Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [325,2,Mod(101,325)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(325, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("325.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 325 = 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 325.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.59513806569\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 16x^{8} + 84x^{6} + 163x^{4} + 118x^{2} + 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(0.887996i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 325.251 |
Dual form | 325.2.n.e.101.4 |
$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).
\(n\) | \(27\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.769027 | + | 0.443998i | 0.543784 | + | 0.313954i | 0.746611 | − | 0.665261i | \(-0.231680\pi\) |
−0.202827 | + | 0.979215i | \(0.565013\pi\) | |||||||
\(3\) | −1.53097 | + | 2.65171i | −0.883904 | + | 1.53097i | −0.0369384 | + | 0.999318i | \(0.511761\pi\) |
−0.846965 | + | 0.531648i | \(0.821573\pi\) | |||||||
\(4\) | −0.605732 | − | 1.04916i | −0.302866 | − | 0.524579i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.35471 | + | 1.35949i | −0.961306 | + | 0.555010i | ||||
\(7\) | −3.08568 | + | 1.78152i | −1.16628 | + | 0.673351i | −0.952801 | − | 0.303597i | \(-0.901812\pi\) |
−0.213477 | + | 0.976948i | \(0.568479\pi\) | |||||||
\(8\) | − | 2.85177i | − | 1.00825i | ||||||
\(9\) | −3.18771 | − | 5.52128i | −1.06257 | − | 1.84043i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.816654 | + | 0.471496i | 0.246231 | + | 0.142161i | 0.618037 | − | 0.786149i | \(-0.287928\pi\) |
−0.371806 | + | 0.928310i | \(0.621262\pi\) | |||||||
\(12\) | 3.70942 | 1.07082 | ||||||||
\(13\) | −3.56247 | + | 0.555692i | −0.988052 | + | 0.154121i | ||||
\(14\) | −3.16396 | −0.845605 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.0547156 | − | 0.0947702i | 0.0136789 | − | 0.0236925i | ||||
\(17\) | −0.479950 | − | 0.831298i | −0.116405 | − | 0.201619i | 0.801936 | − | 0.597411i | \(-0.203804\pi\) |
−0.918341 | + | 0.395791i | \(0.870470\pi\) | |||||||
\(18\) | − | 5.66135i | − | 1.33439i | ||||||
\(19\) | −2.89222 | + | 1.66983i | −0.663521 | + | 0.383084i | −0.793617 | − | 0.608417i | \(-0.791805\pi\) |
0.130096 | + | 0.991501i | \(0.458471\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 10.9098i | − | 2.38071i | ||||||
\(22\) | 0.418686 | + | 0.725186i | 0.0892642 | + | 0.154610i | ||||
\(23\) | 3.29999 | − | 5.71576i | 0.688096 | − | 1.19182i | −0.284357 | − | 0.958718i | \(-0.591780\pi\) |
0.972453 | − | 0.233099i | \(-0.0748866\pi\) | |||||||
\(24\) | 7.56206 | + | 4.36596i | 1.54360 | + | 0.891197i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.98636 | − | 1.15439i | −0.585674 | − | 0.226394i | ||||
\(27\) | 10.3353 | 1.98903 | ||||||||
\(28\) | 3.73819 | + | 2.15824i | 0.706451 | + | 0.407870i | ||||
\(29\) | −4.19863 | + | 7.27224i | −0.779666 | + | 1.35042i | 0.152468 | + | 0.988308i | \(0.451278\pi\) |
−0.932134 | + | 0.362113i | \(0.882056\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.13976i | 0.743524i | 0.928328 | + | 0.371762i | \(0.121246\pi\) | ||||
−0.928328 | + | 0.371762i | \(0.878754\pi\) | |||||||
\(32\) | −4.85525 | + | 2.80318i | −0.858295 | + | 0.495537i | ||||
\(33\) | −2.50054 | + | 1.44369i | −0.435288 | + | 0.251314i | ||||
\(34\) | − | 0.852387i | − | 0.146183i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.86180 | + | 6.68883i | −0.643633 | + | 1.11480i | ||||
\(37\) | −6.90720 | − | 3.98787i | −1.13554 | − | 0.655602i | −0.190215 | − | 0.981743i | \(-0.560918\pi\) |
−0.945321 | + | 0.326141i | \(0.894252\pi\) | |||||||
\(38\) | −2.96560 | −0.481083 | ||||||||
\(39\) | 3.98049 | − | 10.2974i | 0.637389 | − | 1.64890i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.690562 | + | 0.398696i | 0.107848 | + | 0.0622659i | 0.552954 | − | 0.833212i | \(-0.313501\pi\) |
−0.445106 | + | 0.895478i | \(0.646834\pi\) | |||||||
\(42\) | 4.84392 | − | 8.38992i | 0.747433 | − | 1.29459i | ||||
\(43\) | 4.50437 | + | 7.80179i | 0.686910 | + | 1.18976i | 0.972833 | + | 0.231510i | \(0.0743665\pi\) |
−0.285923 | + | 0.958253i | \(0.592300\pi\) | |||||||
\(44\) | − | 1.14240i | − | 0.172223i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.07557 | − | 2.93038i | 0.748352 | − | 0.432061i | ||||
\(47\) | 10.5985i | 1.54595i | 0.634435 | + | 0.772976i | \(0.281233\pi\) | ||||
−0.634435 | + | 0.772976i | \(0.718767\pi\) | |||||||
\(48\) | 0.167535 | + | 0.290180i | 0.0241817 | + | 0.0418839i | ||||
\(49\) | 2.84762 | − | 4.93222i | 0.406803 | − | 0.704603i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.93915 | 0.411563 | ||||||||
\(52\) | 2.74091 | + | 3.40100i | 0.380096 | + | 0.471633i | ||||
\(53\) | −7.44476 | −1.02262 | −0.511308 | − | 0.859397i | \(-0.670839\pi\) | ||||
−0.511308 | + | 0.859397i | \(0.670839\pi\) | |||||||
\(54\) | 7.94815 | + | 4.58886i | 1.08161 | + | 0.624465i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 5.08048 | + | 8.79964i | 0.678907 | + | 1.17590i | ||||
\(57\) | − | 10.2258i | − | 1.35444i | ||||||
\(58\) | −6.45772 | + | 3.72837i | −0.847940 | + | 0.489558i | ||||
\(59\) | 0.869141 | − | 0.501799i | 0.113153 | − | 0.0653287i | −0.442356 | − | 0.896840i | \(-0.645857\pi\) |
0.555508 | + | 0.831511i | \(0.312524\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.26328 | − | 3.92012i | −0.289784 | − | 0.501920i | 0.683974 | − | 0.729506i | \(-0.260250\pi\) |
−0.973758 | + | 0.227586i | \(0.926917\pi\) | |||||||
\(62\) | −1.83805 | + | 3.18359i | −0.233432 | + | 0.404317i | ||||
\(63\) | 19.6725 | + | 11.3579i | 2.47851 | + | 1.43097i | ||||
\(64\) | −5.19729 | −0.649661 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.56398 | −0.315604 | ||||||||
\(67\) | −0.969702 | − | 0.559858i | −0.118468 | − | 0.0683975i | 0.439595 | − | 0.898196i | \(-0.355122\pi\) |
−0.558063 | + | 0.829799i | \(0.688455\pi\) | |||||||
\(68\) | −0.581442 | + | 1.00709i | −0.0705102 | + | 0.122127i | ||||
\(69\) | 10.1044 | + | 17.5013i | 1.21642 | + | 2.10690i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.60542 | + | 0.926890i | −0.190528 | + | 0.110002i | −0.592230 | − | 0.805769i | \(-0.701752\pi\) |
0.401702 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(72\) | −15.7454 | + | 9.09061i | −1.85561 | + | 1.07134i | ||||
\(73\) | 4.69721i | 0.549767i | 0.961478 | + | 0.274884i | \(0.0886393\pi\) | ||||
−0.961478 | + | 0.274884i | \(0.911361\pi\) | |||||||
\(74\) | −3.54121 | − | 6.13356i | −0.411658 | − | 0.713012i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.50382 | + | 2.02293i | 0.401916 | + | 0.232046i | ||||
\(77\) | −3.35991 | −0.382898 | ||||||||
\(78\) | 7.63313 | − | 6.15164i | 0.864281 | − | 0.696536i | ||||
\(79\) | 5.64117 | 0.634681 | 0.317340 | − | 0.948312i | \(-0.397210\pi\) | ||||
0.317340 | + | 0.948312i | \(0.397210\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.25989 | + | 10.8425i | −0.695544 | + | 1.20472i | ||||
\(82\) | 0.354041 | + | 0.613216i | 0.0390972 | + | 0.0677184i | ||||
\(83\) | − | 0.187778i | − | 0.0206114i | −0.999947 | − | 0.0103057i | \(-0.996720\pi\) | ||
0.999947 | − | 0.0103057i | \(-0.00328046\pi\) | |||||||
\(84\) | −11.4461 | + | 6.60840i | −1.24887 | + | 0.721035i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 7.99972i | 0.862632i | ||||||||
\(87\) | −12.8559 | − | 22.2671i | −1.37830 | − | 2.38728i | ||||
\(88\) | 1.34460 | − | 2.32891i | 0.143334 | − | 0.248262i | ||||
\(89\) | 8.21609 | + | 4.74356i | 0.870904 | + | 0.502817i | 0.867649 | − | 0.497178i | \(-0.165630\pi\) |
0.00325556 | + | 0.999995i | \(0.498964\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.0027 | − | 8.06130i | 1.04857 | − | 0.845054i | ||||
\(92\) | −7.99564 | −0.833603 | ||||||||
\(93\) | −10.9775 | − | 6.33784i | −1.13831 | − | 0.657203i | ||||
\(94\) | −4.70572 | + | 8.15054i | −0.485358 | + | 0.840664i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 17.1663i | − | 1.75203i | ||||||
\(97\) | 14.3274 | − | 8.27193i | 1.45473 | − | 0.839887i | 0.455983 | − | 0.889988i | \(-0.349288\pi\) |
0.998744 | + | 0.0501013i | \(0.0159544\pi\) | |||||||
\(98\) | 4.37979 | − | 2.52868i | 0.442426 | − | 0.255435i | ||||
\(99\) | − | 6.01197i | − | 0.604226i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.75291 | + | 4.76817i | −0.273924 | + | 0.474451i | −0.969863 | − | 0.243650i | \(-0.921655\pi\) |
0.695939 | + | 0.718101i | \(0.254988\pi\) | |||||||
\(102\) | 2.26028 | + | 1.30498i | 0.223802 | + | 0.129212i | ||||
\(103\) | 3.49795 | 0.344664 | 0.172332 | − | 0.985039i | \(-0.444870\pi\) | ||||
0.172332 | + | 0.985039i | \(0.444870\pi\) | |||||||
\(104\) | 1.58470 | + | 10.1593i | 0.155393 | + | 0.996205i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.72522 | − | 3.30546i | −0.556083 | − | 0.321054i | ||||
\(107\) | 2.87137 | − | 4.97336i | 0.277586 | − | 0.480793i | −0.693198 | − | 0.720747i | \(-0.743799\pi\) |
0.970784 | + | 0.239954i | \(0.0771324\pi\) | |||||||
\(108\) | −6.26043 | − | 10.8434i | −0.602410 | − | 1.04341i | ||||
