Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 77.16 | ||
Character | \(\chi\) | \(=\) | 570.77 |
Dual form | 570.2.k.b.533.16 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 1.11099 | + | 1.32879i | 0.641433 | + | 0.767179i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.28568 | − | 1.82949i | 0.574973 | − | 0.818172i | ||||
\(6\) | 1.72519 | + | 0.154007i | 0.704306 | + | 0.0628729i | ||||
\(7\) | 1.30605 | + | 1.30605i | 0.493642 | + | 0.493642i | 0.909452 | − | 0.415810i | \(-0.136502\pi\) |
−0.415810 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | −0.531382 | + | 2.95256i | −0.177127 | + | 0.984188i | ||||
\(10\) | −0.384532 | − | 2.20276i | −0.121600 | − | 0.696573i | ||||
\(11\) | 5.15114i | 1.55313i | 0.630038 | + | 0.776564i | \(0.283039\pi\) | ||||
−0.630038 | + | 0.776564i | \(0.716961\pi\) | |||||||
\(12\) | 1.32879 | − | 1.11099i | 0.383589 | − | 0.320717i | ||||
\(13\) | 0.342145 | − | 0.342145i | 0.0948940 | − | 0.0948940i | −0.658066 | − | 0.752960i | \(-0.728625\pi\) |
0.752960 | + | 0.658066i | \(0.228625\pi\) | |||||||
\(14\) | 1.84704 | 0.493642 | ||||||||
\(15\) | 3.85939 | − | 0.324151i | 0.996491 | − | 0.0836954i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.25002 | − | 4.25002i | 1.03078 | − | 1.03078i | 0.0312704 | − | 0.999511i | \(-0.490045\pi\) |
0.999511 | − | 0.0312704i | \(-0.00995530\pi\) | |||||||
\(18\) | 1.71203 | + | 2.46352i | 0.403530 | + | 0.580658i | ||||
\(19\) | − | 1.00000i | − | 0.229416i | ||||||
\(20\) | −1.82949 | − | 1.28568i | −0.409086 | − | 0.287487i | ||||
\(21\) | −0.284456 | + | 3.18649i | −0.0620734 | + | 0.695350i | ||||
\(22\) | 3.64241 | + | 3.64241i | 0.776564 | + | 0.776564i | ||||
\(23\) | −3.32373 | − | 3.32373i | −0.693046 | − | 0.693046i | 0.269855 | − | 0.962901i | \(-0.413024\pi\) |
−0.962901 | + | 0.269855i | \(0.913024\pi\) | |||||||
\(24\) | 0.154007 | − | 1.72519i | 0.0314365 | − | 0.352153i | ||||
\(25\) | −1.69406 | − | 4.70427i | −0.338812 | − | 0.940854i | ||||
\(26\) | − | 0.483866i | − | 0.0948940i | ||||||
\(27\) | −4.51371 | + | 2.57419i | −0.868664 | + | 0.495402i | ||||
\(28\) | 1.30605 | − | 1.30605i | 0.246821 | − | 0.246821i | ||||
\(29\) | 8.73926 | 1.62284 | 0.811420 | − | 0.584463i | \(-0.198695\pi\) | ||||
0.811420 | + | 0.584463i | \(0.198695\pi\) | |||||||
\(30\) | 2.49979 | − | 2.95821i | 0.456398 | − | 0.540093i | ||||
\(31\) | −10.0988 | −1.81380 | −0.906899 | − | 0.421348i | \(-0.861557\pi\) | ||||
−0.906899 | + | 0.421348i | \(0.861557\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −6.84480 | + | 5.72289i | −1.19153 | + | 0.996228i | ||||
\(34\) | − | 6.01044i | − | 1.03078i | ||||||
\(35\) | 4.06858 | − | 0.710245i | 0.687715 | − | 0.120053i | ||||
\(36\) | 2.95256 | + | 0.531382i | 0.492094 | + | 0.0885636i | ||||
\(37\) | 0.317424 | + | 0.317424i | 0.0521842 | + | 0.0521842i | 0.732717 | − | 0.680533i | \(-0.238252\pi\) |
−0.680533 | + | 0.732717i | \(0.738252\pi\) | |||||||
\(38\) | −0.707107 | − | 0.707107i | −0.114708 | − | 0.114708i | ||||
\(39\) | 0.834762 | + | 0.0745186i | 0.133669 | + | 0.0119325i | ||||
\(40\) | −2.20276 | + | 0.384532i | −0.348286 | + | 0.0607998i | ||||
\(41\) | − | 8.89223i | − | 1.38873i | −0.719622 | − | 0.694366i | \(-0.755685\pi\) | ||
0.719622 | − | 0.694366i | \(-0.244315\pi\) | |||||||
\(42\) | 2.05205 | + | 2.45433i | 0.316638 | + | 0.378712i | ||||
\(43\) | −8.84777 | + | 8.84777i | −1.34927 | + | 1.34927i | −0.462820 | + | 0.886452i | \(0.653162\pi\) |
−0.886452 | + | 0.462820i | \(0.846838\pi\) | |||||||
\(44\) | 5.15114 | 0.776564 | ||||||||
\(45\) | 4.71850 | + | 4.76821i | 0.703392 | + | 0.710802i | ||||
\(46\) | −4.70047 | −0.693046 | ||||||||
\(47\) | 2.14509 | − | 2.14509i | 0.312894 | − | 0.312894i | −0.533136 | − | 0.846030i | \(-0.678986\pi\) |
0.846030 | + | 0.533136i | \(0.178986\pi\) | |||||||
\(48\) | −1.11099 | − | 1.32879i | −0.160358 | − | 0.191795i | ||||
\(49\) | − | 3.58845i | − | 0.512636i | ||||||
\(50\) | −4.52430 | − | 2.12854i | −0.639833 | − | 0.301021i | ||||
\(51\) | 10.3691 | + | 0.925647i | 1.45197 | + | 0.129617i | ||||
\(52\) | −0.342145 | − | 0.342145i | −0.0474470 | − | 0.0474470i | ||||
\(53\) | 8.17583 | + | 8.17583i | 1.12304 | + | 1.12304i | 0.991283 | + | 0.131754i | \(0.0420607\pi\) |
0.131754 | + | 0.991283i | \(0.457939\pi\) | |||||||
\(54\) | −1.37145 | + | 5.01190i | −0.186631 | + | 0.682033i | ||||
\(55\) | 9.42396 | + | 6.62272i | 1.27073 | + | 0.893007i | ||||
\(56\) | − | 1.84704i | − | 0.246821i | ||||||
\(57\) | 1.32879 | − | 1.11099i | 0.176003 | − | 0.147155i | ||||
\(58\) | 6.17959 | − | 6.17959i | 0.811420 | − | 0.811420i | ||||
\(59\) | −1.27397 | −0.165856 | −0.0829282 | − | 0.996556i | \(-0.526427\pi\) | ||||
−0.0829282 | + | 0.996556i | \(0.526427\pi\) | |||||||
\(60\) | −0.324151 | − | 3.85939i | −0.0418477 | − | 0.498246i | ||||
\(61\) | −6.26456 | −0.802094 | −0.401047 | − | 0.916057i | \(-0.631354\pi\) | ||||
−0.401047 | + | 0.916057i | \(0.631354\pi\) | |||||||
\(62\) | −7.14093 | + | 7.14093i | −0.906899 | + | 0.906899i | ||||
\(63\) | −4.55022 | + | 3.16219i | −0.573274 | + | 0.398399i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.186062 | − | 1.06584i | −0.0230781 | − | 0.132201i | ||||
\(66\) | −0.793310 | + | 8.88670i | −0.0976498 | + | 1.09388i | ||||
\(67\) | −1.50061 | − | 1.50061i | −0.183328 | − | 0.183328i | 0.609476 | − | 0.792804i | \(-0.291380\pi\) |
−0.792804 | + | 0.609476i | \(0.791380\pi\) | |||||||
\(68\) | −4.25002 | − | 4.25002i | −0.515391 | − | 0.515391i | ||||
\(69\) | 0.723903 | − | 8.10920i | 0.0871477 | − | 0.976233i | ||||
\(70\) | 2.37470 | − | 3.37914i | 0.283831 | − | 0.403884i | ||||
\(71\) | 11.7068i | 1.38935i | 0.719325 | + | 0.694674i | \(0.244451\pi\) | ||||
−0.719325 | + | 0.694674i | \(0.755549\pi\) | |||||||
\(72\) | 2.46352 | − | 1.71203i | 0.290329 | − | 0.201765i | ||||
\(73\) | −2.73639 | + | 2.73639i | −0.320270 | + | 0.320270i | −0.848871 | − | 0.528601i | \(-0.822717\pi\) |
0.528601 | + | 0.848871i | \(0.322717\pi\) | |||||||
\(74\) | 0.448905 | 0.0521842 | ||||||||
\(75\) | 4.36891 | − | 7.47747i | 0.504478 | − | 0.863424i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −6.72767 | + | 6.72767i | −0.766689 | + | 0.766689i | ||||
\(78\) | 0.642958 | − | 0.537573i | 0.0728007 | − | 0.0608682i | ||||
\(79\) | − | 5.23062i | − | 0.588491i | −0.955730 | − | 0.294246i | \(-0.904932\pi\) | ||
0.955730 | − | 0.294246i | \(-0.0950683\pi\) | |||||||
\(80\) | −1.28568 | + | 1.82949i | −0.143743 | + | 0.204543i | ||||
\(81\) | −8.43527 | − | 3.13788i | −0.937252 | − | 0.348653i | ||||
\(82\) | −6.28776 | − | 6.28776i | −0.694366 | − | 0.694366i | ||||
\(83\) | −9.88555 | − | 9.88555i | −1.08508 | − | 1.08508i | −0.996027 | − | 0.0890537i | \(-0.971616\pi\) |
−0.0890537 | − | 0.996027i | \(-0.528384\pi\) | |||||||
\(84\) | 3.18649 | + | 0.284456i | 0.347675 | + | 0.0310367i | ||||
\(85\) | −2.31120 | − | 13.2395i | −0.250685 | − | 1.43603i | ||||
\(86\) | 12.5126i | 1.34927i | ||||||||
\(87\) | 9.70927 | + | 11.6127i | 1.04094 | + | 1.24501i | ||||
\(88\) | 3.64241 | − | 3.64241i | 0.388282 | − | 0.388282i | ||||
\(89\) | −16.2880 | −1.72653 | −0.863264 | − | 0.504753i | \(-0.831584\pi\) | ||||
−0.863264 | + | 0.504753i | \(0.831584\pi\) | |||||||
\(90\) | 6.70811 | + | 0.0351501i | 0.707097 | + | 0.00370514i | ||||
\(91\) | 0.893720 | 0.0936873 | ||||||||
\(92\) | −3.32373 | + | 3.32373i | −0.346523 | + | 0.346523i | ||||
\(93\) | −11.2197 | − | 13.4192i | −1.16343 | − | 1.39151i | ||||
\(94\) | − | 3.03362i | − | 0.312894i | ||||||
\(95\) | −1.82949 | − | 1.28568i | −0.187702 | − | 0.131908i | ||||
\(96\) | −1.72519 | − | 0.154007i | −0.176077 | − | 0.0157182i | ||||
\(97\) | 4.02586 | + | 4.02586i | 0.408765 | + | 0.408765i | 0.881308 | − | 0.472543i | \(-0.156664\pi\) |
−0.472543 | + | 0.881308i | \(0.656664\pi\) | |||||||
\(98\) | −2.53742 | − | 2.53742i | −0.256318 | − | 0.256318i | ||||
\(99\) | −15.2091 | − | 2.73722i | −1.52857 | − | 0.275101i | ||||
\(100\) | −4.70427 | + | 1.69406i | −0.470427 | + | 0.169406i | ||||
\(101\) | 3.68192i | 0.366365i | 0.983079 | + | 0.183183i | \(0.0586400\pi\) | ||||
−0.983079 | + | 0.183183i | \(0.941360\pi\) | |||||||
\(102\) | 7.98663 | − | 6.67756i | 0.790794 | − | 0.661177i | ||||
\(103\) | −5.58428 | + | 5.58428i | −0.550235 | + | 0.550235i | −0.926509 | − | 0.376273i | \(-0.877205\pi\) |
0.376273 | + | 0.926509i | \(0.377205\pi\) | |||||||
\(104\) | −0.483866 | −0.0474470 | ||||||||
\(105\) | 5.46393 | + | 4.61722i | 0.533225 | + | 0.450594i | ||||
\(106\) | 11.5624 | 1.12304 | ||||||||
\(107\) | 2.07440 | − | 2.07440i | 0.200540 | − | 0.200540i | −0.599691 | − | 0.800231i | \(-0.704710\pi\) |
0.800231 | + | 0.599691i | \(0.204710\pi\) | |||||||
\(108\) | 2.57419 | + | 4.51371i | 0.247701 | + | 0.434332i | ||||
\(109\) | − | 4.47191i | − | 0.428331i | −0.976797 | − | 0.214165i | \(-0.931297\pi\) | ||
0.976797 | − | 0.214165i | \(-0.0687032\pi\) | |||||||
\(110\) | 11.3467 | − | 1.98078i | 1.08187 | − | 0.188860i | ||||
\(111\) | −0.0691344 | + | 0.774447i | −0.00656195 | + | 0.0735073i | ||||
\(112\) | −1.30605 | − | 1.30605i | −0.123410 | − | 0.123410i | ||||
\(113\) | 6.24110 | + | 6.24110i | 0.587114 | + | 0.587114i | 0.936849 | − | 0.349735i | \(-0.113728\pi\) |
−0.349735 | + | 0.936849i | \(0.613728\pi\) | |||||||
\(114\) | 0.154007 | − | 1.72519i | 0.0144240 | − | 0.161579i | ||||
\(115\) | −10.3540 | + | 1.80748i | −0.965514 | + | 0.168548i | ||||
\(116\) | − | 8.73926i | − | 0.811420i | ||||||
\(117\) | 0.828396 | + | 1.19202i | 0.0765852 | + | 0.110202i | ||||
\(118\) | −0.900830 | + | 0.900830i | −0.0829282 | + | 0.0829282i | ||||
\(119\) | 11.1015 | 1.01767 | ||||||||
