Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [310,3,Mod(99,310)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(310, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("310.99");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 310 = 2 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 310.i (of order \(6\), 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: | \(8.44688819517\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 99.16 | ||
Character | \(\chi\) | \(=\) | 310.99 |
Dual form | 310.3.i.a.119.32 |
$q$-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 \(\left(\mathbb{Z}/310\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(251\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||
\(3\) | 2.70805 | + | 4.69048i | 0.902683 | + | 1.56349i | 0.823998 | + | 0.566593i | \(0.191739\pi\) |
0.0786852 | + | 0.996900i | \(0.474928\pi\) | |||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 2.12665 | − | 4.52519i | 0.425330 | − | 0.905038i | ||||
\(6\) | 6.63334 | − | 3.82976i | 1.10556 | − | 0.638293i | ||||
\(7\) | −7.85437 | + | 4.53472i | −1.12205 | + | 0.647817i | −0.941924 | − | 0.335826i | \(-0.890985\pi\) |
−0.180129 | + | 0.983643i | \(0.557651\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | −10.1671 | + | 17.6099i | −1.12967 | + | 1.95665i | ||||
\(10\) | −6.39959 | − | 3.00754i | −0.639959 | − | 0.300754i | ||||
\(11\) | 11.8842 | + | 6.86133i | 1.08038 | + | 0.623758i | 0.930999 | − | 0.365022i | \(-0.118939\pi\) |
0.149381 | + | 0.988780i | \(0.452272\pi\) | |||||||
\(12\) | −5.41610 | − | 9.38096i | −0.451341 | − | 0.781746i | ||||
\(13\) | −10.6610 | + | 18.4653i | −0.820074 | + | 1.42041i | 0.0855520 | + | 0.996334i | \(0.472735\pi\) |
−0.905626 | + | 0.424077i | \(0.860599\pi\) | |||||||
\(14\) | 6.41307 | + | 11.1078i | 0.458076 | + | 0.793411i | ||||
\(15\) | 26.9844 | − | 2.27944i | 1.79896 | − | 0.151962i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 2.30156 | + | 3.98641i | 0.135386 | + | 0.234495i | 0.925745 | − | 0.378149i | \(-0.123439\pi\) |
−0.790359 | + | 0.612644i | \(0.790106\pi\) | |||||||
\(18\) | 24.9041 | + | 14.3784i | 1.38356 | + | 0.798799i | ||||
\(19\) | −7.69675 | − | 13.3312i | −0.405092 | − | 0.701640i | 0.589240 | − | 0.807958i | \(-0.299427\pi\) |
−0.994332 | + | 0.106318i | \(0.966094\pi\) | |||||||
\(20\) | −4.25330 | + | 9.05038i | −0.212665 | + | 0.452519i | ||||
\(21\) | −42.5400 | − | 24.5605i | −2.02572 | − | 1.16955i | ||||
\(22\) | 9.70339 | − | 16.8068i | 0.441063 | − | 0.763944i | ||||
\(23\) | 34.1036 | 1.48277 | 0.741384 | − | 0.671082i | \(-0.234170\pi\) | ||||
0.741384 | + | 0.671082i | \(0.234170\pi\) | |||||||
\(24\) | −13.2667 | + | 7.65952i | −0.552778 | + | 0.319147i | ||||
\(25\) | −15.9547 | − | 19.2470i | −0.638189 | − | 0.769880i | ||||
\(26\) | 26.1139 | + | 15.0769i | 1.00438 | + | 0.579880i | ||||
\(27\) | −61.3866 | −2.27358 | ||||||||
\(28\) | 15.7087 | − | 9.06944i | 0.561026 | − | 0.323909i | ||||
\(29\) | 19.5719i | 0.674894i | 0.941345 | + | 0.337447i | \(0.109563\pi\) | ||||
−0.941345 | + | 0.337447i | \(0.890437\pi\) | |||||||
\(30\) | −3.22361 | − | 38.1617i | −0.107454 | − | 1.27206i | ||||
\(31\) | 1.23547 | + | 30.9754i | 0.0398540 | + | 0.999206i | ||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 74.3233i | 2.25222i | ||||||||
\(34\) | 5.63764 | − | 3.25489i | 0.165813 | − | 0.0957321i | ||||
\(35\) | 3.81700 | + | 45.1863i | 0.109057 | + | 1.29104i | ||||
\(36\) | 20.3341 | − | 35.2197i | 0.564836 | − | 0.978325i | ||||
\(37\) | 24.4492 | + | 42.3472i | 0.660789 | + | 1.14452i | 0.980409 | + | 0.196974i | \(0.0631114\pi\) |
−0.319620 | + | 0.947546i | \(0.603555\pi\) | |||||||
\(38\) | −18.8531 | + | 10.8849i | −0.496135 | + | 0.286443i | ||||
\(39\) | −115.482 | −2.96107 | ||||||||
\(40\) | 12.7992 | + | 6.01507i | 0.319979 | + | 0.150377i | ||||
\(41\) | 18.9881 | − | 32.8883i | 0.463123 | − | 0.802153i | −0.535991 | − | 0.844223i | \(-0.680062\pi\) |
0.999115 | + | 0.0420705i | \(0.0133954\pi\) | |||||||
\(42\) | −34.7338 | + | 60.1607i | −0.826995 | + | 1.43240i | ||||
\(43\) | −40.0166 | − | 69.3107i | −0.930618 | − | 1.61188i | −0.782267 | − | 0.622943i | \(-0.785937\pi\) |
−0.148351 | − | 0.988935i | \(-0.547396\pi\) | |||||||
\(44\) | −23.7684 | − | 13.7227i | −0.540190 | − | 0.311879i | ||||
\(45\) | 58.0662 | + | 83.4579i | 1.29036 | + | 1.85462i | ||||
\(46\) | − | 48.2298i | − | 1.04847i | ||||||
\(47\) | 0.952699i | 0.0202702i | 0.999949 | + | 0.0101351i | \(0.00322616\pi\) | ||||
−0.999949 | + | 0.0101351i | \(0.996774\pi\) | |||||||
\(48\) | 10.8322 | + | 18.7619i | 0.225671 | + | 0.390873i | ||||
\(49\) | 16.6274 | − | 28.7995i | 0.339335 | − | 0.587745i | ||||
\(50\) | −27.2194 | + | 22.5634i | −0.544387 | + | 0.451268i | ||||
\(51\) | −12.4654 | + | 21.5908i | −0.244421 | + | 0.423349i | ||||
\(52\) | 21.3219 | − | 36.9307i | 0.410037 | − | 0.710205i | ||||
\(53\) | 11.2960 | − | 19.5652i | 0.213132 | − | 0.369155i | −0.739561 | − | 0.673089i | \(-0.764967\pi\) |
0.952693 | + | 0.303934i | \(0.0983003\pi\) | |||||||
\(54\) | 86.8138i | 1.60766i | ||||||||
\(55\) | 56.3223 | − | 39.1865i | 1.02404 | − | 0.712483i | ||||
\(56\) | −12.8261 | − | 22.2155i | −0.229038 | − | 0.396706i | ||||
\(57\) | 41.6864 | − | 72.2029i | 0.731340 | − | 1.26672i | ||||
\(58\) | 27.6789 | 0.477222 | ||||||||
\(59\) | 2.38563 | + | 4.13204i | 0.0404344 | + | 0.0700345i | 0.885534 | − | 0.464574i | \(-0.153792\pi\) |
−0.845100 | + | 0.534608i | \(0.820459\pi\) | |||||||
\(60\) | −53.9688 | + | 4.55887i | −0.899479 | + | 0.0759812i | ||||
\(61\) | − | 5.24665i | − | 0.0860107i | −0.999075 | − | 0.0430054i | \(-0.986307\pi\) | ||
0.999075 | − | 0.0430054i | \(-0.0136933\pi\) | |||||||
\(62\) | 43.8058 | − | 1.74722i | 0.706545 | − | 0.0281810i | ||||
\(63\) | − | 184.419i | − | 2.92729i | ||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 60.8870 | + | 87.5122i | 0.936724 | + | 1.34634i | ||||
\(66\) | 105.109 | 1.59256 | ||||||||
\(67\) | 29.1149 | + | 16.8095i | 0.434551 | + | 0.250888i | 0.701283 | − | 0.712883i | \(-0.252611\pi\) |
−0.266733 | + | 0.963771i | \(0.585944\pi\) | |||||||
\(68\) | −4.60311 | − | 7.97282i | −0.0676928 | − | 0.117247i | ||||
\(69\) | 92.3543 | + | 159.962i | 1.33847 | + | 2.31830i | ||||
\(70\) | 63.9031 | − | 5.39805i | 0.912901 | − | 0.0771150i | ||||
\(71\) | 25.1077 | − | 43.4878i | 0.353629 | − | 0.612504i | −0.633253 | − | 0.773945i | \(-0.718281\pi\) |
0.986882 | + | 0.161441i | \(0.0516142\pi\) | |||||||
\(72\) | −49.8082 | − | 28.7568i | −0.691780 | − | 0.399400i | ||||
\(73\) | 18.8584 | − | 32.6637i | 0.258334 | − | 0.447448i | −0.707462 | − | 0.706752i | \(-0.750160\pi\) |
0.965796 | + | 0.259304i | \(0.0834932\pi\) | |||||||
\(74\) | 59.8880 | − | 34.5764i | 0.809298 | − | 0.467248i | ||||
\(75\) | 47.0714 | − | 126.957i | 0.627619 | − | 1.69276i | ||||
\(76\) | 15.3935 | + | 26.6623i | 0.202546 | + | 0.350820i | ||||
\(77\) | −124.457 | −1.61632 | ||||||||
\(78\) | 163.316i | 2.09379i | ||||||||
\(79\) | −20.7873 | + | 12.0016i | −0.263131 | + | 0.151919i | −0.625762 | − | 0.780014i | \(-0.715212\pi\) |
0.362631 | + | 0.931933i | \(0.381879\pi\) | |||||||
\(80\) | 8.50660 | − | 18.1008i | 0.106332 | − | 0.226260i | ||||
\(81\) | −74.7345 | − | 129.444i | −0.922648 | − | 1.59807i | ||||
\(82\) | −46.5110 | − | 26.8532i | −0.567208 | − | 0.327478i | ||||
\(83\) | 46.9781 | − | 81.3684i | 0.566001 | − | 0.980342i | −0.430955 | − | 0.902373i | \(-0.641823\pi\) |
0.996956 | − | 0.0779685i | \(-0.0248434\pi\) | |||||||
\(84\) | 85.0801 | + | 49.1210i | 1.01286 | + | 0.584774i | ||||
\(85\) | 22.9339 | − | 1.93728i | 0.269810 | − | 0.0227915i | ||||
\(86\) | −98.0202 | + | 56.5920i | −1.13977 | + | 0.658046i | ||||
\(87\) | −91.8016 | + | 53.0017i | −1.05519 | + | 0.609215i | ||||
\(88\) | −19.4068 | + | 33.6135i | −0.220532 | + | 0.381972i | ||||
\(89\) | − | 45.2974i | − | 0.508959i | −0.967078 | − | 0.254480i | \(-0.918096\pi\) | ||
0.967078 | − | 0.254480i | \(-0.0819042\pi\) | |||||||
\(90\) | 118.027 | − | 82.1180i | 1.31141 | − | 0.912423i | ||||
\(91\) | − | 193.378i | − | 2.12503i | ||||||
\(92\) | −68.2073 | −0.741384 | ||||||||
\(93\) | −141.944 | + | 89.6778i | −1.52627 | + | 0.964277i | ||||
\(94\) | 1.34732 | 0.0143332 | ||||||||
\(95\) | −76.6944 | + | 6.47856i | −0.807309 | + | 0.0681954i | ||||
\(96\) | 26.5333 | − | 15.3190i | 0.276389 | − | 0.159573i | ||||
\(97\) | 139.851i | 1.44177i | 0.693057 | + | 0.720883i | \(0.256263\pi\) | ||||
−0.693057 | + | 0.720883i | \(0.743737\pi\) | |||||||
\(98\) | −40.7287 | − | 23.5147i | −0.415599 | − | 0.239946i | ||||
\(99\) | −241.654 | + | 139.519i | −2.44095 | + | 1.40928i | ||||
\(100\) | 31.9094 | + | 38.4940i | 0.319094 | + | 0.384940i | ||||
\(101\) | 192.514 | 1.90608 | 0.953042 | − | 0.302839i | \(-0.0979344\pi\) | ||||
0.953042 | + | 0.302839i | \(0.0979344\pi\) | |||||||
\(102\) | 30.5340 | + | 17.6288i | 0.299353 | + | 0.172831i | ||||
\(103\) | 39.4183 | + | 22.7582i | 0.382702 | + | 0.220953i | 0.678993 | − | 0.734144i | \(-0.262417\pi\) |
−0.296291 | + | 0.955098i | \(0.595750\pi\) | |||||||
\(104\) | −52.2279 | − | 30.1538i | −0.502191 | − | 0.289940i | ||||
\(105\) | −201.609 | + | 140.270i | −1.92008 | + | 1.33591i | ||||
\(106\) | −27.6694 | − | 15.9749i | −0.261032 | − | 0.150707i | ||||
\(107\) | 78.8892 | − | 45.5467i | 0.737282 | − | 0.425670i | −0.0837981 | − | 0.996483i | \(-0.526705\pi\) |
0.821080 | + | 0.570813i | \(0.193372\pi\) | |||||||
\(108\) | 122.773 | 1.13679 | ||||||||
\(109\) | 79.4627 | 0.729015 | 0.364508 | − | 0.931200i | \(-0.381237\pi\) | ||||
0.364508 | + | 0.931200i | \(0.381237\pi\) | |||||||
\(110\) | −55.4181 | − | 79.6518i | −0.503801 | − | 0.724107i | ||||
\(111\) | −132.419 | + | 229.357i | −1.19297 | + | 2.06628i | ||||
