Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(296,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.296");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.t (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(104\) |
Relative dimension: | \(52\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 296.7 | ||
Character | \(\chi\) | \(=\) | 429.296 |
Dual form | 429.2.t.a.329.7 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.92182 | + | 1.10956i | −1.35893 | + | 0.784581i | −0.989480 | − | 0.144669i | \(-0.953788\pi\) |
−0.369453 | + | 0.929249i | \(0.620455\pi\) | |||||||
\(3\) | −1.59672 | + | 0.671171i | −0.921869 | + | 0.387501i | ||||
\(4\) | 1.46227 | − | 2.53272i | 0.731133 | − | 1.26636i | ||||
\(5\) | 1.97176 | 0.881797 | 0.440899 | − | 0.897557i | \(-0.354660\pi\) | ||||
0.440899 | + | 0.897557i | \(0.354660\pi\) | |||||||
\(6\) | 2.32391 | − | 3.06154i | 0.948733 | − | 1.24987i | ||||
\(7\) | 0.477966 | − | 0.827861i | 0.180654 | − | 0.312902i | −0.761449 | − | 0.648224i | \(-0.775512\pi\) |
0.942103 | + | 0.335322i | \(0.108845\pi\) | |||||||
\(8\) | 2.05166i | 0.725371i | ||||||||
\(9\) | 2.09906 | − | 2.14335i | 0.699686 | − | 0.714450i | ||||
\(10\) | −3.78937 | + | 2.18779i | −1.19830 | + | 0.691841i | ||||
\(11\) | −3.31597 | − | 0.0657479i | −0.999803 | − | 0.0198237i | ||||
\(12\) | −0.634948 | + | 5.02549i | −0.183294 | + | 1.45073i | ||||
\(13\) | −3.43390 | + | 1.09923i | −0.952394 | + | 0.304870i | ||||
\(14\) | 2.12134i | 0.566951i | ||||||||
\(15\) | −3.14836 | + | 1.32339i | −0.812902 | + | 0.341697i | ||||
\(16\) | 0.648086 | + | 1.12252i | 0.162021 | + | 0.280629i | ||||
\(17\) | 1.09581 | − | 1.89800i | 0.265773 | − | 0.460331i | −0.701993 | − | 0.712184i | \(-0.747706\pi\) |
0.967766 | + | 0.251852i | \(0.0810397\pi\) | |||||||
\(18\) | −1.65583 | + | 6.44818i | −0.390283 | + | 1.51985i | ||||
\(19\) | −2.70718 | + | 4.68897i | −0.621069 | + | 1.07572i | 0.368218 | + | 0.929740i | \(0.379968\pi\) |
−0.989287 | + | 0.145984i | \(0.953365\pi\) | |||||||
\(20\) | 2.88324 | − | 4.99391i | 0.644711 | − | 1.11667i | ||||
\(21\) | −0.207543 | + | 1.64266i | −0.0452896 | + | 0.358458i | ||||
\(22\) | 6.44566 | − | 3.55293i | 1.37422 | − | 0.757487i | ||||
\(23\) | −5.88960 | + | 3.40036i | −1.22807 | + | 0.709024i | −0.966625 | − | 0.256196i | \(-0.917531\pi\) |
−0.261441 | + | 0.965220i | \(0.584198\pi\) | |||||||
\(24\) | −1.37701 | − | 3.27593i | −0.281082 | − | 0.668697i | ||||
\(25\) | −1.11217 | −0.222433 | ||||||||
\(26\) | 5.37969 | − | 5.92265i | 1.05504 | − | 1.16153i | ||||
\(27\) | −1.91306 | + | 4.83117i | −0.368169 | + | 0.929759i | ||||
\(28\) | −1.39783 | − | 2.42111i | −0.264164 | − | 0.457546i | ||||
\(29\) | −3.45995 | − | 5.99282i | −0.642497 | − | 1.11284i | −0.984874 | − | 0.173275i | \(-0.944565\pi\) |
0.342376 | − | 0.939563i | \(-0.388768\pi\) | |||||||
\(30\) | 4.58220 | − | 6.03662i | 0.836591 | − | 1.10213i | ||||
\(31\) | − | 9.45661i | − | 1.69846i | −0.528025 | − | 0.849229i | \(-0.677067\pi\) | ||
0.528025 | − | 0.849229i | \(-0.322933\pi\) | |||||||
\(32\) | −6.04459 | − | 3.48984i | −1.06854 | − | 0.616923i | ||||
\(33\) | 5.33882 | − | 2.12060i | 0.929370 | − | 0.369150i | ||||
\(34\) | 4.86348i | 0.834080i | ||||||||
\(35\) | 0.942433 | − | 1.63234i | 0.159300 | − | 0.275916i | ||||
\(36\) | −2.35913 | − | 8.45048i | −0.393188 | − | 1.40841i | ||||
\(37\) | −3.85093 | + | 2.22334i | −0.633090 | + | 0.365515i | −0.781948 | − | 0.623344i | \(-0.785774\pi\) |
0.148858 | + | 0.988859i | \(0.452440\pi\) | |||||||
\(38\) | − | 12.0152i | − | 1.94912i | ||||||
\(39\) | 4.74523 | − | 4.05990i | 0.759845 | − | 0.650104i | ||||
\(40\) | 4.04538i | 0.639630i | ||||||||
\(41\) | 7.34788 | − | 4.24230i | 1.14755 | − | 0.662536i | 0.199258 | − | 0.979947i | \(-0.436147\pi\) |
0.948288 | + | 0.317411i | \(0.102814\pi\) | |||||||
\(42\) | −1.42378 | − | 3.38719i | −0.219694 | − | 0.522654i | ||||
\(43\) | 3.90995 | + | 2.25741i | 0.596261 | + | 0.344252i | 0.767569 | − | 0.640966i | \(-0.221466\pi\) |
−0.171308 | + | 0.985218i | \(0.554799\pi\) | |||||||
\(44\) | −5.01536 | + | 8.30229i | −0.756094 | + | 1.25162i | ||||
\(45\) | 4.13884 | − | 4.22617i | 0.616981 | − | 0.630001i | ||||
\(46\) | 7.54584 | − | 13.0698i | 1.11257 | − | 1.92703i | ||||
\(47\) | −8.69313 | −1.26802 | −0.634012 | − | 0.773323i | \(-0.718593\pi\) | ||||
−0.634012 | + | 0.773323i | \(0.718593\pi\) | |||||||
\(48\) | −1.78822 | − | 1.35737i | −0.258107 | − | 0.195920i | ||||
\(49\) | 3.04310 | + | 5.27080i | 0.434728 | + | 0.752971i | ||||
\(50\) | 2.13739 | − | 1.23402i | 0.302272 | − | 0.174517i | ||||
\(51\) | −0.475824 | + | 3.76605i | −0.0666287 | + | 0.527353i | ||||
\(52\) | −2.23725 | + | 10.3045i | −0.310251 | + | 1.42897i | ||||
\(53\) | − | 0.387082i | − | 0.0531699i | −0.999647 | − | 0.0265849i | \(-0.991537\pi\) | ||
0.999647 | − | 0.0265849i | \(-0.00846324\pi\) | |||||||
\(54\) | −1.68393 | − | 11.4073i | −0.229154 | − | 1.55234i | ||||
\(55\) | −6.53830 | − | 0.129639i | −0.881624 | − | 0.0174805i | ||||
\(56\) | 1.69849 | + | 0.980623i | 0.226970 | + | 0.131041i | ||||
\(57\) | 1.17552 | − | 9.30397i | 0.155701 | − | 1.23234i | ||||
\(58\) | 13.2988 | + | 7.67808i | 1.74622 | + | 1.00818i | ||||
\(59\) | 1.10758 | − | 1.91839i | 0.144195 | − | 0.249753i | −0.784877 | − | 0.619651i | \(-0.787274\pi\) |
0.929072 | + | 0.369898i | \(0.120607\pi\) | |||||||
\(60\) | −1.25196 | + | 9.90905i | −0.161628 | + | 1.27925i | ||||
\(61\) | −8.44034 | − | 4.87303i | −1.08067 | − | 0.623928i | −0.149596 | − | 0.988747i | \(-0.547797\pi\) |
−0.931078 | + | 0.364820i | \(0.881131\pi\) | |||||||
\(62\) | 10.4927 | + | 18.1739i | 1.33258 | + | 2.30809i | ||||
\(63\) | −0.771119 | − | 2.76218i | −0.0971518 | − | 0.348002i | ||||
\(64\) | 12.8965 | 1.61206 | ||||||||
\(65\) | −6.77083 | + | 2.16741i | −0.839818 | + | 0.268834i | ||||
\(66\) | −7.90732 | + | 9.99919i | −0.973324 | + | 1.23082i | ||||
\(67\) | −9.08197 | + | 5.24348i | −1.10954 | + | 0.640593i | −0.938710 | − | 0.344708i | \(-0.887978\pi\) |
−0.170829 | + | 0.985301i | \(0.554645\pi\) | |||||||
\(68\) | −3.20473 | − | 5.55075i | −0.388630 | − | 0.673127i | ||||
\(69\) | 7.12184 | − | 9.38236i | 0.857369 | − | 1.12950i | ||||
\(70\) | 4.18276i | 0.499936i | ||||||||
\(71\) | −2.05660 | + | 3.56214i | −0.244074 | + | 0.422748i | −0.961871 | − | 0.273504i | \(-0.911817\pi\) |
0.717797 | + | 0.696252i | \(0.245151\pi\) | |||||||
\(72\) | 4.39743 | + | 4.30655i | 0.518242 | + | 0.507532i | ||||
\(73\) | −2.33785 | −0.273624 | −0.136812 | − | 0.990597i | \(-0.543686\pi\) | ||||
−0.136812 | + | 0.990597i | \(0.543686\pi\) | |||||||
\(74\) | 4.93387 | − | 8.54572i | 0.573551 | − | 0.993420i | ||||
\(75\) | 1.77582 | − | 0.746454i | 0.205054 | − | 0.0861931i | ||||
\(76\) | 7.91723 | + | 13.7130i | 0.908169 | + | 1.57299i | ||||
\(77\) | −1.63935 | + | 2.71374i | −0.186821 | + | 0.309259i | ||||
\(78\) | −4.61477 | + | 13.0675i | −0.522520 | + | 1.47961i | ||||
\(79\) | − | 8.16220i | − | 0.918320i | −0.888354 | − | 0.459160i | \(-0.848151\pi\) | ||
0.888354 | − | 0.459160i | \(-0.151849\pi\) | |||||||
\(80\) | 1.27787 | + | 2.21333i | 0.142870 | + | 0.247458i | ||||
\(81\) | −0.187909 | − | 8.99804i | −0.0208787 | − | 0.999782i | ||||
\(82\) | −9.41421 | + | 16.3059i | −1.03963 | + | 1.80068i | ||||
\(83\) | 2.78415i | 0.305601i | 0.988257 | + | 0.152800i | \(0.0488291\pi\) | ||||
−0.988257 | + | 0.152800i | \(0.951171\pi\) | |||||||
\(84\) | 3.85692 | + | 2.92766i | 0.420825 | + | 0.319434i | ||||
\(85\) | 2.16067 | − | 3.74239i | 0.234358 | − | 0.405919i | ||||
\(86\) | −10.0190 | −1.08037 | ||||||||
\(87\) | 9.54680 | + | 7.24665i | 1.02352 | + | 0.776923i | ||||
\(88\) | 0.134892 | − | 6.80325i | 0.0143796 | − | 0.725228i | ||||
\(89\) | −2.83303 | − | 4.90695i | −0.300301 | − | 0.520136i | 0.675903 | − | 0.736990i | \(-0.263754\pi\) |
−0.976204 | + | 0.216854i | \(0.930420\pi\) | |||||||
\(90\) | −3.26490 | + | 12.7143i | −0.344150 | + | 1.34020i | ||||
\(91\) | −0.731283 | + | 3.36819i | −0.0766593 | + | 0.353082i | ||||
\(92\) | 19.8889i | 2.07356i | ||||||||
\(93\) | 6.34701 | + | 15.0996i | 0.658154 | + | 1.56576i | ||||
\(94\) | 16.7067 | − | 9.64559i | 1.72316 | − | 0.994867i | ||||
\(95\) | −5.33790 | + | 9.24552i | −0.547657 | + | 0.948570i | ||||
\(96\) | 11.9938 | + | 1.51537i | 1.22411 | + | 0.154661i | ||||
\(97\) | −16.4548 | − | 9.50019i | −1.67073 | − | 0.964598i | −0.967229 | − | 0.253907i | \(-0.918284\pi\) |
−0.703504 | − | 0.710691i | \(-0.748382\pi\) | |||||||
\(98\) | −11.6966 | − | 6.75303i | −1.18153 | − | 0.682159i | ||||
\(99\) | −7.10134 | + | 6.96929i | −0.713712 | + | 0.700440i | ||||
\(100\) | −1.62628 | + | 2.81681i | −0.162628 | + | 0.281681i | ||||
\(101\) | 3.56582 | + | 6.17618i | 0.354812 | + | 0.614553i | 0.987086 | − | 0.160192i | \(-0.0512115\pi\) |
−0.632274 | + | 0.774745i | \(0.717878\pi\) | |||||||
\(102\) | −3.26423 | − | 7.76564i | −0.323207 | − | 0.768913i | ||||
\(103\) | 2.25242 | 0.221937 | 0.110969 | − | 0.993824i | \(-0.464605\pi\) | ||||
0.110969 | + | 0.993824i | \(0.464605\pi\) | |||||||
\(104\) | −2.25524 | − | 7.04520i | −0.221144 | − | 0.690839i | ||||
\(105\) | −0.409225 | + | 3.23893i | −0.0399363 | + | 0.316088i | ||||
\(106\) | 0.429493 | + | 0.743903i | 0.0417160 | + | 0.0722543i | ||||
\(107\) | −0.896452 | − | 1.55270i | −0.0866633 | − | 0.150105i | 0.819435 | − | 0.573171i | \(-0.194287\pi\) |
−0.906099 | + | 0.423066i | \(0.860954\pi\) | |||||||
\(108\) | 9.43859 | + | 11.9097i | 0.908229 | + | 1.14601i | ||||
\(109\) | −5.26402 | −0.504201 | −0.252101 | − | 0.967701i | \(-0.581121\pi\) | ||||
−0.252101 | + | 0.967701i | \(0.581121\pi\) | |||||||
\(110\) | 12.7093 | − | 7.00552i | 1.21178 | − | 0.667950i | ||||
\(111\) | 4.65664 | − | 6.13469i | 0.441989 | − | 0.582279i | ||||
\(112\) | 1.23905 | 0.117079 | ||||||||
\(113\) | 10.9465 | + | 6.31996i | 1.02976 | + | 0.594531i | 0.916916 | − | 0.399081i | \(-0.130671\pi\) |
0.112843 | + | 0.993613i | \(0.464004\pi\) | |||||||
