Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,3,Mod(7,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.7");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.g (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: | \(2.07085000914\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 11.14 | ||
Character | \(\chi\) | \(=\) | 76.11 |
Dual form | 76.3.g.c.7.14 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.72876 | − | 1.00569i | 0.864378 | − | 0.502843i | ||||
\(3\) | −0.443154 | − | 0.255855i | −0.147718 | − | 0.0852850i | 0.424319 | − | 0.905513i | \(-0.360513\pi\) |
−0.572037 | + | 0.820228i | \(0.693847\pi\) | |||||||
\(4\) | 1.97719 | − | 3.47717i | 0.494298 | − | 0.869292i | ||||
\(5\) | 1.99023 | − | 3.44717i | 0.398045 | − | 0.689435i | −0.595439 | − | 0.803400i | \(-0.703022\pi\) |
0.993485 | + | 0.113965i | \(0.0363553\pi\) | |||||||
\(6\) | −1.02341 | + | 0.00336270i | −0.170569 | + | 0.000560450i | ||||
\(7\) | 9.66827i | 1.38118i | 0.723246 | + | 0.690591i | \(0.242649\pi\) | ||||
−0.723246 | + | 0.690591i | \(0.757351\pi\) | |||||||
\(8\) | −0.0788568 | − | 7.99961i | −0.00985710 | − | 0.999951i | ||||
\(9\) | −4.36908 | − | 7.56746i | −0.485453 | − | 0.840829i | ||||
\(10\) | −0.0261575 | − | 7.96087i | −0.00261575 | − | 0.796087i | ||||
\(11\) | − | 2.62030i | − | 0.238209i | −0.992882 | − | 0.119104i | \(-0.961998\pi\) | ||
0.992882 | − | 0.119104i | \(-0.0380023\pi\) | |||||||
\(12\) | −1.76585 | + | 1.03505i | −0.147154 | + | 0.0862538i | ||||
\(13\) | 11.8012 | + | 20.4403i | 0.907787 | + | 1.57233i | 0.817132 | + | 0.576451i | \(0.195563\pi\) |
0.0906551 | + | 0.995882i | \(0.471104\pi\) | |||||||
\(14\) | 9.72324 | + | 16.7141i | 0.694517 | + | 1.19386i | ||||
\(15\) | −1.76395 | + | 1.01842i | −0.117597 | + | 0.0678946i | ||||
\(16\) | −8.18142 | − | 13.7501i | −0.511339 | − | 0.859379i | ||||
\(17\) | −3.40777 | + | 5.90242i | −0.200457 | + | 0.347201i | −0.948676 | − | 0.316251i | \(-0.897576\pi\) |
0.748219 | + | 0.663452i | \(0.230909\pi\) | |||||||
\(18\) | −15.1636 | − | 8.68838i | −0.842420 | − | 0.482688i | ||||
\(19\) | −12.0371 | + | 14.7006i | −0.633530 | + | 0.773718i | ||||
\(20\) | −8.05135 | − | 13.7361i | −0.402567 | − | 0.686804i | ||||
\(21\) | 2.47368 | − | 4.28453i | 0.117794 | − | 0.204025i | ||||
\(22\) | −2.63520 | − | 4.52985i | −0.119782 | − | 0.205902i | ||||
\(23\) | −17.2580 | + | 9.96389i | −0.750346 | + | 0.433213i | −0.825819 | − | 0.563935i | \(-0.809287\pi\) |
0.0754728 | + | 0.997148i | \(0.475953\pi\) | |||||||
\(24\) | −2.01179 | + | 3.56523i | −0.0838247 | + | 0.148551i | ||||
\(25\) | 4.57799 | + | 7.92932i | 0.183120 | + | 0.317173i | ||||
\(26\) | 40.9580 | + | 23.4680i | 1.57531 | + | 0.902616i | ||||
\(27\) | 9.07679i | 0.336177i | ||||||||
\(28\) | 33.6182 | + | 19.1160i | 1.20065 | + | 0.682716i | ||||
\(29\) | 0.445777 | + | 0.772108i | 0.0153716 | + | 0.0266244i | 0.873609 | − | 0.486629i | \(-0.161774\pi\) |
−0.858237 | + | 0.513253i | \(0.828440\pi\) | |||||||
\(30\) | −2.02523 | + | 3.53458i | −0.0675078 | + | 0.117819i | ||||
\(31\) | − | 59.6042i | − | 1.92272i | −0.275303 | − | 0.961358i | \(-0.588778\pi\) | ||
0.275303 | − | 0.961358i | \(-0.411222\pi\) | |||||||
\(32\) | −27.9719 | − | 15.5426i | −0.874123 | − | 0.485705i | ||||
\(33\) | −0.670416 | + | 1.16119i | −0.0203156 | + | 0.0351877i | ||||
\(34\) | 0.0447883 | + | 13.6310i | 0.00131730 | + | 0.400912i | ||||
\(35\) | 33.3282 | + | 19.2421i | 0.952235 | + | 0.549773i | ||||
\(36\) | −34.9519 | + | 0.229690i | −0.970885 | + | 0.00638027i | ||||
\(37\) | −7.80746 | −0.211012 | −0.105506 | − | 0.994419i | \(-0.533646\pi\) | ||||
−0.105506 | + | 0.994419i | \(0.533646\pi\) | |||||||
\(38\) | −6.02492 | + | 37.5193i | −0.158550 | + | 0.987351i | ||||
\(39\) | − | 12.0776i | − | 0.309682i | ||||||
\(40\) | −27.7330 | − | 15.6492i | −0.693325 | − | 0.391230i | ||||
\(41\) | 15.9560 | − | 27.6366i | 0.389171 | − | 0.674063i | −0.603168 | − | 0.797614i | \(-0.706095\pi\) |
0.992338 | + | 0.123551i | \(0.0394283\pi\) | |||||||
\(42\) | −0.0325115 | − | 9.89465i | −0.000774083 | − | 0.235587i | ||||
\(43\) | 6.09346 | + | 3.51806i | 0.141708 | + | 0.0818154i | 0.569178 | − | 0.822214i | \(-0.307262\pi\) |
−0.427470 | + | 0.904030i | \(0.640595\pi\) | |||||||
\(44\) | −9.11122 | − | 5.18083i | −0.207073 | − | 0.117746i | ||||
\(45\) | −34.7818 | −0.772929 | ||||||||
\(46\) | −19.8143 | + | 34.5812i | −0.430745 | + | 0.751766i | ||||
\(47\) | 47.7806 | − | 27.5861i | 1.01661 | − | 0.586939i | 0.103489 | − | 0.994631i | \(-0.466999\pi\) |
0.913120 | + | 0.407692i | \(0.133666\pi\) | |||||||
\(48\) | 0.107603 | + | 8.18665i | 0.00224174 | + | 0.170555i | ||||
\(49\) | −44.4755 | −0.907664 | ||||||||
\(50\) | 15.8886 | + | 9.10383i | 0.317773 | + | 0.182077i | ||||
\(51\) | 3.02033 | − | 1.74379i | 0.0592221 | − | 0.0341919i | ||||
\(52\) | 94.4078 | − | 0.620411i | 1.81553 | − | 0.0119310i | ||||
\(53\) | −33.4862 | − | 57.9998i | −0.631815 | − | 1.09434i | −0.987180 | − | 0.159608i | \(-0.948977\pi\) |
0.355366 | − | 0.934727i | \(-0.384356\pi\) | |||||||
\(54\) | 9.12839 | + | 15.6915i | 0.169044 | + | 0.290584i | ||||
\(55\) | −9.03262 | − | 5.21499i | −0.164230 | − | 0.0948179i | ||||
\(56\) | 77.3424 | − | 0.762409i | 1.38111 | − | 0.0136145i | ||||
\(57\) | 9.09550 | − | 3.43490i | 0.159570 | − | 0.0602615i | ||||
\(58\) | 1.54714 | + | 0.886475i | 0.0266748 | + | 0.0152841i | ||||
\(59\) | −51.3641 | − | 29.6551i | −0.870578 | − | 0.502628i | −0.00303759 | − | 0.999995i | \(-0.500967\pi\) |
−0.867540 | + | 0.497367i | \(0.834300\pi\) | |||||||
\(60\) | 0.0535400 | + | 8.14717i | 0.000892333 | + | 0.135786i | ||||
\(61\) | −1.23664 | − | 2.14192i | −0.0202727 | − | 0.0351134i | 0.855711 | − | 0.517454i | \(-0.173120\pi\) |
−0.875984 | + | 0.482341i | \(0.839787\pi\) | |||||||
\(62\) | −59.9431 | − | 103.041i | −0.966823 | − | 1.66195i | ||||
\(63\) | 73.1643 | − | 42.2414i | 1.16134 | − | 0.670499i | ||||
\(64\) | −63.9876 | + | 1.26165i | −0.999806 | + | 0.0197133i | ||||
\(65\) | 93.9485 | 1.44536 | ||||||||
\(66\) | 0.00881127 | + | 2.68165i | 0.000133504 | + | 0.0406310i | ||||
\(67\) | −36.4967 | + | 21.0714i | −0.544727 | + | 0.314498i | −0.746992 | − | 0.664833i | \(-0.768503\pi\) |
0.202266 | + | 0.979331i | \(0.435170\pi\) | |||||||
\(68\) | 13.7859 | + | 23.5196i | 0.202734 | + | 0.345877i | ||||
\(69\) | 10.1972 | 0.147786 | ||||||||
\(70\) | 76.9678 | − | 0.252898i | 1.09954 | − | 0.00361283i | ||||
\(71\) | 88.6632 | + | 51.1897i | 1.24878 | + | 0.720982i | 0.970866 | − | 0.239625i | \(-0.0770243\pi\) |
0.277912 | + | 0.960607i | \(0.410358\pi\) | |||||||
\(72\) | −60.1922 | + | 35.5477i | −0.836003 | + | 0.493718i | ||||
\(73\) | −7.82182 | + | 13.5478i | −0.107148 | + | 0.185586i | −0.914614 | − | 0.404328i | \(-0.867505\pi\) |
0.807466 | + | 0.589915i | \(0.200839\pi\) | |||||||
\(74\) | −13.4972 | + | 7.85185i | −0.182394 | + | 0.106106i | ||||
\(75\) | − | 4.68521i | − | 0.0624694i | ||||||
\(76\) | 27.3170 | + | 70.9209i | 0.359435 | + | 0.933170i | ||||
\(77\) | 25.3338 | 0.329010 | ||||||||
\(78\) | −12.1463 | − | 20.8792i | −0.155722 | − | 0.267683i | ||||
\(79\) | −63.6689 | − | 36.7592i | −0.805935 | − | 0.465307i | 0.0396072 | − | 0.999215i | \(-0.487389\pi\) |
−0.845542 | + | 0.533908i | \(0.820723\pi\) | |||||||
\(80\) | −63.6818 | + | 0.837019i | −0.796022 | + | 0.0104627i | ||||
\(81\) | −36.9993 | + | 64.0848i | −0.456782 | + | 0.791170i | ||||
\(82\) | −0.209710 | − | 63.8236i | −0.00255743 | − | 0.778337i | ||||
\(83\) | 18.4034i | 0.221728i | 0.993836 | + | 0.110864i | \(0.0353618\pi\) | ||||
−0.993836 | + | 0.110864i | \(0.964638\pi\) | |||||||
\(84\) | −10.0071 | − | 17.0727i | −0.119132 | − | 0.203247i | ||||
\(85\) | 13.5645 | + | 23.4943i | 0.159582 | + | 0.276404i | ||||
\(86\) | 14.0722 | − | 0.0462378i | 0.163630 | − | 0.000537649i | ||||
\(87\) | − | 0.456217i | − | 0.00524387i | ||||||
\(88\) | −20.9614 | + | 0.206628i | −0.238197 | + | 0.00234805i | ||||
\(89\) | −35.4778 | − | 61.4494i | −0.398627 | − | 0.690443i | 0.594929 | − | 0.803778i | \(-0.297180\pi\) |
−0.993557 | + | 0.113335i | \(0.963847\pi\) | |||||||
\(90\) | −60.1293 | + | 34.9796i | −0.668103 | + | 0.388662i | ||||
\(91\) | −197.623 | + | 114.098i | −2.17168 | + | 1.25382i | ||||
\(92\) | 0.523819 | + | 79.7094i | 0.00569368 | + | 0.866406i | ||||
\(93\) | −15.2500 | + | 26.4138i | −0.163979 | + | 0.284019i | ||||
\(94\) | 54.8580 | − | 95.7420i | 0.583596 | − | 1.01853i | ||||
\(95\) | 26.7192 | + | 70.7515i | 0.281255 | + | 0.744753i | ||||
\(96\) | 8.41922 | + | 14.0445i | 0.0877002 | + | 0.146297i | ||||
\(97\) | −39.9967 | + | 69.2763i | −0.412337 | + | 0.714189i | −0.995145 | − | 0.0984213i | \(-0.968621\pi\) |
0.582808 | + | 0.812610i | \(0.301954\pi\) | |||||||
\(98\) | −76.8873 | + | 44.7284i | −0.784564 | + | 0.456412i | ||||
\(99\) | −19.8290 | + | 11.4483i | −0.200293 | + | 0.115639i | ||||
\(100\) | 36.6231 | − | 0.240673i | 0.366231 | − | 0.00240673i | ||||
\(101\) | 70.6125 | + | 122.304i | 0.699133 | + | 1.21093i | 0.968767 | + | 0.247972i | \(0.0797639\pi\) |
−0.269634 | + | 0.962963i | \(0.586903\pi\) | |||||||
\(102\) | 3.46771 | − | 6.05208i | 0.0339971 | − | 0.0593342i | ||||
\(103\) | − | 130.698i | − | 1.26891i | −0.772958 | − | 0.634457i | \(-0.781224\pi\) | ||
0.772958 | − | 0.634457i | \(-0.218776\pi\) | |||||||
\(104\) | 162.584 | − | 96.0171i | 1.56331 | − | 0.923242i | ||||
\(105\) | −9.84635 | − | 17.0544i | −0.0937748 | − | 0.162423i | ||||
\(106\) | −116.219 | − | 66.5909i | −1.09641 | − | 0.628216i | ||||
\(107\) | 83.9587i | 0.784661i | 0.919824 | + | 0.392331i | \(0.128331\pi\) | ||||
−0.919824 | + | 0.392331i | \(0.871669\pi\) | |||||||
\(108\) | 31.5615 | + | 17.9466i | 0.292236 | + | 0.166172i | ||||
\(109\) | −46.1581 | + | 79.9481i | −0.423468 | + | 0.733469i | −0.996276 | − | 0.0862211i | \(-0.972521\pi\) |
0.572808 | + | 0.819690i | \(0.305854\pi\) | |||||||
\(110\) | −20.8598 | + | 0.0685405i | −0.189635 | + | 0.000623096i | ||||
\(111\) | 3.45990 | + | 1.99758i | 0.0311703 | + | 0.0179962i | ||||
\(112\) | 132.939 | − | 79.1002i | 1.18696 | − | 0.706252i | ||||
