Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [585,2,Mod(376,585)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(585, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("585.376");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 585 = 3^{2} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 585.bt (of order \(6\), 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: | \(4.67124851824\) |
Analytic rank: | \(0\) |
Dimension: | \(108\) |
Relative dimension: | \(54\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 571.5 | ||
Character | \(\chi\) | \(=\) | 585.571 |
Dual form | 585.2.bt.b.376.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(496\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.20318 | + | 1.27200i | −1.55788 | + | 0.899443i | −0.560421 | + | 0.828208i | \(0.689361\pi\) |
−0.997460 | + | 0.0712352i | \(0.977306\pi\) | |||||||
\(3\) | 0.350451 | + | 1.69623i | 0.202333 | + | 0.979317i | ||||
\(4\) | 2.23599 | − | 3.87285i | 1.11800 | − | 1.93642i | ||||
\(5\) | −0.866025 | − | 0.500000i | −0.387298 | − | 0.223607i | ||||
\(6\) | −2.92971 | − | 3.29131i | −1.19605 | − | 1.34367i | ||||
\(7\) | −0.586224 | + | 0.338456i | −0.221572 | + | 0.127924i | −0.606678 | − | 0.794948i | \(-0.707498\pi\) |
0.385106 | + | 0.922872i | \(0.374165\pi\) | |||||||
\(8\) | 6.28874i | 2.22341i | ||||||||
\(9\) | −2.75437 | + | 1.18889i | −0.918123 | + | 0.396296i | ||||
\(10\) | 2.54401 | 0.804486 | ||||||||
\(11\) | −3.28964 | + | 1.89927i | −0.991863 | + | 0.572652i | −0.905831 | − | 0.423640i | \(-0.860752\pi\) |
−0.0860322 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(12\) | 7.35283 | + | 2.43550i | 2.12258 | + | 0.703069i | ||||
\(13\) | 2.20335 | + | 2.85399i | 0.611098 | + | 0.791555i | ||||
\(14\) | 0.861036 | − | 1.49136i | 0.230122 | − | 0.398582i | ||||
\(15\) | 0.544614 | − | 1.64420i | 0.140619 | − | 0.424531i | ||||
\(16\) | −3.52732 | − | 6.10950i | −0.881831 | − | 1.52738i | ||||
\(17\) | 0.607547 | 0.147352 | 0.0736759 | − | 0.997282i | \(-0.476527\pi\) | ||||
0.0736759 | + | 0.997282i | \(0.476527\pi\) | |||||||
\(18\) | 4.55609 | − | 6.12290i | 1.07388 | − | 1.44318i | ||||
\(19\) | − | 3.20793i | − | 0.735951i | −0.929836 | − | 0.367975i | \(-0.880051\pi\) | ||
0.929836 | − | 0.367975i | \(-0.119949\pi\) | |||||||
\(20\) | −3.87285 | + | 2.23599i | −0.865995 | + | 0.499983i | ||||
\(21\) | −0.779541 | − | 0.875756i | −0.170110 | − | 0.191106i | ||||
\(22\) | 4.83177 | − | 8.36886i | 1.03014 | − | 1.78425i | ||||
\(23\) | −2.41950 | + | 4.19070i | −0.504501 | + | 0.873821i | 0.495486 | + | 0.868616i | \(0.334990\pi\) |
−0.999986 | + | 0.00520496i | \(0.998343\pi\) | |||||||
\(24\) | −10.6671 | + | 2.20389i | −2.17742 | + | 0.449868i | ||||
\(25\) | 0.500000 | + | 0.866025i | 0.100000 | + | 0.173205i | ||||
\(26\) | −8.48465 | − | 3.48518i | −1.66398 | − | 0.683500i | ||||
\(27\) | −2.98189 | − | 4.25539i | −0.573865 | − | 0.818950i | ||||
\(28\) | 3.02714i | 0.572076i | ||||||||
\(29\) | −3.96123 | − | 6.86105i | −0.735582 | − | 1.27406i | −0.954468 | − | 0.298314i | \(-0.903576\pi\) |
0.218886 | − | 0.975750i | \(-0.429758\pi\) | |||||||
\(30\) | 0.891549 | + | 4.31522i | 0.162774 | + | 0.787847i | ||||
\(31\) | −5.27590 | − | 3.04604i | −0.947579 | − | 0.547085i | −0.0552511 | − | 0.998472i | \(-0.517596\pi\) |
−0.892328 | + | 0.451387i | \(0.850929\pi\) | |||||||
\(32\) | 4.65021 | + | 2.68480i | 0.822049 | + | 0.474610i | ||||
\(33\) | −4.37445 | − | 4.91437i | −0.761494 | − | 0.855482i | ||||
\(34\) | −1.33853 | + | 0.772802i | −0.229556 | + | 0.132534i | ||||
\(35\) | 0.676913 | 0.114419 | ||||||||
\(36\) | −1.55436 | + | 13.3256i | −0.259060 | + | 2.22093i | ||||
\(37\) | − | 2.77571i | − | 0.456324i | −0.973623 | − | 0.228162i | \(-0.926728\pi\) | ||
0.973623 | − | 0.228162i | \(-0.0732715\pi\) | |||||||
\(38\) | 4.08051 | + | 7.06764i | 0.661946 | + | 1.14652i | ||||
\(39\) | −4.06885 | + | 4.73756i | −0.651538 | + | 0.758616i | ||||
\(40\) | 3.14437 | − | 5.44621i | 0.497168 | − | 0.861121i | ||||
\(41\) | 3.24880 | + | 1.87570i | 0.507377 | + | 0.292934i | 0.731755 | − | 0.681568i | \(-0.238702\pi\) |
−0.224378 | + | 0.974502i | \(0.572035\pi\) | |||||||
\(42\) | 2.83143 | + | 0.937865i | 0.436899 | + | 0.144716i | ||||
\(43\) | −5.70599 | − | 9.88307i | −0.870156 | − | 1.50715i | −0.861835 | − | 0.507189i | \(-0.830685\pi\) |
−0.00832073 | − | 0.999965i | \(-0.502649\pi\) | |||||||
\(44\) | 16.9870i | 2.56089i | ||||||||
\(45\) | 2.97980 | + | 0.347578i | 0.444202 | + | 0.0518139i | ||||
\(46\) | − | 12.3105i | − | 1.81508i | ||||||
\(47\) | 7.36875 | − | 4.25435i | 1.07484 | − | 0.620561i | 0.145342 | − | 0.989381i | \(-0.453572\pi\) |
0.929501 | + | 0.368821i | \(0.120238\pi\) | |||||||
\(48\) | 9.12695 | − | 8.12422i | 1.31736 | − | 1.17263i | ||||
\(49\) | −3.27089 | + | 5.66536i | −0.467271 | + | 0.809337i | ||||
\(50\) | −2.20318 | − | 1.27200i | −0.311576 | − | 0.179889i | ||||
\(51\) | 0.212915 | + | 1.03054i | 0.0298141 | + | 0.144304i | ||||
\(52\) | 15.9797 | − | 2.15173i | 2.21599 | − | 0.298391i | ||||
\(53\) | −2.76231 | −0.379432 | −0.189716 | − | 0.981839i | \(-0.560757\pi\) | ||||
−0.189716 | + | 0.981839i | \(0.560757\pi\) | |||||||
\(54\) | 11.9825 | + | 5.58239i | 1.63061 | + | 0.759667i | ||||
\(55\) | 3.79855 | 0.512196 | ||||||||
\(56\) | −2.12846 | − | 3.68661i | −0.284428 | − | 0.492644i | ||||
\(57\) | 5.44138 | − | 1.12422i | 0.720729 | − | 0.148907i | ||||
\(58\) | 17.4546 | + | 10.0774i | 2.29190 | + | 1.32323i | ||||
\(59\) | −2.31312 | − | 1.33548i | −0.301142 | − | 0.173865i | 0.341814 | − | 0.939768i | \(-0.388959\pi\) |
−0.642956 | + | 0.765903i | \(0.722292\pi\) | |||||||
\(60\) | −5.14999 | − | 5.78562i | −0.664861 | − | 0.746921i | ||||
\(61\) | −1.86548 | − | 3.23110i | −0.238850 | − | 0.413700i | 0.721535 | − | 0.692378i | \(-0.243437\pi\) |
−0.960385 | + | 0.278678i | \(0.910104\pi\) | |||||||
\(62\) | 15.4983 | 1.96829 | ||||||||
\(63\) | 1.21229 | − | 1.62919i | 0.152734 | − | 0.205258i | ||||
\(64\) | 0.448974 | 0.0561217 | ||||||||
\(65\) | −0.481159 | − | 3.57330i | −0.0596804 | − | 0.443214i | ||||
\(66\) | 15.8888 | + | 5.26290i | 1.95577 | + | 0.647818i | ||||
\(67\) | 2.92456 | + | 1.68849i | 0.357292 | + | 0.206282i | 0.667892 | − | 0.744258i | \(-0.267197\pi\) |
−0.310600 | + | 0.950541i | \(0.600530\pi\) | |||||||
\(68\) | 1.35847 | − | 2.35294i | 0.164738 | − | 0.285335i | ||||
\(69\) | −7.95629 | − | 2.63539i | −0.957825 | − | 0.317264i | ||||
\(70\) | −1.49136 | + | 0.861036i | −0.178251 | + | 0.102913i | ||||
\(71\) | − | 9.87673i | − | 1.17215i | −0.810256 | − | 0.586076i | \(-0.800672\pi\) | ||
0.810256 | − | 0.586076i | \(-0.199328\pi\) | |||||||
\(72\) | −7.47660 | − | 17.3215i | −0.881126 | − | 2.04136i | ||||
\(73\) | 11.1655i | 1.30682i | 0.757003 | + | 0.653411i | \(0.226663\pi\) | ||||
−0.757003 | + | 0.653411i | \(0.773337\pi\) | |||||||
\(74\) | 3.53071 | + | 6.11537i | 0.410437 | + | 0.710898i | ||||
\(75\) | −1.29375 | + | 1.15161i | −0.149389 | + | 0.132977i | ||||
\(76\) | −12.4238 | − | 7.17291i | −1.42511 | − | 0.822789i | ||||
\(77\) | 1.28564 | − | 2.22680i | 0.146512 | − | 0.253767i | ||||
\(78\) | 2.93820 | − | 15.6133i | 0.332686 | − | 1.76785i | ||||
\(79\) | −2.46916 | − | 4.27671i | −0.277802 | − | 0.481167i | 0.693036 | − | 0.720903i | \(-0.256273\pi\) |
−0.970838 | + | 0.239736i | \(0.922939\pi\) | |||||||
\(80\) | 7.05465i | 0.788733i | ||||||||
\(81\) | 6.17310 | − | 6.54927i | 0.685900 | − | 0.727696i | ||||
\(82\) | −9.54357 | −1.05391 | ||||||||
\(83\) | −10.1895 | + | 5.88288i | −1.11844 | + | 0.645730i | −0.941002 | − | 0.338402i | \(-0.890114\pi\) |
−0.177436 | + | 0.984132i | \(0.556780\pi\) | |||||||
\(84\) | −5.13472 | + | 1.06086i | −0.560243 | + | 0.115750i | ||||
\(85\) | −0.526151 | − | 0.303773i | −0.0570691 | − | 0.0329488i | ||||
\(86\) | 25.1426 | + | 14.5161i | 2.71120 | + | 1.56531i | ||||
\(87\) | 10.2497 | − | 9.12360i | 1.09888 | − | 0.978152i | ||||
\(88\) | −11.9440 | − | 20.6877i | −1.27324 | − | 2.20531i | ||||
\(89\) | − | 16.5506i | − | 1.75436i | −0.480163 | − | 0.877179i | \(-0.659422\pi\) | ||
0.480163 | − | 0.877179i | \(-0.340578\pi\) | |||||||
\(90\) | −7.00714 | + | 3.02454i | −0.738617 | + | 0.318814i | ||||
\(91\) | −2.25761 | − | 0.927340i | −0.236661 | − | 0.0972117i | ||||
\(92\) | 10.8200 | + | 18.7407i | 1.12806 | + | 1.95386i | ||||
\(93\) | 3.31783 | − | 10.0166i | 0.344043 | − | 1.03867i | ||||
\(94\) | −10.8231 | + | 18.7462i | −1.11632 | + | 1.93352i | ||||
\(95\) | −1.60397 | + | 2.77815i | −0.164564 | + | 0.285032i | ||||
\(96\) | −2.92436 | + | 8.82871i | −0.298467 | + | 0.901076i | ||||
\(97\) | −4.48050 | + | 2.58682i | −0.454926 | + | 0.262652i | −0.709908 | − | 0.704294i | \(-0.751264\pi\) |
0.254982 | + | 0.966946i | \(0.417930\pi\) | |||||||
\(98\) | − | 16.6424i | − | 1.68113i | ||||||
\(99\) | 6.80285 | − | 9.14230i | 0.683712 | − | 0.918836i | ||||
\(100\) | 4.47198 | 0.447198 | ||||||||
\(101\) | 9.00439 | + | 15.5961i | 0.895971 | + | 1.55187i | 0.832599 | + | 0.553877i | \(0.186852\pi\) |
0.0633720 | + | 0.997990i | \(0.479815\pi\) | |||||||
\(102\) | −1.77994 | − | 1.99963i | −0.176240 | − | 0.197992i | ||||
\(103\) | −0.202587 | + | 0.350890i | −0.0199615 | + | 0.0345743i | −0.875834 | − | 0.482613i | \(-0.839688\pi\) |
0.855872 | + | 0.517188i | \(0.173021\pi\) | |||||||
\(104\) | −17.9480 | + | 13.8563i | −1.75995 | + | 1.35872i | ||||
\(105\) | 0.237224 | + | 1.14820i | 0.0231507 | + | 0.112053i | ||||
\(106\) | 6.08585 | − | 3.51367i | 0.591110 | − | 0.341278i | ||||
\(107\) | −3.95316 | −0.382167 | −0.191083 | − | 0.981574i | \(-0.561200\pi\) | ||||
−0.191083 | + | 0.981574i | \(0.561200\pi\) | |||||||
\(108\) | −23.1480 | + | 2.03341i | −2.22741 | + | 0.195665i | ||||
\(109\) | 15.2008i | 1.45597i | 0.685592 | + | 0.727986i | \(0.259543\pi\) | ||||
−0.685592 | + | 0.727986i | \(0.740457\pi\) | |||||||
\(110\) | −8.36886 | + | 4.83177i | −0.797940 | + | 0.460691i | ||||