\(114\) | 8.06423 | + | 19.1849i | 0.755284 | + | 1.79683i | ||||
\(115\) | −11.6129 | + | 6.70469i | −1.08291 | + | 0.625216i | ||||
\(116\) | −20.2375 | −1.87900 | ||||||||
\(117\) | −4.85194 | + | 9.66740i | −0.448562 | + | 0.893752i | ||||
\(118\) | 4.91574i | 0.452531i | ||||||||
\(119\) | −1.04752 | − | 1.81435i | −0.0960258 | − | 0.166322i | ||||
\(120\) | −2.71514 | − | 6.45935i | −0.247857 | − | 0.589655i | ||||
\(121\) | 10.9914 | + | 0.436037i | 0.999214 | + | 0.0396397i | ||||
\(122\) | 21.6278 | 1.95809 | ||||||||
\(123\) | −8.88523 | + | 11.7055i | −0.801154 | + | 1.05545i | ||||
\(124\) | −23.9510 | − | 13.8281i | −2.15086 | − | 1.24180i | ||||
\(125\) | −12.0517 | −1.07794 | ||||||||
\(126\) | 4.54677 | + | 4.45281i | 0.405058 | + | 0.396688i | ||||
\(127\) | 8.60329 | − | 4.96711i | 0.763419 | − | 0.440760i | −0.0671031 | − | 0.997746i | \(-0.521376\pi\) |
0.830522 | + | 0.556986i | \(0.188042\pi\) | |||||||
\(128\) | −12.6956 | + | 7.32980i | −1.12214 | + | 0.647868i | ||||
\(129\) | −7.75822 | − | 0.980216i | −0.683073 | − | 0.0863032i | ||||
\(130\) | 10.6075 | − | 11.6780i | 0.930336 | − | 1.02423i | ||||
\(131\) | 3.72037 | 0.325050 | 0.162525 | − | 0.986704i | \(-0.448036\pi\) | ||||
0.162525 | + | 0.986704i | \(0.448036\pi\) | |||||||
\(132\) | 2.43589 | − | 16.6226i | 0.212017 | − | 1.44681i | ||||
\(133\) | 2.58788 | + | 4.48233i | 0.224397 | + | 0.388668i | ||||
\(134\) | 11.6360 | − | 20.1541i | 1.00519 | − | 1.74105i | ||||
\(135\) | −3.77210 | + | 9.52590i | −0.324650 | + | 0.819859i | ||||
\(136\) | 3.89404 | + | 2.24822i | 0.333911 | + | 0.192784i | ||||
\(137\) | 4.60457 | − | 7.97534i | 0.393395 | − | 0.681380i | −0.599500 | − | 0.800375i | \(-0.704634\pi\) |
0.992895 | + | 0.118995i | \(0.0379673\pi\) | |||||||
\(138\) | −3.27657 | + | 25.9334i | −0.278920 | + | 2.20760i | ||||
\(139\) | 1.52965 | + | 0.883145i | 0.129743 | + | 0.0749073i | 0.563467 | − | 0.826139i | \(-0.309467\pi\) |
−0.433724 | + | 0.901046i | \(0.642801\pi\) | |||||||
\(140\) | −2.75618 | − | 4.77384i | −0.232940 | − | 0.403463i | ||||
\(141\) | 13.8805 | − | 5.83458i | 1.16895 | − | 0.491360i | ||||
\(142\) | − | 9.12773i | − | 0.765982i | ||||||
\(143\) | 11.4590 | − | 3.41923i | 0.958250 | − | 0.285930i | ||||
\(144\) | 3.76632 | + | 0.967154i | 0.313860 | + | 0.0805962i | ||||
\(145\) | −6.82219 | − | 11.8164i | −0.566552 | − | 0.981298i | ||||
\(146\) | 4.49293 | − | 2.59399i | 0.371837 | − | 0.214680i | ||||
\(147\) | −8.39660 | − | 6.37358i | −0.692540 | − | 0.525684i | ||||
\(148\) | 13.0045i | 1.06896i | ||||||||
\(149\) | 4.66973 | + | 2.69607i | 0.382559 | + | 0.220870i | 0.678931 | − | 0.734202i | \(-0.262444\pi\) |
−0.296372 | + | 0.955073i | \(0.595777\pi\) | |||||||
\(150\) | −2.58458 | + | 3.40494i | −0.211030 | + | 0.278012i | ||||
\(151\) | −19.7352 | −1.60603 | −0.803013 | − | 0.595962i | \(-0.796771\pi\) | ||||
−0.803013 | + | 0.595962i | \(0.796771\pi\) | |||||||
\(152\) | −9.62017 | − | 5.55421i | −0.780299 | − | 0.450506i | ||||
\(153\) | −1.76791 | − | 6.33270i | −0.142927 | − | 0.511969i | ||||
\(154\) | 0.139473 | − | 7.03429i | 0.0112391 | − | 0.566839i | ||||
\(155\) | − | 18.6462i | − | 1.49770i | ||||||
\(156\) | −3.34379 | − | 17.9550i | −0.267718 | − | 1.43755i | ||||
\(157\) | 15.3245 | 1.22303 | 0.611513 | − | 0.791234i | \(-0.290561\pi\) | ||||
0.611513 | + | 0.791234i | \(0.290561\pi\) | |||||||
\(158\) | 9.05649 | + | 15.6863i | 0.720496 | + | 1.24794i | ||||
\(159\) | 0.259799 | + | 0.618064i | 0.0206034 | + | 0.0490157i | ||||
\(160\) | −11.9185 | − | 6.88113i | −0.942238 | − | 0.544001i | ||||
\(161\) | 6.50102i | 0.512352i | ||||||||
\(162\) | 10.3450 | + | 17.0841i | 0.812782 | + | 1.34226i | ||||
\(163\) | −7.54306 | − | 4.35499i | −0.590818 | − | 0.341109i | 0.174603 | − | 0.984639i | \(-0.444136\pi\) |
−0.765421 | + | 0.643530i | \(0.777469\pi\) | |||||||
\(164\) | − | 24.8135i | − | 1.93761i | ||||||
\(165\) | 10.5269 | − | 4.18132i | 0.819516 | − | 0.325515i | ||||
\(166\) | −3.08920 | − | 5.35065i | −0.239768 | − | 0.415291i | ||||
\(167\) | −10.6863 | + | 6.16976i | −0.826934 | + | 0.477430i | −0.852802 | − | 0.522235i | \(-0.825098\pi\) |
0.0258680 | + | 0.999665i | \(0.491765\pi\) | |||||||
\(168\) | −3.37018 | − | 0.425808i | −0.260015 | − | 0.0328518i | ||||
\(169\) | 10.5834 | − | 7.54927i | 0.814108 | − | 0.580713i | ||||
\(170\) | 9.58961i | 0.735489i | ||||||||
\(171\) | 4.36758 | + | 15.6449i | 0.333998 | + | 1.19639i | ||||
\(172\) | 11.4348 | − | 6.60187i | 0.871893 | − | 0.503388i | ||||
\(173\) | −10.4906 | + | 18.1703i | −0.797587 | + | 1.38146i | 0.123597 | + | 0.992332i | \(0.460557\pi\) |
−0.921184 | + | 0.389128i | \(0.872776\pi\) | |||||||
\(174\) | −26.3879 | − | 3.33399i | −2.00046 | − | 0.252749i | ||||
\(175\) | −0.531577 | + | 0.920719i | −0.0401835 | + | 0.0695998i | ||||
\(176\) | −2.07523 | − | 3.76485i | −0.156426 | − | 0.283786i | ||||
\(177\) | −0.480937 | + | 3.80652i | −0.0361494 | + | 0.286116i | ||||
\(178\) | 10.8892 | + | 6.28686i | 0.816177 | + | 0.471220i | ||||
\(179\) | 1.78408 | − | 1.03004i | 0.133348 | − | 0.0769887i | −0.431842 | − | 0.901949i | \(-0.642136\pi\) |
0.565190 | + | 0.824961i | \(0.308803\pi\) | |||||||
\(180\) | −4.65163 | − | 16.6623i | −0.346712 | − | 1.24194i | ||||
\(181\) | −1.33526 | −0.0992493 | −0.0496246 | − | 0.998768i | \(-0.515803\pi\) | ||||
−0.0496246 | + | 0.998768i | \(0.515803\pi\) | |||||||
\(182\) | −2.33183 | − | 7.28446i | −0.172846 | − | 0.539960i | ||||
\(183\) | 16.7475 | + | 2.11598i | 1.23801 | + | 0.156417i | ||||
\(184\) | −6.97638 | − | 12.0834i | −0.514305 | − | 0.890803i | ||||
\(185\) | −7.59311 | + | 4.38389i | −0.558257 | + | 0.322310i | ||||
\(186\) | −28.9518 | − | 21.9763i | −2.12285 | − | 1.61138i | ||||
\(187\) | −3.75846 | + | 6.22165i | −0.274846 | + | 0.454972i | ||||
\(188\) | −12.7117 | + | 22.0173i | −0.927094 | + | 1.60577i | ||||
\(189\) | 3.08516 | + | 3.89288i | 0.224412 | + | 0.283166i | ||||
\(190\) | − | 23.6910i | − | 1.71873i | ||||||
\(191\) | 7.90490 | + | 4.56389i | 0.571978 | + | 0.330232i | 0.757939 | − | 0.652325i | \(-0.226206\pi\) |
−0.185961 | + | 0.982557i | \(0.559540\pi\) | |||||||
\(192\) | −20.5921 | + | 8.65575i | −1.48611 | + | 0.624675i | ||||
\(193\) | 6.32294 | + | 10.9516i | 0.455135 | + | 0.788317i | 0.998696 | − | 0.0510529i | \(-0.0162577\pi\) |
−0.543561 | + | 0.839370i | \(0.682924\pi\) | |||||||
\(194\) | 42.1643 | 3.02722 | ||||||||
\(195\) | 9.35645 | − | 8.00514i | 0.670030 | − | 0.573260i | ||||
\(196\) | 17.7993 | 1.27138 | ||||||||
\(197\) | 17.8039 | − | 10.2791i | 1.26847 | − | 0.732353i | 0.293774 | − | 0.955875i | \(-0.405089\pi\) |
0.974699 | + | 0.223522i | \(0.0717554\pi\) | |||||||
\(198\) | 5.91464 | − | 21.2731i | 0.420335 | − | 1.51182i | ||||
\(199\) | −3.35659 | + | 5.81378i | −0.237942 | + | 0.412128i | −0.960124 | − | 0.279576i | \(-0.909806\pi\) |
0.722181 | + | 0.691704i | \(0.243140\pi\) | |||||||
\(200\) | − | 2.28179i | − | 0.161347i | ||||||
\(201\) | 10.9821 | − | 14.4679i | 0.774620 | − | 1.02049i | ||||
\(202\) | −13.7057 | − | 7.91301i | −0.964332 | − | 0.556757i | ||||
\(203\) | −6.61496 | −0.464279 | ||||||||
\(204\) | 8.84257 | + | 6.71210i | 0.619104 | + | 0.469941i | ||||
\(205\) | 14.4882 | − | 8.36479i | 1.01190 | − | 0.584222i | ||||
\(206\) | −4.32875 | + | 2.49920i | −0.301598 | + | 0.174128i | ||||
\(207\) | −5.07444 | + | 19.7610i | −0.352698 | + | 1.37349i | ||||
\(208\) | −3.45936 | − | 3.14223i | −0.239864 | − | 0.217874i | ||||
\(209\) | 9.28522 | − | 15.3705i | 0.642272 | − | 1.06320i | ||||
\(210\) | −2.80735 | − | 6.67872i | −0.193726 | − | 0.460875i | ||||
\(211\) | 8.20832 | − | 4.73908i | 0.565084 | − | 0.326251i | −0.190099 | − | 0.981765i | \(-0.560881\pi\) |
0.755184 | + | 0.655513i | \(0.227548\pi\) | |||||||
\(212\) | −0.980371 | − | 0.566018i | −0.0673322 | − | 0.0388743i | ||||
\(213\) | 0.893022 | − | 7.06809i | 0.0611888 | − | 0.484298i | ||||
\(214\) | 3.44564 | + | 1.98934i | 0.235539 | + | 0.135989i | ||||
\(215\) | 7.70947 | + | 4.45107i | 0.525782 | + | 0.303560i | ||||
\(216\) | −9.91191 | − | 3.92495i | −0.674420 | − | 0.267059i | ||||
\(217\) | −7.82876 | − | 4.51994i | −0.531451 | − | 0.306833i | ||||
\(218\) | 10.1165 | − | 5.84077i | 0.685176 | − | 0.395587i | ||||
\(219\) | 3.73290 | − | 1.56910i | 0.252246 | − | 0.106030i | ||||
\(220\) | −9.88908 | + | 16.3701i | −0.666721 | + | 1.10367i | ||||
\(221\) | −1.67658 | + | 7.72208i | −0.112779 | + | 0.519443i | ||||
\(222\) | −2.14240 | + | 16.9566i | −0.143788 | + | 1.13805i | ||||
\(223\) | −0.307378 | + | 0.177465i | −0.0205835 | + | 0.0118839i | −0.510256 | − | 0.860022i | \(-0.670450\pi\) |
0.489673 | + | 0.871906i | \(0.337116\pi\) | |||||||
\(224\) | −5.77821 | + | 3.33605i | −0.386073 | + | 0.222899i | ||||
\(225\) | −2.33450 | + | 2.38376i | −0.155633 | + | 0.158918i | ||||
\(226\) | −28.0496 | −1.86583 | ||||||||
\(227\) | −18.7464 | − | 10.8232i | −1.24424 | − | 0.718362i | −0.274285 | − | 0.961648i | \(-0.588441\pi\) |
−0.969954 | + | 0.243287i | \(0.921774\pi\) | |||||||
\(228\) | −21.8454 | − | 16.5821i | −1.44675 | − | 1.09818i | ||||
\(229\) | 5.36210i | 0.354338i | 0.984180 | + | 0.177169i | \(0.0566938\pi\) | ||||
−0.984180 | + | 0.177169i | \(0.943306\pi\) | |||||||
\(230\) | 14.8786 | − | 25.7704i | 0.981064 | − | 1.69925i | ||||
\(231\) | 0.796209 | − | 5.43338i | 0.0523867 | − | 0.357490i | ||||
\(232\) | 12.2952 | − | 7.09864i | 0.807220 | − | 0.466049i | ||||
\(233\) | −1.04207 | −0.0682685 | −0.0341343 | − | 0.999417i | \(-0.510867\pi\) | ||||
−0.0341343 | + | 0.999417i | \(0.510867\pi\) | |||||||
\(234\) | −1.40204 | − | 23.9626i | −0.0916542 | − | 1.56648i | ||||
\(235\) | −17.1408 | −1.11814 | ||||||||
\(236\) | −3.23917 | − | 5.61040i | −0.210852 | − | 0.365206i | ||||
\(237\) | 5.47824 | + | 13.0328i | 0.355850 | + | 0.846571i | ||||
\(238\) | 4.02628 | + | 2.32458i | 0.260985 | + | 0.150680i | ||||
\(239\) | 12.0549i | 0.779766i | 0.920864 | + | 0.389883i | \(0.127484\pi\) | ||||
−0.920864 | + | 0.389883i | \(0.872516\pi\) | |||||||