\(109\) | − | 10.9903i | − | 1.05268i | −0.850275 | − | 0.526339i | \(-0.823564\pi\) | ||
0.850275 | − | 0.526339i | \(-0.176436\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 21.1494 | − | 12.2106i | 2.00741 | − | 1.15898i | ||||
\(112\) | 0.389908i | 0.0368428i | ||||||||
\(113\) | −6.85841 | − | 11.8791i | −0.645185 | − | 1.11749i | −0.984259 | − | 0.176733i | \(-0.943447\pi\) |
0.339074 | − | 0.940760i | \(-0.389886\pi\) | |||||||
\(114\) | 4.54023 | − | 7.86391i | 0.425231 | − | 0.736522i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.1730 | 0.944536 | ||||||||
\(117\) | 14.4243 | + | 17.8980i | 1.33352 | + | 1.65467i | ||||
\(118\) | 0.891191 | 0.0820408 | ||||||||
\(119\) | 2.96195 | + | 1.71008i | 0.271521 | + | 0.156763i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.05538 | − | 8.75618i | −0.459580 | − | 0.796016i | ||||
\(122\) | − | 4.01957i | − | 0.363915i | ||||||
\(123\) | −2.11445 | + | 1.22078i | −0.190654 | + | 0.110074i | ||||
\(124\) | 4.34327 | − | 2.50759i | 0.390037 | − | 0.225188i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.0858 | + | 17.4691i | 0.898515 | + | 1.55627i | ||||
\(127\) | −1.75673 | + | 3.04275i | −0.155885 | + | 0.270001i | −0.933381 | − | 0.358887i | \(-0.883156\pi\) |
0.777496 | + | 0.628888i | \(0.216490\pi\) | |||||||
\(128\) | 5.71364 | + | 3.29877i | 0.505019 | + | 0.291573i | ||||
\(129\) | −27.5841 | −2.42865 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.0781 | −1.57949 | −0.789744 | − | 0.613437i | \(-0.789787\pi\) | ||||
−0.789744 | + | 0.613437i | \(0.789787\pi\) | |||||||
\(132\) | 3.02931 | + | 1.74897i | 0.263668 | + | 0.152229i | ||||
\(133\) | 5.94965 | − | 10.3051i | 0.515900 | − | 0.893565i | ||||
\(134\) | −0.497152 | − | 0.861092i | −0.0429474 | − | 0.0743870i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.37067 | + | 1.36871i | −0.203283 | + | 0.117366i | ||||
\(137\) | 0.675682 | − | 0.390105i | 0.0577274 | − | 0.0333290i | −0.470858 | − | 0.882209i | \(-0.656056\pi\) |
0.528586 | + | 0.848880i | \(0.322722\pi\) | |||||||
\(138\) | 17.9453i | 1.52760i | ||||||||
\(139\) | −0.139418 | − | 0.241479i | −0.0118253 | − | 0.0204820i | 0.860052 | − | 0.510206i | \(-0.170431\pi\) |
−0.871877 | + | 0.489724i | \(0.837098\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.1042 | − | 16.2260i | −2.36680 | − | 1.36647i | ||||
\(142\) | −1.64615 | −0.138142 | ||||||||
\(143\) | −3.17131 | − | 1.22588i | −0.265199 | − | 0.102513i | ||||
\(144\) | −0.697671 | −0.0581392 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.08555 | + | 3.61228i | −0.172602 | + | 0.298955i | ||||
\(147\) | 8.71922 | + | 15.1021i | 0.719149 | + | 1.24560i | ||||
\(148\) | 9.66232i | 0.794238i | ||||||||
\(149\) | −0.00883675 | + | 0.00510190i | −0.000723935 | + | 0.000417964i | −0.500362 | − | 0.865816i | \(-0.666800\pi\) |
0.499638 | + | 0.866234i | \(0.333466\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.408335i | 0.0332298i | 0.999862 | + | 0.0166149i | \(0.00528893\pi\) | ||||
−0.999862 | + | 0.0166149i | \(0.994711\pi\) | |||||||
\(152\) | 4.76195 | + | 8.24794i | 0.386245 | + | 0.668997i | ||||
\(153\) | −3.05989 | + | 5.29988i | −0.247377 | + | 0.428470i | ||||
\(154\) | −2.58386 | − | 1.49180i | −0.208214 | − | 0.120212i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13.2147 | + | 2.06129i | −1.05802 | + | 0.165035i | ||||
\(157\) | 0.950895 | 0.0758897 | 0.0379448 | − | 0.999280i | \(-0.487919\pi\) | ||||
0.0379448 | + | 0.999280i | \(0.487919\pi\) | |||||||
\(158\) | 4.33821 | + | 2.50467i | 0.345129 | + | 0.199261i | ||||
\(159\) | 11.3977 | − | 19.7413i | 0.903894 | − | 1.56559i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 23.5160i | 1.85332i | ||||||||
\(162\) | −9.62806 | + | 5.55876i | −0.756451 | + | 0.436737i | ||||
\(163\) | −9.09442 | + | 5.25067i | −0.712330 | + | 0.411264i | −0.811923 | − | 0.583764i | \(-0.801579\pi\) |
0.0995930 | + | 0.995028i | \(0.468246\pi\) | |||||||
\(164\) | − | 0.966011i | − | 0.0754328i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.0833732 | − | 0.144407i | 0.00647102 | − | 0.0112081i | ||||
\(167\) | 6.90234 | + | 3.98507i | 0.534119 | + | 0.308374i | 0.742692 | − | 0.669633i | \(-0.233549\pi\) |
−0.208573 | + | 0.978007i | \(0.566882\pi\) | |||||||
\(168\) | −31.1121 | −2.40035 | ||||||||
\(169\) | 12.3824 | − | 3.95927i | 0.952493 | − | 0.304559i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.4392 | + | 10.6459i | 1.41008 | + | 0.814109i | ||||
\(172\) | 5.45688 | − | 9.45158i | 0.416083 | − | 0.720677i | ||||
\(173\) | 4.96645 | + | 8.60214i | 0.377592 | + | 0.654009i | 0.990711 | − | 0.135982i | \(-0.0434188\pi\) |
−0.613119 | + | 0.789990i | \(0.710086\pi\) | |||||||
\(174\) | − | 22.8320i | − | 1.73089i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.0893675 | − | 0.0515963i | 0.00673633 | − | 0.00388922i | ||||
\(177\) | 3.07295i | 0.230977i | ||||||||
\(178\) | 4.21227 | + | 7.29586i | 0.315723 | + | 0.546848i | ||||
\(179\) | −5.31430 | + | 9.20463i | −0.397209 | + | 0.687987i | −0.993380 | − | 0.114871i | \(-0.963355\pi\) |
0.596171 | + | 0.802857i | \(0.296688\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.66166 | 0.643816 | 0.321908 | − | 0.946771i | \(-0.395676\pi\) | ||||
0.321908 | + | 0.946771i | \(0.395676\pi\) | |||||||
\(182\) | 11.2715 | − | 1.75819i | 0.835502 | − | 0.130326i | ||||
\(183\) | 13.8600 | 1.02456 | ||||||||
\(184\) | −16.3000 | − | 9.41081i | −1.20165 | − | 0.693774i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −5.62798 | − | 9.74794i | −0.412663 | − | 0.714754i | ||||
\(187\) | − | 0.905177i | − | 0.0661931i | ||||||
\(188\) | 11.1195 | − | 6.41985i | 0.810974 | − | 0.468216i | ||||
\(189\) | −31.8915 | + | 18.4126i | −2.31977 | + | 1.33932i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.30436 | − | 9.18742i | −0.383810 | − | 0.664779i | 0.607793 | − | 0.794095i | \(-0.292055\pi\) |
−0.991603 | + | 0.129317i | \(0.958722\pi\) | |||||||
\(192\) | 7.95687 | − | 13.7817i | 0.574238 | − | 0.994609i | ||||
\(193\) | −17.7047 | − | 10.2218i | −1.27442 | − | 0.735784i | −0.298600 | − | 0.954378i | \(-0.596520\pi\) |
−0.975816 | + | 0.218594i | \(0.929853\pi\) | |||||||
\(194\) | 14.6909 | 1.05474 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.89957 | −0.492827 | ||||||||
\(197\) | 9.95644 | + | 5.74836i | 0.709367 | + | 0.409553i | 0.810827 | − | 0.585286i | \(-0.199018\pi\) |
−0.101459 | + | 0.994840i | \(0.532351\pi\) | |||||||
\(198\) | 2.66930 | − | 4.62337i | 0.189699 | − | 0.328569i | ||||
\(199\) | −4.97772 | − | 8.62167i | −0.352861 | − | 0.611174i | 0.633888 | − | 0.773425i | \(-0.281458\pi\) |
−0.986750 | + | 0.162251i | \(0.948125\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.96916 | − | 1.71425i | 0.209429 | − | 0.120914i | ||||
\(202\) | −4.23412 | + | 2.44457i | −0.297912 | + | 0.171999i | ||||
\(203\) | − | 29.9198i | − | 2.09995i | ||||||
\(204\) | −1.78033 | − | 3.08363i | −0.124648 | − | 0.215897i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.69002 | + | 1.55308i | 0.187423 | + | 0.108209i | ||||
\(207\) | −42.0777 | −2.92460 | ||||||||
\(208\) | −0.142260 | + | 0.368021i | −0.00986394 | + | 0.0255177i | ||||
\(209\) | −3.14926 | −0.217839 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.72848 | + | 9.92202i | −0.394365 | + | 0.683060i | −0.993020 | − | 0.117947i | \(-0.962369\pi\) |
0.598655 | + | 0.801007i | \(0.295702\pi\) | |||||||
\(212\) | 4.50952 | + | 7.81073i | 0.309715 | + | 0.536443i | ||||
\(213\) | − | 5.67615i | − | 0.388923i | ||||||
\(214\) | 4.41632 | − | 2.54977i | 0.301894 | − | 0.174298i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 29.4739i | − | 2.00545i | ||||||
\(217\) | −7.37507 | − | 12.7740i | −0.500652 | − | 0.867155i | ||||
\(218\) | 4.87967 | − | 8.45183i | 0.330493 | − | 0.572430i | ||||
\(219\) | −12.4557 | − | 7.19127i | −0.841675 | − | 0.485941i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.17175 | + | 2.69477i | 0.146088 | + | 0.181270i | ||||
\(222\) | 21.6859 | 1.45546 | ||||||||
\(223\) | −4.26839 | − | 2.46436i | −0.285833 | − | 0.165026i | 0.350228 | − | 0.936664i | \(-0.386104\pi\) |
−0.636061 | + | 0.771639i | \(0.719437\pi\) | |||||||
\(224\) | 9.98783 | − | 17.2994i | 0.667340 | − | 1.15587i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 12.1805i | − | 0.810233i | ||||||
\(227\) | −21.0243 | + | 12.1384i | −1.39543 | + | 0.805653i | −0.993910 | − | 0.110197i | \(-0.964852\pi\) |
−0.401522 | + | 0.915849i | \(0.631519\pi\) | |||||||
\(228\) | −10.7285 | + | 6.19408i | −0.710510 | + | 0.410213i | ||||
\(229\) | 28.3643i | 1.87437i | 0.348837 | + | 0.937183i | \(0.386577\pi\) | ||||
−0.348837 | + | 0.937183i | \(0.613423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.14391 | − | 8.90952i | 0.338445 | − | 0.586203i | ||||
\(232\) | 20.7387 | + | 11.9735i | 1.36156 | + | 0.786099i | ||||
\(233\) | 12.6827 | 0.830869 | 0.415435 | − | 0.909623i | \(-0.363629\pi\) | ||||
0.415435 | + | 0.909623i | \(0.363629\pi\) | |||||||
