Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(451,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, 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("1050.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.p (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} + 56 x^{10} + 300 x^{9} + 1007 x^{8} + 12456 x^{7} + 209990 x^{6} - 250384 x^{5} + \cdots + 6882692292 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 901.6 | ||
Root | \(5.18297 - 5.32390i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.901 |
Dual form | 1050.3.p.f.451.6 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 1.22474i | 0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 0.866025i | 0.500000 | − | 0.288675i | ||||
\(4\) | −1.00000 | − | 1.73205i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 6.99501 | + | 0.264136i | 0.999288 | + | 0.0377338i | ||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.03457 | + | 3.52398i | 0.184961 | + | 0.320362i | 0.943563 | − | 0.331192i | \(-0.107451\pi\) |
−0.758602 | + | 0.651554i | \(0.774117\pi\) | |||||||
\(12\) | −3.00000 | − | 1.73205i | −0.250000 | − | 0.144338i | ||||
\(13\) | − | 11.1199i | − | 0.855373i | −0.903927 | − | 0.427687i | \(-0.859329\pi\) | ||
0.903927 | − | 0.427687i | \(-0.140671\pi\) | |||||||
\(14\) | 5.26972 | − | 8.38034i | 0.376409 | − | 0.598595i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.50807 | + | 1.44803i | −0.147534 | + | 0.0851785i | −0.571950 | − | 0.820289i | \(-0.693813\pi\) |
0.424416 | + | 0.905467i | \(0.360479\pi\) | |||||||
\(18\) | −2.12132 | − | 3.67423i | −0.117851 | − | 0.204124i | ||||
\(19\) | 17.9363 | + | 10.3556i | 0.944018 | + | 0.545029i | 0.891218 | − | 0.453576i | \(-0.149852\pi\) |
0.0528007 | + | 0.998605i | \(0.483185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.7213 | − | 5.66166i | 0.510537 | − | 0.269603i | ||||
\(22\) | 5.75463 | 0.261574 | ||||||||
\(23\) | 15.3199 | − | 26.5348i | 0.666081 | − | 1.15369i | −0.312910 | − | 0.949783i | \(-0.601304\pi\) |
0.978991 | − | 0.203903i | \(-0.0653628\pi\) | |||||||
\(24\) | −4.24264 | + | 2.44949i | −0.176777 | + | 0.102062i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −13.6190 | − | 7.86292i | −0.523807 | − | 0.302420i | ||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −6.53752 | − | 12.3799i | −0.233483 | − | 0.442138i | ||||
\(29\) | −5.75463 | −0.198436 | −0.0992178 | − | 0.995066i | \(-0.531634\pi\) | ||||
−0.0992178 | + | 0.995066i | \(0.531634\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.32136 | − | 1.91759i | 0.107141 | − | 0.0618576i | −0.445472 | − | 0.895296i | \(-0.646964\pi\) |
0.552613 | + | 0.833438i | \(0.313631\pi\) | |||||||
\(32\) | 2.82843 | + | 4.89898i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 6.10371 | + | 3.52398i | 0.184961 | + | 0.106787i | ||||
\(34\) | 4.09566i | 0.120461i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 4.46151 | − | 7.72755i | 0.120581 | − | 0.208853i | −0.799416 | − | 0.600778i | \(-0.794858\pi\) |
0.919997 | + | 0.391925i | \(0.128191\pi\) | |||||||
\(38\) | 25.3658 | − | 14.6450i | 0.667522 | − | 0.385394i | ||||
\(39\) | −9.63007 | − | 16.6798i | −0.246925 | − | 0.427687i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 56.2622i | − | 1.37225i | −0.727484 | − | 0.686125i | \(-0.759311\pi\) | ||
0.727484 | − | 0.686125i | \(-0.240689\pi\) | |||||||
\(42\) | 0.646999 | − | 17.1342i | 0.0154047 | − | 0.407958i | ||||
\(43\) | 7.16364 | 0.166596 | 0.0832982 | − | 0.996525i | \(-0.473455\pi\) | ||||
0.0832982 | + | 0.996525i | \(0.473455\pi\) | |||||||
\(44\) | 4.06914 | − | 7.04796i | 0.0924805 | − | 0.160181i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −21.6656 | − | 37.5258i | −0.470990 | − | 0.815779i | ||||
\(47\) | 41.2277 | + | 23.8028i | 0.877184 | + | 0.506443i | 0.869729 | − | 0.493530i | \(-0.164294\pi\) |
0.00745542 | + | 0.999972i | \(0.497627\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 48.8605 | + | 3.69527i | 0.997152 | + | 0.0754138i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.50807 | + | 4.34410i | −0.0491778 | + | 0.0851785i | ||||
\(52\) | −19.2601 | + | 11.1199i | −0.370387 | + | 0.213843i | ||||
\(53\) | −16.6629 | − | 28.8610i | −0.314395 | − | 0.544548i | 0.664914 | − | 0.746920i | \(-0.268468\pi\) |
−0.979309 | + | 0.202372i | \(0.935135\pi\) | |||||||
\(54\) | −6.36396 | − | 3.67423i | −0.117851 | − | 0.0680414i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −19.7849 | − | 0.747090i | −0.353302 | − | 0.0133409i | ||||
\(57\) | 35.8727 | 0.629346 | ||||||||
\(58\) | −4.06914 | + | 7.04796i | −0.0701576 | + | 0.121517i | ||||
\(59\) | −38.3489 | + | 22.1407i | −0.649981 | + | 0.375267i | −0.788449 | − | 0.615100i | \(-0.789116\pi\) |
0.138468 | + | 0.990367i | \(0.455782\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −60.3282 | − | 34.8305i | −0.988987 | − | 0.570992i | −0.0840158 | − | 0.996464i | \(-0.526775\pi\) |
−0.904971 | + | 0.425472i | \(0.860108\pi\) | |||||||
\(62\) | − | 5.42375i | − | 0.0874799i | ||||||
\(63\) | 11.1788 | − | 17.7774i | 0.177441 | − | 0.282181i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8.63195 | − | 4.98366i | 0.130787 | − | 0.0755100i | ||||
\(67\) | 46.0565 | + | 79.7722i | 0.687410 | + | 1.19063i | 0.972673 | + | 0.232180i | \(0.0745858\pi\) |
−0.285263 | + | 0.958449i | \(0.592081\pi\) | |||||||
\(68\) | 5.01614 | + | 2.89607i | 0.0737668 | + | 0.0425893i | ||||
\(69\) | − | 53.0695i | − | 0.769124i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.64679 | 0.0936168 | 0.0468084 | − | 0.998904i | \(-0.485095\pi\) | ||||
0.0468084 | + | 0.998904i | \(0.485095\pi\) | |||||||
\(72\) | −4.24264 | + | 7.34847i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 45.3984 | − | 26.2108i | 0.621896 | − | 0.359052i | −0.155711 | − | 0.987803i | \(-0.549767\pi\) |
0.777607 | + | 0.628751i | \(0.216434\pi\) | |||||||
\(74\) | −6.30952 | − | 10.9284i | −0.0852638 | − | 0.147681i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 41.4222i | − | 0.545029i | ||||||
\(77\) | 13.3010 | + | 25.1877i | 0.172741 | + | 0.327113i | ||||
\(78\) | −27.2380 | −0.349205 | ||||||||
\(79\) | 26.7215 | − | 46.2830i | 0.338247 | − | 0.585861i | −0.645856 | − | 0.763459i | \(-0.723499\pi\) |
0.984103 | + | 0.177598i | \(0.0568328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −68.9069 | − | 39.7834i | −0.840327 | − | 0.485163i | ||||
\(83\) | − | 116.101i | − | 1.39880i | −0.714729 | − | 0.699402i | \(-0.753450\pi\) | ||
0.714729 | − | 0.699402i | \(-0.246550\pi\) | |||||||
\(84\) | −20.5275 | − | 12.9081i | −0.244376 | − | 0.153668i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.06546 | − | 8.77363i | 0.0589007 | − | 0.102019i | ||||
\(87\) | −8.63195 | + | 4.98366i | −0.0992178 | + | 0.0572834i | ||||
\(88\) | −5.75463 | − | 9.96732i | −0.0653936 | − | 0.113265i | ||||
\(89\) | −85.6511 | − | 49.4507i | −0.962372 | − | 0.555626i | −0.0654695 | − | 0.997855i | \(-0.520855\pi\) |
−0.896902 | + | 0.442229i | \(0.854188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.93716 | − | 77.7835i | 0.0322764 | − | 0.854764i | ||||
\(92\) | −61.2794 | −0.666081 | ||||||||
\(93\) | 3.32136 | − | 5.75276i | 0.0357135 | − | 0.0618576i | ||||
\(94\) | 58.3047 | − | 33.6623i | 0.620263 | − | 0.358109i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.48528 | + | 4.89898i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | 132.963i | 1.37075i | 0.728189 | + | 0.685377i | \(0.240362\pi\) | ||||
−0.728189 | + | 0.685377i | \(0.759638\pi\) | |||||||
\(98\) | 39.0753 | − | 57.2286i | 0.398728 | − | 0.583966i | ||||
\(99\) | 12.2074 | 0.123307 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −52.3294 | + | 30.2124i | −0.518113 | + | 0.299133i | −0.736162 | − | 0.676805i | \(-0.763364\pi\) |
0.218049 | + | 0.975938i | \(0.430031\pi\) | |||||||
\(102\) | 3.54695 | + | 6.14349i | 0.0347740 | + | 0.0602303i | ||||
\(103\) | 27.1191 | + | 15.6572i | 0.263293 | + | 0.152012i | 0.625836 | − | 0.779955i | \(-0.284758\pi\) |
−0.362543 | + | 0.931967i | \(0.618091\pi\) | |||||||
\(104\) | 31.4517i | 0.302420i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −47.1299 | −0.444622 | ||||||||
\(107\) | −23.5200 | + | 40.7378i | −0.219813 | + | 0.380727i | −0.954751 | − | 0.297407i | \(-0.903878\pi\) |
0.734938 | + | 0.678135i | \(0.237211\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.0833333 | + | 0.0481125i | ||||
\(109\) | −100.779 | − | 174.554i | −0.924576 | − | 1.60141i | −0.792242 | − | 0.610208i | \(-0.791086\pi\) |
−0.132335 | − | 0.991205i | \(-0.542247\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 15.4551i | − | 0.139235i | ||||||
\(112\) | −14.9050 | + | 23.7032i | −0.133081 | + | 0.211635i | ||||
\(113\) | −168.422 | −1.49046 | −0.745230 | − | 0.666807i | \(-0.767661\pi\) | ||||
−0.745230 | + | 0.666807i | \(0.767661\pi\) | |||||||
\(114\) | 25.3658 | − | 43.9349i | 0.222507 | − | 0.385394i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 5.75463 | + | 9.96732i | 0.0496089 | + | 0.0859252i | ||||
