Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [605,2,Mod(362,605)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(605, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("605.362");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 605 = 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 605.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.83094932229\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 362.7 | ||
Character | \(\chi\) | \(=\) | 605.362 |
Dual form | 605.2.e.c.483.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/605\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(486\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.848475 | + | 0.848475i | −0.599963 | + | 0.599963i | −0.940302 | − | 0.340340i | \(-0.889458\pi\) |
0.340340 | + | 0.940302i | \(0.389458\pi\) | |||||||
\(3\) | −0.258670 | + | 0.258670i | −0.149343 | + | 0.149343i | −0.777825 | − | 0.628482i | \(-0.783677\pi\) |
0.628482 | + | 0.777825i | \(0.283677\pi\) | |||||||
\(4\) | 0.560180i | 0.280090i | ||||||||
\(5\) | −0.152228 | − | 2.23088i | −0.0680786 | − | 0.997680i | ||||
\(6\) | − | 0.438950i | − | 0.179200i | ||||||
\(7\) | 1.06376 | − | 1.06376i | 0.402063 | − | 0.402063i | −0.476897 | − | 0.878959i | \(-0.658238\pi\) |
0.878959 | + | 0.476897i | \(0.158238\pi\) | |||||||
\(8\) | −2.17225 | − | 2.17225i | −0.768006 | − | 0.768006i | ||||
\(9\) | 2.86618i | 0.955393i | ||||||||
\(10\) | 2.02201 | + | 1.76368i | 0.639415 | + | 0.557726i | ||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.144901 | − | 0.144901i | −0.0418295 | − | 0.0418295i | ||||
\(13\) | −3.20135 | − | 3.20135i | −0.887895 | − | 0.887895i | 0.106426 | − | 0.994321i | \(-0.466059\pi\) |
−0.994321 | + | 0.106426i | \(0.966059\pi\) | |||||||
\(14\) | 1.80515i | 0.482445i | ||||||||
\(15\) | 0.616438 | + | 0.537684i | 0.159164 | + | 0.138829i | ||||
\(16\) | 2.56584 | 0.641460 | ||||||||
\(17\) | −2.50878 | + | 2.50878i | −0.608469 | + | 0.608469i | −0.942546 | − | 0.334077i | \(-0.891575\pi\) |
0.334077 | + | 0.942546i | \(0.391575\pi\) | |||||||
\(18\) | −2.43188 | − | 2.43188i | −0.573200 | − | 0.573200i | ||||
\(19\) | −7.43246 | −1.70512 | −0.852562 | − | 0.522627i | \(-0.824952\pi\) | ||||
−0.852562 | + | 0.522627i | \(0.824952\pi\) | |||||||
\(20\) | 1.24969 | − | 0.0852752i | 0.279440 | − | 0.0190681i | ||||
\(21\) | 0.550324i | 0.120091i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.84232 | − | 1.84232i | 0.384150 | − | 0.384150i | −0.488445 | − | 0.872595i | \(-0.662436\pi\) |
0.872595 | + | 0.488445i | \(0.162436\pi\) | |||||||
\(24\) | 1.12379 | 0.229393 | ||||||||
\(25\) | −4.95365 | + | 0.679206i | −0.990731 | + | 0.135841i | ||||
\(26\) | 5.43253 | 1.06541 | ||||||||
\(27\) | −1.51740 | − | 1.51740i | −0.292024 | − | 0.292024i | ||||
\(28\) | 0.595896 | + | 0.595896i | 0.112614 | + | 0.112614i | ||||
\(29\) | −0.772905 | −0.143525 | −0.0717624 | − | 0.997422i | \(-0.522862\pi\) | ||||
−0.0717624 | + | 0.997422i | \(0.522862\pi\) | |||||||
\(30\) | −0.979244 | + | 0.0668206i | −0.178785 | + | 0.0121997i | ||||
\(31\) | −6.48429 | −1.16461 | −0.582307 | − | 0.812969i | \(-0.697850\pi\) | ||||
−0.582307 | + | 0.812969i | \(0.697850\pi\) | |||||||
\(32\) | 2.16745 | − | 2.16745i | 0.383154 | − | 0.383154i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 4.25728i | − | 0.730117i | ||||||
\(35\) | −2.53505 | − | 2.21118i | −0.428502 | − | 0.373758i | ||||
\(36\) | −1.60558 | −0.267596 | ||||||||
\(37\) | −2.92535 | − | 2.92535i | −0.480924 | − | 0.480924i | 0.424503 | − | 0.905427i | \(-0.360449\pi\) |
−0.905427 | + | 0.424503i | \(0.860449\pi\) | |||||||
\(38\) | 6.30626 | − | 6.30626i | 1.02301 | − | 1.02301i | ||||
\(39\) | 1.65618 | 0.265202 | ||||||||
\(40\) | −4.51535 | + | 5.17670i | −0.713939 | + | 0.818509i | ||||
\(41\) | − | 6.91063i | − | 1.07926i | −0.841902 | − | 0.539630i | \(-0.818564\pi\) | ||
0.841902 | − | 0.539630i | \(-0.181436\pi\) | |||||||
\(42\) | −0.466936 | − | 0.466936i | −0.0720499 | − | 0.0720499i | ||||
\(43\) | −0.500677 | − | 0.500677i | −0.0763525 | − | 0.0763525i | 0.667899 | − | 0.744252i | \(-0.267194\pi\) |
−0.744252 | + | 0.667899i | \(0.767194\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.39410 | − | 0.436314i | 0.953177 | − | 0.0650418i | ||||
\(46\) | 3.12633i | 0.460952i | ||||||||
\(47\) | 5.46865 | + | 5.46865i | 0.797684 | + | 0.797684i | 0.982730 | − | 0.185046i | \(-0.0592433\pi\) |
−0.185046 | + | 0.982730i | \(0.559243\pi\) | |||||||
\(48\) | −0.663705 | + | 0.663705i | −0.0957976 | + | 0.0957976i | ||||
\(49\) | 4.73684i | 0.676691i | ||||||||
\(50\) | 3.62676 | − | 4.77934i | 0.512902 | − | 0.675901i | ||||
\(51\) | − | 1.29789i | − | 0.181741i | ||||||
\(52\) | 1.79333 | − | 1.79333i | 0.248690 | − | 0.248690i | ||||
\(53\) | 7.53208 | − | 7.53208i | 1.03461 | − | 1.03461i | 0.0352322 | − | 0.999379i | \(-0.488783\pi\) |
0.999379 | − | 0.0352322i | \(-0.0112171\pi\) | |||||||
\(54\) | 2.57496 | 0.350407 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.62150 | −0.617573 | ||||||||
\(57\) | 1.92255 | − | 1.92255i | 0.254648 | − | 0.254648i | ||||
\(58\) | 0.655791 | − | 0.655791i | 0.0861095 | − | 0.0861095i | ||||
\(59\) | − | 12.2294i | − | 1.59214i | −0.605206 | − | 0.796069i | \(-0.706909\pi\) | ||
0.605206 | − | 0.796069i | \(-0.293091\pi\) | |||||||
\(60\) | −0.301200 | + | 0.345316i | −0.0388847 | + | 0.0445801i | ||||
\(61\) | 3.31937i | 0.425001i | 0.977161 | + | 0.212501i | \(0.0681608\pi\) | ||||
−0.977161 | + | 0.212501i | \(0.931839\pi\) | |||||||
\(62\) | 5.50176 | − | 5.50176i | 0.698725 | − | 0.698725i | ||||
\(63\) | 3.04892 | + | 3.04892i | 0.384128 | + | 0.384128i | ||||
\(64\) | 8.80973i | 1.10122i | ||||||||
\(65\) | −6.65449 | + | 7.62916i | −0.825388 | + | 0.946281i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.34899 | − | 3.34899i | −0.409145 | − | 0.409145i | 0.472296 | − | 0.881440i | \(-0.343425\pi\) |
−0.881440 | + | 0.472296i | \(0.843425\pi\) | |||||||
\(68\) | −1.40537 | − | 1.40537i | −0.170426 | − | 0.170426i | ||||
\(69\) | 0.953105i | 0.114740i | ||||||||
\(70\) | 4.02706 | − | 0.274794i | 0.481326 | − | 0.0328442i | ||||
\(71\) | −11.9496 | −1.41815 | −0.709076 | − | 0.705132i | \(-0.750888\pi\) | ||||
−0.709076 | + | 0.705132i | \(0.750888\pi\) | |||||||
\(72\) | 6.22606 | − | 6.22606i | 0.733748 | − | 0.733748i | ||||
\(73\) | −6.73109 | − | 6.73109i | −0.787815 | − | 0.787815i | 0.193321 | − | 0.981136i | \(-0.438074\pi\) |
−0.981136 | + | 0.193321i | \(0.938074\pi\) | |||||||
\(74\) | 4.96417 | 0.577073 | ||||||||
\(75\) | 1.10567 | − | 1.45705i | 0.127672 | − | 0.168246i | ||||
\(76\) | − | 4.16351i | − | 0.477588i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.40523 | + | 1.40523i | −0.159111 | + | 0.159111i | ||||
\(79\) | 11.4583 | 1.28915 | 0.644577 | − | 0.764539i | \(-0.277033\pi\) | ||||
0.644577 | + | 0.764539i | \(0.277033\pi\) | |||||||
\(80\) | −0.390593 | − | 5.72408i | −0.0436697 | − | 0.639972i | ||||
\(81\) | −7.81353 | −0.868170 | ||||||||
\(82\) | 5.86350 | + | 5.86350i | 0.647515 | + | 0.647515i | ||||
\(83\) | 2.80014 | + | 2.80014i | 0.307356 | + | 0.307356i | 0.843883 | − | 0.536527i | \(-0.180264\pi\) |
−0.536527 | + | 0.843883i | \(0.680264\pi\) | |||||||
\(84\) | −0.308280 | −0.0336361 | ||||||||
\(85\) | 5.97870 | + | 5.21488i | 0.648481 | + | 0.565634i | ||||
\(86\) | 0.849623 | 0.0916172 | ||||||||
\(87\) | 0.199927 | − | 0.199927i | 0.0214344 | − | 0.0214344i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.96633i | 1.05643i | 0.849111 | + | 0.528214i | \(0.177138\pi\) | ||||
−0.849111 | + | 0.528214i | \(0.822862\pi\) | |||||||
\(90\) | −5.05504 | + | 5.79544i | −0.532848 | + | 0.610893i | ||||
\(91\) | −6.81093 | −0.713979 | ||||||||
\(92\) | 1.03203 | + | 1.03203i | 0.107597 | + | 0.107597i | ||||
\(93\) | 1.67729 | − | 1.67729i | 0.173927 | − | 0.173927i | ||||
\(94\) | −9.28003 | −0.957162 | ||||||||
\(95\) | 1.13143 | + | 16.5809i | 0.116082 | + | 1.70117i | ||||
\(96\) | 1.12131i | 0.114443i | ||||||||
\(97\) | −8.11524 | − | 8.11524i | −0.823978 | − | 0.823978i | 0.162698 | − | 0.986676i | \(-0.447980\pi\) |
−0.986676 | + | 0.162698i | \(0.947980\pi\) | |||||||
\(98\) | −4.01909 | − | 4.01909i | −0.405989 | − | 0.405989i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.380477 | − | 2.77494i | −0.0380477 | − | 0.277494i | ||||
\(101\) | 3.77428i | 0.375555i | 0.982212 | + | 0.187778i | \(0.0601284\pi\) | ||||
−0.982212 | + | 0.187778i | \(0.939872\pi\) | |||||||
\(102\) | 1.10123 | + | 1.10123i | 0.109038 | + | 0.109038i | ||||
\(103\) | −9.28131 | + | 9.28131i | −0.914515 | + | 0.914515i | −0.996623 | − | 0.0821088i | \(-0.973835\pi\) |
0.0821088 | + | 0.996623i | \(0.473835\pi\) | |||||||
\(104\) | 13.9083i | 1.36382i | ||||||||
\(105\) | 1.22771 | − | 0.0837749i | 0.119812 | − | 0.00817559i | ||||
\(106\) | 12.7816i | 1.24146i | ||||||||
\(107\) | −2.20766 | + | 2.20766i | −0.213423 | + | 0.213423i | −0.805720 | − | 0.592297i | \(-0.798221\pi\) |
0.592297 | + | 0.805720i | \(0.298221\pi\) | |||||||
\(108\) | 0.850018 | − | 0.850018i | 0.0817930 | − | 0.0817930i | ||||
\(109\) | −2.26336 | −0.216791 | −0.108395 | − | 0.994108i | \(-0.534571\pi\) | ||||
−0.108395 | + | 0.994108i | \(0.534571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.51340 | 0.143645 | ||||||||
