Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [425,2,Mod(49,425)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(425, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("425.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 425 = 5^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 425.n (of order \(8\), degree \(4\), not 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: | \(3.39364208590\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{8})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 399.3 | ||
Character | \(\chi\) | \(=\) | 425.399 |
Dual form | 425.2.n.e.49.3 |
$q$-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 \(\left(\mathbb{Z}/425\mathbb{Z}\right)^\times\).
\(n\) | \(52\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{8}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.639117 | − | 0.639117i | −0.451924 | − | 0.451924i | 0.444069 | − | 0.895993i | \(-0.353535\pi\) |
−0.895993 | + | 0.444069i | \(0.853535\pi\) | |||||||
\(3\) | 2.66226 | + | 1.10274i | 1.53706 | + | 0.636670i | 0.980918 | − | 0.194420i | \(-0.0622824\pi\) |
0.556139 | + | 0.831090i | \(0.312282\pi\) | |||||||
\(4\) | − | 1.18306i | − | 0.591530i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.996713 | − | 2.40628i | −0.406906 | − | 0.982359i | ||||
\(7\) | −0.278207 | − | 0.671652i | −0.105152 | − | 0.253861i | 0.862542 | − | 0.505985i | \(-0.168871\pi\) |
−0.967695 | + | 0.252124i | \(0.918871\pi\) | |||||||
\(8\) | −2.03435 | + | 2.03435i | −0.719250 | + | 0.719250i | ||||
\(9\) | 3.75027 | + | 3.75027i | 1.25009 | + | 1.25009i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.958080 | − | 2.31301i | −0.288872 | − | 0.697399i | 0.711112 | − | 0.703079i | \(-0.248192\pi\) |
−0.999984 | + | 0.00567999i | \(0.998192\pi\) | |||||||
\(12\) | 1.30461 | − | 3.14961i | 0.376609 | − | 0.909215i | ||||
\(13\) | 6.29663 | 1.74637 | 0.873186 | − | 0.487388i | \(-0.162050\pi\) | ||||
0.873186 | + | 0.487388i | \(0.162050\pi\) | |||||||
\(14\) | −0.251457 | + | 0.607071i | −0.0672047 | + | 0.162247i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.234252 | 0.0585630 | ||||||||
\(17\) | 3.55925 | − | 2.08128i | 0.863245 | − | 0.504785i | ||||
\(18\) | − | 4.79372i | − | 1.12989i | ||||||
\(19\) | 0.143443 | − | 0.143443i | 0.0329081 | − | 0.0329081i | −0.690461 | − | 0.723369i | \(-0.742592\pi\) |
0.723369 | + | 0.690461i | \(0.242592\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.09490i | − | 0.457146i | ||||||
\(22\) | −0.865959 | + | 2.09061i | −0.184623 | + | 0.445719i | ||||
\(23\) | 0.616148 | − | 0.255217i | 0.128476 | − | 0.0532164i | −0.317519 | − | 0.948252i | \(-0.602850\pi\) |
0.445995 | + | 0.895035i | \(0.352850\pi\) | |||||||
\(24\) | −7.65933 | + | 3.17260i | −1.56345 | + | 0.647604i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.02428 | − | 4.02428i | −0.789227 | − | 0.789227i | ||||
\(27\) | 2.54037 | + | 6.13299i | 0.488894 | + | 1.18030i | ||||
\(28\) | −0.794604 | + | 0.329136i | −0.150166 | + | 0.0622008i | ||||
\(29\) | −7.33161 | − | 3.03685i | −1.36145 | − | 0.563929i | −0.421990 | − | 0.906600i | \(-0.638668\pi\) |
−0.939455 | + | 0.342671i | \(0.888668\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.12864 | + | 5.13900i | −0.382315 | + | 0.922991i | 0.609202 | + | 0.793015i | \(0.291490\pi\) |
−0.991517 | + | 0.129976i | \(0.958510\pi\) | |||||||
\(32\) | 3.91898 | + | 3.91898i | 0.692784 | + | 0.692784i | ||||
\(33\) | − | 7.21436i | − | 1.25586i | ||||||
\(34\) | −3.60496 | − | 0.944595i | −0.618245 | − | 0.161997i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.43679 | − | 4.43679i | 0.739465 | − | 0.739465i | ||||
\(37\) | 7.34010 | + | 3.04037i | 1.20670 | + | 0.499834i | 0.893160 | − | 0.449740i | \(-0.148483\pi\) |
0.313545 | + | 0.949573i | \(0.398483\pi\) | |||||||
\(38\) | −0.183354 | −0.0297439 | ||||||||
\(39\) | 16.7633 | + | 6.94358i | 2.68427 | + | 1.11186i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.73632 | + | 1.96185i | −0.739688 | + | 0.306389i | −0.720526 | − | 0.693427i | \(-0.756100\pi\) |
−0.0191619 | + | 0.999816i | \(0.506100\pi\) | |||||||
\(42\) | −1.33889 | + | 1.33889i | −0.206595 | + | 0.206595i | ||||
\(43\) | −8.45426 | + | 8.45426i | −1.28926 | + | 1.28926i | −0.354028 | + | 0.935235i | \(0.615188\pi\) |
−0.935235 | + | 0.354028i | \(0.884812\pi\) | |||||||
\(44\) | −2.73643 | + | 1.13347i | −0.412532 | + | 0.170876i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.556904 | − | 0.230677i | −0.0821110 | − | 0.0340115i | ||||
\(47\) | −10.9207 | −1.59294 | −0.796472 | − | 0.604675i | \(-0.793303\pi\) | ||||
−0.796472 | + | 0.604675i | \(0.793303\pi\) | |||||||
\(48\) | 0.623640 | + | 0.258320i | 0.0900147 | + | 0.0372853i | ||||
\(49\) | 4.57603 | − | 4.57603i | 0.653719 | − | 0.653719i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 11.7708 | − | 1.61597i | 1.64824 | − | 0.226281i | ||||
\(52\) | − | 7.44929i | − | 1.03303i | ||||||
\(53\) | −2.74061 | − | 2.74061i | −0.376451 | − | 0.376451i | 0.493369 | − | 0.869820i | \(-0.335765\pi\) |
−0.869820 | + | 0.493369i | \(0.835765\pi\) | |||||||
\(54\) | 2.29611 | − | 5.54329i | 0.312461 | − | 0.754347i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.93234 | + | 0.800403i | 0.258220 | + | 0.106958i | ||||
\(57\) | 0.540065 | − | 0.223702i | 0.0715333 | − | 0.0296301i | ||||
\(58\) | 2.74485 | + | 6.62666i | 0.360417 | + | 0.870123i | ||||
\(59\) | 2.38470 | + | 2.38470i | 0.310462 | + | 0.310462i | 0.845088 | − | 0.534626i | \(-0.179548\pi\) |
−0.534626 | + | 0.845088i | \(0.679548\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.04828 | + | 0.434212i | −0.134219 | + | 0.0555952i | −0.448782 | − | 0.893641i | \(-0.648142\pi\) |
0.314563 | + | 0.949237i | \(0.398142\pi\) | |||||||
\(62\) | 4.64487 | − | 1.92397i | 0.589899 | − | 0.244344i | ||||
\(63\) | 1.47552 | − | 3.56223i | 0.185898 | − | 0.448798i | ||||
\(64\) | − | 5.47788i | − | 0.684734i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.61082 | + | 4.61082i | −0.567552 | + | 0.567552i | ||||
\(67\) | − | 5.61946i | − | 0.686526i | −0.939239 | − | 0.343263i | \(-0.888468\pi\) | ||
0.939239 | − | 0.343263i | \(-0.111532\pi\) | |||||||
\(68\) | −2.46228 | − | 4.21081i | −0.298595 | − | 0.510635i | ||||
\(69\) | 1.92179 | 0.231356 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.51683 | + | 3.66196i | −0.180015 | + | 0.434595i | −0.987969 | − | 0.154650i | \(-0.950575\pi\) |
0.807954 | + | 0.589245i | \(0.200575\pi\) | |||||||
\(72\) | −15.2587 | −1.79825 | ||||||||
\(73\) | −1.98578 | + | 4.79409i | −0.232417 | + | 0.561105i | −0.996461 | − | 0.0840596i | \(-0.973211\pi\) |
0.764043 | + | 0.645165i | \(0.223211\pi\) | |||||||
\(74\) | −2.74803 | − | 6.63433i | −0.319452 | − | 0.771225i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.169702 | − | 0.169702i | −0.0194661 | − | 0.0194661i | ||||
\(77\) | −1.28699 | + | 1.28699i | −0.146666 | + | 0.146666i | ||||
\(78\) | −6.27594 | − | 15.1514i | −0.710610 | − | 1.71556i | ||||
\(79\) | −5.37312 | − | 12.9718i | −0.604523 | − | 1.45945i | −0.868880 | − | 0.495022i | \(-0.835160\pi\) |
0.264358 | − | 0.964425i | \(-0.414840\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.21797i | 0.357552i | ||||||||
\(82\) | 4.28091 | + | 1.77321i | 0.472747 | + | 0.195818i | ||||
\(83\) | 8.73235 | + | 8.73235i | 0.958500 | + | 0.958500i | 0.999173 | − | 0.0406730i | \(-0.0129502\pi\) |
−0.0406730 | + | 0.999173i | \(0.512950\pi\) | |||||||
\(84\) | −2.47840 | −0.270415 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 10.8065 | 1.16530 | ||||||||
\(87\) | −16.1698 | − | 16.1698i | −1.73358 | − | 1.73358i | ||||
\(88\) | 6.65453 | + | 2.75640i | 0.709376 | + | 0.293833i | ||||
\(89\) | 13.0419i | 1.38244i | 0.722644 | + | 0.691221i | \(0.242927\pi\) | ||||
−0.722644 | + | 0.691221i | \(0.757073\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.75177 | − | 4.22914i | −0.183635 | − | 0.443335i | ||||
\(92\) | −0.301937 | − | 0.728940i | −0.0314791 | − | 0.0759972i | ||||
\(93\) | −11.3340 | + | 11.3340i | −1.17528 | + | 1.17528i | ||||
\(94\) | 6.97959 | + | 6.97959i | 0.719890 | + | 0.719890i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 6.11171 | + | 14.7550i | 0.623774 | + | 1.50592i | ||||
\(97\) | −4.56330 | + | 11.0168i | −0.463333 | + | 1.11858i | 0.503688 | + | 0.863886i | \(0.331976\pi\) |
−0.967020 | + | 0.254699i | \(0.918024\pi\) | |||||||
\(98\) | −5.84924 | −0.590862 | ||||||||
\(99\) | 5.08135 | − | 12.2675i | 0.510695 | − | 1.23293i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.0642 | −1.00143 | −0.500713 | − | 0.865613i | \(-0.666929\pi\) | ||||
−0.500713 | + | 0.865613i | \(0.666929\pi\) | |||||||
\(102\) | −8.55569 | − | 6.49011i | −0.847140 | − | 0.642617i | ||||
\(103\) | 9.80719i | 0.966331i | 0.875529 | + | 0.483166i | \(0.160513\pi\) | ||||
−0.875529 | + | 0.483166i | \(0.839487\pi\) | |||||||
\(104\) | −12.8095 | + | 12.8095i | −1.25608 | + | 1.25608i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.50314i | 0.340255i | ||||||||
\(107\) | −1.45993 | + | 3.52458i | −0.141137 | + | 0.340734i | −0.978604 | − | 0.205754i | \(-0.934035\pi\) |
0.837467 | + | 0.546488i | \(0.184035\pi\) | |||||||
\(108\) | 7.25570 | − | 3.00541i | 0.698180 | − | 0.289195i | ||||
