Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.47 |
Dual form | 690.2.i.c.323.2 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.292893 | + | 1.70711i | −0.169102 | + | 0.985599i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 1.73205 | + | 1.41421i | 0.774597 | + | 0.632456i | ||||
\(6\) | −1.00000 | − | 1.41421i | −0.408248 | − | 0.577350i | ||||
\(7\) | −2.44949 | − | 2.44949i | −0.925820 | − | 0.925820i | 0.0716124 | − | 0.997433i | \(-0.477186\pi\) |
−0.997433 | + | 0.0716124i | \(0.977186\pi\) | |||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | −2.82843 | − | 1.00000i | −0.942809 | − | 0.333333i | ||||
\(10\) | −2.22474 | + | 0.224745i | −0.703526 | + | 0.0710706i | ||||
\(11\) | − | 5.65685i | − | 1.70561i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||
0.522233 | − | 0.852803i | \(-0.325099\pi\) | |||||||
\(12\) | 1.70711 | + | 0.292893i | 0.492799 | + | 0.0845510i | ||||
\(13\) | 1.44949 | − | 1.44949i | 0.402016 | − | 0.402016i | −0.476927 | − | 0.878943i | \(-0.658249\pi\) |
0.878943 | + | 0.476927i | \(0.158249\pi\) | |||||||
\(14\) | 3.46410 | 0.925820 | ||||||||
\(15\) | −2.92152 | + | 2.54258i | −0.754333 | + | 0.656492i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 5.19615 | − | 5.19615i | 1.26025 | − | 1.26025i | 0.309282 | − | 0.950971i | \(-0.399911\pi\) |
0.950971 | − | 0.309282i | \(-0.100089\pi\) | |||||||
\(18\) | 2.70711 | − | 1.29289i | 0.638071 | − | 0.304738i | ||||
\(19\) | − | 2.44949i | − | 0.561951i | −0.959715 | − | 0.280976i | \(-0.909342\pi\) | ||
0.959715 | − | 0.280976i | \(-0.0906580\pi\) | |||||||
\(20\) | 1.41421 | − | 1.73205i | 0.316228 | − | 0.387298i | ||||
\(21\) | 4.89898 | − | 3.46410i | 1.06904 | − | 0.755929i | ||||
\(22\) | 4.00000 | + | 4.00000i | 0.852803 | + | 0.852803i | ||||
\(23\) | −0.707107 | − | 0.707107i | −0.147442 | − | 0.147442i | ||||
\(24\) | −1.41421 | + | 1.00000i | −0.288675 | + | 0.204124i | ||||
\(25\) | 1.00000 | + | 4.89898i | 0.200000 | + | 0.979796i | ||||
\(26\) | 2.04989i | 0.402016i | ||||||||
\(27\) | 2.53553 | − | 4.53553i | 0.487964 | − | 0.872864i | ||||
\(28\) | −2.44949 | + | 2.44949i | −0.462910 | + | 0.462910i | ||||
\(29\) | −9.12096 | −1.69372 | −0.846859 | − | 0.531817i | \(-0.821510\pi\) | ||||
−0.846859 | + | 0.531817i | \(0.821510\pi\) | |||||||
\(30\) | 0.267949 | − | 3.86370i | 0.0489206 | − | 0.705412i | ||||
\(31\) | −4.89898 | −0.879883 | −0.439941 | − | 0.898027i | \(-0.645001\pi\) | ||||
−0.439941 | + | 0.898027i | \(0.645001\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | 9.65685 | + | 1.65685i | 1.68104 | + | 0.288421i | ||||
\(34\) | 7.34847i | 1.26025i | ||||||||
\(35\) | −0.778539 | − | 7.70674i | −0.131597 | − | 1.30268i | ||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | 2.44949 | + | 2.44949i | 0.402694 | + | 0.402694i | 0.879181 | − | 0.476488i | \(-0.158090\pi\) |
−0.476488 | + | 0.879181i | \(0.658090\pi\) | |||||||
\(38\) | 1.73205 | + | 1.73205i | 0.280976 | + | 0.280976i | ||||
\(39\) | 2.04989 | + | 2.89898i | 0.328245 | + | 0.464208i | ||||
\(40\) | 0.224745 | + | 2.22474i | 0.0355353 | + | 0.351763i | ||||
\(41\) | − | 8.48528i | − | 1.32518i | −0.748983 | − | 0.662589i | \(-0.769458\pi\) | ||
0.748983 | − | 0.662589i | \(-0.230542\pi\) | |||||||
\(42\) | −1.01461 | + | 5.91359i | −0.156558 | + | 0.912487i | ||||
\(43\) | −6.89898 | + | 6.89898i | −1.05208 | + | 1.05208i | −0.0535176 | + | 0.998567i | \(0.517043\pi\) |
−0.998567 | + | 0.0535176i | \(0.982957\pi\) | |||||||
\(44\) | −5.65685 | −0.852803 | ||||||||
\(45\) | −3.48477 | − | 5.73205i | −0.519478 | − | 0.854484i | ||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.04989 | − | 2.04989i | 0.299007 | − | 0.299007i | −0.541618 | − | 0.840625i | \(-0.682188\pi\) |
0.840625 | + | 0.541618i | \(0.182188\pi\) | |||||||
\(48\) | 0.292893 | − | 1.70711i | 0.0422755 | − | 0.246400i | ||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | −4.17121 | − | 2.75699i | −0.589898 | − | 0.389898i | ||||
\(51\) | 7.34847 | + | 10.3923i | 1.02899 | + | 1.45521i | ||||
\(52\) | −1.44949 | − | 1.44949i | −0.201008 | − | 0.201008i | ||||
\(53\) | 9.43879 | + | 9.43879i | 1.29652 | + | 1.29652i | 0.930678 | + | 0.365840i | \(0.119218\pi\) |
0.365840 | + | 0.930678i | \(0.380782\pi\) | |||||||
\(54\) | 1.41421 | + | 5.00000i | 0.192450 | + | 0.680414i | ||||
\(55\) | 8.00000 | − | 9.79796i | 1.07872 | − | 1.32116i | ||||
\(56\) | − | 3.46410i | − | 0.462910i | ||||||
\(57\) | 4.18154 | + | 0.717439i | 0.553859 | + | 0.0950271i | ||||
\(58\) | 6.44949 | − | 6.44949i | 0.846859 | − | 0.846859i | ||||
\(59\) | 8.34242 | 1.08609 | 0.543045 | − | 0.839704i | \(-0.317271\pi\) | ||||
0.543045 | + | 0.839704i | \(0.317271\pi\) | |||||||
\(60\) | 2.54258 | + | 2.92152i | 0.328246 | + | 0.377167i | ||||
\(61\) | −8.89898 | −1.13940 | −0.569699 | − | 0.821854i | \(-0.692940\pi\) | ||||
−0.569699 | + | 0.821854i | \(0.692940\pi\) | |||||||
\(62\) | 3.46410 | − | 3.46410i | 0.439941 | − | 0.439941i | ||||
\(63\) | 4.47871 | + | 9.37769i | 0.564265 | + | 1.18148i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 4.56048 | − | 0.460702i | 0.565658 | − | 0.0571430i | ||||
\(66\) | −8.00000 | + | 5.65685i | −0.984732 | + | 0.696311i | ||||
\(67\) | −1.10102 | − | 1.10102i | −0.134511 | − | 0.134511i | 0.636646 | − | 0.771157i | \(-0.280321\pi\) |
−0.771157 | + | 0.636646i | \(0.780321\pi\) | |||||||
\(68\) | −5.19615 | − | 5.19615i | −0.630126 | − | 0.630126i | ||||
\(69\) | 1.41421 | − | 1.00000i | 0.170251 | − | 0.120386i | ||||
\(70\) | 6.00000 | + | 4.89898i | 0.717137 | + | 0.585540i | ||||
\(71\) | − | 6.14966i | − | 0.729831i | −0.931041 | − | 0.364915i | \(-0.881098\pi\) | ||
0.931041 | − | 0.364915i | \(-0.118902\pi\) | |||||||
\(72\) | −1.29289 | − | 2.70711i | −0.152369 | − | 0.319036i | ||||
\(73\) | 7.89898 | − | 7.89898i | 0.924506 | − | 0.924506i | −0.0728382 | − | 0.997344i | \(-0.523206\pi\) |
0.997344 | + | 0.0728382i | \(0.0232057\pi\) | |||||||
\(74\) | −3.46410 | −0.402694 | ||||||||
\(75\) | −8.65597 | + | 0.272229i | −0.999506 | + | 0.0314343i | ||||
\(76\) | −2.44949 | −0.280976 | ||||||||
\(77\) | −13.8564 | + | 13.8564i | −1.57908 | + | 1.57908i | ||||
\(78\) | −3.49938 | − | 0.600398i | −0.396227 | − | 0.0679817i | ||||
\(79\) | − | 0.449490i | − | 0.0505715i | −0.999680 | − | 0.0252858i | \(-0.991950\pi\) | ||
0.999680 | − | 0.0252858i | \(-0.00804957\pi\) | |||||||
\(80\) | −1.73205 | − | 1.41421i | −0.193649 | − | 0.158114i | ||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 6.00000 | + | 6.00000i | 0.662589 | + | 0.662589i | ||||
\(83\) | 1.41421 | + | 1.41421i | 0.155230 | + | 0.155230i | 0.780449 | − | 0.625219i | \(-0.214990\pi\) |
−0.625219 | + | 0.780449i | \(0.714990\pi\) | |||||||
\(84\) | −3.46410 | − | 4.89898i | −0.377964 | − | 0.534522i | ||||
\(85\) | 16.3485 | − | 1.65153i | 1.77324 | − | 0.179134i | ||||
\(86\) | − | 9.75663i | − | 1.05208i | ||||||
\(87\) | 2.67147 | − | 15.5704i | 0.286411 | − | 1.66933i | ||||
\(88\) | 4.00000 | − | 4.00000i | 0.426401 | − | 0.426401i | ||||
\(89\) | 2.19275 | 0.232431 | 0.116216 | − | 0.993224i | \(-0.462924\pi\) | ||||
0.116216 | + | 0.993224i | \(0.462924\pi\) | |||||||
\(90\) | 6.51727 | + | 1.58907i | 0.686981 | + | 0.167503i | ||||
\(91\) | −7.10102 | −0.744389 | ||||||||
\(92\) | −0.707107 | + | 0.707107i | −0.0737210 | + | 0.0737210i | ||||
\(93\) | 1.43488 | − | 8.36308i | 0.148790 | − | 0.867211i | ||||
\(94\) | 2.89898i | 0.299007i | ||||||||
\(95\) | 3.46410 | − | 4.24264i | 0.355409 | − | 0.435286i | ||||
\(96\) | 1.00000 | + | 1.41421i | 0.102062 | + | 0.144338i | ||||
\(97\) | 4.44949 | + | 4.44949i | 0.451777 | + | 0.451777i | 0.895944 | − | 0.444167i | \(-0.146500\pi\) |
−0.444167 | + | 0.895944i | \(0.646500\pi\) | |||||||
\(98\) | −3.53553 | − | 3.53553i | −0.357143 | − | 0.357143i | ||||
\(99\) | −5.65685 | + | 16.0000i | −0.568535 | + | 1.60806i | ||||
\(100\) | 4.89898 | − | 1.00000i | 0.489898 | − | 0.100000i | ||||
\(101\) | 6.29253i | 0.626130i | 0.949732 | + | 0.313065i | \(0.101356\pi\) | ||||
−0.949732 | + | 0.313065i | \(0.898644\pi\) | |||||||
\(102\) | −12.5446 | − | 2.15232i | −1.24210 | − | 0.213111i | ||||
\(103\) | −1.10102 | + | 1.10102i | −0.108487 | + | 0.108487i | −0.759267 | − | 0.650780i | \(-0.774442\pi\) |
0.650780 | + | 0.759267i | \(0.274442\pi\) | |||||||
\(104\) | 2.04989 | 0.201008 | ||||||||
\(105\) | 13.3843 | + | 0.928203i | 1.30617 | + | 0.0905834i | ||||
\(106\) | −13.3485 | −1.29652 | ||||||||
\(107\) | 0.778539 | − | 0.778539i | 0.0752642 | − | 0.0752642i | −0.668473 | − | 0.743737i | \(-0.733052\pi\) |
0.743737 | + | 0.668473i | \(0.233052\pi\) | |||||||
\(108\) | −4.53553 | − | 2.53553i | −0.436432 | − | 0.243982i | ||||
\(109\) | − | 5.79796i | − | 0.555344i | −0.960676 | − | 0.277672i | \(-0.910437\pi\) | ||
0.960676 | − | 0.277672i | \(-0.0895628\pi\) | |||||||
\(110\) | 1.27135 | + | 12.5851i | 0.121218 | + | 1.19994i | ||||
\(111\) | −4.89898 | + | 3.46410i | −0.464991 | + | 0.328798i | ||||
\(112\) | 2.44949 | + | 2.44949i | 0.231455 | + | 0.231455i | ||||
\(113\) | −2.36773 | − | 2.36773i | −0.222737 | − | 0.222737i | 0.586913 | − | 0.809650i | \(-0.300343\pi\) |
−0.809650 | + | 0.586913i | \(0.800343\pi\) | |||||||
\(114\) | −3.46410 | + | 2.44949i | −0.324443 | + | 0.229416i | ||||
\(115\) | −0.224745 | − | 2.22474i | −0.0209576 | − | 0.207459i | ||||
\(116\) | 9.12096i | 0.846859i | ||||||||
\(117\) | −5.54927 | + | 2.65029i | −0.513030 | + | 0.245019i | ||||
\(118\) | −5.89898 | + | 5.89898i | −0.543045 | + | 0.543045i | ||||
\(119\) | −25.4558 | −2.33353 | ||||||||
