Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(439,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.439");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.o (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 549.19 | ||
Character | \(\chi\) | \(=\) | 770.549 |
Dual form | 770.2.o.b.439.19 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0.781614 | − | 1.35379i | 0.451265 | − | 0.781614i | −0.547200 | − | 0.837002i | \(-0.684306\pi\) |
0.998465 | + | 0.0553881i | \(0.0176396\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −2.11819 | − | 0.716443i | −0.947281 | − | 0.320403i | ||||
\(6\) | 1.56323 | 0.638185 | ||||||||
\(7\) | 0.725302 | + | 2.54439i | 0.274138 | + | 0.961690i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0.278160 | + | 0.481787i | 0.0927199 | + | 0.160596i | ||||
\(10\) | −0.438635 | − | 2.19262i | −0.138708 | − | 0.693369i | ||||
\(11\) | −2.06350 | + | 2.59653i | −0.622169 | + | 0.782883i | ||||
\(12\) | 0.781614 | + | 1.35379i | 0.225632 | + | 0.390807i | ||||
\(13\) | − | 2.41576i | − | 0.670010i | −0.942216 | − | 0.335005i | \(-0.891262\pi\) | ||
0.942216 | − | 0.335005i | \(-0.108738\pi\) | |||||||
\(14\) | −1.84086 | + | 1.90033i | −0.491990 | + | 0.507884i | ||||
\(15\) | −2.62552 | + | 2.30761i | −0.677906 | + | 0.595821i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 6.35472 | + | 3.66890i | 1.54125 | + | 0.889839i | 0.998760 | + | 0.0497746i | \(0.0158503\pi\) |
0.542486 | + | 0.840065i | \(0.317483\pi\) | |||||||
\(18\) | −0.278160 | + | 0.481787i | −0.0655629 | + | 0.113558i | ||||
\(19\) | 2.89975 | + | 5.02252i | 0.665249 | + | 1.15225i | 0.979218 | + | 0.202812i | \(0.0650081\pi\) |
−0.313968 | + | 0.949433i | \(0.601659\pi\) | |||||||
\(20\) | 1.67955 | − | 1.47618i | 0.375559 | − | 0.330084i | ||||
\(21\) | 4.01149 | + | 1.00682i | 0.875379 | + | 0.219707i | ||||
\(22\) | −3.28041 | − | 0.488782i | −0.699386 | − | 0.104209i | ||||
\(23\) | −7.48569 | + | 4.32187i | −1.56087 | + | 0.901171i | −0.563705 | + | 0.825976i | \(0.690625\pi\) |
−0.997169 | + | 0.0751954i | \(0.976042\pi\) | |||||||
\(24\) | −0.781614 | + | 1.35379i | −0.159546 | + | 0.276342i | ||||
\(25\) | 3.97342 | + | 3.03512i | 0.794684 | + | 0.607024i | ||||
\(26\) | 2.09211 | − | 1.20788i | 0.410296 | − | 0.236884i | ||||
\(27\) | 5.55934 | 1.06989 | ||||||||
\(28\) | −2.56616 | − | 0.644067i | −0.484959 | − | 0.121717i | ||||
\(29\) | − | 4.47156i | − | 0.830347i | −0.909742 | − | 0.415174i | \(-0.863721\pi\) | ||
0.909742 | − | 0.415174i | \(-0.136279\pi\) | |||||||
\(30\) | −3.31121 | − | 1.11996i | −0.604541 | − | 0.204476i | ||||
\(31\) | −0.862051 | − | 0.497705i | −0.154829 | − | 0.0893905i | 0.420584 | − | 0.907254i | \(-0.361825\pi\) |
−0.575413 | + | 0.817863i | \(0.695159\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 1.90230 | + | 4.82304i | 0.331149 | + | 0.839584i | ||||
\(34\) | 7.33780i | 1.25842i | ||||||||
\(35\) | 0.286589 | − | 5.90913i | 0.0484423 | − | 0.998826i | ||||
\(36\) | −0.556319 | −0.0927199 | ||||||||
\(37\) | 3.20955 | − | 1.85303i | 0.527646 | − | 0.304637i | −0.212411 | − | 0.977180i | \(-0.568132\pi\) |
0.740057 | + | 0.672544i | \(0.234798\pi\) | |||||||
\(38\) | −2.89975 | + | 5.02252i | −0.470402 | + | 0.814761i | ||||
\(39\) | −3.27044 | − | 1.88819i | −0.523689 | − | 0.302352i | ||||
\(40\) | 2.11819 | + | 0.716443i | 0.334915 | + | 0.113280i | ||||
\(41\) | −6.97297 | −1.08900 | −0.544498 | − | 0.838762i | \(-0.683280\pi\) | ||||
−0.544498 | + | 0.838762i | \(0.683280\pi\) | |||||||
\(42\) | 1.13381 | + | 3.97747i | 0.174951 | + | 0.613736i | ||||
\(43\) | 6.18781 | 0.943632 | 0.471816 | − | 0.881697i | \(-0.343599\pi\) | ||||
0.471816 | + | 0.881697i | \(0.343599\pi\) | |||||||
\(44\) | −1.21691 | − | 3.08531i | −0.183456 | − | 0.465128i | ||||
\(45\) | −0.244021 | − | 1.21980i | −0.0363765 | − | 0.181837i | ||||
\(46\) | −7.48569 | − | 4.32187i | −1.10370 | − | 0.637224i | ||||
\(47\) | 5.29717 | + | 9.17496i | 0.772671 | + | 1.33831i | 0.936094 | + | 0.351750i | \(0.114413\pi\) |
−0.163423 | + | 0.986556i | \(0.552254\pi\) | |||||||
\(48\) | −1.56323 | −0.225632 | ||||||||
\(49\) | −5.94787 | + | 3.69091i | −0.849696 | + | 0.527272i | ||||
\(50\) | −0.641780 | + | 4.95864i | −0.0907615 | + | 0.701258i | ||||
\(51\) | 9.93388 | − | 5.73533i | 1.39102 | − | 0.803107i | ||||
\(52\) | 2.09211 | + | 1.20788i | 0.290123 | + | 0.167502i | ||||
\(53\) | 1.54044 | + | 0.889372i | 0.211595 | + | 0.122165i | 0.602053 | − | 0.798456i | \(-0.294350\pi\) |
−0.390457 | + | 0.920621i | \(0.627683\pi\) | |||||||
\(54\) | 2.77967 | + | 4.81453i | 0.378265 | + | 0.655174i | ||||
\(55\) | 6.23115 | − | 4.02155i | 0.840207 | − | 0.542265i | ||||
\(56\) | −0.725302 | − | 2.54439i | −0.0969226 | − | 0.340009i | ||||
\(57\) | 9.06595 | 1.20081 | ||||||||
\(58\) | 3.87248 | − | 2.23578i | 0.508482 | − | 0.293572i | ||||
\(59\) | −7.38314 | − | 4.26266i | −0.961203 | − | 0.554951i | −0.0646597 | − | 0.997907i | \(-0.520596\pi\) |
−0.896543 | + | 0.442957i | \(0.853930\pi\) | |||||||
\(60\) | −0.685686 | − | 3.42757i | −0.0885217 | − | 0.442497i | ||||
\(61\) | 1.71192 | + | 2.96514i | 0.219189 | + | 0.379647i | 0.954560 | − | 0.298018i | \(-0.0963254\pi\) |
−0.735371 | + | 0.677665i | \(0.762992\pi\) | |||||||
\(62\) | − | 0.995411i | − | 0.126417i | ||||||
\(63\) | −1.02411 | + | 1.05719i | −0.129025 | + | 0.133193i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.73075 | + | 5.11702i | −0.214673 | + | 0.634688i | ||||
\(66\) | −3.22572 | + | 4.05896i | −0.397059 | + | 0.499624i | ||||
\(67\) | −9.76197 | − | 5.63608i | −1.19261 | − | 0.688556i | −0.233716 | − | 0.972305i | \(-0.575089\pi\) |
−0.958899 | + | 0.283749i | \(0.908422\pi\) | |||||||
\(68\) | −6.35472 | + | 3.66890i | −0.770623 | + | 0.444920i | ||||
\(69\) | 13.5121i | 1.62667i | ||||||||
\(70\) | 5.26075 | − | 2.70637i | 0.628780 | − | 0.323474i | ||||
\(71\) | 0.788593 | 0.0935888 | 0.0467944 | − | 0.998905i | \(-0.485099\pi\) | ||||
0.0467944 | + | 0.998905i | \(0.485099\pi\) | |||||||
\(72\) | −0.278160 | − | 0.481787i | −0.0327814 | − | 0.0567791i | ||||
\(73\) | 8.04910 | + | 4.64715i | 0.942076 | + | 0.543908i | 0.890611 | − | 0.454767i | \(-0.150277\pi\) |
0.0514657 | + | 0.998675i | \(0.483611\pi\) | |||||||
\(74\) | 3.20955 | + | 1.85303i | 0.373102 | + | 0.215411i | ||||
\(75\) | 7.21461 | − | 3.00690i | 0.833071 | − | 0.347207i | ||||
\(76\) | −5.79951 | −0.665249 | ||||||||
\(77\) | −8.10325 | − | 3.36710i | −0.923451 | − | 0.383716i | ||||
\(78\) | − | 3.77638i | − | 0.427590i | ||||||
\(79\) | 2.68359 | − | 1.54937i | 0.301927 | − | 0.174318i | −0.341381 | − | 0.939925i | \(-0.610895\pi\) |
0.643308 | + | 0.765607i | \(0.277561\pi\) | |||||||
\(80\) | 0.438635 | + | 2.19262i | 0.0490409 | + | 0.245143i | ||||
\(81\) | 3.51078 | − | 6.08084i | 0.390086 | − | 0.675649i | ||||
\(82\) | −3.48649 | − | 6.03877i | −0.385018 | − | 0.666871i | ||||
\(83\) | − | 11.1034i | − | 1.21875i | −0.792881 | − | 0.609376i | \(-0.791420\pi\) | ||
0.792881 | − | 0.609376i | \(-0.208580\pi\) | |||||||
\(84\) | −2.87768 | + | 2.97064i | −0.313981 | + | 0.324124i | ||||
\(85\) | −10.8319 | − | 12.3242i | −1.17489 | − | 1.33675i | ||||
\(86\) | 3.09391 | + | 5.35880i | 0.333624 | + | 0.577854i | ||||
\(87\) | −6.05357 | − | 3.49503i | −0.649011 | − | 0.374707i | ||||
\(88\) | 2.06350 | − | 2.59653i | 0.219970 | − | 0.276791i | ||||
\(89\) | −3.28611 | + | 1.89724i | −0.348327 | + | 0.201107i | −0.663948 | − | 0.747779i | \(-0.731120\pi\) |
0.315621 | + | 0.948885i | \(0.397787\pi\) | |||||||
\(90\) | 0.934366 | − | 0.821228i | 0.0984909 | − | 0.0865650i | ||||
\(91\) | 6.14663 | − | 1.75215i | 0.644342 | − | 0.183675i | ||||
\(92\) | − | 8.64373i | − | 0.901171i | ||||||
\(93\) | −1.34758 | + | 0.778027i | −0.139738 | + | 0.0806776i | ||||
\(94\) | −5.29717 | + | 9.17496i | −0.546361 | + | 0.946325i | ||||
\(95\) | −2.54387 | − | 12.7161i | −0.260995 | − | 1.30465i | ||||
\(96\) | −0.781614 | − | 1.35379i | −0.0797731 | − | 0.138171i | ||||
\(97\) | 1.37580 | 0.139691 | 0.0698455 | − | 0.997558i | \(-0.477749\pi\) | ||||
0.0698455 | + | 0.997558i | \(0.477749\pi\) | |||||||
\(98\) | −6.17036 | − | 3.30556i | −0.623300 | − | 0.333912i | ||||
\(99\) | −1.82496 | − | 0.271919i | −0.183415 | − | 0.0273289i | ||||
\(100\) | −4.61520 | + | 1.92352i | −0.461520 | + | 0.192352i | ||||
\(101\) | −1.36011 | + | 2.35579i | −0.135336 | + | 0.234409i | −0.925726 | − | 0.378195i | \(-0.876545\pi\) |
0.790390 | + | 0.612605i | \(0.209878\pi\) | |||||||
\(102\) | 9.93388 | + | 5.73533i | 0.983601 | + | 0.567882i | ||||
\(103\) | −9.62535 | − | 16.6716i | −0.948414 | − | 1.64270i | −0.748767 | − | 0.662833i | \(-0.769354\pi\) |
−0.199647 | − | 0.979868i | \(-0.563980\pi\) | |||||||
\(104\) | 2.41576i | 0.236884i | ||||||||
\(105\) | −7.77575 | − | 5.00664i | −0.758836 | − | 0.488598i | ||||
\(106\) | 1.77874i | 0.172767i | ||||||||
\(107\) | 8.42442 | + | 14.5915i | 0.814420 | + | 1.41062i | 0.909744 | + | 0.415170i | \(0.136278\pi\) |
−0.0953239 | + | 0.995446i | \(0.530389\pi\) | |||||||
\(108\) | −2.77967 | + | 4.81453i | −0.267474 | + | 0.463278i | ||||
\(109\) | −13.4790 | − | 7.78209i | −1.29105 | − | 0.745389i | −0.312211 | − | 0.950013i | \(-0.601070\pi\) |
−0.978841 | + | 0.204624i | \(0.934403\pi\) | |||||||
\(110\) | 6.59833 | + | 3.38556i | 0.629126 | + | 0.322800i | ||||
\(111\) | − | 5.79343i | − | 0.549888i | ||||||
\(112\) | 1.84086 | − | 1.90033i | 0.173945 | − | 0.179564i | ||||
\(113\) | − | 7.70432i | − | 0.724762i | −0.932030 | − | 0.362381i | \(-0.881964\pi\) | ||
0.932030 | − | 0.362381i | \(-0.118036\pi\) | |||||||
\(114\) | 4.53298 | + | 7.85134i | 0.424552 | + | 0.735346i | ||||
\(115\) | 18.9525 | − | 3.79144i | 1.76733 | − | 0.353554i | ||||
\(116\) | 3.87248 | + | 2.23578i | 0.359551 | + | 0.207587i | ||||
\(117\) | 1.16388 | − | 0.671966i | 0.107601 | − | 0.0621232i | ||||
\(118\) | − | 8.52531i | − | 0.784819i | ||||||