\(112\) | −31.4175 | + | 18.1389i | −0.280513 | + | 0.161954i | ||||
\(113\) | −153.875 | − | 88.8400i | −1.36173 | − | 0.786195i | −0.371876 | − | 0.928283i | \(-0.621285\pi\) |
−0.989854 | + | 0.142087i | \(0.954619\pi\) | |||||||
\(114\) | −102.110 | − | 58.9534i | −0.895704 | − | 0.517135i | ||||
\(115\) | 72.5265 | − | 154.326i | 0.630665 | − | 1.34196i | ||||
\(116\) | − | 39.1438i | − | 0.337447i | ||||||
\(117\) | −216.781 | − | 375.476i | −1.85283 | − | 3.20920i | ||||
\(118\) | 5.84358 | − | 3.37379i | 0.0495219 | − | 0.0285915i | ||||
\(119\) | −36.1545 | − | 20.8738i | −0.303820 | − | 0.175410i | ||||
\(120\) | 6.44722 | + | 76.3234i | 0.0537268 | + | 0.636028i | ||||
\(121\) | 33.6558 | + | 58.2936i | 0.278147 | + | 0.481765i | ||||
\(122\) | −7.41989 | −0.0608188 | ||||||||
\(123\) | 205.682 | 1.67221 | ||||||||
\(124\) | −2.47095 | − | 61.9507i | −0.0199270 | − | 0.499603i | ||||
\(125\) | −121.026 | + | 31.2666i | −0.968212 | + | 0.250132i | ||||
\(126\) | −260.808 | −2.06990 | ||||||||
\(127\) | −46.5816 | − | 80.6817i | −0.366784 | − | 0.635289i | 0.622277 | − | 0.782797i | \(-0.286208\pi\) |
−0.989061 | + | 0.147509i | \(0.952875\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | 216.734 | − | 375.394i | 1.68011 | − | 2.91003i | ||||
\(130\) | 123.761 | − | 86.1073i | 0.952007 | − | 0.662364i | ||||
\(131\) | 48.6470 | + | 84.2591i | 0.371351 | + | 0.643200i | 0.989774 | − | 0.142646i | \(-0.0455612\pi\) |
−0.618422 | + | 0.785846i | \(0.712228\pi\) | |||||||
\(132\) | − | 148.647i | − | 1.12611i | ||||||
\(133\) | 120.906 | + | 69.8053i | 0.909070 | + | 0.524852i | ||||
\(134\) | 23.7722 | − | 41.1747i | 0.177405 | − | 0.307274i | ||||
\(135\) | −130.548 | + | 277.786i | −0.967021 | + | 2.05768i | ||||
\(136\) | −11.2753 | + | 6.50978i | −0.0829064 | + | 0.0478660i | ||||
\(137\) | 7.16212 | − | 12.4051i | 0.0522782 | − | 0.0905485i | −0.838702 | − | 0.544591i | \(-0.816685\pi\) |
0.890980 | + | 0.454042i | \(0.150018\pi\) | |||||||
\(138\) | 226.221 | − | 130.609i | 1.63928 | − | 0.946440i | ||||
\(139\) | − | 170.310i | − | 1.22525i | −0.790374 | − | 0.612625i | \(-0.790114\pi\) | ||
0.790374 | − | 0.612625i | \(-0.209886\pi\) | |||||||
\(140\) | −7.63399 | − | 90.3726i | −0.0545285 | − | 0.645518i | ||||
\(141\) | −4.46861 | + | 2.57995i | −0.0316923 | + | 0.0182975i | ||||
\(142\) | −61.5010 | − | 35.5076i | −0.433105 | − | 0.250054i | ||||
\(143\) | −253.394 | + | 146.297i | −1.77198 | + | 1.02306i | ||||
\(144\) | −40.6682 | + | 70.4394i | −0.282418 | + | 0.489163i | ||||
\(145\) | 88.5667 | + | 41.6226i | 0.610805 | + | 0.287052i | ||||
\(146\) | −46.1934 | − | 26.6698i | −0.316393 | − | 0.182670i | ||||
\(147\) | 180.111 | 1.22525 | ||||||||
\(148\) | −48.8984 | − | 84.6945i | −0.330394 | − | 0.572260i | ||||
\(149\) | 36.1065 | + | 62.5383i | 0.242325 | + | 0.419720i | 0.961376 | − | 0.275237i | \(-0.0887565\pi\) |
−0.719051 | + | 0.694958i | \(0.755423\pi\) | |||||||
\(150\) | −179.544 | − | 66.5691i | −1.19696 | − | 0.443794i | ||||
\(151\) | − | 11.0907i | − | 0.0734484i | −0.999325 | − | 0.0367242i | \(-0.988308\pi\) | ||
0.999325 | − | 0.0367242i | \(-0.0116923\pi\) | |||||||
\(152\) | 37.7062 | − | 21.7697i | 0.248067 | − | 0.143222i | ||||
\(153\) | −93.6002 | −0.611766 | ||||||||
\(154\) | 176.009i | 1.14291i | ||||||||
\(155\) | 142.797 | + | 60.2830i | 0.921270 | + | 0.388923i | ||||
\(156\) | 230.963 | 1.48053 | ||||||||
\(157\) | 194.366i | 1.23800i | 0.785392 | + | 0.618999i | \(0.212461\pi\) | ||||
−0.785392 | + | 0.618999i | \(0.787539\pi\) | |||||||
\(158\) | 16.9728 | + | 29.3977i | 0.107423 | + | 0.186062i | ||||
\(159\) | 122.360 | 0.769562 | ||||||||
\(160\) | −25.5984 | − | 12.0301i | −0.159990 | − | 0.0751884i | ||||
\(161\) | −267.863 | + | 154.651i | −1.66374 | + | 0.960562i | ||||
\(162\) | −183.061 | + | 105.691i | −1.13001 | + | 0.652411i | ||||
\(163\) | 173.866i | 1.06667i | 0.845906 | + | 0.533333i | \(0.179061\pi\) | ||||
−0.845906 | + | 0.533333i | \(0.820939\pi\) | |||||||
\(164\) | −37.9761 | + | 65.7765i | −0.231562 | + | 0.401076i | ||||
\(165\) | 336.327 | + | 158.060i | 2.03835 | + | 0.957937i | ||||
\(166\) | −115.072 | − | 66.4370i | −0.693206 | − | 0.400223i | ||||
\(167\) | −89.7300 | − | 155.417i | −0.537305 | − | 0.930640i | −0.999048 | − | 0.0436263i | \(-0.986109\pi\) |
0.461742 | − | 0.887014i | \(-0.347224\pi\) | |||||||
\(168\) | 69.4676 | − | 120.321i | 0.413497 | − | 0.716199i | ||||
\(169\) | −142.812 | − | 247.358i | −0.845044 | − | 1.46366i | ||||
\(170\) | −2.73973 | − | 32.4334i | −0.0161160 | − | 0.190785i | ||||
\(171\) | 313.013 | 1.83049 | ||||||||
\(172\) | 80.0332 | + | 138.621i | 0.465309 | + | 0.805939i | ||||
\(173\) | −28.3987 | − | 16.3960i | −0.164154 | − | 0.0947746i | 0.415672 | − | 0.909515i | \(-0.363546\pi\) |
−0.579827 | + | 0.814740i | \(0.696880\pi\) | |||||||
\(174\) | 74.9557 | + | 129.827i | 0.430780 | + | 0.746133i | ||||
\(175\) | 212.594 | + | 78.8228i | 1.21482 | + | 0.450416i | ||||
\(176\) | 47.5367 | + | 27.4453i | 0.270095 | + | 0.155939i | ||||
\(177\) | −12.9208 | + | 22.3795i | −0.0729990 | + | 0.126438i | ||||
\(178\) | −64.0602 | −0.359889 | ||||||||
\(179\) | 260.335 | − | 150.304i | 1.45438 | − | 0.839689i | 0.455659 | − | 0.890154i | \(-0.349404\pi\) |
0.998726 | + | 0.0504650i | \(0.0160703\pi\) | |||||||
\(180\) | −116.132 | − | 166.916i | −0.645180 | − | 0.927310i | ||||
\(181\) | 277.769 | + | 160.370i | 1.53463 | + | 0.886021i | 0.999139 | + | 0.0414816i | \(0.0132078\pi\) |
0.535494 | + | 0.844539i | \(0.320126\pi\) | |||||||
\(182\) | −273.478 | −1.50263 | ||||||||
\(183\) | 24.6093 | − | 14.2082i | 0.134477 | − | 0.0776404i | ||||
\(184\) | 96.4597i | 0.524237i | ||||||||
\(185\) | 243.624 | − | 20.5795i | 1.31689 | − | 0.111241i | ||||
\(186\) | 126.824 | + | 200.739i | 0.681847 | + | 1.07924i | ||||
\(187\) | 63.1670i | 0.337791i | ||||||||
\(188\) | − | 1.90540i | − | 0.0101351i | ||||||
\(189\) | 482.153 | − | 278.371i | 2.55108 | − | 1.47286i | ||||
\(190\) | 9.16207 | + | 108.462i | 0.0482214 | + | 0.570854i | ||||
\(191\) | −86.3346 | + | 149.536i | −0.452014 | + | 0.782910i | −0.998511 | − | 0.0545503i | \(-0.982627\pi\) |
0.546497 | + | 0.837461i | \(0.315961\pi\) | |||||||
\(192\) | −21.6644 | − | 37.5238i | −0.112835 | − | 0.195437i | ||||
\(193\) | 2.10333 | − | 1.21436i | 0.0108981 | − | 0.00629202i | −0.494541 | − | 0.869154i | \(-0.664664\pi\) |
0.505439 | + | 0.862862i | \(0.331331\pi\) | |||||||
\(194\) | 197.780 | 1.01948 | ||||||||
\(195\) | −245.589 | + | 522.577i | −1.25943 | + | 2.67988i | ||||
\(196\) | −33.2548 | + | 57.5990i | −0.169667 | + | 0.293873i | ||||
\(197\) | 26.6461 | − | 46.1525i | 0.135260 | − | 0.234277i | −0.790437 | − | 0.612543i | \(-0.790146\pi\) |
0.925697 | + | 0.378267i | \(0.123480\pi\) | |||||||
\(198\) | 197.310 | + | 341.751i | 0.996514 | + | 1.72601i | ||||
\(199\) | −27.0622 | − | 15.6243i | −0.135991 | − | 0.0785143i | 0.430461 | − | 0.902609i | \(-0.358351\pi\) |
−0.566452 | + | 0.824095i | \(0.691684\pi\) | |||||||
\(200\) | 54.4387 | − | 45.1268i | 0.272194 | − | 0.225634i | ||||
\(201\) | 182.084i | 0.905889i | ||||||||
\(202\) | − | 272.257i | − | 1.34780i | ||||||
\(203\) | −88.7532 | − | 153.725i | −0.437208 | − | 0.757266i | ||||
\(204\) | 24.9309 | − | 43.1816i | 0.122210 | − | 0.211674i | ||||
\(205\) | −108.445 | − | 155.866i | −0.528999 | − | 0.760324i | ||||
\(206\) | 32.1849 | − | 55.7459i | 0.156237 | − | 0.270611i | ||||
\(207\) | −346.734 | + | 600.560i | −1.67504 | + | 2.90126i | ||||
\(208\) | −42.6439 | + | 73.8613i | −0.205019 | + | 0.355103i | ||||
\(209\) | − | 211.240i | − | 1.01072i | ||||||
\(210\) | 198.372 | + | 285.118i | 0.944629 | + | 1.35770i | ||||
\(211\) | 5.80713 | + | 10.0582i | 0.0275219 | + | 0.0476694i | 0.879458 | − | 0.475976i | \(-0.157905\pi\) |
−0.851936 | + | 0.523645i | \(0.824572\pi\) | |||||||
\(212\) | −22.5920 | + | 39.1305i | −0.106566 | + | 0.184578i | ||||
\(213\) | 271.971 | 1.27686 | ||||||||
\(214\) | −64.4128 | − | 111.566i | −0.300994 | − | 0.521337i | ||||
\(215\) | −398.746 | + | 33.6830i | −1.85463 | + | 0.156665i | ||||
\(216\) | − | 173.628i | − | 0.803832i | ||||||
\(217\) | −150.169 | − | 237.689i | −0.692021 | − | 1.09534i | ||||
\(218\) | − | 112.377i | − | 0.515492i | ||||||
\(219\) | 204.278 | 0.932775 | ||||||||
\(220\) | −112.645 | + | 78.3731i | −0.512021 | + | 0.356241i | ||||
\(221\) | −98.1472 | −0.444105 | ||||||||
\(222\) | 324.359 | + | 187.269i | 1.46108 | + | 0.843554i | ||||
\(223\) | 33.3268 | + | 57.7237i | 0.149448 | + | 0.258851i | 0.931023 | − | 0.364959i | \(-0.118917\pi\) |
−0.781576 | + | 0.623810i | \(0.785584\pi\) | |||||||
\(224\) | 25.6523 | + | 44.4310i | 0.114519 | + | 0.198353i | ||||
\(225\) | 501.149 | − | 85.2751i | 2.22733 | − | 0.379000i | ||||
\(226\) | −125.639 | + | 217.613i | −0.555924 | + | 0.962888i | ||||
\(227\) | −155.221 | − | 89.6169i | −0.683793 | − | 0.394788i | 0.117490 | − | 0.993074i | \(-0.462515\pi\) |
−0.801283 | + | 0.598286i | \(0.795849\pi\) | |||||||
\(228\) | −83.3727 | + | 144.406i | −0.365670 | + | 0.633359i | ||||
\(229\) | −341.573 | + | 197.207i | −1.49159 | + | 0.861167i | −0.999954 | − | 0.00963578i | \(-0.996933\pi\) |
−0.491632 | + | 0.870803i | \(0.663599\pi\) | |||||||
\(230\) | −218.249 | − | 102.568i | −0.948910 | − | 0.445948i | ||||
\(231\) | −337.036 | − | 583.763i | −1.45903 | − | 2.52711i | ||||
\(232\) | −55.3577 | −0.238611 | ||||||||
\(233\) | 213.553i | 0.916537i | 0.888814 | + | 0.458269i | \(0.151530\pi\) | ||||
−0.888814 | + | 0.458269i | \(0.848470\pi\) | |||||||
\(234\) | −531.003 | + | 306.575i | −2.26925 | + | 1.31015i | ||||
\(235\) | 4.31114 | + | 2.02606i | 0.0183453 | + | 0.00862152i | ||||
\(236\) | −4.77126 | − | 8.26407i | −0.0202172 | − | 0.0350173i | ||||
