378\pi\) |
0.630024 | + | 0.776575i | \(0.283045\pi\) | |||||||
\(462\) | −4.66645 | + | 2.69418i | −0.217103 | + | 0.125344i | ||||
\(463\) | − | 7.45175i | − | 0.346312i | −0.984894 | − | 0.173156i | \(-0.944604\pi\) | ||
0.984894 | − | 0.173156i | \(-0.0553965\pi\) | |||||||
\(464\) | −2.94169 | − | 5.09516i | −0.136565 | − | 0.236537i | ||||
\(465\) | −4.32855 | + | 7.49727i | −0.200732 | + | 0.347678i | ||||
\(466\) | −8.06468 | − | 4.65615i | −0.373589 | − | 0.215692i | ||||
\(467\) | −32.6098 | −1.50900 | −0.754502 | − | 0.656298i | \(-0.772121\pi\) | ||||
−0.754502 | + | 0.656298i | \(0.772121\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.5429 | −0.533001 | ||||||||
\(470\) | 18.4256 | + | 10.6380i | 0.849909 | + | 0.490695i | ||||
\(471\) | −9.33877 | + | 16.1752i | −0.430308 | + | 0.745315i | ||||
\(472\) | −9.86592 | − | 17.0883i | −0.454116 | − | 0.786552i | ||||
\(473\) | − | 4.60686i | − | 0.211824i | ||||||
\(474\) | 11.0340 | − | 6.37047i | 0.506807 | − | 0.292605i | ||||
\(475\) | −18.2759 | + | 10.5516i | −0.838557 | + | 0.484141i | ||||
\(476\) | − | 8.37867i | − | 0.384036i | ||||||
\(477\) | 4.98039 | + | 8.62628i | 0.228036 | + | 0.394970i | ||||
\(478\) | 0.964361 | − | 1.67032i | 0.0441088 | − | 0.0763987i | ||||
\(479\) | −2.45006 | − | 1.41454i | −0.111946 | − | 0.0646321i | 0.442982 | − | 0.896531i | \(-0.353921\pi\) |
−0.554928 | + | 0.831899i | \(0.687254\pi\) | |||||||
\(480\) | −13.7670 | −0.628376 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.2180 | 0.647614 | ||||||||
\(483\) | −5.41004 | − | 3.12349i | −0.246165 | − | 0.142124i | ||||
\(484\) | 5.10603 | − | 8.84391i | 0.232092 | − | 0.401996i | ||||
\(485\) | −10.9734 | − | 19.0065i | −0.498276 | − | 0.863039i | ||||
\(486\) | 2.35690i | 0.106911i | ||||||||
\(487\) | 35.7612 | − | 20.6468i | 1.62050 | − | 0.935594i | 0.633709 | − | 0.773572i | \(-0.281532\pi\) |
0.986787 | − | 0.162022i | \(-0.0518015\pi\) | |||||||
\(488\) | −42.0750 | + | 24.2920i | −1.90465 | + | 1.09965i | ||||
\(489\) | − | 12.3394i | − | 0.558009i | ||||||
\(490\) | 27.6579 | + | 47.9049i | 1.24946 | + | 2.16412i | ||||
\(491\) | −17.3349 | + | 30.0249i | −0.782313 | + | 1.35501i | 0.148279 | + | 0.988946i | \(0.452627\pi\) |
−0.930591 | + | 0.366060i | \(0.880707\pi\) | |||||||
\(492\) | −2.61951 | − | 1.51238i | −0.118097 | − | 0.0681832i | ||||
\(493\) | −11.3177 | −0.509722 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.5254 | −0.473082 | ||||||||
\(496\) | 3.10248 | + | 1.79122i | 0.139305 | + | 0.0804280i | ||||
\(497\) | 3.25786 | − | 5.64279i | 0.146135 | − | 0.253114i | ||||
\(498\) | −8.30678 | − | 14.3878i | −0.372236 | − | 0.644731i | ||||
\(499\) | − | 17.9409i | − | 0.803146i | −0.915827 | − | 0.401573i | \(-0.868464\pi\) | ||
0.915827 | − | 0.401573i | \(-0.131536\pi\) | |||||||
\(500\) | −41.2723 | + | 23.8286i | −1.84575 | + | 1.06565i | ||||
\(501\) | −9.95406 | + | 5.74698i | −0.444715 | + | 0.256756i | ||||
\(502\) | − | 63.3532i | − | 2.82759i | ||||||
\(503\) | 13.0906 | + | 22.6736i | 0.583681 | + | 1.01096i | 0.995038 | + | 0.0994909i | \(0.0317214\pi\) |
−0.411358 | + | 0.911474i | \(0.634945\pi\) | |||||||
\(504\) | −1.46950 | + | 2.54525i | −0.0654568 | + | 0.113374i | ||||
\(505\) | −14.7900 | − | 8.53899i | −0.658145 | − | 0.379980i | ||||
\(506\) | −52.3414 | −2.32686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.1575 | 0.894345 | ||||||||
\(509\) | −4.76837 | − | 2.75302i | −0.211354 | − | 0.122025i | 0.390586 | − | 0.920566i | \(-0.372272\pi\) |
−0.601941 | + | 0.798541i | \(0.705606\pi\) | |||||||
\(510\) | 12.7872 | − | 22.1480i | 0.566225 | − | 0.980731i | ||||
\(511\) | 4.76659 | + | 8.25598i | 0.210862 | + | 0.365223i | ||||
\(512\) | 16.8955i | 0.746681i | ||||||||
\(513\) | −2.11747 | + | 1.22252i | −0.0934885 | + | 0.0539756i | ||||
\(514\) | −18.4788 | + | 10.6688i | −0.815066 | + | 0.470579i | ||||
\(515\) | 4.45904i | 0.196489i | ||||||||
\(516\) | −2.87233 | − | 4.97502i | −0.126447 | − | 0.219013i | ||||
\(517\) | −3.48523 | + | 6.03660i | −0.153280 | + | 0.265489i | ||||
\(518\) | 12.1865 | + | 7.03588i | 0.535444 | + | 0.309139i | ||||
\(519\) | 12.1142 | 0.531756 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.7211 | −1.17067 | −0.585336 | − | 0.810791i | \(-0.699037\pi\) | ||||
−0.585336 | + | 0.810791i | \(0.699037\pi\) | |||||||
\(522\) | 7.86010 | + | 4.53803i | 0.344027 | + | 0.198624i | ||||
\(523\) | −18.2615 | + | 31.6299i | −0.798520 | + | 1.38308i | 0.122060 | + | 0.992523i | \(0.461050\pi\) |
−0.920580 | + | 0.390555i | \(0.872283\pi\) | |||||||
\(524\) | 32.3907 | + | 56.1023i | 1.41499 | + | 2.45084i | ||||
\(525\) | − | 6.92154i | − | 0.302081i | ||||||
\(526\) | −47.2544 | + | 27.2823i | −2.06039 | + | 1.18957i | ||||
\(527\) | 5.96814 | − | 3.44571i | 0.259976 | − | 0.150097i | ||||
\(528\) | 4.35557i | 0.189552i | ||||||||
\(529\) | −18.8409 | − | 32.6334i | −0.819171 | − | 1.41885i | ||||
\(530\) | −43.3379 | + | 75.0634i | −1.88248 | + | 3.26055i | ||||