\(111\) | 4.70823 | − | 0.972748i | 0.446885 | − | 0.0923292i | ||||
\(112\) | 4.13560 | + | 2.38769i | 0.390777 | + | 0.225615i | ||||
\(113\) | −4.48592 | + | 7.76985i | −0.422000 | + | 0.730926i | −0.996135 | − | 0.0878351i | \(-0.972005\pi\) |
0.574135 | + | 0.818761i | \(0.305338\pi\) | |||||||
\(114\) | −10.5583 | + | 9.39832i | −0.988876 | + | 0.880234i | ||||
\(115\) | 4.19070 | − | 2.41950i | 0.390785 | − | 0.225620i | ||||
\(116\) | −35.4291 | −3.28951 | ||||||||
\(117\) | −9.46190 | − | 5.24141i | −0.874753 | − | 0.484569i | ||||
\(118\) | 6.79494 | 0.625525 | ||||||||
\(119\) | −0.356158 | + | 0.205628i | −0.0326490 | + | 0.0188499i | ||||
\(120\) | 10.3399 | + | 3.42494i | 0.943904 | + | 0.312653i | ||||
\(121\) | 1.71447 | − | 2.96956i | 0.155861 | − | 0.269960i | ||||
\(122\) | 8.21995 | + | 4.74579i | 0.744199 | + | 0.429664i | ||||
\(123\) | −2.04306 | + | 6.16804i | −0.184217 | + | 0.556153i | ||||
\(124\) | −23.5937 | + | 13.6218i | −2.11878 | + | 1.22328i | ||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | −0.598555 | + | 5.13142i | −0.0533235 | + | 0.457144i | ||||
\(127\) | −12.2139 | −1.08380 | −0.541902 | − | 0.840442i | \(-0.682296\pi\) | ||||
−0.541902 | + | 0.840442i | \(0.682296\pi\) | |||||||
\(128\) | −10.2896 | + | 5.94070i | −0.909480 | + | 0.525089i | ||||
\(129\) | 14.7643 | − | 13.1422i | 1.29992 | − | 1.15710i | ||||
\(130\) | 5.60533 | + | 7.26058i | 0.491620 | + | 0.636795i | ||||
\(131\) | 8.71835 | − | 15.1006i | 0.761726 | − | 1.31935i | −0.180234 | − | 0.983624i | \(-0.557686\pi\) |
0.941960 | − | 0.335725i | \(-0.108981\pi\) | |||||||
\(132\) | −28.8138 | + | 5.95311i | −2.50792 | + | 0.518152i | ||||
\(133\) | 1.08575 | + | 1.88057i | 0.0941461 | + | 0.163066i | ||||
\(134\) | −8.59109 | −0.742157 | ||||||||
\(135\) | 0.454700 | + | 5.17622i | 0.0391343 | + | 0.445498i | ||||
\(136\) | 3.82070i | 0.327623i | ||||||||
\(137\) | −10.5939 | + | 6.11637i | −0.905095 | + | 0.522557i | −0.878850 | − | 0.477099i | \(-0.841688\pi\) |
−0.0262452 | + | 0.999656i | \(0.508355\pi\) | |||||||
\(138\) | 20.8813 | − | 4.31421i | 1.77754 | − | 0.367250i | ||||
\(139\) | −2.59598 | + | 4.49636i | −0.220188 | + | 0.381377i | −0.954865 | − | 0.297040i | \(-0.904000\pi\) |
0.734677 | + | 0.678417i | \(0.237334\pi\) | |||||||
\(140\) | 1.51357 | − | 2.62158i | 0.127920 | − | 0.221564i | ||||
\(141\) | 9.79872 | + | 11.0081i | 0.825201 | + | 0.927052i | ||||
\(142\) | 12.5632 | + | 21.7602i | 1.05428 | + | 1.82607i | ||||
\(143\) | −12.6687 | − | 5.20384i | −1.05941 | − | 0.435167i | ||||
\(144\) | 16.9791 | + | 12.6342i | 1.41492 | + | 1.05285i | ||||
\(145\) | 7.92246i | 0.657924i | ||||||||
\(146\) | −14.2026 | − | 24.5995i | −1.17541 | − | 2.03587i | ||||
\(147\) | −10.7560 | − | 3.56275i | −0.887141 | − | 0.293851i | ||||
\(148\) | −10.7499 | − | 6.20645i | −0.883636 | − | 0.510167i | ||||
\(149\) | −8.10115 | − | 4.67720i | −0.663672 | − | 0.383171i | 0.130002 | − | 0.991514i | \(-0.458501\pi\) |
−0.793675 | + | 0.608342i | \(0.791835\pi\) | |||||||
\(150\) | 1.38550 | − | 4.18286i | 0.113126 | − | 0.341529i | ||||
\(151\) | −11.4034 | + | 6.58377i | −0.927997 | + | 0.535779i | −0.886178 | − | 0.463346i | \(-0.846649\pi\) |
−0.0418195 | + | 0.999125i | \(0.513315\pi\) | |||||||
\(152\) | 20.1739 | 1.63632 | ||||||||
\(153\) | −1.67341 | + | 0.722304i | −0.135287 | + | 0.0583948i | ||||
\(154\) | 6.54137i | 0.527118i | ||||||||
\(155\) | 3.04604 | + | 5.27590i | 0.244664 | + | 0.423770i | ||||
\(156\) | 9.24993 | + | 26.3512i | 0.740587 | + | 2.10978i | ||||
\(157\) | −1.74463 | + | 3.02179i | −0.139237 | + | 0.241165i | −0.927208 | − | 0.374547i | \(-0.877798\pi\) |
0.787971 | + | 0.615712i | \(0.211132\pi\) | |||||||
\(158\) | 10.8800 | + | 6.28156i | 0.865565 | + | 0.499734i | ||||
\(159\) | −0.968052 | − | 4.68550i | −0.0767716 | − | 0.371584i | ||||
\(160\) | −2.68480 | − | 4.65021i | −0.212252 | − | 0.367632i | ||||
\(161\) | − | 3.27558i | − | 0.258152i | ||||||
\(162\) | −5.26972 | + | 22.2814i | −0.414029 | + | 1.75059i | ||||
\(163\) | 2.43727i | 0.190902i | 0.995434 | + | 0.0954508i | \(0.0304293\pi\) | ||||
−0.995434 | + | 0.0954508i | \(0.969571\pi\) | |||||||
\(164\) | 14.5286 | − | 8.38807i | 1.13449 | − | 0.654998i | ||||
\(165\) | 1.33120 | + | 6.44319i | 0.103634 | + | 0.501602i | ||||
\(166\) | 14.9661 | − | 25.9221i | 1.16160 | − | 2.01194i | ||||
\(167\) | −3.38013 | − | 1.95152i | −0.261563 | − | 0.151013i | 0.363485 | − | 0.931600i | \(-0.381587\pi\) |
−0.625047 | + | 0.780587i | \(0.714920\pi\) | |||||||
\(168\) | 5.50740 | − | 4.90233i | 0.424905 | − | 0.378223i | ||||
\(169\) | −3.29053 | + | 12.5767i | −0.253118 | + | 0.967436i | ||||
\(170\) | 1.54560 | 0.118542 | ||||||||
\(171\) | 3.81387 | + | 8.83583i | 0.291654 | + | 0.675693i | ||||
\(172\) | −51.0342 | −3.89132 | ||||||||
\(173\) | 12.0167 | + | 20.8135i | 0.913611 | + | 1.58242i | 0.808922 | + | 0.587917i | \(0.200052\pi\) |
0.104690 | + | 0.994505i | \(0.466615\pi\) | |||||||
\(174\) | −10.9766 | + | 33.1385i | −0.832133 | + | 2.51223i | ||||
\(175\) | −0.586224 | − | 0.338456i | −0.0443143 | − | 0.0255849i | ||||
\(176\) | 23.2072 | + | 13.3987i | 1.74931 | + | 1.00996i | ||||
\(177\) | 1.45464 | − | 4.39159i | 0.109338 | − | 0.330092i | ||||
\(178\) | 21.0524 | + | 36.4639i | 1.57795 | + | 2.73308i | ||||
\(179\) | 2.19010 | 0.163696 | 0.0818479 | − | 0.996645i | \(-0.473918\pi\) | ||||
0.0818479 | + | 0.996645i | \(0.473918\pi\) | |||||||
\(180\) | 8.00891 | − | 10.7631i | 0.596949 | − | 0.802236i | ||||
\(181\) | 16.7453 | 1.24466 | 0.622332 | − | 0.782753i | \(-0.286185\pi\) | ||||
0.622332 | + | 0.782753i | \(0.286185\pi\) | |||||||
\(182\) | 6.15348 | − | 0.828590i | 0.456126 | − | 0.0614191i | ||||
\(183\) | 4.82692 | − | 4.29661i | 0.356816 | − | 0.317615i | ||||
\(184\) | −26.3542 | − | 15.2156i | −1.94286 | − | 1.12171i | ||||
\(185\) | −1.38785 | + | 2.40383i | −0.102037 | + | 0.176733i | ||||
\(186\) | 5.43139 | + | 26.2886i | 0.398249 | + | 1.92758i | ||||
\(187\) | −1.99861 | + | 1.15390i | −0.146153 | + | 0.0843813i | ||||
\(188\) | − | 38.0507i | − | 2.77513i | ||||||
\(189\) | 3.18832 | + | 1.48537i | 0.231916 | + | 0.108045i | ||||
\(190\) | − | 8.16101i | − | 0.592062i | ||||||
\(191\) | −10.8226 | − | 18.7453i | −0.783096 | − | 1.35636i | −0.930130 | − | 0.367231i | \(-0.880306\pi\) |
0.147034 | − | 0.989131i | \(-0.453027\pi\) | |||||||
\(192\) | 0.157343 | + | 0.761561i | 0.0113553 | + | 0.0549610i | ||||
\(193\) | 2.65041 | + | 1.53022i | 0.190781 | + | 0.110147i | 0.592348 | − | 0.805682i | \(-0.298201\pi\) |
−0.401567 | + | 0.915830i | \(0.631534\pi\) | |||||||
\(194\) | 6.58089 | − | 11.3984i | 0.472480 | − | 0.818360i | ||||
\(195\) | 5.89251 | − | 2.06842i | 0.421971 | − | 0.148123i | ||||
\(196\) | 14.6274 | + | 25.3354i | 1.04481 | + | 1.80967i | ||||
\(197\) | − | 19.2776i | − | 1.37347i | −0.726906 | − | 0.686737i | \(-0.759042\pi\) | ||
0.726906 | − | 0.686737i | \(-0.240958\pi\) | |||||||
\(198\) | −3.35883 | + | 28.7954i | −0.238702 | + | 2.04640i | ||||
\(199\) | −0.196595 | −0.0139363 | −0.00696813 | − | 0.999976i | \(-0.502218\pi\) | ||||
−0.00696813 | + | 0.999976i | \(0.502218\pi\) | |||||||
\(200\) | −5.44621 | + | 3.14437i | −0.385105 | + | 0.222341i | ||||
\(201\) | −1.83916 | + | 5.55245i | −0.129724 | + | 0.391640i | ||||
\(202\) | −39.6765 | − | 22.9073i | −2.79163 | − | 1.61175i | ||||
\(203\) | 4.64433 | + | 2.68141i | 0.325968 | + | 0.188198i | ||||
\(204\) | 4.46719 | + | 1.47968i | 0.312766 | + | 0.103598i | ||||
\(205\) | −1.87570 | − | 3.24880i | −0.131004 | − | 0.226906i | ||||
\(206\) | − | 1.03076i | − | 0.0718168i | ||||||
\(207\) | 1.68193 | − | 14.4192i | 0.116902 | − | 1.00221i | ||||
\(208\) | 9.66455 | − | 23.5283i | 0.670116 | − | 1.63139i | ||||
\(209\) | 6.09274 | + | 10.5529i | 0.421444 | + | 0.729962i | ||||
\(210\) | −1.98316 | − | 2.22793i | −0.136851 | − | 0.153742i | ||||
\(211\) | 10.5773 | − | 18.3205i | 0.728174 | − | 1.26123i | −0.229480 | − | 0.973313i | \(-0.573703\pi\) |
0.957654 | − | 0.287921i | \(-0.0929641\pi\) | |||||||
\(212\) | −6.17649 | + | 10.6980i | −0.424203 | + | 0.734742i | ||||
\(213\) | 16.7532 | − | 3.46131i | 1.14791 | − | 0.237165i | ||||
\(214\) | 8.70951 | − | 5.02844i | 0.595370 | − | 0.343737i | ||||
\(215\) | 11.4120i | 0.778291i | ||||||||
\(216\) | 26.7610 | − | 18.7523i | 1.82086 | − | 1.27593i | ||||
\(217\) | 4.12381 | 0.279942 | ||||||||
\(218\) | −19.3355 | − | 33.4900i | −1.30956 | − | 2.26823i | ||||
\(219\) | −18.9392 | + | 3.91295i | −1.27979 | + | 0.264413i | ||||
\(220\) | 8.49351 | − | 14.7112i | 0.572632 | − | 0.991828i | ||||
\(221\) | 1.33864 | + | 1.73393i | 0.0900464 | + | 0.116637i | ||||
\(222\) | −9.13572 | + | 8.13202i | −0.613149 | + | 0.545786i | ||||
\(223\) | −17.1482 | + | 9.90054i | −1.14833 | + | 0.662989i | −0.948480 | − | 0.316837i | \(-0.897379\pi\) |
−0.199851 | + | 0.979826i | \(0.564046\pi\) | |||||||
\(224\) | −3.63475 | −0.242857 | ||||||||
\(225\) | −2.40679 | − | 1.79091i | −0.160453 | − | 0.119394i | ||||
\(226\) | − | 22.8245i | − | 1.51826i | ||||||
\(227\) | −0.525321 | + | 0.303295i | −0.0348668 | + | 0.0201304i | −0.517332 | − | 0.855785i | \(-0.673075\pi\) |
0.482465 | + | 0.875915i | \(0.339741\pi\) | |||||||
\(228\) | 7.81294 | − | 23.5874i | 0.517424 | − | 1.56211i | ||||
\(229\) | −19.9475 | − | 11.5167i | −1.31817 | − | 0.761045i | −0.334735 | − | 0.942312i | \(-0.608647\pi\) |
−0.983434 | + | 0.181267i | \(0.941980\pi\) | |||||||
\(230\) | −6.15523 | + | 10.6612i | −0.405864 | + | 0.702977i | ||||
\(231\) | 4.22771 | + | 1.40036i | 0.278163 | + | 0.0921368i | ||||
\(232\) | 43.1473 | − | 24.9111i | 2.83276 | − | 1.63550i | ||||
\(233\) | −18.0736 | −1.18404 | −0.592019 | − | 0.805924i | \(-0.701669\pi\) | ||||
−0.592019 | + | 0.805924i | \(0.701669\pi\) | |||||||
\(234\) | 27.5133 | − | 0.487821i | 1.79860 | − | 0.0318899i | ||||
\(235\) | −8.50870 | −0.555046 | ||||||||
