Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [385,2,Mod(54,385)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(385, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("385.54");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 385 = 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 385.o (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: | \(3.07424047782\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 54.14 | ||
Character | \(\chi\) | \(=\) | 385.54 |
Dual form | 385.2.o.b.164.14 |
$q$-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 \(\left(\mathbb{Z}/385\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(276\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.408979 | + | 0.708373i | −0.289192 | + | 0.500895i | −0.973617 | − | 0.228188i | \(-0.926720\pi\) |
0.684425 | + | 0.729083i | \(0.260053\pi\) | |||||||
\(3\) | 1.44107 | + | 2.49601i | 0.832004 | + | 1.44107i | 0.896446 | + | 0.443152i | \(0.146140\pi\) |
−0.0644421 | + | 0.997921i | \(0.520527\pi\) | |||||||
\(4\) | 0.665472 | + | 1.15263i | 0.332736 | + | 0.576316i | ||||
\(5\) | 0.199440 | − | 2.22716i | 0.0891924 | − | 0.996014i | ||||
\(6\) | −2.35748 | −0.962436 | ||||||||
\(7\) | 2.08705 | − | 1.62611i | 0.788830 | − | 0.614612i | ||||
\(8\) | −2.72457 | −0.963282 | ||||||||
\(9\) | −2.65339 | + | 4.59580i | −0.884462 | + | 1.53193i | ||||
\(10\) | 1.49609 | + | 1.05214i | 0.473105 | + | 0.332715i | ||||
\(11\) | −1.35223 | + | 3.02844i | −0.407714 | + | 0.913110i | ||||
\(12\) | −1.91799 | + | 3.32205i | −0.553676 | + | 0.958994i | ||||
\(13\) | 2.50240i | 0.694040i | 0.937858 | + | 0.347020i | \(0.112806\pi\) | ||||
−0.937858 | + | 0.347020i | \(0.887194\pi\) | |||||||
\(14\) | 0.298333 | + | 2.14345i | 0.0797329 | + | 0.572862i | ||||
\(15\) | 5.84642 | − | 2.71169i | 1.50954 | − | 0.700155i | ||||
\(16\) | −0.216650 | + | 0.375250i | −0.0541626 | + | 0.0938124i | ||||
\(17\) | 4.73654 | − | 2.73464i | 1.14878 | − | 0.663249i | 0.200190 | − | 0.979757i | \(-0.435844\pi\) |
0.948590 | + | 0.316508i | \(0.102511\pi\) | |||||||
\(18\) | −2.17036 | − | 3.75917i | −0.511559 | − | 0.886046i | ||||
\(19\) | −2.68808 | + | 4.65588i | −0.616687 | + | 1.06813i | 0.373399 | + | 0.927671i | \(0.378192\pi\) |
−0.990086 | + | 0.140462i | \(0.955141\pi\) | |||||||
\(20\) | 2.69981 | − | 1.25223i | 0.603696 | − | 0.280007i | ||||
\(21\) | 7.06638 | + | 2.86595i | 1.54201 | + | 0.625402i | ||||
\(22\) | −1.59223 | − | 2.19645i | −0.339465 | − | 0.468286i | ||||
\(23\) | −2.49166 | − | 1.43856i | −0.519548 | − | 0.299961i | 0.217202 | − | 0.976127i | \(-0.430307\pi\) |
−0.736750 | + | 0.676166i | \(0.763640\pi\) | |||||||
\(24\) | −3.92631 | − | 6.80057i | −0.801455 | − | 1.38816i | ||||
\(25\) | −4.92045 | − | 0.888369i | −0.984089 | − | 0.177674i | ||||
\(26\) | −1.77263 | − | 1.02343i | −0.347641 | − | 0.200711i | ||||
\(27\) | −6.64846 | −1.27950 | ||||||||
\(28\) | 3.26318 | + | 1.32347i | 0.616683 | + | 0.250111i | ||||
\(29\) | − | 4.76380i | − | 0.884616i | −0.896863 | − | 0.442308i | \(-0.854160\pi\) | ||
0.896863 | − | 0.442308i | \(-0.145840\pi\) | |||||||
\(30\) | −0.470176 | + | 5.25047i | −0.0858419 | + | 0.958600i | ||||
\(31\) | 6.61332 | − | 3.81820i | 1.18779 | − | 0.685769i | 0.229984 | − | 0.973194i | \(-0.426133\pi\) |
0.957803 | + | 0.287425i | \(0.0927993\pi\) | |||||||
\(32\) | −2.90178 | − | 5.02604i | −0.512968 | − | 0.888486i | ||||
\(33\) | −9.50770 | + | 0.989018i | −1.65508 | + | 0.172166i | ||||
\(34\) | 4.47365i | 0.767224i | ||||||||
\(35\) | −3.20536 | − | 4.97249i | −0.541805 | − | 0.840504i | ||||
\(36\) | −7.06302 | −1.17717 | ||||||||
\(37\) | −3.33285 | − | 1.92422i | −0.547917 | − | 0.316340i | 0.200365 | − | 0.979721i | \(-0.435787\pi\) |
−0.748281 | + | 0.663382i | \(0.769121\pi\) | |||||||
\(38\) | −2.19873 | − | 3.80832i | −0.356682 | − | 0.617791i | ||||
\(39\) | −6.24601 | + | 3.60614i | −1.00016 | + | 0.577444i | ||||
\(40\) | −0.543390 | + | 6.06805i | −0.0859174 | + | 0.959443i | ||||
\(41\) | −2.69547 | −0.420962 | −0.210481 | − | 0.977598i | \(-0.567503\pi\) | ||||
−0.210481 | + | 0.977598i | \(0.567503\pi\) | |||||||
\(42\) | −4.92016 | + | 3.83352i | −0.759198 | + | 0.591524i | ||||
\(43\) | 12.0332 | 1.83505 | 0.917524 | − | 0.397681i | \(-0.130185\pi\) | ||||
0.917524 | + | 0.397681i | \(0.130185\pi\) | |||||||
\(44\) | −4.39055 | + | 0.456718i | −0.661901 | + | 0.0688528i | ||||
\(45\) | 9.70637 | + | 6.82609i | 1.44694 | + | 1.01757i | ||||
\(46\) | 2.03808 | − | 1.17668i | 0.300498 | − | 0.173493i | ||||
\(47\) | 3.99406 | − | 6.91792i | 0.582594 | − | 1.00908i | −0.412577 | − | 0.910923i | \(-0.635371\pi\) |
0.995171 | − | 0.0981596i | \(-0.0312956\pi\) | |||||||
\(48\) | −1.24884 | −0.180254 | ||||||||
\(49\) | 1.71153 | − | 6.78754i | 0.244505 | − | 0.969648i | ||||
\(50\) | 2.64166 | − | 3.12219i | 0.373587 | − | 0.441544i | ||||
\(51\) | 13.6514 | + | 7.88165i | 1.91158 | + | 1.10365i | ||||
\(52\) | −2.88434 | + | 1.66527i | −0.399986 | + | 0.230932i | ||||
\(53\) | 8.24779 | − | 4.76187i | 1.13292 | − | 0.654092i | 0.188253 | − | 0.982120i | \(-0.439717\pi\) |
0.944668 | + | 0.328028i | \(0.106384\pi\) | |||||||
\(54\) | 2.71908 | − | 4.70959i | 0.370020 | − | 0.640894i | ||||
\(55\) | 6.47512 | + | 3.61563i | 0.873106 | + | 0.487531i | ||||
\(56\) | −5.68631 | + | 4.43046i | −0.759866 | + | 0.592045i | ||||
\(57\) | −15.4949 | −2.05234 | ||||||||
\(58\) | 3.37455 | + | 1.94830i | 0.443100 | + | 0.255824i | ||||
\(59\) | −3.95268 | + | 2.28208i | −0.514595 | + | 0.297101i | −0.734720 | − | 0.678370i | \(-0.762687\pi\) |
0.220126 | + | 0.975472i | \(0.429353\pi\) | |||||||
\(60\) | 7.01621 | + | 4.93421i | 0.905789 | + | 0.637004i | ||||
\(61\) | −2.35685 | + | 4.08218i | −0.301764 | + | 0.522670i | −0.976536 | − | 0.215356i | \(-0.930909\pi\) |
0.674772 | + | 0.738026i | \(0.264242\pi\) | |||||||
\(62\) | 6.24626i | 0.793276i | ||||||||
\(63\) | 1.93553 | + | 13.9064i | 0.243854 | + | 1.75204i | ||||
\(64\) | 3.88048 | 0.485059 | ||||||||
\(65\) | 5.57323 | + | 0.499079i | 0.691274 | + | 0.0619031i | ||||
\(66\) | 3.18786 | − | 7.13948i | 0.392398 | − | 0.878810i | ||||
\(67\) | 4.11749 | − | 2.37724i | 0.503032 | − | 0.290426i | −0.226933 | − | 0.973910i | \(-0.572870\pi\) |
0.729965 | + | 0.683485i | \(0.239536\pi\) | |||||||
\(68\) | 6.30407 | + | 3.63966i | 0.764481 | + | 0.441373i | ||||
\(69\) | − | 8.29230i | − | 0.998276i | ||||||
\(70\) | 4.83330 | − | 0.236944i | 0.577690 | − | 0.0283202i | ||||
\(71\) | −4.19042 | −0.497311 | −0.248656 | − | 0.968592i | \(-0.579989\pi\) | ||||
−0.248656 | + | 0.968592i | \(0.579989\pi\) | |||||||
\(72\) | 7.22935 | − | 12.5216i | 0.851987 | − | 1.47568i | ||||
\(73\) | −10.3094 | + | 5.95214i | −1.20663 | + | 0.696646i | −0.962020 | − | 0.272977i | \(-0.911992\pi\) |
−0.244605 | + | 0.969623i | \(0.578658\pi\) | |||||||
\(74\) | 2.72613 | − | 1.57393i | 0.316906 | − | 0.182966i | ||||
\(75\) | −4.87335 | − | 13.5617i | −0.562726 | − | 1.56597i | ||||
\(76\) | −7.15536 | −0.820776 | ||||||||
\(77\) | 2.10241 | + | 8.51938i | 0.239591 | + | 0.970874i | ||||
\(78\) | − | 5.89934i | − | 0.667969i | ||||||
\(79\) | 1.66374 | + | 0.960559i | 0.187185 | + | 0.108071i | 0.590664 | − | 0.806918i | \(-0.298866\pi\) |
−0.403479 | + | 0.914989i | \(0.632199\pi\) | |||||||
\(80\) | 0.792531 | + | 0.557354i | 0.0886076 | + | 0.0623141i | ||||
\(81\) | −1.62076 | − | 2.80724i | −0.180085 | − | 0.311916i | ||||
\(82\) | 1.10239 | − | 1.90940i | 0.121739 | − | 0.210858i | ||||
\(83\) | − | 5.93408i | − | 0.651350i | −0.945482 | − | 0.325675i | \(-0.894408\pi\) | ||
0.945482 | − | 0.325675i | \(-0.105592\pi\) | |||||||
\(84\) | 1.39909 | + | 10.0521i | 0.152653 | + | 1.09678i | ||||
\(85\) | −5.14582 | − | 11.0944i | −0.558143 | − | 1.20336i | ||||
\(86\) | −4.92133 | + | 8.52400i | −0.530681 | + | 0.919167i | ||||
\(87\) | 11.8905 | − | 6.86499i | 1.27480 | − | 0.736004i | ||||
\(88\) | 3.68426 | − | 8.25121i | 0.392743 | − | 0.879582i | ||||
\(89\) | −3.81527 | − | 2.20275i | −0.404418 | − | 0.233491i | 0.283970 | − | 0.958833i | \(-0.408348\pi\) |
−0.688389 | + | 0.725342i | \(0.741682\pi\) | |||||||
\(90\) | −8.80512 | + | 4.08400i | −0.928141 | + | 0.430491i | ||||
\(91\) | 4.06917 | + | 5.22262i | 0.426565 | + | 0.547479i | ||||
\(92\) | − | 3.82929i | − | 0.399232i | ||||||
\(93\) | 19.0606 | + | 11.0046i | 1.97649 | + | 1.14113i | ||||
\(94\) | 3.26698 | + | 5.65857i | 0.336963 | + | 0.583637i | ||||
\(95\) | 9.83327 | + | 6.91533i | 1.00887 | + | 0.709498i | ||||
\(96\) | 8.36337 | − | 14.4858i | 0.853583 | − | 1.47845i | ||||
\(97\) | −16.2827 | −1.65326 | −0.826628 | − | 0.562749i | \(-0.809744\pi\) | ||||
−0.826628 | + | 0.562749i | \(0.809744\pi\) | |||||||
\(98\) | 4.10812 | + | 3.98836i | 0.414983 | + | 0.402886i | ||||
\(99\) | −10.3301 | − | 14.2502i | −1.03822 | − | 1.43220i | ||||
\(100\) | −2.25046 | − | 6.26265i | −0.225046 | − | 0.626265i | ||||
\(101\) | 1.97721 | + | 3.42463i | 0.196740 | + | 0.340763i | 0.947469 | − | 0.319846i | \(-0.103631\pi\) |
−0.750730 | + | 0.660609i | \(0.770298\pi\) | |||||||
\(102\) | −11.1663 | + | 6.44686i | −1.10563 | + | 0.638334i | ||||
\(103\) | 0.806073 | − | 1.39616i | 0.0794247 | − | 0.137568i | −0.823577 | − | 0.567204i | \(-0.808025\pi\) |
0.903002 | + | 0.429637i | \(0.141358\pi\) | |||||||
\(104\) | − | 6.81796i | − | 0.668556i | ||||||
\(105\) | 7.79224 | − | 15.1663i | 0.760445 | − | 1.48008i | ||||
\(106\) | 7.79001i | 0.756633i | ||||||||
\(107\) | 1.85685 | − | 3.21615i | 0.179508 | − | 0.310917i | −0.762204 | − | 0.647337i | \(-0.775883\pi\) |
0.941712 | + | 0.336420i | \(0.109216\pi\) | |||||||
\(108\) | −4.42437 | − | 7.66323i | −0.425735 | − | 0.737394i | ||||
\(109\) | 12.7290 | − | 7.34908i | 1.21921 | − | 0.703914i | 0.254465 | − | 0.967082i | \(-0.418101\pi\) |
0.964750 | + | 0.263168i | \(0.0847673\pi\) | |||||||
\(110\) | −5.20940 | + | 3.10808i | −0.496697 | + | 0.296344i | ||||
\(111\) | − | 11.0918i | − | 1.05278i | ||||||
