Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), not 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} - 102 x^{7} + 144 x^{6} - 432 x^{5} + 502 x^{4} + 288 x^{3} + 72 x^{2} + 12 x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.2 | ||
Root | \(-1.29724 - 0.347596i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.c.1011.2 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | −1.35034 | + | 0.779618i | −0.779618 | + | 0.450113i | −0.836295 | − | 0.548280i | \(-0.815283\pi\) |
0.0566769 | + | 0.998393i | \(0.481950\pi\) | |||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −0.882559 | − | 0.509546i | −0.394692 | − | 0.227876i | 0.289499 | − | 0.957178i | \(-0.406511\pi\) |
−0.684191 | + | 0.729303i | \(0.739845\pi\) | |||||||
\(6\) | 1.55924 | 0.636555 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.284392 | + | 0.492581i | −0.0947972 | + | 0.164194i | ||||
\(10\) | 0.509546 | + | 0.882559i | 0.161132 | + | 0.279090i | ||||
\(11\) | −0.510616 | − | 3.27708i | −0.153957 | − | 0.988078i | ||||
\(12\) | −1.35034 | − | 0.779618i | −0.389809 | − | 0.225056i | ||||
\(13\) | 0.167247 | 0.0463859 | 0.0231929 | − | 0.999731i | \(-0.492617\pi\) | ||||
0.0231929 | + | 0.999731i | \(0.492617\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.58900 | 0.410279 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.47616 | + | 2.55678i | 0.358021 | + | 0.620111i | 0.987630 | − | 0.156801i | \(-0.0501182\pi\) |
−0.629609 | + | 0.776912i | \(0.716785\pi\) | |||||||
\(18\) | 0.492581 | − | 0.284392i | 0.116102 | − | 0.0670318i | ||||
\(19\) | 0.155850 | − | 0.269940i | 0.0357545 | − | 0.0619286i | −0.847594 | − | 0.530645i | \(-0.821950\pi\) |
0.883349 | + | 0.468716i | \(0.155283\pi\) | |||||||
\(20\) | − | 1.01909i | − | 0.227876i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.19633 | + | 3.09335i | −0.255059 | + | 0.659503i | ||||
\(23\) | 0.237719 | − | 0.411742i | 0.0495679 | − | 0.0858541i | −0.840177 | − | 0.542312i | \(-0.817549\pi\) |
0.889745 | + | 0.456458i | \(0.150882\pi\) | |||||||
\(24\) | 0.779618 | + | 1.35034i | 0.159139 | + | 0.275637i | ||||
\(25\) | −1.98073 | − | 3.43072i | −0.396145 | − | 0.686144i | ||||
\(26\) | −0.144840 | − | 0.0836233i | −0.0284054 | − | 0.0163999i | ||||
\(27\) | − | 5.56458i | − | 1.07090i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.89701i | 0.352266i | 0.984366 | + | 0.176133i | \(0.0563589\pi\) | ||||
−0.984366 | + | 0.176133i | \(0.943641\pi\) | |||||||
\(30\) | −1.37612 | − | 0.794502i | −0.251244 | − | 0.145056i | ||||
\(31\) | 2.20834 | − | 1.27498i | 0.396629 | − | 0.228994i | −0.288400 | − | 0.957510i | \(-0.593123\pi\) |
0.685028 | + | 0.728516i | \(0.259790\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 3.24438 | + | 4.02708i | 0.564774 | + | 0.701025i | ||||
\(34\) | − | 2.95232i | − | 0.506318i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.568783 | −0.0947972 | ||||||||
\(37\) | −3.04667 | + | 5.27699i | −0.500870 | + | 0.867532i | 0.499130 | + | 0.866527i | \(0.333653\pi\) |
−0.999999 | + | 0.00100474i | \(0.999680\pi\) | |||||||
\(38\) | −0.269940 | + | 0.155850i | −0.0437901 | + | 0.0252822i | ||||
\(39\) | −0.225839 | + | 0.130388i | −0.0361633 | + | 0.0208789i | ||||
\(40\) | −0.509546 | + | 0.882559i | −0.0805662 | + | 0.139545i | ||||
\(41\) | 10.2084 | 1.59428 | 0.797138 | − | 0.603797i | \(-0.206346\pi\) | ||||
0.797138 | + | 0.603797i | \(0.206346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1222i | 1.54363i | 0.635848 | + | 0.771814i | \(0.280650\pi\) | ||||
−0.635848 | + | 0.771814i | \(0.719350\pi\) | |||||||
\(44\) | 2.58273 | − | 2.08075i | 0.389361 | − | 0.313685i | ||||
\(45\) | 0.501985 | − | 0.289821i | 0.0748315 | − | 0.0432040i | ||||
\(46\) | −0.411742 | + | 0.237719i | −0.0607080 | + | 0.0350498i | ||||
\(47\) | 3.28968 | + | 1.89930i | 0.479849 | + | 0.277041i | 0.720354 | − | 0.693607i | \(-0.243980\pi\) |
−0.240505 | + | 0.970648i | \(0.577313\pi\) | |||||||
\(48\) | − | 1.55924i | − | 0.225056i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.96145i | 0.560234i | ||||||||
\(51\) | −3.98663 | − | 2.30168i | −0.558239 | − | 0.322300i | ||||
\(52\) | 0.0836233 | + | 0.144840i | 0.0115965 | + | 0.0200857i | ||||
\(53\) | −4.21079 | − | 7.29330i | −0.578396 | − | 1.00181i | −0.995664 | − | 0.0930275i | \(-0.970346\pi\) |
0.417268 | − | 0.908784i | \(-0.362988\pi\) | |||||||
\(54\) | −2.78229 | + | 4.81906i | −0.378621 | + | 0.655791i | ||||
\(55\) | −1.21917 | + | 3.15240i | −0.164393 | + | 0.425070i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.486014i | 0.0643742i | ||||||||
\(58\) | 0.948505 | − | 1.64286i | 0.124545 | − | 0.215718i | ||||
\(59\) | −5.40617 | + | 3.12126i | −0.703824 | + | 0.406353i | −0.808770 | − | 0.588125i | \(-0.799866\pi\) |
0.104946 | + | 0.994478i | \(0.466533\pi\) | |||||||
\(60\) | 0.794502 | + | 1.37612i | 0.102570 | + | 0.177656i | ||||
\(61\) | −5.93960 | + | 10.2877i | −0.760488 | + | 1.31720i | 0.182111 | + | 0.983278i | \(0.441707\pi\) |
−0.942599 | + | 0.333926i | \(0.891626\pi\) | |||||||
\(62\) | −2.54997 | −0.323846 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −0.147605 | − | 0.0852198i | −0.0183081 | − | 0.0105702i | ||||
\(66\) | −0.796171 | − | 5.10974i | −0.0980019 | − | 0.628966i | ||||
\(67\) | 5.19151 | + | 8.99196i | 0.634244 | + | 1.09854i | 0.986675 | + | 0.162705i | \(0.0520219\pi\) |
−0.352431 | + | 0.935838i | \(0.614645\pi\) | |||||||
\(68\) | −1.47616 | + | 2.55678i | −0.179011 | + | 0.310055i | ||||
\(69\) | 0.741321i | 0.0892445i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.5206 | 1.72328 | 0.861639 | − | 0.507522i | \(-0.169439\pi\) | ||||
0.861639 | + | 0.507522i | \(0.169439\pi\) | |||||||
\(72\) | 0.492581 | + | 0.284392i | 0.0580512 | + | 0.0335159i | ||||
\(73\) | 4.85385 | + | 8.40712i | 0.568101 | + | 0.983979i | 0.996754 | + | 0.0805099i | \(0.0256549\pi\) |
−0.428653 | + | 0.903469i | \(0.641012\pi\) | |||||||
\(74\) | 5.27699 | − | 3.04667i | 0.613438 | − | 0.354168i | ||||
\(75\) | 5.34930 | + | 3.08842i | 0.617684 | + | 0.356620i | ||||
\(76\) | 0.311700 | 0.0357545 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.260777 | 0.0295272 | ||||||||
\(79\) | 6.06709 | + | 3.50284i | 0.682601 | + | 0.394100i | 0.800834 | − | 0.598886i | \(-0.204390\pi\) |
−0.118233 | + | 0.992986i | \(0.537723\pi\) | |||||||
\(80\) | 0.882559 | − | 0.509546i | 0.0986731 | − | 0.0569689i | ||||
\(81\) | 3.48507 | + | 6.03631i | 0.387230 | + | 0.670702i | ||||
\(82\) | −8.84069 | − | 5.10418i | −0.976291 | − | 0.563662i | ||||
\(83\) | 14.6915 | 1.61261 | 0.806303 | − | 0.591502i | \(-0.201465\pi\) | ||||
0.806303 | + | 0.591502i | \(0.201465\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 3.00868i | − | 0.326337i | ||||||
\(86\) | 5.06112 | − | 8.76612i | 0.545755 | − | 0.945275i | ||||
\(87\) | −1.47894 | − | 2.56161i | −0.158559 | − | 0.274633i | ||||
\(88\) | −3.27708 | + | 0.510616i | −0.349338 | + | 0.0544319i | ||||
\(89\) | −5.97639 | − | 3.45047i | −0.633496 | − | 0.365749i | 0.148609 | − | 0.988896i | \(-0.452520\pi\) |
−0.782105 | + | 0.623147i | \(0.785854\pi\) | |||||||
\(90\) | −0.579642 | −0.0610997 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.475438 | 0.0495679 | ||||||||
\(93\) | −1.98800 | + | 3.44332i | −0.206146 | + | 0.357055i | ||||
\(94\) | −1.89930 | − | 3.28968i | −0.195898 | − | 0.339305i | ||||
\(95\) | −0.275094 | + | 0.158826i | −0.0282240 | + | 0.0162952i | ||||
\(96\) | −0.779618 | + | 1.35034i | −0.0795694 | + | 0.137818i | ||||
\(97\) | 11.0218i | 1.11909i | 0.828799 | + | 0.559547i | \(0.189025\pi\) | ||||
−0.828799 | + | 0.559547i | \(0.810975\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.75944 | + | 0.680455i | 0.176831 | + | 0.0683883i | ||||
\(100\) | 1.98073 | − | 3.43072i | 0.198073 | − | 0.343072i | ||||
\(101\) | 2.66752 | + | 4.62028i | 0.265428 | + | 0.459735i | 0.967676 | − | 0.252198i | \(-0.0811534\pi\) |
−0.702248 | + | 0.711933i | \(0.747820\pi\) | |||||||
\(102\) | 2.30168 | + | 3.98663i | 0.227900 | + | 0.394735i | ||||
\(103\) | 10.7849 | + | 6.22664i | 1.06266 | + | 0.613529i | 0.926168 | − | 0.377112i | \(-0.123083\pi\) |
0.136496 | + | 0.990641i | \(0.456416\pi\) | |||||||
\(104\) | − | 0.167247i | − | 0.0163999i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.42157i | 0.817975i | ||||||||
\(107\) | 6.28227 | + | 3.62707i | 0.607330 | + | 0.350642i | 0.771920 | − | 0.635720i | \(-0.219297\pi\) |
−0.164590 | + | 0.986362i | \(0.552630\pi\) | |||||||
\(108\) | 4.81906 | − | 2.78229i | 0.463715 | − | 0.267726i | ||||
\(109\) | 1.01103 | − | 0.583716i | 0.0968387 | − | 0.0559098i | −0.450799 | − | 0.892626i | \(-0.648861\pi\) |
0.547637 | + | 0.836716i | \(0.315527\pi\) | |||||||
\(110\) | 2.63204 | − | 2.12047i | 0.250955 | − | 0.202179i | ||||
\(111\) | − | 9.50096i | − | 0.901791i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.40135 | −0.790333 | −0.395166 | − | 0.918610i | \(-0.629313\pi\) | ||||
−0.395166 | + | 0.918610i | \(0.629313\pi\) | |||||||
\(114\) | 0.243007 | − | 0.420901i | 0.0227597 | − | 0.0394210i | ||||
\(115\) | −0.419602 | + | 0.242258i | −0.0391281 | + | 0.0225906i | ||||
\(116\) | −1.64286 | + | 0.948505i | −0.152536 | + | 0.0880665i | ||||
\(117\) | −0.0475636 | + | 0.0823825i | −0.00439725 | + | 0.00761626i | ||||