\(236\) | −10.3442 | + | 5.97224i | −0.673351 | + | 0.388760i | ||||
\(237\) | 6.38895 | − | 5.68703i | 0.415007 | − | 0.369412i | ||||
\(238\) | 0.523119 | − | 0.906069i | 0.0339088 | − | 0.0587318i | ||||
\(239\) | 7.36098 | + | 4.24987i | 0.476142 | + | 0.274901i | 0.718807 | − | 0.695209i | \(-0.244688\pi\) |
−0.242665 | + | 0.970110i | \(0.578022\pi\) | |||||||
\(240\) | −11.9663 | + | 2.47230i | −0.772420 | + | 0.159587i | ||||
\(241\) | −12.3577 | + | 7.13471i | −0.796028 | + | 0.459587i | −0.842080 | − | 0.539352i | \(-0.818669\pi\) |
0.0460526 | + | 0.998939i | \(0.485336\pi\) | |||||||
\(242\) | 8.72327i | 0.560753i | ||||||||
\(243\) | 13.2724 | + | 8.17578i | 0.851425 | + | 0.524476i | ||||
\(244\) | −16.6847 | −1.06813 | ||||||||
\(245\) | 5.66536 | − | 3.27089i | 0.361946 | − | 0.208970i | ||||
\(246\) | −3.34455 | − | 16.1881i | −0.213241 | − | 1.03211i | ||||
\(247\) | 9.15542 | − | 7.06819i | 0.582545 | − | 0.449738i | ||||
\(248\) | 19.1558 | − | 33.1787i | 1.21639 | − | 2.10685i | ||||
\(249\) | −13.5496 | − | 15.2220i | −0.858671 | − | 0.964653i | ||||
\(250\) | 1.27200 | + | 2.20318i | 0.0804486 | + | 0.139341i | ||||
\(251\) | −24.8161 | −1.56638 | −0.783190 | − | 0.621782i | \(-0.786409\pi\) | ||||
−0.783190 | + | 0.621782i | \(0.786409\pi\) | |||||||
\(252\) | −3.59893 | − | 8.33786i | −0.226711 | − | 0.525236i | ||||
\(253\) | − | 18.3812i | − | 1.15561i | ||||||
\(254\) | 26.9093 | − | 15.5361i | 1.68844 | − | 0.974820i | ||||
\(255\) | 0.330879 | − | 0.998929i | 0.0207204 | − | 0.0625553i | ||||
\(256\) | 14.6642 | − | 25.3992i | 0.916514 | − | 1.58745i | ||||
\(257\) | 5.36793 | − | 9.29754i | 0.334843 | − | 0.579964i | −0.648612 | − | 0.761119i | \(-0.724650\pi\) |
0.983455 | + | 0.181155i | \(0.0579835\pi\) | |||||||
\(258\) | −15.8113 | + | 47.7347i | −0.984371 | + | 2.97184i | ||||
\(259\) | 0.939456 | + | 1.62719i | 0.0583749 | + | 0.101108i | ||||
\(260\) | −14.9147 | − | 6.12641i | −0.924972 | − | 0.379944i | ||||
\(261\) | 19.0677 | + | 14.1884i | 1.18026 | + | 0.878240i | ||||
\(262\) | 44.3591i | 2.74052i | ||||||||
\(263\) | 6.34254 | + | 10.9856i | 0.391097 | + | 0.677401i | 0.992595 | − | 0.121474i | \(-0.0387622\pi\) |
−0.601497 | + | 0.798875i | \(0.705429\pi\) | |||||||
\(264\) | 30.9052 | − | 27.5098i | 1.90208 | − | 1.69311i | ||||
\(265\) | 2.39223 | + | 1.38115i | 0.146953 | + | 0.0848436i | ||||
\(266\) | −4.78418 | − | 2.76215i | −0.293337 | − | 0.169358i | ||||
\(267\) | 28.0735 | − | 5.80016i | 1.71807 | − | 0.354964i | ||||
\(268\) | 13.0786 | − | 7.55092i | 0.798901 | − | 0.461246i | ||||
\(269\) | 29.1526 | 1.77746 | 0.888732 | − | 0.458427i | \(-0.151587\pi\) | ||||
0.888732 | + | 0.458427i | \(0.151587\pi\) | |||||||
\(270\) | −7.58596 | − | 10.8257i | −0.461667 | − | 0.658834i | ||||
\(271\) | 26.5925i | 1.61538i | 0.589607 | + | 0.807690i | \(0.299282\pi\) | ||||
−0.589607 | + | 0.807690i | \(0.700718\pi\) | |||||||
\(272\) | −2.14301 | − | 3.71181i | −0.129939 | − | 0.225061i | ||||
\(273\) | 0.781800 | − | 4.15440i | 0.0473167 | − | 0.251436i | ||||
\(274\) | 15.5601 | − | 26.9509i | 0.940020 | − | 1.62816i | ||||
\(275\) | −3.28964 | − | 1.89927i | −0.198373 | − | 0.114530i | ||||
\(276\) | −27.9966 | + | 24.9208i | −1.68520 | + | 1.50006i | ||||
\(277\) | 0.909279 | + | 1.57492i | 0.0546333 | + | 0.0946276i | 0.892049 | − | 0.451939i | \(-0.149268\pi\) |
−0.837415 | + | 0.546567i | \(0.815934\pi\) | |||||||
\(278\) | − | 13.2084i | − | 0.792186i | ||||||
\(279\) | 18.1532 | + | 2.11747i | 1.08680 | + | 0.126770i | ||||
\(280\) | 4.25693i | 0.254400i | ||||||||
\(281\) | −17.6054 | + | 10.1645i | −1.05025 | + | 0.606363i | −0.922720 | − | 0.385472i | \(-0.874039\pi\) |
−0.127531 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(282\) | −35.5907 | − | 11.7888i | −2.11940 | − | 0.702015i | ||||
\(283\) | −1.72180 | + | 2.98225i | −0.102351 | + | 0.177276i | −0.912653 | − | 0.408736i | \(-0.865970\pi\) |
0.810302 | + | 0.586012i | \(0.199303\pi\) | |||||||
\(284\) | −38.2511 | − | 22.0843i | −2.26979 | − | 1.31046i | ||||
\(285\) | −5.27449 | − | 1.74709i | −0.312434 | − | 0.103488i | ||||
\(286\) | 34.5307 | − | 4.64969i | 2.04184 | − | 0.274942i | ||||
\(287\) | −2.53936 | −0.149894 | ||||||||
\(288\) | −16.0003 | − | 1.86636i | −0.942828 | − | 0.109976i | ||||
\(289\) | −16.6309 | −0.978287 | ||||||||
\(290\) | −10.0774 | − | 17.4546i | −0.591765 | − | 1.02497i | ||||
\(291\) | −5.95802 | − | 6.69339i | −0.349265 | − | 0.392374i | ||||
\(292\) | 43.2423 | + | 24.9659i | 2.53056 | + | 1.46102i | ||||
\(293\) | 27.1894 | + | 15.6978i | 1.58842 | + | 0.917074i | 0.993568 | + | 0.113238i | \(0.0361222\pi\) |
0.594851 | + | 0.803836i | \(0.297211\pi\) | |||||||
\(294\) | 28.2292 | − | 5.83233i | 1.64636 | − | 0.340148i | ||||
\(295\) | 1.33548 | + | 2.31312i | 0.0777546 | + | 0.134675i | ||||
\(296\) | 17.4557 | 1.01459 | ||||||||
\(297\) | 17.8915 | + | 8.33525i | 1.03817 | + | 0.483661i | ||||
\(298\) | 23.7977 | 1.37856 | ||||||||
\(299\) | −17.2912 | + | 2.32833i | −0.999977 | + | 0.134651i | ||||
\(300\) | 1.56721 | + | 7.58549i | 0.0904828 | + | 0.437949i | ||||
\(301\) | 6.68998 | + | 3.86246i | 0.385604 | + | 0.222628i | ||||
\(302\) | 16.7492 | − | 29.0104i | 0.963806 | − | 1.66936i | ||||
\(303\) | −23.2989 | + | 20.7391i | −1.33849 | + | 1.19143i | ||||
\(304\) | −19.5989 | + | 11.3154i | −1.12407 | + | 0.648984i | ||||
\(305\) | 3.73095i | 0.213634i | ||||||||
\(306\) | 2.76804 | − | 3.71995i | 0.158238 | − | 0.212655i | ||||
\(307\) | 20.5855i | 1.17488i | 0.809268 | + | 0.587439i | \(0.199864\pi\) | ||||
−0.809268 | + | 0.587439i | \(0.800136\pi\) | |||||||
\(308\) | −5.74936 | − | 9.95819i | −0.327600 | − | 0.567421i | ||||
\(309\) | −0.666186 | − | 0.220663i | −0.0378980 | − | 0.0125531i | ||||
\(310\) | −13.4219 | − | 7.74915i | −0.762314 | − | 0.440122i | ||||
\(311\) | −11.5579 | + | 20.0188i | −0.655386 | + | 1.13516i | 0.326411 | + | 0.945228i | \(0.394161\pi\) |
−0.981797 | + | 0.189933i | \(0.939173\pi\) | |||||||
\(312\) | −29.7933 | − | 25.5879i | −1.68671 | − | 1.44863i | ||||
\(313\) | −7.44844 | − | 12.9011i | −0.421011 | − | 0.729212i | 0.575028 | − | 0.818134i | \(-0.304991\pi\) |
−0.996039 | + | 0.0889216i | \(0.971658\pi\) | |||||||
\(314\) | − | 8.87672i | − | 0.500942i | ||||||
\(315\) | −1.86447 | + | 0.804773i | −0.105051 | + | 0.0453438i | ||||
\(316\) | −22.0841 | −1.24232 | ||||||||
\(317\) | 5.64495 | − | 3.25911i | 0.317052 | − | 0.183050i | −0.333026 | − | 0.942918i | \(-0.608070\pi\) |
0.650078 | + | 0.759868i | \(0.274736\pi\) | |||||||
\(318\) | 8.09277 | + | 9.09162i | 0.453820 | + | 0.509833i | ||||
\(319\) | 26.0620 | + | 15.0469i | 1.45919 | + | 0.842465i | ||||
\(320\) | −0.388823 | − | 0.224487i | −0.0217359 | − | 0.0125492i | ||||
\(321\) | −1.38539 | − | 6.70546i | −0.0773248 | − | 0.374262i | ||||
\(322\) | 4.16655 | + | 7.21668i | 0.232193 | + | 0.402170i | ||||
\(323\) | − | 1.94897i | − | 0.108444i | ||||||
\(324\) | −11.5613 | − | 38.5516i | −0.642296 | − | 2.14175i | ||||
\(325\) | −1.36996 | + | 3.33515i | −0.0759915 | + | 0.185001i | ||||
\(326\) | −3.10022 | − | 5.36973i | −0.171705 | − | 0.297402i | ||||
\(327\) | −25.7840 | + | 5.32713i | −1.42586 | + | 0.294591i | ||||
\(328\) | −11.7958 | + | 20.4309i | −0.651312 | + | 1.12811i | ||||
\(329\) | −2.87982 | + | 4.98800i | −0.158770 | + | 0.274997i | ||||
\(330\) | −11.1286 | − | 12.5022i | −0.612612 | − | 0.688223i | ||||
\(331\) | 7.20428 | − | 4.15939i | 0.395983 | − | 0.228621i | −0.288766 | − | 0.957400i | \(-0.593245\pi\) |
0.684749 | + | 0.728779i | \(0.259912\pi\) | |||||||
\(332\) | 52.6163i | 2.88769i | ||||||||
\(333\) | 3.30000 | + | 7.64532i | 0.180839 | + | 0.418961i | ||||
\(334\) | 9.92937 | 0.543311 | ||||||||
\(335\) | −1.68849 | − | 2.92456i | −0.0922523 | − | 0.159786i | ||||
\(336\) | −2.60074 | + | 7.85168i | −0.141882 | + | 0.428344i | ||||
\(337\) | 1.36437 | − | 2.36316i | 0.0743219 | − | 0.128729i | −0.826469 | − | 0.562982i | \(-0.809654\pi\) |
0.900791 | + | 0.434253i | \(0.142987\pi\) | |||||||
\(338\) | −8.74795 | − | 31.8942i | −0.475826 | − | 1.73481i | ||||
\(339\) | −14.7515 | − | 4.88619i | −0.801192 | − | 0.265382i | ||||
\(340\) | −2.35294 | + | 1.35847i | −0.127606 | + | 0.0736733i | ||||
\(341\) | 23.1410 | 1.25316 | ||||||||
\(342\) | −19.6419 | − | 14.6156i | −1.06211 | − | 0.790323i | ||||
\(343\) | − | 9.16661i | − | 0.494950i | ||||||
\(344\) | 62.1520 | − | 35.8835i | 3.35101 | − | 1.93471i | ||||
\(345\) | 5.57265 | + | 6.26046i | 0.300022 | + | 0.337052i | ||||
\(346\) | −52.9497 | − | 30.5705i | −2.84660 | − | 1.64348i | ||||
\(347\) | −14.6740 | + | 25.4161i | −0.787742 | + | 1.36441i | 0.139605 | + | 0.990207i | \(0.455417\pi\) |
−0.927347 | + | 0.374202i | \(0.877917\pi\) | |||||||
\(348\) | −12.4161 | − | 60.0957i | −0.665575 | − | 3.22147i | ||||
\(349\) | 19.9745 | − | 11.5323i | 1.06921 | − | 0.617309i | 0.141245 | − | 0.989975i | \(-0.454889\pi\) |
0.927966 | + | 0.372665i | \(0.121556\pi\) | |||||||
\(350\) | 1.72207 | 0.0920486 | ||||||||
\(351\) | 5.57470 | − | 17.8864i | 0.297555 | − | 0.954705i | ||||
\(352\) | −20.3967 | −1.08715 | ||||||||
\(353\) | 2.12425 | − | 1.22644i | 0.113062 | − | 0.0652766i | −0.442402 | − | 0.896817i | \(-0.645874\pi\) |
0.555465 | + | 0.831540i | \(0.312540\pi\) | |||||||
\(354\) | 2.38129 | + | 11.5258i | 0.126564 | + | 0.612587i | ||||
\(355\) | −4.93837 | + | 8.55350i | −0.262101 | + | 0.453973i | ||||
\(356\) | −64.0979 | − | 37.0070i | −3.39718 | − | 1.96136i | ||||
\(357\) | −0.473608 | − | 0.532063i | −0.0250660 | − | 0.0281597i | ||||
\(358\) | −4.82518 | + | 2.78582i | −0.255019 | + | 0.147235i | ||||
\(359\) | 25.3421i | 1.33750i | 0.743486 | + | 0.668751i | \(0.233171\pi\) | ||||
−0.743486 | + | 0.668751i | \(0.766829\pi\) | |||||||
\(360\) | −2.18583 | + | 18.7392i | −0.115203 | + | 0.987641i | ||||
\(361\) | 8.70916 | 0.458377 | ||||||||
\(362\) | −36.8927 | + | 21.3000i | −1.93904 | + | 1.11951i | ||||