\(120\) | −2.95821 | − | 2.49979i | −0.270047 | − | 0.228199i | ||||
\(121\) | −15.5343 | −1.41221 | ||||||||
\(122\) | −4.42971 | + | 4.42971i | −0.401047 | + | 0.401047i | ||||
\(123\) | 11.8159 | − | 9.87922i | 1.06541 | − | 0.890779i | ||||
\(124\) | 10.0988i | 0.906899i | ||||||||
\(125\) | −10.7844 | − | 2.94892i | −0.964588 | − | 0.263760i | ||||
\(126\) | −0.981482 | + | 5.45350i | −0.0874374 | + | 0.485836i | ||||
\(127\) | 1.82261 | + | 1.82261i | 0.161730 | + | 0.161730i | 0.783333 | − | 0.621603i | \(-0.213518\pi\) |
−0.621603 | + | 0.783333i | \(0.713518\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −21.5867 | − | 1.92703i | −1.90060 | − | 0.169665i | ||||
\(130\) | −0.885228 | − | 0.622097i | −0.0776397 | − | 0.0545615i | ||||
\(131\) | − | 11.4188i | − | 0.997666i | −0.866698 | − | 0.498833i | \(-0.833762\pi\) | ||
0.866698 | − | 0.498833i | \(-0.166238\pi\) | |||||||
\(132\) | 5.72289 | + | 6.84480i | 0.498114 | + | 0.595764i | ||||
\(133\) | 1.30605 | − | 1.30605i | 0.113249 | − | 0.113249i | ||||
\(134\) | −2.12218 | −0.183328 | ||||||||
\(135\) | −1.09373 | + | 11.5674i | −0.0941337 | + | 0.995560i | ||||
\(136\) | −6.01044 | −0.515391 | ||||||||
\(137\) | 11.0007 | − | 11.0007i | 0.939857 | − | 0.939857i | −0.0584339 | − | 0.998291i | \(-0.518611\pi\) |
0.998291 | + | 0.0584339i | \(0.0186107\pi\) | |||||||
\(138\) | −5.22220 | − | 6.24595i | −0.444543 | − | 0.531690i | ||||
\(139\) | − | 1.23352i | − | 0.104626i | −0.998631 | − | 0.0523128i | \(-0.983341\pi\) | ||
0.998631 | − | 0.0523128i | \(-0.0166593\pi\) | |||||||
\(140\) | −0.710245 | − | 4.06858i | −0.0600266 | − | 0.343857i | ||||
\(141\) | 5.23357 | + | 0.467198i | 0.440746 | + | 0.0393452i | ||||
\(142\) | 8.27799 | + | 8.27799i | 0.694674 | + | 0.694674i | ||||
\(143\) | 1.76244 | + | 1.76244i | 0.147383 | + | 0.147383i | ||||
\(144\) | 0.531382 | − | 2.95256i | 0.0442818 | − | 0.246047i | ||||
\(145\) | 11.2359 | − | 15.9884i | 0.933090 | − | 1.32776i | ||||
\(146\) | 3.86983i | 0.320270i | ||||||||
\(147\) | 4.76831 | − | 3.98675i | 0.393283 | − | 0.328821i | ||||
\(148\) | 0.317424 | − | 0.317424i | 0.0260921 | − | 0.0260921i | ||||
\(149\) | 0.607952 | 0.0498053 | 0.0249027 | − | 0.999690i | \(-0.492072\pi\) | ||||
0.0249027 | + | 0.999690i | \(0.492072\pi\) | |||||||
\(150\) | −2.19808 | − | 8.37666i | −0.179473 | − | 0.683951i | ||||
\(151\) | 2.49294 | 0.202873 | 0.101436 | − | 0.994842i | \(-0.467656\pi\) | ||||
0.101436 | + | 0.994842i | \(0.467656\pi\) | |||||||
\(152\) | −0.707107 | + | 0.707107i | −0.0573539 | + | 0.0573539i | ||||
\(153\) | 10.2901 | + | 14.8068i | 0.831903 | + | 1.19706i | ||||
\(154\) | 9.51436i | 0.766689i | ||||||||
\(155\) | −12.9838 | + | 18.4756i | −1.04288 | + | 1.48400i | ||||
\(156\) | 0.0745186 | − | 0.834762i | 0.00596627 | − | 0.0668344i | ||||
\(157\) | 0.0444358 | + | 0.0444358i | 0.00354636 | + | 0.00354636i | 0.708878 | − | 0.705331i | \(-0.249202\pi\) |
−0.705331 | + | 0.708878i | \(0.749202\pi\) | |||||||
\(158\) | −3.69861 | − | 3.69861i | −0.294246 | − | 0.294246i | ||||
\(159\) | −1.78068 | + | 19.9473i | −0.141217 | + | 1.58192i | ||||
\(160\) | 0.384532 | + | 2.20276i | 0.0303999 | + | 0.174143i | ||||
\(161\) | − | 8.68195i | − | 0.684233i | ||||||
\(162\) | −8.18345 | + | 3.74582i | −0.642952 | + | 0.294300i | ||||
\(163\) | 8.99735 | − | 8.99735i | 0.704727 | − | 0.704727i | −0.260694 | − | 0.965421i | \(-0.583952\pi\) |
0.965421 | + | 0.260694i | \(0.0839515\pi\) | |||||||
\(164\) | −8.89223 | −0.694366 | ||||||||
\(165\) | 1.66975 | + | 19.8803i | 0.129990 | + | 1.54768i | ||||
\(166\) | −13.9803 | −1.08508 | ||||||||
\(167\) | −1.17503 | + | 1.17503i | −0.0909264 | + | 0.0909264i | −0.751107 | − | 0.660181i | \(-0.770480\pi\) |
0.660181 | + | 0.751107i | \(0.270480\pi\) | |||||||
\(168\) | 2.45433 | − | 2.05205i | 0.189356 | − | 0.158319i | ||||
\(169\) | 12.7659i | 0.981990i | ||||||||
\(170\) | −10.9960 | − | 7.72749i | −0.843357 | − | 0.592672i | ||||
\(171\) | 2.95256 | + | 0.531382i | 0.225788 | + | 0.0406358i | ||||
\(172\) | 8.84777 | + | 8.84777i | 0.674636 | + | 0.674636i | ||||
\(173\) | 13.5995 | + | 13.5995i | 1.03395 | + | 1.03395i | 0.999403 | + | 0.0345455i | \(0.0109984\pi\) |
0.0345455 | + | 0.999403i | \(0.489002\pi\) | |||||||
\(174\) | 15.0769 | + | 1.34590i | 1.14298 | + | 0.102033i | ||||
\(175\) | 3.93150 | − | 8.35656i | 0.297193 | − | 0.631697i | ||||
\(176\) | − | 5.15114i | − | 0.388282i | ||||||
\(177\) | −1.41537 | − | 1.69284i | −0.106386 | − | 0.127241i | ||||
\(178\) | −11.5174 | + | 11.5174i | −0.863264 | + | 0.863264i | ||||
\(179\) | −17.9786 | −1.34378 | −0.671892 | − | 0.740649i | \(-0.734518\pi\) | ||||
−0.671892 | + | 0.740649i | \(0.734518\pi\) | |||||||
\(180\) | 4.76821 | − | 4.71850i | 0.355401 | − | 0.351696i | ||||
\(181\) | 4.58187 | 0.340568 | 0.170284 | − | 0.985395i | \(-0.445531\pi\) | ||||
0.170284 | + | 0.985395i | \(0.445531\pi\) | |||||||
\(182\) | 0.631955 | − | 0.631955i | 0.0468437 | − | 0.0468437i | ||||
\(183\) | −6.95989 | − | 8.32430i | −0.514490 | − | 0.615350i | ||||
\(184\) | 4.70047i | 0.346523i | ||||||||
\(185\) | 0.988829 | − | 0.172618i | 0.0727002 | − | 0.0126911i | ||||
\(186\) | −17.4223 | − | 1.55528i | −1.27747 | − | 0.114039i | ||||
\(187\) | 21.8925 | + | 21.8925i | 1.60094 | + | 1.60094i | ||||
\(188\) | −2.14509 | − | 2.14509i | −0.156447 | − | 0.156447i | ||||
\(189\) | −9.25717 | − | 2.53312i | −0.673360 | − | 0.184257i | ||||
\(190\) | −2.20276 | + | 0.384532i | −0.159805 | + | 0.0278969i | ||||
\(191\) | − | 12.3225i | − | 0.891626i | −0.895126 | − | 0.445813i | \(-0.852915\pi\) | ||
0.895126 | − | 0.445813i | \(-0.147085\pi\) | |||||||
\(192\) | −1.32879 | + | 1.11099i | −0.0958974 | + | 0.0801791i | ||||
\(193\) | −11.8604 | + | 11.8604i | −0.853728 | + | 0.853728i | −0.990590 | − | 0.136862i | \(-0.956298\pi\) |
0.136862 | + | 0.990590i | \(0.456298\pi\) | |||||||
\(194\) | 5.69343 | 0.408765 | ||||||||
\(195\) | 1.20957 | − | 1.43138i | 0.0866189 | − | 0.102503i | ||||
\(196\) | −3.58845 | −0.256318 | ||||||||
\(197\) | 3.56808 | − | 3.56808i | 0.254215 | − | 0.254215i | −0.568481 | − | 0.822696i | \(-0.692469\pi\) |
0.822696 | + | 0.568481i | \(0.192469\pi\) | |||||||
\(198\) | −12.6900 | + | 8.81894i | −0.901836 | + | 0.626735i | ||||
\(199\) | − | 3.23189i | − | 0.229102i | −0.993417 | − | 0.114551i | \(-0.963457\pi\) | ||
0.993417 | − | 0.114551i | \(-0.0365430\pi\) | |||||||
\(200\) | −2.12854 | + | 4.52430i | −0.150511 | + | 0.319916i | ||||
\(201\) | 0.326830 | − | 3.66116i | 0.0230528 | − | 0.258239i | ||||
\(202\) | 2.60351 | + | 2.60351i | 0.183183 | + | 0.183183i | ||||
\(203\) | 11.4139 | + | 11.4139i | 0.801102 | + | 0.801102i | ||||
\(204\) | 0.925647 | − | 10.3691i | 0.0648083 | − | 0.725986i | ||||
\(205\) | −16.2682 | − | 11.4326i | −1.13622 | − | 0.798484i | ||||
\(206\) | 7.89736i | 0.550235i | ||||||||
\(207\) | 11.5797 | − | 8.04736i | 0.804845 | − | 0.559330i | ||||
\(208\) | −0.342145 | + | 0.342145i | −0.0237235 | + | 0.0237235i | ||||
\(209\) | 5.15114 | 0.356312 | ||||||||
\(210\) | 7.12845 | − | 0.598720i | 0.491910 | − | 0.0413156i | ||||
\(211\) | 13.2442 | 0.911766 | 0.455883 | − | 0.890040i | \(-0.349324\pi\) | ||||
0.455883 | + | 0.890040i | \(0.349324\pi\) | |||||||
\(212\) | 8.17583 | − | 8.17583i | 0.561518 | − | 0.561518i | ||||
\(213\) | −15.5560 | + | 13.0062i | −1.06588 | + | 0.891173i | ||||
\(214\) | − | 2.93365i | − | 0.200540i | ||||||
\(215\) | 4.81150 | + | 27.5623i | 0.328142 | + | 1.87973i | ||||
\(216\) | 5.01190 | + | 1.37145i | 0.341017 | + | 0.0933153i | ||||
\(217\) | −13.1896 | − | 13.1896i | −0.895366 | − | 0.895366i | ||||
\(218\) | −3.16212 | − | 3.16212i | −0.214165 | − | 0.214165i | ||||
\(219\) | −6.67620 | − | 0.595980i | −0.451136 | − | 0.0402726i | ||||
\(220\) | 6.62272 | − | 9.42396i | 0.446504 | − | 0.635363i | ||||
\(221\) | − | 2.90825i | − | 0.195630i | ||||||
\(222\) | 0.498731 | + | 0.596502i | 0.0334727 | + | 0.0400346i | ||||
\(223\) | 3.93298 | − | 3.93298i | 0.263372 | − | 0.263372i | −0.563050 | − | 0.826423i | \(-0.690372\pi\) |
0.826423 | + | 0.563050i | \(0.190372\pi\) | |||||||
\(224\) | −1.84704 | −0.123410 | ||||||||
\(225\) | 14.7899 | − | 2.50205i | 0.985990 | − | 0.166804i | ||||
\(226\) | 8.82625 | 0.587114 | ||||||||
\(227\) | −4.90875 | + | 4.90875i | −0.325805 | + | 0.325805i | −0.850989 | − | 0.525184i | \(-0.823997\pi\) |
0.525184 | + | 0.850989i | \(0.323997\pi\) | |||||||
\(228\) | −1.11099 | − | 1.32879i | −0.0735774 | − | 0.0880015i | ||||
\(229\) | 0.309162i | 0.0204300i | 0.999948 | + | 0.0102150i | \(0.00325159\pi\) | ||||
−0.999948 | + | 0.0102150i | \(0.996748\pi\) | |||||||
\(230\) | −6.04329 | + | 8.59945i | −0.398483 | + | 0.567031i | ||||
\(231\) | −16.4141 | − | 1.46527i | −1.07997 | − | 0.0964080i | ||||
\(232\) | −6.17959 | − | 6.17959i | −0.405710 | − | 0.405710i | ||||
\(233\) | −1.09776 | − | 1.09776i | −0.0719169 | − | 0.0719169i | 0.670233 | − | 0.742150i | \(-0.266194\pi\) |
−0.742150 | + | 0.670233i | \(0.766194\pi\) | |||||||
\(234\) | 1.42865 | + | 0.257118i | 0.0933935 | + | 0.0168083i | ||||
\(235\) | −1.16652 | − | 6.68233i | −0.0760956 | − | 0.435907i | ||||
\(236\) | 1.27397i | 0.0829282i | ||||||||
\(237\) | 6.95041 | − | 5.81119i | 0.451478 | − | 0.377478i | ||||
\(238\) | 7.84995 | − | 7.84995i | 0.508837 | − | 0.508837i | ||||
\(239\) | 24.4016 | 1.57841 | 0.789205 | − | 0.614130i | \(-0.210493\pi\) | ||||
0.789205 | + | 0.614130i | \(0.210493\pi\) | |||||||
\(240\) | −3.85939 | + | 0.324151i | −0.249123 | + | 0.0209239i | ||||
\(241\) | −15.4813 | −0.997235 | −0.498618 | − | 0.866822i | \(-0.666159\pi\) | ||||
−0.498618 | + | 0.866822i | \(0.666159\pi\) | |||||||
\(242\) | −10.9844 | + | 10.9844i | −0.706104 | + | 0.706104i | ||||
