Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [187,2,Mod(100,187)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(187, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("187.100");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 187 = 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 187.h (of order \(8\), degree \(4\), 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: | \(1.49320251780\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 100.12 | ||
Character | \(\chi\) | \(=\) | 187.100 |
Dual form | 187.2.h.a.144.12 |
$q$-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 \(\left(\mathbb{Z}/187\mathbb{Z}\right)^\times\).
\(n\) | \(35\) | \(122\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.12086 | + | 1.12086i | 0.792568 | + | 0.792568i | 0.981911 | − | 0.189343i | \(-0.0606359\pi\) |
−0.189343 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(3\) | −0.951848 | − | 2.29796i | −0.549549 | − | 1.32673i | −0.917815 | − | 0.397009i | \(-0.870048\pi\) |
0.368265 | − | 0.929721i | \(-0.379952\pi\) | |||||||
\(4\) | 0.512654i | 0.256327i | ||||||||
\(5\) | 0.910373 | − | 0.377089i | 0.407131 | − | 0.168639i | −0.169713 | − | 0.985494i | \(-0.554284\pi\) |
0.576844 | + | 0.816854i | \(0.304284\pi\) | |||||||
\(6\) | 1.50881 | − | 3.64258i | 0.615968 | − | 1.48708i | ||||
\(7\) | −2.04824 | − | 0.848409i | −0.774162 | − | 0.320669i | −0.0396053 | − | 0.999215i | \(-0.512610\pi\) |
−0.734557 | + | 0.678547i | \(0.762610\pi\) | |||||||
\(8\) | 1.66711 | − | 1.66711i | 0.589411 | − | 0.589411i | ||||
\(9\) | −2.25330 | + | 2.25330i | −0.751100 | + | 0.751100i | ||||
\(10\) | 1.44307 | + | 0.597737i | 0.456337 | + | 0.189021i | ||||
\(11\) | 0.382683 | − | 0.923880i | 0.115383 | − | 0.278560i | ||||
\(12\) | 1.17806 | − | 0.487969i | 0.340077 | − | 0.140864i | ||||
\(13\) | 0.304786i | 0.0845326i | 0.999106 | + | 0.0422663i | \(0.0134578\pi\) | ||||
−0.999106 | + | 0.0422663i | \(0.986542\pi\) | |||||||
\(14\) | −1.34484 | − | 3.24674i | −0.359425 | − | 0.867728i | ||||
\(15\) | −1.73307 | − | 1.73307i | −0.447478 | − | 0.447478i | ||||
\(16\) | 4.76249 | 1.19062 | ||||||||
\(17\) | 2.10233 | + | 3.54686i | 0.509889 | + | 0.860240i | ||||
\(18\) | −5.05127 | −1.19060 | ||||||||
\(19\) | 5.08065 | + | 5.08065i | 1.16558 | + | 1.16558i | 0.983234 | + | 0.182346i | \(0.0583692\pi\) |
0.182346 | + | 0.983234i | \(0.441631\pi\) | |||||||
\(20\) | 0.193316 | + | 0.466707i | 0.0432268 | + | 0.104359i | ||||
\(21\) | 5.51434i | 1.20333i | ||||||||
\(22\) | 1.46447 | − | 0.606605i | 0.312227 | − | 0.129329i | ||||
\(23\) | 1.10308 | − | 2.66307i | 0.230008 | − | 0.555288i | −0.766170 | − | 0.642638i | \(-0.777840\pi\) |
0.996178 | + | 0.0873499i | \(0.0278398\pi\) | |||||||
\(24\) | −5.41778 | − | 2.24412i | −1.10590 | − | 0.458079i | ||||
\(25\) | −2.84895 | + | 2.84895i | −0.569790 | + | 0.569790i | ||||
\(26\) | −0.341623 | + | 0.341623i | −0.0669978 | + | 0.0669978i | ||||
\(27\) | 0.428912 | + | 0.177661i | 0.0825442 | + | 0.0341909i | ||||
\(28\) | 0.434941 | − | 1.05004i | 0.0821961 | − | 0.198439i | ||||
\(29\) | −7.62083 | + | 3.15665i | −1.41515 | + | 0.586175i | −0.953638 | − | 0.300957i | \(-0.902694\pi\) |
−0.461515 | + | 0.887132i | \(0.652694\pi\) | |||||||
\(30\) | − | 3.88507i | − | 0.709313i | ||||||
\(31\) | −0.0844584 | − | 0.203900i | −0.0151692 | − | 0.0366216i | 0.916113 | − | 0.400919i | \(-0.131309\pi\) |
−0.931283 | + | 0.364297i | \(0.881309\pi\) | |||||||
\(32\) | 2.00388 | + | 2.00388i | 0.354239 | + | 0.354239i | ||||
\(33\) | −2.48730 | −0.432983 | ||||||||
\(34\) | −1.61912 | + | 6.33195i | −0.277677 | + | 1.08592i | ||||
\(35\) | −2.18459 | −0.369263 | ||||||||
\(36\) | −1.15516 | − | 1.15516i | −0.192527 | − | 0.192527i | ||||
\(37\) | 0.566445 | + | 1.36752i | 0.0931231 | + | 0.224819i | 0.963577 | − | 0.267431i | \(-0.0861747\pi\) |
−0.870454 | + | 0.492250i | \(0.836175\pi\) | |||||||
\(38\) | 11.3894i | 1.84760i | ||||||||
\(39\) | 0.700388 | − | 0.290110i | 0.112152 | − | 0.0464548i | ||||
\(40\) | 0.889042 | − | 2.14634i | 0.140570 | − | 0.339366i | ||||
\(41\) | 6.50940 | + | 2.69628i | 1.01660 | + | 0.421089i | 0.827857 | − | 0.560939i | \(-0.189560\pi\) |
0.188740 | + | 0.982027i | \(0.439560\pi\) | |||||||
\(42\) | −6.18080 | + | 6.18080i | −0.953719 | + | 0.953719i | ||||
\(43\) | 4.67834 | − | 4.67834i | 0.713441 | − | 0.713441i | −0.253813 | − | 0.967253i | \(-0.581685\pi\) |
0.967253 | + | 0.253813i | \(0.0816847\pi\) | |||||||
\(44\) | 0.473631 | + | 0.196184i | 0.0714025 | + | 0.0295759i | ||||
\(45\) | −1.20165 | + | 2.90104i | −0.179131 | + | 0.432462i | ||||
\(46\) | 4.22133 | − | 1.74853i | 0.622400 | − | 0.257807i | ||||
\(47\) | − | 3.08276i | − | 0.449666i | −0.974397 | − | 0.224833i | \(-0.927816\pi\) | ||
0.974397 | − | 0.224833i | \(-0.0721837\pi\) | |||||||
\(48\) | −4.53317 | − | 10.9440i | −0.654307 | − | 1.57964i | ||||
\(49\) | −1.47425 | − | 1.47425i | −0.210608 | − | 0.210608i | ||||
\(50\) | −6.38655 | −0.903194 | ||||||||
\(51\) | 6.14946 | − | 8.20714i | 0.861097 | − | 1.14923i | ||||
\(52\) | −0.156250 | −0.0216680 | ||||||||
\(53\) | 3.08641 | + | 3.08641i | 0.423952 | + | 0.423952i | 0.886562 | − | 0.462610i | \(-0.153087\pi\) |
−0.462610 | + | 0.886562i | \(0.653087\pi\) | |||||||
\(54\) | 0.281617 | + | 0.679884i | 0.0383232 | + | 0.0925204i | ||||
\(55\) | − | 0.985381i | − | 0.132869i | ||||||
\(56\) | −4.82902 | + | 2.00025i | −0.645306 | + | 0.267294i | ||||
\(57\) | 6.83914 | − | 16.5111i | 0.905866 | − | 2.18695i | ||||
\(58\) | −12.0800 | − | 5.00372i | −1.58619 | − | 0.657021i | ||||
\(59\) | −8.22327 | + | 8.22327i | −1.07058 | + | 1.07058i | −0.0732660 | + | 0.997312i | \(0.523342\pi\) |
−0.997312 | + | 0.0732660i | \(0.976658\pi\) | |||||||
\(60\) | 0.888468 | − | 0.888468i | 0.114701 | − | 0.114701i | ||||
\(61\) | 6.37840 | + | 2.64202i | 0.816671 | + | 0.338276i | 0.751612 | − | 0.659605i | \(-0.229277\pi\) |
0.0650586 | + | 0.997881i | \(0.479277\pi\) | |||||||
\(62\) | 0.133878 | − | 0.323210i | 0.0170025 | − | 0.0410477i | ||||
\(63\) | 6.52703 | − | 2.70358i | 0.822328 | − | 0.340619i | ||||
\(64\) | − | 5.03286i | − | 0.629107i | ||||||
\(65\) | 0.114932 | + | 0.277469i | 0.0142555 | + | 0.0344159i | ||||
\(66\) | −2.78791 | − | 2.78791i | −0.343168 | − | 0.343168i | ||||
\(67\) | −0.0723373 | −0.00883741 | −0.00441871 | − | 0.999990i | \(-0.501407\pi\) | ||||
−0.00441871 | + | 0.999990i | \(0.501407\pi\) | |||||||
\(68\) | −1.81831 | + | 1.07777i | −0.220503 | + | 0.130698i | ||||
\(69\) | −7.16960 | −0.863118 | ||||||||
\(70\) | −2.44862 | − | 2.44862i | −0.292666 | − | 0.292666i | ||||
\(71\) | −1.32006 | − | 3.18690i | −0.156662 | − | 0.378215i | 0.825987 | − | 0.563689i | \(-0.190618\pi\) |
−0.982649 | + | 0.185473i | \(0.940618\pi\) | |||||||
\(72\) | 7.51298i | 0.885414i | ||||||||
\(73\) | −3.02287 | + | 1.25211i | −0.353800 | + | 0.146549i | −0.552503 | − | 0.833511i | \(-0.686327\pi\) |
0.198703 | + | 0.980060i | \(0.436327\pi\) | |||||||
\(74\) | −0.897893 | + | 2.16771i | −0.104378 | + | 0.251991i | ||||
\(75\) | 9.25855 | + | 3.83502i | 1.06909 | + | 0.442830i | ||||
\(76\) | −2.60462 | + | 2.60462i | −0.298770 | + | 0.298770i | ||||
\(77\) | −1.56766 | + | 1.56766i | −0.178651 | + | 0.178651i | ||||
\(78\) | 1.11021 | + | 0.459864i | 0.125707 | + | 0.0520693i | ||||
\(79\) | 5.35739 | − | 12.9339i | 0.602753 | − | 1.45518i | −0.267982 | − | 0.963424i | \(-0.586357\pi\) |
0.870735 | − | 0.491752i | \(-0.163643\pi\) | |||||||
\(80\) | 4.33565 | − | 1.79588i | 0.484740 | − | 0.200786i | ||||
\(81\) | 8.40522i | 0.933913i | ||||||||
\(82\) | 4.27397 | + | 10.3183i | 0.471981 | + | 1.13946i | ||||
\(83\) | −3.57107 | − | 3.57107i | −0.391976 | − | 0.391976i | 0.483415 | − | 0.875391i | \(-0.339396\pi\) |
−0.875391 | + | 0.483415i | \(0.839396\pi\) | |||||||
\(84\) | −2.82695 | −0.308446 | ||||||||
\(85\) | 3.25138 | + | 2.43620i | 0.352662 | + | 0.264244i | ||||
\(86\) | 10.4875 | 1.13090 | ||||||||
\(87\) | 14.5077 | + | 14.5077i | 1.55539 | + | 1.55539i | ||||
\(88\) | −0.902231 | − | 2.17818i | −0.0961782 | − | 0.232195i | ||||
\(89\) | 11.3144i | 1.19933i | 0.800252 | + | 0.599664i | \(0.204699\pi\) | ||||
−0.800252 | + | 0.599664i | \(0.795301\pi\) | |||||||
\(90\) | −4.59854 | + | 1.90478i | −0.484729 | + | 0.200781i | ||||
\(91\) | 0.258584 | − | 0.624276i | 0.0271069 | − | 0.0654419i | ||||
\(92\) | 1.36523 | + | 0.565499i | 0.142336 | + | 0.0589573i | ||||
\(93\) | −0.388164 | + | 0.388164i | −0.0402508 | + | 0.0402508i | ||||
\(94\) | 3.45534 | − | 3.45534i | 0.356391 | − | 0.356391i | ||||
\(95\) | 6.54114 | + | 2.70943i | 0.671107 | + | 0.277982i | ||||
\(96\) | 2.69745 | − | 6.51222i | 0.275307 | − | 0.664651i | ||||
\(97\) | −0.163202 | + | 0.0676007i | −0.0165707 | + | 0.00686381i | −0.390953 | − | 0.920410i | \(-0.627855\pi\) |
0.374383 | + | 0.927274i | \(0.377855\pi\) | |||||||
\(98\) | − | 3.30486i | − | 0.333842i | ||||||
\(99\) | 1.21948 | + | 2.94408i | 0.122562 | + | 0.295891i | ||||
\(100\) | −1.46053 | − | 1.46053i | −0.146053 | − | 0.146053i | ||||
\(101\) | −6.94906 | −0.691457 | −0.345729 | − | 0.938335i | \(-0.612368\pi\) | ||||
−0.345729 | + | 0.938335i | \(0.612368\pi\) | |||||||
\(102\) | 16.0917 | − | 2.30636i | 1.59332 | − | 0.228364i | ||||
\(103\) | −10.8498 | −1.06907 | −0.534533 | − | 0.845148i | \(-0.679512\pi\) | ||||
−0.534533 | + | 0.845148i | \(0.679512\pi\) | |||||||
\(104\) | 0.508111 | + | 0.508111i | 0.0498244 | + | 0.0498244i | ||||
\(105\) | 2.07940 | + | 5.02011i | 0.202928 | + | 0.489912i | ||||
\(106\) | 6.91888i | 0.672021i | ||||||||
\(107\) | −11.0331 | + | 4.57004i | −1.06661 | + | 0.441802i | −0.845792 | − | 0.533514i | \(-0.820871\pi\) |
−0.220814 | + | 0.975316i | \(0.570871\pi\) | |||||||
\(108\) | −0.0910788 | + | 0.219884i | −0.00876406 | + | 0.0211583i | ||||
\(109\) | 7.29615 | + | 3.02216i | 0.698844 | + | 0.289471i | 0.703679 | − | 0.710518i | \(-0.251539\pi\) |
