Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [240,2,Mod(61,240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(240, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("240.61");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 240 = 2^{4} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 240.s (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: | \(1.91640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 2 x^{18} - 4 x^{17} + 7 x^{16} + 16 x^{15} + 6 x^{14} - 36 x^{13} - 42 x^{12} + 40 x^{11} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 181.7 | ||
Root | \(1.15787 - 0.811989i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 240.181 |
Dual form | 240.2.s.c.61.7 |
$q$-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 \(\left(\mathbb{Z}/240\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(161\) | \(181\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.15787 | − | 0.811989i | 0.818741 | − | 0.574163i | ||||
\(3\) | 0.707107 | − | 0.707107i | 0.408248 | − | 0.408248i | ||||
\(4\) | 0.681349 | − | 1.88036i | 0.340674 | − | 0.940181i | ||||
\(5\) | 0.707107 | + | 0.707107i | 0.316228 | + | 0.316228i | ||||
\(6\) | 0.244579 | − | 1.39290i | 0.0998488 | − | 0.568651i | ||||
\(7\) | 2.18060i | 0.824189i | 0.911141 | + | 0.412094i | \(0.135203\pi\) | ||||
−0.911141 | + | 0.412094i | \(0.864797\pi\) | |||||||
\(8\) | −0.737916 | − | 2.73047i | −0.260893 | − | 0.965368i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 1.39290 | + | 0.244579i | 0.440475 | + | 0.0773425i | ||||
\(11\) | −0.00889637 | − | 0.00889637i | −0.00268236 | − | 0.00268236i | 0.705764 | − | 0.708447i | \(-0.250604\pi\) |
−0.708447 | + | 0.705764i | \(0.750604\pi\) | |||||||
\(12\) | −0.847831 | − | 1.81140i | −0.244748 | − | 0.522907i | ||||
\(13\) | 1.72965 | − | 1.72965i | 0.479719 | − | 0.479719i | −0.425323 | − | 0.905042i | \(-0.639839\pi\) |
0.905042 | + | 0.425323i | \(0.139839\pi\) | |||||||
\(14\) | 1.77062 | + | 2.52486i | 0.473218 | + | 0.674797i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | −3.07153 | − | 2.56237i | −0.767882 | − | 0.640592i | ||||
\(17\) | −5.54943 | −1.34593 | −0.672967 | − | 0.739673i | \(-0.734980\pi\) | ||||
−0.672967 | + | 0.739673i | \(0.734980\pi\) | |||||||
\(18\) | −0.811989 | − | 1.15787i | −0.191388 | − | 0.272914i | ||||
\(19\) | −4.94702 | + | 4.94702i | −1.13493 | + | 1.13493i | −0.145579 | + | 0.989347i | \(0.546504\pi\) |
−0.989347 | + | 0.145579i | \(0.953496\pi\) | |||||||
\(20\) | 1.81140 | − | 0.847831i | 0.405042 | − | 0.189581i | ||||
\(21\) | 1.54192 | + | 1.54192i | 0.336474 | + | 0.336474i | ||||
\(22\) | −0.0175246 | − | 0.00307713i | −0.00373626 | − | 0.000656047i | ||||
\(23\) | 3.01309i | 0.628272i | 0.949378 | + | 0.314136i | \(0.101715\pi\) | ||||
−0.949378 | + | 0.314136i | \(0.898285\pi\) | |||||||
\(24\) | −2.45252 | − | 1.40895i | −0.500619 | − | 0.287601i | ||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0.598263 | − | 3.40718i | 0.117329 | − | 0.668203i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | 4.10031 | + | 1.48575i | 0.774887 | + | 0.280780i | ||||
\(29\) | 3.20471 | − | 3.20471i | 0.595099 | − | 0.595099i | −0.343905 | − | 0.939004i | \(-0.611750\pi\) |
0.939004 | + | 0.343905i | \(0.111750\pi\) | |||||||
\(30\) | 1.15787 | − | 0.811989i | 0.211398 | − | 0.148248i | ||||
\(31\) | 3.58009 | 0.643004 | 0.321502 | − | 0.946909i | \(-0.395812\pi\) | ||||
0.321502 | + | 0.946909i | \(0.395812\pi\) | |||||||
\(32\) | −5.63706 | − | 0.472855i | −0.996500 | − | 0.0835897i | ||||
\(33\) | −0.0125814 | −0.00219013 | ||||||||
\(34\) | −6.42554 | + | 4.50607i | −1.10197 | + | 0.772785i | ||||
\(35\) | −1.54192 | + | 1.54192i | −0.260631 | + | 0.260631i | ||||
\(36\) | −1.88036 | − | 0.681349i | −0.313394 | − | 0.113558i | ||||
\(37\) | 4.97761 | + | 4.97761i | 0.818314 | + | 0.818314i | 0.985864 | − | 0.167550i | \(-0.0535856\pi\) |
−0.167550 | + | 0.985864i | \(0.553586\pi\) | |||||||
\(38\) | −1.71111 | + | 9.74496i | −0.277578 | + | 1.58084i | ||||
\(39\) | − | 2.44610i | − | 0.391689i | ||||||
\(40\) | 1.40895 | − | 2.45252i | 0.222775 | − | 0.387778i | ||||
\(41\) | − | 3.76487i | − | 0.587975i | −0.955809 | − | 0.293987i | \(-0.905018\pi\) | ||
0.955809 | − | 0.293987i | \(-0.0949823\pi\) | |||||||
\(42\) | 3.03736 | + | 0.533328i | 0.468675 | + | 0.0822942i | ||||
\(43\) | 6.81210 | + | 6.81210i | 1.03884 | + | 1.03884i | 0.999215 | + | 0.0396204i | \(0.0126149\pi\) |
0.0396204 | + | 0.999215i | \(0.487385\pi\) | |||||||
\(44\) | −0.0227899 | + | 0.0106669i | −0.00343571 | + | 0.00160809i | ||||
\(45\) | 0.707107 | − | 0.707107i | 0.105409 | − | 0.105409i | ||||
\(46\) | 2.44659 | + | 3.48878i | 0.360730 | + | 0.514392i | ||||
\(47\) | −10.0800 | −1.47032 | −0.735158 | − | 0.677896i | \(-0.762892\pi\) | ||||
−0.735158 | + | 0.677896i | \(0.762892\pi\) | |||||||
\(48\) | −3.98376 | + | 0.360031i | −0.575007 | + | 0.0519660i | ||||
\(49\) | 2.24499 | 0.320713 | ||||||||
\(50\) | 0.811989 | + | 1.15787i | 0.114833 | + | 0.163748i | ||||
\(51\) | −3.92404 | + | 3.92404i | −0.549475 | + | 0.549475i | ||||
\(52\) | −2.07388 | − | 4.43087i | −0.287595 | − | 0.614451i | ||||
\(53\) | −0.932644 | − | 0.932644i | −0.128108 | − | 0.128108i | 0.640145 | − | 0.768254i | \(-0.278874\pi\) |
−0.768254 | + | 0.640145i | \(0.778874\pi\) | |||||||
\(54\) | −1.39290 | − | 0.244579i | −0.189550 | − | 0.0332829i | ||||
\(55\) | − | 0.0125814i | − | 0.00169647i | ||||||
\(56\) | 5.95406 | − | 1.60910i | 0.795645 | − | 0.215025i | ||||
\(57\) | 6.99615i | 0.926663i | ||||||||
\(58\) | 1.10846 | − | 6.31283i | 0.145548 | − | 0.828915i | ||||
\(59\) | −4.60522 | − | 4.60522i | −0.599548 | − | 0.599548i | 0.340644 | − | 0.940192i | \(-0.389355\pi\) |
−0.940192 | + | 0.340644i | \(0.889355\pi\) | |||||||
\(60\) | 0.681349 | − | 1.88036i | 0.0879618 | − | 0.242754i | ||||
\(61\) | 4.17149 | − | 4.17149i | 0.534105 | − | 0.534105i | −0.387686 | − | 0.921791i | \(-0.626726\pi\) |
0.921791 | + | 0.387686i | \(0.126726\pi\) | |||||||
\(62\) | 4.14530 | − | 2.90700i | 0.526454 | − | 0.369189i | ||||
\(63\) | 2.18060 | 0.274730 | ||||||||
\(64\) | −6.91096 | + | 4.02972i | −0.863870 | + | 0.503715i | ||||
\(65\) | 2.44610 | 0.303401 | ||||||||
\(66\) | −0.0145676 | + | 0.0102159i | −0.00179315 | + | 0.00125749i | ||||
\(67\) | −11.0105 | + | 11.0105i | −1.34515 | + | 1.34515i | −0.454293 | + | 0.890852i | \(0.650108\pi\) |
−0.890852 | + | 0.454293i | \(0.849892\pi\) | |||||||
\(68\) | −3.78110 | + | 10.4349i | −0.458525 | + | 1.26542i | ||||
\(69\) | 2.13057 | + | 2.13057i | 0.256491 | + | 0.256491i | ||||
\(70\) | −0.533328 | + | 3.03736i | −0.0637448 | + | 0.363034i | ||||
\(71\) | − | 12.1092i | − | 1.43710i | −0.695475 | − | 0.718550i | \(-0.744806\pi\) | ||
0.695475 | − | 0.718550i | \(-0.255194\pi\) | |||||||
\(72\) | −2.73047 | + | 0.737916i | −0.321789 | + | 0.0869643i | ||||
\(73\) | − | 7.12981i | − | 0.834481i | −0.908796 | − | 0.417240i | \(-0.862997\pi\) | ||
0.908796 | − | 0.417240i | \(-0.137003\pi\) | |||||||
\(74\) | 9.80521 | + | 1.72169i | 1.13983 | + | 0.200142i | ||||
\(75\) | 0.707107 | + | 0.707107i | 0.0816497 | + | 0.0816497i | ||||
\(76\) | 5.93155 | + | 12.6729i | 0.680396 | + | 1.45368i | ||||
\(77\) | 0.0193994 | − | 0.0193994i | 0.00221077 | − | 0.00221077i | ||||
\(78\) | −1.98620 | − | 2.83228i | −0.224893 | − | 0.320692i | ||||
\(79\) | −3.41789 | −0.384543 | −0.192272 | − | 0.981342i | \(-0.561585\pi\) | ||||
−0.192272 | + | 0.981342i | \(0.561585\pi\) | |||||||
\(80\) | −0.360031 | − | 3.98376i | −0.0402527 | − | 0.445398i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −3.05704 | − | 4.35925i | −0.337593 | − | 0.481399i | ||||
\(83\) | 5.31631 | − | 5.31631i | 0.583541 | − | 0.583541i | −0.352333 | − | 0.935875i | \(-0.614612\pi\) |
0.935875 | + | 0.352333i | \(0.114612\pi\) | |||||||
\(84\) | 3.94994 | − | 1.84878i | 0.430974 | − | 0.201718i | ||||
\(85\) | −3.92404 | − | 3.92404i | −0.425622 | − | 0.425622i | ||||
\(86\) | 13.4189 | + | 2.35621i | 1.44700 | + | 0.254077i | ||||
\(87\) | − | 4.53214i | − | 0.485896i | ||||||
\(88\) | −0.0177265 | + | 0.0308561i | −0.00188965 | + | 0.00328927i | ||||
\(89\) | − | 5.06405i | − | 0.536788i | −0.963309 | − | 0.268394i | \(-0.913507\pi\) | ||
0.963309 | − | 0.268394i | \(-0.0864929\pi\) | |||||||
\(90\) | 0.244579 | − | 1.39290i | 0.0257808 | − | 0.146825i | ||||
\(91\) | 3.77168 | + | 3.77168i | 0.395379 | + | 0.395379i | ||||
\(92\) | 5.66569 | + | 2.05296i | 0.590689 | + | 0.214036i | ||||
\(93\) | 2.53151 | − | 2.53151i | 0.262505 | − | 0.262505i | ||||
\(94\) | −11.6714 | + | 8.18483i | −1.20381 | + | 0.844201i | ||||
\(95\) | −6.99615 | −0.717790 | ||||||||
\(96\) | −4.32036 | + | 3.65164i | −0.440945 | + | 0.372694i | ||||
\(97\) | −10.3646 | −1.05237 | −0.526184 | − | 0.850371i | \(-0.676378\pi\) | ||||
−0.526184 | + | 0.850371i | \(0.676378\pi\) | |||||||
\(98\) | 2.59942 | − | 1.82291i | 0.262581 | − | 0.184142i | ||||
\(99\) | −0.00889637 | + | 0.00889637i | −0.000894119 | + | 0.000894119i | ||||
\(100\) | 1.88036 | + | 0.681349i | 0.188036 | + | 0.0681349i | ||||
\(101\) | 9.96414 | + | 9.96414i | 0.991469 | + | 0.991469i | 0.999964 | − | 0.00849458i | \(-0.00270394\pi\) |
−0.00849458 | + | 0.999964i | \(0.502704\pi\) | |||||||
\(102\) | −1.35727 | + | 7.72982i | −0.134390 | + | 0.765366i | ||||
\(103\) | − | 2.25154i | − | 0.221851i | −0.993829 | − | 0.110926i | \(-0.964618\pi\) | ||
0.993829 | − | 0.110926i | \(-0.0353815\pi\) | |||||||
\(104\) | −5.99911 | − | 3.44643i | −0.588261 | − | 0.337950i | ||||
\(105\) | 2.18060i | 0.212805i | ||||||||
\(106\) | −1.83718 | − | 0.322589i | −0.178443 | − | 0.0313326i | ||||
\(107\) | 2.51098 | + | 2.51098i | 0.242746 | + | 0.242746i | 0.817985 | − | 0.575239i | \(-0.195091\pi\) |
−0.575239 | + | 0.817985i | \(0.695091\pi\) | |||||||
\(108\) | −1.81140 | + | 0.847831i | −0.174302 | + | 0.0815825i | ||||
\(109\) | 12.0668 | − | 12.0668i | 1.15579 | − | 1.15579i | 0.170420 | − | 0.985372i | \(-0.445488\pi\) |
