Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,3,Mod(19,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.19");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.f (of order \(2\), degree \(1\), 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: | \(1.63488158616\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.389136420864.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 24x^{4} + 80x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 19.4 | ||
Root | \(-0.656712 + 1.88911i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.19 |
Dual form | 60.3.f.b.19.3 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.656712 | + | 1.88911i | −0.328356 | + | 0.944554i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.13746 | − | 2.48120i | −0.784365 | − | 0.620300i | ||||
\(5\) | −3.27492 | + | 3.77822i | −0.654983 | + | 0.755643i | ||||
\(6\) | 1.13746 | − | 3.27203i | 0.189576 | − | 0.545339i | ||||
\(7\) | −9.55505 | −1.36501 | −0.682504 | − | 0.730882i | \(-0.739109\pi\) | ||||
−0.682504 | + | 0.730882i | \(0.739109\pi\) | |||||||
\(8\) | 6.74766 | − | 4.29756i | 0.843458 | − | 0.537196i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | −4.98678 | − | 8.66787i | −0.498678 | − | 0.866787i | ||||
\(11\) | 9.92480i | 0.902255i | 0.892460 | + | 0.451127i | \(0.148978\pi\) | ||||
−0.892460 | + | 0.451127i | \(0.851022\pi\) | |||||||
\(12\) | 5.43424 | + | 4.29756i | 0.452853 | + | 0.358130i | ||||
\(13\) | − | 7.55643i | − | 0.581264i | −0.956835 | − | 0.290632i | \(-0.906134\pi\) | ||
0.956835 | − | 0.290632i | \(-0.0938655\pi\) | |||||||
\(14\) | 6.27492 | − | 18.0505i | 0.448208 | − | 1.28932i | ||||
\(15\) | 5.67232 | − | 6.54406i | 0.378155 | − | 0.436271i | ||||
\(16\) | 3.68729 | + | 15.5693i | 0.230456 | + | 0.973083i | ||||
\(17\) | 17.1903i | 1.01119i | 0.862770 | + | 0.505596i | \(0.168727\pi\) | ||||
−0.862770 | + | 0.505596i | \(0.831273\pi\) | |||||||
\(18\) | −1.97014 | + | 5.66732i | −0.109452 | + | 0.314851i | ||||
\(19\) | 26.1762i | 1.37770i | 0.724905 | + | 0.688849i | \(0.241884\pi\) | ||||
−0.724905 | + | 0.688849i | \(0.758116\pi\) | |||||||
\(20\) | 19.6494 | − | 3.72827i | 0.982471 | − | 0.186414i | ||||
\(21\) | 16.5498 | 0.788087 | ||||||||
\(22\) | −18.7490 | − | 6.51774i | −0.852228 | − | 0.296261i | ||||
\(23\) | 1.67451 | 0.0728047 | 0.0364023 | − | 0.999337i | \(-0.488410\pi\) | ||||
0.0364023 | + | 0.999337i | \(0.488410\pi\) | |||||||
\(24\) | −11.6873 | + | 7.44360i | −0.486971 | + | 0.310150i | ||||
\(25\) | −3.54983 | − | 24.7467i | −0.141993 | − | 0.989868i | ||||
\(26\) | 14.2749 | + | 4.96240i | 0.549035 | + | 0.190862i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 29.9786 | + | 23.7080i | 1.07066 | + | 0.846714i | ||||
\(29\) | −0.350497 | −0.0120861 | −0.00604305 | − | 0.999982i | \(-0.501924\pi\) | ||||
−0.00604305 | + | 0.999982i | \(0.501924\pi\) | |||||||
\(30\) | 8.63736 | + | 15.0132i | 0.287912 | + | 0.500440i | ||||
\(31\) | − | 46.0258i | − | 1.48470i | −0.670010 | − | 0.742352i | \(-0.733710\pi\) | ||
0.670010 | − | 0.742352i | \(-0.266290\pi\) | |||||||
\(32\) | −31.8336 | − | 3.25887i | −0.994801 | − | 0.101840i | ||||
\(33\) | − | 17.1903i | − | 0.520917i | ||||||
\(34\) | −32.4743 | − | 11.2890i | −0.955125 | − | 0.332031i | ||||
\(35\) | 31.2920 | − | 36.1010i | 0.894057 | − | 1.03146i | ||||
\(36\) | −9.41238 | − | 7.44360i | −0.261455 | − | 0.206767i | ||||
\(37\) | 22.6693i | 0.612684i | 0.951922 | + | 0.306342i | \(0.0991051\pi\) | ||||
−0.951922 | + | 0.306342i | \(0.900895\pi\) | |||||||
\(38\) | −49.4498 | − | 17.1903i | −1.30131 | − | 0.452375i | ||||
\(39\) | 13.0881i | 0.335593i | ||||||||
\(40\) | −5.86091 | + | 39.5683i | −0.146523 | + | 0.989207i | ||||
\(41\) | −77.2990 | −1.88534 | −0.942671 | − | 0.333724i | \(-0.891695\pi\) | ||||
−0.942671 | + | 0.333724i | \(0.891695\pi\) | |||||||
\(42\) | −10.8685 | + | 31.2644i | −0.258773 | + | 0.744391i | ||||
\(43\) | 41.7994 | 0.972079 | 0.486039 | − | 0.873937i | \(-0.338441\pi\) | ||||
0.486039 | + | 0.873937i | \(0.338441\pi\) | |||||||
\(44\) | 24.6254 | − | 31.1386i | 0.559668 | − | 0.707697i | ||||
\(45\) | −9.82475 | + | 11.3346i | −0.218328 | + | 0.251881i | ||||
\(46\) | −1.09967 | + | 3.16332i | −0.0239058 | + | 0.0687679i | ||||
\(47\) | −14.0866 | −0.299715 | −0.149857 | − | 0.988708i | \(-0.547881\pi\) | ||||
−0.149857 | + | 0.988708i | \(0.547881\pi\) | |||||||
\(48\) | −6.38658 | − | 26.9669i | −0.133054 | − | 0.561810i | ||||
\(49\) | 42.2990 | 0.863245 | ||||||||
\(50\) | 49.0804 | + | 9.54543i | 0.981608 | + | 0.190909i | ||||
\(51\) | − | 29.7744i | − | 0.583812i | ||||||
\(52\) | −18.7490 | + | 23.7080i | −0.360558 | + | 0.455923i | ||||
\(53\) | 22.6693i | 0.427723i | 0.976864 | + | 0.213861i | \(0.0686041\pi\) | ||||
−0.976864 | + | 0.213861i | \(0.931396\pi\) | |||||||
\(54\) | 3.41238 | − | 9.81609i | 0.0631921 | − | 0.181780i | ||||
\(55\) | −37.4980 | − | 32.5029i | −0.681783 | − | 0.590962i | ||||
\(56\) | −64.4743 | + | 41.0634i | −1.15133 | + | 0.733276i | ||||
\(57\) | − | 45.3386i | − | 0.795414i | ||||||
\(58\) | 0.230175 | − | 0.662126i | 0.00396854 | − | 0.0114160i | ||||
\(59\) | 94.7802i | 1.60644i | 0.595680 | + | 0.803222i | \(0.296883\pi\) | ||||
−0.595680 | + | 0.803222i | \(0.703117\pi\) | |||||||
\(60\) | −34.0338 | + | 6.45756i | −0.567230 | + | 0.107626i | ||||
\(61\) | 38.0000 | 0.622951 | 0.311475 | − | 0.950254i | \(-0.399177\pi\) | ||||
0.311475 | + | 0.950254i | \(0.399177\pi\) | |||||||
\(62\) | 86.9478 | + | 30.2257i | 1.40238 | + | 0.487512i | ||||
\(63\) | −28.6652 | −0.455002 | ||||||||
\(64\) | 27.0619 | − | 57.9970i | 0.422842 | − | 0.906203i | ||||
\(65\) | 28.5498 | + | 24.7467i | 0.439228 | + | 0.380718i | ||||
\(66\) | 32.4743 | + | 11.2890i | 0.492034 | + | 0.171046i | ||||
\(67\) | 29.8477 | 0.445488 | 0.222744 | − | 0.974877i | \(-0.428499\pi\) | ||||
0.222744 | + | 0.974877i | \(0.428499\pi\) | |||||||
\(68\) | 42.6525 | − | 53.9337i | 0.627242 | − | 0.793143i | ||||
\(69\) | −2.90033 | −0.0420338 | ||||||||
\(70\) | 47.6489 | + | 82.8220i | 0.680699 | + | 1.18317i | ||||
\(71\) | 7.19630i | 0.101356i | 0.998715 | + | 0.0506782i | \(0.0161383\pi\) | ||||
−0.998715 | + | 0.0506782i | \(0.983862\pi\) | |||||||
\(72\) | 20.2430 | − | 12.8927i | 0.281153 | − | 0.179065i | ||||
\(73\) | 34.3805i | 0.470966i | 0.971878 | + | 0.235483i | \(0.0756672\pi\) | ||||
−0.971878 | + | 0.235483i | \(0.924333\pi\) | |||||||
\(74\) | −42.8248 | − | 14.8872i | −0.578713 | − | 0.201178i | ||||
\(75\) | 6.14849 | + | 42.8625i | 0.0819799 | + | 0.571500i | ||||
\(76\) | 64.9485 | − | 82.1269i | 0.854586 | − | 1.08062i | ||||
\(77\) | − | 94.8320i | − | 1.23158i | ||||||
\(78\) | −24.7249 | − | 8.59513i | −0.316986 | − | 0.110194i | ||||
\(79\) | 46.0258i | 0.582606i | 0.956631 | + | 0.291303i | \(0.0940887\pi\) | ||||
−0.956631 | + | 0.291303i | \(0.905911\pi\) | |||||||
\(80\) | −70.8999 | − | 37.0569i | −0.886248 | − | 0.463211i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 50.7632 | − | 146.026i | 0.619063 | − | 1.78081i | ||||
\(83\) | −24.1336 | −0.290767 | −0.145383 | − | 0.989375i | \(-0.546442\pi\) | ||||
−0.145383 | + | 0.989375i | \(0.546442\pi\) | |||||||
\(84\) | −51.9244 | − | 41.0634i | −0.618148 | − | 0.488851i | ||||
\(85\) | −64.9485 | − | 56.2967i | −0.764100 | − | 0.662314i | ||||
\(86\) | −27.4502 | + | 78.9636i | −0.319188 | + | 0.918181i | ||||
\(87\) | 0.607078 | 0.00697791 | ||||||||
\(88\) | 42.6525 | + | 66.9692i | 0.484687 | + | 0.761014i | ||||
\(89\) | 100.199 | 1.12584 | 0.562918 | − | 0.826513i | \(-0.309679\pi\) | ||||
0.562918 | + | 0.826513i | \(0.309679\pi\) | |||||||
\(90\) | −14.9603 | − | 26.0036i | −0.166226 | − | 0.288929i | ||||
\(91\) | 72.2021i | 0.793430i | ||||||||
\(92\) | −5.25370 | − | 4.15479i | −0.0571054 | − | 0.0451607i | ||||
\(93\) | 79.7191i | 0.857195i | ||||||||
\(94\) | 9.25083 | − | 26.6111i | 0.0984131 | − | 0.283097i | ||||
\(95\) | −98.8995 | − | 85.7250i | −1.04105 | − | 0.902369i | ||||
\(96\) | 55.1375 | + | 5.64452i | 0.574349 | + | 0.0587971i | ||||
\(97\) | 131.861i | 1.35939i | 0.733494 | + | 0.679696i | \(0.237888\pi\) | ||||
−0.733494 | + | 0.679696i | \(0.762112\pi\) | |||||||
\(98\) | −27.7783 | + | 79.9074i | −0.283452 | + | 0.815382i | ||||
\(99\) | 29.7744i | 0.300752i | ||||||||
\(100\) | −50.2640 | + | 86.4496i | −0.502640 | + | 0.864496i | ||||
\(101\) | 29.4502 | 0.291586 | 0.145793 | − | 0.989315i | \(-0.453427\pi\) | ||||
0.145793 | + | 0.989315i | \(0.453427\pi\) | |||||||
\(102\) | 56.2471 | + | 19.5532i | 0.551442 | + | 0.191698i | ||||
\(103\) | −143.786 | −1.39598 | −0.697991 | − | 0.716107i | \(-0.745922\pi\) | ||||
−0.697991 | + | 0.716107i | \(0.745922\pi\) | |||||||
\(104\) | −32.4743 | − | 50.9882i | −0.312252 | − | 0.490272i | ||||
\(105\) | −54.1993 | + | 62.5289i | −0.516184 | + | 0.595513i | ||||
\(106\) | −42.8248 | − | 14.8872i | −0.404007 | − | 0.140445i | ||||
\(107\) | 35.1014 | 0.328050 | 0.164025 | − | 0.986456i | \(-0.447552\pi\) | ||||
0.164025 | + | 0.986456i | \(0.447552\pi\) | |||||||
\(108\) | 16.3027 | + | 12.8927i | 0.150951 | + | 0.119377i | ||||
\(109\) | −151.498 | −1.38989 | −0.694947 | − | 0.719061i | \(-0.744572\pi\) | ||||
−0.694947 | + | 0.719061i | \(0.744572\pi\) | |||||||
\(110\) | 86.0269 | − | 49.4928i | 0.782063 | − | 0.449935i | ||||
\(111\) | − | 39.2644i | − | 0.353733i | ||||||
\(112\) | −35.2323 | − | 148.766i | −0.314574 | − | 1.32827i | ||||
\(113\) | − | 32.3031i | − | 0.285868i | −0.989732 | − | 0.142934i | \(-0.954346\pi\) | ||
