Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1110,2,Mod(43,1110)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1110, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1110.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1110.l (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: | \(8.86339462436\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Relative dimension: | \(20\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 697.15 | ||
Character | \(\chi\) | \(=\) | 1110.697 |
Dual form | 1110.2.l.b.43.15 |
$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).
\(n\) | \(371\) | \(631\) | \(667\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 1.88721 | + | 1.19936i | 0.843984 | + | 0.536368i | ||||
\(6\) | −0.707107 | + | 0.707107i | −0.288675 | + | 0.288675i | ||||
\(7\) | −1.50593 | − | 1.50593i | −0.569189 | − | 0.569189i | 0.362712 | − | 0.931901i | \(-0.381851\pi\) |
−0.931901 | + | 0.362712i | \(0.881851\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | −1.19936 | + | 1.88721i | −0.379270 | + | 0.596787i | ||||
\(11\) | 0.249077i | 0.0750994i | 0.999295 | + | 0.0375497i | \(0.0119553\pi\) | ||||
−0.999295 | + | 0.0375497i | \(0.988045\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | 2.83382i | 0.785959i | 0.919547 | + | 0.392980i | \(0.128556\pi\) | ||||
−0.919547 | + | 0.392980i | \(0.871444\pi\) | |||||||
\(14\) | 1.50593 | − | 1.50593i | 0.402478 | − | 0.402478i | ||||
\(15\) | 0.486383 | + | 2.18253i | 0.125583 | + | 0.563527i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.29402 | −1.76906 | −0.884530 | − | 0.466484i | \(-0.845520\pi\) | ||||
−0.884530 | + | 0.466484i | \(0.845520\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.89479 | + | 1.89479i | 0.434694 | + | 0.434694i | 0.890222 | − | 0.455527i | \(-0.150549\pi\) |
−0.455527 | + | 0.890222i | \(0.650549\pi\) | |||||||
\(20\) | −1.88721 | − | 1.19936i | −0.421992 | − | 0.268184i | ||||
\(21\) | − | 2.12971i | − | 0.464741i | ||||||
\(22\) | −0.249077 | −0.0531033 | ||||||||
\(23\) | 8.28835i | 1.72824i | 0.503286 | + | 0.864120i | \(0.332124\pi\) | ||||
−0.503286 | + | 0.864120i | \(0.667876\pi\) | |||||||
\(24\) | 0.707107 | − | 0.707107i | 0.144338 | − | 0.144338i | ||||
\(25\) | 2.12309 | + | 4.52686i | 0.424618 | + | 0.905373i | ||||
\(26\) | −2.83382 | −0.555757 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1.50593 | + | 1.50593i | 0.284595 | + | 0.284595i | ||||
\(29\) | −2.37266 | + | 2.37266i | −0.440592 | + | 0.440592i | −0.892211 | − | 0.451619i | \(-0.850847\pi\) |
0.451619 | + | 0.892211i | \(0.350847\pi\) | |||||||
\(30\) | −2.18253 | + | 0.486383i | −0.398473 | + | 0.0888009i | ||||
\(31\) | 1.83366 | + | 1.83366i | 0.329335 | + | 0.329335i | 0.852334 | − | 0.522999i | \(-0.175187\pi\) |
−0.522999 | + | 0.852334i | \(0.675187\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −0.176124 | + | 0.176124i | −0.0306592 | + | 0.0306592i | ||||
\(34\) | − | 7.29402i | − | 1.25091i | ||||||
\(35\) | −1.03586 | − | 4.64816i | −0.175091 | − | 0.785682i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 3.06084 | − | 5.25654i | 0.503200 | − | 0.864170i | ||||
\(38\) | −1.89479 | + | 1.89479i | −0.307375 | + | 0.307375i | ||||
\(39\) | −2.00381 | + | 2.00381i | −0.320867 | + | 0.320867i | ||||
\(40\) | 1.19936 | − | 1.88721i | 0.189635 | − | 0.298393i | ||||
\(41\) | 10.3232i | 1.61221i | 0.591771 | + | 0.806106i | \(0.298429\pi\) | ||||
−0.591771 | + | 0.806106i | \(0.701571\pi\) | |||||||
\(42\) | 2.12971 | 0.328622 | ||||||||
\(43\) | 7.61240i | 1.16088i | 0.814303 | + | 0.580440i | \(0.197120\pi\) | ||||
−0.814303 | + | 0.580440i | \(0.802880\pi\) | |||||||
\(44\) | − | 0.249077i | − | 0.0375497i | ||||||
\(45\) | −1.19936 | + | 1.88721i | −0.178789 | + | 0.281328i | ||||
\(46\) | −8.28835 | −1.22205 | ||||||||
\(47\) | −2.82753 | − | 2.82753i | −0.412437 | − | 0.412437i | 0.470150 | − | 0.882587i | \(-0.344200\pi\) |
−0.882587 | + | 0.470150i | \(0.844200\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 2.46433i | − | 0.352047i | ||||||
\(50\) | −4.52686 | + | 2.12309i | −0.640195 | + | 0.300250i | ||||
\(51\) | −5.15765 | − | 5.15765i | −0.722215 | − | 0.722215i | ||||
\(52\) | − | 2.83382i | − | 0.392980i | ||||||
\(53\) | 4.20587 | − | 4.20587i | 0.577721 | − | 0.577721i | −0.356554 | − | 0.934275i | \(-0.616048\pi\) |
0.934275 | + | 0.356554i | \(0.116048\pi\) | |||||||
\(54\) | −0.707107 | − | 0.707107i | −0.0962250 | − | 0.0962250i | ||||
\(55\) | −0.298732 | + | 0.470059i | −0.0402810 | + | 0.0633827i | ||||
\(56\) | −1.50593 | + | 1.50593i | −0.201239 | + | 0.201239i | ||||
\(57\) | 2.67964i | 0.354926i | ||||||||
\(58\) | −2.37266 | − | 2.37266i | −0.311546 | − | 0.311546i | ||||
\(59\) | 6.26117 | + | 6.26117i | 0.815135 | + | 0.815135i | 0.985398 | − | 0.170264i | \(-0.0544620\pi\) |
−0.170264 | + | 0.985398i | \(0.554462\pi\) | |||||||
\(60\) | −0.486383 | − | 2.18253i | −0.0627917 | − | 0.281763i | ||||
\(61\) | −3.22008 | − | 3.22008i | −0.412290 | − | 0.412290i | 0.470246 | − | 0.882535i | \(-0.344165\pi\) |
−0.882535 | + | 0.470246i | \(0.844165\pi\) | |||||||
\(62\) | −1.83366 | + | 1.83366i | −0.232875 | + | 0.232875i | ||||
\(63\) | 1.50593 | − | 1.50593i | 0.189730 | − | 0.189730i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.39876 | + | 5.34800i | −0.421564 | + | 0.663337i | ||||
\(66\) | −0.176124 | − | 0.176124i | −0.0216793 | − | 0.0216793i | ||||
\(67\) | 5.68165 | − | 5.68165i | 0.694124 | − | 0.694124i | −0.269013 | − | 0.963137i | \(-0.586697\pi\) |
0.963137 | + | 0.269013i | \(0.0866974\pi\) | |||||||
\(68\) | 7.29402 | 0.884530 | ||||||||
\(69\) | −5.86075 | + | 5.86075i | −0.705551 | + | 0.705551i | ||||
\(70\) | 4.64816 | − | 1.03586i | 0.555561 | − | 0.123808i | ||||
\(71\) | 3.37315 | 0.400320 | 0.200160 | − | 0.979763i | \(-0.435854\pi\) | ||||
0.200160 | + | 0.979763i | \(0.435854\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −7.48228 | − | 7.48228i | −0.875735 | − | 0.875735i | 0.117355 | − | 0.993090i | \(-0.462558\pi\) |
−0.993090 | + | 0.117355i | \(0.962558\pi\) | |||||||
\(74\) | 5.25654 | + | 3.06084i | 0.611061 | + | 0.355816i | ||||
\(75\) | −1.69973 | + | 4.70223i | −0.196267 | + | 0.542966i | ||||
\(76\) | −1.89479 | − | 1.89479i | −0.217347 | − | 0.217347i | ||||
\(77\) | 0.375093 | − | 0.375093i | 0.0427458 | − | 0.0427458i | ||||
\(78\) | −2.00381 | − | 2.00381i | −0.226887 | − | 0.226887i | ||||
\(79\) | 5.99818 | + | 5.99818i | 0.674848 | + | 0.674848i | 0.958830 | − | 0.283982i | \(-0.0916554\pi\) |
−0.283982 | + | 0.958830i | \(0.591655\pi\) | |||||||
\(80\) | 1.88721 | + | 1.19936i | 0.210996 | + | 0.134092i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −10.3232 | −1.14001 | ||||||||
\(83\) | 5.98449 | − | 5.98449i | 0.656883 | − | 0.656883i | −0.297759 | − | 0.954641i | \(-0.596239\pi\) |
0.954641 | + | 0.297759i | \(0.0962390\pi\) | |||||||
\(84\) | 2.12971i | 0.232371i | ||||||||
\(85\) | −13.7653 | − | 8.74813i | −1.49306 | − | 0.948867i | ||||
\(86\) | −7.61240 | −0.820867 | ||||||||
\(87\) | −3.35545 | −0.359742 | ||||||||
\(88\) | 0.249077 | 0.0265517 | ||||||||
\(89\) | 5.37576 | − | 5.37576i | 0.569829 | − | 0.569829i | −0.362251 | − | 0.932081i | \(-0.617992\pi\) |
0.932081 | + | 0.362251i | \(0.117992\pi\) | |||||||
\(90\) | −1.88721 | − | 1.19936i | −0.198929 | − | 0.126423i | ||||
\(91\) | 4.26754 | − | 4.26754i | 0.447360 | − | 0.447360i | ||||
\(92\) | − | 8.28835i | − | 0.864120i | ||||||
\(93\) | 2.59319i | 0.268901i | ||||||||
\(94\) | 2.82753 | − | 2.82753i | 0.291637 | − | 0.291637i | ||||
\(95\) | 1.30333 | + | 5.84838i | 0.133719 | + | 0.600031i | ||||
\(96\) | −0.707107 | + | 0.707107i | −0.0721688 | + | 0.0721688i | ||||
\(97\) | −5.94731 | −0.603858 | −0.301929 | − | 0.953330i | \(-0.597631\pi\) | ||||
−0.301929 | + | 0.953330i | \(0.597631\pi\) | |||||||
\(98\) | 2.46433 | 0.248935 | ||||||||
\(99\) | −0.249077 | −0.0250331 | ||||||||
\(100\) | −2.12309 | − | 4.52686i | −0.212309 | − | 0.452686i | ||||
\(101\) | − | 10.2985i | − | 1.02474i | −0.858766 | − | 0.512368i | \(-0.828768\pi\) | ||
0.858766 | − | 0.512368i | \(-0.171232\pi\) | |||||||
\(102\) | 5.15765 | − | 5.15765i | 0.510683 | − | 0.510683i | ||||
\(103\) | −8.34427 | −0.822186 | −0.411093 | − | 0.911594i | \(-0.634853\pi\) | ||||
−0.411093 | + | 0.911594i | \(0.634853\pi\) | |||||||
\(104\) | 2.83382 | 0.277879 | ||||||||
\(105\) | 2.55428 | − | 4.01920i | 0.249273 | − | 0.392234i | ||||
\(106\) | 4.20587 | + | 4.20587i | 0.408511 | + | 0.408511i | ||||
\(107\) | −2.10671 | − | 2.10671i | −0.203663 | − | 0.203663i | 0.597904 | − | 0.801568i | \(-0.296000\pi\) |
−0.801568 | + | 0.597904i | \(0.796000\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | −10.6743 | − | 10.6743i | −1.02242 | − | 1.02242i | −0.999743 | − | 0.0226738i | \(-0.992782\pi\) |
−0.0226738 | − | 0.999743i | \(-0.507218\pi\) | |||||||
\(110\) | −0.470059 | − | 0.298732i | −0.0448183 | − | 0.0284829i | ||||
\(111\) | 5.88128 | − | 1.55259i | 0.558226 | − | 0.147366i | ||||
\(112\) | −1.50593 | − | 1.50593i | −0.142297 | − | 0.142297i | ||||
\(113\) | 4.25290 | 0.400080 | 0.200040 | − | 0.979788i | \(-0.435893\pi\) | ||||
0.200040 | + | 0.979788i | \(0.435893\pi\) | |||||||
\(114\) | −2.67964 | −0.250971 | ||||||||
\(115\) | −9.94068 | + | 15.6418i | −0.926973 | + | 1.45861i | ||||
