Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,3,Mod(126,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(16))
chi = DirichletCharacter(H, H._module([0, 11]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.126");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.u (of order \(16\), degree \(8\), 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: | \(11.5804112353\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 17) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{16}]$ |
Embedding invariants
Embedding label | 176.1 | ||
Root | \(0.923880 - 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 425.176 |
Dual form | 425.3.u.b.326.1 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{15}{16}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.23044 | − | 0.509666i | −0.615221 | − | 0.254833i | 0.0532379 | − | 0.998582i | \(-0.483046\pi\) |
−0.668459 | + | 0.743749i | \(0.733046\pi\) | |||||||
\(3\) | 2.63099 | − | 0.523336i | 0.876995 | − | 0.174445i | 0.263991 | − | 0.964525i | \(-0.414961\pi\) |
0.613004 | + | 0.790080i | \(0.289961\pi\) | |||||||
\(4\) | −1.57420 | − | 1.57420i | −0.393549 | − | 0.393549i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.50400 | − | 0.696990i | −0.584001 | − | 0.116165i | ||||
\(7\) | −4.92562 | − | 7.37170i | −0.703659 | − | 1.05310i | −0.995325 | − | 0.0965803i | \(-0.969210\pi\) |
0.291666 | − | 0.956520i | \(-0.405790\pi\) | |||||||
\(8\) | 3.17331 | + | 7.66104i | 0.396664 | + | 0.957631i | ||||
\(9\) | −1.66671 | + | 0.690373i | −0.185190 | + | 0.0767081i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.61572 | + | 8.12279i | −0.146884 | + | 0.738436i | 0.835193 | + | 0.549957i | \(0.185356\pi\) |
−0.982077 | + | 0.188479i | \(0.939644\pi\) | |||||||
\(12\) | −4.96553 | − | 3.31786i | −0.413794 | − | 0.276488i | ||||
\(13\) | −16.1480 | + | 16.1480i | −1.24216 | + | 1.24216i | −0.283051 | + | 0.959105i | \(0.591346\pi\) |
−0.959105 | + | 0.283051i | \(0.908654\pi\) | |||||||
\(14\) | 2.30358 | + | 11.5809i | 0.164541 | + | 0.827205i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | − | 2.13880i | − | 0.133675i | ||||||
\(17\) | 15.7060 | + | 6.50562i | 0.923880 | + | 0.382683i | ||||
\(18\) | 2.40265 | 0.133480 | ||||||||
\(19\) | −1.20778 | − | 0.500280i | −0.0635675 | − | 0.0263305i | 0.350673 | − | 0.936498i | \(-0.385953\pi\) |
−0.414241 | + | 0.910167i | \(0.635953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.8171 | − | 16.8171i | −0.800814 | − | 0.800814i | ||||
\(22\) | 6.12797 | − | 9.17115i | 0.278544 | − | 0.416870i | ||||
\(23\) | 26.2400 | + | 5.21946i | 1.14087 | + | 0.226933i | 0.729135 | − | 0.684370i | \(-0.239923\pi\) |
0.411735 | + | 0.911303i | \(0.364923\pi\) | |||||||
\(24\) | 12.3582 | + | 18.4954i | 0.514926 | + | 0.770642i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 28.0993 | − | 11.6391i | 1.08074 | − | 0.447658i | ||||
\(27\) | −24.0978 | + | 16.1016i | −0.892510 | + | 0.596356i | ||||
\(28\) | −3.85063 | + | 19.3584i | −0.137522 | + | 0.691372i | ||||
\(29\) | 13.7583 | + | 9.19303i | 0.474425 | + | 0.317001i | 0.769694 | − | 0.638414i | \(-0.220409\pi\) |
−0.295268 | + | 0.955414i | \(0.595409\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.68003 | + | 13.4734i | 0.0864526 | + | 0.434627i | 0.999633 | + | 0.0270721i | \(0.00861839\pi\) |
−0.913181 | + | 0.407555i | \(0.866382\pi\) | |||||||
\(32\) | 11.6032 | − | 28.0125i | 0.362599 | − | 0.875391i | ||||
\(33\) | 22.2165i | 0.673228i | ||||||||
\(34\) | −16.0096 | − | 16.0096i | −0.470870 | − | 0.470870i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.71051 | + | 1.53694i | 0.103070 | + | 0.0426929i | ||||
\(37\) | −18.9648 | + | 3.77234i | −0.512563 | + | 0.101955i | −0.444594 | − | 0.895732i | \(-0.646652\pi\) |
−0.0679693 | + | 0.997687i | \(0.521652\pi\) | |||||||
\(38\) | 1.23113 | + | 1.23113i | 0.0323982 | + | 0.0323982i | ||||
\(39\) | −34.0344 | + | 50.9361i | −0.872677 | + | 1.30605i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.6853 | − | 21.9781i | −0.358178 | − | 0.536051i | 0.607997 | − | 0.793939i | \(-0.291973\pi\) |
−0.966175 | + | 0.257888i | \(0.916973\pi\) | |||||||
\(42\) | 12.1214 | + | 29.2636i | 0.288604 | + | 0.696752i | ||||
\(43\) | 21.8944 | − | 9.06895i | 0.509172 | − | 0.210906i | −0.113281 | − | 0.993563i | \(-0.536136\pi\) |
0.622453 | + | 0.782657i | \(0.286136\pi\) | |||||||
\(44\) | 15.3303 | − | 10.2434i | 0.348417 | − | 0.232805i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −29.6266 | − | 19.7959i | −0.644058 | − | 0.430345i | ||||
\(47\) | −26.8680 | + | 26.8680i | −0.571660 | + | 0.571660i | −0.932592 | − | 0.360932i | \(-0.882459\pi\) |
0.360932 | + | 0.932592i | \(0.382459\pi\) | |||||||
\(48\) | −1.11931 | − | 5.62714i | −0.0233189 | − | 0.117232i | ||||
\(49\) | −11.3288 | + | 27.3503i | −0.231201 | + | 0.558169i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 44.7268 | + | 8.89671i | 0.876995 | + | 0.174445i | ||||
\(52\) | 50.8404 | 0.977699 | ||||||||
\(53\) | −26.1557 | − | 10.8340i | −0.493503 | − | 0.204416i | 0.122031 | − | 0.992526i | \(-0.461059\pi\) |
−0.615533 | + | 0.788111i | \(0.711059\pi\) | |||||||
\(54\) | 37.8574 | − | 7.53030i | 0.701062 | − | 0.139450i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 40.8445 | − | 61.1281i | 0.729365 | − | 1.09157i | ||||
\(57\) | −3.43947 | − | 0.684154i | −0.0603416 | − | 0.0120027i | ||||
\(58\) | −12.2435 | − | 18.3236i | −0.211094 | − | 0.315925i | ||||
\(59\) | 9.12070 | + | 22.0193i | 0.154588 | + | 0.373209i | 0.982132 | − | 0.188192i | \(-0.0602627\pi\) |
−0.827544 | + | 0.561401i | \(0.810263\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −42.9373 | + | 28.6898i | −0.703890 | + | 0.470324i | −0.855291 | − | 0.518148i | \(-0.826622\pi\) |
0.151401 | + | 0.988472i | \(0.451622\pi\) | |||||||
\(62\) | 3.56932 | − | 17.9442i | 0.0575697 | − | 0.289423i | ||||
\(63\) | 13.2988 | + | 8.88596i | 0.211092 | + | 0.141047i | ||||
\(64\) | −34.6035 | + | 34.6035i | −0.540679 | + | 0.540679i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11.3230 | − | 27.3362i | 0.171561 | − | 0.414184i | ||||
\(67\) | 70.4415i | 1.05137i | 0.850681 | + | 0.525683i | \(0.176190\pi\) | ||||
−0.850681 | + | 0.525683i | \(0.823810\pi\) | |||||||
\(68\) | −14.4831 | − | 34.9654i | −0.212987 | − | 0.514197i | ||||
\(69\) | 71.7687 | 1.04013 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −102.865 | + | 20.4612i | −1.44881 | + | 0.288185i | −0.855923 | − | 0.517104i | \(-0.827010\pi\) |
−0.592883 | + | 0.805289i | \(0.702010\pi\) | |||||||
\(72\) | −10.5780 | − | 10.5780i | −0.146916 | − | 0.146916i | ||||
\(73\) | −19.7693 | + | 29.5868i | −0.270812 | + | 0.405299i | −0.941802 | − | 0.336167i | \(-0.890869\pi\) |
0.670990 | + | 0.741466i | \(0.265869\pi\) | |||||||
\(74\) | 25.2578 | + | 5.02408i | 0.341321 | + | 0.0678930i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.11375 | + | 2.68883i | 0.0146546 | + | 0.0353793i | ||||
\(77\) | 67.8373 | − | 28.0991i | 0.881003 | − | 0.364924i | ||||
\(78\) | 67.8377 | − | 45.3277i | 0.869715 | − | 0.581125i | ||||
\(79\) | −1.41599 | + | 7.11865i | −0.0179239 | + | 0.0901095i | −0.988712 | − | 0.149830i | \(-0.952127\pi\) |
0.970788 | + | 0.239939i | \(0.0771275\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −43.4936 | + | 43.4936i | −0.536958 | + | 0.536958i | ||||
\(82\) | 6.86792 | + | 34.5274i | 0.0837551 | + | 0.421066i | ||||
\(83\) | −51.5218 | + | 124.385i | −0.620745 | + | 1.49861i | 0.230085 | + | 0.973170i | \(0.426099\pi\) |
−0.850830 | + | 0.525441i | \(0.823901\pi\) | |||||||
\(84\) | 52.9469i | 0.630320i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −31.5619 | −0.366999 | ||||||||
\(87\) | 41.0090 | + | 16.9865i | 0.471368 | + | 0.195247i | ||||
\(88\) | −67.3563 | + | 13.3980i | −0.765412 | + | 0.152250i | ||||
\(89\) | 38.6522 | + | 38.6522i | 0.434294 | + | 0.434294i | 0.890086 | − | 0.455792i | \(-0.150644\pi\) |
−0.455792 | + | 0.890086i | \(0.650644\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 198.577 | + | 39.4995i | 2.18217 | + | 0.434060i | ||||
\(92\) | −33.0905 | − | 49.5234i | −0.359679 | − | 0.538298i | ||||
\(93\) | 14.1023 | + | 34.0458i | 0.151637 | + | 0.366084i | ||||
\(94\) | 46.7533 | − | 19.3658i | 0.497375 | − | 0.206020i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 15.8678 | − | 79.7729i | 0.165290 | − | 0.830968i | ||||
\(97\) | −65.9209 | − | 44.0470i | −0.679597 | − | 0.454092i | 0.167260 | − | 0.985913i | \(-0.446508\pi\) |
−0.846857 | + | 0.531820i | \(0.821508\pi\) | |||||||
\(98\) | 27.8790 | − | 27.8790i | 0.284480 | − | 0.284480i | ||||
\(99\) | −2.91482 | − | 14.6538i | −0.0294426 | − | 0.148018i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 140.647i | 1.39254i | 0.717779 | + | 0.696271i | \(0.245159\pi\) | ||||
−0.717779 | + | 0.696271i | \(0.754841\pi\) | |||||||
\(102\) | −50.4994 | − | 33.7426i | −0.495092 | − | 0.330810i | ||||
\(103\) | 42.3283 | 0.410954 | 0.205477 | − | 0.978662i | \(-0.434125\pi\) | ||||
0.205477 | + | 0.978662i | \(0.434125\pi\) | |||||||
\(104\) | −174.953 | − | 72.4681i | −1.68224 | − | 0.696808i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 26.6613 | + | 26.6613i | 0.251522 | + | 0.251522i | ||||
\(107\) | −40.9741 | + | 61.3221i | −0.382936 | + | 0.573104i | −0.972000 | − | 0.234983i | \(-0.924497\pi\) |
0.589064 | + | 0.808086i | \(0.299497\pi\) | |||||||
\(108\) | 63.2818 | + | 12.5875i | 0.585942 | + | 0.116551i | ||||
\(109\) | −116.798 | − | 174.800i | −1.07154 | − | 1.60367i | −0.755770 | − | 0.654837i | \(-0.772737\pi\) |
−0.315770 | − | 0.948836i | \(-0.602263\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −47.9220 | + | 19.8500i | −0.431730 | + | 0.178828i | ||||