\(117\) | −28.8902 | − | 16.6798i | −0.246925 | − | 0.142562i | ||||
\(118\) | 62.6234i | 0.530707i | ||||||||
\(119\) | −17.9265 | + | 9.46655i | −0.150643 | + | 0.0795509i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 52.2210 | − | 90.4495i | 0.431579 | − | 0.747517i | ||||
\(122\) | −85.3170 | + | 49.2578i | −0.699320 | + | 0.403752i | ||||
\(123\) | −48.7245 | − | 84.3933i | −0.396134 | − | 0.686125i | ||||
\(124\) | −6.64271 | − | 3.83517i | −0.0535703 | − | 0.0309288i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −13.8682 | − | 26.2616i | −0.110065 | − | 0.208426i | ||||
\(127\) | 29.1799 | 0.229763 | 0.114882 | − | 0.993379i | \(-0.463351\pi\) | ||||
0.114882 | + | 0.993379i | \(0.463351\pi\) | |||||||
\(128\) | 5.65685 | − | 9.79796i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 10.7455 | − | 6.20390i | 0.0832982 | − | 0.0480922i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 123.441 | + | 71.2688i | 0.942299 | + | 0.544037i | 0.890680 | − | 0.454630i | \(-0.150229\pi\) |
0.0516187 | + | 0.998667i | \(0.483562\pi\) | |||||||
\(132\) | − | 14.0959i | − | 0.106787i | ||||||
\(133\) | 122.730 | + | 77.1749i | 0.922780 | + | 0.580262i | ||||
\(134\) | 130.267 | 0.972145 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.09389 | − | 4.09566i | 0.0521610 | − | 0.0301152i | ||||
\(137\) | 104.297 | + | 180.648i | 0.761295 | + | 1.31860i | 0.942183 | + | 0.335098i | \(0.108769\pi\) |
−0.180889 | + | 0.983504i | \(0.557897\pi\) | |||||||
\(138\) | −64.9967 | − | 37.5258i | −0.470990 | − | 0.271926i | ||||
\(139\) | 152.491i | 1.09706i | 0.836132 | + | 0.548528i | \(0.184812\pi\) | ||||
−0.836132 | + | 0.548528i | \(0.815188\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 82.4553 | 0.584790 | ||||||||
\(142\) | 4.69999 | − | 8.14062i | 0.0330985 | − | 0.0573283i | ||||
\(143\) | 39.1861 | − | 22.6241i | 0.274029 | − | 0.158211i | ||||
\(144\) | 6.00000 | + | 10.3923i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 74.1353i | − | 0.507776i | ||||||
\(147\) | 76.4909 | − | 36.7715i | 0.520346 | − | 0.250146i | ||||
\(148\) | −17.8460 | −0.120581 | ||||||||
\(149\) | −68.2572 | + | 118.225i | −0.458102 | + | 0.793456i | −0.998861 | − | 0.0477221i | \(-0.984804\pi\) |
0.540759 | + | 0.841178i | \(0.318137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −64.7993 | − | 112.236i | −0.429134 | − | 0.743282i | 0.567662 | − | 0.823261i | \(-0.307848\pi\) |
−0.996797 | + | 0.0799793i | \(0.974515\pi\) | |||||||
\(152\) | −50.7317 | − | 29.2899i | −0.333761 | − | 0.192697i | ||||
\(153\) | 8.68821i | 0.0567857i | ||||||||
\(154\) | 40.2538 | + | 1.52001i | 0.261388 | + | 0.00987018i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −19.2601 | + | 33.3596i | −0.123462 | + | 0.213843i | ||||
\(157\) | 116.268 | − | 67.1273i | 0.740560 | − | 0.427562i | −0.0817131 | − | 0.996656i | \(-0.526039\pi\) |
0.822273 | + | 0.569094i | \(0.192706\pi\) | |||||||
\(158\) | −37.7899 | − | 65.4540i | −0.239177 | − | 0.414266i | ||||
\(159\) | −49.9888 | − | 28.8610i | −0.314395 | − | 0.181516i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114.171 | − | 181.565i | 0.709139 | − | 1.12773i | ||||
\(162\) | −12.7279 | −0.0785674 | ||||||||
\(163\) | −80.8126 | + | 139.972i | −0.495783 | + | 0.858721i | −0.999988 | − | 0.00486254i | \(-0.998452\pi\) |
0.504205 | + | 0.863584i | \(0.331786\pi\) | |||||||
\(164\) | −97.4490 | + | 56.2622i | −0.594201 | + | 0.343062i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −142.194 | − | 82.0956i | −0.856589 | − | 0.494552i | ||||
\(167\) | 166.987i | 0.999920i | 0.866049 | + | 0.499960i | \(0.166652\pi\) | ||||
−0.866049 | + | 0.499960i | \(0.833348\pi\) | |||||||
\(168\) | −30.3243 | + | 16.0136i | −0.180502 | + | 0.0953189i | ||||
\(169\) | 45.3489 | 0.268337 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 53.8090 | − | 31.0667i | 0.314673 | − | 0.181676i | ||||
\(172\) | −7.16364 | − | 12.4078i | −0.0416491 | − | 0.0721383i | ||||
\(173\) | −10.1276 | − | 5.84719i | −0.0585412 | − | 0.0337988i | 0.470444 | − | 0.882430i | \(-0.344094\pi\) |
−0.528985 | + | 0.848631i | \(0.677427\pi\) | |||||||
\(174\) | 14.0959i | 0.0810110i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −16.2766 | −0.0924805 | ||||||||
\(177\) | −38.3489 | + | 66.4222i | −0.216660 | + | 0.375267i | ||||
\(178\) | −121.129 | + | 69.9338i | −0.680500 | + | 0.392887i | ||||
\(179\) | −66.8799 | − | 115.839i | −0.373631 | − | 0.647147i | 0.616490 | − | 0.787363i | \(-0.288554\pi\) |
−0.990121 | + | 0.140215i | \(0.955221\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 113.035i | − | 0.624501i | −0.950000 | − | 0.312251i | \(-0.898917\pi\) | ||
0.950000 | − | 0.312251i | \(-0.101083\pi\) | |||||||
\(182\) | −93.1881 | − | 58.5985i | −0.512022 | − | 0.321970i | ||||
\(183\) | −120.656 | −0.659325 | ||||||||
\(184\) | −43.3311 | + | 75.0517i | −0.235495 | + | 0.407890i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −4.69711 | − | 8.13563i | −0.0252533 | − | 0.0437399i | ||||
\(187\) | −10.2057 | − | 5.89226i | −0.0545759 | − | 0.0315094i | ||||
\(188\) | − | 95.2112i | − | 0.506443i | ||||||
\(189\) | 1.37249 | − | 36.3472i | 0.00726187 | − | 0.192313i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −125.518 | + | 217.404i | −0.657163 | + | 1.13824i | 0.324184 | + | 0.945994i | \(0.394910\pi\) |
−0.981347 | + | 0.192245i | \(0.938423\pi\) | |||||||
\(192\) | 12.0000 | − | 6.92820i | 0.0625000 | − | 0.0360844i | ||||
\(193\) | 178.495 | + | 309.163i | 0.924846 | + | 1.60188i | 0.791809 | + | 0.610769i | \(0.209140\pi\) |
0.133038 | + | 0.991111i | \(0.457527\pi\) | |||||||
\(194\) | 162.846 | + | 94.0191i | 0.839412 | + | 0.484635i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −42.4601 | − | 88.3241i | −0.216633 | − | 0.450633i | ||||
\(197\) | −35.1268 | −0.178309 | −0.0891543 | − | 0.996018i | \(-0.528416\pi\) | ||||
−0.0891543 | + | 0.996018i | \(0.528416\pi\) | |||||||
\(198\) | 8.63195 | − | 14.9510i | 0.0435957 | − | 0.0755100i | ||||
\(199\) | −79.3368 | + | 45.8051i | −0.398677 | + | 0.230177i | −0.685913 | − | 0.727683i | \(-0.740597\pi\) |
0.287236 | + | 0.957860i | \(0.407264\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 138.169 | + | 79.7722i | 0.687410 | + | 0.396876i | ||||
\(202\) | 85.4536i | 0.423038i | ||||||||
\(203\) | −40.2538 | − | 1.52001i | −0.198294 | − | 0.00748772i | ||||
\(204\) | 10.0323 | 0.0491778 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 38.3523 | − | 22.1427i | 0.186176 | − | 0.107489i | ||||
\(207\) | −45.9596 | − | 79.6043i | −0.222027 | − | 0.384562i | ||||
\(208\) | 38.5203 | + | 22.2397i | 0.185194 | + | 0.106922i | ||||
\(209\) | 84.2764i | 0.403237i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.70268 | 0.0412449 | 0.0206225 | − | 0.999787i | \(-0.493435\pi\) | ||||
0.0206225 | + | 0.999787i | \(0.493435\pi\) | |||||||
\(212\) | −33.3259 | + | 57.7221i | −0.157197 | + | 0.272274i | ||||
\(213\) | 9.97019 | − | 5.75629i | 0.0468084 | − | 0.0270248i | ||||
\(214\) | 33.2623 | + | 57.6120i | 0.155431 | + | 0.269215i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 23.7394 | − | 12.5363i | 0.109398 | − | 0.0577708i | ||||
\(218\) | −285.045 | −1.30755 | ||||||||
\(219\) | 45.3984 | − | 78.6323i | 0.207299 | − | 0.359052i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.1019 | + | 27.8894i | 0.0728594 | + | 0.126196i | ||||
\(222\) | −18.9286 | − | 10.9284i | −0.0852638 | − | 0.0492271i | ||||
\(223\) | 158.414i | 0.710375i | 0.934795 | + | 0.355187i | \(0.115583\pi\) | ||||
−0.934795 | + | 0.355187i | \(0.884417\pi\) | |||||||
\(224\) | 18.4909 | + | 35.0155i | 0.0825486 | + | 0.156319i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −119.092 | + | 206.274i | −0.526957 | + | 0.912717i | ||||
\(227\) | 343.311 | − | 198.211i | 1.51239 | − | 0.873176i | 0.512490 | − | 0.858693i | \(-0.328723\pi\) |
0.999895 | − | 0.0144830i | \(-0.00461024\pi\) | |||||||
\(228\) | −35.8727 | − | 62.1333i | −0.157336 | − | 0.272515i | ||||
\(229\) | 178.548 | + | 103.085i | 0.779685 | + | 0.450151i | 0.836319 | − | 0.548244i | \(-0.184703\pi\) |
−0.0566339 | + | 0.998395i | \(0.518037\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 41.7647 | + | 26.2625i | 0.180800 | + | 0.113690i | ||||
\(232\) | 16.2766 | 0.0701576 | ||||||||
\(233\) | 55.6555 | − | 96.3981i | 0.238865 | − | 0.413726i | −0.721524 | − | 0.692389i | \(-0.756558\pi\) |
0.960389 | + | 0.278664i | \(0.0898915\pi\) | |||||||
\(234\) | −40.8569 | + | 23.5888i | −0.174602 | + | 0.100807i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 76.6977 | + | 44.2815i | 0.324990 | + | 0.187633i | ||||
\(237\) | − | 92.5660i | − | 0.390574i | ||||||
\(238\) | −1.08181 | + | 28.6492i | −0.00454543 | + | 0.120375i | ||||
\(239\) | −258.839 | −1.08301 | −0.541504 | − | 0.840698i | \(-0.682145\pi\) | ||||
−0.541504 | + | 0.840698i | \(0.682145\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 264.996 | − | 152.995i | 1.09957 | − | 0.634835i | 0.163460 | − | 0.986550i | \(-0.447735\pi\) |