\(118\) | 6.24251 | 0.574670 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | − | 1.58900i | − | 0.145056i | ||||||
\(121\) | −10.4785 | + | 3.34666i | −0.952595 | + | 0.304242i | ||||
\(122\) | 10.2877 | − | 5.93960i | 0.931404 | − | 0.537746i | ||||
\(123\) | −13.7847 | + | 7.95862i | −1.24293 | + | 0.717604i | ||||
\(124\) | 2.20834 | + | 1.27498i | 0.198314 | + | 0.114497i | ||||
\(125\) | 9.13254i | 0.816839i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.53324i | − | 0.313525i | −0.987636 | − | 0.156762i | \(-0.949894\pi\) | ||
0.987636 | − | 0.156762i | \(-0.0501057\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | −7.89149 | − | 13.6685i | −0.694807 | − | 1.20344i | ||||
\(130\) | 0.0852198 | + | 0.147605i | 0.00747427 | + | 0.0129458i | ||||
\(131\) | 6.98984 | − | 12.1068i | 0.610705 | − | 1.05777i | −0.380417 | − | 0.924815i | \(-0.624219\pi\) |
0.991122 | − | 0.132957i | \(-0.0424473\pi\) | |||||||
\(132\) | −1.86537 | + | 4.82325i | −0.162359 | + | 0.419810i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 10.3830i | − | 0.896957i | ||||||
\(135\) | −2.83541 | + | 4.91107i | −0.244033 | + | 0.422677i | ||||
\(136\) | 2.55678 | − | 1.47616i | 0.219242 | − | 0.126580i | ||||
\(137\) | 3.50529 | + | 6.07134i | 0.299477 | + | 0.518709i | 0.976016 | − | 0.217697i | \(-0.0698545\pi\) |
−0.676539 | + | 0.736406i | \(0.736521\pi\) | |||||||
\(138\) | 0.370660 | − | 0.642003i | 0.0315527 | − | 0.0546509i | ||||
\(139\) | −11.4615 | −0.972148 | −0.486074 | − | 0.873918i | \(-0.661571\pi\) | ||||
−0.486074 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92291 | −0.498799 | ||||||||
\(142\) | −12.5752 | − | 7.26030i | −1.05529 | − | 0.609270i | ||||
\(143\) | −0.0853989 | − | 0.548081i | −0.00714141 | − | 0.0458328i | ||||
\(144\) | −0.284392 | − | 0.492581i | −0.0236993 | − | 0.0410484i | ||||
\(145\) | 0.966613 | − | 1.67422i | 0.0802729 | − | 0.139037i | ||||
\(146\) | − | 9.70771i | − | 0.803416i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.09335 | −0.500870 | ||||||||
\(149\) | 12.2602 | + | 7.07841i | 1.00439 | + | 0.579886i | 0.909545 | − | 0.415606i | \(-0.136430\pi\) |
0.0948474 | + | 0.995492i | \(0.469764\pi\) | |||||||
\(150\) | −3.08842 | − | 5.34930i | −0.252168 | − | 0.436768i | ||||
\(151\) | 20.1819 | − | 11.6520i | 1.64238 | − | 0.948228i | 0.662394 | − | 0.749156i | \(-0.269541\pi\) |
0.979985 | − | 0.199072i | \(-0.0637928\pi\) | |||||||
\(152\) | −0.269940 | − | 0.155850i | −0.0218951 | − | 0.0126411i | ||||
\(153\) | −1.67923 | −0.135758 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.59865 | −0.208728 | ||||||||
\(156\) | −0.225839 | − | 0.130388i | −0.0180816 | − | 0.0104394i | ||||
\(157\) | −3.49234 | + | 2.01630i | −0.278719 | + | 0.160919i | −0.632843 | − | 0.774280i | \(-0.718112\pi\) |
0.354124 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(158\) | −3.50284 | − | 6.06709i | −0.278671 | − | 0.482672i | ||||
\(159\) | 11.3720 | + | 6.56561i | 0.901856 | + | 0.520687i | ||||
\(160\) | −1.01909 | −0.0805662 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | − | 6.97014i | − | 0.547626i | ||||||
\(163\) | 2.76994 | − | 4.79768i | 0.216958 | − | 0.375783i | −0.736918 | − | 0.675982i | \(-0.763720\pi\) |
0.953877 | + | 0.300199i | \(0.0970530\pi\) | |||||||
\(164\) | 5.10418 | + | 8.84069i | 0.398569 | + | 0.690342i | ||||
\(165\) | −0.811371 | − | 5.20730i | −0.0631652 | − | 0.405388i | ||||
\(166\) | −12.7233 | − | 7.34577i | −0.987516 | − | 0.570143i | ||||
\(167\) | −21.2252 | −1.64245 | −0.821226 | − | 0.570603i | \(-0.806709\pi\) | ||||
−0.821226 | + | 0.570603i | \(0.806709\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9720 | −0.997848 | ||||||||
\(170\) | −1.50434 | + | 2.60560i | −0.115378 | + | 0.199840i | ||||
\(171\) | 0.0886450 | + | 0.153538i | 0.00677885 | + | 0.0117413i | ||||
\(172\) | −8.76612 | + | 5.06112i | −0.668411 | + | 0.385907i | ||||
\(173\) | 7.53277 | − | 13.0471i | 0.572706 | − | 0.991956i | −0.423581 | − | 0.905858i | \(-0.639227\pi\) |
0.996287 | − | 0.0860973i | \(-0.0274396\pi\) | |||||||
\(174\) | 2.95789i | 0.224237i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.09335 | + | 1.19633i | 0.233170 | + | 0.0901771i | ||||
\(177\) | 4.86677 | − | 8.42950i | 0.365809 | − | 0.633600i | ||||
\(178\) | 3.45047 | + | 5.97639i | 0.258623 | + | 0.447949i | ||||
\(179\) | 1.08088 | + | 1.87214i | 0.0807887 | + | 0.139930i | 0.903589 | − | 0.428401i | \(-0.140923\pi\) |
−0.822800 | + | 0.568331i | \(0.807589\pi\) | |||||||
\(180\) | 0.501985 | + | 0.289821i | 0.0374158 | + | 0.0216020i | ||||
\(181\) | 5.39285i | 0.400848i | 0.979709 | + | 0.200424i | \(0.0642319\pi\) | ||||
−0.979709 | + | 0.200424i | \(0.935768\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 18.5225i | − | 1.36922i | ||||||
\(184\) | −0.411742 | − | 0.237719i | −0.0303540 | − | 0.0175249i | ||||
\(185\) | 5.37774 | − | 3.10484i | 0.395379 | − | 0.228272i | ||||
\(186\) | 3.44332 | − | 1.98800i | 0.252476 | − | 0.145767i | ||||
\(187\) | 7.62504 | − | 6.14303i | 0.557598 | − | 0.449223i | ||||
\(188\) | 3.79859i | 0.277041i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.317651 | 0.0230448 | ||||||||
\(191\) | −3.00000 | + | 5.19615i | −0.217072 | + | 0.375980i | −0.953912 | − | 0.300088i | \(-0.902984\pi\) |
0.736839 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(192\) | 1.35034 | − | 0.779618i | 0.0974522 | − | 0.0562641i | ||||
\(193\) | 8.31348 | − | 4.79979i | 0.598417 | − | 0.345496i | −0.170001 | − | 0.985444i | \(-0.554377\pi\) |
0.768419 | + | 0.639947i | \(0.221044\pi\) | |||||||
\(194\) | 5.51090 | − | 9.54515i | 0.395659 | − | 0.685302i | ||||
\(195\) | 0.265756 | 0.0190311 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.8180i | 1.05574i | 0.849325 | + | 0.527870i | \(0.177009\pi\) | ||||
−0.849325 | + | 0.527870i | \(0.822991\pi\) | |||||||
\(198\) | −1.18350 | − | 1.46901i | −0.0841073 | − | 0.104398i | ||||
\(199\) | −3.55962 | + | 2.05515i | −0.252335 | + | 0.145686i | −0.620833 | − | 0.783943i | \(-0.713205\pi\) |
0.368498 | + | 0.929629i | \(0.379872\pi\) | |||||||
\(200\) | −3.43072 | + | 1.98073i | −0.242588 | + | 0.140059i | ||||
\(201\) | −14.0206 | − | 8.09479i | −0.988936 | − | 0.570963i | ||||
\(202\) | − | 5.33504i | − | 0.375372i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 4.60336i | − | 0.322300i | ||||||
\(205\) | −9.00947 | − | 5.20162i | −0.629249 | − | 0.363297i | ||||
\(206\) | −6.22664 | − | 10.7849i | −0.433831 | − | 0.751417i | ||||
\(207\) | 0.135211 | + | 0.234192i | 0.00939780 | + | 0.0162775i | ||||
\(208\) | −0.0836233 | + | 0.144840i | −0.00579823 | + | 0.0100428i | ||||
\(209\) | −0.964197 | − | 0.372898i | −0.0666949 | − | 0.0257939i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 7.52456i | − | 0.518012i | −0.965876 | − | 0.259006i | \(-0.916605\pi\) | ||
0.965876 | − | 0.259006i | \(-0.0833950\pi\) | |||||||
\(212\) | 4.21079 | − | 7.29330i | 0.289198 | − | 0.500906i | ||||
\(213\) | −19.6077 | + | 11.3205i | −1.34350 | + | 0.775669i | ||||
\(214\) | −3.62707 | − | 6.28227i | −0.247941 | − | 0.429447i | ||||
\(215\) | 5.15775 | − | 8.93348i | 0.351755 | − | 0.609258i | ||||
\(216\) | −5.56458 | −0.378621 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.16743 | −0.0790685 | ||||||||
\(219\) | −13.1087 | − | 7.56830i | −0.885803 | − | 0.511418i | ||||
\(220\) | −3.33965 | + | 0.520365i | −0.225159 | + | 0.0350830i | ||||
\(221\) | 0.246883 | + | 0.427613i | 0.0166071 | + | 0.0287644i | ||||
\(222\) | −4.75048 | + | 8.22807i | −0.318831 | + | 0.552232i | ||||
\(223\) | 13.5885i | 0.909951i | 0.890504 | + | 0.454975i | \(0.150352\pi\) | ||||
−0.890504 | + | 0.454975i | \(0.849648\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.25321 | 0.150214 | ||||||||
\(226\) | 7.27578 | + | 4.20068i | 0.483978 | + | 0.279425i | ||||
\(227\) | 10.8318 | + | 18.7611i | 0.718929 | + | 1.24522i | 0.961425 | + | 0.275069i | \(0.0887006\pi\) |
−0.242496 | + | 0.970152i | \(0.577966\pi\) | |||||||
\(228\) | −0.420901 | + | 0.243007i | −0.0278748 | + | 0.0160935i | ||||
\(229\) | −26.0355 | − | 15.0316i | −1.72047 | − | 0.993317i | −0.917948 | − | 0.396700i | \(-0.870155\pi\) |
−0.802527 | − | 0.596616i | \(-0.796511\pi\) | |||||||
\(230\) | 0.484515 | 0.0319480 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.89701 | 0.124545 | ||||||||
\(233\) | 14.0223 | + | 8.09580i | 0.918633 | + | 0.530373i | 0.883199 | − | 0.468999i | \(-0.155385\pi\) |
0.0354345 | + | 0.999372i | \(0.488718\pi\) | |||||||
\(234\) | 0.0823825 | − | 0.0475636i | 0.00538551 | − | 0.00310933i | ||||
\(235\) | −1.93556 | − | 3.35248i | −0.126262 | − | 0.218692i | ||||
\(236\) | −5.40617 | − | 3.12126i | −0.351912 | − | 0.203176i | ||||
\(237\) | −10.9235 | −0.709558 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 26.0701i | − | 1.68633i | −0.537652 | − | 0.843167i | \(-0.680689\pi\) | ||
0.537652 | − | 0.843167i | \(-0.319311\pi\) | |||||||
\(240\) | −0.794502 | + | 1.37612i | −0.0512849 | + | 0.0888280i | ||||
\(241\) | −6.60221 | − | 11.4354i | −0.425286 | − | 0.736617i | 0.571161 | − | 0.820838i | \(-0.306493\pi\) |
−0.996447 | + | 0.0842210i | \(0.973160\pi\) | |||||||
\(242\) | 10.7480 | + | 2.34098i | 0.690909 | + | 0.150484i | ||||
\(243\) | 5.04515 | + | 2.91282i | 0.323647 | + | 0.186858i | ||||
