Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [357,2,Mod(16,357)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(357, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("357.16");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 357 = 3 \cdot 7 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 357.p (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: | \(2.85065935216\) |
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 | 16.4 | ||
Character | \(\chi\) | \(=\) | 357.16 |
Dual form | 357.2.p.a.67.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/357\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(190\) | \(239\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.11091 | + | 1.92416i | −0.785534 | + | 1.36058i | 0.143145 | + | 0.989702i | \(0.454278\pi\) |
−0.928679 | + | 0.370883i | \(0.879055\pi\) | |||||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.46826 | − | 2.54309i | −0.734128 | − | 1.27155i | ||||
\(5\) | −0.551608 | − | 0.318471i | −0.246687 | − | 0.142425i | 0.371560 | − | 0.928409i | \(-0.378823\pi\) |
−0.618246 | + | 0.785985i | \(0.712157\pi\) | |||||||
\(6\) | 2.22183i | 0.907057i | ||||||||
\(7\) | −1.27391 | − | 2.31887i | −0.481494 | − | 0.876449i | ||||
\(8\) | 2.08076 | 0.735661 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 1.22558 | − | 0.707587i | 0.387561 | − | 0.223759i | ||||
\(11\) | 3.85464 | − | 2.22548i | 1.16222 | − | 0.671007i | 0.210384 | − | 0.977619i | \(-0.432529\pi\) |
0.951835 | + | 0.306612i | \(0.0991954\pi\) | |||||||
\(12\) | −2.54309 | − | 1.46826i | −0.734128 | − | 0.423849i | ||||
\(13\) | −4.96153 | −1.37608 | −0.688040 | − | 0.725673i | \(-0.741529\pi\) | ||||
−0.688040 | + | 0.725673i | \(0.741529\pi\) | |||||||
\(14\) | 5.87707 | + | 0.124849i | 1.57071 | + | 0.0333673i | ||||
\(15\) | −0.636942 | −0.164458 | ||||||||
\(16\) | 0.624963 | − | 1.08247i | 0.156241 | − | 0.270617i | ||||
\(17\) | 4.08405 | + | 0.566148i | 0.990528 | + | 0.137311i | ||||
\(18\) | 1.11091 | + | 1.92416i | 0.261845 | + | 0.453528i | ||||
\(19\) | 2.85195 | − | 4.93972i | 0.654282 | − | 1.13325i | −0.327791 | − | 0.944750i | \(-0.606304\pi\) |
0.982073 | − | 0.188500i | \(-0.0603624\pi\) | |||||||
\(20\) | 1.87039i | 0.418231i | ||||||||
\(21\) | −2.26267 | − | 1.37124i | −0.493756 | − | 0.299229i | ||||
\(22\) | 9.88925i | 2.10840i | ||||||||
\(23\) | 1.06733 | + | 0.616221i | 0.222553 | + | 0.128491i | 0.607132 | − | 0.794601i | \(-0.292320\pi\) |
−0.384579 | + | 0.923092i | \(0.625653\pi\) | |||||||
\(24\) | 1.80199 | − | 1.04038i | 0.367830 | − | 0.212367i | ||||
\(25\) | −2.29715 | − | 3.97878i | −0.459430 | − | 0.795757i | ||||
\(26\) | 5.51183 | − | 9.54676i | 1.08096 | − | 1.87227i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −4.02666 | + | 6.64437i | −0.760968 | + | 1.25567i | ||||
\(29\) | − | 3.35828i | − | 0.623618i | −0.950145 | − | 0.311809i | \(-0.899065\pi\) | ||
0.950145 | − | 0.311809i | \(-0.100935\pi\) | |||||||
\(30\) | 0.707587 | − | 1.22558i | 0.129187 | − | 0.223759i | ||||
\(31\) | 3.14993 | − | 1.81861i | 0.565745 | − | 0.326633i | −0.189703 | − | 0.981841i | \(-0.560753\pi\) |
0.755448 | + | 0.655209i | \(0.227419\pi\) | |||||||
\(32\) | 3.46932 | + | 6.00904i | 0.613296 | + | 1.06226i | ||||
\(33\) | 2.22548 | − | 3.85464i | 0.387406 | − | 0.671007i | ||||
\(34\) | −5.62638 | + | 7.22942i | −0.964917 | + | 1.23983i | ||||
\(35\) | −0.0357911 | + | 1.68481i | −0.00604980 | + | 0.284785i | ||||
\(36\) | −2.93651 | −0.489418 | ||||||||
\(37\) | −2.86890 | − | 1.65636i | −0.471644 | − | 0.272304i | 0.245283 | − | 0.969451i | \(-0.421119\pi\) |
−0.716928 | + | 0.697147i | \(0.754452\pi\) | |||||||
\(38\) | 6.33653 | + | 10.9752i | 1.02792 | + | 1.78041i | ||||
\(39\) | −4.29681 | + | 2.48076i | −0.688040 | + | 0.397240i | ||||
\(40\) | −1.14777 | − | 0.662663i | −0.181478 | − | 0.104776i | ||||
\(41\) | 8.40547i | 1.31271i | 0.754450 | + | 0.656357i | \(0.227903\pi\) | ||||
−0.754450 | + | 0.656357i | \(0.772097\pi\) | |||||||
\(42\) | 5.15212 | − | 2.83041i | 0.794989 | − | 0.436742i | ||||
\(43\) | 2.95338 | 0.450386 | 0.225193 | − | 0.974314i | \(-0.427699\pi\) | ||||
0.225193 | + | 0.974314i | \(0.427699\pi\) | |||||||
\(44\) | −11.3192 | − | 6.53514i | −1.70643 | − | 0.985210i | ||||
\(45\) | −0.551608 | + | 0.318471i | −0.0822289 | + | 0.0474749i | ||||
\(46\) | −2.37141 | + | 1.36914i | −0.349646 | + | 0.201868i | ||||
\(47\) | −5.19336 | + | 8.99516i | −0.757529 | + | 1.31208i | 0.186578 | + | 0.982440i | \(0.440260\pi\) |
−0.944107 | + | 0.329639i | \(0.893073\pi\) | |||||||
\(48\) | − | 1.24993i | − | 0.180411i | ||||||
\(49\) | −3.75429 | + | 5.90807i | −0.536327 | + | 0.844010i | ||||
\(50\) | 10.2077 | 1.44359 | ||||||||
\(51\) | 3.81997 | − | 1.55173i | 0.534902 | − | 0.217285i | ||||
\(52\) | 7.28479 | + | 12.6176i | 1.01022 | + | 1.74975i | ||||
\(53\) | −6.14162 | − | 10.6376i | −0.843616 | − | 1.46119i | −0.886818 | − | 0.462119i | \(-0.847089\pi\) |
0.0432018 | − | 0.999066i | \(-0.486244\pi\) | |||||||
\(54\) | 1.92416 | + | 1.11091i | 0.261845 | + | 0.151176i | ||||
\(55\) | −2.83500 | −0.382272 | ||||||||
\(56\) | −2.65071 | − | 4.82501i | −0.354216 | − | 0.644770i | ||||
\(57\) | − | 5.70390i | − | 0.755500i | ||||||
\(58\) | 6.46187 | + | 3.73076i | 0.848485 | + | 0.489873i | ||||
\(59\) | −0.809436 | − | 1.40198i | −0.105380 | − | 0.182523i | 0.808514 | − | 0.588477i | \(-0.200272\pi\) |
−0.913893 | + | 0.405955i | \(0.866939\pi\) | |||||||
\(60\) | 0.935194 | + | 1.61980i | 0.120733 | + | 0.209116i | ||||
\(61\) | 6.67049 | + | 3.85121i | 0.854069 | + | 0.493097i | 0.862022 | − | 0.506872i | \(-0.169198\pi\) |
−0.00795289 | + | 0.999968i | \(0.502532\pi\) | |||||||
\(62\) | 8.08129i | 1.02632i | ||||||||
\(63\) | −2.64515 | − | 0.0561921i | −0.333258 | − | 0.00707954i | ||||
\(64\) | −12.9166 | −1.61458 | ||||||||
\(65\) | 2.73682 | + | 1.58010i | 0.339461 | + | 0.195988i | ||||
\(66\) | 4.94463 | + | 8.56434i | 0.608641 | + | 1.05420i | ||||
\(67\) | 4.43382 | + | 7.67960i | 0.541677 | + | 0.938213i | 0.998808 | + | 0.0488132i | \(0.0155439\pi\) |
−0.457130 | + | 0.889400i | \(0.651123\pi\) | |||||||
\(68\) | −4.55666 | − | 11.2174i | −0.552577 | − | 1.36031i | ||||
\(69\) | 1.23244 | 0.148369 | ||||||||
\(70\) | −3.20208 | − | 1.94055i | −0.382722 | − | 0.231940i | ||||
\(71\) | − | 9.35212i | − | 1.10989i | −0.831886 | − | 0.554946i | \(-0.812739\pi\) | ||
0.831886 | − | 0.554946i | \(-0.187261\pi\) | |||||||
\(72\) | 1.04038 | − | 1.80199i | 0.122610 | − | 0.212367i | ||||
\(73\) | 7.34831 | − | 4.24255i | 0.860055 | − | 0.496553i | −0.00397574 | − | 0.999992i | \(-0.501266\pi\) |
0.864031 | + | 0.503439i | \(0.167932\pi\) | |||||||
\(74\) | 6.37420 | − | 3.68015i | 0.740986 | − | 0.427808i | ||||
\(75\) | −3.97878 | − | 2.29715i | −0.459430 | − | 0.265252i | ||||
\(76\) | −16.7496 | −1.92131 | ||||||||
\(77\) | −10.0711 | − | 6.10333i | −1.14770 | − | 0.695540i | ||||
\(78\) | − | 11.0237i | − | 1.24818i | ||||||
\(79\) | −12.5774 | − | 7.26158i | −1.41507 | − | 0.816992i | −0.419211 | − | 0.907889i | \(-0.637693\pi\) |
−0.995860 | + | 0.0908965i | \(0.971027\pi\) | |||||||
\(80\) | −0.689470 | + | 0.398066i | −0.0770851 | + | 0.0445051i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −16.1735 | − | 9.33775i | −1.78606 | − | 1.03118i | ||||
\(83\) | 1.17614 | 0.129098 | 0.0645491 | − | 0.997915i | \(-0.479439\pi\) | ||||
0.0645491 | + | 0.997915i | \(0.479439\pi\) | |||||||
\(84\) | −0.165009 | + | 7.76752i | −0.0180039 | + | 0.847506i | ||||
\(85\) | −2.07249 | − | 1.61294i | −0.224794 | − | 0.174948i | ||||
\(86\) | −3.28095 | + | 5.68276i | −0.353793 | + | 0.612788i | ||||
\(87\) | −1.67914 | − | 2.90836i | −0.180023 | − | 0.311809i | ||||
\(88\) | 8.02060 | − | 4.63069i | 0.854999 | − | 0.493634i | ||||
\(89\) | −1.92963 | + | 3.34222i | −0.204541 | + | 0.354275i | −0.949986 | − | 0.312292i | \(-0.898903\pi\) |
0.745446 | + | 0.666566i | \(0.232237\pi\) | |||||||
\(90\) | − | 1.41517i | − | 0.149172i | ||||||
\(91\) | 6.32056 | + | 11.5051i | 0.662575 | + | 1.20606i | ||||
\(92\) | − | 3.61908i | − | 0.377315i | ||||||
\(93\) | 1.81861 | − | 3.14993i | 0.188582 | − | 0.326633i | ||||
\(94\) | −11.5387 | − | 19.9857i | −1.19013 | − | 2.06137i | ||||
\(95\) | −3.14632 | + | 1.81653i | −0.322805 | + | 0.186372i | ||||
\(96\) | 6.00904 | + | 3.46932i | 0.613296 | + | 0.354086i | ||||
\(97\) | − | 12.9435i | − | 1.31421i | −0.753800 | − | 0.657104i | \(-0.771781\pi\) | ||
0.753800 | − | 0.657104i | \(-0.228219\pi\) | |||||||
\(98\) | −7.19737 | − | 13.7872i | −0.727045 | − | 1.39272i | ||||
\(99\) | − | 4.45096i | − | 0.447338i | ||||||
\(100\) | −6.74561 | + | 11.6837i | −0.674561 | + | 1.16837i | ||||
\(101\) | 2.72077 | + | 4.71251i | 0.270727 | + | 0.468912i | 0.969048 | − | 0.246872i | \(-0.0794027\pi\) |
−0.698321 | + | 0.715784i | \(0.746069\pi\) | |||||||
\(102\) | −1.25788 | + | 9.07405i | −0.124549 | + | 0.898465i | ||||
\(103\) | −5.70540 | + | 9.88205i | −0.562170 | + | 0.973707i | 0.435137 | + | 0.900364i | \(0.356700\pi\) |
−0.997307 | + | 0.0733429i | \(0.976633\pi\) | |||||||
\(104\) | −10.3238 | −1.01233 | ||||||||
\(105\) | 0.811409 | + | 1.47698i | 0.0791854 | + | 0.144139i | ||||
\(106\) | 27.2912 | 2.65076 | ||||||||
\(107\) | −10.4912 | − | 6.05708i | −1.01422 | − | 0.585560i | −0.101795 | − | 0.994805i | \(-0.532459\pi\) |
−0.912424 | + | 0.409245i | \(0.865792\pi\) | |||||||
\(108\) | −2.54309 | + | 1.46826i | −0.244709 | + | 0.141283i | ||||
\(109\) | 10.1103 | − | 5.83720i | 0.968394 | − | 0.559103i | 0.0696480 | − | 0.997572i | \(-0.477812\pi\) |
0.898746 | + | 0.438469i | \(0.144479\pi\) | |||||||
\(110\) | 3.14944 | − | 5.45499i | 0.300287 | − | 0.520113i | ||||
\(111\) | −3.31272 | −0.314430 | ||||||||