\(112\) | 0.158037 | + | 1.13546i | 0.0149331 | + | 0.107291i | ||||
\(113\) | 5.83389i | 0.548806i | 0.961615 | + | 0.274403i | \(0.0884803\pi\) | ||||
−0.961615 | + | 0.274403i | \(0.911520\pi\) | |||||||
\(114\) | 6.33707 | − | 10.9761i | 0.593521 | − | 1.02801i | ||||
\(115\) | −3.70084 | + | 5.26242i | −0.345105 | + | 0.490723i | ||||
\(116\) | 5.49091 | − | 3.17018i | 0.509818 | − | 0.294344i | ||||
\(117\) | −11.5005 | − | 6.63983i | −1.06322 | − | 0.613852i | ||||
\(118\) | − | 3.73329i | − | 0.343677i | ||||||
\(119\) | 5.43855 | − | 13.4095i | 0.498552 | − | 1.22924i | ||||
\(120\) | −15.9290 | + | 7.38820i | −1.45411 | + | 0.674447i | ||||
\(121\) | −7.34293 | − | 8.19032i | −0.667539 | − | 0.744575i | ||||
\(122\) | −1.92780 | − | 3.33905i | −0.174535 | − | 0.302304i | ||||
\(123\) | −3.88438 | − | 6.72794i | −0.350242 | − | 0.606638i | ||||
\(124\) | 8.80196 | + | 5.08181i | 0.790439 | + | 0.456360i | ||||
\(125\) | −2.95987 | + | 10.7814i | −0.264739 | + | 0.964320i | ||||
\(126\) | −10.6425 | − | 4.31633i | −0.948107 | − | 0.384529i | ||||
\(127\) | −3.92292 | −0.348103 | −0.174052 | − | 0.984737i | \(-0.555686\pi\) | ||||
−0.174052 | + | 0.984737i | \(0.555686\pi\) | |||||||
\(128\) | 4.21654 | − | 7.30325i | 0.372693 | − | 0.645523i | ||||
\(129\) | 17.3407 | + | 30.0351i | 1.52677 | + | 2.64444i | ||||
\(130\) | −2.63287 | + | 3.74381i | −0.230918 | + | 0.328354i | ||||
\(131\) | −0.0223510 | + | 0.0387130i | −0.00195281 | + | 0.00338237i | −0.867000 | − | 0.498308i | \(-0.833955\pi\) |
0.865047 | + | 0.501690i | \(0.167288\pi\) | |||||||
\(132\) | −7.46708 | − | 10.3007i | −0.649926 | − | 0.896562i | ||||
\(133\) | 1.96084 | + | 14.0882i | 0.170026 | + | 1.22160i | ||||
\(134\) | 3.88896i | 0.335955i | ||||||||
\(135\) | −1.32597 | + | 14.8072i | −0.114121 | + | 1.27440i | ||||
\(136\) | −12.9051 | + | 7.45074i | −1.10660 | + | 0.638895i | ||||
\(137\) | −16.3713 | + | 9.45197i | −1.39869 | + | 0.807536i | −0.994256 | − | 0.107029i | \(-0.965866\pi\) |
−0.404438 | + | 0.914565i | \(0.632533\pi\) | |||||||
\(138\) | 5.87404 | + | 3.39138i | 0.500032 | + | 0.288693i | ||||
\(139\) | 13.4810 | 1.14344 | 0.571721 | − | 0.820448i | \(-0.306276\pi\) | ||||
0.571721 | + | 0.820448i | \(0.306276\pi\) | |||||||
\(140\) | 3.59837 | − | 7.00365i | 0.304118 | − | 0.591917i | ||||
\(141\) | 23.0230 | 1.93888 | ||||||||
\(142\) | 1.71379 | − | 2.96838i | 0.143818 | − | 0.249101i | ||||
\(143\) | −7.57836 | − | 3.38382i | −0.633735 | − | 0.282970i | ||||
\(144\) | −1.14972 | − | 1.99136i | −0.0958096 | − | 0.165947i | ||||
\(145\) | −10.6097 | − | 0.950094i | −0.881090 | − | 0.0789010i | ||||
\(146\) | − | 9.73721i | − | 0.805857i | ||||||
\(147\) | 19.4082 | − | 5.50933i | 1.60076 | − | 0.454402i | ||||
\(148\) | − | 5.12206i | − | 0.421031i | ||||||
\(149\) | −7.90336 | − | 4.56301i | −0.647468 | − | 0.373816i | 0.140017 | − | 0.990149i | \(-0.455284\pi\) |
−0.787486 | + | 0.616333i | \(0.788618\pi\) | |||||||
\(150\) | 11.5998 | + | 2.09431i | 0.947123 | + | 0.171000i | ||||
\(151\) | −6.38502 | + | 3.68639i | −0.519605 | + | 0.299994i | −0.736773 | − | 0.676140i | \(-0.763651\pi\) |
0.217168 | + | 0.976134i | \(0.430318\pi\) | |||||||
\(152\) | 7.32386 | − | 12.6853i | 0.594043 | − | 1.02891i | ||||
\(153\) | 29.0243i | 2.34647i | ||||||||
\(154\) | −6.89474 | − | 1.99496i | −0.555594 | − | 0.160759i | ||||
\(155\) | −7.18477 | − | 15.4904i | −0.577094 | − | 1.24422i | ||||
\(156\) | −8.31310 | − | 4.79957i | −0.665580 | − | 0.384273i | ||||
\(157\) | 4.19474 | + | 7.26550i | 0.334777 | + | 0.579850i | 0.983442 | − | 0.181224i | \(-0.0580058\pi\) |
−0.648665 | + | 0.761074i | \(0.724672\pi\) | |||||||
\(158\) | −1.36087 | + | 0.785697i | −0.108265 | + | 0.0625067i | ||||
\(159\) | 23.7714 | + | 13.7244i | 1.88519 | + | 1.08842i | ||||
\(160\) | −11.7725 | + | 5.46033i | −0.930698 | + | 0.431677i | ||||
\(161\) | −7.53948 | + | 1.04937i | −0.594195 | + | 0.0827021i | ||||
\(162\) | 2.65143 | 0.208316 | ||||||||
\(163\) | −3.66200 | − | 2.11426i | −0.286830 | − | 0.165601i | 0.349681 | − | 0.936869i | \(-0.386290\pi\) |
−0.636511 | + | 0.771267i | \(0.719623\pi\) | |||||||
\(164\) | −1.79376 | − | 3.10689i | −0.140069 | − | 0.242607i | ||||
\(165\) | 0.306479 | + | 21.3724i | 0.0238593 | + | 1.66384i | ||||
\(166\) | 4.20354 | + | 2.42692i | 0.326258 | + | 0.188365i | ||||
\(167\) | 0.690672i | 0.0534458i | 0.999643 | + | 0.0267229i | \(0.00850718\pi\) | ||||
−0.999643 | + | 0.0267229i | \(0.991493\pi\) | |||||||
\(168\) | −19.2529 | − | 7.80850i | −1.48539 | − | 0.602439i | ||||
\(169\) | 6.73801 | 0.518309 | ||||||||
\(170\) | 9.96351 | + | 0.892226i | 0.764167 | + | 0.0684306i | ||||
\(171\) | −14.2650 | − | 24.7077i | −1.09087 | − | 1.88945i | ||||
\(172\) | 8.00777 | + | 13.8699i | 0.610587 | + | 1.05757i | ||||
\(173\) | −1.45495 | − | 0.840015i | −0.110618 | − | 0.0638652i | 0.443670 | − | 0.896190i | \(-0.353676\pi\) |
−0.554288 | + | 0.832325i | \(0.687009\pi\) | |||||||
\(174\) | 11.2305i | 0.851386i | ||||||||
\(175\) | −11.7138 | + | 6.14712i | −0.885479 | + | 0.464679i | ||||
\(176\) | −0.843460 | − | 1.16354i | −0.0635782 | − | 0.0877050i | ||||
\(177\) | −11.3922 | − | 6.57729i | −0.856290 | − | 0.494379i | ||||
\(178\) | 3.12073 | − | 1.80176i | 0.233909 | − | 0.135047i | ||||
\(179\) | −1.30594 | − | 2.26195i | −0.0976102 | − | 0.169066i | 0.813085 | − | 0.582145i | \(-0.197787\pi\) |
−0.910695 | + | 0.413079i | \(0.864453\pi\) | |||||||
\(180\) | −1.40865 | + | 15.7304i | −0.104995 | + | 1.17248i | ||||
\(181\) | 15.9823i | 1.18795i | 0.804482 | + | 0.593977i | \(0.202443\pi\) | ||||
−0.804482 | + | 0.593977i | \(0.797557\pi\) | |||||||
\(182\) | −5.36377 | + | 0.746548i | −0.397589 | + | 0.0553378i | ||||
\(183\) | −13.5856 | −1.00427 | ||||||||
\(184\) | 6.78872 | + | 3.91947i | 0.500471 | + | 0.288947i | ||||
\(185\) | −4.95024 | + | 7.03900i | −0.363949 | + | 0.517518i | ||||
\(186\) | −15.5907 | + | 9.00132i | −1.14317 | + | 0.660009i | ||||
\(187\) | 1.87680 | + | 18.0422i | 0.137245 | + | 1.31938i | ||||
\(188\) | 10.6318 | 0.775400 | ||||||||
\(189\) | −13.8757 | + | 10.8111i | −1.00931 | + | 0.786394i | ||||
\(190\) | −8.92023 | + | 4.13739i | −0.647142 | + | 0.300158i | ||||
\(191\) | 2.34966 | − | 4.06973i | 0.170015 | − | 0.294475i | −0.768410 | − | 0.639958i | \(-0.778952\pi\) |
0.938425 | + | 0.345483i | \(0.112285\pi\) | |||||||
\(192\) | 5.59205 | + | 9.68572i | 0.403572 | + | 0.699006i | ||||
\(193\) | −1.21617 | − | 2.10647i | −0.0875420 | − | 0.151627i | 0.818930 | − | 0.573894i | \(-0.194568\pi\) |
−0.906472 | + | 0.422267i | \(0.861235\pi\) | |||||||
\(194\) | 6.65927 | − | 11.5342i | 0.478108 | − | 0.828107i | ||||
\(195\) | 6.78572 | + | 14.6301i | 0.485936 | + | 1.04768i | ||||
\(196\) | 8.96251 | − | 2.54415i | 0.640179 | − | 0.181725i | ||||
\(197\) | −4.37533 | −0.311730 | −0.155865 | − | 0.987778i | \(-0.549816\pi\) | ||||
−0.155865 | + | 0.987778i | \(0.549816\pi\) | |||||||
\(198\) | 14.3193 | − | 1.48953i | 1.01763 | − | 0.105856i | ||||
\(199\) | −11.1577 | + | 6.44188i | −0.790946 | + | 0.456653i | −0.840295 | − | 0.542129i | \(-0.817618\pi\) |
0.0493496 | + | 0.998782i | \(0.484285\pi\) | |||||||
\(200\) | 13.4061 | + | 2.42043i | 0.947956 | + | 0.171150i | ||||
\(201\) | 11.8672 | + | 6.85155i | 0.837050 | + | 0.483271i | ||||
\(202\) | −3.23455 | −0.227582 | ||||||||
\(203\) | −7.74647 | − | 9.94228i | −0.543695 | − | 0.697811i | ||||
\(204\) | 20.9801i | 1.46890i | ||||||||
\(205\) | −0.537586 | + | 6.00324i | −0.0375466 | + | 0.419285i | ||||
\(206\) | 0.659334 | + | 1.14200i | 0.0459380 | + | 0.0795669i | ||||
\(207\) | 13.2227 | − | 7.63413i | 0.919041 | − | 0.530609i | ||||
\(208\) | −0.939023 | − | 0.542145i | −0.0651096 | − | 0.0375910i | ||||
\(209\) | −10.4652 | − | 14.4365i | −0.723891 | − | 0.998595i | ||||
\(210\) | 7.55656 | + | 11.7225i | 0.521452 | + | 0.808931i | ||||
\(211\) | − | 11.6271i | − | 0.800442i | −0.916419 | − | 0.400221i | \(-0.868933\pi\) | ||
0.916419 | − | 0.400221i | \(-0.131067\pi\) | |||||||
\(212\) | 10.9774 | + | 6.33778i | 0.753928 | + | 0.435280i | ||||
\(213\) | −6.03870 | − | 10.4593i | −0.413765 | − | 0.716662i | ||||
\(214\) | 1.51882 | + | 2.63068i | 0.103825 | + | 0.179829i | ||||
\(215\) | 2.39991 | − | 26.7998i | 0.163672 | − | 1.82773i | ||||
\(216\) | 18.1142 | 1.23252 | ||||||||
\(217\) | 7.59349 | − | 18.7227i | 0.515480 | − | 1.27098i | ||||
\(218\) | 12.0225i | 0.814265i | ||||||||
\(219\) | −29.7132 | − | 17.1550i | −2.00784 | − | 1.15922i | ||||
\(220\) | 0.141529 | + | 9.86953i | 0.00954185 | + | 0.665404i | ||||
\(221\) | 6.84316 | + | 11.8527i | 0.460321 | + | 0.797299i | ||||
\(222\) | 7.85711 | + | 4.53630i | 0.527335 | + | 0.304457i | ||||
\(223\) | 8.56103 | 0.573289 | 0.286644 | − | 0.958037i | \(-0.407460\pi\) | ||||
0.286644 | + | 0.958037i | \(0.407460\pi\) | |||||||
\(224\) | −14.2291 | − | 5.77096i | −0.950719 | − | 0.385588i | ||||
\(225\) | 17.1386 | − | 20.2562i | 1.14257 | − | 1.35041i | ||||
\(226\) | −4.13257 | − | 2.38594i | −0.274894 | − | 0.158710i | ||||
\(227\) | −10.0454 | + | 5.79970i | −0.666735 | + | 0.384940i | −0.794838 | − | 0.606821i | \(-0.792444\pi\) |
0.128103 | + | 0.991761i | \(0.459111\pi\) | |||||||
\(228\) | −10.3114 | − | 17.8599i | −0.682889 | − | 1.18280i | ||||
\(229\) | −16.7546 | − | 9.67325i | −1.10717 | − | 0.639226i | −0.169077 | − | 0.985603i | \(-0.554079\pi\) |
−0.938096 | + | 0.346376i | \(0.887412\pi\) | |||||||
\(230\) | −2.21419 | − | 4.77380i | −0.145999 | − | 0.314775i | ||||
\(231\) | −18.2348 | + | 17.5247i | −1.19976 | + | 1.15304i | ||||
\(232\) | 12.9793i | 0.852135i | ||||||||
\(233\) | 14.4307 | − | 24.9947i | 0.945387 | − | 1.63746i | 0.190413 | − | 0.981704i | \(-0.439017\pi\) |
0.754974 | − | 0.655754i | \(-0.227649\pi\) | |||||||
\(234\) | 9.40694 | − | 5.43110i | 0.614951 | − | 0.355042i | ||||
\(235\) | −14.6107 | − | 10.2751i | −0.953098 | − | 0.670275i | ||||
\(236\) | −5.26079 | − | 3.03732i | −0.342448 | − | 0.197713i | ||||
\(237\) | 5.53694i | 0.359663i | ||||||||