\(119\) | −4.72603 | + | 18.8300i | −0.433235 | + | 1.72614i | ||||
\(120\) | 2.62552 | − | 2.30761i | 0.239676 | − | 0.210655i | ||||
\(121\) | −2.48391 | − | 10.7159i | −0.225810 | − | 0.974171i | ||||
\(122\) | −1.71192 | + | 2.96514i | −0.154990 | + | 0.268451i | ||||
\(123\) | −5.45017 | + | 9.43998i | −0.491426 | + | 0.851174i | ||||
\(124\) | 0.862051 | − | 0.497705i | 0.0774145 | − | 0.0446953i | ||||
\(125\) | −6.24195 | − | 9.27567i | −0.558297 | − | 0.829641i | ||||
\(126\) | −1.42760 | − | 0.358307i | −0.127181 | − | 0.0319205i | ||||
\(127\) | −7.79433 | −0.691635 | −0.345818 | − | 0.938302i | \(-0.612398\pi\) | ||||
−0.345818 | + | 0.938302i | \(0.612398\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 4.83648 | − | 8.37703i | 0.425828 | − | 0.737556i | ||||
\(130\) | −5.29684 | + | 1.05963i | −0.464564 | + | 0.0929361i | ||||
\(131\) | 5.54331 | + | 9.60129i | 0.484321 | + | 0.838869i | 0.999838 | − | 0.0180106i | \(-0.00573328\pi\) |
−0.515517 | + | 0.856880i | \(0.672400\pi\) | |||||||
\(132\) | −5.12803 | − | 0.764077i | −0.446338 | − | 0.0665044i | ||||
\(133\) | −10.6761 | + | 11.0210i | −0.925733 | + | 0.955638i | ||||
\(134\) | − | 11.2722i | − | 0.973766i | ||||||
\(135\) | −11.7757 | − | 3.98295i | −1.01349 | − | 0.342798i | ||||
\(136\) | −6.35472 | − | 3.66890i | −0.544913 | − | 0.314606i | ||||
\(137\) | −7.71390 | − | 4.45362i | −0.659043 | − | 0.380499i | 0.132869 | − | 0.991134i | \(-0.457581\pi\) |
−0.791912 | + | 0.610635i | \(0.790914\pi\) | |||||||
\(138\) | −11.7018 | + | 6.75606i | −0.996127 | + | 0.575114i | ||||
\(139\) | 18.4038 | 1.56099 | 0.780496 | − | 0.625161i | \(-0.214967\pi\) | ||||
0.780496 | + | 0.625161i | \(0.214967\pi\) | |||||||
\(140\) | 4.97417 | + | 3.20276i | 0.420394 | + | 0.270683i | ||||
\(141\) | 16.5614 | 1.39472 | ||||||||
\(142\) | 0.394297 | + | 0.682942i | 0.0330886 | + | 0.0573112i | ||||
\(143\) | 6.27258 | + | 4.98492i | 0.524539 | + | 0.416860i | ||||
\(144\) | 0.278160 | − | 0.481787i | 0.0231800 | − | 0.0401489i | ||||
\(145\) | −3.20362 | + | 9.47159i | −0.266046 | + | 0.786572i | ||||
\(146\) | 9.29430i | 0.769202i | ||||||||
\(147\) | 0.347791 | + | 10.9371i | 0.0286853 | + | 0.902074i | ||||
\(148\) | 3.70607i | 0.304637i | ||||||||
\(149\) | 2.89183 | − | 1.66960i | 0.236908 | − | 0.136779i | −0.376847 | − | 0.926276i | \(-0.622992\pi\) |
0.613755 | + | 0.789497i | \(0.289658\pi\) | |||||||
\(150\) | 6.21136 | + | 4.74458i | 0.507155 | + | 0.387393i | ||||
\(151\) | 0.298524 | + | 0.172353i | 0.0242935 | + | 0.0140259i | 0.512098 | − | 0.858927i | \(-0.328869\pi\) |
−0.487804 | + | 0.872953i | \(0.662202\pi\) | |||||||
\(152\) | −2.89975 | − | 5.02252i | −0.235201 | − | 0.407380i | ||||
\(153\) | 4.08216i | 0.330023i | ||||||||
\(154\) | −1.13564 | − | 8.70117i | −0.0915121 | − | 0.701160i | ||||
\(155\) | 1.46941 | + | 1.67184i | 0.118026 | + | 0.134286i | ||||
\(156\) | 3.27044 | − | 1.88819i | 0.261845 | − | 0.151176i | ||||
\(157\) | 9.08338 | − | 15.7329i | 0.724933 | − | 1.25562i | −0.234069 | − | 0.972220i | \(-0.575204\pi\) |
0.959002 | − | 0.283401i | \(-0.0914626\pi\) | |||||||
\(158\) | 2.68359 | + | 1.54937i | 0.213495 | + | 0.123261i | ||||
\(159\) | 2.40806 | − | 1.39029i | 0.190971 | − | 0.110257i | ||||
\(160\) | −1.67955 | + | 1.47618i | −0.132780 | + | 0.116702i | ||||
\(161\) | −16.4259 | − | 15.9119i | −1.29454 | − | 1.25403i | ||||
\(162\) | 7.02155 | 0.551665 | ||||||||
\(163\) | 5.32629 | − | 3.07513i | 0.417187 | − | 0.240863i | −0.276686 | − | 0.960960i | \(-0.589236\pi\) |
0.693873 | + | 0.720097i | \(0.255903\pi\) | |||||||
\(164\) | 3.48649 | − | 6.03877i | 0.272249 | − | 0.471549i | ||||
\(165\) | −0.573998 | − | 11.5790i | −0.0446857 | − | 0.901423i | ||||
\(166\) | 9.61579 | − | 5.55168i | 0.746330 | − | 0.430894i | ||||
\(167\) | − | 1.94657i | − | 0.150630i | −0.997160 | − | 0.0753152i | \(-0.976004\pi\) | ||
0.997160 | − | 0.0753152i | \(-0.0239963\pi\) | |||||||
\(168\) | −4.01149 | − | 1.00682i | −0.309493 | − | 0.0776781i | ||||
\(169\) | 7.16413 | 0.551087 | ||||||||
\(170\) | 5.25712 | − | 15.5428i | 0.403203 | − | 1.19208i | ||||
\(171\) | −1.61319 | + | 2.79413i | −0.123364 | + | 0.213672i | ||||
\(172\) | −3.09391 | + | 5.35880i | −0.235908 | + | 0.408605i | ||||
\(173\) | 11.4230 | − | 6.59506i | 0.868474 | − | 0.501413i | 0.00163288 | − | 0.999999i | \(-0.499480\pi\) |
0.866841 | + | 0.498585i | \(0.166147\pi\) | |||||||
\(174\) | − | 6.99006i | − | 0.529915i | ||||||
\(175\) | −4.84061 | + | 12.3113i | −0.365915 | + | 0.930648i | ||||
\(176\) | 3.28041 | + | 0.488782i | 0.247270 | + | 0.0368433i | ||||
\(177\) | −11.5415 | + | 6.66350i | −0.867514 | + | 0.500860i | ||||
\(178\) | −3.28611 | − | 1.89724i | −0.246304 | − | 0.142204i | ||||
\(179\) | −5.38578 | + | 9.32844i | −0.402552 | + | 0.697241i | −0.994033 | − | 0.109078i | \(-0.965210\pi\) |
0.591481 | + | 0.806319i | \(0.298543\pi\) | |||||||
\(180\) | 1.17839 | + | 0.398571i | 0.0878318 | + | 0.0297077i | ||||
\(181\) | 4.72166i | 0.350958i | 0.984483 | + | 0.175479i | \(0.0561474\pi\) | ||||
−0.984483 | + | 0.175479i | \(0.943853\pi\) | |||||||
\(182\) | 4.59072 | + | 4.44706i | 0.340287 | + | 0.329638i | ||||
\(183\) | 5.35225 | 0.395650 | ||||||||
\(184\) | 7.48569 | − | 4.32187i | 0.551852 | − | 0.318612i | ||||
\(185\) | −8.12601 | + | 1.62561i | −0.597436 | + | 0.119517i | ||||
\(186\) | −1.34758 | − | 0.778027i | −0.0988095 | − | 0.0570477i | ||||
\(187\) | −22.6394 | + | 8.92943i | −1.65556 | + | 0.652984i | ||||
\(188\) | −10.5943 | −0.772671 | ||||||||
\(189\) | 4.03220 | + | 14.1451i | 0.293299 | + | 1.02891i | ||||
\(190\) | 9.74057 | − | 8.56112i | 0.706655 | − | 0.621089i | ||||
\(191\) | −7.80888 | − | 13.5254i | −0.565031 | − | 0.978662i | −0.997047 | − | 0.0767959i | \(-0.975531\pi\) |
0.432016 | − | 0.901866i | \(-0.357802\pi\) | |||||||
\(192\) | 0.781614 | − | 1.35379i | 0.0564081 | − | 0.0977017i | ||||
\(193\) | 0.956755 | − | 1.65715i | 0.0688687 | − | 0.119284i | −0.829535 | − | 0.558455i | \(-0.811394\pi\) |
0.898404 | + | 0.439171i | \(0.144728\pi\) | |||||||
\(194\) | 0.687898 | + | 1.19147i | 0.0493882 | + | 0.0855429i | ||||
\(195\) | 5.57461 | + | 6.34261i | 0.399206 | + | 0.454204i | ||||
\(196\) | −0.222483 | − | 6.99646i | −0.0158916 | − | 0.499747i | ||||
\(197\) | 14.8366 | 1.05706 | 0.528531 | − | 0.848914i | \(-0.322743\pi\) | ||||
0.528531 | + | 0.848914i | \(0.322743\pi\) | |||||||
\(198\) | −0.676989 | − | 1.71642i | −0.0481115 | − | 0.121980i | ||||
\(199\) | 18.8792 | + | 10.8999i | 1.33831 | + | 0.772675i | 0.986557 | − | 0.163417i | \(-0.0522517\pi\) |
0.351755 | + | 0.936092i | \(0.385585\pi\) | |||||||
\(200\) | −3.97342 | − | 3.03512i | −0.280963 | − | 0.214615i | ||||
\(201\) | −15.2602 | + | 8.81047i | −1.07637 | + | 0.621443i | ||||
\(202\) | −2.72023 | −0.191394 | ||||||||
\(203\) | 11.3774 | − | 3.24323i | 0.798537 | − | 0.227630i | ||||
\(204\) | 11.4707i | 0.803107i | ||||||||
\(205\) | 14.7701 | + | 4.99574i | 1.03159 | + | 0.348918i | ||||
\(206\) | 9.62535 | − | 16.6716i | 0.670630 | − | 1.16157i | ||||
\(207\) | −4.16443 | − | 2.40434i | −0.289448 | − | 0.167113i | ||||
\(208\) | −2.09211 | + | 1.20788i | −0.145061 | + | 0.0837512i | ||||
\(209\) | −19.0248 | − | 2.83469i | −1.31597 | − | 0.196080i | ||||
\(210\) | 0.448003 | − | 9.23732i | 0.0309152 | − | 0.637436i | ||||
\(211\) | 22.3531i | 1.53885i | 0.638738 | + | 0.769425i | \(0.279457\pi\) | ||||
−0.638738 | + | 0.769425i | \(0.720543\pi\) | |||||||
\(212\) | −1.54044 | + | 0.889372i | −0.105798 | + | 0.0610823i | ||||
\(213\) | 0.616375 | − | 1.06759i | 0.0422334 | − | 0.0731503i | ||||
\(214\) | −8.42442 | + | 14.5915i | −0.575882 | + | 0.997456i | ||||
\(215\) | −13.1069 | − | 4.43321i | −0.893885 | − | 0.302343i | ||||
\(216\) | −5.55934 | −0.378265 | ||||||||
\(217\) | 0.641111 | − | 2.55438i | 0.0435214 | − | 0.173403i | ||||
\(218\) | − | 15.5642i | − | 1.05414i | ||||||
\(219\) | 12.5826 | − | 7.26456i | 0.850252 | − | 0.490893i | ||||
\(220\) | 0.367188 | + | 7.40710i | 0.0247558 | + | 0.499387i | ||||
\(221\) | 8.86317 | − | 15.3515i | 0.596201 | − | 1.03265i | ||||
\(222\) | 5.01725 | − | 2.89671i | 0.336736 | − | 0.194415i | ||||
\(223\) | 20.8452 | 1.39590 | 0.697949 | − | 0.716147i | \(-0.254096\pi\) | ||||
0.697949 | + | 0.716147i | \(0.254096\pi\) | |||||||
\(224\) | 2.56616 | + | 0.644067i | 0.171459 | + | 0.0430335i | ||||
\(225\) | −0.357035 | + | 2.75859i | −0.0238023 | + | 0.183906i | ||||
\(226\) | 6.67214 | − | 3.85216i | 0.443824 | − | 0.256242i | ||||
\(227\) | −10.3977 | − | 6.00313i | −0.690122 | − | 0.398442i | 0.113536 | − | 0.993534i | \(-0.463782\pi\) |
−0.803658 | + | 0.595092i | \(0.797116\pi\) | |||||||
\(228\) | −4.53298 | + | 7.85134i | −0.300204 | + | 0.519968i | ||||
\(229\) | 0.995628 | − | 0.574826i | 0.0657930 | − | 0.0379856i | −0.466743 | − | 0.884393i | \(-0.654573\pi\) |
0.532536 | + | 0.846408i | \(0.321239\pi\) | |||||||
\(230\) | 12.7597 | + | 14.5176i | 0.841350 | + | 0.957261i | ||||
\(231\) | −10.8920 | + | 8.33837i | −0.716639 | + | 0.548625i | ||||
\(232\) | 4.47156i | 0.293572i | ||||||||
\(233\) | 0.0103605 | + | 0.0179449i | 0.000678740 | + | 0.00117561i | 0.866365 | − | 0.499412i | \(-0.166451\pi\) |
−0.865686 | + | 0.500588i | \(0.833117\pi\) | |||||||
\(234\) | 1.16388 | + | 0.671966i | 0.0760851 | + | 0.0439278i | ||||
\(235\) | −4.64704 | − | 23.2294i | −0.303140 | − | 1.51532i | ||||
\(236\) | 7.38314 | − | 4.26266i | 0.480601 | − | 0.277475i | ||||
\(237\) | − | 4.84404i | − | 0.314654i | ||||||
\(238\) | −18.6703 | + | 5.32212i | −1.21021 | + | 0.344982i | ||||
\(239\) | 3.74980i | 0.242554i | 0.992619 | + | 0.121277i | \(0.0386990\pi\) | ||||
−0.992619 | + | 0.121277i | \(0.961301\pi\) | |||||||
\(240\) | 3.31121 | + | 1.11996i | 0.213737 | + | 0.0722933i | ||||
\(241\) | 9.64709 | − | 16.7093i | 0.621424 | − | 1.07634i | −0.367797 | − | 0.929906i | \(-0.619888\pi\) |
0.989221 | − | 0.146432i | \(-0.0467789\pi\) | |||||||