\(113\) | 26.6191 | 0.235567 | 0.117784 | − | 0.993039i | \(-0.462421\pi\) | ||||
0.117784 | + | 0.993039i | \(0.462421\pi\) | |||||||
\(114\) | 12.2695 | − | 15.0853i | 0.107627 | − | 0.132327i | ||||
\(115\) | 79.3216i | 0.689753i | ||||||||
\(116\) | 3.56614 | − | 0.0234353i | 0.0307426 | − | 0.000202028i | ||||
\(117\) | 103.121 | − | 178.611i | 0.881376 | − | 1.52659i | ||||
\(118\) | −118.620 | + | 0.389756i | −1.00525 | + | 0.00330302i | ||||
\(119\) | −57.0663 | − | 32.9472i | −0.479548 | − | 0.276867i | ||||
\(120\) | 8.28605 | + | 14.0306i | 0.0690504 | + | 0.116922i | ||||
\(121\) | 114.134 | 0.943257 | ||||||||
\(122\) | −4.29194 | − | 2.45918i | −0.0351798 | − | 0.0201572i | ||||
\(123\) | −14.1419 | + | 8.16484i | −0.114975 | + | 0.0663808i | ||||
\(124\) | −207.254 | − | 117.849i | −1.67140 | − | 0.950394i | ||||
\(125\) | 135.956 | 1.08765 | ||||||||
\(126\) | 84.0016 | − | 146.605i | 0.666679 | − | 1.16353i | ||||
\(127\) | 29.5205 | − | 17.0437i | 0.232445 | − | 0.134202i | −0.379254 | − | 0.925292i | \(-0.623819\pi\) |
0.611700 | + | 0.791090i | \(0.290486\pi\) | |||||||
\(128\) | −109.350 | + | 66.5325i | −0.854297 | + | 0.519785i | ||||
\(129\) | −1.80023 | − | 3.11808i | −0.0139552 | − | 0.0241712i | ||||
\(130\) | 162.414 | − | 94.4827i | 1.24934 | − | 0.726790i | ||||
\(131\) | 163.122 | + | 94.1785i | 1.24521 | + | 0.718920i | 0.970149 | − | 0.242508i | \(-0.0779700\pi\) |
0.275057 | + | 0.961428i | \(0.411303\pi\) | |||||||
\(132\) | 2.71213 | + | 4.62706i | 0.0205464 | + | 0.0350534i | ||||
\(133\) | −142.130 | − | 116.378i | −1.06865 | − | 0.875020i | ||||
\(134\) | −41.9027 | + | 73.1315i | −0.312707 | + | 0.545757i | ||||
\(135\) | 31.2893 | + | 18.0649i | 0.231772 | + | 0.133814i | ||||
\(136\) | 47.4858 | + | 26.7954i | 0.349160 | + | 0.197025i | ||||
\(137\) | −81.9749 | − | 141.985i | −0.598357 | − | 1.03638i | −0.993064 | − | 0.117577i | \(-0.962487\pi\) |
0.394707 | − | 0.918807i | \(-0.370846\pi\) | |||||||
\(138\) | 17.6285 | − | 10.2552i | 0.127743 | − | 0.0743132i | ||||
\(139\) | 33.2670 | − | 19.2067i | 0.239331 | − | 0.138178i | −0.375538 | − | 0.926807i | \(-0.622542\pi\) |
0.614869 | + | 0.788629i | \(0.289209\pi\) | |||||||
\(140\) | 132.804 | − | 77.8426i | 0.948602 | − | 0.556019i | ||||
\(141\) | −28.2322 | −0.200228 | ||||||||
\(142\) | 204.758 | − | 0.672786i | 1.44196 | − | 0.00473793i | ||||
\(143\) | 53.5597 | − | 30.9227i | 0.374544 | − | 0.216243i | ||||
\(144\) | −68.3079 | + | 121.988i | −0.474360 | + | 0.847137i | ||||
\(145\) | 3.54879 | 0.0244744 | ||||||||
\(146\) | 0.102802 | + | 31.2871i | 0.000704124 | + | 0.214295i | ||||
\(147\) | 19.7095 | + | 11.3793i | 0.134078 | + | 0.0774101i | ||||
\(148\) | −15.4368 | + | 27.1479i | −0.104303 | + | 0.183431i | ||||
\(149\) | −115.159 | + | 199.461i | −0.772877 | + | 1.33866i | 0.163104 | + | 0.986609i | \(0.447850\pi\) |
−0.935980 | + | 0.352053i | \(0.885484\pi\) | |||||||
\(150\) | −4.71185 | − | 8.09958i | −0.0314123 | − | 0.0539972i | ||||
\(151\) | − | 186.853i | − | 1.23743i | −0.785614 | − | 0.618717i | \(-0.787653\pi\) | ||
0.785614 | − | 0.618717i | \(-0.212347\pi\) | |||||||
\(152\) | 118.549 | + | 95.1326i | 0.779925 | + | 0.625872i | ||||
\(153\) | 59.5552 | 0.389249 | ||||||||
\(154\) | 43.7959 | − | 25.4778i | 0.284389 | − | 0.165440i | ||||
\(155\) | −205.466 | − | 118.626i | −1.32559 | − | 0.765328i | ||||
\(156\) | −41.9959 | − | 23.8798i | −0.269204 | − | 0.153075i | ||||
\(157\) | 80.6157 | − | 139.630i | 0.513476 | − | 0.889366i | −0.486402 | − | 0.873735i | \(-0.661691\pi\) |
0.999878 | − | 0.0156308i | \(-0.00497563\pi\) | |||||||
\(158\) | −147.036 | + | 0.483127i | −0.930609 | + | 0.00305776i | ||||
\(159\) | 34.2704i | 0.215537i | ||||||||
\(160\) | −109.248 | + | 65.4908i | −0.682803 | + | 0.409318i | ||||
\(161\) | −96.3336 | − | 166.855i | −0.598345 | − | 1.03636i | ||||
\(162\) | 0.486282 | + | 147.997i | 0.00300174 | + | 0.913559i | ||||
\(163\) | 113.722i | 0.697682i | 0.937182 | + | 0.348841i | \(0.113425\pi\) | ||||
−0.937182 | + | 0.348841i | \(0.886575\pi\) | |||||||
\(164\) | −64.5491 | − | 110.125i | −0.393592 | − | 0.671491i | ||||
\(165\) | 2.66856 | + | 4.62208i | 0.0161731 | + | 0.0280126i | ||||
\(166\) | 18.5081 | + | 31.8151i | 0.111494 | + | 0.191657i | ||||
\(167\) | 104.857 | − | 60.5392i | 0.627886 | − | 0.362510i | −0.152047 | − | 0.988373i | \(-0.548586\pi\) |
0.779933 | + | 0.625863i | \(0.215253\pi\) | |||||||
\(168\) | −34.4696 | − | 19.4506i | −0.205176 | − | 0.115777i | ||||
\(169\) | −194.038 | + | 336.084i | −1.14815 | + | 1.98866i | ||||
\(170\) | 47.0775 | + | 26.9744i | 0.276927 | + | 0.158673i | ||||
\(171\) | 163.837 | + | 26.8618i | 0.958114 | + | 0.157087i | ||||
\(172\) | 24.2808 | − | 14.2321i | 0.141168 | − | 0.0827448i | ||||
\(173\) | 59.6985 | − | 103.401i | 0.345078 | − | 0.597693i | −0.640290 | − | 0.768133i | \(-0.721186\pi\) |
0.985368 | + | 0.170441i | \(0.0545191\pi\) | |||||||
\(174\) | −0.458811 | − | 0.788688i | −0.00263684 | − | 0.00453269i | ||||
\(175\) | −76.6628 | + | 44.2613i | −0.438073 | + | 0.252922i | ||||
\(176\) | −36.0293 | + | 21.4378i | −0.204712 | + | 0.121805i | ||||
\(177\) | 15.1748 | + | 26.2835i | 0.0857333 | + | 0.148494i | ||||
\(178\) | −123.131 | − | 70.5515i | −0.691749 | − | 0.396357i | ||||
\(179\) | − | 238.109i | − | 1.33022i | −0.746746 | − | 0.665109i | \(-0.768385\pi\) | ||
0.746746 | − | 0.665109i | \(-0.231615\pi\) | |||||||
\(180\) | −68.7704 | + | 120.942i | −0.382058 | + | 0.671902i | ||||
\(181\) | 76.3894 | + | 132.310i | 0.422041 | + | 0.730996i | 0.996139 | − | 0.0877903i | \(-0.0279805\pi\) |
−0.574098 | + | 0.818787i | \(0.694647\pi\) | |||||||
\(182\) | −226.895 | + | 395.993i | −1.24668 | + | 2.17579i | ||||
\(183\) | 1.26560i | 0.00691584i | ||||||||
\(184\) | 81.0681 | + | 137.271i | 0.440588 | + | 0.746039i | ||||
\(185\) | −15.5386 | + | 26.9137i | −0.0839925 | + | 0.145479i | ||||
\(186\) | 0.200431 | + | 60.9997i | 0.00107759 | + | 0.327956i | ||||
\(187\) | 15.4661 | + | 8.92936i | 0.0827065 | + | 0.0477506i | ||||
\(188\) | −1.45025 | − | 220.684i | −0.00771410 | − | 1.17385i | ||||
\(189\) | −87.7569 | −0.464322 | ||||||||
\(190\) | 117.345 | + | 95.4409i | 0.617604 | + | 0.502321i | ||||
\(191\) | − | 318.713i | − | 1.66865i | −0.551269 | − | 0.834327i | \(-0.685856\pi\) | ||
0.551269 | − | 0.834327i | \(-0.314144\pi\) | |||||||
\(192\) | 28.6791 | + | 15.8124i | 0.149370 | + | 0.0823564i | ||||
\(193\) | 30.7232 | − | 53.2141i | 0.159187 | − | 0.275721i | −0.775388 | − | 0.631485i | \(-0.782446\pi\) |
0.934576 | + | 0.355764i | \(0.115779\pi\) | |||||||
\(194\) | 0.525676 | + | 159.986i | 0.00270967 | + | 0.824670i | ||||
\(195\) | −41.6336 | − | 24.0372i | −0.213506 | − | 0.123268i | ||||
\(196\) | −87.9367 | + | 154.649i | −0.448656 | + | 0.789025i | ||||
\(197\) | −242.851 | −1.23274 | −0.616372 | − | 0.787455i | \(-0.711398\pi\) | ||||
−0.616372 | + | 0.787455i | \(0.711398\pi\) | |||||||
\(198\) | −22.7661 | + | 39.7330i | −0.114980 | + | 0.200672i | ||||
\(199\) | −207.809 | + | 119.979i | −1.04427 | + | 0.602908i | −0.921039 | − | 0.389470i | \(-0.872658\pi\) |
−0.123228 | + | 0.992378i | \(0.539325\pi\) | |||||||
\(200\) | 63.0704 | − | 37.2474i | 0.315352 | − | 0.186237i | ||||
\(201\) | 21.5649 | 0.107288 | ||||||||
\(202\) | 245.071 | + | 140.420i | 1.21323 | + | 0.695151i | ||||
\(203\) | −7.46496 | + | 4.30989i | −0.0367732 | + | 0.0212310i | ||||
\(204\) | −0.0916739 | − | 13.9500i | −0.000449382 | − | 0.0683823i | ||||
\(205\) | −63.5121 | − | 110.006i | −0.309815 | − | 0.536616i | ||||
\(206\) | −131.441 | − | 225.945i | −0.638064 | − | 1.09682i | ||||
\(207\) | 150.803 | + | 87.0660i | 0.728516 | + | 0.420609i | ||||
\(208\) | 184.505 | − | 329.499i | 0.887044 | − | 1.58413i | ||||
\(209\) | 38.5201 | + | 31.5407i | 0.184307 | + | 0.150912i | ||||
\(210\) | −34.1733 | − | 19.5805i | −0.162730 | − | 0.0932406i | ||||
\(211\) | 75.6483 | + | 43.6755i | 0.358523 | + | 0.206993i | 0.668432 | − | 0.743773i | \(-0.266966\pi\) |
−0.309910 | + | 0.950766i | \(0.600299\pi\) | |||||||
\(212\) | −267.884 | + | 1.76043i | −1.26360 | + | 0.00830389i | ||||
\(213\) | −26.1943 | − | 45.3698i | −0.122978 | − | 0.213004i | ||||
\(214\) | 84.4361 | + | 145.144i | 0.394561 | + | 0.678244i | ||||
\(215\) | 24.2547 | − | 14.0035i | 0.112813 | − | 0.0651325i | ||||
\(216\) | 72.6108 | − | 0.715767i | 0.336161 | − | 0.00331373i | ||||
\(217\) | 576.269 | 2.65562 | ||||||||
\(218\) | 0.606655 | + | 184.631i | 0.00278282 | + | 0.846932i | ||||
\(219\) | 6.93254 | − | 4.00250i | 0.0316554 | − | 0.0182763i | ||||
\(220\) | −35.9926 | + | 21.0969i | −0.163603 | + | 0.0958951i | ||||
\(221\) | −160.863 | −0.727888 | ||||||||
\(222\) | 7.99026 | − | 0.0262541i | 0.0359922 | − | 0.000118262i | ||||
\(223\) | 149.218 | + | 86.1509i | 0.669138 | + | 0.386327i | 0.795750 | − | 0.605625i | \(-0.207077\pi\) |
−0.126612 | + | 0.991952i | \(0.540410\pi\) | |||||||
\(224\) | 150.270 | − | 270.440i | 0.670848 | − | 1.20732i | ||||
\(225\) | 40.0032 | − | 69.2876i | 0.177792 | − | 0.307945i | ||||
\(226\) | 46.0179 | − | 26.7704i | 0.203619 | − | 0.118453i | ||||
\(227\) | 249.279i | 1.09814i | 0.835775 | + | 0.549072i | \(0.185019\pi\) | ||||
−0.835775 | + | 0.549072i | \(0.814981\pi\) | |||||||
\(228\) | 6.03982 | − | 38.4181i | 0.0264904 | − | 0.168500i | ||||
\(229\) | 198.117 | 0.865138 | 0.432569 | − | 0.901601i | \(-0.357607\pi\) | ||||
0.432569 | + | 0.901601i | \(0.357607\pi\) | |||||||
\(230\) | 79.7726 | + | 137.128i | 0.346837 | + | 0.596207i | ||||
\(231\) | −11.2267 | − | 6.48176i | −0.0486006 | − | 0.0280596i | ||||
\(232\) | 6.14142 | − | 3.62693i | 0.0264716 | − | 0.0156333i | ||||
\(233\) | −144.366 | + | 250.049i | −0.619596 | + | 1.07317i | 0.369963 | + | 0.929047i | \(0.379370\pi\) |
−0.989559 | + | 0.144126i | \(0.953963\pi\) | |||||||
\(234\) | −1.35532 | − | 412.482i | −0.00579196 | − | 1.76274i | ||||
\(235\) | − | 219.611i | − | 0.934514i | ||||||
\(236\) | −204.672 | + | 119.968i | −0.867256 | + | 0.508338i | ||||
\(237\) | 18.8101 | + | 32.5800i | 0.0793674 | + | 0.137468i | ||||