\(120\) | −3.86370 | − | 0.267949i | −0.352706 | − | 0.0244603i | ||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 6.29253 | − | 6.29253i | 0.569699 | − | 0.569699i | ||||
\(123\) | 14.4853 | + | 2.48528i | 1.30609 | + | 0.224090i | ||||
\(124\) | 4.89898i | 0.439941i | ||||||||
\(125\) | −5.19615 | + | 9.89949i | −0.464758 | + | 0.885438i | ||||
\(126\) | −9.79796 | − | 3.46410i | −0.872872 | − | 0.308607i | ||||
\(127\) | −8.44949 | − | 8.44949i | −0.749771 | − | 0.749771i | 0.224665 | − | 0.974436i | \(-0.427871\pi\) |
−0.974436 | + | 0.224665i | \(0.927871\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −9.75663 | − | 13.7980i | −0.859023 | − | 1.21484i | ||||
\(130\) | −2.89898 | + | 3.55051i | −0.254257 | + | 0.311400i | ||||
\(131\) | − | 13.9993i | − | 1.22312i | −0.791197 | − | 0.611561i | \(-0.790542\pi\) | ||
0.791197 | − | 0.611561i | \(-0.209458\pi\) | |||||||
\(132\) | 1.65685 | − | 9.65685i | 0.144211 | − | 0.840521i | ||||
\(133\) | −6.00000 | + | 6.00000i | −0.520266 | + | 0.520266i | ||||
\(134\) | 1.55708 | 0.134511 | ||||||||
\(135\) | 10.8059 | − | 4.26999i | 0.930023 | − | 0.367502i | ||||
\(136\) | 7.34847 | 0.630126 | ||||||||
\(137\) | −3.28913 | + | 3.28913i | −0.281009 | + | 0.281009i | −0.833511 | − | 0.552502i | \(-0.813673\pi\) |
0.552502 | + | 0.833511i | \(0.313673\pi\) | |||||||
\(138\) | −0.292893 | + | 1.70711i | −0.0249327 | + | 0.145319i | ||||
\(139\) | − | 10.6969i | − | 0.907302i | −0.891179 | − | 0.453651i | \(-0.850121\pi\) | ||
0.891179 | − | 0.453651i | \(-0.149879\pi\) | |||||||
\(140\) | −7.70674 | + | 0.778539i | −0.651339 | + | 0.0657986i | ||||
\(141\) | 2.89898 | + | 4.09978i | 0.244138 | + | 0.345263i | ||||
\(142\) | 4.34847 | + | 4.34847i | 0.364915 | + | 0.364915i | ||||
\(143\) | −8.19955 | − | 8.19955i | −0.685681 | − | 0.685681i | ||||
\(144\) | 2.82843 | + | 1.00000i | 0.235702 | + | 0.0833333i | ||||
\(145\) | −15.7980 | − | 12.8990i | −1.31195 | − | 1.07120i | ||||
\(146\) | 11.1708i | 0.924506i | ||||||||
\(147\) | −8.53553 | − | 1.46447i | −0.703999 | − | 0.120787i | ||||
\(148\) | 2.44949 | − | 2.44949i | 0.201347 | − | 0.201347i | ||||
\(149\) | 16.6848 | 1.36687 | 0.683437 | − | 0.730009i | \(-0.260484\pi\) | ||||
0.683437 | + | 0.730009i | \(0.260484\pi\) | |||||||
\(150\) | 5.92820 | − | 6.31319i | 0.484036 | − | 0.515470i | ||||
\(151\) | 8.89898 | 0.724189 | 0.362094 | − | 0.932141i | \(-0.382062\pi\) | ||||
0.362094 | + | 0.932141i | \(0.382062\pi\) | |||||||
\(152\) | 1.73205 | − | 1.73205i | 0.140488 | − | 0.140488i | ||||
\(153\) | −19.8931 | + | 9.50079i | −1.60826 | + | 0.768093i | ||||
\(154\) | − | 19.5959i | − | 1.57908i | ||||||
\(155\) | −8.48528 | − | 6.92820i | −0.681554 | − | 0.556487i | ||||
\(156\) | 2.89898 | − | 2.04989i | 0.232104 | − | 0.164122i | ||||
\(157\) | −3.55051 | − | 3.55051i | −0.283362 | − | 0.283362i | 0.551087 | − | 0.834448i | \(-0.314213\pi\) |
−0.834448 | + | 0.551087i | \(0.814213\pi\) | |||||||
\(158\) | 0.317837 | + | 0.317837i | 0.0252858 | + | 0.0252858i | ||||
\(159\) | −18.8776 | + | 13.3485i | −1.49709 | + | 1.05860i | ||||
\(160\) | 2.22474 | − | 0.224745i | 0.175882 | − | 0.0177676i | ||||
\(161\) | 3.46410i | 0.273009i | ||||||||
\(162\) | −8.94975 | + | 0.949747i | −0.703159 | + | 0.0746192i | ||||
\(163\) | −4.00000 | + | 4.00000i | −0.313304 | + | 0.313304i | −0.846188 | − | 0.532884i | \(-0.821108\pi\) |
0.532884 | + | 0.846188i | \(0.321108\pi\) | |||||||
\(164\) | −8.48528 | −0.662589 | ||||||||
\(165\) | 14.3830 | + | 16.5266i | 1.11972 | + | 1.28659i | ||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | 5.65685 | − | 5.65685i | 0.437741 | − | 0.437741i | −0.453510 | − | 0.891251i | \(-0.649829\pi\) |
0.891251 | + | 0.453510i | \(0.149829\pi\) | |||||||
\(168\) | 5.91359 | + | 1.01461i | 0.456243 | + | 0.0782790i | ||||
\(169\) | 8.79796i | 0.676766i | ||||||||
\(170\) | −10.3923 | + | 12.7279i | −0.797053 | + | 0.976187i | ||||
\(171\) | −2.44949 | + | 6.92820i | −0.187317 | + | 0.529813i | ||||
\(172\) | 6.89898 | + | 6.89898i | 0.526042 | + | 0.526042i | ||||
\(173\) | 10.5352 | + | 10.5352i | 0.800974 | + | 0.800974i | 0.983248 | − | 0.182274i | \(-0.0583457\pi\) |
−0.182274 | + | 0.983248i | \(0.558346\pi\) | |||||||
\(174\) | 9.12096 | + | 12.8990i | 0.691458 | + | 0.977869i | ||||
\(175\) | 9.55051 | − | 14.4495i | 0.721951 | − | 1.09228i | ||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | −2.44344 | + | 14.2414i | −0.183660 | + | 1.07045i | ||||
\(178\) | −1.55051 | + | 1.55051i | −0.116216 | + | 0.116216i | ||||
\(179\) | 12.4422 | 0.929973 | 0.464987 | − | 0.885318i | \(-0.346059\pi\) | ||||
0.464987 | + | 0.885318i | \(0.346059\pi\) | |||||||
\(180\) | −5.73205 | + | 3.48477i | −0.427242 | + | 0.259739i | ||||
\(181\) | 8.00000 | 0.594635 | 0.297318 | − | 0.954779i | \(-0.403908\pi\) | ||||
0.297318 | + | 0.954779i | \(0.403908\pi\) | |||||||
\(182\) | 5.02118 | − | 5.02118i | 0.372195 | − | 0.372195i | ||||
\(183\) | 2.60645 | − | 15.1915i | 0.192674 | − | 1.12299i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 0.778539 | + | 7.70674i | 0.0572393 | + | 0.566611i | ||||
\(186\) | 4.89898 | + | 6.92820i | 0.359211 | + | 0.508001i | ||||
\(187\) | −29.3939 | − | 29.3939i | −2.14949 | − | 2.14949i | ||||
\(188\) | −2.04989 | − | 2.04989i | −0.149503 | − | 0.149503i | ||||
\(189\) | −17.3205 | + | 4.89898i | −1.25988 | + | 0.356348i | ||||
\(190\) | 0.550510 | + | 5.44949i | 0.0399382 | + | 0.395348i | ||||
\(191\) | − | 23.6130i | − | 1.70858i | −0.519797 | − | 0.854290i | \(-0.673992\pi\) | ||
0.519797 | − | 0.854290i | \(-0.326008\pi\) | |||||||
\(192\) | −1.70711 | − | 0.292893i | −0.123200 | − | 0.0211377i | ||||
\(193\) | −7.89898 | + | 7.89898i | −0.568581 | + | 0.568581i | −0.931731 | − | 0.363150i | \(-0.881701\pi\) |
0.363150 | + | 0.931731i | \(0.381701\pi\) | |||||||
\(194\) | −6.29253 | −0.451777 | ||||||||
\(195\) | −0.549266 | + | 7.92016i | −0.0393337 | + | 0.567174i | ||||
\(196\) | 5.00000 | 0.357143 | ||||||||
\(197\) | −0.778539 | + | 0.778539i | −0.0554686 | + | 0.0554686i | −0.734297 | − | 0.678828i | \(-0.762488\pi\) |
0.678828 | + | 0.734297i | \(0.262488\pi\) | |||||||
\(198\) | −7.31371 | − | 15.3137i | −0.519763 | − | 1.08830i | ||||
\(199\) | 12.4495i | 0.882521i | 0.897379 | + | 0.441260i | \(0.145469\pi\) | ||||
−0.897379 | + | 0.441260i | \(0.854531\pi\) | |||||||
\(200\) | −2.75699 | + | 4.17121i | −0.194949 | + | 0.294949i | ||||
\(201\) | 2.20204 | − | 1.55708i | 0.155320 | − | 0.109828i | ||||
\(202\) | −4.44949 | − | 4.44949i | −0.313065 | − | 0.313065i | ||||
\(203\) | 22.3417 | + | 22.3417i | 1.56808 | + | 1.56808i | ||||
\(204\) | 10.3923 | − | 7.34847i | 0.727607 | − | 0.514496i | ||||
\(205\) | 12.0000 | − | 14.6969i | 0.838116 | − | 1.02648i | ||||
\(206\) | − | 1.55708i | − | 0.108487i | ||||||
\(207\) | 1.29289 | + | 2.70711i | 0.0898623 | + | 0.188157i | ||||
\(208\) | −1.44949 | + | 1.44949i | −0.100504 | + | 0.100504i | ||||
\(209\) | −13.8564 | −0.958468 | ||||||||
\(210\) | −10.1204 | + | 8.80776i | −0.698377 | + | 0.607793i | ||||
\(211\) | −10.6969 | −0.736408 | −0.368204 | − | 0.929745i | \(-0.620027\pi\) | ||||
−0.368204 | + | 0.929745i | \(0.620027\pi\) | |||||||
\(212\) | 9.43879 | − | 9.43879i | 0.648259 | − | 0.648259i | ||||
\(213\) | 10.4981 | + | 1.80119i | 0.719320 | + | 0.123416i | ||||
\(214\) | 1.10102i | 0.0752642i | ||||||||
\(215\) | −21.7060 | + | 2.19275i | −1.48034 | + | 0.149544i | ||||
\(216\) | 5.00000 | − | 1.41421i | 0.340207 | − | 0.0962250i | ||||
\(217\) | 12.0000 | + | 12.0000i | 0.814613 | + | 0.814613i | ||||
\(218\) | 4.09978 | + | 4.09978i | 0.277672 | + | 0.277672i | ||||
\(219\) | 11.1708 | + | 15.7980i | 0.754856 | + | 1.06753i | ||||
\(220\) | −9.79796 | − | 8.00000i | −0.660578 | − | 0.539360i | ||||
\(221\) | − | 15.0635i | − | 1.01328i | ||||||
\(222\) | 1.01461 | − | 5.91359i | 0.0680963 | − | 0.396894i | ||||
\(223\) | −7.55051 | + | 7.55051i | −0.505620 | + | 0.505620i | −0.913179 | − | 0.407559i | \(-0.866380\pi\) |
0.407559 | + | 0.913179i | \(0.366380\pi\) | |||||||
\(224\) | −3.46410 | −0.231455 | ||||||||
\(225\) | 2.07055 | − | 14.8564i | 0.138037 | − | 0.990427i | ||||
\(226\) | 3.34847 | 0.222737 | ||||||||
\(227\) | 7.70674 | − | 7.70674i | 0.511514 | − | 0.511514i | −0.403476 | − | 0.914990i | \(-0.632198\pi\) |
0.914990 | + | 0.403476i | \(0.132198\pi\) | |||||||
\(228\) | 0.717439 | − | 4.18154i | 0.0475136 | − | 0.276929i | ||||
\(229\) | 22.6969i | 1.49986i | 0.661520 | + | 0.749928i | \(0.269912\pi\) | ||||
−0.661520 | + | 0.749928i | \(0.730088\pi\) | |||||||
\(230\) | 1.73205 | + | 1.41421i | 0.114208 | + | 0.0932505i | ||||
\(231\) | −19.5959 | − | 27.7128i | −1.28932 | − | 1.82337i | ||||
\(232\) | −6.44949 | − | 6.44949i | −0.423430 | − | 0.423430i | ||||
\(233\) | −10.5352 | − | 10.5352i | −0.690182 | − | 0.690182i | 0.272090 | − | 0.962272i | \(-0.412285\pi\) |
−0.962272 | + | 0.272090i | \(0.912285\pi\) | |||||||
\(234\) | 2.04989 | − | 5.79796i | 0.134005 | − | 0.379024i | ||||
\(235\) | 6.44949 | − | 0.651531i | 0.420718 | − | 0.0425012i | ||||
\(236\) | − | 8.34242i | − | 0.543045i | ||||||
\(237\) | 0.767327 | + | 0.131652i | 0.0498432 | + | 0.00855175i | ||||
\(238\) | 18.0000 | − | 18.0000i | 1.16677 | − | 1.16677i | ||||
\(239\) | 6.43539 | 0.416271 | 0.208135 | − | 0.978100i | \(-0.433261\pi\) | ||||
0.208135 | + | 0.978100i | \(0.433261\pi\) | |||||||
\(240\) | 2.92152 | − | 2.54258i | 0.188583 | − | 0.164123i | ||||
\(241\) | −18.8990 | −1.21739 | −0.608695 | − | 0.793404i | \(-0.708307\pi\) | ||||
−0.608695 | + | 0.793404i | \(0.708307\pi\) | |||||||
\(242\) | 14.8492 | − | 14.8492i | 0.954545 | − | 0.954545i | ||||
\(243\) | −11.7071 | + | 10.2929i | −0.751011 | + | 0.660289i | ||||