\(240\) | −3.52593 | − | 2.67642i | −0.227598 | − | 0.172762i | ||||
\(241\) | −6.92345 | + | 11.9918i | −0.445979 | + | 0.772458i | −0.998120 | − | 0.0612929i | \(-0.980478\pi\) |
0.552141 | + | 0.833751i | \(0.313811\pi\) | |||||||
\(242\) | −21.6072 | + | 11.3576i | −1.38897 | + | 0.730096i | ||||
\(243\) | 6.33926 | + | 14.2413i | 0.406664 | + | 0.913578i | ||||
\(244\) | −24.6840 | + | 14.2513i | −1.58023 | + | 0.912349i | ||||
\(245\) | 6.00025 | + | 10.3927i | 0.383342 | + | 0.663968i | ||||
\(246\) | 4.08785 | − | 32.3546i | 0.260632 | − | 2.06285i | ||||
\(247\) | 4.14196 | − | 19.0773i | 0.263546 | − | 1.21386i | ||||
\(248\) | 19.4017 | 1.23201 | ||||||||
\(249\) | −1.86864 | − | 4.44553i | −0.118420 | − | 0.281724i | ||||
\(250\) | 23.1613 | − | 13.3722i | 1.46485 | − | 0.845730i | ||||
\(251\) | 7.76115 | + | 4.48090i | 0.489879 | + | 0.282832i | 0.724524 | − | 0.689249i | \(-0.242059\pi\) |
−0.234645 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(252\) | −8.12340 | − | 2.08601i | −0.511726 | − | 0.131406i | ||||
\(253\) | 19.7533 | − | 10.8883i | 1.24188 | − | 0.684540i | ||||
\(254\) | −11.0227 | + | 19.0918i | −0.691623 | + | 1.19793i | ||||
\(255\) | −0.938210 | + | 7.42574i | −0.0587530 | + | 0.465018i | ||||
\(256\) | 3.36927 | − | 5.83575i | 0.210580 | − | 0.364735i | ||||
\(257\) | −7.99043 | + | 4.61328i | −0.498430 | + | 0.287768i | −0.728065 | − | 0.685508i | \(-0.759580\pi\) |
0.229635 | + | 0.973277i | \(0.426247\pi\) | |||||||
\(258\) | 15.9975 | − | 6.72444i | 0.995962 | − | 0.418645i | ||||
\(259\) | 4.25072i | 0.264127i | ||||||||
\(260\) | −4.41133 | + | 20.3180i | −0.273579 | + | 1.26007i | ||||
\(261\) | −20.1074 | − | 5.16337i | −1.24461 | − | 0.319605i | ||||
\(262\) | −7.14988 | + | 4.12799i | −0.441721 | + | 0.255028i | ||||
\(263\) | −5.58664 | − | 9.67634i | −0.344487 | − | 0.596669i | 0.640774 | − | 0.767730i | \(-0.278614\pi\) |
−0.985260 | + | 0.171061i | \(0.945280\pi\) | |||||||
\(264\) | 4.35076 | + | 10.9534i | 0.267771 | + | 0.674138i | ||||
\(265\) | − | 0.763233i | − | 0.0468850i | ||||||
\(266\) | −9.94688 | − | 5.74283i | −0.609882 | − | 0.352116i | ||||
\(267\) | 7.81698 | + | 5.93361i | 0.478391 | + | 0.363131i | ||||
\(268\) | 30.6695i | 1.87343i | ||||||||
\(269\) | −15.4577 | − | 8.92453i | −0.942475 | − | 0.544138i | −0.0517394 | − | 0.998661i | \(-0.516477\pi\) |
−0.890735 | + | 0.454523i | \(0.849810\pi\) | |||||||
\(270\) | −3.32030 | − | 22.4925i | −0.202067 | − | 1.36885i | ||||
\(271\) | −0.989728 | − | 1.71426i | −0.0601217 | − | 0.104134i | 0.834398 | − | 0.551162i | \(-0.185816\pi\) |
−0.894520 | + | 0.447029i | \(0.852482\pi\) | |||||||
\(272\) | 2.84071 | 0.172243 | ||||||||
\(273\) | −1.09297 | − | 5.86888i | −0.0661498 | − | 0.355201i | ||||
\(274\) | 20.4363i | 1.23460i | ||||||||
\(275\) | 3.68791 | + | 0.0731227i | 0.222390 | + | 0.00440946i | ||||
\(276\) | −13.3489 | − | 31.7571i | −0.803508 | − | 1.91156i | ||||
\(277\) | −19.8682 | − | 11.4709i | −1.19377 | − | 0.689222i | −0.234608 | − | 0.972090i | \(-0.575381\pi\) |
−0.959159 | + | 0.282869i | \(0.908714\pi\) | |||||||
\(278\) | −3.91962 | −0.235083 | ||||||||
\(279\) | −20.2688 | − | 19.8500i | −1.21346 | − | 1.18839i | ||||
\(280\) | 3.34901 | + | 1.93355i | 0.200142 | + | 0.115552i | ||||
\(281\) | 16.6033i | 0.990469i | 0.868759 | + | 0.495234i | \(0.164918\pi\) | ||||
−0.868759 | + | 0.495234i | \(0.835082\pi\) | |||||||
\(282\) | −20.2021 | + | 26.6144i | −1.20302 | + | 1.58486i | ||||
\(283\) | −2.54009 | + | 1.46652i | −0.150993 | + | 0.0871758i | −0.573593 | − | 0.819140i | \(-0.694451\pi\) |
0.422600 | + | 0.906316i | \(0.361118\pi\) | |||||||
\(284\) | 6.01460 | + | 10.4176i | 0.356901 | + | 0.618171i | ||||
\(285\) | 2.31783 | − | 18.3452i | 0.137297 | − | 1.08668i | ||||
\(286\) | −18.2283 | + | 19.2857i | −1.07786 | + | 1.14038i | ||||
\(287\) | − | 8.11069i | − | 0.478759i | ||||||
\(288\) | −20.1679 | + | 5.63029i | −1.18841 | + | 0.331768i | ||||
\(289\) | 6.09841 | + | 10.5628i | 0.358730 | + | 0.621339i | ||||
\(290\) | 26.2221 | + | 15.1393i | 1.53981 | + | 0.889012i | ||||
\(291\) | 32.6501 | + | 4.12519i | 1.91398 | + | 0.241823i | ||||
\(292\) | −3.41856 | + | 5.92112i | −0.200056 | + | 0.346507i | ||||
\(293\) | 2.52360 | + | 1.45700i | 0.147430 | + | 0.0851190i | 0.571901 | − | 0.820323i | \(-0.306206\pi\) |
−0.424470 | + | 0.905442i | \(0.639540\pi\) | |||||||
\(294\) | 23.2087 | + | 2.93231i | 1.35356 | + | 0.171016i | ||||
\(295\) | 2.18389 | − | 3.78261i | 0.127151 | − | 0.220232i | ||||
\(296\) | −4.56153 | − | 7.90080i | −0.265134 | − | 0.459225i | ||||
\(297\) | 6.66130 | − | 15.8942i | 0.386528 | − | 0.922278i | ||||
\(298\) | −11.9658 | −0.693163 | ||||||||
\(299\) | 16.4865 | − | 18.1505i | 0.953442 | − | 1.04967i | ||||
\(300\) | 0.706168 | − | 5.58918i | 0.0407706 | − | 0.322691i | ||||
\(301\) | 3.73764 | − | 2.15793i | 0.215434 | − | 0.124381i | ||||
\(302\) | 37.9275 | − | 21.8974i | 2.18248 | − | 1.26006i | ||||
\(303\) | −9.83890 | − | 7.46838i | −0.565230 | − | 0.429047i | ||||
\(304\) | −7.01793 | −0.402506 | ||||||||
\(305\) | −16.6423 | − | 9.60844i | −0.952936 | − | 0.550178i | ||||
\(306\) | 10.4241 | + | 10.2087i | 0.595909 | + | 0.583594i | ||||
\(307\) | 19.3061 | 1.10186 | 0.550928 | − | 0.834553i | \(-0.314274\pi\) | ||||
0.550928 | + | 0.834553i | \(0.314274\pi\) | |||||||
\(308\) | 4.47597 | + | 8.12023i | 0.255042 | + | 0.462693i | ||||
\(309\) | −3.59649 | + | 1.51176i | −0.204597 | + | 0.0860009i | ||||
\(310\) | 20.6891 | + | 35.8346i | 1.17506 | + | 2.03527i | ||||
\(311\) | 34.2031i | 1.93948i | 0.244138 | + | 0.969741i | \(0.421495\pi\) | ||||
−0.244138 | + | 0.969741i | \(0.578505\pi\) | |||||||
\(312\) | 8.32953 | + | 9.73560i | 0.471567 | + | 0.551170i | ||||
\(313\) | 32.2284 | 1.82166 | 0.910828 | − | 0.412786i | \(-0.135444\pi\) | ||||
0.910828 | + | 0.412786i | \(0.135444\pi\) | |||||||
\(314\) | −29.4509 | + | 17.0035i | −1.66201 | + | 0.959562i | ||||
\(315\) | −1.52046 | − | 5.44635i | −0.0856682 | − | 0.306867i | ||||
\(316\) | −20.6726 | − | 11.9353i | −1.16292 | − | 0.671414i | ||||
\(317\) | −16.4465 | −0.923728 | −0.461864 | − | 0.886951i | \(-0.652819\pi\) | ||||
−0.461864 | + | 0.886951i | \(0.652819\pi\) | |||||||
\(318\) | −1.18507 | − | 0.899546i | −0.0664553 | − | 0.0504440i | ||||
\(319\) | 11.0791 | + | 20.0995i | 0.620310 | + | 1.12536i | ||||
\(320\) | 25.4288 | 1.42151 | ||||||||
\(321\) | 2.47351 | + | 1.87756i | 0.138058 | + | 0.104795i | ||||
\(322\) | −7.21330 | − | 12.4938i | −0.401982 | − | 0.696253i | ||||
\(323\) | 5.93310 | + | 10.2764i | 0.330126 | + | 0.571795i | ||||
\(324\) | −23.0643 | − | 12.6816i | −1.28135 | − | 0.704534i | ||||
\(325\) | 3.81907 | − | 1.22252i | 0.211844 | − | 0.0678133i | ||||
\(326\) | 19.3286 | 1.07051 | ||||||||
\(327\) | 8.40519 | − | 3.53306i | 0.464808 | − | 0.195379i | ||||
\(328\) | 8.70375 | + | 15.0753i | 0.480584 | + | 0.832396i | ||||
\(329\) | −4.15502 | + | 7.19670i | −0.229074 | + | 0.396767i | ||||
\(330\) | −15.5913 | + | 19.7160i | −0.858275 | + | 1.08533i | ||||
\(331\) | 18.1116 | + | 10.4568i | 0.995506 | + | 0.574756i | 0.906916 | − | 0.421313i | \(-0.138430\pi\) |
0.0885904 | + | 0.996068i | \(0.471764\pi\) | |||||||
\(332\) | 7.05148 | + | 4.07117i | 0.387000 | + | 0.223435i | ||||
\(333\) | −3.31794 | + | 12.9208i | −0.181822 | + | 0.708057i | ||||
\(334\) | 13.6915 | − | 23.7144i | 0.749165 | − | 1.29759i | ||||
\(335\) | −17.9075 | + | 10.3389i | −0.978389 | + | 0.564873i | ||||
\(336\) | −1.97842 | + | 0.831615i | −0.107932 | + | 0.0453683i | ||||
\(337\) | − | 24.0626i | − | 1.31077i | −0.755293 | − | 0.655387i | \(-0.772505\pi\) | ||
0.755293 | − | 0.655387i | \(-0.227495\pi\) | |||||||
\(338\) | −11.9630 | + | 26.2513i | −0.650703 | + | 1.42788i | ||||
\(339\) | −21.7203 | − | 2.74426i | −1.17968 | − | 0.149048i | ||||
\(340\) | −6.31895 | − | 10.9447i | −0.342693 | − | 0.593562i | ||||
\(341\) | −0.621753 | + | 31.3579i | −0.0336698 | + | 1.69812i | ||||
\(342\) | −25.7527 | − | 25.2205i | −1.39255 | − | 1.36377i | ||||
\(343\) | 12.5095 | 0.675450 | ||||||||
\(344\) | −4.63143 | + | 8.02188i | −0.249710 | + | 0.432511i | ||||
\(345\) | 14.0425 | − | 18.4998i | 0.756025 | − | 0.995994i | ||||
\(346\) | − | 46.5600i | − | 2.50308i | ||||||
\(347\) | −3.14172 | + | 5.44163i | −0.168657 | + | 0.292122i | −0.937948 | − | 0.346777i | \(-0.887276\pi\) |
0.769291 | + | 0.638898i | \(0.220610\pi\) | |||||||
\(348\) | 32.3137 | − | 13.5828i | 1.73220 | − | 0.728116i | ||||
\(349\) | 7.28946 | + | 12.6257i | 0.390196 | + | 0.675839i | 0.992475 | − | 0.122446i | \(-0.0390740\pi\) |
−0.602279 | + | 0.798285i | \(0.705741\pi\) | |||||||
\(350\) | − | 2.35928i | − | 0.126109i | ||||||
\(351\) | 1.25873 | − | 18.6927i | 0.0671860 | − | 0.997740i | ||||
\(352\) | 19.8142 | + | 11.9696i | 1.05610 | + | 0.637984i | ||||
\(353\) | 9.02808 | + | 15.6371i | 0.480516 | + | 0.832278i | 0.999750 | − | 0.0223539i | \(-0.00711608\pi\) |
−0.519234 | + | 0.854632i | \(0.673783\pi\) | |||||||
\(354\) | −3.29931 | − | 7.84909i | −0.175356 | − | 0.417174i | ||||
\(355\) | −4.05512 | + | 7.02368i | −0.215224 | + | 0.372778i | ||||
\(356\) | −16.5706 | −0.878240 | ||||||||
\(357\) | 2.89034 | + | 2.19396i | 0.152973 | + | 0.116117i | ||||
\(358\) | −2.28579 | + | 3.95910i | −0.120808 | + | 0.209245i | ||||
\(359\) | − | 18.9379i | − | 0.999504i | −0.866169 | − | 0.499752i | \(-0.833425\pi\) | ||
0.866169 | − | 0.499752i | \(-0.166575\pi\) | |||||||
\(360\) | 8.67066 | + | 8.49148i | 0.456984 | + | 0.447540i | ||||
\(361\) | −5.15763 | − | 8.93327i | −0.271454 | − | 0.470172i | ||||
\(362\) | 2.56614 | − | 1.48156i | 0.134873 | − | 0.0778691i | ||||
\(363\) | −17.8428 | + | 6.68085i | −0.936505 | + | 0.350654i | ||||
\(364\) | 7.46135 | + | 6.77732i | 0.391081 | + | 0.355228i | ||||
\(365\) | −4.60967 | −0.241281 | ||||||||
\(366\) | −34.5336 | + | 14.5159i | −1.80510 | + | 0.758760i | ||||
\(367\) | 2.20927 | + | 3.82658i | 0.115323 | + | 0.199746i | 0.917909 | − | 0.396791i | \(-0.129876\pi\) |