\(244\) | −11.8792 | −0.760488 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 15.9172 | 1.01485 | ||||||||
\(247\) | 0.0260654 | − | 0.0451466i | 0.00165850 | − | 0.00287261i | ||||
\(248\) | −1.27498 | − | 2.20834i | −0.0809615 | − | 0.140229i | ||||
\(249\) | −19.8386 | + | 11.4538i | −1.25722 | + | 0.725855i | ||||
\(250\) | 4.56627 | − | 7.90901i | 0.288796 | − | 0.500210i | ||||
\(251\) | − | 28.9829i | − | 1.82939i | −0.404149 | − | 0.914693i | \(-0.632432\pi\) | ||
0.404149 | − | 0.914693i | \(-0.367568\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.47070 | − | 0.568783i | −0.0924618 | − | 0.0357591i | ||||
\(254\) | −1.76662 | + | 3.05988i | −0.110848 | + | 0.191994i | ||||
\(255\) | 2.34562 | + | 4.06274i | 0.146889 | + | 0.254419i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.05007 | − | 3.49301i | −0.377393 | − | 0.217888i | 0.299290 | − | 0.954162i | \(-0.403250\pi\) |
−0.676683 | + | 0.736274i | \(0.736583\pi\) | |||||||
\(258\) | 15.7830i | 0.982605i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 0.170440i | − | 0.0105702i | ||||||
\(261\) | −0.934431 | − | 0.539494i | −0.0578398 | − | 0.0333938i | ||||
\(262\) | −12.1068 | + | 6.98984i | −0.747958 | + | 0.431834i | ||||
\(263\) | −3.87174 | + | 2.23535i | −0.238741 | + | 0.137837i | −0.614598 | − | 0.788840i | \(-0.710682\pi\) |
0.375857 | + | 0.926678i | \(0.377348\pi\) | |||||||
\(264\) | 4.02708 | − | 3.24438i | 0.247850 | − | 0.199678i | ||||
\(265\) | 8.58235i | 0.527210i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.7602 | 0.658513 | ||||||||
\(268\) | −5.19151 | + | 8.99196i | −0.317122 | + | 0.549272i | ||||
\(269\) | −1.92024 | + | 1.10865i | −0.117079 | + | 0.0675956i | −0.557396 | − | 0.830247i | \(-0.688199\pi\) |
0.440317 | + | 0.897842i | \(0.354866\pi\) | |||||||
\(270\) | 4.91107 | − | 2.83541i | 0.298878 | − | 0.172557i | ||||
\(271\) | −11.2561 | + | 19.4961i | −0.683759 | + | 1.18431i | 0.290066 | + | 0.957007i | \(0.406323\pi\) |
−0.973825 | + | 0.227299i | \(0.927011\pi\) | |||||||
\(272\) | −2.95232 | −0.179011 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 7.01058i | − | 0.423524i | ||||||
\(275\) | −10.2314 | + | 8.24279i | −0.616974 | + | 0.497059i | ||||
\(276\) | −0.642003 | + | 0.370660i | −0.0386440 | + | 0.0223111i | ||||
\(277\) | −21.1880 | + | 12.2329i | −1.27306 | + | 0.735004i | −0.975563 | − | 0.219718i | \(-0.929486\pi\) |
−0.297500 | + | 0.954722i | \(0.596153\pi\) | |||||||
\(278\) | 9.92591 | + | 5.73073i | 0.595317 | + | 0.343706i | ||||
\(279\) | 1.45038i | 0.0868319i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.3532i | − | 0.677273i | −0.940917 | − | 0.338636i | \(-0.890034\pi\) | ||
0.940917 | − | 0.338636i | \(-0.109966\pi\) | |||||||
\(282\) | 5.12939 | + | 2.96145i | 0.305451 | + | 0.176352i | ||||
\(283\) | −10.8268 | − | 18.7526i | −0.643589 | − | 1.11473i | −0.984626 | − | 0.174679i | \(-0.944111\pi\) |
0.341037 | − | 0.940050i | \(-0.389222\pi\) | |||||||
\(284\) | 7.26030 | + | 12.5752i | 0.430819 | + | 0.746201i | ||||
\(285\) | 0.247646 | − | 0.428936i | 0.0146693 | − | 0.0254080i | ||||
\(286\) | −0.200083 | + | 0.517352i | −0.0118312 | + | 0.0305916i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.568783i | 0.0335159i | ||||||||
\(289\) | 4.14191 | − | 7.17400i | 0.243642 | − | 0.422000i | ||||
\(290\) | −1.67422 | + | 0.966613i | −0.0983138 | + | 0.0567615i | ||||
\(291\) | −8.59279 | − | 14.8831i | −0.503718 | − | 0.872465i | ||||
\(292\) | −4.85385 | + | 8.40712i | −0.284050 | + | 0.491990i | ||||
\(293\) | −12.1233 | −0.708249 | −0.354124 | − | 0.935198i | \(-0.615221\pi\) | ||||
−0.354124 | + | 0.935198i | \(0.615221\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.36169 | 0.370392 | ||||||||
\(296\) | 5.27699 | + | 3.04667i | 0.306719 | + | 0.177084i | ||||
\(297\) | −18.2356 | + | 2.84136i | −1.05814 | + | 0.164873i | ||||
\(298\) | −7.07841 | − | 12.2602i | −0.410041 | − | 0.710213i | ||||
\(299\) | 0.0397577 | − | 0.0688624i | 0.00229925 | − | 0.00398242i | ||||
\(300\) | 6.17684i | 0.356620i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −23.3040 | −1.34100 | ||||||||
\(303\) | −7.20410 | − | 4.15929i | −0.413865 | − | 0.238945i | ||||
\(304\) | 0.155850 | + | 0.269940i | 0.00893862 | + | 0.0154821i | ||||
\(305\) | 10.4841 | − | 6.05300i | 0.600318 | − | 0.346594i | ||||
\(306\) | 1.45426 | + | 0.839615i | 0.0831343 | + | 0.0479976i | ||||
\(307\) | −9.65817 | −0.551221 | −0.275610 | − | 0.961269i | \(-0.588880\pi\) | ||||
−0.275610 | + | 0.961269i | \(0.588880\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.4176 | −1.10463 | ||||||||
\(310\) | 2.25050 | + | 1.29932i | 0.127820 | + | 0.0737967i | ||||
\(311\) | 15.3094 | − | 8.83890i | 0.868118 | − | 0.501208i | 0.00139530 | − | 0.999999i | \(-0.499556\pi\) |
0.866722 | + | 0.498791i | \(0.166223\pi\) | |||||||
\(312\) | 0.130388 | + | 0.225839i | 0.00738179 | + | 0.0127856i | ||||
\(313\) | 24.9505 | + | 14.4052i | 1.41028 | + | 0.814228i | 0.995415 | − | 0.0956530i | \(-0.0304939\pi\) |
0.414869 | + | 0.909881i | \(0.363827\pi\) | |||||||
\(314\) | 4.03261 | 0.227573 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.00567i | 0.394100i | ||||||||
\(317\) | −5.17280 | + | 8.95955i | −0.290533 | + | 0.503218i | −0.973936 | − | 0.226823i | \(-0.927166\pi\) |
0.683403 | + | 0.730042i | \(0.260499\pi\) | |||||||
\(318\) | −6.56561 | − | 11.3720i | −0.368181 | − | 0.637708i | ||||
\(319\) | 6.21666 | − | 0.968644i | 0.348066 | − | 0.0542337i | ||||
\(320\) | 0.882559 | + | 0.509546i | 0.0493366 | + | 0.0284845i | ||||
\(321\) | −11.3109 | −0.631314 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.920239 | 0.0512034 | ||||||||
\(324\) | −3.48507 | + | 6.03631i | −0.193615 | + | 0.335351i | ||||
\(325\) | −0.331270 | − | 0.573776i | −0.0183755 | − | 0.0318274i | ||||
\(326\) | −4.79768 | + | 2.76994i | −0.265719 | + | 0.153413i | ||||
\(327\) | −0.910151 | + | 1.57643i | −0.0503315 | + | 0.0871766i | ||||
\(328\) | − | 10.2084i | − | 0.563662i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −1.90098 | + | 4.91534i | −0.104646 | + | 0.270580i | ||||
\(331\) | 13.4224 | − | 23.2483i | 0.737763 | − | 1.27784i | −0.215737 | − | 0.976451i | \(-0.569215\pi\) |
0.953500 | − | 0.301392i | \(-0.0974512\pi\) | |||||||
\(332\) | 7.34577 | + | 12.7233i | 0.403152 | + | 0.698279i | ||||
\(333\) | −1.73290 | − | 3.00147i | −0.0949622 | − | 0.164479i | ||||
\(334\) | 18.3815 | + | 10.6126i | 1.00579 | + | 0.580694i | ||||
\(335\) | − | 10.5813i | − | 0.578116i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.5505i | 0.792614i | 0.918118 | + | 0.396307i | \(0.129708\pi\) | ||||
−0.918118 | + | 0.396307i | \(0.870292\pi\) | |||||||
\(338\) | 11.2341 | + | 6.48601i | 0.611055 | + | 0.352793i | ||||
\(339\) | 11.3447 | − | 6.54984i | 0.616158 | − | 0.355739i | ||||
\(340\) | 2.60560 | − | 1.50434i | 0.141308 | − | 0.0815844i | ||||
\(341\) | −5.30584 | − | 6.58587i | −0.287327 | − | 0.356645i | ||||
\(342\) | − | 0.177290i | − | 0.00958674i | ||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 10.1222 | 0.545755 | ||||||||
\(345\) | 0.377737 | − | 0.654259i | 0.0203367 | − | 0.0352241i | ||||
\(346\) | −13.0471 | + | 7.53277i | −0.701418 | + | 0.404964i | ||||
\(347\) | −24.7179 | + | 14.2709i | −1.32693 | + | 0.766101i | −0.984823 | − | 0.173562i | \(-0.944472\pi\) |
−0.342102 | + | 0.939663i | \(0.611139\pi\) | |||||||
\(348\) | 1.47894 | − | 2.56161i | 0.0792797 | − | 0.137316i | ||||
\(349\) | 34.6026 | 1.85224 | 0.926118 | − | 0.377235i | \(-0.123125\pi\) | ||||
0.926118 | + | 0.377235i | \(0.123125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 0.930656i | − | 0.0496748i | ||||||
\(352\) | −2.08075 | − | 2.58273i | −0.110904 | − | 0.137660i | ||||
\(353\) | 14.6534 | − | 8.46017i | 0.779924 | − | 0.450289i | −0.0564792 | − | 0.998404i | \(-0.517987\pi\) |
0.836403 | + | 0.548114i | \(0.184654\pi\) | |||||||
\(354\) | −8.42950 | + | 4.86677i | −0.448023 | + | 0.258666i | ||||
\(355\) | −12.8153 | − | 7.39891i | −0.680164 | − | 0.392693i | ||||
\(356\) | − | 6.90094i | − | 0.365749i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 2.16176i | − | 0.114252i | ||||||
\(359\) | 26.2848 | + | 15.1755i | 1.38726 | + | 0.800934i | 0.993006 | − | 0.118067i | \(-0.0376698\pi\) |
0.394254 | + | 0.919002i | \(0.371003\pi\) | |||||||
\(360\) | −0.289821 | − | 0.501985i | −0.0152749 | − | 0.0264569i | ||||
\(361\) | 9.45142 | + | 16.3703i | 0.497443 | + | 0.861597i | ||||
\(362\) | 2.69643 | − | 4.67035i | 0.141721 | − | 0.245468i | ||||
\(363\) | 11.5405 | − | 12.6884i | 0.605717 | − | 0.665968i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 9.89304i | − | 0.517825i | ||||||
\(366\) | −9.26124 | + | 16.0409i | −0.484093 | + | 0.838474i | ||||
\(367\) | 15.0875 | − | 8.71075i | 0.787559 | − | 0.454698i | −0.0515432 | − | 0.998671i | \(-0.516414\pi\) |
0.839103 | + | 0.543973i | \(0.183081\pi\) | |||||||
\(368\) | 0.237719 | + | 0.411742i | 0.0123920 | + | 0.0214635i | ||||
\(369\) | −2.90317 | + | 5.02844i | −0.151133 | + | 0.261770i | ||||
\(370\) | −6.20968 | −0.322826 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3.97600 | −0.206146 | ||||||||
\(373\) | 7.92596 | + | 4.57606i | 0.410391 | + | 0.236939i | 0.690958 | − | 0.722895i | \(-0.257189\pi\) |
