Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (of order \(4\), 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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 32 x^{14} + 152 x^{13} + 1954 x^{12} - 12664 x^{11} + 50336 x^{10} + 231896 x^{9} + \cdots + 2560000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{10}\cdot 5^{2} \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.2 | ||
Root | \(3.60306 + 3.60306i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.43 |
Dual form | 1050.3.l.h.757.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | − | 1.00000i | 0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.44949 | −0.408248 | ||||||||
\(7\) | −1.87083 | + | 1.87083i | −0.267261 | + | 0.267261i | ||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.5847 | 1.05316 | 0.526578 | − | 0.850127i | \(-0.323475\pi\) | ||||
0.526578 | + | 0.850127i | \(0.323475\pi\) | |||||||
\(12\) | −2.44949 | + | 2.44949i | −0.204124 | + | 0.204124i | ||||
\(13\) | 2.01552 | + | 2.01552i | 0.155040 | + | 0.155040i | 0.780365 | − | 0.625325i | \(-0.215034\pi\) |
−0.625325 | + | 0.780365i | \(0.715034\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | −7.75862 | + | 7.75862i | −0.456389 | + | 0.456389i | −0.897468 | − | 0.441079i | \(-0.854596\pi\) |
0.441079 | + | 0.897468i | \(0.354596\pi\) | |||||||
\(18\) | 3.00000 | + | 3.00000i | 0.166667 | + | 0.166667i | ||||
\(19\) | 21.8455i | 1.14976i | 0.818237 | + | 0.574882i | \(0.194952\pi\) | ||||
−0.818237 | + | 0.574882i | \(0.805048\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.58258 | 0.218218 | ||||||||
\(22\) | 11.5847 | − | 11.5847i | 0.526578 | − | 0.526578i | ||||
\(23\) | 7.41192 | + | 7.41192i | 0.322257 | + | 0.322257i | 0.849632 | − | 0.527375i | \(-0.176824\pi\) |
−0.527375 | + | 0.849632i | \(0.676824\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.03103 | 0.155040 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 3.74166 | + | 3.74166i | 0.133631 | + | 0.133631i | ||||
\(29\) | 31.0146i | 1.06947i | 0.845021 | + | 0.534734i | \(0.179588\pi\) | ||||
−0.845021 | + | 0.534734i | \(0.820412\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −11.5743 | −0.373364 | −0.186682 | − | 0.982420i | \(-0.559773\pi\) | ||||
−0.186682 | + | 0.982420i | \(0.559773\pi\) | |||||||
\(32\) | −4.00000 | + | 4.00000i | −0.125000 | + | 0.125000i | ||||
\(33\) | −14.1883 | − | 14.1883i | −0.429949 | − | 0.429949i | ||||
\(34\) | 15.5172i | 0.456389i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 32.0546 | − | 32.0546i | 0.866340 | − | 0.866340i | −0.125725 | − | 0.992065i | \(-0.540126\pi\) |
0.992065 | + | 0.125725i | \(0.0401258\pi\) | |||||||
\(38\) | 21.8455 | + | 21.8455i | 0.574882 | + | 0.574882i | ||||
\(39\) | − | 4.93699i | − | 0.126589i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 39.6845 | 0.967914 | 0.483957 | − | 0.875092i | \(-0.339199\pi\) | ||||
0.483957 | + | 0.875092i | \(0.339199\pi\) | |||||||
\(42\) | 4.58258 | − | 4.58258i | 0.109109 | − | 0.109109i | ||||
\(43\) | 19.3751 | + | 19.3751i | 0.450583 | + | 0.450583i | 0.895548 | − | 0.444965i | \(-0.146784\pi\) |
−0.444965 | + | 0.895548i | \(0.646784\pi\) | |||||||
\(44\) | − | 23.1694i | − | 0.526578i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 14.8238 | 0.322257 | ||||||||
\(47\) | −21.8753 | + | 21.8753i | −0.465432 | + | 0.465432i | −0.900431 | − | 0.434999i | \(-0.856749\pi\) |
0.434999 | + | 0.900431i | \(0.356749\pi\) | |||||||
\(48\) | 4.89898 | + | 4.89898i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 7.00000i | − | 0.142857i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.0047 | 0.372640 | ||||||||
\(52\) | 4.03103 | − | 4.03103i | 0.0775199 | − | 0.0775199i | ||||
\(53\) | 42.4043 | + | 42.4043i | 0.800081 | + | 0.800081i | 0.983108 | − | 0.183027i | \(-0.0585896\pi\) |
−0.183027 | + | 0.983108i | \(0.558590\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 26.7552 | − | 26.7552i | 0.469389 | − | 0.469389i | ||||
\(58\) | 31.0146 | + | 31.0146i | 0.534734 | + | 0.534734i | ||||
\(59\) | − | 89.0234i | − | 1.50887i | −0.656374 | − | 0.754435i | \(-0.727911\pi\) | ||
0.656374 | − | 0.754435i | \(-0.272089\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.07420 | 0.115970 | 0.0579852 | − | 0.998317i | \(-0.481532\pi\) | ||||
0.0579852 | + | 0.998317i | \(0.481532\pi\) | |||||||
\(62\) | −11.5743 | + | 11.5743i | −0.186682 | + | 0.186682i | ||||
\(63\) | −5.61249 | − | 5.61249i | −0.0890871 | − | 0.0890871i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −28.3766 | −0.429949 | ||||||||
\(67\) | −15.6985 | + | 15.6985i | −0.234306 | + | 0.234306i | −0.814487 | − | 0.580181i | \(-0.802982\pi\) |
0.580181 | + | 0.814487i | \(0.302982\pi\) | |||||||
\(68\) | 15.5172 | + | 15.5172i | 0.228195 | + | 0.228195i | ||||
\(69\) | − | 18.1554i | − | 0.263122i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 133.620 | 1.88197 | 0.940986 | − | 0.338447i | \(-0.109901\pi\) | ||||
0.940986 | + | 0.338447i | \(0.109901\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | 92.3644 | + | 92.3644i | 1.26527 | + | 1.26527i | 0.948506 | + | 0.316760i | \(0.102595\pi\) |
0.316760 | + | 0.948506i | \(0.397405\pi\) | |||||||
\(74\) | − | 64.1091i | − | 0.866340i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 43.6910 | 0.574882 | ||||||||
\(77\) | −21.6730 | + | 21.6730i | −0.281468 | + | 0.281468i | ||||
\(78\) | −4.93699 | − | 4.93699i | −0.0632947 | − | 0.0632947i | ||||
\(79\) | − | 126.569i | − | 1.60214i | −0.598569 | − | 0.801071i | \(-0.704264\pi\) | ||
0.598569 | − | 0.801071i | \(-0.295736\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 39.6845 | − | 39.6845i | 0.483957 | − | 0.483957i | ||||
\(83\) | 30.0489 | + | 30.0489i | 0.362035 | + | 0.362035i | 0.864562 | − | 0.502527i | \(-0.167596\pi\) |
−0.502527 | + | 0.864562i | \(0.667596\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 38.7501 | 0.450583 | ||||||||
\(87\) | 37.9849 | − | 37.9849i | 0.436608 | − | 0.436608i | ||||
\(88\) | −23.1694 | − | 23.1694i | −0.263289 | − | 0.263289i | ||||
\(89\) | − | 4.93527i | − | 0.0554525i | −0.999616 | − | 0.0277263i | \(-0.991173\pi\) | ||
0.999616 | − | 0.0277263i | \(-0.00882667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.54137 | −0.0828723 | ||||||||
\(92\) | 14.8238 | − | 14.8238i | 0.161129 | − | 0.161129i | ||||
\(93\) | 14.1755 | + | 14.1755i | 0.152425 | + | 0.152425i | ||||
\(94\) | 43.7506i | 0.465432i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796 | 0.102062 | ||||||||
\(97\) | 30.2346 | − | 30.2346i | 0.311697 | − | 0.311697i | −0.533870 | − | 0.845567i | \(-0.679263\pi\) |
0.845567 | + | 0.533870i | \(0.179263\pi\) | |||||||
\(98\) | −7.00000 | − | 7.00000i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 34.7541i | 0.351052i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −176.319 | −1.74573 | −0.872867 | − | 0.487958i | \(-0.837742\pi\) | ||||
−0.872867 | + | 0.487958i | \(0.837742\pi\) | |||||||
\(102\) | 19.0047 | − | 19.0047i | 0.186320 | − | 0.186320i | ||||
\(103\) | 61.1510 | + | 61.1510i | 0.593699 | + | 0.593699i | 0.938629 | − | 0.344930i | \(-0.112097\pi\) |
−0.344930 | + | 0.938629i | \(0.612097\pi\) | |||||||
\(104\) | − | 8.06207i | − | 0.0775199i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 84.8086 | 0.800081 | ||||||||
\(107\) | 0.766043 | − | 0.766043i | 0.00715928 | − | 0.00715928i | −0.703518 | − | 0.710677i | \(-0.748389\pi\) |
0.710677 | + | 0.703518i | \(0.248389\pi\) | |||||||
\(108\) | −7.34847 | − | 7.34847i | −0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 26.6885i | − | 0.244848i | −0.992478 | − | 0.122424i | \(-0.960933\pi\) | ||
0.992478 | − | 0.122424i | \(-0.0390668\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −78.5173 | −0.707363 | ||||||||
\(112\) | 7.48331 | − | 7.48331i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −133.108 | − | 133.108i | −1.17795 | − | 1.17795i | −0.980267 | − | 0.197680i | \(-0.936659\pi\) |
−0.197680 | − | 0.980267i | \(-0.563341\pi\) | |||||||
\(114\) | − | 53.5103i | − | 0.469389i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 62.0291 | 0.534734 | ||||||||
\(117\) | −6.04655 | + | 6.04655i | −0.0516799 | + | 0.0516799i | ||||
\(118\) | −89.0234 | − | 89.0234i | −0.754435 | − | 0.754435i | ||||