−0.00483526 | + | 0.999988i | \(0.501539\pi\) | |||||||
\(110\) | 1.10447 | − | 1.10447i | 0.105307 | − | 0.105307i | ||||
\(111\) | 2.60334 | − | 2.60334i | 0.247098 | − | 0.247098i | ||||
\(112\) | −9.75474 | − | 4.04054i | −0.921736 | − | 0.381796i | ||||
\(113\) | 5.70321 | − | 13.7688i | 0.536512 | − | 1.29526i | −0.390630 | − | 0.920548i | \(-0.627743\pi\) |
0.927143 | − | 0.374708i | \(-0.122257\pi\) | |||||||
\(114\) | 26.1724 | − | 10.8410i | 2.45127 | − | 1.01535i | ||||
\(115\) | − | 2.84035i | − | 0.264864i | ||||||
\(116\) | −1.61827 | − | 3.90685i | −0.150253 | − | 0.362742i | ||||
\(117\) | −0.686776 | − | 0.686776i | −0.0634924 | − | 0.0634924i | ||||
\(118\) | −18.4343 | −1.69701 | ||||||||
\(119\) | −1.29688 | − | 9.04846i | −0.118885 | − | 0.829471i | ||||
\(120\) | −5.77844 | −0.527497 | ||||||||
\(121\) | −0.707107 | − | 0.707107i | −0.0642824 | − | 0.0642824i | ||||
\(122\) | 4.18796 | + | 10.1106i | 0.379160 | + | 0.915374i | ||||
\(123\) | − | 17.5248i | − | 1.58016i | ||||||
\(124\) | 0.104530 | − | 0.0432979i | 0.00938711 | − | 0.00388827i | ||||
\(125\) | −3.40475 | + | 8.21978i | −0.304530 | + | 0.735200i | ||||
\(126\) | 10.3462 | + | 4.28554i | 0.921715 | + | 0.381787i | ||||
\(127\) | 11.5480 | − | 11.5480i | 1.02472 | − | 1.02472i | 0.0250315 | − | 0.999687i | \(-0.492031\pi\) |
0.999687 | − | 0.0250315i | \(-0.00796861\pi\) | |||||||
\(128\) | 9.64888 | − | 9.64888i | 0.852849 | − | 0.852849i | ||||
\(129\) | −15.2037 | − | 6.29759i | −1.33861 | − | 0.554472i | ||||
\(130\) | −0.182182 | + | 0.439827i | −0.0159784 | + | 0.0385754i | ||||
\(131\) | −15.9803 | + | 6.61928i | −1.39621 | + | 0.578329i | −0.948765 | − | 0.315983i | \(-0.897666\pi\) |
−0.447445 | + | 0.894312i | \(0.647666\pi\) | |||||||
\(132\) | − | 1.27512i | − | 0.110985i | ||||||
\(133\) | −6.09592 | − | 14.7169i | −0.528584 | − | 1.27611i | ||||
\(134\) | −0.0810800 | − | 0.0810800i | −0.00700425 | − | 0.00700425i | ||||
\(135\) | 0.457464 | 0.0393722 | ||||||||
\(136\) | 9.41780 | + | 2.40820i | 0.807569 | + | 0.206501i | ||||
\(137\) | −10.6544 | −0.910270 | −0.455135 | − | 0.890422i | \(-0.650409\pi\) | ||||
−0.455135 | + | 0.890422i | \(0.650409\pi\) | |||||||
\(138\) | −8.03612 | − | 8.03612i | −0.684080 | − | 0.684080i | ||||
\(139\) | 4.63793 | + | 11.1969i | 0.393384 | + | 0.949712i | 0.989197 | + | 0.146590i | \(0.0468297\pi\) |
−0.595814 | + | 0.803123i | \(0.703170\pi\) | |||||||
\(140\) | − | 1.11994i | − | 0.0946522i | ||||||
\(141\) | −7.08406 | + | 2.93431i | −0.596585 | + | 0.247114i | ||||
\(142\) | 2.09247 | − | 5.05167i | 0.175596 | − | 0.423926i | ||||
\(143\) | 0.281586 | + | 0.116637i | 0.0235474 | + | 0.00975365i | ||||
\(144\) | −10.7313 | + | 10.7313i | −0.894278 | + | 0.894278i | ||||
\(145\) | −5.74746 | + | 5.74746i | −0.477301 | + | 0.477301i | ||||
\(146\) | −4.79166 | − | 1.98477i | −0.396560 | − | 0.164261i | ||||
\(147\) | −1.98452 | + | 4.79104i | −0.163680 | + | 0.395159i | ||||
\(148\) | −0.701065 | + | 0.290391i | −0.0576272 | + | 0.0238700i | ||||
\(149\) | − | 13.6059i | − | 1.11464i | −0.830298 | − | 0.557320i | \(-0.811830\pi\) | ||
0.830298 | − | 0.557320i | \(-0.188170\pi\) | |||||||
\(150\) | 6.07902 | + | 14.6761i | 0.496350 | + | 1.19829i | ||||
\(151\) | −4.25390 | − | 4.25390i | −0.346177 | − | 0.346177i | 0.512506 | − | 0.858684i | \(-0.328717\pi\) |
−0.858684 | + | 0.512506i | \(0.828717\pi\) | |||||||
\(152\) | 16.9400 | 1.37401 | ||||||||
\(153\) | −12.7293 | − | 3.25498i | −1.02910 | − | 0.263149i | ||||
\(154\) | −3.51425 | −0.283186 | ||||||||
\(155\) | −0.153777 | − | 0.153777i | −0.0123517 | − | 0.0123517i | ||||
\(156\) | 0.148726 | + | 0.359057i | 0.0119076 | + | 0.0287476i | ||||
\(157\) | − | 22.6873i | − | 1.81064i | −0.424727 | − | 0.905321i | \(-0.639630\pi\) | ||
0.424727 | − | 0.905321i | \(-0.360370\pi\) | |||||||
\(158\) | 20.5020 | − | 8.49219i | 1.63105 | − | 0.675602i | ||||
\(159\) | 4.15467 | − | 10.0303i | 0.329487 | − | 0.795451i | ||||
\(160\) | 2.57992 | + | 1.06864i | 0.203960 | + | 0.0844831i | ||||
\(161\) | −4.51875 | + | 4.51875i | −0.356127 | + | 0.356127i | ||||
\(162\) | −9.42107 | + | 9.42107i | −0.740189 | + | 0.740189i | ||||
\(163\) | −11.1691 | − | 4.62639i | −0.874830 | − | 0.362366i | −0.100341 | − | 0.994953i | \(-0.531993\pi\) |
−0.774490 | + | 0.632587i | \(0.781993\pi\) | |||||||
\(164\) | −1.38226 | + | 3.33707i | −0.107936 | + | 0.260582i | ||||
\(165\) | −2.26437 | + | 0.937933i | −0.176281 | + | 0.0730180i | ||||
\(166\) | − | 8.00534i | − | 0.621335i | ||||||
\(167\) | 8.95471 | + | 21.6186i | 0.692936 | + | 1.67290i | 0.738780 | + | 0.673947i | \(0.235402\pi\) |
−0.0458434 | + | 0.998949i | \(0.514598\pi\) | |||||||
\(168\) | 9.19299 | + | 9.19299i | 0.709255 | + | 0.709255i | ||||
\(169\) | 12.9071 | 0.992854 | ||||||||
\(170\) | 0.913702 | + | 6.37499i | 0.0700777 | + | 0.488939i | ||||
\(171\) | −22.8965 | −1.75094 | ||||||||
\(172\) | 2.39837 | + | 2.39837i | 0.182874 | + | 0.182874i | ||||
\(173\) | 0.467353 | + | 1.12829i | 0.0355322 | + | 0.0857822i | 0.940649 | − | 0.339380i | \(-0.110217\pi\) |
−0.905117 | + | 0.425162i | \(0.860217\pi\) | |||||||
\(174\) | 32.5223i | 2.46551i | ||||||||
\(175\) | 8.25241 | − | 3.41826i | 0.623824 | − | 0.258396i | ||||
\(176\) | 1.82253 | − | 4.39997i | 0.137378 | − | 0.331660i | ||||
\(177\) | 26.7241 | + | 11.0695i | 2.00870 | + | 0.832032i | ||||
\(178\) | −12.6819 | + | 12.6819i | −0.950549 | + | 0.950549i | ||||
\(179\) | −15.4138 | + | 15.4138i | −1.15208 | + | 1.15208i | −0.165947 | + | 0.986135i | \(0.553068\pi\) |
−0.986135 | + | 0.165947i | \(0.946932\pi\) | |||||||
\(180\) | −1.48723 | − | 0.616031i | −0.110852 | − | 0.0459163i | ||||
\(181\) | −6.03596 | + | 14.5721i | −0.448650 | + | 1.08314i | 0.524179 | + | 0.851608i | \(0.324372\pi\) |
−0.972828 | + | 0.231528i | \(0.925628\pi\) | |||||||
\(182\) | 0.989562 | − | 0.409890i | 0.0733512 | − | 0.0303831i | ||||
\(183\) | − | 17.1721i | − | 1.26940i | ||||||
\(184\) | −2.60067 | − | 6.27857i | −0.191724 | − | 0.462862i | ||||
\(185\) | 1.03135 | + | 1.03135i | 0.0758266 | + | 0.0758266i | ||||
\(186\) | −0.870156 | −0.0638029 | ||||||||
\(187\) | 4.08140 | − | 0.584970i | 0.298461 | − | 0.0427773i | ||||
\(188\) | 1.58039 | 0.115262 | ||||||||
\(189\) | −0.727786 | − | 0.727786i | −0.0529386 | − | 0.0529386i | ||||
\(190\) | 4.29481 | + | 10.3686i | 0.311579 | + | 0.752217i | ||||
\(191\) | 8.56666i | 0.619861i | 0.950759 | + | 0.309931i | \(0.100306\pi\) | ||||
−0.950759 | + | 0.309931i | \(0.899694\pi\) | |||||||
\(192\) | −11.5653 | + | 4.79051i | −0.834655 | + | 0.345725i | ||||
\(193\) | −4.58804 | + | 11.0765i | −0.330254 | + | 0.797304i | 0.668318 | + | 0.743876i | \(0.267015\pi\) |
−0.998572 | + | 0.0534279i | \(0.982985\pi\) | |||||||
\(194\) | −0.258698 | − | 0.107156i | −0.0185734 | − | 0.00769337i | ||||
\(195\) | 0.528217 | − | 0.528217i | 0.0378264 | − | 0.0378264i | ||||
\(196\) | 0.755782 | − | 0.755782i | 0.0539845 | − | 0.0539845i | ||||
\(197\) | −17.6970 | − | 7.33033i | −1.26086 | − | 0.522264i | −0.350685 | − | 0.936494i | \(-0.614051\pi\) |
−0.910172 | + | 0.414230i | \(0.864051\pi\) | |||||||
\(198\) | −1.93304 | + | 4.66676i | −0.137375 | + | 0.331653i | ||||
\(199\) | −10.5096 | + | 4.35321i | −0.745005 | + | 0.308591i | −0.722702 | − | 0.691160i | \(-0.757100\pi\) |
−0.0223031 | + | 0.999751i | \(0.507100\pi\) | |||||||
\(200\) | 9.49901i | 0.671681i | ||||||||
\(201\) | 0.0688541 | + | 0.166229i | 0.00485659 | + | 0.0117249i | ||||
\(202\) | −7.78892 | − | 7.78892i | −0.548027 | − | 0.548027i | ||||
\(203\) | 18.2874 | 1.28353 | ||||||||
\(204\) | 4.20743 | + | 3.15255i | 0.294579 | + | 0.220723i | ||||
\(205\) | 6.94272 | 0.484901 | ||||||||
\(206\) | −12.1611 | − | 12.1611i | −0.847307 | − | 0.847307i | ||||
\(207\) | 3.51513 | + | 8.48627i | 0.244318 | + | 0.589836i | ||||
\(208\) | 1.45154i | 0.100646i | ||||||||
\(209\) | 6.63819 | − | 2.74963i | 0.459173 | − | 0.190196i | ||||
\(210\) | −3.29613 | + | 7.95755i | −0.227454 | + | 0.549123i | ||||
\(211\) | −22.4480 | − | 9.29828i | −1.54539 | − | 0.640120i | −0.562912 | − | 0.826517i | \(-0.690319\pi\) |
−0.982475 | + | 0.186397i | \(0.940319\pi\) | |||||||
\(212\) | −1.58226 | + | 1.58226i | −0.108670 | + | 0.108670i | ||||
\(213\) | −6.06688 | + | 6.06688i | −0.415696 | + | 0.415696i | ||||
\(214\) | −17.4889 | − | 7.24413i | −1.19552 | − | 0.495199i | ||||
\(215\) | 2.49489 | − | 6.02319i | 0.170150 | − | 0.410778i | ||||
\(216\) | 1.01122 | − | 0.418862i | 0.0688049 | − | 0.0284999i | ||||
\(217\) | 0.489293i | 0.0332154i | ||||||||
\(218\) | 4.79054 | + | 11.5654i | 0.324456 | + | 0.783307i | ||||
\(219\) | 5.75462 | + | 5.75462i | 0.388861 | + | 0.388861i | ||||
\(220\) | 0.505160 | 0.0340579 | ||||||||
\(221\) | −1.08104 | + | 0.640760i | −0.0727183 | + | 0.0431022i | ||||
\(222\) | 5.83596 | 0.391684 | ||||||||
\(223\) | 10.1047 | + | 10.1047i | 0.676659 | + | 0.676659i | 0.959243 | − | 0.282584i | \(-0.0911916\pi\) |
−0.282584 | + | 0.959243i | \(0.591192\pi\) | |||||||
\(224\) | −2.40432 | − | 5.80453i | −0.160645 | − | 0.387832i | ||||
\(225\) | − | 12.8391i | − | 0.855939i | ||||||
\(226\) | 21.8253 | − | 9.04035i | 1.45180 | − | 0.601355i | ||||
\(227\) | −0.972198 | + | 2.34709i | −0.0645271 | + | 0.155782i | −0.952854 | − | 0.303430i | \(-0.901868\pi\) |
0.888327 | + | 0.459212i | \(0.151868\pi\) | |||||||
\(228\) | 8.46451 | + | 3.50612i | 0.560576 | + | 0.232198i | ||||
\(229\) | 3.66555 | − | 3.66555i | 0.242226 | − | 0.242226i | −0.575544 | − | 0.817771i | \(-0.695210\pi\) |
0.817771 | + | 0.575544i | \(0.195210\pi\) | |||||||
\(230\) | 3.18363 | − | 3.18363i | 0.209922 | − | 0.209922i | ||||
\(231\) | 5.09459 | + | 2.11025i | 0.335199 | + | 0.138844i | ||||
\(232\) | −7.44226 | + | 17.9672i | −0.488608 | + | 1.17960i | ||||
\(233\) | 1.98856 | − | 0.823689i | 0.130275 | − | 0.0539617i | −0.316594 | − | 0.948561i | \(-0.602539\pi\) |
0.446869 | + | 0.894600i | \(0.352539\pi\) | |||||||