\(243\) | −5.20195 | − | 14.6949i | −0.333705 | − | 0.942677i | ||||
\(244\) | 6.26456i | 0.401047i | ||||||||
\(245\) | −6.56503 | − | 4.61359i | −0.419424 | − | 0.294752i | ||||
\(246\) | 1.36946 | − | 15.3408i | 0.0873137 | − | 0.978093i | ||||
\(247\) | −0.342145 | − | 0.342145i | −0.0217702 | − | 0.0217702i | ||||
\(248\) | 7.14093 | + | 7.14093i | 0.453449 | + | 0.453449i | ||||
\(249\) | 2.15306 | − | 24.1187i | 0.136444 | − | 1.52846i | ||||
\(250\) | −9.71094 | + | 5.54054i | −0.614174 | + | 0.350414i | ||||
\(251\) | − | 10.3840i | − | 0.655435i | −0.944776 | − | 0.327718i | \(-0.893721\pi\) | ||
0.944776 | − | 0.327718i | \(-0.106279\pi\) | |||||||
\(252\) | 3.16219 | + | 4.55022i | 0.199199 | + | 0.286637i | ||||
\(253\) | 17.1210 | − | 17.1210i | 1.07639 | − | 1.07639i | ||||
\(254\) | 2.57755 | 0.161730 | ||||||||
\(255\) | 15.0249 | − | 17.7802i | 0.940893 | − | 1.11344i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −10.1303 | + | 10.1303i | −0.631914 | + | 0.631914i | −0.948548 | − | 0.316634i | \(-0.897447\pi\) |
0.316634 | + | 0.948548i | \(0.397447\pi\) | |||||||
\(258\) | −16.6267 | + | 13.9015i | −1.03513 | + | 0.865468i | ||||
\(259\) | 0.829145i | 0.0515206i | ||||||||
\(260\) | −1.06584 | + | 0.186062i | −0.0661006 | + | 0.0115391i | ||||
\(261\) | −4.64388 | + | 25.8032i | −0.287449 | + | 1.59718i | ||||
\(262\) | −8.07432 | − | 8.07432i | −0.498833 | − | 0.498833i | ||||
\(263\) | 18.8740 | + | 18.8740i | 1.16382 | + | 1.16382i | 0.983632 | + | 0.180189i | \(0.0576710\pi\) |
0.180189 | + | 0.983632i | \(0.442329\pi\) | |||||||
\(264\) | 8.88670 | + | 0.793310i | 0.546939 | + | 0.0488249i | ||||
\(265\) | 25.4691 | − | 4.44609i | 1.56455 | − | 0.273121i | ||||
\(266\) | − | 1.84704i | − | 0.113249i | ||||||
\(267\) | −18.0959 | − | 21.6434i | −1.10745 | − | 1.32456i | ||||
\(268\) | −1.50061 | + | 1.50061i | −0.0916642 | + | 0.0916642i | ||||
\(269\) | 6.51981 | 0.397520 | 0.198760 | − | 0.980048i | \(-0.436309\pi\) | ||||
0.198760 | + | 0.980048i | \(0.436309\pi\) | |||||||
\(270\) | 7.40597 | + | 8.95274i | 0.450713 | + | 0.544847i | ||||
\(271\) | 14.4070 | 0.875160 | 0.437580 | − | 0.899179i | \(-0.355836\pi\) | ||||
0.437580 | + | 0.899179i | \(0.355836\pi\) | |||||||
\(272\) | −4.25002 | + | 4.25002i | −0.257695 | + | 0.257695i | ||||
\(273\) | 0.992918 | + | 1.18757i | 0.0600941 | + | 0.0718749i | ||||
\(274\) | − | 15.5574i | − | 0.939857i | ||||||
\(275\) | 24.2324 | − | 8.72634i | 1.46127 | − | 0.526218i | ||||
\(276\) | −8.10920 | − | 0.723903i | −0.488117 | − | 0.0435739i | ||||
\(277\) | 13.9724 | + | 13.9724i | 0.839520 | + | 0.839520i | 0.988796 | − | 0.149276i | \(-0.0476942\pi\) |
−0.149276 | + | 0.988796i | \(0.547694\pi\) | |||||||
\(278\) | −0.872229 | − | 0.872229i | −0.0523128 | − | 0.0523128i | ||||
\(279\) | 5.36632 | − | 29.8173i | 0.321273 | − | 1.78512i | ||||
\(280\) | −3.37914 | − | 2.37470i | −0.201942 | − | 0.141915i | ||||
\(281\) | − | 24.2309i | − | 1.44549i | −0.691113 | − | 0.722747i | \(-0.742879\pi\) | ||
0.691113 | − | 0.722747i | \(-0.257121\pi\) | |||||||
\(282\) | 4.03105 | − | 3.37034i | 0.240046 | − | 0.200701i | ||||
\(283\) | 9.26434 | − | 9.26434i | 0.550708 | − | 0.550708i | −0.375937 | − | 0.926645i | \(-0.622679\pi\) |
0.926645 | + | 0.375937i | \(0.122679\pi\) | |||||||
\(284\) | 11.7068 | 0.694674 | ||||||||
\(285\) | −0.324151 | − | 3.85939i | −0.0192011 | − | 0.228611i | ||||
\(286\) | 2.49247 | 0.147383 | ||||||||
\(287\) | 11.6137 | − | 11.6137i | 0.685537 | − | 0.685537i | ||||
\(288\) | −1.71203 | − | 2.46352i | −0.100883 | − | 0.145164i | ||||
\(289\) | − | 19.1253i | − | 1.12502i | ||||||
\(290\) | −3.36052 | − | 19.2505i | −0.197337 | − | 1.13043i | ||||
\(291\) | −0.876826 | + | 9.82225i | −0.0514005 | + | 0.575791i | ||||
\(292\) | 2.73639 | + | 2.73639i | 0.160135 | + | 0.160135i | ||||
\(293\) | 9.00595 | + | 9.00595i | 0.526133 | + | 0.526133i | 0.919417 | − | 0.393284i | \(-0.128661\pi\) |
−0.393284 | + | 0.919417i | \(0.628661\pi\) | |||||||
\(294\) | 0.552645 | − | 6.19076i | 0.0322309 | − | 0.361052i | ||||
\(295\) | −1.63791 | + | 2.33071i | −0.0953629 | + | 0.135699i | ||||
\(296\) | − | 0.448905i | − | 0.0260921i | ||||||
\(297\) | −13.2600 | − | 23.2508i | −0.769424 | − | 1.34915i | ||||
\(298\) | 0.429887 | − | 0.429887i | 0.0249027 | − | 0.0249027i | ||||
\(299\) | −2.27440 | −0.131532 | ||||||||
\(300\) | −7.47747 | − | 4.36891i | −0.431712 | − | 0.252239i | ||||
\(301\) | −23.1113 | −1.33211 | ||||||||
\(302\) | 1.76278 | − | 1.76278i | 0.101436 | − | 0.101436i | ||||
\(303\) | −4.89252 | + | 4.09060i | −0.281068 | + | 0.234999i | ||||
\(304\) | 1.00000i | 0.0573539i | ||||||||
\(305\) | −8.05421 | + | 11.4609i | −0.461183 | + | 0.656251i | ||||
\(306\) | 17.7462 | + | 3.19384i | 1.01448 | + | 0.182579i | ||||
\(307\) | 4.39219 | + | 4.39219i | 0.250675 | + | 0.250675i | 0.821247 | − | 0.570572i | \(-0.193279\pi\) |
−0.570572 | + | 0.821247i | \(0.693279\pi\) | |||||||
\(308\) | 6.72767 | + | 6.72767i | 0.383345 | + | 0.383345i | ||||
\(309\) | −13.6245 | − | 1.21625i | −0.775068 | − | 0.0691898i | ||||
\(310\) | 3.88331 | + | 22.2452i | 0.220557 | + | 1.26344i | ||||
\(311\) | − | 16.1534i | − | 0.915975i | −0.888959 | − | 0.457988i | \(-0.848570\pi\) | ||
0.888959 | − | 0.457988i | \(-0.151430\pi\) | |||||||
\(312\) | −0.537573 | − | 0.642958i | −0.0304341 | − | 0.0364003i | ||||
\(313\) | −0.493189 | + | 0.493189i | −0.0278767 | + | 0.0278767i | −0.720908 | − | 0.693031i | \(-0.756275\pi\) |
0.693031 | + | 0.720908i | \(0.256275\pi\) | |||||||
\(314\) | 0.0628417 | 0.00354636 | ||||||||
\(315\) | −0.0649235 | + | 12.3901i | −0.00365803 | + | 0.698105i | ||||
\(316\) | −5.23062 | −0.294246 | ||||||||
\(317\) | −16.9755 | + | 16.9755i | −0.953441 | + | 0.953441i | −0.998963 | − | 0.0455227i | \(-0.985505\pi\) |
0.0455227 | + | 0.998963i | \(0.485505\pi\) | |||||||
\(318\) | 12.8457 | + | 15.3640i | 0.720352 | + | 0.861570i | ||||
\(319\) | 45.0172i | 2.52048i | ||||||||
\(320\) | 1.82949 | + | 1.28568i | 0.102272 | + | 0.0718716i | ||||
\(321\) | 5.06110 | + | 0.451801i | 0.282483 | + | 0.0252171i | ||||
\(322\) | −6.13906 | − | 6.13906i | −0.342117 | − | 0.342117i | ||||
\(323\) | −4.25002 | − | 4.25002i | −0.236477 | − | 0.236477i | ||||
\(324\) | −3.13788 | + | 8.43527i | −0.174326 | + | 0.468626i | ||||
\(325\) | −2.18916 | − | 1.02993i | −0.121433 | − | 0.0571302i | ||||
\(326\) | − | 12.7242i | − | 0.704727i | ||||||
\(327\) | 5.94224 | − | 4.96826i | 0.328607 | − | 0.274746i | ||||
\(328\) | −6.28776 | + | 6.28776i | −0.347183 | + | 0.347183i | ||||
\(329\) | 5.60322 | 0.308915 | ||||||||
\(330\) | 15.2382 | + | 12.8768i | 0.838834 | + | 0.708845i | ||||
\(331\) | 14.7118 | 0.808635 | 0.404318 | − | 0.914619i | \(-0.367509\pi\) | ||||
0.404318 | + | 0.914619i | \(0.367509\pi\) | |||||||
\(332\) | −9.88555 | + | 9.88555i | −0.542540 | + | 0.542540i | ||||
\(333\) | −1.10589 | + | 0.768541i | −0.0606023 | + | 0.0421158i | ||||
\(334\) | 1.66174i | 0.0909264i | ||||||||
\(335\) | −4.67464 | + | 0.816045i | −0.255403 | + | 0.0445853i | ||||
\(336\) | 0.284456 | − | 3.18649i | 0.0155184 | − | 0.173837i | ||||
\(337\) | 13.8928 | + | 13.8928i | 0.756787 | + | 0.756787i | 0.975736 | − | 0.218949i | \(-0.0702629\pi\) |
−0.218949 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(338\) | 9.02684 | + | 9.02684i | 0.490995 | + | 0.490995i | ||||
\(339\) | −1.35930 | + | 15.2270i | −0.0738271 | + | 0.827015i | ||||
\(340\) | −13.2395 | + | 2.31120i | −0.718014 | + | 0.125343i | ||||
\(341\) | − | 52.0204i | − | 2.81706i | ||||||
\(342\) | 2.46352 | − | 1.71203i | 0.133212 | − | 0.0925762i | ||||
\(343\) | 13.8291 | − | 13.8291i | 0.746700 | − | 0.746700i | ||||
\(344\) | 12.5126 | 0.674636 | ||||||||
\(345\) | −13.9050 | − | 11.7502i | −0.748619 | − | 0.632610i | ||||
\(346\) | 19.2326 | 1.03395 | ||||||||
\(347\) | 21.0082 | − | 21.0082i | 1.12778 | − | 1.12778i | 0.137245 | − | 0.990537i | \(-0.456175\pi\) |
0.990537 | − | 0.137245i | \(-0.0438246\pi\) | |||||||
\(348\) | 11.6127 | − | 9.70927i | 0.622504 | − | 0.520472i | ||||
\(349\) | − | 18.0913i | − | 0.968404i | −0.874956 | − | 0.484202i | \(-0.839110\pi\) | ||
0.874956 | − | 0.484202i | \(-0.160890\pi\) | |||||||
\(350\) | −3.12899 | − | 8.68897i | −0.167252 | − | 0.464445i | ||||
\(351\) | −0.663598 | + | 2.42509i | −0.0354202 | + | 0.129442i | ||||
\(352\) | −3.64241 | − | 3.64241i | −0.194141 | − | 0.194141i | ||||
\(353\) | 8.95609 | + | 8.95609i | 0.476685 | + | 0.476685i | 0.904070 | − | 0.427385i | \(-0.140565\pi\) |
−0.427385 | + | 0.904070i | \(0.640565\pi\) | |||||||
\(354\) | −2.19783 | − | 0.196199i | −0.116814 | − | 0.0104279i | ||||
\(355\) | 21.4175 | + | 15.0512i | 1.13673 | + | 0.798837i | ||||
\(356\) | 16.2880i | 0.863264i | ||||||||
\(357\) | 12.3337 | + | 14.7516i | 0.652769 | + | 0.780738i | ||||
\(358\) | −12.7128 | + | 12.7128i | −0.671892 | + | 0.671892i | ||||
\(359\) | −13.9018 | −0.733708 | −0.366854 | − | 0.930278i | \(-0.619565\pi\) | ||||
−0.366854 | + | 0.930278i | \(0.619565\pi\) | |||||||
\(360\) | 0.0351501 | − | 6.70811i | 0.00185257 | − | 0.353549i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 3.23987 | − | 3.23987i | 0.170284 | − | 0.170284i | ||||
\(363\) | −17.2585 | − | 20.6419i | −0.905837 | − | 1.08342i | ||||
\(364\) | − | 0.893720i | − | 0.0468437i | ||||||
\(365\) | 1.48807 | + | 8.52430i | 0.0778893 | + | 0.446182i | ||||
\(366\) | −10.8076 | − | 0.964784i | −0.564920 | − | 0.0504300i | ||||
\(367\) | 2.43869 | + | 2.43869i | 0.127299 | + | 0.127299i | 0.767886 | − | 0.640587i | \(-0.221309\pi\) |
−0.640587 | + | 0.767886i | \(0.721309\pi\) | |||||||
\(368\) | 3.32373 | + | 3.32373i | 0.173262 | + | 0.173262i | ||||