\(531\) | 4.66272 | + | 2.69202i | 0.202345 | + | 0.116824i | ||||
\(532\) | −6.97046 | −0.302208 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −2.66727 | −0.115424 | ||||||||
\(535\) | −30.4426 | − | 17.5761i | −1.31615 | − | 0.759880i | ||||
\(536\) | −26.3756 | + | 45.6839i | −1.13925 | + | 1.97324i | ||||
\(537\) | 0.269282 | + | 0.466411i | 0.0116204 | + | 0.0201271i | ||||
\(538\) | 5.70576i | 0.245993i | ||||||||
\(539\) | −15.6946 | + | 9.06129i | −0.676015 | + | 0.390298i | ||||
\(540\) | −11.3666 | + | 6.56249i | −0.489139 | + | 0.282405i | ||||
\(541\) | 18.4655i | 0.793893i | 0.917842 | + | 0.396947i | \(0.129930\pi\) | ||||
−0.917842 | + | 0.396947i | \(0.870070\pi\) | |||||||
\(542\) | 25.2719 | + | 43.7722i | 1.08552 | + | 1.88018i | ||||
\(543\) | 11.6419 | − | 20.1644i | 0.499602 | − | 0.865336i | ||||
\(544\) | 9.49087 | + | 5.47956i | 0.406918 | + | 0.234934i | ||||
\(545\) | 6.58834 | 0.282213 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.8471 | 1.70374 | 0.851870 | − | 0.523753i | \(-0.175468\pi\) | ||||
0.851870 | + | 0.523753i | \(0.175468\pi\) | |||||||
\(548\) | 29.0949 | + | 16.7979i | 1.24287 | + | 0.717572i | ||||
\(549\) | 6.62833 | − | 11.4806i | 0.282890 | − | 0.489981i | ||||
\(550\) | −28.9966 | − | 50.2237i | −1.23642 | − | 2.14154i | ||||
\(551\) | 9.41550i | 0.401114i | ||||||||
\(552\) | −24.7240 | + | 14.2744i | −1.05232 | + | 0.607560i | ||||
\(553\) | −3.75433 | + | 2.16756i | −0.159650 | + | 0.0921741i | ||||
\(554\) | − | 34.8993i | − | 1.48273i | ||||||
\(555\) | 13.7436 | + | 23.8047i | 0.583384 | + | 1.01045i | ||||
\(556\) | 7.13669 | − | 12.3611i | 0.302663 | − | 0.524228i | ||||
\(557\) | −7.97156 | − | 4.60238i | −0.337766 | − | 0.195009i | 0.321518 | − | 0.946904i | \(-0.395807\pi\) |
−0.659284 | + | 0.751894i | \(0.729140\pi\) | |||||||
\(558\) | −5.52648 | −0.233955 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −4.52350 | −0.191153 | ||||||||
\(561\) | 7.25614 | + | 4.18933i | 0.306354 | + | 0.176874i | ||||
\(562\) | −17.0918 | + | 29.6039i | −0.720974 | + | 1.24876i | ||||
\(563\) | −0.487623 | − | 0.844588i | −0.0205509 | − | 0.0355951i | 0.855567 | − | 0.517692i | \(-0.173209\pi\) |
−0.876118 | + | 0.482097i | \(0.839875\pi\) | |||||||
\(564\) | 8.69202i | 0.366000i | ||||||||
\(565\) | −15.8305 | + | 9.13975i | −0.665995 | + | 0.384512i | ||||
\(566\) | 52.4003 | − | 30.2533i | 2.20255 | − | 1.27164i | ||||
\(567\) | − | 0.801938i | − | 0.0336782i | ||||||
\(568\) | −14.8885 | − | 25.7877i | −0.624708 | − | 1.08203i | ||||
\(569\) | −8.44720 | + | 14.6310i | −0.354125 | + | 0.613362i | −0.986968 | − | 0.160918i | \(-0.948555\pi\) |
0.632843 | + | 0.774280i | \(0.281888\pi\) | |||||||
\(570\) | −18.4256 | − | 10.6380i | −0.771763 | − | 0.445578i | ||||
\(571\) | 44.3226 | 1.85484 | 0.927421 | − | 0.374019i | \(-0.122021\pi\) | ||||
0.927421 | + | 0.374019i | \(0.122021\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.7657 | −0.700397 | ||||||||
\(574\) | 1.39273 | + | 0.804094i | 0.0581315 | + | 0.0335622i | ||||
\(575\) | 33.6172 | − | 58.2267i | 1.40193 | − | 2.42822i | ||||
\(576\) | −5.92208 | − | 10.2573i | −0.246753 | − | 0.427389i | ||||
\(577\) | − | 3.56704i | − | 0.148498i | −0.997240 | − | 0.0742489i | \(-0.976344\pi\) | ||
0.997240 | − | 0.0742489i | \(-0.0236559\pi\) | |||||||
\(578\) | 17.0685 | − | 9.85450i | 0.709956 | − | 0.409893i | ||||
\(579\) | −22.2949 | + | 12.8720i | −0.926544 | + | 0.534940i | ||||
\(580\) | 50.5424i | 2.09866i | ||||||||
\(581\) | 2.82640 | + | 4.89546i | 0.117259 | + | 0.203098i | ||||
\(582\) | 7.00514 | − | 12.1333i | 0.290372 | − | 0.502940i | ||||
\(583\) | −24.5923 | − | 14.1984i | −1.01851 | − | 0.588036i | ||||
\(584\) | 43.5669 | 1.80281 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −62.5120 | −2.58235 | ||||||||
\(587\) | −13.9579 | − | 8.05861i | −0.576105 | − | 0.332614i | 0.183479 | − | 0.983024i | \(-0.441264\pi\) |
−0.759584 | + | 0.650409i | \(0.774597\pi\) | |||||||
\(588\) | −11.2992 | + | 19.5709i | −0.465973 | + | 0.807089i | ||||
\(589\) | −2.86658 | − | 4.96507i | −0.118116 | − | 0.204582i | ||||
\(590\) | 46.8504i | 1.92880i | ||||||||
\(591\) | 18.5510 | − | 10.7104i | 0.763087 | − | 0.440569i | ||||
\(592\) | 9.85071 | − | 5.68731i | 0.404862 | − | 0.233747i | ||||
\(593\) | − | 42.8611i | − | 1.76010i | −0.474885 | − | 0.880048i | \(-0.657510\pi\) | ||
0.474885 | − | 0.880048i | \(-0.342490\pi\) | |||||||
\(594\) | −3.35958 | − | 5.81897i | −0.137845 | − | 0.238755i | ||||
\(595\) | −4.35086 | + | 7.53590i | −0.178368 | + | 0.308942i | ||||
\(596\) | −59.7444 | − | 34.4934i | −2.44722 | − | 1.41291i | ||||
\(597\) | 3.52781 | 0.144384 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 40.9420 | 1.67284 | 0.836422 | − | 0.548086i | \(-0.184643\pi\) | ||||
0.836422 | + | 0.548086i | \(0.184643\pi\) | |||||||
\(600\) | −27.3938 | − | 15.8158i | −1.11835 | − | 0.645678i | ||||
\(601\) | −0.593523 | + | 1.02801i | −0.0242103 | + | 0.0419335i | −0.877877 | − | 0.478887i | \(-0.841040\pi\) |