\(234\) | 3.14597 | + | 20.1684i | 0.205658 | + | 1.31845i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.05293 | − | 0.607911i | −0.0685401 | − | 0.0395716i | ||||
\(237\) | −8.63643 | + | 14.9587i | −0.560997 | + | 0.971675i | ||||
\(238\) | 1.51854 | + | 2.63020i | 0.0984326 | + | 0.170490i | ||||
\(239\) | 29.4374i | 1.90415i | 0.305872 | + | 0.952073i | \(0.401052\pi\) | ||||
−0.305872 | + | 0.952073i | \(0.598948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4631 | + | 6.04088i | −0.673989 | + | 0.389128i | −0.797586 | − | 0.603205i | \(-0.793890\pi\) |
0.123598 | + | 0.992332i | \(0.460557\pi\) | |||||||
\(242\) | − | 8.97832i | − | 0.577148i | ||||||
\(243\) | −3.66438 | − | 6.34689i | −0.235070 | − | 0.407153i | ||||
\(244\) | −2.74188 | + | 4.74908i | −0.175531 | + | 0.304029i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.16810 | −0.138233 | ||||||||
\(247\) | 9.37555 | − | 7.55589i | 0.596552 | − | 0.480770i | ||||
\(248\) | 11.8056 | 0.749659 | ||||||||
\(249\) | 0.497934 | + | 0.287482i | 0.0315553 | + | 0.0182184i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.96303 | + | 3.40006i | 0.123905 | + | 0.214610i | 0.921304 | − | 0.388842i | \(-0.127125\pi\) |
−0.797399 | + | 0.603452i | \(0.793791\pi\) | |||||||
\(252\) | − | 27.5195i | − | 1.73356i | ||||||
\(253\) | 5.38991 | − | 3.11186i | 0.338861 | − | 0.195641i | ||||
\(254\) | −2.70195 | + | 1.55997i | −0.169536 | + | 0.0978814i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 8.12658 | + | 14.0757i | 0.507912 | + | 0.879729i | ||||
\(257\) | 10.0300 | − | 17.3725i | 0.625654 | − | 1.08366i | −0.362760 | − | 0.931883i | \(-0.618165\pi\) |
0.988414 | − | 0.151782i | \(-0.0485012\pi\) | |||||||
\(258\) | −21.2129 | − | 12.2473i | −1.32066 | − | 0.762484i | ||||
\(259\) | 28.4179 | 1.76580 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 53.5361 | 3.31380 | ||||||||
\(262\) | −13.9025 | − | 8.02663i | −0.858901 | − | 0.495887i | ||||
\(263\) | −7.97260 | + | 13.8089i | −0.491612 | + | 0.851496i | −0.999953 | − | 0.00965925i | \(-0.996925\pi\) |
0.508342 | + | 0.861155i | \(0.330259\pi\) | |||||||
\(264\) | 4.11706 | + | 7.13096i | 0.253388 | + | 0.438880i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.15089 | − | 5.28327i | 0.561077 | − | 0.323938i | ||||
\(267\) | −25.1571 | + | 14.5245i | −1.53959 | + | 0.888883i | ||||
\(268\) | 1.35649i | 0.0828611i | ||||||||
\(269\) | −10.4030 | − | 18.0185i | −0.634282 | − | 1.09861i | −0.986667 | − | 0.162754i | \(-0.947962\pi\) |
0.352384 | − | 0.935855i | \(-0.385371\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.53510 | − | 4.35039i | −0.457725 | − | 0.264268i | 0.253362 | − | 0.967371i | \(-0.418464\pi\) |
−0.711087 | + | 0.703104i | \(0.751797\pi\) | |||||||
\(272\) | −0.105043 | −0.00636917 | ||||||||
\(273\) | 6.06247 | + | 38.8658i | 0.366917 | + | 2.35226i | ||||
\(274\) | 0.692824 | 0.0418550 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 12.2411 | − | 21.2021i | 0.736825 | − | 1.27622i | ||||
\(277\) | −4.32017 | − | 7.48276i | −0.259574 | − | 0.449595i | 0.706554 | − | 0.707659i | \(-0.250249\pi\) |
−0.966128 | + | 0.258064i | \(0.916915\pi\) | |||||||
\(278\) | − | 0.247605i | − | 0.0148504i | ||||||
\(279\) | 22.8568 | − | 13.1964i | 1.36840 | − | 0.790047i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.5197i | 0.746862i | 0.927658 | + | 0.373431i | \(0.121819\pi\) | ||||
−0.927658 | + | 0.373431i | \(0.878181\pi\) | |||||||
\(282\) | −14.4086 | − | 24.9564i | −0.858019 | − | 1.48613i | ||||
\(283\) | 10.1648 | − | 17.6060i | 0.604236 | − | 1.04657i | −0.387936 | − | 0.921686i | \(-0.626812\pi\) |
0.992172 | − | 0.124880i | \(-0.0398547\pi\) | |||||||
\(284\) | 1.94491 | + | 1.12289i | 0.115409 | + | 0.0666314i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.89454 | − | 2.35079i | −0.112026 | − | 0.139005i | ||||
\(287\) | −2.84114 | −0.167707 | ||||||||
\(288\) | 30.9543 | + | 17.8715i | 1.82400 | + | 1.05309i | ||||
\(289\) | 8.03930 | − | 13.9245i | 0.472900 | − | 0.819086i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 50.6562i | 2.96952i | ||||||||
\(292\) | 4.92812 | − | 2.84525i | 0.288396 | − | 0.166506i | ||||
\(293\) | −22.3448 | + | 12.9008i | −1.30540 | + | 0.753672i | −0.981325 | − | 0.192360i | \(-0.938386\pi\) |
−0.324074 | + | 0.946032i | \(0.605053\pi\) | |||||||
\(294\) | 15.4853i | 0.903119i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −11.3725 | + | 19.6977i | −0.661012 | + | 1.14491i | ||||
\(297\) | 8.44039 | + | 4.87306i | 0.489761 | + | 0.282764i | ||||
\(298\) | −0.00906094 | −0.000524886 | ||||||||
\(299\) | −8.57994 | + | 22.1960i | −0.496191 | + | 1.28363i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −27.7981 | − | 16.0492i | −1.60226 | − | 0.925062i | ||||
\(302\) | −0.181300 | + | 0.314021i | −0.0104326 | + | 0.0180699i | ||||
\(303\) | −8.42921 | − | 14.5998i | −0.484245 | − | 0.838738i | ||||
\(304\) | 0.365462i | 0.0209607i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4.70627 | + | 2.71717i | −0.269040 | + | 0.155330i | ||||
\(307\) | 5.73478i | 0.327301i | 0.986518 | + | 0.163650i | \(0.0523269\pi\) | ||||
−0.986518 | + | 0.163650i | \(0.947673\pi\) | |||||||
\(308\) | 2.03521 | + | 3.52508i | 0.115967 | + | 0.200860i | ||||
\(309\) | −5.35525 | + | 9.27556i | −0.304649 | + | 0.527668i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1145 | −0.913771 | −0.456886 | − | 0.889525i | \(-0.651035\pi\) | ||||
−0.456886 | + | 0.889525i | \(0.651035\pi\) | |||||||
\(312\) | −29.3658 | − | 11.3514i | −1.66251 | − | 0.642648i | ||||
\(313\) | 20.6515 | 1.16729 | 0.583646 | − | 0.812008i | \(-0.301626\pi\) | ||||
0.583646 | + | 0.812008i | \(0.301626\pi\) | |||||||
\(314\) | 0.731264 | + | 0.422196i | 0.0412676 | + | 0.0238259i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.41703 | − | 5.91847i | −0.192223 | − | 0.332940i | ||||
\(317\) | 19.2638i | 1.08196i | 0.841035 | + | 0.540981i | \(0.181947\pi\) | ||||
−0.841035 | + | 0.540981i | \(0.818053\pi\) | |||||||
\(318\) | 17.5302 | − | 10.1211i | 0.983047 | − | 0.567562i | ||||
\(319\) | −6.85766 | + | 3.95927i | −0.383955 | + | 0.221677i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.79194 | + | 15.2281i | 0.490718 | + | 0.849949i | ||||
\(322\) | −10.4411 | + | 18.0844i | −0.581857 | + | 1.00781i | ||||
\(323\) | 2.77624 | + | 1.60287i | 0.154474 | + | 0.0891858i | ||||
\(324\) | 15.1673 | 0.842625 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.32514 | −0.516472 | ||||||||
\(327\) | 29.1431 | + | 16.8258i | 1.61162 | + | 0.930467i | ||||
\(328\) | 1.13699 | − | 1.96932i | 0.0627797 | − | 0.108738i | ||||
\(329\) | −18.8814 | − | 32.7036i | −1.04097 | − | 1.80301i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 17.2245 | − | 9.94456i | 0.946743 | − | 0.546602i | 0.0546755 | − | 0.998504i | \(-0.482588\pi\) |
0.892068 | + | 0.451902i | \(0.149254\pi\) | |||||||
\(332\) | −0.197009 | + | 0.113743i | −0.0108123 | + | 0.00624247i | ||||
\(333\) | 50.8488i | 2.78649i | ||||||||
\(334\) | 3.53872 | + | 6.12925i | 0.193630 | + | 0.335377i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.03392 | − | 0.596935i | −0.0564051 | − | 0.0325655i | ||||
\(337\) | 14.2197 | 0.774599 | 0.387299 | − | 0.921954i | \(-0.373408\pi\) | ||||
0.387299 | + | 0.921954i | \(0.373408\pi\) | |||||||
\(338\) | 11.2803 | + | 2.45298i | 0.613569 | + | 0.133425i | ||||
\(339\) | 42.0000 | 2.28112 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.95188 | + | 3.38076i | −0.105700 | + | 0.183078i | ||||
\(342\) | 9.45347 | + | 16.3739i | 0.511185 | + | 0.885399i | ||||
\(343\) | − | 4.64891i | − | 0.251017i | ||||||
\(344\) | 22.2489 | − | 12.8454i | 1.19958 | − | 0.692578i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.82037i | 0.474186i | ||||||||
\(347\) | −2.74135 | − | 4.74816i | −0.147163 | − | 0.254894i | 0.783015 | − | 0.622003i | \(-0.213681\pi\) |
−0.930178 | + | 0.367109i | \(0.880348\pi\) | |||||||
\(348\) | −15.5745 | + | 26.9758i | −0.834879 | + | 1.44605i | ||||
\(349\) | 4.65835 | + | 2.68950i | 0.249356 | + | 0.143966i | 0.619469 | − | 0.785021i | \(-0.287348\pi\) |
−0.370113 | + | 0.928987i | \(0.620681\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −36.8193 | + | 5.74325i | −1.96527 | + | 0.306552i | ||||
\(352\) | −5.28675 | −0.281785 | ||||||||
\(353\) | 0.206468 | + | 0.119204i | 0.0109892 | + | 0.00634460i | 0.505485 | − | 0.862836i | \(-0.331314\pi\) |
−0.494495 | + | 0.869180i | \(0.664647\pi\) | |||||||
\(354\) | −1.36438 | + | 2.36318i | −0.0725161 | + | 0.125602i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.4933i | − | 0.609144i | ||||||
\(357\) | −9.06928 | + | 5.23615i | −0.479997 | + | 0.277126i | ||||
\(358\) | −8.17368 | + | 4.71908i | −0.431992 | + | 0.249411i | ||||
\(359\) | − | 0.536191i | − | 0.0282991i | −0.999900 | − | 0.0141495i | \(-0.995496\pi\) | ||
0.999900 | − | 0.0141495i | \(-0.00450409\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.92337 | + | 6.79547i | −0.206493 | + | 0.357656i | ||||
\(362\) | 6.66105 | + | 3.84576i | 0.350097 | + | 0.202129i | ||||
