Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.13 | ||
Character | \(\chi\) | \(=\) | 770.43 |
Dual form | 770.2.m.f.197.13 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.888243 | − | 0.888243i | −0.512827 | − | 0.512827i | 0.402564 | − | 0.915392i | \(-0.368119\pi\) |
−0.915392 | + | 0.402564i | \(0.868119\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 1.38828 | + | 1.75290i | 0.620860 | + | 0.783922i | ||||
\(6\) | − | 1.25616i | − | 0.512827i | ||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.42205i | − | 0.474017i | ||||||
\(10\) | −0.257823 | + | 2.22115i | −0.0815308 | + | 0.702391i | ||||
\(11\) | 2.56981 | − | 2.09669i | 0.774826 | − | 0.632174i | ||||
\(12\) | 0.888243 | − | 0.888243i | 0.256414 | − | 0.256414i | ||||
\(13\) | 1.35377 | − | 1.35377i | 0.375469 | − | 0.375469i | −0.493995 | − | 0.869465i | \(-0.664464\pi\) |
0.869465 | + | 0.493995i | \(0.164464\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 0.323868 | − | 2.79014i | 0.0836224 | − | 0.720410i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.87993 | + | 2.87993i | 0.698485 | + | 0.698485i | 0.964084 | − | 0.265599i | \(-0.0855696\pi\) |
−0.265599 | + | 0.964084i | \(0.585570\pi\) | |||||||
\(18\) | 1.00554 | − | 1.00554i | 0.237008 | − | 0.237008i | ||||
\(19\) | −1.47952 | −0.339426 | −0.169713 | − | 0.985494i | \(-0.554284\pi\) | ||||
−0.169713 | + | 0.985494i | \(0.554284\pi\) | |||||||
\(20\) | −1.75290 | + | 1.38828i | −0.391961 | + | 0.310430i | ||||
\(21\) | − | 1.25616i | − | 0.274118i | ||||||
\(22\) | 3.29971 | + | 0.334548i | 0.703500 | + | 0.0713258i | ||||
\(23\) | 4.72879 | + | 4.72879i | 0.986020 | + | 0.986020i | 0.999904 | − | 0.0138832i | \(-0.00441930\pi\) |
−0.0138832 | + | 0.999904i | \(0.504419\pi\) | |||||||
\(24\) | 1.25616 | 0.256414 | ||||||||
\(25\) | −1.14533 | + | 4.86705i | −0.229066 | + | 0.973411i | ||||
\(26\) | 1.91453 | 0.375469 | ||||||||
\(27\) | −3.92785 | + | 3.92785i | −0.755916 | + | 0.755916i | ||||
\(28\) | −0.707107 | + | 0.707107i | −0.133631 | + | 0.133631i | ||||
\(29\) | −8.86980 | −1.64708 | −0.823541 | − | 0.567257i | \(-0.808005\pi\) | ||||
−0.823541 | + | 0.567257i | \(0.808005\pi\) | |||||||
\(30\) | 2.20193 | − | 1.74391i | 0.402016 | − | 0.318394i | ||||
\(31\) | 8.87900 | 1.59472 | 0.797358 | − | 0.603506i | \(-0.206230\pi\) | ||||
0.797358 | + | 0.603506i | \(0.206230\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −4.14498 | − | 0.420247i | −0.721548 | − | 0.0731556i | ||||
\(34\) | 4.07283i | 0.698485i | ||||||||
\(35\) | −0.257823 | + | 2.22115i | −0.0435800 | + | 0.375444i | ||||
\(36\) | 1.42205 | 0.237008 | ||||||||
\(37\) | 1.13673 | − | 1.13673i | 0.186878 | − | 0.186878i | −0.607467 | − | 0.794345i | \(-0.707814\pi\) |
0.794345 | + | 0.607467i | \(0.207814\pi\) | |||||||
\(38\) | −1.04618 | − | 1.04618i | −0.169713 | − | 0.169713i | ||||
\(39\) | −2.40496 | −0.385102 | ||||||||
\(40\) | −2.22115 | − | 0.257823i | −0.351195 | − | 0.0407654i | ||||
\(41\) | 8.24941i | 1.28834i | 0.764881 | + | 0.644171i | \(0.222797\pi\) | ||||
−0.764881 | + | 0.644171i | \(0.777203\pi\) | |||||||
\(42\) | 0.888243 | − | 0.888243i | 0.137059 | − | 0.137059i | ||||
\(43\) | 4.20653 | − | 4.20653i | 0.641490 | − | 0.641490i | −0.309432 | − | 0.950922i | \(-0.600139\pi\) |
0.950922 | + | 0.309432i | \(0.100139\pi\) | |||||||
\(44\) | 2.09669 | + | 2.56981i | 0.316087 | + | 0.387413i | ||||
\(45\) | 2.49271 | − | 1.97421i | 0.371592 | − | 0.294298i | ||||
\(46\) | 6.68752i | 0.986020i | ||||||||
\(47\) | 8.69999 | − | 8.69999i | 1.26902 | − | 1.26902i | 0.322431 | − | 0.946593i | \(-0.395500\pi\) |
0.946593 | − | 0.322431i | \(-0.104500\pi\) | |||||||
\(48\) | 0.888243 | + | 0.888243i | 0.128207 | + | 0.128207i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | −4.25140 | + | 2.63166i | −0.601238 | + | 0.372172i | ||||
\(51\) | − | 5.11615i | − | 0.716404i | ||||||
\(52\) | 1.35377 | + | 1.35377i | 0.187735 | + | 0.187735i | ||||
\(53\) | −0.533202 | − | 0.533202i | −0.0732409 | − | 0.0732409i | 0.669537 | − | 0.742778i | \(-0.266492\pi\) |
−0.742778 | + | 0.669537i | \(0.766492\pi\) | |||||||
\(54\) | −5.55482 | −0.755916 | ||||||||
\(55\) | 7.24291 | + | 1.59382i | 0.976634 | + | 0.214911i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 1.31418 | + | 1.31418i | 0.174067 | + | 0.174067i | ||||
\(58\) | −6.27190 | − | 6.27190i | −0.823541 | − | 0.823541i | ||||
\(59\) | 9.93780i | 1.29379i | 0.762579 | + | 0.646896i | \(0.223933\pi\) | ||||
−0.762579 | + | 0.646896i | \(0.776067\pi\) | |||||||
\(60\) | 2.79014 | + | 0.323868i | 0.360205 | + | 0.0418112i | ||||
\(61\) | − | 2.09421i | − | 0.268136i | −0.990972 | − | 0.134068i | \(-0.957196\pi\) | ||
0.990972 | − | 0.134068i | \(-0.0428040\pi\) | |||||||
\(62\) | 6.27840 | + | 6.27840i | 0.797358 | + | 0.797358i | ||||
\(63\) | 1.00554 | − | 1.00554i | 0.126686 | − | 0.126686i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 4.25246 | + | 0.493609i | 0.527453 | + | 0.0612247i | ||||
\(66\) | −2.63378 | − | 3.22810i | −0.324196 | − | 0.397352i | ||||
\(67\) | 7.31404 | − | 7.31404i | 0.893552 | − | 0.893552i | −0.101303 | − | 0.994856i | \(-0.532301\pi\) |
0.994856 | + | 0.101303i | \(0.0323013\pi\) | |||||||
\(68\) | −2.87993 | + | 2.87993i | −0.349243 | + | 0.349243i | ||||
\(69\) | − | 8.40062i | − | 1.01132i | ||||||
\(70\) | −1.75290 | + | 1.38828i | −0.209512 | + | 0.165932i | ||||
\(71\) | −10.9434 | −1.29874 | −0.649371 | − | 0.760471i | \(-0.724968\pi\) | ||||
−0.649371 | + | 0.760471i | \(0.724968\pi\) | |||||||
\(72\) | 1.00554 | + | 1.00554i | 0.118504 | + | 0.118504i | ||||
\(73\) | −10.4699 | + | 10.4699i | −1.22541 | + | 1.22541i | −0.259733 | + | 0.965680i | \(0.583635\pi\) |
−0.965680 | + | 0.259733i | \(0.916365\pi\) | |||||||
\(74\) | 1.60758 | 0.186878 | ||||||||
\(75\) | 5.34046 | − | 3.30580i | 0.616663 | − | 0.381720i | ||||
\(76\) | − | 1.47952i | − | 0.169713i | ||||||
\(77\) | 3.29971 | + | 0.334548i | 0.376037 | + | 0.0381253i | ||||
\(78\) | −1.70056 | − | 1.70056i | −0.192551 | − | 0.192551i | ||||
\(79\) | −12.8565 | −1.44646 | −0.723232 | − | 0.690605i | \(-0.757344\pi\) | ||||
−0.723232 | + | 0.690605i | \(0.757344\pi\) | |||||||
\(80\) | −1.38828 | − | 1.75290i | −0.155215 | − | 0.195980i | ||||
\(81\) | 2.71162 | 0.301292 | ||||||||
\(82\) | −5.83322 | + | 5.83322i | −0.644171 | + | 0.644171i | ||||
\(83\) | 7.94643 | − | 7.94643i | 0.872234 | − | 0.872234i | −0.120482 | − | 0.992716i | \(-0.538444\pi\) |
0.992716 | + | 0.120482i | \(0.0384439\pi\) | |||||||
\(84\) | 1.25616 | 0.137059 | ||||||||
\(85\) | −1.05007 | + | 9.04639i | −0.113896 | + | 0.981219i | ||||
\(86\) | 5.94893 | 0.641490 | ||||||||
\(87\) | 7.87854 | + | 7.87854i | 0.844668 | + | 0.844668i | ||||
\(88\) | −0.334548 | + | 3.29971i | −0.0356629 | + | 0.351750i | ||||
\(89\) | − | 8.22801i | − | 0.872167i | −0.899906 | − | 0.436084i | \(-0.856365\pi\) | ||
0.899906 | − | 0.436084i | \(-0.143635\pi\) | |||||||
\(90\) | 3.15859 | + | 0.366637i | 0.332945 | + | 0.0386470i | ||||
\(91\) | 1.91453 | 0.200697 | ||||||||
\(92\) | −4.72879 | + | 4.72879i | −0.493010 | + | 0.493010i | ||||
\(93\) | −7.88671 | − | 7.88671i | −0.817814 | − | 0.817814i | ||||
\(94\) | 12.3036 | 1.26902 | ||||||||
\(95\) | −2.05400 | − | 2.59346i | −0.210736 | − | 0.266083i | ||||
\(96\) | 1.25616i | 0.128207i | ||||||||
\(97\) | 1.76695 | − | 1.76695i | 0.179407 | − | 0.179407i | −0.611690 | − | 0.791097i | \(-0.709510\pi\) |
0.791097 | + | 0.611690i | \(0.209510\pi\) | |||||||
\(98\) | −0.707107 | + | 0.707107i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | −2.98159 | − | 3.65439i | −0.299661 | − | 0.367280i | ||||
\(100\) | −4.86705 | − | 1.14533i | −0.486705 | − | 0.114533i | ||||
\(101\) | 1.82071i | 0.181167i | 0.995889 | + | 0.0905835i | \(0.0288732\pi\) | ||||
−0.995889 | + | 0.0905835i | \(0.971127\pi\) | |||||||
\(102\) | 3.61766 | − | 3.61766i | 0.358202 | − | 0.358202i | ||||
\(103\) | −0.202934 | − | 0.202934i | −0.0199957 | − | 0.0199957i | 0.697038 | − | 0.717034i | \(-0.254501\pi\) |
−0.717034 | + | 0.697038i | \(0.754501\pi\) | |||||||
\(104\) | 1.91453i | 0.187735i | ||||||||
\(105\) | 2.20193 | − | 1.74391i | 0.214887 | − | 0.170189i | ||||
\(106\) | − | 0.754061i | − | 0.0732409i | ||||||
\(107\) | −7.06549 | − | 7.06549i | −0.683047 | − | 0.683047i | 0.277639 | − | 0.960686i | \(-0.410448\pi\) |
−0.960686 | + | 0.277639i | \(0.910448\pi\) | |||||||
\(108\) | −3.92785 | − | 3.92785i | −0.377958 | − | 0.377958i | ||||
\(109\) | −8.35194 | −0.799970 | −0.399985 | − | 0.916522i | \(-0.630985\pi\) | ||||
−0.399985 | + | 0.916522i | \(0.630985\pi\) | |||||||
\(110\) | 3.99451 | + | 6.24851i | 0.380861 | + | 0.595772i | ||||
\(111\) | −2.01939 | −0.191672 | ||||||||
\(112\) | −0.707107 | − | 0.707107i | −0.0668153 | − | 0.0668153i | ||||
\(113\) | −6.97441 | − | 6.97441i | −0.656098 | − | 0.656098i | 0.298357 | − | 0.954454i | \(-0.403561\pi\) |
−0.954454 | + | 0.298357i | \(0.903561\pi\) | |||||||
\(114\) | 1.85853i | 0.174067i | ||||||||
\(115\) | −1.72420 | + | 14.8540i | −0.160782 | + | 1.38514i | ||||
\(116\) | − | 8.86980i | − | 0.823541i | ||||||
\(117\) | −1.92513 | − | 1.92513i | −0.177979 | − | 0.177979i | ||||
\(118\) | −7.02708 | + | 7.02708i | −0.646896 | + | 0.646896i | ||||
\(119\) | 4.07283i | 0.373356i | ||||||||
\(120\) | 1.74391 | + | 2.20193i | 0.159197 | + | 0.201008i | ||||