−0.802586 | + | 0.596537i | \(0.796543\pi\) | |||||||
\(368\) | −7.63393 | − | 4.40745i | −0.397946 | − | 0.229754i | ||||
\(369\) | 6.33089 | − | 24.6539i | 0.329573 | − | 1.28343i | ||||
\(370\) | 9.72841 | − | 16.8501i | 0.505756 | − | 0.875995i | ||||
\(371\) | −0.320450 | − | 0.185012i | −0.0166370 | − | 0.00960535i | ||||
\(372\) | 47.5241 | + | 6.00446i | 2.46401 | + | 0.311317i | ||||
\(373\) | 29.9388 | + | 17.2852i | 1.55017 | + | 0.894993i | 0.998127 | + | 0.0611798i | \(0.0194863\pi\) |
0.552047 | + | 0.833813i | \(0.313847\pi\) | |||||||
\(374\) | 0.319764 | − | 16.1272i | 0.0165346 | − | 0.833916i | ||||
\(375\) | 19.2433 | − | 8.08877i | 0.993718 | − | 0.417702i | ||||
\(376\) | − | 17.8353i | − | 0.919787i | ||||||
\(377\) | 18.4686 | + | 16.7755i | 0.951182 | + | 0.863982i | ||||
\(378\) | −10.2485 | − | 4.05825i | −0.527127 | − | 0.208734i | ||||
\(379\) | −12.3499 | + | 7.13023i | −0.634373 | + | 0.366255i | −0.782444 | − | 0.622721i | \(-0.786027\pi\) |
0.148071 | + | 0.988977i | \(0.452694\pi\) | |||||||
\(380\) | 15.6109 | + | 27.0388i | 0.800821 | + | 1.38706i | ||||
\(381\) | −10.4033 | + | 13.7054i | −0.532977 | + | 0.702149i | ||||
\(382\) | −20.2557 | −1.03637 | ||||||||
\(383\) | 17.9515 | − | 31.0929i | 0.917277 | − | 1.58877i | 0.113744 | − | 0.993510i | \(-0.463716\pi\) |
0.803533 | − | 0.595260i | \(-0.202951\pi\) | |||||||
\(384\) | 15.3518 | − | 20.2246i | 0.783418 | − | 1.03208i | ||||
\(385\) | −3.23241 | + | 5.35084i | −0.164739 | + | 0.272704i | ||||
\(386\) | −24.3031 | − | 14.0314i | −1.23700 | − | 0.714180i | ||||
\(387\) | 13.0456 | − | 3.64196i | 0.663146 | − | 0.185131i | ||||
\(388\) | −48.1226 | + | 27.7836i | −2.44306 | + | 1.41050i | ||||
\(389\) | 19.2009i | 0.973524i | 0.873535 | + | 0.486762i | \(0.161822\pi\) | ||||
−0.873535 | + | 0.486762i | \(0.838178\pi\) | |||||||
\(390\) | −9.09922 | + | 25.7660i | −0.460757 | + | 1.30471i | ||||
\(391\) | 14.9046i | 0.753756i | ||||||||
\(392\) | −10.8139 | + | 6.24340i | −0.546184 | + | 0.315339i | ||||
\(393\) | −5.94040 | + | 2.49700i | −0.299654 | + | 0.125957i | ||||
\(394\) | −22.8106 | + | 39.5091i | −1.14918 | + | 1.99044i | ||||
\(395\) | − | 16.0939i | − | 0.809772i | ||||||
\(396\) | 7.26720 | + | 28.1767i | 0.365190 | + | 1.41593i | ||||
\(397\) | 7.80104 | + | 4.50393i | 0.391523 | + | 0.226046i | 0.682820 | − | 0.730587i | \(-0.260753\pi\) |
−0.291297 | + | 0.956633i | \(0.594087\pi\) | |||||||
\(398\) | − | 14.8974i | − | 0.746740i | ||||||
\(399\) | −7.14054 | − | 5.42014i | −0.357474 | − | 0.271347i | ||||
\(400\) | −0.720779 | − | 1.24843i | −0.0360390 | − | 0.0624213i | ||||
\(401\) | −15.8865 | − | 27.5163i | −0.793336 | − | 1.37410i | −0.923890 | − | 0.382658i | \(-0.875009\pi\) |
0.130554 | − | 0.991441i | \(-0.458324\pi\) | |||||||
\(402\) | −5.05258 | + | 39.9902i | −0.252000 | + | 1.99453i | ||||
\(403\) | 10.3949 | + | 32.4731i | 0.517809 | + | 1.61760i | ||||
\(404\) | 20.8567 | 1.03766 | ||||||||
\(405\) | −0.370510 | − | 17.7420i | −0.0184108 | − | 0.881605i | ||||
\(406\) | 12.7128 | − | 7.33972i | 0.630924 | − | 0.364264i | ||||
\(407\) | 12.9158 | − | 7.11934i | 0.640211 | − | 0.352892i | ||||
\(408\) | −7.72665 | − | 0.976228i | −0.382526 | − | 0.0483305i | ||||
\(409\) | −4.32366 | + | 7.48880i | −0.213791 | + | 0.370297i | −0.952898 | − | 0.303291i | \(-0.901915\pi\) |
0.739107 | + | 0.673588i | \(0.235248\pi\) | |||||||
\(410\) | −18.5625 | + | 32.1513i | −0.916739 | + | 1.58784i | ||||
\(411\) | −1.99940 | + | 15.8249i | −0.0986233 | + | 0.780584i | ||||
\(412\) | 3.29364 | − | 5.70475i | 0.162266 | − | 0.281053i | ||||
\(413\) | −1.05877 | − | 1.83385i | −0.0520989 | − | 0.0902379i | ||||
\(414\) | −12.1740 | − | 43.6076i | −0.598318 | − | 2.14320i | ||||
\(415\) | 5.48968i | 0.269478i | ||||||||
\(416\) | 24.5927 | + | 5.33943i | 1.20575 | + | 0.261787i | ||||
\(417\) | −3.03517 | − | 0.383481i | −0.148633 | − | 0.0187791i | ||||
\(418\) | −0.789972 | + | 39.8419i | −0.0386388 | + | 1.94873i | ||||
\(419\) | −4.33374 | + | 2.50209i | −0.211717 | + | 0.122235i | −0.602109 | − | 0.798414i | \(-0.705673\pi\) |
0.390392 | + | 0.920649i | \(0.372339\pi\) | |||||||
\(420\) | 7.60492 | + | 5.77264i | 0.371082 | + | 0.281676i | ||||
\(421\) | 6.12367i | 0.298450i | 0.988803 | + | 0.149225i | \(0.0476778\pi\) | ||||
−0.988803 | + | 0.149225i | \(0.952322\pi\) | |||||||
\(422\) | −10.5166 | + | 18.2153i | −0.511941 | + | 0.886708i | ||||
\(423\) | −18.2474 | + | 18.6324i | −0.887219 | + | 0.905940i | ||||
\(424\) | 0.794161 | 0.0385679 | ||||||||
\(425\) | −1.21872 | + | 2.11089i | −0.0591167 | + | 0.102393i | ||||
\(426\) | 6.12627 | + | 14.5745i | 0.296819 | + | 0.706136i | ||||
\(427\) | −8.06838 | + | 4.65828i | −0.390456 | + | 0.225430i | ||||
\(428\) | −5.24341 | −0.253450 | ||||||||
\(429\) | −16.0020 | + | 13.1505i | −0.772583 | + | 0.634913i | ||||
\(430\) | −19.7550 | −0.952670 | ||||||||
\(431\) | −23.9044 | + | 13.8012i | −1.15144 | + | 0.664782i | −0.949237 | − | 0.314563i | \(-0.898142\pi\) |
−0.202199 | + | 0.979344i | \(0.564809\pi\) | |||||||
\(432\) | −6.66290 | + | 0.983566i | −0.320569 | + | 0.0473218i | ||||
\(433\) | −5.09682 | + | 8.82795i | −0.244938 | + | 0.424244i | −0.962114 | − | 0.272647i | \(-0.912101\pi\) |
0.717176 | + | 0.696892i | \(0.245434\pi\) | |||||||
\(434\) | 20.0606 | 0.962942 | ||||||||
\(435\) | 18.8240 | + | 14.2887i | 0.902541 | + | 0.685089i | ||||
\(436\) | −7.69740 | + | 13.3323i | −0.368638 | + | 0.638501i | ||||
\(437\) | − | 36.8215i | − | 1.76141i | ||||||
\(438\) | −5.43295 | + | 7.15742i | −0.259597 | + | 0.341995i | ||||
\(439\) | −29.8701 | + | 17.2455i | −1.42562 | + | 0.823083i | −0.996771 | − | 0.0802924i | \(-0.974415\pi\) |
−0.428850 | + | 0.903376i | \(0.641081\pi\) | |||||||
\(440\) | 0.265975 | − | 13.4144i | 0.0126799 | − | 0.639504i | ||||
\(441\) | 17.6848 | + | 4.54129i | 0.842134 | + | 0.216252i | ||||
\(442\) | −5.34606 | − | 16.7007i | −0.254286 | − | 0.794372i | ||||
\(443\) | − | 31.8029i | − | 1.51100i | −0.655148 | − | 0.755501i | \(-0.727394\pi\) | ||
0.655148 | − | 0.755501i | \(-0.272606\pi\) | |||||||
\(444\) | −8.72821 | − | 20.7645i | −0.414223 | − | 0.985441i | ||||
\(445\) | −5.58606 | − | 9.67533i | −0.264804 | − | 0.458655i | ||||
\(446\) | 0.393817 | − | 0.682111i | 0.0186478 | − | 0.0322989i | ||||
\(447\) | −9.26579 | − | 1.17069i | −0.438257 | − | 0.0553718i | ||||
\(448\) | 6.16408 | − | 10.6765i | 0.291225 | − | 0.504417i | ||||
\(449\) | 6.75458 | − | 11.6993i | 0.318768 | − | 0.552123i | −0.661463 | − | 0.749978i | \(-0.730064\pi\) |
0.980231 | + | 0.197855i | \(0.0633975\pi\) | |||||||
\(450\) | 1.84156 | − | 7.17145i | 0.0868119 | − | 0.338065i | ||||
\(451\) | −24.6443 | + | 13.5842i | −1.16045 | + | 0.639657i | ||||
\(452\) | 32.0134 | − | 18.4829i | 1.50578 | − | 0.869364i | ||||
\(453\) | 31.5116 | − | 13.2457i | 1.48055 | − | 0.622336i | ||||
\(454\) | 48.0362 | 2.25445 | ||||||||
\(455\) | −1.44191 | + | 6.64125i | −0.0675980 | + | 0.311347i | ||||
\(456\) | 19.0886 | + | 2.41176i | 0.893905 | + | 0.112941i | ||||
\(457\) | −12.3507 | − | 21.3920i | −0.577741 | − | 1.00068i | −0.995738 | − | 0.0922285i | \(-0.970601\pi\) |
0.417997 | − | 0.908449i | \(-0.362732\pi\) | |||||||
\(458\) | −5.94960 | − | 10.3050i | −0.278006 | − | 0.481521i | ||||
\(459\) | 7.07319 | + | 8.92502i | 0.330148 | + | 0.416584i | ||||
\(460\) | 39.2162i | 1.82846i | ||||||||
\(461\) | 2.65199 | + | 1.53112i | 0.123515 | + | 0.0713116i | 0.560485 | − | 0.828165i | \(-0.310615\pi\) |
−0.436969 | + | 0.899476i | \(0.643948\pi\) | |||||||
\(462\) | 4.49851 | + | 11.3254i | 0.209290 | + | 0.526907i | ||||
\(463\) | − | 15.9359i | − | 0.740602i | −0.928912 | − | 0.370301i | \(-0.879255\pi\) | ||
0.928912 | − | 0.370301i | \(-0.120745\pi\) | |||||||
\(464\) | 4.48469 | − | 7.76772i | 0.208197 | − | 0.360607i | ||||
\(465\) | 12.5148 | + | 29.7728i | 0.580358 | + | 1.38068i | ||||
\(466\) | 2.00268 | − | 1.15625i | 0.0927724 | − | 0.0535622i | ||||
\(467\) | − | 38.5307i | − | 1.78299i | −0.453032 | − | 0.891494i | \(-0.649658\pi\) | ||
0.453032 | − | 0.891494i | \(-0.350342\pi\) | |||||||
\(468\) | 17.3900 | + | 26.4249i | 0.803853 | + | 1.22149i | ||||
\(469\) | 10.0248i | 0.462903i | ||||||||
\(470\) | 32.9415 | − | 19.0188i | 1.51948 | − | 0.877271i | ||||
\(471\) | −24.4690 | + | 10.2853i | −1.12747 | + | 0.473924i | ||||
\(472\) | 3.93588 | + | 2.27238i | 0.181164 | + | 0.104595i | ||||
\(473\) | −12.8169 | − | 7.74258i | −0.589320 | − | 0.356004i | ||||
\(474\) | −24.9889 | − | 18.9683i | −1.14778 | − | 0.871241i | ||||
\(475\) | 3.01083 | − | 5.21492i | 0.138146 | − | 0.239277i | ||||
\(476\) | −6.12700 | −0.280831 | ||||||||
\(477\) | −0.829653 | − | 0.812508i | −0.0379872 | − | 0.0372022i | ||||
\(478\) | −13.3757 | − | 23.1673i | −0.611789 | − | 1.05965i | ||||
\(479\) | 35.0623 | − | 20.2432i | 1.60204 | − | 0.924938i | 0.610960 | − | 0.791662i | \(-0.290784\pi\) |
0.991079 | − | 0.133276i | \(-0.0425497\pi\) | |||||||
\(480\) | 23.6489 | + | 2.98794i | 1.07942 | + | 0.136380i | ||||
\(481\) | 10.7798 | − | 11.8678i | 0.491516 | − | 0.541124i | ||||
\(482\) | − | 30.7281i | − | 1.39963i | ||||||
\(483\) | −4.36330 | − | 10.3803i | −0.198537 | − | 0.472322i | ||||
\(484\) | 17.1767 | − | 27.2004i | 0.780757 | − | 1.23638i | ||||
\(485\) | −32.4449 | − | 18.7321i | −1.47325 | − | 0.850580i | ||||
\(486\) | −27.9845 | − | 20.3354i | −1.26940 | − | 0.922431i | ||||
\(487\) | 23.3931 | + | 13.5060i | 1.06004 | + | 0.612015i | 0.925444 | − | 0.378886i | \(-0.123693\pi\) |
0.134597 | + | 0.990900i | \(0.457026\pi\) | |||||||
\(488\) | 9.99779 | − | 17.3167i | 0.452579 | − | 0.783890i | ||||
\(489\) | 14.9671 | + | 1.89103i | 0.676837 | + | 0.0855154i | ||||
\(490\) | −23.0628 | − | 13.3153i | −1.04187 | − | 0.601526i | ||||
\(491\) | 7.35437 | + | 12.7381i | 0.331898 | + | 0.574864i | 0.982884 | − | 0.184226i | \(-0.0589777\pi\) |
−0.650986 | + | 0.759090i | \(0.725644\pi\) | |||||||
\(492\) | 16.6541 | + | 39.6203i | 0.750825 | + | 1.78622i | ||||
