Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,3,Mod(34,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.34");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.e (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: | \(2.86104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 72 x^{14} - 292 x^{13} + 1148 x^{12} - 2304 x^{11} + 4996 x^{10} - 4490 x^{9} + \cdots + 1849 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 34.8 | ||
Root | \(-0.366025 + 0.257094i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.34 |
Dual form | 105.3.e.a.34.10 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 0.702393i | − | 0.351196i | −0.984462 | − | 0.175598i | \(-0.943814\pi\) | ||
0.984462 | − | 0.175598i | \(-0.0561860\pi\) | |||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | 3.50664 | 0.876661 | ||||||||
\(5\) | 0.979490 | − | 4.90312i | 0.195898 | − | 0.980624i | ||||
\(6\) | − | 1.21658i | − | 0.202763i | ||||||
\(7\) | −3.48021 | + | 6.07356i | −0.497172 | + | 0.867652i | ||||
\(8\) | − | 5.27261i | − | 0.659077i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | −3.44392 | − | 0.687987i | −0.344392 | − | 0.0687987i | ||||
\(11\) | 5.39422 | 0.490384 | 0.245192 | − | 0.969475i | \(-0.421149\pi\) | ||||
0.245192 | + | 0.969475i | \(0.421149\pi\) | |||||||
\(12\) | 6.07369 | 0.506141 | ||||||||
\(13\) | −12.5287 | −0.963743 | −0.481871 | − | 0.876242i | \(-0.660043\pi\) | ||||
−0.481871 | + | 0.876242i | \(0.660043\pi\) | |||||||
\(14\) | 4.26603 | + | 2.44447i | 0.304716 | + | 0.174605i | ||||
\(15\) | 1.69653 | − | 8.49246i | 0.113102 | − | 0.566164i | ||||
\(16\) | 10.3231 | 0.645196 | ||||||||
\(17\) | 8.14665 | 0.479215 | 0.239607 | − | 0.970870i | \(-0.422981\pi\) | ||||
0.239607 | + | 0.970870i | \(0.422981\pi\) | |||||||
\(18\) | − | 2.10718i | − | 0.117065i | ||||||
\(19\) | − | 1.94137i | − | 0.102177i | −0.998694 | − | 0.0510886i | \(-0.983731\pi\) | ||
0.998694 | − | 0.0510886i | \(-0.0162691\pi\) | |||||||
\(20\) | 3.43472 | − | 17.1935i | 0.171736 | − | 0.859675i | ||||
\(21\) | −6.02789 | + | 10.5197i | −0.287043 | + | 0.500939i | ||||
\(22\) | − | 3.78886i | − | 0.172221i | ||||||
\(23\) | 11.4362i | 0.497227i | 0.968603 | + | 0.248613i | \(0.0799749\pi\) | ||||
−0.968603 | + | 0.248613i | \(0.920025\pi\) | |||||||
\(24\) | − | 9.13243i | − | 0.380518i | ||||||
\(25\) | −23.0812 | − | 9.60512i | −0.923248 | − | 0.384205i | ||||
\(26\) | 8.80004i | 0.338463i | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −12.2038 | + | 21.2978i | −0.435852 | + | 0.760637i | ||||
\(29\) | −44.2627 | −1.52630 | −0.763150 | − | 0.646221i | \(-0.776348\pi\) | ||||
−0.763150 | + | 0.646221i | \(0.776348\pi\) | |||||||
\(30\) | −5.96504 | − | 1.19163i | −0.198835 | − | 0.0397209i | ||||
\(31\) | 50.4355i | 1.62695i | 0.581598 | + | 0.813476i | \(0.302428\pi\) | ||||
−0.581598 | + | 0.813476i | \(0.697572\pi\) | |||||||
\(32\) | − | 28.3413i | − | 0.885667i | ||||||
\(33\) | 9.34307 | 0.283123 | ||||||||
\(34\) | − | 5.72215i | − | 0.168298i | ||||||
\(35\) | 26.3706 | + | 23.0129i | 0.753445 | + | 0.657511i | ||||
\(36\) | 10.5199 | 0.292220 | ||||||||
\(37\) | 41.7759i | 1.12908i | 0.825406 | + | 0.564540i | \(0.190946\pi\) | ||||
−0.825406 | + | 0.564540i | \(0.809054\pi\) | |||||||
\(38\) | −1.36360 | −0.0358843 | ||||||||
\(39\) | −21.7003 | −0.556417 | ||||||||
\(40\) | −25.8523 | − | 5.16447i | −0.646307 | − | 0.129112i | ||||
\(41\) | 36.0308i | 0.878800i | 0.898292 | + | 0.439400i | \(0.144809\pi\) | ||||
−0.898292 | + | 0.439400i | \(0.855191\pi\) | |||||||
\(42\) | 7.38897 | + | 4.23395i | 0.175928 | + | 0.100808i | ||||
\(43\) | 1.13722i | 0.0264470i | 0.999913 | + | 0.0132235i | \(0.00420929\pi\) | ||||
−0.999913 | + | 0.0132235i | \(0.995791\pi\) | |||||||
\(44\) | 18.9156 | 0.429900 | ||||||||
\(45\) | 2.93847 | − | 14.7094i | 0.0652994 | − | 0.326875i | ||||
\(46\) | 8.03272 | 0.174624 | ||||||||
\(47\) | −24.3975 | −0.519096 | −0.259548 | − | 0.965730i | \(-0.583574\pi\) | ||||
−0.259548 | + | 0.965730i | \(0.583574\pi\) | |||||||
\(48\) | 17.8802 | 0.372504 | ||||||||
\(49\) | −24.7763 | − | 42.2745i | −0.505639 | − | 0.862745i | ||||
\(50\) | −6.74657 | + | 16.2121i | −0.134931 | + | 0.324241i | ||||
\(51\) | 14.1104 | 0.276675 | ||||||||
\(52\) | −43.9335 | −0.844876 | ||||||||
\(53\) | − | 88.3754i | − | 1.66746i | −0.552172 | − | 0.833730i | \(-0.686201\pi\) | ||
0.552172 | − | 0.833730i | \(-0.313799\pi\) | |||||||
\(54\) | − | 3.64974i | − | 0.0675878i | ||||||
\(55\) | 5.28359 | − | 26.4485i | 0.0960652 | − | 0.480882i | ||||
\(56\) | 32.0235 | + | 18.3498i | 0.571849 | + | 0.327675i | ||||
\(57\) | − | 3.36255i | − | 0.0589921i | ||||||
\(58\) | 31.0898i | 0.536031i | ||||||||
\(59\) | − | 46.9226i | − | 0.795298i | −0.917538 | − | 0.397649i | \(-0.869826\pi\) | ||
0.917538 | − | 0.397649i | \(-0.130174\pi\) | |||||||
\(60\) | 5.94912 | − | 29.7800i | 0.0991519 | − | 0.496334i | ||||
\(61\) | 47.5558i | 0.779604i | 0.920899 | + | 0.389802i | \(0.127457\pi\) | ||||
−0.920899 | + | 0.389802i | \(0.872543\pi\) | |||||||
\(62\) | 35.4256 | 0.571380 | ||||||||
\(63\) | −10.4406 | + | 18.2207i | −0.165724 | + | 0.289217i | ||||
\(64\) | 21.3858 | 0.334153 | ||||||||
\(65\) | −12.2717 | + | 61.4295i | −0.188795 | + | 0.945069i | ||||
\(66\) | − | 6.56250i | − | 0.0994319i | ||||||
\(67\) | − | 104.927i | − | 1.56607i | −0.621976 | − | 0.783037i | \(-0.713670\pi\) | ||
0.621976 | − | 0.783037i | \(-0.286330\pi\) | |||||||
\(68\) | 28.5674 | 0.420109 | ||||||||
\(69\) | 19.8081i | 0.287074i | ||||||||
\(70\) | 16.1641 | − | 18.5225i | 0.230915 | − | 0.264607i | ||||
\(71\) | 52.7310 | 0.742690 | 0.371345 | − | 0.928495i | \(-0.378897\pi\) | ||||
0.371345 | + | 0.928495i | \(0.378897\pi\) | |||||||
\(72\) | − | 15.8178i | − | 0.219692i | ||||||
\(73\) | 74.2238 | 1.01676 | 0.508382 | − | 0.861131i | \(-0.330244\pi\) | ||||
0.508382 | + | 0.861131i | \(0.330244\pi\) | |||||||
\(74\) | 29.3431 | 0.396529 | ||||||||
\(75\) | −39.9778 | − | 16.6366i | −0.533037 | − | 0.221821i | ||||
\(76\) | − | 6.80769i | − | 0.0895748i | ||||||
\(77\) | −18.7730 | + | 32.7621i | −0.243805 | + | 0.425482i | ||||
\(78\) | 15.2421i | 0.195412i | ||||||||
\(79\) | 76.3265 | 0.966158 | 0.483079 | − | 0.875577i | \(-0.339518\pi\) | ||||
0.483079 | + | 0.875577i | \(0.339518\pi\) | |||||||
\(80\) | 10.1114 | − | 50.6156i | 0.126393 | − | 0.632695i | ||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 25.3078 | 0.308631 | ||||||||
\(83\) | −140.936 | −1.69802 | −0.849010 | − | 0.528377i | \(-0.822801\pi\) | ||||
−0.849010 | + | 0.528377i | \(0.822801\pi\) | |||||||
\(84\) | −21.1377 | + | 36.8889i | −0.251639 | + | 0.439154i | ||||
\(85\) | 7.97956 | − | 39.9440i | 0.0938772 | − | 0.469929i | ||||
\(86\) | 0.798775 | 0.00928809 | ||||||||
\(87\) | −76.6652 | −0.881210 | ||||||||
\(88\) | − | 28.4416i | − | 0.323201i | ||||||
\(89\) | − | 33.4260i | − | 0.375574i | −0.982210 | − | 0.187787i | \(-0.939869\pi\) | ||
0.982210 | − | 0.187787i | \(-0.0601314\pi\) | |||||||
\(90\) | −10.3318 | − | 2.06396i | −0.114797 | − | 0.0229329i | ||||
\(91\) | 43.6023 | − | 76.0936i | 0.479146 | − | 0.836193i | ||||
\(92\) | 40.1028i | 0.435900i | ||||||||
\(93\) | 87.3569i | 0.939322i | ||||||||
\(94\) | 17.1366i | 0.182305i | ||||||||
\(95\) | −9.51876 | − | 1.90155i | −0.100198 | − | 0.0200163i | ||||
\(96\) | − | 49.0886i | − | 0.511340i | ||||||
\(97\) | 120.963 | 1.24704 | 0.623520 | − | 0.781807i | \(-0.285702\pi\) | ||||
0.623520 | + | 0.781807i | \(0.285702\pi\) | |||||||
\(98\) | −29.6933 | + | 17.4027i | −0.302993 | + | 0.177579i | ||||
\(99\) | 16.1827 | 0.163461 | ||||||||
\(100\) | −80.9376 | − | 33.6817i | −0.809376 | − | 0.336817i | ||||
\(101\) | 47.0704i | 0.466044i | 0.972472 | + | 0.233022i | \(0.0748613\pi\) | ||||
−0.972472 | + | 0.233022i | \(0.925139\pi\) | |||||||
\(102\) | − | 9.91105i | − | 0.0971672i | ||||||
\(103\) | 146.806 | 1.42530 | 0.712648 | − | 0.701522i | \(-0.247496\pi\) | ||||
0.712648 | + | 0.701522i | \(0.247496\pi\) | |||||||
\(104\) | 66.0587i | 0.635180i | ||||||||
\(105\) | 45.6752 | + | 39.8595i | 0.435002 | + | 0.379614i | ||||
\(106\) | −62.0742 | −0.585606 | ||||||||
\(107\) | 111.640i | 1.04337i | 0.853139 | + | 0.521684i | \(0.174696\pi\) | ||||
−0.853139 | + | 0.521684i | \(0.825304\pi\) | |||||||
\(108\) | 18.2211 | 0.168714 | ||||||||
\(109\) | −75.0358 | −0.688402 | −0.344201 | − | 0.938896i | \(-0.611850\pi\) | ||||
−0.344201 | + | 0.938896i | \(0.611850\pi\) | |||||||
\(110\) | −18.5773 | − | 3.71115i | −0.168884 | − | 0.0337378i | ||||
\(111\) | 72.3580i | 0.651874i | ||||||||