\(363\) | 30.9585 | 1.62490 | ||||||||
\(364\) | −14.5165 | − | 5.61141i | −0.760872 | − | 0.294118i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6587 | + | 6.15383i | 0.557141 | + | 0.321666i | ||||
\(367\) | −5.02206 | + | 8.69846i | −0.262149 | + | 0.454056i | −0.966813 | − | 0.255486i | \(-0.917765\pi\) |
0.704663 | + | 0.709542i | \(0.251098\pi\) | |||||||
\(368\) | −0.361122 | − | 0.625482i | −0.0188248 | − | 0.0326055i | ||||
\(369\) | − | 5.08372i | − | 0.264648i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.9722 | − | 13.2630i | 1.19265 | − | 0.688580i | ||||
\(372\) | 15.3561i | 0.796177i | ||||||||
\(373\) | −2.23436 | − | 3.87003i | −0.115691 | − | 0.200382i | 0.802365 | − | 0.596834i | \(-0.203575\pi\) |
−0.918056 | + | 0.396451i | \(0.870242\pi\) | |||||||
\(374\) | 0.401897 | − | 0.696106i | 0.0207816 | − | 0.0359948i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 30.2245 | 1.55871 | ||||||||
\(377\) | 10.9164 | − | 28.2403i | 0.562222 | − | 1.45445i | ||||
\(378\) | −32.7006 | −1.68194 | ||||||||
\(379\) | 22.5652 | + | 13.0280i | 1.15910 | + | 0.669205i | 0.951087 | − | 0.308922i | \(-0.0999682\pi\) |
0.208009 | + | 0.978127i | \(0.433302\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.37900 | − | 9.31670i | −0.275574 | − | 0.477309i | ||||
\(382\) | − | 9.42050i | − | 0.481995i | ||||||
\(383\) | −27.5903 | + | 15.9293i | −1.40980 | + | 0.813947i | −0.995368 | − | 0.0961340i | \(-0.969352\pi\) |
−0.414430 | + | 0.910081i | \(0.636019\pi\) | |||||||
\(384\) | −17.4948 | + | 10.1006i | −0.892777 | + | 0.515445i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.07695 | − | 15.7217i | −0.462005 | − | 0.800216i | ||||
\(387\) | 28.7173 | − | 49.7398i | 1.45978 | − | 2.52841i | ||||
\(388\) | −17.3571 | − | 10.0211i | −0.881174 | − | 0.508746i | ||||
\(389\) | −11.6351 | −0.589923 | −0.294962 | − | 0.955509i | \(-0.595307\pi\) | ||||
−0.294962 | + | 0.955509i | \(0.595307\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.33533 | −0.320391 | ||||||||
\(392\) | −14.0655 | − | 8.12075i | −0.710417 | − | 0.410160i | ||||
\(393\) | 27.6769 | − | 47.9378i | 1.39612 | − | 2.41814i | ||||
\(394\) | 5.10452 | + | 8.84128i | 0.257162 | + | 0.445417i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −6.30751 | + | 3.64164i | −0.316964 | + | 0.182999i | ||||
\(397\) | 6.99421 | − | 4.03811i | 0.351029 | − | 0.202667i | −0.314109 | − | 0.949387i | \(-0.601706\pi\) |
0.665138 | + | 0.746720i | \(0.268373\pi\) | |||||||
\(398\) | − | 8.84039i | − | 0.443129i | ||||||
\(399\) | 18.2174 | + | 31.5535i | 0.912012 | + | 1.57965i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 27.0408 | + | 15.6120i | 1.35035 | + | 0.779625i | 0.988298 | − | 0.152532i | \(-0.0487428\pi\) |
0.362052 | + | 0.932158i | \(0.382076\pi\) | |||||||
\(402\) | 3.04449 | 0.151845 | ||||||||
\(403\) | −2.30043 | − | 14.7478i | −0.114593 | − | 0.734640i | ||||
\(404\) | 6.67009 | 0.331849 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.2843 | − | 23.0091i | 0.659289 | − | 1.14192i | ||||
\(407\) | −3.76053 | − | 6.51343i | −0.186402 | − | 0.322858i | ||||
\(408\) | − | 8.38176i | − | 0.414959i | ||||||
\(409\) | −27.8828 | + | 16.0982i | −1.37872 | + | 0.796003i | −0.992005 | − | 0.126197i | \(-0.959723\pi\) |
−0.386712 | + | 0.922200i | \(0.626389\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.38895i | 0.117838i | ||||||||
\(412\) | −2.11882 | − | 3.66991i | −0.104387 | − | 0.180803i | ||||
\(413\) | −1.78793 | + | 3.09678i | −0.0879782 | + | 0.152383i | ||||
\(414\) | −32.3589 | − | 18.6824i | −1.59035 | − | 0.918191i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 15.7390 | − | 12.6843i | 0.771667 | − | 0.621897i | ||||
\(417\) | 0.853777 | 0.0418096 | ||||||||
\(418\) | −2.42187 | − | 1.39827i | −0.118457 | − | 0.0683914i | ||||
\(419\) | 10.9140 | − | 18.9036i | 0.533185 | − | 0.923503i | −0.466064 | − | 0.884751i | \(-0.654328\pi\) |
0.999249 | − | 0.0387522i | \(-0.0123383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.55712i | 0.222100i | 0.993815 | + | 0.111050i | \(0.0354214\pi\) | ||||
−0.993815 | + | 0.111050i | \(0.964579\pi\) | |||||||
\(422\) | −8.81072 | + | 5.08687i | −0.428899 | + | 0.247625i | ||||
\(423\) | 58.5174 | − | 33.7850i | 2.84521 | − | 1.64268i | ||||
\(424\) | 21.2307i | 1.03105i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.52020 | − | 4.36511i | 0.122104 | − | 0.211490i | ||||
\(427\) | 13.9675 | + | 8.06416i | 0.675936 | + | 0.390252i | ||||
\(428\) | −6.95712 | −0.336285 | ||||||||
\(429\) | 8.10586 | − | 6.53263i | 0.391355 | − | 0.315398i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −25.7415 | − | 14.8619i | −1.23993 | − | 0.715871i | −0.270847 | − | 0.962623i | \(-0.587304\pi\) |
−0.969079 | + | 0.246751i | \(0.920637\pi\) | |||||||
\(432\) | 0.565504 | − | 0.979481i | 0.0272078 | − | 0.0471253i | ||||
\(433\) | −3.89111 | − | 6.73960i | −0.186995 | − | 0.323884i | 0.757252 | − | 0.653123i | \(-0.226541\pi\) |
−0.944247 | + | 0.329238i | \(0.893208\pi\) | |||||||
\(434\) | − | 13.0981i | − | 0.628727i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.5305 | + | 6.65716i | −0.552213 | + | 0.318820i | ||||
\(437\) | 22.0417i | 1.05440i | ||||||||
\(438\) | −6.38582 | − | 11.0606i | −0.305126 | − | 0.528494i | ||||
\(439\) | 2.09941 | − | 3.63629i | 0.100199 | − | 0.173551i | −0.811567 | − | 0.584259i | \(-0.801385\pi\) |
0.911767 | + | 0.410708i | \(0.134719\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −36.3096 | −1.72903 | ||||||||
\(442\) | 0.473664 | + | 3.03661i | 0.0225299 | + | 0.144437i | ||||
\(443\) | −21.5287 | −1.02286 | −0.511430 | − | 0.859325i | \(-0.670884\pi\) | ||||
−0.511430 | + | 0.859325i | \(0.670884\pi\) | |||||||
\(444\) | −25.6217 | − | 14.7927i | −1.21595 | − | 0.702029i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.18834 | − | 3.79032i | −0.103621 | − | 0.179477i | ||||
\(447\) | − | 0.0312433i | − | 0.00147776i | ||||||
\(448\) | 16.0372 | − | 9.25906i | 0.757685 | − | 0.437450i | ||||
\(449\) | −20.8626 | + | 12.0450i | −0.984565 | + | 0.568439i | −0.903645 | − | 0.428282i | \(-0.859119\pi\) |
−0.0809197 | + | 0.996721i | \(0.525786\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.375967 | + | 0.651194i | 0.0177036 | + | 0.0306635i | ||||
\(452\) | −8.30871 | + | 14.3911i | −0.390809 | + | 0.676901i | ||||
\(453\) | −1.08279 | − | 0.625147i | −0.0508737 | − | 0.0293720i | ||||
\(454\) | −21.5577 | −1.01175 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −29.1615 | −1.36561 | ||||||||
\(457\) | −28.4266 | − | 16.4121i | −1.32974 | − | 0.767726i | −0.344481 | − | 0.938793i | \(-0.611945\pi\) |
−0.985259 | + | 0.171068i | \(0.945278\pi\) | |||||||
\(458\) | −12.5937 | + | 21.8129i | −0.588465 | + | 1.01925i | ||||
\(459\) | −4.96044 | − | 8.59173i | −0.231534 | − | 0.401028i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.9815 | − | 12.1137i | 0.977207 | − | 0.564191i | 0.0757814 | − | 0.997124i | \(-0.475855\pi\) |
0.901426 | + | 0.432934i | \(0.142522\pi\) | |||||||
\(462\) | 7.91162 | − | 4.56777i | 0.368082 | − | 0.212512i | ||||
\(463\) | 3.28092i | 0.152477i | 0.997090 | + | 0.0762385i | \(0.0242911\pi\) | ||||
−0.997090 | + | 0.0762385i | \(0.975709\pi\) | |||||||
\(464\) | 0.459461 | + | 0.795810i | 0.0213299 | + | 0.0369445i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 9.75332 | + | 5.63108i | 0.451814 | + | 0.260855i | ||||
\(467\) | 7.88097 | 0.364688 | 0.182344 | − | 0.983235i | \(-0.441632\pi\) | ||||
0.182344 | + | 0.983235i | \(0.441632\pi\) | |||||||
\(468\) | 10.0406 | − | 25.9747i | 0.464128 | − | 1.20068i | ||||
\(469\) | 3.98959 | 0.184222 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.45579 | + | 2.52150i | −0.0670792 | + | 0.116185i | ||||
\(472\) | −1.43101 | − | 2.47859i | −0.0658677 | − | 0.114086i | ||||
\(473\) | 8.49516i | 0.390608i | ||||||||
\(474\) | −13.2833 | + | 7.66912i | −0.610122 | + | 0.352254i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 4.14340i | − | 0.189912i | ||||||
\(477\) | 23.7318 | + | 41.1046i | 1.08660 | + | 1.88205i | ||||
\(478\) | −13.0701 | + | 22.6381i | −0.597814 | + | 1.03544i | ||||
\(479\) | −28.7996 | − | 16.6274i | −1.31589 | − | 0.759727i | −0.332821 | − | 0.942990i | \(-0.608001\pi\) |
−0.983064 | + | 0.183263i | \(0.941334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.8227 | + | 10.3684i | 1.22301 | + | 0.472759i | ||||
\(482\) | −10.7286 | −0.488673 | ||||||||
\(483\) | −62.3576 | − | 36.0022i | −2.83737 | − | 1.63816i | ||||
\(484\) | −6.12441 | + | 10.6078i | −0.278382 | + | 0.482172i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 6.50790i | − | 0.295204i | ||||||
\(487\) | −2.75596 | + | 1.59116i | −0.124885 | + | 0.0721022i | −0.561141 | − | 0.827720i | \(-0.689637\pi\) |
0.436256 | + | 0.899822i | \(0.356304\pi\) | |||||||
\(488\) | −11.1793 | + | 6.45435i | −0.506061 | + | 0.292175i | ||||
\(489\) | − | 32.1544i | − | 1.45407i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.2919 | − | 28.2185i | 0.735245 | − | 1.27348i | −0.219371 | − | 0.975642i | \(-0.570400\pi\) |