\(112\) | −15.7666 | + | 10.5349i | −0.140773 | + | 0.0940615i | ||||
\(113\) | 28.0222 | − | 140.877i | 0.247984 | − | 1.24670i | −0.633224 | − | 0.773969i | \(-0.718269\pi\) |
0.881208 | − | 0.472729i | \(-0.156731\pi\) | |||||||
\(114\) | 3.88338 | + | 2.59479i | 0.0340648 | + | 0.0227613i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.18670 | − | 36.1300i | −0.0619543 | − | 0.311465i | ||||
\(117\) | 15.7659 | − | 38.0622i | 0.134751 | − | 0.325318i | ||||
\(118\) | − | 31.7420i | − | 0.269000i | ||||||
\(119\) | −29.4040 | − | 147.824i | −0.247092 | − | 1.24222i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 48.4202 | + | 20.0563i | 0.400167 | + | 0.165755i | ||||
\(122\) | 67.4541 | − | 13.4175i | 0.552902 | − | 0.109979i | ||||
\(123\) | −50.1387 | − | 50.1387i | −0.407632 | − | 0.407632i | ||||
\(124\) | 16.9909 | − | 25.4287i | 0.137024 | − | 0.205070i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.8345 | − | 17.7116i | −0.0939247 | − | 0.140568i | ||||
\(127\) | −41.4251 | − | 100.009i | −0.326182 | − | 0.787472i | −0.998869 | − | 0.0475454i | \(-0.984860\pi\) |
0.672687 | − | 0.739927i | \(-0.265140\pi\) | |||||||
\(128\) | −51.8363 | + | 21.4713i | −0.404971 | + | 0.167744i | ||||
\(129\) | 52.8577 | − | 35.3184i | 0.409750 | − | 0.273786i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −77.0656 | − | 51.4936i | −0.588287 | − | 0.393081i | 0.225501 | − | 0.974243i | \(-0.427598\pi\) |
−0.813788 | + | 0.581162i | \(0.802598\pi\) | |||||||
\(132\) | 34.9732 | − | 34.9732i | 0.264948 | − | 0.264948i | ||||
\(133\) | 2.26116 | + | 11.3676i | 0.0170012 | + | 0.0854707i | ||||
\(134\) | 35.9016 | − | 86.6742i | 0.267923 | − | 0.646822i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 140.968i | 1.03653i | ||||||||
\(137\) | −102.046 | −0.744863 | −0.372431 | − | 0.928060i | \(-0.621476\pi\) | ||||
−0.372431 | + | 0.928060i | \(0.621476\pi\) | |||||||
\(138\) | −88.3072 | − | 36.5780i | −0.639907 | − | 0.265058i | ||||
\(139\) | 30.2420 | − | 6.01550i | 0.217568 | − | 0.0432770i | −0.0851025 | − | 0.996372i | \(-0.527122\pi\) |
0.302671 | + | 0.953095i | \(0.402122\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −56.6284 | + | 84.7504i | −0.401620 | + | 0.601067i | ||||
\(142\) | 136.998 | + | 27.2506i | 0.964775 | + | 0.191906i | ||||
\(143\) | −105.076 | − | 157.258i | −0.734799 | − | 1.09970i | ||||
\(144\) | 1.47657 | + | 3.56475i | 0.0102539 | + | 0.0247552i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 39.4044 | − | 26.3292i | 0.269893 | − | 0.180337i | ||||
\(147\) | −15.4927 | + | 77.8870i | −0.105392 | + | 0.529843i | ||||
\(148\) | 35.7928 | + | 23.9160i | 0.241843 | + | 0.161595i | ||||
\(149\) | 23.3099 | − | 23.3099i | 0.156443 | − | 0.156443i | −0.624546 | − | 0.780988i | \(-0.714716\pi\) |
0.780988 | + | 0.624546i | \(0.214716\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −53.9466 | + | 130.239i | −0.357262 | + | 0.862507i | 0.638421 | + | 0.769688i | \(0.279588\pi\) |
−0.995683 | + | 0.0928198i | \(0.970412\pi\) | |||||||
\(152\) | − | 10.8404i | − | 0.0713185i | ||||||
\(153\) | −30.6685 | −0.200448 | ||||||||
\(154\) | −97.7910 | −0.635006 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 133.760 | − | 26.6066i | 0.857438 | − | 0.170555i | ||||
\(157\) | 78.3942 | + | 78.3942i | 0.499326 | + | 0.499326i | 0.911228 | − | 0.411902i | \(-0.135135\pi\) |
−0.411902 | + | 0.911228i | \(0.635135\pi\) | |||||||
\(158\) | 5.37042 | − | 8.03741i | 0.0339900 | − | 0.0508697i | ||||
\(159\) | −74.4850 | − | 14.8160i | −0.468459 | − | 0.0931823i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −90.7719 | − | 219.143i | −0.563800 | − | 1.36113i | ||||
\(162\) | 75.6835 | − | 31.3491i | 0.467182 | − | 0.193513i | ||||
\(163\) | 135.804 | − | 90.7416i | 0.833156 | − | 0.556697i | −0.0642345 | − | 0.997935i | \(-0.520461\pi\) |
0.897390 | + | 0.441238i | \(0.145461\pi\) | |||||||
\(164\) | −11.4803 | + | 57.7154i | −0.0700019 | + | 0.351923i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 126.789 | − | 126.789i | 0.763791 | − | 0.763791i | ||||
\(167\) | −32.5256 | − | 163.517i | −0.194764 | − | 0.979145i | −0.947240 | − | 0.320525i | \(-0.896141\pi\) |
0.752476 | − | 0.658620i | \(-0.228859\pi\) | |||||||
\(168\) | 75.4707 | − | 182.202i | 0.449230 | − | 1.08454i | ||||
\(169\) | − | 352.517i | − | 2.08590i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.35840 | 0.0137918 | ||||||||
\(172\) | −48.7424 | − | 20.1898i | −0.283386 | − | 0.117382i | ||||
\(173\) | −16.3948 | + | 3.26113i | −0.0947676 | + | 0.0188504i | −0.242246 | − | 0.970215i | \(-0.577884\pi\) |
0.147479 | + | 0.989065i | \(0.452884\pi\) | |||||||
\(174\) | −41.8018 | − | 41.8018i | −0.240240 | − | 0.240240i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 17.3730 | + | 3.45570i | 0.0987102 | + | 0.0196347i | ||||
\(177\) | 35.5199 | + | 53.1594i | 0.200678 | + | 0.300335i | ||||
\(178\) | −27.8596 | − | 67.2590i | −0.156514 | − | 0.377859i | ||||
\(179\) | −35.7824 | + | 14.8215i | −0.199901 | + | 0.0828019i | −0.480388 | − | 0.877056i | \(-0.659504\pi\) |
0.280487 | + | 0.959858i | \(0.409504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.42674 | − | 42.3641i | 0.0465566 | − | 0.234056i | −0.950500 | − | 0.310724i | \(-0.899428\pi\) |
0.997057 | + | 0.0766687i | \(0.0244284\pi\) | |||||||
\(182\) | −224.207 | − | 149.810i | −1.23190 | − | 0.823132i | ||||
\(183\) | −97.9531 | + | 97.9531i | −0.535263 | + | 0.535263i | ||||
\(184\) | 43.2811 | + | 217.589i | 0.235223 | + | 1.18255i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 49.0789i | − | 0.263865i | ||||||
\(187\) | −78.2203 | + | 117.065i | −0.418290 | + | 0.626015i | ||||
\(188\) | 84.5912 | 0.449953 | ||||||||
\(189\) | 237.393 | + | 98.3313i | 1.25605 | + | 0.520271i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −107.196 | − | 107.196i | −0.561234 | − | 0.561234i | 0.368424 | − | 0.929658i | \(-0.379898\pi\) |
−0.929658 | + | 0.368424i | \(0.879898\pi\) | |||||||
\(192\) | −72.9320 | + | 109.151i | −0.379854 | + | 0.568492i | ||||
\(193\) | 201.713 | + | 40.1233i | 1.04515 | + | 0.207893i | 0.687666 | − | 0.726028i | \(-0.258636\pi\) |
0.357482 | + | 0.933920i | \(0.383636\pi\) | |||||||
\(194\) | 58.6627 | + | 87.7949i | 0.302385 | + | 0.452551i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 60.8886 | − | 25.2209i | 0.310656 | − | 0.128678i | ||||
\(197\) | −116.416 | + | 77.7868i | −0.590945 | + | 0.394857i | −0.814780 | − | 0.579770i | \(-0.803142\pi\) |
0.223835 | + | 0.974627i | \(0.428142\pi\) | |||||||
\(198\) | −3.88201 | + | 19.5162i | −0.0196061 | + | 0.0985667i | ||||
\(199\) | −123.283 | − | 82.3749i | −0.619511 | − | 0.413944i | 0.205823 | − | 0.978589i | \(-0.434013\pi\) |
−0.825334 | + | 0.564645i | \(0.809013\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.8645 | + | 185.331i | 0.183406 | + | 0.922043i | ||||
\(202\) | 71.6828 | − | 173.058i | 0.354865 | − | 0.856721i | ||||
\(203\) | − | 146.704i | − | 0.722678i | ||||||
\(204\) | −56.4036 | − | 84.4140i | −0.276488 | − | 0.413794i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −52.0825 | − | 21.5733i | −0.252828 | − | 0.104725i | ||||
\(207\) | −47.3378 | + | 9.41607i | −0.228685 | + | 0.0454883i | ||||
\(208\) | 34.5373 | + | 34.5373i | 0.166045 | + | 0.166045i | ||||
\(209\) | 6.01511 | − | 9.00225i | 0.0287804 | − | 0.0430730i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 113.713 | + | 170.184i | 0.538925 | + | 0.806559i | 0.996585 | − | 0.0825683i | \(-0.0263123\pi\) |
−0.457660 | + | 0.889127i | \(0.651312\pi\) | |||||||
\(212\) | 24.1193 | + | 58.2291i | 0.113770 | + | 0.274665i | ||||
\(213\) | −259.929 | + | 107.666i | −1.22032 | + | 0.505474i | ||||
\(214\) | 81.6701 | − | 54.5702i | 0.381636 | − | 0.255001i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −199.825 | − | 133.519i | −0.925115 | − | 0.618142i | ||||
\(217\) | 86.1213 | − | 86.1213i | 0.396872 | − | 0.396872i | ||||
\(218\) | 54.6233 | + | 274.610i | 0.250565 | + | 1.25968i | ||||
\(219\) | −36.5289 | + | 88.1885i | −0.166799 | + | 0.402687i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −358.673 | + | 148.567i | −1.62295 | + | 0.672250i | ||||
\(222\) | 69.0821 | 0.311181 | ||||||||
\(223\) | 107.408 | + | 44.4897i | 0.481649 | + | 0.199506i | 0.610278 | − | 0.792187i | \(-0.291058\pi\) |
−0.128629 | + | 0.991693i | \(0.541058\pi\) | |||||||
\(224\) | −263.653 | + | 52.4438i | −1.17702 | + | 0.234124i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −106.280 | + | 159.059i | −0.470265 | + | 0.703801i | ||||
\(227\) | 150.469 | + | 29.9302i | 0.662859 | + | 0.131851i | 0.515044 | − | 0.857164i | \(-0.327776\pi\) |
0.147816 | + | 0.989015i | \(0.452776\pi\) | |||||||
\(228\) | 4.33742 | + | 6.49140i | 0.0190238 | + | 0.0284711i | ||||
\(229\) | 3.69064 | + | 8.91000i | 0.0161164 | + | 0.0389083i | 0.931733 | − | 0.363144i | \(-0.118297\pi\) |
−0.915617 | + | 0.402053i | \(0.868297\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 163.774 | − | 109.430i | 0.708977 | − | 0.473723i | ||||
\(232\) | −26.7687 | + | 134.576i | −0.115382 | + | 0.580067i | ||||
\(233\) | −324.315 | − | 216.700i | −1.39191 | − | 0.930044i | −0.999949 | − | 0.0100614i | \(-0.996797\pi\) |
−0.391960 | − | 0.919982i | \(-0.628203\pi\) | |||||||
\(234\) | −38.7980 | + | 38.7980i | −0.165803 | + | 0.165803i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 20.3050 | − | 49.0206i | 0.0860381 | − | 0.207714i | ||||
\(237\) | 19.4701i | 0.0821523i | ||||||||
\(238\) | −39.1609 | + | 196.875i | −0.164541 | + | 0.827205i | ||||
\(239\) | 372.281 | 1.55766 | 0.778831 | − | 0.627233i | \(-0.215813\pi\) | ||||
