Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,2,Mod(16,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.h (of order \(3\), 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: | \(0.726638658394\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 74.5 | ||
Root | \(-1.02197 + 1.77010i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.74 |
Dual form | 91.2.h.b.16.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(66\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.55469 | 1.09933 | 0.549665 | − | 0.835385i | \(-0.314755\pi\) | ||||
0.549665 | + | 0.835385i | \(0.314755\pi\) | |||||||
\(3\) | 0.244626 | + | 0.423704i | 0.141235 | + | 0.244626i | 0.927962 | − | 0.372675i | \(-0.121559\pi\) |
−0.786727 | + | 0.617301i | \(0.788226\pi\) | |||||||
\(4\) | 0.417051 | 0.208526 | ||||||||
\(5\) | 0.595756 | + | 1.03188i | 0.266430 | + | 0.461470i | 0.967937 | − | 0.251192i | \(-0.0808225\pi\) |
−0.701507 | + | 0.712662i | \(0.747489\pi\) | |||||||
\(6\) | 0.380316 | + | 0.658727i | 0.155264 | + | 0.268924i | ||||
\(7\) | −2.44127 | − | 1.01990i | −0.922713 | − | 0.385488i | ||||
\(8\) | −2.46099 | −0.870091 | ||||||||
\(9\) | 1.38032 | − | 2.39078i | 0.460105 | − | 0.796926i | ||||
\(10\) | 0.926214 | + | 1.60425i | 0.292894 | + | 0.507308i | ||||
\(11\) | −1.05807 | − | 1.83263i | −0.319020 | − | 0.552559i | 0.661264 | − | 0.750153i | \(-0.270020\pi\) |
−0.980284 | + | 0.197595i | \(0.936687\pi\) | |||||||
\(12\) | 0.102021 | + | 0.176706i | 0.0294511 | + | 0.0510107i | ||||
\(13\) | 2.86133 | + | 2.19381i | 0.793590 | + | 0.608453i | ||||
\(14\) | −3.79541 | − | 1.58563i | −1.01437 | − | 0.423778i | ||||
\(15\) | −0.291474 | + | 0.504848i | −0.0752584 | + | 0.130351i | ||||
\(16\) | −4.66017 | −1.16504 | ||||||||
\(17\) | −0.906303 | −0.219811 | −0.109905 | − | 0.993942i | \(-0.535055\pi\) | ||||
−0.109905 | + | 0.993942i | \(0.535055\pi\) | |||||||
\(18\) | 2.14596 | − | 3.71691i | 0.505808 | − | 0.876084i | ||||
\(19\) | −3.34514 | + | 5.79395i | −0.767428 | + | 1.32922i | 0.171525 | + | 0.985180i | \(0.445130\pi\) |
−0.938953 | + | 0.344045i | \(0.888203\pi\) | |||||||
\(20\) | 0.248461 | + | 0.430346i | 0.0555575 | + | 0.0962284i | ||||
\(21\) | −0.165059 | − | 1.28387i | −0.0360189 | − | 0.280164i | ||||
\(22\) | −1.64497 | − | 2.84917i | −0.350708 | − | 0.607444i | ||||
\(23\) | 3.59733 | 0.750095 | 0.375048 | − | 0.927006i | \(-0.377626\pi\) | ||||
0.375048 | + | 0.927006i | \(0.377626\pi\) | |||||||
\(24\) | −0.602021 | − | 1.04273i | −0.122887 | − | 0.212847i | ||||
\(25\) | 1.79015 | − | 3.10063i | 0.358030 | − | 0.620126i | ||||
\(26\) | 4.44847 | + | 3.41068i | 0.872417 | + | 0.668890i | ||||
\(27\) | 2.81840 | 0.542401 | ||||||||
\(28\) | −1.01813 | − | 0.425352i | −0.192409 | − | 0.0803840i | ||||
\(29\) | −4.25772 | + | 7.37459i | −0.790639 | + | 1.36943i | 0.134932 | + | 0.990855i | \(0.456918\pi\) |
−0.925572 | + | 0.378573i | \(0.876415\pi\) | |||||||
\(30\) | −0.453151 | + | 0.784881i | −0.0827337 | + | 0.143299i | ||||
\(31\) | 2.64390 | − | 4.57937i | 0.474859 | − | 0.822479i | −0.524727 | − | 0.851271i | \(-0.675832\pi\) |
0.999585 | + | 0.0287913i | \(0.00916583\pi\) | |||||||
\(32\) | −2.32313 | −0.410675 | ||||||||
\(33\) | 0.517662 | − | 0.896617i | 0.0901134 | − | 0.156081i | ||||
\(34\) | −1.40902 | −0.241644 | ||||||||
\(35\) | −0.401982 | − | 3.12671i | −0.0679473 | − | 0.528510i | ||||
\(36\) | 0.575663 | − | 0.997077i | 0.0959438 | − | 0.166180i | ||||
\(37\) | 4.99159 | 0.820612 | 0.410306 | − | 0.911948i | \(-0.365422\pi\) | ||||
0.410306 | + | 0.911948i | \(0.365422\pi\) | |||||||
\(38\) | −5.20065 | + | 9.00778i | −0.843656 | + | 1.46126i | ||||
\(39\) | −0.229570 | + | 1.74902i | −0.0367606 | + | 0.280067i | ||||
\(40\) | −1.46615 | − | 2.53944i | −0.231818 | − | 0.401521i | ||||
\(41\) | −0.768181 | + | 1.33053i | −0.119970 | + | 0.207794i | −0.919755 | − | 0.392492i | \(-0.871613\pi\) |
0.799786 | + | 0.600286i | \(0.204946\pi\) | |||||||
\(42\) | −0.256616 | − | 1.99602i | −0.0395967 | − | 0.307992i | ||||
\(43\) | −2.71636 | − | 4.70488i | −0.414242 | − | 0.717488i | 0.581107 | − | 0.813827i | \(-0.302620\pi\) |
−0.995349 | + | 0.0963397i | \(0.969286\pi\) | |||||||
\(44\) | −0.441269 | − | 0.764301i | −0.0665238 | − | 0.115223i | ||||
\(45\) | 3.28933 | 0.490344 | ||||||||
\(46\) | 5.59272 | 0.824602 | ||||||||
\(47\) | 1.59337 | + | 2.75979i | 0.232416 | + | 0.402557i | 0.958519 | − | 0.285030i | \(-0.0920035\pi\) |
−0.726102 | + | 0.687587i | \(0.758670\pi\) | |||||||
\(48\) | −1.14000 | − | 1.97453i | −0.164545 | − | 0.284999i | ||||
\(49\) | 4.91959 | + | 4.97972i | 0.702799 | + | 0.711389i | ||||
\(50\) | 2.78312 | − | 4.82051i | 0.393593 | − | 0.681723i | ||||
\(51\) | −0.221705 | − | 0.384004i | −0.0310449 | − | 0.0537714i | ||||
\(52\) | 1.19332 | + | 0.914930i | 0.165484 | + | 0.126878i | ||||
\(53\) | 1.41239 | − | 2.44632i | 0.194006 | − | 0.336029i | −0.752568 | − | 0.658514i | \(-0.771185\pi\) |
0.946574 | + | 0.322486i | \(0.104518\pi\) | |||||||
\(54\) | 4.38173 | 0.596278 | ||||||||
\(55\) | 1.26070 | − | 2.18360i | 0.169993 | − | 0.294436i | ||||
\(56\) | 6.00794 | + | 2.50997i | 0.802844 | + | 0.335409i | ||||
\(57\) | −3.27323 | −0.433550 | ||||||||
\(58\) | −6.61943 | + | 11.4652i | −0.869173 | + | 1.50545i | ||||
\(59\) | −10.2460 | −1.33391 | −0.666956 | − | 0.745097i | \(-0.732403\pi\) | ||||
−0.666956 | + | 0.745097i | \(0.732403\pi\) | |||||||
\(60\) | −0.121560 | + | 0.210548i | −0.0156933 | + | 0.0271816i | ||||
\(61\) | 4.13423 | − | 7.16069i | 0.529333 | − | 0.916832i | −0.470081 | − | 0.882623i | \(-0.655775\pi\) |
0.999415 | − | 0.0342093i | \(-0.0108913\pi\) | |||||||
\(62\) | 4.11044 | − | 7.11949i | 0.522026 | − | 0.904176i | ||||
\(63\) | −5.80809 | + | 4.42874i | −0.731750 | + | 0.557969i | ||||
\(64\) | 5.70861 | 0.713576 | ||||||||
\(65\) | −0.559090 | + | 4.25952i | −0.0693465 | + | 0.528328i | ||||
\(66\) | 0.804802 | − | 1.39396i | 0.0990643 | − | 0.171584i | ||||
\(67\) | 1.87182 | + | 3.24208i | 0.228679 | + | 0.396083i | 0.957417 | − | 0.288709i | \(-0.0932261\pi\) |
−0.728738 | + | 0.684793i | \(0.759893\pi\) | |||||||
\(68\) | −0.377975 | −0.0458362 | ||||||||
\(69\) | 0.880000 | + | 1.52420i | 0.105939 | + | 0.183493i | ||||
\(70\) | −0.624956 | − | 4.86105i | −0.0746965 | − | 0.581007i | ||||
\(71\) | 1.26510 | + | 2.19122i | 0.150140 | + | 0.260050i | 0.931279 | − | 0.364307i | \(-0.118694\pi\) |
−0.781139 | + | 0.624357i | \(0.785361\pi\) | |||||||
\(72\) | −3.39694 | + | 5.88368i | −0.400334 | + | 0.693398i | ||||
\(73\) | 2.86522 | − | 4.96271i | 0.335349 | − | 0.580841i | −0.648203 | − | 0.761468i | \(-0.724479\pi\) |
0.983552 | + | 0.180627i | \(0.0578125\pi\) | |||||||
\(74\) | 7.76035 | 0.902123 | ||||||||
\(75\) | 1.75167 | 0.202265 | ||||||||
\(76\) | −1.39510 | + | 2.41638i | −0.160028 | + | 0.277177i | ||||
\(77\) | 0.713925 | + | 5.55307i | 0.0813593 | + | 0.632831i | ||||
\(78\) | −0.356910 | + | 2.71918i | −0.0404121 | + | 0.307886i | ||||
\(79\) | −3.03620 | − | 5.25885i | −0.341599 | − | 0.591667i | 0.643131 | − | 0.765756i | \(-0.277635\pi\) |
−0.984730 | + | 0.174089i | \(0.944302\pi\) | |||||||
\(80\) | −2.77632 | − | 4.80873i | −0.310402 | − | 0.537633i | ||||
\(81\) | −3.45150 | − | 5.97817i | −0.383500 | − | 0.664241i | ||||
\(82\) | −1.19428 | + | 2.06856i | −0.131886 | + | 0.228434i | ||||
\(83\) | −11.6309 | −1.27665 | −0.638327 | − | 0.769766i | \(-0.720373\pi\) | ||||
−0.638327 | + | 0.769766i | \(0.720373\pi\) | |||||||
\(84\) | −0.0688383 | − | 0.535440i | −0.00751087 | − | 0.0584213i | ||||
\(85\) | −0.539935 | − | 0.935195i | −0.0585642 | − | 0.101436i | ||||
\(86\) | −4.22310 | − | 7.31462i | −0.455388 | − | 0.788755i | ||||
\(87\) | −4.16619 | −0.446663 | ||||||||
\(88\) | 2.60390 | + | 4.51008i | 0.277576 | + | 0.480776i | ||||
\(89\) | −17.7511 | −1.88162 | −0.940808 | − | 0.338939i | \(-0.889932\pi\) | ||||
−0.940808 | + | 0.338939i | \(0.889932\pi\) | |||||||
\(90\) | 5.11387 | 0.539049 | ||||||||
\(91\) | −4.74780 | − | 8.27396i | −0.497705 | − | 0.867346i | ||||
\(92\) | 1.50027 | 0.156414 | ||||||||
\(93\) | 2.58707 | 0.268266 | ||||||||
\(94\) | 2.47719 | + | 4.29061i | 0.255502 | + | 0.442543i | ||||
\(95\) | −7.97155 | −0.817863 | ||||||||
\(96\) | −0.568297 | − | 0.984319i | −0.0580015 | − | 0.100462i | ||||
\(97\) | −3.10217 | − | 5.37312i | −0.314978 | − | 0.545557i | 0.664455 | − | 0.747328i | \(-0.268664\pi\) |
−0.979433 | + | 0.201771i | \(0.935330\pi\) | |||||||
\(98\) | 7.64842 | + | 7.74191i | 0.772607 | + | 0.782051i | ||||
\(99\) | −5.84188 | −0.587131 | ||||||||
\(100\) | 0.746584 | − | 1.29312i | 0.0746584 | − | 0.129312i | ||||
\(101\) | 3.61133 | + | 6.25501i | 0.359341 | + | 0.622397i | 0.987851 | − | 0.155405i | \(-0.0496682\pi\) |
−0.628510 | + | 0.777802i | \(0.716335\pi\) | |||||||
\(102\) | −0.344682 | − | 0.597007i | −0.0341286 | − | 0.0591125i | ||||
\(103\) | −4.96322 | − | 8.59656i | −0.489041 | − | 0.847044i | 0.510879 | − | 0.859652i | \(-0.329320\pi\) |
−0.999921 | + | 0.0126084i | \(0.995987\pi\) | |||||||
\(104\) | −7.04170 | − | 5.39894i | −0.690496 | − | 0.529409i | ||||
\(105\) | 1.22646 | − | 0.935195i | 0.119691 | − | 0.0912657i | ||||
\(106\) | 2.19582 | − | 3.80327i | 0.213277 | − | 0.369406i | ||||
\(107\) | −2.20006 | −0.212688 | −0.106344 | − | 0.994329i | \(-0.533915\pi\) | ||||
−0.106344 | + | 0.994329i | \(0.533915\pi\) | |||||||
\(108\) | 1.17542 | 0.113105 | ||||||||
\(109\) | −6.87291 | + | 11.9042i | −0.658305 | + | 1.14022i | 0.322749 | + | 0.946485i | \(0.395393\pi\) |
−0.981054 | + | 0.193734i | \(0.937940\pi\) | |||||||
\(110\) | 1.96000 | − | 3.39481i | 0.186878 | − | 0.323683i | ||||
\(111\) | 1.22107 | + | 2.11496i | 0.115899 | + | 0.200743i | ||||
\(112\) | 11.3767 | + | 4.75293i | 1.07500 | + | 0.449110i | ||||
\(113\) | 8.04736 | + | 13.9384i | 0.757032 | + | 1.31122i | 0.944358 | + | 0.328920i | \(0.106685\pi\) |
−0.187326 | + | 0.982298i | \(0.559982\pi\) | |||||||