\(112\) | −35.9266 | + | 62.6982i | −0.320774 | + | 0.559805i | ||||
\(113\) | − | 168.123i | − | 1.48781i | −0.668285 | − | 0.743905i | \(-0.732972\pi\) | ||
0.668285 | − | 0.743905i | \(-0.267028\pi\) | |||||||
\(114\) | −2.36183 | −0.0207178 | ||||||||
\(115\) | 56.0732 | + | 11.2017i | 0.487593 | + | 0.0974058i | ||||
\(116\) | −155.214 | −1.33805 | ||||||||
\(117\) | −37.5860 | −0.321248 | ||||||||
\(118\) | −32.9581 | −0.279306 | ||||||||
\(119\) | −28.3520 | + | 49.4792i | −0.238252 | + | 0.415791i | ||||
\(120\) | −44.7774 | − | 8.94513i | −0.373145 | − | 0.0745427i | ||||
\(121\) | −91.9024 | −0.759524 | ||||||||
\(122\) | 33.4029 | 0.273794 | ||||||||
\(123\) | 62.4072i | 0.507375i | ||||||||
\(124\) | 176.860i | 1.42629i | ||||||||
\(125\) | −69.7029 | + | 103.762i | −0.557623 | + | 0.830094i | ||||
\(126\) | 12.7981 | + | 7.33342i | 0.101572 | + | 0.0582017i | ||||
\(127\) | − | 109.069i | − | 0.858812i | −0.903111 | − | 0.429406i | \(-0.858723\pi\) | ||
0.903111 | − | 0.429406i | \(-0.141277\pi\) | |||||||
\(128\) | − | 128.387i | − | 1.00302i | ||||||
\(129\) | 1.96972i | 0.0152692i | ||||||||
\(130\) | 43.1476 | + | 8.61955i | 0.331905 | + | 0.0663042i | ||||
\(131\) | − | 185.046i | − | 1.41257i | −0.707929 | − | 0.706284i | \(-0.750370\pi\) | ||
0.707929 | − | 0.706284i | \(-0.249630\pi\) | |||||||
\(132\) | 32.7628 | 0.248203 | ||||||||
\(133\) | 11.7910 | + | 6.75636i | 0.0886543 | + | 0.0507997i | ||||
\(134\) | −73.6999 | −0.549999 | ||||||||
\(135\) | 5.08958 | − | 25.4774i | 0.0377006 | − | 0.188721i | ||||
\(136\) | − | 42.9541i | − | 0.315839i | ||||||
\(137\) | 161.715i | 1.18040i | 0.807257 | + | 0.590200i | \(0.200951\pi\) | ||||
−0.807257 | + | 0.590200i | \(0.799049\pi\) | |||||||
\(138\) | 13.9131 | 0.100819 | ||||||||
\(139\) | − | 233.420i | − | 1.67928i | −0.543143 | − | 0.839640i | \(-0.682766\pi\) | ||
0.543143 | − | 0.839640i | \(-0.317234\pi\) | |||||||
\(140\) | 92.4723 | + | 80.6980i | 0.660516 | + | 0.576414i | ||||
\(141\) | −42.2577 | −0.299700 | ||||||||
\(142\) | − | 37.0379i | − | 0.260830i | ||||||
\(143\) | −67.5823 | −0.472604 | ||||||||
\(144\) | 30.9694 | 0.215065 | ||||||||
\(145\) | −43.3549 | + | 217.025i | −0.298999 | + | 1.49673i | ||||
\(146\) | − | 52.1343i | − | 0.357084i | ||||||
\(147\) | −42.9139 | − | 73.2216i | −0.291931 | − | 0.498106i | ||||
\(148\) | 146.493i | 0.989820i | ||||||||
\(149\) | −18.6015 | −0.124842 | −0.0624210 | − | 0.998050i | \(-0.519882\pi\) | ||||
−0.0624210 | + | 0.998050i | \(0.519882\pi\) | |||||||
\(150\) | −11.6854 | + | 28.0801i | −0.0779026 | + | 0.187201i | ||||
\(151\) | 82.0432 | 0.543333 | 0.271666 | − | 0.962392i | \(-0.412425\pi\) | ||||
0.271666 | + | 0.962392i | \(0.412425\pi\) | |||||||
\(152\) | −10.2361 | −0.0673427 | ||||||||
\(153\) | 24.4399 | 0.159738 | ||||||||
\(154\) | 23.0119 | + | 13.1860i | 0.149428 | + | 0.0856235i | ||||
\(155\) | 247.292 | + | 49.4011i | 1.59543 | + | 0.318717i | ||||
\(156\) | −76.0951 | −0.487789 | ||||||||
\(157\) | −134.069 | −0.853940 | −0.426970 | − | 0.904266i | \(-0.640419\pi\) | ||||
−0.426970 | + | 0.904266i | \(0.640419\pi\) | |||||||
\(158\) | − | 53.6112i | − | 0.339311i | ||||||
\(159\) | − | 153.071i | − | 0.962709i | ||||||
\(160\) | −138.961 | − | 27.7601i | −0.868507 | − | 0.173500i | ||||
\(161\) | −69.4586 | − | 39.8004i | −0.431420 | − | 0.247207i | ||||
\(162\) | − | 6.32154i | − | 0.0390218i | ||||||
\(163\) | 10.1526i | 0.0622859i | 0.999515 | + | 0.0311429i | \(0.00991471\pi\) | ||||
−0.999515 | + | 0.0311429i | \(0.990085\pi\) | |||||||
\(164\) | 126.347i | 0.770410i | ||||||||
\(165\) | 9.15144 | − | 45.8102i | 0.0554633 | − | 0.277638i | ||||
\(166\) | 98.9921i | 0.596338i | ||||||||
\(167\) | 292.034 | 1.74871 | 0.874353 | − | 0.485290i | \(-0.161286\pi\) | ||||
0.874353 | + | 0.485290i | \(0.161286\pi\) | |||||||
\(168\) | 55.4664 | + | 31.7828i | 0.330157 | + | 0.189183i | ||||
\(169\) | −12.0329 | −0.0712003 | ||||||||
\(170\) | −28.0564 | − | 5.60479i | −0.165038 | − | 0.0329693i | ||||
\(171\) | − | 5.82410i | − | 0.0340591i | ||||||
\(172\) | 3.98783i | 0.0231850i | ||||||||
\(173\) | −193.657 | −1.11941 | −0.559704 | − | 0.828693i | \(-0.689085\pi\) | ||||
−0.559704 | + | 0.828693i | \(0.689085\pi\) | |||||||
\(174\) | 53.8491i | 0.309478i | ||||||||
\(175\) | 138.665 | − | 106.757i | 0.792369 | − | 0.610042i | ||||
\(176\) | 55.6853 | 0.316394 | ||||||||
\(177\) | − | 81.2723i | − | 0.459165i | ||||||
\(178\) | −23.4782 | −0.131900 | ||||||||
\(179\) | 203.588 | 1.13736 | 0.568682 | − | 0.822557i | \(-0.307453\pi\) | ||||
0.568682 | + | 0.822557i | \(0.307453\pi\) | |||||||
\(180\) | 10.3042 | − | 51.5805i | 0.0572454 | − | 0.286558i | ||||
\(181\) | − | 292.439i | − | 1.61569i | −0.589396 | − | 0.807844i | \(-0.700634\pi\) | ||
0.589396 | − | 0.807844i | \(-0.299366\pi\) | |||||||
\(182\) | −53.4476 | − | 30.6259i | −0.293668 | − | 0.168274i | ||||
\(183\) | 82.3691i | 0.450105i | ||||||||
\(184\) | 60.2988 | 0.327711 | ||||||||
\(185\) | 204.832 | + | 40.9191i | 1.10720 | + | 0.221184i | ||||
\(186\) | 61.3589 | 0.329886 | ||||||||
\(187\) | 43.9448 | 0.234999 | ||||||||
\(188\) | −85.5534 | −0.455071 | ||||||||
\(189\) | −18.0837 | + | 31.5592i | −0.0956809 | + | 0.166980i | ||||
\(190\) | −1.33564 | + | 6.68591i | −0.00702966 | + | 0.0351890i | ||||
\(191\) | 81.7472 | 0.427996 | 0.213998 | − | 0.976834i | \(-0.431351\pi\) | ||||
0.213998 | + | 0.976834i | \(0.431351\pi\) | |||||||
\(192\) | 37.0412 | 0.192923 | ||||||||
\(193\) | 270.371i | 1.40089i | 0.713709 | + | 0.700443i | \(0.247014\pi\) | ||||
−0.713709 | + | 0.700443i | \(0.752986\pi\) | |||||||
\(194\) | − | 84.9635i | − | 0.437956i | ||||||
\(195\) | −21.2552 | + | 106.399i | −0.109001 | + | 0.545636i | ||||
\(196\) | −86.8818 | − | 148.242i | −0.443274 | − | 0.756335i | ||||
\(197\) | 40.8502i | 0.207361i | 0.994611 | + | 0.103681i | \(0.0330620\pi\) | ||||
−0.994611 | + | 0.103681i | \(0.966938\pi\) | |||||||
\(198\) | − | 11.3666i | − | 0.0574070i | ||||||
\(199\) | 12.5172i | 0.0629007i | 0.999505 | + | 0.0314503i | \(0.0100126\pi\) | ||||
−0.999505 | + | 0.0314503i | \(0.989987\pi\) | |||||||
\(200\) | −50.6441 | + | 121.698i | −0.253220 | + | 0.608491i | ||||
\(201\) | − | 181.739i | − | 0.904173i | ||||||
\(202\) | 33.0619 | 0.163673 | ||||||||
\(203\) | 154.043 | − | 268.832i | 0.758834 | − | 1.32430i | ||||
\(204\) | 49.4802 | 0.242550 | ||||||||
\(205\) | 176.663 | + | 35.2918i | 0.861772 | + | 0.172155i | ||||
\(206\) | − | 103.115i | − | 0.500559i | ||||||
\(207\) | 34.3087i | 0.165742i | ||||||||
\(208\) | −129.335 | −0.621803 | ||||||||
\(209\) | − | 10.4722i | − | 0.0501061i | ||||||
\(210\) | 27.9970 | − | 32.0819i | 0.133319 | − | 0.152771i | ||||
\(211\) | 22.0149 | 0.104336 | 0.0521681 | − | 0.998638i | \(-0.483387\pi\) | ||||
0.0521681 | + | 0.998638i | \(0.483387\pi\) | |||||||
\(212\) | − | 309.901i | − | 1.46180i | ||||||
\(213\) | 91.3327 | 0.428792 | ||||||||
\(214\) | 78.4154 | 0.366427 | ||||||||
\(215\) | 5.57593 | + | 1.11390i | 0.0259346 | + | 0.00518091i | ||||
\(216\) | − | 27.3973i | − | 0.126839i | ||||||
\(217\) | −306.323 | − | 175.526i | −1.41163 | − | 0.808876i | ||||
\(218\) | 52.7046i | 0.241764i | ||||||||
\(219\) | 128.559 | 0.587029 | ||||||||
\(220\) | 18.5277 | − | 92.7456i | 0.0842167 | − | 0.421571i | ||||
\(221\) | −102.067 | −0.461840 | ||||||||
\(222\) | 50.8238 | 0.228936 | ||||||||
\(223\) | −109.535 | −0.491190 | −0.245595 | − | 0.969373i | \(-0.578983\pi\) | ||||
−0.245595 | + | 0.969373i | \(0.578983\pi\) | |||||||
\(224\) | 172.133 | + | 98.6337i | 0.768451 | + | 0.440329i | ||||
\(225\) | −69.2436 | − | 28.8154i | −0.307749 | − | 0.128068i | ||||
\(226\) | −118.088 | −0.522513 | ||||||||
\(227\) | −369.492 | −1.62772 | −0.813859 | − | 0.581062i | \(-0.802637\pi\) | ||||
−0.813859 | + | 0.581062i | \(0.802637\pi\) | |||||||
\(228\) | − | 11.7913i | − | 0.0517161i | ||||||
\(229\) | 362.391i | 1.58249i | 0.611498 | + | 0.791246i | \(0.290567\pi\) | ||||
−0.611498 | + | 0.791246i | \(0.709433\pi\) | |||||||
\(230\) | 7.86797 | − | 39.3854i | 0.0342086 | − | 0.171241i | ||||
\(231\) | −32.5158 | + | 56.7457i | −0.140761 | + | 0.245652i | ||||
\(232\) | 233.380i | 1.00595i | ||||||||
\(233\) | − | 28.1243i | − | 0.120705i | −0.998177 | − | 0.0603525i | \(-0.980778\pi\) | ||
0.998177 | − | 0.0603525i | \(-0.0192225\pi\) | |||||||
\(234\) | 26.4001i | 0.112821i | ||||||||
\(235\) | −23.8971 | + | 119.624i | −0.101690 | + | 0.509038i | ||||
\(236\) | − | 164.541i | − | 0.697207i | ||||||
\(237\) | 132.201 | 0.557812 | ||||||||
\(238\) | 34.7538 | + | 19.9143i | 0.146024 | + | 0.0836733i | ||||
