Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(31,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.o (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.72208555157\) |
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: | \( x^{16} + 92 x^{14} - 112 x^{13} + 5846 x^{12} - 7728 x^{11} + 197216 x^{10} - 298200 x^{9} + \cdots + 101626561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8}\cdot 7 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 61.2 | ||
Root | \(2.96377 - 5.13339i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 210.61 |
Dual form | 210.3.o.b.31.2 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 1.22474i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | + | 0.866025i | −0.500000 | + | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.93649 | − | 1.11803i | −0.387298 | − | 0.223607i | ||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 5.73733 | − | 4.01037i | 0.819618 | − | 0.572910i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 2.73861 | − | 1.58114i | 0.273861 | − | 0.158114i | ||||
\(11\) | 8.69259 | + | 15.0560i | 0.790236 | + | 1.36873i | 0.925821 | + | 0.377963i | \(0.123375\pi\) |
−0.135585 | + | 0.990766i | \(0.543291\pi\) | |||||||
\(12\) | 3.00000 | + | 1.73205i | 0.250000 | + | 0.144338i | ||||
\(13\) | 7.22559i | 0.555815i | 0.960608 | + | 0.277907i | \(0.0896408\pi\) | ||||
−0.960608 | + | 0.277907i | \(0.910359\pi\) | |||||||
\(14\) | 0.854777 | + | 9.86252i | 0.0610555 | + | 0.704466i | ||||
\(15\) | 3.87298 | 0.258199 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.29669 | + | 1.32600i | −0.135100 | + | 0.0779998i | −0.566027 | − | 0.824387i | \(-0.691520\pi\) |
0.430927 | + | 0.902387i | \(0.358187\pi\) | |||||||
\(18\) | 2.12132 | + | 3.67423i | 0.117851 | + | 0.204124i | ||||
\(19\) | 2.20128 | + | 1.27091i | 0.115857 | + | 0.0668900i | 0.556809 | − | 0.830641i | \(-0.312026\pi\) |
−0.440952 | + | 0.897531i | \(0.645359\pi\) | |||||||
\(20\) | 4.47214i | 0.223607i | ||||||||
\(21\) | −5.13291 | + | 10.9842i | −0.244424 | + | 0.523058i | ||||
\(22\) | −24.5864 | −1.11756 | ||||||||
\(23\) | −20.0507 | + | 34.7289i | −0.871771 | + | 1.50995i | −0.0116074 | + | 0.999933i | \(0.503695\pi\) |
−0.860163 | + | 0.510019i | \(0.829639\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.100000 | + | 0.173205i | ||||
\(26\) | −8.84951 | − | 5.10926i | −0.340366 | − | 0.196510i | ||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | −12.6835 | − | 5.92697i | −0.452982 | − | 0.211678i | ||||
\(29\) | 47.0080 | 1.62096 | 0.810482 | − | 0.585763i | \(-0.199205\pi\) | ||||
0.810482 | + | 0.585763i | \(0.199205\pi\) | |||||||
\(30\) | −2.73861 | + | 4.74342i | −0.0912871 | + | 0.158114i | ||||
\(31\) | 34.9025 | − | 20.1510i | 1.12589 | − | 0.650031i | 0.182990 | − | 0.983115i | \(-0.441422\pi\) |
0.942897 | + | 0.333084i | \(0.108089\pi\) | |||||||
\(32\) | −2.82843 | − | 4.89898i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −26.0778 | − | 15.0560i | −0.790236 | − | 0.456243i | ||||
\(34\) | − | 3.75049i | − | 0.110308i | ||||||
\(35\) | −15.5940 | + | 1.35152i | −0.445543 | + | 0.0386149i | ||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | −16.2514 | + | 28.1482i | −0.439226 | + | 0.760762i | −0.997630 | − | 0.0688071i | \(-0.978081\pi\) |
0.558404 | + | 0.829569i | \(0.311414\pi\) | |||||||
\(38\) | −3.11308 | + | 1.79734i | −0.0819232 | + | 0.0472984i | ||||
\(39\) | −6.25755 | − | 10.8384i | −0.160450 | − | 0.277907i | ||||
\(40\) | −5.47723 | − | 3.16228i | −0.136931 | − | 0.0790569i | ||||
\(41\) | 70.6679i | 1.72361i | 0.507241 | + | 0.861804i | \(0.330665\pi\) | ||||
−0.507241 | + | 0.861804i | \(0.669335\pi\) | |||||||
\(42\) | −9.82336 | − | 14.0535i | −0.233890 | − | 0.334608i | ||||
\(43\) | 37.3732 | 0.869144 | 0.434572 | − | 0.900637i | \(-0.356900\pi\) | ||||
0.434572 | + | 0.900637i | \(0.356900\pi\) | |||||||
\(44\) | 17.3852 | − | 30.1120i | 0.395118 | − | 0.684364i | ||||
\(45\) | −5.80948 | + | 3.35410i | −0.129099 | + | 0.0745356i | ||||
\(46\) | −28.3560 | − | 49.1141i | −0.616435 | − | 1.06770i | ||||
\(47\) | −28.9672 | − | 16.7242i | −0.616324 | − | 0.355835i | 0.159113 | − | 0.987260i | \(-0.449137\pi\) |
−0.775436 | + | 0.631426i | \(0.782470\pi\) | |||||||
\(48\) | − | 6.92820i | − | 0.144338i | ||||||
\(49\) | 16.8339 | − | 46.0176i | 0.343548 | − | 0.939135i | ||||
\(50\) | −7.07107 | −0.141421 | ||||||||
\(51\) | 2.29669 | − | 3.97799i | 0.0450332 | − | 0.0779998i | ||||
\(52\) | 12.5151 | − | 7.22559i | 0.240675 | − | 0.138954i | ||||
\(53\) | 35.4442 | + | 61.3911i | 0.668758 | + | 1.15832i | 0.978252 | + | 0.207422i | \(0.0665073\pi\) |
−0.309493 | + | 0.950902i | \(0.600159\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | − | 38.8745i | − | 0.706808i | ||||||
\(56\) | 16.2276 | − | 11.3430i | 0.289779 | − | 0.202554i | ||||
\(57\) | −4.40256 | −0.0772379 | ||||||||
\(58\) | −33.2397 | + | 57.5728i | −0.573098 | + | 0.992634i | ||||
\(59\) | 87.0863 | − | 50.2793i | 1.47604 | − | 0.852192i | 0.476405 | − | 0.879226i | \(-0.341940\pi\) |
0.999635 | + | 0.0270340i | \(0.00860625\pi\) | |||||||
\(60\) | −3.87298 | − | 6.70820i | −0.0645497 | − | 0.111803i | ||||
\(61\) | −11.1621 | − | 6.44446i | −0.182986 | − | 0.105647i | 0.405709 | − | 0.914002i | \(-0.367025\pi\) |
−0.588695 | + | 0.808355i | \(0.700358\pi\) | |||||||
\(62\) | 56.9955i | 0.919283i | ||||||||
\(63\) | −1.81326 | − | 20.9216i | −0.0287819 | − | 0.332088i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 8.07846 | − | 13.9923i | 0.124284 | − | 0.215266i | ||||
\(66\) | 36.8795 | − | 21.2924i | 0.558781 | − | 0.322612i | ||||
\(67\) | −47.0361 | − | 81.4689i | −0.702031 | − | 1.21595i | −0.967752 | − | 0.251904i | \(-0.918943\pi\) |
0.265721 | − | 0.964050i | \(-0.414390\pi\) | |||||||
\(68\) | 4.59339 | + | 2.65199i | 0.0675498 | + | 0.0389999i | ||||
\(69\) | − | 69.4578i | − | 1.00663i | ||||||
\(70\) | 9.37137 | − | 20.0544i | 0.133877 | − | 0.286491i | ||||
\(71\) | −11.5793 | −0.163088 | −0.0815440 | − | 0.996670i | \(-0.525985\pi\) | ||||
−0.0815440 | + | 0.996670i | \(0.525985\pi\) | |||||||
\(72\) | 4.24264 | − | 7.34847i | 0.0589256 | − | 0.102062i | ||||
\(73\) | −19.6320 | + | 11.3345i | −0.268931 | + | 0.155267i | −0.628402 | − | 0.777889i | \(-0.716291\pi\) |
0.359471 | + | 0.933156i | \(0.382957\pi\) | |||||||
\(74\) | −22.9829 | − | 39.8076i | −0.310580 | − | 0.537940i | ||||
\(75\) | −7.50000 | − | 4.33013i | −0.100000 | − | 0.0577350i | ||||
\(76\) | − | 5.08364i | − | 0.0668900i | ||||||
\(77\) | 110.252 | + | 51.5208i | 1.43185 | + | 0.669101i | ||||
\(78\) | 17.6990 | 0.226910 | ||||||||
\(79\) | 12.0542 | − | 20.8785i | 0.152585 | − | 0.264285i | −0.779592 | − | 0.626287i | \(-0.784574\pi\) |
0.932177 | + | 0.362003i | \(0.117907\pi\) | |||||||
\(80\) | 7.74597 | − | 4.47214i | 0.0968246 | − | 0.0559017i | ||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −86.5502 | − | 49.9698i | −1.05549 | − | 0.609388i | ||||
\(83\) | − | 111.664i | − | 1.34535i | −0.739937 | − | 0.672676i | \(-0.765145\pi\) | ||
0.739937 | − | 0.672676i | \(-0.234855\pi\) | |||||||
\(84\) | 24.1581 | − | 2.09377i | 0.287597 | − | 0.0249258i | ||||
\(85\) | 5.93004 | 0.0697652 | ||||||||
\(86\) | −26.4268 | + | 45.7726i | −0.307289 | + | 0.532240i | ||||
\(87\) | −70.5120 | + | 40.7101i | −0.810482 | + | 0.467932i | ||||
\(88\) | 24.5864 | + | 42.5848i | 0.279390 | + | 0.483919i | ||||
\(89\) | −110.770 | − | 63.9533i | −1.24461 | − | 0.718577i | −0.274582 | − | 0.961564i | \(-0.588540\pi\) |
−0.970030 | + | 0.242987i | \(0.921873\pi\) | |||||||
\(90\) | − | 9.48683i | − | 0.105409i | ||||||
\(91\) | 28.9773 | + | 41.4556i | 0.318432 | + | 0.455556i | ||||
\(92\) | 80.2029 | 0.871771 | ||||||||
\(93\) | −34.9025 | + | 60.4529i | −0.375296 | + | 0.650031i | ||||
\(94\) | 40.9658 | − | 23.6516i | 0.435807 | − | 0.251613i | ||||
\(95\) | −2.84184 | − | 4.92221i | −0.0299141 | − | 0.0518128i | ||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 7.48256i | 0.0771398i | 0.999256 | + | 0.0385699i | \(0.0122802\pi\) | ||||
−0.999256 | + | 0.0385699i | \(0.987720\pi\) | |||||||
\(98\) | 44.4565 | + | 53.1566i | 0.453638 | + | 0.542414i | ||||
\(99\) | 52.1556 | 0.526824 | ||||||||
\(100\) | 5.00000 | − | 8.66025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | −81.9228 | + | 47.2982i | −0.811117 | + | 0.468299i | −0.847344 | − | 0.531045i | \(-0.821799\pi\) |
0.0362267 | + | 0.999344i | \(0.488466\pi\) | |||||||
\(102\) | 3.24802 | + | 5.62573i | 0.0318433 | + | 0.0551542i | ||||
\(103\) | −51.8072 | − | 29.9109i | −0.502982 | − | 0.290397i | 0.226962 | − | 0.973904i | \(-0.427121\pi\) |
−0.729944 | + | 0.683507i | \(0.760454\pi\) | |||||||
\(104\) | 20.4371i | 0.196510i | ||||||||
\(105\) | 22.2206 | − | 15.5321i | 0.211625 | − | 0.147925i | ||||
\(106\) | −100.251 | −0.945767 | ||||||||
\(107\) | −3.23081 | + | 5.59592i | −0.0301945 | + | 0.0522983i | −0.880728 | − | 0.473623i | \(-0.842946\pi\) |
0.850533 | + | 0.525921i | \(0.176279\pi\) | |||||||
\(108\) | 9.00000 | − | 5.19615i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | 81.9201 | + | 141.890i | 0.751560 | + | 1.30174i | 0.947066 | + | 0.321038i | \(0.104032\pi\) |
−0.195506 | + | 0.980703i | \(0.562635\pi\) | |||||||
\(110\) | 47.6113 | + | 27.4884i | 0.432830 | + | 0.249894i | ||||
\(111\) | − | 56.2964i | − | 0.507175i | ||||||
\(112\) | 2.41768 | + | 27.8954i | 0.0215864 | + | 0.249066i | ||||
\(113\) | −105.434 | −0.933040 | −0.466520 | − | 0.884511i | \(-0.654492\pi\) | ||||
−0.466520 | + | 0.884511i | \(0.654492\pi\) | |||||||
\(114\) | 3.11308 | − | 5.39202i | 0.0273077 | − | 0.0472984i | ||||
\(115\) | 77.6561 | − | 44.8348i | 0.675271 | − | 0.389868i | ||||
