Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(7,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.7");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.j (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 7.9 | ||
Character | \(\chi\) | \(=\) | 60.7 |
Dual form | 60.4.j.b.43.9 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05416 | + | 2.62464i | 0.372701 | + | 0.927951i | ||||
\(3\) | 2.12132 | + | 2.12132i | 0.408248 | + | 0.408248i | ||||
\(4\) | −5.77750 | + | 5.53358i | −0.722187 | + | 0.691698i | ||||
\(5\) | 10.9830 | + | 2.09135i | 0.982349 | + | 0.187056i | ||||
\(6\) | −3.33150 | + | 7.80392i | −0.226680 | + | 0.530989i | ||||
\(7\) | −5.27814 | + | 5.27814i | −0.284993 | + | 0.284993i | −0.835096 | − | 0.550104i | \(-0.814588\pi\) |
0.550104 | + | 0.835096i | \(0.314588\pi\) | |||||||
\(8\) | −20.6141 | − | 9.33060i | −0.911022 | − | 0.412358i | ||||
\(9\) | 9.00000i | 0.333333i | ||||||||
\(10\) | 6.08878 | + | 31.0311i | 0.192544 | + | 0.981288i | ||||
\(11\) | 1.40160i | 0.0384181i | 0.999815 | + | 0.0192091i | \(0.00611481\pi\) | ||||
−0.999815 | + | 0.0192091i | \(0.993885\pi\) | |||||||
\(12\) | −23.9944 | − | 0.517429i | −0.577216 | − | 0.0124474i | ||||
\(13\) | 7.55895 | − | 7.55895i | 0.161267 | − | 0.161267i | −0.621861 | − | 0.783128i | \(-0.713623\pi\) |
0.783128 | + | 0.621861i | \(0.213623\pi\) | |||||||
\(14\) | −19.4172 | − | 8.28923i | −0.370676 | − | 0.158242i | ||||
\(15\) | 18.8620 | + | 27.7349i | 0.324677 | + | 0.477408i | ||||
\(16\) | 2.75898 | − | 63.9405i | 0.0431091 | − | 0.999070i | ||||
\(17\) | −51.9561 | − | 51.9561i | −0.741248 | − | 0.741248i | 0.231570 | − | 0.972818i | \(-0.425614\pi\) |
−0.972818 | + | 0.231570i | \(0.925614\pi\) | |||||||
\(18\) | −23.6218 | + | 9.48743i | −0.309317 | + | 0.124234i | ||||
\(19\) | 158.912 | 1.91879 | 0.959395 | − | 0.282067i | \(-0.0910199\pi\) | ||||
0.959395 | + | 0.282067i | \(0.0910199\pi\) | |||||||
\(20\) | −75.0269 | + | 48.6925i | −0.838826 | + | 0.544399i | ||||
\(21\) | −22.3932 | −0.232696 | ||||||||
\(22\) | −3.67871 | + | 1.47751i | −0.0356502 | + | 0.0143185i | ||||
\(23\) | 49.7457 | + | 49.7457i | 0.450987 | + | 0.450987i | 0.895682 | − | 0.444695i | \(-0.146688\pi\) |
−0.444695 | + | 0.895682i | \(0.646688\pi\) | |||||||
\(24\) | −23.9359 | − | 63.5222i | −0.203579 | − | 0.540268i | ||||
\(25\) | 116.253 | + | 45.9386i | 0.930020 | + | 0.367508i | ||||
\(26\) | 27.8079 | + | 11.8712i | 0.209753 | + | 0.0895437i | ||||
\(27\) | −19.0919 | + | 19.0919i | −0.136083 | + | 0.136083i | ||||
\(28\) | 1.28744 | − | 59.7014i | 0.00868937 | − | 0.402947i | ||||
\(29\) | − | 231.773i | − | 1.48411i | −0.670339 | − | 0.742055i | \(-0.733851\pi\) | ||
0.670339 | − | 0.742055i | \(-0.266149\pi\) | |||||||
\(30\) | −52.9106 | + | 78.7431i | −0.322003 | + | 0.479215i | ||||
\(31\) | − | 158.577i | − | 0.918751i | −0.888242 | − | 0.459375i | \(-0.848073\pi\) | ||
0.888242 | − | 0.459375i | \(-0.151927\pi\) | |||||||
\(32\) | 170.729 | − | 60.1621i | 0.943155 | − | 0.332352i | ||||
\(33\) | −2.97325 | + | 2.97325i | −0.0156841 | + | 0.0156841i | ||||
\(34\) | 81.5963 | − | 191.136i | 0.411578 | − | 0.964106i | ||||
\(35\) | −69.0082 | + | 46.9314i | −0.333272 | + | 0.226653i | ||||
\(36\) | −49.8022 | − | 51.9975i | −0.230566 | − | 0.240729i | ||||
\(37\) | 130.982 | + | 130.982i | 0.581981 | + | 0.581981i | 0.935447 | − | 0.353466i | \(-0.114997\pi\) |
−0.353466 | + | 0.935447i | \(0.614997\pi\) | |||||||
\(38\) | 167.519 | + | 417.088i | 0.715136 | + | 1.78054i | ||||
\(39\) | 32.0699 | 0.131674 | ||||||||
\(40\) | −206.891 | − | 145.589i | −0.817808 | − | 0.575492i | ||||
\(41\) | −351.893 | −1.34040 | −0.670201 | − | 0.742180i | \(-0.733792\pi\) | ||||
−0.670201 | + | 0.742180i | \(0.733792\pi\) | |||||||
\(42\) | −23.6060 | − | 58.7743i | −0.0867259 | − | 0.215930i | ||||
\(43\) | −191.372 | − | 191.372i | −0.678696 | − | 0.678696i | 0.281009 | − | 0.959705i | \(-0.409331\pi\) |
−0.959705 | + | 0.281009i | \(0.909331\pi\) | |||||||
\(44\) | −7.75589 | − | 8.09777i | −0.0265737 | − | 0.0277451i | ||||
\(45\) | −18.8221 | + | 98.8470i | −0.0623520 | + | 0.327450i | ||||
\(46\) | −78.1248 | + | 183.004i | −0.250410 | + | 0.586577i | ||||
\(47\) | −286.736 | + | 286.736i | −0.889888 | + | 0.889888i | −0.994512 | − | 0.104624i | \(-0.966636\pi\) |
0.104624 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(48\) | 141.491 | − | 129.786i | 0.425468 | − | 0.390270i | ||||
\(49\) | 287.283i | 0.837558i | ||||||||
\(50\) | 1.97632 | + | 353.548i | 0.00558988 | + | 0.999984i | ||||
\(51\) | − | 220.431i | − | 0.605226i | ||||||
\(52\) | −1.84377 | + | 85.4999i | −0.00491701 | + | 0.228013i | ||||
\(53\) | 89.5861 | − | 89.5861i | 0.232181 | − | 0.232181i | −0.581421 | − | 0.813603i | \(-0.697503\pi\) |
0.813603 | + | 0.581421i | \(0.197503\pi\) | |||||||
\(54\) | −70.2352 | − | 29.9835i | −0.176996 | − | 0.0755599i | ||||
\(55\) | −2.93124 | + | 15.3938i | −0.00718634 | + | 0.0377400i | ||||
\(56\) | 158.052 | − | 59.5557i | 0.377154 | − | 0.142116i | ||||
\(57\) | 337.104 | + | 337.104i | 0.783343 | + | 0.783343i | ||||
\(58\) | 608.322 | − | 244.326i | 1.37718 | − | 0.553130i | ||||
\(59\) | −420.149 | −0.927098 | −0.463549 | − | 0.886071i | \(-0.653424\pi\) | ||||
−0.463549 | + | 0.886071i | \(0.653424\pi\) | |||||||
\(60\) | −262.449 | − | 55.8636i | −0.564699 | − | 0.120199i | ||||
\(61\) | −289.827 | −0.608336 | −0.304168 | − | 0.952618i | \(-0.598378\pi\) | ||||
−0.304168 | + | 0.952618i | \(0.598378\pi\) | |||||||
\(62\) | 416.208 | − | 167.165i | 0.852556 | − | 0.342420i | ||||
\(63\) | −47.5032 | − | 47.5032i | −0.0949976 | − | 0.0949976i | ||||
\(64\) | 337.880 | + | 384.683i | 0.659922 | + | 0.751334i | ||||
\(65\) | 98.8283 | − | 67.2115i | 0.188587 | − | 0.128255i | ||||
\(66\) | −10.9380 | − | 4.66944i | −0.0203996 | − | 0.00870862i | ||||
\(67\) | −689.622 | + | 689.622i | −1.25747 | + | 1.25747i | −0.305179 | + | 0.952295i | \(0.598716\pi\) |
−0.952295 | + | 0.305179i | \(0.901284\pi\) | |||||||
\(68\) | 587.680 | + | 12.6731i | 1.04804 | + | 0.0226005i | ||||
\(69\) | 211.053i | 0.368229i | ||||||||
\(70\) | −195.924 | − | 131.649i | −0.334534 | − | 0.224786i | ||||
\(71\) | − | 1035.24i | − | 1.73043i | −0.501403 | − | 0.865214i | \(-0.667183\pi\) | ||
0.501403 | − | 0.865214i | \(-0.332817\pi\) | |||||||
\(72\) | 83.9754 | − | 185.527i | 0.137453 | − | 0.303674i | ||||
\(73\) | −49.0241 | + | 49.0241i | −0.0786005 | + | 0.0786005i | −0.745314 | − | 0.666714i | \(-0.767700\pi\) |
0.666714 | + | 0.745314i | \(0.267700\pi\) | |||||||
\(74\) | −205.705 | + | 481.857i | −0.323145 | + | 0.756955i | ||||
\(75\) | 149.158 | + | 344.059i | 0.229644 | + | 0.529714i | ||||
\(76\) | −918.116 | + | 879.354i | −1.38573 | + | 1.32722i | ||||
\(77\) | −7.39786 | − | 7.39786i | −0.0109489 | − | 0.0109489i | ||||
\(78\) | 33.8068 | + | 84.1721i | 0.0490752 | + | 0.122187i | ||||
\(79\) | 1148.70 | 1.63594 | 0.817971 | − | 0.575260i | \(-0.195099\pi\) | ||||
0.817971 | + | 0.575260i | \(0.195099\pi\) | |||||||
\(80\) | 164.024 | − | 696.488i | 0.229230 | − | 0.973372i | ||||
\(81\) | −81.0000 | −0.111111 | ||||||||
\(82\) | −370.951 | − | 923.594i | −0.499570 | − | 1.24383i | ||||
\(83\) | −74.7178 | − | 74.7178i | −0.0988114 | − | 0.0988114i | 0.655973 | − | 0.754784i | \(-0.272259\pi\) |
−0.754784 | + | 0.655973i | \(0.772259\pi\) | |||||||
\(84\) | 129.377 | − | 123.915i | 0.168050 | − | 0.160955i | ||||
\(85\) | −461.976 | − | 679.293i | −0.589510 | − | 0.866819i | ||||
\(86\) | 300.546 | − | 704.019i | 0.376846 | − | 0.882748i | ||||
\(87\) | 491.665 | − | 491.665i | 0.605886 | − | 0.605886i | ||||
\(88\) | 13.0778 | − | 28.8928i | 0.0158420 | − | 0.0349998i | ||||
\(89\) | − | 1307.42i | − | 1.55715i | −0.627550 | − | 0.778576i | \(-0.715942\pi\) | ||
0.627550 | − | 0.778576i | \(-0.284058\pi\) | |||||||
\(90\) | −279.280 | + | 54.7990i | −0.327096 | + | 0.0641814i | ||||
\(91\) | 79.7944i | 0.0919200i | ||||||||
\(92\) | −562.677 | − | 12.1339i | −0.637643 | − | 0.0137505i | ||||
\(93\) | 336.393 | − | 336.393i | 0.375078 | − | 0.375078i | ||||
\(94\) | −1054.84 | − | 450.314i | −1.15744 | − | 0.494110i | ||||
\(95\) | 1745.33 | + | 332.341i | 1.88492 | + | 0.358921i | ||||
\(96\) | 489.795 | + | 234.549i | 0.520724 | + | 0.249360i | ||||
\(97\) | 143.267 | + | 143.267i | 0.149964 | + | 0.149964i | 0.778102 | − | 0.628138i | \(-0.216183\pi\) |
−0.628138 | + | 0.778102i | \(0.716183\pi\) | |||||||
\(98\) | −754.014 | + | 302.841i | −0.777213 | + | 0.312159i | ||||
\(99\) | −12.6144 | −0.0128060 | ||||||||
\(100\) | −925.853 | + | 377.883i | −0.925853 | + | 0.377883i | ||||
\(101\) | 643.908 | 0.634369 | 0.317184 | − | 0.948364i | \(-0.397263\pi\) | ||||
0.317184 | + | 0.948364i | \(0.397263\pi\) | |||||||
\(102\) | 578.553 | − | 232.370i | 0.561621 | − | 0.225569i | ||||
\(103\) | −125.454 | − | 125.454i | −0.120013 | − | 0.120013i | 0.644550 | − | 0.764562i | \(-0.277045\pi\) |
−0.764562 | + | 0.644550i | \(0.777045\pi\) | |||||||
\(104\) | −226.350 | + | 85.2912i | −0.213418 | + | 0.0804182i | ||||
\(105\) | −245.945 | − | 46.8321i | −0.228588 | − | 0.0435271i | ||||
\(106\) | 329.569 | + | 140.694i | 0.301987 | + | 0.128919i | ||||
\(107\) | −870.958 | + | 870.958i | −0.786904 | + | 0.786904i | −0.980985 | − | 0.194082i | \(-0.937827\pi\) |
0.194082 | + | 0.980985i | \(0.437827\pi\) | |||||||
\(108\) | 4.65686 | − | 215.950i | 0.00414914 | − | 0.192405i | ||||
\(109\) | 247.031i | 0.217076i | 0.994092 | + | 0.108538i | \(0.0346169\pi\) | ||||
−0.994092 | + | 0.108538i | \(0.965383\pi\) | |||||||
\(110\) | −43.4933 | + | 8.53406i | −0.0376993 | + | 0.00739719i | ||||
\(111\) | 555.709i | 0.475186i | ||||||||
\(112\) | 322.925 | + | 352.049i | 0.272442 | + | 0.297013i | ||||
\(113\) | −1286.39 | + | 1286.39i | −1.07091 | + | 1.07091i | −0.0736249 | + | 0.997286i | \(0.523457\pi\) |
−0.997286 | + | 0.0736249i | \(0.976543\pi\) | |||||||
\(114\) | −529.417 | + | 1240.14i | −0.434951 | + | 1.01886i | ||||