\(239\) | −223.554 | −0.935372 | −0.467686 | − | 0.883895i | \(-0.654912\pi\) | ||||
−0.467686 | + | 0.883895i | \(0.654912\pi\) | |||||||
\(240\) | 17.5135 | − | 87.6687i | 0.0729728 | − | 0.365286i | ||||
\(241\) | 139.669i | 0.579538i | 0.957097 | + | 0.289769i | \(0.0935785\pi\) | ||||
−0.957097 | + | 0.289769i | \(0.906421\pi\) | |||||||
\(242\) | 64.5516i | 0.266742i | ||||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 166.761i | 0.683448i | ||||||||
\(245\) | −231.545 | + | 80.0739i | −0.945082 | + | 0.326832i | ||||
\(246\) | 43.8343 | 0.178188 | ||||||||
\(247\) | 24.3227i | 0.0984726i | ||||||||
\(248\) | 265.927 | 1.07229 | ||||||||
\(249\) | −244.108 | −0.980352 | ||||||||
\(250\) | 72.8815 | + | 48.9588i | 0.291526 | + | 0.195835i | ||||
\(251\) | 332.508i | 1.32473i | 0.749180 | + | 0.662367i | \(0.230448\pi\) | ||||
−0.749180 | + | 0.662367i | \(0.769552\pi\) | |||||||
\(252\) | −36.6115 | + | 63.8935i | −0.145284 | + | 0.253546i | ||||
\(253\) | 61.6895i | 0.243832i | ||||||||
\(254\) | −76.6094 | −0.301612 | ||||||||
\(255\) | 13.8210 | − | 69.1850i | 0.0542000 | − | 0.271314i | ||||
\(256\) | −4.63472 | −0.0181044 | ||||||||
\(257\) | 427.288 | 1.66260 | 0.831300 | − | 0.555824i | \(-0.187597\pi\) | ||||
0.831300 | + | 0.555824i | \(0.187597\pi\) | |||||||
\(258\) | 1.38352 | 0.00536248 | ||||||||
\(259\) | −253.729 | − | 145.389i | −0.979648 | − | 0.561347i | ||||
\(260\) | −43.0325 | + | 215.411i | −0.165509 | + | 0.828506i | ||||
\(261\) | −132.788 | −0.508767 | ||||||||
\(262\) | −129.975 | −0.496089 | ||||||||
\(263\) | 175.650i | 0.667872i | 0.942596 | + | 0.333936i | \(0.108377\pi\) | ||||
−0.942596 | + | 0.333936i | \(0.891623\pi\) | |||||||
\(264\) | − | 49.2624i | − | 0.186600i | ||||||
\(265\) | −433.315 | − | 86.5628i | −1.63515 | − | 0.326652i | ||||
\(266\) | 4.74562 | − | 8.28193i | 0.0178407 | − | 0.0311351i | ||||
\(267\) | − | 57.8956i | − | 0.216837i | ||||||
\(268\) | − | 367.941i | − | 1.37292i | ||||||
\(269\) | − | 283.803i | − | 1.05503i | −0.849546 | − | 0.527515i | \(-0.823124\pi\) | ||
0.849546 | − | 0.527515i | \(-0.176876\pi\) | |||||||
\(270\) | −17.8951 | − | 3.57488i | −0.0662782 | − | 0.0132403i | ||||
\(271\) | 230.603i | 0.850934i | 0.904974 | + | 0.425467i | \(0.139890\pi\) | ||||
−0.904974 | + | 0.425467i | \(0.860110\pi\) | |||||||
\(272\) | 84.0989 | 0.309187 | ||||||||
\(273\) | 75.5214 | − | 131.798i | 0.276635 | − | 0.482776i | ||||
\(274\) | 113.587 | 0.414552 | ||||||||
\(275\) | −124.505 | − | 51.8122i | −0.452746 | − | 0.188408i | ||||
\(276\) | 69.4600i | 0.251667i | ||||||||
\(277\) | 365.707i | 1.32024i | 0.751160 | + | 0.660121i | \(0.229495\pi\) | ||||
−0.751160 | + | 0.660121i | \(0.770505\pi\) | |||||||
\(278\) | −163.952 | −0.589757 | ||||||||
\(279\) | 151.307i | 0.542318i | ||||||||
\(280\) | 121.338 | − | 139.042i | 0.433350 | − | 0.496578i | ||||
\(281\) | −308.169 | −1.09669 | −0.548343 | − | 0.836254i | \(-0.684741\pi\) | ||||
−0.548343 | + | 0.836254i | \(0.684741\pi\) | |||||||
\(282\) | 29.6815i | 0.105254i | ||||||||
\(283\) | 27.0678 | 0.0956458 | 0.0478229 | − | 0.998856i | \(-0.484772\pi\) | ||||
0.0478229 | + | 0.998856i | \(0.484772\pi\) | |||||||
\(284\) | 184.909 | 0.651087 | ||||||||
\(285\) | −16.4870 | − | 3.29358i | −0.0578491 | − | 0.0115564i | ||||
\(286\) | 47.4694i | 0.165977i | ||||||||
\(287\) | −218.835 | − | 125.395i | −0.762492 | − | 0.436915i | ||||
\(288\) | − | 85.0240i | − | 0.295222i | ||||||
\(289\) | −222.632 | −0.770353 | ||||||||
\(290\) | 152.437 | + | 30.4522i | 0.525645 | + | 0.105007i | ||||
\(291\) | 209.514 | 0.719979 | ||||||||
\(292\) | 260.277 | 0.891358 | ||||||||
\(293\) | 178.392 | 0.608845 | 0.304423 | − | 0.952537i | \(-0.401536\pi\) | ||||
0.304423 | + | 0.952537i | \(0.401536\pi\) | |||||||
\(294\) | −51.4303 | + | 30.1424i | −0.174933 | + | 0.102525i | ||||
\(295\) | −230.067 | − | 45.9602i | −0.779888 | − | 0.155797i | ||||
\(296\) | 220.268 | 0.744150 | ||||||||
\(297\) | 28.0292 | 0.0943744 | ||||||||
\(298\) | 13.0655i | 0.0438441i | ||||||||
\(299\) | − | 143.280i | − | 0.479199i | ||||||
\(300\) | −140.188 | − | 58.3385i | −0.467293 | − | 0.194462i | ||||
\(301\) | −6.90698 | − | 3.95776i | −0.0229468 | − | 0.0131487i | ||||
\(302\) | − | 57.6266i | − | 0.190816i | ||||||
\(303\) | 81.5283i | 0.269070i | ||||||||
\(304\) | − | 20.0410i | − | 0.0659243i | ||||||
\(305\) | 233.172 | + | 46.5805i | 0.764499 | + | 0.152723i | ||||
\(306\) | − | 17.1664i | − | 0.0560995i | ||||||
\(307\) | 385.291 | 1.25502 | 0.627510 | − | 0.778609i | \(-0.284074\pi\) | ||||
0.627510 | + | 0.778609i | \(0.284074\pi\) | |||||||
\(308\) | −65.8303 | + | 114.885i | −0.213735 | + | 0.373004i | ||||
\(309\) | 254.275 | 0.822895 | ||||||||
\(310\) | 34.6990 | − | 173.696i | 0.111932 | − | 0.560309i | ||||
\(311\) | 118.862i | 0.382192i | 0.981571 | + | 0.191096i | \(0.0612042\pi\) | ||||
−0.981571 | + | 0.191096i | \(0.938796\pi\) | |||||||
\(312\) | 114.417i | 0.366721i | ||||||||
\(313\) | −171.117 | −0.546701 | −0.273350 | − | 0.961915i | \(-0.588132\pi\) | ||||
−0.273350 | + | 0.961915i | \(0.588132\pi\) | |||||||
\(314\) | 94.1688i | 0.299901i | ||||||||
\(315\) | 79.1118 | + | 69.0386i | 0.251148 | + | 0.219170i | ||||
\(316\) | 267.650 | 0.846993 | ||||||||
\(317\) | 149.801i | 0.472557i | 0.971685 | + | 0.236279i | \(0.0759278\pi\) | ||||
−0.971685 | + | 0.236279i | \(0.924072\pi\) | |||||||
\(318\) | −107.516 | −0.338100 | ||||||||
\(319\) | −238.763 | −0.748473 | ||||||||
\(320\) | 20.9472 | − | 104.857i | 0.0654599 | − | 0.327678i | ||||
\(321\) | 193.367i | 0.602389i | ||||||||
\(322\) | −27.9555 | + | 48.7872i | −0.0868184 | + | 0.151513i | ||||
\(323\) | − | 15.8156i | − | 0.0489648i | ||||||
\(324\) | 31.5598 | 0.0974068 | ||||||||
\(325\) | 289.176 | + | 120.339i | 0.889773 | + | 0.370274i | ||||
\(326\) | 7.13111 | 0.0218746 | ||||||||
\(327\) | −129.966 | −0.397449 | ||||||||
\(328\) | 189.976 | 0.579196 | ||||||||
\(329\) | 84.9084 | − | 148.180i | 0.258080 | − | 0.450395i | ||||
\(330\) | −32.1768 | − | 6.42791i | −0.0975053 | − | 0.0194785i | ||||
\(331\) | 278.204 | 0.840497 | 0.420248 | − | 0.907409i | \(-0.361943\pi\) | ||||
0.420248 | + | 0.907409i | \(0.361943\pi\) | |||||||
\(332\) | −494.211 | −1.48859 | ||||||||
\(333\) | 125.328i | 0.376360i | ||||||||
\(334\) | − | 205.123i | − | 0.614139i | ||||||
\(335\) | −514.469 | − | 102.775i | −1.53573 | − | 0.306791i | ||||
\(336\) | −62.2268 | + | 108.596i | −0.185199 | + | 0.323204i | ||||
\(337\) | − | 346.170i | − | 1.02721i | −0.858027 | − | 0.513605i | \(-0.828310\pi\) | ||
0.858027 | − | 0.513605i | \(-0.171690\pi\) | |||||||
\(338\) | 8.45179i | 0.0250053i | ||||||||
\(339\) | − | 291.197i | − | 0.858987i | ||||||
\(340\) | 27.9815 | − | 140.069i | 0.0822985 | − | 0.411969i | ||||
\(341\) | 272.061i | 0.797832i | ||||||||
\(342\) | −4.09081 | −0.0119614 | ||||||||
\(343\) | 342.984 | − | 3.35656i | 0.999952 | − | 0.00978589i | ||||
\(344\) | 5.99612 | 0.0174306 | ||||||||
\(345\) | 97.1216 | + | 19.4019i | 0.281512 | + | 0.0562373i | ||||
\(346\) | 136.024i | 0.393132i | ||||||||
\(347\) | − | 83.7750i | − | 0.241426i | −0.992687 | − | 0.120713i | \(-0.961482\pi\) | ||
0.992687 | − | 0.120713i | \(-0.0385182\pi\) | |||||||
\(348\) | −268.838 | −0.772522 | ||||||||
\(349\) | − | 304.482i | − | 0.872443i | −0.899839 | − | 0.436221i | \(-0.856316\pi\) | ||
0.899839 | − | 0.436221i | \(-0.143684\pi\) | |||||||
\(350\) | −74.9856 | − | 97.3970i | −0.214244 | − | 0.278277i | ||||
\(351\) | −65.1008 | −0.185472 | ||||||||
\(352\) | − | 152.880i | − | 0.434317i | ||||||
\(353\) | −188.542 | −0.534113 | −0.267056 | − | 0.963681i | \(-0.586051\pi\) | ||||
−0.267056 | + | 0.963681i | \(0.586051\pi\) | |||||||
\(354\) | −57.0851 | −0.161257 | ||||||||
\(355\) | 51.6495 | − | 258.546i | 0.145491 | − | 0.728300i | ||||
\(356\) | − | 117.213i | − | 0.329251i | ||||||
\(357\) | −49.1071 | + | 85.7005i | −0.137555 | + | 0.240057i | ||||
\(358\) | − | 142.999i | − | 0.399438i | ||||||
\(359\) | −359.444 | −1.00124 | −0.500619 | − | 0.865668i | \(-0.666894\pi\) | ||||
−0.500619 | + | 0.865668i | \(0.666894\pi\) | |||||||
\(360\) | −77.5568 | − | 15.4934i | −0.215436 | − | 0.0430373i | ||||
\(361\) | 357.231 | 0.989560 | ||||||||
\(362\) | −205.407 | −0.567424 | ||||||||
\(363\) | −159.180 | −0.438511 | ||||||||
\(364\) | 152.898 | − | 266.833i | 0.420049 | − | 0.733058i | ||||
\(365\) | 72.7015 | − | 363.928i | 0.199182 | − | 0.997064i | ||||
\(366\) | 57.8555 | 0.158075 | ||||||||
\(367\) | 30.8366 | 0.0840235 | 0.0420117 | − | 0.999117i | \(-0.486623\pi\) | ||||