\(112\) | 2.72943 | − | 2.72943i | 0.257907 | − | 0.257907i | ||||
\(113\) | 13.9390 | − | 13.9390i | 1.31127 | − | 1.31127i | 0.390787 | − | 0.920481i | \(-0.372203\pi\) |
0.920481 | − | 0.390787i | \(-0.127797\pi\) | |||||||
\(114\) | 3.26248i | 0.305559i | ||||||||
\(115\) | −4.39045 | − | 3.82954i | −0.409412 | − | 0.357107i | ||||
\(116\) | − | 0.432966i | − | 0.0401998i | ||||||
\(117\) | 9.17565 | − | 9.17565i | 0.848289 | − | 0.848289i | ||||
\(118\) | 10.3764 | + | 10.3764i | 0.955223 | + | 0.955223i | ||||
\(119\) | 5.33748i | 0.489286i | ||||||||
\(120\) | −0.171073 | − | 2.50704i | −0.0156167 | − | 0.228860i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −2.81640 | − | 2.81640i | −0.254985 | − | 0.254985i | ||||
\(123\) | 1.78757 | + | 1.78757i | 0.161180 | + | 0.161180i | ||||
\(124\) | − | 3.63237i | − | 0.326196i | ||||||
\(125\) | 2.26931 | + | 10.9476i | 0.202974 | + | 0.979184i | ||||
\(126\) | −5.17387 | −0.460925 | ||||||||
\(127\) | −14.4700 | + | 14.4700i | −1.28401 | + | 1.28401i | −0.345637 | + | 0.938368i | \(0.612337\pi\) |
−0.938368 | + | 0.345637i | \(0.887663\pi\) | |||||||
\(128\) | −3.13994 | − | 3.13994i | −0.277534 | − | 0.277534i | ||||
\(129\) | 0.259020 | 0.0228054 | ||||||||
\(130\) | −0.826985 | − | 12.1193i | −0.0725314 | − | 1.06294i | ||||
\(131\) | 8.57191i | 0.748931i | 0.927241 | + | 0.374465i | \(0.122174\pi\) | ||||
−0.927241 | + | 0.374465i | \(0.877826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.90634 | + | 7.90634i | −0.685567 | + | 0.685567i | ||||
\(134\) | 5.68307 | 0.490943 | ||||||||
\(135\) | −3.15415 | + | 3.61614i | −0.271466 | + | 0.311227i | ||||
\(136\) | 10.8994 | 0.934616 | ||||||||
\(137\) | −0.590371 | − | 0.590371i | −0.0504388 | − | 0.0504388i | 0.681438 | − | 0.731876i | \(-0.261355\pi\) |
−0.731876 | + | 0.681438i | \(0.761355\pi\) | |||||||
\(138\) | −0.808686 | − | 0.808686i | −0.0688399 | − | 0.0688399i | ||||
\(139\) | 20.0766 | 1.70288 | 0.851438 | − | 0.524455i | \(-0.175731\pi\) | ||||
0.851438 | + | 0.524455i | \(0.175731\pi\) | |||||||
\(140\) | 1.23866 | − | 1.42008i | 0.104686 | − | 0.120019i | ||||
\(141\) | −2.82915 | −0.238257 | ||||||||
\(142\) | 10.1389 | − | 10.1389i | 0.850838 | − | 0.850838i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.35416i | 0.612847i | ||||||||
\(145\) | 0.117658 | + | 1.72426i | 0.00977096 | + | 0.143192i | ||||
\(146\) | 11.4223 | 0.945319 | ||||||||
\(147\) | −1.22528 | − | 1.22528i | −0.101059 | − | 0.101059i | ||||
\(148\) | 1.63872 | − | 1.63872i | 0.134702 | − | 0.134702i | ||||
\(149\) | 2.37943 | 0.194930 | 0.0974651 | − | 0.995239i | \(-0.468927\pi\) | ||||
0.0974651 | + | 0.995239i | \(0.468927\pi\) | |||||||
\(150\) | 0.298137 | + | 2.17440i | 0.0243428 | + | 0.177539i | ||||
\(151\) | 17.9691i | 1.46231i | 0.682214 | + | 0.731153i | \(0.261017\pi\) | ||||
−0.682214 | + | 0.731153i | \(0.738983\pi\) | |||||||
\(152\) | 16.1452 | + | 16.1452i | 1.30954 | + | 1.30954i | ||||
\(153\) | −7.19062 | − | 7.19062i | −0.581327 | − | 0.581327i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.987093 | + | 14.4657i | 0.0792852 | + | 1.16191i | ||||
\(156\) | 0.927761i | 0.0742803i | ||||||||
\(157\) | −2.09908 | − | 2.09908i | −0.167525 | − | 0.167525i | 0.618365 | − | 0.785891i | \(-0.287795\pi\) |
−0.785891 | + | 0.618365i | \(0.787795\pi\) | |||||||
\(158\) | −9.72205 | + | 9.72205i | −0.773445 | + | 0.773445i | ||||
\(159\) | 3.89664i | 0.309024i | ||||||||
\(160\) | −5.16526 | − | 4.50537i | −0.408350 | − | 0.356180i | ||||
\(161\) | − | 3.91957i | − | 0.308905i | ||||||
\(162\) | 6.62958 | − | 6.62958i | 0.520869 | − | 0.520869i | ||||
\(163\) | 2.15084 | − | 2.15084i | 0.168467 | − | 0.168467i | −0.617838 | − | 0.786305i | \(-0.711991\pi\) |
0.786305 | + | 0.617838i | \(0.211991\pi\) | |||||||
\(164\) | 3.87119 | 0.302290 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.75171 | −0.368804 | ||||||||
\(167\) | −2.69793 | + | 2.69793i | −0.208772 | + | 0.208772i | −0.803746 | − | 0.594973i | \(-0.797163\pi\) |
0.594973 | + | 0.803746i | \(0.297163\pi\) | |||||||
\(168\) | 1.19544 | − | 1.19544i | 0.0922303 | − | 0.0922303i | ||||
\(169\) | 7.49728i | 0.576714i | ||||||||
\(170\) | −9.49748 | + | 0.648078i | −0.728423 | + | 0.0497053i | ||||
\(171\) | − | 21.3028i | − | 1.62906i | ||||||
\(172\) | 0.280469 | − | 0.280469i | 0.0213855 | − | 0.0213855i | ||||
\(173\) | 0.824604 | + | 0.824604i | 0.0626935 | + | 0.0626935i | 0.737758 | − | 0.675065i | \(-0.235884\pi\) |
−0.675065 | + | 0.737758i | \(0.735884\pi\) | |||||||
\(174\) | 0.339266i | 0.0257197i | ||||||||
\(175\) | −4.54698 | + | 5.99200i | −0.343719 | + | 0.452953i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.16339 | + | 3.16339i | 0.237775 | + | 0.237775i | ||||
\(178\) | −8.45618 | − | 8.45618i | −0.633818 | − | 0.633818i | ||||
\(179\) | 6.06351i | 0.453208i | 0.973987 | + | 0.226604i | \(0.0727623\pi\) | ||||
−0.973987 | + | 0.226604i | \(0.927238\pi\) | |||||||
\(180\) | 0.244414 | + | 3.58185i | 0.0182175 | + | 0.266975i | ||||
\(181\) | 1.56433 | 0.116276 | 0.0581378 | − | 0.998309i | \(-0.481484\pi\) | ||||
0.0581378 | + | 0.998309i | \(0.481484\pi\) | |||||||
\(182\) | 5.77890 | − | 5.77890i | 0.428361 | − | 0.428361i | ||||
\(183\) | −0.858620 | − | 0.858620i | −0.0634710 | − | 0.0634710i | ||||
\(184\) | −8.00396 | −0.590060 | ||||||||
\(185\) | −6.08078 | + | 6.97142i | −0.447068 | + | 0.512549i | ||||
\(186\) | 2.84628i | 0.208699i | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −3.06342 | + | 3.06342i | −0.223423 | + | 0.223423i | ||||
\(189\) | −3.22830 | −0.234824 | ||||||||
\(190\) | −15.0285 | − | 13.1085i | −1.09028 | − | 0.950992i | ||||
\(191\) | 1.33597 | 0.0966677 | 0.0483338 | − | 0.998831i | \(-0.484609\pi\) | ||||
0.0483338 | + | 0.998831i | \(0.484609\pi\) | |||||||
\(192\) | −2.27881 | − | 2.27881i | −0.164459 | − | 0.164459i | ||||
\(193\) | 1.17411 | + | 1.17411i | 0.0845144 | + | 0.0845144i | 0.748100 | − | 0.663586i | \(-0.230966\pi\) |
−0.663586 | + | 0.748100i | \(0.730966\pi\) | |||||||
\(194\) | 13.7712 | 0.988712 | ||||||||
\(195\) | −0.252118 | − | 3.69475i | −0.0180546 | − | 0.264587i | ||||
\(196\) | −2.65348 | −0.189534 | ||||||||
\(197\) | −3.99064 | + | 3.99064i | −0.284321 | + | 0.284321i | −0.834830 | − | 0.550508i | \(-0.814434\pi\) |
0.550508 | + | 0.834830i | \(0.314434\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.55260i | − | 0.606278i | −0.952946 | − | 0.303139i | \(-0.901965\pi\) | ||
0.952946 | − | 0.303139i | \(-0.0980346\pi\) | |||||||
\(200\) | 12.2360 | + | 9.28516i | 0.865214 | + | 0.656560i | ||||
\(201\) | 1.73257 | 0.122206 | ||||||||
\(202\) | −3.20238 | − | 3.20238i | −0.225319 | − | 0.225319i | ||||
\(203\) | −0.822184 | + | 0.822184i | −0.0577060 | + | 0.0577060i | ||||
\(204\) | 0.727052 | 0.0509038 | ||||||||
\(205\) | −15.4168 | + | 1.05199i | −1.07676 | + | 0.0734744i | ||||
\(206\) | − | 15.7499i | − | 1.09735i | ||||||
\(207\) | 5.28042 | + | 5.28042i | 0.367015 | + | 0.367015i | ||||
\(208\) | −8.21415 | − | 8.21415i | −0.569549 | − | 0.569549i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −0.970598 | + | 1.11276i | −0.0669777 | + | 0.0767878i | ||||
\(211\) | 12.1227i | 0.834564i | 0.908777 | + | 0.417282i | \(0.137017\pi\) | ||||
−0.908777 | + | 0.417282i | \(0.862983\pi\) | |||||||
\(212\) | 4.21932 | + | 4.21932i | 0.289784 | + | 0.289784i | ||||
\(213\) | 3.09099 | − | 3.09099i | 0.211791 | − | 0.211791i | ||||
\(214\) | − | 3.74629i | − | 0.256091i | ||||||
\(215\) | −1.04073 | + | 1.19317i | −0.0709774 | + | 0.0813733i | ||||
\(216\) | 6.59235i | 0.448553i | ||||||||
\(217\) | −6.89772 | + | 6.89772i | −0.468248 | + | 0.468248i | ||||
\(218\) | 1.92040 | − | 1.92040i | 0.130066 | − | 0.130066i | ||||
\(219\) | 3.48226 | 0.235309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.0630 | 1.08051 | ||||||||
\(222\) | −1.28408 | + | 1.28408i | −0.0861818 | + | 0.0861818i | ||||
\(223\) | 3.51789 | − | 3.51789i | 0.235575 | − | 0.235575i | −0.579440 | − | 0.815015i | \(-0.696729\pi\) |
0.815015 | + | 0.579440i | \(0.196729\pi\) | |||||||
\(224\) | − | 4.61128i | − | 0.308104i | ||||||
\(225\) | −1.94673 | − | 14.1981i | −0.129782 | − | 0.946537i | ||||
\(226\) | 23.6537i | 1.57342i | ||||||||
\(227\) | −4.85408 | + | 4.85408i | −0.322177 | + | 0.322177i | −0.849602 | − | 0.527425i | \(-0.823158\pi\) |
0.527425 | + | 0.849602i | \(0.323158\pi\) | |||||||
\(228\) | 1.07697 | + | 1.07697i | 0.0713244 | + | 0.0713244i | ||||
\(229\) | − | 13.1801i | − | 0.870964i | −0.900197 | − | 0.435482i | \(-0.856578\pi\) | ||
0.900197 | − | 0.435482i | \(-0.143422\pi\) | |||||||
\(230\) | 6.97446 | − | 0.475915i | 0.459882 | − | 0.0313809i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.67894 | + | 1.67894i | 0.110228 | + | 0.110228i | ||||
\(233\) | −10.6591 | − | 10.6591i | −0.698301 | − | 0.698301i | 0.265743 | − | 0.964044i | \(-0.414383\pi\) |
−0.964044 | + | 0.265743i | \(0.914383\pi\) | |||||||
\(234\) | 15.5706i | 1.01788i | ||||||||
\(235\) | 11.3674 | − | 13.0324i | 0.741528 | − | 0.850139i | ||||
\(236\) | 6.85068 | 0.445942 | ||||||||
\(237\) | −2.96390 | + | 2.96390i | −0.192526 | + | 0.192526i | ||||
\(238\) | −4.52872 | − | 4.52872i | −0.293553 | − | 0.293553i | ||||
\(239\) | 13.3578 | 0.864047 | 0.432023 | − | 0.901862i | \(-0.357800\pi\) | ||||