0.853666 | + | 0.520820i | \(0.174374\pi\) | |||||||
\(602\) | 1.52715 | + | 2.64510i | 0.0622419 | + | 0.107806i | ||||
\(603\) | − | 14.3937i | − | 0.586158i | ||||||
\(604\) | 38.0595 | − | 21.9737i | 1.54862 | − | 0.894096i | ||||
\(605\) | −9.18489 | + | 5.30290i | −0.373419 | + | 0.215593i | ||||
\(606\) | − | 10.9022i | − | 0.442870i | ||||||
\(607\) | −9.99612 | − | 17.3138i | −0.405730 | − | 0.702745i | 0.588676 | − | 0.808369i | \(-0.299649\pi\) |
−0.994406 | + | 0.105624i | \(0.966316\pi\) | |||||||
\(608\) | 4.55861 | − | 7.89574i | 0.184876 | − | 0.320214i | ||||
\(609\) | −2.67441 | − | 1.54407i | −0.108373 | − | 0.0625690i | ||||
\(610\) | 115.356 | 4.67062 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 10.4480 | 0.422336 | ||||||||
\(613\) | −28.8922 | − | 16.6809i | −1.16694 | − | 0.673735i | −0.213985 | − | 0.976837i | \(-0.568644\pi\) |
−0.952958 | + | 0.303102i | \(0.901978\pi\) | |||||||
\(614\) | 9.71864 | − | 16.8332i | 0.392212 | − | 0.679332i | ||||
\(615\) | 1.57069 | + | 2.72051i | 0.0633362 | + | 0.109702i | ||||
\(616\) | − | 8.37867i | − | 0.337586i | ||||||
\(617\) | −10.0660 | + | 5.81163i | −0.405243 | + | 0.233967i | −0.688744 | − | 0.725005i | \(-0.741838\pi\) |
0.283501 | + | 0.958972i | \(0.408504\pi\) | |||||||
\(618\) | −2.46518 | + | 1.42327i | −0.0991640 | + | 0.0572524i | ||||
\(619\) | − | 16.5381i | − | 0.664722i | −0.943152 | − | 0.332361i | \(-0.892155\pi\) | ||
0.943152 | − | 0.332361i | \(-0.107845\pi\) | |||||||
\(620\) | −15.3878 | − | 26.6525i | −0.617990 | − | 1.07039i | ||||
\(621\) | 3.89493 | − | 6.74621i | 0.156298 | − | 0.270716i | ||||
\(622\) | 29.4288 | + | 16.9907i | 1.17999 | + | 0.681267i | ||||
\(623\) | 0.907542 | 0.0363599 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.33944 | 0.253577 | ||||||||
\(626\) | 29.0531 | + | 16.7738i | 1.16120 | + | 0.670417i | ||||
\(627\) | 3.48523 | − | 6.03660i | 0.139187 | − | 0.241078i | ||||
\(628\) | −33.1989 | − | 57.5023i | −1.32478 | − | 2.29459i | ||||
\(629\) | − | 21.8810i | − | 0.872452i | ||||||
\(630\) | 6.04332 | − | 3.48911i | 0.240772 | − | 0.139010i | ||||
\(631\) | −31.5593 | + | 18.2208i | −1.25636 | + | 0.725358i | −0.972364 | − | 0.233468i | \(-0.924993\pi\) |
−0.283993 | + | 0.958826i | \(0.591659\pi\) | |||||||
\(632\) | 19.8116i | 0.788064i | ||||||||
\(633\) | 0.607760 | + | 1.05267i | 0.0241563 | + | 0.0418399i | ||||
\(634\) | −8.06547 | + | 13.9698i | −0.320321 | + | 0.554812i | ||||
\(635\) | −18.1300 | − | 10.4673i | −0.719466 | − | 0.415384i | ||||
\(636\) | −35.4101 | −1.40410 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −25.8745 | −1.02438 | ||||||||
\(639\) | 7.03644 | + | 4.06249i | 0.278357 | + | 0.160710i | ||||
\(640\) | 37.7652 | − | 65.4112i | 1.49280 | − | 2.58560i | ||||
\(641\) | 13.6033 | + | 23.5617i | 0.537300 | + | 0.930630i | 0.999048 | + | 0.0436195i | \(0.0138889\pi\) |
−0.461748 | + | 0.887011i | \(0.652778\pi\) | |||||||
\(642\) | − | 22.4403i | − | 0.885646i | ||||||
\(643\) | 4.39042 | − | 2.53481i | 0.173141 | − | 0.0999632i | −0.410925 | − | 0.911669i | \(-0.634794\pi\) |
0.584066 | + | 0.811706i | \(0.301461\pi\) | |||||||
\(644\) | 19.2325 | − | 11.1039i | 0.757866 | − | 0.437554i | ||||
\(645\) | 5.96615i | 0.234917i | ||||||||
\(646\) | 8.46830 | + | 14.6675i | 0.333181 | + | 0.577086i | ||||
\(647\) | 9.66033 | − | 16.7322i | 0.379787 | − | 0.657810i | −0.611244 | − | 0.791442i | \(-0.709331\pi\) |
0.991031 | + | 0.133632i | \(0.0426641\pi\) | |||||||
\(648\) | −3.17387 | − | 1.83244i | −0.124682 | − | 0.0719849i | ||||
\(649\) | −15.3491 | −0.602506 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.88040 | 0.0736985 | ||||||||
\(652\) | 37.9892 | + | 21.9331i | 1.48777 | + | 0.858966i | ||||
\(653\) | −17.6177 | + | 30.5148i | −0.689436 | + | 1.19414i | 0.282585 | + | 0.959242i | \(0.408808\pi\) |
−0.972021 | + | 0.234895i | \(0.924525\pi\) | |||||||
\(654\) | 2.10292 | + | 3.64236i | 0.0822305 | + | 0.142427i | ||||
\(655\) | − | 67.2790i | − | 2.62881i | ||||||
\(656\) | 1.12579 | − | 0.649973i | 0.0439546 | − | 0.0253772i | ||||
\(657\) | −10.2950 | + | 5.94385i | −0.401648 | + | 0.231891i | ||||
\(658\) | − | 4.62133i | − | 0.180158i | ||||||
\(659\) | 2.18084 | + | 3.77733i | 0.0849535 | + | 0.147144i | 0.905371 | − | 0.424621i | \(-0.139592\pi\) |
−0.820418 | + | 0.571764i | \(0.806259\pi\) | |||||||
\(660\) | 18.7087 | − | 32.4044i | 0.728236 | − | 1.26134i | ||||
\(661\) | 13.3982 | + | 7.73543i | 0.521128 | + | 0.300873i | 0.737396 | − | 0.675461i | \(-0.236055\pi\) |
−0.216268 | + | 0.976334i | \(0.569389\pi\) | |||||||
\(662\) | −22.2553 | −0.864978 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 25.8334 | 1.00253 | ||||||||
\(665\) | 6.26934 | + | 3.61960i | 0.243115 | + | 0.140362i | ||||
\(666\) | −8.77359 | + | 15.1963i | −0.339970 | + | 0.588845i | ||||
\(667\) | −14.9988 | − | 25.9787i | −0.580756 | − | 1.00590i | ||||
\(668\) | − | 40.8605i | − | 1.58094i | ||||||
\(669\) | −15.0588 | + | 8.69418i | −0.582205 | + | 0.336136i | ||||
