Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(701,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.701");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 701.14 | ||
Character | \(\chi\) | \(=\) | 1050.701 |
Dual form | 1050.3.e.e.701.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 0.554262 | + | 2.94835i | 0.184754 | + | 0.982785i | ||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.16960 | − | 0.783844i | 0.694934 | − | 0.130641i | ||||
\(7\) | −2.64575 | −0.377964 | ||||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −8.38559 | + | 3.26832i | −0.931732 | + | 0.363147i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.58444i | 0.234949i | 0.993076 | + | 0.117475i | \(0.0374799\pi\) | ||||
−0.993076 | + | 0.117475i | \(0.962520\pi\) | |||||||
\(12\) | −1.10852 | − | 5.89671i | −0.0923769 | − | 0.491392i | ||||
\(13\) | 0.180526 | 0.0138866 | 0.00694332 | − | 0.999976i | \(-0.497790\pi\) | ||||
0.00694332 | + | 0.999976i | \(0.497790\pi\) | |||||||
\(14\) | 3.74166i | 0.267261i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 7.25119i | − | 0.426541i | −0.976993 | − | 0.213270i | \(-0.931589\pi\) | ||
0.976993 | − | 0.213270i | \(-0.0684115\pi\) | |||||||
\(18\) | 4.62210 | + | 11.8590i | 0.256783 | + | 0.658834i | ||||
\(19\) | 21.4338 | 1.12809 | 0.564047 | − | 0.825743i | \(-0.309244\pi\) | ||||
0.564047 | + | 0.825743i | \(0.309244\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.46644 | − | 7.80061i | −0.0698304 | − | 0.371458i | ||||
\(22\) | 3.65495 | 0.166134 | ||||||||
\(23\) | 11.8858i | 0.516774i | 0.966042 | + | 0.258387i | \(0.0831909\pi\) | ||||
−0.966042 | + | 0.258387i | \(0.916809\pi\) | |||||||
\(24\) | −8.33921 | + | 1.56769i | −0.347467 | + | 0.0653203i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 0.255303i | − | 0.00981934i | ||||||
\(27\) | −14.2840 | − | 22.9122i | −0.529036 | − | 0.848599i | ||||
\(28\) | 5.29150 | 0.188982 | ||||||||
\(29\) | 29.5458i | 1.01882i | 0.860524 | + | 0.509410i | \(0.170136\pi\) | ||||
−0.860524 | + | 0.509410i | \(0.829864\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −49.5193 | −1.59740 | −0.798699 | − | 0.601731i | \(-0.794478\pi\) | ||||
−0.798699 | + | 0.601731i | \(0.794478\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | −7.61985 | + | 1.43246i | −0.230905 | + | 0.0434078i | ||||
\(34\) | −10.2547 | −0.301610 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 16.7712 | − | 6.53664i | 0.465866 | − | 0.181573i | ||||
\(37\) | −43.2958 | −1.17016 | −0.585078 | − | 0.810977i | \(-0.698936\pi\) | ||||
−0.585078 | + | 0.810977i | \(0.698936\pi\) | |||||||
\(38\) | − | 30.3120i | − | 0.797683i | ||||||
\(39\) | 0.100059 | + | 0.532256i | 0.00256561 | + | 0.0136476i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 20.7847i | − | 0.506944i | −0.967343 | − | 0.253472i | \(-0.918427\pi\) | ||
0.967343 | − | 0.253472i | \(-0.0815726\pi\) | |||||||
\(42\) | −11.0317 | + | 2.07386i | −0.262660 | + | 0.0493775i | ||||
\(43\) | −74.2183 | −1.72601 | −0.863004 | − | 0.505197i | \(-0.831420\pi\) | ||||
−0.863004 | + | 0.505197i | \(0.831420\pi\) | |||||||
\(44\) | − | 5.16888i | − | 0.117475i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 16.8091 | 0.365414 | ||||||||
\(47\) | − | 7.05106i | − | 0.150023i | −0.997183 | − | 0.0750113i | \(-0.976101\pi\) | ||
0.997183 | − | 0.0750113i | \(-0.0238993\pi\) | |||||||
\(48\) | 2.21705 | + | 11.7934i | 0.0461885 | + | 0.245696i | ||||
\(49\) | 7.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 21.3791 | − | 4.01906i | 0.419198 | − | 0.0788050i | ||||
\(52\) | −0.361053 | −0.00694332 | ||||||||
\(53\) | − | 55.0572i | − | 1.03882i | −0.854526 | − | 0.519408i | \(-0.826153\pi\) | ||
0.854526 | − | 0.519408i | \(-0.173847\pi\) | |||||||
\(54\) | −32.4027 | + | 20.2006i | −0.600050 | + | 0.374085i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 7.48331i | − | 0.133631i | ||||||
\(57\) | 11.8799 | + | 63.1944i | 0.208420 | + | 1.10867i | ||||
\(58\) | 41.7841 | 0.720415 | ||||||||
\(59\) | − | 100.110i | − | 1.69678i | −0.529375 | − | 0.848388i | \(-0.677573\pi\) | ||
0.529375 | − | 0.848388i | \(-0.322427\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.44678 | 0.138472 | 0.0692359 | − | 0.997600i | \(-0.477944\pi\) | ||||
0.0692359 | + | 0.997600i | \(0.477944\pi\) | |||||||
\(62\) | 70.0309i | 1.12953i | ||||||||
\(63\) | 22.1862 | − | 8.64716i | 0.352162 | − | 0.137256i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.02580 | + | 10.7761i | 0.0306939 | + | 0.163274i | ||||
\(67\) | −85.7646 | −1.28007 | −0.640034 | − | 0.768347i | \(-0.721080\pi\) | ||||
−0.640034 | + | 0.768347i | \(0.721080\pi\) | |||||||
\(68\) | 14.5024i | 0.213270i | ||||||||
\(69\) | −35.0435 | + | 6.58784i | −0.507877 | + | 0.0954759i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 97.8086i | − | 1.37759i | −0.724958 | − | 0.688793i | \(-0.758141\pi\) | ||
0.724958 | − | 0.688793i | \(-0.241859\pi\) | |||||||
\(72\) | −9.24420 | − | 23.7180i | −0.128392 | − | 0.329417i | ||||
\(73\) | −17.8312 | −0.244264 | −0.122132 | − | 0.992514i | \(-0.538973\pi\) | ||||
−0.122132 | + | 0.992514i | \(0.538973\pi\) | |||||||
\(74\) | 61.2295i | 0.827426i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −42.8676 | −0.564047 | ||||||||
\(77\) | − | 6.83779i | − | 0.0888025i | ||||||
\(78\) | 0.752723 | − | 0.141505i | 0.00965030 | − | 0.00181416i | ||||
\(79\) | 110.652 | 1.40066 | 0.700328 | − | 0.713821i | \(-0.253037\pi\) | ||||
0.700328 | + | 0.713821i | \(0.253037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59.6362 | − | 54.8136i | 0.736249 | − | 0.676711i | ||||
\(82\) | −29.3940 | −0.358464 | ||||||||
\(83\) | − | 3.08611i | − | 0.0371820i | −0.999827 | − | 0.0185910i | \(-0.994082\pi\) | ||
0.999827 | − | 0.0185910i | \(-0.00591804\pi\) | |||||||
\(84\) | 2.93288 | + | 15.6012i | 0.0349152 | + | 0.185729i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 104.961i | 1.22047i | ||||||||
\(87\) | −87.1115 | + | 16.3761i | −1.00128 | + | 0.188231i | ||||
\(88\) | −7.30991 | −0.0830671 | ||||||||
\(89\) | − | 80.1881i | − | 0.900990i | −0.892779 | − | 0.450495i | \(-0.851248\pi\) | ||
0.892779 | − | 0.450495i | \(-0.148752\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.477628 | −0.00524866 | ||||||||
\(92\) | − | 23.7716i | − | 0.258387i | ||||||
\(93\) | −27.4467 | − | 146.001i | −0.295125 | − | 1.56990i | ||||
\(94\) | −9.97171 | −0.106082 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 16.6784 | − | 3.13538i | 0.173733 | − | 0.0326602i | ||||
\(97\) | −105.794 | −1.09066 | −0.545328 | − | 0.838223i | \(-0.683595\pi\) | ||||
−0.545328 | + | 0.838223i | \(0.683595\pi\) | |||||||
\(98\) | − | 9.89949i | − | 0.101015i | ||||||
\(99\) | −8.44678 | − | 21.6721i | −0.0853210 | − | 0.218910i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 120.653i | 1.19459i | 0.802022 | + | 0.597294i | \(0.203757\pi\) | ||||
−0.802022 | + | 0.597294i | \(0.796243\pi\) | |||||||
\(102\) | −5.68380 | − | 30.2346i | −0.0557236 | − | 0.296417i | ||||
\(103\) | −173.031 | −1.67992 | −0.839958 | − | 0.542652i | \(-0.817420\pi\) | ||||
−0.839958 | + | 0.542652i | \(0.817420\pi\) | |||||||
\(104\) | 0.510606i | 0.00490967i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −77.8627 | −0.734554 | ||||||||
\(107\) | − | 82.1335i | − | 0.767603i | −0.923416 | − | 0.383802i | \(-0.874615\pi\) | ||
0.923416 | − | 0.383802i | \(-0.125385\pi\) | |||||||
\(108\) | 28.5679 | + | 45.8244i | 0.264518 | + | 0.424300i | ||||
\(109\) | −63.4890 | −0.582468 | −0.291234 | − | 0.956652i | \(-0.594066\pi\) | ||||
−0.291234 | + | 0.956652i | \(0.594066\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −23.9972 | − | 127.651i | −0.216191 | − | 1.15001i | ||||
\(112\) | −10.5830 | −0.0944911 | ||||||||
\(113\) | 145.494i | 1.28755i | 0.765213 | + | 0.643777i | \(0.222634\pi\) | ||||
−0.765213 | + | 0.643777i | \(0.777366\pi\) | |||||||
\(114\) | 89.3704 | − | 16.8008i | 0.783951 | − | 0.147375i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 59.0916i | − | 0.509410i | ||||||