0.778831 | + | 0.627233i | \(0.215813\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 136.315 | − | 27.1147i | 0.565621 | − | 0.112509i | 0.0960065 | − | 0.995381i | \(-0.469393\pi\) |
0.469614 | + | 0.882872i | \(0.344393\pi\) | |||||||
\(242\) | −49.3563 | − | 49.3563i | −0.203952 | − | 0.203952i | ||||
\(243\) | 53.2453 | − | 79.6872i | 0.219116 | − | 0.327931i | ||||
\(244\) | 112.755 | + | 22.4284i | 0.462111 | + | 0.0919197i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 36.1388 | + | 87.2468i | 0.146906 | + | 0.354662i | ||||
\(247\) | 27.5818 | − | 11.4248i | 0.111667 | − | 0.0462541i | ||||
\(248\) | −94.7160 | + | 63.2872i | −0.381919 | + | 0.255190i | ||||
\(249\) | −70.4583 | + | 354.218i | −0.282965 | + | 1.42256i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 154.052 | − | 154.052i | 0.613754 | − | 0.613754i | −0.330168 | − | 0.943922i | \(-0.607106\pi\) |
0.943922 | + | 0.330168i | \(0.107106\pi\) | |||||||
\(252\) | −6.94665 | − | 34.9232i | −0.0275661 | − | 0.138584i | ||||
\(253\) | −84.7932 | + | 204.709i | −0.335151 | + | 0.809126i | ||||
\(254\) | 144.168i | 0.567591i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 270.472 | 1.05653 | ||||||||
\(257\) | 391.977 | + | 162.362i | 1.52520 | + | 0.631760i | 0.978626 | − | 0.205648i | \(-0.0659301\pi\) |
0.546578 | + | 0.837408i | \(0.315930\pi\) | |||||||
\(258\) | −83.0389 | + | 16.5175i | −0.321856 | + | 0.0640212i | ||||
\(259\) | 121.222 | + | 121.222i | 0.468039 | + | 0.468039i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −29.2777 | − | 5.82370i | −0.112175 | − | 0.0223130i | ||||
\(262\) | 68.5803 | + | 102.638i | 0.261757 | + | 0.391747i | ||||
\(263\) | 54.7003 | + | 132.058i | 0.207986 | + | 0.502122i | 0.993106 | − | 0.117221i | \(-0.0373987\pi\) |
−0.785120 | + | 0.619344i | \(0.787399\pi\) | |||||||
\(264\) | −170.202 | + | 70.4999i | −0.644704 | + | 0.267045i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.01146 | − | 15.1396i | 0.0113213 | − | 0.0569158i | ||||
\(267\) | 121.921 | + | 81.4652i | 0.456634 | + | 0.305113i | ||||
\(268\) | 110.889 | − | 110.889i | 0.413764 | − | 0.413764i | ||||
\(269\) | 8.93614 | + | 44.9250i | 0.0332199 | + | 0.167008i | 0.993834 | − | 0.110878i | \(-0.0353663\pi\) |
−0.960614 | + | 0.277886i | \(0.910366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 329.809i | 1.21701i | 0.793550 | + | 0.608504i | \(0.208230\pi\) | ||||
−0.793550 | + | 0.608504i | \(0.791770\pi\) | |||||||
\(272\) | 13.9142 | − | 33.5918i | 0.0511551 | − | 0.123499i | ||||
\(273\) | 543.126 | 1.98947 | ||||||||
\(274\) | 125.562 | + | 52.0095i | 0.458255 | + | 0.189816i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −112.978 | − | 112.978i | −0.409341 | − | 0.409341i | ||||
\(277\) | −156.783 | + | 234.642i | −0.566002 | + | 0.847082i | −0.998511 | − | 0.0545479i | \(-0.982628\pi\) |
0.432509 | + | 0.901629i | \(0.357628\pi\) | |||||||
\(278\) | −40.2769 | − | 8.01157i | −0.144881 | − | 0.0288186i | ||||
\(279\) | −13.7685 | − | 20.6060i | −0.0493495 | − | 0.0738568i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 141.231 | − | 58.4999i | 0.502603 | − | 0.208185i | −0.116953 | − | 0.993137i | \(-0.537313\pi\) |
0.619556 | + | 0.784953i | \(0.287313\pi\) | |||||||
\(282\) | 112.872 | − | 75.4189i | 0.400257 | − | 0.267443i | ||||
\(283\) | −62.0182 | + | 311.786i | −0.219145 | + | 1.10172i | 0.701904 | + | 0.712272i | \(0.252334\pi\) |
−0.921049 | + | 0.389447i | \(0.872666\pi\) | |||||||
\(284\) | 194.140 | + | 129.720i | 0.683592 | + | 0.456761i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 49.1414 | + | 247.050i | 0.171823 | + | 0.863813i | ||||
\(287\) | −89.6819 | + | 216.511i | −0.312480 | + | 0.754395i | ||||
\(288\) | 54.6992i | 0.189928i | ||||||||
\(289\) | 204.354 | + | 204.354i | 0.707107 | + | 0.707107i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −196.488 | − | 81.3882i | −0.675218 | − | 0.279684i | ||||
\(292\) | 77.6963 | − | 15.4548i | 0.266083 | − | 0.0529272i | ||||
\(293\) | 27.2633 | + | 27.2633i | 0.0930488 | + | 0.0930488i | 0.752099 | − | 0.659050i | \(-0.229042\pi\) |
−0.659050 | + | 0.752099i | \(0.729042\pi\) | |||||||
\(294\) | 58.7592 | − | 87.9393i | 0.199861 | − | 0.299113i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −89.0814 | − | 133.320i | −0.300951 | − | 0.450404i | ||||
\(297\) | −91.8547 | − | 221.757i | −0.309275 | − | 0.746656i | ||||
\(298\) | −40.5618 | + | 16.8013i | −0.136114 | + | 0.0563801i | ||||
\(299\) | −508.008 | + | 339.440i | −1.69902 | + | 1.13525i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −174.697 | − | 116.729i | −0.580388 | − | 0.387803i | ||||
\(302\) | 132.756 | − | 132.756i | 0.439591 | − | 0.439591i | ||||
\(303\) | 73.6054 | + | 370.039i | 0.242922 | + | 1.22125i | ||||
\(304\) | −1.07000 | + | 2.58320i | −0.00351972 | + | 0.00849736i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 37.7359 | + | 15.6307i | 0.123320 | + | 0.0510807i | ||||
\(307\) | 4.80965 | 0.0156666 | 0.00783330 | − | 0.999969i | \(-0.497507\pi\) | ||||
0.00783330 | + | 0.999969i | \(0.497507\pi\) | |||||||
\(308\) | −151.023 | − | 62.5557i | −0.490334 | − | 0.203103i | ||||
\(309\) | 111.365 | − | 22.1519i | 0.360405 | − | 0.0716890i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 267.024 | − | 399.630i | 0.858598 | − | 1.28498i | −0.0984763 | − | 0.995139i | \(-0.531397\pi\) |
0.957074 | − | 0.289843i | \(-0.0936031\pi\) | |||||||
\(312\) | −498.225 | − | 99.1031i | −1.59688 | − | 0.317638i | ||||
\(313\) | 49.2742 | + | 73.7441i | 0.157426 | + | 0.235604i | 0.901795 | − | 0.432164i | \(-0.142250\pi\) |
−0.744369 | + | 0.667768i | \(0.767250\pi\) | |||||||
\(314\) | −56.5047 | − | 136.414i | −0.179951 | − | 0.434441i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.4352 | − | 8.97712i | 0.0425165 | − | 0.0284086i | ||||
\(317\) | 23.4692 | − | 117.988i | 0.0740353 | − | 0.372201i | −0.925950 | − | 0.377647i | \(-0.876733\pi\) |
0.999985 | + | 0.00544574i | \(0.00173344\pi\) | |||||||
\(318\) | 84.0983 | + | 56.1927i | 0.264460 | + | 0.176707i | ||||
\(319\) | −96.9027 | + | 96.9027i | −0.303770 | + | 0.303770i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −75.7103 | + | 182.781i | −0.235858 | + | 0.569411i | ||||
\(322\) | 315.906i | 0.981074i | ||||||||
\(323\) | −15.7147 | − | 15.7147i | −0.0486524 | − | 0.0486524i | ||||
\(324\) | 136.935 | 0.422639 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −213.347 | + | 42.4374i | −0.654440 | + | 0.130176i | ||||
\(327\) | −398.773 | − | 398.773i | −1.21949 | − | 1.21949i | ||||
\(328\) | 121.774 | − | 182.248i | 0.371263 | − | 0.555634i | ||||
\(329\) | 330.405 | + | 65.7216i | 1.00427 | + | 0.199762i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 38.9023 | + | 93.9184i | 0.117530 | + | 0.283741i | 0.971687 | − | 0.236274i | \(-0.0759262\pi\) |
−0.854157 | + | 0.520015i | \(0.825926\pi\) | |||||||
\(332\) | 276.912 | − | 114.701i | 0.834071 | − | 0.345484i | ||||
\(333\) | 29.0045 | − | 19.3802i | 0.0871006 | − | 0.0581988i | ||||
\(334\) | −43.3183 | + | 217.776i | −0.129695 | + | 0.652023i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −35.9683 | + | 35.9683i | −0.107049 | + | 0.107049i | ||||
\(337\) | 107.223 | + | 539.044i | 0.318168 | + | 1.59954i | 0.726807 | + | 0.686842i | \(0.241004\pi\) |
−0.408639 | + | 0.912696i | \(0.633996\pi\) | |||||||
\(338\) | −179.666 | + | 433.752i | −0.531556 | + | 1.28329i | ||||
\(339\) | − | 385.310i | − | 1.13661i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −113.772 | −0.333642 | ||||||||
\(342\) | −2.90187 | − | 1.20200i | −0.00848501 | − | 0.00351461i | ||||
\(343\) | −168.661 | + | 33.5487i | −0.491722 | + | 0.0978097i | ||||
\(344\) | 138.955 | + | 138.955i | 0.403940 | + | 0.403940i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.8349 | + | 4.34324i | 0.0631067 | + | 0.0125527i | ||||
\(347\) | −141.826 | − | 212.258i | −0.408722 | − | 0.611695i | 0.568814 | − | 0.822466i | \(-0.307403\pi\) |
−0.977535 | + | 0.210771i | \(0.932403\pi\) | |||||||
\(348\) | −37.8162 | − | 91.2964i | −0.108667 | − | 0.262346i | ||||
\(349\) | −513.215 | + | 212.580i | −1.47053 | + | 0.609113i | −0.966980 | − | 0.254854i | \(-0.917973\pi\) |
−0.503549 | + | 0.863967i | \(0.667973\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 129.122 | − | 649.141i | 0.367869 | − | 1.84940i | ||||
\(352\) | 208.792 | + | 139.511i | 0.593160 | + | 0.396337i | ||||
\(353\) | 408.644 | − | 408.644i | 1.15763 | − | 1.15763i | 0.172648 | − | 0.984984i | \(-0.444768\pi\) |
0.984984 | − | 0.172648i | \(-0.0552323\pi\) | |||||||
\(354\) | −16.6117 | − | 83.5128i | −0.0469258 | − | 0.235912i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 121.692i | − | 0.341832i | ||||||
\(357\) | −154.723 | − | 373.534i | −0.433398 | − | 1.04631i | ||||
\(358\) | 51.5822 | 0.144084 | ||||||||
\(359\) | −159.526 | − | 66.0778i | −0.444362 | − | 0.184061i | 0.149272 | − | 0.988796i | \(-0.452307\pi\) |
−0.593634 | + | 0.804735i | \(0.702307\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −254.057 | − | 254.057i | −0.703759 | − | 0.703759i | ||||
\(362\) | −31.9602 | + | 47.8317i | −0.0882877 | + | 0.132132i | ||||
\(363\) | 137.889 | + | 27.4279i | 0.379860 | + | 0.0755588i | ||||
\(364\) | −250.420 | − | 374.780i | −0.687967 | − | 1.02962i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 170.449 | − | 70.6023i | 0.465708 | − | 0.192902i | ||||
\(367\) | 16.9759 | − | 11.3429i | 0.0462558 | − | 0.0309071i | −0.532227 | − | 0.846601i | \(-0.678645\pi\) |
0.578483 | + | 0.815694i | \(0.303645\pi\) | |||||||
\(368\) | 11.1634 | − | 56.1220i | 0.0303352 | − | 0.152505i | ||||
\(369\) | 39.6492 | + | 26.4927i | 0.107450 | + | 0.0717960i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 48.9675 | + | 246.176i | 0.131988 | + | 0.663547i | ||||