\(119\) | − | 29.0301i | − | 0.243950i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.2054 | 0.109136 | ||||||||
\(122\) | 7.07420 | − | 7.07420i | 0.0579852 | − | 0.0579852i | ||||
\(123\) | −48.6034 | − | 48.6034i | −0.395149 | − | 0.395149i | ||||
\(124\) | 23.1486i | 0.186682i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | −59.4171 | + | 59.4171i | −0.467851 | + | 0.467851i | −0.901218 | − | 0.433367i | \(-0.857325\pi\) |
0.433367 | + | 0.901218i | \(0.357325\pi\) | |||||||
\(128\) | 8.00000 | + | 8.00000i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 47.4590i | − | 0.367899i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 51.2605 | 0.391302 | 0.195651 | − | 0.980674i | \(-0.437318\pi\) | ||||
0.195651 | + | 0.980674i | \(0.437318\pi\) | |||||||
\(132\) | −28.3766 | + | 28.3766i | −0.214974 | + | 0.214974i | ||||
\(133\) | −40.8692 | − | 40.8692i | −0.307287 | − | 0.307287i | ||||
\(134\) | 31.3970i | 0.234306i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 31.0345 | 0.228195 | ||||||||
\(137\) | 17.6526 | − | 17.6526i | 0.128851 | − | 0.128851i | −0.639740 | − | 0.768591i | \(-0.720958\pi\) |
0.768591 | + | 0.639740i | \(0.220958\pi\) | |||||||
\(138\) | −18.1554 | − | 18.1554i | −0.131561 | − | 0.131561i | ||||
\(139\) | 206.210i | 1.48353i | 0.670662 | + | 0.741763i | \(0.266010\pi\) | ||||
−0.670662 | + | 0.741763i | \(0.733990\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 53.5834 | 0.380024 | ||||||||
\(142\) | 133.620 | − | 133.620i | 0.940986 | − | 0.940986i | ||||
\(143\) | 23.3492 | + | 23.3492i | 0.163281 | + | 0.163281i | ||||
\(144\) | − | 12.0000i | − | 0.0833333i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 184.729 | 1.26527 | ||||||||
\(147\) | −8.57321 | + | 8.57321i | −0.0583212 | + | 0.0583212i | ||||
\(148\) | −64.1091 | − | 64.1091i | −0.433170 | − | 0.433170i | ||||
\(149\) | 256.780i | 1.72336i | 0.507456 | + | 0.861678i | \(0.330586\pi\) | ||||
−0.507456 | + | 0.861678i | \(0.669414\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 255.541 | 1.69232 | 0.846161 | − | 0.532928i | \(-0.178908\pi\) | ||||
0.846161 | + | 0.532928i | \(0.178908\pi\) | |||||||
\(152\) | 43.6910 | − | 43.6910i | 0.287441 | − | 0.287441i | ||||
\(153\) | −23.2759 | − | 23.2759i | −0.152130 | − | 0.152130i | ||||
\(154\) | 43.3460i | 0.281468i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −9.87398 | −0.0632947 | ||||||||
\(157\) | 69.5363 | − | 69.5363i | 0.442906 | − | 0.442906i | −0.450081 | − | 0.892988i | \(-0.648605\pi\) |
0.892988 | + | 0.450081i | \(0.148605\pi\) | |||||||
\(158\) | −126.569 | − | 126.569i | −0.801071 | − | 0.801071i | ||||
\(159\) | − | 103.869i | − | 0.653263i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −27.7328 | −0.172254 | ||||||||
\(162\) | −9.00000 | + | 9.00000i | −0.0555556 | + | 0.0555556i | ||||
\(163\) | 220.179 | + | 220.179i | 1.35079 | + | 1.35079i | 0.884774 | + | 0.466020i | \(0.154313\pi\) |
0.466020 | + | 0.884774i | \(0.345687\pi\) | |||||||
\(164\) | − | 79.3690i | − | 0.483957i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 60.0978 | 0.362035 | ||||||||
\(167\) | −27.6262 | + | 27.6262i | −0.165426 | + | 0.165426i | −0.784966 | − | 0.619539i | \(-0.787319\pi\) |
0.619539 | + | 0.784966i | \(0.287319\pi\) | |||||||
\(168\) | −9.16515 | − | 9.16515i | −0.0545545 | − | 0.0545545i | ||||
\(169\) | − | 160.875i | − | 0.951925i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −65.5365 | −0.383254 | ||||||||
\(172\) | 38.7501 | − | 38.7501i | 0.225291 | − | 0.225291i | ||||
\(173\) | 128.172 | + | 128.172i | 0.740876 | + | 0.740876i | 0.972747 | − | 0.231870i | \(-0.0744845\pi\) |
−0.231870 | + | 0.972747i | \(0.574484\pi\) | |||||||
\(174\) | − | 75.9698i | − | 0.436608i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −46.3388 | −0.263289 | ||||||||
\(177\) | −109.031 | + | 109.031i | −0.615994 | + | 0.615994i | ||||
\(178\) | −4.93527 | − | 4.93527i | −0.0277263 | − | 0.0277263i | ||||
\(179\) | − | 65.6591i | − | 0.366811i | −0.983037 | − | 0.183405i | \(-0.941288\pi\) | ||
0.983037 | − | 0.183405i | \(-0.0587121\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −321.692 | −1.77730 | −0.888651 | − | 0.458584i | \(-0.848357\pi\) | ||||
−0.888651 | + | 0.458584i | \(0.848357\pi\) | |||||||
\(182\) | −7.54137 | + | 7.54137i | −0.0414361 | + | 0.0414361i | ||||
\(183\) | −8.66409 | − | 8.66409i | −0.0473447 | − | 0.0473447i | ||||
\(184\) | − | 29.6477i | − | 0.161129i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 28.3511 | 0.152425 | ||||||||
\(187\) | −89.8813 | + | 89.8813i | −0.480649 | + | 0.480649i | ||||
\(188\) | 43.7506 | + | 43.7506i | 0.232716 | + | 0.232716i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −146.509 | −0.767061 | −0.383531 | − | 0.923528i | \(-0.625292\pi\) | ||||
−0.383531 | + | 0.923528i | \(0.625292\pi\) | |||||||
\(192\) | 9.79796 | − | 9.79796i | 0.0510310 | − | 0.0510310i | ||||
\(193\) | −11.1318 | − | 11.1318i | −0.0576775 | − | 0.0576775i | 0.677680 | − | 0.735357i | \(-0.262986\pi\) |
−0.735357 | + | 0.677680i | \(0.762986\pi\) | |||||||
\(194\) | − | 60.4692i | − | 0.311697i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −22.4067 | + | 22.4067i | −0.113740 | + | 0.113740i | −0.761686 | − | 0.647946i | \(-0.775628\pi\) |
0.647946 | + | 0.761686i | \(0.275628\pi\) | |||||||
\(198\) | 34.7541 | + | 34.7541i | 0.175526 | + | 0.175526i | ||||
\(199\) | − | 163.016i | − | 0.819177i | −0.912270 | − | 0.409589i | \(-0.865672\pi\) | ||
0.912270 | − | 0.409589i | \(-0.134328\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38.4533 | 0.191310 | ||||||||
\(202\) | −176.319 | + | 176.319i | −0.872867 | + | 0.872867i | ||||
\(203\) | −58.0229 | − | 58.0229i | −0.285827 | − | 0.285827i | ||||
\(204\) | − | 38.0093i | − | 0.186320i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 122.302 | 0.593699 | ||||||||
\(207\) | −22.2357 | + | 22.2357i | −0.107419 | + | 0.107419i | ||||
\(208\) | −8.06207 | − | 8.06207i | −0.0387599 | − | 0.0387599i | ||||
\(209\) | 253.074i | 1.21088i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 266.247 | 1.26184 | 0.630918 | − | 0.775850i | \(-0.282678\pi\) | ||||
0.630918 | + | 0.775850i | \(0.282678\pi\) | |||||||
\(212\) | 84.8086 | − | 84.8086i | 0.400040 | − | 0.400040i | ||||
\(213\) | −163.650 | − | 163.650i | −0.768312 | − | 0.768312i | ||||
\(214\) | − | 1.53209i | − | 0.00715928i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −14.6969 | −0.0680414 | ||||||||
\(217\) | 21.6535 | − | 21.6535i | 0.0997857 | − | 0.0997857i | ||||
\(218\) | −26.6885 | − | 26.6885i | −0.122424 | − | 0.122424i | ||||
\(219\) | − | 226.246i | − | 1.03309i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −31.2753 | −0.141517 | ||||||||
\(222\) | −78.5173 | + | 78.5173i | −0.353682 | + | 0.353682i | ||||
\(223\) | 313.209 | + | 313.209i | 1.40453 | + | 1.40453i | 0.784890 | + | 0.619635i | \(0.212719\pi\) |
0.619635 | + | 0.784890i | \(0.287281\pi\) | |||||||
\(224\) | − | 14.9666i | − | 0.0668153i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −266.216 | −1.17795 | ||||||||
\(227\) | −100.753 | + | 100.753i | −0.443847 | + | 0.443847i | −0.893303 | − | 0.449455i | \(-0.851618\pi\) |
0.449455 | + | 0.893303i | \(0.351618\pi\) | |||||||
\(228\) | −53.5103 | − | 53.5103i | −0.234694 | − | 0.234694i | ||||
\(229\) | 120.710i | 0.527119i | 0.964643 | + | 0.263559i | \(0.0848965\pi\) | ||||
−0.964643 | + | 0.263559i | \(0.915104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 53.0878 | 0.229817 | ||||||||
\(232\) | 62.0291 | − | 62.0291i | 0.267367 | − | 0.267367i | ||||
\(233\) | −200.874 | − | 200.874i | −0.862119 | − | 0.862119i | 0.129465 | − | 0.991584i | \(-0.458674\pi\) |
−0.991584 | + | 0.129465i | \(0.958674\pi\) | |||||||
\(234\) | 12.0931i | 0.0516799i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −178.047 | −0.754435 | ||||||||
\(237\) | −155.015 | + | 155.015i | −0.654072 | + | 0.654072i | ||||
\(238\) | −29.0301 | − | 29.0301i | −0.121975 | − | 0.121975i | ||||
\(239\) | 288.534i | 1.20725i | 0.797267 | + | 0.603627i | \(0.206278\pi\) | ||||
−0.797267 | + | 0.603627i | \(0.793722\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −80.3054 | −0.333218 | −0.166609 | − | 0.986023i | \(-0.553282\pi\) | ||||
−0.166609 | + | 0.986023i | \(0.553282\pi\) | |||||||