0.0420117 | + | 0.999117i | \(0.486623\pi\) | |||||||
\(368\) | 118.058i | 0.320809i | ||||||||
\(369\) | 108.092i | 0.292933i | ||||||||
\(370\) | 28.7413 | − | 143.873i | 0.0776792 | − | 0.388845i | ||||
\(371\) | 536.754 | + | 307.565i | 1.44677 | + | 0.829015i | ||||
\(372\) | 306.330i | 0.823467i | ||||||||
\(373\) | 11.2949i | 0.0302813i | 0.999885 | + | 0.0151406i | \(0.00481960\pi\) | ||||
−0.999885 | + | 0.0151406i | \(0.995180\pi\) | |||||||
\(374\) | − | 30.8665i | − | 0.0825308i | ||||||
\(375\) | −120.729 | + | 179.721i | −0.321944 | + | 0.479255i | ||||
\(376\) | 128.639i | 0.342124i | ||||||||
\(377\) | 554.552 | 1.47096 | ||||||||
\(378\) | 22.1669 | + | 12.7018i | 0.0586427 | + | 0.0336028i | ||||
\(379\) | 292.999 | 0.773084 | 0.386542 | − | 0.922272i | \(-0.373669\pi\) | ||||
0.386542 | + | 0.922272i | \(0.373669\pi\) | |||||||
\(380\) | −33.3789 | − | 6.66806i | −0.0878393 | − | 0.0175475i | ||||
\(381\) | − | 188.913i | − | 0.495836i | ||||||
\(382\) | − | 57.4186i | − | 0.150311i | ||||||
\(383\) | 37.2078 | 0.0971484 | 0.0485742 | − | 0.998820i | \(-0.484532\pi\) | ||||
0.0485742 | + | 0.998820i | \(0.484532\pi\) | |||||||
\(384\) | − | 222.372i | − | 0.579094i | ||||||
\(385\) | 142.249 | + | 124.137i | 0.369477 | + | 0.322433i | ||||
\(386\) | 189.907 | 0.491986 | ||||||||
\(387\) | 3.41166i | 0.00881566i | ||||||||
\(388\) | 424.174 | 1.09323 | ||||||||
\(389\) | 164.681 | 0.423345 | 0.211672 | − | 0.977341i | \(-0.432109\pi\) | ||||
0.211672 | + | 0.977341i | \(0.432109\pi\) | |||||||
\(390\) | 74.7339 | + | 14.9295i | 0.191625 | + | 0.0382808i | ||||
\(391\) | 93.1669i | 0.238278i | ||||||||
\(392\) | −222.897 | + | 130.636i | −0.568615 | + | 0.333255i | ||||
\(393\) | − | 320.510i | − | 0.815546i | ||||||
\(394\) | 28.6929 | 0.0728245 | ||||||||
\(395\) | 74.7610 | − | 374.238i | 0.189268 | − | 0.947438i | ||||
\(396\) | 56.7469 | 0.143300 | ||||||||
\(397\) | −149.521 | −0.376627 | −0.188314 | − | 0.982109i | \(-0.560302\pi\) | ||||
−0.188314 | + | 0.982109i | \(0.560302\pi\) | |||||||
\(398\) | 8.79202 | 0.0220905 | ||||||||
\(399\) | 20.4226 | + | 11.7024i | 0.0511846 | + | 0.0293292i | ||||
\(400\) | −238.270 | − | 99.1549i | −0.595676 | − | 0.247887i | ||||
\(401\) | 439.691 | 1.09649 | 0.548244 | − | 0.836319i | \(-0.315297\pi\) | ||||
0.548244 | + | 0.836319i | \(0.315297\pi\) | |||||||
\(402\) | −127.652 | −0.317542 | ||||||||
\(403\) | − | 631.889i | − | 1.56796i | ||||||
\(404\) | 165.059i | 0.408562i | ||||||||
\(405\) | 8.81541 | − | 44.1281i | 0.0217665 | − | 0.108958i | ||||
\(406\) | −188.826 | − | 108.199i | −0.465088 | − | 0.266500i | ||||
\(407\) | 225.349i | 0.553682i | ||||||||
\(408\) | − | 74.3987i | − | 0.182350i | ||||||
\(409\) | 252.435i | 0.617200i | 0.951192 | + | 0.308600i | \(0.0998605\pi\) | ||||
−0.951192 | + | 0.308600i | \(0.900139\pi\) | |||||||
\(410\) | 24.7887 | − | 124.087i | 0.0604603 | − | 0.302651i | ||||
\(411\) | 280.098i | 0.681505i | ||||||||
\(412\) | 514.795 | 1.24950 | ||||||||
\(413\) | 284.987 | + | 163.300i | 0.690042 | + | 0.395400i | ||||
\(414\) | 24.0982 | 0.0582081 | ||||||||
\(415\) | −138.045 | + | 691.024i | −0.332639 | + | 1.66512i | ||||
\(416\) | 355.079i | 0.853555i | ||||||||
\(417\) | − | 404.295i | − | 0.969533i | ||||||
\(418\) | −7.35558 | −0.0175971 | ||||||||
\(419\) | 107.610i | 0.256826i | 0.991721 | + | 0.128413i | \(0.0409884\pi\) | ||||
−0.991721 | + | 0.128413i | \(0.959012\pi\) | |||||||
\(420\) | 160.167 | + | 139.773i | 0.381349 | + | 0.332793i | ||||
\(421\) | −202.537 | −0.481085 | −0.240543 | − | 0.970639i | \(-0.577325\pi\) | ||||
−0.240543 | + | 0.970639i | \(0.577325\pi\) | |||||||
\(422\) | − | 15.4631i | − | 0.0366425i | ||||||
\(423\) | −73.1925 | −0.173032 | ||||||||
\(424\) | −465.969 | −1.09898 | ||||||||
\(425\) | −188.034 | − | 78.2495i | −0.442434 | − | 0.184117i | ||||
\(426\) | − | 64.1514i | − | 0.150590i | ||||||
\(427\) | −288.833 | − | 165.504i | −0.676425 | − | 0.387598i | ||||
\(428\) | 391.483i | 0.914681i | ||||||||
\(429\) | −117.056 | −0.272858 | ||||||||
\(430\) | 0.782393 | − | 3.91649i | 0.00181952 | − | 0.00910812i | ||||
\(431\) | −797.330 | −1.84995 | −0.924977 | − | 0.380023i | \(-0.875916\pi\) | ||||
−0.924977 | + | 0.380023i | \(0.875916\pi\) | |||||||
\(432\) | 53.6406 | 0.124168 | ||||||||
\(433\) | −707.252 | −1.63338 | −0.816689 | − | 0.577079i | \(-0.804193\pi\) | ||||
−0.816689 | + | 0.577079i | \(0.804193\pi\) | |||||||
\(434\) | −123.288 | + | 215.159i | −0.284074 | + | 0.495759i | ||||
\(435\) | −75.0929 | + | 375.899i | −0.172627 | + | 0.864136i | ||||
\(436\) | −263.124 | −0.603495 | ||||||||
\(437\) | 22.2019 | 0.0508053 | ||||||||
\(438\) | − | 90.2992i | − | 0.206163i | ||||||
\(439\) | − | 260.969i | − | 0.594463i | −0.954806 | − | 0.297231i | \(-0.903937\pi\) | ||
0.954806 | − | 0.297231i | \(-0.0960632\pi\) | |||||||
\(440\) | −139.453 | − | 27.8583i | −0.316938 | − | 0.0633144i | ||||
\(441\) | −74.3290 | − | 126.824i | −0.168546 | − | 0.287582i | ||||
\(442\) | 71.6908i | 0.162196i | ||||||||
\(443\) | 690.031i | 1.55763i | 0.627253 | + | 0.778816i | \(0.284179\pi\) | ||||
−0.627253 | + | 0.778816i | \(0.715821\pi\) | |||||||
\(444\) | 253.734i | 0.571473i | ||||||||
\(445\) | −163.892 | − | 32.7405i | −0.368297 | − | 0.0735741i | ||||
\(446\) | 76.9368i | 0.172504i | ||||||||
\(447\) | −32.2187 | −0.0720776 | ||||||||
\(448\) | −74.4269 | + | 129.888i | −0.166131 | + | 0.289928i | ||||
\(449\) | 118.832 | 0.264659 | 0.132329 | − | 0.991206i | \(-0.457754\pi\) | ||||
0.132329 | + | 0.991206i | \(0.457754\pi\) | |||||||
\(450\) | −20.2397 | + | 48.6362i | −0.0449771 | + | 0.108080i | ||||
\(451\) | 194.358i | 0.430949i | ||||||||
\(452\) | − | 589.546i | − | 1.30430i | ||||||
\(453\) | 142.103 | 0.313693 | ||||||||
\(454\) | 259.529i | 0.571649i | ||||||||
\(455\) | −330.388 | − | 288.320i | −0.726127 | − | 0.633671i | ||||
\(456\) | −17.7294 | −0.0388803 | ||||||||
\(457\) | 363.943i | 0.796375i | 0.917304 | + | 0.398187i | \(0.130361\pi\) | ||||
−0.917304 | + | 0.398187i | \(0.869639\pi\) | |||||||
\(458\) | 254.541 | 0.555766 | ||||||||
\(459\) | 42.3312 | 0.0922249 | ||||||||
\(460\) | 196.629 | + | 39.2803i | 0.427454 | + | 0.0853919i | ||||
\(461\) | − | 376.970i | − | 0.817722i | −0.912597 | − | 0.408861i | \(-0.865926\pi\) | ||
0.912597 | − | 0.408861i | \(-0.134074\pi\) | |||||||
\(462\) | 39.8578 | + | 22.8389i | 0.0862722 | + | 0.0494348i | ||||
\(463\) | 206.801i | 0.446654i | 0.974744 | + | 0.223327i | \(0.0716918\pi\) | ||||
−0.974744 | + | 0.223327i | \(0.928308\pi\) | |||||||
\(464\) | −456.930 | −0.984762 | ||||||||
\(465\) | 428.322 | + | 85.5653i | 0.921122 | + | 0.184011i | ||||
\(466\) | −19.7543 | −0.0423912 | ||||||||
\(467\) | 108.098 | 0.231473 | 0.115736 | − | 0.993280i | \(-0.463077\pi\) | ||||
0.115736 | + | 0.993280i | \(0.463077\pi\) | |||||||
\(468\) | −131.801 | −0.281625 | ||||||||
\(469\) | 637.280 | + | 365.167i | 1.35881 | + | 0.778608i | ||||
\(470\) | 84.0230 | + | 16.7852i | 0.178772 | + | 0.0357131i | ||||
\(471\) | −232.214 | −0.493022 | ||||||||
\(472\) | −247.405 | −0.524162 | ||||||||
\(473\) | 6.13442i | 0.0129692i | ||||||||
\(474\) | − | 92.8573i | − | 0.195901i | ||||||
\(475\) | −18.6471 | + | 44.8091i | −0.0392570 | + | 0.0943350i | ||||
\(476\) | −99.4204 | + | 173.506i | −0.208866 | + | 0.364508i | ||||
\(477\) | − | 265.126i | − | 0.555820i | ||||||
\(478\) | 157.023i | 0.328499i | ||||||||
\(479\) | 438.982i | 0.916456i | 0.888835 | + | 0.458228i | \(0.151516\pi\) | ||||
−0.888835 | + | 0.458228i | \(0.848484\pi\) | |||||||
\(480\) | −240.688 | − | 48.0819i | −0.501433 | − | 0.100171i | ||||
\(481\) | − | 523.396i | − | 1.08814i | ||||||
\(482\) | 98.1023 | 0.203532 | ||||||||
\(483\) | −120.306 | − | 68.9363i | −0.249080 | − | 0.142725i | ||||
\(484\) | −322.269 | −0.665845 | ||||||||
\(485\) | 118.482 | − | 593.096i | 0.244293 | − | 1.22288i | ||||
\(486\) | − | 10.9492i | − | 0.0225293i | ||||||
\(487\) | − | 439.990i | − | 0.903471i | −0.892152 | − | 0.451735i | \(-0.850805\pi\) | ||
0.892152 | − | 0.451735i | \(-0.149195\pi\) | |||||||
\(488\) | 250.744 | 0.513819 | ||||||||
\(489\) | 17.5848i | 0.0359608i | ||||||||
\(490\) | 56.2433 | + | 162.636i | 0.114782 | + | 0.331910i | ||||
\(491\) | 111.892 | 0.227886 | 0.113943 | − | 0.993487i | \(-0.463652\pi\) | ||||
0.113943 | + | 0.993487i | \(0.463652\pi\) | |||||||
\(492\) | 218.840i | 0.444796i | ||||||||
\(493\) | −360.593 | −0.731425 | ||||||||
\(494\) | 17.0841 | 0.0345832 | ||||||||
\(495\) | 15.8508 | − | 79.3456i | 0.0320217 | − | 0.160294i | ||||