\(372\) | 31.3952 | − | 75.7946i | 0.0843956 | − | 0.203749i | ||||
\(373\) | − | 690.960i | − | 1.85244i | −0.376983 | − | 0.926220i | \(-0.623039\pi\) | ||
0.376983 | − | 0.926220i | \(-0.376961\pi\) | |||||||
\(374\) | 155.910 | − | 104.175i | 0.416870 | − | 0.278544i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −291.098 | − | 120.577i | −0.774196 | − | 0.320682i | ||||
\(377\) | −370.619 | + | 73.7207i | −0.983075 | + | 0.195546i | ||||
\(378\) | −241.982 | − | 241.982i | −0.640164 | − | 0.640164i | ||||
\(379\) | −97.1405 | + | 145.381i | −0.256308 | + | 0.383591i | −0.937200 | − | 0.348792i | \(-0.886592\pi\) |
0.680893 | + | 0.732383i | \(0.261592\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −161.327 | − | 241.443i | −0.423431 | − | 0.633709i | ||||
\(382\) | 77.2642 | + | 186.532i | 0.202262 | + | 0.488304i | ||||
\(383\) | −440.512 | + | 182.466i | −1.15016 | + | 0.476412i | −0.874588 | − | 0.484868i | \(-0.838868\pi\) |
−0.275574 | + | 0.961280i | \(0.588868\pi\) | |||||||
\(384\) | −125.144 | + | 83.6184i | −0.325895 | + | 0.217756i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −227.747 | − | 152.176i | −0.590019 | − | 0.394238i | ||||
\(387\) | −30.2306 | + | 30.2306i | −0.0781151 | + | 0.0781151i | ||||
\(388\) | 34.4340 | + | 173.111i | 0.0887473 | + | 0.446163i | ||||
\(389\) | 84.5808 | − | 204.196i | 0.217431 | − | 0.524926i | −0.777098 | − | 0.629379i | \(-0.783309\pi\) |
0.994530 | + | 0.104453i | \(0.0333092\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 378.169 | + | 252.684i | 0.967183 | + | 0.646251i | ||||
\(392\) | −245.482 | −0.626228 | ||||||||
\(393\) | −229.707 | − | 95.1478i | −0.584496 | − | 0.242106i | ||||
\(394\) | 182.889 | − | 36.3788i | 0.464184 | − | 0.0923320i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.4794 | + | 27.6564i | −0.0466652 | + | 0.0698395i | ||||
\(397\) | 118.666 | + | 23.6042i | 0.298908 | + | 0.0594565i | 0.342266 | − | 0.939603i | \(-0.388806\pi\) |
−0.0433581 | + | 0.999060i | \(0.513806\pi\) | |||||||
\(398\) | 109.709 | + | 164.191i | 0.275650 | + | 0.412539i | ||||
\(399\) | 11.8981 | + | 28.7246i | 0.0298199 | + | 0.0719916i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 434.146 | − | 290.087i | 1.08266 | − | 0.723409i | 0.119633 | − | 0.992818i | \(-0.461828\pi\) |
0.963026 | + | 0.269409i | \(0.0868282\pi\) | |||||||
\(402\) | 49.0970 | − | 246.827i | 0.122132 | − | 0.613998i | ||||
\(403\) | −260.846 | − | 174.292i | −0.647262 | − | 0.432486i | ||||
\(404\) | 221.406 | − | 221.406i | 0.548034 | − | 0.548034i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −74.7699 | + | 180.510i | −0.184162 | + | 0.444607i | ||||
\(407\) | − | 160.142i | − | 0.393471i | ||||||
\(408\) | 73.7738 | + | 370.886i | 0.180818 | + | 0.909034i | ||||
\(409\) | 136.013 | 0.332550 | 0.166275 | − | 0.986079i | \(-0.446826\pi\) | ||||
0.166275 | + | 0.986079i | \(0.446826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −268.482 | + | 53.4044i | −0.653241 | + | 0.129938i | ||||
\(412\) | −66.6331 | − | 66.6331i | −0.161731 | − | 0.161731i | ||||
\(413\) | 117.395 | − | 175.694i | 0.284249 | − | 0.425409i | ||||
\(414\) | 63.0455 | + | 12.5405i | 0.152284 | + | 0.0302911i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 264.979 | + | 639.715i | 0.636968 | + | 1.53778i | ||||
\(417\) | 76.4181 | − | 31.6534i | 0.183257 | − | 0.0759074i | ||||
\(418\) | −11.9894 | + | 8.01105i | −0.0286827 | + | 0.0191652i | ||||
\(419\) | 73.0669 | − | 367.332i | 0.174384 | − | 0.876687i | −0.790187 | − | 0.612865i | \(-0.790017\pi\) |
0.964571 | − | 0.263822i | \(-0.0849832\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −273.997 | + | 273.997i | −0.650824 | + | 0.650824i | −0.953192 | − | 0.302367i | \(-0.902223\pi\) |
0.302367 | + | 0.953192i | \(0.402223\pi\) | |||||||
\(422\) | −53.1807 | − | 267.357i | −0.126021 | − | 0.633548i | ||||
\(423\) | 26.2322 | − | 63.3301i | 0.0620146 | − | 0.149716i | ||||
\(424\) | − | 234.759i | − | 0.553678i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 374.701 | 0.879580 | ||||||||
\(427\) | 422.985 | + | 175.206i | 0.990598 | + | 0.410319i | ||||
\(428\) | 161.034 | − | 32.0318i | 0.376249 | − | 0.0748405i | ||||
\(429\) | −358.753 | − | 358.753i | −0.836254 | − | 0.836254i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 67.5084 | + | 13.4283i | 0.156632 | + | 0.0311561i | 0.272783 | − | 0.962075i | \(-0.412056\pi\) |
−0.116151 | + | 0.993232i | \(0.537056\pi\) | |||||||
\(432\) | 34.4381 | + | 51.5402i | 0.0797177 | + | 0.119306i | ||||
\(433\) | 104.262 | + | 251.710i | 0.240790 | + | 0.581317i | 0.997362 | − | 0.0725929i | \(-0.0231274\pi\) |
−0.756572 | + | 0.653910i | \(0.773127\pi\) | |||||||
\(434\) | −149.860 | + | 62.0742i | −0.345301 | + | 0.143028i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −91.3074 | + | 459.033i | −0.209421 | + | 1.05283i | ||||
\(437\) | −29.0810 | − | 19.4313i | −0.0665470 | − | 0.0444653i | ||||
\(438\) | 89.8934 | − | 89.8934i | 0.205236 | − | 0.205236i | ||||
\(439\) | −28.7213 | − | 144.392i | −0.0654244 | − | 0.328910i | 0.934187 | − | 0.356783i | \(-0.116127\pi\) |
−0.999611 | + | 0.0278730i | \(0.991127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 53.4060i | − | 0.121102i | ||||||
\(442\) | 517.046 | 1.16979 | ||||||||
\(443\) | 619.331 | 1.39804 | 0.699019 | − | 0.715103i | \(-0.253620\pi\) | ||||
0.699019 | + | 0.715103i | \(0.253620\pi\) | |||||||
\(444\) | 106.687 | + | 44.1910i | 0.240285 | + | 0.0995293i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −109.484 | − | 109.484i | −0.245480 | − | 0.245480i | ||||
\(447\) | 49.1292 | − | 73.5271i | 0.109909 | − | 0.164490i | ||||
\(448\) | 425.530 | + | 84.6432i | 0.949844 | + | 0.188936i | ||||
\(449\) | 348.576 | + | 521.681i | 0.776339 | + | 1.16187i | 0.983026 | + | 0.183466i | \(0.0587318\pi\) |
−0.206687 | + | 0.978407i | \(0.566268\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 202.251 | − | 83.7750i | 0.448450 | − | 0.185754i | ||||
\(452\) | −265.880 | + | 177.656i | −0.588231 | + | 0.393043i | ||||
\(453\) | −73.7743 | + | 370.888i | −0.162857 | + | 0.818738i | ||||
\(454\) | −169.889 | − | 113.516i | −0.374205 | − | 0.250036i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −5.67318 | − | 28.5210i | −0.0124412 | − | 0.0625460i | ||||
\(457\) | 52.9634 | − | 127.865i | 0.115894 | − | 0.279792i | −0.855280 | − | 0.518167i | \(-0.826615\pi\) |
0.971173 | + | 0.238375i | \(0.0766147\pi\) | |||||||
\(458\) | − | 12.8442i | − | 0.0280442i | ||||||
\(459\) | −483.229 | + | 96.1203i | −1.05279 | + | 0.209412i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −135.609 | − | 56.1709i | −0.294162 | − | 0.121846i | 0.230722 | − | 0.973020i | \(-0.425891\pi\) |
−0.524884 | + | 0.851174i | \(0.675891\pi\) | |||||||
\(462\) | −257.287 | + | 51.1775i | −0.556898 | + | 0.110774i | ||||
\(463\) | −522.332 | − | 522.332i | −1.12815 | − | 1.12815i | −0.990478 | − | 0.137669i | \(-0.956039\pi\) |
−0.137669 | − | 0.990478i | \(-0.543961\pi\) | |||||||
\(464\) | 19.6620 | − | 29.4263i | 0.0423750 | − | 0.0634187i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 288.606 | + | 431.929i | 0.619326 | + | 0.926887i | ||||
\(467\) | 2.92741 | + | 7.06740i | 0.00626855 | + | 0.0151336i | 0.926983 | − | 0.375104i | \(-0.122393\pi\) |
−0.920714 | + | 0.390237i | \(0.872393\pi\) | |||||||
\(468\) | −84.7360 | + | 35.0988i | −0.181060 | + | 0.0749974i | ||||
\(469\) | 519.274 | − | 346.968i | 1.10719 | − | 0.739803i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 247.281 | + | 165.228i | 0.525012 | + | 0.350802i | ||||
\(472\) | −139.748 | + | 139.748i | −0.296077 | + | 0.296077i | ||||
\(473\) | 38.2899 | + | 192.496i | 0.0809512 | + | 0.406969i | ||||
\(474\) | 9.92325 | − | 23.9568i | 0.0209351 | − | 0.0505419i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −186.416 | + | 278.992i | −0.391631 | + | 0.586117i | ||||
\(477\) | 51.0733 | 0.107072 | ||||||||
\(478\) | −458.071 | − | 189.739i | −0.958307 | − | 0.396944i | ||||
\(479\) | −742.358 | + | 147.664i | −1.54981 | + | 0.308276i | −0.894493 | − | 0.447081i | \(-0.852464\pi\) |
−0.655314 | + | 0.755357i | \(0.727464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 245.329 | − | 367.160i | 0.510039 | − | 0.763327i | ||||
\(482\) | −181.547 | − | 36.1119i | −0.376653 | − | 0.0749209i | ||||
\(483\) | −353.505 | − | 529.057i | −0.731894 | − | 1.09536i | ||||
\(484\) | −44.6504 | − | 107.796i | −0.0922529 | − | 0.222718i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −106.129 | + | 70.9132i | −0.218373 | + | 0.145912i | ||||
\(487\) | −1.72321 | + | 8.66318i | −0.00353843 | + | 0.0177889i | −0.982514 | − | 0.186188i | \(-0.940387\pi\) |
0.978976 | + | 0.203977i | \(0.0653867\pi\) | |||||||
\(488\) | −356.047 | − | 237.903i | −0.729605 | − | 0.487506i | ||||
\(489\) | 309.811 | − | 309.811i | 0.633561 | − | 0.633561i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −224.608 | + | 542.252i | −0.457450 | + | 1.10438i | 0.511976 | + | 0.859000i | \(0.328914\pi\) |
−0.969426 | + | 0.245383i | \(0.921086\pi\) | |||||||
\(492\) | 157.857i | 0.320847i | ||||||||
\(493\) | 156.281 | + | 233.892i | 0.317001 | + | 0.474425i | ||||
\(494\) | −39.7607 | −0.0804871 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.8169 | − | 5.73204i | 0.0580986 | − | 0.0115565i | ||||
\(497\) | 657.508 | + | 657.508i | 1.32295 | + | 1.32295i | ||||
\(498\) | 267.228 | − | 399.934i | 0.536602 | − | 0.803081i | ||||
\(499\) | −109.936 | − | 21.8676i | −0.220312 | − | 0.0438229i | 0.0836997 | − | 0.996491i | \(-0.473326\pi\) |
