Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1183,2,Mod(170,1183)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1183, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1183.170");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1183 = 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1183.e (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: | \(9.44630255912\) |
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: | no (minimal twist has level 91) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 170.5 | ||
Root | \(-1.02197 - 1.77010i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1183.170 |
Dual form | 1183.2.e.g.508.5 |
$q$-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 \(\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times\).
\(n\) | \(339\) | \(1016\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.777343 | − | 1.34640i | 0.549665 | − | 0.952047i | −0.448632 | − | 0.893716i | \(-0.648089\pi\) |
0.998297 | − | 0.0583310i | \(-0.0185779\pi\) | |||||||
\(3\) | 0.244626 | + | 0.423704i | 0.141235 | + | 0.244626i | 0.927962 | − | 0.372675i | \(-0.121559\pi\) |
−0.786727 | + | 0.617301i | \(0.788226\pi\) | |||||||
\(4\) | −0.208526 | − | 0.361177i | −0.104263 | − | 0.180588i | ||||
\(5\) | −0.595756 | + | 1.03188i | −0.266430 | + | 0.461470i | −0.967937 | − | 0.251192i | \(-0.919177\pi\) |
0.701507 | + | 0.712662i | \(0.252511\pi\) | |||||||
\(6\) | 0.760633 | 0.310527 | ||||||||
\(7\) | −2.10390 | − | 1.60425i | −0.795199 | − | 0.606349i | ||||
\(8\) | 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 | 0.980284 | − | 0.197595i | \(-0.0633130\pi\) |
−0.661264 | + | 0.750153i | \(0.729980\pi\) | |||||||
\(12\) | 0.102021 | − | 0.176706i | 0.0294511 | − | 0.0510107i | ||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −3.79541 | + | 1.58563i | −1.01437 | + | 0.423778i | ||||
\(15\) | −0.582949 | −0.150517 | ||||||||
\(16\) | 2.33009 | − | 4.03583i | 0.582521 | − | 1.00896i | ||||
\(17\) | 0.453151 | + | 0.784881i | 0.109905 | + | 0.190362i | 0.915732 | − | 0.401790i | \(-0.131612\pi\) |
−0.805826 | + | 0.592152i | \(0.798279\pi\) | |||||||
\(18\) | −2.14596 | − | 3.71691i | −0.505808 | − | 0.876084i | ||||
\(19\) | 3.34514 | − | 5.79395i | 0.767428 | − | 1.32922i | −0.171525 | − | 0.985180i | \(-0.554870\pi\) |
0.938953 | − | 0.344045i | \(-0.111797\pi\) | |||||||
\(20\) | 0.496921 | 0.111115 | ||||||||
\(21\) | 0.165059 | − | 1.28387i | 0.0360189 | − | 0.280164i | ||||
\(22\) | 3.28993 | 0.701416 | ||||||||
\(23\) | −1.79866 | + | 3.11538i | −0.375048 | + | 0.649601i | −0.990334 | − | 0.138702i | \(-0.955707\pi\) |
0.615287 | + | 0.788303i | \(0.289040\pi\) | |||||||
\(24\) | 0.602021 | + | 1.04273i | 0.122887 | + | 0.212847i | ||||
\(25\) | 1.79015 | + | 3.10063i | 0.358030 | + | 0.620126i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.81840 | 0.542401 | ||||||||
\(28\) | −0.140701 | + | 1.09441i | −0.0265900 | + | 0.206823i | ||||
\(29\) | 8.51545 | 1.58128 | 0.790639 | − | 0.612282i | \(-0.209748\pi\) | ||||
0.790639 | + | 0.612282i | \(0.209748\pi\) | |||||||
\(30\) | −0.453151 | + | 0.784881i | −0.0827337 | + | 0.143299i | ||||
\(31\) | −2.64390 | − | 4.57937i | −0.474859 | − | 0.822479i | 0.524727 | − | 0.851271i | \(-0.324168\pi\) |
−0.999585 | + | 0.0287913i | \(0.990834\pi\) | |||||||
\(32\) | −1.16156 | − | 2.01189i | −0.205337 | − | 0.355655i | ||||
\(33\) | −0.517662 | + | 0.896617i | −0.0901134 | + | 0.156081i | ||||
\(34\) | 1.40902 | 0.241644 | ||||||||
\(35\) | 2.90880 | − | 1.21523i | 0.491677 | − | 0.205411i | ||||
\(36\) | −1.15133 | −0.191888 | ||||||||
\(37\) | 2.49579 | − | 4.32284i | 0.410306 | − | 0.710670i | −0.584617 | − | 0.811309i | \(-0.698755\pi\) |
0.994923 | + | 0.100639i | \(0.0320886\pi\) | |||||||
\(38\) | −5.20065 | − | 9.00778i | −0.843656 | − | 1.46126i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.46615 | + | 2.53944i | −0.231818 | + | 0.401521i | ||||
\(41\) | −1.53636 | −0.239939 | −0.119970 | − | 0.992778i | \(-0.538280\pi\) | ||||
−0.119970 | + | 0.992778i | \(0.538280\pi\) | |||||||
\(42\) | −1.60029 | − | 1.22024i | −0.246931 | − | 0.188288i | ||||
\(43\) | 5.43273 | 0.828483 | 0.414242 | − | 0.910167i | \(-0.364047\pi\) | ||||
0.414242 | + | 0.910167i | \(0.364047\pi\) | |||||||
\(44\) | 0.441269 | − | 0.764301i | 0.0665238 | − | 0.115223i | ||||
\(45\) | 1.64466 | + | 2.84864i | 0.245172 | + | 0.424650i | ||||
\(46\) | 2.79636 | + | 4.84344i | 0.412301 | + | 0.714126i | ||||
\(47\) | −1.59337 | + | 2.75979i | −0.232416 | + | 0.402557i | −0.958519 | − | 0.285030i | \(-0.907997\pi\) |
0.726102 | + | 0.687587i | \(0.241330\pi\) | |||||||
\(48\) | 2.28000 | 0.329089 | ||||||||
\(49\) | 1.85277 | + | 6.75035i | 0.264682 | + | 0.964336i | ||||
\(50\) | 5.56625 | 0.787186 | ||||||||
\(51\) | −0.221705 | + | 0.384004i | −0.0310449 | + | 0.0537714i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.41239 | + | 2.44632i | 0.194006 | + | 0.336029i | 0.946574 | − | 0.322486i | \(-0.104518\pi\) |
−0.752568 | + | 0.658514i | \(0.771185\pi\) | |||||||
\(54\) | 2.19086 | − | 3.79469i | 0.298139 | − | 0.516391i | ||||
\(55\) | −2.52140 | −0.339986 | ||||||||
\(56\) | −5.17767 | − | 3.94804i | −0.691895 | − | 0.527579i | ||||
\(57\) | 3.27323 | 0.433550 | ||||||||
\(58\) | 6.61943 | − | 11.4652i | 0.869173 | − | 1.50545i | ||||
\(59\) | −5.12298 | − | 8.87327i | −0.666956 | − | 1.15520i | −0.978751 | − | 0.205052i | \(-0.934264\pi\) |
0.311795 | − | 0.950149i | \(-0.399070\pi\) | |||||||
\(60\) | 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 | \(-0.0108913\pi\) | |||||||
\(62\) | −8.22088 | −1.04405 | ||||||||
\(63\) | −6.73945 | + | 2.81558i | −0.849091 | + | 0.354730i | ||||
\(64\) | 5.70861 | 0.713576 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.804802 | + | 1.39396i | 0.0990643 | + | 0.171584i | ||||
\(67\) | −1.87182 | − | 3.24208i | −0.228679 | − | 0.396083i | 0.728738 | − | 0.684793i | \(-0.240107\pi\) |
−0.957417 | + | 0.288709i | \(0.906774\pi\) | |||||||
\(68\) | 0.188987 | − | 0.327336i | 0.0229181 | − | 0.0396953i | ||||
\(69\) | −1.76000 | −0.211879 | ||||||||
\(70\) | 0.624956 | − | 4.86105i | 0.0746965 | − | 0.581007i | ||||
\(71\) | 2.53020 | 0.300280 | 0.150140 | − | 0.988665i | \(-0.452028\pi\) | ||||
0.150140 | + | 0.988665i | \(0.452028\pi\) | |||||||
\(72\) | 3.39694 | − | 5.88368i | 0.400334 | − | 0.693398i | ||||
\(73\) | −2.86522 | − | 4.96271i | −0.335349 | − | 0.580841i | 0.648203 | − | 0.761468i | \(-0.275521\pi\) |
−0.983552 | + | 0.180627i | \(0.942187\pi\) | |||||||
\(74\) | −3.88018 | − | 6.72066i | −0.451061 | − | 0.781261i | ||||
\(75\) | −0.875834 | + | 1.51699i | −0.101133 | + | 0.175167i | ||||
\(76\) | −2.79019 | −0.320057 | ||||||||
\(77\) | 0.713925 | − | 5.55307i | 0.0813593 | − | 0.632831i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.03620 | + | 5.25885i | −0.341599 | + | 0.591667i | −0.984730 | − | 0.174089i | \(-0.944302\pi\) |
0.643131 | + | 0.765756i | \(0.277635\pi\) | |||||||
\(80\) | 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 | \(-0.279627\pi\) | ||||
0.638327 | + | 0.769766i | \(0.279627\pi\) | |||||||
\(84\) | −0.498124 | + | 0.208104i | −0.0543498 | + | 0.0227060i | ||||
\(85\) | −1.07987 | −0.117128 | ||||||||
\(86\) | 4.22310 | − | 7.31462i | 0.455388 | − | 0.788755i | ||||
\(87\) | 2.08310 | + | 3.60803i | 0.223331 | + | 0.386821i | ||||
\(88\) | 2.60390 | + | 4.51008i | 0.277576 | + | 0.480776i | ||||
\(89\) | −8.87557 | + | 15.3729i | −0.940808 | + | 1.62953i | −0.176875 | + | 0.984233i | \(0.556599\pi\) |
−0.763934 | + | 0.645295i | \(0.776735\pi\) | |||||||
\(90\) | 5.11387 | 0.539049 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.50027 | 0.156414 | ||||||||
\(93\) | 1.29353 | − | 2.24046i | 0.134133 | − | 0.232325i | ||||
\(94\) | 2.47719 | + | 4.29061i | 0.255502 | + | 0.442543i | ||||
\(95\) | 3.98577 | + | 6.90356i | 0.408932 | + | 0.708291i | ||||
\(96\) | 0.568297 | − | 0.984319i | 0.0580015 | − | 0.100462i | ||||
\(97\) | −6.20434 | −0.629955 | −0.314978 | − | 0.949099i | \(-0.601997\pi\) | ||||
−0.314978 | + | 0.949099i | \(0.601997\pi\) | |||||||
\(98\) | 10.5289 | + | 2.75277i | 1.06358 | + | 0.278072i | ||||
\(99\) | 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 | −0.999921 | − | 0.0126084i | \(-0.995987\pi\) |
0.510879 | + | 0.859652i | \(0.329320\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.22646 | + | 0.935195i | 0.119691 | + | 0.0912657i | ||||
\(106\) | 4.39164 | 0.426553 | ||||||||
\(107\) | 1.10003 | − | 1.90531i | 0.106344 | − | 0.184193i | −0.807942 | − | 0.589261i | \(-0.799419\pi\) |
0.914287 | + | 0.405068i | \(0.132752\pi\) | |||||||
\(108\) | −0.587708 | − | 1.01794i | −0.0565523 | − | 0.0979514i | ||||
\(109\) | 6.87291 | + | 11.9042i | 0.658305 | + | 1.14022i | 0.981054 | + | 0.193734i | \(0.0620598\pi\) |
−0.322749 | + | 0.946485i | \(0.604607\pi\) | |||||||