\(116\) | 2.37266 | − | 2.37266i | 0.220296 | − | 0.220296i | ||||
\(117\) | −2.83382 | −0.261986 | ||||||||
\(118\) | −6.26117 | + | 6.26117i | −0.576387 | + | 0.576387i | ||||
\(119\) | 10.9843 | + | 10.9843i | 1.00693 | + | 1.00693i | ||||
\(120\) | 2.18253 | − | 0.486383i | 0.199237 | − | 0.0444005i | ||||
\(121\) | 10.9380 | 0.994360 | ||||||||
\(122\) | 3.22008 | − | 3.22008i | 0.291533 | − | 0.291533i | ||||
\(123\) | −7.29960 | + | 7.29960i | −0.658183 | + | 0.658183i | ||||
\(124\) | −1.83366 | − | 1.83366i | −0.164668 | − | 0.164668i | ||||
\(125\) | −1.42262 | + | 11.0895i | −0.127243 | + | 0.991872i | ||||
\(126\) | 1.50593 | + | 1.50593i | 0.134159 | + | 0.134159i | ||||
\(127\) | 12.5469 | + | 12.5469i | 1.11336 | + | 1.11336i | 0.992693 | + | 0.120665i | \(0.0385026\pi\) |
0.120665 | + | 0.992693i | \(0.461497\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −5.38278 | + | 5.38278i | −0.473928 | + | 0.473928i | ||||
\(130\) | −5.34800 | − | 3.39876i | −0.469050 | − | 0.298091i | ||||
\(131\) | 3.81040 | + | 3.81040i | 0.332916 | + | 0.332916i | 0.853693 | − | 0.520777i | \(-0.174358\pi\) |
−0.520777 | + | 0.853693i | \(0.674358\pi\) | |||||||
\(132\) | 0.176124 | − | 0.176124i | 0.0153296 | − | 0.0153296i | ||||
\(133\) | − | 5.70685i | − | 0.494847i | ||||||
\(134\) | 5.68165 | + | 5.68165i | 0.490820 | + | 0.490820i | ||||
\(135\) | −2.18253 | + | 0.486383i | −0.187842 | + | 0.0418612i | ||||
\(136\) | 7.29402i | 0.625457i | ||||||||
\(137\) | −2.72768 | − | 2.72768i | −0.233041 | − | 0.233041i | 0.580920 | − | 0.813961i | \(-0.302693\pi\) |
−0.813961 | + | 0.580920i | \(0.802693\pi\) | |||||||
\(138\) | −5.86075 | − | 5.86075i | −0.498900 | − | 0.498900i | ||||
\(139\) | 2.31516 | 0.196369 | 0.0981847 | − | 0.995168i | \(-0.468696\pi\) | ||||
0.0981847 | + | 0.995168i | \(0.468696\pi\) | |||||||
\(140\) | 1.03586 | + | 4.64816i | 0.0875457 | + | 0.392841i | ||||
\(141\) | − | 3.99873i | − | 0.336753i | ||||||
\(142\) | 3.37315i | 0.283069i | ||||||||
\(143\) | −0.705838 | −0.0590251 | ||||||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −7.32336 | + | 1.63203i | −0.608172 | + | 0.135533i | ||||
\(146\) | 7.48228 | − | 7.48228i | 0.619238 | − | 0.619238i | ||||
\(147\) | 1.74254 | − | 1.74254i | 0.143722 | − | 0.143722i | ||||
\(148\) | −3.06084 | + | 5.25654i | −0.251600 | + | 0.432085i | ||||
\(149\) | 8.45695i | 0.692821i | 0.938083 | + | 0.346410i | \(0.112600\pi\) | ||||
−0.938083 | + | 0.346410i | \(0.887400\pi\) | |||||||
\(150\) | −4.70223 | − | 1.69973i | −0.383935 | − | 0.138782i | ||||
\(151\) | − | 12.3871i | − | 1.00805i | −0.863690 | − | 0.504024i | \(-0.831852\pi\) | ||
0.863690 | − | 0.504024i | \(-0.168148\pi\) | |||||||
\(152\) | 1.89479 | − | 1.89479i | 0.153688 | − | 0.153688i | ||||
\(153\) | − | 7.29402i | − | 0.589686i | ||||||
\(154\) | 0.375093 | + | 0.375093i | 0.0302259 | + | 0.0302259i | ||||
\(155\) | 1.26128 | + | 5.65970i | 0.101309 | + | 0.454598i | ||||
\(156\) | 2.00381 | − | 2.00381i | 0.160433 | − | 0.160433i | ||||
\(157\) | −10.3496 | − | 10.3496i | −0.825986 | − | 0.825986i | 0.160973 | − | 0.986959i | \(-0.448537\pi\) |
−0.986959 | + | 0.160973i | \(0.948537\pi\) | |||||||
\(158\) | −5.99818 | + | 5.99818i | −0.477190 | + | 0.477190i | ||||
\(159\) | 5.94800 | 0.471707 | ||||||||
\(160\) | −1.19936 | + | 1.88721i | −0.0948174 | + | 0.149197i | ||||
\(161\) | 12.4817 | − | 12.4817i | 0.983696 | − | 0.983696i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −8.69039 | −0.680684 | −0.340342 | − | 0.940302i | \(-0.610543\pi\) | ||||
−0.340342 | + | 0.940302i | \(0.610543\pi\) | |||||||
\(164\) | − | 10.3232i | − | 0.806106i | ||||||
\(165\) | −0.543617 | + | 0.121147i | −0.0423205 | + | 0.00943125i | ||||
\(166\) | 5.98449 | + | 5.98449i | 0.464486 | + | 0.464486i | ||||
\(167\) | −18.5233 | −1.43337 | −0.716687 | − | 0.697395i | \(-0.754342\pi\) | ||||
−0.716687 | + | 0.697395i | \(0.754342\pi\) | |||||||
\(168\) | −2.12971 | −0.164311 | ||||||||
\(169\) | 4.96948 | 0.382268 | ||||||||
\(170\) | 8.74813 | − | 13.7653i | 0.670951 | − | 1.05575i | ||||
\(171\) | −1.89479 | + | 1.89479i | −0.144898 | + | 0.144898i | ||||
\(172\) | − | 7.61240i | − | 0.580440i | ||||||
\(173\) | 6.60085 | + | 6.60085i | 0.501854 | + | 0.501854i | 0.912014 | − | 0.410160i | \(-0.134527\pi\) |
−0.410160 | + | 0.912014i | \(0.634527\pi\) | |||||||
\(174\) | − | 3.35545i | − | 0.254376i | ||||||
\(175\) | 3.61993 | − | 10.0144i | 0.273641 | − | 0.757017i | ||||
\(176\) | 0.249077i | 0.0187749i | ||||||||
\(177\) | 8.85463i | 0.665555i | ||||||||
\(178\) | 5.37576 | + | 5.37576i | 0.402930 | + | 0.402930i | ||||
\(179\) | 11.1031 | − | 11.1031i | 0.829883 | − | 0.829883i | −0.157617 | − | 0.987500i | \(-0.550381\pi\) |
0.987500 | + | 0.157617i | \(0.0503812\pi\) | |||||||
\(180\) | 1.19936 | − | 1.88721i | 0.0893947 | − | 0.140664i | ||||
\(181\) | 19.1102 | 1.42045 | 0.710223 | − | 0.703977i | \(-0.248594\pi\) | ||||
0.710223 | + | 0.703977i | \(0.248594\pi\) | |||||||
\(182\) | 4.26754 | + | 4.26754i | 0.316331 | + | 0.316331i | ||||
\(183\) | − | 4.55389i | − | 0.336633i | ||||||
\(184\) | 8.28835 | 0.611025 | ||||||||
\(185\) | 12.0809 | − | 6.24913i | 0.888206 | − | 0.459445i | ||||
\(186\) | −2.59319 | −0.190142 | ||||||||
\(187\) | − | 1.81677i | − | 0.132855i | ||||||
\(188\) | 2.82753 | + | 2.82753i | 0.206219 | + | 0.206219i | ||||
\(189\) | 2.12971 | 0.154914 | ||||||||
\(190\) | −5.84838 | + | 1.30333i | −0.424286 | + | 0.0945534i | ||||
\(191\) | −4.13848 | + | 4.13848i | −0.299450 | + | 0.299450i | −0.840798 | − | 0.541349i | \(-0.817914\pi\) |
0.541349 | + | 0.840798i | \(0.317914\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 1.65600i | 0.119201i | 0.998222 | + | 0.0596007i | \(0.0189827\pi\) | ||||
−0.998222 | + | 0.0596007i | \(0.981017\pi\) | |||||||
\(194\) | − | 5.94731i | − | 0.426992i | ||||||
\(195\) | −6.18489 | + | 1.37832i | −0.442909 | + | 0.0987035i | ||||
\(196\) | 2.46433i | 0.176023i | ||||||||
\(197\) | 14.1878 | + | 14.1878i | 1.01084 | + | 1.01084i | 0.999941 | + | 0.0108958i | \(0.00346830\pi\) |
0.0108958 | + | 0.999941i | \(0.496532\pi\) | |||||||
\(198\) | − | 0.249077i | − | 0.0177011i | ||||||
\(199\) | −3.69181 | + | 3.69181i | −0.261705 | + | 0.261705i | −0.825747 | − | 0.564041i | \(-0.809246\pi\) |
0.564041 | + | 0.825747i | \(0.309246\pi\) | |||||||
\(200\) | 4.52686 | − | 2.12309i | 0.320098 | − | 0.150125i | ||||
\(201\) | 8.03506 | 0.566750 | ||||||||
\(202\) | 10.2985 | 0.724598 | ||||||||
\(203\) | 7.14614 | 0.501561 | ||||||||
\(204\) | 5.15765 | + | 5.15765i | 0.361108 | + | 0.361108i | ||||
\(205\) | −12.3812 | + | 19.4820i | −0.864740 | + | 1.36068i | ||||
\(206\) | − | 8.34427i | − | 0.581373i | ||||||
\(207\) | −8.28835 | −0.576080 | ||||||||
\(208\) | 2.83382i | 0.196490i | ||||||||
\(209\) | −0.471948 | + | 0.471948i | −0.0326453 | + | 0.0326453i | ||||
\(210\) | 4.01920 | + | 2.55428i | 0.277351 | + | 0.176262i | ||||
\(211\) | −8.15505 | −0.561417 | −0.280708 | − | 0.959793i | \(-0.590569\pi\) | ||||
−0.280708 | + | 0.959793i | \(0.590569\pi\) | |||||||
\(212\) | −4.20587 | + | 4.20587i | −0.288861 | + | 0.288861i | ||||
\(213\) | 2.38518 | + | 2.38518i | 0.163430 | + | 0.163430i | ||||
\(214\) | 2.10671 | − | 2.10671i | 0.144012 | − | 0.144012i | ||||
\(215\) | −9.12998 | + | 14.3662i | −0.622660 | + | 0.979765i | ||||
\(216\) | 0.707107 | + | 0.707107i | 0.0481125 | + | 0.0481125i | ||||
\(217\) | − | 5.52274i | − | 0.374908i | ||||||
\(218\) | 10.6743 | − | 10.6743i | 0.722958 | − | 0.722958i | ||||
\(219\) | − | 10.5815i | − | 0.715034i | ||||||
\(220\) | 0.298732 | − | 0.470059i | 0.0201405 | − | 0.0316914i | ||||
\(221\) | − | 20.6699i | − | 1.39041i | ||||||
\(222\) | 1.55259 | + | 5.88128i | 0.104203 | + | 0.394726i | ||||
\(223\) | 18.0980 | − | 18.0980i | 1.21193 | − | 1.21193i | 0.241543 | − | 0.970390i | \(-0.422346\pi\) |
0.970390 | − | 0.241543i | \(-0.0776536\pi\) | |||||||
\(224\) | 1.50593 | − | 1.50593i | 0.100619 | − | 0.100619i | ||||
\(225\) | −4.52686 | + | 2.12309i | −0.301791 | + | 0.141539i | ||||
\(226\) | 4.25290i | 0.282899i | ||||||||
\(227\) | −15.2040 | −1.00913 | −0.504563 | − | 0.863375i | \(-0.668346\pi\) | ||||
−0.504563 | + | 0.863375i | \(0.668346\pi\) | |||||||
\(228\) | − | 2.67964i | − | 0.177463i | ||||||
\(229\) | − | 22.1160i | − | 1.46147i | −0.682662 | − | 0.730735i | \(-0.739178\pi\) | ||
0.682662 | − | 0.730735i | \(-0.260822\pi\) | |||||||
\(230\) | −15.6418 | − | 9.94068i | −1.03139 | − | 0.655469i | ||||
\(231\) | 0.530462 | 0.0349018 | ||||||||
\(232\) | 2.37266 | + | 2.37266i | 0.155773 | + | 0.155773i | ||||
\(233\) | −4.77285 | − | 4.77285i | −0.312680 | − | 0.312680i | 0.533267 | − | 0.845947i | \(-0.320964\pi\) |
−0.845947 | + | 0.533267i | \(0.820964\pi\) | |||||||
\(234\) | − | 2.83382i | − | 0.185252i | ||||||
\(235\) | −1.94491 | − | 8.72733i | −0.126872 | − | 0.569308i | ||||
\(236\) | −6.26117 | − | 6.26117i | −0.407567 | − | 0.407567i | ||||
\(237\) | 8.48271i | 0.551011i | ||||||||
\(238\) | −10.9843 | + | 10.9843i | −0.712007 | + | 0.712007i | ||||
\(239\) | 19.8498 | + | 19.8498i | 1.28398 | + | 1.28398i | 0.938385 | + | 0.345593i | \(0.112322\pi\) |
0.345593 | + | 0.938385i | \(0.387678\pi\) | |||||||
\(240\) | 0.486383 | + | 2.18253i | 0.0313959 | + | 0.140882i | ||||