\(244\) | 8.89898i | 0.569699i | ||||||||
\(245\) | −7.07107 | + | 8.66025i | −0.451754 | + | 0.553283i | ||||
\(246\) | −12.0000 | + | 8.48528i | −0.765092 | + | 0.541002i | ||||
\(247\) | −3.55051 | − | 3.55051i | −0.225914 | − | 0.225914i | ||||
\(248\) | −3.46410 | − | 3.46410i | −0.219971 | − | 0.219971i | ||||
\(249\) | −2.82843 | + | 2.00000i | −0.179244 | + | 0.126745i | ||||
\(250\) | −3.32577 | − | 10.6742i | −0.210340 | − | 0.675098i | ||||
\(251\) | 26.7272i | 1.68701i | 0.537125 | + | 0.843503i | \(0.319510\pi\) | ||||
−0.537125 | + | 0.843503i | \(0.680490\pi\) | |||||||
\(252\) | 9.37769 | − | 4.47871i | 0.590739 | − | 0.282132i | ||||
\(253\) | −4.00000 | + | 4.00000i | −0.251478 | + | 0.251478i | ||||
\(254\) | 11.9494 | 0.749771 | ||||||||
\(255\) | −1.96902 | + | 28.3923i | −0.123305 | + | 1.77800i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 18.0990 | − | 18.0990i | 1.12899 | − | 1.12899i | 0.138645 | − | 0.990342i | \(-0.455725\pi\) |
0.990342 | − | 0.138645i | \(-0.0442748\pi\) | |||||||
\(258\) | 16.6556 | + | 2.85765i | 1.03693 | + | 0.177910i | ||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | −0.460702 | − | 4.56048i | −0.0285715 | − | 0.282829i | ||||
\(261\) | 25.7980 | + | 9.12096i | 1.59685 | + | 0.564573i | ||||
\(262\) | 9.89898 | + | 9.89898i | 0.611561 | + | 0.611561i | ||||
\(263\) | −5.65685 | − | 5.65685i | −0.348817 | − | 0.348817i | 0.510852 | − | 0.859669i | \(-0.329330\pi\) |
−0.859669 | + | 0.510852i | \(0.829330\pi\) | |||||||
\(264\) | 5.65685 | + | 8.00000i | 0.348155 | + | 0.492366i | ||||
\(265\) | 3.00000 | + | 29.6969i | 0.184289 | + | 1.82427i | ||||
\(266\) | − | 8.48528i | − | 0.520266i | ||||||
\(267\) | −0.642242 | + | 3.74326i | −0.0393046 | + | 0.229084i | ||||
\(268\) | −1.10102 | + | 1.10102i | −0.0672555 | + | 0.0672555i | ||||
\(269\) | −0.635674 | −0.0387578 | −0.0193789 | − | 0.999812i | \(-0.506169\pi\) | ||||
−0.0193789 | + | 0.999812i | \(0.506169\pi\) | |||||||
\(270\) | −4.62158 | + | 10.6603i | −0.281260 | + | 0.648762i | ||||
\(271\) | 24.4949 | 1.48796 | 0.743980 | − | 0.668202i | \(-0.232936\pi\) | ||||
0.743980 | + | 0.668202i | \(0.232936\pi\) | |||||||
\(272\) | −5.19615 | + | 5.19615i | −0.315063 | + | 0.315063i | ||||
\(273\) | 2.07984 | − | 12.1222i | 0.125878 | − | 0.733669i | ||||
\(274\) | − | 4.65153i | − | 0.281009i | ||||||
\(275\) | 27.7128 | − | 5.65685i | 1.67115 | − | 0.341121i | ||||
\(276\) | −1.00000 | − | 1.41421i | −0.0601929 | − | 0.0851257i | ||||
\(277\) | −4.55051 | − | 4.55051i | −0.273414 | − | 0.273414i | 0.557059 | − | 0.830473i | \(-0.311930\pi\) |
−0.830473 | + | 0.557059i | \(0.811930\pi\) | |||||||
\(278\) | 7.56388 | + | 7.56388i | 0.453651 | + | 0.453651i | ||||
\(279\) | 13.8564 | + | 4.89898i | 0.829561 | + | 0.293294i | ||||
\(280\) | 4.89898 | − | 6.00000i | 0.292770 | − | 0.358569i | ||||
\(281\) | 5.65685i | 0.337460i | 0.985662 | + | 0.168730i | \(0.0539665\pi\) | ||||
−0.985662 | + | 0.168730i | \(0.946033\pi\) | |||||||
\(282\) | −4.94887 | − | 0.849091i | −0.294701 | − | 0.0505627i | ||||
\(283\) | −9.34847 | + | 9.34847i | −0.555709 | + | 0.555709i | −0.928083 | − | 0.372374i | \(-0.878544\pi\) |
0.372374 | + | 0.928083i | \(0.378544\pi\) | |||||||
\(284\) | −6.14966 | −0.364915 | ||||||||
\(285\) | 6.22803 | + | 7.15623i | 0.368917 | + | 0.423899i | ||||
\(286\) | 11.5959 | 0.685681 | ||||||||
\(287\) | −20.7846 | + | 20.7846i | −1.22688 | + | 1.22688i | ||||
\(288\) | −2.70711 | + | 1.29289i | −0.159518 | + | 0.0761845i | ||||
\(289\) | − | 37.0000i | − | 2.17647i | ||||||
\(290\) | 20.2918 | − | 2.04989i | 1.19158 | − | 0.120374i | ||||
\(291\) | −8.89898 | + | 6.29253i | −0.521667 | + | 0.368875i | ||||
\(292\) | −7.89898 | − | 7.89898i | −0.462253 | − | 0.462253i | ||||
\(293\) | −10.7101 | − | 10.7101i | −0.625693 | − | 0.625693i | 0.321288 | − | 0.946981i | \(-0.395884\pi\) |
−0.946981 | + | 0.321288i | \(0.895884\pi\) | |||||||
\(294\) | 7.07107 | − | 5.00000i | 0.412393 | − | 0.291606i | ||||
\(295\) | 14.4495 | + | 11.7980i | 0.841282 | + | 0.686904i | ||||
\(296\) | 3.46410i | 0.201347i | ||||||||
\(297\) | −25.6569 | − | 14.3431i | −1.48876 | − | 0.832274i | ||||
\(298\) | −11.7980 | + | 11.7980i | −0.683437 | + | 0.683437i | ||||
\(299\) | −2.04989 | −0.118548 | ||||||||
\(300\) | 0.272229 | + | 8.65597i | 0.0157171 | + | 0.499753i | ||||
\(301\) | 33.7980 | 1.94808 | ||||||||
\(302\) | −6.29253 | + | 6.29253i | −0.362094 | + | 0.362094i | ||||
\(303\) | −10.7420 | − | 1.84304i | −0.617113 | − | 0.105880i | ||||
\(304\) | 2.44949i | 0.140488i | ||||||||
\(305\) | −15.4135 | − | 12.5851i | −0.882574 | − | 0.720618i | ||||
\(306\) | 7.34847 | − | 20.7846i | 0.420084 | − | 1.18818i | ||||
\(307\) | 6.69694 | + | 6.69694i | 0.382214 | + | 0.382214i | 0.871899 | − | 0.489685i | \(-0.162888\pi\) |
−0.489685 | + | 0.871899i | \(0.662888\pi\) | |||||||
\(308\) | 13.8564 | + | 13.8564i | 0.789542 | + | 0.789542i | ||||
\(309\) | −1.55708 | − | 2.20204i | −0.0885791 | − | 0.125270i | ||||
\(310\) | 10.8990 | − | 1.10102i | 0.619020 | − | 0.0625338i | ||||
\(311\) | 34.1482i | 1.93637i | 0.250241 | + | 0.968184i | \(0.419490\pi\) | ||||
−0.250241 | + | 0.968184i | \(0.580510\pi\) | |||||||
\(312\) | −0.600398 | + | 3.49938i | −0.0339909 | + | 0.198113i | ||||
\(313\) | 19.1464 | − | 19.1464i | 1.08222 | − | 1.08222i | 0.0859179 | − | 0.996302i | \(-0.472618\pi\) |
0.996302 | − | 0.0859179i | \(-0.0273823\pi\) | |||||||
\(314\) | 5.02118 | 0.283362 | ||||||||
\(315\) | −5.50470 | + | 22.5765i | −0.310155 | + | 1.27204i | ||||
\(316\) | −0.449490 | −0.0252858 | ||||||||
\(317\) | −6.43539 | + | 6.43539i | −0.361448 | + | 0.361448i | −0.864346 | − | 0.502898i | \(-0.832267\pi\) |
0.502898 | + | 0.864346i | \(0.332267\pi\) | |||||||
\(318\) | 3.90968 | − | 22.7873i | 0.219244 | − | 1.27785i | ||||
\(319\) | 51.5959i | 2.88882i | ||||||||
\(320\) | −1.41421 | + | 1.73205i | −0.0790569 | + | 0.0968246i | ||||
\(321\) | 1.10102 | + | 1.55708i | 0.0614530 | + | 0.0869076i | ||||
\(322\) | −2.44949 | − | 2.44949i | −0.136505 | − | 0.136505i | ||||
\(323\) | −12.7279 | − | 12.7279i | −0.708201 | − | 0.708201i | ||||
\(324\) | 5.65685 | − | 7.00000i | 0.314270 | − | 0.388889i | ||||
\(325\) | 8.55051 | + | 5.65153i | 0.474297 | + | 0.313491i | ||||
\(326\) | − | 5.65685i | − | 0.313304i | ||||||
\(327\) | 9.89774 | + | 1.69818i | 0.547346 | + | 0.0939097i | ||||
\(328\) | 6.00000 | − | 6.00000i | 0.331295 | − | 0.331295i | ||||
\(329\) | −10.0424 | −0.553653 | ||||||||
\(330\) | −21.8564 | − | 1.51575i | −1.20316 | − | 0.0834393i | ||||
\(331\) | 10.6969 | 0.587957 | 0.293978 | − | 0.955812i | \(-0.405021\pi\) | ||||
0.293978 | + | 0.955812i | \(0.405021\pi\) | |||||||
\(332\) | 1.41421 | − | 1.41421i | 0.0776151 | − | 0.0776151i | ||||
\(333\) | −4.47871 | − | 9.37769i | −0.245432 | − | 0.513894i | ||||
\(334\) | 8.00000i | 0.437741i | ||||||||
\(335\) | −0.349945 | − | 3.46410i | −0.0191196 | − | 0.189264i | ||||
\(336\) | −4.89898 | + | 3.46410i | −0.267261 | + | 0.188982i | ||||
\(337\) | 9.55051 | + | 9.55051i | 0.520249 | + | 0.520249i | 0.917647 | − | 0.397397i | \(-0.130086\pi\) |
−0.397397 | + | 0.917647i | \(0.630086\pi\) | |||||||
\(338\) | −6.22110 | − | 6.22110i | −0.338383 | − | 0.338383i | ||||
\(339\) | 4.73545 | − | 3.34847i | 0.257194 | − | 0.181864i | ||||
\(340\) | −1.65153 | − | 16.3485i | −0.0895668 | − | 0.886620i | ||||
\(341\) | 27.7128i | 1.50073i | ||||||||
\(342\) | −3.16693 | − | 6.63103i | −0.171248 | − | 0.358565i | ||||
\(343\) | −4.89898 | + | 4.89898i | −0.264520 | + | 0.264520i | ||||
\(344\) | −9.75663 | −0.526042 | ||||||||
\(345\) | 3.86370 | + | 0.267949i | 0.208015 | + | 0.0144259i | ||||
\(346\) | −14.8990 | −0.800974 | ||||||||
\(347\) | −13.9993 | + | 13.9993i | −0.751520 | + | 0.751520i | −0.974763 | − | 0.223243i | \(-0.928336\pi\) |
0.223243 | + | 0.974763i | \(0.428336\pi\) | |||||||
\(348\) | −15.5704 | − | 2.67147i | −0.834663 | − | 0.143206i | ||||
\(349\) | − | 22.0000i | − | 1.17763i | −0.808267 | − | 0.588817i | \(-0.799594\pi\) | ||
0.808267 | − | 0.588817i | \(-0.200406\pi\) | |||||||
\(350\) | 3.46410 | + | 16.9706i | 0.185164 | + | 0.907115i | ||||
\(351\) | −2.89898 | − | 10.2494i | −0.154736 | − | 0.547075i | ||||
\(352\) | −4.00000 | − | 4.00000i | −0.213201 | − | 0.213201i | ||||
\(353\) | 2.33562 | + | 2.33562i | 0.124312 | + | 0.124312i | 0.766526 | − | 0.642213i | \(-0.221984\pi\) |
−0.642213 | + | 0.766526i | \(0.721984\pi\) | |||||||
\(354\) | −8.34242 | − | 11.7980i | −0.443394 | − | 0.627054i | ||||
\(355\) | 8.69694 | − | 10.6515i | 0.461586 | − | 0.565325i | ||||
\(356\) | − | 2.19275i | − | 0.116216i | ||||||
\(357\) | 7.45584 | − | 43.4558i | 0.394605 | − | 2.29993i | ||||
\(358\) | −8.79796 | + | 8.79796i | −0.464987 | + | 0.464987i | ||||
\(359\) | 12.8708 | 0.679294 | 0.339647 | − | 0.940553i | \(-0.389692\pi\) | ||||
0.339647 | + | 0.940553i | \(0.389692\pi\) | |||||||
\(360\) | 1.58907 | − | 6.51727i | 0.0837514 | − | 0.343490i | ||||
\(361\) | 13.0000 | 0.684211 | ||||||||
\(362\) | −5.65685 | + | 5.65685i | −0.297318 | + | 0.297318i | ||||
\(363\) | 6.15076 | − | 35.8492i | 0.322831 | − | 1.88160i | ||||
\(364\) | 7.10102i | 0.372195i | ||||||||
\(365\) | 24.8523 | − | 2.51059i | 1.30083 | − | 0.131410i | ||||
\(366\) | 8.89898 | + | 12.5851i | 0.465157 | + | 0.657831i | ||||
\(367\) | 0.202041 | + | 0.202041i | 0.0105465 | + | 0.0105465i | 0.712360 | − | 0.701814i | \(-0.247626\pi\) |
−0.701814 | + | 0.712360i | \(0.747626\pi\) | |||||||
\(368\) | 0.707107 | + | 0.707107i | 0.0368605 | + | 0.0368605i | ||||
\(369\) | −8.48528 | + | 24.0000i | −0.441726 | + | 1.24939i | ||||
