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: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
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 | 901.6 | ||
Root | \(-0.347596 + 1.29724i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.901 |
Dual form | 1078.2.i.c.1011.6 |
$q$-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 | ||||
\(11\) | −2.58273 | − | 2.08075i | −0.778722 | − | 0.627369i | ||||
\(12\) | −1.35034 | − | 0.779618i | −0.389809 | − | 0.225056i | ||||
\(13\) | −0.167247 | −0.0463859 | −0.0231929 | − | 0.999731i | \(-0.507383\pi\) | ||||
−0.0231929 | + | 0.999731i | \(0.507383\pi\) | |||||||
\(14\) | 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 | 0.629609 | − | 0.776912i | \(-0.283215\pi\) |
−0.987630 | + | 0.156801i | \(0.949882\pi\) | |||||||
\(18\) | −0.492581 | + | 0.284392i | −0.116102 | + | 0.0670318i | ||||
\(19\) | −0.155850 | + | 0.269940i | −0.0357545 | + | 0.0619286i | −0.883349 | − | 0.468716i | \(-0.844717\pi\) |
0.847594 | + | 0.530645i | \(0.178050\pi\) | |||||||
\(20\) | − | 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 | \(-0.943641\pi\) | ||
0.984366 | − | 0.176133i | \(-0.0563589\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 5.10974 | + | 0.796171i | 0.889492 | + | 0.138596i | ||||
\(34\) | − | 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 | \(-0.793654\pi\) | ||||
−0.797138 | + | 0.603797i | \(0.793654\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.1222i | − | 1.54363i | −0.635848 | − | 0.771814i | \(-0.719350\pi\) | ||
0.635848 | − | 0.771814i | \(-0.280650\pi\) | |||||||
\(44\) | 0.510616 | − | 3.27708i | 0.0769783 | − | 0.494039i | ||||
\(45\) | 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 | \(-0.558293\pi\) |
0.942599 | − | 0.333926i | \(-0.108374\pi\) | |||||||
\(62\) | 2.54997 | 0.323846 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.147605 | + | 0.0852198i | 0.0183081 | + | 0.0105702i | ||||
\(66\) | 4.02708 | + | 3.24438i | 0.495700 | + | 0.399355i | ||||
\(67\) | 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 | \(-0.974345\pi\) |
0.428653 | − | 0.903469i | \(-0.358988\pi\) | |||||||
\(74\) | −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 | 0.118233 | − | 0.992986i | \(-0.462277\pi\) |
−0.800834 | + | 0.598886i | \(0.795610\pi\) | |||||||
\(80\) | 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 | \(-0.798535\pi\) | ||||
−0.806303 | + | 0.591502i | \(0.798535\pi\) | |||||||
\(84\) | 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 | ||||
\(88\) | 2.08075 | − | 2.58273i | 0.221808 | − | 0.275320i | ||||
\(89\) | −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 | 0.702248 | − | 0.711933i | \(-0.252180\pi\) |
−0.967676 | + | 0.252198i | \(0.918847\pi\) | |||||||
\(102\) | 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 | 0.164590 | − | 0.986362i | \(-0.447370\pi\) |
−0.771920 | + | 0.635720i | \(0.780703\pi\) | |||||||
\(108\) | 4.81906 | − | 2.78229i | 0.463715 | − | 0.267726i | ||||
\(109\) | −1.01103 | + | 0.583716i | −0.0968387 | + | 0.0559098i | −0.547637 | − | 0.836716i | \(-0.684473\pi\) |
0.450799 | + | 0.892626i | \(0.351139\pi\) | |||||||
\(110\) | −0.520365 | + | 3.33965i | −0.0496148 | + | 0.318423i | ||||
\(111\) | − | 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 | ||||||||
\(121\) | 2.34098 | + | 10.7480i | 0.212816 | + | 0.977092i | ||||
