Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(557,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.557");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.f (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.3317760000.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 25x^{4} + 625 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 743.4 | ||
Root | \(0.578737 + 2.15988i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.743 |
Dual form | 775.2.f.c.557.4 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.73205 | − | 1.73205i | 1.22474 | − | 1.22474i | 0.258819 | − | 0.965926i | \(-0.416667\pi\) |
0.965926 | − | 0.258819i | \(-0.0833333\pi\) | |||||||
\(3\) | 1.58114 | − | 1.58114i | 0.912871 | − | 0.912871i | −0.0836263 | − | 0.996497i | \(-0.526650\pi\) |
0.996497 | + | 0.0836263i | \(0.0266502\pi\) | |||||||
\(4\) | − | 4.00000i | − | 2.00000i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 5.47723i | − | 2.23607i | ||||||
\(7\) | −1.73205 | + | 1.73205i | −0.654654 | + | 0.654654i | −0.954110 | − | 0.299456i | \(-0.903195\pi\) |
0.299456 | + | 0.954110i | \(0.403195\pi\) | |||||||
\(8\) | −3.46410 | − | 3.46410i | −1.22474 | − | 1.22474i | ||||
\(9\) | − | 2.00000i | − | 0.666667i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.47723i | − | 1.65145i | −0.564076 | − | 0.825723i | \(-0.690768\pi\) | ||
0.564076 | − | 0.825723i | \(-0.309232\pi\) | |||||||
\(12\) | −6.32456 | − | 6.32456i | −1.82574 | − | 1.82574i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 6.00000i | 1.60357i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −1.00000 | ||||||||
\(17\) | 1.58114 | + | 1.58114i | 0.383482 | + | 0.383482i | 0.872355 | − | 0.488873i | \(-0.162592\pi\) |
−0.488873 | + | 0.872355i | \(0.662592\pi\) | |||||||
\(18\) | −3.46410 | − | 3.46410i | −0.816497 | − | 0.816497i | ||||
\(19\) | 7.00000i | 1.60591i | 0.596040 | + | 0.802955i | \(0.296740\pi\) | ||||
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.47723i | 1.19523i | ||||||||
\(22\) | −9.48683 | − | 9.48683i | −2.02260 | − | 2.02260i | ||||
\(23\) | 3.16228 | − | 3.16228i | 0.659380 | − | 0.659380i | −0.295853 | − | 0.955233i | \(-0.595604\pi\) |
0.955233 | + | 0.295853i | \(0.0956039\pi\) | |||||||
\(24\) | −10.9545 | −2.23607 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.58114 | + | 1.58114i | 0.304290 | + | 0.304290i | ||||
\(28\) | 6.92820 | + | 6.92820i | 1.30931 | + | 1.30931i | ||||
\(29\) | −5.47723 | −1.01710 | −0.508548 | − | 0.861034i | \(-0.669817\pi\) | ||||
−0.508548 | + | 0.861034i | \(0.669817\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | + | 5.47723i | −0.179605 | + | 0.983739i | ||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −8.66025 | − | 8.66025i | −1.50756 | − | 1.50756i | ||||
\(34\) | 5.47723 | 0.939336 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −8.00000 | −1.33333 | ||||||||
\(37\) | −4.74342 | − | 4.74342i | −0.779813 | − | 0.779813i | 0.199986 | − | 0.979799i | \(-0.435910\pi\) |
−0.979799 | + | 0.199986i | \(0.935910\pi\) | |||||||
\(38\) | 12.1244 | + | 12.1244i | 1.96683 | + | 1.96683i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 9.48683 | + | 9.48683i | 1.46385 | + | 1.46385i | ||||
\(43\) | 4.74342 | − | 4.74342i | 0.723364 | − | 0.723364i | −0.245925 | − | 0.969289i | \(-0.579092\pi\) |
0.969289 | + | 0.245925i | \(0.0790916\pi\) | |||||||
\(44\) | −21.9089 | −3.30289 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 10.9545i | − | 1.61515i | ||||||
\(47\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(48\) | −6.32456 | + | 6.32456i | −0.912871 | + | 0.912871i | ||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.00000 | 0.700140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.90569 | − | 7.90569i | 1.08593 | − | 1.08593i | 0.0899877 | − | 0.995943i | \(-0.471317\pi\) |
0.995943 | − | 0.0899877i | \(-0.0286828\pi\) | |||||||
\(54\) | 5.47723 | 0.745356 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0000 | 1.60357 | ||||||||
\(57\) | 11.0680 | + | 11.0680i | 1.46599 | + | 1.46599i | ||||
\(58\) | −9.48683 | + | 9.48683i | −1.24568 | + | 1.24568i | ||||
\(59\) | 3.00000i | 0.390567i | 0.980747 | + | 0.195283i | \(0.0625627\pi\) | ||||
−0.980747 | + | 0.195283i | \(0.937437\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9545i | 1.40257i | 0.712879 | + | 0.701287i | \(0.247391\pi\) | ||||
−0.712879 | + | 0.701287i | \(0.752609\pi\) | |||||||
\(62\) | 7.75478 | + | 11.2189i | 0.984858 | + | 1.42480i | ||||
\(63\) | 3.46410 | + | 3.46410i | 0.436436 | + | 0.436436i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −30.0000 | −3.69274 | ||||||||
\(67\) | −8.66025 | + | 8.66025i | −1.05802 | + | 1.05802i | −0.0598086 | + | 0.998210i | \(0.519049\pi\) |
−0.998210 | + | 0.0598086i | \(0.980951\pi\) | |||||||
\(68\) | 6.32456 | − | 6.32456i | 0.766965 | − | 0.766965i | ||||
\(69\) | − | 10.0000i | − | 1.20386i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.00000 | −1.06810 | −0.534052 | − | 0.845452i | \(-0.679331\pi\) | ||||
−0.534052 | + | 0.845452i | \(0.679331\pi\) | |||||||
\(72\) | −6.92820 | + | 6.92820i | −0.816497 | + | 0.816497i | ||||
\(73\) | −4.74342 | + | 4.74342i | −0.555175 | + | 0.555175i | −0.927930 | − | 0.372755i | \(-0.878413\pi\) |
0.372755 | + | 0.927930i | \(0.378413\pi\) | |||||||
\(74\) | −16.4317 | −1.91014 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 28.0000 | 3.21182 | ||||||||
\(77\) | 9.48683 | + | 9.48683i | 1.08112 | + | 1.08112i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.47723 | 0.616236 | 0.308118 | − | 0.951348i | \(-0.400301\pi\) | ||||
0.308118 | + | 0.951348i | \(0.400301\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.0000 | 1.22222 | ||||||||
\(82\) | 15.5885 | − | 15.5885i | 1.72146 | − | 1.72146i | ||||
\(83\) | −7.90569 | + | 7.90569i | −0.867763 | + | 0.867763i | −0.992224 | − | 0.124462i | \(-0.960280\pi\) |
0.124462 | + | 0.992224i | \(0.460280\pi\) | |||||||
\(84\) | 21.9089 | 2.39046 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 16.4317i | − | 1.77187i | ||||||
\(87\) | −8.66025 | + | 8.66025i | −0.928477 | + | 0.928477i | ||||
\(88\) | −18.9737 | + | 18.9737i | −2.02260 | + | 2.02260i | ||||
\(89\) | 5.47723 | 0.580585 | 0.290292 | − | 0.956938i | \(-0.406247\pi\) | ||||
0.290292 | + | 0.956938i | \(0.406247\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −12.6491 | − | 12.6491i | −1.31876 | − | 1.31876i | ||||
\(93\) | 7.07912 | + | 10.2414i | 0.734070 | + | 1.06198i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3923 | − | 10.3923i | 1.05518 | − | 1.05518i | 0.0567927 | − | 0.998386i | \(-0.481913\pi\) |
0.998386 | − | 0.0567927i | \(-0.0180874\pi\) | |||||||
\(98\) | 1.73205 | + | 1.73205i | 0.174964 | + | 0.174964i | ||||
\(99\) | −10.9545 | −1.10096 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | 8.66025 | − | 8.66025i | 0.857493 | − | 0.857493i | ||||
\(103\) | −3.46410 | − | 3.46410i | −0.341328 | − | 0.341328i | 0.515538 | − | 0.856866i | \(-0.327592\pi\) |
−0.856866 | + | 0.515538i | \(0.827592\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 27.3861i | − | 2.65998i | ||||||
\(107\) | 10.3923 | − | 10.3923i | 1.00466 | − | 1.00466i | 0.00467295 | − | 0.999989i | \(-0.498513\pi\) |
0.999989 | − | 0.00467295i | \(-0.00148745\pi\) | |||||||
\(108\) | 6.32456 | − | 6.32456i | 0.608581 | − | 0.608581i | ||||
\(109\) | 7.00000i | 0.670478i | 0.942133 | + | 0.335239i | \(0.108817\pi\) | ||||
−0.942133 | + | 0.335239i | \(0.891183\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.0000 | −1.42374 | ||||||||
\(112\) | 6.92820 | − | 6.92820i | 0.654654 | − | 0.654654i | ||||
\(113\) | −5.19615 | − | 5.19615i | −0.488813 | − | 0.488813i | 0.419119 | − | 0.907931i | \(-0.362339\pi\) |
−0.907931 | + | 0.419119i | \(0.862339\pi\) | |||||||