\(116\) | −47.0080 | − | 81.4202i | −0.405241 | − | 0.701898i | ||||
\(117\) | 18.7726 | + | 10.8384i | 0.160450 | + | 0.0926358i | ||||
\(118\) | 142.211i | 1.20518i | ||||||||
\(119\) | −7.85915 | + | 16.8183i | −0.0660433 | + | 0.141330i | ||||
\(120\) | 10.9545 | 0.0912871 | ||||||||
\(121\) | −90.6223 | + | 156.962i | −0.748945 | + | 1.29721i | ||||
\(122\) | 15.7856 | − | 9.11384i | 0.129391 | − | 0.0747036i | ||||
\(123\) | −61.2002 | − | 106.002i | −0.497563 | − | 0.861804i | ||||
\(124\) | −69.8050 | − | 40.3019i | −0.562944 | − | 0.325016i | ||||
\(125\) | − | 11.1803i | − | 0.0894427i | ||||||
\(126\) | 26.9058 | + | 12.5730i | 0.213538 | + | 0.0997858i | ||||
\(127\) | 53.7033 | 0.422860 | 0.211430 | − | 0.977393i | \(-0.432188\pi\) | ||||
0.211430 | + | 0.977393i | \(0.432188\pi\) | |||||||
\(128\) | −5.65685 | + | 9.79796i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −56.0598 | + | 32.3661i | −0.434572 | + | 0.250900i | ||||
\(130\) | 11.4247 | + | 19.7881i | 0.0878820 | + | 0.152216i | ||||
\(131\) | −50.6489 | − | 29.2421i | −0.386632 | − | 0.223222i | 0.294068 | − | 0.955785i | \(-0.404991\pi\) |
−0.680700 | + | 0.732562i | \(0.738324\pi\) | |||||||
\(132\) | 60.2240i | 0.456243i | ||||||||
\(133\) | 17.7263 | − | 1.53632i | 0.133280 | − | 0.0115513i | ||||
\(134\) | 133.038 | 0.992822 | ||||||||
\(135\) | 5.80948 | − | 10.0623i | 0.0430331 | − | 0.0745356i | ||||
\(136\) | −6.49603 | + | 3.75049i | −0.0477650 | + | 0.0275771i | ||||
\(137\) | 6.05848 | + | 10.4936i | 0.0442225 | + | 0.0765956i | 0.887289 | − | 0.461213i | \(-0.152586\pi\) |
−0.843067 | + | 0.537809i | \(0.819252\pi\) | |||||||
\(138\) | 85.0680 | + | 49.1141i | 0.616435 | + | 0.355899i | ||||
\(139\) | − | 45.2562i | − | 0.325584i | −0.986660 | − | 0.162792i | \(-0.947950\pi\) | ||
0.986660 | − | 0.162792i | \(-0.0520500\pi\) | |||||||
\(140\) | 17.9349 | + | 25.6581i | 0.128107 | + | 0.183272i | ||||
\(141\) | 57.9344 | 0.410882 | ||||||||
\(142\) | 8.18777 | − | 14.1816i | 0.0576603 | − | 0.0998706i | ||||
\(143\) | −108.789 | + | 62.8091i | −0.760759 | + | 0.439225i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | −91.0306 | − | 52.5565i | −0.627797 | − | 0.362459i | ||||
\(146\) | − | 32.0589i | − | 0.219581i | ||||||
\(147\) | 14.6016 | + | 83.6050i | 0.0993309 | + | 0.568741i | ||||
\(148\) | 65.0055 | 0.439226 | ||||||||
\(149\) | 25.4474 | − | 44.0762i | 0.170788 | − | 0.295814i | −0.767908 | − | 0.640561i | \(-0.778702\pi\) |
0.938696 | + | 0.344747i | \(0.112035\pi\) | |||||||
\(150\) | 10.6066 | − | 6.12372i | 0.0707107 | − | 0.0408248i | ||||
\(151\) | 78.8476 | + | 136.568i | 0.522169 | + | 0.904424i | 0.999667 | + | 0.0257911i | \(0.00821047\pi\) |
−0.477498 | + | 0.878633i | \(0.658456\pi\) | |||||||
\(152\) | 6.22616 | + | 3.59468i | 0.0409616 | + | 0.0236492i | ||||
\(153\) | 7.95598i | 0.0519999i | ||||||||
\(154\) | −141.060 | + | 98.6004i | −0.915974 | + | 0.640263i | ||||
\(155\) | −90.1179 | −0.581406 | ||||||||
\(156\) | −12.5151 | + | 21.6768i | −0.0802249 | + | 0.138954i | ||||
\(157\) | 145.359 | − | 83.9231i | 0.925854 | − | 0.534542i | 0.0403562 | − | 0.999185i | \(-0.487151\pi\) |
0.885498 | + | 0.464643i | \(0.153817\pi\) | |||||||
\(158\) | 17.0472 | + | 29.5266i | 0.107894 | + | 0.186877i | ||||
\(159\) | −106.333 | − | 61.3911i | −0.668758 | − | 0.386108i | ||||
\(160\) | 12.6491i | 0.0790569i | ||||||||
\(161\) | 24.2381 | + | 279.662i | 0.150547 | + | 1.73703i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | −138.285 | + | 239.517i | −0.848374 | + | 1.46943i | 0.0342839 | + | 0.999412i | \(0.489085\pi\) |
−0.882658 | + | 0.470015i | \(0.844248\pi\) | |||||||
\(164\) | 122.400 | − | 70.6679i | 0.746344 | − | 0.430902i | ||||
\(165\) | 33.6663 | + | 58.3117i | 0.204038 | + | 0.353404i | ||||
\(166\) | 136.760 | + | 78.9586i | 0.823857 | + | 0.475654i | ||||
\(167\) | 48.4258i | 0.289975i | 0.989433 | + | 0.144987i | \(0.0463142\pi\) | ||||
−0.989433 | + | 0.144987i | \(0.953686\pi\) | |||||||
\(168\) | −14.5181 | + | 31.0681i | −0.0864170 | + | 0.184929i | ||||
\(169\) | 116.791 | 0.691070 | ||||||||
\(170\) | −4.19317 | + | 7.26279i | −0.0246657 | + | 0.0427223i | ||||
\(171\) | 6.60384 | − | 3.81273i | 0.0386190 | − | 0.0222967i | ||||
\(172\) | −37.3732 | − | 64.7323i | −0.217286 | − | 0.376351i | ||||
\(173\) | −97.8337 | − | 56.4843i | −0.565513 | − | 0.326499i | 0.189842 | − | 0.981815i | \(-0.439202\pi\) |
−0.755355 | + | 0.655316i | \(0.772536\pi\) | |||||||
\(174\) | − | 115.146i | − | 0.661756i | ||||||
\(175\) | 31.7087 | + | 14.8174i | 0.181193 | + | 0.0846710i | ||||
\(176\) | −69.5407 | −0.395118 | ||||||||
\(177\) | −87.0863 | + | 150.838i | −0.492013 | + | 0.852192i | ||||
\(178\) | 156.653 | − | 90.4437i | 0.880073 | − | 0.508111i | ||||
\(179\) | −165.708 | − | 287.015i | −0.925744 | − | 1.60344i | −0.790360 | − | 0.612642i | \(-0.790107\pi\) |
−0.135384 | − | 0.990793i | \(-0.543227\pi\) | |||||||
\(180\) | 11.6190 | + | 6.70820i | 0.0645497 | + | 0.0372678i | ||||
\(181\) | − | 213.328i | − | 1.17861i | −0.807912 | − | 0.589303i | \(-0.799402\pi\) | ||
0.807912 | − | 0.589303i | \(-0.200598\pi\) | |||||||
\(182\) | −71.2626 | + | 6.17627i | −0.391553 | + | 0.0339356i | ||||
\(183\) | 22.3243 | 0.121991 | ||||||||
\(184\) | −56.7120 | + | 98.2281i | −0.308218 | + | 0.533848i | ||||
\(185\) | 62.9413 | − | 36.3392i | 0.340223 | − | 0.196428i | ||||
\(186\) | −49.3596 | − | 85.4933i | −0.265374 | − | 0.459642i | ||||
\(187\) | −39.9285 | − | 23.0527i | −0.213521 | − | 0.123277i | ||||
\(188\) | 66.8969i | 0.355835i | ||||||||
\(189\) | 20.8385 | + | 29.8120i | 0.110257 | + | 0.157736i | ||||
\(190\) | 8.03794 | 0.0423050 | ||||||||
\(191\) | 33.4517 | − | 57.9400i | 0.175140 | − | 0.303351i | −0.765070 | − | 0.643947i | \(-0.777296\pi\) |
0.940210 | + | 0.340596i | \(0.110629\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 56.3020 | + | 97.5179i | 0.291720 | + | 0.505274i | 0.974217 | − | 0.225615i | \(-0.0724391\pi\) |
−0.682497 | + | 0.730889i | \(0.739106\pi\) | |||||||
\(194\) | −9.16422 | − | 5.29097i | −0.0472383 | − | 0.0272730i | ||||
\(195\) | 27.9846i | 0.143511i | ||||||||
\(196\) | −96.5387 | + | 16.8605i | −0.492544 | + | 0.0860231i | ||||
\(197\) | −61.0211 | −0.309752 | −0.154876 | − | 0.987934i | \(-0.549498\pi\) | ||||
−0.154876 | + | 0.987934i | \(0.549498\pi\) | |||||||
\(198\) | −36.8795 | + | 63.8772i | −0.186260 | + | 0.322612i | ||||
\(199\) | −165.554 | + | 95.5826i | −0.831929 | + | 0.480314i | −0.854513 | − | 0.519431i | \(-0.826144\pi\) |
0.0225837 | + | 0.999745i | \(0.492811\pi\) | |||||||
\(200\) | 7.07107 | + | 12.2474i | 0.0353553 | + | 0.0612372i | ||||
\(201\) | 141.108 | + | 81.4689i | 0.702031 | + | 0.405318i | ||||
\(202\) | − | 133.779i | − | 0.662274i | ||||||
\(203\) | 269.700 | − | 188.519i | 1.32857 | − | 0.928667i | ||||
\(204\) | −9.18678 | −0.0450332 | ||||||||
\(205\) | 79.0092 | − | 136.848i | 0.385410 | − | 0.667551i | ||||
\(206\) | 73.2664 | − | 42.3004i | 0.355662 | − | 0.205342i | ||||
\(207\) | 60.1522 | + | 104.187i | 0.290590 | + | 0.503317i | ||||
\(208\) | −25.0302 | − | 14.4512i | −0.120337 | − | 0.0694768i | ||||
\(209\) | 44.1900i | 0.211435i | ||||||||
\(210\) | 3.31054 | + | 38.1974i | 0.0157645 | + | 0.181892i | ||||
\(211\) | 280.115 | 1.32756 | 0.663781 | − | 0.747927i | \(-0.268951\pi\) | ||||
0.663781 | + | 0.747927i | \(0.268951\pi\) | |||||||
\(212\) | 70.8884 | − | 122.782i | 0.334379 | − | 0.579162i | ||||
\(213\) | 17.3689 | − | 10.0279i | 0.0815440 | − | 0.0470795i | ||||
\(214\) | −4.56905 | − | 7.91383i | −0.0213507 | − | 0.0369805i | ||||
\(215\) | −72.3729 | − | 41.7845i | −0.336618 | − | 0.194347i | ||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 119.434 | − | 255.585i | 0.550388 | − | 1.17781i | ||||
\(218\) | −231.705 | −1.06287 | ||||||||
\(219\) | 19.6320 | − | 34.0036i | 0.0896437 | − | 0.155267i | ||||
\(220\) | −67.3325 | + | 38.8745i | −0.306057 | + | 0.176702i | ||||
\(221\) | −9.58111 | − | 16.5950i | −0.0433535 | − | 0.0750904i | ||||
\(222\) | 68.9487 | + | 39.8076i | 0.310580 | + | 0.179313i | ||||
\(223\) | − | 272.759i | − | 1.22313i | −0.791192 | − | 0.611567i | \(-0.790539\pi\) | ||
0.791192 | − | 0.611567i | \(-0.209461\pi\) | |||||||
\(224\) | −35.8743 | − | 16.7640i | −0.160153 | − | 0.0748393i | ||||
\(225\) | 15.0000 | 0.0666667 | ||||||||
\(226\) | 74.5528 | − | 129.129i | 0.329879 | − | 0.571368i | ||||
\(227\) | 13.9191 | − | 8.03620i | 0.0613176 | − | 0.0354018i | −0.469028 | − | 0.883183i | \(-0.655396\pi\) |
0.530345 | + | 0.847782i | \(0.322062\pi\) | |||||||
\(228\) | 4.40256 | + | 7.62546i | 0.0193095 | + | 0.0334450i | ||||
\(229\) | 128.261 | + | 74.0517i | 0.560093 | + | 0.323370i | 0.753183 | − | 0.657811i | \(-0.228518\pi\) |
−0.193090 | + | 0.981181i | \(0.561851\pi\) | |||||||
\(230\) | 126.812i | 0.551356i | ||||||||
\(231\) | −209.997 | + | 18.2003i | −0.909078 | + | 0.0787891i | ||||
\(232\) | 132.959 | 0.573098 | ||||||||
\(233\) | 149.559 | − | 259.044i | 0.641885 | − | 1.11178i | −0.343127 | − | 0.939289i | \(-0.611486\pi\) |
0.985012 | − | 0.172488i | \(-0.0551806\pi\) | |||||||
\(234\) | −26.5485 | + | 15.3278i | −0.113455 | + | 0.0655034i | ||||
\(235\) | 37.3965 | + | 64.7727i | 0.159134 | + | 0.275628i | ||||
\(236\) | −174.173 | − | 100.559i | −0.738020 | − | 0.426096i | ||||
\(237\) | 41.7570i | 0.176190i | ||||||||
\(238\) | −15.0408 | − | 21.5178i | −0.0631968 | − | 0.0904108i | ||||
\(239\) | −114.253 | −0.478046 | −0.239023 | − | 0.971014i | \(-0.576827\pi\) | ||||
−0.239023 | + | 0.971014i | \(0.576827\pi\) | |||||||
\(240\) | −7.74597 | + | 13.4164i | −0.0322749 | + | 0.0559017i | ||||
\(241\) | −118.162 | + | 68.2209i | −0.490299 | + | 0.283074i | −0.724699 | − | 0.689066i | \(-0.758021\pi\) |