−0.304012 | + | 0.952668i | \(0.598326\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −171.149 | − | 413.190i | −0.341614 | − | 0.824730i | ||||
\(502\) | −268.067 | + | 111.037i | −0.533999 | + | 0.221190i | ||||
\(503\) | 397.401 | − | 265.535i | 0.790061 | − | 0.527902i | −0.0938335 | − | 0.995588i | \(-0.529912\pi\) |
0.883895 | + | 0.467686i | \(0.154912\pi\) | |||||||
\(504\) | −25.8746 | + | 130.080i | −0.0513385 | + | 0.258096i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 208.666 | − | 208.666i | 0.412384 | − | 0.412384i | ||||
\(507\) | −184.485 | − | 927.468i | −0.363875 | − | 1.82933i | ||||
\(508\) | −92.2226 | + | 222.645i | −0.181541 | + | 0.438278i | ||||
\(509\) | − | 235.103i | − | 0.461891i | −0.972967 | − | 0.230946i | \(-0.925818\pi\) | ||
0.972967 | − | 0.230946i | \(-0.0741820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 315.481 | 0.617380 | ||||||||
\(512\) | −125.455 | − | 51.9650i | −0.245029 | − | 0.101494i | ||||
\(513\) | 37.1602 | − | 7.39162i | 0.0724370 | − | 0.0144086i | ||||
\(514\) | −399.555 | − | 399.555i | −0.777345 | − | 0.777345i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −138.807 | − | 27.6104i | −0.269005 | − | 0.0535084i | ||||
\(517\) | −174.832 | − | 261.655i | −0.338166 | − | 0.506102i | ||||
\(518\) | −87.3740 | − | 210.940i | −0.168676 | − | 0.407219i | ||||
\(519\) | −41.4278 | + | 17.1600i | −0.0798223 | + | 0.0330635i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −118.016 | + | 593.308i | −0.226519 | + | 1.13879i | 0.685321 | + | 0.728241i | \(0.259662\pi\) |
−0.911840 | + | 0.410546i | \(0.865338\pi\) | |||||||
\(522\) | 33.0564 | + | 22.0876i | 0.0633265 | + | 0.0423134i | ||||
\(523\) | −721.650 | + | 721.650i | −1.37983 | + | 1.37983i | −0.534934 | + | 0.844894i | \(0.679664\pi\) |
−0.844894 | + | 0.534934i | \(0.820336\pi\) | |||||||
\(524\) | 40.2554 | + | 202.378i | 0.0768233 | + | 0.386217i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 190.369i | − | 0.361918i | ||||||
\(527\) | −45.5605 | + | 229.048i | −0.0864526 | + | 0.434627i | ||||
\(528\) | 47.5166 | 0.0899935 | ||||||||
\(529\) | 172.563 | + | 71.4781i | 0.326207 | + | 0.135119i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −30.4031 | − | 30.4031i | −0.0572563 | − | 0.0572563i | ||||
\(532\) | 14.3353 | − | 21.4544i | 0.0269461 | − | 0.0403277i | ||||
\(533\) | 592.041 | + | 117.764i | 1.11077 | + | 0.220946i | ||||
\(534\) | −108.497 | − | 162.377i | −0.203178 | − | 0.304078i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −539.655 | + | 223.533i | −1.00682 | + | 0.417038i | ||||
\(537\) | −86.3863 | + | 57.7215i | −0.160868 | + | 0.107489i | ||||
\(538\) | 11.9013 | − | 59.8321i | 0.0221215 | − | 0.111212i | ||||
\(539\) | −203.856 | − | 136.212i | −0.378212 | − | 0.252713i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 110.903 | + | 557.546i | 0.204996 | + | 1.03058i | 0.937012 | + | 0.349297i | \(0.113580\pi\) |
−0.732016 | + | 0.681288i | \(0.761420\pi\) | |||||||
\(542\) | 168.093 | − | 405.812i | 0.310134 | − | 0.748730i | ||||
\(543\) | − | 115.869i | − | 0.213387i | ||||||
\(544\) | 364.477 | − | 364.477i | 0.669995 | − | 0.669995i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −668.285 | − | 276.813i | −1.22397 | − | 0.506983i | ||||
\(547\) | 359.860 | − | 71.5805i | 0.657879 | − | 0.130860i | 0.145148 | − | 0.989410i | \(-0.453634\pi\) |
0.512730 | + | 0.858550i | \(0.328634\pi\) | |||||||
\(548\) | 160.641 | + | 160.641i | 0.293140 | + | 0.293140i | ||||
\(549\) | 51.7573 | − | 77.4602i | 0.0942755 | − | 0.141093i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −12.0180 | − | 17.9862i | −0.0218112 | − | 0.0326428i | ||||
\(552\) | 227.744 | + | 549.823i | 0.412580 | + | 0.996056i | ||||
\(553\) | 59.4512 | − | 24.6255i | 0.107507 | − | 0.0445307i | ||||
\(554\) | 312.501 | − | 208.806i | 0.564081 | − | 0.376907i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −57.0764 | − | 38.1372i | −0.102655 | − | 0.0685922i | ||||
\(557\) | 146.512 | − | 146.512i | 0.263038 | − | 0.263038i | −0.563249 | − | 0.826287i | \(-0.690449\pi\) |
0.826287 | + | 0.563249i | \(0.190449\pi\) | |||||||
\(558\) | 6.43917 | + | 32.3719i | 0.0115397 | + | 0.0580141i | ||||
\(559\) | −207.105 | + | 499.996i | −0.370493 | + | 0.894448i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −144.532 | + | 348.932i | −0.257633 | + | 0.621981i | ||||
\(562\) | −203.593 | −0.362264 | ||||||||
\(563\) | −793.273 | − | 328.584i | −1.40901 | − | 0.583631i | −0.456936 | − | 0.889499i | \(-0.651053\pi\) |
−0.952074 | + | 0.305868i | \(0.901053\pi\) | |||||||
\(564\) | 222.558 | − | 44.2696i | 0.394607 | − | 0.0784922i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 235.217 | − | 352.027i | 0.415577 | − | 0.621955i | ||||
\(567\) | 534.854 | + | 106.389i | 0.943306 | + | 0.187635i | ||||
\(568\) | −483.177 | − | 723.125i | −0.850663 | − | 1.27311i | ||||
\(569\) | 120.952 | + | 292.003i | 0.212569 | + | 0.513187i | 0.993817 | − | 0.111034i | \(-0.0354164\pi\) |
−0.781248 | + | 0.624221i | \(0.785416\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 224.810 | − | 150.213i | 0.393713 | − | 0.263071i | −0.342918 | − | 0.939365i | \(-0.611415\pi\) |
0.736631 | + | 0.676294i | \(0.236415\pi\) | |||||||
\(572\) | −82.1440 | + | 412.966i | −0.143608 | + | 0.721968i | ||||
\(573\) | −338.130 | − | 225.931i | −0.590105 | − | 0.394295i | ||||
\(574\) | 220.697 | − | 220.697i | 0.384489 | − | 0.384489i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 33.7846 | − | 81.5632i | 0.0586538 | − | 0.141603i | ||||
\(577\) | − | 63.2031i | − | 0.109537i | −0.998499 | − | 0.0547687i | \(-0.982558\pi\) | ||
0.998499 | − | 0.0547687i | \(-0.0174421\pi\) | |||||||
\(578\) | −147.293 | − | 355.598i | −0.254833 | − | 0.615221i | ||||
\(579\) | 551.703 | 0.952855 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1170.70 | − | 232.868i | 2.01498 | − | 0.400805i | ||||
\(582\) | 200.287 | + | 200.287i | 0.344136 | + | 0.344136i | ||||
\(583\) | 130.263 | − | 194.952i | 0.223435 | − | 0.334395i | ||||
\(584\) | −289.400 | − | 57.5653i | −0.495548 | − | 0.0985706i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.6507 | − | 47.4411i | −0.0335337 | − | 0.0809575i | ||||
\(587\) | −685.040 | + | 283.753i | −1.16702 | + | 0.483395i | −0.880206 | − | 0.474592i | \(-0.842596\pi\) |
−0.286812 | + | 0.957987i | \(0.592596\pi\) | |||||||
\(588\) | 146.998 | − | 98.2209i | 0.249997 | − | 0.167042i | ||||
\(589\) | 3.50359 | − | 17.6137i | 0.00594837 | − | 0.0299045i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −265.581 | + | 265.581i | −0.449375 | + | 0.449375i | ||||
\(592\) | 8.06826 | + | 40.5619i | 0.0136288 | + | 0.0685167i | ||||
\(593\) | 76.8977 | − | 185.647i | 0.129676 | − | 0.313065i | −0.845685 | − | 0.533683i | \(-0.820808\pi\) |
0.975360 | + | 0.220618i | \(0.0708075\pi\) | |||||||
\(594\) | 319.674i | 0.538172i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −73.3889 | −0.123136 | ||||||||
\(597\) | −367.465 | − | 152.209i | −0.615519 | − | 0.254956i | ||||
\(598\) | 798.076 | − | 158.747i | 1.33458 | − | 0.265464i | ||||
\(599\) | 457.825 | + | 457.825i | 0.764316 | + | 0.764316i | 0.977099 | − | 0.212784i | \(-0.0682529\pi\) |
−0.212784 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 703.378 | + | 139.911i | 1.17035 | + | 0.232796i | 0.741735 | − | 0.670693i | \(-0.234003\pi\) |
0.428611 | + | 0.903489i | \(0.359003\pi\) | |||||||
\(602\) | 155.462 | + | 232.665i | 0.258242 | + | 0.386487i | ||||
\(603\) | −48.6309 | − | 117.405i | −0.0806482 | − | 0.194702i | ||||
\(604\) | 289.944 | − | 120.099i | 0.480040 | − | 0.198839i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 98.0293 | − | 492.826i | 0.161764 | − | 0.813245i | ||||
\(607\) | 863.573 | + | 577.021i | 1.42269 | + | 0.950612i | 0.998996 | + | 0.0448067i | \(0.0142672\pi\) |
0.423695 | + | 0.905805i | \(0.360733\pi\) | |||||||
\(608\) | −28.0282 | + | 28.0282i | −0.0460990 | + | 0.0460990i | ||||
\(609\) | −76.7753 | − | 385.975i | −0.126068 | − | 0.633786i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 867.731i | − | 1.42018i | ||||||
\(612\) | 48.2783 | + | 48.2783i | 0.0788861 | + | 0.0788861i | ||||
\(613\) | 626.391 | 1.02185 | 0.510923 | − | 0.859627i | \(-0.329304\pi\) | ||||
0.510923 | + | 0.859627i | \(0.329304\pi\) | |||||||
\(614\) | −5.91799 | − | 2.45131i | −0.00963842 | − | 0.00399237i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 430.537 | + | 430.537i | 0.698924 | + | 0.698924i | ||||
\(617\) | 372.249 | − | 557.109i | 0.603320 | − | 0.902933i | −0.396566 | − | 0.918006i | \(-0.629798\pi\) |
0.999886 | + | 0.0150736i | \(0.00479825\pi\) | |||||||
\(618\) | −148.319 | − | 29.5024i | −0.239998 | − | 0.0477385i | ||||
\(619\) | −437.249 | − | 654.389i | −0.706379 | − | 1.05717i | −0.995014 | − | 0.0997323i | \(-0.968201\pi\) |
0.288635 | − | 0.957439i | \(-0.406799\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −716.368 | + | 296.729i | −1.15357 | + | 0.477825i | ||||
\(622\) | −532.235 | + | 355.628i | −0.855684 | + | 0.571749i | ||||
\(623\) | 94.5466 | − | 475.318i | 0.151760 | − | 0.762950i | ||||
\(624\) | 108.942 | + | 72.7926i | 0.174586 | + | 0.116655i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −23.0442 | − | 115.851i | −0.0368119 | − | 0.185066i | ||||
\(627\) | 11.1145 | − | 26.8327i | 0.0177264 | − | 0.0427954i | ||||
\(628\) | − | 246.816i | − | 0.393019i | ||||||
\(629\) | −322.402 | − | 64.1298i | −0.512563 | − | 0.101955i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −767.465 | − | 317.894i | −1.21627 | − | 0.503794i | −0.320046 | − | 0.947402i | \(-0.603698\pi\) |
−0.896221 | + | 0.443608i | \(0.853698\pi\) | |||||||
\(632\) | −59.0297 | + | 11.7417i | −0.0934013 | + | 0.0185787i | ||||