\(114\) | 38.3406 | 3.59092 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 21.9089i | 2.03419i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 5.19615 | + | 5.19615i | 0.478345 | + | 0.478345i | ||||
\(119\) | −5.47723 | −0.502096 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19.0000 | −1.72727 | ||||||||
\(122\) | 18.9737 | + | 18.9737i | 1.71780 | + | 1.71780i | ||||
\(123\) | 14.2302 | − | 14.2302i | 1.28310 | − | 1.28310i | ||||
\(124\) | 21.9089 | + | 4.00000i | 1.96748 | + | 0.359211i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 12.0000 | 1.06904 | ||||||||
\(127\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(128\) | −13.8564 | − | 13.8564i | −1.22474 | − | 1.22474i | ||||
\(129\) | − | 15.0000i | − | 1.32068i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.00000 | 0.262111 | 0.131056 | − | 0.991375i | \(-0.458163\pi\) | ||||
0.131056 | + | 0.991375i | \(0.458163\pi\) | |||||||
\(132\) | −34.6410 | + | 34.6410i | −3.01511 | + | 3.01511i | ||||
\(133\) | −12.1244 | − | 12.1244i | −1.05131 | − | 1.05131i | ||||
\(134\) | 30.0000i | 2.59161i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 10.9545i | − | 0.939336i | ||||||
\(137\) | −11.0680 | − | 11.0680i | −0.945601 | − | 0.945601i | 0.0529942 | − | 0.998595i | \(-0.483124\pi\) |
−0.998595 | + | 0.0529942i | \(0.983124\pi\) | |||||||
\(138\) | −17.3205 | − | 17.3205i | −1.47442 | − | 1.47442i | ||||
\(139\) | −16.4317 | −1.39372 | −0.696858 | − | 0.717209i | \(-0.745419\pi\) | ||||
−0.696858 | + | 0.717209i | \(0.745419\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.5885 | + | 15.5885i | −1.30815 | + | 1.30815i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 8.00000i | 0.666667i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 16.4317i | 1.35990i | ||||||||
\(147\) | 1.58114 | + | 1.58114i | 0.130410 | + | 0.130410i | ||||
\(148\) | −18.9737 | + | 18.9737i | −1.55963 | + | 1.55963i | ||||
\(149\) | 9.00000i | 0.737309i | 0.929567 | + | 0.368654i | \(0.120181\pi\) | ||||
−0.929567 | + | 0.368654i | \(0.879819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.4317i | 1.33719i | 0.743626 | + | 0.668595i | \(0.233104\pi\) | ||||
−0.743626 | + | 0.668595i | \(0.766896\pi\) | |||||||
\(152\) | 24.2487 | − | 24.2487i | 1.96683 | − | 1.96683i | ||||
\(153\) | 3.16228 | − | 3.16228i | 0.255655 | − | 0.255655i | ||||
\(154\) | 32.8634 | 2.64820 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.73205 | + | 1.73205i | −0.138233 | + | 0.138233i | −0.772837 | − | 0.634604i | \(-0.781163\pi\) |
0.634604 | + | 0.772837i | \(0.281163\pi\) | |||||||
\(158\) | 9.48683 | − | 9.48683i | 0.754732 | − | 0.754732i | ||||
\(159\) | − | 25.0000i | − | 1.98263i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9545i | 0.863332i | ||||||||
\(162\) | 19.0526 | − | 19.0526i | 1.49691 | − | 1.49691i | ||||
\(163\) | 13.8564 | + | 13.8564i | 1.08532 | + | 1.08532i | 0.996004 | + | 0.0893140i | \(0.0284675\pi\) |
0.0893140 | + | 0.996004i | \(0.471533\pi\) | |||||||
\(164\) | − | 36.0000i | − | 2.81113i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 27.3861i | 2.12558i | ||||||||
\(167\) | −1.58114 | − | 1.58114i | −0.122352 | − | 0.122352i | 0.643279 | − | 0.765632i | \(-0.277573\pi\) |
−0.765632 | + | 0.643279i | \(0.777573\pi\) | |||||||
\(168\) | 18.9737 | − | 18.9737i | 1.46385 | − | 1.46385i | ||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.0000 | 1.07061 | ||||||||
\(172\) | −18.9737 | − | 18.9737i | −1.44673 | − | 1.44673i | ||||
\(173\) | −8.66025 | − | 8.66025i | −0.658427 | − | 0.658427i | 0.296581 | − | 0.955008i | \(-0.404154\pi\) |
−0.955008 | + | 0.296581i | \(0.904154\pi\) | |||||||
\(174\) | 30.0000i | 2.27429i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 21.9089i | 1.65145i | ||||||||
\(177\) | 4.74342 | + | 4.74342i | 0.356537 | + | 0.356537i | ||||
\(178\) | 9.48683 | − | 9.48683i | 0.711068 | − | 0.711068i | ||||
\(179\) | −16.4317 | −1.22816 | −0.614081 | − | 0.789243i | \(-0.710473\pi\) | ||||
−0.614081 | + | 0.789243i | \(0.710473\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 10.9545i | − | 0.814238i | −0.913375 | − | 0.407119i | \(-0.866533\pi\) | ||
0.913375 | − | 0.407119i | \(-0.133467\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 17.3205 | + | 17.3205i | 1.28037 | + | 1.28037i | ||||
\(184\) | −21.9089 | −1.61515 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 30.0000 | + | 5.47723i | 2.19971 | + | 0.401610i | ||||
\(187\) | 8.66025 | − | 8.66025i | 0.633300 | − | 0.633300i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.47723 | −0.398410 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | −0.434145 | −0.217072 | − | 0.976156i | \(-0.569651\pi\) | ||||
−0.217072 | + | 0.976156i | \(0.569651\pi\) | |||||||
\(192\) | −12.6491 | − | 12.6491i | −0.912871 | − | 0.912871i | ||||
\(193\) | 3.46410 | + | 3.46410i | 0.249351 | + | 0.249351i | 0.820704 | − | 0.571353i | \(-0.193581\pi\) |
−0.571353 | + | 0.820704i | \(0.693581\pi\) | |||||||
\(194\) | − | 36.0000i | − | 2.58465i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.00000 | 0.285714 | ||||||||
\(197\) | −6.32456 | − | 6.32456i | −0.450606 | − | 0.450606i | 0.444950 | − | 0.895556i | \(-0.353222\pi\) |
−0.895556 | + | 0.444950i | \(0.853222\pi\) | |||||||
\(198\) | −18.9737 | + | 18.9737i | −1.34840 | + | 1.34840i | ||||
\(199\) | −16.4317 | −1.16481 | −0.582405 | − | 0.812899i | \(-0.697888\pi\) | ||||
−0.582405 | + | 0.812899i | \(0.697888\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 27.3861i | 1.93167i | ||||||||
\(202\) | −15.5885 | + | 15.5885i | −1.09680 | + | 1.09680i | ||||
\(203\) | 9.48683 | − | 9.48683i | 0.665845 | − | 0.665845i | ||||
\(204\) | − | 20.0000i | − | 1.40028i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.0000 | −0.836080 | ||||||||
\(207\) | −6.32456 | − | 6.32456i | −0.439587 | − | 0.439587i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 38.3406 | 2.65207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.0000 | 1.10149 | 0.550743 | − | 0.834675i | \(-0.314345\pi\) | ||||
0.550743 | + | 0.834675i | \(0.314345\pi\) | |||||||
\(212\) | −31.6228 | − | 31.6228i | −2.17186 | − | 2.17186i | ||||
\(213\) | −14.2302 | + | 14.2302i | −0.975041 | + | 0.975041i | ||||
\(214\) | − | 36.0000i | − | 2.46091i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 10.9545i | − | 0.745356i | ||||||
\(217\) | −7.75478 | − | 11.2189i | −0.526429 | − | 0.761587i | ||||
\(218\) | 12.1244 | + | 12.1244i | 0.821165 | + | 0.821165i | ||||
\(219\) | 15.0000i | 1.01361i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −25.9808 | + | 25.9808i | −1.74371 | + | 1.74371i | ||||
\(223\) | −14.2302 | + | 14.2302i | −0.952928 | + | 0.952928i | −0.998941 | − | 0.0460129i | \(-0.985348\pi\) |
0.0460129 | + | 0.998941i | \(0.485348\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18.0000 | −1.19734 | ||||||||
\(227\) | −8.66025 | + | 8.66025i | −0.574801 | + | 0.574801i | −0.933466 | − | 0.358665i | \(-0.883232\pi\) |
0.358665 | + | 0.933466i | \(0.383232\pi\) | |||||||
\(228\) | 44.2719 | − | 44.2719i | 2.93198 | − | 2.93198i | ||||
\(229\) | 5.47723 | 0.361945 | 0.180973 | − | 0.983488i | \(-0.442075\pi\) | ||||
0.180973 | + | 0.983488i | \(0.442075\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 30.0000 | 1.97386 | ||||||||
\(232\) | 18.9737 | + | 18.9737i | 1.24568 | + | 1.24568i | ||||
\(233\) | 5.19615 | + | 5.19615i | 0.340411 | + | 0.340411i | 0.856522 | − | 0.516111i | \(-0.172621\pi\) |
−0.516111 | + | 0.856522i | \(0.672621\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 12.0000 | 0.781133 | ||||||||
\(237\) | 8.66025 | − | 8.66025i | 0.562544 | − | 0.562544i | ||||
\(238\) | −9.48683 | + | 9.48683i | −0.614940 | + | 0.614940i | ||||
\(239\) | −10.9545 | −0.708585 | −0.354292 | − | 0.935135i | \(-0.615278\pi\) | ||||