\(238\) | −131.788 | + | 0.433025i | −0.553732 | + | 0.00181943i | ||||
\(239\) | 39.6307i | 0.165819i | 0.996557 | + | 0.0829094i | \(0.0264212\pi\) | ||||
−0.996557 | + | 0.0829094i | \(0.973579\pi\) | |||||||
\(240\) | 28.4350 | + | 15.9224i | 0.118479 | + | 0.0663432i | ||||
\(241\) | −151.983 | − | 263.242i | −0.630634 | − | 1.09229i | −0.987422 | − | 0.158105i | \(-0.949461\pi\) |
0.356788 | − | 0.934185i | \(-0.383872\pi\) | |||||||
\(242\) | 197.310 | − | 114.783i | 0.815330 | − | 0.474310i | ||||
\(243\) | 103.539 | − | 59.7785i | 0.426088 | − | 0.246002i | ||||
\(244\) | −9.89288 | + | 0.0650121i | −0.0405446 | + | 0.000266443i | ||||
\(245\) | −88.5164 | + | 153.315i | −0.361291 | + | 0.625775i | ||||
\(246\) | −16.2367 | + | 28.3373i | −0.0660027 | + | 0.115192i | ||||
\(247\) | −442.538 | − | 72.5559i | −1.79165 | − | 0.293749i | ||||
\(248\) | −476.810 | + | 4.70020i | −1.92262 | + | 0.0189524i | ||||
\(249\) | 4.70861 | − | 8.15555i | 0.0189101 | − | 0.0327532i | ||||
\(250\) | 235.035 | − | 136.729i | 0.940141 | − | 0.546917i | ||||
\(251\) | −346.056 | + | 199.796i | −1.37871 | + | 0.795998i | −0.992004 | − | 0.126205i | \(-0.959720\pi\) |
−0.386705 | + | 0.922203i | \(0.626387\pi\) | |||||||
\(252\) | −2.22070 | − | 337.924i | −0.00881232 | − | 1.34097i | ||||
\(253\) | 26.1084 | + | 45.2210i | 0.103195 | + | 0.178739i | ||||
\(254\) | 33.8932 | − | 59.1527i | 0.133438 | − | 0.232885i | ||||
\(255\) | − | 13.8821i | − | 0.0544397i | ||||||
\(256\) | −122.129 | + | 224.990i | −0.477066 | + | 0.878868i | ||||
\(257\) | −6.41520 | − | 11.1115i | −0.0249619 | − | 0.0432353i | 0.853275 | − | 0.521462i | \(-0.174613\pi\) |
−0.878236 | + | 0.478227i | \(0.841280\pi\) | |||||||
\(258\) | −6.24796 | − | 3.57994i | −0.0242169 | − | 0.0138757i | ||||
\(259\) | − | 75.4846i | − | 0.291447i | ||||||
\(260\) | 185.754 | − | 326.675i | 0.714440 | − | 1.25644i | ||||
\(261\) | 3.89527 | − | 6.74680i | 0.0149244 | − | 0.0258498i | ||||
\(262\) | 376.712 | − | 1.23779i | 1.43783 | − | 0.00472438i | ||||
\(263\) | 206.817 | + | 119.406i | 0.786378 | + | 0.454015i | 0.838686 | − | 0.544616i | \(-0.183324\pi\) |
−0.0523082 | + | 0.998631i | \(0.516658\pi\) | |||||||
\(264\) | 9.34197 | + | 5.27150i | 0.0353863 | + | 0.0199678i | ||||
\(265\) | −266.580 | −1.00596 | ||||||||
\(266\) | −362.747 | − | 58.2505i | −1.36371 | − | 0.218987i | ||||
\(267\) | 36.3087i | 0.135988i | ||||||||
\(268\) | 1.10776 | + | 168.567i | 0.00413343 | + | 0.628983i | ||||
\(269\) | 103.018 | − | 178.433i | 0.382968 | − | 0.663320i | −0.608517 | − | 0.793541i | \(-0.708235\pi\) |
0.991485 | + | 0.130221i | \(0.0415687\pi\) | |||||||
\(270\) | 72.2591 | − | 0.237426i | 0.267626 | − | 0.000879357i | ||||
\(271\) | 378.819 | + | 218.711i | 1.39786 | + | 0.807053i | 0.994168 | − | 0.107843i | \(-0.0343943\pi\) |
0.403690 | + | 0.914896i | \(0.367728\pi\) | |||||||
\(272\) | 109.039 | − | 1.43319i | 0.400879 | − | 0.00526906i | ||||
\(273\) | 116.770 | 0.427728 | ||||||||
\(274\) | −284.507 | − | 163.016i | −1.03834 | − | 0.594948i | ||||
\(275\) | 20.7772 | − | 11.9957i | 0.0755533 | − | 0.0436207i | ||||
\(276\) | 20.1619 | − | 35.4575i | 0.0730504 | − | 0.128469i | ||||
\(277\) | 338.269 | 1.22119 | 0.610594 | − | 0.791943i | \(-0.290931\pi\) | ||||
0.610594 | + | 0.791943i | \(0.290931\pi\) | |||||||
\(278\) | 38.1946 | − | 66.6598i | 0.137391 | − | 0.239783i | ||||
\(279\) | −451.052 | + | 260.415i | −1.61667 | + | 0.933388i | ||||
\(280\) | 151.301 | − | 268.130i | 0.540360 | − | 0.957608i | ||||
\(281\) | −123.429 | − | 213.786i | −0.439250 | − | 0.760804i | 0.558381 | − | 0.829584i | \(-0.311423\pi\) |
−0.997632 | + | 0.0687802i | \(0.978089\pi\) | |||||||
\(282\) | −48.8066 | + | 28.3927i | −0.173073 | + | 0.100683i | ||||
\(283\) | 292.581 | + | 168.921i | 1.03385 | + | 0.596896i | 0.918086 | − | 0.396381i | \(-0.129734\pi\) |
0.115767 | + | 0.993276i | \(0.463067\pi\) | |||||||
\(284\) | 353.300 | − | 207.085i | 1.24401 | − | 0.729173i | ||||
\(285\) | 6.26140 | − | 38.1900i | 0.0219698 | − | 0.134000i | ||||
\(286\) | 61.4932 | − | 107.322i | 0.215011 | − | 0.375252i | ||||
\(287\) | 267.198 | + | 154.267i | 0.931004 | + | 0.537515i | ||||
\(288\) | 4.59362 | + | 279.583i | 0.0159501 | + | 0.970775i | ||||
\(289\) | 121.274 | + | 210.053i | 0.419634 | + | 0.726828i | ||||
\(290\) | 6.13499 | − | 3.56897i | 0.0211551 | − | 0.0123068i | ||||
\(291\) | 35.4494 | − | 20.4667i | 0.121819 | − | 0.0703323i | ||||
\(292\) | 31.6427 | + | 53.9844i | 0.108366 | + | 0.184878i | ||||
\(293\) | 247.442 | 0.844511 | 0.422256 | − | 0.906477i | \(-0.361238\pi\) | ||||
0.422256 | + | 0.906477i | \(0.361238\pi\) | |||||||
\(294\) | 45.5169 | − | 0.149558i | 0.154819 | − | 0.000508700i | ||||
\(295\) | −204.452 | + | 118.041i | −0.693059 | + | 0.400138i | ||||
\(296\) | 0.615671 | + | 62.4566i | 0.00207997 | + | 0.211002i | ||||
\(297\) | 23.7839 | 0.0800804 | ||||||||
\(298\) | 1.51353 | + | 460.632i | 0.00507896 | + | 1.54574i | ||||
\(299\) | −407.330 | − | 235.172i | −1.36231 | − | 0.786529i | ||||
\(300\) | −16.2913 | − | 9.26356i | −0.0543042 | − | 0.0308785i | ||||
\(301\) | −34.0136 | + | 58.9132i | −0.113002 | + | 0.195725i | ||||
\(302\) | −187.915 | − | 323.023i | −0.622235 | − | 1.06961i | ||||
\(303\) | − | 72.2662i | − | 0.238502i | ||||||
\(304\) | 300.615 | + | 45.2383i | 0.988866 | + | 0.148810i | ||||
\(305\) | −9.84475 | −0.0322779 | ||||||||
\(306\) | 102.956 | − | 59.8938i | 0.336459 | − | 0.195731i | ||||
\(307\) | −85.9857 | − | 49.6439i | −0.280084 | − | 0.161706i | 0.353378 | − | 0.935481i | \(-0.385033\pi\) |
−0.633461 | + | 0.773774i | \(0.718366\pi\) | |||||||
\(308\) | 50.0897 | − | 88.0898i | 0.162629 | − | 0.286006i | ||||
\(309\) | −33.4397 | + | 57.9193i | −0.108219 | + | 0.187441i | ||||
\(310\) | −474.501 | + | 1.55910i | −1.53065 | + | 0.00502935i | ||||
\(311\) | 72.4217i | 0.232867i | 0.993198 | + | 0.116434i | \(0.0371462\pi\) | ||||
−0.993198 | + | 0.116434i | \(0.962854\pi\) | |||||||
\(312\) | −96.6162 | + | 0.952402i | −0.309667 | + | 0.00305257i | ||||
\(313\) | −210.651 | − | 364.858i | −0.673006 | − | 1.16568i | −0.977048 | − | 0.213021i | \(-0.931670\pi\) |
0.304042 | − | 0.952659i | \(-0.401664\pi\) | |||||||
\(314\) | −1.05953 | − | 322.461i | −0.00337430 | − | 1.02695i | ||||
\(315\) | − | 336.280i | − | 1.06756i | ||||||
\(316\) | −253.704 | + | 148.707i | −0.802860 | + | 0.470593i | ||||
\(317\) | 142.726 | + | 247.209i | 0.450241 | + | 0.779840i | 0.998401 | − | 0.0565337i | \(-0.0180048\pi\) |
−0.548160 | + | 0.836374i | \(0.684671\pi\) | |||||||
\(318\) | 34.4653 | + | 59.2452i | 0.108381 | + | 0.186306i | ||||
\(319\) | 2.02315 | − | 1.16807i | 0.00634218 | − | 0.00366166i | ||||
\(320\) | −123.001 | + | 223.087i | −0.384377 | + | 0.697148i | ||||
\(321\) | 21.4813 | − | 37.2066i | 0.0669198 | − | 0.115908i | ||||
\(322\) | −334.341 | − | 191.570i | −1.03833 | − | 0.594937i | ||||
\(323\) | −45.7499 | − | 121.144i | −0.141641 | − | 0.375060i | ||||
\(324\) | 149.679 | + | 255.361i | 0.461971 | + | 0.788151i | ||||
\(325\) | −108.052 | + | 187.151i | −0.332467 | + | 0.575850i | ||||
\(326\) | 114.369 | + | 196.598i | 0.350824 | + | 0.603061i | ||||
\(327\) | 40.9102 | − | 23.6195i | 0.125108 | − | 0.0722310i | ||||
\(328\) | −222.340 | − | 125.462i | −0.677867 | − | 0.382507i | ||||
\(329\) | 266.710 | + | 461.956i | 0.810670 | + | 1.40412i | ||||
\(330\) | 9.26165 | + | 5.30672i | 0.0280656 | + | 0.0160810i | ||||
\(331\) | 13.5916i | 0.0410621i | 0.999789 | + | 0.0205311i | \(0.00653570\pi\) | ||||
−0.999789 | + | 0.0205311i | \(0.993464\pi\) | |||||||
\(332\) | 63.9919 | + | 36.3871i | 0.192747 | + | 0.109600i | ||||
\(333\) | 34.1114 | + | 59.0826i | 0.102437 | + | 0.177425i | ||||
\(334\) | 120.389 | − | 210.111i | 0.360445 | − | 0.629074i | ||||
\(335\) | 167.747i | 0.500738i | ||||||||
\(336\) | −79.1508 | + | 1.04034i | −0.235568 | + | 0.00309625i | ||||
\(337\) | −112.071 | + | 194.113i | −0.332556 | + | 0.576003i | −0.983012 | − | 0.183540i | \(-0.941244\pi\) |
0.650456 | + | 0.759544i | \(0.274578\pi\) | |||||||
\(338\) | 2.55024 | + | 776.148i | 0.00754509 | + | 2.29630i | ||||
\(339\) | −11.7963 | − | 6.81062i | −0.0347975 | − | 0.0200903i | ||||
\(340\) | 108.513 | − | 0.713107i | 0.319157 | − | 0.00209737i | ||||
\(341\) | −156.181 | −0.458008 | ||||||||
\(342\) | 310.249 | − | 118.332i | 0.907162 | − | 0.345999i | ||||
\(343\) | 43.7439i | 0.127533i | ||||||||
\(344\) | 27.6626 | − | 49.0227i | 0.0804145 | − | 0.142508i | ||||
\(345\) | 20.2948 | − | 35.1517i | 0.0588256 | − | 0.101889i | ||||
\(346\) | −0.784617 | − | 238.793i | −0.00226768 | − | 0.690152i | ||||
\(347\) | 66.9198 | + | 38.6361i | 0.192852 | + | 0.111343i | 0.593317 | − | 0.804969i | \(-0.297818\pi\) |
−0.400465 | + | 0.916312i | \(0.631151\pi\) | |||||||
\(348\) | −1.58634 | − | 0.902029i | −0.00455846 | − | 0.00259204i | ||||
\(349\) | −137.502 | −0.393990 | −0.196995 | − | 0.980405i | \(-0.563118\pi\) | ||||
−0.196995 | + | 0.980405i | \(0.563118\pi\) | |||||||
\(350\) | −88.0183 | + | 153.616i | −0.251481 | + | 0.438902i | ||||
\(351\) | −185.533 | + | 107.117i | −0.528583 | + | 0.305177i | ||||
\(352\) | −40.7262 | + | 73.2948i | −0.115699 | + | 0.208224i | ||||
\(353\) | −50.4441 | −0.142901 | −0.0714505 | − | 0.997444i | \(-0.522763\pi\) | ||||
−0.0714505 | + | 0.997444i | \(0.522763\pi\) | |||||||
\(354\) | 52.6665 | + | 30.1767i | 0.148775 | + | 0.0852449i | ||||
\(355\) | 352.920 | − | 203.758i | 0.994140 | − | 0.573967i | ||||
\(356\) | −283.817 | + | 1.86513i | −0.797237 | + | 0.00523913i | ||||
\(357\) | 16.8594 | + | 29.2014i | 0.0472252 | + | 0.0817965i | ||||
\(358\) | −239.463 | − | 411.632i | −0.668891 | − | 1.14981i | ||||
\(359\) | −437.654 | − | 252.679i | −1.21909 | − | 0.703843i | −0.254368 | − | 0.967108i | \(-0.581867\pi\) |
−0.964724 | + | 0.263265i | \(0.915201\pi\) | |||||||
\(360\) | 2.74278 | + | 278.241i | 0.00761884 | + | 0.772892i | ||||
\(361\) | −71.2181 | − | 353.905i | −0.197280 | − | 0.980347i | ||||
\(362\) | 265.121 | + | 151.908i | 0.732379 | + | 0.419637i | ||||
\(363\) | −50.5789 | − | 29.2018i | −0.139336 | − | 0.0804456i | ||||