0.936107 | + | 0.351715i | \(0.114401\pi\) | |||||||
\(242\) | −73.8517 | − | 127.915i | −0.305172 | − | 0.528574i | ||||
\(243\) | −13.5000 | − | 7.79423i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 139.322i | 0.570992i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −137.814 | −0.560218 | ||||||||
\(247\) | 115.152 | − | 199.450i | 0.466203 | − | 0.807488i | ||||
\(248\) | −9.39422 | + | 5.42375i | −0.0378799 | + | 0.0218700i | ||||
\(249\) | −100.546 | − | 174.151i | −0.403800 | − | 0.699402i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 415.878i | 1.65688i | 0.560076 | + | 0.828441i | \(0.310772\pi\) | ||||
−0.560076 | + | 0.828441i | \(0.689228\pi\) | |||||||
\(252\) | −41.9701 | − | 1.58482i | −0.166548 | − | 0.00628896i | ||||
\(253\) | 124.677 | 0.492796 | ||||||||
\(254\) | 20.6333 | − | 35.7380i | 0.0812336 | − | 0.140701i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −271.280 | − | 156.624i | −1.05556 | − | 0.609430i | −0.131362 | − | 0.991334i | \(-0.541935\pi\) |
−0.924202 | + | 0.381904i | \(0.875268\pi\) | |||||||
\(258\) | − | 17.5473i | − | 0.0680127i | ||||||
\(259\) | 33.2494 | − | 52.8759i | 0.128376 | − | 0.204154i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −8.63195 | + | 14.9510i | −0.0330726 | + | 0.0572834i | ||||
\(262\) | 174.572 | − | 100.789i | 0.666306 | − | 0.384692i | ||||
\(263\) | −44.2782 | − | 76.6921i | −0.168358 | − | 0.291605i | 0.769485 | − | 0.638665i | \(-0.220513\pi\) |
−0.937843 | + | 0.347061i | \(0.887180\pi\) | |||||||
\(264\) | −17.2639 | − | 9.96732i | −0.0653936 | − | 0.0377550i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 181.303 | − | 95.7417i | 0.681589 | − | 0.359931i | ||||
\(267\) | −171.302 | −0.641581 | ||||||||
\(268\) | 92.1130 | − | 159.544i | 0.343705 | − | 0.595315i | ||||
\(269\) | −70.7545 | + | 40.8501i | −0.263028 | + | 0.151859i | −0.625715 | − | 0.780052i | \(-0.715193\pi\) |
0.362687 | + | 0.931911i | \(0.381859\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 254.904 | + | 147.169i | 0.940604 | + | 0.543058i | 0.890150 | − | 0.455668i | \(-0.150600\pi\) |
0.0504543 | + | 0.998726i | \(0.483933\pi\) | |||||||
\(272\) | − | 11.5843i | − | 0.0425893i | ||||||
\(273\) | −62.9568 | − | 119.219i | −0.230611 | − | 0.436699i | ||||
\(274\) | 294.998 | 1.07663 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −91.9192 | + | 53.0695i | −0.333040 | + | 0.192281i | ||||
\(277\) | 203.122 | + | 351.817i | 0.733292 | + | 1.27010i | 0.955469 | + | 0.295092i | \(0.0953503\pi\) |
−0.222177 | + | 0.975006i | \(0.571316\pi\) | |||||||
\(278\) | 186.762 | + | 107.827i | 0.671807 | + | 0.387868i | ||||
\(279\) | − | 11.5055i | − | 0.0412384i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −234.304 | −0.833823 | −0.416912 | − | 0.908947i | \(-0.636888\pi\) | ||||
−0.416912 | + | 0.908947i | \(0.636888\pi\) | |||||||
\(282\) | 58.3047 | − | 100.987i | 0.206754 | − | 0.358109i | ||||
\(283\) | 237.575 | − | 137.164i | 0.839488 | − | 0.484678i | −0.0176023 | − | 0.999845i | \(-0.505603\pi\) |
0.857090 | + | 0.515167i | \(0.172270\pi\) | |||||||
\(284\) | −6.64679 | − | 11.5126i | −0.0234042 | − | 0.0405372i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 63.9907i | − | 0.223744i | ||||||
\(287\) | 14.8609 | − | 393.555i | 0.0517801 | − | 1.37127i | ||||
\(288\) | 16.9706 | 0.0589256 | ||||||||
\(289\) | −140.306 | + | 243.018i | −0.485489 | + | 0.840892i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 115.149 | + | 199.445i | 0.395702 | + | 0.685377i | ||||
\(292\) | −90.7968 | − | 52.4215i | −0.310948 | − | 0.179526i | ||||
\(293\) | 64.7274i | 0.220913i | 0.993881 | + | 0.110456i | \(0.0352312\pi\) | ||||
−0.993881 | + | 0.110456i | \(0.964769\pi\) | |||||||
\(294\) | 9.05154 | − | 119.683i | 0.0307875 | − | 0.407086i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.6190 | + | 21.8568i | −0.0426319 | + | 0.0738406i | ||||
\(297\) | 18.3111 | − | 10.5719i | 0.0616537 | − | 0.0355958i | ||||
\(298\) | 96.5302 | + | 167.195i | 0.323927 | + | 0.561058i | ||||
\(299\) | −295.063 | − | 170.355i | −0.986832 | − | 0.569748i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 50.1098 | + | 1.89218i | 0.166478 | + | 0.00628631i | ||||
\(302\) | −183.280 | −0.606887 | ||||||||
\(303\) | −52.3294 | + | 90.6372i | −0.172704 | + | 0.299133i | ||||
\(304\) | −71.7454 | + | 41.4222i | −0.236005 | + | 0.136257i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 10.6408 | + | 6.14349i | 0.0347740 | + | 0.0200768i | ||||
\(307\) | 164.065i | 0.534413i | 0.963639 | + | 0.267207i | \(0.0861006\pi\) | ||||
−0.963639 | + | 0.267207i | \(0.913899\pi\) | |||||||
\(308\) | 30.3253 | − | 48.2258i | 0.0984588 | − | 0.156577i | ||||
\(309\) | 54.2383 | 0.175528 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −197.874 | + | 114.243i | −0.636252 | + | 0.367340i | −0.783169 | − | 0.621809i | \(-0.786398\pi\) |
0.146918 | + | 0.989149i | \(0.453065\pi\) | |||||||
\(312\) | 27.2380 | + | 47.1775i | 0.0873012 | + | 0.151210i | ||||
\(313\) | 448.148 | + | 258.738i | 1.43178 | + | 0.826640i | 0.997257 | − | 0.0740194i | \(-0.0235827\pi\) |
0.434526 | + | 0.900659i | \(0.356916\pi\) | |||||||
\(314\) | − | 189.865i | − | 0.604664i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −106.886 | −0.338247 | ||||||||
\(317\) | 147.654 | − | 255.744i | 0.465785 | − | 0.806764i | −0.533451 | − | 0.845831i | \(-0.679105\pi\) |
0.999237 | + | 0.0390670i | \(0.0124386\pi\) | |||||||
\(318\) | −70.6948 | + | 40.8157i | −0.222311 | + | 0.128351i | ||||
\(319\) | −11.7082 | − | 20.2792i | −0.0367029 | − | 0.0635712i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 81.4756i | 0.253818i | ||||||||
\(322\) | −141.639 | − | 268.216i | −0.439872 | − | 0.832970i | ||||
\(323\) | −59.9808 | −0.185699 | ||||||||
\(324\) | −9.00000 | + | 15.5885i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 114.286 | + | 197.950i | 0.350572 | + | 0.607208i | ||||
\(327\) | −302.336 | − | 174.554i | −0.924576 | − | 0.533804i | ||||
\(328\) | 159.134i | 0.485163i | ||||||||
\(329\) | 282.101 | + | 177.391i | 0.857450 | + | 0.539181i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −311.691 | + | 539.864i | −0.941663 | + | 1.63101i | −0.179366 | + | 0.983782i | \(0.557404\pi\) |
−0.762298 | + | 0.647226i | \(0.775929\pi\) | |||||||
\(332\) | −201.092 | + | 116.101i | −0.605700 | + | 0.349701i | ||||
\(333\) | −13.3845 | − | 23.1827i | −0.0401937 | − | 0.0696176i | ||||
\(334\) | 204.516 | + | 118.077i | 0.612323 | + | 0.353525i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.82999 | + | 48.4629i | −0.00544640 | + | 0.144235i | ||||
\(337\) | 0.0404399 | 0.000120000 | 5.99998e−5 | − | 1.00000i | \(-0.499981\pi\) | ||||
5.99998e−5 | 1.00000i | \(0.499981\pi\) | ||||||||
\(338\) | 32.0665 | − | 55.5408i | 0.0948714 | − | 0.164322i | ||||
\(339\) | −252.633 | + | 145.858i | −0.745230 | + | 0.430259i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.5151 | + | 7.80293i | 0.0396336 | + | 0.0228825i | ||||
\(342\) | − | 87.8698i | − | 0.256929i | ||||||
\(343\) | 340.804 | + | 38.7543i | 0.993597 | + | 0.112986i | ||||
\(344\) | −20.2618 | −0.0589007 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.3226 | + | 8.26918i | −0.0413949 | + | 0.0238994i | ||||
\(347\) | 60.8256 | + | 105.353i | 0.175290 | + | 0.303611i | 0.940262 | − | 0.340453i | \(-0.110580\pi\) |
−0.764972 | + | 0.644064i | \(0.777247\pi\) | |||||||
\(348\) | 17.2639 | + | 9.96732i | 0.0496089 | + | 0.0286417i | ||||
\(349\) | 457.192i | 1.31001i | 0.755626 | + | 0.655003i | \(0.227333\pi\) | ||||
−0.755626 | + | 0.655003i | \(0.772667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −57.7804 | −0.164617 | ||||||||
\(352\) | −11.5093 | + | 19.9346i | −0.0326968 | + | 0.0566325i | ||||
\(353\) | 23.6695 | − | 13.6656i | 0.0670525 | − | 0.0387128i | −0.466099 | − | 0.884733i | \(-0.654341\pi\) |
0.533151 | + | 0.846020i | \(0.321008\pi\) | |||||||
\(354\) | 54.2335 | + | 93.9352i | 0.153202 | + | 0.265354i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 197.803i | 0.555626i | ||||||||
\(357\) | −18.6914 | + | 29.7246i | −0.0523569 | + | 0.0832622i | ||||
\(358\) | −189.165 | −0.528394 | ||||||||
\(359\) | 231.018 | − | 400.135i | 0.643504 | − | 1.11458i | −0.341141 | − | 0.940012i | \(-0.610813\pi\) |
0.984645 | − | 0.174569i | \(-0.0558532\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 33.9751 | + | 58.8466i | 0.0941138 | + | 0.163010i | ||||
\(362\) | −138.439 | − | 79.9276i | −0.382427 | − | 0.220794i | ||||
\(363\) | − | 180.899i | − | 0.498344i | ||||||
\(364\) | −137.662 | + | 72.6962i | −0.378193 | + | 0.199715i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −85.3170 | + | 147.773i | −0.233107 | + | 0.403752i | ||||
\(367\) | 372.413 | − | 215.013i | 1.01475 | − | 0.585865i | 0.102170 | − | 0.994767i | \(-0.467421\pi\) |
0.912578 | + | 0.408902i | \(0.134088\pi\) | |||||||
\(368\) | 61.2794 | + | 106.139i | 0.166520 | + | 0.288421i | ||||