0.432023 | + | 0.901862i | \(0.357800\pi\) | |||||||
\(240\) | 1.58168 | + | 1.37961i | 0.102097 | + | 0.0890536i | ||||
\(241\) | − | 6.28913i | − | 0.405119i | −0.979270 | − | 0.202559i | \(-0.935074\pi\) | ||
0.979270 | − | 0.202559i | \(-0.0649259\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.57333 | − | 6.57333i | 0.421679 | − | 0.421679i | ||||
\(244\) | −1.85944 | −0.119039 | ||||||||
\(245\) | 10.5673 | − | 0.721080i | 0.675121 | − | 0.0460681i | ||||
\(246\) | −3.03342 | −0.193404 | ||||||||
\(247\) | 23.7939 | + | 23.7939i | 1.51397 | + | 1.51397i | ||||
\(248\) | 14.0855 | + | 14.0855i | 0.894430 | + | 0.894430i | ||||
\(249\) | −1.44862 | −0.0918029 | ||||||||
\(250\) | −11.2142 | − | 7.36332i | −0.709250 | − | 0.465697i | ||||
\(251\) | −4.11128 | −0.259502 | −0.129751 | − | 0.991547i | \(-0.541418\pi\) | ||||
−0.129751 | + | 0.991547i | \(0.541418\pi\) | |||||||
\(252\) | −1.70794 | + | 1.70794i | −0.107590 | + | 0.107590i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − | 24.5549i | − | 1.54071i | ||||||
\(255\) | −2.89544 | + | 0.197576i | −0.181320 | + | 0.0123727i | ||||
\(256\) | −12.2911 | −0.768195 | ||||||||
\(257\) | −5.68725 | − | 5.68725i | −0.354761 | − | 0.354761i | 0.507117 | − | 0.861877i | \(-0.330711\pi\) |
−0.861877 | + | 0.507117i | \(0.830711\pi\) | |||||||
\(258\) | −0.219772 | + | 0.219772i | −0.0136824 | + | 0.0136824i | ||||
\(259\) | −6.22373 | −0.386724 | ||||||||
\(260\) | −4.27370 | − | 3.72771i | −0.265044 | − | 0.231183i | ||||
\(261\) | − | 2.21528i | − | 0.137123i | ||||||
\(262\) | −7.27305 | − | 7.27305i | −0.449331 | − | 0.449331i | ||||
\(263\) | 16.1103 | + | 16.1103i | 0.993403 | + | 0.993403i | 0.999978 | − | 0.00657518i | \(-0.00209296\pi\) |
−0.00657518 | + | 0.999978i | \(0.502093\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.9498 | − | 15.6566i | −1.10265 | − | 0.961776i | ||||
\(266\) | − | 13.4167i | − | 0.822629i | ||||||
\(267\) | −2.57799 | − | 2.57799i | −0.157770 | − | 0.157770i | ||||
\(268\) | 1.87604 | − | 1.87604i | 0.114597 | − | 0.114597i | ||||
\(269\) | − | 14.0599i | − | 0.857245i | −0.903484 | − | 0.428622i | \(-0.858999\pi\) | ||
0.903484 | − | 0.428622i | \(-0.141001\pi\) | |||||||
\(270\) | −0.391981 | − | 5.74442i | −0.0238552 | − | 0.349594i | ||||
\(271\) | − | 0.0709860i | − | 0.00431209i | −0.999998 | − | 0.00215605i | \(-0.999314\pi\) | ||
0.999998 | − | 0.00215605i | \(-0.000686291\pi\) | |||||||
\(272\) | −6.43713 | + | 6.43713i | −0.390308 | + | 0.390308i | ||||
\(273\) | 1.76178 | − | 1.76178i | 0.106628 | − | 0.106628i | ||||
\(274\) | 1.00183 | 0.0605227 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.533910 | −0.0321376 | ||||||||
\(277\) | 18.2120 | − | 18.2120i | 1.09425 | − | 1.09425i | 0.0991833 | − | 0.995069i | \(-0.468377\pi\) |
0.995069 | − | 0.0991833i | \(-0.0316230\pi\) | |||||||
\(278\) | −17.0345 | + | 17.0345i | −1.02166 | + | 1.02166i | ||||
\(279\) | − | 18.5852i | − | 1.11266i | ||||||
\(280\) | 0.703523 | + | 10.3100i | 0.0420435 | + | 0.616141i | ||||
\(281\) | − | 18.4946i | − | 1.10330i | −0.834077 | − | 0.551648i | \(-0.813999\pi\) | ||
0.834077 | − | 0.551648i | \(-0.186001\pi\) | |||||||
\(282\) | 2.40046 | − | 2.40046i | 0.142945 | − | 0.142945i | ||||
\(283\) | −21.8500 | − | 21.8500i | −1.29885 | − | 1.29885i | −0.929155 | − | 0.369690i | \(-0.879464\pi\) |
−0.369690 | − | 0.929155i | \(-0.620536\pi\) | |||||||
\(284\) | − | 6.69390i | − | 0.397210i | ||||||
\(285\) | −4.58165 | − | 3.99632i | −0.271394 | − | 0.236721i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.35124 | − | 7.35124i | −0.433930 | − | 0.433930i | ||||
\(288\) | 6.21229 | + | 6.21229i | 0.366063 | + | 0.366063i | ||||
\(289\) | 4.41203i | 0.259531i | ||||||||
\(290\) | −1.56282 | − | 1.36316i | −0.0917720 | − | 0.0800475i | ||||
\(291\) | 4.19833 | 0.246111 | ||||||||
\(292\) | 3.77062 | − | 3.77062i | 0.220659 | − | 0.220659i | ||||
\(293\) | −21.0777 | − | 21.0777i | −1.23137 | − | 1.23137i | −0.963437 | − | 0.267936i | \(-0.913659\pi\) |
−0.267936 | − | 0.963437i | \(-0.586341\pi\) | |||||||
\(294\) | 2.07923 | 0.121263 | ||||||||
\(295\) | −27.2824 | + | 1.86167i | −1.58844 | + | 0.108390i | ||||
\(296\) | 12.7092i | 0.738705i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.01888 | + | 2.01888i | −0.116951 | + | 0.116951i | ||||
\(299\) | −11.7958 | −0.682170 | ||||||||
\(300\) | 0.816210 | + | 0.619374i | 0.0471239 | + | 0.0357596i | ||||
\(301\) | −1.06520 | −0.0613970 | ||||||||
\(302\) | −15.2463 | − | 15.2463i | −0.877329 | − | 0.877329i | ||||
\(303\) | −0.976292 | − | 0.976292i | −0.0560865 | − | 0.0560865i | ||||
\(304\) | −19.0705 | −1.09377 | ||||||||
\(305\) | 7.40511 | − | 0.505302i | 0.424015 | − | 0.0289335i | ||||
\(306\) | 12.2021 | 0.697549 | ||||||||
\(307\) | −0.837241 | + | 0.837241i | −0.0477839 | + | 0.0477839i | −0.730595 | − | 0.682811i | \(-0.760757\pi\) |
0.682811 | + | 0.730595i | \(0.260757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.80159i | − | 0.273153i | ||||||
\(310\) | −13.1113 | − | 11.4363i | −0.744672 | − | 0.649535i | ||||
\(311\) | −14.9492 | −0.847689 | −0.423844 | − | 0.905735i | \(-0.639320\pi\) | ||||
−0.423844 | + | 0.905735i | \(0.639320\pi\) | |||||||
\(312\) | −3.59765 | − | 3.59765i | −0.203677 | − | 0.203677i | ||||
\(313\) | 14.7481 | − | 14.7481i | 0.833611 | − | 0.833611i | −0.154398 | − | 0.988009i | \(-0.549344\pi\) |
0.988009 | + | 0.154398i | \(0.0493437\pi\) | |||||||
\(314\) | 3.56204 | 0.201018 | ||||||||
\(315\) | 6.33765 | − | 7.26592i | 0.357086 | − | 0.409388i | ||||
\(316\) | 6.41868i | 0.361079i | ||||||||
\(317\) | 2.90042 | + | 2.90042i | 0.162904 | + | 0.162904i | 0.783852 | − | 0.620948i | \(-0.213252\pi\) |
−0.620948 | + | 0.783852i | \(0.713252\pi\) | |||||||
\(318\) | −3.30621 | − | 3.30621i | −0.185403 | − | 0.185403i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 19.6534 | − | 1.34109i | 1.09866 | − | 0.0749692i | ||||
\(321\) | − | 1.14211i | − | 0.0637463i | ||||||
\(322\) | 3.32566 | + | 3.32566i | 0.185332 | + | 0.185332i | ||||
\(323\) | 18.6464 | − | 18.6464i | 1.03751 | − | 1.03751i | ||||
\(324\) | − | 4.37698i | − | 0.243165i | ||||||
\(325\) | 18.0328 | + | 13.6840i | 1.00028 | + | 0.759052i | ||||
\(326\) | 3.64988i | 0.202148i | ||||||||
\(327\) | 0.585463 | − | 0.585463i | 0.0323762 | − | 0.0323762i | ||||
\(328\) | −15.0116 | + | 15.0116i | −0.828878 | + | 0.828878i | ||||
\(329\) | 11.6346 | 0.641439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.4680 | 0.740270 | 0.370135 | − | 0.928978i | \(-0.379311\pi\) | ||||
0.370135 | + | 0.928978i | \(0.379311\pi\) | |||||||
\(332\) | −1.56858 | + | 1.56858i | −0.0860872 | + | 0.0860872i | ||||
\(333\) | 8.38457 | − | 8.38457i | 0.459472 | − | 0.459472i | ||||
\(334\) | − | 4.57826i | − | 0.250511i | ||||||
\(335\) | −6.96139 | + | 7.98101i | −0.380341 | + | 0.436049i | ||||
\(336\) | 1.41204i | 0.0770333i | ||||||||
\(337\) | −20.1440 | + | 20.1440i | −1.09731 | + | 1.09731i | −0.102589 | + | 0.994724i | \(0.532713\pi\) |
−0.994724 | + | 0.102589i | \(0.967287\pi\) | |||||||
\(338\) | −6.36126 | − | 6.36126i | −0.346007 | − | 0.346007i | ||||
\(339\) | 7.21118i | 0.391658i | ||||||||
\(340\) | −2.92127 | + | 3.34914i | −0.158428 | + | 0.181633i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 18.0749 | + | 18.0749i | 0.977377 | + | 0.977377i | ||||
\(343\) | 12.4852 | + | 12.4852i | 0.674135 | + | 0.674135i | ||||
\(344\) | 2.17519i | 0.117278i | ||||||||
\(345\) | 2.12626 | − | 0.145090i | 0.114474 | − | 0.00781136i | ||||
\(346\) | −1.39931 | −0.0752275 | ||||||||
\(347\) | 8.37190 | − | 8.37190i | 0.449427 | − | 0.449427i | −0.445737 | − | 0.895164i | \(-0.647058\pi\) |
0.895164 | + | 0.445737i | \(0.147058\pi\) | |||||||
\(348\) | 0.111995 | + | 0.111995i | 0.00600357 | + | 0.00600357i | ||||
\(349\) | −8.20105 | −0.438992 | −0.219496 | − | 0.975613i | \(-0.570441\pi\) | ||||
−0.219496 | + | 0.975613i | \(0.570441\pi\) | |||||||
\(350\) | −1.22607 | − | 8.94207i | −0.0655360 | − | 0.477973i | ||||
\(351\) | 9.71548i | 0.518574i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.53600 | − | 9.53600i | 0.507550 | − | 0.507550i | −0.406224 | − | 0.913774i | \(-0.633155\pi\) |
0.913774 | + | 0.406224i | \(0.133155\pi\) | |||||||
\(354\) | −5.36811 | −0.285312 | ||||||||
\(355\) | 1.81906 | + | 26.6580i | 0.0965457 | + | 1.41486i | ||||
\(356\) | −5.58293 | −0.295895 | ||||||||
\(357\) | −1.38064 | − | 1.38064i | −0.0730714 | − | 0.0730714i | ||||
\(358\) | −5.14474 | − | 5.14474i | −0.271908 | − | 0.271908i | ||||
\(359\) | 14.3410 | 0.756889 | 0.378444 | − | 0.925624i | \(-0.376459\pi\) | ||||
0.378444 | + | 0.925624i | \(0.376459\pi\) | |||||||
\(360\) | −14.8374 | − | 12.9418i | −0.781998 | − | 0.682093i | ||||
\(361\) | 36.2415 | 1.90745 | ||||||||
\(362\) | −1.32729 | + | 1.32729i | −0.0697610 | + | 0.0697610i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 3.81534i | − | 0.199978i | ||||||
\(365\) | −13.9916 | + | 16.0409i | −0.732354 | + | 0.839620i | ||||
\(366\) | 1.45704 | 0.0761604 | ||||||||
\(367\) | 14.2153 | + | 14.2153i | 0.742034 | + | 0.742034i | 0.972969 | − | 0.230935i | \(-0.0741784\pi\) |
−0.230935 | + | 0.972969i | \(0.574178\pi\) | |||||||
\(368\) | 4.72710 | − | 4.72710i | 0.246417 | − | 0.246417i | ||||