\(369\) | 26.2549 | + | 4.72517i | 1.36677 | + | 0.245982i | ||||
\(370\) | 0.577148 | − | 0.821267i | 0.0300045 | − | 0.0426957i | ||||
\(371\) | 21.3561i | 1.10876i | ||||||||
\(372\) | −13.4192 | + | 11.2197i | −0.695754 | + | 0.581715i | ||||
\(373\) | −21.0831 | + | 21.0831i | −1.09164 | + | 1.09164i | −0.0962879 | + | 0.995354i | \(0.530697\pi\) |
−0.995354 | + | 0.0962879i | \(0.969303\pi\) | |||||||
\(374\) | 30.9606 | 1.60094 | ||||||||
\(375\) | −8.06294 | − | 17.6065i | −0.416368 | − | 0.909196i | ||||
\(376\) | −3.03362 | −0.156447 | ||||||||
\(377\) | 2.99010 | − | 2.99010i | 0.153998 | − | 0.153998i | ||||
\(378\) | −8.33699 | + | 4.75462i | −0.428809 | + | 0.244551i | ||||
\(379\) | 2.25390i | 0.115775i | 0.998323 | + | 0.0578874i | \(0.0184364\pi\) | ||||
−0.998323 | + | 0.0578874i | \(0.981564\pi\) | |||||||
\(380\) | −1.28568 | + | 1.82949i | −0.0659539 | + | 0.0938508i | ||||
\(381\) | −0.396960 | + | 4.44677i | −0.0203369 | + | 0.227815i | ||||
\(382\) | −8.71334 | − | 8.71334i | −0.445813 | − | 0.445813i | ||||
\(383\) | 4.29081 | + | 4.29081i | 0.219250 | + | 0.219250i | 0.808182 | − | 0.588932i | \(-0.200452\pi\) |
−0.588932 | + | 0.808182i | \(0.700452\pi\) | |||||||
\(384\) | −0.154007 | + | 1.72519i | −0.00785912 | + | 0.0880383i | ||||
\(385\) | 3.65857 | + | 20.9578i | 0.186458 | + | 1.06811i | ||||
\(386\) | 16.7731i | 0.853728i | ||||||||
\(387\) | −21.4221 | − | 30.8252i | −1.08894 | − | 1.56693i | ||||
\(388\) | 4.02586 | − | 4.02586i | 0.204382 | − | 0.204382i | ||||
\(389\) | −21.0267 | −1.06609 | −0.533047 | − | 0.846086i | \(-0.678953\pi\) | ||||
−0.533047 | + | 0.846086i | \(0.678953\pi\) | |||||||
\(390\) | −0.156846 | − | 1.86743i | −0.00794220 | − | 0.0945611i | ||||
\(391\) | −28.2519 | −1.42876 | ||||||||
\(392\) | −2.53742 | + | 2.53742i | −0.128159 | + | 0.128159i | ||||
\(393\) | 15.1732 | − | 12.6862i | 0.765389 | − | 0.639936i | ||||
\(394\) | − | 5.04603i | − | 0.254215i | ||||||
\(395\) | −9.56937 | − | 6.72490i | −0.481487 | − | 0.338367i | ||||
\(396\) | −2.73722 | + | 15.2091i | −0.137551 | + | 0.764285i | ||||
\(397\) | 7.05671 | + | 7.05671i | 0.354166 | + | 0.354166i | 0.861657 | − | 0.507491i | \(-0.169427\pi\) |
−0.507491 | + | 0.861657i | \(0.669427\pi\) | |||||||
\(398\) | −2.28529 | − | 2.28529i | −0.114551 | − | 0.114551i | ||||
\(399\) | 3.18649 | + | 0.284456i | 0.159524 | + | 0.0142406i | ||||
\(400\) | 1.69406 | + | 4.70427i | 0.0847029 | + | 0.235214i | ||||
\(401\) | 3.58548i | 0.179050i | 0.995985 | + | 0.0895252i | \(0.0285350\pi\) | ||||
−0.995985 | + | 0.0895252i | \(0.971465\pi\) | |||||||
\(402\) | −2.35773 | − | 2.81994i | −0.117593 | − | 0.140646i | ||||
\(403\) | −3.45526 | + | 3.45526i | −0.172119 | + | 0.172119i | ||||
\(404\) | 3.68192 | 0.183183 | ||||||||
\(405\) | −16.5858 | + | 11.3979i | −0.824153 | + | 0.566367i | ||||
\(406\) | 16.1418 | 0.801102 | ||||||||
\(407\) | −1.63510 | + | 1.63510i | −0.0810487 | + | 0.0810487i | ||||
\(408\) | −6.67756 | − | 7.98663i | −0.330589 | − | 0.395397i | ||||
\(409\) | 16.2138i | 0.801720i | 0.916139 | + | 0.400860i | \(0.131289\pi\) | ||||
−0.916139 | + | 0.400860i | \(0.868711\pi\) | |||||||
\(410\) | −19.5874 | + | 3.41934i | −0.967354 | + | 0.168869i | ||||
\(411\) | 26.8395 | + | 2.39594i | 1.32389 | + | 0.118183i | ||||
\(412\) | 5.58428 | + | 5.58428i | 0.275118 | + | 0.275118i | ||||
\(413\) | −1.66387 | − | 1.66387i | −0.0818736 | − | 0.0818736i | ||||
\(414\) | 2.49774 | − | 13.8784i | 0.122757 | − | 0.682088i | ||||
\(415\) | −30.7952 | + | 5.37586i | −1.51168 | + | 0.263891i | ||||
\(416\) | 0.483866i | 0.0237235i | ||||||||
\(417\) | 1.63909 | − | 1.37043i | 0.0802666 | − | 0.0671104i | ||||
\(418\) | 3.64241 | − | 3.64241i | 0.178156 | − | 0.178156i | ||||
\(419\) | 7.46153 | 0.364520 | 0.182260 | − | 0.983250i | \(-0.441659\pi\) | ||||
0.182260 | + | 0.983250i | \(0.441659\pi\) | |||||||
\(420\) | 4.61722 | − | 5.46393i | 0.225297 | − | 0.266613i | ||||
\(421\) | 3.53068 | 0.172075 | 0.0860374 | − | 0.996292i | \(-0.472580\pi\) | ||||
0.0860374 | + | 0.996292i | \(0.472580\pi\) | |||||||
\(422\) | 9.36503 | − | 9.36503i | 0.455883 | − | 0.455883i | ||||
\(423\) | 5.19366 | + | 7.47339i | 0.252525 | + | 0.363369i | ||||
\(424\) | − | 11.5624i | − | 0.561518i | ||||||
\(425\) | −27.1930 | − | 12.7935i | −1.31906 | − | 0.620574i | ||||
\(426\) | −1.80293 | + | 20.1965i | −0.0873523 | + | 0.978526i | ||||
\(427\) | −8.18185 | − | 8.18185i | −0.395947 | − | 0.395947i | ||||
\(428\) | −2.07440 | − | 2.07440i | −0.100270 | − | 0.100270i | ||||
\(429\) | −0.383856 | + | 4.29998i | −0.0185328 | + | 0.207605i | ||||
\(430\) | 22.8917 | + | 16.0872i | 1.10394 | + | 0.775795i | ||||
\(431\) | 36.0994i | 1.73885i | 0.494067 | + | 0.869424i | \(0.335510\pi\) | ||||
−0.494067 | + | 0.869424i | \(0.664490\pi\) | |||||||
\(432\) | 4.51371 | − | 2.57419i | 0.217166 | − | 0.123851i | ||||
\(433\) | 8.42713 | − | 8.42713i | 0.404982 | − | 0.404982i | −0.475003 | − | 0.879984i | \(-0.657553\pi\) |
0.879984 | + | 0.475003i | \(0.157553\pi\) | |||||||
\(434\) | −18.6529 | −0.895366 | ||||||||
\(435\) | 33.7283 | − | 2.83284i | 1.61715 | − | 0.135824i | ||||
\(436\) | −4.47191 | −0.214165 | ||||||||
\(437\) | −3.32373 | + | 3.32373i | −0.158996 | + | 0.158996i | ||||
\(438\) | −5.14221 | + | 4.29936i | −0.245704 | + | 0.205432i | ||||
\(439\) | 6.71446i | 0.320464i | 0.987079 | + | 0.160232i | \(0.0512242\pi\) | ||||
−0.987079 | + | 0.160232i | \(0.948776\pi\) | |||||||
\(440\) | −1.98078 | − | 11.3467i | −0.0944299 | − | 0.540933i | ||||
\(441\) | 10.5951 | + | 1.90684i | 0.504530 | + | 0.0908017i | ||||
\(442\) | −2.05644 | − | 2.05644i | −0.0978150 | − | 0.0978150i | ||||
\(443\) | 15.5862 | + | 15.5862i | 0.740522 | + | 0.740522i | 0.972678 | − | 0.232157i | \(-0.0745782\pi\) |
−0.232157 | + | 0.972678i | \(0.574578\pi\) | |||||||
\(444\) | 0.774447 | + | 0.0691344i | 0.0367536 | + | 0.00328097i | ||||
\(445\) | −20.9412 | + | 29.7988i | −0.992707 | + | 1.41260i | ||||
\(446\) | − | 5.56208i | − | 0.263372i | ||||||
\(447\) | 0.675431 | + | 0.807842i | 0.0319468 | + | 0.0382096i | ||||
\(448\) | −1.30605 | + | 1.30605i | −0.0617052 | + | 0.0617052i | ||||
\(449\) | 21.1036 | 0.995941 | 0.497971 | − | 0.867194i | \(-0.334079\pi\) | ||||
0.497971 | + | 0.867194i | \(0.334079\pi\) | |||||||
\(450\) | 8.68879 | − | 12.2272i | 0.409593 | − | 0.576397i | ||||
\(451\) | 45.8052 | 2.15688 | ||||||||
\(452\) | 6.24110 | − | 6.24110i | 0.293557 | − | 0.293557i | ||||
\(453\) | 2.76964 | + | 3.31260i | 0.130129 | + | 0.155640i | ||||
\(454\) | 6.94202i | 0.325805i | ||||||||
\(455\) | 1.14904 | − | 1.63505i | 0.0538677 | − | 0.0766524i | ||||
\(456\) | −1.72519 | − | 0.154007i | −0.0807894 | − | 0.00721202i | ||||
\(457\) | −3.24691 | − | 3.24691i | −0.151884 | − | 0.151884i | 0.627075 | − | 0.778959i | \(-0.284252\pi\) |
−0.778959 | + | 0.627075i | \(0.784252\pi\) | |||||||
\(458\) | 0.218610 | + | 0.218610i | 0.0102150 | + | 0.0102150i | ||||
\(459\) | −8.24301 | + | 30.1237i | −0.384751 | + | 1.40605i | ||||
\(460\) | 1.80748 | + | 10.3540i | 0.0842741 | + | 0.482757i | ||||
\(461\) | − | 31.5064i | − | 1.46740i | −0.679473 | − | 0.733700i | \(-0.737792\pi\) | ||
0.679473 | − | 0.733700i | \(-0.262208\pi\) | |||||||
\(462\) | −12.6426 | + | 10.5704i | −0.588188 | + | 0.491780i | ||||
\(463\) | −8.81741 | + | 8.81741i | −0.409780 | + | 0.409780i | −0.881662 | − | 0.471882i | \(-0.843575\pi\) |
0.471882 | + | 0.881662i | \(0.343575\pi\) | |||||||
\(464\) | −8.73926 | −0.405710 | ||||||||
\(465\) | −38.9752 | + | 3.27354i | −1.80743 | + | 0.151807i | ||||
\(466\) | −1.55247 | −0.0719169 | ||||||||
\(467\) | 4.04048 | − | 4.04048i | 0.186971 | − | 0.186971i | −0.607414 | − | 0.794385i | \(-0.707793\pi\) |
0.794385 | + | 0.607414i | \(0.207793\pi\) | |||||||
\(468\) | 1.19202 | − | 0.828396i | 0.0551009 | − | 0.0382926i | ||||
\(469\) | − | 3.91975i | − | 0.180997i | ||||||
\(470\) | −5.54998 | − | 3.90026i | −0.256001 | − | 0.179906i | ||||
\(471\) | −0.00967804 | + | 0.108414i | −0.000445941 | + | 0.00499545i | ||||
\(472\) | 0.900830 | + | 0.900830i | 0.0414641 | + | 0.0414641i | ||||
\(473\) | −45.5761 | − | 45.5761i | −2.09559 | − | 2.09559i | ||||
\(474\) | 0.805551 | − | 9.02382i | 0.0370002 | − | 0.414478i | ||||
\(475\) | −4.70427 | + | 1.69406i | −0.215847 | + | 0.0777287i | ||||
\(476\) | − | 11.1015i | − | 0.508837i | ||||||
\(477\) | −28.4841 | + | 19.7952i | −1.30420 | + | 0.906358i | ||||
\(478\) | 17.2546 | − | 17.2546i | 0.789205 | − | 0.789205i | ||||
\(479\) | −25.6778 | −1.17325 | −0.586624 | − | 0.809859i | \(-0.699543\pi\) | ||||
−0.586624 | + | 0.809859i | \(0.699543\pi\) | |||||||
\(480\) | −2.49979 | + | 2.95821i | −0.114099 | + | 0.135023i | ||||
\(481\) | 0.217210 | 0.00990393 | ||||||||
\(482\) | −10.9469 | + | 10.9469i | −0.498618 | + | 0.498618i | ||||
\(483\) | 11.5365 | − | 9.64560i | 0.524929 | − | 0.438890i | ||||
\(484\) | 15.5343i | 0.706104i | ||||||||
\(485\) | 12.5412 | − | 2.18930i | 0.569469 | − | 0.0994112i | ||||
\(486\) | −14.0692 | − | 6.71252i | −0.638191 | − | 0.304486i | ||||
\(487\) | −10.1276 | − | 10.1276i | −0.458925 | − | 0.458925i | 0.439377 | − | 0.898303i | \(-0.355199\pi\) |
−0.898303 | + | 0.439377i | \(0.855199\pi\) | |||||||
\(488\) | 4.42971 | + | 4.42971i | 0.200524 | + | 0.200524i | ||||
\(489\) | 21.9516 | + | 1.95961i | 0.992687 | + | 0.0886165i | ||||
\(490\) | −7.90448 | + | 1.37987i | −0.357088 | + | 0.0623363i | ||||
\(491\) | 19.2496i | 0.868723i | 0.900739 | + | 0.434361i | \(0.143026\pi\) | ||||
−0.900739 | + | 0.434361i | \(0.856974\pi\) | |||||||
\(492\) | −9.87922 | − | 11.8159i | −0.445390 | − | 0.532703i | ||||