\(370\) | −6.00000 | − | 4.89898i | −0.311925 | − | 0.254686i | ||||
\(371\) | − | 46.2405i | − | 2.40068i | ||||||
\(372\) | −8.36308 | − | 1.43488i | −0.433606 | − | 0.0743950i | ||||
\(373\) | 7.55051 | − | 7.55051i | 0.390951 | − | 0.390951i | −0.484076 | − | 0.875026i | \(-0.660844\pi\) |
0.875026 | + | 0.484076i | \(0.160844\pi\) | |||||||
\(374\) | 41.5692 | 2.14949 | ||||||||
\(375\) | −15.3776 | − | 11.7699i | −0.794095 | − | 0.607794i | ||||
\(376\) | 2.89898 | 0.149503 | ||||||||
\(377\) | −13.2207 | + | 13.2207i | −0.680902 | + | 0.680902i | ||||
\(378\) | 8.78335 | − | 15.7116i | 0.451767 | − | 0.808115i | ||||
\(379\) | − | 29.1464i | − | 1.49715i | −0.663049 | − | 0.748576i | \(-0.730738\pi\) | ||
0.663049 | − | 0.748576i | \(-0.269262\pi\) | |||||||
\(380\) | −4.24264 | − | 3.46410i | −0.217643 | − | 0.177705i | ||||
\(381\) | 16.8990 | − | 11.9494i | 0.865761 | − | 0.612185i | ||||
\(382\) | 16.6969 | + | 16.6969i | 0.854290 | + | 0.854290i | ||||
\(383\) | 16.0492 | + | 16.0492i | 0.820074 | + | 0.820074i | 0.986118 | − | 0.166045i | \(-0.0530995\pi\) |
−0.166045 | + | 0.986118i | \(0.553100\pi\) | |||||||
\(384\) | 1.41421 | − | 1.00000i | 0.0721688 | − | 0.0510310i | ||||
\(385\) | −43.5959 | + | 4.40408i | −2.22185 | + | 0.224453i | ||||
\(386\) | − | 11.1708i | − | 0.568581i | ||||||
\(387\) | 26.4122 | − | 12.6143i | 1.34261 | − | 0.641220i | ||||
\(388\) | 4.44949 | − | 4.44949i | 0.225889 | − | 0.225889i | ||||
\(389\) | 31.1127 | 1.57748 | 0.788738 | − | 0.614729i | \(-0.210735\pi\) | ||||
0.788738 | + | 0.614729i | \(0.210735\pi\) | |||||||
\(390\) | −5.21201 | − | 5.98879i | −0.263920 | − | 0.303254i | ||||
\(391\) | −7.34847 | −0.371628 | ||||||||
\(392\) | −3.53553 | + | 3.53553i | −0.178571 | + | 0.178571i | ||||
\(393\) | 23.8983 | + | 4.10029i | 1.20551 | + | 0.206832i | ||||
\(394\) | − | 1.10102i | − | 0.0554686i | ||||||
\(395\) | 0.635674 | − | 0.778539i | 0.0319843 | − | 0.0391726i | ||||
\(396\) | 16.0000 | + | 5.65685i | 0.804030 | + | 0.284268i | ||||
\(397\) | 13.4495 | + | 13.4495i | 0.675011 | + | 0.675011i | 0.958867 | − | 0.283856i | \(-0.0916139\pi\) |
−0.283856 | + | 0.958867i | \(0.591614\pi\) | |||||||
\(398\) | −8.80312 | − | 8.80312i | −0.441260 | − | 0.441260i | ||||
\(399\) | −8.48528 | − | 12.0000i | −0.424795 | − | 0.600751i | ||||
\(400\) | −1.00000 | − | 4.89898i | −0.0500000 | − | 0.244949i | ||||
\(401\) | − | 14.7778i | − | 0.737969i | −0.929436 | − | 0.368984i | \(-0.879706\pi\) | ||
0.929436 | − | 0.368984i | \(-0.120294\pi\) | |||||||
\(402\) | −0.456058 | + | 2.65810i | −0.0227461 | + | 0.132574i | ||||
\(403\) | −7.10102 | + | 7.10102i | −0.353727 | + | 0.353727i | ||||
\(404\) | 6.29253 | 0.313065 | ||||||||
\(405\) | 4.12436 | + | 19.6975i | 0.204941 | + | 0.978774i | ||||
\(406\) | −31.5959 | −1.56808 | ||||||||
\(407\) | 13.8564 | − | 13.8564i | 0.686837 | − | 0.686837i | ||||
\(408\) | −2.15232 | + | 12.5446i | −0.106556 | + | 0.621051i | ||||
\(409\) | − | 5.79796i | − | 0.286691i | −0.989673 | − | 0.143345i | \(-0.954214\pi\) | ||
0.989673 | − | 0.143345i | \(-0.0457860\pi\) | |||||||
\(410\) | 1.90702 | + | 18.8776i | 0.0941812 | + | 0.932298i | ||||
\(411\) | −4.65153 | − | 6.57826i | −0.229443 | − | 0.324482i | ||||
\(412\) | 1.10102 | + | 1.10102i | 0.0542434 | + | 0.0542434i | ||||
\(413\) | −20.4347 | − | 20.4347i | −1.00552 | − | 1.00552i | ||||
\(414\) | −2.82843 | − | 1.00000i | −0.139010 | − | 0.0491473i | ||||
\(415\) | 0.449490 | + | 4.44949i | 0.0220646 | + | 0.218417i | ||||
\(416\) | − | 2.04989i | − | 0.100504i | ||||||
\(417\) | 18.2608 | + | 3.13306i | 0.894236 | + | 0.153427i | ||||
\(418\) | 9.79796 | − | 9.79796i | 0.479234 | − | 0.479234i | ||||
\(419\) | −18.2419 | −0.891176 | −0.445588 | − | 0.895238i | \(-0.647005\pi\) | ||||
−0.445588 | + | 0.895238i | \(0.647005\pi\) | |||||||
\(420\) | 0.928203 | − | 13.3843i | 0.0452917 | − | 0.653085i | ||||
\(421\) | −8.89898 | −0.433710 | −0.216855 | − | 0.976204i | \(-0.569580\pi\) | ||||
−0.216855 | + | 0.976204i | \(0.569580\pi\) | |||||||
\(422\) | 7.56388 | − | 7.56388i | 0.368204 | − | 0.368204i | ||||
\(423\) | −7.84785 | + | 3.74807i | −0.381575 | + | 0.182237i | ||||
\(424\) | 13.3485i | 0.648259i | ||||||||
\(425\) | 30.6520 | + | 20.2597i | 1.48684 | + | 0.982739i | ||||
\(426\) | −8.69694 | + | 6.14966i | −0.421368 | + | 0.297952i | ||||
\(427\) | 21.7980 | + | 21.7980i | 1.05488 | + | 1.05488i | ||||
\(428\) | −0.778539 | − | 0.778539i | −0.0376321 | − | 0.0376321i | ||||
\(429\) | 16.3991 | − | 11.5959i | 0.791756 | − | 0.559856i | ||||
\(430\) | 13.7980 | − | 16.8990i | 0.665397 | − | 0.814941i | ||||
\(431\) | − | 5.37113i | − | 0.258718i | −0.991598 | − | 0.129359i | \(-0.958708\pi\) | ||
0.991598 | − | 0.129359i | \(-0.0412920\pi\) | |||||||
\(432\) | −2.53553 | + | 4.53553i | −0.121991 | + | 0.218216i | ||||
\(433\) | 14.6515 | − | 14.6515i | 0.704108 | − | 0.704108i | −0.261182 | − | 0.965290i | \(-0.584112\pi\) |
0.965290 | + | 0.261182i | \(0.0841123\pi\) | |||||||
\(434\) | −16.9706 | −0.814613 | ||||||||
\(435\) | 26.6471 | − | 23.1908i | 1.27763 | − | 1.11191i | ||||
\(436\) | −5.79796 | −0.277672 | ||||||||
\(437\) | −1.73205 | + | 1.73205i | −0.0828552 | + | 0.0828552i | ||||
\(438\) | −19.0698 | − | 3.27186i | −0.911191 | − | 0.156336i | ||||
\(439\) | − | 16.0000i | − | 0.763638i | −0.924237 | − | 0.381819i | \(-0.875298\pi\) | ||
0.924237 | − | 0.381819i | \(-0.124702\pi\) | |||||||
\(440\) | 12.5851 | − | 1.27135i | 0.599969 | − | 0.0606092i | ||||
\(441\) | 5.00000 | − | 14.1421i | 0.238095 | − | 0.673435i | ||||
\(442\) | 10.6515 | + | 10.6515i | 0.506642 | + | 0.506642i | ||||
\(443\) | 11.3137 | + | 11.3137i | 0.537531 | + | 0.537531i | 0.922803 | − | 0.385272i | \(-0.125893\pi\) |
−0.385272 | + | 0.922803i | \(0.625893\pi\) | |||||||
\(444\) | 3.46410 | + | 4.89898i | 0.164399 | + | 0.232495i | ||||
\(445\) | 3.79796 | + | 3.10102i | 0.180041 | + | 0.147002i | ||||
\(446\) | − | 10.6780i | − | 0.505620i | ||||||
\(447\) | −4.88687 | + | 28.4828i | −0.231141 | + | 1.34719i | ||||
\(448\) | 2.44949 | − | 2.44949i | 0.115728 | − | 0.115728i | ||||
\(449\) | −26.4415 | −1.24785 | −0.623925 | − | 0.781484i | \(-0.714463\pi\) | ||||
−0.623925 | + | 0.781484i | \(0.714463\pi\) | |||||||
\(450\) | 9.04096 | + | 11.9692i | 0.426195 | + | 0.564232i | ||||
\(451\) | −48.0000 | −2.26023 | ||||||||
\(452\) | −2.36773 | + | 2.36773i | −0.111368 | + | 0.111368i | ||||
\(453\) | −2.60645 | + | 15.1915i | −0.122462 | + | 0.713759i | ||||
\(454\) | 10.8990i | 0.511514i | ||||||||
\(455\) | −12.2993 | − | 10.0424i | −0.576601 | − | 0.470793i | ||||
\(456\) | 2.44949 | + | 3.46410i | 0.114708 | + | 0.162221i | ||||
\(457\) | 6.44949 | + | 6.44949i | 0.301694 | + | 0.301694i | 0.841677 | − | 0.539982i | \(-0.181569\pi\) |
−0.539982 | + | 0.841677i | \(0.681569\pi\) | |||||||
\(458\) | −16.0492 | − | 16.0492i | −0.749928 | − | 0.749928i | ||||
\(459\) | −10.3923 | − | 36.7423i | −0.485071 | − | 1.71499i | ||||
\(460\) | −2.22474 | + | 0.224745i | −0.103729 | + | 0.0104788i | ||||
\(461\) | 3.17837i | 0.148032i | 0.997257 | + | 0.0740158i | \(0.0235815\pi\) | ||||
−0.997257 | + | 0.0740158i | \(0.976418\pi\) | |||||||
\(462\) | 33.4523 | + | 5.73951i | 1.55634 | + | 0.267026i | ||||
\(463\) | −18.0454 | + | 18.0454i | −0.838641 | + | 0.838641i | −0.988680 | − | 0.150039i | \(-0.952060\pi\) |
0.150039 | + | 0.988680i | \(0.452060\pi\) | |||||||
\(464\) | 9.12096 | 0.423430 | ||||||||
\(465\) | 14.3125 | − | 12.4561i | 0.663725 | − | 0.577636i | ||||
\(466\) | 14.8990 | 0.690182 | ||||||||
\(467\) | −10.5352 | + | 10.5352i | −0.487510 | + | 0.487510i | −0.907519 | − | 0.420010i | \(-0.862027\pi\) |
0.420010 | + | 0.907519i | \(0.362027\pi\) | |||||||
\(468\) | 2.65029 | + | 5.54927i | 0.122510 | + | 0.256515i | ||||
\(469\) | 5.39388i | 0.249066i | ||||||||
\(470\) | −4.09978 | + | 5.02118i | −0.189109 | + | 0.231610i | ||||
\(471\) | 7.10102 | − | 5.02118i | 0.327198 | − | 0.231364i | ||||
\(472\) | 5.89898 | + | 5.89898i | 0.271523 | + | 0.271523i | ||||
\(473\) | 39.0265 | + | 39.0265i | 1.79444 | + | 1.79444i | ||||
\(474\) | −0.635674 | + | 0.449490i | −0.0291975 | + | 0.0206457i | ||||
\(475\) | 12.0000 | − | 2.44949i | 0.550598 | − | 0.112390i | ||||
\(476\) | 25.4558i | 1.16677i | ||||||||
\(477\) | −17.2581 | − | 36.1357i | −0.790196 | − | 1.65454i | ||||
\(478\) | −4.55051 | + | 4.55051i | −0.208135 | + | 0.208135i | ||||
\(479\) | −15.1278 | −0.691205 | −0.345602 | − | 0.938381i | \(-0.612325\pi\) | ||||
−0.345602 | + | 0.938381i | \(0.612325\pi\) | |||||||
\(480\) | −0.267949 | + | 3.86370i | −0.0122302 | + | 0.176353i | ||||
\(481\) | 7.10102 | 0.323779 | ||||||||
\(482\) | 13.3636 | − | 13.3636i | 0.608695 | − | 0.608695i | ||||
\(483\) | −5.91359 | − | 1.01461i | −0.269078 | − | 0.0461664i | ||||
\(484\) | 21.0000i | 0.954545i | ||||||||
\(485\) | 1.41421 | + | 13.9993i | 0.0642161 | + | 0.635674i | ||||
\(486\) | 1.00000 | − | 15.5563i | 0.0453609 | − | 0.705650i | ||||
\(487\) | 4.65153 | + | 4.65153i | 0.210781 | + | 0.210781i | 0.804599 | − | 0.593818i | \(-0.202380\pi\) |
−0.593818 | + | 0.804599i | \(0.702380\pi\) | |||||||
\(488\) | −6.29253 | − | 6.29253i | −0.284849 | − | 0.284849i | ||||
\(489\) | −5.65685 | − | 8.00000i | −0.255812 | − | 0.361773i | ||||
\(490\) | −1.12372 | − | 11.1237i | −0.0507647 | − | 0.502519i | ||||
\(491\) | 11.4566i | 0.517028i | 0.966008 | + | 0.258514i | \(0.0832328\pi\) | ||||
−0.966008 | + | 0.258514i | \(0.916767\pi\) | |||||||
\(492\) | 2.48528 | − | 14.4853i | 0.112045 | − | 0.653047i | ||||
\(493\) | −47.3939 | + | 47.3939i | −2.13451 | + | 2.13451i | ||||
\(494\) | 5.02118 | 0.225914 | ||||||||