0.989732 | − | 0.142934i | \(-0.0456537\pi\) | |||||||
\(114\) | 85.6495 | + | 29.7744i | 0.751311 | + | 0.261179i | ||||
\(115\) | −5.48387 | + | 6.32665i | −0.0476858 | + | 0.0550143i | ||||
\(116\) | 1.09967 | + | 0.869652i | 0.00947990 | + | 0.00749700i | ||||
\(117\) | − | 22.6693i | − | 0.193755i | ||||||
\(118\) | −179.050 | − | 62.2433i | −1.51737 | − | 0.527486i | ||||
\(119\) | − | 164.254i | − | 1.38028i | ||||||
\(120\) | 10.1514 | − | 68.5343i | 0.0845949 | − | 0.571119i | ||||
\(121\) | 22.4983 | 0.185937 | ||||||||
\(122\) | −24.9551 | + | 71.7861i | −0.204550 | + | 0.588411i | ||||
\(123\) | 133.886 | 1.08850 | ||||||||
\(124\) | −114.199 | + | 144.404i | −0.920962 | + | 1.16455i | ||||
\(125\) | 105.124 | + | 67.6313i | 0.840990 | + | 0.541051i | ||||
\(126\) | 18.8248 | − | 54.1516i | 0.149403 | − | 0.429774i | ||||
\(127\) | 192.053 | 1.51223 | 0.756116 | − | 0.654438i | \(-0.227095\pi\) | ||||
0.756116 | + | 0.654438i | \(0.227095\pi\) | |||||||
\(128\) | 91.7908 | + | 89.2102i | 0.717115 | + | 0.696954i | ||||
\(129\) | −72.3987 | −0.561230 | ||||||||
\(130\) | −65.4982 | + | 37.6823i | −0.503832 | + | 0.289864i | ||||
\(131\) | 42.4277i | 0.323876i | 0.986801 | + | 0.161938i | \(0.0517744\pi\) | ||||
−0.986801 | + | 0.161938i | \(0.948226\pi\) | |||||||
\(132\) | −42.6525 | + | 53.9337i | −0.323125 | + | 0.408589i | ||||
\(133\) | − | 250.115i | − | 1.88057i | ||||||
\(134\) | −19.6013 | + | 56.3855i | −0.146279 | + | 0.420787i | ||||
\(135\) | 17.0170 | − | 19.6322i | 0.126052 | − | 0.145424i | ||||
\(136\) | 73.8762 | + | 115.994i | 0.543208 | + | 0.852897i | ||||
\(137\) | − | 206.854i | − | 1.50988i | −0.655791 | − | 0.754942i | \(-0.727665\pi\) | ||
0.655791 | − | 0.754942i | \(-0.272335\pi\) | |||||||
\(138\) | 1.90468 | − | 5.47904i | 0.0138020 | − | 0.0397032i | ||||
\(139\) | − | 46.0258i | − | 0.331121i | −0.986200 | − | 0.165561i | \(-0.947057\pi\) | ||
0.986200 | − | 0.165561i | \(-0.0529433\pi\) | |||||||
\(140\) | −187.751 | + | 35.6238i | −1.34108 | + | 0.254456i | ||||
\(141\) | 24.3987 | 0.173040 | ||||||||
\(142\) | −13.5946 | − | 4.72590i | −0.0957366 | − | 0.0332810i | ||||
\(143\) | 74.9961 | 0.524448 | ||||||||
\(144\) | 11.0619 | + | 46.7080i | 0.0768186 | + | 0.324361i | ||||
\(145\) | 1.14785 | − | 1.32425i | 0.00791619 | − | 0.00913277i | ||||
\(146\) | −64.9485 | − | 22.5781i | −0.444853 | − | 0.154645i | ||||
\(147\) | −73.2640 | −0.498395 | ||||||||
\(148\) | 56.2471 | − | 71.1240i | 0.380048 | − | 0.480567i | ||||
\(149\) | 11.6495 | 0.0781846 | 0.0390923 | − | 0.999236i | \(-0.487553\pi\) | ||||
0.0390923 | + | 0.999236i | \(0.487553\pi\) | |||||||
\(150\) | −85.0097 | − | 16.5332i | −0.566732 | − | 0.110221i | ||||
\(151\) | − | 125.424i | − | 0.830624i | −0.909679 | − | 0.415312i | \(-0.863672\pi\) | ||
0.909679 | − | 0.415312i | \(-0.136328\pi\) | |||||||
\(152\) | 112.494 | + | 176.628i | 0.740093 | + | 1.16203i | ||||
\(153\) | 51.5708i | 0.337064i | ||||||||
\(154\) | 179.148 | + | 62.2773i | 1.16330 | + | 0.404398i | ||||
\(155\) | 173.896 | + | 150.731i | 1.12191 | + | 0.972457i | ||||
\(156\) | 32.4743 | − | 41.0634i | 0.208168 | − | 0.263227i | ||||
\(157\) | 197.220i | 1.25618i | 0.778140 | + | 0.628090i | \(0.216163\pi\) | ||||
−0.778140 | + | 0.628090i | \(0.783837\pi\) | |||||||
\(158\) | −86.9478 | − | 30.2257i | −0.550303 | − | 0.191302i | ||||
\(159\) | − | 39.2644i | − | 0.246946i | ||||||
\(160\) | 116.565 | − | 109.602i | 0.728532 | − | 0.685011i | ||||
\(161\) | −16.0000 | −0.0993789 | ||||||||
\(162\) | −5.91041 | + | 17.0020i | −0.0364840 | + | 0.104950i | ||||
\(163\) | 18.4196 | 0.113004 | 0.0565018 | − | 0.998402i | \(-0.482005\pi\) | ||||
0.0565018 | + | 0.998402i | \(0.482005\pi\) | |||||||
\(164\) | 242.522 | + | 191.794i | 1.47880 | + | 1.16948i | ||||
\(165\) | 64.9485 | + | 56.2967i | 0.393627 | + | 0.341192i | ||||
\(166\) | 15.8488 | − | 45.5910i | 0.0954749 | − | 0.274645i | ||||
\(167\) | −92.8920 | −0.556240 | −0.278120 | − | 0.960546i | \(-0.589711\pi\) | ||||
−0.278120 | + | 0.960546i | \(0.589711\pi\) | |||||||
\(168\) | 111.673 | − | 71.1240i | 0.664718 | − | 0.423357i | ||||
\(169\) | 111.900 | 0.662132 | ||||||||
\(170\) | 149.003 | − | 85.7241i | 0.876488 | − | 0.504259i | ||||
\(171\) | 78.5287i | 0.459232i | ||||||||
\(172\) | −131.144 | − | 103.713i | −0.762464 | − | 0.602981i | ||||
\(173\) | 117.501i | 0.679198i | 0.940570 | + | 0.339599i | \(0.110291\pi\) | ||||
−0.940570 | + | 0.339599i | \(0.889709\pi\) | |||||||
\(174\) | −0.398675 | + | 1.14684i | −0.00229124 | + | 0.00659101i | ||||
\(175\) | 33.9189 | + | 236.456i | 0.193822 | + | 1.35118i | ||||
\(176\) | −154.522 | + | 36.5956i | −0.877968 | + | 0.207930i | ||||
\(177\) | − | 164.164i | − | 0.927481i | ||||||
\(178\) | −65.8021 | + | 189.287i | −0.369675 | + | 1.06341i | ||||
\(179\) | − | 231.988i | − | 1.29602i | −0.761631 | − | 0.648011i | \(-0.775601\pi\) | ||
0.761631 | − | 0.648011i | \(-0.224399\pi\) | |||||||
\(180\) | 58.9483 | − | 11.1848i | 0.327490 | − | 0.0621379i | ||||
\(181\) | −218.096 | −1.20495 | −0.602476 | − | 0.798137i | \(-0.705819\pi\) | ||||
−0.602476 | + | 0.798137i | \(0.705819\pi\) | |||||||
\(182\) | −136.398 | − | 47.4160i | −0.749437 | − | 0.260527i | ||||
\(183\) | −65.8179 | −0.359661 | ||||||||
\(184\) | 11.2990 | − | 7.19630i | 0.0614076 | − | 0.0391103i | ||||
\(185\) | −85.6495 | − | 74.2401i | −0.462970 | − | 0.401298i | ||||
\(186\) | −150.598 | − | 52.3525i | −0.809667 | − | 0.281465i | ||||
\(187\) | −170.610 | −0.912352 | ||||||||
\(188\) | 44.1961 | + | 34.9516i | 0.235085 | + | 0.185913i | ||||
\(189\) | 49.6495 | 0.262696 | ||||||||
\(190\) | 226.892 | − | 130.535i | 1.19417 | − | 0.687027i | ||||
\(191\) | 137.208i | 0.718366i | 0.933267 | + | 0.359183i | \(0.116945\pi\) | ||||
−0.933267 | + | 0.359183i | \(0.883055\pi\) | |||||||
\(192\) | −46.8725 | + | 100.454i | −0.244128 | + | 0.523197i | ||||
\(193\) | 37.0290i | 0.191860i | 0.995388 | + | 0.0959301i | \(0.0305825\pi\) | ||||
−0.995388 | + | 0.0959301i | \(0.969417\pi\) | |||||||
\(194\) | −249.100 | − | 86.5947i | −1.28402 | − | 0.446364i | ||||
\(195\) | −49.4498 | − | 42.8625i | −0.253589 | − | 0.219808i | ||||
\(196\) | −132.711 | − | 104.952i | −0.677099 | − | 0.535471i | ||||
\(197\) | 194.572i | 0.987674i | 0.869554 | + | 0.493837i | \(0.164406\pi\) | ||||
−0.869554 | + | 0.493837i | \(0.835594\pi\) | |||||||
\(198\) | −56.2471 | − | 19.5532i | −0.284076 | − | 0.0987536i | ||||
\(199\) | − | 176.037i | − | 0.884610i | −0.896865 | − | 0.442305i | \(-0.854161\pi\) | ||
0.896865 | − | 0.442305i | \(-0.145839\pi\) | |||||||
\(200\) | −130.304 | − | 151.727i | −0.651518 | − | 0.758633i | ||||
\(201\) | −51.6977 | −0.257202 | ||||||||
\(202\) | −19.3403 | + | 55.6345i | −0.0957440 | + | 0.275419i | ||||
\(203\) | 3.34901 | 0.0164976 | ||||||||
\(204\) | −73.8762 | + | 93.4159i | −0.362138 | + | 0.457921i | ||||
\(205\) | 253.148 | − | 292.052i | 1.23487 | − | 1.42465i | ||||
\(206\) | 94.4261 | − | 271.628i | 0.458379 | − | 1.31858i | ||||
\(207\) | 5.02352 | 0.0242682 | ||||||||
\(208\) | 117.649 | − | 27.8628i | 0.565618 | − | 0.133956i | ||||
\(209\) | −259.794 | −1.24303 | ||||||||
\(210\) | −82.5304 | − | 143.452i | −0.393002 | − | 0.683104i | ||||
\(211\) | 20.7193i | 0.0981955i | 0.998794 | + | 0.0490978i | \(0.0156346\pi\) | ||||
−0.998794 | + | 0.0490978i | \(0.984365\pi\) | |||||||
\(212\) | 56.2471 | − | 71.1240i | 0.265316 | − | 0.335490i | ||||
\(213\) | − | 12.4644i | − | 0.0585181i | ||||||
\(214\) | −23.0515 | + | 66.3103i | −0.107717 | + | 0.309861i | ||||
\(215\) | −136.890 | + | 157.927i | −0.636696 | + | 0.734545i | ||||
\(216\) | −35.0619 | + | 22.3308i | −0.162324 | + | 0.103383i | ||||
\(217\) | 439.779i | 2.02663i | ||||||||
\(218\) | 99.4908 | − | 286.197i | 0.456380 | − | 1.31283i | ||||
\(219\) | − | 59.5488i | − | 0.271912i | ||||||
\(220\) | 37.0024 | + | 195.017i | 0.168193 | + | 0.886439i | ||||
\(221\) | 129.897 | 0.587769 | ||||||||
\(222\) | 74.1746 | + | 25.7854i | 0.334120 | + | 0.116150i | ||||
\(223\) | −97.0265 | −0.435096 | −0.217548 | − | 0.976050i | \(-0.569806\pi\) | ||||
−0.217548 | + | 0.976050i | \(0.569806\pi\) | |||||||
\(224\) | 304.172 | + | 31.1386i | 1.35791 | + | 0.139012i | ||||
\(225\) | −10.6495 | − | 74.2401i | −0.0473311 | − | 0.329956i | ||||
\(226\) | 61.0241 | + | 21.2138i | 0.270018 | + | 0.0938666i | ||||
\(227\) | −407.256 | −1.79408 | −0.897040 | − | 0.441948i | \(-0.854287\pi\) | ||||
−0.897040 | + | 0.441948i | \(0.854287\pi\) | |||||||
\(228\) | −112.494 | + | 142.248i | −0.493395 | + | 0.623895i | ||||
\(229\) | −7.89702 | −0.0344848 | −0.0172424 | − | 0.999851i | \(-0.505489\pi\) | ||||
−0.0172424 | + | 0.999851i | \(0.505489\pi\) | |||||||
\(230\) | −8.35040 | − | 14.5144i | −0.0363061 | − | 0.0631061i | ||||
\(231\) | 164.254i | 0.711055i | ||||||||
\(232\) | −2.36503 | + | 1.50628i | −0.0101941 | + | 0.00649260i | ||||
\(233\) | − | 28.1483i | − | 0.120808i | −0.998174 | − | 0.0604042i | \(-0.980761\pi\) | ||
0.998174 | − | 0.0604042i | \(-0.0192390\pi\) | |||||||
\(234\) | 42.8248 | + | 14.8872i | 0.183012 | + | 0.0636205i | ||||
\(235\) | 46.1324 | − | 53.2222i | 0.196308 | − | 0.226477i | ||||
\(236\) | 235.169 | − | 297.369i | 0.996477 | − | 1.26004i | ||||
\(237\) | − | 79.7191i | − | 0.336368i | ||||||
\(238\) | 310.293 | + | 107.867i | 1.30375 | + | 0.453225i | ||||
\(239\) | 296.005i | 1.23851i | 0.785189 | + | 0.619257i | \(0.212566\pi\) | ||||
−0.785189 | + | 0.619257i | \(0.787434\pi\) | |||||||