\(234\) | − | 1.53956i | − | 0.100644i | ||||||
\(235\) | −1.16247 | − | 2.80646i | −0.0758314 | − | 0.183073i | ||||
\(236\) | −4.21570 | − | 4.21570i | −0.274418 | − | 0.274418i | ||||
\(237\) | −34.8210 | −2.26187 | ||||||||
\(238\) | 8.68844 | − | 11.5957i | 0.563188 | − | 0.751636i | ||||
\(239\) | 25.1415 | 1.62627 | 0.813136 | − | 0.582074i | \(-0.197759\pi\) | ||||
0.813136 | + | 0.582074i | \(0.197759\pi\) | |||||||
\(240\) | −8.25375 | − | 8.25375i | −0.532777 | − | 0.532777i | ||||
\(241\) | −4.30712 | − | 10.3983i | −0.277446 | − | 0.669813i | 0.722318 | − | 0.691561i | \(-0.243077\pi\) |
−0.999763 | + | 0.0217480i | \(0.993077\pi\) | |||||||
\(242\) | − | 1.58514i | − | 0.101896i | ||||||
\(243\) | 20.6016 | − | 8.53347i | 1.32159 | − | 0.547422i | ||||
\(244\) | −1.35444 | + | 3.26992i | −0.0867094 | + | 0.209335i | ||||
\(245\) | −1.89805 | − | 0.786196i | −0.121262 | − | 0.0502282i | ||||
\(246\) | 19.6429 | − | 19.6429i | 1.25238 | − | 1.25238i | ||||
\(247\) | −1.54851 | + | 1.54851i | −0.0985295 | + | 0.0985295i | ||||
\(248\) | −0.480725 | − | 0.199123i | −0.0305261 | − | 0.0126443i | ||||
\(249\) | −4.80708 | + | 11.6053i | −0.304636 | + | 0.735456i | ||||
\(250\) | −13.0295 | + | 5.39698i | −0.824056 | + | 0.341335i | ||||
\(251\) | − | 18.5842i | − | 1.17302i | −0.809941 | − | 0.586511i | \(-0.800501\pi\) | ||
0.809941 | − | 0.586511i | \(-0.199499\pi\) | |||||||
\(252\) | 1.38600 | + | 3.34611i | 0.0873100 | + | 0.210785i | ||||
\(253\) | −2.03823 | − | 2.03823i | −0.128142 | − | 0.128142i | ||||
\(254\) | 25.8874 | 1.62432 | ||||||||
\(255\) | 2.50349 | − | 9.79046i | 0.156774 | − | 0.613102i | ||||
\(256\) | 11.5644 | 0.722774 | ||||||||
\(257\) | −4.97755 | − | 4.97755i | −0.310491 | − | 0.310491i | 0.534609 | − | 0.845100i | \(-0.320459\pi\) |
−0.845100 | + | 0.534609i | \(0.820459\pi\) | |||||||
\(258\) | −9.98254 | − | 24.1000i | −0.621486 | − | 1.50040i | ||||
\(259\) | − | 3.28159i | − | 0.203908i | ||||||
\(260\) | −0.142246 | + | 0.0589202i | −0.00882172 | + | 0.00365408i | ||||
\(261\) | 10.0591 | − | 24.2849i | 0.622645 | − | 1.50320i | ||||
\(262\) | −25.3310 | − | 10.4924i | −1.56496 | − | 0.648226i | ||||
\(263\) | −9.07526 | + | 9.07526i | −0.559605 | + | 0.559605i | −0.929195 | − | 0.369590i | \(-0.879498\pi\) |
0.369590 | + | 0.929195i | \(0.379498\pi\) | |||||||
\(264\) | −4.14659 | + | 4.14659i | −0.255205 | + | 0.255205i | ||||
\(265\) | 3.97364 | + | 1.64594i | 0.244099 | + | 0.101109i | ||||
\(266\) | 9.66287 | − | 23.3282i | 0.592468 | − | 1.43035i | ||||
\(267\) | 26.0002 | − | 10.7696i | 1.59118 | − | 0.659090i | ||||
\(268\) | − | 0.0370840i | − | 0.00226527i | ||||||
\(269\) | −2.92664 | − | 7.06553i | −0.178440 | − | 0.430793i | 0.809199 | − | 0.587534i | \(-0.199901\pi\) |
−0.987640 | + | 0.156741i | \(0.949901\pi\) | |||||||
\(270\) | 0.512753 | + | 0.512753i | 0.0312052 | + | 0.0312052i | ||||
\(271\) | 14.2400 | 0.865016 | 0.432508 | − | 0.901630i | \(-0.357629\pi\) | ||||
0.432508 | + | 0.901630i | \(0.357629\pi\) | |||||||
\(272\) | 10.0123 | + | 16.8919i | 0.607086 | + | 1.02422i | ||||
\(273\) | −1.68070 | −0.101720 | ||||||||
\(274\) | −11.9421 | − | 11.9421i | −0.721451 | − | 0.721451i | ||||
\(275\) | 1.54184 | + | 3.72233i | 0.0929765 | + | 0.224465i | ||||
\(276\) | − | 3.67553i | − | 0.221241i | ||||||
\(277\) | 29.3900 | − | 12.1738i | 1.76588 | − | 0.731450i | 0.770281 | − | 0.637705i | \(-0.220116\pi\) |
0.995596 | − | 0.0937450i | \(-0.0298838\pi\) | |||||||
\(278\) | −7.35174 | + | 17.7487i | −0.440928 | + | 1.06449i | ||||
\(279\) | 0.649759 | + | 0.269139i | 0.0389001 | + | 0.0161129i | ||||
\(280\) | −3.64194 | + | 3.64194i | −0.217648 | + | 0.217648i | ||||
\(281\) | −22.5205 | + | 22.5205i | −1.34346 | + | 1.34346i | −0.450869 | + | 0.892590i | \(0.648886\pi\) |
−0.892590 | + | 0.450869i | \(0.851114\pi\) | |||||||
\(282\) | −11.2292 | − | 4.65128i | −0.668689 | − | 0.276980i | ||||
\(283\) | −3.81994 | + | 9.22216i | −0.227072 | + | 0.548200i | −0.995819 | − | 0.0913533i | \(-0.970881\pi\) |
0.768747 | + | 0.639554i | \(0.220881\pi\) | |||||||
\(284\) | 1.63378 | − | 0.676733i | 0.0969469 | − | 0.0401567i | ||||
\(285\) | − | 17.6103i | − | 1.04314i | ||||||
\(286\) | 0.184885 | + | 0.446352i | 0.0109325 | + | 0.0263933i | ||||
\(287\) | −11.0453 | − | 11.0453i | −0.651982 | − | 0.651982i | ||||
\(288\) | −9.03068 | −0.532138 | ||||||||
\(289\) | −8.16046 | + | 14.9133i | −0.480027 | + | 0.877254i | ||||
\(290\) | −12.8842 | −0.756586 | ||||||||
\(291\) | 0.310688 | + | 0.310688i | 0.0182128 | + | 0.0182128i | ||||
\(292\) | −0.641902 | − | 1.54969i | −0.0375645 | − | 0.0906886i | ||||
\(293\) | − | 4.02872i | − | 0.235360i | −0.993052 | − | 0.117680i | \(-0.962454\pi\) | ||
0.993052 | − | 0.117680i | \(-0.0375458\pi\) | |||||||
\(294\) | −7.59445 | + | 3.14573i | −0.442918 | + | 0.183462i | ||||
\(295\) | −4.38534 | + | 10.5872i | −0.255324 | + | 0.616408i | ||||
\(296\) | 3.22413 | + | 1.33548i | 0.187399 | + | 0.0776230i | ||||
\(297\) | 0.328275 | − | 0.328275i | 0.0190484 | − | 0.0190484i | ||||
\(298\) | 15.2503 | − | 15.2503i | 0.883428 | − | 0.883428i | ||||
\(299\) | 0.811667 | + | 0.336204i | 0.0469399 | + | 0.0194432i | ||||
\(300\) | −1.96604 | + | 4.74644i | −0.113509 | + | 0.274036i | ||||
\(301\) | −13.5515 | + | 5.61323i | −0.781097 | + | 0.323541i | ||||
\(302\) | − | 9.53605i | − | 0.548738i | ||||||
\(303\) | 6.61444 | + | 15.9687i | 0.379990 | + | 0.917377i | ||||
\(304\) | 24.1966 | + | 24.1966i | 1.38777 | + | 1.38777i | ||||
\(305\) | 6.80301 | 0.389539 | ||||||||
\(306\) | −10.6194 | − | 17.9162i | −0.607071 | − | 1.02420i | ||||
\(307\) | 28.5771 | 1.63098 | 0.815490 | − | 0.578771i | \(-0.196468\pi\) | ||||
0.815490 | + | 0.578771i | \(0.196468\pi\) | |||||||
\(308\) | −0.803666 | − | 0.803666i | −0.0457931 | − | 0.0457931i | ||||
\(309\) | 10.3274 | + | 24.9325i | 0.587504 | + | 1.41836i | ||||
\(310\) | − | 0.344726i | − | 0.0195791i | ||||||
\(311\) | −2.09621 | + | 0.868278i | −0.118865 | + | 0.0492355i | −0.441323 | − | 0.897348i | \(-0.645491\pi\) |
0.322458 | + | 0.946584i | \(0.395491\pi\) | |||||||
\(312\) | 0.683977 | − | 1.65127i | 0.0387226 | − | 0.0934845i | ||||
\(313\) | 24.9867 | + | 10.3498i | 1.41233 | + | 0.585008i | 0.952922 | − | 0.303215i | \(-0.0980601\pi\) |
0.459412 | + | 0.888223i | \(0.348060\pi\) | |||||||
\(314\) | 25.4293 | − | 25.4293i | 1.43506 | − | 1.43506i | ||||
\(315\) | 4.92254 | − | 4.92254i | 0.277354 | − | 0.277354i | ||||
\(316\) | 6.63061 | + | 2.74649i | 0.373001 | + | 0.154502i | ||||
\(317\) | 12.6558 | − | 30.5537i | 0.710818 | − | 1.71607i | 0.0128714 | − | 0.999917i | \(-0.495903\pi\) |
0.697947 | − | 0.716150i | \(-0.254097\pi\) | |||||||
\(318\) | 15.8993 | − | 6.58571i | 0.891590 | − | 0.369309i | ||||
\(319\) | 8.24873i | 0.461840i | ||||||||
\(320\) | −1.89784 | − | 4.58178i | −0.106092 | − | 0.256129i | ||||
\(321\) | 21.0036 | + | 21.0036i | 1.17230 | + | 1.17230i | ||||
\(322\) | −10.1298 | −0.564510 | ||||||||
\(323\) | −7.33918 | + | 28.7015i | −0.408363 | + | 1.59700i | ||||
\(324\) | −4.30897 | −0.239387 | ||||||||
\(325\) | −0.868321 | − | 0.868321i | −0.0481658 | − | 0.0481658i | ||||
\(326\) | −7.33345 | − | 17.7045i | −0.406162 | − | 0.980562i | ||||
\(327\) | − | 19.6429i | − | 1.08626i | ||||||
\(328\) | 15.3469 | − | 6.35687i | 0.847388 | − | 0.351000i | ||||
\(329\) | −2.61544 | + | 6.31423i | −0.144194 | + | 0.348115i | ||||
\(330\) | −3.58933 | − | 1.48675i | −0.197586 | − | 0.0818429i | ||||
\(331\) | 0.663758 | − | 0.663758i | 0.0364835 | − | 0.0364835i | −0.688630 | − | 0.725113i | \(-0.741787\pi\) |
0.725113 | + | 0.688630i | \(0.241787\pi\) | |||||||
\(332\) | 1.83073 | − | 1.83073i | 0.100474 | − | 0.100474i | ||||
\(333\) | −4.35781 | − | 1.80506i | −0.238806 | − | 0.0989168i | ||||
\(334\) | −14.1944 | + | 34.2684i | −0.776684 | + | 1.87508i | ||||
\(335\) | −0.0658540 | + | 0.0272776i | −0.00359799 | + | 0.00149034i | ||||
\(336\) | 26.2620i | 1.43271i | ||||||||
\(337\) | 0.248898 | + | 0.600893i | 0.0135583 | + | 0.0327327i | 0.930514 | − | 0.366257i | \(-0.119361\pi\) |
−0.916955 | + | 0.398990i | \(0.869361\pi\) | |||||||
\(338\) | 14.4671 | + | 14.4671i | 0.786904 | + | 0.786904i | ||||
\(339\) | −37.0687 | −2.01329 | ||||||||
\(340\) | −1.24893 | + | 1.66684i | −0.0677328 | + | 0.0903969i | ||||
\(341\) | −0.220700 | −0.0119516 | ||||||||
\(342\) | −25.6637 | − | 25.6637i | −1.38774 | − | 1.38774i | ||||
\(343\) | 7.70772 | + | 18.6081i | 0.416178 | + | 1.00474i | ||||
\(344\) | − | 15.5986i | − | 0.841020i | ||||||
\(345\) | −6.52701 | + | 2.70358i | −0.351403 | + | 0.145556i | ||||
\(346\) | −0.740817 | + | 1.78849i | −0.0398266 | + | 0.0961499i | ||||
\(347\) | −1.27141 | − | 0.526636i | −0.0682529 | − | 0.0282713i | 0.348296 | − | 0.937385i | \(-0.386760\pi\) |
−0.416549 | + | 0.909113i | \(0.636760\pi\) | |||||||
\(348\) | −7.43745 | + | 7.43745i | −0.398689 | + | 0.398689i | ||||
\(349\) | 7.13077 | − | 7.13077i | 0.381701 | − | 0.381701i | −0.490014 | − | 0.871715i | \(-0.663008\pi\) |
0.871715 | + | 0.490014i | \(0.163008\pi\) | |||||||
\(350\) | 13.0812 | + | 5.41841i | 0.699219 | + | 0.289626i | ||||
\(351\) | −0.0541487 | + | 0.130727i | −0.00289024 | + | 0.00697767i | ||||
\(352\) | 2.61819 | − | 1.08449i | 0.139550 | − | 0.0578035i | ||||
\(353\) | − | 29.7786i | − | 1.58495i | −0.609902 | − | 0.792477i | \(-0.708791\pi\) | ||
0.609902 | − | 0.792477i | \(-0.291209\pi\) | |||||||
\(354\) | 17.5466 | + | 42.3613i | 0.932592 | + | 2.25148i | ||||
\(355\) | −2.40349 | − | 2.40349i | −0.127564 | − | 0.127564i | ||||
\(356\) | −5.80040 | −0.307420 | ||||||||
\(357\) | −19.5586 | + | 11.5929i | −1.03515 | + | 0.613563i | ||||
\(358\) | −34.5534 | −1.82621 | ||||||||
\(359\) | −3.99870 | − | 3.99870i | −0.211044 | − | 0.211044i | 0.593667 | − | 0.804711i | \(-0.297680\pi\) |
−0.804711 | + | 0.593667i | \(0.797680\pi\) | |||||||
\(360\) | 2.83306 | + | 6.83962i | 0.149316 | + | 0.360480i | ||||