\(493\) | −15.1658 | −0.683032 | ||||||||
\(494\) | 13.2074 | + | 41.2589i | 0.594227 | + | 1.85633i | ||||
\(495\) | −14.0021 | + | 13.7418i | −0.629349 | + | 0.617646i | ||||
\(496\) | 10.6152 | − | 6.12870i | 0.476637 | − | 0.275187i | ||||
\(497\) | 1.96597 | + | 3.40516i | 0.0881859 | + | 0.152742i | ||||
\(498\) | 8.52380 | + | 6.47013i | 0.381960 | + | 0.289933i | ||||
\(499\) | − | 34.8438i | − | 1.55982i | −0.625889 | − | 0.779912i | \(-0.715264\pi\) | ||
0.625889 | − | 0.779912i | \(-0.284736\pi\) | |||||||
\(500\) | −17.6228 | + | 30.5236i | −0.788117 | + | 1.36506i | ||||
\(501\) | 12.9222 | − | 17.0238i | 0.577320 | − | 0.760566i | ||||
\(502\) | −19.8874 | −0.887618 | ||||||||
\(503\) | −3.73934 | + | 6.47672i | −0.166729 | + | 0.288783i | −0.937268 | − | 0.348610i | \(-0.886654\pi\) |
0.770539 | + | 0.637393i | \(0.219987\pi\) | |||||||
\(504\) | 5.66704 | − | 1.58207i | 0.252430 | − | 0.0704711i | ||||
\(505\) | 7.03093 | + | 12.1779i | 0.312872 | + | 0.541911i | ||||
\(506\) | −25.8811 | + | 42.8429i | −1.15056 | + | 1.90460i | ||||
\(507\) | −11.8319 | + | 19.1574i | −0.525474 | + | 0.850809i | ||||
\(508\) | − | 29.0530i | − | 1.28902i | ||||||
\(509\) | −10.6676 | − | 18.4769i | −0.472835 | − | 0.818974i | 0.526682 | − | 0.850062i | \(-0.323436\pi\) |
−0.999517 | + | 0.0310888i | \(0.990103\pi\) | |||||||
\(510\) | −6.43627 | − | 15.3120i | −0.285003 | − | 0.678025i | ||||
\(511\) | −1.11741 | + | 1.93541i | −0.0494314 | + | 0.0856176i | ||||
\(512\) | − | 14.3655i | − | 0.634870i | ||||||
\(513\) | −17.4742 | − | 22.0491i | −0.771505 | − | 0.973493i | ||||
\(514\) | 10.2375 | − | 17.7318i | 0.451555 | − | 0.782116i | ||||
\(515\) | 4.44123 | 0.195704 | ||||||||
\(516\) | −13.8272 | + | 18.2161i | −0.608708 | + | 0.801917i | ||||
\(517\) | 28.8262 | + | 0.571556i | 1.26777 | + | 0.0251370i | ||||
\(518\) | −4.71645 | − | 8.16912i | −0.207229 | − | 0.358931i | ||||
\(519\) | 4.55525 | − | 36.0539i | 0.199953 | − | 1.58259i | ||||
\(520\) | −4.44678 | − | 13.8914i | −0.195004 | − | 0.609180i | ||||
\(521\) | 0.873932i | 0.0382877i | 0.999817 | + | 0.0191438i | \(0.00609404\pi\) | ||||
−0.999817 | + | 0.0191438i | \(0.993906\pi\) | |||||||
\(522\) | 44.3718 | − | 12.3873i | 1.94210 | − | 0.542178i | ||||
\(523\) | 0.174774 | − | 0.100906i | 0.00764234 | − | 0.00441231i | −0.496174 | − | 0.868223i | \(-0.665262\pi\) |
0.503816 | + | 0.863811i | \(0.331929\pi\) | |||||||
\(524\) | 5.44017 | − | 9.42265i | 0.237655 | − | 0.411630i | ||||
\(525\) | 0.230823 | − | 1.82691i | 0.0100739 | − | 0.0797331i | ||||
\(526\) | 21.4730 | + | 12.3975i | 0.936269 | + | 0.540555i | ||||
\(527\) | −17.9486 | − | 10.3626i | −0.781854 | − | 0.451403i | ||||
\(528\) | 5.84043 | + | 4.61859i | 0.254172 | + | 0.200998i | ||||
\(529\) | 11.6249 | − | 20.1349i | 0.505430 | − | 0.875430i | ||||
\(530\) | 0.846856 | + | 1.46680i | 0.0367851 | + | 0.0637136i | ||||
\(531\) | −1.78690 | − | 6.40076i | −0.0775450 | − | 0.277769i | ||||
\(532\) | 15.1367 | 0.656258 | ||||||||
\(533\) | −20.5687 | + | 22.6446i | −0.890928 | + | 0.980848i | ||||
\(534\) | −21.6066 | − | 2.72989i | −0.935007 | − | 0.118134i | ||||
\(535\) | −1.76759 | − | 3.06155i | −0.0764194 | − | 0.132362i | ||||
\(536\) | −10.7578 | − | 18.6331i | −0.464667 | − | 0.804827i | ||||
\(537\) | −2.15735 | + | 2.84211i | −0.0930966 | + | 0.122646i | ||||
\(538\) | 39.6093 | 1.70768 | ||||||||
\(539\) | −9.74429 | − | 17.6779i | −0.419716 | − | 0.761441i | ||||
\(540\) | 18.6106 | + | 23.4831i | 0.800874 | + | 1.01055i | ||||
\(541\) | −21.2779 | −0.914810 | −0.457405 | − | 0.889259i | \(-0.651221\pi\) | ||||
−0.457405 | + | 0.889259i | \(0.651221\pi\) | |||||||
\(542\) | 3.80416 | + | 2.19633i | 0.163403 | + | 0.0943407i | ||||
\(543\) | 2.13205 | − | 0.896190i | 0.0914949 | − | 0.0384592i | ||||
\(544\) | −13.2474 | + | 7.64840i | −0.567978 | + | 0.327922i | ||||
\(545\) | −10.3794 | −0.444604 | ||||||||
\(546\) | 8.61241 | + | 10.0662i | 0.368577 | + | 0.430795i | ||||
\(547\) | − | 44.8648i | − | 1.91828i | −0.282933 | − | 0.959140i | \(-0.591307\pi\) | ||
0.282933 | − | 0.959140i | \(-0.408693\pi\) | |||||||
\(548\) | −13.4662 | − | 23.3242i | −0.575248 | − | 0.996359i | ||||
\(549\) | −28.1614 | + | 7.86183i | −1.20190 | + | 0.335535i | ||||
\(550\) | −7.16865 | + | 3.95145i | −0.305672 | + | 0.168490i | ||||
\(551\) | 37.4668 | 1.59614 | ||||||||
\(552\) | 19.2494 | + | 14.6116i | 0.819309 | + | 0.621910i | ||||
\(553\) | −6.75717 | − | 3.90125i | −0.287344 | − | 0.165898i | ||||
\(554\) | 50.9110 | 2.16300 | ||||||||
\(555\) | 9.18177 | − | 12.0961i | 0.389745 | − | 0.513453i | ||||
\(556\) | 4.47352 | − | 2.58279i | 0.189719 | − | 0.109535i | ||||
\(557\) | −36.5225 | + | 21.0863i | −1.54751 | + | 0.893453i | −0.549175 | + | 0.835707i | \(0.685058\pi\) |
−0.998331 | + | 0.0577463i | \(0.981609\pi\) | |||||||
\(558\) | 60.9779 | + | 15.6585i | 2.58140 | + | 0.662879i | ||||
\(559\) | −15.9078 | − | 3.45381i | −0.672828 | − | 0.146081i | ||||
\(560\) | 2.44311 | 0.103240 | ||||||||
\(561\) | 1.82543 | − | 12.4568i | 0.0770697 | − | 0.525928i | ||||
\(562\) | −18.4224 | − | 31.9086i | −0.777102 | − | 1.34598i | ||||
\(563\) | −5.60831 | + | 9.71388i | −0.236362 | + | 0.409391i | −0.959668 | − | 0.281137i | \(-0.909289\pi\) |
0.723305 | + | 0.690528i | \(0.242622\pi\) | |||||||
\(564\) | 5.51969 | − | 43.6872i | 0.232421 | − | 1.83956i | ||||
\(565\) | 21.5838 | + | 12.4614i | 0.908039 | + | 0.524256i | ||||
\(566\) | 3.25441 | − | 5.63680i | 0.136793 | − | 0.236932i | ||||
\(567\) | −7.53894 | − | 4.14519i | −0.316606 | − | 0.174082i | ||||
\(568\) | −7.30830 | − | 4.21945i | −0.306649 | − | 0.177044i | ||||
\(569\) | −17.6304 | − | 30.5367i | −0.739103 | − | 1.28016i | −0.952900 | − | 0.303286i | \(-0.901916\pi\) |
0.213797 | − | 0.976878i | \(-0.431417\pi\) | |||||||
\(570\) | 15.9007 | + | 37.8280i | 0.666007 | + | 1.58444i | ||||
\(571\) | − | 10.3174i | − | 0.431769i | −0.976419 | − | 0.215884i | \(-0.930737\pi\) | ||
0.976419 | − | 0.215884i | \(-0.0692634\pi\) | |||||||
\(572\) | 8.09617 | − | 34.0223i | 0.338518 | − | 1.42254i | ||||
\(573\) | −15.6851 | − | 1.98174i | −0.655254 | − | 0.0827885i | ||||
\(574\) | 8.99934 | + | 15.5873i | 0.375625 | + | 0.650602i | ||||
\(575\) | 6.55021 | − | 3.78177i | 0.273163 | − | 0.157711i | ||||
\(576\) | 27.0705 | − | 27.6417i | 1.12794 | − | 1.15174i | ||||
\(577\) | − | 39.9664i | − | 1.66382i | −0.554907 | − | 0.831912i | \(-0.687246\pi\) | ||
0.554907 | − | 0.831912i | \(-0.312754\pi\) | |||||||
\(578\) | −23.4401 | − | 13.5332i | −0.974980 | − | 0.562905i | ||||
\(579\) | −17.4464 | − | 13.2430i | −0.725048 | − | 0.550360i | ||||
\(580\) | −39.9035 | −1.65690 | ||||||||
\(581\) | 2.30489 | + | 1.33073i | 0.0956230 | + | 0.0552080i | ||||
\(582\) | −67.3248 | + | 28.2995i | −2.79070 | + | 1.17305i | ||||
\(583\) | −0.0254499 | + | 1.28355i | −0.00105403 | + | 0.0531594i | ||||
\(584\) | − | 4.79647i | − | 0.198479i | ||||||
\(585\) | −9.56686 | + | 19.0618i | −0.395541 | + | 0.788108i | ||||
\(586\) | −6.46655 | −0.267131 | ||||||||
\(587\) | 9.99810 | + | 17.3172i | 0.412666 | + | 0.714758i | 0.995180 | − | 0.0980623i | \(-0.0312644\pi\) |
−0.582515 | + | 0.812820i | \(0.697931\pi\) | |||||||
\(588\) | −28.4205 | + | 11.9464i | −1.17204 | + | 0.492660i | ||||
\(589\) | 44.3418 | + | 25.6007i | 1.82707 | + | 1.05486i | ||||
\(590\) | 9.69266i | 0.399041i | ||||||||
\(591\) | −21.5289 | + | 28.3623i | −0.885579 | + | 1.16667i | ||||
\(592\) | −4.99147 | − | 2.88183i | −0.205148 | − | 0.118442i | ||||
\(593\) | 44.2238i | 1.81605i | 0.418913 | + | 0.908026i | \(0.362411\pi\) | ||||
−0.418913 | + | 0.908026i | \(0.637589\pi\) | |||||||
\(594\) | 4.83385 | + | 37.9371i | 0.198335 | + | 1.55658i | ||||
\(595\) | −2.06545 | − | 3.57747i | −0.0846753 | − | 0.146662i | ||||
\(596\) | 13.6568 | − | 7.88474i | 0.559403 | − | 0.322971i | ||||
\(597\) | 1.45750 | − | 11.5359i | 0.0596517 | − | 0.472131i | ||||
\(598\) | −11.5451 | + | 53.1749i | −0.472113 | + | 2.17448i | ||||
\(599\) | − | 9.30853i | − | 0.380336i | −0.981752 | − | 0.190168i | \(-0.939097\pi\) | ||
0.981752 | − | 0.190168i | \(-0.0609033\pi\) | |||||||
\(600\) | 1.53147 | + | 3.64338i | 0.0625220 | + | 0.148741i | ||||
\(601\) | 11.2432 | − | 6.49125i | 0.458619 | − | 0.264784i | −0.252844 | − | 0.967507i | \(-0.581366\pi\) |
0.711463 | + | 0.702723i | \(0.248033\pi\) | |||||||
\(602\) | −4.78872 | + | 8.29431i | −0.195174 | + | 0.338051i | ||||
\(603\) | −7.82497 | + | 30.4722i | −0.318657 | + | 1.24092i | ||||
\(604\) | −28.8581 | + | 49.9837i | −1.17422 | + | 2.03381i | ||||
\(605\) | 21.6723 | + | 0.859759i | 0.881104 | + | 0.0349542i | ||||
\(606\) | 27.1953 | + | 3.43600i | 1.10473 | + | 0.139578i | ||||
\(607\) | 23.9591 | + | 13.8328i | 0.972470 | + | 0.561456i | 0.899988 | − | 0.435914i | \(-0.143575\pi\) |
0.0724818 | + | 0.997370i | \(0.476908\pi\) | |||||||
\(608\) | 32.7276 | − | 18.8953i | 1.32728 | − | 0.766304i | ||||
\(609\) | 10.5623 | − | 4.43977i | 0.428005 | − | 0.179909i | ||||
\(610\) | 42.6447 | 1.72664 | ||||||||
\(611\) | 29.8514 | − | 9.55571i | 1.20766 | − | 0.386583i | ||||
\(612\) | −18.6241 | − | 4.78249i | −0.752835 | − | 0.193321i | ||||
\(613\) | 0.701404 | + | 1.21487i | 0.0283295 | + | 0.0490681i | 0.879843 | − | 0.475265i | \(-0.157648\pi\) |
−0.851513 | + | 0.524333i | \(0.824315\pi\) | |||||||
\(614\) | −37.1028 | + | 21.4213i | −1.49735 | + | 0.864494i | ||||
\(615\) | −17.5195 | + | 23.0804i | −0.706455 | + | 0.930690i | ||||
\(616\) | −5.56767 | − | 3.36339i | −0.224328 | − | 0.135515i | ||||
\(617\) | −12.0256 | + | 20.8289i | −0.484132 | + | 0.838541i | −0.999834 | − | 0.0182270i | \(-0.994198\pi\) |
0.515702 | + | 0.856768i | \(0.327531\pi\) | |||||||
\(618\) | 5.23442 | − | 6.89587i | 0.210559 | − | 0.277393i | ||||
\(619\) | 27.0977i | 1.08915i | 0.838713 | + | 0.544574i | \(0.183309\pi\) | ||||
−0.838713 | + | 0.544574i | \(0.816691\pi\) | |||||||
\(620\) | −47.2255 | − | 27.2657i | −1.89662 | − | 1.09502i | ||||