\(242\) | 8.03827 | − | 7.50907i | 0.516720 | − | 0.482702i | ||||
\(243\) | 2.85086 | + | 4.93784i | 0.182883 | + | 0.316763i | ||||
\(244\) | −3.42385 | −0.219189 | ||||||||
\(245\) | 15.2430 | − | 3.55671i | 0.973841 | − | 0.227230i | ||||
\(246\) | −10.9003 | −0.694981 | ||||||||
\(247\) | 12.1332 | − | 7.00510i | 0.772016 | − | 0.445724i | ||||
\(248\) | 0.862051 | + | 0.497705i | 0.0547403 | + | 0.0316043i | ||||
\(249\) | −15.0317 | − | 8.67854i | −0.952593 | − | 0.549980i | ||||
\(250\) | 4.91199 | − | 10.0435i | 0.310662 | − | 0.635208i | ||||
\(251\) | − | 1.86262i | − | 0.117567i | −0.998271 | − | 0.0587836i | \(-0.981278\pi\) | ||
0.998271 | − | 0.0587836i | \(-0.0187222\pi\) | |||||||
\(252\) | −0.403500 | − | 1.41550i | −0.0254181 | − | 0.0891678i | ||||
\(253\) | 4.22490 | − | 28.3550i | 0.265617 | − | 1.78266i | ||||
\(254\) | −3.89717 | − | 6.75009i | −0.244530 | − | 0.423538i | ||||
\(255\) | −25.1508 | + | 5.03143i | −1.57501 | + | 0.315080i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.56618 | − | 4.44475i | −0.160074 | − | 0.277256i | 0.774821 | − | 0.632180i | \(-0.217840\pi\) |
−0.934895 | + | 0.354925i | \(0.884506\pi\) | |||||||
\(258\) | 9.67296 | 0.602212 | ||||||||
\(259\) | 7.04274 | + | 6.82234i | 0.437614 | + | 0.423920i | ||||
\(260\) | −3.56609 | − | 4.05738i | −0.221160 | − | 0.251628i | ||||
\(261\) | 2.15434 | − | 1.24381i | 0.133350 | − | 0.0769897i | ||||
\(262\) | −5.54331 | + | 9.60129i | −0.342467 | + | 0.593170i | ||||
\(263\) | 5.97415 | − | 10.3475i | 0.368382 | − | 0.638056i | −0.620931 | − | 0.783865i | \(-0.713245\pi\) |
0.989313 | + | 0.145809i | \(0.0465785\pi\) | |||||||
\(264\) | −1.90230 | − | 4.82304i | −0.117079 | − | 0.296838i | ||||
\(265\) | −2.62575 | − | 2.98749i | −0.161298 | − | 0.183520i | ||||
\(266\) | −14.8825 | − | 3.73527i | −0.912503 | − | 0.229024i | ||||
\(267\) | 5.93163i | 0.363010i | ||||||||
\(268\) | 9.76197 | − | 5.63608i | 0.596307 | − | 0.344278i | ||||
\(269\) | −9.49594 | − | 5.48248i | −0.578978 | − | 0.334273i | 0.181749 | − | 0.983345i | \(-0.441824\pi\) |
−0.760727 | + | 0.649072i | \(0.775157\pi\) | |||||||
\(270\) | −2.43852 | − | 12.1895i | −0.148404 | − | 0.741831i | ||||
\(271\) | 11.6342 | + | 20.1511i | 0.706730 | + | 1.22409i | 0.966063 | + | 0.258305i | \(0.0831639\pi\) |
−0.259333 | + | 0.965788i | \(0.583503\pi\) | |||||||
\(272\) | − | 7.33780i | − | 0.444920i | ||||||
\(273\) | 2.43224 | − | 9.69078i | 0.147206 | − | 0.586513i | ||||
\(274\) | − | 8.90724i | − | 0.538106i | ||||||
\(275\) | −16.0799 | + | 4.05412i | −0.969656 | + | 0.244472i | ||||
\(276\) | −11.7018 | − | 6.75606i | −0.704368 | − | 0.406667i | ||||
\(277\) | 10.2915 | − | 17.8254i | 0.618356 | − | 1.07102i | −0.371429 | − | 0.928461i | \(-0.621132\pi\) |
0.989786 | − | 0.142564i | \(-0.0455345\pi\) | |||||||
\(278\) | 9.20191 | + | 15.9382i | 0.551894 | + | 0.955909i | ||||
\(279\) | − | 0.553766i | − | 0.0331531i | ||||||
\(280\) | −0.286589 | + | 5.90913i | −0.0171270 | + | 0.353138i | ||||
\(281\) | − | 6.50399i | − | 0.387995i | −0.981002 | − | 0.193998i | \(-0.937855\pi\) | ||
0.981002 | − | 0.193998i | \(-0.0621454\pi\) | |||||||
\(282\) | 8.28068 | + | 14.3426i | 0.493107 | + | 0.854087i | ||||
\(283\) | 12.5405 | + | 7.24027i | 0.745456 | + | 0.430389i | 0.824050 | − | 0.566518i | \(-0.191710\pi\) |
−0.0785938 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(284\) | −0.394297 | + | 0.682942i | −0.0233972 | + | 0.0405251i | ||||
\(285\) | −19.2034 | − | 6.49524i | −1.13751 | − | 0.384745i | ||||
\(286\) | −1.18078 | + | 7.92467i | −0.0698208 | + | 0.468595i | ||||
\(287\) | −5.05751 | − | 17.7420i | −0.298536 | − | 1.04728i | ||||
\(288\) | 0.556319 | 0.0327814 | ||||||||
\(289\) | 18.4217 | + | 31.9073i | 1.08363 | + | 1.87690i | ||||
\(290\) | −9.80444 | + | 1.96138i | −0.575737 | + | 0.115176i | ||||
\(291\) | 1.07534 | − | 1.86255i | 0.0630376 | − | 0.109184i | ||||
\(292\) | −8.04910 | + | 4.64715i | −0.471038 | + | 0.271954i | ||||
\(293\) | − | 19.4674i | − | 1.13730i | −0.822580 | − | 0.568650i | \(-0.807466\pi\) | ||
0.822580 | − | 0.568650i | \(-0.192534\pi\) | |||||||
\(294\) | −9.29788 | + | 5.76973i | −0.542263 | + | 0.336497i | ||||
\(295\) | 12.5849 | + | 14.3187i | 0.732721 | + | 0.833667i | ||||
\(296\) | −3.20955 | + | 1.85303i | −0.186551 | + | 0.107705i | ||||
\(297\) | −11.4717 | + | 14.4350i | −0.665656 | + | 0.837602i | ||||
\(298\) | 2.89183 | + | 1.66960i | 0.167519 | + | 0.0967172i | ||||
\(299\) | 10.4406 | + | 18.0836i | 0.603794 | + | 1.04580i | ||||
\(300\) | −1.00325 | + | 7.75148i | −0.0579226 | + | 0.447532i | ||||
\(301\) | 4.48803 | + | 15.7442i | 0.258686 | + | 0.907482i | ||||
\(302\) | 0.344706i | 0.0198356i | ||||||||
\(303\) | 2.12617 | + | 3.68263i | 0.122145 | + | 0.211562i | ||||
\(304\) | 2.89975 | − | 5.02252i | 0.166312 | − | 0.288061i | ||||
\(305\) | −1.50182 | − | 7.50721i | −0.0859939 | − | 0.429862i | ||||
\(306\) | −3.53526 | + | 2.04108i | −0.202097 | + | 0.116681i | ||||
\(307\) | 7.39584i | 0.422103i | 0.977475 | + | 0.211052i | \(0.0676888\pi\) | ||||
−0.977475 | + | 0.211052i | \(0.932311\pi\) | |||||||
\(308\) | 6.96762 | − | 5.33407i | 0.397017 | − | 0.303937i | ||||
\(309\) | −30.0932 | −1.71194 | ||||||||
\(310\) | −0.713155 | + | 2.10846i | −0.0405045 | + | 0.119753i | ||||
\(311\) | 10.5980 | + | 6.11878i | 0.600960 | + | 0.346964i | 0.769419 | − | 0.638744i | \(-0.220546\pi\) |
−0.168459 | + | 0.985709i | \(0.553879\pi\) | |||||||
\(312\) | 3.27044 | + | 1.88819i | 0.185152 | + | 0.106898i | ||||
\(313\) | 10.3410 | + | 17.9111i | 0.584507 | + | 1.01240i | 0.994937 | + | 0.100504i | \(0.0320454\pi\) |
−0.410430 | + | 0.911892i | \(0.634621\pi\) | |||||||
\(314\) | 18.1668 | 1.02521 | ||||||||
\(315\) | 2.92666 | − | 1.50561i | 0.164899 | − | 0.0848314i | ||||
\(316\) | 3.09874i | 0.174318i | ||||||||
\(317\) | −6.76443 | + | 3.90544i | −0.379928 | + | 0.219352i | −0.677787 | − | 0.735258i | \(-0.737061\pi\) |
0.297859 | + | 0.954610i | \(0.403728\pi\) | |||||||
\(318\) | 2.40806 | + | 1.39029i | 0.135037 | + | 0.0779637i | ||||
\(319\) | 11.6105 | + | 9.22707i | 0.650064 | + | 0.516617i | ||||
\(320\) | −2.11819 | − | 0.716443i | −0.118410 | − | 0.0400504i | ||||
\(321\) | 26.3386 | 1.47008 | ||||||||
\(322\) | 5.56714 | − | 22.1812i | 0.310244 | − | 1.23611i | ||||
\(323\) | 42.5556i | 2.36786i | ||||||||
\(324\) | 3.51078 | + | 6.08084i | 0.195043 | + | 0.337825i | ||||
\(325\) | 7.33210 | − | 9.59881i | 0.406712 | − | 0.532446i | ||||
\(326\) | 5.32629 | + | 3.07513i | 0.294996 | + | 0.170316i | ||||
\(327\) | −21.0707 | + | 12.1652i | −1.16521 | + | 0.672736i | ||||
\(328\) | 6.97297 | 0.385018 | ||||||||
\(329\) | −19.5027 | + | 20.1327i | −1.07522 | + | 1.10995i | ||||
\(330\) | 9.74070 | − | 6.28659i | 0.536208 | − | 0.346065i | ||||
\(331\) | −9.35906 | − | 16.2104i | −0.514421 | − | 0.891002i | −0.999860 | − | 0.0167322i | \(-0.994674\pi\) |
0.485440 | − | 0.874270i | \(-0.338660\pi\) | |||||||
\(332\) | 9.61579 | + | 5.55168i | 0.527735 | + | 0.304688i | ||||
\(333\) | 1.78553 | + | 1.03088i | 0.0978466 | + | 0.0564918i | ||||
\(334\) | 1.68578 | − | 0.973287i | 0.0922419 | − | 0.0532559i | ||||
\(335\) | 16.6397 | + | 18.9322i | 0.909126 | + | 1.03437i | ||||
\(336\) | −1.13381 | − | 3.97747i | −0.0618545 | − | 0.216989i | ||||
\(337\) | 3.10399 | 0.169085 | 0.0845426 | − | 0.996420i | \(-0.473057\pi\) | ||||
0.0845426 | + | 0.996420i | \(0.473057\pi\) | |||||||
\(338\) | 3.58206 | + | 6.20432i | 0.194839 | + | 0.337470i | ||||
\(339\) | −10.4301 | − | 6.02181i | −0.566484 | − | 0.327060i | ||||
\(340\) | 16.0890 | − | 3.21862i | 0.872551 | − | 0.174554i | ||||
\(341\) | 3.07115 | − | 1.21132i | 0.166312 | − | 0.0655968i | ||||
\(342\) | −3.22638 | −0.174463 | ||||||||
\(343\) | −13.7051 | − | 12.4567i | −0.740007 | − | 0.672599i | ||||
\(344\) | −6.18781 | −0.333624 | ||||||||
\(345\) | 9.68066 | − | 28.6212i | 0.521189 | − | 1.54091i | ||||
\(346\) | 11.4230 | + | 6.59506i | 0.614104 | + | 0.354553i | ||||
\(347\) | −7.01443 | + | 12.1493i | −0.376554 | + | 0.652211i | −0.990558 | − | 0.137092i | \(-0.956224\pi\) |
0.614004 | + | 0.789303i | \(0.289558\pi\) | |||||||
\(348\) | 6.05357 | − | 3.49503i | 0.324505 | − | 0.187353i | ||||
\(349\) | −10.9124 | −0.584125 | −0.292063 | − | 0.956399i | \(-0.594342\pi\) | ||||
−0.292063 | + | 0.956399i | \(0.594342\pi\) | |||||||
\(350\) | −13.0822 | + | 1.96357i | −0.699274 | + | 0.104957i | ||||
\(351\) | − | 13.4300i | − | 0.716840i | ||||||
\(352\) | 1.21691 | + | 3.08531i | 0.0648614 | + | 0.164448i | ||||
\(353\) | 1.95844 | − | 3.39212i | 0.104237 | − | 0.180544i | −0.809189 | − | 0.587548i | \(-0.800093\pi\) |
0.913426 | + | 0.407004i | \(0.133427\pi\) | |||||||
\(354\) | −11.5415 | − | 6.66350i | −0.613425 | − | 0.354161i | ||||
\(355\) | −1.67039 | − | 0.564982i | −0.0886549 | − | 0.0299861i | ||||
\(356\) | − | 3.79448i | − | 0.201107i | ||||||
\(357\) | 21.7980 | + | 21.1158i | 1.15367 | + | 1.11757i | ||||
\(358\) | −10.7716 | −0.569295 | ||||||||
\(359\) | −11.8456 | + | 6.83908i | −0.625188 | + | 0.360953i | −0.778886 | − | 0.627165i | \(-0.784215\pi\) |
0.153698 | + | 0.988118i | \(0.450882\pi\) | |||||||
\(360\) | 0.244021 | + | 1.21980i | 0.0128610 | + | 0.0642891i | ||||
\(361\) | −7.31715 | + | 12.6737i | −0.385113 | + | 0.667036i | ||||
\(362\) | −4.08908 | + | 2.36083i | −0.214917 | + | 0.124082i | ||||
\(363\) | −16.4486 | − | 5.01297i | −0.863326 | − | 0.263113i | ||||
\(364\) | −1.55591 | + | 6.19921i | −0.0815517 | + | 0.324927i | ||||
\(365\) | −13.7201 | − | 15.6103i | −0.718141 | − | 0.817078i | ||||
\(366\) | 2.67613 | + | 4.63519i | 0.139883 | + | 0.242285i | ||||
\(367\) | 0.190067 | − | 0.329206i | 0.00992143 | − | 0.0171844i | −0.861022 | − | 0.508568i | \(-0.830175\pi\) |
0.870943 | + | 0.491383i | \(0.163509\pi\) | |||||||
\(368\) | 7.48569 | + | 4.32187i | 0.390219 | + | 0.225293i | ||||
\(369\) | −1.93960 | − | 3.35949i | −0.100972 | − | 0.174888i | ||||