\(110\) | −1.96000 | + | 3.39481i | −0.186878 | + | 0.323683i | ||||
\(111\) | 2.44214 | 0.231798 | ||||||||
\(112\) | −11.3767 | + | 4.75293i | −1.07500 | + | 0.449110i | ||||
\(113\) | −16.0947 | −1.51406 | −0.757032 | − | 0.653378i | \(-0.773351\pi\) | ||||
−0.757032 | + | 0.653378i | \(0.773351\pi\) | |||||||
\(114\) | 2.54442 | − | 4.40707i | 0.238307 | − | 0.412760i | ||||
\(115\) | −2.14313 | − | 3.71201i | −0.199848 | − | 0.346147i | ||||
\(116\) | −1.77569 | − | 3.07558i | −0.164869 | − | 0.285561i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −15.9293 | −1.46641 | ||||||||
\(119\) | 0.305761 | − | 2.37828i | 0.0280290 | − | 0.218016i | ||||
\(120\) | −1.43463 | −0.130963 | ||||||||
\(121\) | 3.26098 | − | 5.64818i | 0.296453 | − | 0.513471i | ||||
\(122\) | −6.42743 | − | 11.1326i | −0.581912 | − | 1.00790i | ||||
\(123\) | −0.375834 | − | 0.650963i | −0.0338878 | − | 0.0586954i | ||||
\(124\) | −1.10264 | + | 1.90983i | −0.0990202 | + | 0.171508i | ||||
\(125\) | −10.2235 | −0.914420 | ||||||||
\(126\) | −1.44797 | + | 11.2627i | −0.128996 | + | 1.00336i | ||||
\(127\) | −15.6784 | −1.39123 | −0.695617 | − | 0.718413i | \(-0.744869\pi\) | ||||
−0.695617 | + | 0.718413i | \(0.744869\pi\) | |||||||
\(128\) | 6.76067 | − | 11.7098i | 0.597565 | − | 1.03501i | ||||
\(129\) | 1.32899 | + | 2.30187i | 0.117011 | + | 0.202668i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.76884 | − | 8.25988i | 0.416656 | − | 0.721669i | −0.578945 | − | 0.815367i | \(-0.696535\pi\) |
0.995601 | + | 0.0936976i | \(0.0298687\pi\) | |||||||
\(132\) | 0.431783 | 0.0375819 | ||||||||
\(133\) | −16.3328 | + | 6.82345i | −1.41623 | + | 0.591668i | ||||
\(134\) | −5.82018 | −0.502787 | ||||||||
\(135\) | −1.67908 | + | 2.90825i | −0.144512 | + | 0.250302i | ||||
\(136\) | 1.11520 | + | 1.93158i | 0.0956277 | + | 0.165632i | ||||
\(137\) | −1.38231 | − | 2.39422i | −0.118098 | − | 0.204552i | 0.800916 | − | 0.598777i | \(-0.204346\pi\) |
−0.919014 | + | 0.394225i | \(0.871013\pi\) | |||||||
\(138\) | −1.36812 | + | 2.36966i | −0.116462 | + | 0.201719i | ||||
\(139\) | −22.7967 | −1.93359 | −0.966795 | − | 0.255554i | \(-0.917742\pi\) | ||||
−0.966795 | + | 0.255554i | \(0.917742\pi\) | |||||||
\(140\) | −1.04547 | − | 0.797185i | −0.0883585 | − | 0.0673745i | ||||
\(141\) | −1.55911 | −0.131301 | ||||||||
\(142\) | 1.96684 | − | 3.40666i | 0.165053 | − | 0.285881i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −6.43251 | − | 11.1414i | −0.536043 | − | 0.928453i | ||||
\(145\) | −5.07312 | + | 8.78691i | −0.421300 | + | 0.729713i | ||||
\(146\) | −8.90904 | −0.737317 | ||||||||
\(147\) | −2.40692 | + | 2.43634i | −0.198519 | + | 0.200946i | ||||
\(148\) | −2.08175 | −0.171119 | ||||||||
\(149\) | −7.20581 | + | 12.4808i | −0.590323 | + | 1.02247i | 0.403866 | + | 0.914818i | \(0.367666\pi\) |
−0.994189 | + | 0.107651i | \(0.965667\pi\) | |||||||
\(150\) | 1.36165 | + | 2.35844i | 0.111178 | + | 0.192566i | ||||
\(151\) | 7.62901 | + | 13.2138i | 0.620840 | + | 1.07533i | 0.989330 | + | 0.145695i | \(0.0465417\pi\) |
−0.368489 | + | 0.929632i | \(0.620125\pi\) | |||||||
\(152\) | 8.23236 | − | 14.2589i | 0.667732 | − | 1.15655i | ||||
\(153\) | 2.50197 | 0.202272 | ||||||||
\(154\) | −6.92168 | − | 5.27787i | −0.557765 | − | 0.425303i | ||||
\(155\) | 6.30048 | 0.506067 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.70745 | + | 9.88559i | 0.455504 | + | 0.788956i | 0.998717 | − | 0.0506387i | \(-0.0161257\pi\) |
−0.543213 | + | 0.839595i | \(0.682792\pi\) | |||||||
\(158\) | 4.72034 | + | 8.17587i | 0.375530 | + | 0.650437i | ||||
\(159\) | −0.691012 | + | 1.19687i | −0.0548008 | + | 0.0949178i | ||||
\(160\) | 2.76803 | 0.218832 | ||||||||
\(161\) | 8.78205 | − | 3.66893i | 0.692122 | − | 0.289152i | ||||
\(162\) | −10.7320 | −0.843185 | ||||||||
\(163\) | −7.20385 | + | 12.4774i | −0.564249 | + | 0.977308i | 0.432870 | + | 0.901456i | \(0.357501\pi\) |
−0.997119 | + | 0.0758514i | \(0.975833\pi\) | |||||||
\(164\) | 0.320371 | + | 0.554899i | 0.0250168 | + | 0.0433303i | ||||
\(165\) | −0.616800 | − | 1.06833i | −0.0480178 | − | 0.0831693i | ||||
\(166\) | 9.04118 | − | 15.6598i | 0.701731 | − | 1.21543i | ||||
\(167\) | −7.77190 | −0.601407 | −0.300704 | − | 0.953718i | \(-0.597222\pi\) | ||||
−0.300704 | + | 0.953718i | \(0.597222\pi\) | |||||||
\(168\) | 0.406210 | − | 3.15959i | 0.0313398 | − | 0.243768i | ||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −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 | ||||||||
\(175\) | 1.20789 | − | 9.39526i | 0.0913080 | − | 0.710215i | ||||
\(176\) | 9.86157 | 0.743344 | ||||||||
\(177\) | 2.50643 | − | 4.34126i | 0.188395 | − | 0.326309i | ||||
\(178\) | 13.7987 | + | 23.9001i | 1.03426 | + | 1.79139i | ||||
\(179\) | −9.26488 | − | 16.0472i | −0.692490 | − | 1.19943i | −0.971020 | − | 0.239000i | \(-0.923181\pi\) |
0.278530 | − | 0.960428i | \(-0.410153\pi\) | |||||||
\(180\) | 0.685909 | − | 1.18803i | 0.0511246 | − | 0.0885504i | ||||
\(181\) | −5.60520 | −0.416631 | −0.208316 | − | 0.978062i | \(-0.566798\pi\) | ||||
−0.208316 | + | 0.978062i | \(0.566798\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.04535 | 0.299041 | ||||||||
\(184\) | −4.42650 | + | 7.66692i | −0.326326 | + | 0.565212i | ||||
\(185\) | 2.97377 | + | 5.15071i | 0.218636 | + | 0.378688i | ||||
\(186\) | −2.01104 | − | 3.48322i | −0.147456 | − | 0.255402i | ||||
\(187\) | −0.958931 | + | 1.66092i | −0.0701240 | + | 0.121458i | ||||
\(188\) | 1.32903 | 0.0969295 | ||||||||
\(189\) | −5.92962 | − | 4.52141i | −0.431317 | − | 0.328884i | ||||
\(190\) | 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 | 0.791453 | − | 0.611230i | \(-0.209325\pi\) |
−0.925067 | + | 0.379804i | \(0.875991\pi\) | |||||||
\(194\) | −4.82290 | + | 8.35351i | −0.346264 | + | 0.599747i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.05172 | − | 2.07680i | 0.146552 | − | 0.148343i | ||||
\(197\) | 7.44451 | 0.530399 | 0.265200 | − | 0.964194i | \(-0.414562\pi\) | ||||
0.265200 | + | 0.964194i | \(0.414562\pi\) | |||||||
\(198\) | 4.54115 | − | 7.86550i | 0.322725 | − | 0.558977i | ||||
\(199\) | −3.75278 | − | 6.50001i | −0.266028 | − | 0.460773i | 0.701805 | − | 0.712369i | \(-0.252378\pi\) |
−0.967832 | + | 0.251596i | \(0.919045\pi\) | |||||||
\(200\) | 4.40554 | + | 7.63062i | 0.311519 | + | 0.539566i | ||||
\(201\) | 0.915789 | − | 1.58619i | 0.0645948 | − | 0.111881i | ||||
\(202\) | 11.2290 | 0.790068 | ||||||||
\(203\) | −17.9156 | − | 13.6609i | −1.25743 | − | 0.958807i | ||||
\(204\) | 0.184925 | 0.0129473 | ||||||||
\(205\) | 0.915297 | − | 1.58534i | 0.0639271 | − | 0.110725i | ||||
\(206\) | 7.71626 | + | 13.3650i | 0.537617 | + | 0.931181i | ||||
\(207\) | 4.96545 | + | 8.60042i | 0.345123 | + | 0.597770i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 14.1576 | 0.979299 | ||||||||
\(210\) | 2.21253 | − | 0.924342i | 0.152679 | − | 0.0637857i | ||||
\(211\) | 3.79063 | 0.260957 | 0.130479 | − | 0.991451i | \(-0.458349\pi\) | ||||
0.130479 | + | 0.991451i | \(0.458349\pi\) | |||||||
\(212\) | 0.589037 | − | 1.02024i | 0.0404553 | − | 0.0700706i | ||||
\(213\) | 0.618953 | + | 1.07206i | 0.0424100 | + | 0.0734562i | ||||
\(214\) | −1.71020 | − | 2.96216i | −0.116907 | − | 0.202489i | ||||
\(215\) | −3.23658 | + | 5.60592i | −0.220733 | + | 0.382320i | ||||
\(216\) | 6.93605 | 0.471938 | ||||||||
\(217\) | −1.78395 | + | 13.8760i | −0.121103 | + | 0.941965i | ||||
\(218\) | 21.3704 | 1.44739 | ||||||||
\(219\) | 1.40181 | − | 2.42801i | 0.0947258 | − | 0.164070i | ||||
\(220\) | 0.525777 | + | 0.910673i | 0.0354479 | + | 0.0613975i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 1.89838 | − | 3.28809i | 0.127411 | − | 0.220682i | ||||
\(223\) | −4.86879 | −0.326039 | −0.163019 | − | 0.986623i | \(-0.552123\pi\) | ||||
−0.163019 | + | 0.986623i | \(0.552123\pi\) | |||||||
\(224\) | −0.783757 | + | 6.09624i | −0.0523669 | + | 0.407322i | ||||
\(225\) | 9.88390 | 0.658926 | ||||||||
\(226\) | −12.5111 | + | 21.6699i | −0.832228 | + | 1.44146i | ||||
\(227\) | 12.0884 | + | 20.9376i | 0.802332 | + | 1.38968i | 0.918077 | + | 0.396402i | \(0.129741\pi\) |
−0.115745 | + | 0.993279i | \(0.536925\pi\) | |||||||
\(228\) | −0.682552 | − | 1.18222i | −0.0452031 | − | 0.0782941i | ||||
\(229\) | −10.8561 | + | 18.8034i | −0.717394 | + | 1.24256i | 0.244635 | + | 0.969615i | \(0.421332\pi\) |
−0.962029 | + | 0.272947i | \(0.912002\pi\) | |||||||
\(230\) | −6.66379 | −0.439397 | ||||||||
\(231\) | 2.52750 | − | 1.05593i | 0.166298 | − | 0.0694752i | ||||
\(232\) | 20.9564 | 1.37586 | ||||||||
\(233\) | −1.89842 | + | 3.28816i | −0.124370 | + | 0.215414i | −0.921486 | − | 0.388411i | \(-0.873024\pi\) |
0.797117 | + | 0.603825i | \(0.206358\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.89851 | − | 3.28832i | −0.123845 | − | 0.214507i | ||||
\(236\) | −2.13655 | + | 3.70061i | −0.139077 | + | 0.240889i | ||||