0.954616 | − | 0.297840i | \(-0.0962662\pi\) | |||||||
\(492\) | 2.56158 | + | 1.47893i | 0.115485 | + | 0.0666753i | ||||
\(493\) | 8.06053 | 0.363028 | ||||||||
\(494\) | 10.5649 | − | 1.64796i | 0.475335 | − | 0.0741451i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.392326 | + | 0.226510i | 0.0176160 | + | 0.0101706i | ||||
\(497\) | 3.30254 | − | 5.72017i | 0.148139 | − | 0.256585i | ||||
\(498\) | 0.255283 | + | 0.442163i | 0.0114395 | + | 0.0198138i | ||||
\(499\) | − | 9.77164i | − | 0.437439i | −0.975788 | − | 0.218719i | \(-0.929812\pi\) | ||
0.975788 | − | 0.218719i | \(-0.0701879\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.1345 | + | 12.2020i | −0.944219 | + | 0.545145i | ||||
\(502\) | 3.48632i | 0.155602i | ||||||||
\(503\) | 9.28730 | + | 16.0861i | 0.414100 | + | 0.717243i | 0.995334 | − | 0.0964943i | \(-0.0307629\pi\) |
−0.581233 | + | 0.813737i | \(0.697430\pi\) | |||||||
\(504\) | 32.3902 | − | 56.1015i | 1.44277 | − | 2.49896i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.52665 | 0.245689 | ||||||||
\(507\) | −8.45821 | + | 38.8961i | −0.375642 | + | 1.72744i | ||||
\(508\) | 4.25644 | 0.188849 | ||||||||
\(509\) | 1.70294 | + | 0.983191i | 0.0754814 | + | 0.0435792i | 0.537266 | − | 0.843413i | \(-0.319457\pi\) |
−0.461784 | + | 0.886992i | \(0.652791\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.36818 | − | 14.4941i | −0.370186 | − | 0.641181i | ||||
\(512\) | 1.23765i | 0.0546971i | ||||||||
\(513\) | −29.8921 | + | 17.2582i | −1.31977 | + | 0.761968i | ||||
\(514\) | 15.4267 | − | 8.90660i | 0.680442 | − | 0.392853i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 16.7086 | + | 28.9401i | 0.735554 | + | 1.27402i | ||||
\(517\) | −4.99715 | + | 8.65532i | −0.219774 | + | 0.380661i | ||||
\(518\) | 21.8541 | + | 12.6175i | 0.960215 | + | 0.554380i | ||||
\(519\) | −30.4139 | −1.33502 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −21.0065 | −0.920312 | −0.460156 | − | 0.887838i | \(-0.652206\pi\) | ||||
−0.460156 | + | 0.887838i | \(0.652206\pi\) | |||||||
\(522\) | 41.1707 | + | 23.7699i | 1.80199 | + | 1.04038i | ||||
\(523\) | −10.1448 | + | 17.5714i | −0.443603 | + | 0.768343i | −0.997954 | − | 0.0639401i | \(-0.979633\pi\) |
0.554351 | + | 0.832283i | \(0.312967\pi\) | |||||||
\(524\) | 10.9505 | + | 18.9667i | 0.478373 | + | 0.828566i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.2623 | + | 7.07964i | −0.534661 | + | 0.308687i | ||||
\(527\) | 3.44138 | − | 1.98688i | 0.149909 | − | 0.0865499i | ||||
\(528\) | 0.315969i | 0.0137508i | ||||||||
\(529\) | −10.2799 | − | 17.8053i | −0.446953 | − | 0.774145i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.54115 | − | 3.19918i | −0.240465 | − | 0.138833i | ||||
\(532\) | −14.4156 | −0.624994 | ||||||||
\(533\) | −2.68166 | − | 1.03660i | −0.116156 | − | 0.0449003i | ||||
\(534\) | −25.7953 | −1.11627 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.59658 | + | 2.76536i | −0.0689619 | + | 0.119446i | ||||
\(537\) | −16.2720 | − | 28.1840i | −0.702189 | − | 1.21623i | ||||
\(538\) | − | 18.4757i | − | 0.796542i | ||||||
\(539\) | 4.65104 | − | 2.68528i | 0.200335 | − | 0.115663i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.0546i | 1.80807i | 0.427458 | + | 0.904035i | \(0.359409\pi\) | ||||
−0.427458 | + | 0.904035i | \(0.640591\pi\) | |||||||
\(542\) | −3.86313 | − | 6.69114i | −0.165936 | − | 0.287409i | ||||
\(543\) | −13.2607 | + | 22.9682i | −0.569072 | + | 0.985661i | ||||
\(544\) | 4.66055 | + | 2.69077i | 0.199820 | + | 0.115366i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −12.5941 | + | 32.5806i | −0.538979 | + | 1.39432i | ||||
\(547\) | −31.0572 | −1.32791 | −0.663956 | − | 0.747772i | \(-0.731124\pi\) | ||||
−0.663956 | + | 0.747772i | \(0.731124\pi\) | |||||||
\(548\) | −0.818564 | − | 0.472598i | −0.0349673 | − | 0.0201884i | ||||
\(549\) | −14.4294 | + | 24.9924i | −0.615831 | + | 1.06665i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 28.0439i | − | 1.19471i | ||||||
\(552\) | 49.9095 | − | 28.8153i | 2.12429 | − | 1.22646i | ||||
\(553\) | −17.4068 | + | 10.0498i | −0.740214 | + | 0.427363i | ||||
\(554\) | − | 7.67259i | − | 0.325977i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −0.168900 | + | 0.292543i | −0.00716294 | + | 0.0124066i | ||||
\(557\) | −2.84783 | − | 1.64420i | −0.120667 | − | 0.0696669i | 0.438452 | − | 0.898755i | \(-0.355527\pi\) |
−0.559118 | + | 0.829088i | \(0.688860\pi\) | |||||||
\(558\) | 23.4367 | 0.992153 | ||||||||
\(559\) | −20.3821 | − | 25.2906i | −0.862070 | − | 1.06968i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.40027 | + | 1.38580i | 0.101339 | + | 0.0585083i | ||||
\(562\) | −5.55872 | + | 9.62798i | −0.234480 | + | 0.406132i | ||||
\(563\) | 18.2500 | + | 31.6100i | 0.769147 | + | 1.33220i | 0.938026 | + | 0.346565i | \(0.112652\pi\) |
−0.168879 | + | 0.985637i | \(0.554015\pi\) | |||||||
\(564\) | 39.3143i | 1.65543i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 15.6340 | − | 9.02632i | 0.657148 | − | 0.379404i | ||||
\(567\) | − | 44.6085i | − | 1.87338i | ||||||
\(568\) | 2.64327 | + | 4.57828i | 0.110909 | + | 0.192101i | ||||
\(569\) | −6.22813 | + | 10.7874i | −0.261097 | + | 0.452233i | −0.966534 | − | 0.256540i | \(-0.917418\pi\) |
0.705437 | + | 0.708773i | \(0.250751\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8215 | 0.536565 | 0.268282 | − | 0.963340i | \(-0.413544\pi\) | ||||
0.268282 | + | 0.963340i | \(0.413544\pi\) | |||||||
\(572\) | 0.634821 | + | 4.06976i | 0.0265432 | + | 0.170165i | ||||
\(573\) | 32.4832 | 1.35700 | ||||||||
\(574\) | −2.18491 | − | 1.26146i | −0.0911965 | − | 0.0526523i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 16.5675 | + | 28.6957i | 0.690311 | + | 1.19565i | ||||
\(577\) | 22.7641i | 0.947681i | 0.880611 | + | 0.473841i | \(0.157133\pi\) | ||||
−0.880611 | + | 0.473841i | \(0.842867\pi\) | |||||||
\(578\) | 12.3649 | − | 7.13886i | 0.514311 | − | 0.296938i | ||||
\(579\) | 54.2107 | − | 31.2986i | 2.25292 | − | 1.30072i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.334531 | + | 0.579424i | 0.0138787 | + | 0.0240386i | ||||
\(582\) | −22.4912 | + | 38.9560i | −0.932292 | + | 1.61478i | ||||
\(583\) | −6.07979 | − | 3.51017i | −0.251799 | − | 0.145376i | ||||
\(584\) | 13.3954 | 0.554304 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.9117 | −0.946474 | ||||||||
\(587\) | −16.1045 | − | 9.29792i | −0.664703 | − | 0.383766i | 0.129364 | − | 0.991597i | \(-0.458707\pi\) |
−0.794067 | + | 0.607831i | \(0.792040\pi\) | |||||||
\(588\) | 10.5630 | − | 18.2957i | 0.435611 | − | 0.754501i | ||||
\(589\) | −6.91268 | − | 11.9731i | −0.284832 | − | 0.493344i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −30.4860 | + | 17.6011i | −1.25402 | + | 0.724011i | ||||
\(592\) | −0.755863 | + | 0.436398i | −0.0310658 | + | 0.0179358i | ||||
\(593\) | − | 36.4829i | − | 1.49817i | −0.662473 | − | 0.749086i | \(-0.730493\pi\) | ||
0.662473 | − | 0.749086i | \(-0.269507\pi\) | |||||||
\(594\) | 4.32726 | + | 7.49503i | 0.177550 | + | 0.307525i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.0107054 | + | 0.00618076i | 0.000438510 | + | 0.000253174i | ||||
\(597\) | 30.4829 | 1.24758 | ||||||||
\(598\) | −16.4532 | + | 13.2598i | −0.672821 | + | 0.542236i | ||||
\(599\) | −46.6153 | −1.90465 | −0.952324 | − | 0.305089i | \(-0.901314\pi\) | ||||
−0.952324 | + | 0.305089i | \(0.901314\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.37814 | − | 2.38701i | 0.0562155 | − | 0.0973682i | −0.836548 | − | 0.547893i | \(-0.815430\pi\) |
0.892764 | + | 0.450525i | \(0.148763\pi\) | |||||||
\(602\) | −14.2517 | − | 24.6846i | −0.580854 | − | 1.00607i | ||||
\(603\) | 7.13867i | 0.290709i | ||||||||
\(604\) | 0.428408 | − | 0.247341i | 0.0174317 | − | 0.0100642i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | − | 14.9702i | − | 0.608123i | ||||||
\(607\) | 3.98927 | + | 6.90961i | 0.161919 | + | 0.280453i | 0.935557 | − | 0.353176i | \(-0.114898\pi\) |
−0.773638 | + | 0.633628i | \(0.781565\pi\) | |||||||
\(608\) | 9.36164 | − | 16.2148i | 0.379665 | − | 0.657598i | ||||
\(609\) | 79.3385 | + | 45.8061i | 3.21496 | + | 1.85616i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.88950 | − | 37.7569i | −0.238264 | − | 1.52748i | ||||
\(612\) | 7.41388 | 0.299688 | ||||||||
\(613\) | 24.5639 | + | 14.1820i | 0.992125 | + | 0.572804i | 0.905909 | − | 0.423473i | \(-0.139189\pi\) |
0.0862164 | + | 0.996276i | \(0.472522\pi\) | |||||||
\(614\) | −2.54623 | + | 4.41020i | −0.102757 | + | 0.177981i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 9.58169i | 0.386057i | ||||||||
\(617\) | 24.9567 | − | 14.4088i | 1.00472 | − | 0.580075i | 0.0950788 | − | 0.995470i | \(-0.469690\pi\) |
0.909641 | + | 0.415394i | \(0.136356\pi\) | |||||||
\(618\) | −8.23666 | + | 4.75544i | −0.331327 | + | 0.191292i | ||||
\(619\) | − | 11.8346i | − | 0.475671i | −0.971305 | − | 0.237836i | \(-0.923562\pi\) | ||
0.971305 | − | 0.237836i | \(-0.0764380\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.1065 | − | 59.0742i | 1.36865 | − | 2.37057i | ||||