\(241\) | 21.3229 | − | 21.3229i | 1.37353 | − | 1.37353i | 0.518380 | − | 0.855150i | \(-0.326535\pi\) |
0.855150 | − | 0.518380i | \(-0.173465\pi\) | |||||||
\(242\) | 10.9380i | 0.703119i | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 3.22008 | + | 3.22008i | 0.206145 | + | 0.206145i | ||||
\(245\) | 2.95561 | − | 4.65069i | 0.188827 | − | 0.297122i | ||||
\(246\) | −7.29960 | − | 7.29960i | −0.465405 | − | 0.465405i | ||||
\(247\) | −5.36948 | + | 5.36948i | −0.341652 | + | 0.341652i | ||||
\(248\) | 1.83366 | − | 1.83366i | 0.116438 | − | 0.116438i | ||||
\(249\) | 8.46334 | 0.536342 | ||||||||
\(250\) | −11.0895 | − | 1.42262i | −0.701359 | − | 0.0899742i | ||||
\(251\) | 14.6439 | + | 14.6439i | 0.924315 | + | 0.924315i | 0.997331 | − | 0.0730156i | \(-0.0232623\pi\) |
−0.0730156 | + | 0.997331i | \(0.523262\pi\) | |||||||
\(252\) | −1.50593 | + | 1.50593i | −0.0948649 | + | 0.0948649i | ||||
\(253\) | −2.06443 | −0.129790 | ||||||||
\(254\) | −12.5469 | + | 12.5469i | −0.787263 | + | 0.787263i | ||||
\(255\) | −3.54768 | − | 15.9194i | −0.222165 | − | 0.996912i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.8930 | 1.11614 | 0.558069 | − | 0.829795i | \(-0.311543\pi\) | ||||
0.558069 | + | 0.829795i | \(0.311543\pi\) | |||||||
\(258\) | −5.38278 | − | 5.38278i | −0.335117 | − | 0.335117i | ||||
\(259\) | −12.5254 | + | 3.30658i | −0.778293 | + | 0.205461i | ||||
\(260\) | 3.39876 | − | 5.34800i | 0.210782 | − | 0.331669i | ||||
\(261\) | −2.37266 | − | 2.37266i | −0.146864 | − | 0.146864i | ||||
\(262\) | −3.81040 | + | 3.81040i | −0.235407 | + | 0.235407i | ||||
\(263\) | 21.7610 | + | 21.7610i | 1.34184 | + | 1.34184i | 0.894225 | + | 0.447617i | \(0.147727\pi\) |
0.447617 | + | 0.894225i | \(0.352273\pi\) | |||||||
\(264\) | 0.176124 | + | 0.176124i | 0.0108397 | + | 0.0108397i | ||||
\(265\) | 12.9817 | − | 2.89301i | 0.797459 | − | 0.177716i | ||||
\(266\) | 5.70685 | 0.349910 | ||||||||
\(267\) | 7.60247 | 0.465264 | ||||||||
\(268\) | −5.68165 | + | 5.68165i | −0.347062 | + | 0.347062i | ||||
\(269\) | 17.8478i | 1.08820i | 0.839020 | + | 0.544101i | \(0.183129\pi\) | ||||
−0.839020 | + | 0.544101i | \(0.816871\pi\) | |||||||
\(270\) | −0.486383 | − | 2.18253i | −0.0296003 | − | 0.132824i | ||||
\(271\) | 2.29360 | 0.139327 | 0.0696633 | − | 0.997571i | \(-0.477808\pi\) | ||||
0.0696633 | + | 0.997571i | \(0.477808\pi\) | |||||||
\(272\) | −7.29402 | −0.442265 | ||||||||
\(273\) | 6.03521 | 0.365268 | ||||||||
\(274\) | 2.72768 | − | 2.72768i | 0.164785 | − | 0.164785i | ||||
\(275\) | −1.12754 | + | 0.528812i | −0.0679930 | + | 0.0318886i | ||||
\(276\) | 5.86075 | − | 5.86075i | 0.352776 | − | 0.352776i | ||||
\(277\) | 1.48608i | 0.0892897i | 0.999003 | + | 0.0446448i | \(0.0142156\pi\) | ||||
−0.999003 | + | 0.0446448i | \(0.985784\pi\) | |||||||
\(278\) | 2.31516i | 0.138854i | ||||||||
\(279\) | −1.83366 | + | 1.83366i | −0.109778 | + | 0.109778i | ||||
\(280\) | −4.64816 | + | 1.03586i | −0.277781 | + | 0.0619042i | ||||
\(281\) | −18.5876 | + | 18.5876i | −1.10884 | + | 1.10884i | −0.115541 | + | 0.993303i | \(0.536860\pi\) |
−0.993303 | + | 0.115541i | \(0.963140\pi\) | |||||||
\(282\) | 3.99873 | 0.238121 | ||||||||
\(283\) | −16.6153 | −0.987676 | −0.493838 | − | 0.869554i | \(-0.664406\pi\) | ||||
−0.493838 | + | 0.869554i | \(0.664406\pi\) | |||||||
\(284\) | −3.37315 | −0.200160 | ||||||||
\(285\) | −3.21384 | + | 5.05702i | −0.190371 | + | 0.299552i | ||||
\(286\) | − | 0.705838i | − | 0.0417371i | ||||||
\(287\) | 15.5460 | − | 15.5460i | 0.917654 | − | 0.917654i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 36.2027 | 2.12957 | ||||||||
\(290\) | −1.63203 | − | 7.32336i | −0.0958362 | − | 0.430043i | ||||
\(291\) | −4.20538 | − | 4.20538i | −0.246524 | − | 0.246524i | ||||
\(292\) | 7.48228 | + | 7.48228i | 0.437867 | + | 0.437867i | ||||
\(293\) | 9.37884 | − | 9.37884i | 0.547918 | − | 0.547918i | −0.377920 | − | 0.925838i | \(-0.623361\pi\) |
0.925838 | + | 0.377920i | \(0.123361\pi\) | |||||||
\(294\) | 1.74254 | + | 1.74254i | 0.101627 | + | 0.101627i | ||||
\(295\) | 4.30674 | + | 19.3255i | 0.250748 | + | 1.12517i | ||||
\(296\) | −5.25654 | − | 3.06084i | −0.305530 | − | 0.177908i | ||||
\(297\) | −0.176124 | − | 0.176124i | −0.0102197 | − | 0.0102197i | ||||
\(298\) | −8.45695 | −0.489898 | ||||||||
\(299\) | −23.4877 | −1.35833 | ||||||||
\(300\) | 1.69973 | − | 4.70223i | 0.0981337 | − | 0.271483i | ||||
\(301\) | 11.4638 | − | 11.4638i | 0.660761 | − | 0.660761i | ||||
\(302\) | 12.3871 | 0.712797 | ||||||||
\(303\) | 7.28212 | − | 7.28212i | 0.418347 | − | 0.418347i | ||||
\(304\) | 1.89479 | + | 1.89479i | 0.108674 | + | 0.108674i | ||||
\(305\) | −2.21493 | − | 9.93899i | −0.126827 | − | 0.569105i | ||||
\(306\) | 7.29402 | 0.416971 | ||||||||
\(307\) | 3.36862 | − | 3.36862i | 0.192258 | − | 0.192258i | −0.604413 | − | 0.796671i | \(-0.706592\pi\) |
0.796671 | + | 0.604413i | \(0.206592\pi\) | |||||||
\(308\) | −0.375093 | + | 0.375093i | −0.0213729 | + | 0.0213729i | ||||
\(309\) | −5.90029 | − | 5.90029i | −0.335656 | − | 0.335656i | ||||
\(310\) | −5.65970 | + | 1.26128i | −0.321450 | + | 0.0716360i | ||||
\(311\) | 22.4334 | + | 22.4334i | 1.27208 | + | 1.27208i | 0.944994 | + | 0.327087i | \(0.106067\pi\) |
0.327087 | + | 0.944994i | \(0.393933\pi\) | |||||||
\(312\) | 2.00381 | + | 2.00381i | 0.113443 | + | 0.113443i | ||||
\(313\) | 19.2752i | 1.08950i | 0.838599 | + | 0.544750i | \(0.183375\pi\) | ||||
−0.838599 | + | 0.544750i | \(0.816625\pi\) | |||||||
\(314\) | 10.3496 | − | 10.3496i | 0.584060 | − | 0.584060i | ||||
\(315\) | 4.64816 | − | 1.03586i | 0.261894 | − | 0.0583638i | ||||
\(316\) | −5.99818 | − | 5.99818i | −0.337424 | − | 0.337424i | ||||
\(317\) | −3.94817 | + | 3.94817i | −0.221751 | + | 0.221751i | −0.809236 | − | 0.587484i | \(-0.800118\pi\) |
0.587484 | + | 0.809236i | \(0.300118\pi\) | |||||||
\(318\) | 5.94800i | 0.333548i | ||||||||
\(319\) | −0.590974 | − | 0.590974i | −0.0330882 | − | 0.0330882i | ||||
\(320\) | −1.88721 | − | 1.19936i | −0.105498 | − | 0.0670461i | ||||
\(321\) | − | 2.97934i | − | 0.166291i | ||||||
\(322\) | 12.4817 | + | 12.4817i | 0.695578 | + | 0.695578i | ||||
\(323\) | −13.8206 | − | 13.8206i | −0.769000 | − | 0.769000i | ||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −12.8283 | + | 6.01645i | −0.711586 | + | 0.333732i | ||||
\(326\) | − | 8.69039i | − | 0.481316i | ||||||
\(327\) | − | 15.0958i | − | 0.834800i | ||||||
\(328\) | 10.3232 | 0.570003 | ||||||||
\(329\) | 8.51613i | 0.469510i | ||||||||
\(330\) | −0.121147 | − | 0.543617i | −0.00666890 | − | 0.0299251i | ||||
\(331\) | −2.89997 | + | 2.89997i | −0.159397 | + | 0.159397i | −0.782299 | − | 0.622902i | \(-0.785953\pi\) |
0.622902 | + | 0.782299i | \(0.285953\pi\) | |||||||
\(332\) | −5.98449 | + | 5.98449i | −0.328441 | + | 0.328441i | ||||
\(333\) | 5.25654 | + | 3.06084i | 0.288057 | + | 0.167733i | ||||
\(334\) | − | 18.5233i | − | 1.01355i | ||||||
\(335\) | 17.5368 | − | 3.90812i | 0.958135 | − | 0.213523i | ||||
\(336\) | − | 2.12971i | − | 0.116185i | ||||||
\(337\) | −1.55976 | + | 1.55976i | −0.0849654 | + | 0.0849654i | −0.748312 | − | 0.663347i | \(-0.769135\pi\) |
0.663347 | + | 0.748312i | \(0.269135\pi\) | |||||||
\(338\) | 4.96948i | 0.270304i | ||||||||
\(339\) | 3.00726 | + | 3.00726i | 0.163332 | + | 0.163332i | ||||
\(340\) | 13.7653 | + | 8.74813i | 0.746529 | + | 0.474434i | ||||
\(341\) | −0.456722 | + | 0.456722i | −0.0247329 | + | 0.0247329i | ||||
\(342\) | −1.89479 | − | 1.89479i | −0.102458 | − | 0.102458i | ||||
\(343\) | −14.2526 | + | 14.2526i | −0.769571 | + | 0.769571i | ||||
\(344\) | 7.61240 | 0.410433 | ||||||||
\(345\) | −18.0896 | + | 4.03131i | −0.973909 | + | 0.217038i | ||||
\(346\) | −6.60085 | + | 6.60085i | −0.354864 | + | 0.354864i | ||||
\(347\) | − | 9.43617i | − | 0.506560i | −0.967393 | − | 0.253280i | \(-0.918491\pi\) | ||
0.967393 | − | 0.253280i | \(-0.0815094\pi\) | |||||||
\(348\) | 3.35545 | 0.179871 | ||||||||
\(349\) | 7.25908i | 0.388569i | 0.980945 | + | 0.194285i | \(0.0622386\pi\) | ||||
−0.980945 | + | 0.194285i | \(0.937761\pi\) | |||||||
\(350\) | 10.0144 | + | 3.61993i | 0.535292 | + | 0.193493i | ||||
\(351\) | −2.00381 | − | 2.00381i | −0.106956 | − | 0.106956i | ||||
\(352\) | −0.249077 | −0.0132758 | ||||||||
\(353\) | −6.63465 | −0.353127 | −0.176563 | − | 0.984289i | \(-0.556498\pi\) | ||||
−0.176563 | + | 0.984289i | \(0.556498\pi\) | |||||||
\(354\) | −8.85463 | −0.470618 | ||||||||
\(355\) | 6.36583 | + | 4.04561i | 0.337863 | + | 0.214719i | ||||
\(356\) | −5.37576 | + | 5.37576i | −0.284915 | + | 0.284915i | ||||
\(357\) | 15.5342i | 0.822155i | ||||||||
\(358\) | 11.1031 | + | 11.1031i | 0.586816 | + | 0.586816i | ||||
\(359\) | − | 3.64712i | − | 0.192488i | −0.995358 | − | 0.0962438i | \(-0.969317\pi\) | ||
0.995358 | − | 0.0962438i | \(-0.0306828\pi\) | |||||||
\(360\) | 1.88721 | + | 1.19936i | 0.0994645 | + | 0.0632116i | ||||
\(361\) | − | 11.8196i | − | 0.622082i | ||||||
\(362\) | 19.1102i | 1.00441i | ||||||||
\(363\) | 7.73431 | + | 7.73431i | 0.405946 | + | 0.405946i | ||||
\(364\) | −4.26754 | + | 4.26754i | −0.223680 | + | 0.223680i | ||||
\(365\) | −5.14668 | − | 23.0945i | −0.269390 | − | 1.20882i | ||||
\(366\) | 4.55389 | 0.238036 | ||||||||