\(369\) | 19.8071 | 1.03112 | ||||||||
\(370\) | −0.755687 | − | 11.0745i | −0.0392863 | − | 0.575734i | ||||
\(371\) | − | 16.0246i | − | 0.831958i | ||||||
\(372\) | 0.939584 | + | 0.939584i | 0.0487151 | + | 0.0487151i | ||||
\(373\) | 0.641626 | + | 0.641626i | 0.0332221 | + | 0.0332221i | 0.723523 | − | 0.690301i | \(-0.242522\pi\) |
−0.690301 | + | 0.723523i | \(0.742522\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.41882 | − | 2.24481i | −0.176547 | − | 0.115922i | ||||
\(376\) | − | 23.7585i | − | 1.22525i | ||||||
\(377\) | 2.47434 | + | 2.47434i | 0.127435 | + | 0.127435i | ||||
\(378\) | 2.73913 | − | 2.73913i | 0.140886 | − | 0.140886i | ||||
\(379\) | − | 10.9413i | − | 0.562018i | −0.959705 | − | 0.281009i | \(-0.909331\pi\) | ||
0.959705 | − | 0.281009i | \(-0.0906691\pi\) | |||||||
\(380\) | −9.28830 | + | 0.633804i | −0.476480 | + | 0.0325135i | ||||
\(381\) | − | 7.48590i | − | 0.383514i | ||||||
\(382\) | −1.13354 | + | 1.13354i | −0.0579970 | + | 0.0579970i | ||||
\(383\) | −6.38190 | + | 6.38190i | −0.326100 | + | 0.326100i | −0.851101 | − | 0.525002i | \(-0.824065\pi\) |
0.525002 | + | 0.851101i | \(0.324065\pi\) | |||||||
\(384\) | 1.62442 | 0.0828957 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.99241 | −0.101411 | ||||||||
\(387\) | 1.43503 | − | 1.43503i | 0.0729466 | − | 0.0729466i | ||||
\(388\) | 4.54599 | − | 4.54599i | 0.230788 | − | 0.230788i | ||||
\(389\) | 16.7680i | 0.850169i | 0.905154 | + | 0.425085i | \(0.139756\pi\) | ||||
−0.905154 | + | 0.425085i | \(0.860244\pi\) | |||||||
\(390\) | 3.34882 | + | 2.92099i | 0.169574 | + | 0.147910i | ||||
\(391\) | 9.24396i | 0.467487i | ||||||||
\(392\) | 10.2896 | − | 10.2896i | 0.519703 | − | 0.519703i | ||||
\(393\) | −2.21729 | − | 2.21729i | −0.111848 | − | 0.111848i | ||||
\(394\) | − | 6.77191i | − | 0.341164i | ||||||
\(395\) | −1.74427 | − | 25.5620i | −0.0877638 | − | 1.28616i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.6796 | − | 11.6796i | −0.586184 | − | 0.586184i | 0.350412 | − | 0.936596i | \(-0.386042\pi\) |
−0.936596 | + | 0.350412i | \(0.886042\pi\) | |||||||
\(398\) | 7.25667 | + | 7.25667i | 0.363744 | + | 0.363744i | ||||
\(399\) | − | 4.09026i | − | 0.204769i | ||||||
\(400\) | −12.7103 | + | 1.74273i | −0.635514 | + | 0.0871367i | ||||
\(401\) | 15.1557 | 0.756841 | 0.378421 | − | 0.925634i | \(-0.376467\pi\) | ||||
0.378421 | + | 0.925634i | \(0.376467\pi\) | |||||||
\(402\) | −1.47004 | + | 1.47004i | −0.0733189 | + | 0.0733189i | ||||
\(403\) | 20.7585 | + | 20.7585i | 1.03405 | + | 1.03405i | ||||
\(404\) | −2.11428 | −0.105189 | ||||||||
\(405\) | 1.18944 | + | 17.4310i | 0.0591037 | + | 0.866156i | ||||
\(406\) | − | 1.39521i | − | 0.0692429i | ||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −2.81934 | + | 2.81934i | −0.139578 | + | 0.139578i | ||||
\(409\) | −17.2482 | −0.852868 | −0.426434 | − | 0.904519i | \(-0.640230\pi\) | ||||
−0.426434 | + | 0.904519i | \(0.640230\pi\) | |||||||
\(410\) | 12.1882 | − | 13.9734i | 0.601931 | − | 0.690095i | ||||
\(411\) | 0.305422 | 0.0150654 | ||||||||
\(412\) | −5.19920 | − | 5.19920i | −0.256146 | − | 0.256146i | ||||
\(413\) | −13.0092 | − | 13.0092i | −0.640140 | − | 0.640140i | ||||
\(414\) | −8.96062 | −0.440390 | ||||||||
\(415\) | 5.82052 | − | 6.67305i | 0.285718 | − | 0.327567i | ||||
\(416\) | −13.8775 | −0.680401 | ||||||||
\(417\) | −5.19321 | + | 5.19321i | −0.254313 | + | 0.254313i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.0003i | 0.928227i | 0.885776 | + | 0.464113i | \(0.153627\pi\) | ||||
−0.885776 | + | 0.464113i | \(0.846373\pi\) | |||||||
\(420\) | 0.0469290 | + | 0.687737i | 0.00228990 | + | 0.0335581i | ||||
\(421\) | −2.15833 | −0.105191 | −0.0525953 | − | 0.998616i | \(-0.516749\pi\) | ||||
−0.0525953 | + | 0.998616i | \(0.516749\pi\) | |||||||
\(422\) | −10.2859 | − | 10.2859i | −0.500707 | − | 0.500707i | ||||
\(423\) | −15.6741 | + | 15.6741i | −0.762102 | + | 0.762102i | ||||
\(424\) | −32.7231 | −1.58918 | ||||||||
\(425\) | 10.7237 | − | 14.1316i | 0.520174 | − | 0.685484i | ||||
\(426\) | 5.24525i | 0.254133i | ||||||||
\(427\) | 3.53100 | + | 3.53100i | 0.170877 | + | 0.170877i | ||||
\(428\) | −1.23669 | − | 1.23669i | −0.0597775 | − | 0.0597775i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.129337 | − | 1.89541i | −0.00623717 | − | 0.0914047i | ||||
\(431\) | − | 7.46697i | − | 0.359671i | −0.983697 | − | 0.179836i | \(-0.942443\pi\) | ||
0.983697 | − | 0.179836i | \(-0.0575566\pi\) | |||||||
\(432\) | −3.89341 | − | 3.89341i | −0.187322 | − | 0.187322i | ||||
\(433\) | −14.8357 | + | 14.8357i | −0.712961 | + | 0.712961i | −0.967154 | − | 0.254193i | \(-0.918190\pi\) |
0.254193 | + | 0.967154i | \(0.418190\pi\) | |||||||
\(434\) | − | 11.7051i | − | 0.561863i | ||||||
\(435\) | −0.476448 | − | 0.415579i | −0.0228439 | − | 0.0199255i | ||||
\(436\) | − | 1.26789i | − | 0.0607208i | ||||||
\(437\) | −13.6930 | + | 13.6930i | −0.655024 | + | 0.655024i | ||||
\(438\) | −2.95461 | + | 2.95461i | −0.141177 | + | 0.141177i | ||||
\(439\) | 28.9958 | 1.38389 | 0.691947 | − | 0.721948i | \(-0.256753\pi\) | ||||
0.691947 | + | 0.721948i | \(0.256753\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.5766 | −0.646506 | ||||||||
\(442\) | −13.6290 | + | 13.6290i | −0.648267 | + | 0.648267i | ||||
\(443\) | −19.8262 | + | 19.8262i | −0.941972 | + | 0.941972i | −0.998406 | − | 0.0564340i | \(-0.982027\pi\) |
0.0564340 | + | 0.998406i | \(0.482027\pi\) | |||||||
\(444\) | 0.847774i | 0.0402336i | ||||||||
\(445\) | 22.2337 | − | 1.51716i | 1.05398 | − | 0.0719201i | ||||
\(446\) | 5.96969i | 0.282673i | ||||||||
\(447\) | −0.615486 | + | 0.615486i | −0.0291115 | + | 0.0291115i | ||||
\(448\) | 9.37142 | + | 9.37142i | 0.442758 | + | 0.442758i | ||||
\(449\) | − | 18.9599i | − | 0.894773i | −0.894341 | − | 0.447387i | \(-0.852355\pi\) | ||
0.894341 | − | 0.447387i | \(-0.147645\pi\) | |||||||
\(450\) | 13.6985 | + | 10.3950i | 0.645751 | + | 0.490023i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 7.80833 | + | 7.80833i | 0.367273 | + | 0.367273i | ||||
\(453\) | −4.64806 | − | 4.64806i | −0.218385 | − | 0.218385i | ||||
\(454\) | − | 8.23714i | − | 0.386588i | ||||||
\(455\) | 1.03682 | + | 15.1944i | 0.0486067 | + | 0.712323i | ||||
\(456\) | −8.35252 | −0.391143 | ||||||||
\(457\) | −11.2549 | + | 11.2549i | −0.526480 | + | 0.526480i | −0.919521 | − | 0.393041i | \(-0.871423\pi\) |
0.393041 | + | 0.919521i | \(0.371423\pi\) | |||||||
\(458\) | 11.1830 | + | 11.1830i | 0.522546 | + | 0.522546i | ||||
\(459\) | 7.61367 | 0.355376 | ||||||||
\(460\) | 2.14523 | − | 2.45944i | 0.100022 | − | 0.114672i | ||||
\(461\) | − | 33.0004i | − | 1.53698i | −0.639859 | − | 0.768492i | \(-0.721007\pi\) | ||
0.639859 | − | 0.768492i | \(-0.278993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.68490 | + | 8.68490i | −0.403622 | + | 0.403622i | −0.879507 | − | 0.475886i | \(-0.842128\pi\) |
0.475886 | + | 0.879507i | \(0.342128\pi\) | |||||||
\(464\) | −1.98315 | −0.0920654 | ||||||||
\(465\) | −3.99717 | − | 3.48650i | −0.185364 | − | 0.161683i | ||||
\(466\) | 18.0880 | 0.837908 | ||||||||
\(467\) | 3.45801 | + | 3.45801i | 0.160018 | + | 0.160018i | 0.782575 | − | 0.622557i | \(-0.213906\pi\) |
−0.622557 | + | 0.782575i | \(0.713906\pi\) | |||||||
\(468\) | 5.14001 | + | 5.14001i | 0.237597 | + | 0.237597i | ||||
\(469\) | −7.12504 | −0.329004 | ||||||||
\(470\) | 1.41268 | + | 20.7026i | 0.0651622 | + | 0.954941i | ||||
\(471\) | 1.08594 | 0.0500374 | ||||||||
\(472\) | −26.5654 | + | 26.5654i | −1.22277 | + | 1.22277i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | − | 5.02960i | − | 0.231017i | ||||||
\(475\) | 36.8178 | − | 5.04817i | 1.68932 | − | 0.231626i | ||||
\(476\) | −2.98994 | −0.137044 | ||||||||
\(477\) | 21.5883 | + | 21.5883i | 0.988461 | + | 0.988461i | ||||
\(478\) | −11.3338 | + | 11.3338i | −0.518396 | + | 0.518396i | ||||
\(479\) | −8.67558 | −0.396397 | −0.198199 | − | 0.980162i | \(-0.563509\pi\) | ||||
−0.198199 | + | 0.980162i | \(0.563509\pi\) | |||||||
\(480\) | 2.50150 | − | 0.170694i | 0.114177 | − | 0.00779110i | ||||
\(481\) | 18.7301i | 0.854020i | ||||||||
\(482\) | 5.33617 | + | 5.33617i | 0.243056 | + | 0.243056i | ||||
\(483\) | 1.01387 | + | 1.01387i | 0.0461329 | + | 0.0461329i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.8688 | + | 19.3395i | −0.765971 | + | 0.878161i | ||||
\(486\) | 11.1546i | 0.505984i | ||||||||
\(487\) | −27.0518 | − | 27.0518i | −1.22584 | − | 1.22584i | −0.965525 | − | 0.260311i | \(-0.916175\pi\) |
−0.260311 | − | 0.965525i | \(-0.583825\pi\) | |||||||
\(488\) | 7.21049 | − | 7.21049i | 0.326404 | − | 0.326404i | ||||
\(489\) | 1.11272i | 0.0503188i | ||||||||
\(490\) | −8.35428 | + | 9.57792i | −0.377408 | + | 0.432686i | ||||
\(491\) | 3.54998i | 0.160208i | 0.996786 | + | 0.0801042i | \(0.0255253\pi\) | ||||
−0.996786 | + | 0.0801042i | \(0.974475\pi\) | |||||||
\(492\) | −1.00136 | + | 1.00136i | −0.0451448 | + | 0.0451448i | ||||
\(493\) | 1.93905 | − | 1.93905i | 0.0873304 | − | 0.0873304i | ||||
\(494\) | −40.3771 | −1.81665 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −16.6377 | −0.747053 | ||||||||
\(497\) | −12.7114 | + | 12.7114i | −0.570186 | + | 0.570186i | ||||
\(498\) | 1.22912 | − | 1.22912i | 0.0550783 | − | 0.0550783i | ||||