0.985372 | − | 0.170420i | \(-0.0545124\pi\) | |||||||
\(110\) | −0.0102159 | − | 0.0145676i | −0.000974050 | − | 0.00138897i | ||||
\(111\) | 7.03940 | 0.668150 | ||||||||
\(112\) | 5.58749 | − | 6.69777i | 0.527968 | − | 0.632879i | ||||
\(113\) | −19.7954 | −1.86219 | −0.931097 | − | 0.364772i | \(-0.881147\pi\) | ||||
−0.931097 | + | 0.364772i | \(0.881147\pi\) | |||||||
\(114\) | 5.68079 | + | 8.10067i | 0.532055 | + | 0.758697i | ||||
\(115\) | −2.13057 | + | 2.13057i | −0.198677 | + | 0.198677i | ||||
\(116\) | −3.84249 | − | 8.20953i | −0.356766 | − | 0.762236i | ||||
\(117\) | −1.72965 | − | 1.72965i | −0.159906 | − | 0.159906i | ||||
\(118\) | −9.07165 | − | 1.59288i | −0.835113 | − | 0.146637i | ||||
\(119\) | − | 12.1011i | − | 1.10930i | ||||||
\(120\) | −0.737916 | − | 2.73047i | −0.0673622 | − | 0.249257i | ||||
\(121\) | − | 10.9998i | − | 0.999986i | ||||||
\(122\) | 1.44286 | − | 8.21727i | 0.130631 | − | 0.743957i | ||||
\(123\) | −2.66217 | − | 2.66217i | −0.240040 | − | 0.240040i | ||||
\(124\) | 2.43929 | − | 6.73188i | 0.219055 | − | 0.604540i | ||||
\(125\) | −0.707107 | + | 0.707107i | −0.0632456 | + | 0.0632456i | ||||
\(126\) | 2.52486 | − | 1.77062i | 0.224932 | − | 0.157739i | ||||
\(127\) | 14.3984 | 1.27765 | 0.638825 | − | 0.769352i | \(-0.279421\pi\) | ||||
0.638825 | + | 0.769352i | \(0.279421\pi\) | |||||||
\(128\) | −4.72994 | + | 10.2775i | −0.418072 | + | 0.908414i | ||||
\(129\) | 9.63376 | 0.848205 | ||||||||
\(130\) | 2.83228 | − | 1.98620i | 0.248407 | − | 0.174202i | ||||
\(131\) | −0.574754 | + | 0.574754i | −0.0502165 | + | 0.0502165i | −0.731769 | − | 0.681553i | \(-0.761305\pi\) |
0.681553 | + | 0.731769i | \(0.261305\pi\) | |||||||
\(132\) | −0.00857230 | + | 0.0236575i | −0.000746123 | + | 0.00205912i | ||||
\(133\) | −10.7875 | − | 10.7875i | −0.935393 | − | 0.935393i | ||||
\(134\) | −3.80838 | + | 21.6892i | −0.328994 | + | 1.87366i | ||||
\(135\) | − | 1.00000i | − | 0.0860663i | ||||||
\(136\) | 4.09501 | + | 15.1526i | 0.351144 | + | 1.29932i | ||||
\(137\) | − | 16.0077i | − | 1.36763i | −0.729654 | − | 0.683817i | \(-0.760319\pi\) | ||
0.729654 | − | 0.683817i | \(-0.239681\pi\) | |||||||
\(138\) | 4.19694 | + | 0.736936i | 0.357267 | + | 0.0627322i | ||||
\(139\) | −1.52424 | − | 1.52424i | −0.129284 | − | 0.129284i | 0.639504 | − | 0.768788i | \(-0.279140\pi\) |
−0.768788 | + | 0.639504i | \(0.779140\pi\) | |||||||
\(140\) | 1.84878 | + | 3.94994i | 0.156250 | + | 0.333831i | ||||
\(141\) | −7.12762 | + | 7.12762i | −0.600254 | + | 0.600254i | ||||
\(142\) | −9.83255 | − | 14.0210i | −0.825129 | − | 1.17661i | ||||
\(143\) | −0.0307753 | −0.00257356 | ||||||||
\(144\) | −2.56237 | + | 3.07153i | −0.213531 | + | 0.255961i | ||||
\(145\) | 4.53214 | 0.376374 | ||||||||
\(146\) | −5.78932 | − | 8.25543i | −0.479128 | − | 0.683224i | ||||
\(147\) | 1.58745 | − | 1.58745i | 0.130931 | − | 0.130931i | ||||
\(148\) | 12.7512 | − | 5.96822i | 1.04814 | − | 0.490585i | ||||
\(149\) | 12.1410 | + | 12.1410i | 0.994629 | + | 0.994629i | 0.999986 | − | 0.00535669i | \(-0.00170510\pi\) |
−0.00535669 | + | 0.999986i | \(0.501705\pi\) | |||||||
\(150\) | 1.39290 | + | 0.244579i | 0.113730 | + | 0.0199698i | ||||
\(151\) | − | 12.7940i | − | 1.04116i | −0.853813 | − | 0.520580i | \(-0.825716\pi\) | ||
0.853813 | − | 0.520580i | \(-0.174284\pi\) | |||||||
\(152\) | 17.1582 | + | 9.85723i | 1.39171 | + | 0.799527i | ||||
\(153\) | 5.54943i | 0.448645i | ||||||||
\(154\) | 0.00670999 | − | 0.0382142i | 0.000540706 | − | 0.00307939i | ||||
\(155\) | 2.53151 | + | 2.53151i | 0.203336 | + | 0.203336i | ||||
\(156\) | −4.59955 | − | 1.66665i | −0.368259 | − | 0.133438i | ||||
\(157\) | −10.3333 | + | 10.3333i | −0.824686 | + | 0.824686i | −0.986776 | − | 0.162090i | \(-0.948177\pi\) |
0.162090 | + | 0.986776i | \(0.448177\pi\) | |||||||
\(158\) | −3.95749 | + | 2.77529i | −0.314841 | + | 0.220790i | ||||
\(159\) | −1.31896 | −0.104600 | ||||||||
\(160\) | −3.65164 | − | 4.32036i | −0.288688 | − | 0.341554i | ||||
\(161\) | −6.57033 | −0.517814 | ||||||||
\(162\) | −1.15787 | + | 0.811989i | −0.0909713 | + | 0.0637959i | ||||
\(163\) | 13.4362 | − | 13.4362i | 1.05241 | − | 1.05241i | 0.0538580 | − | 0.998549i | \(-0.482848\pi\) |
0.998549 | − | 0.0538580i | \(-0.0171518\pi\) | |||||||
\(164\) | −7.07933 | − | 2.56519i | −0.552803 | − | 0.200308i | ||||
\(165\) | −0.00889637 | − | 0.00889637i | −0.000692581 | − | 0.000692581i | ||||
\(166\) | 1.83884 | − | 10.4724i | 0.142722 | − | 0.812817i | ||||
\(167\) | 5.08389i | 0.393403i | 0.980463 | + | 0.196702i | \(0.0630230\pi\) | ||||
−0.980463 | + | 0.196702i | \(0.936977\pi\) | |||||||
\(168\) | 3.07235 | − | 5.34796i | 0.237037 | − | 0.412604i | ||||
\(169\) | 7.01660i | 0.539739i | ||||||||
\(170\) | −7.72982 | − | 1.35727i | −0.592850 | − | 0.104098i | ||||
\(171\) | 4.94702 | + | 4.94702i | 0.378308 | + | 0.378308i | ||||
\(172\) | 17.4506 | − | 8.16780i | 1.33060 | − | 0.622789i | ||||
\(173\) | −10.8821 | + | 10.8821i | −0.827350 | + | 0.827350i | −0.987150 | − | 0.159799i | \(-0.948915\pi\) |
0.159799 | + | 0.987150i | \(0.448915\pi\) | |||||||
\(174\) | −3.68004 | − | 5.24765i | −0.278983 | − | 0.397823i | ||||
\(175\) | −2.18060 | −0.164838 | ||||||||
\(176\) | 0.00452968 | + | 0.0501212i | 0.000341438 | + | 0.00377803i | ||||
\(177\) | −6.51276 | −0.489529 | ||||||||
\(178\) | −4.11195 | − | 5.86353i | −0.308204 | − | 0.439490i | ||||
\(179\) | 11.1719 | − | 11.1719i | 0.835028 | − | 0.835028i | −0.153172 | − | 0.988200i | \(-0.548949\pi\) |
0.988200 | + | 0.153172i | \(0.0489488\pi\) | |||||||
\(180\) | −0.847831 | − | 1.81140i | −0.0631936 | − | 0.135014i | ||||
\(181\) | −10.1479 | − | 10.1479i | −0.754290 | − | 0.754290i | 0.220987 | − | 0.975277i | \(-0.429072\pi\) |
−0.975277 | + | 0.220987i | \(0.929072\pi\) | |||||||
\(182\) | 7.42969 | + | 1.30457i | 0.550725 | + | 0.0967013i | ||||
\(183\) | − | 5.89938i | − | 0.436095i | ||||||
\(184\) | 8.22715 | − | 2.22340i | 0.606513 | − | 0.163912i | ||||
\(185\) | 7.03940i | 0.517547i | ||||||||
\(186\) | 0.875614 | − | 4.98673i | 0.0642032 | − | 0.365645i | ||||
\(187\) | 0.0493697 | + | 0.0493697i | 0.00361027 | + | 0.00361027i | ||||
\(188\) | −6.86798 | + | 18.9540i | −0.500899 | + | 1.38236i | ||||
\(189\) | 1.54192 | − | 1.54192i | 0.112158 | − | 0.112158i | ||||
\(190\) | −8.10067 | + | 5.68079i | −0.587684 | + | 0.412128i | ||||
\(191\) | 13.3716 | 0.967532 | 0.483766 | − | 0.875197i | \(-0.339269\pi\) | ||||
0.483766 | + | 0.875197i | \(0.339269\pi\) | |||||||
\(192\) | −2.03734 | + | 7.73623i | −0.147033 | + | 0.558314i | ||||
\(193\) | 8.32925 | 0.599553 | 0.299776 | − | 0.954009i | \(-0.403088\pi\) | ||||
0.299776 | + | 0.954009i | \(0.403088\pi\) | |||||||
\(194\) | −12.0009 | + | 8.41596i | −0.861617 | + | 0.604230i | ||||
\(195\) | 1.72965 | − | 1.72965i | 0.123863 | − | 0.123863i | ||||
\(196\) | 1.52962 | − | 4.22140i | 0.109259 | − | 0.301529i | ||||
\(197\) | 13.1995 | + | 13.1995i | 0.940427 | + | 0.940427i | 0.998323 | − | 0.0578960i | \(-0.0184392\pi\) |
−0.0578960 | + | 0.998323i | \(0.518439\pi\) | |||||||
\(198\) | −0.00307713 | + | 0.0175246i | −0.000218682 | + | 0.00124542i | ||||
\(199\) | 3.66713i | 0.259956i | 0.991517 | + | 0.129978i | \(0.0414906\pi\) | ||||
−0.991517 | + | 0.129978i | \(0.958509\pi\) | |||||||
\(200\) | 2.73047 | − | 0.737916i | 0.193074 | − | 0.0521786i | ||||
\(201\) | 15.5712i | 1.09831i | ||||||||
\(202\) | 19.6280 | + | 3.44646i | 1.38102 | + | 0.242492i | ||||
\(203\) | 6.98817 | + | 6.98817i | 0.490474 | + | 0.490474i | ||||
\(204\) | 4.70497 | + | 10.0523i | 0.329414 | + | 0.703798i | ||||
\(205\) | 2.66217 | − | 2.66217i | 0.185934 | − | 0.185934i | ||||
\(206\) | −1.82823 | − | 2.60700i | −0.127379 | − | 0.181639i | ||||
\(207\) | 3.01309 | 0.209424 | ||||||||
\(208\) | −9.74468 | + | 0.880672i | −0.675672 | + | 0.0610636i | ||||
\(209\) | 0.0880211 | 0.00608855 | ||||||||
\(210\) | 1.77062 | + | 2.52486i | 0.122184 | + | 0.174232i | ||||
\(211\) | −12.6423 | + | 12.6423i | −0.870332 | + | 0.870332i | −0.992508 | − | 0.122176i | \(-0.961013\pi\) |
0.122176 | + | 0.992508i | \(0.461013\pi\) | |||||||
\(212\) | −2.38916 | + | 1.11825i | −0.164088 | + | 0.0768019i | ||||
\(213\) | −8.56251 | − | 8.56251i | −0.586694 | − | 0.586694i | ||||
\(214\) | 4.94629 | + | 0.868514i | 0.338121 | + | 0.0593704i | ||||
\(215\) | 9.63376i | 0.657017i | ||||||||
\(216\) | −1.40895 | + | 2.45252i | −0.0958669 | + | 0.166873i | ||||
\(217\) | 7.80675i | 0.529956i | ||||||||
\(218\) | 4.17375 | − | 23.7700i | 0.282682 | − | 1.60991i | ||||
\(219\) | −5.04154 | − | 5.04154i | −0.340675 | − | 0.340675i | ||||
\(220\) | −0.0236575 | − | 0.00857230i | −0.00159499 | − | 0.000577944i | ||||
\(221\) | −9.59858 | + | 9.59858i | −0.645670 | + | 0.645670i | ||||
\(222\) | 8.15074 | − | 5.71591i | 0.547042 | − | 0.383627i | ||||
\(223\) | −5.37431 | −0.359891 | −0.179945 | − | 0.983677i | \(-0.557592\pi\) | ||||
−0.179945 | + | 0.983677i | \(0.557592\pi\) | |||||||
\(224\) | 1.03111 | − | 12.2922i | 0.0688936 | − | 0.821304i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −22.9206 | + | 16.0736i | −1.52465 | + | 1.06920i | ||||
\(227\) | 1.92306 | − | 1.92306i | 0.127638 | − | 0.127638i | −0.640402 | − | 0.768040i | \(-0.721232\pi\) |
0.768040 | + | 0.640402i | \(0.221232\pi\) | |||||||
\(228\) | 13.1553 | + | 4.76682i | 0.871231 | + | 0.315690i | ||||
\(229\) | 5.08104 | + | 5.08104i | 0.335765 | + | 0.335765i | 0.854771 | − | 0.519006i | \(-0.173698\pi\) |
−0.519006 | + | 0.854771i | \(0.673698\pi\) | |||||||
\(230\) | −0.736936 | + | 4.19694i | −0.0485921 | + | 0.276738i | ||||
\(231\) | − | 0.0274349i | − | 0.00180508i | ||||||
\(232\) | −11.1152 | − | 6.38556i | −0.729746 | − | 0.419232i | ||||
\(233\) | 26.2417i | 1.71915i | 0.511011 | + | 0.859574i | \(0.329271\pi\) | ||||
−0.511011 | + | 0.859574i | \(0.670729\pi\) | |||||||
\(234\) | −3.40718 | − | 0.598263i | −0.222734 | − | 0.0391097i | ||||
\(235\) | −7.12762 | − | 7.12762i | −0.464955 | − | 0.464955i | ||||
