Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (of order \(3\), 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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 3 x^{19} + 22 x^{18} - 43 x^{17} + 245 x^{16} - 416 x^{15} + 1707 x^{14} - 2021 x^{13} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.10 | ||
Root | \(-1.37000 - 2.37290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.h.277.10 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37000 | − | 2.37290i | 0.968733 | − | 1.67789i | 0.269501 | − | 0.963000i | \(-0.413141\pi\) |
0.699232 | − | 0.714895i | \(-0.253525\pi\) | |||||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −2.75378 | − | 4.76968i | −1.37689 | − | 2.38484i | ||||
\(5\) | 1.69091 | − | 2.92874i | 0.756197 | − | 1.30977i | −0.188581 | − | 0.982058i | \(-0.560389\pi\) |
0.944777 | − | 0.327713i | \(-0.106278\pi\) | |||||||
\(6\) | 2.73999 | 1.11860 | ||||||||
\(7\) | −2.19620 | + | 1.47537i | −0.830084 | + | 0.557638i | ||||
\(8\) | −9.61066 | −3.39788 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −4.63307 | − | 8.02471i | −1.46511 | − | 2.53764i | ||||
\(11\) | −0.941706 | − | 1.63108i | −0.283935 | − | 0.491790i | 0.688415 | − | 0.725317i | \(-0.258307\pi\) |
−0.972350 | + | 0.233527i | \(0.924973\pi\) | |||||||
\(12\) | 2.75378 | − | 4.76968i | 0.794946 | − | 1.37689i | ||||
\(13\) | 1.76938 | 0.490736 | 0.245368 | − | 0.969430i | \(-0.421091\pi\) | ||||
0.245368 | + | 0.969430i | \(0.421091\pi\) | |||||||
\(14\) | 0.492131 | + | 7.23261i | 0.131527 | + | 1.93300i | ||||
\(15\) | 3.38181 | 0.873181 | ||||||||
\(16\) | −7.65901 | + | 13.2658i | −1.91475 | + | 3.31645i | ||||
\(17\) | 2.94798 | + | 5.10605i | 0.714989 | + | 1.23840i | 0.962964 | + | 0.269631i | \(0.0869019\pi\) |
−0.247974 | + | 0.968767i | \(0.579765\pi\) | |||||||
\(18\) | 1.37000 | + | 2.37290i | 0.322911 | + | 0.559298i | ||||
\(19\) | 3.31330 | − | 5.73881i | 0.760123 | − | 1.31657i | −0.182663 | − | 0.983176i | \(-0.558472\pi\) |
0.942787 | − | 0.333397i | \(-0.108195\pi\) | |||||||
\(20\) | −18.6255 | −4.16479 | ||||||||
\(21\) | −2.37581 | − | 1.16428i | −0.518444 | − | 0.254066i | ||||
\(22\) | −5.16053 | −1.10023 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | −4.80533 | − | 8.32307i | −0.980884 | − | 1.69894i | ||||
\(25\) | −3.21833 | − | 5.57432i | −0.643667 | − | 1.11486i | ||||
\(26\) | 2.42404 | − | 4.19855i | 0.475393 | − | 0.823404i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 13.0849 | + | 6.41231i | 2.47281 | + | 1.21181i | ||||
\(29\) | 8.24468 | 1.53100 | 0.765500 | − | 0.643436i | \(-0.222492\pi\) | ||||
0.765500 | + | 0.643436i | \(0.222492\pi\) | |||||||
\(30\) | 4.63307 | − | 8.02471i | 0.845879 | − | 1.46511i | ||||
\(31\) | −1.47179 | − | 2.54922i | −0.264342 | − | 0.457854i | 0.703049 | − | 0.711141i | \(-0.251821\pi\) |
−0.967391 | + | 0.253288i | \(0.918488\pi\) | |||||||
\(32\) | 11.3749 | + | 19.7020i | 2.01083 | + | 3.48285i | ||||
\(33\) | 0.941706 | − | 1.63108i | 0.163930 | − | 0.283935i | ||||
\(34\) | 16.1549 | 2.77054 | ||||||||
\(35\) | 0.607409 | + | 8.92680i | 0.102671 | + | 1.50890i | ||||
\(36\) | 5.50755 | 0.917925 | ||||||||
\(37\) | 2.21781 | − | 3.84136i | 0.364606 | − | 0.631516i | −0.624107 | − | 0.781339i | \(-0.714537\pi\) |
0.988713 | + | 0.149823i | \(0.0478704\pi\) | |||||||
\(38\) | −9.07841 | − | 15.7243i | −1.47271 | − | 2.55081i | ||||
\(39\) | 0.884688 | + | 1.53232i | 0.141663 | + | 0.245368i | ||||
\(40\) | −16.2507 | + | 28.1471i | −2.56947 | + | 4.45044i | ||||
\(41\) | −5.90495 | −0.922198 | −0.461099 | − | 0.887349i | \(-0.652545\pi\) | ||||
−0.461099 | + | 0.887349i | \(0.652545\pi\) | |||||||
\(42\) | −6.01756 | + | 4.04250i | −0.928530 | + | 0.623772i | ||||
\(43\) | 0.669028 | 0.102026 | 0.0510129 | − | 0.998698i | \(-0.483755\pi\) | ||||
0.0510129 | + | 0.998698i | \(0.483755\pi\) | |||||||
\(44\) | −5.18649 | + | 8.98327i | −0.781893 | + | 1.35428i | ||||
\(45\) | 1.69091 | + | 2.92874i | 0.252066 | + | 0.436590i | ||||
\(46\) | 1.37000 | + | 2.37290i | 0.201995 | + | 0.349865i | ||||
\(47\) | −0.897583 | + | 1.55466i | −0.130926 | + | 0.226770i | −0.924034 | − | 0.382311i | \(-0.875128\pi\) |
0.793108 | + | 0.609081i | \(0.208462\pi\) | |||||||
\(48\) | −15.3180 | −2.21096 | ||||||||
\(49\) | 2.64656 | − | 6.48041i | 0.378080 | − | 0.925773i | ||||
\(50\) | −17.6364 | −2.49416 | ||||||||
\(51\) | −2.94798 | + | 5.10605i | −0.412799 | + | 0.714989i | ||||
\(52\) | −4.87246 | − | 8.43935i | −0.675689 | − | 1.17033i | ||||
\(53\) | 4.84250 | + | 8.38746i | 0.665169 | + | 1.15211i | 0.979240 | + | 0.202706i | \(0.0649737\pi\) |
−0.314071 | + | 0.949400i | \(0.601693\pi\) | |||||||
\(54\) | −1.37000 | + | 2.37290i | −0.186433 | + | 0.322911i | ||||
\(55\) | −6.36935 | −0.858843 | ||||||||
\(56\) | 21.1069 | − | 14.1793i | 2.82053 | − | 1.89479i | ||||
\(57\) | 6.62660 | 0.877715 | ||||||||
\(58\) | 11.2952 | − | 19.5638i | 1.48313 | − | 2.56886i | ||||
\(59\) | −0.683613 | − | 1.18405i | −0.0889988 | − | 0.154150i | 0.818089 | − | 0.575091i | \(-0.195033\pi\) |
−0.907088 | + | 0.420941i | \(0.861700\pi\) | |||||||
\(60\) | −9.31276 | − | 16.1302i | −1.20227 | − | 2.08240i | ||||
\(61\) | −4.68170 | + | 8.10894i | −0.599430 | + | 1.03824i | 0.393475 | + | 0.919335i | \(0.371273\pi\) |
−0.992905 | + | 0.118908i | \(0.962061\pi\) | |||||||
\(62\) | −8.06540 | −1.02431 | ||||||||
\(63\) | −0.179610 | − | 2.63965i | −0.0226288 | − | 0.332564i | ||||
\(64\) | 31.6985 | 3.96231 | ||||||||
\(65\) | 2.99185 | − | 5.18203i | 0.371093 | − | 0.642752i | ||||
\(66\) | −2.58027 | − | 4.46915i | −0.317609 | − | 0.550115i | ||||
\(67\) | 4.08947 | + | 7.08317i | 0.499608 | + | 0.865347i | 1.00000 | 0.000452542i | \(-0.000144049\pi\) | |
−0.500392 | + | 0.865799i | \(0.666811\pi\) | |||||||
\(68\) | 16.2361 | − | 28.1218i | 1.96892 | − | 3.41027i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 22.0146 | + | 10.7884i | 2.63124 | + | 1.28945i | ||||
\(71\) | −0.295052 | −0.0350162 | −0.0175081 | − | 0.999847i | \(-0.505573\pi\) | ||||
−0.0175081 | + | 0.999847i | \(0.505573\pi\) | |||||||
\(72\) | 4.80533 | − | 8.32307i | 0.566313 | − | 0.980884i | ||||
\(73\) | 2.22875 | + | 3.86031i | 0.260856 | + | 0.451815i | 0.966470 | − | 0.256781i | \(-0.0826620\pi\) |
−0.705614 | + | 0.708597i | \(0.749329\pi\) | |||||||
\(74\) | −6.07678 | − | 10.5253i | −0.706411 | − | 1.22354i | ||||
\(75\) | 3.21833 | − | 5.57432i | 0.371621 | − | 0.643667i | ||||
\(76\) | −36.4963 | −4.18642 | ||||||||
\(77\) | 4.47462 | + | 2.19281i | 0.509931 | + | 0.249894i | ||||
\(78\) | 4.84807 | 0.548936 | ||||||||
\(79\) | 1.51384 | − | 2.62205i | 0.170320 | − | 0.295004i | −0.768211 | − | 0.640196i | \(-0.778853\pi\) |
0.938532 | + | 0.345192i | \(0.112186\pi\) | |||||||
\(80\) | 25.9013 | + | 44.8624i | 2.89586 | + | 5.01577i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −8.08975 | + | 14.0119i | −0.893363 | + | 1.54735i | ||||
\(83\) | −10.5300 | −1.15582 | −0.577910 | − | 0.816100i | \(-0.696132\pi\) | ||||
−0.577910 | + | 0.816100i | \(0.696132\pi\) | |||||||
\(84\) | 0.989213 | + | 14.5380i | 0.107932 | + | 1.58623i | ||||
\(85\) | 19.9390 | 2.16269 | ||||||||
\(86\) | 0.916565 | − | 1.58754i | 0.0988358 | − | 0.171189i | ||||
\(87\) | 4.12234 | + | 7.14010i | 0.441961 | + | 0.765500i | ||||
\(88\) | 9.05041 | + | 15.6758i | 0.964777 | + | 1.67104i | ||||
\(89\) | 5.35981 | − | 9.28346i | 0.568138 | − | 0.984044i | −0.428612 | − | 0.903489i | \(-0.640997\pi\) |
0.996750 | − | 0.0805556i | \(-0.0256695\pi\) | |||||||
\(90\) | 9.26614 | 0.976737 | ||||||||
\(91\) | −3.88590 | + | 2.61048i | −0.407353 | + | 0.273653i | ||||
\(92\) | 5.50755 | 0.574202 | ||||||||
\(93\) | 1.47179 | − | 2.54922i | 0.152618 | − | 0.264342i | ||||
\(94\) | 2.45937 | + | 4.25975i | 0.253664 | + | 0.439360i | ||||
\(95\) | −11.2050 | − | 19.4076i | −1.14961 | − | 1.99117i | ||||
\(96\) | −11.3749 | + | 19.7020i | −1.16095 | + | 2.01083i | ||||
\(97\) | 15.6290 | 1.58688 | 0.793441 | − | 0.608648i | \(-0.208288\pi\) | ||||
0.793441 | + | 0.608648i | \(0.208288\pi\) | |||||||
\(98\) | −11.7516 | − | 15.1582i | −1.18709 | − | 1.53121i | ||||
\(99\) | 1.88341 | 0.189290 | ||||||||
\(100\) | −17.7251 | + | 30.7008i | −1.77251 | + | 3.07008i | ||||
\(101\) | −3.78458 | − | 6.55508i | −0.376580 | − | 0.652255i | 0.613983 | − | 0.789320i | \(-0.289567\pi\) |
−0.990562 | + | 0.137065i | \(0.956233\pi\) | |||||||
\(102\) | 8.07743 | + | 13.9905i | 0.799785 | + | 1.38527i | ||||
\(103\) | 1.31063 | − | 2.27008i | 0.129141 | − | 0.223678i | −0.794203 | − | 0.607652i | \(-0.792111\pi\) |
0.923344 | + | 0.383974i | \(0.125445\pi\) | |||||||
\(104\) | −17.0049 | −1.66746 | ||||||||
\(105\) | −7.42713 | + | 4.98943i | −0.724814 | + | 0.486919i | ||||
\(106\) | 26.5368 | 2.57748 | ||||||||
\(107\) | −8.66609 | + | 15.0101i | −0.837783 | + | 1.45108i | 0.0539619 | + | 0.998543i | \(0.482815\pi\) |
−0.891745 | + | 0.452539i | \(0.850518\pi\) | |||||||
\(108\) | 2.75378 | + | 4.76968i | 0.264982 | + | 0.458963i | ||||
\(109\) | 6.68403 | + | 11.5771i | 0.640214 | + | 1.10888i | 0.985385 | + | 0.170343i | \(0.0544876\pi\) |
−0.345171 | + | 0.938540i | \(0.612179\pi\) | |||||||
\(110\) | −8.72598 | + | 15.1138i | −0.831990 | + | 1.44105i | ||||
\(111\) | 4.43562 | 0.421011 | ||||||||
\(112\) | −2.75127 | − | 40.4342i | −0.259971 | − | 3.82067i | ||||
\(113\) | −1.18709 | −0.111672 | −0.0558360 | − | 0.998440i | \(-0.517782\pi\) | ||||
−0.0558360 | + | 0.998440i | \(0.517782\pi\) | |||||||
\(114\) | 9.07841 | − | 15.7243i | 0.850271 | − | 1.47271i | ||||