−0.354292 | + | 0.935135i | \(0.615278\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 5.47723i | − | 0.352819i | −0.984317 | − | 0.176410i | \(-0.943552\pi\) | ||
0.984317 | − | 0.176410i | \(-0.0564483\pi\) | |||||||
\(242\) | −32.9090 | + | 32.9090i | −2.11547 | + | 2.11547i | ||||
\(243\) | 12.6491 | − | 12.6491i | 0.811441 | − | 0.811441i | ||||
\(244\) | 43.8178 | 2.80515 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 49.2950i | − | 3.14294i | ||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 22.4378 | − | 15.5096i | 1.42480 | − | 0.984858i | ||||
\(249\) | 25.0000i | 1.58431i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9545i | 0.691439i | 0.938338 | + | 0.345719i | \(0.112365\pi\) | ||||
−0.938338 | + | 0.345719i | \(0.887635\pi\) | |||||||
\(252\) | 13.8564 | − | 13.8564i | 0.872872 | − | 0.872872i | ||||
\(253\) | −17.3205 | − | 17.3205i | −1.08893 | − | 1.08893i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.0000 | −2.00000 | ||||||||
\(257\) | −1.73205 | + | 1.73205i | −0.108042 | + | 0.108042i | −0.759061 | − | 0.651019i | \(-0.774342\pi\) |
0.651019 | + | 0.759061i | \(0.274342\pi\) | |||||||
\(258\) | −25.9808 | − | 25.9808i | −1.61749 | − | 1.61749i | ||||
\(259\) | 16.4317 | 1.02101 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.9545i | 0.678064i | ||||||||
\(262\) | 5.19615 | − | 5.19615i | 0.321019 | − | 0.321019i | ||||
\(263\) | −1.58114 | + | 1.58114i | −0.0974972 | + | 0.0974972i | −0.754173 | − | 0.656676i | \(-0.771962\pi\) |
0.656676 | + | 0.754173i | \(0.271962\pi\) | |||||||
\(264\) | 60.0000i | 3.69274i | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −42.0000 | −2.57519 | ||||||||
\(267\) | 8.66025 | − | 8.66025i | 0.529999 | − | 0.529999i | ||||
\(268\) | 34.6410 | + | 34.6410i | 2.11604 | + | 2.11604i | ||||
\(269\) | 5.47723 | 0.333952 | 0.166976 | − | 0.985961i | \(-0.446600\pi\) | ||||
0.166976 | + | 0.985961i | \(0.446600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 27.3861i | − | 1.66359i | −0.555084 | − | 0.831794i | \(-0.687314\pi\) | ||
0.555084 | − | 0.831794i | \(-0.312686\pi\) | |||||||
\(272\) | −6.32456 | − | 6.32456i | −0.383482 | − | 0.383482i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −38.3406 | −2.31624 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −40.0000 | −2.40772 | ||||||||
\(277\) | −4.74342 | − | 4.74342i | −0.285004 | − | 0.285004i | 0.550097 | − | 0.835101i | \(-0.314591\pi\) |
−0.835101 | + | 0.550097i | \(0.814591\pi\) | |||||||
\(278\) | −28.4605 | + | 28.4605i | −1.70695 | + | 1.70695i | ||||
\(279\) | 10.9545 | + | 2.00000i | 0.655826 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 21.0000 | 1.25275 | 0.626377 | − | 0.779520i | \(-0.284537\pi\) | ||||
0.626377 | + | 0.779520i | \(0.284537\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.3205 | + | 17.3205i | 1.02960 | + | 1.02960i | 0.999548 | + | 0.0300489i | \(0.00956630\pi\) |
0.0300489 | + | 0.999548i | \(0.490434\pi\) | |||||||
\(284\) | 36.0000i | 2.13621i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.5885 | + | 15.5885i | −0.920158 | + | 0.920158i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 12.0000i | − | 0.705882i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 32.8634i | − | 1.92648i | ||||||
\(292\) | 18.9737 | + | 18.9737i | 1.11035 | + | 1.11035i | ||||
\(293\) | 8.66025 | + | 8.66025i | 0.505937 | + | 0.505937i | 0.913277 | − | 0.407339i | \(-0.133543\pi\) |
−0.407339 | + | 0.913277i | \(0.633543\pi\) | |||||||
\(294\) | 5.47723 | 0.319438 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 32.8634i | 1.91014i | ||||||||
\(297\) | 8.66025 | − | 8.66025i | 0.502519 | − | 0.502519i | ||||
\(298\) | 15.5885 | + | 15.5885i | 0.903015 | + | 0.903015i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.4317i | 0.947106i | ||||||||
\(302\) | 28.4605 | + | 28.4605i | 1.63772 | + | 1.63772i | ||||
\(303\) | −14.2302 | + | 14.2302i | −0.817506 | + | 0.817506i | ||||
\(304\) | − | 28.0000i | − | 1.60591i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 10.9545i | − | 0.626224i | ||||||
\(307\) | 1.73205 | − | 1.73205i | 0.0988534 | − | 0.0988534i | −0.655951 | − | 0.754804i | \(-0.727732\pi\) |
0.754804 | + | 0.655951i | \(0.227732\pi\) | |||||||
\(308\) | 37.9473 | − | 37.9473i | 2.16225 | − | 2.16225i | ||||
\(309\) | −10.9545 | −0.623177 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −21.0000 | −1.19080 | −0.595400 | − | 0.803429i | \(-0.703007\pi\) | ||||
−0.595400 | + | 0.803429i | \(0.703007\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.74342 | − | 4.74342i | 0.268114 | − | 0.268114i | −0.560226 | − | 0.828340i | \(-0.689286\pi\) |
0.828340 | + | 0.560226i | \(0.189286\pi\) | |||||||
\(314\) | 6.00000i | 0.338600i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | − | 21.9089i | − | 1.23247i | ||||||
\(317\) | 24.2487 | − | 24.2487i | 1.36194 | − | 1.36194i | 0.490505 | − | 0.871438i | \(-0.336812\pi\) |
0.871438 | − | 0.490505i | \(-0.163188\pi\) | |||||||
\(318\) | −43.3013 | − | 43.3013i | −2.42821 | − | 2.42821i | ||||
\(319\) | 30.0000i | 1.67968i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 32.8634i | − | 1.83425i | ||||||
\(322\) | 18.9737 | + | 18.9737i | 1.05736 | + | 1.05736i | ||||
\(323\) | −11.0680 | + | 11.0680i | −0.615838 | + | 0.615838i | ||||
\(324\) | − | 44.0000i | − | 2.44444i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 48.0000 | 2.65847 | ||||||||
\(327\) | 11.0680 | + | 11.0680i | 0.612060 | + | 0.612060i | ||||
\(328\) | −31.1769 | − | 31.1769i | −1.72146 | − | 1.72146i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 31.6228 | + | 31.6228i | 1.73553 | + | 1.73553i | ||||
\(333\) | −9.48683 | + | 9.48683i | −0.519875 | + | 0.519875i | ||||
\(334\) | −5.47723 | −0.299700 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | − | 21.9089i | − | 1.19523i | ||||||
\(337\) | −14.2302 | − | 14.2302i | −0.775171 | − | 0.775171i | 0.203834 | − | 0.979005i | \(-0.434660\pi\) |
−0.979005 | + | 0.203834i | \(0.934660\pi\) | |||||||
\(338\) | 22.5167 | + | 22.5167i | 1.22474 | + | 1.22474i | ||||
\(339\) | −16.4317 | −0.892446 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 30.0000 | + | 5.47723i | 1.62459 | + | 0.296608i | ||||
\(342\) | 24.2487 | − | 24.2487i | 1.31122 | − | 1.31122i | ||||
\(343\) | −13.8564 | − | 13.8564i | −0.748176 | − | 0.748176i | ||||
\(344\) | −32.8634 | −1.77187 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −30.0000 | −1.61281 | ||||||||
\(347\) | 22.1359 | + | 22.1359i | 1.18832 | + | 1.18832i | 0.977532 | + | 0.210788i | \(0.0676029\pi\) |
0.210788 | + | 0.977532i | \(0.432397\pi\) | |||||||
\(348\) | 34.6410 | + | 34.6410i | 1.85695 | + | 1.85695i | ||||
\(349\) | − | 1.00000i | − | 0.0535288i | −0.999642 | − | 0.0267644i | \(-0.991480\pi\) | ||
0.999642 | − | 0.0267644i | \(-0.00852039\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.32456 | + | 6.32456i | −0.336622 | + | 0.336622i | −0.855094 | − | 0.518472i | \(-0.826501\pi\) |
0.518472 | + | 0.855094i | \(0.326501\pi\) | |||||||
\(354\) | 16.4317 | 0.873334 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 21.9089i | − | 1.16117i | ||||||
\(357\) | −8.66025 | + | 8.66025i | −0.458349 | + | 0.458349i | ||||
\(358\) | −28.4605 | + | 28.4605i | −1.50418 | + | 1.50418i | ||||
\(359\) | − | 18.0000i | − | 0.950004i | −0.879985 | − | 0.475002i | \(-0.842447\pi\) | ||
0.879985 | − | 0.475002i | \(-0.157553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −30.0000 | −1.57895 | ||||||||
\(362\) | −18.9737 | − | 18.9737i | −0.997234 | − | 0.997234i | ||||
\(363\) | −30.0416 | + | 30.0416i | −1.57678 | + | 1.57678i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 60.0000 | 3.13625 | ||||||||