\(112\) | −3.30625 | − | 0.0702360i | −0.312411 | − | 0.00663668i | ||||
\(113\) | − | 4.19208i | − | 0.394358i | −0.980367 | − | 0.197179i | \(-0.936822\pi\) | ||
0.980367 | − | 0.197179i | \(-0.0631780\pi\) | |||||||
\(114\) | 10.9752 | + | 6.33653i | 1.02792 | + | 0.593471i | ||||
\(115\) | −0.392497 | − | 0.679825i | −0.0366006 | − | 0.0633940i | ||||
\(116\) | −8.54043 | + | 4.93082i | −0.792959 | + | 0.457815i | ||||
\(117\) | −2.48076 | + | 4.29681i | −0.229347 | + | 0.397240i | ||||
\(118\) | 3.59685 | 0.331117 | ||||||||
\(119\) | −3.88991 | − | 10.1916i | −0.356587 | − | 0.934262i | ||||
\(120\) | −1.32533 | −0.120985 | ||||||||
\(121\) | 4.40551 | − | 7.63056i | 0.400501 | − | 0.693688i | ||||
\(122\) | −14.8207 | + | 8.55672i | −1.34180 | + | 0.774689i | ||||
\(123\) | 4.20274 | + | 7.27935i | 0.378948 | + | 0.656357i | ||||
\(124\) | −9.24981 | − | 5.34038i | −0.830658 | − | 0.479580i | ||||
\(125\) | 6.11102i | 0.546586i | ||||||||
\(126\) | 3.04666 | − | 5.02727i | 0.271418 | − | 0.447865i | ||||
\(127\) | 17.6363 | 1.56497 | 0.782485 | − | 0.622669i | \(-0.213952\pi\) | ||||
0.782485 | + | 0.622669i | \(0.213952\pi\) | |||||||
\(128\) | 7.41058 | − | 12.8355i | 0.655009 | − | 1.13451i | ||||
\(129\) | 2.55770 | − | 1.47669i | 0.225193 | − | 0.130015i | ||||
\(130\) | −6.08074 | + | 3.51071i | −0.533316 | + | 0.307910i | ||||
\(131\) | 10.7894 | + | 6.22924i | 0.942671 | + | 0.544251i | 0.890797 | − | 0.454402i | \(-0.150147\pi\) |
0.0518742 | + | 0.998654i | \(0.483481\pi\) | |||||||
\(132\) | −13.0703 | −1.13762 | ||||||||
\(133\) | −15.0877 | − | 0.320514i | −1.30827 | − | 0.0277921i | ||||
\(134\) | −19.7024 | −1.70202 | ||||||||
\(135\) | −0.318471 | + | 0.551608i | −0.0274096 | + | 0.0474749i | ||||
\(136\) | 8.49795 | + | 1.17802i | 0.728693 | + | 0.101014i | ||||
\(137\) | 9.11657 | + | 15.7904i | 0.778882 | + | 1.34906i | 0.932587 | + | 0.360946i | \(0.117546\pi\) |
−0.153705 | + | 0.988117i | \(0.549121\pi\) | |||||||
\(138\) | −1.36914 | + | 2.37141i | −0.116549 | + | 0.201868i | ||||
\(139\) | 11.7920i | 1.00019i | 0.865971 | + | 0.500094i | \(0.166701\pi\) | ||||
−0.865971 | + | 0.500094i | \(0.833299\pi\) | |||||||
\(140\) | 4.33718 | − | 2.38271i | 0.366559 | − | 0.201376i | ||||
\(141\) | 10.3867i | 0.874720i | ||||||||
\(142\) | 17.9950 | + | 10.3894i | 1.51010 | + | 0.871858i | ||||
\(143\) | −19.1249 | + | 11.0418i | −1.59931 | + | 0.923360i | ||||
\(144\) | −0.624963 | − | 1.08247i | −0.0520803 | − | 0.0902057i | ||||
\(145\) | −1.06952 | + | 1.85246i | −0.0888185 | + | 0.153838i | ||||
\(146\) | 18.8524i | 1.56024i | ||||||||
\(147\) | −0.297274 | + | 6.99368i | −0.0245187 | + | 0.576829i | ||||
\(148\) | 9.72784i | 0.799624i | ||||||||
\(149\) | −5.60174 | + | 9.70250i | −0.458912 | + | 0.794860i | −0.998904 | − | 0.0468109i | \(-0.985094\pi\) |
0.539991 | + | 0.841671i | \(0.318428\pi\) | |||||||
\(150\) | 8.84017 | − | 5.10387i | 0.721797 | − | 0.416729i | ||||
\(151\) | 6.82085 | + | 11.8141i | 0.555073 | + | 0.961414i | 0.997898 | + | 0.0648064i | \(0.0206430\pi\) |
−0.442825 | + | 0.896608i | \(0.646024\pi\) | |||||||
\(152\) | 5.93423 | − | 10.2784i | 0.481330 | − | 0.833688i | ||||
\(153\) | 2.53232 | − | 3.25382i | 0.204726 | − | 0.263056i | ||||
\(154\) | 22.9319 | − | 12.5981i | 1.84790 | − | 1.01518i | ||||
\(155\) | −2.31670 | −0.186082 | ||||||||
\(156\) | 12.6176 | + | 7.28479i | 1.01022 | + | 0.583250i | ||||
\(157\) | −0.168499 | − | 0.291848i | −0.0134476 | − | 0.0232920i | 0.859223 | − | 0.511601i | \(-0.170947\pi\) |
−0.872671 | + | 0.488309i | \(0.837614\pi\) | |||||||
\(158\) | 27.9449 | − | 16.1340i | 2.22317 | − | 1.28355i | ||||
\(159\) | −10.6376 | − | 6.14162i | −0.843616 | − | 0.487062i | ||||
\(160\) | − | 4.41952i | − | 0.349393i | ||||||
\(161\) | 0.0692535 | − | 3.26000i | 0.00545794 | − | 0.256924i | ||||
\(162\) | 2.22183 | 0.174563 | ||||||||
\(163\) | −4.52040 | − | 2.60985i | −0.354065 | − | 0.204420i | 0.312409 | − | 0.949948i | \(-0.398864\pi\) |
−0.666474 | + | 0.745528i | \(0.732197\pi\) | |||||||
\(164\) | 21.3759 | − | 12.3414i | 1.66918 | − | 0.963700i | ||||
\(165\) | −2.45518 | + | 1.41750i | −0.191136 | + | 0.110352i | ||||
\(166\) | −1.30659 | + | 2.26308i | −0.101411 | + | 0.175649i | ||||
\(167\) | 19.6234i | 1.51850i | 0.650797 | + | 0.759252i | \(0.274435\pi\) | ||||
−0.650797 | + | 0.759252i | \(0.725565\pi\) | |||||||
\(168\) | −4.70809 | − | 2.85323i | −0.363237 | − | 0.220131i | ||||
\(169\) | 11.6168 | 0.893597 | ||||||||
\(170\) | 5.40592 | − | 2.19596i | 0.414615 | − | 0.168423i | ||||
\(171\) | −2.85195 | − | 4.93972i | −0.218094 | − | 0.377750i | ||||
\(172\) | −4.33631 | − | 7.51071i | −0.330641 | − | 0.572687i | ||||
\(173\) | 9.57633 | + | 5.52890i | 0.728075 | + | 0.420354i | 0.817718 | − | 0.575620i | \(-0.195239\pi\) |
−0.0896424 | + | 0.995974i | \(0.528572\pi\) | |||||||
\(174\) | 7.46152 | 0.565657 | ||||||||
\(175\) | −6.29990 | + | 10.3954i | −0.476228 | + | 0.785820i | ||||
\(176\) | − | 5.56337i | − | 0.419355i | ||||||
\(177\) | −1.40198 | − | 0.809436i | −0.105380 | − | 0.0608409i | ||||
\(178\) | −4.28731 | − | 7.42584i | −0.321347 | − | 0.556590i | ||||
\(179\) | 2.93488 | + | 5.08337i | 0.219364 | + | 0.379949i | 0.954614 | − | 0.297847i | \(-0.0962686\pi\) |
−0.735250 | + | 0.677796i | \(0.762935\pi\) | |||||||
\(180\) | 1.61980 | + | 0.935194i | 0.120733 | + | 0.0697052i | ||||
\(181\) | − | 11.6689i | − | 0.867343i | −0.901071 | − | 0.433672i | \(-0.857218\pi\) | ||
0.901071 | − | 0.433672i | \(-0.142782\pi\) | |||||||
\(182\) | −29.1593 | − | 0.619442i | −2.16143 | − | 0.0459161i | ||||
\(183\) | 7.70242 | 0.569379 | ||||||||
\(184\) | 2.22085 | + | 1.28221i | 0.163724 | + | 0.0945258i | ||||
\(185\) | 1.05501 | + | 1.82732i | 0.0775656 | + | 0.134348i | ||||
\(186\) | 4.04065 | + | 6.99860i | 0.296274 | + | 0.513162i | ||||
\(187\) | 17.0025 | − | 6.90667i | 1.24335 | − | 0.505066i | ||||
\(188\) | 30.5007 | 2.22449 | ||||||||
\(189\) | −2.31887 | + | 1.27391i | −0.168673 | + | 0.0926636i | ||||
\(190\) | − | 8.07201i | − | 0.585605i | ||||||
\(191\) | 7.88271 | − | 13.6533i | 0.570373 | − | 0.987915i | −0.426154 | − | 0.904651i | \(-0.640132\pi\) |
0.996527 | − | 0.0832649i | \(-0.0265348\pi\) | |||||||
\(192\) | −11.1861 | + | 6.45831i | −0.807288 | + | 0.466088i | ||||
\(193\) | 1.58028 | − | 0.912377i | 0.113751 | − | 0.0656743i | −0.442045 | − | 0.896993i | \(-0.645747\pi\) |
0.555796 | + | 0.831319i | \(0.312413\pi\) | |||||||
\(194\) | 24.9052 | + | 14.3791i | 1.78809 | + | 1.03236i | ||||
\(195\) | 3.16021 | 0.226307 | ||||||||
\(196\) | 20.5370 | + | 0.872947i | 1.46693 | + | 0.0623534i | ||||
\(197\) | 17.5404i | 1.24970i | 0.780743 | + | 0.624852i | \(0.214841\pi\) | ||||
−0.780743 | + | 0.624852i | \(0.785159\pi\) | |||||||
\(198\) | 8.56434 | + | 4.94463i | 0.608641 | + | 0.351399i | ||||
\(199\) | 10.5663 | − | 6.10043i | 0.749022 | − | 0.432448i | −0.0763186 | − | 0.997083i | \(-0.524317\pi\) |
0.825340 | + | 0.564636i | \(0.190983\pi\) | |||||||
\(200\) | −4.77983 | − | 8.27891i | −0.337985 | − | 0.585407i | ||||
\(201\) | 7.67960 | + | 4.43382i | 0.541677 | + | 0.312738i | ||||
\(202\) | −12.0902 | −0.850660 | ||||||||
\(203\) | −7.78741 | + | 4.27816i | −0.546569 | + | 0.300268i | ||||
\(204\) | −9.55487 | − | 7.43620i | −0.668975 | − | 0.520638i | ||||
\(205\) | 2.67690 | − | 4.63653i | 0.186963 | − | 0.323829i | ||||
\(206\) | −12.6764 | − | 21.9562i | −0.883208 | − | 1.52976i | ||||
\(207\) | 1.06733 | − | 0.616221i | 0.0741843 | − | 0.0428303i | ||||
\(208\) | −3.10077 | + | 5.37070i | −0.215000 | + | 0.372391i | ||||
\(209\) | − | 25.3878i | − | 1.75611i | ||||||
\(210\) | −3.74336 | − | 0.0795216i | −0.258316 | − | 0.00548751i | ||||
\(211\) | − | 3.74811i | − | 0.258030i | −0.991643 | − | 0.129015i | \(-0.958818\pi\) | ||
0.991643 | − | 0.129015i | \(-0.0411816\pi\) | |||||||
\(212\) | −18.0349 | + | 31.2374i | −1.23864 | + | 2.14539i | ||||
\(213\) | −4.67606 | − | 8.09917i | −0.320398 | − | 0.554946i | ||||
\(214\) | 23.3096 | − | 13.4578i | 1.59341 | − | 0.919955i | ||||
\(215\) | −1.62911 | − | 0.940565i | −0.111104 | − | 0.0641460i | ||||
\(216\) | − | 2.08076i | − | 0.141578i | ||||||
\(217\) | −8.22987 | − | 4.98752i | −0.558680 | − | 0.338575i | ||||
\(218\) | 25.9385i | 1.75678i | ||||||||
\(219\) | 4.24255 | − | 7.34831i | 0.286685 | − | 0.496553i | ||||
\(220\) | 4.16251 | + | 7.20967i | 0.280636 | + | 0.486076i | ||||
\(221\) | −20.2631 | − | 2.80896i | −1.36305 | − | 0.188951i | ||||
\(222\) | 3.68015 | − | 6.37420i | 0.246995 | − | 0.427808i | ||||
\(223\) | −10.9773 | −0.735097 | −0.367548 | − | 0.930004i | \(-0.619803\pi\) | ||||
−0.367548 | + | 0.930004i | \(0.619803\pi\) | |||||||
\(224\) | 9.51456 | − | 15.6999i | 0.635718 | − | 1.04899i | ||||
\(225\) | −4.59430 | −0.306287 | ||||||||
\(226\) | 8.06623 | + | 4.65704i | 0.536558 | + | 0.309782i | ||||
\(227\) | −9.40856 | + | 5.43203i | −0.624468 | + | 0.360537i | −0.778606 | − | 0.627513i | \(-0.784073\pi\) |
0.154139 | + | 0.988049i | \(0.450740\pi\) | |||||||
\(228\) | −14.5055 | + | 8.37478i | −0.960653 | + | 0.554633i | ||||
\(229\) | 4.77603 | − | 8.27234i | 0.315609 | − | 0.546651i | −0.663958 | − | 0.747770i | \(-0.731124\pi\) |
0.979567 | + | 0.201119i | \(0.0644578\pi\) | |||||||
\(230\) | 1.74412 | 0.115004 | ||||||||
\(231\) | −11.7735 | − | 0.250109i | −0.774637 | − | 0.0164559i | ||||
\(232\) | − | 6.98779i | − | 0.458771i | ||||||
\(233\) | 8.22414 | + | 4.74821i | 0.538782 | + | 0.311066i | 0.744585 | − | 0.667528i | \(-0.232647\pi\) |
−0.205803 | + | 0.978593i | \(0.565981\pi\) | |||||||
\(234\) | −5.51183 | − | 9.54676i | −0.360319 | − | 0.624091i | ||||
\(235\) | 5.72940 | − | 3.30787i | 0.373745 | − | 0.215782i | ||||