\(238\) | 7.27465 | + | 9.33672i | 0.471545 | + | 0.605209i | ||||
\(239\) | 26.6883i | 1.72632i | 0.504930 | + | 0.863160i | \(0.331518\pi\) | ||||
−0.504930 | + | 0.863160i | \(0.668482\pi\) | |||||||
\(240\) | −0.249068 | + | 2.78136i | −0.0160773 | + | 0.179536i | ||||
\(241\) | 8.86407 | + | 15.3530i | 0.570985 | + | 0.988975i | 0.996465 | + | 0.0840070i | \(0.0267718\pi\) |
−0.425480 | + | 0.904968i | \(0.639895\pi\) | |||||||
\(242\) | 8.80491 | − | 1.85186i | 0.566001 | − | 0.119042i | ||||
\(243\) | −5.30142 | + | 9.18232i | −0.340086 | + | 0.589046i | ||||
\(244\) | −6.27367 | −0.401631 | ||||||||
\(245\) | −14.7756 | − | 5.16556i | −0.943976 | − | 0.330015i | ||||
\(246\) | 6.35452 | 0.405149 | ||||||||
\(247\) | −11.6509 | − | 6.72663i | −0.741327 | − | 0.428005i | ||||
\(248\) | −18.0185 | + | 10.4030i | −1.14417 | + | 0.660589i | ||||
\(249\) | 14.8115 | − | 8.55145i | 0.938644 | − | 0.541926i | ||||
\(250\) | −6.42674 | − | 6.50607i | −0.406463 | − | 0.411480i | ||||
\(251\) | 22.8159i | 1.44013i | 0.693908 | + | 0.720064i | \(0.255888\pi\) | ||||
−0.693908 | + | 0.720064i | \(0.744112\pi\) | |||||||
\(252\) | −14.7409 | + | 11.4852i | −0.928587 | + | 0.723503i | ||||
\(253\) | 7.72592 | − | 5.60059i | 0.485724 | − | 0.352106i | ||||
\(254\) | 1.60439 | − | 2.77889i | 0.100669 | − | 0.174363i | ||||
\(255\) | 20.2763 | − | 28.8319i | 1.26975 | − | 1.80552i | ||||
\(256\) | 7.32943 | + | 12.6949i | 0.458089 | + | 0.793434i | ||||
\(257\) | −2.18282 | + | 3.78076i | −0.136161 | + | 0.235837i | −0.926040 | − | 0.377425i | \(-0.876810\pi\) |
0.789880 | + | 0.613262i | \(0.210143\pi\) | |||||||
\(258\) | −28.3680 | −1.76612 | ||||||||
\(259\) | −10.0848 | + | 1.40364i | −0.626639 | + | 0.0872178i | ||||
\(260\) | 3.13357 | + | 6.75600i | 0.194336 | + | 0.418989i | ||||
\(261\) | 21.8935 | + | 12.6402i | 1.35517 | + | 0.782409i | ||||
\(262\) | −0.0182821 | − | 0.0316656i | −0.00112947 | − | 0.00195631i | ||||
\(263\) | −11.6683 | − | 20.2102i | −0.719501 | − | 1.24621i | −0.961198 | − | 0.275860i | \(-0.911037\pi\) |
0.241697 | − | 0.970352i | \(-0.422296\pi\) | |||||||
\(264\) | 25.9044 | − | 2.69465i | 1.59431 | − | 0.165844i | ||||
\(265\) | −8.96047 | − | 19.3188i | −0.550438 | − | 1.18675i | ||||
\(266\) | −10.7816 | − | 4.37276i | −0.661063 | − | 0.268111i | ||||
\(267\) | − | 12.6973i | − | 0.777062i | ||||||
\(268\) | 5.48016 | + | 3.16397i | 0.334754 | + | 0.193270i | ||||
\(269\) | −18.9045 | + | 10.9145i | −1.15263 | + | 0.665470i | −0.949526 | − | 0.313688i | \(-0.898435\pi\) |
−0.203101 | + | 0.979158i | \(0.565102\pi\) | |||||||
\(270\) | −9.94669 | − | 6.99510i | −0.605336 | − | 0.425708i | ||||
\(271\) | −2.13096 | + | 3.69093i | −0.129446 | + | 0.224208i | −0.923462 | − | 0.383689i | \(-0.874653\pi\) |
0.794016 | + | 0.607897i | \(0.207987\pi\) | |||||||
\(272\) | 2.36985i | 0.143693i | ||||||||
\(273\) | −7.17175 | + | 17.6829i | −0.434054 | + | 1.07022i | ||||
\(274\) | − | 15.4626i | − | 0.934132i | ||||||
\(275\) | 9.34397 | − | 13.7000i | 0.563462 | − | 0.826142i | ||||
\(276\) | 9.55797 | − | 5.51830i | 0.575322 | − | 0.332162i | ||||
\(277\) | −7.13759 | − | 12.3627i | −0.428856 | − | 0.742801i | 0.567915 | − | 0.823087i | \(-0.307750\pi\) |
−0.996772 | + | 0.0802857i | \(0.974417\pi\) | |||||||
\(278\) | −5.51344 | + | 9.54956i | −0.330674 | + | 0.572744i | ||||
\(279\) | 40.5247i | 2.42615i | ||||||||
\(280\) | 8.73324 | + | 13.5479i | 0.521911 | + | 0.809643i | ||||
\(281\) | − | 23.0886i | − | 1.37735i | −0.725070 | − | 0.688676i | \(-0.758192\pi\) | ||
0.725070 | − | 0.688676i | \(-0.241808\pi\) | |||||||
\(282\) | −9.41591 | + | 16.3088i | −0.560709 | + | 0.971177i | ||||
\(283\) | −2.03417 | + | 1.17443i | −0.120919 | + | 0.0698127i | −0.559240 | − | 0.829006i | \(-0.688907\pi\) |
0.438321 | + | 0.898819i | \(0.355573\pi\) | |||||||
\(284\) | −2.78861 | − | 4.83001i | −0.165473 | − | 0.286608i | ||||
\(285\) | −3.09030 | + | 34.5095i | −0.183053 | + | 2.04416i | ||||
\(286\) | 5.49640 | − | 3.98439i | 0.325009 | − | 0.235602i | ||||
\(287\) | −5.62558 | + | 4.38314i | −0.332068 | + | 0.258728i | ||||
\(288\) | 30.7982 | 1.81480 | ||||||||
\(289\) | 6.45655 | − | 11.1831i | 0.379797 | − | 0.657828i | ||||
\(290\) | 5.01218 | − | 7.12707i | 0.294325 | − | 0.418516i | ||||
\(291\) | −23.4645 | − | 40.6418i | −1.37552 | − | 2.38246i | ||||
\(292\) | −13.7213 | − | 7.92197i | −0.802976 | − | 0.463598i | ||||
\(293\) | 6.13847i | 0.358613i | 0.983793 | + | 0.179307i | \(0.0573854\pi\) | ||||
−0.983793 | + | 0.179307i | \(0.942615\pi\) | |||||||
\(294\) | −4.03490 | + | 16.0015i | −0.235320 | + | 0.933224i | ||||
\(295\) | 4.29422 | + | 9.25836i | 0.250019 | + | 0.539043i | ||||
\(296\) | 9.08059 | + | 5.24268i | 0.527798 | + | 0.304725i | ||||
\(297\) | 8.99027 | − | 20.1345i | 0.521668 | − | 1.16832i | ||||
\(298\) | 6.46462 | − | 3.73235i | 0.374485 | − | 0.216209i | ||||
\(299\) | 3.59986 | − | 6.23513i | 0.208185 | − | 0.360587i | ||||
\(300\) | 12.3886 | − | 14.6421i | 0.715255 | − | 0.845363i | ||||
\(301\) | 25.1139 | − | 19.5673i | 1.44754 | − | 1.12784i | ||||
\(302\) | − | 6.03063i | − | 0.347024i | ||||||
\(303\) | −5.69861 | + | 9.87028i | −0.327376 | + | 0.567033i | ||||
\(304\) | −1.16475 | − | 2.01740i | −0.0668027 | − | 0.115706i | ||||
\(305\) | 8.62161 | + | 6.06322i | 0.493672 | + | 0.347179i | ||||
\(306\) | −20.5600 | − | 11.8703i | −1.17534 | − | 0.678581i | ||||
\(307\) | − | 7.19470i | − | 0.410623i | −0.978697 | − | 0.205312i | \(-0.934179\pi\) | ||
0.978697 | − | 0.205312i | \(-0.0658208\pi\) | |||||||
\(308\) | −8.42062 | + | 8.09271i | −0.479809 | + | 0.461125i | ||||
\(309\) | 4.64644 | 0.264327 | ||||||||
\(310\) | 13.9114 | + | 1.24576i | 0.790114 | + | 0.0707542i | ||||
\(311\) | 2.55049 | − | 1.47253i | 0.144625 | − | 0.0834993i | −0.425941 | − | 0.904751i | \(-0.640057\pi\) |
0.570566 | + | 0.821251i | \(0.306724\pi\) | |||||||
\(312\) | 17.0177 | − | 9.82519i | 0.963439 | − | 0.556242i | ||||
\(313\) | 8.24243 | − | 14.2763i | 0.465890 | − | 0.806945i | −0.533352 | − | 0.845894i | \(-0.679068\pi\) |
0.999241 | + | 0.0389491i | \(0.0124010\pi\) | |||||||
\(314\) | −6.86224 | −0.387259 | ||||||||
\(315\) | 31.3576 | − | 1.53725i | 1.76680 | − | 0.0866142i | ||||
\(316\) | 2.55690i | 0.143837i | ||||||||
\(317\) | 9.07329 | + | 5.23847i | 0.509607 | + | 0.294222i | 0.732672 | − | 0.680582i | \(-0.238273\pi\) |
−0.223065 | + | 0.974804i | \(0.571606\pi\) | |||||||
\(318\) | −19.4440 | + | 11.2260i | −1.09036 | + | 0.629522i | ||||
\(319\) | 14.4269 | + | 6.44177i | 0.807751 | + | 0.360670i | ||||
\(320\) | 0.773923 | − | 8.64242i | 0.0432636 | − | 0.483126i | ||||
\(321\) | 10.7034 | 0.597406 | ||||||||
\(322\) | 2.34015 | − | 5.76994i | 0.130411 | − | 0.321546i | ||||
\(323\) | 29.4037i | 1.63607i | ||||||||
\(324\) | 2.15714 | − | 3.73628i | 0.119841 | − | 0.207571i | ||||
\(325\) | 2.22305 | − | 12.3129i | 0.123313 | − | 0.682997i | ||||
\(326\) | 2.99537 | − | 1.72937i | 0.165898 | − | 0.0957812i | ||||
\(327\) | 36.6868 | + | 21.1811i | 2.02878 | + | 1.17132i | ||||
\(328\) | 7.34402 | 0.405506 | ||||||||
\(329\) | −2.91350 | − | 20.9328i | −0.160627 | − | 1.15406i | ||||
\(330\) | −15.2650 | − | 8.52376i | −0.840308 | − | 0.469217i | ||||
\(331\) | −2.26378 | + | 3.92098i | −0.124429 | + | 0.215516i | −0.921509 | − | 0.388356i | \(-0.873043\pi\) |
0.797081 | + | 0.603873i | \(0.206376\pi\) | |||||||
\(332\) | 6.83981 | − | 3.94897i | 0.375383 | − | 0.216728i | ||||
\(333\) | 17.6867 | − | 10.2114i | 0.969223 | − | 0.559581i | ||||
\(334\) | −0.489253 | − | 0.282471i | −0.0267708 | − | 0.0154561i | ||||
\(335\) | −4.47328 | − | 9.64442i | −0.244402 | − | 0.526931i | ||||
\(336\) | −2.60638 | + | 2.03075i | −0.142190 | + | 0.110786i | ||||
\(337\) | −19.4420 | −1.05907 | −0.529536 | − | 0.848287i | \(-0.677634\pi\) | ||||
−0.529536 | + | 0.848287i | \(0.677634\pi\) | |||||||
\(338\) | −2.75571 | + | 4.77302i | −0.149891 | + | 0.259618i | ||||
\(339\) | −14.5615 | + | 8.40707i | −0.790870 | + | 0.456609i | ||||
\(340\) | 9.36337 | − | 13.3143i | 0.507800 | − | 0.722067i | ||||
\(341\) | 2.62045 | + | 25.1912i | 0.141906 | + | 1.36418i | ||||
\(342\) | 23.3364 | 1.26189 | ||||||||
\(343\) | −7.46523 | − | 16.9490i | −0.403085 | − | 0.915163i | ||||
\(344\) | −32.7854 | −1.76767 | ||||||||
\(345\) | −18.4683 | − | 1.65382i | −0.994297 | − | 0.0890386i | ||||
\(346\) | 1.19009 | − | 0.687098i | 0.0639795 | − | 0.0369386i | ||||
\(347\) | 7.13143 | + | 12.3520i | 0.382835 | + | 0.663090i | 0.991466 | − | 0.130363i | \(-0.0416144\pi\) |
−0.608631 | + | 0.793453i | \(0.708281\pi\) | |||||||
\(348\) | 15.8256 | + | 9.13692i | 0.848342 | + | 0.489790i | ||||
\(349\) | −1.84030 | −0.0985092 | −0.0492546 | − | 0.998786i | \(-0.515685\pi\) | ||||
−0.0492546 | + | 0.998786i | \(0.515685\pi\) | |||||||
\(350\) | 0.436245 | − | 10.8118i | 0.0233183 | − | 0.577914i | ||||
\(351\) | − | 16.6371i | − | 0.888022i | ||||||
\(352\) | 19.1450 | − | 1.99151i | 1.02043 | − | 0.106148i | ||||
\(353\) | 7.82224 | + | 13.5485i | 0.416336 | + | 0.721115i | 0.995568 | − | 0.0940479i | \(-0.0299807\pi\) |
−0.579232 | + | 0.815163i | \(0.696647\pi\) | |||||||
\(354\) | 9.31834 | − | 5.37995i | 0.495264 | − | 0.285941i | ||||
\(355\) | −0.835738 | + | 9.33272i | −0.0443564 | + | 0.495329i | ||||
\(356\) | − | 5.86347i | − | 0.310763i | ||||||
\(357\) | 41.3076 | − | 5.74933i | 2.18623 | − | 0.304287i | ||||
\(358\) | 2.13640 | 0.112912 | ||||||||
\(359\) | −17.4109 | − | 10.0522i | −0.918915 | − | 0.530536i | −0.0356260 | − | 0.999365i | \(-0.511342\pi\) |
−0.883289 | + | 0.468830i | \(0.844676\pi\) | |||||||
\(360\) | −26.4457 | − | 18.5982i | −1.39381 | − | 0.980211i | ||||
\(361\) | −4.95150 | − | 8.57624i | −0.260605 | − | 0.451381i | ||||
\(362\) | −11.3214 | − | 6.53643i | −0.595041 | − | 0.343547i | ||||
\(363\) | 9.86144 | − | 30.1309i | 0.517592 | − | 1.58146i | ||||
\(364\) | −3.31184 | + | 8.16576i | −0.173587 | + | 0.428002i | ||||