\(109\) | 2.96319 | − | 1.22739i | 0.283822 | − | 0.117563i | −0.236231 | − | 0.971697i | \(-0.575912\pi\) |
0.520053 | + | 0.854134i | \(0.325912\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.1885 | + | 16.1885i | 1.53655 | + | 1.53655i | ||||
\(112\) | −0.0651706 | − | 0.157336i | −0.00615805 | − | 0.0148668i | ||||
\(113\) | 0.372584 | − | 0.154329i | 0.0350498 | − | 0.0145181i | −0.365090 | − | 0.930972i | \(-0.618962\pi\) |
0.400139 | + | 0.916454i | \(0.368962\pi\) | |||||||
\(114\) | −0.488136 | − | 0.202193i | −0.0457181 | − | 0.0189371i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.59278 | + | 8.67373i | −0.333581 | + | 0.805335i | ||||
\(117\) | 23.6141 | + | 23.6141i | 2.18312 | + | 2.18312i | ||||
\(118\) | − | 3.04821i | − | 0.280610i | ||||||
\(119\) | −2.38811 | − | 1.81155i | −0.218917 | − | 0.166065i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.34607 | − | 3.34607i | 0.304188 | − | 0.304188i | ||||
\(122\) | 0.947487 | + | 0.392462i | 0.0857814 | + | 0.0355318i | ||||
\(123\) | −14.7727 | −1.33201 | ||||||||
\(124\) | 6.07974 | + | 2.51831i | 0.545976 | + | 0.226151i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −3.21971 | + | 1.33365i | −0.286835 | + | 0.118811i | ||||
\(127\) | 1.52815 | − | 1.52815i | 0.135601 | − | 0.135601i | −0.636048 | − | 0.771649i | \(-0.719432\pi\) |
0.771649 | + | 0.636048i | \(0.219432\pi\) | |||||||
\(128\) | 4.33696 | − | 4.33696i | 0.383336 | − | 0.383336i | ||||
\(129\) | −31.8303 | + | 13.1846i | −2.80251 | + | 1.16084i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.43241 | − | 3.07860i | −0.649372 | − | 0.268979i | 0.0335863 | − | 0.999436i | \(-0.489307\pi\) |
−0.682959 | + | 0.730457i | \(0.739307\pi\) | |||||||
\(132\) | −8.53501 | −0.742877 | ||||||||
\(133\) | −0.136251 | − | 0.0564370i | −0.0118144 | − | 0.00489371i | ||||
\(134\) | −3.59149 | + | 3.59149i | −0.310258 | + | 0.310258i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.00670 | + | 11.4748i | −0.257823 | + | 0.983956i | ||||
\(137\) | 7.87082i | 0.672450i | 0.941782 | + | 0.336225i | \(0.109150\pi\) | ||||
−0.941782 | + | 0.336225i | \(0.890850\pi\) | |||||||
\(138\) | −1.22825 | − | 1.22825i | −0.104555 | − | 0.104555i | ||||
\(139\) | 6.68268 | − | 16.1334i | 0.566818 | − | 1.36842i | −0.337405 | − | 0.941359i | \(-0.609549\pi\) |
0.904223 | − | 0.427060i | \(-0.140451\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.0737 | − | 12.0427i | −2.44845 | − | 1.01418i | ||||
\(142\) | 3.30986 | − | 1.37099i | 0.277757 | − | 0.115051i | ||||
\(143\) | −6.03268 | − | 14.5642i | −0.504478 | − | 1.21792i | ||||
\(144\) | 0.878508 | + | 0.878508i | 0.0732090 | + | 0.0732090i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.33312 | − | 1.79484i | 0.358612 | − | 0.148542i | ||||
\(147\) | 17.2288 | − | 7.13639i | 1.42101 | − | 0.588600i | ||||
\(148\) | 3.59694 | − | 8.68377i | 0.295666 | − | 0.713802i | ||||
\(149\) | − | 7.42906i | − | 0.608613i | −0.952574 | − | 0.304306i | \(-0.901575\pi\) | ||
0.952574 | − | 0.304306i | \(-0.0984246\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.55527 | + | 9.55527i | −0.777597 | + | 0.777597i | −0.979422 | − | 0.201825i | \(-0.935313\pi\) |
0.201825 | + | 0.979422i | \(0.435313\pi\) | |||||||
\(152\) | 0.583627i | 0.0473384i | ||||||||
\(153\) | 21.1535 | + | 5.54278i | 1.71016 | + | 0.448107i | ||||
\(154\) | 1.64508 | 0.132564 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 8.21466 | − | 19.8320i | 0.657699 | − | 1.58783i | ||||
\(157\) | −2.75786 | −0.220101 | −0.110051 | − | 0.993926i | \(-0.535101\pi\) | ||||
−0.110051 | + | 0.993926i | \(0.535101\pi\) | |||||||
\(158\) | −4.85648 | + | 11.7246i | −0.386361 | + | 0.932757i | ||||
\(159\) | −4.27402 | − | 10.3184i | −0.338952 | − | 0.818303i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.342834 | − | 0.342834i | −0.0270191 | − | 0.0270191i | ||||
\(162\) | 2.05666 | − | 2.05666i | 0.161586 | − | 0.161586i | ||||
\(163\) | −0.529525 | − | 1.27839i | −0.0414756 | − | 0.100131i | 0.901784 | − | 0.432187i | \(-0.142258\pi\) |
−0.943260 | + | 0.332056i | \(0.892258\pi\) | |||||||
\(164\) | 2.32098 | + | 5.60334i | 0.181238 | + | 0.437548i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 11.1620i | − | 0.866338i | ||||||
\(167\) | −13.5665 | − | 5.61942i | −1.04981 | − | 0.434844i | −0.209983 | − | 0.977705i | \(-0.567341\pi\) |
−0.839822 | + | 0.542861i | \(0.817341\pi\) | |||||||
\(168\) | 4.26176 | + | 4.26176i | 0.328802 | + | 0.328802i | ||||
\(169\) | 26.6476 | 2.04981 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.07590 | 0.0822762 | ||||||||
\(172\) | 10.0019 | + | 10.0019i | 0.762637 | + | 0.762637i | ||||
\(173\) | −13.6265 | − | 5.64428i | −1.03600 | − | 0.429127i | −0.201127 | − | 0.979565i | \(-0.564461\pi\) |
−0.834876 | + | 0.550439i | \(0.814461\pi\) | |||||||
\(174\) | 20.6688i | 1.56689i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.224432 | − | 0.541828i | −0.0169172 | − | 0.0408418i | ||||
\(177\) | 3.71899 | + | 8.97842i | 0.279536 | + | 0.674860i | ||||
\(178\) | 8.33531 | − | 8.33531i | 0.624758 | − | 0.624758i | ||||
\(179\) | 10.0949 | + | 10.0949i | 0.754531 | + | 0.754531i | 0.975321 | − | 0.220790i | \(-0.0708636\pi\) |
−0.220790 | + | 0.975321i | \(0.570864\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.30531 | + | 5.56552i | 0.171353 | + | 0.413682i | 0.986104 | − | 0.166129i | \(-0.0531267\pi\) |
−0.814752 | + | 0.579810i | \(0.803127\pi\) | |||||||
\(182\) | −1.58333 | + | 3.82250i | −0.117364 | + | 0.283343i | ||||
\(183\) | −3.26962 | −0.241698 | ||||||||
\(184\) | −0.734259 | + | 1.77266i | −0.0541303 | + | 0.130682i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 14.4875 | 1.06227 | ||||||||
\(187\) | −8.22408 | − | 6.23855i | −0.601404 | − | 0.456208i | ||||
\(188\) | 12.9198i | 0.942274i | ||||||||
\(189\) | 3.41249 | − | 3.41249i | 0.248222 | − | 0.248222i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 14.1379i | − | 1.02298i | −0.859288 | − | 0.511492i | \(-0.829093\pi\) | ||
0.859288 | − | 0.511492i | \(-0.170907\pi\) | |||||||
\(192\) | 6.04070 | − | 14.5835i | 0.435950 | − | 1.05248i | ||||
\(193\) | 21.5052 | − | 8.90773i | 1.54797 | − | 0.641192i | 0.565026 | − | 0.825073i | \(-0.308866\pi\) |
0.982949 | + | 0.183881i | \(0.0588661\pi\) | |||||||
\(194\) | 9.95749 | − | 4.12453i | 0.714906 | − | 0.296124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.41372 | − | 5.41372i | −0.386694 | − | 0.386694i | ||||
\(197\) | −3.55817 | − | 8.59019i | −0.253509 | − | 0.612026i | 0.744973 | − | 0.667094i | \(-0.232462\pi\) |
−0.998483 | + | 0.0550686i | \(0.982462\pi\) | |||||||
\(198\) | −11.0879 | + | 4.59277i | −0.787984 | + | 0.326394i | ||||
\(199\) | −6.98662 | − | 2.89395i | −0.495268 | − | 0.205147i | 0.121046 | − | 0.992647i | \(-0.461375\pi\) |
−0.616315 | + | 0.787500i | \(0.711375\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.19683 | − | 14.9605i | 0.437090 | − | 1.05523i | ||||
\(202\) | 6.43221 | + | 6.43221i | 0.452569 | + | 0.452569i | ||||
\(203\) | 5.76916i | 0.404916i | ||||||||
\(204\) | −1.91179 | − | 13.9255i | −0.133852 | − | 0.974982i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6.26794 | − | 6.26794i | 0.436708 | − | 0.436708i | ||||
\(207\) | 3.26785 | + | 1.35359i | 0.227131 | + | 0.0940809i | ||||
\(208\) | 1.47500 | 0.102273 | ||||||||
\(209\) | −0.469216 | − | 0.194356i | −0.0324563 | − | 0.0134439i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.0644 | − | 9.55359i | 1.58782 | − | 0.657697i | 0.598192 | − | 0.801353i | \(-0.295886\pi\) |
0.989628 | + | 0.143656i | \(0.0458859\pi\) | |||||||
\(212\) | −3.24230 | + | 3.24230i | −0.222682 | + | 0.222682i | ||||
\(213\) | −8.07642 | + | 8.07642i | −0.553387 | + | 0.553387i | ||||
\(214\) | 3.18568 | − | 1.31955i | 0.217769 | − | 0.0902028i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −17.6446 | − | 7.30864i | −1.20056 | − | 0.497290i | ||||
\(217\) | 4.04382 | 0.274512 | ||||||||
\(218\) | −2.67827 | − | 1.10938i | −0.181395 | − | 0.0751364i | ||||
\(219\) | −10.5733 | + | 10.5733i | −0.714478 | + | 0.714478i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.4113 | − | 13.1051i | 1.50755 | − | 0.881542i | ||||
\(222\) | − | 20.6927i | − | 1.38880i | ||||||
\(223\) | 8.60440 | + | 8.60440i | 0.576193 | + | 0.576193i | 0.933852 | − | 0.357659i | \(-0.116425\pi\) |
−0.357659 | + | 0.933852i | \(0.616425\pi\) | |||||||
\(224\) | 1.54190 | − | 3.72248i | 0.103023 | − | 0.248719i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.336759 | − | 0.139490i | −0.0224009 | − | 0.00927876i | ||||
\(227\) | −1.83530 | + | 0.760206i | −0.121813 | + | 0.0504566i | −0.442757 | − | 0.896641i | \(-0.646000\pi\) |
0.320944 | + | 0.947098i | \(0.396000\pi\) | |||||||
\(228\) | −0.264653 | − | 0.638928i | −0.0175271 | − | 0.0423141i | ||||
\(229\) | −1.62070 | − | 1.62070i | −0.107099 | − | 0.107099i | 0.651527 | − | 0.758626i | \(-0.274129\pi\) |
−0.758626 | + | 0.651527i | \(0.774129\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.84554 | + | 2.00709i | −0.318813 | + | 0.132057i | ||||
\(232\) | 21.0930 | − | 8.73703i | 1.38483 | − | 0.573614i | ||||
\(233\) | 8.68807 | − | 20.9749i | 0.569174 | − | 1.37411i | −0.333078 | − | 0.942899i | \(-0.608087\pi\) |