\(369\) | −146.174 | − | 84.3933i | −0.396134 | − | 0.228708i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −108.934 | − | 206.285i | −0.293623 | − | 0.556024i | ||||
\(372\) | −13.2854 | −0.0357135 | ||||||||
\(373\) | −334.967 | + | 580.179i | −0.898034 | + | 1.55544i | −0.0680300 | + | 0.997683i | \(0.521671\pi\) |
−0.830004 | + | 0.557757i | \(0.811662\pi\) | |||||||
\(374\) | −14.4330 | + | 8.33291i | −0.0385910 | + | 0.0222805i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −116.609 | − | 67.3245i | −0.310132 | − | 0.179055i | ||||
\(377\) | 63.9907i | 0.169737i | ||||||||
\(378\) | −43.5455 | − | 27.3823i | −0.115200 | − | 0.0724399i | ||||
\(379\) | 704.346 | 1.85843 | 0.929216 | − | 0.369536i | \(-0.120483\pi\) | ||||
0.929216 | + | 0.369536i | \(0.120483\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 43.7699 | − | 25.2706i | 0.114882 | − | 0.0663269i | ||||
\(382\) | 177.509 | + | 307.455i | 0.464684 | + | 0.804857i | ||||
\(383\) | 25.6663 | + | 14.8185i | 0.0670139 | + | 0.0386905i | 0.533133 | − | 0.846032i | \(-0.321015\pi\) |
−0.466119 | + | 0.884722i | \(0.654348\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 504.861 | 1.30793 | ||||||||
\(387\) | 10.7455 | − | 18.6117i | 0.0277661 | − | 0.0480922i | ||||
\(388\) | 230.299 | − | 132.963i | 0.593554 | − | 0.342688i | ||||
\(389\) | 18.4085 | + | 31.8844i | 0.0473225 | + | 0.0819650i | 0.888716 | − | 0.458457i | \(-0.151598\pi\) |
−0.841394 | + | 0.540422i | \(0.818264\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 88.7348i | 0.226943i | ||||||||
\(392\) | −138.198 | − | 10.4518i | −0.352547 | − | 0.0266628i | ||||
\(393\) | 246.882 | 0.628199 | ||||||||
\(394\) | −24.8384 | + | 43.0213i | −0.0630416 | + | 0.109191i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −12.2074 | − | 21.1439i | −0.0308268 | − | 0.0533936i | ||||
\(397\) | −79.6635 | − | 45.9937i | −0.200664 | − | 0.115853i | 0.396301 | − | 0.918121i | \(-0.370294\pi\) |
−0.596965 | + | 0.802267i | \(0.703627\pi\) | |||||||
\(398\) | 129.556i | 0.325519i | ||||||||
\(399\) | 250.930 | + | 9.47528i | 0.628897 | + | 0.0237476i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −178.114 | + | 308.502i | −0.444174 | + | 0.769332i | −0.997994 | − | 0.0633041i | \(-0.979836\pi\) |
0.553820 | + | 0.832636i | \(0.313170\pi\) | |||||||
\(402\) | 195.401 | − | 112.815i | 0.486072 | − | 0.280634i | ||||
\(403\) | −21.3233 | − | 36.9330i | −0.0529113 | − | 0.0916451i | ||||
\(404\) | 104.659 | + | 60.4248i | 0.259057 | + | 0.149566i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −30.3253 | + | 48.2258i | −0.0746929 | + | 0.118783i | ||||
\(407\) | 36.3090 | 0.0892113 | ||||||||
\(408\) | 7.09389 | − | 12.2870i | 0.0173870 | − | 0.0301152i | ||||
\(409\) | −20.9491 | + | 12.0950i | −0.0512203 | + | 0.0295720i | −0.525391 | − | 0.850861i | \(-0.676081\pi\) |
0.474171 | + | 0.880433i | \(0.342748\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 312.892 | + | 180.648i | 0.761295 | + | 0.439534i | ||||
\(412\) | − | 62.6290i | − | 0.152012i | ||||||
\(413\) | −274.099 | + | 144.745i | −0.663678 | + | 0.350473i | ||||
\(414\) | −129.993 | −0.313994 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 54.4759 | − | 31.4517i | 0.130952 | − | 0.0756050i | ||||
\(417\) | 132.061 | + | 228.736i | 0.316693 | + | 0.548528i | ||||
\(418\) | 103.217 | + | 59.5924i | 0.246931 | + | 0.142566i | ||||
\(419\) | − | 537.398i | − | 1.28257i | −0.767302 | − | 0.641286i | \(-0.778401\pi\) | ||
0.767302 | − | 0.641286i | \(-0.221599\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −644.404 | −1.53065 | −0.765326 | − | 0.643643i | \(-0.777422\pi\) | ||||
−0.765326 | + | 0.643643i | \(0.777422\pi\) | |||||||
\(422\) | 6.15372 | − | 10.6586i | 0.0145823 | − | 0.0252573i | ||||
\(423\) | 123.683 | − | 71.4084i | 0.292395 | − | 0.168814i | ||||
\(424\) | 47.1299 | + | 81.6314i | 0.111155 | + | 0.192527i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 16.2812i | − | 0.0382189i | ||||||
\(427\) | −412.797 | − | 259.575i | −0.966737 | − | 0.607904i | ||||
\(428\) | 94.0799 | 0.219813 | ||||||||
\(429\) | 39.1861 | − | 67.8724i | 0.0913430 | − | 0.158211i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 233.686 | + | 404.756i | 0.542195 | + | 0.939109i | 0.998778 | + | 0.0494278i | \(0.0157398\pi\) |
−0.456583 | + | 0.889681i | \(0.650927\pi\) | |||||||
\(432\) | 18.0000 | + | 10.3923i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 33.2022i | 0.0766794i | 0.999265 | + | 0.0383397i | \(0.0122069\pi\) | ||||
−0.999265 | + | 0.0383397i | \(0.987793\pi\) | |||||||
\(434\) | 1.43261 | − | 37.9392i | 0.00330094 | − | 0.0874176i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −201.558 | + | 349.108i | −0.462288 | + | 0.800706i | ||||
\(437\) | 549.565 | − | 317.291i | 1.25759 | − | 0.726067i | ||||
\(438\) | −64.2030 | − | 111.203i | −0.146582 | − | 0.253888i | ||||
\(439\) | −44.2179 | − | 25.5292i | −0.100724 | − | 0.0581531i | 0.448792 | − | 0.893636i | \(-0.351855\pi\) |
−0.549516 | + | 0.835483i | \(0.685188\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 82.8913 | − | 121.400i | 0.187962 | − | 0.275284i | ||||
\(442\) | 45.5431 | 0.103039 | ||||||||
\(443\) | −396.329 | + | 686.462i | −0.894648 | + | 1.54958i | −0.0604076 | + | 0.998174i | \(0.519240\pi\) |
−0.834240 | + | 0.551401i | \(0.814093\pi\) | |||||||
\(444\) | −26.7690 | + | 15.4551i | −0.0602906 | + | 0.0348088i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 194.016 | + | 112.015i | 0.435014 | + | 0.251155i | ||||
\(447\) | 236.450i | 0.528970i | ||||||||
\(448\) | 55.9601 | + | 2.11309i | 0.124911 | + | 0.00471672i | ||||
\(449\) | 71.7539 | 0.159808 | 0.0799041 | − | 0.996803i | \(-0.474539\pi\) | ||||
0.0799041 | + | 0.996803i | \(0.474539\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 198.267 | − | 114.469i | 0.439616 | − | 0.253812i | ||||
\(452\) | 168.422 | + | 291.716i | 0.372615 | + | 0.645388i | ||||
\(453\) | −194.398 | − | 112.236i | −0.429134 | − | 0.247761i | ||||
\(454\) | − | 560.625i | − | 1.23486i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −101.463 | −0.222507 | ||||||||
\(457\) | −314.013 | + | 543.886i | −0.687117 | + | 1.19012i | 0.285649 | + | 0.958334i | \(0.407791\pi\) |
−0.972766 | + | 0.231787i | \(0.925543\pi\) | |||||||
\(458\) | 252.505 | − | 145.784i | 0.551320 | − | 0.318305i | ||||
\(459\) | 7.52421 | + | 13.0323i | 0.0163926 | + | 0.0283928i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 475.402i | 1.03124i | 0.856817 | + | 0.515621i | \(0.172439\pi\) | ||||
−0.856817 | + | 0.515621i | \(0.827561\pi\) | |||||||
\(462\) | 61.6970 | − | 32.5808i | 0.133543 | − | 0.0705211i | ||||
\(463\) | 342.588 | 0.739931 | 0.369966 | − | 0.929045i | \(-0.379369\pi\) | ||||
0.369966 | + | 0.929045i | \(0.379369\pi\) | |||||||
\(464\) | 11.5093 | − | 19.9346i | 0.0248045 | − | 0.0429626i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −78.7087 | − | 136.327i | −0.168903 | − | 0.292548i | ||||
\(467\) | −220.056 | − | 127.049i | −0.471211 | − | 0.272054i | 0.245535 | − | 0.969388i | \(-0.421036\pi\) |
−0.716747 | + | 0.697334i | \(0.754370\pi\) | |||||||
\(468\) | 66.7191i | 0.142562i | ||||||||
\(469\) | 301.095 | + | 570.173i | 0.641994 | + | 1.21572i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 116.268 | − | 201.382i | 0.246853 | − | 0.427562i | ||||
\(472\) | 108.467 | − | 62.6234i | 0.229803 | − | 0.132677i | ||||
\(473\) | 14.5749 | + | 25.2445i | 0.0308138 | + | 0.0533711i | ||||
\(474\) | −113.370 | − | 65.4540i | −0.239177 | − | 0.138089i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 34.3230 | + | 21.5830i | 0.0721072 | + | 0.0453424i | ||||
\(477\) | −99.9776 | −0.209597 | ||||||||
\(478\) | −183.027 | + | 317.012i | −0.382901 | + | 0.663204i | ||||
\(479\) | −278.924 | + | 161.037i | −0.582305 | + | 0.336194i | −0.762049 | − | 0.647519i | \(-0.775806\pi\) |
0.179744 | + | 0.983713i | \(0.442473\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −85.9293 | − | 49.6113i | −0.178647 | − | 0.103142i | ||||
\(482\) | − | 432.736i | − | 0.897793i | ||||||
\(483\) | 14.0176 | − | 371.222i | 0.0290219 | − | 0.768576i | ||||
\(484\) | −208.884 | −0.431579 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −19.0919 | + | 11.0227i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −97.1552 | − | 168.278i | −0.199497 | − | 0.345539i | 0.748868 | − | 0.662719i | \(-0.230598\pi\) |
−0.948366 | + | 0.317180i | \(0.897264\pi\) | |||||||
\(488\) | 170.634 | + | 98.5156i | 0.349660 | + | 0.201876i | ||||
\(489\) | 279.943i | 0.572481i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −491.719 | −1.00146 | −0.500732 | − | 0.865602i | \(-0.666936\pi\) | ||||
−0.500732 | + | 0.865602i | \(0.666936\pi\) | |||||||
\(492\) | −97.4490 | + | 168.787i | −0.198067 | + | 0.343062i | ||||
\(493\) | 14.4330 | − | 8.33291i | 0.0292759 | − | 0.0169025i | ||||
\(494\) | −162.850 | − | 282.064i | −0.329656 | − | 0.570980i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 15.3407i | 0.0309288i | ||||||||