\(114\) | −5.08885 | −0.476614 | ||||||||
\(115\) | 2.14313 | + | 3.71201i | 0.199848 | + | 0.346147i | ||||
\(116\) | −1.77569 | + | 3.07558i | −0.164869 | + | 0.285561i | ||||
\(117\) | 9.19445 | − | 3.81266i | 0.850027 | − | 0.352480i | ||||
\(118\) | −15.9293 | −1.46641 | ||||||||
\(119\) | 2.21253 | + | 0.924342i | 0.202822 | + | 0.0847343i | ||||
\(120\) | 0.717315 | − | 1.24243i | 0.0654816 | − | 0.113418i | ||||
\(121\) | 3.26098 | − | 5.64818i | 0.296453 | − | 0.513471i | ||||
\(122\) | 6.42743 | − | 11.1326i | 0.581912 | − | 1.00790i | ||||
\(123\) | −0.751668 | −0.0677756 | ||||||||
\(124\) | 1.10264 | − | 1.90983i | 0.0990202 | − | 0.171508i | ||||
\(125\) | 10.2235 | 0.914420 | ||||||||
\(126\) | −9.02976 | + | 6.88531i | −0.804435 | + | 0.613392i | ||||
\(127\) | 7.83921 | − | 13.5779i | 0.695617 | − | 1.20484i | −0.274355 | − | 0.961628i | \(-0.588464\pi\) |
0.969972 | − | 0.243216i | \(-0.0782023\pi\) | |||||||
\(128\) | 13.5213 | 1.19513 | ||||||||
\(129\) | 1.32899 | − | 2.30187i | 0.117011 | − | 0.202668i | ||||
\(130\) | −0.869209 | + | 6.62222i | −0.0762347 | + | 0.580807i | ||||
\(131\) | 4.76884 | + | 8.25988i | 0.416656 | + | 0.721669i | 0.995601 | − | 0.0936976i | \(-0.0298687\pi\) |
−0.578945 | + | 0.815367i | \(0.696535\pi\) | |||||||
\(132\) | 0.215892 | − | 0.373935i | 0.0187910 | − | 0.0325469i | ||||
\(133\) | 14.0757 | − | 10.7329i | 1.22052 | − | 0.930658i | ||||
\(134\) | 2.91009 | + | 5.04042i | 0.251393 | + | 0.435426i | ||||
\(135\) | 1.67908 | + | 2.90825i | 0.144512 | + | 0.250302i | ||||
\(136\) | 2.23040 | 0.191255 | ||||||||
\(137\) | −2.76461 | −0.236197 | −0.118098 | − | 0.993002i | \(-0.537680\pi\) | ||||
−0.118098 | + | 0.993002i | \(0.537680\pi\) | |||||||
\(138\) | 1.36812 | + | 2.36966i | 0.116462 | + | 0.201719i | ||||
\(139\) | 11.3983 | + | 19.7425i | 0.966795 | + | 1.67454i | 0.704714 | + | 0.709492i | \(0.251075\pi\) |
0.262081 | + | 0.965046i | \(0.415591\pi\) | |||||||
\(140\) | −0.167647 | − | 1.30400i | −0.0141688 | − | 0.110208i | ||||
\(141\) | −0.779557 | + | 1.35023i | −0.0656505 | + | 0.113710i | ||||
\(142\) | 1.96684 | + | 3.40666i | 0.165053 | + | 0.285881i | ||||
\(143\) | 0.992950 | − | 7.56496i | 0.0830346 | − | 0.632614i | ||||
\(144\) | −6.43251 | + | 11.1414i | −0.536043 | + | 0.928453i | ||||
\(145\) | −10.1462 | −0.842600 | ||||||||
\(146\) | 4.45452 | − | 7.71546i | 0.368659 | − | 0.638536i | ||||
\(147\) | −0.906471 | + | 3.30262i | −0.0747645 | + | 0.272395i | ||||
\(148\) | 2.08175 | 0.171119 | ||||||||
\(149\) | 7.20581 | − | 12.4808i | 0.590323 | − | 1.02247i | −0.403866 | − | 0.914818i | \(-0.632334\pi\) |
0.994189 | − | 0.107651i | \(-0.0343329\pi\) | |||||||
\(150\) | 2.72329 | 0.222356 | ||||||||
\(151\) | −7.62901 | + | 13.2138i | −0.620840 | + | 1.07533i | 0.368489 | + | 0.929632i | \(0.379875\pi\) |
−0.989330 | + | 0.145695i | \(0.953458\pi\) | |||||||
\(152\) | 8.23236 | − | 14.2589i | 0.667732 | − | 1.15655i | ||||
\(153\) | −1.25098 | + | 2.16677i | −0.101136 | + | 0.175173i | ||||
\(154\) | 1.10993 | + | 8.63329i | 0.0894407 | + | 0.695690i | ||||
\(155\) | 6.30048 | 0.506067 | ||||||||
\(156\) | −0.0957425 | + | 0.729431i | −0.00766554 | + | 0.0584012i | ||||
\(157\) | 5.70745 | − | 9.88559i | 0.455504 | − | 0.788956i | −0.543213 | − | 0.839595i | \(-0.682792\pi\) |
0.998717 | + | 0.0506387i | \(0.0161257\pi\) | |||||||
\(158\) | −4.72034 | − | 8.17587i | −0.375530 | − | 0.650437i | ||||
\(159\) | 1.38202 | 0.109602 | ||||||||
\(160\) | −1.38402 | − | 2.39719i | −0.109416 | − | 0.189514i | ||||
\(161\) | −8.78205 | − | 3.66893i | −0.692122 | − | 0.289152i | ||||
\(162\) | −5.36600 | − | 9.29418i | −0.421592 | − | 0.730220i | ||||
\(163\) | 7.20385 | − | 12.4774i | 0.564249 | − | 0.977308i | −0.432870 | − | 0.901456i | \(-0.642499\pi\) |
0.997119 | − | 0.0758514i | \(-0.0241675\pi\) | |||||||
\(164\) | −0.320371 | + | 0.554899i | −0.0250168 | + | 0.0433303i | ||||
\(165\) | 1.23360 | 0.0960357 | ||||||||
\(166\) | −18.0824 | −1.40346 | ||||||||
\(167\) | −3.88595 | + | 6.73066i | −0.300704 | + | 0.520834i | −0.976296 | − | 0.216442i | \(-0.930555\pi\) |
0.675592 | + | 0.737276i | \(0.263888\pi\) | |||||||
\(168\) | 0.406210 | + | 3.15959i | 0.0313398 | + | 0.243768i | ||||
\(169\) | 3.37442 | + | 12.5544i | 0.259571 | + | 0.965724i | ||||
\(170\) | −0.839430 | − | 1.45394i | −0.0643813 | − | 0.111512i | ||||
\(171\) | 9.23471 | + | 15.9950i | 0.706196 | + | 1.22317i | ||||
\(172\) | −1.13286 | − | 1.96218i | −0.0863800 | − | 0.149615i | ||||
\(173\) | −3.04731 | + | 5.27809i | −0.231682 | + | 0.401286i | −0.958303 | − | 0.285753i | \(-0.907756\pi\) |
0.726621 | + | 0.687039i | \(0.241090\pi\) | |||||||
\(174\) | −6.47713 | −0.491030 | ||||||||
\(175\) | −7.53259 | + | 5.74369i | −0.569410 | + | 0.434182i | ||||
\(176\) | 4.93078 | + | 8.54037i | 0.371672 | + | 0.643754i | ||||
\(177\) | −2.50643 | − | 4.34126i | −0.188395 | − | 0.326309i | ||||
\(178\) | −27.5975 | −2.06852 | ||||||||
\(179\) | −9.26488 | − | 16.0472i | −0.692490 | − | 1.19943i | −0.971020 | − | 0.239000i | \(-0.923181\pi\) |
0.278530 | − | 0.960428i | \(-0.410153\pi\) | |||||||
\(180\) | 1.37182 | 0.102249 | ||||||||
\(181\) | −5.60520 | −0.416631 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(182\) | −7.38135 | − | 12.8634i | −0.547142 | − | 0.953499i | ||||
\(183\) | 4.04535 | 0.299041 | ||||||||
\(184\) | −8.85299 | −0.652651 | ||||||||
\(185\) | 2.97377 | + | 5.15071i | 0.218636 | + | 0.378688i | ||||
\(186\) | 4.02208 | 0.294913 | ||||||||
\(187\) | 0.958931 | + | 1.66092i | 0.0701240 | + | 0.121458i | ||||
\(188\) | 0.664516 | + | 1.15097i | 0.0484648 | + | 0.0839435i | ||||
\(189\) | −6.88047 | − | 2.87450i | −0.500480 | − | 0.209089i | ||||
\(190\) | −12.3933 | −0.899102 | ||||||||
\(191\) | −0.251851 | + | 0.436219i | −0.0182233 | + | 0.0315637i | −0.874993 | − | 0.484135i | \(-0.839134\pi\) |
0.856770 | + | 0.515699i | \(0.172468\pi\) | |||||||
\(192\) | 1.39647 | + | 2.41876i | 0.100782 | + | 0.174559i | ||||
\(193\) | 1.85622 | + | 3.21507i | 0.133614 | + | 0.231426i | 0.925067 | − | 0.379804i | \(-0.124009\pi\) |
−0.791453 | + | 0.611230i | \(0.790675\pi\) | |||||||
\(194\) | −4.82290 | − | 8.35351i | −0.346264 | − | 0.599747i | ||||
\(195\) | −1.94154 | + | 0.805100i | −0.139037 | + | 0.0576544i | ||||
\(196\) | 2.05172 | + | 2.07680i | 0.146552 | + | 0.148343i | ||||
\(197\) | 3.72225 | − | 6.44713i | 0.265200 | − | 0.459339i | −0.702416 | − | 0.711766i | \(-0.747895\pi\) |
0.967616 | + | 0.252427i | \(0.0812288\pi\) | |||||||
\(198\) | −9.08230 | −0.645451 | ||||||||
\(199\) | 7.50556 | 0.532055 | 0.266028 | − | 0.963965i | \(-0.414289\pi\) | ||||
0.266028 | + | 0.963965i | \(0.414289\pi\) | |||||||
\(200\) | −4.40554 | + | 7.63062i | −0.311519 | + | 0.539566i | ||||
\(201\) | −0.915789 | + | 1.58619i | −0.0645948 | + | 0.111881i | ||||
\(202\) | 5.61449 | + | 9.72458i | 0.395034 | + | 0.684219i | ||||
\(203\) | 17.9156 | − | 13.6609i | 1.25743 | − | 0.958807i | ||||
\(204\) | −0.0924624 | − | 0.160149i | −0.00647366 | − | 0.0112127i | ||||
\(205\) | −1.83059 | −0.127854 | ||||||||
\(206\) | −7.71626 | − | 13.3650i | −0.537617 | − | 0.931181i | ||||
\(207\) | 4.96545 | − | 8.60042i | 0.345123 | − | 0.597770i | ||||
\(208\) | −13.3343 | − | 10.2235i | −0.924567 | − | 0.708873i | ||||
\(209\) | 14.1576 | 0.979299 | ||||||||
\(210\) | 1.90677 | − | 1.45394i | 0.131580 | − | 0.100331i | ||||
\(211\) | −1.89531 | + | 3.28278i | −0.130479 | + | 0.225996i | −0.923861 | − | 0.382728i | \(-0.874985\pi\) |
0.793383 | + | 0.608723i | \(0.208318\pi\) | |||||||
\(212\) | 0.589037 | − | 1.02024i | 0.0404553 | − | 0.0700706i | ||||
\(213\) | −0.618953 | + | 1.07206i | −0.0424100 | + | 0.0734562i | ||||
\(214\) | −3.42041 | −0.233814 | ||||||||
\(215\) | 3.23658 | − | 5.60592i | 0.220733 | − | 0.382320i | ||||
\(216\) | −6.93605 | −0.471938 | ||||||||
\(217\) | −11.1250 | + | 8.48295i | −0.755214 | + | 0.575860i | ||||
\(218\) | −10.6852 | + | 18.5073i | −0.723695 | + | 1.25348i | ||||
\(219\) | 2.80363 | 0.189452 | ||||||||
\(220\) | 0.525777 | − | 0.910673i | 0.0354479 | − | 0.0613975i | ||||
\(221\) | −2.59323 | − | 1.98825i | −0.174440 | − | 0.133744i | ||||
\(222\) | 1.89838 | + | 3.28809i | 0.127411 | + | 0.220682i | ||||
\(223\) | −2.43440 | + | 4.21650i | −0.163019 | + | 0.282358i | −0.935950 | − | 0.352133i | \(-0.885457\pi\) |
0.772931 | + | 0.634490i | \(0.218790\pi\) | |||||||
\(224\) | 5.67138 | + | 2.36937i | 0.378935 | + | 0.158310i | ||||
\(225\) | −4.94195 | − | 8.55971i | −0.329463 | − | 0.570647i | ||||
\(226\) | 12.5111 | + | 21.6699i | 0.832228 | + | 1.44146i | ||||
\(227\) | 24.1767 | 1.60466 | 0.802332 | − | 0.596877i | \(-0.203592\pi\) | ||||
0.802332 | + | 0.596877i | \(0.203592\pi\) | |||||||
\(228\) | −1.36510 | −0.0904063 | ||||||||
\(229\) | 10.8561 | + | 18.8034i | 0.717394 | + | 1.24256i | 0.962029 | + | 0.272947i | \(0.0879985\pi\) |
−0.244635 | + | 0.969615i | \(0.578668\pi\) | |||||||
\(230\) | 3.33190 | + | 5.77101i | 0.219699 | + | 0.380529i | ||||
\(231\) | −2.17822 | + | 1.66092i | −0.143316 | + | 0.109280i | ||||
\(232\) | 10.4782 | − | 18.1488i | 0.687928 | − | 1.19153i | ||||
\(233\) | −1.89842 | − | 3.28816i | −0.124370 | − | 0.215414i | 0.797117 | − | 0.603825i | \(-0.206358\pi\) |
−0.921486 | + | 0.388411i | \(0.873024\pi\) | |||||||
\(234\) | 14.2945 | − | 5.92749i | 0.934460 | − | 0.387492i | ||||
\(235\) | −1.89851 | + | 3.28832i | −0.123845 | + | 0.214507i | ||||
\(236\) | −4.27309 | −0.278155 | ||||||||
\(237\) | 1.48547 | − | 2.57290i | 0.0964914 | − | 0.167128i | ||||
\(238\) | 3.43979 | + | 1.43706i | 0.222968 | + | 0.0931509i | ||||
\(239\) | 21.9100 | 1.41724 | 0.708619 | − | 0.705592i | \(-0.249319\pi\) | ||||
0.708619 | + | 0.705592i | \(0.249319\pi\) | |||||||
\(240\) | 1.35832 | − | 2.35268i | 0.0876792 | − | 0.151865i | ||||
\(241\) | −20.7488 | −1.33655 | −0.668273 | − | 0.743916i | \(-0.732966\pi\) | ||||
−0.668273 | + | 0.743916i | \(0.732966\pi\) | |||||||