\(242\) | 13.2054 | − | 13.2054i | 0.0545679 | − | 0.0545679i | ||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 14.1484i | − | 0.0579852i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −97.2067 | −0.395149 | ||||||||
\(247\) | −44.0300 | + | 44.0300i | −0.178259 | + | 0.178259i | ||||
\(248\) | 23.1486 | + | 23.1486i | 0.0933410 | + | 0.0933410i | ||||
\(249\) | − | 73.6045i | − | 0.295600i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −238.919 | −0.951868 | −0.475934 | − | 0.879481i | \(-0.657890\pi\) | ||||
−0.475934 | + | 0.879481i | \(0.657890\pi\) | |||||||
\(252\) | −11.2250 | + | 11.2250i | −0.0445435 | + | 0.0445435i | ||||
\(253\) | 85.8649 | + | 85.8649i | 0.339387 | + | 0.339387i | ||||
\(254\) | 118.834i | 0.467851i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −357.876 | + | 357.876i | −1.39251 | + | 1.39251i | −0.572859 | + | 0.819654i | \(0.694166\pi\) |
−0.819654 | + | 0.572859i | \(0.805834\pi\) | |||||||
\(258\) | −47.4590 | − | 47.4590i | −0.183950 | − | 0.183950i | ||||
\(259\) | 119.937i | 0.463078i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −93.0437 | −0.356489 | ||||||||
\(262\) | 51.2605 | − | 51.2605i | 0.195651 | − | 0.195651i | ||||
\(263\) | 73.5388 | + | 73.5388i | 0.279615 | + | 0.279615i | 0.832955 | − | 0.553340i | \(-0.186647\pi\) |
−0.553340 | + | 0.832955i | \(0.686647\pi\) | |||||||
\(264\) | 56.7532i | 0.214974i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −81.7384 | −0.307287 | ||||||||
\(267\) | −6.04445 | + | 6.04445i | −0.0226384 | + | 0.0226384i | ||||
\(268\) | 31.3970 | + | 31.3970i | 0.117153 | + | 0.117153i | ||||
\(269\) | − | 63.1334i | − | 0.234697i | −0.993091 | − | 0.117348i | \(-0.962561\pi\) | ||
0.993091 | − | 0.117348i | \(-0.0374394\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −66.1173 | −0.243975 | −0.121988 | − | 0.992532i | \(-0.538927\pi\) | ||||
−0.121988 | + | 0.992532i | \(0.538927\pi\) | |||||||
\(272\) | 31.0345 | − | 31.0345i | 0.114097 | − | 0.114097i | ||||
\(273\) | 9.23626 | + | 9.23626i | 0.0338325 | + | 0.0338325i | ||||
\(274\) | − | 35.3053i | − | 0.128851i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −36.3108 | −0.131561 | ||||||||
\(277\) | 268.807 | − | 268.807i | 0.970423 | − | 0.970423i | −0.0291522 | − | 0.999575i | \(-0.509281\pi\) |
0.999575 | + | 0.0291522i | \(0.00928073\pi\) | |||||||
\(278\) | 206.210 | + | 206.210i | 0.741763 | + | 0.741763i | ||||
\(279\) | − | 34.7229i | − | 0.124455i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −108.591 | −0.386445 | −0.193222 | − | 0.981155i | \(-0.561894\pi\) | ||||
−0.193222 | + | 0.981155i | \(0.561894\pi\) | |||||||
\(282\) | 53.5834 | − | 53.5834i | 0.190012 | − | 0.190012i | ||||
\(283\) | −208.690 | − | 208.690i | −0.737419 | − | 0.737419i | 0.234658 | − | 0.972078i | \(-0.424603\pi\) |
−0.972078 | + | 0.234658i | \(0.924603\pi\) | |||||||
\(284\) | − | 267.240i | − | 0.940986i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 46.6984 | 0.163281 | ||||||||
\(287\) | −74.2429 | + | 74.2429i | −0.258686 | + | 0.258686i | ||||
\(288\) | −12.0000 | − | 12.0000i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | 168.608i | 0.583418i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −74.0593 | −0.254499 | ||||||||
\(292\) | 184.729 | − | 184.729i | 0.632633 | − | 0.632633i | ||||
\(293\) | −315.640 | − | 315.640i | −1.07727 | − | 1.07727i | −0.996753 | − | 0.0805153i | \(-0.974343\pi\) |
−0.0805153 | − | 0.996753i | \(-0.525657\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −128.218 | −0.433170 | ||||||||
\(297\) | 42.5649 | − | 42.5649i | 0.143316 | − | 0.143316i | ||||
\(298\) | 256.780 | + | 256.780i | 0.861678 | + | 0.861678i | ||||
\(299\) | 29.8777i | 0.0999254i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −72.4948 | −0.240847 | ||||||||
\(302\) | 255.541 | − | 255.541i | 0.846161 | − | 0.846161i | ||||
\(303\) | 215.946 | + | 215.946i | 0.712693 | + | 0.712693i | ||||
\(304\) | − | 87.3820i | − | 0.287441i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −46.5517 | −0.152130 | ||||||||
\(307\) | −115.484 | + | 115.484i | −0.376169 | + | 0.376169i | −0.869718 | − | 0.493549i | \(-0.835699\pi\) |
0.493549 | + | 0.869718i | \(0.335699\pi\) | |||||||
\(308\) | 43.3460 | + | 43.3460i | 0.140734 | + | 0.140734i | ||||
\(309\) | − | 149.789i | − | 0.484753i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −489.397 | −1.57362 | −0.786812 | − | 0.617192i | \(-0.788270\pi\) | ||||
−0.786812 | + | 0.617192i | \(0.788270\pi\) | |||||||
\(312\) | −9.87398 | + | 9.87398i | −0.0316474 | + | 0.0316474i | ||||
\(313\) | −95.5816 | − | 95.5816i | −0.305372 | − | 0.305372i | 0.537739 | − | 0.843111i | \(-0.319279\pi\) |
−0.843111 | + | 0.537739i | \(0.819279\pi\) | |||||||
\(314\) | − | 139.073i | − | 0.442906i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −253.138 | −0.801071 | ||||||||
\(317\) | −368.537 | + | 368.537i | −1.16258 | + | 1.16258i | −0.178668 | + | 0.983909i | \(0.557179\pi\) |
−0.983909 | + | 0.178668i | \(0.942821\pi\) | |||||||
\(318\) | −103.869 | − | 103.869i | −0.326632 | − | 0.326632i | ||||
\(319\) | 359.295i | 1.12632i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.87641 | −0.00584553 | ||||||||
\(322\) | −27.7328 | + | 27.7328i | −0.0861269 | + | 0.0861269i | ||||
\(323\) | −169.491 | − | 169.491i | −0.524740 | − | 0.524740i | ||||
\(324\) | 18.0000i | 0.0555556i | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 440.359 | 1.35079 | ||||||||
\(327\) | −32.6866 | + | 32.6866i | −0.0999589 | + | 0.0999589i | ||||
\(328\) | −79.3690 | − | 79.3690i | −0.241979 | − | 0.241979i | ||||
\(329\) | − | 81.8499i | − | 0.248784i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 591.256 | 1.78627 | 0.893135 | − | 0.449788i | \(-0.148501\pi\) | ||||
0.893135 | + | 0.449788i | \(0.148501\pi\) | |||||||
\(332\) | 60.0978 | − | 60.0978i | 0.181017 | − | 0.181017i | ||||
\(333\) | 96.1637 | + | 96.1637i | 0.288780 | + | 0.288780i | ||||
\(334\) | 55.2524i | 0.165426i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −18.3303 | −0.0545545 | ||||||||
\(337\) | 148.222 | − | 148.222i | 0.439827 | − | 0.439827i | −0.452127 | − | 0.891954i | \(-0.649334\pi\) |
0.891954 | + | 0.452127i | \(0.149334\pi\) | |||||||
\(338\) | −160.875 | − | 160.875i | −0.475963 | − | 0.475963i | ||||
\(339\) | 326.047i | 0.961789i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −134.085 | −0.393210 | ||||||||
\(342\) | −65.5365 | + | 65.5365i | −0.191627 | + | 0.191627i | ||||
\(343\) | 13.0958 | + | 13.0958i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 77.5002i | − | 0.225291i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 256.343 | 0.740876 | ||||||||
\(347\) | 299.896 | − | 299.896i | 0.864252 | − | 0.864252i | −0.127577 | − | 0.991829i | \(-0.540720\pi\) |
0.991829 | + | 0.127577i | \(0.0407198\pi\) | |||||||
\(348\) | −75.9698 | − | 75.9698i | −0.218304 | − | 0.218304i | ||||
\(349\) | 421.152i | 1.20674i | 0.797462 | + | 0.603369i | \(0.206176\pi\) | ||||
−0.797462 | + | 0.603369i | \(0.793824\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.8110 | 0.0421965 | ||||||||
\(352\) | −46.3388 | + | 46.3388i | −0.131644 | + | 0.131644i | ||||
\(353\) | −310.590 | − | 310.590i | −0.879858 | − | 0.879858i | 0.113662 | − | 0.993519i | \(-0.463742\pi\) |
−0.993519 | + | 0.113662i | \(0.963742\pi\) | |||||||
\(354\) | 218.062i | 0.615994i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.87055 | −0.0277263 | ||||||||
\(357\) | −35.5545 | + | 35.5545i | −0.0995923 | + | 0.0995923i | ||||
\(358\) | −65.6591 | − | 65.6591i | −0.183405 | − | 0.183405i | ||||
\(359\) | 223.309i | 0.622030i | 0.950405 | + | 0.311015i | \(0.100669\pi\) | ||||
−0.950405 | + | 0.311015i | \(0.899331\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −116.226 | −0.321955 | ||||||||
\(362\) | −321.692 | + | 321.692i | −0.888651 | + | 0.888651i | ||||
\(363\) | −16.1733 | − | 16.1733i | −0.0445545 | − | 0.0445545i | ||||
\(364\) | 15.0827i | 0.0414361i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −17.3282 | −0.0473447 | ||||||||
\(367\) | 262.093 | − | 262.093i | 0.714149 | − | 0.714149i | −0.253251 | − | 0.967401i | \(-0.581500\pi\) |
0.967401 | + | 0.253251i | \(0.0814999\pi\) | |||||||
\(368\) | −29.6477 | − | 29.6477i | −0.0805643 | − | 0.0805643i | ||||