\(364\) | 5.99830 | + | 912.761i | 0.0164788 | + | 2.50758i | ||||
\(365\) | 31.1344 | + | 53.9264i | 0.0852997 | + | 0.147743i | ||||
\(366\) | 1.27279 | + | 2.18791i | 0.00347758 | + | 0.00597790i | ||||
\(367\) | 160.944 | − | 92.9213i | 0.438541 | − | 0.253192i | −0.264438 | − | 0.964403i | \(-0.585186\pi\) |
0.702978 | + | 0.711211i | \(0.251853\pi\) | |||||||
\(368\) | 278.199 | + | 155.779i | 0.755975 | + | 0.423314i | ||||
\(369\) | −278.852 | −0.755696 | ||||||||
\(370\) | 0.204224 | + | 62.1541i | 0.000551957 | + | 0.167984i | ||||
\(371\) | 560.758 | − | 323.754i | 1.51148 | − | 0.872651i | ||||
\(372\) | 61.6931 | + | 105.252i | 0.165842 | + | 0.282936i | ||||
\(373\) | −438.747 | −1.17627 | −0.588133 | − | 0.808764i | \(-0.700137\pi\) | ||||
−0.588133 | + | 0.808764i | \(0.700137\pi\) | |||||||
\(374\) | 35.7173 | − | 0.117359i | 0.0955007 | − | 0.000313793i | ||||
\(375\) | −60.2495 | − | 34.7851i | −0.160665 | − | 0.0927602i | ||||
\(376\) | −224.446 | − | 380.051i | −0.596931 | − | 1.01077i | ||||
\(377\) | −10.5214 | + | 18.2237i | −0.0279083 | + | 0.0483386i | ||||
\(378\) | −151.710 | + | 88.2558i | −0.401350 | + | 0.233481i | ||||
\(379\) | 152.410i | 0.402138i | 0.979577 | + | 0.201069i | \(0.0644416\pi\) | ||||
−0.979577 | + | 0.201069i | \(0.935558\pi\) | |||||||
\(380\) | 298.844 | + | 46.9821i | 0.786431 | + | 0.123637i | ||||
\(381\) | −17.4428 | −0.0457817 | ||||||||
\(382\) | −320.525 | − | 550.977i | −0.839071 | − | 1.44235i | ||||
\(383\) | 68.7065 | + | 39.6677i | 0.179390 | + | 0.103571i | 0.587006 | − | 0.809582i | \(-0.300306\pi\) |
−0.407616 | + | 0.913153i | \(0.633640\pi\) | |||||||
\(384\) | 65.4815 | − | 1.50636i | 0.170525 | − | 0.00392281i | ||||
\(385\) | 50.4199 | − | 87.3299i | 0.130961 | − | 0.226831i | ||||
\(386\) | −0.403795 | − | 122.892i | −0.00104610 | − | 0.318373i | ||||
\(387\) | − | 61.4827i | − | 0.158870i | ||||||
\(388\) | 161.804 | + | 276.048i | 0.417021 | + | 0.711464i | ||||
\(389\) | −241.258 | − | 417.872i | −0.620201 | − | 1.07422i | −0.989448 | − | 0.144889i | \(-0.953718\pi\) |
0.369247 | − | 0.929331i | \(-0.379616\pi\) | |||||||
\(390\) | −96.1482 | + | 0.315921i | −0.246534 | + | 0.000810053i | ||||
\(391\) | − | 135.818i | − | 0.347362i | ||||||
\(392\) | 3.50720 | + | 355.787i | 0.00894693 | + | 0.907620i | ||||
\(393\) | −48.1921 | − | 83.4711i | −0.122626 | − | 0.212395i | ||||
\(394\) | −419.829 | + | 244.231i | −1.06556 | + | 0.619877i | ||||
\(395\) | −253.431 | + | 146.318i | −0.641598 | + | 0.370427i | ||||
\(396\) | 0.601856 | + | 91.5843i | 0.00151984 | + | 0.231273i | ||||
\(397\) | 14.2395 | − | 24.6635i | 0.0358677 | − | 0.0621247i | −0.847534 | − | 0.530741i | \(-0.821914\pi\) |
0.883402 | + | 0.468616i | \(0.155247\pi\) | |||||||
\(398\) | −238.590 | + | 416.405i | −0.599474 | + | 1.04624i | ||||
\(399\) | 33.2096 | + | 87.9378i | 0.0832320 | + | 0.220396i | ||||
\(400\) | 71.5742 | − | 127.821i | 0.178935 | − | 0.319552i | ||||
\(401\) | 98.1016 | − | 169.917i | 0.244642 | − | 0.423733i | −0.717389 | − | 0.696673i | \(-0.754663\pi\) |
0.962031 | + | 0.272940i | \(0.0879961\pi\) | |||||||
\(402\) | 37.2804 | − | 21.6875i | 0.0927372 | − | 0.0539489i | ||||
\(403\) | 1218.33 | − | 703.403i | 3.02315 | − | 1.74542i | ||||
\(404\) | 564.887 | − | 3.71222i | 1.39824 | − | 0.00918866i | ||||
\(405\) | 147.274 | + | 255.086i | 0.363640 | + | 0.629843i | ||||
\(406\) | −8.57069 | + | 14.9582i | −0.0211101 | + | 0.0368427i | ||||
\(407\) | 20.4579i | 0.0502650i | ||||||||
\(408\) | −14.1878 | − | 24.0239i | −0.0347740 | − | 0.0588822i | ||||
\(409\) | 20.7557 | + | 35.9499i | 0.0507474 | + | 0.0878971i | 0.890283 | − | 0.455407i | \(-0.150506\pi\) |
−0.839536 | + | 0.543304i | \(0.817173\pi\) | |||||||
\(410\) | −220.429 | − | 126.301i | −0.537631 | − | 0.308050i | ||||
\(411\) | 83.8947i | 0.204123i | ||||||||
\(412\) | −454.459 | − | 258.415i | −1.10306 | − | 0.627221i | ||||
\(413\) | 286.713 | − | 496.602i | 0.694221 | − | 1.20243i | ||||
\(414\) | 348.262 | − | 1.14431i | 0.841213 | − | 0.00276403i | ||||
\(415\) | 63.4399 | + | 36.6270i | 0.152867 | + | 0.0882579i | ||||
\(416\) | −12.4077 | − | 755.177i | −0.0298263 | − | 1.81533i | ||||
\(417\) | −19.6565 | −0.0471379 | ||||||||
\(418\) | 98.3118 | + | 15.7871i | 0.235196 | + | 0.0377681i | ||||
\(419\) | 207.738i | 0.495794i | 0.968786 | + | 0.247897i | \(0.0797394\pi\) | ||||
−0.968786 | + | 0.247897i | \(0.920261\pi\) | |||||||
\(420\) | −78.7691 | + | 0.517639i | −0.187545 | + | 0.00123247i | ||||
\(421\) | 306.179 | − | 530.317i | 0.727266 | − | 1.25966i | −0.230769 | − | 0.973009i | \(-0.574124\pi\) |
0.958035 | − | 0.286653i | \(-0.0925425\pi\) | |||||||
\(422\) | 174.701 | − | 0.574027i | 0.413984 | − | 0.00136025i | ||||
\(423\) | −417.514 | − | 241.052i | −0.987031 | − | 0.569863i | ||||
\(424\) | −461.335 | + | 272.450i | −1.08805 | + | 0.642571i | ||||
\(425\) | −62.4029 | −0.146830 | ||||||||
\(426\) | −90.9113 | − | 52.0901i | −0.213407 | − | 0.122277i | ||||
\(427\) | 20.7086 | − | 11.9561i | 0.0484980 | − | 0.0280003i | ||||
\(428\) | 291.939 | + | 166.003i | 0.682100 | + | 0.387857i | ||||
\(429\) | −31.6469 | −0.0737691 | ||||||||
\(430\) | 27.8474 | − | 48.6012i | 0.0647614 | − | 0.113026i | ||||
\(431\) | 56.0531 | − | 32.3623i | 0.130054 | − | 0.0750865i | −0.433562 | − | 0.901124i | \(-0.642743\pi\) |
0.563615 | + | 0.826037i | \(0.309410\pi\) | |||||||
\(432\) | 124.806 | − | 74.2610i | 0.288904 | − | 0.171900i | ||||
\(433\) | 73.2567 | + | 126.884i | 0.169184 | + | 0.293036i | 0.938133 | − | 0.346274i | \(-0.112553\pi\) |
−0.768949 | + | 0.639310i | \(0.779220\pi\) | |||||||
\(434\) | 996.229 | − | 579.546i | 2.29546 | − | 1.33536i | ||||
\(435\) | −1.57266 | − | 0.907975i | −0.00361531 | − | 0.00208730i | ||||
\(436\) | 186.730 | + | 318.572i | 0.428279 | + | 0.730670i | ||||
\(437\) | 61.2596 | − | 373.639i | 0.140182 | − | 0.855010i | ||||
\(438\) | 7.95941 | − | 13.8913i | 0.0181722 | − | 0.0317153i | ||||
\(439\) | −333.920 | − | 192.789i | −0.760638 | − | 0.439155i | 0.0688866 | − | 0.997624i | \(-0.478055\pi\) |
−0.829525 | + | 0.558470i | \(0.811389\pi\) | |||||||
\(440\) | −41.0056 | + | 72.6687i | −0.0931945 | + | 0.165156i | ||||
\(441\) | 194.317 | + | 336.567i | 0.440628 | + | 0.763190i | ||||
\(442\) | −278.093 | + | 161.778i | −0.629171 | + | 0.366013i | ||||
\(443\) | 30.9999 | − | 17.8978i | 0.0699771 | − | 0.0404013i | −0.464603 | − | 0.885519i | \(-0.653803\pi\) |
0.534580 | + | 0.845118i | \(0.320470\pi\) | |||||||
\(444\) | 13.7868 | − | 8.08108i | 0.0310514 | − | 0.0182006i | ||||
\(445\) | −282.436 | −0.634687 | ||||||||
\(446\) | 344.602 | − | 1.13228i | 0.772650 | − | 0.00253875i | ||||
\(447\) | 102.066 | − | 58.9278i | 0.228335 | − | 0.131830i | ||||
\(448\) | −12.1980 | − | 618.649i | −0.0272276 | − | 1.38091i | ||||
\(449\) | 729.651 | 1.62506 | 0.812529 | − | 0.582921i | \(-0.198090\pi\) | ||||
0.812529 | + | 0.582921i | \(0.198090\pi\) | |||||||
\(450\) | −0.525762 | − | 160.012i | −0.00116836 | − | 0.355582i | ||||
\(451\) | −72.4161 | − | 41.8095i | −0.160568 | − | 0.0927039i | ||||
\(452\) | 52.6311 | − | 92.5591i | 0.116440 | − | 0.204777i | ||||
\(453\) | −47.8072 | + | 82.8044i | −0.105535 | + | 0.182791i | ||||
\(454\) | 250.696 | + | 430.942i | 0.552193 | + | 0.949211i | ||||
\(455\) | 908.320i | 1.99631i | ||||||||
\(456\) | −28.1951 | − | 72.4896i | −0.0618314 | − | 0.158968i | ||||
\(457\) | −402.710 | −0.881204 | −0.440602 | − | 0.897703i | \(-0.645235\pi\) | ||||
−0.440602 | + | 0.897703i | \(0.645235\pi\) | |||||||
\(458\) | 342.495 | − | 199.243i | 0.747806 | − | 0.435028i | ||||
\(459\) | −53.5750 | − | 30.9316i | −0.116721 | − | 0.0673890i | ||||
\(460\) | 275.815 | + | 156.834i | 0.599597 | + | 0.340944i | ||||
\(461\) | −256.224 | + | 443.793i | −0.555800 | + | 0.962674i | 0.442041 | + | 0.896995i | \(0.354255\pi\) |
−0.997841 | + | 0.0656788i | \(0.979079\pi\) | |||||||
\(462\) | −25.9269 | + | 0.0851898i | −0.0561189 | + | 0.000184394i | ||||
\(463\) | 732.188i | 1.58140i | 0.612204 | + | 0.790700i | \(0.290283\pi\) | ||||
−0.612204 | + | 0.790700i | \(0.709717\pi\) | |||||||
\(464\) | 6.96946 | − | 12.4464i | 0.0150204 | − | 0.0268242i | ||||
\(465\) | 60.7020 | + | 105.139i | 0.130542 | + | 0.226105i | ||||
\(466\) | 1.89740 | + | 577.461i | 0.00407168 | + | 1.23919i | ||||
\(467\) | − | 634.798i | − | 1.35931i | −0.733532 | − | 0.679655i | \(-0.762130\pi\) | ||
0.733532 | − | 0.679655i | \(-0.237870\pi\) | |||||||
\(468\) | −417.170 | − | 711.717i | −0.891389 | − | 1.52076i | ||||
\(469\) | −203.724 | − | 352.860i | −0.434379 | − | 0.752367i | ||||
\(470\) | −220.859 | − | 379.653i | −0.469914 | − | 0.807773i | ||||
\(471\) | −71.4503 | + | 41.2518i | −0.151699 | + | 0.0875835i | ||||
\(472\) | −233.179 | + | 413.231i | −0.494023 | + | 0.875490i | ||||
\(473\) | 9.21836 | − | 15.9667i | 0.0194891 | − | 0.0337562i | ||||
\(474\) | 65.2832 | + | 37.4058i | 0.137728 | + | 0.0789152i | ||||
\(475\) | −171.672 | − | 28.1462i | −0.361414 | − | 0.0592553i | ||||
\(476\) | −227.394 | + | 133.286i | −0.477719 | + | 0.280013i | ||||
\(477\) | −292.607 | + | 506.811i | −0.613433 | + | 1.06250i | ||||
\(478\) | 39.8560 | + | 68.5118i | 0.0833808 | + | 0.143330i | ||||
\(479\) | −194.227 | + | 112.137i | −0.405484 | + | 0.234106i | −0.688847 | − | 0.724906i | \(-0.741883\pi\) |
0.283364 | + | 0.959013i | \(0.408550\pi\) | |||||||
\(480\) | 65.1700 | − | 1.07076i | 0.135771 | − | 0.00223075i | ||||
\(481\) | −92.1376 | − | 159.587i | −0.191554 | − | 0.331782i | ||||
\(482\) | −527.480 | − | 302.234i | −1.09436 | − | 0.627042i | ||||
\(483\) | 98.5897i | 0.204119i | ||||||||
\(484\) | 225.665 | − | 396.863i | 0.466250 | − | 0.819966i | ||||
\(485\) | 159.205 | + | 275.751i | 0.328258 | + | 0.568559i | ||||
\(486\) | 118.876 | − | 207.470i | 0.244601 | − | 0.426894i | ||||
\(487\) | 177.686i | 0.364857i | 0.983219 | + | 0.182429i | \(0.0583959\pi\) | ||||
−0.983219 | + | 0.182429i | \(0.941604\pi\) | |||||||
\(488\) | −17.0370 | + | 10.0615i | −0.0349119 | + | 0.0206179i | ||||
\(489\) | 29.0964 | − | 50.3964i | 0.0595018 | − | 0.103060i | ||||
\(490\) | 1.16337 | + | 354.064i | 0.00237423 | + | 0.722579i | ||||