\(237\) | −112.586 | − | 65.0017i | −0.475047 | − | 0.274269i | ||||
\(238\) | −29.5201 | + | 51.1302i | −0.124034 | + | 0.214833i | ||||
\(239\) | 317.484 | + | 183.299i | 1.32838 | + | 0.766943i | 0.985050 | − | 0.172270i | \(-0.0551100\pi\) |
0.343335 | + | 0.939213i | \(0.388443\pi\) | |||||||
\(240\) | 107.938 | − | 9.11775i | 0.449740 | − | 0.0379906i | ||||
\(241\) | −16.6793 | + | 9.62982i | −0.0692088 | + | 0.0399577i | −0.534205 | − | 0.845355i | \(-0.679389\pi\) |
0.464996 | + | 0.885313i | \(0.346056\pi\) | |||||||
\(242\) | 82.4396 | − | 47.5965i | 0.340660 | − | 0.196680i | ||||
\(243\) | 128.530 | − | 222.620i | 0.528928 | − | 0.916131i | ||||
\(244\) | 10.4933i | 0.0430054i | ||||||||
\(245\) | −94.9627 | − | 136.489i | −0.387603 | − | 0.557097i | ||||
\(246\) | − | 290.879i | − | 1.18243i | ||||||
\(247\) | 328.219 | 1.32882 | ||||||||
\(248\) | −87.6116 | + | 3.49445i | −0.353272 | + | 0.0140905i | ||||
\(249\) | 508.875 | 2.04368 | ||||||||
\(250\) | 44.2176 | + | 171.157i | 0.176870 | + | 0.684629i | ||||
\(251\) | −295.129 | + | 170.393i | −1.17581 | + | 0.678855i | −0.955042 | − | 0.296471i | \(-0.904190\pi\) |
−0.220769 | + | 0.975326i | \(0.570857\pi\) | |||||||
\(252\) | 368.838i | 1.46364i | ||||||||
\(253\) | 405.294 | + | 233.997i | 1.60195 | + | 0.924887i | ||||
\(254\) | −114.101 | + | 65.8763i | −0.449217 | + | 0.259356i | ||||
\(255\) | 71.1928 | + | 102.325i | 0.279188 | + | 0.401273i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −99.2810 | − | 57.3199i | −0.386307 | − | 0.223035i | 0.294252 | − | 0.955728i | \(-0.404930\pi\) |
−0.680559 | + | 0.732693i | \(0.738263\pi\) | |||||||
\(258\) | −530.887 | − | 306.508i | −2.05770 | − | 1.18801i | ||||
\(259\) | −384.066 | − | 221.741i | −1.48288 | − | 0.856141i | ||||
\(260\) | −121.774 | − | 175.024i | −0.468362 | − | 0.673171i | ||||
\(261\) | −344.659 | − | 198.989i | −1.32053 | − | 0.762409i | ||||
\(262\) | 119.160 | − | 68.7973i | 0.454811 | − | 0.262585i | ||||
\(263\) | −249.198 | −0.947522 | −0.473761 | − | 0.880654i | \(-0.657104\pi\) | ||||
−0.473761 | + | 0.880654i | \(0.657104\pi\) | |||||||
\(264\) | −210.218 | −0.796281 | ||||||||
\(265\) | −64.5138 | − | 92.7249i | −0.243448 | − | 0.349905i | ||||
\(266\) | 98.7195 | − | 170.987i | 0.371126 | − | 0.642809i | ||||
\(267\) | 212.466 | − | 122.668i | 0.795754 | − | 0.459429i | ||||
\(268\) | −58.2298 | − | 33.6190i | −0.217275 | − | 0.125444i | ||||
\(269\) | −28.3228 | − | 16.3522i | −0.105289 | − | 0.0607887i | 0.446431 | − | 0.894818i | \(-0.352695\pi\) |
−0.551720 | + | 0.834029i | \(0.686028\pi\) | |||||||
\(270\) | 392.849 | + | 184.623i | 1.45500 | + | 0.683787i | ||||
\(271\) | 172.160i | 0.635278i | 0.948212 | + | 0.317639i | \(0.102890\pi\) | ||||
−0.948212 | + | 0.317639i | \(0.897110\pi\) | |||||||
\(272\) | 9.20622 | + | 15.9456i | 0.0338464 | + | 0.0586237i | ||||
\(273\) | 907.036 | − | 523.677i | 3.32247 | − | 1.91823i | ||||
\(274\) | −17.5435 | − | 10.1288i | −0.0640275 | − | 0.0369663i | ||||
\(275\) | −57.5487 | − | 338.205i | −0.209268 | − | 1.22984i | ||||
\(276\) | −184.709 | − | 319.925i | −0.669234 | − | 1.15915i | ||||
\(277\) | 355.743 | 1.28427 | 0.642136 | − | 0.766591i | \(-0.278049\pi\) | ||||
0.642136 | + | 0.766591i | \(0.278049\pi\) | |||||||
\(278\) | −240.854 | −0.866382 | ||||||||
\(279\) | −558.033 | − | 293.172i | −2.00012 | − | 1.05079i | ||||
\(280\) | −127.806 | + | 10.7961i | −0.456450 | + | 0.0385575i | ||||
\(281\) | 23.2761 | 0.0828330 | 0.0414165 | − | 0.999142i | \(-0.486813\pi\) | ||||
0.0414165 | + | 0.999142i | \(0.486813\pi\) | |||||||
\(282\) | 3.64861 | + | 6.31957i | 0.0129383 | + | 0.0224098i | ||||
\(283\) | − | 338.436i | − | 1.19589i | −0.801538 | − | 0.597944i | \(-0.795985\pi\) | ||
0.801538 | − | 0.597944i | \(-0.204015\pi\) | |||||||
\(284\) | −50.2153 | + | 86.9755i | −0.176815 | + | 0.306252i | ||||
\(285\) | −238.080 | − | 342.189i | −0.835367 | − | 1.20066i | ||||
\(286\) | 206.895 | + | 358.353i | 0.723409 | + | 1.25298i | ||||
\(287\) | 344.422i | 1.20008i | ||||||||
\(288\) | 99.6164 | + | 57.5135i | 0.345890 | + | 0.199700i | ||||
\(289\) | 133.906 | − | 231.931i | 0.463341 | − | 0.802531i | ||||
\(290\) | 58.8633 | − | 125.252i | 0.202977 | − | 0.431904i | ||||
\(291\) | −655.969 | + | 378.724i | −2.25419 | + | 1.30146i | ||||
\(292\) | −37.7168 | + | 65.3273i | −0.129167 | + | 0.223724i | ||||
\(293\) | −443.182 | + | 255.871i | −1.51257 | + | 0.873281i | −0.512675 | + | 0.858583i | \(0.671346\pi\) |
−0.999892 | + | 0.0146985i | \(0.995321\pi\) | |||||||
\(294\) | − | 254.716i | − | 0.866381i | ||||||
\(295\) | 23.7717 | − | 2.00805i | 0.0805819 | − | 0.00680695i | ||||
\(296\) | −119.776 | + | 69.1527i | −0.404649 | + | 0.233624i | ||||
\(297\) | −729.530 | − | 421.194i | −2.45633 | − | 1.41816i | ||||
\(298\) | 88.4425 | − | 51.0623i | 0.296787 | − | 0.171350i | ||||
\(299\) | −363.578 | + | 629.735i | −1.21598 | + | 2.10614i | ||||
\(300\) | −94.1429 | + | 253.914i | −0.313810 | + | 0.846380i | ||||
\(301\) | 628.610 | + | 362.928i | 2.08841 | + | 1.20574i | ||||
\(302\) | −15.6846 | −0.0519358 | ||||||||
\(303\) | 521.338 | + | 902.985i | 1.72059 | + | 2.98015i | ||||
\(304\) | −30.7870 | − | 53.3247i | −0.101273 | − | 0.175410i | ||||
\(305\) | −23.7421 | − | 11.1578i | −0.0778430 | − | 0.0365829i | ||||
\(306\) | 132.371i | 0.432584i | ||||||||
\(307\) | −257.995 | + | 148.953i | −0.840373 | + | 0.485190i | −0.857391 | − | 0.514665i | \(-0.827916\pi\) |
0.0170178 | + | 0.999855i | \(0.494583\pi\) | |||||||
\(308\) | 248.914 | 0.808162 | ||||||||
\(309\) | 246.521i | 0.797803i | ||||||||
\(310\) | 85.2530 | − | 201.945i | 0.275010 | − | 0.651437i | ||||
\(311\) | 191.913 | 0.617085 | 0.308542 | − | 0.951211i | \(-0.400159\pi\) | ||||
0.308542 | + | 0.951211i | \(0.400159\pi\) | |||||||
\(312\) | − | 326.631i | − | 1.04690i | ||||||
\(313\) | 193.112 | + | 334.481i | 0.616973 | + | 1.06863i | 0.990035 | + | 0.140822i | \(0.0449745\pi\) |
−0.373062 | + | 0.927806i | \(0.621692\pi\) | |||||||
\(314\) | 274.875 | 0.875397 | ||||||||
\(315\) | −834.532 | − | 392.195i | −2.64931 | − | 1.24506i | ||||
\(316\) | 41.5747 | − | 24.0031i | 0.131565 | − | 0.0759593i | ||||
\(317\) | 339.129 | − | 195.796i | 1.06981 | − | 0.617653i | 0.141678 | − | 0.989913i | \(-0.454750\pi\) |
0.928129 | + | 0.372260i | \(0.121417\pi\) | |||||||
\(318\) | − | 173.044i | − | 0.544163i | ||||||
\(319\) | −134.289 | + | 232.596i | −0.420970 | + | 0.729142i | ||||
\(320\) | −17.0132 | + | 36.2015i | −0.0531662 | + | 0.113130i | ||||
\(321\) | 427.272 | + | 246.685i | 1.33106 | + | 0.768490i | ||||
\(322\) | 218.709 | + | 378.815i | 0.679220 | + | 1.17644i | ||||
\(323\) | 35.4290 | − | 61.3648i | 0.109687 | − | 0.189984i | ||||
\(324\) | 149.469 | + | 258.888i | 0.461324 | + | 0.799037i | ||||
\(325\) | 525.495 | − | 89.4177i | 1.61691 | − | 0.275131i | ||||
\(326\) | 245.884 | 0.754246 | ||||||||
\(327\) | 215.189 | + | 372.718i | 0.658070 | + | 1.13981i | ||||
\(328\) | 93.0221 | + | 53.7063i | 0.283604 | + | 0.163739i | ||||
\(329\) | −4.32022 | − | 7.48285i | −0.0131314 | − | 0.0227442i | ||||
\(330\) | 223.530 | − | 475.639i | 0.677364 | − | 1.44133i | ||||
\(331\) | −42.7655 | − | 24.6907i | −0.129201 | − | 0.0745941i | 0.434007 | − | 0.900910i | \(-0.357099\pi\) |
−0.563207 | + | 0.826316i | \(0.690433\pi\) | |||||||
\(332\) | −93.9561 | + | 162.737i | −0.283000 | + | 0.490171i | ||||
\(333\) | −994.305 | −2.98590 | ||||||||
\(334\) | −219.793 | + | 126.897i | −0.658062 | + | 0.379932i | ||||
\(335\) | 137.983 | − | 96.0026i | 0.411891 | − | 0.286575i | ||||
\(336\) | −170.160 | − | 98.2420i | −0.506429 | − | 0.292387i | ||||
\(337\) | −370.117 | −1.09827 | −0.549136 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549136 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(338\) | −349.817 | + | 201.967i | −1.03496 | + | 0.597536i | ||||
\(339\) | − | 962.333i | − | 2.83874i | ||||||
\(340\) | −45.8677 | + | 3.87456i | −0.134905 | + | 0.0113958i | ||||
\(341\) | −197.850 | + | 376.594i | −0.580205 | + | 1.10438i | ||||
\(342\) | − | 442.667i | − | 1.29435i | ||||||
\(343\) | − | 142.800i | − | 0.416326i | ||||||
\(344\) | 196.040 | − | 113.184i | 0.569885 | − | 0.329023i | ||||
\(345\) | 920.266 | − | 77.7371i | 2.66744 | − | 0.225325i | ||||
\(346\) | −23.1874 | + | 40.1618i | −0.0670157 | + | 0.116075i | ||||
\(347\) | 57.4812 | + | 99.5604i | 0.165652 | + | 0.286918i | 0.936887 | − | 0.349633i | \(-0.113694\pi\) |
−0.771235 | + | 0.636551i | \(0.780360\pi\) | |||||||
\(348\) | 183.603 | − | 106.003i | 0.527596 | − | 0.304607i | ||||
\(349\) | −85.5971 | −0.245264 | −0.122632 | − | 0.992452i | \(-0.539133\pi\) | ||||
−0.122632 | + | 0.992452i | \(0.539133\pi\) | |||||||
\(350\) | 111.472 | − | 300.653i | 0.318492 | − | 0.859010i | ||||
\(351\) | 654.441 | − | 1133.52i | 1.86450 | − | 3.22942i | ||||
\(352\) | 38.8136 | − | 67.2271i | 0.110266 | − | 0.190986i | ||||
\(353\) | 140.532 | + | 243.408i | 0.398107 | + | 0.689542i | 0.993492 | − | 0.113898i | \(-0.0363338\pi\) |
−0.595385 | + | 0.803440i | \(0.703001\pi\) | |||||||
\(354\) | 31.6494 | + | 18.2728i | 0.0894051 | + | 0.0516181i | ||||
\(355\) | −143.395 | − | 206.100i | −0.403930 | − | 0.580564i | ||||
\(356\) | 90.5948i | 0.254480i | ||||||||
\(357\) | − | 226.109i | − | 0.633360i | ||||||
\(358\) | −212.563 | − | 368.169i | −0.593750 | − | 1.02841i | ||||
\(359\) | −6.42287 | + | 11.1247i | −0.0178910 | + | 0.0309881i | −0.874832 | − | 0.484426i | \(-0.839029\pi\) |
0.856941 | + | 0.515414i | \(0.172362\pi\) | |||||||
\(360\) | −236.055 | + | 164.236i | −0.655707 | + | 0.456211i | ||||
\(361\) | 62.0200 | − | 107.422i | 0.171801 | − | 0.297567i | ||||
\(362\) | 226.797 | − | 392.824i | 0.626511 | − | 1.08515i | ||||