0.902252 | − | 0.431209i | \(-0.141913\pi\) | |||||||
\(234\) | − | 30.1843i | − | 1.97321i | ||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2.82125 | − | 2.82125i | 0.183647 | − | 0.183647i | ||||
\(237\) | − | 40.4596i | − | 2.62813i | ||||||
\(238\) | 0.368487 | + | 2.68407i | 0.0238854 | + | 0.173982i | ||||
\(239\) | −13.2285 | −0.855683 | −0.427841 | − | 0.903854i | \(-0.640726\pi\) | ||||
−0.427841 | + | 0.903854i | \(0.640726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.10950 | − | 2.67856i | 0.0714689 | − | 0.172541i | −0.884108 | − | 0.467282i | \(-0.845233\pi\) |
0.955577 | + | 0.294741i | \(0.0952333\pi\) | |||||||
\(242\) | −4.27706 | −0.274940 | ||||||||
\(243\) | 4.07251 | − | 9.83190i | 0.261251 | − | 0.630717i | ||||
\(244\) | 0.513699 | + | 1.24018i | 0.0328862 | + | 0.0793943i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.44150 | + | 9.44150i | 0.601968 | + | 0.601968i | ||||
\(247\) | 0.903209 | − | 0.903209i | 0.0574698 | − | 0.0574698i | ||||
\(248\) | −6.12410 | − | 14.7849i | −0.388881 | − | 0.938842i | ||||
\(249\) | 13.6182 | + | 32.8773i | 0.863021 | + | 2.08352i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.85445i | 0.622008i | 0.950409 | + | 0.311004i | \(0.100665\pi\) | ||||
−0.950409 | + | 0.311004i | \(0.899335\pi\) | |||||||
\(252\) | −4.21432 | − | 1.74563i | −0.265477 | − | 0.109964i | ||||
\(253\) | −1.18064 | − | 1.18064i | −0.0742261 | − | 0.0742261i | ||||
\(254\) | −1.95333 | −0.122563 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −16.4994 | −1.03121 | ||||||||
\(257\) | 3.74014 | + | 3.74014i | 0.233303 | + | 0.233303i | 0.814070 | − | 0.580767i | \(-0.197247\pi\) |
−0.580767 | + | 0.814070i | \(0.697247\pi\) | |||||||
\(258\) | 28.7698 | + | 11.9168i | 1.79113 | + | 0.741910i | ||||
\(259\) | − | 5.77584i | − | 0.358893i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −16.1065 | − | 38.8845i | −0.996967 | − | 2.40689i | ||||
\(262\) | 2.78259 | + | 6.71776i | 0.171909 | + | 0.415025i | ||||
\(263\) | 8.89552 | − | 8.89552i | 0.548521 | − | 0.548521i | −0.377492 | − | 0.926013i | \(-0.623213\pi\) |
0.926013 | + | 0.377492i | \(0.123213\pi\) | |||||||
\(264\) | 14.6765 | + | 14.6765i | 0.903276 | + | 0.903276i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.0510104 | + | 0.123150i | 0.00312765 | + | 0.00755081i | ||||
\(267\) | −14.3819 | + | 34.7210i | −0.880159 | + | 2.12489i | ||||
\(268\) | −6.64815 | −0.406101 | ||||||||
\(269\) | −3.52167 | + | 8.50207i | −0.214720 | + | 0.518380i | −0.994137 | − | 0.108125i | \(-0.965515\pi\) |
0.779417 | + | 0.626505i | \(0.215515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.6023 | −0.887028 | −0.443514 | − | 0.896267i | \(-0.646268\pi\) | ||||
−0.443514 | + | 0.896267i | \(0.646268\pi\) | |||||||
\(272\) | 0.833762 | − | 0.487545i | 0.0505543 | − | 0.0295617i | ||||
\(273\) | − | 13.1908i | − | 0.798346i | ||||||
\(274\) | 5.03038 | − | 5.03038i | 0.303896 | − | 0.303896i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 2.27359i | − | 0.136854i | ||||||
\(277\) | −5.00008 | + | 12.0713i | −0.300425 | + | 0.725291i | 0.699518 | + | 0.714615i | \(0.253398\pi\) |
−0.999943 | + | 0.0106758i | \(0.996602\pi\) | |||||||
\(278\) | −14.5822 | + | 6.04013i | −0.874580 | + | 0.362263i | ||||
\(279\) | −27.2556 | + | 11.2896i | −1.63175 | + | 0.675892i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.34654 | + | 5.34654i | 0.318948 | + | 0.318948i | 0.848363 | − | 0.529415i | \(-0.177589\pi\) |
−0.529415 | + | 0.848363i | \(0.677589\pi\) | |||||||
\(282\) | 10.8848 | + | 26.2782i | 0.648179 | + | 1.56484i | ||||
\(283\) | 3.80456 | − | 1.57590i | 0.226157 | − | 0.0936775i | −0.266727 | − | 0.963772i | \(-0.585942\pi\) |
0.492885 | + | 0.870095i | \(0.335942\pi\) | |||||||
\(284\) | 4.33232 | + | 1.79450i | 0.257076 | + | 0.106484i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.45262 | + | 13.1638i | −0.322420 | + | 0.778392i | ||||
\(287\) | 2.63536 | + | 2.63536i | 0.155560 | + | 0.155560i | ||||
\(288\) | 29.3944i | 1.73208i | ||||||||
\(289\) | 8.33654 | − | 14.8156i | 0.490385 | − | 0.871506i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.2974 | + | 24.2974i | −1.42434 | + | 1.42434i | ||||
\(292\) | 5.67169 | + | 2.34929i | 0.331911 | + | 0.137482i | ||||
\(293\) | 18.5803 | 1.08547 | 0.542736 | − | 0.839903i | \(-0.317388\pi\) | ||||
0.542736 | + | 0.839903i | \(0.317388\pi\) | |||||||
\(294\) | −15.5722 | − | 6.45021i | −0.908189 | − | 0.376184i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.1175 | + | 8.74714i | −1.22743 | + | 0.508417i | ||||
\(297\) | 11.7518 | − | 11.7518i | 0.681909 | − | 0.681909i | ||||
\(298\) | −4.74804 | + | 4.74804i | −0.275047 | + | 0.275047i | ||||
\(299\) | 3.87966 | − | 1.60701i | 0.224366 | − | 0.0929356i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.03036 | + | 3.32628i | 0.462862 | + | 0.191724i | ||||
\(302\) | 12.2139 | 0.702829 | ||||||||
\(303\) | −26.7936 | − | 11.0983i | −1.53925 | − | 0.637578i | ||||
\(304\) | 0.0336019 | − | 0.0336019i | 0.00192720 | − | 0.00192720i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.97708 | − | 17.0620i | −0.570351 | − | 0.975372i | ||||
\(307\) | 9.82624i | 0.560813i | 0.959881 | + | 0.280407i | \(0.0904693\pi\) | ||||
−0.959881 | + | 0.280407i | \(0.909531\pi\) | |||||||
\(308\) | 1.52259 | + | 1.52259i | 0.0867576 | + | 0.0867576i | ||||
\(309\) | −10.8148 | + | 26.1093i | −0.615234 | + | 1.48531i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.5045 | + | 10.9785i | 1.50293 | + | 0.622536i | 0.974086 | − | 0.226180i | \(-0.0726237\pi\) |
0.528849 | + | 0.848716i | \(0.322624\pi\) | |||||||
\(312\) | −48.2280 | + | 19.9767i | −2.73037 | + | 1.13096i | ||||
\(313\) | 0.370684 | + | 0.894911i | 0.0209523 | + | 0.0505834i | 0.934009 | − | 0.357248i | \(-0.116285\pi\) |
−0.913057 | + | 0.407832i | \(0.866285\pi\) | |||||||
\(314\) | 1.76259 | + | 1.76259i | 0.0994689 | + | 0.0994689i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.3465 | + | 6.35671i | −0.863306 | + | 0.357593i | ||||
\(317\) | 24.5058 | − | 10.1506i | 1.37638 | − | 0.570116i | 0.432870 | − | 0.901456i | \(-0.357501\pi\) |
0.943511 | + | 0.331341i | \(0.107501\pi\) | |||||||
\(318\) | −3.86307 | + | 9.32626i | −0.216630 | + | 0.522991i | ||||
\(319\) | 19.8676i | 1.11237i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.77342 | + | 7.77342i | −0.433870 | + | 0.433870i | ||||
\(322\) | 0.438222i | 0.0244211i | ||||||||
\(323\) | 0.212005 | − | 0.809096i | 0.0117963 | − | 0.0450193i | ||||
\(324\) | 3.80705 | 0.211503 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −0.478610 | + | 1.15547i | −0.0265077 | + | 0.0639953i | ||||
\(327\) | 9.24228 | 0.511099 | ||||||||
\(328\) | 5.64423 | − | 13.6264i | 0.311651 | − | 0.752391i | ||||
\(329\) | 3.03821 | + | 7.33489i | 0.167502 | + | 0.404386i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.33174 | + | 4.33174i | 0.238094 | + | 0.238094i | 0.816060 | − | 0.577967i | \(-0.196154\pi\) |
−0.577967 | + | 0.816060i | \(0.696154\pi\) | |||||||
\(332\) | 10.3309 | − | 10.3309i | 0.566981 | − | 0.566981i | ||||
\(333\) | 16.1251 | + | 38.9295i | 0.883652 | + | 2.13333i | ||||
\(334\) | 5.07910 | + | 12.2620i | 0.277916 | + | 0.670949i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 0.490736i | − | 0.0267718i | ||||||
\(337\) | −14.6668 | − | 6.07517i | −0.798950 | − | 0.330936i | −0.0544140 | − | 0.998518i | \(-0.517329\pi\) |
−0.744536 | + | 0.667583i | \(0.767329\pi\) | |||||||
\(338\) | −17.0309 | − | 17.0309i | −0.926360 | − | 0.926360i | ||||
\(339\) | 1.16210 | 0.0631167 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.9260 | 0.754133 | ||||||||
\(342\) | −0.687626 | − | 0.687626i | −0.0371826 | − | 0.0371826i | ||||
\(343\) | −9.04815 | − | 3.74787i | −0.488554 | − | 0.202366i | ||||
\(344\) | − | 34.3978i | − | 1.85461i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5.10157 | + | 12.3163i | 0.274262 | + | 0.662127i | ||||
\(347\) | −0.651859 | − | 1.57373i | −0.0349936 | − | 0.0844821i | 0.905417 | − | 0.424524i | \(-0.139559\pi\) |
−0.940410 | + | 0.340042i | \(0.889559\pi\) | |||||||
\(348\) | −19.1298 | + | 19.1298i | −1.02547 | + | 1.02547i | ||||
\(349\) | −24.9284 | − | 24.9284i | −1.33439 | − | 1.33439i | −0.901401 | − | 0.432985i | \(-0.857460\pi\) |
−0.432985 | − | 0.901401i | \(-0.642540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.9958 | + | 38.6172i | 0.853791 | + | 2.06123i | ||||
\(352\) | 5.30994 | − | 12.8193i | 0.283021 | − | 0.683273i | ||||
\(353\) | 22.4928 | 1.19717 | 0.598586 | − | 0.801059i | \(-0.295730\pi\) | ||||
0.598586 | + | 0.801059i | \(0.295730\pi\) | |||||||
\(354\) | 3.36140 | − | 8.11513i | 0.178656 | − | 0.431314i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 15.4294 | 0.817755 | ||||||||
\(357\) | −4.36008 | − | 7.45629i | −0.230760 | − | 0.394629i | ||||
\(358\) | − | 12.9037i | − | 0.681981i | ||||||
\(359\) | 12.7307 | − | 12.7307i | 0.671898 | − | 0.671898i | −0.286255 | − | 0.958153i | \(-0.592410\pi\) |
0.958153 | + | 0.286255i | \(0.0924105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9588i | 0.997834i | ||||||||
\(362\) | 2.08365 | − | 5.03038i | 0.109514 | − | 0.264391i | ||||
\(363\) | 12.5980 | − | 5.21826i | 0.661223 | − | 0.273887i | ||||