\(117\) | −1.51382 | + | 0.590018i | −0.0129386 | + | 0.00504289i | ||||
\(118\) | −141.577 | −1.19980 | ||||||||
\(119\) | 19.1848i | 0.161217i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.321 | 0.944799 | ||||||||
\(122\) | − | 11.9456i | − | 0.0979144i | ||||||
\(123\) | 61.2807 | − | 11.5202i | 0.498217 | − | 0.0936599i | ||||
\(124\) | 99.0387 | 0.798699 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −12.2289 | − | 31.3760i | −0.0970550 | − | 0.249016i | ||||
\(127\) | −153.065 | −1.20523 | −0.602616 | − | 0.798031i | \(-0.705875\pi\) | ||||
−0.602616 | + | 0.798031i | \(0.705875\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | −41.1364 | − | 218.822i | −0.318887 | − | 1.69629i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 176.646i | 1.34844i | 0.738529 | + | 0.674222i | \(0.235521\pi\) | ||||
−0.738529 | + | 0.674222i | \(0.764479\pi\) | |||||||
\(132\) | 15.2397 | − | 2.86491i | 0.115452 | − | 0.0217039i | ||||
\(133\) | −56.7085 | −0.426380 | ||||||||
\(134\) | 121.289i | 0.905145i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 20.5095 | 0.150805 | ||||||||
\(137\) | − | 229.315i | − | 1.67383i | −0.547333 | − | 0.836915i | \(-0.684357\pi\) | ||
0.547333 | − | 0.836915i | \(-0.315643\pi\) | |||||||
\(138\) | 9.31661 | + | 49.5591i | 0.0675117 | + | 0.359124i | ||||
\(139\) | −7.93236 | −0.0570673 | −0.0285337 | − | 0.999593i | \(-0.509084\pi\) | ||||
−0.0285337 | + | 0.999593i | \(0.509084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 20.7890 | − | 3.90813i | 0.147440 | − | 0.0277173i | ||||
\(142\) | −138.322 | −0.974101 | ||||||||
\(143\) | 0.466560i | 0.00326266i | ||||||||
\(144\) | −33.5424 | + | 13.0733i | −0.232933 | + | 0.0907866i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.2172i | 0.172720i | ||||||||
\(147\) | 3.87983 | + | 20.6385i | 0.0263934 | + | 0.140398i | ||||
\(148\) | 86.5916 | 0.585078 | ||||||||
\(149\) | − | 111.886i | − | 0.750910i | −0.926841 | − | 0.375455i | \(-0.877487\pi\) | ||
0.926841 | − | 0.375455i | \(-0.122513\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −73.7503 | −0.488412 | −0.244206 | − | 0.969723i | \(-0.578527\pi\) | ||||
−0.244206 | + | 0.969723i | \(0.578527\pi\) | |||||||
\(152\) | 60.6239i | 0.398842i | ||||||||
\(153\) | 23.6992 | + | 60.8055i | 0.154897 | + | 0.397421i | ||||
\(154\) | −9.67010 | −0.0627928 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.200118 | − | 1.06451i | −0.00128281 | − | 0.00682379i | ||||
\(157\) | −52.3958 | −0.333731 | −0.166866 | − | 0.985980i | \(-0.553365\pi\) | ||||
−0.166866 | + | 0.985980i | \(0.553365\pi\) | |||||||
\(158\) | − | 156.485i | − | 0.990414i | ||||||
\(159\) | 162.328 | − | 30.5161i | 1.02093 | − | 0.191925i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 31.4469i | − | 0.195322i | ||||||
\(162\) | −77.5181 | − | 84.3383i | −0.478507 | − | 0.520607i | ||||
\(163\) | 16.9135 | 0.103764 | 0.0518819 | − | 0.998653i | \(-0.483478\pi\) | ||||
0.0518819 | + | 0.998653i | \(0.483478\pi\) | |||||||
\(164\) | 41.5694i | 0.253472i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.36442 | −0.0262917 | ||||||||
\(167\) | − | 2.03625i | − | 0.0121931i | −0.999981 | − | 0.00609657i | \(-0.998059\pi\) | ||
0.999981 | − | 0.00609657i | \(-0.00194061\pi\) | |||||||
\(168\) | 22.0635 | − | 4.14771i | 0.131330 | − | 0.0246888i | ||||
\(169\) | −168.967 | −0.999807 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −179.735 | + | 70.0525i | −1.05108 | + | 0.409664i | ||||
\(172\) | 148.437 | 0.863004 | ||||||||
\(173\) | 258.927i | 1.49669i | 0.663312 | + | 0.748343i | \(0.269150\pi\) | ||||
−0.663312 | + | 0.748343i | \(0.730850\pi\) | |||||||
\(174\) | 23.1593 | + | 123.194i | 0.133099 | + | 0.708013i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 10.3378i | 0.0587373i | ||||||||
\(177\) | 295.159 | − | 55.4870i | 1.66757 | − | 0.313486i | ||||
\(178\) | −113.403 | −0.637096 | ||||||||
\(179\) | 38.3599i | 0.214301i | 0.994243 | + | 0.107150i | \(0.0341727\pi\) | ||||
−0.994243 | + | 0.107150i | \(0.965827\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 213.719 | 1.18077 | 0.590384 | − | 0.807122i | \(-0.298976\pi\) | ||||
0.590384 | + | 0.807122i | \(0.298976\pi\) | |||||||
\(182\) | 0.675468i | 0.00371136i | ||||||||
\(183\) | 4.68173 | + | 24.9041i | 0.0255832 | + | 0.136088i | ||||
\(184\) | −33.6181 | −0.182707 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −206.476 | + | 38.8154i | −1.11009 | + | 0.208685i | ||||
\(187\) | 18.7403 | 0.100215 | ||||||||
\(188\) | 14.1021i | 0.0750113i | ||||||||
\(189\) | 37.7918 | + | 60.6199i | 0.199957 | + | 0.320740i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 245.546i | 1.28558i | 0.766043 | + | 0.642790i | \(0.222223\pi\) | ||||
−0.766043 | + | 0.642790i | \(0.777777\pi\) | |||||||
\(192\) | −4.43409 | − | 23.5868i | −0.0230942 | − | 0.122848i | ||||
\(193\) | 32.9007 | 0.170470 | 0.0852350 | − | 0.996361i | \(-0.472836\pi\) | ||||
0.0852350 | + | 0.996361i | \(0.472836\pi\) | |||||||
\(194\) | 149.615i | 0.771210i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | 219.340i | 1.11340i | 0.830714 | + | 0.556700i | \(0.187933\pi\) | ||||
−0.830714 | + | 0.556700i | \(0.812067\pi\) | |||||||
\(198\) | −30.6489 | + | 11.9456i | −0.154793 | + | 0.0603311i | ||||
\(199\) | −100.635 | −0.505703 | −0.252852 | − | 0.967505i | \(-0.581368\pi\) | ||||
−0.252852 | + | 0.967505i | \(0.581368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −47.5360 | − | 252.864i | −0.236498 | − | 1.25803i | ||||
\(202\) | 170.630 | 0.844701 | ||||||||
\(203\) | − | 78.1708i | − | 0.385078i | ||||||
\(204\) | −42.7582 | + | 8.03811i | −0.209599 | + | 0.0394025i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 244.703i | 1.18788i | ||||||||
\(207\) | −38.8466 | − | 99.6694i | −0.187665 | − | 0.481495i | ||||
\(208\) | 0.722106 | 0.00347166 | ||||||||
\(209\) | 55.3944i | 0.265045i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 119.865 | 0.568082 | 0.284041 | − | 0.958812i | \(-0.408325\pi\) | ||||
0.284041 | + | 0.958812i | \(0.408325\pi\) | |||||||
\(212\) | 110.114i | 0.519408i | ||||||||
\(213\) | 288.375 | − | 54.2116i | 1.35387 | − | 0.254514i | ||||
\(214\) | −116.154 | −0.542777 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 64.8054 | − | 40.4012i | 0.300025 | − | 0.187042i | ||||
\(217\) | 131.016 | 0.603760 | ||||||||
\(218\) | 89.7870i | 0.411867i | ||||||||
\(219\) | −9.88317 | − | 52.5728i | −0.0451286 | − | 0.240059i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.30903i | − | 0.00592322i | ||||||
\(222\) | −180.526 | + | 33.9372i | −0.813182 | + | 0.152870i | ||||
\(223\) | 315.561 | 1.41507 | 0.707536 | − | 0.706677i | \(-0.249807\pi\) | ||||
0.707536 | + | 0.706677i | \(0.249807\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 205.759 | 0.910438 | ||||||||
\(227\) | 315.509i | 1.38991i | 0.719054 | + | 0.694954i | \(0.244575\pi\) | ||||
−0.719054 | + | 0.694954i | \(0.755425\pi\) | |||||||
\(228\) | −23.7599 | − | 126.389i | −0.104210 | − | 0.554337i | ||||
\(229\) | −66.8556 | −0.291946 | −0.145973 | − | 0.989289i | \(-0.546631\pi\) | ||||
−0.145973 | + | 0.989289i | \(0.546631\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 20.1602 | − | 3.78992i | 0.0872737 | − | 0.0164066i | ||||
\(232\) | −83.5681 | −0.360207 | ||||||||
\(233\) | − | 301.826i | − | 1.29539i | −0.761900 | − | 0.647695i | \(-0.775733\pi\) | ||
0.761900 | − | 0.647695i | \(-0.224267\pi\) | |||||||
\(234\) | 0.834411 | + | 2.14086i | 0.00356586 | + | 0.00914899i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 200.220i | 0.848388i | ||||||||
\(237\) | 61.3301 | + | 326.241i | 0.258777 | + | 1.37654i | ||||
\(238\) | 27.1315 | 0.113998 | ||||||||
\(239\) | 241.028i | 1.00849i | 0.863562 | + | 0.504243i | \(0.168229\pi\) | ||||
−0.863562 | + | 0.504243i | \(0.831771\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −196.843 | −0.816775 | −0.408388 | − | 0.912809i | \(-0.633909\pi\) | ||||