\(236\) | −11.7972 | + | 5.52172i | −0.767935 | + | 0.359433i | ||||
\(237\) | −2.41682 | + | 2.41682i | −0.156989 | + | 0.156989i | ||||
\(238\) | −9.82593 | − | 14.0115i | −0.636920 | − | 0.908232i | ||||
\(239\) | −7.40931 | −0.479268 | −0.239634 | − | 0.970863i | \(-0.577027\pi\) | ||||
−0.239634 | + | 0.970863i | \(0.577027\pi\) | |||||||
\(240\) | −3.07153 | − | 2.56237i | −0.198266 | − | 0.165400i | ||||
\(241\) | −19.6231 | −1.26404 | −0.632019 | − | 0.774953i | \(-0.717773\pi\) | ||||
−0.632019 | + | 0.774953i | \(0.717773\pi\) | |||||||
\(242\) | −8.93175 | − | 12.7364i | −0.574154 | − | 0.818729i | ||||
\(243\) | −0.707107 | + | 0.707107i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | −5.00168 | − | 10.6862i | −0.320200 | − | 0.684112i | ||||
\(245\) | 1.58745 | + | 1.58745i | 0.101418 | + | 0.101418i | ||||
\(246\) | −5.24411 | − | 0.920808i | −0.334352 | − | 0.0587085i | ||||
\(247\) | 17.1133i | 1.08889i | ||||||||
\(248\) | −2.64181 | − | 9.77535i | −0.167755 | − | 0.620735i | ||||
\(249\) | − | 7.51840i | − | 0.476459i | ||||||
\(250\) | −0.244579 | + | 1.39290i | −0.0154685 | + | 0.0880950i | ||||
\(251\) | 1.23610 | + | 1.23610i | 0.0780217 | + | 0.0780217i | 0.745041 | − | 0.667019i | \(-0.232430\pi\) |
−0.667019 | + | 0.745041i | \(0.732430\pi\) | |||||||
\(252\) | 1.48575 | − | 4.10031i | 0.0935933 | − | 0.258296i | ||||
\(253\) | 0.0268055 | − | 0.0268055i | 0.00168525 | − | 0.00168525i | ||||
\(254\) | 16.6715 | − | 11.6913i | 1.04606 | − | 0.733579i | ||||
\(255\) | −5.54943 | −0.347519 | ||||||||
\(256\) | 2.86856 | + | 15.7408i | 0.179285 | + | 0.983797i | ||||
\(257\) | 3.01050 | 0.187790 | 0.0938948 | − | 0.995582i | \(-0.470068\pi\) | ||||
0.0938948 | + | 0.995582i | \(0.470068\pi\) | |||||||
\(258\) | 11.1547 | − | 7.82250i | 0.694461 | − | 0.487008i | ||||
\(259\) | −10.8542 | + | 10.8542i | −0.674445 | + | 0.674445i | ||||
\(260\) | 1.66665 | − | 4.59955i | 0.103361 | − | 0.285252i | ||||
\(261\) | −3.20471 | − | 3.20471i | −0.198366 | − | 0.198366i | ||||
\(262\) | −0.198800 | + | 1.13219i | −0.0122819 | + | 0.0699468i | ||||
\(263\) | 11.9000i | 0.733788i | 0.930263 | + | 0.366894i | \(0.119579\pi\) | ||||
−0.930263 | + | 0.366894i | \(0.880421\pi\) | |||||||
\(264\) | 0.00928399 | + | 0.0343531i | 0.000571390 | + | 0.00211429i | ||||
\(265\) | − | 1.31896i | − | 0.0810229i | ||||||
\(266\) | −21.2498 | − | 3.73124i | −1.30291 | − | 0.228777i | ||||
\(267\) | −3.58082 | − | 3.58082i | −0.219143 | − | 0.219143i | ||||
\(268\) | 13.2017 | + | 28.2057i | 0.806424 | + | 1.72294i | ||||
\(269\) | −15.4949 | + | 15.4949i | −0.944742 | + | 0.944742i | −0.998551 | − | 0.0538091i | \(-0.982864\pi\) |
0.0538091 | + | 0.998551i | \(0.482864\pi\) | |||||||
\(270\) | −0.811989 | − | 1.15787i | −0.0494161 | − | 0.0704660i | ||||
\(271\) | 7.30492 | 0.443742 | 0.221871 | − | 0.975076i | \(-0.428784\pi\) | ||||
0.221871 | + | 0.975076i | \(0.428784\pi\) | |||||||
\(272\) | 17.0452 | + | 14.2197i | 1.03352 | + | 0.862194i | ||||
\(273\) | 5.33396 | 0.322826 | ||||||||
\(274\) | −12.9981 | − | 18.5350i | −0.785244 | − | 1.11974i | ||||
\(275\) | 0.00889637 | − | 0.00889637i | 0.000536471 | − | 0.000536471i | ||||
\(276\) | 5.45791 | − | 2.55459i | 0.328528 | − | 0.153768i | ||||
\(277\) | 2.23718 | + | 2.23718i | 0.134419 | + | 0.134419i | 0.771115 | − | 0.636696i | \(-0.219699\pi\) |
−0.636696 | + | 0.771115i | \(0.719699\pi\) | |||||||
\(278\) | −3.00254 | − | 0.527212i | −0.180080 | − | 0.0316201i | ||||
\(279\) | − | 3.58009i | − | 0.214335i | ||||||
\(280\) | 5.34796 | + | 3.07235i | 0.319602 | + | 0.183608i | ||||
\(281\) | − | 4.85036i | − | 0.289348i | −0.989479 | − | 0.144674i | \(-0.953787\pi\) | ||
0.989479 | − | 0.144674i | \(-0.0462134\pi\) | |||||||
\(282\) | −2.46535 | + | 14.0404i | −0.146809 | + | 0.836096i | ||||
\(283\) | 11.4295 | + | 11.4295i | 0.679414 | + | 0.679414i | 0.959867 | − | 0.280454i | \(-0.0904850\pi\) |
−0.280454 | + | 0.959867i | \(0.590485\pi\) | |||||||
\(284\) | −22.7697 | − | 8.25060i | −1.35113 | − | 0.489583i | ||||
\(285\) | −4.94702 | + | 4.94702i | −0.293036 | + | 0.293036i | ||||
\(286\) | −0.0356339 | + | 0.0249892i | −0.00210708 | + | 0.00147764i | ||||
\(287\) | 8.20968 | 0.484602 | ||||||||
\(288\) | −0.472855 | + | 5.63706i | −0.0278632 | + | 0.332167i | ||||
\(289\) | 13.7961 | 0.811537 | ||||||||
\(290\) | 5.24765 | − | 3.68004i | 0.308153 | − | 0.216100i | ||||
\(291\) | −7.32890 | + | 7.32890i | −0.429627 | + | 0.429627i | ||||
\(292\) | −13.4066 | − | 4.85789i | −0.784563 | − | 0.284286i | ||||
\(293\) | −11.1686 | − | 11.1686i | −0.652475 | − | 0.652475i | 0.301113 | − | 0.953588i | \(-0.402642\pi\) |
−0.953588 | + | 0.301113i | \(0.902642\pi\) | |||||||
\(294\) | 0.549077 | − | 3.12706i | 0.0320228 | − | 0.182374i | ||||
\(295\) | − | 6.51276i | − | 0.379188i | ||||||
\(296\) | 9.91816 | − | 17.2643i | 0.576481 | − | 1.00347i | ||||
\(297\) | 0.0125814i | 0.000730045i | ||||||||
\(298\) | 23.9161 | + | 4.19940i | 1.38542 | + | 0.243265i | ||||
\(299\) | 5.21159 | + | 5.21159i | 0.301394 | + | 0.301394i | ||||
\(300\) | 1.81140 | − | 0.847831i | 0.104581 | − | 0.0489495i | ||||
\(301\) | −14.8544 | + | 14.8544i | −0.856196 | + | 0.856196i | ||||
\(302\) | −10.3886 | − | 14.8138i | −0.597795 | − | 0.852440i | ||||
\(303\) | 14.0914 | 0.809531 | ||||||||
\(304\) | 27.8710 | − | 2.51883i | 1.59851 | − | 0.144465i | ||||
\(305\) | 5.89938 | 0.337798 | ||||||||
\(306\) | 4.50607 | + | 6.42554i | 0.257595 | + | 0.367324i | ||||
\(307\) | 13.5366 | − | 13.5366i | 0.772575 | − | 0.772575i | −0.205981 | − | 0.978556i | \(-0.566038\pi\) |
0.978556 | + | 0.205981i | \(0.0660384\pi\) | |||||||
\(308\) | −0.0232602 | − | 0.0496957i | −0.00132537 | − | 0.00283167i | ||||
\(309\) | −1.59208 | − | 1.59208i | −0.0905703 | − | 0.0905703i | ||||
\(310\) | 4.98673 | + | 0.875614i | 0.283227 | + | 0.0497316i | ||||
\(311\) | 16.4956i | 0.935378i | 0.883893 | + | 0.467689i | \(0.154913\pi\) | ||||
−0.883893 | + | 0.467689i | \(0.845087\pi\) | |||||||
\(312\) | −6.67900 | + | 1.80502i | −0.378124 | + | 0.102189i | ||||
\(313\) | 27.2549i | 1.54054i | 0.637719 | + | 0.770269i | \(0.279878\pi\) | ||||
−0.637719 | + | 0.770269i | \(0.720122\pi\) | |||||||
\(314\) | −3.57414 | + | 20.3552i | −0.201701 | + | 1.14871i | ||||
\(315\) | 1.54192 | + | 1.54192i | 0.0868771 | + | 0.0868771i | ||||
\(316\) | −2.32878 | + | 6.42688i | −0.131004 | + | 0.361540i | ||||
\(317\) | 23.2962 | − | 23.2962i | 1.30845 | − | 1.30845i | 0.385911 | − | 0.922536i | \(-0.373887\pi\) |
0.922536 | − | 0.385911i | \(-0.126113\pi\) | |||||||
\(318\) | −1.52719 | + | 1.07098i | −0.0856404 | + | 0.0600575i | ||||
\(319\) | −0.0570205 | −0.00319253 | ||||||||
\(320\) | −7.73623 | − | 2.03734i | −0.432468 | − | 0.113891i | ||||
\(321\) | 3.55106 | 0.198201 | ||||||||
\(322\) | −7.60762 | + | 5.33503i | −0.423956 | + | 0.297310i | ||||
\(323\) | 27.4531 | − | 27.4531i | 1.52753 | − | 1.52753i | ||||
\(324\) | −0.681349 | + | 1.88036i | −0.0378527 | + | 0.104465i | ||||
\(325\) | 1.72965 | + | 1.72965i | 0.0959439 | + | 0.0959439i | ||||
\(326\) | 4.64741 | − | 26.4675i | 0.257396 | − | 1.46590i | ||||
\(327\) | − | 17.0651i | − | 0.943700i | ||||||
\(328\) | −10.2799 | + | 2.77816i | −0.567612 | + | 0.153398i | ||||
\(329\) | − | 21.9804i | − | 1.21182i | ||||||
\(330\) | −0.0175246 | − | 0.00307713i | −0.000964699 | − | 0.000169391i | ||||
\(331\) | −15.9057 | − | 15.9057i | −0.874257 | − | 0.874257i | 0.118676 | − | 0.992933i | \(-0.462135\pi\) |
−0.992933 | + | 0.118676i | \(0.962135\pi\) | |||||||
\(332\) | −6.37433 | − | 13.6189i | −0.349837 | − | 0.747432i | ||||
\(333\) | 4.97761 | − | 4.97761i | 0.272771 | − | 0.272771i | ||||
\(334\) | 4.12806 | + | 5.88651i | 0.225877 | + | 0.322096i | ||||
\(335\) | −15.5712 | −0.850745 | ||||||||
\(336\) | −0.785083 | − | 8.68699i | −0.0428298 | − | 0.473914i | ||||
\(337\) | 7.15503 | 0.389759 | 0.194880 | − | 0.980827i | \(-0.437568\pi\) | ||||
0.194880 | + | 0.980827i | \(0.437568\pi\) | |||||||
\(338\) | 5.69740 | + | 8.12435i | 0.309898 | + | 0.441906i | ||||
\(339\) | −13.9975 | + | 13.9975i | −0.760237 | + | 0.760237i | ||||
\(340\) | −10.0523 | + | 4.70497i | −0.545160 | + | 0.255163i | ||||
\(341\) | −0.0318498 | − | 0.0318498i | −0.00172477 | − | 0.00172477i | ||||
\(342\) | 9.74496 | + | 1.71111i | 0.526947 | + | 0.0925261i | ||||
\(343\) | 20.1596i | 1.08852i | ||||||||
\(344\) | 13.5735 | − | 23.6270i | 0.731833 | − | 1.27388i | ||||
\(345\) | 3.01309i | 0.162219i | ||||||||
\(346\) | −3.76397 | + | 21.4362i | −0.202352 | + | 1.15242i | ||||
\(347\) | −9.64716 | − | 9.64716i | −0.517887 | − | 0.517887i | 0.399045 | − | 0.916931i | \(-0.369342\pi\) |
−0.916931 | + | 0.399045i | \(0.869342\pi\) | |||||||
\(348\) | −8.52206 | − | 3.08797i | −0.456830 | − | 0.165532i | ||||
\(349\) | 20.3332 | − | 20.3332i | 1.08841 | − | 1.08841i | 0.0927209 | − | 0.995692i | \(-0.470444\pi\) |
0.995692 | − | 0.0927209i | \(-0.0295564\pi\) | |||||||
\(350\) | −2.52486 | + | 1.77062i | −0.134959 | + | 0.0946437i | ||||
\(351\) | −2.44610 | −0.130563 | ||||||||
\(352\) | 0.0459426 | + | 0.0543560i | 0.00244875 | + | 0.00289719i | ||||
\(353\) | 32.1660 | 1.71202 | 0.856010 | − | 0.516958i | \(-0.172936\pi\) | ||||
0.856010 | + | 0.516958i | \(0.172936\pi\) | |||||||
\(354\) | −7.54096 | + | 5.28829i | −0.400798 | + | 0.281069i | ||||
\(355\) | 8.56251 | − | 8.56251i | 0.454451 | − | 0.454451i | ||||
\(356\) | −9.52225 | − | 3.45038i | −0.504678 | − | 0.182870i | ||||
\(357\) | −8.55675 | − | 8.55675i | −0.452871 | − | 0.452871i | ||||
\(358\) | 3.86421 | − | 22.0071i | 0.204230 | − | 1.16311i | ||||
\(359\) | 15.8239i | 0.835155i | 0.908641 | + | 0.417578i | \(0.137121\pi\) | ||||
−0.908641 | + | 0.417578i | \(0.862879\pi\) | |||||||
\(360\) | −2.45252 | − | 1.40895i | −0.129259 | − | 0.0742582i | ||||
\(361\) | − | 29.9461i | − | 1.57611i | ||||||
\(362\) | −19.9901 | − | 3.51003i | −1.05065 | − | 0.184483i | ||||
\(363\) | −7.77806 | − | 7.77806i | −0.408242 | − | 0.408242i | ||||