\(122\) | 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 | \(0.0501057\pi\) | ||||
−0.987636 | + | 0.156762i | \(0.949894\pi\) | |||||||
\(128\) | −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 | \(0.375781\pi\) |
−0.991122 | + | 0.132957i | \(0.957553\pi\) | |||||||
\(132\) | 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 | \(-0.338429\pi\) | ||||
0.486074 | + | 0.873918i | \(0.338429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.92291 | −0.498799 | ||||||||
\(142\) | 12.5752 | + | 7.26030i | 1.05529 | + | 0.609270i | ||||
\(143\) | 0.431953 | + | 0.347998i | 0.0361217 | + | 0.0291011i | ||||
\(144\) | −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 | −0.0948474 | − | 0.995492i | \(-0.530236\pi\) |
−0.909545 | + | 0.415606i | \(0.863570\pi\) | |||||||
\(150\) | 3.08842 | + | 5.34930i | 0.252168 | + | 0.436768i | ||||
\(151\) | −20.1819 | + | 11.6520i | −1.64238 | + | 0.948228i | −0.662394 | + | 0.749156i | \(0.730459\pi\) |
−0.979985 | + | 0.199072i | \(0.936207\pi\) | |||||||
\(152\) | −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 | ||||
\(165\) | −4.10397 | − | 3.30632i | −0.319493 | − | 0.257396i | ||||
\(166\) | −12.7233 | − | 7.34577i | −0.987516 | − | 0.570143i | ||||
\(167\) | 21.2252 | 1.64245 | 0.821226 | − | 0.570603i | \(-0.193291\pi\) | ||||
0.821226 | + | 0.570603i | \(0.193291\pi\) | |||||||
\(168\) | 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 | \(0.360773\pi\) |
−0.996287 | + | 0.0860973i | \(0.972560\pi\) | |||||||
\(174\) | 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 | ||||
\(187\) | −1.50750 | + | 9.67499i | −0.110239 | + | 0.707505i | ||||
\(188\) | 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 | −0.768419 | − | 0.639947i | \(-0.778956\pi\) |
0.170001 | + | 0.985444i | \(0.445623\pi\) | |||||||
\(194\) | −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 | \(-0.822991\pi\) | ||
0.849325 | − | 0.527870i | \(-0.177009\pi\) | |||||||
\(198\) | 1.86395 | + | 0.290430i | 0.132465 | + | 0.0206400i | ||||
\(199\) | −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 | \(0.0833950\pi\) | ||||
−0.965876 | + | 0.259006i | \(0.916605\pi\) | |||||||
\(212\) | 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 | ||||
\(220\) | −2.12047 | + | 2.63204i | −0.142962 | + | 0.177452i | ||||
\(221\) | 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 | \(-0.911299\pi\) |
0.242496 | − | 0.970152i | \(-0.422034\pi\) | |||||||
\(228\) | 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 | −0.0354345 | − | 0.999372i | \(-0.511282\pi\) |
−0.883199 | + | 0.468999i | \(0.844615\pi\) | |||||||
\(234\) | 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 | \(0.319311\pi\) | ||||
−0.537652 | + | 0.843167i | \(0.680689\pi\) | |||||||
\(240\) | −0.794502 | + | 1.37612i | −0.0512849 | + | 0.0888280i | ||||
\(241\) | 6.60221 | + | 11.4354i | 0.425286 | + | 0.736617i | 0.996447 | − | 0.0842210i | \(-0.0268402\pi\) |
−0.571161 | + | 0.820838i | \(0.693507\pi\) | |||||||
\(242\) | −3.34666 | + | 10.4785i | −0.215132 | + | 0.673586i | ||||
\(243\) | 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 | −0.375857 | − | 0.926678i | \(-0.622652\pi\) |
0.614598 | + | 0.788840i | \(0.289318\pi\) | |||||||
\(264\) | −0.796171 | + | 5.10974i | −0.0490010 | + | 0.314483i | ||||