\(499\) | 25.7772i | 1.15395i | 0.816763 | + | 0.576973i | \(0.195766\pi\) | ||||
−0.816763 | + | 0.576973i | \(0.804234\pi\) | |||||||
\(500\) | −6.13263 | + | 1.27122i | −0.274259 | + | 0.0568508i | ||||
\(501\) | − | 1.39575i | − | 0.0623574i | ||||||
\(502\) | 3.48832 | − | 3.48832i | 0.155691 | − | 0.155691i | ||||
\(503\) | −2.77955 | − | 2.77955i | −0.123934 | − | 0.123934i | 0.642419 | − | 0.766353i | \(-0.277931\pi\) |
−0.766353 | + | 0.642419i | \(0.777931\pi\) | |||||||
\(504\) | − | 13.2460i | − | 0.590026i | ||||||
\(505\) | 8.41997 | − | 0.574552i | 0.374684 | − | 0.0255673i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.93932 | − | 1.93932i | −0.0861282 | − | 0.0861282i | ||||
\(508\) | −8.10580 | − | 8.10580i | −0.359637 | − | 0.359637i | ||||
\(509\) | − | 18.6485i | − | 0.826579i | −0.910600 | − | 0.413289i | \(-0.864380\pi\) | ||
0.910600 | − | 0.413289i | \(-0.135620\pi\) | |||||||
\(510\) | 2.28907 | − | 2.62435i | 0.101362 | − | 0.116208i | ||||
\(511\) | −14.3205 | −0.633502 | ||||||||
\(512\) | 16.7086 | − | 16.7086i | 0.738423 | − | 0.738423i | ||||
\(513\) | 11.2780 | + | 11.2780i | 0.497938 | + | 0.497938i | ||||
\(514\) | 9.65098 | 0.425686 | ||||||||
\(515\) | 22.1184 | + | 19.2926i | 0.974652 | + | 0.850134i | ||||
\(516\) | 0.145098i | 0.00638756i | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 5.28068 | − | 5.28068i | 0.232020 | − | 0.232020i | ||||
\(519\) | −0.426600 | −0.0187257 | ||||||||
\(520\) | 31.0277 | − | 2.11723i | 1.36065 | − | 0.0928467i | ||||
\(521\) | −13.7453 | −0.602194 | −0.301097 | − | 0.953594i | \(-0.597353\pi\) | ||||
−0.301097 | + | 0.953594i | \(0.597353\pi\) | |||||||
\(522\) | 1.87961 | + | 1.87961i | 0.0822685 | + | 0.0822685i | ||||
\(523\) | −13.9488 | − | 13.9488i | −0.609938 | − | 0.609938i | 0.332992 | − | 0.942930i | \(-0.391942\pi\) |
−0.942930 | + | 0.332992i | \(0.891942\pi\) | |||||||
\(524\) | −4.80181 | −0.209768 | ||||||||
\(525\) | −0.373784 | − | 2.72612i | −0.0163133 | − | 0.118977i | ||||
\(526\) | −27.3384 | −1.19201 | ||||||||
\(527\) | 16.2677 | − | 16.2677i | 0.708631 | − | 0.708631i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.2117i | 0.704857i | ||||||||
\(530\) | 28.5142 | − | 1.94572i | 1.23858 | − | 0.0845166i | ||||
\(531\) | 35.0518 | 1.52112 | ||||||||
\(532\) | −4.42897 | − | 4.42897i | −0.192020 | − | 0.192020i | ||||
\(533\) | −22.1234 | + | 22.1234i | −0.958269 | + | 0.958269i | ||||
\(534\) | 4.37472 | 0.189312 | ||||||||
\(535\) | 5.26109 | + | 4.58896i | 0.227457 | + | 0.198398i | ||||
\(536\) | 14.5497i | 0.628451i | ||||||||
\(537\) | −1.56845 | − | 1.56845i | −0.0676835 | − | 0.0676835i | ||||
\(538\) | 11.9294 | + | 11.9294i | 0.514315 | + | 0.514315i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −2.02569 | − | 1.76689i | −0.0871716 | − | 0.0760349i | ||||
\(541\) | 16.0662i | 0.690738i | 0.938467 | + | 0.345369i | \(0.112246\pi\) | ||||
−0.938467 | + | 0.345369i | \(0.887754\pi\) | |||||||
\(542\) | 0.0602299 | + | 0.0602299i | 0.00258709 | + | 0.00258709i | ||||
\(543\) | −0.404644 | + | 0.404644i | −0.0173649 | + | 0.0173649i | ||||
\(544\) | 10.8753i | 0.466275i | ||||||||
\(545\) | 0.344547 | + | 5.04928i | 0.0147588 | + | 0.216288i | ||||
\(546\) | 2.98965i | 0.127945i | ||||||||
\(547\) | 23.6289 | − | 23.6289i | 1.01030 | − | 1.01030i | 0.0103542 | − | 0.999946i | \(-0.496704\pi\) |
0.999946 | − | 0.0103542i | \(-0.00329590\pi\) | |||||||
\(548\) | 0.330714 | − | 0.330714i | 0.0141274 | − | 0.0141274i | ||||
\(549\) | −9.51390 | −0.406043 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.74459 | 0.244728 | ||||||||
\(552\) | 2.07038 | − | 2.07038i | 0.0881213 | − | 0.0881213i | ||||
\(553\) | 12.1888 | − | 12.1888i | 0.518321 | − | 0.518321i | ||||
\(554\) | 30.9048i | 1.31302i | ||||||||
\(555\) | −0.230382 | − | 3.37621i | −0.00977917 | − | 0.143312i | ||||
\(556\) | 11.2465i | 0.476958i | ||||||||
\(557\) | −25.6652 | + | 25.6652i | −1.08747 | + | 1.08747i | −0.0916796 | + | 0.995789i | \(0.529224\pi\) |
−0.995789 | + | 0.0916796i | \(0.970776\pi\) | |||||||
\(558\) | 15.7690 | + | 15.7690i | 0.667557 | + | 0.667557i | ||||
\(559\) | 3.20568i | 0.135586i | ||||||||
\(560\) | −6.50454 | − | 5.67354i | −0.274867 | − | 0.239751i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 15.6922 | + | 15.6922i | 0.661936 | + | 0.661936i | ||||
\(563\) | 22.7913 | + | 22.7913i | 0.960538 | + | 0.960538i | 0.999250 | − | 0.0387120i | \(-0.0123255\pi\) |
−0.0387120 | + | 0.999250i | \(0.512325\pi\) | |||||||
\(564\) | − | 1.58483i | − | 0.0667334i | ||||||
\(565\) | −33.2181 | − | 28.9743i | −1.39750 | − | 1.21896i | ||||
\(566\) | 37.0783 | 1.55852 | ||||||||
\(567\) | −8.31171 | + | 8.31171i | −0.349059 | + | 0.349059i | ||||
\(568\) | 25.9574 | + | 25.9574i | 1.08915 | + | 1.08915i | ||||
\(569\) | 24.8116 | 1.04016 | 0.520078 | − | 0.854119i | \(-0.325903\pi\) | ||||
0.520078 | + | 0.854119i | \(0.325903\pi\) | |||||||
\(570\) | 7.27819 | − | 0.496641i | 0.304850 | − | 0.0208020i | ||||
\(571\) | − | 9.17242i | − | 0.383854i | −0.981409 | − | 0.191927i | \(-0.938526\pi\) | ||
0.981409 | − | 0.191927i | \(-0.0614737\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.345576 | + | 0.345576i | −0.0144366 | + | 0.0144366i | ||||
\(574\) | 12.4747 | 0.520684 | ||||||||
\(575\) | −7.87490 | + | 10.3775i | −0.328406 | + | 0.432773i | ||||
\(576\) | −25.2503 | −1.05209 | ||||||||
\(577\) | −11.2891 | − | 11.2891i | −0.469973 | − | 0.469973i | 0.431933 | − | 0.901906i | \(-0.357832\pi\) |
−0.901906 | + | 0.431933i | \(0.857832\pi\) | |||||||
\(578\) | −3.74350 | − | 3.74350i | −0.155709 | − | 0.155709i | ||||
\(579\) | −0.607414 | −0.0252433 | ||||||||
\(580\) | −0.965894 | + | 0.0659096i | −0.0401066 | + | 0.00273675i | ||||
\(581\) | 5.95735 | 0.247153 | ||||||||
\(582\) | −3.56218 | + | 3.56218i | −0.147657 | + | 0.147657i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 29.2432i | 1.21009i | ||||||||
\(585\) | −21.8666 | − | 19.0730i | −0.904071 | − | 0.788570i | ||||
\(586\) | 35.7678 | 1.47755 | ||||||||
\(587\) | −11.2955 | − | 11.2955i | −0.466215 | − | 0.466215i | 0.434471 | − | 0.900686i | \(-0.356935\pi\) |
−0.900686 | + | 0.434471i | \(0.856935\pi\) | |||||||
\(588\) | 0.686374 | − | 0.686374i | 0.0283056 | − | 0.0283056i | ||||
\(589\) | 48.1943 | 1.98581 | ||||||||
\(590\) | 21.5689 | − | 24.7280i | 0.887977 | − | 1.01804i | ||||
\(591\) | − | 2.06451i | − | 0.0849228i | ||||||
\(592\) | −7.50597 | − | 7.50597i | −0.308494 | − | 0.308494i | ||||
\(593\) | −18.2153 | − | 18.2153i | −0.748014 | − | 0.748014i | 0.226092 | − | 0.974106i | \(-0.427405\pi\) |
−0.974106 | + | 0.226092i | \(0.927405\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.9073 | − | 0.812515i | 0.488150 | − | 0.0333099i | ||||
\(596\) | 1.33291i | 0.0545980i | ||||||||
\(597\) | 2.21230 | + | 2.21230i | 0.0905434 | + | 0.0905434i | ||||
\(598\) | 10.0085 | − | 10.0085i | 0.409277 | − | 0.409277i | ||||
\(599\) | 22.2495i | 0.909090i | 0.890724 | + | 0.454545i | \(0.150198\pi\) | ||||
−0.890724 | + | 0.454545i | \(0.849802\pi\) | |||||||
\(600\) | −5.56687 | + | 0.763285i | −0.227266 | + | 0.0311610i | ||||
\(601\) | − | 30.5129i | − | 1.24465i | −0.782760 | − | 0.622324i | \(-0.786189\pi\) | ||
0.782760 | − | 0.622324i | \(-0.213811\pi\) | |||||||
\(602\) | 0.903794 | − | 0.903794i | 0.0368359 | − | 0.0368359i | ||||
\(603\) | 9.59882 | − | 9.59882i | 0.390894 | − | 0.390894i | ||||
\(604\) | −10.0659 | −0.409577 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.65672 | 0.0672996 | ||||||||
\(607\) | 11.2506 | − | 11.2506i | 0.456648 | − | 0.456648i | −0.440905 | − | 0.897554i | \(-0.645343\pi\) |
0.897554 | + | 0.440905i | \(0.145343\pi\) | |||||||
\(608\) | −16.1095 | + | 16.1095i | −0.653325 | + | 0.653325i | ||||
\(609\) | − | 0.425348i | − | 0.0172360i | ||||||
\(610\) | −5.85432 | + | 6.71179i | −0.237034 | + | 0.271752i | ||||
\(611\) | − | 35.0141i | − | 1.41652i | ||||||
\(612\) | 4.02804 | − | 4.02804i | 0.162824 | − | 0.162824i | ||||
\(613\) | 12.1960 | + | 12.1960i | 0.492591 | + | 0.492591i | 0.909122 | − | 0.416531i | \(-0.136754\pi\) |
−0.416531 | + | 0.909122i | \(0.636754\pi\) | |||||||
\(614\) | − | 1.42076i | − | 0.0573371i | ||||||
\(615\) | 3.71574 | − | 4.25998i | 0.149833 | − | 0.171779i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −8.28834 | − | 8.28834i | −0.333676 | − | 0.333676i | 0.520305 | − | 0.853981i | \(-0.325818\pi\) |
−0.853981 | + | 0.520305i | \(0.825818\pi\) | |||||||
\(618\) | 4.07403 | + | 4.07403i | 0.163881 | + | 0.163881i | ||||
\(619\) | − | 8.34814i | − | 0.335540i | −0.985826 | − | 0.167770i | \(-0.946343\pi\) | ||
0.985826 | − | 0.167770i | \(-0.0536566\pi\) | |||||||
\(620\) | −8.10338 | + | 0.552949i | −0.325440 | + | 0.0222070i | ||||
\(621\) | −5.59109 | −0.224363 | ||||||||
\(622\) | 12.6840 | − | 12.6840i | 0.508582 | − | 0.508582i | ||||
\(623\) | 10.6018 | + | 10.6018i | 0.424751 | + | 0.424751i | ||||
\(624\) | 4.24950 | 0.170116 | ||||||||
\(625\) | 24.0774 | − | 6.72910i | 0.963094 | − | 0.269164i | ||||
\(626\) | 25.0268i | 1.00027i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.17586 | − | 1.17586i | 0.0469221 | − | 0.0469221i | ||||
\(629\) | 14.6781 | 0.585255 | ||||||||
\(630\) | 0.787610 | + | 11.5423i | 0.0313791 | + | 0.459856i | ||||