−0.280567 | + | 0.959834i | \(0.590522\pi\) | |||||||
\(374\) | −9.67499 | + | 1.50750i | −0.500282 | + | 0.0779511i | ||||
\(375\) | −7.11989 | − | 12.3320i | −0.367670 | − | 0.636822i | ||||
\(376\) | 1.89930 | − | 3.28968i | 0.0979488 | − | 0.169652i | ||||
\(377\) | 0.317269i | 0.0163402i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.15382 | −0.316100 | −0.158050 | − | 0.987431i | \(-0.550521\pi\) | ||||
−0.158050 | + | 0.987431i | \(0.550521\pi\) | |||||||
\(380\) | −0.275094 | − | 0.158826i | −0.0141120 | − | 0.00814758i | ||||
\(381\) | 2.75458 | + | 4.77107i | 0.141121 | + | 0.244429i | ||||
\(382\) | 5.19615 | − | 3.00000i | 0.265858 | − | 0.153493i | ||||
\(383\) | −11.2281 | − | 6.48253i | −0.573728 | − | 0.331242i | 0.184909 | − | 0.982756i | \(-0.440801\pi\) |
−0.758637 | + | 0.651514i | \(0.774134\pi\) | |||||||
\(384\) | −1.55924 | −0.0795694 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.59958 | −0.488606 | ||||||||
\(387\) | −4.98603 | − | 2.87868i | −0.253454 | − | 0.146332i | ||||
\(388\) | −9.54515 | + | 5.51090i | −0.484582 | + | 0.279773i | ||||
\(389\) | −2.58323 | − | 4.47429i | −0.130975 | − | 0.226856i | 0.793078 | − | 0.609121i | \(-0.208477\pi\) |
−0.924053 | + | 0.382265i | \(0.875144\pi\) | |||||||
\(390\) | −0.230151 | − | 0.132878i | −0.0116542 | − | 0.00672853i | ||||
\(391\) | 1.40365 | 0.0709854 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.7976i | 1.09954i | ||||||||
\(394\) | 7.40901 | − | 12.8328i | 0.373261 | − | 0.646506i | ||||
\(395\) | −3.56971 | − | 6.18292i | −0.179612 | − | 0.311097i | ||||
\(396\) | 0.290430 | + | 1.86395i | 0.0145947 | + | 0.0936670i | ||||
\(397\) | −8.01690 | − | 4.62856i | −0.402357 | − | 0.232301i | 0.285144 | − | 0.958485i | \(-0.407959\pi\) |
−0.687500 | + | 0.726184i | \(0.741292\pi\) | |||||||
\(398\) | 4.11030 | 0.206030 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.96145 | 0.198073 | ||||||||
\(401\) | 15.4624 | − | 26.7816i | 0.772155 | − | 1.33741i | −0.164225 | − | 0.986423i | \(-0.552512\pi\) |
0.936380 | − | 0.350988i | \(-0.114154\pi\) | |||||||
\(402\) | 8.09479 | + | 14.0206i | 0.403732 | + | 0.699284i | ||||
\(403\) | 0.369337 | − | 0.213237i | 0.0183980 | − | 0.0106221i | ||||
\(404\) | −2.66752 | + | 4.62028i | −0.132714 | + | 0.229867i | ||||
\(405\) | − | 7.10320i | − | 0.352961i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.8488 | + | 7.28968i | 0.934301 | + | 0.361336i | ||||
\(408\) | −2.30168 | + | 3.98663i | −0.113950 | + | 0.197367i | ||||
\(409\) | 11.9198 | + | 20.6458i | 0.589399 | + | 1.02087i | 0.994311 | + | 0.106513i | \(0.0339686\pi\) |
−0.404913 | + | 0.914355i | \(0.632698\pi\) | |||||||
\(410\) | 5.20162 | + | 9.00947i | 0.256890 | + | 0.444946i | ||||
\(411\) | −9.46665 | − | 5.46557i | −0.466955 | − | 0.269597i | ||||
\(412\) | 12.4533i | 0.613529i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 0.270422i | − | 0.0132905i | ||||||
\(415\) | −12.9662 | − | 7.48601i | −0.636484 | − | 0.367474i | ||||
\(416\) | 0.144840 | − | 0.0836233i | 0.00710136 | − | 0.00409997i | ||||
\(417\) | 15.4768 | − | 8.93556i | 0.757904 | − | 0.437576i | ||||
\(418\) | 0.648570 | + | 0.805037i | 0.0317226 | + | 0.0393757i | ||||
\(419\) | − | 5.03426i | − | 0.245940i | −0.992410 | − | 0.122970i | \(-0.960758\pi\) | ||
0.992410 | − | 0.122970i | \(-0.0392418\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.9250 | −0.824872 | −0.412436 | − | 0.910987i | \(-0.635322\pi\) | ||||
−0.412436 | + | 0.910987i | \(0.635322\pi\) | |||||||
\(422\) | −3.76228 | + | 6.51646i | −0.183145 | + | 0.317216i | ||||
\(423\) | −1.87112 | + | 1.08029i | −0.0909767 | + | 0.0525254i | ||||
\(424\) | −7.29330 | + | 4.21079i | −0.354194 | + | 0.204494i | ||||
\(425\) | 5.84773 | − | 10.1286i | 0.283657 | − | 0.491308i | ||||
\(426\) | 22.6410 | 1.09696 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.25414i | 0.350642i | ||||||||
\(429\) | 0.542611 | + | 0.673516i | 0.0261975 | + | 0.0325177i | ||||
\(430\) | −8.93348 | + | 5.15775i | −0.430811 | + | 0.248729i | ||||
\(431\) | −5.19535 | + | 2.99953i | −0.250251 | + | 0.144482i | −0.619879 | − | 0.784697i | \(-0.712818\pi\) |
0.369628 | + | 0.929180i | \(0.379485\pi\) | |||||||
\(432\) | 4.81906 | + | 2.78229i | 0.231857 | + | 0.133863i | ||||
\(433\) | 36.1175i | 1.73570i | 0.496829 | + | 0.867849i | \(0.334498\pi\) | ||||
−0.496829 | + | 0.867849i | \(0.665502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.01436i | 0.144527i | ||||||||
\(436\) | 1.01103 | + | 0.583716i | 0.0484193 | + | 0.0279549i | ||||
\(437\) | −0.0740971 | − | 0.128340i | −0.00354455 | − | 0.00613934i | ||||
\(438\) | 7.56830 | + | 13.1087i | 0.361627 | + | 0.626357i | ||||
\(439\) | −5.67481 | + | 9.82906i | −0.270844 | + | 0.469116i | −0.969078 | − | 0.246754i | \(-0.920636\pi\) |
0.698234 | + | 0.715869i | \(0.253969\pi\) | |||||||
\(440\) | 3.15240 | + | 1.21917i | 0.150285 | + | 0.0581219i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 0.493765i | − | 0.0234860i | ||||||
\(443\) | 2.37538 | − | 4.11428i | 0.112858 | − | 0.195475i | −0.804064 | − | 0.594543i | \(-0.797333\pi\) |
0.916921 | + | 0.399068i | \(0.130666\pi\) | |||||||
\(444\) | 8.22807 | − | 4.75048i | 0.390487 | − | 0.225448i | ||||
\(445\) | 3.51634 | + | 6.09048i | 0.166691 | + | 0.288717i | ||||
\(446\) | 6.79423 | − | 11.7680i | 0.321716 | − | 0.557229i | ||||
\(447\) | −22.0738 | −1.04406 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.33297 | 0.346064 | 0.173032 | − | 0.984916i | \(-0.444644\pi\) | ||||
0.173032 | + | 0.984916i | \(0.444644\pi\) | |||||||
\(450\) | −1.95134 | − | 1.12660i | −0.0919869 | − | 0.0531086i | ||||
\(451\) | −5.21255 | − | 33.4536i | −0.245449 | − | 1.57527i | ||||
\(452\) | −4.20068 | − | 7.27578i | −0.197583 | − | 0.342224i | ||||
\(453\) | −18.1682 | + | 31.4683i | −0.853619 | + | 1.47851i | ||||
\(454\) | − | 21.6635i | − | 1.01672i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.486014 | 0.0227597 | ||||||||
\(457\) | −11.7066 | − | 6.75879i | −0.547610 | − | 0.316163i | 0.200547 | − | 0.979684i | \(-0.435728\pi\) |
−0.748158 | + | 0.663521i | \(0.769061\pi\) | |||||||
\(458\) | 15.0316 | + | 26.0355i | 0.702381 | + | 1.21656i | ||||
\(459\) | 14.2274 | − | 8.21420i | 0.664079 | − | 0.383406i | ||||
\(460\) | −0.419602 | − | 0.242258i | −0.0195641 | − | 0.0112953i | ||||
\(461\) | 18.5730 | 0.865033 | 0.432516 | − | 0.901626i | \(-0.357626\pi\) | ||||
0.432516 | + | 0.901626i | \(0.357626\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.2849 | 1.31451 | 0.657256 | − | 0.753667i | \(-0.271717\pi\) | ||||
0.657256 | + | 0.753667i | \(0.271717\pi\) | |||||||
\(464\) | −1.64286 | − | 0.948505i | −0.0762678 | − | 0.0440332i | ||||
\(465\) | 3.50905 | − | 2.02595i | 0.162728 | − | 0.0939513i | ||||
\(466\) | −8.09580 | − | 14.0223i | −0.375030 | − | 0.649572i | ||||
\(467\) | 18.6881 | + | 10.7896i | 0.864782 | + | 0.499282i | 0.865611 | − | 0.500717i | \(-0.166930\pi\) |
−0.000828665 | 1.00000i | \(0.500264\pi\) | ||||||||
\(468\) | −0.0951271 | −0.00439725 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 3.87112i | 0.178561i | ||||||||
\(471\) | 3.14389 | − | 5.44538i | 0.144863 | − | 0.250910i | ||||
\(472\) | 3.12126 | + | 5.40617i | 0.143667 | + | 0.248839i | ||||
\(473\) | 33.1714 | − | 5.16859i | 1.52522 | − | 0.237652i | ||||
\(474\) | 9.46003 | + | 5.46175i | 0.434513 | + | 0.250866i | ||||
\(475\) | −1.23479 | −0.0566559 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.79005 | 0.219321 | ||||||||
\(478\) | −13.0350 | + | 22.5774i | −0.596209 | + | 1.03266i | ||||
\(479\) | 3.46780 | + | 6.00641i | 0.158448 | + | 0.274440i | 0.934309 | − | 0.356464i | \(-0.116018\pi\) |
−0.775861 | + | 0.630904i | \(0.782684\pi\) | |||||||
\(480\) | 1.37612 | − | 0.794502i | 0.0628109 | − | 0.0362639i | ||||
\(481\) | −0.509546 | + | 0.882559i | −0.0232333 | + | 0.0402412i | ||||
\(482\) | 13.2044i | 0.601445i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.13757 | − | 7.40135i | −0.369889 | − | 0.336425i | ||||
\(485\) | 5.61611 | − | 9.72738i | 0.255014 | − | 0.441698i | ||||
\(486\) | −2.91282 | − | 5.04515i | −0.132128 | − | 0.228853i | ||||
\(487\) | 6.08702 | + | 10.5430i | 0.275829 | + | 0.477750i | 0.970344 | − | 0.241728i | \(-0.0777143\pi\) |
−0.694515 | + | 0.719478i | \(0.744381\pi\) | |||||||
\(488\) | 10.2877 | + | 5.93960i | 0.465702 | + | 0.268873i | ||||
\(489\) | 8.63798i | 0.390623i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 2.37152i | − | 0.107025i | −0.998567 | − | 0.0535125i | \(-0.982958\pi\) | ||
0.998567 | − | 0.0535125i | \(-0.0170417\pi\) | |||||||
\(492\) | −13.7847 | − | 7.95862i | −0.621463 | − | 0.358802i | ||||
\(493\) | −4.85024 | + | 2.80029i | −0.218444 | + | 0.126119i | ||||
\(494\) | −0.0451466 | + | 0.0260654i | −0.00203124 | + | 0.00117274i | ||||
\(495\) | −1.20609 | − | 1.49706i | −0.0542097 | − | 0.0672878i | ||||
\(496\) | 2.54997i | 0.114497i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 22.9076 | 1.02651 | ||||||||
\(499\) | 1.96446 | − | 3.40255i | 0.0879413 | − | 0.152319i | −0.818699 | − | 0.574222i | \(-0.805305\pi\) |
0.906641 | + | 0.421903i | \(0.138638\pi\) | |||||||
\(500\) | −7.90901 | + | 4.56627i | −0.353702 | + | 0.204210i | ||||
\(501\) | 28.6611 | − | 16.5475i | 1.28048 | − | 0.739288i | ||||