\(115\) | 442.321 | + | 650.392i | 0.358667 | + | 0.527386i | ||||
\(116\) | 1282.54 | + | 1339.07i | 1.02656 | + | 1.07181i | ||||
\(117\) | 68.0305 | + | 68.0305i | 0.0537558 | + | 0.0537558i | ||||
\(118\) | −442.904 | − | 1102.74i | −0.345531 | − | 0.860302i | ||||
\(119\) | 548.463 | 0.422500 | ||||||||
\(120\) | −130.040 | − | 747.723i | −0.0989251 | − | 0.568812i | ||||
\(121\) | 1329.04 | 0.998524 | ||||||||
\(122\) | −305.523 | − | 760.692i | −0.226728 | − | 0.564507i | ||||
\(123\) | −746.478 | − | 746.478i | −0.547217 | − | 0.547217i | ||||
\(124\) | 877.499 | + | 916.178i | 0.635498 | + | 0.663510i | ||||
\(125\) | 1180.73 | + | 747.668i | 0.844860 | + | 0.534987i | ||||
\(126\) | 74.6031 | − | 174.755i | 0.0527474 | − | 0.123559i | ||||
\(127\) | 459.299 | − | 459.299i | 0.320915 | − | 0.320915i | −0.528203 | − | 0.849118i | \(-0.677134\pi\) |
0.849118 | + | 0.528203i | \(0.177134\pi\) | |||||||
\(128\) | −653.477 | + | 1292.33i | −0.451248 | + | 0.892399i | ||||
\(129\) | − | 811.922i | − | 0.554153i | ||||||
\(130\) | 280.587 | + | 188.537i | 0.189301 | + | 0.127199i | ||||
\(131\) | 860.399i | 0.573843i | 0.957954 | + | 0.286922i | \(0.0926319\pi\) | ||||
−0.957954 | + | 0.286922i | \(0.907368\pi\) | |||||||
\(132\) | 0.725231 | − | 33.6307i | 0.000478207 | − | 0.0221756i | ||||
\(133\) | −838.762 | + | 838.762i | −0.546841 | + | 0.546841i | ||||
\(134\) | −2536.98 | − | 1083.04i | −1.63554 | − | 0.698212i | ||||
\(135\) | −249.614 | + | 169.758i | −0.159136 | + | 0.108226i | ||||
\(136\) | 586.246 | + | 1555.81i | 0.369634 | + | 0.980953i | ||||
\(137\) | 352.457 | + | 352.457i | 0.219799 | + | 0.219799i | 0.808414 | − | 0.588615i | \(-0.200326\pi\) |
−0.588615 | + | 0.808414i | \(0.700326\pi\) | |||||||
\(138\) | −553.939 | + | 222.483i | −0.341699 | + | 0.137239i | ||||
\(139\) | −1240.08 | −0.756709 | −0.378355 | − | 0.925661i | \(-0.623510\pi\) | ||||
−0.378355 | + | 0.925661i | \(0.623510\pi\) | |||||||
\(140\) | 138.996 | − | 653.008i | 0.0839096 | − | 0.394209i | ||||
\(141\) | −1216.52 | −0.726591 | ||||||||
\(142\) | 2717.14 | − | 1091.31i | 1.60575 | − | 0.644933i | ||||
\(143\) | 10.5947 | + | 10.5947i | 0.00619559 | + | 0.00619559i | ||||
\(144\) | 575.465 | + | 24.8308i | 0.333023 | + | 0.0143697i | ||||
\(145\) | 484.719 | − | 2545.57i | 0.277612 | − | 1.45791i | ||||
\(146\) | −180.350 | − | 76.9915i | −0.102232 | − | 0.0436429i | ||||
\(147\) | −609.418 | + | 609.418i | −0.341932 | + | 0.341932i | ||||
\(148\) | −1481.55 | − | 31.9489i | −0.822854 | − | 0.0177445i | ||||
\(149\) | 1724.45i | 0.948136i | 0.880488 | + | 0.474068i | \(0.157215\pi\) | ||||
−0.880488 | + | 0.474068i | \(0.842785\pi\) | |||||||
\(150\) | −745.796 | + | 754.181i | −0.405960 | + | 0.410524i | ||||
\(151\) | − | 1213.38i | − | 0.653932i | −0.945036 | − | 0.326966i | \(-0.893974\pi\) | ||
0.945036 | − | 0.326966i | \(-0.106026\pi\) | |||||||
\(152\) | −3275.83 | − | 1482.75i | −1.74806 | − | 0.791228i | ||||
\(153\) | 467.605 | − | 467.605i | 0.247083 | − | 0.247083i | ||||
\(154\) | 11.6182 | − | 27.2153i | 0.00607937 | − | 0.0142407i | ||||
\(155\) | 331.640 | − | 1741.65i | 0.171858 | − | 0.902534i | ||||
\(156\) | −185.284 | + | 177.461i | −0.0950935 | + | 0.0910787i | ||||
\(157\) | −1316.84 | − | 1316.84i | −0.669395 | − | 0.669395i | 0.288181 | − | 0.957576i | \(-0.406949\pi\) |
−0.957576 | + | 0.288181i | \(0.906949\pi\) | |||||||
\(158\) | 1210.92 | + | 3014.94i | 0.609718 | + | 1.51807i | ||||
\(159\) | 380.082 | 0.189575 | ||||||||
\(160\) | 2000.94 | − | 303.706i | 0.988676 | − | 0.150063i | ||||
\(161\) | −525.129 | −0.257056 | ||||||||
\(162\) | −85.3869 | − | 212.596i | −0.0414113 | − | 0.103106i | ||||
\(163\) | −1463.80 | − | 1463.80i | −0.703395 | − | 0.703395i | 0.261742 | − | 0.965138i | \(-0.415703\pi\) |
−0.965138 | + | 0.261742i | \(0.915703\pi\) | |||||||
\(164\) | 2033.06 | − | 1947.23i | 0.968021 | − | 0.927153i | ||||
\(165\) | −38.8733 | + | 26.4371i | −0.0183411 | + | 0.0124735i | ||||
\(166\) | 117.343 | − | 274.872i | 0.0548650 | − | 0.128519i | ||||
\(167\) | 695.722 | − | 695.722i | 0.322375 | − | 0.322375i | −0.527303 | − | 0.849678i | \(-0.676797\pi\) |
0.849678 | + | 0.527303i | \(0.176797\pi\) | |||||||
\(168\) | 461.616 | + | 208.942i | 0.211991 | + | 0.0959539i | ||||
\(169\) | 2082.72i | 0.947986i | ||||||||
\(170\) | 1295.90 | − | 1928.60i | 0.584655 | − | 0.870101i | ||||
\(171\) | 1430.21i | 0.639597i | ||||||||
\(172\) | 2164.62 | + | 46.6791i | 0.959598 | + | 0.0206933i | ||||
\(173\) | −252.659 | + | 252.659i | −0.111037 | + | 0.111037i | −0.760442 | − | 0.649406i | \(-0.775018\pi\) |
0.649406 | + | 0.760442i | \(0.275018\pi\) | |||||||
\(174\) | 1808.74 | + | 772.152i | 0.788047 | + | 0.336418i | ||||
\(175\) | −856.067 | + | 371.127i | −0.369786 | + | 0.160312i | ||||
\(176\) | 89.6193 | + | 3.86700i | 0.0383824 | + | 0.00165617i | ||||
\(177\) | −891.271 | − | 891.271i | −0.378486 | − | 0.378486i | ||||
\(178\) | 3431.52 | − | 1378.23i | 1.44496 | − | 0.580353i | ||||
\(179\) | −2471.68 | −1.03208 | −0.516040 | − | 0.856565i | \(-0.672594\pi\) | ||||
−0.516040 | + | 0.856565i | \(0.672594\pi\) | |||||||
\(180\) | −438.233 | − | 675.242i | −0.181466 | − | 0.279609i | ||||
\(181\) | 2598.92 | 1.06727 | 0.533635 | − | 0.845715i | \(-0.320826\pi\) | ||||
0.533635 | + | 0.845715i | \(0.320826\pi\) | |||||||
\(182\) | −209.432 | + | 84.1159i | −0.0852973 | + | 0.0342587i | ||||
\(183\) | −614.815 | − | 614.815i | −0.248352 | − | 0.248352i | ||||
\(184\) | −561.304 | − | 1489.62i | −0.224891 | − | 0.596827i | ||||
\(185\) | 1164.65 | + | 1712.50i | 0.462846 | + | 0.680572i | ||||
\(186\) | 1237.52 | + | 528.299i | 0.487847 | + | 0.208262i | ||||
\(187\) | 72.8220 | − | 72.8220i | 0.0284774 | − | 0.0284774i | ||||
\(188\) | 69.9402 | − | 3243.29i | 0.0271325 | − | 1.25820i | ||||
\(189\) | − | 201.539i | − | 0.0775652i | ||||||
\(190\) | 967.583 | + | 4931.22i | 0.369452 | + | 1.88289i | ||||
\(191\) | − | 52.1327i | − | 0.0197497i | −0.999951 | − | 0.00987484i | \(-0.996857\pi\) | ||
0.999951 | − | 0.00987484i | \(-0.00314331\pi\) | |||||||
\(192\) | −99.2849 | + | 1532.79i | −0.0373191 | + | 0.576143i | ||||
\(193\) | −139.514 | + | 139.514i | −0.0520335 | + | 0.0520335i | −0.732645 | − | 0.680611i | \(-0.761714\pi\) |
0.680611 | + | 0.732645i | \(0.261714\pi\) | |||||||
\(194\) | −224.998 | + | 527.051i | −0.0832678 | + | 0.195052i | ||||
\(195\) | 352.224 | + | 67.0694i | 0.129350 | + | 0.0246304i | ||||
\(196\) | −1589.70 | − | 1659.77i | −0.579337 | − | 0.604874i | ||||
\(197\) | 109.513 | + | 109.513i | 0.0396066 | + | 0.0396066i | 0.726633 | − | 0.687026i | \(-0.241084\pi\) |
−0.687026 | + | 0.726633i | \(0.741084\pi\) | |||||||
\(198\) | −13.2976 | − | 33.1084i | −0.00477283 | − | 0.0118834i | ||||
\(199\) | 1076.03 | 0.383305 | 0.191653 | − | 0.981463i | \(-0.438615\pi\) | ||||
0.191653 | + | 0.981463i | \(0.438615\pi\) | |||||||
\(200\) | −1967.80 | − | 2031.69i | −0.695724 | − | 0.718310i | ||||
\(201\) | −2925.82 | −1.02672 | ||||||||
\(202\) | 678.781 | + | 1690.03i | 0.236430 | + | 0.588663i | ||||
\(203\) | 1223.33 | + | 1223.33i | 0.422961 | + | 0.422961i | ||||
\(204\) | 1219.77 | + | 1273.54i | 0.418634 | + | 0.437087i | ||||
\(205\) | −3864.84 | − | 735.931i | −1.31674 | − | 0.250730i | ||||
\(206\) | 197.023 | − | 461.519i | 0.0666371 | − | 0.156095i | ||||
\(207\) | −447.711 | + | 447.711i | −0.150329 | + | 0.150329i | ||||
\(208\) | −462.468 | − | 504.178i | −0.154165 | − | 0.168070i | ||||
\(209\) | 222.732i | 0.0737163i | ||||||||
\(210\) | −136.348 | − | 694.886i | −0.0448042 | − | 0.228341i | ||||
\(211\) | − | 649.062i | − | 0.211769i | −0.994378 | − | 0.105885i | \(-0.966233\pi\) | ||
0.994378 | − | 0.105885i | \(-0.0337674\pi\) | |||||||
\(212\) | −21.8517 | + | 1013.32i | −0.00707916 | + | 0.328277i | ||||
\(213\) | 2196.08 | − | 2196.08i | 0.706444 | − | 0.706444i | ||||
\(214\) | −3204.08 | − | 1367.83i | −1.02349 | − | 0.436928i | ||||
\(215\) | −1701.61 | − | 2502.06i | −0.539763 | − | 0.793671i | ||||
\(216\) | 571.700 | − | 215.423i | 0.180089 | − | 0.0678595i | ||||
\(217\) | 836.991 | + | 836.991i | 0.261837 | + | 0.261837i | ||||
\(218\) | −648.369 | + | 260.410i | −0.201436 | + | 0.0809046i | ||||
\(219\) | −207.992 | −0.0641770 | ||||||||
\(220\) | −68.2477 | − | 105.158i | −0.0209148 | − | 0.0322262i | ||||
\(221\) | −785.468 | −0.239078 | ||||||||
\(222\) | −1458.54 | + | 585.806i | −0.440949 | + | 0.177102i | ||||
\(223\) | 3774.71 | + | 3774.71i | 1.13351 | + | 1.13351i | 0.989589 | + | 0.143924i | \(0.0459721\pi\) |
0.143924 | + | 0.989589i | \(0.454028\pi\) | |||||||
\(224\) | −583.589 | + | 1218.68i | −0.174075 | + | 0.363510i | ||||
\(225\) | −413.447 | + | 1046.27i | −0.122503 | + | 0.310007i | ||||
\(226\) | −4732.36 | − | 2020.25i | −1.39288 | − | 0.594623i | ||||
\(227\) | 1110.47 | − | 1110.47i | 0.324690 | − | 0.324690i | −0.525873 | − | 0.850563i | \(-0.676261\pi\) |
0.850563 | + | 0.525873i | \(0.176261\pi\) | |||||||
\(228\) | −3813.01 | − | 82.2259i | −1.10756 | − | 0.0238840i | ||||
\(229\) | 144.576i | 0.0417199i | 0.999782 | + | 0.0208600i | \(0.00664042\pi\) | ||||
−0.999782 | + | 0.0208600i | \(0.993360\pi\) | |||||||
\(230\) | −1240.77 | + | 1846.55i | −0.355713 | + | 0.529383i | ||||
\(231\) | − | 31.3865i | − | 0.00893973i | ||||||
\(232\) | −2162.58 | + | 4777.79i | −0.611985 | + | 1.35206i | ||||
\(233\) | 3097.20 | − | 3097.20i | 0.870833 | − | 0.870833i | −0.121730 | − | 0.992563i | \(-0.538844\pi\) |
0.992563 | + | 0.121730i | \(0.0388443\pi\) | |||||||
\(234\) | −106.841 | + | 250.271i | −0.0298479 | + | 0.0699176i | ||||
\(235\) | −3748.89 | + | 2549.56i | −1.04064 | + | 0.707722i | ||||
\(236\) | 2427.41 | − | 2324.93i | 0.669539 | − | 0.641272i | ||||
\(237\) | 2436.77 | + | 2436.77i | 0.667870 | + | 0.667870i | ||||
\(238\) | 578.167 | + | 1439.52i | 0.157467 | + | 0.392060i | ||||
\(239\) | 1721.09 | 0.465808 | 0.232904 | − | 0.972500i | \(-0.425177\pi\) | ||||
0.232904 | + | 0.972500i | \(0.425177\pi\) | |||||||