\(364\) | −5.00333 | + | 2.07245i | −0.262246 | + | 0.108626i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.08967 | + | 2.08967i | 0.109229 | + | 0.109229i | ||||
\(367\) | 11.9711 | + | 28.9008i | 0.624887 | + | 1.50861i | 0.845901 | + | 0.533340i | \(0.179063\pi\) |
−0.221015 | + | 0.975271i | \(0.570937\pi\) | |||||||
\(368\) | 0.144334 | − | 0.0597851i | 0.00752393 | − | 0.00311651i | ||||
\(369\) | −25.1199 | − | 10.4050i | −1.30769 | − | 0.541663i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.07828 | + | 2.60319i | −0.0559814 | + | 0.135151i | ||||
\(372\) | 13.4088 | + | 13.4088i | 0.695213 | + | 0.695213i | ||||
\(373\) | − | 24.3521i | − | 1.26091i | −0.776228 | − | 0.630453i | \(-0.782869\pi\) | ||
0.776228 | − | 0.630453i | \(-0.217131\pi\) | |||||||
\(374\) | 1.26898 | + | 9.24331i | 0.0656175 | + | 0.477960i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 22.2164 | − | 22.2164i | 1.14573 | − | 1.14573i | ||||
\(377\) | −46.1644 | − | 19.1219i | −2.37759 | − | 0.984830i | ||||
\(378\) | −4.36196 | −0.224355 | ||||||||
\(379\) | −6.04944 | − | 2.50576i | −0.310739 | − | 0.128712i | 0.221864 | − | 0.975078i | \(-0.428786\pi\) |
−0.532603 | + | 0.846365i | \(0.678786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.75348 | − | 2.38317i | 0.294760 | − | 0.122093i | ||||
\(382\) | −9.03578 | + | 9.03578i | −0.462311 | + | 0.462311i | ||||
\(383\) | −13.0036 | + | 13.0036i | −0.664451 | + | 0.664451i | −0.956426 | − | 0.291975i | \(-0.905688\pi\) |
0.291975 | + | 0.956426i | \(0.405688\pi\) | |||||||
\(384\) | 16.3287 | − | 6.76355i | 0.833269 | − | 0.345151i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −19.4374 | − | 8.05123i | −0.989337 | − | 0.409797i | ||||
\(387\) | −63.4115 | −3.22339 | ||||||||
\(388\) | 13.0335 | + | 5.39865i | 0.661676 | + | 0.274075i | ||||
\(389\) | −1.52050 | + | 1.52050i | −0.0770922 | + | 0.0770922i | −0.744602 | − | 0.667509i | \(-0.767360\pi\) |
0.667509 | + | 0.744602i | \(0.267360\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.66185 | − | 2.19076i | 0.0840433 | − | 0.110791i | ||||
\(392\) | 18.6185i | 0.940375i | ||||||||
\(393\) | −16.3921 | − | 16.3921i | −0.826872 | − | 0.826872i | ||||
\(394\) | −3.21605 | + | 7.76423i | −0.162022 | + | 0.391156i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −14.5131 | − | 6.01154i | −0.729313 | − | 0.302091i | ||||
\(397\) | 0.358143 | − | 0.148348i | 0.0179747 | − | 0.00744535i | −0.373678 | − | 0.927558i | \(-0.621903\pi\) |
0.391653 | + | 0.920113i | \(0.371903\pi\) | |||||||
\(398\) | 2.61569 | + | 6.31484i | 0.131113 | + | 0.316534i | ||||
\(399\) | −0.300500 | − | 0.300500i | −0.0150438 | − | 0.0150438i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.4465 | + | 6.39816i | −0.771362 | + | 0.319509i | −0.733424 | − | 0.679771i | \(-0.762079\pi\) |
−0.0379382 | + | 0.999280i | \(0.512079\pi\) | |||||||
\(402\) | −13.5220 | + | 5.60099i | −0.674415 | + | 0.279352i | ||||
\(403\) | −13.4033 | + | 32.3584i | −0.667665 | + | 1.61188i | ||||
\(404\) | 11.9066i | 0.592374i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.68717 | − | 3.68717i | 0.182991 | − | 0.182991i | ||||
\(407\) | − | 19.8906i | − | 0.985943i | ||||||
\(408\) | −20.6584 | + | 27.2333i | −1.02274 | + | 1.34825i | ||||
\(409\) | 15.7306 | 0.777828 | 0.388914 | − | 0.921274i | \(-0.372850\pi\) | ||||
0.388914 | + | 0.921274i | \(0.372850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.67951 | + | 20.9542i | −0.428129 | + | 1.03359i | ||||
\(412\) | 11.6025 | 0.571613 | ||||||||
\(413\) | 0.938249 | − | 2.26513i | 0.0461682 | − | 0.111460i | ||||
\(414\) | −1.22344 | − | 2.95364i | −0.0601287 | − | 0.145164i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.6764 | + | 24.6764i | 1.20986 | + | 1.20986i | ||||
\(417\) | 35.5821 | − | 35.5821i | 1.74246 | − | 1.74246i | ||||
\(418\) | 0.175668 | + | 0.424100i | 0.00859220 | + | 0.0207434i | ||||
\(419\) | 4.06462 | + | 9.81286i | 0.198570 | + | 0.479390i | 0.991529 | − | 0.129885i | \(-0.0414608\pi\) |
−0.792959 | + | 0.609274i | \(0.791461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 17.0231i | − | 0.829656i | −0.909900 | − | 0.414828i | \(-0.863842\pi\) | ||
0.909900 | − | 0.414828i | \(-0.136158\pi\) | |||||||
\(422\) | −20.8467 | − | 8.63499i | −1.01480 | − | 0.420345i | ||||
\(423\) | −40.9555 | − | 40.9555i | −1.99132 | − | 1.99132i | ||||
\(424\) | 11.1507 | 0.541526 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 10.3235 | 0.500178 | ||||||||
\(427\) | 0.583279 | + | 0.583279i | 0.0282269 | + | 0.0282269i | ||||
\(428\) | 4.16979 | + | 1.72718i | 0.201554 | + | 0.0834865i | ||||
\(429\) | − | 45.4261i | − | 2.19320i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −7.53530 | − | 18.1918i | −0.362963 | − | 0.876270i | −0.994864 | − | 0.101221i | \(-0.967725\pi\) |
0.631901 | − | 0.775049i | \(-0.282275\pi\) | |||||||
\(432\) | 0.595087 | + | 1.43667i | 0.0286311 | + | 0.0691217i | ||||
\(433\) | 15.5266 | − | 15.5266i | 0.746159 | − | 0.746159i | −0.227597 | − | 0.973755i | \(-0.573087\pi\) |
0.973755 | + | 0.227597i | \(0.0730868\pi\) | |||||||
\(434\) | −2.58447 | − | 2.58447i | −0.124059 | − | 0.124059i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.45208 | − | 3.50563i | −0.0695419 | − | 0.167889i | ||||
\(437\) | 0.0517732 | − | 0.124991i | 0.00247665 | − | 0.00597915i | ||||
\(438\) | 13.5152 | 0.645779 | ||||||||
\(439\) | 3.25235 | − | 7.85186i | 0.155226 | − | 0.374749i | −0.827066 | − | 0.562105i | \(-0.809992\pi\) |
0.982292 | + | 0.187356i | \(0.0599918\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 34.3227 | 1.63441 | ||||||||
\(442\) | −22.6991 | − | 5.94777i | −1.07969 | − | 0.282907i | ||||
\(443\) | 4.70952i | 0.223756i | 0.993722 | + | 0.111878i | \(0.0356866\pi\) | ||||
−0.993722 | + | 0.111878i | \(0.964313\pi\) | |||||||
\(444\) | 19.1520 | − | 19.1520i | 0.908912 | − | 0.908912i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 10.9984i | − | 0.520791i | ||||||
\(447\) | 8.19236 | − | 19.7781i | 0.387485 | − | 0.935472i | ||||
\(448\) | −3.67923 | + | 1.52398i | −0.173827 | + | 0.0720015i | ||||
\(449\) | 24.2399 | − | 10.0405i | 1.14395 | − | 0.473839i | 0.271449 | − | 0.962453i | \(-0.412497\pi\) |
0.872500 | + | 0.488613i | \(0.162497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.07554 | + | 9.07554i | 0.427351 | + | 0.427351i | ||||
\(452\) | −0.182581 | − | 0.440789i | −0.00858788 | − | 0.0207330i | ||||
\(453\) | −35.9756 | + | 14.9016i | −1.69028 | + | 0.700138i | ||||
\(454\) | 1.65883 | + | 0.687110i | 0.0778528 | + | 0.0322477i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.643591 | + | 1.55377i | −0.0301389 | + | 0.0727618i | ||||
\(457\) | −14.6247 | − | 14.6247i | −0.684115 | − | 0.684115i | 0.276810 | − | 0.960925i | \(-0.410723\pi\) |
−0.960925 | + | 0.276810i | \(0.910723\pi\) | |||||||
\(458\) | 2.07163i | 0.0968009i | ||||||||
\(459\) | 21.8063 | + | 16.5416i | 1.01783 | + | 0.772098i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.37250 | + | 1.37250i | −0.0639239 | + | 0.0639239i | −0.738346 | − | 0.674422i | \(-0.764393\pi\) |
0.674422 | + | 0.738346i | \(0.264393\pi\) | |||||||
\(462\) | 4.37963 | + | 1.81410i | 0.203759 | + | 0.0843996i | ||||
\(463\) | −10.6872 | −0.496676 | −0.248338 | − | 0.968673i | \(-0.579884\pi\) | ||||
−0.248338 | + | 0.968673i | \(0.579884\pi\) | |||||||
\(464\) | −1.71744 | − | 0.711389i | −0.0797304 | − | 0.0330254i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −18.9581 | + | 7.85269i | −0.878216 | + | 0.363769i | ||||
\(467\) | 3.43207 | − | 3.43207i | 0.158817 | − | 0.158817i | −0.623225 | − | 0.782042i | \(-0.714178\pi\) |
0.782042 | + | 0.623225i | \(0.214178\pi\) | |||||||
\(468\) | 27.9368 | − | 27.9368i | 1.29138 | − | 1.29138i | ||||
\(469\) | −3.77432 | + | 1.56337i | −0.174282 | + | 0.0721899i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.34214 | − | 3.04121i | −0.338308 | − | 0.140132i | ||||
\(472\) | −9.70263 | −0.446600 | ||||||||
\(473\) | 27.6547 | + | 11.4549i | 1.27156 | + | 0.526699i | ||||
\(474\) | −25.8584 | + | 25.8584i | −1.18772 | + | 1.18772i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.14317 | + | 2.82527i | −0.0982321 | + | 0.129496i | ||||
\(477\) | − | 20.5560i | − | 0.941196i | ||||||
\(478\) | 8.45458 | + | 8.45458i | 0.386703 | + | 0.386703i | ||||
\(479\) | −2.91185 | + | 7.02983i | −0.133046 | + | 0.321201i | −0.976337 | − | 0.216256i | \(-0.930615\pi\) |
0.843291 | + | 0.537458i | \(0.180615\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 46.2179 | + | 19.1441i | 2.10736 | + | 0.872895i | ||||
\(482\) | −2.42101 | + | 1.00282i | −0.110274 | + | 0.0456770i | ||||
\(483\) | −0.534655 | − | 1.29077i | −0.0243276 | − | 0.0587321i | ||||
\(484\) | −3.95860 | − | 3.95860i | −0.179937 | − | 0.179937i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −8.88654 | + | 3.68093i | −0.403102 | + | 0.166970i | ||||
\(487\) | −0.393190 | + | 0.162865i | −0.0178171 | + | 0.00738010i | −0.391574 | − | 0.920147i | \(-0.628069\pi\) |
0.373757 | + | 0.927527i | \(0.378069\pi\) | |||||||
\(488\) | 1.24923 | − | 3.01591i | 0.0565500 | − | 0.136524i | ||||
\(489\) | − | 3.98733i | − | 0.180313i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0.197439 | − | 0.197439i | 0.00891028 | − | 0.00891028i | −0.702638 | − | 0.711548i | \(-0.747994\pi\) |