\(121\) | 2.20782 | − | 10.7762i | 0.200711 | − | 0.979651i | ||||
\(122\) | 1.48083 | − | 1.48083i | 0.134068 | − | 0.134068i | ||||
\(123\) | 7.32748 | − | 7.32748i | 0.660697 | − | 0.660697i | ||||
\(124\) | 8.87900i | 0.797358i | ||||||||
\(125\) | −10.1215 | + | 4.74921i | −0.905296 | + | 0.424782i | ||||
\(126\) | 1.42205 | 0.126686 | ||||||||
\(127\) | −11.9485 | − | 11.9485i | −1.06026 | − | 1.06026i | −0.998064 | − | 0.0621978i | \(-0.980189\pi\) |
−0.0621978 | − | 0.998064i | \(-0.519811\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −7.47284 | −0.657947 | ||||||||
\(130\) | 2.65791 | + | 3.35598i | 0.233114 | + | 0.294339i | ||||
\(131\) | − | 6.02808i | − | 0.526676i | −0.964704 | − | 0.263338i | \(-0.915177\pi\) | ||
0.964704 | − | 0.263338i | \(-0.0848234\pi\) | |||||||
\(132\) | 0.420247 | − | 4.14498i | 0.0365778 | − | 0.360774i | ||||
\(133\) | −1.04618 | − | 1.04618i | −0.0907154 | − | 0.0907154i | ||||
\(134\) | 10.3436 | 0.893552 | ||||||||
\(135\) | −12.3381 | − | 1.43216i | −1.06190 | − | 0.123261i | ||||
\(136\) | −4.07283 | −0.349243 | ||||||||
\(137\) | 2.39805 | − | 2.39805i | 0.204879 | − | 0.204879i | −0.597207 | − | 0.802087i | \(-0.703723\pi\) |
0.802087 | + | 0.597207i | \(0.203723\pi\) | |||||||
\(138\) | 5.94014 | − | 5.94014i | 0.505658 | − | 0.505658i | ||||
\(139\) | 3.78375 | 0.320933 | 0.160467 | − | 0.987041i | \(-0.448700\pi\) | ||||
0.160467 | + | 0.987041i | \(0.448700\pi\) | |||||||
\(140\) | −2.22115 | − | 0.257823i | −0.187722 | − | 0.0217900i | ||||
\(141\) | −15.4554 | −1.30158 | ||||||||
\(142\) | −7.73815 | − | 7.73815i | −0.649371 | − | 0.649371i | ||||
\(143\) | 0.640500 | − | 6.31738i | 0.0535613 | − | 0.528286i | ||||
\(144\) | 1.42205i | 0.118504i | ||||||||
\(145\) | −12.3138 | − | 15.5479i | −1.02261 | − | 1.29118i | ||||
\(146\) | −14.8067 | −1.22541 | ||||||||
\(147\) | 0.888243 | − | 0.888243i | 0.0732610 | − | 0.0732610i | ||||
\(148\) | 1.13673 | + | 1.13673i | 0.0934389 | + | 0.0934389i | ||||
\(149\) | 0.493471 | 0.0404267 | 0.0202134 | − | 0.999796i | \(-0.493565\pi\) | ||||
0.0202134 | + | 0.999796i | \(0.493565\pi\) | |||||||
\(150\) | 6.11382 | + | 1.43872i | 0.499192 | + | 0.117471i | ||||
\(151\) | − | 19.0310i | − | 1.54872i | −0.632746 | − | 0.774359i | \(-0.718072\pi\) | ||
0.632746 | − | 0.774359i | \(-0.281928\pi\) | |||||||
\(152\) | 1.04618 | − | 1.04618i | 0.0848565 | − | 0.0848565i | ||||
\(153\) | 4.09540 | − | 4.09540i | 0.331094 | − | 0.331094i | ||||
\(154\) | 2.09669 | + | 2.56981i | 0.168956 | + | 0.207081i | ||||
\(155\) | 12.3266 | + | 15.5640i | 0.990095 | + | 1.25013i | ||||
\(156\) | − | 2.40496i | − | 0.192551i | ||||||
\(157\) | −12.7843 | + | 12.7843i | −1.02030 | + | 1.02030i | −0.0205125 | + | 0.999790i | \(0.506530\pi\) |
−0.999790 | + | 0.0205125i | \(0.993470\pi\) | |||||||
\(158\) | −9.09089 | − | 9.09089i | −0.723232 | − | 0.723232i | ||||
\(159\) | 0.947225i | 0.0751198i | ||||||||
\(160\) | 0.257823 | − | 2.22115i | 0.0203827 | − | 0.175598i | ||||
\(161\) | 6.68752i | 0.527050i | ||||||||
\(162\) | 1.91741 | + | 1.91741i | 0.150646 | + | 0.150646i | ||||
\(163\) | −1.69054 | − | 1.69054i | −0.132413 | − | 0.132413i | 0.637794 | − | 0.770207i | \(-0.279847\pi\) |
−0.770207 | + | 0.637794i | \(0.779847\pi\) | |||||||
\(164\) | −8.24941 | −0.644171 | ||||||||
\(165\) | −5.01776 | − | 7.84916i | −0.390632 | − | 0.611056i | ||||
\(166\) | 11.2379 | 0.872234 | ||||||||
\(167\) | 15.3944 | + | 15.3944i | 1.19126 | + | 1.19126i | 0.976715 | + | 0.214542i | \(0.0688259\pi\) |
0.214542 | + | 0.976715i | \(0.431174\pi\) | |||||||
\(168\) | 0.888243 | + | 0.888243i | 0.0685294 | + | 0.0685294i | ||||
\(169\) | 9.33459i | 0.718045i | ||||||||
\(170\) | −7.13928 | + | 5.65425i | −0.547558 | + | 0.433661i | ||||
\(171\) | 2.10396i | 0.160894i | ||||||||
\(172\) | 4.20653 | + | 4.20653i | 0.320745 | + | 0.320745i | ||||
\(173\) | 5.59818 | − | 5.59818i | 0.425622 | − | 0.425622i | −0.461512 | − | 0.887134i | \(-0.652693\pi\) |
0.887134 | + | 0.461512i | \(0.152693\pi\) | |||||||
\(174\) | 11.1419i | 0.844668i | ||||||||
\(175\) | −4.25140 | + | 2.63166i | −0.321375 | + | 0.198935i | ||||
\(176\) | −2.56981 | + | 2.09669i | −0.193707 | + | 0.158044i | ||||
\(177\) | 8.82718 | − | 8.82718i | 0.663491 | − | 0.663491i | ||||
\(178\) | 5.81808 | − | 5.81808i | 0.436084 | − | 0.436084i | ||||
\(179\) | − | 1.60494i | − | 0.119959i | −0.998200 | − | 0.0599794i | \(-0.980897\pi\) | ||
0.998200 | − | 0.0599794i | \(-0.0191035\pi\) | |||||||
\(180\) | 1.97421 | + | 2.49271i | 0.147149 | + | 0.185796i | ||||
\(181\) | −24.0351 | −1.78652 | −0.893258 | − | 0.449544i | \(-0.851586\pi\) | ||||
−0.893258 | + | 0.449544i | \(0.851586\pi\) | |||||||
\(182\) | 1.35377 | + | 1.35377i | 0.100348 | + | 0.100348i | ||||
\(183\) | −1.86016 | + | 1.86016i | −0.137507 | + | 0.137507i | ||||
\(184\) | −6.68752 | −0.493010 | ||||||||
\(185\) | 3.57069 | + | 0.414472i | 0.262523 | + | 0.0304726i | ||||
\(186\) | − | 11.1535i | − | 0.817814i | ||||||
\(187\) | 13.4392 | + | 1.36256i | 0.982769 | + | 0.0996401i | ||||
\(188\) | 8.69999 | + | 8.69999i | 0.634512 | + | 0.634512i | ||||
\(189\) | −5.55482 | −0.404054 | ||||||||
\(190\) | 0.381455 | − | 3.28625i | 0.0276737 | − | 0.238410i | ||||
\(191\) | −5.76500 | −0.417141 | −0.208570 | − | 0.978007i | \(-0.566881\pi\) | ||||
−0.208570 | + | 0.978007i | \(0.566881\pi\) | |||||||
\(192\) | −0.888243 | + | 0.888243i | −0.0641034 | + | 0.0641034i | ||||
\(193\) | −2.53288 | + | 2.53288i | −0.182321 | + | 0.182321i | −0.792366 | − | 0.610046i | \(-0.791151\pi\) |
0.610046 | + | 0.792366i | \(0.291151\pi\) | |||||||
\(194\) | 2.49885 | 0.179407 | ||||||||
\(195\) | −3.33877 | − | 4.21566i | −0.239094 | − | 0.301890i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 9.40601 | + | 9.40601i | 0.670150 | + | 0.670150i | 0.957751 | − | 0.287600i | \(-0.0928575\pi\) |
−0.287600 | + | 0.957751i | \(0.592857\pi\) | |||||||
\(198\) | 0.475744 | − | 4.69235i | 0.0338096 | − | 0.333471i | ||||
\(199\) | − | 9.67486i | − | 0.685833i | −0.939366 | − | 0.342916i | \(-0.888585\pi\) | ||
0.939366 | − | 0.342916i | \(-0.111415\pi\) | |||||||
\(200\) | −2.63166 | − | 4.25140i | −0.186086 | − | 0.300619i | ||||
\(201\) | −12.9933 | −0.916476 | ||||||||
\(202\) | −1.28743 | + | 1.28743i | −0.0905835 | + | 0.0905835i | ||||
\(203\) | −6.27190 | − | 6.27190i | −0.440201 | − | 0.440201i | ||||
\(204\) | 5.11615 | 0.358202 | ||||||||
\(205\) | −14.4604 | + | 11.4525i | −1.00996 | + | 0.799880i | ||||
\(206\) | − | 0.286992i | − | 0.0199957i | ||||||
\(207\) | 6.72457 | − | 6.72457i | 0.467390 | − | 0.467390i | ||||
\(208\) | −1.35377 | + | 1.35377i | −0.0938674 | + | 0.0938674i | ||||
\(209\) | −3.80209 | + | 3.10210i | −0.262996 | + | 0.214577i | ||||
\(210\) | 2.79014 | + | 0.323868i | 0.192538 | + | 0.0223490i | ||||
\(211\) | − | 11.1990i | − | 0.770971i | −0.922714 | − | 0.385485i | \(-0.874034\pi\) | ||
0.922714 | − | 0.385485i | \(-0.125966\pi\) | |||||||
\(212\) | 0.533202 | − | 0.533202i | 0.0366204 | − | 0.0366204i | ||||
\(213\) | 9.72040 | + | 9.72040i | 0.666031 | + | 0.666031i | ||||
\(214\) | − | 9.99212i | − | 0.683047i | ||||||
\(215\) | 13.2135 | + | 1.53377i | 0.901153 | + | 0.104602i | ||||
\(216\) | − | 5.55482i | − | 0.377958i | ||||||
\(217\) | 6.27840 | + | 6.27840i | 0.426206 | + | 0.426206i | ||||
\(218\) | −5.90571 | − | 5.90571i | −0.399985 | − | 0.399985i | ||||
\(219\) | 18.5997 | 1.25685 | ||||||||
\(220\) | −1.59382 | + | 7.24291i | −0.107456 | + | 0.488317i | ||||
\(221\) | 7.79755 | 0.524520 | ||||||||
\(222\) | −1.42792 | − | 1.42792i | −0.0958360 | − | 0.0958360i | ||||
\(223\) | 1.71338 | + | 1.71338i | 0.114736 | + | 0.114736i | 0.762144 | − | 0.647408i | \(-0.224147\pi\) |
−0.647408 | + | 0.762144i | \(0.724147\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | 6.92119 | + | 1.62872i | 0.461413 | + | 0.108581i | ||||
\(226\) | − | 9.86331i | − | 0.656098i | ||||||
\(227\) | −5.86091 | − | 5.86091i | −0.389002 | − | 0.389002i | 0.485329 | − | 0.874332i | \(-0.338700\pi\) |
−0.874332 | + | 0.485329i | \(0.838700\pi\) | |||||||
\(228\) | −1.31418 | + | 1.31418i | −0.0870335 | + | 0.0870335i | ||||
\(229\) | − | 1.08317i | − | 0.0715777i | −0.999359 | − | 0.0357888i | \(-0.988606\pi\) | ||
0.999359 | − | 0.0357888i | \(-0.0113944\pi\) | |||||||
\(230\) | −11.7226 | + | 9.28418i | −0.772963 | + | 0.612181i | ||||
\(231\) | −2.63378 | − | 3.22810i | −0.173290 | − | 0.212394i | ||||
\(232\) | 6.27190 | − | 6.27190i | 0.411770 | − | 0.411770i | ||||
\(233\) | 13.0962 | − | 13.0962i | 0.857963 | − | 0.857963i | −0.133135 | − | 0.991098i | \(-0.542504\pi\) |
0.991098 | + | 0.133135i | \(0.0425043\pi\) | |||||||
\(234\) | − | 2.72255i | − | 0.177979i | ||||||
\(235\) | 27.3283 | + | 3.17216i | 1.78270 | + | 0.206929i | ||||
\(236\) | −9.93780 | −0.646896 | ||||||||
\(237\) | 11.4197 | + | 11.4197i | 0.741786 | + | 0.741786i | ||||
\(238\) | −2.87993 | + | 2.87993i | −0.186678 | + | 0.186678i | ||||
\(239\) | 27.4149 | 1.77332 | 0.886661 | − | 0.462419i | \(-0.153018\pi\) | ||||
0.886661 | + | 0.462419i | \(0.153018\pi\) | |||||||
\(240\) | −0.323868 | + | 2.79014i | −0.0209056 | + | 0.180103i | ||||
\(241\) | − | 1.81865i | − | 0.117149i | −0.998283 | − | 0.0585747i | \(-0.981344\pi\) | ||
0.998283 | − | 0.0585747i | \(-0.0186556\pi\) | |||||||
\(242\) | 9.18106 | − | 6.05873i | 0.590181 | − | 0.389470i | ||||