\(240\) | 1825.42 | − | 1129.53i | 0.490960 | − | 0.303795i | ||||
\(241\) | 1740.30 | 0.465156 | 0.232578 | − | 0.972578i | \(-0.425284\pi\) | ||||
0.232578 | + | 0.972578i | \(0.425284\pi\) | |||||||
\(242\) | 1401.01 | + | 3488.24i | 0.372151 | + | 0.926582i | ||||
\(243\) | −171.827 | − | 171.827i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 1674.47 | − | 1603.78i | 0.439333 | − | 0.420785i | ||||
\(245\) | −600.808 | + | 3155.22i | −0.156670 | + | 0.822775i | ||||
\(246\) | 1172.33 | − | 2746.14i | 0.303842 | − | 0.711739i | ||||
\(247\) | 1201.21 | − | 1201.21i | 0.309438 | − | 0.309438i | ||||
\(248\) | −1479.62 | + | 3268.92i | −0.378854 | + | 0.837002i | ||||
\(249\) | − | 317.001i | − | 0.0806791i | ||||||
\(250\) | −717.686 | + | 3887.15i | −0.181562 | + | 0.983380i | ||||
\(251\) | 4230.64i | 1.06389i | 0.846780 | + | 0.531944i | \(0.178538\pi\) | ||||
−0.846780 | + | 0.531944i | \(0.821462\pi\) | |||||||
\(252\) | 537.313 | + | 11.5869i | 0.134316 | + | 0.00289646i | ||||
\(253\) | −69.7238 | + | 69.7238i | −0.0173261 | + | 0.0173261i | ||||
\(254\) | 1689.67 | + | 721.321i | 0.417399 | + | 0.178188i | ||||
\(255\) | 460.999 | − | 2421.00i | 0.113211 | − | 0.594544i | ||||
\(256\) | −4080.78 | − | 352.821i | −0.996283 | − | 0.0861380i | ||||
\(257\) | 376.741 | + | 376.741i | 0.0914416 | + | 0.0914416i | 0.751348 | − | 0.659906i | \(-0.229404\pi\) |
−0.659906 | + | 0.751348i | \(0.729404\pi\) | |||||||
\(258\) | 2131.01 | − | 855.895i | 0.514227 | − | 0.206534i | ||||
\(259\) | −1382.68 | −0.331721 | ||||||||
\(260\) | −199.060 | + | 935.189i | −0.0474815 | + | 0.223069i | ||||
\(261\) | 2085.96 | 0.494704 | ||||||||
\(262\) | −2258.24 | + | 906.998i | −0.532498 | + | 0.213872i | ||||
\(263\) | 3363.14 | + | 3363.14i | 0.788517 | + | 0.788517i | 0.981251 | − | 0.192734i | \(-0.0617355\pi\) |
−0.192734 | + | 0.981251i | \(0.561736\pi\) | |||||||
\(264\) | 89.0330 | − | 33.5486i | 0.0207561 | − | 0.00782111i | ||||
\(265\) | 1171.28 | − | 796.568i | 0.271514 | − | 0.184652i | ||||
\(266\) | −3085.64 | − | 1317.26i | −0.711250 | − | 0.303633i | ||||
\(267\) | 2773.46 | − | 2773.46i | 0.635705 | − | 0.635705i | ||||
\(268\) | 168.212 | − | 7800.37i | 0.0383402 | − | 1.77792i | ||||
\(269\) | − | 6368.38i | − | 1.44345i | −0.692182 | − | 0.721723i | \(-0.743351\pi\) | ||
0.692182 | − | 0.721723i | \(-0.256649\pi\) | |||||||
\(270\) | −708.688 | − | 476.195i | −0.159738 | − | 0.107334i | ||||
\(271\) | − | 1806.78i | − | 0.404997i | −0.979283 | − | 0.202499i | \(-0.935094\pi\) | ||
0.979283 | − | 0.202499i | \(-0.0649061\pi\) | |||||||
\(272\) | −3465.45 | + | 3178.76i | −0.772513 | + | 0.708604i | ||||
\(273\) | −169.269 | + | 169.269i | −0.0375262 | + | 0.0375262i | ||||
\(274\) | −553.529 | + | 1296.62i | −0.122043 | + | 0.285882i | ||||
\(275\) | −64.3877 | + | 162.940i | −0.0141190 | + | 0.0357297i | ||||
\(276\) | −1167.88 | − | 1219.36i | −0.254703 | − | 0.265930i | ||||
\(277\) | −5532.86 | − | 5532.86i | −1.20014 | − | 1.20014i | −0.974125 | − | 0.226010i | \(-0.927432\pi\) |
−0.226010 | − | 0.974125i | \(-0.572568\pi\) | |||||||
\(278\) | −1307.25 | − | 3254.78i | −0.282027 | − | 0.702189i | ||||
\(279\) | 1427.19 | 0.306250 | ||||||||
\(280\) | 1860.44 | − | 323.559i | 0.397080 | − | 0.0690583i | ||||
\(281\) | −4840.59 | −1.02763 | −0.513817 | − | 0.857900i | \(-0.671769\pi\) | ||||
−0.513817 | + | 0.857900i | \(0.671769\pi\) | |||||||
\(282\) | −1282.40 | − | 3192.92i | −0.270801 | − | 0.674241i | ||||
\(283\) | 5155.62 | + | 5155.62i | 1.08293 | + | 1.08293i | 0.996235 | + | 0.0866976i | \(0.0276314\pi\) |
0.0866976 | + | 0.996235i | \(0.472369\pi\) | |||||||
\(284\) | 5728.58 | + | 5981.10i | 1.19693 | + | 1.24969i | ||||
\(285\) | 2997.41 | + | 4407.42i | 0.622987 | + | 0.916045i | ||||
\(286\) | −16.6387 | + | 38.9756i | −0.00344010 | + | 0.00805831i | ||||
\(287\) | 1857.34 | − | 1857.34i | 0.382005 | − | 0.382005i | ||||
\(288\) | 541.459 | + | 1536.56i | 0.110784 | + | 0.314385i | ||||
\(289\) | 485.881i | 0.0988971i | ||||||||
\(290\) | 7192.17 | − | 1411.22i | 1.45634 | − | 0.285757i | ||||
\(291\) | 607.830i | 0.122445i | ||||||||
\(292\) | 11.9579 | − | 554.515i | 0.00239651 | − | 0.111132i | ||||
\(293\) | 2981.51 | − | 2981.51i | 0.594476 | − | 0.594476i | −0.344361 | − | 0.938837i | \(-0.611905\pi\) |
0.938837 | + | 0.344361i | \(0.111905\pi\) | |||||||
\(294\) | −2241.93 | − | 957.082i | −0.444734 | − | 0.189858i | ||||
\(295\) | −4614.50 | − | 878.679i | −0.910734 | − | 0.173419i | ||||
\(296\) | −1477.93 | − | 3922.21i | −0.290213 | − | 0.770182i | ||||
\(297\) | −26.7593 | − | 26.7593i | −0.00522805 | − | 0.00522805i | ||||
\(298\) | −4526.06 | + | 1817.84i | −0.879824 | + | 0.353372i | ||||
\(299\) | 752.050 | 0.145459 | ||||||||
\(300\) | −2765.64 | − | 1162.42i | −0.532248 | − | 0.223708i | ||||
\(301\) | 2020.17 | 0.386847 | ||||||||
\(302\) | 3184.70 | − | 1279.10i | 0.606817 | − | 0.243721i | ||||
\(303\) | 1365.94 | + | 1365.94i | 0.258980 | + | 0.258980i | ||||
\(304\) | 438.436 | − | 10160.9i | 0.0827173 | − | 1.91701i | ||||
\(305\) | −3183.17 | − | 606.129i | −0.597599 | − | 0.113793i | ||||
\(306\) | 1720.23 | + | 734.367i | 0.321369 | + | 0.137193i | ||||
\(307\) | 4165.72 | − | 4165.72i | 0.774430 | − | 0.774430i | −0.204447 | − | 0.978878i | \(-0.565540\pi\) |
0.978878 | + | 0.204447i | \(0.0655397\pi\) | |||||||
\(308\) | 83.6778 | + | 1.80448i | 0.0154805 | + | 0.000333830i | ||||
\(309\) | − | 532.255i | − | 0.0979900i | ||||||
\(310\) | 4920.81 | − | 965.541i | 0.901559 | − | 0.176900i | ||||
\(311\) | − | 1118.75i | − | 0.203983i | −0.994785 | − | 0.101991i | \(-0.967479\pi\) | ||
0.994785 | − | 0.101991i | \(-0.0325214\pi\) | |||||||
\(312\) | −661.091 | − | 299.231i | −0.119958 | − | 0.0542969i | ||||
\(313\) | −6105.65 | + | 6105.65i | −1.10259 | + | 1.10259i | −0.108496 | + | 0.994097i | \(0.534604\pi\) |
−0.994097 | + | 0.108496i | \(0.965396\pi\) | |||||||
\(314\) | 2068.07 | − | 4844.38i | 0.371681 | − | 0.870650i | ||||
\(315\) | −422.382 | − | 621.074i | −0.0755509 | − | 0.111091i | ||||
\(316\) | −6636.64 | + | 6356.45i | −1.18146 | + | 1.13158i | ||||
\(317\) | −2218.47 | − | 2218.47i | −0.393065 | − | 0.393065i | 0.482714 | − | 0.875778i | \(-0.339651\pi\) |
−0.875778 | + | 0.482714i | \(0.839651\pi\) | |||||||
\(318\) | 400.666 | + | 997.578i | 0.0706549 | + | 0.175916i | ||||
\(319\) | 324.854 | 0.0570168 | ||||||||
\(320\) | 2906.43 | + | 4931.60i | 0.507732 | + | 0.861515i | ||||
\(321\) | −3695.16 | −0.642504 | ||||||||
\(322\) | −553.569 | − | 1378.28i | −0.0958050 | − | 0.238535i | ||||
\(323\) | −8256.47 | − | 8256.47i | −1.42230 | − | 1.42230i | ||||
\(324\) | 467.977 | − | 448.220i | 0.0802430 | − | 0.0768553i | ||||
\(325\) | 1225.99 | − | 531.500i | 0.209249 | − | 0.0907148i | ||||
\(326\) | 2298.87 | − | 5385.02i | 0.390560 | − | 0.914873i | ||||
\(327\) | −524.032 | + | 524.032i | −0.0886209 | + | 0.0886209i | ||||
\(328\) | 7253.95 | + | 3283.37i | 1.22114 | + | 0.552725i | ||||
\(329\) | − | 3026.86i | − | 0.507223i | ||||||
\(330\) | −110.367 | − | 74.1597i | −0.0184106 | − | 0.0123708i | ||||
\(331\) | 3749.37i | 0.622611i | 0.950310 | + | 0.311306i | \(0.100766\pi\) | ||||
−0.950310 | + | 0.311306i | \(0.899234\pi\) | |||||||
\(332\) | 845.139 | + | 18.2251i | 0.139708 | + | 0.00301274i | ||||
\(333\) | −1178.84 | + | 1178.84i | −0.193994 | + | 0.193994i | ||||
\(334\) | 2559.42 | + | 1092.62i | 0.419298 | + | 0.178999i | ||||
\(335\) | −9016.36 | + | 6131.88i | −1.47050 | + | 1.00006i | ||||
\(336\) | −61.7825 | + | 1431.84i | −0.0100313 | + | 0.232479i | ||||
\(337\) | 5399.37 | + | 5399.37i | 0.872767 | + | 0.872767i | 0.992773 | − | 0.120006i | \(-0.0382914\pi\) |
−0.120006 | + | 0.992773i | \(0.538291\pi\) | |||||||
\(338\) | −5466.41 | + | 2195.52i | −0.879685 | + | 0.353316i | ||||
\(339\) | −5457.67 | −0.874395 | ||||||||
\(340\) | 6427.99 | + | 1368.23i | 1.02531 | + | 0.218244i | ||||
\(341\) | 222.262 | 0.0352967 | ||||||||
\(342\) | −3753.79 | + | 1507.67i | −0.593514 | + | 0.238379i | ||||
\(343\) | −3326.72 | − | 3326.72i | −0.523691 | − | 0.523691i | ||||
\(344\) | 2159.34 | + | 5730.57i | 0.338441 | + | 0.898173i | ||||
\(345\) | −441.385 | + | 2318.00i | −0.0688794 | + | 0.361729i | ||||
\(346\) | −929.483 | − | 396.797i | −0.144420 | − | 0.0616530i | ||||
\(347\) | −215.533 | + | 215.533i | −0.0333442 | + | 0.0333442i | −0.723582 | − | 0.690238i | \(-0.757506\pi\) |
0.690238 | + | 0.723582i | \(0.257506\pi\) | |||||||
\(348\) | −119.926 | + | 5561.26i | −0.0184733 | + | 0.856653i | ||||
\(349\) | 8313.82i | 1.27515i | 0.770387 | + | 0.637577i | \(0.220063\pi\) | ||||
−0.770387 | + | 0.637577i | \(0.779937\pi\) | |||||||
\(350\) | −1876.51 | − | 1855.64i | −0.286581 | − | 0.283395i | ||||
\(351\) | 288.629i | 0.0438914i | ||||||||
\(352\) | 84.3235 | + | 239.295i | 0.0127683 | + | 0.0362343i | ||||
\(353\) | 1199.56 | − | 1199.56i | 0.180867 | − | 0.180867i | −0.610867 | − | 0.791734i | \(-0.709179\pi\) |
0.791734 | + | 0.610867i | \(0.209179\pi\) | |||||||
\(354\) | 1399.73 | − | 3278.81i | 0.210154 | − | 0.492279i | ||||
\(355\) | 2165.05 | − | 11370.0i | 0.323687 | − | 1.69988i | ||||
\(356\) | 7234.73 | + | 7553.63i | 1.07708 | + | 1.12456i | ||||
\(357\) | 1163.47 | + | 1163.47i | 0.172485 | + | 0.172485i | ||||
\(358\) | −2605.54 | − | 6487.28i | −0.384657 | − | 0.957719i | ||||
\(359\) | −10201.8 | −1.49981 | −0.749905 | − | 0.661545i | \(-0.769901\pi\) | ||||
−0.749905 | + | 0.661545i | \(0.769901\pi\) | |||||||
\(360\) | 1310.30 | − | 1862.02i | 0.191831 | − | 0.272603i | ||||
\(361\) | 18394.1 | 2.68175 | ||||||||
\(362\) | 2739.67 | + | 6821.22i | 0.397773 | + | 0.990374i | ||||
\(363\) | 2819.31 | + | 2819.31i | 0.407646 | + | 0.407646i | ||||
\(364\) | −441.548 | − | 461.012i | −0.0635808 | − | 0.0663835i | ||||
\(365\) | −640.958 | + | 435.905i | −0.0919158 | + | 0.0625104i | ||||
\(366\) | 965.558 | − | 2261.78i | 0.137898 | − | 0.323020i | ||||
\(367\) | −7970.47 | + | 7970.47i | −1.13367 | + | 1.13367i | −0.144103 | + | 0.989563i | \(0.546030\pi\) |