\(367\) | −23.7171 | − | 23.7171i | −1.23802 | − | 1.23802i | −0.960808 | − | 0.277213i | \(-0.910589\pi\) |
−0.277213 | − | 0.960808i | \(-0.589411\pi\) | |||||||
\(368\) | −12.6491 | + | 12.6491i | −0.659380 | + | 0.659380i | ||||
\(369\) | − | 18.0000i | − | 0.937043i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.3861i | 1.42182i | ||||||||
\(372\) | 40.9656 | − | 28.3165i | 2.12397 | − | 1.46814i | ||||
\(373\) | 5.19615 | + | 5.19615i | 0.269047 | + | 0.269047i | 0.828716 | − | 0.559669i | \(-0.189072\pi\) |
−0.559669 | + | 0.828716i | \(0.689072\pi\) | |||||||
\(374\) | − | 30.0000i | − | 1.55126i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −9.48683 | + | 9.48683i | −0.487950 | + | 0.487950i | ||||
\(379\) | − | 11.0000i | − | 0.565032i | −0.959263 | − | 0.282516i | \(-0.908831\pi\) | ||
0.959263 | − | 0.282516i | \(-0.0911690\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.3923 | + | 10.3923i | −0.531717 | + | 0.531717i | ||||
\(383\) | −17.3925 | + | 17.3925i | −0.888717 | + | 0.888717i | −0.994400 | − | 0.105683i | \(-0.966297\pi\) |
0.105683 | + | 0.994400i | \(0.466297\pi\) | |||||||
\(384\) | −43.8178 | −2.23607 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.0000 | 0.610784 | ||||||||
\(387\) | −9.48683 | − | 9.48683i | −0.482243 | − | 0.482243i | ||||
\(388\) | −41.5692 | − | 41.5692i | −2.11036 | − | 2.11036i | ||||
\(389\) | 21.9089 | 1.11083 | 0.555413 | − | 0.831575i | \(-0.312560\pi\) | ||||
0.555413 | + | 0.831575i | \(0.312560\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000 | 0.505722 | ||||||||
\(392\) | 3.46410 | − | 3.46410i | 0.174964 | − | 0.174964i | ||||
\(393\) | 4.74342 | − | 4.74342i | 0.239274 | − | 0.239274i | ||||
\(394\) | −21.9089 | −1.10375 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 43.8178i | 2.20193i | ||||||||
\(397\) | −6.92820 | + | 6.92820i | −0.347717 | + | 0.347717i | −0.859258 | − | 0.511542i | \(-0.829075\pi\) |
0.511542 | + | 0.859258i | \(0.329075\pi\) | |||||||
\(398\) | −28.4605 | + | 28.4605i | −1.42660 | + | 1.42660i | ||||
\(399\) | −38.3406 | −1.91943 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.4317i | 0.820559i | 0.911960 | + | 0.410279i | \(0.134569\pi\) | ||||
−0.911960 | + | 0.410279i | \(0.865431\pi\) | |||||||
\(402\) | 47.4342 | + | 47.4342i | 2.36580 | + | 2.36580i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 36.0000i | 1.79107i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 32.8634i | − | 1.63098i | ||||||
\(407\) | −25.9808 | + | 25.9808i | −1.28782 | + | 1.28782i | ||||
\(408\) | −17.3205 | − | 17.3205i | −0.857493 | − | 0.857493i | ||||
\(409\) | −5.47723 | −0.270831 | −0.135416 | − | 0.990789i | \(-0.543237\pi\) | ||||
−0.135416 | + | 0.990789i | \(0.543237\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −35.0000 | −1.72642 | ||||||||
\(412\) | −13.8564 | + | 13.8564i | −0.682656 | + | 0.682656i | ||||
\(413\) | −5.19615 | − | 5.19615i | −0.255686 | − | 0.255686i | ||||
\(414\) | −21.9089 | −1.07676 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.9808 | + | 25.9808i | −1.27228 | + | 1.27228i | ||||
\(418\) | 66.4078 | − | 66.4078i | 3.24811 | − | 3.24811i | ||||
\(419\) | 3.00000i | 0.146560i | 0.997311 | + | 0.0732798i | \(0.0233466\pi\) | ||||
−0.997311 | + | 0.0732798i | \(0.976653\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.00000 | −0.0487370 | −0.0243685 | − | 0.999703i | \(-0.507758\pi\) | ||||
−0.0243685 | + | 0.999703i | \(0.507758\pi\) | |||||||
\(422\) | 27.7128 | − | 27.7128i | 1.34904 | − | 1.34904i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −54.7723 | −2.65998 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 49.2950i | 2.38835i | ||||||||
\(427\) | −18.9737 | − | 18.9737i | −0.918200 | − | 0.918200i | ||||
\(428\) | −41.5692 | − | 41.5692i | −2.00932 | − | 2.00932i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.0000 | −1.30054 | −0.650272 | − | 0.759701i | \(-0.725345\pi\) | ||||
−0.650272 | + | 0.759701i | \(0.725345\pi\) | |||||||
\(432\) | −6.32456 | − | 6.32456i | −0.304290 | − | 0.304290i | ||||
\(433\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(434\) | −32.8634 | − | 6.00000i | −1.57749 | − | 0.288009i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 28.0000 | 1.34096 | ||||||||
\(437\) | 22.1359 | + | 22.1359i | 1.05891 | + | 1.05891i | ||||
\(438\) | 25.9808 | + | 25.9808i | 1.24141 | + | 1.24141i | ||||
\(439\) | − | 17.0000i | − | 0.811366i | −0.914014 | − | 0.405683i | \(-0.867034\pi\) | ||
0.914014 | − | 0.405683i | \(-0.132966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.46410 | + | 3.46410i | 0.164584 | + | 0.164584i | 0.784594 | − | 0.620010i | \(-0.212871\pi\) |
−0.620010 | + | 0.784594i | \(0.712871\pi\) | |||||||
\(444\) | 60.0000i | 2.84747i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 49.2950i | 2.33419i | ||||||||
\(447\) | 14.2302 | + | 14.2302i | 0.673068 | + | 0.673068i | ||||
\(448\) | 13.8564 | + | 13.8564i | 0.654654 | + | 0.654654i | ||||
\(449\) | 21.9089 | 1.03395 | 0.516973 | − | 0.856002i | \(-0.327059\pi\) | ||||
0.516973 | + | 0.856002i | \(0.327059\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 49.2950i | − | 2.32121i | ||||||
\(452\) | −20.7846 | + | 20.7846i | −0.977626 | + | 0.977626i | ||||
\(453\) | 25.9808 | + | 25.9808i | 1.22068 | + | 1.22068i | ||||
\(454\) | 30.0000i | 1.40797i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − | 76.6812i | − | 3.59092i | ||||||
\(457\) | −18.9737 | − | 18.9737i | −0.887551 | − | 0.887551i | 0.106737 | − | 0.994287i | \(-0.465960\pi\) |
−0.994287 | + | 0.106737i | \(0.965960\pi\) | |||||||
\(458\) | 9.48683 | − | 9.48683i | 0.443291 | − | 0.443291i | ||||
\(459\) | 5.00000i | 0.233380i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 38.3406i | 1.78570i | 0.450355 | + | 0.892849i | \(0.351297\pi\) | ||||
−0.450355 | + | 0.892849i | \(0.648703\pi\) | |||||||
\(462\) | 51.9615 | − | 51.9615i | 2.41747 | − | 2.41747i | ||||
\(463\) | 9.48683 | − | 9.48683i | 0.440891 | − | 0.440891i | −0.451421 | − | 0.892311i | \(-0.649083\pi\) |
0.892311 | + | 0.451421i | \(0.149083\pi\) | |||||||
\(464\) | 21.9089 | 1.01710 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 18.0000 | 0.833834 | ||||||||
\(467\) | 24.2487 | − | 24.2487i | 1.12210 | − | 1.12210i | 0.130671 | − | 0.991426i | \(-0.458287\pi\) |
0.991426 | − | 0.130671i | \(-0.0417131\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 30.0000i | − | 1.38527i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.47723i | 0.252377i | ||||||||
\(472\) | 10.3923 | − | 10.3923i | 0.478345 | − | 0.478345i | ||||
\(473\) | −25.9808 | − | 25.9808i | −1.19460 | − | 1.19460i | ||||
\(474\) | − | 30.0000i | − | 1.37795i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 21.9089i | 1.00419i | ||||||||
\(477\) | −15.8114 | − | 15.8114i | −0.723954 | − | 0.723954i | ||||
\(478\) | −18.9737 | + | 18.9737i | −0.867835 | + | 0.867835i | ||||
\(479\) | 18.0000i | 0.822441i | 0.911536 | + | 0.411220i | \(0.134897\pi\) | ||||
−0.911536 | + | 0.411220i | \(0.865103\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −9.48683 | − | 9.48683i | −0.432113 | − | 0.432113i | ||||
\(483\) | 17.3205 | + | 17.3205i | 0.788110 | + | 0.788110i | ||||
\(484\) | 76.0000i | 3.45455i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 43.8178i | − | 1.98762i | ||||||
\(487\) | 14.2302 | + | 14.2302i | 0.644834 | + | 0.644834i | 0.951740 | − | 0.306906i | \(-0.0992936\pi\) |
−0.306906 | + | 0.951740i | \(0.599294\pi\) | |||||||
\(488\) | 37.9473 | − | 37.9473i | 1.71780 | − | 1.71780i | ||||
\(489\) | 43.8178 | 1.98151 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.9545i | 0.494367i | 0.968969 | + | 0.247184i | \(0.0795051\pi\) | ||||
−0.968969 | + | 0.247184i | \(0.920495\pi\) | |||||||
\(492\) | −56.9210 | − | 56.9210i | −2.56620 | − | 2.56620i | ||||