−0.408388 | + | 0.912809i | \(0.633909\pi\) | |||||||
\(242\) | − | 161.674i | − | 0.668074i | ||||||
\(243\) | 194.664 | + | 145.448i | 0.801086 | + | 0.598550i | ||||
\(244\) | −16.8936 | −0.0692359 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −16.2920 | − | 86.6640i | −0.0662275 | − | 0.352293i | ||||
\(247\) | 3.86937 | 0.0156654 | ||||||||
\(248\) | − | 140.062i | − | 0.564766i | ||||||
\(249\) | 9.09894 | − | 1.71051i | 0.0365419 | − | 0.00686952i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 349.301i | 1.39164i | 0.718217 | + | 0.695819i | \(0.244959\pi\) | ||||
−0.718217 | + | 0.695819i | \(0.755041\pi\) | |||||||
\(252\) | −44.3724 | + | 17.2943i | −0.176081 | + | 0.0686282i | ||||
\(253\) | −30.7182 | −0.121416 | ||||||||
\(254\) | 216.466i | 0.852228i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | − | 4.18732i | − | 0.0162931i | −0.999967 | − | 0.00814653i | \(-0.997407\pi\) | ||
0.999967 | − | 0.00814653i | \(-0.00259315\pi\) | |||||||
\(258\) | −309.461 | + | 58.1756i | −1.19946 | + | 0.225487i | ||||
\(259\) | 114.550 | 0.442278 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −96.5651 | − | 247.759i | −0.369981 | − | 0.949267i | ||||
\(262\) | 249.815 | 0.953493 | ||||||||
\(263\) | − | 268.485i | − | 1.02086i | −0.859921 | − | 0.510428i | \(-0.829487\pi\) | ||
0.859921 | − | 0.510428i | \(-0.170513\pi\) | |||||||
\(264\) | −4.05160 | − | 21.5522i | −0.0153470 | − | 0.0816371i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 80.1979i | 0.301496i | ||||||||
\(267\) | 236.423 | − | 44.4452i | 0.885479 | − | 0.166461i | ||||
\(268\) | 171.529 | 0.640034 | ||||||||
\(269\) | 59.1206i | 0.219779i | 0.993944 | + | 0.109890i | \(0.0350497\pi\) | ||||
−0.993944 | + | 0.109890i | \(0.964950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −206.348 | −0.761433 | −0.380717 | − | 0.924692i | \(-0.624323\pi\) | ||||
−0.380717 | + | 0.924692i | \(0.624323\pi\) | |||||||
\(272\) | − | 29.0048i | − | 0.106635i | ||||||
\(273\) | −0.264731 | − | 1.40822i | −0.000969710 | − | 0.00515830i | ||||
\(274\) | −324.300 | −1.18358 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 70.0871 | − | 13.1757i | 0.253939 | − | 0.0477380i | ||||
\(277\) | 370.482 | 1.33748 | 0.668740 | − | 0.743496i | \(-0.266834\pi\) | ||||
0.668740 | + | 0.743496i | \(0.266834\pi\) | |||||||
\(278\) | 11.2180i | 0.0403527i | ||||||||
\(279\) | 415.249 | − | 161.845i | 1.48835 | − | 0.580090i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 71.0258i | 0.252761i | 0.991982 | + | 0.126380i | \(0.0403360\pi\) | ||||
−0.991982 | + | 0.126380i | \(0.959664\pi\) | |||||||
\(282\) | −5.52693 | − | 29.4001i | −0.0195991 | − | 0.104256i | ||||
\(283\) | −255.816 | −0.903944 | −0.451972 | − | 0.892032i | \(-0.649279\pi\) | ||||
−0.451972 | + | 0.892032i | \(0.649279\pi\) | |||||||
\(284\) | 195.617i | 0.688793i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.659816 | 0.00230705 | ||||||||
\(287\) | 54.9912i | 0.191607i | ||||||||
\(288\) | 18.4884 | + | 47.4361i | 0.0641958 | + | 0.164709i | ||||
\(289\) | 236.420 | 0.818063 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −58.6373 | − | 311.917i | −0.201503 | − | 1.07188i | ||||
\(292\) | 35.6625 | 0.122132 | ||||||||
\(293\) | 162.409i | 0.554297i | 0.960827 | + | 0.277148i | \(0.0893894\pi\) | ||||
−0.960827 | + | 0.277148i | \(0.910611\pi\) | |||||||
\(294\) | 29.1872 | − | 5.48691i | 0.0992763 | − | 0.0186630i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 122.459i | − | 0.413713i | ||||||
\(297\) | 59.2152 | − | 36.9161i | 0.199378 | − | 0.124297i | ||||
\(298\) | −158.230 | −0.530973 | ||||||||
\(299\) | 2.14570i | 0.00717625i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 196.363 | 0.652370 | ||||||||
\(302\) | 104.299i | 0.345360i | ||||||||
\(303\) | −355.729 | + | 66.8735i | −1.17402 | + | 0.220705i | ||||
\(304\) | 85.7352 | 0.282024 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 85.9919 | − | 33.5157i | 0.281019 | − | 0.109529i | ||||
\(307\) | −532.774 | −1.73542 | −0.867709 | − | 0.497072i | \(-0.834408\pi\) | ||||
−0.867709 | + | 0.497072i | \(0.834408\pi\) | |||||||
\(308\) | 13.6756i | 0.0444012i | ||||||||
\(309\) | −95.9046 | − | 510.158i | −0.310371 | − | 1.65100i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 353.139i | − | 1.13549i | −0.823203 | − | 0.567747i | \(-0.807815\pi\) | ||
0.823203 | − | 0.567747i | \(-0.192185\pi\) | |||||||
\(312\) | −1.50545 | + | 0.283009i | −0.00482515 | + | 0.000907081i | ||||
\(313\) | −113.835 | −0.363689 | −0.181845 | − | 0.983327i | \(-0.558207\pi\) | ||||
−0.181845 | + | 0.983327i | \(0.558207\pi\) | |||||||
\(314\) | 74.0989i | 0.235984i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −221.304 | −0.700328 | ||||||||
\(317\) | − | 73.1423i | − | 0.230733i | −0.993323 | − | 0.115366i | \(-0.963196\pi\) | ||
0.993323 | − | 0.115366i | \(-0.0368042\pi\) | |||||||
\(318\) | −43.1563 | − | 229.567i | −0.135712 | − | 0.721908i | ||||
\(319\) | −76.3594 | −0.239371 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 242.159 | − | 45.5235i | 0.754389 | − | 0.141818i | ||||
\(322\) | −44.4726 | −0.138114 | ||||||||
\(323\) | − | 155.420i | − | 0.481178i | ||||||
\(324\) | −119.272 | + | 109.627i | −0.368125 | + | 0.338355i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 23.9193i | − | 0.0733720i | ||||||
\(327\) | −35.1895 | − | 187.188i | −0.107613 | − | 0.572441i | ||||
\(328\) | 58.7880 | 0.179232 | ||||||||
\(329\) | 18.6554i | 0.0567032i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −244.549 | −0.738818 | −0.369409 | − | 0.929267i | \(-0.620440\pi\) | ||||
−0.369409 | + | 0.929267i | \(0.620440\pi\) | |||||||
\(332\) | 6.17222i | 0.0185910i | ||||||||
\(333\) | 363.061 | − | 141.505i | 1.09027 | − | 0.424938i | ||||
\(334\) | −2.87970 | −0.00862185 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −5.86575 | − | 31.2025i | −0.0174576 | − | 0.0928644i | ||||
\(337\) | 360.620 | 1.07009 | 0.535045 | − | 0.844824i | \(-0.320295\pi\) | ||||
0.535045 | + | 0.844824i | \(0.320295\pi\) | |||||||
\(338\) | 238.956i | 0.706970i | ||||||||
\(339\) | −428.967 | + | 80.6415i | −1.26539 | + | 0.237881i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 127.980i | − | 0.375308i | ||||||
\(342\) | 99.0692 | + | 254.184i | 0.289676 | + | 0.743227i | ||||
\(343\) | −18.5203 | −0.0539949 | ||||||||
\(344\) | − | 209.921i | − | 0.610236i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 366.178 | 1.05832 | ||||||||
\(347\) | − | 320.079i | − | 0.922417i | −0.887292 | − | 0.461209i | \(-0.847416\pi\) | ||
0.887292 | − | 0.461209i | \(-0.152584\pi\) | |||||||
\(348\) | 174.223 | − | 32.7522i | 0.500641 | − | 0.0941155i | ||||
\(349\) | 656.250 | 1.88037 | 0.940187 | − | 0.340660i | \(-0.110650\pi\) | ||||
0.940187 | + | 0.340660i | \(0.110650\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.57863 | − | 4.13625i | −0.00734654 | − | 0.0117842i | ||||
\(352\) | 14.6198 | 0.0415336 | ||||||||
\(353\) | 307.348i | 0.870673i | 0.900268 | + | 0.435337i | \(0.143371\pi\) | ||||
−0.900268 | + | 0.435337i | \(0.856629\pi\) | |||||||
\(354\) | −78.4705 | − | 417.418i | −0.221668 | − | 1.17915i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 160.376i | 0.450495i | ||||||||
\(357\) | −56.5637 | + | 10.6334i | −0.158442 | + | 0.0297855i | ||||
\(358\) | 54.2490 | 0.151534 | ||||||||
\(359\) | − | 149.072i | − | 0.415244i | −0.978209 | − | 0.207622i | \(-0.933428\pi\) | ||
0.978209 | − | 0.207622i | \(-0.0665723\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 98.4076 | 0.272597 | ||||||||
\(362\) | − | 302.245i | − | 0.834930i | ||||||
\(363\) | 63.3635 | + | 337.058i | 0.174555 | + | 0.928534i | ||||
\(364\) | 0.955256 | 0.00262433 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 35.2197 | − | 6.62096i | 0.0962287 | − | 0.0180901i | ||||
\(367\) | 394.930 | 1.07610 | 0.538052 | − | 0.842912i | \(-0.319160\pi\) | ||||
0.538052 | + | 0.842912i | \(0.319160\pi\) | |||||||
\(368\) | 47.5432i | 0.129193i | ||||||||