\(491\) | −463.870 | − | 267.815i | −0.944745 | − | 0.545449i | −0.0533002 | − | 0.998579i | \(-0.516974\pi\) |
−0.891444 | + | 0.453130i | \(0.850307\pi\) | |||||||
\(492\) | 0.429239 | + | 65.3173i | 0.000872438 | + | 0.132759i | ||||
\(493\) | −6.07642 | −0.0123254 | ||||||||
\(494\) | −838.009 | + | 319.623i | −1.69637 | + | 0.647010i | ||||
\(495\) | 91.1387i | 0.184119i | ||||||||
\(496\) | −819.561 | + | 487.647i | −1.65234 | + | 0.983159i | ||||
\(497\) | −494.916 | + | 857.220i | −0.995807 | + | 1.72479i | ||||
\(498\) | −0.0618852 | − | 18.8343i | −0.000124268 | − | 0.0378200i | ||||
\(499\) | 419.926 | + | 242.445i | 0.841536 | + | 0.485861i | 0.857786 | − | 0.514007i | \(-0.171840\pi\) |
−0.0162502 | + | 0.999868i | \(0.505173\pi\) | |||||||
\(500\) | 268.812 | − | 472.743i | 0.537624 | − | 0.945486i | ||||
\(501\) | −61.9570 | −0.123667 | ||||||||
\(502\) | −397.315 | + | 693.421i | −0.791464 | + | 1.38132i | ||||
\(503\) | −279.526 | + | 161.384i | −0.555718 | + | 0.320844i | −0.751425 | − | 0.659819i | \(-0.770633\pi\) |
0.195707 | + | 0.980662i | \(0.437300\pi\) | |||||||
\(504\) | −343.685 | − | 581.955i | −0.681914 | − | 1.15467i | ||||
\(505\) | 562.139 | 1.11315 | ||||||||
\(506\) | 90.6131 | + | 51.9193i | 0.179077 | + | 0.102607i | ||||
\(507\) | 171.977 | − | 99.2912i | 0.339206 | − | 0.195841i | ||||
\(508\) | −0.896015 | − | 136.347i | −0.00176381 | − | 0.268399i | ||||
\(509\) | 213.275 | + | 369.403i | 0.419008 | + | 0.725742i | 0.995840 | − | 0.0911201i | \(-0.0290447\pi\) |
−0.576832 | + | 0.816863i | \(0.695711\pi\) | |||||||
\(510\) | −13.9611 | − | 23.9988i | −0.0273746 | − | 0.0470565i | ||||
\(511\) | −130.984 | − | 75.6235i | −0.256328 | − | 0.147991i | ||||
\(512\) | 15.1386 | + | 511.776i | 0.0295675 | + | 0.999563i | ||||
\(513\) | −133.435 | − | 109.258i | −0.260107 | − | 0.212978i | ||||
\(514\) | −22.2650 | − | 12.7573i | −0.0433170 | − | 0.0248197i | ||||
\(515\) | −450.539 | − | 260.119i | −0.874833 | − | 0.505085i | ||||
\(516\) | −14.4015 | + | 0.0946409i | −0.0279099 | + | 0.000183413i | ||||
\(517\) | −72.2839 | − | 125.199i | −0.139814 | − | 0.242165i | ||||
\(518\) | −75.9138 | − | 130.495i | −0.146552 | − | 0.251920i | ||||
\(519\) | −52.9112 | + | 30.5483i | −0.101948 | + | 0.0588599i | ||||
\(520\) | −7.40848 | − | 751.552i | −0.0142471 | − | 1.44529i | ||||
\(521\) | 528.882 | 1.01513 | 0.507564 | − | 0.861614i | \(-0.330546\pi\) | ||||
0.507564 | + | 0.861614i | \(0.330546\pi\) | |||||||
\(522\) | −0.0511955 | − | 15.5810i | −9.80756e−5 | − | 0.0298486i | ||||
\(523\) | −402.414 | + | 232.334i | −0.769434 | + | 0.444233i | −0.832673 | − | 0.553765i | \(-0.813190\pi\) |
0.0632386 | + | 0.997998i | \(0.479857\pi\) | |||||||
\(524\) | 649.998 | − | 380.994i | 1.24046 | − | 0.727088i | ||||
\(525\) | 45.2979 | 0.0862816 | ||||||||
\(526\) | 477.622 | − | 1.56935i | 0.908026 | − | 0.00298356i | ||||
\(527\) | 351.809 | + | 203.117i | 0.667569 | + | 0.385421i | ||||
\(528\) | 21.4515 | − | 0.281953i | 0.0406278 | − | 0.000534002i | ||||
\(529\) | −65.9418 | + | 114.215i | −0.124654 | + | 0.215907i | ||||
\(530\) | −460.852 | + | 268.096i | −0.869533 | + | 0.505842i | ||||
\(531\) | 518.261i | 0.976010i | ||||||||
\(532\) | −685.683 | + | 264.109i | −1.28888 | + | 0.496445i | ||||
\(533\) | 753.201 | 1.41314 | ||||||||
\(534\) | 36.5151 | + | 62.7689i | 0.0683804 | + | 0.117545i | ||||
\(535\) | 289.420 | + | 167.097i | 0.540973 | + | 0.312331i | ||||
\(536\) | 171.441 | + | 290.298i | 0.319852 | + | 0.541600i | ||||
\(537\) | −60.9214 | + | 105.519i | −0.113448 | + | 0.196497i | ||||
\(538\) | −1.35397 | − | 412.071i | −0.00251667 | − | 0.765931i | ||||
\(539\) | 116.539i | 0.216214i | ||||||||
\(540\) | 124.680 | − | 73.0804i | 0.230888 | − | 0.135334i | ||||
\(541\) | 318.729 | + | 552.054i | 0.589147 | + | 1.02043i | 0.994344 | + | 0.106204i | \(0.0338696\pi\) |
−0.405197 | + | 0.914229i | \(0.632797\pi\) | |||||||
\(542\) | 874.841 | − | 2.87452i | 1.61410 | − | 0.00530355i | ||||
\(543\) | − | 78.1784i | − | 0.143975i | ||||||
\(544\) | 187.061 | − | 112.137i | 0.343861 | − | 0.206134i | ||||
\(545\) | 183.730 | + | 318.230i | 0.337119 | + | 0.583908i | ||||
\(546\) | 201.866 | − | 117.434i | 0.369718 | − | 0.215080i | ||||
\(547\) | −16.4275 | + | 9.48444i | −0.0300320 | + | 0.0173390i | −0.514941 | − | 0.857226i | \(-0.672186\pi\) |
0.484909 | + | 0.874565i | \(0.338853\pi\) | |||||||
\(548\) | −655.785 | + | 4.30956i | −1.19669 | + | 0.00786416i | ||||
\(549\) | −10.8059 | + | 18.7164i | −0.0196829 | + | 0.0340918i | ||||
\(550\) | 23.8547 | − | 41.6329i | 0.0433723 | − | 0.0756963i | ||||
\(551\) | −16.7163 | − | 2.74071i | −0.0303382 | − | 0.00497407i | ||||
\(552\) | −0.804122 | − | 81.5739i | −0.00145674 | − | 0.147779i | ||||
\(553\) | 355.398 | − | 615.568i | 0.642673 | − | 1.11314i | ||||
\(554\) | 584.785 | − | 340.193i | 1.05557 | − | 0.614066i | ||||
\(555\) | 13.7720 | − | 7.95126i | 0.0248144 | − | 0.0143266i | ||||
\(556\) | −1.00973 | − | 153.650i | −0.00181606 | − | 0.276349i | ||||
\(557\) | −496.557 | − | 860.062i | −0.891485 | − | 1.54410i | −0.838096 | − | 0.545523i | \(-0.816331\pi\) |
−0.0533887 | − | 0.998574i | \(-0.517002\pi\) | |||||||
\(558\) | −517.863 | + | 903.811i | −0.928071 | + | 1.61973i | ||||
\(559\) | 166.070i | 0.297084i | ||||||||
\(560\) | −8.09253 | − | 615.693i | −0.0144509 | − | 1.09945i | ||||
\(561\) | −4.56924 | − | 7.91416i | −0.00814482 | − | 0.0141072i | ||||
\(562\) | −428.381 | − | 245.453i | −0.762243 | − | 0.436748i | ||||
\(563\) | 412.624i | 0.732903i | 0.930437 | + | 0.366451i | \(0.119427\pi\) | ||||
−0.930437 | + | 0.366451i | \(0.880573\pi\) | |||||||
\(564\) | −55.8205 | + | 98.1681i | −0.0989725 | + | 0.174057i | ||||
\(565\) | 52.9780 | − | 91.7606i | 0.0937664 | − | 0.162408i | ||||
\(566\) | 675.682 | − | 2.22013i | 1.19378 | − | 0.00392250i | ||||
\(567\) | −619.589 | − | 357.720i | −1.09275 | − | 0.630899i | ||||
\(568\) | 402.506 | − | 713.308i | 0.708638 | − | 1.25582i | ||||
\(569\) | −749.109 | −1.31654 | −0.658268 | − | 0.752784i | \(-0.728711\pi\) | ||||
−0.658268 | + | 0.752784i | \(0.728711\pi\) | |||||||
\(570\) | −27.5827 | − | 72.3182i | −0.0483907 | − | 0.126874i | ||||
\(571\) | − | 530.406i | − | 0.928907i | −0.885598 | − | 0.464453i | \(-0.846251\pi\) | ||
0.885598 | − | 0.464453i | \(-0.153749\pi\) | |||||||
\(572\) | −1.62566 | − | 247.377i | −0.00284206 | − | 0.432476i | ||||
\(573\) | −81.5443 | + | 141.239i | −0.142311 | + | 0.246490i | ||||
\(574\) | 617.064 | − | 2.02753i | 1.07503 | − | 0.00353228i | ||||
\(575\) | −158.014 | − | 91.2292i | −0.274806 | − | 0.158660i | ||||
\(576\) | 289.114 | + | 478.711i | 0.501934 | + | 0.831096i | ||||
\(577\) | −103.722 | −0.179762 | −0.0898808 | − | 0.995953i | \(-0.528649\pi\) | ||||
−0.0898808 | + | 0.995953i | \(0.528649\pi\) | |||||||
\(578\) | 420.901 | + | 241.167i | 0.728202 | + | 0.417244i | ||||
\(579\) | −27.2302 | + | 15.7214i | −0.0470297 | + | 0.0271526i | ||||
\(580\) | 7.01664 | − | 12.3397i | 0.0120977 | − | 0.0212754i | ||||
\(581\) | −177.929 | −0.306247 | ||||||||
\(582\) | 40.7002 | − | 71.0328i | 0.0699317 | − | 0.122050i | ||||
\(583\) | −151.977 | + | 87.7438i | −0.260680 | + | 0.150504i | ||||
\(584\) | 108.994 | + | 61.5032i | 0.186633 | + | 0.105314i | ||||
\(585\) | −410.468 | − | 710.952i | −0.701655 | − | 1.21530i | ||||
\(586\) | 427.767 | − | 248.849i | 0.729977 | − | 0.424657i | ||||
\(587\) | −491.362 | − | 283.688i | −0.837074 | − | 0.483285i | 0.0191946 | − | 0.999816i | \(-0.493890\pi\) |
−0.856269 | + | 0.516531i | \(0.827223\pi\) | |||||||
\(588\) | 78.5371 | − | 46.0342i | 0.133567 | − | 0.0782895i | ||||
\(589\) | 876.220 | + | 717.459i | 1.48764 | + | 1.21810i | ||||
\(590\) | −234.736 | + | 409.678i | −0.397858 | + | 0.694370i | ||||
\(591\) | 107.620 | + | 62.1345i | 0.182098 | + | 0.105135i | ||||
\(592\) | 63.8761 | + | 107.353i | 0.107899 | + | 0.181340i | ||||
\(593\) | −157.268 | − | 272.396i | −0.265207 | − | 0.459352i | 0.702411 | − | 0.711772i | \(-0.252107\pi\) |
−0.967618 | + | 0.252420i | \(0.918774\pi\) | |||||||
\(594\) | 41.1165 | − | 23.9191i | 0.0692197 | − | 0.0402679i | ||||
\(595\) | −227.150 | + | 131.145i | −0.381764 | + | 0.220412i | ||||
\(596\) | 465.868 | + | 794.798i | 0.781657 | + | 1.33355i | ||||
\(597\) | 122.789 | 0.205676 | ||||||||
\(598\) | −940.684 | + | 3.09087i | −1.57305 | + | 0.00516868i | ||||
\(599\) | 503.360 | − | 290.615i | 0.840333 | − | 0.485167i | −0.0170441 | − | 0.999855i | \(-0.505426\pi\) |
0.857378 | + | 0.514688i | \(0.172092\pi\) | |||||||
\(600\) | −37.4798 | + | 0.369461i | −0.0624664 | + | 0.000615768i | ||||
\(601\) | −191.970 | −0.319418 | −0.159709 | − | 0.987164i | \(-0.551056\pi\) | ||||
−0.159709 | + | 0.987164i | \(0.551056\pi\) | |||||||
\(602\) | 0.447040 | + | 136.054i | 0.000742592 | + | 0.226003i | ||||
\(603\) | 318.914 | + | 184.125i | 0.528878 | + | 0.305348i | ||||
\(604\) | −649.718 | − | 369.444i | −1.07569 | − | 0.611662i | ||||
\(605\) | 227.153 | − | 393.440i | 0.375459 | − | 0.650314i | ||||
\(606\) | −72.6771 | − | 124.931i | −0.119929 | − | 0.206156i | ||||
\(607\) | − | 503.612i | − | 0.829675i | −0.909896 | − | 0.414837i | \(-0.863838\pi\) | ||
0.909896 | − | 0.414837i | \(-0.136162\pi\) | |||||||
\(608\) | 565.186 | − | 224.118i | 0.929582 | − | 0.368616i | ||||
\(609\) | 4.41083 | 0.00724274 | ||||||||
\(610\) | −17.0192 | + | 9.90072i | −0.0279003 | + | 0.0162307i | ||||
\(611\) | 1127.74 | + | 651.101i | 1.84573 | + | 1.06563i | ||||
\(612\) | 117.752 | − | 207.083i | 0.192405 | − | 0.338372i | ||||
\(613\) | −72.2021 | + | 125.058i | −0.117785 | + | 0.204009i | −0.918890 | − | 0.394515i | \(-0.870913\pi\) |
0.801105 | + | 0.598524i | \(0.204246\pi\) | |||||||
\(614\) | −198.574 | + | 0.652469i | −0.323411 | + | 0.00106265i | ||||
\(615\) | 64.9995i | 0.105690i | ||||||||
\(616\) | −1.99774 | − | 202.660i | −0.00324308 | − | 0.328994i | ||||
\(617\) | −73.7633 | − | 127.762i | −0.119552 | − | 0.207069i | 0.800038 | − | 0.599949i | \(-0.204812\pi\) |
−0.919590 | + | 0.392879i | \(0.871479\pi\) | |||||||