\(497\) | 46.4944 | + | 1.75566i | 0.0935501 | + | 0.00353251i | ||||
\(498\) | −284.388 | −0.571059 | ||||||||
\(499\) | −38.5757 | + | 66.8150i | −0.0773060 | + | 0.133898i | −0.902087 | − | 0.431555i | \(-0.857965\pi\) |
0.824781 | + | 0.565453i | \(0.191298\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 144.615 | + | 250.480i | 0.288652 | + | 0.499960i | ||||
\(502\) | 509.344 | + | 294.070i | 1.01463 | + | 0.585797i | ||||
\(503\) | − | 772.176i | − | 1.53514i | −0.640965 | − | 0.767571i | \(-0.721465\pi\) | ||
0.640965 | − | 0.767571i | \(-0.278535\pi\) | |||||||
\(504\) | −31.6183 | + | 50.2820i | −0.0627348 | + | 0.0997659i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 88.1602 | − | 152.698i | 0.174230 | − | 0.301775i | ||||
\(507\) | 68.0234 | − | 39.2733i | 0.134168 | − | 0.0774621i | ||||
\(508\) | −29.1799 | − | 50.5411i | −0.0574408 | − | 0.0994904i | ||||
\(509\) | 583.669 | + | 336.981i | 1.14670 | + | 0.662046i | 0.948080 | − | 0.318032i | \(-0.103022\pi\) |
0.198617 | + | 0.980077i | \(0.436355\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 324.486 | − | 171.353i | 0.635001 | − | 0.335329i | ||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 53.8090 | − | 93.2000i | 0.104891 | − | 0.181676i | ||||
\(514\) | −383.648 | + | 221.499i | −0.746396 | + | 0.430932i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −21.4909 | − | 12.4078i | −0.0416491 | − | 0.0240461i | ||||
\(517\) | 193.714i | 0.374689i | ||||||||
\(518\) | −41.2486 | − | 78.1110i | −0.0796305 | − | 0.150793i | ||||
\(519\) | −20.2553 | −0.0390275 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 275.030 | − | 158.788i | 0.527888 | − | 0.304776i | −0.212268 | − | 0.977211i | \(-0.568085\pi\) |
0.740156 | + | 0.672435i | \(0.234752\pi\) | |||||||
\(522\) | 12.2074 | + | 21.1439i | 0.0233859 | + | 0.0405055i | ||||
\(523\) | −606.691 | − | 350.273i | −1.16002 | − | 0.669739i | −0.208713 | − | 0.977977i | \(-0.566927\pi\) |
−0.951309 | + | 0.308238i | \(0.900261\pi\) | |||||||
\(524\) | − | 285.075i | − | 0.544037i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −125.238 | −0.238094 | ||||||||
\(527\) | −5.55346 | + | 9.61888i | −0.0105379 | + | 0.0182521i | ||||
\(528\) | −24.4148 | + | 14.0959i | −0.0462402 | + | 0.0266968i | ||||
\(529\) | −204.896 | − | 354.891i | −0.387327 | − | 0.670871i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 132.844i | 0.250178i | ||||||||
\(532\) | 10.9411 | − | 289.749i | 0.0205660 | − | 0.544641i | ||||
\(533\) | −625.627 | −1.17379 | ||||||||
\(534\) | −121.129 | + | 209.801i | −0.226833 | + | 0.392887i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −130.267 | − | 225.630i | −0.243036 | − | 0.420951i | ||||
\(537\) | −200.640 | − | 115.839i | −0.373631 | − | 0.215716i | ||||
\(538\) | 115.542i | 0.214761i | ||||||||
\(539\) | 86.3880 | + | 179.702i | 0.160275 | + | 0.333398i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3027 | + | 40.3614i | −0.0430733 | + | 0.0746052i | −0.886758 | − | 0.462233i | \(-0.847048\pi\) |
0.843685 | + | 0.536839i | \(0.180382\pi\) | |||||||
\(542\) | 360.488 | − | 208.128i | 0.665107 | − | 0.384000i | ||||
\(543\) | −97.8909 | − | 169.552i | −0.180278 | − | 0.312251i | ||||
\(544\) | −14.1878 | − | 8.19132i | −0.0260805 | − | 0.0150576i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −190.530 | − | 7.19454i | −0.348956 | − | 0.0131768i | ||||
\(547\) | −886.307 | −1.62031 | −0.810153 | − | 0.586219i | \(-0.800616\pi\) | ||||
−0.810153 | + | 0.586219i | \(0.800616\pi\) | |||||||
\(548\) | 208.595 | − | 361.297i | 0.380647 | − | 0.659301i | ||||
\(549\) | −180.985 | + | 104.492i | −0.329662 | + | 0.190331i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −103.217 | − | 59.5924i | −0.187327 | − | 0.108153i | ||||
\(552\) | 150.103i | 0.271926i | ||||||||
\(553\) | 199.142 | − | 316.692i | 0.360113 | − | 0.572680i | ||||
\(554\) | 574.515 | 1.03703 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 264.122 | − | 152.491i | 0.475039 | − | 0.274264i | ||||
\(557\) | 289.104 | + | 500.743i | 0.519038 | + | 0.899000i | 0.999755 | + | 0.0221246i | \(0.00704307\pi\) |
−0.480717 | + | 0.876876i | \(0.659624\pi\) | |||||||
\(558\) | −14.0913 | − | 8.13563i | −0.0252533 | − | 0.0145800i | ||||
\(559\) | − | 79.6586i | − | 0.142502i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.4114 | −0.0363839 | ||||||||
\(562\) | −165.678 | + | 286.963i | −0.294801 | + | 0.510610i | ||||
\(563\) | −129.465 | + | 74.7467i | −0.229956 | + | 0.132765i | −0.610552 | − | 0.791976i | \(-0.709052\pi\) |
0.380596 | + | 0.924741i | \(0.375719\pi\) | |||||||
\(564\) | −82.4553 | − | 142.817i | −0.146197 | − | 0.253221i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 387.958i | − | 0.685439i | ||||||
\(567\) | −29.4188 | − | 55.7094i | −0.0518851 | − | 0.0982528i | ||||
\(568\) | −18.8000 | −0.0330985 | ||||||||
\(569\) | −79.3178 | + | 137.382i | −0.139399 | + | 0.241446i | −0.927269 | − | 0.374395i | \(-0.877850\pi\) |
0.787871 | + | 0.615841i | \(0.211184\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.86886 | + | 13.6293i | 0.0137808 | + | 0.0238691i | 0.872834 | − | 0.488018i | \(-0.162280\pi\) |
−0.859053 | + | 0.511887i | \(0.828947\pi\) | |||||||
\(572\) | −78.3723 | − | 45.2482i | −0.137014 | − | 0.0791053i | ||||
\(573\) | 434.807i | 0.758826i | ||||||||
\(574\) | −471.496 | − | 296.486i | −0.821422 | − | 0.516526i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 12.0000 | − | 20.7846i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −143.510 | + | 82.8557i | −0.248718 | + | 0.143597i | −0.619177 | − | 0.785251i | \(-0.712534\pi\) |
0.370459 | + | 0.928849i | \(0.379200\pi\) | |||||||
\(578\) | 198.423 | + | 343.679i | 0.343293 | + | 0.594600i | ||||
\(579\) | 535.486 | + | 309.163i | 0.924846 | + | 0.533960i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 30.6664 | − | 812.126i | 0.0527821 | − | 1.39781i | ||||
\(582\) | 325.692 | 0.559608 | ||||||||
\(583\) | 67.8038 | − | 117.440i | 0.116302 | − | 0.201440i | ||||
\(584\) | −128.406 | + | 74.1353i | −0.219873 | + | 0.126944i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 79.2745 | + | 45.7692i | 0.135281 | + | 0.0781044i | ||||
\(587\) | − | 466.624i | − | 0.794929i | −0.917617 | − | 0.397465i | \(-0.869890\pi\) | ||
0.917617 | − | 0.397465i | \(-0.130110\pi\) | |||||||
\(588\) | −140.181 | − | 95.7146i | −0.238403 | − | 0.162780i | ||||
\(589\) | 79.4307 | 0.134857 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −52.6902 | + | 30.4207i | −0.0891543 | + | 0.0514732i | ||||
\(592\) | 17.8460 | + | 30.9102i | 0.0301453 | + | 0.0522132i | ||||
\(593\) | 193.493 | + | 111.713i | 0.326295 | + | 0.188386i | 0.654195 | − | 0.756326i | \(-0.273008\pi\) |
−0.327900 | + | 0.944712i | \(0.606341\pi\) | |||||||
\(594\) | − | 29.9020i | − | 0.0503400i | ||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 273.029 | 0.458102 | ||||||||
\(597\) | −79.3368 | + | 137.415i | −0.132892 | + | 0.230177i | ||||
\(598\) | −417.282 | + | 240.918i | −0.697796 | + | 0.402872i | ||||
\(599\) | −389.927 | − | 675.373i | −0.650963 | − | 1.12750i | −0.982890 | − | 0.184196i | \(-0.941032\pi\) |
0.331926 | − | 0.943305i | \(-0.392301\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 917.029i | − | 1.52584i | −0.646494 | − | 0.762919i | \(-0.723766\pi\) | ||
0.646494 | − | 0.762919i | \(-0.276234\pi\) | |||||||
\(602\) | 37.7504 | − | 60.0337i | 0.0627083 | − | 0.0997238i | ||||
\(603\) | 276.339 | 0.458273 | ||||||||
\(604\) | −129.599 | + | 224.471i | −0.214567 | + | 0.371641i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 74.0050 | + | 128.180i | 0.122120 | + | 0.211519i | ||||
\(607\) | −189.426 | − | 109.365i | −0.312070 | − | 0.180174i | 0.335783 | − | 0.941940i | \(-0.390999\pi\) |
−0.647852 | + | 0.761766i | \(0.724333\pi\) | |||||||
\(608\) | 117.160i | 0.192697i | ||||||||
\(609\) | −61.6970 | + | 32.5808i | −0.101309 | + | 0.0534988i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 264.684 | − | 458.446i | 0.433197 | − | 0.750320i | ||||
\(612\) | 15.0484 | − | 8.68821i | 0.0245889 | − | 0.0141964i | ||||
\(613\) | 448.607 | + | 777.010i | 0.731822 | + | 1.26755i | 0.956104 | + | 0.293029i | \(0.0946631\pi\) |
−0.224282 | + | 0.974524i | \(0.572004\pi\) | |||||||
\(614\) | 200.938 | + | 116.011i | 0.327260 | + | 0.188944i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −37.6210 | − | 71.2416i | −0.0610731 | − | 0.115652i | ||||
\(617\) | −1227.93 | −1.99016 | −0.995080 | − | 0.0990738i | \(-0.968412\pi\) | ||||
−0.995080 | + | 0.0990738i | \(0.968412\pi\) | |||||||
\(618\) | 38.3523 | − | 66.4281i | 0.0620587 | − | 0.107489i | ||||
\(619\) | 359.910 | − | 207.794i | 0.581437 | − | 0.335693i | −0.180267 | − | 0.983618i | \(-0.557696\pi\) |
0.761704 | + | 0.647925i | \(0.224363\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −137.879 | − | 79.6043i | −0.222027 | − | 0.128187i | ||||