\(493\) | 37.1420 | − | 37.1420i | 1.67279 | − | 1.67279i | ||||
\(494\) | −0.483866 | −0.0217702 | ||||||||
\(495\) | −24.5617 | + | 24.3057i | −1.10397 | + | 1.09246i | ||||
\(496\) | 10.0988 | 0.453449 | ||||||||
\(497\) | −15.2898 | + | 15.2898i | −0.685840 | + | 0.685840i | ||||
\(498\) | −15.5320 | − | 18.5769i | −0.696007 | − | 0.832451i | ||||
\(499\) | − | 19.5782i | − | 0.876439i | −0.898868 | − | 0.438220i | \(-0.855609\pi\) | ||
0.898868 | − | 0.438220i | \(-0.144391\pi\) | |||||||
\(500\) | −2.94892 | + | 10.7844i | −0.131880 | + | 0.482294i | ||||
\(501\) | −2.86682 | − | 0.255919i | −0.128080 | − | 0.0114336i | ||||
\(502\) | −7.34263 | − | 7.34263i | −0.327718 | − | 0.327718i | ||||
\(503\) | −18.0640 | − | 18.0640i | −0.805434 | − | 0.805434i | 0.178505 | − | 0.983939i | \(-0.442874\pi\) |
−0.983939 | + | 0.178505i | \(0.942874\pi\) | |||||||
\(504\) | 5.45350 | + | 0.981482i | 0.242918 | + | 0.0437187i | ||||
\(505\) | 6.73604 | + | 4.73377i | 0.299750 | + | 0.210650i | ||||
\(506\) | − | 24.2128i | − | 1.07639i | ||||||
\(507\) | −16.9632 | + | 14.1828i | −0.753362 | + | 0.629881i | ||||
\(508\) | 1.82261 | − | 1.82261i | 0.0808651 | − | 0.0808651i | ||||
\(509\) | 24.2848 | 1.07640 | 0.538202 | − | 0.842816i | \(-0.319104\pi\) | ||||
0.538202 | + | 0.842816i | \(0.319104\pi\) | |||||||
\(510\) | −1.94829 | − | 23.1966i | −0.0862717 | − | 1.02716i | ||||
\(511\) | −7.14773 | −0.316197 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 2.57419 | + | 4.51371i | 0.113653 | + | 0.199285i | ||||
\(514\) | 14.3265i | 0.631914i | ||||||||
\(515\) | 3.03678 | + | 17.3960i | 0.133817 | + | 0.766558i | ||||
\(516\) | −1.92703 | + | 21.5867i | −0.0848327 | + | 0.950301i | ||||
\(517\) | 11.0497 | + | 11.0497i | 0.485965 | + | 0.485965i | ||||
\(518\) | 0.586294 | + | 0.586294i | 0.0257603 | + | 0.0257603i | ||||
\(519\) | −2.96194 | + | 33.1798i | −0.130015 | + | 1.45643i | ||||
\(520\) | −0.622097 | + | 0.885228i | −0.0272808 | + | 0.0388198i | ||||
\(521\) | − | 19.1374i | − | 0.838425i | −0.907888 | − | 0.419213i | \(-0.862306\pi\) | ||
0.907888 | − | 0.419213i | \(-0.137694\pi\) | |||||||
\(522\) | 14.9619 | + | 21.5294i | 0.654865 | + | 0.942315i | ||||
\(523\) | −3.69849 | + | 3.69849i | −0.161724 | + | 0.161724i | −0.783330 | − | 0.621606i | \(-0.786480\pi\) |
0.621606 | + | 0.783330i | \(0.286480\pi\) | |||||||
\(524\) | −11.4188 | −0.498833 | ||||||||
\(525\) | 15.4720 | − | 4.05995i | 0.675254 | − | 0.177191i | ||||
\(526\) | 26.6919 | 1.16382 | ||||||||
\(527\) | −42.9201 | + | 42.9201i | −1.86963 | + | 1.86963i | ||||
\(528\) | 6.84480 | − | 5.72289i | 0.297882 | − | 0.249057i | ||||
\(529\) | − | 0.905600i | − | 0.0393739i | ||||||
\(530\) | 14.8655 | − | 21.1532i | 0.645716 | − | 0.918837i | ||||
\(531\) | 0.676962 | − | 3.76147i | 0.0293777 | − | 0.163234i | ||||
\(532\) | −1.30605 | − | 1.30605i | −0.0566246 | − | 0.0566246i | ||||
\(533\) | −3.04243 | − | 3.04243i | −0.131782 | − | 0.131782i | ||||
\(534\) | −28.0999 | − | 2.50846i | −1.21600 | − | 0.108552i | ||||
\(535\) | −1.12808 | − | 6.46211i | −0.0487711 | − | 0.279381i | ||||
\(536\) | 2.12218i | 0.0916642i | ||||||||
\(537\) | −19.9741 | − | 23.8899i | −0.861948 | − | 1.03092i | ||||
\(538\) | 4.61020 | − | 4.61020i | 0.198760 | − | 0.198760i | ||||
\(539\) | 18.4846 | 0.796189 | ||||||||
\(540\) | 11.5674 | + | 1.09373i | 0.497780 | + | 0.0470668i | ||||
\(541\) | −15.7000 | −0.674995 | −0.337498 | − | 0.941326i | \(-0.609581\pi\) | ||||
−0.337498 | + | 0.941326i | \(0.609581\pi\) | |||||||
\(542\) | 10.1873 | − | 10.1873i | 0.437580 | − | 0.437580i | ||||
\(543\) | 5.09044 | + | 6.08836i | 0.218452 | + | 0.261277i | ||||
\(544\) | 6.01044i | 0.257695i | ||||||||
\(545\) | −8.18130 | − | 5.74944i | −0.350449 | − | 0.246279i | ||||
\(546\) | 1.54184 | + | 0.137639i | 0.0659845 | + | 0.00589040i | ||||
\(547\) | 6.76457 | + | 6.76457i | 0.289232 | + | 0.289232i | 0.836777 | − | 0.547545i | \(-0.184437\pi\) |
−0.547545 | + | 0.836777i | \(0.684437\pi\) | |||||||
\(548\) | −11.0007 | − | 11.0007i | −0.469929 | − | 0.469929i | ||||
\(549\) | 3.32887 | − | 18.4965i | 0.142073 | − | 0.789412i | ||||
\(550\) | 10.9644 | − | 23.3053i | 0.467525 | − | 0.993743i | ||||
\(551\) | − | 8.73926i | − | 0.372305i | ||||||
\(552\) | −6.24595 | + | 5.22220i | −0.265845 | + | 0.222271i | ||||
\(553\) | 6.83147 | − | 6.83147i | 0.290504 | − | 0.290504i | ||||
\(554\) | 19.7600 | 0.839520 | ||||||||
\(555\) | 1.32796 | + | 1.12217i | 0.0563687 | + | 0.0476335i | ||||
\(556\) | −1.23352 | −0.0523128 | ||||||||
\(557\) | −7.92409 | + | 7.92409i | −0.335754 | + | 0.335754i | −0.854767 | − | 0.519012i | \(-0.826300\pi\) |
0.519012 | + | 0.854767i | \(0.326300\pi\) | |||||||
\(558\) | −17.2895 | − | 24.8786i | −0.731922 | − | 1.05320i | ||||
\(559\) | 6.05445i | 0.256076i | ||||||||
\(560\) | −4.06858 | + | 0.710245i | −0.171929 | + | 0.0300133i | ||||
\(561\) | −4.76814 | + | 53.4130i | −0.201311 | + | 2.25510i | ||||
\(562\) | −17.1338 | − | 17.1338i | −0.722747 | − | 0.722747i | ||||
\(563\) | 2.50755 | + | 2.50755i | 0.105681 | + | 0.105681i | 0.757970 | − | 0.652289i | \(-0.226191\pi\) |
−0.652289 | + | 0.757970i | \(0.726191\pi\) | |||||||
\(564\) | 0.467198 | − | 5.23357i | 0.0196726 | − | 0.220373i | ||||
\(565\) | 19.4421 | − | 3.39397i | 0.817935 | − | 0.142786i | ||||
\(566\) | − | 13.1018i | − | 0.550708i | ||||||
\(567\) | −6.91868 | − | 15.1151i | −0.290557 | − | 0.634776i | ||||
\(568\) | 8.27799 | − | 8.27799i | 0.347337 | − | 0.347337i | ||||
\(569\) | −19.7316 | −0.827190 | −0.413595 | − | 0.910461i | \(-0.635727\pi\) | ||||
−0.413595 | + | 0.910461i | \(0.635727\pi\) | |||||||
\(570\) | −2.95821 | − | 2.49979i | −0.123906 | − | 0.104705i | ||||
\(571\) | 11.2502 | 0.470807 | 0.235403 | − | 0.971898i | \(-0.424359\pi\) | ||||
0.235403 | + | 0.971898i | \(0.424359\pi\) | |||||||
\(572\) | 1.76244 | − | 1.76244i | 0.0736913 | − | 0.0736913i | ||||
\(573\) | 16.3741 | − | 13.6903i | 0.684037 | − | 0.571919i | ||||
\(574\) | − | 16.4243i | − | 0.685537i | ||||||
\(575\) | −10.0051 | + | 21.2663i | −0.417243 | + | 0.886868i | ||||
\(576\) | −2.95256 | − | 0.531382i | −0.123023 | − | 0.0221409i | ||||
\(577\) | 22.9715 | + | 22.9715i | 0.956315 | + | 0.956315i | 0.999085 | − | 0.0427697i | \(-0.0136182\pi\) |
−0.0427697 | + | 0.999085i | \(0.513618\pi\) | |||||||
\(578\) | −13.5237 | − | 13.5237i | −0.562510 | − | 0.562510i | ||||
\(579\) | −28.9368 | − | 2.58317i | −1.20257 | − | 0.107353i | ||||
\(580\) | −15.9884 | − | 11.2359i | −0.663881 | − | 0.466545i | ||||
\(581\) | − | 25.8221i | − | 1.07128i | ||||||
\(582\) | 6.32537 | + | 7.56539i | 0.262195 | + | 0.313596i | ||||
\(583\) | −42.1149 | + | 42.1149i | −1.74422 | + | 1.74422i | ||||
\(584\) | 3.86983 | 0.160135 | ||||||||
\(585\) | 3.24583 | + | 0.0170079i | 0.134199 | + | 0.000703192i | ||||
\(586\) | 12.7363 | 0.526133 | ||||||||
\(587\) | 20.3746 | − | 20.3746i | 0.840951 | − | 0.840951i | −0.148032 | − | 0.988983i | \(-0.547294\pi\) |
0.988983 | + | 0.148032i | \(0.0472939\pi\) | |||||||
\(588\) | −3.98675 | − | 4.76831i | −0.164411 | − | 0.196642i | ||||
\(589\) | 10.0988i | 0.416114i | ||||||||
\(590\) | 0.489880 | + | 2.80624i | 0.0201681 | + | 0.115531i | ||||
\(591\) | 8.70536 | + | 0.777122i | 0.358091 | + | 0.0319665i | ||||
\(592\) | −0.317424 | − | 0.317424i | −0.0130460 | − | 0.0130460i | ||||
\(593\) | −7.81504 | − | 7.81504i | −0.320925 | − | 0.320925i | 0.528197 | − | 0.849122i | \(-0.322868\pi\) |
−0.849122 | + | 0.528197i | \(0.822868\pi\) | |||||||
\(594\) | −25.8170 | − | 7.06453i | −1.05928 | − | 0.289861i | ||||
\(595\) | 14.2730 | − | 20.3101i | 0.585135 | − | 0.832632i | ||||
\(596\) | − | 0.607952i | − | 0.0249027i | ||||||
\(597\) | 4.29451 | − | 3.59061i | 0.175762 | − | 0.146954i | ||||
\(598\) | −1.60824 | + | 1.60824i | −0.0657659 | + | 0.0657659i | ||||
\(599\) | −6.25932 | −0.255749 | −0.127874 | − | 0.991790i | \(-0.540815\pi\) | ||||
−0.127874 | + | 0.991790i | \(0.540815\pi\) | |||||||
\(600\) | −8.37666 | + | 2.19808i | −0.341976 | + | 0.0897364i | ||||
\(601\) | −13.5081 | −0.551009 | −0.275504 | − | 0.961300i | \(-0.588845\pi\) | ||||
−0.275504 | + | 0.961300i | \(0.588845\pi\) | |||||||
\(602\) | −16.3422 | + | 16.3422i | −0.666057 | + | 0.666057i | ||||
\(603\) | 5.22803 | − | 3.63324i | 0.212902 | − | 0.147957i | ||||
\(604\) | − | 2.49294i | − | 0.101436i | ||||||
\(605\) | −19.9721 | + | 28.4198i | −0.811982 | + | 1.15543i | ||||
\(606\) | −0.567041 | + | 6.35202i | −0.0230345 | + | 0.258033i | ||||
\(607\) | −19.7516 | − | 19.7516i | −0.801691 | − | 0.801691i | 0.181669 | − | 0.983360i | \(-0.441850\pi\) |
−0.983360 | + | 0.181669i | \(0.941850\pi\) | |||||||
\(608\) | 0.707107 | + | 0.707107i | 0.0286770 | + | 0.0286770i | ||||
\(609\) | −2.48594 | + | 27.8476i | −0.100735 | + | 1.12844i | ||||
\(610\) | 2.40892 | + | 13.7993i | 0.0975343 | + | 0.558717i | ||||
\(611\) | − | 1.46787i | − | 0.0593836i | ||||||
\(612\) | 14.8068 | − | 10.2901i | 0.598531 | − | 0.415952i | ||||
\(613\) | −8.37167 | + | 8.37167i | −0.338129 | + | 0.338129i | −0.855663 | − | 0.517534i | \(-0.826850\pi\) |
0.517534 | + | 0.855663i | \(0.326850\pi\) | |||||||
\(614\) | 6.21149 | 0.250675 | ||||||||
\(615\) | −2.88243 | − | 34.3186i | −0.116231 | − | 1.38386i | ||||
\(616\) | 9.51436 | 0.383345 | ||||||||
\(617\) | 18.8481 | − | 18.8481i | 0.758795 | − | 0.758795i | −0.217308 | − | 0.976103i | \(-0.569728\pi\) |
0.976103 | + | 0.217308i | \(0.0697277\pi\) | |||||||
\(618\) | −10.4940 | + | 8.77393i | −0.422129 | + | 0.352939i | ||||
\(619\) | − | 19.7510i | − | 0.793860i | −0.917849 | − | 0.396930i | \(-0.870076\pi\) | ||
0.917849 | − | 0.396930i | \(-0.129924\pi\) | |||||||