\(618\) | 0.439498 | + | 133.758i | 0.000711162 | + | 0.216437i | ||||
\(619\) | 240.726i | 0.388895i | 0.980913 | + | 0.194448i | \(0.0622915\pi\) | ||||
−0.980913 | + | 0.194448i | \(0.937709\pi\) | |||||||
\(620\) | −818.728 | + | 479.894i | −1.32053 | + | 0.774022i | ||||
\(621\) | −90.4401 | − | 156.647i | −0.145636 | − | 0.252249i | ||||
\(622\) | 72.8335 | + | 125.199i | 0.117096 | + | 0.201285i | ||||
\(623\) | 594.110 | − | 343.009i | 0.953627 | − | 0.550577i | ||||
\(624\) | −166.068 | + | 98.8120i | −0.266135 | + | 0.158353i | ||||
\(625\) | 156.134 | − | 270.432i | 0.249815 | − | 0.432692i | ||||
\(626\) | −731.096 | − | 418.902i | −1.16788 | − | 0.669172i | ||||
\(627\) | −9.00047 | − | 23.8329i | −0.0143548 | − | 0.0380110i | ||||
\(628\) | −326.126 | − | 556.391i | −0.519309 | − | 0.885972i | ||||
\(629\) | 26.6060 | − | 46.0829i | 0.0422989 | − | 0.0732638i | ||||
\(630\) | −338.192 | − | 581.346i | −0.536813 | − | 0.922772i | ||||
\(631\) | 641.965 | − | 370.639i | 1.01738 | − | 0.587383i | 0.104034 | − | 0.994574i | \(-0.466825\pi\) |
0.913343 | + | 0.407191i | \(0.133492\pi\) | |||||||
\(632\) | −289.039 | + | 512.225i | −0.457340 | + | 0.810483i | ||||
\(633\) | −22.3492 | − | 38.7100i | −0.0353068 | − | 0.0611532i | ||||
\(634\) | 495.354 | + | 283.827i | 0.781315 | + | 0.447676i | ||||
\(635\) | − | 135.683i | − | 0.213674i | ||||||
\(636\) | 119.164 | + | 67.7592i | 0.187365 | + | 0.106540i | ||||
\(637\) | −524.866 | − | 909.094i | −0.823965 | − | 1.42715i | ||||
\(638\) | 2.32283 | − | 4.05396i | 0.00364080 | − | 0.00635417i | ||||
\(639\) | − | 894.607i | − | 1.40001i | ||||||
\(640\) | 11.7176 | + | 509.363i | 0.0183087 | + | 0.795880i | ||||
\(641\) | −168.177 | + | 291.291i | −0.262366 | + | 0.454432i | −0.966870 | − | 0.255268i | \(-0.917836\pi\) |
0.704504 | + | 0.709700i | \(0.251169\pi\) | |||||||
\(642\) | −0.282328 | − | 85.9246i | −0.000439763 | − | 0.133839i | ||||
\(643\) | 530.178 | + | 306.098i | 0.824538 | + | 0.476047i | 0.851979 | − | 0.523576i | \(-0.175402\pi\) |
−0.0274407 | + | 0.999623i | \(0.508736\pi\) | |||||||
\(644\) | −770.652 | + | 5.06442i | −1.19666 | + | 0.00786401i | ||||
\(645\) | −14.3314 | −0.0222193 | ||||||||
\(646\) | −200.924 | − | 163.419i | −0.311027 | − | 0.252970i | ||||
\(647\) | 22.0321i | 0.0340527i | 0.999855 | + | 0.0170263i | \(0.00541992\pi\) | ||||
−0.999855 | + | 0.0170263i | \(0.994580\pi\) | |||||||
\(648\) | 515.571 | + | 290.927i | 0.795634 | + | 0.448961i | ||||
\(649\) | −77.7051 | + | 134.589i | −0.119731 | + | 0.207379i | ||||
\(650\) | 1.42013 | + | 432.205i | 0.00218481 | + | 0.664931i | ||||
\(651\) | −255.376 | − | 147.441i | −0.392282 | − | 0.226484i | ||||
\(652\) | 395.431 | + | 224.851i | 0.606490 | + | 0.344863i | ||||
\(653\) | 432.929 | 0.662984 | 0.331492 | − | 0.943458i | \(-0.392448\pi\) | ||||
0.331492 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(654\) | 46.9700 | − | 81.9752i | 0.0718195 | − | 0.125344i | ||||
\(655\) | 649.300 | − | 374.873i | 0.991297 | − | 0.572326i | ||||
\(656\) | −510.548 | + | 6.71052i | −0.778274 | + | 0.0102295i | ||||
\(657\) | 136.697 | 0.208062 | ||||||||
\(658\) | 925.659 | + | 530.382i | 1.40678 | + | 0.806052i | ||||
\(659\) | −550.072 | + | 317.584i | −0.834707 | + | 0.481918i | −0.855462 | − | 0.517866i | \(-0.826726\pi\) |
0.0207547 | + | 0.999785i | \(0.493393\pi\) | |||||||
\(660\) | 21.3480 | − | 0.140291i | 0.0323455 | − | 0.000212562i | ||||
\(661\) | 555.362 | + | 961.915i | 0.840184 | + | 1.45524i | 0.889739 | + | 0.456470i | \(0.150887\pi\) |
−0.0495545 | + | 0.998771i | \(0.515780\pi\) | |||||||
\(662\) | 13.6688 | + | 23.4965i | 0.0206478 | + | 0.0354932i | ||||
\(663\) | 71.2872 | + | 41.1577i | 0.107522 | + | 0.0620779i | ||||
\(664\) | 147.220 | − | 1.45124i | 0.221717 | − | 0.00218560i | ||||
\(665\) | −684.045 | + | 258.329i | −1.02864 | + | 0.388464i | ||||
\(666\) | 118.389 | + | 67.8341i | 0.177761 | + | 0.101853i | ||||
\(667\) | −15.3864 | − | 8.88335i | −0.0230681 | − | 0.0133184i | ||||
\(668\) | −3.18265 | − | 484.303i | −0.00476445 | − | 0.725005i | ||||
\(669\) | −44.0843 | − | 76.3562i | −0.0658958 | − | 0.114135i | ||||
\(670\) | 168.701 | + | 289.994i | 0.251793 | + | 0.432827i | ||||
\(671\) | −5.61246 | + | 3.24036i | −0.00836432 | + | 0.00482914i | ||||
\(672\) | −135.786 | + | 81.3993i | −0.202063 | + | 0.121130i | ||||
\(673\) | −1159.87 | −1.72344 | −0.861718 | − | 0.507388i | \(-0.830611\pi\) | ||||
−0.861718 | + | 0.507388i | \(0.830611\pi\) | |||||||
\(674\) | 1.47295 | + | 448.283i | 0.00218539 | + | 0.665108i | ||||
\(675\) | −71.9727 | + | 41.5535i | −0.106626 | + | 0.0615607i | ||||
\(676\) | 784.970 | + | 1339.21i | 1.16120 | + | 1.98107i | ||||
\(677\) | −1044.27 | −1.54250 | −0.771248 | − | 0.636535i | \(-0.780367\pi\) | ||||
−0.771248 | + | 0.636535i | \(0.780367\pi\) | |||||||
\(678\) | −27.2423 | + | 0.0895120i | −0.0401805 | + | 0.000132024i | ||||
\(679\) | −669.782 | − | 386.699i | −0.986425 | − | 0.569513i | ||||
\(680\) | 186.876 | − | 110.363i | 0.274817 | − | 0.162299i | ||||
\(681\) | 63.7791 | − | 110.469i | 0.0936551 | − | 0.162215i | ||||
\(682\) | −269.998 | + | 157.069i | −0.395892 | + | 0.230306i | ||||
\(683\) | − | 1038.26i | − | 1.52014i | −0.649841 | − | 0.760070i | \(-0.725165\pi\) | ||
0.649841 | − | 0.760070i | \(-0.274835\pi\) | |||||||
\(684\) | 417.341 | − | 516.580i | 0.610148 | − | 0.755234i | ||||
\(685\) | −652.595 | −0.952693 | ||||||||
\(686\) | 43.9927 | + | 75.6226i | 0.0641292 | + | 0.110237i | ||||
\(687\) | −87.7961 | − | 50.6891i | −0.127796 | − | 0.0737833i | ||||
\(688\) | −1.47957 | − | 112.568i | −0.00215054 | − | 0.163617i | ||||
\(689\) | 790.356 | − | 1368.94i | 1.14711 | − | 1.98685i | ||||
\(690\) | −0.266735 | − | 81.1788i | −0.000386572 | − | 0.117650i | ||||
\(691\) | − | 240.378i | − | 0.347870i | −0.984757 | − | 0.173935i | \(-0.944352\pi\) | ||
0.984757 | − | 0.173935i | \(-0.0556483\pi\) | |||||||
\(692\) | −241.507 | − | 412.025i | −0.348998 | − | 0.595412i | ||||
\(693\) | −110.685 | − | 191.712i | −0.159719 | − | 0.276641i | ||||
\(694\) | 154.544 | − | 0.507795i | 0.222685 | − | 0.000731692i | ||||
\(695\) | − | 152.903i | − | 0.220004i | ||||||
\(696\) | −3.64956 | + | 0.0359758i | −0.00524362 | + | 5.16894e-5i | ||||
\(697\) | 108.749 | + | 188.358i | 0.156024 | + | 0.270241i | ||||
\(698\) | −237.708 | + | 138.284i | −0.340556 | + | 0.198115i | ||||
\(699\) | 127.953 | − | 73.8735i | 0.183051 | − | 0.105685i | ||||
\(700\) | 2.32689 | + | 354.083i | 0.00332413 | + | 0.505832i | ||||
\(701\) | 52.8209 | − | 91.4885i | 0.0753508 | − | 0.130511i | −0.825888 | − | 0.563834i | \(-0.809326\pi\) |
0.901239 | + | 0.433323i | \(0.142659\pi\) | |||||||
\(702\) | −213.014 | + | 371.767i | −0.303439 | + | 0.529583i | ||||
\(703\) | 93.9789 | − | 114.775i | 0.133683 | − | 0.163264i | ||||
\(704\) | 3.30589 | + | 167.666i | 0.00469587 | + | 0.238163i | ||||
\(705\) | −56.1885 | + | 97.3213i | −0.0797000 | + | 0.138044i | ||||
\(706\) | −87.2054 | + | 50.7309i | −0.123520 | + | 0.0718567i | ||||
\(707\) | −1182.47 | + | 682.701i | −1.67252 | + | 0.965630i | ||||
\(708\) | 121.396 | − | 0.797764i | 0.171463 | − | 0.00112679i | ||||
\(709\) | 133.751 | + | 231.663i | 0.188647 | + | 0.326747i | 0.944799 | − | 0.327649i | \(-0.106256\pi\) |
−0.756152 | + | 0.654396i | \(0.772923\pi\) | |||||||
\(710\) | 405.195 | − | 707.175i | 0.570698 | − | 0.996021i | ||||
\(711\) | 642.416i | 0.903538i | ||||||||
\(712\) | −488.774 | + | 288.655i | −0.686480 | + | 0.405414i | ||||
\(713\) | 593.889 | + | 1028.65i | 0.832944 | + | 1.44270i | ||||
\(714\) | 58.5132 | + | 33.5267i | 0.0819513 | + | 0.0469562i | ||||
\(715\) | − | 246.173i | − | 0.344298i | ||||||
\(716\) | −827.946 | − | 470.787i | −1.15635 | − | 0.657524i | ||||
\(717\) | 10.1397 | − | 17.5625i | 0.0141418 | − | 0.0244944i | ||||
\(718\) | −1010.71 | + | 3.32097i | −1.40768 | + | 0.00462530i | ||||
\(719\) | 931.697 | + | 537.915i | 1.29582 | + | 0.748144i | 0.979680 | − | 0.200567i | \(-0.0642786\pi\) |
0.316143 | + | 0.948711i | \(0.397612\pi\) | |||||||
\(720\) | 284.565 | + | 478.252i | 0.395229 | + | 0.664239i | ||||
\(721\) | 1263.62 | 1.75260 | ||||||||
\(722\) | −479.036 | − | 540.193i | −0.663485 | − | 0.748190i | ||||
\(723\) | 155.542i | 0.215134i | ||||||||
\(724\) | 611.102 | − | 4.01592i | 0.844063 | − | 0.00554685i | ||||
\(725\) | −4.08153 | + | 7.06941i | −0.00562969 | + | 0.00975092i | ||||
\(726\) | −116.806 | + | 0.383798i | −0.160890 | + | 0.000528648i | ||||
\(727\) | 231.915 | + | 133.896i | 0.319003 | + | 0.184176i | 0.650948 | − | 0.759122i | \(-0.274372\pi\) |
−0.331945 | + | 0.943299i | \(0.607705\pi\) | |||||||
\(728\) | 928.320 | + | 1571.91i | 1.27516 | + | 2.15921i | ||||
\(729\) | 604.810 | 0.829643 | ||||||||
\(730\) | 108.057 | + | 61.9141i | 0.148023 | + | 0.0848138i | ||||
\(731\) | −41.5302 | + | 23.9775i | −0.0568128 | + | 0.0328009i | ||||
\(732\) | 4.40070 | + | 2.50233i | 0.00601188 | + | 0.00341848i | ||||
\(733\) | −517.076 | −0.705424 | −0.352712 | − | 0.935732i | \(-0.614740\pi\) | ||||
−0.352712 | + | 0.935732i | \(0.614740\pi\) | |||||||
\(734\) | 184.784 | − | 322.498i | 0.251749 | − | 0.439370i | ||||
\(735\) | 78.4527 | − | 45.2947i | 0.106738 | − | 0.0616254i | ||||
\(736\) | 637.603 | − | 10.4760i | 0.866308 | − | 0.0142337i | ||||
\(737\) | 55.2133 | + | 95.6322i | 0.0749162 | + | 0.129759i | ||||
\(738\) | −482.067 | + | 280.437i | −0.653207 | + | 0.379996i | ||||
\(739\) | 74.5529 | + | 43.0432i | 0.100884 | + | 0.0582451i | 0.549593 | − | 0.835433i | \(-0.314783\pi\) |
−0.448709 | + | 0.893678i | \(0.648116\pi\) | |||||||
\(740\) | 62.8606 | + | 107.244i | 0.0849467 | + | 0.144924i | ||||
\(741\) | 177.549 | + | 145.379i | 0.239607 | + | 0.196193i | ||||
\(742\) | 643.819 | − | 1123.64i | 0.867680 | − | 1.51434i | ||||
\(743\) | 22.5854 | + | 13.0397i | 0.0303976 | + | 0.0175501i | 0.515122 | − | 0.857117i | \(-0.327747\pi\) |
−0.484724 | + | 0.874667i | \(0.661080\pi\) | |||||||
\(744\) | 212.503 | + | 119.911i | 0.285622 | + | 0.161171i | ||||
\(745\) | 458.384 | + | 793.944i | 0.615280 | + | 1.06570i | ||||