\(115\) | 1.69091 | + | 2.92874i | 0.157678 | + | 0.273106i | ||||
\(116\) | −22.7040 | − | 39.3245i | −2.10801 | − | 3.65119i | ||||
\(117\) | −0.884688 | + | 1.53232i | −0.0817894 | + | 0.141663i | ||||
\(118\) | −3.74618 | −0.344864 | ||||||||
\(119\) | −14.0076 | − | 6.86452i | −1.28408 | − | 0.629270i | ||||
\(120\) | −32.5015 | −2.96696 | ||||||||
\(121\) | 3.72638 | − | 6.45428i | 0.338762 | − | 0.586753i | ||||
\(122\) | 12.8278 | + | 22.2184i | 1.16138 | + | 2.01156i | ||||
\(123\) | −2.95247 | − | 5.11383i | −0.266216 | − | 0.461099i | ||||
\(124\) | −8.10598 | + | 14.0400i | −0.727938 | + | 1.26083i | ||||
\(125\) | −4.85853 | −0.434560 | ||||||||
\(126\) | −6.50969 | − | 3.19011i | −0.579929 | − | 0.284197i | ||||
\(127\) | −12.2311 | −1.08533 | −0.542667 | − | 0.839948i | \(-0.682585\pi\) | ||||
−0.542667 | + | 0.839948i | \(0.682585\pi\) | |||||||
\(128\) | 20.6769 | − | 35.8134i | 1.82760 | − | 3.16549i | ||||
\(129\) | 0.334514 | + | 0.579395i | 0.0294523 | + | 0.0510129i | ||||
\(130\) | −8.19764 | − | 14.1987i | −0.718981 | − | 1.24531i | ||||
\(131\) | 3.02835 | − | 5.24526i | 0.264588 | − | 0.458280i | −0.702868 | − | 0.711321i | \(-0.748097\pi\) |
0.967456 | + | 0.253041i | \(0.0814307\pi\) | |||||||
\(132\) | −10.3730 | −0.902853 | ||||||||
\(133\) | 1.19021 | + | 17.4919i | 0.103204 | + | 1.51674i | ||||
\(134\) | 22.4102 | 1.93595 | ||||||||
\(135\) | −1.69091 | + | 2.92874i | −0.145530 | + | 0.252066i | ||||
\(136\) | −28.3320 | − | 49.0725i | −2.42945 | − | 4.20793i | ||||
\(137\) | 7.14630 | + | 12.3778i | 0.610550 | + | 1.05750i | 0.991148 | + | 0.132763i | \(0.0423848\pi\) |
−0.380598 | + | 0.924741i | \(0.624282\pi\) | |||||||
\(138\) | −1.37000 | + | 2.37290i | −0.116622 | + | 0.201995i | ||||
\(139\) | −16.4290 | −1.39349 | −0.696743 | − | 0.717321i | \(-0.745368\pi\) | ||||
−0.696743 | + | 0.717321i | \(0.745368\pi\) | |||||||
\(140\) | 40.9053 | − | 27.4795i | 3.45713 | − | 2.32244i | ||||
\(141\) | −1.79517 | −0.151180 | ||||||||
\(142\) | −0.404220 | + | 0.700129i | −0.0339214 | + | 0.0587535i | ||||
\(143\) | −1.66623 | − | 2.88600i | −0.139337 | − | 0.241339i | ||||
\(144\) | −7.65901 | − | 13.2658i | −0.638250 | − | 1.10548i | ||||
\(145\) | 13.9410 | − | 24.1465i | 1.15774 | − | 2.00526i | ||||
\(146\) | 12.2135 | 1.01080 | ||||||||
\(147\) | 6.93548 | − | 0.948216i | 0.572029 | − | 0.0782075i | ||||
\(148\) | −24.4294 | −2.00809 | ||||||||
\(149\) | −6.90181 | + | 11.9543i | −0.565418 | + | 0.979333i | 0.431593 | + | 0.902069i | \(0.357952\pi\) |
−0.997011 | + | 0.0772640i | \(0.975382\pi\) | |||||||
\(150\) | −8.81820 | − | 15.2736i | −0.720003 | − | 1.24708i | ||||
\(151\) | 2.12357 | + | 3.67813i | 0.172814 | + | 0.299322i | 0.939403 | − | 0.342816i | \(-0.111381\pi\) |
−0.766589 | + | 0.642138i | \(0.778047\pi\) | |||||||
\(152\) | −31.8430 | + | 55.1537i | −2.58281 | + | 4.47355i | ||||
\(153\) | −5.89595 | −0.476660 | ||||||||
\(154\) | 11.3335 | − | 7.61370i | 0.913283 | − | 0.613529i | ||||
\(155\) | −9.95467 | −0.799578 | ||||||||
\(156\) | 4.87246 | − | 8.43935i | 0.390109 | − | 0.675689i | ||||
\(157\) | 0.333896 | + | 0.578325i | 0.0266478 | + | 0.0461554i | 0.879042 | − | 0.476745i | \(-0.158183\pi\) |
−0.852394 | + | 0.522900i | \(0.824850\pi\) | |||||||
\(158\) | −4.14791 | − | 7.18440i | −0.329990 | − | 0.571560i | ||||
\(159\) | −4.84250 | + | 8.38746i | −0.384035 | + | 0.665169i | ||||
\(160\) | 76.9359 | 6.08232 | ||||||||
\(161\) | −0.179610 | − | 2.63965i | −0.0141553 | − | 0.208033i | ||||
\(162\) | −2.73999 | −0.215274 | ||||||||
\(163\) | 0.363590 | − | 0.629757i | 0.0284786 | − | 0.0493263i | −0.851435 | − | 0.524460i | \(-0.824267\pi\) |
0.879913 | + | 0.475134i | \(0.157600\pi\) | |||||||
\(164\) | 16.2609 | + | 28.1647i | 1.26976 | + | 2.19929i | ||||
\(165\) | −3.18467 | − | 5.51602i | −0.247927 | − | 0.429421i | ||||
\(166\) | −14.4261 | + | 24.9867i | −1.11968 | + | 1.93935i | ||||
\(167\) | 9.42526 | 0.729349 | 0.364674 | − | 0.931135i | \(-0.381180\pi\) | ||||
0.364674 | + | 0.931135i | \(0.381180\pi\) | |||||||
\(168\) | 22.8331 | + | 11.1895i | 1.76161 | + | 0.863286i | ||||
\(169\) | −9.86931 | −0.759178 | ||||||||
\(170\) | 27.3164 | − | 47.3133i | 2.09507 | − | 3.62877i | ||||
\(171\) | 3.31330 | + | 5.73881i | 0.253374 | + | 0.438857i | ||||
\(172\) | −1.84235 | − | 3.19105i | −0.140478 | − | 0.243315i | ||||
\(173\) | −5.42568 | + | 9.39756i | −0.412507 | + | 0.714483i | −0.995163 | − | 0.0982357i | \(-0.968680\pi\) |
0.582656 | + | 0.812719i | \(0.302013\pi\) | |||||||
\(174\) | 22.5904 | 1.71257 | ||||||||
\(175\) | 15.2923 | + | 7.49406i | 1.15599 | + | 0.566498i | ||||
\(176\) | 28.8501 | 2.17466 | ||||||||
\(177\) | 0.683613 | − | 1.18405i | 0.0513835 | − | 0.0889988i | ||||
\(178\) | −14.6858 | − | 25.4366i | −1.10075 | − | 1.90655i | ||||
\(179\) | 4.97180 | + | 8.61141i | 0.371610 | + | 0.643647i | 0.989813 | − | 0.142371i | \(-0.0454726\pi\) |
−0.618204 | + | 0.786018i | \(0.712139\pi\) | |||||||
\(180\) | 9.31276 | − | 16.1302i | 0.694132 | − | 1.20227i | ||||
\(181\) | −0.975614 | −0.0725168 | −0.0362584 | − | 0.999342i | \(-0.511544\pi\) | ||||
−0.0362584 | + | 0.999342i | \(0.511544\pi\) | |||||||
\(182\) | 0.870764 | + | 12.7972i | 0.0645453 | + | 0.948592i | ||||
\(183\) | −9.36339 | −0.692162 | ||||||||
\(184\) | 4.80533 | − | 8.32307i | 0.354254 | − | 0.613585i | ||||
\(185\) | −7.50022 | − | 12.9908i | −0.551427 | − | 0.955100i | ||||
\(186\) | −4.03270 | − | 6.98484i | −0.295692 | − | 0.512154i | ||||
\(187\) | 5.55226 | − | 9.61679i | 0.406021 | − | 0.703249i | ||||
\(188\) | 9.88696 | 0.721081 | ||||||||
\(189\) | 2.19620 | − | 1.47537i | 0.159750 | − | 0.107317i | ||||
\(190\) | −61.4030 | −4.45464 | ||||||||
\(191\) | −3.50335 | + | 6.06798i | −0.253494 | + | 0.439064i | −0.964485 | − | 0.264137i | \(-0.914913\pi\) |
0.710992 | + | 0.703200i | \(0.248246\pi\) | |||||||
\(192\) | 15.8492 | + | 27.4517i | 1.14382 | + | 1.98116i | ||||
\(193\) | −6.26011 | − | 10.8428i | −0.450613 | − | 0.780484i | 0.547812 | − | 0.836602i | \(-0.315461\pi\) |
−0.998424 | + | 0.0561178i | \(0.982128\pi\) | |||||||
\(194\) | 21.4116 | − | 37.0860i | 1.53726 | − | 2.66262i | ||||
\(195\) | 5.98370 | 0.428502 | ||||||||
\(196\) | −38.1975 | + | 5.22235i | −2.72839 | + | 0.373025i | ||||
\(197\) | −25.3287 | −1.80459 | −0.902296 | − | 0.431116i | \(-0.858120\pi\) | ||||
−0.902296 | + | 0.431116i | \(0.858120\pi\) | |||||||
\(198\) | 2.58027 | − | 4.46915i | 0.183372 | − | 0.317609i | ||||
\(199\) | −0.324280 | − | 0.561669i | −0.0229876 | − | 0.0398156i | 0.854303 | − | 0.519776i | \(-0.173984\pi\) |
−0.877290 | + | 0.479960i | \(0.840651\pi\) | |||||||
\(200\) | 30.9303 | + | 53.5728i | 2.18710 | + | 3.78817i | ||||
\(201\) | −4.08947 | + | 7.08317i | −0.288449 | + | 0.499608i | ||||
\(202\) | −20.7394 | −1.45922 | ||||||||
\(203\) | −18.1069 | + | 12.1640i | −1.27086 | + | 0.853743i | ||||
\(204\) | 32.4723 | 2.27351 | ||||||||
\(205\) | −9.98471 | + | 17.2940i | −0.697363 | + | 1.20787i | ||||
\(206\) | −3.59113 | − | 6.22001i | −0.250206 | − | 0.433369i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | −13.5517 | + | 23.4722i | −0.939638 | + | 1.62750i | ||||
\(209\) | −12.4806 | −0.863303 | ||||||||
\(210\) | 1.66429 | + | 24.4593i | 0.114847 | + | 1.68786i | ||||
\(211\) | 14.4647 | 0.995790 | 0.497895 | − | 0.867237i | \(-0.334106\pi\) | ||||
0.497895 | + | 0.867237i | \(0.334106\pi\) | |||||||
\(212\) | 26.6703 | − | 46.1944i | 1.83173 | − | 3.17264i | ||||
\(213\) | −0.147526 | − | 0.255522i | −0.0101083 | − | 0.0175081i | ||||
\(214\) | 23.7450 | + | 41.1276i | 1.62318 | + | 2.81142i | ||||
\(215\) | 1.13126 | − | 1.95941i | 0.0771516 | − | 0.133630i | ||||
\(216\) | 9.61066 | 0.653922 | ||||||||
\(217\) | 6.99340 | + | 3.42715i | 0.474743 | + | 0.232650i | ||||
\(218\) | 36.6284 | 2.48079 | ||||||||
\(219\) | −2.22875 | + | 3.86031i | −0.150605 | + | 0.260856i | ||||
\(220\) | 17.5398 | + | 30.3798i | 1.18253 | + | 2.04820i | ||||
\(221\) | 5.21608 | + | 9.03451i | 0.350871 | + | 0.607727i | ||||
\(222\) | 6.07678 | − | 10.5253i | 0.407847 | − | 0.706411i | ||||
\(223\) | −29.7327 | −1.99105 | −0.995525 | − | 0.0945015i | \(-0.969874\pi\) | ||||
−0.995525 | + | 0.0945015i | \(0.969874\pi\) | |||||||
\(224\) | −54.0494 | − | 26.4872i | −3.61133 | − | 1.76975i | ||||
\(225\) | 6.43667 | 0.429111 | ||||||||
\(226\) | −1.62631 | + | 2.81685i | −0.108180 | + | 0.187374i | ||||
\(227\) | 3.24510 | + | 5.62067i | 0.215385 | + | 0.373057i | 0.953391 | − | 0.301736i | \(-0.0975662\pi\) |
−0.738007 | + | 0.674793i | \(0.764233\pi\) | |||||||
\(228\) | −18.2482 | − | 31.6068i | −1.20851 | − | 2.09321i | ||||
\(229\) | 0.618039 | − | 1.07048i | 0.0408412 | − | 0.0707390i | −0.844882 | − | 0.534952i | \(-0.820330\pi\) |
0.885723 | + | 0.464213i | \(0.153663\pi\) | |||||||
\(230\) | 9.26614 | 0.610991 | ||||||||
\(231\) | 0.338280 | + | 4.97154i | 0.0222572 | + | 0.327104i | ||||
\(232\) | −79.2368 | −5.20215 | ||||||||
\(233\) | −12.1781 | + | 21.0931i | −0.797814 | + | 1.38185i | 0.123223 | + | 0.992379i | \(0.460677\pi\) |
−0.921037 | + | 0.389475i | \(0.872656\pi\) | |||||||
\(234\) | 2.42404 | + | 4.19855i | 0.158464 | + | 0.274468i | ||||
\(235\) | 3.03546 | + | 5.25757i | 0.198011 | + | 0.342966i | ||||
\(236\) | −3.76503 | + | 6.52123i | −0.245083 | + | 0.424496i | ||||
\(237\) | 3.02768 | 0.196669 | ||||||||
\(238\) | −35.4793 | + | 23.8344i | −2.29978 | + | 1.54496i | ||||
\(239\) | 15.2471 | 0.986251 | 0.493126 | − | 0.869958i | \(-0.335854\pi\) | ||||