0.234399 | + | 0.972140i | \(0.424688\pi\) | |||||||
\(242\) | −128.159 | − | 221.978i | −0.529584 | − | 0.917266i | ||||
\(243\) | 13.5000 | + | 7.79423i | 0.0555556 | + | 0.0320750i | ||||
\(244\) | 25.7778i | 0.105647i | ||||||||
\(245\) | −84.0479 | + | 70.2919i | −0.343053 | + | 0.286906i | ||||
\(246\) | 173.100 | 0.703660 | ||||||||
\(247\) | −9.18308 | + | 15.9056i | −0.0371785 | + | 0.0643950i | ||||
\(248\) | 98.7192 | − | 56.9955i | 0.398061 | − | 0.229821i | ||||
\(249\) | 96.7041 | + | 167.496i | 0.388370 | + | 0.672676i | ||||
\(250\) | 13.6931 | + | 7.90569i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | − | 457.024i | − | 1.82081i | −0.413717 | − | 0.910406i | \(-0.635770\pi\) | ||
0.413717 | − | 0.910406i | \(-0.364230\pi\) | |||||||
\(252\) | −34.4240 | + | 24.0622i | −0.136603 | + | 0.0954850i | ||||
\(253\) | −697.171 | −2.75562 | ||||||||
\(254\) | −37.9739 | + | 65.7728i | −0.149504 | + | 0.258948i | ||||
\(255\) | −8.89506 | + | 5.13557i | −0.0348826 | + | 0.0201395i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 43.2997 | + | 24.9991i | 0.168481 | + | 0.0972726i | 0.581869 | − | 0.813282i | \(-0.302321\pi\) |
−0.413388 | + | 0.910555i | \(0.635655\pi\) | |||||||
\(258\) | − | 91.5453i | − | 0.354827i | ||||||
\(259\) | 19.6453 | + | 226.669i | 0.0758505 | + | 0.875172i | ||||
\(260\) | −32.3138 | −0.124284 | ||||||||
\(261\) | 70.5120 | − | 122.130i | 0.270161 | − | 0.467932i | ||||
\(262\) | 71.6283 | − | 41.3546i | 0.273390 | − | 0.157842i | ||||
\(263\) | −91.1388 | − | 157.857i | −0.346535 | − | 0.600217i | 0.639096 | − | 0.769127i | \(-0.279309\pi\) |
−0.985631 | + | 0.168910i | \(0.945975\pi\) | |||||||
\(264\) | −73.7591 | − | 42.5848i | −0.279390 | − | 0.161306i | ||||
\(265\) | − | 158.511i | − | 0.598156i | ||||||
\(266\) | −10.6528 | + | 22.7965i | −0.0400480 | + | 0.0857012i | ||||
\(267\) | 221.541 | 0.829741 | ||||||||
\(268\) | −94.0722 | + | 162.938i | −0.351016 | + | 0.607977i | ||||
\(269\) | −32.5814 | + | 18.8109i | −0.121120 | + | 0.0699289i | −0.559336 | − | 0.828941i | \(-0.688944\pi\) |
0.438216 | + | 0.898870i | \(0.355611\pi\) | |||||||
\(270\) | 8.21584 | + | 14.2302i | 0.0304290 | + | 0.0527046i | ||||
\(271\) | 175.576 | + | 101.369i | 0.647880 | + | 0.374054i | 0.787644 | − | 0.616131i | \(-0.211301\pi\) |
−0.139763 | + | 0.990185i | \(0.544634\pi\) | |||||||
\(272\) | − | 10.6080i | − | 0.0389999i | ||||||
\(273\) | −79.3675 | − | 37.0883i | −0.290724 | − | 0.135855i | ||||
\(274\) | −17.1360 | −0.0625401 | ||||||||
\(275\) | −43.4630 | + | 75.2801i | −0.158047 | + | 0.273746i | ||||
\(276\) | −120.304 | + | 69.4578i | −0.435885 | + | 0.251659i | ||||
\(277\) | −128.121 | − | 221.912i | −0.462530 | − | 0.801126i | 0.536556 | − | 0.843865i | \(-0.319725\pi\) |
−0.999086 | + | 0.0427390i | \(0.986392\pi\) | |||||||
\(278\) | 55.4273 | + | 32.0010i | 0.199379 | + | 0.115111i | ||||
\(279\) | − | 120.906i | − | 0.433354i | ||||||
\(280\) | −44.1065 | + | 3.82268i | −0.157523 | + | 0.0136524i | ||||
\(281\) | −141.462 | −0.503423 | −0.251711 | − | 0.967802i | \(-0.580993\pi\) | ||||
−0.251711 | + | 0.967802i | \(0.580993\pi\) | |||||||
\(282\) | −40.9658 | + | 70.9549i | −0.145269 | + | 0.251613i | ||||
\(283\) | 470.571 | − | 271.684i | 1.66279 | − | 0.960014i | 0.691421 | − | 0.722452i | \(-0.256985\pi\) |
0.971372 | − | 0.237562i | \(-0.0763483\pi\) | |||||||
\(284\) | 11.5793 | + | 20.0559i | 0.0407720 | + | 0.0706192i | ||||
\(285\) | 8.52553 | + | 4.92221i | 0.0299141 | + | 0.0172709i | ||||
\(286\) | − | 177.651i | − | 0.621157i | ||||||
\(287\) | 283.405 | + | 405.445i | 0.987472 | + | 1.41270i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −140.983 | + | 244.191i | −0.487832 | + | 0.844950i | ||||
\(290\) | 128.737 | − | 74.3261i | 0.443920 | − | 0.256297i | ||||
\(291\) | −6.48008 | − | 11.2238i | −0.0222683 | − | 0.0385699i | ||||
\(292\) | 39.2639 | + | 22.6690i | 0.134466 | + | 0.0776337i | ||||
\(293\) | 375.289i | 1.28085i | 0.768021 | + | 0.640424i | \(0.221241\pi\) | ||||
−0.768021 | + | 0.640424i | \(0.778759\pi\) | |||||||
\(294\) | −112.720 | − | 41.2344i | −0.383400 | − | 0.140253i | ||||
\(295\) | −224.856 | −0.762224 | ||||||||
\(296\) | −45.9658 | + | 79.6151i | −0.155290 | + | 0.268970i | ||||
\(297\) | −78.2333 | + | 45.1680i | −0.263412 | + | 0.152081i | ||||
\(298\) | 35.9881 | + | 62.3332i | 0.120765 | + | 0.209172i | ||||
\(299\) | −250.937 | − | 144.878i | −0.839253 | − | 0.484543i | ||||
\(300\) | 17.3205i | 0.0577350i | ||||||||
\(301\) | 214.422 | − | 149.880i | 0.712367 | − | 0.497942i | ||||
\(302\) | −223.015 | −0.738459 | ||||||||
\(303\) | 81.9228 | − | 141.894i | 0.270372 | − | 0.468299i | ||||
\(304\) | −8.80512 | + | 5.08364i | −0.0289642 | + | 0.0167225i | ||||
\(305\) | 14.4103 | + | 24.9593i | 0.0472467 | + | 0.0818337i | ||||
\(306\) | −9.74405 | − | 5.62573i | −0.0318433 | − | 0.0183847i | ||||
\(307\) | − | 41.3436i | − | 0.134670i | −0.997730 | − | 0.0673349i | \(-0.978550\pi\) | ||
0.997730 | − | 0.0673349i | \(-0.0214496\pi\) | |||||||
\(308\) | −21.0159 | − | 242.484i | −0.0682333 | − | 0.787284i | ||||
\(309\) | 103.614 | 0.335321 | ||||||||
\(310\) | 63.7230 | − | 110.371i | 0.205558 | − | 0.356037i | ||||
\(311\) | −126.924 | + | 73.2794i | −0.408115 | + | 0.235625i | −0.689979 | − | 0.723829i | \(-0.742380\pi\) |
0.281865 | + | 0.959454i | \(0.409047\pi\) | |||||||
\(312\) | −17.6990 | − | 30.6556i | −0.0567276 | − | 0.0982551i | ||||
\(313\) | 194.744 | + | 112.435i | 0.622184 | + | 0.359218i | 0.777719 | − | 0.628612i | \(-0.216377\pi\) |
−0.155535 | + | 0.987830i | \(0.549710\pi\) | |||||||
\(314\) | 237.370i | 0.755957i | ||||||||
\(315\) | −19.8797 | + | 42.5417i | −0.0631101 | + | 0.135053i | ||||
\(316\) | −48.2168 | −0.152585 | ||||||||
\(317\) | 113.113 | − | 195.918i | 0.356825 | − | 0.618038i | −0.630604 | − | 0.776105i | \(-0.717193\pi\) |
0.987428 | + | 0.158067i | \(0.0505261\pi\) | |||||||
\(318\) | 150.377 | − | 86.8202i | 0.472884 | − | 0.273019i | ||||
\(319\) | 408.621 | + | 707.753i | 1.28094 | + | 2.21866i | ||||
\(320\) | −15.4919 | − | 8.94427i | −0.0484123 | − | 0.0279508i | ||||
\(321\) | − | 11.1918i | − | 0.0348656i | ||||||
\(322\) | −359.653 | − | 168.065i | −1.11694 | − | 0.521942i | ||||
\(323\) | −6.74089 | −0.0208696 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −31.2877 | + | 18.0640i | −0.0962699 | + | 0.0555815i | ||||
\(326\) | −195.565 | − | 338.728i | −0.599891 | − | 1.03904i | ||||
\(327\) | −245.760 | − | 141.890i | −0.751560 | − | 0.433914i | ||||
\(328\) | 199.879i | 0.609388i | ||||||||
\(329\) | −233.265 | + | 20.2169i | −0.709011 | + | 0.0614495i | ||||
\(330\) | −95.2226 | −0.288553 | ||||||||
\(331\) | −69.9082 | + | 121.085i | −0.211203 | + | 0.365814i | −0.952091 | − | 0.305814i | \(-0.901071\pi\) |
0.740888 | + | 0.671628i | \(0.234405\pi\) | |||||||
\(332\) | −193.408 | + | 111.664i | −0.582555 | + | 0.336338i | ||||
\(333\) | 48.7541 | + | 84.4446i | 0.146409 | + | 0.253587i | ||||
\(334\) | −59.3093 | − | 34.2422i | −0.177573 | − | 0.102522i | ||||
\(335\) | 210.352i | 0.627916i | ||||||||
\(336\) | −27.7847 | − | 39.7494i | −0.0826924 | − | 0.118302i | ||||
\(337\) | 30.1128 | 0.0893556 | 0.0446778 | − | 0.999001i | \(-0.485774\pi\) | ||||
0.0446778 | + | 0.999001i | \(0.485774\pi\) | |||||||
\(338\) | −82.5836 | + | 143.039i | −0.244330 | + | 0.423192i | ||||
\(339\) | 158.150 | − | 91.3081i | 0.466520 | − | 0.269345i | ||||
\(340\) | −5.93004 | − | 10.2711i | −0.0174413 | − | 0.0302092i | ||||
\(341\) | 606.786 | + | 350.328i | 1.77943 | + | 1.02736i | ||||
\(342\) | 10.7840i | 0.0315323i | ||||||||
\(343\) | −87.9664 | − | 331.528i | −0.256462 | − | 0.966554i | ||||
\(344\) | 105.707 | 0.307289 | ||||||||
\(345\) | −77.6561 | + | 134.504i | −0.225090 | + | 0.389868i | ||||
\(346\) | 138.358 | − | 79.8809i | 0.399878 | − | 0.230870i | ||||
\(347\) | 207.954 | + | 360.186i | 0.599290 | + | 1.03800i | 0.992926 | + | 0.118734i | \(0.0378836\pi\) |
−0.393636 | + | 0.919266i | \(0.628783\pi\) | |||||||
\(348\) | 141.024 | + | 81.4202i | 0.405241 | + | 0.233966i | ||||
\(349\) | 594.950i | 1.70473i | 0.522950 | + | 0.852363i | \(0.324831\pi\) | ||||
−0.522950 | + | 0.852363i | \(0.675169\pi\) | |||||||
\(350\) | −40.5690 | + | 28.3576i | −0.115912 | + | 0.0810217i | ||||
\(351\) | −37.5453 | −0.106967 | ||||||||
\(352\) | 49.1727 | − | 85.1697i | 0.139695 | − | 0.241959i | ||||
\(353\) | 315.509 | − | 182.159i | 0.893793 | − | 0.516031i | 0.0186116 | − | 0.999827i | \(-0.494075\pi\) |
0.875181 | + | 0.483795i | \(0.160742\pi\) | |||||||
\(354\) | −123.159 | − | 213.317i | −0.347906 | − | 0.602591i | ||||
\(355\) | 22.4231 | + | 12.9460i | 0.0631637 | + | 0.0364676i | ||||
\(356\) | 255.813i | 0.718577i | ||||||||
\(357\) | −2.77633 | − | 32.0336i | −0.00777684 | − | 0.0897301i | ||||
\(358\) | 468.693 | 1.30920 | ||||||||
\(359\) | 306.381 | − | 530.668i | 0.853430 | − | 1.47818i | −0.0246647 | − | 0.999696i | \(-0.507852\pi\) |
0.878094 | − | 0.478488i | \(-0.158815\pi\) | |||||||
\(360\) | −16.4317 | + | 9.48683i | −0.0456435 | + | 0.0263523i | ||||
\(361\) | −177.270 | − | 307.040i | −0.491051 | − | 0.850526i | ||||
\(362\) | 261.272 | + | 150.846i | 0.721746 | + | 0.416700i | ||||
\(363\) | − | 313.925i | − | 0.864807i | ||||||
\(364\) | 42.8259 | − | 91.6457i | 0.117654 | − | 0.251774i | ||||
\(365\) | 50.6895 | 0.138875 | ||||||||
\(366\) | −15.7856 | + | 27.3415i | −0.0431302 | + | 0.0747036i | ||||
\(367\) | −426.967 | + | 246.509i | −1.16340 | + | 0.671687i | −0.952116 | − | 0.305738i | \(-0.901097\pi\) |
−0.211281 | + | 0.977425i | \(0.567764\pi\) | |||||||
\(368\) | −80.2029 | − | 138.916i | −0.217943 | − | 0.377488i | ||||
\(369\) | 183.601 | + | 106.002i | 0.497563 | + | 0.287268i | ||||