\(496\) | 520.653i | 1.04970i | ||||||||
\(497\) | −183.515 | + | 320.265i | −0.369245 | + | 0.644396i | ||||
\(498\) | 171.459i | 0.344296i | ||||||||
\(499\) | 78.8110 | 0.157938 | 0.0789689 | − | 0.996877i | \(-0.474837\pi\) | ||||
0.0789689 | + | 0.996877i | \(0.474837\pi\) | |||||||
\(500\) | −244.423 | + | 363.856i | −0.488846 | + | 0.727711i | ||||
\(501\) | 505.818 | 1.00962 | ||||||||
\(502\) | 233.551 | 0.465241 | ||||||||
\(503\) | −37.3888 | −0.0743316 | −0.0371658 | − | 0.999309i | \(-0.511833\pi\) | ||||
−0.0371658 | + | 0.999309i | \(0.511833\pi\) | |||||||
\(504\) | 96.0706 | + | 55.0493i | 0.190616 | + | 0.109225i | ||||
\(505\) | 230.792 | + | 46.1050i | 0.457014 | + | 0.0912970i | ||||
\(506\) | 43.3303 | 0.0856329 | ||||||||
\(507\) | −20.8415 | −0.0411075 | ||||||||
\(508\) | − | 382.467i | − | 0.752887i | ||||||
\(509\) | 114.044i | 0.224055i | 0.993705 | + | 0.112027i | \(0.0357345\pi\) | ||||
−0.993705 | + | 0.112027i | \(0.964266\pi\) | |||||||
\(510\) | −48.5951 | − | 9.70778i | −0.0952845 | − | 0.0190349i | ||||
\(511\) | −258.314 | + | 450.803i | −0.505507 | + | 0.882198i | ||||
\(512\) | − | 510.291i | − | 0.996662i | ||||||
\(513\) | − | 10.0876i | − | 0.0196640i | ||||||
\(514\) | − | 300.124i | − | 0.583899i | ||||||
\(515\) | 143.795 | − | 719.805i | 0.279213 | − | 1.39768i | ||||
\(516\) | 6.90712i | 0.0133859i | ||||||||
\(517\) | −131.606 | −0.254556 | ||||||||
\(518\) | −102.120 | + | 178.217i | −0.197143 | + | 0.344049i | ||||
\(519\) | −335.425 | −0.646290 | ||||||||
\(520\) | 323.894 | + | 64.7039i | 0.622873 | + | 0.124431i | ||||
\(521\) | − | 921.332i | − | 1.76839i | −0.467116 | − | 0.884196i | \(-0.654707\pi\) | ||
0.467116 | − | 0.884196i | \(-0.345293\pi\) | |||||||
\(522\) | 93.2694i | 0.178677i | ||||||||
\(523\) | 21.3685 | 0.0408575 | 0.0204287 | − | 0.999791i | \(-0.493497\pi\) | ||||
0.0204287 | + | 0.999791i | \(0.493497\pi\) | |||||||
\(524\) | − | 648.892i | − | 1.23834i | ||||||
\(525\) | 240.174 | − | 184.909i | 0.457475 | − | 0.352208i | ||||
\(526\) | 123.376 | 0.234554 | ||||||||
\(527\) | 410.881i | 0.779660i | ||||||||
\(528\) | 96.4497 | 0.182670 | ||||||||
\(529\) | 398.213 | 0.752765 | ||||||||
\(530\) | −60.8011 | + | 304.358i | −0.114719 | + | 0.574260i | ||||
\(531\) | − | 140.768i | − | 0.265099i | ||||||
\(532\) | 41.3469 | + | 23.6922i | 0.0777198 | + | 0.0445341i | ||||
\(533\) | − | 451.417i | − | 0.846937i | ||||||
\(534\) | −40.6655 | −0.0761525 | ||||||||
\(535\) | 547.387 | + | 109.351i | 1.02315 | + | 0.204394i | ||||
\(536\) | −553.239 | −1.03216 | ||||||||
\(537\) | 352.625 | 0.656658 | ||||||||
\(538\) | −199.341 | −0.370523 | ||||||||
\(539\) | −133.649 | − | 228.038i | −0.247957 | − | 0.423076i | ||||
\(540\) | 17.8473 | − | 89.3401i | 0.0330506 | − | 0.165445i | ||||
\(541\) | −352.307 | −0.651215 | −0.325607 | − | 0.945505i | \(-0.605569\pi\) | ||||
−0.325607 | + | 0.945505i | \(0.605569\pi\) | |||||||
\(542\) | 161.974 | 0.298845 | ||||||||
\(543\) | − | 506.520i | − | 0.932818i | ||||||
\(544\) | − | 230.887i | − | 0.424425i | ||||||
\(545\) | −73.4969 | + | 367.910i | −0.134857 | + | 0.675064i | ||||
\(546\) | −92.5739 | − | 53.0457i | −0.169549 | − | 0.0971533i | ||||
\(547\) | 424.917i | 0.776814i | 0.921488 | + | 0.388407i | \(0.126974\pi\) | ||||
−0.921488 | + | 0.388407i | \(0.873026\pi\) | |||||||
\(548\) | 567.077i | 1.03481i | ||||||||
\(549\) | 142.668i | 0.259868i | ||||||||
\(550\) | −36.3925 | + | 87.4515i | −0.0661681 | + | 0.159003i | ||||
\(551\) | 85.9302i | 0.155953i | ||||||||
\(552\) | 104.441 | 0.189204 | ||||||||
\(553\) | −265.632 | + | 463.574i | −0.480347 | + | 0.838289i | ||||
\(554\) | 256.870 | 0.463664 | ||||||||
\(555\) | 354.780 | + | 70.8740i | 0.639244 | + | 0.127701i | ||||
\(556\) | − | 818.521i | − | 1.47216i | ||||||
\(557\) | − | 130.707i | − | 0.234662i | −0.993093 | − | 0.117331i | \(-0.962566\pi\) | ||
0.993093 | − | 0.117331i | \(-0.0374338\pi\) | |||||||
\(558\) | 106.277 | 0.190460 | ||||||||
\(559\) | − | 14.2478i | − | 0.0254881i | ||||||
\(560\) | 272.227 | + | 237.565i | 0.486120 | + | 0.424223i | ||||
\(561\) | 76.1147 | 0.135677 | ||||||||
\(562\) | 216.455i | 0.385152i | ||||||||
\(563\) | −30.8033 | −0.0547129 | −0.0273564 | − | 0.999626i | \(-0.508709\pi\) | ||||
−0.0273564 | + | 0.999626i | \(0.508709\pi\) | |||||||
\(564\) | −148.183 | −0.262735 | ||||||||
\(565\) | −824.325 | − | 164.674i | −1.45898 | − | 0.291459i | ||||
\(566\) | − | 19.0122i | − | 0.0335905i | ||||||
\(567\) | −31.3219 | + | 54.6621i | −0.0552414 | + | 0.0964058i | ||||
\(568\) | − | 278.030i | − | 0.489489i | ||||||
\(569\) | 636.391 | 1.11844 | 0.559219 | − | 0.829020i | \(-0.311101\pi\) | ||||
0.559219 | + | 0.829020i | \(0.311101\pi\) | |||||||
\(570\) | −2.31339 | + | 11.5803i | −0.00405858 | + | 0.0203164i | ||||
\(571\) | 565.901 | 0.991070 | 0.495535 | − | 0.868588i | \(-0.334972\pi\) | ||||
0.495535 | + | 0.868588i | \(0.334972\pi\) | |||||||
\(572\) | −236.987 | −0.414313 | ||||||||
\(573\) | 141.590 | 0.247103 | ||||||||
\(574\) | −88.0762 | + | 153.708i | −0.153443 | + | 0.267784i | ||||
\(575\) | 109.846 | − | 263.962i | 0.191037 | − | 0.459064i | ||||
\(576\) | 64.1573 | 0.111384 | ||||||||
\(577\) | −775.389 | −1.34383 | −0.671914 | − | 0.740629i | \(-0.734528\pi\) | ||||
−0.671914 | + | 0.740629i | \(0.734528\pi\) | |||||||
\(578\) | 156.375i | 0.270545i | ||||||||
\(579\) | 468.296i | 0.808801i | ||||||||
\(580\) | −152.030 | + | 761.031i | −0.262121 | + | 1.31212i | ||||
\(581\) | 490.485 | − | 855.981i | 0.844208 | − | 1.47329i | ||||
\(582\) | − | 147.161i | − | 0.252854i | ||||||
\(583\) | − | 476.717i | − | 0.817696i | ||||||
\(584\) | − | 391.354i | − | 0.670126i | ||||||
\(585\) | −36.8151 | + | 184.289i | −0.0629318 | + | 0.315023i | ||||
\(586\) | − | 125.301i | − | 0.213824i | ||||||
\(587\) | 386.248 | 0.658003 | 0.329001 | − | 0.944329i | \(-0.393288\pi\) | ||||
0.329001 | + | 0.944329i | \(0.393288\pi\) | |||||||
\(588\) | −150.484 | − | 256.762i | −0.255925 | − | 0.436670i | ||||
\(589\) | 97.9140 | 0.166238 | ||||||||
\(590\) | −32.2821 | + | 161.597i | −0.0547154 | + | 0.273894i | ||||
\(591\) | 70.7546i | 0.119720i | ||||||||
\(592\) | 431.258i | 0.728477i | ||||||||
\(593\) | 918.373 | 1.54869 | 0.774345 | − | 0.632764i | \(-0.218080\pi\) | ||||
0.774345 | + | 0.632764i | \(0.218080\pi\) | |||||||
\(594\) | − | 19.6875i | − | 0.0331440i | ||||||
\(595\) | 214.832 | + | 187.478i | 0.361062 | + | 0.315089i | ||||
\(596\) | −65.2287 | −0.109444 | ||||||||
\(597\) | 21.6805i | 0.0363157i | ||||||||
\(598\) | −100.639 | −0.168293 | ||||||||
\(599\) | −52.1903 | −0.0871291 | −0.0435645 | − | 0.999051i | \(-0.513871\pi\) | ||||
−0.0435645 | + | 0.999051i | \(0.513871\pi\) | |||||||
\(600\) | −87.7181 | + | 210.787i | −0.146197 | + | 0.351312i | ||||
\(601\) | − | 474.802i | − | 0.790020i | −0.918677 | − | 0.395010i | \(-0.870741\pi\) | ||
0.918677 | − | 0.395010i | \(-0.129259\pi\) | |||||||
\(602\) | −2.77990 | + | 4.85141i | −0.00461778 | + | 0.00805882i | ||||
\(603\) | − | 314.781i | − | 0.522024i | ||||||
\(604\) | 287.696 | 0.476318 | ||||||||
\(605\) | −90.0175 | + | 450.608i | −0.148789 | + | 0.744807i | ||||
\(606\) | 57.2649 | 0.0944965 | ||||||||
\(607\) | −187.465 | −0.308839 | −0.154420 | − | 0.988005i | \(-0.549351\pi\) | ||||
−0.154420 | + | 0.988005i | \(0.549351\pi\) | |||||||
\(608\) | −55.0210 | −0.0904950 | ||||||||
\(609\) | 266.811 | − | 465.631i | 0.438113 | − | 0.764583i | ||||
\(610\) | 32.7178 | − | 163.778i | 0.0536357 | − | 0.268489i | ||||
\(611\) | 305.668 | 0.500275 | ||||||||
\(612\) | 85.7022 | 0.140036 | ||||||||
\(613\) | − | 24.8739i | − | 0.0405774i | −0.999794 | − | 0.0202887i | \(-0.993541\pi\) | ||
0.999794 | − | 0.0202887i | \(-0.00645854\pi\) | |||||||
\(614\) | − | 270.626i | − | 0.440758i | ||||||
\(615\) | 305.990 | + | 61.1272i | 0.497544 | + | 0.0993938i | ||||
\(616\) | 172.742 | + | 98.9828i | 0.280426 | + | 0.160686i | ||||
\(617\) | − | 154.454i | − | 0.250331i | −0.992136 | − | 0.125165i | \(-0.960054\pi\) | ||
0.992136 | − | 0.125165i | \(-0.0399461\pi\) | |||||||
\(618\) | − | 178.601i | − | 0.288998i | ||||||
\(619\) | 305.924i | 0.494223i | 0.968987 | + | 0.247111i | \(0.0794813\pi\) | ||||
−0.968987 | + | 0.247111i | \(0.920519\pi\) | |||||||
\(620\) | 867.164 | + | 173.232i | 1.39865 | + | 0.279407i | ||||
\(621\) | 59.4243i | 0.0956914i | ||||||||
\(622\) | 83.4877 | 0.134225 | ||||||||
\(623\) | 203.015 | + | 116.330i | 0.325867 | + | 0.186725i | ||||
\(624\) | −224.015 | −0.358998 | ||||||||
\(625\) | 440.483 | + | 443.395i | 0.704773 | + | 0.709433i | ||||