\(237\) | −2.97093 | −0.192983 | ||||||||
\(238\) | −2.96443 | − | 2.26041i | −0.192155 | − | 0.146521i | ||||
\(239\) | −21.9100 | −1.41724 | −0.708619 | − | 0.705592i | \(-0.750681\pi\) | ||||
−0.708619 | + | 0.705592i | \(0.750681\pi\) | |||||||
\(240\) | −1.35832 | + | 2.35268i | −0.0876792 | + | 0.151865i | ||||
\(241\) | −10.3744 | − | 17.9690i | −0.668273 | − | 1.15748i | −0.978387 | − | 0.206783i | \(-0.933701\pi\) |
0.310114 | − | 0.950699i | \(-0.399633\pi\) | |||||||
\(242\) | −5.06980 | − | 8.78115i | −0.325899 | − | 0.564474i | ||||
\(243\) | 5.91625 | − | 10.2472i | 0.379527 | − | 0.657361i | ||||
\(244\) | −3.44837 | −0.220759 | ||||||||
\(245\) | −8.06935 | − | 2.10972i | −0.515532 | − | 0.134785i | ||||
\(246\) | −1.16861 | −0.0745077 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.50661 | − | 11.2698i | −0.413170 | − | 0.715632i | ||||
\(249\) | 2.84521 | + | 4.92805i | 0.180308 | + | 0.312302i | ||||
\(250\) | −7.94719 | + | 13.7649i | −0.502624 | + | 0.870571i | ||||
\(251\) | 13.2578 | 0.836827 | 0.418413 | − | 0.908257i | \(-0.362586\pi\) | ||||
0.418413 | + | 0.908257i | \(0.362586\pi\) | |||||||
\(252\) | 2.42227 | + | 1.84701i | 0.152589 | + | 0.116351i | ||||
\(253\) | −7.61245 | −0.478591 | ||||||||
\(254\) | −12.1875 | + | 21.1094i | −0.764713 | + | 1.32452i | ||||
\(255\) | −0.264164 | − | 0.457546i | −0.0165426 | − | 0.0286526i | ||||
\(256\) | −4.80213 | − | 8.31753i | −0.300133 | − | 0.519845i | ||||
\(257\) | 6.58555 | − | 11.4065i | 0.410795 | − | 0.711518i | −0.584182 | − | 0.811623i | \(-0.698584\pi\) |
0.994977 | + | 0.100105i | \(0.0319178\pi\) | |||||||
\(258\) | 4.13231 | 0.257266 | ||||||||
\(259\) | −12.1858 | + | 5.09094i | −0.757189 | + | 0.316336i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 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 | ||||||||
\(266\) | −3.50910 | + | 27.2946i | −0.215157 | + | 1.67354i | ||||
\(267\) | −8.68477 | −0.531499 | ||||||||
\(268\) | −0.780643 | + | 1.35211i | −0.0476854 | + | 0.0825935i | ||||
\(269\) | 14.2411 | + | 24.6663i | 0.868296 | + | 1.50393i | 0.863737 | + | 0.503943i | \(0.168118\pi\) |
0.00455867 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(270\) | 2.61044 | + | 4.52141i | 0.158866 | + | 0.275164i | ||||
\(271\) | 8.97371 | − | 15.5429i | 0.545114 | − | 0.944165i | −0.453486 | − | 0.891263i | \(-0.649820\pi\) |
0.998600 | − | 0.0529014i | \(-0.0168469\pi\) | |||||||
\(272\) | 4.22353 | 0.256089 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.29811 | −0.259658 | ||||||||
\(275\) | −3.78821 | + | 6.56137i | −0.228437 | + | 0.395665i | ||||
\(276\) | 0.367005 | + | 0.635671i | 0.0220911 | + | 0.0382629i | ||||
\(277\) | −6.71943 | − | 11.6384i | −0.403732 | − | 0.699284i | 0.590441 | − | 0.807081i | \(-0.298954\pi\) |
−0.994173 | + | 0.107797i | \(0.965620\pi\) | |||||||
\(278\) | −17.7209 | + | 30.6934i | −1.06283 | + | 1.84087i | ||||
\(279\) | −14.5977 | −0.873940 | ||||||||
\(280\) | 7.15853 | − | 2.99066i | 0.427804 | − | 0.178726i | ||||
\(281\) | 29.9530 | 1.78685 | 0.893424 | − | 0.449214i | \(-0.148296\pi\) | ||||
0.893424 | + | 0.449214i | \(0.148296\pi\) | |||||||
\(282\) | −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 | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.23235 | + | 2.46471i | 0.190800 | + | 0.145487i | ||||
\(288\) | −6.41330 | −0.377907 | ||||||||
\(289\) | 8.08931 | − | 14.0111i | 0.475842 | − | 0.824182i | ||||
\(290\) | 7.88712 | + | 13.6609i | 0.463148 | + | 0.802195i | ||||
\(291\) | −1.51774 | − | 2.62881i | −0.0889716 | − | 0.154103i | ||||
\(292\) | −1.19494 | + | 2.06970i | −0.0699288 | + | 0.121120i | ||||
\(293\) | −7.91058 | −0.462141 | −0.231071 | − | 0.972937i | \(-0.574223\pi\) | ||||
−0.231071 | + | 0.972937i | \(0.574223\pi\) | |||||||
\(294\) | 1.40928 | + | 5.13454i | 0.0821908 | + | 0.299452i | ||||
\(295\) | 12.2082 | 0.710788 | ||||||||
\(296\) | 6.14212 | − | 10.6385i | 0.357003 | − | 0.618348i | ||||
\(297\) | 2.98206 | + | 5.16508i | 0.173037 | + | 0.299708i | ||||
\(298\) | 11.2028 | + | 19.4038i | 0.648959 | + | 1.12403i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0.730535 | 0.0421775 | ||||||||
\(301\) | −11.4299 | − | 8.71545i | −0.658809 | − | 0.502350i | ||||
\(302\) | 23.7214 | 1.36502 | ||||||||
\(303\) | −1.76685 | + | 3.06027i | −0.101503 | + | 0.175808i | ||||
\(304\) | −15.5889 | − | 27.0008i | −0.894086 | − | 1.54860i | ||||
\(305\) | 4.92598 | + | 8.53204i | 0.282061 | + | 0.488543i | ||||
\(306\) | 1.94489 | − | 3.36865i | 0.111182 | − | 0.192573i | ||||
\(307\) | −1.27238 | −0.0726187 | −0.0363094 | − | 0.999341i | \(-0.511560\pi\) | ||||
−0.0363094 | + | 0.999341i | \(0.511560\pi\) | |||||||
\(308\) | −2.15451 | + | 0.900105i | −0.122765 | + | 0.0512882i | ||||
\(309\) | −4.85653 | −0.276278 | ||||||||
\(310\) | 4.89763 | − | 8.48295i | 0.278167 | − | 0.481799i | ||||
\(311\) | −12.3817 | − | 21.4458i | −0.702103 | − | 1.21608i | −0.967727 | − | 0.252002i | \(-0.918911\pi\) |
0.265624 | − | 0.964077i | \(-0.414422\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.18826 | + | 2.05812i | −0.0671642 | + | 0.116332i | −0.897652 | − | 0.440705i | \(-0.854728\pi\) |
0.830488 | + | 0.557037i | \(0.188062\pi\) | |||||||
\(314\) | 17.7466 | 1.00150 | ||||||||
\(315\) | 1.10972 | − | 8.63169i | 0.0625259 | − | 0.486341i | ||||
\(316\) | 2.53250 | 0.142464 | ||||||||
\(317\) | −9.88979 | + | 17.1296i | −0.555466 | + | 0.962096i | 0.442401 | + | 0.896817i | \(0.354127\pi\) |
−0.997867 | + | 0.0652782i | \(0.979207\pi\) | |||||||
\(318\) | 1.07431 | + | 1.86076i | 0.0602442 | + | 0.104346i | ||||
\(319\) | 9.00993 | + | 15.6057i | 0.504459 | + | 0.873749i | ||||
\(320\) | −3.40093 | + | 5.89059i | −0.190118 | + | 0.329294i | ||||
\(321\) | 1.07638 | 0.0600779 | ||||||||
\(322\) | 1.88682 | − | 14.6762i | 0.105149 | − | 0.817870i | ||||
\(323\) | 6.06342 | 0.337378 | ||||||||
\(324\) | −1.43945 | + | 2.49320i | −0.0799695 | + | 0.138511i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 11.1997 | + | 19.3985i | 0.620295 | + | 1.07438i | ||||
\(327\) | −3.36258 | + | 5.82416i | −0.185951 | + | 0.322077i | ||||
\(328\) | −3.78097 | −0.208769 | ||||||||
\(329\) | 7.77967 | − | 3.25016i | 0.428907 | − | 0.179187i | ||||
\(330\) | −1.91786 | −0.105575 | ||||||||
\(331\) | 1.96386 | − | 3.40151i | 0.107944 | − | 0.186964i | −0.806993 | − | 0.590561i | \(-0.798907\pi\) |
0.914937 | + | 0.403596i | \(0.132240\pi\) | |||||||
\(332\) | −2.42533 | − | 4.20080i | −0.133107 | − | 0.230549i | ||||
\(333\) | −6.88997 | − | 11.9338i | −0.377568 | − | 0.653967i | ||||
\(334\) | −6.04143 | + | 10.4641i | −0.330572 | + | 0.572568i | ||||
\(335\) | 4.46058 | 0.243708 | ||||||||
\(336\) | −4.79688 | − | 3.65768i | −0.261691 | − | 0.199543i | ||||
\(337\) | −7.14099 | −0.388995 | −0.194497 | − | 0.980903i | \(-0.562308\pi\) | ||||
−0.194497 | + | 0.980903i | \(0.562308\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.93718 | − | 6.81940i | −0.213838 | − | 0.370379i | ||||
\(340\) | 0.225181 | + | 0.390024i | 0.0122121 | + | 0.0211520i | ||||
\(341\) | 5.59486 | − | 9.69059i | 0.302979 | − | 0.524775i | ||||
\(342\) | −28.7142 | −1.55268 | ||||||||
\(343\) | 6.93120 | − | 17.1744i | 0.374250 | − | 0.927328i | ||||
\(344\) | 13.3699 | 0.720856 | ||||||||
\(345\) | 1.04853 | − | 1.81611i | 0.0564509 | − | 0.0977759i | ||||
\(346\) | 4.73761 | + | 8.20578i | 0.254695 | + | 0.441145i | ||||
\(347\) | −5.03498 | − | 8.72085i | −0.270292 | − | 0.468160i | 0.698644 | − | 0.715469i | \(-0.253787\pi\) |
−0.968937 | + | 0.247309i | \(0.920454\pi\) | |||||||
\(348\) | 0.868758 | − | 1.50473i | 0.0465703 | − | 0.0806622i | ||||
\(349\) | 6.28837 | 0.336609 | 0.168304 | − | 0.985735i | \(-0.446171\pi\) | ||||
0.168304 | + | 0.985735i | \(0.446171\pi\) | |||||||
\(350\) | −11.7108 | − | 8.92964i | −0.625969 | − | 0.477310i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.45803 | − | 4.25743i | 0.131013 | − | 0.226922i | ||||
\(353\) | 17.0836 | + | 29.5897i | 0.909269 | + | 1.57490i | 0.815083 | + | 0.579345i | \(0.196692\pi\) |
0.0941861 | + | 0.995555i | \(0.469975\pi\) | |||||||
\(354\) | −3.89671 | − | 6.74930i | −0.207108 | − | 0.358721i | ||||
\(355\) | −1.50738 | + | 2.61087i | −0.0800036 | + | 0.138570i | ||||
\(356\) | 7.40313 | 0.392365 | ||||||||
\(357\) | 1.08248 | − | 0.452236i | 0.0572911 | − | 0.0239349i | ||||
\(358\) | −28.8080 | −1.52255 | ||||||||
\(359\) | 9.34327 | − | 16.1830i | 0.493119 | − | 0.854107i | −0.506850 | − | 0.862034i | \(-0.669190\pi\) |
0.999969 | + | 0.00792750i | \(0.00252343\pi\) | |||||||
\(360\) | 4.04750 | + | 7.01047i | 0.213322 | + | 0.369484i | ||||
\(361\) | −12.8799 | − | 22.3087i | −0.677891 | − | 1.17414i | ||||
\(362\) | −4.35716 | + | 7.54683i | −0.229007 | + | 0.396653i | ||||
\(363\) | 3.19088 | 0.167478 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.82788 | 0.357388 | ||||||||