\(631\) | 20.1258 | 0.801194 | 0.400597 | − | 0.916254i | \(-0.368803\pi\) | ||||
0.400597 | + | 0.916254i | \(0.368803\pi\) | |||||||
\(632\) | −24.8902 | − | 24.8902i | −0.990078 | − | 0.990078i | ||||
\(633\) | −3.13579 | − | 3.13579i | −0.124636 | − | 0.124636i | ||||
\(634\) | −4.92186 | −0.195472 | ||||||||
\(635\) | 34.4836 | + | 30.0781i | 1.36844 | + | 1.19361i | ||||
\(636\) | −2.18282 | −0.0865545 | ||||||||
\(637\) | 15.1643 | − | 15.1643i | 0.600830 | − | 0.600830i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 34.2496i | − | 1.35489i | ||||||
\(640\) | −6.52685 | + | 7.48283i | −0.257996 | + | 0.295785i | ||||
\(641\) | −15.7080 | −0.620427 | −0.310214 | − | 0.950667i | \(-0.600401\pi\) | ||||
−0.310214 | + | 0.950667i | \(0.600401\pi\) | |||||||
\(642\) | 0.969051 | + | 0.969051i | 0.0382454 | + | 0.0382454i | ||||
\(643\) | −35.1585 | + | 35.1585i | −1.38652 | + | 1.38652i | −0.553999 | + | 0.832517i | \(0.686899\pi\) |
−0.832517 | + | 0.553999i | \(0.813101\pi\) | |||||||
\(644\) | 2.19566 | 0.0865212 | ||||||||
\(645\) | −0.0394301 | − | 0.577842i | −0.00155256 | − | 0.0227525i | ||||
\(646\) | 31.6421i | 1.24494i | ||||||||
\(647\) | −25.2859 | − | 25.2859i | −0.994091 | − | 0.994091i | 0.00589156 | − | 0.999983i | \(-0.498125\pi\) |
−0.999983 | + | 0.00589156i | \(0.998125\pi\) | |||||||
\(648\) | 16.9729 | + | 16.9729i | 0.666760 | + | 0.666760i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −26.9109 | + | 3.68981i | −1.05553 | + | 0.144726i | ||||
\(651\) | − | 3.56846i | − | 0.139859i | ||||||
\(652\) | 1.20486 | + | 1.20486i | 0.0471859 | + | 0.0471859i | ||||
\(653\) | 8.27696 | − | 8.27696i | 0.323902 | − | 0.323902i | −0.526360 | − | 0.850262i | \(-0.676443\pi\) |
0.850262 | + | 0.526360i | \(0.176443\pi\) | |||||||
\(654\) | 0.993501i | 0.0388490i | ||||||||
\(655\) | 19.1229 | − | 1.30489i | 0.747193 | − | 0.0509861i | ||||
\(656\) | − | 17.7316i | − | 0.692302i | ||||||
\(657\) | 19.2925 | − | 19.2925i | 0.752673 | − | 0.752673i | ||||
\(658\) | −9.87171 | + | 9.87171i | −0.384839 | + | 0.384839i | ||||
\(659\) | −44.7867 | −1.74464 | −0.872322 | − | 0.488933i | \(-0.837386\pi\) | ||||
−0.872322 | + | 0.488933i | \(0.837386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.9940 | −0.816573 | −0.408286 | − | 0.912854i | \(-0.633873\pi\) | ||||
−0.408286 | + | 0.912854i | \(0.633873\pi\) | |||||||
\(662\) | −11.4273 | + | 11.4273i | −0.444134 | + | 0.444134i | ||||
\(663\) | −4.15501 | + | 4.15501i | −0.161367 | + | 0.161367i | ||||
\(664\) | − | 12.1652i | − | 0.472102i | ||||||
\(665\) | 18.8417 | + | 16.4345i | 0.730649 | + | 0.637304i | ||||
\(666\) | 14.2282i | 0.551332i | ||||||||
\(667\) | −1.42394 | + | 1.42394i | −0.0551351 | + | 0.0551351i | ||||
\(668\) | −1.51133 | − | 1.51133i | −0.0584750 | − | 0.0584750i | ||||
\(669\) | 1.81994i | 0.0703631i | ||||||||
\(670\) | −0.865125 | − | 12.6783i | −0.0334227 | − | 0.489804i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 1.19280 | + | 1.19280i | 0.0460132 | + | 0.0460132i | ||||
\(673\) | 12.8325 | + | 12.8325i | 0.494655 | + | 0.494655i | 0.909769 | − | 0.415114i | \(-0.136258\pi\) |
−0.415114 | + | 0.909769i | \(0.636258\pi\) | |||||||
\(674\) | − | 34.1834i | − | 1.31669i | ||||||
\(675\) | 8.54732 | + | 6.48606i | 0.328986 | + | 0.249649i | ||||
\(676\) | −4.19982 | −0.161532 | ||||||||
\(677\) | −10.6666 | + | 10.6666i | −0.409951 | + | 0.409951i | −0.881721 | − | 0.471770i | \(-0.843615\pi\) |
0.471770 | + | 0.881721i | \(0.343615\pi\) | |||||||
\(678\) | −6.11851 | − | 6.11851i | −0.234980 | − | 0.234980i | ||||
\(679\) | −17.2653 | −0.662582 | ||||||||
\(680\) | −1.65920 | − | 24.3152i | −0.0636273 | − | 0.932447i | ||||
\(681\) | − | 2.51121i | − | 0.0962297i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.5210 | − | 12.5210i | 0.479102 | − | 0.479102i | −0.425743 | − | 0.904844i | \(-0.639987\pi\) |
0.904844 | + | 0.425743i | \(0.139987\pi\) | |||||||
\(684\) | 11.9334 | 0.456284 | ||||||||
\(685\) | −1.22718 | + | 1.40692i | −0.0468879 | + | 0.0537555i | ||||
\(686\) | −21.1867 | −0.808912 | ||||||||
\(687\) | 3.40929 | + | 3.40929i | 0.130072 | + | 0.130072i | ||||
\(688\) | −1.28466 | − | 1.28466i | −0.0489771 | − | 0.0489771i | ||||
\(689\) | −48.2257 | −1.83725 | ||||||||
\(690\) | −1.68098 | + | 1.92719i | −0.0639937 | + | 0.0733667i | ||||
\(691\) | 27.4323 | 1.04358 | 0.521788 | − | 0.853075i | \(-0.325265\pi\) | ||||
0.521788 | + | 0.853075i | \(0.325265\pi\) | |||||||
\(692\) | −0.461926 | + | 0.461926i | −0.0175598 | + | 0.0175598i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 14.2067i | 0.539279i | ||||||||
\(695\) | −3.05623 | − | 44.7885i | −0.115929 | − | 1.69893i | ||||
\(696\) | −0.868583 | −0.0329235 | ||||||||
\(697\) | 17.3373 | + | 17.3373i | 0.656696 | + | 0.656696i | ||||
\(698\) | 6.95838 | − | 6.95838i | 0.263379 | − | 0.263379i | ||||
\(699\) | 5.51437 | 0.208573 | ||||||||
\(700\) | −3.35660 | − | 2.54712i | −0.126867 | − | 0.0962723i | ||||
\(701\) | − | 33.8539i | − | 1.27864i | −0.768939 | − | 0.639322i | \(-0.779215\pi\) | ||
0.768939 | − | 0.639322i | \(-0.220785\pi\) | |||||||
\(702\) | −8.24334 | − | 8.24334i | −0.311125 | − | 0.311125i | ||||
\(703\) | 21.7425 | + | 21.7425i | 0.820035 | + | 0.820035i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.430676 | + | 6.31149i | 0.0162202 | + | 0.237704i | ||||
\(706\) | 16.1821i | 0.609022i | ||||||||
\(707\) | 4.01492 | + | 4.01492i | 0.150997 | + | 0.150997i | ||||
\(708\) | −1.77206 | + | 1.77206i | −0.0665983 | + | 0.0665983i | ||||
\(709\) | − | 22.3780i | − | 0.840424i | −0.907426 | − | 0.420212i | \(-0.861956\pi\) | ||
0.907426 | − | 0.420212i | \(-0.138044\pi\) | |||||||
\(710\) | −24.1621 | − | 21.0752i | −0.906788 | − | 0.790940i | ||||
\(711\) | 32.8414i | 1.23165i | ||||||||
\(712\) | 21.6493 | − | 21.6493i | 0.811343 | − | 0.811343i | ||||
\(713\) | −11.9461 | + | 11.9461i | −0.447387 | + | 0.447387i | ||||
\(714\) | 2.34288 | 0.0876802 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.39665 | −0.126939 | ||||||||
\(717\) | −3.45527 | + | 3.45527i | −0.129039 | + | 0.129039i | ||||
\(718\) | −12.1680 | + | 12.1680i | −0.454105 | + | 0.454105i | ||||
\(719\) | − | 37.8017i | − | 1.40976i | −0.709325 | − | 0.704882i | \(-0.751000\pi\) | ||
0.709325 | − | 0.704882i | \(-0.249000\pi\) | |||||||
\(720\) | 16.4062 | − | 1.11951i | 0.611425 | − | 0.0417217i | ||||
\(721\) | 19.7461i | 0.735385i | ||||||||
\(722\) | −30.7500 | + | 30.7500i | −1.14440 | + | 1.14440i | ||||
\(723\) | 1.62681 | + | 1.62681i | 0.0605016 | + | 0.0605016i | ||||
\(724\) | 0.876305i | 0.0325676i | ||||||||
\(725\) | 3.82870 | − | 0.524962i | 0.142194 | − | 0.0194966i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9838 | − | 13.9838i | −0.518630 | − | 0.518630i | 0.398527 | − | 0.917157i | \(-0.369522\pi\) |
−0.917157 | + | 0.398527i | \(0.869522\pi\) | |||||||
\(728\) | 14.7950 | + | 14.7950i | 0.548340 | + | 0.548340i | ||||
\(729\) | − | 20.0399i | − | 0.742220i | ||||||
\(730\) | −1.73880 | − | 25.4818i | −0.0643559 | − | 0.943126i | ||||
\(731\) | 2.51218 | 0.0929162 | ||||||||
\(732\) | 0.480981 | − | 0.480981i | 0.0177776 | − | 0.0177776i | ||||
\(733\) | 19.6728 | + | 19.6728i | 0.726630 | + | 0.726630i | 0.969947 | − | 0.243317i | \(-0.0782354\pi\) |
−0.243317 | + | 0.969947i | \(0.578235\pi\) | |||||||
\(734\) | −24.1227 | −0.890386 | ||||||||
\(735\) | −2.54692 | + | 2.91997i | −0.0939446 | + | 0.107705i | ||||
\(736\) | − | 7.98626i | − | 0.294378i | ||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −16.8058 | + | 16.8058i | −0.618632 | + | 0.618632i | ||||
\(739\) | −30.2242 | −1.11182 | −0.555908 | − | 0.831244i | \(-0.687629\pi\) | ||||
−0.555908 | + | 0.831244i | \(0.687629\pi\) | |||||||
\(740\) | −3.90525 | − | 3.40633i | −0.143560 | − | 0.125219i | ||||
\(741\) | −12.3095 | −0.452202 | ||||||||
\(742\) | 13.5965 | + | 13.5965i | 0.499144 | + | 0.499144i | ||||
\(743\) | 5.51933 | + | 5.51933i | 0.202485 | + | 0.202485i | 0.801064 | − | 0.598579i | \(-0.204268\pi\) |
−0.598579 | + | 0.801064i | \(0.704268\pi\) | |||||||
\(744\) | −7.28698 | −0.267154 | ||||||||
\(745\) | −0.362216 | − | 5.30822i | −0.0132706 | − | 0.194478i | ||||
\(746\) | −1.08881 | −0.0398640 | ||||||||
\(747\) | −8.02572 | + | 8.02572i | −0.293646 | + | 0.293646i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.69683i | 0.171619i | ||||||||
\(750\) | 4.80545 | − | 0.996115i | 0.175470 | − | 0.0363730i | ||||
\(751\) | 5.23553 | 0.191047 | 0.0955236 | − | 0.995427i | \(-0.469547\pi\) | ||||
0.0955236 | + | 0.995427i | \(0.469547\pi\) | |||||||
\(752\) | 14.0317 | + | 14.0317i | 0.511683 | + | 0.511683i | ||||
\(753\) | 1.06346 | − | 1.06346i | 0.0387548 | − | 0.0387548i | ||||
\(754\) | −4.19883 | −0.152912 | ||||||||
\(755\) | 40.0869 | − | 2.73541i | 1.45891 | − | 0.0995517i | ||||
\(756\) | − | 1.80843i | − | 0.0657719i | ||||||
\(757\) | −14.2275 | − | 14.2275i | −0.517109 | − | 0.517109i | 0.399587 | − | 0.916695i | \(-0.369154\pi\) |
−0.916695 | + | 0.399587i | \(0.869154\pi\) | |||||||
\(758\) | 9.28344 | + | 9.28344i | 0.337190 | + | 0.337190i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 33.5602 | − | 38.4757i | 1.21735 | − | 1.39566i | ||||
\(761\) | − | 31.5754i | − | 1.14461i | −0.820041 | − | 0.572304i | \(-0.806050\pi\) | ||