\(369\) | 119.053i | 0.322638i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −158.662 | −0.427661 | ||||||||
\(372\) | 28.3511 | − | 28.3511i | 0.0762126 | − | 0.0762126i | ||||
\(373\) | −56.2361 | − | 56.2361i | −0.150767 | − | 0.150767i | 0.627694 | − | 0.778461i | \(-0.283999\pi\) |
−0.778461 | + | 0.627694i | \(0.783999\pi\) | |||||||
\(374\) | 179.763i | 0.480649i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 87.5012 | 0.232716 | ||||||||
\(377\) | −62.5104 | + | 62.5104i | −0.165810 | + | 0.165810i | ||||
\(378\) | 13.7477 | + | 13.7477i | 0.0363696 | + | 0.0363696i | ||||
\(379\) | 179.724i | 0.474206i | 0.971485 | + | 0.237103i | \(0.0761979\pi\) | ||||
−0.971485 | + | 0.237103i | \(0.923802\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 145.541 | 0.381999 | ||||||||
\(382\) | −146.509 | + | 146.509i | −0.383531 | + | 0.383531i | ||||
\(383\) | 285.701 | + | 285.701i | 0.745956 | + | 0.745956i | 0.973717 | − | 0.227761i | \(-0.0731405\pi\) |
−0.227761 | + | 0.973717i | \(0.573141\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.2635 | −0.0576775 | ||||||||
\(387\) | −58.1252 | + | 58.1252i | −0.150194 | + | 0.150194i | ||||
\(388\) | −60.4692 | − | 60.4692i | −0.155848 | − | 0.155848i | ||||
\(389\) | − | 728.870i | − | 1.87370i | −0.349730 | − | 0.936851i | \(-0.613727\pi\) | ||
0.349730 | − | 0.936851i | \(-0.386273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −115.012 | −0.294149 | ||||||||
\(392\) | −14.0000 | + | 14.0000i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | −62.7811 | − | 62.7811i | −0.159748 | − | 0.159748i | ||||
\(394\) | 44.8135i | 0.113740i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 69.5082 | 0.175526 | ||||||||
\(397\) | −19.6549 | + | 19.6549i | −0.0495086 | + | 0.0495086i | −0.731428 | − | 0.681919i | \(-0.761146\pi\) |
0.681919 | + | 0.731428i | \(0.261146\pi\) | |||||||
\(398\) | −163.016 | − | 163.016i | −0.409589 | − | 0.409589i | ||||
\(399\) | 100.109i | 0.250899i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 230.054 | 0.573701 | 0.286851 | − | 0.957975i | \(-0.407392\pi\) | ||||
0.286851 | + | 0.957975i | \(0.407392\pi\) | |||||||
\(402\) | 38.4533 | − | 38.4533i | 0.0956550 | − | 0.0956550i | ||||
\(403\) | −23.3282 | − | 23.3282i | −0.0578863 | − | 0.0578863i | ||||
\(404\) | 352.638i | 0.872867i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −116.046 | −0.285827 | ||||||||
\(407\) | 371.343 | − | 371.343i | 0.912390 | − | 0.912390i | ||||
\(408\) | −38.0093 | − | 38.0093i | −0.0931601 | − | 0.0931601i | ||||
\(409\) | 420.833i | 1.02893i | 0.857511 | + | 0.514466i | \(0.172010\pi\) | ||||
−0.857511 | + | 0.514466i | \(0.827990\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −43.2400 | −0.105207 | ||||||||
\(412\) | 122.302 | − | 122.302i | 0.296849 | − | 0.296849i | ||||
\(413\) | 166.547 | + | 166.547i | 0.403263 | + | 0.403263i | ||||
\(414\) | 44.4715i | 0.107419i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −16.1241 | −0.0387599 | ||||||||
\(417\) | 252.555 | − | 252.555i | 0.605647 | − | 0.605647i | ||||
\(418\) | 253.074 | + | 253.074i | 0.605439 | + | 0.605439i | ||||
\(419\) | 196.613i | 0.469243i | 0.972087 | + | 0.234621i | \(0.0753850\pi\) | ||||
−0.972087 | + | 0.234621i | \(0.924615\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −169.718 | −0.403132 | −0.201566 | − | 0.979475i | \(-0.564603\pi\) | ||||
−0.201566 | + | 0.979475i | \(0.564603\pi\) | |||||||
\(422\) | 266.247 | − | 266.247i | 0.630918 | − | 0.630918i | ||||
\(423\) | −65.6259 | − | 65.6259i | −0.155144 | − | 0.155144i | ||||
\(424\) | − | 169.617i | − | 0.400040i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −327.301 | −0.768312 | ||||||||
\(427\) | −13.2346 | + | 13.2346i | −0.0309944 | + | 0.0309944i | ||||
\(428\) | −1.53209 | − | 1.53209i | −0.00357964 | − | 0.00357964i | ||||
\(429\) | − | 57.1936i | − | 0.133318i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −279.559 | −0.648628 | −0.324314 | − | 0.945949i | \(-0.605133\pi\) | ||||
−0.324314 | + | 0.945949i | \(0.605133\pi\) | |||||||
\(432\) | −14.6969 | + | 14.6969i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 354.216 | + | 354.216i | 0.818050 | + | 0.818050i | 0.985825 | − | 0.167776i | \(-0.0536584\pi\) |
−0.167776 | + | 0.985825i | \(0.553658\pi\) | |||||||
\(434\) | − | 43.3070i | − | 0.0997857i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −53.3770 | −0.122424 | ||||||||
\(437\) | −161.917 | + | 161.917i | −0.370519 | + | 0.370519i | ||||
\(438\) | −226.246 | − | 226.246i | −0.516543 | − | 0.516543i | ||||
\(439\) | 506.541i | 1.15385i | 0.816797 | + | 0.576926i | \(0.195748\pi\) | ||||
−0.816797 | + | 0.576926i | \(0.804252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −31.2753 | + | 31.2753i | −0.0707585 | + | 0.0707585i | ||||
\(443\) | −443.138 | − | 443.138i | −1.00031 | − | 1.00031i | −1.00000 | 0.000312670i | \(-0.999900\pi\) | |
−0.000312670 | − | 1.00000i | \(-0.500100\pi\) | |||||||
\(444\) | 157.035i | 0.353682i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 626.418 | 1.40453 | ||||||||
\(447\) | 314.490 | − | 314.490i | 0.703557 | − | 0.703557i | ||||
\(448\) | −14.9666 | − | 14.9666i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | − | 360.679i | − | 0.803294i | −0.915795 | − | 0.401647i | \(-0.868438\pi\) | ||
0.915795 | − | 0.401647i | \(-0.131562\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 459.733 | 1.01936 | ||||||||
\(452\) | −266.216 | + | 266.216i | −0.588973 | + | 0.588973i | ||||
\(453\) | −312.972 | − | 312.972i | −0.690887 | − | 0.690887i | ||||
\(454\) | 201.507i | 0.443847i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −107.021 | −0.234694 | ||||||||
\(457\) | −206.799 | + | 206.799i | −0.452514 | + | 0.452514i | −0.896188 | − | 0.443674i | \(-0.853675\pi\) |
0.443674 | + | 0.896188i | \(0.353675\pi\) | |||||||
\(458\) | 120.710 | + | 120.710i | 0.263559 | + | 0.263559i | ||||
\(459\) | 57.0140i | 0.124213i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −649.704 | −1.40934 | −0.704668 | − | 0.709537i | \(-0.748904\pi\) | ||||
−0.704668 | + | 0.709537i | \(0.748904\pi\) | |||||||
\(462\) | 53.0878 | − | 53.0878i | 0.114909 | − | 0.114909i | ||||
\(463\) | −199.904 | − | 199.904i | −0.431759 | − | 0.431759i | 0.457467 | − | 0.889226i | \(-0.348757\pi\) |
−0.889226 | + | 0.457467i | \(0.848757\pi\) | |||||||
\(464\) | − | 124.058i | − | 0.267367i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −401.747 | −0.862119 | ||||||||
\(467\) | 120.654 | − | 120.654i | 0.258359 | − | 0.258359i | −0.566027 | − | 0.824386i | \(-0.691520\pi\) |
0.824386 | + | 0.566027i | \(0.191520\pi\) | |||||||
\(468\) | 12.0931 | + | 12.0931i | 0.0258400 | + | 0.0258400i | ||||
\(469\) | − | 58.7384i | − | 0.125242i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −170.328 | −0.361632 | ||||||||
\(472\) | −178.047 | + | 178.047i | −0.377218 | + | 0.377218i | ||||
\(473\) | 224.454 | + | 224.454i | 0.474534 | + | 0.474534i | ||||
\(474\) | 310.030i | 0.654072i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −58.0602 | −0.121975 | ||||||||
\(477\) | −127.213 | + | 127.213i | −0.266694 | + | 0.266694i | ||||
\(478\) | 288.534 | + | 288.534i | 0.603627 | + | 0.603627i | ||||
\(479\) | − | 527.483i | − | 1.10122i | −0.834764 | − | 0.550609i | \(-0.814396\pi\) | ||
0.834764 | − | 0.550609i | \(-0.185604\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 129.213 | 0.268634 | ||||||||
\(482\) | −80.3054 | + | 80.3054i | −0.166609 | + | 0.166609i | ||||
\(483\) | 33.9657 | + | 33.9657i | 0.0703223 | + | 0.0703223i | ||||
\(484\) | − | 26.4109i | − | 0.0545679i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454 | 0.0453609 | ||||||||
\(487\) | 361.051 | − | 361.051i | 0.741378 | − | 0.741378i | −0.231465 | − | 0.972843i | \(-0.574352\pi\) |
0.972843 | + | 0.231465i | \(0.0743519\pi\) | |||||||
\(488\) | −14.1484 | − | 14.1484i | −0.0289926 | − | 0.0289926i | ||||
\(489\) | − | 539.327i | − | 1.10292i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 579.301 | 1.17984 | 0.589920 | − | 0.807462i | \(-0.299159\pi\) | ||||
0.589920 | + | 0.807462i | \(0.299159\pi\) | |||||||
\(492\) | −97.2067 | + | 97.2067i | −0.197575 | + | 0.197575i | ||||
\(493\) | −240.630 | − | 240.630i | −0.488093 | − | 0.488093i | ||||