\(366\) | 3.14463 | − | 5.44666i | 0.164372 | − | 0.284701i | ||||
\(367\) | 15.5305 | + | 26.8997i | 0.810687 | + | 1.40415i | 0.912384 | + | 0.409336i | \(0.134240\pi\) |
−0.101696 | + | 0.994816i | \(0.532427\pi\) | |||||||
\(368\) | 8.38209 | + | 14.5182i | 0.436946 | + | 0.756813i | ||||
\(369\) | −2.12067 | + | 3.67310i | −0.110397 | + | 0.191214i | ||||
\(370\) | 9.24655 | 0.480705 | ||||||||
\(371\) | 0.952998 | − | 7.41264i | 0.0494772 | − | 0.384845i | ||||
\(372\) | −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 | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −10.6970 | + | 4.46894i | −0.550193 | + | 0.229858i | ||||
\(379\) | −10.0851 | −0.518036 | −0.259018 | − | 0.965872i | \(-0.583399\pi\) | ||||
−0.259018 | + | 0.965872i | \(0.583399\pi\) | |||||||
\(380\) | 1.66227 | − | 2.87914i | 0.0852727 | − | 0.147697i | ||||
\(381\) | −3.83534 | − | 6.64301i | −0.196491 | − | 0.340332i | ||||
\(382\) | 0.391550 | + | 0.678184i | 0.0200334 | + | 0.0346989i | ||||
\(383\) | 1.84466 | − | 3.19504i | 0.0942576 | − | 0.163259i | −0.815041 | − | 0.579403i | \(-0.803286\pi\) |
0.909299 | + | 0.416144i | \(0.136619\pi\) | |||||||
\(384\) | 6.61534 | 0.337588 | ||||||||
\(385\) | 5.30477 | + | 4.04496i | 0.270356 | + | 0.206150i | ||||
\(386\) | −5.77168 | −0.293771 | ||||||||
\(387\) | 7.49888 | − | 12.9884i | 0.381190 | − | 0.660240i | ||||
\(388\) | 1.29376 | + | 2.24086i | 0.0656809 | + | 0.113763i | ||||
\(389\) | −11.3333 | − | 19.6299i | −0.574623 | − | 0.995277i | −0.996082 | − | 0.0884295i | \(-0.971815\pi\) |
0.421459 | − | 0.906847i | \(-0.361518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.26027 | −0.164879 | ||||||||
\(392\) | 4.55965 | + | 16.6125i | 0.230297 | + | 0.839060i | ||||
\(393\) | 4.66633 | 0.235385 | ||||||||
\(394\) | 5.78694 | − | 10.0233i | 0.291542 | − | 0.504965i | ||||
\(395\) | −3.61767 | − | 6.26598i | −0.182025 | − | 0.315276i | ||||
\(396\) | −1.21818 | − | 2.10995i | −0.0612160 | − | 0.106029i | ||||
\(397\) | −14.5680 | + | 25.2325i | −0.731146 | + | 1.26638i | 0.225248 | + | 0.974302i | \(0.427681\pi\) |
−0.956394 | + | 0.292080i | \(0.905652\pi\) | |||||||
\(398\) | −11.6688 | −0.584904 | ||||||||
\(399\) | −6.88654 | − | 5.25108i | −0.344758 | − | 0.262883i | ||||
\(400\) | 16.6848 | 0.834241 | ||||||||
\(401\) | 4.06026 | − | 7.03258i | 0.202760 | − | 0.351190i | −0.746657 | − | 0.665209i | \(-0.768342\pi\) |
0.949417 | + | 0.314019i | \(0.101676\pi\) | |||||||
\(402\) | −1.42377 | − | 2.46603i | −0.0710110 | − | 0.122995i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.50611 | − | 2.60866i | 0.0749318 | − | 0.129786i | ||||
\(405\) | 8.22499 | 0.408703 | ||||||||
\(406\) | −32.3196 | + | 13.5024i | −1.60399 | + | 0.670111i | ||||
\(407\) | 10.5629 | 0.523583 | ||||||||
\(408\) | −0.545614 | + | 0.945031i | −0.0270119 | + | 0.0467860i | ||||
\(409\) | −4.16131 | − | 7.20759i | −0.205763 | − | 0.356393i | 0.744612 | − | 0.667497i | \(-0.232634\pi\) |
−0.950376 | + | 0.311105i | \(0.899301\pi\) | |||||||
\(410\) | −1.42300 | − | 2.46471i | −0.0702769 | − | 0.121723i | ||||
\(411\) | 0.676295 | − | 1.17138i | 0.0333592 | − | 0.0577798i | ||||
\(412\) | 4.13984 | 0.203955 | ||||||||
\(413\) | −3.45670 | + | 26.8870i | −0.170093 | + | 1.32302i | ||||
\(414\) | 15.4395 | 0.758808 | ||||||||
\(415\) | −6.92915 | + | 12.0016i | −0.340139 | + | 0.589138i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −5.57666 | − | 9.65905i | −0.273090 | − | 0.473006i | ||||
\(418\) | 11.0053 | − | 19.0617i | 0.538286 | − | 0.932339i | ||||
\(419\) | −13.0166 | −0.635905 | −0.317952 | − | 0.948107i | \(-0.602995\pi\) | ||||
−0.317952 | + | 0.948107i | \(0.602995\pi\) | |||||||
\(420\) | 0.0820216 | − | 0.637983i | 0.00400224 | − | 0.0311304i | ||||
\(421\) | 8.89681 | 0.433604 | 0.216802 | − | 0.976216i | \(-0.430437\pi\) | ||||
0.216802 | + | 0.976216i | \(0.430437\pi\) | |||||||
\(422\) | 2.94662 | − | 5.10369i | 0.143439 | − | 0.248444i | ||||
\(423\) | 4.39870 | + | 7.61877i | 0.213872 | + | 0.370437i | ||||
\(424\) | 3.47587 | + | 6.02038i | 0.168803 | + | 0.292376i | ||||
\(425\) | −1.62242 | + | 2.81011i | −0.0786988 | + | 0.136310i | ||||
\(426\) | 1.92456 | 0.0932451 | ||||||||
\(427\) | −20.1855 | + | 8.43303i | −0.976846 | + | 0.408103i | ||||
\(428\) | −0.917539 | −0.0443509 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.03187 | + | 8.71545i | 0.242658 | + | 0.420296i | ||||
\(431\) | −4.47872 | − | 7.75736i | −0.215732 | − | 0.373659i | 0.737767 | − | 0.675056i | \(-0.235880\pi\) |
−0.953499 | + | 0.301397i | \(0.902547\pi\) | |||||||
\(432\) | 6.56711 | − | 11.3746i | 0.315960 | − | 0.547259i | ||||
\(433\) | −0.172909 | −0.00830950 | −0.00415475 | − | 0.999991i | \(-0.501323\pi\) | ||||
−0.00415475 | + | 0.999991i | \(0.501323\pi\) | |||||||
\(434\) | 17.2959 | + | 13.1883i | 0.830229 | + | 0.633060i | ||||
\(435\) | −4.96407 | −0.238009 | ||||||||
\(436\) | 2.86636 | − | 4.96467i | 0.137274 | − | 0.237765i | ||||
\(437\) | 12.0336 | + | 20.8428i | 0.575644 | + | 0.997045i | ||||
\(438\) | −2.17938 | − | 3.77480i | −0.104135 | − | 0.180367i | ||||
\(439\) | −4.77080 | + | 8.26327i | −0.227698 | + | 0.394384i | −0.957125 | − | 0.289674i | \(-0.906453\pi\) |
0.729428 | + | 0.684058i | \(0.239787\pi\) | |||||||
\(440\) | −6.20515 | −0.295819 | ||||||||
\(441\) | 18.6960 | + | 4.88806i | 0.890286 | + | 0.232765i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.93676 | − | 12.0148i | 0.329576 | − | 0.570842i | −0.652852 | − | 0.757485i | \(-0.726428\pi\) |
0.982428 | + | 0.186644i | \(0.0597610\pi\) | |||||||
\(444\) | −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 | ||||||||
\(448\) | −12.0103 | − | 9.15803i | −0.567434 | − | 0.432676i | ||||
\(449\) | 21.2913 | 1.00480 | 0.502398 | − | 0.864636i | \(-0.332451\pi\) | ||||
0.502398 | + | 0.864636i | \(0.332451\pi\) | |||||||
\(450\) | 7.68318 | − | 13.3077i | 0.362189 | − | 0.627329i | ||||
\(451\) | −1.62558 | − | 2.81558i | −0.0765455 | − | 0.132581i | ||||
\(452\) | 3.35616 | + | 5.81304i | 0.157861 | + | 0.273423i | ||||
\(453\) | −3.73251 | + | 6.46489i | −0.175368 | + | 0.303747i | ||||
\(454\) | 37.5872 | 1.76406 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 8.05539 | 0.377228 | ||||||||
\(457\) | 4.84282 | − | 8.38801i | 0.226538 | − | 0.392375i | −0.730242 | − | 0.683189i | \(-0.760593\pi\) |
0.956780 | + | 0.290814i | \(0.0939261\pi\) | |||||||
\(458\) | 16.8779 | + | 29.2334i | 0.788652 | + | 1.36599i | ||||
\(459\) | 1.27716 | + | 2.21211i | 0.0596128 | + | 0.103252i | ||||
\(460\) | −0.893795 | + | 1.54810i | −0.0416734 | + | 0.0721804i | ||||
\(461\) | 1.37436 | 0.0640101 | 0.0320051 | − | 0.999488i | \(-0.489811\pi\) | ||||
0.0320051 | + | 0.999488i | \(0.489811\pi\) | |||||||
\(462\) | 0.543035 | − | 4.22385i | 0.0252643 | − | 0.196511i | ||||
\(463\) | −31.7710 | −1.47653 | −0.738263 | − | 0.674513i | \(-0.764354\pi\) | ||||
−0.738263 | + | 0.674513i | \(0.764354\pi\) | |||||||
\(464\) | 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 | −0.303046 | − | 0.952976i | \(-0.598004\pi\) |
0.976824 | − | 0.214042i | \(-0.0686629\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.26299 | + | 9.82387i | −0.0583197 | + | 0.453624i | ||||
\(470\) | −5.90319 | −0.272294 | ||||||||
\(471\) | −2.79238 | + | 4.83654i | −0.128666 | + | 0.222856i | ||||
\(472\) | −12.6076 | − | 21.8370i | −0.580312 | − | 1.00513i | ||||
\(473\) | 5.74820 | + | 9.95618i | 0.264303 | + | 0.457786i | ||||
\(474\) | −2.30943 | + | 4.00006i | −0.106076 | + | 0.183729i | ||||
\(475\) | 23.9532 | 1.09905 | ||||||||
\(476\) | −0.922738 | + | 0.385498i | −0.0422936 | + | 0.0176693i | ||||
\(477\) | 7.79816 | 0.357053 | ||||||||
\(478\) | −17.0316 | + | 29.4995i | −0.779005 | + | 1.34928i | ||||
\(479\) | 4.86092 | + | 8.41936i | 0.222101 | + | 0.384690i | 0.955446 | − | 0.295167i | \(-0.0953752\pi\) |
−0.733345 | + | 0.679857i | \(0.762042\pi\) | |||||||
\(480\) | 0.677132 | + | 1.17283i | 0.0309067 | + | 0.0535320i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −32.2578 | −1.46930 | ||||||||
\(483\) | 3.70286 | + | 2.82348i | 0.168486 | + | 0.128473i | ||||
\(484\) | −2.71999 | −0.123636 | ||||||||
\(485\) | 3.69627 | − | 6.40213i | 0.167839 | − | 0.290706i | ||||
\(486\) | −9.19791 | − | 15.9313i | −0.417226 | − | 0.722656i | ||||
\(487\) | −8.55666 | − | 14.8206i | −0.387739 | − | 0.671584i | 0.604406 | − | 0.796676i | \(-0.293411\pi\) |
−0.992145 | + | 0.125093i | \(0.960077\pi\) | |||||||
\(488\) | 10.1743 | − | 17.6224i | 0.460568 | − | 0.797728i | ||||
\(489\) | −7.04899 | −0.318766 | ||||||||
\(490\) | −9.11318 | + | 9.22457i | −0.411692 | + | 0.416724i | ||||
\(491\) | −25.7213 | −1.16079 | −0.580394 | − | 0.814336i | \(-0.697101\pi\) | ||||
−0.580394 | + | 0.814336i | \(0.697101\pi\) | |||||||
\(492\) | −0.156742 | + | 0.271485i | −0.00706647 | + | 0.0122395i | ||||