\(746\) | −758.487 | + | 441.242i | −1.01674 | + | 0.591477i | ||||
\(747\) | 139.267 | − | 80.4060i | 0.186436 | − | 0.107639i | ||||
\(748\) | 61.6284 | − | 36.1232i | 0.0823909 | − | 0.0482931i | ||||
\(749\) | −811.736 | −1.08376 | ||||||||
\(750\) | −139.140 | + | 0.457180i | −0.185519 | + | 0.000609574i | ||||
\(751\) | −715.806 | + | 413.271i | −0.953137 | + | 0.550294i | −0.894054 | − | 0.447959i | \(-0.852151\pi\) |
−0.0590833 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(752\) | −770.224 | − | 431.293i | −1.02423 | − | 0.573528i | ||||
\(753\) | 204.475 | 0.271547 | ||||||||
\(754\) | 0.138283 | + | 42.0855i | 0.000183399 | + | 0.0558163i | ||||
\(755\) | −644.114 | − | 371.879i | −0.853131 | − | 0.492555i | ||||
\(756\) | −173.512 | + | 305.145i | −0.229513 | + | 0.403632i | ||||
\(757\) | −6.25471 | + | 10.8335i | −0.00826249 | + | 0.0143111i | −0.870127 | − | 0.492827i | \(-0.835963\pi\) |
0.861865 | + | 0.507138i | \(0.169297\pi\) | |||||||
\(758\) | 153.277 | + | 263.480i | 0.202212 | + | 0.347599i | ||||
\(759\) | − | 26.7198i | − | 0.0352040i | ||||||
\(760\) | 563.877 | − | 219.322i | 0.741944 | − | 0.288582i | ||||
\(761\) | −722.622 | −0.949568 | −0.474784 | − | 0.880102i | \(-0.657474\pi\) | ||||
−0.474784 | + | 0.880102i | \(0.657474\pi\) | |||||||
\(762\) | −30.1544 | + | 17.5420i | −0.0395727 | + | 0.0230210i | ||||
\(763\) | −772.960 | − | 446.269i | −1.01305 | − | 0.584887i | ||||
\(764\) | −1108.22 | − | 630.157i | −1.45055 | − | 0.824813i | ||||
\(765\) | 118.528 | − | 205.297i | 0.154939 | − | 0.268362i | ||||
\(766\) | 158.670 | − | 0.521352i | 0.207141 | − | 0.000680617i | ||||
\(767\) | − | 1399.87i | − | 1.82512i | ||||||
\(768\) | 111.687 | − | 68.4580i | 0.145425 | − | 0.0891380i | ||||
\(769\) | 173.928 | + | 301.252i | 0.226174 | + | 0.391745i | 0.956671 | − | 0.291171i | \(-0.0940448\pi\) |
−0.730497 | + | 0.682916i | \(0.760711\pi\) | |||||||
\(770\) | −0.662669 | − | 201.679i | −0.000860609 | − | 0.261920i | ||||
\(771\) | 6.56545i | 0.00851549i | ||||||||
\(772\) | −124.289 | − | 212.044i | −0.160996 | − | 0.274669i | ||||
\(773\) | 224.641 | + | 389.089i | 0.290609 | + | 0.503349i | 0.973954 | − | 0.226746i | \(-0.0728088\pi\) |
−0.683345 | + | 0.730096i | \(0.739475\pi\) | |||||||
\(774\) | −61.8323 | − | 106.289i | −0.0798867 | − | 0.137324i | ||||
\(775\) | 472.620 | − | 272.867i | 0.609833 | − | 0.352087i | ||||
\(776\) | 557.338 | + | 314.495i | 0.718219 | + | 0.405277i | ||||
\(777\) | −19.3131 | + | 33.4513i | −0.0248560 | + | 0.0430519i | ||||
\(778\) | −837.324 | − | 479.768i | −1.07625 | − | 0.616668i | ||||
\(779\) | 214.212 | + | 567.227i | 0.274984 | + | 0.728148i | ||||
\(780\) | −165.899 | + | 97.2410i | −0.212691 | + | 0.124668i | ||||
\(781\) | 134.132 | − | 232.324i | 0.171744 | − | 0.297470i | ||||
\(782\) | −136.591 | − | 234.797i | −0.174668 | − | 0.300252i | ||||
\(783\) | −7.00826 | + | 4.04622i | −0.00895053 | + | 0.00516759i | ||||
\(784\) | 363.873 | + | 611.541i | 0.464124 | + | 0.780027i | ||||
\(785\) | −320.887 | − | 555.792i | −0.408773 | − | 0.708016i | ||||
\(786\) | −167.258 | − | 95.8351i | −0.212797 | − | 0.121928i | ||||
\(787\) | 1044.41i | 1.32708i | 0.748140 | + | 0.663541i | \(0.230947\pi\) | ||||
−0.748140 | + | 0.663541i | \(0.769053\pi\) | |||||||
\(788\) | −480.162 | + | 844.433i | −0.609343 | + | 1.07162i | ||||
\(789\) | −61.1012 | − | 105.830i | −0.0774414 | − | 0.134132i | ||||
\(790\) | −290.970 | + | 507.821i | −0.368316 | + | 0.642811i | ||||
\(791\) | 257.361i | 0.325361i | ||||||||
\(792\) | 93.1454 | + | 157.722i | 0.117608 | + | 0.199143i | ||||
\(793\) | 29.1877 | − | 50.5545i | 0.0368066 | − | 0.0637510i | ||||
\(794\) | −0.187149 | − | 56.9576i | −0.000235705 | − | 0.0717351i | ||||
\(795\) | 118.136 | + | 68.2059i | 0.148599 | + | 0.0857936i | ||||
\(796\) | 6.30748 | + | 959.809i | 0.00792397 | + | 1.20579i | ||||
\(797\) | 950.188 | 1.19221 | 0.596103 | − | 0.802908i | \(-0.296715\pi\) | ||||
0.596103 | + | 0.802908i | \(0.296715\pi\) | |||||||
\(798\) | 145.849 | + | 118.625i | 0.182768 | + | 0.148652i | ||||
\(799\) | 376.028i | 0.470624i | ||||||||
\(800\) | −4.81327 | − | 292.952i | −0.00601659 | − | 0.366190i | ||||
\(801\) | −310.011 | + | 536.954i | −0.387030 | + | 0.670355i | ||||
\(802\) | −1.28935 | − | 392.404i | −0.00160767 | − | 0.489282i | ||||
\(803\) | 35.4992 | + | 20.4955i | 0.0442083 | + | 0.0255237i | ||||
\(804\) | 42.6379 | − | 74.9847i | 0.0530322 | − | 0.0932645i | ||||
\(805\) | −766.903 | −0.952675 | ||||||||
\(806\) | 1398.79 | − | 2441.27i | 1.73547 | − | 3.02887i | ||||
\(807\) | −91.3059 | + | 52.7155i | −0.113142 | + | 0.0653228i | ||||
\(808\) | 972.819 | − | 574.517i | 1.20398 | − | 0.711036i | ||||
\(809\) | −640.785 | −0.792070 | −0.396035 | − | 0.918235i | \(-0.629614\pi\) | ||||
−0.396035 | + | 0.918235i | \(0.629614\pi\) | |||||||
\(810\) | 511.138 | + | 292.871i | 0.631034 | + | 0.361569i | ||||
\(811\) | −625.445 | + | 361.101i | −0.771202 | + | 0.445253i | −0.833303 | − | 0.552816i | \(-0.813553\pi\) |
0.0621015 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(812\) | 0.226578 | + | 34.4784i | 0.000279038 | + | 0.0424611i | ||||
\(813\) | −111.917 | − | 193.846i | −0.137659 | − | 0.238432i | ||||
\(814\) | 20.5742 | + | 35.3666i | 0.0252754 | + | 0.0434480i | ||||
\(815\) | 392.020 | + | 226.333i | 0.481006 | + | 0.277709i | ||||
\(816\) | −48.6878 | − | 27.2631i | −0.0596664 | − | 0.0334106i | ||||
\(817\) | −125.065 | + | 47.2307i | −0.153079 | + | 0.0578099i | ||||
\(818\) | 72.0359 | + | 41.2749i | 0.0880634 | + | 0.0504584i | ||||
\(819\) | 1726.86 | + | 997.002i | 2.10850 | + | 1.21734i | ||||
\(820\) | −508.086 | + | 3.33894i | −0.619617 | + | 0.00407188i | ||||
\(821\) | −448.792 | − | 777.331i | −0.546641 | − | 0.946810i | −0.998502 | − | 0.0547215i | \(-0.982573\pi\) |
0.451861 | − | 0.892089i | \(-0.350760\pi\) | |||||||
\(822\) | 84.3717 | + | 145.033i | 0.102642 | + | 0.176440i | ||||
\(823\) | −1018.02 | + | 587.755i | −1.23696 | + | 0.714162i | −0.968473 | − | 0.249120i | \(-0.919858\pi\) |
−0.268492 | + | 0.963282i | \(0.586525\pi\) | |||||||
\(824\) | −1045.53 | + | 10.3064i | −1.26885 | + | 0.0125078i | ||||
\(825\) | −12.2766 | −0.0148808 | ||||||||
\(826\) | −3.76827 | − | 1146.85i | −0.00456207 | − | 1.38843i | ||||
\(827\) | −388.645 | + | 224.384i | −0.469945 | + | 0.271323i | −0.716217 | − | 0.697878i | \(-0.754128\pi\) |
0.246272 | + | 0.969201i | \(0.420795\pi\) | |||||||
\(828\) | 600.909 | − | 352.220i | 0.725736 | − | 0.425387i | ||||
\(829\) | 316.454 | 0.381730 | 0.190865 | − | 0.981616i | \(-0.438871\pi\) | ||||
0.190865 | + | 0.981616i | \(0.438871\pi\) | |||||||
\(830\) | 146.507 | − | 0.481389i | 0.176515 | − | 0.000579986i | ||||
\(831\) | −149.905 | − | 86.5479i | −0.180391 | − | 0.104149i | ||||
\(832\) | −780.920 | − | 1293.04i | −0.938606 | − | 1.55413i | ||||
\(833\) | 151.562 | − | 262.513i | 0.181947 | − | 0.315142i | ||||
\(834\) | −33.9813 | + | 19.7683i | −0.0407450 | + | 0.0237030i | ||||
\(835\) | − | 481.947i | − | 0.577182i | ||||||
\(836\) | 185.834 | − | 71.5788i | 0.222289 | − | 0.0856206i | ||||
\(837\) | 541.014 | 0.646373 | ||||||||
\(838\) | 208.919 | + | 359.128i | 0.249306 | + | 0.428553i | ||||
\(839\) | 34.7062 | + | 20.0376i | 0.0413661 | + | 0.0238828i | 0.520540 | − | 0.853837i | \(-0.325730\pi\) |
−0.479174 | + | 0.877720i | \(0.659064\pi\) | |||||||
\(840\) | −135.652 | + | 80.1118i | −0.161490 | + | 0.0953712i | ||||
\(841\) | 420.103 | − | 727.639i | 0.499527 | − | 0.865207i | ||||
\(842\) | −4.02411 | − | 1224.71i | −0.00477922 | − | 1.45452i | ||||
\(843\) | 126.320i | 0.149846i | ||||||||
\(844\) | 301.438 | − | 176.687i | 0.357155 | − | 0.209345i | ||||
\(845\) | 772.360 | + | 1337.77i | 0.914035 | + | 1.58316i | ||||
\(846\) | −964.202 | + | 3.16814i | −1.13972 | + | 0.00374485i | ||||
\(847\) | 1103.48i | 1.30281i | ||||||||
\(848\) | −523.536 | + | 934.958i | −0.617378 | + | 1.10254i | ||||
\(849\) | −86.4388 | − | 149.716i | −0.101812 | − | 0.176344i | ||||
\(850\) | −107.879 | + | 62.7577i | −0.126917 | + | 0.0738326i | ||||
\(851\) | 134.741 | − | 77.7926i | 0.158332 | − | 0.0914132i | ||||
\(852\) | −209.550 | + | 1.37708i | −0.245950 | + | 0.00161629i | ||||
\(853\) | 483.234 | − | 836.987i | 0.566512 | − | 0.981227i | −0.430396 | − | 0.902640i | \(-0.641626\pi\) |
0.996907 | − | 0.0785867i | \(-0.0250407\pi\) | |||||||
\(854\) | 23.7761 | − | 41.4956i | 0.0278408 | − | 0.0485897i | ||||
\(855\) | 418.671 | − | 511.315i | 0.489674 | − | 0.598030i | ||||
\(856\) | 671.637 | − | 6.62072i | 0.784623 | − | 0.00773449i | ||||
\(857\) | −278.085 | + | 481.657i | −0.324486 | + | 0.562026i | −0.981408 | − | 0.191932i | \(-0.938525\pi\) |
0.656922 | + | 0.753958i | \(0.271858\pi\) | |||||||
\(858\) | −54.7098 | + | 31.8269i | −0.0637644 | + | 0.0370943i | ||||
\(859\) | −1018.26 | + | 587.890i | −1.18540 | + | 0.684389i | −0.957257 | − | 0.289239i | \(-0.906598\pi\) |
−0.228140 | + | 0.973628i | \(0.573264\pi\) | |||||||
\(860\) | −0.736187 | − | 112.025i | −0.000856031 | − | 0.130262i | ||||
\(861\) | −78.9399 | − | 136.728i | −0.0916840 | − | 0.158801i | ||||
\(862\) | 64.3559 | − | 112.318i | 0.0746588 | − | 0.130300i | ||||
\(863\) | − | 1372.56i | − | 1.59045i | −0.606316 | − | 0.795224i | \(-0.707353\pi\) | ||
0.606316 | − | 0.795224i | \(-0.292647\pi\) | |||||||
\(864\) | 141.077 | − | 253.895i | 0.163283 | − | 0.293860i | ||||
\(865\) | −237.627 | − | 411.582i | −0.274713 | − | 0.475818i | ||||
\(866\) | 254.249 | + | 145.679i | 0.293590 | + | 0.168220i | ||||
\(867\) | − | 124.114i | − | 0.143154i | ||||||
\(868\) | 1139.40 | − | 2003.79i | 1.31267 | − | 2.30851i | ||||
\(869\) | −96.3201 | + | 166.831i | −0.110840 | + | 0.191981i | ||||
\(870\) | −3.63188 | + | 0.0119335i | −0.00417458 | + | 1.37167e-5i | ||||
\(871\) | −861.412 | − | 497.336i | −0.988992 | − | 0.570995i | ||||
\(872\) | 643.194 | + | 362.942i | 0.737607 | + | 0.416218i | ||||
\(873\) | 698.994 | 0.800681 | ||||||||
\(874\) | −269.861 | − | 707.539i | −0.308765 | − | 0.809541i | ||||
\(875\) | 1314.46i | 1.50224i | ||||||||
\(876\) | −0.210418 | − | 32.0193i | −0.000240204 | − | 0.0365517i | ||||