\(494\) | 88.0600i | 0.178259i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 46.2971 | 0.0933410 | ||||||||
\(497\) | −249.980 | + | 249.980i | −0.502978 | + | 0.502978i | ||||
\(498\) | −73.6045 | − | 73.6045i | −0.147800 | − | 0.147800i | ||||
\(499\) | − | 269.123i | − | 0.539324i | −0.962955 | − | 0.269662i | \(-0.913088\pi\) | ||
0.962955 | − | 0.269662i | \(-0.0869120\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 67.6701 | 0.135070 | ||||||||
\(502\) | −238.919 | + | 238.919i | −0.475934 | + | 0.475934i | ||||
\(503\) | 297.017 | + | 297.017i | 0.590492 | + | 0.590492i | 0.937764 | − | 0.347273i | \(-0.112892\pi\) |
−0.347273 | + | 0.937764i | \(0.612892\pi\) | |||||||
\(504\) | 22.4499i | 0.0445435i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 171.730 | 0.339387 | ||||||||
\(507\) | −197.031 | + | 197.031i | −0.388622 | + | 0.388622i | ||||
\(508\) | 118.834 | + | 118.834i | 0.233925 | + | 0.233925i | ||||
\(509\) | − | 518.564i | − | 1.01879i | −0.860533 | − | 0.509395i | \(-0.829869\pi\) | ||
0.860533 | − | 0.509395i | \(-0.170131\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −345.596 | −0.676313 | ||||||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 80.2655 | + | 80.2655i | 0.156463 | + | 0.156463i | ||||
\(514\) | 715.752i | 1.39251i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −94.9180 | −0.183950 | ||||||||
\(517\) | −253.419 | + | 253.419i | −0.490172 | + | 0.490172i | ||||
\(518\) | 119.937 | + | 119.937i | 0.231539 | + | 0.231539i | ||||
\(519\) | − | 313.955i | − | 0.604923i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 583.187 | 1.11936 | 0.559680 | − | 0.828709i | \(-0.310924\pi\) | ||||
0.559680 | + | 0.828709i | \(0.310924\pi\) | |||||||
\(522\) | −93.0437 | + | 93.0437i | −0.178245 | + | 0.178245i | ||||
\(523\) | 135.776 | + | 135.776i | 0.259610 | + | 0.259610i | 0.824895 | − | 0.565286i | \(-0.191234\pi\) |
−0.565286 | + | 0.824895i | \(0.691234\pi\) | |||||||
\(524\) | − | 102.521i | − | 0.195651i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 147.078 | 0.279615 | ||||||||
\(527\) | 89.8004 | − | 89.8004i | 0.170399 | − | 0.170399i | ||||
\(528\) | 56.7532 | + | 56.7532i | 0.107487 | + | 0.107487i | ||||
\(529\) | − | 419.127i | − | 0.792301i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 267.070 | 0.502957 | ||||||||
\(532\) | −81.7384 | + | 81.7384i | −0.153644 | + | 0.153644i | ||||
\(533\) | 79.9847 | + | 79.9847i | 0.150065 | + | 0.150065i | ||||
\(534\) | 12.0889i | 0.0226384i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 62.7940 | 0.117153 | ||||||||
\(537\) | −80.4157 | + | 80.4157i | −0.149750 | + | 0.149750i | ||||
\(538\) | −63.1334 | − | 63.1334i | −0.117348 | − | 0.117348i | ||||
\(539\) | − | 81.0929i | − | 0.150451i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −631.949 | −1.16811 | −0.584057 | − | 0.811713i | \(-0.698535\pi\) | ||||
−0.584057 | + | 0.811713i | \(0.698535\pi\) | |||||||
\(542\) | −66.1173 | + | 66.1173i | −0.121988 | + | 0.121988i | ||||
\(543\) | 393.990 | + | 393.990i | 0.725581 | + | 0.725581i | ||||
\(544\) | − | 62.0689i | − | 0.114097i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 18.4725 | 0.0338325 | ||||||||
\(547\) | 465.158 | − | 465.158i | 0.850381 | − | 0.850381i | −0.139799 | − | 0.990180i | \(-0.544646\pi\) |
0.990180 | + | 0.139799i | \(0.0446457\pi\) | |||||||
\(548\) | −35.3053 | − | 35.3053i | −0.0644257 | − | 0.0644257i | ||||
\(549\) | 21.2226i | 0.0386568i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −677.529 | −1.22963 | ||||||||
\(552\) | −36.3108 | + | 36.3108i | −0.0657805 | + | 0.0657805i | ||||
\(553\) | 236.789 | + | 236.789i | 0.428190 | + | 0.428190i | ||||
\(554\) | − | 537.614i | − | 0.970423i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 412.421 | 0.741763 | ||||||||
\(557\) | −432.756 | + | 432.756i | −0.776941 | + | 0.776941i | −0.979309 | − | 0.202368i | \(-0.935136\pi\) |
0.202368 | + | 0.979309i | \(0.435136\pi\) | |||||||
\(558\) | −34.7229 | − | 34.7229i | −0.0622273 | − | 0.0622273i | ||||
\(559\) | 78.1015i | 0.139717i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 220.163 | 0.392448 | ||||||||
\(562\) | −108.591 | + | 108.591i | −0.193222 | + | 0.193222i | ||||
\(563\) | −382.111 | − | 382.111i | −0.678706 | − | 0.678706i | 0.281002 | − | 0.959707i | \(-0.409333\pi\) |
−0.959707 | + | 0.281002i | \(0.909333\pi\) | |||||||
\(564\) | − | 107.167i | − | 0.190012i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −417.379 | −0.737419 | ||||||||
\(567\) | 16.8375 | − | 16.8375i | 0.0296957 | − | 0.0296957i | ||||
\(568\) | −267.240 | − | 267.240i | −0.470493 | − | 0.470493i | ||||
\(569\) | 298.102i | 0.523905i | 0.965081 | + | 0.261952i | \(0.0843663\pi\) | ||||
−0.965081 | + | 0.261952i | \(0.915634\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 769.585 | 1.34778 | 0.673892 | − | 0.738830i | \(-0.264621\pi\) | ||||
0.673892 | + | 0.738830i | \(0.264621\pi\) | |||||||
\(572\) | 46.6984 | − | 46.6984i | 0.0816405 | − | 0.0816405i | ||||
\(573\) | 179.436 | + | 179.436i | 0.313151 | + | 0.313151i | ||||
\(574\) | 148.486i | 0.258686i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 357.027 | − | 357.027i | 0.618765 | − | 0.618765i | −0.326450 | − | 0.945215i | \(-0.605852\pi\) |
0.945215 | + | 0.326450i | \(0.105852\pi\) | |||||||
\(578\) | 168.608 | + | 168.608i | 0.291709 | + | 0.291709i | ||||
\(579\) | 27.2671i | 0.0470935i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −112.433 | −0.193516 | ||||||||
\(582\) | −74.0593 | + | 74.0593i | −0.127250 | + | 0.127250i | ||||
\(583\) | 491.241 | + | 491.241i | 0.842609 | + | 0.842609i | ||||
\(584\) | − | 369.458i | − | 0.632633i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −631.279 | −1.07727 | ||||||||
\(587\) | 107.406 | − | 107.406i | 0.182974 | − | 0.182974i | −0.609677 | − | 0.792650i | \(-0.708701\pi\) |
0.792650 | + | 0.609677i | \(0.208701\pi\) | |||||||
\(588\) | 17.1464 | + | 17.1464i | 0.0291606 | + | 0.0291606i | ||||
\(589\) | − | 252.846i | − | 0.429280i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 54.8851 | 0.0928682 | ||||||||
\(592\) | −128.218 | + | 128.218i | −0.216585 | + | 0.216585i | ||||
\(593\) | −108.955 | − | 108.955i | −0.183735 | − | 0.183735i | 0.609246 | − | 0.792981i | \(-0.291472\pi\) |
−0.792981 | + | 0.609246i | \(0.791472\pi\) | |||||||
\(594\) | − | 85.1299i | − | 0.143316i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 513.560 | 0.861678 | ||||||||
\(597\) | −199.653 | + | 199.653i | −0.334428 | + | 0.334428i | ||||
\(598\) | 29.8777 | + | 29.8777i | 0.0499627 | + | 0.0499627i | ||||
\(599\) | − | 641.351i | − | 1.07070i | −0.844629 | − | 0.535352i | \(-0.820179\pi\) | ||
0.844629 | − | 0.535352i | \(-0.179821\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 52.4826 | 0.0873255 | 0.0436627 | − | 0.999046i | \(-0.486097\pi\) | ||||
0.0436627 | + | 0.999046i | \(0.486097\pi\) | |||||||
\(602\) | −72.4948 | + | 72.4948i | −0.120423 | + | 0.120423i | ||||
\(603\) | −47.0955 | − | 47.0955i | −0.0781020 | − | 0.0781020i | ||||
\(604\) | − | 511.081i | − | 0.846161i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 431.892 | 0.712693 | ||||||||
\(607\) | −318.678 | + | 318.678i | −0.525005 | + | 0.525005i | −0.919079 | − | 0.394074i | \(-0.871065\pi\) |
0.394074 | + | 0.919079i | \(0.371065\pi\) | |||||||
\(608\) | −87.3820 | − | 87.3820i | −0.143720 | − | 0.143720i | ||||
\(609\) | 142.127i | 0.233377i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −88.1801 | −0.144321 | ||||||||
\(612\) | −46.5517 | + | 46.5517i | −0.0760649 | + | 0.0760649i | ||||
\(613\) | −102.852 | − | 102.852i | −0.167784 | − | 0.167784i | 0.618220 | − | 0.786005i | \(-0.287854\pi\) |
−0.786005 | + | 0.618220i | \(0.787854\pi\) | |||||||
\(614\) | 230.968i | 0.376169i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 86.6920 | 0.140734 | ||||||||
\(617\) | 433.993 | − | 433.993i | 0.703392 | − | 0.703392i | −0.261745 | − | 0.965137i | \(-0.584298\pi\) |
0.965137 | + | 0.261745i | \(0.0842980\pi\) | |||||||
\(618\) | −149.789 | − | 149.789i | −0.242377 | − | 0.242377i | ||||
\(619\) | − | 642.310i | − | 1.03766i | −0.854878 | − | 0.518828i | \(-0.826368\pi\) | ||
0.854878 | − | 0.518828i | \(-0.173632\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 54.4662 | 0.0877073 | ||||||||