0.820041 | − | 0.572304i | \(-0.193950\pi\) | |||||||
\(762\) | 6.35160 | + | 6.35160i | 0.230094 | + | 0.230094i | ||||
\(763\) | −2.40767 | + | 2.40767i | −0.0871634 | + | 0.0871634i | ||||
\(764\) | 0.748385i | 0.0270756i | ||||||||
\(765\) | −14.9468 | + | 17.1360i | −0.540403 | + | 0.619554i | ||||
\(766\) | − | 10.8298i | − | 0.391295i | ||||||
\(767\) | −39.1507 | + | 39.1507i | −1.41365 | + | 1.41365i | ||||
\(768\) | 3.17934 | − | 3.17934i | 0.114725 | − | 0.114725i | ||||
\(769\) | −22.1089 | −0.797269 | −0.398634 | − | 0.917110i | \(-0.630516\pi\) | ||||
−0.398634 | + | 0.917110i | \(0.630516\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.94224 | 0.105962 | ||||||||
\(772\) | −0.657713 | + | 0.657713i | −0.0236716 | + | 0.0236716i | ||||
\(773\) | −2.46526 | + | 2.46526i | −0.0886693 | + | 0.0886693i | −0.750050 | − | 0.661381i | \(-0.769971\pi\) |
0.661381 | + | 0.750050i | \(0.269971\pi\) | |||||||
\(774\) | 2.43517i | 0.0875305i | ||||||||
\(775\) | 32.1209 | − | 4.40417i | 1.15382 | − | 0.158203i | ||||
\(776\) | 35.2566i | 1.26564i | ||||||||
\(777\) | 1.60989 | − | 1.60989i | 0.0577545 | − | 0.0577545i | ||||
\(778\) | −14.2272 | − | 14.2272i | −0.510070 | − | 0.510070i | ||||
\(779\) | 51.3630i | 1.84027i | ||||||||
\(780\) | 2.06972 | − | 0.141231i | 0.0741080 | − | 0.00505690i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −7.84327 | − | 7.84327i | −0.280475 | − | 0.280475i | ||||
\(783\) | 1.17281 | + | 1.17281i | 0.0419128 | + | 0.0419128i | ||||
\(784\) | 12.1540i | 0.434070i | ||||||||
\(785\) | −4.36327 | + | 5.00235i | −0.155732 | + | 0.178541i | ||||
\(786\) | 3.76264 | 0.134209 | ||||||||
\(787\) | 18.5691 | − | 18.5691i | 0.661917 | − | 0.661917i | −0.293915 | − | 0.955832i | \(-0.594958\pi\) |
0.955832 | + | 0.293915i | \(0.0949582\pi\) | |||||||
\(788\) | −2.23547 | − | 2.23547i | −0.0796354 | − | 0.0796354i | ||||
\(789\) | −8.33449 | −0.296716 | ||||||||
\(790\) | 23.1687 | + | 20.2088i | 0.824305 | + | 0.718995i | ||||
\(791\) | − | 29.6554i | − | 1.05442i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.6265 | − | 10.6265i | 0.377356 | − | 0.377356i | ||||
\(794\) | 19.8198 | 0.703377 | ||||||||
\(795\) | 8.69295 | − | 0.593179i | 0.308307 | − | 0.0210379i | ||||
\(796\) | 4.79099 | 0.169812 | ||||||||
\(797\) | −2.48582 | − | 2.48582i | −0.0880523 | − | 0.0880523i | 0.661709 | − | 0.749761i | \(-0.269832\pi\) |
−0.749761 | + | 0.661709i | \(0.769832\pi\) | |||||||
\(798\) | 3.47049 | + | 3.47049i | 0.122854 | + | 0.122854i | ||||
\(799\) | −27.4393 | −0.970732 | ||||||||
\(800\) | −9.26463 | + | 12.2089i | −0.327554 | + | 0.431651i | ||||
\(801\) | −28.5653 | −1.00930 | ||||||||
\(802\) | −12.8593 | + | 12.8593i | −0.454076 | + | 0.454076i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0.970548i | 0.0342286i | ||||||||
\(805\) | −8.74409 | + | 0.596669i | −0.308189 | + | 0.0210298i | ||||
\(806\) | −35.2261 | −1.24079 | ||||||||
\(807\) | 3.63686 | + | 3.63686i | 0.128023 | + | 0.128023i | ||||
\(808\) | 8.19868 | − | 8.19868i | 0.288429 | − | 0.288429i | ||||
\(809\) | −10.8292 | −0.380735 | −0.190367 | − | 0.981713i | \(-0.560968\pi\) | ||||
−0.190367 | + | 0.981713i | \(0.560968\pi\) | |||||||
\(810\) | −15.7990 | − | 13.7806i | −0.555121 | − | 0.484201i | ||||
\(811\) | − | 36.2429i | − | 1.27266i | −0.771416 | − | 0.636331i | \(-0.780451\pi\) | ||
0.771416 | − | 0.636331i | \(-0.219549\pi\) | |||||||
\(812\) | −0.460571 | − | 0.460571i | −0.0161629 | − | 0.0161629i | ||||
\(813\) | 0.0183619 | + | 0.0183619i | 0.000643981 | + | 0.000643981i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.12569 | − | 4.47086i | −0.179545 | − | 0.156607i | ||||
\(816\) | − | 3.33018i | − | 0.116580i | ||||||
\(817\) | 3.72126 | + | 3.72126i | 0.130190 | + | 0.130190i | ||||
\(818\) | 14.6347 | − | 14.6347i | 0.511689 | − | 0.511689i | ||||
\(819\) | − | 19.5213i | − | 0.682131i | ||||||
\(820\) | −0.589305 | − | 8.63617i | −0.0205794 | − | 0.301588i | ||||
\(821\) | − | 43.9586i | − | 1.53417i | −0.641548 | − | 0.767083i | \(-0.721708\pi\) | ||
0.641548 | − | 0.767083i | \(-0.278292\pi\) | |||||||
\(822\) | −0.259143 | + | 0.259143i | −0.00903865 | + | 0.00903865i | ||||
\(823\) | 16.9211 | − | 16.9211i | 0.589832 | − | 0.589832i | −0.347754 | − | 0.937586i | \(-0.613056\pi\) |
0.937586 | + | 0.347754i | \(0.113056\pi\) | |||||||
\(824\) | 40.3226 | 1.40471 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 22.0759 | 0.768120 | ||||||||
\(827\) | −37.6563 | + | 37.6563i | −1.30944 | + | 1.30944i | −0.387618 | + | 0.921820i | \(0.626702\pi\) |
−0.921820 | + | 0.387618i | \(0.873298\pi\) | |||||||
\(828\) | −2.95798 | + | 2.95798i | −0.102797 | + | 0.102797i | ||||
\(829\) | 28.4366i | 0.987645i | 0.869563 | + | 0.493822i | \(0.164401\pi\) | ||||
−0.869563 | + | 0.493822i | \(0.835599\pi\) | |||||||
\(830\) | 0.723344 | + | 10.6005i | 0.0251076 | + | 0.367948i | ||||
\(831\) | 9.42178i | 0.326838i | ||||||||
\(832\) | 28.2030 | − | 28.2030i | 0.977764 | − | 0.977764i | ||||
\(833\) | −11.8837 | − | 11.8837i | −0.411745 | − | 0.411745i | ||||
\(834\) | − | 8.81262i | − | 0.305156i | ||||||
\(835\) | 6.42947 | + | 5.60806i | 0.222501 | + | 0.194075i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.83929 | + | 9.83929i | 0.340096 | + | 0.340096i | ||||
\(838\) | −16.1213 | − | 16.1213i | −0.556901 | − | 0.556901i | ||||
\(839\) | 5.92526i | 0.204563i | 0.994756 | + | 0.102281i | \(0.0326142\pi\) | ||||
−0.994756 | + | 0.102281i | \(0.967386\pi\) | |||||||
\(840\) | −2.84887 | − | 2.48491i | −0.0982952 | − | 0.0857374i | ||||
\(841\) | −28.4026 | −0.979401 | ||||||||
\(842\) | 1.83129 | − | 1.83129i | 0.0631104 | − | 0.0631104i | ||||
\(843\) | 4.78399 | + | 4.78399i | 0.164769 | + | 0.164769i | ||||
\(844\) | −6.79092 | −0.233753 | ||||||||
\(845\) | 16.7255 | − | 1.14130i | 0.575376 | − | 0.0392619i | ||||
\(846\) | − | 26.5982i | − | 0.914466i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 19.3261 | − | 19.3261i | 0.663662 | − | 0.663662i | ||||
\(849\) | 11.3038 | 0.387947 | ||||||||
\(850\) | 2.89157 | + | 21.0891i | 0.0991800 | + | 0.723350i | ||||
\(851\) | −10.7789 | −0.369495 | ||||||||
\(852\) | 1.73151 | + | 1.73151i | 0.0593205 | + | 0.0593205i | ||||
\(853\) | −15.7577 | − | 15.7577i | −0.539535 | − | 0.539535i | 0.383858 | − | 0.923392i | \(-0.374595\pi\) |
−0.923392 | + | 0.383858i | \(0.874595\pi\) | |||||||
\(854\) | −5.99194 | −0.205040 | ||||||||
\(855\) | −47.5239 | + | 3.24288i | −1.62528 | + | 0.110904i | ||||
\(856\) | 9.59117 | 0.327820 | ||||||||
\(857\) | 25.6632 | − | 25.6632i | 0.876637 | − | 0.876637i | −0.116548 | − | 0.993185i | \(-0.537183\pi\) |
0.993185 | + | 0.116548i | \(0.0371830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 30.6311i | 1.04512i | 0.852603 | + | 0.522559i | \(0.175023\pi\) | ||||
−0.852603 | + | 0.522559i | \(0.824977\pi\) | |||||||
\(860\) | −0.668388 | − | 0.582997i | −0.0227918 | − | 0.0198800i | ||||
\(861\) | 3.80309 | 0.129609 | ||||||||
\(862\) | 6.33554 | + | 6.33554i | 0.215789 | + | 0.215789i | ||||
\(863\) | 33.6775 | − | 33.6775i | 1.14639 | − | 1.14639i | 0.159138 | − | 0.987256i | \(-0.449129\pi\) |
0.987256 | − | 0.159138i | \(-0.0508714\pi\) | |||||||
\(864\) | −6.57778 | −0.223781 | ||||||||
\(865\) | 1.71406 | − | 1.96512i | 0.0582799 | − | 0.0668161i | ||||
\(866\) | − | 25.1755i | − | 0.855499i | ||||||
\(867\) | −1.14126 | − | 1.14126i | −0.0387592 | − | 0.0387592i | ||||
\(868\) | −3.86396 | − | 3.86396i | −0.131151 | − | 0.131151i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.756863 | − | 0.0516459i | 0.0256600 | − | 0.00175096i | ||||
\(871\) | 21.4426i | 0.726555i | ||||||||
\(872\) | 4.91658 | + | 4.91658i | 0.166496 | + | 0.166496i | ||||
\(873\) | 23.2597 | − | 23.2597i | 0.787223 | − | 0.787223i | ||||
\(874\) | − | 23.2363i | − | 0.785980i | ||||||
\(875\) | 14.0596 | + | 9.23161i | 0.475302 | + | 0.312086i | ||||
\(876\) | 1.95069i | 0.0659077i | ||||||||
\(877\) | 6.03697 | − | 6.03697i | 0.203854 | − | 0.203854i | −0.597795 | − | 0.801649i | \(-0.703956\pi\) |
0.801649 | + | 0.597795i | \(0.203956\pi\) | |||||||
\(878\) | −24.6022 | + | 24.6022i | −0.830285 | + | 0.830285i | ||||
\(879\) | 10.9043 | 0.367794 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 18.6414 | 0.628046 | 0.314023 | − | 0.949415i | \(-0.398323\pi\) | ||||
0.314023 | + | 0.949415i | \(0.398323\pi\) | |||||||
\(882\) | 11.5194 | − | 11.5194i | 0.387879 | − | 0.387879i | ||||
\(883\) | −31.3527 | + | 31.3527i | −1.05510 | + | 1.05510i | −0.0567125 | + | 0.998391i | \(0.518062\pi\) |
−0.998391 | + | 0.0567125i | \(0.981938\pi\) | |||||||
\(884\) | 8.99815i | 0.302641i | ||||||||
\(885\) | 6.57558 | − | 7.53869i | 0.221036 | − | 0.253410i | ||||
\(886\) | − | 33.6441i | − | 1.13030i | ||||||
\(887\) | 2.34082 | − | 2.34082i | 0.0785972 | − | 0.0785972i | −0.666715 | − | 0.745312i | \(-0.732300\pi\) |
0.745312 | + | 0.666715i | \(0.232300\pi\) | |||||||
\(888\) | −3.28748 | − | 3.28748i | −0.110321 | − | 0.110321i | ||||
\(889\) | 30.7852i | 1.03250i | ||||||||
\(890\) | −17.5775 | + | 20.1520i | −0.589198 | + | 0.675497i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.97065 | + | 1.97065i | 0.0659823 | + | 0.0659823i | ||||
\(893\) | −40.6455 | − | 40.6455i | −1.36015 | − | 1.36015i | ||||