\(626\) | 120.192i | 0.191999i | ||||||||
\(627\) | − | 18.1383i | − | 0.0289288i | ||||||
\(628\) | −470.131 | −0.748616 | ||||||||
\(629\) | 340.334i | 0.541071i | ||||||||
\(630\) | 48.4922 | − | 55.5675i | 0.0769718 | − | 0.0882024i | ||||
\(631\) | −622.718 | −0.986875 | −0.493438 | − | 0.869781i | \(-0.664260\pi\) | ||||
−0.493438 | + | 0.869781i | \(0.664260\pi\) | |||||||
\(632\) | − | 402.440i | − | 0.636772i | ||||||
\(633\) | 38.1310 | 0.0602386 | ||||||||
\(634\) | 105.219 | 0.165960 | ||||||||
\(635\) | −534.779 | − | 106.832i | −0.842172 | − | 0.168240i | ||||
\(636\) | − | 536.764i | − | 0.843969i | ||||||
\(637\) | 310.414 | + | 529.643i | 0.487306 | + | 0.831464i | ||||
\(638\) | 167.705i | 0.262861i | ||||||||
\(639\) | 158.193 | 0.247563 | ||||||||
\(640\) | −629.495 | − | 125.753i | −0.983586 | − | 0.196490i | ||||
\(641\) | −915.315 | −1.42795 | −0.713974 | − | 0.700172i | \(-0.753107\pi\) | ||||
−0.713974 | + | 0.700172i | \(0.753107\pi\) | |||||||
\(642\) | 135.820 | 0.211557 | ||||||||
\(643\) | 232.129 | 0.361009 | 0.180505 | − | 0.983574i | \(-0.442227\pi\) | ||||
0.180505 | + | 0.983574i | \(0.442227\pi\) | |||||||
\(644\) | −243.567 | − | 139.566i | −0.378209 | − | 0.216717i | ||||
\(645\) | 9.65779 | + | 1.92932i | 0.0149733 | + | 0.00299120i | ||||
\(646\) | −11.1088 | −0.0171963 | ||||||||
\(647\) | 267.653 | 0.413683 | 0.206842 | − | 0.978374i | \(-0.433682\pi\) | ||||
0.206842 | + | 0.978374i | \(0.433682\pi\) | |||||||
\(648\) | − | 47.4535i | − | 0.0732307i | ||||||
\(649\) | − | 253.111i | − | 0.390001i | ||||||
\(650\) | 84.5254 | − | 203.115i | 0.130039 | − | 0.312485i | ||||
\(651\) | −530.568 | − | 304.020i | −0.815004 | − | 0.467005i | ||||
\(652\) | 35.6016i | 0.0546036i | ||||||||
\(653\) | − | 157.117i | − | 0.240608i | −0.992737 | − | 0.120304i | \(-0.961613\pi\) | ||
0.992737 | − | 0.120304i | \(-0.0383869\pi\) | |||||||
\(654\) | 91.2871i | 0.139583i | ||||||||
\(655\) | −907.305 | − | 181.251i | −1.38520 | − | 0.276719i | ||||
\(656\) | 371.951i | 0.566998i | ||||||||
\(657\) | 222.671 | 0.338922 | ||||||||
\(658\) | −104.080 | − | 59.6390i | −0.158177 | − | 0.0906368i | ||||
\(659\) | 162.032 | 0.245876 | 0.122938 | − | 0.992414i | \(-0.460768\pi\) | ||||
0.122938 | + | 0.992414i | \(0.460768\pi\) | |||||||
\(660\) | 32.0909 | − | 160.640i | 0.0486225 | − | 0.243394i | ||||
\(661\) | − | 908.541i | − | 1.37450i | −0.726423 | − | 0.687248i | \(-0.758819\pi\) | ||
0.726423 | − | 0.687248i | \(-0.241181\pi\) | |||||||
\(662\) | − | 195.409i | − | 0.295179i | ||||||
\(663\) | −176.784 | −0.266643 | ||||||||
\(664\) | 743.099i | 1.11912i | ||||||||
\(665\) | 44.6765 | − | 51.1950i | 0.0671826 | − | 0.0769850i | ||||
\(666\) | 88.0293 | 0.132176 | ||||||||
\(667\) | − | 506.198i | − | 0.758917i | ||||||
\(668\) | 1024.06 | 1.53302 | ||||||||
\(669\) | −189.721 | −0.283589 | ||||||||
\(670\) | −72.1883 | + | 361.360i | −0.107744 | + | 0.539343i | ||||
\(671\) | 256.527i | 0.382305i | ||||||||
\(672\) | 298.143 | + | 170.839i | 0.443665 | + | 0.254224i | ||||
\(673\) | − | 44.7205i | − | 0.0664495i | −0.999448 | − | 0.0332247i | \(-0.989422\pi\) | ||
0.999448 | − | 0.0332247i | \(-0.0105777\pi\) | |||||||
\(674\) | −243.147 | −0.360753 | ||||||||
\(675\) | −119.933 | − | 49.9097i | −0.177679 | − | 0.0739402i | ||||
\(676\) | −42.1949 | −0.0624185 | ||||||||
\(677\) | −315.654 | −0.466254 | −0.233127 | − | 0.972446i | \(-0.574896\pi\) | ||||
−0.233127 | + | 0.972446i | \(0.574896\pi\) | |||||||
\(678\) | −204.534 | −0.301673 | ||||||||
\(679\) | −420.976 | + | 734.676i | −0.619994 | + | 1.08200i | ||||
\(680\) | −210.609 | − | 42.0731i | −0.309720 | − | 0.0618723i | ||||
\(681\) | −639.979 | −0.939764 | ||||||||
\(682\) | 191.093 | 0.280196 | ||||||||
\(683\) | 191.841i | 0.280879i | 0.990089 | + | 0.140440i | \(0.0448516\pi\) | ||||
−0.990089 | + | 0.140440i | \(0.955148\pi\) | |||||||
\(684\) | − | 20.4231i | − | 0.0298583i | ||||||
\(685\) | 792.908 | + | 158.398i | 1.15753 | + | 0.231238i | ||||
\(686\) | −2.35762 | − | 240.909i | −0.00343677 | − | 0.351180i | ||||
\(687\) | 627.679i | 0.913652i | ||||||||
\(688\) | 11.7397i | 0.0170635i | ||||||||
\(689\) | 1107.22i | 1.60700i | ||||||||
\(690\) | 13.6277 | − | 68.2175i | 0.0197503 | − | 0.0988659i | ||||
\(691\) | − | 569.279i | − | 0.823849i | −0.911218 | − | 0.411924i | \(-0.864857\pi\) | ||
0.911218 | − | 0.411924i | \(-0.135143\pi\) | |||||||
\(692\) | −679.088 | −0.981341 | ||||||||
\(693\) | −56.3190 | + | 98.2864i | −0.0812684 | + | 0.141827i | ||||
\(694\) | −58.8429 | −0.0847881 | ||||||||
\(695\) | −1144.49 | − | 228.633i | −1.64674 | − | 0.328968i | ||||
\(696\) | 404.226i | 0.580785i | ||||||||
\(697\) | 293.530i | 0.421134i | ||||||||
\(698\) | −213.866 | −0.306399 | ||||||||
\(699\) | − | 48.7127i | − | 0.0696891i | ||||||
\(700\) | 486.248 | − | 374.360i | 0.694639 | − | 0.534800i | ||||
\(701\) | −1169.70 | −1.66862 | −0.834308 | − | 0.551298i | \(-0.814133\pi\) | ||||
−0.834308 | + | 0.551298i | \(0.814133\pi\) | |||||||
\(702\) | 45.7263i | 0.0651372i | ||||||||
\(703\) | 81.1025 | 0.115366 | ||||||||
\(704\) | 115.360 | 0.163863 | ||||||||
\(705\) | −41.3910 | + | 207.195i | −0.0587107 | + | 0.293893i | ||||
\(706\) | 132.430i | 0.187578i | ||||||||
\(707\) | −285.885 | − | 163.815i | −0.404364 | − | 0.231704i | ||||
\(708\) | − | 284.993i | − | 0.402532i | ||||||
\(709\) | 174.767 | 0.246499 | 0.123249 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123249 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(710\) | −181.601 | − | 36.2782i | −0.255776 | − | 0.0510961i | ||||
\(711\) | 228.979 | 0.322053 | ||||||||
\(712\) | −176.243 | −0.247532 | ||||||||
\(713\) | −576.792 | −0.808965 | ||||||||
\(714\) | 60.1954 | + | 34.4925i | 0.0843073 | + | 0.0483088i | ||||
\(715\) | −66.1963 | + | 331.364i | −0.0925822 | + | 0.463447i | ||||
\(716\) | 713.911 | 0.997083 | ||||||||
\(717\) | −387.207 | −0.540037 | ||||||||
\(718\) | 252.471i | 0.351631i | ||||||||
\(719\) | 1311.82i | 1.82451i | 0.409622 | + | 0.912255i | \(0.365661\pi\) | ||||
−0.409622 | + | 0.912255i | \(0.634339\pi\) | |||||||
\(720\) | 30.3342 | − | 151.847i | 0.0421309 | − | 0.210898i | ||||
\(721\) | −510.914 | + | 891.633i | −0.708618 | + | 1.23666i | ||||
\(722\) | − | 250.917i | − | 0.347530i | ||||||
\(723\) | 241.913i | 0.334597i | ||||||||
\(724\) | − | 1025.48i | − | 1.41641i | ||||||
\(725\) | 1021.64 | + | 425.148i | 1.40915 | + | 0.586412i | ||||
\(726\) | 111.807i | 0.154004i | ||||||||
\(727\) | 422.239 | 0.580796 | 0.290398 | − | 0.956906i | \(-0.406212\pi\) | ||||
0.290398 | + | 0.956906i | \(0.406212\pi\) | |||||||
\(728\) | −401.212 | − | 229.898i | −0.551115 | − | 0.315794i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −255.621 | − | 51.0650i | −0.350165 | − | 0.0699521i | ||||
\(731\) | 9.26453i | 0.0126738i | ||||||||
\(732\) | 288.839i | 0.394589i | ||||||||
\(733\) | 952.458 | 1.29940 | 0.649699 | − | 0.760192i | \(-0.274895\pi\) | ||||
0.649699 | + | 0.760192i | \(0.274895\pi\) | |||||||
\(734\) | − | 21.6594i | − | 0.0295087i | ||||||
\(735\) | −401.048 | + | 138.692i | −0.545644 | + | 0.188697i | ||||
\(736\) | 324.118 | 0.440378 | ||||||||
\(737\) | − | 565.999i | − | 0.767977i | ||||||
\(738\) | 75.9233 | 0.102877 | ||||||||
\(739\) | −19.1678 | −0.0259375 | −0.0129687 | − | 0.999916i | \(-0.504128\pi\) | ||||
−0.0129687 | + | 0.999916i | \(0.504128\pi\) | |||||||
\(740\) | 718.275 | + | 143.489i | 0.970641 | + | 0.193904i | ||||
\(741\) | 42.1282i | 0.0568532i | ||||||||
\(742\) | 216.031 | − | 377.012i | 0.291147 | − | 0.508102i | ||||
\(743\) | 1326.11i | 1.78480i | 0.451246 | + | 0.892400i | \(0.350980\pi\) | ||||
−0.451246 | + | 0.892400i | \(0.649020\pi\) | |||||||
\(744\) | 460.599 | 0.619085 | ||||||||
\(745\) | −18.2199 | + | 91.2052i | −0.0244563 | + | 0.122423i | ||||
\(746\) | 7.93346 | 0.0106347 | ||||||||
\(747\) | −422.807 | −0.566006 | ||||||||
\(748\) | 154.099 | 0.206015 | ||||||||
\(749\) | −678.055 | − | 388.532i | −0.905281 | − | 0.518734i | ||||
\(750\) | 126.235 | + | 84.7991i | 0.168313 | + | 0.113065i | ||||
\(751\) | −866.144 | −1.15332 | −0.576660 | − | 0.816984i | \(-0.695644\pi\) | ||||
−0.576660 | + | 0.816984i | \(0.695644\pi\) | |||||||
\(752\) | −251.859 | −0.334919 | ||||||||
\(753\) | 575.921i | 0.764835i | ||||||||
\(754\) | − | 389.513i | − | 0.516596i | ||||||
\(755\) | 80.3605 | − | 402.268i | 0.106438 | − | 0.532805i | ||||
\(756\) | −63.4130 | + | 110.667i | −0.0838797 | + | 0.146385i | ||||
\(757\) | − | 1069.24i | − | 1.41248i | −0.707975 | − | 0.706238i | \(-0.750391\pi\) | ||