\(370\) | 102.783i | 0.277791i | ||||||||
\(371\) | 449.556 | + | 210.077i | 1.21174 | + | 0.566245i | ||||
\(372\) | 139.610 | 0.375296 | ||||||||
\(373\) | −82.7013 | + | 143.243i | −0.221719 | + | 0.384029i | −0.955330 | − | 0.295541i | \(-0.904500\pi\) |
0.733611 | + | 0.679570i | \(0.237834\pi\) | |||||||
\(374\) | 56.4674 | − | 32.6015i | 0.150982 | − | 0.0871697i | ||||
\(375\) | 9.68246 | + | 16.7705i | 0.0258199 | + | 0.0447214i | ||||
\(376\) | −81.9317 | − | 47.3033i | −0.217903 | − | 0.125807i | ||||
\(377\) | 339.660i | 0.900956i | ||||||||
\(378\) | −51.2472 | + | 4.44155i | −0.135575 | + | 0.0117501i | ||||
\(379\) | −179.349 | −0.473215 | −0.236608 | − | 0.971605i | \(-0.576036\pi\) | ||||
−0.236608 | + | 0.971605i | \(0.576036\pi\) | |||||||
\(380\) | −5.68368 | + | 9.84443i | −0.0149571 | + | 0.0259064i | ||||
\(381\) | −80.5549 | + | 46.5084i | −0.211430 | + | 0.122069i | ||||
\(382\) | 47.3078 | + | 81.9395i | 0.123842 | + | 0.214501i | ||||
\(383\) | 233.108 | + | 134.585i | 0.608636 | + | 0.351396i | 0.772432 | − | 0.635098i | \(-0.219040\pi\) |
−0.163795 | + | 0.986494i | \(0.552374\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | −155.901 | − | 223.035i | −0.404938 | − | 0.579313i | ||||
\(386\) | −159.246 | −0.412554 | ||||||||
\(387\) | 56.0598 | − | 97.0984i | 0.144857 | − | 0.250900i | ||||
\(388\) | 12.9602 | − | 7.48256i | 0.0334025 | − | 0.0192849i | ||||
\(389\) | 236.874 | + | 410.277i | 0.608930 | + | 1.05470i | 0.991417 | + | 0.130737i | \(0.0417344\pi\) |
−0.382487 | + | 0.923961i | \(0.624932\pi\) | |||||||
\(390\) | −34.2740 | − | 19.7881i | −0.0878820 | − | 0.0507387i | ||||
\(391\) | − | 106.349i | − | 0.271992i | ||||||
\(392\) | 47.6133 | − | 130.157i | 0.121463 | − | 0.332034i | ||||
\(393\) | 101.298 | 0.257755 | ||||||||
\(394\) | 43.1484 | − | 74.7353i | 0.109514 | − | 0.189683i | ||||
\(395\) | −46.6857 | + | 26.9540i | −0.118192 | + | 0.0682380i | ||||
\(396\) | −52.1556 | − | 90.3361i | −0.131706 | − | 0.228121i | ||||
\(397\) | −445.080 | − | 256.967i | −1.12111 | − | 0.647271i | −0.179424 | − | 0.983772i | \(-0.557423\pi\) |
−0.941683 | + | 0.336500i | \(0.890757\pi\) | |||||||
\(398\) | − | 270.348i | − | 0.679267i | ||||||
\(399\) | −25.2589 | + | 17.6559i | −0.0633056 | + | 0.0442504i | ||||
\(400\) | −20.0000 | −0.0500000 | ||||||||
\(401\) | 203.367 | − | 352.242i | 0.507150 | − | 0.878410i | −0.492816 | − | 0.870134i | \(-0.664032\pi\) |
0.999966 | − | 0.00827591i | \(-0.00263433\pi\) | |||||||
\(402\) | −199.557 | + | 115.214i | −0.496411 | + | 0.286603i | ||||
\(403\) | 145.603 | + | 252.191i | 0.361297 | + | 0.625785i | ||||
\(404\) | 163.846 | + | 94.5963i | 0.405558 | + | 0.234149i | ||||
\(405\) | 20.1246i | 0.0496904i | ||||||||
\(406\) | 40.1814 | + | 463.617i | 0.0989689 | + | 1.14191i | ||||
\(407\) | −565.066 | −1.38837 | ||||||||
\(408\) | 6.49603 | − | 11.2515i | 0.0159217 | − | 0.0275771i | ||||
\(409\) | −422.173 | + | 243.742i | −1.03221 | + | 0.595946i | −0.917617 | − | 0.397467i | \(-0.869889\pi\) |
−0.114592 | + | 0.993413i | \(0.536556\pi\) | |||||||
\(410\) | 111.736 | + | 193.532i | 0.272526 | + | 0.472030i | ||||
\(411\) | −18.1755 | − | 10.4936i | −0.0442225 | − | 0.0255319i | ||||
\(412\) | 119.643i | 0.290397i | ||||||||
\(413\) | 298.004 | − | 637.717i | 0.721560 | − | 1.54411i | ||||
\(414\) | −170.136 | −0.410957 | ||||||||
\(415\) | −124.844 | + | 216.237i | −0.300830 | + | 0.521053i | ||||
\(416\) | 35.3980 | − | 20.4371i | 0.0850914 | − | 0.0491275i | ||||
\(417\) | 39.1930 | + | 67.8843i | 0.0939881 | + | 0.162792i | ||||
\(418\) | −54.1215 | − | 31.2471i | −0.129477 | − | 0.0747537i | ||||
\(419\) | 552.257i | 1.31804i | 0.752127 | + | 0.659018i | \(0.229028\pi\) | ||||
−0.752127 | + | 0.659018i | \(0.770972\pi\) | |||||||
\(420\) | −49.1230 | − | 22.9551i | −0.116959 | − | 0.0546549i | ||||
\(421\) | −74.6870 | −0.177404 | −0.0887019 | − | 0.996058i | \(-0.528272\pi\) | ||||
−0.0887019 | + | 0.996058i | \(0.528272\pi\) | |||||||
\(422\) | −198.072 | + | 343.070i | −0.469364 | + | 0.812962i | ||||
\(423\) | −86.9016 | + | 50.1727i | −0.205441 | + | 0.118612i | ||||
\(424\) | 100.251 | + | 173.640i | 0.236442 | + | 0.409529i | ||||
\(425\) | −11.4835 | − | 6.62999i | −0.0270199 | − | 0.0156000i | ||||
\(426\) | 28.3633i | 0.0665804i | ||||||||
\(427\) | −89.8855 | + | 7.79031i | −0.210505 | + | 0.0182443i | ||||
\(428\) | 12.9232 | 0.0301945 | ||||||||
\(429\) | 108.789 | − | 188.427i | 0.253586 | − | 0.439225i | ||||
\(430\) | 102.351 | − | 59.0922i | 0.238025 | − | 0.137424i | ||||
\(431\) | −242.339 | − | 419.743i | −0.562271 | − | 0.973881i | −0.997298 | − | 0.0734641i | \(-0.976595\pi\) |
0.435027 | − | 0.900417i | \(-0.356739\pi\) | |||||||
\(432\) | −18.0000 | − | 10.3923i | −0.0416667 | − | 0.0240563i | ||||
\(433\) | − | 458.196i | − | 1.05819i | −0.848563 | − | 0.529094i | \(-0.822532\pi\) | ||
0.848563 | − | 0.529094i | \(-0.177468\pi\) | |||||||
\(434\) | 228.573 | + | 327.002i | 0.526667 | + | 0.753461i | ||||
\(435\) | 182.061 | 0.418531 | ||||||||
\(436\) | 163.840 | − | 283.779i | 0.375780 | − | 0.650870i | ||||
\(437\) | −88.2746 | + | 50.9653i | −0.202001 | + | 0.116626i | ||||
\(438\) | 27.7638 | + | 48.0883i | 0.0633877 | + | 0.109791i | ||||
\(439\) | 121.167 | + | 69.9559i | 0.276007 | + | 0.159353i | 0.631614 | − | 0.775283i | \(-0.282393\pi\) |
−0.355607 | + | 0.934635i | \(0.615726\pi\) | |||||||
\(440\) | − | 109.954i | − | 0.249894i | ||||||
\(441\) | −94.3065 | − | 112.762i | −0.213847 | − | 0.255696i | ||||
\(442\) | 27.0995 | 0.0613110 | ||||||||
\(443\) | 8.04616 | − | 13.9364i | 0.0181629 | − | 0.0314591i | −0.856801 | − | 0.515647i | \(-0.827552\pi\) |
0.874964 | + | 0.484188i | \(0.160885\pi\) | |||||||
\(444\) | −97.5082 | + | 56.2964i | −0.219613 | + | 0.126794i | ||||
\(445\) | 143.004 | + | 247.690i | 0.321357 | + | 0.556607i | ||||
\(446\) | 334.060 | + | 192.870i | 0.749014 | + | 0.432444i | ||||
\(447\) | 88.1524i | 0.197209i | ||||||||
\(448\) | 45.8986 | − | 32.0830i | 0.102452 | − | 0.0716138i | ||||
\(449\) | −329.314 | −0.733439 | −0.366720 | − | 0.930332i | \(-0.619519\pi\) | ||||
−0.366720 | + | 0.930332i | \(0.619519\pi\) | |||||||
\(450\) | −10.6066 | + | 18.3712i | −0.0235702 | + | 0.0408248i | ||||
\(451\) | −1063.98 | + | 614.288i | −2.35915 | + | 1.36206i | ||||
\(452\) | 105.434 | + | 182.616i | 0.233260 | + | 0.404018i | ||||
\(453\) | −236.543 | − | 136.568i | −0.522169 | − | 0.301475i | ||||
\(454\) | 22.7298i | 0.0500657i | ||||||||
\(455\) | −9.76554 | − | 112.676i | −0.0214627 | − | 0.247640i | ||||
\(456\) | −12.4523 | −0.0273077 | ||||||||
\(457\) | 445.459 | − | 771.557i | 0.974745 | − | 1.68831i | 0.293972 | − | 0.955814i | \(-0.405023\pi\) |
0.680773 | − | 0.732494i | \(-0.261644\pi\) | |||||||
\(458\) | −181.389 | + | 104.725i | −0.396046 | + | 0.228657i | ||||
\(459\) | −6.89008 | − | 11.9340i | −0.0150111 | − | 0.0259999i | ||||
\(460\) | −155.312 | − | 89.6696i | −0.337635 | − | 0.194934i | ||||
\(461\) | 534.019i | 1.15839i | 0.815188 | + | 0.579196i | \(0.196633\pi\) | ||||
−0.815188 | + | 0.579196i | \(0.803367\pi\) | |||||||
\(462\) | 126.200 | − | 270.062i | 0.273159 | − | 0.584550i | ||||
\(463\) | 158.679 | 0.342719 | 0.171359 | − | 0.985209i | \(-0.445184\pi\) | ||||
0.171359 | + | 0.985209i | \(0.445184\pi\) | |||||||
\(464\) | −94.0160 | + | 162.840i | −0.202621 | + | 0.350949i | ||||
\(465\) | 135.177 | − | 78.0444i | 0.290703 | − | 0.167837i | ||||
\(466\) | 211.509 | + | 366.344i | 0.453881 | + | 0.786145i | ||||
\(467\) | −97.1671 | − | 56.0995i | −0.208067 | − | 0.120127i | 0.392346 | − | 0.919818i | \(-0.371664\pi\) |
−0.600413 | + | 0.799690i | \(0.704997\pi\) | |||||||
\(468\) | − | 43.3535i | − | 0.0926358i | ||||||
\(469\) | −596.582 | − | 278.782i | −1.27203 | − | 0.594417i | ||||
\(470\) | −105.773 | −0.225050 | ||||||||
\(471\) | −145.359 | + | 251.769i | −0.308618 | + | 0.534542i | ||||
\(472\) | 246.317 | − | 142.211i | 0.521859 | − | 0.301295i | ||||
\(473\) | 324.870 | + | 562.691i | 0.686829 | + | 1.18962i | ||||
\(474\) | −51.1416 | − | 29.5266i | −0.107894 | − | 0.0622925i | ||||
\(475\) | 12.7091i | 0.0267560i | ||||||||
\(476\) | 36.9893 | − | 3.20583i | 0.0777085 | − | 0.00673494i | ||||
\(477\) | 212.665 | 0.445839 | ||||||||
\(478\) | 80.7891 | − | 139.931i | 0.169015 | − | 0.292742i | ||||
\(479\) | −598.669 | + | 345.642i | −1.24983 | + | 0.721590i | −0.971076 | − | 0.238772i | \(-0.923255\pi\) |
−0.278755 | + | 0.960362i | \(0.589922\pi\) | |||||||
\(480\) | −10.9545 | − | 18.9737i | −0.0228218 | − | 0.0395285i | ||||
\(481\) | −203.387 | − | 117.426i | −0.422843 | − | 0.244128i | ||||
\(482\) | − | 192.958i | − | 0.400328i | ||||||
\(483\) | −278.551 | − | 398.502i | −0.576711 | − | 0.825056i | ||||
\(484\) | 362.489 | 0.748945 | ||||||||
\(485\) | 8.36575 | − | 14.4899i | 0.0172490 | − | 0.0298761i | ||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −360.410 | − | 624.248i | −0.740062 | − | 1.28182i | −0.952467 | − | 0.304643i | \(-0.901463\pi\) |
0.212405 | − | 0.977182i | \(-0.431870\pi\) | |||||||
\(488\) | −31.5713 | − | 18.2277i | −0.0646953 | − | 0.0373518i | ||||
\(489\) | − | 479.033i | − | 0.979618i | ||||||
\(490\) | −26.6588 | − | 152.641i | −0.0544058 | − | 0.311512i | ||||
\(491\) | 589.995 | 1.20162 | 0.600809 | − | 0.799392i | \(-0.294845\pi\) | ||||
0.600809 | + | 0.799392i | \(0.294845\pi\) | |||||||
\(492\) | −122.400 | + | 212.004i | −0.248781 | + | 0.430902i | ||||
\(493\) | −107.963 | + | 62.3325i | −0.218992 | + | 0.126435i | ||||
\(494\) | −12.9868 | − | 22.4939i | −0.0262891 | − | 0.0455341i | ||||
\(495\) | −100.999 | − | 58.3117i | −0.204038 | − | 0.117801i | ||||
\(496\) | 161.208i | 0.325016i | ||||||||