\(622\) | −12.3925 | − | 7.15482i | −0.496895 | − | 0.286882i | ||||
\(623\) | −33.8030 | −1.35429 | ||||||||
\(624\) | −0.758091 | − | 0.940660i | −0.0303479 | − | 0.0376565i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.8816 | + | 9.16923i | 0.634755 | + | 0.366476i | ||||
\(627\) | 4.82141 | − | 8.35093i | 0.192549 | − | 0.333504i | ||||
\(628\) | −0.575987 | − | 0.997639i | −0.0229844 | − | 0.0398101i | ||||
\(629\) | 7.65592i | 0.305261i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0631 | − | 11.0061i | 0.758889 | − | 0.438145i | −0.0700074 | − | 0.997546i | \(-0.522302\pi\) |
0.828897 | + | 0.559401i | \(0.188969\pi\) | |||||||
\(632\) | − | 16.0873i | − | 0.639918i | ||||||
\(633\) | −17.5402 | − | 30.3806i | −0.697161 | − | 1.20752i | ||||
\(634\) | −8.55309 | + | 14.8144i | −0.339687 | + | 0.588354i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −27.6157 | −1.09503 | ||||||||
\(637\) | −7.40377 | + | 19.1533i | −0.293348 | + | 0.758882i | ||||
\(638\) | −7.03163 | −0.278385 | ||||||||
\(639\) | 10.2352 | + | 5.90932i | 0.404900 | + | 0.233769i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.18143 | − | 2.04629i | −0.0466636 | − | 0.0808237i | 0.841750 | − | 0.539867i | \(-0.181526\pi\) |
−0.888414 | + | 0.459043i | \(0.848192\pi\) | |||||||
\(642\) | 15.6144i | 0.616252i | ||||||||
\(643\) | −24.7766 | + | 14.3048i | −0.977093 | + | 0.564125i | −0.901391 | − | 0.433005i | \(-0.857453\pi\) |
−0.0757019 | + | 0.997130i | \(0.524120\pi\) | |||||||
\(644\) | 24.6720 | − | 14.2444i | 0.972213 | − | 0.561307i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.42334 | + | 2.46529i | 0.0560005 | + | 0.0969957i | ||||
\(647\) | 15.5023 | − | 26.8508i | 0.609458 | − | 1.05561i | −0.381872 | − | 0.924215i | \(-0.624720\pi\) |
0.991330 | − | 0.131397i | \(-0.0419462\pi\) | |||||||
\(648\) | 30.9201 | + | 17.8518i | 1.21466 | + | 0.701283i | ||||
\(649\) | 0.946384 | 0.0371488 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 45.1639 | 1.77011 | ||||||||
\(652\) | 11.0176 | + | 6.36099i | 0.431481 | + | 0.249116i | ||||
\(653\) | −9.87093 | + | 17.0970i | −0.386279 | + | 0.669056i | −0.991946 | − | 0.126663i | \(-0.959573\pi\) |
0.605666 | + | 0.795719i | \(0.292907\pi\) | |||||||
\(654\) | 14.9412 | + | 25.8789i | 0.584247 | + | 1.01195i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.0755690 | − | 0.0436298i | 0.00295047 | − | 0.00170346i | ||||
\(657\) | 25.9346 | − | 14.9734i | 1.01181 | − | 0.584167i | ||||
\(658\) | − | 33.5333i | − | 1.30726i | ||||||
\(659\) | 17.1915 | + | 29.7766i | 0.669687 | + | 1.15993i | 0.977992 | + | 0.208645i | \(0.0669052\pi\) |
−0.308304 | + | 0.951288i | \(0.599761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.52798 | + | 1.45953i | 0.0983271 | + | 0.0567692i | 0.548357 | − | 0.836244i | \(-0.315253\pi\) |
−0.450030 | + | 0.893013i | \(0.648587\pi\) | |||||||
\(662\) | 17.6615 | 0.686432 | ||||||||
\(663\) | −10.4706 | + | 1.63326i | −0.406646 | + | 0.0634306i | ||||
\(664\) | −0.535500 | −0.0207814 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −22.5767 | + | 39.1041i | −0.874831 | + | 1.51525i | ||||
\(667\) | 27.7109 | + | 47.9967i | 1.07297 | + | 1.85844i | ||||
\(668\) | − | 9.65552i | − | 0.373583i | ||||||
\(669\) | 13.0695 | − | 7.54569i | 0.505297 | − | 0.291733i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 4.26851i | − | 0.164784i | ||||||
\(672\) | 30.5821 | + | 52.9697i | 1.17973 | + | 2.04335i | ||||
\(673\) | 18.0933 | − | 31.3384i | 0.697444 | − | 1.20801i | −0.271906 | − | 0.962324i | \(-0.587654\pi\) |
0.969350 | − | 0.245684i | \(-0.0790126\pi\) | |||||||
\(674\) | 10.9354 | + | 6.31354i | 0.421215 | + | 0.243188i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.6543 | − | 10.5929i | −0.448243 | − | 0.407417i | ||||
\(677\) | −17.8383 | −0.685580 | −0.342790 | − | 0.939412i | \(-0.611372\pi\) | ||||
−0.342790 | + | 0.939412i | \(0.611372\pi\) | |||||||
\(678\) | 32.2991 | + | 18.6479i | 1.24044 | + | 0.716168i | ||||
\(679\) | −29.4732 | + | 51.0491i | −1.13108 | + | 1.95908i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 74.3338i | − | 2.84848i | ||||||
\(682\) | −3.00210 | + | 1.73326i | −0.114956 | + | 0.0663701i | ||||
\(683\) | 41.5607 | − | 23.9951i | 1.59028 | − | 0.918147i | 0.597018 | − | 0.802227i | \(-0.296352\pi\) |
0.993259 | − | 0.115919i | \(-0.0369814\pi\) | |||||||
\(684\) | − | 25.7941i | − | 0.986262i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 2.06411 | − | 3.57514i | 0.0788079 | − | 0.136499i | ||||
\(687\) | −75.2140 | − | 43.4248i | −2.86959 | − | 1.65676i | ||||
\(688\) | 0.985837 | 0.0375847 | ||||||||
\(689\) | 26.5217 | − | 4.13699i | 1.01040 | − | 0.157607i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.6535 | + | 15.3884i | 1.01395 | + | 0.585403i | 0.912345 | − | 0.409422i | \(-0.134270\pi\) |
0.101603 | + | 0.994825i | \(0.467603\pi\) | |||||||
\(692\) | 6.01667 | − | 10.4212i | 0.228719 | − | 0.396154i | ||||
\(693\) | 10.7104 | + | 18.5510i | 0.406856 | + | 0.704695i | ||||
\(694\) | − | 4.86861i | − | 0.184810i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −63.5006 | + | 36.6621i | −2.40698 | + | 1.38967i | ||||
\(697\) | − | 0.765417i | − | 0.0289922i | ||||||
\(698\) | 2.38827 | + | 4.13660i | 0.0903972 | + | 0.156573i | ||||
\(699\) | −19.4167 | + | 33.6308i | −0.734408 | + | 1.27203i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.69487 | 0.252862 | 0.126431 | − | 0.991975i | \(-0.459648\pi\) | ||||
0.126431 | + | 0.991975i | \(0.459648\pi\) | |||||||
\(702\) | −30.8650 | − | 11.9310i | −1.16493 | − | 0.450306i | ||||
\(703\) | 26.6362 | 1.00460 | ||||||||
\(704\) | −4.24439 | − | 2.45050i | −0.159966 | − | 0.0923566i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.105853 | + | 0.183342i | 0.00398382 | + | 0.00690018i | ||||
\(707\) | − | 19.6174i | − | 0.737789i | ||||||
\(708\) | 3.22401 | − | 1.86138i | 0.121166 | − | 0.0699550i | ||||
\(709\) | 12.6384 | − | 7.29676i | 0.474644 | − | 0.274036i | −0.243538 | − | 0.969891i | \(-0.578308\pi\) |
0.718182 | + | 0.695856i | \(0.244975\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.9824 | − | 31.1465i | −0.674394 | − | 1.16808i | ||||
\(712\) | 13.5275 | − | 23.4304i | 0.506966 | − | 0.878091i | ||||
\(713\) | 23.6619 | + | 13.6612i | 0.886144 | + | 0.511616i | ||||
\(714\) | −9.29936 | −0.348020 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.8762 | 0.481204 | ||||||||
\(717\) | −78.0594 | − | 45.0676i | −2.91518 | − | 1.68308i | ||||
\(718\) | 0.238068 | − | 0.412346i | 0.00888461 | − | 0.0153886i | ||||
\(719\) | −7.52798 | − | 13.0388i | −0.280746 | − | 0.486267i | 0.690822 | − | 0.723024i | \(-0.257249\pi\) |
−0.971569 | + | 0.236757i | \(0.923915\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.7936 | + | 6.23167i | −0.401974 | + | 0.232080i | ||||
\(722\) | −6.03435 | + | 3.48393i | −0.224575 | + | 0.129659i | ||||
\(723\) | − | 36.9936i | − | 1.37581i | ||||||
\(724\) | −5.24664 | − | 9.08745i | −0.194990 | − | 0.337732i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.8079 | + | 13.7455i | 0.883594 | + | 0.510144i | ||||
\(727\) | −38.0451 | −1.41102 | −0.705508 | − | 0.708702i | \(-0.749281\pi\) | ||||
−0.705508 | + | 0.708702i | \(0.749281\pi\) | |||||||
\(728\) | −22.9889 | − | 28.5253i | −0.852027 | − | 1.05722i | ||||
\(729\) | −15.1192 | −0.559971 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.32374 | − | 7.48894i | 0.159919 | − | 0.276989i | ||||
\(732\) | −8.39546 | − | 14.5414i | −0.310305 | − | 0.537464i | ||||
\(733\) | − | 1.60488i | − | 0.0592776i | −0.999561 | − | 0.0296388i | \(-0.990564\pi\) | ||
0.999561 | − | 0.0296388i | \(-0.00943570\pi\) | |||||||
\(734\) | −7.72420 | + | 4.45957i | −0.285106 | + | 0.164606i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.0019i | 1.36391i | ||||||||
\(737\) | −0.527941 | − | 0.914421i | −0.0194470 | − | 0.0336831i | ||||
\(738\) | 2.25716 | − | 3.90951i | 0.0830872 | − | 0.143911i | ||||
\(739\) | 32.6221 | + | 18.8344i | 1.20002 | + | 0.692833i | 0.960560 | − | 0.278073i | \(-0.0896957\pi\) |
0.239462 | + | 0.970906i | \(0.423029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.68238 | + | 36.4291i | 0.208747 | + | 1.33826i | ||||
\(742\) | 23.5549 | 0.864729 | ||||||||
\(743\) | 39.5689 | + | 22.8451i | 1.45164 | + | 0.838106i | 0.998575 | − | 0.0533694i | \(-0.0169961\pi\) |
0.453068 | + | 0.891476i | \(0.350329\pi\) | |||||||
\(744\) | −18.0740 | + | 31.3051i | −0.662626 | + | 1.14770i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 3.96821i | − | 0.145286i | ||||||
\(747\) | −1.03678 | + | 0.598584i | −0.0379337 | + | 0.0219010i | ||||
\(748\) | −0.949674 | + | 0.548294i | −0.0347235 | + | 0.0200476i | ||||
\(749\) | 20.4616i | 0.747651i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19.1650 | + | 33.1948i | −0.699342 | + | 1.21130i | 0.269352 | + | 0.963042i | \(0.413190\pi\) |
−0.968695 | + | 0.248255i | \(0.920143\pi\) | |||||||
\(752\) | 1.00442 | + | 0.579904i | 0.0366275 | + | 0.0211469i | ||||