\(502\) | −14.4915 | + | 25.1000i | −0.646786 | + | 1.12027i | ||||
\(503\) | 19.8703 | 0.885971 | 0.442986 | − | 0.896529i | \(-0.353919\pi\) | ||||
0.442986 | + | 0.896529i | \(0.353919\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.43689i | − | 0.241938i | ||||||
\(506\) | 0.989268 | + | 1.22793i | 0.0439783 | + | 0.0545881i | ||||
\(507\) | 17.5166 | − | 10.1132i | 0.777940 | − | 0.449144i | ||||
\(508\) | 3.05988 | − | 1.76662i | 0.135760 | − | 0.0783812i | ||||
\(509\) | −13.2438 | − | 7.64634i | −0.587023 | − | 0.338918i | 0.176896 | − | 0.984229i | \(-0.443394\pi\) |
−0.763920 | + | 0.645312i | \(0.776728\pi\) | |||||||
\(510\) | − | 4.69125i | − | 0.207732i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −1.50210 | − | 0.867240i | −0.0663195 | − | 0.0382896i | ||||
\(514\) | 3.49301 | + | 6.05007i | 0.154070 | + | 0.266857i | ||||
\(515\) | −6.34552 | − | 10.9908i | −0.279617 | − | 0.484311i | ||||
\(516\) | 7.89149 | − | 13.6685i | 0.347403 | − | 0.601720i | ||||
\(517\) | 4.54439 | − | 11.7504i | 0.199862 | − | 0.516780i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.4907i | 1.03113i | ||||||||
\(520\) | −0.0852198 | + | 0.147605i | −0.00373714 | + | 0.00647291i | ||||
\(521\) | 0.121861 | − | 0.0703565i | 0.00533883 | − | 0.00308237i | −0.497328 | − | 0.867562i | \(-0.665686\pi\) |
0.502667 | + | 0.864480i | \(0.332352\pi\) | |||||||
\(522\) | 0.539494 | + | 0.934431i | 0.0236130 | + | 0.0408989i | ||||
\(523\) | 4.56153 | − | 7.90081i | 0.199462 | − | 0.345478i | −0.748892 | − | 0.662692i | \(-0.769414\pi\) |
0.948354 | + | 0.317214i | \(0.102747\pi\) | |||||||
\(524\) | 13.9797 | 0.610705 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.47070 | 0.194932 | ||||||||
\(527\) | 6.51971 | + | 3.76416i | 0.284003 | + | 0.163969i | ||||
\(528\) | −5.10974 | + | 0.796171i | −0.222373 | + | 0.0346489i | ||||
\(529\) | 11.3870 | + | 19.7228i | 0.495086 | + | 0.857514i | ||||
\(530\) | 4.29118 | − | 7.43253i | 0.186397 | − | 0.322849i | ||||
\(531\) | − | 3.55064i | − | 0.154085i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.70731 | 0.0739519 | ||||||||
\(534\) | −9.31859 | − | 5.38009i | −0.403255 | − | 0.232819i | ||||
\(535\) | −3.69632 | − | 6.40221i | −0.159806 | − | 0.276792i | ||||
\(536\) | 8.99196 | − | 5.19151i | 0.388394 | − | 0.224239i | ||||
\(537\) | −2.91910 | − | 1.68534i | −0.125969 | − | 0.0727280i | ||||
\(538\) | 2.21730 | 0.0955946 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.67081 | −0.244033 | ||||||||
\(541\) | −21.6730 | − | 12.5129i | −0.931797 | − | 0.537973i | −0.0444172 | − | 0.999013i | \(-0.514143\pi\) |
−0.887379 | + | 0.461040i | \(0.847476\pi\) | |||||||
\(542\) | 19.4961 | − | 11.2561i | 0.837430 | − | 0.483491i | ||||
\(543\) | −4.20437 | − | 7.28217i | −0.180427 | − | 0.312508i | ||||
\(544\) | 2.55678 | + | 1.47616i | 0.109621 | + | 0.0632898i | ||||
\(545\) | −1.18972 | −0.0509620 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 36.7246i | 1.57023i | 0.619348 | + | 0.785116i | \(0.287397\pi\) | ||||
−0.619348 | + | 0.785116i | \(0.712603\pi\) | |||||||
\(548\) | −3.50529 | + | 6.07134i | −0.149738 | + | 0.259355i | ||||
\(549\) | −3.37835 | − | 5.85147i | −0.144184 | − | 0.249735i | ||||
\(550\) | 12.9820 | − | 2.02278i | 0.553555 | − | 0.0862517i | ||||
\(551\) | 0.512080 | + | 0.295649i | 0.0218153 | + | 0.0125951i | ||||
\(552\) | 0.741321 | 0.0315527 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 24.4658 | 1.03945 | ||||||||
\(555\) | −4.84117 | + | 8.38516i | −0.205496 | + | 0.355930i | ||||
\(556\) | −5.73073 | − | 9.92591i | −0.243037 | − | 0.420952i | ||||
\(557\) | −33.5815 | + | 19.3883i | −1.42290 | + | 0.821509i | −0.996545 | − | 0.0830490i | \(-0.973534\pi\) |
−0.426350 | + | 0.904558i | \(0.640201\pi\) | |||||||
\(558\) | 0.725189 | − | 1.25606i | 0.0306997 | − | 0.0531735i | ||||
\(559\) | 1.69291i | 0.0716025i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.50716 | + | 14.2398i | −0.232512 | + | 0.601204i | ||||
\(562\) | −5.67658 | + | 9.83212i | −0.239452 | + | 0.414743i | ||||
\(563\) | 21.6247 | + | 37.4550i | 0.911371 | + | 1.57854i | 0.812129 | + | 0.583477i | \(0.198308\pi\) |
0.0992415 | + | 0.995063i | \(0.468358\pi\) | |||||||
\(564\) | −2.96145 | − | 5.12939i | −0.124700 | − | 0.215986i | ||||
\(565\) | 7.41469 | + | 4.28087i | 0.311938 | + | 0.180098i | ||||
\(566\) | 21.6537i | 0.910172i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 14.5206i | − | 0.609270i | ||||||
\(569\) | −18.4783 | − | 10.6685i | −0.774651 | − | 0.447245i | 0.0598803 | − | 0.998206i | \(-0.480928\pi\) |
−0.834531 | + | 0.550961i | \(0.814261\pi\) | |||||||
\(570\) | −0.428936 | + | 0.247646i | −0.0179662 | + | 0.0103728i | ||||
\(571\) | 19.5677 | − | 11.2974i | 0.818883 | − | 0.472782i | −0.0311482 | − | 0.999515i | \(-0.509916\pi\) |
0.850031 | + | 0.526733i | \(0.176583\pi\) | |||||||
\(572\) | 0.431953 | − | 0.347998i | 0.0180608 | − | 0.0145505i | ||||
\(573\) | − | 9.35542i | − | 0.390828i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.88343 | −0.0785443 | ||||||||
\(576\) | 0.284392 | − | 0.492581i | 0.0118497 | − | 0.0205242i | ||||
\(577\) | 29.3358 | − | 16.9370i | 1.22126 | − | 0.705097i | 0.256077 | − | 0.966656i | \(-0.417570\pi\) |
0.965187 | + | 0.261559i | \(0.0842366\pi\) | |||||||
\(578\) | −7.17400 | + | 4.14191i | −0.298399 | + | 0.172281i | ||||
\(579\) | −7.48400 | + | 12.9627i | −0.311025 | + | 0.538710i | ||||
\(580\) | 1.93323 | 0.0802729 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.1856i | 0.712365i | ||||||||
\(583\) | −21.7506 | + | 17.5232i | −0.900819 | + | 0.725736i | ||||
\(584\) | 8.40712 | − | 4.85385i | 0.347889 | − | 0.200854i | ||||
\(585\) | 0.0839553 | − | 0.0484716i | 0.00347112 | − | 0.00200405i | ||||
\(586\) | 10.4991 | + | 6.06163i | 0.433712 | + | 0.250404i | ||||
\(587\) | − | 6.07819i | − | 0.250874i | −0.992102 | − | 0.125437i | \(-0.959967\pi\) | ||
0.992102 | − | 0.125437i | \(-0.0400332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.794825i | − | 0.0327502i | ||||||
\(590\) | −5.50939 | − | 3.18085i | −0.226818 | − | 0.130953i | ||||
\(591\) | −11.5524 | − | 20.0093i | −0.475202 | − | 0.823074i | ||||
\(592\) | −3.04667 | − | 5.27699i | −0.125217 | − | 0.216883i | ||||
\(593\) | 0.809196 | − | 1.40157i | 0.0332297 | − | 0.0575555i | −0.848932 | − | 0.528502i | \(-0.822754\pi\) |
0.882162 | + | 0.470946i | \(0.156087\pi\) | |||||||
\(594\) | 17.2132 | + | 6.65709i | 0.706264 | + | 0.273144i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 14.1568i | 0.579886i | ||||||||
\(597\) | 3.20446 | − | 5.55029i | 0.131150 | − | 0.227158i | ||||
\(598\) | −0.0688624 | + | 0.0397577i | −0.00281599 | + | 0.00162581i | ||||
\(599\) | −2.63955 | − | 4.57184i | −0.107849 | − | 0.186800i | 0.807050 | − | 0.590484i | \(-0.201063\pi\) |
−0.914899 | + | 0.403684i | \(0.867730\pi\) | |||||||
\(600\) | 3.08842 | − | 5.34930i | 0.126084 | − | 0.218384i | ||||
\(601\) | 32.7945 | 1.33771 | 0.668857 | − | 0.743391i | \(-0.266784\pi\) | ||||
0.668857 | + | 0.743391i | \(0.266784\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.90569 | −0.240498 | ||||||||
\(604\) | 20.1819 | + | 11.6520i | 0.821189 | + | 0.474114i | ||||
\(605\) | 10.9532 | + | 2.38567i | 0.445311 | + | 0.0969912i | ||||
\(606\) | 4.15929 | + | 7.20410i | 0.168960 | + | 0.292647i | ||||
\(607\) | −0.332910 | + | 0.576616i | −0.0135124 | + | 0.0234041i | −0.872703 | − | 0.488252i | \(-0.837635\pi\) |
0.859190 | + | 0.511656i | \(0.170968\pi\) | |||||||
\(608\) | − | 0.311700i | − | 0.0126411i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.1060 | −0.490158 | ||||||||
\(611\) | 0.550188 | + | 0.317651i | 0.0222582 | + | 0.0128508i | ||||
\(612\) | −0.839615 | − | 1.45426i | −0.0339394 | − | 0.0587848i | ||||
\(613\) | 3.71908 | − | 2.14721i | 0.150212 | − | 0.0867251i | −0.423010 | − | 0.906125i | \(-0.639027\pi\) |
0.573222 | + | 0.819400i | \(0.305693\pi\) | |||||||
\(614\) | 8.36422 | + | 4.82908i | 0.337552 | + | 0.194886i | ||||
\(615\) | 16.2211 | 0.654098 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −30.9913 | −1.24766 | −0.623831 | − | 0.781559i | \(-0.714425\pi\) | ||||
−0.623831 | + | 0.781559i | \(0.714425\pi\) | |||||||
\(618\) | 16.8161 | + | 9.70880i | 0.676444 | + | 0.390545i | ||||
\(619\) | 0.685357 | − | 0.395691i | 0.0275468 | − | 0.0159042i | −0.486163 | − | 0.873868i | \(-0.661604\pi\) |
0.513710 | + | 0.857964i | \(0.328271\pi\) | |||||||
\(620\) | −1.29932 | − | 2.25050i | −0.0521821 | − | 0.0903821i | ||||
\(621\) | −2.29117 | − | 1.32281i | −0.0919414 | − | 0.0530824i | ||||
\(622\) | −17.6778 | −0.708815 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.260777i | − | 0.0104394i | ||||||
\(625\) | −5.25019 | + | 9.09359i | −0.210007 | + | 0.363744i | ||||
\(626\) | −14.4052 | − | 24.9505i | −0.575746 | − | 0.997222i | ||||
\(627\) | 1.59271 | − | 0.248167i | 0.0636067 | − | 0.00991083i | ||||
\(628\) | −3.49234 | − | 2.01630i | −0.139360 | − | 0.0804593i | ||||
\(629\) | −17.9895 | −0.717288 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −34.3677 | −1.36816 | −0.684078 | − | 0.729409i | \(-0.739795\pi\) | ||||
−0.684078 | + | 0.729409i | \(0.739795\pi\) | |||||||
\(632\) | 3.50284 | − | 6.06709i | 0.139335 | − | 0.241336i | ||||
\(633\) | 5.86628 | + | 10.1607i | 0.233164 | + | 0.403852i | ||||