\(370\) | −5.47082 | − | 6.22453i | −0.284415 | − | 0.323598i | ||||
\(371\) | −1.14563 | + | 4.56454i | −0.0594782 | + | 0.236979i | ||||
\(372\) | − | 1.55605i | − | 0.0806776i | ||||||
\(373\) | 3.71164 | + | 6.42875i | 0.192182 | + | 0.332868i | 0.945973 | − | 0.324246i | \(-0.105110\pi\) |
−0.753791 | + | 0.657114i | \(0.771777\pi\) | |||||||
\(374\) | −19.0528 | − | 15.1416i | −0.985197 | − | 0.782952i | ||||
\(375\) | −17.4361 | + | 1.20032i | −0.900399 | + | 0.0619844i | ||||
\(376\) | −5.29717 | − | 9.17496i | −0.273181 | − | 0.473163i | ||||
\(377\) | −10.8022 | −0.556341 | ||||||||
\(378\) | −10.2340 | + | 10.5646i | −0.526378 | + | 0.543382i | ||||
\(379\) | −12.0907 | −0.621059 | −0.310529 | − | 0.950564i | \(-0.600506\pi\) | ||||
−0.310529 | + | 0.950564i | \(0.600506\pi\) | |||||||
\(380\) | 12.2844 | + | 4.15502i | 0.630178 | + | 0.213148i | ||||
\(381\) | −6.09216 | + | 10.5519i | −0.312111 | + | 0.540592i | ||||
\(382\) | 7.80888 | − | 13.5254i | 0.399537 | − | 0.692018i | ||||
\(383\) | −7.34126 | − | 12.7154i | −0.375121 | − | 0.649729i | 0.615224 | − | 0.788352i | \(-0.289066\pi\) |
−0.990345 | + | 0.138624i | \(0.955732\pi\) | |||||||
\(384\) | 1.56323 | 0.0797731 | ||||||||
\(385\) | 14.7519 | + | 12.9376i | 0.751824 | + | 0.659364i | ||||
\(386\) | 1.91351 | 0.0973951 | ||||||||
\(387\) | 1.72120 | + | 2.98121i | 0.0874935 | + | 0.151543i | ||||
\(388\) | −0.687898 | + | 1.19147i | −0.0349227 | + | 0.0604880i | ||||
\(389\) | −12.3561 | + | 21.4013i | −0.626478 | + | 1.08509i | 0.361776 | + | 0.932265i | \(0.382171\pi\) |
−0.988253 | + | 0.152826i | \(0.951163\pi\) | |||||||
\(390\) | −2.70556 | + | 7.99906i | −0.137001 | + | 0.405048i | ||||
\(391\) | −63.4260 | −3.20759 | ||||||||
\(392\) | 5.94787 | − | 3.69091i | 0.300413 | − | 0.186419i | ||||
\(393\) | 17.3309 | 0.874229 | ||||||||
\(394\) | 7.41829 | + | 12.8489i | 0.373728 | + | 0.647316i | ||||
\(395\) | −6.79438 | + | 1.35922i | −0.341862 | + | 0.0683896i | ||||
\(396\) | 1.14797 | − | 1.44450i | 0.0576875 | − | 0.0725888i | ||||
\(397\) | 9.10381 | + | 15.7683i | 0.456907 | + | 0.791386i | 0.998796 | − | 0.0490641i | \(-0.0156238\pi\) |
−0.541889 | + | 0.840450i | \(0.682291\pi\) | |||||||
\(398\) | 21.7998i | 1.09273i | ||||||||
\(399\) | 6.57555 | + | 23.0673i | 0.329189 | + | 1.15481i | ||||
\(400\) | 0.641780 | − | 4.95864i | 0.0320890 | − | 0.247932i | ||||
\(401\) | 11.0903 | + | 19.2090i | 0.553825 | + | 0.959252i | 0.997994 | + | 0.0633096i | \(0.0201656\pi\) |
−0.444169 | + | 0.895943i | \(0.646501\pi\) | |||||||
\(402\) | −15.2602 | − | 8.81047i | −0.761109 | − | 0.439426i | ||||
\(403\) | −1.20233 | + | 2.08250i | −0.0598925 | + | 0.103737i | ||||
\(404\) | −1.36011 | − | 2.35579i | −0.0676682 | − | 0.117205i | ||||
\(405\) | −11.7930 | + | 10.3651i | −0.586001 | + | 0.515045i | ||||
\(406\) | 8.49742 | + | 8.23150i | 0.421720 | + | 0.408523i | ||||
\(407\) | −1.81146 | + | 12.1574i | −0.0897906 | + | 0.602621i | ||||
\(408\) | −9.93388 | + | 5.73533i | −0.491800 | + | 0.283941i | ||||
\(409\) | −11.3050 | + | 19.5808i | −0.558995 | + | 0.968207i | 0.438586 | + | 0.898689i | \(0.355479\pi\) |
−0.997581 | + | 0.0695178i | \(0.977854\pi\) | |||||||
\(410\) | 3.05859 | + | 15.2891i | 0.151053 | + | 0.755075i | ||||
\(411\) | −12.0586 | + | 6.96202i | −0.594806 | + | 0.343411i | ||||
\(412\) | 19.2507 | 0.948414 | ||||||||
\(413\) | 5.49087 | − | 21.8773i | 0.270188 | − | 1.07651i | ||||
\(414\) | − | 4.80867i | − | 0.236333i | ||||||
\(415\) | −7.95493 | + | 23.5190i | −0.390492 | + | 1.15450i | ||||
\(416\) | −2.09211 | − | 1.20788i | −0.102574 | − | 0.0592211i | ||||
\(417\) | 14.3847 | − | 24.9150i | 0.704421 | − | 1.22009i | ||||
\(418\) | −7.05747 | − | 17.8933i | −0.345192 | − | 0.875189i | ||||
\(419\) | − | 22.1700i | − | 1.08307i | −0.840677 | − | 0.541537i | \(-0.817843\pi\) | ||
0.840677 | − | 0.541537i | \(-0.182157\pi\) | |||||||
\(420\) | 8.22376 | − | 4.23068i | 0.401278 | − | 0.206436i | ||||
\(421\) | −5.06729 | −0.246964 | −0.123482 | − | 0.992347i | \(-0.539406\pi\) | ||||
−0.123482 | + | 0.992347i | \(0.539406\pi\) | |||||||
\(422\) | −19.3583 | + | 11.1765i | −0.942349 | + | 0.544065i | ||||
\(423\) | −2.94692 | + | 5.10421i | −0.143284 | + | 0.248175i | ||||
\(424\) | −1.54044 | − | 0.889372i | −0.0748103 | − | 0.0431917i | ||||
\(425\) | 14.1144 | + | 33.8654i | 0.684650 | + | 1.64271i | ||||
\(426\) | 1.23275 | 0.0597270 | ||||||||
\(427\) | −6.30282 | + | 6.50643i | −0.305015 | + | 0.314868i | ||||
\(428\) | −16.8488 | −0.814420 | ||||||||
\(429\) | 11.6513 | − | 4.59550i | 0.562529 | − | 0.221873i | ||||
\(430\) | −2.71419 | − | 13.5675i | −0.130890 | − | 0.654285i | ||||
\(431\) | −1.49673 | − | 0.864138i | −0.0720950 | − | 0.0416241i | 0.463519 | − | 0.886087i | \(-0.346587\pi\) |
−0.535614 | + | 0.844463i | \(0.679920\pi\) | |||||||
\(432\) | −2.77967 | − | 4.81453i | −0.133737 | − | 0.231639i | ||||
\(433\) | −1.16651 | −0.0560588 | −0.0280294 | − | 0.999607i | \(-0.508923\pi\) | ||||
−0.0280294 | + | 0.999607i | \(0.508923\pi\) | |||||||
\(434\) | 2.53272 | − | 0.721973i | 0.121574 | − | 0.0346558i | ||||
\(435\) | 10.3186 | + | 11.7402i | 0.494739 | + | 0.562898i | ||||
\(436\) | 13.4790 | − | 7.78209i | 0.645526 | − | 0.372695i | ||||
\(437\) | −43.4133 | − | 25.0647i | −2.07674 | − | 1.19901i | ||||
\(438\) | 12.5826 | + | 7.26456i | 0.601219 | + | 0.347114i | ||||
\(439\) | −7.42466 | − | 12.8599i | −0.354360 | − | 0.613769i | 0.632649 | − | 0.774439i | \(-0.281968\pi\) |
−0.987008 | + | 0.160670i | \(0.948634\pi\) | |||||||
\(440\) | −6.23115 | + | 4.02155i | −0.297058 | + | 0.191720i | ||||
\(441\) | −3.43269 | − | 1.83894i | −0.163461 | − | 0.0875688i | ||||
\(442\) | 17.7263 | 0.843156 | ||||||||
\(443\) | 27.9784 | − | 16.1533i | 1.32929 | − | 0.767468i | 0.344104 | − | 0.938932i | \(-0.388183\pi\) |
0.985191 | + | 0.171463i | \(0.0548495\pi\) | |||||||
\(444\) | 5.01725 | + | 2.89671i | 0.238108 | + | 0.137472i | ||||
\(445\) | 8.31986 | − | 1.66439i | 0.394399 | − | 0.0788996i | ||||
\(446\) | 10.4226 | + | 18.0525i | 0.493525 | + | 0.854810i | ||||
\(447\) | − | 5.21992i | − | 0.246894i | ||||||
\(448\) | 0.725302 | + | 2.54439i | 0.0342673 | + | 0.120211i | ||||
\(449\) | −31.2597 | −1.47524 | −0.737618 | − | 0.675218i | \(-0.764049\pi\) | ||||
−0.737618 | + | 0.675218i | \(0.764049\pi\) | |||||||
\(450\) | −2.56752 | + | 1.07009i | −0.121034 | + | 0.0504447i | ||||
\(451\) | 14.3888 | − | 18.1055i | 0.677540 | − | 0.852556i | ||||
\(452\) | 6.67214 | + | 3.85216i | 0.313831 | + | 0.181190i | ||||
\(453\) | 0.466661 | − | 0.269427i | 0.0219257 | − | 0.0126588i | ||||
\(454\) | − | 12.0063i | − | 0.563482i | ||||||
\(455\) | −14.2750 | − | 0.692328i | −0.669223 | − | 0.0324568i | ||||
\(456\) | −9.06595 | −0.424552 | ||||||||
\(457\) | −20.0531 | − | 34.7330i | −0.938044 | − | 1.62474i | −0.769114 | − | 0.639112i | \(-0.779302\pi\) |
−0.168930 | − | 0.985628i | \(-0.554031\pi\) | |||||||
\(458\) | 0.995628 | + | 0.574826i | 0.0465227 | + | 0.0268599i | ||||
\(459\) | 35.3280 | + | 20.3967i | 1.64897 | + | 0.952034i | ||||
\(460\) | −6.19274 | + | 18.3090i | −0.288738 | + | 0.853663i | ||||
\(461\) | −21.3818 | −0.995848 | −0.497924 | − | 0.867221i | \(-0.665904\pi\) | ||||
−0.497924 | + | 0.867221i | \(0.665904\pi\) | |||||||
\(462\) | −12.6672 | − | 5.26354i | −0.589333 | − | 0.244882i | ||||
\(463\) | 20.7517i | 0.964415i | 0.876057 | + | 0.482207i | \(0.160165\pi\) | ||||
−0.876057 | + | 0.482207i | \(0.839835\pi\) | |||||||
\(464\) | −3.87248 | + | 2.23578i | −0.179775 | + | 0.103793i | ||||
\(465\) | 3.41184 | − | 0.682539i | 0.158220 | − | 0.0316520i | ||||
\(466\) | −0.0103605 | + | 0.0179449i | −0.000479942 | + | 0.000831283i | ||||
\(467\) | −0.436949 | − | 0.756818i | −0.0202196 | − | 0.0350213i | 0.855739 | − | 0.517408i | \(-0.173103\pi\) |
−0.875958 | + | 0.482387i | \(0.839770\pi\) | |||||||
\(468\) | 1.34393i | 0.0621232i | ||||||||
\(469\) | 7.26002 | − | 28.9261i | 0.335236 | − | 1.33569i | ||||
\(470\) | 17.7937 | − | 15.6392i | 0.820763 | − | 0.721380i | ||||
\(471\) | −14.1994 | − | 24.5941i | −0.654274 | − | 1.13324i | ||||
\(472\) | 7.38314 | + | 4.26266i | 0.339836 | + | 0.196205i | ||||
\(473\) | −12.7686 | + | 16.0668i | −0.587099 | + | 0.738753i | ||||
\(474\) | 4.19506 | − | 2.42202i | 0.192686 | − | 0.111247i | ||||
\(475\) | −3.72201 | + | 28.7577i | −0.170778 | + | 1.31949i | ||||
\(476\) | −13.9442 | − | 13.5079i | −0.639132 | − | 0.619131i | ||||
\(477\) | 0.989550i | 0.0453084i | ||||||||
\(478\) | −3.24742 | + | 1.87490i | −0.148534 | + | 0.0857559i | ||||
\(479\) | −2.01746 | + | 3.49434i | −0.0921801 | + | 0.159661i | −0.908428 | − | 0.418041i | \(-0.862717\pi\) |
0.816248 | + | 0.577702i | \(0.196050\pi\) | |||||||
\(480\) | 0.685686 | + | 3.42757i | 0.0312971 | + | 0.156446i | ||||
\(481\) | −4.47647 | − | 7.75348i | −0.204110 | − | 0.353528i | ||||
\(482\) | 19.2942 | 0.878826 | ||||||||
\(483\) | −34.3801 | + | 9.80037i | −1.56435 | + | 0.445932i | ||||
\(484\) | 10.5222 | + | 3.20681i | 0.478281 | + | 0.145764i | ||||
\(485\) | −2.91419 | − | 0.985680i | −0.132327 | − | 0.0447574i | ||||
\(486\) | −2.85086 | + | 4.93784i | −0.129318 | + | 0.223985i | ||||
\(487\) | 10.6366 | + | 6.14105i | 0.481991 | + | 0.278277i | 0.721246 | − | 0.692679i | \(-0.243570\pi\) |
−0.239255 | + | 0.970957i | \(0.576903\pi\) | |||||||
\(488\) | −1.71192 | − | 2.96514i | −0.0774952 | − | 0.134226i | ||||
\(489\) | − | 9.61427i | − | 0.434772i | ||||||
\(490\) | 10.7017 | + | 11.4225i | 0.483454 | + | 0.516015i | ||||
\(491\) | − | 6.98569i | − | 0.315260i | −0.987498 | − | 0.157630i | \(-0.949615\pi\) | ||
0.987498 | − | 0.157630i | \(-0.0503853\pi\) | |||||||
\(492\) | −5.45017 | − | 9.43998i | −0.245713 | − | 0.425587i | ||||
\(493\) | 16.4057 | − | 28.4155i | 0.738876 | − | 1.27977i | ||||
\(494\) | 12.1332 | + | 7.00510i | 0.545898 | + | 0.315174i | ||||
\(495\) | 3.67078 | + | 1.88345i | 0.164989 | + | 0.0846548i | ||||