\(242\) | 5.06980 | − | 8.78115i | 0.325899 | − | 0.564474i | ||||
\(243\) | 5.91625 | − | 10.2472i | 0.379527 | − | 0.657361i | ||||
\(244\) | 1.72418 | − | 2.98637i | 0.110380 | − | 0.191183i | ||||
\(245\) | −2.20760 | + | 8.04312i | −0.141038 | + | 0.513856i | ||||
\(246\) | −1.16861 | −0.0745077 | ||||||||
\(247\) | −22.2824 | + | 9.23982i | −1.41779 | + | 0.587916i | ||||
\(248\) | −6.50661 | + | 11.2698i | −0.413170 | + | 0.715632i | ||||
\(249\) | −2.84521 | − | 4.92805i | −0.180308 | − | 0.312302i | ||||
\(250\) | 15.8944 | 1.00525 | ||||||||
\(251\) | −6.62891 | − | 11.4816i | −0.418413 | − | 0.724713i | 0.577367 | − | 0.816485i | \(-0.304080\pi\) |
−0.995780 | + | 0.0917718i | \(0.970747\pi\) | |||||||
\(252\) | −2.42227 | + | 1.84701i | −0.152589 | + | 0.116351i | ||||
\(253\) | −3.80622 | − | 6.59257i | −0.239295 | − | 0.414472i | ||||
\(254\) | 12.1875 | − | 21.1094i | 0.764713 | − | 1.32452i | ||||
\(255\) | 0.264164 | − | 0.457546i | 0.0165426 | − | 0.0286526i | ||||
\(256\) | 9.60425 | 0.600266 | ||||||||
\(257\) | −13.1711 | −0.821590 | −0.410795 | − | 0.911728i | \(-0.634749\pi\) | ||||
−0.410795 | + | 0.911728i | \(0.634749\pi\) | |||||||
\(258\) | 2.06616 | − | 3.57869i | 0.128633 | − | 0.222799i | ||||
\(259\) | −12.1858 | − | 5.09094i | −0.757189 | − | 0.316336i | ||||
\(260\) | −0.233169 | + | 1.77644i | −0.0144605 | + | 0.110170i | ||||
\(261\) | 11.7540 | + | 20.3585i | 0.727555 | + | 1.26016i | ||||
\(262\) | 7.41406 | + | 12.8415i | 0.458042 | + | 0.793352i | ||||
\(263\) | 9.57028 | + | 16.5762i | 0.590129 | + | 1.02213i | 0.994215 | + | 0.107412i | \(0.0342564\pi\) |
−0.404086 | + | 0.914721i | \(0.632410\pi\) | |||||||
\(264\) | −1.27396 | + | 2.20657i | −0.0784069 | + | 0.135805i | ||||
\(265\) | 3.36575 | 0.206756 | ||||||||
\(266\) | 21.8833 | − | 16.6863i | 1.34175 | − | 1.02310i | ||||
\(267\) | −4.34239 | − | 7.52123i | −0.265750 | − | 0.460292i | ||||
\(268\) | 0.780643 | + | 1.35211i | 0.0476854 | + | 0.0825935i | ||||
\(269\) | −28.4822 | −1.73659 | −0.868296 | − | 0.496047i | \(-0.834784\pi\) | ||||
−0.868296 | + | 0.496047i | \(0.834784\pi\) | |||||||
\(270\) | 2.61044 | + | 4.52141i | 0.158866 | + | 0.275164i | ||||
\(271\) | 17.9474 | 1.09023 | 0.545114 | − | 0.838362i | \(-0.316486\pi\) | ||||
0.545114 | + | 0.838362i | \(0.316486\pi\) | |||||||
\(272\) | 4.22353 | 0.256089 | ||||||||
\(273\) | 2.34428 | − | 4.03569i | 0.141882 | − | 0.244251i | ||||
\(274\) | −4.29811 | −0.259658 | ||||||||
\(275\) | −7.57641 | −0.456875 | ||||||||
\(276\) | 0.367005 | + | 0.635671i | 0.0220911 | + | 0.0382629i | ||||
\(277\) | 13.4389 | 0.807463 | 0.403732 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403732 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(278\) | 17.7209 | + | 30.6934i | 1.06283 | + | 1.84087i | ||||
\(279\) | −7.29884 | − | 12.6420i | −0.436970 | − | 0.756855i | ||||
\(280\) | 0.989273 | + | 7.69480i | 0.0591204 | + | 0.459852i | ||||
\(281\) | −29.9530 | −1.78685 | −0.893424 | − | 0.449214i | \(-0.851704\pi\) | ||||
−0.893424 | + | 0.449214i | \(0.851704\pi\) | |||||||
\(282\) | −1.21197 | + | 2.09919i | −0.0721716 | + | 0.125005i | ||||
\(283\) | 4.94561 | + | 8.56604i | 0.293986 | + | 0.509199i | 0.974748 | − | 0.223306i | \(-0.0716848\pi\) |
−0.680763 | + | 0.732504i | \(0.738351\pi\) | |||||||
\(284\) | 0.527613 | + | 0.913852i | 0.0313080 | + | 0.0542271i | ||||
\(285\) | −1.95005 | − | 3.37758i | −0.115511 | − | 0.200070i | ||||
\(286\) | 1.54373 | − | 11.7611i | 0.0912824 | − | 0.695451i | ||||
\(287\) | 3.23235 | − | 2.46471i | 0.190800 | − | 0.145487i | ||||
\(288\) | −3.20665 | + | 5.55408i | −0.188954 | + | 0.327277i | ||||
\(289\) | −16.1786 | −0.951683 | ||||||||
\(290\) | −15.7742 | −0.926295 | ||||||||
\(291\) | 1.51774 | − | 2.62881i | 0.0889716 | − | 0.154103i | ||||
\(292\) | 1.19494 | − | 2.06970i | 0.0699288 | − | 0.121120i | ||||
\(293\) | −3.95529 | − | 6.85076i | −0.231071 | − | 0.400226i | 0.727053 | − | 0.686581i | \(-0.240889\pi\) |
−0.958123 | + | 0.286356i | \(0.907556\pi\) | |||||||
\(294\) | −1.40928 | + | 5.13454i | −0.0821908 | + | 0.299452i | ||||
\(295\) | −6.10409 | − | 10.5726i | −0.355394 | − | 0.615561i | ||||
\(296\) | −12.2842 | −0.714007 | ||||||||
\(297\) | −2.98206 | − | 5.16508i | −0.173037 | − | 0.299708i | ||||
\(298\) | 11.2028 | − | 19.4038i | 0.648959 | − | 1.12403i | ||||
\(299\) | 10.2931 | + | 7.89185i | 0.595268 | + | 0.456397i | ||||
\(300\) | 0.730535 | 0.0421775 | ||||||||
\(301\) | 1.83285 | + | 14.2563i | 0.105644 | + | 0.821720i | ||||
\(302\) | −11.8607 | + | 20.5434i | −0.682508 | + | 1.18214i | ||||
\(303\) | −1.76685 | + | 3.06027i | −0.101503 | + | 0.175808i | ||||
\(304\) | 15.5889 | − | 27.0008i | 0.894086 | − | 1.54860i | ||||
\(305\) | 9.85196 | 0.564121 | ||||||||
\(306\) | −1.94489 | + | 3.36865i | −0.111182 | + | 0.192573i | ||||
\(307\) | 1.27238 | 0.0726187 | 0.0363094 | − | 0.999341i | \(-0.488440\pi\) | ||||
0.0363094 | + | 0.999341i | \(0.488440\pi\) | |||||||
\(308\) | 0.297743 | + | 2.31592i | 0.0169655 | + | 0.131962i | ||||
\(309\) | 2.42827 | − | 4.20588i | 0.138139 | − | 0.239264i | ||||
\(310\) | 9.79527 | 0.556334 | ||||||||
\(311\) | −12.3817 | + | 21.4458i | −0.702103 | + | 1.21608i | 0.265624 | + | 0.964077i | \(0.414422\pi\) |
−0.967727 | + | 0.252002i | \(0.918911\pi\) | |||||||
\(312\) | 0.564970 | − | 4.30432i | 0.0319851 | − | 0.243684i | ||||
\(313\) | −1.18826 | − | 2.05812i | −0.0671642 | − | 0.116332i | 0.830488 | − | 0.557037i | \(-0.188062\pi\) |
−0.897652 | + | 0.440705i | \(0.854728\pi\) | |||||||
\(314\) | 8.87330 | − | 15.3690i | 0.500749 | − | 0.867323i | ||||
\(315\) | −8.03013 | − | 3.35480i | −0.452446 | − | 0.189021i | ||||
\(316\) | −1.26625 | − | 2.19321i | −0.0712322 | − | 0.123378i | ||||
\(317\) | 9.88979 | + | 17.1296i | 0.555466 | + | 0.962096i | 0.997867 | + | 0.0652782i | \(0.0207935\pi\) |
−0.442401 | + | 0.896817i | \(0.645873\pi\) | |||||||
\(318\) | 2.14862 | 0.120488 | ||||||||
\(319\) | 18.0199 | 1.00892 | ||||||||
\(320\) | 3.40093 | + | 5.89059i | 0.190118 | + | 0.329294i | ||||
\(321\) | −0.538192 | − | 0.932176i | −0.0300390 | − | 0.0520290i | ||||
\(322\) | −13.6533 | − | 5.70404i | −0.760871 | − | 0.317874i | ||||
\(323\) | 3.03171 | − | 5.25108i | 0.168689 | − | 0.292178i | ||||
\(324\) | −1.43945 | − | 2.49320i | −0.0799695 | − | 0.138511i | ||||
\(325\) | 11.9244 | − | 4.94469i | 0.661447 | − | 0.274282i | ||||
\(326\) | 11.1997 | − | 19.3985i | 0.620295 | − | 1.07438i | ||||
\(327\) | −6.72516 | −0.371902 | ||||||||
\(328\) | 1.89049 | − | 3.27442i | 0.104385 | − | 0.180799i | ||||
\(329\) | −1.07511 | − | 8.36248i | −0.0592729 | − | 0.461038i | ||||
\(330\) | 1.91786 | 0.105575 | ||||||||
\(331\) | −1.96386 | + | 3.40151i | −0.107944 | + | 0.186964i | −0.914937 | − | 0.403596i | \(-0.867760\pi\) |
0.806993 | + | 0.590561i | \(0.201093\pi\) | |||||||
\(332\) | −4.85067 | −0.266215 | ||||||||
\(333\) | 6.88997 | − | 11.9338i | 0.377568 | − | 0.653967i | ||||
\(334\) | −6.04143 | + | 10.4641i | −0.330572 | + | 0.572568i | ||||
\(335\) | −2.23029 | + | 3.86298i | −0.121854 | + | 0.211057i | ||||
\(336\) | 0.769205 | + | 5.98306i | 0.0419636 | + | 0.326403i | ||||
\(337\) | −7.14099 | −0.388995 | −0.194497 | − | 0.980903i | \(-0.562308\pi\) | ||||
−0.194497 | + | 0.980903i | \(0.562308\pi\) | |||||||
\(338\) | 5.24617 | + | 19.5182i | 0.285354 | + | 1.06165i | ||||
\(339\) | −3.93718 | + | 6.81940i | −0.213838 | + | 0.370379i | ||||
\(340\) | −0.225181 | − | 0.390024i | −0.0122121 | − | 0.0211520i | ||||
\(341\) | −11.1897 | −0.605958 | ||||||||
\(342\) | 14.3571 | + | 24.8672i | 0.776342 | + | 1.34466i | ||||
\(343\) | −6.93120 | − | 17.1744i | −0.374250 | − | 0.927328i | ||||
\(344\) | 6.68494 | + | 11.5787i | 0.360428 | + | 0.624280i | ||||
\(345\) | −1.04853 | + | 1.81611i | −0.0564509 | + | 0.0977759i | ||||
\(346\) | −4.73761 | + | 8.20578i | −0.254695 | + | 0.441145i | ||||
\(347\) | 10.0700 | 0.540584 | 0.270292 | − | 0.962778i | \(-0.412880\pi\) | ||||
0.270292 | + | 0.962778i | \(0.412880\pi\) | |||||||
\(348\) | −1.73752 | −0.0931407 | ||||||||
\(349\) | 3.14418 | − | 5.44588i | 0.168304 | − | 0.291512i | −0.769520 | − | 0.638623i | \(-0.779504\pi\) |
0.937824 | + | 0.347112i | \(0.112838\pi\) | |||||||
\(350\) | −11.7108 | + | 8.92964i | −0.625969 | + | 0.477310i | ||||
\(351\) | 8.06437 | + | 6.18302i | 0.430444 | + | 0.330025i | ||||
\(352\) | 2.45803 | + | 4.25743i | 0.131013 | + | 0.226922i | ||||
\(353\) | −17.0836 | − | 29.5897i | −0.909269 | − | 1.57490i | −0.815083 | − | 0.579345i | \(-0.803308\pi\) |
−0.0941861 | − | 0.995555i | \(-0.530025\pi\) | |||||||
\(354\) | −3.89671 | − | 6.74930i | −0.207108 | − | 0.358721i | ||||
\(355\) | −1.50738 | + | 2.61087i | −0.0800036 | + | 0.138570i | ||||
\(356\) | −7.40313 | −0.392365 | ||||||||
\(357\) | 0.149594 | + | 1.16358i | 0.00791735 | + | 0.0615830i | ||||
\(358\) | −14.4040 | − | 24.9484i | −0.761274 | − | 1.31857i | ||||
\(359\) | −9.34327 | − | 16.1830i | −0.493119 | − | 0.854107i | 0.506850 | − | 0.862034i | \(-0.330810\pi\) |
−0.999969 | + | 0.00792750i | \(0.997477\pi\) | |||||||
\(360\) | −8.09500 | −0.426644 | ||||||||
\(361\) | −12.8799 | − | 22.3087i | −0.677891 | − | 1.17414i | ||||
\(362\) | −8.71433 | −0.458015 | ||||||||
\(363\) | 3.19088 | 0.167478 | ||||||||
\(364\) | −1.98008 | − | 3.45066i | −0.103784 | − | 0.180864i | ||||
\(365\) | 6.82788 | 0.357388 | ||||||||
\(366\) | 6.28926 | 0.328745 | ||||||||
\(367\) | 15.5305 | + | 26.8997i | 0.810687 | + | 1.40415i | 0.912384 | + | 0.409336i | \(0.134240\pi\) |
−0.101696 | + | 0.994816i | \(0.532427\pi\) | |||||||
\(368\) | −16.7642 | −0.873893 | ||||||||
\(369\) | 2.12067 | + | 3.67310i | 0.110397 | + | 0.191214i | ||||
\(370\) | 4.62327 | + | 8.00775i | 0.240353 | + | 0.416303i | ||||
\(371\) | −5.94303 | + | 4.53164i | −0.308547 | + | 0.235271i | ||||
\(372\) | 1.07894 | 0.0559404 | ||||||||
\(373\) | 1.46852 | − | 2.54355i | 0.0760371 | − | 0.131700i | −0.825500 | − | 0.564403i | \(-0.809107\pi\) |