\(240\) | 122.802 | + | 64.1844i | 0.511676 | + | 0.267435i | ||||
\(241\) | 465.794 | 1.93276 | 0.966378 | − | 0.257127i | \(-0.0827758\pi\) | ||||
0.966378 | + | 0.257127i | \(0.0827758\pi\) | |||||||
\(242\) | −14.7749 | + | 42.5018i | −0.0610534 | + | 0.175627i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | −119.223 | − | 94.2856i | −0.488621 | − | 0.386416i | ||||
\(245\) | −138.526 | + | 159.815i | −0.565411 | + | 0.652305i | ||||
\(246\) | −87.9244 | + | 252.925i | −0.357416 | + | 1.02815i | ||||
\(247\) | 197.799 | 0.800806 | ||||||||
\(248\) | −197.799 | − | 310.567i | −0.797577 | − | 1.25229i | ||||
\(249\) | 41.8007 | 0.167874 | ||||||||
\(250\) | −196.799 | + | 154.176i | −0.787196 | + | 0.616703i | ||||
\(251\) | − | 141.676i | − | 0.564445i | −0.959349 | − | 0.282223i | \(-0.908928\pi\) | ||
0.959349 | − | 0.282223i | \(-0.0910716\pi\) | |||||||
\(252\) | 89.9357 | + | 71.1240i | 0.356888 | + | 0.282238i | ||||
\(253\) | 16.6191i | 0.0656883i | ||||||||
\(254\) | −126.124 | + | 362.810i | −0.496550 | + | 1.42838i | ||||
\(255\) | 112.494 | + | 97.5087i | 0.441153 | + | 0.382387i | ||||
\(256\) | −228.808 | + | 114.817i | −0.893780 | + | 0.448505i | ||||
\(257\) | − | 41.7549i | − | 0.162470i | −0.996695 | − | 0.0812352i | \(-0.974113\pi\) | ||
0.996695 | − | 0.0812352i | \(-0.0258865\pi\) | |||||||
\(258\) | 47.5451 | − | 136.769i | 0.184283 | − | 0.530112i | ||||
\(259\) | − | 216.606i | − | 0.836318i | ||||||
\(260\) | −28.1724 | − | 148.480i | −0.108356 | − | 0.571075i | ||||
\(261\) | −1.05149 | −0.00402870 | ||||||||
\(262\) | −80.1505 | − | 27.8628i | −0.305918 | − | 0.106346i | ||||
\(263\) | 203.283 | 0.772939 | 0.386469 | − | 0.922302i | \(-0.373694\pi\) | ||||
0.386469 | + | 0.922302i | \(0.373694\pi\) | |||||||
\(264\) | −73.8762 | − | 115.994i | −0.279834 | − | 0.439371i | ||||
\(265\) | −85.6495 | − | 74.2401i | −0.323206 | − | 0.280151i | ||||
\(266\) | 472.495 | + | 164.254i | 1.77630 | + | 0.617495i | ||||
\(267\) | −173.550 | −0.650001 | ||||||||
\(268\) | −93.6458 | − | 74.0580i | −0.349425 | − | 0.276336i | ||||
\(269\) | −244.048 | −0.907242 | −0.453621 | − | 0.891195i | \(-0.649868\pi\) | ||||
−0.453621 | + | 0.891195i | \(0.649868\pi\) | |||||||
\(270\) | 25.9121 | + | 45.0396i | 0.0959706 | + | 0.166813i | ||||
\(271\) | 466.585i | 1.72172i | 0.508845 | + | 0.860858i | \(0.330073\pi\) | ||||
−0.508845 | + | 0.860858i | \(0.669927\pi\) | |||||||
\(272\) | −267.641 | + | 63.3855i | −0.983973 | + | 0.233035i | ||||
\(273\) | − | 125.058i | − | 0.458087i | ||||||
\(274\) | 390.770 | + | 135.844i | 1.42617 | + | 0.495780i | ||||
\(275\) | 245.606 | − | 35.2314i | 0.893113 | − | 0.128114i | ||||
\(276\) | 9.09967 | + | 7.19630i | 0.0329698 | + | 0.0260736i | ||||
\(277\) | − | 494.181i | − | 1.78405i | −0.451990 | − | 0.892023i | \(-0.649286\pi\) | ||
0.451990 | − | 0.892023i | \(-0.350714\pi\) | |||||||
\(278\) | 86.9478 | + | 30.2257i | 0.312762 | + | 0.108726i | ||||
\(279\) | − | 138.078i | − | 0.494902i | ||||||
\(280\) | 56.0013 | − | 378.077i | 0.200005 | − | 1.35028i | ||||
\(281\) | −43.4020 | −0.154455 | −0.0772277 | − | 0.997013i | \(-0.524607\pi\) | ||||
−0.0772277 | + | 0.997013i | \(0.524607\pi\) | |||||||
\(282\) | −16.0229 | + | 46.0917i | −0.0568188 | + | 0.163446i | ||||
\(283\) | 310.785 | 1.09818 | 0.549090 | − | 0.835763i | \(-0.314974\pi\) | ||||
0.549090 | + | 0.835763i | \(0.314974\pi\) | |||||||
\(284\) | 17.8555 | − | 22.5781i | 0.0628714 | − | 0.0795003i | ||||
\(285\) | 171.299 | + | 148.480i | 0.601049 | + | 0.520983i | ||||
\(286\) | −49.2508 | + | 141.676i | −0.172206 | + | 0.495370i | ||||
\(287\) | 738.596 | 2.57351 | ||||||||
\(288\) | −95.5009 | − | 9.77660i | −0.331600 | − | 0.0339465i | ||||
\(289\) | −6.50497 | −0.0225085 | ||||||||
\(290\) | 1.74785 | + | 3.03806i | 0.00602707 | + | 0.0104761i | ||||
\(291\) | − | 228.390i | − | 0.784845i | ||||||
\(292\) | 85.3049 | − | 107.867i | 0.292140 | − | 0.369409i | ||||
\(293\) | 245.207i | 0.836886i | 0.908243 | + | 0.418443i | \(0.137424\pi\) | ||||
−0.908243 | + | 0.418443i | \(0.862576\pi\) | |||||||
\(294\) | 48.1134 | − | 138.404i | 0.163651 | − | 0.470761i | ||||
\(295\) | −358.100 | − | 310.397i | −1.21390 | − | 1.05219i | ||||
\(296\) | 97.4228 | + | 152.965i | 0.329131 | + | 0.516773i | ||||
\(297\) | − | 51.5708i | − | 0.173639i | ||||||
\(298\) | −7.65037 | + | 22.0072i | −0.0256724 | + | 0.0738496i | ||||
\(299\) | − | 12.6533i | − | 0.0423187i | ||||||
\(300\) | 87.0599 | − | 149.735i | 0.290200 | − | 0.499117i | ||||
\(301\) | −399.395 | −1.32689 | ||||||||
\(302\) | 236.940 | + | 82.3676i | 0.784569 | + | 0.272740i | ||||
\(303\) | −51.0092 | −0.168347 | ||||||||
\(304\) | −407.547 | + | 96.5195i | −1.34061 | + | 0.317498i | ||||
\(305\) | −124.447 | + | 143.572i | −0.408022 | + | 0.470729i | ||||
\(306\) | −97.4228 | − | 33.8671i | −0.318375 | − | 0.110677i | ||||
\(307\) | −337.514 | −1.09939 | −0.549697 | − | 0.835364i | \(-0.685257\pi\) | ||||
−0.549697 | + | 0.835364i | \(0.685257\pi\) | |||||||
\(308\) | −235.297 | + | 297.531i | −0.763952 | + | 0.966011i | ||||
\(309\) | 249.045 | 0.805970 | ||||||||
\(310\) | −398.946 | + | 229.521i | −1.28692 | + | 0.740390i | ||||
\(311\) | − | 427.756i | − | 1.37542i | −0.725986 | − | 0.687710i | \(-0.758616\pi\) | ||
0.725986 | − | 0.687710i | \(-0.241384\pi\) | |||||||
\(312\) | 56.2471 | + | 88.3142i | 0.180279 | + | 0.283058i | ||||
\(313\) | − | 83.8739i | − | 0.267968i | −0.990984 | − | 0.133984i | \(-0.957223\pi\) | ||
0.990984 | − | 0.133984i | \(-0.0427770\pi\) | |||||||
\(314\) | −372.571 | − | 129.517i | −1.18653 | − | 0.412475i | ||||
\(315\) | 93.8760 | − | 108.303i | 0.298019 | − | 0.343820i | ||||
\(316\) | 114.199 | − | 144.404i | 0.361390 | − | 0.456975i | ||||
\(317\) | − | 112.204i | − | 0.353957i | −0.984215 | − | 0.176978i | \(-0.943368\pi\) | ||
0.984215 | − | 0.176978i | \(-0.0566323\pi\) | |||||||
\(318\) | 74.1746 | + | 25.7854i | 0.233254 | + | 0.0810861i | ||||
\(319\) | − | 3.47861i | − | 0.0109047i | ||||||
\(320\) | 130.500 | + | 292.181i | 0.407812 | + | 0.913066i | ||||
\(321\) | −60.7974 | −0.189400 | ||||||||
\(322\) | 10.5074 | − | 30.2257i | 0.0326317 | − | 0.0938687i | ||||
\(323\) | −449.976 | −1.39312 | ||||||||
\(324\) | −28.2371 | − | 22.3308i | −0.0871516 | − | 0.0689222i | ||||
\(325\) | −186.997 | + | 26.8241i | −0.575374 | + | 0.0825356i | ||||
\(326\) | −12.0964 | + | 34.7966i | −0.0371054 | + | 0.106738i | ||||
\(327\) | 262.403 | 0.802455 | ||||||||
\(328\) | −521.588 | + | 332.197i | −1.59021 | + | 1.01280i | ||||
\(329\) | 134.598 | 0.409113 | ||||||||
\(330\) | −149.003 | + | 85.7241i | −0.451524 | + | 0.259770i | ||||
\(331\) | − | 132.621i | − | 0.400666i | −0.979728 | − | 0.200333i | \(-0.935798\pi\) | ||
0.979728 | − | 0.200333i | \(-0.0642025\pi\) | |||||||
\(332\) | 75.7182 | + | 59.8803i | 0.228067 | + | 0.180362i | ||||
\(333\) | 68.0079i | 0.204228i | ||||||||
\(334\) | 61.0033 | − | 175.483i | 0.182645 | − | 0.525398i | ||||
\(335\) | −97.7487 | + | 112.771i | −0.291787 | + | 0.336630i | ||||
\(336\) | 61.0241 | + | 257.670i | 0.181619 | + | 0.766874i | ||||
\(337\) | − | 20.7739i | − | 0.0616437i | −0.999525 | − | 0.0308219i | \(-0.990188\pi\) | ||
0.999525 | − | 0.0308219i | \(-0.00981246\pi\) | |||||||
\(338\) | −73.4863 | + | 211.392i | −0.217415 | + | 0.625420i | ||||
\(339\) | 55.9506i | 0.165046i | ||||||||
\(340\) | 64.0900 | + | 337.779i | 0.188500 | + | 0.993467i | ||||
\(341\) | 456.797 | 1.33958 | ||||||||
\(342\) | −148.349 | − | 51.5708i | −0.433770 | − | 0.150792i | ||||
\(343\) | 64.0283 | 0.186672 | ||||||||
\(344\) | 282.048 | − | 179.636i | 0.819907 | − | 0.522196i | ||||
\(345\) | 9.49834 | − | 10.9581i | 0.0275314 | − | 0.0317625i | ||||
\(346\) | −221.973 | − | 77.1645i | −0.641539 | − | 0.223019i | ||||
\(347\) | −8.89616 | −0.0256374 | −0.0128187 | − | 0.999918i | \(-0.504080\pi\) | ||||
−0.0128187 | + | 0.999918i | \(0.504080\pi\) | |||||||
\(348\) | −1.90468 | − | 1.50628i | −0.00547323 | − | 0.00432840i | ||||
\(349\) | 19.4020 | 0.0555931 | 0.0277965 | − | 0.999614i | \(-0.491151\pi\) | ||||
0.0277965 | + | 0.999614i | \(0.491151\pi\) | |||||||
\(350\) | −468.966 | − | 91.2071i | −1.33990 | − | 0.260592i | ||||
\(351\) | 39.2644i | 0.111864i | ||||||||
\(352\) | 32.3436 | − | 315.942i | 0.0918853 | − | 0.897564i | ||||
\(353\) | − | 80.2902i | − | 0.227451i | −0.993512 | − | 0.113726i | \(-0.963722\pi\) | ||
0.993512 | − | 0.113726i | \(-0.0362784\pi\) | |||||||
\(354\) | 310.124 | + | 107.809i | 0.876056 | + | 0.304544i | ||||
\(355\) | −27.1892 | − | 23.5673i | −0.0765892 | − | 0.0663867i | ||||
\(356\) | −314.371 | − | 248.615i | −0.883065 | − | 0.698356i | ||||
\(357\) | 284.496i | 0.796907i | ||||||||
\(358\) | 438.251 | + | 152.349i | 1.22416 | + | 0.425557i | ||||
\(359\) | 314.115i | 0.874972i | 0.899225 | + | 0.437486i | \(0.144131\pi\) | ||||
−0.899225 | + | 0.437486i | \(0.855869\pi\) | |||||||
\(360\) | −17.5827 | + | 118.705i | −0.0488409 | + | 0.329736i | ||||
\(361\) | −324.196 | −0.898050 | ||||||||
\(362\) | 143.227 | − | 412.008i | 0.395653 | − | 1.13814i | ||||
\(363\) | −38.9683 | −0.107351 | ||||||||
\(364\) | 179.148 | − | 226.531i | 0.492164 | − | 0.622338i | ||||
\(365\) | −129.897 | − | 112.593i | −0.355882 | − | 0.308475i | ||||
\(366\) | 43.2234 | − | 124.337i | 0.118097 | − | 0.339719i | ||||
\(367\) | 476.800 | 1.29918 | 0.649592 | − | 0.760283i | \(-0.274940\pi\) | ||||
0.649592 | + | 0.760283i | \(0.274940\pi\) | |||||||
\(368\) | 6.17440 | + | 26.0709i | 0.0167783 | + | 0.0708450i | ||||