\(495\) | −32.4254 | + | 19.7128i | −1.45741 | + | 0.886025i | ||||
\(496\) | 4.89898 | 0.219971 | ||||||||
\(497\) | −15.0635 | + | 15.0635i | −0.675692 | + | 0.675692i | ||||
\(498\) | 0.585786 | − | 3.41421i | 0.0262497 | − | 0.152995i | ||||
\(499\) | − | 14.2020i | − | 0.635771i | −0.948129 | − | 0.317885i | \(-0.897027\pi\) | ||
0.948129 | − | 0.317885i | \(-0.102973\pi\) | |||||||
\(500\) | 9.89949 | + | 5.19615i | 0.442719 | + | 0.232379i | ||||
\(501\) | 8.00000 | + | 11.3137i | 0.357414 | + | 0.505459i | ||||
\(502\) | −18.8990 | − | 18.8990i | −0.843503 | − | 0.843503i | ||||
\(503\) | 18.8776 | + | 18.8776i | 0.841710 | + | 0.841710i | 0.989081 | − | 0.147371i | \(-0.0470812\pi\) |
−0.147371 | + | 0.989081i | \(0.547081\pi\) | |||||||
\(504\) | −3.46410 | + | 9.79796i | −0.154303 | + | 0.436436i | ||||
\(505\) | −8.89898 | + | 10.8990i | −0.395999 | + | 0.484998i | ||||
\(506\) | − | 5.65685i | − | 0.251478i | ||||||
\(507\) | −15.0191 | − | 2.57686i | −0.667020 | − | 0.114442i | ||||
\(508\) | −8.44949 | + | 8.44949i | −0.374885 | + | 0.374885i | ||||
\(509\) | 42.4906 | 1.88336 | 0.941682 | − | 0.336504i | \(-0.109245\pi\) | ||||
0.941682 | + | 0.336504i | \(0.109245\pi\) | |||||||
\(510\) | −18.6841 | − | 21.4687i | −0.827345 | − | 0.950650i | ||||
\(511\) | −38.6969 | −1.71185 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −11.1097 | − | 6.21076i | −0.490507 | − | 0.274212i | ||||
\(514\) | 25.5959i | 1.12899i | ||||||||
\(515\) | −3.46410 | + | 0.349945i | −0.152647 | + | 0.0154204i | ||||
\(516\) | −13.7980 | + | 9.75663i | −0.607421 | + | 0.429512i | ||||
\(517\) | −11.5959 | − | 11.5959i | −0.509988 | − | 0.509988i | ||||
\(518\) | 8.48528 | + | 8.48528i | 0.372822 | + | 0.372822i | ||||
\(519\) | −21.0703 | + | 14.8990i | −0.924885 | + | 0.653993i | ||||
\(520\) | 3.55051 | + | 2.89898i | 0.155700 | + | 0.127129i | ||||
\(521\) | − | 42.4906i | − | 1.86155i | −0.365595 | − | 0.930774i | \(-0.619134\pi\) | ||
0.365595 | − | 0.930774i | \(-0.380866\pi\) | |||||||
\(522\) | −24.6914 | + | 11.7924i | −1.08071 | + | 0.516140i | ||||
\(523\) | 2.24745 | − | 2.24745i | 0.0982741 | − | 0.0982741i | −0.656260 | − | 0.754534i | \(-0.727863\pi\) |
0.754534 | + | 0.656260i | \(0.227863\pi\) | |||||||
\(524\) | −13.9993 | −0.611561 | ||||||||
\(525\) | 21.8695 | + | 20.5359i | 0.954465 | + | 0.896260i | ||||
\(526\) | 8.00000 | 0.348817 | ||||||||
\(527\) | −25.4558 | + | 25.4558i | −1.10887 | + | 1.10887i | ||||
\(528\) | −9.65685 | − | 1.65685i | −0.420261 | − | 0.0721053i | ||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −23.1202 | − | 18.8776i | −1.00428 | − | 0.819990i | ||||
\(531\) | −23.5959 | − | 8.34242i | −1.02398 | − | 0.362030i | ||||
\(532\) | 6.00000 | + | 6.00000i | 0.260133 | + | 0.260133i | ||||
\(533\) | −12.2993 | − | 12.2993i | −0.532743 | − | 0.532743i | ||||
\(534\) | −2.19275 | − | 3.10102i | −0.0948897 | − | 0.134194i | ||||
\(535\) | 2.44949 | − | 0.247449i | 0.105901 | − | 0.0106981i | ||||
\(536\) | − | 1.55708i | − | 0.0672555i | ||||||
\(537\) | −3.64423 | + | 21.2402i | −0.157260 | + | 0.916580i | ||||
\(538\) | 0.449490 | − | 0.449490i | 0.0193789 | − | 0.0193789i | ||||
\(539\) | 28.2843 | 1.21829 | ||||||||
\(540\) | −4.26999 | − | 10.8059i | −0.183751 | − | 0.465011i | ||||
\(541\) | −10.6969 | −0.459897 | −0.229949 | − | 0.973203i | \(-0.573856\pi\) | ||||
−0.229949 | + | 0.973203i | \(0.573856\pi\) | |||||||
\(542\) | −17.3205 | + | 17.3205i | −0.743980 | + | 0.743980i | ||||
\(543\) | −2.34315 | + | 13.6569i | −0.100554 | + | 0.586072i | ||||
\(544\) | − | 7.34847i | − | 0.315063i | ||||||
\(545\) | 8.19955 | − | 10.0424i | 0.351230 | − | 0.430167i | ||||
\(546\) | 7.10102 | + | 10.0424i | 0.303896 | + | 0.429773i | ||||
\(547\) | 27.5959 | + | 27.5959i | 1.17992 | + | 1.17992i | 0.979765 | + | 0.200151i | \(0.0641433\pi\) |
0.200151 | + | 0.979765i | \(0.435857\pi\) | |||||||
\(548\) | 3.28913 | + | 3.28913i | 0.140505 | + | 0.140505i | ||||
\(549\) | 25.1701 | + | 8.89898i | 1.07423 | + | 0.379799i | ||||
\(550\) | −15.5959 | + | 23.5959i | −0.665012 | + | 1.00613i | ||||
\(551\) | 22.3417i | 0.951788i | ||||||||
\(552\) | 1.70711 | + | 0.292893i | 0.0726593 | + | 0.0124664i | ||||
\(553\) | −1.10102 | + | 1.10102i | −0.0468202 | + | 0.0468202i | ||||
\(554\) | 6.43539 | 0.273414 | ||||||||
\(555\) | −13.3843 | − | 0.928203i | −0.568130 | − | 0.0394000i | ||||
\(556\) | −10.6969 | −0.453651 | ||||||||
\(557\) | −23.9309 | + | 23.9309i | −1.01398 | + | 1.01398i | −0.0140828 | + | 0.999901i | \(0.504483\pi\) |
−0.999901 | + | 0.0140828i | \(0.995517\pi\) | |||||||
\(558\) | −13.2621 | + | 6.33386i | −0.561428 | + | 0.268134i | ||||
\(559\) | 20.0000i | 0.845910i | ||||||||
\(560\) | 0.778539 | + | 7.70674i | 0.0328993 | + | 0.325669i | ||||
\(561\) | 58.7878 | − | 41.5692i | 2.48202 | − | 1.75505i | ||||
\(562\) | −4.00000 | − | 4.00000i | −0.168730 | − | 0.168730i | ||||
\(563\) | 1.12848 | + | 1.12848i | 0.0475599 | + | 0.0475599i | 0.730487 | − | 0.682927i | \(-0.239293\pi\) |
−0.682927 | + | 0.730487i | \(0.739293\pi\) | |||||||
\(564\) | 4.09978 | − | 2.89898i | 0.172632 | − | 0.122069i | ||||
\(565\) | −0.752551 | − | 7.44949i | −0.0316601 | − | 0.313402i | ||||
\(566\) | − | 13.2207i | − | 0.555709i | ||||||
\(567\) | −3.29002 | − | 31.0028i | −0.138168 | − | 1.30200i | ||||
\(568\) | 4.34847 | − | 4.34847i | 0.182458 | − | 0.182458i | ||||
\(569\) | −10.0424 | −0.420998 | −0.210499 | − | 0.977594i | \(-0.567509\pi\) | ||||
−0.210499 | + | 0.977594i | \(0.567509\pi\) | |||||||
\(570\) | −9.46410 | − | 0.656339i | −0.396408 | − | 0.0274910i | ||||
\(571\) | 26.4495 | 1.10688 | 0.553438 | − | 0.832890i | \(-0.313315\pi\) | ||||
0.553438 | + | 0.832890i | \(0.313315\pi\) | |||||||
\(572\) | −8.19955 | + | 8.19955i | −0.342841 | + | 0.342841i | ||||
\(573\) | 40.3100 | + | 6.91610i | 1.68397 | + | 0.288924i | ||||
\(574\) | − | 29.3939i | − | 1.22688i | ||||||
\(575\) | 2.75699 | − | 4.17121i | 0.114975 | − | 0.173951i | ||||
\(576\) | 1.00000 | − | 2.82843i | 0.0416667 | − | 0.117851i | ||||
\(577\) | 18.7980 | + | 18.7980i | 0.782569 | + | 0.782569i | 0.980264 | − | 0.197694i | \(-0.0633454\pi\) |
−0.197694 | + | 0.980264i | \(0.563345\pi\) | |||||||
\(578\) | 26.1630 | + | 26.1630i | 1.08824 | + | 1.08824i | ||||
\(579\) | −11.1708 | − | 15.7980i | −0.464244 | − | 0.656541i | ||||
\(580\) | −12.8990 | + | 15.7980i | −0.535601 | + | 0.655975i | ||||
\(581\) | − | 6.92820i | − | 0.287430i | ||||||
\(582\) | 1.84304 | − | 10.7420i | 0.0763964 | − | 0.445271i | ||||
\(583\) | 53.3939 | − | 53.3939i | 2.21135 | − | 2.21135i | ||||
\(584\) | 11.1708 | 0.462253 | ||||||||
\(585\) | −13.3597 | − | 3.25742i | −0.552355 | − | 0.134678i | ||||
\(586\) | 15.1464 | 0.625693 | ||||||||
\(587\) | 0.142865 | − | 0.142865i | 0.00589665 | − | 0.00589665i | −0.704152 | − | 0.710049i | \(-0.748673\pi\) |
0.710049 | + | 0.704152i | \(0.248673\pi\) | |||||||
\(588\) | −1.46447 | + | 8.53553i | −0.0603936 | + | 0.351999i | ||||
\(589\) | 12.0000i | 0.494451i | ||||||||
\(590\) | −18.5597 | + | 1.87492i | −0.764093 | + | 0.0771890i | ||||
\(591\) | −1.10102 | − | 1.55708i | −0.0452899 | − | 0.0640496i | ||||
\(592\) | −2.44949 | − | 2.44949i | −0.100673 | − | 0.100673i | ||||
\(593\) | 2.68556 | + | 2.68556i | 0.110283 | + | 0.110283i | 0.760095 | − | 0.649812i | \(-0.225152\pi\) |
−0.649812 | + | 0.760095i | \(0.725152\pi\) | |||||||
\(594\) | 28.2843 | − | 8.00000i | 1.16052 | − | 0.328244i | ||||
\(595\) | −44.0908 | − | 36.0000i | −1.80755 | − | 1.47586i | ||||
\(596\) | − | 16.6848i | − | 0.683437i | ||||||
\(597\) | −21.2526 | − | 3.64637i | −0.869811 | − | 0.149236i | ||||
\(598\) | 1.44949 | − | 1.44949i | 0.0592740 | − | 0.0592740i | ||||
\(599\) | −17.4634 | −0.713534 | −0.356767 | − | 0.934193i | \(-0.616121\pi\) | ||||
−0.356767 | + | 0.934193i | \(0.616121\pi\) | |||||||
\(600\) | −6.31319 | − | 5.92820i | −0.257735 | − | 0.242018i | ||||
\(601\) | −35.7980 | −1.46023 | −0.730115 | − | 0.683325i | \(-0.760533\pi\) | ||||
−0.730115 | + | 0.683325i | \(0.760533\pi\) | |||||||
\(602\) | −23.8988 | + | 23.8988i | −0.974041 | + | 0.974041i | ||||
\(603\) | 2.01314 | + | 4.21518i | 0.0819812 | + | 0.171655i | ||||
\(604\) | − | 8.89898i | − | 0.362094i | ||||||
\(605\) | −36.3731 | − | 29.6985i | −1.47878 | − | 1.20742i | ||||
\(606\) | 8.89898 | − | 6.29253i | 0.361496 | − | 0.255617i | ||||
\(607\) | 7.34847 | + | 7.34847i | 0.298265 | + | 0.298265i | 0.840334 | − | 0.542069i | \(-0.182359\pi\) |
−0.542069 | + | 0.840334i | \(0.682359\pi\) | |||||||
\(608\) | −1.73205 | − | 1.73205i | −0.0702439 | − | 0.0702439i | ||||
\(609\) | −44.6834 | + | 31.5959i | −1.81066 | + | 1.28033i | ||||
\(610\) | 19.7980 | − | 2.00000i | 0.801596 | − | 0.0809776i | ||||
\(611\) | − | 5.94258i | − | 0.240411i | ||||||
\(612\) | 9.50079 | + | 19.8931i | 0.384047 | + | 0.804131i | ||||
\(613\) | −11.3485 | + | 11.3485i | −0.458360 | + | 0.458360i | −0.898117 | − | 0.439757i | \(-0.855065\pi\) |
0.439757 | + | 0.898117i | \(0.355065\pi\) | |||||||
\(614\) | −9.47090 | −0.382214 | ||||||||
\(615\) | 21.5745 | + | 24.7899i | 0.869969 | + | 0.999626i | ||||
\(616\) | −19.5959 | −0.789542 | ||||||||
\(617\) | −12.7600 | + | 12.7600i | −0.513699 | + | 0.513699i | −0.915658 | − | 0.401958i | \(-0.868330\pi\) |
0.401958 | + | 0.915658i | \(0.368330\pi\) | |||||||
\(618\) | 2.65810 | + | 0.456058i | 0.106924 | + | 0.0183453i | ||||
\(619\) | − | 14.0454i | − | 0.564533i | −0.959336 | − | 0.282266i | \(-0.908914\pi\) | ||
0.959336 | − | 0.282266i | \(-0.0910862\pi\) | |||||||
\(620\) | −6.92820 | + | 8.48528i | −0.278243 | + | 0.340777i | ||||