\(236\) | −2.37692 | + | 4.11694i | −0.154724 | + | 0.267990i | ||||
\(237\) | −14.5232 | −0.943381 | ||||||||
\(238\) | 23.9316 | + | 3.83718i | 1.55125 | + | 0.248728i | ||||
\(239\) | 11.4897 | 0.743209 | 0.371605 | − | 0.928391i | \(-0.378808\pi\) | ||||
0.371605 | + | 0.928391i | \(0.378808\pi\) | |||||||
\(240\) | −0.398066 | + | 0.689470i | −0.0256950 | + | 0.0445051i | ||||
\(241\) | −11.4533 | + | 6.61255i | −0.737771 | + | 0.425952i | −0.821258 | − | 0.570557i | \(-0.806727\pi\) |
0.0834876 | + | 0.996509i | \(0.473394\pi\) | |||||||
\(242\) | 9.78827 | + | 16.9538i | 0.629214 | + | 1.08983i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | − | 22.6182i | − | 1.44798i | ||||||
\(245\) | 3.95245 | − | 2.06331i | 0.252512 | − | 0.131820i | ||||
\(246\) | −18.6755 | −1.19071 | ||||||||
\(247\) | −14.1500 | + | 24.5086i | −0.900345 | + | 1.55944i | ||||
\(248\) | 6.55427 | − | 3.78411i | 0.416196 | − | 0.240291i | ||||
\(249\) | 1.01857 | − | 0.588071i | 0.0645491 | − | 0.0372675i | ||||
\(250\) | −11.7586 | − | 6.78881i | −0.743677 | − | 0.429362i | ||||
\(251\) | 1.84848 | 0.116675 | 0.0583376 | − | 0.998297i | \(-0.481420\pi\) | ||||
0.0583376 | + | 0.998297i | \(0.481420\pi\) | |||||||
\(252\) | 3.74086 | + | 6.80938i | 0.235652 | + | 0.428950i | ||||
\(253\) | 5.48555 | 0.344873 | ||||||||
\(254\) | −19.5924 | + | 33.9351i | −1.22934 | + | 2.12927i | ||||
\(255\) | −2.60130 | − | 0.360603i | −0.162900 | − | 0.0225819i | ||||
\(256\) | 3.54842 | + | 6.14604i | 0.221776 | + | 0.384128i | ||||
\(257\) | 3.50196 | − | 6.06558i | 0.218446 | − | 0.378360i | −0.735887 | − | 0.677105i | \(-0.763234\pi\) |
0.954333 | + | 0.298744i | \(0.0965678\pi\) | |||||||
\(258\) | 6.56189i | 0.408526i | ||||||||
\(259\) | −0.186149 | + | 8.76266i | −0.0115667 | + | 0.544485i | ||||
\(260\) | − | 9.27998i | − | 0.575520i | ||||||
\(261\) | −2.90836 | − | 1.67914i | −0.180023 | − | 0.103936i | ||||
\(262\) | −23.9721 | + | 13.8403i | −1.48100 | + | 0.855056i | ||||
\(263\) | 2.41099 | + | 4.17595i | 0.148668 | + | 0.257500i | 0.930735 | − | 0.365694i | \(-0.119168\pi\) |
−0.782068 | + | 0.623194i | \(0.785835\pi\) | |||||||
\(264\) | 4.63069 | − | 8.02060i | 0.285000 | − | 0.493634i | ||||
\(265\) | 7.82371i | 0.480607i | ||||||||
\(266\) | 17.3778 | − | 28.6750i | 1.06550 | − | 1.75818i | ||||
\(267\) | 3.85927i | 0.236183i | ||||||||
\(268\) | 13.0200 | − | 22.5512i | 0.795321 | − | 1.37754i | ||||
\(269\) | 13.9286 | − | 8.04171i | 0.849244 | − | 0.490311i | −0.0111515 | − | 0.999938i | \(-0.503550\pi\) |
0.860396 | + | 0.509626i | \(0.170216\pi\) | |||||||
\(270\) | −0.707587 | − | 1.22558i | −0.0430624 | − | 0.0745862i | ||||
\(271\) | −14.1230 | + | 24.4617i | −0.857909 | + | 1.48594i | 0.0160101 | + | 0.999872i | \(0.494904\pi\) |
−0.873919 | + | 0.486071i | \(0.838430\pi\) | |||||||
\(272\) | 3.16522 | − | 4.06703i | 0.191920 | − | 0.246600i | ||||
\(273\) | 11.2263 | + | 6.80345i | 0.679448 | + | 0.411764i | ||||
\(274\) | −40.5109 | −2.44735 | ||||||||
\(275\) | −17.7094 | − | 10.2245i | −1.06792 | − | 0.616562i | ||||
\(276\) | −1.80954 | − | 3.13422i | −0.108922 | − | 0.188658i | ||||
\(277\) | 9.82327 | − | 5.67146i | 0.590223 | − | 0.340765i | −0.174963 | − | 0.984575i | \(-0.555981\pi\) |
0.765186 | + | 0.643810i | \(0.222647\pi\) | |||||||
\(278\) | −22.6898 | − | 13.0999i | −1.36084 | − | 0.785682i | ||||
\(279\) | − | 3.63723i | − | 0.217755i | ||||||
\(280\) | −0.0744728 | + | 3.50569i | −0.00445060 | + | 0.209505i | ||||
\(281\) | 0.839507 | 0.0500808 | 0.0250404 | − | 0.999686i | \(-0.492029\pi\) | ||||
0.0250404 | + | 0.999686i | \(0.492029\pi\) | |||||||
\(282\) | −19.9857 | − | 11.5387i | −1.19013 | − | 0.687122i | ||||
\(283\) | −16.1532 | + | 9.32607i | −0.960210 | + | 0.554377i | −0.896238 | − | 0.443574i | \(-0.853710\pi\) |
−0.0639721 | + | 0.997952i | \(0.520377\pi\) | |||||||
\(284\) | −23.7833 | + | 13.7313i | −1.41128 | + | 0.814803i | ||||
\(285\) | −1.81653 | + | 3.14632i | −0.107602 | + | 0.186372i | ||||
\(286\) | − | 49.0658i | − | 2.90132i | ||||||
\(287\) | 19.4912 | − | 10.7078i | 1.15053 | − | 0.632064i | ||||
\(288\) | 6.93865 | 0.408864 | ||||||||
\(289\) | 16.3590 | + | 4.62436i | 0.962291 | + | 0.272021i | ||||
\(290\) | −2.37628 | − | 4.11584i | −0.139540 | − | 0.241690i | ||||
\(291\) | −6.47173 | − | 11.2094i | −0.379379 | − | 0.657104i | ||||
\(292\) | −21.5784 | − | 12.4583i | −1.26278 | − | 0.729066i | ||||
\(293\) | −2.99309 | −0.174858 | −0.0874292 | − | 0.996171i | \(-0.527865\pi\) | ||||
−0.0874292 | + | 0.996171i | \(0.527865\pi\) | |||||||
\(294\) | −13.1267 | − | 8.34138i | −0.765565 | − | 0.486479i | ||||
\(295\) | 1.03113i | 0.0600346i | ||||||||
\(296\) | −5.96950 | − | 3.44649i | −0.346970 | − | 0.200323i | ||||
\(297\) | −2.22548 | − | 3.85464i | −0.129135 | − | 0.223669i | ||||
\(298\) | −12.4461 | − | 21.5573i | −0.720983 | − | 1.24878i | ||||
\(299\) | −5.29557 | − | 3.05740i | −0.306251 | − | 0.176814i | ||||
\(300\) | 13.4912i | 0.778916i | ||||||||
\(301\) | −3.76235 | − | 6.84849i | −0.216858 | − | 0.394740i | ||||
\(302\) | −30.3095 | −1.74411 | ||||||||
\(303\) | 4.71251 | + | 2.72077i | 0.270727 | + | 0.156304i | ||||
\(304\) | −3.56473 | − | 6.17429i | −0.204451 | − | 0.354120i | ||||
\(305\) | −2.45300 | − | 4.24872i | −0.140458 | − | 0.243281i | ||||
\(306\) | 3.44767 | + | 8.48730i | 0.197090 | + | 0.485187i | ||||
\(307\) | 25.0511 | 1.42974 | 0.714871 | − | 0.699256i | \(-0.246485\pi\) | ||||
0.714871 | + | 0.699256i | \(0.246485\pi\) | |||||||
\(308\) | −0.734447 | + | 34.5729i | −0.0418490 | + | 1.96997i | ||||
\(309\) | 11.4108i | 0.649138i | ||||||||
\(310\) | 2.57366 | − | 4.45770i | 0.146174 | − | 0.253181i | ||||
\(311\) | 1.39150 | − | 0.803381i | 0.0789045 | − | 0.0455555i | −0.460029 | − | 0.887904i | \(-0.652161\pi\) |
0.538933 | + | 0.842349i | \(0.318828\pi\) | |||||||
\(312\) | −8.94064 | + | 5.16188i | −0.506164 | + | 0.292234i | ||||
\(313\) | −8.09544 | − | 4.67390i | −0.457581 | − | 0.264185i | 0.253446 | − | 0.967350i | \(-0.418436\pi\) |
−0.711027 | + | 0.703165i | \(0.751769\pi\) | |||||||
\(314\) | 0.748749 | 0.0422543 | ||||||||
\(315\) | 1.44119 | + | 0.873401i | 0.0812020 | + | 0.0492106i | ||||
\(316\) | 42.6474i | 2.39911i | ||||||||
\(317\) | 19.3820 | + | 11.1902i | 1.08860 | + | 0.628506i | 0.933204 | − | 0.359346i | \(-0.117000\pi\) |
0.155399 | + | 0.987852i | \(0.450334\pi\) | |||||||
\(318\) | 23.6349 | − | 13.6456i | 1.32538 | − | 0.765207i | ||||
\(319\) | −7.47379 | − | 12.9450i | −0.418452 | − | 0.724780i | ||||
\(320\) | 7.12491 | + | 4.11357i | 0.398294 | + | 0.229955i | ||||
\(321\) | −12.1142 | −0.676146 | ||||||||
\(322\) | 6.19582 | + | 3.75483i | 0.345280 | + | 0.209249i | ||||
\(323\) | 14.4441 | − | 18.5594i | 0.803692 | − | 1.03268i | ||||
\(324\) | −1.46826 | + | 2.54309i | −0.0815697 | + | 0.141283i | ||||
\(325\) | 11.3974 | + | 19.7409i | 0.632213 | + | 1.09503i | ||||
\(326\) | 10.0435 | − | 5.79864i | 0.556260 | − | 0.321157i | ||||
\(327\) | 5.83720 | − | 10.1103i | 0.322798 | − | 0.559103i | ||||
\(328\) | 17.4898i | 0.965712i | ||||||||
\(329\) | 27.4745 | + | 0.583652i | 1.51472 | + | 0.0321778i | ||||
\(330\) | − | 6.29888i | − | 0.346742i | ||||||
\(331\) | −9.19545 | + | 15.9270i | −0.505427 | + | 0.875426i | 0.494553 | + | 0.869148i | \(0.335332\pi\) |
−0.999980 | + | 0.00627837i | \(0.998002\pi\) | |||||||
\(332\) | −1.72688 | − | 2.99104i | −0.0947746 | − | 0.164154i | ||||
\(333\) | −2.86890 | + | 1.65636i | −0.157215 | + | 0.0907680i | ||||
\(334\) | −37.7585 | − | 21.7999i | −2.06605 | − | 1.19284i | ||||
\(335\) | − | 5.64817i | − | 0.308593i | ||||||
\(336\) | −2.89841 | + | 1.59230i | −0.158121 | + | 0.0868670i | ||||
\(337\) | − | 11.8137i | − | 0.643535i | −0.946819 | − | 0.321768i | \(-0.895723\pi\) | ||
0.946819 | − | 0.321768i | \(-0.104277\pi\) | |||||||
\(338\) | −12.9052 | + | 22.3525i | −0.701951 | + | 1.21582i | ||||
\(339\) | −2.09604 | − | 3.63045i | −0.113841 | − | 0.197179i | ||||
\(340\) | −1.05892 | + | 7.63876i | −0.0574278 | + | 0.414270i | ||||
\(341\) | 8.09458 | − | 14.0202i | 0.438346 | − | 0.759237i | ||||
\(342\) | 12.6731 | 0.685281 | ||||||||
\(343\) | 18.4827 | + | 1.17932i | 0.997971 | + | 0.0636775i | ||||
\(344\) | 6.14528 | 0.331331 | ||||||||
\(345\) | −0.679825 | − | 0.392497i | −0.0366006 | − | 0.0211313i | ||||
\(346\) | −21.2769 | + | 12.2843i | −1.14386 | + | 0.660405i | ||||
\(347\) | 14.5661 | − | 8.40971i | 0.781947 | − | 0.451457i | −0.0551731 | − | 0.998477i | \(-0.517571\pi\) |
0.837120 | + | 0.547020i | \(0.184238\pi\) | |||||||
\(348\) | −4.93082 | + | 8.54043i | −0.264320 | + | 0.457815i | ||||
\(349\) | 26.7376 | 1.43123 | 0.715616 | − | 0.698494i | \(-0.246146\pi\) | ||||
0.715616 | + | 0.698494i | \(0.246146\pi\) | |||||||
\(350\) | −13.0038 | − | 23.6704i | −0.695082 | − | 1.26524i | ||||
\(351\) | 4.96153i | 0.264827i | ||||||||
\(352\) | 26.7460 | + | 15.4418i | 1.42557 | + | 0.823051i | ||||
\(353\) | −5.56692 | − | 9.64219i | −0.296297 | − | 0.513202i | 0.678989 | − | 0.734149i | \(-0.262419\pi\) |
−0.975286 | + | 0.220947i | \(0.929085\pi\) | |||||||
\(354\) | 3.11496 | − | 1.79843i | 0.165558 | − | 0.0955852i | ||||
\(355\) | −2.97838 | + | 5.15870i | −0.158076 | + | 0.273796i | ||||
\(356\) | 11.3328 | 0.600636 | ||||||||
\(357\) | −8.46456 | − | 6.88123i | −0.447992 | − | 0.364193i | ||||
\(358\) | −13.0416 | −0.689270 | ||||||||
\(359\) | 3.39000 | − | 5.87165i | 0.178917 | − | 0.309894i | −0.762593 | − | 0.646879i | \(-0.776074\pi\) |
0.941510 | + | 0.336985i | \(0.109407\pi\) | |||||||
\(360\) | −1.14777 | + | 0.662663i | −0.0604926 | + | 0.0349254i | ||||
\(361\) | −6.76723 | − | 11.7212i | −0.356170 | − | 0.616904i | ||||
\(362\) | 22.4528 | + | 12.9631i | 1.18009 | + | 0.681328i | ||||