\(670\) | 108.470 | − | 62.6250i | 4.19055 | − | 2.41942i | ||||
\(671\) | 37.7928i | 1.45898i | ||||||||
\(672\) | 1.49516 | + | 2.58969i | 0.0576769 | + | 0.0998993i | ||||
\(673\) | −5.87047 | + | 10.1680i | −0.226290 | + | 0.391946i | −0.956706 | − | 0.291057i | \(-0.905993\pi\) |
0.730416 | + | 0.683003i | \(0.239326\pi\) | |||||||
\(674\) | −5.39492 | − | 3.11476i | −0.207805 | − | 0.119976i | ||||
\(675\) | 8.63102 | 0.332208 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.44504 | 0.132404 | 0.0662019 | − | 0.997806i | \(-0.478912\pi\) | ||||
0.0662019 | + | 0.997806i | \(0.478912\pi\) | |||||||
\(678\) | −10.1058 | − | 5.83459i | −0.388111 | − | 0.224076i | ||||
\(679\) | −2.38351 | + | 4.12836i | −0.0914707 | + | 0.158432i | ||||
\(680\) | 19.8835 | + | 34.4393i | 0.762498 | + | 1.32068i | ||||
\(681\) | 17.4155i | 0.667363i | ||||||||
\(682\) | 13.6444 | − | 7.87760i | 0.522471 | − | 0.301649i | ||||
\(683\) | 17.6720 | − | 10.2029i | 0.676198 | − | 0.390403i | −0.122223 | − | 0.992503i | \(-0.539002\pi\) |
0.798421 | + | 0.602099i | \(0.205669\pi\) | |||||||
\(684\) | − | 8.69202i | − | 0.332348i | ||||||
\(685\) | −17.4456 | − | 30.2166i | −0.666561 | − | 1.15452i | ||||
\(686\) | 12.6228 | − | 21.8634i | 0.481942 | − | 0.834748i | ||||
\(687\) | 16.2469 | + | 9.38016i | 0.619858 | + | 0.357875i | ||||
\(688\) | 2.46888 | 0.0941251 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 67.7851 | 2.58053 | ||||||||
\(691\) | 24.0788 | + | 13.9019i | 0.916002 | + | 0.528854i | 0.882358 | − | 0.470580i | \(-0.155955\pi\) |
0.0336449 | + | 0.999434i | \(0.489288\pi\) | |||||||
\(692\) | −21.5328 | + | 37.2959i | −0.818554 | + | 1.41778i | ||||
\(693\) | 1.14310 | + | 1.97991i | 0.0434229 | + | 0.0752107i | ||||
\(694\) | 23.9433i | 0.908876i | ||||||||
\(695\) | −12.8377 | + | 7.41185i | −0.486962 | + | 0.281148i | ||||
\(696\) | −12.2221 | + | 7.05645i | −0.463279 | + | 0.267474i | ||||
\(697\) | − | 2.50066i | − | 0.0947194i | ||||||
\(698\) | −12.3026 | − | 21.3087i | −0.465660 | − | 0.806547i | ||||
\(699\) | −1.97554 | + | 3.42174i | −0.0747218 | + | 0.129422i | ||||
\(700\) | 21.3092 | + | 12.3029i | 0.805414 | + | 0.465006i | ||||
\(701\) | −11.9715 | −0.452158 | −0.226079 | − | 0.974109i | \(-0.572591\pi\) | ||||
−0.226079 | + | 0.974109i | \(0.572591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2034 | −0.686556 | ||||||||
\(704\) | 29.2422 | + | 16.8830i | 1.10211 | + | 0.636301i | ||||
\(705\) | 4.51357 | − | 7.81774i | 0.169991 | − | 0.294433i | ||||
\(706\) | 21.5551 | + | 37.3346i | 0.811238 | + | 1.40510i | ||||
\(707\) | 3.70948i | 0.139509i | ||||||||
\(708\) | −16.5758 | + | 9.57002i | −0.622955 | + | 0.359664i | ||||
\(709\) | 27.9435 | − | 16.1332i | 1.04944 | − | 0.605894i | 0.126947 | − | 0.991909i | \(-0.459482\pi\) |
0.922492 | + | 0.386015i | \(0.126149\pi\) | |||||||
\(710\) | 70.7012i | 2.65337i | ||||||||
\(711\) | −2.70291 | − | 4.68157i | −0.101367 | − | 0.175573i | ||||
\(712\) | 2.07374 | − | 3.59183i | 0.0777169 | − | 0.134610i | ||||
\(713\) | 15.8186 | + | 9.13288i | 0.592412 | + | 0.342029i | ||||
\(714\) | −5.55496 | −0.207889 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.91457 | −0.0715510 | ||||||||
\(717\) | −0.708696 | − | 0.409166i | −0.0264667 | − | 0.0152806i | ||||
\(718\) | 17.9985 | − | 31.1743i | 0.671698 | − | 1.16342i | ||||
\(719\) | 6.05429 | + | 10.4863i | 0.225787 | + | 0.391075i | 0.956555 | − | 0.291551i | \(-0.0941713\pi\) |
−0.730768 | + | 0.682626i | \(0.760838\pi\) | |||||||
\(720\) | − | 5.64071i | − | 0.210217i | ||||||
\(721\) | 0.838781 | − | 0.484271i | 0.0312378 | − | 0.0180352i | ||||
\(722\) | −26.5791 | + | 15.3455i | −0.989173 | + | 0.571100i | ||||
\(723\) | − | 6.03252i | − | 0.224352i | ||||||
\(724\) | 41.3865 | + | 71.6835i | 1.53812 | + | 2.66410i | ||||
\(725\) | 16.6184 | − | 28.7839i | 0.617192 | − | 1.06901i | ||||
\(726\) | −5.86341 | − | 3.38524i | −0.217611 | − | 0.125638i | ||||
\(727\) | 16.6200 | 0.616402 | 0.308201 | − | 0.951321i | \(-0.400273\pi\) | ||||
0.308201 | + | 0.951321i | \(0.400273\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −89.5845 | − | 51.7216i | −3.31567 | − | 1.91430i | ||||
\(731\) | 2.37465 | − | 4.11301i | 0.0878296 | − | 0.152125i | ||||
\(732\) | 23.5635 | + | 40.8131i | 0.870930 | + | 1.50850i | ||||
\(733\) | − | 17.7912i | − | 0.657132i | −0.944481 | − | 0.328566i | \(-0.893435\pi\) | ||
0.944481 | − | 0.328566i | \(-0.106565\pi\) | |||||||
\(734\) | 45.4595 | − | 26.2461i | 1.67794 | − | 0.968760i | ||||
\(735\) | 20.3254 | − | 11.7349i | 0.749715 | − | 0.432848i | ||||
\(736\) | 29.0473i | 1.07070i | ||||||||
\(737\) | 20.5172 | + | 35.5369i | 0.755762 | + | 1.30902i | ||||
\(738\) | −1.00269 | + | 1.73671i | −0.0369095 | + | 0.0639291i | ||||
\(739\) | 23.6960 | + | 13.6809i | 0.871672 | + | 0.503260i | 0.867903 | − | 0.496733i | \(-0.165467\pi\) |
0.00376844 | + | 0.999993i | \(0.498800\pi\) | |||||||
\(740\) | −97.7160 | −3.59211 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 18.8267 | 0.691150 | ||||||||