0.711548 | + | 0.702638i | \(0.247994\pi\) | |||||||
\(492\) | 17.4770i | 0.787924i | ||||||||
\(493\) | −32.4156 | + | 4.45022i | −1.45992 | + | 0.200428i | ||||
\(494\) | −1.15451 | −0.0519440 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.498639 | + | 1.20382i | −0.0223895 | + | 0.0540531i | ||||
\(497\) | 2.88156 | 0.129256 | ||||||||
\(498\) | 12.3088 | − | 29.7161i | 0.551571 | − | 1.33161i | ||||
\(499\) | −7.08936 | − | 17.1152i | −0.317363 | − | 0.766183i | −0.999392 | − | 0.0348579i | \(-0.988902\pi\) |
0.682029 | − | 0.731325i | \(-0.261098\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −29.9207 | − | 29.9207i | −1.33676 | − | 1.33676i | ||||
\(502\) | 6.29815 | − | 6.29815i | 0.281100 | − | 0.281100i | ||||
\(503\) | −3.10919 | − | 7.50624i | −0.138632 | − | 0.334687i | 0.839282 | − | 0.543697i | \(-0.182976\pi\) |
−0.977913 | + | 0.209010i | \(0.932976\pi\) | |||||||
\(504\) | 4.24508 | + | 10.2485i | 0.189091 | + | 0.456506i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.50913i | 0.0670891i | ||||||||
\(507\) | 70.9428 | + | 29.3855i | 3.15068 | + | 1.30505i | ||||
\(508\) | −1.80789 | − | 1.80789i | −0.0802120 | − | 0.0802120i | ||||
\(509\) | −15.1877 | −0.673181 | −0.336590 | − | 0.941651i | \(-0.609274\pi\) | ||||
−0.336590 | + | 0.941651i | \(0.609274\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.77241 | 0.166882 | ||||||||
\(512\) | 1.87113 | + | 1.87113i | 0.0826930 | + | 0.0826930i | ||||
\(513\) | 1.24414 | + | 0.515338i | 0.0549299 | + | 0.0227527i | ||||
\(514\) | − | 4.78077i | − | 0.210871i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 15.5981 | + | 37.6572i | 0.686669 | + | 1.65777i | ||||
\(517\) | 10.4629 | + | 25.2596i | 0.460157 | + | 1.11092i | ||||
\(518\) | −3.69144 | + | 3.69144i | −0.162193 | + | 0.162193i | ||||
\(519\) | −30.0531 | − | 30.0531i | −1.31918 | − | 1.31918i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2931 | − | 34.5065i | −0.626190 | − | 1.51176i | −0.844321 | − | 0.535837i | \(-0.819996\pi\) |
0.218131 | − | 0.975919i | \(-0.430004\pi\) | |||||||
\(522\) | −14.5578 | + | 35.1457i | −0.637178 | + | 1.53828i | ||||
\(523\) | −8.03541 | −0.351364 | −0.175682 | − | 0.984447i | \(-0.556213\pi\) | ||||
−0.175682 | + | 0.984447i | \(0.556213\pi\) | |||||||
\(524\) | −3.64217 | + | 8.79298i | −0.159109 | + | 0.384123i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.3706 | −0.495780 | ||||||||
\(527\) | 3.11932 | + | 22.7213i | 0.135880 | + | 0.989754i | ||||
\(528\) | − | 1.68998i | − | 0.0735469i | ||||||
\(529\) | −15.9490 | + | 15.9490i | −0.693433 | + | 0.693433i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.8866i | 0.776210i | ||||||||
\(532\) | −0.0667683 | + | 0.161193i | −0.00289477 | + | 0.00698860i | ||||
\(533\) | −29.8228 | + | 12.3530i | −1.29177 | + | 0.535069i | ||||
\(534\) | 31.3825 | − | 12.9991i | 1.35805 | − | 0.562524i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.4319 | + | 11.4319i | 0.493784 | + | 0.493784i | ||||
\(537\) | 15.7432 | + | 38.0075i | 0.679370 | + | 1.64014i | ||||
\(538\) | 7.68457 | − | 3.18306i | 0.331306 | − | 0.137231i | ||||
\(539\) | −14.9686 | − | 6.20020i | −0.644744 | − | 0.267062i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.24786 | − | 15.0837i | 0.268616 | − | 0.648498i | −0.730802 | − | 0.682589i | \(-0.760854\pi\) |
0.999419 | + | 0.0340917i | \(0.0108538\pi\) | |||||||
\(542\) | 9.33259 | + | 9.33259i | 0.400869 | + | 0.400869i | ||||
\(543\) | 17.3590i | 0.744947i | ||||||||
\(544\) | 22.1051 | + | 5.79213i | 0.947750 | + | 0.248336i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −8.43049 | + | 8.43049i | −0.360792 | + | 0.360792i | ||||
\(547\) | −26.6116 | − | 11.0229i | −1.13783 | − | 0.471304i | −0.267394 | − | 0.963587i | \(-0.586162\pi\) |
−0.870435 | + | 0.492283i | \(0.836162\pi\) | |||||||
\(548\) | 9.31165 | 0.397774 | ||||||||
\(549\) | −5.55975 | − | 2.30292i | −0.237284 | − | 0.0982864i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.48729 | + | 0.616054i | −0.0633605 | + | 0.0262448i | ||||
\(552\) | −3.90958 | + | 3.90958i | −0.166403 | + | 0.166403i | ||||
\(553\) | −7.21773 | + | 7.21773i | −0.306929 | + | 0.306929i | ||||
\(554\) | 10.9106 | − | 4.51931i | 0.463546 | − | 0.192007i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.0868 | − | 7.90601i | −0.809461 | − | 0.335290i | ||||
\(557\) | 7.64838 | 0.324072 | 0.162036 | − | 0.986785i | \(-0.448194\pi\) | ||||
0.162036 | + | 0.986785i | \(0.448194\pi\) | |||||||
\(558\) | 24.6349 | + | 10.2041i | 1.04288 | + | 0.431974i | ||||
\(559\) | −53.2334 | + | 53.2334i | −2.25153 | + | 2.25153i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.0151 | − | 25.6777i | −0.633938 | − | 1.08411i | ||||
\(562\) | − | 6.83413i | − | 0.288280i | ||||||
\(563\) | 29.9736 | + | 29.9736i | 1.26324 | + | 1.26324i | 0.949514 | + | 0.313724i | \(0.101577\pi\) |
0.313724 | + | 0.949514i | \(0.398423\pi\) | |||||||
\(564\) | −14.2472 | + | 34.3959i | −0.599917 | + | 1.44833i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.43874 | − | 1.42437i | −0.144541 | − | 0.0598709i | ||||
\(567\) | 2.16136 | − | 0.895263i | 0.0907684 | − | 0.0375975i | ||||
\(568\) | −4.36393 | − | 10.5355i | −0.183107 | − | 0.442058i | ||||
\(569\) | 21.7924 | + | 21.7924i | 0.913584 | + | 0.913584i | 0.996552 | − | 0.0829686i | \(-0.0264401\pi\) |
−0.0829686 | + | 0.996552i | \(0.526440\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.3678 | + | 8.43662i | −0.852366 | + | 0.353062i | −0.765717 | − | 0.643177i | \(-0.777616\pi\) |
−0.0866487 | + | 0.996239i | \(0.527616\pi\) | |||||||
\(572\) | −17.2303 | + | 7.13702i | −0.720434 | + | 0.298414i | ||||
\(573\) | 15.5905 | − | 37.6388i | 0.651303 | − | 1.57238i | ||||
\(574\) | − | 3.36860i | − | 0.140603i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 20.5435 | − | 20.5435i | 0.855979 | − | 0.855979i | ||||
\(577\) | 20.2437i | 0.842755i | 0.906885 | + | 0.421378i | \(0.138453\pi\) | ||||
−0.906885 | + | 0.421378i | \(0.861547\pi\) | |||||||
\(578\) | −14.7969 | + | 4.14088i | −0.615471 | + | 0.172238i | ||||
\(579\) | 67.0753 | 2.78755 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43569 | − | 8.29450i | 0.142537 | − | 0.344114i | ||||
\(582\) | 31.0577 | 1.28738 | ||||||||
\(583\) | −3.71333 | + | 8.96478i | −0.153791 | + | 0.371283i | ||||
\(584\) | −5.71308 | − | 13.7926i | −0.236409 | − | 0.570742i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8750 | − | 11.8750i | −0.490551 | − | 0.490551i | ||||
\(587\) | 9.02526 | − | 9.02526i | 0.372513 | − | 0.372513i | −0.495879 | − | 0.868392i | \(-0.665154\pi\) |
0.868392 | + | 0.495879i | \(0.165154\pi\) | |||||||
\(588\) | −8.44278 | − | 20.3827i | −0.348174 | − | 0.840567i | ||||
\(589\) | 0.431815 | + | 1.04249i | 0.0177926 | + | 0.0429552i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 26.7931i | − | 1.10212i | ||||||
\(592\) | 1.71943 | + | 0.712213i | 0.0706683 | + | 0.0292718i | ||||
\(593\) | −2.03582 | − | 2.03582i | −0.0836009 | − | 0.0836009i | 0.664070 | − | 0.747671i | \(-0.268828\pi\) |
−0.747671 | + | 0.664070i | \(0.768828\pi\) | |||||||
\(594\) | −15.0216 | −0.616342 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.78902 | −0.360012 | ||||||||
\(597\) | −15.4089 | − | 15.4089i | −0.630645 | − | 0.630645i | ||||
\(598\) | −3.50662 | − | 1.45249i | −0.143396 | − | 0.0593967i | ||||
\(599\) | − | 12.6720i | − | 0.517762i | −0.965909 | − | 0.258881i | \(-0.916646\pi\) | ||
0.965909 | − | 0.258881i | \(-0.0833538\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.25226 | − | 12.6801i | −0.214244 | − | 0.517231i | 0.779823 | − | 0.626000i | \(-0.215309\pi\) |
−0.994067 | + | 0.108769i | \(0.965309\pi\) | |||||||
\(602\) | −3.00645 | − | 7.25822i | −0.122534 | − | 0.295823i | ||||
\(603\) | 21.0745 | − | 21.0745i | 0.858219 | − | 0.858219i | ||||
\(604\) | 11.3045 | + | 11.3045i | 0.459972 | + | 0.459972i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 10.0311 | + | 24.2173i | 0.407487 | + | 0.983760i | ||||
\(607\) | 2.98647 | − | 7.20998i | 0.121217 | − | 0.292644i | −0.851610 | − | 0.524175i | \(-0.824374\pi\) |
0.972827 | + | 0.231531i | \(0.0743736\pi\) | |||||||
\(608\) | 1.12430 | 0.0455965 | ||||||||
\(609\) | −6.36191 | + | 15.3590i | −0.257798 | + | 0.622379i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −68.7635 | −2.78187 | ||||||||
\(612\) | 6.55744 | − | 25.0258i | 0.265069 | − | 1.01161i | ||||
\(613\) | 44.7999i | 1.80945i | 0.425994 | + | 0.904726i | \(0.359924\pi\) | ||||
−0.425994 | + | 0.904726i | \(0.640076\pi\) | |||||||
\(614\) | 6.28011 | − | 6.28011i | 0.253445 | − | 0.253445i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 5.23638i | − | 0.210980i | ||||||
\(617\) | 8.25893 | − | 19.9388i | 0.332492 | − | 0.802707i | −0.665901 | − | 0.746040i | \(-0.731953\pi\) |
0.998393 | − | 0.0566667i | \(-0.0180472\pi\) | |||||||
\(618\) | 23.5988 | − | 9.77495i | 0.949284 | − | 0.393206i | ||||
\(619\) | −35.6401 | + | 14.7626i | −1.43250 | + | 0.593360i | −0.957967 | − | 0.286879i | \(-0.907382\pi\) |
−0.474530 | + | 0.880239i | \(0.657382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.13049 | + | 3.13049i | 0.125622 | + | 0.125622i | ||||