\(622\) | 323.127i | 0.519497i | ||||||||
\(623\) | −586.069 | − | 368.532i | −0.940720 | − | 0.591544i | ||||
\(624\) | 77.0406 | 0.123462 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 633.777 | − | 365.911i | 1.01242 | − | 0.584523i | ||||
\(627\) | 72.9855 | + | 126.415i | 0.116404 | + | 0.201618i | ||||
\(628\) | −232.536 | − | 134.255i | −0.370280 | − | 0.213781i | ||||
\(629\) | 25.8417i | 0.0410837i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −67.1152 | −0.106363 | −0.0531816 | − | 0.998585i | \(-0.516936\pi\) | ||||
−0.0531816 | + | 0.998585i | \(0.516936\pi\) | |||||||
\(632\) | −75.5798 | + | 130.908i | −0.119588 | + | 0.207133i | ||||
\(633\) | 13.0540 | − | 7.53674i | 0.0206225 | − | 0.0119064i | ||||
\(634\) | −208.814 | − | 361.677i | −0.329360 | − | 0.570468i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 115.444i | 0.181516i | ||||||||
\(637\) | 41.0909 | − | 543.321i | 0.0645069 | − | 0.852937i | ||||
\(638\) | −33.1158 | −0.0519057 | ||||||||
\(639\) | 9.97019 | − | 17.2689i | 0.0156028 | − | 0.0270248i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −459.366 | − | 795.645i | −0.716639 | − | 1.24126i | −0.962324 | − | 0.271905i | \(-0.912346\pi\) |
0.245685 | − | 0.969350i | \(-0.420987\pi\) | |||||||
\(642\) | 99.7868 | + | 57.6120i | 0.155431 | + | 0.0897383i | ||||
\(643\) | − | 881.952i | − | 1.37162i | −0.727780 | − | 0.685810i | \(-0.759448\pi\) | ||
0.727780 | − | 0.685810i | \(-0.240552\pi\) | |||||||
\(644\) | −428.651 | − | 16.1861i | −0.665606 | − | 0.0251337i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −42.4129 | + | 73.4612i | −0.0656546 | + | 0.113717i | ||||
\(647\) | 768.152 | − | 443.493i | 1.18725 | − | 0.685460i | 0.229571 | − | 0.973292i | \(-0.426268\pi\) |
0.957681 | + | 0.287832i | \(0.0929344\pi\) | |||||||
\(648\) | 12.7279 | + | 22.0454i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −156.047 | − | 90.0938i | −0.240442 | − | 0.138819i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 24.7525 | − | 39.3633i | 0.0380222 | − | 0.0604660i | ||||
\(652\) | 323.251 | 0.495783 | ||||||||
\(653\) | −500.073 | + | 866.151i | −0.765808 | + | 1.32642i | 0.174010 | + | 0.984744i | \(0.444327\pi\) |
−0.939818 | + | 0.341675i | \(0.889006\pi\) | |||||||
\(654\) | −427.568 | + | 246.857i | −0.653774 | + | 0.377457i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 194.898 | + | 112.524i | 0.297101 | + | 0.171531i | ||||
\(657\) | − | 157.265i | − | 0.239368i | ||||||
\(658\) | 416.734 | − | 220.068i | 0.633334 | − | 0.334449i | ||||
\(659\) | −825.607 | −1.25282 | −0.626409 | − | 0.779495i | \(-0.715476\pi\) | ||||
−0.626409 | + | 0.779495i | \(0.715476\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 923.294 | − | 533.064i | 1.39681 | − | 0.806451i | 0.402757 | − | 0.915307i | \(-0.368052\pi\) |
0.994058 | + | 0.108856i | \(0.0347188\pi\) | |||||||
\(662\) | 440.797 | + | 763.483i | 0.665857 | + | 1.15330i | ||||
\(663\) | 48.3058 | + | 27.8894i | 0.0728594 | + | 0.0420654i | ||||
\(664\) | 328.382i | 0.494552i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −37.8571 | −0.0568425 | ||||||||
\(667\) | −88.1602 | + | 152.698i | −0.132174 | + | 0.228932i | ||||
\(668\) | 289.229 | − | 166.987i | 0.432978 | − | 0.249980i | ||||
\(669\) | 137.190 | + | 237.620i | 0.205068 | + | 0.355187i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 283.461i | − | 0.422445i | ||||||
\(672\) | 58.0607 | + | 36.5097i | 0.0863998 | + | 0.0543299i | ||||
\(673\) | −115.190 | −0.171159 | −0.0855796 | − | 0.996331i | \(-0.527274\pi\) | ||||
−0.0855796 | + | 0.996331i | \(0.527274\pi\) | |||||||
\(674\) | 0.0285953 | − | 0.0495285i | 4.24263e−5 | − | 7.34845e-5i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −45.3489 | − | 78.5466i | −0.0670842 | − | 0.116193i | ||||
\(677\) | 490.897 | + | 283.420i | 0.725107 | + | 0.418641i | 0.816629 | − | 0.577162i | \(-0.195840\pi\) |
−0.0915226 | + | 0.995803i | \(0.529173\pi\) | |||||||
\(678\) | 412.548i | 0.608478i | ||||||||
\(679\) | −35.1204 | + | 930.079i | −0.0517237 | + | 1.36978i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 343.311 | − | 594.633i | 0.504128 | − | 0.873176i | ||||
\(682\) | 19.1132 | − | 11.0350i | 0.0280252 | − | 0.0161804i | ||||
\(683\) | 11.8357 | + | 20.5001i | 0.0173290 | + | 0.0300147i | 0.874560 | − | 0.484918i | \(-0.161150\pi\) |
−0.857231 | + | 0.514932i | \(0.827817\pi\) | |||||||
\(684\) | −107.618 | − | 62.1333i | −0.157336 | − | 0.0908382i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 288.449 | − | 389.994i | 0.420479 | − | 0.568504i | ||||
\(687\) | 357.096 | 0.519790 | ||||||||
\(688\) | −14.3273 | + | 24.8156i | −0.0208245 | + | 0.0360692i | ||||
\(689\) | −320.931 | + | 185.289i | −0.465792 | + | 0.268925i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −922.771 | − | 532.762i | −1.33541 | − | 0.771002i | −0.349290 | − | 0.937014i | \(-0.613577\pi\) |
−0.986124 | + | 0.166013i | \(0.946911\pi\) | |||||||
\(692\) | 23.3888i | 0.0337988i | ||||||||
\(693\) | 85.3911 | + | 3.22442i | 0.123219 | + | 0.00465285i | ||||
\(694\) | 172.041 | 0.247897 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 24.4148 | − | 14.0959i | 0.0350788 | − | 0.0202528i | ||||
\(697\) | 81.4696 | + | 141.110i | 0.116886 | + | 0.202453i | ||||
\(698\) | 559.944 | + | 323.284i | 0.802212 | + | 0.463157i | ||||
\(699\) | − | 192.796i | − | 0.275817i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1086.46 | −1.54987 | −0.774936 | − | 0.632040i | \(-0.782218\pi\) | ||||
−0.774936 | + | 0.632040i | \(0.782218\pi\) | |||||||
\(702\) | −40.8569 | + | 70.7663i | −0.0582008 | + | 0.100807i | ||||
\(703\) | 160.046 | − | 92.4027i | 0.227662 | − | 0.131441i | ||||
\(704\) | 16.2766 | + | 28.1918i | 0.0231201 | + | 0.0400452i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 38.6522i | − | 0.0547481i | ||||||
\(707\) | −374.025 | + | 197.514i | −0.529032 | + | 0.279369i | ||||
\(708\) | 153.395 | 0.216660 | ||||||||
\(709\) | 299.823 | − | 519.309i | 0.422881 | − | 0.732452i | −0.573339 | − | 0.819319i | \(-0.694352\pi\) |
0.996220 | + | 0.0868665i | \(0.0276854\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −80.1645 | − | 138.849i | −0.112749 | − | 0.195287i | ||||
\(712\) | 242.258 | + | 139.868i | 0.340250 | + | 0.196443i | ||||
\(713\) | − | 117.509i | − | 0.164809i | ||||||
\(714\) | 23.1882 | + | 43.9107i | 0.0324765 | + | 0.0614996i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −133.760 | + | 231.679i | −0.186815 | + | 0.323574i | ||||
\(717\) | −388.258 | + | 224.161i | −0.541504 | + | 0.312637i | ||||
\(718\) | −326.709 | − | 565.876i | −0.455026 | − | 0.788128i | ||||
\(719\) | 286.589 | + | 165.462i | 0.398594 | + | 0.230128i | 0.685877 | − | 0.727717i | \(-0.259419\pi\) |
−0.287283 | + | 0.957846i | \(0.592752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 185.563 | + | 116.686i | 0.257369 | + | 0.161839i | ||||
\(722\) | 96.0961 | 0.133097 | ||||||||
\(723\) | 264.996 | − | 458.986i | 0.366522 | − | 0.634835i | ||||
\(724\) | −195.782 | + | 113.035i | −0.270417 | + | 0.156125i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −221.555 | − | 127.915i | −0.305172 | − | 0.176191i | ||||
\(727\) | 1104.90i | 1.51980i | 0.650039 | + | 0.759901i | \(0.274753\pi\) | ||||
−0.650039 | + | 0.759901i | \(0.725247\pi\) | |||||||
\(728\) | −8.30753 | + | 220.005i | −0.0114114 | + | 0.302205i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.9669 | + | 10.3732i | −0.0245785 | + | 0.0141904i | ||||
\(732\) | 120.656 | + | 208.983i | 0.164831 | + | 0.285496i | ||||
\(733\) | −869.845 | − | 502.205i | −1.18669 | − | 0.685137i | −0.229138 | − | 0.973394i | \(-0.573591\pi\) |
−0.957553 | + | 0.288257i | \(0.906924\pi\) | |||||||
\(734\) | − | 608.147i | − | 0.828539i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 173.324 | 0.235495 | ||||||||
\(737\) | −187.410 | + | 324.604i | −0.254288 | + | 0.440440i | ||||
\(738\) | −206.721 | + | 119.350i | −0.280109 | + | 0.161721i | ||||
\(739\) | −545.640 | − | 945.075i | −0.738348 | − | 1.27886i | −0.953239 | − | 0.302219i | \(-0.902273\pi\) |
0.214890 | − | 0.976638i | \(-0.431061\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 398.899i | − | 0.538325i | ||||||
\(742\) | −329.674 | − | 12.4487i | −0.444305 | − | 0.0167772i | ||||
\(743\) | −876.833 | −1.18013 | −0.590063 | − | 0.807358i | \(-0.700897\pi\) | ||||
−0.590063 | + | 0.807358i | \(0.700897\pi\) | |||||||
\(744\) | −9.39422 | + | 16.2713i | −0.0126266 | + | 0.0218700i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 473.714 | + | 820.498i | 0.635006 | + | 1.09986i | ||||
\(747\) | −301.639 | − | 174.151i | −0.403800 | − | 0.233134i | ||||
\(748\) | 23.5690i | 0.0315094i | ||||||||
\(749\) | −175.283 | + | 278.749i | −0.234023 | + | 0.372162i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 56.4095 | − | 97.7042i | 0.0751126 | − | 0.130099i | −0.826023 | − | 0.563637i | \(-0.809402\pi\) |
0.901135 | + | 0.433538i | \(0.142735\pi\) | |||||||
