Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(901,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.i (of order \(6\), degree \(2\), 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: | \(8.60787333789\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} + 34 x^{12} + 18 x^{11} - 72 x^{10} + 132 x^{9} - 93 x^{8} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1011.7 | ||
Root | \(0.430324 + 1.60599i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.1011 |
Dual form | 1078.2.i.c.901.7 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.889740 | + | 0.513691i | 0.513691 | + | 0.296580i | 0.734350 | − | 0.678771i | \(-0.237487\pi\) |
−0.220658 | + | 0.975351i | \(0.570821\pi\) | |||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.09005 | + | 0.629341i | −0.487486 | + | 0.281450i | −0.723531 | − | 0.690292i | \(-0.757482\pi\) |
0.236045 | + | 0.971742i | \(0.424149\pi\) | |||||||
\(6\) | 1.02738 | 0.419427 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −0.972242 | − | 1.68397i | −0.324081 | − | 0.561324i | ||||
\(10\) | −0.629341 | + | 1.09005i | −0.199015 | + | 0.344704i | ||||
\(11\) | 1.45007 | − | 2.98283i | 0.437213 | − | 0.899358i | ||||
\(12\) | 0.889740 | − | 0.513691i | 0.256846 | − | 0.148290i | ||||
\(13\) | 4.08338 | 1.13253 | 0.566263 | − | 0.824224i | \(-0.308388\pi\) | ||||
0.566263 | + | 0.824224i | \(0.308388\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.29315 | −0.333890 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.60096 | − | 2.77294i | 0.388289 | − | 0.672537i | −0.603930 | − | 0.797037i | \(-0.706400\pi\) |
0.992220 | + | 0.124501i | \(0.0397329\pi\) | |||||||
\(18\) | −1.68397 | − | 0.972242i | −0.396916 | − | 0.229160i | ||||
\(19\) | −3.81407 | − | 6.60616i | −0.875007 | − | 1.51556i | −0.856756 | − | 0.515723i | \(-0.827524\pi\) |
−0.0182510 | − | 0.999833i | \(-0.505810\pi\) | |||||||
\(20\) | 1.25868i | 0.281450i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.235617 | − | 3.30824i | −0.0502337 | − | 0.705320i | ||||
\(23\) | 4.12636 | + | 7.14707i | 0.860407 | + | 1.49027i | 0.871537 | + | 0.490330i | \(0.163124\pi\) |
−0.0111305 | + | 0.999938i | \(0.503543\pi\) | |||||||
\(24\) | 0.513691 | − | 0.889740i | 0.104857 | − | 0.181617i | ||||
\(25\) | −1.70786 | + | 2.95810i | −0.341572 | + | 0.591620i | ||||
\(26\) | 3.53631 | − | 2.04169i | 0.693528 | − | 0.400409i | ||||
\(27\) | − | 5.07988i | − | 0.977623i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 3.54386i | − | 0.658079i | −0.944316 | − | 0.329039i | \(-0.893275\pi\) | ||
0.944316 | − | 0.329039i | \(-0.106725\pi\) | |||||||
\(30\) | −1.11990 | + | 0.646574i | −0.204465 | + | 0.118048i | ||||
\(31\) | 7.95304 | + | 4.59169i | 1.42841 | + | 0.824692i | 0.996995 | − | 0.0774626i | \(-0.0246818\pi\) |
0.431413 | + | 0.902155i | \(0.358015\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 2.82244 | − | 1.90905i | 0.491324 | − | 0.332324i | ||||
\(34\) | − | 3.20191i | − | 0.549124i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.94448 | −0.324081 | ||||||||
\(37\) | 0.154122 | + | 0.266948i | 0.0253376 | + | 0.0438860i | 0.878416 | − | 0.477896i | \(-0.158601\pi\) |
−0.853079 | + | 0.521782i | \(0.825267\pi\) | |||||||
\(38\) | −6.60616 | − | 3.81407i | −1.07166 | − | 0.618723i | ||||
\(39\) | 3.63315 | + | 2.09760i | 0.581769 | + | 0.335885i | ||||
\(40\) | 0.629341 | + | 1.09005i | 0.0995076 | + | 0.172352i | ||||
\(41\) | 6.05276 | 0.945283 | 0.472641 | − | 0.881255i | \(-0.343301\pi\) | ||||
0.472641 | + | 0.881255i | \(0.343301\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 7.57607i | − | 1.15534i | −0.816270 | − | 0.577670i | \(-0.803962\pi\) | ||
0.816270 | − | 0.577670i | \(-0.196038\pi\) | |||||||
\(44\) | −1.85817 | − | 2.74722i | −0.280130 | − | 0.414158i | ||||
\(45\) | 2.11959 | + | 1.22374i | 0.315969 | + | 0.182425i | ||||
\(46\) | 7.14707 | + | 4.12636i | 1.05378 | + | 0.608399i | ||||
\(47\) | −4.07263 | + | 2.35133i | −0.594054 | + | 0.342977i | −0.766699 | − | 0.642007i | \(-0.778102\pi\) |
0.172645 | + | 0.984984i | \(0.444769\pi\) | |||||||
\(48\) | − | 1.02738i | − | 0.148290i | ||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.41572i | 0.483056i | ||||||||
\(51\) | 2.84887 | − | 1.64480i | 0.398922 | − | 0.230317i | ||||
\(52\) | 2.04169 | − | 3.53631i | 0.283132 | − | 0.490399i | ||||
\(53\) | 2.39830 | − | 4.15397i | 0.329431 | − | 0.570592i | −0.652968 | − | 0.757386i | \(-0.726476\pi\) |
0.982399 | + | 0.186794i | \(0.0598097\pi\) | |||||||
\(54\) | −2.53994 | − | 4.39930i | −0.345642 | − | 0.598669i | ||||
\(55\) | 0.296567 | + | 4.16403i | 0.0399891 | + | 0.561478i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 7.83701i | − | 1.03804i | ||||||
\(58\) | −1.77193 | − | 3.06907i | −0.232666 | − | 0.402989i | ||||
\(59\) | −2.36710 | − | 1.36664i | −0.308170 | − | 0.177922i | 0.337938 | − | 0.941169i | \(-0.390271\pi\) |
−0.646107 | + | 0.763247i | \(0.723604\pi\) | |||||||
\(60\) | −0.646574 | + | 1.11990i | −0.0834724 | + | 0.144578i | ||||
\(61\) | 0.755050 | + | 1.30779i | 0.0966743 | + | 0.167445i | 0.910306 | − | 0.413936i | \(-0.135846\pi\) |
−0.813632 | + | 0.581380i | \(0.802513\pi\) | |||||||
\(62\) | 9.18338 | 1.16629 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −4.45110 | + | 2.56984i | −0.552090 | + | 0.318750i | ||||
\(66\) | 1.48978 | − | 3.06451i | 0.183379 | − | 0.377215i | ||||
\(67\) | −1.69044 | + | 2.92792i | −0.206520 | + | 0.357703i | −0.950616 | − | 0.310370i | \(-0.899547\pi\) |
0.744096 | + | 0.668073i | \(0.232880\pi\) | |||||||
\(68\) | −1.60096 | − | 2.77294i | −0.194145 | − | 0.336268i | ||||
\(69\) | 8.47871i | 1.02072i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.50810 | 0.416334 | 0.208167 | − | 0.978093i | \(-0.433250\pi\) | ||||
0.208167 | + | 0.978093i | \(0.433250\pi\) | |||||||
\(72\) | −1.68397 | + | 0.972242i | −0.198458 | + | 0.114580i | ||||
\(73\) | −0.483428 | + | 0.837321i | −0.0565809 | + | 0.0980011i | −0.892929 | − | 0.450198i | \(-0.851353\pi\) |
0.836348 | + | 0.548200i | \(0.184687\pi\) | |||||||
\(74\) | 0.266948 | + | 0.154122i | 0.0310321 | + | 0.0179164i | ||||
\(75\) | −3.03910 | + | 1.75463i | −0.350925 | + | 0.202607i | ||||
\(76\) | −7.62813 | −0.875007 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.19520 | 0.475013 | ||||||||
\(79\) | −13.5212 | + | 7.80647i | −1.52125 | + | 0.878296i | −0.521568 | + | 0.853210i | \(0.674653\pi\) |
−0.999685 | + | 0.0250865i | \(0.992014\pi\) | |||||||
\(80\) | 1.09005 | + | 0.629341i | 0.121871 | + | 0.0703625i | ||||
\(81\) | −0.307237 | + | 0.532150i | −0.0341374 | + | 0.0591278i | ||||
\(82\) | 5.24185 | − | 3.02638i | 0.578865 | − | 0.334208i | ||||
\(83\) | 1.32998 | 0.145984 | 0.0729921 | − | 0.997333i | \(-0.476745\pi\) | ||||
0.0729921 | + | 0.997333i | \(0.476745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.03019i | 0.437136i | ||||||||
\(86\) | −3.78804 | − | 6.56107i | −0.408474 | − | 0.707498i | ||||
\(87\) | 1.82045 | − | 3.15311i | 0.195173 | − | 0.338049i | ||||
\(88\) | −2.98283 | − | 1.45007i | −0.317971 | − | 0.154578i | ||||
\(89\) | −9.22296 | + | 5.32488i | −0.977631 | + | 0.564436i | −0.901554 | − | 0.432666i | \(-0.857573\pi\) |
−0.0760772 | + | 0.997102i | \(0.524240\pi\) | |||||||
\(90\) | 2.44749 | 0.257988 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.25273 | 0.860407 | ||||||||
\(93\) | 4.71742 | + | 8.17082i | 0.489174 | + | 0.847274i | ||||
\(94\) | −2.35133 | + | 4.07263i | −0.242521 | + | 0.420059i | ||||
\(95\) | 8.31505 | + | 4.80070i | 0.853106 | + | 0.492541i | ||||
\(96\) | −0.513691 | − | 0.889740i | −0.0524284 | − | 0.0908087i | ||||
\(97\) | 10.6748i | 1.08386i | 0.840424 | + | 0.541930i | \(0.182306\pi\) | ||||
−0.840424 | + | 0.541930i | \(0.817694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.43283 | + | 0.458154i | −0.646524 | + | 0.0460462i | ||||
\(100\) | 1.70786 | + | 2.95810i | 0.170786 | + | 0.295810i | ||||
\(101\) | −5.03242 | + | 8.71642i | −0.500745 | + | 0.867316i | 0.499255 | + | 0.866455i | \(0.333607\pi\) |
−1.00000 | 0.000860457i | \(0.999726\pi\) | ||||||||
\(102\) | 1.64480 | − | 2.84887i | 0.162859 | − | 0.282080i | ||||
\(103\) | −2.49868 | + | 1.44261i | −0.246202 | + | 0.142145i | −0.618024 | − | 0.786159i | \(-0.712067\pi\) |
0.371822 | + | 0.928304i | \(0.378733\pi\) | |||||||
\(104\) | − | 4.08338i | − | 0.400409i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 4.79659i | − | 0.465886i | ||||||
\(107\) | 14.1162 | − | 8.15002i | 1.36467 | − | 0.787892i | 0.374428 | − | 0.927256i | \(-0.377839\pi\) |
0.990241 | + | 0.139364i | \(0.0445059\pi\) | |||||||
\(108\) | −4.39930 | − | 2.53994i | −0.423323 | − | 0.244406i | ||||
\(109\) | −9.96227 | − | 5.75172i | −0.954213 | − | 0.550915i | −0.0598257 | − | 0.998209i | \(-0.519054\pi\) |
−0.894387 | + | 0.447294i | \(0.852388\pi\) | |||||||
\(110\) | 2.33885 | + | 3.45787i | 0.223001 | + | 0.329695i | ||||
\(111\) | 0.316686i | 0.0300585i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.558958 | 0.0525824 | 0.0262912 | − | 0.999654i | \(-0.491630\pi\) | ||||
0.0262912 | + | 0.999654i | \(0.491630\pi\) | |||||||
\(114\) | −3.91851 | − | 6.78705i | −0.367002 | − | 0.635666i | ||||
\(115\) | −8.99589 | − | 5.19378i | −0.838872 | − | 0.484323i | ||||