\(369\) | −231.897 | −0.628447 | ||||||||
\(370\) | 196.495 | − | 113.047i | 0.531066 | − | 0.305532i | ||||
\(371\) | − | 216.606i | − | 0.583844i | ||||||
\(372\) | 197.799 | − | 250.115i | 0.531718 | − | 0.672353i | ||||
\(373\) | 86.1333i | 0.230920i | 0.993312 | + | 0.115460i | \(0.0368343\pi\) | ||||
−0.993312 | + | 0.115460i | \(0.963166\pi\) | |||||||
\(374\) | 112.042 | − | 322.300i | 0.299576 | − | 0.861766i | ||||
\(375\) | −182.080 | − | 117.141i | −0.485546 | − | 0.312376i | ||||
\(376\) | −95.0515 | + | 60.5380i | −0.252797 | + | 0.161005i | ||||
\(377\) | 2.64850i | 0.00702521i | ||||||||
\(378\) | −32.6054 | + | 93.7933i | −0.0862577 | + | 0.248130i | ||||
\(379\) | 638.035i | 1.68347i | 0.539891 | + | 0.841735i | \(0.318466\pi\) | ||||
−0.539891 | + | 0.841735i | \(0.681534\pi\) | |||||||
\(380\) | 97.5922 | + | 514.348i | 0.256822 | + | 1.35355i | ||||
\(381\) | −332.646 | −0.873087 | ||||||||
\(382\) | −259.201 | − | 90.1061i | −0.678535 | − | 0.235880i | ||||
\(383\) | −216.742 | −0.565907 | −0.282953 | − | 0.959134i | \(-0.591314\pi\) | ||||
−0.282953 | + | 0.959134i | \(0.591314\pi\) | |||||||
\(384\) | −158.986 | − | 154.517i | −0.414027 | − | 0.402387i | ||||
\(385\) | 358.296 | + | 310.567i | 0.930638 | + | 0.806667i | ||||
\(386\) | −69.9518 | − | 24.3174i | −0.181222 | − | 0.0629985i | ||||
\(387\) | 125.398 | 0.324026 | ||||||||
\(388\) | 327.174 | − | 413.708i | 0.843231 | − | 1.06626i | ||||
\(389\) | 476.640 | 1.22529 | 0.612647 | − | 0.790356i | \(-0.290105\pi\) | ||||
0.612647 | + | 0.790356i | \(0.290105\pi\) | |||||||
\(390\) | 113.446 | − | 65.2676i | 0.290888 | − | 0.167353i | ||||
\(391\) | 28.7852i | 0.0736195i | ||||||||
\(392\) | 285.419 | − | 181.783i | 0.728111 | − | 0.463731i | ||||
\(393\) | − | 73.4869i | − | 0.186990i | ||||||
\(394\) | −367.567 | − | 127.778i | −0.932912 | − | 0.324309i | ||||
\(395\) | −173.896 | − | 150.731i | −0.440242 | − | 0.381597i | ||||
\(396\) | 73.8762 | − | 93.4159i | 0.186556 | − | 0.235899i | ||||
\(397\) | − | 43.0792i | − | 0.108512i | −0.998527 | − | 0.0542559i | \(-0.982721\pi\) | ||
0.998527 | − | 0.0542559i | \(-0.0172787\pi\) | |||||||
\(398\) | 332.554 | + | 115.606i | 0.835562 | + | 0.290467i | ||||
\(399\) | 433.213i | 1.08575i | ||||||||
\(400\) | 372.200 | − | 146.517i | 0.930500 | − | 0.366292i | ||||
\(401\) | −168.694 | −0.420684 | −0.210342 | − | 0.977628i | \(-0.567458\pi\) | ||||
−0.210342 | + | 0.977628i | \(0.567458\pi\) | |||||||
\(402\) | 33.9505 | − | 97.6625i | 0.0844540 | − | 0.242942i | ||||
\(403\) | −347.791 | −0.863005 | ||||||||
\(404\) | −92.3987 | − | 73.0718i | −0.228710 | − | 0.180871i | ||||
\(405\) | −29.4743 | + | 34.0039i | −0.0727759 | + | 0.0839604i | ||||
\(406\) | −2.19934 | + | 6.32665i | −0.00541709 | + | 0.0155829i | ||||
\(407\) | −224.988 | −0.552797 | ||||||||
\(408\) | −127.957 | − | 200.908i | −0.313621 | − | 0.492421i | ||||
\(409\) | 373.890 | 0.914157 | 0.457079 | − | 0.889426i | \(-0.348896\pi\) | ||||
0.457079 | + | 0.889426i | \(0.348896\pi\) | |||||||
\(410\) | 385.473 | + | 670.018i | 0.940179 | + | 1.63419i | ||||
\(411\) | 358.282i | 0.871732i | ||||||||
\(412\) | 451.123 | + | 356.762i | 1.09496 | + | 0.865927i | ||||
\(413\) | − | 905.630i | − | 2.19281i | ||||||
\(414\) | −3.29901 | + | 9.48997i | −0.00796862 | + | 0.0229226i | ||||
\(415\) | 79.0356 | − | 91.1820i | 0.190447 | − | 0.219716i | ||||
\(416\) | −24.6254 | + | 240.549i | −0.0591957 | + | 0.578242i | ||||
\(417\) | 79.7191i | 0.191173i | ||||||||
\(418\) | 170.610 | − | 490.779i | 0.408158 | − | 1.17411i | ||||
\(419\) | 87.5839i | 0.209031i | 0.994523 | + | 0.104515i | \(0.0333291\pi\) | ||||
−0.994523 | + | 0.104515i | \(0.966671\pi\) | |||||||
\(420\) | 325.195 | − | 61.7023i | 0.774273 | − | 0.146910i | ||||
\(421\) | 70.3023 | 0.166989 | 0.0834944 | − | 0.996508i | \(-0.473392\pi\) | ||||
0.0834944 | + | 0.996508i | \(0.473392\pi\) | |||||||
\(422\) | −39.1409 | − | 13.6066i | −0.0927510 | − | 0.0322431i | ||||
\(423\) | −42.2597 | −0.0999048 | ||||||||
\(424\) | 97.4228 | + | 152.965i | 0.229771 | + | 0.360766i | ||||
\(425\) | 425.402 | − | 61.0226i | 1.00095 | − | 0.143583i | ||||
\(426\) | 23.5465 | + | 8.18550i | 0.0552735 | + | 0.0192148i | ||||
\(427\) | −363.092 | −0.850332 | ||||||||
\(428\) | −110.129 | − | 87.0935i | −0.257311 | − | 0.203490i | ||||
\(429\) | −129.897 | −0.302790 | ||||||||
\(430\) | −208.444 | − | 362.312i | −0.484754 | − | 0.842586i | ||||
\(431\) | 247.370i | 0.573944i | 0.957939 | + | 0.286972i | \(0.0926487\pi\) | ||||
−0.957939 | + | 0.286972i | \(0.907351\pi\) | |||||||
\(432\) | −19.1597 | − | 80.9006i | −0.0443512 | − | 0.187270i | ||||
\(433\) | 636.247i | 1.46939i | 0.678397 | + | 0.734696i | \(0.262675\pi\) | ||||
−0.678397 | + | 0.734696i | \(0.737325\pi\) | |||||||
\(434\) | −830.791 | − | 288.808i | −1.91426 | − | 0.665457i | ||||
\(435\) | −1.98813 | + | 2.29367i | −0.00457041 | + | 0.00527281i | ||||
\(436\) | 475.320 | + | 375.898i | 1.09018 | + | 0.862151i | ||||
\(437\) | 43.8323i | 0.100303i | ||||||||
\(438\) | 112.494 | + | 39.1064i | 0.256836 | + | 0.0892840i | ||||
\(439\) | 769.786i | 1.75350i | 0.480947 | + | 0.876750i | \(0.340293\pi\) | ||||
−0.480947 | + | 0.876750i | \(0.659707\pi\) | |||||||
\(440\) | −392.707 | − | 58.1683i | −0.892517 | − | 0.132201i | ||||
\(441\) | 126.897 | 0.287748 | ||||||||
\(442\) | −85.3049 | + | 245.390i | −0.192998 | + | 0.555180i | ||||
\(443\) | 612.214 | 1.38197 | 0.690986 | − | 0.722868i | \(-0.257177\pi\) | ||||
0.690986 | + | 0.722868i | \(0.257177\pi\) | |||||||
\(444\) | −97.4228 | + | 123.190i | −0.219421 | + | 0.277456i | ||||
\(445\) | −328.145 | + | 378.575i | −0.737403 | + | 0.850730i | ||||
\(446\) | 63.7185 | − | 183.294i | 0.142867 | − | 0.410972i | ||||
\(447\) | −20.1775 | −0.0451399 | ||||||||
\(448\) | −258.578 | + | 554.165i | −0.577182 | + | 1.23697i | ||||
\(449\) | 175.897 | 0.391753 | 0.195876 | − | 0.980629i | \(-0.437245\pi\) | ||||
0.195876 | + | 0.980629i | \(0.437245\pi\) | |||||||
\(450\) | 147.241 | + | 28.6363i | 0.327203 | + | 0.0636362i | ||||
\(451\) | − | 767.177i | − | 1.70106i | ||||||
\(452\) | −80.1505 | + | 101.350i | −0.177324 | + | 0.224225i | ||||
\(453\) | 217.241i | 0.479561i | ||||||||
\(454\) | 267.450 | − | 769.351i | 0.589097 | − | 1.69461i | ||||
\(455\) | −272.795 | − | 236.456i | −0.599550 | − | 0.519683i | ||||
\(456\) | −194.846 | − | 305.929i | −0.427293 | − | 0.670898i | ||||
\(457\) | − | 365.357i | − | 0.799469i | −0.916631 | − | 0.399734i | \(-0.869102\pi\) | ||
0.916631 | − | 0.399734i | \(-0.130898\pi\) | |||||||
\(458\) | 5.18607 | − | 14.9183i | 0.0113233 | − | 0.0325728i | ||||
\(459\) | − | 89.3232i | − | 0.194604i | ||||||
\(460\) | 32.9031 | − | 6.24302i | 0.0715285 | − | 0.0135718i | ||||
\(461\) | 308.350 | 0.668873 | 0.334437 | − | 0.942418i | \(-0.391454\pi\) | ||||
0.334437 | + | 0.942418i | \(0.391454\pi\) | |||||||
\(462\) | −310.293 | − | 107.867i | −0.671630 | − | 0.233479i | ||||
\(463\) | 92.6302 | 0.200065 | 0.100033 | − | 0.994984i | \(-0.468105\pi\) | ||||
0.100033 | + | 0.994984i | \(0.468105\pi\) | |||||||
\(464\) | −1.29238 | − | 5.45700i | −0.00278531 | − | 0.0117608i | ||||
\(465\) | −301.196 | − | 261.073i | −0.647733 | − | 0.561448i | ||||
\(466\) | 53.1752 | + | 18.4854i | 0.114110 | + | 0.0396681i | ||||
\(467\) | −606.103 | −1.29786 | −0.648932 | − | 0.760846i | \(-0.724784\pi\) | ||||
−0.648932 | + | 0.760846i | \(0.724784\pi\) | |||||||
\(468\) | −56.2471 | + | 71.1240i | −0.120186 | + | 0.151974i | ||||
\(469\) | −285.196 | −0.608094 | ||||||||
\(470\) | 70.2467 | + | 122.101i | 0.149461 | + | 0.259789i | ||||
\(471\) | − | 341.596i | − | 0.725256i | ||||||
\(472\) | 407.324 | + | 639.545i | 0.862975 | + | 1.35497i | ||||
\(473\) | 414.851i | 0.877063i | ||||||||
\(474\) | 150.598 | + | 52.3525i | 0.317717 | + | 0.110448i | ||||
\(475\) | 647.776 | − | 92.9214i | 1.36374 | − | 0.195624i | ||||
\(476\) | −407.547 | + | 515.339i | −0.856190 | + | 1.08265i | ||||
\(477\) | 68.0079i | 0.142574i | ||||||||
\(478\) | −559.185 | − | 194.390i | −1.16984 | − | 0.406673i | ||||
\(479\) | − | 138.947i | − | 0.290078i | −0.989426 | − | 0.145039i | \(-0.953669\pi\) | ||
0.989426 | − | 0.145039i | \(-0.0463307\pi\) | |||||||
\(480\) | −201.897 | + | 189.836i | −0.420618 | + | 0.395491i | ||||
\(481\) | 171.299 | 0.356131 | ||||||||
\(482\) | −305.893 | + | 879.935i | −0.634632 | + | 1.82559i | ||||
\(483\) | 27.7128 | 0.0573764 | ||||||||
\(484\) | −70.5876 | − | 55.8229i | −0.145842 | − | 0.115337i | ||||
\(485\) | −498.199 | − | 431.834i | −1.02722 | − | 0.890379i | ||||
\(486\) | 10.2371 | − | 29.4483i | 0.0210640 | − | 0.0605932i | ||||
\(487\) | 201.243 | 0.413230 | 0.206615 | − | 0.978422i | \(-0.433755\pi\) | ||||
0.206615 | + | 0.978422i | \(0.433755\pi\) | |||||||
\(488\) | 256.411 | − | 163.307i | 0.525433 | − | 0.334646i | ||||
\(489\) | −31.9036 | −0.0652426 | ||||||||
\(490\) | −210.936 | − | 366.642i | −0.430481 | − | 0.748250i | ||||
\(491\) | 347.368i | 0.707470i | 0.935346 | + | 0.353735i | \(0.115089\pi\) | ||||
−0.935346 | + | 0.353735i | \(0.884911\pi\) | |||||||
\(492\) | −420.061 | − | 332.197i | −0.853783 | − | 0.675198i | ||||
\(493\) | − | 6.02513i | − | 0.0122214i | ||||||
\(494\) | −129.897 | + | 373.664i | −0.262949 | + | 0.756404i | ||||
\(495\) | −112.494 | − | 97.5087i | −0.227261 | − | 0.196987i | ||||
\(496\) | 716.591 | − | 169.711i | 1.44474 | − | 0.342159i | ||||
\(497\) | − | 68.7610i | − | 0.138352i | ||||||