−0.989563 | + | 0.144103i | \(0.953970\pi\) | |||||||
\(368\) | 3318.01 | − | 3043.52i | 0.470009 | − | 0.431126i | ||||
\(369\) | − | 3167.04i | − | 0.446801i | ||||||
\(370\) | −3266.99 | + | 4862.03i | −0.459034 | + | 0.683148i | ||||
\(371\) | 945.695i | 0.132340i | ||||||||
\(372\) | −82.0524 | + | 3804.96i | −0.0114361 | + | 0.530318i | ||||
\(373\) | −3104.50 | + | 3104.50i | −0.430951 | + | 0.430951i | −0.888952 | − | 0.458001i | \(-0.848566\pi\) |
0.458001 | + | 0.888952i | \(0.348566\pi\) | |||||||
\(374\) | 267.898 | + | 114.366i | 0.0370392 | + | 0.0158121i | ||||
\(375\) | 918.659 | + | 4090.74i | 0.126505 | + | 0.563320i | ||||
\(376\) | 8586.22 | − | 3235.38i | 1.17766 | − | 0.443755i | ||||
\(377\) | −1751.96 | − | 1751.96i | −0.239339 | − | 0.239339i | ||||
\(378\) | 528.968 | − | 212.454i | 0.0719767 | − | 0.0289086i | ||||
\(379\) | 4144.26 | 0.561678 | 0.280839 | − | 0.959755i | \(-0.409387\pi\) | ||||
0.280839 | + | 0.959755i | \(0.409387\pi\) | |||||||
\(380\) | −11922.7 | + | 7737.85i | −1.60953 | + | 1.04459i | ||||
\(381\) | 1948.64 | 0.262026 | ||||||||
\(382\) | 136.830 | − | 54.9561i | 0.0183267 | − | 0.00736073i | ||||
\(383\) | −1571.99 | − | 1571.99i | −0.209726 | − | 0.209726i | 0.594425 | − | 0.804151i | \(-0.297380\pi\) |
−0.804151 | + | 0.594425i | \(0.797380\pi\) | |||||||
\(384\) | −4127.68 | + | 1355.21i | −0.548541 | + | 0.180099i | ||||
\(385\) | −65.7792 | − | 96.7222i | −0.00870758 | − | 0.0128037i | ||||
\(386\) | −513.246 | − | 219.105i | −0.0676775 | − | 0.0288916i | ||||
\(387\) | 1722.35 | − | 1722.35i | 0.226232 | − | 0.226232i | ||||
\(388\) | −1620.50 | − | 34.9455i | −0.212033 | − | 0.00457239i | ||||
\(389\) | 5657.83i | 0.737438i | 0.929541 | + | 0.368719i | \(0.120204\pi\) | ||||
−0.929541 | + | 0.368719i | \(0.879796\pi\) | |||||||
\(390\) | 195.267 | + | 995.163i | 0.0253531 | + | 0.129210i | ||||
\(391\) | − | 5169.19i | − | 0.668586i | ||||||
\(392\) | 2680.52 | − | 5922.06i | 0.345374 | − | 0.763034i | ||||
\(393\) | −1825.18 | + | 1825.18i | −0.234270 | + | 0.234270i | ||||
\(394\) | −171.989 | + | 402.878i | −0.0219916 | + | 0.0515145i | ||||
\(395\) | 12616.2 | + | 2402.34i | 1.60707 | + | 0.306012i | ||||
\(396\) | 72.8799 | − | 69.8030i | 0.00924837 | − | 0.00885791i | ||||
\(397\) | −5486.74 | − | 5486.74i | −0.693631 | − | 0.693631i | 0.269398 | − | 0.963029i | \(-0.413175\pi\) |
−0.963029 | + | 0.269398i | \(0.913175\pi\) | |||||||
\(398\) | 1134.31 | + | 2824.19i | 0.142858 | + | 0.355689i | ||||
\(399\) | −3558.56 | −0.446494 | ||||||||
\(400\) | 3258.07 | − | 7306.50i | 0.407259 | − | 0.913313i | ||||
\(401\) | −9093.30 | −1.13241 | −0.566207 | − | 0.824263i | \(-0.691590\pi\) | ||||
−0.566207 | + | 0.824263i | \(0.691590\pi\) | |||||||
\(402\) | −3084.28 | − | 7679.23i | −0.382661 | − | 0.952749i | ||||
\(403\) | −1198.68 | − | 1198.68i | −0.148164 | − | 0.148164i | ||||
\(404\) | −3720.18 | + | 3563.12i | −0.458133 | + | 0.438791i | ||||
\(405\) | −889.623 | − | 169.399i | −0.109150 | − | 0.0207840i | ||||
\(406\) | −1921.22 | + | 4500.39i | −0.234849 | + | 0.550125i | ||||
\(407\) | −183.585 | + | 183.585i | −0.0223586 | + | 0.0223586i | ||||
\(408\) | −2056.76 | + | 4543.99i | −0.249570 | + | 0.551374i | ||||
\(409\) | 5147.04i | 0.622261i | 0.950367 | + | 0.311130i | \(0.100708\pi\) | ||||
−0.950367 | + | 0.311130i | \(0.899292\pi\) | |||||||
\(410\) | −2142.60 | − | 10919.6i | −0.258087 | − | 1.31532i | ||||
\(411\) | 1495.35i | 0.179465i | ||||||||
\(412\) | 1419.02 | + | 30.6005i | 0.169684 | + | 0.00365917i | ||||
\(413\) | 2217.61 | − | 2217.61i | 0.264216 | − | 0.264216i | ||||
\(414\) | −1647.04 | − | 703.123i | −0.195526 | − | 0.0834701i | ||||
\(415\) | −664.364 | − | 976.886i | −0.0785840 | − | 0.115551i | ||||
\(416\) | 835.773 | − | 1745.30i | 0.0985027 | − | 0.205698i | ||||
\(417\) | −2630.62 | − | 2630.62i | −0.308925 | − | 0.308925i | ||||
\(418\) | −584.593 | + | 234.795i | −0.0684052 | + | 0.0274742i | ||||
\(419\) | 8395.93 | 0.978922 | 0.489461 | − | 0.872025i | \(-0.337194\pi\) | ||||
0.489461 | + | 0.872025i | \(0.337194\pi\) | |||||||
\(420\) | 1680.10 | − | 1090.38i | 0.195191 | − | 0.126679i | ||||
\(421\) | −13595.9 | −1.57393 | −0.786963 | − | 0.617000i | \(-0.788348\pi\) | ||||
−0.786963 | + | 0.617000i | \(0.788348\pi\) | |||||||
\(422\) | 1703.56 | − | 684.215i | 0.196512 | − | 0.0789267i | ||||
\(423\) | −2580.62 | − | 2580.62i | −0.296629 | − | 0.296629i | ||||
\(424\) | −2682.63 | + | 1010.84i | −0.307264 | + | 0.115780i | ||||
\(425\) | −3653.24 | − | 8426.82i | −0.416961 | − | 0.961790i | ||||
\(426\) | 8078.93 | + | 3448.90i | 0.918839 | + | 0.392253i | ||||
\(427\) | 1529.75 | − | 1529.75i | 0.173371 | − | 0.173371i | ||||
\(428\) | 212.443 | − | 9851.48i | 0.0239926 | − | 1.11259i | ||||
\(429\) | 44.9493i | 0.00505868i | ||||||||
\(430\) | 4773.25 | − | 7103.69i | 0.535318 | − | 0.796676i | ||||
\(431\) | 9613.29i | 1.07438i | 0.843463 | + | 0.537188i | \(0.180513\pi\) | ||||
−0.843463 | + | 0.537188i | \(0.819487\pi\) | |||||||
\(432\) | 1168.07 | + | 1273.42i | 0.130090 | + | 0.141823i | ||||
\(433\) | 9384.90 | − | 9384.90i | 1.04159 | − | 1.04159i | 0.0424958 | − | 0.999097i | \(-0.486469\pi\) |
0.999097 | − | 0.0424958i | \(-0.0135309\pi\) | |||||||
\(434\) | −1314.48 | + | 3079.12i | −0.145385 | + | 0.340559i | ||||
\(435\) | 6428.20 | − | 4371.72i | 0.708526 | − | 0.481857i | ||||
\(436\) | −1366.97 | − | 1427.22i | −0.150151 | − | 0.156770i | ||||
\(437\) | 7905.20 | + | 7905.20i | 0.865348 | + | 0.865348i | ||||
\(438\) | −219.256 | − | 545.903i | −0.0239189 | − | 0.0595531i | ||||
\(439\) | 4968.42 | 0.540159 | 0.270079 | − | 0.962838i | \(-0.412950\pi\) | ||||
0.270079 | + | 0.962838i | \(0.412950\pi\) | |||||||
\(440\) | 204.058 | − | 289.979i | 0.0221093 | − | 0.0314187i | ||||
\(441\) | −2585.54 | −0.279186 | ||||||||
\(442\) | −828.008 | − | 2061.57i | −0.0891048 | − | 0.221853i | ||||
\(443\) | 1271.39 | + | 1271.39i | 0.136356 | + | 0.136356i | 0.771990 | − | 0.635635i | \(-0.219261\pi\) |
−0.635635 | + | 0.771990i | \(0.719261\pi\) | |||||||
\(444\) | −3075.06 | − | 3210.61i | −0.328685 | − | 0.343173i | ||||
\(445\) | 2734.28 | − | 14359.4i | 0.291274 | − | 1.52967i | ||||
\(446\) | −5928.12 | + | 13886.4i | −0.629383 | + | 1.47431i | ||||
\(447\) | −3658.11 | + | 3658.11i | −0.387075 | + | 0.387075i | ||||
\(448\) | −3813.79 | − | 247.034i | −0.402198 | − | 0.0260520i | ||||
\(449\) | 7777.90i | 0.817509i | 0.912644 | + | 0.408755i | \(0.134037\pi\) | ||||
−0.912644 | + | 0.408755i | \(0.865963\pi\) | |||||||
\(450\) | −3181.93 | + | 17.7869i | −0.333328 | + | 0.00186329i | ||||
\(451\) | − | 493.215i | − | 0.0514958i | ||||||
\(452\) | 313.773 | − | 14550.4i | 0.0326519 | − | 1.51414i | ||||
\(453\) | 2573.97 | − | 2573.97i | 0.266967 | − | 0.266967i | ||||
\(454\) | 4085.20 | + | 1743.98i | 0.422308 | + | 0.180284i | ||||
\(455\) | −166.878 | + | 876.381i | −0.0171942 | + | 0.0902976i | ||||
\(456\) | −3803.71 | − | 10094.5i | −0.390625 | − | 1.03666i | ||||
\(457\) | −3937.51 | − | 3937.51i | −0.403039 | − | 0.403039i | 0.476264 | − | 0.879303i | \(-0.341991\pi\) |
−0.879303 | + | 0.476264i | \(0.841991\pi\) | |||||||
\(458\) | −379.461 | + | 152.406i | −0.0387141 | + | 0.0155491i | ||||
\(459\) | 1983.88 | 0.201742 | ||||||||
\(460\) | −6154.51 | − | 1310.02i | −0.623816 | − | 0.132783i | ||||
\(461\) | 10816.8 | 1.09282 | 0.546408 | − | 0.837519i | \(-0.315995\pi\) | ||||
0.546408 | + | 0.837519i | \(0.315995\pi\) | |||||||
\(462\) | 82.3783 | − | 33.0863i | 0.00829564 | − | 0.00333185i | ||||
\(463\) | 4575.12 | + | 4575.12i | 0.459231 | + | 0.459231i | 0.898403 | − | 0.439172i | \(-0.144728\pi\) |
−0.439172 | + | 0.898403i | \(0.644728\pi\) | |||||||
\(464\) | −14819.7 | − | 639.458i | −1.48273 | − | 0.0639787i | ||||
\(465\) | 4398.11 | − | 2991.09i | 0.438619 | − | 0.298297i | ||||
\(466\) | 11394.0 | + | 4864.10i | 1.13265 | + | 0.483530i | ||||
\(467\) | 10845.2 | − | 10845.2i | 1.07464 | − | 1.07464i | 0.0776630 | − | 0.996980i | \(-0.475254\pi\) |
0.996980 | − | 0.0776630i | \(-0.0247458\pi\) | |||||||
\(468\) | −769.499 | − | 16.5939i | −0.0760045 | − | 0.00163900i | ||||
\(469\) | − | 7279.84i | − | 0.716742i | ||||||
\(470\) | −10643.6 | − | 7151.85i | −1.04458 | − | 0.701894i | ||||
\(471\) | − | 5586.86i | − | 0.546558i | ||||||
\(472\) | 8660.99 | + | 3920.25i | 0.844607 | + | 0.382296i | ||||
\(473\) | 268.228 | − | 268.228i | 0.0260743 | − | 0.0260743i | ||||
\(474\) | −3826.91 | + | 8964.39i | −0.370835 | + | 0.868667i | ||||
\(475\) | 18474.0 | + | 7300.21i | 1.78451 | + | 0.705171i | ||||
\(476\) | −3168.75 | + | 3034.97i | −0.305124 | + | 0.292243i | ||||
\(477\) | 806.275 | + | 806.275i | 0.0773937 | + | 0.0773937i | ||||
\(478\) | 1814.30 | + | 4517.25i | 0.173607 | + | 0.432247i | ||||
\(479\) | 10214.6 | 0.974361 | 0.487180 | − | 0.873301i | \(-0.338025\pi\) | ||||
0.487180 | + | 0.873301i | \(0.338025\pi\) | |||||||
\(480\) | 4888.89 | + | 3600.38i | 0.464888 | + | 0.342363i | ||||
\(481\) | 1980.17 | 0.187709 | ||||||||
\(482\) | 1834.55 | + | 4567.67i | 0.173364 | + | 0.431642i | ||||
\(483\) | −1113.97 | − | 1113.97i | −0.104943 | − | 0.104943i | ||||
\(484\) | −7678.50 | + | 7354.32i | −0.721121 | + | 0.690677i | ||||
\(485\) | 1273.88 | + | 1873.12i | 0.119266 | + | 0.175369i | ||||
\(486\) | 269.851 | − | 632.117i | 0.0251866 | − | 0.0589988i | ||||
\(487\) | −10616.5 | + | 10616.5i | −0.987846 | + | 0.987846i | −0.999927 | − | 0.0120806i | \(-0.996155\pi\) |
0.0120806 | + | 0.999927i | \(0.496155\pi\) | |||||||
\(488\) | 5974.51 | + | 2704.26i | 0.554208 | + | 0.250852i | ||||
\(489\) | − | 6210.37i | − | 0.574320i | ||||||
\(490\) | −8914.68 | + | 1749.20i | −0.821886 | + | 0.161267i | ||||
\(491\) | 3824.37i | 0.351510i | 0.984434 | + | 0.175755i | \(0.0562366\pi\) | ||||
−0.984434 | + | 0.175755i | \(0.943763\pi\) | |||||||
\(492\) | 8443.47 | + | 182.080i | 0.773701 | + | 0.0166845i | ||||
\(493\) | −12042.0 | + | 12042.0i | −1.10009 | + | 1.10009i | ||||