\(633\) | 388.241 | + | 388.241i | 0.613336 | + | 0.613336i | ||||
\(634\) | −89.0118 | + | 133.216i | −0.140397 | + | 0.210119i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 93.9308 | + | 140.577i | 0.147690 | + | 0.221034i | ||||
\(637\) | −258.714 | − | 624.591i | −0.406145 | − | 0.980520i | ||||
\(638\) | 168.621 | − | 69.8452i | 0.264297 | − | 0.109475i | ||||
\(639\) | 157.320 | − | 105.118i | 0.246198 | − | 0.164504i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −703.209 | − | 469.870i | −1.09705 | − | 0.733026i | −0.131001 | − | 0.991382i | \(-0.541819\pi\) |
−0.966050 | + | 0.258357i | \(0.916819\pi\) | |||||||
\(642\) | 186.314 | − | 186.314i | 0.290209 | − | 0.290209i | ||||
\(643\) | 144.203 | + | 724.957i | 0.224266 | + | 1.12746i | 0.914721 | + | 0.404085i | \(0.132410\pi\) |
−0.690456 | + | 0.723375i | \(0.742590\pi\) | |||||||
\(644\) | −202.081 | + | 487.867i | −0.313790 | + | 0.757557i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 11.3268 | + | 27.3453i | 0.0175338 | + | 0.0423303i | ||||
\(647\) | −874.070 | −1.35096 | −0.675479 | − | 0.737379i | \(-0.736063\pi\) | ||||
−0.675479 | + | 0.737379i | \(0.736063\pi\) | |||||||
\(648\) | −471.225 | − | 195.188i | −0.727199 | − | 0.301216i | ||||
\(649\) | −193.595 | + | 38.5084i | −0.298297 | + | 0.0593350i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 181.514 | − | 271.654i | 0.278823 | − | 0.417288i | ||||
\(652\) | −356.628 | − | 70.9377i | −0.546976 | − | 0.108800i | ||||
\(653\) | 642.117 | + | 960.997i | 0.983335 | + | 1.47166i | 0.878827 | + | 0.477140i | \(0.158327\pi\) |
0.104507 | + | 0.994524i | \(0.466673\pi\) | |||||||
\(654\) | 287.426 | + | 693.908i | 0.439489 | + | 1.06102i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −47.0066 | + | 31.4088i | −0.0716565 | + | 0.0478793i | ||||
\(657\) | 12.5237 | − | 62.9607i | 0.0190619 | − | 0.0958307i | ||||
\(658\) | −373.048 | − | 249.263i | −0.566942 | − | 0.378819i | ||||
\(659\) | −318.726 | + | 318.726i | −0.483651 | + | 0.483651i | −0.906295 | − | 0.422645i | \(-0.861102\pi\) |
0.422645 | + | 0.906295i | \(0.361102\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 191.121 | − | 461.408i | 0.289140 | − | 0.698045i | −0.710846 | − | 0.703347i | \(-0.751688\pi\) |
0.999986 | + | 0.00530241i | \(0.00168782\pi\) | |||||||
\(662\) | − | 135.388i | − | 0.204514i | ||||||
\(663\) | −865.913 | + | 578.585i | −1.30605 | + | 0.872677i | ||||
\(664\) | −1116.41 | −1.68134 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −45.5658 | + | 9.06360i | −0.0684171 | + | 0.0136090i | ||||
\(667\) | 313.036 | + | 313.036i | 0.469320 | + | 0.469320i | ||||
\(668\) | −206.207 | + | 308.610i | −0.308693 | + | 0.461991i | ||||
\(669\) | 305.871 | + | 60.8416i | 0.457207 | + | 0.0909441i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −163.666 | − | 395.126i | −0.243914 | − | 0.588861i | ||||
\(672\) | −666.221 | + | 275.958i | −0.991400 | + | 0.410651i | ||||
\(673\) | 781.320 | − | 522.061i | 1.16095 | − | 0.775722i | 0.182704 | − | 0.983168i | \(-0.441515\pi\) |
0.978247 | + | 0.207446i | \(0.0665151\pi\) | |||||||
\(674\) | 142.801 | − | 717.911i | 0.211871 | − | 1.06515i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −554.932 | + | 554.932i | −0.820905 | + | 0.820905i | ||||
\(677\) | −217.100 | − | 1091.43i | −0.320679 | − | 1.61216i | −0.719065 | − | 0.694943i | \(-0.755430\pi\) |
0.398386 | − | 0.917218i | \(-0.369570\pi\) | |||||||
\(678\) | −196.379 | + | 474.102i | −0.289645 | + | 0.699265i | ||||
\(679\) | 702.908i | 1.03521i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 411.546 | 0.604325 | ||||||||
\(682\) | 139.990 | + | 57.9857i | 0.205264 | + | 0.0850231i | ||||
\(683\) | −1289.29 | + | 256.456i | −1.88769 | + | 0.375484i | −0.996882 | − | 0.0789027i | \(-0.974858\pi\) |
−0.890804 | + | 0.454387i | \(0.849858\pi\) | |||||||
\(684\) | −3.71259 | − | 3.71259i | −0.00542776 | − | 0.00542776i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 224.626 | + | 44.6809i | 0.327443 | + | 0.0651325i | ||||
\(687\) | 14.3730 | + | 21.5107i | 0.0209213 | + | 0.0313110i | ||||
\(688\) | −19.3966 | − | 46.8276i | −0.0281928 | − | 0.0680634i | ||||
\(689\) | 597.310 | − | 247.414i | 0.866923 | − | 0.359091i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 93.4894 | − | 470.003i | 0.135296 | − | 0.680178i | −0.852286 | − | 0.523075i | \(-0.824785\pi\) |
0.987582 | − | 0.157103i | \(-0.0502154\pi\) | |||||||
\(692\) | 30.9423 | + | 20.6750i | 0.0447143 | + | 0.0298771i | ||||
\(693\) | −93.6660 | + | 93.6660i | −0.135160 | + | 0.135160i | ||||
\(694\) | 66.3285 | + | 333.456i | 0.0955742 | + | 0.480484i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 368.075i | 0.528844i | ||||||||
\(697\) | −87.6654 | − | 440.724i | −0.125775 | − | 0.632315i | ||||
\(698\) | 739.826 | 1.05992 | ||||||||
\(699\) | −966.675 | − | 400.410i | −1.38294 | − | 0.572832i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 777.458 | + | 777.458i | 1.10907 | + | 1.10907i | 0.993273 | + | 0.115796i | \(0.0369420\pi\) |
0.115796 | + | 0.993273i | \(0.463058\pi\) | |||||||
\(702\) | −489.722 | + | 732.921i | −0.697610 | + | 1.04405i | ||||
\(703\) | 24.7926 | + | 4.93156i | 0.0352669 | + | 0.00701502i | ||||
\(704\) | −225.167 | − | 336.987i | −0.319840 | − | 0.478674i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −711.085 | + | 294.541i | −1.00720 | + | 0.417197i | ||||
\(707\) | 1036.81 | − | 692.771i | 1.46649 | − | 0.979875i | ||||
\(708\) | 27.7679 | − | 139.599i | 0.0392202 | − | 0.197173i | ||||
\(709\) | 433.937 | + | 289.947i | 0.612041 | + | 0.408953i | 0.822593 | − | 0.568630i | \(-0.192526\pi\) |
−0.210553 | + | 0.977583i | \(0.567526\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.55448 | − | 12.8423i | −0.00359281 | − | 0.0180623i | ||||
\(712\) | −173.461 | + | 418.771i | −0.243625 | + | 0.588162i | ||||
\(713\) | 367.531i | 0.515472i | ||||||||
\(714\) | 538.469i | 0.754159i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 79.6605 | + | 32.9965i | 0.111258 | + | 0.0460845i | ||||
\(717\) | 979.467 | − | 194.828i | 1.36606 | − | 0.271727i | ||||
\(718\) | 162.610 | + | 162.610i | 0.226476 | + | 0.226476i | ||||
\(719\) | −345.349 | + | 516.851i | −0.480318 | + | 0.718847i | −0.989930 | − | 0.141557i | \(-0.954789\pi\) |
0.509612 | + | 0.860404i | \(0.329789\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −208.493 | − | 312.032i | −0.289172 | − | 0.432776i | ||||
\(722\) | 183.118 | + | 442.087i | 0.253627 | + | 0.612309i | ||||
\(723\) | 344.452 | − | 142.677i | 0.476420 | − | 0.197340i | ||||
\(724\) | −79.9548 | + | 53.4241i | −0.110435 | + | 0.0737902i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −155.686 | − | 104.026i | −0.214443 | − | 0.143286i | ||||
\(727\) | −181.405 | + | 181.405i | −0.249526 | + | 0.249526i | −0.820776 | − | 0.571250i | \(-0.806459\pi\) |
0.571250 | + | 0.820776i | \(0.306459\pi\) | |||||||
\(728\) | 327.540 | + | 1646.65i | 0.449917 | + | 2.26189i | ||||
\(729\) | 310.231 | − | 748.965i | 0.425557 | − | 1.02739i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 402.871 | 0.551123 | ||||||||
\(732\) | 308.395 | 0.421305 | ||||||||
\(733\) | −204.776 | − | 84.8211i | −0.279367 | − | 0.115718i | 0.238600 | − | 0.971118i | \(-0.423311\pi\) |
−0.517968 | + | 0.855400i | \(0.673311\pi\) | |||||||
\(734\) | −26.6690 | + | 5.30478i | −0.0363337 | + | 0.00722723i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 450.677 | − | 674.487i | 0.612334 | − | 0.916422i | ||||
\(737\) | −572.182 | − | 113.814i | −0.776366 | − | 0.154429i | ||||
\(738\) | −35.2836 | − | 52.8056i | −0.0478097 | − | 0.0715523i | ||||
\(739\) | 113.071 | + | 272.978i | 0.153006 | + | 0.369388i | 0.981733 | − | 0.190265i | \(-0.0609346\pi\) |
−0.828727 | + | 0.559653i | \(0.810935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 66.5884 | − | 44.4929i | 0.0898629 | − | 0.0600445i | ||||
\(742\) | 65.2159 | − | 327.862i | 0.0878920 | − | 0.441863i | ||||
\(743\) | 622.570 | + | 415.988i | 0.837914 | + | 0.559876i | 0.898846 | − | 0.438265i | \(-0.144407\pi\) |
−0.0609312 | + | 0.998142i | \(0.519407\pi\) | |||||||
\(744\) | −216.076 | + | 216.076i | −0.290425 | + | 0.290425i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −352.159 | + | 850.187i | −0.472063 | + | 1.13966i | ||||
\(747\) | − | 242.882i | − | 0.325143i | ||||||
\(748\) | 307.417 | − | 61.1491i | 0.410986 | − | 0.0817502i | ||||
\(749\) | 653.871 | 0.872992 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −683.178 | + | 135.892i | −0.909691 | + | 0.180949i | −0.627688 | − | 0.778465i | \(-0.715999\pi\) |
−0.282003 | + | 0.959414i | \(0.590999\pi\) | |||||||
\(752\) | 57.4652 | + | 57.4652i | 0.0764165 | + | 0.0764165i | ||||
\(753\) | 324.688 | − | 485.930i | 0.431193 | − | 0.645326i | ||||
\(754\) | 493.598 | + | 98.1828i | 0.654640 | + | 0.130216i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −218.910 | − | 528.496i | −0.289564 | − | 0.699069i | ||||
\(757\) | 633.525 | − | 262.415i | 0.836889 | − | 0.346651i | 0.0772631 | − | 0.997011i | \(-0.475382\pi\) |
0.759626 | + | 0.650360i | \(0.225382\pi\) | |||||||
\(758\) | 193.622 | − | 129.374i | 0.255438 | − | 0.170678i | ||||
\(759\) | −115.958 | + | 582.962i | −0.152778 | + | 0.768066i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −305.005 | + | 305.005i | −0.400795 | + | 0.400795i | −0.878513 | − | 0.477718i | \(-0.841464\pi\) |
0.477718 | + | 0.878513i | \(0.341464\pi\) | |||||||
\(762\) | 75.4484 | + | 379.305i | 0.0990136 | + | 0.497775i | ||||
\(763\) | −713.275 | + | 1722.00i | −0.934830 | + | 2.25688i | ||||
\(764\) | 337.495i | 0.441747i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 635.021 | 0.829009 | ||||||||