\(364\) | 9.66195 | − | 4.52229i | 0.506424 | − | 0.237033i | ||||
\(365\) | 5.04154 | − | 5.04154i | 0.263886 | − | 0.263886i | ||||
\(366\) | −4.79023 | − | 6.83075i | −0.250389 | − | 0.357049i | ||||
\(367\) | 4.34838 | 0.226984 | 0.113492 | − | 0.993539i | \(-0.463796\pi\) | ||||
0.113492 | + | 0.993539i | \(0.463796\pi\) | |||||||
\(368\) | 7.72063 | − | 9.25477i | 0.402466 | − | 0.482438i | ||||
\(369\) | −3.76487 | −0.195992 | ||||||||
\(370\) | 5.71591 | + | 8.15074i | 0.297156 | + | 0.423737i | ||||
\(371\) | 2.03372 | − | 2.03372i | 0.105586 | − | 0.105586i | ||||
\(372\) | −3.03531 | − | 6.48500i | −0.157374 | − | 0.336231i | ||||
\(373\) | −17.3659 | − | 17.3659i | −0.899171 | − | 0.899171i | 0.0961919 | − | 0.995363i | \(-0.469334\pi\) |
−0.995363 | + | 0.0961919i | \(0.969334\pi\) | |||||||
\(374\) | 0.0972517 | + | 0.0170763i | 0.00502876 | + | 0.000882996i | ||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 7.43818 | + | 27.5231i | 0.383595 | + | 1.41940i | ||||
\(377\) | − | 11.0861i | − | 0.570961i | ||||||
\(378\) | 0.533328 | − | 3.03736i | 0.0274314 | − | 0.156225i | ||||
\(379\) | −15.3936 | − | 15.3936i | −0.790717 | − | 0.790717i | 0.190893 | − | 0.981611i | \(-0.438862\pi\) |
−0.981611 | + | 0.190893i | \(0.938862\pi\) | |||||||
\(380\) | −4.76682 | + | 13.1553i | −0.244533 | + | 0.674853i | ||||
\(381\) | 10.1812 | − | 10.1812i | 0.521598 | − | 0.521598i | ||||
\(382\) | 15.4826 | − | 10.8576i | 0.792159 | − | 0.555521i | ||||
\(383\) | −15.6393 | −0.799129 | −0.399564 | − | 0.916705i | \(-0.630839\pi\) | ||||
−0.399564 | + | 0.916705i | \(0.630839\pi\) | |||||||
\(384\) | 3.92274 | + | 10.6119i | 0.200181 | + | 0.541536i | ||||
\(385\) | 0.0274349 | 0.00139821 | ||||||||
\(386\) | 9.64423 | − | 6.76326i | 0.490879 | − | 0.344241i | ||||
\(387\) | 6.81210 | − | 6.81210i | 0.346278 | − | 0.346278i | ||||
\(388\) | −7.06193 | + | 19.4893i | −0.358515 | + | 0.989417i | ||||
\(389\) | 17.0067 | + | 17.0067i | 0.862276 | + | 0.862276i | 0.991602 | − | 0.129326i | \(-0.0412813\pi\) |
−0.129326 | + | 0.991602i | \(0.541281\pi\) | |||||||
\(390\) | 0.598263 | − | 3.40718i | 0.0302942 | − | 0.172529i | ||||
\(391\) | − | 16.7209i | − | 0.845612i | ||||||
\(392\) | −1.65662 | − | 6.12989i | −0.0836717 | − | 0.309606i | ||||
\(393\) | 0.812825i | 0.0410016i | ||||||||
\(394\) | 26.0012 | + | 4.56553i | 1.30992 | + | 0.230008i | ||||
\(395\) | −2.41682 | − | 2.41682i | −0.121603 | − | 0.121603i | ||||
\(396\) | 0.0106669 | + | 0.0227899i | 0.000536030 | + | 0.00114524i | ||||
\(397\) | −12.5043 | + | 12.5043i | −0.627572 | + | 0.627572i | −0.947457 | − | 0.319884i | \(-0.896356\pi\) |
0.319884 | + | 0.947457i | \(0.396356\pi\) | |||||||
\(398\) | 2.97767 | + | 4.24608i | 0.149257 | + | 0.212837i | ||||
\(399\) | −15.2558 | −0.763745 | ||||||||
\(400\) | 2.56237 | − | 3.07153i | 0.128118 | − | 0.153576i | ||||
\(401\) | −14.6398 | −0.731079 | −0.365539 | − | 0.930796i | \(-0.619115\pi\) | ||||
−0.365539 | + | 0.930796i | \(0.619115\pi\) | |||||||
\(402\) | 12.6436 | + | 18.0295i | 0.630607 | + | 0.899229i | ||||
\(403\) | 6.19232 | − | 6.19232i | 0.308461 | − | 0.308461i | ||||
\(404\) | 25.5253 | − | 11.9471i | 1.26993 | − | 0.594393i | ||||
\(405\) | −0.707107 | − | 0.707107i | −0.0351364 | − | 0.0351364i | ||||
\(406\) | 13.7657 | + | 2.41711i | 0.683183 | + | 0.119959i | ||||
\(407\) | − | 0.0885653i | − | 0.00439002i | ||||||
\(408\) | 13.6101 | + | 7.81886i | 0.673800 | + | 0.387091i | ||||
\(409\) | 33.5504i | 1.65896i | 0.558537 | + | 0.829479i | \(0.311363\pi\) | ||||
−0.558537 | + | 0.829479i | \(0.688637\pi\) | |||||||
\(410\) | 0.920808 | − | 5.24411i | 0.0454754 | − | 0.258988i | ||||
\(411\) | −11.3192 | − | 11.3192i | −0.558334 | − | 0.558334i | ||||
\(412\) | −4.23372 | − | 1.53409i | −0.208580 | − | 0.0755790i | ||||
\(413\) | 10.0421 | − | 10.0421i | 0.494141 | − | 0.494141i | ||||
\(414\) | 3.48878 | − | 2.44659i | 0.171464 | − | 0.120243i | ||||
\(415\) | 7.51840 | 0.369064 | ||||||||
\(416\) | −10.5680 | + | 8.93227i | −0.518140 | + | 0.437941i | ||||
\(417\) | −2.15559 | −0.105560 | ||||||||
\(418\) | 0.101917 | − | 0.0714721i | 0.00498495 | − | 0.00349582i | ||||
\(419\) | 16.5641 | − | 16.5641i | 0.809211 | − | 0.809211i | −0.175303 | − | 0.984514i | \(-0.556091\pi\) |
0.984514 | + | 0.175303i | \(0.0560906\pi\) | |||||||
\(420\) | 4.10031 | + | 1.48575i | 0.200075 | + | 0.0724971i | ||||
\(421\) | 14.1472 | + | 14.1472i | 0.689492 | + | 0.689492i | 0.962120 | − | 0.272628i | \(-0.0878928\pi\) |
−0.272628 | + | 0.962120i | \(0.587893\pi\) | |||||||
\(422\) | −4.37280 | + | 24.9036i | −0.212865 | + | 1.21229i | ||||
\(423\) | 10.0800i | 0.490105i | ||||||||
\(424\) | −1.85834 | + | 3.23477i | −0.0902492 | + | 0.157094i | ||||
\(425\) | − | 5.54943i | − | 0.269187i | ||||||
\(426\) | −16.8670 | − | 2.96166i | −0.817208 | − | 0.143493i | ||||
\(427\) | 9.09635 | + | 9.09635i | 0.440203 | + | 0.440203i | ||||
\(428\) | 6.43241 | − | 3.01070i | 0.310922 | − | 0.145528i | ||||
\(429\) | −0.0217614 | + | 0.0217614i | −0.00105065 | + | 0.00105065i | ||||
\(430\) | 7.82250 | + | 11.1547i | 0.377235 | + | 0.537927i | ||||
\(431\) | 13.1169 | 0.631819 | 0.315909 | − | 0.948789i | \(-0.397690\pi\) | ||||
0.315909 | + | 0.948789i | \(0.397690\pi\) | |||||||
\(432\) | 0.360031 | + | 3.98376i | 0.0173220 | + | 0.191669i | ||||
\(433\) | 0.300976 | 0.0144640 | 0.00723199 | − | 0.999974i | \(-0.497698\pi\) | ||||
0.00723199 | + | 0.999974i | \(0.497698\pi\) | |||||||
\(434\) | 6.33899 | + | 9.03924i | 0.304281 | + | 0.433897i | ||||
\(435\) | 3.20471 | − | 3.20471i | 0.153654 | − | 0.153654i | ||||
\(436\) | −14.4683 | − | 30.9117i | −0.692905 | − | 1.48040i | ||||
\(437\) | −14.9058 | − | 14.9058i | −0.713041 | − | 0.713041i | ||||
\(438\) | −9.93114 | − | 1.74380i | −0.474528 | − | 0.0833219i | ||||
\(439\) | 30.3358i | 1.44785i | 0.689879 | + | 0.723925i | \(0.257664\pi\) | ||||
−0.689879 | + | 0.723925i | \(0.742336\pi\) | |||||||
\(440\) | −0.0343531 | + | 0.00928399i | −0.00163772 | + | 0.000442597i | ||||
\(441\) | − | 2.24499i | − | 0.106904i | ||||||
\(442\) | −3.32002 | + | 18.9079i | −0.157917 | + | 0.899357i | ||||
\(443\) | −3.99367 | − | 3.99367i | −0.189745 | − | 0.189745i | 0.605841 | − | 0.795586i | \(-0.292837\pi\) |
−0.795586 | + | 0.605841i | \(0.792837\pi\) | |||||||
\(444\) | 4.79629 | − | 13.2366i | 0.227622 | − | 0.628182i | ||||
\(445\) | 3.58082 | − | 3.58082i | 0.169747 | − | 0.169747i | ||||
\(446\) | −6.22278 | + | 4.36388i | −0.294657 | + | 0.206636i | ||||
\(447\) | 17.1700 | 0.812111 | ||||||||
\(448\) | −8.78720 | − | 15.0700i | −0.415156 | − | 0.711992i | ||||
\(449\) | −10.4806 | −0.494610 | −0.247305 | − | 0.968938i | \(-0.579545\pi\) | ||||
−0.247305 | + | 0.968938i | \(0.579545\pi\) | |||||||
\(450\) | 1.15787 | − | 0.811989i | 0.0545828 | − | 0.0382775i | ||||
\(451\) | −0.0334937 | + | 0.0334937i | −0.00157716 | + | 0.00157716i | ||||
\(452\) | −13.4876 | + | 37.2225i | −0.634402 | + | 1.75080i | ||||
\(453\) | −9.04671 | − | 9.04671i | −0.425052 | − | 0.425052i | ||||
\(454\) | 0.665160 | − | 3.78816i | 0.0312175 | − | 0.177787i | ||||
\(455\) | 5.33396i | 0.250060i | ||||||||
\(456\) | 19.1028 | − | 5.16257i | 0.894570 | − | 0.241760i | ||||
\(457\) | − | 5.70188i | − | 0.266723i | −0.991067 | − | 0.133361i | \(-0.957423\pi\) | ||
0.991067 | − | 0.133361i | \(-0.0425771\pi\) | |||||||
\(458\) | 10.0090 | + | 1.75746i | 0.467688 | + | 0.0821208i | ||||
\(459\) | 3.92404 | + | 3.92404i | 0.183158 | + | 0.183158i | ||||
\(460\) | 2.55459 | + | 5.45791i | 0.119108 | + | 0.254477i | ||||
\(461\) | 1.78282 | − | 1.78282i | 0.0830341 | − | 0.0830341i | −0.664370 | − | 0.747404i | \(-0.731300\pi\) |
0.747404 | + | 0.664370i | \(0.231300\pi\) | |||||||
\(462\) | −0.0222768 | − | 0.0317662i | −0.00103641 | − | 0.00147790i | ||||
\(463\) | −37.2015 | −1.72890 | −0.864451 | − | 0.502717i | \(-0.832334\pi\) | ||||
−0.864451 | + | 0.502717i | \(0.832334\pi\) | |||||||
\(464\) | −18.0550 | + | 1.63171i | −0.838181 | + | 0.0757503i | ||||
\(465\) | 3.58009 | 0.166023 | ||||||||
\(466\) | 21.3079 | + | 30.3846i | 0.987071 | + | 1.40754i | ||||
\(467\) | −14.3669 | + | 14.3669i | −0.664822 | + | 0.664822i | −0.956513 | − | 0.291691i | \(-0.905782\pi\) |
0.291691 | + | 0.956513i | \(0.405782\pi\) | |||||||
\(468\) | −4.43087 | + | 2.07388i | −0.204817 | + | 0.0958650i | ||||
\(469\) | −24.0094 | − | 24.0094i | −1.10865 | − | 1.10865i | ||||
\(470\) | −14.0404 | − | 2.46535i | −0.647637 | − | 0.113718i | ||||
\(471\) | 14.6135i | 0.673353i | ||||||||
\(472\) | −9.17616 | + | 15.9727i | −0.422367 | + | 0.735202i | ||||
\(473\) | − | 0.121206i | − | 0.00557305i | ||||||
\(474\) | −0.835944 | + | 4.76080i | −0.0383962 | + | 0.218671i | ||||
\(475\) | −4.94702 | − | 4.94702i | −0.226985 | − | 0.226985i | ||||
\(476\) | −22.7544 | − | 8.24505i | −1.04295 | − | 0.377911i | ||||
\(477\) | −0.932644 | + | 0.932644i | −0.0427028 | + | 0.0427028i | ||||
\(478\) | −8.57905 | + | 6.01627i | −0.392397 | + | 0.275178i | ||||
\(479\) | −36.6561 | −1.67486 | −0.837431 | − | 0.546544i | \(-0.815943\pi\) | ||||
−0.837431 | + | 0.546544i | \(0.815943\pi\) | |||||||
\(480\) | −5.63706 | − | 0.472855i | −0.257295 | − | 0.0215828i | ||||
\(481\) | 17.2191 | 0.785122 | ||||||||
\(482\) | −22.7211 | + | 15.9338i | −1.03492 | + | 0.725763i | ||||
\(483\) | −4.64592 | + | 4.64592i | −0.211397 | + | 0.211397i | ||||
\(484\) | −20.6837 | − | 7.49473i | −0.940168 | − | 0.340670i | ||||
\(485\) | −7.32890 | − | 7.32890i | −0.332788 | − | 0.332788i | ||||
\(486\) | −0.244579 | + | 1.39290i | −0.0110943 | + | 0.0631834i | ||||
\(487\) | − | 34.3322i | − | 1.55574i | −0.628425 | − | 0.777870i | \(-0.716300\pi\) | ||
0.628425 | − | 0.777870i | \(-0.283700\pi\) | |||||||
\(488\) | −14.4684 | − | 8.31194i | −0.654952 | − | 0.376264i | ||||
\(489\) | − | 19.0017i | − | 0.859286i | ||||||
\(490\) | 3.12706 | + | 0.549077i | 0.141266 | + | 0.0248048i | ||||
\(491\) | 17.6224 | + | 17.6224i | 0.795287 | + | 0.795287i | 0.982348 | − | 0.187061i | \(-0.0598963\pi\) |