0.901537 | + | 0.432702i | \(0.142440\pi\) | |||||||
\(374\) | 1.49084 | + | 2.58221i | 0.0770894 | + | 0.133523i | ||||
\(375\) | 2.50094 | + | 4.33175i | 0.129148 | + | 0.223691i | ||||
\(376\) | −3.92126 | − | 6.79182i | −0.202223 | − | 0.350261i | ||||
\(377\) | −28.3612 | + | 11.7605i | −1.46068 | + | 0.605698i | ||||
\(378\) | −10.6970 | − | 4.46894i | −0.550193 | − | 0.229858i | ||||
\(379\) | −5.04254 | + | 8.73394i | −0.259018 | + | 0.448632i | −0.965979 | − | 0.258620i | \(-0.916732\pi\) |
0.706961 | + | 0.707252i | \(0.250066\pi\) | |||||||
\(380\) | −3.32454 | −0.170545 | ||||||||
\(381\) | 7.67069 | 0.392981 | ||||||||
\(382\) | −0.391550 | + | 0.678184i | −0.0200334 | + | 0.0346989i | ||||
\(383\) | −1.84466 | + | 3.19504i | −0.0942576 | + | 0.163259i | −0.909299 | − | 0.416144i | \(-0.863381\pi\) |
0.815041 | + | 0.579403i | \(0.196714\pi\) | |||||||
\(384\) | 3.30767 | + | 5.72905i | 0.168794 | + | 0.292360i | ||||
\(385\) | −5.30477 | + | 4.04496i | −0.270356 | + | 0.206150i | ||||
\(386\) | 2.88584 | + | 4.99842i | 0.146885 | + | 0.254413i | ||||
\(387\) | −14.9978 | −0.762379 | ||||||||
\(388\) | −1.29376 | − | 2.24086i | −0.0656809 | − | 0.113763i | ||||
\(389\) | −11.3333 | + | 19.6299i | −0.574623 | + | 0.995277i | 0.421459 | + | 0.906847i | \(0.361518\pi\) |
−0.996082 | + | 0.0884295i | \(0.971815\pi\) | |||||||
\(390\) | −3.01849 | + | 1.25168i | −0.152847 | + | 0.0633812i | ||||
\(391\) | −3.26027 | −0.164879 | ||||||||
\(392\) | −12.1071 | − | 12.2550i | −0.611499 | − | 0.618973i | ||||
\(393\) | −2.33316 | + | 4.04116i | −0.117693 | + | 0.203849i | ||||
\(394\) | 5.78694 | − | 10.0233i | 0.291542 | − | 0.504965i | ||||
\(395\) | 3.61767 | − | 6.26598i | 0.182025 | − | 0.315276i | ||||
\(396\) | −2.43636 | −0.122432 | ||||||||
\(397\) | 14.5680 | − | 25.2325i | 0.731146 | − | 1.26638i | −0.225248 | − | 0.974302i | \(-0.572319\pi\) |
0.956394 | − | 0.292080i | \(-0.0943475\pi\) | |||||||
\(398\) | 11.6688 | 0.584904 | ||||||||
\(399\) | 7.99084 | + | 3.33838i | 0.400042 | + | 0.167128i | ||||
\(400\) | −8.34241 | + | 14.4495i | −0.417120 | + | 0.722474i | ||||
\(401\) | 8.12052 | 0.405519 | 0.202760 | − | 0.979229i | \(-0.435009\pi\) | ||||
0.202760 | + | 0.979229i | \(0.435009\pi\) | |||||||
\(402\) | −1.42377 | + | 2.46603i | −0.0710110 | + | 0.122995i | ||||
\(403\) | 17.6113 | − | 7.30289i | 0.877283 | − | 0.363783i | ||||
\(404\) | 1.50611 | + | 2.60866i | 0.0749318 | + | 0.129786i | ||||
\(405\) | 4.11250 | − | 7.12305i | 0.204352 | − | 0.353947i | ||||
\(406\) | 27.8532 | − | 21.2384i | 1.38233 | − | 1.05404i | ||||
\(407\) | −5.28144 | − | 9.14773i | −0.261791 | − | 0.453436i | ||||
\(408\) | 0.545614 | + | 0.945031i | 0.0270119 | + | 0.0467860i | ||||
\(409\) | −8.32261 | −0.411527 | −0.205763 | − | 0.978602i | \(-0.565968\pi\) | ||||
−0.205763 | + | 0.978602i | \(0.565968\pi\) | |||||||
\(410\) | −2.84600 | −0.140554 | ||||||||
\(411\) | −0.676295 | − | 1.17138i | −0.0333592 | − | 0.0577798i | ||||
\(412\) | −2.06992 | − | 3.58520i | −0.101978 | − | 0.176630i | ||||
\(413\) | 25.0132 | + | 10.4499i | 1.23082 | + | 0.514206i | ||||
\(414\) | 7.71973 | − | 13.3710i | 0.379404 | − | 0.657147i | ||||
\(415\) | −6.92915 | − | 12.0016i | −0.340139 | − | 0.589138i | ||||
\(416\) | −6.64723 | − | 5.09649i | −0.325907 | − | 0.249876i | ||||
\(417\) | −5.57666 | + | 9.65905i | −0.273090 | + | 0.473006i | ||||
\(418\) | 22.0106 | 1.07657 | ||||||||
\(419\) | 6.50832 | − | 11.2727i | 0.317952 | − | 0.550710i | −0.662108 | − | 0.749408i | \(-0.730338\pi\) |
0.980061 | + | 0.198699i | \(0.0636715\pi\) | |||||||
\(420\) | 0.511499 | − | 0.390024i | 0.0249586 | − | 0.0190312i | ||||
\(421\) | −8.89681 | −0.433604 | −0.216802 | − | 0.976216i | \(-0.569563\pi\) | ||||
−0.216802 | + | 0.976216i | \(0.569563\pi\) | |||||||
\(422\) | −2.94662 | + | 5.10369i | −0.143439 | + | 0.248444i | ||||
\(423\) | 8.79740 | 0.427744 | ||||||||
\(424\) | −3.47587 | + | 6.02038i | −0.168803 | + | 0.292376i | ||||
\(425\) | −1.62242 | + | 2.81011i | −0.0786988 | + | 0.136310i | ||||
\(426\) | −0.962279 | + | 1.66672i | −0.0466225 | + | 0.0807526i | ||||
\(427\) | −17.3960 | + | 13.2647i | −0.841850 | + | 0.641922i | ||||
\(428\) | −0.917539 | −0.0443509 | ||||||||
\(429\) | 3.44821 | − | 1.42987i | 0.166481 | − | 0.0690346i | ||||
\(430\) | 5.03187 | − | 8.71545i | 0.242658 | − | 0.420296i | ||||
\(431\) | 4.47872 | + | 7.75736i | 0.215732 | + | 0.373659i | 0.953499 | − | 0.301397i | \(-0.0974529\pi\) |
−0.737767 | + | 0.675056i | \(0.764120\pi\) | |||||||
\(432\) | −13.1342 | −0.631920 | ||||||||
\(433\) | 0.0864547 | + | 0.149744i | 0.00415475 | + | 0.00719624i | 0.868095 | − | 0.496398i | \(-0.165344\pi\) |
−0.863941 | + | 0.503594i | \(0.832011\pi\) | |||||||
\(434\) | −17.2959 | + | 13.1883i | −0.830229 | + | 0.633060i | ||||
\(435\) | −2.48203 | − | 4.29901i | −0.119004 | − | 0.206122i | ||||
\(436\) | −2.86636 | + | 4.96467i | −0.137274 | + | 0.237765i | ||||
\(437\) | −12.0336 | + | 20.8428i | −0.575644 | + | 0.997045i | ||||
\(438\) | 4.35876 | 0.208270 | ||||||||
\(439\) | 9.54160 | 0.455396 | 0.227698 | − | 0.973732i | \(-0.426880\pi\) | ||||
0.227698 | + | 0.973732i | \(0.426880\pi\) | |||||||
\(440\) | −3.10257 | + | 5.37382i | −0.147909 | + | 0.256187i | ||||
\(441\) | 18.6960 | − | 4.88806i | 0.890286 | − | 0.232765i | ||||
\(442\) | −4.03166 | − | 3.09111i | −0.191767 | − | 0.147029i | ||||
\(443\) | 6.93676 | + | 12.0148i | 0.329576 | + | 0.570842i | 0.982428 | − | 0.186644i | \(-0.0597610\pi\) |
−0.652852 | + | 0.757485i | \(0.726428\pi\) | |||||||
\(444\) | 0.509249 | + | 0.882045i | 0.0241679 | + | 0.0418600i | ||||
\(445\) | −10.5753 | − | 18.3170i | −0.501319 | − | 0.868310i | ||||
\(446\) | −3.78473 | + | 6.55534i | −0.179212 | + | 0.310404i | ||||
\(447\) | 7.05091 | 0.333496 | ||||||||
\(448\) | −13.9362 | − | 5.82223i | −0.658426 | − | 0.275075i | ||||
\(449\) | 10.6456 | + | 18.4388i | 0.502398 | + | 0.870180i | 0.999996 | + | 0.00277167i | \(0.000882252\pi\) |
−0.497598 | + | 0.867408i | \(0.665784\pi\) | |||||||
\(450\) | −7.68318 | − | 13.3077i | −0.362189 | − | 0.627329i | ||||
\(451\) | 3.25116 | 0.153091 | ||||||||
\(452\) | 3.35616 | + | 5.81304i | 0.157861 | + | 0.273423i | ||||
\(453\) | −7.46501 | −0.350737 | ||||||||
\(454\) | 37.5872 | 1.76406 | ||||||||
\(455\) | 5.70919 | − | 9.82842i | 0.267651 | − | 0.460763i | ||||
\(456\) | 8.05539 | 0.377228 | ||||||||
\(457\) | 9.68564 | 0.453075 | 0.226538 | − | 0.974002i | \(-0.427259\pi\) | ||||
0.226538 | + | 0.974002i | \(0.427259\pi\) | |||||||
\(458\) | 16.8779 | + | 29.2334i | 0.788652 | + | 1.36599i | ||||
\(459\) | −2.55432 | −0.119226 | ||||||||
\(460\) | 0.893795 | + | 1.54810i | 0.0416734 | + | 0.0721804i | ||||
\(461\) | 0.687178 | + | 1.19023i | 0.0320051 | + | 0.0554344i | 0.881584 | − | 0.472027i | \(-0.156477\pi\) |
−0.849579 | + | 0.527461i | \(0.823144\pi\) | |||||||
\(462\) | −3.38644 | + | 2.58221i | −0.157552 | + | 0.120135i | ||||
\(463\) | 31.7710 | 1.47653 | 0.738263 | − | 0.674513i | \(-0.235646\pi\) | ||||
0.738263 | + | 0.674513i | \(0.235646\pi\) | |||||||
\(464\) | 19.8417 | − | 34.3669i | 0.921128 | − | 1.59544i | ||||
\(465\) | 1.54126 | + | 2.66954i | 0.0714742 | + | 0.123797i | ||||
\(466\) | −2.95145 | − | 5.11206i | −0.136723 | − | 0.236812i | ||||
\(467\) | 14.5605 | + | 25.2195i | 0.673778 | + | 1.16702i | 0.976824 | + | 0.214042i | \(0.0686629\pi\) |
−0.303046 | + | 0.952976i | \(0.598004\pi\) | |||||||
\(468\) | 3.83456 | − | 1.59007i | 0.177252 | − | 0.0735012i | ||||
\(469\) | −1.26299 | − | 9.82387i | −0.0583197 | − | 0.453624i | ||||
\(470\) | −2.95160 | + | 5.11231i | −0.136147 | + | 0.235813i | ||||
\(471\) | 5.58476 | 0.257332 | ||||||||
\(472\) | 25.2152 | 1.16062 | ||||||||
\(473\) | −5.74820 | + | 9.95618i | −0.264303 | + | 0.457786i | ||||
\(474\) | 2.30943 | − | 4.00006i | 0.106076 | − | 0.183729i | ||||
\(475\) | 11.9766 | + | 20.7441i | 0.549525 | + | 0.951804i | ||||
\(476\) | 0.922738 | + | 0.385498i | 0.0422936 | + | 0.0176693i | ||||
\(477\) | −3.89908 | − | 6.75341i | −0.178527 | − | 0.309217i | ||||
\(478\) | 34.0631 | 1.55801 | ||||||||
\(479\) | −4.86092 | − | 8.41936i | −0.222101 | − | 0.384690i | 0.733345 | − | 0.679857i | \(-0.237958\pi\) |
−0.955446 | + | 0.295167i | \(0.904625\pi\) | |||||||
\(480\) | 0.677132 | − | 1.17283i | 0.0309067 | − | 0.0535320i | ||||
\(481\) | 14.2826 | + | 10.9506i | 0.651229 | + | 0.499303i | ||||
\(482\) | −32.2578 | −1.46930 | ||||||||
\(483\) | −0.593773 | − | 4.61851i | −0.0270176 | − | 0.210149i | ||||
\(484\) | 1.36000 | − | 2.35558i | 0.0618180 | − | 0.107072i | ||||
\(485\) | 3.69627 | − | 6.40213i | 0.167839 | − | 0.290706i | ||||
\(486\) | 9.19791 | − | 15.9313i | 0.417226 | − | 0.722656i | ||||
\(487\) | −17.1133 | −0.775478 | −0.387739 | − | 0.921769i | \(-0.626744\pi\) | ||||
−0.387739 | + | 0.921769i | \(0.626744\pi\) | |||||||
\(488\) | −10.1743 | + | 17.6224i | −0.460568 | + | 0.797728i | ||||
\(489\) | 7.04899 | 0.318766 | ||||||||
\(490\) | −3.43212 | + | 12.5045i | −0.155048 | + | 0.564897i | ||||
\(491\) | 12.8607 | − | 22.2753i | 0.580394 | − | 1.00527i | −0.415038 | − | 0.909804i | \(-0.636232\pi\) |
0.995432 | − | 0.0954681i | \(-0.0304348\pi\) | |||||||
\(492\) | −0.313484 | −0.0141329 | ||||||||
\(493\) | 3.85879 | − | 6.68361i | 0.173791 | − | 0.301015i | ||||
\(494\) | −34.6421 | + | 14.3650i | −1.55862 | + | 0.646313i | ||||
\(495\) | −3.48033 | − | 6.02812i | −0.156429 | − | 0.270944i | ||||
\(496\) | −12.3210 | + | 21.3407i | −0.553231 | + | 0.958224i | ||||
\(497\) | −0.853619 | − | 6.63965i | −0.0382900 | − | 0.297829i | ||||
\(498\) | −4.42341 | − | 7.66157i | −0.198218 | − | 0.343323i | ||||
\(499\) | −2.70198 | − | 4.67996i | −0.120957 | − | 0.209504i | 0.799188 | − | 0.601081i | \(-0.205263\pi\) |
−0.920145 | + | 0.391577i | \(0.871930\pi\) | |||||||
\(500\) | 4.26373 | 0.190680 | ||||||||
\(501\) | −3.80241 | −0.169879 | ||||||||