\(116\) | −3.06907 | − | 1.77193i | −0.284956 | − | 0.164520i | ||||
\(117\) | −3.97004 | − | 6.87631i | −0.367030 | − | 0.635715i | ||||
\(118\) | −2.73329 | −0.251619 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.29315i | 0.118048i | ||||||||
\(121\) | −6.79458 | − | 8.65064i | −0.617689 | − | 0.786422i | ||||
\(122\) | 1.30779 | + | 0.755050i | 0.118401 | + | 0.0683590i | ||||
\(123\) | 5.38538 | + | 3.10925i | 0.485584 | + | 0.280352i | ||||
\(124\) | 7.95304 | − | 4.59169i | 0.714204 | − | 0.412346i | ||||
\(125\) | − | 10.5927i | − | 0.947441i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2829i | 1.00120i | 0.865679 | + | 0.500599i | \(0.166887\pi\) | ||||
−0.865679 | + | 0.500599i | \(0.833113\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 3.89176 | − | 6.74073i | 0.342651 | − | 0.593488i | ||||
\(130\) | −2.56984 | + | 4.45110i | −0.225390 | + | 0.390387i | ||||
\(131\) | 3.51694 | + | 6.09152i | 0.307276 | + | 0.532218i | 0.977766 | − | 0.209701i | \(-0.0672490\pi\) |
−0.670489 | + | 0.741919i | \(0.733916\pi\) | |||||||
\(132\) | −0.242069 | − | 3.39883i | −0.0210694 | − | 0.295831i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.38087i | 0.292063i | ||||||||
\(135\) | 3.19698 | + | 5.53733i | 0.275152 | + | 0.476577i | ||||
\(136\) | −2.77294 | − | 1.60096i | −0.237778 | − | 0.137281i | ||||
\(137\) | −4.54487 | + | 7.87195i | −0.388294 | + | 0.672546i | −0.992220 | − | 0.124495i | \(-0.960269\pi\) |
0.603926 | + | 0.797041i | \(0.293602\pi\) | |||||||
\(138\) | 4.23936 | + | 7.34278i | 0.360878 | + | 0.625059i | ||||
\(139\) | −7.86546 | −0.667140 | −0.333570 | − | 0.942725i | \(-0.608253\pi\) | ||||
−0.333570 | + | 0.942725i | \(0.608253\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.83144 | −0.406880 | ||||||||
\(142\) | 3.03810 | − | 1.75405i | 0.254952 | − | 0.147196i | ||||
\(143\) | 5.92120 | − | 12.1801i | 0.495156 | − | 1.01855i | ||||
\(144\) | −0.972242 | + | 1.68397i | −0.0810202 | + | 0.140331i | ||||
\(145\) | 2.23030 | + | 3.86299i | 0.185216 | + | 0.320804i | ||||
\(146\) | 0.966855i | 0.0800175i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.308245 | 0.0253376 | ||||||||
\(149\) | 5.39617 | − | 3.11548i | 0.442072 | − | 0.255230i | −0.262404 | − | 0.964958i | \(-0.584515\pi\) |
0.704476 | + | 0.709728i | \(0.251182\pi\) | |||||||
\(150\) | −1.75463 | + | 3.03910i | −0.143265 | + | 0.248142i | ||||
\(151\) | −15.1642 | − | 8.75506i | −1.23405 | − | 0.712476i | −0.266175 | − | 0.963925i | \(-0.585760\pi\) |
−0.967871 | + | 0.251448i | \(0.919093\pi\) | |||||||
\(152\) | −6.60616 | + | 3.81407i | −0.535830 | + | 0.309362i | ||||
\(153\) | −6.22607 | −0.503348 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.5590 | −0.928438 | ||||||||
\(156\) | 3.63315 | − | 2.09760i | 0.290885 | − | 0.167942i | ||||
\(157\) | 6.73252 | + | 3.88702i | 0.537314 | + | 0.310218i | 0.743989 | − | 0.668191i | \(-0.232931\pi\) |
−0.206676 | + | 0.978409i | \(0.566265\pi\) | |||||||
\(158\) | −7.80647 | + | 13.5212i | −0.621049 | + | 1.07569i | ||||
\(159\) | 4.26772 | − | 2.46397i | 0.338452 | − | 0.195405i | ||||
\(160\) | 1.25868 | 0.0995076 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.614474i | 0.0482776i | ||||||||
\(163\) | 9.10616 | + | 15.7723i | 0.713249 | + | 1.23538i | 0.963631 | + | 0.267237i | \(0.0861105\pi\) |
−0.250382 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(164\) | 3.02638 | − | 5.24185i | 0.236321 | − | 0.409319i | ||||
\(165\) | −1.87516 | + | 3.85725i | −0.145981 | + | 0.300286i | ||||
\(166\) | 1.15180 | − | 0.664990i | 0.0893967 | − | 0.0516132i | ||||
\(167\) | 14.3653 | 1.11162 | 0.555809 | − | 0.831310i | \(-0.312409\pi\) | ||||
0.555809 | + | 0.831310i | \(0.312409\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.67402 | 0.282617 | ||||||||
\(170\) | 2.01510 | + | 3.49025i | 0.154551 | + | 0.267690i | ||||
\(171\) | −7.41639 | + | 12.8456i | −0.567146 | + | 0.982325i | ||||
\(172\) | −6.56107 | − | 3.78804i | −0.500277 | − | 0.288835i | ||||
\(173\) | 2.38160 | + | 4.12505i | 0.181069 | + | 0.313621i | 0.942245 | − | 0.334924i | \(-0.108711\pi\) |
−0.761176 | + | 0.648546i | \(0.775377\pi\) | |||||||
\(174\) | − | 3.64090i | − | 0.276016i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3.30824 | + | 0.235617i | −0.249368 | + | 0.0177603i | ||||
\(177\) | −1.40407 | − | 2.43191i | −0.105536 | − | 0.182794i | ||||
\(178\) | −5.32488 | + | 9.22296i | −0.399116 | + | 0.691290i | ||||
\(179\) | 1.94526 | − | 3.36928i | 0.145395 | − | 0.251832i | −0.784125 | − | 0.620603i | \(-0.786888\pi\) |
0.929520 | + | 0.368771i | \(0.120221\pi\) | |||||||
\(180\) | 2.11959 | − | 1.22374i | 0.157985 | − | 0.0912125i | ||||
\(181\) | 13.0698i | 0.971474i | 0.874105 | + | 0.485737i | \(0.161449\pi\) | ||||
−0.874105 | + | 0.485737i | \(0.838551\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.55145i | 0.114687i | ||||||||
\(184\) | 7.14707 | − | 4.12636i | 0.526889 | − | 0.304200i | ||||
\(185\) | −0.336003 | − | 0.193991i | −0.0247034 | − | 0.0142625i | ||||
\(186\) | 8.17082 | + | 4.71742i | 0.599113 | + | 0.345898i | ||||
\(187\) | −5.94971 | − | 8.79635i | −0.435086 | − | 0.643253i | ||||
\(188\) | 4.70267i | 0.342977i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.60139 | 0.696558 | ||||||||
\(191\) | −3.00000 | − | 5.19615i | −0.217072 | − | 0.375980i | 0.736839 | − | 0.676068i | \(-0.236317\pi\) |
−0.953912 | + | 0.300088i | \(0.902984\pi\) | |||||||
\(192\) | −0.889740 | − | 0.513691i | −0.0642114 | − | 0.0370725i | ||||
\(193\) | 8.12582 | + | 4.69144i | 0.584909 | + | 0.337698i | 0.763082 | − | 0.646302i | \(-0.223685\pi\) |
−0.178173 | + | 0.983999i | \(0.557019\pi\) | |||||||
\(194\) | 5.33739 | + | 9.24463i | 0.383202 | + | 0.663726i | ||||
\(195\) | −5.28042 | −0.378139 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.3471i | 1.23593i | 0.786205 | + | 0.617966i | \(0.212043\pi\) | ||||
−0.786205 | + | 0.617966i | \(0.787957\pi\) | |||||||
\(198\) | −5.34192 | + | 3.61319i | −0.379634 | + | 0.256778i | ||||
\(199\) | −2.53353 | − | 1.46273i | −0.179597 | − | 0.103690i | 0.407506 | − | 0.913202i | \(-0.366398\pi\) |
−0.587103 | + | 0.809512i | \(0.699732\pi\) | |||||||
\(200\) | 2.95810 | + | 1.70786i | 0.209169 | + | 0.120764i | ||||
\(201\) | −3.00810 | + | 1.73673i | −0.212175 | + | 0.122499i | ||||
\(202\) | 10.0648i | 0.708160i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 3.28959i | − | 0.230317i | ||||||
\(205\) | −6.59782 | + | 3.80925i | −0.460812 | + | 0.266050i | ||||
\(206\) | −1.44261 | + | 2.49868i | −0.100512 | + | 0.174091i | ||||
\(207\) | 8.02365 | − | 13.8974i | 0.557682 | − | 0.965934i | ||||
\(208\) | −2.04169 | − | 3.53631i | −0.141566 | − | 0.245199i | ||||
\(209\) | −25.2357 | + | 1.79732i | −1.74559 | + | 0.124323i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.252729i | 0.0173986i | 0.999962 | + | 0.00869931i | \(0.00276911\pi\) | ||||
−0.999962 | + | 0.00869931i | \(0.997231\pi\) | |||||||
\(212\) | −2.39830 | − | 4.15397i | −0.164716 | − | 0.285296i | ||||
\(213\) | 3.12129 | + | 1.80208i | 0.213867 | + | 0.123476i | ||||
\(214\) | 8.15002 | − | 14.1162i | 0.557124 | − | 0.964967i | ||||
\(215\) | 4.76793 | + | 8.25830i | 0.325170 | + | 0.563212i | ||||
\(216\) | −5.07988 | −0.345642 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −11.5034 | −0.779111 | ||||||||
\(219\) | −0.860250 | + | 0.496665i | −0.0581303 | + | 0.0335615i | ||||
\(220\) | 3.75444 | + | 1.82518i | 0.253124 | + | 0.123054i | ||||
\(221\) | 6.53732 | − | 11.3230i | 0.439748 | − | 0.761666i | ||||
\(222\) | 0.158343 | + | 0.274258i | 0.0106273 | + | 0.0184070i | ||||
\(223\) | − | 19.0370i | − | 1.27482i | −0.770527 | − | 0.637408i | \(-0.780007\pi\) | ||
0.770527 | − | 0.637408i | \(-0.219993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 6.64181 | 0.442788 | ||||||||
\(226\) | 0.484072 | − | 0.279479i | 0.0322000 | − | 0.0185907i | ||||
\(227\) | −9.20350 | + | 15.9409i | −0.610858 | + | 1.05804i | 0.380238 | + | 0.924888i | \(0.375842\pi\) |
−0.991096 | + | 0.133148i | \(0.957491\pi\) | |||||||
\(228\) | −6.78705 | − | 3.91851i | −0.449483 | − | 0.259509i | ||||
\(229\) | 4.59674 | − | 2.65393i | 0.303761 | − | 0.175377i | −0.340370 | − | 0.940292i | \(-0.610552\pi\) |
0.644131 | + | 0.764915i | \(0.277219\pi\) | |||||||
\(230\) | −10.3876 | −0.684936 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.54386 | −0.232666 | ||||||||
\(233\) | 18.4629 | − | 10.6596i | 1.20955 | − | 0.698332i | 0.246887 | − | 0.969044i | \(-0.420592\pi\) |
0.962660 | + | 0.270712i | \(0.0872591\pi\) | |||||||
\(234\) | −6.87631 | − | 3.97004i | −0.449518 | − | 0.259530i | ||||
\(235\) | 2.95958 | − | 5.12614i | 0.193062 | − | 0.334393i | ||||
\(236\) | −2.36710 | + | 1.36664i | −0.154085 | + | 0.0889609i | ||||
\(237\) | −16.0405 | −1.04194 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.25163i | 0.469069i | 0.972108 | + | 0.234535i | \(0.0753566\pi\) | ||||
−0.972108 | + | 0.234535i | \(0.924643\pi\) | |||||||
\(240\) | 0.646574 | + | 1.11990i | 0.0417362 | + | 0.0722892i | ||||
\(241\) | 1.77705 | − | 3.07794i | 0.114470 | − | 0.198267i | −0.803098 | − | 0.595847i | \(-0.796816\pi\) |
0.917568 | + | 0.397580i | \(0.130150\pi\) | |||||||
\(242\) | −10.2096 | − | 4.09439i | −0.656298 | − | 0.263197i | ||||