\(620\) | 18.4756 | + | 12.9838i | 0.741999 | + | 0.521442i | ||||
\(621\) | 23.5583 | + | 6.44645i | 0.945361 | + | 0.258687i | ||||
\(622\) | −11.4222 | − | 11.4222i | −0.457988 | − | 0.457988i | ||||
\(623\) | −21.2730 | − | 21.2730i | −0.852286 | − | 0.852286i | ||||
\(624\) | −0.834762 | − | 0.0745186i | −0.0334172 | − | 0.00298313i | ||||
\(625\) | −19.2603 | + | 15.9386i | −0.770413 | + | 0.637545i | ||||
\(626\) | 0.697474i | 0.0278767i | ||||||||
\(627\) | 5.72289 | + | 6.84480i | 0.228550 | + | 0.273355i | ||||
\(628\) | 0.0444358 | − | 0.0444358i | 0.00177318 | − | 0.00177318i | ||||
\(629\) | 2.69812 | 0.107581 | ||||||||
\(630\) | 8.71524 | + | 8.80706i | 0.347224 | + | 0.350882i | ||||
\(631\) | 16.2630 | 0.647418 | 0.323709 | − | 0.946157i | \(-0.395070\pi\) | ||||
0.323709 | + | 0.946157i | \(0.395070\pi\) | |||||||
\(632\) | −3.69861 | + | 3.69861i | −0.147123 | + | 0.147123i | ||||
\(633\) | 14.7142 | + | 17.5987i | 0.584837 | + | 0.699487i | ||||
\(634\) | 24.0070i | 0.953441i | ||||||||
\(635\) | 5.67772 | − | 0.991151i | 0.225314 | − | 0.0393326i | ||||
\(636\) | 19.9473 | + | 1.78068i | 0.790961 | + | 0.0706086i | ||||
\(637\) | −1.22777 | − | 1.22777i | −0.0486460 | − | 0.0486460i | ||||
\(638\) | 31.8320 | + | 31.8320i | 1.26024 | + | 1.26024i | ||||
\(639\) | −34.5652 | − | 6.22080i | −1.36738 | − | 0.246091i | ||||
\(640\) | 2.20276 | − | 0.384532i | 0.0870716 | − | 0.0151999i | ||||
\(641\) | 16.4351i | 0.649146i | 0.945861 | + | 0.324573i | \(0.105221\pi\) | ||||
−0.945861 | + | 0.324573i | \(0.894779\pi\) | |||||||
\(642\) | 3.89821 | − | 3.25926i | 0.153850 | − | 0.128633i | ||||
\(643\) | 16.1113 | − | 16.1113i | 0.635369 | − | 0.635369i | −0.314041 | − | 0.949409i | \(-0.601683\pi\) |
0.949409 | + | 0.314041i | \(0.101683\pi\) | |||||||
\(644\) | −8.68195 | −0.342117 | ||||||||
\(645\) | −31.2790 | + | 37.0151i | −1.23161 | + | 1.45747i | ||||
\(646\) | −6.01044 | −0.236477 | ||||||||
\(647\) | −33.8022 | + | 33.8022i | −1.32890 | + | 1.32890i | −0.422570 | + | 0.906330i | \(0.638872\pi\) |
−0.906330 | + | 0.422570i | \(0.861128\pi\) | |||||||
\(648\) | 3.74582 | + | 8.18345i | 0.147150 | + | 0.321476i | ||||
\(649\) | − | 6.56239i | − | 0.257596i | ||||||
\(650\) | −2.27624 | + | 0.819698i | −0.0892814 | + | 0.0321512i | ||||
\(651\) | 2.87267 | − | 32.1797i | 0.112589 | − | 1.26122i | ||||
\(652\) | −8.99735 | − | 8.99735i | −0.352363 | − | 0.352363i | ||||
\(653\) | 6.58374 | + | 6.58374i | 0.257642 | + | 0.257642i | 0.824094 | − | 0.566453i | \(-0.191685\pi\) |
−0.566453 | + | 0.824094i | \(0.691685\pi\) | |||||||
\(654\) | 0.688703 | − | 7.71489i | 0.0269304 | − | 0.301676i | ||||
\(655\) | −20.8906 | − | 14.6809i | −0.816263 | − | 0.573631i | ||||
\(656\) | 8.89223i | 0.347183i | ||||||||
\(657\) | −6.62529 | − | 9.53342i | −0.258477 | − | 0.371934i | ||||
\(658\) | 3.96207 | − | 3.96207i | 0.154458 | − | 0.154458i | ||||
\(659\) | −0.843524 | −0.0328590 | −0.0164295 | − | 0.999865i | \(-0.505230\pi\) | ||||
−0.0164295 | + | 0.999865i | \(0.505230\pi\) | |||||||
\(660\) | 19.8803 | − | 1.66975i | 0.773840 | − | 0.0649949i | ||||
\(661\) | 20.3317 | 0.790813 | 0.395406 | − | 0.918506i | \(-0.370604\pi\) | ||||
0.395406 | + | 0.918506i | \(0.370604\pi\) | |||||||
\(662\) | 10.4028 | − | 10.4028i | 0.404318 | − | 0.404318i | ||||
\(663\) | 3.86446 | − | 3.23105i | 0.150083 | − | 0.125484i | ||||
\(664\) | 13.9803i | 0.542540i | ||||||||
\(665\) | −0.710245 | − | 4.06858i | −0.0275421 | − | 0.157773i | ||||
\(666\) | −0.238540 | + | 1.32542i | −0.00924324 | + | 0.0513590i | ||||
\(667\) | −29.0470 | − | 29.0470i | −1.12470 | − | 1.12470i | ||||
\(668\) | 1.17503 | + | 1.17503i | 0.0454632 | + | 0.0454632i | ||||
\(669\) | 9.59564 | + | 0.856597i | 0.370989 | + | 0.0331180i | ||||
\(670\) | −2.72844 | + | 3.88250i | −0.105409 | + | 0.149994i | ||||
\(671\) | − | 32.2696i | − | 1.24576i | ||||||
\(672\) | −2.05205 | − | 2.45433i | −0.0791595 | − | 0.0946779i | ||||
\(673\) | −23.9996 | + | 23.9996i | −0.925115 | + | 0.925115i | −0.997385 | − | 0.0722701i | \(-0.976976\pi\) |
0.0722701 | + | 0.997385i | \(0.476976\pi\) | |||||||
\(674\) | 19.6473 | 0.756787 | ||||||||
\(675\) | 19.7562 | + | 16.8729i | 0.760415 | + | 0.649438i | ||||
\(676\) | 12.7659 | 0.490995 | ||||||||
\(677\) | 18.9600 | − | 18.9600i | 0.728691 | − | 0.728691i | −0.241668 | − | 0.970359i | \(-0.577695\pi\) |
0.970359 | + | 0.241668i | \(0.0776946\pi\) | |||||||
\(678\) | 9.80592 | + | 11.7283i | 0.376594 | + | 0.450421i | ||||
\(679\) | 10.5160i | 0.403567i | ||||||||
\(680\) | −7.72749 | + | 10.9960i | −0.296336 | + | 0.421678i | ||||
\(681\) | −11.9763 | − | 1.06912i | −0.458933 | − | 0.0409686i | ||||
\(682\) | −36.7840 | − | 36.7840i | −1.40853 | − | 1.40853i | ||||
\(683\) | −6.99901 | − | 6.99901i | −0.267810 | − | 0.267810i | 0.560407 | − | 0.828217i | \(-0.310645\pi\) |
−0.828217 | + | 0.560407i | \(0.810645\pi\) | |||||||
\(684\) | 0.531382 | − | 2.95256i | 0.0203179 | − | 0.112894i | ||||
\(685\) | −5.98231 | − | 34.2692i | −0.228572 | − | 1.30936i | ||||
\(686\) | − | 19.5573i | − | 0.746700i | ||||||
\(687\) | −0.410812 | + | 0.343477i | −0.0156735 | + | 0.0131045i | ||||
\(688\) | 8.84777 | − | 8.84777i | 0.337318 | − | 0.337318i | ||||
\(689\) | 5.59464 | 0.213139 | ||||||||
\(690\) | −18.1410 | + | 1.52366i | −0.690615 | + | 0.0580048i | ||||
\(691\) | −44.2770 | −1.68438 | −0.842189 | − | 0.539183i | \(-0.818733\pi\) | ||||
−0.842189 | + | 0.539183i | \(0.818733\pi\) | |||||||
\(692\) | 13.5995 | − | 13.5995i | 0.516974 | − | 0.516974i | ||||
\(693\) | −16.2889 | − | 23.4388i | −0.618765 | − | 0.890368i | ||||
\(694\) | − | 29.7101i | − | 1.12778i | ||||||
\(695\) | −2.25671 | − | 1.58591i | −0.0856018 | − | 0.0601570i | ||||
\(696\) | 1.34590 | − | 15.0769i | 0.0510164 | − | 0.571488i | ||||
\(697\) | −37.7922 | − | 37.7922i | −1.43148 | − | 1.43148i | ||||
\(698\) | −12.7925 | − | 12.7925i | −0.484202 | − | 0.484202i | ||||
\(699\) | 0.239091 | − | 2.67831i | 0.00904325 | − | 0.101303i | ||||
\(700\) | −8.35656 | − | 3.93150i | −0.315848 | − | 0.148597i | ||||
\(701\) | 47.5139i | 1.79458i | 0.441445 | + | 0.897288i | \(0.354466\pi\) | ||||
−0.441445 | + | 0.897288i | \(0.645534\pi\) | |||||||
\(702\) | 1.24556 | + | 2.18403i | 0.0470107 | + | 0.0824310i | ||||
\(703\) | 0.317424 | − | 0.317424i | 0.0119719 | − | 0.0119719i | ||||
\(704\) | −5.15114 | −0.194141 | ||||||||
\(705\) | 7.58343 | − | 8.97410i | 0.285609 | − | 0.337984i | ||||
\(706\) | 12.6658 | 0.476685 | ||||||||
\(707\) | −4.80879 | + | 4.80879i | −0.180853 | + | 0.180853i | ||||
\(708\) | −1.69284 | + | 1.41537i | −0.0636207 | + | 0.0531929i | ||||
\(709\) | 34.9010i | 1.31073i | 0.755311 | + | 0.655367i | \(0.227486\pi\) | ||||
−0.755311 | + | 0.655367i | \(0.772514\pi\) | |||||||
\(710\) | 25.7873 | − | 4.50165i | 0.967781 | − | 0.168944i | ||||
\(711\) | 15.4437 | + | 2.77946i | 0.579186 | + | 0.104238i | ||||
\(712\) | 11.5174 | + | 11.5174i | 0.431632 | + | 0.431632i | ||||
\(713\) | 33.5657 | + | 33.5657i | 1.25705 | + | 1.25705i | ||||
\(714\) | 19.1522 | + | 1.70971i | 0.716754 | + | 0.0639841i | ||||
\(715\) | 5.49029 | − | 0.958432i | 0.205325 | − | 0.0358433i | ||||
\(716\) | 17.9786i | 0.671892i | ||||||||
\(717\) | 27.1101 | + | 32.4247i | 1.01244 | + | 1.21092i | ||||
\(718\) | −9.83005 | + | 9.83005i | −0.366854 | + | 0.366854i | ||||
\(719\) | −31.1460 | −1.16155 | −0.580775 | − | 0.814064i | \(-0.697250\pi\) | ||||
−0.580775 | + | 0.814064i | \(0.697250\pi\) | |||||||
\(720\) | −4.71850 | − | 4.76821i | −0.175848 | − | 0.177701i | ||||
\(721\) | −14.5867 | −0.543238 | ||||||||
\(722\) | −0.707107 | + | 0.707107i | −0.0263158 | + | 0.0263158i | ||||
\(723\) | −17.1996 | − | 20.5714i | −0.639660 | − | 0.765058i | ||||
\(724\) | − | 4.58187i | − | 0.170284i | ||||||
\(725\) | −14.8048 | − | 41.1119i | −0.549837 | − | 1.52686i | ||||
\(726\) | −26.7996 | − | 2.39238i | −0.994627 | − | 0.0887897i | ||||
\(727\) | 18.0500 | + | 18.0500i | 0.669439 | + | 0.669439i | 0.957586 | − | 0.288147i | \(-0.0930393\pi\) |
−0.288147 | + | 0.957586i | \(0.593039\pi\) | |||||||
\(728\) | −0.631955 | − | 0.631955i | −0.0234218 | − | 0.0234218i | ||||
\(729\) | 13.7471 | − | 23.2383i | 0.509153 | − | 0.860676i | ||||
\(730\) | 7.07982 | + | 4.97536i | 0.262036 | + | 0.184146i | ||||
\(731\) | 75.2064i | 2.78161i | ||||||||
\(732\) | −8.32430 | + | 6.95989i | −0.307675 | + | 0.257245i | ||||
\(733\) | −9.66033 | + | 9.66033i | −0.356812 | + | 0.356812i | −0.862637 | − | 0.505824i | \(-0.831188\pi\) |
0.505824 | + | 0.862637i | \(0.331188\pi\) | |||||||
\(734\) | 3.44883 | 0.127299 | ||||||||
\(735\) | −1.16320 | − | 13.8492i | −0.0429053 | − | 0.510837i | ||||
\(736\) | 4.70047 | 0.173262 | ||||||||
\(737\) | 7.72984 | − | 7.72984i | 0.284732 | − | 0.284732i | ||||
\(738\) | 21.9062 | − | 15.2238i | 0.806378 | − | 0.560396i | ||||
\(739\) | − | 5.67646i | − | 0.208812i | −0.994535 | − | 0.104406i | \(-0.966706\pi\) | ||
0.994535 | − | 0.104406i | \(-0.0332941\pi\) | |||||||
\(740\) | −0.172618 | − | 0.988829i | −0.00634557 | − | 0.0363501i | ||||
\(741\) | 0.0745186 | − | 0.834762i | 0.00273751 | − | 0.0306657i | ||||
\(742\) | 15.1011 | + | 15.1011i | 0.554378 | + | 0.554378i | ||||
\(743\) | 31.4477 | + | 31.4477i | 1.15370 | + | 1.15370i | 0.985804 | + | 0.167901i | \(0.0536988\pi\) |
0.167901 | + | 0.985804i | \(0.446301\pi\) | |||||||
\(744\) | −1.55528 | + | 17.4223i | −0.0570194 | + | 0.638734i | ||||
\(745\) | 0.781631 | − | 1.11224i | 0.0286367 | − | 0.0407494i | ||||
\(746\) | 29.8160i | 1.09164i | ||||||||
\(747\) | 34.4407 | − | 23.9347i | 1.26012 | − | 0.875726i | ||||
\(748\) | 21.8925 | − | 21.8925i | 0.800468 | − | 0.800468i | ||||
\(749\) | 5.41856 | 0.197990 | ||||||||