\(621\) | −5.00000 | + | 1.41421i | −0.200643 | + | 0.0567504i | ||||
\(622\) | −24.1464 | − | 24.1464i | −0.968184 | − | 0.968184i | ||||
\(623\) | −5.37113 | − | 5.37113i | −0.215190 | − | 0.215190i | ||||
\(624\) | −2.04989 | − | 2.89898i | −0.0820612 | − | 0.116052i | ||||
\(625\) | −23.0000 | + | 9.79796i | −0.920000 | + | 0.391918i | ||||
\(626\) | 27.0771i | 1.08222i | ||||||||
\(627\) | 4.05845 | − | 23.6544i | 0.162079 | − | 0.944664i | ||||
\(628\) | −3.55051 | + | 3.55051i | −0.141681 | + | 0.141681i | ||||
\(629\) | 25.4558 | 1.01499 | ||||||||
\(630\) | −12.0716 | − | 19.8564i | −0.480943 | − | 0.791098i | ||||
\(631\) | 19.5505 | 0.778294 | 0.389147 | − | 0.921176i | \(-0.372770\pi\) | ||||
0.389147 | + | 0.921176i | \(0.372770\pi\) | |||||||
\(632\) | 0.317837 | − | 0.317837i | 0.0126429 | − | 0.0126429i | ||||
\(633\) | 3.13306 | − | 18.2608i | 0.124528 | − | 0.725802i | ||||
\(634\) | − | 9.10102i | − | 0.361448i | ||||||
\(635\) | −2.68556 | − | 26.5843i | −0.106573 | − | 1.05497i | ||||
\(636\) | 13.3485 | + | 18.8776i | 0.529301 | + | 0.748545i | ||||
\(637\) | 7.24745 | + | 7.24745i | 0.287154 | + | 0.287154i | ||||
\(638\) | −36.4838 | − | 36.4838i | −1.44441 | − | 1.44441i | ||||
\(639\) | −6.14966 | + | 17.3939i | −0.243277 | + | 0.688091i | ||||
\(640\) | −0.224745 | − | 2.22474i | −0.00888382 | − | 0.0879408i | ||||
\(641\) | 13.5065i | 0.533473i | 0.963769 | + | 0.266737i | \(0.0859454\pi\) | ||||
−0.963769 | + | 0.266737i | \(0.914055\pi\) | |||||||
\(642\) | −1.87956 | − | 0.322481i | −0.0741803 | − | 0.0127273i | ||||
\(643\) | −13.1010 | + | 13.1010i | −0.516654 | + | 0.516654i | −0.916557 | − | 0.399903i | \(-0.869044\pi\) |
0.399903 | + | 0.916557i | \(0.369044\pi\) | |||||||
\(644\) | 3.46410 | 0.136505 | ||||||||
\(645\) | 2.61428 | − | 37.6967i | 0.102937 | − | 1.48431i | ||||
\(646\) | 18.0000 | 0.708201 | ||||||||
\(647\) | −13.6493 | + | 13.6493i | −0.536610 | + | 0.536610i | −0.922532 | − | 0.385921i | \(-0.873884\pi\) |
0.385921 | + | 0.922532i | \(0.373884\pi\) | |||||||
\(648\) | 0.949747 | + | 8.94975i | 0.0373096 | + | 0.351579i | ||||
\(649\) | − | 47.1918i | − | 1.85244i | ||||||
\(650\) | −10.0424 | + | 2.04989i | −0.393894 | + | 0.0804032i | ||||
\(651\) | −24.0000 | + | 16.9706i | −0.940634 | + | 0.665129i | ||||
\(652\) | 4.00000 | + | 4.00000i | 0.156652 | + | 0.156652i | ||||
\(653\) | −9.26382 | − | 9.26382i | −0.362521 | − | 0.362521i | 0.502219 | − | 0.864740i | \(-0.332517\pi\) |
−0.864740 | + | 0.502219i | \(0.832517\pi\) | |||||||
\(654\) | −8.19955 | + | 5.79796i | −0.320628 | + | 0.226718i | ||||
\(655\) | 19.7980 | − | 24.2474i | 0.773570 | − | 0.947426i | ||||
\(656\) | 8.48528i | 0.331295i | ||||||||
\(657\) | −30.2407 | + | 14.4427i | −1.17980 | + | 0.563464i | ||||
\(658\) | 7.10102 | − | 7.10102i | 0.276827 | − | 0.276827i | ||||
\(659\) | 4.09978 | 0.159705 | 0.0798523 | − | 0.996807i | \(-0.474555\pi\) | ||||
0.0798523 | + | 0.996807i | \(0.474555\pi\) | |||||||
\(660\) | 16.5266 | − | 14.3830i | 0.643297 | − | 0.559858i | ||||
\(661\) | 7.10102 | 0.276198 | 0.138099 | − | 0.990418i | \(-0.455901\pi\) | ||||
0.138099 | + | 0.990418i | \(0.455901\pi\) | |||||||
\(662\) | −7.56388 | + | 7.56388i | −0.293978 | + | 0.293978i | ||||
\(663\) | 25.7151 | + | 4.41201i | 0.998691 | + | 0.171348i | ||||
\(664\) | 2.00000i | 0.0776151i | ||||||||
\(665\) | −18.8776 | + | 1.90702i | −0.732041 | + | 0.0739512i | ||||
\(666\) | 9.79796 | + | 3.46410i | 0.379663 | + | 0.134231i | ||||
\(667\) | 6.44949 | + | 6.44949i | 0.249725 | + | 0.249725i | ||||
\(668\) | −5.65685 | − | 5.65685i | −0.218870 | − | 0.218870i | ||||
\(669\) | −10.6780 | − | 15.1010i | −0.412837 | − | 0.583839i | ||||
\(670\) | 2.69694 | + | 2.20204i | 0.104192 | + | 0.0850723i | ||||
\(671\) | 50.3402i | 1.94336i | ||||||||
\(672\) | 1.01461 | − | 5.91359i | 0.0391395 | − | 0.228122i | ||||
\(673\) | 3.00000 | − | 3.00000i | 0.115642 | − | 0.115642i | −0.646918 | − | 0.762560i | \(-0.723942\pi\) |
0.762560 | + | 0.646918i | \(0.223942\pi\) | |||||||
\(674\) | −13.5065 | −0.520249 | ||||||||
\(675\) | 24.7550 | + | 7.88599i | 0.952821 | + | 0.303532i | ||||
\(676\) | 8.79796 | 0.338383 | ||||||||
\(677\) | 22.6595 | − | 22.6595i | 0.870876 | − | 0.870876i | −0.121692 | − | 0.992568i | \(-0.538832\pi\) |
0.992568 | + | 0.121692i | \(0.0388319\pi\) | |||||||
\(678\) | −0.980744 | + | 5.71619i | −0.0376652 | + | 0.219529i | ||||
\(679\) | − | 21.7980i | − | 0.836529i | ||||||
\(680\) | 12.7279 | + | 10.3923i | 0.488094 | + | 0.398527i | ||||
\(681\) | 10.8990 | + | 15.4135i | 0.417650 | + | 0.590646i | ||||
\(682\) | −19.5959 | − | 19.5959i | −0.750366 | − | 0.750366i | ||||
\(683\) | 4.24264 | + | 4.24264i | 0.162340 | + | 0.162340i | 0.783603 | − | 0.621262i | \(-0.213380\pi\) |
−0.621262 | + | 0.783603i | \(0.713380\pi\) | |||||||
\(684\) | 6.92820 | + | 2.44949i | 0.264906 | + | 0.0936586i | ||||
\(685\) | −10.3485 | + | 1.04541i | −0.395395 | + | 0.0399430i | ||||
\(686\) | − | 6.92820i | − | 0.264520i | ||||||
\(687\) | −38.7461 | − | 6.64778i | −1.47826 | − | 0.253629i | ||||
\(688\) | 6.89898 | − | 6.89898i | 0.263021 | − | 0.263021i | ||||
\(689\) | 27.3629 | 1.04244 | ||||||||
\(690\) | −2.92152 | + | 2.54258i | −0.111220 | + | 0.0967944i | ||||
\(691\) | −28.0000 | −1.06517 | −0.532585 | − | 0.846376i | \(-0.678779\pi\) | ||||
−0.532585 | + | 0.846376i | \(0.678779\pi\) | |||||||
\(692\) | 10.5352 | − | 10.5352i | 0.400487 | − | 0.400487i | ||||
\(693\) | 53.0482 | − | 25.3354i | 2.01514 | − | 0.962413i | ||||
\(694\) | − | 19.7980i | − | 0.751520i | ||||||
\(695\) | 15.1278 | − | 18.5276i | 0.573828 | − | 0.702793i | ||||
\(696\) | 12.8990 | − | 9.12096i | 0.488935 | − | 0.345729i | ||||
\(697\) | −44.0908 | − | 44.0908i | −1.67006 | − | 1.67006i | ||||
\(698\) | 15.5563 | + | 15.5563i | 0.588817 | + | 0.588817i | ||||
\(699\) | 21.0703 | − | 14.8990i | 0.796953 | − | 0.563531i | ||||
\(700\) | −14.4495 | − | 9.55051i | −0.546139 | − | 0.360975i | ||||
\(701\) | 43.0621i | 1.62643i | 0.581962 | + | 0.813216i | \(0.302285\pi\) | ||||
−0.581962 | + | 0.813216i | \(0.697715\pi\) | |||||||
\(702\) | 9.29734 | + | 5.19756i | 0.350905 | + | 0.196169i | ||||
\(703\) | 6.00000 | − | 6.00000i | 0.226294 | − | 0.226294i | ||||
\(704\) | 5.65685 | 0.213201 | ||||||||
\(705\) | −0.776779 | + | 11.2008i | −0.0292552 | + | 0.421846i | ||||
\(706\) | −3.30306 | −0.124312 | ||||||||
\(707\) | 15.4135 | − | 15.4135i | 0.579684 | − | 0.579684i | ||||
\(708\) | 14.2414 | + | 2.44344i | 0.535224 | + | 0.0918300i | ||||
\(709\) | − | 7.10102i | − | 0.266684i | −0.991070 | − | 0.133342i | \(-0.957429\pi\) | ||
0.991070 | − | 0.133342i | \(-0.0425709\pi\) | |||||||
\(710\) | 1.38211 | + | 13.6814i | 0.0518695 | + | 0.513455i | ||||
\(711\) | −0.449490 | + | 1.27135i | −0.0168572 | + | 0.0476793i | ||||
\(712\) | 1.55051 | + | 1.55051i | 0.0581078 | + | 0.0581078i | ||||
\(713\) | 3.46410 | + | 3.46410i | 0.129732 | + | 0.129732i | ||||
\(714\) | 25.4558 | + | 36.0000i | 0.952661 | + | 1.34727i | ||||
\(715\) | −2.60612 | − | 25.7980i | −0.0974635 | − | 0.964789i | ||||
\(716\) | − | 12.4422i | − | 0.464987i | ||||||
\(717\) | −1.88488 | + | 10.9859i | −0.0703922 | + | 0.410276i | ||||
\(718\) | −9.10102 | + | 9.10102i | −0.339647 | + | 0.339647i | ||||
\(719\) | −32.8769 | −1.22610 | −0.613050 | − | 0.790044i | \(-0.710058\pi\) | ||||
−0.613050 | + | 0.790044i | \(0.710058\pi\) | |||||||
\(720\) | 3.48477 | + | 5.73205i | 0.129870 | + | 0.213621i | ||||
\(721\) | 5.39388 | 0.200878 | ||||||||
\(722\) | −9.19239 | + | 9.19239i | −0.342105 | + | 0.342105i | ||||
\(723\) | 5.53538 | − | 32.2626i | 0.205863 | − | 1.19986i | ||||
\(724\) | − | 8.00000i | − | 0.297318i | ||||||
\(725\) | −9.12096 | − | 44.6834i | −0.338744 | − | 1.65950i | ||||
\(726\) | 21.0000 | + | 29.6985i | 0.779383 | + | 1.10221i | ||||
\(727\) | −0.247449 | − | 0.247449i | −0.00917736 | − | 0.00917736i | 0.702503 | − | 0.711681i | \(-0.252066\pi\) |
−0.711681 | + | 0.702503i | \(0.752066\pi\) | |||||||
\(728\) | −5.02118 | − | 5.02118i | −0.186097 | − | 0.186097i | ||||
\(729\) | −14.1421 | − | 23.0000i | −0.523783 | − | 0.851852i | ||||
\(730\) | −15.7980 | + | 19.3485i | −0.584709 | + | 0.716119i | ||||
\(731\) | 71.6963i | 2.65178i | ||||||||
\(732\) | −15.1915 | − | 2.60645i | −0.561494 | − | 0.0963372i | ||||
\(733\) | 9.14643 | − | 9.14643i | 0.337831 | − | 0.337831i | −0.517719 | − | 0.855550i | \(-0.673219\pi\) |
0.855550 | + | 0.517719i | \(0.173219\pi\) | |||||||
\(734\) | −0.285729 | −0.0105465 | ||||||||
\(735\) | −12.7129 | − | 14.6076i | −0.468923 | − | 0.538809i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −6.22831 | + | 6.22831i | −0.229423 | + | 0.229423i | ||||
\(738\) | −10.9706 | − | 22.9706i | −0.403832 | − | 0.845558i | ||||
\(739\) | 1.30306i | 0.0479339i | 0.999713 | + | 0.0239669i | \(0.00762965\pi\) | ||||
−0.999713 | + | 0.0239669i | \(0.992370\pi\) | |||||||
\(740\) | 7.70674 | − | 0.778539i | 0.283305 | − | 0.0286197i | ||||
\(741\) | 7.10102 | − | 5.02118i | 0.260863 | − | 0.184458i | ||||
\(742\) | 32.6969 | + | 32.6969i | 1.20034 | + | 1.20034i | ||||
\(743\) | 17.6062 | + | 17.6062i | 0.645910 | + | 0.645910i | 0.952002 | − | 0.306092i | \(-0.0990215\pi\) |
−0.306092 | + | 0.952002i | \(0.599021\pi\) | |||||||
\(744\) | 6.92820 | − | 4.89898i | 0.254000 | − | 0.179605i | ||||
\(745\) | 28.8990 | + | 23.5959i | 1.05878 | + | 0.864488i | ||||
\(746\) | 10.6780i | 0.390951i | ||||||||
\(747\) | −2.58579 | − | 5.41421i | −0.0946090 | − | 0.198096i | ||||
\(748\) | −29.3939 | + | 29.3939i | −1.07475 | + | 1.07475i | ||||
\(749\) | −3.81405 | −0.139362 | ||||||||