\(363\) | 5.63788 | + | 1.86745i | 0.295912 | + | 0.0980159i | ||||
\(364\) | −8.63943 | + | 6.66984i | −0.452829 | + | 0.349595i | ||||
\(365\) | 5.58274 | − | 9.66960i | 0.292214 | − | 0.506130i | ||||
\(366\) | −5.16925 | + | 15.6061i | −0.270201 | + | 0.815742i | ||||
\(367\) | −6.18953 | − | 10.7206i | −0.323091 | − | 0.559609i | 0.658033 | − | 0.752989i | \(-0.271389\pi\) |
−0.981124 | + | 0.193379i | \(0.938055\pi\) | |||||||
\(368\) | 34.1375 | 1.77954 | ||||||||
\(369\) | −11.1784 | − | 1.30390i | −0.581923 | − | 0.0678784i | ||||
\(370\) | − | 7.06142i | − | 0.367106i | ||||||
\(371\) | 1.61933 | − | 0.934921i | 0.0840715 | − | 0.0485387i | ||||
\(372\) | −31.3741 | − | 35.2465i | −1.62667 | − | 1.82745i | ||||
\(373\) | −13.6097 | + | 23.5726i | −0.704681 | + | 1.22054i | 0.262125 | + | 0.965034i | \(0.415577\pi\) |
−0.966806 | + | 0.255510i | \(0.917757\pi\) | |||||||
\(374\) | 2.93552 | − | 5.08448i | 0.151792 | − | 0.262912i | ||||
\(375\) | 1.69623 | − | 0.350451i | 0.0875928 | − | 0.0180972i | ||||
\(376\) | 26.7545 | + | 46.3401i | 1.37976 | + | 2.38981i | ||||
\(377\) | 10.8534 | − | 26.4226i | 0.558979 | − | 1.36083i | ||||
\(378\) | −8.91382 | + | 0.783026i | −0.458478 | + | 0.0402745i | ||||
\(379\) | − | 5.72921i | − | 0.294290i | −0.989115 | − | 0.147145i | \(-0.952992\pi\) | ||
0.989115 | − | 0.147145i | \(-0.0470083\pi\) | |||||||
\(380\) | 7.17291 | + | 12.4238i | 0.367962 | + | 0.637330i | ||||
\(381\) | −4.28035 | − | 20.7175i | −0.219289 | − | 1.06139i | ||||
\(382\) | 47.6882 | + | 27.5328i | 2.43994 | + | 1.40870i | ||||
\(383\) | 0.496892 | + | 0.286881i | 0.0253900 | + | 0.0146589i | 0.512641 | − | 0.858603i | \(-0.328667\pi\) |
−0.487251 | + | 0.873262i | \(0.662000\pi\) | |||||||
\(384\) | −13.6828 | − | 15.3716i | −0.698246 | − | 0.784427i | ||||
\(385\) | −2.22680 | + | 1.28564i | −0.113488 | + | 0.0655224i | ||||
\(386\) | −7.78577 | −0.396285 | ||||||||
\(387\) | 27.4663 | + | 20.4378i | 1.39619 | + | 1.03891i | ||||
\(388\) | 23.1364i | 1.17457i | ||||||||
\(389\) | 12.0269 | + | 20.8311i | 0.609786 | + | 1.05618i | 0.991275 | + | 0.131807i | \(0.0420780\pi\) |
−0.381489 | + | 0.924373i | \(0.624589\pi\) | |||||||
\(390\) | −10.3512 | + | 12.0524i | −0.524153 | + | 0.610296i | ||||
\(391\) | −1.46996 | + | 2.54605i | −0.0743391 | + | 0.128759i | ||||
\(392\) | −35.6279 | − | 20.5698i | −1.79948 | − | 1.03893i | ||||
\(393\) | 28.6694 | + | 9.49628i | 1.44618 | + | 0.479024i | ||||
\(394\) | 24.5212 | + | 42.4720i | 1.23536 | + | 2.13971i | ||||
\(395\) | 4.93832i | 0.248474i | ||||||||
\(396\) | −20.1956 | − | 46.7885i | −1.01487 | − | 2.35121i | ||||
\(397\) | − | 8.67254i | − | 0.435262i | −0.976031 | − | 0.217631i | \(-0.930167\pi\) | ||
0.976031 | − | 0.217631i | \(-0.0698330\pi\) | |||||||
\(398\) | 0.433133 | − | 0.250070i | 0.0217110 | − | 0.0125349i | ||||
\(399\) | −2.80937 | + | 2.50072i | −0.140644 | + | 0.125192i | ||||
\(400\) | 3.52732 | − | 6.10950i | 0.176366 | − | 0.305475i | ||||
\(401\) | 0.00995431 | + | 0.00574712i | 0.000497095 | + | 0.000286998i | 0.500249 | − | 0.865882i | \(-0.333242\pi\) |
−0.499751 | + | 0.866169i | \(0.666575\pi\) | |||||||
\(402\) | −3.01075 | − | 14.5724i | −0.150163 | − | 0.726807i | ||||
\(403\) | −2.93126 | − | 21.7688i | −0.146016 | − | 1.08438i | ||||
\(404\) | 80.5349 | 4.00676 | ||||||||
\(405\) | −8.62069 | + | 2.58528i | −0.428366 | + | 0.128464i | ||||
\(406\) | −13.6430 | −0.677093 | ||||||||
\(407\) | 5.27183 | + | 9.13107i | 0.261315 | + | 0.452610i | ||||
\(408\) | −6.48078 | + | 1.33897i | −0.320846 | + | 0.0662887i | ||||
\(409\) | 26.5614 | + | 15.3352i | 1.31338 | + | 0.758279i | 0.982654 | − | 0.185449i | \(-0.0593738\pi\) |
0.330724 | + | 0.943728i | \(0.392707\pi\) | |||||||
\(410\) | 8.26497 | + | 4.77179i | 0.408178 | + | 0.235662i | ||||
\(411\) | −14.0874 | − | 15.8261i | −0.694879 | − | 0.780644i | ||||
\(412\) | 0.905963 | + | 1.56917i | 0.0446336 | + | 0.0773077i | ||||
\(413\) | 1.80801 | 0.0889662 | ||||||||
\(414\) | 14.6357 | + | 33.9076i | 0.719308 | + | 1.66647i | ||||
\(415\) | 11.7658 | 0.577559 | ||||||||
\(416\) | 2.58363 | + | 19.1872i | 0.126673 | + | 0.940731i | ||||
\(417\) | −8.53661 | − | 2.82761i | −0.418040 | − | 0.138469i | ||||
\(418\) | −26.8468 | − | 15.5000i | −1.31312 | − | 0.758129i | ||||
\(419\) | 11.3914 | − | 19.7304i | 0.556505 | − | 0.963895i | −0.441280 | − | 0.897370i | \(-0.645475\pi\) |
0.997785 | − | 0.0665255i | \(-0.0211914\pi\) | |||||||
\(420\) | 4.97723 | + | 1.64862i | 0.242864 | + | 0.0804446i | ||||
\(421\) | −15.2034 | + | 8.77766i | −0.740966 | + | 0.427797i | −0.822421 | − | 0.568880i | \(-0.807377\pi\) |
0.0814542 | + | 0.996677i | \(0.474044\pi\) | |||||||
\(422\) | 53.8177i | 2.61980i | ||||||||
\(423\) | −15.2383 | + | 20.4787i | −0.740912 | + | 0.995706i | ||||
\(424\) | − | 17.3714i | − | 0.843632i | ||||||
\(425\) | 0.303773 | + | 0.526151i | 0.0147352 | + | 0.0255221i | ||||
\(426\) | −32.5074 | + | 28.9360i | −1.57499 | + | 1.40195i | ||||
\(427\) | 2.18717 | + | 1.26276i | 0.105845 | + | 0.0611095i | ||||
\(428\) | −8.83923 | + | 15.3100i | −0.427260 | + | 0.740037i | ||||
\(429\) | 4.38713 | − | 23.3127i | 0.211813 | − | 1.12555i | ||||
\(430\) | −14.5161 | − | 25.1426i | −0.700028 | − | 1.21248i | ||||
\(431\) | 1.01234i | 0.0487625i | 0.999703 | + | 0.0243813i | \(0.00776157\pi\) | ||||
−0.999703 | + | 0.0243813i | \(0.992238\pi\) | |||||||
\(432\) | −15.4802 | + | 33.2280i | −0.744792 | + | 1.59868i | ||||
\(433\) | −10.0230 | −0.481676 | −0.240838 | − | 0.970565i | \(-0.577422\pi\) | ||||
−0.240838 | + | 0.970565i | \(0.577422\pi\) | |||||||
\(434\) | −9.08547 | + | 5.24550i | −0.436117 | + | 0.251792i | ||||
\(435\) | −13.4383 | + | 2.77643i | −0.644316 | + | 0.133120i | ||||
\(436\) | 58.8704 | + | 33.9888i | 2.81938 | + | 1.62777i | ||||
\(437\) | 13.4435 | + | 7.76160i | 0.643089 | + | 0.371288i | ||||
\(438\) | 36.7491 | − | 32.7117i | 1.75594 | − | 1.56302i | ||||
\(439\) | 20.6121 | + | 35.7012i | 0.983762 | + | 1.70393i | 0.647313 | + | 0.762224i | \(0.275893\pi\) |
0.336449 | + | 0.941702i | \(0.390774\pi\) | |||||||
\(440\) | 23.8881i | 1.13882i | ||||||||
\(441\) | 2.27378 | − | 19.4932i | 0.108275 | − | 0.928248i | ||||
\(442\) | −5.15482 | − | 2.11741i | −0.245190 | − | 0.100715i | ||||
\(443\) | −1.58945 | − | 2.75302i | −0.0755173 | − | 0.130800i | 0.825794 | − | 0.563972i | \(-0.190727\pi\) |
−0.901311 | + | 0.433172i | \(0.857394\pi\) | |||||||
\(444\) | 6.76025 | − | 20.4093i | 0.320827 | − | 0.968583i | ||||
\(445\) | −8.27529 | + | 14.3332i | −0.392287 | + | 0.679460i | ||||
\(446\) | 25.1871 | − | 43.6253i | 1.19264 | − | 2.06572i | ||||
\(447\) | 5.09454 | − | 15.3805i | 0.240964 | − | 0.727474i | ||||
\(448\) | −0.263199 | + | 0.151958i | −0.0124350 | + | 0.00717934i | ||||
\(449\) | − | 14.5997i | − | 0.689001i | −0.938786 | − | 0.344500i | \(-0.888048\pi\) | ||
0.938786 | − | 0.344500i | \(-0.111952\pi\) | |||||||
\(450\) | 7.58063 | + | 0.884242i | 0.357354 | + | 0.0416836i | ||||
\(451\) | −14.2498 | −0.670998 | ||||||||
\(452\) | 20.0610 | + | 34.7466i | 0.943588 | + | 1.63434i | ||||
\(453\) | −15.1639 | − | 17.0355i | −0.712462 | − | 0.800397i | ||||
\(454\) | 0.771584 | − | 1.33642i | 0.0362122 | − | 0.0627214i | ||||
\(455\) | 1.49147 | + | 1.93190i | 0.0699213 | + | 0.0905690i | ||||
\(456\) | 7.06994 | + | 34.2194i | 0.331080 | + | 1.60247i | ||||
\(457\) | 7.43635 | − | 4.29338i | 0.347858 | − | 0.200836i | −0.315884 | − | 0.948798i | \(-0.602301\pi\) |
0.663741 | + | 0.747962i | \(0.268968\pi\) | |||||||
\(458\) | 58.5972 | 2.73807 | ||||||||
\(459\) | −1.81164 | − | 2.58535i | −0.0845600 | − | 0.120674i | ||||
\(460\) | − | 21.6399i | − | 1.00897i | ||||||
\(461\) | −7.22786 | + | 4.17301i | −0.336635 | + | 0.194356i | −0.658783 | − | 0.752333i | \(-0.728928\pi\) |
0.322148 | + | 0.946689i | \(0.395595\pi\) | |||||||
\(462\) | −11.0956 | + | 2.29243i | −0.516216 | + | 0.106653i | ||||
\(463\) | −18.6874 | − | 10.7892i | −0.868479 | − | 0.501417i | −0.00163665 | − | 0.999999i | \(-0.500521\pi\) |
−0.866843 | + | 0.498582i | \(0.833854\pi\) | |||||||
\(464\) | −27.9451 | + | 48.4023i | −1.29732 | + | 2.24702i | ||||
\(465\) | −7.88163 | + | 7.01572i | −0.365502 | + | 0.325346i | ||||
\(466\) | 39.8192 | − | 22.9897i | 1.84459 | − | 1.06498i | ||||
\(467\) | 11.1741 | 0.517078 | 0.258539 | − | 0.966001i | \(-0.416759\pi\) | ||||
0.258539 | + | 0.966001i | \(0.416759\pi\) | |||||||
\(468\) | −41.4559 | + | 24.9248i | −1.91630 | + | 1.15215i | ||||
\(469\) | −2.28593 | −0.105554 | ||||||||
\(470\) | 18.7462 | − | 10.8231i | 0.864696 | − | 0.499232i | ||||
\(471\) | −5.73705 | − | 1.90030i | −0.264349 | − | 0.0875613i | ||||
\(472\) | 8.39848 | − | 14.5466i | 0.386572 | − | 0.669562i | ||||
\(473\) | 37.5413 | + | 21.6745i | 1.72615 | + | 0.996593i | ||||
\(474\) | −6.84205 | + | 20.6563i | −0.314266 | + | 0.948775i | ||||
\(475\) | 2.77815 | − | 1.60397i | 0.127470 | − | 0.0735951i | ||||
\(476\) | 1.83913i | 0.0842963i | ||||||||
\(477\) | 7.60842 | − | 3.28407i | 0.348365 | − | 0.150367i | ||||
\(478\) | −21.6234 | −0.989031 | ||||||||
\(479\) | 14.9034 | − | 8.60450i | 0.680955 | − | 0.393150i | −0.119260 | − | 0.992863i | \(-0.538052\pi\) |
0.800215 | + | 0.599713i | \(0.204719\pi\) | |||||||
\(480\) | 6.94693 | − | 6.18370i | 0.317082 | − | 0.282246i | ||||
\(481\) | 7.92184 | − | 6.11585i | 0.361205 | − | 0.278859i | ||||
\(482\) | 18.1508 | − | 31.4380i | 0.826744 | − | 1.43196i | ||||
\(483\) | 5.55613 | − | 1.14793i | 0.252813 | − | 0.0522326i | ||||
\(484\) | −7.66709 | − | 13.2798i | −0.348504 | − | 0.603627i | ||||
\(485\) | 5.17364 | 0.234923 | ||||||||
\(486\) | −39.6411 | − | 1.13012i | −1.79816 | − | 0.0512632i | ||||
\(487\) | − | 11.0744i | − | 0.501829i | −0.968009 | − | 0.250915i | \(-0.919269\pi\) | ||
0.968009 | − | 0.250915i | \(-0.0807314\pi\) | |||||||
\(488\) | 20.3195 | − | 11.7315i | 0.919823 | − | 0.531060i | ||||