\(767\) | −502.850 | − | 208.287i | −0.655606 | − | 0.271561i | ||||
\(768\) | 711.607 | − | 141.547i | 0.926572 | − | 0.184307i | ||||
\(769\) | 303.275 | + | 303.275i | 0.394376 | + | 0.394376i | 0.876244 | − | 0.481868i | \(-0.160041\pi\) |
−0.481868 | + | 0.876244i | \(0.660041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1116.26 | + | 222.037i | 1.44780 | + | 0.287986i | ||||
\(772\) | −254.375 | − | 380.699i | −0.329501 | − | 0.493133i | ||||
\(773\) | 79.8088 | + | 192.675i | 0.103246 | + | 0.249257i | 0.967058 | − | 0.254557i | \(-0.0819297\pi\) |
−0.863812 | + | 0.503814i | \(0.831930\pi\) | |||||||
\(774\) | 52.6045 | − | 21.7895i | 0.0679644 | − | 0.0281518i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 128.258 | − | 644.798i | 0.165281 | − | 0.830925i | ||||
\(777\) | 382.373 | + | 255.494i | 0.492115 | + | 0.328821i | ||||
\(778\) | −208.144 | + | 208.144i | −0.267537 | + | 0.267537i | ||||
\(779\) | 6.74144 | + | 33.8915i | 0.00865396 | + | 0.0435064i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 868.612i | − | 1.11218i | ||||||
\(782\) | −336.530 | − | 503.653i | −0.430345 | − | 0.644058i | ||||
\(783\) | −479.568 | −0.612475 | ||||||||
\(784\) | 58.4966 | + | 24.2301i | 0.0746130 | + | 0.0309057i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 234.148 | + | 234.148i | 0.297898 | + | 0.297898i | ||||
\(787\) | −614.498 | + | 919.662i | −0.780811 | + | 1.16857i | 0.201164 | + | 0.979558i | \(0.435527\pi\) |
−0.981975 | + | 0.189009i | \(0.939473\pi\) | |||||||
\(788\) | 305.714 | + | 60.8102i | 0.387962 | + | 0.0771703i | ||||
\(789\) | 213.027 | + | 318.817i | 0.269996 | + | 0.404077i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1176.53 | + | 487.334i | −1.48739 | + | 0.616099i | ||||
\(792\) | 103.014 | − | 68.8315i | 0.130068 | − | 0.0869084i | ||||
\(793\) | 230.069 | − | 1156.64i | 0.290125 | − | 1.45856i | ||||
\(794\) | −133.982 | − | 89.5239i | −0.168743 | − | 0.112750i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 64.3970 | + | 323.746i | 0.0809008 | + | 0.406716i | ||||
\(797\) | 23.4701 | − | 56.6619i | 0.0294481 | − | 0.0710940i | −0.908471 | − | 0.417947i | \(-0.862750\pi\) |
0.937919 | + | 0.346853i | \(0.112750\pi\) | |||||||
\(798\) | − | 41.4081i | − | 0.0518899i | ||||||
\(799\) | −596.781 | + | 247.195i | −0.746910 | + | 0.309380i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −91.1062 | − | 37.7374i | −0.113741 | − | 0.0471129i | ||||
\(802\) | −682.039 | + | 135.666i | −0.850423 | + | 0.169160i | ||||
\(803\) | −208.386 | − | 208.386i | −0.259509 | − | 0.259509i | ||||
\(804\) | 233.715 | − | 349.779i | 0.290690 | − | 0.435049i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 232.126 | + | 347.401i | 0.287997 | + | 0.431018i | ||||
\(807\) | 47.0217 | + | 113.521i | 0.0582673 | + | 0.140670i | ||||
\(808\) | −1077.50 | + | 446.315i | −1.33354 | + | 0.552370i | ||||
\(809\) | 676.209 | − | 451.829i | 0.835858 | − | 0.558503i | −0.0623592 | − | 0.998054i | \(-0.519862\pi\) |
0.898218 | + | 0.439551i | \(0.144862\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 961.868 | + | 642.700i | 1.18603 | + | 0.792478i | 0.982440 | − | 0.186579i | \(-0.0597399\pi\) |
0.203587 | + | 0.979057i | \(0.434740\pi\) | |||||||
\(812\) | −230.941 | + | 230.941i | −0.284410 | + | 0.284410i | ||||
\(813\) | 172.601 | + | 867.724i | 0.212301 | + | 1.06731i | ||||
\(814\) | −81.6192 | + | 197.046i | −0.100269 | + | 0.242071i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 19.0282 | − | 95.6614i | 0.0233189 | − | 0.117232i | ||||
\(817\) | −30.9806 | −0.0379200 | ||||||||
\(818\) | −167.356 | − | 69.3211i | −0.204592 | − | 0.0847446i | ||||
\(819\) | −358.240 | + | 71.2583i | −0.437411 | + | 0.0870065i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 555.958 | − | 832.050i | 0.677172 | − | 1.01346i | −0.320631 | − | 0.947204i | \(-0.603895\pi\) |
0.997803 | − | 0.0662547i | \(-0.0211050\pi\) | |||||||
\(822\) | 357.570 | + | 71.1252i | 0.435000 | + | 0.0865270i | ||||
\(823\) | −30.1009 | − | 45.0492i | −0.0365746 | − | 0.0547378i | 0.812732 | − | 0.582638i | \(-0.197979\pi\) |
−0.849306 | + | 0.527900i | \(0.822979\pi\) | |||||||
\(824\) | 134.321 | + | 324.279i | 0.163011 | + | 0.393542i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −233.993 | + | 156.349i | −0.283284 | + | 0.189285i | ||||
\(827\) | −80.0267 | + | 402.321i | −0.0967675 | + | 0.486483i | 0.901760 | + | 0.432237i | \(0.142276\pi\) |
−0.998528 | + | 0.0542461i | \(0.982724\pi\) | |||||||
\(828\) | 89.3418 | + | 59.6963i | 0.107901 | + | 0.0720970i | ||||
\(829\) | −153.097 | + | 153.097i | −0.184677 | + | 0.184677i | −0.793390 | − | 0.608713i | \(-0.791686\pi\) |
0.608713 | + | 0.793390i | \(0.291686\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −289.696 | + | 699.389i | −0.348612 | + | 0.841623i | ||||
\(832\) | − | 1117.56i | − | 1.34322i | ||||||
\(833\) | −355.861 | + | 355.861i | −0.427204 | + | 0.427204i | ||||
\(834\) | −110.161 | −0.132087 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −23.6403 | + | 4.70235i | −0.0282779 | + | 0.00562482i | ||||
\(837\) | −281.527 | − | 281.527i | −0.336352 | − | 0.336352i | ||||
\(838\) | −277.121 | + | 414.741i | −0.330694 | + | 0.494918i | ||||
\(839\) | −278.253 | − | 55.3480i | −0.331648 | − | 0.0659690i | 0.0264576 | − | 0.999650i | \(-0.491577\pi\) |
−0.358106 | + | 0.933681i | \(0.616577\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −217.057 | − | 524.021i | −0.258094 | − | 0.623093i | ||||
\(842\) | 476.785 | − | 197.491i | 0.566252 | − | 0.234549i | ||||
\(843\) | 340.963 | − | 227.824i | 0.404463 | − | 0.270254i | ||||
\(844\) | 88.8960 | − | 446.910i | 0.105327 | − | 0.529515i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −64.5544 | + | 64.5544i | −0.0763054 | + | 0.0763054i | ||||
\(847\) | −90.6502 | − | 455.729i | −0.107025 | − | 0.538051i | ||||
\(848\) | −23.1718 | + | 55.9416i | −0.0273252 | + | 0.0659689i | ||||
\(849\) | 852.762i | 1.00443i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −517.327 | −0.607905 | ||||||||
\(852\) | 578.667 | + | 239.692i | 0.679187 | + | 0.281328i | ||||
\(853\) | 559.124 | − | 111.217i | 0.655479 | − | 0.130383i | 0.143864 | − | 0.989598i | \(-0.454047\pi\) |
0.511615 | + | 0.859215i | \(0.329047\pi\) | |||||||
\(854\) | −431.162 | − | 431.162i | −0.504874 | − | 0.504874i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −599.815 | − | 119.311i | −0.700718 | − | 0.139382i | ||||
\(857\) | 738.200 | + | 1104.79i | 0.861377 | + | 1.28914i | 0.955922 | + | 0.293622i | \(0.0948605\pi\) |
−0.0945445 | + | 0.995521i | \(0.530139\pi\) | |||||||
\(858\) | 258.581 | + | 624.269i | 0.301376 | + | 0.727586i | ||||
\(859\) | 260.316 | − | 107.826i | 0.303046 | − | 0.125526i | −0.225979 | − | 0.974132i | \(-0.572558\pi\) |
0.529024 | + | 0.848607i | \(0.322558\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −122.644 | + | 616.572i | −0.142443 | + | 0.716111i | ||||
\(862\) | −76.2213 | − | 50.9295i | −0.0884238 | − | 0.0590829i | ||||
\(863\) | −44.4457 | + | 44.4457i | −0.0515014 | + | 0.0515014i | −0.732388 | − | 0.680887i | \(-0.761594\pi\) |
0.680887 | + | 0.732388i | \(0.261594\pi\) | |||||||
\(864\) | 171.436 | + | 861.869i | 0.198422 | + | 0.997533i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 362.854i | − | 0.419000i | ||||||
\(867\) | 644.598 | + | 430.707i | 0.743481 | + | 0.496778i | ||||
\(868\) | −271.144 | −0.312378 | ||||||||
\(869\) | −55.5355 | − | 23.0035i | −0.0639073 | − | 0.0264713i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1137.49 | − | 1137.49i | −1.30596 | − | 1.30596i | ||||
\(872\) | 968.518 | − | 1449.49i | 1.11069 | − | 1.66226i | ||||
\(873\) | 140.280 | + | 27.9034i | 0.160687 | + | 0.0319626i | ||||
\(874\) | 25.8790 | + | 38.7307i | 0.0296099 | + | 0.0443143i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 196.330 | − | 81.3225i | 0.224121 | − | 0.0928339i | ||||
\(877\) | −374.931 | + | 250.521i | −0.427515 | + | 0.285657i | −0.750655 | − | 0.660695i | \(-0.770262\pi\) |
0.323139 | + | 0.946351i | \(0.395262\pi\) | |||||||
\(878\) | −38.2516 | + | 192.304i | −0.0435668 | + | 0.219025i | ||||
\(879\) | 85.9972 | + | 57.4615i | 0.0978353 | + | 0.0653714i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 192.046 | + | 965.483i | 0.217987 | + | 1.09589i | 0.922439 | + | 0.386143i | \(0.126193\pi\) |
−0.704452 | + | 0.709752i | \(0.748807\pi\) | |||||||
\(882\) | −27.2192 | + | 65.7130i | −0.0308608 | + | 0.0745046i | ||||
\(883\) | 908.452i | 1.02882i | 0.857543 | + | 0.514412i | \(0.171990\pi\) | ||||
−0.857543 | + | 0.514412i | \(0.828010\pi\) | |||||||
\(884\) | 798.496 | + | 330.748i | 0.903276 | + | 0.374149i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −762.051 | − | 315.652i | −0.860103 | − | 0.356266i | ||||
\(887\) | −245.627 | + | 48.8583i | −0.276919 | + | 0.0550827i | −0.331596 | − | 0.943421i | \(-0.607587\pi\) |
0.0546769 | + | 0.998504i | \(0.482587\pi\) | |||||||
\(888\) | −304.143 | − | 304.143i | −0.342503 | − | 0.342503i | ||||
\(889\) | −533.193 | + | 797.979i | −0.599767 | + | 0.897614i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −283.016 | − | 423.563i | −0.317638 | − | 0.475379i | ||||
\(892\) | −99.0454 | − | 239.117i | −0.111037 | − | 0.268068i | ||||
\(893\) | 45.8922 | − | 19.0092i | 0.0513911 | − | 0.0212869i | ||||
\(894\) | −97.9249 | + | 65.4313i | −0.109536 | + | 0.0731894i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 413.605 | + | 276.362i | 0.461613 | + | 0.308440i | ||||
\(897\) | −1158.92 | + | 1158.92i | −1.29200 | + | 1.29200i | ||||
\(898\) | −163.020 | − | 819.556i | −0.181537 | − | 0.912646i | ||||