\(243\) | −13.7446 | + | 7.93547i | −0.881719 | + | 0.509060i | ||||
\(244\) | 1.51010 | 0.0966743 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 6.21850 | 0.396477 | ||||||||
\(247\) | −15.5743 | − | 26.9755i | −0.990968 | − | 1.71641i | ||||
\(248\) | 4.59169 | − | 7.95304i | 0.291573 | − | 0.505019i | ||||
\(249\) | 1.18334 | + | 0.683199i | 0.0749908 | + | 0.0432960i | ||||
\(250\) | −5.29636 | − | 9.17356i | −0.334971 | − | 0.580187i | ||||
\(251\) | − | 0.735728i | − | 0.0464387i | −0.999730 | − | 0.0232194i | \(-0.992608\pi\) | ||
0.999730 | − | 0.0232194i | \(-0.00739162\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.3021 | − | 1.94448i | 1.71647 | − | 0.122249i | ||||
\(254\) | 5.64146 | + | 9.77130i | 0.353977 | + | 0.613106i | ||||
\(255\) | −2.07028 | + | 3.58582i | −0.129646 | + | 0.224553i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.0352 | − | 8.10325i | 0.875494 | − | 0.505467i | 0.00632378 | − | 0.999980i | \(-0.497987\pi\) |
0.869170 | + | 0.494513i | \(0.164654\pi\) | |||||||
\(258\) | − | 7.78352i | − | 0.484581i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 5.13968i | 0.318750i | ||||||||
\(261\) | −5.96777 | + | 3.44549i | −0.369396 | + | 0.213271i | ||||
\(262\) | 6.09152 | + | 3.51694i | 0.376335 | + | 0.217277i | ||||
\(263\) | −21.0462 | − | 12.1510i | −1.29776 | − | 0.749264i | −0.317746 | − | 0.948176i | \(-0.602926\pi\) |
−0.980017 | + | 0.198911i | \(0.936259\pi\) | |||||||
\(264\) | −1.90905 | − | 2.82244i | −0.117494 | − | 0.173709i | ||||
\(265\) | 6.03738i | 0.370874i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.9414 | −0.669601 | ||||||||
\(268\) | 1.69044 | + | 2.92792i | 0.103260 | + | 0.178851i | ||||
\(269\) | 23.4246 | + | 13.5242i | 1.42822 | + | 0.824586i | 0.996981 | − | 0.0776498i | \(-0.0247416\pi\) |
0.431244 | + | 0.902236i | \(0.358075\pi\) | |||||||
\(270\) | 5.53733 | + | 3.19698i | 0.336991 | + | 0.194562i | ||||
\(271\) | 5.22166 | + | 9.04417i | 0.317193 | + | 0.549394i | 0.979901 | − | 0.199483i | \(-0.0639264\pi\) |
−0.662708 | + | 0.748878i | \(0.730593\pi\) | |||||||
\(272\) | −3.20191 | −0.194145 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.08974i | 0.549131i | ||||||||
\(275\) | 6.34700 | + | 9.38372i | 0.382738 | + | 0.565859i | ||||
\(276\) | 7.34278 | + | 4.23936i | 0.441983 | + | 0.255179i | ||||
\(277\) | 17.6675 | + | 10.2003i | 1.06153 | + | 0.612877i | 0.925856 | − | 0.377876i | \(-0.123345\pi\) |
0.135678 | + | 0.990753i | \(0.456679\pi\) | |||||||
\(278\) | −6.81169 | + | 3.93273i | −0.408538 | + | 0.235869i | ||||
\(279\) | − | 17.8569i | − | 1.06907i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.99535i | 0.596272i | 0.954523 | + | 0.298136i | \(0.0963650\pi\) | ||||
−0.954523 | + | 0.298136i | \(0.903635\pi\) | |||||||
\(282\) | −4.18415 | + | 2.41572i | −0.249162 | + | 0.143854i | ||||
\(283\) | 1.74448 | − | 3.02153i | 0.103699 | − | 0.179611i | −0.809507 | − | 0.587110i | \(-0.800266\pi\) |
0.913206 | + | 0.407499i | \(0.133599\pi\) | |||||||
\(284\) | 1.75405 | − | 3.03810i | 0.104084 | − | 0.180278i | ||||
\(285\) | 4.93215 | + | 8.54274i | 0.292156 | + | 0.506028i | ||||
\(286\) | −0.962115 | − | 13.5088i | −0.0568911 | − | 0.798794i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.94448i | 0.114580i | ||||||||
\(289\) | 3.37387 | + | 5.84372i | 0.198463 | + | 0.343748i | ||||
\(290\) | 3.86299 | + | 2.23030i | 0.226843 | + | 0.130968i | ||||
\(291\) | −5.48354 | + | 9.49778i | −0.321451 | + | 0.556770i | ||||
\(292\) | 0.483428 | + | 0.837321i | 0.0282905 | + | 0.0490005i | ||||
\(293\) | 17.3549 | 1.01388 | 0.506942 | − | 0.861980i | \(-0.330776\pi\) | ||||
0.506942 | + | 0.861980i | \(0.330776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44034 | 0.200304 | ||||||||
\(296\) | 0.266948 | − | 0.154122i | 0.0155160 | − | 0.00895819i | ||||
\(297\) | −15.1524 | − | 7.36619i | −0.879233 | − | 0.427430i | ||||
\(298\) | 3.11548 | − | 5.39617i | 0.180475 | − | 0.312592i | ||||
\(299\) | 16.8495 | + | 29.1842i | 0.974433 | + | 1.68777i | ||||
\(300\) | 3.50925i | 0.202607i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −17.5101 | −1.00759 | ||||||||
\(303\) | −8.95510 | + | 5.17023i | −0.514457 | + | 0.297022i | ||||
\(304\) | −3.81407 | + | 6.60616i | −0.218752 | + | 0.378889i | ||||
\(305\) | −1.64609 | − | 0.950368i | −0.0942546 | − | 0.0544179i | ||||
\(306\) | −5.39194 | + | 3.11304i | −0.308237 | + | 0.177960i | ||||
\(307\) | −22.6829 | −1.29458 | −0.647290 | − | 0.762244i | \(-0.724098\pi\) | ||||
−0.647290 | + | 0.762244i | \(0.724098\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.96423 | −0.168629 | ||||||||
\(310\) | −10.0104 | + | 5.77948i | −0.568550 | + | 0.328252i | ||||
\(311\) | −5.75141 | − | 3.32058i | −0.326133 | − | 0.188293i | 0.327990 | − | 0.944681i | \(-0.393629\pi\) |
−0.654123 | + | 0.756388i | \(0.726962\pi\) | |||||||
\(312\) | 2.09760 | − | 3.63315i | 0.118753 | − | 0.205687i | ||||
\(313\) | 0.435583 | − | 0.251484i | 0.0246206 | − | 0.0142147i | −0.487639 | − | 0.873045i | \(-0.662142\pi\) |
0.512260 | + | 0.858831i | \(0.328809\pi\) | |||||||
\(314\) | 7.77404 | 0.438715 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.6129i | 0.878296i | ||||||||
\(317\) | 5.27437 | + | 9.13547i | 0.296238 | + | 0.513099i | 0.975272 | − | 0.221008i | \(-0.0709345\pi\) |
−0.679034 | + | 0.734107i | \(0.737601\pi\) | |||||||
\(318\) | 2.46397 | − | 4.26772i | 0.138172 | − | 0.239322i | ||||
\(319\) | −10.5707 | − | 5.13886i | −0.591848 | − | 0.287721i | ||||
\(320\) | 1.09005 | − | 0.629341i | 0.0609357 | − | 0.0351812i | ||||
\(321\) | 16.7464 | 0.934692 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −24.4246 | −1.35902 | ||||||||
\(324\) | 0.307237 | + | 0.532150i | 0.0170687 | + | 0.0295639i | ||||
\(325\) | −6.97385 | + | 12.0791i | −0.386839 | + | 0.670025i | ||||
\(326\) | 15.7723 | + | 9.10616i | 0.873548 | + | 0.504343i | ||||
\(327\) | −5.90922 | − | 10.2351i | −0.326781 | − | 0.566001i | ||||
\(328\) | − | 6.05276i | − | 0.334208i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.304688 | + | 4.27805i | 0.0167725 | + | 0.235499i | ||||
\(331\) | 2.89029 | + | 5.00613i | 0.158865 | + | 0.275162i | 0.934460 | − | 0.356069i | \(-0.115883\pi\) |
−0.775595 | + | 0.631231i | \(0.782550\pi\) | |||||||
\(332\) | 0.664990 | − | 1.15180i | 0.0364960 | − | 0.0632130i | ||||
\(333\) | 0.299689 | − | 0.519076i | 0.0164228 | − | 0.0284452i | ||||
\(334\) | 12.4407 | − | 7.18264i | 0.680724 | − | 0.393016i | ||||
\(335\) | − | 4.25544i | − | 0.232500i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.1226i | 0.605885i | 0.953009 | + | 0.302943i | \(0.0979690\pi\) | ||||
−0.953009 | + | 0.302943i | \(0.902031\pi\) | |||||||
\(338\) | 3.18180 | − | 1.83701i | 0.173067 | − | 0.0999202i | ||||
\(339\) | 0.497327 | + | 0.287132i | 0.0270111 | + | 0.0155949i | ||||
\(340\) | 3.49025 | + | 2.01510i | 0.189285 | + | 0.109284i | ||||
\(341\) | 25.2287 | − | 17.0643i | 1.36621 | − | 0.924084i | ||||
\(342\) | 14.8328i | 0.802065i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −7.57607 | −0.408474 | ||||||||
\(345\) | −5.33600 | − | 9.24223i | −0.287281 | − | 0.497585i | ||||
\(346\) | 4.12505 | + | 2.38160i | 0.221764 | + | 0.128035i | ||||
\(347\) | −12.7058 | − | 7.33569i | −0.682083 | − | 0.393801i | 0.118557 | − | 0.992947i | \(-0.462173\pi\) |
−0.800639 | + | 0.599147i | \(0.795507\pi\) | |||||||
\(348\) | −1.82045 | − | 3.15311i | −0.0975864 | − | 0.169025i | ||||
\(349\) | −24.6769 | −1.32093 | −0.660463 | − | 0.750859i | \(-0.729640\pi\) | ||||
−0.660463 | + | 0.750859i | \(0.729640\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 20.7431i | − | 1.10718i | ||||||
\(352\) | −2.74722 | + | 1.85817i | −0.146427 | + | 0.0990409i | ||||
\(353\) | 16.6664 | + | 9.62237i | 0.887065 | + | 0.512147i | 0.872981 | − | 0.487754i | \(-0.162184\pi\) |
0.0140834 | + | 0.999901i | \(0.495517\pi\) | |||||||
\(354\) | −2.43191 | − | 1.40407i | −0.129255 | − | 0.0746252i | ||||
\(355\) | −3.82400 | + | 2.20779i | −0.202957 | + | 0.117177i | ||||
\(356\) | 10.6498i | 0.564436i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 3.89051i | − | 0.205620i | ||||||
\(359\) | 2.85275 | − | 1.64703i | 0.150562 | − | 0.0869271i | −0.422826 | − | 0.906211i | \(-0.638962\pi\) |
0.573388 | + | 0.819284i | \(0.305629\pi\) | |||||||
\(360\) | 1.22374 | − | 2.11959i | 0.0644970 | − | 0.111712i | ||||
\(361\) | −19.5942 | + | 33.9381i | −1.03127 | + | 1.78622i | ||||
\(362\) | 6.53492 | + | 11.3188i | 0.343468 | + | 0.594904i | ||||
\(363\) | −1.60165 | − | 11.1871i | −0.0840647 | − | 0.587173i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.21696i | − | 0.0636988i | ||||||
\(366\) | 0.775726 | + | 1.34360i | 0.0405478 | + | 0.0702309i | ||||
\(367\) | −26.7957 | − | 15.4705i | −1.39873 | − | 0.807555i | −0.404467 | − | 0.914553i | \(-0.632543\pi\) |
−0.994259 | + | 0.106998i | \(0.965876\pi\) | |||||||
\(368\) | 4.12636 | − | 7.14707i | 0.215102 | − | 0.372567i | ||||
\(369\) | −5.88475 | − | 10.1927i | −0.306348 | − | 0.530610i | ||||
\(370\) | −0.387982 | −0.0201702 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 9.43485 | 0.489174 | ||||||||
\(373\) | 0.832767 | − | 0.480798i | 0.0431191 | − | 0.0248948i | −0.478286 | − | 0.878204i | \(-0.658742\pi\) |