\(489\) | −4.13416 | + | 0.854142i | −0.186953 | + | 0.0386257i | ||||
\(490\) | −8.32118 | + | 14.4127i | −0.375913 | + | 0.651100i | ||||
\(491\) | −10.5950 | + | 18.3511i | −0.478147 | + | 0.828174i | −0.999686 | − | 0.0250528i | \(-0.992025\pi\) |
0.521539 | + | 0.853227i | \(0.325358\pi\) | |||||||
\(492\) | 19.3196 | + | 21.7041i | 0.870996 | + | 0.978498i | ||||
\(493\) | −2.40663 | − | 4.16841i | −0.108389 | − | 0.187736i | ||||
\(494\) | −11.1802 | + | 27.2182i | −0.503022 | + | 1.22460i | ||||
\(495\) | −10.4626 | + | 4.51604i | −0.470259 | + | 0.202981i | ||||
\(496\) | 42.9775i | 1.92975i | ||||||||
\(497\) | 3.34284 | + | 5.78997i | 0.149947 | + | 0.259716i | ||||
\(498\) | 49.2146 | + | 16.3015i | 2.20536 | + | 0.730488i | ||||
\(499\) | −14.4857 | − | 8.36330i | −0.648467 | − | 0.374393i | 0.139402 | − | 0.990236i | \(-0.455482\pi\) |
−0.787869 | + | 0.615843i | \(0.788815\pi\) | |||||||
\(500\) | −3.87285 | − | 2.23599i | −0.173199 | − | 0.0999965i | ||||
\(501\) | 2.12565 | − | 6.41738i | 0.0949671 | − | 0.286708i | ||||
\(502\) | 54.6743 | − | 31.5662i | 2.44023 | − | 1.40887i | ||||
\(503\) | −16.8199 | −0.749962 | −0.374981 | − | 0.927033i | \(-0.622351\pi\) | ||||
−0.374981 | + | 0.927033i | \(0.622351\pi\) | |||||||
\(504\) | 10.2455 | + | 7.62377i | 0.456372 | + | 0.339590i | ||||
\(505\) | − | 18.0088i | − | 0.801381i | ||||||
\(506\) | 23.3809 | + | 40.4970i | 1.03941 | + | 1.80031i | ||||
\(507\) | −22.4860 | − | 1.17398i | −0.998640 | − | 0.0521385i | ||||
\(508\) | −27.3101 | + | 47.3024i | −1.21169 | + | 2.09870i | ||||
\(509\) | −24.2677 | − | 14.0110i | −1.07565 | − | 0.621025i | −0.145928 | − | 0.989295i | \(-0.546617\pi\) |
−0.929719 | + | 0.368270i | \(0.879950\pi\) | |||||||
\(510\) | 0.541658 | + | 2.62169i | 0.0239850 | + | 0.116091i | ||||
\(511\) | −3.77903 | − | 6.54547i | −0.167174 | − | 0.289555i | ||||
\(512\) | 50.8490i | 2.24723i | ||||||||
\(513\) | −13.6510 | + | 9.56571i | −0.602707 | + | 0.422337i | ||||
\(514\) | 27.3121i | 1.20469i | ||||||||
\(515\) | 0.350890 | − | 0.202587i | 0.0154621 | − | 0.00892703i | ||||
\(516\) | −17.8850 | − | 86.5655i | −0.787341 | − | 3.81083i | ||||
\(517\) | −16.1603 | + | 27.9905i | −0.710731 | + | 1.23102i | ||||
\(518\) | −4.13957 | − | 2.38998i | −0.181882 | − | 0.105010i | ||||
\(519\) | −31.0932 | + | 27.6771i | −1.36484 | + | 1.21489i | ||||
\(520\) | 22.4716 | − | 3.02588i | 0.985443 | − | 0.132694i | ||||
\(521\) | −26.2509 | −1.15007 | −0.575037 | − | 0.818127i | \(-0.695012\pi\) | ||||
−0.575037 | + | 0.818127i | \(0.695012\pi\) | |||||||
\(522\) | −60.0572 | − | 7.00537i | −2.62863 | − | 0.306617i | ||||
\(523\) | −2.41985 | −0.105812 | −0.0529062 | − | 0.998599i | \(-0.516848\pi\) | ||||
−0.0529062 | + | 0.998599i | \(0.516848\pi\) | |||||||
\(524\) | −38.9883 | − | 67.5297i | −1.70321 | − | 2.95005i | ||||
\(525\) | 0.368656 | − | 1.11298i | 0.0160895 | − | 0.0485744i | ||||
\(526\) | −27.9474 | − | 16.1355i | −1.21857 | − | 0.703540i | ||||
\(527\) | −3.20535 | − | 1.85061i | −0.139627 | − | 0.0806139i | ||||
\(528\) | −14.5942 | + | 44.0603i | −0.635133 | + | 1.91748i | ||||
\(529\) | −0.207971 | − | 0.360217i | −0.00904223 | − | 0.0156616i | ||||
\(530\) | −7.02734 | −0.305248 | ||||||||
\(531\) | 7.95892 | + | 0.928367i | 0.345388 | + | 0.0402877i | ||||
\(532\) | 9.71087 | 0.421019 | ||||||||
\(533\) | 1.80501 | + | 13.4049i | 0.0781838 | + | 0.580629i | ||||
\(534\) | −54.4731 | + | 48.4885i | −2.35728 | + | 2.09830i | ||||
\(535\) | 3.42354 | + | 1.97658i | 0.148013 | + | 0.0854551i | ||||
\(536\) | −10.6185 | + | 18.3918i | −0.458650 | + | 0.794404i | ||||
\(537\) | 0.767522 | + | 3.71491i | 0.0331210 | + | 0.160310i | ||||
\(538\) | −64.2283 | + | 37.0822i | −2.76908 | + | 1.59873i | ||||
\(539\) | − | 24.8493i | − | 1.07033i | ||||||
\(540\) | 21.0634 | + | 9.81299i | 0.906425 | + | 0.422284i | ||||
\(541\) | 19.8249i | 0.852339i | 0.904643 | + | 0.426169i | \(0.140137\pi\) | ||||
−0.904643 | + | 0.426169i | \(0.859863\pi\) | |||||||
\(542\) | −33.8258 | − | 58.5880i | −1.45294 | − | 2.51657i | ||||
\(543\) | 5.86838 | + | 28.4037i | 0.251836 | + | 1.21892i | ||||
\(544\) | 2.82522 | + | 1.63114i | 0.121130 | + | 0.0699347i | ||||
\(545\) | 7.60040 | − | 13.1643i | 0.325565 | − | 0.563895i | ||||
\(546\) | 3.56197 | + | 10.1473i | 0.152438 | + | 0.434265i | ||||
\(547\) | −15.9204 | − | 27.5749i | −0.680706 | − | 1.17902i | −0.974766 | − | 0.223230i | \(-0.928340\pi\) |
0.294060 | − | 0.955787i | \(-0.404994\pi\) | |||||||
\(548\) | 54.7046i | 2.33686i | ||||||||
\(549\) | 8.97962 | + | 6.68180i | 0.383241 | + | 0.285172i | ||||
\(550\) | 9.66353 | 0.412054 | ||||||||
\(551\) | −22.0098 | + | 12.7074i | −0.937649 | + | 0.541352i | ||||
\(552\) | 16.5733 | − | 50.0350i | 0.705406 | − | 2.12963i | ||||
\(553\) | 2.89496 | + | 1.67140i | 0.123106 | + | 0.0710753i | ||||
\(554\) | −4.00660 | − | 2.31321i | −0.170224 | − | 0.0982790i | ||||
\(555\) | −4.56382 | − | 1.51169i | −0.193723 | − | 0.0641677i | ||||
\(556\) | 11.6092 | + | 20.1076i | 0.492338 | + | 0.852754i | ||||
\(557\) | 2.96054i | 0.125442i | 0.998031 | + | 0.0627210i | \(0.0199778\pi\) | ||||
−0.998031 | + | 0.0627210i | \(0.980022\pi\) | |||||||
\(558\) | −42.6881 | + | 18.4257i | −1.80713 | + | 0.780024i | ||||
\(559\) | 15.6339 | − | 38.0607i | 0.661244 | − | 1.60980i | ||||
\(560\) | −2.38769 | − | 4.13560i | −0.100898 | − | 0.174761i | ||||
\(561\) | −2.65768 | − | 2.98571i | −0.112207 | − | 0.126057i | ||||
\(562\) | 25.8586 | − | 44.7883i | 1.09078 | − | 1.88928i | ||||
\(563\) | −20.3611 | + | 35.2664i | −0.858117 | + | 1.48630i | 0.0156058 | + | 0.999878i | \(0.495032\pi\) |
−0.873723 | + | 0.486424i | \(0.838301\pi\) | |||||||
\(564\) | 64.5427 | − | 13.3349i | 2.71774 | − | 0.561501i | ||||
\(565\) | 7.76985 | − | 4.48592i | 0.326880 | − | 0.188724i | ||||
\(566\) | − | 8.76056i | − | 0.368234i | ||||||
\(567\) | −1.40217 | + | 5.92866i | −0.0588858 | + | 0.248980i | ||||
\(568\) | 62.1122 | 2.60617 | ||||||||
\(569\) | −8.27447 | − | 14.3318i | −0.346884 | − | 0.600821i | 0.638810 | − | 0.769364i | \(-0.279427\pi\) |
−0.985694 | + | 0.168544i | \(0.946094\pi\) | |||||||
\(570\) | 13.8429 | − | 2.86003i | 0.579816 | − | 0.119794i | ||||
\(571\) | 18.2882 | − | 31.6762i | 0.765339 | − | 1.32561i | −0.174728 | − | 0.984617i | \(-0.555905\pi\) |
0.940067 | − | 0.340990i | \(-0.110762\pi\) | |||||||
\(572\) | −48.4808 | + | 37.4283i | −2.02708 | + | 1.56496i | ||||
\(573\) | 28.0035 | − | 24.9269i | 1.16986 | − | 1.04134i | ||||
\(574\) | 5.59467 | − | 3.23008i | 0.233517 | − | 0.134821i | ||||
\(575\) | −4.83900 | −0.201800 | ||||||||
\(576\) | −1.23664 | + | 0.533779i | −0.0515266 | + | 0.0222408i | ||||
\(577\) | − | 31.6106i | − | 1.31596i | −0.753033 | − | 0.657982i | \(-0.771410\pi\) | ||
0.753033 | − | 0.657982i | \(-0.228590\pi\) | |||||||
\(578\) | 36.6408 | − | 21.1546i | 1.52406 | − | 0.879914i | ||||
\(579\) | −1.66676 | + | 5.03197i | −0.0692680 | + | 0.209121i | ||||
\(580\) | 30.6825 | + | 17.7145i | 1.27402 | + | 0.735556i | ||||
\(581\) | 3.98220 | − | 6.89737i | 0.165209 | − | 0.286151i | ||||
\(582\) | 21.6406 | + | 7.16809i | 0.897031 | + | 0.297127i | ||||
\(583\) | 9.08699 | − | 5.24638i | 0.376345 | − | 0.217283i | ||||
\(584\) | −70.2169 | −2.90559 | ||||||||
\(585\) | 5.57354 | + | 9.27015i | 0.230438 | + | 0.383273i | ||||
\(586\) | −79.8706 | −3.29942 | ||||||||
\(587\) | 2.34354 | − | 1.35304i | 0.0967283 | − | 0.0558461i | −0.450856 | − | 0.892597i | \(-0.648881\pi\) |
0.547584 | + | 0.836751i | \(0.315548\pi\) | |||||||
\(588\) | −37.8483 | + | 33.6901i | −1.56084 | + | 1.38936i | ||||
\(589\) | −9.77150 | + | 16.9247i | −0.402628 | + | 0.697371i | ||||
\(590\) | −5.88459 | − | 3.39747i | −0.242265 | − | 0.139872i | ||||
\(591\) | 32.6992 | − | 6.75585i | 1.34507 | − | 0.277899i | ||||
\(592\) | −16.9582 | + | 9.79082i | −0.696978 | + | 0.402400i | ||||
\(593\) | − | 29.8580i | − | 1.22612i | −0.790036 | − | 0.613060i | \(-0.789938\pi\) | ||
0.790036 | − | 0.613060i | \(-0.210062\pi\) | |||||||
\(594\) | −50.0206 | + | 4.39401i | −2.05237 | + | 0.180288i | ||||
\(595\) | 0.411256 | 0.0168599 | ||||||||
\(596\) | −36.2282 | + | 20.9164i | −1.48396 | + | 0.856768i | ||||
\(597\) | −0.0688968 | − | 0.333470i | −0.00281976 | − | 0.0136480i | ||||
\(598\) | 35.1340 | − | 27.1242i | 1.43673 | − | 1.10919i | ||||
\(599\) | 8.09772 | − | 14.0257i | 0.330864 | − | 0.573073i | −0.651818 | − | 0.758376i | \(-0.725993\pi\) |
0.982681 | + | 0.185303i | \(0.0593266\pi\) | |||||||
\(600\) | −7.24219 | − | 8.13606i | −0.295661 | − | 0.332153i | ||||
\(601\) | −24.3153 | − | 42.1154i | −0.991843 | − | 1.71792i | −0.606313 | − | 0.795226i | \(-0.707352\pi\) |
−0.385530 | − | 0.922695i | \(-0.625981\pi\) | |||||||
\(602\) | −19.6523 | −0.800966 | ||||||||
\(603\) | −10.0627 | − | 1.17377i | −0.409787 | − | 0.0477995i | ||||
\(604\) | 58.8849i | 2.39599i | ||||||||
\(605\) | −2.96956 | + | 1.71447i | −0.120730 | + | 0.0697033i | ||||
\(606\) | 24.9512 | − | 75.3282i | 1.01357 | − | 3.06000i | ||||
\(607\) | −13.0014 | + | 22.5191i | −0.527710 | + | 0.914021i | 0.471768 | + | 0.881723i | \(0.343616\pi\) |
−0.999478 | + | 0.0322985i | \(0.989717\pi\) | |||||||
\(608\) | 8.61267 | − | 14.9176i | 0.349290 | − | 0.604988i | ||||
\(609\) | −2.92066 | + | 8.81754i | −0.118351 | + | 0.357305i | ||||
\(610\) | −4.74579 | − | 8.21995i | −0.192151 | − | 0.332816i | ||||
\(611\) | 28.3778 | + | 11.6565i | 1.14804 | + | 0.471573i | ||||
\(612\) | −0.944348 | + | 8.09592i | −0.0381730 | + | 0.327258i | ||||
\(613\) | − | 37.1209i | − | 1.49930i | −0.661834 | − | 0.749650i | \(-0.730222\pi\) | ||
0.661834 | − | 0.749650i | \(-0.269778\pi\) | |||||||
\(614\) | −26.1849 | − | 45.3536i | −1.05674 | − | 1.83032i | ||||
\(615\) | 4.85336 | − | 4.32015i | 0.195706 | − | 0.174205i | ||||
\(616\) | 14.0037 | + | 8.08507i | 0.564227 | + | 0.325757i | ||||
\(617\) | 4.76857 | + | 2.75313i | 0.191975 | + | 0.110837i | 0.592907 | − | 0.805271i | \(-0.297980\pi\) |