\(243\) | 9.37498 | + | 9.37498i | 0.601405 | + | 0.601405i | ||||
\(244\) | 2.09421 | 0.134068 | ||||||||
\(245\) | −1.75290 | + | 1.38828i | −0.111989 | + | 0.0886943i | ||||
\(246\) | 10.3626 | 0.660697 | ||||||||
\(247\) | −2.00294 | + | 2.00294i | −0.127444 | + | 0.127444i | ||||
\(248\) | −6.27840 | + | 6.27840i | −0.398679 | + | 0.398679i | ||||
\(249\) | −14.1167 | −0.894610 | ||||||||
\(250\) | −10.5152 | − | 3.79879i | −0.665039 | − | 0.240257i | ||||
\(251\) | −11.0968 | −0.700423 | −0.350212 | − | 0.936671i | \(-0.613890\pi\) | ||||
−0.350212 | + | 0.936671i | \(0.613890\pi\) | |||||||
\(252\) | 1.00554 | + | 1.00554i | 0.0633431 | + | 0.0633431i | ||||
\(253\) | 22.0669 | + | 2.23729i | 1.38733 | + | 0.140657i | ||||
\(254\) | − | 16.8978i | − | 1.06026i | ||||||
\(255\) | 8.96811 | − | 7.10267i | 0.561605 | − | 0.444787i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.77824 | + | 3.77824i | −0.235680 | + | 0.235680i | −0.815059 | − | 0.579378i | \(-0.803295\pi\) |
0.579378 | + | 0.815059i | \(0.303295\pi\) | |||||||
\(258\) | −5.28409 | − | 5.28409i | −0.328973 | − | 0.328973i | ||||
\(259\) | 1.60758 | 0.0998904 | ||||||||
\(260\) | −0.493609 | + | 4.25246i | −0.0306123 | + | 0.263726i | ||||
\(261\) | 12.6133i | 0.780744i | ||||||||
\(262\) | 4.26249 | − | 4.26249i | 0.263338 | − | 0.263338i | ||||
\(263\) | −17.0224 | + | 17.0224i | −1.04965 | + | 1.04965i | −0.0509451 | + | 0.998701i | \(0.516223\pi\) |
−0.998701 | + | 0.0509451i | \(0.983777\pi\) | |||||||
\(264\) | 3.22810 | − | 2.63378i | 0.198676 | − | 0.162098i | ||||
\(265\) | 0.194414 | − | 1.67489i | 0.0119428 | − | 0.102887i | ||||
\(266\) | − | 1.47952i | − | 0.0907154i | ||||||
\(267\) | −7.30847 | + | 7.30847i | −0.447271 | + | 0.447271i | ||||
\(268\) | 7.31404 | + | 7.31404i | 0.446776 | + | 0.446776i | ||||
\(269\) | − | 21.8470i | − | 1.33204i | −0.745936 | − | 0.666018i | \(-0.767997\pi\) | ||
0.745936 | − | 0.666018i | \(-0.232003\pi\) | |||||||
\(270\) | −7.71168 | − | 9.73706i | −0.469318 | − | 0.592579i | ||||
\(271\) | 11.6241i | 0.706114i | 0.935602 | + | 0.353057i | \(0.114858\pi\) | ||||
−0.935602 | + | 0.353057i | \(0.885142\pi\) | |||||||
\(272\) | −2.87993 | − | 2.87993i | −0.174621 | − | 0.174621i | ||||
\(273\) | −1.70056 | − | 1.70056i | −0.102923 | − | 0.102923i | ||||
\(274\) | 3.39136 | 0.204879 | ||||||||
\(275\) | 7.26141 | + | 14.9088i | 0.437879 | + | 0.899034i | ||||
\(276\) | 8.40062 | 0.505658 | ||||||||
\(277\) | −20.9515 | − | 20.9515i | −1.25885 | − | 1.25885i | −0.951641 | − | 0.307213i | \(-0.900604\pi\) |
−0.307213 | − | 0.951641i | \(-0.599396\pi\) | |||||||
\(278\) | 2.67551 | + | 2.67551i | 0.160467 | + | 0.160467i | ||||
\(279\) | − | 12.6264i | − | 0.755922i | ||||||
\(280\) | −1.38828 | − | 1.75290i | −0.0829659 | − | 0.104756i | ||||
\(281\) | 12.0990i | 0.721763i | 0.932612 | + | 0.360881i | \(0.117524\pi\) | ||||
−0.932612 | + | 0.360881i | \(0.882476\pi\) | |||||||
\(282\) | −10.9286 | − | 10.9286i | −0.650790 | − | 0.650790i | ||||
\(283\) | −11.0577 | + | 11.0577i | −0.657315 | + | 0.657315i | −0.954744 | − | 0.297429i | \(-0.903871\pi\) |
0.297429 | + | 0.954744i | \(0.403871\pi\) | |||||||
\(284\) | − | 10.9434i | − | 0.649371i | ||||||
\(285\) | −0.479171 | + | 4.12807i | −0.0283836 | + | 0.244526i | ||||
\(286\) | 4.91996 | − | 4.01416i | 0.290924 | − | 0.237362i | ||||
\(287\) | −5.83322 | + | 5.83322i | −0.344324 | + | 0.344324i | ||||
\(288\) | −1.00554 | + | 1.00554i | −0.0592521 | + | 0.0592521i | ||||
\(289\) | − | 0.412027i | − | 0.0242369i | ||||||
\(290\) | 2.28684 | − | 19.7012i | 0.134288 | − | 1.15689i | ||||
\(291\) | −3.13897 | −0.184010 | ||||||||
\(292\) | −10.4699 | − | 10.4699i | −0.612707 | − | 0.612707i | ||||
\(293\) | 19.5279 | − | 19.5279i | 1.14083 | − | 1.14083i | 0.152533 | − | 0.988298i | \(-0.451257\pi\) |
0.988298 | − | 0.152533i | \(-0.0487429\pi\) | |||||||
\(294\) | 1.25616 | 0.0732610 | ||||||||
\(295\) | −17.4200 | + | 13.7965i | −1.01423 | + | 0.803263i | ||||
\(296\) | 1.60758i | 0.0934389i | ||||||||
\(297\) | −1.85835 | + | 18.3293i | −0.107833 | + | 1.06357i | ||||
\(298\) | 0.348937 | + | 0.348937i | 0.0202134 | + | 0.0202134i | ||||
\(299\) | 12.8034 | 0.740441 | ||||||||
\(300\) | 3.30580 | + | 5.34046i | 0.190860 | + | 0.308331i | ||||
\(301\) | 5.94893 | 0.342891 | ||||||||
\(302\) | 13.4569 | − | 13.4569i | 0.774359 | − | 0.774359i | ||||
\(303\) | 1.61723 | − | 1.61723i | 0.0929074 | − | 0.0929074i | ||||
\(304\) | 1.47952 | 0.0848565 | ||||||||
\(305\) | 3.67094 | − | 2.90735i | 0.210197 | − | 0.166475i | ||||
\(306\) | 5.79177 | 0.331094 | ||||||||
\(307\) | 12.1977 | + | 12.1977i | 0.696157 | + | 0.696157i | 0.963579 | − | 0.267422i | \(-0.0861718\pi\) |
−0.267422 | + | 0.963579i | \(0.586172\pi\) | |||||||
\(308\) | −0.334548 | + | 3.29971i | −0.0190626 | + | 0.188018i | ||||
\(309\) | 0.360509i | 0.0205086i | ||||||||
\(310\) | −2.28921 | + | 19.7216i | −0.130019 | + | 1.12011i | ||||
\(311\) | −28.6968 | −1.62725 | −0.813623 | − | 0.581393i | \(-0.802508\pi\) | ||||
−0.813623 | + | 0.581393i | \(0.802508\pi\) | |||||||
\(312\) | 1.70056 | − | 1.70056i | 0.0962755 | − | 0.0962755i | ||||
\(313\) | −8.12218 | − | 8.12218i | −0.459093 | − | 0.459093i | 0.439265 | − | 0.898358i | \(-0.355239\pi\) |
−0.898358 | + | 0.439265i | \(0.855239\pi\) | |||||||
\(314\) | −18.0798 | −1.02030 | ||||||||
\(315\) | 3.15859 | + | 0.366637i | 0.177967 | + | 0.0206577i | ||||
\(316\) | − | 12.8565i | − | 0.723232i | ||||||
\(317\) | 9.80486 | − | 9.80486i | 0.550696 | − | 0.550696i | −0.375946 | − | 0.926642i | \(-0.622682\pi\) |
0.926642 | + | 0.375946i | \(0.122682\pi\) | |||||||
\(318\) | −0.669789 | + | 0.669789i | −0.0375599 | + | 0.0375599i | ||||
\(319\) | −22.7937 | + | 18.5972i | −1.27620 | + | 1.04124i | ||||
\(320\) | 1.75290 | − | 1.38828i | 0.0979902 | − | 0.0776075i | ||||
\(321\) | 12.5517i | 0.700570i | ||||||||
\(322\) | −4.72879 | + | 4.72879i | −0.263525 | + | 0.263525i | ||||
\(323\) | −4.26092 | − | 4.26092i | −0.237084 | − | 0.237084i | ||||
\(324\) | 2.71162i | 0.150646i | ||||||||
\(325\) | 5.03838 | + | 8.13941i | 0.279479 | + | 0.451493i | ||||
\(326\) | − | 2.39078i | − | 0.132413i | ||||||
\(327\) | 7.41855 | + | 7.41855i | 0.410247 | + | 0.410247i | ||||
\(328\) | −5.83322 | − | 5.83322i | −0.322086 | − | 0.322086i | ||||
\(329\) | 12.3036 | 0.678322 | ||||||||
\(330\) | 2.00210 | − | 9.09829i | 0.110212 | − | 0.500844i | ||||
\(331\) | 5.87481 | 0.322909 | 0.161454 | − | 0.986880i | \(-0.448382\pi\) | ||||
0.161454 | + | 0.986880i | \(0.448382\pi\) | |||||||
\(332\) | 7.94643 | + | 7.94643i | 0.436117 | + | 0.436117i | ||||
\(333\) | −1.61649 | − | 1.61649i | −0.0885832 | − | 0.0885832i | ||||
\(334\) | 21.7710i | 1.19126i | ||||||||
\(335\) | 22.9748 | + | 2.66682i | 1.25525 | + | 0.145704i | ||||
\(336\) | 1.25616i | 0.0685294i | ||||||||
\(337\) | 12.0573 | + | 12.0573i | 0.656805 | + | 0.656805i | 0.954623 | − | 0.297818i | \(-0.0962589\pi\) |
−0.297818 | + | 0.954623i | \(0.596259\pi\) | |||||||
\(338\) | −6.60055 | + | 6.60055i | −0.359023 | + | 0.359023i | ||||
\(339\) | 12.3899i | 0.672929i | ||||||||
\(340\) | −9.04639 | − | 1.05007i | −0.490610 | − | 0.0569481i | ||||
\(341\) | 22.8173 | − | 18.6165i | 1.23563 | − | 1.00814i | ||||
\(342\) | −1.48772 | + | 1.48772i | −0.0804468 | + | 0.0804468i | ||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 5.94893i | 0.320745i | ||||||||
\(345\) | 14.7255 | − | 11.6625i | 0.792792 | − | 0.627886i | ||||
\(346\) | 7.91702 | 0.425622 | ||||||||
\(347\) | 11.5264 | + | 11.5264i | 0.618768 | + | 0.618768i | 0.945215 | − | 0.326447i | \(-0.105852\pi\) |
−0.326447 | + | 0.945215i | \(0.605852\pi\) | |||||||
\(348\) | −7.87854 | + | 7.87854i | −0.422334 | + | 0.422334i | ||||
\(349\) | −33.2970 | −1.78235 | −0.891175 | − | 0.453661i | \(-0.850118\pi\) | ||||
−0.891175 | + | 0.453661i | \(0.850118\pi\) | |||||||
\(350\) | −4.86705 | − | 1.14533i | −0.260155 | − | 0.0612204i | ||||
\(351\) | 10.6349i | 0.567647i | ||||||||
\(352\) | −3.29971 | − | 0.334548i | −0.175875 | − | 0.0178315i | ||||
\(353\) | 20.8810 | + | 20.8810i | 1.11138 | + | 1.11138i | 0.992964 | + | 0.118420i | \(0.0377830\pi\) |
0.118420 | + | 0.992964i | \(0.462217\pi\) | |||||||
\(354\) | 12.4835 | 0.663491 | ||||||||
\(355\) | −15.1926 | − | 19.1827i | −0.806337 | − | 1.01811i | ||||
\(356\) | 8.22801 | 0.436084 | ||||||||
\(357\) | 3.61766 | − | 3.61766i | 0.191467 | − | 0.191467i | ||||
\(358\) | 1.13486 | − | 1.13486i | 0.0599794 | − | 0.0599794i | ||||
\(359\) | −24.4482 | −1.29032 | −0.645162 | − | 0.764046i | \(-0.723210\pi\) | ||||
−0.645162 | + | 0.764046i | \(0.723210\pi\) | |||||||
\(360\) | −0.366637 | + | 3.15859i | −0.0193235 | + | 0.166472i | ||||
\(361\) | −16.8110 | −0.884790 | ||||||||
\(362\) | −16.9954 | − | 16.9954i | −0.893258 | − | 0.893258i | ||||
\(363\) | −11.5329 | + | 7.61076i | −0.605321 | + | 0.399461i | ||||
\(364\) | 1.91453i | 0.100348i | ||||||||
\(365\) | −32.8880 | − | 3.81752i | −1.72144 | − | 0.199818i | ||||
\(366\) | −2.63067 | −0.137507 | ||||||||
\(367\) | −17.6498 | + | 17.6498i | −0.921310 | + | 0.921310i | −0.997122 | − | 0.0758120i | \(-0.975845\pi\) |
0.0758120 | + | 0.997122i | \(0.475845\pi\) | |||||||
\(368\) | −4.72879 | − | 4.72879i | −0.246505 | − | 0.246505i | ||||
\(369\) | 11.7311 | 0.610696 | ||||||||
\(370\) | 2.23178 | + | 2.81794i | 0.116025 | + | 0.146498i | ||||