\(365\) | 11.2002 | + | 24.1478i | 0.586247 | + | 1.26395i | ||||
\(366\) | 5.55622 | − | 9.62365i | 0.290428 | − | 0.503036i | ||||
\(367\) | −11.1080 | − | 19.2397i | −0.579835 | − | 1.00430i | −0.995498 | − | 0.0947844i | \(-0.969784\pi\) |
0.415663 | − | 0.909519i | \(-0.363550\pi\) | |||||||
\(368\) | 1.07964 | − | 0.623331i | 0.0562802 | − | 0.0324934i | ||||
\(369\) | 7.15214 | − | 12.3879i | 0.372325 | − | 0.644886i | ||||
\(370\) | −2.96169 | − | 6.38542i | −0.153971 | − | 0.331962i | ||||
\(371\) | 9.47022 | − | 23.3501i | 0.491669 | − | 1.21227i | ||||
\(372\) | 29.2931i | 1.51877i | ||||||||
\(373\) | −10.4633 | + | 18.1230i | −0.541770 | + | 0.938372i | 0.457033 | + | 0.889450i | \(0.348912\pi\) |
−0.998803 | + | 0.0489227i | \(0.984421\pi\) | |||||||
\(374\) | −13.5482 | − | 6.04942i | −0.700560 | − | 0.312808i | ||||
\(375\) | −31.1760 | + | 8.14895i | −1.60992 | + | 0.420810i | ||||
\(376\) | −10.8821 | + | 18.8484i | −0.561202 | + | 0.972031i | ||||
\(377\) | 11.9209 | 0.613959 | ||||||||
\(378\) | −1.98346 | − | 14.2507i | −0.102018 | − | 0.732975i | ||||
\(379\) | −2.53873 | −0.130406 | −0.0652030 | − | 0.997872i | \(-0.520769\pi\) | ||||
−0.0652030 | + | 0.997872i | \(0.520769\pi\) | |||||||
\(380\) | −1.42707 | + | 15.9361i | −0.0732069 | + | 0.817504i | ||||
\(381\) | −5.65322 | − | 9.79166i | −0.289623 | − | 0.501642i | ||||
\(382\) | 1.92192 | + | 3.32887i | 0.0983342 | + | 0.170320i | ||||
\(383\) | −2.89690 | + | 5.01758i | −0.148025 | + | 0.256386i | −0.930497 | − | 0.366299i | \(-0.880625\pi\) |
0.782473 | + | 0.622685i | \(0.213958\pi\) | |||||||
\(384\) | 24.3054 | 1.24033 | ||||||||
\(385\) | 19.3933 | − | 2.98328i | 0.988374 | − | 0.152042i | ||||
\(386\) | 1.98956 | 0.101266 | ||||||||
\(387\) | −31.9288 | + | 55.3023i | −1.62303 | + | 2.81117i | ||||
\(388\) | −10.8357 | − | 18.7679i | −0.550098 | − | 0.952797i | ||||
\(389\) | 2.24668 | + | 3.89137i | 0.113911 | + | 0.197300i | 0.917344 | − | 0.398095i | \(-0.130329\pi\) |
−0.803433 | + | 0.595396i | \(0.796995\pi\) | |||||||
\(390\) | −13.1388 | − | 1.17657i | −0.665306 | − | 0.0595777i | ||||
\(391\) | −15.7358 | −0.795795 | ||||||||
\(392\) | −4.66320 | + | 18.4931i | −0.235527 | + | 0.934045i | ||||
\(393\) | −0.128837 | −0.00649899 | ||||||||
\(394\) | 1.78942 | − | 3.09937i | 0.0901497 | − | 0.156144i | ||||
\(395\) | 2.47113 | − | 3.51383i | 0.124336 | − | 0.176800i | ||||
\(396\) | 9.55085 | − | 21.3900i | 0.479948 | − | 1.07489i | ||||
\(397\) | 13.3536 | − | 23.1291i | 0.670198 | − | 1.16082i | −0.307649 | − | 0.951500i | \(-0.599542\pi\) |
0.977848 | − | 0.209318i | \(-0.0671243\pi\) | |||||||
\(398\) | − | 10.5384i | − | 0.528241i | ||||||
\(399\) | −32.3385 | + | 25.1963i | −1.61895 | + | 1.26139i | ||||
\(400\) | 1.39938 | − | 1.65393i | 0.0699689 | − | 0.0826965i | ||||
\(401\) | −5.42527 | + | 9.39685i | −0.270925 | + | 0.469256i | −0.969099 | − | 0.246672i | \(-0.920663\pi\) |
0.698174 | + | 0.715928i | \(0.253996\pi\) | |||||||
\(402\) | −9.70690 | + | 5.60428i | −0.484136 | + | 0.279516i | ||||
\(403\) | 9.55465 | + | 16.5491i | 0.475951 | + | 0.824371i | ||||
\(404\) | −2.63155 | + | 4.55799i | −0.130925 | + | 0.226768i | ||||
\(405\) | −6.57541 | + | 3.04981i | −0.326735 | + | 0.151546i | ||||
\(406\) | 10.2110 | − | 1.42120i | 0.506763 | − | 0.0705330i | ||||
\(407\) | 10.3342 | − | 7.49134i | 0.512246 | − | 0.371332i | ||||
\(408\) | −37.1943 | − | 21.4741i | −1.84139 | − | 1.06313i | ||||
\(409\) | 16.8829 | + | 29.2420i | 0.834805 | + | 1.44593i | 0.894189 | + | 0.447690i | \(0.147753\pi\) |
−0.0593834 | + | 0.998235i | \(0.518913\pi\) | |||||||
\(410\) | −4.03267 | − | 2.83601i | −0.199159 | − | 0.140061i | ||||
\(411\) | −47.1845 | − | 27.2420i | −2.32744 | − | 1.34375i | ||||
\(412\) | 2.14568 | 0.105710 | ||||||||
\(413\) | −4.53851 | + | 11.1903i | −0.223326 | + | 0.550638i | ||||
\(414\) | 12.4888i | 0.613791i | ||||||||
\(415\) | −13.2161 | − | 1.18350i | −0.648754 | − | 0.0580955i | ||||
\(416\) | 12.5771 | − | 7.26141i | 0.616645 | − | 0.356020i | ||||
\(417\) | 19.4271 | + | 33.6487i | 0.951349 | + | 1.64778i | ||||
\(418\) | 14.5065 | − | 1.50900i | 0.709535 | − | 0.0738078i | ||||
\(419\) | − | 17.3492i | − | 0.847562i | −0.905765 | − | 0.423781i | \(-0.860703\pi\) | ||
0.905765 | − | 0.423781i | \(-0.139297\pi\) | |||||||
\(420\) | 22.6667 | − | 1.11119i | 1.10602 | − | 0.0542207i | ||||
\(421\) | −33.3348 | −1.62464 | −0.812319 | − | 0.583213i | \(-0.801795\pi\) | ||||
−0.812319 | + | 0.583213i | \(0.801795\pi\) | |||||||
\(422\) | 8.23632 | + | 4.75524i | 0.400938 | + | 0.231481i | ||||
\(423\) | 21.1956 | + | 36.7118i | 1.03056 | + | 1.78499i | ||||
\(424\) | −22.4717 | + | 12.9741i | −1.09132 | + | 0.630076i | ||||
\(425\) | −25.7353 | + | 9.24787i | −1.24834 | + | 0.448588i | ||||
\(426\) | 9.87882 | 0.478630 | ||||||||
\(427\) | 1.71922 | + | 12.3522i | 0.0831990 | + | 0.597765i | ||||
\(428\) | 4.94271 | 0.238915 | ||||||||
\(429\) | −2.47491 | − | 23.7920i | −0.119490 | − | 1.14869i | ||||
\(430\) | 18.0028 | + | 12.6606i | 0.868170 | + | 0.610549i | ||||
\(431\) | −15.0543 | + | 8.69160i | −0.725140 | + | 0.418660i | −0.816641 | − | 0.577145i | \(-0.804167\pi\) |
0.0915017 | + | 0.995805i | \(0.470833\pi\) | |||||||
\(432\) | 1.44039 | − | 2.49483i | 0.0693009 | − | 0.120033i | ||||
\(433\) | 0.584483 | 0.0280885 | 0.0140442 | − | 0.999901i | \(-0.495529\pi\) | ||||
0.0140442 | + | 0.999901i | \(0.495529\pi\) | |||||||
\(434\) | 10.1571 | + | 13.0362i | 0.487557 | + | 0.625759i | ||||
\(435\) | −12.9180 | − | 27.8512i | −0.619369 | − | 1.33536i | ||||
\(436\) | 16.9416 | + | 9.78121i | 0.811354 | + | 0.468435i | ||||
\(437\) | 13.3956 | − | 7.73393i | 0.640797 | − | 0.369964i | ||||
\(438\) | 24.3042 | − | 14.0320i | 1.16130 | − | 0.670477i | ||||
\(439\) | 8.83334 | − | 15.2998i | 0.421593 | − | 0.730220i | −0.574503 | − | 0.818503i | \(-0.694805\pi\) |
0.996095 | + | 0.0882829i | \(0.0281379\pi\) | |||||||
\(440\) | −17.6420 | − | 9.85104i | −0.841047 | − | 0.469630i | ||||
\(441\) | 26.6528 | + | 25.8758i | 1.26918 | + | 1.23218i | ||||
\(442\) | −11.1948 | −0.532484 | ||||||||
\(443\) | −14.6701 | − | 8.46976i | −0.696995 | − | 0.402410i | 0.109232 | − | 0.994016i | \(-0.465161\pi\) |
−0.806227 | + | 0.591606i | \(0.798494\pi\) | |||||||
\(444\) | 12.7847 | − | 7.38127i | 0.606736 | − | 0.350299i | ||||
\(445\) | −5.66678 | + | 8.05789i | −0.268631 | + | 0.381981i | ||||
\(446\) | −3.50128 | + | 6.06440i | −0.165791 | + | 0.287158i | ||||
\(447\) | − | 26.3025i | − | 1.24407i | ||||||
\(448\) | 8.09874 | − | 6.31008i | 0.382629 | − | 0.298123i | ||||
\(449\) | 20.3183 | 0.958878 | 0.479439 | − | 0.877575i | \(-0.340840\pi\) | ||||
0.479439 | + | 0.877575i | \(0.340840\pi\) | |||||||
\(450\) | 7.33961 | + | 20.4249i | 0.345992 | + | 0.962839i | ||||
\(451\) | 3.64491 | − | 8.16309i | 0.171632 | − | 0.384385i | ||||
\(452\) | −6.72433 | + | 3.88229i | −0.316286 | + | 0.182608i | ||||
\(453\) | −18.4026 | − | 10.6247i | −0.864628 | − | 0.499193i | ||||
\(454\) | − | 9.48783i | − | 0.445286i | ||||||
\(455\) | 12.4431 | − | 8.02108i | 0.583344 | − | 0.376034i | ||||
\(456\) | 42.2169 | 1.97699 | ||||||||
\(457\) | −7.46388 | + | 12.9278i | −0.349146 | + | 0.604738i | −0.986098 | − | 0.166165i | \(-0.946862\pi\) |
0.636952 | + | 0.770903i | \(0.280195\pi\) | |||||||
\(458\) | 13.7045 | − | 7.91232i | 0.640371 | − | 0.369718i | ||||
\(459\) | −31.4907 | + | 18.1812i | −1.46986 | + | 0.848624i | ||||
\(460\) | −8.52844 | − | 0.763716i | −0.397640 | − | 0.0356084i | ||||
\(461\) | 6.31188 | 0.293973 | 0.146987 | − | 0.989138i | \(-0.453043\pi\) | ||||
0.146987 | + | 0.989138i | \(0.453043\pi\) | |||||||
\(462\) | −4.95637 | − | 20.0842i | −0.230591 | − | 0.934404i | ||||
\(463\) | − | 34.8340i | − | 1.61887i | −0.587208 | − | 0.809436i | \(-0.699773\pi\) | ||
0.587208 | − | 0.809436i | \(-0.300227\pi\) | |||||||
\(464\) | 1.78761 | + | 1.03208i | 0.0829879 | + | 0.0479131i | ||||
\(465\) | 28.3104 | − | 40.2561i | 1.31287 | − | 1.86683i | ||||
\(466\) | 11.8037 | + | 20.4446i | 0.546797 | + | 0.947080i | ||||
\(467\) | 2.10166 | − | 3.64018i | 0.0972532 | − | 0.168447i | −0.813294 | − | 0.581854i | \(-0.802328\pi\) |
0.910547 | + | 0.413406i | \(0.135661\pi\) | |||||||
\(468\) | − | 17.6745i | − | 0.817003i | ||||||
\(469\) | 4.72776 | − | 11.6569i | 0.218308 | − | 0.538266i | ||||
\(470\) | 13.2541 | − | 6.14752i | 0.611365 | − | 0.283564i | ||||
\(471\) | −12.0899 | + | 20.9402i | −0.557071 | + | 0.964875i | ||||
\(472\) | 10.7694 | − | 6.21769i | 0.495700 | − | 0.286192i | ||||
\(473\) | −16.2717 | + | 36.4419i | −0.748174 | + | 1.67560i | ||||
\(474\) | −3.92222 | − | 2.26449i | −0.180153 | − | 0.104012i | ||||
\(475\) | 17.3627 | − | 20.5210i | 0.796654 | − | 0.941569i | ||||
\(476\) | 19.0754 | − | 2.65498i | 0.874319 | − | 0.121691i | ||||
\(477\) | 50.5403i | 2.31408i | ||||||||
\(478\) | −18.9052 | − | 10.9149i | −0.864706 | − | 0.499238i | ||||
\(479\) | 5.88450 | + | 10.1923i | 0.268870 | + | 0.465696i | 0.968570 | − | 0.248740i | \(-0.0800166\pi\) |
−0.699701 | + | 0.714436i | \(0.746683\pi\) | |||||||
\(480\) | −30.5941 | − | 21.5156i | −1.39642 | − | 0.982047i | ||||
\(481\) | 4.81516 | − | 8.34011i | 0.219552 | − | 0.380276i | ||||
\(482\) | −14.5009 | −0.660497 | ||||||||
\(483\) | −13.4842 | − | 17.3064i | −0.613552 | − | 0.787470i | ||||
\(484\) | 4.55391 | − | 13.9141i | 0.206996 | − | 0.632460i | ||||
\(485\) | −3.24742 | + | 36.2641i | −0.147458 | + | 1.64667i | ||||
\(486\) | −4.33634 | − | 7.51076i | −0.196700 | − | 0.340695i | ||||
\(487\) | 10.5269 | − | 6.07769i | 0.477018 | − | 0.275406i | −0.242155 | − | 0.970238i | \(-0.577854\pi\) |
0.719173 | + | 0.694831i | \(0.244521\pi\) | |||||||
\(488\) | 6.42141 | − | 11.1222i | 0.290683 | − | 0.503479i | ||||
\(489\) | − | 12.1872i | − | 0.551125i | ||||||
\(490\) | 9.70203 | − | 8.35399i | 0.438293 | − | 0.377395i | ||||
\(491\) | 20.4766i | 0.924096i | 0.886855 | + | 0.462048i | \(0.152885\pi\) | ||||