\(498\) | −27.4510 | + | 78.9660i | −0.0551225 | + | 0.158566i | ||||
\(499\) | − | 672.277i | − | 1.34725i | −0.739074 | − | 0.673625i | \(-0.764736\pi\) | ||
0.739074 | − | 0.673625i | \(-0.235264\pi\) | |||||||
\(500\) | −162.015 | − | 473.024i | −0.324029 | − | 0.946047i | ||||
\(501\) | 160.894 | 0.321145 | ||||||||
\(502\) | 267.641 | + | 93.0401i | 0.533149 | + | 0.185339i | ||||
\(503\) | −436.350 | −0.867496 | −0.433748 | − | 0.901034i | \(-0.642809\pi\) | ||||
−0.433748 | + | 0.901034i | \(0.642809\pi\) | |||||||
\(504\) | −193.423 | + | 123.190i | −0.383775 | + | 0.244425i | ||||
\(505\) | −96.4469 | + | 111.269i | −0.190984 | + | 0.220335i | ||||
\(506\) | −31.3954 | − | 10.9140i | −0.0620462 | − | 0.0215692i | ||||
\(507\) | −193.817 | −0.382282 | ||||||||
\(508\) | −602.559 | − | 476.523i | −1.18614 | − | 0.938037i | ||||
\(509\) | −109.547 | −0.215219 | −0.107610 | − | 0.994193i | \(-0.534320\pi\) | ||||
−0.107610 | + | 0.994193i | \(0.534320\pi\) | |||||||
\(510\) | −258.081 | + | 148.478i | −0.506041 | + | 0.291134i | ||||
\(511\) | − | 328.508i | − | 0.642872i | ||||||
\(512\) | −66.6415 | − | 507.644i | −0.130159 | − | 0.991493i | ||||
\(513\) | − | 136.016i | − | 0.265138i | ||||||
\(514\) | 78.8796 | + | 27.4210i | 0.153462 | + | 0.0533482i | ||||
\(515\) | 470.888 | − | 543.255i | 0.914345 | − | 1.05486i | ||||
\(516\) | 227.148 | + | 179.636i | 0.440209 | + | 0.348131i | ||||
\(517\) | − | 139.807i | − | 0.270419i | ||||||
\(518\) | 409.193 | + | 142.248i | 0.789947 | + | 0.274610i | ||||
\(519\) | − | 203.518i | − | 0.392135i | ||||||
\(520\) | 298.995 | + | 44.2875i | 0.574991 | + | 0.0851683i | ||||
\(521\) | −743.100 | −1.42629 | −0.713147 | − | 0.701014i | \(-0.752731\pi\) | ||||
−0.713147 | + | 0.701014i | \(0.752731\pi\) | |||||||
\(522\) | 0.690526 | − | 1.98638i | 0.00132285 | − | 0.00380532i | ||||
\(523\) | 366.211 | 0.700212 | 0.350106 | − | 0.936710i | \(-0.386146\pi\) | ||||
0.350106 | + | 0.936710i | \(0.386146\pi\) | |||||||
\(524\) | 105.272 | − | 133.115i | 0.200900 | − | 0.254037i | ||||
\(525\) | −58.7492 | − | 409.554i | −0.111903 | − | 0.780102i | ||||
\(526\) | −133.498 | + | 384.023i | −0.253799 | + | 0.730083i | ||||
\(527\) | 791.196 | 1.50132 | ||||||||
\(528\) | 267.641 | − | 63.3855i | 0.506895 | − | 0.120048i | ||||
\(529\) | −526.196 | −0.994699 | ||||||||
\(530\) | 196.495 | − | 113.047i | 0.370744 | − | 0.213296i | ||||
\(531\) | 284.341i | 0.535481i | ||||||||
\(532\) | −620.586 | + | 784.727i | −1.16652 | + | 1.47505i | ||||
\(533\) | 584.105i | 1.09588i | ||||||||
\(534\) | 113.973 | − | 327.855i | 0.213432 | − | 0.613961i | ||||
\(535\) | −114.954 | + | 132.621i | −0.214867 | + | 0.247889i | ||||
\(536\) | 201.402 | − | 128.272i | 0.375750 | − | 0.239314i | ||||
\(537\) | 401.815i | 0.748259i | ||||||||
\(538\) | 160.269 | − | 461.033i | 0.297898 | − | 0.856939i | ||||
\(539\) | 419.809i | 0.778867i | ||||||||
\(540\) | −102.101 | + | 19.3727i | −0.189077 | + | 0.0358753i | ||||
\(541\) | 170.688 | 0.315504 | 0.157752 | − | 0.987479i | \(-0.449575\pi\) | ||||
0.157752 | + | 0.987479i | \(0.449575\pi\) | |||||||
\(542\) | −881.430 | − | 306.412i | −1.62625 | − | 0.565336i | ||||
\(543\) | 377.754 | 0.695680 | ||||||||
\(544\) | 56.0208 | − | 547.228i | 0.102979 | − | 1.00593i | ||||
\(545\) | 496.145 | − | 572.393i | 0.910357 | − | 1.05026i | ||||
\(546\) | 236.248 | + | 82.1269i | 0.432688 | + | 0.150416i | ||||
\(547\) | −507.600 | −0.927971 | −0.463986 | − | 0.885843i | \(-0.653581\pi\) | ||||
−0.463986 | + | 0.885843i | \(0.653581\pi\) | |||||||
\(548\) | −513.247 | + | 648.997i | −0.936581 | + | 1.18430i | ||||
\(549\) | 114.000 | 0.207650 | ||||||||
\(550\) | −94.7365 | + | 487.113i | −0.172248 | + | 0.885660i | ||||
\(551\) | − | 9.17469i | − | 0.0166510i | ||||||
\(552\) | −19.5705 | + | 12.4644i | −0.0354537 | + | 0.0225804i | ||||
\(553\) | − | 439.779i | − | 0.795261i | ||||||
\(554\) | 933.561 | + | 324.534i | 1.68513 | + | 0.585802i | ||||
\(555\) | 148.349 | + | 128.588i | 0.267296 | + | 0.231689i | ||||
\(556\) | −114.199 | + | 144.404i | −0.205394 | + | 0.259720i | ||||
\(557\) | 788.492i | 1.41561i | 0.706410 | + | 0.707803i | \(0.250314\pi\) | ||||
−0.706410 | + | 0.707803i | \(0.749686\pi\) | |||||||
\(558\) | 260.843 | + | 90.6772i | 0.467461 | + | 0.162504i | ||||
\(559\) | − | 315.854i | − | 0.565035i | ||||||
\(560\) | 677.452 | + | 354.080i | 1.20974 | + | 0.632286i | ||||
\(561\) | 295.505 | 0.526747 | ||||||||
\(562\) | 28.5026 | − | 81.9910i | 0.0507164 | − | 0.145892i | ||||
\(563\) | 936.102 | 1.66270 | 0.831351 | − | 0.555747i | \(-0.187568\pi\) | ||||
0.831351 | + | 0.555747i | \(0.187568\pi\) | |||||||
\(564\) | −76.5498 | − | 60.5380i | −0.135727 | − | 0.107337i | ||||
\(565\) | 122.048 | + | 105.790i | 0.216014 | + | 0.187239i | ||||
\(566\) | −204.096 | + | 587.107i | −0.360594 | + | 1.03729i | ||||
\(567\) | −85.9955 | −0.151667 | ||||||||
\(568\) | 30.9266 | + | 48.5582i | 0.0544482 | + | 0.0854898i | ||||
\(569\) | −95.4983 | −0.167835 | −0.0839177 | − | 0.996473i | \(-0.526743\pi\) | ||||
−0.0839177 | + | 0.996473i | \(0.526743\pi\) | |||||||
\(570\) | −392.989 | + | 226.094i | −0.689455 | + | 0.396656i | ||||
\(571\) | 889.123i | 1.55713i | 0.627562 | + | 0.778566i | \(0.284053\pi\) | ||||
−0.627562 | + | 0.778566i | \(0.715947\pi\) | |||||||
\(572\) | −235.297 | − | 186.080i | −0.411359 | − | 0.325315i | ||||
\(573\) | − | 237.651i | − | 0.414749i | ||||||
\(574\) | −485.045 | + | 1395.29i | −0.845026 | + | 2.43081i | ||||
\(575\) | −5.94422 | − | 41.4385i | −0.0103378 | − | 0.0720670i | ||||
\(576\) | 81.1856 | − | 173.991i | 0.140947 | − | 0.302068i | ||||
\(577\) | − | 522.147i | − | 0.904934i | −0.891781 | − | 0.452467i | \(-0.850544\pi\) | ||
0.891781 | − | 0.452467i | \(-0.149456\pi\) | |||||||
\(578\) | 4.27189 | − | 12.2886i | 0.00739081 | − | 0.0212605i | ||||
\(579\) | − | 64.1361i | − | 0.110771i | ||||||
\(580\) | −6.88706 | + | 1.30675i | −0.0118742 | + | 0.00225301i | ||||
\(581\) | 230.598 | 0.396898 | ||||||||
\(582\) | 431.453 | + | 149.986i | 0.741329 | + | 0.257709i | ||||
\(583\) | −224.988 | −0.385915 | ||||||||
\(584\) | 147.752 | + | 231.988i | 0.253001 | + | 0.397240i | ||||
\(585\) | 85.6495 | + | 74.2401i | 0.146409 | + | 0.126906i | ||||
\(586\) | −463.223 | − | 161.031i | −0.790484 | − | 0.274796i | ||||
\(587\) | −95.8440 | −0.163278 | −0.0816388 | − | 0.996662i | \(-0.526015\pi\) | ||||
−0.0816388 | + | 0.996662i | \(0.526015\pi\) | |||||||
\(588\) | 229.863 | + | 181.783i | 0.390923 | + | 0.309154i | ||||
\(589\) | 1204.78 | 2.04547 | ||||||||
\(590\) | 821.543 | − | 472.648i | 1.39245 | − | 0.801098i | ||||
\(591\) | − | 337.008i | − | 0.570234i | ||||||
\(592\) | −352.946 | + | 83.5883i | −0.596192 | + | 0.141197i | ||||
\(593\) | − | 878.624i | − | 1.48166i | −0.671693 | − | 0.740829i | \(-0.734433\pi\) | ||
0.671693 | − | 0.740829i | \(-0.265567\pi\) | |||||||
\(594\) | 97.4228 | + | 33.8671i | 0.164011 | + | 0.0570154i | ||||
\(595\) | 620.586 | + | 537.918i | 1.04300 | + | 0.904063i | ||||
\(596\) | −36.5498 | − | 28.9047i | −0.0613252 | − | 0.0484979i | ||||
\(597\) | 304.906i | 0.510730i | ||||||||
\(598\) | 23.9034 | + | 8.30957i | 0.0399723 | + | 0.0138956i | ||||
\(599\) | − | 967.652i | − | 1.61545i | −0.589563 | − | 0.807723i | \(-0.700700\pi\) | ||
0.589563 | − | 0.807723i | \(-0.299300\pi\) | |||||||
\(600\) | 225.692 | + | 262.798i | 0.376154 | + | 0.437997i | ||||
\(601\) | 279.704 | 0.465398 | 0.232699 | − | 0.972549i | \(-0.425244\pi\) | ||||
0.232699 | + | 0.972549i | \(0.425244\pi\) | |||||||
\(602\) | 262.288 | − | 754.501i | 0.435694 | − | 1.25332i | ||||
\(603\) | 89.5430 | 0.148496 | ||||||||
\(604\) | −311.203 | + | 393.513i | −0.515236 | + | 0.651512i | ||||
\(605\) | −73.6802 | + | 85.0036i | −0.121785 | + | 0.140502i | ||||
\(606\) | 33.4983 | − | 96.3619i | 0.0552778 | − | 0.159013i | ||||
\(607\) | −747.564 | −1.23157 | −0.615786 | − | 0.787914i | \(-0.711161\pi\) | ||||
−0.615786 | + | 0.787914i | \(0.711161\pi\) | |||||||
\(608\) | 85.3049 | − | 833.285i | 0.140304 | − | 1.37053i | ||||
\(609\) | −5.80066 | −0.00952490 | ||||||||
\(610\) | −189.498 | − | 329.379i | −0.310652 | − | 0.539966i | ||||
\(611\) | 106.444i | 0.174213i | ||||||||
\(612\) | 127.957 | − | 161.801i | 0.209081 | − | 0.264381i | ||||
\(613\) | − | 457.152i | − | 0.745761i | −0.927879 | − | 0.372881i | \(-0.878370\pi\) | ||
0.927879 | − | 0.372881i | \(-0.121630\pi\) | |||||||
\(614\) | 221.650 | − | 637.600i | 0.360993 | − | 1.03844i | ||||
\(615\) | −438.465 | + | 505.850i | −0.712951 | + | 0.822520i | ||||
\(616\) | −407.547 | − | 639.894i | −0.661601 | − | 1.03879i | ||||
\(617\) | 764.888i | 1.23969i | 0.784725 | + | 0.619844i | \(0.212804\pi\) | ||||
−0.784725 | + | 0.619844i | \(0.787196\pi\) | |||||||
\(618\) | −163.551 | + | 470.473i | −0.264645 | + | 0.761283i | ||||
\(619\) | 365.359i | 0.590240i | 0.955460 | + | 0.295120i | \(0.0953597\pi\) | ||||
−0.955460 | + | 0.295120i | \(0.904640\pi\) | |||||||
\(620\) | −171.597 | − | 904.382i | −0.276769 | − | 1.45868i | ||||
\(621\) | −8.70099 | −0.0140113 | ||||||||
\(622\) | 808.077 | + | 280.912i | 1.29916 | + | 0.451627i | ||||
\(623\) | −957.410 | −1.53677 | ||||||||
\(624\) | −203.773 | + | 48.2598i | −0.326560 | + | 0.0773393i | ||||
\(625\) | −599.797 | + | 175.693i | −0.959676 | + | 0.281109i | ||||
\(626\) | 158.447 | + | 55.0810i | 0.253110 | + | 0.0879888i | ||||
\(627\) | 449.976 | 0.717666 | ||||||||
\(628\) | 489.343 | − | 618.771i | 0.779209 | − | 0.985304i | ||||