\(367\) | −2.67398 | − | 2.67398i | −0.139580 | − | 0.139580i | 0.633864 | − | 0.773444i | \(-0.281468\pi\) |
−0.773444 | + | 0.633864i | \(0.781468\pi\) | |||||||
\(368\) | 8.28835i | 0.432060i | ||||||||
\(369\) | −10.3232 | −0.537404 | ||||||||
\(370\) | 6.24913 | + | 12.0809i | 0.324877 | + | 0.628057i | ||||
\(371\) | −12.6675 | −0.657666 | ||||||||
\(372\) | − | 2.59319i | − | 0.134450i | ||||||
\(373\) | 8.22916 | + | 8.22916i | 0.426090 | + | 0.426090i | 0.887294 | − | 0.461204i | \(-0.152582\pi\) |
−0.461204 | + | 0.887294i | \(0.652582\pi\) | |||||||
\(374\) | 1.81677 | 0.0939429 | ||||||||
\(375\) | −8.84738 | + | 6.83549i | −0.456877 | + | 0.352983i | ||||
\(376\) | −2.82753 | + | 2.82753i | −0.145819 | + | 0.145819i | ||||
\(377\) | −6.72369 | − | 6.72369i | −0.346287 | − | 0.346287i | ||||
\(378\) | 2.12971i | 0.109541i | ||||||||
\(379\) | 23.2988i | 1.19678i | 0.801206 | + | 0.598389i | \(0.204192\pi\) | ||||
−0.801206 | + | 0.598389i | \(0.795808\pi\) | |||||||
\(380\) | −1.30333 | − | 5.84838i | −0.0668593 | − | 0.300016i | ||||
\(381\) | 17.7440i | 0.909053i | ||||||||
\(382\) | −4.13848 | − | 4.13848i | −0.211743 | − | 0.211743i | ||||
\(383\) | − | 1.82589i | − | 0.0932984i | −0.998911 | − | 0.0466492i | \(-0.985146\pi\) | ||
0.998911 | − | 0.0466492i | \(-0.0148543\pi\) | |||||||
\(384\) | 0.707107 | − | 0.707107i | 0.0360844 | − | 0.0360844i | ||||
\(385\) | 1.15775 | − | 0.258007i | 0.0590043 | − | 0.0131493i | ||||
\(386\) | −1.65600 | −0.0842881 | ||||||||
\(387\) | −7.61240 | −0.386960 | ||||||||
\(388\) | 5.94731 | 0.301929 | ||||||||
\(389\) | 1.87840 | + | 1.87840i | 0.0952388 | + | 0.0952388i | 0.753121 | − | 0.657882i | \(-0.228547\pi\) |
−0.657882 | + | 0.753121i | \(0.728547\pi\) | |||||||
\(390\) | −1.37832 | − | 6.18489i | −0.0697939 | − | 0.313184i | ||||
\(391\) | − | 60.4554i | − | 3.05736i | ||||||
\(392\) | −2.46433 | −0.124467 | ||||||||
\(393\) | 5.38872i | 0.271825i | ||||||||
\(394\) | −14.1878 | + | 14.1878i | −0.714769 | + | 0.714769i | ||||
\(395\) | 4.12584 | + | 18.5138i | 0.207594 | + | 0.931528i | ||||
\(396\) | 0.249077 | 0.0125166 | ||||||||
\(397\) | 12.0046 | − | 12.0046i | 0.602492 | − | 0.602492i | −0.338481 | − | 0.940973i | \(-0.609913\pi\) |
0.940973 | + | 0.338481i | \(0.109913\pi\) | |||||||
\(398\) | −3.69181 | − | 3.69181i | −0.185054 | − | 0.185054i | ||||
\(399\) | 4.03535 | − | 4.03535i | 0.202020 | − | 0.202020i | ||||
\(400\) | 2.12309 | + | 4.52686i | 0.106154 | + | 0.226343i | ||||
\(401\) | −23.2046 | − | 23.2046i | −1.15878 | − | 1.15878i | −0.984738 | − | 0.174043i | \(-0.944317\pi\) |
−0.174043 | − | 0.984738i | \(-0.555683\pi\) | |||||||
\(402\) | 8.03506i | 0.400753i | ||||||||
\(403\) | −5.19626 | + | 5.19626i | −0.258844 | + | 0.258844i | ||||
\(404\) | 10.2985i | 0.512368i | ||||||||
\(405\) | −1.88721 | − | 1.19936i | −0.0937760 | − | 0.0595965i | ||||
\(406\) | 7.14614i | 0.354657i | ||||||||
\(407\) | 1.30928 | + | 0.762385i | 0.0648987 | + | 0.0377900i | ||||
\(408\) | −5.15765 | + | 5.15765i | −0.255342 | + | 0.255342i | ||||
\(409\) | 12.7469 | − | 12.7469i | 0.630292 | − | 0.630292i | −0.317850 | − | 0.948141i | \(-0.602961\pi\) |
0.948141 | + | 0.317850i | \(0.102961\pi\) | |||||||
\(410\) | −19.4820 | − | 12.3812i | −0.962147 | − | 0.611463i | ||||
\(411\) | − | 3.85752i | − | 0.190278i | ||||||
\(412\) | 8.34427 | 0.411093 | ||||||||
\(413\) | − | 18.8578i | − | 0.927932i | ||||||
\(414\) | − | 8.28835i | − | 0.407350i | ||||||
\(415\) | 18.4715 | − | 4.11642i | 0.906729 | − | 0.202067i | ||||
\(416\) | −2.83382 | −0.138939 | ||||||||
\(417\) | 1.63707 | + | 1.63707i | 0.0801675 | + | 0.0801675i | ||||
\(418\) | −0.471948 | − | 0.471948i | −0.0230837 | − | 0.0230837i | ||||
\(419\) | − | 22.1539i | − | 1.08229i | −0.840929 | − | 0.541145i | \(-0.817991\pi\) | ||
0.840929 | − | 0.541145i | \(-0.182009\pi\) | |||||||
\(420\) | −2.55428 | + | 4.01920i | −0.124636 | + | 0.196117i | ||||
\(421\) | −18.3106 | − | 18.3106i | −0.892404 | − | 0.892404i | 0.102345 | − | 0.994749i | \(-0.467365\pi\) |
−0.994749 | + | 0.102345i | \(0.967365\pi\) | |||||||
\(422\) | − | 8.15505i | − | 0.396981i | ||||||
\(423\) | 2.82753 | − | 2.82753i | 0.137479 | − | 0.137479i | ||||
\(424\) | −4.20587 | − | 4.20587i | −0.204255 | − | 0.204255i | ||||
\(425\) | −15.4858 | − | 33.0190i | −0.751174 | − | 1.60166i | ||||
\(426\) | −2.38518 | + | 2.38518i | −0.115562 | + | 0.115562i | ||||
\(427\) | 9.69847i | 0.469342i | ||||||||
\(428\) | 2.10671 | + | 2.10671i | 0.101832 | + | 0.101832i | ||||
\(429\) | −0.499103 | − | 0.499103i | −0.0240969 | − | 0.0240969i | ||||
\(430\) | −14.3662 | − | 9.12998i | −0.692798 | − | 0.440287i | ||||
\(431\) | −8.32782 | − | 8.32782i | −0.401137 | − | 0.401137i | 0.477497 | − | 0.878634i | \(-0.341544\pi\) |
−0.878634 | + | 0.477497i | \(0.841544\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | −6.11268 | + | 6.11268i | −0.293757 | + | 0.293757i | −0.838562 | − | 0.544806i | \(-0.816603\pi\) |
0.544806 | + | 0.838562i | \(0.316603\pi\) | |||||||
\(434\) | 5.52274 | 0.265100 | ||||||||
\(435\) | −6.33242 | − | 4.02438i | −0.303616 | − | 0.192954i | ||||
\(436\) | 10.6743 | + | 10.6743i | 0.511208 | + | 0.511208i | ||||
\(437\) | −15.7047 | + | 15.7047i | −0.751256 | + | 0.751256i | ||||
\(438\) | 10.5815 | 0.505606 | ||||||||
\(439\) | 16.2052 | − | 16.2052i | 0.773431 | − | 0.773431i | −0.205273 | − | 0.978705i | \(-0.565808\pi\) |
0.978705 | + | 0.205273i | \(0.0658084\pi\) | |||||||
\(440\) | 0.470059 | + | 0.298732i | 0.0224092 | + | 0.0142415i | ||||
\(441\) | 2.46433 | 0.117349 | ||||||||
\(442\) | 20.6699 | 0.983167 | ||||||||
\(443\) | −6.30399 | − | 6.30399i | −0.299512 | − | 0.299512i | 0.541311 | − | 0.840823i | \(-0.317928\pi\) |
−0.840823 | + | 0.541311i | \(0.817928\pi\) | |||||||
\(444\) | −5.88128 | + | 1.55259i | −0.279113 | + | 0.0736828i | ||||
\(445\) | 16.5926 | − | 3.69771i | 0.786565 | − | 0.175288i | ||||
\(446\) | 18.0980 | + | 18.0980i | 0.856966 | + | 0.856966i | ||||
\(447\) | −5.97997 | + | 5.97997i | −0.282843 | + | 0.282843i | ||||
\(448\) | 1.50593 | + | 1.50593i | 0.0711487 | + | 0.0711487i | ||||
\(449\) | −19.8634 | − | 19.8634i | −0.937412 | − | 0.937412i | 0.0607412 | − | 0.998154i | \(-0.480654\pi\) |
−0.998154 | + | 0.0607412i | \(0.980654\pi\) | |||||||
\(450\) | −2.12309 | − | 4.52686i | −0.100083 | − | 0.213398i | ||||
\(451\) | −2.57127 | −0.121076 | ||||||||
\(452\) | −4.25290 | −0.200040 | ||||||||
\(453\) | 8.75900 | − | 8.75900i | 0.411534 | − | 0.411534i | ||||
\(454\) | − | 15.2040i | − | 0.713560i | ||||||
\(455\) | 13.1720 | − | 2.93542i | 0.617514 | − | 0.137615i | ||||
\(456\) | 2.67964 | 0.125485 | ||||||||
\(457\) | −40.2606 | −1.88331 | −0.941657 | − | 0.336575i | \(-0.890731\pi\) | ||||
−0.941657 | + | 0.336575i | \(0.890731\pi\) | |||||||
\(458\) | 22.1160 | 1.03341 | ||||||||
\(459\) | 5.15765 | − | 5.15765i | 0.240738 | − | 0.240738i | ||||
\(460\) | 9.94068 | − | 15.6418i | 0.463487 | − | 0.729303i | ||||
\(461\) | −15.0948 | + | 15.0948i | −0.703036 | + | 0.703036i | −0.965061 | − | 0.262025i | \(-0.915610\pi\) |
0.262025 | + | 0.965061i | \(0.415610\pi\) | |||||||
\(462\) | 0.530462i | 0.0246793i | ||||||||
\(463\) | 25.5478i | 1.18730i | 0.804722 | + | 0.593652i | \(0.202315\pi\) | ||||
−0.804722 | + | 0.593652i | \(0.797685\pi\) | |||||||
\(464\) | −2.37266 | + | 2.37266i | −0.110148 | + | 0.110148i | ||||
\(465\) | −3.11015 | + | 4.89388i | −0.144230 | + | 0.226948i | ||||
\(466\) | 4.77285 | − | 4.77285i | 0.221098 | − | 0.221098i | ||||
\(467\) | −30.7343 | −1.42221 | −0.711106 | − | 0.703085i | \(-0.751805\pi\) | ||||
−0.711106 | + | 0.703085i | \(0.751805\pi\) | |||||||
\(468\) | 2.83382 | 0.130993 | ||||||||
\(469\) | −17.1124 | −0.790176 | ||||||||
\(470\) | 8.72733 | − | 1.94491i | 0.402562 | − | 0.0897121i | ||||
\(471\) | − | 14.6365i | − | 0.674415i | ||||||
\(472\) | 6.26117 | − | 6.26117i | 0.288194 | − | 0.288194i | ||||
\(473\) | −1.89607 | −0.0871815 | ||||||||
\(474\) | −8.48271 | −0.389624 | ||||||||
\(475\) | −4.55464 | + | 12.6003i | −0.208981 | + | 0.578139i | ||||
\(476\) | −10.9843 | − | 10.9843i | −0.503465 | − | 0.503465i | ||||
\(477\) | 4.20587 | + | 4.20587i | 0.192574 | + | 0.192574i | ||||
\(478\) | −19.8498 | + | 19.8498i | −0.907909 | + | 0.907909i | ||||
\(479\) | −0.00977229 | − | 0.00977229i | −0.000446507 | − | 0.000446507i | 0.706883 | − | 0.707330i | \(-0.250100\pi\) |
−0.707330 | + | 0.706883i | \(0.750100\pi\) | |||||||
\(480\) | −2.18253 | + | 0.486383i | −0.0996184 | + | 0.0222002i | ||||
\(481\) | 14.8961 | + | 8.67387i | 0.679203 | + | 0.395495i | ||||
\(482\) | 21.3229 | + | 21.3229i | 0.971233 | + | 0.971233i | ||||
\(483\) | 17.6518 | 0.803184 | ||||||||
\(484\) | −10.9380 | −0.497180 | ||||||||
\(485\) | −11.2238 | − | 7.13294i | −0.509646 | − | 0.323890i | ||||
\(486\) | 0.707107 | − | 0.707107i | 0.0320750 | − | 0.0320750i | ||||
\(487\) | −0.0126739 | −0.000574311 | −0.000287155 | − | 1.00000i | \(-0.500091\pi\) | ||||
−0.000287155 | 1.00000i | \(0.500091\pi\) | ||||||||
\(488\) | −3.22008 | + | 3.22008i | −0.145766 | + | 0.145766i | ||||
\(489\) | −6.14503 | − | 6.14503i | −0.277888 | − | 0.277888i | ||||
\(490\) | 4.65069 | + | 2.95561i | 0.210097 | + | 0.133521i | ||||
\(491\) | 24.8512 | 1.12152 | 0.560760 | − | 0.827979i | \(-0.310509\pi\) | ||||
0.560760 | + | 0.827979i | \(0.310509\pi\) | |||||||