−0.187061 | + | 0.982348i | \(0.559896\pi\) | |||||||
\(492\) | −6.81971 | + | 3.19198i | −0.307456 | + | 0.143905i | ||||
\(493\) | −17.7843 | + | 17.7843i | −0.800963 | + | 0.800963i | ||||
\(494\) | 13.8958 | + | 19.8150i | 0.625201 | + | 0.891520i | ||||
\(495\) | −0.0125814 | −0.000565490 | ||||||||
\(496\) | −10.9964 | − | 9.17351i | −0.493751 | − | 0.411903i | ||||
\(497\) | 26.4053 | 1.18444 | ||||||||
\(498\) | −6.10486 | − | 8.70537i | −0.273565 | − | 0.390097i | ||||
\(499\) | −14.6801 | + | 14.6801i | −0.657173 | + | 0.657173i | −0.954710 | − | 0.297537i | \(-0.903835\pi\) |
0.297537 | + | 0.954710i | \(0.403835\pi\) | |||||||
\(500\) | 0.847831 | + | 1.81140i | 0.0379161 | + | 0.0810084i | ||||
\(501\) | 3.59485 | + | 3.59485i | 0.160606 | + | 0.160606i | ||||
\(502\) | 2.43494 | + | 0.427549i | 0.108677 | + | 0.0190824i | ||||
\(503\) | 13.0618i | 0.582398i | 0.956663 | + | 0.291199i | \(0.0940541\pi\) | ||||
−0.956663 | + | 0.291199i | \(0.905946\pi\) | |||||||
\(504\) | −1.60910 | − | 5.95406i | −0.0716749 | − | 0.265215i | ||||
\(505\) | 14.0914i | 0.627060i | ||||||||
\(506\) | 0.00927166 | − | 0.0528032i | 0.000412176 | − | 0.00234739i | ||||
\(507\) | 4.96149 | + | 4.96149i | 0.220347 | + | 0.220347i | ||||
\(508\) | 9.81032 | − | 27.0742i | 0.435263 | − | 1.20122i | ||||
\(509\) | −22.0202 | + | 22.0202i | −0.976027 | + | 0.976027i | −0.999719 | − | 0.0236921i | \(-0.992458\pi\) |
0.0236921 | + | 0.999719i | \(0.492458\pi\) | |||||||
\(510\) | −6.42554 | + | 4.50607i | −0.284528 | + | 0.199532i | ||||
\(511\) | 15.5472 | 0.687770 | ||||||||
\(512\) | 16.1027 | + | 15.8966i | 0.711648 | + | 0.702537i | ||||
\(513\) | 6.99615 | 0.308888 | ||||||||
\(514\) | 3.48578 | − | 2.44449i | 0.153751 | − | 0.107822i | ||||
\(515\) | 1.59208 | − | 1.59208i | 0.0701555 | − | 0.0701555i | ||||
\(516\) | 6.56395 | − | 18.1150i | 0.288962 | − | 0.797467i | ||||
\(517\) | 0.0896752 | + | 0.0896752i | 0.00394391 | + | 0.00394391i | ||||
\(518\) | −3.75431 | + | 21.3812i | −0.164955 | + | 0.939437i | ||||
\(519\) | 15.3896i | 0.675529i | ||||||||
\(520\) | −1.80502 | − | 6.67900i | −0.0791552 | − | 0.292894i | ||||
\(521\) | − | 22.0123i | − | 0.964375i | −0.876068 | − | 0.482188i | \(-0.839842\pi\) | ||
0.876068 | − | 0.482188i | \(-0.160158\pi\) | |||||||
\(522\) | −6.31283 | − | 1.10846i | −0.276305 | − | 0.0485161i | ||||
\(523\) | −14.7575 | − | 14.7575i | −0.645299 | − | 0.645299i | 0.306554 | − | 0.951853i | \(-0.400824\pi\) |
−0.951853 | + | 0.306554i | \(0.900824\pi\) | |||||||
\(524\) | 0.689138 | + | 1.47235i | 0.0301051 | + | 0.0643201i | ||||
\(525\) | −1.54192 | + | 1.54192i | −0.0672947 | + | 0.0672947i | ||||
\(526\) | 9.66269 | + | 13.7788i | 0.421313 | + | 0.600782i | ||||
\(527\) | −19.8675 | −0.865441 | ||||||||
\(528\) | 0.0386440 | + | 0.0322381i | 0.00168176 | + | 0.00140298i | ||||
\(529\) | 13.9213 | 0.605275 | ||||||||
\(530\) | −1.07098 | − | 1.52719i | −0.0465203 | − | 0.0663368i | ||||
\(531\) | −4.60522 | + | 4.60522i | −0.199849 | + | 0.199849i | ||||
\(532\) | −27.6344 | + | 12.9343i | −1.19810 | + | 0.560774i | ||||
\(533\) | −6.51192 | − | 6.51192i | −0.282063 | − | 0.282063i | ||||
\(534\) | −7.05373 | − | 1.23856i | −0.305245 | − | 0.0535976i | ||||
\(535\) | 3.55106i | 0.153526i | ||||||||
\(536\) | 38.1887 | + | 21.9390i | 1.64950 | + | 0.947621i | ||||
\(537\) | − | 15.7995i | − | 0.681797i | ||||||
\(538\) | −5.35948 | + | 30.5229i | −0.231064 | + | 1.31593i | ||||
\(539\) | −0.0199723 | − | 0.0199723i | −0.000860267 | − | 0.000860267i | ||||
\(540\) | −1.88036 | − | 0.681349i | −0.0809179 | − | 0.0293206i | ||||
\(541\) | 8.39925 | − | 8.39925i | 0.361112 | − | 0.361112i | −0.503110 | − | 0.864222i | \(-0.667811\pi\) |
0.864222 | + | 0.503110i | \(0.167811\pi\) | |||||||
\(542\) | 8.45818 | − | 5.93151i | 0.363310 | − | 0.254780i | ||||
\(543\) | −14.3513 | −0.615875 | ||||||||
\(544\) | 31.2824 | + | 2.62407i | 1.34122 | + | 0.112506i | ||||
\(545\) | 17.0651 | 0.730987 | ||||||||
\(546\) | 6.17605 | − | 4.33111i | 0.264311 | − | 0.185354i | ||||
\(547\) | −8.81903 | + | 8.81903i | −0.377074 | + | 0.377074i | −0.870046 | − | 0.492971i | \(-0.835911\pi\) |
0.492971 | + | 0.870046i | \(0.335911\pi\) | |||||||
\(548\) | −30.1003 | − | 10.9069i | −1.28582 | − | 0.465918i | ||||
\(549\) | −4.17149 | − | 4.17149i | −0.178035 | − | 0.178035i | ||||
\(550\) | 0.00307713 | − | 0.0175246i | 0.000131209 | − | 0.000747253i | ||||
\(551\) | 31.7075i | 1.35079i | ||||||||
\(552\) | 4.24529 | − | 7.38965i | 0.180691 | − | 0.314525i | ||||
\(553\) | − | 7.45305i | − | 0.316936i | ||||||
\(554\) | 4.40694 | + | 0.773810i | 0.187233 | + | 0.0328760i | ||||
\(555\) | 4.97761 | + | 4.97761i | 0.211288 | + | 0.211288i | ||||
\(556\) | −3.90465 | + | 1.82758i | −0.165594 | + | 0.0775066i | ||||
\(557\) | 6.98592 | − | 6.98592i | 0.296003 | − | 0.296003i | −0.543443 | − | 0.839446i | \(-0.682880\pi\) |
0.839446 | + | 0.543443i | \(0.182880\pi\) | |||||||
\(558\) | −2.90700 | − | 4.14530i | −0.123063 | − | 0.175485i | ||||
\(559\) | 23.5651 | 0.996699 | ||||||||
\(560\) | 8.68699 | − | 0.785083i | 0.367092 | − | 0.0331758i | ||||
\(561\) | 0.0698194 | 0.00294778 | ||||||||
\(562\) | −3.93844 | − | 5.61612i | −0.166133 | − | 0.236902i | ||||
\(563\) | 3.94396 | − | 3.94396i | 0.166218 | − | 0.166218i | −0.619097 | − | 0.785315i | \(-0.712501\pi\) |
0.785315 | + | 0.619097i | \(0.212501\pi\) | |||||||
\(564\) | 8.54612 | + | 18.2589i | 0.359856 | + | 0.768839i | ||||
\(565\) | −13.9975 | − | 13.9975i | −0.588877 | − | 0.588877i | ||||
\(566\) | 22.5146 | + | 3.95331i | 0.946358 | + | 0.166170i | ||||
\(567\) | − | 2.18060i | − | 0.0915765i | ||||||
\(568\) | −33.0639 | + | 8.93559i | −1.38733 | + | 0.374929i | ||||
\(569\) | 31.6307i | 1.32603i | 0.748607 | + | 0.663014i | \(0.230723\pi\) | ||||
−0.748607 | + | 0.663014i | \(0.769277\pi\) | |||||||
\(570\) | −1.71111 | + | 9.74496i | −0.0716704 | + | 0.408172i | ||||
\(571\) | 5.70590 | + | 5.70590i | 0.238785 | + | 0.238785i | 0.816347 | − | 0.577562i | \(-0.195996\pi\) |
−0.577562 | + | 0.816347i | \(0.695996\pi\) | |||||||
\(572\) | −0.0209687 | + | 0.0578686i | −0.000876745 | + | 0.00241961i | ||||
\(573\) | 9.45512 | − | 9.45512i | 0.394993 | − | 0.394993i | ||||
\(574\) | 9.50578 | − | 6.66616i | 0.396764 | − | 0.278240i | ||||
\(575\) | −3.01309 | −0.125654 | ||||||||
\(576\) | 4.02972 | + | 6.91096i | 0.167905 | + | 0.287957i | ||||
\(577\) | 21.9772 | 0.914921 | 0.457461 | − | 0.889230i | \(-0.348759\pi\) | ||||
0.457461 | + | 0.889230i | \(0.348759\pi\) | |||||||
\(578\) | 15.9742 | − | 11.2023i | 0.664439 | − | 0.465954i | ||||
\(579\) | 5.88967 | − | 5.88967i | 0.244766 | − | 0.244766i | ||||
\(580\) | 3.08797 | − | 8.52206i | 0.128221 | − | 0.353859i | ||||
\(581\) | 11.5927 | + | 11.5927i | 0.480948 | + | 0.480948i | ||||
\(582\) | −2.53497 | + | 14.4369i | −0.105078 | + | 0.598430i | ||||
\(583\) | 0.0165943i | 0.000687265i | ||||||||
\(584\) | −19.4677 | + | 5.26120i | −0.805581 | + | 0.217710i | ||||
\(585\) | − | 2.44610i | − | 0.101134i | ||||||
\(586\) | −22.0006 | − | 3.86306i | −0.908835 | − | 0.159581i | ||||
\(587\) | −15.3747 | − | 15.3747i | −0.634583 | − | 0.634583i | 0.314631 | − | 0.949214i | \(-0.398119\pi\) |
−0.949214 | + | 0.314631i | \(0.898119\pi\) | |||||||
\(588\) | −1.90337 | − | 4.06659i | −0.0784938 | − | 0.167703i | ||||
\(589\) | −17.7108 | + | 17.7108i | −0.729761 | + | 0.729761i | ||||
\(590\) | −5.28829 | − | 7.54096i | −0.217715 | − | 0.310457i | ||||
\(591\) | 18.6669 | 0.767855 | ||||||||
\(592\) | −2.53440 | − | 28.0433i | −0.104163 | − | 1.15257i | ||||
\(593\) | −16.9206 | −0.694846 | −0.347423 | − | 0.937708i | \(-0.612943\pi\) | ||||
−0.347423 | + | 0.937708i | \(0.612943\pi\) | |||||||
\(594\) | 0.0102159 | + | 0.0145676i | 0.000419165 | + | 0.000597718i | ||||
\(595\) | 8.55675 | − | 8.55675i | 0.350792 | − | 0.350792i | ||||
\(596\) | 31.1017 | − | 14.5572i | 1.27398 | − | 0.596287i | ||||
\(597\) | 2.59305 | + | 2.59305i | 0.106127 | + | 0.106127i | ||||
\(598\) | 10.2661 | + | 1.80262i | 0.419813 | + | 0.0737145i | ||||
\(599\) | − | 19.1715i | − | 0.783327i | −0.920109 | − | 0.391663i | \(-0.871900\pi\) | ||
0.920109 | − | 0.391663i | \(-0.128100\pi\) | |||||||
\(600\) | 1.40895 | − | 2.45252i | 0.0575201 | − | 0.100124i | ||||
\(601\) | − | 10.1428i | − | 0.413735i | −0.978369 | − | 0.206867i | \(-0.933673\pi\) | ||
0.978369 | − | 0.206867i | \(-0.0663269\pi\) | |||||||
\(602\) | −5.13795 | + | 29.2612i | −0.209407 | + | 1.19260i | ||||
\(603\) | 11.0105 | + | 11.0105i | 0.448382 | + | 0.448382i | ||||
\(604\) | −24.0573 | − | 8.71717i | −0.978879 | − | 0.354696i | ||||
\(605\) | 7.77806 | − | 7.77806i | 0.316223 | − | 0.316223i | ||||
\(606\) | 16.3161 | − | 11.4421i | 0.662797 | − | 0.464803i | ||||
\(607\) | 6.80048 | 0.276023 | 0.138011 | − | 0.990431i | \(-0.455929\pi\) | ||||
0.138011 | + | 0.990431i | \(0.455929\pi\) | |||||||
\(608\) | 30.2259 | − | 25.5474i | 1.22582 | − | 1.03609i | ||||
\(609\) | 9.88277 | 0.400470 | ||||||||
\(610\) | 6.83075 | − | 4.79023i | 0.276569 | − | 0.193951i | ||||
\(611\) | −17.4349 | + | 17.4349i | −0.705339 | + | 0.705339i | ||||
\(612\) | 10.4349 | + | 3.78110i | 0.421807 | + | 0.152842i | ||||
\(613\) | 18.1431 | + | 18.1431i | 0.732793 | + | 0.732793i | 0.971172 | − | 0.238379i | \(-0.0766161\pi\) |
−0.238379 | + | 0.971172i | \(0.576616\pi\) | |||||||
\(614\) | 4.68213 | − | 26.6653i | 0.188955 | − | 1.07612i | ||||
\(615\) | − | 3.76487i | − | 0.151814i | ||||||
\(616\) | −0.0672847 | − | 0.0386544i | −0.00271098 | − | 0.00155743i | ||||
\(617\) | − | 30.4488i | − | 1.22582i | −0.790151 | − | 0.612912i | \(-0.789998\pi\) | ||
0.790151 | − | 0.612912i | \(-0.210002\pi\) | |||||||
\(618\) | −3.13618 | − | 0.550679i | −0.126156 | − | 0.0221516i | ||||
\(619\) | −12.1946 | − | 12.1946i | −0.490143 | − | 0.490143i | 0.418208 | − | 0.908351i | \(-0.362658\pi\) |
−0.908351 | + | 0.418208i | \(0.862658\pi\) | |||||||
\(620\) | 6.48500 | − | 3.03531i | 0.260444 | − | 0.121901i | ||||