0.521405 | + | 0.853310i | \(0.325408\pi\) | |||||||
\(374\) | −9.55077 | − | 4.64301i | −0.493859 | − | 0.240084i | ||||
\(375\) | 5.44139 | − | 9.42476i | 0.280992 | − | 0.486692i | ||||
\(376\) | 2.35133 | + | 4.07263i | 0.121261 | + | 0.210030i | ||||
\(377\) | − | 14.4709i | − | 0.745292i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.41216 | −0.0725379 | −0.0362689 | − | 0.999342i | \(-0.511547\pi\) | ||||
−0.0362689 | + | 0.999342i | \(0.511547\pi\) | |||||||
\(380\) | 8.31505 | − | 4.80070i | 0.426553 | − | 0.246271i | ||||
\(381\) | −5.79594 | + | 10.0389i | −0.296935 | + | 0.514307i | ||||
\(382\) | −5.19615 | − | 3.00000i | −0.265858 | − | 0.153493i | ||||
\(383\) | −3.27426 | + | 1.89039i | −0.167307 | + | 0.0965946i | −0.581315 | − | 0.813678i | \(-0.697462\pi\) |
0.414009 | + | 0.910273i | \(0.364128\pi\) | |||||||
\(384\) | −1.02738 | −0.0524284 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.38289 | 0.477576 | ||||||||
\(387\) | −12.7579 | + | 7.36578i | −0.648520 | + | 0.374423i | ||||
\(388\) | 9.24463 | + | 5.33739i | 0.469325 | + | 0.270965i | ||||
\(389\) | 1.68943 | − | 2.92618i | 0.0856574 | − | 0.148363i | −0.820014 | − | 0.572344i | \(-0.806034\pi\) |
0.905671 | + | 0.423981i | \(0.139368\pi\) | |||||||
\(390\) | −4.57298 | + | 2.64021i | −0.231562 | + | 0.133692i | ||||
\(391\) | 26.4245 | 1.33635 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.22649i | 0.364528i | ||||||||
\(394\) | 8.67356 | + | 15.0230i | 0.436968 | + | 0.756850i | ||||
\(395\) | 9.82586 | − | 17.0189i | 0.494393 | − | 0.856313i | ||||
\(396\) | −2.81964 | + | 5.80007i | −0.141692 | + | 0.291465i | ||||
\(397\) | 9.98525 | − | 5.76499i | 0.501145 | − | 0.289336i | −0.228041 | − | 0.973652i | \(-0.573232\pi\) |
0.729186 | + | 0.684315i | \(0.239899\pi\) | |||||||
\(398\) | −2.92547 | −0.146640 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.41572 | 0.170786 | ||||||||
\(401\) | −13.0261 | − | 22.5619i | −0.650494 | − | 1.12669i | −0.983003 | − | 0.183588i | \(-0.941229\pi\) |
0.332509 | − | 0.943100i | \(-0.392105\pi\) | |||||||
\(402\) | −1.73673 | + | 3.00810i | −0.0866200 | + | 0.150030i | ||||
\(403\) | 32.4753 | + | 18.7496i | 1.61771 | + | 0.933986i | ||||
\(404\) | 5.03242 | + | 8.71642i | 0.250372 | + | 0.433658i | ||||
\(405\) | − | 0.773427i | − | 0.0384319i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.01975 | − | 0.0726278i | 0.0505471 | − | 0.00360003i | ||||
\(408\) | −1.64480 | − | 2.84887i | −0.0814295 | − | 0.141040i | ||||
\(409\) | −17.5109 | + | 30.3297i | −0.865856 | + | 1.49971i | 0.000338063 | 1.00000i | \(0.499892\pi\) | |
−0.866194 | + | 0.499707i | \(0.833441\pi\) | |||||||
\(410\) | −3.80925 | + | 6.59782i | −0.188126 | + | 0.325843i | ||||
\(411\) | −8.08750 | + | 4.66932i | −0.398927 | + | 0.230321i | ||||
\(412\) | 2.88523i | 0.142145i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 16.0473i | − | 0.788682i | ||||||
\(415\) | −1.44974 | + | 0.837011i | −0.0711652 | + | 0.0410872i | ||||
\(416\) | −3.53631 | − | 2.04169i | −0.173382 | − | 0.100102i | ||||
\(417\) | −6.99821 | − | 4.04042i | −0.342704 | − | 0.197860i | ||||
\(418\) | −20.9561 | + | 14.1744i | −1.02500 | + | 0.693292i | ||||
\(419\) | 12.1242i | 0.592307i | 0.955140 | + | 0.296154i | \(0.0957040\pi\) | ||||
−0.955140 | + | 0.296154i | \(0.904296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.6940 | 0.911089 | 0.455545 | − | 0.890213i | \(-0.349445\pi\) | ||||
0.455545 | + | 0.890213i | \(0.349445\pi\) | |||||||
\(422\) | 0.126365 | + | 0.218870i | 0.00615134 | + | 0.0106544i | ||||
\(423\) | 7.91916 | + | 4.57213i | 0.385043 | + | 0.222305i | ||||
\(424\) | −4.15397 | − | 2.39830i | −0.201735 | − | 0.116472i | ||||
\(425\) | 5.46842 | + | 9.47158i | 0.265257 | + | 0.459439i | ||||
\(426\) | 3.60416 | 0.174622 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 16.3000i | − | 0.787892i | ||||||
\(429\) | 11.5251 | − | 7.79540i | 0.556438 | − | 0.376366i | ||||
\(430\) | 8.25830 | + | 4.76793i | 0.398251 | + | 0.229930i | ||||
\(431\) | 29.3945 | + | 16.9709i | 1.41588 | + | 0.817461i | 0.995934 | − | 0.0900869i | \(-0.0287145\pi\) |
0.419949 | + | 0.907548i | \(0.362048\pi\) | |||||||
\(432\) | −4.39930 | + | 2.53994i | −0.211662 | + | 0.122203i | ||||
\(433\) | 27.0949i | 1.30210i | 0.759037 | + | 0.651048i | \(0.225670\pi\) | ||||
−0.759037 | + | 0.651048i | \(0.774330\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.58274i | 0.219726i | ||||||||
\(436\) | −9.96227 | + | 5.75172i | −0.477106 | + | 0.275458i | ||||
\(437\) | 31.4765 | − | 54.5188i | 1.50572 | − | 2.60799i | ||||
\(438\) | −0.496665 | + | 0.860250i | −0.0237316 | + | 0.0411043i | ||||
\(439\) | −10.2269 | − | 17.7135i | −0.488104 | − | 0.845421i | 0.511802 | − | 0.859103i | \(-0.328978\pi\) |
−0.999906 | + | 0.0136821i | \(0.995645\pi\) | |||||||
\(440\) | 4.16403 | − | 0.296567i | 0.198512 | − | 0.0141383i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 13.0746i | − | 0.621897i | ||||||
\(443\) | 1.79868 | + | 3.11541i | 0.0854579 | + | 0.148017i | 0.905586 | − | 0.424162i | \(-0.139431\pi\) |
−0.820128 | + | 0.572180i | \(0.806098\pi\) | |||||||
\(444\) | 0.274258 | + | 0.158343i | 0.0130157 | + | 0.00751462i | ||||
\(445\) | 6.70233 | − | 11.6088i | 0.317721 | − | 0.550309i | ||||
\(446\) | −9.51852 | − | 16.4866i | −0.450715 | − | 0.780662i | ||||
\(447\) | 6.40159 | 0.302785 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.0664 | 1.74927 | 0.874637 | − | 0.484779i | \(-0.161100\pi\) | ||||
0.874637 | + | 0.484779i | \(0.161100\pi\) | |||||||
\(450\) | 5.75198 | − | 3.32091i | 0.271151 | − | 0.156549i | ||||
\(451\) | 8.77694 | − | 18.0544i | 0.413290 | − | 0.850148i | ||||
\(452\) | 0.279479 | − | 0.484072i | 0.0131456 | − | 0.0227688i | ||||
\(453\) | −8.99479 | − | 15.5794i | −0.422612 | − | 0.731986i | ||||
\(454\) | 18.4070i | 0.863883i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.83701 | −0.367002 | ||||||||
\(457\) | 15.7194 | − | 9.07561i | 0.735323 | − | 0.424539i | −0.0850431 | − | 0.996377i | \(-0.527103\pi\) |
0.820366 | + | 0.571838i | \(0.193769\pi\) | |||||||
\(458\) | 2.65393 | − | 4.59674i | 0.124010 | − | 0.214792i | ||||
\(459\) | −14.0862 | − | 8.13267i | −0.657487 | − | 0.379600i | ||||
\(460\) | −8.99589 | + | 5.19378i | −0.419436 | + | 0.242161i | ||||
\(461\) | 22.4278 | 1.04457 | 0.522284 | − | 0.852772i | \(-0.325080\pi\) | ||||
0.522284 | + | 0.852772i | \(0.325080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.6274 | −0.726267 | −0.363134 | − | 0.931737i | \(-0.618293\pi\) | ||||
−0.363134 | + | 0.931737i | \(0.618293\pi\) | |||||||
\(464\) | −3.06907 | + | 1.77193i | −0.142478 | + | 0.0822598i | ||||
\(465\) | −10.2845 | − | 5.93774i | −0.476931 | − | 0.275356i | ||||
\(466\) | 10.6596 | − | 18.4629i | 0.493796 | − | 0.855279i | ||||
\(467\) | 5.27860 | − | 3.04760i | 0.244264 | − | 0.141026i | −0.372871 | − | 0.927883i | \(-0.621626\pi\) |
0.617135 | + | 0.786857i | \(0.288293\pi\) | |||||||
\(468\) | −7.94008 | −0.367030 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 5.91916i | − | 0.273031i | ||||||
\(471\) | 3.99346 | + | 6.91688i | 0.184009 | + | 0.318713i | ||||
\(472\) | −1.36664 | + | 2.36710i | −0.0629048 | + | 0.108954i | ||||
\(473\) | −22.5982 | − | 10.9858i | −1.03906 | − | 0.505130i | ||||
\(474\) | −13.8914 | + | 8.02023i | −0.638055 | + | 0.368381i | ||||
\(475\) | 26.0556 | 1.19551 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.32690 | −0.427049 | ||||||||
\(478\) | 3.62582 | + | 6.28010i | 0.165841 | + | 0.287245i | ||||
\(479\) | 15.3138 | − | 26.5242i | 0.699704 | − | 1.21192i | −0.268865 | − | 0.963178i | \(-0.586648\pi\) |
0.968569 | − | 0.248745i | \(-0.0800182\pi\) | |||||||
\(480\) | 1.11990 | + | 0.646574i | 0.0511162 | + | 0.0295119i | ||||
\(481\) | 0.629341 | + | 1.09005i | 0.0286955 | + | 0.0497020i | ||||
\(482\) | − | 3.55410i | − | 0.161885i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.8890 | + | 1.55896i | −0.494953 | + | 0.0708617i | ||||
\(485\) | −6.71808 | − | 11.6361i | −0.305052 | − | 0.528366i | ||||
\(486\) | −7.93547 | + | 13.7446i | −0.359960 | + | 0.623469i | ||||
\(487\) | 1.58726 | − | 2.74922i | 0.0719258 | − | 0.124579i | −0.827819 | − | 0.560995i | \(-0.810419\pi\) |
0.899745 | + | 0.436415i | \(0.143752\pi\) | |||||||
\(488\) | 1.30779 | − | 0.755050i | 0.0592007 | − | 0.0341795i | ||||
\(489\) | 18.7110i | 0.846141i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 32.6507i | − | 1.47351i | −0.676162 | − | 0.736753i | \(-0.736358\pi\) | ||
0.676162 | − | 0.736753i | \(-0.263642\pi\) | |||||||
\(492\) | 5.38538 | − | 3.10925i | 0.242792 | − | 0.140176i | ||||
\(493\) | −9.82691 | − | 5.67357i | −0.442582 | − | 0.255525i | ||||
\(494\) | −26.9755 | − | 15.5743i | −1.21368 | − | 0.700721i | ||||
\(495\) | 6.72378 | − | 4.54786i | 0.302211 | − | 0.204411i | ||||
\(496\) | − | 9.18338i | − | 0.412346i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 1.36640 | 0.0612297 | ||||||||
\(499\) | −14.2274 | − | 24.6426i | −0.636906 | − | 1.10315i | −0.986108 | − | 0.166106i | \(-0.946881\pi\) |
0.349202 | − | 0.937048i | \(-0.386453\pi\) | |||||||
\(500\) | −9.17356 | − | 5.29636i | −0.410254 | − | 0.236860i | ||||
\(501\) | 12.7814 | + | 7.37932i | 0.571029 | + | 0.329684i | ||||