\(621\) | −5.16055 | − | 34.9587i | −0.207086 | − | 1.40285i | ||||
\(622\) | −37.9506 | − | 65.7323i | −1.52168 | − | 2.63563i | ||||
\(623\) | −5.41637 | −0.217002 | ||||||||
\(624\) | 7.63262 | + | 2.69544i | 0.305549 | + | 0.107904i | ||||
\(625\) | −18.2023 | −0.728090 | ||||||||
\(626\) | −61.9372 | + | 35.7595i | −2.47551 | + | 1.42924i | ||||
\(627\) | −4.50970 | + | 30.7744i | −0.180100 | + | 1.22901i | ||||
\(628\) | 22.4085 | − | 38.8126i | 0.894195 | − | 1.54879i | ||||
\(629\) | 9.74541i | 0.388575i | ||||||||
\(630\) | 8.96513 | + | 8.77986i | 0.357179 | + | 0.349798i | ||||
\(631\) | −28.2667 | − | 16.3198i | −1.12528 | − | 0.649681i | −0.182537 | − | 0.983199i | \(-0.558431\pi\) |
−0.942744 | + | 0.333517i | \(0.891764\pi\) | |||||||
\(632\) | 16.7461 | 0.666122 | ||||||||
\(633\) | −9.92569 | + | 13.0762i | −0.394511 | + | 0.519732i | ||||
\(634\) | 31.6073 | − | 18.2485i | 1.25528 | − | 0.724739i | ||||
\(635\) | 16.9636 | − | 9.79395i | 0.673181 | − | 0.388661i | ||||
\(636\) | 1.94528 | + | 0.245777i | 0.0771353 | + | 0.00974570i | ||||
\(637\) | −16.2435 | − | 14.7544i | −0.643591 | − | 0.584590i | ||||
\(638\) | −43.5937 | − | 26.3347i | −1.72589 | − | 1.04260i | ||||
\(639\) | 3.31799 | + | 11.8852i | 0.131258 | + | 0.470170i | ||||
\(640\) | −25.0326 | + | 14.4526i | −0.989501 | + | 0.571289i | ||||
\(641\) | −21.8328 | − | 12.6052i | −0.862345 | − | 0.497875i | 0.00245202 | − | 0.999997i | \(-0.499219\pi\) |
−0.864797 | + | 0.502122i | \(0.832553\pi\) | |||||||
\(642\) | −6.83693 | − | 0.863816i | −0.269832 | − | 0.0340921i | ||||
\(643\) | 0.598409 | + | 0.345491i | 0.0235989 | + | 0.0136249i | 0.511753 | − | 0.859133i | \(-0.328996\pi\) |
−0.488154 | + | 0.872757i | \(0.662330\pi\) | |||||||
\(644\) | 16.4653 | + | 9.50623i | 0.648822 | + | 0.374598i | ||||
\(645\) | −15.2973 | − | 1.93275i | −0.602332 | − | 0.0761020i | ||||
\(646\) | −22.8047 | − | 13.1663i | −0.897239 | − | 0.518021i | ||||
\(647\) | −1.37109 | + | 0.791601i | −0.0539032 | + | 0.0311211i | −0.526709 | − | 0.850045i | \(-0.676574\pi\) |
0.472806 | + | 0.881166i | \(0.343241\pi\) | |||||||
\(648\) | 18.4609 | − | 0.385524i | 0.725213 | − | 0.0151448i | ||||
\(649\) | −3.79885 | + | 6.28851i | −0.149118 | + | 0.246846i | ||||
\(650\) | −5.98311 | + | 6.58698i | −0.234677 | + | 0.258363i | ||||
\(651\) | 15.5340 | + | 1.96266i | 0.608826 | + | 0.0769225i | ||||
\(652\) | −22.0599 | + | 12.7363i | −0.863934 | + | 0.498793i | ||||
\(653\) | −3.20106 | + | 1.84813i | −0.125267 | + | 0.0723230i | −0.561324 | − | 0.827596i | \(-0.689708\pi\) |
0.436057 | + | 0.899919i | \(0.356375\pi\) | |||||||
\(654\) | −12.2331 | + | 16.1160i | −0.478353 | + | 0.630186i | ||||
\(655\) | 7.33567 | 0.286628 | ||||||||
\(656\) | 9.52411 | + | 5.49875i | 0.371854 | + | 0.214690i | ||||
\(657\) | −4.90728 | + | 5.01083i | −0.191451 | + | 0.195491i | ||||
\(658\) | − | 18.4410i | − | 0.718907i | ||||||
\(659\) | −7.75247 | + | 13.4277i | −0.301993 | + | 0.523068i | −0.976587 | − | 0.215121i | \(-0.930985\pi\) |
0.674594 | + | 0.738189i | \(0.264319\pi\) | |||||||
\(660\) | 4.80298 | − | 32.7758i | 0.186956 | − | 1.27580i | ||||
\(661\) | −0.385420 | + | 0.222522i | −0.0149911 | + | 0.00865512i | −0.507477 | − | 0.861665i | \(-0.669422\pi\) |
0.492486 | + | 0.870321i | \(0.336088\pi\) | |||||||
\(662\) | −46.4098 | −1.80377 | ||||||||
\(663\) | −2.50581 | − | 13.4553i | −0.0973174 | − | 0.522560i | ||||
\(664\) | −5.71213 | −0.221674 | ||||||||
\(665\) | 5.10267 | + | 8.83808i | 0.197873 | + | 0.342726i | ||||
\(666\) | −7.95999 | − | 28.5130i | −0.308443 | − | 1.10486i | ||||
\(667\) | 40.7555 | + | 23.5302i | 1.57806 | + | 0.911092i | ||||
\(668\) | 36.0873i | 1.39626i | ||||||||
\(669\) | 0.371688 | − | 0.489665i | 0.0143703 | − | 0.0189316i | ||||
\(670\) | 22.9433 | − | 39.7390i | 0.886377 | − | 1.53525i | ||||
\(671\) | 27.6675 | + | 16.7138i | 1.06809 | + | 0.645228i | ||||
\(672\) | 6.98715 | − | 9.20493i | 0.269535 | − | 0.355088i | ||||
\(673\) | −40.4168 | + | 23.3347i | −1.55795 | + | 0.899485i | −0.560501 | + | 0.828154i | \(0.689391\pi\) |
−0.997453 | + | 0.0713312i | \(0.977275\pi\) | |||||||
\(674\) | 26.6990 | + | 46.2441i | 1.02841 | + | 1.78126i | ||||
\(675\) | 2.12764 | − | 5.37306i | 0.0818930 | − | 0.206809i | ||||
\(676\) | −3.64443 | − | 37.8439i | −0.140170 | − | 1.45553i | ||||
\(677\) | −18.6397 | −0.716382 | −0.358191 | − | 0.933648i | \(-0.616606\pi\) | ||||
−0.358191 | + | 0.933648i | \(0.616606\pi\) | |||||||
\(678\) | 44.7875 | − | 18.8261i | 1.72005 | − | 0.723011i | ||||
\(679\) | −15.7297 | + | 9.08153i | −0.603649 | + | 0.348517i | ||||
\(680\) | 7.67811 | + | 4.43296i | 0.294442 | + | 0.169996i | ||||
\(681\) | 37.1970 | + | 4.69968i | 1.42539 | + | 0.180092i | ||||
\(682\) | −33.5987 | − | 60.9541i | −1.28656 | − | 2.33405i | ||||
\(683\) | −15.0046 | + | 25.9887i | −0.574133 | + | 0.994428i | 0.422002 | + | 0.906595i | \(0.361328\pi\) |
−0.996135 | + | 0.0878331i | \(0.972006\pi\) | |||||||
\(684\) | 46.0106 | + | 11.8151i | 1.75926 | + | 0.451761i | ||||
\(685\) | 9.07910 | − | 15.7255i | 0.346894 | − | 0.600839i | ||||
\(686\) | −24.0410 | + | 13.8801i | −0.917891 | + | 0.529945i | ||||
\(687\) | −3.59889 | − | 8.56180i | −0.137306 | − | 0.326653i | ||||
\(688\) | 5.85198i | 0.223105i | ||||||||
\(689\) | 0.425491 | + | 1.32920i | 0.0162099 | + | 0.0506386i | ||||
\(690\) | −6.46060 | + | 51.1344i | −0.245951 | + | 1.94665i | ||||
\(691\) | 6.97257 | − | 4.02561i | 0.265249 | − | 0.153142i | −0.361478 | − | 0.932381i | \(-0.617728\pi\) |
0.626727 | + | 0.779239i | \(0.284394\pi\) | |||||||
\(692\) | 30.6801 | + | 53.1396i | 1.16628 | + | 2.02006i | ||||
\(693\) | 2.37540 | + | 9.21000i | 0.0902340 | + | 0.349859i | ||||
\(694\) | − | 13.9438i | − | 0.529299i | ||||||
\(695\) | 3.01610 | + | 1.74135i | 0.114407 | + | 0.0660531i | ||||
\(696\) | −14.8677 | + | 19.5868i | −0.563557 | + | 0.742435i | ||||
\(697\) | − | 18.5950i | − | 0.704335i | ||||||
\(698\) | −28.0181 | − | 16.1762i | −1.06050 | − | 0.612280i | ||||
\(699\) | 1.66391 | − | 0.699410i | 0.0629347 | − | 0.0264541i | ||||
\(700\) | 1.55462 | + | 2.69267i | 0.0587590 | + | 0.101774i | ||||
\(701\) | 24.7407 | 0.934442 | 0.467221 | − | 0.884141i | \(-0.345255\pi\) | ||||
0.467221 | + | 0.884141i | \(0.345255\pi\) | |||||||
\(702\) | 18.3217 | + | 37.3206i | 0.691506 | + | 1.40858i | ||||
\(703\) | − | 24.0759i | − | 0.908039i | ||||||
\(704\) | −42.7644 | − | 0.847917i | −1.61174 | − | 0.0319571i | ||||
\(705\) | 27.3691 | − | 11.5044i | 1.03078 | − | 0.433280i | ||||
\(706\) | −34.7007 | − | 20.0345i | −1.30598 | − | 0.754007i | ||||
\(707\) | 6.81735 | 0.256393 | ||||||||
\(708\) | 8.93760 | + | 6.78423i | 0.335895 | + | 0.254967i | ||||
\(709\) | −0.770952 | − | 0.445109i | −0.0289537 | − | 0.0167164i | 0.485453 | − | 0.874263i | \(-0.338655\pi\) |
−0.514407 | + | 0.857546i | \(0.671988\pi\) | |||||||
\(710\) | − | 17.9977i | − | 0.675441i | ||||||
\(711\) | −17.4945 | − | 17.1329i | −0.656094 | − | 0.642536i | ||||
\(712\) | 10.0674 | − | 5.81241i | 0.377292 | − | 0.217829i | ||||
\(713\) | 32.1559 | + | 55.6956i | 1.20425 | + | 2.08582i | ||||
\(714\) | −7.98906 | − | 1.00938i | −0.298983 | − | 0.0377752i | ||||
\(715\) | 22.5944 | − | 6.74190i | 0.844983 | − | 0.252133i | ||||
\(716\) | − | 6.02477i | − | 0.225156i | ||||||
\(717\) | −8.09089 | − | 19.2483i | −0.302160 | − | 0.718842i | ||||
\(718\) | 21.0128 | + | 36.3953i | 0.784191 | + | 1.35826i | ||||
\(719\) | −32.6474 | − | 18.8490i | −1.21754 | − | 0.702948i | −0.253151 | − | 0.967427i | \(-0.581467\pi\) |
−0.964392 | + | 0.264478i | \(0.914800\pi\) | |||||||
\(720\) | 7.42627 | + | 1.90699i | 0.276761 | + | 0.0710695i | ||||
\(721\) | 1.07658 | − | 1.86469i | 0.0400939 | − | 0.0694447i | ||||
\(722\) | 19.8241 | + | 11.4454i | 0.737776 | + | 0.425955i | ||||
\(723\) | 3.00631 | − | 23.7944i | 0.111806 | − | 0.884922i | ||||
\(724\) | −1.95251 | + | 3.38185i | −0.0725645 | + | 0.125685i | ||||
\(725\) | 3.84804 | + | 6.66501i | 0.142913 | + | 0.247532i | ||||
\(726\) | 26.8779 | − | 32.6372i | 0.997532 | − | 1.21128i | ||||
\(727\) | −12.5075 | −0.463877 | −0.231938 | − | 0.972730i | \(-0.574507\pi\) | ||||
−0.231938 | + | 0.972730i | \(0.574507\pi\) | |||||||
\(728\) | −6.91037 | − | 1.50034i | −0.256115 | − | 0.0556064i | ||||
\(729\) | −19.6804 | − | 18.4847i | −0.728903 | − | 0.684617i | ||||
\(730\) | 8.85897 | − | 5.11473i | 0.327885 | − | 0.189305i | ||||
\(731\) | 8.56910 | − | 4.94737i | 0.316940 | − | 0.182985i | ||||
\(732\) | 29.8485 | − | 39.3227i | 1.10323 | − | 1.45341i | ||||
\(733\) | −28.5101 | −1.05304 | −0.526522 | − | 0.850161i | \(-0.676504\pi\) | ||||
−0.526522 | + | 0.850161i | \(0.676504\pi\) | |||||||
\(734\) | −8.49166 | − | 4.90266i | −0.313433 | − | 0.180961i | ||||
\(735\) | −16.5561 | − | 12.5672i | −0.610680 | − | 0.463546i | ||||
\(736\) | 47.4669 | 1.74965 | ||||||||
\(737\) | 30.4603 | − | 16.7901i | 1.12202 | − | 0.618472i | ||||
\(738\) | 15.1883 | + | 54.4050i | 0.559088 | + | 2.00267i | ||||
\(739\) | 14.3761 | + | 24.9002i | 0.528835 | + | 0.915968i | 0.999435 | + | 0.0336218i | \(0.0107042\pi\) |
−0.470600 | + | 0.882347i | \(0.655963\pi\) | |||||||
\(740\) | 25.6416i | 0.942606i | ||||||||
\(741\) | 6.19056 | + | 33.2411i | 0.227416 | + | 1.22114i | ||||
\(742\) | 0.821131 | 0.0301447 | ||||||||
\(743\) | 22.6209 | − | 13.0602i | 0.829879 | − | 0.479131i | −0.0239320 | − | 0.999714i | \(-0.507619\pi\) |
0.853811 | + | 0.520583i | \(0.174285\pi\) | |||||||
\(744\) | −30.9792 | + | 13.0219i | −1.13575 | + | 0.477406i | ||||
\(745\) | 9.20757 | + | 5.31599i | 0.337339 | + | 0.194763i | ||||
\(746\) | −76.7161 | −2.80878 | ||||||||
\(747\) | 5.96742 | + | 5.84410i | 0.218336 | + | 0.213824i | ||||
\(748\) | 10.2618 | + | 18.6168i | 0.375210 | + | 0.680699i | ||||
\(749\) | −1.71389 | −0.0626243 | ||||||||
\(750\) | −28.0071 | + | 36.8968i | −1.02268 | + | 1.34728i | ||||
\(751\) | −10.9343 | − | 18.9388i | −0.398999 | − | 0.691086i | 0.594604 | − | 0.804019i | \(-0.297309\pi\) |
−0.993603 | + | 0.112933i | \(0.963976\pi\) | |||||||