\(622\) | −489.397 | + | 489.397i | −0.786812 | + | 0.786812i | ||||
\(623\) | 9.23305 | + | 9.23305i | 0.0148203 | + | 0.0148203i | ||||
\(624\) | 19.7480i | 0.0316474i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −191.163 | −0.305372 | ||||||||
\(627\) | 309.951 | − | 309.951i | 0.494339 | − | 0.494339i | ||||
\(628\) | −139.073 | − | 139.073i | −0.221453 | − | 0.221453i | ||||
\(629\) | 497.398i | 0.790776i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −571.788 | −0.906162 | −0.453081 | − | 0.891469i | \(-0.649675\pi\) | ||||
−0.453081 | + | 0.891469i | \(0.649675\pi\) | |||||||
\(632\) | −253.138 | + | 253.138i | −0.400535 | + | 0.400535i | ||||
\(633\) | −326.085 | − | 326.085i | −0.515142 | − | 0.515142i | ||||
\(634\) | 737.074i | 1.16258i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −207.738 | −0.326632 | ||||||||
\(637\) | 14.1086 | − | 14.1086i | 0.0221485 | − | 0.0221485i | ||||
\(638\) | 359.295 | + | 359.295i | 0.563158 | + | 0.563158i | ||||
\(639\) | 400.860i | 0.627324i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −530.212 | −0.827164 | −0.413582 | − | 0.910467i | \(-0.635722\pi\) | ||||
−0.413582 | + | 0.910467i | \(0.635722\pi\) | |||||||
\(642\) | −1.87641 | + | 1.87641i | −0.00292276 | + | 0.00292276i | ||||
\(643\) | −314.561 | − | 314.561i | −0.489208 | − | 0.489208i | 0.418848 | − | 0.908056i | \(-0.362434\pi\) |
−0.908056 | + | 0.418848i | \(0.862434\pi\) | |||||||
\(644\) | 55.4657i | 0.0861269i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −338.982 | −0.524740 | ||||||||
\(647\) | 62.4615 | − | 62.4615i | 0.0965401 | − | 0.0965401i | −0.657187 | − | 0.753727i | \(-0.728254\pi\) |
0.753727 | + | 0.657187i | \(0.228254\pi\) | |||||||
\(648\) | 18.0000 | + | 18.0000i | 0.0277778 | + | 0.0277778i | ||||
\(649\) | − | 1031.31i | − | 1.58907i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −53.0400 | −0.0814747 | ||||||||
\(652\) | 440.359 | − | 440.359i | 0.675397 | − | 0.675397i | ||||
\(653\) | −666.847 | − | 666.847i | −1.02121 | − | 1.02121i | −0.999770 | − | 0.0214354i | \(-0.993176\pi\) |
−0.0214354 | − | 0.999770i | \(-0.506824\pi\) | |||||||
\(654\) | 65.3731i | 0.0999589i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −158.738 | −0.241979 | ||||||||
\(657\) | −277.093 | + | 277.093i | −0.421755 | + | 0.421755i | ||||
\(658\) | −81.8499 | − | 81.8499i | −0.124392 | − | 0.124392i | ||||
\(659\) | 594.414i | 0.901994i | 0.892525 | + | 0.450997i | \(0.148932\pi\) | ||||
−0.892525 | + | 0.450997i | \(0.851068\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1114.18 | 1.68560 | 0.842799 | − | 0.538228i | \(-0.180906\pi\) | ||||
0.842799 | + | 0.538228i | \(0.180906\pi\) | |||||||
\(662\) | 591.256 | − | 591.256i | 0.893135 | − | 0.893135i | ||||
\(663\) | 38.3042 | + | 38.3042i | 0.0577741 | + | 0.0577741i | ||||
\(664\) | − | 120.196i | − | 0.181017i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 192.327 | 0.288780 | ||||||||
\(667\) | −229.877 | + | 229.877i | −0.344644 | + | 0.344644i | ||||
\(668\) | 55.2524 | + | 55.2524i | 0.0827132 | + | 0.0827132i | ||||
\(669\) | − | 767.202i | − | 1.14679i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 81.9525 | 0.122135 | ||||||||
\(672\) | −18.3303 | + | 18.3303i | −0.0272772 | + | 0.0272772i | ||||
\(673\) | −171.862 | − | 171.862i | −0.255367 | − | 0.255367i | 0.567800 | − | 0.823167i | \(-0.307795\pi\) |
−0.823167 | + | 0.567800i | \(0.807795\pi\) | |||||||
\(674\) | − | 296.444i | − | 0.439827i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −321.751 | −0.475963 | ||||||||
\(677\) | 920.701 | − | 920.701i | 1.35997 | − | 1.35997i | 0.486029 | − | 0.873943i | \(-0.338445\pi\) |
0.873943 | − | 0.486029i | \(-0.161555\pi\) | |||||||
\(678\) | 326.047 | + | 326.047i | 0.480895 | + | 0.480895i | ||||
\(679\) | 113.127i | 0.166609i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 246.794 | 0.362400 | ||||||||
\(682\) | −134.085 | + | 134.085i | −0.196605 | + | 0.196605i | ||||
\(683\) | −272.628 | − | 272.628i | −0.399162 | − | 0.399162i | 0.478775 | − | 0.877937i | \(-0.341081\pi\) |
−0.877937 | + | 0.478775i | \(0.841081\pi\) | |||||||
\(684\) | 131.073i | 0.191627i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | 147.839 | − | 147.839i | 0.215195 | − | 0.215195i | ||||
\(688\) | −77.5002 | − | 77.5002i | −0.112646 | − | 0.112646i | ||||
\(689\) | 170.933i | 0.248089i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 418.117 | 0.605090 | 0.302545 | − | 0.953135i | \(-0.402164\pi\) | ||||
0.302545 | + | 0.953135i | \(0.402164\pi\) | |||||||
\(692\) | 256.343 | − | 256.343i | 0.370438 | − | 0.370438i | ||||
\(693\) | −65.0190 | − | 65.0190i | −0.0938225 | − | 0.0938225i | ||||
\(694\) | − | 599.791i | − | 0.864252i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −151.940 | −0.218304 | ||||||||
\(697\) | −307.897 | + | 307.897i | −0.441746 | + | 0.441746i | ||||
\(698\) | 421.152 | + | 421.152i | 0.603369 | + | 0.603369i | ||||
\(699\) | 492.038i | 0.703917i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1093.07 | 1.55930 | 0.779651 | − | 0.626214i | \(-0.215396\pi\) | ||||
0.779651 | + | 0.626214i | \(0.215396\pi\) | |||||||
\(702\) | 14.8110 | − | 14.8110i | 0.0210982 | − | 0.0210982i | ||||
\(703\) | 700.248 | + | 700.248i | 0.996085 | + | 0.996085i | ||||
\(704\) | 92.6777i | 0.131644i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −621.179 | −0.879858 | ||||||||
\(707\) | 329.863 | − | 329.863i | 0.466567 | − | 0.466567i | ||||
\(708\) | 218.062 | + | 218.062i | 0.307997 | + | 0.307997i | ||||
\(709\) | − | 80.7065i | − | 0.113831i | −0.998379 | − | 0.0569157i | \(-0.981873\pi\) | ||
0.998379 | − | 0.0569157i | \(-0.0181266\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 379.708 | 0.534047 | ||||||||
\(712\) | −9.87055 | + | 9.87055i | −0.0138631 | + | 0.0138631i | ||||
\(713\) | −85.7876 | − | 85.7876i | −0.120319 | − | 0.120319i | ||||
\(714\) | 71.1089i | 0.0995923i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −131.318 | −0.183405 | ||||||||
\(717\) | 353.380 | − | 353.380i | 0.492860 | − | 0.492860i | ||||
\(718\) | 223.309 | + | 223.309i | 0.311015 | + | 0.311015i | ||||
\(719\) | 266.201i | 0.370238i | 0.982716 | + | 0.185119i | \(0.0592670\pi\) | ||||
−0.982716 | + | 0.185119i | \(0.940733\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −228.806 | −0.317345 | ||||||||
\(722\) | −116.226 | + | 116.226i | −0.160978 | + | 0.160978i | ||||
\(723\) | 98.3537 | + | 98.3537i | 0.136035 | + | 0.136035i | ||||
\(724\) | 643.383i | 0.888651i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −32.3466 | −0.0445545 | ||||||||
\(727\) | −551.246 | + | 551.246i | −0.758248 | + | 0.758248i | −0.976003 | − | 0.217756i | \(-0.930126\pi\) |
0.217756 | + | 0.976003i | \(0.430126\pi\) | |||||||
\(728\) | 15.0827 | + | 15.0827i | 0.0207181 | + | 0.0207181i | ||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −300.647 | −0.411282 | ||||||||
\(732\) | −17.3282 | + | 17.3282i | −0.0236724 | + | 0.0236724i | ||||
\(733\) | −439.355 | − | 439.355i | −0.599393 | − | 0.599393i | 0.340758 | − | 0.940151i | \(-0.389316\pi\) |
−0.940151 | + | 0.340758i | \(0.889316\pi\) | |||||||
\(734\) | − | 524.186i | − | 0.714149i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −59.2953 | −0.0805643 | ||||||||
\(737\) | −181.862 | + | 181.862i | −0.246761 | + | 0.246761i | ||||
\(738\) | 119.053 | + | 119.053i | 0.161319 | + | 0.161319i | ||||
\(739\) | 1138.45i | 1.54053i | 0.637722 | + | 0.770267i | \(0.279877\pi\) | ||||
−0.637722 | + | 0.770267i | \(0.720123\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 107.851 | 0.145548 | ||||||||
\(742\) | −158.662 | + | 158.662i | −0.213831 | + | 0.213831i | ||||
\(743\) | −334.460 | − | 334.460i | −0.450148 | − | 0.450148i | 0.445256 | − | 0.895404i | \(-0.353113\pi\) |
−0.895404 | + | 0.445256i | \(0.853113\pi\) | |||||||
\(744\) | − | 56.7022i | − | 0.0762126i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −112.472 | −0.150767 | ||||||||
\(747\) | −90.1467 | + | 90.1467i | −0.120678 | + | 0.120678i | ||||
\(748\) | 179.763 | + | 179.763i | 0.240324 | + | 0.240324i | ||||
\(749\) | 2.86627i | 0.00382680i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1204.09 | 1.60331 | 0.801656 | − | 0.597785i | \(-0.203953\pi\) | ||||