\(496\) | 0.995411i | 0.0446953i | ||||||||
\(497\) | 0.571968 | + | 2.00649i | 0.0256563 | + | 0.0900034i | ||||
\(498\) | − | 17.3571i | − | 0.777789i | ||||||
\(499\) | 15.3366 | + | 26.5638i | 0.686561 | + | 1.18916i | 0.972944 | + | 0.231043i | \(0.0742137\pi\) |
−0.286383 | + | 0.958115i | \(0.592453\pi\) | |||||||
\(500\) | 11.1539 | − | 0.767849i | 0.498819 | − | 0.0343393i | ||||
\(501\) | −2.63526 | − | 1.52147i | −0.117735 | − | 0.0679742i | ||||
\(502\) | 1.61307 | − | 0.931308i | 0.0719950 | − | 0.0415663i | ||||
\(503\) | 15.2089i | 0.678133i | 0.940762 | + | 0.339067i | \(0.110111\pi\) | ||||
−0.940762 | + | 0.339067i | \(0.889889\pi\) | |||||||
\(504\) | 1.02411 | − | 1.05719i | 0.0456173 | − | 0.0470909i | ||||
\(505\) | 4.56876 | − | 4.01555i | 0.203307 | − | 0.178689i | ||||
\(506\) | 26.6686 | − | 10.5186i | 1.18556 | − | 0.467610i | ||||
\(507\) | 5.59958 | − | 9.69876i | 0.248686 | − | 0.430737i | ||||
\(508\) | 3.89717 | − | 6.75009i | 0.172909 | − | 0.299487i | ||||
\(509\) | 15.7863 | − | 9.11423i | 0.699716 | − | 0.403981i | −0.107526 | − | 0.994202i | \(-0.534293\pi\) |
0.807242 | + | 0.590221i | \(0.200959\pi\) | |||||||
\(510\) | −16.9328 | − | 19.2655i | −0.749795 | − | 0.853093i | ||||
\(511\) | −5.98615 | + | 23.8507i | −0.264812 | + | 1.05509i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.1207 | + | 27.9219i | 0.711747 | + | 1.23278i | ||||
\(514\) | 2.56618 | − | 4.44475i | 0.113189 | − | 0.196049i | ||||
\(515\) | 8.44403 | + | 42.2095i | 0.372088 | + | 1.85998i | ||||
\(516\) | 4.83648 | + | 8.37703i | 0.212914 | + | 0.368778i | ||||
\(517\) | −34.7538 | − | 5.17832i | −1.52847 | − | 0.227742i | ||||
\(518\) | −2.38695 | + | 9.51036i | −0.104877 | + | 0.417861i | ||||
\(519\) | − | 20.6192i | − | 0.905081i | ||||||
\(520\) | 1.73075 | − | 5.11702i | 0.0758985 | − | 0.224396i | ||||
\(521\) | 20.3030 | + | 11.7220i | 0.889492 | + | 0.513549i | 0.873776 | − | 0.486328i | \(-0.161664\pi\) |
0.0157158 | + | 0.999876i | \(0.494997\pi\) | |||||||
\(522\) | 2.15434 | + | 1.24381i | 0.0942927 | + | 0.0544399i | ||||
\(523\) | 20.7215 | − | 11.9635i | 0.906086 | − | 0.523129i | 0.0269161 | − | 0.999638i | \(-0.491431\pi\) |
0.879170 | + | 0.476509i | \(0.158098\pi\) | |||||||
\(524\) | −11.0866 | −0.484321 | ||||||||
\(525\) | 12.8835 | + | 16.1759i | 0.562283 | + | 0.705973i | ||||
\(526\) | 11.9483 | 0.520971 | ||||||||
\(527\) | −3.65206 | − | 6.32556i | −0.159086 | − | 0.275546i | ||||
\(528\) | 3.22572 | − | 4.05896i | 0.140382 | − | 0.176644i | ||||
\(529\) | 25.8570 | − | 44.7857i | 1.12422 | − | 1.94720i | ||||
\(530\) | 1.27437 | − | 3.76771i | 0.0553551 | − | 0.163659i | ||||
\(531\) | − | 4.74280i | − | 0.205820i | ||||||
\(532\) | −4.20640 | − | 14.7562i | −0.182370 | − | 0.639764i | ||||
\(533\) | 16.8450i | 0.729638i | ||||||||
\(534\) | −5.13694 | + | 2.96581i | −0.222297 | + | 0.128343i | ||||
\(535\) | −7.39049 | − | 36.9432i | −0.319519 | − | 1.59719i | ||||
\(536\) | 9.76197 | + | 5.63608i | 0.421653 | + | 0.243441i | ||||
\(537\) | 8.41920 | + | 14.5825i | 0.363315 | + | 0.629281i | ||||
\(538\) | − | 10.9650i | − | 0.472733i | ||||||
\(539\) | 2.68991 | − | 23.0600i | 0.115863 | − | 0.993265i | ||||
\(540\) | 9.33719 | − | 8.20659i | 0.401809 | − | 0.353155i | ||||
\(541\) | 31.8171 | − | 18.3696i | 1.36792 | − | 0.789770i | 0.377260 | − | 0.926107i | \(-0.376866\pi\) |
0.990662 | + | 0.136337i | \(0.0435331\pi\) | |||||||
\(542\) | −11.6342 | + | 20.1511i | −0.499734 | + | 0.865564i | ||||
\(543\) | 6.39216 | + | 3.69051i | 0.274314 | + | 0.158375i | ||||
\(544\) | 6.35472 | − | 3.66890i | 0.272457 | − | 0.157303i | ||||
\(545\) | 22.9755 | + | 26.1408i | 0.984164 | + | 1.11975i | ||||
\(546\) | 9.60858 | − | 2.73901i | 0.411209 | − | 0.117219i | ||||
\(547\) | −33.9176 | −1.45021 | −0.725106 | − | 0.688637i | \(-0.758209\pi\) | ||||
−0.725106 | + | 0.688637i | \(0.758209\pi\) | |||||||
\(548\) | 7.71390 | − | 4.45362i | 0.329521 | − | 0.190249i | ||||
\(549\) | −0.952377 | + | 1.64956i | −0.0406464 | + | 0.0704017i | ||||
\(550\) | −11.5509 | − | 11.8986i | −0.492533 | − | 0.507357i | ||||
\(551\) | 22.4585 | − | 12.9664i | 0.956764 | − | 0.552388i | ||||
\(552\) | − | 13.5121i | − | 0.575114i | ||||||
\(553\) | 5.88862 | + | 5.70434i | 0.250410 | + | 0.242573i | ||||
\(554\) | 20.5830 | 0.874488 | ||||||||
\(555\) | −4.15066 | + | 12.2715i | −0.176186 | + | 0.520898i | ||||
\(556\) | −9.20191 | + | 15.9382i | −0.390248 | + | 0.675929i | ||||
\(557\) | 7.99756 | − | 13.8522i | 0.338868 | − | 0.586936i | −0.645352 | − | 0.763885i | \(-0.723289\pi\) |
0.984220 | + | 0.176949i | \(0.0566228\pi\) | |||||||
\(558\) | 0.479576 | − | 0.276883i | 0.0203021 | − | 0.0117214i | ||||
\(559\) | − | 14.9482i | − | 0.632243i | ||||||
\(560\) | −5.26075 | + | 2.70637i | −0.222307 | + | 0.114365i | ||||
\(561\) | −5.60665 | + | 37.6285i | −0.236713 | + | 1.58867i | ||||
\(562\) | 5.63262 | − | 3.25199i | 0.237598 | − | 0.137177i | ||||
\(563\) | 39.3395 | + | 22.7127i | 1.65796 | + | 0.957226i | 0.973653 | + | 0.228035i | \(0.0732300\pi\) |
0.684310 | + | 0.729191i | \(0.260103\pi\) | |||||||
\(564\) | −8.28068 | + | 14.3426i | −0.348679 | + | 0.603930i | ||||
\(565\) | −5.51971 | + | 16.3192i | −0.232216 | + | 0.686553i | ||||
\(566\) | 14.4805i | 0.608662i | ||||||||
\(567\) | 18.0184 | + | 4.52235i | 0.756703 | + | 0.189921i | ||||
\(568\) | −0.788593 | −0.0330886 | ||||||||
\(569\) | −22.2683 | + | 12.8566i | −0.933537 | + | 0.538978i | −0.887929 | − | 0.459981i | \(-0.847856\pi\) |
−0.0456086 | + | 0.998959i | \(0.514523\pi\) | |||||||
\(570\) | −3.97664 | − | 19.8782i | −0.166563 | − | 0.832607i | ||||
\(571\) | 1.28028 | + | 0.739171i | 0.0535781 | + | 0.0309333i | 0.526550 | − | 0.850144i | \(-0.323485\pi\) |
−0.472972 | + | 0.881078i | \(0.656819\pi\) | |||||||
\(572\) | −7.45335 | + | 2.93975i | −0.311640 | + | 0.122917i | ||||
\(573\) | −24.4141 | −1.01991 | ||||||||
\(574\) | 12.8363 | − | 13.2509i | 0.535775 | − | 0.553083i | ||||
\(575\) | −42.8612 | − | 5.54738i | −1.78743 | − | 0.231342i | ||||
\(576\) | 0.278160 | + | 0.481787i | 0.0115900 | + | 0.0200744i | ||||
\(577\) | 20.1440 | − | 34.8905i | 0.838608 | − | 1.45251i | −0.0524512 | − | 0.998623i | \(-0.516703\pi\) |
0.891059 | − | 0.453888i | \(-0.149963\pi\) | |||||||
\(578\) | −18.4217 | + | 31.9073i | −0.766241 | + | 1.32717i | ||||
\(579\) | −1.49563 | − | 2.59050i | −0.0621561 | − | 0.107658i | ||||
\(580\) | −6.60083 | − | 7.51021i | −0.274084 | − | 0.311844i | ||||
\(581\) | 28.2513 | − | 8.05329i | 1.17206 | − | 0.334107i | ||||
\(582\) | 2.15068 | 0.0891487 | ||||||||
\(583\) | −5.48798 | + | 2.16457i | −0.227289 | + | 0.0896473i | ||||
\(584\) | −8.04910 | − | 4.64715i | −0.333074 | − | 0.192301i | ||||
\(585\) | −2.94674 | + | 0.589495i | −0.121833 | + | 0.0243726i | ||||
\(586\) | 16.8593 | − | 9.73371i | 0.696451 | − | 0.402096i | ||||
\(587\) | 15.4414 | 0.637335 | 0.318667 | − | 0.947867i | \(-0.396765\pi\) | ||||
0.318667 | + | 0.947867i | \(0.396765\pi\) | |||||||
\(588\) | −9.64567 | − | 5.16734i | −0.397781 | − | 0.213097i | ||||
\(589\) | − | 5.77289i | − | 0.237868i | ||||||
\(590\) | −6.10790 | + | 18.0582i | −0.251458 | + | 0.743444i | ||||
\(591\) | 11.5965 | − | 20.0857i | 0.477015 | − | 0.826215i | ||||
\(592\) | −3.20955 | − | 1.85303i | −0.131912 | − | 0.0761592i | ||||
\(593\) | 12.7767 | − | 7.37664i | 0.524677 | − | 0.302922i | −0.214169 | − | 0.976797i | \(-0.568704\pi\) |
0.738846 | + | 0.673874i | \(0.235371\pi\) | |||||||
\(594\) | −18.2369 | − | 2.71730i | −0.748269 | − | 0.111492i | ||||
\(595\) | 23.5012 | − | 36.4994i | 0.963456 | − | 1.49633i | ||||
\(596\) | 3.33920i | 0.136779i | ||||||||
\(597\) | 29.5125 | − | 17.0391i | 1.20787 | − | 0.697362i | ||||
\(598\) | −10.4406 | + | 18.0836i | −0.426947 | + | 0.739493i | ||||
\(599\) | 17.6585 | − | 30.5853i | 0.721505 | − | 1.24968i | −0.238892 | − | 0.971046i | \(-0.576784\pi\) |
0.960397 | − | 0.278637i | \(-0.0898826\pi\) | |||||||
\(600\) | −7.21461 | + | 3.00690i | −0.294535 | + | 0.122756i | ||||
\(601\) | −17.7029 | −0.722115 | −0.361057 | − | 0.932544i | \(-0.617584\pi\) | ||||
−0.361057 | + | 0.932544i | \(0.617584\pi\) | |||||||
\(602\) | −11.3909 | + | 11.7589i | −0.464258 | + | 0.479255i | ||||
\(603\) | − | 6.27092i | − | 0.255371i | ||||||
\(604\) | −0.298524 | + | 0.172353i | −0.0121468 | + | 0.00701294i | ||||
\(605\) | −2.41593 | + | 24.4778i | −0.0982216 | + | 0.995165i | ||||
\(606\) | −2.12617 | + | 3.68263i | −0.0863696 | + | 0.149597i | ||||
\(607\) | −8.30150 | + | 4.79288i | −0.336948 | + | 0.194537i | −0.658921 | − | 0.752212i | \(-0.728987\pi\) |
0.321974 | + | 0.946749i | \(0.395654\pi\) | |||||||
\(608\) | 5.79951 | 0.235201 | ||||||||
\(609\) | 4.50207 | − | 17.9376i | 0.182433 | − | 0.726869i | ||||
\(610\) | 5.75053 | − | 5.05422i | 0.232832 | − | 0.204639i | ||||
\(611\) | 22.1645 | − | 12.7967i | 0.896678 | − | 0.517697i | ||||
\(612\) | −3.53526 | − | 2.04108i | −0.142904 | − | 0.0825058i | ||||
\(613\) | 1.69971 | − | 2.94399i | 0.0686508 | − | 0.118907i | −0.829657 | − | 0.558274i | \(-0.811464\pi\) |
0.898308 | + | 0.439367i | \(0.144797\pi\) | |||||||
\(614\) | −6.40499 | + | 3.69792i | −0.258484 | + | 0.149236i | ||||
\(615\) | 18.3077 | − | 16.0909i | 0.738237 | − | 0.648847i | ||||
\(616\) | 8.10325 | + | 3.36710i | 0.326489 | + | 0.135664i | ||||
\(617\) | − | 2.52801i | − | 0.101774i | −0.998704 | − | 0.0508870i | \(-0.983795\pi\) | ||
0.998704 | − | 0.0508870i | \(-0.0162048\pi\) | |||||||
\(618\) | −15.0466 | − | 26.0615i | −0.605264 | − | 1.04835i | ||||
\(619\) | 10.7041 | + | 6.18003i | 0.430235 | + | 0.248396i | 0.699447 | − | 0.714685i | \(-0.253430\pi\) |
−0.269212 | + | 0.963081i | \(0.586763\pi\) | |||||||
\(620\) | −2.18256 | + | 0.436622i | −0.0876538 | + | 0.0175351i | ||||
\(621\) | −41.6155 | + | 24.0267i | −1.66997 | + | 0.964158i | ||||
\(622\) | 12.2376i | 0.490682i | ||||||||