\(752\) | −5.63389 | − | 9.75819i | −0.205447 | − | 0.355845i | ||||
\(753\) | −15.3999 | − | 1.94571i | −0.561202 | − | 0.0709054i | ||||
\(754\) | −54.1069 | − | 11.7474i | −1.97046 | − | 0.427815i | ||||
\(755\) | −38.9130 | −1.41619 | ||||||||
\(756\) | 14.3709 | − | 2.12141i | 0.522665 | − | 0.0771549i | ||||
\(757\) | 9.56102 | + | 16.5602i | 0.347501 | + | 0.601890i | 0.985805 | − | 0.167895i | \(-0.0536969\pi\) |
−0.638304 | + | 0.769785i | \(0.720364\pi\) | |||||||
\(758\) | 15.8229 | − | 27.4061i | 0.574714 | − | 0.995433i | ||||
\(759\) | −24.2327 | + | 30.6434i | −0.879591 | + | 1.11229i | ||||
\(760\) | −18.9686 | − | 10.9516i | −0.688065 | − | 0.397255i | ||||
\(761\) | 27.6886 | + | 15.9860i | 1.00371 | + | 0.579493i | 0.909344 | − | 0.416045i | \(-0.136584\pi\) |
0.0943666 | + | 0.995538i | \(0.469917\pi\) | |||||||
\(762\) | 4.78628 | − | 37.8825i | 0.173389 | − | 1.37234i | ||||
\(763\) | −2.51602 | + | 4.35787i | −0.0910860 | + | 0.157766i | ||||
\(764\) | 23.1181 | − | 13.3473i | 0.836385 | − | 0.482887i | ||||
\(765\) | −3.48588 | − | 12.4866i | −0.126032 | − | 0.451453i | ||||
\(766\) | 79.6732i | 2.87871i | ||||||||
\(767\) | −1.69459 | + | 7.80506i | −0.0611882 | + | 0.281824i | ||||
\(768\) | −1.46301 | + | 11.5794i | −0.0527919 | + | 0.417837i | ||||
\(769\) | −18.2288 | − | 31.5733i | −0.657349 | − | 1.13856i | −0.981299 | − | 0.192488i | \(-0.938344\pi\) |
0.323950 | − | 0.946074i | \(-0.394989\pi\) | |||||||
\(770\) | 0.275008 | − | 13.8699i | 0.00991060 | − | 0.499837i | ||||
\(771\) | 9.66222 | − | 12.7291i | 0.347976 | − | 0.458427i | ||||
\(772\) | 36.9833 | 1.33106 | ||||||||
\(773\) | 10.1061 | − | 17.5043i | 0.363492 | − | 0.629587i | −0.625041 | − | 0.780592i | \(-0.714918\pi\) |
0.988533 | + | 0.151005i | \(0.0482510\pi\) | |||||||
\(774\) | −21.0304 | + | 21.4742i | −0.755922 | + | 0.771873i | ||||
\(775\) | 10.5173i | 0.377794i | ||||||||
\(776\) | 19.4911 | − | 33.7597i | 0.699691 | − | 1.21190i | ||||
\(777\) | −2.85296 | − | 6.78722i | −0.102349 | − | 0.243490i | ||||
\(778\) | −21.3046 | − | 36.9007i | −0.763808 | − | 1.32295i | ||||
\(779\) | 45.9386i | 1.64592i | ||||||||
\(780\) | −6.59315 | − | 35.4029i | −0.236073 | − | 1.26763i | ||||
\(781\) | 7.05384 | − | 11.6767i | 0.252406 | − | 0.417827i | ||||
\(782\) | −16.5376 | − | 28.6439i | −0.591383 | − | 1.02430i | ||||
\(783\) | 35.5714 | − | 5.25099i | 1.27122 | − | 0.187655i | ||||
\(784\) | −3.94438 | + | 6.83186i | −0.140871 | + | 0.243995i | ||||
\(785\) | 30.2162 | 1.07846 | ||||||||
\(786\) | 8.64581 | − | 11.3901i | 0.308386 | − | 0.406270i | ||||
\(787\) | 5.32454 | − | 9.22237i | 0.189799 | − | 0.328742i | −0.755384 | − | 0.655282i | \(-0.772550\pi\) |
0.945183 | + | 0.326540i | \(0.105883\pi\) | |||||||
\(788\) | − | 60.1229i | − | 2.14179i | ||||||
\(789\) | 15.4148 | + | 11.7009i | 0.548782 | + | 0.416562i | ||||
\(790\) | 17.8572 | + | 30.9296i | 0.635331 | + | 1.10043i | ||||
\(791\) | 10.4641 | − | 6.04144i | 0.372060 | − | 0.214809i | ||||
\(792\) | −14.2986 | − | 14.5695i | −0.508078 | − | 0.517706i | ||||
\(793\) | 34.3399 | + | 7.45569i | 1.21944 | + | 0.264759i | ||||
\(794\) | −19.9896 | −0.709405 | ||||||||
\(795\) | 0.512260 | + | 1.21867i | 0.0181680 | + | 0.0432219i | ||||
\(796\) | 9.81646 | + | 17.0026i | 0.347935 | + | 0.602641i | ||||
\(797\) | −26.3888 | − | 15.2356i | −0.934739 | − | 0.539672i | −0.0464317 | − | 0.998921i | \(-0.514785\pi\) |
−0.888307 | + | 0.459250i | \(0.848118\pi\) | |||||||
\(798\) | 19.7368 | + | 2.49366i | 0.698677 | + | 0.0882747i | ||||
\(799\) | −9.52601 | + | 16.4995i | −0.337006 | + | 0.583711i | ||||
\(800\) | 6.72259 | + | 3.88129i | 0.237679 | + | 0.137224i | ||||
\(801\) | −16.4640 | − | 4.22780i | −0.581728 | − | 0.149382i | ||||
\(802\) | 61.0622 | + | 35.2543i | 2.15618 | + | 1.24487i | ||||
\(803\) | 7.75224 | + | 0.153709i | 0.273571 | + | 0.00542426i | ||||
\(804\) | −20.5845 | − | 48.9707i | −0.725958 | − | 1.72706i | ||||
\(805\) | 12.8184i | 0.451791i | ||||||||
\(806\) | −56.0083 | − | 50.8737i | −1.97281 | − | 1.79195i | ||||
\(807\) | 30.6716 | + | 3.87522i | 1.07969 | + | 0.136414i | ||||
\(808\) | −12.6714 | + | 7.31584i | −0.445779 | + | 0.257370i | ||||
\(809\) | 8.54272 | + | 14.7964i | 0.300346 | + | 0.520215i | 0.976214 | − | 0.216808i | \(-0.0695645\pi\) |
−0.675868 | + | 0.737022i | \(0.736231\pi\) | |||||||
\(810\) | 20.3979 | + | 33.6858i | 0.716709 | + | 1.18360i | ||||
\(811\) | 24.3459 | 0.854901 | 0.427450 | − | 0.904039i | \(-0.359412\pi\) | ||||
0.427450 | + | 0.904039i | \(0.359412\pi\) | |||||||
\(812\) | −9.67283 | + | 16.7538i | −0.339450 | + | 0.587944i | ||||
\(813\) | 2.73089 | + | 2.07292i | 0.0957763 | + | 0.0727006i | ||||
\(814\) | −16.9225 | + | 28.0130i | −0.593132 | + | 0.981855i | ||||
\(815\) | −14.8731 | − | 8.58699i | −0.520982 | − | 0.300789i | ||||
\(816\) | −4.53583 | + | 1.90660i | −0.158786 | + | 0.0667445i | ||||
\(817\) | −21.1698 | + | 12.2224i | −0.740639 | + | 0.427608i | ||||
\(818\) | − | 19.1895i | − | 0.670945i | ||||||
\(819\) | 5.68420 | + | 8.63742i | 0.198622 | + | 0.301816i | ||||
\(820\) | − | 48.9262i | − | 1.70858i | ||||||
\(821\) | 4.76317 | − | 2.75002i | 0.166236 | − | 0.0959763i | −0.414574 | − | 0.910016i | \(-0.636069\pi\) |
0.580810 | + | 0.814039i | \(0.302736\pi\) | |||||||
\(822\) | −13.7162 | − | 32.6311i | −0.478408 | − | 1.13814i | ||||
\(823\) | 19.6095 | − | 33.9646i | 0.683543 | − | 1.18393i | −0.290349 | − | 0.956921i | \(-0.593771\pi\) |
0.973892 | − | 0.227011i | \(-0.0728953\pi\) | |||||||
\(824\) | 4.62119i | 0.160987i | ||||||||
\(825\) | −5.93766 | + | 2.35847i | −0.206723 | + | 0.0821112i | ||||
\(826\) | 4.06955 | + | 2.34956i | 0.141598 | + | 0.0817515i | ||||
\(827\) | 3.99661i | 0.138976i | 0.997583 | + | 0.0694879i | \(0.0221365\pi\) | ||||
−0.997583 | + | 0.0694879i | \(0.977863\pi\) | |||||||
\(828\) | 42.6290 | + | 41.7480i | 1.48146 | + | 1.45084i | ||||
\(829\) | −10.0608 | − | 17.4258i | −0.349426 | − | 0.605223i | 0.636722 | − | 0.771094i | \(-0.280290\pi\) |
−0.986148 | + | 0.165870i | \(0.946957\pi\) | |||||||
\(830\) | −6.09115 | − | 10.5502i | −0.211427 | − | 0.366202i | ||||
\(831\) | 39.4231 | + | 4.98093i | 1.36757 | + | 0.172787i | ||||
\(832\) | −44.2853 | + | 14.1761i | −1.53532 | + | 0.491469i | ||||
\(833\) | 13.3386 | 0.462155 | ||||||||
\(834\) | 6.25856 | − | 2.63074i | 0.216716 | − | 0.0910950i | ||||
\(835\) | −21.0709 | + | 12.1653i | −0.729188 | + | 0.420997i | ||||
\(836\) | −25.3517 | − | 45.9926i | −0.876808 | − | 1.59069i | ||||
\(837\) | 45.6865 | + | 18.0911i | 1.57916 | + | 0.625319i | ||||
\(838\) | 5.55246 | − | 9.61714i | 0.191806 | − | 0.332218i | ||||
\(839\) | 6.49242 | − | 11.2452i | 0.224143 | − | 0.388228i | −0.731919 | − | 0.681392i | \(-0.761375\pi\) |
0.956062 | + | 0.293164i | \(0.0947083\pi\) | |||||||
\(840\) | −6.64519 | − | 0.839590i | −0.229281 | − | 0.0289686i | ||||
\(841\) | −9.44255 | + | 16.3550i | −0.325605 | + | 0.563965i | ||||
\(842\) | −6.79461 | − | 11.7686i | −0.234158 | − | 0.405573i | ||||
\(843\) | −11.1436 | − | 26.5109i | −0.383808 | − | 0.913083i | ||||
\(844\) | − | 27.7192i | − | 0.954133i | ||||||
\(845\) | 20.8679 | − | 14.8853i | 0.717879 | − | 0.512071i | ||||
\(846\) | 14.3944 | − | 56.0549i | 0.494888 | − | 1.92721i | ||||
\(847\) | 5.61447 | − | 8.89090i | 0.192915 | − | 0.305495i | ||||
\(848\) | 0.434507 | − | 0.250863i | 0.0149210 | − | 0.00861465i | ||||
\(849\) | 3.07154 | − | 4.04647i | 0.105415 | − | 0.138875i | ||||
\(850\) | − | 5.40900i | − | 0.185527i | ||||||
\(851\) | 15.1203 | − | 26.1891i | 0.518317 | − | 0.897752i | ||||
\(852\) | −16.5957 | − | 12.5972i | −0.568558 | − | 0.431573i | ||||
\(853\) | −29.8292 | −1.02133 | −0.510666 | − | 0.859779i | \(-0.670601\pi\) | ||||
−0.510666 | + | 0.859779i | \(0.670601\pi\) | |||||||
\(854\) | 10.3373 | − | 17.9048i | 0.353736 | − | 0.612689i | ||||
\(855\) | 8.61182 | + | 30.8479i | 0.294518 | + | 1.05498i | ||||
\(856\) | 3.18561 | − | 1.83921i | 0.108882 | − | 0.0628630i | ||||
\(857\) | 7.98798 | 0.272864 | 0.136432 | − | 0.990649i | \(-0.456436\pi\) | ||||
0.136432 | + | 0.990649i | \(0.456436\pi\) | |||||||
\(858\) | 16.1616 | − | 43.0282i | 0.551749 | − | 1.46896i | ||||
\(859\) | −17.7875 | −0.606900 | −0.303450 | − | 0.952847i | \(-0.598139\pi\) | ||||
−0.303450 | + | 0.952847i | \(0.598139\pi\) | |||||||
\(860\) | 22.5466 | − | 13.0173i | 0.768833 | − | 0.443886i | ||||
\(861\) | 5.44366 | + | 12.9505i | 0.185520 | + | 0.441353i | ||||
\(862\) | 30.6267 | − | 53.0470i | 1.04315 | − | 1.80679i | ||||
\(863\) | 31.1502 | 1.06037 | 0.530183 | − | 0.847883i | \(-0.322123\pi\) | ||||
0.530183 | + | 0.847883i | \(0.322123\pi\) | |||||||
\(864\) | 28.4237 | − | 22.5261i | 0.966994 | − | 0.766355i | ||||
\(865\) | −20.6850 | + | 35.8274i | −0.703310 | + | 1.21817i | ||||
\(866\) | − | 22.6210i | − | 0.768693i | ||||||
\(867\) | −16.8269 | − | 12.7727i | −0.571471 | − | 0.433785i | ||||
\(868\) | −22.8955 | + | 13.2187i | −0.777123 | + | 0.448672i | ||||
\(869\) | −0.536648 | + | 27.0657i | −0.0182045 | + | 0.918139i | ||||
\(870\) | −52.0305 | − | 6.57383i | −1.76400 | − | 0.222874i | ||||
\(871\) | 25.4229 | − | 27.9887i | 0.861421 | − | 0.948362i | ||||
\(872\) | − | 10.8000i | − | 0.365733i | ||||||
\(873\) | −54.9018 | + | 15.3270i | −1.85815 | + | 0.518740i | ||||
\(874\) | 40.8558 | + | 70.7644i | 1.38197 | + | 2.39364i | ||||
\(875\) | −5.76031 | + | 9.97715i | −0.194734 | + | 0.337289i | ||||
\(876\) | 1.48441 | − | 11.7488i | 0.0501536 | − | 0.396956i | ||||
\(877\) | 11.2319 | − | 19.4542i | 0.379274 | − | 0.656922i | −0.611683 | − | 0.791103i | \(-0.709507\pi\) |
0.990957 | + | 0.134181i | \(0.0428405\pi\) | |||||||
\(878\) | 38.2700 | − | 66.2856i | 1.29155 | − | 2.23703i | ||||
\(879\) | −5.00740 | − | 0.632662i | −0.168895 | − | 0.0213392i | ||||
\(880\) | −4.09186 | − | 7.42337i | −0.137936 | − | 0.250242i | ||||
\(881\) | −4.24725 | + | 2.45215i | −0.143094 | + | 0.0826151i | −0.569838 | − | 0.821757i | \(-0.692994\pi\) |