\(361\) | 32.6260i | 1.71716i | ||||||||
\(362\) | −23.0988 | + | 9.56782i | −1.21404 | + | 0.502874i | ||||
\(363\) | −0.951848 | + | 2.29796i | −0.0499590 | + | 0.120612i | ||||
\(364\) | 0.320038 | + | 0.132564i | 0.0167745 | + | 0.00694824i | ||||
\(365\) | −2.27978 | + | 2.27978i | −0.119329 | + | 0.119329i | ||||
\(366\) | 19.2476 | − | 19.2476i | 1.00609 | − | 1.00609i | ||||
\(367\) | −28.2228 | − | 11.6903i | −1.47322 | − | 0.610228i | −0.505629 | − | 0.862751i | \(-0.668740\pi\) |
−0.967591 | + | 0.252523i | \(0.918740\pi\) | |||||||
\(368\) | 5.25341 | − | 12.6829i | 0.273853 | − | 0.661139i | ||||
\(369\) | −20.7432 | + | 8.59210i | −1.07985 | + | 0.447287i | ||||
\(370\) | 2.31201i | 0.120196i | ||||||||
\(371\) | −3.70318 | − | 8.94026i | −0.192259 | − | 0.464155i | ||||
\(372\) | −0.198994 | − | 0.198994i | −0.0103174 | − | 0.0103174i | ||||
\(373\) | 0.755973 | 0.0391428 | 0.0195714 | − | 0.999808i | \(-0.493770\pi\) | ||||
0.0195714 | + | 0.999808i | \(0.493770\pi\) | |||||||
\(374\) | 5.23035 | + | 3.91901i | 0.270455 | + | 0.202647i | ||||
\(375\) | 22.1296 | 1.14277 | ||||||||
\(376\) | −5.13928 | − | 5.13928i | −0.265038 | − | 0.265038i | ||||
\(377\) | −0.962104 | − | 2.32273i | −0.0495509 | − | 0.119626i | ||||
\(378\) | − | 1.63149i | − | 0.0839149i | ||||||
\(379\) | 10.0781 | − | 4.17447i | 0.517675 | − | 0.214428i | −0.108520 | − | 0.994094i | \(-0.534611\pi\) |
0.626195 | + | 0.779666i | \(0.284611\pi\) | |||||||
\(380\) | −1.38900 | + | 3.35335i | −0.0712543 | + | 0.172023i | ||||
\(381\) | −37.5288 | − | 15.5449i | −1.92266 | − | 0.796391i | ||||
\(382\) | −9.60202 | + | 9.60202i | −0.491282 | + | 0.491282i | ||||
\(383\) | 24.0793 | − | 24.0793i | 1.23039 | − | 1.23039i | 0.266582 | − | 0.963812i | \(-0.414106\pi\) |
0.963812 | − | 0.266582i | \(-0.0858944\pi\) | |||||||
\(384\) | −31.3570 | − | 12.9885i | −1.60018 | − | 0.662817i | ||||
\(385\) | −0.836007 | + | 2.01830i | −0.0426068 | + | 0.102862i | ||||
\(386\) | −17.5578 | + | 7.27266i | −0.893666 | + | 0.370169i | ||||
\(387\) | 21.0834i | 1.07173i | ||||||||
\(388\) | −0.0346558 | − | 0.0836664i | −0.00175938 | − | 0.00424752i | ||||
\(389\) | −7.33123 | − | 7.33123i | −0.371708 | − | 0.371708i | 0.496391 | − | 0.868099i | \(-0.334658\pi\) |
−0.868099 | + | 0.496391i | \(0.834658\pi\) | |||||||
\(390\) | 1.18412 | 0.0599600 | ||||||||
\(391\) | 11.7646 | − | 1.68617i | 0.594960 | − | 0.0852732i | ||||
\(392\) | −4.91547 | −0.248269 | ||||||||
\(393\) | 30.4217 | + | 30.4217i | 1.53457 | + | 1.53457i | ||||
\(394\) | −11.6196 | − | 28.0521i | −0.585385 | − | 1.41324i | ||||
\(395\) | − | 13.7949i | − | 0.694096i | ||||||
\(396\) | −1.50930 | + | 0.625171i | −0.0758449 | + | 0.0314160i | ||||
\(397\) | −1.21286 | + | 2.92811i | −0.0608719 | + | 0.146958i | −0.951389 | − | 0.307992i | \(-0.900343\pi\) |
0.890517 | + | 0.454950i | \(0.150343\pi\) | |||||||
\(398\) | −16.6591 | − | 6.90043i | −0.835046 | − | 0.345887i | ||||
\(399\) | −28.0164 | + | 28.0164i | −1.40258 | + | 1.40258i | ||||
\(400\) | −13.5681 | + | 13.5681i | −0.678405 | + | 0.678405i | ||||
\(401\) | −11.5944 | − | 4.80255i | −0.578995 | − | 0.239828i | 0.0739129 | − | 0.997265i | \(-0.476451\pi\) |
−0.652908 | + | 0.757437i | \(0.726451\pi\) | |||||||
\(402\) | −0.109143 | + | 0.263495i | −0.00544356 | + | 0.0131419i | ||||
\(403\) | 0.0621461 | − | 0.0257418i | 0.00309572 | − | 0.00128229i | ||||
\(404\) | − | 3.56246i | − | 0.177239i | ||||||
\(405\) | 3.16951 | + | 7.65189i | 0.157494 | + | 0.380225i | ||||
\(406\) | 20.4977 | + | 20.4977i | 1.01728 | + | 1.01728i | ||||
\(407\) | 1.48019 | 0.0733705 | ||||||||
\(408\) | −3.43036 | − | 23.9340i | −0.169828 | − | 1.18491i | ||||
\(409\) | 40.3629 | 1.99582 | 0.997909 | − | 0.0646276i | \(-0.0205859\pi\) | ||||
0.997909 | + | 0.0646276i | \(0.0205859\pi\) | |||||||
\(410\) | 7.78182 | + | 7.78182i | 0.384317 | + | 0.384317i | ||||
\(411\) | 10.1414 | + | 24.4835i | 0.500238 | + | 1.20768i | ||||
\(412\) | − | 5.56221i | − | 0.274030i | ||||||
\(413\) | 23.8199 | − | 9.86654i | 1.17210 | − | 0.485501i | ||||
\(414\) | −5.57195 | + | 13.4519i | −0.273846 | + | 0.661124i | ||||
\(415\) | −4.59762 | − | 1.90440i | −0.225688 | − | 0.0934832i | ||||
\(416\) | −0.610755 | + | 0.610755i | −0.0299447 | + | 0.0299447i | ||||
\(417\) | 21.3156 | − | 21.3156i | 1.04383 | − | 1.04383i | ||||
\(418\) | 10.5224 | + | 4.35853i | 0.514669 | + | 0.213183i | ||||
\(419\) | −12.0348 | + | 29.0546i | −0.587940 | + | 1.41941i | 0.297529 | + | 0.954713i | \(0.403838\pi\) |
−0.885469 | + | 0.464699i | \(0.846162\pi\) | |||||||
\(420\) | −2.57358 | + | 1.06601i | −0.125578 | + | 0.0520161i | ||||
\(421\) | 33.3000i | 1.62294i | 0.584394 | + | 0.811470i | \(0.301332\pi\) | ||||
−0.584394 | + | 0.811470i | \(0.698668\pi\) | |||||||
\(422\) | −14.7390 | − | 35.5832i | −0.717485 | − | 1.73216i | ||||
\(423\) | 6.94638 | + | 6.94638i | 0.337744 | + | 0.337744i | ||||
\(424\) | 10.2908 | 0.499763 | ||||||||
\(425\) | −16.0943 | − | 4.11541i | −0.780686 | − | 0.199627i | ||||
\(426\) | −13.6003 | −0.658934 | ||||||||
\(427\) | −10.8230 | − | 10.8230i | −0.523761 | − | 0.523761i | ||||
\(428\) | −2.34285 | − | 5.65614i | −0.113246 | − | 0.273400i | ||||
\(429\) | − | 0.758095i | − | 0.0366012i | ||||||
\(430\) | 9.54757 | − | 3.95473i | 0.460425 | − | 0.190714i | ||||
\(431\) | 5.16813 | − | 12.4770i | 0.248940 | − | 0.600994i | −0.749175 | − | 0.662373i | \(-0.769550\pi\) |
0.998115 | + | 0.0613782i | \(0.0195496\pi\) | |||||||
\(432\) | 2.04269 | + | 0.846110i | 0.0982790 | + | 0.0407085i | ||||
\(433\) | 26.6016 | − | 26.6016i | 1.27839 | − | 1.27839i | 0.336825 | − | 0.941567i | \(-0.390647\pi\) |
0.941567 | − | 0.336825i | \(-0.109353\pi\) | |||||||
\(434\) | −0.548429 | + | 0.548429i | −0.0263254 | + | 0.0263254i | ||||
\(435\) | 18.6782 | + | 7.73675i | 0.895550 | + | 0.370949i | ||||
\(436\) | −1.54933 | + | 3.74040i | −0.0741992 | + | 0.179133i | ||||
\(437\) | 19.1345 | − | 7.92576i | 0.915326 | − | 0.379141i | ||||
\(438\) | 12.9003i | 0.616398i | ||||||||
\(439\) | −0.0710817 | − | 0.171606i | −0.00339254 | − | 0.00819033i | 0.922174 | − | 0.386775i | \(-0.126411\pi\) |
−0.925567 | + | 0.378585i | \(0.876411\pi\) | |||||||
\(440\) | −1.64274 | − | 1.64274i | −0.0783143 | − | 0.0783143i | ||||
\(441\) | 6.64387 | 0.316375 | ||||||||
\(442\) | −1.92989 | − | 0.493487i | −0.0917956 | − | 0.0234728i | ||||
\(443\) | −20.3984 | −0.969159 | −0.484580 | − | 0.874747i | \(-0.661027\pi\) | ||||
−0.484580 | + | 0.874747i | \(0.661027\pi\) | |||||||
\(444\) | 1.33461 | + | 1.33461i | 0.0633380 | + | 0.0633380i | ||||
\(445\) | 4.26655 | + | 10.3004i | 0.202254 | + | 0.488284i | ||||
\(446\) | 22.6518i | 1.07260i | ||||||||
\(447\) | −31.2659 | + | 12.9508i | −1.47883 | + | 0.612550i | ||||
\(448\) | −4.26992 | + | 10.3085i | −0.201735 | + | 0.487031i | ||||
\(449\) | 24.9357 | + | 10.3287i | 1.17679 | + | 0.487441i | 0.883431 | − | 0.468562i | \(-0.155228\pi\) |
0.293356 | + | 0.956003i | \(0.405228\pi\) | |||||||
\(450\) | 14.3908 | − | 14.3908i | 0.678390 | − | 0.678390i | ||||
\(451\) | 4.98208 | − | 4.98208i | 0.234597 | − | 0.234597i | ||||
\(452\) | 7.05861 | + | 2.92377i | 0.332009 | + | 0.137523i | ||||
\(453\) | −5.72624 | + | 13.8244i | −0.269042 | + | 0.649525i | ||||
\(454\) | −3.72046 | + | 1.54107i | −0.174610 | + | 0.0723258i | ||||
\(455\) | − | 0.665834i | − | 0.0312148i | ||||||
\(456\) | −16.1243 | − | 38.9274i | −0.755088 | − | 1.82294i | ||||
\(457\) | 7.23033 | + | 7.23033i | 0.338221 | + | 0.338221i | 0.855697 | − | 0.517477i | \(-0.173129\pi\) |
−0.517477 | + | 0.855697i | \(0.673129\pi\) | |||||||
\(458\) | 8.21713 | 0.383961 | ||||||||
\(459\) | 0.271573 | + | 1.89479i | 0.0126759 | + | 0.0884414i | ||||
\(460\) | 1.45612 | 0.0678918 | ||||||||
\(461\) | −14.1356 | − | 14.1356i | −0.658360 | − | 0.658360i | 0.296632 | − | 0.954992i | \(-0.404137\pi\) |
−0.954992 | + | 0.296632i | \(0.904137\pi\) | |||||||
\(462\) | 3.34503 | + | 8.07561i | 0.155625 | + | 0.375711i | ||||
\(463\) | − | 27.8496i | − | 1.29428i | −0.762371 | − | 0.647140i | \(-0.775965\pi\) | ||
0.762371 | − | 0.647140i | \(-0.224035\pi\) | |||||||
\(464\) | −36.2942 | + | 15.0335i | −1.68491 | + | 0.697914i | ||||
\(465\) | −0.207002 | + | 0.499747i | −0.00959949 | + | 0.0231752i | ||||
\(466\) | 3.15214 | + | 1.30566i | 0.146020 | + | 0.0604835i | ||||
\(467\) | −6.53346 | + | 6.53346i | −0.302333 | + | 0.302333i | −0.841926 | − | 0.539593i | \(-0.818578\pi\) |
0.539593 | + | 0.841926i | \(0.318578\pi\) | |||||||
\(468\) | 0.352079 | − | 0.352079i | 0.0162748 | − | 0.0162748i | ||||
\(469\) | 0.148164 | + | 0.0613717i | 0.00684159 | + | 0.00283388i | ||||
\(470\) | 1.84268 | − | 4.44862i | 0.0849964 | − | 0.205199i | ||||
\(471\) | −52.1346 | + | 21.5948i | −2.40223 | + | 0.995038i | ||||
\(472\) | 27.4181i | 1.26202i | ||||||||
\(473\) | −2.53190 | − | 6.11255i | −0.116417 | − | 0.281055i | ||||
\(474\) | −39.0295 | − | 39.0295i | −1.79268 | − | 1.79268i | ||||
\(475\) | −28.9490 | −1.32827 | ||||||||
\(476\) | 4.63873 | − | 0.664851i | 0.212616 | − | 0.0304734i | ||||
\(477\) | −13.9092 | −0.636860 | ||||||||
\(478\) | 28.1801 | + | 28.1801i | 1.28893 | + | 1.28893i | ||||
\(479\) | 4.94552 | + | 11.9395i | 0.225967 | + | 0.545532i | 0.995679 | − | 0.0928587i | \(-0.0296005\pi\) |
−0.769713 | + | 0.638391i | \(0.779601\pi\) | |||||||
\(480\) | − | 6.94573i | − | 0.317028i | ||||||
\(481\) | −0.416802 | + | 0.172645i | −0.0190045 | + | 0.00787193i | ||||
\(482\) | 6.82736 | − | 16.4827i | 0.310978 | − | 0.750767i | ||||
\(483\) | 14.6851 | + | 6.08275i | 0.668194 | + | 0.276775i | ||||
\(484\) | 0.362501 | − | 0.362501i | 0.0164773 | − | 0.0164773i | ||||
\(485\) | −0.123084 | + | 0.123084i | −0.00558894 | + | 0.00558894i | ||||
\(486\) | 32.6563 | + | 13.5267i | 1.48132 | + | 0.613584i | ||||
\(487\) | −0.795130 | + | 1.91961i | −0.0360308 | + | 0.0869860i | −0.940871 | − | 0.338766i | \(-0.889990\pi\) |