\(363\) | −182.283 | + | 315.724i | −0.502158 | + | 0.869763i | ||||
\(364\) | 386.756i | 1.06252i | ||||||||
\(365\) | −107.704 | − | 154.802i | −0.295080 | − | 0.424115i | ||||
\(366\) | −20.0934 | − | 34.8028i | −0.0549001 | − | 0.0950897i | ||||
\(367\) | 73.4489 | − | 127.217i | 0.200133 | − | 0.346641i | −0.748438 | − | 0.663205i | \(-0.769196\pi\) |
0.948571 | + | 0.316564i | \(0.102529\pi\) | |||||||
\(368\) | 136.415 | 0.370692 | ||||||||
\(369\) | 386.105 | + | 668.754i | 1.04636 | + | 1.81234i | ||||
\(370\) | −29.1038 | − | 344.537i | −0.0786590 | − | 0.931180i | ||||
\(371\) | 204.897i | 0.552282i | ||||||||
\(372\) | 283.887 | − | 179.356i | 0.763137 | − | 0.482139i | ||||
\(373\) | − | 560.211i | − | 1.50191i | −0.660356 | − | 0.750953i | \(-0.729595\pi\) | ||
0.660356 | − | 0.750953i | \(-0.270405\pi\) | |||||||
\(374\) | 89.3316 | 0.238854 | ||||||||
\(375\) | −474.401 | − | 483.001i | −1.26507 | − | 1.28800i | ||||
\(376\) | −2.69464 | −0.00716659 | ||||||||
\(377\) | −361.402 | − | 208.656i | −0.958626 | − | 0.553463i | ||||
\(378\) | −393.677 | − | 681.868i | −1.04147 | − | 1.80388i | ||||
\(379\) | 99.6752 | + | 172.642i | 0.262995 | + | 0.455521i | 0.967036 | − | 0.254638i | \(-0.0819563\pi\) |
−0.704041 | + | 0.710159i | \(0.748623\pi\) | |||||||
\(380\) | 153.389 | − | 12.9571i | 0.403655 | − | 0.0340977i | ||||
\(381\) | 252.290 | − | 436.980i | 0.662180 | − | 1.14693i | ||||
\(382\) | 211.476 | + | 122.096i | 0.553601 | + | 0.319622i | ||||
\(383\) | 167.926 | − | 290.857i | 0.438450 | − | 0.759418i | −0.559120 | − | 0.829087i | \(-0.688861\pi\) |
0.997570 | + | 0.0696687i | \(0.0221942\pi\) | |||||||
\(384\) | −53.0667 | + | 30.6381i | −0.138195 | + | 0.0797866i | ||||
\(385\) | −264.676 | + | 563.192i | −0.687471 | + | 1.46284i | ||||
\(386\) | −1.71736 | − | 2.97456i | −0.00444913 | − | 0.00770612i | ||||
\(387\) | 1627.40 | 4.20518 | ||||||||
\(388\) | − | 279.703i | − | 0.720883i | ||||||
\(389\) | −546.194 | + | 315.345i | −1.40410 | + | 0.810656i | −0.994810 | − | 0.101749i | \(-0.967556\pi\) |
−0.409288 | + | 0.912405i | \(0.634223\pi\) | |||||||
\(390\) | 739.035 | + | 347.315i | 1.89496 | + | 0.890552i | ||||
\(391\) | 78.4914 | + | 135.951i | 0.200745 | + | 0.347701i | ||||
\(392\) | 81.4574 | + | 47.0294i | 0.207799 | + | 0.119973i | ||||
\(393\) | −263.477 | + | 456.356i | −0.670425 | + | 1.16121i | ||||
\(394\) | −65.2695 | − | 37.6833i | −0.165659 | − | 0.0956430i | ||||
\(395\) | 10.1020 | + | 119.590i | 0.0255748 | + | 0.302759i | ||||
\(396\) | 483.308 | − | 279.038i | 1.22048 | − | 0.704642i | ||||
\(397\) | −305.777 | + | 176.540i | −0.770218 | + | 0.444686i | −0.832952 | − | 0.553345i | \(-0.813351\pi\) |
0.0627342 | + | 0.998030i | \(0.480018\pi\) | |||||||
\(398\) | −22.0962 | + | 38.2717i | −0.0555180 | + | 0.0961600i | ||||
\(399\) | 756.144i | 1.89510i | ||||||||
\(400\) | −63.8189 | − | 76.9880i | −0.159547 | − | 0.192470i | ||||
\(401\) | 381.323i | 0.950930i | 0.879735 | + | 0.475465i | \(0.157720\pi\) | ||||
−0.879735 | + | 0.475465i | \(0.842280\pi\) | |||||||
\(402\) | 257.505 | 0.640560 | ||||||||
\(403\) | −585.142 | − | 307.414i | −1.45197 | − | 0.762814i | ||||
\(404\) | −385.029 | −0.953042 | ||||||||
\(405\) | −744.693 | + | 62.9060i | −1.83875 | + | 0.155324i | ||||
\(406\) | −217.400 | + | 125.516i | −0.535468 | + | 0.309153i | ||||
\(407\) | 671.016i | 1.64869i | ||||||||
\(408\) | −61.0680 | − | 35.2576i | −0.149676 | − | 0.0864157i | ||||
\(409\) | 46.8236 | − | 27.0336i | 0.114483 | − | 0.0660969i | −0.441665 | − | 0.897180i | \(-0.645612\pi\) |
0.556148 | + | 0.831083i | \(0.312279\pi\) | |||||||
\(410\) | −220.428 | + | 153.364i | −0.537630 | + | 0.374059i | ||||
\(411\) | 77.5814 | 0.188763 | ||||||||
\(412\) | −78.8366 | − | 45.5164i | −0.191351 | − | 0.110477i | ||||
\(413\) | −37.4753 | − | 21.6364i | −0.0907391 | − | 0.0523883i | ||||
\(414\) | 849.320 | + | 490.355i | 2.05150 | + | 1.18443i | ||||
\(415\) | −268.302 | − | 385.627i | −0.646510 | − | 0.929221i | ||||
\(416\) | 104.456 | + | 60.3075i | 0.251095 | + | 0.144970i | ||||
\(417\) | 798.834 | − | 461.207i | 1.91567 | − | 1.10601i | ||||
\(418\) | −298.738 | −0.714685 | ||||||||
\(419\) | 395.030 | 0.942792 | 0.471396 | − | 0.881922i | \(-0.343750\pi\) | ||||
0.471396 | + | 0.881922i | \(0.343750\pi\) | |||||||
\(420\) | 403.217 | − | 280.540i | 0.960041 | − | 0.667953i | ||||
\(421\) | −59.6070 | + | 103.242i | −0.141584 | + | 0.245231i | −0.928093 | − | 0.372348i | \(-0.878553\pi\) |
0.786509 | + | 0.617579i | \(0.211886\pi\) | |||||||
\(422\) | 14.2245 | − | 8.21252i | 0.0337074 | − | 0.0194609i | ||||
\(423\) | −16.7769 | − | 9.68614i | −0.0396617 | − | 0.0228987i | ||||
\(424\) | 55.3388 | + | 31.9499i | 0.130516 | + | 0.0753535i | ||||
\(425\) | 40.0058 | − | 107.900i | 0.0941312 | − | 0.253883i | ||||
\(426\) | − | 384.625i | − | 0.902876i | ||||||
\(427\) | 23.7921 | + | 41.2092i | 0.0557192 | + | 0.0965086i | ||||
\(428\) | −157.778 | + | 91.0934i | −0.368641 | + | 0.212835i | ||||
\(429\) | −1372.40 | − | 792.358i | −3.19908 | − | 1.84699i | ||||
\(430\) | 47.6350 | + | 563.912i | 0.110779 | + | 1.31142i | ||||
\(431\) | −371.615 | − | 643.656i | −0.862216 | − | 1.49340i | −0.869785 | − | 0.493431i | \(-0.835743\pi\) |
0.00756874 | − | 0.999971i | \(-0.497591\pi\) | |||||||
\(432\) | −245.547 | −0.568395 | ||||||||
\(433\) | 649.567 | 1.50016 | 0.750078 | − | 0.661350i | \(-0.230016\pi\) | ||||
0.750078 | + | 0.661350i | \(0.230016\pi\) | |||||||
\(434\) | −336.144 | + | 212.370i | −0.774525 | + | 0.489333i | ||||
\(435\) | 44.6129 | + | 528.136i | 0.102558 | + | 1.21411i | ||||
\(436\) | −158.925 | −0.364508 | ||||||||
\(437\) | −262.487 | − | 454.641i | −0.600657 | − | 1.04037i | ||||
\(438\) | − | 288.892i | − | 0.659571i | ||||||
\(439\) | 80.6393 | − | 139.671i | 0.183689 | − | 0.318158i | −0.759445 | − | 0.650571i | \(-0.774530\pi\) |
0.943134 | + | 0.332413i | \(0.107863\pi\) | |||||||
\(440\) | 110.836 | + | 159.304i | 0.251901 | + | 0.362054i | ||||
\(441\) | 338.104 | + | 585.613i | 0.766675 | + | 1.32792i | ||||
\(442\) | 138.801i | 0.314030i | ||||||||
\(443\) | −329.231 | − | 190.082i | −0.743185 | − | 0.429078i | 0.0800413 | − | 0.996792i | \(-0.474495\pi\) |
−0.823226 | + | 0.567714i | \(0.807828\pi\) | |||||||
\(444\) | 264.838 | − | 458.713i | 0.596483 | − | 1.03314i | ||||
\(445\) | −204.979 | − | 96.3317i | −0.460628 | − | 0.216476i | ||||
\(446\) | 81.6337 | − | 47.1312i | 0.183035 | − | 0.105675i | ||||
\(447\) | −195.556 | + | 338.713i | −0.437486 | + | 0.757748i | ||||
\(448\) | 62.8350 | − | 36.2778i | 0.140257 | − | 0.0809772i | ||||
\(449\) | − | 663.535i | − | 1.47781i | −0.673811 | − | 0.738904i | \(-0.735344\pi\) | ||
0.673811 | − | 0.738904i | \(-0.264656\pi\) | |||||||
\(450\) | −120.597 | − | 708.732i | −0.267994 | − | 1.57496i | ||||
\(451\) | 451.315 | − | 260.567i | 1.00070 | − | 0.577753i | ||||
\(452\) | 307.751 | + | 177.680i | 0.680865 | + | 0.393098i | ||||
\(453\) | 52.0207 | − | 30.0342i | 0.114836 | − | 0.0663006i | ||||
\(454\) | −126.737 | + | 219.516i | −0.279157 | + | 0.483515i | ||||
\(455\) | −875.073 | − | 411.247i | −1.92324 | − | 0.903840i | ||||
\(456\) | 204.221 | + | 117.907i | 0.447852 | + | 0.258568i | ||||
\(457\) | −805.856 | −1.76336 | −0.881680 | − | 0.471848i | \(-0.843587\pi\) | ||||
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(458\) | 278.893 | + | 483.057i | 0.608937 | + | 1.05471i | ||||
\(459\) | −141.285 | − | 244.712i | −0.307810 | − | 0.533142i | ||||
\(460\) | −145.053 | + | 308.651i | −0.315333 | + | 0.670981i | ||||
\(461\) | − | 553.021i | − | 1.19961i | −0.800146 | − | 0.599806i | \(-0.795244\pi\) | ||
0.800146 | − | 0.599806i | \(-0.204756\pi\) | |||||||
\(462\) | −825.565 | + | 476.640i | −1.78694 | + | 1.03169i | ||||
\(463\) | 522.496 | 1.12850 | 0.564250 | − | 0.825604i | \(-0.309165\pi\) | ||||
0.564250 | + | 0.825604i | \(0.309165\pi\) | |||||||
\(464\) | 78.2877i | 0.168723i | ||||||||
\(465\) | 103.945 | + | 833.035i | 0.223537 | + | 1.79147i | ||||
\(466\) | 302.010 | 0.648090 | ||||||||
\(467\) | − | 354.874i | − | 0.759901i | −0.925007 | − | 0.379951i | \(-0.875941\pi\) | ||
0.925007 | − | 0.379951i | \(-0.124059\pi\) | |||||||
\(468\) | 433.563 | + | 750.952i | 0.926416 | + | 1.60460i | ||||
\(469\) | −304.905 | −0.650118 | ||||||||
\(470\) | 2.86528 | − | 6.09688i | 0.00609633 | − | 0.0129721i | ||||
\(471\) | −911.668 | + | 526.352i | −1.93560 | + | 1.11752i | ||||
\(472\) | −11.6872 | + | 6.74759i | −0.0247609 | + | 0.0142957i | ||||
\(473\) | − | 1098.27i | − | 2.32192i | ||||||
\(474\) | −91.9263 | + | 159.221i | −0.193937 | + | 0.335909i | ||||
\(475\) | −133.785 | + | 360.834i | −0.281653 | + | 0.759651i | ||||
\(476\) | 72.3091 | + | 41.7477i | 0.151910 | + | 0.0877052i | ||||
\(477\) | 229.694 | + | 397.842i | 0.481539 | + | 0.834049i | ||||
\(478\) | 259.225 | − | 448.990i | 0.542311 | − | 0.939310i | ||||
\(479\) | 152.869 | + | 264.776i | 0.319141 | + | 0.552769i | 0.980309 | − | 0.197469i | \(-0.0632723\pi\) |
−0.661168 | + | 0.750238i | \(0.729939\pi\) | |||||||
\(480\) | −12.8944 | − | 152.647i | −0.0268634 | − | 0.318014i | ||||
\(481\) | −1042.61 | −2.16758 | ||||||||
\(482\) | 13.6186 | + | 23.5881i | 0.0282544 | + | 0.0489380i | ||||
\(483\) | −1450.77 | − | 837.602i | −3.00366 | − | 1.73417i | ||||
\(484\) | −67.3117 | − | 116.587i | −0.139074 | − | 0.240883i | ||||
\(485\) | 632.854 | + | 297.415i | 1.30485 | + | 0.613226i | ||||
\(486\) | −314.832 | − | 181.768i | −0.647802 | − | 0.374009i | ||||
\(487\) | 99.1184 | − | 171.678i | 0.203529 | − | 0.352522i | −0.746134 | − | 0.665795i | \(-0.768092\pi\) |
0.949663 | + | 0.313274i | \(0.101426\pi\) | |||||||
\(488\) | 14.8398 | 0.0304094 | ||||||||