\(502\) | −0.367864 | − | 0.637159i | −0.0164186 | − | 0.0284378i | ||||
\(503\) | −22.5058 | −1.00348 | −0.501741 | − | 0.865018i | \(-0.667307\pi\) | ||||
−0.501741 | + | 0.865018i | \(0.667307\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 12.6684i | − | 0.563739i | ||||||
\(506\) | 22.6720 | − | 15.3350i | 1.00789 | − | 0.681724i | ||||
\(507\) | 3.26892 | + | 1.88731i | 0.145178 | + | 0.0838185i | ||||
\(508\) | 9.77130 | + | 5.64146i | 0.433531 | + | 0.250299i | ||||
\(509\) | 11.6437 | − | 6.72249i | 0.516098 | − | 0.297969i | −0.219239 | − | 0.975671i | \(-0.570357\pi\) |
0.735337 | + | 0.677702i | \(0.237024\pi\) | |||||||
\(510\) | 4.14055i | 0.183347i | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −33.5585 | + | 19.3750i | −1.48164 | + | 0.855427i | ||||
\(514\) | 8.10325 | − | 14.0352i | 0.357419 | − | 0.619068i | ||||
\(515\) | 1.81579 | − | 3.14505i | 0.0800134 | − | 0.138587i | ||||
\(516\) | −3.89176 | − | 6.74073i | −0.171325 | − | 0.296744i | ||||
\(517\) | 1.10803 | + | 15.5576i | 0.0487310 | + | 0.684221i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.89362i | 0.214806i | ||||||||
\(520\) | 2.56984 | + | 4.45110i | 0.112695 | + | 0.195193i | ||||
\(521\) | −34.2339 | − | 19.7649i | −1.49981 | − | 0.865918i | −0.499813 | − | 0.866133i | \(-0.666598\pi\) |
−1.00000 | 0.000215610i | \(0.999931\pi\) | ||||||||
\(522\) | −3.44549 | + | 5.96777i | −0.150805 | + | 0.261202i | ||||
\(523\) | −14.8061 | − | 25.6449i | −0.647425 | − | 1.12137i | −0.983736 | − | 0.179622i | \(-0.942512\pi\) |
0.336310 | − | 0.941751i | \(-0.390821\pi\) | |||||||
\(524\) | 7.03388 | 0.307276 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.3021 | −1.05962 | ||||||||
\(527\) | 25.4650 | − | 14.7022i | 1.10927 | − | 0.640438i | ||||
\(528\) | −3.06451 | − | 1.48978i | −0.133366 | − | 0.0648343i | ||||
\(529\) | −22.5538 | + | 39.0643i | −0.980599 | + | 1.69845i | ||||
\(530\) | 3.01869 | + | 5.22853i | 0.131124 | + | 0.227113i | ||||
\(531\) | 5.31483i | 0.230644i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.7158 | 1.07056 | ||||||||
\(534\) | −9.47551 | + | 5.47069i | −0.410045 | + | 0.236740i | ||||
\(535\) | −10.2583 | + | 17.7679i | −0.443504 | + | 0.768172i | ||||
\(536\) | 2.92792 | + | 1.69044i | 0.126467 | + | 0.0730157i | ||||
\(537\) | 3.46154 | − | 1.99852i | 0.149377 | − | 0.0862426i | ||||
\(538\) | 27.0484 | 1.16614 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 6.39395 | 0.275152 | ||||||||
\(541\) | −15.1111 | + | 8.72442i | −0.649679 | + | 0.375092i | −0.788333 | − | 0.615249i | \(-0.789056\pi\) |
0.138654 | + | 0.990341i | \(0.455722\pi\) | |||||||
\(542\) | 9.04417 | + | 5.22166i | 0.388480 | + | 0.224289i | ||||
\(543\) | −6.71387 | + | 11.6288i | −0.288120 | + | 0.499038i | ||||
\(544\) | −2.77294 | + | 1.60096i | −0.118889 | + | 0.0686405i | ||||
\(545\) | 14.4792 | 0.620220 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 1.16878i | − | 0.0499734i | −0.999688 | − | 0.0249867i | \(-0.992046\pi\) | ||
0.999688 | − | 0.0249867i | \(-0.00795434\pi\) | |||||||
\(548\) | 4.54487 | + | 7.87195i | 0.194147 | + | 0.336273i | ||||
\(549\) | 1.46818 | − | 2.54297i | 0.0626605 | − | 0.108531i | ||||
\(550\) | 10.1885 | + | 4.95304i | 0.434440 | + | 0.211198i | ||||
\(551\) | −23.4113 | + | 13.5165i | −0.997355 | + | 0.575823i | ||||
\(552\) | 8.47871 | 0.360878 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 20.4006 | 0.866739 | ||||||||
\(555\) | −0.199303 | − | 0.345203i | −0.00845995 | − | 0.0146531i | ||||
\(556\) | −3.93273 | + | 6.81169i | −0.166785 | + | 0.288880i | ||||
\(557\) | −4.20151 | − | 2.42574i | −0.178024 | − | 0.102782i | 0.408340 | − | 0.912830i | \(-0.366108\pi\) |
−0.586364 | + | 0.810048i | \(0.699441\pi\) | |||||||
\(558\) | −8.92847 | − | 15.4646i | −0.377972 | − | 0.654667i | ||||
\(559\) | − | 30.9360i | − | 1.30845i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.775084 | − | 10.8828i | −0.0327241 | − | 0.459471i | ||||
\(562\) | 4.99767 | + | 8.65622i | 0.210814 | + | 0.365141i | ||||
\(563\) | −13.0572 | + | 22.6158i | −0.550297 | + | 0.953143i | 0.447956 | + | 0.894056i | \(0.352152\pi\) |
−0.998253 | + | 0.0590869i | \(0.981181\pi\) | |||||||
\(564\) | −2.41572 | + | 4.18415i | −0.101720 | + | 0.176184i | ||||
\(565\) | −0.609293 | + | 0.351776i | −0.0256332 | + | 0.0147993i | ||||
\(566\) | − | 3.48896i | − | 0.146652i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 3.50810i | − | 0.147196i | ||||||
\(569\) | 6.47913 | − | 3.74073i | 0.271619 | − | 0.156820i | −0.358004 | − | 0.933720i | \(-0.616543\pi\) |
0.629623 | + | 0.776901i | \(0.283209\pi\) | |||||||
\(570\) | 8.54274 | + | 4.93215i | 0.357816 | + | 0.206585i | ||||
\(571\) | 28.5249 | + | 16.4688i | 1.19373 | + | 0.689199i | 0.959150 | − | 0.282898i | \(-0.0912958\pi\) |
0.234578 | + | 0.972097i | \(0.424629\pi\) | |||||||
\(572\) | −7.58763 | − | 11.2179i | −0.317255 | − | 0.469045i | ||||
\(573\) | − | 6.16430i | − | 0.257517i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −28.1890 | −1.17556 | ||||||||
\(576\) | 0.972242 | + | 1.68397i | 0.0405101 | + | 0.0701655i | ||||
\(577\) | −1.34703 | − | 0.777711i | −0.0560778 | − | 0.0323765i | 0.471699 | − | 0.881760i | \(-0.343641\pi\) |
−0.527777 | + | 0.849383i | \(0.676974\pi\) | |||||||
\(578\) | 5.84372 | + | 3.37387i | 0.243067 | + | 0.140335i | ||||
\(579\) | 4.81991 | + | 8.34833i | 0.200309 | + | 0.346945i | ||||
\(580\) | 4.46060 | 0.185216 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.9671i | 0.454600i | ||||||||
\(583\) | −8.91290 | − | 13.1773i | −0.369134 | − | 0.545747i | ||||
\(584\) | 0.837321 | + | 0.483428i | 0.0346486 | + | 0.0200044i | ||||
\(585\) | 8.65509 | + | 4.99702i | 0.357844 | + | 0.206601i | ||||
\(586\) | 15.0298 | − | 8.67744i | 0.620874 | − | 0.358462i | ||||
\(587\) | − | 42.8124i | − | 1.76706i | −0.468376 | − | 0.883529i | \(-0.655161\pi\) | ||
0.468376 | − | 0.883529i | \(-0.344839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 70.0520i | − | 2.88644i | ||||||
\(590\) | 2.97942 | − | 1.72017i | 0.122661 | − | 0.0708183i | ||||
\(591\) | −8.91107 | + | 15.4344i | −0.366552 | + | 0.634887i | ||||
\(592\) | 0.154122 | − | 0.266948i | 0.00633439 | − | 0.0109715i | ||||
\(593\) | −16.7711 | − | 29.0484i | −0.688707 | − | 1.19288i | −0.972256 | − | 0.233918i | \(-0.924845\pi\) |
0.283549 | − | 0.958958i | \(-0.408488\pi\) | |||||||
\(594\) | −16.8055 | + | 1.19691i | −0.689537 | + | 0.0491097i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 6.23096i | − | 0.255230i | ||||||
\(597\) | −1.50279 | − | 2.60290i | −0.0615050 | − | 0.106530i | ||||
\(598\) | 29.1842 | + | 16.8495i | 1.19343 | + | 0.689029i | ||||
\(599\) | −7.00856 | + | 12.1392i | −0.286362 | + | 0.495993i | −0.972939 | − | 0.231064i | \(-0.925779\pi\) |
0.686577 | + | 0.727057i | \(0.259113\pi\) | |||||||
\(600\) | 1.75463 | + | 3.03910i | 0.0716323 | + | 0.124071i | ||||
\(601\) | 36.1513 | 1.47464 | 0.737322 | − | 0.675542i | \(-0.236090\pi\) | ||||
0.737322 | + | 0.675542i | \(0.236090\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.57405 | 0.267716 | ||||||||
\(604\) | −15.1642 | + | 8.75506i | −0.617023 | + | 0.356238i | ||||
\(605\) | 12.8506 | + | 5.15353i | 0.522453 | + | 0.209521i | ||||
\(606\) | −5.17023 | + | 8.95510i | −0.210026 | + | 0.363776i | ||||
\(607\) | −14.8196 | − | 25.6684i | −0.601511 | − | 1.04185i | −0.992593 | − | 0.121491i | \(-0.961232\pi\) |
0.391082 | − | 0.920356i | \(-0.372101\pi\) | |||||||
\(608\) | 7.62813i | 0.309362i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.90074 | −0.0769586 | ||||||||
\(611\) | −16.6301 | + | 9.60139i | −0.672782 | + | 0.388431i | ||||
\(612\) | −3.11304 | + | 5.39194i | −0.125837 | + | 0.217956i | ||||
\(613\) | −28.9964 | − | 16.7411i | −1.17115 | − | 0.676166i | −0.217202 | − | 0.976127i | \(-0.569693\pi\) |
−0.953951 | + | 0.299961i | \(0.903026\pi\) | |||||||
\(614\) | −19.6439 | + | 11.3414i | −0.792765 | + | 0.457703i | ||||
\(615\) | −7.82712 | −0.315620 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.79395 | 0.354031 | 0.177016 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177016 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(618\) | −2.56710 | + | 1.48212i | −0.103264 | + | 0.0596195i | ||||
\(619\) | −24.2445 | − | 13.9976i | −0.974469 | − | 0.562610i | −0.0738736 | − | 0.997268i | \(-0.523536\pi\) |
−0.900596 | + | 0.434657i | \(0.856869\pi\) | |||||||
\(620\) | −5.77948 | + | 10.0104i | −0.232109 | + | 0.402025i | ||||
\(621\) | 36.3063 | − | 20.9614i | 1.45692 | − | 0.841153i | ||||
\(622\) | −6.64116 | −0.266286 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 4.19520i | − | 0.167942i | ||||||
\(625\) | −1.87286 | − | 3.24390i | −0.0749146 | − | 0.129756i | ||||
\(626\) | 0.251484 | − | 0.435583i | 0.0100513 | − | 0.0174094i | ||||
\(627\) | −23.3765 | − | 11.3642i | −0.933567 | − | 0.453844i | ||||
\(628\) | 6.73252 | − | 3.88702i | 0.268657 | − | 0.155109i | ||||
\(629\) | 0.986974 | 0.0393532 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.154087 | −0.00613412 | −0.00306706 | − | 0.999995i | \(-0.500976\pi\) | ||||
−0.00306706 | + | 0.999995i | \(0.500976\pi\) | |||||||
\(632\) | 7.80647 | + | 13.5212i | 0.310525 | + | 0.537844i | ||||