−0.400932 | + | 0.916108i | \(0.631314\pi\) | |||||||
\(618\) | 1.74841 | − | 0.361232i | 0.0703314 | − | 0.0145309i | ||||
\(619\) | 14.9154 | − | 8.61139i | 0.599499 | − | 0.346121i | −0.169345 | − | 0.985557i | \(-0.554165\pi\) |
0.768845 | + | 0.639436i | \(0.220832\pi\) | |||||||
\(620\) | 27.2437 | 1.09413 | ||||||||
\(621\) | 25.0477 | − | 2.20029i | 1.00513 | − | 0.0882948i | ||||
\(622\) | − | 58.8066i | − | 2.35793i | ||||||
\(623\) | 5.60165 | + | 9.70235i | 0.224425 | + | 0.388716i | ||||
\(624\) | 43.2963 | + | 8.14776i | 1.73324 | + | 0.326172i | ||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 32.8205 | + | 18.9489i | 1.31177 | + | 0.757351i | ||||
\(627\) | −15.7650 | + | 14.0330i | −0.629592 | + | 0.560422i | ||||
\(628\) | 7.80196 | + | 13.5134i | 0.311332 | + | 0.539243i | ||||
\(629\) | − | 1.68637i | − | 0.0672400i | ||||||
\(630\) | 3.08408 | − | 4.14467i | 0.122873 | − | 0.165127i | ||||
\(631\) | 26.4212i | 1.05181i | 0.850543 | + | 0.525905i | \(0.176273\pi\) | ||||
−0.850543 | + | 0.525905i | \(0.823727\pi\) | |||||||
\(632\) | 26.8951 | − | 15.5279i | 1.06983 | − | 0.617666i | ||||
\(633\) | 34.7825 | + | 11.5211i | 1.38248 | + | 0.457924i | ||||
\(634\) | −8.29121 | + | 14.3608i | −0.329286 | + | 0.570340i | ||||
\(635\) | 10.5775 | + | 6.10693i | 0.419756 | + | 0.242346i | ||||
\(636\) | −20.3108 | − | 6.72761i | −0.805375 | − | 0.266767i | ||||
\(637\) | −23.3758 | + | 3.14764i | −0.926182 | + | 0.124714i | ||||
\(638\) | −76.5589 | −3.03100 | ||||||||
\(639\) | 11.7423 | + | 27.2042i | 0.464519 | + | 1.07618i | ||||
\(640\) | 11.8814 | 0.469654 | ||||||||
\(641\) | 15.8245 | + | 27.4089i | 0.625031 | + | 1.08258i | 0.988535 | + | 0.150992i | \(0.0482469\pi\) |
−0.363504 | + | 0.931593i | \(0.618420\pi\) | |||||||
\(642\) | 11.5816 | + | 13.0111i | 0.457090 | + | 0.513507i | ||||
\(643\) | −2.52194 | − | 1.45605i | −0.0994558 | − | 0.0574208i | 0.449447 | − | 0.893307i | \(-0.351621\pi\) |
−0.548903 | + | 0.835886i | \(0.684954\pi\) | |||||||
\(644\) | −12.6858 | − | 7.32417i | −0.499892 | − | 0.288613i | ||||
\(645\) | −19.3573 | + | 3.99934i | −0.762193 | + | 0.157474i | ||||
\(646\) | 2.47910 | + | 4.29392i | 0.0975388 | + | 0.168942i | ||||
\(647\) | −26.7669 | −1.05232 | −0.526158 | − | 0.850387i | \(-0.676368\pi\) | ||||
−0.526158 | + | 0.850387i | \(0.676368\pi\) | |||||||
\(648\) | 41.1866 | + | 38.8210i | 1.61796 | + | 1.52503i | ||||
\(649\) | 10.1458 | 0.398256 | ||||||||
\(650\) | −1.22407 | − | 9.09051i | −0.0480120 | − | 0.356559i | ||||
\(651\) | 1.44519 | + | 6.99491i | 0.0566415 | + | 0.274152i | ||||
\(652\) | 9.43918 | + | 5.44971i | 0.369667 | + | 0.213427i | ||||
\(653\) | 11.5619 | − | 20.0259i | 0.452454 | − | 0.783673i | −0.546084 | − | 0.837731i | \(-0.683882\pi\) |
0.998538 | + | 0.0540572i | \(0.0172153\pi\) | |||||||
\(654\) | 50.0305 | − | 44.5339i | 1.95635 | − | 1.74141i | ||||
\(655\) | −15.1006 | + | 8.71835i | −0.590031 | + | 0.340654i | ||||
\(656\) | − | 26.4647i | − | 1.03327i | ||||||
\(657\) | −13.2745 | − | 30.7539i | −0.517888 | − | 1.19982i | ||||
\(658\) | − | 14.6526i | − | 0.571217i | ||||||
\(659\) | −6.08359 | − | 10.5371i | −0.236983 | − | 0.410467i | 0.722864 | − | 0.690990i | \(-0.242825\pi\) |
−0.959847 | + | 0.280524i | \(0.909492\pi\) | |||||||
\(660\) | 27.9301 | + | 9.25137i | 1.08718 | + | 0.360109i | ||||
\(661\) | −0.348155 | − | 0.201008i | −0.0135417 | − | 0.00781829i | 0.493214 | − | 0.869908i | \(-0.335822\pi\) |
−0.506756 | + | 0.862090i | \(0.669155\pi\) | |||||||
\(662\) | −10.5815 | + | 18.3278i | −0.411263 | + | 0.712328i | ||||
\(663\) | −2.47202 | + | 2.87829i | −0.0960052 | + | 0.111783i | ||||
\(664\) | −36.9959 | − | 64.0788i | −1.43572 | − | 2.48674i | ||||
\(665\) | − | 2.17149i | − | 0.0842068i | ||||||
\(666\) | −16.9954 | − | 12.6464i | −0.658557 | − | 0.490037i | ||||
\(667\) | 38.3368 | 1.48441 | ||||||||
\(668\) | −15.1159 | + | 8.72716i | −0.584851 | + | 0.337664i | ||||
\(669\) | −22.8032 | − | 25.6176i | −0.881621 | − | 0.990436i | ||||
\(670\) | 7.44010 | + | 4.29555i | 0.287436 | + | 0.165951i | ||||
\(671\) | 12.2735 | + | 7.08610i | 0.473812 | + | 0.273556i | ||||
\(672\) | −1.27380 | − | 6.16536i | −0.0491379 | − | 0.237834i | ||||
\(673\) | −14.4416 | − | 25.0137i | −0.556685 | − | 0.964206i | −0.997770 | − | 0.0667411i | \(-0.978740\pi\) |
0.441086 | − | 0.897465i | \(-0.354593\pi\) | |||||||
\(674\) | 6.94193i | 0.267393i | ||||||||
\(675\) | 2.19433 | − | 4.71009i | 0.0844597 | − | 0.181291i | ||||
\(676\) | 41.3499 | + | 40.8650i | 1.59038 | + | 1.57173i | ||||
\(677\) | 9.71809 | + | 16.8322i | 0.373496 | + | 0.646915i | 0.990101 | − | 0.140358i | \(-0.0448255\pi\) |
−0.616604 | + | 0.787273i | \(0.711492\pi\) | |||||||
\(678\) | 38.7154 | − | 7.99884i | 1.48686 | − | 0.307194i | ||||
\(679\) | 1.75105 | − | 3.03291i | 0.0671991 | − | 0.116392i | ||||
\(680\) | 1.91035 | − | 3.30883i | 0.0732586 | − | 0.126888i | ||||
\(681\) | −0.698555 | − | 0.784775i | −0.0267687 | − | 0.0300726i | ||||
\(682\) | −50.9838 | + | 29.4355i | −1.95227 | + | 1.12714i | ||||
\(683\) | 17.6204i | 0.674225i | 0.941464 | + | 0.337112i | \(0.109450\pi\) | ||||
−0.941464 | + | 0.337112i | \(0.890550\pi\) | |||||||
\(684\) | 42.7476 | + | 4.98629i | 1.63450 | + | 0.190656i | ||||
\(685\) | 12.2327 | 0.467389 | ||||||||
\(686\) | 11.6600 | + | 20.1957i | 0.445180 | + | 0.771074i | ||||
\(687\) | 12.5443 | − | 37.8715i | 0.478596 | − | 1.44489i | ||||
\(688\) | −40.2538 | + | 69.7216i | −1.53466 | + | 2.65811i | ||||
\(689\) | −6.08632 | − | 7.88360i | −0.231870 | − | 0.300341i | ||||
\(690\) | −20.2409 | − | 6.70445i | −0.770557 | − | 0.255234i | ||||
\(691\) | 13.8877 | − | 8.01809i | 0.528315 | − | 0.305023i | −0.212015 | − | 0.977266i | \(-0.568003\pi\) |
0.740330 | + | 0.672244i | \(0.234669\pi\) | |||||||
\(692\) | 107.477 | 4.08565 | ||||||||
\(693\) | −0.893722 | + | 7.66190i | −0.0339497 | + | 0.291052i | ||||
\(694\) | − | 74.6616i | − | 2.83412i | ||||||
\(695\) | 4.49636 | − | 2.59598i | 0.170557 | − | 0.0984710i | ||||
\(696\) | 57.3759 | + | 64.4576i | 2.17483 | + | 2.44326i | ||||
\(697\) | 1.97380 | + | 1.13957i | 0.0747629 | + | 0.0431644i | ||||
\(698\) | −29.3382 | + | 50.8153i | −1.11047 | + | 1.92339i | ||||
\(699\) | −6.33389 | − | 30.6569i | −0.239570 | − | 1.15955i | ||||
\(700\) | −2.62158 | + | 1.51357i | −0.0990864 | + | 0.0572076i | ||||
\(701\) | 3.23764 | 0.122284 | 0.0611420 | − | 0.998129i | \(-0.480526\pi\) | ||||
0.0611420 | + | 0.998129i | \(0.480526\pi\) | |||||||
\(702\) | 10.4695 | + | 46.4979i | 0.395147 | + | 1.75495i | ||||
\(703\) | −8.90429 | −0.335832 | ||||||||
\(704\) | −1.47696 | + | 0.852724i | −0.0556651 | + | 0.0321382i | ||||
\(705\) | −2.98188 | − | 14.4327i | −0.112304 | − | 0.543566i | ||||
\(706\) | −3.12006 | + | 5.40411i | −0.117425 | + | 0.203386i | ||||
\(707\) | −10.5572 | − | 6.09519i | −0.397043 | − | 0.229233i | ||||
\(708\) | −13.7554 | − | 15.4532i | −0.516960 | − | 0.580766i | ||||
\(709\) | 10.8929 | − | 6.28902i | 0.409091 | − | 0.236189i | −0.281308 | − | 0.959618i | \(-0.590768\pi\) |
0.690399 | + | 0.723429i | \(0.257435\pi\) | |||||||
\(710\) | − | 25.1265i | − | 0.942981i | ||||||
\(711\) | 11.8855 | + | 8.84408i | 0.445741 | + | 0.331679i | ||||
\(712\) | 104.082 | 3.90065 | ||||||||
\(713\) | 25.5301 | − | 14.7398i | 0.956109 | − | 0.552010i | ||||
\(714\) | 1.72023 | + | 0.569797i | 0.0643779 | + | 0.0213241i | ||||
\(715\) | 8.36951 | + | 10.8410i | 0.313002 | + | 0.405431i | ||||
\(716\) | 4.89705 | − | 8.48193i | 0.183011 | − | 0.316985i | ||||
\(717\) | −4.62907 | + | 13.9753i | −0.172876 | + | 0.521916i | ||||
\(718\) | −32.2352 | − | 55.8330i | −1.20301 | − | 2.08367i | ||||
\(719\) | −22.2780 | −0.830831 | −0.415415 | − | 0.909632i | \(-0.636364\pi\) | ||||
−0.415415 | + | 0.909632i | \(0.636364\pi\) | |||||||
\(720\) | −8.38718 | − | 19.4311i | −0.312572 | − | 0.724154i | ||||
\(721\) | − | 0.274267i | − | 0.0102142i | ||||||
\(722\) | −19.1878 | + | 11.0781i | −0.714096 | + | 0.412284i | ||||
\(723\) | −16.4328 | − | 18.4611i | −0.611144 | − | 0.686574i | ||||
\(724\) | 37.4422 | − | 64.8518i | 1.39153 | − | 2.41020i | ||||
\(725\) | 3.96123 | − | 6.86105i | 0.147116 | − | 0.254813i | ||||
\(726\) | −14.7966 | + | 3.05707i | −0.549155 | + | 0.113459i | ||||
\(727\) | −3.64784 | − | 6.31824i | −0.135291 | − | 0.234331i | 0.790418 | − | 0.612568i | \(-0.209864\pi\) |
−0.925709 | + | 0.378238i | \(0.876530\pi\) | |||||||
\(728\) | 5.83180 | − | 14.1975i | 0.216141 | − | 0.526194i | ||||
\(729\) | −9.21665 | + | 25.3782i | −0.341357 | + | 0.939934i | ||||
\(730\) | 28.4051i | 1.05132i | ||||||||
\(731\) | −3.46666 | − | 6.00443i | −0.128219 | − | 0.222082i | ||||
\(732\) | −5.84718 | − | 28.3011i | −0.216118 | − | 1.04604i | ||||
\(733\) | 20.2232 | + | 11.6758i | 0.746960 | + | 0.431257i | 0.824594 | − | 0.565725i | \(-0.191403\pi\) |
−0.0776347 | + | 0.996982i | \(0.524737\pi\) | |||||||
\(734\) | 27.2732 | + | 15.7462i | 1.00667 | + | 0.581203i | ||||
\(735\) | 7.53360 | + | 8.46344i | 0.277881 | + | 0.312179i | ||||
\(736\) | −22.5024 | + | 12.9918i | −0.829449 | + | 0.478883i | ||||
\(737\) | −12.8276 | −0.472513 | ||||||||
\(738\) | 26.2865 | − | 11.3462i | 0.967620 | − | 0.417660i | ||||
\(739\) | 13.1702i | 0.484474i | 0.970217 | + | 0.242237i | \(0.0778811\pi\) | ||||
−0.970217 | + | 0.242237i | \(0.922119\pi\) | |||||||
\(740\) | 6.20645 | + | 10.7499i | 0.228154 | + | 0.395174i | ||||
\(741\) | 15.1978 | + | 13.0526i | 0.558304 | + | 0.479500i | ||||
\(742\) | −2.37845 | + | 4.11959i | −0.0873155 | + | 0.151235i | ||||
\(743\) | 22.6663 | + | 13.0864i | 0.831546 | + | 0.480093i | 0.854382 | − | 0.519646i | \(-0.173936\pi\) |
−0.0228357 | + | 0.999739i | \(0.507269\pi\) | |||||||
\(744\) | 62.9918 | + | 20.8650i | 2.30939 | + | 0.764948i | ||||
\(745\) | 4.67720 | + | 8.10115i | 0.171359 | + | 0.296803i | ||||
\(746\) | − | 69.2462i | − | 2.53528i | ||||||