\(494\) | 4419.02 | + | 1886.48i | 0.402472 | + | 0.171815i | ||||
\(495\) | −138.544 | − | 26.3812i | −0.0125800 | − | 0.00239545i | ||||
\(496\) | −10139.5 | − | 437.511i | −0.917897 | − | 0.0396065i | ||||
\(497\) | 5464.14 | + | 5464.14i | 0.493159 | + | 0.493159i | ||||
\(498\) | 832.014 | − | 334.169i | 0.0748663 | − | 0.0300692i | ||||
\(499\) | −5757.97 | −0.516557 | −0.258279 | − | 0.966070i | \(-0.583155\pi\) | ||||
−0.258279 | + | 0.966070i | \(0.583155\pi\) | |||||||
\(500\) | −10958.9 | + | 2214.00i | −0.980197 | + | 0.198026i | ||||
\(501\) | 2951.70 | 0.263218 | ||||||||
\(502\) | −11103.9 | + | 4459.77i | −0.987235 | + | 0.396512i | ||||
\(503\) | −2576.09 | − | 2576.09i | −0.228354 | − | 0.228354i | 0.583651 | − | 0.812005i | \(-0.301624\pi\) |
−0.812005 | + | 0.583651i | \(0.801624\pi\) | |||||||
\(504\) | 536.002 | + | 1422.47i | 0.0473718 | + | 0.125718i | ||||
\(505\) | 7072.04 | + | 1346.64i | 0.623172 | + | 0.118662i | ||||
\(506\) | −256.500 | − | 109.500i | −0.0225352 | − | 0.00962030i | ||||
\(507\) | −4418.13 | + | 4418.13i | −0.387014 | + | 0.387014i | ||||
\(508\) | −112.031 | + | 5195.16i | −0.00978463 | + | 0.453736i | ||||
\(509\) | 7306.41i | 0.636249i | 0.948049 | + | 0.318125i | \(0.103053\pi\) | ||||
−0.948049 | + | 0.318125i | \(0.896947\pi\) | |||||||
\(510\) | 6840.22 | − | 1342.16i | 0.593902 | − | 0.116533i | ||||
\(511\) | − | 517.512i | − | 0.0448011i | ||||||
\(512\) | −3375.76 | − | 11082.5i | −0.291384 | − | 0.956606i | ||||
\(513\) | −3033.94 | + | 3033.94i | −0.261114 | + | 0.261114i | ||||
\(514\) | −591.666 | + | 1385.96i | −0.0507729 | + | 0.118934i | ||||
\(515\) | −1115.49 | − | 1640.22i | −0.0954454 | − | 0.140344i | ||||
\(516\) | 4492.84 | + | 4690.88i | 0.383306 | + | 0.400202i | ||||
\(517\) | −401.890 | − | 401.890i | −0.0341879 | − | 0.0341879i | ||||
\(518\) | −1457.57 | − | 3629.05i | −0.123633 | − | 0.307821i | ||||
\(519\) | −1071.94 | −0.0906609 | ||||||||
\(520\) | −2664.38 | + | 463.376i | −0.224694 | + | 0.0390777i | ||||
\(521\) | −774.456 | −0.0651238 | −0.0325619 | − | 0.999470i | \(-0.510367\pi\) | ||||
−0.0325619 | + | 0.999470i | \(0.510367\pi\) | |||||||
\(522\) | 2198.93 | + | 5474.90i | 0.184377 | + | 0.459061i | ||||
\(523\) | −10529.4 | − | 10529.4i | −0.880340 | − | 0.880340i | 0.113229 | − | 0.993569i | \(-0.463881\pi\) |
−0.993569 | + | 0.113229i | \(0.963881\pi\) | |||||||
\(524\) | −4761.09 | − | 4970.96i | −0.396926 | − | 0.414422i | ||||
\(525\) | −2603.27 | − | 1028.71i | −0.216412 | − | 0.0855176i | ||||
\(526\) | −5281.75 | + | 12372.3i | −0.437824 | + | 1.02559i | ||||
\(527\) | −8239.05 | + | 8239.05i | −0.681022 | + | 0.681022i | ||||
\(528\) | 181.908 | + | 198.314i | 0.0149934 | + | 0.0163457i | ||||
\(529\) | − | 7217.74i | − | 0.593222i | ||||||
\(530\) | 3325.42 | + | 2234.48i | 0.272542 | + | 0.183131i | ||||
\(531\) | − | 3781.34i | − | 0.309033i | ||||||
\(532\) | 204.589 | − | 9487.30i | 0.0166731 | − | 0.773170i | ||||
\(533\) | −2659.94 | + | 2659.94i | −0.216163 | + | 0.216163i | ||||
\(534\) | 10203.0 | + | 4355.68i | 0.826831 | + | 0.352975i | ||||
\(535\) | −11387.2 | + | 7744.26i | −0.920209 | + | 0.625819i | ||||
\(536\) | 20650.5 | − | 7781.33i | 1.66412 | − | 0.627057i | ||||
\(537\) | −5243.23 | − | 5243.23i | −0.421345 | − | 0.421345i | ||||
\(538\) | 16714.7 | − | 6713.28i | 1.33945 | − | 0.537974i | ||||
\(539\) | −402.656 | −0.0321774 | ||||||||
\(540\) | 502.773 | − | 2362.04i | 0.0400665 | − | 0.188233i | ||||
\(541\) | −5769.32 | −0.458489 | −0.229244 | − | 0.973369i | \(-0.573625\pi\) | ||||
−0.229244 | + | 0.973369i | \(0.573625\pi\) | |||||||
\(542\) | 4742.16 | − | 1904.64i | 0.375818 | − | 0.150943i | ||||
\(543\) | 5513.13 | + | 5513.13i | 0.435711 | + | 0.435711i | ||||
\(544\) | −11996.2 | − | 5744.65i | −0.945467 | − | 0.452757i | ||||
\(545\) | −516.628 | + | 2713.14i | −0.0406054 | + | 0.213245i | ||||
\(546\) | −622.708 | − | 265.835i | −0.0488085 | − | 0.0208364i | ||||
\(547\) | −6028.69 | + | 6028.69i | −0.471240 | + | 0.471240i | −0.902316 | − | 0.431076i | \(-0.858134\pi\) |
0.431076 | + | 0.902316i | \(0.358134\pi\) | |||||||
\(548\) | −3986.67 | − | 85.9709i | −0.310770 | − | 0.00670163i | ||||
\(549\) | − | 2608.44i | − | 0.202779i | ||||||
\(550\) | −495.534 | + | 2.77002i | −0.0384175 | + | 0.000214753i | ||||
\(551\) | − | 36831.6i | − | 2.84770i | ||||||
\(552\) | 1969.25 | − | 4350.66i | 0.151842 | − | 0.335465i | ||||
\(553\) | −6063.02 | + | 6063.02i | −0.466231 | + | 0.466231i | ||||
\(554\) | 8689.27 | − | 20354.3i | 0.666375 | − | 1.56096i | ||||
\(555\) | −1162.18 | + | 6103.36i | −0.0888863 | + | 0.466798i | ||||
\(556\) | 7164.58 | − | 6862.10i | 0.546486 | − | 0.523414i | ||||
\(557\) | 14823.7 | + | 14823.7i | 1.12765 | + | 1.12765i | 0.990558 | + | 0.137091i | \(0.0437752\pi\) |
0.137091 | + | 0.990558i | \(0.456225\pi\) | |||||||
\(558\) | 1504.49 | + | 3745.87i | 0.114140 | + | 0.284185i | ||||
\(559\) | −2893.14 | −0.218903 | ||||||||
\(560\) | 2810.42 | + | 4541.90i | 0.212075 | + | 0.342733i | ||||
\(561\) | 308.957 | 0.0232517 | ||||||||
\(562\) | −5102.75 | − | 12704.8i | −0.383001 | − | 0.953595i | ||||
\(563\) | −11122.6 | − | 11122.6i | −0.832611 | − | 0.832611i | 0.155263 | − | 0.987873i | \(-0.450378\pi\) |
−0.987873 | + | 0.155263i | \(0.950378\pi\) | |||||||
\(564\) | 7028.43 | − | 6731.70i | 0.524735 | − | 0.502581i | ||||
\(565\) | −16818.6 | + | 11438.1i | −1.25233 | + | 0.851688i | ||||
\(566\) | −8096.82 | + | 18966.5i | −0.601298 | + | 1.40852i | ||||
\(567\) | 427.529 | − | 427.529i | 0.0316659 | − | 0.0316659i | ||||
\(568\) | −9659.41 | + | 21340.5i | −0.713556 | + | 1.57646i | ||||
\(569\) | − | 85.0828i | − | 0.00626864i | −0.999995 | − | 0.00313432i | \(-0.999002\pi\) | ||
0.999995 | − | 0.00313432i | \(-0.000997687\pi\) | |||||||
\(570\) | −8408.14 | + | 12513.3i | −0.617857 | + | 0.919513i | ||||
\(571\) | 9200.81i | 0.674329i | 0.941446 | + | 0.337164i | \(0.109468\pi\) | ||||
−0.941446 | + | 0.337164i | \(0.890532\pi\) | |||||||
\(572\) | −119.837 | − | 2.58423i | −0.00875985 | − | 0.000188902i | ||||
\(573\) | 110.590 | − | 110.590i | 0.00806277 | − | 0.00806277i | ||||
\(574\) | 6832.79 | + | 2916.92i | 0.496855 | + | 0.212108i | ||||
\(575\) | 3497.82 | + | 8068.30i | 0.253685 | + | 0.585168i | ||||
\(576\) | −3462.15 | + | 3040.92i | −0.250445 | + | 0.219974i | ||||
\(577\) | 7574.02 | + | 7574.02i | 0.546466 | + | 0.546466i | 0.925417 | − | 0.378951i | \(-0.123715\pi\) |
−0.378951 | + | 0.925417i | \(0.623715\pi\) | |||||||
\(578\) | −1275.26 | + | 512.196i | −0.0917717 | + | 0.0368591i | ||||
\(579\) | −591.910 | −0.0424852 | ||||||||
\(580\) | 11285.6 | + | 17389.2i | 0.807949 | + | 1.24491i | ||||
\(581\) | 788.742 | 0.0563210 | ||||||||
\(582\) | −1595.34 | + | 640.750i | −0.113623 | + | 0.0456356i | ||||
\(583\) | 125.564 | + | 125.564i | 0.00891997 | + | 0.00891997i | ||||
\(584\) | 1468.01 | − | 553.162i | 0.104018 | − | 0.0391952i | ||||
\(585\) | 604.904 | + | 889.455i | 0.0427516 | + | 0.0628623i | ||||
\(586\) | 10968.4 | + | 4682.41i | 0.773207 | + | 0.330083i | ||||
\(587\) | −6773.84 | + | 6773.84i | −0.476297 | + | 0.476297i | −0.903945 | − | 0.427648i | \(-0.859342\pi\) |
0.427648 | + | 0.903945i | \(0.359342\pi\) | |||||||
\(588\) | 148.648 | − | 6893.18i | 0.0104254 | − | 0.483452i | ||||
\(589\) | − | 25199.9i | − | 1.76289i | ||||||
\(590\) | −2558.20 | − | 13037.7i | −0.178507 | − | 0.909751i | ||||
\(591\) | 464.626i | 0.0323387i | ||||||||
\(592\) | 8736.43 | − | 8013.68i | 0.606529 | − | 0.556351i | ||||
\(593\) | −7866.71 | + | 7866.71i | −0.544767 | + | 0.544767i | −0.924923 | − | 0.380155i | \(-0.875871\pi\) |
0.380155 | + | 0.924923i | \(0.375871\pi\) | |||||||
\(594\) | 42.0250 | − | 98.4420i | 0.00290287 | − | 0.00679987i | ||||
\(595\) | 6023.77 | + | 1147.03i | 0.415043 | + | 0.0790312i | ||||
\(596\) | −9542.37 | − | 9962.99i | −0.655823 | − | 0.684732i | ||||
\(597\) | 2282.60 | + | 2282.60i | 0.156484 | + | 0.156484i | ||||
\(598\) | 792.780 | + | 1973.86i | 0.0542127 | + | 0.134979i | ||||
\(599\) | 5663.67 | 0.386330 | 0.193165 | − | 0.981166i | \(-0.438125\pi\) | ||||
0.193165 | + | 0.981166i | \(0.438125\pi\) | |||||||
\(600\) | 135.515 | − | 8484.20i | 0.00922065 | − | 0.577277i | ||||
\(601\) | −7673.02 | −0.520780 | −0.260390 | − | 0.965503i | \(-0.583851\pi\) | ||||
−0.260390 | + | 0.965503i | \(0.583851\pi\) | |||||||
\(602\) | 2129.58 | + | 5302.24i | 0.144178 | + | 0.358975i | ||||
\(603\) | −6206.60 | − | 6206.60i | −0.419158 | − | 0.419158i | ||||
\(604\) | 6714.35 | + | 7010.32i | 0.452323 | + | 0.472261i | ||||
\(605\) | 14596.8 | + | 2779.48i | 0.980899 | + | 0.186780i | ||||
\(606\) | −2145.18 | + | 5025.01i | −0.143799 | + | 0.336843i | ||||
\(607\) | 5437.64 | − | 5437.64i | 0.363603 | − | 0.363603i | −0.501535 | − | 0.865137i | \(-0.667231\pi\) |
0.865137 | + | 0.501535i | \(0.167231\pi\) | |||||||
\(608\) | 27131.0 | − | 9560.50i | 1.80972 | − | 0.637713i | ||||
\(609\) | 5190.15i | 0.345346i | ||||||||
\(610\) | −1764.69 | − | 8993.63i | −0.117132 | − | 0.596953i | ||||
\(611\) | 4334.85i | 0.287020i | ||||||||
\(612\) | −114.058 | + | 5289.12i | −0.00753350 | + | 0.349346i | ||||
\(613\) | 13245.8 | − | 13245.8i | 0.872745 | − | 0.872745i | −0.120026 | − | 0.992771i | \(-0.538298\pi\) |
0.992771 | + | 0.120026i | \(0.0382977\pi\) | |||||||
\(614\) | 15324.9 | + | 6542.19i | 1.00727 | + | 0.430002i | ||||
\(615\) | −6637.42 | − | 9759.71i | −0.435198 | − | 0.639918i | ||||
\(616\) | 83.4736 | + | 221.527i | 0.00545981 | + | 0.0144895i | ||||
\(617\) | −13290.6 | − | 13290.6i | −0.867195 | − | 0.867195i | 0.124966 | − | 0.992161i | \(-0.460118\pi\) |
−0.992161 | + | 0.124966i | \(0.960118\pi\) | |||||||
\(618\) | 1396.98 | − | 561.081i | 0.0909300 | − | 0.0365210i | ||||
\(619\) | −1651.71 | −0.107250 | −0.0536249 | − | 0.998561i | \(-0.517078\pi\) | ||||
−0.0536249 | + | 0.998561i | \(0.517078\pi\) | |||||||
\(620\) | 7721.52 | + | 11897.5i | 0.500167 | + | 0.770672i | ||||