0.493126 | + | 0.869958i | \(0.335854\pi\) | |||||||
\(240\) | −25.9013 | + | 44.8624i | −1.67192 | + | 2.89586i | ||||
\(241\) | −2.06351 | − | 3.57411i | −0.132923 | − | 0.230229i | 0.791879 | − | 0.610678i | \(-0.209103\pi\) |
−0.924802 | + | 0.380449i | \(0.875769\pi\) | |||||||
\(242\) | −10.2102 | − | 17.6847i | −0.656339 | − | 1.13681i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 51.5694 | 3.30139 | ||||||||
\(245\) | −14.5043 | − | 18.7089i | −0.926647 | − | 1.19526i | ||||
\(246\) | −16.1795 | −1.03157 | ||||||||
\(247\) | 5.86247 | − | 10.1541i | 0.373020 | − | 0.646090i | ||||
\(248\) | 14.1449 | + | 24.4997i | 0.898202 | + | 1.55573i | ||||
\(249\) | −5.26501 | − | 9.11927i | −0.333657 | − | 0.577910i | ||||
\(250\) | −6.65617 | + | 11.5288i | −0.420973 | + | 0.729147i | ||||
\(251\) | 4.82682 | 0.304666 | 0.152333 | − | 0.988329i | \(-0.451321\pi\) | ||||
0.152333 | + | 0.988329i | \(0.451321\pi\) | |||||||
\(252\) | −12.0957 | + | 8.12568i | −0.761955 | + | 0.511870i | ||||
\(253\) | 1.88341 | 0.118409 | ||||||||
\(254\) | −16.7565 | + | 29.0232i | −1.05140 | + | 1.82108i | ||||
\(255\) | 9.96951 | + | 17.2677i | 0.624315 | + | 1.08135i | ||||
\(256\) | −24.9560 | − | 43.2251i | −1.55975 | − | 2.70157i | ||||
\(257\) | 2.37570 | − | 4.11483i | 0.148192 | − | 0.256676i | −0.782367 | − | 0.622817i | \(-0.785988\pi\) |
0.930559 | + | 0.366141i | \(0.119321\pi\) | |||||||
\(258\) | 1.83313 | 0.114126 | ||||||||
\(259\) | 0.796683 | + | 11.7085i | 0.0495035 | + | 0.727529i | ||||
\(260\) | −32.9555 | −2.04381 | ||||||||
\(261\) | −4.12234 | + | 7.14010i | −0.255167 | + | 0.441961i | ||||
\(262\) | −8.29765 | − | 14.3720i | −0.512631 | − | 0.887902i | ||||
\(263\) | 8.07074 | + | 13.9789i | 0.497663 | + | 0.861978i | 0.999996 | − | 0.00269631i | \(-0.000858265\pi\) |
−0.502333 | + | 0.864674i | \(0.667525\pi\) | |||||||
\(264\) | −9.05041 | + | 15.6758i | −0.557014 | + | 0.964777i | ||||
\(265\) | 32.7529 | 2.01199 | ||||||||
\(266\) | 43.1371 | + | 21.1396i | 2.64491 | + | 1.29615i | ||||
\(267\) | 10.7196 | 0.656030 | ||||||||
\(268\) | 22.5230 | − | 39.0109i | 1.37581 | − | 2.38297i | ||||
\(269\) | −4.79781 | − | 8.31006i | −0.292528 | − | 0.506673i | 0.681879 | − | 0.731465i | \(-0.261163\pi\) |
−0.974407 | + | 0.224792i | \(0.927830\pi\) | |||||||
\(270\) | 4.63307 | + | 8.02471i | 0.281960 | + | 0.488368i | ||||
\(271\) | −10.4810 | + | 18.1537i | −0.636677 | + | 1.10276i | 0.349480 | + | 0.936944i | \(0.386358\pi\) |
−0.986157 | + | 0.165813i | \(0.946975\pi\) | |||||||
\(272\) | −90.3143 | −5.47611 | ||||||||
\(273\) | −4.20369 | − | 2.06004i | −0.254419 | − | 0.124679i | ||||
\(274\) | 39.1616 | 2.36584 | ||||||||
\(275\) | −6.06145 | + | 10.4987i | −0.365519 | + | 0.633097i | ||||
\(276\) | 2.75378 | + | 4.76968i | 0.165758 | + | 0.287101i | ||||
\(277\) | −7.29118 | − | 12.6287i | −0.438085 | − | 0.758785i | 0.559457 | − | 0.828859i | \(-0.311010\pi\) |
−0.997542 | + | 0.0700746i | \(0.977676\pi\) | |||||||
\(278\) | −22.5076 | + | 38.9843i | −1.34992 | + | 2.33812i | ||||
\(279\) | 2.94359 | 0.176228 | ||||||||
\(280\) | −5.83760 | − | 85.7924i | −0.348863 | − | 5.12708i | ||||
\(281\) | −10.2706 | −0.612694 | −0.306347 | − | 0.951920i | \(-0.599107\pi\) | ||||
−0.306347 | + | 0.951920i | \(0.599107\pi\) | |||||||
\(282\) | −2.45937 | + | 4.25975i | −0.146453 | + | 0.253664i | ||||
\(283\) | −8.54651 | − | 14.8030i | −0.508037 | − | 0.879946i | −0.999957 | − | 0.00930538i | \(-0.997038\pi\) |
0.491920 | − | 0.870641i | \(-0.336295\pi\) | |||||||
\(284\) | 0.812507 | + | 1.40730i | 0.0482134 | + | 0.0835081i | ||||
\(285\) | 11.2050 | − | 19.4076i | 0.663725 | − | 1.14961i | ||||
\(286\) | −9.13092 | −0.539923 | ||||||||
\(287\) | 12.9684 | − | 8.71199i | 0.765502 | − | 0.514252i | ||||
\(288\) | −22.7499 | −1.34055 | ||||||||
\(289\) | −8.88114 | + | 15.3826i | −0.522420 | + | 0.904858i | ||||
\(290\) | −38.1982 | − | 66.1612i | −2.24307 | − | 3.88512i | ||||
\(291\) | 7.81449 | + | 13.5351i | 0.458093 | + | 0.793441i | ||||
\(292\) | 12.2750 | − | 21.2609i | 0.718338 | − | 1.24420i | ||||
\(293\) | 10.9029 | 0.636955 | 0.318478 | − | 0.947930i | \(-0.396828\pi\) | ||||
0.318478 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(294\) | 7.25155 | − | 17.7563i | 0.422919 | − | 1.03557i | ||||
\(295\) | −4.62370 | −0.269202 | ||||||||
\(296\) | −21.3146 | + | 36.9180i | −1.23889 | + | 2.14582i | ||||
\(297\) | 0.941706 | + | 1.63108i | 0.0546433 | + | 0.0946450i | ||||
\(298\) | 18.9109 | + | 32.7546i | 1.09548 | + | 1.89742i | ||||
\(299\) | −0.884688 | + | 1.53232i | −0.0511628 | + | 0.0886166i | ||||
\(300\) | −35.4503 | −2.04672 | ||||||||
\(301\) | −1.46932 | + | 0.987064i | −0.0846900 | + | 0.0568934i | ||||
\(302\) | 11.6371 | 0.669642 | ||||||||
\(303\) | 3.78458 | − | 6.55508i | 0.217418 | − | 0.376580i | ||||
\(304\) | 50.7532 | + | 87.9071i | 2.91089 | + | 5.04182i | ||||
\(305\) | 15.8326 | + | 27.4229i | 0.906574 | + | 1.57023i | ||||
\(306\) | −8.07743 | + | 13.9905i | −0.461756 | + | 0.799785i | ||||
\(307\) | 26.7973 | 1.52940 | 0.764700 | − | 0.644386i | \(-0.222887\pi\) | ||||
0.764700 | + | 0.644386i | \(0.222887\pi\) | |||||||
\(308\) | −1.86310 | − | 27.3810i | −0.106160 | − | 1.56018i | ||||
\(309\) | 2.62127 | 0.149119 | ||||||||
\(310\) | −13.6378 | + | 23.6214i | −0.774578 | + | 1.34161i | ||||
\(311\) | −8.93077 | − | 15.4685i | −0.506417 | − | 0.877141i | −0.999972 | − | 0.00742604i | \(-0.997636\pi\) |
0.493555 | − | 0.869715i | \(-0.335697\pi\) | |||||||
\(312\) | −8.50243 | − | 14.7266i | −0.481355 | − | 0.833732i | ||||
\(313\) | 14.5650 | − | 25.2272i | 0.823260 | − | 1.42593i | −0.0799820 | − | 0.996796i | \(-0.525486\pi\) |
0.903242 | − | 0.429132i | \(-0.141180\pi\) | |||||||
\(314\) | 1.82975 | 0.103258 | ||||||||
\(315\) | −8.03454 | − | 3.93737i | −0.452695 | − | 0.221846i | ||||
\(316\) | −16.6751 | −0.938049 | ||||||||
\(317\) | −10.9687 | + | 18.9983i | −0.616062 | + | 1.06705i | 0.374135 | + | 0.927374i | \(0.377940\pi\) |
−0.990197 | + | 0.139676i | \(0.955394\pi\) | |||||||
\(318\) | 13.2684 | + | 22.9816i | 0.744056 | + | 1.28874i | ||||
\(319\) | −7.76407 | − | 13.4478i | −0.434704 | − | 0.752930i | ||||
\(320\) | 53.5992 | − | 92.8365i | 2.99629 | − | 5.18972i | ||||
\(321\) | −17.3322 | −0.967388 | ||||||||
\(322\) | −6.50969 | − | 3.19011i | −0.362771 | − | 0.177778i | ||||
\(323\) | 39.0701 | 2.17392 | ||||||||
\(324\) | −2.75378 | + | 4.76968i | −0.152988 | + | 0.264982i | ||||
\(325\) | −5.69444 | − | 9.86306i | −0.315871 | − | 0.547104i | ||||
\(326\) | −0.996234 | − | 1.72553i | −0.0551763 | − | 0.0955681i | ||||
\(327\) | −6.68403 | + | 11.5771i | −0.369628 | + | 0.640214i | ||||
\(328\) | 56.7504 | 3.13352 | ||||||||
\(329\) | −0.322430 | − | 4.73860i | −0.0177762 | − | 0.261248i | ||||
\(330\) | −17.4520 | −0.960699 | ||||||||
\(331\) | 2.81522 | − | 4.87611i | 0.154739 | − | 0.268015i | −0.778225 | − | 0.627985i | \(-0.783880\pi\) |
0.932964 | + | 0.359970i | \(0.117213\pi\) | |||||||
\(332\) | 28.9973 | + | 50.2249i | 1.59144 | + | 2.75645i | ||||
\(333\) | 2.21781 | + | 3.84136i | 0.121535 | + | 0.210505i | ||||
\(334\) | 12.9126 | − | 22.3652i | 0.706544 | − | 1.22377i | ||||
\(335\) | 27.6596 | 1.51121 | ||||||||
\(336\) | 33.6414 | − | 22.5997i | 1.83529 | − | 1.23292i | ||||
\(337\) | 21.7330 | 1.18387 | 0.591936 | − | 0.805985i | \(-0.298364\pi\) | ||||
0.591936 | + | 0.805985i | \(0.298364\pi\) | |||||||
\(338\) | −13.5209 | + | 23.4189i | −0.735441 | + | 1.27382i | ||||
\(339\) | −0.593544 | − | 1.02805i | −0.0322369 | − | 0.0558360i | ||||
\(340\) | −54.9076 | − | 95.1027i | −2.97778 | − | 5.15767i | ||||
\(341\) | −2.77199 | + | 4.80124i | −0.150112 | + | 0.260001i | ||||
\(342\) | 18.1568 | 0.981809 | ||||||||
\(343\) | 3.74864 | + | 18.1369i | 0.202408 | + | 0.979301i | ||||
\(344\) | −6.42980 | −0.346671 | ||||||||
\(345\) | −1.69091 | + | 2.92874i | −0.0910354 | + | 0.157678i | ||||
\(346\) | 14.8663 | + | 25.7492i | 0.799218 | + | 1.38429i | ||||
\(347\) | −16.2403 | − | 28.1289i | −0.871822 | − | 1.51004i | −0.860110 | − | 0.510109i | \(-0.829605\pi\) |
−0.0117127 | − | 0.999931i | \(-0.503728\pi\) | |||||||
\(348\) | 22.7040 | − | 39.3245i | 1.21706 | − | 2.10801i | ||||
\(349\) | 0.230635 | 0.0123456 | 0.00617281 | − | 0.999981i | \(-0.498035\pi\) | ||||
0.00617281 | + | 0.999981i | \(0.498035\pi\) | |||||||
\(350\) | 38.7330 | − | 26.0202i | 2.07037 | − | 1.39084i | ||||
\(351\) | −1.76938 | −0.0944423 | ||||||||
\(352\) | 21.4237 | − | 37.1070i | 1.14189 | − | 1.97781i | ||||
\(353\) | −13.9482 | − | 24.1590i | −0.742388 | − | 1.28585i | −0.951405 | − | 0.307942i | \(-0.900360\pi\) |
0.209017 | − | 0.977912i | \(-0.432974\pi\) | |||||||
\(354\) | −1.87309 | − | 3.24429i | −0.0995537 | − | 0.172432i | ||||
\(355\) | −0.498905 | + | 0.864129i | −0.0264791 | + | 0.0458632i | ||||
\(356\) | −59.0388 | −3.12905 | ||||||||
\(357\) | −1.05897 | − | 15.5632i | −0.0560469 | − | 0.823694i | ||||
\(358\) | 27.2454 | 1.43996 | ||||||||
\(359\) | −8.18126 | + | 14.1704i | −0.431790 | + | 0.747883i | −0.997028 | − | 0.0770455i | \(-0.975451\pi\) |
0.565237 | + | 0.824928i | \(0.308785\pi\) | |||||||
\(360\) | −16.2507 | − | 28.1471i | −0.856488 | − | 1.48348i | ||||
\(361\) | −12.4559 | − | 21.5743i | −0.655575 | − | 1.13549i | ||||
\(362\) | −1.33659 | + | 2.31504i | −0.0702494 | + | 0.121676i | ||||
\(363\) | 7.45276 | 0.391168 | ||||||||
\(364\) | 23.1521 | + | 11.3458i | 1.21350 | + | 0.594681i | ||||
\(365\) | 15.0745 | 0.789033 | ||||||||