−0.886855 | + | 0.462048i | \(0.847115\pi\) | |||||||
\(492\) | 5.16989 | − | 8.95451i | 0.233077 | − | 0.403701i | ||||
\(493\) | −13.0273 | − | 22.5639i | −0.586720 | − | 1.01623i | ||||
\(494\) | 9.52992 | − | 5.50210i | 0.428771 | − | 0.247551i | ||||
\(495\) | −33.7977 | + | 20.1647i | −1.51909 | + | 0.906337i | ||||
\(496\) | 3.30886i | 0.148572i | ||||||||
\(497\) | −8.74560 | + | 6.81408i | −0.392294 | + | 0.305653i | ||||
\(498\) | 13.9895i | 0.626883i | ||||||||
\(499\) | 5.92616 | − | 10.2644i | 0.265291 | − | 0.459498i | −0.702348 | − | 0.711833i | \(-0.747865\pi\) |
0.967640 | + | 0.252335i | \(0.0811985\pi\) | |||||||
\(500\) | −14.3967 | + | 3.76310i | −0.643841 | + | 0.168291i | ||||
\(501\) | −1.72393 | + | 0.995310i | −0.0770194 | + | 0.0444672i | ||||
\(502\) | −16.1622 | − | 9.33123i | −0.721353 | − | 0.416473i | ||||
\(503\) | 15.7747i | 0.703357i | 0.936121 | + | 0.351679i | \(0.114389\pi\) | ||||
−0.936121 | + | 0.351679i | \(0.885611\pi\) | |||||||
\(504\) | −5.27351 | − | 37.8889i | −0.234901 | − | 1.68770i | ||||
\(505\) | 8.02151 | − | 3.72054i | 0.356953 | − | 0.165562i | ||||
\(506\) | 0.807566 | + | 7.76335i | 0.0359007 | + | 0.345123i | ||||
\(507\) | 9.70997 | + | 16.8182i | 0.431235 | + | 0.746921i | ||||
\(508\) | −2.61060 | − | 4.52168i | −0.115826 | − | 0.200617i | ||||
\(509\) | 21.7215 | + | 12.5409i | 0.962789 | + | 0.555866i | 0.897030 | − | 0.441969i | \(-0.145720\pi\) |
0.0657584 | + | 0.997836i | \(0.479053\pi\) | |||||||
\(510\) | 12.1312 | + | 26.1548i | 0.537176 | + | 1.15815i | ||||
\(511\) | −11.8374 | + | 29.1866i | −0.523655 | + | 1.29114i | ||||
\(512\) | 4.87581 | 0.215483 | ||||||||
\(513\) | 17.8716 | − | 30.9545i | 0.789049 | − | 1.36667i | ||||
\(514\) | −1.78546 | − | 3.09250i | −0.0787532 | − | 0.136404i | ||||
\(515\) | −2.94870 | − | 2.07370i | −0.129935 | − | 0.0913781i | ||||
\(516\) | −23.0796 | + | 39.9750i | −1.01602 | + | 1.75980i | ||||
\(517\) | 15.5496 | + | 21.4504i | 0.683872 | + | 0.943389i | ||||
\(518\) | 3.13018 | − | 7.71786i | 0.137532 | − | 0.339103i | ||||
\(519\) | − | 4.84210i | − | 0.212544i | ||||||
\(520\) | −15.1847 | − | 1.35978i | −0.665892 | − | 0.0596301i | ||||
\(521\) | −39.2520 | + | 22.6621i | −1.71966 | + | 0.992847i | −0.800132 | + | 0.599824i | \(0.795237\pi\) |
−0.919529 | + | 0.393022i | \(0.871429\pi\) | |||||||
\(522\) | −17.9080 | + | 10.3392i | −0.783810 | + | 0.452533i | ||||
\(523\) | 29.6979 | + | 17.1461i | 1.29860 | + | 0.749747i | 0.980162 | − | 0.198197i | \(-0.0635084\pi\) |
0.318438 | + | 0.947944i | \(0.396842\pi\) | |||||||
\(524\) | −0.0594957 | −0.00259908 | ||||||||
\(525\) | −32.2237 | − | 20.3793i | −1.40636 | − | 0.889426i | ||||
\(526\) | 19.0884 | 0.832295 | ||||||||
\(527\) | 20.8828 | − | 36.1701i | 0.909671 | − | 1.57560i | ||||
\(528\) | 1.68872 | − | 3.78203i | 0.0734921 | − | 0.164592i | ||||
\(529\) | −7.36107 | − | 12.7497i | −0.320047 | − | 0.554337i | ||||
\(530\) | 17.3496 | + | 1.55364i | 0.753617 | + | 0.0674859i | ||||
\(531\) | − | 24.2209i | − | 1.05110i | ||||||
\(532\) | −14.9336 | + | 11.6354i | −0.647452 | + | 0.504458i | ||||
\(533\) | − | 6.74514i | − | 0.292165i | ||||||
\(534\) | 8.99442 | + | 5.19293i | 0.389226 | + | 0.224720i | ||||
\(535\) | −6.79254 | − | 4.77691i | −0.293667 | − | 0.206524i | ||||
\(536\) | −11.2184 | + | 6.47696i | −0.484562 | + | 0.279762i | ||||
\(537\) | 3.76390 | − | 6.51926i | 0.162424 | − | 0.281327i | ||||
\(538\) | − | 17.8552i | − | 0.769794i | ||||||
\(539\) | 18.2413 | + | 14.3616i | 0.785707 | + | 0.618598i | ||||
\(540\) | −17.9496 | + | 8.32540i | −0.772428 | + | 0.358268i | ||||
\(541\) | −4.89784 | − | 2.82777i | −0.210574 | − | 0.121575i | 0.391004 | − | 0.920389i | \(-0.372128\pi\) |
−0.601578 | + | 0.798814i | \(0.705461\pi\) | |||||||
\(542\) | −1.74303 | − | 3.01902i | −0.0748697 | − | 0.129678i | ||||
\(543\) | −39.8920 | + | 23.0317i | −1.71193 | + | 0.988383i | ||||
\(544\) | −27.4888 | − | 15.8707i | −1.17857 | − | 0.680450i | ||||
\(545\) | −13.8289 | − | 29.8151i | −0.592364 | − | 1.27714i | ||||
\(546\) | −9.59298 | − | 12.3122i | −0.410541 | − | 0.526914i | ||||
\(547\) | 1.59722 | 0.0682922 | 0.0341461 | − | 0.999417i | \(-0.489129\pi\) | ||||
0.0341461 | + | 0.999417i | \(0.489129\pi\) | |||||||
\(548\) | −21.7893 | − | 12.5800i | −0.930792 | − | 0.537393i | ||||
\(549\) | −12.5073 | − | 21.6632i | −0.533797 | − | 0.924564i | ||||
\(550\) | 5.88323 | + | 12.2220i | 0.250862 | + | 0.521149i | ||||
\(551\) | 22.1797 | + | 12.8055i | 0.944887 | + | 0.545531i | ||||
\(552\) | 22.5930i | 0.961621i | ||||||||
\(553\) | 5.03427 | − | 0.700687i | 0.214079 | − | 0.0297963i | ||||
\(554\) | 11.6765 | 0.496087 | ||||||||
\(555\) | −24.7031 | − | 2.21215i | −1.04859 | − | 0.0939004i | ||||
\(556\) | 8.97122 | + | 15.5386i | 0.380464 | + | 0.658984i | ||||
\(557\) | 2.91725 | + | 5.05282i | 0.123608 | + | 0.214095i | 0.921188 | − | 0.389118i | \(-0.127220\pi\) |
−0.797580 | + | 0.603213i | \(0.793887\pi\) | |||||||
\(558\) | −28.7066 | − | 16.5737i | −1.21525 | − | 0.701622i | ||||
\(559\) | 30.1119i | 1.27360i | ||||||||
\(560\) | 2.56037 | − | 0.125517i | 0.108195 | − | 0.00530407i | ||||
\(561\) | −42.3290 | + | 30.6847i | −1.78713 | + | 1.29551i | ||||
\(562\) | 16.3553 | + | 9.44276i | 0.689908 | + | 0.398319i | ||||
\(563\) | −18.6852 | + | 10.7879i | −0.787487 | + | 0.454656i | −0.839077 | − | 0.544013i | \(-0.816904\pi\) |
0.0515902 | + | 0.998668i | \(0.483571\pi\) | |||||||
\(564\) | 15.3211 | + | 26.5370i | 0.645136 | + | 1.11741i | ||||
\(565\) | 12.9930 | + | 1.16351i | 0.546619 | + | 0.0489494i | ||||
\(566\) | − | 1.92127i | − | 0.0807570i | ||||||
\(567\) | −7.94749 | − | 3.22331i | −0.333763 | − | 0.135366i | ||||
\(568\) | 11.4171 | 0.479051 | ||||||||
\(569\) | 21.2938 | + | 12.2940i | 0.892682 | + | 0.515390i | 0.874819 | − | 0.484450i | \(-0.160980\pi\) |
0.0178634 | + | 0.999840i | \(0.494314\pi\) | |||||||
\(570\) | −23.1817 | − | 16.3027i | −0.970974 | − | 0.682846i | ||||
\(571\) | 33.9663 | − | 19.6104i | 1.42144 | − | 0.820672i | 0.425022 | − | 0.905183i | \(-0.360266\pi\) |
0.996423 | + | 0.0845113i | \(0.0269329\pi\) | |||||||
\(572\) | −1.14289 | − | 10.9869i | −0.0477866 | − | 0.459385i | ||||
\(573\) | 13.5441 | 0.565814 | ||||||||
\(574\) | −0.804149 | − | 5.77762i | −0.0335645 | − | 0.241153i | ||||
\(575\) | 10.9821 | + | 9.29189i | 0.457986 | + | 0.387499i | ||||
\(576\) | −10.2964 | + | 17.8339i | −0.429017 | + | 0.743079i | ||||
\(577\) | 15.8525 | + | 27.4573i | 0.659948 | + | 1.14306i | 0.980629 | + | 0.195877i | \(0.0627552\pi\) |
−0.320680 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(578\) | 5.28119 | + | 9.14729i | 0.219669 | + | 0.380477i | ||||
\(579\) | 3.50519 | − | 6.07116i | 0.145671 | − | 0.252309i | ||||
\(580\) | −5.96537 | − | 12.8614i | −0.247699 | − | 0.534039i | ||||
\(581\) | −9.64947 | − | 12.3847i | −0.400328 | − | 0.513804i | ||||
\(582\) | 38.3860 | 1.59115 | ||||||||
\(583\) | 3.26810 | + | 31.4171i | 0.135351 | + | 1.30116i | ||||
\(584\) | 28.0888 | − | 16.2170i | 1.16232 | − | 0.671066i | ||||
\(585\) | −17.0816 | + | 24.2892i | −0.706237 | + | 1.00423i | ||||
\(586\) | −4.34832 | − | 2.51051i | −0.179628 | − | 0.103708i | ||||
\(587\) | 7.82663 | 0.323040 | 0.161520 | − | 0.986869i | \(-0.448360\pi\) | ||||
0.161520 | + | 0.986869i | \(0.448360\pi\) | |||||||
\(588\) | 19.2659 | + | 18.7042i | 0.794511 | + | 0.771349i | ||||
\(589\) | 41.0544i | 1.69162i | ||||||||
\(590\) | −8.31462 | − | 0.744568i | −0.342307 | − | 0.0306534i | ||||
\(591\) | −6.30518 | − | 10.9209i | −0.259360 | − | 0.449225i | ||||
\(592\) | 1.44413 | − | 0.833767i | 0.0593532 | − | 0.0342676i | ||||
\(593\) | −37.0010 | − | 21.3625i | −1.51945 | − | 0.877254i | −0.999737 | − | 0.0229115i | \(-0.992706\pi\) |
−0.519711 | − | 0.854342i | \(-0.673960\pi\) | |||||||
\(594\) | 10.5859 | + | 14.6030i | 0.434344 | + | 0.599170i | ||||
\(595\) | −28.7803 | − | 14.7869i | −1.17988 | − | 0.606204i | ||||
\(596\) | − | 12.1462i | − | 0.497528i | ||||||
\(597\) | −32.1580 | − | 18.5664i | −1.31614 | − | 0.759874i | ||||
\(598\) | 2.94453 | + | 5.10008i | 0.120411 | + | 0.208558i | ||||
\(599\) | 2.31031 | + | 4.00157i | 0.0943965 | + | 0.163500i | 0.909357 | − | 0.416018i | \(-0.136575\pi\) |
−0.814960 | + | 0.579517i | \(0.803241\pi\) | |||||||
\(600\) | 13.2778 | + | 36.9499i | 0.542063 | + | 1.50847i | ||||
\(601\) | −41.3301 | −1.68589 | −0.842945 | − | 0.538000i | \(-0.819180\pi\) | ||||
−0.842945 | + | 0.538000i | \(0.819180\pi\) | |||||||
\(602\) | 3.58991 | + | 25.7926i | 0.146314 | + | 1.05123i | ||||
\(603\) | 25.2309i | 1.02748i | ||||||||
\(604\) | −8.49810 | − | 4.90638i | −0.345783 | − | 0.199638i | ||||
\(605\) | −19.7056 | + | 14.7204i | −0.801147 | + | 0.598468i | ||||
\(606\) | −4.66122 | − | 8.07348i | −0.189349 | − | 0.327963i | ||||
\(607\) | 2.83581 | + | 1.63726i | 0.115102 | + | 0.0664542i | 0.556446 | − | 0.830884i | \(-0.312165\pi\) |
−0.441344 | + | 0.897338i | \(0.645498\pi\) | |||||||
\(608\) | 31.2009 | 1.26536 | ||||||||
\(609\) | 13.6528 | − | 33.6628i | 0.553241 | − | 1.36409i | ||||
\(610\) | −7.82108 | + | 3.62758i | −0.316666 | + | 0.146876i | ||||
\(611\) | 17.3114 | + | 9.99473i | 0.700343 | + | 0.404343i | ||||
\(612\) | −33.4543 | + | 19.3148i | −1.35231 | + | 0.780756i | ||||
\(613\) | 3.71261 | + | 6.43042i | 0.149951 | + | 0.259722i | 0.931209 | − | 0.364486i | \(-0.118755\pi\) |
−0.781258 | + | 0.624208i | \(0.785422\pi\) | |||||||
\(614\) | 5.09653 | + | 2.94248i | 0.205679 | + | 0.118749i | ||||
\(615\) | −15.7589 | + | 7.30929i | −0.635459 | + | 0.294739i | ||||
\(616\) | −5.72816 | − | 23.2117i | −0.230794 | − | 0.935225i | ||||
\(617\) | − | 0.911253i | − | 0.0366857i | −0.999832 | − | 0.0183428i | \(-0.994161\pi\) | ||
0.999832 | − | 0.0183428i | \(-0.00583903\pi\) | |||||||
\(618\) | −1.90030 | + | 3.29141i | −0.0764412 | + | 0.132400i | ||||
\(619\) | 27.2769 | − | 15.7483i | 1.09635 | − | 0.632979i | 0.161091 | − | 0.986940i | \(-0.448499\pi\) |