\(265\) | 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 | \(-0.593677\pi\) |
0.973825 | − | 0.227299i | \(-0.0729893\pi\) | |||||||
\(272\) | 2.95232 | 0.179011 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.01058i | 0.423524i | ||||||||
\(275\) | −2.02278 | + | 12.9820i | −0.121978 | + | 0.782845i | ||||
\(276\) | −0.642003 | + | 0.370660i | −0.0386440 | + | 0.0223111i | ||||
\(277\) | 21.1880 | − | 12.2329i | 1.27306 | − | 0.735004i | 0.297500 | − | 0.954722i | \(-0.403847\pi\) |
0.975563 | + | 0.219718i | \(0.0705138\pi\) | |||||||
\(278\) | 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 | \(0.109966\pi\) | ||||
−0.940917 | + | 0.338636i | \(0.890034\pi\) | |||||||
\(282\) | −5.12939 | − | 2.96145i | −0.305451 | − | 0.176352i | ||||
\(283\) | 10.8268 | + | 18.7526i | 0.643589 | + | 1.11473i | 0.984626 | + | 0.174679i | \(0.0558886\pi\) |
−0.341037 | + | 0.940050i | \(0.610778\pi\) | |||||||
\(284\) | 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 | \(-0.384779\pi\) | ||||
0.354124 | + | 0.935198i | \(0.384779\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.36169 | 0.370392 | ||||||||
\(296\) | −5.27699 | − | 3.04667i | −0.306719 | − | 0.177084i | ||||
\(297\) | −11.5785 | + | 14.3718i | −0.671852 | + | 0.833936i | ||||
\(298\) | −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 | \(-0.411120\pi\) | ||||
0.275610 | + | 0.961269i | \(0.411120\pi\) | |||||||
\(308\) | 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 | ||||
\(319\) | −3.94720 | + | 4.89946i | −0.221001 | + | 0.274317i | ||||
\(320\) | 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 | \(-0.870292\pi\) | ||
0.918118 | − | 0.396307i | \(-0.129708\pi\) | |||||||
\(338\) | −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 | ||||
\(341\) | −8.35645 | − | 1.30205i | −0.452527 | − | 0.0705102i | ||||
\(342\) | − | 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 | 0.342102 | − | 0.939663i | \(-0.388861\pi\) |
0.984823 | + | 0.173562i | \(0.0555278\pi\) | |||||||
\(348\) | −1.47894 | + | 2.56161i | −0.0792797 | + | 0.137316i | ||||
\(349\) | −34.6026 | −1.85224 | −0.926118 | − | 0.377235i | \(-0.876875\pi\) | ||||
−0.926118 | + | 0.377235i | \(0.876875\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.930656i | 0.0496748i | ||||||||
\(352\) | 3.27708 | + | 0.510616i | 0.174669 | + | 0.0272159i | ||||
\(353\) | 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 | −0.394254 | − | 0.919002i | \(-0.628997\pi\) |
−0.993006 | + | 0.118067i | \(0.962330\pi\) | |||||||
\(360\) | 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 | 0.280567 | − | 0.959834i | \(-0.409478\pi\) |
−0.690958 | + | 0.722895i | \(0.742811\pi\) | |||||||
\(374\) | −6.14303 | + | 7.62504i | −0.317649 | + | 0.394281i | ||||
\(375\) | −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 | ||||
\(396\) | 1.46901 | + | 1.18350i | 0.0738207 | + | 0.0594729i | ||||
\(397\) | −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 | \(-0.966031\pi\) |
0.404913 | − | 0.914355i | \(-0.367302\pi\) | |||||||
\(410\) | 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 | ||||
\(418\) | 1.02147 | + | 0.159159i | 0.0499616 | + | 0.00778473i | ||||
\(419\) | − | 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 | ||||||
\(429\) | −0.854588 | − | 0.133157i | −0.0412599 | − | 0.00642888i | ||||
\(430\) | −8.93348 | + | 5.15775i | −0.430811 | + | 0.248729i | ||||