\(621\) | 2.13057 | − | 2.13057i | 0.0854969 | − | 0.0854969i | ||||
\(622\) | 13.3942 | + | 19.0998i | 0.537059 | + | 0.765833i | ||||
\(623\) | 11.0427 | 0.442415 | ||||||||
\(624\) | −6.26780 | + | 7.51326i | −0.250913 | + | 0.300771i | ||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 22.1307 | + | 31.5578i | 0.884519 | + | 1.26130i | ||||
\(627\) | 0.0622403 | − | 0.0622403i | 0.00248564 | − | 0.00248564i | ||||
\(628\) | 12.3898 | + | 26.4709i | 0.494405 | + | 1.05630i | ||||
\(629\) | −27.6229 | − | 27.6229i | −1.10140 | − | 1.10140i | ||||
\(630\) | 3.03736 | + | 0.533328i | 0.121011 | + | 0.0212483i | ||||
\(631\) | − | 27.9943i | − | 1.11444i | −0.830366 | − | 0.557218i | \(-0.811869\pi\) | ||
0.830366 | − | 0.557218i | \(-0.188131\pi\) | |||||||
\(632\) | 2.52212 | + | 9.33246i | 0.100324 | + | 0.371225i | ||||
\(633\) | 17.8789i | 0.710623i | ||||||||
\(634\) | 8.05785 | − | 45.8904i | 0.320018 | − | 1.82254i | ||||
\(635\) | 10.1812 | + | 10.1812i | 0.404028 | + | 0.404028i | ||||
\(636\) | −0.898670 | + | 2.48012i | −0.0356346 | + | 0.0983431i | ||||
\(637\) | 3.88306 | − | 3.88306i | 0.153852 | − | 0.153852i | ||||
\(638\) | −0.0660226 | + | 0.0463000i | −0.00261386 | + | 0.00183303i | ||||
\(639\) | −12.1092 | −0.479033 | ||||||||
\(640\) | −10.6119 | + | 3.92274i | −0.419472 | + | 0.155060i | ||||
\(641\) | 5.01913 | 0.198244 | 0.0991219 | − | 0.995075i | \(-0.468397\pi\) | ||||
0.0991219 | + | 0.995075i | \(0.468397\pi\) | |||||||
\(642\) | 4.11169 | − | 2.88342i | 0.162275 | − | 0.113800i | ||||
\(643\) | 1.55218 | − | 1.55218i | 0.0612118 | − | 0.0612118i | −0.675838 | − | 0.737050i | \(-0.736218\pi\) |
0.737050 | + | 0.675838i | \(0.236218\pi\) | |||||||
\(644\) | −4.47669 | + | 12.3546i | −0.176406 | + | 0.486839i | ||||
\(645\) | 6.81210 | + | 6.81210i | 0.268226 | + | 0.268226i | ||||
\(646\) | 9.49567 | − | 54.0790i | 0.373602 | − | 2.12771i | ||||
\(647\) | 24.6915i | 0.970722i | 0.874314 | + | 0.485361i | \(0.161312\pi\) | ||||
−0.874314 | + | 0.485361i | \(0.838688\pi\) | |||||||
\(648\) | 0.737916 | + | 2.73047i | 0.0289881 | + | 0.107263i | ||||
\(649\) | 0.0819394i | 0.00321640i | ||||||||
\(650\) | 3.40718 | + | 0.598263i | 0.133641 | + | 0.0234658i | ||||
\(651\) | 5.52020 | + | 5.52020i | 0.216354 | + | 0.216354i | ||||
\(652\) | −16.1102 | − | 34.4197i | −0.630925 | − | 1.34798i | ||||
\(653\) | −10.4301 | + | 10.4301i | −0.408161 | + | 0.408161i | −0.881097 | − | 0.472936i | \(-0.843194\pi\) |
0.472936 | + | 0.881097i | \(0.343194\pi\) | |||||||
\(654\) | −13.8566 | − | 19.7592i | −0.541837 | − | 0.772646i | ||||
\(655\) | −0.812825 | −0.0317597 | ||||||||
\(656\) | −9.64699 | + | 11.5639i | −0.376652 | + | 0.451495i | ||||
\(657\) | −7.12981 | −0.278160 | ||||||||
\(658\) | −17.8478 | − | 25.4505i | −0.695781 | − | 0.992165i | ||||
\(659\) | −15.4151 | + | 15.4151i | −0.600487 | + | 0.600487i | −0.940442 | − | 0.339955i | \(-0.889588\pi\) |
0.339955 | + | 0.940442i | \(0.389588\pi\) | |||||||
\(660\) | −0.0227899 | + | 0.0106669i | −0.000887097 | + | 0.000415207i | ||||
\(661\) | 17.9150 | + | 17.9150i | 0.696813 | + | 0.696813i | 0.963722 | − | 0.266909i | \(-0.0860022\pi\) |
−0.266909 | + | 0.963722i | \(0.586002\pi\) | |||||||
\(662\) | −31.3321 | − | 5.50157i | −1.21776 | − | 0.213825i | ||||
\(663\) | 13.5744i | 0.527188i | ||||||||
\(664\) | −18.4390 | − | 10.5931i | −0.715574 | − | 0.411090i | ||||
\(665\) | − | 15.2558i | − | 0.591594i | ||||||
\(666\) | 1.72169 | − | 9.80521i | 0.0667140 | − | 0.379944i | ||||
\(667\) | 9.65605 | + | 9.65605i | 0.373884 | + | 0.373884i | ||||
\(668\) | 9.55956 | + | 3.46390i | 0.369870 | + | 0.134022i | ||||
\(669\) | −3.80021 | + | 3.80021i | −0.146925 | + | 0.146925i | ||||
\(670\) | −18.0295 | + | 12.6436i | −0.696540 | + | 0.488466i | ||||
\(671\) | −0.0742223 | −0.00286532 | ||||||||
\(672\) | −7.96276 | − | 9.42097i | −0.307170 | − | 0.363422i | ||||
\(673\) | 28.8891 | 1.11359 | 0.556796 | − | 0.830649i | \(-0.312030\pi\) | ||||
0.556796 | + | 0.830649i | \(0.312030\pi\) | |||||||
\(674\) | 8.28463 | − | 5.80981i | 0.319112 | − | 0.223785i | ||||
\(675\) | 0.707107 | − | 0.707107i | 0.0272166 | − | 0.0272166i | ||||
\(676\) | 13.1938 | + | 4.78076i | 0.507452 | + | 0.183875i | ||||
\(677\) | 10.8421 | + | 10.8421i | 0.416695 | + | 0.416695i | 0.884063 | − | 0.467368i | \(-0.154798\pi\) |
−0.467368 | + | 0.884063i | \(0.654798\pi\) | |||||||
\(678\) | −4.84153 | + | 27.5731i | −0.185938 | + | 1.05894i | ||||
\(679\) | − | 22.6011i | − | 0.867350i | ||||||
\(680\) | −7.81886 | + | 13.6101i | −0.299840 | + | 0.521923i | ||||
\(681\) | − | 2.71961i | − | 0.104216i | ||||||
\(682\) | −0.0627398 | − | 0.0110164i | −0.00240243 | − | 0.000421841i | ||||
\(683\) | −2.04256 | − | 2.04256i | −0.0781564 | − | 0.0781564i | 0.666948 | − | 0.745104i | \(-0.267600\pi\) |
−0.745104 | + | 0.666948i | \(0.767600\pi\) | |||||||
\(684\) | 12.6729 | − | 5.93155i | 0.484559 | − | 0.226799i | ||||
\(685\) | 11.3192 | − | 11.3192i | 0.432484 | − | 0.432484i | ||||
\(686\) | 16.3694 | + | 23.3423i | 0.624986 | + | 0.891214i | ||||
\(687\) | 7.18568 | 0.274151 | ||||||||
\(688\) | −3.46845 | − | 38.3786i | −0.132234 | − | 1.46317i | ||||
\(689\) | −3.22630 | −0.122912 | ||||||||
\(690\) | 2.44659 | + | 3.48878i | 0.0931401 | + | 0.132815i | ||||
\(691\) | 33.4347 | − | 33.4347i | 1.27192 | − | 1.27192i | 0.326837 | − | 0.945081i | \(-0.394017\pi\) |
0.945081 | − | 0.326837i | \(-0.105983\pi\) | |||||||
\(692\) | 13.0478 | + | 27.8768i | 0.496002 | + | 1.05972i | ||||
\(693\) | −0.0193994 | − | 0.0193994i | −0.000736922 | − | 0.000736922i | ||||
\(694\) | −19.0036 | − | 3.33682i | −0.721366 | − | 0.126664i | ||||
\(695\) | − | 2.15559i | − | 0.0817664i | ||||||
\(696\) | −12.3749 | + | 3.34434i | −0.469068 | + | 0.126767i | ||||
\(697\) | 20.8929i | 0.791375i | ||||||||
\(698\) | 7.03299 | − | 40.0537i | 0.266203 | − | 1.51605i | ||||
\(699\) | 18.5557 | + | 18.5557i | 0.701839 | + | 0.701839i | ||||
\(700\) | −1.48575 | + | 4.10031i | −0.0561560 | + | 0.154977i | ||||
\(701\) | 4.02037 | − | 4.02037i | 0.151847 | − | 0.151847i | −0.627095 | − | 0.778943i | \(-0.715756\pi\) |
0.778943 | + | 0.627095i | \(0.215756\pi\) | |||||||
\(702\) | −2.83228 | + | 1.98620i | −0.106897 | + | 0.0749644i | ||||
\(703\) | −49.2487 | −1.85745 | ||||||||
\(704\) | 0.0973323 | + | 0.0256326i | 0.00366835 | + | 0.000966064i | ||||
\(705\) | −10.0800 | −0.379634 | ||||||||
\(706\) | 37.2442 | − | 26.1184i | 1.40170 | − | 0.982978i | ||||
\(707\) | −21.7278 | + | 21.7278i | −0.817158 | + | 0.817158i | ||||
\(708\) | −4.43746 | + | 12.2464i | −0.166770 | + | 0.460246i | ||||
\(709\) | 18.0101 | + | 18.0101i | 0.676385 | + | 0.676385i | 0.959180 | − | 0.282795i | \(-0.0912617\pi\) |
−0.282795 | + | 0.959180i | \(0.591262\pi\) | |||||||
\(710\) | 2.96166 | − | 16.8670i | 0.111149 | − | 0.633006i | ||||
\(711\) | 3.41789i | 0.128181i | ||||||||
\(712\) | −13.8272 | + | 3.73684i | −0.518198 | + | 0.140044i | ||||
\(713\) | 10.7871i | 0.403981i | ||||||||
\(714\) | −16.8556 | − | 2.95966i | −0.630806 | − | 0.110763i | ||||
\(715\) | −0.0217614 | − | 0.0217614i | −0.000813830 | − | 0.000813830i | ||||
\(716\) | −13.3953 | − | 28.6192i | −0.500605 | − | 1.06955i | ||||
\(717\) | −5.23917 | + | 5.23917i | −0.195660 | + | 0.195660i | ||||
\(718\) | 12.8489 | + | 18.3221i | 0.479515 | + | 0.683776i | ||||
\(719\) | 50.2917 | 1.87556 | 0.937782 | − | 0.347224i | \(-0.112876\pi\) | ||||
0.937782 | + | 0.347224i | \(0.112876\pi\) | |||||||
\(720\) | −3.98376 | + | 0.360031i | −0.148466 | + | 0.0134176i | ||||
\(721\) | 4.90971 | 0.182847 | ||||||||
\(722\) | −24.3159 | − | 34.6739i | −0.904944 | − | 1.29043i | ||||
\(723\) | −13.8757 | + | 13.8757i | −0.516041 | + | 0.516041i | ||||
\(724\) | −25.9961 | + | 12.1675i | −0.966137 | + | 0.452202i | ||||
\(725\) | 3.20471 | + | 3.20471i | 0.119020 | + | 0.119020i | ||||
\(726\) | −15.3217 | − | 2.69033i | −0.568642 | − | 0.0998474i | ||||
\(727\) | − | 15.1799i | − | 0.562991i | −0.959562 | − | 0.281496i | \(-0.909169\pi\) | ||
0.959562 | − | 0.281496i | \(-0.0908305\pi\) | |||||||
\(728\) | 7.51528 | − | 13.0816i | 0.278535 | − | 0.484838i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 1.74380 | − | 9.93114i | 0.0645409 | − | 0.367568i | ||||
\(731\) | −37.8032 | − | 37.8032i | −1.39820 | − | 1.39820i | ||||
\(732\) | −11.0930 | − | 4.01954i | −0.410008 | − | 0.148566i | ||||
\(733\) | −12.1524 | + | 12.1524i | −0.448859 | + | 0.448859i | −0.894975 | − | 0.446116i | \(-0.852807\pi\) |
0.446116 | + | 0.894975i | \(0.352807\pi\) | |||||||
\(734\) | 5.03488 | − | 3.53084i | 0.185841 | − | 0.130326i | ||||
\(735\) | 2.24499 | 0.0828078 | ||||||||
\(736\) | 1.42475 | − | 16.9849i | 0.0525170 | − | 0.626073i | ||||
\(737\) | 0.195907 | 0.00721632 | ||||||||
\(738\) | −4.35925 | + | 3.05704i | −0.160466 | + | 0.112531i | ||||
\(739\) | −17.9947 | + | 17.9947i | −0.661947 | + | 0.661947i | −0.955839 | − | 0.293892i | \(-0.905050\pi\) |
0.293892 | + | 0.955839i | \(0.405050\pi\) | |||||||
\(740\) | 13.2366 | + | 4.79629i | 0.486588 | + | 0.176315i | ||||
\(741\) | 12.1009 | + | 12.1009i | 0.444538 | + | 0.444538i | ||||
\(742\) | 0.703436 | − | 4.00615i | 0.0258240 | − | 0.147070i | ||||
\(743\) | − | 19.2456i | − | 0.706051i | −0.935614 | − | 0.353026i | \(-0.885153\pi\) | ||
0.935614 | − | 0.353026i | \(-0.114847\pi\) | |||||||
\(744\) | −8.78026 | − | 5.04417i | −0.321900 | − | 0.184928i | ||||
\(745\) | 17.1700i | 0.629059i | ||||||||
\(746\) | −34.2084 | − | 6.00662i | −1.25246 | − | 0.219918i | ||||
\(747\) | −5.31631 | − | 5.31631i | −0.194514 | − | 0.194514i | ||||
\(748\) | 0.126471 | − | 0.0591950i | 0.00462424 | − | 0.00216438i | ||||
\(749\) | −5.47544 | + | 5.47544i | −0.200068 | + | 0.200068i | ||||
\(750\) | 0.811989 | + | 1.15787i | 0.0296496 | + | 0.0422796i | ||||
\(751\) | −53.5813 | −1.95521 | −0.977604 | − | 0.210451i | \(-0.932507\pi\) | ||||
−0.977604 | + | 0.210451i | \(0.932507\pi\) | |||||||