\(622\) | −9.92293 | − | 23.9561i | −0.397873 | − | 0.960551i | ||||
\(623\) | 8.75963 | − | 3.62836i | 0.350947 | − | 0.145367i | ||||
\(624\) | 3.92683 | + | 1.62655i | 0.157199 | + | 0.0651140i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.335042 | − | 0.808864i | 0.0133910 | − | 0.0323287i | ||||
\(627\) | −1.03485 | − | 1.03485i | −0.0413280 | − | 0.0413280i | ||||
\(628\) | 3.26271i | 0.130196i | ||||||||
\(629\) | 32.4531 | − | 4.45538i | 1.29399 | − | 0.177647i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1283 | − | 17.1283i | 0.681866 | − | 0.681866i | −0.278555 | − | 0.960420i | \(-0.589855\pi\) |
0.960420 | + | 0.278555i | \(0.0898553\pi\) | |||||||
\(632\) | 37.3200 | + | 15.4585i | 1.48451 | + | 0.614904i | ||||
\(633\) | 71.9387 | 2.85931 | ||||||||
\(634\) | −22.1495 | − | 9.17461i | −0.879668 | − | 0.364370i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.2073 | + | 5.05642i | −0.484050 | + | 0.200500i | ||||
\(637\) | 28.8136 | − | 28.8136i | 1.14164 | − | 1.14164i | ||||
\(638\) | 12.6977 | − | 12.6977i | 0.502708 | − | 0.502708i | ||||
\(639\) | −19.4219 | + | 8.04480i | −0.768317 | + | 0.318247i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 40.1257 | + | 16.6206i | 1.58487 | + | 0.656475i | 0.989176 | − | 0.146737i | \(-0.0468770\pi\) |
0.595694 | + | 0.803211i | \(0.296877\pi\) | |||||||
\(642\) | 9.93625 | 0.392152 | ||||||||
\(643\) | −32.7815 | − | 13.5786i | −1.29278 | − | 0.535486i | −0.372965 | − | 0.927845i | \(-0.621659\pi\) |
−0.919812 | + | 0.392359i | \(0.871659\pi\) | |||||||
\(644\) | −0.405593 | + | 0.405593i | −0.0159826 | + | 0.0159826i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.652603 | + | 0.381611i | −0.0256763 | + | 0.0150143i | ||||
\(647\) | − | 28.2269i | − | 1.10971i | −0.831946 | − | 0.554857i | \(-0.812773\pi\) | ||
0.831946 | − | 0.554857i | \(-0.187227\pi\) | |||||||
\(648\) | −6.54647 | − | 6.54647i | −0.257170 | − | 0.257170i | ||||
\(649\) | 3.23111 | − | 7.80059i | 0.126832 | − | 0.306200i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7657 | + | 4.45930i | 0.421941 | + | 0.174774i | ||||
\(652\) | −1.51241 | + | 0.626459i | −0.0592304 | + | 0.0245340i | ||||
\(653\) | −1.42702 | − | 3.44513i | −0.0558436 | − | 0.134818i | 0.893495 | − | 0.449073i | \(-0.148246\pi\) |
−0.949339 | + | 0.314254i | \(0.898246\pi\) | |||||||
\(654\) | −5.90689 | − | 5.90689i | −0.230978 | − | 0.230978i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.10949 | + | 0.459567i | −0.0433184 | + | 0.0179431i | ||||
\(657\) | −25.4263 | + | 10.5319i | −0.991974 | + | 0.410889i | ||||
\(658\) | 2.74608 | − | 6.62962i | 0.107053 | − | 0.258450i | ||||
\(659\) | 16.0238i | 0.624200i | 0.950049 | + | 0.312100i | \(0.101032\pi\) | ||||
−0.950049 | + | 0.312100i | \(0.898968\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.4741 | + | 19.4741i | −0.757454 | + | 0.757454i | −0.975858 | − | 0.218404i | \(-0.929915\pi\) |
0.218404 | + | 0.975858i | \(0.429915\pi\) | |||||||
\(662\) | − | 5.53698i | − | 0.215201i | ||||||
\(663\) | 74.1162 | − | 10.1752i | 2.87844 | − | 0.395171i | ||||
\(664\) | −35.5292 | −1.37880 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14.5747 | − | 35.1864i | 0.564757 | − | 1.36344i | ||||
\(667\) | −5.29241 | −0.204923 | ||||||||
\(668\) | −6.64811 | + | 16.0500i | −0.257223 | + | 0.620991i | ||||
\(669\) | 13.4187 | + | 32.3956i | 0.518797 | + | 1.25249i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.00868 | + | 2.00868i | 0.0775441 | + | 0.0775441i | ||||
\(672\) | 8.20989 | − | 8.20989i | 0.316703 | − | 0.316703i | ||||
\(673\) | 7.24825 | + | 17.4988i | 0.279400 | + | 0.674530i | 0.999819 | − | 0.0190080i | \(-0.00605081\pi\) |
−0.720420 | + | 0.693538i | \(0.756051\pi\) | |||||||
\(674\) | 5.49103 | + | 13.2565i | 0.211507 | + | 0.510622i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | − | 31.5257i | − | 1.21253i | ||||||
\(677\) | −9.78472 | − | 4.05297i | −0.376058 | − | 0.155768i | 0.186645 | − | 0.982427i | \(-0.440238\pi\) |
−0.562703 | + | 0.826659i | \(0.690238\pi\) | |||||||
\(678\) | −0.742719 | − | 0.742719i | −0.0285240 | − | 0.0285240i | ||||
\(679\) | 8.66898 | 0.332685 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.72436 | −0.219358 | ||||||||
\(682\) | −8.90032 | − | 8.90032i | −0.340811 | − | 0.340811i | ||||
\(683\) | −41.6347 | − | 17.2457i | −1.59311 | − | 0.659887i | −0.602688 | − | 0.797977i | \(-0.705904\pi\) |
−0.990420 | + | 0.138090i | \(0.955904\pi\) | |||||||
\(684\) | − | 1.27285i | − | 0.0486688i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.38750 | + | 8.17815i | 0.129335 | + | 0.312243i | ||||
\(687\) | −2.52750 | − | 6.10193i | −0.0964303 | − | 0.232803i | ||||
\(688\) | −1.98043 | + | 1.98043i | −0.0755031 | + | 0.0755031i | ||||
\(689\) | −17.2566 | − | 17.2566i | −0.657424 | − | 0.657424i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.99288 | − | 12.0539i | −0.189938 | − | 0.458551i | 0.800009 | − | 0.599988i | \(-0.204828\pi\) |
−0.989947 | + | 0.141437i | \(0.954828\pi\) | |||||||
\(692\) | −6.67752 | + | 16.1209i | −0.253841 | + | 0.612827i | ||||
\(693\) | −9.65314 | −0.366692 | ||||||||
\(694\) | −0.589181 | + | 1.42241i | −0.0223650 | + | 0.0539939i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 65.7899 | 2.49376 | ||||||||
\(697\) | −12.7746 | + | 16.8403i | −0.483872 | + | 0.637872i | ||||
\(698\) | 31.8643i | 1.20608i | ||||||||
\(699\) | 46.2598 | − | 46.2598i | 1.74971 | − | 1.74971i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.42228i | − | 0.167027i | −0.996507 | − | 0.0835136i | \(-0.973386\pi\) | ||
0.996507 | − | 0.0835136i | \(-0.0266142\pi\) | |||||||
\(702\) | 14.4577 | − | 34.9041i | 0.545672 | − | 1.31737i | ||||
\(703\) | 1.48901 | − | 0.616767i | 0.0561590 | − | 0.0232618i | ||||
\(704\) | −12.6704 | + | 5.24825i | −0.477533 | + | 0.197801i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.3755 | − | 14.3755i | −0.541030 | − | 0.541030i | ||||
\(707\) | 2.79994 | + | 6.75965i | 0.105302 | + | 0.254223i | ||||
\(708\) | 10.6220 | − | 4.39978i | 0.399200 | − | 0.165354i | ||||
\(709\) | 29.6088 | + | 12.2644i | 1.11198 | + | 0.460597i | 0.861619 | − | 0.507555i | \(-0.169451\pi\) |
0.250361 | + | 0.968152i | \(0.419451\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 28.4973 | − | 68.7985i | 1.06873 | − | 2.58015i | ||||
\(712\) | −26.5318 | − | 26.5318i | −0.994321 | − | 0.994321i | ||||
\(713\) | 3.70965i | 0.138927i | ||||||||
\(714\) | −1.97884 | + | 7.55204i | −0.0740561 | + | 0.282628i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 11.9429 | − | 11.9429i | 0.446327 | − | 0.446327i | ||||
\(717\) | −35.2178 | − | 14.5877i | −1.31523 | − | 0.544787i | ||||
\(718\) | −16.2728 | −0.607294 | ||||||||
\(719\) | −25.6163 | − | 10.6106i | −0.955329 | − | 0.395710i | −0.150098 | − | 0.988671i | \(-0.547959\pi\) |
−0.805231 | + | 0.592961i | \(0.797959\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.58702 | − | 2.72843i | 0.245313 | − | 0.101612i | ||||
\(722\) | 12.1169 | − | 12.1169i | 0.450945 | − | 0.450945i | ||||
\(723\) | 5.90754 | − | 5.90754i | 0.219704 | − | 0.219704i | ||||
\(724\) | 6.58434 | − | 2.72732i | 0.244705 | − | 0.101360i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −11.3867 | − | 4.71651i | −0.422599 | − | 0.175046i | ||||
\(727\) | 10.5407 | 0.390934 | 0.195467 | − | 0.980710i | \(-0.437378\pi\) | ||||
0.195467 | + | 0.980710i | \(0.437378\pi\) | |||||||
\(728\) | 12.1673 | + | 5.03984i | 0.450948 | + | 0.186789i | ||||
\(729\) | 28.5105 | − | 28.5105i | 1.05594 | − | 1.05594i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.4951 | + | 47.6865i | −0.462150 | + | 1.76375i | ||||
\(732\) | 3.86816i | 0.142971i | ||||||||
\(733\) | 11.6126 | + | 11.6126i | 0.428920 | + | 0.428920i | 0.888260 | − | 0.459340i | \(-0.151914\pi\) |
−0.459340 | + | 0.888260i | \(0.651914\pi\) | |||||||
\(734\) | 10.8201 | − | 26.1219i | 0.399376 | − | 0.964178i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.41486 | + | 1.41448i | 0.125873 | + | 0.0521385i | ||||
\(737\) | −12.9979 | + | 5.38389i | −0.478783 | + | 0.198318i | ||||
\(738\) | 9.40454 | + | 22.7046i | 0.346186 | + | 0.835767i | ||||
\(739\) | −1.27919 | − | 1.27919i | −0.0470556 | − | 0.0470556i | 0.683187 | − | 0.730243i | \(-0.260593\pi\) |
−0.730243 | + | 0.683187i | \(0.760593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.40059 | − | 1.40857i | 0.124924 | − | 0.0517451i | ||||
\(742\) | 2.35289 | − | 0.974598i | 0.0863773 | − | 0.0357786i | ||||
\(743\) | −16.4954 | + | 39.8234i | −0.605157 | + | 1.46098i | 0.263052 | + | 0.964782i | \(0.415271\pi\) |
−0.868210 | + | 0.496198i | \(0.834729\pi\) | |||||||
\(744\) | − | 46.1146i | − | 1.69064i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −15.5639 | + | 15.5639i | −0.569833 | + | 0.569833i | ||||
\(747\) | 65.4973i | 2.39642i | ||||||||
\(748\) | −7.38058 | + | 9.72957i | −0.269861 | + | 0.355748i | ||||
\(749\) | 2.77345 | 0.101340 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.2128 | + | 27.0700i | −0.409160 | + | 0.987799i | 0.576199 | + | 0.817309i | \(0.304535\pi\) |
−0.985359 | + | 0.170490i | \(0.945465\pi\) | |||||||
\(752\) | −2.55819 | −0.0932876 | ||||||||
\(753\) | −10.8669 | + | 26.2351i | −0.396013 | + | 0.956061i | ||||