\(493\) | 3.85879 | + | 6.68361i | 0.173791 | + | 0.301015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.48033 | + | 6.02812i | −0.156429 | + | 0.270944i | ||||
\(496\) | −24.6421 | −1.10646 | ||||||||
\(497\) | −5.32329 | − | 4.05908i | −0.238782 | − | 0.182075i | ||||
\(498\) | 8.84682 | 0.396435 | ||||||||
\(499\) | 2.70198 | − | 4.67996i | 0.120957 | − | 0.209504i | −0.799188 | − | 0.601081i | \(-0.794737\pi\) |
0.920145 | + | 0.391577i | \(0.128070\pi\) | |||||||
\(500\) | 2.13187 | + | 3.69250i | 0.0953400 | + | 0.165134i | ||||
\(501\) | −1.90121 | − | 3.29299i | −0.0849396 | − | 0.147120i | ||||
\(502\) | 10.3059 | − | 17.8503i | 0.459974 | − | 0.796699i | ||||
\(503\) | −12.6169 | −0.562562 | −0.281281 | − | 0.959625i | \(-0.590759\pi\) | ||||
−0.281281 | + | 0.959625i | \(0.590759\pi\) | |||||||
\(504\) | −16.5857 | + | 6.92912i | −0.738786 | + | 0.308647i | ||||
\(505\) | −8.60589 | −0.382957 | ||||||||
\(506\) | −5.91749 | + | 10.2494i | −0.263064 | + | 0.455641i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.26935 | + | 5.66268i | 0.145054 | + | 0.251241i | ||||
\(509\) | −0.979379 | + | 1.69633i | −0.0434102 | + | 0.0751887i | −0.886914 | − | 0.461934i | \(-0.847156\pi\) |
0.843504 | + | 0.537123i | \(0.180489\pi\) | |||||||
\(510\) | −0.821385 | −0.0363715 | ||||||||
\(511\) | −1.93329 | + | 15.0376i | −0.0855236 | + | 0.665222i | ||||
\(512\) | 12.1111 | 0.535240 | ||||||||
\(513\) | 9.42794 | − | 16.3297i | 0.416254 | − | 0.720973i | ||||
\(514\) | −10.2385 | − | 17.7335i | −0.451599 | − | 0.782193i | ||||
\(515\) | −5.91374 | − | 10.2429i | −0.260590 | − | 0.451356i | ||||
\(516\) | 0.554255 | − | 0.959998i | 0.0243997 | − | 0.0422615i | ||||
\(517\) | −6.74357 | −0.296582 | ||||||||
\(518\) | −2.61812 | + | 20.3644i | −0.115034 | + | 0.894758i | ||||
\(519\) | −2.98180 | −0.130886 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.5477 | + | 33.8576i | 0.856401 | + | 1.48333i | 0.875339 | + | 0.483509i | \(0.160638\pi\) |
−0.0189387 | + | 0.999821i | \(0.506029\pi\) | |||||||
\(522\) | −18.2738 | − | 31.6512i | −0.799823 | − | 1.38533i | ||||
\(523\) | 4.35634 | − | 7.54540i | 0.190489 | − | 0.329937i | −0.754923 | − | 0.655813i | \(-0.772326\pi\) |
0.945413 | + | 0.325876i | \(0.105659\pi\) | |||||||
\(524\) | −3.97770 | −0.173767 | ||||||||
\(525\) | 4.27629 | − | 1.78653i | 0.186633 | − | 0.0779707i | ||||
\(526\) | 29.7576 | 1.29749 | ||||||||
\(527\) | 2.39618 | − | 4.15030i | 0.104379 | − | 0.180790i | ||||
\(528\) | 2.41239 | + | 4.17839i | 0.104986 | + | 0.181841i | ||||
\(529\) | 5.02961 | + | 8.71154i | 0.218679 | + | 0.378763i | ||||
\(530\) | −2.61634 | + | 4.53164i | −0.113647 | + | 0.196842i | ||||
\(531\) | −28.2854 | −1.22748 | ||||||||
\(532\) | 5.87028 | + | 4.47616i | 0.254509 | + | 0.194066i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −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 | ||||||||
\(539\) | −10.4105 | + | 10.5378i | −0.448413 | + | 0.453894i | ||||
\(540\) | 1.40052 | 0.0602689 | ||||||||
\(541\) | −10.7497 | + | 18.6190i | −0.462165 | + | 0.800493i | −0.999069 | − | 0.0431505i | \(-0.986260\pi\) |
0.536904 | + | 0.843644i | \(0.319594\pi\) | |||||||
\(542\) | −13.9513 | − | 24.1644i | −0.599260 | − | 1.03795i | ||||
\(543\) | −1.37118 | − | 2.37495i | −0.0588428 | − | 0.101919i | ||||
\(544\) | 1.05273 | − | 1.82338i | 0.0451353 | − | 0.0781767i | ||||
\(545\) | −16.3783 | −0.701569 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −30.2968 | −1.29540 | −0.647699 | − | 0.761896i | \(-0.724269\pi\) | ||||
−0.647699 | + | 0.761896i | \(0.724269\pi\) | |||||||
\(548\) | −0.576493 | + | 0.998514i | −0.0246265 | + | 0.0426544i | ||||
\(549\) | −11.4131 | − | 19.7680i | −0.487098 | − | 0.843679i | ||||
\(550\) | 5.88947 | + | 10.2009i | 0.251128 | + | 0.434967i | ||||
\(551\) | 28.4854 | − | 49.3381i | 1.21352 | − | 2.10187i | ||||
\(552\) | −4.33134 | −0.184354 | ||||||||
\(553\) | 14.8244 | − | 6.19327i | 0.630396 | − | 0.263365i | ||||
\(554\) | −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 | 0.615626 | − | 0.788038i | \(-0.288903\pi\) |
−0.990274 | + | 0.139129i | \(0.955570\pi\) | |||||||
\(558\) | −11.3474 | + | 19.6543i | −0.480374 | + | 0.832033i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.87330 | − | 14.5710i | 0.0791616 | − | 0.615737i | ||||
\(561\) | −0.938317 | −0.0396158 | ||||||||
\(562\) | 23.2838 | − | 40.3287i | 0.982167 | − | 1.70116i | ||||
\(563\) | 20.8695 | + | 36.1471i | 0.879545 | + | 1.52342i | 0.851841 | + | 0.523801i | \(0.175486\pi\) |
0.0277042 | + | 0.999616i | \(0.491180\pi\) | |||||||
\(564\) | 0.325115 | + | 0.563116i | 0.0136898 | + | 0.0237115i | ||||
\(565\) | 9.58852 | − | 16.6078i | 0.403392 | − | 0.698696i | ||||
\(566\) | 15.3777 | 0.646375 | ||||||||
\(567\) | −2.32887 | + | 18.1145i | −0.0978035 | + | 0.760738i | ||||
\(568\) | 6.22681 | 0.261271 | ||||||||
\(569\) | −2.73388 | + | 4.73521i | −0.114610 | + | 0.198510i | −0.917624 | − | 0.397450i | \(-0.869895\pi\) |
0.803014 | + | 0.595960i | \(0.203229\pi\) | |||||||
\(570\) | 3.03171 | + | 5.25108i | 0.126984 | + | 0.219943i | ||||
\(571\) | −4.67621 | − | 8.09944i | −0.195693 | − | 0.338951i | 0.751434 | − | 0.659808i | \(-0.229362\pi\) |
−0.947128 | + | 0.320857i | \(0.896029\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.246437 | −0.0102951 | ||||||||
\(574\) | 5.83112 | − | 2.43611i | 0.243386 | − | 0.101681i | ||||
\(575\) | −12.8795 | −0.537113 | ||||||||
\(576\) | 7.87968 | − | 13.6480i | 0.328320 | − | 0.568667i | ||||
\(577\) | −1.68462 | − | 2.91786i | −0.0701318 | − | 0.121472i | 0.828827 | − | 0.559505i | \(-0.189009\pi\) |
−0.898959 | + | 0.438033i | \(0.855675\pi\) | |||||||
\(578\) | −12.5763 | − | 21.7829i | −0.523107 | − | 0.906048i | ||||
\(579\) | 0.908159 | − | 1.57298i | 0.0377418 | − | 0.0653707i | ||||
\(580\) | 4.23151 | 0.175704 | ||||||||
\(581\) | −24.4702 | − | 18.6588i | −1.01519 | − | 0.774098i | ||||
\(582\) | −4.71923 | −0.195618 | ||||||||
\(583\) | −2.98881 | + | 5.17676i | −0.123784 | + | 0.214400i | ||||
\(584\) | −7.05128 | − | 12.2132i | −0.291784 | − | 0.505385i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.14924 | + | 10.6508i | −0.254023 | + | 0.439980i | ||||
\(587\) | 13.1528 | 0.542873 | 0.271437 | − | 0.962456i | \(-0.412501\pi\) | ||||
0.271437 | + | 0.962456i | \(0.412501\pi\) | |||||||
\(588\) | 1.38185 | + | 0.361284i | 0.0569866 | + | 0.0148991i | ||||
\(589\) | −35.3769 | −1.45768 | ||||||||
\(590\) | 9.48995 | − | 16.4371i | 0.390695 | − | 0.676704i | ||||
\(591\) | 1.82112 | + | 3.15427i | 0.0749108 | + | 0.129749i | ||||
\(592\) | −11.6308 | − | 20.1452i | −0.478024 | − | 0.827961i | ||||
\(593\) | 19.2958 | − | 33.4213i | 0.792384 | − | 1.37245i | −0.132102 | − | 0.991236i | \(-0.542173\pi\) |
0.924487 | − | 0.381214i | \(-0.124494\pi\) | |||||||
\(594\) | 9.27234 | 0.380449 | ||||||||
\(595\) | 2.27194 | + | 1.73238i | 0.0931403 | + | 0.0710207i | ||||
\(596\) | 6.01038 | 0.246195 | ||||||||
\(597\) | 1.83605 | − | 3.18014i | 0.0751447 | − | 0.130154i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.20762 | − | 15.9481i | −0.376213 | − | 0.651620i | 0.614295 | − | 0.789077i | \(-0.289441\pi\) |
−0.990508 | + | 0.137457i | \(0.956107\pi\) | |||||||
\(600\) | −2.15542 | + | 3.73329i | −0.0879946 | + | 0.152411i | ||||
\(601\) | −41.4037 | −1.68889 | −0.844445 | − | 0.535642i | \(-0.820070\pi\) | ||||
−0.844445 | + | 0.535642i | \(0.820070\pi\) | |||||||
\(602\) | −20.6194 | + | 8.61431i | −0.840385 | + | 0.351093i | ||||
\(603\) | −10.3348 | −0.420865 | ||||||||
\(604\) | 3.18169 | − | 5.51085i | 0.129461 | − | 0.224233i | ||||
\(605\) | 3.88549 | + | 6.72987i | 0.157968 | + | 0.273608i | ||||
\(606\) | 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 | \(0.247007\pi\) | |||||||
\(608\) | −15.5424 | −0.630327 | ||||||||
\(609\) | 1.40556 | − | 10.9327i | 0.0569560 | − | 0.443017i | ||||
\(610\) | 15.3167 | 0.620155 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −0.521725 | − | 0.903654i | −0.0210895 | − | 0.0365280i | ||||
\(613\) | 13.1112 | + | 22.7093i | 0.529556 | + | 0.917219i | 0.999406 | + | 0.0344720i | \(0.0109749\pi\) |
−0.469849 | + | 0.882747i | \(0.655692\pi\) | |||||||
\(614\) | −0.989078 | + | 1.71313i | −0.0399160 | + | 0.0691365i | ||||
\(615\) | 0.895620 | 0.0361149 | ||||||||
\(616\) | 1.75696 | − | 13.6661i | 0.0707900 | − | 0.550621i | ||||
\(617\) | 18.8252 | 0.757873 | 0.378936 | − | 0.925423i | \(-0.376290\pi\) | ||||
0.378936 | + | 0.925423i | \(0.376290\pi\) | |||||||
\(618\) | −3.77519 | + | 6.53882i | −0.151860 | + | 0.263030i | ||||
\(619\) | −7.90415 | − | 13.6904i | −0.317695 | − | 0.550263i | 0.662312 | − | 0.749228i | \(-0.269575\pi\) |
−0.980007 | + | 0.198965i | \(0.936242\pi\) | |||||||
\(620\) | −1.31381 | − | 2.27559i | −0.0527639 | − | 0.0913898i | ||||
\(621\) | −5.06935 | + | 8.78038i | −0.203426 | + | 0.352344i | ||||
\(622\) | −38.4994 | −1.54369 | ||||||||