\(497\) | −66.4340 | + | 46.4371i | −0.133670 | + | 0.0934348i | ||||
\(498\) | −273.521 | −0.549238 | ||||||||
\(499\) | 437.845 | − | 758.370i | 0.877445 | − | 1.51978i | 0.0233104 | − | 0.999728i | \(-0.492579\pi\) |
0.854135 | − | 0.520052i | \(-0.174087\pi\) | |||||||
\(500\) | −19.3649 | + | 11.1803i | −0.0387298 | + | 0.0223607i | ||||
\(501\) | −41.9380 | − | 72.6387i | −0.0837085 | − | 0.144987i | ||||
\(502\) | 559.737 | + | 323.165i | 1.11501 | + | 0.643754i | ||||
\(503\) | 817.809i | 1.62586i | 0.582360 | + | 0.812931i | \(0.302129\pi\) | ||||
−0.582360 | + | 0.812931i | \(0.697871\pi\) | |||||||
\(504\) | −5.12866 | − | 59.1751i | −0.0101759 | − | 0.117411i | ||||
\(505\) | 211.524 | 0.418859 | ||||||||
\(506\) | 492.974 | − | 853.857i | 0.974258 | − | 1.68746i | ||||
\(507\) | −175.186 | + | 101.144i | −0.345535 | + | 0.199495i | ||||
\(508\) | −53.7033 | − | 93.0168i | −0.105715 | − | 0.183104i | ||||
\(509\) | −657.585 | − | 379.657i | −1.29191 | − | 0.745887i | −0.312921 | − | 0.949779i | \(-0.601308\pi\) |
−0.978993 | + | 0.203892i | \(0.934641\pi\) | |||||||
\(510\) | − | 14.5256i | − | 0.0284815i | ||||||
\(511\) | −67.1794 | + | 143.761i | −0.131467 | + | 0.281333i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −6.60384 | + | 11.4382i | −0.0128730 | + | 0.0222967i | ||||
\(514\) | −61.2350 | + | 35.3540i | −0.119134 | + | 0.0687821i | ||||
\(515\) | 66.8827 | + | 115.844i | 0.129869 | + | 0.224940i | ||||
\(516\) | 112.120 | + | 64.7323i | 0.217286 | + | 0.125450i | ||||
\(517\) | − | 581.508i | − | 1.12477i | ||||||
\(518\) | −291.504 | − | 136.219i | −0.562748 | − | 0.262971i | ||||
\(519\) | 195.667 | 0.377009 | ||||||||
\(520\) | 22.8493 | − | 39.5762i | 0.0439410 | − | 0.0761081i | ||||
\(521\) | −153.671 | + | 88.7220i | −0.294954 | + | 0.170292i | −0.640174 | − | 0.768230i | \(-0.721138\pi\) |
0.345220 | + | 0.938522i | \(0.387804\pi\) | |||||||
\(522\) | 99.7190 | + | 172.718i | 0.191033 | + | 0.330878i | ||||
\(523\) | 91.1221 | + | 52.6094i | 0.174230 | + | 0.100592i | 0.584579 | − | 0.811337i | \(-0.301260\pi\) |
−0.410349 | + | 0.911929i | \(0.634593\pi\) | |||||||
\(524\) | 116.969i | 0.223222i | ||||||||
\(525\) | −60.3954 | + | 5.23442i | −0.115039 | + | 0.00997033i | ||||
\(526\) | 257.780 | 0.490075 | ||||||||
\(527\) | −53.4403 | + | 92.5612i | −0.101405 | + | 0.175638i | ||||
\(528\) | 104.311 | − | 60.2240i | 0.197559 | − | 0.114061i | ||||
\(529\) | −539.563 | − | 934.551i | −1.01997 | − | 1.76664i | ||||
\(530\) | 194.136 | + | 112.084i | 0.366294 | + | 0.211480i | ||||
\(531\) | − | 301.676i | − | 0.568128i | ||||||
\(532\) | −20.3873 | − | 29.1665i | −0.0383220 | − | 0.0548243i | ||||
\(533\) | −510.618 | −0.958007 | ||||||||
\(534\) | −156.653 | + | 271.331i | −0.293358 | + | 0.508111i | ||||
\(535\) | 12.5129 | − | 7.22430i | 0.0233885 | − | 0.0135034i | ||||
\(536\) | −133.038 | − | 230.429i | −0.248206 | − | 0.429905i | ||||
\(537\) | 497.125 | + | 287.015i | 0.925744 | + | 0.534479i | ||||
\(538\) | − | 53.2051i | − | 0.0988943i | ||||||
\(539\) | 839.172 | − | 146.562i | 1.55690 | − | 0.271914i | ||||
\(540\) | −23.2379 | −0.0430331 | ||||||||
\(541\) | 138.181 | − | 239.337i | 0.255419 | − | 0.442398i | −0.709591 | − | 0.704614i | \(-0.751120\pi\) |
0.965009 | + | 0.262216i | \(0.0844534\pi\) | |||||||
\(542\) | −248.301 | + | 143.357i | −0.458121 | + | 0.264496i | ||||
\(543\) | 184.747 | + | 319.992i | 0.340234 | + | 0.589303i | ||||
\(544\) | 12.9921 | + | 7.50097i | 0.0238825 | + | 0.0137886i | ||||
\(545\) | − | 366.358i | − | 0.672216i | ||||||
\(546\) | 101.545 | − | 70.9796i | 0.185980 | − | 0.129999i | ||||
\(547\) | 918.409 | 1.67899 | 0.839496 | − | 0.543366i | \(-0.182850\pi\) | ||||
0.839496 | + | 0.543366i | \(0.182850\pi\) | |||||||
\(548\) | 12.1170 | − | 20.9872i | 0.0221113 | − | 0.0382978i | ||||
\(549\) | −33.4864 | + | 19.3334i | −0.0609953 | + | 0.0352156i | ||||
\(550\) | −61.4659 | − | 106.462i | −0.111756 | − | 0.193567i | ||||
\(551\) | 103.478 | + | 59.7429i | 0.187800 | + | 0.108426i | ||||
\(552\) | − | 196.456i | − | 0.355899i | ||||||
\(553\) | −14.5716 | − | 168.128i | −0.0263500 | − | 0.304030i | ||||
\(554\) | 362.380 | 0.654116 | ||||||||
\(555\) | −62.9413 | + | 109.018i | −0.113408 | + | 0.196428i | ||||
\(556\) | −78.3861 | + | 45.2562i | −0.140982 | + | 0.0813961i | ||||
\(557\) | −367.505 | − | 636.538i | −0.659794 | − | 1.14280i | −0.980669 | − | 0.195675i | \(-0.937310\pi\) |
0.320875 | − | 0.947122i | \(-0.396023\pi\) | |||||||
\(558\) | 148.079 | + | 85.4933i | 0.265374 | + | 0.153214i | ||||
\(559\) | 270.044i | 0.483083i | ||||||||
\(560\) | 26.5062 | − | 56.7223i | 0.0473325 | − | 0.101290i | ||||
\(561\) | 79.8569 | 0.142347 | ||||||||
\(562\) | 100.029 | − | 173.255i | 0.177987 | − | 0.308282i | ||||
\(563\) | 715.827 | − | 413.283i | 1.27145 | − | 0.734073i | 0.296191 | − | 0.955129i | \(-0.404284\pi\) |
0.975261 | + | 0.221056i | \(0.0709502\pi\) | |||||||
\(564\) | −57.9344 | − | 100.345i | −0.102721 | − | 0.177917i | ||||
\(565\) | 204.171 | + | 117.878i | 0.361365 | + | 0.208634i | ||||
\(566\) | 768.438i | 1.35767i | ||||||||
\(567\) | −57.0757 | − | 26.6714i | −0.100663 | − | 0.0470395i | ||||
\(568\) | −32.7511 | −0.0576603 | ||||||||
\(569\) | 216.546 | − | 375.069i | 0.380573 | − | 0.659172i | −0.610571 | − | 0.791961i | \(-0.709060\pi\) |
0.991144 | + | 0.132790i | \(0.0423935\pi\) | |||||||
\(570\) | −12.0569 | + | 6.96106i | −0.0211525 | + | 0.0122124i | ||||
\(571\) | −240.036 | − | 415.754i | −0.420378 | − | 0.728116i | 0.575598 | − | 0.817733i | \(-0.304769\pi\) |
−0.995976 | + | 0.0896166i | \(0.971436\pi\) | |||||||
\(572\) | 217.577 | + | 125.618i | 0.380380 | + | 0.219612i | ||||
\(573\) | 115.880i | 0.202234i | ||||||||
\(574\) | −696.964 | + | 60.4054i | −1.21422 | + | 0.105236i | ||||
\(575\) | −200.507 | −0.348708 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −75.4646 | + | 43.5695i | −0.130788 | + | 0.0755104i | −0.563966 | − | 0.825798i | \(-0.690725\pi\) |
0.433179 | + | 0.901308i | \(0.357392\pi\) | |||||||
\(578\) | −199.381 | − | 345.338i | −0.344949 | − | 0.597470i | ||||
\(579\) | −168.906 | − | 97.5179i | −0.291720 | − | 0.168425i | ||||
\(580\) | 210.226i | 0.362459i | ||||||||
\(581\) | −447.815 | − | 640.655i | −0.770766 | − | 1.10268i | ||||
\(582\) | 18.3284 | 0.0314922 | ||||||||
\(583\) | −616.204 | + | 1067.30i | −1.05695 | + | 1.83070i | ||||
\(584\) | −55.5276 | + | 32.0589i | −0.0950815 | + | 0.0548953i | ||||
\(585\) | −24.2354 | − | 41.9769i | −0.0414280 | − | 0.0717554i | ||||
\(586\) | −459.633 | − | 265.369i | −0.784356 | − | 0.452848i | ||||
\(587\) | − | 104.332i | − | 0.177737i | −0.996043 | − | 0.0888687i | \(-0.971675\pi\) | ||
0.996043 | − | 0.0888687i | \(-0.0283252\pi\) | |||||||
\(588\) | 130.206 | − | 108.896i | 0.221439 | − | 0.185197i | ||||
\(589\) | 102.440 | 0.173922 | ||||||||
\(590\) | 158.997 | − | 275.391i | 0.269487 | − | 0.466765i | ||||
\(591\) | 91.5316 | − | 52.8458i | 0.154876 | − | 0.0894176i | ||||
\(592\) | −65.0055 | − | 112.593i | −0.109807 | − | 0.190191i | ||||
\(593\) | 252.421 | + | 145.735i | 0.425668 | + | 0.245760i | 0.697499 | − | 0.716585i | \(-0.254296\pi\) |
−0.271831 | + | 0.962345i | \(0.587629\pi\) | |||||||
\(594\) | − | 127.754i | − | 0.215075i | ||||||
\(595\) | 34.0226 | − | 23.7817i | 0.0571808 | − | 0.0399692i | ||||
\(596\) | −101.790 | −0.170788 | ||||||||
\(597\) | 165.554 | − | 286.748i | 0.277310 | − | 0.480314i | ||||
\(598\) | 354.878 | − | 204.889i | 0.593442 | − | 0.342624i | ||||
\(599\) | −298.839 | − | 517.604i | −0.498896 | − | 0.864114i | 0.501103 | − | 0.865388i | \(-0.332928\pi\) |
−0.999999 | + | 0.00127378i | \(0.999595\pi\) | |||||||
\(600\) | −21.2132 | − | 12.2474i | −0.0353553 | − | 0.0204124i | ||||
\(601\) | − | 447.444i | − | 0.744499i | −0.928133 | − | 0.372250i | \(-0.878587\pi\) | ||
0.928133 | − | 0.372250i | \(-0.121413\pi\) | |||||||
\(602\) | 31.9458 | + | 368.594i | 0.0530661 | + | 0.612283i | ||||
\(603\) | −282.217 | −0.468021 | ||||||||
\(604\) | 157.695 | − | 273.136i | 0.261085 | − | 0.452212i | ||||
\(605\) | 350.979 | − | 202.638i | 0.580130 | − | 0.334938i | ||||
\(606\) | 115.856 | + | 200.669i | 0.191182 | + | 0.331137i | ||||
\(607\) | 533.739 | + | 308.155i | 0.879307 | + | 0.507668i | 0.870430 | − | 0.492293i | \(-0.163841\pi\) |
0.00887709 | + | 0.999961i | \(0.497174\pi\) | |||||||
\(608\) | − | 14.3787i | − | 0.0236492i | ||||||
\(609\) | −241.288 | + | 516.346i | −0.396203 | + | 0.847859i | ||||
\(610\) | −40.7584 | −0.0668170 | ||||||||
\(611\) | 120.842 | − | 209.305i | 0.197778 | − | 0.342562i | ||||
\(612\) | 13.7802 | − | 7.95598i | 0.0225166 | − | 0.0130000i | ||||
\(613\) | 63.5384 | + | 110.052i | 0.103651 | + | 0.179530i | 0.913186 | − | 0.407542i | \(-0.133614\pi\) |
−0.809535 | + | 0.587072i | \(0.800281\pi\) | |||||||
\(614\) | 50.6354 | + | 29.2344i | 0.0824681 | + | 0.0476130i | ||||
\(615\) | 273.696i | 0.445034i | ||||||||
\(616\) | 311.841 | + | 145.723i | 0.506235 | + | 0.236563i | ||||
\(617\) | 68.5630 | 0.111123 | 0.0555616 | − | 0.998455i | \(-0.482305\pi\) | ||||
0.0555616 | + | 0.998455i | \(0.482305\pi\) | |||||||
\(618\) | −73.2664 | + | 126.901i | −0.118554 | + | 0.205342i | ||||
\(619\) | 833.529 | − | 481.238i | 1.34657 | − | 0.777445i | 0.358812 | − | 0.933410i | \(-0.383182\pi\) |
0.987763 | + | 0.155965i | \(0.0498487\pi\) | |||||||
\(620\) | 90.1179 | + | 156.089i | 0.145351 | + | 0.251756i | ||||
\(621\) | −180.457 | − | 104.187i | −0.290590 | − | 0.167772i | ||||
\(622\) | − | 207.265i | − | 0.333224i | ||||||
\(623\) | −892.003 | + | 77.3092i | −1.43179 | + | 0.124092i | ||||
\(624\) | 50.0604 | 0.0802249 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −275.409 | + | 159.008i | −0.439951 | + | 0.254006i | ||||