\(431\) | 5.19535 | − | 2.99953i | 0.250251 | − | 0.144482i | −0.369628 | − | 0.929180i | \(-0.620515\pi\) |
0.619879 | + | 0.784697i | \(0.287182\pi\) | |||||||
\(432\) | 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 | −0.698234 | − | 0.715869i | \(-0.746031\pi\) |
0.969078 | + | 0.246754i | \(0.0793639\pi\) | |||||||
\(440\) | −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 | ||||
\(451\) | 26.3654 | + | 21.2410i | 1.24150 | + | 1.00020i | ||||
\(452\) | −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 | 0.748158 | − | 0.663521i | \(-0.230939\pi\) |
−0.200547 | + | 0.979684i | \(0.564272\pi\) | |||||||
\(458\) | −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 | \(-0.642374\pi\) | ||||
−0.432516 | + | 0.901626i | \(0.642374\pi\) | |||||||
\(462\) | 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 | ||||
\(473\) | −21.0618 | + | 26.1430i | −0.968425 | + | 1.20206i | ||||
\(474\) | 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 | 0.775861 | − | 0.630904i | \(-0.217316\pi\) |
−0.934309 | + | 0.356464i | \(0.883982\pi\) | |||||||
\(480\) | −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 | \(0.0170417\pi\) | ||||
−0.998567 | + | 0.0535125i | \(0.982958\pi\) | |||||||
\(492\) | 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 | ||||
\(495\) | −1.89954 | − | 0.295975i | −0.0853778 | − | 0.0133031i | ||||
\(496\) | 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 | \(-0.646081\pi\) | ||||
−0.442986 | + | 0.896529i | \(0.646081\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.43689i | 0.241938i | ||||||||
\(506\) | −1.55805 | − | 0.242767i | −0.0692638 | − | 0.0107923i | ||||
\(507\) | 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 | −0.948354 | − | 0.317214i | \(-0.897253\pi\) |
0.748892 | + | 0.662692i | \(0.230586\pi\) | |||||||
\(524\) | −13.9797 | −0.610705 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.47070 | 0.194932 | ||||||||
\(527\) | −6.51971 | − | 3.76416i | −0.284003 | − | 0.163969i | ||||
\(528\) | −3.24438 | + | 4.02708i | −0.141193 | + | 0.175256i | ||||
\(529\) | 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 | 0.887379 | − | 0.461040i | \(-0.152524\pi\) |
0.0444172 | + | 0.999013i | \(0.485857\pi\) | |||||||
\(542\) | 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 | \(-0.712603\pi\) | ||
0.619348 | − | 0.785116i | \(-0.287397\pi\) | |||||||
\(548\) | −3.50529 | + | 6.07134i | −0.149738 | + | 0.259355i | ||||
\(549\) | 3.37835 | + | 5.85147i | 0.144184 | + | 0.249735i | ||||
\(550\) | −8.24279 | + | 10.2314i | −0.351474 | + | 0.436267i | ||||
\(551\) | 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 | 0.426350 | − | 0.904558i | \(-0.359799\pi\) |
0.996545 | + | 0.0830490i | \(0.0264658\pi\) | |||||||
\(558\) | −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 | \(-0.801692\pi\) |
−0.0992415 | − | 0.995063i | \(-0.531642\pi\) | |||||||
\(564\) | −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 | 0.834531 | − | 0.550961i | \(-0.185739\pi\) |
−0.0598803 | + | 0.998206i | \(0.519072\pi\) | |||||||
\(570\) | −0.428936 | + | 0.247646i | −0.0179662 | + | 0.0103728i | ||||
\(571\) | −19.5677 | + | 11.2974i | −0.818883 | + | 0.472782i | −0.850031 | − | 0.526733i | \(-0.823417\pi\) |
0.0311482 | + | 0.999515i | \(0.490084\pi\) | |||||||
\(572\) | −0.0853989 | + | 0.548081i | −0.00357071 | + | 0.0229164i | ||||