\(502\) | −10.3059 | − | 17.8503i | −0.459974 | − | 0.796699i | ||||
\(503\) | 6.30847 | + | 10.9266i | 0.281281 | + | 0.487193i | 0.971700 | − | 0.236216i | \(-0.0759074\pi\) |
−0.690420 | + | 0.723409i | \(0.742574\pi\) | |||||||
\(504\) | 14.2936 | − | 10.8991i | 0.636690 | − | 0.485484i | ||||
\(505\) | −4.30294 | + | 7.45292i | −0.191478 | + | 0.331650i | ||||
\(506\) | −5.91749 | − | 10.2494i | −0.263064 | − | 0.455641i | ||||
\(507\) | −4.49389 | + | 4.50089i | −0.199581 | + | 0.199892i | ||||
\(508\) | 3.26935 | − | 5.66268i | 0.145054 | − | 0.251241i | ||||
\(509\) | −1.95876 | −0.0868204 | −0.0434102 | − | 0.999057i | \(-0.513822\pi\) | ||||
−0.0434102 | + | 0.999057i | \(0.513822\pi\) | |||||||
\(510\) | 0.410692 | − | 0.711340i | 0.0181858 | − | 0.0314987i | ||||
\(511\) | −12.0563 | + | 9.19305i | −0.533338 | + | 0.406677i | ||||
\(512\) | −12.1111 | −0.535240 | ||||||||
\(513\) | −9.42794 | + | 16.3297i | −0.416254 | + | 0.720973i | ||||
\(514\) | −20.4769 | −0.903198 | ||||||||
\(515\) | 5.91374 | − | 10.2429i | 0.260590 | − | 0.451356i | ||||
\(516\) | 0.554255 | − | 0.959998i | 0.0243997 | − | 0.0422615i | ||||
\(517\) | 3.37178 | − | 5.84010i | 0.148291 | − | 0.256847i | ||||
\(518\) | −18.9451 | − | 7.91482i | −0.832400 | − | 0.347757i | ||||
\(519\) | −2.98180 | −0.130886 | ||||||||
\(520\) | 1.37591 | − | 10.4826i | 0.0603378 | − | 0.459694i | ||||
\(521\) | 19.5477 | − | 33.8576i | 0.856401 | − | 1.48333i | −0.0189387 | − | 0.999821i | \(-0.506029\pi\) |
0.875339 | − | 0.483509i | \(-0.160638\pi\) | |||||||
\(522\) | 18.2738 | + | 31.6512i | 0.799823 | + | 1.38533i | ||||
\(523\) | −8.71268 | −0.380979 | −0.190489 | − | 0.981689i | \(-0.561007\pi\) | ||||
−0.190489 | + | 0.981689i | \(0.561007\pi\) | |||||||
\(524\) | 1.98885 | + | 3.44479i | 0.0868834 | + | 0.150486i | ||||
\(525\) | −4.27629 | − | 1.78653i | −0.186633 | − | 0.0779707i | ||||
\(526\) | 14.8788 | + | 25.7708i | 0.648746 | + | 1.12366i | ||||
\(527\) | −2.39618 | + | 4.15030i | −0.104379 | + | 0.180790i | ||||
\(528\) | −2.41239 | + | 4.17839i | −0.104986 | + | 0.181841i | ||||
\(529\) | −10.0592 | −0.437357 | ||||||||
\(530\) | 5.23269 | 0.227293 | ||||||||
\(531\) | −14.1427 | + | 24.4958i | −0.613740 | + | 1.06303i | ||||
\(532\) | 5.87028 | − | 4.47616i | 0.254509 | − | 0.194066i | ||||
\(533\) | −5.11694 | + | 2.12184i | −0.221639 | + | 0.0919072i | ||||
\(534\) | −6.75105 | − | 11.6932i | −0.292147 | − | 0.506013i | ||||
\(535\) | −1.31070 | − | 2.27020i | −0.0566665 | − | 0.0981493i | ||||
\(536\) | −4.60652 | − | 7.97873i | −0.198971 | − | 0.344629i | ||||
\(537\) | 4.53286 | − | 7.85114i | 0.195607 | − | 0.338802i | ||||
\(538\) | −44.2809 | −1.90909 | ||||||||
\(539\) | 3.92072 | − | 14.2847i | 0.168877 | − | 0.615285i | ||||
\(540\) | 0.700261 | + | 1.21289i | 0.0301344 | + | 0.0521944i | ||||
\(541\) | 10.7497 | + | 18.6190i | 0.462165 | + | 0.800493i | 0.999069 | − | 0.0431505i | \(-0.0137395\pi\) |
−0.536904 | + | 0.843644i | \(0.680406\pi\) | |||||||
\(542\) | 27.9026 | 1.19852 | ||||||||
\(543\) | −1.37118 | − | 2.37495i | −0.0588428 | − | 0.101919i | ||||
\(544\) | 2.10546 | 0.0902707 | ||||||||
\(545\) | −16.3783 | −0.701569 | ||||||||
\(546\) | 3.64461 | − | 6.27423i | 0.155975 | − | 0.268512i | ||||
\(547\) | −30.2968 | −1.29540 | −0.647699 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647699 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(548\) | −1.15299 | −0.0492531 | ||||||||
\(549\) | −11.4131 | − | 19.7680i | −0.487098 | − | 0.843679i | ||||
\(550\) | −11.7789 | −0.502256 | ||||||||
\(551\) | −28.4854 | − | 49.3381i | −1.21352 | − | 2.10187i | ||||
\(552\) | −2.16567 | − | 3.75105i | −0.0921770 | − | 0.159655i | ||||
\(553\) | 2.04865 | + | 15.9349i | 0.0871176 | + | 0.677621i | ||||
\(554\) | 20.8932 | 0.887668 | ||||||||
\(555\) | −1.45492 | + | 2.51999i | −0.0617579 | + | 0.106968i | ||||
\(556\) | 4.75369 | + | 8.23364i | 0.201601 | + | 0.349184i | ||||
\(557\) | 8.84201 | + | 15.3148i | 0.374648 | + | 0.648909i | 0.990274 | − | 0.139129i | \(-0.0444302\pi\) |
−0.615626 | + | 0.788038i | \(0.711097\pi\) | |||||||
\(558\) | −11.3474 | − | 19.6543i | −0.480374 | − | 0.832033i | ||||
\(559\) | 2.54918 | − | 19.4214i | 0.107819 | − | 0.821437i | ||||
\(560\) | 1.87330 | + | 14.5710i | 0.0791616 | + | 0.615737i | ||||
\(561\) | −0.469159 | + | 0.812606i | −0.0198079 | + | 0.0343083i | ||||
\(562\) | −46.5676 | −1.96433 | ||||||||
\(563\) | −41.7390 | −1.75909 | −0.879545 | − | 0.475816i | \(-0.842153\pi\) | ||||
−0.879545 | + | 0.475816i | \(0.842153\pi\) | |||||||
\(564\) | −0.325115 | + | 0.563116i | −0.0136898 | + | 0.0237115i | ||||
\(565\) | −9.58852 | + | 16.6078i | −0.403392 | + | 0.698696i | ||||
\(566\) | 7.68887 | + | 13.3175i | 0.323187 | + | 0.559777i | ||||
\(567\) | 2.32887 | + | 18.1145i | 0.0978035 | + | 0.760738i | ||||
\(568\) | −3.11340 | − | 5.39257i | −0.130636 | − | 0.226267i | ||||
\(569\) | 5.46775 | 0.229220 | 0.114610 | − | 0.993411i | \(-0.463438\pi\) | ||||
0.114610 | + | 0.993411i | \(0.463438\pi\) | |||||||
\(570\) | −3.03171 | − | 5.25108i | −0.126984 | − | 0.219943i | ||||
\(571\) | −4.67621 | + | 8.09944i | −0.195693 | + | 0.338951i | −0.947128 | − | 0.320857i | \(-0.896029\pi\) |
0.751434 | + | 0.659808i | \(0.229362\pi\) | |||||||
\(572\) | 0.414111 | − | 3.15498i | 0.0173149 | − | 0.131916i | ||||
\(573\) | −0.246437 | −0.0102951 | ||||||||
\(574\) | 5.02529 | − | 3.83185i | 0.209752 | − | 0.159938i | ||||
\(575\) | 6.43976 | − | 11.1540i | 0.268557 | − | 0.465154i | ||||
\(576\) | 7.87968 | − | 13.6480i | 0.328320 | − | 0.568667i | ||||
\(577\) | 1.68462 | − | 2.91786i | 0.0701318 | − | 0.121472i | −0.828827 | − | 0.559505i | \(-0.810991\pi\) |
0.898959 | + | 0.438033i | \(0.144325\pi\) | |||||||
\(578\) | −25.1527 | −1.04621 | ||||||||
\(579\) | −0.908159 | + | 1.57298i | −0.0377418 | + | 0.0653707i | ||||
\(580\) | −4.23151 | −0.175704 | ||||||||
\(581\) | 28.3941 | + | 11.8624i | 1.17798 | + | 0.492134i | ||||
\(582\) | 2.35961 | − | 4.08697i | 0.0978091 | − | 0.169410i | ||||
\(583\) | −5.97761 | −0.247567 | ||||||||
\(584\) | −7.05128 | + | 12.2132i | −0.291784 | + | 0.505385i | ||||
\(585\) | 9.41185 | + | 7.21614i | 0.389132 | + | 0.298351i | ||||
\(586\) | −6.14924 | − | 10.6508i | −0.254023 | − | 0.439980i | ||||
\(587\) | 6.57639 | − | 11.3906i | 0.271437 | − | 0.470142i | −0.697793 | − | 0.716299i | \(-0.745835\pi\) |
0.969230 | + | 0.246157i | \(0.0791679\pi\) | |||||||
\(588\) | −0.378045 | + | 1.37736i | −0.0155903 | + | 0.0568014i | ||||
\(589\) | 17.6884 | + | 30.6373i | 0.728840 | + | 1.26239i | ||||
\(590\) | −9.48995 | − | 16.4371i | −0.390695 | − | 0.676704i | ||||
\(591\) | 3.64224 | 0.149822 | ||||||||
\(592\) | −23.2616 | −0.956048 | ||||||||
\(593\) | −19.2958 | − | 33.4213i | −0.792384 | − | 1.37245i | −0.924487 | − | 0.381214i | \(-0.875506\pi\) |
0.132102 | − | 0.991236i | \(-0.457827\pi\) | |||||||
\(594\) | −4.63617 | − | 8.03008i | −0.190224 | − | 0.329478i | ||||
\(595\) | 0.364317 | + | 2.83374i | 0.0149356 | + | 0.116172i | ||||
\(596\) | 3.00519 | − | 5.20515i | 0.123097 | − | 0.213211i | ||||
\(597\) | 1.83605 | + | 3.18014i | 0.0751447 | + | 0.130154i | ||||
\(598\) | 16.0026 | + | 12.2694i | 0.654396 | + | 0.501731i | ||||
\(599\) | −9.20762 | + | 15.9481i | −0.376213 | + | 0.651620i | −0.990508 | − | 0.137457i | \(-0.956107\pi\) |
0.614295 | + | 0.789077i | \(0.289441\pi\) | |||||||
\(600\) | −4.31084 | −0.175989 | ||||||||
\(601\) | 20.7018 | − | 35.8566i | 0.844445 | − | 1.46262i | −0.0416571 | − | 0.999132i | \(-0.513264\pi\) |
0.886102 | − | 0.463490i | \(-0.153403\pi\) | |||||||
\(602\) | 2.84950 | + | 22.1641i | 0.116137 | + | 0.903341i | ||||
\(603\) | 10.3348 | 0.420865 | ||||||||
\(604\) | −3.18169 | + | 5.51085i | −0.129461 | + | 0.224233i | ||||
\(605\) | 7.77099 | 0.315936 | ||||||||
\(606\) | −2.74690 | + | 4.75777i | −0.111585 | + | 0.193271i | ||||
\(607\) | −6.15255 | + | 10.6565i | −0.249724 | + | 0.432535i | −0.963449 | − | 0.267891i | \(-0.913673\pi\) |
0.713725 | + | 0.700426i | \(0.247007\pi\) | |||||||
\(608\) | 7.77119 | − | 13.4601i | 0.315163 | − | 0.545879i | ||||
\(609\) | 10.1708 | + | 4.24912i | 0.412142 | + | 0.172183i | ||||
\(610\) | 15.3167 | 0.620155 | ||||||||
\(611\) | −1.49530 | + | 11.3922i | −0.0604934 | + | 0.460880i | ||||
\(612\) | −0.521725 | + | 0.903654i | −0.0210895 | + | 0.0365280i | ||||
\(613\) | −13.1112 | − | 22.7093i | −0.529556 | − | 0.917219i | −0.999406 | − | 0.0344720i | \(-0.989025\pi\) |
0.469849 | − | 0.882747i | \(-0.344308\pi\) | |||||||
\(614\) | 1.97816 | 0.0798319 | ||||||||
\(615\) | −0.447810 | − | 0.775630i | −0.0180575 | − | 0.0312764i | ||||
\(616\) | −1.75696 | − | 13.6661i | −0.0707900 | − | 0.550621i | ||||
\(617\) | 9.41259 | + | 16.3031i | 0.378936 | + | 0.656337i | 0.990908 | − | 0.134543i | \(-0.0429565\pi\) |
−0.611971 | + | 0.790880i | \(0.709623\pi\) | |||||||
\(618\) | 3.77519 | − | 6.53882i | 0.151860 | − | 0.263030i | ||||
\(619\) | 7.90415 | − | 13.6904i | 0.317695 | − | 0.550263i | −0.662312 | − | 0.749228i | \(-0.730425\pi\) |
0.980007 | + | 0.198965i | \(0.0637580\pi\) | |||||||
\(620\) | 2.62762 | 0.105528 | ||||||||
\(621\) | 10.1387 | 0.406852 | ||||||||
\(622\) | −19.2497 | + | 33.3415i | −0.771843 | + | 1.33687i | ||||
\(623\) | 43.3353 | + | 18.1045i | 1.73619 | + | 0.725340i | ||||
\(624\) | 1.06984 | − | 8.15073i | 0.0428277 | − | 0.326290i | ||||
\(625\) | −2.86003 | − | 4.95371i | −0.114401 | − | 0.198149i | ||||
\(626\) | −1.84737 | − | 3.19973i | −0.0738356 | − | 0.127887i | ||||
\(627\) | 3.46331 | + | 5.99862i | 0.138311 | + | 0.239562i | ||||
\(628\) | 2.38030 | − | 4.12280i | 0.0949843 | − | 0.164518i | ||||
\(629\) | −4.52389 | −0.180379 | ||||||||
\(630\) | −12.4843 | − | 5.21566i | −0.497388 | − | 0.207797i | ||||
\(631\) | 8.33817 | + | 14.4421i | 0.331937 | + | 0.574933i | 0.982892 | − | 0.184184i | \(-0.0589644\pi\) |
−0.650954 | + | 0.759117i | \(0.725631\pi\) | |||||||