0.935260 | + | 0.353961i | \(0.115165\pi\) | |||||||
\(620\) | 13.0735 | − | 18.5898i | 0.525043 | − | 0.746585i | ||||
\(621\) | 16.5657 | + | 9.56423i | 0.664760 | + | 0.383799i | ||||
\(622\) | 2.40893i | 0.0965893i | ||||||||
\(623\) | −11.5446 | + | 1.60681i | −0.462523 | + | 0.0643756i | ||||
\(624\) | − | 3.12509i | − | 0.125104i | ||||||
\(625\) | 23.4216 | + | 8.74235i | 0.936864 | + | 0.349694i | ||||
\(626\) | 6.74196 | + | 11.6774i | 0.269463 | + | 0.466724i | ||||
\(627\) | 20.9527 | − | 46.9253i | 0.836769 | − | 1.87402i | ||||
\(628\) | −5.58296 | + | 9.66998i | −0.222784 | + | 0.385874i | ||||
\(629\) | −21.0482 | −0.839248 | ||||||||
\(630\) | −11.7357 | + | 22.8416i | −0.467560 | + | 0.910031i | ||||
\(631\) | −17.7376 | −0.706122 | −0.353061 | − | 0.935600i | \(-0.614859\pi\) | ||||
−0.353061 | + | 0.935600i | \(0.614859\pi\) | |||||||
\(632\) | −4.53297 | − | 2.61711i | −0.180312 | − | 0.104103i | ||||
\(633\) | 29.0214 | − | 16.7555i | 1.15350 | − | 0.665971i | ||||
\(634\) | −7.42157 | + | 4.28485i | −0.294748 | + | 0.170173i | ||||
\(635\) | −0.782389 | + | 8.73696i | −0.0310481 | + | 0.346716i | ||||
\(636\) | 36.5328i | 1.44862i | ||||||||
\(637\) | 16.9851 | + | 4.28293i | 0.672974 | + | 0.169696i | ||||
\(638\) | −10.4635 | + | 7.58507i | −0.414253 | + | 0.300296i | ||||
\(639\) | 11.1188 | − | 19.2583i | 0.439853 | − | 0.761848i | ||||
\(640\) | −15.4245 | − | 10.8474i | −0.609708 | − | 0.428783i | ||||
\(641\) | 22.5671 | + | 39.0873i | 0.891345 | + | 1.54386i | 0.838264 | + | 0.545265i | \(0.183571\pi\) |
0.0530816 | + | 0.998590i | \(0.483096\pi\) | |||||||
\(642\) | −4.37747 | + | 7.58200i | −0.172765 | + | 0.299238i | ||||
\(643\) | 26.7815 | 1.05616 | 0.528080 | − | 0.849194i | \(-0.322912\pi\) | ||||
0.528080 | + | 0.849194i | \(0.322912\pi\) | |||||||
\(644\) | −6.22686 | − | 7.99192i | −0.245372 | − | 0.314926i | ||||
\(645\) | 70.3512 | − | 32.6303i | 2.77008 | − | 1.28482i | ||||
\(646\) | −20.8288 | − | 12.0255i | −0.819498 | − | 0.473137i | ||||
\(647\) | −7.12283 | − | 12.3371i | −0.280027 | − | 0.485022i | 0.691364 | − | 0.722507i | \(-0.257010\pi\) |
−0.971391 | + | 0.237485i | \(0.923677\pi\) | |||||||
\(648\) | 4.41589 | + | 7.64854i | 0.173472 | + | 0.300463i | ||||
\(649\) | −1.56620 | − | 15.0564i | −0.0614789 | − | 0.591014i | ||||
\(650\) | 7.81295 | + | 6.61047i | 0.306449 | + | 0.259284i | ||||
\(651\) | 57.6750 | − | 8.02741i | 2.26046 | − | 0.314619i | ||||
\(652\) | − | 5.62792i | − | 0.220406i | ||||||
\(653\) | 40.8763 | + | 23.5999i | 1.59961 | + | 0.923537i | 0.991561 | + | 0.129641i | \(0.0413823\pi\) |
0.608053 | + | 0.793897i | \(0.291951\pi\) | |||||||
\(654\) | −30.0083 | + | 17.3253i | −1.17342 | + | 0.677472i | ||||
\(655\) | 0.0817622 | + | 0.0575000i | 0.00319471 | + | 0.00224671i | ||||
\(656\) | 0.583976 | − | 1.01148i | 0.0228004 | − | 0.0394915i | ||||
\(657\) | − | 63.1733i | − | 2.46463i | ||||||
\(658\) | 16.0198 | + | 6.49724i | 0.624517 | + | 0.253289i | ||||
\(659\) | 21.3029i | 0.829841i | 0.909858 | + | 0.414921i | \(0.136191\pi\) | ||||
−0.909858 | + | 0.414921i | \(0.863809\pi\) | |||||||
\(660\) | −24.4305 | + | 14.5760i | −0.950957 | + | 0.567369i | ||||
\(661\) | −2.77887 | + | 1.60438i | −0.108086 | + | 0.0624032i | −0.553068 | − | 0.833136i | \(-0.686543\pi\) |
0.444983 | + | 0.895539i | \(0.353210\pi\) | |||||||
\(662\) | −1.85168 | − | 3.20720i | −0.0719674 | − | 0.124651i | ||||
\(663\) | −19.7230 | + | 34.1612i | −0.765978 | + | 1.32671i | ||||
\(664\) | 16.1678i | 0.627434i | ||||||||
\(665\) | 31.7676 | − | 1.55735i | 1.23189 | − | 0.0603913i | ||||
\(666\) | 16.7050i | 0.647306i | ||||||||
\(667\) | −6.85303 | + | 11.8698i | −0.265350 | + | 0.459600i | ||||
\(668\) | −0.796091 | + | 0.459623i | −0.0308017 | + | 0.0177834i | ||||
\(669\) | 12.3371 | + | 21.3684i | 0.476979 | + | 0.826152i | ||||
\(670\) | 8.66132 | + | 0.775615i | 0.334616 | + | 0.0299646i | ||||
\(671\) | −9.17565 | − | 12.6576i | −0.354222 | − | 0.488643i | ||||
\(672\) | −6.10073 | − | 43.8323i | −0.235341 | − | 1.69087i | ||||
\(673\) | −0.164082 | −0.00632491 | −0.00316245 | − | 0.999995i | \(-0.501007\pi\) | ||||
−0.00316245 | + | 0.999995i | \(0.501007\pi\) | |||||||
\(674\) | 7.95136 | − | 13.7722i | 0.306275 | − | 0.530484i | ||||
\(675\) | 32.7134 | + | 5.90629i | 1.25914 | + | 0.227333i | ||||
\(676\) | 4.48396 | + | 7.76645i | 0.172460 | + | 0.298709i | ||||
\(677\) | −3.47551 | − | 2.00659i | −0.133575 | − | 0.0771194i | 0.431724 | − | 0.902006i | \(-0.357906\pi\) |
−0.565298 | + | 0.824887i | \(0.691239\pi\) | |||||||
\(678\) | − | 13.7533i | − | 0.528191i | ||||||
\(679\) | −33.9827 | + | 26.4774i | −1.30414 | + | 1.01611i | ||||
\(680\) | 14.0202 | + | 30.2275i | 0.537649 | + | 1.15917i | ||||
\(681\) | −28.9523 | − | 16.7156i | −1.10945 | − | 0.640543i | ||||
\(682\) | −18.9164 | − | 8.44640i | −0.724348 | − | 0.323429i | ||||
\(683\) | −22.4174 | + | 12.9427i | −0.857778 | + | 0.495238i | −0.863267 | − | 0.504747i | \(-0.831586\pi\) |
0.00548973 | + | 0.999985i | \(0.498253\pi\) | |||||||
\(684\) | 18.9859 | − | 32.8846i | 0.725945 | − | 1.25737i | ||||
\(685\) | 17.7859 | + | 38.3465i | 0.679565 | + | 1.46515i | ||||
\(686\) | 15.0594 | + | 1.64364i | 0.574969 | + | 0.0627545i | ||||
\(687\) | − | 55.7595i | − | 2.12736i | ||||||
\(688\) | −2.60700 | + | 4.51546i | −0.0993910 | + | 0.172150i | ||||
\(689\) | 11.9161 | + | 20.6392i | 0.453966 | + | 0.786293i | ||||
\(690\) | 8.72465 | − | 12.4060i | 0.332142 | − | 0.472289i | ||||
\(691\) | −13.8886 | − | 8.01859i | −0.528347 | − | 0.305042i | 0.211996 | − | 0.977271i | \(-0.432004\pi\) |
−0.740343 | + | 0.672229i | \(0.765337\pi\) | |||||||
\(692\) | − | 2.23603i | − | 0.0850010i | ||||||
\(693\) | −44.7319 | − | 12.9430i | −1.69922 | − | 0.491663i | ||||
\(694\) | −11.6664 | −0.442851 | ||||||||
\(695\) | 2.68865 | − | 30.0242i | 0.101986 | − | 1.13888i | ||||
\(696\) | −32.3966 | + | 18.7042i | −1.22799 | + | 0.708980i | ||||
\(697\) | −12.7672 | + | 7.37116i | −0.483593 | + | 0.279203i | ||||
\(698\) | 0.752646 | − | 1.30362i | 0.0284881 | − | 0.0493428i | ||||
\(699\) | 83.1828 | 3.14626 | ||||||||
\(700\) | −14.8806 | − | 9.41095i | −0.562433 | − | 0.355700i | ||||
\(701\) | 12.4384i | 0.469793i | 0.972020 | + | 0.234897i | \(0.0754752\pi\) | ||||
−0.972020 | + | 0.234897i | \(0.924525\pi\) | |||||||
\(702\) | 11.7853 | + | 6.80422i | 0.444806 | + | 0.256809i | ||||
\(703\) | 17.9179 | − | 10.3449i | 0.675786 | − | 0.390165i | ||||
\(704\) | −5.24731 | + | 11.7518i | −0.197765 | + | 0.442913i | ||||
\(705\) | 4.59171 | − | 51.2757i | 0.172934 | − | 1.93116i | ||||
\(706\) | −12.7965 | −0.481604 | ||||||||
\(707\) | 9.69535 | + | 3.93220i | 0.364631 | + | 0.147886i | ||||
\(708\) | − | 17.5080i | − | 0.657991i | ||||||
\(709\) | 18.3423 | − | 31.7697i | 0.688858 | − | 1.19314i | −0.283350 | − | 0.959017i | \(-0.591446\pi\) |
0.972208 | − | 0.234120i | \(-0.0752209\pi\) | |||||||
\(710\) | −6.26924 | − | 4.40890i | −0.235280 | − | 0.165463i | ||||
\(711\) | −8.82907 | + | 5.09747i | −0.331116 | + | 0.191170i | ||||
\(712\) | 10.3950 | + | 6.00155i | 0.389569 | + | 0.224918i | ||||
\(713\) | −21.9709 | −0.822816 | ||||||||
\(714\) | −12.8213 | + | 31.6125i | −0.479824 | + | 1.18307i | ||||
\(715\) | −9.04773 | + | 16.2033i | −0.338366 | + | 0.605970i | ||||
\(716\) | 1.73813 | − | 3.01052i | 0.0649569 | − | 0.112509i | ||||
\(717\) | −66.6143 | + | 38.4598i | −2.48776 | + | 1.43631i | ||||
\(718\) | 14.2414 | − | 8.22229i | 0.531485 | − | 0.306853i | ||||
\(719\) | 14.7756 | + | 8.53070i | 0.551037 | + | 0.318141i | 0.749540 | − | 0.661959i | \(-0.230275\pi\) |
−0.198503 | + | 0.980100i | \(0.563608\pi\) | |||||||
\(720\) | −4.66438 | + | 2.16344i | −0.173831 | + | 0.0806265i | ||||
\(721\) | −0.587996 | − | 4.22461i | −0.0218981 | − | 0.157333i | ||||
\(722\) | 8.10023 | 0.301459 | ||||||||
\(723\) | −25.5475 | + | 44.2496i | −0.950124 | + | 1.64566i | ||||
\(724\) | −18.4217 | + | 10.6358i | −0.684637 | + | 0.395275i | ||||
\(725\) | −4.23201 | + | 23.4400i | −0.157173 | + | 0.870541i | ||||
\(726\) | 17.3108 | + | 19.3085i | 0.642464 | + | 0.716605i | ||||
\(727\) | −36.3728 | −1.34899 | −0.674496 | − | 0.738278i | \(-0.735639\pi\) | ||||
−0.674496 | + | 0.738278i | \(0.735639\pi\) | |||||||
\(728\) | −11.0868 | − | 14.2294i | −0.410903 | − | 0.527377i | ||||
\(729\) | −40.2835 | −1.49198 | ||||||||
\(730\) | −21.6863 | − | 1.94199i | −0.802645 | − | 0.0718763i | ||||
\(731\) | 56.9958 | − | 32.9066i | 2.10807 | − | 1.21709i | ||||
\(732\) | −9.04082 | − | 15.6592i | −0.334158 | − | 0.578779i | ||||
\(733\) | 28.2237 | + | 16.2950i | 1.04247 | + | 0.601869i | 0.920531 | − | 0.390669i | \(-0.127756\pi\) |
0.121936 | + | 0.992538i | \(0.461090\pi\) | |||||||
\(734\) | 18.1718 | 0.670734 | ||||||||
\(735\) | −8.39937 | − | 44.3239i | −0.309815 | − | 1.63491i | ||||
\(736\) | 16.6976i | 0.615482i | ||||||||
\(737\) | 1.63151 | + | 15.6842i | 0.0600975 | + | 0.577734i | ||||
\(738\) | 5.85015 | + | 10.1328i | 0.215347 | + | 0.372992i | ||||
\(739\) | 2.50620 | − | 1.44695i | 0.0921919 | − | 0.0532270i | −0.453195 | − | 0.891411i | \(-0.649716\pi\) |
0.545387 | + | 0.838184i | \(0.316383\pi\) | |||||||
\(740\) | −11.4076 | − | 1.02155i | −0.419353 | − | 0.0375527i | ||||
\(741\) | − | 38.7743i | − | 1.42441i | ||||||
\(742\) | 12.6674 | + | 16.2581i | 0.465036 | + | 0.596855i | ||||
\(743\) | 18.6676 | 0.684849 | 0.342425 | − | 0.939545i | \(-0.388752\pi\) | ||||
0.342425 | + | 0.939545i | \(0.388752\pi\) | |||||||
\(744\) | −51.9319 | − | 29.9829i | −1.90392 | − | 1.09923i | ||||
\(745\) | −11.7388 | + | 16.6920i | −0.430075 | + | 0.611546i | ||||
\(746\) | −8.55855 | − | 14.8238i | −0.313351 | − | 0.542739i | ||||
\(747\) | 27.2719 | + | 15.7454i | 0.997825 | + | 0.576095i | ||||
\(748\) | −19.5471 | + | 14.1699i | −0.714712 | + | 0.518101i | ||||
\(749\) | −1.35449 | − | 9.73169i | −0.0494920 | − | 0.355588i | ||||
\(750\) | 6.97783 | − | 25.4170i | 0.254794 | − | 0.928096i | ||||