0.904840 | + | 0.425752i | \(0.139990\pi\) | |||||||
\(488\) | 15.0380 | − | 6.22895i | 0.680738 | − | 0.281971i | ||||
\(489\) | 30.0698i | 1.35980i | ||||||||
\(490\) | −1.24623 | − | 3.00866i | −0.0562988 | − | 0.135917i | ||||
\(491\) | −9.21640 | − | 9.21640i | −0.415930 | − | 0.415930i | 0.467868 | − | 0.883798i | \(-0.345022\pi\) |
−0.883798 | + | 0.467868i | \(0.845022\pi\) | |||||||
\(492\) | 8.98417 | 0.405038 | ||||||||
\(493\) | −27.2177 | − | 20.3937i | −1.22582 | − | 0.918487i | ||||
\(494\) | −3.47133 | −0.156183 | ||||||||
\(495\) | 2.22036 | + | 2.22036i | 0.0997978 | + | 0.0997978i | ||||
\(496\) | −0.402232 | − | 0.971075i | −0.0180608 | − | 0.0436026i | ||||
\(497\) | 7.64749i | 0.343037i | ||||||||
\(498\) | −18.3960 | + | 7.61987i | −0.824344 | + | 0.341454i | ||||
\(499\) | 4.94409 | − | 11.9361i | 0.221328 | − | 0.534333i | −0.773743 | − | 0.633500i | \(-0.781618\pi\) |
0.995071 | + | 0.0991670i | \(0.0316178\pi\) | |||||||
\(500\) | −4.21391 | − | 1.74546i | −0.188452 | − | 0.0780593i | ||||
\(501\) | 41.1552 | − | 41.1552i | 1.83868 | − | 1.83868i | ||||
\(502\) | 20.8302 | − | 20.8302i | 0.929699 | − | 0.929699i | ||||
\(503\) | 13.6361 | + | 5.64827i | 0.608006 | + | 0.251844i | 0.665375 | − | 0.746509i | \(-0.268271\pi\) |
−0.0573700 | + | 0.998353i | \(0.518271\pi\) | |||||||
\(504\) | 6.37409 | − | 15.3884i | 0.283924 | − | 0.685454i | ||||
\(505\) | −6.32624 | + | 2.62041i | −0.281514 | + | 0.116607i | ||||
\(506\) | − | 4.56913i | − | 0.203123i | ||||||
\(507\) | −12.2856 | − | 29.6601i | −0.545622 | − | 1.31725i | ||||
\(508\) | 5.92013 | + | 5.92013i | 0.262663 | + | 0.262663i | ||||
\(509\) | 11.9929 | 0.531577 | 0.265789 | − | 0.964031i | \(-0.414368\pi\) | ||||
0.265789 | + | 0.964031i | \(0.414368\pi\) | |||||||
\(510\) | 13.7798 | − | 8.16767i | 0.610179 | − | 0.361671i | ||||
\(511\) | 7.25387 | 0.320892 | ||||||||
\(512\) | −6.33572 | − | 6.33572i | −0.280002 | − | 0.280002i | ||||
\(513\) | 1.27652 | + | 3.08178i | 0.0563596 | + | 0.136064i | ||||
\(514\) | − | 11.1583i | − | 0.492170i | ||||||
\(515\) | −9.87739 | + | 4.09135i | −0.435250 | + | 0.180286i | ||||
\(516\) | 3.22849 | − | 7.79426i | 0.142126 | − | 0.343123i | ||||
\(517\) | −2.84810 | − | 1.17972i | −0.125259 | − | 0.0518840i | ||||
\(518\) | 3.67820 | − | 3.67820i | 0.161611 | − | 0.161611i | ||||
\(519\) | 2.14792 | − | 2.14792i | 0.0942831 | − | 0.0942831i | ||||
\(520\) | 0.654174 | + | 0.270968i | 0.0286874 | + | 0.0118827i | ||||
\(521\) | 5.57772 | − | 13.4658i | 0.244364 | − | 0.589948i | −0.753343 | − | 0.657628i | \(-0.771560\pi\) |
0.997707 | + | 0.0676804i | \(0.0215598\pi\) | |||||||
\(522\) | 38.4949 | − | 15.9451i | 1.68487 | − | 0.697898i | ||||
\(523\) | 15.2307i | 0.665993i | 0.942928 | + | 0.332997i | \(0.108060\pi\) | ||||
−0.942928 | + | 0.332997i | \(0.891940\pi\) | |||||||
\(524\) | −3.39340 | − | 8.19240i | −0.148241 | − | 0.357886i | ||||
\(525\) | −15.7101 | − | 15.7101i | −0.685644 | − | 0.685644i | ||||
\(526\) | −20.3442 | −0.887049 | ||||||||
\(527\) | 0.545648 | − | 0.728227i | 0.0237688 | − | 0.0317221i | ||||
\(528\) | −11.8457 | −0.515520 | ||||||||
\(529\) | 10.3883 | + | 10.3883i | 0.451665 | + | 0.451665i | ||||
\(530\) | 2.60903 | + | 6.29876i | 0.113329 | + | 0.273601i | ||||
\(531\) | − | 37.0590i | − | 1.60822i | ||||||
\(532\) | 7.54466 | − | 3.12510i | 0.327103 | − | 0.135490i | ||||
\(533\) | −0.821790 | + | 1.98398i | −0.0355957 | + | 0.0859356i | ||||
\(534\) | 41.2138 | + | 17.0713i | 1.78350 | + | 0.738748i | ||||
\(535\) | −8.32089 | + | 8.32089i | −0.359743 | + | 0.359743i | ||||
\(536\) | −0.120594 | + | 0.120594i | −0.00520887 | + | 0.00520887i | ||||
\(537\) | 50.0919 | + | 20.7488i | 2.16163 | + | 0.895375i | ||||
\(538\) | 4.63912 | − | 11.1998i | 0.200007 | − | 0.482859i | ||||
\(539\) | −1.92620 | + | 0.797860i | −0.0829675 | + | 0.0343663i | ||||
\(540\) | 0.234521i | 0.0100922i | ||||||||
\(541\) | 7.71994 | + | 18.6376i | 0.331906 | + | 0.801293i | 0.998441 | + | 0.0558186i | \(0.0177768\pi\) |
−0.666535 | + | 0.745474i | \(0.732223\pi\) | |||||||
\(542\) | 15.9610 | + | 15.9610i | 0.685584 | + | 0.685584i | ||||
\(543\) | 39.2315 | 1.68358 | ||||||||
\(544\) | −2.89467 | + | 11.3203i | −0.124108 | + | 0.485353i | ||||
\(545\) | 7.78184 | 0.333338 | ||||||||
\(546\) | −1.88382 | − | 1.88382i | −0.0806203 | − | 0.0806203i | ||||
\(547\) | −3.95124 | − | 9.53913i | −0.168943 | − | 0.407864i | 0.816620 | − | 0.577176i | \(-0.195845\pi\) |
−0.985562 | + | 0.169312i | \(0.945845\pi\) | |||||||
\(548\) | − | 5.46204i | − | 0.233327i | ||||||
\(549\) | −20.3257 | + | 8.41919i | −0.867481 | + | 0.359322i | ||||
\(550\) | −2.44403 | + | 5.90040i | −0.104214 | + | 0.251594i | ||||
\(551\) | −54.7566 | − | 22.6809i | −2.33271 | − | 0.966240i | ||||
\(552\) | −11.9525 | + | 11.9525i | −0.508731 | + | 0.508731i | ||||
\(553\) | −21.9465 | + | 21.9465i | −0.933258 | + | 0.933258i | ||||
\(554\) | 46.5872 | + | 19.2971i | 1.97930 | + | 0.819853i | ||||
\(555\) | 1.38832 | − | 3.35170i | 0.0589310 | − | 0.142272i | ||||
\(556\) | −5.74016 | + | 2.37765i | −0.243437 | + | 0.100835i | ||||
\(557\) | − | 4.27787i | − | 0.181259i | −0.995885 | − | 0.0906297i | \(-0.971112\pi\) | ||
0.995885 | − | 0.0906297i | \(-0.0288880\pi\) | |||||||
\(558\) | 0.426622 | + | 1.02996i | 0.0180603 | + | 0.0436015i | ||||
\(559\) | 1.42590 | + | 1.42590i | 0.0603090 | + | 0.0603090i | ||||
\(560\) | −10.4041 | −0.439653 | ||||||||
\(561\) | −5.22911 | − | 8.82210i | −0.220773 | − | 0.372469i | ||||
\(562\) | −50.4846 | −2.12956 | ||||||||
\(563\) | −3.93666 | − | 3.93666i | −0.165910 | − | 0.165910i | 0.619269 | − | 0.785179i | \(-0.287429\pi\) |
−0.785179 | + | 0.619269i | \(0.787429\pi\) | |||||||
\(564\) | −1.50429 | − | 3.63167i | −0.0633420 | − | 0.152921i | ||||
\(565\) | − | 14.6853i | − | 0.617816i | ||||||
\(566\) | −14.6184 | + | 6.05513i | −0.614456 | + | 0.254516i | ||||
\(567\) | 7.13106 | − | 17.2159i | 0.299477 | − | 0.723000i | ||||
\(568\) | −7.51357 | − | 3.11222i | −0.315262 | − | 0.130586i | ||||
\(569\) | 7.02098 | − | 7.02098i | 0.294335 | − | 0.294335i | −0.544455 | − | 0.838790i | \(-0.683264\pi\) |
0.838790 | + | 0.544455i | \(0.183264\pi\) | |||||||
\(570\) | 19.7387 | − | 19.7387i | 0.826761 | − | 0.826761i | ||||
\(571\) | 10.6172 | + | 4.39779i | 0.444317 | + | 0.184042i | 0.593613 | − | 0.804750i | \(-0.297701\pi\) |
−0.149297 | + | 0.988792i | \(0.547701\pi\) | |||||||
\(572\) | −0.0597943 | + | 0.144356i | −0.00250013 | + | 0.00603584i | ||||
\(573\) | 19.6859 | − | 8.15415i | 0.822389 | − | 0.340644i | ||||
\(574\) | − | 24.7604i | − | 1.03348i | ||||||
\(575\) | 4.44433 | + | 10.7296i | 0.185342 | + | 0.447454i | ||||
\(576\) | 11.3405 | + | 11.3405i | 0.472523 | + | 0.472523i | ||||
\(577\) | −3.16478 | −0.131751 | −0.0658757 | − | 0.997828i | \(-0.520984\pi\) | ||||
−0.0658757 | + | 0.997828i | \(0.520984\pi\) | |||||||
\(578\) | −25.8625 | + | 7.56901i | −1.07574 | + | 0.314829i | ||||
\(579\) | 29.8205 | 1.23930 | ||||||||
\(580\) | −2.94646 | − | 2.94646i | −0.122345 | − | 0.122345i | ||||
\(581\) | 4.28469 | + | 10.3441i | 0.177759 | + | 0.429148i | ||||
\(582\) | 0.696475i | 0.0288698i | ||||||||
\(583\) | 4.03259 | − | 1.67036i | 0.167013 | − | 0.0691790i | ||||
\(584\) | −2.95204 | + | 7.12685i | −0.122156 | + | 0.294911i | ||||
\(585\) | −0.884198 | − | 0.366247i | −0.0365571 | − | 0.0151424i | ||||
\(586\) | 4.51563 | − | 4.51563i | 0.186539 | − | 0.186539i | ||||
\(587\) | −16.5085 | + | 16.5085i | −0.681378 | + | 0.681378i | −0.960311 | − | 0.278933i | \(-0.910019\pi\) |
0.278933 | + | 0.960311i | \(0.410019\pi\) | |||||||
\(588\) | −2.45615 | − | 1.01737i | −0.101290 | − | 0.0419557i | ||||
\(589\) | 0.606844 | − | 1.46505i | 0.0250046 | − | 0.0603663i | ||||
\(590\) | −16.7821 | + | 6.95136i | −0.690907 | + | 0.286183i | ||||
\(591\) | 47.6443i | 1.95983i | ||||||||
\(592\) | 2.69769 | + | 6.51281i | 0.110875 | + | 0.267675i | ||||
\(593\) | −4.00981 | − | 4.00981i | −0.164663 | − | 0.164663i | 0.619966 | − | 0.784629i | \(-0.287146\pi\) |
−0.784629 | + | 0.619966i | \(0.787146\pi\) | |||||||
\(594\) | 0.735901 | 0.0301944 | ||||||||
\(595\) | −4.59272 | − | 7.74844i | −0.188283 | − | 0.317655i | ||||
\(596\) | 6.97514 | 0.285713 | ||||||||
\(597\) | 20.0070 | + | 20.0070i | 0.818834 | + | 0.818834i | ||||
\(598\) | 0.532928 | + | 1.28660i | 0.0217931 | + | 0.0526131i | ||||
\(599\) | − | 34.0787i | − | 1.39242i | −0.717839 | − | 0.696209i | \(-0.754869\pi\) | ||
0.717839 | − | 0.696209i | \(-0.245131\pi\) | |||||||
\(600\) | 21.8284 | − | 9.04160i | 0.891139 | − | 0.369122i | ||||
\(601\) | 4.41452 | − | 10.6576i | 0.180072 | − | 0.434732i | −0.807909 | − | 0.589307i | \(-0.799401\pi\) |
0.987981 | + | 0.154575i | \(0.0494008\pi\) | |||||||
\(602\) | −21.4810 | − | 8.89772i | −0.875500 | − | 0.362644i | ||||
\(603\) | 0.162998 | − | 0.162998i | 0.00663778 | − | 0.00663778i | ||||
\(604\) | 2.18078 | − | 2.18078i | 0.0887347 | − | 0.0887347i | ||||
\(605\) | −0.910373 | − | 0.377089i | −0.0370119 | − | 0.0153308i | ||||
\(606\) | −10.4848 | + | 25.3125i | −0.425915 | + | 1.02825i | ||||
\(607\) | −12.8938 | + | 5.34079i | −0.523343 | + | 0.216776i | −0.628685 | − | 0.777660i | \(-0.716406\pi\) |
0.105341 | + | 0.994436i | \(0.466406\pi\) | |||||||
\(608\) | 20.3620i | 0.825788i | ||||||||
\(609\) | −17.4068 | − | 42.0238i | −0.705361 | − | 1.70289i | ||||
\(610\) | 7.62522 | + | 7.62522i | 0.308736 | + | 0.308736i | ||||
\(611\) | 0.939582 | 0.0380114 | ||||||||
\(612\) | 1.66868 | − | 6.52574i | 0.0674523 | − | 0.263787i | ||||
\(613\) | −7.57108 | −0.305793 | −0.152896 | − | 0.988242i | \(-0.548860\pi\) | ||||
−0.152896 | + | 0.988242i | \(0.548860\pi\) | |||||||
\(614\) | 32.0309 | + | 32.0309i | 1.29266 | + | 1.29266i | ||||
\(615\) | −6.60842 | − | 15.9541i | −0.266477 | − | 0.643332i | ||||
\(616\) | 5.22690i | 0.210598i | ||||||||