\(747\) | 21.0714 | − | 28.3177i | 0.770963 | − | 1.03609i | ||||
\(748\) | 10.3204i | 0.377351i | ||||||||
\(749\) | 2.31744 | − | 1.33797i | 0.0846773 | − | 0.0488885i | ||||
\(750\) | −3.29131 | + | 2.92971i | −0.120182 | + | 0.106978i | ||||
\(751\) | −24.8206 | + | 42.9905i | −0.905715 | + | 1.56875i | −0.0857616 | + | 0.996316i | \(0.527332\pi\) |
−0.819954 | + | 0.572430i | \(0.806001\pi\) | |||||||
\(752\) | −51.9839 | − | 30.0129i | −1.89566 | − | 1.09446i | ||||
\(753\) | −8.69683 | − | 42.0938i | −0.316930 | − | 1.53398i | ||||
\(754\) | 9.69765 | + | 72.0192i | 0.353168 | + | 2.62278i | ||||
\(755\) | 13.1675 | 0.479216 | ||||||||
\(756\) | 12.8817 | − | 9.02660i | 0.468501 | − | 0.328294i | ||||
\(757\) | 40.3143 | 1.46525 | 0.732624 | − | 0.680634i | \(-0.238296\pi\) | ||||
0.732624 | + | 0.680634i | \(0.238296\pi\) | |||||||
\(758\) | 7.28757 | + | 12.6224i | 0.264697 | + | 0.458468i | ||||
\(759\) | 31.1786 | − | 6.44169i | 1.13171 | − | 0.233819i | ||||
\(760\) | −17.4711 | − | 10.0869i | −0.633743 | − | 0.365891i | ||||
\(761\) | 27.5453 | + | 15.9033i | 0.998518 | + | 0.576494i | 0.907809 | − | 0.419383i | \(-0.137754\pi\) |
0.0907082 | + | 0.995878i | \(0.471087\pi\) | |||||||
\(762\) | 35.7831 | + | 40.1996i | 1.29628 | + | 1.45628i | ||||
\(763\) | −5.14480 | − | 8.91106i | −0.186254 | − | 0.322602i | ||||
\(764\) | −96.7969 | −3.50199 | ||||||||
\(765\) | 1.81037 | + | 0.211170i | 0.0654539 | + | 0.00763487i | ||||
\(766\) | −1.45965 | −0.0527394 | ||||||||
\(767\) | −1.28516 | − | 9.54414i | −0.0464043 | − | 0.344619i | ||||
\(768\) | 48.2218 | + | 15.9727i | 1.74006 | + | 0.576365i | ||||
\(769\) | −28.4535 | − | 16.4276i | −1.02606 | − | 0.592395i | −0.110206 | − | 0.993909i | \(-0.535151\pi\) |
−0.915853 | + | 0.401513i | \(0.868484\pi\) | |||||||
\(770\) | 3.27068 | − | 5.66499i | 0.117867 | − | 0.204152i | ||||
\(771\) | 17.6519 | + | 5.84691i | 0.635718 | + | 0.210571i | ||||
\(772\) | 11.8526 | − | 6.84310i | 0.426584 | − | 0.246289i | ||||
\(773\) | 17.5635i | 0.631715i | 0.948807 | + | 0.315858i | \(0.102292\pi\) | ||||
−0.948807 | + | 0.315858i | \(0.897708\pi\) | |||||||
\(774\) | −86.5100 | − | 10.0910i | −3.10954 | − | 0.362712i | ||||
\(775\) | − | 6.09208i | − | 0.218834i | ||||||
\(776\) | −16.2678 | − | 28.1767i | −0.583981 | − | 1.01148i | ||||
\(777\) | −2.43084 | + | 2.16378i | −0.0872060 | + | 0.0776251i | ||||
\(778\) | −52.9946 | − | 30.5964i | −1.89995 | − | 1.09694i | ||||
\(779\) | 6.01711 | − | 10.4219i | 0.215585 | − | 0.373405i | ||||
\(780\) | 5.16491 | − | 27.4458i | 0.184934 | − | 0.982716i | ||||
\(781\) | 18.7586 | + | 32.4909i | 0.671236 | + | 1.16261i | ||||
\(782\) | − | 7.47918i | − | 0.267455i | ||||||
\(783\) | −17.3845 | + | 37.3155i | −0.621270 | + | 1.33355i | ||||
\(784\) | 46.1500 | 1.64821 | ||||||||
\(785\) | 3.02179 | − | 1.74463i | 0.107852 | − | 0.0622686i | ||||
\(786\) | −75.2431 | + | 15.5457i | −2.68383 | + | 0.554496i | ||||
\(787\) | −37.4340 | − | 21.6125i | −1.33438 | − | 0.770404i | −0.348411 | − | 0.937342i | \(-0.613279\pi\) |
−0.985967 | + | 0.166938i | \(0.946612\pi\) | |||||||
\(788\) | −74.6593 | − | 43.1046i | −2.65963 | − | 1.53554i | ||||
\(789\) | −16.4113 | + | 14.6083i | −0.584258 | + | 0.520069i | ||||
\(790\) | −6.28156 | − | 10.8800i | −0.223488 | − | 0.387092i | ||||
\(791\) | − | 6.07316i | − | 0.215937i | ||||||
\(792\) | 57.4936 | + | 42.7814i | 2.04294 | + | 1.52017i | ||||
\(793\) | 5.11124 | − | 12.4433i | 0.181505 | − | 0.441874i | ||||
\(794\) | 11.0315 | + | 19.1071i | 0.391494 | + | 0.678087i | ||||
\(795\) | −1.50439 | + | 4.54179i | −0.0533553 | + | 0.161081i | ||||
\(796\) | −0.439585 | + | 0.761383i | −0.0155807 | + | 0.0269865i | ||||
\(797\) | −7.21071 | + | 12.4893i | −0.255416 | + | 0.442394i | −0.965009 | − | 0.262218i | \(-0.915546\pi\) |
0.709592 | + | 0.704613i | \(0.248879\pi\) | |||||||
\(798\) | 3.00861 | − | 9.08305i | 0.106504 | − | 0.321536i | ||||
\(799\) | 4.47686 | − | 2.58472i | 0.158380 | − | 0.0914407i | ||||
\(800\) | 5.36960i | 0.189844i | ||||||||
\(801\) | 19.6768 | + | 45.5864i | 0.695245 | + | 1.61072i | ||||
\(802\) | −0.0292415 | −0.00103255 | ||||||||
\(803\) | −21.2063 | − | 36.7304i | −0.748354 | − | 1.29619i | ||||
\(804\) | 17.3915 | + | 19.5380i | 0.613349 | + | 0.689052i | ||||
\(805\) | −1.63779 | + | 2.83674i | −0.0577245 | + | 0.0999819i | ||||
\(806\) | 34.1481 | + | 44.2320i | 1.20282 | + | 1.55801i | ||||
\(807\) | 10.2165 | + | 49.4494i | 0.359639 | + | 1.74070i | ||||
\(808\) | −98.0796 | + | 56.6263i | −3.45043 | + | 1.99211i | ||||
\(809\) | 37.1222 | 1.30515 | 0.652574 | − | 0.757725i | \(-0.273689\pi\) | ||||
0.652574 | + | 0.757725i | \(0.273689\pi\) | |||||||
\(810\) | 15.7044 | − | 16.6614i | 0.551797 | − | 0.585422i | ||||
\(811\) | − | 47.4834i | − | 1.66737i | −0.552242 | − | 0.833684i | \(-0.686228\pi\) | ||
0.552242 | − | 0.833684i | \(-0.313772\pi\) | |||||||
\(812\) | 20.7694 | − | 11.9912i | 0.728862 | − | 0.420808i | ||||
\(813\) | −45.1069 | + | 9.31936i | −1.58197 | + | 0.326844i | ||||
\(814\) | −23.2295 | − | 13.4116i | −0.814194 | − | 0.470075i | ||||
\(815\) | 1.21863 | − | 2.11074i | 0.0426869 | − | 0.0739359i | ||||
\(816\) | 5.54505 | − | 4.93584i | 0.194115 | − | 0.172789i | ||||
\(817\) | −31.7042 | + | 18.3045i | −1.10919 | + | 0.640392i | ||||
\(818\) | −78.0260 | −2.72811 | ||||||||
\(819\) | 7.32078 | − | 0.129800i | 0.255809 | − | 0.00453558i | ||||
\(820\) | −16.7761 | −0.585848 | ||||||||
\(821\) | 13.7316 | − | 7.92794i | 0.479236 | − | 0.276687i | −0.240862 | − | 0.970559i | \(-0.577430\pi\) |
0.720098 | + | 0.693872i | \(0.244097\pi\) | |||||||
\(822\) | 51.1678 | + | 16.9485i | 1.78468 | + | 0.591147i | ||||
\(823\) | 6.45752 | − | 11.1847i | 0.225095 | − | 0.389876i | −0.731253 | − | 0.682106i | \(-0.761064\pi\) |
0.956348 | + | 0.292230i | \(0.0943974\pi\) | |||||||
\(824\) | −2.20666 | − | 1.27401i | −0.0768726 | − | 0.0443824i | ||||
\(825\) | 2.06874 | − | 6.24557i | 0.0720243 | − | 0.217443i | ||||
\(826\) | −3.98336 | + | 2.29979i | −0.138599 | + | 0.0800200i | ||||
\(827\) | − | 17.5745i | − | 0.611126i | −0.952172 | − | 0.305563i | \(-0.901155\pi\) | ||
0.952172 | − | 0.305563i | \(-0.0988447\pi\) | |||||||
\(828\) | −52.0828 | − | 38.7552i | −1.81000 | − | 1.34683i | ||||
\(829\) | −31.8757 | −1.10709 | −0.553545 | − | 0.832820i | \(-0.686725\pi\) | ||||
−0.553545 | + | 0.832820i | \(0.686725\pi\) | |||||||
\(830\) | −25.9221 | + | 14.9661i | −0.899768 | + | 0.519481i | ||||
\(831\) | −2.35276 | + | 2.09427i | −0.0816163 | + | 0.0726495i | ||||
\(832\) | 0.989245 | + | 1.28137i | 0.0342959 | + | 0.0444234i | ||||
\(833\) | −1.98722 | + | 3.44197i | −0.0688531 | + | 0.119257i | ||||
\(834\) | 22.4044 | − | 4.62888i | 0.775801 | − | 0.160285i | ||||
\(835\) | 1.95152 | + | 3.38013i | 0.0675352 | + | 0.116974i | ||||
\(836\) | 54.4932 | 1.88469 | ||||||||
\(837\) | 2.77007 | + | 31.5340i | 0.0957476 | + | 1.08997i | ||||
\(838\) | 57.9595i | 2.00218i | ||||||||
\(839\) | 43.4135 | − | 25.0648i | 1.49880 | − | 0.865334i | 0.498803 | − | 0.866715i | \(-0.333773\pi\) |
0.999999 | + | 0.00138153i | \(0.000439754\pi\) | |||||||
\(840\) | −7.22071 | + | 1.49184i | −0.249138 | + | 0.0514735i | ||||
\(841\) | −16.8827 | + | 29.2416i | −0.582161 | + | 1.00833i | ||||
\(842\) | 22.3305 | − | 38.6775i | 0.769558 | − | 1.33291i | ||||
\(843\) | −23.4111 | − | 26.3006i | −0.806321 | − | 0.905841i | ||||
\(844\) | −47.3016 | − | 81.9289i | −1.62819 | − | 2.82011i | ||||
\(845\) | 9.13801 | − | 9.24644i | 0.314357 | − | 0.318087i | ||||
\(846\) | 7.52375 | − | 64.5013i | 0.258672 | − | 2.21760i | ||||
\(847\) | 2.32110i | 0.0797539i | ||||||||
\(848\) | 9.74356 | + | 16.8763i | 0.334595 | + | 0.579536i | ||||
\(849\) | −5.66198 | − | 1.87544i | −0.194319 | − | 0.0643648i | ||||
\(850\) | −1.33853 | − | 0.772802i | −0.0459113 | − | 0.0265069i | ||||
\(851\) | 11.6322 | + | 6.71583i | 0.398745 | + | 0.230216i | ||||
\(852\) | 24.0548 | − | 72.6220i | 0.824105 | − | 2.48799i | ||||
\(853\) | 47.0551 | − | 27.1673i | 1.61114 | − | 0.930190i | 0.622028 | − | 0.782995i | \(-0.286309\pi\) |
0.989108 | − | 0.147195i | \(-0.0470244\pi\) | |||||||
\(854\) | −6.42497 | −0.219858 | ||||||||
\(855\) | 1.11501 | − | 9.55899i | 0.0381325 | − | 0.326911i | ||||
\(856\) | − | 24.8604i | − | 0.849711i | ||||||
\(857\) | −9.11178 | − | 15.7821i | −0.311252 | − | 0.539105i | 0.667381 | − | 0.744716i | \(-0.267415\pi\) |
−0.978634 | + | 0.205611i | \(0.934082\pi\) | |||||||
\(858\) | 19.9882 | + | 56.9424i | 0.682387 | + | 1.94398i | ||||
\(859\) | 11.4096 | − | 19.7621i | 0.389292 | − | 0.674273i | −0.603063 | − | 0.797694i | \(-0.706053\pi\) |
0.992354 | + | 0.123420i | \(0.0393864\pi\) | |||||||
\(860\) | 44.1969 | + | 25.5171i | 1.50710 | + | 0.870125i | ||||
\(861\) | −0.889921 | − | 4.30734i | −0.0303284 | − | 0.146794i | ||||
\(862\) | −1.28770 | − | 2.23036i | −0.0438591 | − | 0.0759662i | ||||
\(863\) | 49.9680i | 1.70093i | 0.526032 | + | 0.850465i | \(0.323679\pi\) | ||||
−0.526032 | + | 0.850465i | \(0.676321\pi\) | |||||||
\(864\) | −2.44156 | − | 27.7942i | −0.0830635 | − | 0.945580i | ||||
\(865\) | − | 24.0334i | − | 0.817159i | ||||||
\(866\) | 22.0825 | − | 12.7493i | 0.750394 | − | 0.433240i | ||||
\(867\) | −5.82830 | − | 28.2098i | −0.197940 | − | 0.958053i | ||||
\(868\) | 9.22079 | − | 15.9709i | 0.312974 | − | 0.542087i | ||||
\(869\) | 16.2453 | + | 9.37921i | 0.551083 | + | 0.318168i | ||||
\(870\) | 26.0753 | − | 23.2105i | 0.884035 | − | 0.786910i | ||||
\(871\) | 1.62487 | + | 12.0670i | 0.0550565 | + | 0.408875i | ||||
\(872\) | −95.5938 | −3.23722 | ||||||||
\(873\) | 9.26551 | − | 12.4519i | 0.313590 | − | 0.421432i | ||||
\(874\) | −39.4912 | −1.33581 | ||||||||
\(875\) | 0.338456 | + | 0.586224i | 0.0114419 | + | 0.0198180i | ||||
\(876\) | −27.1936 | + | 82.0980i | −0.918786 | + | 2.77383i | ||||
\(877\) | −9.00754 | − | 5.20050i | −0.304163 | − | 0.175609i | 0.340149 | − | 0.940372i | \(-0.389523\pi\) |