\(743\) | 7.26246 | + | 4.19298i | 0.266434 | + | 0.153826i | 0.627266 | − | 0.778805i | \(-0.284174\pi\) |
−0.360832 | + | 0.932631i | \(0.617507\pi\) | |||||||
\(744\) | 4.29672 | − | 7.44215i | 0.157526 | − | 0.272842i | ||||
\(745\) | 35.8233 | + | 62.0478i | 1.31247 | + | 2.27326i | ||||
\(746\) | − | 9.72528i | − | 0.356068i | ||||||
\(747\) | −6.10454 | + | 3.52446i | −0.223353 | + | 0.128953i | ||||
\(748\) | −25.7953 | + | 14.8929i | −0.943168 | + | 0.544538i | ||||
\(749\) | 7.63533i | 0.278989i | ||||||||
\(750\) | 15.7981 | + | 27.3630i | 0.576863 | + | 0.999157i | ||||
\(751\) | −19.3889 | + | 33.5825i | −0.707511 | + | 1.22544i | 0.258267 | + | 0.966073i | \(0.416848\pi\) |
−0.965778 | + | 0.259371i | \(0.916485\pi\) | |||||||
\(752\) | −3.23509 | − | 1.86778i | −0.117972 | − | 0.0681110i | ||||
\(753\) | −26.8799 | −0.979559 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −45.6418 | −1.66107 | ||||||||
\(756\) | 2.46891 | + | 1.42543i | 0.0897935 | + | 0.0518423i | ||||
\(757\) | −6.48643 | + | 11.2348i | −0.235753 | + | 0.408336i | −0.959491 | − | 0.281738i | \(-0.909089\pi\) |
0.723738 | + | 0.690075i | \(0.242422\pi\) | |||||||
\(758\) | −12.6177 | − | 21.8546i | −0.458297 | − | 0.793794i | ||||
\(759\) | 22.2078i | 0.806090i | ||||||||
\(760\) | 28.6510 | − | 16.5417i | 1.03928 | − | 0.600030i | ||||
\(761\) | −4.46510 | + | 2.57792i | −0.161860 | + | 0.0934497i | −0.578742 | − | 0.815511i | \(-0.696456\pi\) |
0.416882 | + | 0.908961i | \(0.363123\pi\) | |||||||
\(762\) | − | 13.3642i | − | 0.484134i | ||||||
\(763\) | −0.715521 | − | 1.23932i | −0.0259036 | − | 0.0448663i | ||||
\(764\) | 29.8007 | − | 51.6163i | 1.07815 | − | 1.86741i | ||||
\(765\) | −9.39712 | − | 5.42543i | −0.339753 | − | 0.196157i | ||||
\(766\) | −15.3822 | −0.555783 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 24.5284 | 0.885092 | ||||||||
\(769\) | −30.7450 | − | 17.7506i | −1.10869 | − | 0.640104i | −0.170202 | − | 0.985409i | \(-0.554442\pi\) |
−0.938490 | + | 0.345305i | \(0.887775\pi\) | |||||||
\(770\) | −9.94696 | + | 17.2286i | −0.358464 | + | 0.620877i | ||||
\(771\) | 4.52661 | + | 7.84033i | 0.163022 | + | 0.282362i | ||||
\(772\) | − | 91.5186i | − | 3.29383i | ||||||
\(773\) | 5.33112 | − | 3.07792i | 0.191747 | − | 0.110705i | −0.401053 | − | 0.916055i | \(-0.631356\pi\) |
0.592800 | + | 0.805350i | \(0.298022\pi\) | |||||||
\(774\) | −3.29838 | + | 1.90432i | −0.118558 | + | 0.0684494i | ||||
\(775\) | 20.2381i | 0.726976i | ||||||||
\(776\) | 10.8927 | + | 18.8667i | 0.391025 | + | 0.677275i | ||||
\(777\) | 2.98523 | − | 5.17057i | 0.107095 | − | 0.185493i | ||||
\(778\) | 24.0695 | + | 13.8966i | 0.862935 | + | 0.498216i | ||||
\(779\) | −2.08038 | −0.0745372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.1631 | −0.828843 | ||||||||
\(782\) | −46.7305 | − | 26.9799i | −1.67108 | − | 0.964798i | ||||
\(783\) | 1.92543 | − | 3.33494i | 0.0688092 | − | 0.119181i | ||||
\(784\) | −4.85607 | − | 8.41096i | −0.173431 | − | 0.300391i | ||||
\(785\) | 68.9579i | 2.46121i | ||||||||
\(786\) | 37.1952 | − | 21.4746i | 1.32671 | − | 0.765975i | ||||
\(787\) | 12.3069 | − | 7.10537i | 0.438692 | − | 0.253279i | −0.264351 | − | 0.964427i | \(-0.585158\pi\) |
0.703043 | + | 0.711148i | \(0.251824\pi\) | |||||||
\(788\) | 76.1503i | 2.71274i | ||||||||
\(789\) | 11.5755 | + | 20.0494i | 0.412100 | + | 0.713778i | ||||
\(790\) | 23.5199 | − | 40.7377i | 0.836801 | − | 1.44938i | ||||
\(791\) | 3.43852 | + | 1.98523i | 0.122260 | + | 0.0705867i | ||||
\(792\) | 10.4480 | 0.371254 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −29.5623 | −1.04913 | ||||||||
\(795\) | 31.8484 | + | 18.3877i | 1.12955 | + | 0.652144i | ||||
\(796\) | −6.27061 | + | 10.8610i | −0.222256 | + | 0.384958i | ||||
\(797\) | 5.95108 | + | 10.3076i | 0.210798 | + | 0.365113i | 0.951965 | − | 0.306208i | \(-0.0990604\pi\) |
−0.741166 | + | 0.671321i | \(0.765727\pi\) | |||||||
\(798\) | 4.62133i | 0.163593i | ||||||||
\(799\) | −6.22324 | + | 3.59299i | −0.220162 | + | 0.127111i | ||||
\(800\) | −27.8720 | + | 16.0919i | −0.985425 | + | 0.568935i | ||||
\(801\) | 1.13169i | 0.0399862i | ||||||||
\(802\) | −21.0591 | − | 36.4755i | −0.743624 | − | 1.28799i | ||||
\(803\) | 16.9450 | − | 29.3497i | 0.597978 | − | 1.03573i | ||||
\(804\) | 44.3138 | + | 25.5846i | 1.56283 | + | 0.902298i | ||||
\(805\) | −23.0640 | −0.812899 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.42088 | 0.0852190 | ||||||||
\(808\) | 14.6812 | + | 8.47621i | 0.516483 | + | 0.298192i | ||||
\(809\) | −0.807979 | + | 1.39946i | −0.0284070 | + | 0.0492024i | −0.879879 | − | 0.475197i | \(-0.842377\pi\) |
0.851472 | + | 0.524399i | \(0.175710\pi\) | |||||||
\(810\) | 4.35086 | + | 7.53590i | 0.152873 | + | 0.264785i | ||||
\(811\) | 51.9657i | 1.82476i | 0.409342 | + | 0.912381i | \(0.365758\pi\) | ||||
−0.409342 | + | 0.912381i | \(0.634242\pi\) | |||||||
\(812\) | 9.50743 | − | 5.48911i | 0.333645 | − | 0.192630i | ||||