0.707975 | − | 0.706238i | \(-0.249609\pi\) | |||||||
\(758\) | − | 205.800i | − | 0.271504i | ||||||
\(759\) | 106.849i | 0.140777i | ||||||||
\(760\) | −10.0261 | + | 50.1888i | −0.0131923 | + | 0.0660378i | ||||
\(761\) | − | 371.263i | − | 0.487863i | −0.969793 | − | 0.243931i | \(-0.921563\pi\) | ||
0.969793 | − | 0.243931i | \(-0.0784371\pi\) | |||||||
\(762\) | −132.691 | −0.174136 | ||||||||
\(763\) | 261.140 | − | 455.735i | 0.342255 | − | 0.597293i | ||||
\(764\) | 286.658 | 0.375207 | ||||||||
\(765\) | 23.9387 | − | 119.832i | 0.0312924 | − | 0.156643i | ||||
\(766\) | − | 26.1345i | − | 0.0341182i | ||||||
\(767\) | 587.877i | 0.766462i | ||||||||
\(768\) | −8.02757 | −0.0104526 | ||||||||
\(769\) | 388.419i | 0.505096i | 0.967584 | + | 0.252548i | \(0.0812686\pi\) | ||||
−0.967584 | + | 0.252548i | \(0.918731\pi\) | |||||||
\(770\) | 87.1926 | − | 99.9145i | 0.113237 | − | 0.129759i | ||||
\(771\) | 740.085 | 0.959903 | ||||||||
\(772\) | 948.094i | 1.22810i | ||||||||
\(773\) | −732.499 | −0.947605 | −0.473803 | − | 0.880631i | \(-0.657119\pi\) | ||||
−0.473803 | + | 0.880631i | \(0.657119\pi\) | |||||||
\(774\) | 2.39633 | 0.00309603 | ||||||||
\(775\) | 484.439 | − | 1164.11i | 0.625083 | − | 1.50208i | ||||
\(776\) | − | 637.791i | − | 0.821895i | ||||||
\(777\) | −439.471 | − | 251.821i | −0.565600 | − | 0.324094i | ||||
\(778\) | − | 115.671i | − | 0.148677i | ||||||
\(779\) | 69.9490 | 0.0897934 | ||||||||
\(780\) | −74.5344 | + | 373.104i | −0.0955569 | + | 0.478338i | ||||
\(781\) | 284.443 | 0.364203 | ||||||||
\(782\) | 65.4397 | 0.0836825 | ||||||||
\(783\) | −229.996 | −0.293737 | ||||||||
\(784\) | −255.769 | − | 436.405i | −0.326236 | − | 0.556639i | ||||
\(785\) | −131.319 | + | 657.354i | −0.167285 | + | 0.837394i | ||||
\(786\) | −225.124 | −0.286417 | ||||||||
\(787\) | 1123.40 | 1.42745 | 0.713725 | − | 0.700426i | \(-0.247007\pi\) | ||||
0.713725 | + | 0.700426i | \(0.247007\pi\) | |||||||
\(788\) | 143.247i | 0.181786i | ||||||||
\(789\) | 304.235i | 0.385596i | ||||||||
\(790\) | −262.862 | − | 52.5116i | −0.332737 | − | 0.0664704i | ||||
\(791\) | 1021.10 | + | 585.101i | 1.29090 | + | 0.739698i | ||||
\(792\) | − | 85.3249i | − | 0.107734i | ||||||
\(793\) | − | 595.811i | − | 0.751337i | ||||||
\(794\) | 105.022i | 0.132270i | ||||||||
\(795\) | −750.524 | − | 149.931i | −0.944056 | − | 0.188593i | ||||
\(796\) | 43.8935i | 0.0551426i | ||||||||
\(797\) | −1107.27 | −1.38929 | −0.694646 | − | 0.719351i | \(-0.744439\pi\) | ||||
−0.694646 | + | 0.719351i | \(0.744439\pi\) | |||||||
\(798\) | 8.21966 | − | 14.3447i | 0.0103003 | − | 0.0179758i | ||||
\(799\) | −198.758 | −0.248758 | ||||||||
\(800\) | −272.222 | + | 654.152i | −0.340278 | + | 0.817690i | ||||
\(801\) | − | 100.278i | − | 0.125191i | ||||||
\(802\) | − | 308.836i | − | 0.385082i | ||||||
\(803\) | 400.380 | 0.498605 | ||||||||
\(804\) | − | 637.293i | − | 0.792653i | ||||||
\(805\) | −263.180 | + | 301.580i | −0.326932 | + | 0.374633i | ||||
\(806\) | −443.835 | −0.550663 | ||||||||
\(807\) | − | 491.561i | − | 0.609122i | ||||||
\(808\) | 248.184 | 0.307158 | ||||||||
\(809\) | 358.280 | 0.442867 | 0.221434 | − | 0.975175i | \(-0.428926\pi\) | ||||
0.221434 | + | 0.975175i | \(0.428926\pi\) | |||||||
\(810\) | −30.9953 | − | 6.19188i | −0.0382657 | − | 0.00764430i | ||||
\(811\) | 272.867i | 0.336458i | 0.985748 | + | 0.168229i | \(0.0538047\pi\) | ||||
−0.985748 | + | 0.168229i | \(0.946195\pi\) | |||||||
\(812\) | 540.175 | − | 942.699i | 0.665240 | − | 1.16096i | ||||
\(813\) | 399.416i | 0.491287i | ||||||||
\(814\) | 158.283 | 0.194451 | ||||||||
\(815\) | 49.7794 | + | 9.94437i | 0.0610790 | + | 0.0122017i | ||||
\(816\) | 145.664 | 0.178509 | ||||||||
\(817\) | 2.20776 | 0.00270228 | ||||||||
\(818\) | 177.308 | 0.216759 | ||||||||
\(819\) | 130.807 | − | 228.281i | 0.159715 | − | 0.278731i | ||||
\(820\) | 619.495 | + | 123.756i | 0.755482 | + | 0.150922i | ||||
\(821\) | 669.181 | 0.815080 | 0.407540 | − | 0.913187i | \(-0.366387\pi\) | ||||
0.407540 | + | 0.913187i | \(0.366387\pi\) | |||||||
\(822\) | 196.739 | 0.239342 | ||||||||
\(823\) | 71.5057i | 0.0868843i | 0.999056 | + | 0.0434421i | \(0.0138324\pi\) | ||||
−0.999056 | + | 0.0434421i | \(0.986168\pi\) | |||||||
\(824\) | − | 774.049i | − | 0.939380i | ||||||
\(825\) | −215.649 | − | 89.7413i | −0.261393 | − | 0.108777i | ||||
\(826\) | 114.701 | − | 200.173i | 0.138863 | − | 0.242340i | ||||
\(827\) | 1255.08i | 1.51763i | 0.651306 | + | 0.758815i | \(0.274221\pi\) | ||||
−0.651306 | + | 0.758815i | \(0.725779\pi\) | |||||||
\(828\) | 120.308i | 0.145300i | ||||||||
\(829\) | 398.796i | 0.481057i | 0.970642 | + | 0.240528i | \(0.0773207\pi\) | ||||
−0.970642 | + | 0.240528i | \(0.922679\pi\) | |||||||
\(830\) | 485.370 | + | 96.9618i | 0.584784 | + | 0.116821i | ||||
\(831\) | 633.423i | 0.762242i | ||||||||
\(832\) | −267.935 | −0.322037 | ||||||||
\(833\) | −201.844 | − | 344.396i | −0.242310 | − | 0.413440i | ||||
\(834\) | −283.974 | −0.340496 | ||||||||
\(835\) | 286.044 | − | 1431.88i | 0.342568 | − | 1.71482i | ||||
\(836\) | − | 36.7222i | − | 0.0439261i | ||||||
\(837\) | 262.071i | 0.313107i | ||||||||
\(838\) | 75.5847 | 0.0901965 | ||||||||
\(839\) | − | 72.2323i | − | 0.0860934i | −0.999073 | − | 0.0430467i | \(-0.986294\pi\) | ||
0.999073 | − | 0.0430467i | \(-0.0137064\pi\) | |||||||
\(840\) | 210.164 | − | 240.828i | 0.250195 | − | 0.286700i | ||||
\(841\) | 1118.19 | 1.32959 | ||||||||
\(842\) | 142.260i | 0.168955i | ||||||||
\(843\) | −533.764 | −0.633172 | ||||||||
\(844\) | 77.1986 | 0.0914675 | ||||||||
\(845\) | −11.7861 | + | 58.9985i | −0.0139480 | + | 0.0698208i | ||||
\(846\) | 51.4099i | 0.0607682i | ||||||||
\(847\) | 319.839 | − | 558.175i | 0.377614 | − | 0.659002i | ||||
\(848\) | − | 912.311i | − | 1.07584i | ||||||
\(849\) | 46.8827 | 0.0552211 | ||||||||
\(850\) | −54.9619 | + | 132.074i | −0.0646611 | + | 0.155381i | ||||
\(851\) | −477.759 | −0.561409 | ||||||||
\(852\) | 320.271 | 0.375905 | ||||||||
\(853\) | 977.259 | 1.14567 | 0.572836 | − | 0.819670i | \(-0.305843\pi\) | ||||
0.572836 | + | 0.819670i | \(0.305843\pi\) | |||||||
\(854\) | −116.249 | + | 202.874i | −0.136123 | + | 0.237558i | ||||
\(855\) | −28.5563 | − | 5.70465i | −0.0333992 | − | 0.00667211i | ||||
\(856\) | 588.637 | 0.687660 | ||||||||
\(857\) | 919.007 | 1.07235 | 0.536177 | − | 0.844106i | \(-0.319868\pi\) | ||||
0.536177 | + | 0.844106i | \(0.319868\pi\) | |||||||
\(858\) | 82.2193i | 0.0958267i | ||||||||
\(859\) | − | 1258.07i | − | 1.46457i | −0.680996 | − | 0.732287i | \(-0.738453\pi\) | ||
0.680996 | − | 0.732287i | \(-0.261547\pi\) | |||||||
\(860\) | 19.5528 | + | 3.90604i | 0.0227358 | + | 0.00454190i | ||||
\(861\) | −379.034 | − | 217.190i | −0.440225 | − | 0.252253i | ||||
\(862\) | 560.039i | 0.649697i | ||||||||
\(863\) | − | 740.363i | − | 0.857895i | −0.903329 | − | 0.428947i | \(-0.858885\pi\) | ||
0.903329 | − | 0.428947i | \(-0.141115\pi\) | |||||||
\(864\) | − | 147.266i | − | 0.170447i | ||||||
\(865\) | −189.686 | + | 949.526i | −0.219290 | + | 1.09772i | ||||
\(866\) | 496.769i | 0.573636i | ||||||||
\(867\) | −385.610 | −0.444764 | ||||||||
\(868\) | −1074.17 | − | 615.508i | −1.23752 | − | 0.709110i | ||||
\(869\) | 411.722 | 0.473788 | ||||||||
\(870\) | 264.029 | + | 52.7447i | 0.303481 | + | 0.0606261i | ||||
\(871\) | 1314.59i | 1.50929i | ||||||||
\(872\) | 395.635i | 0.453710i | ||||||||
\(873\) | 362.889 | 0.415680 | ||||||||
\(874\) | − | 15.5945i | − | 0.0178426i | ||||||
\(875\) | −387.623 | − | 784.457i | −0.442998 | − | 0.896523i | ||||
\(876\) | 450.812 | 0.514626 | ||||||||
\(877\) | − | 1161.99i | − | 1.32496i | −0.749078 | − | 0.662482i | \(-0.769503\pi\) | ||
0.749078 | − | 0.662482i | \(-0.230497\pi\) | |||||||
\(878\) | −183.303 | −0.208773 | ||||||||
\(879\) | 308.983 | 0.351517 | ||||||||
\(880\) | 54.5432 | − | 273.032i | 0.0619809 | − | 0.310263i | ||||
\(881\) | − | 434.212i | − | 0.492863i | −0.969160 | − | 0.246431i | \(-0.920742\pi\) | ||
0.969160 | − | 0.246431i | \(-0.0792580\pi\) | |||||||
\(882\) | −89.0799 | + | 52.2081i | −0.100998 | + | 0.0591929i | ||||
\(883\) | 1390.88i | 1.57518i | 0.616200 | + | 0.787589i | \(0.288671\pi\) | ||||
−0.616200 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(884\) | −357.911 | −0.404877 | ||||||||
\(885\) | −398.488 | − | 79.6054i | −0.450269 | − | 0.0899496i | ||||
\(886\) | 484.673 | 0.547034 | ||||||||
\(887\) | −505.489 | −0.569886 | −0.284943 | − | 0.958544i | \(-0.591975\pi\) | ||||
−0.284943 | + | 0.958544i | \(0.591975\pi\) | |||||||