\(617\) | −13.1801 | + | 5.45939i | −0.530612 | + | 0.219787i | −0.631871 | − | 0.775073i | \(-0.717713\pi\) |
0.101259 | + | 0.994860i | \(0.467713\pi\) | |||||||
\(618\) | −16.3703 | + | 39.5214i | −0.658510 | + | 1.58978i | ||||
\(619\) | −11.2081 | − | 4.64255i | −0.450492 | − | 0.186600i | 0.145890 | − | 0.989301i | \(-0.453396\pi\) |
−0.596382 | + | 0.802701i | \(0.703396\pi\) | |||||||
\(620\) | 0.0788346 | − | 0.0788346i | 0.00316607 | − | 0.00316607i | ||||
\(621\) | 0.946248 | − | 0.946248i | 0.0379716 | − | 0.0379716i | ||||
\(622\) | −3.32277 | − | 1.37634i | −0.133231 | − | 0.0551861i | ||||
\(623\) | 9.59928 | − | 23.1747i | 0.384587 | − | 0.928475i | ||||
\(624\) | 3.33559 | − | 1.38165i | 0.133531 | − | 0.0553102i | ||||
\(625\) | − | 11.3782i | − | 0.455126i | ||||||
\(626\) | 16.4059 | + | 39.6074i | 0.655712 | + | 1.58303i | ||||
\(627\) | −12.6371 | − | 12.6371i | −0.504677 | − | 0.504677i | ||||
\(628\) | 11.6307 | 0.464117 | ||||||||
\(629\) | −3.65955 | + | 4.88408i | −0.145916 | + | 0.194741i | ||||
\(630\) | 11.0350 | 0.439643 | ||||||||
\(631\) | −23.8985 | − | 23.8985i | −0.951386 | − | 0.951386i | 0.0474859 | − | 0.998872i | \(-0.484879\pi\) |
−0.998872 | + | 0.0474859i | \(0.984879\pi\) | |||||||
\(632\) | −12.6308 | − | 30.4935i | −0.502427 | − | 1.21297i | ||||
\(633\) | 60.4353i | 2.40209i | ||||||||
\(634\) | 48.4318 | − | 20.0611i | 1.92347 | − | 0.796728i | ||||
\(635\) | 6.15836 | − | 14.8676i | 0.244387 | − | 0.590003i | ||||
\(636\) | 5.14206 | + | 2.12991i | 0.203896 | + | 0.0844564i | ||||
\(637\) | 0.449332 | − | 0.449332i | 0.0178032 | − | 0.0178032i | ||||
\(638\) | −9.24567 | + | 9.24567i | −0.366039 | + | 0.366039i | ||||
\(639\) | 10.1555 | + | 4.20656i | 0.401746 | + | 0.166409i | ||||
\(640\) | 5.14560 | − | 12.4226i | 0.203398 | − | 0.491045i | ||||
\(641\) | 33.8610 | − | 14.0257i | 1.33743 | − | 0.553982i | 0.404665 | − | 0.914465i | \(-0.367388\pi\) |
0.932766 | + | 0.360483i | \(0.117388\pi\) | |||||||
\(642\) | 47.0841i | 1.85826i | ||||||||
\(643\) | −12.4766 | − | 30.1211i | −0.492029 | − | 1.18786i | −0.953686 | − | 0.300804i | \(-0.902745\pi\) |
0.461657 | − | 0.887058i | \(-0.347255\pi\) | |||||||
\(644\) | −2.31655 | − | 2.31655i | −0.0912850 | − | 0.0912850i | ||||
\(645\) | −16.2158 | −0.638498 | ||||||||
\(646\) | −40.3966 | + | 23.9442i | −1.58938 | + | 0.942072i | ||||
\(647\) | −14.3019 | −0.562267 | −0.281133 | − | 0.959669i | \(-0.590710\pi\) | ||||
−0.281133 | + | 0.959669i | \(0.590710\pi\) | |||||||
\(648\) | 14.0124 | + | 14.0124i | 0.550459 | + | 0.550459i | ||||
\(649\) | 4.45040 | + | 10.7442i | 0.174694 | + | 0.421747i | ||||
\(650\) | − | 1.94653i | − | 0.0763493i | ||||||
\(651\) | 1.12438 | − | 0.465732i | 0.0440678 | − | 0.0182535i | ||||
\(652\) | 2.37174 | − | 5.72588i | 0.0928844 | − | 0.224243i | ||||
\(653\) | 18.7089 | + | 7.74946i | 0.732134 | + | 0.303260i | 0.717429 | − | 0.696632i | \(-0.245319\pi\) |
0.0147056 | + | 0.999892i | \(0.495319\pi\) | |||||||
\(654\) | 22.0170 | − | 22.0170i | 0.860931 | − | 0.860931i | ||||
\(655\) | −12.0520 | + | 12.0520i | −0.470912 | + | 0.470912i | ||||
\(656\) | 31.0010 | + | 12.8410i | 1.21039 | + | 0.501358i | ||||
\(657\) | 3.99005 | − | 9.63283i | 0.155667 | − | 0.375812i | ||||
\(658\) | −10.0089 | + | 4.14583i | −0.390188 | + | 0.161621i | ||||
\(659\) | − | 9.12180i | − | 0.355335i | −0.984091 | − | 0.177667i | \(-0.943145\pi\) | ||
0.984091 | − | 0.177667i | \(-0.0568551\pi\) | |||||||
\(660\) | −0.480835 | − | 1.16084i | −0.0187165 | − | 0.0451856i | ||||
\(661\) | −9.08758 | − | 9.08758i | −0.353466 | − | 0.353466i | 0.507932 | − | 0.861397i | \(-0.330410\pi\) |
−0.861397 | + | 0.507932i | \(0.830410\pi\) | |||||||
\(662\) | 1.48796 | 0.0578312 | ||||||||
\(663\) | 2.50142 | + | 1.87427i | 0.0971473 | + | 0.0727907i | ||||
\(664\) | −11.9067 | −0.462070 | ||||||||
\(665\) | −11.0991 | − | 11.0991i | −0.430406 | − | 0.430406i | ||||
\(666\) | −2.86127 | − | 6.90771i | −0.110872 | − | 0.267669i | ||||
\(667\) | 23.7768i | 0.920643i | ||||||||
\(668\) | −11.0829 | + | 4.59067i | −0.428809 | + | 0.177618i | ||||
\(669\) | 13.6021 | − | 32.8383i | 0.525886 | − | 1.26960i | ||||
\(670\) | −0.104387 | − | 0.0432387i | −0.00403284 | − | 0.00167046i | ||||
\(671\) | 4.88182 | − | 4.88182i | 0.188460 | − | 0.188460i | ||||
\(672\) | −11.0501 | + | 11.0501i | −0.426265 | + | 0.426265i | ||||
\(673\) | −23.2066 | − | 9.61249i | −0.894549 | − | 0.370534i | −0.112427 | − | 0.993660i | \(-0.535863\pi\) |
−0.782122 | + | 0.623125i | \(0.785863\pi\) | |||||||
\(674\) | −0.394537 | + | 0.952496i | −0.0151970 | + | 0.0366888i | ||||
\(675\) | −1.72810 | + | 0.715801i | −0.0665145 | + | 0.0275512i | ||||
\(676\) | 6.61688i | 0.254496i | ||||||||
\(677\) | 0.102880 | + | 0.248374i | 0.00395400 | + | 0.00954579i | 0.925844 | − | 0.377905i | \(-0.123356\pi\) |
−0.921890 | + | 0.387451i | \(0.873356\pi\) | |||||||
\(678\) | −41.5488 | − | 41.5488i | −1.59567 | − | 1.59567i | ||||
\(679\) | 0.391631 | 0.0150294 | ||||||||
\(680\) | 9.48181 | − | 1.35899i | 0.363611 | − | 0.0521149i | ||||
\(681\) | 6.31892 | 0.242142 | ||||||||
\(682\) | −0.247374 | − | 0.247374i | −0.00947245 | − | 0.00947245i | ||||
\(683\) | 0.549145 | + | 1.32575i | 0.0210125 | + | 0.0507286i | 0.934038 | − | 0.357175i | \(-0.116260\pi\) |
−0.913025 | + | 0.407903i | \(0.866260\pi\) | |||||||
\(684\) | − | 11.7380i | − | 0.448813i | ||||||
\(685\) | −9.69952 | + | 4.01767i | −0.370600 | + | 0.153507i | ||||
\(686\) | −12.2178 | + | 29.4963i | −0.466477 | + | 1.12618i | ||||
\(687\) | −11.9123 | − | 4.93425i | −0.454484 | − | 0.188253i | ||||
\(688\) | 22.2806 | − | 22.2806i | 0.849439 | − | 0.849439i | ||||
\(689\) | −0.940697 | + | 0.940697i | −0.0358377 | + | 0.0358377i | ||||
\(690\) | −10.3462 | − | 4.28554i | −0.393873 | − | 0.163148i | ||||
\(691\) | −5.55056 | + | 13.4002i | −0.211153 | + | 0.509769i | −0.993601 | − | 0.112947i | \(-0.963971\pi\) |
0.782448 | + | 0.622716i | \(0.213971\pi\) | |||||||
\(692\) | −0.578422 | + | 0.239590i | −0.0219883 | + | 0.00910786i | ||||
\(693\) | − | 7.06480i | − | 0.268370i | ||||||
\(694\) | −0.834789 | − | 2.01536i | −0.0316881 | − | 0.0765020i | ||||
\(695\) | 8.44449 | + | 8.44449i | 0.320318 | + | 0.320318i | ||||
\(696\) | 48.3719 | 1.83353 | ||||||||
\(697\) | 4.12154 | + | 28.7564i | 0.156114 | + | 1.08923i | ||||
\(698\) | 15.9852 | 0.605048 | ||||||||
\(699\) | −3.78562 | − | 3.78562i | −0.143185 | − | 0.143185i | ||||
\(700\) | 1.75239 | + | 4.23064i | 0.0662340 | + | 0.159903i | ||||
\(701\) | 35.8282i | 1.35321i | 0.736346 | + | 0.676606i | \(0.236550\pi\) | ||||
−0.736346 | + | 0.676606i | \(0.763450\pi\) | |||||||
\(702\) | −0.207219 | + | 0.0858330i | −0.00782099 | + | 0.00323956i | ||||
\(703\) | −4.06998 | + | 9.82580i | −0.153502 | + | 0.370587i | ||||
\(704\) | −4.64975 | − | 1.92599i | −0.175244 | − | 0.0725885i | ||||
\(705\) | −5.34264 | + | 5.34264i | −0.201216 | + | 0.201216i | ||||
\(706\) | 33.3776 | − | 33.3776i | 1.25618 | − | 1.25618i | ||||
\(707\) | 14.2333 | + | 5.89565i | 0.535300 | + | 0.221729i | ||||
\(708\) | −5.67481 | + | 13.7002i | −0.213273 | + | 0.514885i | ||||
\(709\) | −22.4913 | + | 9.31622i | −0.844680 | + | 0.349878i | −0.762697 | − | 0.646756i | \(-0.776125\pi\) |
−0.0819829 | + | 0.996634i | \(0.526125\pi\) | |||||||
\(710\) | − | 5.38795i | − | 0.202206i | ||||||
\(711\) | 17.0721 | + | 41.2157i | 0.640255 | + | 1.54571i | ||||
\(712\) | 18.8624 | + | 18.8624i | 0.706897 | + | 0.706897i | ||||
\(713\) | −0.636165 | −0.0238246 | ||||||||
\(714\) | −34.9165 | − | 8.92839i | −1.30672 | − | 0.334137i | ||||
\(715\) | 0.300331 | 0.0112317 | ||||||||
\(716\) | −7.90195 | − | 7.90195i | −0.295310 | − | 0.295310i | ||||
\(717\) | −23.9309 | − | 57.7743i | −0.893716 | − | 2.15762i | ||||
\(718\) | − | 8.96397i | − | 0.334533i | ||||||
\(719\) | 5.13640 | − | 2.12757i | 0.191555 | − | 0.0793449i | −0.284844 | − | 0.958574i | \(-0.591942\pi\) |
0.476399 | + | 0.879229i | \(0.341942\pi\) | |||||||
\(720\) | −5.72285 | + | 13.8162i | −0.213278 | + | 0.514899i | ||||
\(721\) | 22.2231 | + | 9.20509i | 0.827630 | + | 0.342816i | ||||
\(722\) | −36.5691 | + | 36.5691i | −1.36096 | + | 1.36096i | ||||
\(723\) | −19.7952 | + | 19.7952i | −0.736191 | + | 0.736191i | ||||
\(724\) | −7.47046 | − | 3.09436i | −0.277637 | − | 0.115001i | ||||
\(725\) | 12.7182 | − | 30.7045i | 0.472343 | − | 1.14034i | ||||
\(726\) | −3.64258 | + | 1.50881i | −0.135189 | + | 0.0559971i | ||||
\(727\) | 2.96865i | 0.110101i | 0.998484 | + | 0.0550506i | \(0.0175320\pi\) | ||||
−0.998484 | + | 0.0550506i | \(0.982468\pi\) | |||||||
\(728\) | −0.609648 | − | 1.47182i | −0.0225951 | − | 0.0545493i | ||||
\(729\) | −21.3890 | − | 21.3890i | −0.792186 | − | 0.792186i | ||||
\(730\) | −5.11063 | −0.189153 | ||||||||
\(731\) | 26.4288 | + | 6.75804i | 0.977506 | + | 0.249955i | ||||
\(732\) | 8.80337 | 0.325382 | ||||||||
\(733\) | −19.7202 | − | 19.7202i | −0.728384 | − | 0.728384i | 0.241914 | − | 0.970298i | \(-0.422225\pi\) |
−0.970298 | + | 0.241914i | \(0.922225\pi\) | |||||||
\(734\) | −18.5307 | − | 44.7370i | −0.683980 | − | 1.65127i | ||||
\(735\) | 5.10998i | 0.188484i | ||||||||
\(736\) | 7.54690 | − | 3.12603i | 0.278182 | − | 0.115227i | ||||
\(737\) | −0.0276823 | + | 0.0668310i | −0.00101969 | + | 0.00246175i | ||||
\(738\) | −32.8807 | − | 13.6196i | −1.21036 | − | 0.501346i | ||||
\(739\) | −10.2158 | + | 10.2158i | −0.375795 | + | 0.375795i | −0.869582 | − | 0.493788i | \(-0.835612\pi\) |
0.493788 | + | 0.869582i | \(0.335612\pi\) | |||||||
\(740\) | −0.528728 | + | 0.528728i | −0.0194364 | + | 0.0194364i | ||||
\(741\) | 5.03237 | + | 2.08448i | 0.184869 | + | 0.0765752i | ||||
\(742\) | 5.87004 | − | 14.1715i | 0.215496 | − | 0.520253i | ||||
\(743\) | −49.9110 | + | 20.6738i | −1.83106 | + | 0.758449i | −0.864193 | + | 0.503161i | \(0.832170\pi\) |
−0.966865 | + | 0.255288i | \(0.917830\pi\) | |||||||
\(744\) | 1.29422i | 0.0474485i | ||||||||