\(752\) | 30.9609 | + | 25.8286i | 1.12903 | + | 0.941872i | ||||
\(753\) | 1.74810 | 0.0637044 | ||||||||
\(754\) | −9.00175 | − | 12.8363i | −0.327824 | − | 0.467469i | ||||
\(755\) | 9.04671 | − | 9.04671i | 0.329244 | − | 0.329244i | ||||
\(756\) | −1.84878 | − | 3.94994i | −0.0672394 | − | 0.143658i | ||||
\(757\) | 10.4133 | + | 10.4133i | 0.378477 | + | 0.378477i | 0.870552 | − | 0.492076i | \(-0.163762\pi\) |
−0.492076 | + | 0.870552i | \(0.663762\pi\) | |||||||
\(758\) | −30.3233 | − | 5.32445i | −1.10139 | − | 0.193393i | ||||
\(759\) | − | 0.0379087i | − | 0.00137600i | ||||||
\(760\) | 5.16257 | + | 19.1028i | 0.187266 | + | 0.692931i | ||||
\(761\) | 38.1651i | 1.38348i | 0.722145 | + | 0.691742i | \(0.243156\pi\) | ||||
−0.722145 | + | 0.691742i | \(0.756844\pi\) | |||||||
\(762\) | 3.52154 | − | 20.0556i | 0.127572 | − | 0.726536i | ||||
\(763\) | 26.3129 | + | 26.3129i | 0.952590 | + | 0.952590i | ||||
\(764\) | 9.11070 | − | 25.1434i | 0.329614 | − | 0.909656i | ||||
\(765\) | −3.92404 | + | 3.92404i | −0.141874 | + | 0.141874i | ||||
\(766\) | −18.1083 | + | 12.6989i | −0.654279 | + | 0.458830i | ||||
\(767\) | −15.9309 | −0.575230 | ||||||||
\(768\) | 13.1588 | + | 9.10202i | 0.474826 | + | 0.328441i | ||||
\(769\) | −38.1071 | −1.37418 | −0.687089 | − | 0.726573i | \(-0.741112\pi\) | ||||
−0.687089 | + | 0.726573i | \(0.741112\pi\) | |||||||
\(770\) | 0.0317662 | − | 0.0222768i | 0.00114477 | − | 0.000802801i | ||||
\(771\) | 2.12874 | − | 2.12874i | 0.0766648 | − | 0.0766648i | ||||
\(772\) | 5.67513 | − | 15.6620i | 0.204252 | − | 0.563688i | ||||
\(773\) | −32.9401 | − | 32.9401i | −1.18477 | − | 1.18477i | −0.978493 | − | 0.206280i | \(-0.933864\pi\) |
−0.206280 | − | 0.978493i | \(-0.566136\pi\) | |||||||
\(774\) | 2.35621 | − | 13.4189i | 0.0846923 | − | 0.482333i | ||||
\(775\) | 3.58009i | 0.128601i | ||||||||
\(776\) | 7.64822 | + | 28.3003i | 0.274555 | + | 1.01592i | ||||
\(777\) | 15.3501i | 0.550682i | ||||||||
\(778\) | 33.5010 | + | 5.88240i | 1.20107 | + | 0.210894i | ||||
\(779\) | 18.6249 | + | 18.6249i | 0.667307 | + | 0.667307i | ||||
\(780\) | −2.07388 | − | 4.43087i | −0.0742567 | − | 0.158651i | ||||
\(781\) | −0.107728 | + | 0.107728i | −0.00385481 | + | 0.00385481i | ||||
\(782\) | −13.5772 | − | 19.3607i | −0.485519 | − | 0.692337i | ||||
\(783\) | −4.53214 | −0.161965 | ||||||||
\(784\) | −6.89556 | − | 5.75249i | −0.246270 | − | 0.205446i | ||||
\(785\) | −14.6135 | −0.521577 | ||||||||
\(786\) | 0.660005 | + | 0.941150i | 0.0235416 | + | 0.0335697i | ||||
\(787\) | 21.5631 | − | 21.5631i | 0.768642 | − | 0.768642i | −0.209225 | − | 0.977867i | \(-0.567094\pi\) |
0.977867 | + | 0.209225i | \(0.0670942\pi\) | |||||||
\(788\) | 33.8134 | − | 15.8264i | 1.20455 | − | 0.563792i | ||||
\(789\) | 8.41460 | + | 8.41460i | 0.299568 | + | 0.299568i | ||||
\(790\) | −4.76080 | − | 0.835944i | −0.169382 | − | 0.0297415i | ||||
\(791\) | − | 43.1658i | − | 1.53480i | ||||||
\(792\) | 0.0308561 | + | 0.0177265i | 0.00109642 | + | 0.000629884i | ||||
\(793\) | − | 14.4305i | − | 0.512441i | ||||||
\(794\) | −4.32506 | + | 24.6317i | −0.153491 | + | 0.874148i | ||||
\(795\) | −0.932644 | − | 0.932644i | −0.0330775 | − | 0.0330775i | ||||
\(796\) | 6.89553 | + | 2.49859i | 0.244406 | + | 0.0885603i | ||||
\(797\) | 7.81695 | − | 7.81695i | 0.276891 | − | 0.276891i | −0.554976 | − | 0.831866i | \(-0.687273\pi\) |
0.831866 | + | 0.554976i | \(0.187273\pi\) | |||||||
\(798\) | −17.6643 | + | 12.3875i | −0.625309 | + | 0.438514i | ||||
\(799\) | 55.9381 | 1.97895 | ||||||||
\(800\) | 0.472855 | − | 5.63706i | 0.0167179 | − | 0.199300i | ||||
\(801\) | −5.06405 | −0.178929 | ||||||||
\(802\) | −16.9511 | + | 11.8874i | −0.598564 | + | 0.419758i | ||||
\(803\) | −0.0634294 | + | 0.0634294i | −0.00223837 | + | 0.00223837i | ||||
\(804\) | 29.2795 | + | 10.6094i | 1.03261 | + | 0.374165i | ||||
\(805\) | −4.64592 | − | 4.64592i | −0.163747 | − | 0.163747i | ||||
\(806\) | 2.14184 | − | 12.1980i | 0.0754430 | − | 0.429657i | ||||
\(807\) | 21.9131i | 0.771379i | ||||||||
\(808\) | 19.8541 | − | 34.5595i | 0.698465 | − | 1.21580i | ||||
\(809\) | − | 8.21009i | − | 0.288651i | −0.989530 | − | 0.144326i | \(-0.953899\pi\) | ||
0.989530 | − | 0.144326i | \(-0.0461013\pi\) | |||||||
\(810\) | −1.39290 | − | 0.244579i | −0.0489417 | − | 0.00859362i | ||||
\(811\) | −0.466318 | − | 0.466318i | −0.0163746 | − | 0.0163746i | 0.698872 | − | 0.715247i | \(-0.253686\pi\) |
−0.715247 | + | 0.698872i | \(0.753686\pi\) | |||||||
\(812\) | 17.9017 | − | 8.37892i | 0.628226 | − | 0.294042i | ||||
\(813\) | 5.16536 | − | 5.16536i | 0.181157 | − | 0.181157i | ||||
\(814\) | −0.0719140 | − | 0.102547i | −0.00252058 | − | 0.00359429i | ||||
\(815\) | 19.0017 | 0.665600 | ||||||||
\(816\) | 22.1076 | − | 1.99797i | 0.773921 | − | 0.0699428i | ||||
\(817\) | −67.3992 | −2.35800 | ||||||||
\(818\) | 27.2425 | + | 38.8471i | 0.952512 | + | 1.35826i | ||||
\(819\) | 3.77168 | − | 3.77168i | 0.131793 | − | 0.131793i | ||||
\(820\) | −3.19198 | − | 6.81971i | −0.111469 | − | 0.238154i | ||||
\(821\) | 22.1688 | + | 22.1688i | 0.773696 | + | 0.773696i | 0.978751 | − | 0.205054i | \(-0.0657371\pi\) |
−0.205054 | + | 0.978751i | \(0.565737\pi\) | |||||||
\(822\) | −22.2972 | − | 3.91515i | −0.777706 | − | 0.136557i | ||||
\(823\) | 14.7926i | 0.515636i | 0.966193 | + | 0.257818i | \(0.0830035\pi\) | ||||
−0.966193 | + | 0.257818i | \(0.916996\pi\) | |||||||
\(824\) | −6.14777 | + | 1.66145i | −0.214168 | + | 0.0578793i | ||||
\(825\) | − | 0.0125814i | − | 0.000438027i | ||||||
\(826\) | 3.47344 | − | 19.7816i | 0.120856 | − | 0.688291i | ||||
\(827\) | 27.9227 | + | 27.9227i | 0.970967 | + | 0.970967i | 0.999590 | − | 0.0286237i | \(-0.00911246\pi\) |
−0.0286237 | + | 0.999590i | \(0.509112\pi\) | |||||||
\(828\) | 2.05296 | − | 5.66569i | 0.0713454 | − | 0.196896i | ||||
\(829\) | −0.798074 | + | 0.798074i | −0.0277182 | + | 0.0277182i | −0.720830 | − | 0.693112i | \(-0.756239\pi\) |
0.693112 | + | 0.720830i | \(0.256239\pi\) | |||||||
\(830\) | 8.70537 | − | 6.10486i | 0.302168 | − | 0.211903i | ||||
\(831\) | 3.16385 | 0.109753 | ||||||||
\(832\) | −4.98354 | + | 18.9236i | −0.172773 | + | 0.656057i | ||||
\(833\) | −12.4584 | −0.431659 | ||||||||
\(834\) | −2.49591 | + | 1.75032i | −0.0864263 | + | 0.0606086i | ||||
\(835\) | −3.59485 | + | 3.59485i | −0.124405 | + | 0.124405i | ||||
\(836\) | 0.0599731 | − | 0.165512i | 0.00207421 | − | 0.00572434i | ||||
\(837\) | −2.53151 | − | 2.53151i | −0.0875018 | − | 0.0875018i | ||||
\(838\) | 5.72931 | − | 32.6291i | 0.197916 | − | 1.12715i | ||||
\(839\) | − | 29.3983i | − | 1.01494i | −0.861669 | − | 0.507470i | \(-0.830581\pi\) | ||
0.861669 | − | 0.507470i | \(-0.169419\pi\) | |||||||
\(840\) | 5.95406 | − | 1.60910i | 0.205435 | − | 0.0555192i | ||||
\(841\) | 8.45973i | 0.291715i | ||||||||
\(842\) | 27.8680 | + | 4.89332i | 0.960396 | + | 0.168635i | ||||
\(843\) | −3.42973 | − | 3.42973i | −0.118126 | − | 0.118126i | ||||
\(844\) | 15.1583 | + | 32.3859i | 0.521770 | + | 1.11477i | ||||
\(845\) | −4.96149 | + | 4.96149i | −0.170680 | + | 0.170680i | ||||
\(846\) | 8.18483 | + | 11.6714i | 0.281400 | + | 0.401270i | ||||
\(847\) | 23.9862 | 0.824177 | ||||||||
\(848\) | 0.474866 | + | 5.25441i | 0.0163070 | + | 0.180437i | ||||
\(849\) | 16.1638 | 0.554739 | ||||||||
\(850\) | −4.50607 | − | 6.42554i | −0.154557 | − | 0.220394i | ||||
\(851\) | −14.9980 | + | 14.9980i | −0.514123 | + | 0.514123i | ||||
\(852\) | −21.9347 | + | 10.2666i | −0.751470 | + | 0.351727i | ||||
\(853\) | 24.2137 | + | 24.2137i | 0.829060 | + | 0.829060i | 0.987387 | − | 0.158326i | \(-0.0506098\pi\) |
−0.158326 | + | 0.987387i | \(0.550610\pi\) | |||||||
\(854\) | 17.9186 | + | 3.14630i | 0.613161 | + | 0.107664i | ||||
\(855\) | 6.99615i | 0.239263i | ||||||||
\(856\) | 5.00327 | − | 8.70906i | 0.171008 | − | 0.297669i | ||||
\(857\) | − | 16.2011i | − | 0.553419i | −0.960954 | − | 0.276709i | \(-0.910756\pi\) | ||
0.960954 | − | 0.276709i | \(-0.0892440\pi\) | |||||||
\(858\) | −0.00752697 | + | 0.0428670i | −0.000256966 | + | 0.00146345i | ||||
\(859\) | 0.266646 | + | 0.266646i | 0.00909783 | + | 0.00909783i | 0.711641 | − | 0.702543i | \(-0.247952\pi\) |
−0.702543 | + | 0.711641i | \(0.747952\pi\) | |||||||
\(860\) | 18.1150 | + | 6.56395i | 0.617715 | + | 0.223829i | ||||
\(861\) | 5.80512 | − | 5.80512i | 0.197838 | − | 0.197838i | ||||
\(862\) | 15.1877 | − | 10.6508i | 0.517296 | − | 0.362767i | ||||
\(863\) | 10.2561 | 0.349121 | 0.174560 | − | 0.984646i | \(-0.444150\pi\) | ||||
0.174560 | + | 0.984646i | \(0.444150\pi\) | |||||||
\(864\) | 3.65164 | + | 4.32036i | 0.124231 | + | 0.146982i | ||||
\(865\) | −15.3896 | −0.523262 | ||||||||
\(866\) | 0.348492 | − | 0.244389i | 0.0118422 | − | 0.00830467i | ||||
\(867\) | 9.75534 | − | 9.75534i | 0.331309 | − | 0.331309i | ||||
\(868\) | 14.6795 | + | 5.31912i | 0.498255 | + | 0.180543i | ||||
\(869\) | 0.0304068 | + | 0.0304068i | 0.00103148 | + | 0.00103148i | ||||
\(870\) | 1.10846 | − | 6.31283i | 0.0375804 | − | 0.214025i | ||||
\(871\) | 38.0886i | 1.29058i | ||||||||
\(872\) | −41.8524 | − | 24.0438i | −1.41730 | − | 0.814226i | ||||
\(873\) | 10.3646i | 0.350789i | ||||||||
\(874\) | −29.3624 | − | 5.15572i | −0.993198 | − | 0.174395i | ||||
\(875\) | −1.54192 | − | 1.54192i | −0.0521263 | − | 0.0521263i | ||||
\(876\) | −12.9150 | + | 6.04487i | −0.436356 | + | 0.204237i | ||||
\(877\) | −20.4974 | + | 20.4974i | −0.692149 | + | 0.692149i | −0.962704 | − | 0.270555i | \(-0.912793\pi\) |
0.270555 | + | 0.962704i | \(0.412793\pi\) | |||||||
\(878\) | 24.6323 | + | 35.1251i | 0.831301 | + | 1.18541i | ||||
\(879\) | −15.7948 | −0.532744 | ||||||||
\(880\) | −0.0322381 | + | 0.0386440i | −0.00108675 | + | 0.00130269i | ||||
\(881\) | −56.8144 | −1.91413 | −0.957063 | − | 0.289881i | \(-0.906384\pi\) | ||||
−0.957063 | + | 0.289881i | \(0.906384\pi\) | |||||||
\(882\) | −1.82291 | − | 2.59942i | −0.0613805 | − | 0.0875270i | ||||