\(363\) | − | 8.81102i | − | 0.462458i | ||||||
\(364\) | 19.9784 | − | 32.9662i | 1.04715 | − | 1.72790i | ||||
\(365\) | −5.40452 | −0.282885 | ||||||||
\(366\) | −8.55672 | + | 14.8207i | −0.447267 | + | 0.774689i | ||||
\(367\) | 23.9881 | − | 13.8495i | 1.25217 | − | 0.722940i | 0.280629 | − | 0.959816i | \(-0.409457\pi\) |
0.971540 | + | 0.236876i | \(0.0761236\pi\) | |||||||
\(368\) | 1.33408 | − | 0.770232i | 0.0695437 | − | 0.0401511i | ||||
\(369\) | 7.27935 | + | 4.20274i | 0.378948 | + | 0.218786i | ||||
\(370\) | −4.68808 | −0.243722 | ||||||||
\(371\) | −16.8433 | + | 27.7930i | −0.874459 | + | 1.44294i | ||||
\(372\) | −10.6808 | −0.553772 | ||||||||
\(373\) | 14.3114 | − | 24.7881i | 0.741016 | − | 1.28348i | −0.211018 | − | 0.977482i | \(-0.567678\pi\) |
0.952033 | − | 0.305994i | \(-0.0989889\pi\) | |||||||
\(374\) | −5.59878 | + | 40.3882i | −0.289506 | + | 2.08842i | ||||
\(375\) | 3.05551 | + | 5.29230i | 0.157786 | + | 0.273293i | ||||
\(376\) | −10.8062 | + | 18.7168i | −0.557285 | + | 0.965246i | ||||
\(377\) | 16.6622i | 0.858148i | ||||||||
\(378\) | 0.124849 | − | 5.87707i | 0.00642154 | − | 0.302284i | ||||
\(379\) | 27.2491i | 1.39969i | 0.714294 | + | 0.699845i | \(0.246748\pi\) | ||||
−0.714294 | + | 0.699845i | \(0.753252\pi\) | |||||||
\(380\) | 9.23919 | + | 5.33425i | 0.473960 | + | 0.273641i | ||||
\(381\) | 15.2735 | − | 8.81816i | 0.782485 | − | 0.451768i | ||||
\(382\) | 17.5140 | + | 30.3352i | 0.896095 | + | 1.55208i | ||||
\(383\) | −17.7384 | + | 30.7238i | −0.906391 | + | 1.56991i | −0.0873512 | + | 0.996178i | \(0.527840\pi\) |
−0.819039 | + | 0.573737i | \(0.805493\pi\) | |||||||
\(384\) | − | 14.8212i | − | 0.756340i | ||||||
\(385\) | 3.61155 | + | 6.57399i | 0.184061 | + | 0.335042i | ||||
\(386\) | 4.05428i | 0.206358i | ||||||||
\(387\) | 1.47669 | − | 2.55770i | 0.0750643 | − | 0.130015i | ||||
\(388\) | −32.9164 | + | 19.0043i | −1.67108 | + | 0.964797i | ||||
\(389\) | −8.97450 | − | 15.5443i | −0.455025 | − | 0.788126i | 0.543665 | − | 0.839303i | \(-0.317036\pi\) |
−0.998690 | + | 0.0511761i | \(0.983703\pi\) | |||||||
\(390\) | −3.51071 | + | 6.08074i | −0.177772 | + | 0.307910i | ||||
\(391\) | 4.01014 | + | 3.12094i | 0.202802 | + | 0.157833i | ||||
\(392\) | −7.81179 | + | 12.2933i | −0.394555 | + | 0.620905i | ||||
\(393\) | 12.4585 | 0.628447 | ||||||||
\(394\) | −33.7506 | − | 19.4859i | −1.70033 | − | 0.981686i | ||||
\(395\) | 4.62521 | + | 8.01110i | 0.232720 | + | 0.403082i | ||||
\(396\) | −11.3192 | + | 6.53514i | −0.568811 | + | 0.328403i | ||||
\(397\) | −14.5890 | − | 8.42296i | −0.732201 | − | 0.422736i | 0.0870261 | − | 0.996206i | \(-0.472264\pi\) |
−0.819227 | + | 0.573470i | \(0.805597\pi\) | |||||||
\(398\) | 27.1082i | 1.35881i | ||||||||
\(399\) | −13.2266 | + | 7.26627i | −0.662157 | + | 0.363769i | ||||
\(400\) | −5.74255 | −0.287127 | ||||||||
\(401\) | −27.4843 | − | 15.8681i | −1.37250 | − | 0.792413i | −0.381257 | − | 0.924469i | \(-0.624509\pi\) |
−0.991242 | + | 0.132056i | \(0.957842\pi\) | |||||||
\(402\) | −17.0627 | + | 9.85118i | −0.851012 | + | 0.491332i | ||||
\(403\) | −15.6285 | + | 9.02311i | −0.778510 | + | 0.449473i | ||||
\(404\) | 7.98957 | − | 13.8383i | 0.397496 | − | 0.688483i | ||||
\(405\) | 0.636942i | 0.0316499i | ||||||||
\(406\) | 0.419279 | − | 19.7369i | 0.0208084 | − | 0.979525i | ||||
\(407\) | −14.7448 | −0.730872 | ||||||||
\(408\) | 7.94845 | − | 3.22878i | 0.393507 | − | 0.159848i | ||||
\(409\) | −7.11957 | − | 12.3315i | −0.352040 | − | 0.609751i | 0.634567 | − | 0.772868i | \(-0.281179\pi\) |
−0.986607 | + | 0.163117i | \(0.947845\pi\) | |||||||
\(410\) | 5.94760 | + | 10.3016i | 0.293731 | + | 0.508757i | ||||
\(411\) | 15.7904 | + | 9.11657i | 0.778882 | + | 0.449687i | ||||
\(412\) | 33.5080 | 1.65082 | ||||||||
\(413\) | −2.21986 | + | 3.66298i | −0.109232 | + | 0.180243i | ||||
\(414\) | 2.73827i | 0.134579i | ||||||||
\(415\) | −0.648769 | − | 0.374567i | −0.0318468 | − | 0.0183868i | ||||
\(416\) | −17.2131 | − | 29.8140i | −0.843944 | − | 1.46175i | ||||
\(417\) | 5.89602 | + | 10.2122i | 0.288729 | + | 0.500094i | ||||
\(418\) | 48.8501 | + | 28.2036i | 2.38934 | + | 1.37949i | ||||
\(419\) | 2.91045i | 0.142185i | 0.997470 | + | 0.0710923i | \(0.0226485\pi\) | ||||
−0.997470 | + | 0.0710923i | \(0.977352\pi\) | |||||||
\(420\) | 2.56475 | − | 4.23208i | 0.125147 | − | 0.206504i | ||||
\(421\) | 0.521247 | 0.0254040 | 0.0127020 | − | 0.999919i | \(-0.495957\pi\) | ||||
0.0127020 | + | 0.999919i | \(0.495957\pi\) | |||||||
\(422\) | 7.21195 | + | 4.16382i | 0.351072 | + | 0.202692i | ||||
\(423\) | 5.19336 | + | 8.99516i | 0.252510 | + | 0.437360i | ||||
\(424\) | −12.7793 | − | 22.1343i | −0.620615 | − | 1.07494i | ||||
\(425\) | −7.12911 | − | 17.5501i | −0.345813 | − | 0.851304i | ||||
\(426\) | 20.7788 | 1.00674 | ||||||||
\(427\) | 0.432815 | − | 20.3741i | 0.0209454 | − | 0.985971i | ||||
\(428\) | 35.5734i | 1.71950i | ||||||||
\(429\) | −11.0418 | + | 19.1249i | −0.533102 | + | 0.923360i | ||||
\(430\) | 3.61959 | − | 2.08977i | 0.174552 | − | 0.100778i | ||||
\(431\) | −21.6103 | + | 12.4767i | −1.04093 | + | 0.600981i | −0.920097 | − | 0.391691i | \(-0.871890\pi\) |
−0.120834 | + | 0.992673i | \(0.538557\pi\) | |||||||
\(432\) | −1.08247 | − | 0.624963i | −0.0520803 | − | 0.0300686i | ||||
\(433\) | −8.79699 | −0.422756 | −0.211378 | − | 0.977404i | \(-0.567795\pi\) | ||||
−0.211378 | + | 0.977404i | \(0.567795\pi\) | |||||||
\(434\) | 18.7394 | − | 10.2949i | 0.899522 | − | 0.494169i | ||||
\(435\) | 2.13903i | 0.102559i | ||||||||
\(436\) | −29.6891 | − | 17.1410i | −1.42185 | − | 0.820906i | ||||
\(437\) | 6.08792 | − | 3.51486i | 0.291225 | − | 0.168139i | ||||
\(438\) | 9.42621 | + | 16.3267i | 0.450402 | + | 0.780119i | ||||
\(439\) | 3.85640 | + | 2.22649i | 0.184056 | + | 0.106265i | 0.589197 | − | 0.807989i | \(-0.299444\pi\) |
−0.405141 | + | 0.914254i | \(0.632778\pi\) | |||||||
\(440\) | −5.89897 | −0.281222 | ||||||||
\(441\) | 3.23940 | + | 6.20535i | 0.154257 | + | 0.295493i | ||||
\(442\) | 27.9155 | − | 35.8690i | 1.32780 | − | 1.70611i | ||||
\(443\) | 15.5992 | − | 27.0186i | 0.741141 | − | 1.28369i | −0.210835 | − | 0.977522i | \(-0.567618\pi\) |
0.951976 | − | 0.306173i | \(-0.0990485\pi\) | |||||||
\(444\) | 4.86392 | + | 8.42456i | 0.230831 | + | 0.399812i | ||||
\(445\) | 2.12880 | − | 1.22906i | 0.100915 | − | 0.0582632i | ||||
\(446\) | 12.1949 | − | 21.1221i | 0.577444 | − | 1.00016i | ||||
\(447\) | 11.2035i | 0.529906i | ||||||||
\(448\) | 16.4546 | + | 29.9519i | 0.777409 | + | 1.41509i | ||||
\(449\) | − | 35.1190i | − | 1.65737i | −0.559716 | − | 0.828685i | \(-0.689090\pi\) | ||
0.559716 | − | 0.828685i | \(-0.310910\pi\) | |||||||
\(450\) | 5.10387 | − | 8.84017i | 0.240599 | − | 0.416729i | ||||
\(451\) | 18.7062 | + | 32.4001i | 0.880840 | + | 1.52566i | ||||
\(452\) | −10.6609 | + | 6.15505i | −0.501445 | + | 0.289509i | ||||
\(453\) | 11.8141 | + | 6.82085i | 0.555073 | + | 0.320471i | ||||
\(454\) | − | 24.1381i | − | 1.13286i | ||||||
\(455\) | 0.177579 | − | 8.35923i | 0.00832501 | − | 0.391887i | ||||
\(456\) | − | 11.8685i | − | 0.555792i | ||||||
\(457\) | 4.26769 | − | 7.39186i | 0.199634 | − | 0.345777i | −0.748776 | − | 0.662824i | \(-0.769358\pi\) |
0.948410 | + | 0.317047i | \(0.102691\pi\) | |||||||
\(458\) | 10.6115 | + | 18.3797i | 0.495844 | + | 0.858826i | ||||
\(459\) | 0.566148 | − | 4.08405i | 0.0264255 | − | 0.190627i | ||||
\(460\) | −1.15257 | + | 1.99631i | −0.0537390 | + | 0.0930786i | ||||
\(461\) | 16.5716 | 0.771819 | 0.385909 | − | 0.922537i | \(-0.373888\pi\) | ||||
0.385909 | + | 0.922537i | \(0.373888\pi\) | |||||||
\(462\) | 13.5605 | − | 22.3762i | 0.630894 | − | 1.04103i | ||||
\(463\) | −9.46742 | −0.439989 | −0.219994 | − | 0.975501i | \(-0.570604\pi\) | ||||
−0.219994 | + | 0.975501i | \(0.570604\pi\) | |||||||
\(464\) | −3.63524 | − | 2.09880i | −0.168762 | − | 0.0974346i | ||||
\(465\) | −2.00632 | + | 1.15835i | −0.0930411 | + | 0.0537173i | ||||
\(466\) | −18.2726 | + | 10.5497i | −0.846463 | + | 0.488705i | ||||
\(467\) | −4.59009 | + | 7.95027i | −0.212404 | + | 0.367895i | −0.952466 | − | 0.304644i | \(-0.901463\pi\) |
0.740062 | + | 0.672538i | \(0.234796\pi\) | |||||||
\(468\) | 14.5696 | 0.673479 | ||||||||
\(469\) | 12.1597 | − | 20.0646i | 0.561482 | − | 0.926497i | ||||
\(470\) | 14.6990i | 0.678015i | ||||||||
\(471\) | −0.291848 | − | 0.168499i | −0.0134476 | − | 0.00776400i | ||||
\(472\) | −1.68424 | − | 2.91720i | −0.0775236 | − | 0.134275i | ||||
\(473\) | 11.3842 | − | 6.57268i | 0.523447 | − | 0.302212i | ||||
\(474\) | 16.1340 | − | 27.9449i | 0.741058 | − | 1.28355i | ||||
\(475\) | −26.2054 | −1.20239 | ||||||||
\(476\) | −20.2068 | + | 24.8563i | −0.926177 | + | 1.13928i | ||||
\(477\) | −12.2832 | −0.562411 | ||||||||
\(478\) | −12.7641 | + | 22.1081i | −0.583816 | + | 1.01120i | ||||
\(479\) | −17.4440 | + | 10.0713i | −0.797037 | + | 0.460169i | −0.842434 | − | 0.538800i | \(-0.818878\pi\) |
0.0453972 | + | 0.998969i | \(0.485545\pi\) | |||||||
\(480\) | −2.20976 | − | 3.82741i | −0.100861 | − | 0.174697i | ||||
\(481\) | 14.2341 | + | 8.21808i | 0.649021 | + | 0.374712i | ||||
\(482\) | − | 29.3839i | − | 1.33840i | ||||||
\(483\) | −1.57003 | − | 2.85787i | −0.0714386 | − | 0.130038i | ||||
\(484\) | −25.8736 | −1.17607 | ||||||||
\(485\) | −4.12212 | + | 7.13971i | −0.187176 | + | 0.324198i | ||||
\(486\) | 1.92416 | − | 1.11091i | 0.0872816 | − | 0.0503920i | ||||
\(487\) | −4.67401 | + | 2.69854i | −0.211800 | + | 0.122283i | −0.602148 | − | 0.798385i | \(-0.705688\pi\) |
0.390348 | + | 0.920667i | \(0.372355\pi\) | |||||||
\(488\) | 13.8797 | + | 8.01345i | 0.628305 | + | 0.362752i | ||||
\(489\) | −5.21971 | −0.236043 | ||||||||