\(492\) | 7.29960 | − | 7.29960i | 0.329091 | − | 0.329091i | ||||
\(493\) | 17.3062 | − | 17.3062i | 0.779433 | − | 0.779433i | ||||
\(494\) | −5.36948 | − | 5.36948i | −0.241584 | − | 0.241584i | ||||
\(495\) | −0.470059 | − | 0.298732i | −0.0211276 | − | 0.0134270i | ||||
\(496\) | 1.83366 | + | 1.83366i | 0.0823338 | + | 0.0823338i | ||||
\(497\) | −5.07975 | − | 5.07975i | −0.227858 | − | 0.227858i | ||||
\(498\) | 8.46334i | 0.379251i | ||||||||
\(499\) | 30.1549 | − | 30.1549i | 1.34992 | − | 1.34992i | 0.464175 | − | 0.885744i | \(-0.346351\pi\) |
0.885744 | − | 0.464175i | \(-0.153649\pi\) | |||||||
\(500\) | 1.42262 | − | 11.0895i | 0.0636214 | − | 0.495936i | ||||
\(501\) | −13.0979 | − | 13.0979i | −0.585172 | − | 0.585172i | ||||
\(502\) | −14.6439 | + | 14.6439i | −0.653590 | + | 0.653590i | ||||
\(503\) | 33.2862i | 1.48416i | 0.670312 | + | 0.742080i | \(0.266160\pi\) | ||||
−0.670312 | + | 0.742080i | \(0.733840\pi\) | |||||||
\(504\) | −1.50593 | − | 1.50593i | −0.0670796 | − | 0.0670796i | ||||
\(505\) | 12.3515 | − | 19.4353i | 0.549636 | − | 0.864861i | ||||
\(506\) | − | 2.06443i | − | 0.0917753i | ||||||
\(507\) | 3.51395 | + | 3.51395i | 0.156060 | + | 0.156060i | ||||
\(508\) | −12.5469 | − | 12.5469i | −0.556679 | − | 0.556679i | ||||
\(509\) | 35.6979 | 1.58228 | 0.791140 | − | 0.611635i | \(-0.209488\pi\) | ||||
0.791140 | + | 0.611635i | \(0.209488\pi\) | |||||||
\(510\) | 15.9194 | − | 3.54768i | 0.704923 | − | 0.157094i | ||||
\(511\) | 22.5356i | 0.996918i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −2.67964 | −0.118309 | ||||||||
\(514\) | 17.8930i | 0.789228i | ||||||||
\(515\) | −15.7474 | − | 10.0078i | −0.693911 | − | 0.440994i | ||||
\(516\) | 5.38278 | − | 5.38278i | 0.236964 | − | 0.236964i | ||||
\(517\) | 0.704271 | − | 0.704271i | 0.0309738 | − | 0.0309738i | ||||
\(518\) | −3.30658 | − | 12.5254i | −0.145283 | − | 0.550336i | ||||
\(519\) | 9.33502i | 0.409762i | ||||||||
\(520\) | 5.34800 | + | 3.39876i | 0.234525 | + | 0.149045i | ||||
\(521\) | 0.701242i | 0.0307220i | 0.999882 | + | 0.0153610i | \(0.00488975\pi\) | ||||
−0.999882 | + | 0.0153610i | \(0.995110\pi\) | |||||||
\(522\) | 2.37266 | − | 2.37266i | 0.103849 | − | 0.103849i | ||||
\(523\) | 35.1652i | 1.53767i | 0.639449 | + | 0.768833i | \(0.279162\pi\) | ||||
−0.639449 | + | 0.768833i | \(0.720838\pi\) | |||||||
\(524\) | −3.81040 | − | 3.81040i | −0.166458 | − | 0.166458i | ||||
\(525\) | 9.64092 | − | 4.52157i | 0.420764 | − | 0.197337i | ||||
\(526\) | −21.7610 | + | 21.7610i | −0.948826 | + | 0.948826i | ||||
\(527\) | −13.3747 | − | 13.3747i | −0.582613 | − | 0.582613i | ||||
\(528\) | −0.176124 | + | 0.176124i | −0.00766480 | + | 0.00766480i | ||||
\(529\) | −45.6967 | −1.98681 | ||||||||
\(530\) | 2.89301 | + | 12.9817i | 0.125664 | + | 0.563889i | ||||
\(531\) | −6.26117 | + | 6.26117i | −0.271712 | + | 0.271712i | ||||
\(532\) | 5.70685i | 0.247423i | ||||||||
\(533\) | −29.2540 | −1.26713 | ||||||||
\(534\) | 7.60247i | 0.328991i | ||||||||
\(535\) | −1.44910 | − | 6.50250i | −0.0626500 | − | 0.281127i | ||||
\(536\) | −5.68165 | − | 5.68165i | −0.245410 | − | 0.245410i | ||||
\(537\) | 15.7021 | 0.677597 | ||||||||
\(538\) | −17.8478 | −0.769475 | ||||||||
\(539\) | 0.613806 | 0.0264385 | ||||||||
\(540\) | 2.18253 | − | 0.486383i | 0.0939211 | − | 0.0209306i | ||||
\(541\) | −5.47295 | + | 5.47295i | −0.235300 | + | 0.235300i | −0.814901 | − | 0.579600i | \(-0.803209\pi\) |
0.579600 | + | 0.814901i | \(0.303209\pi\) | |||||||
\(542\) | 2.29360i | 0.0985188i | ||||||||
\(543\) | 13.5129 | + | 13.5129i | 0.579895 | + | 0.579895i | ||||
\(544\) | − | 7.29402i | − | 0.312728i | ||||||
\(545\) | −7.34234 | − | 32.9470i | −0.314511 | − | 1.41130i | ||||
\(546\) | 6.03521i | 0.258283i | ||||||||
\(547\) | 14.4568i | 0.618127i | 0.951041 | + | 0.309064i | \(0.100016\pi\) | ||||
−0.951041 | + | 0.309064i | \(0.899984\pi\) | |||||||
\(548\) | 2.72768 | + | 2.72768i | 0.116521 | + | 0.116521i | ||||
\(549\) | 3.22008 | − | 3.22008i | 0.137430 | − | 0.137430i | ||||
\(550\) | −0.528812 | − | 1.12754i | −0.0225486 | − | 0.0480783i | ||||
\(551\) | −8.99138 | −0.383046 | ||||||||
\(552\) | 5.86075 | + | 5.86075i | 0.249450 | + | 0.249450i | ||||
\(553\) | − | 18.0657i | − | 0.768233i | ||||||
\(554\) | −1.48608 | −0.0631373 | ||||||||
\(555\) | 12.9613 | + | 4.12369i | 0.550176 | + | 0.175041i | ||||
\(556\) | −2.31516 | −0.0981847 | ||||||||
\(557\) | 16.2684i | 0.689316i | 0.938728 | + | 0.344658i | \(0.112005\pi\) | ||||
−0.938728 | + | 0.344658i | \(0.887995\pi\) | |||||||
\(558\) | −1.83366 | − | 1.83366i | −0.0776250 | − | 0.0776250i | ||||
\(559\) | −21.5722 | −0.912405 | ||||||||
\(560\) | −1.03586 | − | 4.64816i | −0.0437729 | − | 0.196421i | ||||
\(561\) | 1.28465 | − | 1.28465i | 0.0542380 | − | 0.0542380i | ||||
\(562\) | −18.5876 | − | 18.5876i | −0.784071 | − | 0.784071i | ||||
\(563\) | − | 6.03926i | − | 0.254525i | −0.991869 | − | 0.127262i | \(-0.959381\pi\) | ||
0.991869 | − | 0.127262i | \(-0.0406190\pi\) | |||||||
\(564\) | 3.99873i | 0.168377i | ||||||||
\(565\) | 8.02610 | + | 5.10075i | 0.337661 | + | 0.214590i | ||||
\(566\) | − | 16.6153i | − | 0.698392i | ||||||
\(567\) | 1.50593 | + | 1.50593i | 0.0632433 | + | 0.0632433i | ||||
\(568\) | − | 3.37315i | − | 0.141534i | ||||||
\(569\) | −13.8974 | + | 13.8974i | −0.582609 | + | 0.582609i | −0.935620 | − | 0.353010i | \(-0.885158\pi\) |
0.353010 | + | 0.935620i | \(0.385158\pi\) | |||||||
\(570\) | −5.05702 | − | 3.21384i | −0.211815 | − | 0.134613i | ||||
\(571\) | −28.3787 | −1.18761 | −0.593805 | − | 0.804609i | \(-0.702375\pi\) | ||||
−0.593805 | + | 0.804609i | \(0.702375\pi\) | |||||||
\(572\) | 0.705838 | 0.0295126 | ||||||||
\(573\) | −5.85269 | −0.244500 | ||||||||
\(574\) | 15.5460 | + | 15.5460i | 0.648879 | + | 0.648879i | ||||
\(575\) | −37.5202 | + | 17.5969i | −1.56470 | + | 0.733841i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | −35.3160 | −1.47023 | −0.735113 | − | 0.677945i | \(-0.762871\pi\) | ||||
−0.735113 | + | 0.677945i | \(0.762871\pi\) | |||||||
\(578\) | 36.2027i | 1.50583i | ||||||||
\(579\) | −1.17097 | + | 1.17097i | −0.0486638 | + | 0.0486638i | ||||
\(580\) | 7.32336 | − | 1.63203i | 0.304086 | − | 0.0677665i | ||||
\(581\) | −18.0245 | −0.747781 | ||||||||
\(582\) | 4.20538 | − | 4.20538i | 0.174319 | − | 0.174319i | ||||
\(583\) | 1.04759 | + | 1.04759i | 0.0433865 | + | 0.0433865i | ||||
\(584\) | −7.48228 | + | 7.48228i | −0.309619 | + | 0.309619i | ||||
\(585\) | −5.34800 | − | 3.39876i | −0.221112 | − | 0.140521i | ||||
\(586\) | 9.37884 | + | 9.37884i | 0.387436 | + | 0.387436i | ||||
\(587\) | − | 33.3247i | − | 1.37546i | −0.725968 | − | 0.687729i | \(-0.758608\pi\) | ||
0.725968 | − | 0.687729i | \(-0.241392\pi\) | |||||||
\(588\) | −1.74254 | + | 1.74254i | −0.0718612 | + | 0.0718612i | ||||
\(589\) | 6.94879i | 0.286320i | ||||||||
\(590\) | −19.3255 | + | 4.30674i | −0.795617 | + | 0.177306i | ||||
\(591\) | 20.0645i | 0.825344i | ||||||||
\(592\) | 3.06084 | − | 5.25654i | 0.125800 | − | 0.216043i | ||||
\(593\) | 29.5804 | − | 29.5804i | 1.21472 | − | 1.21472i | 0.245266 | − | 0.969456i | \(-0.421125\pi\) |
0.969456 | − | 0.245266i | \(-0.0788753\pi\) | |||||||
\(594\) | 0.176124 | − | 0.176124i | 0.00722645 | − | 0.00722645i | ||||
\(595\) | 7.55555 | + | 33.9037i | 0.309747 | + | 1.38992i | ||||
\(596\) | − | 8.45695i | − | 0.346410i | ||||||
\(597\) | −5.22101 | −0.213682 | ||||||||
\(598\) | − | 23.4877i | − | 0.960482i | ||||||
\(599\) | 16.4095i | 0.670473i | 0.942134 | + | 0.335236i | \(0.108816\pi\) | ||||
−0.942134 | + | 0.335236i | \(0.891184\pi\) | |||||||
\(600\) | 4.70223 | + | 1.69973i | 0.191968 | + | 0.0693910i | ||||
\(601\) | −24.3063 | −0.991473 | −0.495736 | − | 0.868473i | \(-0.665102\pi\) | ||||
−0.495736 | + | 0.868473i | \(0.665102\pi\) | |||||||
\(602\) | 11.4638 | + | 11.4638i | 0.467229 | + | 0.467229i | ||||
\(603\) | 5.68165 | + | 5.68165i | 0.231375 | + | 0.231375i | ||||
\(604\) | 12.3871i | 0.504024i | ||||||||
\(605\) | 20.6422 | + | 13.1185i | 0.839224 | + | 0.533343i | ||||
\(606\) | 7.28212 | + | 7.28212i | 0.295816 | + | 0.295816i | ||||
\(607\) | − | 2.93171i | − | 0.118994i | −0.998228 | − | 0.0594972i | \(-0.981050\pi\) | ||
0.998228 | − | 0.0594972i | \(-0.0189497\pi\) | |||||||
\(608\) | −1.89479 | + | 1.89479i | −0.0768438 | + | 0.0768438i | ||||
\(609\) | 5.05308 | + | 5.05308i | 0.204761 | + | 0.204761i | ||||
\(610\) | 9.93899 | − | 2.21493i | 0.402418 | − | 0.0896800i | ||||
\(611\) | 8.01269 | − | 8.01269i | 0.324159 | − | 0.324159i | ||||
\(612\) | 7.29402i | 0.294843i | ||||||||
\(613\) | −15.0778 | − | 15.0778i | −0.608986 | − | 0.608986i | 0.333695 | − | 0.942681i | \(-0.391704\pi\) |
−0.942681 | + | 0.333695i | \(0.891704\pi\) | |||||||
\(614\) | 3.36862 | + | 3.36862i | 0.135947 | + | 0.135947i | ||||
\(615\) | −22.5307 | + | 5.02102i | −0.908524 | + | 0.202467i | ||||
\(616\) | −0.375093 | − | 0.375093i | −0.0151129 | − | 0.0151129i | ||||
\(617\) | −31.1997 | + | 31.1997i | −1.25605 | + | 1.25605i | −0.303091 | + | 0.952962i | \(0.598019\pi\) |
−0.952962 | + | 0.303091i | \(0.901981\pi\) | |||||||
\(618\) | 5.90029 | − | 5.90029i | 0.237345 | − | 0.237345i | ||||
\(619\) | −11.1366 | −0.447619 | −0.223809 | − | 0.974633i | \(-0.571849\pi\) | ||||