\(629\) | −389.691 | −0.619541 | ||||||||
\(630\) | 142.947 | + | 248.466i | 0.226900 | + | 0.394390i | ||||
\(631\) | − | 62.1578i | − | 0.0985067i | −0.998786 | − | 0.0492534i | \(-0.984316\pi\) | ||
0.998786 | − | 0.0492534i | \(-0.0156842\pi\) | |||||||
\(632\) | 197.799 | + | 310.567i | 0.312973 | + | 0.491403i | ||||
\(633\) | − | 35.8868i | − | 0.0566932i | ||||||
\(634\) | 211.966 | + | 73.6859i | 0.334331 | + | 0.116224i | ||||
\(635\) | −628.959 | + | 725.619i | −0.990486 | + | 1.14271i | ||||
\(636\) | −97.4228 | + | 123.190i | −0.153180 | + | 0.193696i | ||||
\(637\) | − | 319.630i | − | 0.501773i | ||||||
\(638\) | 6.57147 | + | 2.28444i | 0.0103001 | + | 0.00358063i | ||||
\(639\) | 21.5889i | 0.0337855i | ||||||||
\(640\) | −637.662 | + | 54.6495i | −0.996348 | + | 0.0853899i | ||||
\(641\) | −1111.69 | −1.73431 | −0.867154 | − | 0.498041i | \(-0.834053\pi\) | ||||
−0.867154 | + | 0.498041i | \(0.834053\pi\) | |||||||
\(642\) | 39.9264 | − | 114.853i | 0.0621906 | − | 0.178898i | ||||
\(643\) | −468.983 | −0.729367 | −0.364683 | − | 0.931132i | \(-0.618823\pi\) | ||||
−0.364683 | + | 0.931132i | \(0.618823\pi\) | |||||||
\(644\) | 50.1993 | + | 39.6992i | 0.0779493 | + | 0.0616447i | ||||
\(645\) | 237.100 | − | 273.538i | 0.367596 | − | 0.424090i | ||||
\(646\) | 295.505 | − | 850.054i | 0.457438 | − | 1.31587i | ||||
\(647\) | 96.7647 | 0.149559 | 0.0747795 | − | 0.997200i | \(-0.476175\pi\) | ||||
0.0747795 | + | 0.997200i | \(0.476175\pi\) | |||||||
\(648\) | 60.7290 | − | 38.6781i | 0.0937175 | − | 0.0596884i | ||||
\(649\) | −940.675 | −1.44942 | ||||||||
\(650\) | 72.1294 | − | 370.873i | 0.110968 | − | 0.570573i | ||||
\(651\) | − | 761.720i | − | 1.17008i | ||||||
\(652\) | −57.7907 | − | 45.7027i | −0.0886360 | − | 0.0700961i | ||||
\(653\) | 920.353i | 1.40942i | 0.709494 | + | 0.704712i | \(0.248924\pi\) | ||||
−0.709494 | + | 0.704712i | \(0.751076\pi\) | |||||||
\(654\) | −172.323 | + | 495.707i | −0.263491 | + | 0.757962i | ||||
\(655\) | −160.301 | − | 138.947i | −0.244734 | − | 0.212133i | ||||
\(656\) | −285.024 | − | 1203.49i | −0.434488 | − | 1.83459i | ||||
\(657\) | 103.142i | 0.156989i | ||||||||
\(658\) | −88.3921 | + | 254.270i | −0.134335 | + | 0.386429i | ||||
\(659\) | 591.020i | 0.896844i | 0.893822 | + | 0.448422i | \(0.148014\pi\) | ||||
−0.893822 | + | 0.448422i | \(0.851986\pi\) | |||||||
\(660\) | −64.0900 | − | 337.779i | −0.0971060 | − | 0.511786i | ||||
\(661\) | −306.193 | −0.463226 | −0.231613 | − | 0.972808i | \(-0.574400\pi\) | ||||
−0.231613 | + | 0.972808i | \(0.574400\pi\) | |||||||
\(662\) | 250.535 | + | 87.0935i | 0.378451 | + | 0.131561i | ||||
\(663\) | −224.988 | −0.339349 | ||||||||
\(664\) | −162.846 | + | 103.716i | −0.245249 | + | 0.156198i | ||||
\(665\) | 944.990 | + | 819.107i | 1.42104 | + | 1.23174i | ||||
\(666\) | −128.474 | − | 44.6616i | −0.192904 | − | 0.0670595i | ||||
\(667\) | −0.586909 | −0.000879924 | ||||||||
\(668\) | 291.445 | + | 230.484i | 0.436295 | + | 0.345035i | ||||
\(669\) | 168.055 | 0.251203 | ||||||||
\(670\) | −148.844 | − | 258.716i | −0.222155 | − | 0.386143i | ||||
\(671\) | 377.142i | 0.562060i | ||||||||
\(672\) | −526.841 | − | 53.9337i | −0.783990 | − | 0.0802585i | ||||
\(673\) | 556.892i | 0.827476i | 0.910396 | + | 0.413738i | \(0.135777\pi\) | ||||
−0.910396 | + | 0.413738i | \(0.864223\pi\) | |||||||
\(674\) | 39.2442 | + | 13.6425i | 0.0582258 | + | 0.0202411i | ||||
\(675\) | 18.4455 | + | 128.588i | 0.0273266 | + | 0.190500i | ||||
\(676\) | −351.083 | − | 277.647i | −0.519353 | − | 0.410721i | ||||
\(677\) | 58.1920i | 0.0859557i | 0.999076 | + | 0.0429779i | \(0.0136845\pi\) | ||||
−0.999076 | + | 0.0429779i | \(0.986316\pi\) | |||||||
\(678\) | −105.697 | − | 36.7435i | −0.155895 | − | 0.0541939i | ||||
\(679\) | − | 1259.94i | − | 1.85558i | ||||||
\(680\) | −680.189 | − | 100.750i | −1.00028 | − | 0.148162i | ||||
\(681\) | 705.389 | 1.03581 | ||||||||
\(682\) | −299.984 | + | 862.940i | −0.439860 | + | 1.26531i | ||||
\(683\) | 357.274 | 0.523096 | 0.261548 | − | 0.965191i | \(-0.415767\pi\) | ||||
0.261548 | + | 0.965191i | \(0.415767\pi\) | |||||||
\(684\) | 194.846 | − | 246.381i | 0.284862 | − | 0.360206i | ||||
\(685\) | 781.540 | + | 677.430i | 1.14093 | + | 0.988949i | ||||
\(686\) | −42.0482 | + | 120.956i | −0.0612947 | + | 0.176321i | ||||
\(687\) | 13.6780 | 0.0199098 | ||||||||
\(688\) | 154.127 | + | 650.788i | 0.224021 | + | 0.945913i | ||||
\(689\) | 171.299 | 0.248620 | ||||||||
\(690\) | 14.4633 | + | 25.1397i | 0.0209613 | + | 0.0364343i | ||||
\(691\) | 614.707i | 0.889590i | 0.895632 | + | 0.444795i | \(0.146724\pi\) | ||||
−0.895632 | + | 0.444795i | \(0.853276\pi\) | |||||||
\(692\) | 291.544 | − | 368.655i | 0.421307 | − | 0.532739i | ||||
\(693\) | − | 284.496i | − | 0.410528i | ||||||
\(694\) | 5.84222 | − | 16.8058i | 0.00841818 | − | 0.0242159i | ||||
\(695\) | 173.896 | + | 150.731i | 0.250210 | + | 0.216879i | ||||
\(696\) | 4.09636 | − | 2.60896i | 0.00588557 | − | 0.00374850i | ||||
\(697\) | − | 1328.79i | − | 1.90644i | ||||||
\(698\) | −12.7415 | + | 36.6524i | −0.0182543 | + | 0.0525107i | ||||
\(699\) | 48.7543i | 0.0697487i | ||||||||
\(700\) | 480.275 | − | 826.030i | 0.686108 | − | 1.18004i | ||||
\(701\) | −886.028 | −1.26395 | −0.631975 | − | 0.774989i | \(-0.717755\pi\) | ||||
−0.631975 | + | 0.774989i | \(0.717755\pi\) | |||||||
\(702\) | −74.1746 | − | 25.7854i | −0.105662 | − | 0.0367313i | ||||
\(703\) | −593.397 | −0.844093 | ||||||||
\(704\) | 575.609 | + | 268.584i | 0.817626 | + | 0.381511i | ||||
\(705\) | −79.9036 | + | 92.1835i | −0.113338 | + | 0.130757i | ||||
\(706\) | 151.677 | + | 52.7276i | 0.214840 | + | 0.0746849i | ||||
\(707\) | −281.398 | −0.398017 | ||||||||
\(708\) | −407.324 | + | 515.058i | −0.575316 | + | 0.727483i | ||||
\(709\) | −760.887 | −1.07318 | −0.536592 | − | 0.843842i | \(-0.680288\pi\) | ||||
−0.536592 | + | 0.843842i | \(0.680288\pi\) | |||||||
\(710\) | 62.3766 | − | 35.8864i | 0.0878544 | − | 0.0505442i | ||||
\(711\) | 138.078i | 0.194202i | ||||||||
\(712\) | 676.111 | − | 430.613i | 0.949594 | − | 0.604794i | ||||
\(713\) | − | 77.0706i | − | 0.108093i | ||||||
\(714\) | −537.444 | − | 186.832i | −0.752722 | − | 0.261669i | ||||
\(715\) | −245.606 | + | 283.351i | −0.343505 | + | 0.396296i | ||||
\(716\) | −575.609 | + | 727.853i | −0.803923 | + | 1.01655i | ||||
\(717\) | − | 512.695i | − | 0.715056i | ||||||
\(718\) | −593.397 | − | 206.283i | −0.826458 | − | 0.287302i | ||||
\(719\) | − | 575.877i | − | 0.800942i | −0.916309 | − | 0.400471i | \(-0.868846\pi\) | ||
0.916309 | − | 0.400471i | \(-0.131154\pi\) | |||||||
\(720\) | −212.700 | − | 111.171i | −0.295416 | − | 0.154404i | ||||
\(721\) | 1373.88 | 1.90553 | ||||||||
\(722\) | 212.903 | − | 612.441i | 0.294880 | − | 0.848257i | ||||
\(723\) | −806.779 | −1.11588 | ||||||||
\(724\) | 684.268 | + | 541.141i | 0.945122 | + | 0.747432i | ||||
\(725\) | 1.24421 | + | 8.67363i | 0.00171615 | + | 0.0119636i | ||||
\(726\) | 25.5909 | − | 73.6153i | 0.0352492 | − | 0.101398i | ||||
\(727\) | 327.332 | 0.450250 | 0.225125 | − | 0.974330i | \(-0.427721\pi\) | ||||
0.225125 | + | 0.974330i | \(0.427721\pi\) | |||||||
\(728\) | 310.293 | + | 487.195i | 0.426227 | + | 0.669224i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 298.006 | − | 171.448i | 0.408227 | − | 0.234860i | ||||
\(731\) | 718.542i | 0.982958i | ||||||||
\(732\) | 206.501 | + | 163.307i | 0.282105 | + | 0.223098i | ||||
\(733\) | 947.567i | 1.29272i | 0.763031 | + | 0.646362i | \(0.223710\pi\) | ||||
−0.763031 | + | 0.646362i | \(0.776290\pi\) | |||||||
\(734\) | −313.120 | + | 900.727i | −0.426595 | + | 1.22715i | ||||
\(735\) | 239.934 | − | 276.807i | 0.326440 | − | 0.376609i | ||||
\(736\) | −53.3056 | − | 5.45700i | −0.0724261 | − | 0.00741440i | ||||
\(737\) | 296.232i | 0.401943i | ||||||||
\(738\) | 152.290 | − | 438.079i | 0.206354 | − | 0.593602i | ||||
\(739\) | 183.234i | 0.247948i | 0.992285 | + | 0.123974i | \(0.0395640\pi\) | ||||
−0.992285 | + | 0.123974i | \(0.960436\pi\) | |||||||
\(740\) | 84.5173 | + | 445.439i | 0.114213 | + | 0.601944i | ||||
\(741\) | −342.598 | −0.462345 | ||||||||
\(742\) | 409.193 | + | 142.248i | 0.551473 | + | 0.191709i | ||||
\(743\) | 183.712 | 0.247258 | 0.123629 | − | 0.992329i | \(-0.460547\pi\) | ||||
0.123629 | + | 0.992329i | \(0.460547\pi\) | |||||||
\(744\) | 342.598 | + | 537.918i | 0.460481 | + | 0.723008i | ||||
\(745\) | −38.1512 | + | 44.0143i | −0.0512096 | + | 0.0590797i | ||||
\(746\) | −162.715 | − | 56.5648i | −0.218117 | − | 0.0758241i | ||||
\(747\) | −72.4009 | −0.0969222 | ||||||||
\(748\) | 535.281 | + | 423.317i | 0.715617 | + | 0.565932i | ||||
\(749\) | −335.395 | −0.447791 | ||||||||
\(750\) | 340.866 | − | 267.040i | 0.454488 | − | 0.356054i | ||||
\(751\) | − | 345.748i | − | 0.460384i | −0.973145 | − | 0.230192i | \(-0.926065\pi\) | ||
0.973145 | − | 0.230192i | \(-0.0739354\pi\) | |||||||
\(752\) | −51.9414 | − | 219.319i | −0.0690710 | − | 0.291647i | ||||
\(753\) | 245.390i | 0.325882i | ||||||||
\(754\) | −5.00331 | − | 1.73930i | −0.00663569 | − | 0.00230677i | ||||
\(755\) | 473.880 | + | 410.754i | 0.627656 | + | 0.544045i | ||||
\(756\) | −155.773 | − | 123.190i | −0.206049 | − | 0.162950i | ||||
\(757\) | − | 549.335i | − | 0.725674i | −0.931853 | − | 0.362837i | \(-0.881808\pi\) | ||
0.931853 | − | 0.362837i | \(-0.118192\pi\) | |||||||
\(758\) | −1205.32 | − | 419.005i | −1.59013 | − | 0.552778i | ||||