\(813\) | 18.5720 | − | 10.7225i | 0.651347 | − | 0.376055i | ||||
\(814\) | − | 50.0245i | − | 1.75336i | ||||||
\(815\) | −22.7787 | − | 39.4539i | −0.797904 | − | 1.38201i | ||||
\(816\) | −2.24512 | + | 3.88866i | −0.0785949 | + | 0.136130i | ||||
\(817\) | −3.42174 | − | 1.97554i | −0.119711 | − | 0.0691154i | ||||
\(818\) | 65.7853 | 2.30013 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11.1675 | −0.389985 | ||||||||
\(821\) | 47.4865 | + | 27.4163i | 1.65729 | + | 0.956837i | 0.973958 | + | 0.226728i | \(0.0728029\pi\) |
0.683331 | + | 0.730108i | \(0.260530\pi\) | |||||||
\(822\) | 11.1368 | − | 19.2895i | 0.388441 | − | 0.672800i | ||||
\(823\) | −23.4257 | − | 40.5745i | −0.816569 | − | 1.41434i | −0.908196 | − | 0.418546i | \(-0.862540\pi\) |
0.0916262 | − | 0.995793i | \(-0.470794\pi\) | |||||||
\(824\) | − | 4.42626i | − | 0.154196i | ||||||
\(825\) | −21.3092 | + | 12.3029i | −0.741893 | + | 0.428332i | ||||
\(826\) | 8.81293 | − | 5.08815i | 0.306641 | − | 0.177039i | ||||
\(827\) | 21.2021i | 0.737270i | 0.929574 | + | 0.368635i | \(0.120175\pi\) | ||||
−0.929574 | + | 0.368635i | \(0.879825\pi\) | |||||||
\(828\) | 13.8463 | + | 23.9825i | 0.481192 | + | 0.833450i | ||||
\(829\) | 9.14861 | − | 15.8459i | 0.317744 | − | 0.550350i | −0.662273 | − | 0.749263i | \(-0.730408\pi\) |
0.980017 | + | 0.198913i | \(0.0637413\pi\) | |||||||
\(830\) | −53.1200 | − | 30.6688i | −1.84382 | − | 1.06453i | ||||
\(831\) | −14.8073 | −0.513660 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.6829 | −0.647325 | ||||||||
\(834\) | −8.19528 | − | 4.73155i | −0.283779 | − | 0.163840i | ||||
\(835\) | −21.2180 | + | 36.7506i | −0.734278 | + | 1.27181i | ||||
\(836\) | 12.3898 | + | 21.4598i | 0.428512 | + | 0.742204i | ||||
\(837\) | 2.34481i | 0.0810486i | ||||||||
\(838\) | 33.4815 | − | 19.3306i | 1.15660 | − | 0.667764i | ||||
\(839\) | 18.3090 | − | 10.5707i | 0.632096 | − | 0.364941i | −0.149468 | − | 0.988767i | \(-0.547756\pi\) |
0.781563 | + | 0.623826i | \(0.214423\pi\) | |||||||
\(840\) | 10.8509i | 0.374390i | ||||||||
\(841\) | 7.08546 | + | 12.2724i | 0.244326 | + | 0.423185i | ||||
\(842\) | −3.57875 | + | 6.19858i | −0.123332 | + | 0.213617i | ||||
\(843\) | 12.5605 | + | 7.25182i | 0.432608 | + | 0.249766i | ||||
\(844\) | −4.32113 | −0.148739 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 5.76271 | 0.198126 | ||||||||
\(847\) | 1.99503 | + | 1.15183i | 0.0685502 | + | 0.0395775i | ||||
\(848\) | 7.60909 | − | 13.1793i | 0.261297 | − | 0.452580i | ||||
\(849\) | −12.8361 | − | 22.2328i | −0.440533 | − | 0.763026i | ||||
\(850\) | − | 59.7864i | − | 2.05066i | ||||||
\(851\) | 50.2258 | − | 28.9979i | 1.72172 | − | 0.994035i | ||||
\(852\) | −25.0143 | + | 14.4420i | −0.856974 | + | 0.494774i | ||||
\(853\) | − | 7.13036i | − | 0.244139i | −0.992522 | − | 0.122069i | \(-0.961047\pi\) | ||
0.992522 | − | 0.122069i | \(-0.0389531\pi\) | |||||||
\(854\) | −12.5281 | − | 21.6993i | −0.428703 | − | 0.742535i | ||||
\(855\) | −4.51357 | + | 7.81774i | −0.154361 | + | 0.267361i | ||||
\(856\) | 30.2188 | + | 17.4468i | 1.03286 | + | 0.596320i | ||||
\(857\) | 44.7741 | 1.52945 | 0.764726 | − | 0.644355i | \(-0.222874\pi\) | ||||
0.764726 | + | 0.644355i | \(0.222874\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.3782 | 1.95772 | 0.978859 | − | 0.204535i | \(-0.0655681\pi\) | ||||
0.978859 | + | 0.204535i | \(0.0655681\pi\) | |||||||
\(860\) | −18.3679 | − | 10.6047i | −0.626340 | − | 0.361617i | ||||
\(861\) | 0.341166 | − | 0.590918i | 0.0116269 | − | 0.0201384i | ||||
\(862\) | −3.93379 | − | 6.81352i | −0.133985 | − | 0.232069i | ||||
\(863\) | 6.67563i | 0.227241i | 0.993524 | + | 0.113621i | \(0.0362448\pi\) | ||||
−0.993524 | + | 0.113621i | \(0.963755\pi\) | |||||||
\(864\) | −3.22929 | + | 1.86443i | −0.109863 | + | 0.0634291i | ||||
\(865\) | 38.7338 | − | 22.3630i | 1.31699 | − | 0.760365i | ||||
\(866\) | 28.0536i | 0.953299i | ||||||||
\(867\) | −4.18114 | − | 7.24194i | −0.141999 | − | 0.245949i | ||||
\(868\) | −3.34236 | + | 5.78914i | −0.113447 | + | 0.196496i | ||||
\(869\) | 13.3465 | + | 7.70560i | 0.452748 | + | 0.261394i | ||||
\(870\) | 33.5090 | 1.13606 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −6.53989 | −0.221469 | ||||||||
\(873\) | −5.14798 | − | 2.97219i | −0.174233 | − | 0.100593i | ||||
\(874\) | −22.4453 | + | 38.8765i | −0.759225 | + | 1.31502i | ||||
\(875\) | −5.37531 | − | 9.31032i | −0.181719 | − | 0.314746i | ||||
\(876\) | − | 42.2602i | − | 1.42784i | ||||||
\(877\) | −21.9090 | + | 12.6491i | −0.739813 | + | 0.427131i | −0.822001 | − | 0.569486i | \(-0.807142\pi\) |
0.0821883 | + | 0.996617i | \(0.473809\pi\) | |||||||
\(878\) | 7.58914 | − | 4.38159i | 0.256121 | − | 0.147872i | ||||
\(879\) | 26.5230i | 0.894599i | ||||||||
\(880\) | 8.04043 | + | 13.9264i | 0.271043 | + | 0.469460i | ||||
\(881\) | −17.6893 | + | 30.6388i | −0.595969 | + | 1.03225i | 0.397441 | + | 0.917628i | \(0.369898\pi\) |
−0.993409 | + | 0.114620i | \(0.963435\pi\) | |||||||