\(750\) | 19.1962 | − | 2.55103i | 0.700944 | − | 0.0931503i | ||||
\(751\) | −17.7526 | −0.647800 | −0.323900 | − | 0.946091i | \(-0.604994\pi\) | ||||
−0.323900 | + | 0.946091i | \(0.604994\pi\) | |||||||
\(752\) | −2.04989 | + | 2.04989i | −0.0747517 | + | 0.0747517i | ||||
\(753\) | −45.6262 | − | 7.82821i | −1.66271 | − | 0.285276i | ||||
\(754\) | − | 18.6969i | − | 0.680902i | ||||||
\(755\) | 15.4135 | + | 12.5851i | 0.560954 | + | 0.458017i | ||||
\(756\) | 4.89898 | + | 17.3205i | 0.178174 | + | 0.629941i | ||||
\(757\) | −10.6515 | − | 10.6515i | −0.387136 | − | 0.387136i | 0.486528 | − | 0.873665i | \(-0.338263\pi\) |
−0.873665 | + | 0.486528i | \(0.838263\pi\) | |||||||
\(758\) | 20.6096 | + | 20.6096i | 0.748576 | + | 0.748576i | ||||
\(759\) | −5.65685 | − | 8.00000i | −0.205331 | − | 0.290382i | ||||
\(760\) | 5.44949 | − | 0.550510i | 0.197674 | − | 0.0199691i | ||||
\(761\) | − | 14.4279i | − | 0.523010i | −0.965202 | − | 0.261505i | \(-0.915781\pi\) | ||
0.965202 | − | 0.261505i | \(-0.0842187\pi\) | |||||||
\(762\) | −3.49989 | + | 20.3989i | −0.126788 | + | 0.738973i | ||||
\(763\) | −14.2020 | + | 14.2020i | −0.514148 | + | 0.514148i | ||||
\(764\) | −23.6130 | −0.854290 | ||||||||
\(765\) | −47.8920 | − | 11.6772i | −1.73154 | − | 0.422191i | ||||
\(766\) | −22.6969 | −0.820074 | ||||||||
\(767\) | 12.0922 | − | 12.0922i | 0.436626 | − | 0.436626i | ||||
\(768\) | −0.292893 | + | 1.70711i | −0.0105689 | + | 0.0615999i | ||||
\(769\) | − | 0.696938i | − | 0.0251322i | −0.999921 | − | 0.0125661i | \(-0.996000\pi\) | ||
0.999921 | − | 0.0125661i | \(-0.00400003\pi\) | |||||||
\(770\) | 27.7128 | − | 33.9411i | 0.998700 | − | 1.22315i | ||||
\(771\) | 25.5959 | + | 36.1981i | 0.921814 | + | 1.30364i | ||||
\(772\) | 7.89898 | + | 7.89898i | 0.284290 | + | 0.284290i | ||||
\(773\) | −18.2740 | − | 18.2740i | −0.657271 | − | 0.657271i | 0.297463 | − | 0.954733i | \(-0.403860\pi\) |
−0.954733 | + | 0.297463i | \(0.903860\pi\) | |||||||
\(774\) | −9.75663 | + | 27.5959i | −0.350695 | + | 0.991915i | ||||
\(775\) | −4.89898 | − | 24.0000i | −0.175977 | − | 0.862105i | ||||
\(776\) | 6.29253i | 0.225889i | ||||||||
\(777\) | 20.4853 | + | 3.51472i | 0.734905 | + | 0.126090i | ||||
\(778\) | −22.0000 | + | 22.0000i | −0.788738 | + | 0.788738i | ||||
\(779\) | −20.7846 | −0.744686 | ||||||||
\(780\) | 7.92016 | + | 0.549266i | 0.283587 | + | 0.0196669i | ||||
\(781\) | −34.7878 | −1.24480 | ||||||||
\(782\) | 5.19615 | − | 5.19615i | 0.185814 | − | 0.185814i | ||||
\(783\) | −23.1265 | + | 41.3684i | −0.826473 | + | 1.47839i | ||||
\(784\) | − | 5.00000i | − | 0.178571i | ||||||
\(785\) | −1.12848 | − | 11.1708i | −0.0402773 | − | 0.398705i | ||||
\(786\) | −19.7980 | + | 13.9993i | −0.706170 | + | 0.499337i | ||||
\(787\) | 30.8990 | + | 30.8990i | 1.10143 | + | 1.10143i | 0.994238 | + | 0.107191i | \(0.0341857\pi\) |
0.107191 | + | 0.994238i | \(0.465814\pi\) | |||||||
\(788\) | 0.778539 | + | 0.778539i | 0.0277343 | + | 0.0277343i | ||||
\(789\) | 11.3137 | − | 8.00000i | 0.402779 | − | 0.284808i | ||||
\(790\) | 0.101021 | + | 1.00000i | 0.00359415 | + | 0.0355784i | ||||
\(791\) | 11.5994i | 0.412429i | ||||||||
\(792\) | −15.3137 | + | 7.31371i | −0.544149 | + | 0.259881i | ||||
\(793\) | −12.8990 | + | 12.8990i | −0.458056 | + | 0.458056i | ||||
\(794\) | −19.0205 | −0.675011 | ||||||||
\(795\) | −51.5745 | − | 3.57671i | −1.82916 | − | 0.126853i | ||||
\(796\) | 12.4495 | 0.441260 | ||||||||
\(797\) | 37.4373 | − | 37.4373i | 1.32610 | − | 1.32610i | 0.417355 | − | 0.908744i | \(-0.362957\pi\) |
0.908744 | − | 0.417355i | \(-0.137043\pi\) | |||||||
\(798\) | 14.4853 | + | 2.48528i | 0.512773 | + | 0.0879780i | ||||
\(799\) | − | 21.3031i | − | 0.753648i | ||||||
\(800\) | 4.17121 | + | 2.75699i | 0.147474 | + | 0.0974745i | ||||
\(801\) | −6.20204 | − | 2.19275i | −0.219138 | − | 0.0774771i | ||||
\(802\) | 10.4495 | + | 10.4495i | 0.368984 | + | 0.368984i | ||||
\(803\) | −44.6834 | − | 44.6834i | −1.57684 | − | 1.57684i | ||||
\(804\) | −1.55708 | − | 2.20204i | −0.0549139 | − | 0.0776600i | ||||
\(805\) | −4.89898 | + | 6.00000i | −0.172666 | + | 0.211472i | ||||
\(806\) | − | 10.0424i | − | 0.353727i | ||||||
\(807\) | 0.186185 | − | 1.08516i | 0.00655401 | − | 0.0381996i | ||||
\(808\) | −4.44949 | + | 4.44949i | −0.156533 | + | 0.156533i | ||||
\(809\) | 8.48528 | 0.298327 | 0.149163 | − | 0.988813i | \(-0.452342\pi\) | ||||
0.149163 | + | 0.988813i | \(0.452342\pi\) | |||||||
\(810\) | −16.8446 | − | 11.0118i | −0.591858 | − | 0.386917i | ||||
\(811\) | 7.59592 | 0.266729 | 0.133364 | − | 0.991067i | \(-0.457422\pi\) | ||||
0.133364 | + | 0.991067i | \(0.457422\pi\) | |||||||
\(812\) | 22.3417 | − | 22.3417i | 0.784040 | − | 0.784040i | ||||
\(813\) | −7.17439 | + | 41.8154i | −0.251617 | + | 1.46653i | ||||
\(814\) | 19.5959i | 0.686837i | ||||||||
\(815\) | −12.5851 | + | 1.27135i | −0.440835 | + | 0.0445334i | ||||
\(816\) | −7.34847 | − | 10.3923i | −0.257248 | − | 0.363803i | ||||
\(817\) | 16.8990 | + | 16.8990i | 0.591220 | + | 0.591220i | ||||
\(818\) | 4.09978 | + | 4.09978i | 0.143345 | + | 0.143345i | ||||
\(819\) | 20.0847 | + | 7.10102i | 0.701817 | + | 0.248130i | ||||
\(820\) | −14.6969 | − | 12.0000i | −0.513239 | − | 0.419058i | ||||
\(821\) | − | 24.8202i | − | 0.866230i | −0.901339 | − | 0.433115i | \(-0.857414\pi\) | ||
0.901339 | − | 0.433115i | \(-0.142586\pi\) | |||||||
\(822\) | 7.94066 | + | 1.36240i | 0.276962 | + | 0.0475192i | ||||
\(823\) | −5.14643 | + | 5.14643i | −0.179393 | + | 0.179393i | −0.791091 | − | 0.611698i | \(-0.790487\pi\) |
0.611698 | + | 0.791091i | \(0.290487\pi\) | |||||||
\(824\) | −1.55708 | −0.0542434 | ||||||||
\(825\) | 1.53996 | + | 48.9656i | 0.0536145 | + | 1.70476i | ||||
\(826\) | 28.8990 | 1.00552 | ||||||||
\(827\) | 21.8489 | − | 21.8489i | 0.759760 | − | 0.759760i | −0.216519 | − | 0.976278i | \(-0.569470\pi\) |
0.976278 | + | 0.216519i | \(0.0694702\pi\) | |||||||
\(828\) | 2.70711 | − | 1.29289i | 0.0940785 | − | 0.0449311i | ||||
\(829\) | − | 23.1010i | − | 0.802332i | −0.916005 | − | 0.401166i | \(-0.868605\pi\) | ||
0.916005 | − | 0.401166i | \(-0.131395\pi\) | |||||||
\(830\) | −3.46410 | − | 2.82843i | −0.120241 | − | 0.0981761i | ||||
\(831\) | 9.10102 | − | 6.43539i | 0.315711 | − | 0.223241i | ||||
\(832\) | 1.44949 | + | 1.44949i | 0.0502520 | + | 0.0502520i | ||||
\(833\) | 25.9808 | + | 25.9808i | 0.900180 | + | 0.900180i | ||||
\(834\) | −15.1278 | + | 10.6969i | −0.523831 | + | 0.370405i | ||||
\(835\) | 17.7980 | − | 1.79796i | 0.615924 | − | 0.0622209i | ||||
\(836\) | 13.8564i | 0.479234i | ||||||||
\(837\) | −12.4215 | + | 22.2195i | −0.429351 | + | 0.768018i | ||||
\(838\) | 12.8990 | − | 12.8990i | 0.445588 | − | 0.445588i | ||||
\(839\) | −0.285729 | −0.00986447 | −0.00493223 | − | 0.999988i | \(-0.501570\pi\) | ||||
−0.00493223 | + | 0.999988i | \(0.501570\pi\) | |||||||
\(840\) | 8.80776 | + | 10.1204i | 0.303897 | + | 0.349188i | ||||
\(841\) | 54.1918 | 1.86868 | ||||||||
\(842\) | 6.29253 | − | 6.29253i | 0.216855 | − | 0.216855i | ||||
\(843\) | −9.65685 | − | 1.65685i | −0.332600 | − | 0.0570651i | ||||
\(844\) | 10.6969i | 0.368204i | ||||||||
\(845\) | −12.4422 | + | 15.2385i | −0.428024 | + | 0.524221i | ||||
\(846\) | 2.89898 | − | 8.19955i | 0.0996690 | − | 0.281906i | ||||
\(847\) | 51.4393 | + | 51.4393i | 1.76747 | + | 1.76747i | ||||
\(848\) | −9.43879 | − | 9.43879i | −0.324129 | − | 0.324129i | ||||
\(849\) | −13.2207 | − | 18.6969i | −0.453734 | − | 0.641677i | ||||
\(850\) | −36.0000 | + | 7.34847i | −1.23479 | + | 0.252050i | ||||
\(851\) | − | 3.46410i | − | 0.118748i | ||||||
\(852\) | 1.80119 | − | 10.4981i | 0.0617079 | − | 0.359660i | ||||
\(853\) | −19.2474 | + | 19.2474i | −0.659020 | + | 0.659020i | −0.955148 | − | 0.296128i | \(-0.904304\pi\) |
0.296128 | + | 0.955148i | \(0.404304\pi\) | |||||||
\(854\) | −30.8270 | −1.05488 | ||||||||
\(855\) | −14.0406 | + | 8.53590i | −0.480178 | + | 0.291922i | ||||
\(856\) | 1.10102 | 0.0376321 | ||||||||
\(857\) | 9.89949 | − | 9.89949i | 0.338160 | − | 0.338160i | −0.517514 | − | 0.855675i | \(-0.673143\pi\) |
0.855675 | + | 0.517514i | \(0.173143\pi\) | |||||||
\(858\) | −3.39637 | + | 19.7955i | −0.115950 | + | 0.675806i | ||||
\(859\) | − | 35.1010i | − | 1.19763i | −0.800887 | − | 0.598816i | \(-0.795638\pi\) | ||
0.800887 | − | 0.598816i | \(-0.204362\pi\) | |||||||
\(860\) | 2.19275 | + | 21.7060i | 0.0747722 | + | 0.740169i | ||||
\(861\) | −29.3939 | − | 41.5692i | −1.00174 | − | 1.41668i | ||||
\(862\) | 3.79796 | + | 3.79796i | 0.129359 | + | 0.129359i | ||||
\(863\) | 5.65685 | + | 5.65685i | 0.192562 | + | 0.192562i | 0.796802 | − | 0.604240i | \(-0.206523\pi\) |
−0.604240 | + | 0.796802i | \(0.706523\pi\) | |||||||
\(864\) | −1.41421 | − | 5.00000i | −0.0481125 | − | 0.170103i | ||||
\(865\) | 3.34847 | + | 33.1464i | 0.113851 | + | 1.12701i | ||||
\(866\) | 20.7204i | 0.704108i | ||||||||
\(867\) | 63.1630 | + | 10.8370i | 2.14513 | + | 0.368045i | ||||
\(868\) | 12.0000 | − | 12.0000i | 0.407307 | − | 0.407307i | ||||
\(869\) | −2.54270 | −0.0862551 | ||||||||
\(870\) | −2.44395 | + | 35.2407i | −0.0828578 | + | 1.19477i | ||||
\(871\) | −3.19184 | −0.108151 | ||||||||
\(872\) | 4.09978 | − | 4.09978i | 0.138836 | − | 0.138836i | ||||
\(873\) | −8.13557 | − | 17.0345i | −0.275347 | − | 0.576532i | ||||
\(874\) | − | 2.44949i | − | 0.0828552i | ||||||
\(875\) | 36.9766 | − | 11.5208i | 1.25004 | − | 0.389474i | ||||
\(876\) | 15.7980 | − | 11.1708i | 0.533764 | − | 0.377428i | ||||
\(877\) | 11.2474 | + | 11.2474i | 0.379799 | + | 0.379799i | 0.871030 | − | 0.491230i | \(-0.163453\pi\) |