\(573\) | − | 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 | ||||||
\(583\) | −4.30019 | + | 27.5982i | −0.178096 | + | 1.14300i | ||||
\(584\) | 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 | −0.882162 | − | 0.470946i | \(-0.843913\pi\) |
0.848932 | + | 0.528502i | \(0.177246\pi\) | |||||||
\(594\) | −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 | \(-0.733216\pi\) | ||||
−0.668857 | + | 0.743391i | \(0.733216\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.90569 | −0.240498 | ||||||||
\(604\) | −20.1819 | − | 11.6520i | −0.821189 | − | 0.474114i | ||||
\(605\) | 3.41056 | − | 10.6786i | 0.138659 | − | 0.434147i | ||||
\(606\) | 4.15929 | + | 7.20410i | 0.168960 | + | 0.292647i | ||||
\(607\) | 0.332910 | − | 0.576616i | 0.0135124 | − | 0.0234041i | −0.859190 | − | 0.511656i | \(-0.829032\pi\) |
0.872703 | + | 0.488252i | \(0.162365\pi\) | |||||||
\(608\) | − | 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 | −0.573222 | − | 0.819400i | \(-0.694307\pi\) |
0.423010 | + | 0.906125i | \(0.360973\pi\) | |||||||
\(614\) | 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 | ||||
\(627\) | −1.01127 | + | 1.25524i | −0.0403864 | + | 0.0501296i | ||||
\(628\) | −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 | ||||
\(649\) | 20.4572 | + | 3.18753i | 0.803016 | + | 0.125121i | ||||
\(650\) | 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 | \(0.159234\pi\) | ||||
−0.877464 | + | 0.479643i | \(0.840766\pi\) | |||||||
\(660\) | 0.811371 | − | 5.20730i | 0.0315826 | − | 0.202694i | ||||
\(661\) | −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 | \(0.0994752\pi\) | ||||
−0.951565 | + | 0.307449i | \(0.900525\pi\) | |||||||
\(674\) | 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 | −0.684390 | − | 0.729116i | \(-0.739932\pi\) |
0.973628 | + | 0.228141i | \(0.0732649\pi\) | |||||||
\(678\) | 13.0997 | 0.503091 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −3.00868 | −0.115378 | ||||||||
\(681\) | 29.2531 | + | 16.8893i | 1.12098 | + | 0.647198i | ||||
\(682\) | −6.58587 | − | 5.30584i | −0.252186 | − | 0.203171i | ||||
\(683\) | 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 | \(-0.877204\pi\) | ||
0.926507 | − | 0.376278i | \(-0.122796\pi\) | |||||||
\(702\) | −0.465328 | + | 0.805972i | −0.0175627 | + | 0.0304195i | ||||
\(703\) | −0.949649 | − | 1.64484i | −0.0358167 | − | 0.0620363i | ||||
\(704\) | 2.58273 | + | 2.08075i | 0.0973403 | + | 0.0784211i | ||||
\(705\) | 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 | ||||
\(726\) | −3.65013 | − | 16.7587i | −0.135469 | − | 0.621973i | ||||
\(727\) | 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 | −0.773157 | − | 0.634214i | \(-0.781324\pi\) |
0.935824 | + | 0.352467i | \(0.114657\pi\) | |||||||
\(734\) | 17.4215 | 0.643040 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.475438i | 0.0175249i | ||||||||
\(737\) | 5.30174 | − | 34.0260i | 0.195292 | − | 1.25336i | ||||
\(738\) | 5.02844 | − | 2.90317i | 0.185099 | − | 0.106867i | ||||
\(739\) | 28.4003 | − | 16.3969i | 1.04472 | − | 0.603170i | 0.123555 | − | 0.992338i | \(-0.460571\pi\) |
0.921167 | + | 0.389167i | \(0.127237\pi\) | |||||||
\(740\) | 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 | \(-0.843360\pi\) | ||
0.881344 | − | 0.472476i | \(-0.156640\pi\) | |||||||