\(369\) | 67.9311 | + | 174.292i | 0.184095 | + | 0.472336i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 145.668i | 0.392635i | ||||||||
\(372\) | 54.8933 | + | 292.001i | 0.147563 | + | 0.784949i | ||||
\(373\) | 567.874 | 1.52245 | 0.761225 | − | 0.648488i | \(-0.224598\pi\) | ||||
0.761225 | + | 0.648488i | \(0.224598\pi\) | |||||||
\(374\) | − | 26.5028i | − | 0.0708630i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 19.9434 | 0.0530410 | ||||||||
\(377\) | 5.33379i | 0.0141480i | ||||||||
\(378\) | 85.7295 | − | 53.4457i | 0.226798 | − | 0.141391i | ||||
\(379\) | −641.443 | −1.69246 | −0.846230 | − | 0.532817i | \(-0.821133\pi\) | ||||
−0.846230 | + | 0.532817i | \(0.821133\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −84.8378 | − | 451.289i | −0.222671 | − | 1.18448i | ||||
\(382\) | 347.254 | 0.909042 | ||||||||
\(383\) | 340.090i | 0.887963i | 0.896036 | + | 0.443982i | \(0.146434\pi\) | ||||
−0.896036 | + | 0.443982i | \(0.853566\pi\) | |||||||
\(384\) | −33.3568 | + | 6.27075i | −0.0868667 | + | 0.0163301i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 46.5286i | − | 0.120541i | ||||||
\(387\) | 622.365 | − | 242.569i | 1.60818 | − | 0.626794i | ||||
\(388\) | 211.587 | 0.545328 | ||||||||
\(389\) | − | 432.582i | − | 1.11204i | −0.831170 | − | 0.556018i | \(-0.812328\pi\) | ||
0.831170 | − | 0.556018i | \(-0.187672\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 86.1862 | 0.220425 | ||||||||
\(392\) | 19.7990i | 0.0505076i | ||||||||
\(393\) | −520.815 | + | 97.9081i | −1.32523 | + | 0.249130i | ||||
\(394\) | 310.193 | 0.787292 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.8936 | + | 43.3441i | 0.0426605 | + | 0.109455i | ||||
\(397\) | 471.352 | 1.18728 | 0.593642 | − | 0.804729i | \(-0.297690\pi\) | ||||
0.593642 | + | 0.804729i | \(0.297690\pi\) | |||||||
\(398\) | 142.319i | 0.357586i | ||||||||
\(399\) | −31.4313 | − | 167.197i | −0.0787753 | − | 0.419039i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 180.124i | − | 0.449186i | −0.974453 | − | 0.224593i | \(-0.927895\pi\) | ||
0.974453 | − | 0.224593i | \(-0.0721053\pi\) | |||||||
\(402\) | −357.604 | + | 67.2261i | −0.889563 | + | 0.167229i | ||||
\(403\) | −8.93955 | −0.0221825 | ||||||||
\(404\) | − | 241.307i | − | 0.597294i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −110.550 | −0.272291 | ||||||||
\(407\) | − | 111.896i | − | 0.274928i | ||||||
\(408\) | 11.3676 | + | 60.4692i | 0.0278618 | + | 0.148209i | ||||
\(409\) | −259.241 | −0.633842 | −0.316921 | − | 0.948452i | \(-0.602649\pi\) | ||||
−0.316921 | + | 0.948452i | \(0.602649\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 676.101 | − | 127.100i | 1.64501 | − | 0.309246i | ||||
\(412\) | 346.063 | 0.839958 | ||||||||
\(413\) | 264.866i | 0.641321i | ||||||||
\(414\) | −140.954 | + | 54.9374i | −0.340468 | + | 0.132699i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 1.02121i | − | 0.00245484i | ||||||
\(417\) | −4.39660 | − | 23.3874i | −0.0105434 | − | 0.0560849i | ||||
\(418\) | 78.3395 | 0.187415 | ||||||||
\(419\) | 146.134i | 0.348769i | 0.984678 | + | 0.174384i | \(0.0557935\pi\) | ||||
−0.984678 | + | 0.174384i | \(0.944207\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −599.808 | −1.42472 | −0.712361 | − | 0.701813i | \(-0.752374\pi\) | ||||
−0.712361 | + | 0.701813i | \(0.752374\pi\) | |||||||
\(422\) | − | 169.515i | − | 0.401695i | ||||||
\(423\) | 23.0451 | + | 59.1273i | 0.0544802 | + | 0.139781i | ||||
\(424\) | 155.725 | 0.367277 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −76.6667 | − | 407.823i | −0.179969 | − | 0.957331i | ||||
\(427\) | −22.3481 | −0.0523374 | ||||||||
\(428\) | 164.267i | 0.383802i | ||||||||
\(429\) | −1.37558 | + | 0.258596i | −0.00320649 | + | 0.000602789i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 825.631i | 1.91562i | 0.287409 | + | 0.957808i | \(0.407206\pi\) | ||||
−0.287409 | + | 0.957808i | \(0.592794\pi\) | |||||||
\(432\) | −57.1359 | − | 91.6487i | −0.132259 | − | 0.212150i | ||||
\(433\) | 185.307 | 0.427962 | 0.213981 | − | 0.976838i | \(-0.431357\pi\) | ||||
0.213981 | + | 0.976838i | \(0.431357\pi\) | |||||||
\(434\) | − | 185.284i | − | 0.426923i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 126.978 | 0.291234 | ||||||||
\(437\) | 254.758i | 0.582970i | ||||||||
\(438\) | −74.3492 | + | 13.9769i | −0.169747 | + | 0.0319108i | ||||
\(439\) | 809.103 | 1.84306 | 0.921529 | − | 0.388309i | \(-0.126941\pi\) | ||||
0.921529 | + | 0.388309i | \(0.126941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −58.6991 | + | 22.8782i | −0.133105 | + | 0.0518781i | ||||
\(442\) | −1.85125 | −0.00418835 | ||||||||
\(443\) | − | 449.922i | − | 1.01563i | −0.861467 | − | 0.507813i | \(-0.830454\pi\) | ||
0.861467 | − | 0.507813i | \(-0.169546\pi\) | |||||||
\(444\) | 47.9944 | + | 255.303i | 0.108095 | + | 0.575006i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 446.271i | − | 1.00061i | ||||||
\(447\) | 329.878 | − | 62.0138i | 0.737983 | − | 0.138733i | ||||
\(448\) | 21.1660 | 0.0472456 | ||||||||
\(449\) | − | 676.008i | − | 1.50559i | −0.658257 | − | 0.752793i | \(-0.728706\pi\) | ||
0.658257 | − | 0.752793i | \(-0.271294\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 53.7169 | 0.119106 | ||||||||
\(452\) | − | 290.987i | − | 0.643777i | ||||||
\(453\) | −40.8769 | − | 217.442i | −0.0902361 | − | 0.480004i | ||||
\(454\) | 446.198 | 0.982814 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −178.741 | + | 33.6015i | −0.391975 | + | 0.0736875i | ||||
\(457\) | −588.327 | −1.28737 | −0.643683 | − | 0.765292i | \(-0.722595\pi\) | ||||
−0.643683 | + | 0.765292i | \(0.722595\pi\) | |||||||
\(458\) | 94.5481i | 0.206437i | ||||||||
\(459\) | −166.141 | + | 103.576i | −0.361962 | + | 0.225655i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 344.268i | − | 0.746785i | −0.927673 | − | 0.373393i | \(-0.878194\pi\) | ||
0.927673 | − | 0.373393i | \(-0.121806\pi\) | |||||||
\(462\) | −5.35976 | − | 28.5109i | −0.0116012 | − | 0.0617119i | ||||
\(463\) | 220.223 | 0.475643 | 0.237821 | − | 0.971309i | \(-0.423567\pi\) | ||||
0.237821 | + | 0.971309i | \(0.423567\pi\) | |||||||
\(464\) | 118.183i | 0.254705i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −426.846 | −0.915978 | ||||||||
\(467\) | 595.502i | 1.27516i | 0.770382 | + | 0.637582i | \(0.220065\pi\) | ||||
−0.770382 | + | 0.637582i | \(0.779935\pi\) | |||||||
\(468\) | 3.02764 | − | 1.18004i | 0.00646932 | − | 0.00252144i | ||||
\(469\) | 226.912 | 0.483820 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −29.0410 | − | 154.481i | −0.0616581 | − | 0.327986i | ||||
\(472\) | 283.153 | 0.599901 | ||||||||
\(473\) | − | 191.813i | − | 0.405524i | ||||||
\(474\) | 461.374 | − | 86.7338i | 0.973364 | − | 0.182983i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 38.3697i | − | 0.0806086i | ||||||
\(477\) | 179.945 | + | 461.687i | 0.377242 | + | 0.967898i | ||||
\(478\) | 340.865 | 0.713108 | ||||||||
\(479\) | 710.354i | 1.48299i | 0.670956 | + | 0.741497i | \(0.265884\pi\) | ||||
−0.670956 | + | 0.741497i | \(0.734116\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.81604 | −0.0162496 | ||||||||
\(482\) | 278.378i | 0.577547i | ||||||||
\(483\) | 92.7165 | − | 17.4298i | 0.191960 | − | 0.0360865i | ||||
\(484\) | −228.641 | −0.472399 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 205.694 | − | 275.296i | 0.423239 | − | 0.566453i | ||||
\(487\) | −325.987 | −0.669378 | −0.334689 | − | 0.942329i | \(-0.608631\pi\) | ||||
−0.334689 | + | 0.942329i | \(0.608631\pi\) | |||||||
\(488\) | 23.8911i | 0.0489572i | ||||||||
\(489\) | 9.37450 | + | 49.8670i | 0.0191708 | + | 0.101977i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 573.407i | 1.16784i | 0.811813 | + | 0.583918i | \(0.198481\pi\) | ||||
−0.811813 | + | 0.583918i | \(0.801519\pi\) | |||||||
\(492\) | −122.561 | + | 23.0403i | −0.249108 | + | 0.0468299i | ||||
\(493\) | 214.242 | 0.434568 | ||||||||
\(494\) | − | 5.47211i | − | 0.0110771i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −198.077 | −0.399350 | ||||||||