\(759\) | − | 28.7852i | − | 0.0379252i | ||||||
\(760\) | −1035.75 | − | 153.417i | −1.36283 | − | 0.201864i | ||||
\(761\) | 251.485 | 0.330467 | 0.165233 | − | 0.986255i | \(-0.447162\pi\) | ||||
0.165233 | + | 0.986255i | \(0.447162\pi\) | |||||||
\(762\) | 218.453 | − | 628.405i | 0.286683 | − | 0.824678i | ||||
\(763\) | 1447.57 | 1.89721 | ||||||||
\(764\) | 340.440 | − | 430.484i | 0.445602 | − | 0.563461i | ||||
\(765\) | −194.846 | − | 168.890i | −0.254700 | − | 0.220771i | ||||
\(766\) | 142.337 | − | 409.450i | 0.185819 | − | 0.534529i | ||||
\(767\) | 716.200 | 0.933768 | ||||||||
\(768\) | 396.307 | − | 198.869i | 0.516024 | − | 0.258945i | ||||
\(769\) | 583.691 | 0.759026 | 0.379513 | − | 0.925186i | \(-0.376092\pi\) | ||||
0.379513 | + | 0.925186i | \(0.376092\pi\) | |||||||
\(770\) | −821.991 | + | 472.906i | −1.06752 | + | 0.614164i | ||||
\(771\) | 72.3216i | 0.0938024i | ||||||||
\(772\) | 91.8764 | − | 116.177i | 0.119011 | − | 0.150488i | ||||
\(773\) | − | 1328.04i | − | 1.71803i | −0.511951 | − | 0.859015i | \(-0.671077\pi\) | ||
0.511951 | − | 0.859015i | \(-0.328923\pi\) | |||||||
\(774\) | −82.3505 | + | 236.891i | −0.106396 | + | 0.306060i | ||||
\(775\) | −1138.99 | + | 163.384i | −1.46966 | + | 0.210818i | ||||
\(776\) | 566.681 | + | 889.753i | 0.730259 | + | 1.14659i | ||||
\(777\) | 375.173i | 0.482848i | ||||||||
\(778\) | −313.015 | + | 900.424i | −0.402333 | + | 1.15736i | ||||
\(779\) | − | 2023.40i | − | 2.59743i | ||||||
\(780\) | 48.7961 | + | 257.174i | 0.0625591 | + | 0.329710i | ||||
\(781\) | −71.4219 | −0.0914492 | ||||||||
\(782\) | −54.3784 | − | 18.9036i | −0.0695376 | − | 0.0241734i | ||||
\(783\) | 1.82123 | 0.00232597 | ||||||||
\(784\) | 155.969 | + | 658.567i | 0.198940 | + | 0.840009i | ||||
\(785\) | −745.141 | − | 645.880i | −0.949224 | − | 0.822778i | ||||
\(786\) | 138.825 | + | 48.2598i | 0.176622 | + | 0.0613992i | ||||
\(787\) | 1318.83 | 1.67577 | 0.837883 | − | 0.545850i | \(-0.183793\pi\) | ||||
0.837883 | + | 0.545850i | \(0.183793\pi\) | |||||||
\(788\) | 482.772 | − | 610.461i | 0.612654 | − | 0.774697i | ||||
\(789\) | −352.096 | −0.446256 | ||||||||
\(790\) | 398.946 | − | 229.521i | 0.504995 | − | 0.290533i | ||||
\(791\) | 308.658i | 0.390212i | ||||||||
\(792\) | 127.957 | + | 200.908i | 0.161562 | + | 0.253671i | ||||
\(793\) | − | 287.144i | − | 0.362099i | ||||||
\(794\) | 81.3812 | + | 28.2906i | 0.102495 | + | 0.0356305i | ||||
\(795\) | 148.349 | + | 128.588i | 0.186603 | + | 0.161745i | ||||
\(796\) | −436.784 | + | 552.310i | −0.548724 | + | 0.693857i | ||||
\(797\) | − | 1277.40i | − | 1.60276i | −0.598154 | − | 0.801381i | \(-0.704099\pi\) | ||
0.598154 | − | 0.801381i | \(-0.295901\pi\) | |||||||
\(798\) | −818.385 | − | 284.496i | −1.02555 | − | 0.356511i | ||||
\(799\) | − | 242.152i | − | 0.303069i | ||||||
\(800\) | 32.3579 | + | 799.345i | 0.0404474 | + | 0.999182i | ||||
\(801\) | 300.598 | 0.375278 | ||||||||
\(802\) | 110.784 | − | 318.682i | 0.138134 | − | 0.397359i | ||||
\(803\) | −341.220 | −0.424931 | ||||||||
\(804\) | 162.199 | + | 128.272i | 0.201740 | + | 0.159543i | ||||
\(805\) | 52.3987 | − | 60.4515i | 0.0650915 | − | 0.0750950i | ||||
\(806\) | 228.399 | − | 657.015i | 0.283373 | − | 0.815155i | ||||
\(807\) | 422.704 | 0.523797 | ||||||||
\(808\) | 198.720 | − | 126.564i | 0.245940 | − | 0.156639i | ||||
\(809\) | 321.093 | 0.396901 | 0.198451 | − | 0.980111i | \(-0.436409\pi\) | ||||
0.198451 | + | 0.980111i | \(0.436409\pi\) | |||||||
\(810\) | −44.8810 | − | 78.0109i | −0.0554087 | − | 0.0963097i | ||||
\(811\) | − | 946.932i | − | 1.16761i | −0.811894 | − | 0.583805i | \(-0.801563\pi\) | ||
0.811894 | − | 0.583805i | \(-0.198437\pi\) | |||||||
\(812\) | −10.5074 | − | 8.30957i | −0.0129401 | − | 0.0102335i | ||||
\(813\) | − | 808.149i | − | 0.994033i | ||||||
\(814\) | 147.752 | − | 425.027i | 0.181514 | − | 0.522146i | ||||
\(815\) | −60.3226 | + | 69.5931i | −0.0740154 | + | 0.0853904i | ||||
\(816\) | 463.567 | − | 109.787i | 0.568097 | − | 0.134543i | ||||
\(817\) | 1094.15i | 1.33923i | ||||||||
\(818\) | −245.538 | + | 706.319i | −0.300169 | + | 0.863471i | ||||
\(819\) | 216.606i | 0.264477i | ||||||||
\(820\) | −1518.88 | + | 288.192i | −1.85229 | + | 0.351453i | ||||
\(821\) | 1169.34 | 1.42429 | 0.712144 | − | 0.702033i | \(-0.247724\pi\) | ||||
0.712144 | + | 0.702033i | \(0.247724\pi\) | |||||||
\(822\) | −676.833 | − | 235.288i | −0.823398 | − | 0.286239i | ||||
\(823\) | 1251.71 | 1.52091 | 0.760457 | − | 0.649389i | \(-0.224975\pi\) | ||||
0.760457 | + | 0.649389i | \(0.224975\pi\) | |||||||
\(824\) | −970.220 | + | 617.930i | −1.17745 | + | 0.749915i | ||||
\(825\) | −425.402 | + | 61.0226i | −0.515639 | + | 0.0739668i | ||||
\(826\) | 1710.83 | + | 594.738i | 2.07123 | + | 0.720022i | ||||
\(827\) | 892.104 | 1.07872 | 0.539362 | − | 0.842074i | \(-0.318666\pi\) | ||||
0.539362 | + | 0.842074i | \(0.318666\pi\) | |||||||
\(828\) | −15.7611 | − | 12.4644i | −0.0190351 | − | 0.0150536i | ||||
\(829\) | 998.688 | 1.20469 | 0.602345 | − | 0.798236i | \(-0.294233\pi\) | ||||
0.602345 | + | 0.798236i | \(0.294233\pi\) | |||||||
\(830\) | 120.349 | + | 209.187i | 0.144999 | + | 0.252033i | ||||
\(831\) | 855.946i | 1.03002i | ||||||||
\(832\) | −438.251 | − | 204.491i | −0.526743 | − | 0.245783i | ||||
\(833\) | 727.131i | 0.872906i | ||||||||
\(834\) | −150.598 | − | 52.3525i | −0.180573 | − | 0.0627728i | ||||
\(835\) | 304.214 | − | 350.966i | 0.364328 | − | 0.420319i | ||||
\(836\) | 815.093 | + | 644.601i | 0.974992 | + | 0.771054i | ||||
\(837\) | 239.157i | 0.285732i | ||||||||
\(838\) | −165.455 | − | 57.5174i | −0.197441 | − | 0.0686365i | ||||
\(839\) | 610.359i | 0.727484i | 0.931500 | + | 0.363742i | \(0.118501\pi\) | ||||
−0.931500 | + | 0.363742i | \(0.881499\pi\) | |||||||
\(840\) | −96.9970 | + | 654.849i | −0.115473 | + | 0.779582i | ||||
\(841\) | −840.877 | −0.999854 | ||||||||
\(842\) | −46.1684 | + | 132.809i | −0.0548318 | + | 0.157730i | ||||
\(843\) | 75.1744 | 0.0891749 | ||||||||
\(844\) | 51.4086 | − | 65.0058i | 0.0609107 | − | 0.0770211i | ||||
\(845\) | −366.464 | + | 422.784i | −0.433686 | + | 0.500336i | ||||
\(846\) | 27.7525 | − | 79.8332i | 0.0328044 | − | 0.0943655i | ||||
\(847\) | −214.973 | −0.253805 | ||||||||
\(848\) | −352.946 | + | 83.5883i | −0.416209 | + | 0.0985712i | ||||
\(849\) | −538.296 | −0.634035 | ||||||||
\(850\) | −164.088 | + | 843.705i | −0.193045 | + | 0.992594i | ||||
\(851\) | 37.9599i | 0.0446062i | ||||||||
\(852\) | −30.9266 | + | 39.1064i | −0.0362988 | + | 0.0458995i | ||||
\(853\) | 832.689i | 0.976189i | 0.872791 | + | 0.488094i | \(0.162308\pi\) | ||||
−0.872791 | + | 0.488094i | \(0.837692\pi\) | |||||||
\(854\) | 238.447 | − | 685.920i | 0.279212 | − | 0.803185i | ||||
\(855\) | −296.699 | − | 257.175i | −0.347016 | − | 0.300790i | ||||
\(856\) | 236.852 | − | 150.850i | 0.276696 | − | 0.176227i | ||||
\(857\) | 149.415i | 0.174347i | 0.996193 | + | 0.0871735i | \(0.0277834\pi\) | ||||
−0.996193 | + | 0.0871735i | \(0.972217\pi\) | |||||||
\(858\) | 85.3049 | − | 245.390i | 0.0994230 | − | 0.286002i | ||||
\(859\) | − | 394.144i | − | 0.458840i | −0.973327 | − | 0.229420i | \(-0.926317\pi\) | ||
0.973327 | − | 0.229420i | \(-0.0736830\pi\) | |||||||
\(860\) | 821.334 | − | 155.840i | 0.955040 | − | 0.181209i | ||||
\(861\) | −1279.29 | −1.48581 | ||||||||
\(862\) | −467.308 | − | 162.451i | −0.542121 | − | 0.188458i | ||||
\(863\) | −1409.58 | −1.63335 | −0.816677 | − | 0.577095i | \(-0.804186\pi\) | ||||
−0.816677 | + | 0.577095i | \(0.804186\pi\) | |||||||
\(864\) | 165.412 | + | 16.9336i | 0.191450 | + | 0.0195990i | ||||
\(865\) | −443.945 | − | 384.807i | −0.513231 | − | 0.444864i | ||||
\(866\) | −1201.94 | − | 417.831i | −1.38792 | − | 0.482484i | ||||
\(867\) | 11.2669 | 0.0129953 | ||||||||
\(868\) | 1091.18 | − | 1379.79i | 1.25712 | − | 1.58962i | ||||
\(869\) | −456.797 | −0.525659 | ||||||||
\(870\) | −3.02737 | − | 5.26208i | −0.00347973 | − | 0.00604836i | ||||
\(871\) | − | 225.542i | − | 0.258946i | ||||||
\(872\) | −1022.26 | + | 651.074i | −1.17232 | + | 0.746644i | ||||
\(873\) | 395.583i | 0.453131i | ||||||||
\(874\) | −82.8040 | − | 28.7852i | −0.0947414 | − | 0.0329350i | ||||
\(875\) | −1004.46 | − | 646.221i | −1.14796 | − | 0.738538i | ||||
\(876\) | −147.752 | + | 186.832i | −0.168667 | + | 0.213278i | ||||
\(877\) | 872.780i | 0.995189i | 0.867410 | + | 0.497594i | \(0.165783\pi\) | ||||
−0.867410 | + | 0.497594i | \(0.834217\pi\) | |||||||
\(878\) | −1454.21 | − | 505.528i | −1.65627 | − | 0.575772i | ||||
\(879\) | − | 424.712i | − | 0.483176i | ||||||
\(880\) | 367.782 | − | 703.667i | 0.417934 | − | 0.799621i | ||||
\(881\) | 1103.38 | 1.25241 | 0.626206 | − | 0.779657i | \(-0.284607\pi\) | ||||
0.626206 | + | 0.779657i | \(0.284607\pi\) | |||||||
\(882\) | −83.3348 | + | 239.722i | −0.0944839 | + | 0.271794i | ||||
\(883\) | −536.884 | −0.608023 | −0.304011 | − | 0.952668i | \(-0.598326\pi\) | ||||
−0.304011 | + | 0.952668i | \(0.598326\pi\) | |||||||
\(884\) | −407.547 | − | 322.300i | −0.461025 | − | 0.364593i | ||||
\(885\) | 620.248 | + | 537.624i | 0.700845 | + | 0.607485i | ||||
\(886\) | −402.048 | + | 1156.54i | −0.453779 | + | 1.30535i | ||||
\(887\) | −888.945 | −1.00219 | −0.501096 | − | 0.865392i | \(-0.667070\pi\) | ||||
−0.501096 | + | 0.865392i | \(0.667070\pi\) | |||||||
\(888\) | −168.741 | − | 264.943i | −0.190024 | − | 0.298359i | ||||
\(889\) | −1835.08 | −2.06421 | ||||||||
\(890\) | −499.672 | − | 868.515i | −0.561429 | − | 0.975860i | ||||