\(633\) | −0.129825 | + | 0.224863i | −0.00516008 | + | 0.00893752i | ||||
\(634\) | 9.13547 | + | 5.27437i | 0.362816 | + | 0.209472i | ||||
\(635\) | −7.10081 | − | 12.2990i | −0.281787 | − | 0.488069i | ||||
\(636\) | − | 4.92794i | − | 0.195405i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −11.7240 | + | 0.834995i | −0.464156 | + | 0.0330578i | ||||
\(639\) | −3.41072 | − | 5.90754i | −0.134926 | − | 0.233699i | ||||
\(640\) | 0.629341 | − | 1.09005i | 0.0248769 | − | 0.0430880i | ||||
\(641\) | 9.92017 | − | 17.1822i | 0.391823 | − | 0.678658i | −0.600867 | − | 0.799349i | \(-0.705178\pi\) |
0.992690 | + | 0.120691i | \(0.0385112\pi\) | |||||||
\(642\) | 14.5028 | − | 8.37319i | 0.572379 | − | 0.330463i | ||||
\(643\) | 25.2948i | 0.997529i | 0.866737 | + | 0.498765i | \(0.166213\pi\) | ||||
−0.866737 | + | 0.498765i | \(0.833787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.79699i | 0.385756i | ||||||||
\(646\) | −21.1523 | + | 12.2123i | −0.832228 | + | 0.480487i | ||||
\(647\) | −0.813596 | − | 0.469730i | −0.0319857 | − | 0.0184670i | 0.483922 | − | 0.875111i | \(-0.339212\pi\) |
−0.515908 | + | 0.856644i | \(0.672545\pi\) | |||||||
\(648\) | 0.532150 | + | 0.307237i | 0.0209048 | + | 0.0120694i | ||||
\(649\) | −7.50893 | + | 5.07892i | −0.294751 | + | 0.199365i | ||||
\(650\) | 13.9477i | 0.547073i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 18.2123 | 0.713249 | ||||||||
\(653\) | 5.50375 | + | 9.53278i | 0.215379 | + | 0.373047i | 0.953390 | − | 0.301742i | \(-0.0975681\pi\) |
−0.738011 | + | 0.674789i | \(0.764235\pi\) | |||||||
\(654\) | −10.2351 | − | 5.90922i | −0.400223 | − | 0.231069i | ||||
\(655\) | −7.66729 | − | 4.42671i | −0.299586 | − | 0.172966i | ||||
\(656\) | −3.02638 | − | 5.24185i | −0.118160 | − | 0.204660i | ||||
\(657\) | 1.88004 | 0.0733472 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 29.9068i | 1.16500i | 0.812830 | + | 0.582501i | \(0.197926\pi\) | ||||
−0.812830 | + | 0.582501i | \(0.802074\pi\) | |||||||
\(660\) | 2.40289 | + | 3.55256i | 0.0935325 | + | 0.138283i | ||||
\(661\) | −2.32896 | − | 1.34463i | −0.0905861 | − | 0.0522999i | 0.454023 | − | 0.890990i | \(-0.349989\pi\) |
−0.544609 | + | 0.838690i | \(0.683322\pi\) | |||||||
\(662\) | 5.00613 | + | 2.89029i | 0.194569 | + | 0.112334i | ||||
\(663\) | 11.6330 | − | 6.71633i | 0.451789 | − | 0.260841i | ||||
\(664\) | − | 1.32998i | − | 0.0516132i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − | 0.599378i | − | 0.0232254i | ||||||
\(667\) | 25.3282 | − | 14.6233i | 0.980713 | − | 0.566215i | ||||
\(668\) | 7.18264 | − | 12.4407i | 0.277905 | − | 0.481345i | ||||
\(669\) | 9.77917 | − | 16.9380i | 0.378084 | − | 0.654862i | ||||
\(670\) | −2.12772 | − | 3.68532i | −0.0822011 | − | 0.142376i | ||||
\(671\) | 4.99578 | − | 0.355806i | 0.192860 | − | 0.0137357i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.56361i | − | 0.137367i | −0.997638 | − | 0.0686836i | \(-0.978120\pi\) | ||
0.997638 | − | 0.0686836i | \(-0.0218799\pi\) | |||||||
\(674\) | 5.56129 | + | 9.63243i | 0.214213 | + | 0.371027i | ||||
\(675\) | 15.0268 | + | 8.67572i | 0.578381 | + | 0.333929i | ||||
\(676\) | 1.83701 | − | 3.18180i | 0.0706543 | − | 0.122377i | ||||
\(677\) | 15.5901 | + | 27.0029i | 0.599178 | + | 1.03781i | 0.992943 | + | 0.118595i | \(0.0378390\pi\) |
−0.393765 | + | 0.919211i | \(0.628828\pi\) | |||||||
\(678\) | 0.574264 | 0.0220545 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.03019 | 0.154551 | ||||||||
\(681\) | −16.3774 | + | 9.45552i | −0.627585 | + | 0.362336i | ||||
\(682\) | 13.3166 | − | 27.3925i | 0.509918 | − | 1.04891i | ||||
\(683\) | 7.79993 | − | 13.5099i | 0.298456 | − | 0.516941i | −0.677327 | − | 0.735682i | \(-0.736862\pi\) |
0.975783 | + | 0.218741i | \(0.0701951\pi\) | |||||||
\(684\) | 7.41639 | + | 12.8456i | 0.283573 | + | 0.491163i | ||||
\(685\) | − | 11.4411i | − | 0.437142i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.45320 | 0.208053 | ||||||||
\(688\) | −6.56107 | + | 3.78804i | −0.250138 | + | 0.144417i | ||||
\(689\) | 9.79316 | − | 16.9623i | 0.373090 | − | 0.646210i | ||||
\(690\) | −9.24223 | − | 5.33600i | −0.351846 | − | 0.203138i | ||||
\(691\) | 31.8902 | − | 18.4118i | 1.21316 | − | 0.700419i | 0.249714 | − | 0.968320i | \(-0.419663\pi\) |
0.963447 | + | 0.267901i | \(0.0863299\pi\) | |||||||
\(692\) | 4.76319 | 0.181069 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6714 | −0.556918 | ||||||||
\(695\) | 8.57375 | − | 4.95006i | 0.325221 | − | 0.187766i | ||||
\(696\) | −3.15311 | − | 1.82045i | −0.119518 | − | 0.0690040i | ||||
\(697\) | 9.69021 | − | 16.7839i | 0.367043 | − | 0.635737i | ||||
\(698\) | −21.3708 | + | 12.3385i | −0.808899 | + | 0.467018i | ||||
\(699\) | 21.9029 | 0.828445 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 15.6940i | − | 0.592754i | −0.955071 | − | 0.296377i | \(-0.904222\pi\) | ||
0.955071 | − | 0.296377i | \(-0.0957784\pi\) | |||||||
\(702\) | −10.3715 | − | 17.9640i | −0.391449 | − | 0.678009i | ||||
\(703\) | 1.17567 | − | 2.03631i | 0.0443411 | − | 0.0768010i | ||||
\(704\) | −1.45007 | + | 2.98283i | −0.0546516 | + | 0.112420i | ||||
\(705\) | 5.26651 | − | 3.04062i | 0.198348 | − | 0.114516i | ||||
\(706\) | 19.2447 | 0.724285 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.80813 | −0.105536 | ||||||||
\(709\) | 12.1733 | + | 21.0847i | 0.457176 | + | 0.791852i | 0.998810 | − | 0.0487621i | \(-0.0155276\pi\) |
−0.541634 | + | 0.840614i | \(0.682194\pi\) | |||||||
\(710\) | −2.20779 | + | 3.82400i | −0.0828569 | + | 0.143512i | ||||
\(711\) | 26.2918 | + | 15.1796i | 0.986018 | + | 0.569278i | ||||
\(712\) | 5.32488 | + | 9.22296i | 0.199558 | + | 0.345645i | ||||
\(713\) | 75.7880i | 2.83828i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.21100 | + | 17.0033i | 0.0452887 | + | 0.635888i | ||||
\(716\) | −1.94526 | − | 3.36928i | −0.0726976 | − | 0.125916i | ||||
\(717\) | −3.72510 | + | 6.45207i | −0.139116 | + | 0.240957i | ||||
\(718\) | 1.64703 | − | 2.85275i | 0.0614668 | − | 0.106464i | ||||
\(719\) | −36.9070 | + | 21.3083i | −1.37640 | + | 0.794665i | −0.991724 | − | 0.128386i | \(-0.959020\pi\) |
−0.384676 | + | 0.923051i | \(0.625687\pi\) | |||||||
\(720\) | − | 2.44749i | − | 0.0912125i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 39.1884i | 1.45844i | ||||||||
\(723\) | 3.16222 | − | 1.82571i | 0.117604 | − | 0.0678988i | ||||
\(724\) | 11.3188 | + | 6.53492i | 0.420661 | + | 0.242868i | ||||
\(725\) | 10.4831 | + | 6.05242i | 0.389332 | + | 0.224781i | ||||
\(726\) | −6.98064 | − | 8.88752i | −0.259076 | − | 0.329847i | ||||
\(727\) | − | 23.2698i | − | 0.863031i | −0.902106 | − | 0.431515i | \(-0.857979\pi\) | ||
0.902106 | − | 0.431515i | \(-0.142021\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.4621 | −0.535633 | ||||||||
\(730\) | −0.608482 | − | 1.05392i | −0.0225209 | − | 0.0390074i | ||||
\(731\) | −21.0080 | − | 12.1290i | −0.777008 | − | 0.448606i | ||||
\(732\) | 1.34360 | + | 0.775726i | 0.0496607 | + | 0.0286716i | ||||
\(733\) | 18.8378 | + | 32.6281i | 0.695791 | + | 1.20515i | 0.969913 | + | 0.243450i | \(0.0782793\pi\) |
−0.274122 | + | 0.961695i | \(0.588387\pi\) | |||||||
\(734\) | −30.9410 | −1.14205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 8.25273i | − | 0.304200i | ||||||
\(737\) | 6.28225 | + | 9.28799i | 0.231410 | + | 0.342127i | ||||
\(738\) | −10.1927 | − | 5.88475i | −0.375198 | − | 0.216621i | ||||
\(739\) | 0.479784 | + | 0.277003i | 0.0176491 | + | 0.0101897i | 0.508799 | − | 0.860886i | \(-0.330090\pi\) |
−0.491149 | + | 0.871075i | \(0.663423\pi\) | |||||||
\(740\) | −0.336003 | + | 0.193991i | −0.0123517 | + | 0.00713126i | ||||
\(741\) | − | 32.0015i | − | 1.17561i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20.1974i | − | 0.740972i | −0.928838 | − | 0.370486i | \(-0.879191\pi\) | ||
0.928838 | − | 0.370486i | \(-0.120809\pi\) | |||||||
\(744\) | 8.17082 | − | 4.71742i | 0.299557 | − | 0.172949i | ||||
\(745\) | −3.92140 | + | 6.79207i | −0.143669 | + | 0.248842i | ||||
\(746\) | 0.480798 | − | 0.832767i | 0.0176033 | − | 0.0304898i | ||||
\(747\) | −1.29306 | − | 2.23965i | −0.0473107 | − | 0.0819445i | ||||
\(748\) | −10.5927 | + | 0.754426i | −0.387308 | + | 0.0275845i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 10.8828i | − | 0.397383i | ||||||
\(751\) | −3.70031 | − | 6.40913i | −0.135026 | − | 0.233872i | 0.790581 | − | 0.612357i | \(-0.209779\pi\) |
−0.925607 | + | 0.378485i | \(0.876445\pi\) | |||||||
\(752\) | 4.07263 | + | 2.35133i | 0.148513 | + | 0.0857443i | ||||
\(753\) | 0.377937 | − | 0.654606i | 0.0137728 | − | 0.0238552i | ||||
\(754\) | −7.23547 | − | 12.5322i | −0.263500 | − | 0.456396i | ||||
\(755\) | 22.0397 | 0.802106 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.1994 | −1.06127 | −0.530636 | − | 0.847600i | \(-0.678047\pi\) | ||||
−0.530636 | + | 0.847600i | \(0.678047\pi\) | |||||||
\(758\) | −1.22297 | + | 0.706081i | −0.0444202 | + | 0.0256460i | ||||
\(759\) | 25.2906 | + | 12.2947i | 0.917990 | + | 0.446271i | ||||
\(760\) | 4.80070 | − | 8.31505i | 0.174140 | − | 0.301619i | ||||
\(761\) | 25.4831 | + | 44.1380i | 0.923761 | + | 1.60000i | 0.793541 | + | 0.608517i | \(0.208235\pi\) |
0.130220 | + | 0.991485i | \(0.458432\pi\) | |||||||