\(752\) | −164.911 | + | 95.2112i | −0.219296 | + | 0.126611i | ||||
\(753\) | 360.161 | + | 623.816i | 0.478301 | + | 0.828441i | ||||
\(754\) | 78.3723 | + | 45.2482i | 0.103942 | + | 0.0600109i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −64.3276 | + | 33.9699i | −0.0850895 | + | 0.0449338i | ||||
\(757\) | −1279.08 | −1.68966 | −0.844832 | − | 0.535032i | \(-0.820300\pi\) | ||||
−0.844832 | + | 0.535032i | \(0.820300\pi\) | |||||||
\(758\) | 498.048 | − | 862.644i | 0.657055 | − | 1.13805i | ||||
\(759\) | 187.016 | − | 107.974i | 0.246398 | − | 0.142258i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −794.534 | − | 458.724i | −1.04407 | − | 0.602791i | −0.123083 | − | 0.992396i | \(-0.539278\pi\) |
−0.920982 | + | 0.389605i | \(0.872612\pi\) | |||||||
\(762\) | − | 71.4759i | − | 0.0938004i | ||||||
\(763\) | −658.843 | − | 1247.63i | −0.863490 | − | 1.63516i | ||||
\(764\) | 502.072 | 0.657163 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36.2977 | − | 20.9565i | 0.0473860 | − | 0.0273583i | ||||
\(767\) | 246.202 | + | 426.434i | 0.320993 | + | 0.555976i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 187.311i | 0.243577i | 0.992556 | + | 0.121789i | \(0.0388630\pi\) | ||||
−0.992556 | + | 0.121789i | \(0.961137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −542.560 | −0.703709 | ||||||||
\(772\) | 356.991 | − | 618.326i | 0.462423 | − | 0.800940i | ||||
\(773\) | 169.320 | − | 97.7567i | 0.219042 | − | 0.126464i | −0.386464 | − | 0.922304i | \(-0.626304\pi\) |
0.605507 | + | 0.795840i | \(0.292970\pi\) | |||||||
\(774\) | −15.1964 | − | 26.3209i | −0.0196336 | − | 0.0340063i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 376.076i | − | 0.484635i | ||||||
\(777\) | 4.08226 | − | 108.109i | 0.00525387 | − | 0.139136i | ||||
\(778\) | 52.0670 | 0.0669241 | ||||||||
\(779\) | 582.626 | − | 1009.14i | 0.747916 | − | 1.29543i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5234 | + | 23.4232i | 0.0173154 | + | 0.0299912i | ||||
\(782\) | 108.677 | + | 62.7450i | 0.138974 | + | 0.0802365i | ||||
\(783\) | 29.9020i | 0.0381890i | ||||||||
\(784\) | −110.522 | + | 161.867i | −0.140972 | + | 0.206463i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 174.572 | − | 302.368i | 0.222102 | − | 0.384692i | ||||
\(787\) | 426.846 | − | 246.440i | 0.542371 | − | 0.313138i | −0.203668 | − | 0.979040i | \(-0.565286\pi\) |
0.746040 | + | 0.665902i | \(0.231953\pi\) | |||||||
\(788\) | 35.1268 | + | 60.8414i | 0.0445771 | + | 0.0772099i | ||||
\(789\) | −132.835 | − | 76.6921i | −0.168358 | − | 0.0972016i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1178.11 | − | 44.4864i | −1.48940 | − | 0.0562407i | ||||
\(792\) | −34.5278 | −0.0435957 | ||||||||
\(793\) | −387.310 | + | 670.841i | −0.488411 | + | 0.845953i | ||||
\(794\) | −112.661 | + | 65.0450i | −0.141891 | + | 0.0819206i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 158.674 | + | 91.6103i | 0.199339 | + | 0.115088i | ||||
\(797\) | 283.436i | 0.355629i | 0.984064 | + | 0.177814i | \(0.0569027\pi\) | ||||
−0.984064 | + | 0.177814i | \(0.943097\pi\) | |||||||
\(798\) | 189.039 | − | 300.625i | 0.236891 | − | 0.376723i | ||||
\(799\) | −137.869 | −0.172552 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −256.953 | + | 148.352i | −0.320791 | + | 0.185209i | ||||
\(802\) | 251.891 | + | 436.288i | 0.314079 | + | 0.544000i | ||||
\(803\) | 184.732 | + | 106.655i | 0.230053 | + | 0.132821i | ||||
\(804\) | − | 319.089i | − | 0.396876i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −60.3113 | −0.0748279 | ||||||||
\(807\) | −70.7545 | + | 122.550i | −0.0876759 | + | 0.151859i | ||||
\(808\) | 148.010 | − | 85.4536i | 0.183181 | − | 0.105759i | ||||
\(809\) | 63.7961 | + | 110.498i | 0.0788580 | + | 0.136586i | 0.902757 | − | 0.430150i | \(-0.141539\pi\) |
−0.823899 | + | 0.566736i | \(0.808206\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1029.60i | 1.26955i | 0.772697 | + | 0.634774i | \(0.218907\pi\) | ||||
−0.772697 | + | 0.634774i | \(0.781093\pi\) | |||||||
\(812\) | 37.6210 | + | 71.2416i | 0.0463313 | + | 0.0877359i | ||||
\(813\) | 509.807 | 0.627069 | ||||||||
\(814\) | 25.6743 | − | 44.4693i | 0.0315410 | − | 0.0546305i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −10.0323 | − | 17.3764i | −0.0122945 | − | 0.0212946i | ||||
\(817\) | 128.490 | + | 74.1835i | 0.157270 | + | 0.0907999i | ||||
\(818\) | 34.2097i | 0.0418212i | ||||||||
\(819\) | −197.682 | − | 124.306i | −0.241370 | − | 0.151778i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 357.710 | − | 619.572i | 0.435701 | − | 0.754656i | −0.561652 | − | 0.827374i | \(-0.689834\pi\) |
0.997353 | + | 0.0727181i | \(0.0231673\pi\) | |||||||
\(822\) | 442.496 | − | 255.475i | 0.538317 | − | 0.310797i | ||||
\(823\) | −594.806 | − | 1030.23i | −0.722729 | − | 1.25180i | −0.959902 | − | 0.280336i | \(-0.909554\pi\) |
0.237173 | − | 0.971467i | \(-0.423779\pi\) | |||||||
\(824\) | −76.7045 | − | 44.2854i | −0.0930880 | − | 0.0537444i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.5411 | + | 438.052i | −0.0200256 | + | 0.530329i | ||||
\(827\) | −764.411 | −0.924318 | −0.462159 | − | 0.886797i | \(-0.652925\pi\) | ||||
−0.462159 | + | 0.886797i | \(0.652925\pi\) | |||||||
\(828\) | −91.9192 | + | 159.209i | −0.111013 | + | 0.192281i | ||||
\(829\) | 623.257 | − | 359.837i | 0.751818 | − | 0.434062i | −0.0745327 | − | 0.997219i | \(-0.523747\pi\) |
0.826350 | + | 0.563156i | \(0.190413\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 609.365 | + | 351.817i | 0.733292 | + | 0.423366i | ||||
\(832\) | − | 88.9588i | − | 0.106922i | ||||||
\(833\) | −127.896 | + | 61.4837i | −0.153537 | + | 0.0738099i | ||||
\(834\) | 373.525 | 0.447871 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 145.971 | − | 84.2764i | 0.174607 | − | 0.100809i | ||||
\(837\) | −9.96407 | − | 17.2583i | −0.0119045 | − | 0.0206192i | ||||
\(838\) | −658.175 | − | 379.997i | −0.785412 | − | 0.453458i | ||||
\(839\) | − | 622.729i | − | 0.742228i | −0.928587 | − | 0.371114i | \(-0.878976\pi\) | ||
0.928587 | − | 0.371114i | \(-0.121024\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −807.884 | −0.960623 | ||||||||
\(842\) | −455.663 | + | 789.231i | −0.541167 | + | 0.937329i | ||||
\(843\) | −351.456 | + | 202.913i | −0.416912 | + | 0.240704i | ||||
\(844\) | −8.70268 | − | 15.0735i | −0.0103112 | − | 0.0178596i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 201.974i | − | 0.238739i | ||||||
\(847\) | 389.178 | − | 618.902i | 0.459478 | − | 0.730699i | ||||
\(848\) | 133.303 | 0.157197 | ||||||||
\(849\) | 237.575 | − | 411.492i | 0.279829 | − | 0.484678i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −136.699 | − | 236.770i | −0.160634 | − | 0.278226i | ||||
\(852\) | −19.9404 | − | 11.5126i | −0.0234042 | − | 0.0135124i | ||||
\(853\) | − | 748.971i | − | 0.878044i | −0.898476 | − | 0.439022i | \(-0.855325\pi\) | ||
0.898476 | − | 0.439022i | \(-0.144675\pi\) | |||||||
\(854\) | −609.804 | + | 322.024i | −0.714057 | + | 0.377077i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 66.5246 | − | 115.224i | 0.0777156 | − | 0.134607i | ||||
\(857\) | 902.421 | − | 521.013i | 1.05300 | − | 0.607950i | 0.129512 | − | 0.991578i | \(-0.458659\pi\) |
0.923488 | + | 0.383628i | \(0.125325\pi\) | |||||||
\(858\) | −55.4176 | − | 95.9860i | −0.0645892 | − | 0.111872i | ||||
\(859\) | −483.193 | − | 278.972i | −0.562506 | − | 0.324763i | 0.191644 | − | 0.981464i | \(-0.438618\pi\) |
−0.754151 | + | 0.656701i | \(0.771951\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −318.537 | − | 603.202i | −0.369962 | − | 0.700584i | ||||
\(862\) | 660.963 | 0.766779 | ||||||||
\(863\) | 729.238 | − | 1263.08i | 0.845004 | − | 1.46359i | −0.0406140 | − | 0.999175i | \(-0.512931\pi\) |
0.885618 | − | 0.464415i | \(-0.153735\pi\) | |||||||
\(864\) | 25.4558 | − | 14.6969i | 0.0294628 | − | 0.0170103i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 40.6642 | + | 23.4775i | 0.0469563 | + | 0.0271103i | ||||
\(867\) | 486.036i | 0.560595i | ||||||||
\(868\) | −45.4529 | − | 28.5817i | −0.0523651 | − | 0.0329282i | ||||
\(869\) | 217.467 | 0.250250 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 887.055 | − | 512.141i | 1.01843 | − | 0.587992i | ||||
\(872\) | 285.045 | + | 493.713i | 0.326887 | + | 0.566185i | ||||
\(873\) | 345.448 | + | 199.445i | 0.395702 | + | 0.228459i | ||||
\(874\) | − | 897.435i | − | 1.02681i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −181.594 | −0.207299 | ||||||||
\(877\) | 347.719 | − | 602.267i | 0.396487 | − | 0.686736i | −0.596803 | − | 0.802388i | \(-0.703563\pi\) |
0.993290 | + | 0.115652i | \(0.0368959\pi\) | |||||||
\(878\) | −62.5336 | + | 36.1038i | −0.0712228 | + | 0.0411205i | ||||
\(879\) | 56.0556 | + | 97.0911i | 0.0637720 | + | 0.110456i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 795.045i | 0.902435i | 0.892414 | + | 0.451218i | \(0.149010\pi\) | ||||
−0.892414 | + | 0.451218i | \(0.850990\pi\) | |||||||