\(754\) | 17.2833 | + | 41.7256i | 0.629421 | + | 1.51956i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.03717 | − | 4.03717i | −0.146831 | − | 0.146831i | ||||
\(757\) | −7.31966 | + | 7.31966i | −0.266038 | + | 0.266038i | −0.827501 | − | 0.561464i | \(-0.810238\pi\) |
0.561464 | + | 0.827501i | \(0.310238\pi\) | |||||||
\(758\) | 2.26483 | + | 5.46777i | 0.0822622 | + | 0.198598i | ||||
\(759\) | −1.84123 | − | 4.44511i | −0.0668323 | − | 0.161347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 40.0677i | − | 1.45245i | −0.687455 | − | 0.726227i | \(-0.741272\pi\) | ||
0.687455 | − | 0.726227i | \(-0.258728\pi\) | |||||||
\(762\) | −5.20027 | − | 2.15402i | −0.188386 | − | 0.0780319i | ||||
\(763\) | −1.64876 | − | 1.64876i | −0.0596891 | − | 0.0596891i | ||||
\(764\) | −16.7260 | −0.605125 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 16.6216 | 0.600562 | ||||||||
\(767\) | 15.0156 | + | 15.0156i | 0.542182 | + | 0.542182i | ||||
\(768\) | −43.9257 | − | 18.1946i | −1.58503 | − | 0.656542i | ||||
\(769\) | 40.8532i | 1.47320i | 0.676327 | + | 0.736602i | \(0.263571\pi\) | ||||
−0.676327 | + | 0.736602i | \(0.736429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.83281 | + | 14.0816i | 0.210063 | + | 0.507138i | ||||
\(772\) | −10.5384 | − | 25.4419i | −0.379284 | − | 0.915673i | ||||
\(773\) | 12.0994 | − | 12.0994i | 0.435183 | − | 0.435183i | −0.455204 | − | 0.890387i | \(-0.650434\pi\) |
0.890387 | + | 0.455204i | \(0.150434\pi\) | |||||||
\(774\) | 40.5273 | + | 40.5273i | 1.45673 | + | 1.45673i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.1286 | − | 31.6953i | −0.471290 | − | 1.13779i | ||||
\(777\) | 6.36928 | − | 15.3768i | 0.228497 | − | 0.551640i | ||||
\(778\) | 1.94355 | 0.0696796 | ||||||||
\(779\) | −0.397979 | + | 0.960806i | −0.0142591 | + | 0.0344245i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.92341 | 0.355087 | ||||||||
\(782\) | −2.46227 | + | 0.338036i | −0.0880504 | + | 0.0120881i | ||||
\(783\) | − | 52.6794i | − | 1.88261i | ||||||
\(784\) | 1.07194 | − | 1.07194i | 0.0382837 | − | 0.0382837i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 20.9529i | 0.747366i | ||||||||
\(787\) | −7.04943 | + | 17.0188i | −0.251285 | + | 0.606655i | −0.998308 | − | 0.0581423i | \(-0.981482\pi\) |
0.747023 | + | 0.664798i | \(0.231482\pi\) | |||||||
\(788\) | −10.1627 | + | 4.20953i | −0.362031 | + | 0.149958i | ||||
\(789\) | 33.4917 | − | 13.8727i | 1.19234 | − | 0.493882i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.207311 | − | 0.207311i | −0.00737114 | − | 0.00737114i | ||||
\(792\) | 14.6191 | + | 35.2935i | 0.519465 | + | 1.25410i | ||||
\(793\) | −6.60064 | + | 2.73408i | −0.234396 | + | 0.0970899i | ||||
\(794\) | −0.323707 | − | 0.134084i | −0.0114879 | − | 0.00475845i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.42372 | + | 8.26559i | −0.121350 | + | 0.292966i | ||||
\(797\) | 20.2228 | + | 20.2228i | 0.716328 | + | 0.716328i | 0.967851 | − | 0.251523i | \(-0.0809314\pi\) |
−0.251523 | + | 0.967851i | \(0.580931\pi\) | |||||||
\(798\) | 0.384109i | 0.0135973i | ||||||||
\(799\) | −38.8694 | + | 22.7290i | −1.37510 | + | 0.804094i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.9107 | + | 48.9107i | −1.72817 | + | 1.72817i | ||||
\(802\) | 13.9613 | + | 5.78296i | 0.492991 | + | 0.204203i | ||||
\(803\) | 12.9913 | 0.458453 | ||||||||
\(804\) | −17.6991 | − | 7.33121i | −0.624200 | − | 0.258552i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 29.2470 | − | 12.1145i | 1.03018 | − | 0.426716i | ||||
\(807\) | −18.7512 | + | 18.7512i | −0.660074 | + | 0.660074i | ||||
\(808\) | 20.4741 | − | 20.4741i | 0.720276 | − | 0.720276i | ||||
\(809\) | 25.1095 | − | 10.4007i | 0.882801 | − | 0.365668i | 0.105219 | − | 0.994449i | \(-0.466446\pi\) |
0.777583 | + | 0.628781i | \(0.216446\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.5782 | + | 7.28112i | 0.617254 | + | 0.255675i | 0.669326 | − | 0.742968i | \(-0.266583\pi\) |
−0.0520727 | + | 0.998643i | \(0.516583\pi\) | |||||||
\(812\) | 6.82526 | 0.239520 | ||||||||
\(813\) | −38.8752 | − | 16.1026i | −1.36341 | − | 0.564744i | ||||
\(814\) | −12.7124 | + | 12.7124i | −0.445571 | + | 0.445571i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.75733 | − | 0.378544i | 0.0965258 | − | 0.0132517i | ||||
\(817\) | 2.42541i | 0.0848545i | ||||||||
\(818\) | −10.0537 | − | 10.0537i | −0.351519 | − | 0.351519i | ||||
\(819\) | 9.29082 | − | 22.4300i | 0.324648 | − | 0.783768i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.6213 | − | 11.0269i | −0.929089 | − | 0.384841i | −0.133756 | − | 0.991014i | \(-0.542704\pi\) |
−0.795333 | + | 0.606173i | \(0.792704\pi\) | |||||||
\(822\) | 18.9394 | − | 7.84495i | 0.660587 | − | 0.273624i | ||||
\(823\) | −15.9651 | − | 38.5431i | −0.556507 | − | 1.34353i | −0.912514 | − | 0.409044i | \(-0.865862\pi\) |
0.356007 | − | 0.934483i | \(-0.384138\pi\) | |||||||
\(824\) | −19.9512 | − | 19.9512i | −0.695034 | − | 0.695034i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.04734 | + | 0.848034i | −0.0712359 | + | 0.0295069i | ||||
\(827\) | 25.0091 | − | 10.3591i | 0.869650 | − | 0.360221i | 0.0971760 | − | 0.995267i | \(-0.469019\pi\) |
0.772474 | + | 0.635046i | \(0.219019\pi\) | |||||||
\(828\) | 1.60138 | − | 3.86606i | 0.0556516 | − | 0.134355i | ||||
\(829\) | − | 21.8341i | − | 0.758331i | −0.925329 | − | 0.379165i | \(-0.876211\pi\) | ||
0.925329 | − | 0.379165i | \(-0.123789\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.6230 | + | 26.6230i | −0.923542 | + | 0.923542i | ||||
\(832\) | − | 34.4922i | − | 1.19580i | ||||||
\(833\) | 6.76324 | − | 25.8112i | 0.234332 | − | 0.894307i | ||||
\(834\) | −45.4822 | −1.57492 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −0.229934 | + | 0.555110i | −0.00795244 | + | 0.0191989i | ||||
\(837\) | −36.9250 | −1.27631 | ||||||||
\(838\) | 3.67380 | − | 8.86933i | 0.126909 | − | 0.306386i | ||||
\(839\) | −17.4844 | − | 42.2111i | −0.603629 | − | 1.45729i | −0.869820 | − | 0.493369i | \(-0.835765\pi\) |
0.266191 | − | 0.963920i | \(-0.414235\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.0239 | + | 24.0239i | 0.828411 | + | 0.828411i | ||||
\(842\) | −10.8798 | + | 10.8798i | −0.374942 | + | 0.374942i | ||||
\(843\) | 8.33802 | + | 20.1298i | 0.287177 | + | 0.693305i | ||||
\(844\) | −11.3025 | − | 27.2866i | −0.389047 | − | 0.939243i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 52.3506i | 1.79985i | ||||||||
\(847\) | −3.17830 | − | 1.31649i | −0.109208 | − | 0.0452353i | ||||
\(848\) | −0.641993 | − | 0.641993i | −0.0220461 | − | 0.0220461i | ||||
\(849\) | 11.8665 | 0.407259 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.29854 | 0.181632 | ||||||||
\(852\) | 9.55488 | + | 9.55488i | 0.327345 | + | 0.327345i | ||||
\(853\) | 0.0896578 | + | 0.0371375i | 0.00306983 | + | 0.00127156i | 0.384218 | − | 0.923242i | \(-0.374471\pi\) |
−0.381148 | + | 0.924514i | \(0.624471\pi\) | |||||||
\(854\) | − | 0.745567i | − | 0.0255128i | ||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.20022 | − | 10.1402i | −0.143560 | − | 0.346585i | ||||
\(857\) | 17.8974 | + | 43.2082i | 0.611364 | + | 1.47596i | 0.861503 | + | 0.507753i | \(0.169524\pi\) |
−0.250139 | + | 0.968210i | \(0.580476\pi\) | |||||||
\(858\) | −29.0326 | + | 29.0326i | −0.991157 | + | 0.991157i | ||||
\(859\) | 18.6065 | + | 18.6065i | 0.634845 | + | 0.634845i | 0.949279 | − | 0.314434i | \(-0.101815\pi\) |
−0.314434 | + | 0.949279i | \(0.601815\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.10988 | + | 9.92213i | 0.140064 | + | 0.338145i | ||||
\(862\) | −6.81077 | + | 16.4426i | −0.231976 | + | 0.560039i | ||||
\(863\) | 33.5202 | 1.14104 | 0.570520 | − | 0.821284i | \(-0.306742\pi\) | ||||
0.570520 | + | 0.821284i | \(0.306742\pi\) | |||||||
\(864\) | −14.0794 | + | 33.9907i | −0.478992 | + | 1.15639i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −19.8466 | −0.674414 | ||||||||
\(867\) | 38.5319 | − | 30.2499i | 1.30861 | − | 1.02734i | ||||
\(868\) | − | 4.78408i | − | 0.162382i | ||||||
\(869\) | −24.8561 | + | 24.8561i | −0.843187 | + | 0.843187i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 35.3837i | − | 1.19893i | ||||||
\(872\) | −3.53121 | + | 8.52509i | −0.119582 | + | 0.288696i | ||||
\(873\) | −58.4295 | + | 24.2023i | −1.97754 | + | 0.819123i | ||||
\(874\) | −0.112973 | + | 0.0467950i | −0.00382138 | + | 0.00158287i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.5088 | + | 12.5088i | 0.422635 | + | 0.422635i | ||||
\(877\) | −1.51846 | − | 3.66588i | −0.0512747 | − | 0.123788i | 0.896167 | − | 0.443718i | \(-0.146341\pi\) |
−0.947441 | + | 0.319930i | \(0.896341\pi\) | |||||||
\(878\) | −7.09689 | + | 2.93963i | −0.239508 | + | 0.0992076i | ||||
\(879\) | 49.4656 | + | 20.4893i | 1.66843 | + | 0.691088i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.1301 | + | 41.3558i | −0.577129 | + | 1.39331i | 0.318249 | + | 0.948007i | \(0.396905\pi\) |
−0.895378 | + | 0.445306i | \(0.853095\pi\) | |||||||
\(882\) | −21.9362 | − | 21.9362i | −0.738630 | − | 0.738630i | ||||
\(883\) | − | 6.22372i | − | 0.209445i | −0.994501 | − | 0.104722i | \(-0.966605\pi\) | ||
0.994501 | − | 0.104722i | \(-0.0333954\pi\) | |||||||