\(632\) | 7.47206 | + | 12.9420i | 0.297222 | + | 0.514804i | ||||
\(633\) | −1.85457 | −0.0737125 | ||||||||
\(634\) | 15.3755 | + | 26.6312i | 0.610640 | + | 1.05766i | ||||
\(635\) | 18.6810 | 0.741333 | ||||||||
\(636\) | 0.576375 | 0.0228548 | ||||||||
\(637\) | 3.15202 | + | 25.0413i | 0.124888 | + | 0.992171i | ||||
\(638\) | 28.0152 | 1.10913 | ||||||||
\(639\) | 6.98497 | 0.276321 | ||||||||
\(640\) | 8.05542 | + | 13.9524i | 0.318418 | + | 0.551517i | ||||
\(641\) | 49.2464 | 1.94512 | 0.972559 | − | 0.232658i | \(-0.0747422\pi\) | ||||
0.972559 | + | 0.232658i | \(0.0747422\pi\) | |||||||
\(642\) | −0.836720 | − | 1.44924i | −0.0330227 | − | 0.0571970i | ||||
\(643\) | −21.4355 | − | 37.1275i | −0.845335 | − | 1.46416i | −0.885330 | − | 0.464964i | \(-0.846067\pi\) |
0.0399940 | − | 0.999200i | \(-0.487266\pi\) | |||||||
\(644\) | −3.66256 | − | 1.53013i | −0.144325 | − | 0.0602957i | ||||
\(645\) | 3.16700 | 0.124701 | ||||||||
\(646\) | 4.71336 | − | 8.16378i | 0.185445 | − | 0.321200i | ||||
\(647\) | −2.12929 | − | 3.68804i | −0.0837112 | − | 0.144992i | 0.821130 | − | 0.570741i | \(-0.193344\pi\) |
−0.904841 | + | 0.425749i | \(0.860011\pi\) | |||||||
\(648\) | 8.49410 | + | 14.7122i | 0.333680 | + | 0.577950i | ||||
\(649\) | 10.8409 | + | 18.7771i | 0.425544 | + | 0.737064i | ||||
\(650\) | 18.5387 | − | 7.68744i | 0.727148 | − | 0.301526i | ||||
\(651\) | −6.31572 | − | 2.63856i | −0.247533 | − | 0.103413i | ||||
\(652\) | 3.00437 | − | 5.20373i | 0.117660 | − | 0.203794i | ||||
\(653\) | −2.09552 | −0.0820040 | −0.0410020 | − | 0.999159i | \(-0.513055\pi\) | ||||
−0.0410020 | + | 0.999159i | \(0.513055\pi\) | |||||||
\(654\) | −10.4555 | −0.408843 | ||||||||
\(655\) | −5.68213 | + | 9.84174i | −0.222019 | + | 0.384549i | ||||
\(656\) | 3.57986 | − | 6.20049i | 0.139770 | − | 0.242089i | ||||
\(657\) | −7.90982 | − | 13.7002i | −0.308592 | − | 0.534496i | ||||
\(658\) | −1.67146 | − | 13.0010i | −0.0651604 | − | 0.506833i | ||||
\(659\) | −12.7259 | − | 22.0419i | −0.495732 | − | 0.858632i | 0.504256 | − | 0.863554i | \(-0.331767\pi\) |
−0.999988 | + | 0.00492170i | \(0.998433\pi\) | |||||||
\(660\) | 0.514475 | 0.0200259 | ||||||||
\(661\) | −13.9054 | − | 24.0848i | −0.540857 | − | 0.936792i | −0.998855 | − | 0.0478387i | \(-0.984767\pi\) |
0.457998 | − | 0.888953i | \(-0.348567\pi\) | |||||||
\(662\) | −3.05319 | + | 5.28829i | −0.118666 | + | 0.205535i | ||||
\(663\) | 0.208060 | − | 1.58514i | 0.00808038 | − | 0.0615618i | ||||
\(664\) | 28.6234 | 1.11080 | ||||||||
\(665\) | 19.4607 | + | 8.13022i | 0.754653 | + | 0.315276i | ||||
\(666\) | 10.7117 | − | 18.5533i | 0.415072 | − | 0.718925i | ||||
\(667\) | −15.3164 | + | 26.5288i | −0.593055 | + | 1.02720i | ||||
\(668\) | −1.62064 | + | 2.80703i | −0.0627044 | + | 0.108607i | ||||
\(669\) | −2.38207 | −0.0920960 | ||||||||
\(670\) | −3.46740 | + | 6.00572i | −0.133957 | + | 0.232021i | ||||
\(671\) | −17.4972 | −0.675472 | ||||||||
\(672\) | 0.383454 | + | 2.98260i | 0.0147921 | + | 0.115056i | ||||
\(673\) | −7.76033 | + | 13.4413i | −0.299139 | + | 0.518124i | −0.975939 | − | 0.218043i | \(-0.930033\pi\) |
0.676800 | + | 0.736167i | \(0.263366\pi\) | |||||||
\(674\) | −11.1020 | −0.427633 | ||||||||
\(675\) | 5.04536 | − | 8.73881i | 0.194196 | − | 0.336357i | ||||
\(676\) | 1.40731 | + | 5.23583i | 0.0541272 | + | 0.201378i | ||||
\(677\) | −17.2813 | − | 29.9321i | −0.664175 | − | 1.15038i | −0.979508 | − | 0.201403i | \(-0.935450\pi\) |
0.315334 | − | 0.948981i | \(-0.397884\pi\) | |||||||
\(678\) | −6.12109 | + | 10.6020i | −0.235079 | + | 0.407169i | ||||
\(679\) | 2.09317 | + | 16.2811i | 0.0803284 | + | 0.624813i | ||||
\(680\) | 1.32877 | + | 2.30150i | 0.0509562 | + | 0.0882587i | ||||
\(681\) | 5.91425 | + | 10.2438i | 0.226634 | + | 0.392542i | ||||
\(682\) | −17.3965 | −0.666147 | ||||||||
\(683\) | 47.0064 | 1.79865 | 0.899325 | − | 0.437281i | \(-0.144058\pi\) | ||||
0.899325 | + | 0.437281i | \(0.144058\pi\) | |||||||
\(684\) | 3.85135 | + | 6.67073i | 0.147260 | + | 0.255062i | ||||
\(685\) | −1.64703 | − | 2.85275i | −0.0629299 | − | 0.108998i | ||||
\(686\) | −10.7758 | − | 26.7007i | −0.411424 | − | 1.01944i | ||||
\(687\) | −5.31138 | + | 9.19958i | −0.202642 | + | 0.350986i | ||||
\(688\) | 12.6587 | + | 21.9255i | 0.482609 | + | 0.835904i | ||||
\(689\) | 9.40807 | − | 3.90124i | 0.358419 | − | 0.148625i | ||||
\(690\) | −1.63013 | + | 2.82348i | −0.0620582 | + | 0.107488i | ||||
\(691\) | 19.0060 | 0.723023 | 0.361512 | − | 0.932368i | \(-0.382261\pi\) | ||||
0.361512 | + | 0.932368i | \(0.382261\pi\) | |||||||
\(692\) | −1.27088 | + | 2.20123i | −0.0483117 | + | 0.0836784i | ||||
\(693\) | 14.2616 | + | 5.95816i | 0.541754 | + | 0.226332i | ||||
\(694\) | 15.6556 | 0.594280 | ||||||||
\(695\) | −13.5813 | + | 23.5234i | −0.515166 | + | 0.892294i | ||||
\(696\) | 10.2530 | 0.388638 | ||||||||
\(697\) | 0.696205 | − | 1.20586i | 0.0263706 | − | 0.0456753i | ||||
\(698\) | 4.88822 | − | 8.46665i | 0.185022 | − | 0.320467i | ||||
\(699\) | 0.928805 | − | 1.60874i | 0.0351306 | − | 0.0608480i | ||||
\(700\) | −3.14147 | + | 2.39541i | −0.118737 | + | 0.0905382i | ||||
\(701\) | −45.4648 | −1.71718 | −0.858591 | − | 0.512662i | \(-0.828659\pi\) | ||||
−0.858591 | + | 0.512662i | \(0.828659\pi\) | |||||||
\(702\) | 12.5376 | + | 9.61266i | 0.473200 | + | 0.362807i | ||||
\(703\) | −16.6976 | + | 28.9210i | −0.629760 | + | 1.09078i | ||||
\(704\) | −6.04010 | − | 10.4618i | −0.227645 | − | 0.394293i | ||||
\(705\) | −1.85770 | −0.0699651 | ||||||||
\(706\) | −26.5597 | − | 46.0027i | −0.999586 | − | 1.73133i | ||||
\(707\) | −2.43672 | − | 18.9534i | −0.0916423 | − | 0.712815i | ||||
\(708\) | −1.04531 | − | 1.81053i | −0.0392851 | − | 0.0680438i | ||||
\(709\) | 4.89390 | − | 8.47648i | 0.183794 | − | 0.318341i | −0.759375 | − | 0.650653i | \(-0.774495\pi\) |
0.943170 | + | 0.332312i | \(0.107829\pi\) | |||||||
\(710\) | −2.34351 | + | 4.05908i | −0.0879504 | + | 0.152334i | ||||
\(711\) | −16.7637 | −0.628687 | ||||||||
\(712\) | 43.6854 | 1.63718 | ||||||||
\(713\) | 9.51099 | − | 16.4735i | 0.356189 | − | 0.616938i | ||||
\(714\) | 0.232572 | + | 1.80900i | 0.00870377 | + | 0.0677000i | ||||
\(715\) | 8.39768 | − | 3.48226i | 0.314055 | − | 0.130229i | ||||
\(716\) | −3.86393 | − | 6.69252i | −0.144402 | − | 0.250111i | ||||
\(717\) | 5.35974 | + | 9.28334i | 0.200163 | + | 0.346693i | ||||
\(718\) | −14.5259 | − | 25.1595i | −0.542100 | − | 0.938945i | ||||
\(719\) | 13.9201 | − | 24.1104i | 0.519133 | − | 0.899165i | −0.480620 | − | 0.876929i | \(-0.659588\pi\) |
0.999753 | − | 0.0222358i | \(-0.00707846\pi\) | |||||||
\(720\) | −15.3288 | −0.571271 | ||||||||
\(721\) | 3.34890 | + | 26.0485i | 0.124720 | + | 0.970098i | ||||
\(722\) | −20.0243 | − | 34.6830i | −0.745226 | − | 1.29077i | ||||
\(723\) | −5.07568 | − | 8.79134i | −0.188767 | − | 0.326953i | ||||
\(724\) | −2.33766 | −0.0868783 | ||||||||
\(725\) | 15.2439 | + | 26.4033i | 0.566145 | + | 0.980592i | ||||
\(726\) | 4.96082 | 0.184113 | ||||||||
\(727\) | −14.5650 | −0.540186 | −0.270093 | − | 0.962834i | \(-0.587055\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587055\pi\) | |||||||
\(728\) | 11.6843 | + | 20.3621i | 0.433049 | + | 0.754670i | ||||
\(729\) | −14.9199 | −0.552589 | ||||||||
\(730\) | 10.6152 | 0.392887 | ||||||||
\(731\) | 2.46185 | + | 4.26405i | 0.0910547 | + | 0.157711i | ||||
\(732\) | 1.68712 | 0.0623577 | ||||||||
\(733\) | −8.83030 | − | 15.2945i | −0.326155 | − | 0.564916i | 0.655591 | − | 0.755116i | \(-0.272420\pi\) |
−0.981745 | + | 0.190200i | \(0.939086\pi\) | |||||||
\(734\) | 24.1451 | + | 41.8206i | 0.891213 | + | 1.54363i | ||||
\(735\) | −3.94794 | + | 1.03219i | −0.145622 | + | 0.0380727i | ||||
\(736\) | −8.35705 | −0.308045 | ||||||||
\(737\) | 3.96102 | − | 6.86069i | 0.145906 | − | 0.252717i | ||||
\(738\) | 3.29697 | + | 5.71052i | 0.121363 | + | 0.210207i | ||||
\(739\) | −4.48279 | − | 7.76443i | −0.164902 | − | 0.285619i | 0.771718 | − | 0.635964i | \(-0.219398\pi\) |
−0.936621 | + | 0.350345i | \(0.886064\pi\) | |||||||
\(740\) | 1.24021 | + | 2.14811i | 0.0455911 | + | 0.0789661i | ||||
\(741\) | −9.36579 | − | 7.18084i | −0.344061 | − | 0.263795i | ||||
\(742\) | −9.23955 | + | 7.04528i | −0.339195 | + | 0.258640i | ||||
\(743\) | 13.1839 | − | 22.8352i | 0.483671 | − | 0.837743i | −0.516153 | − | 0.856497i | \(-0.672636\pi\) |
0.999824 | + | 0.0187532i | \(0.00596968\pi\) | |||||||
\(744\) | −6.36674 | −0.233416 | ||||||||
\(745\) | 17.1716 | 0.629119 | ||||||||
\(746\) | 2.28309 | − | 3.95442i | 0.0835898 | − | 0.144782i | ||||
\(747\) | −16.0543 | + | 27.8068i | −0.587395 | + | 1.01740i | ||||
\(748\) | 0.399923 | + | 0.692688i | 0.0146226 | + | 0.0253272i | ||||
\(749\) | 5.37095 | + | 2.24385i | 0.196250 | + | 0.0819887i | ||||
\(750\) | 3.88818 | + | 6.73452i | 0.141976 | + | 0.245910i | ||||
\(751\) | −20.2876 | −0.740305 | −0.370152 | − | 0.928971i | \(-0.620695\pi\) | ||||
−0.370152 | + | 0.928971i | \(0.620695\pi\) | |||||||
\(752\) | −7.42536 | − | 12.8611i | −0.270775 | − | 0.468996i | ||||
\(753\) | 3.24321 | − | 5.61740i | 0.118189 | − | 0.204709i | ||||
\(754\) | −44.0928 | + | 18.2839i | −1.60576 | + | 0.665861i | ||||
\(755\) | −18.1801 | −0.661642 | ||||||||
\(756\) | −2.86951 | − | 1.19881i | −0.104363 | − | 0.0436004i | ||||
\(757\) | −12.4992 | + | 21.6493i | −0.454292 | + | 0.786857i | −0.998647 | − | 0.0519981i | \(-0.983441\pi\) |
0.544355 | + | 0.838855i | \(0.316774\pi\) | |||||||
\(758\) | −7.83957 | + | 13.5785i | −0.284746 | + | 0.493195i | ||||
\(759\) | 1.86220 | − | 3.22543i | 0.0675936 | − | 0.117076i | ||||
\(760\) | 19.6179 | 0.711616 | ||||||||
\(761\) | −10.0711 | + | 17.4436i | −0.365077 | + | 0.632332i | −0.988789 | − | 0.149323i | \(-0.952291\pi\) |
0.623712 | + | 0.781655i | \(0.285624\pi\) | |||||||
\(762\) | 11.9255 | 0.432016 | ||||||||
\(763\) | 28.9198 | − | 22.0517i | 1.04697 | − | 0.798326i | ||||