\(371\) | − | 0.754061i | − | 0.0391489i | ||||||
\(372\) | 7.88671 | − | 7.88671i | 0.408907 | − | 0.408907i | ||||
\(373\) | −3.47802 | + | 3.47802i | −0.180085 | + | 0.180085i | −0.791393 | − | 0.611308i | \(-0.790644\pi\) |
0.611308 | + | 0.791393i | \(0.290644\pi\) | |||||||
\(374\) | 8.53945 | + | 10.4664i | 0.441564 | + | 0.541205i | ||||
\(375\) | 13.2088 | + | 4.77191i | 0.682100 | + | 0.246420i | ||||
\(376\) | 12.3036i | 0.634512i | ||||||||
\(377\) | −12.0077 | + | 12.0077i | −0.618429 | + | 0.618429i | ||||
\(378\) | −3.92785 | − | 3.92785i | −0.202027 | − | 0.202027i | ||||
\(379\) | 20.7313i | 1.06490i | 0.846463 | + | 0.532448i | \(0.178728\pi\) | ||||
−0.846463 | + | 0.532448i | \(0.821272\pi\) | |||||||
\(380\) | 2.59346 | − | 2.05400i | 0.133042 | − | 0.105368i | ||||
\(381\) | 21.2264i | 1.08746i | ||||||||
\(382\) | −4.07647 | − | 4.07647i | −0.208570 | − | 0.208570i | ||||
\(383\) | −0.806297 | − | 0.806297i | −0.0411998 | − | 0.0411998i | 0.686207 | − | 0.727407i | \(-0.259275\pi\) |
−0.727407 | + | 0.686207i | \(0.759275\pi\) | |||||||
\(384\) | −1.25616 | −0.0641034 | ||||||||
\(385\) | 3.99451 | + | 6.24851i | 0.203579 | + | 0.318454i | ||||
\(386\) | −3.58203 | −0.182321 | ||||||||
\(387\) | −5.98189 | − | 5.98189i | −0.304077 | − | 0.304077i | ||||
\(388\) | 1.76695 | + | 1.76695i | 0.0897035 | + | 0.0897035i | ||||
\(389\) | − | 35.0385i | − | 1.77652i | −0.459340 | − | 0.888260i | \(-0.651914\pi\) | ||
0.459340 | − | 0.888260i | \(-0.348086\pi\) | |||||||
\(390\) | 0.620054 | − | 5.34179i | 0.0313977 | − | 0.270492i | ||||
\(391\) | 27.2371i | 1.37744i | ||||||||
\(392\) | −0.707107 | − | 0.707107i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | −5.35440 | + | 5.35440i | −0.270094 | + | 0.270094i | ||||
\(394\) | 13.3021i | 0.670150i | ||||||||
\(395\) | −17.8484 | − | 22.5361i | −0.898052 | − | 1.13391i | ||||
\(396\) | 3.65439 | − | 2.98159i | 0.183640 | − | 0.149831i | ||||
\(397\) | 0.531094 | − | 0.531094i | 0.0266548 | − | 0.0266548i | −0.693654 | − | 0.720309i | \(-0.744000\pi\) |
0.720309 | + | 0.693654i | \(0.244000\pi\) | |||||||
\(398\) | 6.84116 | − | 6.84116i | 0.342916 | − | 0.342916i | ||||
\(399\) | 1.85853i | 0.0930427i | ||||||||
\(400\) | 1.14533 | − | 4.86705i | 0.0572665 | − | 0.243353i | ||||
\(401\) | −11.5324 | −0.575903 | −0.287951 | − | 0.957645i | \(-0.592974\pi\) | ||||
−0.287951 | + | 0.957645i | \(0.592974\pi\) | |||||||
\(402\) | −9.18764 | − | 9.18764i | −0.458238 | − | 0.458238i | ||||
\(403\) | 12.0202 | − | 12.0202i | 0.598767 | − | 0.598767i | ||||
\(404\) | −1.82071 | −0.0905835 | ||||||||
\(405\) | 3.76451 | + | 4.75321i | 0.187060 | + | 0.236189i | ||||
\(406\) | − | 8.86980i | − | 0.440201i | ||||||
\(407\) | 0.537814 | − | 5.30456i | 0.0266584 | − | 0.262937i | ||||
\(408\) | 3.61766 | + | 3.61766i | 0.179101 | + | 0.179101i | ||||
\(409\) | 9.69828 | 0.479549 | 0.239775 | − | 0.970829i | \(-0.422926\pi\) | ||||
0.239775 | + | 0.970829i | \(0.422926\pi\) | |||||||
\(410\) | −18.3232 | − | 2.12689i | −0.904919 | − | 0.105040i | ||||
\(411\) | −4.26011 | −0.210136 | ||||||||
\(412\) | 0.202934 | − | 0.202934i | 0.00999784 | − | 0.00999784i | ||||
\(413\) | −7.02708 | + | 7.02708i | −0.345780 | + | 0.345780i | ||||
\(414\) | 9.50998 | 0.467390 | ||||||||
\(415\) | 24.9612 | + | 2.89740i | 1.22530 | + | 0.142228i | ||||
\(416\) | −1.91453 | −0.0938674 | ||||||||
\(417\) | −3.36089 | − | 3.36089i | −0.164583 | − | 0.164583i | ||||
\(418\) | −4.88200 | − | 0.494971i | −0.238786 | − | 0.0242098i | ||||
\(419\) | − | 28.3703i | − | 1.38598i | −0.720946 | − | 0.692991i | \(-0.756292\pi\) | ||
0.720946 | − | 0.692991i | \(-0.243708\pi\) | |||||||
\(420\) | 1.74391 | + | 2.20193i | 0.0850943 | + | 0.107443i | ||||
\(421\) | −6.66942 | −0.325048 | −0.162524 | − | 0.986705i | \(-0.551963\pi\) | ||||
−0.162524 | + | 0.986705i | \(0.551963\pi\) | |||||||
\(422\) | 7.91889 | − | 7.91889i | 0.385485 | − | 0.385485i | ||||
\(423\) | −12.3718 | − | 12.3718i | −0.601538 | − | 0.601538i | ||||
\(424\) | 0.754061 | 0.0366204 | ||||||||
\(425\) | −17.3152 | + | 10.7183i | −0.839912 | + | 0.519914i | ||||
\(426\) | 13.7467i | 0.666031i | ||||||||
\(427\) | 1.48083 | − | 1.48083i | 0.0716623 | − | 0.0716623i | ||||
\(428\) | 7.06549 | − | 7.06549i | 0.341524 | − | 0.341524i | ||||
\(429\) | −6.18029 | + | 5.04245i | −0.298387 | + | 0.243452i | ||||
\(430\) | 8.25881 | + | 10.4279i | 0.398275 | + | 0.502878i | ||||
\(431\) | − | 0.660707i | − | 0.0318251i | −0.999873 | − | 0.0159126i | \(-0.994935\pi\) | ||
0.999873 | − | 0.0159126i | \(-0.00506534\pi\) | |||||||
\(432\) | 3.92785 | − | 3.92785i | 0.188979 | − | 0.188979i | ||||
\(433\) | −0.909235 | − | 0.909235i | −0.0436950 | − | 0.0436950i | 0.684922 | − | 0.728617i | \(-0.259836\pi\) |
−0.728617 | + | 0.684922i | \(0.759836\pi\) | |||||||
\(434\) | 8.87900i | 0.426206i | ||||||||
\(435\) | −2.87265 | + | 24.7480i | −0.137733 | + | 1.18657i | ||||
\(436\) | − | 8.35194i | − | 0.399985i | ||||||
\(437\) | −6.99636 | − | 6.99636i | −0.334681 | − | 0.334681i | ||||
\(438\) | 13.1520 | + | 13.1520i | 0.628425 | + | 0.628425i | ||||
\(439\) | 3.74444 | 0.178712 | 0.0893562 | − | 0.996000i | \(-0.471519\pi\) | ||||
0.0893562 | + | 0.996000i | \(0.471519\pi\) | |||||||
\(440\) | −6.24851 | + | 3.99451i | −0.297886 | + | 0.190431i | ||||
\(441\) | 1.42205 | 0.0677167 | ||||||||
\(442\) | 5.51370 | + | 5.51370i | 0.262260 | + | 0.262260i | ||||
\(443\) | 13.7718 | + | 13.7718i | 0.654319 | + | 0.654319i | 0.954030 | − | 0.299711i | \(-0.0968902\pi\) |
−0.299711 | + | 0.954030i | \(0.596890\pi\) | |||||||
\(444\) | − | 2.01939i | − | 0.0958360i | ||||||
\(445\) | 14.4229 | − | 11.4228i | 0.683711 | − | 0.541494i | ||||
\(446\) | 2.42308i | 0.114736i | ||||||||
\(447\) | −0.438322 | − | 0.438322i | −0.0207319 | − | 0.0207319i | ||||
\(448\) | 0.707107 | − | 0.707107i | 0.0334077 | − | 0.0334077i | ||||
\(449\) | 31.7894i | 1.50023i | 0.661305 | + | 0.750117i | \(0.270003\pi\) | ||||
−0.661305 | + | 0.750117i | \(0.729997\pi\) | |||||||
\(450\) | 3.74235 | + | 6.04570i | 0.176416 | + | 0.284997i | ||||
\(451\) | 17.2964 | + | 21.1994i | 0.814457 | + | 0.998241i | ||||
\(452\) | 6.97441 | − | 6.97441i | 0.328049 | − | 0.328049i | ||||
\(453\) | −16.9041 | + | 16.9041i | −0.794225 | + | 0.794225i | ||||
\(454\) | − | 8.28858i | − | 0.389002i | ||||||
\(455\) | 2.65791 | + | 3.35598i | 0.124605 | + | 0.157331i | ||||
\(456\) | −1.85853 | −0.0870335 | ||||||||
\(457\) | 2.54612 | + | 2.54612i | 0.119102 | + | 0.119102i | 0.764146 | − | 0.645044i | \(-0.223161\pi\) |
−0.645044 | + | 0.764146i | \(0.723161\pi\) | |||||||
\(458\) | 0.765915 | − | 0.765915i | 0.0357888 | − | 0.0357888i | ||||
\(459\) | −22.6239 | −1.05599 | ||||||||
\(460\) | −14.8540 | − | 1.72420i | −0.692572 | − | 0.0803910i | ||||
\(461\) | 14.4788i | 0.674343i | 0.941443 | + | 0.337172i | \(0.109470\pi\) | ||||
−0.941443 | + | 0.337172i | \(0.890530\pi\) | |||||||
\(462\) | 0.420247 | − | 4.14498i | 0.0195517 | − | 0.192842i | ||||
\(463\) | 18.1240 | + | 18.1240i | 0.842292 | + | 0.842292i | 0.989157 | − | 0.146865i | \(-0.0469183\pi\) |
−0.146865 | + | 0.989157i | \(0.546918\pi\) | |||||||
\(464\) | 8.86980 | 0.411770 | ||||||||
\(465\) | 2.87563 | − | 24.7736i | 0.133354 | − | 1.14885i | ||||
\(466\) | 18.5209 | 0.857963 | ||||||||
\(467\) | 14.5407 | − | 14.5407i | 0.672866 | − | 0.672866i | −0.285510 | − | 0.958376i | \(-0.592163\pi\) |
0.958376 | + | 0.285510i | \(0.0921630\pi\) | |||||||
\(468\) | 1.92513 | − | 1.92513i | 0.0889894 | − | 0.0889894i | ||||
\(469\) | 10.3436 | 0.477624 | ||||||||
\(470\) | 17.0810 | + | 21.5671i | 0.787886 | + | 0.994815i | ||||
\(471\) | 22.7112 | 1.04648 | ||||||||
\(472\) | −7.02708 | − | 7.02708i | −0.323448 | − | 0.323448i | ||||
\(473\) | 1.99020 | − | 19.6297i | 0.0915095 | − | 0.902576i | ||||
\(474\) | 16.1498i | 0.741786i | ||||||||
\(475\) | 1.69454 | − | 7.20092i | 0.0777510 | − | 0.330401i | ||||
\(476\) | −4.07283 | −0.186678 | ||||||||
\(477\) | −0.758239 | + | 0.758239i | −0.0347174 | + | 0.0347174i | ||||
\(478\) | 19.3853 | + | 19.3853i | 0.886661 | + | 0.886661i | ||||
\(479\) | 38.0893 | 1.74035 | 0.870173 | − | 0.492747i | \(-0.164007\pi\) | ||||
0.870173 | + | 0.492747i | \(0.164007\pi\) | |||||||
\(480\) | −2.20193 | + | 1.74391i | −0.100504 | + | 0.0795985i | ||||
\(481\) | − | 3.07776i | − | 0.140334i | ||||||
\(482\) | 1.28598 | − | 1.28598i | 0.0585747 | − | 0.0585747i | ||||
\(483\) | 5.94014 | − | 5.94014i | 0.270286 | − | 0.270286i | ||||
\(484\) | 10.7762 | + | 2.20782i | 0.489825 | + | 0.100355i | ||||
\(485\) | 5.55033 | + | 0.644261i | 0.252028 | + | 0.0292544i | ||||
\(486\) | 13.2582i | 0.601405i | ||||||||
\(487\) | −19.6660 | + | 19.6660i | −0.891152 | + | 0.891152i | −0.994632 | − | 0.103480i | \(-0.967002\pi\) |
0.103480 | + | 0.994632i | \(0.467002\pi\) | |||||||
\(488\) | 1.48083 | + | 1.48083i | 0.0670339 | + | 0.0670339i | ||||
\(489\) | 3.00322i | 0.135810i | ||||||||
\(490\) | −2.22115 | − | 0.257823i | −0.100342 | − | 0.0116473i | ||||
\(491\) | − | 6.03773i | − | 0.272479i | −0.990676 | − | 0.136240i | \(-0.956498\pi\) | ||
0.990676 | − | 0.136240i | \(-0.0435017\pi\) | |||||||
\(492\) | 7.32748 | + | 7.32748i | 0.330348 | + | 0.330348i | ||||
\(493\) | −25.5444 | − | 25.5444i | −1.15046 | − | 1.15046i | ||||
\(494\) | −2.83259 | −0.127444 | ||||||||