\(744\) | −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 | ||||
\(759\) | 1.54250 | − | 1.91463i | 0.0559893 | − | 0.0694967i | ||||
\(760\) | 0.158826 | + | 0.275094i | 0.00576121 | + | 0.00997871i | ||||
\(761\) | 13.0047 | − | 22.5249i | 0.471421 | − | 0.816526i | −0.528044 | − | 0.849217i | \(-0.677074\pi\) |
0.999466 | + | 0.0326910i | \(0.0104077\pi\) | |||||||
\(762\) | − | 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 | \(-0.763759\pi\) | ||||
−0.737001 | + | 0.675891i | \(0.763759\pi\) | |||||||
\(770\) | 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 | ||||
\(781\) | −37.5027 | − | 30.2137i | −1.34195 | − | 1.08113i | ||||
\(782\) | −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 | 0.996909 | − | 0.0785692i | \(-0.0250352\pi\) |
−0.566497 | + | 0.824064i | \(0.691702\pi\) | |||||||
\(788\) | 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 | ||||
\(803\) | −4.95691 | + | 31.8130i | −0.174926 | + | 1.12265i | ||||
\(804\) | − | 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 | −0.0274911 | − | 0.999622i | \(-0.508752\pi\) |
0.851953 | + | 0.523619i | \(0.175418\pi\) | |||||||
\(810\) | 3.55160 | − | 6.15156i | 0.124791 | − | 0.216144i | ||||
\(811\) | 23.5808 | 0.828033 | 0.414016 | − | 0.910269i | \(-0.364126\pi\) | ||||
0.414016 | + | 0.910269i | \(0.364126\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 35.1018i | 1.23107i | ||||||||
\(814\) | 19.9684 | + | 3.11136i | 0.699892 | + | 0.109053i | ||||
\(815\) | −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 | −0.110826 | − | 0.993840i | \(-0.535350\pi\) |
−0.916104 | + | 0.400942i | \(0.868683\pi\) | |||||||
\(822\) | −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 | \(0.0958557\pi\) | ||||
−0.954999 | + | 0.296609i | \(0.904144\pi\) | |||||||
\(828\) | −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 | ||||
\(836\) | 0.805037 | + | 0.648570i | 0.0278428 | + | 0.0224313i | ||||
\(837\) | −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 | \(-0.141700\pi\) | ||||
0.902541 | + | 0.430605i | \(0.141700\pi\) | |||||||
\(854\) | 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 | 0.616466 | − | 0.787382i | \(-0.288564\pi\) |
−0.990125 | + | 0.140184i | \(0.955230\pi\) | |||||||
\(858\) | −0.673516 | − | 0.542611i | −0.0229935 | − | 0.0185244i | ||||
\(859\) | −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 | 0.692773 | − | 0.721156i | \(-0.256389\pi\) |
−0.278153 | + | 0.960537i | \(0.589722\pi\) | |||||||
\(878\) | 9.82906 | − | 5.67481i | 0.331715 | − | 0.191516i | ||||
\(879\) | −16.3705 | + | 9.45151i | −0.552163 | + | 0.318792i | ||||
\(880\) | −3.33965 | − | 0.520365i | −0.112579 | − | 0.0175415i | ||||
\(881\) | 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 | −0.931639 | − | 0.363385i | \(-0.881621\pi\) |
0.780520 | + | 0.625131i | \(0.214954\pi\) | |||||||
\(888\) | 9.50096 | 0.318831 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.03268i | 0.235736i | ||||||||
\(891\) | 3.55906 | − | 22.8417i | 0.119233 | − | 0.765226i | ||||
\(892\) | −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 | ||||
\(913\) | 37.9443 | + | 30.5694i | 1.25577 | + | 1.01170i | ||||
\(914\) | 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 | 0.168181 | − | 0.985756i | \(-0.446211\pi\) |
−0.769600 | + | 0.638527i | \(0.779544\pi\) | |||||||