\(497\) | 258.777i | 0.520679i | ||||||||
\(498\) | −2.41903 | − | 12.8678i | −0.00485749 | − | 0.0258390i | ||||
\(499\) | −410.671 | −0.822989 | −0.411494 | − | 0.911412i | \(-0.634993\pi\) | ||||
−0.411494 | + | 0.911412i | \(0.634993\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6.00360 | − | 1.12862i | 0.0119832 | − | 0.00225273i | ||||
\(502\) | 493.987 | 0.984037 | ||||||||
\(503\) | − | 903.370i | − | 1.79596i | −0.440032 | − | 0.897982i | \(-0.645033\pi\) | ||
0.440032 | − | 0.897982i | \(-0.354967\pi\) | |||||||
\(504\) | 24.4579 | + | 62.7520i | 0.0485275 | + | 0.124508i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 43.4420i | 0.0858538i | ||||||||
\(507\) | −93.6521 | − | 498.176i | −0.184718 | − | 0.982595i | ||||
\(508\) | 306.129 | 0.602616 | ||||||||
\(509\) | 323.535i | 0.635628i | 0.948153 | + | 0.317814i | \(0.102949\pi\) | ||||
−0.948153 | + | 0.317814i | \(0.897051\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 47.1770 | 0.0923230 | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −306.160 | − | 491.095i | −0.596803 | − | 0.957300i | ||||
\(514\) | −5.92176 | −0.0115209 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 82.2728 | + | 437.644i | 0.159443 | + | 0.848147i | ||||
\(517\) | 18.2231 | 0.0352477 | ||||||||
\(518\) | − | 161.998i | − | 0.312738i | ||||||
\(519\) | −763.408 | + | 143.513i | −1.47092 | + | 0.276519i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 687.287i | − | 1.31917i | −0.751631 | − | 0.659584i | \(-0.770732\pi\) | ||
0.751631 | − | 0.659584i | \(-0.229268\pi\) | |||||||
\(522\) | −350.384 | + | 136.564i | −0.671233 | + | 0.261616i | ||||
\(523\) | −760.416 | −1.45395 | −0.726975 | − | 0.686664i | \(-0.759074\pi\) | ||||
−0.726975 | + | 0.686664i | \(0.759074\pi\) | |||||||
\(524\) | − | 353.292i | − | 0.674222i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −379.695 | −0.721854 | ||||||||
\(527\) | 359.074i | 0.681355i | ||||||||
\(528\) | −30.4794 | + | 5.72983i | −0.0577262 | + | 0.0108519i | ||||
\(529\) | 387.728 | 0.732945 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 327.191 | + | 839.480i | 0.616179 | + | 1.58094i | ||||
\(532\) | 113.417 | 0.213190 | ||||||||
\(533\) | − | 3.75219i | − | 0.00703975i | ||||||
\(534\) | −62.8550 | − | 334.353i | −0.117706 | − | 0.626128i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 242.579i | − | 0.452572i | ||||||
\(537\) | −113.098 | + | 21.2614i | −0.210612 | + | 0.0395929i | ||||
\(538\) | 83.6091 | 0.155407 | ||||||||
\(539\) | 18.0911i | 0.0335642i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 472.370 | 0.873142 | 0.436571 | − | 0.899670i | \(-0.356193\pi\) | ||||
0.436571 | + | 0.899670i | \(0.356193\pi\) | |||||||
\(542\) | 291.821i | 0.538415i | ||||||||
\(543\) | 118.456 | + | 630.120i | 0.218152 | + | 1.16044i | ||||
\(544\) | −41.0189 | −0.0754024 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.99152 | + | 0.374386i | −0.00364747 | + | 0.000685688i | ||||
\(547\) | −536.508 | −0.980818 | −0.490409 | − | 0.871492i | \(-0.663153\pi\) | ||||
−0.490409 | + | 0.871492i | \(0.663153\pi\) | |||||||
\(548\) | 458.629i | 0.836915i | ||||||||
\(549\) | −70.8312 | + | 27.6068i | −0.129019 | + | 0.0502856i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 633.278i | 1.14933i | ||||||||
\(552\) | −18.6332 | − | 99.1181i | −0.0337558 | − | 0.179562i | ||||
\(553\) | −292.757 | −0.529398 | ||||||||
\(554\) | − | 523.941i | − | 0.945741i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.8647 | 0.0285337 | ||||||||
\(557\) | − | 288.061i | − | 0.517165i | −0.965989 | − | 0.258583i | \(-0.916745\pi\) | ||
0.965989 | − | 0.258583i | \(-0.0832554\pi\) | |||||||
\(558\) | −228.883 | − | 587.250i | −0.410185 | − | 1.05242i | ||||
\(559\) | −13.3984 | −0.0239685 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10.3870 | + | 55.2530i | 0.0185152 | + | 0.0984902i | ||||
\(562\) | 100.446 | 0.178729 | ||||||||
\(563\) | 16.4938i | 0.0292963i | 0.999893 | + | 0.0146482i | \(0.00466282\pi\) | ||||
−0.999893 | + | 0.0146482i | \(0.995337\pi\) | |||||||
\(564\) | −41.5781 | + | 7.81627i | −0.0737200 | + | 0.0138586i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 361.779i | 0.639185i | ||||||||
\(567\) | −157.783 | + | 145.023i | −0.278276 | + | 0.255773i | ||||
\(568\) | 276.645 | 0.487050 | ||||||||
\(569\) | 1076.66i | 1.89219i | 0.323889 | + | 0.946095i | \(0.395009\pi\) | ||||
−0.323889 | + | 0.946095i | \(0.604991\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1009.39 | 1.76775 | 0.883876 | − | 0.467721i | \(-0.154925\pi\) | ||||
0.883876 | + | 0.467721i | \(0.154925\pi\) | |||||||
\(572\) | − | 0.933120i | − | 0.00163133i | ||||||
\(573\) | −723.956 | + | 136.097i | −1.26345 | + | 0.237516i | ||||
\(574\) | 77.7693 | 0.135487 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 67.0847 | − | 26.1466i | 0.116467 | − | 0.0453933i | ||||
\(577\) | −901.098 | −1.56169 | −0.780847 | − | 0.624722i | \(-0.785212\pi\) | ||||
−0.780847 | + | 0.624722i | \(0.785212\pi\) | |||||||
\(578\) | − | 334.349i | − | 0.578458i | ||||||
\(579\) | 18.2356 | + | 97.0030i | 0.0314950 | + | 0.167535i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.16507i | 0.0140535i | ||||||||
\(582\) | −441.117 | + | 82.9257i | −0.757933 | + | 0.142484i | ||||
\(583\) | 142.292 | 0.244069 | ||||||||
\(584\) | − | 50.4344i | − | 0.0863602i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 229.681 | 0.391947 | ||||||||
\(587\) | 265.739i | 0.452707i | 0.974045 | + | 0.226354i | \(0.0726805\pi\) | ||||
−0.974045 | + | 0.226354i | \(0.927319\pi\) | |||||||
\(588\) | −7.75966 | − | 41.2770i | −0.0131967 | − | 0.0701989i | ||||
\(589\) | −1061.39 | −1.80202 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −646.691 | + | 121.572i | −1.09423 | + | 0.205705i | ||||
\(592\) | −173.183 | −0.292539 | ||||||||
\(593\) | − | 548.447i | − | 0.924869i | −0.886653 | − | 0.462435i | \(-0.846976\pi\) | ||
0.886653 | − | 0.462435i | \(-0.153024\pi\) | |||||||
\(594\) | −52.2073 | − | 83.7430i | −0.0878910 | − | 0.140981i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 223.771i | 0.375455i | ||||||||
\(597\) | −55.7781 | − | 296.708i | −0.0934306 | − | 0.496998i | ||||
\(598\) | 3.03448 | 0.00507438 | ||||||||
\(599\) | − | 237.976i | − | 0.397289i | −0.980072 | − | 0.198644i | \(-0.936346\pi\) | ||
0.980072 | − | 0.198644i | \(-0.0636538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −566.317 | −0.942291 | −0.471146 | − | 0.882055i | \(-0.656159\pi\) | ||||
−0.471146 | + | 0.882055i | \(0.656159\pi\) | |||||||
\(602\) | − | 277.700i | − | 0.461295i | ||||||
\(603\) | 719.186 | − | 280.306i | 1.19268 | − | 0.464852i | ||||
\(604\) | 147.501 | 0.244206 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 94.5734 | + | 503.077i | 0.156062 | + | 0.830159i | ||||
\(607\) | −60.4291 | −0.0995537 | −0.0497769 | − | 0.998760i | \(-0.515851\pi\) | ||||
−0.0497769 | + | 0.998760i | \(0.515851\pi\) | |||||||
\(608\) | − | 121.248i | − | 0.199421i | ||||||
\(609\) | 230.475 | − | 43.3271i | 0.378449 | − | 0.0711446i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 1.27290i | − | 0.00208331i | ||||||
\(612\) | −47.3984 | − | 121.611i | −0.0774484 | − | 0.198711i | ||||
\(613\) | −307.983 | −0.502419 | −0.251210 | − | 0.967933i | \(-0.580828\pi\) | ||||
−0.251210 | + | 0.967933i | \(0.580828\pi\) | |||||||
\(614\) | 753.456i | 1.22713i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.3402 | 0.0313964 | ||||||||
\(617\) | − | 780.226i | − | 1.26455i | −0.774745 | − | 0.632274i | \(-0.782122\pi\) | ||
0.774745 | − | 0.632274i | \(-0.217878\pi\) | |||||||
\(618\) | −721.472 | + | 135.630i | −1.16743 | + | 0.219465i | ||||
\(619\) | −838.604 | −1.35477 | −0.677386 | − | 0.735627i | \(-0.736887\pi\) | ||||
−0.677386 | + | 0.735627i | \(0.736887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 272.330 | − | 169.776i | 0.438534 | − | 0.273392i | ||||
\(622\) | −499.413 | −0.802916 | ||||||||
\(623\) | 212.158i | 0.340542i | ||||||||