\(883\) | 26.2082 | − | 26.2082i | 0.881978 | − | 0.881978i | −0.111758 | − | 0.993735i | \(-0.535648\pi\) |
0.993735 | + | 0.111758i | \(0.0356481\pi\) | |||||||
\(884\) | 11.5088 | + | 24.5888i | 0.387084 | + | 0.827011i | ||||
\(885\) | −4.60522 | − | 4.60522i | −0.154803 | − | 0.154803i | ||||
\(886\) | −7.86698 | − | 1.38136i | −0.264296 | − | 0.0464075i | ||||
\(887\) | − | 26.0161i | − | 0.873537i | −0.899574 | − | 0.436768i | \(-0.856123\pi\) | ||
0.899574 | − | 0.436768i | \(-0.143877\pi\) | |||||||
\(888\) | −5.19449 | − | 19.2209i | −0.174316 | − | 0.645011i | ||||
\(889\) | 31.3971i | 1.05302i | ||||||||
\(890\) | 1.23856 | − | 7.05373i | 0.0415165 | − | 0.236442i | ||||
\(891\) | 0.00889637 | + | 0.00889637i | 0.000298040 | + | 0.000298040i | ||||
\(892\) | −3.66178 | + | 10.1057i | −0.122606 | + | 0.338362i | ||||
\(893\) | 49.8659 | − | 49.8659i | 1.66870 | − | 1.66870i | ||||
\(894\) | 19.8807 | − | 13.9418i | 0.664909 | − | 0.466284i | ||||
\(895\) | 15.7995 | 0.528118 | ||||||||
\(896\) | −22.4112 | − | 10.3141i | −0.748704 | − | 0.344570i | ||||
\(897\) | 7.37030 | 0.246087 | ||||||||
\(898\) | −12.1352 | + | 8.51013i | −0.404958 | + | 0.283987i | ||||
\(899\) | 11.4731 | − | 11.4731i | 0.382651 | − | 0.382651i | ||||
\(900\) | 0.681349 | − | 1.88036i | 0.0227116 | − | 0.0626788i | ||||
\(901\) | 5.17564 | + | 5.17564i | 0.172425 | + | 0.172425i | ||||
\(902\) | −0.0115850 | + | 0.0659780i | −0.000385739 | + | 0.00219683i | ||||
\(903\) | 21.0074i | 0.699081i | ||||||||
\(904\) | 14.6073 | + | 54.0508i | 0.485833 | + | 1.79770i | ||||
\(905\) | − | 14.3513i | − | 0.477055i | ||||||
\(906\) | −17.8208 | − | 3.12913i | −0.592056 | − | 0.103959i | ||||
\(907\) | −27.6233 | − | 27.6233i | −0.917218 | − | 0.917218i | 0.0796085 | − | 0.996826i | \(-0.474633\pi\) |
−0.996826 | + | 0.0796085i | \(0.974633\pi\) | |||||||
\(908\) | −2.30577 | − | 4.92632i | −0.0765198 | − | 0.163486i | ||||
\(909\) | 9.96414 | − | 9.96414i | 0.330490 | − | 0.330490i | ||||
\(910\) | 4.33111 | + | 6.17605i | 0.143575 | + | 0.204734i | ||||
\(911\) | −5.83194 | −0.193221 | −0.0966104 | − | 0.995322i | \(-0.530800\pi\) | ||||
−0.0966104 | + | 0.995322i | \(0.530800\pi\) | |||||||
\(912\) | 17.9267 | − | 21.4889i | 0.593612 | − | 0.711567i | ||||
\(913\) | −0.0945918 | −0.00313053 | ||||||||
\(914\) | −4.62986 | − | 6.60207i | −0.153142 | − | 0.218377i | ||||
\(915\) | 4.17149 | − | 4.17149i | 0.137905 | − | 0.137905i | ||||
\(916\) | 13.0162 | − | 6.09224i | 0.430066 | − | 0.201293i | ||||
\(917\) | −1.25331 | − | 1.25331i | −0.0413879 | − | 0.0413879i | ||||
\(918\) | 7.72982 | + | 1.35727i | 0.255122 | + | 0.0447966i | ||||
\(919\) | − | 11.8292i | − | 0.390208i | −0.980783 | − | 0.195104i | \(-0.937496\pi\) | ||
0.980783 | − | 0.195104i | \(-0.0625045\pi\) | |||||||
\(920\) | 7.38965 | + | 4.24529i | 0.243630 | + | 0.139963i | ||||
\(921\) | − | 19.1437i | − | 0.630805i | ||||||
\(922\) | 0.616653 | − | 3.51191i | 0.0203084 | − | 0.115659i | ||||
\(923\) | −20.9447 | − | 20.9447i | −0.689405 | − | 0.689405i | ||||
\(924\) | −0.0515876 | − | 0.0186927i | −0.00169711 | − | 0.000614946i | ||||
\(925\) | −4.97761 | + | 4.97761i | −0.163663 | + | 0.163663i | ||||
\(926\) | −43.0747 | + | 30.2072i | −1.41552 | + | 0.992671i | ||||
\(927\) | −2.25154 | −0.0739503 | ||||||||
\(928\) | −19.5805 | + | 16.5497i | −0.642760 | + | 0.543272i | ||||
\(929\) | −45.8141 | −1.50311 | −0.751556 | − | 0.659669i | \(-0.770696\pi\) | ||||
−0.751556 | + | 0.659669i | \(0.770696\pi\) | |||||||
\(930\) | 4.14530 | − | 2.90700i | 0.135930 | − | 0.0953242i | ||||
\(931\) | −11.1060 | + | 11.1060i | −0.363986 | + | 0.363986i | ||||
\(932\) | 49.3438 | + | 17.8797i | 1.61631 | + | 0.585670i | ||||
\(933\) | 11.6641 | + | 11.6641i | 0.381867 | + | 0.381867i | ||||
\(934\) | −4.96932 | + | 28.3009i | −0.162601 | + | 0.926033i | ||||
\(935\) | 0.0698194i | 0.00228334i | ||||||||
\(936\) | −3.44643 | + | 5.99911i | −0.112650 | + | 0.196087i | ||||
\(937\) | 6.21014i | 0.202876i | 0.994842 | + | 0.101438i | \(0.0323444\pi\) | ||||
−0.994842 | + | 0.101438i | \(0.967656\pi\) | |||||||
\(938\) | −47.2953 | − | 8.30454i | −1.54425 | − | 0.271153i | ||||
\(939\) | 19.2721 | + | 19.2721i | 0.628922 | + | 0.628922i | ||||
\(940\) | −18.2589 | + | 8.54612i | −0.595540 | + | 0.278744i | ||||
\(941\) | −2.43886 | + | 2.43886i | −0.0795045 | + | 0.0795045i | −0.745741 | − | 0.666236i | \(-0.767904\pi\) |
0.666236 | + | 0.745741i | \(0.267904\pi\) | |||||||
\(942\) | 11.8660 | + | 16.9206i | 0.386614 | + | 0.551302i | ||||
\(943\) | 11.3439 | 0.369408 | ||||||||
\(944\) | 2.34480 | + | 25.9453i | 0.0763167 | + | 0.844448i | ||||
\(945\) | 2.18060 | 0.0709349 | ||||||||
\(946\) | −0.0984178 | − | 0.140341i | −0.00319984 | − | 0.00456289i | ||||
\(947\) | −33.4856 | + | 33.4856i | −1.08814 | + | 1.08814i | −0.0924159 | + | 0.995720i | \(0.529459\pi\) |
−0.995720 | + | 0.0924159i | \(0.970541\pi\) | |||||||
\(948\) | 2.89779 | + | 6.19118i | 0.0941160 | + | 0.201080i | ||||
\(949\) | −12.3321 | − | 12.3321i | −0.400317 | − | 0.400317i | ||||
\(950\) | −9.74496 | − | 1.71111i | −0.316168 | − | 0.0555157i | ||||
\(951\) | − | 32.9459i | − | 1.06834i | ||||||
\(952\) | −33.0416 | + | 8.92957i | −1.07089 | + | 0.289409i | ||||
\(953\) | 14.3013i | 0.463266i | 0.972803 | + | 0.231633i | \(0.0744068\pi\) | ||||
−0.972803 | + | 0.231633i | \(0.925593\pi\) | |||||||
\(954\) | −0.322589 | + | 1.83718i | −0.0104442 | + | 0.0594809i | ||||
\(955\) | 9.45512 | + | 9.45512i | 0.305961 | + | 0.305961i | ||||
\(956\) | −5.04832 | + | 13.9322i | −0.163274 | + | 0.450599i | ||||
\(957\) | −0.0403196 | + | 0.0403196i | −0.00130335 | + | 0.00130335i | ||||
\(958\) | −42.4432 | + | 29.7644i | −1.37128 | + | 0.961643i | ||||
\(959\) | 34.9064 | 1.12719 | ||||||||
\(960\) | −6.91096 | + | 4.02972i | −0.223050 | + | 0.130059i | ||||
\(961\) | −18.1829 | −0.586546 | ||||||||
\(962\) | 19.9375 | − | 13.9817i | 0.642811 | − | 0.450787i | ||||
\(963\) | 2.51098 | − | 2.51098i | 0.0809152 | − | 0.0809152i | ||||
\(964\) | −13.3702 | + | 36.8986i | −0.430625 | + | 1.18842i | ||||
\(965\) | 5.88967 | + | 5.88967i | 0.189595 | + | 0.189595i | ||||
\(966\) | −1.60696 | + | 9.15183i | −0.0517031 | + | 0.294455i | ||||
\(967\) | − | 53.0546i | − | 1.70612i | −0.521812 | − | 0.853060i | \(-0.674744\pi\) | ||
0.521812 | − | 0.853060i | \(-0.325256\pi\) | |||||||
\(968\) | −30.0348 | + | 8.11696i | −0.965354 | + | 0.260889i | ||||
\(969\) | − | 38.8246i | − | 1.24723i | ||||||
\(970\) | −14.4369 | − | 2.53497i | −0.463542 | − | 0.0813928i | ||||
\(971\) | 4.58090 | + | 4.58090i | 0.147008 | + | 0.147008i | 0.776780 | − | 0.629772i | \(-0.216852\pi\) |
−0.629772 | + | 0.776780i | \(0.716852\pi\) | |||||||
\(972\) | 0.847831 | + | 1.81140i | 0.0271942 | + | 0.0581008i | ||||
\(973\) | 3.32375 | − | 3.32375i | 0.106554 | − | 0.106554i | ||||
\(974\) | −27.8774 | − | 39.7524i | −0.893248 | − | 1.27375i | ||||
\(975\) | 2.44610 | 0.0783378 | ||||||||
\(976\) | −23.5018 | + | 2.12396i | −0.752273 | + | 0.0679864i | ||||
\(977\) | 11.2092 | 0.358614 | 0.179307 | − | 0.983793i | \(-0.442615\pi\) | ||||
0.179307 | + | 0.983793i | \(0.442615\pi\) | |||||||
\(978\) | −15.4292 | − | 22.0016i | −0.493370 | − | 0.703533i | ||||
\(979\) | −0.0450516 | + | 0.0450516i | −0.00143986 | + | 0.00143986i | ||||
\(980\) | 4.06659 | − | 1.90337i | 0.129902 | − | 0.0608010i | ||||
\(981\) | −12.0668 | − | 12.0668i | −0.385264 | − | 0.385264i | ||||
\(982\) | 34.7137 | + | 6.09534i | 1.10776 | + | 0.194510i | ||||
\(983\) | − | 20.1018i | − | 0.641147i | −0.947224 | − | 0.320573i | \(-0.896124\pi\) | ||
0.947224 | − | 0.320573i | \(-0.103876\pi\) | |||||||
\(984\) | −5.30452 | + | 9.23343i | −0.169102 | + | 0.294351i | ||||
\(985\) | 18.6669i | 0.594778i | ||||||||
\(986\) | −6.15134 | + | 35.0326i | −0.195899 | + | 1.11567i | ||||
\(987\) | −15.5425 | − | 15.5425i | −0.494723 | − | 0.494723i | ||||
\(988\) | 32.1791 | + | 11.6601i | 1.02376 | + | 0.370957i | ||||
\(989\) | −20.5254 | + | 20.5254i | −0.652671 | + | 0.652671i | ||||
\(990\) | −0.0145676 | + | 0.0102159i | −0.000462990 | + | 0.000324683i | ||||
\(991\) | 20.7088 | 0.657835 | 0.328918 | − | 0.944359i | \(-0.393316\pi\) | ||||
0.328918 | + | 0.944359i | \(0.393316\pi\) | |||||||
\(992\) | −20.1812 | − | 1.69286i | −0.640754 | − | 0.0537485i | ||||
\(993\) | −22.4941 | −0.713828 | ||||||||
\(994\) | 30.5741 | − | 21.4408i | 0.969751 | − | 0.680062i | ||||
\(995\) | −2.59305 | + | 2.59305i | −0.0822052 | + | 0.0822052i | ||||
\(996\) | −14.1373 | − | 5.12266i | −0.447958 | − | 0.162318i | ||||
\(997\) | 0.704128 | + | 0.704128i | 0.0223000 | + | 0.0223000i | 0.718169 | − | 0.695869i | \(-0.244981\pi\) |
−0.695869 | + | 0.718169i | \(0.744981\pi\) | |||||||
\(998\) | −5.07766 | + | 28.9179i | −0.160730 | + | 0.915379i | ||||
\(999\) | − | 7.03940i | − | 0.222717i |
(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 | 240.2.s.c.181.7 | yes | 20 | |
3.2 | odd | 2 | 720.2.t.d.181.4 | 20 | |||
4.3 | odd | 2 | 960.2.s.c.241.2 | 20 | |||
8.3 | odd | 2 | 1920.2.s.f.481.7 | 20 | |||
8.5 | even | 2 | 1920.2.s.e.481.4 | 20 | |||
12.11 | even | 2 | 2880.2.t.d.2161.2 | 20 | |||
16.3 | odd | 4 | 960.2.s.c.721.4 | 20 | |||
16.5 | even | 4 | 1920.2.s.e.1441.2 | 20 | |||
16.11 | odd | 4 | 1920.2.s.f.1441.9 | 20 | |||
16.13 | even | 4 | inner | 240.2.s.c.61.7 | ✓ | 20 | |
48.29 | odd | 4 | 720.2.t.d.541.4 | 20 | |||
48.35 | even | 4 | 2880.2.t.d.721.4 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
240.2.s.c.61.7 | ✓ | 20 | 16.13 | even | 4 | inner | |
240.2.s.c.181.7 | yes | 20 | 1.1 | even | 1 | trivial | |
720.2.t.d.181.4 | 20 | 3.2 | odd | 2 | |||
720.2.t.d.541.4 | 20 | 48.29 | odd | 4 | |||
960.2.s.c.241.2 | 20 | 4.3 | odd | 2 | |||
960.2.s.c.721.4 | 20 | 16.3 | odd | 4 | |||
1920.2.s.e.481.4 | 20 | 8.5 | even | 2 | |||
1920.2.s.e.1441.2 | 20 | 16.5 | even | 4 | |||
1920.2.s.f.481.7 | 20 | 8.3 | odd | 2 | |||
1920.2.s.f.1441.9 | 20 | 16.11 | odd | 4 | |||
2880.2.t.d.721.4 | 20 | 48.35 | even | 4 | |||
2880.2.t.d.2161.2 | 20 | 12.11 | even | 2 |