\(623\) | 43.3353 | − | 18.1045i | 1.73619 | − | 0.725340i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −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 | ||||||||
\(630\) | −10.7591 | − | 8.20392i | −0.428651 | − | 0.326852i | ||||
\(631\) | 16.6763 | 0.663875 | 0.331937 | − | 0.943301i | \(-0.392298\pi\) | ||||
0.331937 | + | 0.943301i | \(0.392298\pi\) | |||||||
\(632\) | −7.47206 | + | 12.9420i | −0.297222 | + | 0.514804i | ||||
\(633\) | 0.927285 | + | 1.60610i | 0.0368563 | + | 0.0638369i | ||||
\(634\) | 15.3755 | + | 26.6312i | 0.610640 | + | 1.05766i | ||||
\(635\) | 9.34050 | − | 16.1782i | 0.370667 | − | 0.642013i | ||||
\(636\) | 0.576375 | 0.0228548 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 28.0152 | 1.10913 | ||||||||
\(639\) | 3.49248 | − | 6.04916i | 0.138161 | − | 0.239301i | ||||
\(640\) | 8.05542 | + | 13.9524i | 0.318418 | + | 0.551517i | ||||
\(641\) | −24.6232 | − | 42.6487i | −0.972559 | − | 1.68452i | −0.687767 | − | 0.725932i | \(-0.741409\pi\) |
−0.284792 | − | 0.958589i | \(-0.591925\pi\) | |||||||
\(642\) | 0.836720 | − | 1.44924i | 0.0330227 | − | 0.0571970i | ||||
\(643\) | −42.8711 | −1.69067 | −0.845335 | − | 0.534236i | \(-0.820599\pi\) | ||||
−0.845335 | + | 0.534236i | \(0.820599\pi\) | |||||||
\(644\) | −3.15642 | − | 2.40681i | −0.124380 | − | 0.0948415i | ||||
\(645\) | −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 | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.31572 | + | 2.63856i | −0.247533 | + | 0.103413i | ||||
\(652\) | 6.00875 | 0.235321 | ||||||||
\(653\) | 1.04776 | − | 1.81477i | 0.0410020 | − | 0.0710176i | −0.844796 | − | 0.535088i | \(-0.820278\pi\) |
0.885798 | + | 0.464071i | \(0.153612\pi\) | |||||||
\(654\) | 5.22776 | + | 9.05475i | 0.204422 | + | 0.354069i | ||||
\(655\) | 5.68213 | + | 9.84174i | 0.222019 | + | 0.384549i | ||||
\(656\) | −3.57986 | + | 6.20049i | −0.139770 | + | 0.242089i | ||||
\(657\) | −15.8196 | −0.617183 | ||||||||
\(658\) | 1.67146 | − | 13.0010i | 0.0651604 | − | 0.506833i | ||||
\(659\) | 25.4518 | 0.991463 | 0.495732 | − | 0.868476i | \(-0.334900\pi\) | ||||
0.495732 | + | 0.868476i | \(0.334900\pi\) | |||||||
\(660\) | −0.257237 | + | 0.445548i | −0.0100129 | + | 0.0173429i | ||||
\(661\) | 13.9054 | + | 24.0848i | 0.540857 | + | 0.936792i | 0.998855 | + | 0.0478387i | \(0.0152333\pi\) |
−0.457998 | + | 0.888953i | \(0.651433\pi\) | |||||||
\(662\) | −3.05319 | − | 5.28829i | −0.118666 | − | 0.205535i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 28.6234 | 1.11080 | ||||||||
\(665\) | 2.68937 | − | 20.9186i | 0.104289 | − | 0.811187i | ||||
\(666\) | −21.4235 | −0.830143 | ||||||||
\(667\) | −15.3164 | + | 26.5288i | −0.593055 | + | 1.02720i | ||||
\(668\) | 1.62064 | + | 2.80703i | 0.0627044 | + | 0.108607i | ||||
\(669\) | −1.19103 | − | 2.06293i | −0.0460480 | − | 0.0797574i | ||||
\(670\) | 3.46740 | − | 6.00572i | 0.133957 | − | 0.232021i | ||||
\(671\) | 17.4972 | 0.675472 | ||||||||
\(672\) | −2.77473 | + | 1.15922i | −0.107038 | + | 0.0447178i | ||||
\(673\) | 15.5207 | 0.598278 | 0.299139 | − | 0.954210i | \(-0.403301\pi\) | ||||
0.299139 | + | 0.954210i | \(0.403301\pi\) | |||||||
\(674\) | −5.55100 | + | 9.61462i | −0.213817 | + | 0.370341i | ||||
\(675\) | 5.04536 | + | 8.73881i | 0.194196 | + | 0.336357i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.2813 | + | 29.9321i | −0.664175 | + | 1.15038i | 0.315334 | + | 0.948981i | \(0.397884\pi\) |
−0.979508 | + | 0.201403i | \(0.935450\pi\) | |||||||
\(678\) | −12.2422 | −0.470158 | ||||||||
\(679\) | 13.0533 | + | 9.95331i | 0.500940 | + | 0.381973i | ||||
\(680\) | −2.65755 | −0.101912 | ||||||||
\(681\) | −5.91425 | + | 10.2438i | −0.226634 | + | 0.392542i | ||||
\(682\) | −8.69826 | − | 15.0658i | −0.333074 | − | 0.576900i | ||||
\(683\) | 23.5032 | + | 40.7087i | 0.899325 | + | 1.55768i | 0.828359 | + | 0.560198i | \(0.189275\pi\) |
0.0709661 | + | 0.997479i | \(0.477392\pi\) | |||||||
\(684\) | −3.85135 | + | 6.67073i | −0.147260 | + | 0.255062i | ||||
\(685\) | 3.29407 | 0.125860 | ||||||||
\(686\) | −17.7356 | − | 22.6825i | −0.677148 | − | 0.866023i | ||||
\(687\) | −10.6228 | −0.405284 | ||||||||
\(688\) | 12.6587 | − | 21.9255i | 0.482609 | − | 0.835904i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −1.63013 | − | 2.82348i | −0.0620582 | − | 0.107488i | ||||
\(691\) | 9.50301 | − | 16.4597i | 0.361512 | − | 0.626156i | −0.626698 | − | 0.779262i | \(-0.715594\pi\) |
0.988210 | + | 0.153106i | \(0.0489275\pi\) | |||||||
\(692\) | 2.54177 | 0.0966235 | ||||||||
\(693\) | −12.2907 | − | 9.37183i | −0.466886 | − | 0.356006i | ||||
\(694\) | −15.6556 | −0.594280 | ||||||||
\(695\) | 13.5813 | − | 23.5234i | 0.515166 | − | 0.892294i | ||||
\(696\) | 5.12648 | + | 8.87933i | 0.194319 | + | 0.336570i | ||||
\(697\) | −0.696205 | − | 1.20586i | −0.0263706 | − | 0.0456753i | ||||
\(698\) | 4.88822 | − | 8.46665i | 0.185022 | − | 0.320467i | ||||
\(699\) | −1.85761 | −0.0702612 | ||||||||
\(700\) | −3.64523 | + | 1.52289i | −0.137777 | + | 0.0575598i | ||||
\(701\) | −45.4648 | −1.71718 | −0.858591 | − | 0.512662i | \(-0.828659\pi\) | ||||
−0.858591 | + | 0.512662i | \(0.828659\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.6976 | − | 28.9210i | −0.629760 | − | 1.09078i | ||||
\(704\) | 6.04010 | + | 10.4618i | 0.227645 | + | 0.394293i | ||||
\(705\) | 0.928851 | − | 1.60882i | 0.0349826 | − | 0.0605916i | ||||
\(706\) | 53.1193 | 1.99917 | ||||||||
\(707\) | 2.43672 | − | 18.9534i | 0.0916423 | − | 0.712815i | ||||
\(708\) | −2.09062 | −0.0785702 | ||||||||
\(709\) | −4.89390 | + | 8.47648i | −0.183794 | + | 0.318341i | −0.943170 | − | 0.332312i | \(-0.892171\pi\) |
0.759375 | + | 0.650653i | \(0.225505\pi\) | |||||||
\(710\) | 2.34351 | + | 4.05908i | 0.0879504 | + | 0.152334i | ||||
\(711\) | 8.38183 | + | 14.5178i | 0.314343 | + | 0.544459i | ||||
\(712\) | −21.8427 | + | 37.8326i | −0.818589 | + | 1.41784i | ||||
\(713\) | 19.0220 | 0.712378 | ||||||||
\(714\) | 0.232572 | − | 1.80900i | 0.00870377 | − | 0.0677000i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −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 | ||||||||
\(721\) | 24.2331 | − | 10.1240i | 0.902489 | − | 0.377039i | ||||
\(722\) | −40.0485 | −1.49045 | ||||||||
\(723\) | 5.07568 | − | 8.79134i | 0.188767 | − | 0.326953i | ||||
\(724\) | 1.16883 | + | 2.02447i | 0.0434391 | + | 0.0752388i | ||||
\(725\) | 15.2439 | + | 26.4033i | 0.566145 | + | 0.980592i | ||||
\(726\) | 2.48041 | − | 4.29619i | 0.0920566 | − | 0.159447i | ||||
\(727\) | −14.5650 | −0.540186 | −0.270093 | − | 0.962834i | \(-0.587055\pi\) | ||||
−0.270093 | + | 0.962834i | \(0.587055\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.9199 | −0.552589 | ||||||||
\(730\) | 5.30761 | − | 9.19305i | 0.196444 | − | 0.340250i | ||||
\(731\) | 2.46185 | + | 4.26405i | 0.0910547 | + | 0.157711i | ||||
\(732\) | −0.843560 | − | 1.46109i | −0.0311789 | − | 0.0540034i | ||||
\(733\) | 8.83030 | − | 15.2945i | 0.326155 | − | 0.564916i | −0.655591 | − | 0.755116i | \(-0.727580\pi\) |
0.981745 | + | 0.190200i | \(0.0609136\pi\) | |||||||
\(734\) | 48.2902 | 1.78243 | ||||||||
\(735\) | −1.08007 | − | 3.93511i | −0.0398390 | − | 0.145149i | ||||
\(736\) | 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 | 0.936621 | − | 0.350345i | \(-0.113936\pi\) |
−0.771718 | + | 0.635964i | \(0.780602\pi\) | |||||||
\(740\) | 1.24021 | − | 2.14811i | 0.0455911 | − | 0.0789661i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −9.23955 | − | 7.04528i | −0.339195 | − | 0.258640i | ||||
\(743\) | 26.3679 | 0.967343 | 0.483671 | − | 0.875250i | \(-0.339303\pi\) | ||||
0.483671 | + | 0.875250i | \(0.339303\pi\) | |||||||
\(744\) | 3.18337 | − | 5.51376i | 0.116708 | − | 0.202144i | ||||
\(745\) | −8.58580 | − | 14.8710i | −0.314560 | − | 0.544833i | ||||
\(746\) | −2.28309 | − | 3.95442i | −0.0835898 | − | 0.144782i | ||||
\(747\) | 16.0543 | − | 27.8068i | 0.587395 | − | 1.01740i | ||||
\(748\) | 0.799847 | 0.0292453 | ||||||||
\(749\) | −5.37095 | + | 2.24385i | −0.196250 | + | 0.0819887i | ||||
\(750\) | −7.77635 | −0.283952 | ||||||||
\(751\) | 10.1438 | − | 17.5696i | 0.370152 | − | 0.641123i | −0.619436 | − | 0.785047i | \(-0.712639\pi\) |
0.989589 | + | 0.143924i | \(0.0459721\pi\) | |||||||
\(752\) | 7.42536 | + | 12.8611i | 0.270775 | + | 0.468996i | ||||
\(753\) | 3.24321 | + | 5.61740i | 0.118189 | + | 0.204709i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18.1801 | −0.661642 | ||||||||
\(756\) | −0.396552 | + | 3.08447i | −0.0144225 | + | 0.112181i | ||||
\(757\) | 24.9984 | 0.908584 | 0.454292 | − | 0.890853i | \(-0.349892\pi\) | ||||
0.454292 | + | 0.890853i | \(0.349892\pi\) | |||||||
\(758\) | −7.83957 | + | 13.5785i | −0.284746 | + | 0.493195i | ||||
\(759\) | −1.86220 | − | 3.22543i | −0.0675936 | − | 0.117076i | ||||
\(760\) | 9.80895 | + | 16.9896i | 0.355808 | + | 0.616277i | ||||