−0.491230 | + | 0.871030i | \(0.663453\pi\) | |||||||
\(878\) | 11.3137 | + | 11.3137i | 0.381819 | + | 0.381819i | ||||
\(879\) | 21.4203 | − | 15.1464i | 0.722488 | − | 0.510876i | ||||
\(880\) | −8.00000 | + | 9.79796i | −0.269680 | + | 0.330289i | ||||
\(881\) | 22.6274i | 0.762337i | 0.924506 | + | 0.381169i | \(0.124478\pi\) | ||||
−0.924506 | + | 0.381169i | \(0.875522\pi\) | |||||||
\(882\) | 6.46447 | + | 13.5355i | 0.217670 | + | 0.455765i | ||||
\(883\) | 41.3939 | − | 41.3939i | 1.39301 | − | 1.39301i | 0.574535 | − | 0.818480i | \(-0.305183\pi\) |
0.818480 | − | 0.574535i | \(-0.194817\pi\) | |||||||
\(884\) | −15.0635 | −0.506642 | ||||||||
\(885\) | −24.3725 | + | 21.2113i | −0.819274 | + | 0.713009i | ||||
\(886\) | −16.0000 | −0.537531 | ||||||||
\(887\) | −2.54270 | + | 2.54270i | −0.0853754 | + | 0.0853754i | −0.748505 | − | 0.663129i | \(-0.769228\pi\) |
0.663129 | + | 0.748505i | \(0.269228\pi\) | |||||||
\(888\) | −5.91359 | − | 1.01461i | −0.198447 | − | 0.0340481i | ||||
\(889\) | 41.3939i | 1.38831i | ||||||||
\(890\) | −4.87832 | + | 0.492810i | −0.163521 | + | 0.0165190i | ||||
\(891\) | 32.0000 | − | 39.5980i | 1.07204 | − | 1.32658i | ||||
\(892\) | 7.55051 | + | 7.55051i | 0.252810 | + | 0.252810i | ||||
\(893\) | −5.02118 | − | 5.02118i | −0.168027 | − | 0.168027i | ||||
\(894\) | −16.6848 | − | 23.5959i | −0.558024 | − | 0.789166i | ||||
\(895\) | 21.5505 | + | 17.5959i | 0.720354 | + | 0.588167i | ||||
\(896\) | 3.46410i | 0.115728i | ||||||||
\(897\) | 0.600398 | − | 3.49938i | 0.0200467 | − | 0.116841i | ||||
\(898\) | 18.6969 | − | 18.6969i | 0.623925 | − | 0.623925i | ||||
\(899\) | 44.6834 | 1.49027 | ||||||||
\(900\) | −14.8564 | − | 2.07055i | −0.495214 | − | 0.0690184i | ||||
\(901\) | 98.0908 | 3.26788 | ||||||||
\(902\) | 33.9411 | − | 33.9411i | 1.13012 | − | 1.13012i | ||||
\(903\) | −9.89919 | + | 57.6967i | −0.329425 | + | 1.92003i | ||||
\(904\) | − | 3.34847i | − | 0.111368i | ||||||
\(905\) | 13.8564 | + | 11.3137i | 0.460603 | + | 0.376080i | ||||
\(906\) | −8.89898 | − | 12.5851i | −0.295649 | − | 0.418111i | ||||
\(907\) | 8.44949 | + | 8.44949i | 0.280561 | + | 0.280561i | 0.833333 | − | 0.552772i | \(-0.186430\pi\) |
−0.552772 | + | 0.833333i | \(0.686430\pi\) | |||||||
\(908\) | −7.70674 | − | 7.70674i | −0.255757 | − | 0.255757i | ||||
\(909\) | 6.29253 | − | 17.7980i | 0.208710 | − | 0.590321i | ||||
\(910\) | 15.7980 | − | 1.59592i | 0.523697 | − | 0.0529042i | ||||
\(911\) | 33.3697i | 1.10559i | 0.833318 | + | 0.552793i | \(0.186438\pi\) | ||||
−0.833318 | + | 0.552793i | \(0.813562\pi\) | |||||||
\(912\) | −4.18154 | − | 0.717439i | −0.138465 | − | 0.0237568i | ||||
\(913\) | 8.00000 | − | 8.00000i | 0.264761 | − | 0.264761i | ||||
\(914\) | −9.12096 | −0.301694 | ||||||||
\(915\) | 25.9985 | − | 22.6264i | 0.859485 | − | 0.748005i | ||||
\(916\) | 22.6969 | 0.749928 | ||||||||
\(917\) | −34.2911 | + | 34.2911i | −1.13239 | + | 1.13239i | ||||
\(918\) | 33.3292 | + | 18.6323i | 1.10003 | + | 0.614957i | ||||
\(919\) | 32.4495i | 1.07041i | 0.844722 | + | 0.535205i | \(0.179766\pi\) | ||||
−0.844722 | + | 0.535205i | \(0.820234\pi\) | |||||||
\(920\) | 1.41421 | − | 1.73205i | 0.0466252 | − | 0.0571040i | ||||
\(921\) | −13.3939 | + | 9.47090i | −0.441343 | + | 0.312077i | ||||
\(922\) | −2.24745 | − | 2.24745i | −0.0740158 | − | 0.0740158i | ||||
\(923\) | −8.91388 | − | 8.91388i | −0.293404 | − | 0.293404i | ||||
\(924\) | −27.7128 | + | 19.5959i | −0.911685 | + | 0.644658i | ||||
\(925\) | −9.55051 | + | 14.4495i | −0.314019 | + | 0.475096i | ||||
\(926\) | − | 25.5201i | − | 0.838641i | ||||||
\(927\) | 4.21518 | − | 2.01314i | 0.138445 | − | 0.0661201i | ||||
\(928\) | −6.44949 | + | 6.44949i | −0.211715 | + | 0.211715i | ||||
\(929\) | 41.5692 | 1.36384 | 0.681921 | − | 0.731426i | \(-0.261145\pi\) | ||||
0.681921 | + | 0.731426i | \(0.261145\pi\) | |||||||
\(930\) | −1.31268 | + | 18.9282i | −0.0430444 | + | 0.620680i | ||||
\(931\) | 12.2474 | 0.401394 | ||||||||
\(932\) | −10.5352 | + | 10.5352i | −0.345091 | + | 0.345091i | ||||
\(933\) | −58.2946 | − | 10.0018i | −1.90848 | − | 0.327444i | ||||
\(934\) | − | 14.8990i | − | 0.487510i | ||||||
\(935\) | −9.34247 | − | 92.4809i | −0.305531 | − | 3.02445i | ||||
\(936\) | −5.79796 | − | 2.04989i | −0.189512 | − | 0.0670027i | ||||
\(937\) | 4.85357 | + | 4.85357i | 0.158559 | + | 0.158559i | 0.781928 | − | 0.623369i | \(-0.214236\pi\) |
−0.623369 | + | 0.781928i | \(0.714236\pi\) | |||||||
\(938\) | −3.81405 | − | 3.81405i | −0.124533 | − | 0.124533i | ||||
\(939\) | 27.0771 | + | 38.2929i | 0.883629 | + | 1.24964i | ||||
\(940\) | −0.651531 | − | 6.44949i | −0.0212506 | − | 0.210359i | ||||
\(941\) | − | 6.64247i | − | 0.216538i | −0.994122 | − | 0.108269i | \(-0.965469\pi\) | ||
0.994122 | − | 0.108269i | \(-0.0345309\pi\) | |||||||
\(942\) | −1.47067 | + | 8.57169i | −0.0479170 | + | 0.279281i | ||||
\(943\) | −6.00000 | + | 6.00000i | −0.195387 | + | 0.195387i | ||||
\(944\) | −8.34242 | −0.271523 | ||||||||
\(945\) | −36.9282 | − | 16.0096i | −1.20127 | − | 0.520793i | ||||
\(946\) | −55.1918 | −1.79444 | ||||||||
\(947\) | 25.4558 | − | 25.4558i | 0.827204 | − | 0.827204i | −0.159925 | − | 0.987129i | \(-0.551125\pi\) |
0.987129 | + | 0.159925i | \(0.0511253\pi\) | |||||||
\(948\) | 0.131652 | − | 0.767327i | 0.00427587 | − | 0.0249216i | ||||
\(949\) | − | 22.8990i | − | 0.743332i | ||||||
\(950\) | −6.75323 | + | 10.2173i | −0.219104 | + | 0.331494i | ||||
\(951\) | −9.10102 | − | 12.8708i | −0.295121 | − | 0.417364i | ||||
\(952\) | −18.0000 | − | 18.0000i | −0.583383 | − | 0.583383i | ||||
\(953\) | −4.21053 | − | 4.21053i | −0.136393 | − | 0.136393i | 0.635614 | − | 0.772007i | \(-0.280747\pi\) |
−0.772007 | + | 0.635614i | \(0.780747\pi\) | |||||||
\(954\) | 37.7552 | + | 13.3485i | 1.22237 | + | 0.432173i | ||||
\(955\) | 33.3939 | − | 40.8990i | 1.08060 | − | 1.32346i | ||||
\(956\) | − | 6.43539i | − | 0.208135i | ||||||
\(957\) | −88.0797 | − | 15.1121i | −2.84721 | − | 0.488505i | ||||
\(958\) | 10.6969 | − | 10.6969i | 0.345602 | − | 0.345602i | ||||
\(959\) | 16.1134 | 0.520328 | ||||||||
\(960\) | −2.54258 | − | 2.92152i | −0.0820615 | − | 0.0942916i | ||||
\(961\) | −7.00000 | −0.225806 | ||||||||
\(962\) | −5.02118 | + | 5.02118i | −0.161889 | + | 0.161889i | ||||
\(963\) | −2.98058 | + | 1.42350i | −0.0960479 | + | 0.0458717i | ||||
\(964\) | 18.8990i | 0.608695i | ||||||||
\(965\) | −24.8523 | + | 2.51059i | −0.800023 | + | 0.0808187i | ||||
\(966\) | 4.89898 | − | 3.46410i | 0.157622 | − | 0.111456i | ||||
\(967\) | −2.44949 | − | 2.44949i | −0.0787703 | − | 0.0787703i | 0.666624 | − | 0.745394i | \(-0.267739\pi\) |
−0.745394 | + | 0.666624i | \(0.767739\pi\) | |||||||
\(968\) | −14.8492 | − | 14.8492i | −0.477273 | − | 0.477273i | ||||
\(969\) | 25.4558 | − | 18.0000i | 0.817760 | − | 0.578243i | ||||
\(970\) | −10.8990 | − | 8.89898i | −0.349945 | − | 0.285729i | ||||
\(971\) | 15.6992i | 0.503812i | 0.967752 | + | 0.251906i | \(0.0810573\pi\) | ||||
−0.967752 | + | 0.251906i | \(0.918943\pi\) | |||||||
\(972\) | 10.2929 | + | 11.7071i | 0.330145 | + | 0.375506i | ||||
\(973\) | −26.2020 | + | 26.2020i | −0.839999 | + | 0.839999i | ||||
\(974\) | −6.57826 | −0.210781 | ||||||||
\(975\) | −12.1522 | + | 12.9413i | −0.389180 | + | 0.414455i | ||||
\(976\) | 8.89898 | 0.284849 | ||||||||
\(977\) | 39.7730 | − | 39.7730i | 1.27245 | − | 1.27245i | 0.327650 | − | 0.944799i | \(-0.393743\pi\) |
0.944799 | − | 0.327650i | \(-0.106257\pi\) | |||||||
\(978\) | 9.65685 | + | 1.65685i | 0.308792 | + | 0.0529804i | ||||
\(979\) | − | 12.4041i | − | 0.396436i | ||||||
\(980\) | 8.66025 | + | 7.07107i | 0.276642 | + | 0.225877i | ||||
\(981\) | −5.79796 | + | 16.3991i | −0.185115 | + | 0.523583i | ||||
\(982\) | −8.10102 | − | 8.10102i | −0.258514 | − | 0.258514i | ||||
\(983\) | 16.3991 | + | 16.3991i | 0.523050 | + | 0.523050i | 0.918491 | − | 0.395441i | \(-0.129408\pi\) |
−0.395441 | + | 0.918491i | \(0.629408\pi\) | |||||||
\(984\) | 8.48528 | + | 12.0000i | 0.270501 | + | 0.382546i | ||||
\(985\) | −2.44949 | + | 0.247449i | −0.0780472 | + | 0.00788437i | ||||
\(986\) | − | 67.0251i | − | 2.13451i | ||||||
\(987\) | 2.94134 | − | 17.1434i | 0.0936239 | − | 0.545680i | ||||
\(988\) | −3.55051 | + | 3.55051i | −0.112957 | + | 0.112957i | ||||
\(989\) | 9.75663 | 0.310243 | ||||||||
\(990\) | 8.98914 | − | 36.8673i | 0.285694 | − | 1.17172i | ||||
\(991\) | 5.79796 | 0.184178 | 0.0920891 | − | 0.995751i | \(-0.470646\pi\) | ||||
0.0920891 | + | 0.995751i | \(0.470646\pi\) | |||||||
\(992\) | −3.46410 | + | 3.46410i | −0.109985 | + | 0.109985i | ||||
\(993\) | −3.13306 | + | 18.2608i | −0.0994247 | + | 0.579489i | ||||
\(994\) | − | 21.3031i | − | 0.675692i | ||||||
\(995\) | −17.6062 | + | 21.5631i | −0.558155 | + | 0.683598i | ||||
\(996\) | 2.00000 | + | 2.82843i | 0.0633724 | + | 0.0896221i | ||||
\(997\) | 0.550510 | + | 0.550510i | 0.0174348 | + | 0.0174348i | 0.715770 | − | 0.698336i | \(-0.246076\pi\) |
−0.698336 | + | 0.715770i | \(0.746076\pi\) | |||||||
\(998\) | 10.0424 | + | 10.0424i | 0.317885 | + | 0.317885i | ||||
\(999\) | 17.3205 | − | 4.89898i | 0.547997 | − | 0.154997i |
(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 | 690.2.i.c.47.2 | ✓ | 8 | |
3.2 | odd | 2 | inner | 690.2.i.c.47.3 | yes | 8 | |
5.3 | odd | 4 | inner | 690.2.i.c.323.3 | yes | 8 | |
15.8 | even | 4 | inner | 690.2.i.c.323.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.c.47.2 | ✓ | 8 | 1.1 | even | 1 | trivial | |
690.2.i.c.47.3 | yes | 8 | 3.2 | odd | 2 | inner | |
690.2.i.c.323.2 | yes | 8 | 15.8 | even | 4 | inner | |
690.2.i.c.323.3 | yes | 8 | 5.3 | odd | 4 | inner |