\(490\) | −0.420694 | + | 9.89728i | −0.0190050 | + | 0.447114i | ||||
\(491\) | −4.61469 | −0.208258 | −0.104129 | − | 0.994564i | \(-0.533206\pi\) | ||||
−0.104129 | + | 0.994564i | \(0.533206\pi\) | |||||||
\(492\) | 12.3414 | − | 21.3759i | 0.556392 | − | 0.963700i | ||||
\(493\) | 1.90129 | − | 13.7154i | 0.0856296 | − | 0.617711i | ||||
\(494\) | −31.4389 | − | 54.4538i | −1.41450 | − | 2.44999i | ||||
\(495\) | −1.41750 | + | 2.45518i | −0.0637119 | + | 0.110352i | ||||
\(496\) | − | 4.54627i | − | 0.204134i | ||||||
\(497\) | −21.6863 | + | 11.9138i | −0.972765 | + | 0.534407i | ||||
\(498\) | 2.61318i | 0.117099i | ||||||||
\(499\) | 35.0782 | + | 20.2524i | 1.57031 | + | 0.906621i | 0.996130 | + | 0.0878956i | \(0.0280142\pi\) |
0.574185 | + | 0.818726i | \(0.305319\pi\) | |||||||
\(500\) | 15.5409 | − | 8.97253i | 0.695009 | − | 0.401264i | ||||
\(501\) | 9.81170 | + | 16.9944i | 0.438354 | + | 0.759252i | ||||
\(502\) | −2.05350 | + | 3.55677i | −0.0916523 | + | 0.158746i | ||||
\(503\) | 0.342609i | 0.0152762i | 0.999971 | + | 0.00763808i | \(0.00243130\pi\) | ||||
−0.999971 | + | 0.00763808i | \(0.997569\pi\) | |||||||
\(504\) | −5.50394 | − | 0.116922i | −0.245165 | − | 0.00520814i | ||||
\(505\) | − | 3.46595i | − | 0.154233i | ||||||
\(506\) | −6.09397 | + | 10.5551i | −0.270910 | + | 0.469230i | ||||
\(507\) | 10.0604 | − | 5.80838i | 0.446799 | − | 0.257959i | ||||
\(508\) | −25.8946 | − | 44.8508i | −1.14889 | − | 1.98993i | ||||
\(509\) | 9.05619 | − | 15.6858i | 0.401409 | − | 0.695260i | −0.592488 | − | 0.805580i | \(-0.701854\pi\) |
0.993896 | + | 0.110320i | \(0.0351874\pi\) | |||||||
\(510\) | 3.58368 | − | 4.60472i | 0.158688 | − | 0.203900i | ||||
\(511\) | −19.1990 | − | 11.6351i | −0.849315 | − | 0.514707i | ||||
\(512\) | 13.8744 | 0.613168 | ||||||||
\(513\) | −4.93972 | − | 2.85195i | −0.218094 | − | 0.125917i | ||||
\(514\) | 7.78075 | + | 13.4767i | 0.343194 | + | 0.594430i | ||||
\(515\) | 6.29429 | − | 3.63401i | 0.277360 | − | 0.160134i | ||||
\(516\) | −7.51071 | − | 4.33631i | −0.330641 | − | 0.190896i | ||||
\(517\) | 46.2308i | 2.03323i | ||||||||
\(518\) | −16.6539 | − | 10.0927i | −0.731732 | − | 0.443449i | ||||
\(519\) | 11.0578 | 0.485383 | ||||||||
\(520\) | 5.69467 | + | 3.28782i | 0.249728 | + | 0.144180i | ||||
\(521\) | 1.69820 | − | 0.980458i | 0.0743996 | − | 0.0429546i | −0.462339 | − | 0.886703i | \(-0.652990\pi\) |
0.536738 | + | 0.843749i | \(0.319656\pi\) | |||||||
\(522\) | 6.46187 | − | 3.73076i | 0.282828 | − | 0.163291i | ||||
\(523\) | −17.6024 | + | 30.4883i | −0.769700 | + | 1.33316i | 0.168026 | + | 0.985783i | \(0.446261\pi\) |
−0.937726 | + | 0.347377i | \(0.887073\pi\) | |||||||
\(524\) | − | 36.5845i | − | 1.59820i | ||||||
\(525\) | −0.258164 | + | 12.1526i | −0.0112672 | + | 0.530385i | ||||
\(526\) | −10.7136 | −0.467134 | ||||||||
\(527\) | 13.8941 | − | 5.64399i | 0.605236 | − | 0.245856i | ||||
\(528\) | −2.78169 | − | 4.81802i | −0.121057 | − | 0.209677i | ||||
\(529\) | −10.7405 | − | 18.6032i | −0.466980 | − | 0.808833i | ||||
\(530\) | −15.0540 | − | 8.69146i | −0.653906 | − | 0.377533i | ||||
\(531\) | −1.61887 | −0.0702530 | ||||||||
\(532\) | 21.3375 | + | 38.8400i | 0.925097 | + | 1.68393i | ||||
\(533\) | − | 41.7040i | − | 1.80640i | ||||||
\(534\) | −7.42584 | − | 4.28731i | −0.321347 | − | 0.185530i | ||||
\(535\) | 3.85801 | + | 6.68227i | 0.166796 | + | 0.288900i | ||||
\(536\) | 9.22573 | + | 15.9794i | 0.398491 | + | 0.690207i | ||||
\(537\) | 5.08337 | + | 2.93488i | 0.219364 | + | 0.126650i | ||||
\(538\) | 35.7345i | 1.54063i | ||||||||
\(539\) | −1.32315 | + | 31.1286i | −0.0569922 | + | 1.34080i | ||||
\(540\) | 1.87039 | 0.0804886 | ||||||||
\(541\) | −15.6944 | − | 9.06116i | −0.674754 | − | 0.389570i | 0.123121 | − | 0.992392i | \(-0.460710\pi\) |
−0.797876 | + | 0.602822i | \(0.794043\pi\) | |||||||
\(542\) | −31.3788 | − | 54.3496i | −1.34783 | − | 2.33452i | ||||
\(543\) | −5.83446 | − | 10.1056i | −0.250380 | − | 0.433672i | ||||
\(544\) | 10.7669 | + | 26.5054i | 0.461626 | + | 1.13641i | ||||
\(545\) | −7.43592 | −0.318520 | ||||||||
\(546\) | −25.5624 | + | 14.0432i | −1.09397 | + | 0.600993i | ||||
\(547\) | − | 3.48512i | − | 0.149013i | −0.997221 | − | 0.0745065i | \(-0.976262\pi\) | ||
0.997221 | − | 0.0745065i | \(-0.0237382\pi\) | |||||||
\(548\) | 26.7709 | − | 46.3686i | 1.14360 | − | 1.98077i | ||||
\(549\) | 6.67049 | − | 3.85121i | 0.284690 | − | 0.164366i | ||||
\(550\) | 39.3472 | − | 22.7171i | 1.67777 | − | 0.968661i | ||||
\(551\) | −16.5890 | − | 9.57766i | −0.706715 | − | 0.408022i | ||||
\(552\) | 2.56442 | 0.109149 | ||||||||
\(553\) | −0.816087 | + | 38.4160i | −0.0347036 | + | 1.63362i | ||||
\(554\) | 25.2020i | 1.07073i | ||||||||
\(555\) | 1.82732 | + | 1.05501i | 0.0775656 | + | 0.0447825i | ||||
\(556\) | 29.9883 | − | 17.3137i | 1.27179 | − | 0.734266i | ||||
\(557\) | 11.3343 | + | 19.6315i | 0.480249 | + | 0.831815i | 0.999743 | − | 0.0226584i | \(-0.00721302\pi\) |
−0.519494 | + | 0.854474i | \(0.673880\pi\) | |||||||
\(558\) | 6.99860 | + | 4.04065i | 0.296274 | + | 0.171054i | ||||
\(559\) | −14.6533 | −0.619767 | ||||||||
\(560\) | 1.80139 | + | 1.09169i | 0.0761224 | + | 0.0461322i | ||||
\(561\) | 11.2713 | − | 14.4826i | 0.475873 | − | 0.611456i | ||||
\(562\) | −0.932619 | + | 1.61534i | −0.0393402 | + | 0.0681392i | ||||
\(563\) | −4.36066 | − | 7.55289i | −0.183780 | − | 0.318316i | 0.759385 | − | 0.650642i | \(-0.225500\pi\) |
−0.943165 | + | 0.332326i | \(0.892167\pi\) | |||||||
\(564\) | 26.4144 | − | 15.2504i | 1.11225 | − | 0.642156i | ||||
\(565\) | −1.33506 | + | 2.31239i | −0.0561663 | + | 0.0972829i | ||||
\(566\) | − | 41.4418i | − | 1.74193i | ||||||
\(567\) | −1.37124 | + | 2.26267i | −0.0575867 | + | 0.0950234i | ||||
\(568\) | − | 19.4595i | − | 0.816505i | ||||||
\(569\) | 18.9894 | − | 32.8906i | 0.796078 | − | 1.37885i | −0.126074 | − | 0.992021i | \(-0.540238\pi\) |
0.922152 | − | 0.386827i | \(-0.126429\pi\) | |||||||
\(570\) | −4.03601 | − | 6.99057i | −0.169050 | − | 0.292803i | ||||
\(571\) | 35.6117 | − | 20.5604i | 1.49030 | − | 0.860426i | 0.490363 | − | 0.871518i | \(-0.336864\pi\) |
0.999938 | + | 0.0110921i | \(0.00353079\pi\) | |||||||
\(572\) | 56.1605 | + | 32.4243i | 2.34819 | + | 1.35573i | ||||
\(573\) | − | 15.7654i | − | 0.658610i | ||||||
\(574\) | −1.04942 | + | 49.3996i | −0.0438017 | + | 2.06190i | ||||
\(575\) | − | 5.66222i | − | 0.236131i | ||||||
\(576\) | −6.45831 | + | 11.1861i | −0.269096 | + | 0.466088i | ||||
\(577\) | −11.7385 | − | 20.3316i | −0.488679 | − | 0.846417i | 0.511236 | − | 0.859440i | \(-0.329188\pi\) |
−0.999915 | + | 0.0130235i | \(0.995854\pi\) | |||||||
\(578\) | −27.0714 | + | 26.3399i | −1.12602 | + | 1.09560i | ||||
\(579\) | 0.912377 | − | 1.58028i | 0.0379171 | − | 0.0656743i | ||||
\(580\) | 6.28129 | 0.260816 | ||||||||
\(581\) | −1.49830 | − | 2.72732i | −0.0621600 | − | 0.113148i | ||||
\(582\) | 28.7581 | 1.19206 | ||||||||
\(583\) | −47.3475 | − | 27.3361i | −1.96093 | − | 1.13214i | ||||
\(584\) | 15.2901 | − | 8.82774i | 0.632709 | − | 0.365295i | ||||
\(585\) | 2.73682 | − | 1.58010i | 0.113154 | − | 0.0653292i | ||||
\(586\) | 3.32507 | − | 5.75918i | 0.137357 | − | 0.237910i | ||||
\(587\) | −23.3181 | −0.962443 | −0.481221 | − | 0.876599i | \(-0.659807\pi\) | ||||
−0.481221 | + | 0.876599i | \(0.659807\pi\) | |||||||
\(588\) | 18.2221 | − | 9.51252i | 0.751465 | − | 0.392290i | ||||
\(589\) | − | 20.7464i | − | 0.854840i | ||||||
\(590\) | −1.98405 | − | 1.14549i | −0.0816821 | − | 0.0471592i | ||||
\(591\) | 8.77022 | + | 15.1905i | 0.360759 | + | 0.624852i | ||||
\(592\) | −3.58592 | + | 2.07033i | −0.147380 | + | 0.0850900i | ||||
\(593\) | −7.23725 | + | 12.5353i | −0.297198 | + | 0.514763i | −0.975494 | − | 0.220026i | \(-0.929386\pi\) |
0.678295 | + | 0.734789i | \(0.262719\pi\) | |||||||
\(594\) | 9.88925 | 0.405761 | ||||||||
\(595\) | −1.10002 | + | 6.86059i | −0.0450966 | + | 0.281257i | ||||
\(596\) | 32.8991 | 1.34760 | ||||||||
\(597\) | 6.10043 | − | 10.5663i | 0.249674 | − | 0.432448i | ||||
\(598\) | 11.7658 | − | 6.79301i | 0.481141 | − | 0.277787i | ||||
\(599\) | 0.156806 | + | 0.271596i | 0.00640692 | + | 0.0110971i | 0.869211 | − | 0.494441i | \(-0.164627\pi\) |
−0.862804 | + | 0.505538i | \(0.831294\pi\) | |||||||
\(600\) | −8.27891 | − | 4.77983i | −0.337985 | − | 0.195136i | ||||
\(601\) | 39.9343i | 1.62896i | 0.580195 | + | 0.814478i | \(0.302976\pi\) | ||||
−0.580195 | + | 0.814478i | \(0.697024\pi\) | |||||||
\(602\) | 17.3572 | + | 0.368726i | 0.707427 | + | 0.0150282i | ||||
\(603\) | 8.86764 | 0.361118 | ||||||||
\(604\) | 20.0295 | − | 34.6921i | 0.814989 | − | 1.41160i | ||||
\(605\) | −4.86023 | + | 2.80605i | −0.197596 | + | 0.114082i | ||||
\(606\) | −10.4704 | + | 6.04508i | −0.425330 | + | 0.245564i | ||||
\(607\) | −7.80981 | − | 4.50900i | −0.316990 | − | 0.183015i | 0.333060 | − | 0.942906i | \(-0.391919\pi\) |
−0.650050 | + | 0.759891i | \(0.725252\pi\) | |||||||
\(608\) | 39.5773 | 1.60507 | ||||||||
\(609\) | −4.60502 | + | 7.59871i | −0.186605 | + | 0.307915i | ||||
\(610\) | 10.9003 | 0.441339 | ||||||||
\(611\) | 25.7670 | − | 44.6298i | 1.04242 | − | 1.80553i | ||||
\(612\) | −11.9929 | − | 1.66250i | −0.484783 | − | 0.0672026i | ||||
\(613\) | 9.03406 | + | 15.6475i | 0.364882 | + | 0.631995i | 0.988757 | − | 0.149529i | \(-0.0477759\pi\) |
−0.623875 | + | 0.781524i | \(0.714443\pi\) | |||||||
\(614\) | −27.8296 | + | 48.2023i | −1.12311 | + | 1.94529i | ||||
\(615\) | − | 5.35380i | − | 0.215886i | ||||||
\(616\) | −20.9555 | − | 12.6996i | −0.844322 | − | 0.511681i | ||||
\(617\) | 44.6374i | 1.79703i | 0.438938 | + | 0.898517i | \(0.355355\pi\) | ||||
−0.438938 | + | 0.898517i | \(0.644645\pi\) | |||||||