\(753\) | −12.0213 | −0.438081 | ||||||||
\(754\) | 20.9336 | − | 16.8707i | 0.762358 | − | 0.614395i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 38.6354 | + | 22.3062i | 1.40516 | + | 0.811267i | ||||
\(757\) | 18.0528 | − | 31.2684i | 0.656141 | − | 1.13647i | −0.325466 | − | 0.945554i | \(-0.605521\pi\) |
0.981607 | − | 0.190915i | \(-0.0611455\pi\) | |||||||
\(758\) | 11.5688 | + | 20.0378i | 0.420199 | + | 0.727806i | ||||
\(759\) | 19.0566i | 0.691712i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.92472 | + | 5.73004i | −0.359771 | + | 0.207714i | −0.668980 | − | 0.743280i | \(-0.733269\pi\) |
0.309209 | + | 0.950994i | \(0.399936\pi\) | |||||||
\(762\) | − | 9.55306i | − | 0.346071i | ||||||
\(763\) | 19.5794 | + | 33.9125i | 0.708822 | + | 1.22772i | ||||
\(764\) | −6.42604 | + | 11.1302i | −0.232486 | + | 0.402677i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −28.2902 | −1.02217 | ||||||||
\(767\) | −2.81745 | + | 2.27062i | −0.101732 | + | 0.0819873i | ||||
\(768\) | −49.7661 | −1.79578 | ||||||||
\(769\) | 17.2077 | + | 9.93487i | 0.620525 | + | 0.358260i | 0.777073 | − | 0.629410i | \(-0.216703\pi\) |
−0.156548 | + | 0.987670i | \(0.550037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.7112 | + | 53.1933i | 1.10604 | + | 1.91571i | ||||
\(772\) | 24.7668i | 0.891375i | ||||||||
\(773\) | −40.1408 | + | 23.1753i | −1.44376 | + | 0.833558i | −0.998098 | − | 0.0616411i | \(-0.980367\pi\) |
−0.445666 | + | 0.895199i | \(0.647033\pi\) | |||||||
\(774\) | 44.1687 | − | 25.5008i | 1.58761 | − | 0.916608i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −23.5896 | − | 40.8584i | −0.846818 | − | 1.46673i | ||||
\(777\) | −43.5068 | + | 75.3560i | −1.56080 | + | 2.70338i | ||||
\(778\) | −8.94771 | − | 5.16596i | −0.320791 | − | 0.185209i | ||||
\(779\) | −2.66301 | −0.0954123 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.74810 | −0.0625519 | ||||||||
\(782\) | −4.87204 | − | 2.81287i | −0.174224 | − | 0.100588i | ||||
\(783\) | −43.3942 | + | 75.1610i | −1.55078 | + | 2.68603i | ||||
\(784\) | −0.311618 | − | 0.539739i | −0.0111292 | − | 0.0192764i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 42.5686 | − | 24.5770i | 1.51837 | − | 0.876632i | ||||
\(787\) | 30.8013 | − | 17.7832i | 1.09795 | − | 0.633901i | 0.162267 | − | 0.986747i | \(-0.448119\pi\) |
0.935681 | + | 0.352846i | \(0.114786\pi\) | |||||||
\(788\) | − | 13.9278i | − | 0.496159i | ||||||
\(789\) | −24.4116 | − | 42.2821i | −0.869074 | − | 1.50528i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 42.3257 | + | 24.4368i | 1.50493 | + | 0.868872i | ||||
\(792\) | −17.1447 | −0.609212 | ||||||||
\(793\) | 10.2413 | + | 12.7076i | 0.363678 | + | 0.451261i | ||||
\(794\) | 7.17165 | 0.254512 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.03033 | + | 10.4448i | −0.213739 | + | 0.370207i | ||||
\(797\) | −7.85502 | − | 13.6053i | −0.278239 | − | 0.481924i | 0.692708 | − | 0.721218i | \(-0.256417\pi\) |
−0.970947 | + | 0.239294i | \(0.923084\pi\) | |||||||
\(798\) | 32.3540i | 1.14532i | ||||||||
\(799\) | 8.81052 | − | 5.08676i | 0.311694 | − | 0.179956i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 60.4845i | − | 2.13711i | ||||||
\(802\) | 13.8634 | + | 24.0121i | 0.489533 | + | 0.847896i | ||||
\(803\) | −2.21472 | + | 3.83600i | −0.0781556 | + | 0.135370i | ||||
\(804\) | −3.59703 | − | 2.07675i | −0.126857 | − | 0.0732412i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.77890 | − | 12.3628i | 0.168329 | − | 0.435463i | ||||
\(807\) | 63.7066 | 2.24258 | ||||||||
\(808\) | 13.5977 | + | 7.85064i | 0.478366 | + | 0.276185i | ||||
\(809\) | 24.9367 | − | 43.1916i | 0.876728 | − | 1.51854i | 0.0218171 | − | 0.999762i | \(-0.493055\pi\) |
0.854911 | − | 0.518775i | \(-0.173612\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 38.3395i | 1.34628i | 0.739514 | + | 0.673141i | \(0.235055\pi\) | ||||
−0.739514 | + | 0.673141i | \(0.764945\pi\) | |||||||
\(812\) | −31.3905 | + | 18.1233i | −1.10159 | + | 0.636004i | ||||
\(813\) | 23.0720 | − | 13.3206i | 0.809170 | − | 0.467174i | ||||
\(814\) | − | 6.67867i | − | 0.234087i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0.160817 | − | 0.278544i | 0.00562973 | − | 0.00975098i | ||||
\(817\) | −26.0553 | − | 15.0430i | −0.911559 | − | 0.526289i | ||||
\(818\) | −28.5902 | −0.999633 | ||||||||
\(819\) | −76.3944 | − | 29.5305i | −2.66944 | − | 1.03188i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.8633 | − | 16.0869i | −0.972436 | − | 0.561436i | −0.0724577 | − | 0.997371i | \(-0.523084\pi\) |
−0.899978 | + | 0.435936i | \(0.856418\pi\) | |||||||
\(822\) | −1.06069 | + | 1.83717i | −0.0369958 | + | 0.0640786i | ||||
\(823\) | −5.60008 | − | 9.69962i | −0.195207 | − | 0.338108i | 0.751762 | − | 0.659435i | \(-0.229204\pi\) |
−0.946968 | + | 0.321327i | \(0.895871\pi\) | |||||||
\(824\) | − | 9.97535i | − | 0.347508i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.74993 | + | 1.58767i | −0.0956823 | + | 0.0552422i | ||||
\(827\) | 8.21374i | 0.285620i | 0.989750 | + | 0.142810i | \(0.0456138\pi\) | ||||
−0.989750 | + | 0.142810i | \(0.954386\pi\) | |||||||
\(828\) | 25.4878 | + | 44.1462i | 0.885763 | + | 1.53419i | ||||
\(829\) | 17.5474 | − | 30.3930i | 0.609447 | − | 1.05559i | −0.381884 | − | 0.924210i | \(-0.624725\pi\) |
0.991332 | − | 0.131383i | \(-0.0419419\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 26.4561 | 0.917753 | ||||||||
\(832\) | 18.5152 | − | 2.88809i | 0.641899 | − | 0.100126i | ||||
\(833\) | −5.46686 | −0.189416 | ||||||||
\(834\) | 0.656577 | + | 0.379075i | 0.0227354 | + | 0.0131263i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 1.90761 | + | 3.30407i | 0.0659760 | + | 0.114274i | ||||
\(837\) | 42.7858i | 1.47889i | ||||||||
\(838\) | 16.7864 | − | 9.69161i | 0.579875 | − | 0.334791i | ||||
\(839\) | 15.3296 | − | 8.85053i | 0.529235 | − | 0.305554i | −0.211470 | − | 0.977385i | \(-0.567825\pi\) |
0.740705 | + | 0.671830i | \(0.234492\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.7570 | − | 35.9521i | −0.715758 | − | 1.23973i | ||||
\(842\) | −2.02335 | + | 3.50455i | −0.0697293 | + | 0.120775i | ||||
\(843\) | −33.1986 | − | 19.1672i | −1.14342 | − | 0.660154i | ||||
\(844\) | 13.8797 | 0.477759 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 60.0019 | 2.06291 | ||||||||
\(847\) | 31.1986 | + | 18.0125i | 1.07200 | + | 0.618918i | ||||
\(848\) | −0.407344 | + | 0.705541i | −0.0139883 | + | 0.0242284i | ||||
\(849\) | 31.1240 | + | 53.9083i | 1.06817 | + | 1.85013i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −45.5874 | + | 26.3199i | −1.56272 | + | 0.902234i | ||||
\(852\) | −5.95517 | + | 3.43822i | −0.204021 | + | 0.117792i | ||||
\(853\) | 20.4558i | 0.700394i | 0.936676 | + | 0.350197i | \(0.113885\pi\) | ||||
−0.936676 | + | 0.350197i | \(0.886115\pi\) | |||||||
\(854\) | 7.16094 | + | 12.4031i | 0.245042 | + | 0.424426i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.1829 | − | 8.18848i | −0.484760 | − | 0.279876i | ||||
\(857\) | 36.3625 | 1.24212 | 0.621060 | − | 0.783763i | \(-0.286702\pi\) | ||||
0.621060 | + | 0.783763i | \(0.286702\pi\) | |||||||
\(858\) | 9.13410 | − | 1.42478i | 0.311833 | − | 0.0486412i | ||||
\(859\) | −51.0474 | −1.74172 | −0.870858 | − | 0.491534i | \(-0.836436\pi\) | ||||
−0.870858 | + | 0.491534i | \(0.836436\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.34969 | − | 7.53388i | 0.148237 | − | 0.256754i | ||||
\(862\) | −13.1973 | − | 22.8584i | −0.449501 | − | 0.778559i | ||||
\(863\) | 24.9638i | 0.849776i | 0.905246 | + | 0.424888i | \(0.139687\pi\) | ||||
−0.905246 | + | 0.424888i | \(0.860313\pi\) | |||||||
\(864\) | −50.1806 | + | 28.9718i | −1.70718 | + | 0.985640i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 6.91058i | − | 0.234831i | ||||||
\(867\) | 24.6158 | + | 42.6358i | 0.835996 | + | 1.44799i | ||||
\(868\) | −8.93462 | + | 15.4752i | −0.303261 | + | 0.525263i | ||||
\(869\) | 4.60688 | + | 2.65979i | 0.156278 | + | 0.0902270i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.76565 | + | 1.45562i | 0.127594 | + | 0.0493219i | ||||
\(872\) | −31.3417 | −1.06137 | ||||||||
\(873\) | −91.3433 | − | 52.7371i | −3.09150 | − | 1.78488i | ||||
\(874\) | −9.78645 | + | 16.9506i | −0.331032 | + | 0.573364i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 17.4239i | 0.588700i | ||||||||
\(877\) | 31.1542 | − | 17.9869i | 1.05200 | − | 0.607374i | 0.128794 | − | 0.991671i | \(-0.458889\pi\) |
0.923210 | + | 0.384297i | \(0.125556\pi\) | |||||||
\(878\) | 3.22901 | − | 1.86427i | 0.108974 | − | 0.0629161i | ||||
\(879\) | − | 79.0027i | − | 2.66469i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.88848 | + | 6.73505i | −0.131006 | + | 0.226910i | −0.924065 | − | 0.382236i | \(-0.875154\pi\) |
0.793058 | + | 0.609146i | \(0.208487\pi\) | |||||||
\(882\) | −27.9231 | − | 16.1214i | −0.940218 | − | 0.542835i | ||||
\(883\) | 38.0635 | 1.28094 | 0.640470 | − | 0.767983i | \(-0.278740\pi\) | ||||
0.640470 | + | 0.767983i | \(0.278740\pi\) | |||||||