\(366\) | −12.8278 | + | 22.2184i | −0.670520 | + | 1.16138i | ||||
\(367\) | −7.73982 | − | 13.4058i | −0.404016 | − | 0.699775i | 0.590191 | − | 0.807264i | \(-0.299053\pi\) |
−0.994206 | + | 0.107488i | \(0.965719\pi\) | |||||||
\(368\) | −7.65901 | − | 13.2658i | −0.399253 | − | 0.691527i | ||||
\(369\) | 2.95247 | − | 5.11383i | 0.153700 | − | 0.266216i | ||||
\(370\) | −41.1011 | −2.13674 | ||||||||
\(371\) | −23.0097 | − | 11.2760i | −1.19460 | − | 0.585422i | ||||
\(372\) | −16.2120 | −0.840551 | ||||||||
\(373\) | 14.7036 | − | 25.4674i | 0.761325 | − | 1.31865i | −0.180843 | − | 0.983512i | \(-0.557883\pi\) |
0.942168 | − | 0.335141i | \(-0.108784\pi\) | |||||||
\(374\) | −15.2131 | − | 26.3499i | −0.786652 | − | 1.36252i | ||||
\(375\) | −2.42927 | − | 4.20761i | −0.125447 | − | 0.217280i | ||||
\(376\) | 8.62636 | − | 14.9413i | 0.444870 | − | 0.770538i | ||||
\(377\) | 14.5879 | 0.751317 | ||||||||
\(378\) | −0.492131 | − | 7.23261i | −0.0253125 | − | 0.372005i | ||||
\(379\) | 23.7449 | 1.21969 | 0.609846 | − | 0.792520i | \(-0.291231\pi\) | ||||
0.609846 | + | 0.792520i | \(0.291231\pi\) | |||||||
\(380\) | −61.7119 | + | 106.888i | −3.16575 | + | 5.48325i | ||||
\(381\) | −6.11554 | − | 10.5924i | −0.313309 | − | 0.542667i | ||||
\(382\) | 9.59915 | + | 16.6262i | 0.491135 | + | 0.850671i | ||||
\(383\) | −2.39500 | + | 4.14826i | −0.122379 | + | 0.211966i | −0.920705 | − | 0.390259i | \(-0.872386\pi\) |
0.798327 | + | 0.602225i | \(0.205719\pi\) | |||||||
\(384\) | 41.3538 | 2.11033 | ||||||||
\(385\) | 13.9883 | − | 9.39715i | 0.712912 | − | 0.478923i | ||||
\(386\) | −34.3053 | −1.74609 | ||||||||
\(387\) | −0.334514 | + | 0.579395i | −0.0170043 | + | 0.0294523i | ||||
\(388\) | −43.0387 | − | 74.5452i | −2.18496 | − | 3.78446i | ||||
\(389\) | −11.2776 | − | 19.5334i | −0.571798 | − | 0.990384i | −0.996381 | − | 0.0849949i | \(-0.972913\pi\) |
0.424583 | − | 0.905389i | \(-0.360421\pi\) | |||||||
\(390\) | 8.19764 | − | 14.1987i | 0.415104 | − | 0.718981i | ||||
\(391\) | −5.89595 | −0.298171 | ||||||||
\(392\) | −25.4352 | + | 62.2810i | −1.28467 | + | 3.14567i | ||||
\(393\) | 6.05670 | 0.305520 | ||||||||
\(394\) | −34.7002 | + | 60.1024i | −1.74817 | + | 3.02792i | ||||
\(395\) | −5.11953 | − | 8.86729i | −0.257592 | − | 0.446162i | ||||
\(396\) | −5.18649 | − | 8.98327i | −0.260631 | − | 0.451426i | ||||
\(397\) | −1.79437 | + | 3.10794i | −0.0900570 | + | 0.155983i | −0.907535 | − | 0.419977i | \(-0.862038\pi\) |
0.817478 | + | 0.575960i | \(0.195372\pi\) | |||||||
\(398\) | −1.77705 | −0.0890753 | ||||||||
\(399\) | −14.5533 | + | 9.77670i | −0.728577 | + | 0.489447i | ||||
\(400\) | 98.5969 | 4.92985 | ||||||||
\(401\) | −5.31679 | + | 9.20895i | −0.265508 | + | 0.459873i | −0.967697 | − | 0.252118i | \(-0.918873\pi\) |
0.702189 | + | 0.711991i | \(0.252206\pi\) | |||||||
\(402\) | 11.2051 | + | 19.4078i | 0.558860 | + | 0.967974i | ||||
\(403\) | −2.60416 | − | 4.51053i | −0.129722 | − | 0.224685i | ||||
\(404\) | −20.8438 | + | 36.1024i | −1.03702 | + | 1.79616i | ||||
\(405\) | −3.38181 | −0.168044 | ||||||||
\(406\) | 4.05746 | + | 59.6306i | 0.201368 | + | 2.95942i | ||||
\(407\) | −8.35410 | −0.414098 | ||||||||
\(408\) | 28.3320 | − | 49.0725i | 1.40264 | − | 2.42945i | ||||
\(409\) | −7.26614 | − | 12.5853i | −0.359288 | − | 0.622304i | 0.628554 | − | 0.777766i | \(-0.283647\pi\) |
−0.987842 | + | 0.155461i | \(0.950314\pi\) | |||||||
\(410\) | 27.3580 | + | 47.3855i | 1.35112 | + | 2.34020i | ||||
\(411\) | −7.14630 | + | 12.3778i | −0.352501 | + | 0.610550i | ||||
\(412\) | −14.4368 | −0.711248 | ||||||||
\(413\) | 3.24826 | + | 1.59183i | 0.159837 | + | 0.0783288i | ||||
\(414\) | −2.73999 | −0.134663 | ||||||||
\(415\) | −17.8053 | + | 30.8397i | −0.874028 | + | 1.51386i | ||||
\(416\) | 20.1266 | + | 34.8602i | 0.986786 | + | 1.70916i | ||||
\(417\) | −8.21448 | − | 14.2279i | −0.402265 | − | 0.696743i | ||||
\(418\) | −17.0984 | + | 29.6153i | −0.836310 | + | 1.44853i | ||||
\(419\) | −28.8287 | −1.40837 | −0.704187 | − | 0.710015i | \(-0.748688\pi\) | ||||
−0.704187 | + | 0.710015i | \(0.748688\pi\) | |||||||
\(420\) | 44.2506 | + | 21.6852i | 2.15921 | + | 1.05813i | ||||
\(421\) | 25.2897 | 1.23254 | 0.616271 | − | 0.787534i | \(-0.288643\pi\) | ||||
0.616271 | + | 0.787534i | \(0.288643\pi\) | |||||||
\(422\) | 19.8166 | − | 34.3233i | 0.964655 | − | 1.67083i | ||||
\(423\) | −0.897583 | − | 1.55466i | −0.0436420 | − | 0.0755901i | ||||
\(424\) | −46.5396 | − | 80.6090i | −2.26016 | − | 3.91472i | ||||
\(425\) | 18.9751 | − | 32.8659i | 0.920430 | − | 1.59423i | ||||
\(426\) | −0.808440 | −0.0391690 | ||||||||
\(427\) | −1.68176 | − | 24.7161i | −0.0813862 | − | 1.19609i | ||||
\(428\) | 95.4579 | 4.61413 | ||||||||
\(429\) | 1.66623 | − | 2.88600i | 0.0804464 | − | 0.139337i | ||||
\(430\) | −3.09965 | − | 5.36876i | −0.149479 | − | 0.258904i | ||||
\(431\) | 0.666648 | + | 1.15467i | 0.0321113 | + | 0.0556184i | 0.881634 | − | 0.471933i | \(-0.156444\pi\) |
−0.849523 | + | 0.527551i | \(0.823110\pi\) | |||||||
\(432\) | 7.65901 | − | 13.2658i | 0.368494 | − | 0.638250i | ||||
\(433\) | −12.4620 | −0.598887 | −0.299444 | − | 0.954114i | \(-0.596801\pi\) | ||||
−0.299444 | + | 0.954114i | \(0.596801\pi\) | |||||||
\(434\) | 17.7132 | − | 11.8995i | 0.850261 | − | 0.571192i | ||||
\(435\) | 27.8820 | 1.33684 | ||||||||
\(436\) | 36.8126 | − | 63.7613i | 1.76301 | − | 3.05361i | ||||
\(437\) | 3.31330 | + | 5.73881i | 0.158497 | + | 0.274524i | ||||
\(438\) | 6.10676 | + | 10.5772i | 0.291792 | + | 0.505399i | ||||
\(439\) | −6.88278 | + | 11.9213i | −0.328497 | + | 0.568974i | −0.982214 | − | 0.187766i | \(-0.939875\pi\) |
0.653717 | + | 0.756739i | \(0.273209\pi\) | |||||||
\(440\) | 61.2136 | 2.91825 | ||||||||
\(441\) | 4.28892 | + | 5.53219i | 0.204234 | + | 0.263438i | ||||
\(442\) | 28.5840 | 1.35960 | ||||||||
\(443\) | 3.53406 | − | 6.12117i | 0.167908 | − | 0.290826i | −0.769776 | − | 0.638314i | \(-0.779632\pi\) |
0.937684 | + | 0.347489i | \(0.112965\pi\) | |||||||
\(444\) | −12.2147 | − | 21.1565i | −0.579684 | − | 1.00404i | ||||
\(445\) | −18.1259 | − | 31.3949i | −0.859248 | − | 1.48826i | ||||
\(446\) | −40.7337 | + | 70.5528i | −1.92880 | + | 3.34077i | ||||
\(447\) | −13.8036 | −0.652888 | ||||||||
\(448\) | −69.6161 | + | 46.7670i | −3.28905 | + | 2.20953i | ||||
\(449\) | −22.4140 | −1.05778 | −0.528892 | − | 0.848689i | \(-0.677392\pi\) | ||||
−0.528892 | + | 0.848689i | \(0.677392\pi\) | |||||||
\(450\) | 8.81820 | − | 15.2736i | 0.415694 | − | 0.720003i | ||||
\(451\) | 5.56072 | + | 9.63146i | 0.261844 | + | 0.453528i | ||||
\(452\) | 3.26898 | + | 5.66203i | 0.153760 | + | 0.266320i | ||||
\(453\) | −2.12357 | + | 3.67813i | −0.0997741 | + | 0.172814i | ||||
\(454\) | 17.7831 | 0.834601 | ||||||||
\(455\) | 1.07473 | + | 15.7949i | 0.0503843 | + | 0.740474i | ||||
\(456\) | −63.6860 | −2.98237 | ||||||||
\(457\) | 1.34517 | − | 2.32990i | 0.0629244 | − | 0.108988i | −0.832847 | − | 0.553503i | \(-0.813291\pi\) |
0.895771 | + | 0.444515i | \(0.146624\pi\) | |||||||
\(458\) | −1.69342 | − | 2.93309i | −0.0791284 | − | 0.137054i | ||||
\(459\) | −2.94798 | − | 5.10605i | −0.137600 | − | 0.238330i | ||||
\(460\) | 9.31276 | − | 16.1302i | 0.434209 | − | 0.752073i | ||||
\(461\) | 30.1064 | 1.40220 | 0.701098 | − | 0.713065i | \(-0.252693\pi\) | ||||
0.701098 | + | 0.713065i | \(0.252693\pi\) | |||||||
\(462\) | 12.2604 | + | 6.00829i | 0.570407 | + | 0.279531i | ||||
\(463\) | −14.0463 | −0.652787 | −0.326394 | − | 0.945234i | \(-0.605834\pi\) | ||||
−0.326394 | + | 0.945234i | \(0.605834\pi\) | |||||||
\(464\) | −63.1461 | + | 109.372i | −2.93148 | + | 5.07748i | ||||
\(465\) | −4.97733 | − | 8.62099i | −0.230818 | − | 0.399789i | ||||
\(466\) | 33.3679 | + | 57.7949i | 1.54574 | + | 2.67730i | ||||
\(467\) | 5.30205 | − | 9.18342i | 0.245350 | − | 0.424958i | −0.716880 | − | 0.697196i | \(-0.754431\pi\) |
0.962230 | + | 0.272238i | \(0.0877639\pi\) | |||||||
\(468\) | 9.74492 | 0.450459 | ||||||||
\(469\) | −19.4316 | − | 9.52255i | −0.897267 | − | 0.439710i | ||||
\(470\) | 16.6343 | 0.767281 | ||||||||
\(471\) | −0.333896 | + | 0.578325i | −0.0153851 | + | 0.0266478i | ||||
\(472\) | 6.56997 | + | 11.3795i | 0.302407 | + | 0.523785i | ||||
\(473\) | −0.630028 | − | 1.09124i | −0.0289687 | − | 0.0501753i | ||||
\(474\) | 4.14791 | − | 7.18440i | 0.190520 | − | 0.329990i | ||||
\(475\) | −42.6532 | −1.95706 | ||||||||
\(476\) | 5.83235 | + | 85.7153i | 0.267326 | + | 3.92876i | ||||
\(477\) | −9.68500 | −0.443446 | ||||||||
\(478\) | 20.8884 | − | 36.1798i | 0.955414 | − | 1.65483i | ||||
\(479\) | 5.63196 | + | 9.75483i | 0.257331 | + | 0.445710i | 0.965526 | − | 0.260307i | \(-0.0838237\pi\) |
−0.708195 | + | 0.706017i | \(0.750490\pi\) | |||||||
\(480\) | 38.4680 | + | 66.6285i | 1.75581 | + | 3.04116i | ||||
\(481\) | 3.92414 | − | 6.79681i | 0.178925 | − | 0.309908i | ||||
\(482\) | −11.3080 | −0.515066 | ||||||||
\(483\) | 2.19620 | − | 1.47537i | 0.0999304 | − | 0.0671317i | ||||
\(484\) | −41.0464 | −1.86575 | ||||||||
\(485\) | 26.4271 | − | 45.7731i | 1.19999 | − | 2.07845i | ||||
\(486\) | −1.37000 | − | 2.37290i | −0.0621443 | − | 0.107637i | ||||
\(487\) | −0.951673 | − | 1.64835i | −0.0431244 | − | 0.0746937i | 0.843658 | − | 0.536882i | \(-0.180398\pi\) |
−0.886782 | + | 0.462188i | \(0.847065\pi\) | |||||||
\(488\) | 44.9942 | − | 77.9322i | 2.03679 | − | 3.52783i | ||||
\(489\) | 0.727180 | 0.0328842 | ||||||||
\(490\) | −64.2651 | + | 8.78630i | −2.90320 | + | 0.396925i | ||||