\(493\) | −8.66025 | − | 8.66025i | −0.390038 | − | 0.390038i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.00000 | − | 21.9089i | 0.179605 | − | 0.983739i | ||||
\(497\) | 15.5885 | − | 15.5885i | 0.699238 | − | 0.699238i | ||||
\(498\) | 43.3013 | + | 43.3013i | 1.94038 | + | 1.94038i | ||||
\(499\) | 5.47723 | 0.245194 | 0.122597 | − | 0.992457i | \(-0.460878\pi\) | ||||
0.122597 | + | 0.992457i | \(0.460878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.00000 | −0.223384 | ||||||||
\(502\) | 18.9737 | + | 18.9737i | 0.846836 | + | 0.846836i | ||||
\(503\) | −12.1244 | − | 12.1244i | −0.540598 | − | 0.540598i | 0.383106 | − | 0.923704i | \(-0.374854\pi\) |
−0.923704 | + | 0.383106i | \(0.874854\pi\) | |||||||
\(504\) | − | 24.0000i | − | 1.06904i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −60.0000 | −2.66733 | ||||||||
\(507\) | 20.5548 | + | 20.5548i | 0.912871 | + | 0.912871i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.9545 | 0.485548 | 0.242774 | − | 0.970083i | \(-0.421943\pi\) | ||||
0.242774 | + | 0.970083i | \(0.421943\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.4317i | − | 0.726895i | ||||||
\(512\) | −27.7128 | + | 27.7128i | −1.22474 | + | 1.22474i | ||||
\(513\) | −11.0680 | + | 11.0680i | −0.488663 | + | 0.488663i | ||||
\(514\) | 6.00000i | 0.264649i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −60.0000 | −2.64135 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 28.4605 | − | 28.4605i | 1.25048 | − | 1.25048i | ||||
\(519\) | −27.3861 | −1.20212 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −27.0000 | −1.18289 | −0.591446 | − | 0.806345i | \(-0.701443\pi\) | ||||
−0.591446 | + | 0.806345i | \(0.701443\pi\) | |||||||
\(522\) | 18.9737 | + | 18.9737i | 0.830455 | + | 0.830455i | ||||
\(523\) | 23.7171 | − | 23.7171i | 1.03708 | − | 1.03708i | 0.0377899 | − | 0.999286i | \(-0.487968\pi\) |
0.999286 | − | 0.0377899i | \(-0.0120318\pi\) | |||||||
\(524\) | − | 12.0000i | − | 0.524222i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.47723i | 0.238818i | ||||||||
\(527\) | −10.2414 | + | 7.07912i | −0.446122 | + | 0.308371i | ||||
\(528\) | 34.6410 | + | 34.6410i | 1.50756 | + | 1.50756i | ||||
\(529\) | 3.00000i | 0.130435i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | −48.4974 | + | 48.4974i | −2.10263 | + | 2.10263i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | − | 30.0000i | − | 1.29823i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 60.0000 | 2.59161 | ||||||||
\(537\) | −25.9808 | + | 25.9808i | −1.12115 | + | 1.12115i | ||||
\(538\) | 9.48683 | − | 9.48683i | 0.409006 | − | 0.409006i | ||||
\(539\) | 5.47723 | 0.235921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.00000 | −0.171973 | −0.0859867 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859867 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(542\) | −47.4342 | − | 47.4342i | −2.03747 | − | 2.03747i | ||||
\(543\) | −17.3205 | − | 17.3205i | −0.743294 | − | 0.743294i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5885 | − | 15.5885i | 0.666514 | − | 0.666514i | −0.290393 | − | 0.956907i | \(-0.593786\pi\) |
0.956907 | + | 0.290393i | \(0.0937861\pi\) | |||||||
\(548\) | −44.2719 | + | 44.2719i | −1.89120 | + | 1.89120i | ||||
\(549\) | 21.9089 | 0.935049 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 38.3406i | − | 1.63336i | ||||||
\(552\) | −34.6410 | + | 34.6410i | −1.47442 | + | 1.47442i | ||||
\(553\) | −9.48683 | + | 9.48683i | −0.403421 | + | 0.403421i | ||||
\(554\) | −16.4317 | −0.698115 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 65.7267i | 2.78743i | ||||||||
\(557\) | −3.16228 | − | 3.16228i | −0.133990 | − | 0.133990i | 0.636931 | − | 0.770921i | \(-0.280204\pi\) |
−0.770921 | + | 0.636931i | \(0.780204\pi\) | |||||||
\(558\) | 22.4378 | − | 15.5096i | 0.949866 | − | 0.656572i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 27.3861i | − | 1.15624i | ||||||
\(562\) | 36.3731 | − | 36.3731i | 1.53431 | − | 1.53431i | ||||
\(563\) | −5.19615 | − | 5.19615i | −0.218992 | − | 0.218992i | 0.589082 | − | 0.808073i | \(-0.299490\pi\) |
−0.808073 | + | 0.589082i | \(0.799490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 60.0000 | 2.52199 | ||||||||
\(567\) | −19.0526 | + | 19.0526i | −0.800132 | + | 0.800132i | ||||
\(568\) | 31.1769 | + | 31.1769i | 1.30815 | + | 1.30815i | ||||
\(569\) | 21.9089 | 0.918469 | 0.459234 | − | 0.888315i | \(-0.348124\pi\) | ||||
0.459234 | + | 0.888315i | \(0.348124\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.47723i | 0.229215i | 0.993411 | + | 0.114607i | \(0.0365610\pi\) | ||||
−0.993411 | + | 0.114607i | \(0.963439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.48683 | + | 9.48683i | −0.396318 | + | 0.396318i | ||||
\(574\) | 54.0000i | 2.25392i | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −16.0000 | −0.666667 | ||||||||
\(577\) | −8.66025 | + | 8.66025i | −0.360531 | + | 0.360531i | −0.864008 | − | 0.503477i | \(-0.832054\pi\) |
0.503477 | + | 0.864008i | \(0.332054\pi\) | |||||||
\(578\) | −20.7846 | − | 20.7846i | −0.864526 | − | 0.864526i | ||||
\(579\) | 10.9545 | 0.455251 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 27.3861i | − | 1.13617i | ||||||
\(582\) | −56.9210 | − | 56.9210i | −2.35945 | − | 2.35945i | ||||
\(583\) | −43.3013 | − | 43.3013i | −1.79336 | − | 1.79336i | ||||
\(584\) | 32.8634 | 1.35990 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 30.0000 | 1.23929 | ||||||||
\(587\) | −22.1359 | − | 22.1359i | −0.913648 | − | 0.913648i | 0.0829090 | − | 0.996557i | \(-0.473579\pi\) |
−0.996557 | + | 0.0829090i | \(0.973579\pi\) | |||||||
\(588\) | 6.32456 | − | 6.32456i | 0.260820 | − | 0.260820i | ||||
\(589\) | −38.3406 | − | 7.00000i | −1.57980 | − | 0.288430i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −20.0000 | −0.822690 | ||||||||
\(592\) | 18.9737 | + | 18.9737i | 0.779813 | + | 0.779813i | ||||
\(593\) | 13.8564 | + | 13.8564i | 0.569014 | + | 0.569014i | 0.931852 | − | 0.362838i | \(-0.118192\pi\) |
−0.362838 | + | 0.931852i | \(0.618192\pi\) | |||||||
\(594\) | − | 30.0000i | − | 1.23091i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 36.0000 | 1.47462 | ||||||||
\(597\) | −25.9808 | + | 25.9808i | −1.06332 | + | 1.06332i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.0000i | 0.490307i | 0.969484 | + | 0.245153i | \(0.0788383\pi\) | ||||
−0.969484 | + | 0.245153i | \(0.921162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 5.47723i | − | 0.223421i | −0.993741 | − | 0.111710i | \(-0.964367\pi\) | ||
0.993741 | − | 0.111710i | \(-0.0356329\pi\) | |||||||
\(602\) | 28.4605 | + | 28.4605i | 1.15996 | + | 1.15996i | ||||
\(603\) | 17.3205 | + | 17.3205i | 0.705346 | + | 0.705346i | ||||
\(604\) | 65.7267 | 2.67438 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 49.2950i | 2.00247i | ||||||||
\(607\) | −25.9808 | + | 25.9808i | −1.05453 | + | 1.05453i | −0.0561015 | + | 0.998425i | \(0.517867\pi\) |
−0.998425 | + | 0.0561015i | \(0.982133\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 30.0000i | − | 1.21566i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −12.6491 | − | 12.6491i | −0.511310 | − | 0.511310i | ||||
\(613\) | 23.7171 | − | 23.7171i | 0.957924 | − | 0.957924i | −0.0412259 | − | 0.999150i | \(-0.513126\pi\) |
0.999150 | + | 0.0412259i | \(0.0131263\pi\) | |||||||
\(614\) | − | 6.00000i | − | 0.242140i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 65.7267i | − | 2.64820i | ||||||
\(617\) | 8.66025 | − | 8.66025i | 0.348649 | − | 0.348649i | −0.510957 | − | 0.859606i | \(-0.670709\pi\) |
0.859606 | + | 0.510957i | \(0.170709\pi\) | |||||||
\(618\) | −18.9737 | + | 18.9737i | −0.763233 | + | 0.763233i | ||||
\(619\) | −32.8634 | −1.32089 | −0.660445 | − | 0.750875i | \(-0.729632\pi\) | ||||