\(621\) | −1899.48 | −0.122743 | ||||||||
\(622\) | 2936.33 | − | 1179.34i | 0.189286 | − | 0.0760247i | ||||
\(623\) | 6900.76 | + | 6900.76i | 0.443777 | + | 0.443777i | ||||
\(624\) | 88.4803 | − | 2050.57i | 0.00567636 | − | 0.131552i | ||||
\(625\) | 11404.3 | + | 10680.9i | 0.729875 | + | 0.683581i | ||||
\(626\) | −22461.5 | − | 9588.82i | −1.43409 | − | 0.612215i | ||||
\(627\) | −472.487 | + | 472.487i | −0.0300946 | + | 0.0300946i | ||||
\(628\) | 14894.8 | + | 321.201i | 0.946447 | + | 0.0204097i | ||||
\(629\) | − | 13610.6i | − | 0.862785i | ||||||
\(630\) | 1184.84 | − | 1763.31i | 0.0749288 | − | 0.111511i | ||||
\(631\) | − | 30428.9i | − | 1.91974i | −0.280442 | − | 0.959871i | \(-0.590481\pi\) | ||
0.280442 | − | 0.959871i | \(-0.409519\pi\) | |||||||
\(632\) | −23679.5 | − | 10718.1i | −1.49038 | − | 0.674594i | ||||
\(633\) | 1376.87 | − | 1376.87i | 0.0864544 | − | 0.0864544i | ||||
\(634\) | 3484.07 | − | 8161.30i | 0.218249 | − | 0.511241i | ||||
\(635\) | 6005.03 | − | 4083.92i | 0.375279 | − | 0.255221i | ||||
\(636\) | −2195.92 | + | 2103.21i | −0.136909 | + | 0.131129i | ||||
\(637\) | 2171.55 | + | 2171.55i | 0.135071 | + | 0.135071i | ||||
\(638\) | 342.448 | + | 852.627i | 0.0212502 | + | 0.0529088i | ||||
\(639\) | 9317.16 | 0.576809 | ||||||||
\(640\) | −9879.85 | + | 12827.0i | −0.610212 | + | 0.792238i | ||||
\(641\) | 341.972 | 0.0210719 | 0.0105359 | − | 0.999944i | \(-0.496646\pi\) | ||||
0.0105359 | + | 0.999944i | \(0.496646\pi\) | |||||||
\(642\) | −3895.29 | − | 9698.48i | −0.239462 | − | 0.596213i | ||||
\(643\) | −7618.85 | − | 7618.85i | −0.467275 | − | 0.467275i | 0.433755 | − | 0.901031i | \(-0.357188\pi\) |
−0.901031 | + | 0.433755i | \(0.857188\pi\) | |||||||
\(644\) | 3033.93 | − | 2905.84i | 0.185642 | − | 0.177805i | ||||
\(645\) | 1698.01 | − | 8917.34i | 0.103658 | − | 0.544372i | ||||
\(646\) | 12966.7 | − | 30373.9i | 0.789731 | − | 1.84992i | ||||
\(647\) | −15349.3 | + | 15349.3i | −0.932677 | + | 0.932677i | −0.997872 | − | 0.0651957i | \(-0.979233\pi\) |
0.0651957 | + | 0.997872i | \(0.479233\pi\) | |||||||
\(648\) | 1669.74 | + | 755.778i | 0.101225 | + | 0.0458176i | ||||
\(649\) | − | 588.883i | − | 0.0356174i | ||||||
\(650\) | 2687.39 | + | 2657.51i | 0.162166 | + | 0.160363i | ||||
\(651\) | 3551.05i | 0.213789i | ||||||||
\(652\) | 16557.1 | + | 357.047i | 0.994520 | + | 0.0214464i | ||||
\(653\) | −3802.77 | + | 3802.77i | −0.227893 | + | 0.227893i | −0.811812 | − | 0.583919i | \(-0.801518\pi\) |
0.583919 | + | 0.811812i | \(0.301518\pi\) | |||||||
\(654\) | −1927.81 | − | 822.984i | −0.115265 | − | 0.0492068i | ||||
\(655\) | −1799.39 | + | 9449.77i | −0.107341 | + | 0.563714i | ||||
\(656\) | −970.867 | + | 22500.2i | −0.0577835 | + | 1.33916i | ||||
\(657\) | −441.217 | − | 441.217i | −0.0262002 | − | 0.0262002i | ||||
\(658\) | 7944.44 | − | 3190.80i | 0.470678 | − | 0.189043i | ||||
\(659\) | −4982.51 | −0.294524 | −0.147262 | − | 0.989098i | \(-0.547046\pi\) | ||||
−0.147262 | + | 0.989098i | \(0.547046\pi\) | |||||||
\(660\) | 78.2987 | − | 367.849i | 0.00461784 | − | 0.0216947i | ||||
\(661\) | −19650.1 | −1.15628 | −0.578139 | − | 0.815939i | \(-0.696221\pi\) | ||||
−0.578139 | + | 0.815939i | \(0.696221\pi\) | |||||||
\(662\) | −9840.77 | + | 3952.44i | −0.577753 | + | 0.232048i | ||||
\(663\) | −1666.23 | − | 1666.23i | −0.0976033 | − | 0.0976033i | ||||
\(664\) | 843.076 | + | 2237.40i | 0.0492737 | + | 0.130765i | ||||
\(665\) | −10966.3 | + | 7457.97i | −0.639479 | + | 0.434899i | ||||
\(666\) | −4336.71 | − | 1851.35i | −0.252318 | − | 0.107715i | ||||
\(667\) | 11529.7 | − | 11529.7i | 0.669314 | − | 0.669314i | ||||
\(668\) | −169.700 | + | 7869.37i | −0.00982915 | + | 0.455801i | ||||
\(669\) | 16014.7i | 0.925509i | ||||||||
\(670\) | −25598.7 | − | 17200.8i | −1.47606 | − | 0.991825i | ||||
\(671\) | − | 406.222i | − | 0.0233712i | ||||||
\(672\) | −3823.18 | + | 1347.22i | −0.219468 | + | 0.0773368i | ||||
\(673\) | 13172.1 | − | 13172.1i | 0.754455 | − | 0.754455i | −0.220853 | − | 0.975307i | \(-0.570884\pi\) |
0.975307 | + | 0.220853i | \(0.0708840\pi\) | |||||||
\(674\) | −8479.63 | + | 19863.2i | −0.484604 | + | 1.13517i | ||||
\(675\) | −3096.53 | + | 1342.43i | −0.176571 | + | 0.0765482i | ||||
\(676\) | −11524.9 | − | 12032.9i | −0.655719 | − | 0.684623i | ||||
\(677\) | −16647.6 | − | 16647.6i | −0.945078 | − | 0.945078i | 0.0534901 | − | 0.998568i | \(-0.482965\pi\) |
−0.998568 | + | 0.0534901i | \(0.982965\pi\) | |||||||
\(678\) | −5753.25 | − | 14324.4i | −0.325888 | − | 0.811396i | ||||
\(679\) | −1512.37 | −0.0854776 | ||||||||
\(680\) | 3185.00 | + | 18313.5i | 0.179616 | + | 1.03278i | ||||
\(681\) | 4711.33 | 0.265108 | ||||||||
\(682\) | 234.300 | + | 583.359i | 0.0131551 | + | 0.0327536i | ||||
\(683\) | 15171.4 | + | 15171.4i | 0.849954 | + | 0.849954i | 0.990127 | − | 0.140173i | \(-0.0447657\pi\) |
−0.140173 | + | 0.990127i | \(0.544766\pi\) | |||||||
\(684\) | −7914.19 | − | 8263.05i | −0.442407 | − | 0.461909i | ||||
\(685\) | 3133.93 | + | 4608.15i | 0.174805 | + | 0.257034i | ||||
\(686\) | 5224.56 | − | 12238.3i | 0.290779 | − | 0.681140i | ||||
\(687\) | −306.692 | + | 306.692i | −0.0170321 | + | 0.0170321i | ||||
\(688\) | −12764.4 | + | 11708.4i | −0.707323 | + | 0.648807i | ||||
\(689\) | − | 1354.35i | − | 0.0748864i | ||||||
\(690\) | −6549.20 | + | 1285.06i | −0.361339 | + | 0.0709003i | ||||
\(691\) | − | 1675.28i | − | 0.0922297i | −0.998936 | − | 0.0461148i | \(-0.985316\pi\) | ||
0.998936 | − | 0.0461148i | \(-0.0146840\pi\) | |||||||
\(692\) | 61.6282 | − | 2857.85i | 0.00338548 | − | 0.156993i | ||||
\(693\) | 66.5807 | − | 66.5807i | 0.00364963 | − | 0.00364963i | ||||
\(694\) | −792.904 | − | 338.491i | −0.0433692 | − | 0.0185144i | ||||
\(695\) | −13619.8 | − | 2593.45i | −0.743353 | − | 0.141547i | ||||
\(696\) | −14722.8 | + | 5547.69i | −0.801817 | + | 0.302133i | ||||
\(697\) | 18283.0 | + | 18283.0i | 0.993570 | + | 0.993570i | ||||
\(698\) | −21820.8 | + | 8764.09i | −1.18328 | + | 0.475251i | ||||
\(699\) | 13140.3 | 0.711032 | ||||||||
\(700\) | 2892.27 | − | 6881.30i | 0.156168 | − | 0.371555i | ||||
\(701\) | −11625.6 | −0.626381 | −0.313190 | − | 0.949690i | \(-0.601398\pi\) | ||||
−0.313190 | + | 0.949690i | \(0.601398\pi\) | |||||||
\(702\) | −757.548 | + | 304.261i | −0.0407291 | + | 0.0163584i | ||||
\(703\) | 20814.7 | + | 20814.7i | 1.11670 | + | 1.11670i | ||||
\(704\) | −539.174 | + | 473.574i | −0.0288649 | + | 0.0253530i | ||||
\(705\) | −13361.0 | − | 2544.16i | −0.713766 | − | 0.135913i | ||||
\(706\) | 4412.94 | + | 1883.89i | 0.235245 | + | 0.100426i | ||||
\(707\) | −3398.64 | + | 3398.64i | −0.180790 | + | 0.180790i | ||||
\(708\) | 10081.2 | + | 217.398i | 0.535136 | + | 0.0115400i | ||||
\(709\) | 25418.8i | 1.34644i | 0.739444 | + | 0.673219i | \(0.235089\pi\) | ||||
−0.739444 | + | 0.673219i | \(0.764911\pi\) | |||||||
\(710\) | 32124.6 | − | 6303.35i | 1.69805 | − | 0.333184i | ||||
\(711\) | 10338.3i | 0.545314i | ||||||||
\(712\) | −12199.0 | + | 26951.3i | −0.642104 | + | 1.41860i | ||||
\(713\) | 7888.52 | − | 7888.52i | 0.414344 | − | 0.414344i | ||||
\(714\) | −1827.21 | + | 4280.16i | −0.0957723 | + | 0.224343i | ||||
\(715\) | 94.2040 | + | 138.518i | 0.00492731 | + | 0.00724516i | ||||
\(716\) | 14280.1 | − | 13677.2i | 0.745354 | − | 0.713887i | ||||
\(717\) | 3650.99 | + | 3650.99i | 0.190165 | + | 0.190165i | ||||
\(718\) | −10754.3 | − | 26776.2i | −0.558982 | − | 1.39175i | ||||
\(719\) | 27090.8 | 1.40517 | 0.702586 | − | 0.711599i | \(-0.252029\pi\) | ||||
0.702586 | + | 0.711599i | \(0.252029\pi\) | |||||||
\(720\) | 6268.40 | + | 1476.21i | 0.324457 | + | 0.0764101i | ||||
\(721\) | 1324.32 | 0.0684055 | ||||||||
\(722\) | 19390.4 | + | 48278.1i | 0.999493 | + | 2.48854i | ||||
\(723\) | 3691.73 | + | 3691.73i | 0.189899 | + | 0.189899i | ||||
\(724\) | −15015.2 | + | 14381.3i | −0.770769 | + | 0.738228i | ||||
\(725\) | 10647.3 | − | 26944.2i | 0.545423 | − | 1.38025i | ||||
\(726\) | −4427.68 | + | 10371.7i | −0.226345 | + | 0.530206i | ||||
\(727\) | 18281.4 | − | 18281.4i | 0.932627 | − | 0.932627i | −0.0652427 | − | 0.997869i | \(-0.520782\pi\) |
0.997869 | + | 0.0652427i | \(0.0207822\pi\) | |||||||
\(728\) | 744.529 | − | 1644.89i | 0.0379040 | − | 0.0837411i | ||||
\(729\) | − | 729.000i | − | 0.0370370i | ||||||
\(730\) | −1819.77 | − | 1222.77i | −0.0922638 | − | 0.0619957i | ||||
\(731\) | 19885.9i | 1.00616i | ||||||||
\(732\) | 6954.23 | + | 149.965i | 0.351142 | + | 0.00757222i | ||||
\(733\) | 17901.9 | − | 17901.9i | 0.902074 | − | 0.902074i | −0.0935411 | − | 0.995615i | \(-0.529819\pi\) |
0.995615 | + | 0.0935411i | \(0.0298186\pi\) | |||||||
\(734\) | −29321.8 | − | 12517.5i | −1.47451 | − | 0.629468i | ||||
\(735\) | −7967.75 | + | 5418.73i | −0.399857 | + | 0.271936i | ||||
\(736\) | 11485.9 | + | 5500.24i | 0.575237 | + | 0.275464i | ||||
\(737\) | −966.578 | − | 966.578i | −0.0483098 | − | 0.0483098i | ||||
\(738\) | 8312.34 | − | 3338.56i | 0.414609 | − | 0.166523i | ||||
\(739\) | −15909.2 | −0.791922 | −0.395961 | − | 0.918267i | \(-0.629588\pi\) | ||||
−0.395961 | + | 0.918267i | \(0.629588\pi\) | |||||||
\(740\) | −16205.0 | − | 3449.33i | −0.805011 | − | 0.171351i | ||||
\(741\) | 5096.31 | 0.252655 | ||||||||
\(742\) | −2482.11 | + | 996.913i | −0.122805 | + | 0.0493232i | ||||
\(743\) | 5683.09 | + | 5683.09i | 0.280609 | + | 0.280609i | 0.833352 | − | 0.552743i | \(-0.186419\pi\) |
−0.552743 | + | 0.833352i | \(0.686419\pi\) | |||||||
\(744\) | −10073.2 | + | 3795.68i | −0.496371 | + | 0.187038i | ||||
\(745\) | −3606.42 | + | 18939.6i | −0.177354 | + | 0.931400i | ||||
\(746\) | −11420.8 | − | 4875.57i | −0.560518 | − | 0.239286i | ||||
\(747\) | 672.460 | − | 672.460i | 0.0329371 | − | 0.0329371i | ||||
\(748\) | −17.7626 | + | 823.695i | −0.000868270 | + | 0.0402637i | ||||
\(749\) | − | 9194.07i | − | 0.448524i | ||||||
\(750\) | −9768.33 | + | 6723.45i | −0.475585 | + | 0.327341i | ||||