\(764\) | −0.105035 | + | 0.181926i | −0.00380003 | + | 0.00658184i | ||||
\(765\) | −2.98112 | −0.107783 | ||||||||
\(766\) | −2.86786 | + | 4.96729i | −0.103620 | + | 0.179475i | ||||
\(767\) | −29.3171 | − | 22.4777i | −1.05858 | − | 0.811622i | ||||
\(768\) | 2.34945 | + | 4.06936i | 0.0847784 | + | 0.146840i | ||||
\(769\) | −4.33610 | + | 7.51034i | −0.156364 | + | 0.270830i | −0.933555 | − | 0.358435i | \(-0.883311\pi\) |
0.777191 | + | 0.629265i | \(0.216644\pi\) | |||||||
\(770\) | −8.24726 | + | 6.28864i | −0.297211 | + | 0.226627i | ||||
\(771\) | −3.22199 | − | 5.58065i | −0.116037 | − | 0.200982i | ||||
\(772\) | 0.774139 | + | 1.34085i | 0.0278619 | + | 0.0482582i | ||||
\(773\) | 2.34567 | 0.0843679 | 0.0421839 | − | 0.999110i | \(-0.486568\pi\) | ||||
0.0421839 | + | 0.999110i | \(0.486568\pi\) | |||||||
\(774\) | −23.3168 | −0.838106 | ||||||||
\(775\) | −9.46596 | − | 16.3955i | −0.340027 | − | 0.588945i | ||||
\(776\) | 7.63441 | + | 13.2232i | 0.274059 | + | 0.474685i | ||||
\(777\) | −0.823909 | − | 6.40855i | −0.0295576 | − | 0.229906i | ||||
\(778\) | −17.6198 | + | 30.5184i | −0.631701 | + | 1.09414i | ||||
\(779\) | −5.13935 | − | 8.90161i | −0.184136 | − | 0.318933i | ||||
\(780\) | −0.809724 | + | 0.335768i | −0.0289928 | + | 0.0120224i | ||||
\(781\) | 2.67713 | − | 4.63693i | 0.0957953 | − | 0.165922i | ||||
\(782\) | −5.06870 | −0.181256 | ||||||||
\(783\) | −12.0000 | + | 20.7845i | −0.428844 | + | 0.742779i | ||||
\(784\) | −22.9261 | − | 23.2064i | −0.818790 | − | 0.828798i | ||||
\(785\) | 13.6010 | 0.485440 | ||||||||
\(786\) | −3.62734 | + | 6.28274i | −0.129383 | + | 0.224098i | ||||
\(787\) | −34.1166 | −1.21613 | −0.608063 | − | 0.793889i | \(-0.708053\pi\) | ||||
−0.608063 | + | 0.793889i | \(0.708053\pi\) | |||||||
\(788\) | 1.55237 | − | 2.68878i | 0.0553009 | − | 0.0957840i | ||||
\(789\) | −4.68228 | + | 8.10994i | −0.166693 | + | 0.288721i | ||||
\(790\) | 5.62434 | − | 9.74164i | 0.200105 | − | 0.346592i | ||||
\(791\) | −5.42990 | − | 42.2350i | −0.193065 | − | 1.50170i | ||||
\(792\) | 14.3768 | 0.510858 | ||||||||
\(793\) | 27.5386 | − | 11.4194i | 0.977923 | − | 0.405515i | ||||
\(794\) | 22.6486 | − | 39.2286i | 0.803770 | − | 1.39217i | ||||
\(795\) | 0.823349 | + | 1.42608i | 0.0292012 | + | 0.0505779i | ||||
\(796\) | 3.13020 | 0.110947 | ||||||||
\(797\) | 17.0422 | + | 29.5180i | 0.603666 | + | 1.04558i | 0.992261 | + | 0.124172i | \(0.0396275\pi\) |
−0.388594 | + | 0.921409i | \(0.627039\pi\) | |||||||
\(798\) | 12.4232 | + | 5.19014i | 0.439778 | + | 0.183729i | ||||
\(799\) | −1.44407 | − | 2.50121i | −0.0510876 | − | 0.0884863i | ||||
\(800\) | −4.15875 | + | 7.20316i | −0.147034 | + | 0.254670i | ||||
\(801\) | −24.5022 | + | 42.4390i | −0.865742 | + | 1.49951i | ||||
\(802\) | 12.6249 | 0.445800 | ||||||||
\(803\) | −12.1264 | −0.427932 | ||||||||
\(804\) | −0.381931 | + | 0.661524i | −0.0134697 | + | 0.0233302i | ||||
\(805\) | −1.44606 | − | 11.2478i | −0.0509670 | − | 0.396433i | ||||
\(806\) | 27.3801 | − | 11.3537i | 0.964423 | − | 0.399917i | ||||
\(807\) | −6.96748 | − | 12.0680i | −0.245267 | − | 0.424815i | ||||
\(808\) | −8.88745 | − | 15.3935i | −0.312659 | − | 0.541542i | ||||
\(809\) | 13.2603 | + | 22.9675i | 0.466206 | + | 0.807493i | 0.999255 | − | 0.0385914i | \(-0.0122871\pi\) |
−0.533049 | + | 0.846085i | \(0.678954\pi\) | |||||||
\(810\) | 6.39365 | − | 11.0741i | 0.224650 | − | 0.389105i | ||||
\(811\) | 52.5463 | 1.84515 | 0.922575 | − | 0.385818i | \(-0.126081\pi\) | ||||
0.922575 | + | 0.385818i | \(0.126081\pi\) | |||||||
\(812\) | 7.47173 | − | 5.69729i | 0.262206 | − | 0.199936i | ||||
\(813\) | 4.39040 | + | 7.60439i | 0.153978 | + | 0.266698i | ||||
\(814\) | −8.21099 | − | 14.2219i | −0.287795 | − | 0.498476i | ||||
\(815\) | 17.1669 | 0.601331 | ||||||||
\(816\) | 1.03318 | + | 1.78953i | 0.0361686 | + | 0.0626459i | ||||
\(817\) | 36.3465 | 1.27160 | ||||||||
\(818\) | −12.9391 | −0.452403 | ||||||||
\(819\) | −26.3347 | − | 0.0697311i | −0.920208 | − | 0.00243660i | ||||
\(820\) | −0.763451 | −0.0266609 | ||||||||
\(821\) | −30.7546 | −1.07334 | −0.536671 | − | 0.843791i | \(-0.680318\pi\) | ||||
−0.536671 | + | 0.843791i | \(0.680318\pi\) | |||||||
\(822\) | −1.05143 | − | 1.82113i | −0.0366728 | − | 0.0635191i | ||||
\(823\) | −29.7038 | −1.03541 | −0.517705 | − | 0.855559i | \(-0.673213\pi\) | ||||
−0.517705 | + | 0.855559i | \(0.673213\pi\) | |||||||
\(824\) | 12.2144 | + | 21.1560i | 0.425510 | + | 0.737006i | ||||
\(825\) | −1.85339 | − | 3.21016i | −0.0645266 | − | 0.111763i | ||||
\(826\) | 38.8876 | + | 16.2463i | 1.35307 | + | 0.565282i | ||||
\(827\) | 14.8351 | 0.515866 | 0.257933 | − | 0.966163i | \(-0.416959\pi\) | ||||
0.257933 | + | 0.966163i | \(0.416959\pi\) | |||||||
\(828\) | 2.07085 | − | 3.58681i | 0.0719670 | − | 0.124650i | ||||
\(829\) | −7.29244 | − | 12.6309i | −0.253277 | − | 0.438688i | 0.711149 | − | 0.703041i | \(-0.248175\pi\) |
−0.964426 | + | 0.264353i | \(0.914842\pi\) | |||||||
\(830\) | −10.7727 | − | 18.6588i | −0.373925 | − | 0.647657i | ||||
\(831\) | 3.28749 | + | 5.69411i | 0.114042 | + | 0.197526i | ||||
\(832\) | 16.3342 | + | 12.5236i | 0.566287 | + | 0.434177i | ||||
\(833\) | −4.45864 | − | 4.51314i | −0.154483 | − | 0.156371i | ||||
\(834\) | −8.66995 | + | 15.0168i | −0.300216 | + | 0.519989i | ||||
\(835\) | −9.26030 | −0.320466 | ||||||||
\(836\) | 5.90443 | 0.204209 | ||||||||
\(837\) | 7.45157 | − | 12.9065i | 0.257564 | − | 0.446114i | ||||
\(838\) | 10.1184 | − | 17.5256i | 0.349534 | − | 0.605411i | ||||
\(839\) | −18.4043 | − | 31.8772i | −0.635386 | − | 1.10052i | −0.986433 | − | 0.164164i | \(-0.947508\pi\) |
0.351047 | − | 0.936358i | \(-0.385826\pi\) | |||||||
\(840\) | −3.01832 | + | 2.30150i | −0.104142 | + | 0.0794095i | ||||
\(841\) | −21.7564 | − | 37.6832i | −0.750221 | − | 1.29942i | ||||
\(842\) | −13.8318 | −0.476674 | ||||||||
\(843\) | −7.32728 | − | 12.6912i | −0.252365 | − | 0.437109i | ||||
\(844\) | −0.790442 | + | 1.36909i | −0.0272082 | + | 0.0471259i | ||||
\(845\) | −10.9443 | + | 10.9614i | −0.376496 | + | 0.377082i | ||||
\(846\) | 13.6772 | 0.470232 | ||||||||
\(847\) | −13.7215 | + | 10.4628i | −0.471477 | + | 0.359508i | ||||
\(848\) | −6.58196 | + | 11.4003i | −0.226025 | + | 0.391488i | ||||
\(849\) | −2.41965 | + | 4.19095i | −0.0830421 | + | 0.143833i | ||||
\(850\) | −2.52235 | + | 4.36884i | −0.0865160 | + | 0.149850i | ||||
\(851\) | 17.9564 | 0.615537 | ||||||||
\(852\) | −0.258135 | + | 0.447103i | −0.00884357 | + | 0.0153175i | ||||
\(853\) | −4.10728 | −0.140630 | −0.0703152 | − | 0.997525i | \(-0.522401\pi\) | ||||
−0.0703152 | + | 0.997525i | \(0.522401\pi\) | |||||||
\(854\) | −27.0453 | + | 20.6224i | −0.925471 | + | 0.705684i | ||||
\(855\) | −11.0033 | + | 19.0582i | −0.376303 | + | 0.651777i | ||||
\(856\) | 5.41433 | 0.185058 | ||||||||
\(857\) | 19.1656 | − | 33.1958i | 0.654684 | − | 1.13395i | −0.327288 | − | 0.944925i | \(-0.606135\pi\) |
0.981973 | − | 0.189022i | \(-0.0605318\pi\) | |||||||
\(858\) | 5.36088 | − | 2.22300i | 0.183017 | − | 0.0758918i | ||||
\(859\) | 19.7185 | + | 34.1534i | 0.672785 | + | 1.16530i | 0.977111 | + | 0.212730i | \(0.0682356\pi\) |
−0.304326 | + | 0.952568i | \(0.598431\pi\) | |||||||
\(860\) | 1.34982 | − | 2.33796i | 0.0460284 | − | 0.0797236i | ||||
\(861\) | 1.83502 | + | 0.766629i | 0.0625374 | + | 0.0261267i | ||||
\(862\) | 6.96300 | + | 12.0603i | 0.237161 | + | 0.410775i | ||||
\(863\) | 19.3220 | + | 33.4667i | 0.657728 | + | 1.13922i | 0.981202 | + | 0.192982i | \(0.0618159\pi\) |
−0.323474 | + | 0.946237i | \(0.604851\pi\) | |||||||
\(864\) | −6.54750 | −0.222750 | ||||||||
\(865\) | −7.26180 | −0.246909 | ||||||||
\(866\) | 0.134410 | + | 0.232805i | 0.00456744 | + | 0.00791104i | ||||
\(867\) | −3.95771 | − | 6.85495i | −0.134411 | − | 0.232806i | ||||
\(868\) | −4.63969 | + | 3.53783i | −0.157481 | + | 0.120082i | ||||
\(869\) | −6.42502 | + | 11.1285i | −0.217954 | + | 0.377507i | ||||
\(870\) | −3.85879 | − | 6.68361i | −0.130825 | − | 0.226596i | ||||
\(871\) | −1.75661 | + | 13.3831i | −0.0595206 | + | 0.453468i | ||||
\(872\) | 16.9142 | − | 29.2962i | 0.572786 | − | 0.992094i | ||||
\(873\) | −17.1279 | −0.579692 | ||||||||
\(874\) | −18.7084 | + | 32.4040i | −0.632822 | + | 1.09608i | ||||
\(875\) | −24.9584 | − | 10.4270i | −0.843747 | − | 0.352498i | ||||
\(876\) | 1.16926 | 0.0395055 | ||||||||
\(877\) | 29.0371 | − | 50.2937i | 0.980512 | − | 1.69830i | 0.320118 | − | 0.947378i | \(-0.396277\pi\) |
0.660394 | − | 0.750919i | \(-0.270389\pi\) | |||||||
\(878\) | 14.8342 | 0.500630 | ||||||||
\(879\) | 1.93513 | − | 3.35175i | 0.0652704 | − | 0.113052i | ||||
\(880\) | −5.87508 | + | 10.1759i | −0.198049 | + | 0.343031i | ||||
\(881\) | −10.8118 | + | 18.7266i | −0.364259 | + | 0.630916i | −0.988657 | − | 0.150191i | \(-0.952011\pi\) |
0.624398 | + | 0.781107i | \(0.285345\pi\) | |||||||
\(882\) | 29.0664 | − | 7.59940i | 0.978718 | − | 0.255885i | ||||
\(883\) | −22.7329 | −0.765022 | −0.382511 | − | 0.923951i | \(-0.624941\pi\) | ||||
−0.382511 | + | 0.923951i | \(0.624941\pi\) | |||||||
\(884\) | −1.08151 | − | 0.829203i | −0.0363751 | − | 0.0278891i | ||||
\(885\) | 2.98644 | − | 5.17266i | 0.100388 | − | 0.173877i | ||||
\(886\) | 10.7845 | + | 18.6793i | 0.362312 | + | 0.627543i | ||||
\(887\) | −16.3317 | −0.548365 | −0.274182 | − | 0.961678i | \(-0.588407\pi\) | ||||
−0.274182 | + | 0.961678i | \(0.588407\pi\) | |||||||
\(888\) | −3.00504 | − | 5.20488i | −0.100843 | − | 0.174664i | ||||
\(889\) | −32.9858 | + | 25.1521i | −1.10631 | + | 0.843574i | ||||
\(890\) | −16.4413 | − | 28.4772i | −0.551115 | − | 0.954559i | ||||
\(891\) | −7.30385 | + | 12.6506i | −0.244688 | + | 0.423812i | ||||
\(892\) | −1.01527 | + | 1.75850i | −0.0339937 | + | 0.0588788i | ||||
\(893\) | −21.3201 | −0.713451 | ||||||||
\(894\) | 10.9620 | 0.366623 | ||||||||
\(895\) | 11.0392 | − | 19.1205i | 0.369000 | − | 0.639127i | ||||