\(899\) | −86.9888 | + | 210.010i | −0.0967617 | + | 0.233604i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −340.317 | − | 340.317i | −0.377711 | − | 0.377711i | ||||
\(902\) | −291.555 | −0.323232 | ||||||||
\(903\) | −520.713 | − | 215.687i | −0.576648 | − | 0.238856i | ||||
\(904\) | 1168.19 | − | 232.367i | 1.29224 | − | 0.257043i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 279.804 | − | 418.756i | 0.308835 | − | 0.462204i | ||||
\(907\) | −1703.05 | − | 338.757i | −1.87767 | − | 0.373492i | −0.882387 | − | 0.470524i | \(-0.844065\pi\) |
−0.995281 | + | 0.0970321i | \(0.969065\pi\) | |||||||
\(908\) | −189.752 | − | 283.984i | −0.208978 | − | 0.312758i | ||||
\(909\) | −97.0986 | − | 234.417i | −0.106819 | − | 0.257884i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1492.51 | − | 997.265i | 1.63832 | − | 1.09469i | 0.723922 | − | 0.689882i | \(-0.242337\pi\) |
0.914401 | − | 0.404811i | \(-0.132663\pi\) | |||||||
\(912\) | −1.46326 | + | 7.35633i | −0.00160446 | + | 0.00806615i | ||||
\(913\) | −927.106 | − | 619.472i | −1.01545 | − | 0.678502i | ||||
\(914\) | −130.337 | + | 130.337i | −0.142600 | + | 0.142600i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.21630 | − | 19.8359i | 0.00896976 | − | 0.0216549i | ||||
\(917\) | 821.743i | 0.896121i | ||||||||
\(918\) | 643.575 | + | 128.015i | 0.701062 | + | 0.139450i | ||||
\(919\) | −506.869 | −0.551544 | −0.275772 | − | 0.961223i | \(-0.588933\pi\) | ||||
−0.275772 | + | 0.961223i | \(0.588933\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12.6541 | − | 2.51706i | 0.0137395 | − | 0.00273296i | ||||
\(922\) | 138.230 | + | 138.230i | 0.149924 | + | 0.149924i | ||||
\(923\) | 1330.66 | − | 1991.48i | 1.44167 | − | 2.15761i | ||||
\(924\) | −430.077 | − | 85.5476i | −0.465451 | − | 0.0925839i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 376.485 | + | 908.914i | 0.406571 | + | 0.981549i | ||||
\(927\) | −70.5489 | + | 29.2223i | −0.0761045 | + | 0.0315235i | ||||
\(928\) | 417.160 | − | 278.737i | 0.449526 | − | 0.300364i | ||||
\(929\) | 272.070 | − | 1367.79i | 0.292863 | − | 1.47232i | −0.501646 | − | 0.865073i | \(-0.667272\pi\) |
0.794510 | − | 0.607251i | \(-0.207728\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.3656 | − | 27.3656i | 0.0293937 | − | 0.0293937i | ||||
\(932\) | 169.407 | + | 851.665i | 0.181767 | + | 0.913803i | ||||
\(933\) | 493.396 | − | 1191.16i | 0.528827 | − | 1.27670i | ||||
\(934\) | − | 10.1880i | − | 0.0109080i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 341.626 | 0.364985 | ||||||||
\(937\) | 185.233 | + | 76.7261i | 0.197687 | + | 0.0818848i | 0.479331 | − | 0.877634i | \(-0.340879\pi\) |
−0.281643 | + | 0.959519i | \(0.590879\pi\) | |||||||
\(938\) | −815.774 | + | 162.268i | −0.869695 | + | 0.172993i | ||||
\(939\) | 168.233 | + | 168.233i | 0.179162 | + | 0.179162i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1497.87 | − | 297.945i | −1.59179 | − | 0.316626i | −0.681889 | − | 0.731456i | \(-0.738841\pi\) |
−0.909899 | + | 0.414830i | \(0.863841\pi\) | |||||||
\(942\) | −220.054 | − | 329.334i | −0.233603 | − | 0.349611i | ||||
\(943\) | −270.628 | − | 653.355i | −0.286987 | − | 0.692847i | ||||
\(944\) | 47.0948 | − | 19.5073i | 0.0498886 | − | 0.0206645i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 50.9953 | − | 256.371i | 0.0539063 | − | 0.271005i | ||||
\(947\) | 845.726 | + | 565.096i | 0.893058 | + | 0.596723i | 0.915186 | − | 0.403033i | \(-0.132044\pi\) |
−0.0221273 | + | 0.999755i | \(0.507044\pi\) | |||||||
\(948\) | 30.6498 | − | 30.6498i | 0.0323310 | − | 0.0323310i | ||||
\(949\) | −158.534 | − | 797.004i | −0.167054 | − | 0.839835i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 322.706i | − | 0.339334i | ||||||
\(952\) | 1039.18 | − | 694.356i | 1.09157 | − | 0.729365i | ||||
\(953\) | −297.230 | −0.311889 | −0.155945 | − | 0.987766i | \(-0.549842\pi\) | ||||
−0.155945 | + | 0.987766i | \(0.549842\pi\) | |||||||
\(954\) | −62.8428 | − | 26.0303i | −0.0658730 | − | 0.0272855i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −586.045 | − | 586.045i | −0.613017 | − | 0.613017i | ||||
\(957\) | −204.237 | + | 305.662i | −0.213414 | + | 0.319396i | ||||
\(958\) | 988.688 | + | 196.662i | 1.03203 | + | 0.205284i | ||||
\(959\) | 502.640 | + | 752.255i | 0.524130 | + | 0.784416i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 713.498 | − | 295.540i | 0.742453 | − | 0.307534i | ||||
\(962\) | −488.992 | + | 326.734i | −0.508308 | + | 0.339640i | ||||
\(963\) | 25.9567 | − | 130.493i | 0.0269540 | − | 0.135507i | ||||
\(964\) | −257.270 | − | 171.902i | −0.266878 | − | 0.178322i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 165.325 | + | 831.144i | 0.171144 | + | 0.860397i | ||||
\(967\) | 452.787 | − | 1093.12i | 0.468239 | − | 1.13043i | −0.496692 | − | 0.867927i | \(-0.665452\pi\) |
0.964931 | − | 0.262502i | \(-0.0845477\pi\) | |||||||
\(968\) | 434.595i | 0.448961i | ||||||||
\(969\) | −49.5693 | − | 33.1212i | −0.0511551 | − | 0.0341808i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 510.211 | + | 211.336i | 0.525449 | + | 0.217648i | 0.629608 | − | 0.776913i | \(-0.283215\pi\) |
−0.104160 | + | 0.994561i | \(0.533215\pi\) | |||||||
\(972\) | −209.262 | + | 41.6248i | −0.215290 | + | 0.0428239i | ||||
\(973\) | −193.305 | − | 193.305i | −0.198669 | − | 0.198669i | ||||
\(974\) | 6.53565 | − | 9.78129i | 0.00671011 | − | 0.0100424i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 61.3616 | + | 91.8341i | 0.0628705 | + | 0.0940923i | ||||
\(977\) | 125.177 | + | 302.204i | 0.128124 | + | 0.309318i | 0.974904 | − | 0.222624i | \(-0.0714623\pi\) |
−0.846781 | + | 0.531942i | \(0.821462\pi\) | |||||||
\(978\) | −539.105 | + | 223.305i | −0.551232 | + | 0.228328i | ||||
\(979\) | −376.415 | + | 251.512i | −0.384489 | + | 0.256907i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 315.345 | + | 210.707i | 0.321453 | + | 0.214788i | ||||
\(982\) | 552.735 | − | 552.735i | 0.562866 | − | 0.562866i | ||||
\(983\) | −199.903 | − | 1004.98i | −0.203360 | − | 1.02236i | −0.938719 | − | 0.344683i | \(-0.887986\pi\) |
0.735359 | − | 0.677678i | \(-0.237014\pi\) | |||||||
\(984\) | 225.009 | − | 543.221i | 0.228668 | − | 0.552053i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −73.0887 | − | 367.442i | −0.0741265 | − | 0.372659i | ||||
\(987\) | 903.685 | 0.915587 | ||||||||
\(988\) | −61.4041 | − | 25.4344i | −0.0621499 | − | 0.0257433i | ||||
\(989\) | 621.844 | − | 123.692i | 0.628760 | − | 0.125068i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −229.264 | + | 343.118i | −0.231346 | + | 0.346234i | −0.928921 | − | 0.370278i | \(-0.879262\pi\) |
0.697575 | + | 0.716512i | \(0.254262\pi\) | |||||||
\(992\) | 408.521 | + | 81.2600i | 0.411816 | + | 0.0819153i | ||||
\(993\) | 151.502 | + | 226.739i | 0.152570 | + | 0.228338i | ||||
\(994\) | −473.916 | − | 1144.14i | −0.476777 | − | 1.15104i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 668.524 | − | 446.693i | 0.671209 | − | 0.448487i | ||||
\(997\) | −245.429 | + | 1233.85i | −0.246167 | + | 1.23757i | 0.637867 | + | 0.770146i | \(0.279817\pi\) |
−0.884035 | + | 0.467421i | \(0.845183\pi\) | |||||||
\(998\) | 124.125 | + | 82.9374i | 0.124373 | + | 0.0831037i | ||||
\(999\) | 396.270 | − | 396.270i | 0.396666 | − | 0.396666i |
(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 | 425.3.u.b.176.1 | 8 | ||
5.2 | odd | 4 | 425.3.t.c.74.1 | 8 | |||
5.3 | odd | 4 | 425.3.t.a.74.1 | 8 | |||
5.4 | even | 2 | 17.3.e.a.6.1 | yes | 8 | ||
15.14 | odd | 2 | 153.3.p.b.91.1 | 8 | |||
17.3 | odd | 16 | inner | 425.3.u.b.326.1 | 8 | ||
20.19 | odd | 2 | 272.3.bh.c.193.1 | 8 | |||
85.3 | even | 16 | 425.3.t.c.224.1 | 8 | |||
85.4 | even | 4 | 289.3.e.i.249.1 | 8 | |||
85.9 | even | 8 | 289.3.e.l.214.1 | 8 | |||
85.14 | odd | 16 | 289.3.e.c.224.1 | 8 | |||
85.19 | even | 8 | 289.3.e.b.75.1 | 8 | |||
85.24 | odd | 16 | 289.3.e.d.158.1 | 8 | |||
85.29 | odd | 16 | 289.3.e.m.65.1 | 8 | |||
85.37 | even | 16 | 425.3.t.a.224.1 | 8 | |||
85.39 | odd | 16 | 289.3.e.i.65.1 | 8 | |||
85.44 | odd | 16 | 289.3.e.b.158.1 | 8 | |||
85.49 | even | 8 | 289.3.e.d.75.1 | 8 | |||
85.54 | odd | 16 | 17.3.e.a.3.1 | ✓ | 8 | ||
85.59 | even | 8 | 289.3.e.k.214.1 | 8 | |||
85.64 | even | 4 | 289.3.e.m.249.1 | 8 | |||
85.74 | odd | 16 | 289.3.e.l.131.1 | 8 | |||
85.79 | odd | 16 | 289.3.e.k.131.1 | 8 | |||
85.84 | even | 2 | 289.3.e.c.40.1 | 8 | |||
255.224 | even | 16 | 153.3.p.b.37.1 | 8 | |||
340.139 | even | 16 | 272.3.bh.c.241.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.3.e.a.3.1 | ✓ | 8 | 85.54 | odd | 16 | ||
17.3.e.a.6.1 | yes | 8 | 5.4 | even | 2 | ||
153.3.p.b.37.1 | 8 | 255.224 | even | 16 | |||
153.3.p.b.91.1 | 8 | 15.14 | odd | 2 | |||
272.3.bh.c.193.1 | 8 | 20.19 | odd | 2 | |||
272.3.bh.c.241.1 | 8 | 340.139 | even | 16 | |||
289.3.e.b.75.1 | 8 | 85.19 | even | 8 | |||
289.3.e.b.158.1 | 8 | 85.44 | odd | 16 | |||
289.3.e.c.40.1 | 8 | 85.84 | even | 2 | |||
289.3.e.c.224.1 | 8 | 85.14 | odd | 16 | |||
289.3.e.d.75.1 | 8 | 85.49 | even | 8 | |||
289.3.e.d.158.1 | 8 | 85.24 | odd | 16 | |||
289.3.e.i.65.1 | 8 | 85.39 | odd | 16 | |||
289.3.e.i.249.1 | 8 | 85.4 | even | 4 | |||
289.3.e.k.131.1 | 8 | 85.79 | odd | 16 | |||
289.3.e.k.214.1 | 8 | 85.59 | even | 8 | |||
289.3.e.l.131.1 | 8 | 85.74 | odd | 16 | |||
289.3.e.l.214.1 | 8 | 85.9 | even | 8 | |||
289.3.e.m.65.1 | 8 | 85.29 | odd | 16 | |||
289.3.e.m.249.1 | 8 | 85.64 | even | 4 | |||
425.3.t.a.74.1 | 8 | 5.3 | odd | 4 | |||
425.3.t.a.224.1 | 8 | 85.37 | even | 16 | |||
425.3.t.c.74.1 | 8 | 5.2 | odd | 4 | |||
425.3.t.c.224.1 | 8 | 85.3 | even | 16 | |||
425.3.u.b.176.1 | 8 | 1.1 | even | 1 | trivial | ||
425.3.u.b.326.1 | 8 | 17.3 | odd | 16 | inner |