\(495\) | 2.26650 | − | 10.2998i | 0.101871 | − | 0.462941i | ||||
\(496\) | −8.87900 | −0.398679 | ||||||||
\(497\) | −7.73815 | − | 7.73815i | −0.347104 | − | 0.347104i | ||||
\(498\) | −9.98202 | − | 9.98202i | −0.447305 | − | 0.447305i | ||||
\(499\) | − | 12.4443i | − | 0.557081i | −0.960424 | − | 0.278541i | \(-0.910149\pi\) | ||
0.960424 | − | 0.278541i | \(-0.0898507\pi\) | |||||||
\(500\) | −4.74921 | − | 10.1215i | −0.212391 | − | 0.452648i | ||||
\(501\) | − | 27.3480i | − | 1.22182i | ||||||
\(502\) | −7.84662 | − | 7.84662i | −0.350212 | − | 0.350212i | ||||
\(503\) | −8.83489 | + | 8.83489i | −0.393928 | + | 0.393928i | −0.876085 | − | 0.482157i | \(-0.839854\pi\) |
0.482157 | + | 0.876085i | \(0.339854\pi\) | |||||||
\(504\) | 1.42205i | 0.0633431i | ||||||||
\(505\) | −3.19152 | + | 2.52766i | −0.142021 | + | 0.112479i | ||||
\(506\) | 14.0216 | + | 17.1856i | 0.623337 | + | 0.763994i | ||||
\(507\) | 8.29138 | − | 8.29138i | 0.368233 | − | 0.368233i | ||||
\(508\) | 11.9485 | − | 11.9485i | 0.530131 | − | 0.530131i | ||||
\(509\) | 1.45865i | 0.0646534i | 0.999477 | + | 0.0323267i | \(0.0102917\pi\) | ||||
−0.999477 | + | 0.0323267i | \(0.989708\pi\) | |||||||
\(510\) | 11.3638 | + | 1.31906i | 0.503196 | + | 0.0584090i | ||||
\(511\) | −14.8067 | −0.655011 | ||||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 5.81135 | − | 5.81135i | 0.256578 | − | 0.256578i | ||||
\(514\) | −5.34324 | −0.235680 | ||||||||
\(515\) | 0.0739931 | − | 0.637453i | 0.00326053 | − | 0.0280895i | ||||
\(516\) | − | 7.47284i | − | 0.328973i | ||||||
\(517\) | 4.11616 | − | 40.5984i | 0.181028 | − | 1.78552i | ||||
\(518\) | 1.13673 | + | 1.13673i | 0.0499452 | + | 0.0499452i | ||||
\(519\) | −9.94508 | −0.436541 | ||||||||
\(520\) | −3.35598 | + | 2.65791i | −0.147169 | + | 0.116557i | ||||
\(521\) | 28.3008 | 1.23988 | 0.619941 | − | 0.784648i | \(-0.287157\pi\) | ||||
0.619941 | + | 0.784648i | \(0.287157\pi\) | |||||||
\(522\) | −8.91895 | + | 8.91895i | −0.390372 | + | 0.390372i | ||||
\(523\) | 5.44347 | − | 5.44347i | 0.238026 | − | 0.238026i | −0.578006 | − | 0.816032i | \(-0.696169\pi\) |
0.816032 | + | 0.578006i | \(0.196169\pi\) | |||||||
\(524\) | 6.02808 | 0.263338 | ||||||||
\(525\) | 6.11382 | + | 1.43872i | 0.266829 | + | 0.0627910i | ||||
\(526\) | −24.0733 | −1.04965 | ||||||||
\(527\) | 25.5709 | + | 25.5709i | 1.11389 | + | 1.11389i | ||||
\(528\) | 4.14498 | + | 0.420247i | 0.180387 | + | 0.0182889i | ||||
\(529\) | 21.7229i | 0.944473i | ||||||||
\(530\) | 1.32179 | − | 1.04685i | 0.0574151 | − | 0.0454723i | ||||
\(531\) | 14.1320 | 0.613278 | ||||||||
\(532\) | 1.04618 | − | 1.04618i | 0.0453577 | − | 0.0453577i | ||||
\(533\) | 11.1678 | + | 11.1678i | 0.483733 | + | 0.483733i | ||||
\(534\) | −10.3357 | −0.447271 | ||||||||
\(535\) | 2.57620 | − | 22.1940i | 0.111379 | − | 0.959532i | ||||
\(536\) | 10.3436i | 0.446776i | ||||||||
\(537\) | −1.42557 | + | 1.42557i | −0.0615181 | + | 0.0615181i | ||||
\(538\) | 15.4482 | − | 15.4482i | 0.666018 | − | 0.666018i | ||||
\(539\) | 2.09669 | + | 2.56981i | 0.0903106 | + | 0.110689i | ||||
\(540\) | 1.43216 | − | 12.3381i | 0.0616304 | − | 0.530948i | ||||
\(541\) | 38.4666i | 1.65381i | 0.562344 | + | 0.826903i | \(0.309900\pi\) | ||||
−0.562344 | + | 0.826903i | \(0.690100\pi\) | |||||||
\(542\) | −8.21948 | + | 8.21948i | −0.353057 | + | 0.353057i | ||||
\(543\) | 21.3490 | + | 21.3490i | 0.916174 | + | 0.916174i | ||||
\(544\) | − | 4.07283i | − | 0.174621i | ||||||
\(545\) | −11.5949 | − | 14.6401i | −0.496670 | − | 0.627114i | ||||
\(546\) | − | 2.40496i | − | 0.102923i | ||||||
\(547\) | −16.7490 | − | 16.7490i | −0.716137 | − | 0.716137i | 0.251675 | − | 0.967812i | \(-0.419019\pi\) |
−0.967812 | + | 0.251675i | \(0.919019\pi\) | |||||||
\(548\) | 2.39805 | + | 2.39805i | 0.102440 | + | 0.102440i | ||||
\(549\) | −2.97807 | −0.127101 | ||||||||
\(550\) | −5.40752 | + | 15.6767i | −0.230577 | + | 0.668457i | ||||
\(551\) | 13.1231 | 0.559062 | ||||||||
\(552\) | 5.94014 | + | 5.94014i | 0.252829 | + | 0.252829i | ||||
\(553\) | −9.09089 | − | 9.09089i | −0.386584 | − | 0.386584i | ||||
\(554\) | − | 29.6299i | − | 1.25885i | ||||||
\(555\) | −2.80349 | − | 3.53979i | −0.119002 | − | 0.150256i | ||||
\(556\) | 3.78375i | 0.160467i | ||||||||
\(557\) | 28.2389 | + | 28.2389i | 1.19652 | + | 1.19652i | 0.975201 | + | 0.221319i | \(0.0710362\pi\) |
0.221319 | + | 0.975201i | \(0.428964\pi\) | |||||||
\(558\) | 8.92820 | − | 8.92820i | 0.377961 | − | 0.377961i | ||||
\(559\) | − | 11.3894i | − | 0.481720i | ||||||
\(560\) | 0.257823 | − | 2.22115i | 0.0108950 | − | 0.0938609i | ||||
\(561\) | −10.7270 | − | 13.1475i | −0.452893 | − | 0.555089i | ||||
\(562\) | −8.55525 | + | 8.55525i | −0.360881 | + | 0.360881i | ||||
\(563\) | 3.94828 | − | 3.94828i | 0.166400 | − | 0.166400i | −0.618995 | − | 0.785395i | \(-0.712460\pi\) |
0.785395 | + | 0.618995i | \(0.212460\pi\) | |||||||
\(564\) | − | 15.4554i | − | 0.650790i | ||||||
\(565\) | 2.54299 | − | 21.9079i | 0.106984 | − | 0.921674i | ||||
\(566\) | −15.6380 | −0.657315 | ||||||||
\(567\) | 1.91741 | + | 1.91741i | 0.0805236 | + | 0.0805236i | ||||
\(568\) | 7.73815 | − | 7.73815i | 0.324686 | − | 0.324686i | ||||
\(569\) | 30.6319 | 1.28416 | 0.642079 | − | 0.766639i | \(-0.278072\pi\) | ||||
0.642079 | + | 0.766639i | \(0.278072\pi\) | |||||||
\(570\) | −3.25781 | + | 2.58016i | −0.136455 | + | 0.108071i | ||||
\(571\) | 15.1172i | 0.632635i | 0.948653 | + | 0.316318i | \(0.102447\pi\) | ||||
−0.948653 | + | 0.316318i | \(0.897553\pi\) | |||||||
\(572\) | 6.31738 | + | 0.640500i | 0.264143 | + | 0.0267807i | ||||
\(573\) | 5.12072 | + | 5.12072i | 0.213921 | + | 0.213921i | ||||
\(574\) | −8.24941 | −0.344324 | ||||||||
\(575\) | −28.4313 | + | 17.5992i | −1.18567 | + | 0.733939i | ||||
\(576\) | −1.42205 | −0.0592521 | ||||||||
\(577\) | −24.9260 | + | 24.9260i | −1.03768 | + | 1.03768i | −0.0384196 | + | 0.999262i | \(0.512232\pi\) |
−0.999262 | + | 0.0384196i | \(0.987768\pi\) | |||||||
\(578\) | 0.291347 | − | 0.291347i | 0.0121185 | − | 0.0121185i | ||||
\(579\) | 4.49962 | 0.186998 | ||||||||
\(580\) | 15.5479 | − | 12.3138i | 0.645591 | − | 0.511303i | ||||
\(581\) | 11.2379 | 0.466229 | ||||||||
\(582\) | −2.21959 | − | 2.21959i | −0.0920048 | − | 0.0920048i | ||||
\(583\) | −2.48818 | − | 0.252269i | −0.103050 | − | 0.0104479i | ||||
\(584\) | − | 14.8067i | − | 0.612707i | ||||||
\(585\) | 0.701937 | − | 6.04721i | 0.0290215 | − | 0.250021i | ||||
\(586\) | 27.6166 | 1.14083 | ||||||||
\(587\) | 9.40740 | − | 9.40740i | 0.388285 | − | 0.388285i | −0.485790 | − | 0.874075i | \(-0.661468\pi\) |
0.874075 | + | 0.485790i | \(0.161468\pi\) | |||||||
\(588\) | 0.888243 | + | 0.888243i | 0.0366305 | + | 0.0366305i | ||||
\(589\) | −13.1367 | −0.541288 | ||||||||
\(590\) | −22.0734 | − | 2.56219i | −0.908747 | − | 0.105484i | ||||
\(591\) | − | 16.7096i | − | 0.687342i | ||||||
\(592\) | −1.13673 | + | 1.13673i | −0.0467195 | + | 0.0467195i | ||||
\(593\) | 7.99804 | − | 7.99804i | 0.328440 | − | 0.328440i | −0.523553 | − | 0.851993i | \(-0.675394\pi\) |
0.851993 | + | 0.523553i | \(0.175394\pi\) | |||||||
\(594\) | −14.2748 | + | 11.6467i | −0.585703 | + | 0.477871i | ||||
\(595\) | −7.13928 | + | 5.65425i | −0.292682 | + | 0.231802i | ||||
\(596\) | 0.493471i | 0.0202134i | ||||||||
\(597\) | −8.59362 | + | 8.59362i | −0.351714 | + | 0.351714i | ||||
\(598\) | 9.05339 | + | 9.05339i | 0.370221 | + | 0.370221i | ||||
\(599\) | − | 14.1834i | − | 0.579518i | −0.957100 | − | 0.289759i | \(-0.906425\pi\) | ||
0.957100 | − | 0.289759i | \(-0.0935752\pi\) | |||||||
\(600\) | −1.43872 | + | 6.11382i | −0.0587356 | + | 0.249596i | ||||
\(601\) | 22.0502i | 0.899447i | 0.893168 | + | 0.449724i | \(0.148478\pi\) | ||||
−0.893168 | + | 0.449724i | \(0.851522\pi\) | |||||||
\(602\) | 4.20653 | + | 4.20653i | 0.171445 | + | 0.171445i | ||||
\(603\) | −10.4009 | − | 10.4009i | −0.423559 | − | 0.423559i | ||||
\(604\) | 19.0310 | 0.774359 | ||||||||
\(605\) | 21.9546 | − | 11.0903i | 0.892582 | − | 0.450884i | ||||
\(606\) | 2.28711 | 0.0929074 | ||||||||
\(607\) | −20.1106 | − | 20.1106i | −0.816265 | − | 0.816265i | 0.169299 | − | 0.985565i | \(-0.445850\pi\) |
−0.985565 | + | 0.169299i | \(0.945850\pi\) | |||||||
\(608\) | 1.04618 | + | 1.04618i | 0.0424283 | + | 0.0424283i | ||||
\(609\) | 11.1419i | 0.451494i | ||||||||
\(610\) | 4.65156 | + | 0.539935i | 0.188336 | + | 0.0218613i | ||||
\(611\) | − | 23.5556i | − | 0.952959i | ||||||
\(612\) | 4.09540 | + | 4.09540i | 0.165547 | + | 0.165547i | ||||
\(613\) | 7.51374 | − | 7.51374i | 0.303477 | − | 0.303477i | −0.538895 | − | 0.842373i | \(-0.681158\pi\) |
0.842373 | + | 0.538895i | \(0.181158\pi\) | |||||||
\(614\) | 17.2501i | 0.696157i | ||||||||
\(615\) | 23.0170 | + | 2.67172i | 0.928135 | + | 0.107734i | ||||
\(616\) | −2.56981 | + | 2.09669i | −0.103540 | + | 0.0844779i | ||||
\(617\) | 13.3597 | − | 13.3597i | 0.537841 | − | 0.537841i | −0.385054 | − | 0.922894i | \(-0.625817\pi\) |
0.922894 | + | 0.385054i | \(0.125817\pi\) | |||||||
\(618\) | −0.254918 | + | 0.254918i | −0.0102543 | + | 0.0102543i | ||||
\(619\) | 11.1084i | 0.446484i | 0.974763 | + | 0.223242i | \(0.0716640\pi\) | ||||
−0.974763 | + | 0.223242i | \(0.928336\pi\) | |||||||
\(620\) | −15.5640 | + | 12.3266i | −0.625066 | + | 0.495048i | ||||
\(621\) | −37.1480 | −1.49070 | ||||||||