\(489\) | −815.517 | + | 470.839i | −1.66772 | + | 0.962860i | ||||
\(490\) | −193.024 | + | 134.298i | −0.393927 | + | 0.274077i | ||||
\(491\) | 407.331 | + | 235.172i | 0.829594 | + | 0.478966i | 0.853714 | − | 0.520743i | \(-0.174345\pi\) |
−0.0241198 | + | 0.999709i | \(0.507678\pi\) | |||||||
\(492\) | −411.365 | −0.836107 | ||||||||
\(493\) | −78.0217 | + | 45.0458i | −0.158259 | + | 0.0913709i | ||||
\(494\) | − | 464.172i | − | 0.939620i | ||||||
\(495\) | 117.437 | + | 1390.24i | 0.237246 | + | 2.80857i | ||||
\(496\) | 4.94190 | + | 123.901i | 0.00996350 | + | 0.249801i | ||||
\(497\) | 455.425i | 0.916349i | ||||||||
\(498\) | − | 719.658i | − | 1.44510i | ||||||
\(499\) | 60.9240 | − | 35.1745i | 0.122092 | − | 0.0704900i | −0.437710 | − | 0.899116i | \(-0.644210\pi\) |
0.559802 | + | 0.828626i | \(0.310877\pi\) | |||||||
\(500\) | 242.053 | − | 62.5331i | 0.484106 | − | 0.125066i | ||||
\(501\) | 485.986 | − | 841.753i | 0.970033 | − | 1.68015i | ||||
\(502\) | 240.971 | + | 417.375i | 0.480023 | + | 0.831424i | ||||
\(503\) | 20.0204 | − | 11.5588i | 0.0398020 | − | 0.0229797i | −0.479967 | − | 0.877287i | \(-0.659351\pi\) |
0.519769 | + | 0.854307i | \(0.326018\pi\) | |||||||
\(504\) | 521.616 | 1.03495 | ||||||||
\(505\) | 409.411 | − | 871.165i | 0.810714 | − | 1.72508i | ||||
\(506\) | 330.921 | − | 573.172i | 0.653994 | − | 1.13275i | ||||
\(507\) | 773.486 | − | 1339.72i | 1.52561 | − | 2.64244i | ||||
\(508\) | 93.1632 | + | 161.363i | 0.183392 | + | 0.317644i | ||||
\(509\) | −228.165 | − | 131.731i | −0.448262 | − | 0.258804i | 0.258834 | − | 0.965922i | \(-0.416662\pi\) |
−0.707096 | + | 0.707118i | \(0.749995\pi\) | |||||||
\(510\) | 144.709 | − | 100.682i | 0.283743 | − | 0.197415i | ||||
\(511\) | 342.070i | 0.669413i | ||||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | 472.478 | + | 818.355i | 0.921009 | + | 1.59523i | ||||
\(514\) | −81.0626 | + | 140.404i | −0.157709 | + | 0.273160i | ||||
\(515\) | 186.814 | − | 129.977i | 0.362746 | − | 0.252382i | ||||
\(516\) | −433.467 | + | 750.787i | −0.840053 | + | 1.45501i | ||||
\(517\) | −6.53678 | + | 11.3220i | −0.0126437 | + | 0.0218995i | ||||
\(518\) | −313.588 | + | 543.151i | −0.605383 | + | 1.04855i | ||||
\(519\) | − | 177.605i | − | 0.342206i | ||||||
\(520\) | −247.522 | + | 172.215i | −0.476004 | + | 0.331182i | ||||
\(521\) | −202.021 | − | 349.910i | −0.387756 | − | 0.671613i | 0.604391 | − | 0.796687i | \(-0.293416\pi\) |
−0.992147 | + | 0.125075i | \(0.960083\pi\) | |||||||
\(522\) | −281.413 | + | 487.421i | −0.539105 | + | 0.933756i | ||||
\(523\) | 306.267 | 0.585597 | 0.292798 | − | 0.956174i | \(-0.405413\pi\) | ||||
0.292798 | + | 0.956174i | \(0.405413\pi\) | |||||||
\(524\) | −97.2941 | − | 168.518i | −0.185676 | − | 0.321600i | ||||
\(525\) | 205.999 | + | 1210.62i | 0.392378 | + | 2.30595i | ||||
\(526\) | 352.419i | 0.669999i | ||||||||
\(527\) | −120.637 | + | 76.2166i | −0.228913 | + | 0.144624i | ||||
\(528\) | 297.293i | 0.563055i | ||||||||
\(529\) | 634.059 | 1.19860 | ||||||||
\(530\) | −131.133 | + | 91.2363i | −0.247420 | + | 0.172144i | ||||
\(531\) | −97.0194 | −0.182711 | ||||||||
\(532\) | −241.813 | − | 139.611i | −0.454535 | − | 0.262426i | ||||
\(533\) | 404.862 | + | 701.241i | 0.759591 | + | 1.31565i | ||||
\(534\) | −173.478 | − | 300.473i | −0.324865 | − | 0.562683i | ||||
\(535\) | −38.3379 | − | 453.851i | −0.0716596 | − | 0.848319i | ||||
\(536\) | −47.5444 | + | 82.3493i | −0.0887023 | + | 0.153637i | ||||
\(537\) | 1410.00 | + | 814.063i | 2.62570 | + | 1.51595i | ||||
\(538\) | −23.1255 | + | 40.0545i | −0.0429841 | + | 0.0744507i | ||||
\(539\) | 395.206 | − | 228.172i | 0.733221 | − | 0.423326i | ||||
\(540\) | 261.096 | − | 555.573i | 0.483511 | − | 1.02884i | ||||
\(541\) | −3.77161 | − | 6.53263i | −0.00697156 | − | 0.0120751i | 0.862519 | − | 0.506025i | \(-0.168886\pi\) |
−0.869490 | + | 0.493950i | \(0.835552\pi\) | |||||||
\(542\) | 243.471 | 0.449209 | ||||||||
\(543\) | 1737.16i | 3.19918i | ||||||||
\(544\) | 22.5505 | − | 13.0196i | 0.0414532 | − | 0.0239330i | ||||
\(545\) | 168.989 | − | 359.584i | 0.310072 | − | 0.659787i | ||||
\(546\) | −740.591 | − | 1282.74i | −1.35639 | − | 2.34934i | ||||
\(547\) | −63.2052 | − | 36.4916i | −0.115549 | − | 0.0667122i | 0.441112 | − | 0.897452i | \(-0.354584\pi\) |
−0.556661 | + | 0.830740i | \(0.687918\pi\) | |||||||
\(548\) | −14.3242 | + | 24.8103i | −0.0261391 | + | 0.0452743i | ||||
\(549\) | 92.3928 | + | 53.3430i | 0.168293 | + | 0.0971640i | ||||
\(550\) | −478.295 | + | 81.3862i | −0.869627 | + | 0.147975i | ||||
\(551\) | 260.916 | − | 150.640i | 0.473532 | − | 0.273394i | ||||
\(552\) | −452.442 | + | 261.217i | −0.819641 | + | 0.473220i | ||||
\(553\) | 108.848 | − | 188.530i | 0.196831 | − | 0.340921i | ||||
\(554\) | − | 503.097i | − | 0.908117i | ||||||
\(555\) | 756.274 | + | 1086.98i | 1.36266 | + | 1.95853i | ||||
\(556\) | 340.619i | 0.612625i | ||||||||
\(557\) | −245.009 | −0.439873 | −0.219936 | − | 0.975514i | \(-0.570585\pi\) | ||||
−0.219936 | + | 0.975514i | \(0.570585\pi\) | |||||||
\(558\) | −414.608 | + | 789.178i | −0.743024 | + | 1.41430i | ||||
\(559\) | 1706.46 | 3.05270 | ||||||||
\(560\) | 15.2680 | + | 180.745i | 0.0272643 | + | 0.322759i | ||||
\(561\) | −296.283 | + | 171.059i | −0.528134 | + | 0.304918i | ||||
\(562\) | − | 32.9173i | − | 0.0585718i | ||||||
\(563\) | −142.081 | − | 82.0304i | −0.252364 | − | 0.145702i | 0.368482 | − | 0.929635i | \(-0.379878\pi\) |
−0.620846 | + | 0.783932i | \(0.713211\pi\) | |||||||
\(564\) | 8.93722 | − | 5.15991i | 0.0158461 | − | 0.00914877i | ||||
\(565\) | −729.257 | + | 507.384i | −1.29072 | + | 0.898025i | ||||
\(566\) | −478.621 | −0.845621 | ||||||||
\(567\) | 1173.99 | + | 677.801i | 2.07052 | + | 1.19542i | ||||
\(568\) | 123.002 | + | 71.0152i | 0.216553 | + | 0.125027i | ||||
\(569\) | 475.912 | + | 274.768i | 0.836401 | + | 0.482896i | 0.856039 | − | 0.516911i | \(-0.172918\pi\) |
−0.0196382 | + | 0.999807i | \(0.506251\pi\) | |||||||
\(570\) | −483.928 | + | 336.695i | −0.848997 | + | 0.590694i | ||||
\(571\) | −158.710 | − | 91.6311i | −0.277950 | − | 0.160475i | 0.354545 | − | 0.935039i | \(-0.384636\pi\) |
−0.632495 | + | 0.774564i | \(0.717969\pi\) | |||||||
\(572\) | 506.787 | − | 292.594i | 0.885992 | − | 0.511528i | ||||
\(573\) | −935.193 | −1.63210 | ||||||||
\(574\) | 487.087 | 0.848583 | ||||||||
\(575\) | −544.114 | − | 656.393i | −0.946286 | − | 1.14155i | ||||
\(576\) | 81.3364 | − | 140.879i | 0.141209 | − | 0.244581i | ||||
\(577\) | −447.584 | + | 258.413i | −0.775709 | + | 0.447856i | −0.834907 | − | 0.550391i | \(-0.814479\pi\) |
0.0591985 | + | 0.998246i | \(0.481145\pi\) | |||||||
\(578\) | −328.001 | − | 189.371i | −0.567475 | − | 0.327632i | ||||
\(579\) | 11.3919 | + | 6.57709i | 0.0196751 | + | 0.0113594i | ||||
\(580\) | −177.133 | − | 83.2452i | −0.305402 | − | 0.143526i | ||||
\(581\) | 852.130i | 1.46666i | ||||||||
\(582\) | 535.597 | + | 927.681i | 0.920269 | + | 1.59395i | ||||
\(583\) | 268.487 | − | 155.011i | 0.460527 | − | 0.265885i | ||||
\(584\) | 92.3868 | + | 53.3396i | 0.158197 | + | 0.0913349i | ||||
\(585\) | −2160.12 | + | 182.471i | −3.69251 | + | 0.311915i | ||||
\(586\) | 361.857 | + | 626.754i | 0.617503 | + | 1.06955i | ||||
\(587\) | −178.951 | −0.304857 | −0.152428 | − | 0.988315i | \(-0.548709\pi\) | ||||
−0.152428 | + | 0.988315i | \(0.548709\pi\) | |||||||
\(588\) | −360.223 | −0.612624 | ||||||||
\(589\) | 403.429 | − | 254.880i | 0.684938 | − | 0.432734i | ||||
\(590\) | −2.83981 | − | 33.6182i | −0.00481324 | − | 0.0569800i | ||||
\(591\) | 288.636 | 0.488386 | ||||||||
\(592\) | 97.7967 | + | 169.389i | 0.165197 | + | 0.286130i | ||||
\(593\) | 129.321i | 0.218079i | 0.994037 | + | 0.109039i | \(0.0347775\pi\) | ||||
−0.994037 | + | 0.109039i | \(0.965223\pi\) | |||||||
\(594\) | −595.659 | + | 1031.71i | −1.00279 | + | 1.73689i | ||||
\(595\) | −171.346 | + | 119.215i | −0.287977 | + | 0.200361i | ||||
\(596\) | −72.2130 | − | 125.077i | −0.121163 | − | 0.209860i | ||||
\(597\) | − | 169.246i | − | 0.283494i | ||||||
\(598\) | 890.580 | + | 514.177i | 1.48926 | + | 0.859827i | ||||
\(599\) | 56.8801 | − | 98.5192i | 0.0949584 | − | 0.164473i | −0.814633 | − | 0.579977i | \(-0.803062\pi\) |
0.909591 | + | 0.415504i | \(0.136395\pi\) | |||||||
\(600\) | 359.089 | + | 133.138i | 0.598481 | + | 0.221897i | ||||
\(601\) | −536.918 | + | 309.990i | −0.893374 | + | 0.515790i | −0.875045 | − | 0.484042i | \(-0.839168\pi\) |
−0.0183293 | + | 0.999832i | \(0.505835\pi\) | |||||||
\(602\) | 513.258 | − | 888.989i | 0.852588 | − | 1.47673i | ||||
\(603\) | −592.025 | + | 341.806i | −0.981800 | + | 0.566842i | ||||
\(604\) | 22.1814i | 0.0367242i | ||||||||
\(605\) | 335.364 | − | 28.3290i | 0.554321 | − | 0.0468248i | ||||
\(606\) | 1277.01 | − | 737.284i | 2.10728 | − | 1.21664i | ||||
\(607\) | 31.0626 | + | 17.9340i | 0.0511740 | + | 0.0295453i | 0.525369 | − | 0.850875i | \(-0.323927\pi\) |
−0.474195 | + | 0.880420i | \(0.657261\pi\) | |||||||
\(608\) | −75.4125 | + | 43.5394i | −0.124034 | + | 0.0716109i | ||||
\(609\) | 480.696 | − | 832.590i | 0.789320 | − | 1.36714i | ||||
\(610\) | −15.7795 | + | 33.5764i | −0.0258680 | + | 0.0550433i | ||||
\(611\) | −17.5919 | − | 10.1567i | −0.0287920 | − | 0.0166231i | ||||
\(612\) | 187.200 | 0.305883 | ||||||||
\(613\) | −318.064 | − | 550.902i | −0.518864 | − | 0.898699i | −0.999760 | − | 0.0219211i | \(-0.993022\pi\) |
0.480896 | − | 0.876778i | \(-0.340312\pi\) | |||||||
\(614\) | 210.652 | + | 364.859i | 0.343081 | + | 0.594234i | ||||
\(615\) | 437.414 | − | 930.752i | 0.711243 | − | 1.51342i | ||||
\(616\) | − | 352.018i | − | 0.571457i | ||||||
\(617\) | 551.654 | − | 318.498i | 0.894091 | − | 0.516204i | 0.0188126 | − | 0.999823i | \(-0.494011\pi\) |