\(751\) | 20133.5i | 0.978271i | 0.872208 | + | 0.489135i | \(0.162688\pi\) | ||||
−0.872208 | + | 0.489135i | \(0.837312\pi\) | |||||||
\(752\) | 17542.9 | + | 19125.1i | 0.850699 | + | 0.927423i | ||||
\(753\) | −8974.54 | + | 8974.54i | −0.434330 | + | 0.434330i | ||||
\(754\) | 2751.43 | − | 6445.12i | 0.132893 | − | 0.311296i | ||||
\(755\) | 2537.61 | − | 13326.6i | 0.122322 | − | 0.642390i | ||||
\(756\) | 1115.23 | + | 1164.39i | 0.0536516 | + | 0.0560166i | ||||
\(757\) | 19878.4 | + | 19878.4i | 0.954417 | + | 0.954417i | 0.999005 | − | 0.0445880i | \(-0.0141975\pi\) |
−0.0445880 | + | 0.999005i | \(0.514198\pi\) | |||||||
\(758\) | 4368.70 | + | 10877.2i | 0.209338 | + | 0.521210i | ||||
\(759\) | −295.813 | −0.0141467 | ||||||||
\(760\) | −32877.5 | − | 23135.9i | −1.56920 | − | 1.10425i | ||||
\(761\) | 16214.1 | 0.772355 | 0.386177 | − | 0.922425i | \(-0.373795\pi\) | ||||
0.386177 | + | 0.922425i | \(0.373795\pi\) | |||||||
\(762\) | 2054.17 | + | 5114.48i | 0.0976574 | + | 0.243147i | ||||
\(763\) | −1303.86 | − | 1303.86i | −0.0618651 | − | 0.0618651i | ||||
\(764\) | 288.480 | + | 301.197i | 0.0136608 | + | 0.0142630i | ||||
\(765\) | 6113.63 | − | 4157.78i | 0.288940 | − | 0.196503i | ||||
\(766\) | 2468.79 | − | 5783.04i | 0.116450 | − | 0.272781i | ||||
\(767\) | −3175.89 | + | 3175.89i | −0.149511 | + | 0.149511i | ||||
\(768\) | −7908.19 | − | 9405.08i | −0.371565 | − | 0.441897i | ||||
\(769\) | − | 1687.15i | − | 0.0791161i | −0.999217 | − | 0.0395581i | \(-0.987405\pi\) | ||
0.999217 | − | 0.0395581i | \(-0.0125950\pi\) | |||||||
\(770\) | 184.520 | − | 274.607i | 0.00863587 | − | 0.0128522i | ||||
\(771\) | 1598.38i | 0.0746617i | ||||||||
\(772\) | 34.0302 | − | 1578.06i | 0.00158649 | − | 0.0735694i | ||||
\(773\) | −11843.8 | + | 11843.8i | −0.551087 | + | 0.551087i | −0.926755 | − | 0.375667i | \(-0.877414\pi\) |
0.375667 | + | 0.926755i | \(0.377414\pi\) | |||||||
\(774\) | 6336.17 | + | 2704.92i | 0.294249 | + | 0.125615i | ||||
\(775\) | 7284.80 | − | 18435.0i | 0.337649 | − | 0.854457i | ||||
\(776\) | −1616.55 | − | 4290.08i | −0.0747819 | − | 0.198460i | ||||
\(777\) | −2933.11 | − | 2933.11i | −0.135424 | − | 0.135424i | ||||
\(778\) | −14849.8 | + | 5964.25i | −0.684307 | + | 0.274844i | ||||
\(779\) | −55920.2 | −2.57195 | ||||||||
\(780\) | −2406.11 | + | 1561.57i | −0.110452 | + | 0.0716833i | ||||
\(781\) | 1451.00 | 0.0664798 | ||||||||
\(782\) | 13567.3 | − | 5449.14i | 0.620415 | − | 0.249183i | ||||
\(783\) | 4424.99 | + | 4424.99i | 0.201962 | + | 0.201962i | ||||
\(784\) | 18369.0 | + | 792.607i | 0.836780 | + | 0.0361064i | ||||
\(785\) | −11708.8 | − | 17216.8i | −0.532365 | − | 0.782794i | ||||
\(786\) | −6714.48 | − | 2866.42i | −0.304705 | − | 0.130079i | ||||
\(787\) | 8086.40 | − | 8086.40i | 0.366263 | − | 0.366263i | −0.499849 | − | 0.866112i | \(-0.666611\pi\) |
0.866112 | + | 0.499849i | \(0.166611\pi\) | |||||||
\(788\) | −1238.72 | − | 26.7124i | −0.0559992 | − | 0.00120760i | ||||
\(789\) | 14268.6i | 0.643821i | ||||||||
\(790\) | 6994.21 | + | 35645.5i | 0.314991 | + | 1.60533i | ||||
\(791\) | − | 13579.4i | − | 0.610403i | ||||||
\(792\) | 260.035 | + | 117.700i | 0.0116666 | + | 0.00528068i | ||||
\(793\) | −2190.79 | + | 2190.79i | −0.0981048 | + | 0.0981048i | ||||
\(794\) | 8616.84 | − | 20184.6i | 0.385139 | − | 0.902173i | ||||
\(795\) | 4174.44 | + | 794.883i | 0.186229 | + | 0.0354611i | ||||
\(796\) | −6216.76 | + | 5954.30i | −0.276818 | + | 0.265131i | ||||
\(797\) | −27180.0 | − | 27180.0i | −1.20799 | − | 1.20799i | −0.971678 | − | 0.236308i | \(-0.924062\pi\) |
−0.236308 | − | 0.971678i | \(-0.575938\pi\) | |||||||
\(798\) | −3751.29 | − | 9339.96i | −0.166409 | − | 0.414324i | ||||
\(799\) | 29795.4 | 1.31926 | ||||||||
\(800\) | 22611.5 | + | 849.065i | 0.999296 | + | 0.0375237i | ||||
\(801\) | 11766.8 | 0.519051 | ||||||||
\(802\) | −9585.78 | − | 23866.7i | −0.422052 | − | 1.05082i | ||||
\(803\) | −68.7124 | − | 68.7124i | −0.00301968 | − | 0.00301968i | ||||
\(804\) | 16903.9 | − | 16190.3i | 0.741487 | − | 0.710182i | ||||
\(805\) | −5767.49 | − | 1098.23i | −0.252518 | − | 0.0480838i | ||||
\(806\) | 1882.50 | − | 4409.69i | 0.0822683 | − | 0.192711i | ||||
\(807\) | 13509.4 | − | 13509.4i | 0.589284 | − | 0.589284i | ||||
\(808\) | −13273.6 | − | 6008.05i | −0.577924 | − | 0.261587i | ||||
\(809\) | − | 24.5910i | − | 0.00106870i | −1.00000 | 0.000534348i | \(-0.999830\pi\) | |||
1.00000 | 0.000534348i | \(-0.000170088\pi\) | ||||||||
\(810\) | −493.191 | − | 2513.52i | −0.0213938 | − | 0.109032i | ||||
\(811\) | 45766.8i | 1.98162i | 0.135276 | + | 0.990808i | \(0.456808\pi\) | ||||
−0.135276 | + | 0.990808i | \(0.543192\pi\) | |||||||
\(812\) | −13837.2 | − | 298.393i | −0.598018 | − | 0.0128960i | ||||
\(813\) | 3832.76 | − | 3832.76i | 0.165339 | − | 0.165339i | ||||
\(814\) | −675.372 | − | 288.317i | −0.0290808 | − | 0.0124146i | ||||
\(815\) | −13015.6 | − | 19138.2i | −0.559406 | − | 0.822554i | ||||
\(816\) | −14094.5 | − | 608.166i | −0.604664 | − | 0.0260908i | ||||
\(817\) | −30411.4 | − | 30411.4i | −1.30228 | − | 1.30228i | ||||
\(818\) | −13509.1 | + | 5425.79i | −0.577427 | + | 0.231917i | ||||
\(819\) | −718.149 | −0.0306400 | ||||||||
\(820\) | 26401.5 | − | 17134.6i | 1.12436 | − | 0.729714i | ||||
\(821\) | 19818.7 | 0.842483 | 0.421242 | − | 0.906948i | \(-0.361594\pi\) | ||||
0.421242 | + | 0.906948i | \(0.361594\pi\) | |||||||
\(822\) | −3924.76 | + | 1576.34i | −0.166535 | + | 0.0668869i | ||||
\(823\) | −11931.2 | − | 11931.2i | −0.505339 | − | 0.505339i | 0.407753 | − | 0.913092i | \(-0.366312\pi\) |
−0.913092 | + | 0.407753i | \(0.866312\pi\) | |||||||
\(824\) | 1415.55 | + | 3756.67i | 0.0598460 | + | 0.158823i | ||||
\(825\) | −482.235 | + | 209.061i | −0.0203506 | + | 0.00882251i | ||||
\(826\) | 8158.13 | + | 3482.72i | 0.343653 | + | 0.146706i | ||||
\(827\) | 22543.2 | − | 22543.2i | 0.947889 | − | 0.947889i | −0.0508193 | − | 0.998708i | \(-0.516183\pi\) |
0.998708 | + | 0.0508193i | \(0.0161832\pi\) | |||||||
\(828\) | 109.205 | − | 5064.10i | 0.00458350 | − | 0.212548i | ||||
\(829\) | − | 9845.03i | − | 0.412463i | −0.978503 | − | 0.206232i | \(-0.933880\pi\) | ||
0.978503 | − | 0.206232i | \(-0.0661200\pi\) | |||||||
\(830\) | 1863.63 | − | 2773.51i | 0.0779369 | − | 0.115988i | ||||
\(831\) | − | 23473.9i | − | 0.979906i | ||||||
\(832\) | 5461.82 | + | 353.784i | 0.227590 | + | 0.0147419i | ||||
\(833\) | 14926.1 | − | 14926.1i | 0.620838 | − | 0.620838i | ||||
\(834\) | 4131.34 | − | 9677.51i | 0.171531 | − | 0.401804i | ||||
\(835\) | 9096.11 | − | 6186.12i | 0.376987 | − | 0.256383i | ||||
\(836\) | −1232.51 | − | 1286.84i | −0.0509894 | − | 0.0532370i | ||||
\(837\) | 3027.53 | + | 3027.53i | 0.125026 | + | 0.125026i | ||||
\(838\) | 8850.65 | + | 22036.3i | 0.364845 | + | 0.908392i | ||||
\(839\) | 2289.14 | 0.0941953 | 0.0470977 | − | 0.998890i | \(-0.485003\pi\) | ||||
0.0470977 | + | 0.998890i | \(0.485003\pi\) | |||||||
\(840\) | 4632.96 | + | 3260.21i | 0.190300 | + | 0.133914i | ||||
\(841\) | −29329.8 | −1.20258 | ||||||||
\(842\) | −14332.2 | − | 35684.4i | −0.586605 | − | 1.46053i | ||||
\(843\) | −10268.4 | − | 10268.4i | −0.419530 | − | 0.419530i | ||||
\(844\) | 3591.64 | + | 3749.96i | 0.146480 | + | 0.152937i | ||||
\(845\) | −4355.70 | + | 22874.6i | −0.177326 | + | 0.931253i | ||||
\(846\) | 4052.83 | − | 9493.60i | 0.164703 | − | 0.385812i | ||||
\(847\) | −7014.83 | + | 7014.83i | −0.284572 | + | 0.284572i | ||||
\(848\) | −5481.01 | − | 5975.35i | −0.221956 | − | 0.241974i | ||||
\(849\) | 21873.4i | 0.884211i | ||||||||
\(850\) | 18266.3 | − | 18471.7i | 0.737093 | − | 0.745380i | ||||
\(851\) | 13031.6i | 0.524931i | ||||||||
\(852\) | −535.664 | + | 24840.0i | −0.0215394 | + | 0.998831i | ||||
\(853\) | 842.336 | − | 842.336i | 0.0338113 | − | 0.0338113i | −0.689999 | − | 0.723810i | \(-0.742389\pi\) |
0.723810 | + | 0.689999i | \(0.242389\pi\) | |||||||
\(854\) | 5627.63 | + | 2402.44i | 0.225496 | + | 0.0962645i | ||||
\(855\) | −2991.07 | + | 15708.0i | −0.119640 | + | 0.628307i | ||||
\(856\) | 26080.6 | − | 9827.43i | 1.04137 | − | 0.392400i | ||||
\(857\) | −4975.55 | − | 4975.55i | −0.198321 | − | 0.198321i | 0.600959 | − | 0.799280i | \(-0.294786\pi\) |
−0.799280 | + | 0.600959i | \(0.794786\pi\) | |||||||
\(858\) | −117.976 | + | 47.3837i | −0.00469421 | + | 0.00188538i | ||||
\(859\) | −30452.1 | −1.20956 | −0.604781 | − | 0.796392i | \(-0.706739\pi\) | ||||
−0.604781 | + | 0.796392i | \(0.706739\pi\) | |||||||
\(860\) | 23676.4 | + | 5039.66i | 0.938790 | + | 0.199827i | ||||
\(861\) | 7880.03 | 0.311905 | ||||||||
\(862\) | −25231.5 | + | 10133.9i | −0.996968 | + | 0.400421i | ||||
\(863\) | 18215.5 | + | 18215.5i | 0.718498 | + | 0.718498i | 0.968298 | − | 0.249799i | \(-0.0803646\pi\) |
−0.249799 | + | 0.968298i | \(0.580365\pi\) | |||||||
\(864\) | −2110.94 | + | 4408.15i | −0.0831199 | + | 0.173575i | ||||
\(865\) | −3303.35 | + | 2246.56i | −0.129847 | + | 0.0883066i | ||||
\(866\) | 34525.2 | + | 14738.8i | 1.35475 | + | 0.578344i | ||||
\(867\) | −1030.71 | + | 1030.71i | −0.0403746 | + | 0.0403746i | ||||
\(868\) | −9467.27 | − | 204.158i | −0.370208 | − | 0.00798337i | ||||
\(869\) | 1610.03i | 0.0628498i | ||||||||
\(870\) | 18250.5 | + | 12263.3i | 0.711208 | + | 0.477889i | ||||
\(871\) | 10425.6i | 0.405579i | ||||||||
\(872\) | 2304.95 | − | 5092.32i | 0.0895131 | − | 0.197761i | ||||
\(873\) | −1289.40 | + | 1289.40i | −0.0499882 | + | 0.0499882i | ||||
\(874\) | −12415.0 | + | 29081.7i | −0.480485 | + | 1.12552i | ||||
\(875\) | −10178.3 | + | 2285.75i | −0.393246 | + | 0.0883114i | ||||
\(876\) | 1201.67 | − | 1150.94i | 0.0463478 | − | 0.0443911i | ||||
\(877\) | 3474.76 | + | 3474.76i | 0.133790 | + | 0.133790i | 0.770831 | − | 0.637040i | \(-0.219841\pi\) |
−0.637040 | + | 0.770831i | \(0.719841\pi\) | |||||||
\(878\) | 5237.50 | + | 13040.3i | 0.201318 | + | 0.501241i | ||||
\(879\) | 12649.5 | 0.485387 | ||||||||
\(880\) | 976.201 | + | 229.896i | 0.0373952 | + | 0.00880660i | ||||