\(896\) | −33.0093 | − | 13.7905i | −1.10276 | − | 0.460708i | ||||
\(897\) | −0.825840 | + | 6.29180i | −0.0275740 | + | 0.210077i | ||||
\(898\) | 16.5506 | + | 28.6665i | 0.552301 | + | 0.956614i | ||||
\(899\) | 22.5140 | + | 38.9954i | 0.750884 | + | 1.30057i | ||||
\(900\) | −2.06105 | − | 3.56984i | −0.0687015 | − | 0.118995i | ||||
\(901\) | −1.28005 | + | 2.21711i | −0.0426446 | + | 0.0738627i | ||||
\(902\) | 5.05453 | 0.168297 | ||||||||
\(903\) | −5.59210 | + | 4.26405i | −0.186093 | + | 0.141899i | ||||
\(904\) | −19.8045 | − | 34.3023i | −0.658687 | − | 1.14088i | ||||
\(905\) | −3.33933 | − | 5.78389i | −0.111003 | − | 0.192263i | ||||
\(906\) | −11.6058 | −0.385575 | ||||||||
\(907\) | −7.20480 | − | 12.4791i | −0.239232 | − | 0.414361i | 0.721262 | − | 0.692662i | \(-0.243562\pi\) |
−0.960494 | + | 0.278301i | \(0.910229\pi\) | |||||||
\(908\) | 10.0829 | 0.334614 | ||||||||
\(909\) | 19.9391 | 0.661339 | ||||||||
\(910\) | 8.87600 | − | 15.2801i | 0.294237 | − | 0.506531i | ||||
\(911\) | −1.32236 | −0.0438118 | −0.0219059 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219059 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(912\) | 15.2538 | 0.505104 | ||||||||
\(913\) | 12.3063 | + | 21.3151i | 0.407278 | + | 0.705426i | ||||
\(914\) | 15.0581 | 0.498079 | ||||||||
\(915\) | 2.41004 | + | 4.17432i | 0.0796735 | + | 0.137999i | ||||
\(916\) | 4.52757 | + | 7.84197i | 0.149595 | + | 0.259106i | ||||
\(917\) | −3.21774 | − | 25.0284i | −0.106259 | − | 0.826509i | ||||
\(918\) | −3.97117 | −0.131068 | ||||||||
\(919\) | 13.7229 | − | 23.7688i | 0.452677 | − | 0.784059i | −0.545875 | − | 0.837867i | \(-0.683802\pi\) |
0.998551 | + | 0.0538078i | \(0.0171358\pi\) | |||||||
\(920\) | −5.27422 | − | 9.13522i | −0.173886 | − | 0.301179i | ||||
\(921\) | 0.311258 | + | 0.539114i | 0.0102563 | + | 0.0177644i | ||||
\(922\) | 1.06835 | + | 1.85043i | 0.0351841 | + | 0.0609407i | ||||
\(923\) | −1.18724 | + | 9.04520i | −0.0390785 | + | 0.297726i | ||||
\(924\) | −0.908428 | + | 0.692688i | −0.0298851 | + | 0.0227878i | ||||
\(925\) | 8.93569 | − | 15.4771i | 0.293804 | − | 0.508883i | ||||
\(926\) | 49.3940 | 1.62319 | ||||||||
\(927\) | −27.4033 | −0.900042 | ||||||||
\(928\) | 9.89123 | − | 17.1321i | 0.324696 | − | 0.562389i | ||||
\(929\) | 14.3194 | − | 24.8020i | 0.469805 | − | 0.813727i | −0.529599 | − | 0.848248i | \(-0.677657\pi\) |
0.999404 | + | 0.0345217i | \(0.0109908\pi\) | |||||||
\(930\) | 2.39618 | + | 4.15030i | 0.0785737 | + | 0.136094i | ||||
\(931\) | −45.3090 | + | 11.8460i | −1.48494 | + | 0.388237i | ||||
\(932\) | −0.791738 | − | 1.37133i | −0.0259343 | − | 0.0449194i | ||||
\(933\) | −12.1156 | −0.396646 | ||||||||
\(934\) | 22.6370 | + | 39.2084i | 0.740704 | + | 1.28294i | ||||
\(935\) | −1.14258 | + | 1.97900i | −0.0373663 | + | 0.0647203i | ||||
\(936\) | −22.6274 | + | 9.38291i | −0.739601 | + | 0.306690i | ||||
\(937\) | 27.9990 | 0.914688 | 0.457344 | − | 0.889290i | \(-0.348801\pi\) | ||||
0.457344 | + | 0.889290i | \(0.348801\pi\) | |||||||
\(938\) | −1.96356 | − | 15.2730i | −0.0641126 | − | 0.498682i | ||||
\(939\) | 0.581356 | − | 1.00694i | 0.0189718 | − | 0.0328602i | ||||
\(940\) | −0.791778 | + | 1.37140i | −0.0258249 | + | 0.0447301i | ||||
\(941\) | −14.4502 | + | 25.0284i | −0.471062 | + | 0.815903i | −0.999452 | − | 0.0330983i | \(-0.989463\pi\) |
0.528390 | + | 0.849002i | \(0.322796\pi\) | |||||||
\(942\) | 8.68255 | 0.282893 | ||||||||
\(943\) | −2.76340 | + | 4.78635i | −0.0899887 | + | 0.155865i | ||||
\(944\) | 47.7480 | 1.55406 | ||||||||
\(945\) | −1.13295 | − | 8.81231i | −0.0368547 | − | 0.286664i | ||||
\(946\) | −8.93666 | + | 15.4787i | −0.290556 | + | 0.503257i | ||||
\(947\) | 30.1235 | 0.978881 | 0.489441 | − | 0.872037i | \(-0.337201\pi\) | ||||
0.489441 | + | 0.872037i | \(0.337201\pi\) | |||||||
\(948\) | 0.619515 | − | 1.07303i | 0.0201209 | − | 0.0348505i | ||||
\(949\) | 19.0856 | − | 7.91420i | 0.619544 | − | 0.256906i | ||||
\(950\) | 18.6199 | + | 32.2506i | 0.604109 | + | 1.04635i | ||||
\(951\) | −4.83860 | + | 8.38070i | −0.156902 | + | 0.271763i | ||||
\(952\) | −5.44501 | − | 2.27480i | −0.176474 | − | 0.0737266i | ||||
\(953\) | −2.46511 | − | 4.26969i | −0.0798527 | − | 0.138309i | 0.823334 | − | 0.567558i | \(-0.192112\pi\) |
−0.903186 | + | 0.429249i | \(0.858778\pi\) | |||||||
\(954\) | −6.06185 | − | 10.4994i | −0.196260 | − | 0.339932i | ||||
\(955\) | −0.600167 | −0.0194210 | ||||||||
\(956\) | 9.13757 | 0.295530 | ||||||||
\(957\) | 4.40812 | + | 7.63509i | 0.142494 | + | 0.246808i | ||||
\(958\) | −7.55721 | − | 13.0895i | −0.244162 | − | 0.422902i | ||||
\(959\) | 6.74916 | + | 2.81964i | 0.217942 | + | 0.0910509i | ||||
\(960\) | −1.66391 | + | 2.88198i | −0.0537025 | + | 0.0930155i | ||||
\(961\) | 1.51957 | + | 2.63197i | 0.0490184 | + | 0.0849024i | ||||
\(962\) | 22.2049 | + | 17.0247i | 0.715916 | + | 0.548899i | ||||
\(963\) | −3.03678 | + | 5.25986i | −0.0978590 | + | 0.169497i | ||||
\(964\) | −8.65330 | −0.278704 | ||||||||
\(965\) | −2.21171 | + | 3.83079i | −0.0711974 | + | 0.123317i | ||||
\(966\) | −0.923132 | − | 7.18033i | −0.0297013 | − | 0.231023i | ||||
\(967\) | 29.1431 | 0.937180 | 0.468590 | − | 0.883416i | \(-0.344762\pi\) | ||||
0.468590 | + | 0.883416i | \(0.344762\pi\) | |||||||
\(968\) | −8.02523 | + | 13.9001i | −0.257941 | + | 0.446767i | ||||
\(969\) | 2.96654 | 0.0952989 | ||||||||
\(970\) | 5.74654 | − | 9.95331i | 0.184510 | − | 0.319581i | ||||
\(971\) | −7.28843 | + | 12.6239i | −0.233897 | + | 0.405121i | −0.958952 | − | 0.283570i | \(-0.908481\pi\) |
0.725055 | + | 0.688691i | \(0.241814\pi\) | |||||||
\(972\) | 2.46738 | − | 4.27362i | 0.0791412 | − | 0.137077i | ||||
\(973\) | −7.69095 | − | 59.8220i | −0.246561 | − | 1.91780i | ||||
\(974\) | −26.6058 | −0.852506 | ||||||||
\(975\) | 5.01210 | + | 3.84282i | 0.160516 | + | 0.123069i | ||||
\(976\) | −19.2662 | + | 33.3700i | −0.616696 | + | 1.06815i | ||||
\(977\) | −26.2609 | − | 45.4852i | −0.840161 | − | 1.45520i | −0.889758 | − | 0.456432i | \(-0.849127\pi\) |
0.0495974 | − | 0.998769i | \(-0.484206\pi\) | |||||||
\(978\) | 10.9590 | 0.350429 | ||||||||
\(979\) | 18.7819 | + | 32.5313i | 0.600273 | + | 1.03970i | ||||
\(980\) | −0.920681 | + | 3.35439i | −0.0294101 | + | 0.107152i | ||||
\(981\) | 18.9736 | + | 32.8632i | 0.605780 | + | 1.04924i | ||||
\(982\) | 19.9943 | − | 34.6312i | 0.638044 | − | 1.10513i | ||||
\(983\) | 3.01884 | − | 5.22879i | 0.0962862 | − | 0.166773i | −0.813858 | − | 0.581063i | \(-0.802637\pi\) |
0.910145 | + | 0.414291i | \(0.135970\pi\) | |||||||
\(984\) | 1.84985 | 0.0589709 | ||||||||
\(985\) | 8.87022 | 0.282629 | ||||||||
\(986\) | 5.99920 | − | 10.3909i | 0.191054 | − | 0.330914i | ||||
\(987\) | 3.28022 | − | 2.50121i | 0.104410 | − | 0.0796143i | ||||
\(988\) | −9.29289 | + | 3.85348i | −0.295646 | + | 0.122596i | ||||
\(989\) | −9.77166 | − | 16.9250i | −0.310721 | − | 0.538184i | ||||
\(990\) | −5.41083 | − | 9.37183i | −0.171967 | − | 0.297856i | ||||
\(991\) | −15.6742 | − | 27.1485i | −0.497907 | − | 0.862400i | 0.502090 | − | 0.864815i | \(-0.332564\pi\) |
−0.999997 | + | 0.00241558i | \(0.999231\pi\) | |||||||
\(992\) | −6.14212 | + | 10.6385i | −0.195012 | + | 0.337771i | ||||
\(993\) | −1.92165 | −0.0609816 | ||||||||
\(994\) | −1.32711 | − | 10.3226i | −0.0420934 | − | 0.327412i | ||||
\(995\) | 4.47148 | + | 7.74483i | 0.141755 | + | 0.245528i | ||||
\(996\) | −1.18660 | − | 2.05525i | −0.0375988 | − | 0.0651230i | ||||
\(997\) | 5.48033 | 0.173564 | 0.0867819 | − | 0.996227i | \(-0.472342\pi\) | ||||
0.0867819 | + | 0.996227i | \(0.472342\pi\) | |||||||
\(998\) | −4.20073 | − | 7.27588i | −0.132972 | − | 0.230314i | ||||
\(999\) | 14.0683 | 0.445101 |
(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 | 91.2.h.b.74.5 | yes | 12 | |
3.2 | odd | 2 | 819.2.s.d.802.2 | 12 | |||
7.2 | even | 3 | 91.2.g.b.9.2 | ✓ | 12 | ||
7.3 | odd | 6 | 637.2.f.j.295.2 | 12 | |||
7.4 | even | 3 | 637.2.f.k.295.2 | 12 | |||
7.5 | odd | 6 | 637.2.g.l.373.2 | 12 | |||
7.6 | odd | 2 | 637.2.h.l.165.5 | 12 | |||
13.3 | even | 3 | 91.2.g.b.81.2 | yes | 12 | ||
13.4 | even | 6 | 1183.2.e.g.508.5 | 12 | |||
13.9 | even | 3 | 1183.2.e.h.508.2 | 12 | |||
21.2 | odd | 6 | 819.2.n.d.100.5 | 12 | |||
39.29 | odd | 6 | 819.2.n.d.172.5 | 12 | |||
91.3 | odd | 6 | 637.2.f.j.393.2 | 12 | |||
91.4 | even | 6 | 8281.2.a.ce.1.2 | 6 | |||
91.9 | even | 3 | 1183.2.e.h.170.2 | 12 | |||
91.16 | even | 3 | inner | 91.2.h.b.16.5 | yes | 12 | |
91.17 | odd | 6 | 8281.2.a.cf.1.2 | 6 | |||
91.30 | even | 6 | 1183.2.e.g.170.5 | 12 | |||
91.55 | odd | 6 | 637.2.g.l.263.2 | 12 | |||
91.68 | odd | 6 | 637.2.h.l.471.5 | 12 | |||
91.74 | even | 3 | 8281.2.a.bz.1.5 | 6 | |||
91.81 | even | 3 | 637.2.f.k.393.2 | 12 | |||
91.87 | odd | 6 | 8281.2.a.ca.1.5 | 6 | |||
273.107 | odd | 6 | 819.2.s.d.289.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.2 | ✓ | 12 | 7.2 | even | 3 | ||
91.2.g.b.81.2 | yes | 12 | 13.3 | even | 3 | ||
91.2.h.b.16.5 | yes | 12 | 91.16 | even | 3 | inner | |
91.2.h.b.74.5 | yes | 12 | 1.1 | even | 1 | trivial | |
637.2.f.j.295.2 | 12 | 7.3 | odd | 6 | |||
637.2.f.j.393.2 | 12 | 91.3 | odd | 6 | |||
637.2.f.k.295.2 | 12 | 7.4 | even | 3 | |||
637.2.f.k.393.2 | 12 | 91.81 | even | 3 | |||
637.2.g.l.263.2 | 12 | 91.55 | odd | 6 | |||
637.2.g.l.373.2 | 12 | 7.5 | odd | 6 | |||
637.2.h.l.165.5 | 12 | 7.6 | odd | 2 | |||
637.2.h.l.471.5 | 12 | 91.68 | odd | 6 | |||
819.2.n.d.100.5 | 12 | 21.2 | odd | 6 | |||
819.2.n.d.172.5 | 12 | 39.29 | odd | 6 | |||
819.2.s.d.289.2 | 12 | 273.107 | odd | 6 | |||
819.2.s.d.802.2 | 12 | 3.2 | odd | 2 | |||
1183.2.e.g.170.5 | 12 | 91.30 | even | 6 | |||
1183.2.e.g.508.5 | 12 | 13.4 | even | 6 | |||
1183.2.e.h.170.2 | 12 | 91.9 | even | 3 | |||
1183.2.e.h.508.2 | 12 | 13.9 | even | 3 | |||
8281.2.a.bz.1.5 | 6 | 91.74 | even | 3 | |||
8281.2.a.ca.1.5 | 6 | 91.87 | odd | 6 | |||
8281.2.a.ce.1.2 | 6 | 91.4 | even | 6 | |||
8281.2.a.cf.1.2 | 6 | 91.17 | odd | 6 |