0.875278 | + | 0.483619i | \(0.160678\pi\) | |||||||
\(618\) | 348.633 | 0.564132 | ||||||||
\(619\) | − | 848.040i | − | 1.37002i | −0.728535 | − | 0.685008i | \(-0.759799\pi\) | ||
0.728535 | − | 0.685008i | \(-0.240201\pi\) | |||||||
\(620\) | −285.594 | − | 120.566i | −0.460635 | − | 0.194461i | ||||
\(621\) | −2093.51 | −3.37119 | ||||||||
\(622\) | − | 271.406i | − | 0.436345i | ||||||
\(623\) | 205.411 | + | 355.782i | 0.329713 | + | 0.571079i | ||||
\(624\) | −461.927 | −0.740267 | ||||||||
\(625\) | −115.894 | + | 614.161i | −0.185430 | + | 0.982657i | ||||
\(626\) | 473.027 | − | 273.102i | 0.755634 | − | 0.436266i | ||||
\(627\) | 990.816 | − | 572.048i | 1.58025 | − | 0.912357i | ||||
\(628\) | − | 388.731i | − | 0.618999i | ||||||
\(629\) | −112.542 | + | 194.929i | −0.178923 | + | 0.309903i | ||||
\(630\) | −554.647 | + | 1180.21i | −0.880392 | + | 1.87334i | ||||
\(631\) | −270.764 | − | 156.326i | −0.429103 | − | 0.247743i | 0.269861 | − | 0.962899i | \(-0.413022\pi\) |
−0.698965 | + | 0.715156i | \(0.746355\pi\) | |||||||
\(632\) | −33.9456 | − | 58.7955i | −0.0537113 | − | 0.0930308i | ||||
\(633\) | −31.4520 | + | 54.4764i | −0.0496872 | + | 0.0860607i | ||||
\(634\) | −276.897 | − | 479.600i | −0.436747 | − | 0.756467i | ||||
\(635\) | −464.163 | + | 39.2090i | −0.730965 | + | 0.0617464i | ||||
\(636\) | −244.721 | −0.384781 | ||||||||
\(637\) | 354.529 | + | 614.061i | 0.556560 | + | 0.963990i | ||||
\(638\) | 328.941 | + | 189.914i | 0.515581 | + | 0.297671i | ||||
\(639\) | 510.542 | + | 884.285i | 0.798970 | + | 1.38386i | ||||
\(640\) | 51.1967 | + | 24.0603i | 0.0799948 | + | 0.0375942i | ||||
\(641\) | 947.241 | + | 546.890i | 1.47776 | + | 0.853182i | 0.999684 | − | 0.0251385i | \(-0.00800267\pi\) |
0.478071 | + | 0.878321i | \(0.341336\pi\) | |||||||
\(642\) | 348.866 | − | 604.253i | 0.543405 | − | 0.941204i | ||||
\(643\) | −215.375 | −0.334953 | −0.167476 | − | 0.985876i | \(-0.553562\pi\) | ||||
−0.167476 | + | 0.985876i | \(0.553562\pi\) | |||||||
\(644\) | 535.725 | − | 309.301i | 0.831871 | − | 0.480281i | ||||
\(645\) | −1237.81 | − | 1779.09i | −1.91909 | − | 2.75828i | ||||
\(646\) | −86.7830 | − | 50.1042i | −0.134339 | − | 0.0775606i | ||||
\(647\) | 505.621 | 0.781485 | 0.390743 | − | 0.920500i | \(-0.372218\pi\) | ||||
0.390743 | + | 0.920500i | \(0.372218\pi\) | |||||||
\(648\) | 366.123 | − | 211.381i | 0.565004 | − | 0.326205i | ||||
\(649\) | 65.4745i | 0.100885i | ||||||||
\(650\) | −126.456 | − | 743.162i | −0.194547 | − | 1.14333i | ||||
\(651\) | 708.213 | − | 1348.04i | 1.08789 | − | 2.07072i | ||||
\(652\) | − | 347.733i | − | 0.533333i | ||||||
\(653\) | 490.344i | 0.750910i | 0.926841 | + | 0.375455i | \(0.122513\pi\) | ||||
−0.926841 | + | 0.375455i | \(0.877487\pi\) | |||||||
\(654\) | 527.103 | − | 304.323i | 0.805967 | − | 0.465325i | ||||
\(655\) | 484.744 | − | 40.9475i | 0.740067 | − | 0.0625153i | ||||
\(656\) | 75.9522 | − | 131.553i | 0.115781 | − | 0.200538i | ||||
\(657\) | 383.468 | + | 664.187i | 0.583666 | + | 1.01094i | ||||
\(658\) | −10.5823 | + | 6.10972i | −0.0160826 | + | 0.00928529i | ||||
\(659\) | 363.202 | 0.551141 | 0.275570 | − | 0.961281i | \(-0.411133\pi\) | ||||
0.275570 | + | 0.961281i | \(0.411133\pi\) | |||||||
\(660\) | −672.655 | − | 316.119i | −1.01917 | − | 0.478969i | ||||
\(661\) | 70.9059 | − | 122.813i | 0.107271 | − | 0.185798i | −0.807393 | − | 0.590014i | \(-0.799122\pi\) |
0.914664 | + | 0.404216i | \(0.132456\pi\) | |||||||
\(662\) | −34.9179 | + | 60.4795i | −0.0527460 | + | 0.0913588i | ||||
\(663\) | −265.787 | − | 460.357i | −0.400886 | − | 0.694355i | ||||
\(664\) | 230.145 | + | 132.874i | 0.346603 | + | 0.200111i | ||||
\(665\) | 573.007 | − | 398.673i | 0.861665 | − | 0.599508i | ||||
\(666\) | 1406.16i | 2.11135i | ||||||||
\(667\) | 667.474i | 1.00071i | ||||||||
\(668\) | 179.460 | + | 310.834i | 0.268653 | + | 0.465320i | ||||
\(669\) | −180.501 | + | 312.637i | −0.269807 | + | 0.467320i | ||||
\(670\) | −135.768 | − | 195.138i | −0.202639 | − | 0.291251i | ||||
\(671\) | 35.9990 | − | 62.3522i | 0.0536498 | − | 0.0929243i | ||||
\(672\) | −138.935 | + | 240.643i | −0.206749 | + | 0.358099i | ||||
\(673\) | −93.0491 | + | 161.166i | −0.138260 | + | 0.239474i | −0.926838 | − | 0.375461i | \(-0.877484\pi\) |
0.788578 | + | 0.614935i | \(0.210818\pi\) | |||||||
\(674\) | 523.425i | 0.776595i | ||||||||
\(675\) | 979.407 | + | 1181.51i | 1.45097 | + | 1.75038i | ||||
\(676\) | 285.625 | + | 494.717i | 0.422522 | + | 0.731829i | ||||
\(677\) | 120.480 | − | 208.678i | 0.177962 | − | 0.308239i | −0.763220 | − | 0.646138i | \(-0.776383\pi\) |
0.941182 | + | 0.337899i | \(0.109716\pi\) | |||||||
\(678\) | −1360.94 | −2.00729 | ||||||||
\(679\) | −634.187 | − | 1098.44i | −0.934001 | − | 1.61774i | ||||
\(680\) | 5.47946 | + | 64.8668i | 0.00805802 | + | 0.0953923i | ||||
\(681\) | − | 970.747i | − | 1.42547i | ||||||
\(682\) | 532.584 | + | 279.802i | 0.780915 | + | 0.410267i | ||||
\(683\) | − | 1207.66i | − | 1.76817i | −0.467326 | − | 0.884085i | \(-0.654783\pi\) | ||
0.467326 | − | 0.884085i | \(-0.345217\pi\) | |||||||
\(684\) | −626.026 | −0.915243 | ||||||||
\(685\) | −40.9044 | − | 58.7913i | −0.0597144 | − | 0.0858268i | ||||
\(686\) | −201.950 | −0.294387 | ||||||||
\(687\) | −1849.99 | − | 1068.09i | −2.69286 | − | 1.55472i | ||||
\(688\) | −160.066 | − | 277.243i | −0.232655 | − | 0.402969i | ||||
\(689\) | 240.852 | + | 417.169i | 0.349568 | + | 0.605470i | ||||
\(690\) | −109.937 | − | 1301.45i | −0.159329 | − | 1.88616i | ||||
\(691\) | 166.424 | − | 288.255i | 0.240845 | − | 0.417156i | −0.720110 | − | 0.693860i | \(-0.755909\pi\) |
0.960955 | + | 0.276704i | \(0.0892421\pi\) | |||||||
\(692\) | 56.7974 | + | 32.7920i | 0.0820772 | + | 0.0473873i | ||||
\(693\) | 1265.36 | − | 2191.67i | 1.82592 | − | 3.16258i | ||||
\(694\) | 140.800 | − | 81.2907i | 0.202881 | − | 0.117134i | ||||
\(695\) | −770.684 | − | 362.189i | −1.10890 | − | 0.521135i | ||||
\(696\) | −149.911 | − | 259.654i | −0.215390 | − | 0.373066i | ||||
\(697\) | 174.808 | 0.250801 | ||||||||
\(698\) | 121.053i | 0.173428i | ||||||||
\(699\) | −1001.67 | + | 578.313i | −1.43300 | + | 0.827343i | ||||
\(700\) | −425.188 | − | 157.646i | −0.607412 | − | 0.225208i | ||||
\(701\) | 612.390 | + | 1060.69i | 0.873595 | + | 1.51311i | 0.858252 | + | 0.513229i | \(0.171551\pi\) |
0.0153434 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(702\) | −1603.05 | − | 925.519i | −2.28354 | − | 1.31840i | ||||
\(703\) | 376.359 | − | 651.872i | 0.535361 | − | 0.927272i | ||||
\(704\) | −95.0734 | − | 54.8907i | −0.135048 | − | 0.0779697i | ||||
\(705\) | 2.17162 | + | 25.7080i | 0.00308031 | + | 0.0364652i | ||||
\(706\) | 344.231 | − | 198.742i | 0.487580 | − | 0.281504i | ||||
\(707\) | −1512.08 | + | 873.000i | −2.13873 | + | 1.23479i | ||||
\(708\) | 25.8416 | − | 44.7590i | 0.0364995 | − | 0.0632189i | ||||
\(709\) | − | 413.482i | − | 0.583191i | −0.956542 | − | 0.291595i | \(-0.905814\pi\) | ||
0.956542 | − | 0.291595i | \(-0.0941861\pi\) | |||||||
\(710\) | −291.470 | + | 202.791i | −0.410521 | + | 0.285622i | ||||
\(711\) | − | 488.083i | − | 0.686473i | ||||||
\(712\) | 128.120 | 0.179944 | ||||||||
\(713\) | 42.1342 | + | 1056.37i | 0.0590942 | + | 1.48159i | ||||
\(714\) | −319.767 | −0.447853 | ||||||||
\(715\) | 123.142 | + | 1457.78i | 0.172227 | + | 2.03885i | ||||
\(716\) | −520.670 | + | 300.609i | −0.727192 | + | 0.419845i | ||||
\(717\) | 1985.54i | 2.76923i | ||||||||
\(718\) | 15.7328 | + | 9.08331i | 0.0219119 | + | 0.0126508i | ||||
\(719\) | 950.752 | − | 548.917i | 1.32233 | − | 0.763445i | 0.338226 | − | 0.941065i | \(-0.390173\pi\) |
0.984099 | + | 0.177620i | \(0.0568398\pi\) | |||||||
\(720\) | 232.265 | + | 333.831i | 0.322590 | + | 0.463655i | ||||
\(721\) | −412.808 | −0.572549 | ||||||||
\(722\) | −151.917 | − | 87.7096i | −0.210412 | − | 0.121481i | ||||
\(723\) | −90.3369 | − | 52.1560i | −0.124947 | − | 0.0721383i | ||||
\(724\) | −555.537 | − | 320.740i | −0.767316 | − | 0.443010i | ||||
\(725\) | 376.701 | − | 312.264i | 0.519587 | − | 0.430710i | ||||
\(726\) | 446.501 | + | 257.787i | 0.615015 | + | 0.355079i | ||||
\(727\) | −957.797 | + | 552.984i | −1.31746 | + | 0.760638i | −0.983320 | − | 0.181884i | \(-0.941781\pi\) |
−0.334144 | + | 0.942522i | \(0.608447\pi\) | |||||||
\(728\) | 546.956 | 0.751313 | ||||||||
\(729\) | 47.0358 | 0.0645210 | ||||||||
\(730\) | −218.923 | + | 152.317i | −0.299895 | + | 0.208653i | ||||
\(731\) | 184.201 | − | 319.045i | 0.251985 | − | 0.436450i | ||||
\(732\) | −49.2186 | + | 28.4164i | −0.0672386 | + | 0.0388202i | ||||
\(733\) | 189.883 | + | 109.629i | 0.259050 | + | 0.149562i | 0.623901 | − | 0.781503i | \(-0.285547\pi\) |
−0.364851 | + | 0.931066i | \(0.618880\pi\) | |||||||
\(734\) | −179.912 | − | 103.872i | −0.245112 | − | 0.141516i | ||||
\(735\) | 383.034 | − | 815.039i | 0.521134 | − | 1.10890i | ||||
\(736\) | − | 192.919i | − | 0.262119i | ||||||
\(737\) | 230.671 | + | 399.534i | 0.312986 | + | 0.542109i | ||||
\(738\) | 945.761 | − | 546.035i | 1.28152 | − | 0.739885i | ||||
\(739\) | −621.959 | − | 359.088i | −0.841623 | − | 0.485911i | 0.0161928 | − | 0.999869i | \(-0.494845\pi\) |
−0.857815 | + | 0.513958i | \(0.828179\pi\) | |||||||
\(740\) | −487.248 | + | 41.1591i | −0.658444 | + | 0.0556203i | ||||
\(741\) | 888.834 | + | 1539.50i | 1.19951 | + | 2.07760i | ||||
\(742\) | 289.768 | 0.390523 | ||||||||
\(743\) | −263.700 | −0.354912 | −0.177456 | − | 0.984129i | \(-0.556787\pi\) | ||||
−0.177456 | + | 0.984129i | \(0.556787\pi\) | |||||||
\(744\) | −253.647 | − | 401.477i | −0.340923 | − | 0.539620i | ||||
\(745\) | 359.784 | − | 30.3918i | 0.482931 | − | 0.0407944i | ||||