\(762\) | 11.5919i | 0.419930i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −6.00000 | −0.217072 | ||||||||
\(765\) | 6.78674 | − | 3.91832i | 0.245375 | − | 0.141667i | ||||
\(766\) | −1.89039 | + | 3.27426i | −0.0683027 | + | 0.118304i | ||||
\(767\) | −9.66576 | − | 5.58053i | −0.349010 | − | 0.201501i | ||||
\(768\) | −0.889740 | + | 0.513691i | −0.0321057 | + | 0.0185362i | ||||
\(769\) | −32.9963 | −1.18988 | −0.594938 | − | 0.803771i | \(-0.702824\pi\) | ||||
−0.594938 | + | 0.803771i | \(0.702824\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.6503 | 0.599645 | ||||||||
\(772\) | 8.12582 | − | 4.69144i | 0.292455 | − | 0.168849i | ||||
\(773\) | 28.1797 | + | 16.2696i | 1.01355 | + | 0.585175i | 0.912230 | − | 0.409678i | \(-0.134359\pi\) |
0.101323 | + | 0.994854i | \(0.467692\pi\) | |||||||
\(774\) | −7.36578 | + | 12.7579i | −0.264757 | + | 0.458573i | ||||
\(775\) | −27.1654 | + | 15.6839i | −0.975808 | + | 0.563383i | ||||
\(776\) | 10.6748 | 0.383202 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 3.37886i | − | 0.121138i | ||||||
\(779\) | −23.0856 | − | 39.9855i | −0.827129 | − | 1.43263i | ||||
\(780\) | −2.64021 | + | 4.57298i | −0.0945347 | + | 0.163739i | ||||
\(781\) | 5.08699 | − | 10.4641i | 0.182027 | − | 0.374434i | ||||
\(782\) | 22.8843 | − | 13.2123i | 0.818341 | − | 0.472470i | ||||
\(783\) | −18.0024 | −0.643353 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.78505 | −0.349243 | ||||||||
\(786\) | 3.61324 | + | 6.25832i | 0.128880 | + | 0.223227i | ||||
\(787\) | 10.0577 | − | 17.4205i | 0.358519 | − | 0.620973i | −0.629195 | − | 0.777248i | \(-0.716615\pi\) |
0.987714 | + | 0.156275i | \(0.0499485\pi\) | |||||||
\(788\) | 15.0230 | + | 8.67356i | 0.535174 | + | 0.308983i | ||||
\(789\) | −12.4838 | − | 21.6225i | −0.444433 | − | 0.769781i | ||||
\(790\) | − | 19.6517i | − | 0.699177i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.458154 | + | 6.43283i | 0.0162798 | + | 0.228581i | ||||
\(793\) | 3.08316 | + | 5.34019i | 0.109486 | + | 0.189636i | ||||
\(794\) | 5.76499 | − | 9.98525i | 0.204592 | − | 0.354363i | ||||
\(795\) | −3.10135 | + | 5.37170i | −0.109994 | + | 0.190515i | ||||
\(796\) | −2.53353 | + | 1.46273i | −0.0897985 | + | 0.0518452i | ||||
\(797\) | − | 31.1568i | − | 1.10363i | −0.833966 | − | 0.551816i | \(-0.813935\pi\) | ||
0.833966 | − | 0.551816i | \(-0.186065\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0575i | 0.532697i | ||||||||
\(800\) | 2.95810 | − | 1.70786i | 0.104585 | − | 0.0603819i | ||||
\(801\) | 17.9339 | + | 10.3541i | 0.633663 | + | 0.365846i | ||||
\(802\) | −22.5619 | − | 13.0261i | −0.796689 | − | 0.459969i | ||||
\(803\) | 1.79658 | + | 2.65616i | 0.0634001 | + | 0.0937339i | ||||
\(804\) | 3.47345i | 0.122499i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 37.4993 | 1.32086 | ||||||||
\(807\) | 13.8945 | + | 24.0661i | 0.489111 | + | 0.847165i | ||||
\(808\) | 8.71642 | + | 5.03242i | 0.306642 | + | 0.177040i | ||||
\(809\) | 12.6960 | + | 7.33001i | 0.446366 | + | 0.257709i | 0.706294 | − | 0.707918i | \(-0.250366\pi\) |
−0.259928 | + | 0.965628i | \(0.583699\pi\) | |||||||
\(810\) | −0.386714 | − | 0.669808i | −0.0135877 | − | 0.0235346i | ||||
\(811\) | −45.7501 | −1.60650 | −0.803251 | − | 0.595640i | \(-0.796898\pi\) | ||||
−0.803251 | + | 0.595640i | \(0.796898\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.7293i | 0.376292i | ||||||||
\(814\) | 0.846815 | − | 0.572772i | 0.0296809 | − | 0.0200757i | ||||
\(815\) | −19.8523 | − | 11.4618i | −0.695397 | − | 0.401488i | ||||
\(816\) | −2.84887 | − | 1.64480i | −0.0997304 | − | 0.0575794i | ||||
\(817\) | −50.0487 | + | 28.8956i | −1.75098 | + | 1.01093i | ||||
\(818\) | 35.0217i | 1.22451i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 7.61851i | 0.266050i | ||||||||
\(821\) | −6.11121 | + | 3.52831i | −0.213283 | + | 0.123139i | −0.602836 | − | 0.797865i | \(-0.705963\pi\) |
0.389553 | + | 0.921004i | \(0.372629\pi\) | |||||||
\(822\) | −4.66932 | + | 8.08750i | −0.162861 | + | 0.282084i | ||||
\(823\) | 14.2038 | − | 24.6016i | 0.495112 | − | 0.857559i | −0.504872 | − | 0.863194i | \(-0.668460\pi\) |
0.999984 | + | 0.00563530i | \(0.00179378\pi\) | |||||||
\(824\) | 1.44261 | + | 2.49868i | 0.0502559 | + | 0.0870457i | ||||
\(825\) | 0.826840 | + | 11.6095i | 0.0287869 | + | 0.404190i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.161893i | 0.00562957i | 0.999996 | + | 0.00281478i | \(0.000895975\pi\) | ||||
−0.999996 | + | 0.00281478i | \(0.999104\pi\) | |||||||
\(828\) | −8.02365 | − | 13.8974i | −0.278841 | − | 0.482967i | ||||
\(829\) | 21.0966 | + | 12.1801i | 0.732715 | + | 0.423033i | 0.819415 | − | 0.573201i | \(-0.194299\pi\) |
−0.0866997 | + | 0.996234i | \(0.527632\pi\) | |||||||
\(830\) | −0.837011 | + | 1.44974i | −0.0290531 | + | 0.0503214i | ||||
\(831\) | 10.4796 | + | 18.1512i | 0.363534 | + | 0.629660i | ||||
\(832\) | −4.08338 | −0.141566 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −8.08084 | −0.279817 | ||||||||
\(835\) | −15.6589 | + | 9.04066i | −0.541898 | + | 0.312865i | ||||
\(836\) | −11.0613 | + | 22.7534i | −0.382564 | + | 0.786944i | ||||
\(837\) | 23.3252 | − | 40.4005i | 0.806238 | − | 1.39644i | ||||
\(838\) | 6.06211 | + | 10.4999i | 0.209412 | + | 0.362713i | ||||
\(839\) | − | 3.31341i | − | 0.114392i | −0.998363 | − | 0.0571958i | \(-0.981784\pi\) | ||
0.998363 | − | 0.0571958i | \(-0.0182159\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.4410 | 0.566932 | ||||||||
\(842\) | 16.1895 | − | 9.34699i | 0.557926 | − | 0.322119i | ||||
\(843\) | −5.13452 | + | 8.89326i | −0.176842 | + | 0.306300i | ||||
\(844\) | 0.218870 | + | 0.126365i | 0.00753382 | + | 0.00434965i | ||||
\(845\) | −4.00487 | + | 2.31221i | −0.137772 | + | 0.0795425i | ||||
\(846\) | 9.14426 | 0.314386 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.79659 | −0.164716 | ||||||||
\(849\) | 3.10427 | − | 1.79225i | 0.106538 | − | 0.0615098i | ||||
\(850\) | 9.47158 | + | 5.46842i | 0.324873 | + | 0.187565i | ||||
\(851\) | −1.27193 | + | 2.20305i | −0.0436012 | + | 0.0755196i | ||||
\(852\) | 3.12129 | − | 1.80208i | 0.106934 | − | 0.0617382i | ||||
\(853\) | −17.0905 | −0.585169 | −0.292584 | − | 0.956240i | \(-0.594515\pi\) | ||||
−0.292584 | + | 0.956240i | \(0.594515\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 18.6698i | − | 0.638492i | ||||||
\(856\) | −8.15002 | − | 14.1162i | −0.278562 | − | 0.482483i | ||||
\(857\) | 11.2484 | − | 19.4827i | 0.384237 | − | 0.665517i | −0.607426 | − | 0.794376i | \(-0.707798\pi\) |
0.991663 | + | 0.128859i | \(0.0411314\pi\) | |||||||
\(858\) | 6.08334 | − | 12.5136i | 0.207682 | − | 0.427206i | ||||
\(859\) | 33.3698 | − | 19.2661i | 1.13856 | − | 0.657350i | 0.192489 | − | 0.981299i | \(-0.438344\pi\) |
0.946074 | + | 0.323950i | \(0.105011\pi\) | |||||||
\(860\) | 9.53587 | 0.325170 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 33.9418 | 1.15606 | ||||||||
\(863\) | 12.8730 | + | 22.2967i | 0.438202 | + | 0.758989i | 0.997551 | − | 0.0699437i | \(-0.0222820\pi\) |
−0.559348 | + | 0.828933i | \(0.688949\pi\) | |||||||
\(864\) | −2.53994 | + | 4.39930i | −0.0864105 | + | 0.149667i | ||||
\(865\) | −5.19212 | − | 2.99767i | −0.176537 | − | 0.101924i | ||||
\(866\) | 13.5474 | + | 23.4648i | 0.460360 | + | 0.797368i | ||||
\(867\) | 6.93252i | 0.235441i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.67867 | + | 51.6514i | 0.124790 | + | 1.75215i | ||||
\(870\) | 2.29137 | + | 3.96877i | 0.0776847 | + | 0.134554i | ||||
\(871\) | −6.90270 | + | 11.9558i | −0.233889 | + | 0.405108i | ||||
\(872\) | −5.75172 | + | 9.96227i | −0.194778 | + | 0.337365i | ||||
\(873\) | 17.9760 | − | 10.3785i | 0.608397 | − | 0.351258i | ||||
\(874\) | − | 62.9529i | − | 2.12941i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0.993331i | 0.0335615i | ||||||||
\(877\) | −14.7676 | + | 8.52609i | −0.498667 | + | 0.287906i | −0.728163 | − | 0.685404i | \(-0.759626\pi\) |
0.229496 | + | 0.973310i | \(0.426292\pi\) | |||||||
\(878\) | −17.7135 | − | 10.2269i | −0.597803 | − | 0.345142i | ||||
\(879\) | 15.4413 | + | 8.91506i | 0.520823 | + | 0.300697i | ||||
\(880\) | 3.45787 | − | 2.33885i | 0.116565 | − | 0.0788426i | ||||
\(881\) | − | 38.3968i | − | 1.29362i | −0.762651 | − | 0.646811i | \(-0.776102\pi\) | ||
0.762651 | − | 0.646811i | \(-0.223898\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.3727 | −1.19038 | −0.595192 | − | 0.803583i | \(-0.702924\pi\) | ||||
−0.595192 | + | 0.803583i | \(0.702924\pi\) | |||||||
\(884\) | −6.53732 | − | 11.3230i | −0.219874 | − | 0.380833i | ||||
\(885\) | 3.06101 | + | 1.76727i | 0.102895 | + | 0.0594062i | ||||
\(886\) | 3.11541 | + | 1.79868i | 0.104664 | + | 0.0604279i | ||||
\(887\) | −1.05289 | − | 1.82365i | −0.0353525 | − | 0.0612322i | 0.847808 | − | 0.530304i | \(-0.177922\pi\) |
−0.883160 | + | 0.469071i | \(0.844589\pi\) | |||||||
\(888\) | 0.316686 | 0.0106273 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 13.4047i | − | 0.449325i | ||||||
\(891\) | 1.14180 | + | 1.68809i | 0.0382517 | + | 0.0565532i | ||||
\(892\) | −16.4866 | − | 9.51852i | −0.552011 | − | 0.318704i | ||||
\(893\) | 31.0665 | + | 17.9363i | 1.03960 | + | 0.600215i | ||||
\(894\) | 5.54394 | − | 3.20079i | 0.185417 | − | 0.107051i | ||||