\(618\) | −21.9562 | − | 12.6764i | −0.883208 | − | 0.509920i | ||||
\(619\) | −29.1522 | + | 16.8310i | −1.17173 | + | 0.676496i | −0.954086 | − | 0.299533i | \(-0.903169\pi\) |
−0.217639 | + | 0.976029i | \(0.569836\pi\) | |||||||
\(620\) | 3.40151 | + | 5.89159i | 0.136608 | + | 0.236612i | ||||
\(621\) | 0.616221 | − | 1.06733i | 0.0247281 | − | 0.0428303i | ||||
\(622\) | 3.56994i | 0.143142i | ||||||||
\(623\) | 10.2084 | + | 0.216860i | 0.408989 | + | 0.00868832i | ||||
\(624\) | 6.20155i | 0.248261i | ||||||||
\(625\) | −9.53958 | + | 16.5230i | −0.381583 | + | 0.660922i | ||||
\(626\) | 17.9867 | − | 10.3846i | 0.718891 | − | 0.415052i | ||||
\(627\) | −12.6939 | − | 21.9865i | −0.506946 | − | 0.878056i | ||||
\(628\) | −0.494798 | + | 0.857015i | −0.0197446 | + | 0.0341986i | ||||
\(629\) | −10.7790 | − | 8.38888i | −0.429787 | − | 0.334487i | ||||
\(630\) | −3.28160 | + | 1.80281i | −0.130742 | + | 0.0718257i | ||||
\(631\) | 46.1081 | 1.83553 | 0.917767 | − | 0.397120i | \(-0.129990\pi\) | ||||
0.917767 | + | 0.397120i | \(0.129990\pi\) | |||||||
\(632\) | −26.1707 | − | 15.1096i | −1.04101 | − | 0.601029i | ||||
\(633\) | −1.87405 | − | 3.24596i | −0.0744869 | − | 0.129015i | ||||
\(634\) | −43.0635 | + | 24.8627i | −1.71027 | + | 0.987425i | ||||
\(635\) | −9.72833 | − | 5.61666i | −0.386057 | − | 0.222890i | ||||
\(636\) | 36.0698i | 1.43026i | ||||||||
\(637\) | 18.6270 | − | 29.3131i | 0.738029 | − | 1.16143i | ||||
\(638\) | 33.2109 | 1.31483 | ||||||||
\(639\) | −8.09917 | − | 4.67606i | −0.320398 | − | 0.184982i | ||||
\(640\) | −8.17548 | + | 4.72011i | −0.323164 | + | 0.186579i | ||||
\(641\) | −31.3749 | + | 18.1143i | −1.23924 | + | 0.715473i | −0.968938 | − | 0.247304i | \(-0.920455\pi\) |
−0.270298 | + | 0.962777i | \(0.587122\pi\) | |||||||
\(642\) | 13.4578 | − | 23.3096i | 0.531136 | − | 0.919955i | ||||
\(643\) | − | 42.9418i | − | 1.69346i | −0.532022 | − | 0.846731i | \(-0.678568\pi\) | ||
0.532022 | − | 0.846731i | \(-0.321432\pi\) | |||||||
\(644\) | −8.39217 | + | 4.61040i | −0.330698 | + | 0.181675i | ||||
\(645\) | −1.88113 | −0.0740694 | ||||||||
\(646\) | 19.6651 | + | 48.4107i | 0.773715 | + | 1.90469i | ||||
\(647\) | 11.9012 | + | 20.6134i | 0.467884 | + | 0.810398i | 0.999326 | − | 0.0366959i | \(-0.0116833\pi\) |
−0.531443 | + | 0.847094i | \(0.678350\pi\) | |||||||
\(648\) | −1.04038 | − | 1.80199i | −0.0408701 | − | 0.0707890i | ||||
\(649\) | −6.24017 | − | 3.60276i | −0.244948 | − | 0.141421i | ||||
\(650\) | −50.6460 | −1.98650 | ||||||||
\(651\) | −9.62103 | − | 0.204384i | −0.377078 | − | 0.00801042i | ||||
\(652\) | 15.3277i | 0.600280i | ||||||||
\(653\) | −16.8061 | − | 9.70301i | −0.657673 | − | 0.379708i | 0.133716 | − | 0.991020i | \(-0.457309\pi\) |
−0.791390 | + | 0.611312i | \(0.790642\pi\) | |||||||
\(654\) | 12.9693 | + | 22.4634i | 0.507138 | + | 0.878389i | ||||
\(655\) | −3.96766 | − | 6.87220i | −0.155029 | − | 0.268519i | ||||
\(656\) | 9.09866 | + | 5.25311i | 0.355243 | + | 0.205100i | ||||
\(657\) | − | 8.48510i | − | 0.331035i | ||||||
\(658\) | −31.6448 | + | 52.2168i | −1.23364 | + | 2.03562i | ||||
\(659\) | −5.28871 | −0.206019 | −0.103009 | − | 0.994680i | \(-0.532847\pi\) | ||||
−0.103009 | + | 0.994680i | \(0.532847\pi\) | |||||||
\(660\) | 7.20967 | + | 4.16251i | 0.280636 | + | 0.162025i | ||||
\(661\) | 4.45043 | + | 7.70836i | 0.173102 | + | 0.299821i | 0.939503 | − | 0.342542i | \(-0.111288\pi\) |
−0.766401 | + | 0.642362i | \(0.777954\pi\) | |||||||
\(662\) | −20.4307 | − | 35.3870i | −0.794061 | − | 1.37535i | ||||
\(663\) | −18.9529 | + | 7.69894i | −0.736069 | + | 0.299002i | ||||
\(664\) | 2.44727 | 0.0949726 | ||||||||
\(665\) | 8.22042 | + | 4.98179i | 0.318774 | + | 0.193186i | ||||
\(666\) | − | 7.36029i | − | 0.285205i | ||||||
\(667\) | 2.06945 | − | 3.58439i | 0.0801293 | − | 0.138788i | ||||
\(668\) | 49.9041 | − | 28.8122i | 1.93085 | − | 1.11478i | ||||
\(669\) | −9.50665 | + | 5.48867i | −0.367548 | + | 0.212204i | ||||
\(670\) | 10.8680 | + | 6.27463i | 0.419867 | + | 0.242410i | ||||
\(671\) | 34.2831 | 1.32349 | ||||||||
\(672\) | 0.389897 | − | 18.3538i | 0.0150406 | − | 0.708013i | ||||
\(673\) | 25.1549i | 0.969650i | 0.874611 | + | 0.484825i | \(0.161117\pi\) | ||||
−0.874611 | + | 0.484825i | \(0.838883\pi\) | |||||||
\(674\) | 22.7315 | + | 13.1240i | 0.875584 | + | 0.505519i | ||||
\(675\) | −3.97878 | + | 2.29715i | −0.153143 | + | 0.0884174i | ||||
\(676\) | −17.0564 | − | 29.5425i | −0.656015 | − | 1.13625i | ||||
\(677\) | −20.9761 | − | 12.1106i | −0.806178 | − | 0.465447i | 0.0394489 | − | 0.999222i | \(-0.487440\pi\) |
−0.845627 | + | 0.533775i | \(0.820773\pi\) | |||||||
\(678\) | 9.31408 | 0.357705 | ||||||||
\(679\) | −30.0142 | + | 16.4888i | −1.15184 | + | 0.632784i | ||||
\(680\) | −4.31237 | − | 3.35615i | −0.165372 | − | 0.128703i | ||||
\(681\) | −5.43203 | + | 9.40856i | −0.208156 | + | 0.360537i | ||||
\(682\) | 17.9847 | + | 31.1505i | 0.688671 | + | 1.19281i | ||||
\(683\) | 10.2643 | − | 5.92609i | 0.392752 | − | 0.226756i | −0.290600 | − | 0.956845i | \(-0.593855\pi\) |
0.683352 | + | 0.730089i | \(0.260521\pi\) | |||||||
\(684\) | −8.37478 | + | 14.5055i | −0.320218 | + | 0.554633i | ||||
\(685\) | − | 11.6135i | − | 0.443727i | ||||||
\(686\) | −22.8018 | + | 34.2535i | −0.870579 | + | 1.30780i | ||||
\(687\) | − | 9.55207i | − | 0.364434i | ||||||
\(688\) | 1.84575 | − | 3.19694i | 0.0703687 | − | 0.121882i | ||||
\(689\) | 30.4718 | + | 52.7787i | 1.16088 | + | 2.01071i | ||||
\(690\) | 1.51045 | − | 0.872061i | 0.0575020 | − | 0.0331988i | ||||
\(691\) | 33.3914 | + | 19.2785i | 1.27027 | + | 0.733390i | 0.975038 | − | 0.222036i | \(-0.0712704\pi\) |
0.295230 | + | 0.955426i | \(0.404604\pi\) | |||||||
\(692\) | − | 32.4713i | − | 1.23438i | ||||||
\(693\) | −10.3212 | + | 5.67013i | −0.392069 | + | 0.215391i | ||||
\(694\) | 37.3698i | 1.41854i | ||||||||
\(695\) | 3.75542 | − | 6.50459i | 0.142451 | − | 0.246733i | ||||
\(696\) | −3.49390 | − | 6.05161i | −0.132436 | − | 0.229386i | ||||
\(697\) | −4.75874 | + | 34.3284i | −0.180250 | + | 1.30028i | ||||
\(698\) | −29.7032 | + | 51.4474i | −1.12428 | + | 1.94731i | ||||
\(699\) | 9.49642 | 0.359188 | ||||||||
\(700\) | 35.6864 | + | 0.758100i | 1.34882 | + | 0.0286535i | ||||
\(701\) | −25.5314 | −0.964308 | −0.482154 | − | 0.876087i | \(-0.660145\pi\) | ||||
−0.482154 | + | 0.876087i | \(0.660145\pi\) | |||||||
\(702\) | −9.54676 | − | 5.51183i | −0.360319 | − | 0.208030i | ||||
\(703\) | −16.3639 | + | 9.44771i | −0.617177 | + | 0.356327i | ||||
\(704\) | −49.7889 | + | 28.7456i | −1.87649 | + | 1.08339i | ||||
\(705\) | 3.30787 | − | 5.72940i | 0.124582 | − | 0.215782i | ||||
\(706\) | 24.7375 | 0.931007 | ||||||||
\(707\) | 7.46166 | − | 12.3124i | 0.280625 | − | 0.463057i | ||||
\(708\) | 4.75383i | 0.178660i | ||||||||
\(709\) | −30.6327 | − | 17.6858i | −1.15043 | − | 0.664203i | −0.201441 | − | 0.979501i | \(-0.564562\pi\) |
−0.948993 | + | 0.315297i | \(0.897896\pi\) | |||||||
\(710\) | −6.61744 | − | 11.4617i | −0.248348 | − | 0.430152i | ||||
\(711\) | −12.5774 | + | 7.26158i | −0.471691 | + | 0.272331i | ||||
\(712\) | −4.01511 | + | 6.95438i | −0.150473 | + | 0.260626i | ||||
\(713\) | 4.48268 | 0.167878 | ||||||||
\(714\) | 22.6440 | − | 8.64269i | 0.847429 | − | 0.323445i | ||||
\(715\) | 14.0659 | 0.526036 | ||||||||
\(716\) | 8.61832 | − | 14.9274i | 0.322082 | − | 0.557862i | ||||
\(717\) | 9.95040 | − | 5.74487i | 0.371605 | − | 0.214546i | ||||
\(718\) | 7.53199 | + | 13.0458i | 0.281091 | + | 0.486864i | ||||
\(719\) | −0.253848 | − | 0.146559i | −0.00946693 | − | 0.00546573i | 0.495259 | − | 0.868745i | \(-0.335073\pi\) |
−0.504726 | + | 0.863280i | \(0.668406\pi\) | |||||||
\(720\) | 0.796131i | 0.0296701i | ||||||||
\(721\) | 30.1834 | + | 0.641197i | 1.12409 | + | 0.0238794i | ||||
\(722\) | 30.0712 | 1.11913 | ||||||||
\(723\) | −6.61255 | + | 11.4533i | −0.245924 | + | 0.425952i | ||||
\(724\) | −29.6751 | + | 17.1329i | −1.10287 | + | 0.636741i | ||||
\(725\) | −13.3619 | + | 7.71449i | −0.496248 | + | 0.286509i | ||||
\(726\) | 16.9538 | + | 9.78827i | 0.629214 | + | 0.363277i | ||||
\(727\) | −8.78145 | −0.325686 | −0.162843 | − | 0.986652i | \(-0.552066\pi\) | ||||
−0.162843 | + | 0.986652i | \(0.552066\pi\) | |||||||
\(728\) | 13.1516 | + | 23.9394i | 0.487430 | + | 0.887255i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 6.00395 | − | 10.3991i | 0.222216 | − | 0.384890i | ||||
\(731\) | 12.0617 | + | 1.67205i | 0.446120 | + | 0.0618430i | ||||
\(732\) | −11.3091 | − | 19.5880i | −0.417997 | − | 0.723992i | ||||
\(733\) | 17.9304 | − | 31.0564i | 0.662275 | − | 1.14709i | −0.317741 | − | 0.948177i | \(-0.602924\pi\) |
0.980016 | − | 0.198917i | \(-0.0637423\pi\) | |||||||
\(734\) | 61.5425i | 2.27158i | ||||||||
\(735\) | 2.39126 | − | 3.76310i | 0.0882031 | − | 0.138804i | ||||
\(736\) | 8.55148i | 0.315212i | ||||||||
\(737\) | 34.1816 | + | 19.7347i | 1.25909 | + | 0.726939i | ||||
\(738\) | −16.1735 | + | 9.33775i | −0.595353 | + | 0.343727i | ||||
\(739\) | −11.0541 | − | 19.1462i | −0.406631 | − | 0.704306i | 0.587879 | − | 0.808949i | \(-0.299963\pi\) |
−0.994510 | + | 0.104643i | \(0.966630\pi\) | |||||||
\(740\) | 3.09804 | − | 5.36596i | 0.113886 | − | 0.197256i | ||||
\(741\) | 28.3001i | 1.03963i | ||||||||
\(742\) | −34.7666 | − | 63.2847i | −1.27632 | − | 2.32325i | ||||
\(743\) | − | 22.7670i | − | 0.835241i | −0.908622 | − | 0.417620i | \(-0.862864\pi\) | ||
0.908622 | − | 0.417620i | \(-0.137136\pi\) | |||||||
\(744\) | 3.78411 | − | 6.55427i | 0.138732 | − | 0.240291i | ||||
\(745\) | 6.17993 | − | 3.56798i | 0.226415 | − | 0.130721i | ||||
\(746\) | 31.7974 | + | 55.0747i | 1.16419 | + | 2.01643i | ||||
\(747\) | 0.588071 | − | 1.01857i | 0.0215164 | − | 0.0372675i | ||||