\(761\) | 10.0711 | − | 17.4436i | 0.365077 | − | 0.632332i | −0.623712 | − | 0.781655i | \(-0.714376\pi\) |
0.988789 | + | 0.149323i | \(0.0477094\pi\) | |||||||
\(762\) | −11.9255 | −0.432016 | ||||||||
\(763\) | 4.63745 | − | 36.0711i | 0.167887 | − | 1.30586i | ||||
\(764\) | 0.210070 | 0.00760006 | ||||||||
\(765\) | −1.49056 | + | 2.58173i | −0.0538914 | + | 0.0933426i | ||||
\(766\) | −2.86786 | − | 4.96729i | −0.103620 | − | 0.179475i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 2.34945 | − | 4.06936i | 0.0847784 | − | 0.146840i | ||||
\(769\) | −8.67220 | −0.312727 | −0.156364 | − | 0.987700i | \(-0.549977\pi\) | ||||
−0.156364 | + | 0.987700i | \(0.549977\pi\) | |||||||
\(770\) | 9.56976 | − | 3.99802i | 0.344870 | − | 0.144079i | ||||
\(771\) | 6.44398 | 0.232074 | ||||||||
\(772\) | −0.774139 | + | 1.34085i | −0.0278619 | + | 0.0482582i | ||||
\(773\) | 1.17283 | + | 2.03141i | 0.0421839 | + | 0.0730647i | 0.886346 | − | 0.463023i | \(-0.153235\pi\) |
−0.844163 | + | 0.536087i | \(0.819902\pi\) | |||||||
\(774\) | −11.6584 | − | 20.1930i | −0.419053 | − | 0.725821i | ||||
\(775\) | 9.46596 | − | 16.3955i | 0.340027 | − | 0.588945i | ||||
\(776\) | −15.2688 | −0.548119 | ||||||||
\(777\) | −5.13801 | − | 3.91780i | −0.184325 | − | 0.140550i | ||||
\(778\) | −35.2396 | −1.26340 | ||||||||
\(779\) | −5.13935 | + | 8.90161i | −0.184136 | + | 0.318933i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.67713 | + | 4.63693i | 0.0957953 | + | 0.165922i | ||||
\(782\) | −2.53435 | + | 4.38962i | −0.0906281 | + | 0.156973i | ||||
\(783\) | 23.9999 | 0.857687 | ||||||||
\(784\) | 31.5604 | + | 8.25143i | 1.12716 | + | 0.294694i | ||||
\(785\) | −13.6010 | −0.485440 | ||||||||
\(786\) | 3.62734 | − | 6.28274i | 0.129383 | − | 0.224098i | ||||
\(787\) | −17.0583 | − | 29.5459i | −0.608063 | − | 1.05320i | −0.991559 | − | 0.129654i | \(-0.958613\pi\) |
0.383496 | − | 0.923543i | \(-0.374720\pi\) | |||||||
\(788\) | −1.55237 | − | 2.68878i | −0.0553009 | − | 0.0957840i | ||||
\(789\) | −4.68228 | + | 8.10994i | −0.166693 | + | 0.288721i | ||||
\(790\) | −11.2487 | −0.400210 | ||||||||
\(791\) | 33.8616 | + | 25.8199i | 1.20398 | + | 0.918051i | ||||
\(792\) | 14.3768 | 0.510858 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 22.6486 | + | 39.2286i | 0.803770 | + | 1.39217i | ||||
\(795\) | −0.823349 | − | 1.42608i | −0.0292012 | − | 0.0505779i | ||||
\(796\) | −1.56510 | + | 2.71084i | −0.0554736 | + | 0.0960830i | ||||
\(797\) | −34.0844 | −1.20733 | −0.603666 | − | 0.797237i | \(-0.706294\pi\) | ||||
−0.603666 | + | 0.797237i | \(0.706294\pi\) | |||||||
\(798\) | −12.4232 | + | 5.19014i | −0.439778 | + | 0.183729i | ||||
\(799\) | −2.88815 | −0.102175 | ||||||||
\(800\) | 4.15875 | − | 7.20316i | 0.147034 | − | 0.254670i | ||||
\(801\) | 24.5022 | + | 42.4390i | 0.865742 | + | 1.49951i | ||||
\(802\) | −6.31243 | − | 10.9335i | −0.222900 | − | 0.386074i | ||||
\(803\) | 6.06320 | − | 10.5018i | 0.213966 | − | 0.370600i | ||||
\(804\) | −0.763862 | −0.0269393 | ||||||||
\(805\) | −1.44606 | + | 11.2478i | −0.0509670 | + | 0.396433i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −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 | \(-0.873919\pi\) | ||||
−0.922575 | + | 0.385818i | \(0.873919\pi\) | |||||||
\(812\) | −1.19813 | + | 9.31936i | −0.0420462 | + | 0.327045i | ||||
\(813\) | 8.78080 | 0.307956 | ||||||||
\(814\) | 8.21099 | − | 14.2219i | 0.287795 | − | 0.498476i | ||||
\(815\) | −8.58347 | − | 14.8670i | −0.300666 | − | 0.520768i | ||||
\(816\) | 1.03318 | + | 1.78953i | 0.0361686 | + | 0.0626459i | ||||
\(817\) | 18.1732 | − | 31.4770i | 0.635801 | − | 1.10124i | ||||
\(818\) | −12.9391 | −0.452403 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.763451 | −0.0266609 | ||||||||
\(821\) | −15.3773 | + | 26.6343i | −0.536671 | + | 0.929542i | 0.462409 | + | 0.886667i | \(0.346985\pi\) |
−0.999080 | + | 0.0428753i | \(0.986348\pi\) | |||||||
\(822\) | −1.05143 | − | 1.82113i | −0.0366728 | − | 0.0635191i | ||||
\(823\) | 14.8519 | + | 25.7243i | 0.517705 | + | 0.896691i | 0.999789 | + | 0.0205659i | \(0.00654678\pi\) |
−0.482084 | + | 0.876125i | \(0.660120\pi\) | |||||||
\(824\) | −12.2144 | + | 21.1560i | −0.425510 | + | 0.737006i | ||||
\(825\) | −3.70677 | −0.129053 | ||||||||
\(826\) | 33.5136 | + | 25.5545i | 1.16609 | + | 0.889155i | ||||
\(827\) | −14.8351 | −0.515866 | −0.257933 | − | 0.966163i | \(-0.583041\pi\) | ||||
−0.257933 | + | 0.966163i | \(0.583041\pi\) | |||||||
\(828\) | 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 | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.45864 | + | 4.51314i | −0.154483 | + | 0.156371i | ||||
\(834\) | −17.3399 | −0.600432 | ||||||||
\(835\) | 4.63015 | − | 8.01966i | 0.160233 | − | 0.277532i | ||||
\(836\) | −2.95221 | − | 5.11339i | −0.102104 | − | 0.176850i | ||||
\(837\) | −7.45157 | − | 12.9065i | −0.257564 | − | 0.446114i | ||||
\(838\) | −10.1184 | + | 17.5256i | −0.349534 | + | 0.605411i | ||||
\(839\) | −36.8086 | −1.27077 | −0.635386 | − | 0.772194i | \(-0.719159\pi\) | ||||
−0.635386 | + | 0.772194i | \(0.719159\pi\) | |||||||
\(840\) | 3.01832 | + | 2.30150i | 0.104142 | + | 0.0794095i | ||||
\(841\) | 43.5128 | 1.50044 | ||||||||
\(842\) | 6.91588 | − | 11.9787i | 0.238337 | − | 0.412812i | ||||
\(843\) | 7.32728 | + | 12.6912i | 0.252365 | + | 0.437109i | ||||
\(844\) | −0.790442 | − | 1.36909i | −0.0272082 | − | 0.0471259i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 13.6772 | 0.470232 | ||||||||
\(847\) | −15.9219 | + | 6.65177i | −0.547081 | + | 0.228558i | ||||
\(848\) | 13.1639 | 0.452051 | ||||||||
\(849\) | −2.41965 | + | 4.19095i | −0.0830421 | + | 0.143833i | ||||
\(850\) | 2.52235 | + | 4.36884i | 0.0865160 | + | 0.149850i | ||||
\(851\) | 8.97819 | + | 15.5507i | 0.307768 | + | 0.533070i | ||||
\(852\) | 0.258135 | − | 0.447103i | 0.00884357 | − | 0.0153175i | ||||
\(853\) | 4.10728 | 0.140630 | 0.0703152 | − | 0.997525i | \(-0.477599\pi\) | ||||
0.0703152 | + | 0.997525i | \(0.477599\pi\) | |||||||
\(854\) | −4.33686 | + | 33.7331i | −0.148404 | + | 1.15432i | ||||
\(855\) | 22.0065 | 0.752607 | ||||||||
\(856\) | 2.70717 | − | 4.68895i | 0.0925291 | − | 0.160265i | ||||
\(857\) | 19.1656 | + | 33.1958i | 0.654684 | + | 1.13395i | 0.981973 | + | 0.189022i | \(0.0605318\pi\) |
−0.327288 | + | 0.944925i | \(0.606135\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.7185 | − | 34.1534i | 0.672785 | − | 1.16530i | −0.304326 | − | 0.952568i | \(-0.598431\pi\) |
0.977111 | − | 0.212730i | \(-0.0682356\pi\) | |||||||
\(860\) | 2.69964 | 0.0920569 | ||||||||
\(861\) | −0.253591 | + | 1.97249i | −0.00864236 | + | 0.0672223i | ||||
\(862\) | −13.9260 | −0.474322 | ||||||||
\(863\) | −19.3220 | + | 33.4667i | −0.657728 | + | 1.13922i | 0.323474 | + | 0.946237i | \(0.395149\pi\) |
−0.981202 | + | 0.192982i | \(0.938184\pi\) | |||||||
\(864\) | −3.27375 | − | 5.67030i | −0.111375 | − | 0.192907i | ||||
\(865\) | −3.63090 | − | 6.28891i | −0.123454 | − | 0.213829i | ||||
\(866\) | −0.134410 | + | 0.232805i | −0.00456744 | + | 0.00791104i | ||||
\(867\) | 7.91541 | 0.268821 | ||||||||
\(868\) | 5.38369 | − | 2.24918i | 0.182734 | − | 0.0763421i | ||||
\(869\) | −12.8500 | −0.435908 | ||||||||
\(870\) | −3.85879 | + | 6.68361i | −0.130825 | + | 0.226596i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 16.9142 | + | 29.2962i | 0.572786 | + | 0.992094i | ||||
\(873\) | −8.56395 | + | 14.8332i | −0.289846 | + | 0.502028i | ||||
\(874\) | 37.4169 | 1.26564 | ||||||||
\(875\) | 21.5093 | + | 16.4011i | 0.727145 | + | 0.554458i | ||||
\(876\) | −1.16926 | −0.0395055 | ||||||||
\(877\) | −29.0371 | + | 50.2937i | −0.980512 | + | 1.69830i | −0.320118 | + | 0.947378i | \(0.603723\pi\) |
−0.660394 | + | 0.750919i | \(0.729611\pi\) | |||||||
\(878\) | 7.41710 | + | 12.8468i | 0.250315 | + | 0.433558i | ||||
\(879\) | −1.93513 | − | 3.35175i | −0.0652704 | − | 0.113052i | ||||
\(880\) | −5.87508 | + | 10.1759i | −0.198049 | + | 0.343031i | ||||
\(881\) | 21.6236 | 0.728519 | 0.364259 | − | 0.931298i | \(-0.381322\pi\) | ||||
0.364259 | + | 0.931298i | \(0.381322\pi\) | |||||||
\(882\) | 21.1145 | − | 21.3726i | 0.710962 | − | 0.719652i | ||||
\(883\) | −22.7329 | −0.765022 | −0.382511 | − | 0.923951i | \(-0.624941\pi\) | ||||
−0.382511 | + | 0.923951i | \(0.624941\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.98644 | + | 5.17266i | 0.100388 | + | 0.173877i | ||||
\(886\) | −10.7845 | − | 18.6793i | −0.362312 | − | 0.627543i | ||||
\(887\) | 8.16585 | − | 14.1437i | 0.274182 | − | 0.474898i | −0.695746 | − | 0.718288i | \(-0.744926\pi\) |
0.969929 | + | 0.243390i | \(0.0782595\pi\) | |||||||
\(888\) | 6.01008 | 0.201685 | ||||||||
\(889\) | 32.9858 | + | 25.1521i | 1.10631 | + | 0.843574i | ||||
\(890\) | −32.8827 | −1.10223 | ||||||||
\(891\) | 7.30385 | − | 12.6506i | 0.244688 | − | 0.423812i | ||||