\(622\) | −20.2917 | − | 20.2917i | −0.813623 | − | 0.813623i | ||||
\(623\) | 5.81808 | − | 5.81808i | 0.233096 | − | 0.233096i | ||||
\(624\) | 2.40496 | 0.0962755 | ||||||||
\(625\) | −22.3764 | − | 11.1488i | −0.895058 | − | 0.445951i | ||||
\(626\) | − | 11.4865i | − | 0.459093i | ||||||
\(627\) | 6.13260 | + | 0.621766i | 0.244912 | + | 0.0248309i | ||||
\(628\) | −12.7843 | − | 12.7843i | −0.510151 | − | 0.510151i | ||||
\(629\) | 6.54742 | 0.261063 | ||||||||
\(630\) | 1.97421 | + | 2.49271i | 0.0786544 | + | 0.0993121i | ||||
\(631\) | 43.0780 | 1.71491 | 0.857454 | − | 0.514561i | \(-0.172045\pi\) | ||||
0.857454 | + | 0.514561i | \(0.172045\pi\) | |||||||
\(632\) | 9.09089 | − | 9.09089i | 0.361616 | − | 0.361616i | ||||
\(633\) | −9.94743 | + | 9.94743i | −0.395375 | + | 0.395375i | ||||
\(634\) | 13.8662 | 0.550696 | ||||||||
\(635\) | 4.35664 | − | 37.5326i | 0.172888 | − | 1.48944i | ||||
\(636\) | −0.947225 | −0.0375599 | ||||||||
\(637\) | 1.35377 | + | 1.35377i | 0.0536385 | + | 0.0536385i | ||||
\(638\) | −29.2678 | − | 2.96737i | −1.15872 | − | 0.117479i | ||||
\(639\) | 15.5621i | 0.615626i | ||||||||
\(640\) | 2.22115 | + | 0.257823i | 0.0877988 | + | 0.0101914i | ||||
\(641\) | −18.9643 | −0.749044 | −0.374522 | − | 0.927218i | \(-0.622193\pi\) | ||||
−0.374522 | + | 0.927218i | \(0.622193\pi\) | |||||||
\(642\) | −8.87542 | + | 8.87542i | −0.350285 | + | 0.350285i | ||||
\(643\) | −16.1431 | − | 16.1431i | −0.636622 | − | 0.636622i | 0.313099 | − | 0.949721i | \(-0.398633\pi\) |
−0.949721 | + | 0.313099i | \(0.898633\pi\) | |||||||
\(644\) | −6.68752 | −0.263525 | ||||||||
\(645\) | −10.3744 | − | 13.0991i | −0.408493 | − | 0.515778i | ||||
\(646\) | − | 6.02586i | − | 0.237084i | ||||||
\(647\) | −20.7235 | + | 20.7235i | −0.814725 | + | 0.814725i | −0.985338 | − | 0.170613i | \(-0.945425\pi\) |
0.170613 | + | 0.985338i | \(0.445425\pi\) | |||||||
\(648\) | −1.91741 | + | 1.91741i | −0.0753229 | + | 0.0753229i | ||||
\(649\) | 20.8364 | + | 25.5382i | 0.817902 | + | 1.00246i | ||||
\(650\) | −2.19276 | + | 9.31810i | −0.0860073 | + | 0.365486i | ||||
\(651\) | − | 11.1535i | − | 0.437140i | ||||||
\(652\) | 1.69054 | − | 1.69054i | 0.0662066 | − | 0.0662066i | ||||
\(653\) | 2.78208 | + | 2.78208i | 0.108871 | + | 0.108871i | 0.759444 | − | 0.650573i | \(-0.225471\pi\) |
−0.650573 | + | 0.759444i | \(0.725471\pi\) | |||||||
\(654\) | 10.4914i | 0.410247i | ||||||||
\(655\) | 10.5666 | − | 8.36869i | 0.412872 | − | 0.326992i | ||||
\(656\) | − | 8.24941i | − | 0.322086i | ||||||
\(657\) | 14.8888 | + | 14.8888i | 0.580866 | + | 0.580866i | ||||
\(658\) | 8.69999 | + | 8.69999i | 0.339161 | + | 0.339161i | ||||
\(659\) | −34.4321 | −1.34128 | −0.670642 | − | 0.741781i | \(-0.733981\pi\) | ||||
−0.670642 | + | 0.741781i | \(0.733981\pi\) | |||||||
\(660\) | 7.84916 | − | 5.01776i | 0.305528 | − | 0.195316i | ||||
\(661\) | −28.1721 | −1.09577 | −0.547884 | − | 0.836554i | \(-0.684567\pi\) | ||||
−0.547884 | + | 0.836554i | \(0.684567\pi\) | |||||||
\(662\) | 4.15412 | + | 4.15412i | 0.161454 | + | 0.161454i | ||||
\(663\) | −6.92611 | − | 6.92611i | −0.268988 | − | 0.268988i | ||||
\(664\) | 11.2379i | 0.436117i | ||||||||
\(665\) | 0.381455 | − | 3.28625i | 0.0147922 | − | 0.127435i | ||||
\(666\) | − | 2.28606i | − | 0.0885832i | ||||||
\(667\) | −41.9434 | − | 41.9434i | −1.62406 | − | 1.62406i | ||||
\(668\) | −15.3944 | + | 15.3944i | −0.595628 | + | 0.595628i | ||||
\(669\) | − | 3.04379i | − | 0.117680i | ||||||
\(670\) | 14.3599 | + | 18.1313i | 0.554771 | + | 0.700475i | ||||
\(671\) | −4.39089 | − | 5.38171i | −0.169508 | − | 0.207758i | ||||
\(672\) | −0.888243 | + | 0.888243i | −0.0342647 | + | 0.0342647i | ||||
\(673\) | −25.6689 | + | 25.6689i | −0.989465 | + | 0.989465i | −0.999945 | − | 0.0104805i | \(-0.996664\pi\) |
0.0104805 | + | 0.999945i | \(0.496664\pi\) | |||||||
\(674\) | 17.0516i | 0.656805i | ||||||||
\(675\) | −14.6184 | − | 23.6158i | −0.562662 | − | 0.908971i | ||||
\(676\) | −9.33459 | −0.359023 | ||||||||
\(677\) | 1.67884 | + | 1.67884i | 0.0645231 | + | 0.0645231i | 0.738632 | − | 0.674109i | \(-0.235472\pi\) |
−0.674109 | + | 0.738632i | \(0.735472\pi\) | |||||||
\(678\) | −8.76101 | + | 8.76101i | −0.336465 | + | 0.336465i | ||||
\(679\) | 2.49885 | 0.0958971 | ||||||||
\(680\) | −5.65425 | − | 7.13928i | −0.216831 | − | 0.273779i | ||||
\(681\) | 10.4118i | 0.398982i | ||||||||
\(682\) | 29.2981 | + | 2.97045i | 1.12188 | + | 0.113744i | ||||
\(683\) | −8.58431 | − | 8.58431i | −0.328470 | − | 0.328470i | 0.523535 | − | 0.852004i | \(-0.324613\pi\) |
−0.852004 | + | 0.523535i | \(0.824613\pi\) | |||||||
\(684\) | −2.10396 | −0.0804468 | ||||||||
\(685\) | 7.53273 | + | 0.874371i | 0.287811 | + | 0.0334080i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −0.962115 | + | 0.962115i | −0.0367070 | + | 0.0367070i | ||||
\(688\) | −4.20653 | + | 4.20653i | −0.160372 | + | 0.160372i | ||||
\(689\) | −1.44367 | −0.0549994 | ||||||||
\(690\) | 18.6591 | + | 2.16587i | 0.710339 | + | 0.0824534i | ||||
\(691\) | 8.46405 | 0.321988 | 0.160994 | − | 0.986955i | \(-0.448530\pi\) | ||||
0.160994 | + | 0.986955i | \(0.448530\pi\) | |||||||
\(692\) | 5.59818 | + | 5.59818i | 0.212811 | + | 0.212811i | ||||
\(693\) | 0.475744 | − | 4.69235i | 0.0180720 | − | 0.178248i | ||||
\(694\) | 16.3007i | 0.618768i | ||||||||
\(695\) | 5.25292 | + | 6.63254i | 0.199255 | + | 0.251587i | ||||
\(696\) | −11.1419 | −0.422334 | ||||||||
\(697\) | −23.7577 | + | 23.7577i | −0.899888 | + | 0.899888i | ||||
\(698\) | −23.5446 | − | 23.5446i | −0.891175 | − | 0.891175i | ||||
\(699\) | −23.2653 | −0.879974 | ||||||||
\(700\) | −2.63166 | − | 4.25140i | −0.0994673 | − | 0.160688i | ||||
\(701\) | − | 8.58739i | − | 0.324341i | −0.986763 | − | 0.162171i | \(-0.948151\pi\) | ||
0.986763 | − | 0.162171i | \(-0.0518495\pi\) | |||||||
\(702\) | −7.51998 | + | 7.51998i | −0.283823 | + | 0.283823i | ||||
\(703\) | −1.68182 | + | 1.68182i | −0.0634312 | + | 0.0634312i | ||||
\(704\) | −2.09669 | − | 2.56981i | −0.0790218 | − | 0.0968533i | ||||
\(705\) | −21.4565 | − | 27.0918i | −0.808099 | − | 1.02034i | ||||
\(706\) | 29.5302i | 1.11138i | ||||||||
\(707\) | −1.28743 | + | 1.28743i | −0.0484189 | + | 0.0484189i | ||||
\(708\) | 8.82718 | + | 8.82718i | 0.331746 | + | 0.331746i | ||||
\(709\) | − | 9.13828i | − | 0.343195i | −0.985167 | − | 0.171598i | \(-0.945107\pi\) | ||
0.985167 | − | 0.171598i | \(-0.0548929\pi\) | |||||||
\(710\) | 2.82146 | − | 24.3070i | 0.105888 | − | 0.912225i | ||||
\(711\) | 18.2825i | 0.685648i | ||||||||
\(712\) | 5.81808 | + | 5.81808i | 0.218042 | + | 0.218042i | ||||
\(713\) | 41.9869 | + | 41.9869i | 1.57242 | + | 1.57242i | ||||
\(714\) | 5.11615 | 0.191467 | ||||||||
\(715\) | 11.9629 | − | 7.64759i | 0.447389 | − | 0.286004i | ||||
\(716\) | 1.60494 | 0.0599794 | ||||||||
\(717\) | −24.3511 | − | 24.3511i | −0.909408 | − | 0.909408i | ||||
\(718\) | −17.2875 | − | 17.2875i | −0.645162 | − | 0.645162i | ||||
\(719\) | − | 17.4983i | − | 0.652578i | −0.945270 | − | 0.326289i | \(-0.894202\pi\) | ||
0.945270 | − | 0.326289i | \(-0.105798\pi\) | |||||||
\(720\) | −2.49271 | + | 1.97421i | −0.0928980 | + | 0.0735745i | ||||
\(721\) | − | 0.286992i | − | 0.0106881i | ||||||
\(722\) | −11.8872 | − | 11.8872i | −0.442395 | − | 0.442395i | ||||
\(723\) | −1.61540 | + | 1.61540i | −0.0600774 | + | 0.0600774i | ||||
\(724\) | − | 24.0351i | − | 0.893258i | ||||||
\(725\) | 10.1589 | − | 43.1698i | 0.377290 | − | 1.60329i | ||||
\(726\) | −13.5366 | − | 2.77339i | −0.502391 | − | 0.102930i | ||||
\(727\) | −27.3661 | + | 27.3661i | −1.01495 | + | 1.01495i | −0.0150668 | + | 0.999886i | \(0.504796\pi\) |
−0.999886 | + | 0.0150668i | \(0.995204\pi\) | |||||||
\(728\) | −1.35377 | + | 1.35377i | −0.0501742 | + | 0.0501742i | ||||
\(729\) | − | 24.7894i | − | 0.918126i | ||||||
\(730\) | −20.5560 | − | 25.9547i | −0.760810 | − | 0.960628i | ||||
\(731\) | 24.2290 | 0.896142 | ||||||||
\(732\) | −1.86016 | − | 1.86016i | −0.0687536 | − | 0.0687536i | ||||
\(733\) | −0.449878 | + | 0.449878i | −0.0166166 | + | 0.0166166i | −0.715366 | − | 0.698750i | \(-0.753740\pi\) |
0.698750 | + | 0.715366i | \(0.253740\pi\) | |||||||
\(734\) | −24.9605 | −0.921310 | ||||||||
\(735\) | 2.79014 | + | 0.323868i | 0.102916 | + | 0.0119461i | ||||
\(736\) | − | 6.68752i | − | 0.246505i | ||||||
\(737\) | 3.46043 | − | 34.1309i | 0.127467 | − | 1.25723i | ||||
\(738\) | 8.29512 | + | 8.29512i | 0.305348 | + | 0.305348i | ||||
\(739\) | −6.02634 | −0.221683 | −0.110841 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110841 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(740\) | −0.414472 | + | 3.57069i | −0.0152363 | + | 0.131261i | ||||
\(741\) | 3.55820 | 0.130714 | ||||||||
\(742\) | 0.533202 | − | 0.533202i | 0.0195744 | − | 0.0195744i | ||||
\(743\) | −20.6171 | + | 20.6171i | −0.756368 | + | 0.756368i | −0.975659 | − | 0.219291i | \(-0.929625\pi\) |
0.219291 | + | 0.975659i | \(0.429625\pi\) | |||||||
\(744\) | 11.1535 | 0.408907 | ||||||||
\(745\) | 0.685078 | + | 0.865006i | 0.0250993 | + | 0.0316914i | ||||
\(746\) | −4.91867 | −0.180085 | ||||||||
\(747\) | −11.3002 | − | 11.3002i | −0.413453 | − | 0.413453i | ||||
\(748\) | −1.36256 | + | 13.4392i | −0.0498200 | + | 0.491385i | ||||
\(749\) | − | 9.99212i | − | 0.365104i | ||||||
\(750\) | 5.96579 | + | 12.7143i | 0.217840 | + | 0.464260i | ||||