\(745\) | −5.13064 | − | 12.3865i | −0.187972 | − | 0.453805i | ||||
\(746\) | 0.847340 | + | 0.847340i | 0.0310233 | + | 0.0310233i | ||||
\(747\) | 16.0934 | 0.588827 | ||||||||
\(748\) | 0.299888 | + | 2.09235i | 0.0109650 | + | 0.0765038i | ||||
\(749\) | 26.4756 | 0.967398 | ||||||||
\(750\) | 24.8041 | + | 24.8041i | 0.905719 | + | 0.905719i | ||||
\(751\) | −2.87153 | − | 6.93249i | −0.104784 | − | 0.252970i | 0.862788 | − | 0.505565i | \(-0.168716\pi\) |
−0.967572 | + | 0.252595i | \(0.918716\pi\) | |||||||
\(752\) | − | 14.6816i | − | 0.535383i | ||||||
\(753\) | −42.7057 | + | 17.6893i | −1.55628 | + | 0.644633i | ||||
\(754\) | 1.52507 | − | 3.68183i | 0.0555396 | − | 0.134085i | ||||
\(755\) | −5.47673 | − | 2.26854i | −0.199319 | − | 0.0825605i | ||||
\(756\) | 0.373103 | − | 0.373103i | 0.0135696 | − | 0.0135696i | ||||
\(757\) | −1.93330 | + | 1.93330i | −0.0702670 | + | 0.0702670i | −0.741367 | − | 0.671100i | \(-0.765822\pi\) |
0.671100 | + | 0.741367i | \(0.265822\pi\) | |||||||
\(758\) | 15.9751 | + | 6.61710i | 0.580241 | + | 0.240344i | ||||
\(759\) | −2.74369 | + | 6.62385i | −0.0995895 | + | 0.240430i | ||||
\(760\) | 15.4217 | − | 6.38787i | 0.559404 | − | 0.231713i | ||||
\(761\) | − | 19.9761i | − | 0.724132i | −0.932152 | − | 0.362066i | \(-0.882071\pi\) | ||
0.932152 | − | 0.362066i | \(-0.117929\pi\) | |||||||
\(762\) | −24.6408 | − | 59.4882i | −0.892643 | − | 2.15503i | ||||
\(763\) | −12.3802 | − | 12.3802i | −0.448195 | − | 0.448195i | ||||
\(764\) | −4.39173 | −0.158887 | ||||||||
\(765\) | −12.8158 | + | 1.83684i | −0.463358 | + | 0.0664112i | ||||
\(766\) | 53.9790 | 1.95034 | ||||||||
\(767\) | −2.50634 | − | 2.50634i | −0.0904987 | − | 0.0904987i | ||||
\(768\) | −11.0075 | − | 26.5745i | −0.397200 | − | 0.958925i | ||||
\(769\) | − | 14.6466i | − | 0.528171i | −0.964499 | − | 0.264085i | \(-0.914930\pi\) | ||
0.964499 | − | 0.264085i | \(-0.0850701\pi\) | |||||||
\(770\) | −3.19928 | + | 1.32518i | −0.115294 | + | 0.0477563i | ||||
\(771\) | −6.70035 | + | 16.1761i | −0.241307 | + | 0.582567i | ||||
\(772\) | −5.67842 | − | 2.35208i | −0.204371 | − | 0.0846531i | ||||
\(773\) | −32.3353 | + | 32.3353i | −1.16302 | + | 1.16302i | −0.179210 | + | 0.983811i | \(0.557354\pi\) |
−0.983811 | + | 0.179210i | \(0.942646\pi\) | |||||||
\(774\) | −23.6316 | + | 23.6316i | −0.849419 | + | 0.849419i | ||||
\(775\) | 0.821520 | + | 0.340285i | 0.0295099 | + | 0.0122234i | ||||
\(776\) | −0.159378 | + | 0.384773i | −0.00572135 | + | 0.0138126i | ||||
\(777\) | −7.54097 | + | 3.12357i | −0.270531 | + | 0.112058i | ||||
\(778\) | − | 16.4346i | − | 0.589208i | ||||||
\(779\) | 19.3731 | + | 46.7708i | 0.694114 | + | 1.67574i | ||||
\(780\) | 0.270793 | + | 0.270793i | 0.00969594 | + | 0.00969594i | ||||
\(781\) | −3.44947 | −0.123432 | ||||||||
\(782\) | 15.0764 | + | 11.2965i | 0.539131 | + | 0.403961i | ||||
\(783\) | −3.82948 | −0.136854 | ||||||||
\(784\) | −7.02112 | − | 7.02112i | −0.250754 | − | 0.250754i | ||||
\(785\) | −8.55513 | − | 20.6539i | −0.305346 | − | 0.737170i | ||||
\(786\) | 68.1970i | 2.43250i | ||||||||
\(787\) | 7.09216 | − | 2.93767i | 0.252808 | − | 0.104717i | −0.252681 | − | 0.967550i | \(-0.581312\pi\) |
0.505489 | + | 0.862833i | \(0.331312\pi\) | |||||||
\(788\) | 3.75792 | − | 9.07243i | 0.133870 | − | 0.323192i | ||||
\(789\) | 29.4929 | + | 12.2164i | 1.04997 | + | 0.434914i | ||||
\(790\) | 15.4621 | − | 15.4621i | 0.550118 | − | 0.550118i | ||||
\(791\) | −23.3631 | + | 23.3631i | −0.830696 | + | 0.830696i | ||||
\(792\) | 6.94109 | + | 2.87509i | 0.246641 | + | 0.102162i | ||||
\(793\) | −0.805252 | + | 1.94405i | −0.0285953 | + | 0.0690353i | ||||
\(794\) | −4.64146 | + | 1.92256i | −0.164719 | + | 0.0682289i | ||||
\(795\) | − | 10.6980i | − | 0.379418i | ||||||
\(796\) | −2.23169 | − | 5.38779i | −0.0791003 | − | 0.190965i | ||||
\(797\) | 35.3095 | + | 35.3095i | 1.25073 | + | 1.25073i | 0.955395 | + | 0.295330i | \(0.0954295\pi\) |
0.295330 | + | 0.955395i | \(0.404570\pi\) | |||||||
\(798\) | −62.8050 | −2.22327 | ||||||||
\(799\) | 10.9341 | − | 6.48096i | 0.386821 | − | 0.229280i | ||||
\(800\) | −11.4179 | −0.403683 | ||||||||
\(801\) | −25.4948 | − | 25.4948i | −0.900816 | − | 0.900816i | ||||
\(802\) | −7.61269 | − | 18.3787i | −0.268813 | − | 0.648973i | ||||
\(803\) | 3.27193i | 0.115464i | ||||||||
\(804\) | −0.0852178 | + | 0.0352984i | −0.00300540 | + | 0.00124488i | ||||
\(805\) | −2.40978 | + | 5.81772i | −0.0849335 | + | 0.205048i | ||||
\(806\) | 0.0985100 | + | 0.0408042i | 0.00346987 | + | 0.00143727i | ||||
\(807\) | −13.4506 | + | 13.4506i | −0.473484 | + | 0.473484i | ||||
\(808\) | −11.5848 | + | 11.5848i | −0.407552 | + | 0.407552i | ||||
\(809\) | 33.8746 | + | 14.0313i | 1.19097 | + | 0.493314i | 0.888070 | − | 0.459709i | \(-0.152046\pi\) |
0.302897 | + | 0.953023i | \(0.402046\pi\) | |||||||
\(810\) | −5.02411 | + | 12.1293i | −0.176529 | + | 0.426179i | ||||
\(811\) | 32.7313 | − | 13.5577i | 1.14935 | − | 0.476076i | 0.275035 | − | 0.961434i | \(-0.411311\pi\) |
0.874316 | + | 0.485358i | \(0.161311\pi\) | |||||||
\(812\) | 9.37513i | 0.329003i | ||||||||
\(813\) | −13.5543 | − | 32.7229i | −0.475369 | − | 1.14764i | ||||
\(814\) | 1.65909 | + | 1.65909i | 0.0581511 | + | 0.0581511i | ||||
\(815\) | −11.9126 | −0.417280 | ||||||||
\(816\) | 29.2868 | − | 39.0864i | 1.02524 | − | 1.36830i | ||||
\(817\) | 47.5380 | 1.66315 | ||||||||
\(818\) | 45.2412 | + | 45.2412i | 1.58182 | + | 1.58182i | ||||
\(819\) | 0.824015 | + | 1.98935i | 0.0287934 | + | 0.0695135i | ||||
\(820\) | 3.55922i | 0.124293i | ||||||||
\(821\) | −24.2758 | + | 10.0554i | −0.847231 | + | 0.350935i | −0.763701 | − | 0.645570i | \(-0.776620\pi\) |
−0.0835307 | + | 0.996505i | \(0.526620\pi\) | |||||||
\(822\) | −16.0755 | + | 38.8097i | −0.560697 | + | 1.35364i | ||||
\(823\) | −44.8293 | − | 18.5689i | −1.56265 | − | 0.647272i | −0.577104 | − | 0.816671i | \(-0.695817\pi\) |
−0.985548 | + | 0.169399i | \(0.945817\pi\) | |||||||
\(824\) | −18.0878 | + | 18.0878i | −0.630119 | + | 0.630119i | ||||
\(825\) | 7.08619 | − | 7.08619i | 0.246709 | − | 0.246709i | ||||
\(826\) | 37.7578 | + | 15.6398i | 1.31376 | + | 0.544178i | ||||
\(827\) | −11.2669 | + | 27.2007i | −0.391788 | + | 0.945861i | 0.597762 | + | 0.801674i | \(0.296057\pi\) |
−0.989550 | + | 0.144187i | \(0.953943\pi\) | |||||||
\(828\) | −4.35052 | + | 1.80205i | −0.151191 | + | 0.0626254i | ||||
\(829\) | − | 40.5713i | − | 1.40910i | −0.709654 | − | 0.704550i | \(-0.751149\pi\) | ||
0.709654 | − | 0.704550i | \(-0.248851\pi\) | |||||||
\(830\) | −3.01873 | − | 7.28785i | −0.104782 | − | 0.252965i | ||||
\(831\) | −55.9497 | − | 55.9497i | −1.94087 | − | 1.94087i | ||||
\(832\) | 1.53395 | 0.0531800 | ||||||||
\(833\) | 2.12961 | − | 8.32833i | 0.0737867 | − | 0.288560i | ||||
\(834\) | 47.7835 | 1.65461 | ||||||||
\(835\) | 16.3043 | + | 16.3043i | 0.564232 | + | 0.564232i | ||||
\(836\) | 1.40961 | + | 3.40310i | 0.0487523 | + | 0.117699i | ||||
\(837\) | − | 0.102460i | − | 0.00354155i | ||||||
\(838\) | −46.0555 | + | 19.0768i | −1.59096 | + | 0.658998i | ||||
\(839\) | 0.759740 | − | 1.83418i | 0.0262291 | − | 0.0633228i | −0.910222 | − | 0.414120i | \(-0.864089\pi\) |
0.936451 | + | 0.350797i | \(0.114089\pi\) | |||||||
\(840\) | 11.8356 | + | 4.90248i | 0.408368 | + | 0.169152i | ||||
\(841\) | 27.6065 | − | 27.6065i | 0.951948 | − | 0.951948i | ||||
\(842\) | −37.3246 | + | 37.3246i | −1.28629 | + | 1.28629i | ||||
\(843\) | 73.1873 | + | 30.3152i | 2.52070 | + | 1.04411i | ||||
\(844\) | 4.76680 | − | 11.5081i | 0.164080 | − | 0.396125i | ||||
\(845\) | 11.7503 | − | 4.86713i | 0.404222 | − | 0.167434i | ||||
\(846\) | 15.5718i | 0.535371i | ||||||||
\(847\) | 0.848409 | + | 2.04824i | 0.0291517 | + | 0.0703784i | ||||
\(848\) | 14.6990 | + | 14.6990i | 0.504767 | + | 0.504767i | ||||
\(849\) | 24.8282 | 0.852101 | ||||||||
\(850\) | −13.4266 | − | 22.6522i | −0.460529 | − | 0.776964i | ||||
\(851\) | 4.26664 | 0.146258 | ||||||||
\(852\) | −3.11021 | − | 3.11021i | −0.106554 | − | 0.106554i | ||||
\(853\) | −9.61832 | − | 23.2207i | −0.329325 | − | 0.795061i | −0.998643 | − | 0.0520844i | \(-0.983414\pi\) |
0.669318 | − | 0.742976i | \(-0.266586\pi\) | |||||||
\(854\) | − | 24.2621i | − | 0.830233i | ||||||
\(855\) | −20.8443 | + | 8.63400i | −0.712861 | + | 0.295277i | ||||
\(856\) | −10.7745 | + | 26.0120i | −0.368266 | + | 0.889072i | ||||
\(857\) | 18.2056 | + | 7.54102i | 0.621893 | + | 0.257596i | 0.671304 | − | 0.741182i | \(-0.265734\pi\) |
−0.0494112 | + | 0.998779i | \(0.515734\pi\) | |||||||
\(858\) | 0.849718 | − | 0.849718i | 0.0290089 | − | 0.0290089i | ||||
\(859\) | −9.65385 | + | 9.65385i | −0.329385 | + | 0.329385i | −0.852353 | − | 0.522968i | \(-0.824825\pi\) |
0.522968 | + | 0.852353i | \(0.324825\pi\) | |||||||
\(860\) | 3.08782 | + | 1.27902i | 0.105294 | + | 0.0436141i | ||||
\(861\) | −14.8682 | + | 35.8950i | −0.506707 | + | 1.22330i | ||||
\(862\) | 19.7777 | − | 8.19219i | 0.673631 | − | 0.279027i | ||||
\(863\) | 15.9712i | 0.543667i | 0.962344 | + | 0.271833i | \(0.0876300\pi\) | ||||
−0.962344 | + | 0.271833i | \(0.912370\pi\) | |||||||
\(864\) | 0.503476 | + | 1.21550i | 0.0171286 | + | 0.0413521i | ||||
\(865\) | 0.850931 | + | 0.850931i | 0.0289325 | + | 0.0289325i | ||||
\(866\) | 59.6334 | 2.02643 | ||||||||
\(867\) | 42.0378 | + | 4.55723i | 1.42768 | + | 0.154771i | ||||
\(868\) | −0.250838 | −0.00851400 | ||||||||
\(869\) | −9.89917 | − | 9.89917i | −0.335806 | − | 0.335806i | ||||
\(870\) | 12.2638 | + | 29.6074i | 0.415782 | + | 1.00379i | ||||
\(871\) | − | 0.0220474i | − | 0.000747049i | ||||||
\(872\) | 17.2017 | − | 7.12519i | 0.582524 | − | 0.241289i | ||||
\(873\) | 0.215420 | − | 0.520069i | 0.00729085 | − | 0.0176017i | ||||
\(874\) | 30.3307 | + | 12.5634i | 1.02595 | + | 0.424963i | ||||
\(875\) | 13.9475 | − | 13.9475i | 0.471511 | − | 0.471511i | ||||