\(892\) | 1.01527 | + | 1.75850i | 0.0339937 | + | 0.0588788i | ||||
\(893\) | 10.6601 | + | 18.4638i | 0.356726 | + | 0.617867i | ||||
\(894\) | −5.48098 | + | 9.49333i | −0.183311 | + | 0.317504i | ||||
\(895\) | 22.0784 | 0.738000 | ||||||||
\(896\) | −33.0093 | + | 13.7905i | −1.10276 | + | 0.460708i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||||||
\(903\) | 0.896723 | − | 6.97492i | 0.0298411 | − | 0.232111i | ||||
\(904\) | −39.6089 | −1.31737 | ||||||||
\(905\) | 3.33933 | − | 5.78389i | 0.111003 | − | 0.192263i | ||||
\(906\) | 5.80288 | + | 10.0509i | 0.192788 | + | 0.333918i | ||||
\(907\) | −7.20480 | − | 12.4791i | −0.239232 | − | 0.414361i | 0.721262 | − | 0.692662i | \(-0.243562\pi\) |
−0.960494 | + | 0.278301i | \(0.910229\pi\) | |||||||
\(908\) | 5.04146 | − | 8.73207i | 0.167307 | − | 0.289784i | ||||
\(909\) | 19.9391 | 0.661339 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.32236 | −0.0438118 | −0.0219059 | − | 0.999760i | \(-0.506973\pi\) | ||||
−0.0219059 | + | 0.999760i | \(0.506973\pi\) | |||||||
\(912\) | 7.62691 | − | 13.2102i | 0.252552 | − | 0.437433i | ||||
\(913\) | 12.3063 | + | 21.3151i | 0.407278 | + | 0.705426i | ||||
\(914\) | −7.52907 | − | 13.0407i | −0.249039 | − | 0.431349i | ||||
\(915\) | −2.41004 | + | 4.17432i | −0.0796735 | + | 0.137999i | ||||
\(916\) | 9.05513 | 0.299190 | ||||||||
\(917\) | −23.2841 | + | 9.72753i | −0.768907 | + | 0.321231i | ||||
\(918\) | 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 | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −0.908428 | − | 0.692688i | −0.0298851 | − | 0.0227878i | ||||
\(925\) | 17.8714 | 0.587607 | ||||||||
\(926\) | −24.6970 | + | 42.7765i | −0.811594 | + | 1.40572i | ||||
\(927\) | 13.7016 | + | 23.7319i | 0.450021 | + | 0.779459i | ||||
\(928\) | −9.89123 | − | 17.1321i | −0.324696 | − | 0.562389i | ||||
\(929\) | −14.3194 | + | 24.8020i | −0.469805 | + | 0.813727i | −0.999404 | − | 0.0345217i | \(-0.989009\pi\) |
0.529599 | + | 0.848248i | \(0.322343\pi\) | |||||||
\(930\) | 4.79235 | 0.157147 | ||||||||
\(931\) | 45.3090 | + | 11.8460i | 1.48494 | + | 0.388237i | ||||
\(932\) | 1.58348 | 0.0518685 | ||||||||
\(933\) | 6.05778 | − | 10.4924i | 0.198323 | − | 0.343505i | ||||
\(934\) | −22.6370 | − | 39.2084i | −0.740704 | − | 1.28294i | ||||
\(935\) | −1.14258 | − | 1.97900i | −0.0373663 | − | 0.0647203i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.9990 | 0.914688 | 0.457344 | − | 0.889290i | \(-0.348801\pi\) | ||||
0.457344 | + | 0.889290i | \(0.348801\pi\) | |||||||
\(938\) | 12.2451 | + | 9.33701i | 0.399815 | + | 0.304864i | ||||
\(939\) | −1.16271 | −0.0379437 | ||||||||
\(940\) | −0.791778 | + | 1.37140i | −0.0258249 | + | 0.0447301i | ||||
\(941\) | 14.4502 | + | 25.0284i | 0.471062 | + | 0.815903i | 0.999452 | − | 0.0330983i | \(-0.0105375\pi\) |
−0.528390 | + | 0.849002i | \(0.677204\pi\) | |||||||
\(942\) | 4.34127 | + | 7.51931i | 0.141446 | + | 0.244992i | ||||
\(943\) | 2.76340 | − | 4.78635i | 0.0899887 | − | 0.155865i | ||||
\(944\) | −47.7480 | −1.55406 | ||||||||
\(945\) | 8.19816 | − | 3.42500i | 0.266686 | − | 0.111415i | ||||
\(946\) | 17.8733 | 0.581111 | ||||||||
\(947\) | 15.0617 | − | 26.0877i | 0.489441 | − | 0.847736i | −0.510486 | − | 0.859886i | \(-0.670534\pi\) |
0.999926 | + | 0.0121504i | \(0.00386769\pi\) | |||||||
\(948\) | 0.619515 | + | 1.07303i | 0.0201209 | + | 0.0348505i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 18.6199 | − | 32.2506i | 0.604109 | − | 1.04635i | ||||
\(951\) | −9.67719 | −0.313805 | ||||||||
\(952\) | 0.752474 | − | 5.85292i | 0.0243878 | − | 0.189694i | ||||
\(953\) | 4.93022 | 0.159705 | 0.0798527 | − | 0.996807i | \(-0.474555\pi\) | ||||
0.0798527 | + | 0.996807i | \(0.474555\pi\) | |||||||
\(954\) | 6.06185 | − | 10.4994i | 0.196260 | − | 0.339932i | ||||
\(955\) | −0.300084 | − | 0.519760i | −0.00971048 | − | 0.0168190i | ||||
\(956\) | 4.56879 | + | 7.91337i | 0.147765 | + | 0.255937i | ||||
\(957\) | −4.40812 | + | 7.63509i | −0.142494 | + | 0.246808i | ||||
\(958\) | 15.1144 | 0.488325 | ||||||||
\(959\) | −0.932701 | + | 7.25477i | −0.0301185 | + | 0.234269i | ||||
\(960\) | −3.32783 | −0.107405 | ||||||||
\(961\) | 1.51957 | − | 2.63197i | 0.0490184 | − | 0.0849024i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −3.03678 | − | 5.25986i | −0.0978590 | − | 0.169497i | ||||
\(964\) | −4.32665 | + | 7.49398i | −0.139352 | + | 0.241365i | ||||
\(965\) | 4.42341 | 0.142395 | ||||||||
\(966\) | 6.67992 | − | 2.79071i | 0.214923 | − | 0.0897896i | ||||
\(967\) | −29.1431 | −0.937180 | −0.468590 | − | 0.883416i | \(-0.655238\pi\) | ||||
−0.468590 | + | 0.883416i | \(0.655238\pi\) | |||||||
\(968\) | 8.02523 | − | 13.9001i | 0.257941 | − | 0.446767i | ||||
\(969\) | 1.48327 | + | 2.56910i | 0.0476495 | + | 0.0825313i | ||||
\(970\) | −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 | \(0.241814\pi\) | |||||||
\(972\) | −4.93476 | −0.158282 | ||||||||
\(973\) | 47.9619 | + | 36.5716i | 1.53759 | + | 1.17243i | ||||
\(974\) | −26.6058 | −0.852506 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.2662 | − | 33.3700i | −0.616696 | − | 1.06815i | ||||
\(977\) | 26.2609 | + | 45.4852i | 0.840161 | + | 1.45520i | 0.889758 | + | 0.456432i | \(0.150873\pi\) |
−0.0495974 | + | 0.998769i | \(0.515794\pi\) | |||||||
\(978\) | −5.47948 | + | 9.49074i | −0.175215 | + | 0.303481i | ||||
\(979\) | −37.5639 | −1.20055 | ||||||||
\(980\) | 0.920681 | + | 3.35439i | 0.0294101 | + | 0.107152i | ||||
\(981\) | 37.9472 | 1.21156 | ||||||||
\(982\) | −19.9943 | + | 34.6312i | −0.638044 | + | 1.10513i | ||||
\(983\) | −3.01884 | − | 5.22879i | −0.0962862 | − | 0.166773i | 0.813858 | − | 0.581063i | \(-0.197363\pi\) |
−0.910145 | + | 0.414291i | \(0.864030\pi\) | |||||||
\(984\) | −0.924923 | − | 1.60201i | −0.0294855 | − | 0.0510703i | ||||
\(985\) | −4.43511 | + | 7.68183i | −0.141314 | + | 0.244764i | ||||
\(986\) | 11.9984 | 0.382107 | ||||||||
\(987\) | 3.28022 | + | 2.50121i | 0.104410 | + | 0.0796143i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −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 | ||||||||
\(994\) | −9.60316 | + | 4.01197i | −0.304594 | + | 0.127252i | ||||
\(995\) | 8.94296 | 0.283511 | ||||||||
\(996\) | 1.18660 | − | 2.05525i | 0.0375988 | − | 0.0651230i | ||||
\(997\) | −2.74017 | − | 4.74611i | −0.0867819 | − | 0.150311i | 0.819367 | − | 0.573269i | \(-0.194325\pi\) |
−0.906149 | + | 0.422958i | \(0.860992\pi\) | |||||||
\(998\) | −4.20073 | − | 7.27588i | −0.132972 | − | 0.230314i | ||||
\(999\) | 7.03414 | − | 12.1835i | 0.222550 | − | 0.385468i |
(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 | 1183.2.e.g.170.5 | 12 | ||
7.2 | even | 3 | 8281.2.a.ce.1.2 | 6 | |||
7.4 | even | 3 | inner | 1183.2.e.g.508.5 | 12 | ||
7.5 | odd | 6 | 8281.2.a.cf.1.2 | 6 | |||
13.4 | even | 6 | 91.2.h.b.16.5 | yes | 12 | ||
13.10 | even | 6 | 91.2.g.b.9.2 | ✓ | 12 | ||
13.12 | even | 2 | 1183.2.e.h.170.2 | 12 | |||
39.17 | odd | 6 | 819.2.s.d.289.2 | 12 | |||
39.23 | odd | 6 | 819.2.n.d.100.5 | 12 | |||
91.4 | even | 6 | 91.2.g.b.81.2 | yes | 12 | ||
91.10 | odd | 6 | 637.2.h.l.165.5 | 12 | |||
91.12 | odd | 6 | 8281.2.a.ca.1.5 | 6 | |||
91.17 | odd | 6 | 637.2.g.l.263.2 | 12 | |||
91.23 | even | 6 | 637.2.f.k.295.2 | 12 | |||
91.25 | even | 6 | 1183.2.e.h.508.2 | 12 | |||
91.30 | even | 6 | 637.2.f.k.393.2 | 12 | |||
91.51 | even | 6 | 8281.2.a.bz.1.5 | 6 | |||
91.62 | odd | 6 | 637.2.g.l.373.2 | 12 | |||
91.69 | odd | 6 | 637.2.h.l.471.5 | 12 | |||
91.75 | odd | 6 | 637.2.f.j.295.2 | 12 | |||
91.82 | odd | 6 | 637.2.f.j.393.2 | 12 | |||
91.88 | even | 6 | 91.2.h.b.74.5 | yes | 12 | ||
273.95 | odd | 6 | 819.2.n.d.172.5 | 12 | |||
273.179 | odd | 6 | 819.2.s.d.802.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.2.g.b.9.2 | ✓ | 12 | 13.10 | even | 6 | ||
91.2.g.b.81.2 | yes | 12 | 91.4 | even | 6 | ||
91.2.h.b.16.5 | yes | 12 | 13.4 | even | 6 | ||
91.2.h.b.74.5 | yes | 12 | 91.88 | even | 6 | ||
637.2.f.j.295.2 | 12 | 91.75 | odd | 6 | |||
637.2.f.j.393.2 | 12 | 91.82 | odd | 6 | |||
637.2.f.k.295.2 | 12 | 91.23 | even | 6 | |||
637.2.f.k.393.2 | 12 | 91.30 | even | 6 | |||
637.2.g.l.263.2 | 12 | 91.17 | odd | 6 | |||
637.2.g.l.373.2 | 12 | 91.62 | odd | 6 | |||
637.2.h.l.165.5 | 12 | 91.10 | odd | 6 | |||
637.2.h.l.471.5 | 12 | 91.69 | odd | 6 | |||
819.2.n.d.100.5 | 12 | 39.23 | odd | 6 | |||
819.2.n.d.172.5 | 12 | 273.95 | odd | 6 | |||
819.2.s.d.289.2 | 12 | 39.17 | odd | 6 | |||
819.2.s.d.802.2 | 12 | 273.179 | odd | 6 | |||
1183.2.e.g.170.5 | 12 | 1.1 | even | 1 | trivial | ||
1183.2.e.g.508.5 | 12 | 7.4 | even | 3 | inner | ||
1183.2.e.h.170.2 | 12 | 13.12 | even | 2 | |||
1183.2.e.h.508.2 | 12 | 91.25 | even | 6 | |||
8281.2.a.bz.1.5 | 6 | 91.51 | even | 6 | |||
8281.2.a.ca.1.5 | 6 | 91.12 | odd | 6 | |||
8281.2.a.ce.1.2 | 6 | 7.2 | even | 3 | |||
8281.2.a.cf.1.2 | 6 | 7.5 | odd | 6 |