\(491\) | 20.8742 | 0.942040 | 0.471020 | − | 0.882123i | \(-0.343886\pi\) | ||||
0.471020 | + | 0.882123i | \(0.343886\pi\) | |||||||
\(492\) | −16.2609 | + | 28.1647i | −0.733098 | + | 1.26976i | ||||
\(493\) | 24.3051 | + | 42.0977i | 1.09465 | + | 1.89599i | ||||
\(494\) | −16.0631 | − | 27.8221i | −0.722714 | − | 1.25178i | ||||
\(495\) | 3.18467 | − | 5.51602i | 0.143140 | − | 0.247927i | ||||
\(496\) | 45.0899 | 2.02460 | ||||||||
\(497\) | 0.647992 | − | 0.435311i | 0.0290664 | − | 0.0195264i | ||||
\(498\) | −28.8522 | −1.29290 | ||||||||
\(499\) | 18.5467 | − | 32.1239i | 0.830266 | − | 1.43806i | −0.0675618 | − | 0.997715i | \(-0.521522\pi\) |
0.897828 | − | 0.440347i | \(-0.145145\pi\) | |||||||
\(500\) | 13.3793 | + | 23.1736i | 0.598341 | + | 1.03636i | ||||
\(501\) | 4.71263 | + | 8.16252i | 0.210545 | + | 0.364674i | ||||
\(502\) | 6.61272 | − | 11.4536i | 0.295140 | − | 0.511198i | ||||
\(503\) | 0.702967 | 0.0313437 | 0.0156719 | − | 0.999877i | \(-0.495011\pi\) | ||||
0.0156719 | + | 0.999877i | \(0.495011\pi\) | |||||||
\(504\) | 1.72617 | + | 25.3687i | 0.0768899 | + | 1.13001i | ||||
\(505\) | −25.5975 | −1.13907 | ||||||||
\(506\) | 2.58027 | − | 4.46915i | 0.114707 | − | 0.198678i | ||||
\(507\) | −4.93466 | − | 8.54707i | −0.219156 | − | 0.379589i | ||||
\(508\) | 33.6817 | + | 58.3384i | 1.49438 | + | 2.58835i | ||||
\(509\) | −9.46193 | + | 16.3885i | −0.419393 | + | 0.726409i | −0.995878 | − | 0.0906978i | \(-0.971090\pi\) |
0.576486 | + | 0.817107i | \(0.304424\pi\) | |||||||
\(510\) | 54.6327 | 2.41918 | ||||||||
\(511\) | −10.5902 | − | 5.18977i | −0.468482 | − | 0.229582i | ||||
\(512\) | −54.0509 | −2.38874 | ||||||||
\(513\) | −3.31330 | + | 5.73881i | −0.146286 | + | 0.253374i | ||||
\(514\) | −6.50939 | − | 11.2746i | −0.287117 | − | 0.497301i | ||||
\(515\) | −4.43232 | − | 7.67700i | −0.195311 | − | 0.338289i | ||||
\(516\) | 1.84235 | − | 3.19105i | 0.0811050 | − | 0.140478i | ||||
\(517\) | 3.38104 | 0.148698 | ||||||||
\(518\) | 28.8745 | + | 14.1501i | 1.26867 | + | 0.621720i | ||||
\(519\) | −10.8514 | −0.476322 | ||||||||
\(520\) | −28.7536 | + | 49.8028i | −1.26093 | + | 2.18400i | ||||
\(521\) | −9.57227 | − | 16.5797i | −0.419369 | − | 0.726368i | 0.576507 | − | 0.817092i | \(-0.304415\pi\) |
−0.995876 | + | 0.0907240i | \(0.971082\pi\) | |||||||
\(522\) | 11.2952 | + | 19.5638i | 0.494376 | + | 0.856285i | ||||
\(523\) | −6.95888 | + | 12.0531i | −0.304291 | + | 0.527047i | −0.977103 | − | 0.212766i | \(-0.931753\pi\) |
0.672813 | + | 0.739813i | \(0.265086\pi\) | |||||||
\(524\) | −33.3576 | −1.45723 | ||||||||
\(525\) | 1.15609 | + | 16.9905i | 0.0504560 | + | 0.741527i | ||||
\(526\) | 44.2275 | 1.92841 | ||||||||
\(527\) | 8.67763 | − | 15.0301i | 0.378003 | − | 0.654721i | ||||
\(528\) | 14.4251 | + | 24.9849i | 0.627770 | + | 1.08733i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 44.8713 | − | 77.7194i | 1.94908 | − | 3.37591i | ||||
\(531\) | 1.36723 | 0.0593325 | ||||||||
\(532\) | 80.1532 | − | 53.8456i | 3.47508 | − | 2.33450i | ||||
\(533\) | −10.4481 | −0.452556 | ||||||||
\(534\) | 14.6858 | − | 25.4366i | 0.635518 | − | 1.10075i | ||||
\(535\) | 29.3071 | + | 50.7614i | 1.26706 | + | 2.19461i | ||||
\(536\) | −39.3025 | − | 68.0739i | −1.69761 | − | 2.94034i | ||||
\(537\) | −4.97180 | + | 8.61141i | −0.214549 | + | 0.371610i | ||||
\(538\) | −26.2919 | −1.13353 | ||||||||
\(539\) | −13.0624 | + | 1.78588i | −0.562636 | + | 0.0769234i | ||||
\(540\) | 18.6255 | 0.801514 | ||||||||
\(541\) | −14.3756 | + | 24.8992i | −0.618053 | + | 1.07050i | 0.371787 | + | 0.928318i | \(0.378745\pi\) |
−0.989841 | + | 0.142182i | \(0.954588\pi\) | |||||||
\(542\) | 28.7179 | + | 49.7409i | 1.23354 | + | 2.13656i | ||||
\(543\) | −0.487807 | − | 0.844906i | −0.0209338 | − | 0.0362584i | ||||
\(544\) | −67.0662 | + | 116.162i | −2.87544 | + | 4.98041i | ||||
\(545\) | 45.2083 | 1.93651 | ||||||||
\(546\) | −10.6473 | + | 7.15271i | −0.455663 | + | 0.306108i | ||||
\(547\) | 25.9067 | 1.10769 | 0.553845 | − | 0.832620i | \(-0.313160\pi\) | ||||
0.553845 | + | 0.832620i | \(0.313160\pi\) | |||||||
\(548\) | 39.3586 | − | 68.1711i | 1.68132 | − | 2.91213i | ||||
\(549\) | −4.68170 | − | 8.10894i | −0.199810 | − | 0.346081i | ||||
\(550\) | 16.6083 | + | 28.7664i | 0.708181 | + | 1.22660i | ||||
\(551\) | 27.3171 | − | 47.3146i | 1.16375 | − | 2.01567i | ||||
\(552\) | 9.61066 | 0.409057 | ||||||||
\(553\) | 0.543803 | + | 7.99202i | 0.0231249 | + | 0.339855i | ||||
\(554\) | −39.9555 | −1.69755 | ||||||||
\(555\) | 7.50022 | − | 12.9908i | 0.318367 | − | 0.551427i | ||||
\(556\) | 45.2416 | + | 78.3608i | 1.91867 | + | 3.32324i | ||||
\(557\) | 2.31799 | + | 4.01488i | 0.0982164 | + | 0.170116i | 0.910946 | − | 0.412525i | \(-0.135353\pi\) |
−0.812730 | + | 0.582640i | \(0.802020\pi\) | |||||||
\(558\) | 4.03270 | − | 6.98484i | 0.170718 | − | 0.295692i | ||||
\(559\) | 1.18376 | 0.0500678 | ||||||||
\(560\) | −123.073 | − | 60.3126i | −5.20079 | − | 2.54867i | ||||
\(561\) | 11.1045 | 0.468833 | ||||||||
\(562\) | −14.0707 | + | 24.3712i | −0.593537 | + | 1.02804i | ||||
\(563\) | −2.61558 | − | 4.53031i | −0.110233 | − | 0.190930i | 0.805631 | − | 0.592418i | \(-0.201827\pi\) |
−0.915864 | + | 0.401488i | \(0.868493\pi\) | |||||||
\(564\) | 4.94348 | + | 8.56236i | 0.208158 | + | 0.360540i | ||||
\(565\) | −2.00726 | + | 3.47667i | −0.0844459 | + | 0.146265i | ||||
\(566\) | −46.8347 | −1.96861 | ||||||||
\(567\) | 2.37581 | + | 1.16428i | 0.0997745 | + | 0.0488950i | ||||
\(568\) | 2.83564 | 0.118981 | ||||||||
\(569\) | −3.85568 | + | 6.67823i | −0.161638 | + | 0.279966i | −0.935456 | − | 0.353442i | \(-0.885011\pi\) |
0.773818 | + | 0.633408i | \(0.218344\pi\) | |||||||
\(570\) | −30.7015 | − | 53.1766i | −1.28594 | − | 2.22732i | ||||
\(571\) | −8.77576 | − | 15.2001i | −0.367254 | − | 0.636103i | 0.621881 | − | 0.783112i | \(-0.286369\pi\) |
−0.989135 | + | 0.147009i | \(0.953035\pi\) | |||||||
\(572\) | −9.17685 | + | 15.8948i | −0.383704 | + | 0.664594i | ||||
\(573\) | −7.00670 | −0.292709 | ||||||||
\(574\) | −2.90601 | − | 42.7082i | −0.121294 | − | 1.78260i | ||||
\(575\) | 6.43667 | 0.268427 | ||||||||
\(576\) | −15.8492 | + | 27.4517i | −0.660385 | + | 1.14382i | ||||
\(577\) | −7.82632 | − | 13.5556i | −0.325814 | − | 0.564327i | 0.655863 | − | 0.754880i | \(-0.272305\pi\) |
−0.981677 | + | 0.190554i | \(0.938972\pi\) | |||||||
\(578\) | 24.3342 | + | 42.1481i | 1.01217 | + | 1.75313i | ||||
\(579\) | 6.26011 | − | 10.8428i | 0.260161 | − | 0.450613i | ||||
\(580\) | −153.561 | −6.37629 | ||||||||
\(581\) | 23.1260 | − | 15.5357i | 0.959429 | − | 0.644529i | ||||
\(582\) | 42.8232 | 1.77508 | ||||||||
\(583\) | 9.12043 | − | 15.7970i | 0.377729 | − | 0.654247i | ||||
\(584\) | −21.4198 | − | 37.1001i | −0.886357 | − | 1.53521i | ||||
\(585\) | 2.99185 | + | 5.18203i | 0.123698 | + | 0.214251i | ||||
\(586\) | 14.9369 | − | 25.8715i | 0.617039 | − | 1.06874i | ||||
\(587\) | 29.3900 | 1.21305 | 0.606527 | − | 0.795063i | \(-0.292562\pi\) | ||||
0.606527 | + | 0.795063i | \(0.292562\pi\) | |||||||
\(588\) | −23.6214 | − | 30.4688i | −0.974132 | − | 1.25651i | ||||
\(589\) | −19.5060 | −0.803730 | ||||||||
\(590\) | −6.33445 | + | 10.9716i | −0.260785 | + | 0.451693i | ||||
\(591\) | −12.6643 | − | 21.9353i | −0.520941 | − | 0.902296i | ||||
\(592\) | 33.9724 | + | 58.8420i | 1.39626 | + | 2.41839i | ||||
\(593\) | 9.00362 | − | 15.5947i | 0.369734 | − | 0.640399i | −0.619789 | − | 0.784768i | \(-0.712782\pi\) |
0.989524 | + | 0.144369i | \(0.0461154\pi\) | |||||||
\(594\) | 5.16053 | 0.211739 | ||||||||
\(595\) | −43.7900 | + | 29.4175i | −1.79522 | + | 1.20600i | ||||
\(596\) | 76.0241 | 3.11407 | ||||||||
\(597\) | 0.324280 | − | 0.561669i | 0.0132719 | − | 0.0229876i | ||||
\(598\) | 2.42404 | + | 4.19855i | 0.0991262 | + | 0.171692i | ||||
\(599\) | 6.16954 | + | 10.6860i | 0.252081 | + | 0.436617i | 0.964099 | − | 0.265545i | \(-0.0855518\pi\) |
−0.712018 | + | 0.702161i | \(0.752218\pi\) | |||||||
\(600\) | −30.9303 | + | 53.5728i | −1.26272 | + | 2.18710i | ||||
\(601\) | 0.594459 | 0.0242485 | 0.0121243 | − | 0.999926i | \(-0.496141\pi\) | ||||
0.0121243 | + | 0.999926i | \(0.496141\pi\) | |||||||
\(602\) | 0.329249 | + | 4.83882i | 0.0134192 | + | 0.197216i | ||||
\(603\) | −8.17894 | −0.333072 | ||||||||
\(604\) | 11.6957 | − | 20.2575i | 0.475890 | − | 0.824266i | ||||
\(605\) | −12.6019 | − | 21.8272i | −0.512341 | − | 0.887401i | ||||
\(606\) | −10.3697 | − | 17.9609i | −0.421241 | − | 0.729610i | ||||
\(607\) | 0.0338873 | − | 0.0586945i | 0.00137544 | − | 0.00238233i | −0.865337 | − | 0.501191i | \(-0.832896\pi\) |
0.866712 | + | 0.498808i | \(0.166229\pi\) | |||||||
\(608\) | 150.755 | 6.11390 | ||||||||
\(609\) | −19.5878 | − | 9.59909i | −0.793737 | − | 0.388975i | ||||
\(610\) | 86.7625 | 3.51291 | ||||||||
\(611\) | −1.58816 | + | 2.75077i | −0.0642501 | + | 0.111284i | ||||
\(612\) | 16.2361 | + | 28.1218i | 0.656307 | + | 1.13676i | ||||
\(613\) | −10.7516 | − | 18.6224i | −0.434254 | − | 0.752150i | 0.562980 | − | 0.826470i | \(-0.309655\pi\) |
−0.997234 | + | 0.0743201i | \(0.976321\pi\) | |||||||
\(614\) | 36.7121 | − | 63.5873i | 1.48158 | − | 2.56617i | ||||
\(615\) | −19.9694 | −0.805245 | ||||||||
\(616\) | −43.0041 | − | 21.0744i | −1.73268 | − | 0.849111i | ||||
\(617\) | 10.0024 | 0.402683 | 0.201341 | − | 0.979521i | \(-0.435470\pi\) | ||||
0.201341 | + | 0.979521i | \(0.435470\pi\) | |||||||
\(618\) | 3.59113 | − | 6.22001i | 0.144456 | − | 0.250206i | ||||