\(920\) | −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 | ||||
\(935\) | 6.26031 | − | 7.77061i | 0.204734 | − | 0.254126i | ||||
\(936\) | 0.0823825 | + | 0.0475636i | 0.00269276 | + | 0.00155466i | ||||
\(937\) | 43.2128 | 1.41170 | 0.705850 | − | 0.708362i | \(-0.250565\pi\) | ||||
0.705850 | + | 0.708362i | \(0.250565\pi\) | |||||||
\(938\) | 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 | 0.964141 | − | 0.265390i | \(-0.0855006\pi\) |
−0.711905 | + | 0.702276i | \(0.752167\pi\) | |||||||
\(942\) | 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 | \(0.135422\pi\) | ||||
−0.910857 | + | 0.412722i | \(0.864578\pi\) | |||||||
\(954\) | 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 | ||||
\(957\) | 1.51035 | − | 9.69324i | 0.0488225 | − | 0.313338i | ||||
\(958\) | − | 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 | \(0.219988\pi\) | ||||
−0.770537 | + | 0.637395i | \(0.780012\pi\) | |||||||
\(968\) | −10.7480 | + | 2.34098i | −0.345454 | + | 0.0752418i | ||||
\(969\) | −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 | ||||
\(990\) | −1.49706 | − | 1.20609i | −0.0475797 | − | 0.0383320i | ||||
\(991\) | 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 | 0.831587 | − | 0.555395i | \(-0.187433\pi\) |
−0.896779 | + | 0.442478i | \(0.854100\pi\) | |||||||
\(998\) | 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.901.6 | 16 | ||
7.2 | even | 3 | 1078.2.c.b.1077.3 | 16 | |||
7.3 | odd | 6 | inner | 1078.2.i.c.1011.2 | 16 | ||
7.4 | even | 3 | 154.2.i.a.87.3 | ✓ | 16 | ||
7.5 | odd | 6 | 1078.2.c.b.1077.6 | 16 | |||
7.6 | odd | 2 | 154.2.i.a.131.7 | yes | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.c.901.2 | 16 | ||
21.11 | odd | 6 | 1386.2.bk.c.703.6 | 16 | |||
21.20 | even | 2 | 1386.2.bk.c.901.2 | 16 | |||
28.11 | odd | 6 | 1232.2.bn.b.241.3 | 16 | |||
28.27 | even | 2 | 1232.2.bn.b.593.4 | 16 | |||
77.10 | even | 6 | inner | 1078.2.i.c.1011.6 | 16 | ||
77.32 | odd | 6 | 154.2.i.a.87.7 | yes | 16 | ||
77.54 | even | 6 | 1078.2.c.b.1077.14 | 16 | |||
77.65 | odd | 6 | 1078.2.c.b.1077.11 | 16 | |||
77.76 | even | 2 | 154.2.i.a.131.3 | yes | 16 | ||
231.32 | even | 6 | 1386.2.bk.c.703.2 | 16 | |||
231.230 | odd | 2 | 1386.2.bk.c.901.6 | 16 | |||
308.263 | even | 6 | 1232.2.bn.b.241.4 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.b.593.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.3 | ✓ | 16 | 7.4 | even | 3 | ||
154.2.i.a.87.7 | yes | 16 | 77.32 | odd | 6 | ||
154.2.i.a.131.3 | yes | 16 | 77.76 | even | 2 | ||
154.2.i.a.131.7 | yes | 16 | 7.6 | odd | 2 | ||
1078.2.c.b.1077.3 | 16 | 7.2 | even | 3 | |||
1078.2.c.b.1077.6 | 16 | 7.5 | odd | 6 | |||
1078.2.c.b.1077.11 | 16 | 77.65 | odd | 6 | |||
1078.2.c.b.1077.14 | 16 | 77.54 | even | 6 | |||
1078.2.i.c.901.2 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.c.901.6 | 16 | 1.1 | even | 1 | trivial | ||
1078.2.i.c.1011.2 | 16 | 7.3 | odd | 6 | inner | ||
1078.2.i.c.1011.6 | 16 | 77.10 | even | 6 | inner | ||
1232.2.bn.b.241.3 | 16 | 28.11 | odd | 6 | |||
1232.2.bn.b.241.4 | 16 | 308.263 | even | 6 | |||
1232.2.bn.b.593.3 | 16 | 308.307 | odd | 2 | |||
1232.2.bn.b.593.4 | 16 | 28.27 | even | 2 | |||
1386.2.bk.c.703.2 | 16 | 231.32 | even | 6 | |||
1386.2.bk.c.703.6 | 16 | 21.11 | odd | 6 | |||
1386.2.bk.c.901.2 | 16 | 21.20 | even | 2 | |||
1386.2.bk.c.901.6 | 16 | 231.230 | odd | 2 |