\(634\) | 8.95955 | − | 5.17280i | 0.355829 | − | 0.205438i | ||||
\(635\) | −1.80035 | + | 3.11830i | −0.0714447 | + | 0.123746i | ||||
\(636\) | 13.1312i | 0.520687i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.86811 | − | 2.26946i | −0.232321 | − | 0.0898488i | ||||
\(639\) | −4.12954 | + | 7.15257i | −0.163362 | + | 0.282951i | ||||
\(640\) | −0.509546 | − | 0.882559i | −0.0201416 | − | 0.0348862i | ||||
\(641\) | −2.47939 | − | 4.29443i | −0.0979301 | − | 0.169620i | 0.812898 | − | 0.582407i | \(-0.197889\pi\) |
−0.910828 | + | 0.412787i | \(0.864556\pi\) | |||||||
\(642\) | 9.79554 | + | 5.65546i | 0.386599 | + | 0.223203i | ||||
\(643\) | − | 48.1404i | − | 1.89847i | −0.314562 | − | 0.949237i | \(-0.601858\pi\) | ||
0.314562 | − | 0.949237i | \(-0.398142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.0843i | 0.633318i | ||||||||
\(646\) | −0.796950 | − | 0.460119i | −0.0313556 | − | 0.0181031i | ||||
\(647\) | 2.74160 | − | 1.58286i | 0.107783 | − | 0.0622287i | −0.445139 | − | 0.895461i | \(-0.646846\pi\) |
0.552923 | + | 0.833233i | \(0.313513\pi\) | |||||||
\(648\) | 6.03631 | − | 3.48507i | 0.237129 | − | 0.136906i | ||||
\(649\) | 12.9891 | + | 16.1227i | 0.509867 | + | 0.632872i | ||||
\(650\) | 0.662540i | 0.0259869i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.53988 | 0.216958 | ||||||||
\(653\) | 11.0606 | − | 19.1575i | 0.432833 | − | 0.749689i | −0.564283 | − | 0.825582i | \(-0.690847\pi\) |
0.997116 | + | 0.0758922i | \(0.0241805\pi\) | |||||||
\(654\) | 1.57643 | − | 0.910151i | 0.0616432 | − | 0.0355897i | ||||
\(655\) | −12.3379 | + | 7.12329i | −0.482081 | + | 0.278330i | ||||
\(656\) | −5.10418 | + | 8.84069i | −0.199285 | + | 0.345171i | ||||
\(657\) | −5.52158 | −0.215417 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 24.6258i | − | 0.959286i | −0.877464 | − | 0.479643i | \(-0.840766\pi\) | ||
0.877464 | − | 0.479643i | \(-0.159234\pi\) | |||||||
\(660\) | 4.10397 | − | 3.30632i | 0.159747 | − | 0.128698i | ||||
\(661\) | −24.0205 | + | 13.8682i | −0.934289 | + | 0.539412i | −0.888166 | − | 0.459524i | \(-0.848020\pi\) |
−0.0461236 | + | 0.998936i | \(0.514687\pi\) | |||||||
\(662\) | −23.2483 | + | 13.4224i | −0.903572 | + | 0.521677i | ||||
\(663\) | −0.666750 | − | 0.384948i | −0.0258944 | − | 0.0149502i | ||||
\(664\) | − | 14.6915i | − | 0.570143i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.46579i | 0.134297i | ||||||||
\(667\) | 0.781078 | + | 0.450956i | 0.0302435 | + | 0.0174611i | ||||
\(668\) | −10.6126 | − | 18.3815i | −0.410613 | − | 0.711202i | ||||
\(669\) | −10.5938 | − | 18.3490i | −0.409580 | − | 0.709414i | ||||
\(670\) | −5.29063 | + | 9.16363i | −0.204395 | + | 0.354022i | ||||
\(671\) | 36.7465 | + | 14.2115i | 1.41858 | + | 0.548629i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 15.9518i | − | 0.614897i | −0.951565 | − | 0.307449i | \(-0.900525\pi\) | ||
0.951565 | − | 0.307449i | \(-0.0994752\pi\) | |||||||
\(674\) | 7.27523 | − | 12.6011i | 0.280231 | − | 0.485375i | ||||
\(675\) | −19.0905 | + | 11.0219i | −0.734793 | + | 0.424233i | ||||
\(676\) | −6.48601 | − | 11.2341i | −0.249462 | − | 0.432081i | ||||
\(677\) | −7.52574 | + | 13.0350i | −0.289238 | + | 0.500974i | −0.973628 | − | 0.228141i | \(-0.926735\pi\) |
0.684390 | + | 0.729116i | \(0.260068\pi\) | |||||||
\(678\) | −13.0997 | −0.503091 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00868 | −0.115378 | ||||||||
\(681\) | −29.2531 | − | 16.8893i | −1.12098 | − | 0.647198i | ||||
\(682\) | 1.30205 | + | 8.35645i | 0.0498582 | + | 0.319985i | ||||
\(683\) | 2.64673 | + | 4.58427i | 0.101274 | + | 0.175412i | 0.912210 | − | 0.409723i | \(-0.134375\pi\) |
−0.810936 | + | 0.585135i | \(0.801041\pi\) | |||||||
\(684\) | −0.0886450 | + | 0.153538i | −0.00338943 | + | 0.00587066i | ||||
\(685\) | − | 7.14442i | − | 0.272974i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 46.8756 | 1.78842 | ||||||||
\(688\) | −8.76612 | − | 5.06112i | −0.334205 | − | 0.192954i | ||||
\(689\) | −0.704240 | − | 1.21978i | −0.0268294 | − | 0.0464699i | ||||
\(690\) | −0.654259 | + | 0.377737i | −0.0249072 | + | 0.0143802i | ||||
\(691\) | 23.4089 | + | 13.5151i | 0.890517 | + | 0.514140i | 0.874112 | − | 0.485725i | \(-0.161444\pi\) |
0.0164055 | + | 0.999865i | \(0.494778\pi\) | |||||||
\(692\) | 15.0655 | 0.572706 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.5417 | 1.08343 | ||||||||
\(695\) | 10.1154 | + | 5.84014i | 0.383699 | + | 0.221529i | ||||
\(696\) | −2.56161 | + | 1.47894i | −0.0970974 | + | 0.0560592i | ||||
\(697\) | 15.0692 | + | 26.1005i | 0.570785 | + | 0.988629i | ||||
\(698\) | −29.9667 | − | 17.3013i | −1.13426 | − | 0.654864i | ||||
\(699\) | −25.2465 | −0.954911 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19.9250i | 0.752555i | 0.926507 | + | 0.376278i | \(0.122796\pi\) | ||||
−0.926507 | + | 0.376278i | \(0.877204\pi\) | |||||||
\(702\) | −0.465328 | + | 0.805972i | −0.0175627 | + | 0.0304195i | ||||
\(703\) | 0.949649 | + | 1.64484i | 0.0358167 | + | 0.0620363i | ||||
\(704\) | 0.510616 | + | 3.27708i | 0.0192446 | + | 0.123510i | ||||
\(705\) | 5.22731 | + | 3.01799i | 0.196872 | + | 0.113664i | ||||
\(706\) | −16.9203 | −0.636805 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.73355 | 0.365809 | ||||||||
\(709\) | −4.98412 | + | 8.63276i | −0.187183 | + | 0.324210i | −0.944310 | − | 0.329058i | \(-0.893269\pi\) |
0.757127 | + | 0.653268i | \(0.226602\pi\) | |||||||
\(710\) | 7.39891 | + | 12.8153i | 0.277676 | + | 0.480949i | ||||
\(711\) | −3.45086 | + | 1.99236i | −0.129417 | + | 0.0747192i | ||||
\(712\) | −3.45047 | + | 5.97639i | −0.129312 | + | 0.223975i | ||||
\(713\) | − | 1.21235i | − | 0.0454029i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.203903 | + | 0.527228i | −0.00762553 | + | 0.0197172i | ||||
\(716\) | −1.08088 | + | 1.87214i | −0.0403943 | + | 0.0699650i | ||||
\(717\) | 20.3247 | + | 35.2034i | 0.759040 | + | 1.31470i | ||||
\(718\) | −15.1755 | − | 26.2848i | −0.566346 | − | 0.980940i | ||||
\(719\) | −35.6817 | − | 20.6008i | −1.33070 | − | 0.768282i | −0.345295 | − | 0.938494i | \(-0.612221\pi\) |
−0.985407 | + | 0.170212i | \(0.945555\pi\) | |||||||
\(720\) | 0.579642i | 0.0216020i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.9028i | − | 0.703491i | ||||||
\(723\) | 17.8304 | + | 10.2944i | 0.663121 | + | 0.382853i | ||||
\(724\) | −4.67035 | + | 2.69643i | −0.173572 | + | 0.100212i | ||||
\(725\) | 6.50811 | − | 3.75746i | 0.241705 | − | 0.139549i | ||||
\(726\) | −16.3385 | + | 5.21824i | −0.606379 | + | 0.193667i | ||||
\(727\) | 0.0415718i | 0.00154181i | 1.00000 | 0.000770906i | \(0.000245387\pi\) | |||||
−1.00000 | 0.000770906i | \(0.999755\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.9940 | −1.11089 | ||||||||
\(730\) | −4.94652 | + | 8.56762i | −0.183079 | + | 0.317102i | ||||
\(731\) | −25.8804 | + | 14.9420i | −0.957221 | + | 0.552652i | ||||
\(732\) | 16.0409 | − | 9.26124i | 0.592890 | − | 0.342305i | ||||
\(733\) | −4.40404 | + | 7.62803i | −0.162667 | + | 0.281748i | −0.935824 | − | 0.352467i | \(-0.885343\pi\) |
0.773157 | + | 0.634214i | \(0.218676\pi\) | |||||||
\(734\) | −17.4215 | −0.643040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 0.475438i | − | 0.0175249i | ||||||
\(737\) | 26.8165 | − | 21.6045i | 0.987800 | − | 0.795810i | ||||
\(738\) | 5.02844 | − | 2.90317i | 0.185099 | − | 0.106867i | ||||
\(739\) | −28.4003 | + | 16.3969i | −1.04472 | + | 0.603170i | −0.921167 | − | 0.389167i | \(-0.872763\pi\) |
−0.123555 | + | 0.992338i | \(0.539429\pi\) | |||||||
\(740\) | 5.37774 | + | 3.10484i | 0.197690 | + | 0.114136i | ||||
\(741\) | 0.0812842i | 0.00298605i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 25.7575i | 0.944952i | 0.881344 | + | 0.472476i | \(0.156640\pi\) | ||||
−0.881344 | + | 0.472476i | \(0.843360\pi\) | |||||||
\(744\) | 3.44332 | + | 1.98800i | 0.126238 | + | 0.0728836i | ||||
\(745\) | −7.21355 | − | 12.4942i | −0.264284 | − | 0.457753i | ||||
\(746\) | −4.57606 | − | 7.92596i | −0.167541 | − | 0.290190i | ||||
\(747\) | −4.17815 | + | 7.23678i | −0.152871 | + | 0.264780i | ||||
\(748\) | 9.13254 | + | 3.53196i | 0.333919 | + | 0.129141i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 14.2398i | 0.519963i | ||||||||
\(751\) | −5.73290 | + | 9.92967i | −0.209196 | + | 0.362339i | −0.951462 | − | 0.307767i | \(-0.900418\pi\) |
0.742265 | + | 0.670106i | \(0.233751\pi\) | |||||||
\(752\) | −3.28968 | + | 1.89930i | −0.119962 | + | 0.0692603i | ||||
\(753\) | 22.5956 | + | 39.1367i | 0.823430 | + | 1.42622i | ||||
\(754\) | 0.158634 | − | 0.274763i | 0.00577712 | − | 0.0100063i | ||||
\(755\) | −23.7489 | −0.864313 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.9741 | 0.798661 | 0.399331 | − | 0.916807i | \(-0.369243\pi\) | ||||
0.399331 | + | 0.916807i | \(0.369243\pi\) | |||||||
\(758\) | 5.32936 | + | 3.07691i | 0.193571 | + | 0.111758i | ||||
\(759\) | 2.42937 | − | 0.378530i | 0.0881805 | − | 0.0137398i | ||||
\(760\) | 0.158826 | + | 0.275094i | 0.00576121 | + | 0.00997871i | ||||
\(761\) | −13.0047 | + | 22.5249i | −0.471421 | + | 0.816526i | −0.999466 | − | 0.0326910i | \(-0.989592\pi\) |
0.528044 | + | 0.849217i | \(0.322926\pi\) | |||||||