\(624\) | 0.400235 | + | 2.12902i | 0.000641403 | + | 0.00341190i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 160.987i | 0.257167i | ||||||||
\(627\) | −163.322 | + | 30.7030i | −0.260482 | + | 0.0489681i | ||||
\(628\) | 104.792 | 0.166866 | ||||||||
\(629\) | 313.946i | 0.499119i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −433.178 | −0.686494 | −0.343247 | − | 0.939245i | \(-0.611527\pi\) | ||||
−0.343247 | + | 0.939245i | \(0.611527\pi\) | |||||||
\(632\) | 312.971i | 0.495207i | ||||||||
\(633\) | 66.4368 | + | 353.406i | 0.104955 | + | 0.558303i | ||||
\(634\) | −103.439 | −0.163153 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −324.656 | + | 61.0322i | −0.510466 | + | 0.0959626i | ||||
\(637\) | 1.26368 | 0.00198381 | ||||||||
\(638\) | 107.988i | 0.169261i | ||||||||
\(639\) | 319.670 | + | 820.183i | 0.500266 | + | 1.28354i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 571.035i | 0.890850i | 0.895319 | + | 0.445425i | \(0.146947\pi\) | ||||
−0.895319 | + | 0.445425i | \(0.853053\pi\) | |||||||
\(642\) | −64.3799 | − | 342.464i | −0.100280 | − | 0.533433i | ||||
\(643\) | −194.578 | −0.302609 | −0.151304 | − | 0.988487i | \(-0.548347\pi\) | ||||
−0.151304 | + | 0.988487i | \(0.548347\pi\) | |||||||
\(644\) | 62.8937i | 0.0976611i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −219.798 | −0.340244 | ||||||||
\(647\) | 432.986i | 0.669220i | 0.942357 | + | 0.334610i | \(0.108605\pi\) | ||||
−0.942357 | + | 0.334610i | \(0.891395\pi\) | |||||||
\(648\) | 155.036 | + | 168.677i | 0.239253 | + | 0.260303i | ||||
\(649\) | 258.728 | 0.398656 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 72.6171 | + | 386.281i | 0.111547 | + | 0.593366i | ||||
\(652\) | −33.8270 | −0.0518819 | ||||||||
\(653\) | 870.907i | 1.33370i | 0.745192 | + | 0.666850i | \(0.232358\pi\) | ||||
−0.745192 | + | 0.666850i | \(0.767642\pi\) | |||||||
\(654\) | −264.724 | + | 49.7655i | −0.404777 | + | 0.0760940i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 83.1388i | − | 0.126736i | ||||||
\(657\) | 149.525 | − | 58.2782i | 0.227588 | − | 0.0887035i | ||||
\(658\) | 26.3827 | 0.0400952 | ||||||||
\(659\) | 95.3946i | 0.144757i | 0.997377 | + | 0.0723783i | \(0.0230589\pi\) | ||||
−0.997377 | + | 0.0723783i | \(0.976941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −532.252 | −0.805222 | −0.402611 | − | 0.915371i | \(-0.631897\pi\) | ||||
−0.402611 | + | 0.915371i | \(0.631897\pi\) | |||||||
\(662\) | 345.844i | 0.522423i | ||||||||
\(663\) | 3.85949 | − | 0.725546i | 0.00582125 | − | 0.00109434i | ||||
\(664\) | 8.72883 | 0.0131458 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −200.118 | − | 513.446i | −0.300477 | − | 0.770939i | ||||
\(667\) | −351.175 | −0.526500 | ||||||||
\(668\) | 4.07251i | 0.00609657i | ||||||||
\(669\) | 174.903 | + | 930.386i | 0.261440 | + | 1.39071i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 21.8302i | 0.0325339i | ||||||||
\(672\) | −44.1269 | + | 8.29543i | −0.0656651 | + | 0.0123444i | ||||
\(673\) | −256.746 | −0.381494 | −0.190747 | − | 0.981639i | \(-0.561091\pi\) | ||||
−0.190747 | + | 0.981639i | \(0.561091\pi\) | |||||||
\(674\) | − | 509.994i | − | 0.756667i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 337.935 | 0.499904 | ||||||||
\(677\) | − | 962.182i | − | 1.42124i | −0.703574 | − | 0.710622i | \(-0.748414\pi\) | ||
0.703574 | − | 0.710622i | \(-0.251586\pi\) | |||||||
\(678\) | 114.044 | + | 606.651i | 0.168207 | + | 0.894765i | ||||
\(679\) | 279.903 | 0.412229 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −930.233 | + | 174.875i | −1.36598 | + | 0.256791i | ||||
\(682\) | −180.991 | −0.265383 | ||||||||
\(683\) | 981.986i | 1.43775i | 0.695137 | + | 0.718877i | \(0.255344\pi\) | ||||
−0.695137 | + | 0.718877i | \(0.744656\pi\) | |||||||
\(684\) | 359.470 | − | 140.105i | 0.525541 | − | 0.204832i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916i | 0.0381802i | ||||||||
\(687\) | −37.0555 | − | 197.114i | −0.0539381 | − | 0.286920i | ||||
\(688\) | −296.873 | −0.431502 | ||||||||
\(689\) | − | 9.93928i | − | 0.0144257i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −38.5649 | −0.0558103 | −0.0279052 | − | 0.999611i | \(-0.508884\pi\) | ||||
−0.0279052 | + | 0.999611i | \(0.508884\pi\) | |||||||
\(692\) | − | 517.853i | − | 0.748343i | ||||||
\(693\) | 22.3481 | + | 57.3389i | 0.0322483 | + | 0.0827401i | ||||
\(694\) | −452.660 | −0.652247 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −46.3186 | − | 246.388i | −0.0665497 | − | 0.354006i | ||||
\(697\) | −150.714 | −0.216232 | ||||||||
\(698\) | − | 928.078i | − | 1.32962i | ||||||
\(699\) | 889.889 | − | 167.290i | 1.27309 | − | 0.239328i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 301.635i | − | 0.430293i | −0.976582 | − | 0.215146i | \(-0.930977\pi\) | ||
0.976582 | − | 0.215146i | \(-0.0690228\pi\) | |||||||
\(702\) | −5.84955 | + | 3.64674i | −0.00833269 | + | 0.00519478i | ||||
\(703\) | −927.993 | −1.32005 | ||||||||
\(704\) | − | 20.6755i | − | 0.0293687i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 434.655 | 0.615659 | ||||||||
\(707\) | − | 319.219i | − | 0.451512i | ||||||
\(708\) | −590.318 | + | 110.974i | −0.833783 | + | 0.156743i | ||||
\(709\) | 910.699 | 1.28448 | 0.642242 | − | 0.766502i | \(-0.278005\pi\) | ||||
0.642242 | + | 0.766502i | \(0.278005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −927.881 | + | 361.646i | −1.30504 | + | 0.508644i | ||||
\(712\) | 226.806 | 0.318548 | ||||||||
\(713\) | − | 588.577i | − | 0.825493i | ||||||
\(714\) | 15.0379 | + | 79.9932i | 0.0210615 | + | 0.112035i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 76.7197i | − | 0.107150i | ||||||
\(717\) | −710.637 | + | 133.593i | −0.991125 | + | 0.186322i | ||||
\(718\) | −210.820 | −0.293622 | ||||||||
\(719\) | 526.394i | 0.732119i | 0.930591 | + | 0.366060i | \(0.119293\pi\) | ||||
−0.930591 | + | 0.366060i | \(0.880707\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 457.798 | 0.634948 | ||||||||
\(722\) | − | 139.169i | − | 0.192755i | ||||||
\(723\) | −109.102 | − | 580.362i | −0.150902 | − | 0.802714i | ||||
\(724\) | −427.438 | −0.590384 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 476.672 | − | 89.6096i | 0.656573 | − | 0.123429i | ||||
\(727\) | −348.251 | −0.479025 | −0.239513 | − | 0.970893i | \(-0.576988\pi\) | ||||
−0.239513 | + | 0.970893i | \(0.576988\pi\) | |||||||
\(728\) | − | 1.35094i | − | 0.00185568i | ||||||
\(729\) | −320.936 | + | 654.554i | −0.440242 | + | 0.897879i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 538.171i | 0.736212i | ||||||||
\(732\) | −9.36345 | − | 49.8082i | −0.0127916 | − | 0.0680440i | ||||
\(733\) | 1270.52 | 1.73332 | 0.866658 | − | 0.498903i | \(-0.166264\pi\) | ||||
0.866658 | + | 0.498903i | \(0.166264\pi\) | |||||||
\(734\) | − | 558.515i | − | 0.760920i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 67.2362 | 0.0913536 | ||||||||
\(737\) | − | 221.654i | − | 0.300751i | ||||||
\(738\) | 246.486 | − | 96.0690i | 0.333992 | − | 0.130175i | ||||
\(739\) | −1072.31 | −1.45103 | −0.725514 | − | 0.688207i | \(-0.758398\pi\) | ||||
−0.725514 | + | 0.688207i | \(0.758398\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.14464 | + | 11.4083i | 0.00289425 | + | 0.0153958i | ||||
\(742\) | 206.005 | 0.277635 | ||||||||
\(743\) | − | 205.210i | − | 0.276191i | −0.990419 | − | 0.138095i | \(-0.955902\pi\) | ||
0.990419 | − | 0.138095i | \(-0.0440981\pi\) | |||||||
\(744\) | 412.952 | − | 77.6309i | 0.555043 | − | 0.104343i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 803.094i | − | 1.07653i | ||||||
\(747\) | 10.0864 | + | 25.8788i | 0.0135025 | + | 0.0346437i | ||||
\(748\) | −37.4806 | −0.0501077 | ||||||||
\(749\) | 217.305i | 0.290127i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −167.702 | −0.223306 | −0.111653 | − | 0.993747i | \(-0.535614\pi\) | ||||
−0.111653 | + | 0.993747i | \(0.535614\pi\) | |||||||
\(752\) | − | 28.2043i | − | 0.0375057i | ||||||