\(884\) | 1.51174 | − | 3.91082i | 0.0508453 | − | 0.131535i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −16.5562 | − | 9.55870i | −0.556215 | − | 0.321131i | ||||
\(887\) | −11.1820 | + | 19.3678i | −0.375455 | + | 0.650307i | −0.990395 | − | 0.138267i | \(-0.955847\pi\) |
0.614940 | + | 0.788574i | \(0.289180\pi\) | |||||||
\(888\) | −34.8218 | − | 60.3130i | −1.16854 | − | 2.02397i | ||||
\(889\) | − | 12.5186i | − | 0.419861i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −10.2243 | + | 5.90302i | −0.342528 | + | 0.197759i | ||||
\(892\) | 5.97096i | 0.199922i | ||||||||
\(893\) | −17.6977 | − | 30.6533i | −0.592230 | − | 1.02577i | ||||
\(894\) | 0.0138720 | − | 0.0240270i | 0.000463949 | − | 0.000803582i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −23.5073 | −0.785324 | ||||||||
\(897\) | −45.7218 | − | 56.7328i | −1.52661 | − | 1.89425i | ||||
\(898\) | −21.3918 | −0.713855 | ||||||||
\(899\) | −30.1054 | − | 17.3813i | −1.00407 | − | 0.579700i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.57311 | + | 6.18881i | 0.119038 | + | 0.206179i | ||||
\(902\) | 0.667714i | 0.0222325i | ||||||||
\(903\) | 85.1159 | − | 49.1417i | 2.83248 | − | 1.63533i | ||||
\(904\) | −33.8765 | + | 19.5586i | −1.12671 | + | 0.650509i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −0.555128 | − | 0.961510i | −0.0184429 | − | 0.0319440i | ||||
\(907\) | −19.7115 | + | 34.1414i | −0.654510 | + | 1.13365i | 0.327506 | + | 0.944849i | \(0.393792\pi\) |
−0.982016 | + | 0.188796i | \(0.939541\pi\) | |||||||
\(908\) | 25.4702 | + | 14.7052i | 0.845257 | + | 0.488009i | ||||
\(909\) | 35.1019 | 1.16426 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.8525 | −1.08845 | −0.544227 | − | 0.838938i | \(-0.683177\pi\) | ||||
−0.544227 | + | 0.838938i | \(0.683177\pi\) | |||||||
\(912\) | −0.969100 | − | 0.559510i | −0.0320901 | − | 0.0185272i | ||||
\(913\) | 0.0885367 | − | 0.153350i | 0.00293014 | − | 0.00507514i | ||||
\(914\) | −14.5739 | − | 25.2427i | −0.482061 | − | 0.834954i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 29.7586 | − | 17.1812i | 0.983253 | − | 0.567682i | ||||
\(917\) | 55.7832 | − | 32.2064i | 1.84212 | − | 1.06355i | ||||
\(918\) | − | 8.80970i | − | 0.290764i | ||||||
\(919\) | −4.27163 | − | 7.39867i | −0.140908 | − | 0.244060i | 0.786931 | − | 0.617041i | \(-0.211669\pi\) |
−0.927839 | + | 0.372981i | \(0.878335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.2070 | − | 8.77975i | −0.501087 | − | 0.289303i | ||||
\(922\) | 21.5138 | 0.708520 | ||||||||
\(923\) | 5.20420 | − | 4.19414i | 0.171298 | − | 0.138052i | ||||
\(924\) | −12.4633 | −0.410013 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.45672 | + | 2.52311i | −0.0478708 | + | 0.0829146i | ||||
\(927\) | −11.1505 | − | 19.3132i | −0.366230 | − | 0.634328i | ||||
\(928\) | − | 47.0780i | − | 1.54541i | ||||||
\(929\) | −0.316653 | + | 0.182820i | −0.0103891 | + | 0.00599812i | −0.505186 | − | 0.863011i | \(-0.668576\pi\) |
0.494796 | + | 0.869009i | \(0.335243\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.0201i | 0.623359i | ||||||||
\(932\) | −7.68229 | − | 13.3061i | −0.251642 | − | 0.435856i | ||||
\(933\) | 24.6708 | − | 42.7311i | 0.807686 | − | 1.39895i | ||||
\(934\) | 6.06068 | + | 3.49913i | 0.198311 | + | 0.114495i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 51.0410 | − | 41.1346i | 1.66833 | − | 1.34453i | ||||
\(937\) | −9.19666 | −0.300442 | −0.150221 | − | 0.988652i | \(-0.547999\pi\) | ||||
−0.150221 | + | 0.988652i | \(0.547999\pi\) | |||||||
\(938\) | 3.06810 | + | 1.77137i | 0.100177 | + | 0.0578373i | ||||
\(939\) | −31.6168 | + | 54.7618i | −1.03177 | + | 1.78708i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.66316i | 0.119416i | 0.998216 | + | 0.0597078i | \(0.0190169\pi\) | ||||
−0.998216 | + | 0.0597078i | \(0.980983\pi\) | |||||||
\(942\) | −2.23908 | + | 1.29273i | −0.0729532 | + | 0.0421196i | ||||
\(943\) | 4.55770 | − | 2.63139i | 0.148419 | − | 0.0856898i | ||||
\(944\) | − | 0.109825i | − | 0.00357450i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.77183 | + | 6.53301i | −0.122633 | + | 0.212406i | ||||
\(947\) | 26.5382 | + | 15.3219i | 0.862377 | + | 0.497893i | 0.864807 | − | 0.502104i | \(-0.167440\pi\) |
−0.00243083 | + | 0.999997i | \(0.500774\pi\) | |||||||
\(948\) | 20.9254 | 0.679627 | ||||||||
\(949\) | −2.61020 | − | 16.7337i | −0.0847307 | − | 0.543199i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −51.0820 | − | 29.4922i | −1.65645 | − | 0.956351i | ||||
\(952\) | 4.87675 | − | 8.44678i | 0.158056 | − | 0.273762i | ||||
\(953\) | 2.97388 | + | 5.15090i | 0.0963333 | + | 0.166854i | 0.910164 | − | 0.414248i | \(-0.135955\pi\) |
−0.813831 | + | 0.581102i | \(0.802622\pi\) | |||||||
\(954\) | 42.1474i | 1.36457i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 30.8844 | − | 17.8311i | 0.998874 | − | 0.576700i | ||||
\(957\) | − | 24.2460i | − | 0.783763i | ||||||
\(958\) | −14.7651 | − | 25.5739i | −0.477038 | − | 0.826255i | ||||
\(959\) | −1.38996 | + | 2.40748i | −0.0448842 | + | 0.0777417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.8623 | 0.447173 | ||||||||
\(962\) | 16.0238 | + | 19.8828i | 0.516629 | + | 0.641048i | ||||
\(963\) | −36.6124 | −1.17982 | ||||||||
\(964\) | 12.6757 | + | 7.31831i | 0.408256 | + | 0.235707i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −31.9698 | − | 55.3733i | −1.02861 | − | 1.78161i | ||||
\(967\) | − | 1.71181i | − | 0.0550482i | −0.999621 | − | 0.0275241i | \(-0.991238\pi\) | ||
0.999621 | − | 0.0275241i | \(-0.00876229\pi\) | |||||||
\(968\) | −24.9706 | + | 14.4168i | −0.802585 | + | 0.463373i | ||||
\(969\) | −8.50067 | + | 4.90787i | −0.273081 | + | 0.157663i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.13340 | + | 12.3554i | 0.228922 | + | 0.396504i | 0.957489 | − | 0.288470i | \(-0.0931467\pi\) |
−0.728567 | + | 0.684974i | \(0.759813\pi\) | |||||||
\(972\) | −4.43926 | + | 7.68902i | −0.142389 | + | 0.246625i | ||||
\(973\) | 0.860399 | + | 0.496752i | 0.0275831 | + | 0.0159251i | ||||
\(974\) | −2.82588 | −0.0905471 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.495347 | −0.0158557 | ||||||||
\(977\) | 41.1517 | + | 23.7589i | 1.31656 | + | 0.760115i | 0.983173 | − | 0.182676i | \(-0.0584758\pi\) |
0.333385 | + | 0.942791i | \(0.391809\pi\) | |||||||
\(978\) | 14.2765 | − | 24.7276i | 0.456511 | − | 0.790701i | ||||
\(979\) | 4.47314 | + | 7.74770i | 0.142962 | + | 0.247618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −60.6805 | + | 35.0339i | −1.93738 | + | 1.11855i | ||||
\(982\) | 25.0579 | − | 14.4672i | 0.799629 | − | 0.461666i | ||||
\(983\) | 35.3161i | 1.12641i | 0.826318 | + | 0.563204i | \(0.190432\pi\) | ||||
−0.826318 | + | 0.563204i | \(0.809568\pi\) | |||||||
\(984\) | 3.48138 | + | 6.02993i | 0.110982 | + | 0.192227i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 6.19877 | + | 3.57886i | 0.197409 | + | 0.113974i | ||||
\(987\) | 115.627 | 3.68046 | ||||||||
\(988\) | −13.6064 | − | 5.25960i | −0.432877 | − | 0.167330i | ||||
\(989\) | 59.4575 | 1.89064 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 30.6644 | − | 53.1123i | 0.974087 | − | 1.68717i | 0.291172 | − | 0.956671i | \(-0.405955\pi\) |
0.682915 | − | 0.730498i | \(-0.260712\pi\) | |||||||
\(992\) | −11.6045 | − | 20.0996i | −0.368443 | − | 0.638163i | ||||
\(993\) | 60.8991i | 1.93258i | ||||||||
\(994\) | 5.07949 | − | 2.93265i | 0.161112 | − | 0.0930179i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 0.696548i | − | 0.0220710i | ||||||
\(997\) | −10.3298 | − | 17.8917i | −0.327148 | − | 0.566636i | 0.654797 | − | 0.755805i | \(-0.272754\pi\) |
−0.981945 | + | 0.189169i | \(0.939421\pi\) | |||||||
\(998\) | 4.33859 | − | 7.51465i | 0.137336 | − | 0.237872i | ||||
\(999\) | −71.3881 | − | 41.2160i | −2.25862 | − | 1.30401i |
(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 | 325.2.n.e.251.4 | yes | 10 | |
5.2 | odd | 4 | 325.2.m.d.199.4 | 20 | |||
5.3 | odd | 4 | 325.2.m.d.199.7 | 20 | |||
5.4 | even | 2 | 325.2.n.f.251.2 | yes | 10 | ||
13.6 | odd | 12 | 4225.2.a.bv.1.4 | 10 | |||
13.7 | odd | 12 | 4225.2.a.bv.1.7 | 10 | |||
13.10 | even | 6 | inner | 325.2.n.e.101.4 | ✓ | 10 | |
65.19 | odd | 12 | 4225.2.a.bu.1.7 | 10 | |||
65.23 | odd | 12 | 325.2.m.d.49.4 | 20 | |||
65.49 | even | 6 | 325.2.n.f.101.2 | yes | 10 | ||
65.59 | odd | 12 | 4225.2.a.bu.1.4 | 10 | |||
65.62 | odd | 12 | 325.2.m.d.49.7 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
325.2.m.d.49.4 | 20 | 65.23 | odd | 12 | |||
325.2.m.d.49.7 | 20 | 65.62 | odd | 12 | |||
325.2.m.d.199.4 | 20 | 5.2 | odd | 4 | |||
325.2.m.d.199.7 | 20 | 5.3 | odd | 4 | |||
325.2.n.e.101.4 | ✓ | 10 | 13.10 | even | 6 | inner | |
325.2.n.e.251.4 | yes | 10 | 1.1 | even | 1 | trivial | |
325.2.n.f.101.2 | yes | 10 | 65.49 | even | 6 | ||
325.2.n.f.251.2 | yes | 10 | 5.4 | even | 2 | ||
4225.2.a.bu.1.4 | 10 | 65.59 | odd | 12 | |||
4225.2.a.bu.1.7 | 10 | 65.19 | odd | 12 | |||
4225.2.a.bv.1.4 | 10 | 13.6 | odd | 12 | |||
4225.2.a.bv.1.7 | 10 | 13.7 | odd | 12 |