\(888\) | 381.516 | 0.429635 | ||||||||
\(889\) | 662.438 | + | 379.583i | 0.745150 | + | 0.426978i | ||||
\(890\) | −22.9967 | + | 115.117i | −0.0258390 | + | 0.129344i | ||||
\(891\) | 48.5480 | 0.0544871 | ||||||||
\(892\) | −384.101 | −0.430607 | ||||||||
\(893\) | 47.3646i | 0.0530398i | ||||||||
\(894\) | 22.6302i | 0.0253134i | ||||||||
\(895\) | 199.413 | − | 998.218i | 0.222807 | − | 1.11533i | ||||
\(896\) | 779.764 | + | 446.812i | 0.870272 | + | 0.498674i | ||||
\(897\) | − | 248.169i | − | 0.276666i | ||||||
\(898\) | − | 83.4666i | − | 0.0929472i | ||||||
\(899\) | − | 2232.41i | − | 2.48322i | ||||||
\(900\) | −242.813 | − | 101.045i | −0.269792 | − | 0.112272i | ||||
\(901\) | − | 719.963i | − | 0.799071i | ||||||
\(902\) | 136.516 | 0.151348 | ||||||||
\(903\) | −11.9632 | − | 6.85504i | −0.0132483 | − | 0.00759141i | ||||
\(904\) | −886.445 | −0.980581 | ||||||||
\(905\) | −1433.87 | − | 286.442i | −1.58438 | − | 0.316510i | ||||
\(906\) | − | 99.8121i | − | 0.110168i | ||||||
\(907\) | 158.597i | 0.174859i | 0.996171 | + | 0.0874293i | \(0.0278652\pi\) | ||||
−0.996171 | + | 0.0874293i | \(0.972135\pi\) | |||||||
\(908\) | −1295.68 | −1.42696 | ||||||||
\(909\) | 141.211i | 0.155348i | ||||||||
\(910\) | −202.514 | + | 232.062i | −0.222543 | + | 0.255013i | ||||
\(911\) | 700.060 | 0.768452 | 0.384226 | − | 0.923239i | \(-0.374468\pi\) | ||||
0.384226 | + | 0.923239i | \(0.374468\pi\) | |||||||
\(912\) | − | 34.7120i | − | 0.0380614i | ||||||
\(913\) | −760.238 | −0.832681 | ||||||||
\(914\) | 255.631 | 0.279684 | ||||||||
\(915\) | 403.866 | + | 80.6798i | 0.441383 | + | 0.0881746i | ||||
\(916\) | 1270.78i | 1.38731i | ||||||||
\(917\) | 1123.89 | + | 643.999i | 1.22562 | + | 0.702290i | ||||
\(918\) | − | 29.7331i | − | 0.0323891i | ||||||
\(919\) | 91.7379 | 0.0998236 | 0.0499118 | − | 0.998754i | \(-0.484106\pi\) | ||||
0.0499118 | + | 0.998754i | \(0.484106\pi\) | |||||||
\(920\) | 59.0620 | − | 295.652i | 0.0641979 | − | 0.321361i | ||||
\(921\) | 667.344 | 0.724586 | ||||||||
\(922\) | −264.781 | −0.287181 | ||||||||
\(923\) | −660.648 | −0.715762 | ||||||||
\(924\) | −114.021 | + | 198.987i | −0.123400 | + | 0.215354i | ||||
\(925\) | 401.263 | − | 964.238i | 0.433798 | − | 1.04242i | ||||
\(926\) | 145.255 | 0.156863 | ||||||||
\(927\) | 440.417 | 0.475099 | ||||||||
\(928\) | 1254.46i | 1.35179i | ||||||||
\(929\) | 411.879i | 0.443358i | 0.975120 | + | 0.221679i | \(0.0711537\pi\) | ||||
−0.975120 | + | 0.221679i | \(0.928846\pi\) | |||||||
\(930\) | 60.1004 | − | 300.850i | 0.0646241 | − | 0.323495i | ||||
\(931\) | −82.0704 | + | 48.1000i | −0.0881529 | + | 0.0516648i | ||||
\(932\) | − | 98.6218i | − | 0.105817i | ||||||
\(933\) | 205.875i | 0.220659i | ||||||||
\(934\) | − | 75.9272i | − | 0.0812925i | ||||||
\(935\) | 43.0435 | − | 215.467i | 0.0460359 | − | 0.230446i | ||||
\(936\) | 198.176i | 0.211727i | ||||||||
\(937\) | −1257.62 | −1.34218 | −0.671091 | − | 0.741375i | \(-0.734174\pi\) | ||||
−0.671091 | + | 0.741375i | \(0.734174\pi\) | |||||||
\(938\) | 256.491 | − | 447.621i | 0.273444 | − | 0.477208i | ||||
\(939\) | −296.384 | −0.315638 | ||||||||
\(940\) | −83.7987 | + | 419.479i | −0.0891476 | + | 0.446254i | ||||
\(941\) | 1353.18i | 1.43802i | 0.694998 | + | 0.719012i | \(0.255405\pi\) | ||||
−0.694998 | + | 0.719012i | \(0.744595\pi\) | |||||||
\(942\) | 163.105i | 0.173148i | ||||||||
\(943\) | −412.056 | −0.436963 | ||||||||
\(944\) | − | 484.388i | − | 0.513123i | ||||||
\(945\) | 137.026 | + | 119.578i | 0.145001 | + | 0.126538i | ||||
\(946\) | 4.30877 | 0.00455473 | ||||||||
\(947\) | − | 413.235i | − | 0.436362i | −0.975908 | − | 0.218181i | \(-0.929988\pi\) | ||
0.975908 | − | 0.218181i | \(-0.0700124\pi\) | |||||||
\(948\) | 463.583 | 0.489012 | ||||||||
\(949\) | −929.925 | −0.979899 | ||||||||
\(950\) | 31.4736 | + | 13.0976i | 0.0331301 | + | 0.0137869i | ||||
\(951\) | 259.462i | 0.272831i | ||||||||
\(952\) | 260.885 | + | 149.489i | 0.274038 | + | 0.157026i | ||||
\(953\) | − | 1488.70i | − | 1.56212i | −0.624455 | − | 0.781061i | \(-0.714679\pi\) | ||
0.624455 | − | 0.781061i | \(-0.285321\pi\) | |||||||
\(954\) | −186.223 | −0.195202 | ||||||||
\(955\) | 80.0706 | − | 400.816i | 0.0838435 | − | 0.419703i | ||||
\(956\) | −783.924 | −0.820005 | ||||||||
\(957\) | −413.549 | −0.432131 | ||||||||
\(958\) | 308.338 | 0.321856 | ||||||||
\(959\) | −982.186 | − | 562.801i | −1.02418 | − | 0.586863i | ||||
\(960\) | 36.2815 | − | 181.618i | 0.0377933 | − | 0.189185i | ||||
\(961\) | −1582.74 | −1.64698 | ||||||||
\(962\) | −367.630 | −0.382151 | ||||||||
\(963\) | 334.921i | 0.347789i | ||||||||
\(964\) | 489.769i | 0.508059i | ||||||||
\(965\) | 1325.66 | + | 264.826i | 1.37374 | + | 0.274431i | ||||
\(966\) | −48.4204 | + | 84.5019i | −0.0501246 | + | 0.0874761i | ||||
\(967\) | 329.641i | 0.340890i | 0.985367 | + | 0.170445i | \(0.0545205\pi\) | ||||
−0.985367 | + | 0.170445i | \(0.945479\pi\) | |||||||
\(968\) | 484.566i | 0.500584i | ||||||||
\(969\) | − | 27.3935i | − | 0.0282699i | ||||||
\(970\) | −416.586 | − | 83.2209i | −0.429470 | − | 0.0857948i | ||||
\(971\) | 1814.32i | 1.86851i | 0.356610 | + | 0.934253i | \(0.383933\pi\) | ||||
−0.356610 | + | 0.934253i | \(0.616067\pi\) | |||||||
\(972\) | 54.6632 | 0.0562378 | ||||||||
\(973\) | 1417.69 | + | 812.350i | 1.45703 | + | 0.834892i | ||||
\(974\) | −309.046 | −0.317296 | ||||||||
\(975\) | 500.868 | + | 208.434i | 0.513711 | + | 0.213778i | ||||
\(976\) | 490.925i | 0.502997i | ||||||||
\(977\) | 1615.80i | 1.65384i | 0.562318 | + | 0.826921i | \(0.309910\pi\) | ||||
−0.562318 | + | 0.826921i | \(0.690090\pi\) | |||||||
\(978\) | 12.3514 | 0.0126293 | ||||||||
\(979\) | − | 180.308i | − | 0.184175i | ||||||
\(980\) | −811.947 | + | 280.791i | −0.828517 | + | 0.286521i | ||||
\(981\) | −225.108 | −0.229467 | ||||||||
\(982\) | − | 78.5923i | − | 0.0800329i | ||||||
\(983\) | −657.745 | −0.669120 | −0.334560 | − | 0.942374i | \(-0.608588\pi\) | ||||
−0.334560 | + | 0.942374i | \(0.608588\pi\) | |||||||
\(984\) | 329.049 | 0.334399 | ||||||||
\(985\) | 200.293 | + | 40.0123i | 0.203344 | + | 0.0406217i | ||||
\(986\) | 253.278i | 0.256874i | ||||||||
\(987\) | 147.066 | − | 256.655i | 0.149003 | − | 0.260035i | ||||
\(988\) | 85.2912i | 0.0863271i | ||||||||
\(989\) | −13.0055 | −0.0131502 | ||||||||
\(990\) | −55.7318 | − | 11.1335i | −0.0562947 | − | 0.0112459i | ||||
\(991\) | 1191.09 | 1.20191 | 0.600956 | − | 0.799282i | \(-0.294787\pi\) | ||||
0.600956 | + | 0.799282i | \(0.294787\pi\) | |||||||
\(992\) | 1429.41 | 1.44094 | ||||||||
\(993\) | 481.864 | 0.485261 | ||||||||
\(994\) | 224.952 | + | 128.899i | 0.226310 | + | 0.129677i | ||||
\(995\) | 61.3735 | + | 12.2605i | 0.0616819 | + | 0.0123221i | ||||
\(996\) | −855.999 | −0.859436 | ||||||||
\(997\) | 1231.00 | 1.23470 | 0.617350 | − | 0.786689i | \(-0.288206\pi\) | ||||
0.617350 | + | 0.786689i | \(0.288206\pi\) | |||||||
\(998\) | − | 55.3563i | − | 0.0554672i | ||||||
\(999\) | 217.074i | 0.217291i |
(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 | 105.3.e.a.34.8 | yes | 16 | |
3.2 | odd | 2 | 315.3.e.e.244.9 | 16 | |||
4.3 | odd | 2 | 1680.3.bd.c.769.3 | 16 | |||
5.2 | odd | 4 | 525.3.h.e.76.9 | 16 | |||
5.3 | odd | 4 | 525.3.h.e.76.8 | 16 | |||
5.4 | even | 2 | inner | 105.3.e.a.34.9 | yes | 16 | |
7.6 | odd | 2 | inner | 105.3.e.a.34.7 | ✓ | 16 | |
15.14 | odd | 2 | 315.3.e.e.244.8 | 16 | |||
20.19 | odd | 2 | 1680.3.bd.c.769.13 | 16 | |||
21.20 | even | 2 | 315.3.e.e.244.10 | 16 | |||
28.27 | even | 2 | 1680.3.bd.c.769.14 | 16 | |||
35.13 | even | 4 | 525.3.h.e.76.7 | 16 | |||
35.27 | even | 4 | 525.3.h.e.76.10 | 16 | |||
35.34 | odd | 2 | inner | 105.3.e.a.34.10 | yes | 16 | |
105.104 | even | 2 | 315.3.e.e.244.7 | 16 | |||
140.139 | even | 2 | 1680.3.bd.c.769.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.e.a.34.7 | ✓ | 16 | 7.6 | odd | 2 | inner | |
105.3.e.a.34.8 | yes | 16 | 1.1 | even | 1 | trivial | |
105.3.e.a.34.9 | yes | 16 | 5.4 | even | 2 | inner | |
105.3.e.a.34.10 | yes | 16 | 35.34 | odd | 2 | inner | |
315.3.e.e.244.7 | 16 | 105.104 | even | 2 | |||
315.3.e.e.244.8 | 16 | 15.14 | odd | 2 | |||
315.3.e.e.244.9 | 16 | 3.2 | odd | 2 | |||
315.3.e.e.244.10 | 16 | 21.20 | even | 2 | |||
525.3.h.e.76.7 | 16 | 35.13 | even | 4 | |||
525.3.h.e.76.8 | 16 | 5.3 | odd | 4 | |||
525.3.h.e.76.9 | 16 | 5.2 | odd | 4 | |||
525.3.h.e.76.10 | 16 | 35.27 | even | 4 | |||
1680.3.bd.c.769.3 | 16 | 4.3 | odd | 2 | |||
1680.3.bd.c.769.4 | 16 | 140.139 | even | 2 | |||
1680.3.bd.c.769.13 | 16 | 20.19 | odd | 2 | |||
1680.3.bd.c.769.14 | 16 | 28.27 | even | 2 |