\(753\) | −1029.86 | + | 193.604i | −1.36768 | + | 0.257111i | ||||
\(754\) | 7.54312 | 0.0100041 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −75.5837 | − | 121.240i | −0.0999784 | − | 0.160370i | ||||
\(757\) | −468.004 | −0.618236 | −0.309118 | − | 0.951024i | \(-0.600034\pi\) | ||||
−0.309118 | + | 0.951024i | \(0.600034\pi\) | |||||||
\(758\) | 907.137i | 1.19675i | ||||||||
\(759\) | −17.0259 | − | 90.5680i | −0.0224320 | − | 0.119325i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 252.487i | − | 0.331784i | −0.986144 | − | 0.165892i | \(-0.946950\pi\) | ||
0.986144 | − | 0.165892i | \(-0.0530503\pi\) | |||||||
\(762\) | −638.218 | + | 119.979i | −0.837557 | + | 0.157452i | ||||
\(763\) | 167.976 | 0.220152 | ||||||||
\(764\) | − | 491.091i | − | 0.642790i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 480.960 | 0.627885 | ||||||||
\(767\) | − | 18.0725i | − | 0.0235625i | ||||||
\(768\) | 8.86818 | + | 47.1737i | 0.0115471 | + | 0.0614241i | ||||
\(769\) | −146.391 | −0.190366 | −0.0951828 | − | 0.995460i | \(-0.530344\pi\) | ||||
−0.0951828 | + | 0.995460i | \(0.530344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.3457 | − | 2.32087i | 0.0160126 | − | 0.00301021i | ||||
\(772\) | −65.8014 | −0.0852350 | ||||||||
\(773\) | 1105.53i | 1.43018i | 0.699032 | + | 0.715091i | \(0.253615\pi\) | ||||
−0.699032 | + | 0.715091i | \(0.746385\pi\) | |||||||
\(774\) | −343.045 | − | 880.156i | −0.443210 | − | 1.13715i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 299.229i | − | 0.385605i | ||||||
\(777\) | 63.4906 | + | 337.734i | 0.0817125 | + | 0.434664i | ||||
\(778\) | −611.764 | −0.786328 | ||||||||
\(779\) | − | 445.495i | − | 0.571881i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 252.781 | 0.323663 | ||||||||
\(782\) | − | 121.886i | − | 0.155864i | ||||||
\(783\) | 676.958 | − | 422.031i | 0.864570 | − | 0.538993i | ||||
\(784\) | 28.0000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 138.463 | + | 736.544i | 0.176162 | + | 0.937079i | ||||
\(787\) | 1176.01 | 1.49430 | 0.747150 | − | 0.664655i | \(-0.231422\pi\) | ||||
0.747150 | + | 0.664655i | \(0.231422\pi\) | |||||||
\(788\) | − | 438.679i | − | 0.556700i | ||||||
\(789\) | 791.589 | − | 148.811i | 1.00328 | − | 0.188607i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 384.940i | − | 0.486650i | ||||||
\(792\) | 61.2979 | − | 23.8911i | 0.0773963 | − | 0.0301655i | ||||
\(793\) | 1.52487 | 0.00192291 | ||||||||
\(794\) | − | 666.592i | − | 0.839536i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 201.270 | 0.252852 | ||||||||
\(797\) | − | 1123.49i | − | 1.40965i | −0.709383 | − | 0.704823i | \(-0.751027\pi\) | ||
0.709383 | − | 0.704823i | \(-0.248973\pi\) | |||||||
\(798\) | −236.452 | + | 44.4506i | −0.296306 | + | 0.0557025i | ||||
\(799\) | −51.1286 | −0.0639907 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 262.080 | + | 672.424i | 0.327191 | + | 0.839481i | ||||
\(802\) | −254.733 | −0.317623 | ||||||||
\(803\) | − | 46.0838i | − | 0.0573896i | ||||||
\(804\) | 95.0720 | + | 505.729i | 0.118249 | + | 0.629016i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.6424i | 0.0156854i | ||||||||
\(807\) | −174.308 | + | 32.7683i | −0.215996 | + | 0.0406050i | ||||
\(808\) | −341.259 | −0.422351 | ||||||||
\(809\) | − | 539.089i | − | 0.666365i | −0.942862 | − | 0.333182i | \(-0.891878\pi\) | ||
0.942862 | − | 0.333182i | \(-0.108122\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 435.885 | 0.537467 | 0.268733 | − | 0.963215i | \(-0.413395\pi\) | ||||
0.268733 | + | 0.963215i | \(0.413395\pi\) | |||||||
\(812\) | 156.342i | 0.192539i | ||||||||
\(813\) | −114.371 | − | 608.388i | −0.140678 | − | 0.748325i | ||||
\(814\) | −158.244 | −0.194403 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 85.5163 | − | 16.0762i | 0.104799 | − | 0.0197013i | ||||
\(817\) | −1590.78 | −1.94710 | ||||||||
\(818\) | 366.623i | 0.448194i | ||||||||
\(819\) | 4.00519 | − | 1.56104i | 0.00489034 | − | 0.00190603i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 811.354i | − | 0.988251i | −0.869391 | − | 0.494126i | \(-0.835488\pi\) | ||
0.869391 | − | 0.494126i | \(-0.164512\pi\) | |||||||
\(822\) | −179.747 | − | 956.151i | −0.218670 | − | 1.16320i | ||||
\(823\) | −283.495 | −0.344465 | −0.172233 | − | 0.985056i | \(-0.555098\pi\) | ||||
−0.172233 | + | 0.985056i | \(0.555098\pi\) | |||||||
\(824\) | − | 489.406i | − | 0.593940i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 374.577 | 0.453483 | ||||||||
\(827\) | − | 406.820i | − | 0.491923i | −0.969280 | − | 0.245962i | \(-0.920896\pi\) | ||
0.969280 | − | 0.245962i | \(-0.0791037\pi\) | |||||||
\(828\) | 77.6931 | + | 199.339i | 0.0938323 | + | 0.240747i | ||||
\(829\) | −553.326 | −0.667462 | −0.333731 | − | 0.942668i | \(-0.608308\pi\) | ||||
−0.333731 | + | 0.942668i | \(0.608308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 205.344 | + | 1092.31i | 0.247105 | + | 1.31446i | ||||
\(832\) | −1.44421 | −0.00173583 | ||||||||
\(833\) | − | 50.7583i | − | 0.0609344i | ||||||
\(834\) | −33.0748 | + | 6.21773i | −0.0396580 | + | 0.00745532i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 110.789i | − | 0.132522i | ||||||
\(837\) | 707.333 | + | 1134.60i | 0.845081 | + | 1.35555i | ||||
\(838\) | 206.665 | 0.246617 | ||||||||
\(839\) | 1325.58i | 1.57996i | 0.613136 | + | 0.789978i | \(0.289908\pi\) | ||||
−0.613136 | + | 0.789978i | \(0.710092\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −31.9535 | −0.0379946 | ||||||||
\(842\) | 848.256i | 1.00743i | ||||||||
\(843\) | −209.409 | + | 39.3669i | −0.248409 | + | 0.0466985i | ||||
\(844\) | −239.731 | −0.284041 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 83.6186 | − | 32.5907i | 0.0988400 | − | 0.0385233i | ||||
\(847\) | −302.464 | −0.357100 | ||||||||
\(848\) | − | 220.229i | − | 0.259704i | ||||||
\(849\) | −141.789 | − | 754.237i | −0.167007 | − | 0.888382i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 514.605i | − | 0.604706i | ||||||
\(852\) | −576.749 | + | 108.423i | −0.676936 | + | 0.127257i | ||||
\(853\) | −273.098 | −0.320162 | −0.160081 | − | 0.987104i | \(-0.551175\pi\) | ||||
−0.160081 | + | 0.987104i | \(0.551175\pi\) | |||||||
\(854\) | 31.6050i | 0.0370082i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 232.309 | 0.271389 | ||||||||
\(857\) | 1236.47i | 1.44278i | 0.692527 | + | 0.721392i | \(0.256497\pi\) | ||||
−0.692527 | + | 0.721392i | \(0.743503\pi\) | |||||||
\(858\) | 0.365710 | + | 1.94537i | 0.000426236 | + | 0.00226733i | ||||
\(859\) | 1117.68 | 1.30114 | 0.650569 | − | 0.759447i | \(-0.274530\pi\) | ||||
0.650569 | + | 0.759447i | \(0.274530\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −162.133 | + | 30.4795i | −0.188308 | + | 0.0354001i | ||||
\(862\) | 1167.62 | 1.35455 | ||||||||
\(863\) | − | 95.0081i | − | 0.110090i | −0.998484 | − | 0.0550452i | \(-0.982470\pi\) | ||
0.998484 | − | 0.0550452i | \(-0.0175303\pi\) | |||||||
\(864\) | −129.611 | + | 80.8023i | −0.150013 | + | 0.0935212i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 262.064i | − | 0.302615i | ||||||
\(867\) | 131.039 | + | 697.051i | 0.151140 | + | 0.803980i | ||||
\(868\) | −262.032 | −0.301880 | ||||||||
\(869\) | 285.973i | 0.329083i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.4828 | −0.0177759 | ||||||||
\(872\) | − | 179.574i | − | 0.205934i | ||||||
\(873\) | 887.141 | − | 345.767i | 1.01620 | − | 0.396068i | ||||
\(874\) | 360.282 | 0.412222 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 19.7663 | + | 105.146i | 0.0225643 | + | 0.120029i | ||||
\(877\) | −749.945 | −0.855125 | −0.427563 | − | 0.903986i | \(-0.640628\pi\) | ||||
−0.427563 | + | 0.903986i | \(0.640628\pi\) | |||||||
\(878\) | − | 1144.24i | − | 1.30324i | ||||||
\(879\) | −478.839 | + | 90.0171i | −0.544755 | + | 0.102408i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1369.06i | − | 1.55399i | −0.629508 | − | 0.776994i | \(-0.716744\pi\) | ||
0.629508 | − | 0.776994i | \(-0.283256\pi\) | |||||||
\(882\) | 32.3547 | + | 83.0131i | 0.0366833 | + | 0.0941191i | ||||