\(882\) | 12.9753 | + | 7.49127i | 0.436900 | + | 0.252244i | ||||
\(883\) | 11.5851 | 0.389869 | 0.194935 | − | 0.980816i | \(-0.437551\pi\) | ||||
0.194935 | + | 0.980816i | \(0.437551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8780 | 0.668192 | ||||||||
\(886\) | 2.97418 | + | 1.71714i | 0.0999196 | + | 0.0576886i | ||||
\(887\) | 13.6446 | − | 23.6331i | 0.458141 | − | 0.793523i | −0.540722 | − | 0.841201i | \(-0.681849\pi\) |
0.998863 | + | 0.0476784i | \(0.0151822\pi\) | |||||||
\(888\) | −13.6426 | − | 23.6296i | −0.457815 | − | 0.792958i | ||||
\(889\) | 4.54719i | 0.152508i | ||||||||
\(890\) | −8.52828 | + | 4.92380i | −0.285869 | + | 0.165046i | ||||
\(891\) | −2.46891 | + | 1.42543i | −0.0827117 | + | 0.0477536i | ||||
\(892\) | − | 61.8149i | − | 2.06972i | ||||||
\(893\) | 2.98911 | + | 5.17730i | 0.100027 | + | 0.173252i | ||||
\(894\) | −22.8687 | + | 39.6098i | −0.764845 | + | 1.32475i | ||||
\(895\) | 1.72200 | + | 0.994196i | 0.0575601 | + | 0.0332323i | ||||
\(896\) | −16.4058 | −0.548080 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −28.5830 | −0.953826 | ||||||||
\(899\) | 7.81981 | + | 4.51477i | 0.260805 | + | 0.150576i | ||||
\(900\) | −15.3415 | + | 26.5722i | −0.511382 | + | 0.885740i | ||||
\(901\) | −14.6374 | − | 25.3526i | −0.487641 | − | 0.844619i | ||||
\(902\) | − | 5.71704i | − | 0.190357i | ||||||
\(903\) | 1.12228 | − | 0.647948i | 0.0373471 | − | 0.0215624i | ||||
\(904\) | 15.7141 | − | 9.07255i | 0.522644 | − | 0.301748i | ||||
\(905\) | − | 85.9643i | − | 2.85755i | ||||||
\(906\) | −14.5683 | − | 25.2330i | −0.483999 | − | 0.838311i | ||||
\(907\) | −15.2110 | + | 26.3462i | −0.505072 | + | 0.874810i | 0.494911 | + | 0.868944i | \(0.335201\pi\) |
−0.999983 | + | 0.00586661i | \(0.998133\pi\) | |||||||
\(908\) | −53.6168 | − | 30.9557i | −1.77934 | − | 1.02730i | ||||
\(909\) | −4.62565 | −0.153423 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 53.5719 | 1.77492 | 0.887459 | − | 0.460887i | \(-0.152469\pi\) | ||||
0.887459 | + | 0.460887i | \(0.152469\pi\) | |||||||
\(912\) | 3.23509 | + | 1.86778i | 0.107125 | + | 0.0618484i | ||||
\(913\) | 10.0477 | − | 17.4032i | 0.332531 | − | 0.575961i | ||||
\(914\) | −4.06332 | − | 7.03787i | −0.134403 | − | 0.232792i | ||||
\(915\) | − | 48.9439i | − | 1.61804i | ||||||
\(916\) | −57.7571 | + | 33.3461i | −1.90835 | + | 1.10179i | ||||
\(917\) | −12.6557 | + | 7.30678i | −0.417929 | + | 0.241291i | ||||
\(918\) | − | 6.92692i | − | 0.228622i | ||||||
\(919\) | 18.0836 | + | 31.3217i | 0.596523 | + | 1.03321i | 0.993330 | + | 0.115306i | \(0.0367848\pi\) |
−0.396807 | + | 0.917902i | \(0.629882\pi\) | |||||||
\(920\) | −52.7015 | + | 91.2816i | −1.73752 | + | 3.00947i | ||||
\(921\) | −7.14209 | − | 4.12349i | −0.235340 | − | 0.135874i | ||||
\(922\) | 15.9232 | 0.524403 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −8.12737 | −0.267371 | ||||||||
\(925\) | 55.6493 | + | 32.1292i | 1.82974 | + | 1.05640i | ||||
\(926\) | 8.78150 | − | 15.2100i | 0.288578 | − | 0.499831i | ||||
\(927\) | 0.603875 | + | 1.04594i | 0.0198339 | + | 0.0343533i | ||||
\(928\) | 14.3593i | 0.471367i | ||||||||
\(929\) | 11.5595 | − | 6.67390i | 0.379256 | − | 0.218964i | −0.298239 | − | 0.954491i | \(-0.596399\pi\) |
0.677494 | + | 0.735528i | \(0.263066\pi\) | |||||||
\(930\) | −17.6703 | + | 10.2019i | −0.579432 | + | 0.334535i | ||||
\(931\) | 15.5429i | 0.509397i | ||||||||
\(932\) | −7.02297 | − | 12.1641i | −0.230045 | − | 0.398449i | ||||
\(933\) | 7.20895 | − | 12.4863i | 0.236010 | − | 0.408782i | ||||
\(934\) | −66.5610 | − | 38.4290i | −2.17794 | − | 1.25744i | ||||
\(935\) | 30.9342 | 1.01166 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 38.6872 | 1.26386 | 0.631928 | − | 0.775027i | \(-0.282264\pi\) | ||||
0.631928 | + | 0.775027i | \(0.282264\pi\) | |||||||
\(938\) | −23.5605 | − | 13.6027i | −0.769279 | − | 0.444143i | ||||
\(939\) | 7.11692 | − | 12.3269i | 0.232252 | − | 0.402272i | ||||
\(940\) | 16.0456 | + | 27.7917i | 0.523349 | + | 0.906466i | ||||
\(941\) | − | 35.7275i | − | 1.16468i | −0.812944 | − | 0.582342i | \(-0.802136\pi\) | ||
0.812944 | − | 0.582342i | \(-0.197864\pi\) | |||||||
\(942\) | −38.1233 | + | 22.0105i | −1.24213 | + | 0.717141i | ||||
\(943\) | 5.74005 | − | 3.31402i | 0.186922 | − | 0.107919i | ||||
\(944\) | − | 8.22580i | − | 0.267727i | ||||||
\(945\) | −1.48039 | − | 2.56410i | −0.0481569 | − | 0.0834103i | ||||
\(946\) | 5.42894 | − | 9.40321i | 0.176510 | − | 0.305725i | ||||
\(947\) | 15.4530 | + | 8.92178i | 0.502154 | + | 0.289919i | 0.729603 | − | 0.683871i | \(-0.239705\pi\) |
−0.227448 | + | 0.973790i | \(0.573038\pi\) | |||||||
\(948\) | 19.2174 | 0.624153 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −49.7381 | −1.61372 | ||||||||
\(951\) | 5.92721 | + | 3.42208i | 0.192203 | + | 0.110968i | ||||
\(952\) | 4.31886 | − | 7.48049i | 0.139975 | − | 0.242444i | ||||
\(953\) | 10.0846 | + | 17.4670i | 0.326671 | + | 0.565810i | 0.981849 | − | 0.189664i | \(-0.0607398\pi\) |