−0.660445 | + | 0.750875i | \(0.729632\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.0000 | 0.401286 | ||||||||
\(622\) | −36.3731 | + | 36.3731i | −1.45843 | + | 1.45843i | ||||
\(623\) | −9.48683 | + | 9.48683i | −0.380082 | + | 0.380082i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 16.4317i | − | 0.656742i | ||||||
\(627\) | 60.6218 | − | 60.6218i | 2.42100 | − | 2.42100i | ||||
\(628\) | 6.92820 | + | 6.92820i | 0.276465 | + | 0.276465i | ||||
\(629\) | − | 15.0000i | − | 0.598089i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 21.9089i | − | 0.872180i | −0.899903 | − | 0.436090i | \(-0.856363\pi\) | ||
0.899903 | − | 0.436090i | \(-0.143637\pi\) | |||||||
\(632\) | −18.9737 | − | 18.9737i | −0.754732 | − | 0.754732i | ||||
\(633\) | 25.2982 | − | 25.2982i | 1.00551 | − | 1.00551i | ||||
\(634\) | − | 84.0000i | − | 3.33607i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −100.000 | −3.96526 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 51.9615 | + | 51.9615i | 2.05718 | + | 2.05718i | ||||
\(639\) | 18.0000i | 0.712069i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 32.8634i | − | 1.29802i | −0.760778 | − | 0.649012i | \(-0.775182\pi\) | ||
0.760778 | − | 0.649012i | \(-0.224818\pi\) | |||||||
\(642\) | −56.9210 | − | 56.9210i | −2.24649 | − | 2.24649i | ||||
\(643\) | 33.2039 | − | 33.2039i | 1.30943 | − | 1.30943i | 0.387612 | − | 0.921823i | \(-0.373300\pi\) |
0.921823 | − | 0.387612i | \(-0.126700\pi\) | |||||||
\(644\) | 43.8178 | 1.72666 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 38.3406i | 1.50849i | ||||||||
\(647\) | −1.58114 | − | 1.58114i | −0.0621610 | − | 0.0621610i | 0.675343 | − | 0.737504i | \(-0.263996\pi\) |
−0.737504 | + | 0.675343i | \(0.763996\pi\) | |||||||
\(648\) | −38.1051 | − | 38.1051i | −1.49691 | − | 1.49691i | ||||
\(649\) | 16.4317 | 0.645000 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −30.0000 | − | 5.47723i | −1.17579 | − | 0.214669i | ||||
\(652\) | 55.4256 | − | 55.4256i | 2.17064 | − | 2.17064i | ||||
\(653\) | 17.3205 | + | 17.3205i | 0.677804 | + | 0.677804i | 0.959503 | − | 0.281699i | \(-0.0908980\pi\) |
−0.281699 | + | 0.959503i | \(0.590898\pi\) | |||||||
\(654\) | 38.3406 | 1.49924 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −36.0000 | −1.40556 | ||||||||
\(657\) | 9.48683 | + | 9.48683i | 0.370117 | + | 0.370117i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 33.0000i | − | 1.28550i | −0.766077 | − | 0.642749i | \(-0.777794\pi\) | ||
0.766077 | − | 0.642749i | \(-0.222206\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.0000 | 1.59472 | 0.797358 | − | 0.603507i | \(-0.206231\pi\) | ||||
0.797358 | + | 0.603507i | \(0.206231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 54.7723 | 2.12558 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 32.8634i | 1.27343i | ||||||||
\(667\) | −17.3205 | + | 17.3205i | −0.670653 | + | 0.670653i | ||||
\(668\) | −6.32456 | + | 6.32456i | −0.244704 | + | 0.244704i | ||||
\(669\) | 45.0000i | 1.73980i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 60.0000 | 2.31627 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.74342 | − | 4.74342i | 0.182845 | − | 0.182845i | −0.609749 | − | 0.792594i | \(-0.708730\pi\) |
0.792594 | + | 0.609749i | \(0.208730\pi\) | |||||||
\(674\) | −49.2950 | −1.89877 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 52.0000 | 2.00000 | ||||||||
\(677\) | 1.58114 | + | 1.58114i | 0.0607681 | + | 0.0607681i | 0.736838 | − | 0.676070i | \(-0.236318\pi\) |
−0.676070 | + | 0.736838i | \(0.736318\pi\) | |||||||
\(678\) | −28.4605 | + | 28.4605i | −1.09302 | + | 1.09302i | ||||
\(679\) | 36.0000i | 1.38155i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.3861i | 1.04944i | ||||||||
\(682\) | 61.4484 | − | 42.4747i | 2.35298 | − | 1.62644i | ||||
\(683\) | −22.5167 | − | 22.5167i | −0.861576 | − | 0.861576i | 0.129945 | − | 0.991521i | \(-0.458520\pi\) |
−0.991521 | + | 0.129945i | \(0.958520\pi\) | |||||||
\(684\) | − | 56.0000i | − | 2.14121i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −48.0000 | −1.83265 | ||||||||
\(687\) | 8.66025 | − | 8.66025i | 0.330409 | − | 0.330409i | ||||
\(688\) | −18.9737 | + | 18.9737i | −0.723364 | + | 0.723364i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.0000 | 0.722794 | 0.361397 | − | 0.932412i | \(-0.382300\pi\) | ||||
0.361397 | + | 0.932412i | \(0.382300\pi\) | |||||||
\(692\) | −34.6410 | + | 34.6410i | −1.31685 | + | 1.31685i | ||||
\(693\) | 18.9737 | − | 18.9737i | 0.720750 | − | 0.720750i | ||||
\(694\) | 76.6812 | 2.91078 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 60.0000 | 2.27429 | ||||||||
\(697\) | 14.2302 | + | 14.2302i | 0.539009 | + | 0.539009i | ||||
\(698\) | −1.73205 | − | 1.73205i | −0.0655591 | − | 0.0655591i | ||||
\(699\) | 16.4317 | 0.621503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.00000 | −0.226617 | −0.113308 | − | 0.993560i | \(-0.536145\pi\) | ||||
−0.113308 | + | 0.993560i | \(0.536145\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 33.2039 | − | 33.2039i | 1.25231 | − | 1.25231i | ||||
\(704\) | −43.8178 | −1.65145 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 21.9089i | 0.824552i | ||||||||
\(707\) | 15.5885 | − | 15.5885i | 0.586264 | − | 0.586264i | ||||
\(708\) | 18.9737 | − | 18.9737i | 0.713074 | − | 0.713074i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.9545i | − | 0.410824i | ||||||
\(712\) | −18.9737 | − | 18.9737i | −0.711068 | − | 0.711068i | ||||
\(713\) | 14.1582 | + | 20.4828i | 0.530230 | + | 0.767086i | ||||
\(714\) | 30.0000i | 1.12272i | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 65.7267i | 2.45632i | ||||||||
\(717\) | −17.3205 | + | 17.3205i | −0.646846 | + | 0.646846i | ||||
\(718\) | −31.1769 | − | 31.1769i | −1.16351 | − | 1.16351i | ||||
\(719\) | 10.9545 | 0.408532 | 0.204266 | − | 0.978915i | \(-0.434519\pi\) | ||||
0.204266 | + | 0.978915i | \(0.434519\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.0000 | 0.446903 | ||||||||
\(722\) | −51.9615 | + | 51.9615i | −1.93381 | + | 1.93381i | ||||
\(723\) | −8.66025 | − | 8.66025i | −0.322078 | − | 0.322078i | ||||
\(724\) | −43.8178 | −1.62848 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 104.067i | 3.86230i | ||||||||
\(727\) | −24.2487 | + | 24.2487i | −0.899335 | + | 0.899335i | −0.995377 | − | 0.0960423i | \(-0.969382\pi\) |
0.0960423 | + | 0.995377i | \(0.469382\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 7.00000i | − | 0.259259i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 15.0000 | 0.554795 | ||||||||
\(732\) | 69.2820 | − | 69.2820i | 2.56074 | − | 2.56074i | ||||
\(733\) | 3.46410 | + | 3.46410i | 0.127950 | + | 0.127950i | 0.768182 | − | 0.640232i | \(-0.221162\pi\) |
−0.640232 | + | 0.768182i | \(0.721162\pi\) | |||||||
\(734\) | −82.1584 | −3.03252 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 47.4342 | + | 47.4342i | 1.74726 | + | 1.74726i | ||||
\(738\) | −31.1769 | − | 31.1769i | −1.14764 | − | 1.14764i | ||||
\(739\) | 43.8178 | 1.61186 | 0.805932 | − | 0.592008i | \(-0.201665\pi\) | ||||
0.805932 | + | 0.592008i | \(0.201665\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 47.4342 | + | 47.4342i | 1.74136 | + | 1.74136i | ||||
\(743\) | −20.5548 | + | 20.5548i | −0.754083 | + | 0.754083i | −0.975238 | − | 0.221156i | \(-0.929017\pi\) |
0.221156 | + | 0.975238i | \(0.429017\pi\) | |||||||
\(744\) | 10.9545 | − | 60.0000i | 0.401610 | − | 2.19971i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.0000 | 0.659027 | ||||||||
\(747\) | 15.8114 | + | 15.8114i | 0.578508 | + | 0.578508i | ||||
\(748\) | −34.6410 | − | 34.6410i | −1.26660 | − | 1.26660i | ||||
\(749\) | 36.0000i | 1.31541i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.0000 | −0.510867 | −0.255434 | − | 0.966827i | \(-0.582218\pi\) | ||||