\(876\) | −2.95013 | + | 2.95013i | −0.0996757 | + | 0.0996757i | ||||
\(877\) | −52.7803 | − | 21.8623i | −1.78226 | − | 0.738238i | −0.992116 | − | 0.125322i | \(-0.960004\pi\) |
−0.790148 | − | 0.612916i | \(-0.789996\pi\) | |||||||
\(878\) | 0.112674 | − | 0.272019i | 0.00380257 | − | 0.00918021i | ||||
\(879\) | −9.25785 | + | 3.83473i | −0.312260 | + | 0.129342i | ||||
\(880\) | − | 4.69287i | − | 0.158197i | ||||||
\(881\) | 12.5161 | + | 30.2165i | 0.421678 | + | 1.01802i | 0.981853 | + | 0.189646i | \(0.0607340\pi\) |
−0.560175 | + | 0.828375i | \(0.689266\pi\) | |||||||
\(882\) | 7.44685 | + | 7.44685i | 0.250749 | + | 0.250749i | ||||
\(883\) | 41.5063 | 1.39680 | 0.698399 | − | 0.715709i | \(-0.253896\pi\) | ||||
0.698399 | + | 0.715709i | \(0.253896\pi\) | |||||||
\(884\) | −0.328489 | − | 0.554198i | −0.0110483 | − | 0.0186397i | ||||
\(885\) | 28.5031 | 0.958120 | ||||||||
\(886\) | −22.8638 | − | 22.8638i | −0.768124 | − | 0.768124i | ||||
\(887\) | 16.0381 | + | 38.7193i | 0.538505 | + | 1.30007i | 0.925766 | + | 0.378096i | \(0.123421\pi\) |
−0.387261 | + | 0.921970i | \(0.626579\pi\) | |||||||
\(888\) | − | 8.68009i | − | 0.291285i | ||||||
\(889\) | −33.4505 | + | 13.8556i | −1.12189 | + | 0.464703i | ||||
\(890\) | −6.76306 | + | 16.3275i | −0.226698 | + | 0.547298i | ||||
\(891\) | 7.76541 | + | 3.21654i | 0.260151 | + | 0.107758i | ||||
\(892\) | −5.18020 | + | 5.18020i | −0.173446 | + | 0.173446i | ||||
\(893\) | 15.6624 | − | 15.6624i | 0.524122 | − | 0.524122i | ||||
\(894\) | −49.5607 | − | 20.5287i | −1.65756 | − | 0.686583i | ||||
\(895\) | −8.21994 | + | 19.8447i | −0.274762 | + | 0.663335i | ||||
\(896\) | −27.9494 | + | 11.5770i | −0.933725 | + | 0.386762i | ||||
\(897\) | − | 2.18520i | − | 0.0729616i | ||||||
\(898\) | 16.3724 | + | 39.5264i | 0.546353 | + | 1.31901i | ||||
\(899\) | 1.28729 | + | 1.28729i | 0.0429334 | + | 0.0429334i | ||||
\(900\) | 6.58201 | 0.219400 | ||||||||
\(901\) | −4.45844 | + | 17.4357i | −0.148532 | + | 0.580868i | ||||
\(902\) | 11.1684 | 0.371868 | ||||||||
\(903\) | 25.7980 | + | 25.7980i | 0.858503 | + | 0.858503i | ||||
\(904\) | −13.4461 | − | 32.4618i | −0.447212 | − | 1.07966i | ||||
\(905\) | 15.5422i | 0.516639i | ||||||||
\(906\) | −21.9135 | + | 9.07686i | −0.728027 | + | 0.301559i | ||||
\(907\) | 0.00921302 | − | 0.0222422i | 0.000305913 | − | 0.000738540i | −0.923727 | − | 0.383053i | \(-0.874873\pi\) |
0.924032 | + | 0.382314i | \(0.124873\pi\) | |||||||
\(908\) | −1.20325 | − | 0.498402i | −0.0399312 | − | 0.0165400i | ||||
\(909\) | 15.6583 | − | 15.6583i | 0.519354 | − | 0.519354i | ||||
\(910\) | 0.746306 | − | 0.746306i | 0.0247398 | − | 0.0247398i | ||||
\(911\) | 11.1580 | + | 4.62179i | 0.369681 | + | 0.153127i | 0.559787 | − | 0.828637i | \(-0.310883\pi\) |
−0.190106 | + | 0.981764i | \(0.560883\pi\) | |||||||
\(912\) | 32.5714 | − | 78.6342i | 1.07855 | − | 2.60384i | ||||
\(913\) | −4.66583 | + | 1.93265i | −0.154416 | + | 0.0639614i | ||||
\(914\) | 16.2084i | 0.536125i | ||||||||
\(915\) | −6.47542 | − | 15.6331i | −0.214071 | − | 0.516813i | ||||
\(916\) | 1.87916 | + | 1.87916i | 0.0620892 | + | 0.0620892i | ||||
\(917\) | 38.3475 | 1.26634 | ||||||||
\(918\) | −1.81940 | + | 2.42819i | −0.0600492 | + | 0.0801423i | ||||
\(919\) | 7.31860 | 0.241418 | 0.120709 | − | 0.992688i | \(-0.461483\pi\) | ||||
0.120709 | + | 0.992688i | \(0.461483\pi\) | |||||||
\(920\) | −4.73516 | − | 4.73516i | −0.156114 | − | 0.156114i | ||||
\(921\) | −27.2010 | − | 65.6691i | −0.896304 | − | 2.16387i | ||||
\(922\) | − | 31.6880i | − | 1.04359i | ||||||
\(923\) | 0.971323 | − | 0.402335i | 0.0319715 | − | 0.0132430i | ||||
\(924\) | −1.08183 | + | 2.61176i | −0.0355895 | + | 0.0859207i | ||||
\(925\) | −5.50977 | − | 2.28222i | −0.181160 | − | 0.0750390i | ||||
\(926\) | 31.2155 | − | 31.2155i | 1.02580 | − | 1.02580i | ||||
\(927\) | 24.4479 | − | 24.4479i | 0.802975 | − | 0.802975i | ||||
\(928\) | −21.5967 | − | 8.94566i | −0.708948 | − | 0.293656i | ||||
\(929\) | −0.291137 | + | 0.702868i | −0.00955191 | + | 0.0230603i | −0.928584 | − | 0.371123i | \(-0.878973\pi\) |
0.919032 | + | 0.394184i | \(0.128973\pi\) | |||||||
\(930\) | −0.792167 | + | 0.328126i | −0.0259762 | + | 0.0107597i | ||||
\(931\) | − | 14.9803i | − | 0.490960i | ||||||
\(932\) | 0.422268 | + | 1.01945i | 0.0138318 | + | 0.0333930i | ||||
\(933\) | 3.99054 | + | 3.99054i | 0.130644 | + | 0.130644i | ||||
\(934\) | −14.6462 | −0.479238 | ||||||||
\(935\) | 3.49501 | − | 2.07159i | 0.114299 | − | 0.0677483i | ||||
\(936\) | −2.28986 | −0.0748463 | ||||||||
\(937\) | 10.8080 | + | 10.8080i | 0.353081 | + | 0.353081i | 0.861254 | − | 0.508174i | \(-0.169679\pi\) |
−0.508174 | + | 0.861254i | \(0.669679\pi\) | |||||||
\(938\) | 0.0972824 | + | 0.234860i | 0.00317638 | + | 0.00766847i | ||||
\(939\) | − | 67.2701i | − | 2.19528i | ||||||
\(940\) | 1.43874 | − | 0.595947i | 0.0469266 | − | 0.0194377i | ||||
\(941\) | 19.6363 | − | 47.4063i | 0.640126 | − | 1.54540i | −0.186383 | − | 0.982477i | \(-0.559676\pi\) |
0.826509 | − | 0.562924i | \(-0.190324\pi\) | |||||||
\(942\) | −82.6403 | − | 34.2307i | −2.69257 | − | 1.11530i | ||||
\(943\) | 14.3608 | − | 14.3608i | 0.467651 | − | 0.467651i | ||||
\(944\) | −39.1633 | + | 39.1633i | −1.27466 | + | 1.27466i | ||||
\(945\) | −0.936997 | − | 0.388117i | −0.0304805 | − | 0.0126254i | ||||
\(946\) | 4.01341 | − | 9.68922i | 0.130487 | − | 0.315024i | ||||
\(947\) | 24.1279 | − | 9.99411i | 0.784052 | − | 0.324765i | 0.0455026 | − | 0.998964i | \(-0.485511\pi\) |
0.738550 | + | 0.674199i | \(0.235511\pi\) | |||||||
\(948\) | − | 17.8511i | − | 0.579778i | ||||||
\(949\) | −0.381627 | − | 0.921330i | −0.0123881 | − | 0.0299076i | ||||
\(950\) | −32.4478 | − | 32.4478i | −1.05275 | − | 1.05275i | ||||
\(951\) | −82.2576 | −2.66739 | ||||||||
\(952\) | −17.2468 | − | 12.9227i | −0.558971 | − | 0.418827i | ||||
\(953\) | −16.9120 | −0.547835 | −0.273917 | − | 0.961753i | \(-0.588319\pi\) | ||||
−0.273917 | + | 0.961753i | \(0.588319\pi\) | |||||||
\(954\) | −15.5903 | − | 15.5903i | −0.504755 | − | 0.504755i | ||||
\(955\) | 3.23039 | + | 7.79886i | 0.104533 | + | 0.252365i | ||||
\(956\) | 12.8889i | 0.416858i | ||||||||
\(957\) | 18.9553 | − | 7.85153i | 0.612737 | − | 0.253804i | ||||
\(958\) | −7.83932 | + | 18.9258i | −0.253277 | + | 0.611465i | ||||
\(959\) | 21.8229 | + | 9.03933i | 0.704697 | + | 0.291895i | ||||
\(960\) | −8.72231 | + | 8.72231i | −0.281511 | + | 0.281511i | ||||
\(961\) | 21.8859 | − | 21.8859i | 0.705996 | − | 0.705996i | ||||
\(962\) | −0.660687 | − | 0.273666i | −0.0213014 | − | 0.00882333i | ||||
\(963\) | 14.5631 | − | 35.1585i | 0.469290 | − | 1.13297i | ||||
\(964\) | 5.33073 | − | 2.20806i | 0.171691 | − | 0.0711169i | ||||
\(965\) | 11.8139i | 0.380301i | ||||||||
\(966\) | 9.64199 | + | 23.2778i | 0.310226 | + | 0.748952i | ||||
\(967\) | 26.1949 | + | 26.1949i | 0.842372 | + | 0.842372i | 0.989167 | − | 0.146795i | \(-0.0468959\pi\) |
−0.146795 | + | 0.989167i | \(0.546896\pi\) | |||||||
\(968\) | −2.35764 | −0.0757776 | ||||||||
\(969\) | 72.9408 | − | 10.4543i | 2.34320 | − | 0.335841i | ||||
\(970\) | −0.275919 | −0.00885923 | ||||||||
\(971\) | −34.7881 | − | 34.7881i | −1.11640 | − | 1.11640i | −0.992265 | − | 0.124137i | \(-0.960384\pi\) |
−0.124137 | − | 0.992265i | \(-0.539616\pi\) | |||||||
\(972\) | 4.37472 | + | 10.5615i | 0.140319 | + | 0.338761i | ||||
\(973\) | − | 26.8689i | − | 0.861377i | ||||||
\(974\) | −3.04285 | + | 1.26039i | −0.0974991 | + | 0.0403855i | ||||
\(975\) | −1.16886 | + | 2.82188i | −0.0374335 | + | 0.0903725i | ||||
\(976\) | 30.3771 | + | 12.5826i | 0.972347 | + | 0.402759i | ||||
\(977\) | 1.86938 | − | 1.86938i | 0.0598069 | − | 0.0598069i | −0.676571 | − | 0.736378i | \(-0.736535\pi\) |
0.736378 | + | 0.676571i | \(0.236535\pi\) | |||||||
\(978\) | −33.7040 | + | 33.7040i | −1.07773 | + | 1.07773i | ||||
\(979\) | 10.4532 | + | 4.32985i | 0.334085 | + | 0.138383i | ||||
\(980\) | 0.403047 | − | 0.973041i | 0.0128749 | − | 0.0310827i | ||||
\(981\) | −23.2503 | + | 9.63057i | −0.742324 | + | 0.307481i | ||||
\(982\) | − | 20.6606i | − | 0.659306i | ||||||
\(983\) | −4.20395 | − | 10.1492i | −0.134085 | − | 0.323710i | 0.842549 | − | 0.538620i | \(-0.181054\pi\) |
−0.976634 | + | 0.214910i | \(0.931054\pi\) | |||||||
\(984\) | −29.2157 | − | 29.2157i | −0.931363 | − | 0.931363i | ||||
\(985\) | −18.8750 | −0.601409 | ||||||||
\(986\) | −7.64869 | − | 53.3657i | −0.243584 | − | 1.69951i | ||||
\(987\) | 16.9994 | 0.541096 | ||||||||
\(988\) | −0.793852 | − | 0.793852i | −0.0252558 | − | 0.0252558i | ||||
\(989\) | −7.29817 | − | 17.6193i | −0.232068 | − | 0.560262i | ||||
\(990\) | 4.97743i | 0.158193i | ||||||||
\(991\) | 36.4187 | − | 15.0851i | 1.15688 | − | 0.479195i | 0.280044 | − | 0.959987i | \(-0.409651\pi\) |
0.876835 | + | 0.480792i | \(0.159651\pi\) | |||||||
\(992\) | 0.239347 | − | 0.577836i | 0.00759929 | − | 0.0183463i | ||||
\(993\) | −2.15709 | − | 0.893496i | −0.0684532 | − | 0.0283542i | ||||
\(994\) | −8.57176 | + | 8.57176i | −0.271880 | + | 0.271880i | ||||
\(995\) | −7.92610 | + | 7.92610i | −0.251274 | + | 0.251274i | ||||
\(996\) | −5.94951 | − | 2.46437i | −0.188517 | − | 0.0780865i | ||||
\(997\) | −11.3308 | + | 27.3550i | −0.358850 | + | 0.866340i | 0.636612 | + | 0.771184i | \(0.280335\pi\) |
−0.995462 | + | 0.0951564i | \(0.969665\pi\) | |||||||
\(998\) | 18.9203 | − | 7.83705i | 0.598912 | − | 0.248078i | ||||
\(999\) | 0.687181i | 0.0217415i |
(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 | 187.2.h.a.100.12 | ✓ | 56 | |
17.5 | odd | 16 | 3179.2.a.bh.1.7 | 28 | |||
17.8 | even | 8 | inner | 187.2.h.a.144.12 | yes | 56 | |
17.12 | odd | 16 | 3179.2.a.bi.1.7 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
187.2.h.a.100.12 | ✓ | 56 | 1.1 | even | 1 | trivial | |
187.2.h.a.144.12 | yes | 56 | 17.8 | even | 8 | inner | |
3179.2.a.bh.1.7 | 28 | 17.5 | odd | 16 | |||
3179.2.a.bi.1.7 | 28 | 17.12 | odd | 16 |