−0.655178 | + | 0.755474i | \(0.727406\pi\) | |||||||
\(954\) | 23.4765i | 0.760080i | ||||||||
\(955\) | −53.6064 | + | 30.9496i | −1.73466 | + | 1.00151i | ||||
\(956\) | 2.51938 | − | 1.45457i | 0.0814827 | − | 0.0470440i | ||||
\(957\) | 10.9782i | 0.354876i | ||||||||
\(958\) | −3.33393 | − | 5.77453i | −0.107714 | − | 0.186567i | ||||
\(959\) | −3.78932 | + | 6.56330i | −0.122364 | + | 0.211940i | ||||
\(960\) | −37.8703 | − | 21.8644i | −1.22226 | − | 0.705671i | ||||
\(961\) | 25.5018 | 0.822640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −9.52111 | −0.306813 | ||||||||
\(964\) | 18.5722 | + | 10.7227i | 0.598171 | + | 0.345354i | ||||
\(965\) | −47.5236 | + | 82.3132i | −1.52984 | + | 2.64976i | ||||
\(966\) | −7.36174 | − | 12.7509i | −0.236860 | − | 0.410254i | ||||
\(967\) | 32.7894i | 1.05444i | 0.849730 | + | 0.527218i | \(0.176765\pi\) | ||||
−0.849730 | + | 0.527218i | \(0.823235\pi\) | |||||||
\(968\) | 9.11735 | − | 5.26391i | 0.293043 | − | 0.169188i | ||||
\(969\) | 6.22324 | − | 3.59299i | 0.199919 | − | 0.115423i | ||||
\(970\) | − | 51.7263i | − | 1.66083i | ||||||
\(971\) | 13.4922 | + | 23.3692i | 0.432986 | + | 0.749954i | 0.997129 | − | 0.0757231i | \(-0.0241265\pi\) |
−0.564143 | + | 0.825677i | \(0.690793\pi\) | |||||||
\(972\) | −1.77748 | + | 3.07868i | −0.0570127 | + | 0.0987488i | ||||
\(973\) | 2.78846 | + | 1.60992i | 0.0893938 | + | 0.0516115i | ||||
\(974\) | 97.3245 | 3.11848 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −20.2537 | −0.648305 | ||||||||
\(977\) | −14.6852 | − | 8.47853i | −0.469822 | − | 0.271252i | 0.246343 | − | 0.969183i | \(-0.420771\pi\) |
−0.716165 | + | 0.697931i | \(0.754104\pi\) | |||||||
\(978\) | 14.5414 | − | 25.1864i | 0.464982 | − | 0.805373i | ||||
\(979\) | −1.61314 | − | 2.79404i | −0.0515561 | − | 0.0892978i | ||||
\(980\) | 83.4341i | 2.66521i | ||||||||
\(981\) | 1.54540 | − | 0.892240i | 0.0493410 | − | 0.0284870i | ||||
\(982\) | −70.7656 | + | 40.8565i | −2.25822 | + | 1.30378i | ||||
\(983\) | − | 32.6631i | − | 1.04179i | −0.853621 | − | 0.520895i | \(-0.825598\pi\) | ||
0.853621 | − | 0.520895i | \(-0.174402\pi\) | |||||||
\(984\) | −1.55914 | − | 2.70051i | −0.0497035 | − | 0.0860890i | ||||
\(985\) | 39.5432 | − | 68.4908i | 1.25995 | − | 2.18230i | ||||
\(986\) | −23.1008 | − | 13.3373i | −0.735681 | − | 0.424746i | ||||
\(987\) | −1.96077 | −0.0624120 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.5881 | 0.400277 | ||||||||
\(990\) | −21.4838 | − | 12.4037i | −0.682799 | − | 0.394214i | ||||
\(991\) | −3.82155 | + | 6.61912i | −0.121396 | + | 0.210263i | −0.920318 | − | 0.391170i | \(-0.872070\pi\) |
0.798923 | + | 0.601434i | \(0.205404\pi\) | |||||||
\(992\) | −4.37174 | − | 7.57207i | −0.138803 | − | 0.240414i | ||||
\(993\) | 9.44265i | 0.299653i | ||||||||
\(994\) | 13.2995 | − | 7.67845i | 0.421833 | − | 0.243546i | ||||
\(995\) | 11.2798 | − | 6.51238i | 0.357593 | − | 0.206456i | ||||
\(996\) | − | 25.0586i | − | 0.794012i | ||||||
\(997\) | −18.0628 | − | 31.2857i | −0.572054 | − | 0.990827i | −0.996355 | − | 0.0853055i | \(-0.972813\pi\) |
0.424301 | − | 0.905521i | \(-0.360520\pi\) | |||||||
\(998\) | 21.1424 | − | 36.6198i | 0.669252 | − | 1.15918i | ||||
\(999\) | 6.44760 | + | 3.72252i | 0.203993 | + | 0.117775i |
(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 | 507.2.j.i.316.5 | 12 | ||
13.2 | odd | 12 | 507.2.e.l.484.2 | 6 | |||
13.3 | even | 3 | inner | 507.2.j.i.361.2 | 12 | ||
13.4 | even | 6 | 507.2.b.f.337.5 | 6 | |||
13.5 | odd | 4 | 507.2.e.l.22.2 | 6 | |||
13.6 | odd | 12 | 507.2.a.i.1.2 | ✓ | 3 | ||
13.7 | odd | 12 | 507.2.a.l.1.2 | yes | 3 | ||
13.8 | odd | 4 | 507.2.e.i.22.2 | 6 | |||
13.9 | even | 3 | 507.2.b.f.337.2 | 6 | |||
13.10 | even | 6 | inner | 507.2.j.i.361.5 | 12 | ||
13.11 | odd | 12 | 507.2.e.i.484.2 | 6 | |||
13.12 | even | 2 | inner | 507.2.j.i.316.2 | 12 | ||
39.17 | odd | 6 | 1521.2.b.k.1351.2 | 6 | |||
39.20 | even | 12 | 1521.2.a.n.1.2 | 3 | |||
39.32 | even | 12 | 1521.2.a.s.1.2 | 3 | |||
39.35 | odd | 6 | 1521.2.b.k.1351.5 | 6 | |||
52.7 | even | 12 | 8112.2.a.cp.1.3 | 3 | |||
52.19 | even | 12 | 8112.2.a.cg.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
507.2.a.i.1.2 | ✓ | 3 | 13.6 | odd | 12 | ||
507.2.a.l.1.2 | yes | 3 | 13.7 | odd | 12 | ||
507.2.b.f.337.2 | 6 | 13.9 | even | 3 | |||
507.2.b.f.337.5 | 6 | 13.4 | even | 6 | |||
507.2.e.i.22.2 | 6 | 13.8 | odd | 4 | |||
507.2.e.i.484.2 | 6 | 13.11 | odd | 12 | |||
507.2.e.l.22.2 | 6 | 13.5 | odd | 4 | |||
507.2.e.l.484.2 | 6 | 13.2 | odd | 12 | |||
507.2.j.i.316.2 | 12 | 13.12 | even | 2 | inner | ||
507.2.j.i.316.5 | 12 | 1.1 | even | 1 | trivial | ||
507.2.j.i.361.2 | 12 | 13.3 | even | 3 | inner | ||
507.2.j.i.361.5 | 12 | 13.10 | even | 6 | inner | ||
1521.2.a.n.1.2 | 3 | 39.20 | even | 12 | |||
1521.2.a.s.1.2 | 3 | 39.32 | even | 12 | |||
1521.2.b.k.1351.2 | 6 | 39.17 | odd | 6 | |||
1521.2.b.k.1351.5 | 6 | 39.35 | odd | 6 | |||
8112.2.a.cg.1.1 | 3 | 52.19 | even | 12 | |||
8112.2.a.cp.1.3 | 3 | 52.7 | even | 12 |