\(623\) | −7.21074 | − | 6.98509i | −0.288892 | − | 0.279852i | ||||
\(624\) | 3.77638i | 0.151176i | ||||||||
\(625\) | 6.57611 | + | 24.1196i | 0.263044 | + | 0.964784i | ||||
\(626\) | −10.3410 | + | 17.9111i | −0.413309 | + | 0.715872i | ||||
\(627\) | −18.7076 | + | 23.5400i | −0.747110 | + | 0.940097i | ||||
\(628\) | 9.08338 | + | 15.7329i | 0.362466 | + | 0.627810i | ||||
\(629\) | 27.1944 | 1.08431 | ||||||||
\(630\) | 2.76722 | + | 1.78176i | 0.110249 | + | 0.0709869i | ||||
\(631\) | −3.86853 | −0.154004 | −0.0770018 | − | 0.997031i | \(-0.524535\pi\) | ||||
−0.0770018 | + | 0.997031i | \(0.524535\pi\) | |||||||
\(632\) | −2.68359 | + | 1.54937i | −0.106747 | + | 0.0616307i | ||||
\(633\) | 30.2615 | + | 17.4715i | 1.20279 | + | 0.694429i | ||||
\(634\) | −6.76443 | − | 3.90544i | −0.268650 | − | 0.155105i | ||||
\(635\) | 16.5098 | + | 5.58420i | 0.655173 | + | 0.221602i | ||||
\(636\) | 2.78058i | 0.110257i | ||||||||
\(637\) | 8.91633 | + | 14.3686i | 0.353278 | + | 0.569305i | ||||
\(638\) | −2.18562 | + | 14.6685i | −0.0865293 | + | 0.580733i | ||||
\(639\) | 0.219355 | + | 0.379934i | 0.00867754 | + | 0.0150299i | ||||
\(640\) | −0.438635 | − | 2.19262i | −0.0173386 | − | 0.0866711i | ||||
\(641\) | 4.08934 | − | 7.08294i | 0.161519 | − | 0.279760i | −0.773895 | − | 0.633315i | \(-0.781694\pi\) |
0.935414 | + | 0.353555i | \(0.115027\pi\) | |||||||
\(642\) | 13.1693 | + | 22.8099i | 0.519751 | + | 0.900234i | ||||
\(643\) | −28.2230 | −1.11301 | −0.556504 | − | 0.830845i | \(-0.687858\pi\) | ||||
−0.556504 | + | 0.830845i | \(0.687858\pi\) | |||||||
\(644\) | 21.9930 | − | 6.26932i | 0.866648 | − | 0.247046i | ||||
\(645\) | −16.2462 | + | 14.2790i | −0.639694 | + | 0.562236i | ||||
\(646\) | −36.8543 | + | 21.2778i | −1.45001 | + | 0.837165i | ||||
\(647\) | −8.01674 | + | 13.8854i | −0.315171 | + | 0.545892i | −0.979474 | − | 0.201572i | \(-0.935395\pi\) |
0.664303 | + | 0.747463i | \(0.268728\pi\) | |||||||
\(648\) | −3.51078 | + | 6.08084i | −0.137916 | + | 0.238878i | ||||
\(649\) | 26.3032 | − | 10.3745i | 1.03249 | − | 0.407236i | ||||
\(650\) | 11.9789 | + | 1.55038i | 0.469850 | + | 0.0608111i | ||||
\(651\) | −2.95701 | − | 2.86447i | −0.115894 | − | 0.112268i | ||||
\(652\) | 6.15027i | 0.240863i | ||||||||
\(653\) | −39.3535 | + | 22.7208i | −1.54002 | + | 0.889132i | −0.541185 | + | 0.840904i | \(0.682024\pi\) |
−0.998836 | + | 0.0482281i | \(0.984643\pi\) | |||||||
\(654\) | −21.0707 | − | 12.1652i | −0.823930 | − | 0.475696i | ||||
\(655\) | −4.86298 | − | 24.3088i | −0.190012 | − | 0.949823i | ||||
\(656\) | 3.48649 | + | 6.03877i | 0.136124 | + | 0.235774i | ||||
\(657\) | 5.17060i | 0.201724i | ||||||||
\(658\) | −27.1868 | − | 6.82346i | −1.05985 | − | 0.266006i | ||||
\(659\) | − | 48.4979i | − | 1.88921i | −0.328212 | − | 0.944604i | \(-0.606446\pi\) | ||
0.328212 | − | 0.944604i | \(-0.393554\pi\) | |||||||
\(660\) | 10.3147 | + | 5.29240i | 0.401499 | + | 0.206006i | ||||
\(661\) | −17.2004 | − | 9.93066i | −0.669018 | − | 0.386258i | 0.126686 | − | 0.991943i | \(-0.459566\pi\) |
−0.795705 | + | 0.605685i | \(0.792899\pi\) | |||||||
\(662\) | 9.35906 | − | 16.2104i | 0.363750 | − | 0.630034i | ||||
\(663\) | −13.8551 | − | 23.9978i | −0.538089 | − | 0.931998i | ||||
\(664\) | 11.1034i | 0.430894i | ||||||||
\(665\) | 30.5098 | − | 15.6956i | 1.18312 | − | 0.608651i | ||||
\(666\) | 2.06176i | 0.0798914i | ||||||||
\(667\) | 19.3255 | + | 33.4727i | 0.748285 | + | 1.29607i | ||||
\(668\) | 1.68578 | + | 0.973287i | 0.0652249 | + | 0.0376576i | ||||
\(669\) | 16.2929 | − | 28.2201i | 0.629920 | − | 1.09105i | ||||
\(670\) | −8.07586 | + | 23.8765i | −0.311998 | + | 0.922430i | ||||
\(671\) | −11.2316 | − | 1.67351i | −0.433592 | − | 0.0646053i | ||||
\(672\) | 2.87768 | − | 2.97064i | 0.111009 | − | 0.114595i | ||||
\(673\) | −15.0386 | −0.579695 | −0.289848 | − | 0.957073i | \(-0.593605\pi\) | ||||
−0.289848 | + | 0.957073i | \(0.593605\pi\) | |||||||
\(674\) | 1.55200 | + | 2.68814i | 0.0597806 | + | 0.103543i | ||||
\(675\) | 22.0896 | + | 16.8732i | 0.850228 | + | 0.649452i | ||||
\(676\) | −3.58206 | + | 6.20432i | −0.137772 | + | 0.238628i | ||||
\(677\) | 3.39917 | − | 1.96251i | 0.130641 | − | 0.0754254i | −0.433255 | − | 0.901271i | \(-0.642635\pi\) |
0.563896 | + | 0.825846i | \(0.309302\pi\) | |||||||
\(678\) | − | 12.0436i | − | 0.462532i | ||||||
\(679\) | 0.997868 | + | 3.50057i | 0.0382947 | + | 0.134339i | ||||
\(680\) | 10.8319 | + | 12.3242i | 0.415385 | + | 0.472612i | ||||
\(681\) | −16.2540 | + | 9.38426i | −0.622855 | + | 0.359606i | ||||
\(682\) | 2.58461 | + | 2.05403i | 0.0989699 | + | 0.0786530i | ||||
\(683\) | −38.8580 | − | 22.4347i | −1.48686 | − | 0.858440i | −0.486974 | − | 0.873417i | \(-0.661899\pi\) |
−0.999888 | + | 0.0149766i | \(0.995233\pi\) | |||||||
\(684\) | −1.61319 | − | 2.79413i | −0.0616818 | − | 0.106836i | ||||
\(685\) | 13.1487 | + | 14.9602i | 0.502386 | + | 0.571599i | ||||
\(686\) | 3.93526 | − | 18.0973i | 0.150249 | − | 0.690960i | ||||
\(687\) | − | 1.79717i | − | 0.0685663i | ||||||
\(688\) | −3.09391 | − | 5.35880i | −0.117954 | − | 0.204302i | ||||
\(689\) | 2.14851 | − | 3.72132i | 0.0818516 | − | 0.141771i | ||||
\(690\) | 29.6270 | − | 5.92689i | 1.12788 | − | 0.225633i | ||||
\(691\) | −16.0707 | + | 9.27845i | −0.611360 | + | 0.352969i | −0.773498 | − | 0.633799i | \(-0.781495\pi\) |
0.162137 | + | 0.986768i | \(0.448161\pi\) | |||||||
\(692\) | 13.1901i | 0.501413i | ||||||||
\(693\) | −0.631776 | − | 4.84063i | −0.0239992 | − | 0.183880i | ||||
\(694\) | −14.0289 | −0.532528 | ||||||||
\(695\) | −38.9827 | − | 13.1853i | −1.47870 | − | 0.500147i | ||||
\(696\) | 6.05357 | + | 3.49503i | 0.229460 | + | 0.132479i | ||||
\(697\) | −44.3113 | − | 25.5832i | −1.67841 | − | 0.969031i | ||||
\(698\) | −5.45618 | − | 9.45038i | −0.206520 | − | 0.357702i | ||||
\(699\) | 0.0323917 | 0.00122517 | ||||||||
\(700\) | −8.24161 | − | 10.3477i | −0.311504 | − | 0.391108i | ||||
\(701\) | 20.4291i | 0.771598i | 0.922583 | + | 0.385799i | \(0.126074\pi\) | ||||
−0.922583 | + | 0.385799i | \(0.873926\pi\) | |||||||
\(702\) | 11.6307 | − | 6.71500i | 0.438973 | − | 0.253441i | ||||
\(703\) | 18.6138 | + | 10.7467i | 0.702033 | + | 0.405319i | ||||
\(704\) | −2.06350 | + | 2.59653i | −0.0777712 | + | 0.0978603i | ||||
\(705\) | −35.0800 | − | 11.8653i | −1.32119 | − | 0.446872i | ||||
\(706\) | 3.91688 | 0.147414 | ||||||||
\(707\) | −6.98054 | − | 1.75201i | −0.262530 | − | 0.0658910i | ||||
\(708\) | − | 13.3270i | − | 0.500860i | ||||||
\(709\) | −13.1689 | − | 22.8093i | −0.494570 | − | 0.856620i | 0.505411 | − | 0.862879i | \(-0.331341\pi\) |
−0.999980 | + | 0.00625917i | \(0.998008\pi\) | |||||||
\(710\) | −0.345904 | − | 1.72909i | −0.0129816 | − | 0.0648915i | ||||
\(711\) | 1.49293 | + | 0.861945i | 0.0559893 | + | 0.0323255i | ||||
\(712\) | 3.28611 | − | 1.89724i | 0.123152 | − | 0.0711020i | ||||
\(713\) | 8.60406 | 0.322225 | ||||||||
\(714\) | −7.38787 | + | 29.4355i | −0.276484 | + | 1.10160i | ||||
\(715\) | −9.71507 | − | 15.0529i | −0.363323 | − | 0.562947i | ||||
\(716\) | −5.38578 | − | 9.32844i | −0.201276 | − | 0.348620i | ||||
\(717\) | 5.07646 | + | 2.93089i | 0.189584 | + | 0.109456i | ||||
\(718\) | −11.8456 | − | 6.83908i | −0.442075 | − | 0.255232i | ||||
\(719\) | 39.2384 | − | 22.6543i | 1.46335 | − | 0.844863i | 0.464181 | − | 0.885740i | \(-0.346349\pi\) |
0.999164 | + | 0.0408772i | \(0.0130152\pi\) | |||||||
\(720\) | −0.934366 | + | 0.821228i | −0.0348218 | + | 0.0306054i | ||||
\(721\) | 35.4378 | − | 36.5826i | 1.31977 | − | 1.36241i | ||||
\(722\) | −14.6343 | −0.544632 | ||||||||
\(723\) | −15.0806 | − | 26.1204i | −0.560854 | − | 0.971427i | ||||
\(724\) | −4.08908 | − | 2.36083i | −0.151969 | − | 0.0877395i | ||||
\(725\) | 13.5717 | − | 17.7674i | 0.504040 | − | 0.659863i | ||||
\(726\) | −3.88292 | − | 16.7514i | −0.144109 | − | 0.621702i | ||||
\(727\) | −18.1010 | −0.671329 | −0.335665 | − | 0.941982i | \(-0.608961\pi\) | ||||
−0.335665 | + | 0.941982i | \(0.608961\pi\) | |||||||
\(728\) | −6.14663 | + | 1.75215i | −0.227809 | + | 0.0649391i | ||||
\(729\) | 29.9778 | 1.11029 | ||||||||
\(730\) | 6.65884 | − | 19.6871i | 0.246455 | − | 0.728651i | ||||
\(731\) | 39.3218 | + | 22.7025i | 1.45437 | + | 0.839681i | ||||
\(732\) | −2.67613 | + | 4.63519i | −0.0989125 | + | 0.171321i | ||||
\(733\) | 9.66386 | − | 5.57943i | 0.356943 | − | 0.206081i | −0.310796 | − | 0.950477i | \(-0.600596\pi\) |
0.667739 | + | 0.744396i | \(0.267262\pi\) | |||||||
\(734\) | 0.380135 | 0.0140310 | ||||||||
\(735\) | 7.09910 | − | 23.4159i | 0.261854 | − | 0.863709i | ||||
\(736\) | 8.64373i | 0.318612i | ||||||||
\(737\) | 34.7781 | − | 13.7172i | 1.28107 | − | 0.505278i | ||||
\(738\) | 1.93960 | − | 3.35949i | 0.0713977 | − | 0.123664i | ||||
\(739\) | −39.9416 | − | 23.0603i | −1.46928 | − | 0.848287i | −0.469870 | − | 0.882735i | \(-0.655699\pi\) |
−0.999406 | + | 0.0344480i | \(0.989033\pi\) | |||||||
\(740\) | 2.65519 | − | 7.85014i | 0.0976066 | − | 0.288577i | ||||
\(741\) | − | 21.9011i | − | 0.804558i | ||||||
\(742\) | −4.52583 | + | 1.29013i | −0.166148 | + | 0.0473621i | ||||
\(743\) | 17.7370 | 0.650706 | 0.325353 | − | 0.945593i | \(-0.394517\pi\) | ||||
0.325353 | + | 0.945593i | \(0.394517\pi\) | |||||||
\(744\) | 1.34758 | − | 0.778027i | 0.0494047 | − | 0.0285238i | ||||
\(745\) | −7.32160 | + | 1.46469i | −0.268243 | + | 0.0536620i | ||||
\(746\) | −3.71164 | + | 6.42875i | −0.135893 | + | 0.235373i | ||||
\(747\) | 5.34945 | − | 3.08851i | 0.195726 | − | 0.113003i | ||||
\(748\) | 3.58658 | − | 24.0710i | 0.131138 | − | 0.880123i | ||||
\(749\) | −31.0163 | + | 32.0183i | −1.13331 | + | 1.16992i | ||||
\(750\) | −9.75759 | − | 14.5000i | −0.356297 | − | 0.529465i | ||||
\(751\) | 15.9123 | + | 27.5609i | 0.580648 | + | 1.00571i | 0.995403 | + | 0.0957789i | \(0.0305342\pi\) |
−0.414754 | + | 0.909933i | \(0.636132\pi\) | |||||||