\(619\) | 6.57468 | + | 11.3877i | 0.264259 | + | 0.457710i | 0.967369 | − | 0.253371i | \(-0.0815394\pi\) |
−0.703110 | + | 0.711081i | \(0.748206\pi\) | |||||||
\(620\) | 27.4129 | + | 47.4806i | 1.10093 | + | 1.90686i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | −48.9404 | −1.96233 | ||||||||
\(623\) | 1.92535 | + | 28.2960i | 0.0771376 | + | 1.13366i | ||||
\(624\) | −27.1033 | −1.08500 | ||||||||
\(625\) | 7.87633 | − | 13.6422i | 0.315053 | − | 0.545688i | ||||
\(626\) | −39.9078 | − | 69.1224i | −1.59504 | − | 2.76269i | ||||
\(627\) | −6.24031 | − | 10.8085i | −0.249214 | − | 0.431651i | ||||
\(628\) | 1.83895 | − | 3.18516i | 0.0733821 | − | 0.127102i | ||||
\(629\) | 26.1522 | 1.04276 | ||||||||
\(630\) | −20.3503 | + | 13.6710i | −0.810774 | + | 0.544665i | ||||
\(631\) | 27.0831 | 1.07816 | 0.539081 | − | 0.842254i | \(-0.318772\pi\) | ||||
0.539081 | + | 0.842254i | \(0.318772\pi\) | |||||||
\(632\) | −14.5490 | + | 25.1996i | −0.578729 | + | 1.00239i | ||||
\(633\) | 7.23235 | + | 12.5268i | 0.287460 | + | 0.497895i | ||||
\(634\) | 30.0541 | + | 52.0552i | 1.19360 | + | 2.06737i | ||||
\(635\) | −20.6816 | + | 35.8216i | −0.820725 | + | 1.42154i | ||||
\(636\) | 53.3406 | 2.11509 | ||||||||
\(637\) | 4.68276 | − | 11.4663i | 0.185538 | − | 0.454310i | ||||
\(638\) | −42.5469 | −1.68445 | ||||||||
\(639\) | 0.147526 | − | 0.255522i | 0.00583604 | − | 0.0101083i | ||||
\(640\) | −69.9254 | − | 121.114i | −2.76404 | − | 4.78747i | ||||
\(641\) | 18.8298 | + | 32.6142i | 0.743733 | + | 1.28818i | 0.950784 | + | 0.309854i | \(0.100280\pi\) |
−0.207051 | + | 0.978330i | \(0.566387\pi\) | |||||||
\(642\) | −23.7450 | + | 41.1276i | −0.937141 | + | 1.62318i | ||||
\(643\) | 0.584100 | 0.0230347 | 0.0115173 | − | 0.999934i | \(-0.496334\pi\) | ||||
0.0115173 | + | 0.999934i | \(0.496334\pi\) | |||||||
\(644\) | −12.0957 | + | 8.12568i | −0.476636 | + | 0.320197i | ||||
\(645\) | 2.26253 | 0.0890869 | ||||||||
\(646\) | 53.5259 | − | 92.7096i | 2.10595 | − | 3.64761i | ||||
\(647\) | −2.90401 | − | 5.02990i | −0.114169 | − | 0.197746i | 0.803279 | − | 0.595604i | \(-0.203087\pi\) |
−0.917447 | + | 0.397858i | \(0.869754\pi\) | |||||||
\(648\) | 4.80533 | + | 8.32307i | 0.188771 | + | 0.326961i | ||||
\(649\) | −1.28752 | + | 2.23006i | −0.0505398 | + | 0.0875374i | ||||
\(650\) | −31.2054 | −1.22398 | ||||||||
\(651\) | 0.528699 | + | 7.77003i | 0.0207213 | + | 0.304532i | ||||
\(652\) | −4.00498 | −0.156847 | ||||||||
\(653\) | −12.3522 | + | 21.3946i | −0.483378 | + | 0.837235i | −0.999818 | − | 0.0190884i | \(-0.993924\pi\) |
0.516440 | + | 0.856323i | \(0.327257\pi\) | |||||||
\(654\) | 18.3142 | + | 31.7211i | 0.716141 | + | 1.24039i | ||||
\(655\) | −10.2413 | − | 17.7385i | −0.400161 | − | 0.693100i | ||||
\(656\) | 45.2260 | − | 78.3338i | 1.76578 | − | 3.05842i | ||||
\(657\) | −4.45751 | −0.173904 | ||||||||
\(658\) | −11.6860 | − | 5.72677i | −0.455567 | − | 0.223253i | ||||
\(659\) | 24.0716 | 0.937697 | 0.468848 | − | 0.883279i | \(-0.344669\pi\) | ||||
0.468848 | + | 0.883279i | \(0.344669\pi\) | |||||||
\(660\) | −17.5398 | + | 30.3798i | −0.682734 | + | 1.18253i | ||||
\(661\) | −5.08195 | − | 8.80219i | −0.197665 | − | 0.342366i | 0.750106 | − | 0.661318i | \(-0.230002\pi\) |
−0.947771 | + | 0.318952i | \(0.896669\pi\) | |||||||
\(662\) | −7.71369 | − | 13.3605i | −0.299801 | − | 0.519271i | ||||
\(663\) | −5.21608 | + | 9.03451i | −0.202576 | + | 0.350871i | ||||
\(664\) | 101.200 | 3.92734 | ||||||||
\(665\) | 53.2417 | + | 26.0914i | 2.06462 | + | 1.01178i | ||||
\(666\) | 12.1536 | 0.470941 | ||||||||
\(667\) | −4.12234 | + | 7.14010i | −0.159618 | + | 0.276466i | ||||
\(668\) | −25.9550 | − | 44.9555i | −1.00423 | − | 1.73938i | ||||
\(669\) | −14.8664 | − | 25.7493i | −0.574766 | − | 0.995525i | ||||
\(670\) | 37.8936 | − | 65.6336i | 1.46396 | − | 2.53565i | ||||
\(671\) | 17.6351 | 0.680797 | ||||||||
\(672\) | −4.08612 | − | 60.0517i | −0.157625 | − | 2.31655i | ||||
\(673\) | 21.4374 | 0.826350 | 0.413175 | − | 0.910652i | \(-0.364420\pi\) | ||||
0.413175 | + | 0.910652i | \(0.364420\pi\) | |||||||
\(674\) | 29.7741 | − | 51.5703i | 1.14686 | − | 1.98641i | ||||
\(675\) | 3.21833 | + | 5.57432i | 0.123874 | + | 0.214556i | ||||
\(676\) | 27.1779 | + | 47.0734i | 1.04530 | + | 1.81052i | ||||
\(677\) | −14.5934 | + | 25.2765i | −0.560869 | + | 0.971454i | 0.436552 | + | 0.899679i | \(0.356200\pi\) |
−0.997421 | + | 0.0717746i | \(0.977134\pi\) | |||||||
\(678\) | −3.25261 | −0.124916 | ||||||||
\(679\) | −34.3243 | + | 23.0585i | −1.31725 | + | 0.884905i | ||||
\(680\) | −191.627 | −7.34856 | ||||||||
\(681\) | −3.24510 | + | 5.62067i | −0.124352 | + | 0.215385i | ||||
\(682\) | 7.59524 | + | 13.1553i | 0.290837 | + | 0.503744i | ||||
\(683\) | 24.8388 | + | 43.0221i | 0.950432 | + | 1.64620i | 0.744492 | + | 0.667631i | \(0.232692\pi\) |
0.205940 | + | 0.978565i | \(0.433975\pi\) | |||||||
\(684\) | 18.2482 | − | 31.6068i | 0.697736 | − | 1.20851i | ||||
\(685\) | 48.3349 | 1.84678 | ||||||||
\(686\) | 48.1727 | + | 15.9523i | 1.83924 | + | 0.609063i | ||||
\(687\) | 1.23608 | 0.0471593 | ||||||||
\(688\) | −5.12409 | + | 8.87518i | −0.195354 | + | 0.338363i | ||||
\(689\) | 8.56820 | + | 14.8406i | 0.326423 | + | 0.565380i | ||||
\(690\) | 4.63307 | + | 8.02471i | 0.176378 | + | 0.305496i | ||||
\(691\) | −3.61070 | + | 6.25391i | −0.137357 | + | 0.237910i | −0.926496 | − | 0.376306i | \(-0.877194\pi\) |
0.789138 | + | 0.614216i | \(0.210528\pi\) | |||||||
\(692\) | 59.7644 | 2.27190 | ||||||||
\(693\) | −4.13634 | + | 2.77873i | −0.157127 | + | 0.105555i | ||||
\(694\) | −88.9963 | −3.37825 | ||||||||
\(695\) | −27.7798 | + | 48.1161i | −1.05375 | + | 1.82515i | ||||
\(696\) | −39.6184 | − | 68.6211i | −1.50173 | − | 2.60108i | ||||
\(697\) | −17.4076 | − | 30.1509i | −0.659362 | − | 1.14205i | ||||
\(698\) | 0.315969 | − | 0.547274i | 0.0119596 | − | 0.0207146i | ||||
\(699\) | −24.3562 | −0.921236 | ||||||||
\(700\) | −6.36723 | − | 93.5762i | −0.240659 | − | 3.53685i | ||||
\(701\) | −43.4759 | −1.64206 | −0.821031 | − | 0.570884i | \(-0.806601\pi\) | ||||
−0.821031 | + | 0.570884i | \(0.806601\pi\) | |||||||
\(702\) | −2.42404 | + | 4.19855i | −0.0914894 | + | 0.158464i | ||||
\(703\) | −14.6965 | − | 25.4552i | −0.554291 | − | 0.960060i | ||||
\(704\) | −29.8507 | − | 51.7029i | −1.12504 | − | 1.94863i | ||||
\(705\) | −3.03546 | + | 5.25757i | −0.114322 | + | 0.198011i | ||||
\(706\) | −76.4359 | −2.87670 | ||||||||
\(707\) | 17.9829 | + | 8.81259i | 0.676315 | + | 0.331432i | ||||
\(708\) | −7.53006 | −0.282997 | ||||||||
\(709\) | −11.6132 | + | 20.1146i | −0.436143 | + | 0.755421i | −0.997388 | − | 0.0722280i | \(-0.976989\pi\) |
0.561245 | + | 0.827649i | \(0.310322\pi\) | |||||||
\(710\) | 1.36700 | + | 2.36771i | 0.0513024 | + | 0.0888584i | ||||
\(711\) | 1.51384 | + | 2.62205i | 0.0567735 | + | 0.0983346i | ||||
\(712\) | −51.5112 | + | 89.2201i | −1.93047 | + | 3.34366i | ||||
\(713\) | 2.94359 | 0.110238 | ||||||||
\(714\) | −38.3808 | − | 18.8087i | −1.43637 | − | 0.703899i | ||||
\(715\) | −11.2698 | −0.421466 | ||||||||
\(716\) | 27.3824 | − | 47.4278i | 1.02333 | − | 1.77246i | ||||
\(717\) | 7.62354 | + | 13.2044i | 0.284706 | + | 0.493126i | ||||
\(718\) | 22.4166 | + | 38.8267i | 0.836579 | + | 1.44900i | ||||
\(719\) | −19.9020 | + | 34.4712i | −0.742218 | + | 1.28556i | 0.209265 | + | 0.977859i | \(0.432893\pi\) |
−0.951483 | + | 0.307701i | \(0.900440\pi\) | |||||||
\(720\) | −51.8027 | −1.93057 | ||||||||
\(721\) | 0.470807 | + | 6.91922i | 0.0175338 | + | 0.257685i | ||||
\(722\) | −68.2582 | −2.54031 | ||||||||
\(723\) | 2.06351 | − | 3.57411i | 0.0767429 | − | 0.132923i | ||||
\(724\) | 2.68662 | + | 4.65336i | 0.0998475 | + | 0.172941i | ||||
\(725\) | −26.5341 | − | 45.9585i | −0.985453 | − | 1.70685i | ||||
\(726\) | 10.2102 | − | 17.6847i | 0.378938 | − | 0.656339i | ||||
\(727\) | −22.3786 | −0.829978 | −0.414989 | − | 0.909826i | \(-0.636215\pi\) | ||||
−0.414989 | + | 0.909826i | \(0.636215\pi\) | |||||||
\(728\) | 37.3460 | − | 25.0885i | 1.38414 | − | 0.929841i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 20.6519 | − | 35.7702i | 0.764362 | − | 1.32391i | ||||
\(731\) | 1.97228 | + | 3.41609i | 0.0729474 | + | 0.126349i | ||||
\(732\) | 25.7847 | + | 44.6604i | 0.953029 | + | 1.65070i | ||||
\(733\) | 15.6130 | − | 27.0426i | 0.576681 | − | 0.998840i | −0.419176 | − | 0.907905i | \(-0.637681\pi\) |
0.995857 | − | 0.0909352i | \(-0.0289856\pi\) | |||||||
\(734\) | −42.4141 | −1.56553 | ||||||||
\(735\) | 8.95018 | − | 21.9155i | 0.330132 | − | 0.808367i | ||||
\(736\) | −22.7499 | −0.838572 | ||||||||
\(737\) | 7.70215 | − | 13.3405i | 0.283712 | − | 0.491404i | ||||
\(738\) | −8.08975 | − | 14.0119i | −0.297788 | − | 0.515784i | ||||
\(739\) | −17.3219 | − | 30.0024i | −0.637197 | − | 1.10366i | −0.986045 | − | 0.166478i | \(-0.946760\pi\) |
0.348848 | − | 0.937179i | \(-0.386573\pi\) | |||||||
\(740\) | −41.3079 | + | 71.5473i | −1.51851 | + | 2.63013i | ||||
\(741\) | 11.7249 | 0.430727 | ||||||||
\(742\) | −58.2801 | + | 39.1517i | −2.13953 | + | 1.43730i | ||||
\(743\) | −23.7961 | −0.872996 | −0.436498 | − | 0.899705i | \(-0.643781\pi\) | ||||
−0.436498 | + | 0.899705i | \(0.643781\pi\) | |||||||
\(744\) | −14.1449 | + | 24.4997i | −0.518577 | + | 0.898202i | ||||
\(745\) | 23.3406 | + | 40.4271i | 0.855134 | + | 1.48114i | ||||
\(746\) | −40.2878 | − | 69.7805i | −1.47504 | − | 2.55485i | ||||
\(747\) | 5.26501 | − | 9.11927i | 0.192637 | − | 0.333657i | ||||