−0.223809 | + | 0.974633i | \(0.571849\pi\) | |||||||
\(620\) | −1.26128 | − | 5.65970i | −0.0506543 | − | 0.227299i | ||||
\(621\) | −5.86075 | − | 5.86075i | −0.235184 | − | 0.235184i | ||||
\(622\) | −22.4334 | + | 22.4334i | −0.899497 | + | 0.899497i | ||||
\(623\) | −16.1911 | −0.648682 | ||||||||
\(624\) | −2.00381 | + | 2.00381i | −0.0802166 | + | 0.0802166i | ||||
\(625\) | −15.9850 | + | 19.2219i | −0.639399 | + | 0.768875i | ||||
\(626\) | −19.2752 | −0.770393 | ||||||||
\(627\) | −0.667435 | −0.0266548 | ||||||||
\(628\) | 10.3496 | + | 10.3496i | 0.412993 | + | 0.412993i | ||||
\(629\) | −22.3259 | + | 38.3413i | −0.890190 | + | 1.52877i | ||||
\(630\) | 1.03586 | + | 4.64816i | 0.0412695 | + | 0.185187i | ||||
\(631\) | 19.2236 | + | 19.2236i | 0.765279 | + | 0.765279i | 0.977271 | − | 0.211992i | \(-0.0679951\pi\) |
−0.211992 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(632\) | 5.99818 | − | 5.99818i | 0.238595 | − | 0.238595i | ||||
\(633\) | −5.76649 | − | 5.76649i | −0.229197 | − | 0.229197i | ||||
\(634\) | −3.94817 | − | 3.94817i | −0.156802 | − | 0.156802i | ||||
\(635\) | 8.63038 | + | 38.7268i | 0.342486 | + | 1.53683i | ||||
\(636\) | −5.94800 | −0.235854 | ||||||||
\(637\) | 6.98345 | 0.276694 | ||||||||
\(638\) | 0.590974 | − | 0.590974i | 0.0233969 | − | 0.0233969i | ||||
\(639\) | 3.37315i | 0.133440i | ||||||||
\(640\) | 1.19936 | − | 1.88721i | 0.0474087 | − | 0.0745983i | ||||
\(641\) | 8.52699 | 0.336796 | 0.168398 | − | 0.985719i | \(-0.446141\pi\) | ||||
0.168398 | + | 0.985719i | \(0.446141\pi\) | |||||||
\(642\) | 2.97934 | 0.117585 | ||||||||
\(643\) | −11.8650 | −0.467910 | −0.233955 | − | 0.972247i | \(-0.575167\pi\) | ||||
−0.233955 | + | 0.972247i | \(0.575167\pi\) | |||||||
\(644\) | −12.4817 | + | 12.4817i | −0.491848 | + | 0.491848i | ||||
\(645\) | −16.6143 | + | 3.70254i | −0.654187 | + | 0.145787i | ||||
\(646\) | 13.8206 | − | 13.8206i | 0.543765 | − | 0.543765i | ||||
\(647\) | − | 1.01194i | − | 0.0397836i | −0.999802 | − | 0.0198918i | \(-0.993668\pi\) | ||
0.999802 | − | 0.0198918i | \(-0.00633217\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −1.55951 | + | 1.55951i | −0.0612161 | + | 0.0612161i | ||||
\(650\) | −6.01645 | − | 12.8283i | −0.235984 | − | 0.503167i | ||||
\(651\) | 3.90517 | − | 3.90517i | 0.153056 | − | 0.153056i | ||||
\(652\) | 8.69039 | 0.340342 | ||||||||
\(653\) | 14.7798 | 0.578377 | 0.289189 | − | 0.957272i | \(-0.406614\pi\) | ||||
0.289189 | + | 0.957272i | \(0.406614\pi\) | |||||||
\(654\) | 15.0958 | 0.590293 | ||||||||
\(655\) | 2.62098 | + | 11.7610i | 0.102410 | + | 0.459541i | ||||
\(656\) | 10.3232i | 0.403053i | ||||||||
\(657\) | 7.48228 | − | 7.48228i | 0.291912 | − | 0.291912i | ||||
\(658\) | −8.51613 | −0.331993 | ||||||||
\(659\) | −1.79646 | −0.0699802 | −0.0349901 | − | 0.999388i | \(-0.511140\pi\) | ||||
−0.0349901 | + | 0.999388i | \(0.511140\pi\) | |||||||
\(660\) | 0.543617 | − | 0.121147i | 0.0211603 | − | 0.00471562i | ||||
\(661\) | 11.0318 | + | 11.0318i | 0.429086 | + | 0.429086i | 0.888317 | − | 0.459231i | \(-0.151875\pi\) |
−0.459231 | + | 0.888317i | \(0.651875\pi\) | |||||||
\(662\) | −2.89997 | − | 2.89997i | −0.112711 | − | 0.112711i | ||||
\(663\) | 14.6158 | − | 14.6158i | 0.567632 | − | 0.567632i | ||||
\(664\) | −5.98449 | − | 5.98449i | −0.232243 | − | 0.232243i | ||||
\(665\) | 6.84455 | − | 10.7700i | 0.265420 | − | 0.417643i | ||||
\(666\) | −3.06084 | + | 5.25654i | −0.118605 | + | 0.203687i | ||||
\(667\) | −19.6654 | − | 19.6654i | −0.761449 | − | 0.761449i | ||||
\(668\) | 18.5233 | 0.716687 | ||||||||
\(669\) | 25.5945 | 0.989539 | ||||||||
\(670\) | 3.90812 | + | 17.5368i | 0.150984 | + | 0.677504i | ||||
\(671\) | 0.802048 | − | 0.802048i | 0.0309627 | − | 0.0309627i | ||||
\(672\) | 2.12971 | 0.0821554 | ||||||||
\(673\) | 12.5759 | − | 12.5759i | 0.484766 | − | 0.484766i | −0.421884 | − | 0.906650i | \(-0.638631\pi\) |
0.906650 | + | 0.421884i | \(0.138631\pi\) | |||||||
\(674\) | −1.55976 | − | 1.55976i | −0.0600796 | − | 0.0600796i | ||||
\(675\) | −4.70223 | − | 1.69973i | −0.180989 | − | 0.0654225i | ||||
\(676\) | −4.96948 | −0.191134 | ||||||||
\(677\) | −18.9213 | + | 18.9213i | −0.727203 | + | 0.727203i | −0.970062 | − | 0.242859i | \(-0.921915\pi\) |
0.242859 | + | 0.970062i | \(0.421915\pi\) | |||||||
\(678\) | −3.00726 | + | 3.00726i | −0.115493 | + | 0.115493i | ||||
\(679\) | 8.95625 | + | 8.95625i | 0.343710 | + | 0.343710i | ||||
\(680\) | −8.74813 | + | 13.7653i | −0.335475 | + | 0.527876i | ||||
\(681\) | −10.7509 | − | 10.7509i | −0.411974 | − | 0.411974i | ||||
\(682\) | −0.456722 | − | 0.456722i | −0.0174888 | − | 0.0174888i | ||||
\(683\) | − | 36.6018i | − | 1.40053i | −0.713883 | − | 0.700265i | \(-0.753065\pi\) | ||
0.713883 | − | 0.700265i | \(-0.246935\pi\) | |||||||
\(684\) | 1.89479 | − | 1.89479i | 0.0724490 | − | 0.0724490i | ||||
\(685\) | −1.87623 | − | 8.41915i | −0.0716871 | − | 0.321679i | ||||
\(686\) | −14.2526 | − | 14.2526i | −0.544169 | − | 0.544169i | ||||
\(687\) | 15.6384 | − | 15.6384i | 0.596642 | − | 0.596642i | ||||
\(688\) | 7.61240i | 0.290220i | ||||||||
\(689\) | 11.9187 | + | 11.9187i | 0.454066 | + | 0.454066i | ||||
\(690\) | −4.03131 | − | 18.0896i | −0.153469 | − | 0.688658i | ||||
\(691\) | 23.7209i | 0.902385i | 0.892427 | + | 0.451193i | \(0.149001\pi\) | ||||
−0.892427 | + | 0.451193i | \(0.850999\pi\) | |||||||
\(692\) | −6.60085 | − | 6.60085i | −0.250927 | − | 0.250927i | ||||
\(693\) | 0.375093 | + | 0.375093i | 0.0142486 | + | 0.0142486i | ||||
\(694\) | 9.43617 | 0.358192 | ||||||||
\(695\) | 4.36918 | + | 2.77670i | 0.165733 | + | 0.105326i | ||||
\(696\) | 3.35545i | 0.127188i | ||||||||
\(697\) | − | 75.2975i | − | 2.85210i | ||||||
\(698\) | −7.25908 | −0.274760 | ||||||||
\(699\) | − | 6.74984i | − | 0.255302i | ||||||
\(700\) | −3.61993 | + | 10.0144i | −0.136820 | + | 0.378508i | ||||
\(701\) | −12.5087 | + | 12.5087i | −0.472447 | + | 0.472447i | −0.902706 | − | 0.430259i | \(-0.858422\pi\) |
0.430259 | + | 0.902706i | \(0.358422\pi\) | |||||||
\(702\) | 2.00381 | − | 2.00381i | 0.0756290 | − | 0.0756290i | ||||
\(703\) | 15.7597 | − | 4.16038i | 0.594388 | − | 0.156912i | ||||
\(704\) | − | 0.249077i | − | 0.00938743i | ||||||
\(705\) | 4.79590 | − | 7.54642i | 0.180624 | − | 0.284214i | ||||
\(706\) | − | 6.63465i | − | 0.249698i | ||||||
\(707\) | −15.5088 | + | 15.5088i | −0.583269 | + | 0.583269i | ||||
\(708\) | − | 8.85463i | − | 0.332777i | ||||||
\(709\) | −16.9567 | − | 16.9567i | −0.636822 | − | 0.636822i | 0.312948 | − | 0.949770i | \(-0.398683\pi\) |
−0.949770 | + | 0.312948i | \(0.898683\pi\) | |||||||
\(710\) | −4.04561 | + | 6.36583i | −0.151829 | + | 0.238906i | ||||
\(711\) | −5.99818 | + | 5.99818i | −0.224949 | + | 0.224949i | ||||
\(712\) | −5.37576 | − | 5.37576i | −0.201465 | − | 0.201465i | ||||
\(713\) | −15.1980 | + | 15.1980i | −0.569170 | + | 0.569170i | ||||
\(714\) | −15.5342 | −0.581351 | ||||||||
\(715\) | −1.33206 | − | 0.846551i | −0.0498162 | − | 0.0316592i | ||||
\(716\) | −11.1031 | + | 11.1031i | −0.414942 | + | 0.414942i | ||||
\(717\) | 28.0719i | 1.04836i | ||||||||
\(718\) | 3.64712 | 0.136109 | ||||||||
\(719\) | 6.40855i | 0.238998i | 0.992834 | + | 0.119499i | \(0.0381289\pi\) | ||||
−0.992834 | + | 0.119499i | \(0.961871\pi\) | |||||||
\(720\) | −1.19936 | + | 1.88721i | −0.0446974 | + | 0.0703320i | ||||
\(721\) | 12.5659 | + | 12.5659i | 0.467979 | + | 0.467979i | ||||
\(722\) | 11.8196 | 0.439878 | ||||||||
\(723\) | 30.1552 | 1.12148 | ||||||||
\(724\) | −19.1102 | −0.710223 | ||||||||
\(725\) | −15.7781 | − | 5.70334i | −0.585983 | − | 0.211817i | ||||
\(726\) | −7.73431 | + | 7.73431i | −0.287047 | + | 0.287047i | ||||
\(727\) | − | 6.09536i | − | 0.226064i | −0.993591 | − | 0.113032i | \(-0.963944\pi\) | ||
0.993591 | − | 0.113032i | \(-0.0360563\pi\) | |||||||
\(728\) | −4.26754 | − | 4.26754i | −0.158166 | − | 0.158166i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 23.0945 | − | 5.14668i | 0.854767 | − | 0.190487i | ||||
\(731\) | − | 55.5250i | − | 2.05367i | ||||||
\(732\) | 4.55389i | 0.168317i | ||||||||
\(733\) | 5.99617 | + | 5.99617i | 0.221474 | + | 0.221474i | 0.809119 | − | 0.587645i | \(-0.199945\pi\) |
−0.587645 | + | 0.809119i | \(0.699945\pi\) | |||||||
\(734\) | 2.67398 | − | 2.67398i | 0.0986982 | − | 0.0986982i | ||||
\(735\) | 5.37846 | − | 1.19861i | 0.198388 | − | 0.0442113i | ||||
\(736\) | −8.28835 | −0.305513 | ||||||||
\(737\) | 1.41517 | + | 1.41517i | 0.0521283 | + | 0.0521283i | ||||
\(738\) | − | 10.3232i | − | 0.380002i | ||||||
\(739\) | 31.2325 | 1.14891 | 0.574453 | − | 0.818538i | \(-0.305215\pi\) | ||||
0.574453 | + | 0.818538i | \(0.305215\pi\) | |||||||
\(740\) | −12.0809 | + | 6.24913i | −0.444103 | + | 0.229723i | ||||
\(741\) | −7.59360 | −0.278958 | ||||||||
\(742\) | − | 12.6675i | − | 0.465040i | ||||||
\(743\) | −28.7095 | − | 28.7095i | −1.05325 | − | 1.05325i | −0.998500 | − | 0.0547482i | \(-0.982564\pi\) |
−0.0547482 | − | 0.998500i | \(-0.517436\pi\) | |||||||
\(744\) | 2.59319 | 0.0950708 | ||||||||
\(745\) | −10.1429 | + | 15.9600i | −0.371607 | + | 0.584730i | ||||
\(746\) | −8.22916 | + | 8.22916i | −0.301291 | + | 0.301291i | ||||
\(747\) | 5.98449 | + | 5.98449i | 0.218961 | + | 0.218961i | ||||
\(748\) | 1.81677i | 0.0664277i | ||||||||