\(752\) | 5.29717 | − | 9.17496i | 0.193168 | − | 0.334576i | ||||
\(753\) | −2.52160 | − | 1.45585i | −0.0918922 | − | 0.0530540i | ||||
\(754\) | −5.40109 | − | 9.35497i | −0.196696 | − | 0.340688i | ||||
\(755\) | −0.508848 | − | 0.578951i | −0.0185189 | − | 0.0210702i | ||||
\(756\) | −14.2661 | − | 3.58058i | −0.518855 | − | 0.130225i | ||||
\(757\) | − | 30.9859i | − | 1.12620i | −0.826388 | − | 0.563101i | \(-0.809608\pi\) | ||
0.826388 | − | 0.563101i | \(-0.190392\pi\) | |||||||
\(758\) | −6.04536 | − | 10.4709i | −0.219577 | − | 0.380319i | ||||
\(759\) | −35.0846 | − | 27.8823i | −1.27349 | − | 1.01206i | ||||
\(760\) | 2.54387 | + | 12.7161i | 0.0922757 | + | 0.461263i | ||||
\(761\) | −12.4190 | − | 21.5103i | −0.450187 | − | 0.779747i | 0.548210 | − | 0.836341i | \(-0.315309\pi\) |
−0.998397 | + | 0.0565938i | \(0.981976\pi\) | |||||||
\(762\) | −12.1843 | −0.441391 | ||||||||
\(763\) | 10.0244 | − | 39.9402i | 0.362907 | − | 1.44593i | ||||
\(764\) | 15.6178 | 0.565031 | ||||||||
\(765\) | 2.92464 | − | 8.64677i | 0.105740 | − | 0.312625i | ||||
\(766\) | 7.34126 | − | 12.7154i | 0.265251 | − | 0.459428i | ||||
\(767\) | −10.2975 | + | 17.8359i | −0.371822 | + | 0.644015i | ||||
\(768\) | 0.781614 | + | 1.35379i | 0.0282041 | + | 0.0488509i | ||||
\(769\) | 16.6967 | 0.602099 | 0.301049 | − | 0.953609i | \(-0.402663\pi\) | ||||
0.301049 | + | 0.953609i | \(0.402663\pi\) | |||||||
\(770\) | −3.82841 | + | 19.2443i | −0.137966 | + | 0.693517i | ||||
\(771\) | −8.02303 | −0.288942 | ||||||||
\(772\) | 0.956755 | + | 1.65715i | 0.0344344 | + | 0.0596421i | ||||
\(773\) | 1.87123 | − | 3.24107i | 0.0673036 | − | 0.116573i | −0.830410 | − | 0.557153i | \(-0.811894\pi\) |
0.897714 | + | 0.440580i | \(0.145227\pi\) | |||||||
\(774\) | −1.72120 | + | 2.98121i | −0.0618672 | + | 0.107157i | ||||
\(775\) | −1.91469 | − | 4.59402i | −0.0687779 | − | 0.165022i | ||||
\(776\) | −1.37580 | −0.0493882 | ||||||||
\(777\) | 14.7408 | − | 4.20198i | 0.528822 | − | 0.150745i | ||||
\(778\) | −24.7121 | −0.885973 | ||||||||
\(779\) | −20.2199 | − | 35.0219i | −0.724454 | − | 1.25479i | ||||
\(780\) | −8.28017 | + | 1.65645i | −0.296478 | + | 0.0593104i | ||||
\(781\) | −1.62726 | + | 2.04760i | −0.0582281 | + | 0.0732691i | ||||
\(782\) | −31.7130 | − | 54.9285i | −1.13405 | − | 1.96424i | ||||
\(783\) | − | 24.8589i | − | 0.888384i | ||||||
\(784\) | 6.17036 | + | 3.30556i | 0.220370 | + | 0.118056i | ||||
\(785\) | −30.5120 | + | 26.8174i | −1.08902 | + | 0.957155i | ||||
\(786\) | 8.66545 | + | 15.0090i | 0.309087 | + | 0.535354i | ||||
\(787\) | 29.5678 | + | 17.0710i | 1.05398 | + | 0.608514i | 0.923760 | − | 0.382971i | \(-0.125099\pi\) |
0.130218 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(788\) | −7.41829 | + | 12.8489i | −0.264266 | + | 0.457722i | ||||
\(789\) | −9.33896 | − | 16.1756i | −0.332476 | − | 0.575865i | ||||
\(790\) | −4.57430 | − | 5.20449i | −0.162746 | − | 0.185168i | ||||
\(791\) | 19.6028 | − | 5.58796i | 0.696996 | − | 0.198685i | ||||
\(792\) | 1.82496 | + | 0.271919i | 0.0648470 | + | 0.00966221i | ||||
\(793\) | 7.16305 | − | 4.13559i | 0.254367 | − | 0.146859i | ||||
\(794\) | −9.10381 | + | 15.7683i | −0.323082 | + | 0.559595i | ||||
\(795\) | −6.09677 | + | 1.21966i | −0.216230 | + | 0.0432569i | ||||
\(796\) | −18.8792 | + | 10.8999i | −0.669156 | + | 0.386337i | ||||
\(797\) | −48.7853 | −1.72806 | −0.864032 | − | 0.503438i | \(-0.832068\pi\) | ||||
−0.864032 | + | 0.503438i | \(0.832068\pi\) | |||||||
\(798\) | −16.6891 | + | 17.2283i | −0.590789 | + | 0.609874i | ||||
\(799\) | 77.7391i | 2.75021i | ||||||||
\(800\) | 4.61520 | − | 1.92352i | 0.163172 | − | 0.0680068i | ||||
\(801\) | −1.82813 | − | 1.05547i | −0.0645937 | − | 0.0372932i | ||||
\(802\) | −11.0903 | + | 19.2090i | −0.391613 | + | 0.678294i | ||||
\(803\) | −28.6758 | + | 11.3103i | −1.01195 | + | 0.399132i | ||||
\(804\) | − | 17.6209i | − | 0.621443i | ||||||
\(805\) | 23.3932 | + | 45.4725i | 0.824501 | + | 1.60270i | ||||
\(806\) | −2.40467 | −0.0847008 | ||||||||
\(807\) | −14.8443 | + | 8.57037i | −0.522545 | + | 0.301691i | ||||
\(808\) | 1.36011 | − | 2.35579i | 0.0478486 | − | 0.0828762i | ||||
\(809\) | 2.38177 | + | 1.37512i | 0.0837386 | + | 0.0483465i | 0.541285 | − | 0.840839i | \(-0.317938\pi\) |
−0.457546 | + | 0.889186i | \(0.651271\pi\) | |||||||
\(810\) | −14.8729 | − | 5.03054i | −0.522582 | − | 0.176755i | ||||
\(811\) | 30.7840 | 1.08097 | 0.540486 | − | 0.841353i | \(-0.318240\pi\) | ||||
0.540486 | + | 0.841353i | \(0.318240\pi\) | |||||||
\(812\) | −2.87998 | + | 11.4747i | −0.101068 | + | 0.402684i | ||||
\(813\) | 36.3740 | 1.27569 | ||||||||
\(814\) | −11.4344 | + | 4.50994i | −0.400774 | + | 0.158073i | ||||
\(815\) | −13.4852 | + | 2.69772i | −0.472367 | + | 0.0944970i | ||||
\(816\) | −9.93388 | − | 5.73533i | −0.347755 | − | 0.200777i | ||||
\(817\) | 17.9431 | + | 31.0784i | 0.627751 | + | 1.08730i | ||||
\(818\) | −22.6099 | −0.790538 | ||||||||
\(819\) | 2.55391 | + | 2.47399i | 0.0892408 | + | 0.0864481i | ||||
\(820\) | −11.7115 | + | 10.2934i | −0.408982 | + | 0.359460i | ||||
\(821\) | −21.9663 | + | 12.6823i | −0.766630 | + | 0.442614i | −0.831671 | − | 0.555269i | \(-0.812615\pi\) |
0.0650411 | + | 0.997883i | \(0.479282\pi\) | |||||||
\(822\) | −12.0586 | − | 6.96202i | −0.420591 | − | 0.242828i | ||||
\(823\) | 8.96688 | + | 5.17703i | 0.312566 | + | 0.180460i | 0.648074 | − | 0.761577i | \(-0.275575\pi\) |
−0.335508 | + | 0.942037i | \(0.608908\pi\) | |||||||
\(824\) | 9.62535 | + | 16.6716i | 0.335315 | + | 0.580783i | ||||
\(825\) | −7.07985 | + | 24.9377i | −0.246489 | + | 0.868219i | ||||
\(826\) | 21.6918 | − | 6.18343i | 0.754753 | − | 0.215149i | ||||
\(827\) | 42.0465 | 1.46210 | 0.731049 | − | 0.682325i | \(-0.239031\pi\) | ||||
0.731049 | + | 0.682325i | \(0.239031\pi\) | |||||||
\(828\) | 4.16443 | − | 2.40434i | 0.144724 | − | 0.0835565i | ||||
\(829\) | 4.88779 | + | 2.82197i | 0.169760 | + | 0.0980109i | 0.582473 | − | 0.812850i | \(-0.302085\pi\) |
−0.412713 | + | 0.910861i | \(0.635419\pi\) | |||||||
\(830\) | −24.3455 | + | 4.87032i | −0.845044 | + | 0.169051i | ||||
\(831\) | −16.0880 | − | 27.8652i | −0.558085 | − | 0.966632i | ||||
\(832\) | − | 2.41576i | − | 0.0837512i | ||||||
\(833\) | −51.3387 | + | 1.63253i | −1.77878 | + | 0.0565639i | ||||
\(834\) | 28.7694 | 0.996202 | ||||||||
\(835\) | −1.39461 | + | 4.12320i | −0.0482624 | + | 0.142689i | ||||
\(836\) | 11.9673 | − | 15.0586i | 0.413898 | − | 0.520812i | ||||
\(837\) | −4.79243 | − | 2.76691i | −0.165651 | − | 0.0956384i | ||||
\(838\) | 19.1998 | − | 11.0850i | 0.663245 | − | 0.382924i | ||||
\(839\) | 18.9602i | 0.654579i | 0.944924 | + | 0.327290i | \(0.106135\pi\) | ||||
−0.944924 | + | 0.327290i | \(0.893865\pi\) | |||||||
\(840\) | 7.77575 | + | 5.00664i | 0.268289 | + | 0.172746i | ||||
\(841\) | 9.00518 | 0.310523 | ||||||||
\(842\) | −2.53364 | − | 4.38840i | −0.0873151 | − | 0.151234i | ||||
\(843\) | −8.80507 | − | 5.08361i | −0.303263 | − | 0.175089i | ||||
\(844\) | −19.3583 | − | 11.1765i | −0.666341 | − | 0.384712i | ||||
\(845\) | −15.1749 | − | 5.13269i | −0.522034 | − | 0.176570i | ||||
\(846\) | −5.89383 | −0.202634 | ||||||||
\(847\) | 25.4638 | − | 14.0923i | 0.874948 | − | 0.484217i | ||||
\(848\) | − | 1.77874i | − | 0.0610823i | ||||||
\(849\) | 19.6037 | − | 11.3182i | 0.672796 | − | 0.388439i | ||||
\(850\) | −22.2711 | + | 29.1562i | −0.763892 | + | 1.00005i | ||||
\(851\) | −16.0171 | + | 27.7425i | −0.549060 | + | 0.950999i | ||||
\(852\) | 0.616375 | + | 1.06759i | 0.0211167 | + | 0.0365752i | ||||
\(853\) | − | 27.6201i | − | 0.945693i | −0.881145 | − | 0.472846i | \(-0.843227\pi\) | ||
0.881145 | − | 0.472846i | \(-0.156773\pi\) | |||||||
\(854\) | −8.78614 | − | 2.20519i | −0.300656 | − | 0.0754599i | ||||
\(855\) | 5.41887 | − | 4.76272i | 0.185321 | − | 0.162882i | ||||
\(856\) | −8.42442 | − | 14.5915i | −0.287941 | − | 0.498728i | ||||
\(857\) | −17.2917 | − | 9.98337i | −0.590673 | − | 0.341025i | 0.174690 | − | 0.984623i | \(-0.444108\pi\) |
−0.765364 | + | 0.643598i | \(0.777441\pi\) | |||||||
\(858\) | 9.80546 | + | 7.79256i | 0.334753 | + | 0.266034i | ||||
\(859\) | 13.2809 | − | 7.66771i | 0.453137 | − | 0.261619i | −0.256017 | − | 0.966672i | \(-0.582410\pi\) |
0.709154 | + | 0.705053i | \(0.249077\pi\) | |||||||
\(860\) | 10.3927 | − | 9.13433i | 0.354390 | − | 0.311478i | ||||
\(861\) | −27.9720 | − | 7.02055i | −0.953284 | − | 0.239260i | ||||
\(862\) | − | 1.72828i | − | 0.0588653i | ||||||
\(863\) | −43.9294 | + | 25.3627i | −1.49538 | + | 0.863355i | −0.999986 | − | 0.00531596i | \(-0.998308\pi\) |
−0.495389 | + | 0.868671i | \(0.664975\pi\) | |||||||
\(864\) | 2.77967 | − | 4.81453i | 0.0945662 | − | 0.163794i | ||||
\(865\) | −28.9210 | + | 5.78565i | −0.983343 | + | 0.196718i | ||||
\(866\) | −0.583254 | − | 1.01023i | −0.0198198 | − | 0.0343289i | ||||
\(867\) | 57.5945 | 1.95601 | ||||||||
\(868\) | 1.89161 | + | 1.83241i | 0.0642053 | + | 0.0621960i | ||||
\(869\) | −1.51461 | + | 10.1651i | −0.0513796 | + | 0.344829i | ||||
\(870\) | −5.00798 | + | 14.8062i | −0.169786 | + | 0.501979i | ||||
\(871\) | −13.6154 | + | 23.5825i | −0.461340 | + | 0.799064i | ||||
\(872\) | 13.4790 | + | 7.78209i | 0.456456 | + | 0.263535i | ||||
\(873\) | 0.382691 | + | 0.662840i | 0.0129521 | + | 0.0224337i | ||||
\(874\) | − | 50.1294i | − | 1.69565i | ||||||
\(875\) | 19.0737 | − | 22.6096i | 0.644807 | − | 0.764345i | ||||
\(876\) | 14.5291i | 0.490893i | ||||||||
\(877\) | −12.0867 | − | 20.9347i | −0.408137 | − | 0.706915i | 0.586544 | − | 0.809918i | \(-0.300488\pi\) |
−0.994681 | + | 0.103003i | \(0.967155\pi\) | |||||||
\(878\) | 7.42466 | − | 12.8599i | 0.250570 | − | 0.434000i | ||||
\(879\) | −26.3549 | − | 15.2160i | −0.888929 | − | 0.513223i | ||||
\(880\) | −6.59833 | − | 3.38556i | −0.222430 | − | 0.114127i | ||||
\(881\) | − | 36.0228i | − | 1.21364i | −0.794840 | − | 0.606819i | \(-0.792445\pi\) | ||