\(751\) | 16.2406 | − | 28.1295i | 0.592628 | − | 1.02646i | −0.401249 | − | 0.915969i | \(-0.631424\pi\) |
0.993877 | − | 0.110492i | \(-0.0352428\pi\) | |||||||
\(752\) | 1.73063 | + | 2.99754i | 0.0631096 | + | 0.109309i | ||||
\(753\) | −56.9488 | + | 32.8794i | −2.07533 | + | 1.19819i | ||||
\(754\) | −4.87541 | + | 8.44445i | −0.177552 | + | 0.307529i | ||||
\(755\) | 6.93674 | + | 14.9556i | 0.252454 | + | 0.544292i | ||||
\(756\) | −21.6951 | − | 8.79901i | −0.789043 | − | 0.320017i | ||||
\(757\) | − | 0.192111i | − | 0.00698239i | −0.999994 | − | 0.00349119i | \(-0.998889\pi\) | ||
0.999994 | − | 0.00349119i | \(-0.00111128\pi\) | |||||||
\(758\) | 1.03829 | − | 1.79837i | 0.0377124 | − | 0.0653197i | ||||
\(759\) | 25.1128 | + | 11.2131i | 0.911536 | + | 0.407011i | ||||
\(760\) | −26.7915 | − | 18.8413i | −0.971828 | − | 0.683447i | ||||
\(761\) | 15.9644 | − | 27.6512i | 0.578710 | − | 1.00236i | −0.416918 | − | 0.908944i | \(-0.636890\pi\) |
0.995628 | − | 0.0934108i | \(-0.0297770\pi\) | |||||||
\(762\) | 9.24820 | 0.335027 | ||||||||
\(763\) | 14.6156 | − | 36.0366i | 0.529119 | − | 1.30461i | ||||
\(764\) | 6.25453 | 0.226281 | ||||||||
\(765\) | 64.6416 | + | 5.78861i | 2.33712 | + | 0.209288i | ||||
\(766\) | −2.36954 | − | 4.10417i | −0.0856150 | − | 0.148290i | ||||
\(767\) | −5.71066 | − | 9.89116i | −0.206200 | − | 0.357149i | ||||
\(768\) | −21.1245 | + | 36.5887i | −0.762264 | + | 1.32028i | ||||
\(769\) | 32.2718 | 1.16375 | 0.581875 | − | 0.813278i | \(-0.302319\pi\) | ||||
0.581875 | + | 0.813278i | \(0.302319\pi\) | |||||||
\(770\) | −5.81818 | + | 14.9578i | −0.209673 | + | 0.539041i | ||||
\(771\) | −12.5824 | −0.453145 | ||||||||
\(772\) | 1.61866 | − | 2.80360i | 0.0582567 | − | 0.100904i | ||||
\(773\) | −3.25566 | − | 5.63896i | −0.117098 | − | 0.202819i | 0.801519 | − | 0.597970i | \(-0.204026\pi\) |
−0.918616 | + | 0.395151i | \(0.870692\pi\) | |||||||
\(774\) | −26.1164 | − | 45.2349i | −0.938735 | − | 1.62594i | ||||
\(775\) | −35.9325 | + | 12.9122i | −1.29073 | + | 0.463819i | ||||
\(776\) | 44.3633 | 1.59255 | ||||||||
\(777\) | −18.0364 | − | 23.1491i | −0.647054 | − | 0.830468i | ||||
\(778\) | −3.67538 | −0.131769 | ||||||||
\(779\) | 7.24564 | − | 12.5498i | 0.259602 | − | 0.449644i | ||||
\(780\) | −12.3474 | + | 17.5573i | −0.442106 | + | 0.628653i | ||||
\(781\) | 5.66642 | − | 12.6904i | 0.202761 | − | 0.454100i | ||||
\(782\) | 6.43563 | − | 11.1468i | 0.230138 | − | 0.398610i | ||||
\(783\) | 31.6720i | 1.13186i | ||||||||
\(784\) | 2.17622 | + | 2.11277i | 0.0777220 | + | 0.0754562i | ||||
\(785\) | 17.0180 | − | 7.89330i | 0.607399 | − | 0.281724i | ||||
\(786\) | 0.0526918 | − | 0.0912649i | 0.00187946 | − | 0.00325531i | ||||
\(787\) | 23.1360 | − | 13.3576i | 0.824710 | − | 0.476146i | −0.0273282 | − | 0.999627i | \(-0.508700\pi\) |
0.852038 | + | 0.523480i | \(0.175367\pi\) | |||||||
\(788\) | −2.91166 | − | 5.04315i | −0.103724 | − | 0.179655i | ||||
\(789\) | 33.6299 | − | 58.2487i | 1.19726 | − | 2.07371i | ||||
\(790\) | 1.47846 | + | 3.18756i | 0.0526012 | + | 0.113408i | ||||
\(791\) | 9.48655 | + | 12.1756i | 0.337303 | + | 0.432915i | ||||
\(792\) | 28.1452 | + | 38.8258i | 1.00010 | + | 1.37961i | ||||
\(793\) | −10.2152 | − | 5.89777i | −0.362754 | − | 0.209436i | ||||
\(794\) | 10.9227 | + | 18.9187i | 0.387632 | + | 0.671398i | ||||
\(795\) | 35.3073 | − | 50.2053i | 1.25222 | − | 1.78060i | ||||
\(796\) | −14.8502 | − | 8.57378i | −0.526352 | − | 0.303890i | ||||
\(797\) | −11.2146 | −0.397243 | −0.198621 | − | 0.980076i | \(-0.563646\pi\) | ||||
−0.198621 | + | 0.980076i | \(0.563646\pi\) | |||||||
\(798\) | −4.62263 | − | 33.2125i | −0.163639 | − | 1.17571i | ||||
\(799\) | − | 43.6894i | − | 1.54562i | ||||||
\(800\) | 9.81310 | + | 27.3082i | 0.346945 | + | 0.965491i | ||||
\(801\) | 20.2468 | − | 11.6895i | 0.715385 | − | 0.413028i | ||||
\(802\) | −4.43765 | − | 7.68623i | −0.156699 | − | 0.271410i | ||||
\(803\) | −4.08499 | − | 39.2702i | −0.144156 | − | 1.38581i | ||||
\(804\) | 18.2381i | 0.643206i | ||||||||
\(805\) | 0.833437 | + | 17.0009i | 0.0293748 | + | 0.599203i | ||||
\(806\) | −15.6306 | −0.550565 | ||||||||
\(807\) | −54.4855 | − | 31.4572i | −1.91798 | − | 1.10735i | ||||
\(808\) | −5.38705 | − | 9.33065i | −0.189516 | − | 0.328251i | ||||
\(809\) | −0.479900 | + | 0.277070i | −0.0168724 | + | 0.00974128i | −0.508412 | − | 0.861114i | \(-0.669767\pi\) |
0.491540 | + | 0.870855i | \(0.336434\pi\) | |||||||
\(810\) | 0.528802 | − | 5.90515i | 0.0185802 | − | 0.207486i | ||||
\(811\) | −46.7849 | −1.64284 | −0.821421 | − | 0.570323i | \(-0.806818\pi\) | ||||
−0.821421 | + | 0.570323i | \(0.806818\pi\) | |||||||
\(812\) | 6.30473 | − | 15.5451i | 0.221253 | − | 0.545527i | ||||
\(813\) | −12.2835 | −0.430800 | ||||||||
\(814\) | 1.08020 | + | 10.3843i | 0.0378610 | + | 0.363968i | ||||
\(815\) | −5.43913 | + | 7.73418i | −0.190525 | + | 0.270917i | ||||
\(816\) | −5.91517 | + | 3.41512i | −0.207072 | + | 0.119553i | ||||
\(817\) | −32.3462 | + | 56.0252i | −1.13165 | + | 1.96007i | ||||
\(818\) | −27.6190 | −0.965676 | ||||||||
\(819\) | −34.7992 | + | 4.84347i | −1.21598 | + | 0.169245i | ||||
\(820\) | −7.27727 | + | 3.37535i | −0.254133 | + | 0.117872i | ||||
\(821\) | −44.1456 | − | 25.4875i | −1.54069 | − | 0.889518i | −0.998795 | − | 0.0490725i | \(-0.984373\pi\) |
−0.541896 | − | 0.840446i | \(-0.682293\pi\) | |||||||
\(822\) | 38.5949 | − | 22.2828i | 1.34615 | − | 0.777202i | ||||
\(823\) | 40.3221 | − | 23.2800i | 1.40554 | − | 0.811489i | 0.410586 | − | 0.911822i | \(-0.365324\pi\) |
0.994954 | + | 0.100333i | \(0.0319908\pi\) | |||||||
\(824\) | −2.19620 | + | 3.80394i | −0.0765084 | + | 0.132516i | ||||
\(825\) | 47.6607 | + | 3.57994i | 1.65933 | + | 0.124637i | ||||
\(826\) | −6.07074 | − | 7.79155i | −0.211228 | − | 0.271103i | ||||
\(827\) | −38.2998 | −1.33182 | −0.665908 | − | 0.746034i | \(-0.731956\pi\) | ||||
−0.665908 | + | 0.746034i | \(0.731956\pi\) | |||||||
\(828\) | 17.5987 | + | 10.1606i | 0.611596 | + | 0.353105i | ||||
\(829\) | −36.5937 | + | 21.1274i | −1.27095 | + | 0.733784i | −0.975167 | − | 0.221471i | \(-0.928914\pi\) |
−0.295784 | + | 0.955255i | \(0.595581\pi\) | |||||||
\(830\) | 6.24348 | − | 8.87792i | 0.216714 | − | 0.308157i | ||||
\(831\) | 20.5716 | − | 35.6311i | 0.713621 | − | 1.23603i | ||||
\(832\) | 9.71049i | 0.336651i | ||||||||
\(833\) | −10.4548 | − | 36.8299i | −0.362236 | − | 1.27608i | ||||
\(834\) | −31.7811 | −1.10049 | ||||||||
\(835\) | 1.53824 | + | 0.137748i | 0.0532328 | + | 0.00476696i | ||||
\(836\) | 9.67571 | − | 21.6696i | 0.334641 | − | 0.749458i | ||||
\(837\) | −43.9684 | + | 25.3852i | −1.51977 | + | 0.877440i | ||||
\(838\) | 12.2897 | + | 7.09544i | 0.424540 | + | 0.245108i | ||||
\(839\) | 3.52229i | 0.121603i | 0.998150 | + | 0.0608016i | \(0.0193657\pi\) | ||||
−0.998150 | + | 0.0608016i | \(0.980634\pi\) | |||||||
\(840\) | −21.2305 | + | 41.3218i | −0.732523 | + | 1.42574i | ||||
\(841\) | 6.30619 | 0.217455 | ||||||||
\(842\) | 13.6332 | − | 23.6135i | 0.469832 | − | 0.813774i | ||||
\(843\) | 57.6295 | − | 33.2724i | 1.98486 | − | 1.14596i | ||||
\(844\) | 13.4018 | − | 7.73751i | 0.461307 | − | 0.266336i | ||||
\(845\) | 1.34383 | − | 15.0066i | 0.0462292 | − | 0.516243i | ||||
\(846\) | −34.6742 | −1.19212 | ||||||||
\(847\) | −28.6434 | − | 5.15317i | −0.984199 | − | 0.177065i | ||||
\(848\) | 4.12664i | 0.141709i | ||||||||
\(849\) | −5.86279 | − | 3.38488i | −0.201210 | − | 0.116169i | ||||
\(850\) | 3.97425 | − | 22.0124i | 0.136316 | − | 0.755017i | ||||
\(851\) | 5.53623 | + | 9.58902i | 0.189779 | + | 0.328708i | ||||
\(852\) | 8.03718 | − | 13.9208i | 0.275349 | − | 0.476919i | ||||
\(853\) | − | 19.6762i | − | 0.673701i | −0.941558 | − | 0.336851i | \(-0.890638\pi\) | ||
0.941558 | − | 0.336851i | \(-0.109362\pi\) | |||||||
\(854\) | −9.45309 | − | 3.83394i | −0.323478 | − | 0.131195i | ||||
\(855\) | −57.8729 | + | 26.8427i | −1.97921 | + | 0.918000i | ||||
\(856\) | −5.05911 | + | 8.76264i | −0.172917 | + | 0.299501i | ||||
\(857\) | −3.48466 | + | 2.01187i | −0.119034 | + | 0.0687241i | −0.558335 | − | 0.829616i | \(-0.688559\pi\) |
0.439301 | + | 0.898340i | \(0.355226\pi\) | |||||||
\(858\) | 17.8658 | + | 7.97728i | 0.609929 | + | 0.272340i | ||||
\(859\) | 35.0908 | + | 20.2597i | 1.19728 | + | 0.691251i | 0.959948 | − | 0.280177i | \(-0.0903933\pi\) |
0.237333 | + | 0.971428i | \(0.423727\pi\) | |||||||
\(860\) | 32.4874 | − | 15.0683i | 1.10781 | − | 0.513826i | ||||
\(861\) | −19.0472 | − | 7.72510i | −0.649128 | − | 0.263271i | ||||
\(862\) | − | 14.2187i | − | 0.484292i | ||||||
\(863\) | −22.7296 | − | 13.1229i | −0.773724 | − | 0.446710i | 0.0604773 | − | 0.998170i | \(-0.480738\pi\) |
−0.834202 | + | 0.551460i | \(0.814071\pi\) | |||||||
\(864\) | 19.2924 | + | 33.4154i | 0.656341 | + | 1.13682i | ||||
\(865\) | −2.16102 | + | 3.07287i | −0.0734769 | + | 0.104481i | ||||
\(866\) | −0.239042 | + | 0.414032i | −0.00812296 | + | 0.0140694i | ||||
\(867\) | 37.2175 | 1.26397 | ||||||||
\(868\) | 26.6337 | − | 3.70697i | 0.904006 | − | 0.125823i | ||||
\(869\) | −5.15876 | + | 3.73963i | −0.174999 | + | 0.126858i | ||||
\(870\) | 25.0122 | + | 2.23982i | 0.847993 | + | 0.0759371i | ||||
\(871\) | 5.94879 | + | 10.3036i | 0.201567 | + | 0.349124i | ||||
\(872\) | −34.6810 | + | 20.0231i | −1.17445 | + | 0.678068i | ||||
\(873\) | 43.2042 | − | 74.8319i | 1.46224 | − | 2.53268i | ||||
\(874\) | 12.6521i | 0.427963i | ||||||||
\(875\) | 11.3544 | + | 27.3144i | 0.383849 | + | 0.923396i | ||||
\(876\) | − | 45.6646i | − | 1.54286i | ||||||
\(877\) | 10.7439 | − | 18.6089i | 0.362795 | − | 0.628379i | −0.625625 | − | 0.780124i | \(-0.715156\pi\) |
0.988420 | + | 0.151745i | \(0.0484893\pi\) | |||||||
\(878\) | 7.22531 | + | 12.5146i | 0.243842 | + | 0.422347i | ||||
\(879\) | −15.3217 | + | 8.84599i | −0.516788 | + | 0.298368i | ||||
\(880\) | −2.75960 | + | 1.64646i | −0.0930262 | + | 0.0555022i | ||||