−0.255434 | + | 0.966827i | \(0.582218\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.3205 | + | 17.3205i | 0.631194 | + | 0.631194i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 21.9089i | 0.796819i | ||||||||
\(757\) | −14.2302 | − | 14.2302i | −0.517207 | − | 0.517207i | 0.399518 | − | 0.916725i | \(-0.369177\pi\) |
−0.916725 | + | 0.399518i | \(0.869177\pi\) | |||||||
\(758\) | −19.0526 | − | 19.0526i | −0.692020 | − | 0.692020i | ||||
\(759\) | −54.7723 | −1.98811 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 32.8634i | − | 1.19130i | −0.803246 | − | 0.595648i | \(-0.796895\pi\) | ||
0.803246 | − | 0.595648i | \(-0.203105\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.1244 | − | 12.1244i | −0.438931 | − | 0.438931i | ||||
\(764\) | 24.0000i | 0.868290i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 60.2495i | 2.17690i | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −50.5964 | + | 50.5964i | −1.82574 | + | 1.82574i | ||||
\(769\) | − | 47.0000i | − | 1.69486i | −0.530904 | − | 0.847432i | \(-0.678148\pi\) | ||
0.530904 | − | 0.847432i | \(-0.321852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47723i | 0.197257i | ||||||||
\(772\) | 13.8564 | − | 13.8564i | 0.498703 | − | 0.498703i | ||||
\(773\) | 22.1359 | − | 22.1359i | 0.796175 | − | 0.796175i | −0.186315 | − | 0.982490i | \(-0.559655\pi\) |
0.982490 | + | 0.186315i | \(0.0596546\pi\) | |||||||
\(774\) | −32.8634 | −1.18125 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −72.0000 | −2.58465 | ||||||||
\(777\) | 25.9808 | − | 25.9808i | 0.932055 | − | 0.932055i | ||||
\(778\) | 37.9473 | − | 37.9473i | 1.36048 | − | 1.36048i | ||||
\(779\) | 63.0000i | 2.25721i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 49.2950i | 1.76391i | ||||||||
\(782\) | 17.3205 | − | 17.3205i | 0.619380 | − | 0.619380i | ||||
\(783\) | −8.66025 | − | 8.66025i | −0.309492 | − | 0.309492i | ||||
\(784\) | − | 4.00000i | − | 0.142857i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | − | 16.4317i | − | 0.586098i | ||||||
\(787\) | 9.48683 | + | 9.48683i | 0.338169 | + | 0.338169i | 0.855678 | − | 0.517509i | \(-0.173141\pi\) |
−0.517509 | + | 0.855678i | \(0.673141\pi\) | |||||||
\(788\) | −25.2982 | + | 25.2982i | −0.901212 | + | 0.901212i | ||||
\(789\) | 5.00000i | 0.178005i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | 0.640006 | ||||||||
\(792\) | 37.9473 | + | 37.9473i | 1.34840 | + | 1.34840i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 24.0000i | 0.851728i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 65.7267i | 2.32962i | ||||||||
\(797\) | −3.16228 | − | 3.16228i | −0.112014 | − | 0.112014i | 0.648878 | − | 0.760892i | \(-0.275238\pi\) |
−0.760892 | + | 0.648878i | \(0.775238\pi\) | |||||||
\(798\) | −66.4078 | + | 66.4078i | −2.35081 | + | 2.35081i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.9545i | − | 0.387056i | ||||||
\(802\) | 28.4605 | + | 28.4605i | 1.00498 | + | 1.00498i | ||||
\(803\) | 25.9808 | + | 25.9808i | 0.916841 | + | 0.916841i | ||||
\(804\) | 109.545 | 3.86334 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.66025 | − | 8.66025i | 0.304855 | − | 0.304855i | ||||
\(808\) | 31.1769 | + | 31.1769i | 1.09680 | + | 1.09680i | ||||
\(809\) | 16.4317 | 0.577707 | 0.288853 | − | 0.957373i | \(-0.406726\pi\) | ||||
0.288853 | + | 0.957373i | \(0.406726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.0000 | −0.456492 | −0.228246 | − | 0.973604i | \(-0.573299\pi\) | ||||
−0.228246 | + | 0.973604i | \(0.573299\pi\) | |||||||
\(812\) | −37.9473 | − | 37.9473i | −1.33169 | − | 1.33169i | ||||
\(813\) | −43.3013 | − | 43.3013i | −1.51864 | − | 1.51864i | ||||
\(814\) | 90.0000i | 3.15450i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −20.0000 | −0.700140 | ||||||||
\(817\) | 33.2039 | + | 33.2039i | 1.16166 | + | 1.16166i | ||||
\(818\) | −9.48683 | + | 9.48683i | −0.331699 | + | 0.331699i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 49.2950i | 1.72041i | 0.509950 | + | 0.860204i | \(0.329664\pi\) | ||||
−0.509950 | + | 0.860204i | \(0.670336\pi\) | |||||||
\(822\) | −60.6218 | + | 60.6218i | −2.11443 | + | 2.11443i | ||||
\(823\) | −14.2302 | + | 14.2302i | −0.496035 | + | 0.496035i | −0.910201 | − | 0.414166i | \(-0.864073\pi\) |
0.414166 | + | 0.910201i | \(0.364073\pi\) | |||||||
\(824\) | 24.0000i | 0.836080i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −18.0000 | −0.626300 | ||||||||
\(827\) | 7.90569 | + | 7.90569i | 0.274908 | + | 0.274908i | 0.831072 | − | 0.556164i | \(-0.187728\pi\) |
−0.556164 | + | 0.831072i | \(0.687728\pi\) | |||||||
\(828\) | −25.2982 | + | 25.2982i | −0.879174 | + | 0.879174i | ||||
\(829\) | 32.8634 | 1.14139 | 0.570696 | − | 0.821162i | \(-0.306674\pi\) | ||||
0.570696 | + | 0.821162i | \(0.306674\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0000 | −0.520344 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.58114 | + | 1.58114i | −0.0547832 | + | 0.0547832i | ||||
\(834\) | 90.0000i | 3.11645i | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 153.362i | − | 5.30415i | ||||||
\(837\) | −10.2414 | + | 7.07912i | −0.353994 | + | 0.244690i | ||||
\(838\) | 5.19615 | + | 5.19615i | 0.179498 | + | 0.179498i | ||||
\(839\) | − | 39.0000i | − | 1.34643i | −0.739447 | − | 0.673215i | \(-0.764913\pi\) | ||
0.739447 | − | 0.673215i | \(-0.235087\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | −1.73205 | + | 1.73205i | −0.0596904 | + | 0.0596904i | ||||
\(843\) | 33.2039 | − | 33.2039i | 1.14360 | − | 1.14360i | ||||
\(844\) | − | 64.0000i | − | 2.20297i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.9090 | − | 32.9090i | 1.13077 | − | 1.13077i | ||||
\(848\) | −31.6228 | + | 31.6228i | −1.08593 | + | 1.08593i | ||||
\(849\) | 54.7723 | 1.87978 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.0000 | −1.02839 | ||||||||
\(852\) | 56.9210 | + | 56.9210i | 1.95008 | + | 1.95008i | ||||
\(853\) | 17.3205 | + | 17.3205i | 0.593043 | + | 0.593043i | 0.938452 | − | 0.345409i | \(-0.112260\pi\) |
−0.345409 | + | 0.938452i | \(0.612260\pi\) | |||||||
\(854\) | −65.7267 | −2.24912 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −72.0000 | −2.46091 | ||||||||
\(857\) | 8.66025 | − | 8.66025i | 0.295829 | − | 0.295829i | −0.543549 | − | 0.839378i | \(-0.682920\pi\) |
0.839378 | + | 0.543549i | \(0.182920\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.3406 | −1.30816 | −0.654082 | − | 0.756424i | \(-0.726945\pi\) | ||||
−0.654082 | + | 0.756424i | \(0.726945\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 49.2950i | 1.67997i | ||||||||
\(862\) | −46.7654 | + | 46.7654i | −1.59283 | + | 1.59283i | ||||
\(863\) | −30.0416 | + | 30.0416i | −1.02263 | + | 1.02263i | −0.0228913 | + | 0.999738i | \(0.507287\pi\) |
−0.999738 | + | 0.0228913i | \(0.992713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.9737 | − | 18.9737i | −0.644379 | − | 0.644379i | ||||
\(868\) | −44.8755 | + | 31.0191i | −1.52317 | + | 1.05286i | ||||
\(869\) | − | 30.0000i | − | 1.01768i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 24.2487 | − | 24.2487i | 0.821165 | − | 0.821165i | ||||
\(873\) | −20.7846 | − | 20.7846i | −0.703452 | − | 0.703452i | ||||
\(874\) | 76.6812 | 2.59378 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 60.0000 | 2.02721 | ||||||||
\(877\) | 36.3731 | − | 36.3731i | 1.22823 | − | 1.22823i | 0.263599 | − | 0.964632i | \(-0.415091\pi\) |
0.964632 | − | 0.263599i | \(-0.0849095\pi\) | |||||||
\(878\) | −29.4449 | − | 29.4449i | −0.993716 | − | 0.993716i | ||||
\(879\) | 27.3861 | 0.923711 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 38.3406i | − | 1.29173i | −0.763453 | − | 0.645863i | \(-0.776498\pi\) | ||
0.763453 | − | 0.645863i | \(-0.223502\pi\) | |||||||