\(762\) | − | 5.50916i | − | 0.199576i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 1.48202 | + | 0.855644i | 0.0535825 | + | 0.0309359i | ||||
\(766\) | 6.48253 | + | 11.2281i | 0.234223 | + | 0.405687i | ||||
\(767\) | −0.904164 | + | 0.522020i | −0.0326475 | + | 0.0188490i | ||||
\(768\) | 1.35034 | + | 0.779618i | 0.0487261 | + | 0.0281320i | ||||
\(769\) | 40.8753 | 1.47400 | 0.737001 | − | 0.675891i | \(-0.236241\pi\) | ||||
0.737001 | + | 0.675891i | \(0.236241\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.8929 | 0.392296 | ||||||||
\(772\) | 8.31348 | + | 4.79979i | 0.299209 | + | 0.172748i | ||||
\(773\) | −40.8229 | + | 23.5691i | −1.46830 | + | 0.847722i | −0.999369 | − | 0.0355144i | \(-0.988693\pi\) |
−0.468928 | + | 0.883236i | \(0.655360\pi\) | |||||||
\(774\) | 2.87868 | + | 4.98603i | 0.103472 | + | 0.179219i | ||||
\(775\) | −8.74822 | − | 5.05078i | −0.314245 | − | 0.181430i | ||||
\(776\) | 11.0218 | 0.395659 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.16647i | 0.185227i | ||||||||
\(779\) | 1.59097 | − | 2.75565i | 0.0570025 | − | 0.0987313i | ||||
\(780\) | 0.132878 | + | 0.230151i | 0.00475779 | + | 0.00824073i | ||||
\(781\) | −7.41445 | − | 47.5852i | −0.265310 | − | 1.70273i | ||||
\(782\) | −1.21559 | − | 0.701823i | −0.0434695 | − | 0.0250971i | ||||
\(783\) | 10.5561 | 0.377243 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.10960 | 0.146678 | ||||||||
\(786\) | 10.8988 | − | 18.8773i | 0.388748 | − | 0.673331i | ||||
\(787\) | −12.0746 | − | 20.9137i | −0.430411 | − | 0.745494i | 0.566497 | − | 0.824064i | \(-0.308298\pi\) |
−0.996909 | + | 0.0785692i | \(0.974965\pi\) | |||||||
\(788\) | −12.8328 | + | 7.40901i | −0.457149 | + | 0.263935i | ||||
\(789\) | 3.48543 | − | 6.03695i | 0.124085 | − | 0.214921i | ||||
\(790\) | 7.13942i | 0.254009i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.680455 | − | 1.75944i | 0.0241789 | − | 0.0625191i | ||||
\(793\) | −0.993379 | + | 1.72058i | −0.0352759 | + | 0.0610997i | ||||
\(794\) | 4.62856 | + | 8.01690i | 0.164261 | + | 0.284509i | ||||
\(795\) | −6.69096 | − | 11.5891i | −0.237304 | − | 0.411022i | ||||
\(796\) | −3.55962 | − | 2.05515i | −0.126167 | − | 0.0728428i | ||||
\(797\) | − | 20.3073i | − | 0.719321i | −0.933083 | − | 0.359660i | \(-0.882893\pi\) | ||
0.933083 | − | 0.359660i | \(-0.117107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.2147i | 0.396746i | ||||||||
\(800\) | −3.43072 | − | 1.98073i | −0.121294 | − | 0.0700293i | ||||
\(801\) | 3.39927 | − | 1.96257i | 0.120107 | − | 0.0693440i | ||||
\(802\) | −26.7816 | + | 15.4624i | −0.945692 | + | 0.545996i | ||||
\(803\) | 25.0724 | − | 20.1993i | 0.884785 | − | 0.712818i | ||||
\(804\) | − | 16.1896i | − | 0.570963i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −0.426473 | −0.0150219 | ||||||||
\(807\) | 1.72865 | − | 2.99410i | 0.0608513 | − | 0.105397i | ||||
\(808\) | 4.62028 | − | 2.66752i | 0.162541 | − | 0.0938430i | ||||
\(809\) | −23.4501 | + | 13.5389i | −0.824461 | + | 0.476003i | −0.851953 | − | 0.523619i | \(-0.824582\pi\) |
0.0274911 | + | 0.999622i | \(0.491248\pi\) | |||||||
\(810\) | −3.55160 | + | 6.15156i | −0.124791 | + | 0.216144i | ||||
\(811\) | −23.5808 | −0.828033 | −0.414016 | − | 0.910269i | \(-0.635874\pi\) | ||||
−0.414016 | + | 0.910269i | \(0.635874\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 35.1018i | − | 1.23107i | ||||||
\(814\) | −12.6787 | − | 15.7375i | −0.444389 | − | 0.551598i | ||||
\(815\) | −4.88927 | + | 2.82282i | −0.171264 | + | 0.0988792i | ||||
\(816\) | 3.98663 | − | 2.30168i | 0.139560 | − | 0.0805749i | ||||
\(817\) | 2.73240 | + | 1.57755i | 0.0955947 | + | 0.0551916i | ||||
\(818\) | − | 23.8397i | − | 0.833535i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 10.4032i | − | 0.363297i | ||||||
\(821\) | 29.4247 | + | 16.9884i | 1.02693 | + | 0.592898i | 0.916104 | − | 0.400942i | \(-0.131317\pi\) |
0.110826 | + | 0.993840i | \(0.464650\pi\) | |||||||
\(822\) | 5.46557 | + | 9.46665i | 0.190634 | + | 0.330187i | ||||
\(823\) | 5.90033 | + | 10.2197i | 0.205673 | + | 0.356235i | 0.950347 | − | 0.311193i | \(-0.100728\pi\) |
−0.744674 | + | 0.667428i | \(0.767395\pi\) | |||||||
\(824\) | 6.22664 | − | 10.7849i | 0.216915 | − | 0.375708i | ||||
\(825\) | 7.38957 | − | 19.1071i | 0.257272 | − | 0.665224i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 17.0595i | − | 0.593217i | −0.954999 | − | 0.296609i | \(-0.904144\pi\) | ||
0.954999 | − | 0.296609i | \(-0.0958557\pi\) | |||||||
\(828\) | −0.135211 | + | 0.234192i | −0.00469890 | + | 0.00813873i | ||||
\(829\) | 21.7387 | − | 12.5508i | 0.755015 | − | 0.435908i | −0.0724880 | − | 0.997369i | \(-0.523094\pi\) |
0.827503 | + | 0.561461i | \(0.189761\pi\) | |||||||
\(830\) | 7.48601 | + | 12.9662i | 0.259843 | + | 0.450062i | ||||
\(831\) | 19.0740 | − | 33.0371i | 0.661669 | − | 1.14604i | ||||
\(832\) | −0.167247 | −0.00579823 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −17.8711 | −0.618826 | ||||||||
\(835\) | 18.7324 | + | 10.8152i | 0.648263 | + | 0.374275i | ||||
\(836\) | −0.159159 | − | 1.02147i | −0.00550464 | − | 0.0353282i | ||||
\(837\) | −7.09474 | − | 12.2884i | −0.245230 | − | 0.424751i | ||||
\(838\) | −2.51713 | + | 4.35980i | −0.0869528 | + | 0.150607i | ||||
\(839\) | 41.1030i | 1.41903i | 0.704688 | + | 0.709517i | \(0.251087\pi\) | ||||
−0.704688 | + | 0.709517i | \(0.748913\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.4014 | 0.875909 | ||||||||
\(842\) | 14.6574 | + | 8.46248i | 0.505129 | + | 0.291636i | ||||
\(843\) | 8.85113 | + | 15.3306i | 0.304849 | + | 0.528014i | ||||
\(844\) | 6.51646 | − | 3.76228i | 0.224306 | − | 0.129503i | ||||
\(845\) | 11.4486 | + | 6.60984i | 0.393843 | + | 0.227385i | ||||
\(846\) | 2.16058 | 0.0742822 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.42157 | 0.289198 | ||||||||
\(849\) | 29.2398 | + | 16.8816i | 1.00351 | + | 0.579375i | ||||
\(850\) | −10.1286 | + | 5.84773i | −0.347407 | + | 0.200576i | ||||
\(851\) | 1.44851 | + | 2.50888i | 0.0496541 | + | 0.0860035i | ||||
\(852\) | −19.6077 | − | 11.3205i | −0.671749 | − | 0.387834i | ||||
\(853\) | −52.7195 | −1.80508 | −0.902541 | − | 0.430605i | \(-0.858300\pi\) | ||||
−0.902541 | + | 0.430605i | \(0.858300\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 0.180675i | − | 0.00617894i | ||||||
\(856\) | 3.62707 | − | 6.28227i | 0.123971 | − | 0.214724i | ||||
\(857\) | 10.9387 | + | 18.9464i | 0.373659 | + | 0.647197i | 0.990125 | − | 0.140184i | \(-0.0447695\pi\) |
−0.616466 | + | 0.787382i | \(0.711436\pi\) | |||||||
\(858\) | −0.133157 | − | 0.854588i | −0.00454590 | − | 0.0291751i | ||||
\(859\) | −11.8529 | − | 6.84326i | −0.404415 | − | 0.233489i | 0.283972 | − | 0.958832i | \(-0.408348\pi\) |
−0.688387 | + | 0.725344i | \(0.741681\pi\) | |||||||
\(860\) | 10.3155 | 0.351755 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.99907 | 0.204329 | ||||||||
\(863\) | −15.0240 | + | 26.0223i | −0.511423 | + | 0.885810i | 0.488490 | + | 0.872570i | \(0.337548\pi\) |
−0.999912 | + | 0.0132402i | \(0.995785\pi\) | |||||||
\(864\) | −2.78229 | − | 4.81906i | −0.0946553 | − | 0.163948i | ||||
\(865\) | −13.2962 | + | 7.67658i | −0.452085 | + | 0.261012i | ||||
\(866\) | 18.0588 | − | 31.2787i | 0.613662 | − | 1.06289i | ||||
\(867\) | 12.9164i | 0.438665i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.38113 | − | 21.6710i | 0.284310 | − | 0.735137i | ||||
\(870\) | 1.50718 | − | 2.61051i | 0.0510981 | − | 0.0885046i | ||||
\(871\) | 0.868263 | + | 1.50388i | 0.0294200 | + | 0.0509569i | ||||
\(872\) | −0.583716 | − | 1.01103i | −0.0197671 | − | 0.0342377i | ||||
\(873\) | −5.42913 | − | 3.13451i | −0.183748 | − | 0.106087i | ||||
\(874\) | 0.148194i | 0.00501275i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 15.1366i | − | 0.511418i | ||||||
\(877\) | −12.2786 | − | 7.08908i | −0.414620 | − | 0.239381i | 0.278153 | − | 0.960537i | \(-0.410278\pi\) |
−0.692773 | + | 0.721156i | \(0.743611\pi\) | |||||||
\(878\) | 9.82906 | − | 5.67481i | 0.331715 | − | 0.191516i | ||||
\(879\) | 16.3705 | − | 9.45151i | 0.552163 | − | 0.318792i | ||||
\(880\) | −2.12047 | − | 2.63204i | −0.0714811 | − | 0.0887259i | ||||
\(881\) | 22.3264i | 0.752196i | 0.926580 | + | 0.376098i | \(0.122734\pi\) | ||||
−0.926580 | + | 0.376098i | \(0.877266\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.45618 | −0.149962 | −0.0749812 | − | 0.997185i | \(-0.523890\pi\) | ||||
−0.0749812 | + | 0.997185i | \(0.523890\pi\) | |||||||
\(884\) | −0.246883 | + | 0.427613i | −0.00830356 | + | 0.0143822i | ||||
\(885\) | −8.59043 | + | 4.95969i | −0.288764 | + | 0.166718i | ||||
\(886\) | −4.11428 | + | 2.37538i | −0.138222 | + | 0.0798025i | ||||
\(887\) | 4.50070 | − | 7.79545i | 0.151119 | − | 0.261746i | −0.780520 | − | 0.625131i | \(-0.785046\pi\) |
0.931639 | + | 0.363385i | \(0.118379\pi\) | |||||||
\(888\) | −9.50096 | −0.318831 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 7.03268i | − | 0.235736i | ||||||
\(891\) | 18.0020 | − | 14.5031i | 0.603089 | − | 0.485872i | ||||
\(892\) | −11.7680 | + | 6.79423i | −0.394020 | + | 0.227488i | ||||
\(893\) | 1.02539 | − | 0.592012i | 0.0343135 | − | 0.0198109i | ||||
\(894\) | 19.1165 | + | 11.0369i | 0.639351 | + | 0.369130i | ||||
\(895\) | − | 2.20303i | − | 0.0736391i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.123983i | 0.00413968i | ||||||||