\(881\) | − | 23.3214i | − | 0.785718i | −0.919599 | − | 0.392859i | \(-0.871486\pi\) | ||
0.919599 | − | 0.392859i | \(-0.128514\pi\) | |||||||
\(882\) | −29.2302 | + | 8.29745i | −0.984231 | + | 0.279390i | ||||
\(883\) | − | 46.6256i | − | 1.56908i | −0.620081 | − | 0.784538i | \(-0.712900\pi\) | ||
0.620081 | − | 0.784538i | \(-0.287100\pi\) | |||||||
\(884\) | −9.10787 | + | 15.7753i | −0.306331 | + | 0.530580i | ||||
\(885\) | −16.9207 | + | 24.0604i | −0.568783 | + | 0.808782i | ||||
\(886\) | 11.9995 | − | 6.92791i | 0.403131 | − | 0.232748i | ||||
\(887\) | 20.8582 | + | 12.0425i | 0.700349 | + | 0.404347i | 0.807477 | − | 0.589899i | \(-0.200832\pi\) |
−0.107128 | + | 0.994245i | \(0.534166\pi\) | |||||||
\(888\) | 30.2204i | 1.01413i | ||||||||
\(889\) | −8.18732 | + | 6.37910i | −0.274594 | + | 0.213948i | ||||
\(890\) | −3.39039 | − | 7.30971i | −0.113646 | − | 0.245022i | ||||
\(891\) | 10.6932 | − | 1.11234i | 0.358236 | − | 0.0372648i | ||||
\(892\) | 5.69713 | + | 9.86771i | 0.190754 | + | 0.330395i | ||||
\(893\) | 21.4727 | + | 37.1918i | 0.718556 | + | 1.24458i | ||||
\(894\) | 18.6320 | + | 10.7572i | 0.623147 | + | 0.359774i | ||||
\(895\) | −5.29816 | + | 2.45740i | −0.177098 | + | 0.0821418i | ||||
\(896\) | −3.07579 | − | 22.0988i | −0.102755 | − | 0.738269i | ||||
\(897\) | 20.7506 | 0.692843 | ||||||||
\(898\) | −8.30974 | + | 14.3929i | −0.277300 | + | 0.480297i | ||||
\(899\) | −18.1892 | − | 31.5045i | −0.606642 | − | 1.05074i | ||||
\(900\) | 34.7532 | + | 6.27457i | 1.15844 | + | 0.209152i | ||||
\(901\) | 26.0440 | − | 45.1095i | 0.867652 | − | 1.50282i | ||||
\(902\) | 4.29182 | + | 5.92049i | 0.142902 | + | 0.197131i | ||||
\(903\) | 85.0313 | + | 34.4866i | 2.82966 | + | 1.14764i | ||||
\(904\) | − | 15.8949i | − | 0.528655i | ||||||
\(905\) | 35.5951 | + | 3.18751i | 1.18322 | + | 0.105957i | ||||
\(906\) | 15.0525 | − | 8.69058i | 0.500087 | − | 0.288725i | ||||
\(907\) | 27.9508 | − | 16.1374i | 0.928090 | − | 0.535833i | 0.0418827 | − | 0.999123i | \(-0.486664\pi\) |
0.886207 | + | 0.463290i | \(0.153331\pi\) | |||||||
\(908\) | −13.3698 | − | 7.71908i | −0.443694 | − | 0.256167i | ||||
\(909\) | −20.9852 | −0.696035 | ||||||||
\(910\) | 0.592927 | + | 12.0948i | 0.0196553 | + | 0.400940i | ||||
\(911\) | −6.54639 | −0.216892 | −0.108446 | − | 0.994102i | \(-0.534587\pi\) | ||||
−0.108446 | + | 0.994102i | \(0.534587\pi\) | |||||||
\(912\) | 3.35697 | − | 5.81444i | 0.111160 | − | 0.192535i | ||||
\(913\) | 17.9710 | + | 8.02426i | 0.594754 | + | 0.265564i | ||||
\(914\) | −6.10514 | − | 10.5744i | −0.201940 | − | 0.349771i | ||||
\(915\) | −2.70951 | + | 30.2572i | −0.0895736 | + | 1.00027i | ||||
\(916\) | − | 25.7491i | − | 0.850775i | ||||||
\(917\) | 0.0163041 | + | 0.117141i | 0.000538408 | + | 0.00386833i | ||||
\(918\) | − | 29.7429i | − | 0.981661i | ||||||
\(919\) | −44.9307 | − | 25.9407i | −1.48213 | − | 0.855706i | −0.482331 | − | 0.875989i | \(-0.660210\pi\) |
−0.999794 | + | 0.0202831i | \(0.993543\pi\) | |||||||
\(920\) | 10.0832 | − | 14.3378i | 0.332434 | − | 0.472705i | ||||
\(921\) | 17.9581 | − | 10.3681i | 0.591738 | − | 0.341640i | ||||
\(922\) | −2.58143 | + | 4.47116i | −0.0850147 | + | 0.147250i | ||||
\(923\) | − | 10.4861i | − | 0.345154i | ||||||
\(924\) | −32.3342 | − | 9.35577i | −1.06372 | − | 0.307782i | ||||
\(925\) | 14.6897 | + | 12.4288i | 0.482994 | + | 0.408657i | ||||
\(926\) | 24.6754 | + | 14.2464i | 0.810885 | + | 0.468165i | ||||
\(927\) | 4.27764 | + | 7.40910i | 0.140496 | + | 0.243347i | ||||
\(928\) | −23.9430 | + | 13.8235i | −0.785969 | + | 0.453779i | ||||
\(929\) | 6.50895 | + | 3.75795i | 0.213552 | + | 0.123294i | 0.602961 | − | 0.797771i | \(-0.293987\pi\) |
−0.389409 | + | 0.921065i | \(0.627321\pi\) | |||||||
\(930\) | 16.9379 | + | 36.5182i | 0.555416 | + | 1.19748i | ||||
\(931\) | 27.0012 | + | 26.2141i | 0.884930 | + | 0.859132i | ||||
\(932\) | 38.4129 | 1.25826 | ||||||||
\(933\) | 7.35089 | + | 4.24404i | 0.240657 | + | 0.138944i | ||||
\(934\) | 1.71907 | + | 2.97752i | 0.0562497 | + | 0.0974273i | ||||
\(935\) | 40.5572 | − | 0.581587i | 1.32636 | − | 0.0190199i | ||||
\(936\) | 31.3340 | + | 18.0907i | 1.02418 | + | 0.591313i | ||||
\(937\) | − | 14.0976i | − | 0.460548i | −0.973126 | − | 0.230274i | \(-0.926038\pi\) | ||
0.973126 | − | 0.230274i | \(-0.0739623\pi\) | |||||||
\(938\) | 6.32388 | + | 8.11644i | 0.206482 | + | 0.265011i | ||||
\(939\) | 47.5118 | 1.55049 | ||||||||
\(940\) | 2.12040 | − | 23.6786i | 0.0691598 | − | 0.772310i | ||||
\(941\) | 29.8070 | + | 51.6272i | 0.971680 | + | 1.68300i | 0.690481 | + | 0.723350i | \(0.257399\pi\) |
0.281199 | + | 0.959650i | \(0.409268\pi\) | |||||||
\(942\) | −9.88900 | − | 17.1282i | −0.322201 | − | 0.558068i | ||||
\(943\) | 6.71622 | + | 3.87761i | 0.218710 | + | 0.126272i | ||||
\(944\) | − | 1.97765i | − | 0.0643671i | ||||||
\(945\) | 21.3107 | + | 33.0594i | 0.693237 | + | 1.07542i | ||||
\(946\) | −19.1597 | − | 26.4304i | −0.622934 | − | 0.859327i | ||||
\(947\) | 32.5177 | + | 18.7741i | 1.05668 | + | 0.610076i | 0.924513 | − | 0.381151i | \(-0.124472\pi\) |
0.132169 | + | 0.991227i | \(0.457806\pi\) | |||||||
\(948\) | −6.38206 | + | 3.68468i | −0.207280 | + | 0.119673i | ||||
\(949\) | −14.8946 | − | 25.7982i | −0.483500 | − | 0.837446i | ||||
\(950\) | 7.43556 | + | 20.6919i | 0.241241 | + | 0.671334i | ||||
\(951\) | 30.1961i | 0.979174i | ||||||||
\(952\) | −14.8177 | + | 36.5351i | −0.480246 | + | 1.18411i | ||||
\(953\) | −48.2083 | −1.56162 | −0.780810 | − | 0.624769i | \(-0.785193\pi\) | ||||
−0.780810 | + | 0.624769i | \(0.785193\pi\) | |||||||
\(954\) | −35.8014 | − | 20.6699i | −1.15911 | − | 0.669213i | ||||
\(955\) | −8.59531 | − | 6.04473i | −0.278138 | − | 0.195603i | ||||
\(956\) | −30.7617 | + | 17.7603i | −0.994906 | + | 0.574409i | ||||
\(957\) | 4.71148 | + | 45.2928i | 0.152301 | + | 1.46411i | ||||
\(958\) | −9.62655 | −0.311020 | ||||||||
\(959\) | −18.7977 | + | 46.3482i | −0.607010 | + | 1.49666i | ||||
\(960\) | 22.6869 | − | 10.5226i | 0.732216 | − | 0.339617i | ||||
\(961\) | 13.6573 | − | 23.6552i | 0.440559 | − | 0.763070i | ||||
\(962\) | 3.93860 | + | 6.82186i | 0.126986 | + | 0.219946i | ||||
\(963\) | 9.85386 | + | 17.0674i | 0.317536 | + | 0.549989i | ||||
\(964\) | −11.7976 | + | 20.4340i | −0.379974 | + | 0.658135i | ||||
\(965\) | −4.93399 | + | 2.28849i | −0.158831 | + | 0.0736691i | ||||
\(966\) | 17.7742 | − | 2.47387i | 0.571874 | − | 0.0795954i | ||||
\(967\) | −20.8217 | −0.669579 | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(968\) | 20.0064 | + | 22.3151i | 0.643029 | + | 0.717236i | ||||
\(969\) | −73.3920 | + | 42.3729i | −2.35769 | + | 1.36121i | ||||
\(970\) | −24.3603 | − | 17.1316i | −0.782163 | − | 0.550063i | ||||
\(971\) | −4.04418 | − | 2.33491i | −0.129784 | − | 0.0749307i | 0.433702 | − | 0.901056i | \(-0.357207\pi\) |
−0.563486 | + | 0.826125i | \(0.690540\pi\) | |||||||
\(972\) | −14.1118 | −0.452635 | ||||||||
\(973\) | 28.1354 | − | 21.9216i | 0.901981 | − | 0.702773i | ||||
\(974\) | 9.94260i | 0.318581i | ||||||||
\(975\) | 33.9368 | − | 12.1950i | 1.08685 | − | 0.390554i | ||||
\(976\) | −1.02122 | − | 1.76881i | −0.0326886 | − | 0.0566183i | ||||
\(977\) | 3.20589 | − | 1.85092i | 0.102565 | − | 0.0592162i | −0.447840 | − | 0.894114i | \(-0.647807\pi\) |
0.550405 | + | 0.834898i | \(0.314473\pi\) | |||||||
\(978\) | 8.63308 | + | 4.98431i | 0.276056 | + | 0.159381i | ||||
\(979\) | 11.8300 | − | 8.57571i | 0.378090 | − | 0.274081i | ||||
\(980\) | −3.87874 | − | 20.4683i | −0.123902 | − | 0.653836i | ||||
\(981\) | 77.9998i | 2.49034i | ||||||||
\(982\) | −14.5051 | − | 8.37451i | −0.462875 | − | 0.267241i | ||||
\(983\) | 22.1124 | + | 38.2999i | 0.705277 | + | 1.22158i | 0.966591 | + | 0.256322i | \(0.0825107\pi\) |
−0.261315 | + | 0.965254i | \(0.584156\pi\) | |||||||
\(984\) | 10.5833 | + | 18.3308i | 0.337382 | + | 0.584363i | ||||
\(985\) | −0.872618 | + | 9.74455i | −0.0278039 | + | 0.310487i | ||||
\(986\) | 21.3116 | 0.678699 | ||||||||
\(987\) | 48.0500 | − | 37.4379i | 1.52945 | − | 1.19166i | ||||
\(988\) | − | 17.9055i | − | 0.569651i | ||||||
\(989\) | −29.9827 | − | 17.3105i | −0.953395 | − | 0.550443i | ||||
\(990\) | −0.461579 | − | 32.1883i | −0.0146699 | − | 1.02301i | ||||
\(991\) | 19.8299 | + | 34.3463i | 0.629916 | + | 1.09105i | 0.987568 | + | 0.157192i | \(0.0502441\pi\) |
−0.357652 | + | 0.933855i | \(0.616423\pi\) | |||||||
\(992\) | −38.3808 | − | 22.1592i | −1.21859 | − | 0.703555i | ||||
\(993\) | −13.0491 | −0.414100 | ||||||||
\(994\) | −1.25014 | − | 8.98196i | −0.0396521 | − | 0.284891i | ||||
\(995\) | 12.1218 | + | 26.1346i | 0.384286 | + | 0.828523i | ||||
\(996\) | 19.7133 | + | 11.3815i | 0.624641 | + | 0.360637i | ||||
\(997\) | −23.3948 | + | 13.5070i | −0.740920 | + | 0.427770i | −0.822404 | − | 0.568904i | \(-0.807367\pi\) |
0.0814837 | + | 0.996675i | \(0.474034\pi\) | |||||||
\(998\) | 4.84735 | + | 8.39586i | 0.153440 | + | 0.265766i | ||||
\(999\) | 22.1583 | + | 12.7931i | 0.701058 | + | 0.404756i |
(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 | 385.2.o.b.54.14 | yes | 72 | |
5.4 | even | 2 | inner | 385.2.o.b.54.23 | yes | 72 | |
7.3 | odd | 6 | inner | 385.2.o.b.164.13 | yes | 72 | |
11.10 | odd | 2 | inner | 385.2.o.b.54.24 | yes | 72 | |
35.24 | odd | 6 | inner | 385.2.o.b.164.24 | yes | 72 | |
55.54 | odd | 2 | inner | 385.2.o.b.54.13 | ✓ | 72 | |
77.10 | even | 6 | inner | 385.2.o.b.164.23 | yes | 72 | |
385.164 | even | 6 | inner | 385.2.o.b.164.14 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
385.2.o.b.54.13 | ✓ | 72 | 55.54 | odd | 2 | inner | |
385.2.o.b.54.14 | yes | 72 | 1.1 | even | 1 | trivial | |
385.2.o.b.54.23 | yes | 72 | 5.4 | even | 2 | inner | |
385.2.o.b.54.24 | yes | 72 | 11.10 | odd | 2 | inner | |
385.2.o.b.164.13 | yes | 72 | 7.3 | odd | 6 | inner | |
385.2.o.b.164.14 | yes | 72 | 385.164 | even | 6 | inner | |
385.2.o.b.164.23 | yes | 72 | 77.10 | even | 6 | inner | |
385.2.o.b.164.24 | yes | 72 | 35.24 | odd | 6 | inner |