\(881\) | 31547.7 | 1.20644 | 0.603218 | − | 0.797577i | \(-0.293885\pi\) | ||||
0.603218 | + | 0.797577i | \(0.293885\pi\) | |||||||
\(882\) | −2725.57 | − | 6786.13i | −0.104053 | − | 0.259071i | ||||
\(883\) | −23531.5 | − | 23531.5i | −0.896827 | − | 0.896827i | 0.0983271 | − | 0.995154i | \(-0.468651\pi\) |
−0.995154 | + | 0.0983271i | \(0.968651\pi\) | |||||||
\(884\) | 4538.04 | − | 4346.45i | 0.172659 | − | 0.165370i | ||||
\(885\) | −7924.87 | − | 11652.8i | −0.301008 | − | 0.442604i | ||||
\(886\) | −1996.70 | + | 4677.19i | −0.0757114 | + | 0.177351i | ||||
\(887\) | 24361.7 | − | 24361.7i | 0.922194 | − | 0.922194i | −0.0749901 | − | 0.997184i | \(-0.523893\pi\) |
0.997184 | + | 0.0749901i | \(0.0238925\pi\) | |||||||
\(888\) | 5185.10 | − | 11455.4i | 0.195947 | − | 0.432904i | ||||
\(889\) | 4848.48i | 0.182917i | ||||||||
\(890\) | 40570.7 | − | 7960.61i | 1.52802 | − | 0.299821i | ||||
\(891\) | − | 113.530i | − | 0.00426868i | ||||||
\(892\) | −42696.1 | − | 920.722i | −1.60266 | − | 0.0345606i | ||||
\(893\) | −45565.9 | + | 45565.9i | −1.70751 | + | 1.70751i | ||||
\(894\) | −13457.4 | − | 5745.00i | −0.503450 | − | 0.214923i | ||||
\(895\) | −27146.5 | − | 5169.15i | −1.01386 | − | 0.193056i | ||||
\(896\) | −3371.96 | − | 10270.2i | −0.125725 | − | 0.382929i | ||||
\(897\) | 1595.34 | + | 1595.34i | 0.0593833 | + | 0.0593833i | ||||
\(898\) | −20414.2 | + | 8199.14i | −0.758609 | + | 0.304687i | ||||
\(899\) | −36753.9 | −1.36353 | ||||||||
\(900\) | −3400.94 | − | 8332.68i | −0.125961 | − | 0.308618i | ||||
\(901\) | −9309.10 | −0.344207 | ||||||||
\(902\) | 1294.51 | − | 519.927i | 0.0477856 | − | 0.0191925i | ||||
\(903\) | 4285.44 | + | 4285.44i | 0.157930 | + | 0.157930i | ||||
\(904\) | 38520.4 | − | 14514.9i | 1.41722 | − | 0.534025i | ||||
\(905\) | 28543.9 | + | 5435.24i | 1.04843 | + | 0.199639i | ||||
\(906\) | 9469.14 | + | 4042.39i | 0.347231 | + | 0.148233i | ||||
\(907\) | −19097.8 | + | 19097.8i | −0.699154 | + | 0.699154i | −0.964228 | − | 0.265074i | \(-0.914604\pi\) |
0.265074 | + | 0.964228i | \(0.414604\pi\) | |||||||
\(908\) | −270.864 | + | 12560.6i | −0.00989972 | + | 0.459074i | ||||
\(909\) | 5795.17i | 0.211456i | ||||||||
\(910\) | −2476.10 | + | 485.850i | −0.0902000 | + | 0.0176987i | ||||
\(911\) | − | 4084.84i | − | 0.148558i | −0.997237 | − | 0.0742792i | \(-0.976334\pi\) | ||
0.997237 | − | 0.0742792i | \(-0.0236656\pi\) | |||||||
\(912\) | 22484.7 | − | 20624.5i | 0.816384 | − | 0.748845i | ||||
\(913\) | 104.725 | − | 104.725i | 0.00379615 | − | 0.00379615i | ||||
\(914\) | 6183.79 | − | 14485.3i | 0.223787 | − | 0.524214i | ||||
\(915\) | −5466.72 | − | 8038.31i | −0.197513 | − | 0.290424i | ||||
\(916\) | −800.024 | − | 835.289i | −0.0288576 | − | 0.0301296i | ||||
\(917\) | −4541.31 | − | 4541.31i | −0.163541 | − | 0.163541i | ||||
\(918\) | 2091.33 | + | 5206.98i | 0.0751896 | + | 0.187207i | ||||
\(919\) | −8349.81 | −0.299712 | −0.149856 | − | 0.988708i | \(-0.547881\pi\) | ||||
−0.149856 | + | 0.988708i | \(0.547881\pi\) | |||||||
\(920\) | −3049.49 | − | 17534.4i | −0.109281 | − | 0.628359i | ||||
\(921\) | 17673.6 | 0.632320 | ||||||||
\(922\) | 11402.6 | + | 28390.2i | 0.407294 | + | 1.01408i | ||||
\(923\) | −7825.33 | − | 7825.33i | −0.279062 | − | 0.279062i | ||||
\(924\) | 173.680 | + | 181.335i | 0.00618359 | + | 0.00645616i | ||||
\(925\) | 9209.86 | + | 21244.1i | 0.327371 | + | 0.755137i | ||||
\(926\) | −7185.15 | + | 16831.0i | −0.254988 | + | 0.597300i | ||||
\(927\) | 1129.08 | − | 1129.08i | 0.0400043 | − | 0.0400043i | ||||
\(928\) | −13944.0 | − | 39570.5i | −0.493247 | − | 1.39975i | ||||
\(929\) | 30013.5i | 1.05997i | 0.848008 | + | 0.529984i | \(0.177802\pi\) | ||||
−0.848008 | + | 0.529984i | \(0.822198\pi\) | |||||||
\(930\) | 12486.8 | + | 8390.40i | 0.440279 | + | 0.295841i | ||||
\(931\) | 45652.8i | 1.60710i | ||||||||
\(932\) | −755.463 | + | 35032.6i | −0.0265515 | + | 1.23126i | ||||
\(933\) | 2373.23 | − | 2373.23i | 0.0832756 | − | 0.0832756i | ||||
\(934\) | 39897.5 | + | 17032.3i | 1.39774 | + | 0.596695i | ||||
\(935\) | 952.100 | − | 647.507i | 0.0333016 | − | 0.0226479i | ||||
\(936\) | −767.621 | − | 2037.15i | −0.0268061 | − | 0.0711393i | ||||
\(937\) | −17115.8 | − | 17115.8i | −0.596743 | − | 0.596743i | 0.342701 | − | 0.939444i | \(-0.388658\pi\) |
−0.939444 | + | 0.342701i | \(0.888658\pi\) | |||||||
\(938\) | 19107.0 | − | 7674.11i | 0.665101 | − | 0.267131i | ||||
\(939\) | −25904.1 | −0.900263 | ||||||||
\(940\) | 7551.01 | − | 35474.8i | 0.262007 | − | 1.23092i | ||||
\(941\) | 19806.9 | 0.686170 | 0.343085 | − | 0.939304i | \(-0.388528\pi\) | ||||
0.343085 | + | 0.939304i | \(0.388528\pi\) | |||||||
\(942\) | 14663.5 | − | 5889.44i | 0.507180 | − | 0.203703i | ||||
\(943\) | −17505.2 | − | 17505.2i | −0.604503 | − | 0.604503i | ||||
\(944\) | −1159.18 | + | 26864.6i | −0.0399664 | + | 0.926236i | ||||
\(945\) | 421.489 | − | 2213.50i | 0.0145090 | − | 0.0761961i | ||||
\(946\) | 986.756 | + | 421.247i | 0.0339135 | + | 0.0144777i | ||||
\(947\) | −15101.6 | + | 15101.6i | −0.518199 | + | 0.518199i | −0.917026 | − | 0.398827i | \(-0.869417\pi\) |
0.398827 | + | 0.917026i | \(0.369417\pi\) | |||||||
\(948\) | −27562.5 | − | 594.373i | −0.944291 | − | 0.0203632i | ||||
\(949\) | 741.141i | 0.0253514i | ||||||||
\(950\) | 314.062 | + | 56183.1i | 0.0107258 | + | 1.91876i | ||||
\(951\) | − | 9412.16i | − | 0.320936i | ||||||
\(952\) | −11306.1 | − | 5117.49i | −0.384907 | − | 0.174221i | ||||
\(953\) | −13808.5 | + | 13808.5i | −0.469359 | + | 0.469359i | −0.901707 | − | 0.432348i | \(-0.857685\pi\) |
0.432348 | + | 0.901707i | \(0.357685\pi\) | |||||||
\(954\) | −1266.24 | + | 2966.13i | −0.0429728 | + | 0.100662i | ||||
\(955\) | 109.028 | − | 572.573i | 0.00369429 | − | 0.0194011i | ||||
\(956\) | −9943.60 | + | 9523.79i | −0.336401 | + | 0.322198i | ||||
\(957\) | 689.120 | + | 689.120i | 0.0232770 | + | 0.0232770i | ||||
\(958\) | 10767.8 | + | 26809.8i | 0.363146 | + | 0.904159i | ||||
\(959\) | −3720.64 | −0.125282 | ||||||||
\(960\) | −4296.04 | + | 16627.0i | −0.144431 | + | 0.558993i | ||||
\(961\) | 4644.33 | 0.155897 | ||||||||
\(962\) | 2087.42 | + | 5197.24i | 0.0699594 | + | 0.174185i | ||||
\(963\) | −7838.62 | − | 7838.62i | −0.262301 | − | 0.262301i | ||||
\(964\) | −10054.6 | + | 9630.09i | −0.335930 | + | 0.321747i | ||||
\(965\) | −1824.06 | + | 1240.51i | −0.0608483 | + | 0.0413819i | ||||
\(966\) | 1749.47 | − | 4098.06i | 0.0582693 | − | 0.136494i | ||||
\(967\) | 36563.4 | − | 36563.4i | 1.21593 | − | 1.21593i | 0.246879 | − | 0.969046i | \(-0.420595\pi\) |
0.969046 | − | 0.246879i | \(-0.0794051\pi\) | |||||||
\(968\) | −27396.8 | − | 12400.7i | −0.909677 | − | 0.411749i | ||||
\(969\) | − | 35029.3i | − | 1.16130i | ||||||
\(970\) | −3573.40 | + | 5318.05i | −0.118284 | + | 0.176033i | ||||
\(971\) | 17522.2i | 0.579108i | 0.957162 | + | 0.289554i | \(0.0935070\pi\) | ||||
−0.957162 | + | 0.289554i | \(0.906493\pi\) | |||||||
\(972\) | 1943.55 | + | 41.9118i | 0.0641351 | + | 0.00138305i | ||||
\(973\) | 6545.33 | − | 6545.33i | 0.215657 | − | 0.215657i | ||||
\(974\) | −39056.1 | − | 16673.1i | −1.28485 | − | 0.548502i | ||||
\(975\) | 3728.21 | + | 1473.25i | 0.122460 | + | 0.0483914i | ||||
\(976\) | −799.627 | + | 18531.7i | −0.0262248 | + | 0.607771i | ||||
\(977\) | 12863.3 | + | 12863.3i | 0.421222 | + | 0.421222i | 0.885624 | − | 0.464402i | \(-0.153731\pi\) |
−0.464402 | + | 0.885624i | \(0.653731\pi\) | |||||||
\(978\) | 16300.0 | − | 6546.71i | 0.532941 | − | 0.214050i | ||||
\(979\) | 1832.49 | 0.0598229 | ||||||||
\(980\) | −13988.5 | − | 21553.9i | −0.455966 | − | 0.702566i | ||||
\(981\) | −2223.28 | −0.0723587 | ||||||||
\(982\) | −10037.6 | + | 4031.49i | −0.326184 | + | 0.131008i | ||||
\(983\) | 27962.6 | + | 27962.6i | 0.907294 | + | 0.907294i | 0.996053 | − | 0.0887593i | \(-0.0282902\pi\) |
−0.0887593 | + | 0.996053i | \(0.528290\pi\) | |||||||
\(984\) | 8422.87 | + | 22353.0i | 0.272877 | + | 0.724176i | ||||
\(985\) | 973.755 | + | 1431.82i | 0.0314989 | + | 0.0463162i | ||||
\(986\) | −44300.3 | − | 18911.8i | −1.43084 | − | 0.610827i | ||||
\(987\) | 6420.95 | − | 6420.95i | 0.207073 | − | 0.207073i | ||||
\(988\) | −292.998 | + | 13587.0i | −0.00943471 | + | 0.437510i | ||||
\(989\) | − | 19039.8i | − | 0.612166i | ||||||
\(990\) | −76.8066 | − | 391.439i | −0.00246573 | − | 0.0125664i | ||||
\(991\) | − | 22684.4i | − | 0.727139i | −0.931567 | − | 0.363570i | \(-0.881558\pi\) | ||
0.931567 | − | 0.363570i | \(-0.118442\pi\) | |||||||
\(992\) | −9540.33 | − | 27073.8i | −0.305348 | − | 0.866525i | ||||
\(993\) | −7953.63 | + | 7953.63i | −0.254180 | + | 0.254180i | ||||
\(994\) | −8581.34 | + | 20101.5i | −0.273827 | + | 0.641429i | ||||
\(995\) | 11818.0 | + | 2250.35i | 0.376540 | + | 0.0716995i | ||||
\(996\) | 1754.15 | + | 1831.47i | 0.0558056 | + | 0.0582655i | ||||
\(997\) | 19120.7 | + | 19120.7i | 0.607382 | + | 0.607382i | 0.942261 | − | 0.334879i | \(-0.108695\pi\) |
−0.334879 | + | 0.942261i | \(0.608695\pi\) | |||||||
\(998\) | −6069.82 | − | 15112.6i | −0.192522 | − | 0.479340i | ||||
\(999\) | −5001.38 | −0.158395 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 60.4.j.b.7.9 | ✓ | 28 | |
3.2 | odd | 2 | 180.4.k.f.127.6 | 28 | |||
4.3 | odd | 2 | inner | 60.4.j.b.7.12 | yes | 28 | |
5.3 | odd | 4 | inner | 60.4.j.b.43.12 | yes | 28 | |
12.11 | even | 2 | 180.4.k.f.127.3 | 28 | |||
15.8 | even | 4 | 180.4.k.f.163.3 | 28 | |||
20.3 | even | 4 | inner | 60.4.j.b.43.9 | yes | 28 | |
60.23 | odd | 4 | 180.4.k.f.163.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.j.b.7.9 | ✓ | 28 | 1.1 | even | 1 | trivial | |
60.4.j.b.7.12 | yes | 28 | 4.3 | odd | 2 | inner | |
60.4.j.b.43.9 | yes | 28 | 20.3 | even | 4 | inner | |
60.4.j.b.43.12 | yes | 28 | 5.3 | odd | 4 | inner | |
180.4.k.f.127.3 | 28 | 12.11 | even | 2 | |||
180.4.k.f.127.6 | 28 | 3.2 | odd | 2 | |||
180.4.k.f.163.3 | 28 | 15.8 | even | 4 | |||
180.4.k.f.163.6 | 28 | 60.23 | odd | 4 |