\(877\) | 57.4006 | − | 99.4207i | 0.0654511 | − | 0.113365i | −0.831443 | − | 0.555610i | \(-0.812485\pi\) |
0.896894 | + | 0.442246i | \(0.145818\pi\) | |||||||
\(878\) | −771.151 | + | 2.53382i | −0.878305 | + | 0.00288590i | ||||
\(879\) | −109.655 | − | 63.3092i | −0.124749 | − | 0.0720241i | ||||
\(880\) | 2.19324 | + | 166.865i | 0.00249232 | + | 0.189620i | ||||
\(881\) | 318.598 | 0.361632 | 0.180816 | − | 0.983517i | \(-0.442126\pi\) | ||||
0.180816 | + | 0.983517i | \(0.442126\pi\) | |||||||
\(882\) | 674.407 | + | 386.420i | 0.764634 | + | 0.438118i | ||||
\(883\) | −316.390 | + | 182.668i | −0.358313 | + | 0.206872i | −0.668340 | − | 0.743856i | \(-0.732995\pi\) |
0.310028 | + | 0.950728i | \(0.399662\pi\) | |||||||
\(884\) | −318.058 | + | 559.349i | −0.359794 | + | 0.632748i | ||||
\(885\) | 120.805 | 0.136503 | ||||||||
\(886\) | 35.5916 | − | 62.1170i | 0.0401711 | − | 0.0701095i | ||||
\(887\) | 1482.78 | − | 856.081i | 1.67167 | − | 0.965142i | 0.704973 | − | 0.709234i | \(-0.250959\pi\) |
0.966701 | − | 0.255908i | \(-0.0823743\pi\) | |||||||
\(888\) | 15.7070 | − | 27.8354i | 0.0176881 | − | 0.0313462i | ||||
\(889\) | 164.783 | + | 285.413i | 0.185358 | + | 0.321049i | ||||
\(890\) | −488.262 | + | 284.042i | −0.548610 | + | 0.319148i | ||||
\(891\) | 167.921 | + | 96.9493i | 0.188464 | + | 0.108810i | ||||
\(892\) | 594.594 | − | 348.519i | 0.666585 | − | 0.390716i | ||||
\(893\) | −169.604 | + | 1034.46i | −0.189926 | + | 1.15841i | ||||
\(894\) | 117.184 | − | 204.518i | 0.131079 | − | 0.228767i | ||||
\(895\) | −820.803 | − | 473.891i | −0.917099 | − | 0.529487i | ||||
\(896\) | −643.254 | − | 1057.23i | −0.717917 | − | 1.17994i | ||||
\(897\) | 120.340 | + | 208.435i | 0.134158 | + | 0.232369i | ||||
\(898\) | 1261.39 | − | 733.799i | 1.40466 | − | 0.817149i | ||||
\(899\) | 46.0209 | − | 26.5702i | 0.0511912 | − | 0.0295552i | ||||
\(900\) | −161.831 | − | 276.093i | −0.179812 | − | 0.306770i | ||||
\(901\) | 456.452 | 0.506606 | ||||||||
\(902\) | −167.237 | + | 0.549501i | −0.185407 | + | 0.000609203i | ||||
\(903\) | 30.1465 | − | 17.4051i | 0.0333848 | − | 0.0192747i | ||||
\(904\) | −2.09910 | − | 212.942i | −0.00232201 | − | 0.235556i | ||||
\(905\) | 608.129 | 0.671966 | ||||||||
\(906\) | 0.628329 | + | 191.228i | 0.000693520 | + | 0.211068i | ||||
\(907\) | 1449.68 | + | 836.973i | 1.59832 | + | 0.922792i | 0.991810 | + | 0.127719i | \(0.0407655\pi\) |
0.606513 | + | 0.795074i | \(0.292568\pi\) | |||||||
\(908\) | 866.784 | + | 492.872i | 0.954608 | + | 0.542810i | ||||
\(909\) | 617.023 | − | 1068.71i | 0.678793 | − | 1.17570i | ||||
\(910\) | 913.484 | + | 1570.26i | 1.00383 | + | 1.72556i | ||||
\(911\) | − | 758.092i | − | 0.832153i | −0.909330 | − | 0.416077i | \(-0.863405\pi\) | ||
0.909330 | − | 0.416077i | \(-0.136595\pi\) | |||||||
\(912\) | −121.644 | − | 96.9614i | −0.133382 | − | 0.106317i | ||||
\(913\) | 48.2225 | 0.0528176 | ||||||||
\(914\) | −696.187 | + | 405.000i | −0.761693 | + | 0.443107i | ||||
\(915\) | 4.36274 | + | 2.51883i | 0.00476802 | + | 0.00275282i | ||||
\(916\) | 391.715 | − | 688.885i | 0.427636 | − | 0.752058i | ||||
\(917\) | −910.544 | + | 1577.11i | −0.992960 | + | 1.71986i | ||||
\(918\) | −123.726 | + | 0.406533i | −0.134777 | + | 0.000442847i | ||||
\(919\) | − | 1173.48i | − | 1.27691i | −0.769660 | − | 0.638454i | \(-0.779574\pi\) | ||
0.769660 | − | 0.638454i | \(-0.220426\pi\) | |||||||
\(920\) | 634.542 | − | 6.25505i | 0.689720 | − | 0.00679897i | ||||
\(921\) | 25.4033 | + | 43.9997i | 0.0275823 | + | 0.0477739i | ||||
\(922\) | 3.36755 | + | 1024.89i | 0.00365244 | + | 1.11159i | ||||
\(923\) | 2416.41i | 2.61799i | ||||||||
\(924\) | −44.7356 | + | 26.2216i | −0.0484152 | + | 0.0283784i | ||||
\(925\) | −35.7425 | − | 61.9078i | −0.0386405 | − | 0.0669274i | ||||
\(926\) | 736.351 | + | 1265.77i | 0.795196 | + | 1.36693i | ||||
\(927\) | −989.053 | + | 571.030i | −1.06694 | + | 0.615998i | ||||
\(928\) | −0.468687 | − | 28.5259i | −0.000505051 | − | 0.0307391i | ||||
\(929\) | 741.767 | − | 1284.78i | 0.798457 | − | 1.38297i | −0.122164 | − | 0.992510i | \(-0.538983\pi\) |
0.920621 | − | 0.390458i | \(-0.127683\pi\) | |||||||
\(930\) | 210.676 | + | 120.712i | 0.226533 | + | 0.129798i | ||||
\(931\) | 535.355 | − | 653.819i | 0.575032 | − | 0.702276i | ||||
\(932\) | 584.024 | + | 996.380i | 0.626635 | + | 1.06908i | ||||
\(933\) | 18.5295 | − | 32.0940i | 0.0198601 | − | 0.0343987i | ||||
\(934\) | −638.407 | − | 1097.41i | −0.683519 | − | 1.17496i | ||||
\(935\) | 61.5621 | − | 35.5429i | 0.0658419 | − | 0.0380138i | ||||
\(936\) | −1436.95 | − | 810.843i | −1.53520 | − | 0.866285i | ||||
\(937\) | −489.796 | − | 848.351i | −0.522728 | − | 0.905391i | −0.999650 | − | 0.0264456i | \(-0.991581\pi\) |
0.476923 | − | 0.878945i | \(-0.341752\pi\) | |||||||
\(938\) | −707.055 | − | 405.127i | −0.753790 | − | 0.431905i | ||||
\(939\) | 215.584i | 0.229589i | ||||||||
\(940\) | −763.624 | − | 434.213i | −0.812366 | − | 0.461928i | ||||
\(941\) | −631.521 | − | 1093.83i | −0.671117 | − | 1.16241i | −0.977588 | − | 0.210528i | \(-0.932482\pi\) |
0.306471 | − | 0.951880i | \(-0.400852\pi\) | |||||||
\(942\) | −82.0337 | + | 143.171i | −0.0870846 | + | 0.151986i | ||||
\(943\) | 635.935i | 0.674374i | ||||||||
\(944\) | 12.4719 | + | 948.880i | 0.0132117 | + | 1.00517i | ||||
\(945\) | −174.656 | + | 302.513i | −0.184821 | + | 0.320120i | ||||
\(946\) | −0.121157 | − | 36.8733i | −0.000128073 | − | 0.0389781i | ||||
\(947\) | −1520.70 | − | 877.977i | −1.60581 | − | 0.927114i | −0.990294 | − | 0.138989i | \(-0.955615\pi\) |
−0.615515 | − | 0.788125i | \(-0.711052\pi\) | |||||||
\(948\) | 150.477 | − | 0.988877i | 0.158731 | − | 0.00104312i | ||||
\(949\) | −369.229 | −0.389071 | ||||||||
\(950\) | −325.085 | + | 123.990i | −0.342194 | + | 0.130516i | ||||
\(951\) | − | 146.069i | − | 0.153595i | ||||||
\(952\) | −259.065 | + | 459.106i | −0.272127 | + | 0.482254i | ||||
\(953\) | −285.372 | + | 494.279i | −0.299446 | + | 0.518656i | −0.976009 | − | 0.217729i | \(-0.930135\pi\) |
0.676563 | + | 0.736384i | \(0.263468\pi\) | |||||||
\(954\) | 3.84574 | + | 1170.42i | 0.00403117 | + | 1.22686i | ||||
\(955\) | −1098.66 | − | 634.311i | −1.15043 | − | 0.664200i | ||||
\(956\) | 137.803 | + | 78.3575i | 0.144145 | + | 0.0819639i | ||||
\(957\) | −1.19542 | −0.00124914 | ||||||||
\(958\) | −222.996 | + | 389.188i | −0.232773 | + | 0.406251i | ||||
\(959\) | 1372.75 | − | 792.556i | 1.43144 | − | 0.826440i | ||||
\(960\) | 111.586 | − | 67.3916i | 0.116236 | − | 0.0701996i | ||||
\(961\) | −2591.66 | −2.69683 | ||||||||
\(962\) | −319.778 | − | 183.226i | −0.332409 | − | 0.190463i | ||||
\(963\) | 635.355 | − | 366.822i | 0.659766 | − | 0.380916i | ||||
\(964\) | −1215.84 | + | 7.99000i | −1.26124 | + | 0.00828838i | ||||
\(965\) | −122.292 | − | 211.816i | −0.126728 | − | 0.219499i | ||||
\(966\) | 99.1502 | + | 170.438i | 0.102640 | + | 0.176436i | ||||
\(967\) | 722.083 | + | 416.895i | 0.746725 | + | 0.431122i | 0.824509 | − | 0.565848i | \(-0.191451\pi\) |
−0.0777842 | + | 0.996970i | \(0.524785\pi\) | |||||||
\(968\) | −9.00025 | − | 913.028i | −0.00929778 | − | 0.943211i | ||||
\(969\) | −10.7211 | + | 65.3909i | −0.0110641 | + | 0.0674828i | ||||
\(970\) | 552.546 | + | 316.596i | 0.569635 | + | 0.326388i | ||||
\(971\) | −353.825 | − | 204.281i | −0.364393 | − | 0.210382i | 0.306613 | − | 0.951834i | \(-0.400804\pi\) |
−0.671006 | + | 0.741452i | \(0.734138\pi\) | |||||||
\(972\) | −3.14266 | − | 478.217i | −0.00323318 | − | 0.491993i | ||||
\(973\) | 185.696 | + | 321.634i | 0.190849 | + | 0.330559i | ||||
\(974\) | 178.696 | + | 307.175i | 0.183466 | + | 0.315375i | ||||
\(975\) | 95.7672 | − | 55.2912i | 0.0982228 | − | 0.0567089i | ||||
\(976\) | −19.3341 | + | 34.5278i | −0.0198095 | + | 0.0353768i | ||||
\(977\) | −649.188 | −0.664471 | −0.332236 | − | 0.943196i | \(-0.607803\pi\) | ||||
−0.332236 | + | 0.943196i | \(0.607803\pi\) | |||||||
\(978\) | −0.382413 | − | 116.385i | −0.000391016 | − | 0.119003i | ||||
\(979\) | −161.016 | + | 92.9625i | −0.164470 | + | 0.0949566i | ||||
\(980\) | 358.088 | + | 610.919i | 0.365396 | + | 0.623387i | ||||
\(981\) | 806.672 | 0.822296 | ||||||||
\(982\) | −1071.26 | + | 3.51989i | −1.09089 | + | 0.00358441i | ||||
\(983\) | −282.210 | − | 162.934i | −0.287091 | − | 0.165752i | 0.349538 | − | 0.936922i | \(-0.386338\pi\) |
−0.636629 | + | 0.771170i | \(0.719672\pi\) | |||||||
\(984\) | 66.4307 | + | 112.486i | 0.0675109 | + | 0.114315i | ||||
\(985\) | −483.328 | + | 837.148i | −0.490688 | + | 0.849897i | ||||
\(986\) | −10.5046 | + | 6.11096i | −0.0106538 | + | 0.00619773i | ||||
\(987\) | − | 272.957i | − | 0.276552i | ||||||
\(988\) | −1127.27 | + | 1395.32i | −1.14096 | + | 1.41227i | ||||
\(989\) | −140.214 | −0.141774 | ||||||||
\(990\) | 91.6569 | + | 157.557i | 0.0925827 | + | 0.159148i | ||||
\(991\) | −698.600 | − | 403.337i | −0.704945 | − | 0.407000i | 0.104242 | − | 0.994552i | \(-0.466758\pi\) |
−0.809187 | + | 0.587552i | \(0.800092\pi\) | |||||||
\(992\) | −926.402 | + | 1667.24i | −0.933873 | + | 1.68069i | ||||
\(993\) | 3.47747 | − | 6.02315i | 0.00350198 | − | 0.00606561i | ||||
\(994\) | 6.50468 | + | 1979.65i | 0.00654395 | + | 1.99160i | ||||
\(995\) | 955.139i | 0.959939i | ||||||||
\(996\) | −19.0484 | − | 32.4977i | −0.0191249 | − | 0.0326282i | ||||
\(997\) | 648.363 | + | 1123.00i | 0.650314 | + | 1.12638i | 0.983047 | + | 0.183356i | \(0.0586962\pi\) |
−0.332732 | + | 0.943021i | \(0.607970\pi\) | |||||||
\(998\) | 969.773 | − | 3.18645i | 0.971716 | − | 0.00319283i | ||||
\(999\) | − | 70.8666i | − | 0.0709376i |
(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 | 76.3.g.c.11.14 | yes | 28 | |
4.3 | odd | 2 | inner | 76.3.g.c.11.8 | yes | 28 | |
19.7 | even | 3 | inner | 76.3.g.c.7.8 | ✓ | 28 | |
76.7 | odd | 6 | inner | 76.3.g.c.7.14 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.3.g.c.7.8 | ✓ | 28 | 19.7 | even | 3 | inner | |
76.3.g.c.7.14 | yes | 28 | 76.7 | odd | 6 | inner | |
76.3.g.c.11.8 | yes | 28 | 4.3 | odd | 2 | inner | |
76.3.g.c.11.14 | yes | 28 | 1.1 | even | 1 | trivial |