\(882\) | −90.0714 | − | 187.364i | −0.102122 | − | 0.212430i | ||||
\(883\) | 1060.28 | 1.20077 | 0.600384 | − | 0.799712i | \(-0.295014\pi\) | ||||
0.600384 | + | 0.799712i | \(0.295014\pi\) | |||||||
\(884\) | 32.2039 | − | 55.7787i | 0.0364297 | − | 0.0630981i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 560.494 | + | 970.804i | 0.632611 | + | 1.09572i | ||||
\(887\) | −1005.08 | − | 580.285i | −1.13313 | − | 0.654211i | −0.188407 | − | 0.982091i | \(-0.560333\pi\) |
−0.944719 | + | 0.327880i | \(0.893666\pi\) | |||||||
\(888\) | 43.7137i | 0.0492271i | ||||||||
\(889\) | 204.114 | + | 7.70748i | 0.229600 | + | 0.00866983i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 18.3111 | − | 31.7158i | 0.0205512 | − | 0.0355958i | ||||
\(892\) | 274.380 | − | 158.414i | 0.307601 | − | 0.177594i | ||||
\(893\) | 492.983 | + | 853.871i | 0.552052 | + | 0.956182i | ||||
\(894\) | 289.591 | + | 167.195i | 0.323927 | + | 0.187019i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 42.1578 | − | 67.0427i | 0.0470511 | − | 0.0748244i | ||||
\(897\) | −590.125 | −0.657888 | ||||||||
\(898\) | 50.7376 | − | 87.8802i | 0.0565007 | − | 0.0978621i | ||||
\(899\) | −19.1132 | + | 11.0350i | −0.0212605 | + | 0.0122748i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 83.5836 | + | 48.2570i | 0.0927676 | + | 0.0535594i | ||||
\(902\) | − | 323.768i | − | 0.358945i | ||||||
\(903\) | 76.8034 | − | 40.5581i | 0.0850535 | − | 0.0449148i | ||||
\(904\) | 476.370 | 0.526957 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −274.920 | + | 158.725i | −0.303444 | + | 0.175193i | ||||
\(907\) | 724.984 | + | 1255.71i | 0.799320 | + | 1.38446i | 0.920059 | + | 0.391779i | \(0.128140\pi\) |
−0.120739 | + | 0.992684i | \(0.538526\pi\) | |||||||
\(908\) | −686.623 | − | 396.422i | −0.756193 | − | 0.436588i | ||||
\(909\) | 181.274i | 0.199422i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 803.838 | 0.882369 | 0.441185 | − | 0.897416i | \(-0.354558\pi\) | ||||
0.441185 | + | 0.897416i | \(0.354558\pi\) | |||||||
\(912\) | −71.7454 | + | 124.267i | −0.0786682 | + | 0.136257i | ||||
\(913\) | 409.137 | − | 236.215i | 0.448123 | − | 0.258724i | ||||
\(914\) | 444.081 | + | 769.170i | 0.485865 | + | 0.841543i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 412.338i | − | 0.450151i | ||||||
\(917\) | 844.648 | + | 531.131i | 0.921099 | + | 0.579206i | ||||
\(918\) | 21.2817 | 0.0231827 | ||||||||
\(919\) | 190.607 | − | 330.140i | 0.207407 | − | 0.359239i | −0.743490 | − | 0.668747i | \(-0.766831\pi\) |
0.950897 | + | 0.309508i | \(0.100164\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 142.084 | + | 246.097i | 0.154272 | + | 0.267207i | ||||
\(922\) | 582.247 | + | 336.160i | 0.631504 | + | 0.364599i | ||||
\(923\) | − | 73.9113i | − | 0.0800773i | ||||||
\(924\) | 3.72324 | − | 98.6012i | 0.00402948 | − | 0.106711i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 242.246 | − | 419.583i | 0.261605 | − | 0.453114i | ||||
\(927\) | 81.3574 | − | 46.9717i | 0.0877642 | − | 0.0506707i | ||||
\(928\) | −16.2766 | − | 28.1918i | −0.0175394 | − | 0.0303791i | ||||
\(929\) | 1182.30 | + | 682.603i | 1.27266 | + | 0.734772i | 0.975488 | − | 0.220051i | \(-0.0706225\pi\) |
0.297174 | + | 0.954823i | \(0.403956\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 838.112 | + | 572.257i | 0.900227 | + | 0.614669i | ||||
\(932\) | −222.622 | −0.238865 | ||||||||
\(933\) | −197.874 | + | 342.728i | −0.212084 | + | 0.367340i | ||||
\(934\) | −311.206 | + | 179.675i | −0.333197 | + | 0.192371i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 81.7139 | + | 47.1775i | 0.0873012 | + | 0.0504033i | ||||
\(937\) | − | 836.234i | − | 0.892459i | −0.894918 | − | 0.446230i | \(-0.852766\pi\) | ||
0.894918 | − | 0.446230i | \(-0.147234\pi\) | |||||||
\(938\) | 911.222 | + | 34.4083i | 0.971452 | + | 0.0366827i | ||||
\(939\) | 896.296 | 0.954522 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −846.732 | + | 488.861i | −0.899822 | + | 0.519512i | −0.877142 | − | 0.480230i | \(-0.840553\pi\) |
−0.0226794 | + | 0.999743i | \(0.507220\pi\) | |||||||
\(942\) | −164.428 | − | 284.797i | −0.174552 | − | 0.302332i | ||||
\(943\) | −1492.91 | − | 861.929i | −1.58314 | − | 0.914029i | ||||
\(944\) | − | 177.126i | − | 0.187633i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 41.2241 | 0.0435773 | ||||||||
\(947\) | −477.919 | + | 827.780i | −0.504667 | + | 0.874108i | 0.495319 | + | 0.868711i | \(0.335051\pi\) |
−0.999985 | + | 0.00539682i | \(0.998282\pi\) | |||||||
\(948\) | −160.329 | + | 92.5660i | −0.169123 | + | 0.0976435i | ||||
\(949\) | −291.460 | − | 504.823i | −0.307123 | − | 0.531953i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 511.488i | − | 0.537843i | ||||||
\(952\) | 50.7037 | − | 26.7755i | 0.0532602 | − | 0.0281255i | ||||
\(953\) | 156.597 | 0.164320 | 0.0821598 | − | 0.996619i | \(-0.473818\pi\) | ||||
0.0821598 | + | 0.996619i | \(0.473818\pi\) | |||||||
\(954\) | −70.6948 | + | 122.447i | −0.0741036 | + | 0.128351i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 258.839 | + | 448.322i | 0.270752 | + | 0.468956i | ||||
\(957\) | −35.1246 | − | 20.2792i | −0.0367029 | − | 0.0211904i | ||||
\(958\) | 455.481i | 0.475450i | ||||||||
\(959\) | 681.846 | + | 1291.19i | 0.710997 | + | 1.34639i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −473.146 | + | 819.512i | −0.492347 | + | 0.852770i | ||||
\(962\) | −121.522 | + | 70.1609i | −0.126323 | + | 0.0729324i | ||||
\(963\) | 70.5600 | + | 122.213i | 0.0732710 | + | 0.126909i | ||||
\(964\) | −529.991 | − | 305.991i | −0.549784 | − | 0.317418i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −444.741 | − | 279.662i | −0.460394 | − | 0.289505i | ||||
\(967\) | −1344.56 | −1.39045 | −0.695224 | − | 0.718793i | \(-0.744695\pi\) | ||||
−0.695224 | + | 0.718793i | \(0.744695\pi\) | |||||||
\(968\) | −147.703 | + | 255.830i | −0.152586 | + | 0.264287i | ||||
\(969\) | −89.9712 | + | 51.9449i | −0.0928496 | + | 0.0536067i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1311.13 | − | 756.983i | −1.35029 | − | 0.779591i | −0.362001 | − | 0.932178i | \(-0.617906\pi\) |
−0.988290 | + | 0.152586i | \(0.951240\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | −40.2784 | + | 1066.68i | −0.0413961 | + | 1.09627i | ||||
\(974\) | −274.796 | −0.282132 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 241.313 | − | 139.322i | 0.247247 | − | 0.142748i | ||||
\(977\) | 16.6886 | + | 28.9055i | 0.0170815 | + | 0.0295860i | 0.874440 | − | 0.485134i | \(-0.161229\pi\) |
−0.857358 | + | 0.514720i | \(0.827896\pi\) | |||||||
\(978\) | 342.859 | + | 197.950i | 0.350572 | + | 0.202403i | ||||
\(979\) | − | 402.444i | − | 0.411076i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −604.673 | −0.616384 | ||||||||
\(982\) | −347.698 | + | 602.230i | −0.354071 | + | 0.613269i | ||||
\(983\) | 1672.03 | − | 965.345i | 1.70094 | − | 0.982039i | 0.756133 | − | 0.654418i | \(-0.227086\pi\) |
0.944809 | − | 0.327621i | \(-0.106247\pi\) | |||||||
\(984\) | 137.814 | + | 238.700i | 0.140055 | + | 0.242582i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 23.5690i | − | 0.0239037i | ||||||
\(987\) | 576.776 | + | 21.7794i | 0.584373 | + | 0.0220663i | ||||
\(988\) | −460.609 | −0.466203 | ||||||||
\(989\) | 109.746 | − | 190.086i | 0.110967 | − | 0.192200i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 670.602 | + | 1161.52i | 0.676692 | + | 1.17206i | 0.975971 | + | 0.217899i | \(0.0699205\pi\) |
−0.299279 | + | 0.954166i | \(0.596746\pi\) | |||||||
\(992\) | 18.7884 | + | 10.8475i | 0.0189400 | + | 0.0109350i | ||||
\(993\) | 1079.73i | 1.08734i | ||||||||
\(994\) | 35.0267 | − | 55.7023i | 0.0352382 | − | 0.0560386i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −201.092 | + | 348.302i | −0.201900 | + | 0.349701i | ||||
\(997\) | −159.613 | + | 92.1525i | −0.160093 | + | 0.0924298i | −0.577906 | − | 0.816103i | \(-0.696130\pi\) |
0.417813 | + | 0.908533i | \(0.362797\pi\) | |||||||
\(998\) | 54.5542 | + | 94.4907i | 0.0546636 | + | 0.0946801i | ||||
\(999\) | −40.1536 | − | 23.1827i | −0.0401937 | − | 0.0232059i |
(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 | 1050.3.p.f.901.6 | yes | 12 | |
5.2 | odd | 4 | 1050.3.q.d.649.10 | 24 | |||
5.3 | odd | 4 | 1050.3.q.d.649.4 | 24 | |||
5.4 | even | 2 | 1050.3.p.e.901.1 | yes | 12 | ||
7.3 | odd | 6 | inner | 1050.3.p.f.451.6 | yes | 12 | |
35.3 | even | 12 | 1050.3.q.d.199.10 | 24 | |||
35.17 | even | 12 | 1050.3.q.d.199.4 | 24 | |||
35.24 | odd | 6 | 1050.3.p.e.451.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.p.e.451.1 | ✓ | 12 | 35.24 | odd | 6 | ||
1050.3.p.e.901.1 | yes | 12 | 5.4 | even | 2 | ||
1050.3.p.f.451.6 | yes | 12 | 7.3 | odd | 6 | inner | |
1050.3.p.f.901.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1050.3.q.d.199.4 | 24 | 35.17 | even | 12 | |||
1050.3.q.d.199.10 | 24 | 35.3 | even | 12 | |||
1050.3.q.d.649.4 | 24 | 5.3 | odd | 4 | |||
1050.3.q.d.649.10 | 24 | 5.2 | odd | 4 |