\(748\) | −61.1587 | −2.23618 | ||||||||
\(749\) | −3.11304 | − | 45.7509i | −0.113748 | − | 1.67170i | ||||
\(750\) | −13.3123 | −0.486098 | ||||||||
\(751\) | 1.27430 | − | 2.20715i | 0.0464999 | − | 0.0805401i | −0.841839 | − | 0.539729i | \(-0.818527\pi\) |
0.888339 | + | 0.459189i | \(0.151860\pi\) | |||||||
\(752\) | −13.7492 | − | 23.8143i | −0.501381 | − | 0.868417i | ||||
\(753\) | 2.41341 | + | 4.18015i | 0.0879495 | + | 0.152333i | ||||
\(754\) | 19.9854 | − | 34.6157i | 0.727826 | − | 1.26063i | ||||
\(755\) | 14.3630 | 0.522725 | ||||||||
\(756\) | −13.0849 | − | 6.41231i | −0.475892 | − | 0.233214i | ||||
\(757\) | −35.5043 | −1.29042 | −0.645212 | − | 0.764004i | \(-0.723231\pi\) | ||||
−0.645212 | + | 0.764004i | \(0.723231\pi\) | |||||||
\(758\) | 32.5303 | − | 56.3442i | 1.18156 | − | 2.04651i | ||||
\(759\) | 0.941706 | + | 1.63108i | 0.0341818 | + | 0.0592046i | ||||
\(760\) | 107.687 | + | 186.520i | 3.90622 | + | 6.76577i | ||||
\(761\) | 15.0000 | − | 25.9808i | 0.543749 | − | 0.941802i | −0.454935 | − | 0.890525i | \(-0.650338\pi\) |
0.998684 | − | 0.0512770i | \(-0.0163291\pi\) | |||||||
\(762\) | −33.5131 | −1.21405 | ||||||||
\(763\) | −31.7599 | − | 15.5641i | −1.14979 | − | 0.563459i | ||||
\(764\) | 38.5898 | 1.39613 | ||||||||
\(765\) | −9.96951 | + | 17.2677i | −0.360448 | + | 0.624315i | ||||
\(766\) | 6.56228 | + | 11.3662i | 0.237105 | + | 0.410677i | ||||
\(767\) | −1.20957 | − | 2.09503i | −0.0436749 | − | 0.0756472i | ||||
\(768\) | 24.9560 | − | 43.2251i | 0.900523 | − | 1.55975i | ||||
\(769\) | 39.7222 | 1.43242 | 0.716210 | − | 0.697885i | \(-0.245875\pi\) | ||||
0.716210 | + | 0.697885i | \(0.245875\pi\) | |||||||
\(770\) | −3.13455 | − | 46.0670i | −0.112961 | − | 1.66014i | ||||
\(771\) | 4.75140 | 0.171117 | ||||||||
\(772\) | −34.4779 | + | 59.7174i | −1.24089 | + | 2.14928i | ||||
\(773\) | −5.99665 | − | 10.3865i | −0.215684 | − | 0.373576i | 0.737800 | − | 0.675020i | \(-0.235865\pi\) |
−0.953484 | + | 0.301443i | \(0.902532\pi\) | |||||||
\(774\) | 0.916565 | + | 1.58754i | 0.0329453 | + | 0.0570629i | ||||
\(775\) | −9.47344 | + | 16.4085i | −0.340296 | + | 0.589410i | ||||
\(776\) | −150.205 | −5.39203 | ||||||||
\(777\) | −9.74150 | + | 6.54419i | −0.349474 | + | 0.234771i | ||||
\(778\) | −61.8012 | −2.21568 | ||||||||
\(779\) | −19.5649 | + | 33.8873i | −0.700984 | + | 1.21414i | ||||
\(780\) | −16.4778 | − | 28.5403i | −0.589998 | − | 1.02191i | ||||
\(781\) | 0.277852 | + | 0.481254i | 0.00994233 | + | 0.0172206i | ||||
\(782\) | −8.07743 | + | 13.9905i | −0.288848 | + | 0.500300i | ||||
\(783\) | −8.24468 | −0.294641 | ||||||||
\(784\) | 65.6977 | + | 84.7422i | 2.34635 | + | 3.02651i | ||||
\(785\) | 2.25835 | 0.0806040 | ||||||||
\(786\) | 8.29765 | − | 14.3720i | 0.295967 | − | 0.512631i | ||||
\(787\) | 4.02056 | + | 6.96382i | 0.143318 | + | 0.248233i | 0.928744 | − | 0.370722i | \(-0.120890\pi\) |
−0.785426 | + | 0.618955i | \(0.787556\pi\) | |||||||
\(788\) | 69.7495 | + | 120.810i | 2.48472 | + | 4.30366i | ||||
\(789\) | −8.07074 | + | 13.9789i | −0.287326 | + | 0.497663i | ||||
\(790\) | −28.0549 | −0.998150 | ||||||||
\(791\) | 2.60708 | − | 1.75140i | 0.0926971 | − | 0.0622725i | ||||
\(792\) | −18.1008 | −0.643185 | ||||||||
\(793\) | −8.28368 | + | 14.3478i | −0.294162 | + | 0.509504i | ||||
\(794\) | 4.91656 | + | 8.51574i | 0.174482 | + | 0.302212i | ||||
\(795\) | 16.3764 | + | 28.3648i | 0.580812 | + | 1.00600i | ||||
\(796\) | −1.78599 | + | 3.09342i | −0.0633026 | + | 0.109643i | ||||
\(797\) | −27.9672 | −0.990651 | −0.495325 | − | 0.868708i | \(-0.664951\pi\) | ||||
−0.495325 | + | 0.868708i | \(0.664951\pi\) | |||||||
\(798\) | 3.26115 | + | 47.9276i | 0.115444 | + | 1.69662i | ||||
\(799\) | −10.5842 | −0.374443 | ||||||||
\(800\) | 73.2167 | − | 126.815i | 2.58860 | − | 4.48359i | ||||
\(801\) | 5.35981 | + | 9.28346i | 0.189379 | + | 0.328015i | ||||
\(802\) | 14.5680 | + | 25.2324i | 0.514412 | + | 0.890988i | ||||
\(803\) | 4.19766 | − | 7.27056i | 0.148132 | − | 0.256573i | ||||
\(804\) | 45.0459 | 1.58865 | ||||||||
\(805\) | −8.03454 | − | 3.93737i | −0.283180 | − | 0.138774i | ||||
\(806\) | −14.2707 | −0.502665 | ||||||||
\(807\) | 4.79781 | − | 8.31006i | 0.168891 | − | 0.292528i | ||||
\(808\) | 36.3723 | + | 62.9986i | 1.27957 | + | 2.21628i | ||||
\(809\) | −4.65850 | − | 8.06876i | −0.163784 | − | 0.283682i | 0.772439 | − | 0.635089i | \(-0.219037\pi\) |
−0.936223 | + | 0.351407i | \(0.885703\pi\) | |||||||
\(810\) | −4.63307 | + | 8.02471i | −0.162789 | + | 0.281960i | ||||
\(811\) | −18.5550 | −0.651553 | −0.325776 | − | 0.945447i | \(-0.605626\pi\) | ||||
−0.325776 | + | 0.945447i | \(0.605626\pi\) | |||||||
\(812\) | 107.881 | + | 52.8675i | 3.78587 | + | 1.85528i | ||||
\(813\) | −20.9621 | −0.735172 | ||||||||
\(814\) | −11.4451 | + | 19.8235i | −0.401150 | + | 0.694812i | ||||
\(815\) | −1.22959 | − | 2.12972i | −0.0430708 | − | 0.0746008i | ||||
\(816\) | −45.1571 | − | 78.2145i | −1.58082 | − | 2.73805i | ||||
\(817\) | 2.21669 | − | 3.83942i | 0.0775522 | − | 0.134324i | ||||
\(818\) | −39.8183 | −1.39222 | ||||||||
\(819\) | −0.317798 | − | 4.67053i | −0.0111048 | − | 0.163201i | ||||
\(820\) | 109.983 | 3.84076 | ||||||||
\(821\) | 10.8387 | − | 18.7733i | 0.378275 | − | 0.655191i | −0.612537 | − | 0.790442i | \(-0.709851\pi\) |
0.990811 | + | 0.135251i | \(0.0431841\pi\) | |||||||
\(822\) | 19.5808 | + | 33.9150i | 0.682959 | + | 1.18292i | ||||
\(823\) | −1.61481 | − | 2.79694i | −0.0562888 | − | 0.0974951i | 0.836508 | − | 0.547955i | \(-0.184593\pi\) |
−0.892797 | + | 0.450460i | \(0.851260\pi\) | |||||||
\(824\) | −12.5961 | + | 21.8170i | −0.438804 | + | 0.760031i | ||||
\(825\) | −12.1229 | −0.422065 | ||||||||
\(826\) | 8.22736 | − | 5.52701i | 0.286266 | − | 0.192309i | ||||
\(827\) | 34.5890 | 1.20278 | 0.601388 | − | 0.798957i | \(-0.294614\pi\) | ||||
0.601388 | + | 0.798957i | \(0.294614\pi\) | |||||||
\(828\) | −2.75378 | + | 4.76968i | −0.0957003 | + | 0.165758i | ||||
\(829\) | −8.55391 | − | 14.8158i | −0.297090 | − | 0.514574i | 0.678379 | − | 0.734712i | \(-0.262683\pi\) |
−0.975469 | + | 0.220138i | \(0.929349\pi\) | |||||||
\(830\) | 48.7864 | + | 84.5005i | 1.69340 | + | 2.93305i | ||||
\(831\) | 7.29118 | − | 12.6287i | 0.252928 | − | 0.438085i | ||||
\(832\) | 56.0865 | 1.94445 | ||||||||
\(833\) | 40.8913 | − | 5.59064i | 1.41680 | − | 0.193704i | ||||
\(834\) | −45.0152 | −1.55875 | ||||||||
\(835\) | 15.9372 | − | 27.6041i | 0.551531 | − | 0.955280i | ||||
\(836\) | 34.3688 | + | 59.5286i | 1.18867 | + | 2.05884i | ||||
\(837\) | 1.47179 | + | 2.54922i | 0.0508726 | + | 0.0881140i | ||||
\(838\) | −39.4952 | + | 68.4077i | −1.36434 | + | 2.36310i | ||||
\(839\) | −16.7696 | −0.578951 | −0.289476 | − | 0.957185i | \(-0.593481\pi\) | ||||
−0.289476 | + | 0.957185i | \(0.593481\pi\) | |||||||
\(840\) | 71.3796 | − | 47.9517i | 2.46283 | − | 1.65449i | ||||
\(841\) | 38.9748 | 1.34396 | ||||||||
\(842\) | 34.6467 | − | 60.0099i | 1.19400 | − | 2.06808i | ||||
\(843\) | −5.13531 | − | 8.89462i | −0.176870 | − | 0.306347i | ||||
\(844\) | −39.8325 | − | 68.9919i | −1.37109 | − | 2.37480i | ||||
\(845\) | −16.6881 | + | 28.9046i | −0.574088 | + | 0.994349i | ||||
\(846\) | −4.91874 | −0.169110 | ||||||||
\(847\) | 1.33859 | + | 19.6727i | 0.0459946 | + | 0.675960i | ||||
\(848\) | −148.355 | −5.09453 | ||||||||
\(849\) | 8.54651 | − | 14.8030i | 0.293315 | − | 0.508037i | ||||
\(850\) | −51.9917 | − | 90.0523i | −1.78330 | − | 3.08877i | ||||
\(851\) | 2.21781 | + | 3.84136i | 0.0760256 | + | 0.131680i | ||||
\(852\) | −0.812507 | + | 1.40730i | −0.0278360 | + | 0.0482134i | ||||
\(853\) | 51.7879 | 1.77318 | 0.886591 | − | 0.462554i | \(-0.153067\pi\) | ||||
0.886591 | + | 0.462554i | \(0.153067\pi\) | |||||||
\(854\) | −60.9528 | − | 29.8702i | −2.08576 | − | 1.02214i | ||||
\(855\) | 22.4099 | 0.766404 | ||||||||
\(856\) | 83.2868 | − | 144.257i | 2.84669 | − | 4.93060i | ||||
\(857\) | 21.5998 | + | 37.4119i | 0.737835 | + | 1.27797i | 0.953469 | + | 0.301493i | \(0.0974849\pi\) |
−0.215634 | + | 0.976474i | \(0.569182\pi\) | |||||||
\(858\) | −4.56546 | − | 7.90761i | −0.155862 | − | 0.269961i | ||||
\(859\) | 1.15276 | − | 1.99665i | 0.0393318 | − | 0.0681247i | −0.845689 | − | 0.533675i | \(-0.820810\pi\) |
0.885021 | + | 0.465551i | \(0.154144\pi\) | |||||||
\(860\) | −12.4610 | −0.424916 | ||||||||
\(861\) | 14.0290 | + | 6.87499i | 0.478107 | + | 0.234299i | ||||
\(862\) | 3.65322 | 0.124429 | ||||||||
\(863\) | 12.7359 | − | 22.0592i | 0.433535 | − | 0.750904i | −0.563640 | − | 0.826020i | \(-0.690600\pi\) |
0.997175 | + | 0.0751164i | \(0.0239328\pi\) | |||||||
\(864\) | −11.3749 | − | 19.7020i | −0.386984 | − | 0.670275i | ||||
\(865\) | 18.3486 | + | 31.7808i | 0.623873 | + | 1.08058i | ||||
\(866\) | −17.0729 | + | 29.5712i | −0.580162 | + | 1.00487i | ||||
\(867\) | −17.7623 | −0.603238 | ||||||||
\(868\) | −2.91184 | − | 42.7939i | −0.0988341 | − | 1.45252i | ||||
\(869\) | −5.70238 | −0.193440 | ||||||||
\(870\) | 38.1982 | − | 66.1612i | 1.29504 | − | 2.24307i | ||||
\(871\) | 7.23580 | + | 12.5328i | 0.245176 | + | 0.424657i | ||||
\(872\) | −64.2379 | − | 111.263i | −2.17537 | − | 3.76785i | ||||
\(873\) | −7.81449 | + | 13.5351i | −0.264480 | + | 0.458093i | ||||
\(874\) | 18.1568 | 0.614164 | ||||||||
\(875\) | 10.6703 | − | 7.16814i | 0.360722 | − | 0.242327i | ||||
\(876\) | 24.5499 | 0.829465 | ||||||||
\(877\) | 3.55031 | − | 6.14931i | 0.119885 | − | 0.207647i | −0.799837 | − | 0.600218i | \(-0.795081\pi\) |