\(883\) | 1039.06 | 1.17673 | 0.588367 | − | 0.808594i | \(-0.299771\pi\) | ||||
0.588367 | + | 0.808594i | \(0.299771\pi\) | |||||||
\(884\) | 2.61806i | 0.00296161i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −636.286 | −0.718156 | ||||||||
\(887\) | 217.425i | 0.245124i | 0.992461 | + | 0.122562i | \(0.0391111\pi\) | ||||
−0.992461 | + | 0.122562i | \(0.960889\pi\) | |||||||
\(888\) | 361.053 | − | 67.8743i | 0.406591 | − | 0.0764351i | ||||
\(889\) | 404.971 | 0.455535 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 141.662 | + | 154.126i | 0.158993 | + | 0.172981i | ||||
\(892\) | −631.122 | −0.707536 | ||||||||
\(893\) | − | 151.131i | − | 0.169240i | ||||||
\(894\) | −87.7008 | − | 466.518i | −0.0980994 | − | 0.521833i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 29.9333i | − | 0.0334077i | ||||||
\(897\) | −6.32628 | + | 1.18928i | −0.00705271 | + | 0.00132584i | ||||
\(898\) | −956.020 | −1.06461 | ||||||||
\(899\) | − | 1463.09i | − | 1.62746i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −399.230 | −0.443097 | ||||||||
\(902\) | − | 75.9671i | − | 0.0842208i | ||||||
\(903\) | 108.837 | + | 578.949i | 0.120528 | + | 0.641139i | ||||
\(904\) | −411.518 | −0.455219 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −307.509 | + | 57.8087i | −0.339414 | + | 0.0638065i | ||||
\(907\) | −331.700 | −0.365711 | −0.182855 | − | 0.983140i | \(-0.558534\pi\) | ||||
−0.182855 | + | 0.983140i | \(0.558534\pi\) | |||||||
\(908\) | − | 631.019i | − | 0.694954i | ||||||
\(909\) | −394.334 | − | 1011.75i | −0.433810 | − | 1.11304i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 500.840i | − | 0.549769i | −0.961477 | − | 0.274885i | \(-0.911360\pi\) | ||
0.961477 | − | 0.274885i | \(-0.0886396\pi\) | |||||||
\(912\) | 47.5197 | + | 252.778i | 0.0521049 | + | 0.277169i | ||||
\(913\) | 7.97587 | 0.00873589 | ||||||||
\(914\) | 832.020i | 0.910306i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 133.711 | 0.145973 | ||||||||
\(917\) | − | 467.362i | − | 0.509664i | ||||||
\(918\) | 146.478 | + | 234.958i | 0.159562 | + | 0.255946i | ||||
\(919\) | 634.767 | 0.690715 | 0.345357 | − | 0.938471i | \(-0.387758\pi\) | ||||
0.345357 | + | 0.938471i | \(0.387758\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −295.296 | − | 1570.81i | −0.320625 | − | 1.70554i | ||||
\(922\) | −486.868 | −0.528057 | ||||||||
\(923\) | − | 17.6570i | − | 0.0191301i | ||||||
\(924\) | −40.3205 | + | 7.57985i | −0.0436369 | + | 0.00820330i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 311.442i | − | 0.336330i | ||||||
\(927\) | 1450.97 | − | 565.521i | 1.56523 | − | 0.610055i | ||||
\(928\) | 167.136 | 0.180104 | ||||||||
\(929\) | − | 1222.10i | − | 1.31551i | −0.753234 | − | 0.657753i | \(-0.771507\pi\) | ||
0.753234 | − | 0.657753i | \(-0.228493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 150.037 | 0.161156 | ||||||||
\(932\) | 603.651i | 0.647695i | ||||||||
\(933\) | 1041.18 | − | 195.731i | 1.11595 | − | 0.209787i | ||||
\(934\) | 842.167 | 0.901678 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.66882 | − | 4.28173i | −0.00178293 | − | 0.00457450i | ||||
\(937\) | 689.991 | 0.736383 | 0.368191 | − | 0.929750i | \(-0.379977\pi\) | ||||
0.368191 | + | 0.929750i | \(0.379977\pi\) | |||||||
\(938\) | − | 320.902i | − | 0.342113i | ||||||
\(939\) | −63.0942 | − | 335.625i | −0.0671930 | − | 0.357428i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 83.4328i | 0.0886639i | 0.999017 | + | 0.0443320i | \(0.0141159\pi\) | ||||
−0.999017 | + | 0.0443320i | \(0.985884\pi\) | |||||||
\(942\) | −218.470 | + | 41.0701i | −0.231921 | + | 0.0435989i | ||||
\(943\) | 247.043 | 0.261975 | ||||||||
\(944\) | − | 400.439i | − | 0.424194i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −271.265 | −0.286749 | ||||||||
\(947\) | 528.948i | 0.558551i | 0.960211 | + | 0.279276i | \(0.0900943\pi\) | ||||
−0.960211 | + | 0.279276i | \(0.909906\pi\) | |||||||
\(948\) | −122.660 | − | 652.482i | −0.129388 | − | 0.688272i | ||||
\(949\) | −3.21901 | −0.00339200 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 215.649 | − | 40.5400i | 0.226761 | − | 0.0426288i | ||||
\(952\) | −54.2629 | −0.0569989 | ||||||||
\(953\) | − | 1017.29i | − | 1.06746i | −0.845654 | − | 0.533732i | \(-0.820789\pi\) | ||
0.845654 | − | 0.533732i | \(-0.179211\pi\) | |||||||
\(954\) | 652.924 | − | 254.480i | 0.684407 | − | 0.266751i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | − | 482.057i | − | 0.504243i | ||||||
\(957\) | −42.3231 | − | 225.135i | −0.0442247 | − | 0.235250i | ||||
\(958\) | 1004.59 | 1.04864 | ||||||||
\(959\) | 606.710i | 0.632648i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1491.17 | 1.55168 | ||||||||
\(962\) | 11.0535i | 0.0114902i | ||||||||
\(963\) | 268.439 | + | 688.738i | 0.278752 | + | 0.715200i | ||||
\(964\) | 393.686 | 0.408388 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −24.6494 | − | 131.121i | −0.0255170 | − | 0.135736i | ||||
\(967\) | 12.4388 | 0.0128633 | 0.00643164 | − | 0.999979i | \(-0.497953\pi\) | ||||
0.00643164 | + | 0.999979i | \(0.497953\pi\) | |||||||
\(968\) | 323.348i | 0.334037i | ||||||||
\(969\) | 458.235 | − | 86.1436i | 0.472894 | − | 0.0888995i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 855.268i | − | 0.880812i | −0.897799 | − | 0.440406i | \(-0.854835\pi\) | ||
0.897799 | − | 0.440406i | \(-0.145165\pi\) | |||||||
\(972\) | −389.328 | − | 290.895i | −0.400543 | − | 0.299275i | ||||
\(973\) | 20.9870 | 0.0215694 | ||||||||
\(974\) | 461.016i | 0.473322i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 33.7871 | 0.0346180 | ||||||||
\(977\) | 939.920i | 0.962047i | 0.876708 | + | 0.481023i | \(0.159735\pi\) | ||||
−0.876708 | + | 0.481023i | \(0.840265\pi\) | |||||||
\(978\) | 70.5225 | − | 13.2575i | 0.0721089 | − | 0.0135558i | ||||
\(979\) | 207.242 | 0.211687 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 532.393 | − | 207.502i | 0.542704 | − | 0.211521i | ||||
\(982\) | 810.920 | 0.825784 | ||||||||
\(983\) | 564.622i | 0.574387i | 0.957873 | + | 0.287194i | \(0.0927223\pi\) | ||||
−0.957873 | + | 0.287194i | \(0.907278\pi\) | |||||||
\(984\) | 32.5839 | + | 173.328i | 0.0331138 | + | 0.176146i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 302.984i | − | 0.307286i | ||||||
\(987\) | −55.0026 | + | 10.3399i | −0.0557271 | + | 0.0104761i | ||||
\(988\) | −7.73873 | −0.00783272 | ||||||||
\(989\) | − | 882.144i | − | 0.891956i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1156.30 | −1.16680 | −0.583400 | − | 0.812185i | \(-0.698278\pi\) | ||||
−0.583400 | + | 0.812185i | \(0.698278\pi\) | |||||||
\(992\) | 280.124i | 0.282383i | ||||||||
\(993\) | −135.544 | − | 721.016i | −0.136499 | − | 0.726099i | ||||
\(994\) | 365.966 | 0.368175 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −18.1979 | + | 3.42102i | −0.0182710 | + | 0.00343476i | ||||
\(997\) | −807.864 | −0.810295 | −0.405148 | − | 0.914251i | \(-0.632780\pi\) | ||||
−0.405148 | + | 0.914251i | \(0.632780\pi\) | |||||||
\(998\) | 580.777i | 0.581941i | ||||||||
\(999\) | 618.436 | + | 992.001i | 0.619055 | + | 0.992994i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.3.e.e.701.14 | 24 | ||
3.2 | odd | 2 | inner | 1050.3.e.e.701.16 | 24 | ||
5.2 | odd | 4 | 210.3.c.a.29.23 | yes | 24 | ||
5.3 | odd | 4 | 210.3.c.a.29.2 | yes | 24 | ||
5.4 | even | 2 | inner | 1050.3.e.e.701.15 | 24 | ||
15.2 | even | 4 | 210.3.c.a.29.1 | ✓ | 24 | ||
15.8 | even | 4 | 210.3.c.a.29.24 | yes | 24 | ||
15.14 | odd | 2 | inner | 1050.3.e.e.701.13 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.c.a.29.1 | ✓ | 24 | 15.2 | even | 4 | ||
210.3.c.a.29.2 | yes | 24 | 5.3 | odd | 4 | ||
210.3.c.a.29.23 | yes | 24 | 5.2 | odd | 4 | ||
210.3.c.a.29.24 | yes | 24 | 15.8 | even | 4 | ||
1050.3.e.e.701.13 | 24 | 15.14 | odd | 2 | inner | ||
1050.3.e.e.701.14 | 24 | 1.1 | even | 1 | trivial | ||
1050.3.e.e.701.15 | 24 | 5.4 | even | 2 | inner | ||
1050.3.e.e.701.16 | 24 | 3.2 | odd | 2 | inner |