\(749\) | 6.34514i | 0.231846i | ||||||||
\(750\) | −6.83549 | − | 8.84738i | −0.249597 | − | 0.323060i | ||||
\(751\) | − | 4.99355i | − | 0.182217i | −0.995841 | − | 0.0911086i | \(-0.970959\pi\) | ||
0.995841 | − | 0.0911086i | \(-0.0290410\pi\) | |||||||
\(752\) | −2.82753 | − | 2.82753i | −0.103109 | − | 0.103109i | ||||
\(753\) | 20.7096i | 0.754700i | ||||||||
\(754\) | 6.72369 | − | 6.72369i | 0.244862 | − | 0.244862i | ||||
\(755\) | 14.8565 | − | 23.3770i | 0.540685 | − | 0.850776i | ||||
\(756\) | −2.12971 | −0.0774569 | ||||||||
\(757\) | 20.7849 | 0.755438 | 0.377719 | − | 0.925920i | \(-0.376708\pi\) | ||||
0.377719 | + | 0.925920i | \(0.376708\pi\) | |||||||
\(758\) | −23.2988 | −0.846250 | ||||||||
\(759\) | −1.45978 | − | 1.45978i | −0.0529865 | − | 0.0529865i | ||||
\(760\) | 5.84838 | − | 1.30333i | 0.212143 | − | 0.0472767i | ||||
\(761\) | 10.4423i | 0.378532i | 0.981926 | + | 0.189266i | \(0.0606109\pi\) | ||||
−0.981926 | + | 0.189266i | \(0.939389\pi\) | |||||||
\(762\) | −17.7440 | −0.642798 | ||||||||
\(763\) | 32.1497i | 1.16390i | ||||||||
\(764\) | 4.13848 | − | 4.13848i | 0.149725 | − | 0.149725i | ||||
\(765\) | 8.74813 | − | 13.7653i | 0.316289 | − | 0.497686i | ||||
\(766\) | 1.82589 | 0.0659719 | ||||||||
\(767\) | −17.7430 | + | 17.7430i | −0.640663 | + | 0.640663i | ||||
\(768\) | 0.707107 | + | 0.707107i | 0.0255155 | + | 0.0255155i | ||||
\(769\) | 36.5206 | − | 36.5206i | 1.31697 | − | 1.31697i | 0.400801 | − | 0.916165i | \(-0.368732\pi\) |
0.916165 | − | 0.400801i | \(-0.131268\pi\) | |||||||
\(770\) | 0.258007 | + | 1.15775i | 0.00929794 | + | 0.0417223i | ||||
\(771\) | 12.6523 | + | 12.6523i | 0.455661 | + | 0.455661i | ||||
\(772\) | − | 1.65600i | − | 0.0596007i | ||||||
\(773\) | 36.9436 | − | 36.9436i | 1.32877 | − | 1.32877i | 0.422323 | − | 0.906445i | \(-0.361215\pi\) |
0.906445 | − | 0.422323i | \(-0.138785\pi\) | |||||||
\(774\) | − | 7.61240i | − | 0.273622i | ||||||
\(775\) | −4.40771 | + | 12.1938i | −0.158329 | + | 0.438012i | ||||
\(776\) | 5.94731i | 0.213496i | ||||||||
\(777\) | −11.1949 | − | 6.51872i | −0.401616 | − | 0.233858i | ||||
\(778\) | −1.87840 | + | 1.87840i | −0.0673440 | + | 0.0673440i | ||||
\(779\) | −19.5603 | + | 19.5603i | −0.700819 | + | 0.700819i | ||||
\(780\) | 6.18489 | − | 1.37832i | 0.221454 | − | 0.0493518i | ||||
\(781\) | 0.840174i | 0.0300638i | ||||||||
\(782\) | 60.4554 | 2.16188 | ||||||||
\(783\) | − | 3.35545i | − | 0.119914i | ||||||
\(784\) | − | 2.46433i | − | 0.0880117i | ||||||
\(785\) | −7.11895 | − | 31.9446i | −0.254086 | − | 1.14015i | ||||
\(786\) | −5.38872 | −0.192209 | ||||||||
\(787\) | −5.06401 | − | 5.06401i | −0.180512 | − | 0.180512i | 0.611067 | − | 0.791579i | \(-0.290741\pi\) |
−0.791579 | + | 0.611067i | \(0.790741\pi\) | |||||||
\(788\) | −14.1878 | − | 14.1878i | −0.505418 | − | 0.505418i | ||||
\(789\) | 30.7747i | 1.09561i | ||||||||
\(790\) | −18.5138 | + | 4.12584i | −0.658690 | + | 0.146791i | ||||
\(791\) | −6.40459 | − | 6.40459i | −0.227721 | − | 0.227721i | ||||
\(792\) | 0.249077i | 0.00885055i | ||||||||
\(793\) | 9.12513 | − | 9.12513i | 0.324043 | − | 0.324043i | ||||
\(794\) | 12.0046 | + | 12.0046i | 0.426026 | + | 0.426026i | ||||
\(795\) | 11.2251 | + | 7.13378i | 0.398114 | + | 0.253009i | ||||
\(796\) | 3.69181 | − | 3.69181i | 0.130853 | − | 0.130853i | ||||
\(797\) | − | 21.7157i | − | 0.769210i | −0.923081 | − | 0.384605i | \(-0.874338\pi\) | ||
0.923081 | − | 0.384605i | \(-0.125662\pi\) | |||||||
\(798\) | 4.03535 | + | 4.03535i | 0.142850 | + | 0.142850i | ||||
\(799\) | 20.6240 | + | 20.6240i | 0.729625 | + | 0.729625i | ||||
\(800\) | −4.52686 | + | 2.12309i | −0.160049 | + | 0.0750625i | ||||
\(801\) | 5.37576 | + | 5.37576i | 0.189943 | + | 0.189943i | ||||
\(802\) | 23.2046 | − | 23.2046i | 0.819382 | − | 0.819382i | ||||
\(803\) | 1.86366 | − | 1.86366i | 0.0657672 | − | 0.0657672i | ||||
\(804\) | −8.03506 | −0.283375 | ||||||||
\(805\) | 38.5255 | − | 8.58553i | 1.35785 | − | 0.302600i | ||||
\(806\) | −5.19626 | − | 5.19626i | −0.183030 | − | 0.183030i | ||||
\(807\) | −12.6203 | + | 12.6203i | −0.444257 | + | 0.444257i | ||||
\(808\) | −10.2985 | −0.362299 | ||||||||
\(809\) | −23.1152 | + | 23.1152i | −0.812687 | + | 0.812687i | −0.985036 | − | 0.172349i | \(-0.944864\pi\) |
0.172349 | + | 0.985036i | \(0.444864\pi\) | |||||||
\(810\) | 1.19936 | − | 1.88721i | 0.0421411 | − | 0.0663096i | ||||
\(811\) | 45.9301 | 1.61282 | 0.806412 | − | 0.591354i | \(-0.201407\pi\) | ||||
0.806412 | + | 0.591354i | \(0.201407\pi\) | |||||||
\(812\) | −7.14614 | −0.250780 | ||||||||
\(813\) | 1.62182 | + | 1.62182i | 0.0568798 | + | 0.0568798i | ||||
\(814\) | −0.762385 | + | 1.30928i | −0.0267216 | + | 0.0458903i | ||||
\(815\) | −16.4006 | − | 10.4229i | −0.574486 | − | 0.365097i | ||||
\(816\) | −5.15765 | − | 5.15765i | −0.180554 | − | 0.180554i | ||||
\(817\) | −14.4239 | + | 14.4239i | −0.504628 | + | 0.504628i | ||||
\(818\) | 12.7469 | + | 12.7469i | 0.445683 | + | 0.445683i | ||||
\(819\) | 4.26754 | + | 4.26754i | 0.149120 | + | 0.149120i | ||||
\(820\) | 12.3812 | − | 19.4820i | 0.432370 | − | 0.680340i | ||||
\(821\) | −31.8102 | −1.11018 | −0.555092 | − | 0.831789i | \(-0.687317\pi\) | ||||
−0.555092 | + | 0.831789i | \(0.687317\pi\) | |||||||
\(822\) | 3.85752 | 0.134547 | ||||||||
\(823\) | 0.924037 | − | 0.924037i | 0.0322099 | − | 0.0322099i | −0.690818 | − | 0.723028i | \(-0.742750\pi\) |
0.723028 | + | 0.690818i | \(0.242750\pi\) | |||||||
\(824\) | 8.34427i | 0.290686i | ||||||||
\(825\) | −1.17121 | − | 0.423362i | −0.0407765 | − | 0.0147396i | ||||
\(826\) | 18.8578 | 0.656147 | ||||||||
\(827\) | 5.29174 | 0.184012 | 0.0920059 | − | 0.995758i | \(-0.470672\pi\) | ||||
0.0920059 | + | 0.995758i | \(0.470672\pi\) | |||||||
\(828\) | 8.28835 | 0.288040 | ||||||||
\(829\) | −14.0039 | + | 14.0039i | −0.486376 | + | 0.486376i | −0.907161 | − | 0.420784i | \(-0.861755\pi\) |
0.420784 | + | 0.907161i | \(0.361755\pi\) | |||||||
\(830\) | 4.11642 | + | 18.4715i | 0.142883 | + | 0.641155i | ||||
\(831\) | −1.05081 | + | 1.05081i | −0.0364523 | + | 0.0364523i | ||||
\(832\) | − | 2.83382i | − | 0.0982449i | ||||||
\(833\) | 17.9748i | 0.622791i | ||||||||
\(834\) | −1.63707 | + | 1.63707i | −0.0566870 | + | 0.0566870i | ||||
\(835\) | −34.9572 | − | 22.2160i | −1.20974 | − | 0.768816i | ||||
\(836\) | 0.471948 | − | 0.471948i | 0.0163226 | − | 0.0163226i | ||||
\(837\) | −2.59319 | −0.0896336 | ||||||||
\(838\) | 22.1539 | 0.765295 | ||||||||
\(839\) | 5.45096 | 0.188188 | 0.0940941 | − | 0.995563i | \(-0.470005\pi\) | ||||
0.0940941 | + | 0.995563i | \(0.470005\pi\) | |||||||
\(840\) | −4.01920 | − | 2.55428i | −0.138676 | − | 0.0881312i | ||||
\(841\) | 17.7410i | 0.611757i | ||||||||
\(842\) | 18.3106 | − | 18.3106i | 0.631025 | − | 0.631025i | ||||
\(843\) | −26.2868 | −0.905367 | ||||||||
\(844\) | 8.15505 | 0.280708 | ||||||||
\(845\) | 9.37843 | + | 5.96018i | 0.322628 | + | 0.205036i | ||||
\(846\) | 2.82753 | + | 2.82753i | 0.0972123 | + | 0.0972123i | ||||
\(847\) | −16.4718 | − | 16.4718i | −0.565979 | − | 0.565979i | ||||
\(848\) | 4.20587 | − | 4.20587i | 0.144430 | − | 0.144430i | ||||
\(849\) | −11.7488 | − | 11.7488i | −0.403217 | − | 0.403217i | ||||
\(850\) | 33.0190 | − | 15.4858i | 1.13254 | − | 0.531160i | ||||
\(851\) | 43.5680 | + | 25.3693i | 1.49349 | + | 0.869650i | ||||
\(852\) | −2.38518 | − | 2.38518i | −0.0817149 | − | 0.0817149i | ||||
\(853\) | 1.69992 | 0.0582041 | 0.0291021 | − | 0.999576i | \(-0.490735\pi\) | ||||
0.0291021 | + | 0.999576i | \(0.490735\pi\) | |||||||
\(854\) | −9.69847 | −0.331875 | ||||||||
\(855\) | −5.84838 | + | 1.30333i | −0.200010 | + | 0.0445729i | ||||
\(856\) | −2.10671 | + | 2.10671i | −0.0720059 | + | 0.0720059i | ||||
\(857\) | 48.8147 | 1.66748 | 0.833738 | − | 0.552160i | \(-0.186196\pi\) | ||||
0.833738 | + | 0.552160i | \(0.186196\pi\) | |||||||
\(858\) | 0.499103 | − | 0.499103i | 0.0170391 | − | 0.0170391i | ||||
\(859\) | −2.09107 | − | 2.09107i | −0.0713463 | − | 0.0713463i | 0.670533 | − | 0.741879i | \(-0.266065\pi\) |
−0.741879 | + | 0.670533i | \(0.766065\pi\) | |||||||
\(860\) | 9.12998 | − | 14.3662i | 0.311330 | − | 0.489882i | ||||
\(861\) | 21.9854 | 0.749261 | ||||||||
\(862\) | 8.32782 | − | 8.32782i | 0.283647 | − | 0.283647i | ||||
\(863\) | −5.37396 | + | 5.37396i | −0.182932 | + | 0.182932i | −0.792632 | − | 0.609700i | \(-0.791290\pi\) |
0.609700 | + | 0.792632i | \(0.291290\pi\) | |||||||
\(864\) | −0.707107 | − | 0.707107i | −0.0240563 | − | 0.0240563i | ||||
\(865\) | 4.54039 | + | 20.3739i | 0.154378 | + | 0.692735i | ||||
\(866\) | −6.11268 | − | 6.11268i | −0.207717 | − | 0.207717i | ||||
\(867\) | 25.5992 | + | 25.5992i | 0.869393 | + | 0.869393i | ||||
\(868\) | 5.52274i | 0.187454i | ||||||||
\(869\) | −1.49401 | + | 1.49401i | −0.0506807 | + | 0.0506807i | ||||
\(870\) | 4.02438 | − | 6.33242i | 0.136439 | − | 0.214689i | ||||
\(871\) | 16.1008 | + | 16.1008i | 0.545553 | + | 0.545553i | ||||
\(872\) | −10.6743 | + | 10.6743i | −0.361479 | + | 0.361479i | ||||
\(873\) | − | 5.94731i | − | 0.201286i | ||||||
\(874\) | −15.7047 | − | 15.7047i | −0.531218 | − | 0.531218i | ||||
\(875\) | 18.8424 | − | 14.5576i | 0.636988 | − | 0.492138i | ||||
\(876\) | 10.5815i | 0.357517i | ||||||||