\(627\) | −38.2697 | − | 66.2850i | −0.0610362 | − | 0.105718i | ||||
\(628\) | −290.718 | − | 167.846i | −0.462927 | − | 0.267271i | ||||
\(629\) | − | 86.1971i | − | 0.137038i | ||||||
\(630\) | −38.0457 | − | 54.4291i | −0.0603900 | − | 0.0863953i | ||||
\(631\) | 412.586 | 0.653860 | 0.326930 | − | 0.945048i | \(-0.393986\pi\) | ||||
0.326930 | + | 0.945048i | \(0.393986\pi\) | |||||||
\(632\) | 34.0944 | − | 59.0533i | 0.0539469 | − | 0.0934387i | ||||
\(633\) | −420.173 | + | 242.587i | −0.663781 | + | 0.383234i | ||||
\(634\) | 159.966 | + | 277.070i | 0.252313 | + | 0.437019i | ||||
\(635\) | −103.996 | − | 60.0421i | −0.163773 | − | 0.0945545i | ||||
\(636\) | 245.565i | 0.386108i | ||||||||
\(637\) | 332.504 | + | 121.635i | 0.521985 | + | 0.190949i | ||||
\(638\) | −1155.76 | −1.81153 | ||||||||
\(639\) | −17.3689 | + | 30.0838i | −0.0271813 | + | 0.0470795i | ||||
\(640\) | 21.9089 | − | 12.6491i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | 71.3374 | + | 123.560i | 0.111291 | + | 0.192761i | 0.916291 | − | 0.400513i | \(-0.131168\pi\) |
−0.805000 | + | 0.593275i | \(0.797835\pi\) | |||||||
\(642\) | 13.7072 | + | 7.91383i | 0.0213507 | + | 0.0123268i | ||||
\(643\) | 239.942i | 0.373160i | 0.982440 | + | 0.186580i | \(0.0597403\pi\) | ||||
−0.982440 | + | 0.186580i | \(0.940260\pi\) | |||||||
\(644\) | 460.150 | − | 321.643i | 0.714519 | − | 0.499446i | ||||
\(645\) | 144.746 | 0.224412 | ||||||||
\(646\) | 4.76653 | − | 8.25588i | 0.00737853 | − | 0.0127800i | ||||
\(647\) | −128.817 | + | 74.3724i | −0.199098 | + | 0.114950i | −0.596235 | − | 0.802810i | \(-0.703337\pi\) |
0.397136 | + | 0.917760i | \(0.370004\pi\) | |||||||
\(648\) | −12.7279 | − | 22.0454i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 1514.01 | + | 874.115i | 2.33284 | + | 1.34686i | ||||
\(650\) | − | 51.0926i | − | 0.0786041i | ||||||
\(651\) | 42.1915 | + | 486.810i | 0.0648102 | + | 0.747788i | ||||
\(652\) | 553.140 | 0.848374 | ||||||||
\(653\) | −144.011 | + | 249.434i | −0.220537 | + | 0.381982i | −0.954971 | − | 0.296698i | \(-0.904114\pi\) |
0.734434 | + | 0.678680i | \(0.237448\pi\) | |||||||
\(654\) | 347.557 | − | 200.662i | 0.531433 | − | 0.306823i | ||||
\(655\) | 65.3874 | + | 113.254i | 0.0998281 | + | 0.172907i | ||||
\(656\) | −244.801 | − | 141.336i | −0.373172 | − | 0.215451i | ||||
\(657\) | 68.0071i | 0.103512i | ||||||||
\(658\) | 140.183 | − | 299.985i | 0.213043 | − | 0.455905i | ||||
\(659\) | −175.647 | −0.266536 | −0.133268 | − | 0.991080i | \(-0.542547\pi\) | ||||
−0.133268 | + | 0.991080i | \(0.542547\pi\) | |||||||
\(660\) | 67.3325 | − | 116.623i | 0.102019 | − | 0.176702i | ||||
\(661\) | −615.015 | + | 355.079i | −0.930432 | + | 0.537185i | −0.886948 | − | 0.461869i | \(-0.847179\pi\) |
−0.0434835 | + | 0.999054i | \(0.513846\pi\) | |||||||
\(662\) | −98.8651 | − | 171.239i | −0.149343 | − | 0.258670i | ||||
\(663\) | 28.7433 | + | 16.5950i | 0.0433535 | + | 0.0250301i | ||||
\(664\) | − | 315.834i | − | 0.475654i | ||||||
\(665\) | −36.0445 | − | 16.8435i | −0.0542022 | − | 0.0253286i | ||||
\(666\) | −137.897 | −0.207053 | ||||||||
\(667\) | −942.544 | + | 1632.53i | −1.41311 | + | 2.44758i | ||||
\(668\) | 83.8760 | − | 48.4258i | 0.125563 | − | 0.0724937i | ||||
\(669\) | 236.216 | + | 409.139i | 0.353089 | + | 0.611567i | ||||
\(670\) | −257.627 | − | 148.741i | −0.384518 | − | 0.222002i | ||||
\(671\) | − | 224.076i | − | 0.333944i | ||||||
\(672\) | 68.3296 | − | 5.92207i | 0.101681 | − | 0.00881261i | ||||
\(673\) | −1173.04 | −1.74301 | −0.871504 | − | 0.490389i | \(-0.836855\pi\) | ||||
−0.871504 | + | 0.490389i | \(0.836855\pi\) | |||||||
\(674\) | −21.2930 | + | 36.8806i | −0.0315920 | + | 0.0547189i | ||||
\(675\) | −22.5000 | + | 12.9904i | −0.0333333 | + | 0.0192450i | ||||
\(676\) | −116.791 | − | 202.288i | −0.172768 | − | 0.299242i | ||||
\(677\) | 586.699 | + | 338.731i | 0.866616 | + | 0.500341i | 0.866222 | − | 0.499659i | \(-0.166541\pi\) |
0.000393478 | 1.00000i | \(0.499875\pi\) | ||||||||
\(678\) | 258.258i | 0.380912i | ||||||||
\(679\) | 30.0078 | + | 42.9299i | 0.0441941 | + | 0.0632252i | ||||
\(680\) | 16.7727 | 0.0246657 | ||||||||
\(681\) | −13.9191 | + | 24.1086i | −0.0204392 | + | 0.0354018i | ||||
\(682\) | −858.126 | + | 495.439i | −1.25825 | + | 0.726450i | ||||
\(683\) | 415.514 | + | 719.691i | 0.608366 | + | 1.05372i | 0.991510 | + | 0.130032i | \(0.0415079\pi\) |
−0.383144 | + | 0.923689i | \(0.625159\pi\) | |||||||
\(684\) | −13.2077 | − | 7.62546i | −0.0193095 | − | 0.0111483i | ||||
\(685\) | − | 27.0944i | − | 0.0395538i | ||||||
\(686\) | 468.239 | + | 126.689i | 0.682564 | + | 0.184679i | ||||
\(687\) | −256.523 | −0.373395 | ||||||||
\(688\) | −74.7464 | + | 129.465i | −0.108643 | + | 0.188175i | ||||
\(689\) | −443.587 | + | 256.105i | −0.643813 | + | 0.371706i | ||||
\(690\) | −109.822 | − | 190.218i | −0.159163 | − | 0.275678i | ||||
\(691\) | 541.436 | + | 312.598i | 0.783554 | + | 0.452385i | 0.837688 | − | 0.546149i | \(-0.183907\pi\) |
−0.0541345 | + | 0.998534i | \(0.517240\pi\) | |||||||
\(692\) | 225.937i | 0.326499i | ||||||||
\(693\) | 299.233 | − | 209.163i | 0.431794 | − | 0.301823i | ||||
\(694\) | −588.181 | −0.847524 | ||||||||
\(695\) | −50.5980 | + | 87.6383i | −0.0728029 | + | 0.126098i | ||||
\(696\) | −199.438 | + | 115.146i | −0.286549 | + | 0.165439i | ||||
\(697\) | −93.7055 | − | 162.303i | −0.134441 | − | 0.232859i | ||||
\(698\) | −728.661 | − | 420.693i | −1.04393 | − | 0.602712i | ||||
\(699\) | 518.088i | 0.741185i | ||||||||
\(700\) | −6.04419 | − | 69.7386i | −0.00863456 | − | 0.0996265i | ||||
\(701\) | 1030.02 | 1.46936 | 0.734678 | − | 0.678416i | \(-0.237333\pi\) | ||||
0.734678 | + | 0.678416i | \(0.237333\pi\) | |||||||
\(702\) | 26.5485 | − | 45.9834i | 0.0378184 | − | 0.0655034i | ||||
\(703\) | −71.5477 | + | 41.3081i | −0.101775 | + | 0.0587597i | ||||
\(704\) | 69.5407 | + | 120.448i | 0.0987795 | + | 0.171091i | ||||
\(705\) | −112.190 | − | 64.7727i | −0.159134 | − | 0.0918761i | ||||
\(706\) | 515.224i | 0.729779i | ||||||||
\(707\) | −280.335 | + | 599.906i | −0.396513 | + | 0.848523i | ||||
\(708\) | 348.345 | 0.492013 | ||||||||
\(709\) | 329.126 | − | 570.062i | 0.464211 | − | 0.804037i | −0.534955 | − | 0.844881i | \(-0.679671\pi\) |
0.999166 | + | 0.0408438i | \(0.0130046\pi\) | |||||||
\(710\) | −31.7111 | + | 18.3084i | −0.0446635 | + | 0.0257865i | ||||
\(711\) | −36.1626 | − | 62.6354i | −0.0508616 | − | 0.0880949i | ||||
\(712\) | −313.306 | − | 180.887i | −0.440037 | − | 0.254055i | ||||
\(713\) | 1616.17i | 2.26671i | ||||||||
\(714\) | 41.1962 | + | 19.2509i | 0.0576978 | + | 0.0269621i | ||||
\(715\) | 280.891 | 0.392854 | ||||||||
\(716\) | −331.416 | + | 574.030i | −0.462872 | + | 0.801718i | ||||
\(717\) | 171.380 | − | 98.9461i | 0.239023 | − | 0.138000i | ||||
\(718\) | 433.288 | + | 750.478i | 0.603466 | + | 1.04523i | ||||
\(719\) | −1166.99 | − | 673.760i | −1.62307 | − | 0.937079i | −0.986093 | − | 0.166195i | \(-0.946852\pi\) |
−0.636975 | − | 0.770884i | \(-0.719815\pi\) | |||||||
\(720\) | − | 26.8328i | − | 0.0372678i | ||||||
\(721\) | −417.188 | + | 36.1574i | −0.578625 | + | 0.0501490i | ||||
\(722\) | 501.394 | 0.694452 | ||||||||
\(723\) | 118.162 | − | 204.663i | 0.163433 | − | 0.283074i | ||||
\(724\) | −369.495 | + | 213.328i | −0.510352 | + | 0.294652i | ||||
\(725\) | 117.520 | + | 203.551i | 0.162096 | + | 0.280759i | ||||
\(726\) | 384.478 | + | 221.978i | 0.529584 | + | 0.305755i | ||||
\(727\) | 1126.18i | 1.54907i | 0.632530 | + | 0.774536i | \(0.282017\pi\) | ||||
−0.632530 | + | 0.774536i | \(0.717983\pi\) | |||||||
\(728\) | 81.9602 | + | 117.254i | 0.112583 | + | 0.161063i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | −35.8429 | + | 62.0817i | −0.0490999 | + | 0.0850435i | ||||
\(731\) | −85.8348 | + | 49.5568i | −0.117421 | + | 0.0677931i | ||||
\(732\) | −22.3243 | − | 38.6668i | −0.0304976 | − | 0.0528235i | ||||
\(733\) | 525.395 | + | 303.337i | 0.716773 | + | 0.413829i | 0.813564 | − | 0.581476i | \(-0.197524\pi\) |
−0.0967907 | + | 0.995305i | \(0.530858\pi\) | |||||||
\(734\) | − | 697.233i | − | 0.949909i | ||||||
\(735\) | 65.1972 | − | 178.225i | 0.0887037 | − | 0.242484i | ||||
\(736\) | 226.848 | 0.308218 | ||||||||
\(737\) | 817.731 | − | 1416.35i | 1.10954 | − | 1.92178i | ||||
\(738\) | −259.651 | + | 149.909i | −0.351830 | + | 0.203129i | ||||
\(739\) | −461.084 | − | 798.622i | −0.623930 | − | 1.08068i | −0.988747 | − | 0.149599i | \(-0.952202\pi\) |
0.364817 | − | 0.931079i | \(-0.381132\pi\) | |||||||
\(740\) | −125.883 | − | 72.6783i | −0.170112 | − | 0.0982140i | ||||
\(741\) | − | 31.8111i | − | 0.0429300i | ||||||
\(742\) | −575.175 | + | 402.045i | −0.775168 | + | 0.541840i | ||||
\(743\) | 13.3994 | 0.0180342 | 0.00901712 | − | 0.999959i | \(-0.497130\pi\) | ||||
0.00901712 | + | 0.999959i | \(0.497130\pi\) | |||||||
\(744\) | −98.7192 | + | 170.987i | −0.132687 | + | 0.229821i | ||||
\(745\) | −98.5574 | + | 56.9022i | −0.132292 | + | 0.0763787i | ||||
\(746\) | −116.957 | − | 202.576i | −0.156779 | − | 0.271550i | ||||
\(747\) | −290.112 | − | 167.496i | −0.388370 | − | 0.224225i | ||||
\(748\) | 92.2108i | 0.123277i | ||||||||
\(749\) | 3.90552 | + | 45.0624i | 0.00521431 | + | 0.0601634i | ||||
\(750\) | −27.3861 | −0.0365148 | ||||||||
\(751\) | −538.071 | + | 931.967i | −0.716473 | + | 1.24097i | 0.245916 | + | 0.969291i | \(0.420911\pi\) |
−0.962389 | + | 0.271676i | \(0.912422\pi\) | |||||||
\(752\) | 115.869 | − | 66.8969i | 0.154081 | − | 0.0889587i | ||||
\(753\) | 395.794 | + | 685.536i | 0.525623 | + | 0.910406i | ||||
\(754\) | −415.997 | − | 240.176i | −0.551721 | − | 0.318536i | ||||
\(755\) | − | 352.617i | − | 0.467043i | ||||||