\(894\) | − | 1.04445i | − | 0.0349316i | ||||||
\(895\) | 13.5270 | − | 0.923038i | 0.452157 | − | 0.0308538i | ||||
\(896\) | −6.68029 | −0.223173 | ||||||||
\(897\) | 3.05122 | − | 3.05122i | 0.101877 | − | 0.101877i | ||||
\(898\) | 16.0870 | + | 16.0870i | 0.536830 | + | 0.536830i | ||||
\(899\) | 5.01174 | 0.167151 | ||||||||
\(900\) | 7.95346 | − | 1.09052i | 0.265115 | − | 0.0363506i | ||||
\(901\) | 37.7927i | 1.25906i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.275534 | − | 0.275534i | 0.00916921 | − | 0.00916921i | ||||
\(904\) | −60.5578 | −2.01412 | ||||||||
\(905\) | −0.238135 | − | 3.48983i | −0.00791587 | − | 0.116006i | ||||
\(906\) | 7.88754 | 0.262046 | ||||||||
\(907\) | −37.8445 | − | 37.8445i | −1.25661 | − | 1.25661i | −0.952703 | − | 0.303903i | \(-0.901710\pi\) |
−0.303903 | − | 0.952703i | \(-0.598290\pi\) | |||||||
\(908\) | −2.71916 | − | 2.71916i | −0.0902384 | − | 0.0902384i | ||||
\(909\) | −10.8178 | −0.358803 | ||||||||
\(910\) | −13.7718 | − | 12.0123i | −0.456529 | − | 0.398205i | ||||
\(911\) | −30.2935 | −1.00367 | −0.501834 | − | 0.864964i | \(-0.667341\pi\) | ||||
−0.501834 | + | 0.864964i | \(0.667341\pi\) | |||||||
\(912\) | 4.93296 | − | 4.93296i | 0.163347 | − | 0.163347i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 19.0990i | − | 0.631737i | ||||||
\(915\) | −1.78477 | + | 2.04618i | −0.0590027 | + | 0.0676447i | ||||
\(916\) | 7.38321 | 0.243948 | ||||||||
\(917\) | 9.11844 | + | 9.11844i | 0.301117 | + | 0.301117i | ||||
\(918\) | −6.46001 | + | 6.46001i | −0.213212 | + | 0.213212i | ||||
\(919\) | −16.1318 | −0.532140 | −0.266070 | − | 0.963954i | \(-0.585725\pi\) | ||||
−0.266070 | + | 0.963954i | \(0.585725\pi\) | |||||||
\(920\) | 1.21843 | + | 17.8559i | 0.0401704 | + | 0.588691i | ||||
\(921\) | − | 0.433138i | − | 0.0142724i | ||||||
\(922\) | 28.0001 | + | 28.0001i | 0.922133 | + | 0.922133i | ||||
\(923\) | 38.2547 | + | 38.2547i | 1.25917 | + | 1.25917i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 16.4781 | + | 12.5042i | 0.541796 | + | 0.411137i | ||||
\(926\) | − | 14.7378i | − | 0.484316i | ||||||
\(927\) | −26.6019 | − | 26.6019i | −0.873721 | − | 0.873721i | ||||
\(928\) | −1.67523 | + | 1.67523i | −0.0549921 | + | 0.0549921i | ||||
\(929\) | − | 3.84293i | − | 0.126082i | −0.998011 | − | 0.0630411i | \(-0.979920\pi\) | ||
0.998011 | − | 0.0630411i | \(-0.0200799\pi\) | |||||||
\(930\) | 6.34971 | − | 0.433284i | 0.208215 | − | 0.0142079i | ||||
\(931\) | − | 35.2063i | − | 1.15384i | ||||||
\(932\) | 5.97101 | − | 5.97101i | 0.195587 | − | 0.195587i | ||||
\(933\) | 3.86689 | − | 3.86689i | 0.126596 | − | 0.126596i | ||||
\(934\) | −5.86807 | −0.192009 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −39.8636 | −1.30298 | ||||||||
\(937\) | 12.2864 | − | 12.2864i | 0.401380 | − | 0.401380i | −0.477339 | − | 0.878719i | \(-0.658399\pi\) |
0.878719 | + | 0.477339i | \(0.158399\pi\) | |||||||
\(938\) | 6.04542 | − | 6.04542i | 0.197390 | − | 0.197390i | ||||
\(939\) | 7.62977i | 0.248988i | ||||||||
\(940\) | 7.30047 | + | 6.36779i | 0.238115 | + | 0.207695i | ||||
\(941\) | − | 4.12356i | − | 0.134424i | −0.997739 | − | 0.0672120i | \(-0.978590\pi\) | ||
0.997739 | − | 0.0672120i | \(-0.0214104\pi\) | |||||||
\(942\) | −0.921393 | + | 0.921393i | −0.0300206 | + | 0.0300206i | ||||
\(943\) | −12.7316 | − | 12.7316i | −0.414598 | − | 0.414598i | ||||
\(944\) | − | 31.3788i | − | 1.02129i | ||||||
\(945\) | 0.491439 | + | 7.20195i | 0.0159865 | + | 0.234280i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −9.37085 | − | 9.37085i | −0.304512 | − | 0.304512i | 0.538264 | − | 0.842776i | \(-0.319080\pi\) |
−0.842776 | + | 0.538264i | \(0.819080\pi\) | |||||||
\(948\) | −1.66032 | − | 1.66032i | −0.0539246 | − | 0.0539246i | ||||
\(949\) | 43.0972i | 1.39899i | ||||||||
\(950\) | −26.9558 | + | 35.5223i | −0.874561 | + | 1.15249i | ||||
\(951\) | −1.50050 | −0.0486570 | ||||||||
\(952\) | 11.5943 | − | 11.5943i | 0.375774 | − | 0.375774i | ||||
\(953\) | −9.73307 | − | 9.73307i | −0.315285 | − | 0.315285i | 0.531668 | − | 0.846953i | \(-0.321565\pi\) |
−0.846953 | + | 0.531668i | \(0.821565\pi\) | |||||||
\(954\) | −36.6343 | −1.18608 | ||||||||
\(955\) | −0.203373 | − | 2.98040i | −0.00658100 | − | 0.0964434i | ||||
\(956\) | 7.48279i | 0.242011i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.36101 | − | 7.36101i | 0.237823 | − | 0.237823i | ||||
\(959\) | −1.25602 | −0.0405591 | ||||||||
\(960\) | −4.73685 | + | 5.43065i | −0.152881 | + | 0.175274i | ||||
\(961\) | 11.0461 | 0.356325 | ||||||||
\(962\) | −15.8920 | − | 15.8920i | −0.512380 | − | 0.512380i | ||||
\(963\) | −6.32755 | − | 6.32755i | −0.203902 | − | 0.203902i | ||||
\(964\) | 3.52304 | 0.113470 | ||||||||
\(965\) | 2.44057 | − | 2.79803i | 0.0785647 | − | 0.0900719i | ||||
\(966\) | −1.72049 | −0.0553560 | ||||||||
\(967\) | −33.1678 | + | 33.1678i | −1.06660 | + | 1.06660i | −0.0689861 | + | 0.997618i | \(0.521976\pi\) |
−0.997618 | + | 0.0689861i | \(0.978024\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.64653i | 0.309891i | ||||||||
\(970\) | −2.09636 | − | 30.7218i | −0.0673101 | − | 0.986418i | ||||
\(971\) | 34.8809 | 1.11938 | 0.559691 | − | 0.828702i | \(-0.310920\pi\) | ||||
0.559691 | + | 0.828702i | \(0.310920\pi\) | |||||||
\(972\) | 3.68225 | + | 3.68225i | 0.118108 | + | 0.118108i | ||||
\(973\) | 21.3567 | − | 21.3567i | 0.684663 | − | 0.684663i | ||||
\(974\) | 45.9056 | 1.47091 | ||||||||
\(975\) | −8.20416 | + | 1.12489i | −0.262744 | + | 0.0360253i | ||||
\(976\) | 8.51696i | 0.272621i | ||||||||
\(977\) | −14.7673 | − | 14.7673i | −0.472448 | − | 0.472448i | 0.430258 | − | 0.902706i | \(-0.358423\pi\) |
−0.902706 | + | 0.430258i | \(0.858423\pi\) | |||||||
\(978\) | −0.944112 | − | 0.944112i | −0.0301894 | − | 0.0301894i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.403934 | + | 5.91959i | 0.0129032 | + | 0.189094i | ||||
\(981\) | − | 6.48720i | − | 0.207120i | ||||||
\(982\) | −3.01207 | − | 3.01207i | −0.0961190 | − | 0.0961190i | ||||
\(983\) | −5.93055 | + | 5.93055i | −0.189155 | + | 0.189155i | −0.795331 | − | 0.606176i | \(-0.792703\pi\) |
0.606176 | + | 0.795331i | \(0.292703\pi\) | |||||||
\(984\) | − | 7.76610i | − | 0.247574i | ||||||
\(985\) | 9.51012 | + | 8.29515i | 0.303018 | + | 0.264305i | ||||
\(986\) | 3.29047i | 0.104790i | ||||||||
\(987\) | −3.00953 | + | 3.00953i | −0.0957944 | + | 0.0957944i | ||||
\(988\) | −13.3289 | + | 13.3289i | −0.424048 | + | 0.424048i | ||||
\(989\) | −1.84481 | −0.0586617 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.22056 | 0.0387723 | 0.0193861 | − | 0.999812i | \(-0.493829\pi\) | ||||
0.0193861 | + | 0.999812i | \(0.493829\pi\) | |||||||
\(992\) | −14.0544 | + | 14.0544i | −0.446226 | + | 0.446226i | ||||
\(993\) | −3.48377 | + | 3.48377i | −0.110554 | + | 0.110554i | ||||
\(994\) | − | 21.5707i | − | 0.684181i | ||||||
\(995\) | −19.0798 | + | 1.30195i | −0.604871 | + | 0.0412745i | ||||
\(996\) | − | 0.811490i | − | 0.0257130i | ||||||
\(997\) | 6.09123 | − | 6.09123i | 0.192911 | − | 0.192911i | −0.604042 | − | 0.796953i | \(-0.706444\pi\) |
0.796953 | + | 0.604042i | \(0.206444\pi\) | |||||||
\(998\) | −21.8713 | − | 21.8713i | −0.692325 | − | 0.692325i | ||||
\(999\) | 8.87786i | 0.280883i |
(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 | 605.2.e.c.362.7 | ✓ | 40 | |
5.3 | odd | 4 | inner | 605.2.e.c.483.14 | yes | 40 | |
11.2 | odd | 10 | 605.2.m.g.282.7 | 160 | |||
11.3 | even | 5 | 605.2.m.g.112.14 | 160 | |||
11.4 | even | 5 | 605.2.m.g.457.7 | 160 | |||
11.5 | even | 5 | 605.2.m.g.602.14 | 160 | |||
11.6 | odd | 10 | 605.2.m.g.602.7 | 160 | |||
11.7 | odd | 10 | 605.2.m.g.457.14 | 160 | |||
11.8 | odd | 10 | 605.2.m.g.112.7 | 160 | |||
11.9 | even | 5 | 605.2.m.g.282.14 | 160 | |||
11.10 | odd | 2 | inner | 605.2.e.c.362.14 | yes | 40 | |
55.3 | odd | 20 | 605.2.m.g.233.14 | 160 | |||
55.8 | even | 20 | 605.2.m.g.233.7 | 160 | |||
55.13 | even | 20 | 605.2.m.g.403.14 | 160 | |||
55.18 | even | 20 | 605.2.m.g.578.14 | 160 | |||
55.28 | even | 20 | 605.2.m.g.118.14 | 160 | |||
55.38 | odd | 20 | 605.2.m.g.118.7 | 160 | |||
55.43 | even | 4 | inner | 605.2.e.c.483.7 | yes | 40 | |
55.48 | odd | 20 | 605.2.m.g.578.7 | 160 | |||
55.53 | odd | 20 | 605.2.m.g.403.7 | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
605.2.e.c.362.7 | ✓ | 40 | 1.1 | even | 1 | trivial | |
605.2.e.c.362.14 | yes | 40 | 11.10 | odd | 2 | inner | |
605.2.e.c.483.7 | yes | 40 | 55.43 | even | 4 | inner | |
605.2.e.c.483.14 | yes | 40 | 5.3 | odd | 4 | inner | |
605.2.m.g.112.7 | 160 | 11.8 | odd | 10 | |||
605.2.m.g.112.14 | 160 | 11.3 | even | 5 | |||
605.2.m.g.118.7 | 160 | 55.38 | odd | 20 | |||
605.2.m.g.118.14 | 160 | 55.28 | even | 20 | |||
605.2.m.g.233.7 | 160 | 55.8 | even | 20 | |||
605.2.m.g.233.14 | 160 | 55.3 | odd | 20 | |||
605.2.m.g.282.7 | 160 | 11.2 | odd | 10 | |||
605.2.m.g.282.14 | 160 | 11.9 | even | 5 | |||
605.2.m.g.403.7 | 160 | 55.53 | odd | 20 | |||
605.2.m.g.403.14 | 160 | 55.13 | even | 20 | |||
605.2.m.g.457.7 | 160 | 11.4 | even | 5 | |||
605.2.m.g.457.14 | 160 | 11.7 | odd | 10 | |||
605.2.m.g.578.7 | 160 | 55.48 | odd | 20 | |||
605.2.m.g.578.14 | 160 | 55.18 | even | 20 | |||
605.2.m.g.602.7 | 160 | 11.6 | odd | 10 | |||
605.2.m.g.602.14 | 160 | 11.5 | even | 5 |