−0.644311 | + | 0.764763i | \(0.722856\pi\) | |||||||
\(878\) | −90.8242 | − | 52.4374i | −3.06517 | − | 1.76968i | ||||
\(879\) | −17.0985 | + | 51.6206i | −0.576717 | + | 1.74112i | ||||
\(880\) | −13.3987 | − | 23.2072i | −0.451670 | − | 0.782315i | ||||
\(881\) | 0.359362 | 0.0121072 | 0.00605360 | − | 0.999982i | \(-0.498073\pi\) | ||||
0.00605360 | + | 0.999982i | \(0.498073\pi\) | |||||||
\(882\) | 19.7859 | + | 45.8392i | 0.666226 | + | 1.54349i | ||||
\(883\) | 14.5057 | 0.488156 | 0.244078 | − | 0.969756i | \(-0.421515\pi\) | ||||
0.244078 | + | 0.969756i | \(0.421515\pi\) | |||||||
\(884\) | 9.70843 | − | 1.30728i | 0.326530 | − | 0.0439685i | ||||
\(885\) | −3.45555 | + | 3.07591i | −0.116157 | + | 0.103396i | ||||
\(886\) | 7.00370 | + | 4.04359i | 0.235294 | + | 0.135847i | ||||
\(887\) | 8.58749 | − | 14.8740i | 0.288340 | − | 0.499419i | −0.685074 | − | 0.728474i | \(-0.740230\pi\) |
0.973414 | + | 0.229055i | \(0.0735634\pi\) | |||||||
\(888\) | 6.11736 | + | 29.6088i | 0.205285 | + | 0.993607i | ||||
\(889\) | 7.16005 | − | 4.13386i | 0.240140 | − | 0.138645i | ||||
\(890\) | − | 42.1048i | − | 1.41136i | ||||||
\(891\) | −7.86840 | + | 33.2691i | −0.263601 | + | 1.11456i | ||||
\(892\) | 88.5500i | 2.96487i | ||||||||
\(893\) | −13.6477 | − | 23.6385i | −0.456702 | − | 0.791031i | ||||
\(894\) | 8.33991 | + | 40.3663i | 0.278928 | + | 1.35005i | ||||
\(895\) | −1.89668 | − | 1.09505i | −0.0633991 | − | 0.0366035i | ||||
\(896\) | 4.02134 | − | 6.96516i | 0.134343 | − | 0.232690i | ||||
\(897\) | −10.0091 | − | 28.5139i | −0.334194 | − | 0.952050i | ||||
\(898\) | 18.5708 | + | 32.1656i | 0.619717 | + | 1.07338i | ||||
\(899\) | 48.2643i | 1.60970i | ||||||||
\(900\) | −12.3175 | + | 5.31668i | −0.410583 | + | 0.177223i | ||||
\(901\) | −1.67823 | −0.0559100 | ||||||||
\(902\) | 31.3949 | − | 18.1258i | 1.04534 | − | 0.603525i | ||||
\(903\) | −4.20710 | + | 12.7013i | −0.140004 | + | 0.422673i | ||||
\(904\) | −48.8625 | − | 28.2108i | −1.62514 | − | 0.938277i | ||||
\(905\) | −14.5018 | − | 8.37263i | −0.482057 | − | 0.278316i | ||||
\(906\) | 55.0780 | + | 18.2437i | 1.82984 | + | 0.606105i | ||||
\(907\) | −17.6773 | − | 30.6180i | −0.586966 | − | 1.01666i | −0.994627 | − | 0.103522i | \(-0.966989\pi\) |
0.407661 | − | 0.913133i | \(-0.366345\pi\) | |||||||
\(908\) | 2.71265i | 0.0900226i | ||||||||
\(909\) | −43.3434 | − | 32.2521i | −1.43761 | − | 1.06974i | ||||
\(910\) | −5.74337 | − | 2.35916i | −0.190391 | − | 0.0782054i | ||||
\(911\) | 20.4838 | + | 35.4789i | 0.678658 | + | 1.17547i | 0.975385 | + | 0.220508i | \(0.0707714\pi\) |
−0.296727 | + | 0.954962i | \(0.595895\pi\) | |||||||
\(912\) | −26.0620 | − | 29.2787i | −0.862998 | − | 0.969513i | ||||
\(913\) | 22.3464 | − | 38.7051i | 0.739558 | − | 1.28095i | ||||
\(914\) | −10.9224 | + | 18.9181i | −0.361281 | + | 0.625756i | ||||
\(915\) | −6.32854 | + | 1.30751i | −0.209215 | + | 0.0432251i | ||||
\(916\) | −89.2049 | + | 51.5025i | −2.94741 | + | 1.70169i | ||||
\(917\) | 11.8031i | 0.389774i | ||||||||
\(918\) | 7.27993 | + | 3.39156i | 0.240273 | + | 0.111938i | ||||
\(919\) | −55.3482 | −1.82577 | −0.912884 | − | 0.408219i | \(-0.866150\pi\) | ||||
−0.912884 | + | 0.408219i | \(0.866150\pi\) | |||||||
\(920\) | 15.2156 | + | 26.3542i | 0.501644 | + | 0.868873i | ||||
\(921\) | −34.9177 | + | 7.21421i | −1.15058 | + | 0.237716i | ||||
\(922\) | 10.6162 | − | 18.3877i | 0.349625 | − | 0.605568i | ||||
\(923\) | 28.1881 | − | 21.7619i | 0.927823 | − | 0.716301i | ||||
\(924\) | 14.8765 | − | 13.2421i | 0.489400 | − | 0.435632i | ||||
\(925\) | 2.40383 | − | 1.38785i | 0.0790376 | − | 0.0456324i | ||||
\(926\) | 54.8956 | 1.80398 | ||||||||
\(927\) | 0.140829 | − | 1.20733i | 0.00462544 | − | 0.0396541i | ||||
\(928\) | − | 42.5405i | − | 1.39646i | ||||||
\(929\) | −4.79009 | + | 2.76556i | −0.157158 | + | 0.0907352i | −0.576516 | − | 0.817086i | \(-0.695588\pi\) |
0.419359 | + | 0.907821i | \(0.362255\pi\) | |||||||
\(930\) | 8.44060 | − | 25.4823i | 0.276778 | − | 0.835598i | ||||
\(931\) | 18.1741 | + | 10.4928i | 0.595632 | + | 0.343888i | ||||
\(932\) | −40.4123 | + | 69.9962i | −1.32375 | + | 2.29280i | ||||
\(933\) | −38.0069 | − | 12.5891i | −1.24429 | − | 0.412150i | ||||
\(934\) | −24.6186 | + | 14.2136i | −0.805546 | + | 0.465082i | ||||
\(935\) | 2.30779 | 0.0754729 | ||||||||
\(936\) | 32.9619 | − | 59.5034i | 1.07739 | − | 1.94493i | ||||
\(937\) | −16.6722 | −0.544657 | −0.272329 | − | 0.962204i | \(-0.587794\pi\) | ||||
−0.272329 | + | 0.962204i | \(0.587794\pi\) | |||||||
\(938\) | 5.03630 | − | 2.90771i | 0.164441 | − | 0.0949401i | ||||
\(939\) | 19.2728 | − | 17.1554i | 0.628946 | − | 0.559847i | ||||
\(940\) | −19.0254 | + | 32.9529i | −0.620539 | + | 1.07481i | ||||
\(941\) | −37.4236 | − | 21.6065i | −1.21997 | − | 0.704353i | −0.255062 | − | 0.966925i | \(-0.582096\pi\) |
−0.964912 | + | 0.262572i | \(0.915429\pi\) | |||||||
\(942\) | 15.0569 | − | 3.11085i | 0.490581 | − | 0.101357i | ||||
\(943\) | −15.7209 | + | 9.07649i | −0.511945 | + | 0.295571i | ||||
\(944\) | 18.8427i | 0.613277i | ||||||||
\(945\) | −2.01848 | − | 2.88053i | −0.0656612 | − | 0.0937035i | ||||
\(946\) | −110.280 | −3.58552 | ||||||||
\(947\) | −11.0435 | + | 6.37595i | −0.358864 | + | 0.207190i | −0.668583 | − | 0.743638i | \(-0.733099\pi\) |
0.309718 | + | 0.950828i | \(0.399765\pi\) | |||||||
\(948\) | −7.73937 | − | 37.4596i | −0.251363 | − | 1.21663i | ||||
\(949\) | −31.8662 | + | 24.6014i | −1.03442 | + | 0.798597i | ||||
\(950\) | −4.08051 | + | 7.06764i | −0.132389 | + | 0.229305i | ||||
\(951\) | 7.50647 | + | 8.43295i | 0.243414 | + | 0.273457i | ||||
\(952\) | −1.29314 | − | 2.23979i | −0.0419109 | − | 0.0725919i | ||||
\(953\) | 57.2328 | 1.85395 | 0.926977 | − | 0.375119i | \(-0.122398\pi\) | ||||
0.926977 | + | 0.375119i | \(0.122398\pi\) | |||||||
\(954\) | −12.5853 | + | 16.9133i | −0.407465 | + | 0.547589i | ||||
\(955\) | 21.6452i | 0.700423i | ||||||||
\(956\) | 32.9182 | − | 19.0053i | 1.06465 | − | 0.614676i | ||||
\(957\) | −16.3895 | + | 49.4803i | −0.529798 | + | 1.59947i | ||||
\(958\) | −21.8899 | + | 37.9145i | −0.707232 | + | 1.22496i | ||||
\(959\) | 4.14025 | − | 7.17112i | 0.133696 | − | 0.231568i | ||||
\(960\) | 0.244518 | − | 0.738203i | 0.00789177 | − | 0.0238254i | ||||
\(961\) | 3.05673 | + | 5.29441i | 0.0986041 | + | 0.170787i | ||||
\(962\) | −9.67384 | + | 23.5509i | −0.311897 | + | 0.759312i | ||||
\(963\) | 10.8885 | − | 4.69986i | 0.350876 | − | 0.151451i | ||||
\(964\) | 63.8125i | 2.05526i | ||||||||
\(965\) | −1.53022 | − | 2.65041i | −0.0492594 | − | 0.0853198i | ||||
\(966\) | −10.7810 | + | 9.59651i | −0.346872 | + | 0.308763i | ||||
\(967\) | 17.8188 | + | 10.2877i | 0.573016 | + | 0.330831i | 0.758353 | − | 0.651844i | \(-0.226004\pi\) |
−0.185337 | + | 0.982675i | \(0.559338\pi\) | |||||||
\(968\) | 18.6748 | + | 10.7819i | 0.600229 | + | 0.346543i | ||||
\(969\) | 3.30589 | − | 0.683017i | 0.106201 | − | 0.0219417i | ||||
\(970\) | −11.3984 | + | 6.58089i | −0.365982 | + | 0.211300i | ||||
\(971\) | −47.2658 | −1.51683 | −0.758416 | − | 0.651771i | \(-0.774026\pi\) | ||||
−0.758416 | + | 0.651771i | \(0.774026\pi\) | |||||||
\(972\) | 61.3405 | − | 33.1211i | 1.96750 | − | 1.06236i | ||||
\(973\) | − | 3.51450i | − | 0.112670i | ||||||
\(974\) | 14.0867 | + | 24.3989i | 0.451367 | + | 0.781790i | ||||
\(975\) | −6.13727 | − | 1.15495i | −0.196550 | − | 0.0369880i | ||||
\(976\) | −13.1603 | + | 22.7943i | −0.421250 | + | 0.729627i | ||||
\(977\) | −3.64672 | − | 2.10544i | −0.116669 | − | 0.0673589i | 0.440530 | − | 0.897738i | \(-0.354791\pi\) |
−0.557199 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(978\) | 8.02181 | − | 7.14050i | 0.256509 | − | 0.228328i | ||||
\(979\) | 31.4341 | + | 54.4454i | 1.00464 | + | 1.74008i | ||||
\(980\) | − | 29.2548i | − | 0.934509i | ||||||
\(981\) | −18.0720 | − | 41.8686i | −0.576995 | − | 1.33676i | ||||
\(982\) | − | 53.9077i | − | 1.72026i | ||||||
\(983\) | −23.7727 | + | 13.7252i | −0.758231 | + | 0.437765i | −0.828660 | − | 0.559752i | \(-0.810897\pi\) |
0.0704290 | + | 0.997517i | \(0.477563\pi\) | |||||||
\(984\) | −38.7892 | − | 12.8483i | −1.23655 | − | 0.409588i | ||||
\(985\) | −9.63881 | + | 16.6949i | −0.307118 | + | 0.531944i | ||||
\(986\) | 10.6045 | + | 6.12249i | 0.337715 | + | 0.194980i | ||||
\(987\) | −9.47001 | − | 3.13679i | −0.301434 | − | 0.0998450i | ||||
\(988\) | −6.90261 | − | 51.2619i | −0.219601 | − | 1.63086i | ||||
\(989\) | 55.2226 | 1.75598 | ||||||||
\(990\) | 17.3065 | − | 23.2581i | 0.550037 | − | 0.739191i | ||||
\(991\) | −24.1246 | −0.766345 | −0.383172 | − | 0.923677i | \(-0.625168\pi\) | ||||
−0.383172 | + | 0.923677i | \(0.625168\pi\) | |||||||
\(992\) | −16.3560 | − | 28.3295i | −0.519305 | − | 0.899462i | ||||
\(993\) | 9.58002 | + | 10.7624i | 0.304013 | + | 0.341535i | ||||
\(994\) | −14.7297 | − | 8.50422i | −0.467199 | − | 0.269738i | ||||
\(995\) | 0.170256 | + | 0.0982975i | 0.00539749 | + | 0.00311624i | ||||
\(996\) | −89.2491 | + | 18.4394i | −2.82797 | + | 0.584275i | ||||
\(997\) | 0.378662 | + | 0.655861i | 0.0119923 | + | 0.0207713i | 0.871959 | − | 0.489578i | \(-0.162849\pi\) |
−0.859967 | + | 0.510350i | \(0.829516\pi\) | |||||||
\(998\) | 42.5526 | 1.34698 | ||||||||
\(999\) | −11.8117 | + | 8.27686i | −0.373706 | + | 0.261868i |
(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 | 585.2.bt.b.571.5 | yes | 108 | |
9.7 | even | 3 | inner | 585.2.bt.b.376.50 | yes | 108 | |
13.12 | even | 2 | inner | 585.2.bt.b.571.50 | yes | 108 | |
117.25 | even | 6 | inner | 585.2.bt.b.376.5 | ✓ | 108 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
585.2.bt.b.376.5 | ✓ | 108 | 117.25 | even | 6 | inner | |
585.2.bt.b.376.50 | yes | 108 | 9.7 | even | 3 | inner | |
585.2.bt.b.571.5 | yes | 108 | 1.1 | even | 1 | trivial | |
585.2.bt.b.571.50 | yes | 108 | 13.12 | even | 2 | inner |