\(891\) | 89.3232i | 0.100251i | ||||||||
\(892\) | 304.417 | + | 240.742i | 0.341274 | + | 0.269890i | ||||
\(893\) | − | 368.734i | − | 0.412916i | ||||||
\(894\) | 13.2508 | − | 38.1175i | 0.0148220 | − | 0.0426371i | ||||
\(895\) | 876.501 | + | 759.742i | 0.979331 | + | 0.848874i | ||||
\(896\) | −877.066 | − | 852.408i | −0.978868 | − | 0.951348i | ||||
\(897\) | 21.9162i | 0.0244327i | ||||||||
\(898\) | −115.514 | + | 332.288i | −0.128634 | + | 0.370032i | ||||
\(899\) | 16.1319i | 0.0179443i | ||||||||
\(900\) | −150.792 | + | 259.349i | −0.167547 | + | 0.288165i | ||||
\(901\) | −389.691 | −0.432510 | ||||||||
\(902\) | 1449.28 | + | 503.814i | 1.60674 | + | 0.558553i | ||||
\(903\) | 691.773 | 0.766083 | ||||||||
\(904\) | −138.825 | − | 217.971i | −0.153567 | − | 0.241118i | ||||
\(905\) | 714.248 | − | 824.015i | 0.789224 | − | 0.910514i | ||||
\(906\) | −410.392 | − | 142.665i | −0.452971 | − | 0.157467i | ||||
\(907\) | −1668.40 | −1.83947 | −0.919734 | − | 0.392543i | \(-0.871595\pi\) | ||||
−0.919734 | + | 0.392543i | \(0.871595\pi\) | |||||||
\(908\) | 1277.75 | + | 1010.48i | 1.40721 | + | 1.11287i | ||||
\(909\) | 88.3505 | 0.0971953 | ||||||||
\(910\) | 625.839 | − | 360.056i | 0.687735 | − | 0.395666i | ||||
\(911\) | − | 1498.13i | − | 1.64449i | −0.569131 | − | 0.822247i | \(-0.692720\pi\) | ||
0.569131 | − | 0.822247i | \(-0.307280\pi\) | |||||||
\(912\) | 705.891 | − | 167.177i | 0.774004 | − | 0.183308i | ||||
\(913\) | − | 239.521i | − | 0.262345i | ||||||
\(914\) | 690.199 | + | 239.935i | 0.755142 | + | 0.262510i | ||||
\(915\) | 215.548 | − | 248.674i | 0.235572 | − | 0.271775i | ||||
\(916\) | 24.7766 | + | 19.5941i | 0.0270487 | + | 0.0213909i | ||||
\(917\) | − | 405.399i | − | 0.442093i | ||||||
\(918\) | 168.741 | + | 58.6596i | 0.183814 | + | 0.0638994i | ||||
\(919\) | 1094.82i | 1.19131i | 0.803240 | + | 0.595656i | \(0.203108\pi\) | ||||
−0.803240 | + | 0.595656i | \(0.796892\pi\) | |||||||
\(920\) | −9.81413 | + | 66.2574i | −0.0106675 | + | 0.0720189i | ||||
\(921\) | 584.591 | 0.634735 | ||||||||
\(922\) | −202.497 | + | 582.507i | −0.219629 | + | 0.631787i | ||||
\(923\) | 54.3784 | 0.0589148 | ||||||||
\(924\) | 407.547 | − | 515.339i | 0.441068 | − | 0.557727i | ||||
\(925\) | 560.990 | − | 80.4723i | 0.606476 | − | 0.0869970i | ||||
\(926\) | −60.8314 | + | 174.988i | −0.0656926 | + | 0.188972i | ||||
\(927\) | −431.358 | −0.465327 | ||||||||
\(928\) | 11.1576 | + | 1.14222i | 0.0120233 | + | 0.00123084i | ||||
\(929\) | 1145.90 | 1.23348 | 0.616740 | − | 0.787167i | \(-0.288453\pi\) | ||||
0.616740 | + | 0.787167i | \(0.288453\pi\) | |||||||
\(930\) | 690.995 | − | 397.542i | 0.743005 | − | 0.427464i | ||||
\(931\) | 1107.23i | 1.18929i | ||||||||
\(932\) | −69.8417 | + | 88.3142i | −0.0749374 | + | 0.0947578i | ||||
\(933\) | 740.894i | 0.794099i | ||||||||
\(934\) | 398.035 | − | 1144.99i | 0.426162 | − | 1.22590i | ||||
\(935\) | 558.733 | − | 644.601i | 0.597576 | − | 0.689413i | ||||
\(936\) | −97.4228 | − | 152.965i | −0.104084 | − | 0.163424i | ||||
\(937\) | − | 1272.49i | − | 1.35805i | −0.734115 | − | 0.679025i | \(-0.762403\pi\) | ||
0.734115 | − | 0.679025i | \(-0.237597\pi\) | |||||||
\(938\) | 187.292 | − | 538.766i | 0.199671 | − | 0.574378i | ||||
\(939\) | 145.274i | 0.154711i | ||||||||
\(940\) | −276.793 | + | 52.5186i | −0.294461 | + | 0.0558709i | ||||
\(941\) | 707.360 | 0.751711 | 0.375856 | − | 0.926678i | \(-0.377349\pi\) | ||||
0.375856 | + | 0.926678i | \(0.377349\pi\) | |||||||
\(942\) | 645.311 | + | 224.330i | 0.685044 | + | 0.238142i | ||||
\(943\) | −129.438 | −0.137262 | ||||||||
\(944\) | −1475.66 | + | 349.482i | −1.56320 | + | 0.370214i | ||||
\(945\) | −162.598 | + | 187.587i | −0.172061 | + | 0.198504i | ||||
\(946\) | −783.698 | − | 272.437i | −0.828433 | − | 0.287989i | ||||
\(947\) | −284.977 | −0.300926 | −0.150463 | − | 0.988616i | \(-0.548076\pi\) | ||||
−0.150463 | + | 0.988616i | \(0.548076\pi\) | |||||||
\(948\) | −197.799 | + | 250.115i | −0.208649 | + | 0.263835i | ||||
\(949\) | 259.794 | 0.273756 | ||||||||
\(950\) | −249.864 | + | 1284.74i | −0.263014 | + | 1.35236i | ||||
\(951\) | 194.343i | 0.204357i | ||||||||
\(952\) | −705.891 | − | 1108.33i | −0.741482 | − | 1.16421i | ||||
\(953\) | 295.247i | 0.309808i | 0.987930 | + | 0.154904i | \(0.0495068\pi\) | ||||
−0.987930 | + | 0.154904i | \(0.950493\pi\) | |||||||
\(954\) | −128.474 | − | 44.6616i | −0.134669 | − | 0.0468151i | ||||
\(955\) | −518.401 | − | 449.344i | −0.542828 | − | 0.470518i | ||||
\(956\) | 734.447 | − | 928.702i | 0.768250 | − | 0.971446i | ||||
\(957\) | 6.02513i | 0.00629585i | ||||||||
\(958\) | 262.486 | + | 91.2483i | 0.273994 | + | 0.0952487i | ||||
\(959\) | 1976.50i | 2.06100i | ||||||||
\(960\) | −226.032 | − | 506.072i | −0.235450 | − | 0.527159i | ||||
\(961\) | −1157.38 | −1.20435 | ||||||||
\(962\) | −112.494 | + | 323.602i | −0.116938 | + | 0.336385i | ||||
\(963\) | 105.304 | 0.109350 | ||||||||
\(964\) | −1461.41 | − | 1155.73i | −1.51598 | − | 1.19889i | ||||
\(965\) | −139.904 | − | 121.267i | −0.144978 | − | 0.125665i | ||||
\(966\) | −18.1993 | + | 52.3525i | −0.0188399 | + | 0.0541951i | ||||
\(967\) | −348.013 | −0.359889 | −0.179945 | − | 0.983677i | \(-0.557592\pi\) | ||||
−0.179945 | + | 0.983677i | \(0.557592\pi\) | |||||||
\(968\) | 151.811 | − | 96.6881i | 0.156830 | − | 0.0998844i | ||||
\(969\) | 779.382 | 0.804316 | ||||||||
\(970\) | 1142.95 | − | 657.562i | 1.17830 | − | 0.677899i | ||||
\(971\) | − | 798.691i | − | 0.822545i | −0.911513 | − | 0.411272i | \(-0.865085\pi\) | ||
0.911513 | − | 0.411272i | \(-0.134915\pi\) | |||||||
\(972\) | 48.9081 | + | 38.6781i | 0.0503170 | + | 0.0397923i | ||||
\(973\) | 439.779i | 0.451983i | ||||||||
\(974\) | −132.159 | + | 380.170i | −0.135687 | + | 0.390318i | ||||
\(975\) | 323.888 | − | 46.4607i | 0.332193 | − | 0.0476520i | ||||
\(976\) | 140.117 | + | 591.634i | 0.143563 | + | 0.606183i | ||||
\(977\) | − | 721.834i | − | 0.738827i | −0.929265 | − | 0.369413i | \(-0.879559\pi\) | ||
0.929265 | − | 0.369413i | \(-0.120441\pi\) | |||||||
\(978\) | 20.9515 | − | 60.2694i | 0.0214228 | − | 0.0616252i | ||||
\(979\) | 994.458i | 1.01579i | ||||||||
\(980\) | 831.151 | − | 157.702i | 0.848114 | − | 0.160921i | ||||
\(981\) | −454.495 | −0.463298 | ||||||||
\(982\) | −656.216 | − | 228.121i | −0.668244 | − | 0.232302i | ||||
\(983\) | 1717.25 | 1.74695 | 0.873474 | − | 0.486870i | \(-0.161861\pi\) | ||||
0.873474 | + | 0.486870i | \(0.161861\pi\) | |||||||
\(984\) | 903.416 | − | 575.383i | 0.918106 | − | 0.584739i | ||||
\(985\) | −735.135 | − | 637.207i | −0.746330 | − | 0.646910i | ||||
\(986\) | 11.3821 | + | 3.95677i | 0.0115437 | + | 0.00401296i | ||||
\(987\) | −233.131 | −0.236201 | ||||||||
\(988\) | −620.586 | − | 490.779i | −0.628124 | − | 0.496740i | ||||
\(989\) | 69.9934 | 0.0707719 | ||||||||
\(990\) | 258.081 | − | 148.478i | 0.260688 | − | 0.149978i | ||||
\(991\) | 342.270i | 0.345378i | 0.984976 | + | 0.172689i | \(0.0552456\pi\) | ||||
−0.984976 | + | 0.172689i | \(0.944754\pi\) | |||||||
\(992\) | −149.992 | + | 1465.17i | −0.151202 | + | 1.47699i | ||||
\(993\) | 229.706i | 0.231325i | ||||||||
\(994\) | 129.897 | + | 45.1562i | 0.130681 | + | 0.0454288i | ||||
\(995\) | 665.108 | + | 576.508i | 0.668450 | + | 0.579405i | ||||
\(996\) | −131.148 | − | 103.716i | −0.131675 | − | 0.104132i | ||||
\(997\) | 1586.05i | 1.59082i | 0.606072 | + | 0.795410i | \(0.292744\pi\) | ||||
−0.606072 | + | 0.795410i | \(0.707256\pi\) | |||||||
\(998\) | 1270.00 | + | 441.493i | 1.27255 | + | 0.442377i | ||||
\(999\) | − | 117.793i | − | 0.117911i |
(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 | 60.3.f.b.19.4 | yes | 8 | |
3.2 | odd | 2 | 180.3.f.h.19.5 | 8 | |||
4.3 | odd | 2 | inner | 60.3.f.b.19.6 | yes | 8 | |
5.2 | odd | 4 | 300.3.c.f.151.1 | 8 | |||
5.3 | odd | 4 | 300.3.c.f.151.8 | 8 | |||
5.4 | even | 2 | inner | 60.3.f.b.19.5 | yes | 8 | |
8.3 | odd | 2 | 960.3.j.e.319.3 | 8 | |||
8.5 | even | 2 | 960.3.j.e.319.7 | 8 | |||
12.11 | even | 2 | 180.3.f.h.19.3 | 8 | |||
15.2 | even | 4 | 900.3.c.r.451.8 | 8 | |||
15.8 | even | 4 | 900.3.c.r.451.1 | 8 | |||
15.14 | odd | 2 | 180.3.f.h.19.4 | 8 | |||
20.3 | even | 4 | 300.3.c.f.151.7 | 8 | |||
20.7 | even | 4 | 300.3.c.f.151.2 | 8 | |||
20.19 | odd | 2 | inner | 60.3.f.b.19.3 | ✓ | 8 | |
40.19 | odd | 2 | 960.3.j.e.319.8 | 8 | |||
40.29 | even | 2 | 960.3.j.e.319.4 | 8 | |||
60.23 | odd | 4 | 900.3.c.r.451.2 | 8 | |||
60.47 | odd | 4 | 900.3.c.r.451.7 | 8 | |||
60.59 | even | 2 | 180.3.f.h.19.6 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.3.f.b.19.3 | ✓ | 8 | 20.19 | odd | 2 | inner | |
60.3.f.b.19.4 | yes | 8 | 1.1 | even | 1 | trivial | |
60.3.f.b.19.5 | yes | 8 | 5.4 | even | 2 | inner | |
60.3.f.b.19.6 | yes | 8 | 4.3 | odd | 2 | inner | |
180.3.f.h.19.3 | 8 | 12.11 | even | 2 | |||
180.3.f.h.19.4 | 8 | 15.14 | odd | 2 | |||
180.3.f.h.19.5 | 8 | 3.2 | odd | 2 | |||
180.3.f.h.19.6 | 8 | 60.59 | even | 2 | |||
300.3.c.f.151.1 | 8 | 5.2 | odd | 4 | |||
300.3.c.f.151.2 | 8 | 20.7 | even | 4 | |||
300.3.c.f.151.7 | 8 | 20.3 | even | 4 | |||
300.3.c.f.151.8 | 8 | 5.3 | odd | 4 | |||
900.3.c.r.451.1 | 8 | 15.8 | even | 4 | |||
900.3.c.r.451.2 | 8 | 60.23 | odd | 4 | |||
900.3.c.r.451.7 | 8 | 60.47 | odd | 4 | |||
900.3.c.r.451.8 | 8 | 15.2 | even | 4 | |||
960.3.j.e.319.3 | 8 | 8.3 | odd | 2 | |||
960.3.j.e.319.4 | 8 | 40.29 | even | 2 | |||
960.3.j.e.319.7 | 8 | 8.5 | even | 2 | |||
960.3.j.e.319.8 | 8 | 40.19 | odd | 2 |