\(756\) | 30.7975 | − | 65.9054i | 0.0407374 | − | 0.0871764i | ||||
\(757\) | −254.117 | −0.335690 | −0.167845 | − | 0.985813i | \(-0.553681\pi\) | ||||
−0.167845 | + | 0.985813i | \(0.553681\pi\) | |||||||
\(758\) | 126.819 | − | 219.656i | 0.167307 | − | 0.289784i | ||||
\(759\) | 1045.76 | − | 603.768i | 1.37781 | − | 0.795478i | ||||
\(760\) | −8.03794 | − | 13.9221i | −0.0105762 | − | 0.0183186i | ||||
\(761\) | −685.095 | − | 395.540i | −0.900256 | − | 0.519763i | −0.0229729 | − | 0.999736i | \(-0.507313\pi\) |
−0.877283 | + | 0.479973i | \(0.840646\pi\) | |||||||
\(762\) | − | 131.546i | − | 0.172632i | ||||||
\(763\) | 1039.03 | + | 485.538i | 1.36177 | + | 0.636354i | ||||
\(764\) | −133.807 | −0.175140 | ||||||||
\(765\) | 8.89506 | − | 15.4067i | 0.0116275 | − | 0.0201395i | ||||
\(766\) | −329.664 | + | 190.332i | −0.430371 | + | 0.248475i | ||||
\(767\) | 363.298 | + | 629.250i | 0.473661 | + | 0.820405i | ||||
\(768\) | 24.0000 | + | 13.8564i | 0.0312500 | + | 0.0180422i | ||||
\(769\) | − | 464.403i | − | 0.603905i | −0.953323 | − | 0.301952i | \(-0.902362\pi\) | ||
0.953323 | − | 0.301952i | \(-0.0976384\pi\) | |||||||
\(770\) | 383.400 | − | 33.2290i | 0.497922 | − | 0.0431546i | ||||
\(771\) | −86.5993 | −0.112321 | ||||||||
\(772\) | 112.604 | − | 195.036i | 0.145860 | − | 0.252637i | ||||
\(773\) | 675.608 | − | 390.063i | 0.874008 | − | 0.504609i | 0.00533002 | − | 0.999986i | \(-0.498303\pi\) |
0.868678 | + | 0.495377i | \(0.164970\pi\) | |||||||
\(774\) | 79.2805 | + | 137.318i | 0.102430 | + | 0.177413i | ||||
\(775\) | 174.513 | + | 100.755i | 0.225177 | + | 0.130006i | ||||
\(776\) | 21.1639i | 0.0272730i | ||||||||
\(777\) | −225.769 | − | 322.991i | −0.290566 | − | 0.415690i | ||||
\(778\) | −669.980 | −0.861157 | ||||||||
\(779\) | −89.8126 | + | 155.560i | −0.115292 | + | 0.199692i | ||||
\(780\) | 48.4707 | − | 27.9846i | 0.0621420 | − | 0.0358777i | ||||
\(781\) | −100.654 | − | 174.337i | −0.128878 | − | 0.223223i | ||||
\(782\) | 130.250 | + | 75.2000i | 0.166560 | + | 0.0961637i | ||||
\(783\) | 244.261i | 0.311955i | ||||||||
\(784\) | 125.742 | + | 150.349i | 0.160385 | + | 0.191772i | ||||
\(785\) | −375.316 | −0.478109 | ||||||||
\(786\) | −71.6283 | + | 124.064i | −0.0911302 | + | 0.157842i | ||||
\(787\) | 998.358 | − | 576.402i | 1.26856 | − | 0.732404i | 0.293845 | − | 0.955853i | \(-0.405065\pi\) |
0.974716 | + | 0.223449i | \(0.0717316\pi\) | |||||||
\(788\) | 61.0211 | + | 105.692i | 0.0774379 | + | 0.134126i | ||||
\(789\) | 273.416 | + | 157.857i | 0.346535 | + | 0.200072i | ||||
\(790\) | − | 76.2374i | − | 0.0965031i | ||||||
\(791\) | −604.907 | + | 422.827i | −0.764737 | + | 0.534548i | ||||
\(792\) | 147.518 | 0.186260 | ||||||||
\(793\) | 46.5650 | − | 80.6530i | 0.0587201 | − | 0.101706i | ||||
\(794\) | 629.437 | − | 363.406i | 0.792742 | − | 0.457690i | ||||
\(795\) | 137.275 | + | 237.767i | 0.172673 | + | 0.299078i | ||||
\(796\) | 331.108 | + | 191.165i | 0.415964 | + | 0.240157i | ||||
\(797\) | − | 1475.63i | − | 1.85148i | −0.378156 | − | 0.925742i | \(-0.623442\pi\) | ||
0.378156 | − | 0.925742i | \(-0.376558\pi\) | |||||||
\(798\) | −3.76321 | − | 43.4204i | −0.00471580 | − | 0.0544115i | ||||
\(799\) | 88.7051 | 0.111020 | ||||||||
\(800\) | 14.1421 | − | 24.4949i | 0.0176777 | − | 0.0306186i | ||||
\(801\) | −332.311 | + | 191.860i | −0.414871 | + | 0.239526i | ||||
\(802\) | 287.605 | + | 498.146i | 0.358609 | + | 0.621129i | ||||
\(803\) | −341.305 | − | 197.053i | −0.425038 | − | 0.245396i | ||||
\(804\) | − | 325.876i | − | 0.405318i | ||||||
\(805\) | 265.735 | − | 568.662i | 0.330105 | − | 0.706412i | ||||
\(806\) | −411.827 | −0.510951 | ||||||||
\(807\) | 32.5814 | − | 56.4326i | 0.0403734 | − | 0.0699289i | ||||
\(808\) | −231.713 | + | 133.779i | −0.286773 | + | 0.165569i | ||||
\(809\) | 6.88050 | + | 11.9174i | 0.00850495 | + | 0.0147310i | 0.870247 | − | 0.492616i | \(-0.163959\pi\) |
−0.861742 | + | 0.507347i | \(0.830626\pi\) | |||||||
\(810\) | −24.6475 | − | 14.2302i | −0.0304290 | − | 0.0175682i | ||||
\(811\) | − | 1274.65i | − | 1.57170i | −0.618416 | − | 0.785851i | \(-0.712225\pi\) | ||
0.618416 | − | 0.785851i | \(-0.287775\pi\) | |||||||
\(812\) | −596.225 | − | 278.615i | −0.734268 | − | 0.343122i | ||||
\(813\) | −351.151 | −0.431920 | ||||||||
\(814\) | 399.562 | − | 692.062i | 0.490863 | − | 0.850199i | ||||
\(815\) | 535.576 | − | 309.215i | 0.657148 | − | 0.379405i | ||||
\(816\) | 9.18678 | + | 15.9120i | 0.0112583 | + | 0.0195000i | ||||
\(817\) | 82.2689 | + | 47.4980i | 0.100696 | + | 0.0581371i | ||||
\(818\) | − | 689.406i | − | 0.842795i | ||||||
\(819\) | 151.171 | − | 13.1019i | 0.184580 | − | 0.0159974i | ||||
\(820\) | −316.037 | −0.385410 | ||||||||
\(821\) | −292.249 | + | 506.190i | −0.355967 | + | 0.616553i | −0.987283 | − | 0.158973i | \(-0.949182\pi\) |
0.631316 | + | 0.775526i | \(0.282515\pi\) | |||||||
\(822\) | 25.7040 | − | 14.8402i | 0.0312700 | − | 0.0180538i | ||||
\(823\) | 40.4835 | + | 70.1196i | 0.0491902 | + | 0.0851999i | 0.889572 | − | 0.456795i | \(-0.151003\pi\) |
−0.840382 | + | 0.541995i | \(0.817669\pi\) | |||||||
\(824\) | −146.533 | − | 84.6007i | −0.177831 | − | 0.102671i | ||||
\(825\) | − | 150.560i | − | 0.182497i | ||||||
\(826\) | 570.320 | + | 815.913i | 0.690461 | + | 0.987789i | ||||
\(827\) | −1628.46 | −1.96911 | −0.984556 | − | 0.175072i | \(-0.943984\pi\) | ||||
−0.984556 | + | 0.175072i | \(0.943984\pi\) | |||||||
\(828\) | 120.304 | − | 208.373i | 0.145295 | − | 0.251659i | ||||
\(829\) | −761.982 | + | 439.931i | −0.919158 | + | 0.530676i | −0.883366 | − | 0.468683i | \(-0.844729\pi\) |
−0.0357920 | + | 0.999359i | \(0.511395\pi\) | |||||||
\(830\) | −176.557 | − | 305.805i | −0.212719 | − | 0.368440i | ||||
\(831\) | 384.362 | + | 221.912i | 0.462530 | + | 0.267042i | ||||
\(832\) | 57.8047i | 0.0694768i | ||||||||
\(833\) | 22.3570 | + | 128.010i | 0.0268391 | + | 0.153674i | ||||
\(834\) | −110.855 | −0.132919 | ||||||||
\(835\) | 54.1417 | − | 93.7762i | 0.0648404 | − | 0.112307i | ||||
\(836\) | 76.5394 | − | 44.1900i | 0.0915543 | − | 0.0528589i | ||||
\(837\) | 104.708 | + | 181.359i | 0.125099 | + | 0.216677i | ||||
\(838\) | −676.374 | − | 390.505i | −0.807129 | − | 0.465996i | ||||
\(839\) | − | 647.389i | − | 0.771619i | −0.922578 | − | 0.385810i | \(-0.873922\pi\) | ||
0.922578 | − | 0.385810i | \(-0.126078\pi\) | |||||||
\(840\) | 62.8493 | − | 43.9314i | 0.0748206 | − | 0.0522993i | ||||
\(841\) | 1368.75 | 1.62753 | ||||||||
\(842\) | 52.8117 | − | 91.4725i | 0.0627217 | − | 0.108637i | ||||
\(843\) | 212.193 | − | 122.510i | 0.251711 | − | 0.145326i | ||||
\(844\) | −280.115 | − | 485.174i | −0.331890 | − | 0.574851i | ||||
\(845\) | −226.164 | − | 130.576i | −0.267650 | − | 0.154528i | ||||
\(846\) | − | 141.910i | − | 0.167742i | ||||||
\(847\) | 109.548 | + | 1263.97i | 0.129336 | + | 1.49230i | ||||
\(848\) | −283.554 | −0.334379 | ||||||||
\(849\) | −470.571 | + | 815.052i | −0.554264 | + | 0.960014i | ||||
\(850\) | 16.2401 | − | 9.37622i | 0.0191060 | − | 0.0110308i | ||||
\(851\) | −651.704 | − | 1128.78i | −0.765809 | − | 1.32642i | ||||
\(852\) | −34.7378 | − | 20.0559i | −0.0407720 | − | 0.0235397i | ||||
\(853\) | 569.518i | 0.667665i | 0.942632 | + | 0.333833i | \(0.108342\pi\) | ||||
−0.942632 | + | 0.333833i | \(0.891658\pi\) | |||||||
\(854\) | 54.0175 | − | 115.595i | 0.0632524 | − | 0.135358i | ||||
\(855\) | −17.0511 | −0.0199427 | ||||||||
\(856\) | −9.13810 | + | 15.8277i | −0.0106754 | + | 0.0184903i | ||||
\(857\) | 553.041 | − | 319.299i | 0.645322 | − | 0.372577i | −0.141339 | − | 0.989961i | \(-0.545141\pi\) |
0.786662 | + | 0.617384i | \(0.211808\pi\) | |||||||
\(858\) | 153.850 | + | 266.477i | 0.179313 | + | 0.310579i | ||||
\(859\) | 1097.36 | + | 633.562i | 1.27749 | + | 0.737558i | 0.976386 | − | 0.216034i | \(-0.0693122\pi\) |
0.301102 | + | 0.953592i | \(0.402645\pi\) | |||||||
\(860\) | 167.138i | 0.194347i | ||||||||
\(861\) | −776.233 | − | 362.732i | −0.901548 | − | 0.421292i | ||||
\(862\) | 685.437 | 0.795171 | ||||||||
\(863\) | 103.017 | − | 178.430i | 0.119371 | − | 0.206756i | −0.800148 | − | 0.599803i | \(-0.795246\pi\) |
0.919518 | + | 0.393047i | \(0.128579\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 126.303 | + | 218.763i | 0.146015 | + | 0.252905i | ||||
\(866\) | 561.173 | + | 323.993i | 0.648006 | + | 0.374126i | ||||
\(867\) | − | 488.381i | − | 0.563300i | ||||||
\(868\) | −562.120 | + | 48.7185i | −0.647604 | + | 0.0561273i | ||||
\(869\) | 419.129 | 0.482312 | ||||||||
\(870\) | −128.737 | + | 222.978i | −0.147973 | + | 0.256297i | ||||
\(871\) | 588.661 | − | 339.864i | 0.675845 | − | 0.390199i | ||||
\(872\) | 231.705 | + | 401.325i | 0.265717 | + | 0.460235i | ||||
\(873\) | 19.4403 | + | 11.2238i | 0.0222683 | + | 0.0128566i | ||||
\(874\) | − | 144.152i | − | 0.164933i | ||||||
\(875\) | −44.8373 | − | 64.1453i | −0.0512426 | − | 0.0733089i | ||||
\(876\) | −78.5279 | −0.0896437 | ||||||||
\(877\) | −412.272 | + | 714.076i | −0.470093 | + | 0.814226i | −0.999415 | − | 0.0341955i | \(-0.989113\pi\) |
0.529322 | + | 0.848421i | \(0.322446\pi\) | |||||||
\(878\) | −171.356 | + | 98.9325i | −0.195167 | + | 0.112679i | ||||
\(879\) | −325.009 | − | 562.933i | −0.369749 | − | 0.640424i | ||||
\(880\) | 134.665 | + | 77.7489i | 0.153028 | + | 0.0883510i | ||||
\(881\) | 416.337i | 0.472574i | 0.971683 | + | 0.236287i | \(0.0759305\pi\) | ||||
−0.971683 | + | 0.236287i | \(0.924070\pi\) | |||||||
\(882\) | 204.790 | − | 35.7666i | 0.232188 | − | 0.0405517i | ||||
\(883\) | 650.529 | 0.736726 | 0.368363 | − | 0.929682i | \(-0.379918\pi\) | ||||
0.368363 | + | 0.929682i | \(0.379918\pi\) | |||||||