\(750\) | −18.1510 | − | 6.74832i | −0.662782 | − | 0.246414i | ||||
\(751\) | 35.7096 | 1.30306 | 0.651532 | − | 0.758622i | \(-0.274127\pi\) | ||||
0.651532 | + | 0.758622i | \(0.274127\pi\) | |||||||
\(752\) | −2.14509 | + | 2.14509i | −0.0782235 | + | 0.0782235i | ||||
\(753\) | 13.7983 | − | 11.5366i | 0.502836 | − | 0.420418i | ||||
\(754\) | − | 4.22864i | − | 0.153998i | ||||||
\(755\) | 3.20512 | − | 4.56081i | 0.116646 | − | 0.165985i | ||||
\(756\) | −2.53312 | + | 9.25717i | −0.0921286 | + | 0.336680i | ||||
\(757\) | −16.5848 | − | 16.5848i | −0.602785 | − | 0.602785i | 0.338266 | − | 0.941051i | \(-0.390160\pi\) |
−0.941051 | + | 0.338266i | \(0.890160\pi\) | |||||||
\(758\) | 1.59375 | + | 1.59375i | 0.0578874 | + | 0.0578874i | ||||
\(759\) | 41.7717 | + | 3.72893i | 1.51622 | + | 0.135352i | ||||
\(760\) | 0.384532 | + | 2.20276i | 0.0139484 | + | 0.0799024i | ||||
\(761\) | 34.9067i | 1.26537i | 0.774411 | + | 0.632683i | \(0.218047\pi\) | ||||
−0.774411 | + | 0.632683i | \(0.781953\pi\) | |||||||
\(762\) | 2.86365 | + | 3.42504i | 0.103739 | + | 0.124076i | ||||
\(763\) | 5.84055 | − | 5.84055i | 0.211442 | − | 0.211442i | ||||
\(764\) | −12.3225 | −0.445813 | ||||||||
\(765\) | 40.3187 | + | 0.211267i | 1.45772 | + | 0.00763838i | ||||
\(766\) | 6.06812 | 0.219250 | ||||||||
\(767\) | −0.435882 | + | 0.435882i | −0.0157388 | + | 0.0157388i | ||||
\(768\) | 1.11099 | + | 1.32879i | 0.0400896 | + | 0.0479487i | ||||
\(769\) | 37.8613i | 1.36531i | 0.730739 | + | 0.682657i | \(0.239176\pi\) | ||||
−0.730739 | + | 0.682657i | \(0.760824\pi\) | |||||||
\(770\) | 17.4064 | + | 12.2324i | 0.627284 | + | 0.440826i | ||||
\(771\) | −24.7159 | − | 2.20637i | −0.890121 | − | 0.0794605i | ||||
\(772\) | 11.8604 | + | 11.8604i | 0.426864 | + | 0.426864i | ||||
\(773\) | 12.9141 | + | 12.9141i | 0.464488 | + | 0.464488i | 0.900123 | − | 0.435635i | \(-0.143476\pi\) |
−0.435635 | + | 0.900123i | \(0.643476\pi\) | |||||||
\(774\) | −36.9444 | − | 6.64899i | −1.32794 | − | 0.238993i | ||||
\(775\) | 17.1080 | + | 47.5075i | 0.614536 | + | 1.70652i | ||||
\(776\) | − | 5.69343i | − | 0.204382i | ||||||
\(777\) | −1.10176 | + | 0.921176i | −0.0395255 | + | 0.0330470i | ||||
\(778\) | −14.8681 | + | 14.8681i | −0.533047 | + | 0.533047i | ||||
\(779\) | −8.89223 | −0.318597 | ||||||||
\(780\) | −1.43138 | − | 1.20957i | −0.0512516 | − | 0.0433094i | ||||
\(781\) | −60.3037 | −2.15783 | ||||||||
\(782\) | −19.9771 | + | 19.9771i | −0.714379 | + | 0.714379i | ||||
\(783\) | −39.4465 | + | 22.4965i | −1.40970 | + | 0.803959i | ||||
\(784\) | 3.58845i | 0.128159i | ||||||||
\(785\) | 0.138425 | − | 0.0241646i | 0.00494060 | − | 0.000862473i | ||||
\(786\) | 1.75857 | − | 19.6996i | 0.0627262 | − | 0.702662i | ||||
\(787\) | −11.4900 | − | 11.4900i | −0.409575 | − | 0.409575i | 0.472015 | − | 0.881590i | \(-0.343527\pi\) |
−0.881590 | + | 0.472015i | \(0.843527\pi\) | |||||||
\(788\) | −3.56808 | − | 3.56808i | −0.127108 | − | 0.127108i | ||||
\(789\) | −4.11073 | + | 46.0486i | −0.146346 | + | 1.63937i | ||||
\(790\) | −11.5218 | + | 2.01134i | −0.409927 | + | 0.0715603i | ||||
\(791\) | 16.3024i | 0.579648i | ||||||||
\(792\) | 8.81894 | + | 12.6900i | 0.313367 | + | 0.450918i | ||||
\(793\) | −2.14339 | + | 2.14339i | −0.0761140 | + | 0.0761140i | ||||
\(794\) | 9.97969 | 0.354166 | ||||||||
\(795\) | 34.2039 | + | 28.9035i | 1.21309 | + | 1.02510i | ||||
\(796\) | −3.23189 | −0.114551 | ||||||||
\(797\) | 26.4864 | − | 26.4864i | 0.938196 | − | 0.938196i | −0.0600027 | − | 0.998198i | \(-0.519111\pi\) |
0.998198 | + | 0.0600027i | \(0.0191109\pi\) | |||||||
\(798\) | 2.45433 | − | 2.05205i | 0.0868824 | − | 0.0726418i | ||||
\(799\) | − | 18.2334i | − | 0.645051i | ||||||
\(800\) | 4.52430 | + | 2.12854i | 0.159958 | + | 0.0752553i | ||||
\(801\) | 8.65516 | − | 48.0914i | 0.305815 | − | 1.69923i | ||||
\(802\) | 2.53532 | + | 2.53532i | 0.0895252 | + | 0.0895252i | ||||
\(803\) | −14.0955 | − | 14.0955i | −0.497420 | − | 0.497420i | ||||
\(804\) | −3.66116 | − | 0.326830i | −0.129119 | − | 0.0115264i | ||||
\(805\) | −15.8835 | − | 11.1622i | −0.559821 | − | 0.393416i | ||||
\(806\) | 4.88647i | 0.172119i | ||||||||
\(807\) | 7.24347 | + | 8.66348i | 0.254982 | + | 0.304969i | ||||
\(808\) | 2.60351 | − | 2.60351i | 0.0915913 | − | 0.0915913i | ||||
\(809\) | −3.31684 | −0.116614 | −0.0583069 | − | 0.998299i | \(-0.518570\pi\) | ||||
−0.0583069 | + | 0.998299i | \(0.518570\pi\) | |||||||
\(810\) | −3.66835 | + | 19.7875i | −0.128893 | + | 0.695260i | ||||
\(811\) | −31.1363 | −1.09334 | −0.546671 | − | 0.837347i | \(-0.684105\pi\) | ||||
−0.546671 | + | 0.837347i | \(0.684105\pi\) | |||||||
\(812\) | 11.4139 | − | 11.4139i | 0.400551 | − | 0.400551i | ||||
\(813\) | 16.0061 | + | 19.1439i | 0.561357 | + | 0.671405i | ||||
\(814\) | 2.31238i | 0.0810487i | ||||||||
\(815\) | −4.89285 | − | 28.0283i | −0.171389 | − | 0.981787i | ||||
\(816\) | −10.3691 | − | 0.925647i | −0.362993 | − | 0.0324041i | ||||
\(817\) | 8.84777 | + | 8.84777i | 0.309544 | + | 0.309544i | ||||
\(818\) | 11.4649 | + | 11.4649i | 0.400860 | + | 0.400860i | ||||
\(819\) | −0.474906 | + | 2.63877i | −0.0165946 | + | 0.0922059i | ||||
\(820\) | −11.4326 | + | 16.2682i | −0.399242 | + | 0.568111i | ||||
\(821\) | − | 11.7993i | − | 0.411797i | −0.978573 | − | 0.205899i | \(-0.933988\pi\) | ||
0.978573 | − | 0.205899i | \(-0.0660117\pi\) | |||||||
\(822\) | 20.6726 | − | 17.2842i | 0.721039 | − | 0.602856i | ||||
\(823\) | 2.49272 | − | 2.49272i | 0.0868909 | − | 0.0868909i | −0.662325 | − | 0.749216i | \(-0.730430\pi\) |
0.749216 | + | 0.662325i | \(0.230430\pi\) | |||||||
\(824\) | 7.89736 | 0.275118 | ||||||||
\(825\) | 38.5175 | + | 22.5049i | 1.34101 | + | 0.783520i | ||||
\(826\) | −2.35307 | −0.0818736 | ||||||||
\(827\) | 8.72992 | − | 8.72992i | 0.303569 | − | 0.303569i | −0.538839 | − | 0.842408i | \(-0.681137\pi\) |
0.842408 | + | 0.538839i | \(0.181137\pi\) | |||||||
\(828\) | −8.04736 | − | 11.5797i | −0.279665 | − | 0.402423i | ||||
\(829\) | 3.58566i | 0.124535i | 0.998059 | + | 0.0622676i | \(0.0198332\pi\) | ||||
−0.998059 | + | 0.0622676i | \(0.980167\pi\) | |||||||
\(830\) | −17.9742 | + | 25.5768i | −0.623892 | + | 0.887783i | ||||
\(831\) | −3.04316 | + | 34.0897i | −0.105566 | + | 1.18256i | ||||
\(832\) | 0.342145 | + | 0.342145i | 0.0118618 | + | 0.0118618i | ||||
\(833\) | −15.2510 | − | 15.2510i | −0.528415 | − | 0.528415i | ||||
\(834\) | 0.189970 | − | 2.12805i | 0.00657812 | − | 0.0736885i | ||||
\(835\) | 0.638992 | + | 3.66041i | 0.0221132 | + | 0.126674i | ||||
\(836\) | − | 5.15114i | − | 0.178156i | ||||||
\(837\) | 45.5830 | − | 25.9962i | 1.57558 | − | 0.898560i | ||||
\(838\) | 5.27610 | − | 5.27610i | 0.182260 | − | 0.182260i | ||||
\(839\) | 35.9702 | 1.24183 | 0.620914 | − | 0.783879i | \(-0.286762\pi\) | ||||
0.620914 | + | 0.783879i | \(0.286762\pi\) | |||||||
\(840\) | −0.598720 | − | 7.12845i | −0.0206578 | − | 0.245955i | ||||
\(841\) | 47.3747 | 1.63361 | ||||||||
\(842\) | 2.49657 | − | 2.49657i | 0.0860374 | − | 0.0860374i | ||||
\(843\) | 32.1978 | − | 26.9204i | 1.10895 | − | 0.927188i | ||||
\(844\) | − | 13.2442i | − | 0.455883i | ||||||
\(845\) | 23.3550 | + | 16.4128i | 0.803437 | + | 0.564618i | ||||
\(846\) | 8.95696 | + | 1.61201i | 0.307947 | + | 0.0554221i | ||||
\(847\) | −20.2886 | − | 20.2886i | −0.697125 | − | 0.697125i | ||||
\(848\) | −8.17583 | − | 8.17583i | −0.280759 | − | 0.280759i | ||||
\(849\) | 22.6030 | + | 2.01776i | 0.775734 | + | 0.0692492i | ||||
\(850\) | −28.2747 | + | 10.1820i | −0.969815 | + | 0.349241i | ||||
\(851\) | − | 2.11007i | − | 0.0723321i | ||||||
\(852\) | 13.0062 | + | 15.5560i | 0.445587 | + | 0.532939i | ||||
\(853\) | −22.0095 | + | 22.0095i | −0.753591 | + | 0.753591i | −0.975148 | − | 0.221556i | \(-0.928886\pi\) |
0.221556 | + | 0.975148i | \(0.428886\pi\) | |||||||
\(854\) | −11.5709 | −0.395947 | ||||||||
\(855\) | 4.76821 | − | 4.71850i | 0.163069 | − | 0.161369i | ||||
\(856\) | −2.93365 | −0.100270 | ||||||||
\(857\) | −11.8490 | + | 11.8490i | −0.404754 | + | 0.404754i | −0.879905 | − | 0.475150i | \(-0.842394\pi\) |
0.475150 | + | 0.879905i | \(0.342394\pi\) | |||||||
\(858\) | 2.76912 | + | 3.31197i | 0.0945361 | + | 0.113069i | ||||
\(859\) | − | 24.7373i | − | 0.844025i | −0.906590 | − | 0.422013i | \(-0.861324\pi\) | ||
0.906590 | − | 0.422013i | \(-0.138676\pi\) | |||||||
\(860\) | 27.5623 | − | 4.81150i | 0.939866 | − | 0.164071i | ||||
\(861\) | 28.3350 | + | 2.52945i | 0.965655 | + | 0.0862034i | ||||
\(862\) | 25.5261 | + | 25.5261i | 0.869424 | + | 0.869424i | ||||
\(863\) | −15.8562 | − | 15.8562i | −0.539752 | − | 0.539752i | 0.383704 | − | 0.923456i | \(-0.374648\pi\) |
−0.923456 | + | 0.383704i | \(0.874648\pi\) | |||||||
\(864\) | 1.37145 | − | 5.01190i | 0.0466576 | − | 0.170508i | ||||
\(865\) | 42.3646 | − | 7.39553i | 1.44044 | − | 0.251455i | ||||
\(866\) | − | 11.9178i | − | 0.404982i | ||||||
\(867\) | 25.4136 | − | 21.2482i | 0.863092 | − | 0.721625i | ||||
\(868\) | −13.1896 | + | 13.1896i | −0.447683 | + | 0.447683i | ||||
\(869\) | 26.9437 | 0.914002 | ||||||||
\(870\) | 21.8464 | − | 25.8526i | 0.740661 | − | 0.876485i | ||||
\(871\) | −1.02685 | −0.0347935 | ||||||||
\(872\) | −3.16212 | + | 3.16212i | −0.107083 | + | 0.107083i | ||||
\(873\) | −14.0259 | + | 9.74735i | −0.474705 | + | 0.329898i | ||||
\(874\) | 4.70047i | 0.158996i | ||||||||
\(875\) | −10.2336 | − | 17.9365i | −0.345958 | − | 0.606364i | ||||
\(876\) | −0.595980 | + | 6.67620i | −0.0201363 | + | 0.225568i | ||||
\(877\) | −4.84768 | − | 4.84768i | −0.163694 | − | 0.163694i | 0.620507 | − | 0.784201i | \(-0.286927\pi\) |
−0.784201 | + | 0.620507i | \(0.786927\pi\) | |||||||