\(898\) | −6.35054 | − | 3.66649i | −0.211920 | − | 0.122352i | ||||
\(899\) | 2.41866 | + | 4.18924i | 0.0806667 | + | 0.139719i | ||||
\(900\) | 1.12660 | + | 1.95134i | 0.0375535 | + | 0.0650445i | ||||
\(901\) | 12.4316 | − | 21.5321i | 0.414156 | − | 0.717339i | ||||
\(902\) | −12.2126 | + | 31.5780i | −0.406635 | + | 1.05143i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.40135i | 0.279425i | ||||||||
\(905\) | 2.74791 | − | 4.75951i | 0.0913435 | − | 0.158212i | ||||
\(906\) | 31.4683 | − | 18.1682i | 1.04547 | − | 0.603600i | ||||
\(907\) | −10.6872 | − | 18.5107i | −0.354862 | − | 0.614638i | 0.632233 | − | 0.774779i | \(-0.282139\pi\) |
−0.987094 | + | 0.160140i | \(0.948805\pi\) | |||||||
\(908\) | −10.8318 | + | 18.7611i | −0.359464 | + | 0.622611i | ||||
\(909\) | −3.03448 | −0.100647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.4299 | −0.941924 | −0.470962 | − | 0.882153i | \(-0.656093\pi\) | ||||
−0.470962 | + | 0.882153i | \(0.656093\pi\) | |||||||
\(912\) | −0.420901 | − | 0.243007i | −0.0139374 | − | 0.00804677i | ||||
\(913\) | −7.50174 | − | 48.1454i | −0.248271 | − | 1.59338i | ||||
\(914\) | 6.75879 | + | 11.7066i | 0.223561 | + | 0.387219i | ||||
\(915\) | −9.43805 | + | 16.3472i | −0.312012 | + | 0.540421i | ||||
\(916\) | − | 30.0632i | − | 0.993317i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.4284 | −0.542218 | ||||||||
\(919\) | 18.2320 | + | 10.5263i | 0.601419 | + | 0.347229i | 0.769600 | − | 0.638527i | \(-0.220456\pi\) |
−0.168181 | + | 0.985756i | \(0.553789\pi\) | |||||||
\(920\) | 0.242258 | + | 0.419602i | 0.00798700 | + | 0.0138339i | ||||
\(921\) | 13.0418 | − | 7.52968i | 0.429741 | − | 0.248111i | ||||
\(922\) | −16.0847 | − | 9.28652i | −0.529722 | − | 0.305835i | ||||
\(923\) | 2.42852 | 0.0799357 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1385 | 0.793669 | ||||||||
\(926\) | −24.4955 | − | 14.1425i | −0.804971 | − | 0.464750i | ||||
\(927\) | −6.13425 | + | 3.54161i | −0.201475 | + | 0.116322i | ||||
\(928\) | 0.948505 | + | 1.64286i | 0.0311362 | + | 0.0539295i | ||||
\(929\) | −10.8055 | − | 6.23858i | −0.354518 | − | 0.204681i | 0.312155 | − | 0.950031i | \(-0.398949\pi\) |
−0.666674 | + | 0.745350i | \(0.732282\pi\) | |||||||
\(930\) | −4.05191 | −0.132867 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 16.1916i | 0.530373i | ||||||||
\(933\) | −13.7819 | + | 23.8710i | −0.451200 | + | 0.781501i | ||||
\(934\) | −10.7896 | − | 18.6881i | −0.353046 | − | 0.611493i | ||||
\(935\) | −9.85970 | + | 1.53628i | −0.322447 | + | 0.0502418i | ||||
\(936\) | 0.0823825 | + | 0.0475636i | 0.00269276 | + | 0.00155466i | ||||
\(937\) | −43.2128 | −1.41170 | −0.705850 | − | 0.708362i | \(-0.749435\pi\) | ||||
−0.705850 | + | 0.708362i | \(0.749435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −44.9221 | −1.46598 | ||||||||
\(940\) | 1.93556 | − | 3.35248i | 0.0631309 | − | 0.109346i | ||||
\(941\) | −7.73754 | − | 13.4018i | −0.252236 | − | 0.436886i | 0.711905 | − | 0.702276i | \(-0.247833\pi\) |
−0.964141 | + | 0.265390i | \(0.914499\pi\) | |||||||
\(942\) | −5.44538 | + | 3.14389i | −0.177420 | + | 0.102434i | ||||
\(943\) | 2.42672 | − | 4.20321i | 0.0790249 | − | 0.136875i | ||||
\(944\) | − | 6.24251i | − | 0.203176i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −31.3116 | − | 12.1096i | −1.01803 | − | 0.393717i | ||||
\(947\) | −16.7488 | + | 29.0098i | −0.544264 | + | 0.942693i | 0.454389 | + | 0.890803i | \(0.349858\pi\) |
−0.998653 | + | 0.0518895i | \(0.983476\pi\) | |||||||
\(948\) | −5.46175 | − | 9.46003i | −0.177389 | − | 0.307247i | ||||
\(949\) | 0.811791 | + | 1.40606i | 0.0263518 | + | 0.0456427i | ||||
\(950\) | 1.06936 | + | 0.617393i | 0.0346945 | + | 0.0200309i | ||||
\(951\) | − | 16.1312i | − | 0.523091i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 25.4820i | − | 0.825444i | −0.910857 | − | 0.412722i | \(-0.864578\pi\) | ||
0.910857 | − | 0.412722i | \(-0.135422\pi\) | |||||||
\(954\) | −4.14831 | − | 2.39503i | −0.134306 | − | 0.0775418i | ||||
\(955\) | 5.29535 | − | 3.05727i | 0.171354 | − | 0.0989311i | ||||
\(956\) | 22.5774 | − | 13.0350i | 0.730204 | − | 0.421583i | ||||
\(957\) | −7.63942 | + | 6.15462i | −0.246947 | + | 0.198951i | ||||
\(958\) | − | 6.93560i | − | 0.224079i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −1.58900 | −0.0512849 | ||||||||
\(961\) | −12.2488 | + | 21.2156i | −0.395124 | + | 0.684374i | ||||
\(962\) | 0.882559 | − | 0.509546i | 0.0284548 | − | 0.0164284i | ||||
\(963\) | −3.57325 | + | 2.06302i | −0.115146 | + | 0.0664798i | ||||
\(964\) | 6.60221 | − | 11.4354i | 0.212643 | − | 0.368309i | ||||
\(965\) | −9.78285 | −0.314921 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 39.6417i | − | 1.27479i | −0.770537 | − | 0.637395i | \(-0.780012\pi\) | ||
0.770537 | − | 0.637395i | \(-0.219988\pi\) | |||||||
\(968\) | 3.34666 | + | 10.4785i | 0.107566 | + | 0.336793i | ||||
\(969\) | −1.24263 | + | 0.717434i | −0.0399191 | + | 0.0230473i | ||||
\(970\) | −9.72738 | + | 5.61611i | −0.312327 | + | 0.180322i | ||||
\(971\) | 16.5082 | + | 9.53101i | 0.529773 | + | 0.305865i | 0.740924 | − | 0.671589i | \(-0.234388\pi\) |
−0.211151 | + | 0.977454i | \(0.567721\pi\) | |||||||
\(972\) | 5.82564i | 0.186858i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 12.1740i | − | 0.390081i | ||||||
\(975\) | 0.894652 | + | 0.516528i | 0.0286518 | + | 0.0165421i | ||||
\(976\) | −5.93960 | − | 10.2877i | −0.190122 | − | 0.329301i | ||||
\(977\) | −23.8348 | − | 41.2832i | −0.762544 | − | 1.32077i | −0.941535 | − | 0.336915i | \(-0.890617\pi\) |
0.178991 | − | 0.983851i | \(-0.442717\pi\) | |||||||
\(978\) | 4.31899 | − | 7.48071i | 0.138106 | − | 0.239207i | ||||
\(979\) | −8.25583 | + | 21.3470i | −0.263857 | + | 0.682252i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.664016i | 0.0212004i | ||||||||
\(982\) | −1.18576 | + | 2.05379i | −0.0378391 | + | 0.0655392i | ||||
\(983\) | −40.2377 | + | 23.2312i | −1.28338 | + | 0.740961i | −0.977465 | − | 0.211097i | \(-0.932296\pi\) |
−0.305917 | + | 0.952058i | \(0.598963\pi\) | |||||||
\(984\) | 7.95862 | + | 13.7847i | 0.253711 | + | 0.439441i | ||||
\(985\) | 7.55046 | − | 13.0778i | 0.240578 | − | 0.416693i | ||||
\(986\) | 5.60058 | 0.178359 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.0521308 | 0.00165850 | ||||||||
\(989\) | 4.16775 | + | 2.40625i | 0.132527 | + | 0.0765144i | ||||
\(990\) | 0.295975 | + | 1.89954i | 0.00940670 | + | 0.0603712i | ||||
\(991\) | 7.28588 | + | 12.6195i | 0.231444 | + | 0.400872i | 0.958233 | − | 0.285988i | \(-0.0923218\pi\) |
−0.726790 | + | 0.686860i | \(0.758988\pi\) | |||||||
\(992\) | 1.27498 | − | 2.20834i | 0.0404808 | − | 0.0701147i | ||||
\(993\) | 41.8575i | 1.32831i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.18877 | 0.132793 | ||||||||
\(996\) | −19.8386 | − | 11.4538i | −0.628609 | − | 0.362927i | ||||
\(997\) | 2.05848 | + | 3.56539i | 0.0651927 | + | 0.112917i | 0.896779 | − | 0.442478i | \(-0.145900\pi\) |
−0.831587 | + | 0.555395i | \(0.812567\pi\) | |||||||
\(998\) | −3.40255 | + | 1.96446i | −0.107706 | + | 0.0621839i | ||||
\(999\) | 29.3642 | + | 16.9534i | 0.929043 | + | 0.536383i |
(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 | 1078.2.i.c.901.2 | 16 | ||
7.2 | even | 3 | 1078.2.c.b.1077.11 | 16 | |||
7.3 | odd | 6 | inner | 1078.2.i.c.1011.6 | 16 | ||
7.4 | even | 3 | 154.2.i.a.87.7 | yes | 16 | ||
7.5 | odd | 6 | 1078.2.c.b.1077.14 | 16 | |||
7.6 | odd | 2 | 154.2.i.a.131.3 | yes | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.c.901.6 | 16 | ||
21.11 | odd | 6 | 1386.2.bk.c.703.2 | 16 | |||
21.20 | even | 2 | 1386.2.bk.c.901.6 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.b.241.4 | 16 | |||
28.27 | even | 2 | 1232.2.bn.b.593.3 | 16 | |||
77.10 | even | 6 | inner | 1078.2.i.c.1011.2 | 16 | ||
77.32 | odd | 6 | 154.2.i.a.87.3 | ✓ | 16 | ||
77.54 | even | 6 | 1078.2.c.b.1077.6 | 16 | |||
77.65 | odd | 6 | 1078.2.c.b.1077.3 | 16 | |||
77.76 | even | 2 | 154.2.i.a.131.7 | yes | 16 | ||
231.32 | even | 6 | 1386.2.bk.c.703.6 | 16 | |||
231.230 | odd | 2 | 1386.2.bk.c.901.2 | 16 | |||
308.263 | even | 6 | 1232.2.bn.b.241.3 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.b.593.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.3 | ✓ | 16 | 77.32 | odd | 6 | ||
154.2.i.a.87.7 | yes | 16 | 7.4 | even | 3 | ||
154.2.i.a.131.3 | yes | 16 | 7.6 | odd | 2 | ||
154.2.i.a.131.7 | yes | 16 | 77.76 | even | 2 | ||
1078.2.c.b.1077.3 | 16 | 77.65 | odd | 6 | |||
1078.2.c.b.1077.6 | 16 | 77.54 | even | 6 | |||
1078.2.c.b.1077.11 | 16 | 7.2 | even | 3 | |||
1078.2.c.b.1077.14 | 16 | 7.5 | odd | 6 | |||
1078.2.i.c.901.2 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.c.901.6 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.c.1011.2 | 16 | 77.10 | even | 6 | inner | ||
1078.2.i.c.1011.6 | 16 | 7.3 | odd | 6 | inner | ||
1232.2.bn.b.241.3 | 16 | 308.263 | even | 6 | |||
1232.2.bn.b.241.4 | 16 | 28.11 | odd | 6 | |||
1232.2.bn.b.593.3 | 16 | 28.27 | even | 2 | |||
1232.2.bn.b.593.4 | 16 | 308.307 | odd | 2 | |||
1386.2.bk.c.703.2 | 16 | 21.11 | odd | 6 | |||
1386.2.bk.c.703.6 | 16 | 231.32 | even | 6 | |||
1386.2.bk.c.901.2 | 16 | 231.230 | odd | 2 | |||
1386.2.bk.c.901.6 | 16 | 21.20 | even | 2 |