\(884\) | −19.1622 | + | 33.1900i | −0.0216767 | + | 0.0375452i | ||||
\(885\) | 337.284 | − | 194.731i | 0.381112 | − | 0.220035i | ||||
\(886\) | 11.3790 | + | 19.7090i | 0.0128431 | + | 0.0222449i | ||||
\(887\) | −299.987 | − | 173.198i | −0.338204 | − | 0.195262i | 0.321273 | − | 0.946987i | \(-0.395889\pi\) |
−0.659478 | + | 0.751724i | \(0.729223\pi\) | |||||||
\(888\) | − | 159.230i | − | 0.179313i | ||||||
\(889\) | 308.113 | − | 215.370i | 0.346584 | − | 0.242261i | ||||
\(890\) | −404.476 | −0.454468 | ||||||||
\(891\) | 78.2333 | − | 135.504i | 0.0878040 | − | 0.152081i | ||||
\(892\) | −472.433 | + | 272.759i | −0.529633 | + | 0.305784i | ||||
\(893\) | −42.5100 | − | 73.6295i | −0.0476036 | − | 0.0824518i | ||||
\(894\) | −107.964 | − | 62.3332i | −0.120765 | − | 0.0697239i | ||||
\(895\) | 741.069i | 0.828011i | ||||||||
\(896\) | 6.83822 | + | 78.9002i | 0.00763194 | + | 0.0880582i | ||||
\(897\) | 501.873 | 0.559502 | ||||||||
\(898\) | 232.860 | − | 403.326i | 0.259310 | − | 0.449138i | ||||
\(899\) | 1640.70 | − | 947.256i | 1.82502 | − | 1.05368i | ||||
\(900\) | −15.0000 | − | 25.9808i | −0.0166667 | − | 0.0288675i | ||||
\(901\) | −162.809 | − | 93.9978i | −0.180698 | − | 0.104326i | ||||
\(902\) | − | 1737.47i | − | 1.92624i | ||||||
\(903\) | −191.833 | + | 410.516i | −0.212440 | + | 0.454613i | ||||
\(904\) | −298.211 | −0.329879 | ||||||||
\(905\) | −238.508 | + | 413.107i | −0.263544 | + | 0.456472i | ||||
\(906\) | 334.522 | − | 193.136i | 0.369230 | − | 0.213175i | ||||
\(907\) | −210.091 | − | 363.888i | −0.231633 | − | 0.401199i | 0.726656 | − | 0.687001i | \(-0.241073\pi\) |
−0.958289 | + | 0.285802i | \(0.907740\pi\) | |||||||
\(908\) | −27.8382 | − | 16.0724i | −0.0306588 | − | 0.0177009i | ||||
\(909\) | 283.789i | 0.312199i | ||||||||
\(910\) | 144.905 | + | 67.7137i | 0.159236 | + | 0.0744106i | ||||
\(911\) | 717.087 | 0.787142 | 0.393571 | − | 0.919294i | \(-0.371239\pi\) | ||||
0.393571 | + | 0.919294i | \(0.371239\pi\) | |||||||
\(912\) | 8.80512 | − | 15.2509i | 0.00965474 | − | 0.0167225i | ||||
\(913\) | 1681.22 | − | 970.652i | 1.84142 | − | 1.06315i | ||||
\(914\) | 629.974 | + | 1091.15i | 0.689249 | + | 1.19381i | ||||
\(915\) | −43.2308 | − | 24.9593i | −0.0472467 | − | 0.0272779i | ||||
\(916\) | − | 296.207i | − | 0.323370i | ||||||
\(917\) | −407.861 | + | 35.3490i | −0.444777 | + | 0.0385485i | ||||
\(918\) | 19.4881 | 0.0212289 | ||||||||
\(919\) | 59.5137 | − | 103.081i | 0.0647592 | − | 0.112166i | −0.831828 | − | 0.555034i | \(-0.812705\pi\) |
0.896587 | + | 0.442867i | \(0.146039\pi\) | |||||||
\(920\) | 219.645 | − | 126.812i | 0.238744 | − | 0.137839i | ||||
\(921\) | 35.8046 | + | 62.0154i | 0.0388758 | + | 0.0673349i | ||||
\(922\) | −654.037 | − | 377.608i | −0.709367 | − | 0.409553i | ||||
\(923\) | − | 83.6669i | − | 0.0906467i | ||||||
\(924\) | 241.521 | + | 345.525i | 0.261386 | + | 0.373945i | ||||
\(925\) | −162.514 | −0.175691 | ||||||||
\(926\) | −112.203 | + | 194.341i | −0.121169 | + | 0.209872i | ||||
\(927\) | −155.421 | + | 89.7326i | −0.167661 | + | 0.0967989i | ||||
\(928\) | −132.959 | − | 230.291i | −0.143274 | − | 0.248159i | ||||
\(929\) | 328.049 | + | 189.399i | 0.353121 | + | 0.203874i | 0.666059 | − | 0.745899i | \(-0.267980\pi\) |
−0.312938 | + | 0.949773i | \(0.601313\pi\) | |||||||
\(930\) | 220.743i | 0.237358i | ||||||||
\(931\) | 95.5403 | − | 79.9034i | 0.102621 | − | 0.0858253i | ||||
\(932\) | −598.237 | −0.641885 | ||||||||
\(933\) | 126.924 | − | 219.838i | 0.136038 | − | 0.235625i | ||||
\(934\) | 137.415 | − | 79.3366i | 0.147125 | − | 0.0849429i | ||||
\(935\) | 51.5474 | + | 89.2827i | 0.0551309 | + | 0.0954896i | ||||
\(936\) | 53.0970 | + | 30.6556i | 0.0567276 | + | 0.0327517i | ||||
\(937\) | 365.585i | 0.390165i | 0.980787 | + | 0.195083i | \(0.0624975\pi\) | ||||
−0.980787 | + | 0.195083i | \(0.937503\pi\) | |||||||
\(938\) | 763.284 | − | 533.532i | 0.813735 | − | 0.568798i | ||||
\(939\) | −389.487 | −0.414790 | ||||||||
\(940\) | 74.7930 | − | 129.545i | 0.0795670 | − | 0.137814i | ||||
\(941\) | −1193.22 | + | 688.903i | −1.26803 | + | 0.732097i | −0.974615 | − | 0.223889i | \(-0.928125\pi\) |
−0.293414 | + | 0.955985i | \(0.594791\pi\) | |||||||
\(942\) | −205.569 | − | 356.056i | −0.218226 | − | 0.377978i | ||||
\(943\) | −2454.22 | − | 1416.94i | −2.60256 | − | 1.50259i | ||||
\(944\) | 402.235i | 0.426096i | ||||||||
\(945\) | −7.02271 | − | 81.0289i | −0.00743144 | − | 0.0857449i | ||||
\(946\) | −918.871 | −0.971323 | ||||||||
\(947\) | −237.417 | + | 411.218i | −0.250704 | + | 0.434232i | −0.963720 | − | 0.266916i | \(-0.913995\pi\) |
0.713016 | + | 0.701148i | \(0.247329\pi\) | |||||||
\(948\) | 72.3252 | − | 41.7570i | 0.0762924 | − | 0.0440474i | ||||
\(949\) | −81.8986 | − | 141.853i | −0.0862999 | − | 0.149476i | ||||
\(950\) | −15.5654 | − | 8.98669i | −0.0163846 | − | 0.00945968i | ||||
\(951\) | 391.836i | 0.412025i | ||||||||
\(952\) | −22.2290 | + | 47.5693i | −0.0233498 | + | 0.0499677i | ||||
\(953\) | −172.839 | −0.181363 | −0.0906813 | − | 0.995880i | \(-0.528904\pi\) | ||||
−0.0906813 | + | 0.995880i | \(0.528904\pi\) | |||||||
\(954\) | −150.377 | + | 260.461i | −0.157628 | + | 0.273019i | ||||
\(955\) | −129.558 | + | 74.8002i | −0.135663 | + | 0.0783248i | ||||
\(956\) | 114.253 | + | 197.892i | 0.119512 | + | 0.207000i | ||||
\(957\) | −1225.86 | − | 707.753i | −1.28094 | − | 0.739554i | ||||
\(958\) | − | 977.622i | − | 1.02048i | ||||||
\(959\) | 76.8427 | + | 35.9085i | 0.0801280 | + | 0.0374437i | ||||
\(960\) | 30.9839 | 0.0322749 | ||||||||
\(961\) | 331.623 | − | 574.388i | 0.345081 | − | 0.597698i | ||||
\(962\) | 287.633 | − | 166.065i | 0.298995 | − | 0.172625i | ||||
\(963\) | 9.69242 | + | 16.7878i | 0.0100648 | + | 0.0174328i | ||||
\(964\) | 236.324 | + | 136.442i | 0.245150 | + | 0.141537i | ||||
\(965\) | − | 251.790i | − | 0.260922i | ||||||
\(966\) | 685.029 | − | 59.3709i | 0.709139 | − | 0.0614606i | ||||
\(967\) | −1209.88 | −1.25117 | −0.625583 | − | 0.780158i | \(-0.715139\pi\) | ||||
−0.625583 | + | 0.780158i | \(0.715139\pi\) | |||||||
\(968\) | −256.319 | + | 443.957i | −0.264792 | + | 0.458633i | ||||
\(969\) | 10.1113 | − | 5.83779i | 0.0104348 | − | 0.00602455i | ||||
\(970\) | 11.8310 | + | 20.4918i | 0.0121969 | + | 0.0211256i | ||||
\(971\) | −675.990 | − | 390.283i | −0.696180 | − | 0.401939i | 0.109743 | − | 0.993960i | \(-0.464997\pi\) |
−0.805923 | + | 0.592020i | \(0.798330\pi\) | |||||||
\(972\) | − | 31.1769i | − | 0.0320750i | ||||||
\(973\) | −181.494 | − | 259.650i | −0.186531 | − | 0.266855i | ||||
\(974\) | 1019.39 | 1.04661 | ||||||||
\(975\) | 31.2877 | − | 54.1919i | 0.0320900 | − | 0.0555815i | ||||
\(976\) | 44.6485 | − | 25.7778i | 0.0457465 | − | 0.0264117i | ||||
\(977\) | −794.931 | − | 1376.86i | −0.813644 | − | 1.40927i | −0.910297 | − | 0.413955i | \(-0.864147\pi\) |
0.0966527 | − | 0.995318i | \(-0.469186\pi\) | |||||||
\(978\) | 586.694 | + | 338.728i | 0.599891 | + | 0.346347i | ||||
\(979\) | − | 2223.68i | − | 2.27138i | ||||||
\(980\) | 205.797 | + | 75.2833i | 0.209997 | + | 0.0768197i | ||||
\(981\) | 491.520 | 0.501040 | ||||||||
\(982\) | −417.189 | + | 722.593i | −0.424836 | + | 0.735838i | ||||
\(983\) | 607.577 | − | 350.785i | 0.618084 | − | 0.356851i | −0.158039 | − | 0.987433i | \(-0.550517\pi\) |
0.776123 | + | 0.630582i | \(0.217184\pi\) | |||||||
\(984\) | −173.100 | − | 299.819i | −0.175915 | − | 0.304694i | ||||
\(985\) | 118.167 | + | 68.2237i | 0.119966 | + | 0.0692626i | ||||
\(986\) | − | 176.303i | − | 0.178806i | ||||||
\(987\) | 332.389 | − | 232.339i | 0.336767 | − | 0.235399i | ||||
\(988\) | 36.7323 | 0.0371785 | ||||||||
\(989\) | −749.360 | + | 1297.93i | −0.757695 | + | 1.31237i | ||||
\(990\) | 142.834 | − | 82.4652i | 0.144277 | − | 0.0832982i | ||||
\(991\) | −203.359 | − | 352.228i | −0.205206 | − | 0.355427i | 0.744992 | − | 0.667073i | \(-0.232453\pi\) |
−0.950198 | + | 0.311646i | \(0.899120\pi\) | |||||||
\(992\) | −197.438 | − | 113.991i | −0.199031 | − | 0.114910i | ||||
\(993\) | − | 242.169i | − | 0.243876i | ||||||
\(994\) | −9.89768 | − | 114.201i | −0.00995743 | − | 0.114890i | ||||
\(995\) | 427.458 | 0.429606 | ||||||||
\(996\) | 193.408 | − | 334.993i | 0.194185 | − | 0.336338i | ||||
\(997\) | −655.372 | + | 378.379i | −0.657344 | + | 0.379518i | −0.791264 | − | 0.611474i | \(-0.790577\pi\) |
0.133920 | + | 0.990992i | \(0.457243\pi\) | |||||||
\(998\) | 619.207 | + | 1072.50i | 0.620448 | + | 1.07465i | ||||
\(999\) | −146.262 | − | 84.4446i | −0.146409 | − | 0.0845291i |
(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 | 210.3.o.b.61.2 | yes | 16 | |
3.2 | odd | 2 | 630.3.v.c.271.8 | 16 | |||
5.2 | odd | 4 | 1050.3.q.e.649.2 | 32 | |||
5.3 | odd | 4 | 1050.3.q.e.649.15 | 32 | |||
5.4 | even | 2 | 1050.3.p.i.901.5 | 16 | |||
7.2 | even | 3 | 1470.3.f.d.391.11 | 16 | |||
7.3 | odd | 6 | inner | 210.3.o.b.31.2 | ✓ | 16 | |
7.5 | odd | 6 | 1470.3.f.d.391.13 | 16 | |||
21.17 | even | 6 | 630.3.v.c.451.8 | 16 | |||
35.3 | even | 12 | 1050.3.q.e.199.2 | 32 | |||
35.17 | even | 12 | 1050.3.q.e.199.15 | 32 | |||
35.24 | odd | 6 | 1050.3.p.i.451.5 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.o.b.31.2 | ✓ | 16 | 7.3 | odd | 6 | inner | |
210.3.o.b.61.2 | yes | 16 | 1.1 | even | 1 | trivial | |
630.3.v.c.271.8 | 16 | 3.2 | odd | 2 | |||
630.3.v.c.451.8 | 16 | 21.17 | even | 6 | |||
1050.3.p.i.451.5 | 16 | 35.24 | odd | 6 | |||
1050.3.p.i.901.5 | 16 | 5.4 | even | 2 | |||
1050.3.q.e.199.2 | 32 | 35.3 | even | 12 | |||
1050.3.q.e.199.15 | 32 | 35.17 | even | 12 | |||
1050.3.q.e.649.2 | 32 | 5.2 | odd | 4 | |||
1050.3.q.e.649.15 | 32 | 5.3 | odd | 4 | |||
1470.3.f.d.391.11 | 16 | 7.2 | even | 3 | |||
1470.3.f.d.391.13 | 16 | 7.5 | odd | 6 |