0.801656 | + | 0.597785i | \(0.203953\pi\) | |||||||
\(752\) | 87.5012 | − | 87.5012i | 0.116358 | − | 0.116358i | ||||
\(753\) | 292.615 | + | 292.615i | 0.388599 | + | 0.388599i | ||||
\(754\) | 125.021i | 0.165810i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.4955 | 0.0363696 | ||||||||
\(757\) | 343.214 | − | 343.214i | 0.453387 | − | 0.453387i | −0.443090 | − | 0.896477i | \(-0.646118\pi\) |
0.896477 | + | 0.443090i | \(0.146118\pi\) | |||||||
\(758\) | 179.724 | + | 179.724i | 0.237103 | + | 0.237103i | ||||
\(759\) | − | 210.325i | − | 0.277108i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −210.154 | −0.276155 | −0.138078 | − | 0.990421i | \(-0.544092\pi\) | ||||
−0.138078 | + | 0.990421i | \(0.544092\pi\) | |||||||
\(762\) | 145.541 | − | 145.541i | 0.190999 | − | 0.190999i | ||||
\(763\) | 49.9296 | + | 49.9296i | 0.0654385 | + | 0.0654385i | ||||
\(764\) | 293.017i | 0.383531i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 571.402 | 0.745956 | ||||||||
\(767\) | 179.428 | − | 179.428i | 0.233935 | − | 0.233935i | ||||
\(768\) | −19.5959 | − | 19.5959i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 1250.27i | − | 1.62583i | −0.582381 | − | 0.812916i | \(-0.697879\pi\) | ||
0.582381 | − | 0.812916i | \(-0.302121\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 876.613 | 1.13698 | ||||||||
\(772\) | −22.2635 | + | 22.2635i | −0.0288388 | + | 0.0288388i | ||||
\(773\) | −734.887 | − | 734.887i | −0.950695 | − | 0.950695i | 0.0481453 | − | 0.998840i | \(-0.484669\pi\) |
−0.998840 | + | 0.0481453i | \(0.984669\pi\) | |||||||
\(774\) | 116.250i | 0.150194i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −120.938 | −0.155848 | ||||||||
\(777\) | 146.892 | − | 146.892i | 0.189051 | − | 0.189051i | ||||
\(778\) | −728.870 | − | 728.870i | −0.936851 | − | 0.936851i | ||||
\(779\) | 866.927i | 1.11287i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1547.95 | 1.98201 | ||||||||
\(782\) | −115.012 | + | 115.012i | −0.147075 | + | 0.147075i | ||||
\(783\) | 113.955 | + | 113.955i | 0.145536 | + | 0.145536i | ||||
\(784\) | 28.0000i | 0.0357143i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −125.562 | −0.159748 | ||||||||
\(787\) | 787.788 | − | 787.788i | 1.00100 | − | 1.00100i | 0.00100239 | − | 0.999999i | \(-0.499681\pi\) |
0.999999 | − | 0.00100239i | \(-0.000319071\pi\) | |||||||
\(788\) | 44.8135 | + | 44.8135i | 0.0568699 | + | 0.0568699i | ||||
\(789\) | − | 180.132i | − | 0.228305i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 498.044 | 0.629639 | ||||||||
\(792\) | 69.5082 | − | 69.5082i | 0.0877629 | − | 0.0877629i | ||||
\(793\) | 14.2582 | + | 14.2582i | 0.0179800 | + | 0.0179800i | ||||
\(794\) | 39.3098i | 0.0495086i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −326.032 | −0.409589 | ||||||||
\(797\) | −603.311 | + | 603.311i | −0.756977 | + | 0.756977i | −0.975771 | − | 0.218794i | \(-0.929788\pi\) |
0.218794 | + | 0.975771i | \(0.429788\pi\) | |||||||
\(798\) | 100.109 | + | 100.109i | 0.125449 | + | 0.125449i | ||||
\(799\) | − | 339.444i | − | 0.424836i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8058 | 0.0184842 | ||||||||
\(802\) | 230.054 | − | 230.054i | 0.286851 | − | 0.286851i | ||||
\(803\) | 1070.01 | + | 1070.01i | 1.33252 | + | 1.33252i | ||||
\(804\) | − | 76.9066i | − | 0.0956550i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −46.6563 | −0.0578863 | ||||||||
\(807\) | −77.3223 | + | 77.3223i | −0.0958145 | + | 0.0958145i | ||||
\(808\) | 352.638 | + | 352.638i | 0.436434 | + | 0.436434i | ||||
\(809\) | 637.421i | 0.787912i | 0.919129 | + | 0.393956i | \(0.128894\pi\) | ||||
−0.919129 | + | 0.393956i | \(0.871106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 262.276 | 0.323399 | 0.161699 | − | 0.986840i | \(-0.448303\pi\) | ||||
0.161699 | + | 0.986840i | \(0.448303\pi\) | |||||||
\(812\) | −116.046 | + | 116.046i | −0.142914 | + | 0.142914i | ||||
\(813\) | 80.9768 | + | 80.9768i | 0.0996025 | + | 0.0996025i | ||||
\(814\) | − | 742.686i | − | 0.912390i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −76.0186 | −0.0931601 | ||||||||
\(817\) | −423.258 | + | 423.258i | −0.518064 | + | 0.518064i | ||||
\(818\) | 420.833 | + | 420.833i | 0.514466 | + | 0.514466i | ||||
\(819\) | − | 22.6241i | − | 0.0276241i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0.899179 | 0.00109522 | 0.000547612 | − | 1.00000i | \(-0.499826\pi\) | ||||
0.000547612 | 1.00000i | \(0.499826\pi\) | ||||||||
\(822\) | −43.2400 | + | 43.2400i | −0.0526034 | + | 0.0526034i | ||||
\(823\) | −805.679 | − | 805.679i | −0.978954 | − | 0.978954i | 0.0208291 | − | 0.999783i | \(-0.493369\pi\) |
−0.999783 | + | 0.0208291i | \(0.993369\pi\) | |||||||
\(824\) | − | 244.604i | − | 0.296849i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 333.095 | 0.403263 | ||||||||
\(827\) | 1086.99 | − | 1086.99i | 1.31438 | − | 1.31438i | 0.396232 | − | 0.918150i | \(-0.370317\pi\) |
0.918150 | − | 0.396232i | \(-0.129683\pi\) | |||||||
\(828\) | 44.4715 | + | 44.4715i | 0.0537095 | + | 0.0537095i | ||||
\(829\) | − | 1385.23i | − | 1.67097i | −0.549514 | − | 0.835485i | \(-0.685187\pi\) | ||
0.549514 | − | 0.835485i | \(-0.314813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −658.440 | −0.792347 | ||||||||
\(832\) | −16.1241 | + | 16.1241i | −0.0193800 | + | 0.0193800i | ||||
\(833\) | 54.3103 | + | 54.3103i | 0.0651985 | + | 0.0651985i | ||||
\(834\) | − | 505.110i | − | 0.605647i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 506.147 | 0.605439 | ||||||||
\(837\) | −42.5266 | + | 42.5266i | −0.0508084 | + | 0.0508084i | ||||
\(838\) | 196.613 | + | 196.613i | 0.234621 | + | 0.234621i | ||||
\(839\) | 1077.27i | 1.28399i | 0.766707 | + | 0.641997i | \(0.221894\pi\) | ||||
−0.766707 | + | 0.641997i | \(0.778106\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −120.903 | −0.143761 | ||||||||
\(842\) | −169.718 | + | 169.718i | −0.201566 | + | 0.201566i | ||||
\(843\) | 132.996 | + | 132.996i | 0.157765 | + | 0.157765i | ||||
\(844\) | − | 532.495i | − | 0.630918i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −131.252 | −0.155144 | ||||||||
\(847\) | −24.7051 | + | 24.7051i | −0.0291678 | + | 0.0291678i | ||||
\(848\) | −169.617 | − | 169.617i | −0.200020 | − | 0.200020i | ||||
\(849\) | 511.183i | 0.602100i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 475.171 | 0.558368 | ||||||||
\(852\) | −327.301 | + | 327.301i | −0.384156 | + | 0.384156i | ||||
\(853\) | 447.775 | + | 447.775i | 0.524942 | + | 0.524942i | 0.919060 | − | 0.394118i | \(-0.128950\pi\) |
−0.394118 | + | 0.919060i | \(0.628950\pi\) | |||||||
\(854\) | 26.4692i | 0.0309944i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.06417 | −0.00357964 | ||||||||
\(857\) | 223.510 | − | 223.510i | 0.260805 | − | 0.260805i | −0.564576 | − | 0.825381i | \(-0.690960\pi\) |
0.825381 | + | 0.564576i | \(0.190960\pi\) | |||||||
\(858\) | −57.1936 | − | 57.1936i | −0.0666592 | − | 0.0666592i | ||||
\(859\) | − | 1389.27i | − | 1.61731i | −0.588280 | − | 0.808657i | \(-0.700195\pi\) | ||
0.588280 | − | 0.808657i | \(-0.299805\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 181.857 | 0.211216 | ||||||||
\(862\) | −279.559 | + | 279.559i | −0.324314 | + | 0.324314i | ||||
\(863\) | 1076.82 | + | 1076.82i | 1.24776 | + | 1.24776i | 0.956707 | + | 0.291051i | \(0.0940051\pi\) |
0.291051 | + | 0.956707i | \(0.405995\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 708.431 | 0.818050 | ||||||||
\(867\) | 206.501 | − | 206.501i | 0.238179 | − | 0.238179i | ||||
\(868\) | −43.3070 | − | 43.3070i | −0.0498929 | − | 0.0498929i | ||||
\(869\) | − | 1466.27i | − | 1.68730i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63.2812 | −0.0726535 | ||||||||
\(872\) | −53.3770 | + | 53.3770i | −0.0612121 | + | 0.0612121i | ||||
\(873\) | 90.7038 | + | 90.7038i | 0.103899 | + | 0.103899i | ||||
\(874\) | 323.834i | 0.370519i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −452.491 | −0.516543 | ||||||||
\(877\) | 114.375 | − | 114.375i | 0.130417 | − | 0.130417i | −0.638885 | − | 0.769302i | \(-0.720604\pi\) |
0.769302 | + | 0.638885i | \(0.220604\pi\) | |||||||
\(878\) | 506.541 | + | 506.541i | 0.576926 | + | 0.576926i | ||||