\(746\) | −792.257 | −1.06201 | ||||||||
\(747\) | 955.257 | + | 1654.55i | 1.27879 | + | 2.21493i | ||||
\(748\) | − | 126.334i | − | 0.168896i | ||||||
\(749\) | −413.083 | + | 715.481i | −0.551513 | + | 0.955249i | ||||
\(750\) | −683.066 | + | 670.904i | −0.910755 | + | 0.894538i | ||||
\(751\) | −364.911 | − | 632.044i | −0.485899 | − | 0.841603i | 0.513969 | − | 0.857809i | \(-0.328175\pi\) |
−0.999869 | + | 0.0162061i | \(0.994841\pi\) | |||||||
\(752\) | 3.81079i | 0.00506755i | ||||||||
\(753\) | −1598.44 | − | 922.863i | −2.12277 | − | 1.22558i | ||||
\(754\) | −295.083 | + | 511.100i | −0.391357 | + | 0.677851i | ||||
\(755\) | −50.1876 | − | 23.5860i | −0.0664736 | − | 0.0312398i | ||||
\(756\) | −964.307 | + | 556.743i | −1.27554 | + | 0.736432i | ||||
\(757\) | 316.039 | − | 547.396i | 0.417489 | − | 0.723113i | −0.578197 | − | 0.815897i | \(-0.696243\pi\) |
0.995686 | + | 0.0927845i | \(0.0295768\pi\) | |||||||
\(758\) | 244.153 | − | 140.962i | 0.322102 | − | 0.185966i | ||||
\(759\) | 2534.70i | 3.33952i | ||||||||
\(760\) | −18.3241 | − | 216.924i | −0.0241107 | − | 0.285427i | ||||
\(761\) | −1027.33 | + | 593.128i | −1.34997 | + | 0.779407i | −0.988245 | − | 0.152877i | \(-0.951146\pi\) |
−0.361727 | + | 0.932284i | \(0.617813\pi\) | |||||||
\(762\) | −617.983 | − | 356.793i | −0.811001 | − | 0.468232i | ||||
\(763\) | −624.129 | + | 360.341i | −0.817993 | + | 0.472269i | ||||
\(764\) | 172.669 | − | 299.072i | 0.226007 | − | 0.391455i | ||||
\(765\) | −199.055 | + | 423.559i | −0.260202 | + | 0.553671i | ||||
\(766\) | −411.334 | − | 237.484i | −0.536990 | − | 0.310031i | ||||
\(767\) | −101.733 | −0.132637 | ||||||||
\(768\) | 43.3288 | + | 75.0476i | 0.0564177 | + | 0.0977183i | ||||
\(769\) | −23.9096 | − | 41.4127i | −0.0310918 | − | 0.0538526i | 0.850061 | − | 0.526685i | \(-0.176565\pi\) |
−0.881153 | + | 0.472832i | \(0.843232\pi\) | |||||||
\(770\) | 796.473 | + | 374.309i | 1.03438 | + | 0.486116i | ||||
\(771\) | − | 620.900i | − | 0.805318i | ||||||
\(772\) | −4.20667 | + | 2.42872i | −0.00544905 | + | 0.00314601i | ||||
\(773\) | 17.4533 | 0.0225786 | 0.0112893 | − | 0.999936i | \(-0.496406\pi\) | ||||
0.0112893 | + | 0.999936i | \(0.496406\pi\) | |||||||
\(774\) | − | 2301.50i | − | 2.97351i | ||||||
\(775\) | 576.471 | − | 517.983i | 0.743834 | − | 0.668365i | ||||
\(776\) | −395.559 | −0.509741 | ||||||||
\(777\) | − | 2401.94i | − | 3.09130i | ||||||
\(778\) | 445.966 | + | 772.435i | 0.573221 | + | 0.992847i | ||||
\(779\) | −584.585 | −0.750430 | ||||||||
\(780\) | 491.178 | − | 1045.15i | 0.629715 | − | 1.33994i | ||||
\(781\) | 596.768 | − | 344.544i | 0.764108 | − | 0.441158i | ||||
\(782\) | 192.264 | − | 111.004i | 0.245862 | − | 0.141948i | ||||
\(783\) | − | 1201.45i | − | 1.53442i | ||||||
\(784\) | 66.5097 | − | 115.198i | 0.0848337 | − | 0.146936i | ||||
\(785\) | 879.542 | + | 413.348i | 1.12044 | + | 0.526557i | ||||
\(786\) | 645.384 | + | 372.613i | 0.821100 | + | 0.474062i | ||||
\(787\) | −676.493 | − | 1171.72i | −0.859584 | − | 1.48884i | −0.872326 | − | 0.488925i | \(-0.837389\pi\) |
0.0127413 | − | 0.999919i | \(-0.495944\pi\) | |||||||
\(788\) | −53.2923 | + | 92.3050i | −0.0676298 | + | 0.117138i | ||||
\(789\) | −674.841 | − | 1168.86i | −0.855312 | − | 1.48144i | ||||
\(790\) | 169.126 | − | 14.2864i | 0.214083 | − | 0.0180841i | ||||
\(791\) | 1611.46 | 2.03724 | ||||||||
\(792\) | −394.620 | − | 683.501i | −0.498257 | − | 0.863007i | ||||
\(793\) | 96.8812 | + | 55.9344i | 0.122171 | + | 0.0705352i | ||||
\(794\) | 249.666 | + | 432.434i | 0.314440 | + | 0.544627i | ||||
\(795\) | 260.218 | − | 553.704i | 0.327318 | − | 0.696483i | ||||
\(796\) | 54.1243 | + | 31.2487i | 0.0679954 | + | 0.0392571i | ||||
\(797\) | 471.307 | − | 816.328i | 0.591352 | − | 1.02425i | −0.402699 | − | 0.915332i | \(-0.631928\pi\) |
0.994051 | − | 0.108919i | \(-0.0347388\pi\) | |||||||
\(798\) | 1069.35 | 1.34004 | ||||||||
\(799\) | −3.79785 | + | 2.19269i | −0.00475325 | + | 0.00274429i | ||||
\(800\) | −108.877 | + | 90.2535i | −0.136097 | + | 0.112817i | ||||
\(801\) | 797.680 | + | 460.541i | 0.995856 | + | 0.574958i | ||||
\(802\) | 539.272 | 0.672409 | ||||||||
\(803\) | 448.233 | − | 258.787i | 0.558198 | − | 0.322276i | ||||
\(804\) | − | 364.167i | − | 0.452944i | ||||||
\(805\) | 130.173 | + | 1541.02i | 0.161706 | + | 1.91431i | ||||
\(806\) | −434.749 | + | 827.516i | −0.539391 | + | 1.02669i | ||||
\(807\) | − | 177.130i | − | 0.219492i | ||||||
\(808\) | 544.513i | 0.673902i | ||||||||
\(809\) | 211.142 | − | 121.903i | 0.260991 | − | 0.150683i | −0.363796 | − | 0.931479i | \(-0.618519\pi\) |
0.624787 | + | 0.780796i | \(0.285186\pi\) | |||||||
\(810\) | 88.9626 | + | 1053.16i | 0.109830 | + | 1.30019i | ||||
\(811\) | 495.278 | − | 857.847i | 0.610701 | − | 1.05776i | −0.380422 | − | 0.924813i | \(-0.624221\pi\) |
0.991123 | − | 0.132951i | \(-0.0424454\pi\) | |||||||
\(812\) | 177.506 | + | 307.450i | 0.218604 | + | 0.378633i | ||||
\(813\) | −807.514 | + | 466.218i | −0.993252 | + | 0.573454i | ||||
\(814\) | 948.960 | 1.16580 | ||||||||
\(815\) | 786.779 | + | 369.753i | 0.965373 | + | 0.453685i | ||||
\(816\) | −49.8618 | + | 86.3632i | −0.0611051 | + | 0.105837i | ||||
\(817\) | −615.995 | + | 1066.94i | −0.753972 | + | 1.30592i | ||||
\(818\) | −38.2313 | − | 66.2186i | −0.0467376 | − | 0.0809518i | ||||
\(819\) | 3405.36 | + | 1966.09i | 4.15795 | + | 2.40059i | ||||
\(820\) | 216.890 | + | 311.733i | 0.264500 | + | 0.380162i | ||||
\(821\) | − | 126.179i | − | 0.153690i | −0.997043 | − | 0.0768448i | \(-0.975515\pi\) | ||
0.997043 | − | 0.0768448i | \(-0.0244846\pi\) | |||||||
\(822\) | − | 109.717i | − | 0.133475i | ||||||
\(823\) | −402.561 | − | 697.256i | −0.489138 | − | 0.847212i | 0.510784 | − | 0.859709i | \(-0.329355\pi\) |
−0.999922 | + | 0.0124969i | \(0.996022\pi\) | |||||||
\(824\) | −64.3698 | + | 111.492i | −0.0781187 | + | 0.135306i | ||||
\(825\) | 1430.50 | − | 1185.81i | 1.73394 | − | 1.43734i | ||||
\(826\) | −30.5984 | + | 52.9980i | −0.0370441 | + | 0.0641623i | ||||
\(827\) | 202.582 | − | 350.882i | 0.244960 | − | 0.424283i | −0.717161 | − | 0.696908i | \(-0.754559\pi\) |
0.962120 | + | 0.272625i | \(0.0878919\pi\) | |||||||
\(828\) | 693.467 | − | 1201.12i | 0.837521 | − | 1.45063i | ||||
\(829\) | − | 529.451i | − | 0.638662i | −0.947643 | − | 0.319331i | \(-0.896542\pi\) | ||
0.947643 | − | 0.319331i | \(-0.103458\pi\) | |||||||
\(830\) | −545.359 | + | 379.436i | −0.657058 | + | 0.457152i | ||||
\(831\) | 963.370 | + | 1668.61i | 1.15929 | + | 2.00795i | ||||
\(832\) | 85.2877 | − | 147.723i | 0.102509 | − | 0.177551i | ||||
\(833\) | 153.076 | 0.183764 | ||||||||
\(834\) | −652.245 | − | 1129.72i | −0.782068 | − | 1.35458i | ||||
\(835\) | −894.116 | + | 75.5281i | −1.07080 | + | 0.0904529i | ||||
\(836\) | 422.480i | 0.505359i | ||||||||
\(837\) | −75.8416 | − | 1901.47i | −0.0906112 | − | 2.27177i | ||||
\(838\) | − | 558.656i | − | 0.666654i | ||||||
\(839\) | −1409.99 | −1.68056 | −0.840282 | − | 0.542150i | \(-0.817611\pi\) | ||||
−0.840282 | + | 0.542150i | \(0.817611\pi\) | |||||||
\(840\) | −396.744 | − | 570.236i | −0.472314 | − | 0.678852i | ||||
\(841\) | 457.940 | 0.544519 | ||||||||
\(842\) | 146.007 | + | 84.2970i | 0.173405 | + | 0.100115i | ||||
\(843\) | 63.0328 | + | 109.176i | 0.0747720 | + | 0.129509i | ||||
\(844\) | −11.6143 | − | 20.1165i | −0.0137610 | − | 0.0238347i | ||||
\(845\) | −1423.06 | + | 120.209i | −1.68409 | + | 0.142259i | ||||
\(846\) | −13.6983 | + | 23.7261i | −0.0161918 | + | 0.0280450i | ||||
\(847\) | −528.691 | − | 305.240i | −0.624192 | − | 0.360377i | ||||
\(848\) | 45.1840 | − | 78.2609i | 0.0532830 | − | 0.0922888i | ||||
\(849\) | 1587.43 | − | 916.502i | 1.86976 | − | 1.07951i | ||||
\(850\) | −152.594 | − | 56.5767i | −0.179522 | − | 0.0665608i | ||||
\(851\) | 833.806 | + | 1444.19i | 0.979796 | + | 1.69706i | ||||
\(852\) | −543.942 | −0.638430 | ||||||||
\(853\) | − | 353.272i | − | 0.414153i | −0.978325 | − | 0.207076i | \(-0.933605\pi\) | ||
0.978325 | − | 0.207076i | \(-0.0663948\pi\) | |||||||
\(854\) | 58.2786 | − | 33.6471i | 0.0682419 | − | 0.0393995i | ||||
\(855\) | 665.669 | − | 1416.44i | 0.778561 | − | 1.65666i | ||||
\(856\) | 128.826 | + | 223.132i | 0.150497 | + | 0.260669i | ||||
\(857\) | 391.116 | + | 225.811i | 0.456378 | + | 0.263490i | 0.710520 | − | 0.703677i | \(-0.248460\pi\) |
−0.254142 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(858\) | −1120.56 | + | 1940.87i | −1.30602 | + | 2.26209i | ||||
\(859\) | −215.027 | − | 124.146i | −0.250323 | − | 0.144524i | 0.369589 | − | 0.929195i | \(-0.379498\pi\) |
−0.619912 | + | 0.784671i | \(0.712832\pi\) | |||||||
\(860\) | 797.491 | − | 67.3660i | 0.927315 | − | 0.0783326i | ||||
\(861\) | −1615.50 | + | 932.712i | −1.87631 | + | 1.08329i | ||||
\(862\) | −910.268 | + | 525.543i | −1.05599 | + | 0.609679i | ||||
\(863\) | 502.444 | − | 870.259i | 0.582207 | − | 1.00841i | −0.413011 | − | 0.910726i | \(-0.635523\pi\) |
0.995217 | − | 0.0976853i | \(-0.0311439\pi\) | |||||||
\(864\) | 347.255i | 0.401916i | ||||||||
\(865\) | −134.589 | + | 93.6411i | −0.155594 | + | 0.108256i | ||||
\(866\) | − | 918.627i | − | 1.06077i | ||||||
\(867\) | 1450.49 | 1.67300 | ||||||||
\(868\) | 300.337 | + | 475.379i | 0.346011 | + | 0.547672i | ||||
\(869\) | −329.387 | −0.379042 | ||||||||
\(870\) | 746.897 | − | 63.0922i | 0.858502 | − | 0.0725198i | ||||
\(871\) | −620.786 | + | 358.411i | −0.712727 | + | 0.411493i | ||||
\(872\) | 224.754i | 0.257746i | ||||||||
\(873\) | −2462.76 | − | 1421.88i | −2.82103 | − | 1.62872i | ||||
\(874\) | −642.960 | + | 371.213i | −0.735652 | + | 0.424729i | ||||
\(875\) | 808.801 | − | 794.400i | 0.924344 | − | 0.907886i | ||||
\(876\) | −408.555 | −0.466387 | ||||||||