\(877\) | −6.91171 | − | 6.91171i | −0.233392 | − | 0.233392i | 0.580715 | − | 0.814107i | \(-0.302773\pi\) |
−0.814107 | + | 0.580715i | \(0.802773\pi\) | |||||||
\(878\) | 16.2052 | + | 16.2052i | 0.546899 | + | 0.546899i | ||||
\(879\) | 13.2637 | 0.447373 | ||||||||
\(880\) | −0.298732 | + | 0.470059i | −0.0100702 | + | 0.0158457i | ||||
\(881\) | − | 8.64906i | − | 0.291394i | −0.989329 | − | 0.145697i | \(-0.953457\pi\) | ||
0.989329 | − | 0.145697i | \(-0.0465425\pi\) | |||||||
\(882\) | 2.46433i | 0.0829782i | ||||||||
\(883\) | 18.4508 | 0.620919 | 0.310460 | − | 0.950587i | \(-0.399517\pi\) | ||||
0.310460 | + | 0.950587i | \(0.399517\pi\) | |||||||
\(884\) | 20.6699i | 0.695204i | ||||||||
\(885\) | −10.6199 | + | 16.7105i | −0.356982 | + | 0.561717i | ||||
\(886\) | 6.30399 | − | 6.30399i | 0.211787 | − | 0.211787i | ||||
\(887\) | 27.1337 | − | 27.1337i | 0.911062 | − | 0.911062i | −0.0852937 | − | 0.996356i | \(-0.527183\pi\) |
0.996356 | + | 0.0852937i | \(0.0271829\pi\) | |||||||
\(888\) | −1.55259 | − | 5.88128i | −0.0521016 | − | 0.197363i | ||||
\(889\) | − | 37.7896i | − | 1.26742i | ||||||
\(890\) | 3.69771 | + | 16.5926i | 0.123948 | + | 0.556186i | ||||
\(891\) | − | 0.249077i | − | 0.00834438i | ||||||
\(892\) | −18.0980 | + | 18.0980i | −0.605967 | + | 0.605967i | ||||
\(893\) | − | 10.7151i | − | 0.358568i | ||||||
\(894\) | −5.97997 | − | 5.97997i | −0.200000 | − | 0.200000i | ||||
\(895\) | 34.2703 | − | 7.63724i | 1.14553 | − | 0.255285i | ||||
\(896\) | −1.50593 | + | 1.50593i | −0.0503097 | + | 0.0503097i | ||||
\(897\) | −16.6083 | − | 16.6083i | −0.554534 | − | 0.554534i | ||||
\(898\) | 19.8634 | − | 19.8634i | 0.662851 | − | 0.662851i | ||||
\(899\) | −8.70130 | −0.290205 | ||||||||
\(900\) | 4.52686 | − | 2.12309i | 0.150895 | − | 0.0707696i | ||||
\(901\) | −30.6777 | + | 30.6777i | −1.02202 | + | 1.02202i | ||||
\(902\) | − | 2.57127i | − | 0.0856138i | ||||||
\(903\) | 16.2122 | 0.539509 | ||||||||
\(904\) | − | 4.25290i | − | 0.141449i | ||||||
\(905\) | 36.0648 | + | 22.9199i | 1.19883 | + | 0.761883i | ||||
\(906\) | 8.75900 | + | 8.75900i | 0.290998 | + | 0.290998i | ||||
\(907\) | 20.4243 | 0.678179 | 0.339090 | − | 0.940754i | \(-0.389881\pi\) | ||||
0.339090 | + | 0.940754i | \(0.389881\pi\) | |||||||
\(908\) | 15.2040 | 0.504563 | ||||||||
\(909\) | 10.2985 | 0.341579 | ||||||||
\(910\) | 2.93542 | + | 13.1720i | 0.0973084 | + | 0.436648i | ||||
\(911\) | 26.7806 | − | 26.7806i | 0.887279 | − | 0.887279i | −0.106982 | − | 0.994261i | \(-0.534119\pi\) |
0.994261 | + | 0.106982i | \(0.0341186\pi\) | |||||||
\(912\) | 2.67964i | 0.0887316i | ||||||||
\(913\) | 1.49060 | + | 1.49060i | 0.0493315 | + | 0.0493315i | ||||
\(914\) | − | 40.2606i | − | 1.33170i | ||||||
\(915\) | 5.46173 | − | 8.59412i | 0.180559 | − | 0.284113i | ||||
\(916\) | 22.1160i | 0.730735i | ||||||||
\(917\) | − | 11.4764i | − | 0.378985i | ||||||
\(918\) | 5.15765 | + | 5.15765i | 0.170228 | + | 0.170228i | ||||
\(919\) | 31.0865 | − | 31.0865i | 1.02545 | − | 1.02545i | 0.0257801 | − | 0.999668i | \(-0.491793\pi\) |
0.999668 | − | 0.0257801i | \(-0.00820698\pi\) | |||||||
\(920\) | 15.6418 | + | 9.94068i | 0.515695 | + | 0.327735i | ||||
\(921\) | 4.76395 | 0.156978 | ||||||||
\(922\) | −15.0948 | − | 15.0948i | −0.497121 | − | 0.497121i | ||||
\(923\) | 9.55890i | 0.314635i | ||||||||
\(924\) | −0.530462 | −0.0174509 | ||||||||
\(925\) | 30.2941 | + | 2.69592i | 0.996064 | + | 0.0886413i | ||||
\(926\) | −25.5478 | −0.839551 | ||||||||
\(927\) | − | 8.34427i | − | 0.274062i | ||||||
\(928\) | −2.37266 | − | 2.37266i | −0.0778864 | − | 0.0778864i | ||||
\(929\) | −47.3305 | −1.55286 | −0.776431 | − | 0.630202i | \(-0.782972\pi\) | ||||
−0.776431 | + | 0.630202i | \(0.782972\pi\) | |||||||
\(930\) | −4.89388 | − | 3.11015i | −0.160477 | − | 0.101986i | ||||
\(931\) | 4.66938 | − | 4.66938i | 0.153033 | − | 0.153033i | ||||
\(932\) | 4.77285 | + | 4.77285i | 0.156340 | + | 0.156340i | ||||
\(933\) | 31.7256i | 1.03865i | ||||||||
\(934\) | − | 30.7343i | − | 1.00566i | ||||||
\(935\) | 2.17895 | − | 3.42862i | 0.0712594 | − | 0.112128i | ||||
\(936\) | 2.83382i | 0.0926262i | ||||||||
\(937\) | −17.0130 | − | 17.0130i | −0.555791 | − | 0.555791i | 0.372315 | − | 0.928106i | \(-0.378564\pi\) |
−0.928106 | + | 0.372315i | \(0.878564\pi\) | |||||||
\(938\) | − | 17.1124i | − | 0.558739i | ||||||
\(939\) | −13.6296 | + | 13.6296i | −0.444787 | + | 0.444787i | ||||
\(940\) | 1.94491 | + | 8.72733i | 0.0634360 | + | 0.284654i | ||||
\(941\) | 19.9394 | 0.650005 | 0.325002 | − | 0.945713i | \(-0.394635\pi\) | ||||
0.325002 | + | 0.945713i | \(0.394635\pi\) | |||||||
\(942\) | 14.6365 | 0.476883 | ||||||||
\(943\) | −85.5622 | −2.78629 | ||||||||
\(944\) | 6.26117 | + | 6.26117i | 0.203784 | + | 0.203784i | ||||
\(945\) | 4.01920 | + | 2.55428i | 0.130745 | + | 0.0830908i | ||||
\(946\) | − | 1.89607i | − | 0.0616466i | ||||||
\(947\) | 51.9641 | 1.68861 | 0.844304 | − | 0.535865i | \(-0.180014\pi\) | ||||
0.844304 | + | 0.535865i | \(0.180014\pi\) | |||||||
\(948\) | − | 8.48271i | − | 0.275506i | ||||||
\(949\) | 21.2034 | − | 21.2034i | 0.688292 | − | 0.688292i | ||||
\(950\) | −12.6003 | − | 4.55464i | −0.408806 | − | 0.147772i | ||||
\(951\) | −5.58356 | −0.181059 | ||||||||
\(952\) | 10.9843 | − | 10.9843i | 0.356003 | − | 0.356003i | ||||
\(953\) | 1.57228 | + | 1.57228i | 0.0509312 | + | 0.0509312i | 0.732114 | − | 0.681182i | \(-0.238534\pi\) |
−0.681182 | + | 0.732114i | \(0.738534\pi\) | |||||||
\(954\) | −4.20587 | + | 4.20587i | −0.136170 | + | 0.136170i | ||||
\(955\) | −12.7737 | + | 2.84665i | −0.413346 | + | 0.0921154i | ||||
\(956\) | −19.8498 | − | 19.8498i | −0.641989 | − | 0.641989i | ||||
\(957\) | − | 0.835764i | − | 0.0270164i | ||||||
\(958\) | 0.00977229 | − | 0.00977229i | 0.000315728 | − | 0.000315728i | ||||
\(959\) | 8.21541i | 0.265289i | ||||||||
\(960\) | −0.486383 | − | 2.18253i | −0.0156979 | − | 0.0704408i | ||||
\(961\) | − | 24.2754i | − | 0.783077i | ||||||
\(962\) | −8.67387 | + | 14.8961i | −0.279657 | + | 0.480269i | ||||
\(963\) | 2.10671 | − | 2.10671i | 0.0678878 | − | 0.0678878i | ||||
\(964\) | −21.3229 | + | 21.3229i | −0.686765 | + | 0.686765i | ||||
\(965\) | −1.98613 | + | 3.12521i | −0.0639358 | + | 0.100604i | ||||
\(966\) | 17.6518i | 0.567937i | ||||||||
\(967\) | 31.3573 | 1.00838 | 0.504192 | − | 0.863592i | \(-0.331790\pi\) | ||||
0.504192 | + | 0.863592i | \(0.331790\pi\) | |||||||
\(968\) | − | 10.9380i | − | 0.351559i | ||||||
\(969\) | − | 19.5453i | − | 0.627886i | ||||||
\(970\) | 7.13294 | − | 11.2238i | 0.229025 | − | 0.360374i | ||||
\(971\) | −32.7570 | −1.05122 | −0.525611 | − | 0.850725i | \(-0.676163\pi\) | ||||
−0.525611 | + | 0.850725i | \(0.676163\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −3.48648 | − | 3.48648i | −0.111771 | − | 0.111771i | ||||
\(974\) | − | 0.0126739i | − | 0.000406099i | ||||||
\(975\) | −13.3252 | − | 4.81671i | −0.426750 | − | 0.154258i | ||||
\(976\) | −3.22008 | − | 3.22008i | −0.103072 | − | 0.103072i | ||||
\(977\) | − | 10.8286i | − | 0.346436i | −0.984883 | − | 0.173218i | \(-0.944583\pi\) | ||
0.984883 | − | 0.173218i | \(-0.0554166\pi\) | |||||||
\(978\) | 6.14503 | − | 6.14503i | 0.196497 | − | 0.196497i | ||||
\(979\) | 1.33898 | + | 1.33898i | 0.0427939 | + | 0.0427939i | ||||
\(980\) | −2.95561 | + | 4.65069i | −0.0944134 | + | 0.148561i | ||||
\(981\) | 10.6743 | − | 10.6743i | 0.340806 | − | 0.340806i | ||||
\(982\) | 24.8512i | 0.793034i | ||||||||
\(983\) | 32.0672 | + | 32.0672i | 1.02279 | + | 1.02279i | 0.999734 | + | 0.0230521i | \(0.00733836\pi\) |
0.0230521 | + | 0.999734i | \(0.492662\pi\) | |||||||
\(984\) | 7.29960 | + | 7.29960i | 0.232703 | + | 0.232703i | ||||
\(985\) | 9.75904 | + | 43.7914i | 0.310949 | + | 1.39531i | ||||
\(986\) | 17.3062 | + | 17.3062i | 0.551142 | + | 0.551142i | ||||
\(987\) | −6.02182 | + | 6.02182i | −0.191677 | + | 0.191677i | ||||
\(988\) | 5.36948 | − | 5.36948i | 0.170826 | − | 0.170826i | ||||
\(989\) | −63.0943 | −2.00628 | ||||||||
\(990\) | 0.298732 | − | 0.470059i | 0.00949431 | − | 0.0149394i | ||||
\(991\) | 10.7854 | + | 10.7854i | 0.342609 | + | 0.342609i | 0.857347 | − | 0.514738i | \(-0.172111\pi\) |
−0.514738 | + | 0.857347i | \(0.672111\pi\) | |||||||
\(992\) | −1.83366 | + | 1.83366i | −0.0582188 | + | 0.0582188i | ||||
\(993\) | −4.10118 | −0.130147 | ||||||||
\(994\) | 5.07975 | − | 5.07975i | 0.161120 | − | 0.161120i | ||||
\(995\) | −11.3950 | + | 2.53941i | −0.361246 | + | 0.0805046i | ||||
\(996\) | −8.46334 | −0.268171 | ||||||||
\(997\) | 27.7799 | 0.879799 | 0.439900 | − | 0.898047i | \(-0.355014\pi\) | ||||
0.439900 | + | 0.898047i | \(0.355014\pi\) | |||||||
\(998\) | 30.1549 | + | 30.1549i | 0.954536 | + | 0.954536i | ||||
\(999\) | 1.55259 | + | 5.88128i | 0.0491219 | + | 0.186075i |
(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 | 1110.2.l.b.697.15 | yes | 40 | |
5.3 | odd | 4 | 1110.2.o.b.253.6 | yes | 40 | ||
37.6 | odd | 4 | 1110.2.o.b.487.6 | yes | 40 | ||
185.43 | even | 4 | inner | 1110.2.l.b.43.15 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1110.2.l.b.43.15 | ✓ | 40 | 185.43 | even | 4 | inner | |
1110.2.l.b.697.15 | yes | 40 | 1.1 | even | 1 | trivial | |
1110.2.o.b.253.6 | yes | 40 | 5.3 | odd | 4 | ||
1110.2.o.b.487.6 | yes | 40 | 37.6 | odd | 4 |