\(882\) | 3.46410 | − | 3.46410i | 0.116642 | − | 0.116642i | ||||
\(883\) | −23.7171 | + | 23.7171i | −0.798143 | + | 0.798143i | −0.982803 | − | 0.184659i | \(-0.940882\pi\) |
0.184659 | + | 0.982803i | \(0.440882\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.0000 | 0.403148 | ||||||||
\(887\) | 19.0526 | − | 19.0526i | 0.639722 | − | 0.639722i | −0.310765 | − | 0.950487i | \(-0.600585\pi\) |
0.950487 | + | 0.310765i | \(0.100585\pi\) | |||||||
\(888\) | 51.9615 | + | 51.9615i | 1.74371 | + | 1.74371i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 60.2495i | − | 2.01843i | ||||||
\(892\) | 56.9210 | + | 56.9210i | 1.90586 | + | 1.90586i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 49.2950 | 1.64867 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.0000 | 1.60357 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 37.9473 | − | 37.9473i | 1.26632 | − | 1.26632i | ||||
\(899\) | 5.47723 | − | 30.0000i | 0.182676 | − | 1.00056i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.0000 | 0.832871 | ||||||||
\(902\) | −85.3815 | − | 85.3815i | −2.84289 | − | 2.84289i | ||||
\(903\) | 25.9808 | + | 25.9808i | 0.864586 | + | 0.864586i | ||||
\(904\) | 36.0000i | 1.19734i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 90.0000 | 2.99005 | ||||||||
\(907\) | 6.92820 | − | 6.92820i | 0.230047 | − | 0.230047i | −0.582665 | − | 0.812712i | \(-0.697990\pi\) |
0.812712 | + | 0.582665i | \(0.197990\pi\) | |||||||
\(908\) | 34.6410 | + | 34.6410i | 1.14960 | + | 1.14960i | ||||
\(909\) | 18.0000i | 0.597022i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 5.47723i | − | 0.181469i | −0.995875 | − | 0.0907343i | \(-0.971079\pi\) | ||
0.995875 | − | 0.0907343i | \(-0.0289214\pi\) | |||||||
\(912\) | −44.2719 | − | 44.2719i | −1.46599 | − | 1.46599i | ||||
\(913\) | 43.3013 | + | 43.3013i | 1.43306 | + | 1.43306i | ||||
\(914\) | −65.7267 | −2.17405 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 21.9089i | − | 0.723891i | ||||||
\(917\) | −5.19615 | + | 5.19615i | −0.171592 | + | 0.171592i | ||||
\(918\) | 8.66025 | + | 8.66025i | 0.285831 | + | 0.285831i | ||||
\(919\) | 31.0000i | 1.02260i | 0.859404 | + | 0.511298i | \(0.170835\pi\) | ||||
−0.859404 | + | 0.511298i | \(0.829165\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 5.47723i | − | 0.180481i | ||||||
\(922\) | 66.4078 | + | 66.4078i | 2.18703 | + | 2.18703i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | − | 120.000i | − | 3.94771i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 32.8634i | − | 1.07996i | ||||||
\(927\) | −6.92820 | + | 6.92820i | −0.227552 | + | 0.227552i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.9545 | −0.359404 | −0.179702 | − | 0.983721i | \(-0.557513\pi\) | ||||
−0.179702 | + | 0.983721i | \(0.557513\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.00000 | −0.229416 | ||||||||
\(932\) | 20.7846 | − | 20.7846i | 0.680823 | − | 0.680823i | ||||
\(933\) | −33.2039 | + | 33.2039i | −1.08705 | + | 1.08705i | ||||
\(934\) | − | 84.0000i | − | 2.74856i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.66025 | + | 8.66025i | −0.282918 | + | 0.282918i | −0.834272 | − | 0.551354i | \(-0.814112\pi\) |
0.551354 | + | 0.834272i | \(0.314112\pi\) | |||||||
\(938\) | −51.9615 | − | 51.9615i | −1.69660 | − | 1.69660i | ||||
\(939\) | − | 15.0000i | − | 0.489506i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(942\) | 9.48683 | + | 9.48683i | 0.309098 | + | 0.309098i | ||||
\(943\) | 28.4605 | − | 28.4605i | 0.926801 | − | 0.926801i | ||||
\(944\) | − | 12.0000i | − | 0.390567i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −90.0000 | −2.92615 | ||||||||
\(947\) | −17.3925 | − | 17.3925i | −0.565181 | − | 0.565181i | 0.365593 | − | 0.930775i | \(-0.380866\pi\) |
−0.930775 | + | 0.365593i | \(0.880866\pi\) | |||||||
\(948\) | −34.6410 | − | 34.6410i | −1.12509 | − | 1.12509i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 76.6812i | − | 2.48656i | ||||||
\(952\) | 18.9737 | + | 18.9737i | 0.614940 | + | 0.614940i | ||||
\(953\) | 1.58114 | − | 1.58114i | 0.0512181 | − | 0.0512181i | −0.681034 | − | 0.732252i | \(-0.738469\pi\) |
0.732252 | + | 0.681034i | \(0.238469\pi\) | |||||||
\(954\) | −54.7723 | −1.77332 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 43.8178i | 1.41717i | ||||||||
\(957\) | 47.4342 | + | 47.4342i | 1.53333 | + | 1.53333i | ||||
\(958\) | 31.1769 | + | 31.1769i | 1.00728 | + | 1.00728i | ||||
\(959\) | 38.3406 | 1.23808 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.0000 | − | 10.9545i | −0.935484 | − | 0.353369i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7846 | − | 20.7846i | −0.669775 | − | 0.669775i | ||||
\(964\) | −21.9089 | −0.705638 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 60.0000 | 1.93047 | ||||||||
\(967\) | −37.9473 | − | 37.9473i | −1.22030 | − | 1.22030i | −0.967524 | − | 0.252780i | \(-0.918655\pi\) |
−0.252780 | − | 0.967524i | \(-0.581345\pi\) | |||||||
\(968\) | 65.8179 | + | 65.8179i | 2.11547 | + | 2.11547i | ||||
\(969\) | 35.0000i | 1.12436i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.0000 | −1.05902 | −0.529510 | − | 0.848304i | \(-0.677624\pi\) | ||||
−0.529510 | + | 0.848304i | \(0.677624\pi\) | |||||||
\(972\) | −50.5964 | − | 50.5964i | −1.62288 | − | 1.62288i | ||||
\(973\) | 28.4605 | − | 28.4605i | 0.912402 | − | 0.912402i | ||||
\(974\) | 49.2950 | 1.57951 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 43.8178i | − | 1.40257i | ||||||
\(977\) | −15.5885 | + | 15.5885i | −0.498719 | + | 0.498719i | −0.911039 | − | 0.412320i | \(-0.864719\pi\) |
0.412320 | + | 0.911039i | \(0.364719\pi\) | |||||||
\(978\) | 75.8947 | − | 75.8947i | 2.42684 | − | 2.42684i | ||||
\(979\) | − | 30.0000i | − | 0.958804i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 14.0000 | 0.446986 | ||||||||
\(982\) | 18.9737 | + | 18.9737i | 0.605474 | + | 0.605474i | ||||
\(983\) | 34.7851 | − | 34.7851i | 1.10947 | − | 1.10947i | 0.116251 | − | 0.993220i | \(-0.462912\pi\) |
0.993220 | − | 0.116251i | \(-0.0370877\pi\) | |||||||
\(984\) | −98.5901 | −3.14294 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −30.0000 | −0.955395 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 30.0000i | − | 0.953945i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 5.47723i | − | 0.173990i | −0.996209 | − | 0.0869949i | \(-0.972274\pi\) | ||
0.996209 | − | 0.0869949i | \(-0.0277264\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 54.0000i | − | 1.71278i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 100.000 | 3.16862 | ||||||||
\(997\) | 6.92820 | − | 6.92820i | 0.219418 | − | 0.219418i | −0.588835 | − | 0.808253i | \(-0.700413\pi\) |
0.808253 | + | 0.588835i | \(0.200413\pi\) | |||||||
\(998\) | 9.48683 | − | 9.48683i | 0.300300 | − | 0.300300i | ||||
\(999\) | − | 15.0000i | − | 0.474579i |
(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 | 775.2.f.c.743.4 | yes | 8 | |
5.2 | odd | 4 | inner | 775.2.f.c.557.3 | yes | 8 | |
5.3 | odd | 4 | inner | 775.2.f.c.557.2 | yes | 8 | |
5.4 | even | 2 | inner | 775.2.f.c.743.1 | yes | 8 | |
31.30 | odd | 2 | inner | 775.2.f.c.743.3 | yes | 8 | |
155.92 | even | 4 | inner | 775.2.f.c.557.4 | yes | 8 | |
155.123 | even | 4 | inner | 775.2.f.c.557.1 | ✓ | 8 | |
155.154 | odd | 2 | inner | 775.2.f.c.743.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
775.2.f.c.557.1 | ✓ | 8 | 155.123 | even | 4 | inner | |
775.2.f.c.557.2 | yes | 8 | 5.3 | odd | 4 | inner | |
775.2.f.c.557.3 | yes | 8 | 5.2 | odd | 4 | inner | |
775.2.f.c.557.4 | yes | 8 | 155.92 | even | 4 | inner | |
775.2.f.c.743.1 | yes | 8 | 5.4 | even | 2 | inner | |
775.2.f.c.743.2 | yes | 8 | 155.154 | odd | 2 | inner | |
775.2.f.c.743.3 | yes | 8 | 31.30 | odd | 2 | inner | |
775.2.f.c.743.4 | yes | 8 | 1.1 | even | 1 | trivial |