\(877\) | −553.474 | − | 319.549i | −0.631100 | − | 0.364366i | 0.150078 | − | 0.988674i | \(-0.452047\pi\) |
−0.781178 | + | 0.624309i | \(0.785381\pi\) | |||||||
\(878\) | −197.525 | − | 114.041i | −0.224972 | − | 0.129887i | ||||
\(879\) | −2400.32 | − | 1385.82i | −2.73074 | − | 1.57659i | ||||
\(880\) | 225.289 | − | 156.746i | 0.256011 | − | 0.178121i | ||||
\(881\) | −459.951 | − | 265.553i | −0.522079 | − | 0.301422i | 0.215706 | − | 0.976458i | \(-0.430795\pi\) |
−0.737785 | + | 0.675036i | \(0.764128\pi\) | |||||||
\(882\) | 828.181 | − | 478.151i | 0.938981 | − | 0.542121i | ||||
\(883\) | 1373.15 | 1.55510 | 0.777548 | − | 0.628824i | \(-0.216463\pi\) | ||||
0.777548 | + | 0.628824i | \(0.216463\pi\) | |||||||
\(884\) | 196.294 | 0.222053 | ||||||||
\(885\) | 73.7935 | + | 106.063i | 0.0833825 | + | 0.119845i | ||||
\(886\) | −268.816 | + | 465.603i | −0.303404 | + | 0.525511i | ||||
\(887\) | 203.455 | − | 117.465i | 0.229374 | − | 0.132429i | −0.380909 | − | 0.924612i | \(-0.624389\pi\) |
0.610283 | + | 0.792183i | \(0.291056\pi\) | |||||||
\(888\) | −648.719 | − | 374.538i | −0.730539 | − | 0.421777i | ||||
\(889\) | 731.738 | + | 422.469i | 0.823102 | + | 0.475218i | ||||
\(890\) | −136.234 | + | 289.885i | −0.153071 | + | 0.325713i | ||||
\(891\) | − | 2051.11i | − | 2.30204i | ||||||
\(892\) | −66.6536 | − | 115.447i | −0.0747238 | − | 0.129425i | ||||
\(893\) | 12.7006 | − | 7.33268i | 0.0142224 | − | 0.00821129i | ||||
\(894\) | 479.013 | + | 276.558i | 0.535809 | + | 0.309349i | ||||
\(895\) | −126.515 | − | 1497.71i | −0.141358 | − | 1.67342i | ||||
\(896\) | −51.3045 | − | 88.8620i | −0.0572595 | − | 0.0991764i | ||||
\(897\) | −3938.35 | −4.39057 | ||||||||
\(898\) | −938.381 | −1.04497 | ||||||||
\(899\) | −606.247 | + | 24.1806i | −0.674357 | + | 0.0268972i | ||||
\(900\) | −1002.30 | + | 170.550i | −1.11367 | + | 0.189500i | ||||
\(901\) | 103.993 | 0.115420 | ||||||||
\(902\) | −368.497 | − | 638.256i | −0.408533 | − | 0.707600i | ||||
\(903\) | 3931.31i | 4.35361i | ||||||||
\(904\) | 251.278 | − | 435.226i | 0.277962 | − | 0.481444i | ||||
\(905\) | 1316.42 | − | 915.906i | 1.45461 | − | 1.01205i | ||||
\(906\) | −42.4747 | − | 73.5684i | −0.0468816 | − | 0.0812013i | ||||
\(907\) | − | 102.195i | − | 0.112674i | −0.998412 | − | 0.0563370i | \(-0.982058\pi\) | ||
0.998412 | − | 0.0563370i | \(-0.0179421\pi\) | |||||||
\(908\) | 310.442 | + | 179.234i | 0.341896 | + | 0.197394i | ||||
\(909\) | −1957.30 | + | 3390.15i | −2.15325 | + | 3.72954i | ||||
\(910\) | −581.592 | + | 1237.54i | −0.639112 | + | 1.35993i | ||||
\(911\) | 1277.32 | − | 737.462i | 1.40211 | − | 0.809508i | 0.407501 | − | 0.913205i | \(-0.366400\pi\) |
0.994609 | + | 0.103697i | \(0.0330671\pi\) | |||||||
\(912\) | 166.745 | − | 288.812i | 0.182835 | − | 0.316679i | ||||
\(913\) | 1116.59 | − | 644.664i | 1.22299 | − | 0.706094i | ||||
\(914\) | 1139.65i | 1.24688i | ||||||||
\(915\) | −11.9594 | − | 141.578i | −0.0130704 | − | 0.154730i | ||||
\(916\) | 683.146 | − | 394.415i | 0.745793 | − | 0.430584i | ||||
\(917\) | −764.184 | − | 441.202i | −0.833352 | − | 0.481136i | ||||
\(918\) | −346.076 | + | 199.807i | −0.376989 | + | 0.217654i | ||||
\(919\) | −617.267 | + | 1069.14i | −0.671672 | + | 1.16337i | 0.305758 | + | 0.952109i | \(0.401090\pi\) |
−0.977430 | + | 0.211261i | \(0.932243\pi\) | |||||||
\(920\) | 436.499 | + | 205.136i | 0.474455 | + | 0.222974i | ||||
\(921\) | −1397.32 | − | 806.745i | −1.51718 | − | 0.875945i | ||||
\(922\) | −782.090 | −0.848254 | ||||||||
\(923\) | 535.344 | + | 927.243i | 0.580004 | + | 1.00460i | ||||
\(924\) | 674.071 | + | 1167.53i | 0.729514 | + | 1.26356i | ||||
\(925\) | 424.977 | − | 1146.21i | 0.459435 | − | 1.23915i | ||||
\(926\) | − | 738.920i | − | 0.797970i | ||||||
\(927\) | −801.536 | + | 462.767i | −0.864656 | + | 0.499210i | ||||
\(928\) | 110.715 | 0.119305 | ||||||||
\(929\) | 190.481i | 0.205038i | 0.994731 | + | 0.102519i | \(0.0326903\pi\) | ||||
−0.994731 | + | 0.102519i | \(0.967310\pi\) | |||||||
\(930\) | 1178.09 | − | 147.000i | 1.26676 | − | 0.158065i | ||||
\(931\) | −511.908 | −0.549848 | ||||||||
\(932\) | − | 427.106i | − | 0.458269i | ||||||
\(933\) | 519.711 | + | 900.165i | 0.557032 | + | 0.964808i | ||||
\(934\) | −501.867 | −0.537331 | ||||||||
\(935\) | 285.843 | + | 134.334i | 0.305714 | + | 0.143673i | ||||
\(936\) | 1062.01 | − | 613.150i | 1.13462 | − | 0.655075i | ||||
\(937\) | 971.440 | − | 560.861i | 1.03676 | − | 0.598571i | 0.117843 | − | 0.993032i | \(-0.462402\pi\) |
0.918913 | + | 0.394461i | \(0.129069\pi\) | |||||||
\(938\) | 431.201i | 0.459703i | ||||||||
\(939\) | −1045.92 | + | 1811.58i | −1.11386 | + | 1.92926i | ||||
\(940\) | −8.62229 | − | 4.05211i | −0.00917265 | − | 0.00431076i | ||||
\(941\) | −111.557 | − | 64.4077i | −0.118552 | − | 0.0684460i | 0.439551 | − | 0.898217i | \(-0.355137\pi\) |
−0.558103 | + | 0.829771i | \(0.688471\pi\) | |||||||
\(942\) | 744.374 | + | 1289.29i | 0.790206 | + | 1.36868i | ||||
\(943\) | 647.562 | − | 1121.61i | 0.686704 | − | 1.18941i | ||||
\(944\) | 9.54253 | + | 16.5281i | 0.0101086 | + | 0.0175086i | ||||
\(945\) | −234.313 | − | 2773.83i | −0.247950 | − | 2.93528i | ||||
\(946\) | −1553.19 | −1.64185 | ||||||||
\(947\) | 424.724 | + | 735.644i | 0.448494 | + | 0.776815i | 0.998288 | − | 0.0584852i | \(-0.0186270\pi\) |
−0.549794 | + | 0.835300i | \(0.685294\pi\) | |||||||
\(948\) | 225.172 | + | 130.003i | 0.237524 | + | 0.137134i | ||||
\(949\) | 402.097 | + | 696.453i | 0.423706 | + | 0.733880i | ||||
\(950\) | 510.297 | + | 189.201i | 0.537155 | + | 0.199159i | ||||
\(951\) | 1836.75 | + | 1060.45i | 1.93139 | + | 1.11509i | ||||
\(952\) | 59.0401 | − | 102.260i | 0.0620169 | − | 0.107416i | ||||
\(953\) | 1363.21 | 1.43044 | 0.715219 | − | 0.698900i | \(-0.246327\pi\) | ||||
0.715219 | + | 0.698900i | \(0.246327\pi\) | |||||||
\(954\) | 562.633 | − | 324.836i | 0.589762 | − | 0.340499i | ||||
\(955\) | 493.075 | + | 708.691i | 0.516309 | + | 0.742085i | ||||
\(956\) | −634.968 | − | 366.599i | −0.664192 | − | 0.383472i | ||||
\(957\) | −1454.65 | −1.52001 | ||||||||
\(958\) | 374.450 | − | 216.189i | 0.390866 | − | 0.225667i | ||||
\(959\) | 129.913i | 0.135467i | ||||||||
\(960\) | −215.875 | + | 18.2355i | −0.224870 | + | 0.0189953i | ||||
\(961\) | −957.947 | + | 76.5385i | −0.996823 | + | 0.0796447i | ||||
\(962\) | 1474.47i | 1.53271i | ||||||||
\(963\) | 1852.30i | 1.92347i | ||||||||
\(964\) | 33.3587 | − | 19.2596i | 0.0346044 | − | 0.0199789i | ||||
\(965\) | −1.02216 | − | 12.1005i | −0.00105923 | − | 0.0125394i | ||||
\(966\) | −1184.55 | + | 2051.70i | −1.22624 | + | 2.12391i | ||||
\(967\) | −679.170 | − | 1176.36i | −0.702347 | − | 1.21650i | −0.967640 | − | 0.252333i | \(-0.918802\pi\) |
0.265293 | − | 0.964168i | \(-0.414531\pi\) | |||||||
\(968\) | −164.879 | + | 95.1931i | −0.170330 | + | 0.0983399i | ||||
\(969\) | 383.774 | 0.396051 | ||||||||
\(970\) | 420.608 | − | 894.991i | 0.433616 | − | 0.922671i | ||||
\(971\) | −488.655 | + | 846.375i | −0.503249 | + | 0.871652i | 0.496744 | + | 0.867897i | \(0.334529\pi\) |
−0.999993 | + | 0.00375546i | \(0.998805\pi\) | |||||||
\(972\) | −257.059 | + | 445.239i | −0.264464 | + | 0.458065i | ||||
\(973\) | 772.307 | + | 1337.67i | 0.793738 | + | 1.37479i | ||||
\(974\) | −242.789 | − | 140.175i | −0.249271 | − | 0.143916i | ||||
\(975\) | 1842.48 | + | 2222.67i | 1.88972 | + | 2.27967i | ||||
\(976\) | − | 20.9866i | − | 0.0215027i | ||||||
\(977\) | 1682.30i | 1.72191i | 0.508682 | + | 0.860954i | \(0.330133\pi\) | ||||
−0.508682 | + | 0.860954i | \(0.669867\pi\) | |||||||
\(978\) | 665.867 | + | 1153.31i | 0.680845 | + | 1.17926i | ||||
\(979\) | 310.800 | − | 538.322i | 0.317467 | − | 0.549869i | ||||
\(980\) | 189.925 | + | 272.977i | 0.193801 | + | 0.278548i | ||||
\(981\) | −807.901 | + | 1399.33i | −0.823549 | + | 1.42643i | ||||
\(982\) | 332.584 | − | 576.052i | 0.338680 | − | 0.586611i | ||||
\(983\) | −72.7672 | + | 126.037i | −0.0740257 | + | 0.128216i | −0.900662 | − | 0.434520i | \(-0.856918\pi\) |
0.826636 | + | 0.562736i | \(0.190251\pi\) | |||||||
\(984\) | 581.757i | 0.591217i | ||||||||
\(985\) | −152.182 | − | 218.729i | −0.154499 | − | 0.222060i | ||||
\(986\) | 63.7044 | + | 110.339i | 0.0646090 | + | 0.111906i | ||||
\(987\) | 23.3988 | − | 40.5278i | 0.0237069 | − | 0.0410616i | ||||
\(988\) | −656.438 | −0.664411 | ||||||||
\(989\) | −1364.71 | − | 2363.75i | −1.37989 | − | 2.39004i | ||||
\(990\) | 1966.10 | − | 166.081i | 1.98596 | − | 0.167759i | ||||
\(991\) | − | 1859.24i | − | 1.87612i | −0.346468 | − | 0.938062i | \(-0.612619\pi\) | ||
0.346468 | − | 0.938062i | \(-0.387381\pi\) | |||||||
\(992\) | 175.223 | − | 6.98890i | 0.176636 | − | 0.00704526i | ||||
\(993\) | − | 267.454i | − | 0.269339i | ||||||
\(994\) | 644.069 | 0.647956 | ||||||||
\(995\) | −128.255 | + | 89.2339i | −0.128899 | + | 0.0896823i | ||||
\(996\) | −1017.75 | −1.02184 | ||||||||
\(997\) | 1085.46 | + | 626.691i | 1.08873 | + | 0.628577i | 0.933237 | − | 0.359261i | \(-0.116971\pi\) |
0.155489 | + | 0.987838i | \(0.450305\pi\) | |||||||
\(998\) | −49.7443 | − | 86.1596i | −0.0498439 | − | 0.0863322i | ||||
\(999\) | −1500.85 | − | 2599.55i | −1.50236 | − | 2.60216i |
(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 | 310.3.i.a.99.16 | ✓ | 64 | |
5.4 | even | 2 | inner | 310.3.i.a.99.17 | yes | 64 | |
31.26 | odd | 6 | inner | 310.3.i.a.119.1 | yes | 64 | |
155.119 | odd | 6 | inner | 310.3.i.a.119.32 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
310.3.i.a.99.16 | ✓ | 64 | 1.1 | even | 1 | trivial | |
310.3.i.a.99.17 | yes | 64 | 5.4 | even | 2 | inner | |
310.3.i.a.119.1 | yes | 64 | 31.26 | odd | 6 | inner | |
310.3.i.a.119.32 | yes | 64 | 155.119 | odd | 6 | inner |