\(748\) | −42.5283 | − | 33.0982i | −1.55499 | − | 1.21019i | ||||
\(749\) | −0.680720 | + | 32.0438i | −0.0248730 | + | 1.17086i | ||||
\(750\) | −13.5776 | −0.495784 | ||||||||
\(751\) | −29.3570 | − | 16.9493i | −1.07125 | − | 0.618488i | −0.142729 | − | 0.989762i | \(-0.545588\pi\) |
−0.928523 | + | 0.371274i | \(0.878921\pi\) | |||||||
\(752\) | 6.49132 | + | 11.2433i | 0.236714 | + | 0.410001i | ||||
\(753\) | 1.60083 | − | 0.924241i | 0.0583376 | − | 0.0336812i | ||||
\(754\) | −32.0607 | − | 18.5103i | −1.16758 | − | 0.674105i | ||||
\(755\) | − | 8.68897i | − | 0.316224i | ||||||
\(756\) | 6.64437 | + | 4.02666i | 0.241653 | + | 0.146448i | ||||
\(757\) | −47.8187 | −1.73800 | −0.869000 | − | 0.494813i | \(-0.835237\pi\) | ||||
−0.869000 | + | 0.494813i | \(0.835237\pi\) | |||||||
\(758\) | −52.4315 | − | 30.2713i | −1.90440 | − | 1.09950i | ||||
\(759\) | 4.75062 | − | 2.74277i | 0.172437 | − | 0.0995564i | ||||
\(760\) | −6.54674 | + | 3.77976i | −0.237475 | + | 0.137106i | ||||
\(761\) | −8.17259 | + | 14.1553i | −0.296256 | + | 0.513131i | −0.975276 | − | 0.220989i | \(-0.929072\pi\) |
0.679020 | + | 0.734120i | \(0.262405\pi\) | |||||||
\(762\) | 39.1848i | 1.41952i | ||||||||
\(763\) | −26.4154 | − | 16.0084i | −0.956301 | − | 0.579544i | ||||
\(764\) | −46.2954 | −1.67491 | ||||||||
\(765\) | −2.43310 | + | 0.988360i | −0.0879688 | + | 0.0357342i | ||||
\(766\) | −39.4117 | − | 68.2630i | −1.42400 | − | 2.46644i | ||||
\(767\) | 4.01604 | + | 6.95598i | 0.145011 | + | 0.251166i | ||||
\(768\) | 6.14604 | + | 3.54842i | 0.221776 | + | 0.128043i | ||||
\(769\) | 4.74962 | 0.171276 | 0.0856378 | − | 0.996326i | \(-0.472707\pi\) | ||||
0.0856378 | + | 0.996326i | \(0.472707\pi\) | |||||||
\(770\) | −16.6615 | − | 0.353947i | −0.600439 | − | 0.0127554i | ||||
\(771\) | − | 7.00393i | − | 0.252240i | ||||||
\(772\) | −4.64052 | − | 2.67920i | −0.167016 | − | 0.0964267i | ||||
\(773\) | 6.84878 | + | 11.8624i | 0.246333 | + | 0.426662i | 0.962506 | − | 0.271262i | \(-0.0874408\pi\) |
−0.716172 | + | 0.697924i | \(0.754108\pi\) | |||||||
\(774\) | 3.28095 | + | 5.68276i | 0.117931 | + | 0.204263i | ||||
\(775\) | −14.4718 | − | 8.35527i | −0.519841 | − | 0.300130i | ||||
\(776\) | − | 26.9323i | − | 0.966812i | ||||||
\(777\) | 4.22012 | + | 7.68176i | 0.151396 | + | 0.275582i | ||||
\(778\) | 39.8795 | 1.42975 | ||||||||
\(779\) | 41.5207 | + | 23.9720i | 1.48763 | + | 0.858885i | ||||
\(780\) | −4.63999 | − | 8.03670i | −0.166138 | − | 0.287760i | ||||
\(781\) | −20.8129 | − | 36.0491i | −0.744746 | − | 1.28994i | ||||
\(782\) | −10.4601 | + | 4.24905i | −0.374053 | + | 0.151946i | ||||
\(783\) | −3.35828 | −0.120015 | ||||||||
\(784\) | 4.04901 | + | 7.75623i | 0.144607 | + | 0.277008i | ||||
\(785\) | 0.214648i | 0.00766110i | ||||||||
\(786\) | −13.8403 | + | 23.9721i | −0.493667 | + | 0.855056i | ||||
\(787\) | 42.8464 | − | 24.7374i | 1.52731 | − | 0.881793i | 0.527838 | − | 0.849345i | \(-0.323003\pi\) |
0.999473 | − | 0.0324481i | \(-0.0103304\pi\) | |||||||
\(788\) | 44.6070 | − | 25.7538i | 1.58906 | − | 0.917443i | ||||
\(789\) | 4.17595 | + | 2.41099i | 0.148668 | + | 0.0858333i | ||||
\(790\) | −20.5528 | −0.731236 | ||||||||
\(791\) | −9.72089 | + | 5.34035i | −0.345635 | + | 0.189881i | ||||
\(792\) | − | 9.26139i | − | 0.329089i | ||||||
\(793\) | −33.0958 | − | 19.1079i | −1.17527 | − | 0.678541i | ||||
\(794\) | 32.4142 | − | 18.7143i | 1.15034 | − | 0.664147i | ||||
\(795\) | 3.91185 | + | 6.77553i | 0.138739 | + | 0.240303i | ||||
\(796\) | −31.0279 | − | 17.9140i | −1.09976 | − | 0.634944i | ||||
\(797\) | −19.8771 | −0.704082 | −0.352041 | − | 0.935985i | \(-0.614512\pi\) | ||||
−0.352041 | + | 0.935985i | \(0.614512\pi\) | |||||||
\(798\) | 0.712126 | − | 33.5222i | 0.0252090 | − | 1.18667i | ||||
\(799\) | −26.3025 | + | 33.7965i | −0.930517 | + | 1.19563i | ||||
\(800\) | 15.9391 | − | 27.6074i | 0.563533 | − | 0.976068i | ||||
\(801\) | 1.92963 | + | 3.34222i | 0.0681802 | + | 0.118092i | ||||
\(802\) | 61.0653 | − | 35.2561i | 2.15629 | − | 1.24493i | ||||
\(803\) | 18.8834 | − | 32.7070i | 0.666381 | − | 1.15421i | ||||
\(804\) | − | 26.0399i | − | 0.918357i | ||||||
\(805\) | −1.07642 | + | 1.77619i | −0.0379387 | + | 0.0626024i | ||||
\(806\) | − | 40.0956i | − | 1.41231i | ||||||
\(807\) | 8.04171 | − | 13.9286i | 0.283081 | − | 0.490311i | ||||
\(808\) | 5.66128 | + | 9.80562i | 0.199163 | + | 0.344961i | ||||
\(809\) | −18.8332 | + | 10.8734i | −0.662140 | + | 0.382287i | −0.793092 | − | 0.609102i | \(-0.791530\pi\) |
0.130952 | + | 0.991389i | \(0.458197\pi\) | |||||||
\(810\) | −1.22558 | − | 0.707587i | −0.0430624 | − | 0.0248621i | ||||
\(811\) | − | 1.15024i | − | 0.0403905i | −0.999796 | − | 0.0201952i | \(-0.993571\pi\) | ||
0.999796 | − | 0.0201952i | \(-0.00642878\pi\) | |||||||
\(812\) | 22.3137 | + | 13.5227i | 0.783057 | + | 0.474553i | ||||
\(813\) | 28.2459i | 0.990628i | ||||||||
\(814\) | 16.3802 | − | 28.3713i | 0.574125 | − | 0.994413i | ||||
\(815\) | 1.66233 | + | 2.87923i | 0.0582287 | + | 0.100855i | ||||
\(816\) | 0.707644 | − | 5.10477i | 0.0247725 | − | 0.178703i | ||||
\(817\) | 8.42288 | − | 14.5889i | 0.294679 | − | 0.510400i | ||||
\(818\) | 31.6369 | 1.10616 | ||||||||
\(819\) | 13.1240 | + | 0.278799i | 0.458590 | + | 0.00974201i | ||||
\(820\) | −15.7215 | −0.549018 | ||||||||
\(821\) | 42.8081 | + | 24.7153i | 1.49401 | + | 0.862569i | 0.999976 | − | 0.00687127i | \(-0.00218721\pi\) |
0.494038 | + | 0.869441i | \(0.335521\pi\) | |||||||
\(822\) | −35.0835 | + | 20.2554i | −1.22368 | + | 0.706490i | ||||
\(823\) | −8.27176 | + | 4.77570i | −0.288335 | + | 0.166471i | −0.637191 | − | 0.770706i | \(-0.719904\pi\) |
0.348856 | + | 0.937177i | \(0.386570\pi\) | |||||||
\(824\) | −11.8716 | + | 20.5622i | −0.413567 | + | 0.716318i | ||||
\(825\) | −20.4491 | −0.711945 | ||||||||
\(826\) | −4.58208 | − | 8.34062i | −0.159431 | − | 0.290207i | ||||
\(827\) | − | 56.8626i | − | 1.97731i | −0.150219 | − | 0.988653i | \(-0.547998\pi\) | ||
0.150219 | − | 0.988653i | \(-0.452002\pi\) | |||||||
\(828\) | −3.13422 | − | 1.80954i | −0.108922 | − | 0.0628859i | ||||
\(829\) | 21.4785 | + | 37.2019i | 0.745981 | + | 1.29208i | 0.949735 | + | 0.313055i | \(0.101352\pi\) |
−0.203754 | + | 0.979022i | \(0.565314\pi\) | |||||||
\(830\) | 1.44145 | − | 0.832223i | 0.0500335 | − | 0.0288869i | ||||
\(831\) | 5.67146 | − | 9.82327i | 0.196741 | − | 0.340765i | ||||
\(832\) | 64.0861 | 2.22179 | ||||||||
\(833\) | −18.6776 | + | 22.0034i | −0.647139 | + | 0.762372i | ||||
\(834\) | −26.1999 | −0.907227 | ||||||||
\(835\) | 6.24948 | − | 10.8244i | 0.216272 | − | 0.374595i | ||||
\(836\) | −64.5635 | + | 37.2758i | −2.23298 | + | 1.28921i | ||||
\(837\) | −1.81861 | − | 3.14993i | −0.0628605 | − | 0.108878i | ||||
\(838\) | −5.60016 | − | 3.23325i | −0.193454 | − | 0.111691i | ||||
\(839\) | − | 47.9465i | − | 1.65530i | −0.561246 | − | 0.827649i | \(-0.689678\pi\) | ||
0.561246 | − | 0.827649i | \(-0.310322\pi\) | |||||||
\(840\) | 1.68835 | + | 3.07325i | 0.0582536 | + | 0.106037i | ||||
\(841\) | 17.7219 | 0.611101 | ||||||||
\(842\) | −0.579061 | + | 1.00296i | −0.0199557 | + | 0.0345644i | ||||
\(843\) | 0.727034 | − | 0.419754i | 0.0250404 | − | 0.0144571i | ||||
\(844\) | −9.53178 | + | 5.50318i | −0.328097 | + | 0.189427i | ||||
\(845\) | −6.40790 | − | 3.69960i | −0.220438 | − | 0.127270i | ||||
\(846\) | −23.0775 | −0.793420 | ||||||||
\(847\) | −23.3065 | − | 0.495110i | −0.800821 | − | 0.0170122i | ||||
\(848\) | −15.3531 | −0.527229 | ||||||||
\(849\) | −9.32607 | + | 16.1532i | −0.320070 | + | 0.554377i | ||||
\(850\) | 41.6890 | + | 5.77909i | 1.42992 | + | 0.198221i | ||||
\(851\) | −2.04137 | − | 3.53576i | −0.0699772 | − | 0.121204i | ||||
\(852\) | −13.7313 | + | 23.7833i | −0.470427 | + | 0.814803i | ||||
\(853\) | 22.5926i | 0.773556i | 0.922173 | + | 0.386778i | \(0.126412\pi\) | ||||
−0.922173 | + | 0.386778i | \(0.873588\pi\) | |||||||
\(854\) | 38.7221 | + | 23.4666i | 1.32504 | + | 0.803012i | ||||
\(855\) | 3.63305i | 0.124248i | ||||||||
\(856\) | −21.8296 | − | 12.6034i | −0.746122 | − | 0.430774i | ||||
\(857\) | 36.3637 | − | 20.9946i | 1.24216 | − | 0.717161i | 0.272626 | − | 0.962120i | \(-0.412108\pi\) |
0.969533 | + | 0.244959i | \(0.0787746\pi\) | |||||||
\(858\) | −24.5329 | − | 42.4922i | −0.837539 | − | 1.45066i | ||||
\(859\) | 27.1729 | − | 47.0649i | 0.927128 | − | 1.60583i | 0.139024 | − | 0.990289i | \(-0.455603\pi\) |
0.788103 | − | 0.615543i | \(-0.211063\pi\) | |||||||
\(860\) | 5.52396i | 0.188365i | ||||||||
\(861\) | 11.5259 | − | 19.0188i | 0.392803 | − | 0.648161i | ||||
\(862\) | − | 55.4421i | − | 1.88837i | ||||||
\(863\) | −27.7443 | + | 48.0545i | −0.944426 | + | 1.63579i | −0.187530 | + | 0.982259i | \(0.560048\pi\) |
−0.756896 | + | 0.653535i | \(0.773285\pi\) | |||||||
\(864\) | 6.00904 | − | 3.46932i | 0.204432 | − | 0.118029i | ||||
\(865\) | −3.52159 | − | 6.09957i | −0.119738 | − | 0.207392i | ||||
\(866\) | 9.77269 | − | 16.9268i | 0.332089 | − | 0.575196i | ||||
\(867\) | 16.4794 | − | 4.17467i | 0.559671 | − | 0.141779i | ||||
\(868\) | −0.600174 | + | 28.2523i | −0.0203712 | + | 0.958944i | ||||
\(869\) | −64.6420 | −2.19283 | ||||||||
\(870\) | −4.11584 | − | 2.37628i | −0.139540 | − | 0.0805634i | ||||
\(871\) | −21.9985 | − | 38.1026i | −0.745392 | − | 1.29106i | ||||
\(872\) | 21.0372 | − | 12.1458i | 0.712410 | − | 0.411310i | ||||
\(873\) | −11.2094 | − | 6.47173i | −0.379379 | − | 0.219035i | ||||
\(874\) | 15.6188i | 0.528315i | ||||||||
\(875\) | 14.1706 | − | 7.78491i | 0.479055 | − | 0.263178i | ||||
\(876\) | −24.9166 | −0.841853 | ||||||||
\(877\) | −9.07889 | − | 5.24170i | −0.306572 | − | 0.177000i | 0.338819 | − | 0.940851i | \(-0.389972\pi\) |