\(751\) | 24.6959 | 0.901166 | 0.450583 | − | 0.892734i | \(-0.351216\pi\) | ||||
0.450583 | + | 0.892734i | \(0.351216\pi\) | |||||||
\(752\) | −8.69999 | + | 8.69999i | −0.317256 | + | 0.317256i | ||||
\(753\) | 9.85664 | + | 9.85664i | 0.359196 | + | 0.359196i | ||||
\(754\) | −16.9815 | −0.618429 | ||||||||
\(755\) | 33.3594 | − | 26.4204i | 1.21407 | − | 0.961537i | ||||
\(756\) | − | 5.55482i | − | 0.202027i | ||||||
\(757\) | 24.1915 | − | 24.1915i | 0.879256 | − | 0.879256i | −0.114202 | − | 0.993458i | \(-0.536431\pi\) |
0.993458 | + | 0.114202i | \(0.0364311\pi\) | |||||||
\(758\) | −14.6592 | + | 14.6592i | −0.532448 | + | 0.532448i | ||||
\(759\) | −17.6135 | − | 21.5880i | −0.639328 | − | 0.783594i | ||||
\(760\) | 3.28625 | + | 0.381455i | 0.119205 | + | 0.0138368i | ||||
\(761\) | − | 18.9888i | − | 0.688344i | −0.938907 | − | 0.344172i | \(-0.888160\pi\) | ||
0.938907 | − | 0.344172i | \(-0.111840\pi\) | |||||||
\(762\) | −15.0093 | + | 15.0093i | −0.543731 | + | 0.543731i | ||||
\(763\) | −5.90571 | − | 5.90571i | −0.213801 | − | 0.213801i | ||||
\(764\) | − | 5.76500i | − | 0.208570i | ||||||
\(765\) | 12.8644 | + | 1.49325i | 0.465114 | + | 0.0539887i | ||||
\(766\) | − | 1.14028i | − | 0.0411998i | ||||||
\(767\) | 13.4535 | + | 13.4535i | 0.485779 | + | 0.485779i | ||||
\(768\) | −0.888243 | − | 0.888243i | −0.0320517 | − | 0.0320517i | ||||
\(769\) | −17.1249 | −0.617538 | −0.308769 | − | 0.951137i | \(-0.599917\pi\) | ||||
−0.308769 | + | 0.951137i | \(0.599917\pi\) | |||||||
\(770\) | −1.59382 | + | 7.24291i | −0.0574374 | + | 0.261016i | ||||
\(771\) | 6.71200 | 0.241727 | ||||||||
\(772\) | −2.53288 | − | 2.53288i | −0.0911603 | − | 0.0911603i | ||||
\(773\) | 21.8670 | + | 21.8670i | 0.786502 | + | 0.786502i | 0.980919 | − | 0.194417i | \(-0.0622815\pi\) |
−0.194417 | + | 0.980919i | \(0.562282\pi\) | |||||||
\(774\) | − | 8.45967i | − | 0.304077i | ||||||
\(775\) | −10.1694 | + | 43.2146i | −0.365295 | + | 1.55231i | ||||
\(776\) | 2.49885i | 0.0897035i | ||||||||
\(777\) | −1.42792 | − | 1.42792i | −0.0512265 | − | 0.0512265i | ||||
\(778\) | 24.7759 | − | 24.7759i | 0.888260 | − | 0.888260i | ||||
\(779\) | − | 12.2052i | − | 0.437297i | ||||||
\(780\) | 4.21566 | − | 3.33877i | 0.150945 | − | 0.119547i | ||||
\(781\) | −28.1224 | + | 22.9449i | −1.00630 | + | 0.821032i | ||||
\(782\) | −19.2596 | + | 19.2596i | −0.688721 | + | 0.688721i | ||||
\(783\) | 34.8393 | − | 34.8393i | 1.24505 | − | 1.24505i | ||||
\(784\) | − | 1.00000i | − | 0.0357143i | ||||||
\(785\) | −40.1580 | − | 4.66139i | −1.43330 | − | 0.166372i | ||||
\(786\) | −7.57226 | −0.270094 | ||||||||
\(787\) | 7.04060 | + | 7.04060i | 0.250970 | + | 0.250970i | 0.821368 | − | 0.570398i | \(-0.193211\pi\) |
−0.570398 | + | 0.821368i | \(0.693211\pi\) | |||||||
\(788\) | −9.40601 | + | 9.40601i | −0.335075 | + | 0.335075i | ||||
\(789\) | 30.2401 | 1.07657 | ||||||||
\(790\) | 3.31469 | − | 28.5562i | 0.117931 | − | 1.01598i | ||||
\(791\) | − | 9.86331i | − | 0.350699i | ||||||
\(792\) | 4.69235 | + | 0.475744i | 0.166735 | + | 0.0169048i | ||||
\(793\) | −2.83508 | − | 2.83508i | −0.100677 | − | 0.100677i | ||||
\(794\) | 0.751080 | 0.0266548 | ||||||||
\(795\) | −1.66039 | + | 1.31502i | −0.0588880 | + | 0.0466389i | ||||
\(796\) | 9.67486 | 0.342916 | ||||||||
\(797\) | −16.2064 | + | 16.2064i | −0.574059 | + | 0.574059i | −0.933260 | − | 0.359201i | \(-0.883049\pi\) |
0.359201 | + | 0.933260i | \(0.383049\pi\) | |||||||
\(798\) | −1.31418 | + | 1.31418i | −0.0465213 | + | 0.0465213i | ||||
\(799\) | 50.1107 | 1.77279 | ||||||||
\(800\) | 4.25140 | − | 2.63166i | 0.150310 | − | 0.0930431i | ||||
\(801\) | −11.7006 | −0.413422 | ||||||||
\(802\) | −8.15467 | − | 8.15467i | −0.287951 | − | 0.287951i | ||||
\(803\) | −4.95356 | + | 48.8579i | −0.174807 | + | 1.72416i | ||||
\(804\) | − | 12.9933i | − | 0.458238i | ||||||
\(805\) | −11.7226 | + | 9.28418i | −0.413166 | + | 0.327224i | ||||
\(806\) | 16.9991 | 0.598767 | ||||||||
\(807\) | −19.4055 | + | 19.4055i | −0.683104 | + | 0.683104i | ||||
\(808\) | −1.28743 | − | 1.28743i | −0.0452918 | − | 0.0452918i | ||||
\(809\) | −1.28331 | −0.0451188 | −0.0225594 | − | 0.999746i | \(-0.507181\pi\) | ||||
−0.0225594 | + | 0.999746i | \(0.507181\pi\) | |||||||
\(810\) | −0.699119 | + | 6.02294i | −0.0245646 | + | 0.211624i | ||||
\(811\) | − | 38.2967i | − | 1.34478i | −0.740198 | − | 0.672389i | \(-0.765268\pi\) | ||
0.740198 | − | 0.672389i | \(-0.234732\pi\) | |||||||
\(812\) | 6.27190 | − | 6.27190i | 0.220101 | − | 0.220101i | ||||
\(813\) | 10.3250 | − | 10.3250i | 0.362115 | − | 0.362115i | ||||
\(814\) | 4.13118 | − | 3.37060i | 0.144798 | − | 0.118139i | ||||
\(815\) | 0.616399 | − | 5.31030i | 0.0215915 | − | 0.186012i | ||||
\(816\) | 5.11615i | 0.179101i | ||||||||
\(817\) | −6.22366 | + | 6.22366i | −0.217738 | + | 0.217738i | ||||
\(818\) | 6.85772 | + | 6.85772i | 0.239775 | + | 0.239775i | ||||
\(819\) | − | 2.72255i | − | 0.0951337i | ||||||
\(820\) | −11.4525 | − | 14.4604i | −0.399940 | − | 0.504980i | ||||
\(821\) | − | 4.69422i | − | 0.163829i | −0.996639 | − | 0.0819147i | \(-0.973897\pi\) | ||
0.996639 | − | 0.0819147i | \(-0.0261035\pi\) | |||||||
\(822\) | −3.01235 | − | 3.01235i | −0.105068 | − | 0.105068i | ||||
\(823\) | −33.8017 | − | 33.8017i | −1.17825 | − | 1.17825i | −0.980189 | − | 0.198065i | \(-0.936534\pi\) |
−0.198065 | − | 0.980189i | \(-0.563466\pi\) | |||||||
\(824\) | 0.286992 | 0.00999784 | ||||||||
\(825\) | 6.79273 | − | 19.6925i | 0.236493 | − | 0.685605i | ||||
\(826\) | −9.93780 | −0.345780 | ||||||||
\(827\) | −19.0259 | − | 19.0259i | −0.661594 | − | 0.661594i | 0.294161 | − | 0.955756i | \(-0.404960\pi\) |
−0.955756 | + | 0.294161i | \(0.904960\pi\) | |||||||
\(828\) | 6.72457 | + | 6.72457i | 0.233695 | + | 0.233695i | ||||
\(829\) | − | 0.385397i | − | 0.0133854i | −0.999978 | − | 0.00669270i | \(-0.997870\pi\) | ||
0.999978 | − | 0.00669270i | \(-0.00213037\pi\) | |||||||
\(830\) | 15.6015 | + | 19.6990i | 0.541535 | + | 0.683763i | ||||
\(831\) | 37.2200i | 1.29115i | ||||||||
\(832\) | −1.35377 | − | 1.35377i | −0.0469337 | − | 0.0469337i | ||||
\(833\) | −2.87993 | + | 2.87993i | −0.0997836 | + | 0.0997836i | ||||
\(834\) | − | 4.75301i | − | 0.164583i | ||||||
\(835\) | −5.61307 | + | 48.3568i | −0.194248 | + | 1.67346i | ||||
\(836\) | −3.10210 | − | 3.80209i | −0.107288 | − | 0.131498i | ||||
\(837\) | −34.8754 | + | 34.8754i | −1.20547 | + | 1.20547i | ||||
\(838\) | 20.0609 | − | 20.0609i | 0.692991 | − | 0.692991i | ||||
\(839\) | − | 18.6298i | − | 0.643173i | −0.946880 | − | 0.321587i | \(-0.895784\pi\) | ||
0.946880 | − | 0.321587i | \(-0.104216\pi\) | |||||||
\(840\) | −0.323868 | + | 2.79014i | −0.0111745 | + | 0.0962688i | ||||
\(841\) | 49.6734 | 1.71288 | ||||||||
\(842\) | −4.71599 | − | 4.71599i | −0.162524 | − | 0.162524i | ||||
\(843\) | 10.7468 | − | 10.7468i | 0.370140 | − | 0.370140i | ||||
\(844\) | 11.1990 | 0.385485 | ||||||||
\(845\) | −16.3626 | + | 12.9591i | −0.562891 | + | 0.445806i | ||||
\(846\) | − | 17.4964i | − | 0.601538i | ||||||
\(847\) | 9.18106 | − | 6.05873i | 0.315465 | − | 0.208180i | ||||
\(848\) | 0.533202 | + | 0.533202i | 0.0183102 | + | 0.0183102i | ||||
\(849\) | 19.6439 | 0.674178 | ||||||||
\(850\) | −19.8227 | − | 4.66474i | −0.679913 | − | 0.159999i | ||||
\(851\) | 10.7507 | 0.368531 | ||||||||
\(852\) | −9.72040 | + | 9.72040i | −0.333015 | + | 0.333015i | ||||
\(853\) | 10.2175 | − | 10.2175i | 0.349842 | − | 0.349842i | −0.510209 | − | 0.860051i | \(-0.670432\pi\) |
0.860051 | + | 0.510209i | \(0.170432\pi\) | |||||||
\(854\) | 2.09421 | 0.0716623 | ||||||||
\(855\) | −3.68803 | + | 2.92089i | −0.126128 | + | 0.0998924i | ||||
\(856\) | 9.99212 | 0.341524 | ||||||||
\(857\) | −34.2775 | − | 34.2775i | −1.17090 | − | 1.17090i | −0.981996 | − | 0.188903i | \(-0.939507\pi\) |
−0.188903 | − | 0.981996i | \(-0.560493\pi\) | |||||||
\(858\) | −7.93567 | − | 0.804574i | −0.270919 | − | 0.0274677i | ||||
\(859\) | − | 13.2629i | − | 0.452525i | −0.974066 | − | 0.226263i | \(-0.927349\pi\) | ||
0.974066 | − | 0.226263i | \(-0.0726508\pi\) | |||||||
\(860\) | −1.53377 | + | 13.2135i | −0.0523012 | + | 0.450576i | ||||
\(861\) | 10.3626 | 0.353157 | ||||||||
\(862\) | 0.467190 | − | 0.467190i | 0.0159126 | − | 0.0159126i | ||||
\(863\) | −21.1845 | − | 21.1845i | −0.721129 | − | 0.721129i | 0.247706 | − | 0.968835i | \(-0.420323\pi\) |
−0.968835 | + | 0.247706i | \(0.920323\pi\) | |||||||
\(864\) | 5.55482 | 0.188979 | ||||||||
\(865\) | 17.5849 | + | 2.04119i | 0.597905 | + | 0.0694025i | ||||
\(866\) | − | 1.28585i | − | 0.0436950i | ||||||
\(867\) | −0.365980 | + | 0.365980i | −0.0124293 | + | 0.0124293i | ||||
\(868\) | −6.27840 | + | 6.27840i | −0.213103 | + | 0.213103i | ||||
\(869\) | −33.0386 | + | 26.9560i | −1.12076 | + | 0.914418i | ||||
\(870\) | −19.5307 | + | 15.4682i | −0.662153 | + | 0.524421i | ||||
\(871\) | − | 19.8031i | − | 0.671003i | ||||||
\(872\) | 5.90571 | − | 5.90571i | 0.199993 | − | 0.199993i | ||||
\(873\) | −2.51270 | − | 2.51270i | −0.0850419 | − | 0.0850419i | ||||
\(874\) | − | 9.89434i | − | 0.334681i | ||||||
\(875\) | −10.5152 | − | 3.79879i | −0.355478 | − | 0.128423i | ||||
\(876\) | 18.5997i | 0.628425i | ||||||||
\(877\) | −21.2067 | − | 21.2067i | −0.716099 | − | 0.716099i | 0.251705 | − | 0.967804i | \(-0.419009\pi\) |