\(895\) | 4.89692i | 0.163686i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 34.6218i | 1.15599i | ||||||||
\(898\) | 32.1005 | − | 18.5332i | 1.07121 | − | 0.618461i | ||||
\(899\) | 16.2723 | − | 28.1845i | 0.542712 | − | 0.940005i | ||||
\(900\) | 3.32091 | − | 5.75198i | 0.110697 | − | 0.191733i | ||||
\(901\) | −7.67914 | − | 13.3007i | −0.255829 | − | 0.443109i | ||||
\(902\) | −1.42613 | − | 20.0240i | −0.0474851 | − | 0.666727i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.558958i | − | 0.0185907i | ||||||
\(905\) | −8.22539 | − | 14.2468i | −0.273421 | − | 0.473579i | ||||
\(906\) | −15.5794 | − | 8.99479i | −0.517592 | − | 0.298832i | ||||
\(907\) | −25.2204 | + | 43.6831i | −0.837431 | + | 1.45047i | 0.0546043 | + | 0.998508i | \(0.482610\pi\) |
−0.892035 | + | 0.451965i | \(0.850723\pi\) | |||||||
\(908\) | 9.20350 | + | 15.9409i | 0.305429 | + | 0.529018i | ||||
\(909\) | 19.5709 | 0.649127 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.24825 | −0.0413565 | −0.0206782 | − | 0.999786i | \(-0.506583\pi\) | ||||
−0.0206782 | + | 0.999786i | \(0.506583\pi\) | |||||||
\(912\) | −6.78705 | + | 3.91851i | −0.224742 | + | 0.129755i | ||||
\(913\) | 1.92857 | − | 3.96711i | 0.0638262 | − | 0.131292i | ||||
\(914\) | 9.07561 | − | 15.7194i | 0.300195 | − | 0.519952i | ||||
\(915\) | −0.976392 | − | 1.69116i | −0.0322785 | − | 0.0559080i | ||||
\(916\) | − | 5.30786i | − | 0.175377i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −16.2653 | −0.536836 | ||||||||
\(919\) | −14.0660 | + | 8.12103i | −0.463996 | + | 0.267888i | −0.713723 | − | 0.700428i | \(-0.752992\pi\) |
0.249727 | + | 0.968316i | \(0.419659\pi\) | |||||||
\(920\) | −5.19378 | + | 8.99589i | −0.171234 | + | 0.296586i | ||||
\(921\) | −20.1818 | − | 11.6520i | −0.665014 | − | 0.383946i | ||||
\(922\) | 19.4231 | − | 11.2139i | 0.639665 | − | 0.369311i | ||||
\(923\) | 14.3249 | 0.471510 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05288 | −0.0346184 | ||||||||
\(926\) | −13.5337 | + | 7.81370i | −0.444746 | + | 0.256774i | ||||
\(927\) | 4.85865 | + | 2.80514i | 0.159579 | + | 0.0921329i | ||||
\(928\) | −1.77193 | + | 3.06907i | −0.0581665 | + | 0.100747i | ||||
\(929\) | 20.7072 | − | 11.9553i | 0.679382 | − | 0.392242i | −0.120240 | − | 0.992745i | \(-0.538366\pi\) |
0.799622 | + | 0.600503i | \(0.205033\pi\) | |||||||
\(930\) | −11.8755 | −0.389412 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 21.3192i | − | 0.698332i | ||||||
\(933\) | −3.41151 | − | 5.90890i | −0.111688 | − | 0.193449i | ||||
\(934\) | 3.04760 | − | 5.27860i | 0.0997206 | − | 0.172721i | ||||
\(935\) | 12.0214 | + | 5.84407i | 0.393142 | + | 0.191122i | ||||
\(936\) | −6.87631 | + | 3.97004i | −0.224759 | + | 0.129765i | ||||
\(937\) | −28.2482 | −0.922827 | −0.461414 | − | 0.887185i | \(-0.652658\pi\) | ||||
−0.461414 | + | 0.887185i | \(0.652658\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.516740 | 0.0168632 | ||||||||
\(940\) | −2.95958 | − | 5.12614i | −0.0965309 | − | 0.167196i | ||||
\(941\) | −29.3512 | + | 50.8377i | −0.956821 | + | 1.65726i | −0.226677 | + | 0.973970i | \(0.572786\pi\) |
−0.730144 | + | 0.683293i | \(0.760547\pi\) | |||||||
\(942\) | 6.91688 | + | 3.99346i | 0.225364 | + | 0.130114i | ||||
\(943\) | 24.9759 | + | 43.2595i | 0.813327 | + | 1.40872i | ||||
\(944\) | 2.73329i | 0.0889609i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −25.0635 | + | 1.78505i | −0.814885 | + | 0.0580371i | ||||
\(947\) | 22.1672 | + | 38.3948i | 0.720338 | + | 1.24766i | 0.960864 | + | 0.277020i | \(0.0893468\pi\) |
−0.240526 | + | 0.970643i | \(0.577320\pi\) | |||||||
\(948\) | −8.02023 | + | 13.8914i | −0.260485 | + | 0.451173i | ||||
\(949\) | −1.97402 | + | 3.41910i | −0.0640794 | + | 0.110989i | ||||
\(950\) | 22.5648 | − | 13.0278i | 0.732098 | − | 0.422677i | ||||
\(951\) | 10.8376i | 0.351433i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 13.9238i | − | 0.451037i | −0.974239 | − | 0.225518i | \(-0.927592\pi\) | ||
0.974239 | − | 0.225518i | \(-0.0724075\pi\) | |||||||
\(954\) | −8.07733 | + | 4.66345i | −0.261513 | + | 0.150985i | ||||
\(955\) | 6.54031 | + | 3.77605i | 0.211639 | + | 0.122190i | ||||
\(956\) | 6.28010 | + | 3.62582i | 0.203113 | + | 0.117267i | ||||
\(957\) | −6.76543 | − | 10.0023i | −0.218695 | − | 0.323330i | ||||
\(958\) | − | 30.6275i | − | 0.989531i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.29315 | 0.0417362 | ||||||||
\(961\) | 26.6672 | + | 46.1890i | 0.860233 | + | 1.48997i | ||||
\(962\) | 1.09005 | + | 0.629341i | 0.0351447 | + | 0.0202908i | ||||
\(963\) | −27.4488 | − | 15.8476i | −0.884526 | − | 0.510681i | ||||
\(964\) | −1.77705 | − | 3.07794i | −0.0572349 | − | 0.0991337i | ||||
\(965\) | −11.8101 | −0.380180 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.3085i | 0.942499i | 0.882000 | + | 0.471250i | \(0.156197\pi\) | ||||
−0.882000 | + | 0.471250i | \(0.843803\pi\) | |||||||
\(968\) | −8.65064 | + | 6.79458i | −0.278042 | + | 0.218386i | ||||
\(969\) | −21.7316 | − | 12.5467i | −0.698118 | − | 0.403059i | ||||
\(970\) | −11.6361 | − | 6.71808i | −0.373611 | − | 0.215705i | ||||
\(971\) | 0.0286574 | − | 0.0165453i | 0.000919659 | − | 0.000530965i | −0.499540 | − | 0.866291i | \(-0.666498\pi\) |
0.500460 | + | 0.865760i | \(0.333164\pi\) | |||||||
\(972\) | 15.8709i | 0.509060i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 3.17453i | − | 0.101718i | ||||||
\(975\) | −12.4098 | + | 7.16481i | −0.397432 | + | 0.229458i | ||||
\(976\) | 0.755050 | − | 1.30779i | 0.0241686 | − | 0.0418612i | ||||
\(977\) | −21.0948 | + | 36.5373i | −0.674883 | + | 1.16893i | 0.301620 | + | 0.953428i | \(0.402473\pi\) |
−0.976503 | + | 0.215503i | \(0.930861\pi\) | |||||||
\(978\) | 9.35551 | + | 16.2042i | 0.299156 | + | 0.518154i | ||||
\(979\) | 2.50926 | + | 35.2320i | 0.0801964 | + | 1.12602i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 22.3683i | 0.714164i | ||||||||
\(982\) | −16.3254 | − | 28.2763i | −0.520963 | − | 0.902335i | ||||
\(983\) | 44.0056 | + | 25.4067i | 1.40356 | + | 0.810347i | 0.994756 | − | 0.102274i | \(-0.0326120\pi\) |
0.408806 | + | 0.912621i | \(0.365945\pi\) | |||||||
\(984\) | 3.10925 | − | 5.38538i | 0.0991193 | − | 0.171680i | ||||
\(985\) | −10.9173 | − | 18.9092i | −0.347853 | − | 0.602499i | ||||
\(986\) | −11.3471 | −0.361367 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.1486 | −0.990968 | ||||||||
\(989\) | 54.1467 | − | 31.2616i | 1.72177 | − | 0.994062i | ||||
\(990\) | 3.54903 | − | 7.30045i | 0.112796 | − | 0.232023i | ||||
\(991\) | −23.2614 | + | 40.2899i | −0.738923 | + | 1.27985i | 0.214058 | + | 0.976821i | \(0.431332\pi\) |
−0.952981 | + | 0.303030i | \(0.902002\pi\) | |||||||
\(992\) | −4.59169 | − | 7.95304i | −0.145786 | − | 0.252509i | ||||
\(993\) | 5.93886i | 0.188464i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.68223 | 0.116735 | ||||||||
\(996\) | 1.18334 | − | 0.683199i | 0.0374954 | − | 0.0216480i | ||||
\(997\) | −2.26888 | + | 3.92981i | −0.0718560 | + | 0.124458i | −0.899715 | − | 0.436478i | \(-0.856226\pi\) |
0.827859 | + | 0.560937i | \(0.189559\pi\) | |||||||
\(998\) | −24.6426 | − | 14.2274i | −0.780048 | − | 0.450361i | ||||
\(999\) | 1.35606 | − | 0.782923i | 0.0429039 | − | 0.0247706i |
(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 | 1078.2.i.c.1011.7 | 16 | ||
7.2 | even | 3 | 154.2.i.a.131.2 | yes | 16 | ||
7.3 | odd | 6 | 1078.2.c.b.1077.13 | 16 | |||
7.4 | even | 3 | 1078.2.c.b.1077.12 | 16 | |||
7.5 | odd | 6 | inner | 1078.2.i.c.901.3 | 16 | ||
7.6 | odd | 2 | 154.2.i.a.87.6 | yes | 16 | ||
11.10 | odd | 2 | inner | 1078.2.i.c.1011.3 | 16 | ||
21.2 | odd | 6 | 1386.2.bk.c.901.5 | 16 | |||
21.20 | even | 2 | 1386.2.bk.c.703.1 | 16 | |||
28.23 | odd | 6 | 1232.2.bn.b.593.6 | 16 | |||
28.27 | even | 2 | 1232.2.bn.b.241.5 | 16 | |||
77.10 | even | 6 | 1078.2.c.b.1077.5 | 16 | |||
77.32 | odd | 6 | 1078.2.c.b.1077.4 | 16 | |||
77.54 | even | 6 | inner | 1078.2.i.c.901.7 | 16 | ||
77.65 | odd | 6 | 154.2.i.a.131.6 | yes | 16 | ||
77.76 | even | 2 | 154.2.i.a.87.2 | ✓ | 16 | ||
231.65 | even | 6 | 1386.2.bk.c.901.1 | 16 | |||
231.230 | odd | 2 | 1386.2.bk.c.703.5 | 16 | |||
308.219 | even | 6 | 1232.2.bn.b.593.5 | 16 | |||
308.307 | odd | 2 | 1232.2.bn.b.241.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.i.a.87.2 | ✓ | 16 | 77.76 | even | 2 | ||
154.2.i.a.87.6 | yes | 16 | 7.6 | odd | 2 | ||
154.2.i.a.131.2 | yes | 16 | 7.2 | even | 3 | ||
154.2.i.a.131.6 | yes | 16 | 77.65 | odd | 6 | ||
1078.2.c.b.1077.4 | 16 | 77.32 | odd | 6 | |||
1078.2.c.b.1077.5 | 16 | 77.10 | even | 6 | |||
1078.2.c.b.1077.12 | 16 | 7.4 | even | 3 | |||
1078.2.c.b.1077.13 | 16 | 7.3 | odd | 6 | |||
1078.2.i.c.901.3 | 16 | 7.5 | odd | 6 | inner | ||
1078.2.i.c.901.7 | 16 | 77.54 | even | 6 | inner | ||
1078.2.i.c.1011.3 | 16 | 11.10 | odd | 2 | inner | ||
1078.2.i.c.1011.7 | 16 | 1.1 | even | 1 | trivial | ||
1232.2.bn.b.241.5 | 16 | 28.27 | even | 2 | |||
1232.2.bn.b.241.6 | 16 | 308.307 | odd | 2 | |||
1232.2.bn.b.593.5 | 16 | 308.219 | even | 6 | |||
1232.2.bn.b.593.6 | 16 | 28.23 | odd | 6 | |||
1386.2.bk.c.703.1 | 16 | 21.20 | even | 2 | |||
1386.2.bk.c.703.5 | 16 | 231.230 | odd | 2 | |||
1386.2.bk.c.901.1 | 16 | 231.65 | even | 6 | |||
1386.2.bk.c.901.5 | 16 | 21.2 | odd | 6 |