\(884\) | −15.5041 | − | 26.5139i | −0.521458 | − | 0.891759i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.00993 | − | 3.00993i | 0.101121 | − | 0.101121i | ||||
\(887\) | 15.5607 | + | 6.44546i | 0.522478 | + | 0.216417i | 0.628305 | − | 0.777967i | \(-0.283749\pi\) |
−0.105827 | + | 0.994385i | \(0.533749\pi\) | |||||||
\(888\) | −65.8661 | −2.21032 | ||||||||
\(889\) | −1.45152 | − | 0.601240i | −0.0486825 | − | 0.0201650i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.44320 | − | 3.08308i | 0.249357 | − | 0.103287i | ||||
\(892\) | 10.1795 | − | 10.1795i | 0.340835 | − | 0.340835i | ||||
\(893\) | −1.56650 | + | 1.56650i | −0.0524208 | + | 0.0524208i | ||||
\(894\) | −17.8764 | + | 7.40465i | −0.597876 | + | 0.247648i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −4.11950 | − | 1.70635i | −0.137623 | − | 0.0570052i | ||||
\(897\) | 12.1008 | 0.404033 | ||||||||
\(898\) | −21.9091 | − | 9.07506i | −0.731118 | − | 0.302839i | ||||
\(899\) | 31.2127 | − | 31.2127i | 1.04100 | − | 1.04100i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.4585 | − | 4.05054i | −0.514997 | − | 0.134943i | ||||
\(902\) | − | 11.6007i | − | 0.386260i | ||||||
\(903\) | 17.7109 | + | 17.7109i | 0.589381 | + | 0.589381i | ||||
\(904\) | −0.444006 | + | 1.07193i | −0.0147674 | + | 0.0356517i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 32.5165 | + | 13.4688i | 1.08029 | + | 0.447470i | ||||
\(907\) | −26.7345 | + | 11.0738i | −0.887705 | + | 0.367699i | −0.779480 | − | 0.626427i | \(-0.784517\pi\) |
−0.108225 | + | 0.994126i | \(0.534517\pi\) | |||||||
\(908\) | 0.899369 | + | 2.17127i | 0.0298466 | + | 0.0720561i | ||||
\(909\) | −37.7435 | − | 37.7435i | −1.25187 | − | 1.25187i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.2044 | − | 5.88367i | 0.470614 | − | 0.194935i | −0.134756 | − | 0.990879i | \(-0.543025\pi\) |
0.605370 | + | 0.795944i | \(0.293025\pi\) | |||||||
\(912\) | 0.126511 | − | 0.0524027i | 0.00418921 | − | 0.00173523i | ||||
\(913\) | 11.8317 | − | 28.5643i | 0.391573 | − | 0.945340i | ||||
\(914\) | 18.6938i | 0.618336i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.91738 | + | 1.91738i | −0.0633521 | + | 0.0633521i | ||||
\(917\) | 5.84848i | 0.193134i | ||||||||
\(918\) | −3.36473 | − | 24.5088i | −0.111053 | − | 0.808911i | ||||
\(919\) | −9.89298 | −0.326339 | −0.163170 | − | 0.986598i | \(-0.552172\pi\) | ||||
−0.163170 | + | 0.986598i | \(0.552172\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.8358 | + | 26.1600i | −0.357053 | + | 0.862002i | ||||
\(922\) | 1.75438 | 0.0577774 | ||||||||
\(923\) | −9.55095 | + | 23.0580i | −0.314373 | + | 0.758964i | ||||
\(924\) | 2.37450 | + | 5.73256i | 0.0781154 | + | 0.188587i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.83036 | + | 6.83036i | 0.224460 | + | 0.224460i | ||||
\(927\) | −36.7796 | + | 36.7796i | −1.20800 | + | 1.20800i | ||||
\(928\) | −16.8311 | − | 40.6338i | −0.552507 | − | 1.33387i | ||||
\(929\) | 2.76136 | + | 6.66651i | 0.0905973 | + | 0.218721i | 0.962683 | − | 0.270632i | \(-0.0872328\pi\) |
−0.872085 | + | 0.489354i | \(0.837233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.31280i | − | 0.0430253i | ||||||
\(932\) | −24.8145 | − | 10.2785i | −0.812826 | − | 0.336684i | ||||
\(933\) | 58.4555 | + | 58.4555i | 1.91375 | + | 1.91375i | ||||
\(934\) | −4.38699 | −0.143547 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −96.0783 | −3.14042 | ||||||||
\(937\) | 3.46962 | + | 3.46962i | 0.113348 | + | 0.113348i | 0.761506 | − | 0.648158i | \(-0.224460\pi\) |
−0.648158 | + | 0.761506i | \(0.724460\pi\) | |||||||
\(938\) | 3.41141 | + | 1.41305i | 0.111386 | + | 0.0461378i | ||||
\(939\) | 2.79126i | 0.0910892i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 10.0630 | + | 24.2941i | 0.328043 | + | 0.791966i | 0.998738 | + | 0.0502322i | \(0.0159961\pi\) |
−0.670695 | + | 0.741734i | \(0.734004\pi\) | |||||||
\(942\) | 2.74879 | + | 6.63617i | 0.0895605 | + | 0.216218i | ||||
\(943\) | −2.41758 | + | 2.41758i | −0.0787271 | + | 0.0787271i | ||||
\(944\) | 0.558622 | + | 0.558622i | 0.0181816 | + | 0.0181816i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.3535 | − | 24.9956i | −0.336622 | − | 0.812677i | ||||
\(947\) | −12.6418 | + | 30.5201i | −0.410804 | + | 0.991770i | 0.574118 | + | 0.818773i | \(0.305345\pi\) |
−0.984922 | + | 0.172997i | \(0.944655\pi\) | |||||||
\(948\) | −47.8661 | −1.55462 | ||||||||
\(949\) | −12.5037 | + | 30.1866i | −0.405887 | + | 0.979899i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 76.4343 | 2.47855 | ||||||||
\(952\) | 8.54356 | − | 1.17292i | 0.276898 | − | 0.0380144i | ||||
\(953\) | − | 51.4399i | − | 1.66630i | −0.553046 | − | 0.833151i | \(-0.686535\pi\) | ||
0.553046 | − | 0.833151i | \(-0.313465\pi\) | |||||||
\(954\) | −13.1377 | + | 13.1377i | −0.425349 | + | 0.425349i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 15.6501i | 0.506162i | ||||||||
\(957\) | −21.9089 | + | 52.8928i | −0.708215 | + | 1.70978i | ||||
\(958\) | 6.35390 | − | 2.63187i | 0.205285 | − | 0.0850319i | ||||
\(959\) | 5.28645 | − | 2.18972i | 0.170708 | − | 0.0707098i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0421545 | + | 0.0421545i | 0.00135982 | + | 0.00135982i | ||||
\(962\) | −17.3033 | − | 41.7739i | −0.557882 | − | 1.34685i | ||||
\(963\) | −18.6932 | + | 7.74299i | −0.602381 | + | 0.249514i | ||||
\(964\) | −3.16890 | − | 1.31260i | −0.102063 | − | 0.0422760i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −0.483247 | + | 1.16666i | −0.0155482 | + | 0.0375367i | ||||
\(967\) | −21.4243 | − | 21.4243i | −0.688960 | − | 0.688960i | 0.273042 | − | 0.962002i | \(-0.411970\pi\) |
−0.962002 | + | 0.273042i | \(0.911970\pi\) | |||||||
\(968\) | 13.6141i | 0.437575i | ||||||||
\(969\) | 1.45664 | − | 1.92024i | 0.0467940 | − | 0.0616869i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.6251 | + | 24.6251i | −0.790256 | + | 0.790256i | −0.981536 | − | 0.191279i | \(-0.938736\pi\) |
0.191279 | + | 0.981536i | \(0.438736\pi\) | |||||||
\(972\) | −11.6317 | − | 4.81802i | −0.373088 | − | 0.154538i | ||||
\(973\) | −12.6952 | −0.406990 | ||||||||
\(974\) | 0.355384 | + | 0.147205i | 0.0113872 | + | 0.00471675i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −0.245562 | + | 0.101715i | −0.00786025 | + | 0.00325582i | ||||
\(977\) | −14.6363 | + | 14.6363i | −0.468257 | + | 0.468257i | −0.901349 | − | 0.433092i | \(-0.857422\pi\) |
0.433092 | + | 0.901349i | \(0.357422\pi\) | |||||||
\(978\) | −2.54837 | + | 2.54837i | −0.0814878 | + | 0.0814878i | ||||
\(979\) | 30.1661 | − | 12.4952i | 0.964113 | − | 0.399349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.7158 | + | 6.50969i | 0.501767 | + | 0.207839i | ||||
\(982\) | −0.252373 | −0.00805354 | ||||||||
\(983\) | 40.9497 | + | 16.9619i | 1.30609 | + | 0.541002i | 0.923742 | − | 0.383015i | \(-0.125114\pi\) |
0.382352 | + | 0.924017i | \(0.375114\pi\) | |||||||
\(984\) | 30.0528 | − | 30.0528i | 0.958050 | − | 0.958050i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 23.5616 | + | 17.8731i | 0.750353 | + | 0.569196i | ||||
\(987\) | 22.8778i | 0.728207i | ||||||||
\(988\) | −1.06855 | − | 1.06855i | −0.0339951 | − | 0.0339951i | ||||
\(989\) | −3.05141 | + | 7.36675i | −0.0970291 | + | 0.234249i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1426 | + | 10.0002i | 0.766915 | + | 0.317667i | 0.731622 | − | 0.681710i | \(-0.238764\pi\) |
0.0352929 | + | 0.999377i | \(0.488764\pi\) | |||||||
\(992\) | −28.4817 | + | 11.7975i | −0.904295 | + | 0.374571i | ||||
\(993\) | 6.75542 | + | 16.3090i | 0.214377 | + | 0.517551i | ||||
\(994\) | −1.84165 | − | 1.84165i | −0.0584137 | − | 0.0584137i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.8958 | − | 16.1112i | 1.23246 | − | 0.510502i | ||||
\(997\) | 24.2756 | − | 10.0553i | 0.768816 | − | 0.318454i | 0.0364232 | − | 0.999336i | \(-0.488404\pi\) |
0.732393 | + | 0.680882i | \(0.238404\pi\) | |||||||
\(998\) | −6.40770 | + | 15.4696i | −0.202832 | + | 0.489681i | ||||
\(999\) | 52.7404i | 1.66863i |
(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 | 425.2.n.e.399.3 | 24 | ||
5.2 | odd | 4 | 425.2.m.c.76.4 | ✓ | 24 | ||
5.3 | odd | 4 | 425.2.m.d.76.3 | yes | 24 | ||
5.4 | even | 2 | 425.2.n.d.399.4 | 24 | |||
17.15 | even | 8 | 425.2.n.d.49.4 | 24 | |||
85.7 | even | 16 | 7225.2.a.bx.1.11 | 24 | |||
85.27 | even | 16 | 7225.2.a.bx.1.12 | 24 | |||
85.32 | odd | 8 | 425.2.m.c.151.4 | yes | 24 | ||
85.49 | even | 8 | inner | 425.2.n.e.49.3 | 24 | ||
85.58 | even | 16 | 7225.2.a.cb.1.14 | 24 | |||
85.78 | even | 16 | 7225.2.a.cb.1.13 | 24 | |||
85.83 | odd | 8 | 425.2.m.d.151.3 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
425.2.m.c.76.4 | ✓ | 24 | 5.2 | odd | 4 | ||
425.2.m.c.151.4 | yes | 24 | 85.32 | odd | 8 | ||
425.2.m.d.76.3 | yes | 24 | 5.3 | odd | 4 | ||
425.2.m.d.151.3 | yes | 24 | 85.83 | odd | 8 | ||
425.2.n.d.49.4 | 24 | 17.15 | even | 8 | |||
425.2.n.d.399.4 | 24 | 5.4 | even | 2 | |||
425.2.n.e.49.3 | 24 | 85.49 | even | 8 | inner | ||
425.2.n.e.399.3 | 24 | 1.1 | even | 1 | trivial | ||
7225.2.a.bx.1.11 | 24 | 85.7 | even | 16 | |||
7225.2.a.bx.1.12 | 24 | 85.27 | even | 16 | |||
7225.2.a.cb.1.13 | 24 | 85.78 | even | 16 | |||
7225.2.a.cb.1.14 | 24 | 85.58 | even | 16 |