\(879\) | 773.156i | 0.879586i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 909.307 | 1.03213 | 0.516065 | − | 0.856549i | \(-0.327396\pi\) | ||||
0.516065 | + | 0.856549i | \(0.327396\pi\) | |||||||
\(882\) | 21.0000 | − | 21.0000i | 0.0238095 | − | 0.0238095i | ||||
\(883\) | −745.228 | − | 745.228i | −0.843973 | − | 0.843973i | 0.145400 | − | 0.989373i | \(-0.453553\pi\) |
−0.989373 | + | 0.145400i | \(0.953553\pi\) | |||||||
\(884\) | 62.5505i | 0.0707585i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −886.277 | −1.00031 | ||||||||
\(887\) | 138.997 | − | 138.997i | 0.156704 | − | 0.156704i | −0.624400 | − | 0.781105i | \(-0.714657\pi\) |
0.781105 | + | 0.624400i | \(0.214657\pi\) | |||||||
\(888\) | 157.035 | + | 157.035i | 0.176841 | + | 0.176841i | ||||
\(889\) | − | 222.318i | − | 0.250077i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −104.262 | −0.117017 | ||||||||
\(892\) | 626.418 | − | 626.418i | 0.702263 | − | 0.702263i | ||||
\(893\) | −477.877 | − | 477.877i | −0.535137 | − | 0.535137i | ||||
\(894\) | − | 628.980i | − | 0.703557i | ||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 36.5925 | − | 36.5925i | 0.0407944 | − | 0.0407944i | ||||
\(898\) | −360.679 | − | 360.679i | −0.401647 | − | 0.401647i | ||||
\(899\) | − | 358.971i | − | 0.399301i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −657.997 | −0.730296 | ||||||||
\(902\) | 459.733 | − | 459.733i | 0.509682 | − | 0.509682i | ||||
\(903\) | 88.7877 | + | 88.7877i | 0.0983252 | + | 0.0983252i | ||||
\(904\) | 532.432i | 0.588973i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −625.944 | −0.690887 | ||||||||
\(907\) | −475.689 | + | 475.689i | −0.524464 | + | 0.524464i | −0.918916 | − | 0.394452i | \(-0.870934\pi\) |
0.394452 | + | 0.918916i | \(0.370934\pi\) | |||||||
\(908\) | 201.507 | + | 201.507i | 0.221924 | + | 0.221924i | ||||
\(909\) | − | 528.958i | − | 0.581912i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 197.368 | 0.216650 | 0.108325 | − | 0.994116i | \(-0.465451\pi\) | ||||
0.108325 | + | 0.994116i | \(0.465451\pi\) | |||||||
\(912\) | −107.021 | + | 107.021i | −0.117347 | + | 0.117347i | ||||
\(913\) | 348.108 | + | 348.108i | 0.381279 | + | 0.381279i | ||||
\(914\) | 413.598i | 0.452514i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 241.420 | 0.263559 | ||||||||
\(917\) | −95.8997 | + | 95.8997i | −0.104580 | + | 0.104580i | ||||
\(918\) | 57.0140 | + | 57.0140i | 0.0621067 | + | 0.0621067i | ||||
\(919\) | 227.388i | 0.247430i | 0.992318 | + | 0.123715i | \(0.0394809\pi\) | ||||
−0.992318 | + | 0.123715i | \(0.960519\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 282.876 | 0.307140 | ||||||||
\(922\) | −649.704 | + | 649.704i | −0.704668 | + | 0.704668i | ||||
\(923\) | 269.313 | + | 269.313i | 0.291780 | + | 0.291780i | ||||
\(924\) | − | 106.176i | − | 0.114909i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −399.809 | −0.431759 | ||||||||
\(927\) | −183.453 | + | 183.453i | −0.197900 | + | 0.197900i | ||||
\(928\) | −124.058 | − | 124.058i | −0.133683 | − | 0.133683i | ||||
\(929\) | 1423.69i | 1.53250i | 0.642542 | + | 0.766250i | \(0.277880\pi\) | ||||
−0.642542 | + | 0.766250i | \(0.722120\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 152.918 | 0.164252 | ||||||||
\(932\) | −401.747 | + | 401.747i | −0.431060 | + | 0.431060i | ||||
\(933\) | 599.387 | + | 599.387i | 0.642430 | + | 0.642430i | ||||
\(934\) | − | 241.307i | − | 0.258359i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 24.1862 | 0.0258400 | ||||||||
\(937\) | −333.167 | + | 333.167i | −0.355567 | + | 0.355567i | −0.862176 | − | 0.506609i | \(-0.830899\pi\) |
0.506609 | + | 0.862176i | \(0.330899\pi\) | |||||||
\(938\) | −58.7384 | − | 58.7384i | −0.0626209 | − | 0.0626209i | ||||
\(939\) | 234.126i | 0.249336i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −703.676 | −0.747796 | −0.373898 | − | 0.927470i | \(-0.621979\pi\) | ||||
−0.373898 | + | 0.927470i | \(0.621979\pi\) | |||||||
\(942\) | −170.328 | + | 170.328i | −0.180816 | + | 0.180816i | ||||
\(943\) | 294.138 | + | 294.138i | 0.311917 | + | 0.311917i | ||||
\(944\) | 356.093i | 0.377218i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 448.909 | 0.474534 | ||||||||
\(947\) | −457.028 | + | 457.028i | −0.482606 | + | 0.482606i | −0.905963 | − | 0.423357i | \(-0.860852\pi\) |
0.423357 | + | 0.905963i | \(0.360852\pi\) | |||||||
\(948\) | 310.030 | + | 310.030i | 0.327036 | + | 0.327036i | ||||
\(949\) | 372.324i | 0.392333i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 902.727 | 0.949240 | ||||||||
\(952\) | −58.0602 | + | 58.0602i | −0.0609876 | + | 0.0609876i | ||||
\(953\) | 705.067 | + | 705.067i | 0.739839 | + | 0.739839i | 0.972547 | − | 0.232707i | \(-0.0747585\pi\) |
−0.232707 | + | 0.972547i | \(0.574758\pi\) | |||||||
\(954\) | 254.426i | 0.266694i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 577.068 | 0.603627 | ||||||||
\(957\) | 440.044 | − | 440.044i | 0.459816 | − | 0.459816i | ||||
\(958\) | −527.483 | − | 527.483i | −0.550609 | − | 0.550609i | ||||
\(959\) | 66.0501i | 0.0688740i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −827.036 | −0.860599 | ||||||||
\(962\) | 129.213 | − | 129.213i | 0.134317 | − | 0.134317i | ||||
\(963\) | 2.29813 | + | 2.29813i | 0.00238643 | + | 0.00238643i | ||||
\(964\) | 160.611i | 0.166609i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 67.9313 | 0.0703223 | ||||||||
\(967\) | 509.515 | − | 509.515i | 0.526902 | − | 0.526902i | −0.392745 | − | 0.919647i | \(-0.628475\pi\) |
0.919647 | + | 0.392745i | \(0.128475\pi\) | |||||||
\(968\) | −26.4109 | − | 26.4109i | −0.0272840 | − | 0.0272840i | ||||
\(969\) | 415.166i | 0.428448i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 68.3318 | 0.0703727 | 0.0351863 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351863 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(972\) | 22.0454 | − | 22.0454i | 0.0226805 | − | 0.0226805i | ||||
\(973\) | −385.784 | − | 385.784i | −0.396489 | − | 0.396489i | ||||
\(974\) | − | 722.102i | − | 0.741378i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −28.2968 | −0.0289926 | ||||||||
\(977\) | 69.5422 | − | 69.5422i | 0.0711793 | − | 0.0711793i | −0.670621 | − | 0.741800i | \(-0.733972\pi\) |
0.741800 | + | 0.670621i | \(0.233972\pi\) | |||||||
\(978\) | −539.327 | − | 539.327i | −0.551459 | − | 0.551459i | ||||
\(979\) | − | 57.1737i | − | 0.0584001i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 80.0654 | 0.0816161 | ||||||||
\(982\) | 579.301 | − | 579.301i | 0.589920 | − | 0.589920i | ||||
\(983\) | 554.809 | + | 554.809i | 0.564403 | + | 0.564403i | 0.930555 | − | 0.366152i | \(-0.119325\pi\) |
−0.366152 | + | 0.930555i | \(0.619325\pi\) | |||||||
\(984\) | 194.413i | 0.197575i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −481.260 | −0.488093 | ||||||||
\(987\) | −100.245 | + | 100.245i | −0.101566 | + | 0.101566i | ||||
\(988\) | 88.0600 | + | 88.0600i | 0.0891295 | + | 0.0891295i | ||||
\(989\) | 287.213i | 0.290407i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1286.89 | −1.29858 | −0.649291 | − | 0.760540i | \(-0.724934\pi\) | ||||
−0.649291 | + | 0.760540i | \(0.724934\pi\) | |||||||
\(992\) | 46.2971 | − | 46.2971i | 0.0466705 | − | 0.0466705i | ||||
\(993\) | −724.137 | − | 724.137i | −0.729242 | − | 0.729242i | ||||
\(994\) | 499.960i | 0.502978i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −147.209 | −0.147800 | ||||||||
\(997\) | 637.153 | − | 637.153i | 0.639071 | − | 0.639071i | −0.311256 | − | 0.950326i | \(-0.600750\pi\) |
0.950326 | + | 0.311256i | \(0.100750\pi\) | |||||||
\(998\) | −269.123 | − | 269.123i | −0.269662 | − | 0.269662i | ||||
\(999\) | − | 235.552i | − | 0.235788i |
(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 | 1050.3.l.h.43.2 | 16 | ||
5.2 | odd | 4 | inner | 1050.3.l.h.757.2 | 16 | ||
5.3 | odd | 4 | 210.3.l.b.127.8 | yes | 16 | ||
5.4 | even | 2 | 210.3.l.b.43.8 | ✓ | 16 | ||
15.8 | even | 4 | 630.3.o.f.127.2 | 16 | |||
15.14 | odd | 2 | 630.3.o.f.253.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.l.b.43.8 | ✓ | 16 | 5.4 | even | 2 | ||
210.3.l.b.127.8 | yes | 16 | 5.3 | odd | 4 | ||
630.3.o.f.127.2 | 16 | 15.8 | even | 4 | |||
630.3.o.f.253.2 | 16 | 15.14 | odd | 2 | |||
1050.3.l.h.43.2 | 16 | 1.1 | even | 1 | trivial | ||
1050.3.l.h.757.2 | 16 | 5.2 | odd | 4 | inner |