−0.645392 | + | 0.763852i | \(0.723306\pi\) | |||||||
\(878\) | −8.56825 | + | 4.94688i | −0.289165 | + | 0.166949i | ||||
\(879\) | −2.59209 | + | 1.49655i | −0.0874292 | + | 0.0504772i | ||||
\(880\) | −1.77177 | + | 3.06880i | −0.0597264 | + | 0.103449i | ||||
\(881\) | − | 36.9043i | − | 1.24334i | −0.783280 | − | 0.621669i | \(-0.786455\pi\) | ||
0.783280 | − | 0.621669i | \(-0.213545\pi\) | |||||||
\(882\) | −15.5388 | − | 0.660490i | −0.523217 | − | 0.0222399i | ||||
\(883\) | 12.2155 | 0.411086 | 0.205543 | − | 0.978648i | \(-0.434104\pi\) | ||||
0.205543 | + | 0.978648i | \(0.434104\pi\) | |||||||
\(884\) | 22.6080 | + | 55.6553i | 0.760390 | + | 1.87189i | ||||
\(885\) | 0.515564 | + | 0.892983i | 0.0173305 | + | 0.0300173i | ||||
\(886\) | 34.6587 | + | 60.0307i | 1.16438 | + | 2.01677i | ||||
\(887\) | −26.0598 | − | 15.0457i | −0.875003 | − | 0.505183i | −0.00599576 | − | 0.999982i | \(-0.501909\pi\) |
−0.869008 | + | 0.494799i | \(0.835242\pi\) | |||||||
\(888\) | −6.89299 | −0.231314 | ||||||||
\(889\) | −22.4671 | − | 40.8963i | −0.753524 | − | 1.37162i | ||||
\(890\) | 5.46154i | 0.183071i | ||||||||
\(891\) | −3.85464 | − | 2.22548i | −0.129135 | − | 0.0745563i | ||||
\(892\) | 16.1175 | + | 27.9164i | 0.539655 | + | 0.934710i | ||||
\(893\) | 29.6224 | + | 51.3075i | 0.991276 | + | 1.71694i | ||||
\(894\) | −21.5573 | − | 12.4461i | −0.720983 | − | 0.416260i | ||||
\(895\) | − | 3.73870i | − | 0.124971i | ||||||
\(896\) | −39.2043 | − | 0.832833i | −1.30972 | − | 0.0278230i | ||||
\(897\) | −6.11480 | −0.204167 | ||||||||
\(898\) | 67.5745 | + | 39.0142i | 2.25499 | + | 1.30192i | ||||
\(899\) | −6.10742 | − | 10.5784i | −0.203694 | − | 0.352808i | ||||
\(900\) | 6.74561 | + | 11.6837i | 0.224854 | + | 0.389458i | ||||
\(901\) | −19.0602 | − | 46.9215i | −0.634988 | − | 1.56318i | ||||
\(902\) | −83.1238 | −2.76772 | ||||||||
\(903\) | −6.68253 | − | 4.04979i | −0.222381 | − | 0.134769i | ||||
\(904\) | − | 8.72273i | − | 0.290114i | ||||||
\(905\) | −3.71621 | + | 6.43666i | −0.123531 | + | 0.213962i | ||||
\(906\) | −26.2488 | + | 15.1547i | −0.872057 | + | 0.503483i | ||||
\(907\) | −19.0675 | + | 11.0086i | −0.633125 | + | 0.365535i | −0.781961 | − | 0.623327i | \(-0.785781\pi\) |
0.148836 | + | 0.988862i | \(0.452447\pi\) | |||||||
\(908\) | 27.6283 | + | 15.9512i | 0.916878 | + | 0.529360i | ||||
\(909\) | 5.44154 | 0.180484 | ||||||||
\(910\) | 15.8872 | + | 9.62807i | 0.526656 | + | 0.319167i | ||||
\(911\) | − | 7.91228i | − | 0.262146i | −0.991373 | − | 0.131073i | \(-0.958158\pi\) | ||
0.991373 | − | 0.131073i | \(-0.0418422\pi\) | |||||||
\(912\) | −6.17429 | − | 3.56473i | −0.204451 | − | 0.118040i | ||||
\(913\) | 4.53360 | − | 2.61748i | 0.150040 | − | 0.0866258i | ||||
\(914\) | 9.48207 | + | 16.4234i | 0.313639 | + | 0.543239i | ||||
\(915\) | −4.24872 | − | 2.45300i | −0.140458 | − | 0.0810936i | ||||
\(916\) | −28.0498 | −0.926790 | ||||||||
\(917\) | 0.700068 | − | 32.9546i | 0.0231183 | − | 1.08826i | ||||
\(918\) | 7.22942 | + | 5.62638i | 0.238606 | + | 0.185698i | ||||
\(919\) | −27.6410 | + | 47.8756i | −0.911792 | + | 1.57927i | −0.100261 | + | 0.994961i | \(0.531968\pi\) |
−0.811531 | + | 0.584309i | \(0.801366\pi\) | |||||||
\(920\) | −0.816694 | − | 1.41456i | −0.0269256 | − | 0.0466365i | ||||
\(921\) | 21.6949 | − | 12.5256i | 0.714871 | − | 0.412731i | ||||
\(922\) | −18.4097 | + | 31.8865i | −0.606290 | + | 1.05012i | ||||
\(923\) | 46.4008i | 1.52730i | ||||||||
\(924\) | 16.6504 | + | 30.3082i | 0.547758 | + | 0.997068i | ||||
\(925\) | 15.2197i | 0.500419i | ||||||||
\(926\) | 10.5175 | − | 18.2168i | 0.345626 | − | 0.598642i | ||||
\(927\) | 5.70540 | + | 9.88205i | 0.187390 | + | 0.324569i | ||||
\(928\) | 20.1801 | − | 11.6510i | 0.662444 | − | 0.382462i | ||||
\(929\) | −4.83852 | − | 2.79352i | −0.158747 | − | 0.0916524i | 0.418522 | − | 0.908207i | \(-0.362548\pi\) |
−0.577269 | + | 0.816554i | \(0.695882\pi\) | |||||||
\(930\) | − | 5.14731i | − | 0.168787i | ||||||
\(931\) | 18.4772 | + | 35.3947i | 0.605565 | + | 1.16001i | ||||
\(932\) | − | 27.8863i | − | 0.913448i | ||||||
\(933\) | 0.803381 | − | 1.39150i | 0.0263015 | − | 0.0455555i | ||||
\(934\) | −10.1984 | − | 17.6641i | −0.333701 | − | 0.577988i | ||||
\(935\) | −11.5783 | − | 1.60503i | −0.378651 | − | 0.0524901i | ||||
\(936\) | −5.16188 | + | 8.94064i | −0.168721 | + | 0.292234i | ||||
\(937\) | −35.3405 | −1.15452 | −0.577262 | − | 0.816559i | \(-0.695879\pi\) | ||||
−0.577262 | + | 0.816559i | \(0.695879\pi\) | |||||||
\(938\) | 25.0991 | + | 45.6871i | 0.819515 | + | 1.49174i | ||||
\(939\) | −9.34780 | −0.305054 | ||||||||
\(940\) | −16.8244 | − | 9.71359i | −0.548753 | − | 0.316823i | ||||
\(941\) | 1.01029 | − | 0.583291i | 0.0329345 | − | 0.0190147i | −0.483442 | − | 0.875376i | \(-0.660614\pi\) |
0.516377 | + | 0.856361i | \(0.327280\pi\) | |||||||
\(942\) | 0.648436 | − | 0.374374i | 0.0211272 | − | 0.0121978i | ||||
\(943\) | −5.17963 | + | 8.97138i | −0.168672 | + | 0.292148i | ||||
\(944\) | −2.02347 | −0.0658584 | ||||||||
\(945\) | 1.68481 | + | 0.0357911i | 0.0548069 | + | 0.00116428i | ||||
\(946\) | 29.2067i | 0.949592i | ||||||||
\(947\) | 44.5572 | + | 25.7251i | 1.44792 | + | 0.835955i | 0.998357 | − | 0.0572964i | \(-0.0182480\pi\) |
0.449558 | + | 0.893251i | \(0.351581\pi\) | |||||||
\(948\) | 21.3237 | + | 36.9338i | 0.692562 | + | 1.19955i | ||||
\(949\) | −36.4589 | + | 21.0495i | −1.18350 | + | 0.683297i | ||||
\(950\) | 29.1120 | − | 50.4234i | 0.944517 | − | 1.63595i | ||||
\(951\) | 22.3804 | 0.725736 | ||||||||
\(952\) | −8.09397 | − | 21.2063i | −0.262327 | − | 0.687300i | ||||
\(953\) | −36.9788 | −1.19786 | −0.598930 | − | 0.800801i | \(-0.704407\pi\) | ||||
−0.598930 | + | 0.800801i | \(0.704407\pi\) | |||||||
\(954\) | 13.6456 | − | 23.6349i | 0.441793 | − | 0.765207i | ||||
\(955\) | −8.69634 | + | 5.02083i | −0.281407 | + | 0.162470i | ||||
\(956\) | −16.8699 | − | 29.2195i | −0.545610 | − | 0.945025i | ||||
\(957\) | −12.9450 | − | 7.47379i | −0.418452 | − | 0.241593i | ||||
\(958\) | − | 44.7533i | − | 1.44591i | ||||||
\(959\) | 25.0020 | − | 41.2557i | 0.807358 | − | 1.33222i | ||||
\(960\) | 8.22713 | 0.265530 | ||||||||
\(961\) | −8.88528 | + | 15.3898i | −0.286622 | + | 0.496444i | ||||
\(962\) | −31.6258 | + | 18.2591i | −1.01966 | + | 0.588698i | ||||
\(963\) | −10.4912 | + | 6.05708i | −0.338073 | + | 0.195187i | ||||
\(964\) | 33.6327 | + | 19.4178i | 1.08324 | + | 0.625406i | ||||
\(965\) | −1.16226 | −0.0374145 | ||||||||
\(966\) | 7.24315 | + | 0.153869i | 0.233045 | + | 0.00495066i | ||||
\(967\) | 11.5339 | 0.370905 | 0.185453 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185453 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(968\) | 9.16682 | − | 15.8774i | 0.294633 | − | 0.510319i | ||||
\(969\) | 3.22925 | − | 23.2950i | 0.103738 | − | 0.748344i | ||||
\(970\) | −9.15862 | − | 15.8632i | −0.294066 | − | 0.509337i | ||||
\(971\) | 4.18925 | − | 7.25599i | 0.134439 | − | 0.232856i | −0.790944 | − | 0.611889i | \(-0.790410\pi\) |
0.925383 | + | 0.379033i | \(0.123743\pi\) | |||||||
\(972\) | 2.93651i | 0.0941886i | ||||||||
\(973\) | 27.3442 | − | 15.0220i | 0.876614 | − | 0.481585i | ||||
\(974\) | − | 11.9914i | − | 0.384229i | ||||||
\(975\) | 19.7409 | + | 11.3974i | 0.632213 | + | 0.365009i | ||||
\(976\) | 8.33762 | − | 4.81373i | 0.266881 | − | 0.154084i | ||||
\(977\) | −3.37704 | − | 5.84921i | −0.108041 | − | 0.187133i | 0.806935 | − | 0.590640i | \(-0.201124\pi\) |
−0.914977 | + | 0.403507i | \(0.867791\pi\) | |||||||
\(978\) | 5.79864 | − | 10.0435i | 0.185420 | − | 0.321157i | ||||
\(979\) | 17.1774i | 0.548993i | ||||||||
\(980\) | −11.0504 | − | 7.02197i | −0.352991 | − | 0.224309i | ||||
\(981\) | − | 11.6744i | − | 0.372735i | ||||||
\(982\) | 5.12652 | − | 8.87940i | 0.163594 | − | 0.283353i | ||||
\(983\) | −11.1391 | + | 6.43115i | −0.355281 | + | 0.205122i | −0.667009 | − | 0.745050i | \(-0.732426\pi\) |
0.311728 | + | 0.950171i | \(0.399092\pi\) | |||||||
\(984\) | 8.74490 | + | 15.1466i | 0.278777 | + | 0.482856i | ||||
\(985\) | 5.58612 | − | 9.67545i | 0.177989 | − | 0.308285i | ||||
\(986\) | 24.2784 | + | 18.8950i | 0.773183 | + | 0.601739i | ||||
\(987\) | 24.0854 | − | 13.2318i | 0.766647 | − | 0.421172i | ||||
\(988\) | 83.1034 | 2.64387 | ||||||||
\(989\) | 3.15222 | + | 1.81993i | 0.100235 | + | 0.0578705i | ||||
\(990\) | −3.14944 | − | 5.45499i | −0.100096 | − | 0.173371i | ||||
\(991\) | 45.5283 | − | 26.2858i | 1.44625 | − | 0.834995i | 0.447998 | − | 0.894034i | \(-0.352137\pi\) |
0.998256 | + | 0.0590392i | \(0.0188037\pi\) | |||||||
\(992\) | 21.8563 | + | 12.6187i | 0.693937 | + | 0.400645i | ||||
\(993\) | 18.3909i | 0.583617i | ||||||||
\(994\) | 1.16760 | − | 54.9631i | 0.0370341 | − | 1.74332i | ||||
\(995\) | −7.77124 | −0.246365 | ||||||||
\(996\) | −2.99104 | − | 1.72688i | −0.0947746 | − | 0.0547181i | ||||
\(997\) | 4.36058 | − | 2.51758i | 0.138101 | − | 0.0797326i | −0.429358 | − | 0.903135i | \(-0.641260\pi\) |
0.567459 | + | 0.823402i | \(0.307927\pi\) | |||||||
\(998\) | −77.9376 | + | 44.9973i | −2.46707 | + | 1.42436i | ||||
\(999\) | −1.65636 | + | 2.86890i | −0.0524049 | + | 0.0907680i |
(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 | 357.2.p.a.16.4 | yes | 48 | |
7.4 | even | 3 | inner | 357.2.p.a.67.3 | yes | 48 | |
17.16 | even | 2 | inner | 357.2.p.a.16.3 | ✓ | 48 | |
119.67 | even | 6 | inner | 357.2.p.a.67.4 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
357.2.p.a.16.3 | ✓ | 48 | 17.16 | even | 2 | inner | |
357.2.p.a.16.4 | yes | 48 | 1.1 | even | 1 | trivial | |
357.2.p.a.67.3 | yes | 48 | 7.4 | even | 3 | inner | |
357.2.p.a.67.4 | yes | 48 | 119.67 | even | 6 | inner |