0.919722 | + | 0.392570i | \(0.128414\pi\) | |||||||
\(878\) | 18.8588 | + | 32.6643i | 0.636452 | + | 1.10237i | ||||
\(879\) | 5.45146 | + | 9.44220i | 0.183873 | + | 0.318478i | ||||
\(880\) | 48.7829 | − | 84.4944i | 1.64447 | − | 2.84831i | ||||
\(881\) | −29.0434 | −0.978497 | −0.489249 | − | 0.872144i | \(-0.662729\pi\) | ||||
−0.489249 | + | 0.872144i | \(0.662729\pi\) | |||||||
\(882\) | 19.0032 | − | 2.59810i | 0.639869 | − | 0.0874827i | ||||
\(883\) | −30.2662 | −1.01854 | −0.509269 | − | 0.860608i | \(-0.670084\pi\) | ||||
−0.509269 | + | 0.860608i | \(0.670084\pi\) | |||||||
\(884\) | 28.7278 | − | 49.7580i | 0.966221 | − | 1.67354i | ||||
\(885\) | −2.31185 | − | 4.00424i | −0.0777120 | − | 0.134601i | ||||
\(886\) | −9.68329 | − | 16.7720i | −0.325316 | − | 0.563465i | ||||
\(887\) | 15.6878 | − | 27.1721i | 0.526746 | − | 0.912350i | −0.472769 | − | 0.881187i | \(-0.656745\pi\) |
0.999514 | − | 0.0311636i | \(-0.00992130\pi\) | |||||||
\(888\) | −42.6292 | −1.43054 | ||||||||
\(889\) | 26.8619 | − | 18.0454i | 0.900918 | − | 0.605223i | ||||
\(890\) | −99.3294 | −3.32953 | ||||||||
\(891\) | −0.941706 | + | 1.63108i | −0.0315483 | + | 0.0546433i | ||||
\(892\) | 81.8772 | + | 141.815i | 2.74145 | + | 4.74833i | ||||
\(893\) | 5.94792 | + | 10.3021i | 0.199040 | + | 0.344747i | ||||
\(894\) | −18.9109 | + | 32.7546i | −0.632475 | + | 1.09548i | ||||
\(895\) | 33.6274 | 1.12404 | ||||||||
\(896\) | 7.42757 | + | 109.159i | 0.248138 | + | 3.64676i | ||||
\(897\) | −1.76938 | −0.0590777 | ||||||||
\(898\) | −30.7071 | + | 53.1863i | −1.02471 | + | 1.77485i | ||||
\(899\) | −12.1345 | − | 21.0175i | −0.404707 | − | 0.700974i | ||||
\(900\) | −17.7251 | − | 30.7008i | −0.590838 | − | 1.02336i | ||||
\(901\) | −28.5512 | + | 49.4521i | −0.951177 | + | 1.64749i | ||||
\(902\) | 30.4727 | 1.01463 | ||||||||
\(903\) | −1.58948 | − | 0.778934i | −0.0528946 | − | 0.0259213i | ||||
\(904\) | 11.4087 | 0.379448 | ||||||||
\(905\) | −1.64967 | + | 2.85732i | −0.0548370 | + | 0.0949804i | ||||
\(906\) | 5.81857 | + | 10.0781i | 0.193309 | + | 0.334821i | ||||
\(907\) | −11.2817 | − | 19.5405i | −0.374604 | − | 0.648833i | 0.615664 | − | 0.788009i | \(-0.288888\pi\) |
−0.990268 | + | 0.139176i | \(0.955555\pi\) | |||||||
\(908\) | 17.8725 | − | 30.9561i | 0.593121 | − | 1.02732i | ||||
\(909\) | 7.56916 | 0.251053 | ||||||||
\(910\) | 38.9520 | + | 19.0886i | 1.29125 | + | 0.632782i | ||||
\(911\) | 55.2986 | 1.83212 | 0.916062 | − | 0.401038i | \(-0.131350\pi\) | ||||
0.916062 | + | 0.401038i | \(0.131350\pi\) | |||||||
\(912\) | −50.7532 | + | 87.9071i | −1.68061 | + | 2.91089i | ||||
\(913\) | 9.91619 | + | 17.1754i | 0.328178 | + | 0.568421i | ||||
\(914\) | −3.68576 | − | 6.38392i | −0.121914 | − | 0.211161i | ||||
\(915\) | −15.8326 | + | 27.4229i | −0.523411 | + | 0.906574i | ||||
\(916\) | −6.80776 | −0.224935 | ||||||||
\(917\) | 1.08785 | + | 15.9876i | 0.0359238 | + | 0.527955i | ||||
\(918\) | −16.1549 | −0.533190 | ||||||||
\(919\) | −12.7123 | + | 22.0184i | −0.419341 | + | 0.726320i | −0.995873 | − | 0.0907546i | \(-0.971072\pi\) |
0.576532 | + | 0.817074i | \(0.304405\pi\) | |||||||
\(920\) | −16.2507 | − | 28.1471i | −0.535771 | − | 0.927982i | ||||
\(921\) | 13.3986 | + | 23.2071i | 0.441500 | + | 0.764700i | ||||
\(922\) | 41.2457 | − | 71.4396i | 1.35835 | − | 2.35274i | ||||
\(923\) | −0.522058 | −0.0171837 | ||||||||
\(924\) | 22.7811 | − | 15.3040i | 0.749444 | − | 0.503465i | ||||
\(925\) | −28.5506 | −0.938738 | ||||||||
\(926\) | −19.2434 | + | 33.3305i | −0.632377 | + | 1.09531i | ||||
\(927\) | 1.31063 | + | 2.27008i | 0.0430469 | + | 0.0745594i | ||||
\(928\) | 93.7828 | + | 162.437i | 3.07857 | + | 5.33224i | ||||
\(929\) | 17.1281 | − | 29.6668i | 0.561956 | − | 0.973337i | −0.435370 | − | 0.900252i | \(-0.643382\pi\) |
0.997326 | − | 0.0730848i | \(-0.0232844\pi\) | |||||||
\(930\) | −27.2757 | −0.894405 | ||||||||
\(931\) | −28.4210 | − | 36.6596i | −0.931459 | − | 1.20147i | ||||
\(932\) | 134.143 | 4.39400 | ||||||||
\(933\) | 8.93077 | − | 15.4685i | 0.292380 | − | 0.506417i | ||||
\(934\) | −14.5276 | − | 25.1625i | −0.475357 | − | 0.823342i | ||||
\(935\) | −18.7767 | − | 32.5222i | −0.614064 | − | 1.06359i | ||||
\(936\) | 8.50243 | − | 14.7266i | 0.277911 | − | 0.481355i | ||||
\(937\) | 54.0699 | 1.76639 | 0.883193 | − | 0.469010i | \(-0.155389\pi\) | ||||
0.883193 | + | 0.469010i | \(0.155389\pi\) | |||||||
\(938\) | −49.2172 | + | 33.0634i | −1.60700 | + | 1.07956i | ||||
\(939\) | 29.1299 | 0.950619 | ||||||||
\(940\) | 16.7179 | − | 28.9563i | 0.545279 | − | 0.944451i | ||||
\(941\) | 8.52884 | + | 14.7724i | 0.278032 | + | 0.481566i | 0.970896 | − | 0.239503i | \(-0.0769845\pi\) |
−0.692863 | + | 0.721069i | \(0.743651\pi\) | |||||||
\(942\) | 0.914873 | + | 1.58461i | 0.0298082 | + | 0.0516292i | ||||
\(943\) | 2.95247 | − | 5.11383i | 0.0961457 | − | 0.166529i | ||||
\(944\) | 20.9432 | 0.681642 | ||||||||
\(945\) | −0.607409 | − | 8.92680i | −0.0197590 | − | 0.290389i | ||||
\(946\) | −3.45254 | −0.112252 | ||||||||
\(947\) | −16.9738 | + | 29.3995i | −0.551575 | + | 0.955356i | 0.446586 | + | 0.894741i | \(0.352640\pi\) |
−0.998161 | + | 0.0606156i | \(0.980694\pi\) | |||||||
\(948\) | −8.33756 | − | 14.4411i | −0.270791 | − | 0.469024i | ||||
\(949\) | 3.94350 | + | 6.83034i | 0.128011 | + | 0.221722i | ||||
\(950\) | −58.4347 | + | 101.212i | −1.89587 | + | 3.28375i | ||||
\(951\) | −21.9373 | −0.711367 | ||||||||
\(952\) | 134.623 | + | 65.9726i | 4.36315 | + | 2.13818i | ||||
\(953\) | −22.1762 | −0.718358 | −0.359179 | − | 0.933269i | \(-0.616943\pi\) | ||||
−0.359179 | + | 0.933269i | \(0.616943\pi\) | |||||||
\(954\) | −13.2684 | + | 22.9816i | −0.429581 | + | 0.744056i | ||||
\(955\) | 11.8477 | + | 20.5208i | 0.383382 | + | 0.664037i | ||||
\(956\) | −41.9870 | − | 72.7236i | −1.35796 | − | 2.35205i | ||||
\(957\) | 7.76407 | − | 13.4478i | 0.250977 | − | 0.434704i | ||||
\(958\) | 30.8630 | 0.997139 | ||||||||
\(959\) | −33.9565 | − | 16.6405i | −1.09651 | − | 0.537351i | ||||
\(960\) | 107.198 | 3.45981 | ||||||||
\(961\) | 11.1676 | − | 19.3429i | 0.360247 | − | 0.623965i | ||||
\(962\) | −10.7521 | − | 18.6232i | −0.346662 | − | 0.600436i | ||||
\(963\) | −8.66609 | − | 15.0101i | −0.279261 | − | 0.483694i | ||||
\(964\) | −11.3649 | + | 19.6846i | −0.366039 | + | 0.633998i | ||||
\(965\) | −42.3411 | −1.36301 | ||||||||
\(966\) | −0.492131 | − | 7.23261i | −0.0158340 | − | 0.232705i | ||||
\(967\) | 15.9540 | 0.513045 | 0.256523 | − | 0.966538i | \(-0.417423\pi\) | ||||
0.256523 | + | 0.966538i | \(0.417423\pi\) | |||||||
\(968\) | −35.8130 | + | 62.0298i | −1.15107 | + | 1.99371i | ||||
\(969\) | 19.5351 | + | 33.8357i | 0.627557 | + | 1.08696i | ||||
\(970\) | −72.4101 | − | 125.418i | −2.32495 | − | 4.02693i | ||||
\(971\) | −18.6549 | + | 32.3113i | −0.598665 | + | 1.03692i | 0.394353 | + | 0.918959i | \(0.370969\pi\) |
−0.993018 | + | 0.117960i | \(0.962365\pi\) | |||||||
\(972\) | −5.50755 | −0.176655 | ||||||||
\(973\) | 36.0812 | − | 24.2388i | 1.15671 | − | 0.777060i | ||||
\(974\) | −5.21515 | −0.167104 | ||||||||
\(975\) | 5.69444 | − | 9.86306i | 0.182368 | − | 0.315871i | ||||
\(976\) | −71.7143 | − | 124.213i | −2.29552 | − | 3.97595i | ||||
\(977\) | 18.5645 | + | 32.1546i | 0.593930 | + | 1.02872i | 0.993697 | + | 0.112100i | \(0.0357576\pi\) |
−0.399767 | + | 0.916617i | \(0.630909\pi\) | |||||||
\(978\) | 0.996234 | − | 1.72553i | 0.0318560 | − | 0.0551763i | ||||
\(979\) | −20.1894 | −0.645258 | ||||||||
\(980\) | −49.2935 | + | 120.701i | −1.57462 | + | 3.85565i | ||||
\(981\) | −13.3681 | −0.426809 | ||||||||
\(982\) | 28.5976 | − | 49.5324i | 0.912585 | − | 1.58064i | ||||
\(983\) | 10.0202 | + | 17.3554i | 0.319594 | + | 0.553553i | 0.980403 | − | 0.197001i | \(-0.0631202\pi\) |
−0.660809 | + | 0.750554i | \(0.729787\pi\) | |||||||
\(984\) | 28.3752 | + | 49.1473i | 0.904568 | + | 1.56676i | ||||
\(985\) | −42.8284 | + | 74.1810i | −1.36463 | + | 2.36360i | ||||
\(986\) | 133.192 | 4.24169 | ||||||||
\(987\) | 3.94254 | − | 2.64853i | 0.125492 | − | 0.0843038i | ||||
\(988\) | −64.5757 | −2.05443 | ||||||||
\(989\) | −0.334514 | + | 0.579395i | −0.0106369 | + | 0.0184237i | ||||
\(990\) | −8.72598 | − | 15.1138i | −0.277330 | − | 0.480349i | ||||
\(991\) | −20.1728 | − | 34.9403i | −0.640810 | − | 1.10992i | −0.985252 | − | 0.171108i | \(-0.945265\pi\) |
0.344442 | − | 0.938808i | \(-0.388068\pi\) | |||||||
\(992\) | 33.4832 | − | 57.9945i | 1.06309 | − | 1.84133i | ||||
\(993\) | 5.63045 | 0.178677 | ||||||||
\(994\) | −0.145204 | − | 2.13400i | −0.00460559 | − | 0.0676862i | ||||
\(995\) | −2.19331 | −0.0695325 | ||||||||
\(996\) | −28.9973 | + | 50.2249i | −0.918816 | + | 1.59144i | ||||
\(997\) | −2.28550 | − | 3.95861i | −0.0723826 | − | 0.125370i | 0.827562 | − | 0.561374i | \(-0.189727\pi\) |
−0.899945 | + | 0.436003i | \(0.856394\pi\) | |||||||
\(998\) | −50.8179 | − | 88.0191i | −1.60861 | − | 2.78620i | ||||
\(999\) | −2.21781 | + | 3.84136i | −0.0701684 | + | 0.121535i |
(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 | 483.2.i.h.415.10 | yes | 20 | |
7.2 | even | 3 | 3381.2.a.bi.1.1 | 10 | |||
7.4 | even | 3 | inner | 483.2.i.h.277.10 | ✓ | 20 | |
7.5 | odd | 6 | 3381.2.a.bj.1.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.h.277.10 | ✓ | 20 | 7.4 | even | 3 | inner | |
483.2.i.h.415.10 | yes | 20 | 1.1 | even | 1 | trivial | |
3381.2.a.bi.1.1 | 10 | 7.2 | even | 3 | |||
3381.2.a.bj.1.1 | 10 | 7.5 | odd | 6 |