\(878\) | 4.74784 | + | 4.74784i | 0.160232 | + | 0.160232i | ||||
\(879\) | −1.96148 | + | 21.9726i | −0.0661591 | + | 0.741117i | ||||
\(880\) | −9.42396 | − | 6.62272i | −0.317682 | − | 0.223252i | ||||
\(881\) | − | 41.5364i | − | 1.39940i | −0.714439 | − | 0.699698i | \(-0.753318\pi\) | ||
0.714439 | − | 0.699698i | \(-0.246682\pi\) | |||||||
\(882\) | 8.84022 | − | 6.14355i | 0.297666 | − | 0.206864i | ||||
\(883\) | 39.1569 | − | 39.1569i | 1.31773 | − | 1.31773i | 0.402167 | − | 0.915566i | \(-0.368257\pi\) |
0.915566 | − | 0.402167i | \(-0.131743\pi\) | |||||||
\(884\) | −2.90825 | −0.0978150 | ||||||||
\(885\) | −4.91674 | + | 0.412958i | −0.165274 | + | 0.0138814i | ||||
\(886\) | 22.0422 | 0.740522 | ||||||||
\(887\) | 21.3528 | − | 21.3528i | 0.716958 | − | 0.716958i | −0.251023 | − | 0.967981i | \(-0.580767\pi\) |
0.967981 | + | 0.251023i | \(0.0807670\pi\) | |||||||
\(888\) | 0.596502 | − | 0.498731i | 0.0200173 | − | 0.0167363i | ||||
\(889\) | 4.76084i | 0.159674i | ||||||||
\(890\) | 6.26326 | + | 35.8786i | 0.209945 | + | 1.20265i | ||||
\(891\) | 16.1637 | − | 43.4513i | 0.541503 | − | 1.45567i | ||||
\(892\) | −3.93298 | − | 3.93298i | −0.131686 | − | 0.131686i | ||||
\(893\) | −2.14509 | − | 2.14509i | −0.0717828 | − | 0.0717828i | ||||
\(894\) | 1.04883 | + | 0.0936286i | 0.0350782 | + | 0.00313141i | ||||
\(895\) | −23.1147 | + | 32.8917i | −0.772640 | + | 1.09945i | ||||
\(896\) | 1.84704i | 0.0617052i | ||||||||
\(897\) | −2.52684 | − | 3.02221i | −0.0843689 | − | 0.100908i | ||||
\(898\) | 14.9225 | − | 14.9225i | 0.497971 | − | 0.497971i | ||||
\(899\) | −88.2560 | −2.94350 | ||||||||
\(900\) | −2.50205 | − | 14.7899i | −0.0834018 | − | 0.492995i | ||||
\(901\) | 69.4949 | 2.31521 | ||||||||
\(902\) | 32.3891 | − | 32.3891i | 1.07844 | − | 1.07844i | ||||
\(903\) | −25.6766 | − | 30.7102i | −0.854462 | − | 1.02197i | ||||
\(904\) | − | 8.82625i | − | 0.293557i | ||||||
\(905\) | 5.89082 | − | 8.38249i | 0.195817 | − | 0.278643i | ||||
\(906\) | 4.30080 | + | 0.383929i | 0.142884 | + | 0.0127552i | ||||
\(907\) | −10.8871 | − | 10.8871i | −0.361499 | − | 0.361499i | 0.502866 | − | 0.864364i | \(-0.332279\pi\) |
−0.864364 | + | 0.502866i | \(0.832279\pi\) | |||||||
\(908\) | 4.90875 | + | 4.90875i | 0.162903 | + | 0.162903i | ||||
\(909\) | −10.8711 | − | 1.95651i | −0.360572 | − | 0.0648932i | ||||
\(910\) | −0.343664 | − | 1.96865i | −0.0113923 | − | 0.0652600i | ||||
\(911\) | 17.7253i | 0.587264i | 0.955919 | + | 0.293632i | \(0.0948640\pi\) | ||||
−0.955919 | + | 0.293632i | \(0.905136\pi\) | |||||||
\(912\) | −1.32879 | + | 1.11099i | −0.0440007 | + | 0.0367887i | ||||
\(913\) | 50.9219 | − | 50.9219i | 1.68527 | − | 1.68527i | ||||
\(914\) | −4.59183 | −0.151884 | ||||||||
\(915\) | −24.1774 | + | 2.03066i | −0.799280 | + | 0.0671317i | ||||
\(916\) | 0.309162 | 0.0102150 | ||||||||
\(917\) | 14.9136 | − | 14.9136i | 0.492490 | − | 0.492490i | ||||
\(918\) | 15.4720 | + | 27.1294i | 0.510652 | + | 0.895402i | ||||
\(919\) | − | 41.6528i | − | 1.37400i | −0.726658 | − | 0.686999i | \(-0.758928\pi\) | ||
0.726658 | − | 0.686999i | \(-0.241072\pi\) | |||||||
\(920\) | 8.59945 | + | 6.04329i | 0.283516 | + | 0.199241i | ||||
\(921\) | −0.956611 | + | 10.7160i | −0.0315214 | + | 0.353104i | ||||
\(922\) | −22.2784 | − | 22.2784i | −0.733700 | − | 0.733700i | ||||
\(923\) | 4.00544 | + | 4.00544i | 0.131841 | + | 0.131841i | ||||
\(924\) | −1.46527 | + | 16.4141i | −0.0482040 | + | 0.539984i | ||||
\(925\) | 0.955514 | − | 2.03098i | 0.0314171 | − | 0.0667783i | ||||
\(926\) | 12.4697i | 0.409780i | ||||||||
\(927\) | −13.5206 | − | 19.4553i | −0.444073 | − | 0.638996i | ||||
\(928\) | −6.17959 | + | 6.17959i | −0.202855 | + | 0.202855i | ||||
\(929\) | −5.97512 | −0.196037 | −0.0980187 | − | 0.995185i | \(-0.531250\pi\) | ||||
−0.0980187 | + | 0.995185i | \(0.531250\pi\) | |||||||
\(930\) | −25.2449 | + | 29.8744i | −0.827814 | + | 0.979620i | ||||
\(931\) | −3.58845 | −0.117607 | ||||||||
\(932\) | −1.09776 | + | 1.09776i | −0.0359584 | + | 0.0359584i | ||||
\(933\) | 21.4645 | − | 17.9463i | 0.702717 | − | 0.587537i | ||||
\(934\) | − | 5.71410i | − | 0.186971i | ||||||
\(935\) | 68.1987 | − | 11.9053i | 2.23034 | − | 0.389346i | ||||
\(936\) | 0.257118 | − | 1.42865i | 0.00840416 | − | 0.0466968i | ||||
\(937\) | 30.6142 | + | 30.6142i | 1.00012 | + | 1.00012i | 1.00000 | 0.000123448i | \(3.92947e-5\pi\) | |
0.000123448 | 1.00000i | \(0.499961\pi\) | ||||||||
\(938\) | −2.77168 | − | 2.77168i | −0.0904985 | − | 0.0904985i | ||||
\(939\) | −1.20328 | − | 0.107416i | −0.0392674 | − | 0.00350538i | ||||
\(940\) | −6.68233 | + | 1.16652i | −0.217954 | + | 0.0380478i | ||||
\(941\) | − | 6.27661i | − | 0.204611i | −0.994753 | − | 0.102306i | \(-0.967378\pi\) | ||
0.994753 | − | 0.102306i | \(-0.0326220\pi\) | |||||||
\(942\) | 0.0698168 | + | 0.0835037i | 0.00227476 | + | 0.00272070i | ||||
\(943\) | −29.5554 | + | 29.5554i | −0.962456 | + | 0.962456i | ||||
\(944\) | 1.27397 | 0.0414641 | ||||||||
\(945\) | −16.5361 | + | 13.6791i | −0.537918 | + | 0.444981i | ||||
\(946\) | −64.4544 | −2.09559 | ||||||||
\(947\) | −7.98043 | + | 7.98043i | −0.259329 | + | 0.259329i | −0.824781 | − | 0.565452i | \(-0.808702\pi\) |
0.565452 | + | 0.824781i | \(0.308702\pi\) | |||||||
\(948\) | −5.81119 | − | 6.95041i | −0.188739 | − | 0.225739i | ||||
\(949\) | 1.87248i | 0.0607833i | ||||||||
\(950\) | −2.12854 | + | 4.52430i | −0.0690590 | + | 0.146788i | ||||
\(951\) | −41.4167 | − | 3.69724i | −1.34303 | − | 0.119891i | ||||
\(952\) | −7.84995 | − | 7.84995i | −0.254418 | − | 0.254418i | ||||
\(953\) | 12.3683 | + | 12.3683i | 0.400650 | + | 0.400650i | 0.878462 | − | 0.477812i | \(-0.158570\pi\) |
−0.477812 | + | 0.878462i | \(0.658570\pi\) | |||||||
\(954\) | −6.14403 | + | 34.1386i | −0.198920 | + | 1.10528i | ||||
\(955\) | −22.5439 | − | 15.8428i | −0.729504 | − | 0.512661i | ||||
\(956\) | − | 24.4016i | − | 0.789205i | ||||||
\(957\) | −59.8185 | + | 50.0139i | −1.93366 | + | 1.61672i | ||||
\(958\) | −18.1569 | + | 18.1569i | −0.586624 | + | 0.586624i | ||||
\(959\) | 28.7351 | 0.927906 | ||||||||
\(960\) | 0.324151 | + | 3.85939i | 0.0104619 | + | 0.124561i | ||||
\(961\) | 70.9857 | 2.28986 | ||||||||
\(962\) | 0.153591 | − | 0.153591i | 0.00495197 | − | 0.00495197i | ||||
\(963\) | 5.02250 | + | 7.22710i | 0.161848 | + | 0.232890i | ||||
\(964\) | 15.4813i | 0.498618i | ||||||||
\(965\) | 6.44978 | + | 36.9470i | 0.207626 | + | 1.18937i | ||||
\(966\) | 1.33708 | − | 14.9780i | 0.0430198 | − | 0.481910i | ||||
\(967\) | −17.7605 | − | 17.7605i | −0.571140 | − | 0.571140i | 0.361307 | − | 0.932447i | \(-0.382331\pi\) |
−0.932447 | + | 0.361307i | \(0.882331\pi\) | |||||||
\(968\) | 10.9844 | + | 10.9844i | 0.353052 | + | 0.353052i | ||||
\(969\) | 0.925647 | − | 10.3691i | 0.0297361 | − | 0.333105i | ||||
\(970\) | 7.31993 | − | 10.4161i | 0.235029 | − | 0.334440i | ||||
\(971\) | − | 22.5253i | − | 0.722872i | −0.932397 | − | 0.361436i | \(-0.882287\pi\) | ||
0.932397 | − | 0.361436i | \(-0.117713\pi\) | |||||||
\(972\) | −14.6949 | + | 5.20195i | −0.471339 | + | 0.166853i | ||||
\(973\) | 1.61104 | − | 1.61104i | 0.0516476 | − | 0.0516476i | ||||
\(974\) | −14.3226 | −0.458925 | ||||||||
\(975\) | −1.06358 | − | 4.05318i | −0.0340618 | − | 0.129806i | ||||
\(976\) | 6.26456 | 0.200524 | ||||||||
\(977\) | −32.1177 | + | 32.1177i | −1.02754 | + | 1.02754i | −0.0279276 | + | 0.999610i | \(0.508891\pi\) |
−0.999610 | + | 0.0279276i | \(0.991109\pi\) | |||||||
\(978\) | 16.9078 | − | 14.1365i | 0.540652 | − | 0.452035i | ||||
\(979\) | − | 83.9020i | − | 2.68152i | ||||||
\(980\) | −4.61359 | + | 6.56503i | −0.147376 | + | 0.209712i | ||||
\(981\) | 13.2036 | + | 2.37629i | 0.421558 | + | 0.0758691i | ||||
\(982\) | 13.6115 | + | 13.6115i | 0.434361 | + | 0.434361i | ||||
\(983\) | 2.22712 | + | 2.22712i | 0.0710340 | + | 0.0710340i | 0.741731 | − | 0.670697i | \(-0.234005\pi\) |
−0.670697 | + | 0.741731i | \(0.734005\pi\) | |||||||
\(984\) | −15.3408 | − | 1.36946i | −0.489047 | − | 0.0436569i | ||||
\(985\) | −1.94036 | − | 11.1152i | −0.0618250 | − | 0.354159i | ||||
\(986\) | − | 52.5268i | − | 1.67279i | ||||||
\(987\) | 6.22514 | + | 7.44551i | 0.198148 | + | 0.236993i | ||||
\(988\) | −0.342145 | + | 0.342145i | −0.0108851 | + | 0.0108851i | ||||
\(989\) | 58.8153 | 1.87022 | ||||||||
\(990\) | −0.181063 | + | 34.5545i | −0.00575456 | + | 1.09821i | ||||
\(991\) | −11.1667 | −0.354723 | −0.177361 | − | 0.984146i | \(-0.556756\pi\) | ||||
−0.177361 | + | 0.984146i | \(0.556756\pi\) | |||||||
\(992\) | 7.14093 | − | 7.14093i | 0.226725 | − | 0.226725i | ||||
\(993\) | 16.3448 | + | 19.5490i | 0.518685 | + | 0.620368i | ||||
\(994\) | 21.6230i | 0.685840i | ||||||||
\(995\) | −5.91270 | − | 4.15517i | −0.187445 | − | 0.131728i | ||||
\(996\) | −24.1187 | − | 2.15306i | −0.764229 | − | 0.0682222i | ||||
\(997\) | −10.8789 | − | 10.8789i | −0.344538 | − | 0.344538i | 0.513533 | − | 0.858070i | \(-0.328337\pi\) |
−0.858070 | + | 0.513533i | \(0.828337\pi\) | |||||||
\(998\) | −13.8439 | − | 13.8439i | −0.438220 | − | 0.438220i | ||||
\(999\) | −2.24987 | − | 0.615651i | −0.0711827 | − | 0.0194783i |
(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 | 570.2.k.b.77.16 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.77.3 | ✓ | 36 | |
5.3 | odd | 4 | inner | 570.2.k.b.533.3 | yes | 36 | |
15.8 | even | 4 | inner | 570.2.k.b.533.16 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.3 | ✓ | 36 | 3.2 | odd | 2 | inner | |
570.2.k.b.77.16 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.533.3 | yes | 36 | 5.3 | odd | 4 | inner | |
570.2.k.b.533.16 | yes | 36 | 15.8 | even | 4 | inner |