0.426744 | + | 0.904372i | \(0.359661\pi\) | |||||||
\(882\) | −39.0259 | + | 10.8949i | −1.31407 | + | 0.366850i | ||||
\(883\) | −8.70611 | −0.292984 | −0.146492 | − | 0.989212i | \(-0.546798\pi\) | ||||
−0.146492 | + | 0.989212i | \(0.546798\pi\) | |||||||
\(884\) | 17.1063 | + | 15.5380i | 0.575346 | + | 0.522601i | ||||
\(885\) | −0.948292 | + | 7.50554i | −0.0318765 | + | 0.252296i | ||||
\(886\) | 35.2874 | + | 61.1195i | 1.18550 | + | 2.05335i | ||||
\(887\) | −7.63792 | − | 13.2293i | −0.256456 | − | 0.444195i | 0.708834 | − | 0.705376i | \(-0.249222\pi\) |
−0.965290 | + | 0.261180i | \(0.915888\pi\) | |||||||
\(888\) | 12.5863 | + | 9.55384i | 0.422369 | + | 0.320606i | ||||
\(889\) | − | 9.49644i | − | 0.318500i | ||||||
\(890\) | 21.4708 | + | 12.3962i | 0.719703 | + | 0.415521i | ||||
\(891\) | 0.0314971 | + | 29.8496i | 0.00105519 | + | 0.999999i | ||||
\(892\) | 1.03800i | 0.0347549i | ||||||||
\(893\) | 23.5339 | − | 40.7618i | 0.787531 | − | 1.36404i | ||||
\(894\) | 19.1062 | − | 8.03113i | 0.639005 | − | 0.268601i | ||||
\(895\) | 3.51778 | − | 2.03099i | 0.117586 | − | 0.0678885i | ||||
\(896\) | 14.0136i | 0.468160i | ||||||||
\(897\) | −14.1424 | + | 40.0467i | −0.472200 | + | 1.33712i | ||||
\(898\) | 29.9786i | 1.00040i | ||||||||
\(899\) | −56.6717 | + | 32.7194i | −1.89011 | + | 1.09125i | ||||
\(900\) | 2.62374 | + | 9.39834i | 0.0874580 | + | 0.313278i | ||||
\(901\) | −0.734680 | − | 0.424168i | −0.0244758 | − | 0.0141311i | ||||
\(902\) | 32.2893 | − | 53.4509i | 1.07512 | − | 1.77972i | ||||
\(903\) | −4.51964 | + | 5.95421i | −0.150404 | + | 0.198144i | ||||
\(904\) | −12.9664 | + | 22.4585i | −0.431256 | + | 0.746957i | ||||
\(905\) | −2.63282 | −0.0875178 | ||||||||
\(906\) | −45.8628 | + | 60.4200i | −1.52369 | + | 2.00732i | ||||
\(907\) | 11.9712 | + | 20.7348i | 0.397499 | + | 0.688488i | 0.993417 | − | 0.114557i | \(-0.0365449\pi\) |
−0.595918 | + | 0.803045i | \(0.703212\pi\) | |||||||
\(908\) | −54.8243 | + | 31.6529i | −1.81941 | + | 1.05044i | ||||
\(909\) | 20.7226 | + | 5.32136i | 0.687324 | + | 0.176498i | ||||
\(910\) | −4.59780 | − | 14.3632i | −0.152416 | − | 0.476136i | ||||
\(911\) | − | 8.04747i | − | 0.266624i | −0.991074 | − | 0.133312i | \(-0.957439\pi\) | ||
0.991074 | − | 0.133312i | \(-0.0425613\pi\) | |||||||
\(912\) | 11.2057 | − | 4.71024i | 0.371058 | − | 0.155971i | ||||
\(913\) | 0.183052 | − | 9.23218i | 0.00605815 | − | 0.305540i | ||||
\(914\) | 47.4717 | + | 27.4078i | 1.57022 | + | 0.906569i | ||||
\(915\) | 33.0221 | + | 4.17219i | 1.09168 | + | 0.137928i | ||||
\(916\) | 13.5807 | + | 7.84082i | 0.448719 | + | 0.259068i | ||||
\(917\) | 1.77821 | − | 3.07995i | 0.0587216 | − | 0.101709i | ||||
\(918\) | −23.4963 | − | 9.30414i | −0.775493 | − | 0.307082i | ||||
\(919\) | −21.0124 | − | 12.1315i | −0.693135 | − | 0.400181i | 0.111651 | − | 0.993748i | \(-0.464386\pi\) |
−0.804785 | + | 0.593566i | \(0.797720\pi\) | |||||||
\(920\) | −13.7557 | − | 23.8256i | −0.453513 | − | 0.785508i | ||||
\(921\) | −30.8265 | + | 12.9577i | −1.01577 | + | 0.426970i | ||||
\(922\) | −6.79553 | −0.223799 | ||||||||
\(923\) | 3.14658 | − | 14.4927i | 0.103571 | − | 0.477034i | ||||
\(924\) | −12.5970 | − | 9.96162i | −0.414410 | − | 0.327713i | ||||
\(925\) | 4.28288 | − | 2.47272i | 0.140820 | − | 0.0813026i | ||||
\(926\) | 17.6819 | + | 30.6259i | 0.581062 | + | 1.00643i | ||||
\(927\) | 4.72796 | − | 4.82772i | 0.155286 | − | 0.158563i | ||||
\(928\) | 48.2988i | 1.58549i | ||||||||
\(929\) | −3.26981 | + | 5.66349i | −0.107279 | + | 0.185813i | −0.914667 | − | 0.404208i | \(-0.867547\pi\) |
0.807388 | + | 0.590021i | \(0.200881\pi\) | |||||||
\(930\) | −57.0860 | − | 43.3320i | −1.87192 | − | 1.42091i | ||||
\(931\) | −32.9528 | −1.07999 | ||||||||
\(932\) | −1.52379 | + | 2.63928i | −0.0499134 | + | 0.0864526i | ||||
\(933\) | −22.9562 | − | 54.6130i | −0.751551 | − | 1.78795i | ||||
\(934\) | 42.7523 | + | 74.0492i | 1.39890 | + | 2.42296i | ||||
\(935\) | −7.41078 | + | 12.2676i | −0.242358 | + | 0.401193i | ||||
\(936\) | −19.8342 | − | 9.95453i | −0.648301 | − | 0.325374i | ||||
\(937\) | 50.8866i | 1.66239i | 0.555979 | + | 0.831196i | \(0.312343\pi\) | ||||
−0.555979 | + | 0.831196i | \(0.687657\pi\) | |||||||
\(938\) | −11.1232 | − | 19.2659i | −0.363185 | − | 0.629054i | ||||
\(939\) | −51.4599 | + | 21.6308i | −1.67933 | + | 0.705893i | ||||
\(940\) | −25.0644 | + | 43.4128i | −0.817509 | + | 1.41597i | ||||
\(941\) | 9.85705i | 0.321331i | 0.987009 | + | 0.160665i | \(0.0513640\pi\) | ||||
−0.987009 | + | 0.160665i | \(0.948636\pi\) | |||||||
\(942\) | 35.6127 | − | 46.9165i | 1.16033 | − | 1.52862i | ||||
\(943\) | −28.8507 | + | 49.9708i | −0.939507 | + | 1.62727i | ||||
\(944\) | 2.87124 | 0.0934508 | ||||||||
\(945\) | 6.08319 | + | 7.67583i | 0.197886 | + | 0.249695i | ||||
\(946\) | 33.2226 | + | 0.658726i | 1.08016 | + | 0.0214170i | ||||
\(947\) | −9.91084 | − | 17.1661i | −0.322059 | − | 0.557823i | 0.658854 | − | 0.752271i | \(-0.271042\pi\) |
−0.980913 | + | 0.194448i | \(0.937708\pi\) | |||||||
\(948\) | 41.0191 | + | 5.18258i | 1.33224 | + | 0.168322i | ||||
\(949\) | 8.02795 | − | 2.56982i | 0.260598 | − | 0.0834200i | ||||
\(950\) | 13.3629i | 0.433548i | ||||||||
\(951\) | 26.2605 | − | 11.0384i | 0.851557 | − | 0.357945i | ||||
\(952\) | 3.72243 | − | 2.14915i | 0.120645 | − | 0.0696543i | ||||
\(953\) | 25.9105 | − | 44.8783i | 0.839324 | − | 1.45375i | −0.0511362 | − | 0.998692i | \(-0.516284\pi\) |
0.890460 | − | 0.455061i | \(-0.150382\pi\) | |||||||
\(954\) | 2.49598 | + | 0.640943i | 0.0808102 | + | 0.0207513i | ||||
\(955\) | 15.5866 | + | 8.99890i | 0.504369 | + | 0.291198i | ||||
\(956\) | 30.5316 | + | 17.6275i | 0.987464 | + | 0.570113i | ||||
\(957\) | −31.1805 | − | 24.6574i | −1.00792 | − | 0.797060i | ||||
\(958\) | −44.9224 | + | 77.8078i | −1.45138 | + | 2.51386i | ||||
\(959\) | −4.40165 | − | 7.62388i | −0.142137 | − | 0.246188i | ||||
\(960\) | −40.6027 | + | 17.0671i | −1.31045 | + | 0.550837i | ||||
\(961\) | −58.4275 | −1.88476 | ||||||||
\(962\) | −7.54878 | + | 34.7686i | −0.243382 | + | 1.12099i | ||||
\(963\) | −5.20969 | − | 1.33780i | −0.167880 | − | 0.0431099i | ||||
\(964\) | 20.2479 | + | 35.0703i | 0.652140 | + | 1.12954i | ||||
\(965\) | 12.4673 | + | 21.5940i | 0.401337 | + | 0.695136i | ||||
\(966\) | 19.9031 | + | 15.1078i | 0.640373 | + | 0.486086i | ||||
\(967\) | −9.43118 | −0.303286 | −0.151643 | − | 0.988435i | \(-0.548456\pi\) | ||||
−0.151643 | + | 0.988435i | \(0.548456\pi\) | |||||||
\(968\) | −0.894599 | + | 22.5505i | −0.0287535 | + | 0.724801i | ||||
\(969\) | −16.3708 | − | 12.4265i | −0.525905 | − | 0.399196i | ||||
\(970\) | 83.1378 | 2.66939 | ||||||||
\(971\) | 34.5687 | + | 19.9583i | 1.10936 | + | 0.640491i | 0.938664 | − | 0.344832i | \(-0.112064\pi\) |
0.170698 | + | 0.985323i | \(0.445398\pi\) | |||||||
\(972\) | 45.3388 | + | 4.76895i | 1.45424 | + | 0.152964i | ||||
\(973\) | 1.46224 | − | 0.844226i | 0.0468773 | − | 0.0270646i | ||||
\(974\) | −59.9431 | −1.92070 | ||||||||
\(975\) | −5.27749 | + | 4.51528i | −0.169015 | + | 0.144605i | ||||
\(976\) | − | 12.6326i | − | 0.404359i | ||||||
\(977\) | −2.95283 | − | 5.11445i | −0.0944694 | − | 0.163626i | 0.814918 | − | 0.579577i | \(-0.196782\pi\) |
−0.909387 | + | 0.415951i | \(0.863449\pi\) | |||||||
\(978\) | −30.8624 | + | 12.9728i | −0.986871 | + | 0.414824i | ||||
\(979\) | 9.07163 | + | 16.4576i | 0.289931 | + | 0.525987i | ||||
\(980\) | 35.0959 | 1.12110 | ||||||||
\(981\) | −11.0495 | + | 11.2826i | −0.352783 | + | 0.360227i | ||||
\(982\) | −28.2676 | − | 16.3203i | −0.902054 | − | 0.520801i | ||||
\(983\) | −11.0187 | −0.351442 | −0.175721 | − | 0.984440i | \(-0.556226\pi\) | ||||
−0.175721 | + | 0.984440i | \(0.556226\pi\) | |||||||
\(984\) | −24.0156 | − | 18.2295i | −0.765590 | − | 0.581134i | ||||
\(985\) | 35.1049 | − | 20.2678i | 1.11854 | − | 0.645787i | ||||
\(986\) | 29.1459 | − | 16.8274i | 0.928195 | − | 0.535894i | ||||
\(987\) | 1.80420 | − | 14.2799i | 0.0574283 | − | 0.454534i | ||||
\(988\) | −42.2608 | − | 38.3865i | −1.34449 | − | 1.22124i | ||||
\(989\) | −30.7040 | −0.976331 | ||||||||
\(990\) | 11.6623 | − | 41.9455i | 0.370651 | − | 1.33311i | ||||
\(991\) | −0.257650 | − | 0.446263i | −0.00818452 | − | 0.0141760i | 0.861904 | − | 0.507071i | \(-0.169272\pi\) |
−0.870089 | + | 0.492895i | \(0.835939\pi\) | |||||||
\(992\) | −33.0021 | + | 57.1613i | −1.04782 | + | 1.81487i | ||||
\(993\) | −35.9376 | − | 4.54055i | −1.14044 | − | 0.144090i | ||||
\(994\) | −7.55649 | − | 4.36274i | −0.239677 | − | 0.138378i | ||||
\(995\) | −6.61839 | + | 11.4634i | −0.209817 | + | 0.363414i | ||||
\(996\) | −13.9917 | − | 1.76779i | −0.443345 | − | 0.0560147i | ||||
\(997\) | 9.52856 | + | 5.50132i | 0.301773 | + | 0.174229i | 0.643239 | − | 0.765665i | \(-0.277590\pi\) |
−0.341466 | + | 0.939894i | \(0.610924\pi\) | |||||||
\(998\) | 38.6615 | + | 66.9636i | 1.22381 | + | 2.11970i | ||||
\(999\) | −3.37424 | − | 22.8579i | −0.106756 | − | 0.723192i |
(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 | 429.2.t.a.296.7 | ✓ | 104 | |
3.2 | odd | 2 | inner | 429.2.t.a.296.46 | yes | 104 | |
11.10 | odd | 2 | inner | 429.2.t.a.296.45 | yes | 104 | |
13.4 | even | 6 | inner | 429.2.t.a.329.8 | yes | 104 | |
33.32 | even | 2 | inner | 429.2.t.a.296.8 | yes | 104 | |
39.17 | odd | 6 | inner | 429.2.t.a.329.45 | yes | 104 | |
143.43 | odd | 6 | inner | 429.2.t.a.329.46 | yes | 104 | |
429.329 | even | 6 | inner | 429.2.t.a.329.7 | yes | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.t.a.296.7 | ✓ | 104 | 1.1 | even | 1 | trivial | |
429.2.t.a.296.8 | yes | 104 | 33.32 | even | 2 | inner | |
429.2.t.a.296.45 | yes | 104 | 11.10 | odd | 2 | inner | |
429.2.t.a.296.46 | yes | 104 | 3.2 | odd | 2 | inner | |
429.2.t.a.329.7 | yes | 104 | 429.329 | even | 6 | inner | |
429.2.t.a.329.8 | yes | 104 | 13.4 | even | 6 | inner | |
429.2.t.a.329.45 | yes | 104 | 39.17 | odd | 6 | inner | |
429.2.t.a.329.46 | yes | 104 | 143.43 | odd | 6 | inner |