−0.967804 | + | 0.251705i | \(0.919009\pi\) | |||||||
\(878\) | 2.64772 | + | 2.64772i | 0.0893562 | + | 0.0893562i | ||||
\(879\) | −34.6910 | −1.17010 | ||||||||
\(880\) | −7.24291 | − | 1.59382i | −0.244158 | − | 0.0537278i | ||||
\(881\) | 3.46287 | 0.116667 | 0.0583335 | − | 0.998297i | \(-0.481421\pi\) | ||||
0.0583335 | + | 0.998297i | \(0.481421\pi\) | |||||||
\(882\) | 1.00554 | + | 1.00554i | 0.0338583 | + | 0.0338583i | ||||
\(883\) | −26.2872 | − | 26.2872i | −0.884634 | − | 0.884634i | 0.109368 | − | 0.994001i | \(-0.465117\pi\) |
−0.994001 | + | 0.109368i | \(0.965117\pi\) | |||||||
\(884\) | 7.79755i | 0.262260i | ||||||||
\(885\) | 27.7278 | + | 3.21854i | 0.932060 | + | 0.108190i | ||||
\(886\) | 19.4763i | 0.654319i | ||||||||
\(887\) | 13.2703 | + | 13.2703i | 0.445573 | + | 0.445573i | 0.893880 | − | 0.448307i | \(-0.147973\pi\) |
−0.448307 | + | 0.893880i | \(0.647973\pi\) | |||||||
\(888\) | 1.42792 | − | 1.42792i | 0.0479180 | − | 0.0479180i | ||||
\(889\) | − | 16.8978i | − | 0.566734i | ||||||
\(890\) | 18.2757 | + | 2.12137i | 0.612602 | + | 0.0711085i | ||||
\(891\) | 6.96835 | − | 5.68542i | 0.233449 | − | 0.190469i | ||||
\(892\) | −1.71338 | + | 1.71338i | −0.0573681 | + | 0.0573681i | ||||
\(893\) | −12.8718 | + | 12.8718i | −0.430740 | + | 0.430740i | ||||
\(894\) | − | 0.619881i | − | 0.0207319i | ||||||
\(895\) | 2.81330 | − | 2.22811i | 0.0940382 | − | 0.0744776i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | −11.3725 | − | 11.3725i | −0.379718 | − | 0.379718i | ||||
\(898\) | −22.4785 | + | 22.4785i | −0.750117 | + | 0.750117i | ||||
\(899\) | −78.7550 | −2.62663 | ||||||||
\(900\) | −1.62872 | + | 6.92119i | −0.0542905 | + | 0.230706i | ||||
\(901\) | − | 3.07116i | − | 0.102315i | ||||||
\(902\) | −2.75982 | + | 27.2207i | −0.0918920 | + | 0.906349i | ||||
\(903\) | −5.28409 | − | 5.28409i | −0.175844 | − | 0.175844i | ||||
\(904\) | 9.86331 | 0.328049 | ||||||||
\(905\) | −33.3676 | − | 42.1312i | −1.10918 | − | 1.40049i | ||||
\(906\) | −23.9060 | −0.794225 | ||||||||
\(907\) | 12.1339 | − | 12.1339i | 0.402899 | − | 0.402899i | −0.476355 | − | 0.879253i | \(-0.658042\pi\) |
0.879253 | + | 0.476355i | \(0.158042\pi\) | |||||||
\(908\) | 5.86091 | − | 5.86091i | 0.194501 | − | 0.194501i | ||||
\(909\) | 2.58914 | 0.0858762 | ||||||||
\(910\) | −0.493609 | + | 4.25246i | −0.0163630 | + | 0.140968i | ||||
\(911\) | −16.8498 | −0.558259 | −0.279130 | − | 0.960253i | \(-0.590046\pi\) | ||||
−0.279130 | + | 0.960253i | \(0.590046\pi\) | |||||||
\(912\) | −1.31418 | − | 1.31418i | −0.0435167 | − | 0.0435167i | ||||
\(913\) | 3.75963 | − | 37.0819i | 0.124426 | − | 1.22723i | ||||
\(914\) | 3.60075i | 0.119102i | ||||||||
\(915\) | −5.84312 | − | 0.678247i | −0.193168 | − | 0.0224222i | ||||
\(916\) | 1.08317 | 0.0357888 | ||||||||
\(917\) | 4.26249 | − | 4.26249i | 0.140760 | − | 0.140760i | ||||
\(918\) | −15.9975 | − | 15.9975i | −0.527996 | − | 0.527996i | ||||
\(919\) | 25.4965 | 0.841051 | 0.420526 | − | 0.907281i | \(-0.361846\pi\) | ||||
0.420526 | + | 0.907281i | \(0.361846\pi\) | |||||||
\(920\) | −9.28418 | − | 11.7226i | −0.306090 | − | 0.386481i | ||||
\(921\) | − | 21.6690i | − | 0.714017i | ||||||
\(922\) | −10.2380 | + | 10.2380i | −0.337172 | + | 0.337172i | ||||
\(923\) | −14.8149 | + | 14.8149i | −0.487638 | + | 0.487638i | ||||
\(924\) | 3.22810 | − | 2.63378i | 0.106197 | − | 0.0866451i | ||||
\(925\) | 4.23061 | + | 6.83448i | 0.139102 | + | 0.224716i | ||||
\(926\) | 25.6311i | 0.842292i | ||||||||
\(927\) | −0.288582 | + | 0.288582i | −0.00947828 | + | 0.00947828i | ||||
\(928\) | 6.27190 | + | 6.27190i | 0.205885 | + | 0.205885i | ||||
\(929\) | − | 12.7297i | − | 0.417648i | −0.977953 | − | 0.208824i | \(-0.933036\pi\) | ||
0.977953 | − | 0.208824i | \(-0.0669637\pi\) | |||||||
\(930\) | 19.5510 | − | 15.4842i | 0.641102 | − | 0.507748i | ||||
\(931\) | − | 1.47952i | − | 0.0484894i | ||||||
\(932\) | 13.0962 | + | 13.0962i | 0.428982 | + | 0.428982i | ||||
\(933\) | 25.4897 | + | 25.4897i | 0.834496 | + | 0.834496i | ||||
\(934\) | 20.5637 | 0.672866 | ||||||||
\(935\) | 16.2690 | + | 25.4492i | 0.532052 | + | 0.832276i | ||||
\(936\) | 2.72255 | 0.0889894 | ||||||||
\(937\) | 12.4492 | + | 12.4492i | 0.406698 | + | 0.406698i | 0.880585 | − | 0.473888i | \(-0.157150\pi\) |
−0.473888 | + | 0.880585i | \(0.657150\pi\) | |||||||
\(938\) | 7.31404 | + | 7.31404i | 0.238812 | + | 0.238812i | ||||
\(939\) | 14.4289i | 0.470870i | ||||||||
\(940\) | −3.17216 | + | 27.3283i | −0.103465 | + | 0.891351i | ||||
\(941\) | 47.8865i | 1.56106i | 0.625121 | + | 0.780528i | \(0.285050\pi\) | ||||
−0.625121 | + | 0.780528i | \(0.714950\pi\) | |||||||
\(942\) | 16.0592 | + | 16.0592i | 0.523239 | + | 0.523239i | ||||
\(943\) | −39.0097 | + | 39.0097i | −1.27033 | + | 1.27033i | ||||
\(944\) | − | 9.93780i | − | 0.323448i | ||||||
\(945\) | −7.71168 | − | 9.73706i | −0.250861 | − | 0.316747i | ||||
\(946\) | 15.2876 | − | 12.4730i | 0.497043 | − | 0.405533i | ||||
\(947\) | −17.4772 | + | 17.4772i | −0.567932 | + | 0.567932i | −0.931549 | − | 0.363617i | \(-0.881542\pi\) |
0.363617 | + | 0.931549i | \(0.381542\pi\) | |||||||
\(948\) | −11.4197 | + | 11.4197i | −0.370893 | + | 0.370893i | ||||
\(949\) | 28.3479i | 0.920211i | ||||||||
\(950\) | 6.29005 | − | 3.89360i | 0.204076 | − | 0.126325i | ||||
\(951\) | −17.4182 | −0.564824 | ||||||||
\(952\) | −2.87993 | − | 2.87993i | −0.0933390 | − | 0.0933390i | ||||
\(953\) | 3.85767 | − | 3.85767i | 0.124962 | − | 0.124962i | −0.641860 | − | 0.766822i | \(-0.721837\pi\) |
0.766822 | + | 0.641860i | \(0.221837\pi\) | |||||||
\(954\) | −1.07231 | −0.0347174 | ||||||||
\(955\) | −8.00346 | − | 10.1055i | −0.258986 | − | 0.327006i | ||||
\(956\) | 27.4149i | 0.886661i | ||||||||
\(957\) | 36.7651 | + | 3.72751i | 1.18845 | + | 0.120493i | ||||
\(958\) | 26.9332 | + | 26.9332i | 0.870173 | + | 0.870173i | ||||
\(959\) | 3.39136 | 0.109513 | ||||||||
\(960\) | −2.79014 | − | 0.323868i | −0.0900513 | − | 0.0104528i | ||||
\(961\) | 47.8367 | 1.54312 | ||||||||
\(962\) | 2.17631 | − | 2.17631i | 0.0701669 | − | 0.0701669i | ||||
\(963\) | −10.0475 | + | 10.0475i | −0.323776 | + | 0.323776i | ||||
\(964\) | 1.81865 | 0.0585747 | ||||||||
\(965\) | −7.95624 | − | 0.923530i | −0.256121 | − | 0.0297295i | ||||
\(966\) | 8.40062 | 0.270286 | ||||||||
\(967\) | 32.6022 | + | 32.6022i | 1.04842 | + | 1.04842i | 0.998767 | + | 0.0496495i | \(0.0158104\pi\) |
0.0496495 | + | 0.998767i | \(0.484190\pi\) | |||||||
\(968\) | 6.05873 | + | 9.18106i | 0.194735 | + | 0.295090i | ||||
\(969\) | 7.56947i | 0.243166i | ||||||||
\(970\) | 3.46912 | + | 4.38024i | 0.111387 | + | 0.140641i | ||||
\(971\) | 24.9573 | 0.800919 | 0.400460 | − | 0.916314i | \(-0.368851\pi\) | ||||
0.400460 | + | 0.916314i | \(0.368851\pi\) | |||||||
\(972\) | −9.37498 | + | 9.37498i | −0.300703 | + | 0.300703i | ||||
\(973\) | 2.67551 | + | 2.67551i | 0.0857731 | + | 0.0857731i | ||||
\(974\) | −27.8119 | −0.891152 | ||||||||
\(975\) | 2.75447 | − | 11.7051i | 0.0882137 | − | 0.374862i | ||||
\(976\) | 2.09421i | 0.0670339i | ||||||||
\(977\) | 26.9726 | − | 26.9726i | 0.862931 | − | 0.862931i | −0.128746 | − | 0.991678i | \(-0.541095\pi\) |
0.991678 | + | 0.128746i | \(0.0410953\pi\) | |||||||
\(978\) | −2.12360 | + | 2.12360i | −0.0679051 | + | 0.0679051i | ||||
\(979\) | −17.2515 | − | 21.1444i | −0.551362 | − | 0.675778i | ||||
\(980\) | −1.38828 | − | 1.75290i | −0.0443471 | − | 0.0559944i | ||||
\(981\) | 11.8769i | 0.379199i | ||||||||
\(982\) | 4.26932 | − | 4.26932i | 0.136240 | − | 0.136240i | ||||
\(983\) | 1.63673 | + | 1.63673i | 0.0522037 | + | 0.0522037i | 0.732727 | − | 0.680523i | \(-0.238247\pi\) |
−0.680523 | + | 0.732727i | \(0.738247\pi\) | |||||||
\(984\) | 10.3626i | 0.330348i | ||||||||
\(985\) | −3.42959 | + | 29.5460i | −0.109276 | + | 0.941414i | ||||
\(986\) | − | 36.1252i | − | 1.15046i | ||||||
\(987\) | −10.9286 | − | 10.9286i | −0.347862 | − | 0.347862i | ||||
\(988\) | −2.00294 | − | 2.00294i | −0.0637221 | − | 0.0637221i | ||||
\(989\) | 39.7836 | 1.26504 | ||||||||
\(990\) | 8.88570 | − | 5.68039i | 0.282406 | − | 0.180535i | ||||
\(991\) | −5.70763 | −0.181309 | −0.0906543 | − | 0.995882i | \(-0.528896\pi\) | ||||
−0.0906543 | + | 0.995882i | \(0.528896\pi\) | |||||||
\(992\) | −6.27840 | − | 6.27840i | −0.199340 | − | 0.199340i | ||||
\(993\) | −5.21826 | − | 5.21826i | −0.165596 | − | 0.165596i | ||||
\(994\) | − | 10.9434i | − | 0.347104i | ||||||
\(995\) | 16.9591 | − | 13.4315i | 0.537639 | − | 0.425806i | ||||
\(996\) | − | 14.1167i | − | 0.447305i | ||||||
\(997\) | 1.75802 | + | 1.75802i | 0.0556771 | + | 0.0556771i | 0.734397 | − | 0.678720i | \(-0.237465\pi\) |
−0.678720 | + | 0.734397i | \(0.737465\pi\) | |||||||
\(998\) | 8.79942 | − | 8.79942i | 0.278541 | − | 0.278541i | ||||
\(999\) | 8.92985i | 0.282528i |
(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 | 770.2.m.f.43.13 | yes | 36 | |
5.2 | odd | 4 | inner | 770.2.m.f.197.4 | yes | 36 | |
11.10 | odd | 2 | inner | 770.2.m.f.43.4 | ✓ | 36 | |
55.32 | even | 4 | inner | 770.2.m.f.197.13 | yes | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.f.43.4 | ✓ | 36 | 11.10 | odd | 2 | inner | |
770.2.m.f.43.13 | yes | 36 | 1.1 | even | 1 | trivial | |
770.2.m.f.197.4 | yes | 36 | 5.2 | odd | 4 | inner | |
770.2.m.f.197.13 | yes | 36 | 55.32 | even | 4 | inner |