0.794840 | − | 0.606819i | \(-0.207555\pi\) | |||||||
\(882\) | −0.123771 | − | 3.89227i | −0.00416760 | − | 0.131059i | ||||
\(883\) | − | 1.47027i | − | 0.0494785i | −0.999694 | − | 0.0247393i | \(-0.992124\pi\) | ||
0.999694 | − | 0.0247393i | \(-0.00787556\pi\) | |||||||
\(884\) | 8.86317 | + | 15.3515i | 0.298101 | + | 0.516325i | ||||
\(885\) | 29.2211 | − | 5.84569i | 0.982257 | − | 0.196501i | ||||
\(886\) | 27.9784 | + | 16.1533i | 0.939953 | + | 0.542682i | ||||
\(887\) | 23.8127 | − | 13.7483i | 0.799552 | − | 0.461622i | −0.0437623 | − | 0.999042i | \(-0.513934\pi\) |
0.843315 | + | 0.537420i | \(0.180601\pi\) | |||||||
\(888\) | 5.79343i | 0.194415i | ||||||||
\(889\) | −5.65325 | − | 19.8319i | −0.189604 | − | 0.665139i | ||||
\(890\) | 5.60133 | + | 6.37301i | 0.187757 | + | 0.213624i | ||||
\(891\) | 8.54458 | + | 21.6637i | 0.286254 | + | 0.725760i | ||||
\(892\) | −10.4226 | + | 18.0525i | −0.348975 | + | 0.604442i | ||||
\(893\) | −30.7210 | + | 53.2103i | −1.02804 | + | 1.78061i | ||||
\(894\) | 4.52059 | − | 2.60996i | 0.151191 | − | 0.0872902i | ||||
\(895\) | 18.0914 | − | 15.9008i | 0.604728 | − | 0.531504i | ||||
\(896\) | −1.84086 | + | 1.90033i | −0.0614988 | + | 0.0634855i | ||||
\(897\) | 32.6420 | 1.08988 | ||||||||
\(898\) | −15.6298 | − | 27.0717i | −0.521575 | − | 0.903394i | ||||
\(899\) | −2.22552 | + | 3.85471i | −0.0742252 | + | 0.128562i | ||||
\(900\) | −2.21049 | − | 1.68850i | −0.0736830 | − | 0.0562832i | ||||
\(901\) | 6.52604 | + | 11.3034i | 0.217414 | + | 0.376572i | ||||
\(902\) | 22.8742 | + | 3.40826i | 0.761628 | + | 0.113483i | ||||
\(903\) | 24.8224 | + | 6.23003i | 0.826036 | + | 0.207322i | ||||
\(904\) | 7.70432i | 0.256242i | ||||||||
\(905\) | 3.38280 | − | 10.0013i | 0.112448 | − | 0.332456i | ||||
\(906\) | 0.466661 | + | 0.269427i | 0.0155038 | + | 0.00895111i | ||||
\(907\) | 1.99949 | + | 1.15440i | 0.0663918 | + | 0.0383313i | 0.532828 | − | 0.846223i | \(-0.321129\pi\) |
−0.466437 | + | 0.884555i | \(0.654462\pi\) | |||||||
\(908\) | 10.3977 | − | 6.00313i | 0.345061 | − | 0.199221i | ||||
\(909\) | −1.51331 | −0.0501935 | ||||||||
\(910\) | −6.53794 | − | 12.7087i | −0.216730 | − | 0.421289i | ||||
\(911\) | 15.2046 | 0.503752 | 0.251876 | − | 0.967760i | \(-0.418953\pi\) | ||||
0.251876 | + | 0.967760i | \(0.418953\pi\) | |||||||
\(912\) | −4.53298 | − | 7.85134i | −0.150102 | − | 0.259984i | ||||
\(913\) | 28.8302 | + | 22.9118i | 0.954140 | + | 0.758270i | ||||
\(914\) | 20.0531 | − | 34.7330i | 0.663297 | − | 1.14886i | ||||
\(915\) | −11.3371 | − | 3.83459i | −0.374792 | − | 0.126767i | ||||
\(916\) | 1.14965i | 0.0379856i | ||||||||
\(917\) | −20.4089 | + | 21.0682i | −0.673961 | + | 0.695733i | ||||
\(918\) | 40.7933i | 1.34638i | ||||||||
\(919\) | −1.33444 | + | 0.770439i | −0.0440191 | + | 0.0254144i | −0.521848 | − | 0.853038i | \(-0.674757\pi\) |
0.477829 | + | 0.878453i | \(0.341424\pi\) | |||||||
\(920\) | −18.9525 | + | 3.79144i | −0.624844 | + | 0.125000i | ||||
\(921\) | 10.0125 | + | 5.78069i | 0.329922 | + | 0.190480i | ||||
\(922\) | −10.6909 | − | 18.5171i | −0.352085 | − | 0.609830i | ||||
\(923\) | − | 1.90505i | − | 0.0627054i | ||||||
\(924\) | −1.77526 | − | 13.6019i | −0.0584017 | − | 0.447470i | ||||
\(925\) | 18.3771 | + | 2.37848i | 0.604234 | + | 0.0782040i | ||||
\(926\) | −17.9715 | + | 10.3759i | −0.590581 | + | 0.340972i | ||||
\(927\) | 5.35477 | − | 9.27473i | 0.175874 | − | 0.304622i | ||||
\(928\) | −3.87248 | − | 2.23578i | −0.127120 | − | 0.0733930i | ||||
\(929\) | −4.87979 | + | 2.81735i | −0.160101 | + | 0.0924342i | −0.577910 | − | 0.816101i | \(-0.696131\pi\) |
0.417809 | + | 0.908535i | \(0.362798\pi\) | |||||||
\(930\) | 2.29702 | + | 2.61347i | 0.0753221 | + | 0.0856991i | ||||
\(931\) | −35.7850 | − | 19.1706i | −1.17281 | − | 0.628291i | ||||
\(932\) | −0.0207210 | −0.000678740 | ||||||||
\(933\) | 16.5671 | − | 9.56505i | 0.542384 | − | 0.313146i | ||||
\(934\) | 0.436949 | − | 0.756818i | 0.0142974 | − | 0.0247638i | ||||
\(935\) | 54.3519 | − | 2.69435i | 1.77750 | − | 0.0881147i | ||||
\(936\) | −1.16388 | + | 0.671966i | −0.0380426 | + | 0.0219639i | ||||
\(937\) | 53.8656i | 1.75971i | 0.475241 | + | 0.879855i | \(0.342361\pi\) | ||||
−0.475241 | + | 0.879855i | \(0.657639\pi\) | |||||||
\(938\) | 28.6808 | − | 8.17572i | 0.936461 | − | 0.266947i | ||||
\(939\) | 32.3306 | 1.05507 | ||||||||
\(940\) | 22.4408 | + | 7.59024i | 0.731937 | + | 0.247566i | ||||
\(941\) | −9.19669 | + | 15.9291i | −0.299804 | + | 0.519275i | −0.976091 | − | 0.217363i | \(-0.930254\pi\) |
0.676287 | + | 0.736638i | \(0.263588\pi\) | |||||||
\(942\) | 14.1994 | − | 24.5941i | 0.462641 | − | 0.801318i | ||||
\(943\) | 52.1975 | − | 30.1363i | 1.69979 | − | 0.981372i | ||||
\(944\) | 8.52531i | 0.277475i | ||||||||
\(945\) | 1.59324 | − | 32.8509i | 0.0518282 | − | 1.06864i | ||||
\(946\) | −20.2986 | − | 3.02449i | −0.659963 | − | 0.0983346i | ||||
\(947\) | 19.5459 | − | 11.2848i | 0.635156 | − | 0.366707i | −0.147590 | − | 0.989049i | \(-0.547152\pi\) |
0.782746 | + | 0.622341i | \(0.213818\pi\) | |||||||
\(948\) | 4.19506 | + | 2.42202i | 0.136249 | + | 0.0786635i | ||||
\(949\) | 11.2264 | − | 19.4447i | 0.364424 | − | 0.631200i | ||||
\(950\) | −26.7659 | + | 11.1555i | −0.868400 | + | 0.361932i | ||||
\(951\) | 12.2102i | 0.395943i | ||||||||
\(952\) | 4.72603 | − | 18.8300i | 0.153172 | − | 0.610283i | ||||
\(953\) | −48.0685 | −1.55709 | −0.778546 | − | 0.627587i | \(-0.784043\pi\) | ||||
−0.778546 | + | 0.627587i | \(0.784043\pi\) | |||||||
\(954\) | −0.856976 | + | 0.494775i | −0.0277456 | + | 0.0160189i | ||||
\(955\) | 6.85049 | + | 34.2439i | 0.221677 | + | 1.10811i | ||||
\(956\) | −3.24742 | − | 1.87490i | −0.105029 | − | 0.0606386i | ||||
\(957\) | 21.5665 | − | 8.50626i | 0.697146 | − | 0.274968i | ||||
\(958\) | −4.03492 | −0.130362 | ||||||||
\(959\) | 5.73686 | − | 22.8574i | 0.185253 | − | 0.738104i | ||||
\(960\) | −2.62552 | + | 2.30761i | −0.0847383 | + | 0.0744777i | ||||
\(961\) | −15.0046 | − | 25.9887i | −0.484019 | − | 0.838345i | ||||
\(962\) | 4.47647 | − | 7.75348i | 0.144327 | − | 0.249982i | ||||
\(963\) | −4.68667 | + | 8.11755i | −0.151026 | + | 0.261584i | ||||
\(964\) | 9.64709 | + | 16.7093i | 0.310712 | + | 0.538169i | ||||
\(965\) | −3.21384 | + | 2.82469i | −0.103457 | + | 0.0909299i | ||||
\(966\) | −25.6774 | − | 24.8739i | −0.826158 | − | 0.800304i | ||||
\(967\) | −33.6784 | −1.08302 | −0.541512 | − | 0.840693i | \(-0.682148\pi\) | ||||
−0.541512 | + | 0.840693i | \(0.682148\pi\) | |||||||
\(968\) | 2.48391 | + | 10.7159i | 0.0798360 | + | 0.344422i | ||||
\(969\) | 57.6116 | + | 33.2621i | 1.85075 | + | 1.06853i | ||||
\(970\) | −0.603472 | − | 3.01660i | −0.0193763 | − | 0.0968573i | ||||
\(971\) | 4.09133 | − | 2.36213i | 0.131297 | − | 0.0758043i | −0.432913 | − | 0.901436i | \(-0.642514\pi\) |
0.564210 | + | 0.825631i | \(0.309181\pi\) | |||||||
\(972\) | −5.70173 | −0.182883 | ||||||||
\(973\) | 13.3483 | + | 46.8266i | 0.427928 | + | 1.50119i | ||||
\(974\) | 12.2821i | 0.393544i | ||||||||
\(975\) | −7.26394 | − | 17.4287i | −0.232632 | − | 0.558166i | ||||
\(976\) | 1.71192 | − | 2.96514i | 0.0547974 | − | 0.0949118i | ||||
\(977\) | 23.7125 | + | 13.6904i | 0.758629 | + | 0.437995i | 0.828803 | − | 0.559540i | \(-0.189022\pi\) |
−0.0701744 | + | 0.997535i | \(0.522356\pi\) | |||||||
\(978\) | 8.32620 | − | 4.80713i | 0.266242 | − | 0.153715i | ||||
\(979\) | 1.85467 | − | 12.4474i | 0.0592755 | − | 0.397822i | ||||
\(980\) | −4.54131 | + | 14.9792i | −0.145067 | + | 0.478493i | ||||
\(981\) | − | 8.65866i | − | 0.276450i | ||||||
\(982\) | 6.04979 | − | 3.49285i | 0.193057 | − | 0.111461i | ||||
\(983\) | 19.8353 | − | 34.3557i | 0.632646 | − | 1.09578i | −0.354362 | − | 0.935108i | \(-0.615302\pi\) |
0.987009 | − | 0.160668i | \(-0.0513647\pi\) | |||||||
\(984\) | 5.45017 | − | 9.43998i | 0.173745 | − | 0.300935i | ||||
\(985\) | −31.4266 | − | 10.6296i | −1.00134 | − | 0.338686i | ||||
\(986\) | 32.8114 | 1.04493 | ||||||||
\(987\) | 12.0120 | + | 42.1386i | 0.382346 | + | 1.34129i | ||||
\(988\) | 14.0102i | 0.445724i | ||||||||
\(989\) | −46.3200 | + | 26.7429i | −1.47289 | + | 0.850374i | ||||
\(990\) | 0.204274 | + | 4.12071i | 0.00649224 | + | 0.130965i | ||||
\(991\) | −29.7219 | + | 51.4798i | −0.944147 | + | 1.63531i | −0.186697 | + | 0.982418i | \(0.559778\pi\) |
−0.757450 | + | 0.652893i | \(0.773555\pi\) | |||||||
\(992\) | −0.862051 | + | 0.497705i | −0.0273701 | + | 0.0158022i | ||||
\(993\) | −29.2607 | −0.928560 | ||||||||
\(994\) | −1.45169 | + | 1.49858i | −0.0460448 | + | 0.0475322i | ||||
\(995\) | −32.1805 | − | 36.6139i | −1.02019 | − | 1.16074i | ||||
\(996\) | 15.0317 | − | 8.67854i | 0.476297 | − | 0.274990i | ||||
\(997\) | 16.6501 | + | 9.61297i | 0.527315 | + | 0.304446i | 0.739923 | − | 0.672692i | \(-0.234862\pi\) |
−0.212607 | + | 0.977138i | \(0.568195\pi\) | |||||||
\(998\) | −15.3366 | + | 26.5638i | −0.485472 | + | 0.840862i | ||||
\(999\) | 17.8430 | − | 10.3016i | 0.564526 | − | 0.325929i |
(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 | 770.2.o.b.549.19 | yes | 48 | |
5.4 | even | 2 | 770.2.o.a.549.6 | yes | 48 | ||
7.5 | odd | 6 | inner | 770.2.o.b.439.6 | yes | 48 | |
11.10 | odd | 2 | 770.2.o.a.549.19 | yes | 48 | ||
35.19 | odd | 6 | 770.2.o.a.439.19 | yes | 48 | ||
55.54 | odd | 2 | inner | 770.2.o.b.549.6 | yes | 48 | |
77.54 | even | 6 | 770.2.o.a.439.6 | ✓ | 48 | ||
385.54 | even | 6 | inner | 770.2.o.b.439.19 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.o.a.439.6 | ✓ | 48 | 77.54 | even | 6 | ||
770.2.o.a.439.19 | yes | 48 | 35.19 | odd | 6 | ||
770.2.o.a.549.6 | yes | 48 | 5.4 | even | 2 | ||
770.2.o.a.549.19 | yes | 48 | 11.10 | odd | 2 | ||
770.2.o.b.439.6 | yes | 48 | 7.5 | odd | 6 | inner | |
770.2.o.b.439.19 | yes | 48 | 385.54 | even | 6 | inner | |
770.2.o.b.549.6 | yes | 48 | 55.54 | odd | 2 | inner | |
770.2.o.b.549.19 | yes | 48 | 1.1 | even | 1 | trivial |