Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,3,Mod(28,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([4, 9]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.28");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.l (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.0354507066\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 3^{2} \) |
Twist minimal: | no (minimal twist has level 15) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 352.2 | ||
Root | \(-0.258819 + 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.352 |
Dual form | 405.3.l.h.298.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0822623 | − | 0.307007i | 0.0411312 | − | 0.153504i | −0.942306 | − | 0.334752i | \(-0.891347\pi\) |
0.983437 | + | 0.181249i | \(0.0580140\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.37662 | + | 1.94949i | 0.844154 | + | 0.487372i | ||||
\(5\) | 0.799701 | − | 4.93563i | 0.159940 | − | 0.987127i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.26260 | − | 4.71209i | 0.180372 | − | 0.673156i | −0.815203 | − | 0.579176i | \(-0.803374\pi\) |
0.995574 | − | 0.0939798i | \(-0.0299589\pi\) | |||||||
\(8\) | 1.77526 | − | 1.77526i | 0.221907 | − | 0.221907i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.44949 | − | 0.651531i | −0.144949 | − | 0.0651531i | ||||
\(11\) | −5.67423 | − | 9.82806i | −0.515840 | − | 0.893460i | −0.999831 | − | 0.0183875i | \(-0.994147\pi\) |
0.483991 | − | 0.875073i | \(-0.339187\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.03163 | − | 7.58214i | −0.156279 | − | 0.583241i | −0.998992 | − | 0.0448789i | \(-0.985710\pi\) |
0.842713 | − | 0.538362i | \(-0.180957\pi\) | |||||||
\(14\) | −1.34278 | − | 0.775255i | −0.0959129 | − | 0.0553754i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7.39898 | + | 12.8154i | 0.462436 | + | 0.800963i | ||||
\(17\) | −17.3485 | − | 17.3485i | −1.02050 | − | 1.02050i | −0.999785 | − | 0.0207127i | \(-0.993406\pi\) |
−0.0207127 | − | 0.999785i | \(-0.506594\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.69694i | 0.457734i | 0.973458 | + | 0.228867i | \(0.0735020\pi\) | ||||
−0.973458 | + | 0.228867i | \(0.926498\pi\) | |||||||
\(20\) | 12.3223 | − | 15.1067i | 0.616113 | − | 0.755336i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.48406 | + | 0.933552i | −0.158366 | + | 0.0424342i | ||||
\(23\) | 4.22778 | + | 15.7783i | 0.183817 | + | 0.686013i | 0.994881 | + | 0.101056i | \(0.0322220\pi\) |
−0.811064 | + | 0.584957i | \(0.801111\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −23.7210 | − | 7.89406i | −0.948838 | − | 0.315763i | ||||
\(26\) | −2.49490 | −0.0959576 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 13.4495 | − | 13.4495i | 0.480339 | − | 0.480339i | ||||
\(29\) | 30.4377 | − | 17.5732i | 1.04958 | − | 0.605973i | 0.127045 | − | 0.991897i | \(-0.459451\pi\) |
0.922531 | + | 0.385924i | \(0.126117\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.34847 | + | 9.26382i | −0.172531 | + | 0.298833i | −0.939304 | − | 0.343086i | \(-0.888528\pi\) |
0.766773 | + | 0.641918i | \(0.221861\pi\) | |||||||
\(32\) | 14.2433 | − | 3.81647i | 0.445102 | − | 0.119265i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.75323 | + | 3.89898i | −0.198624 | + | 0.114676i | ||||
\(35\) | −22.2474 | − | 10.0000i | −0.635641 | − | 0.285714i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.04541 | − | 6.04541i | −0.163389 | − | 0.163389i | 0.620677 | − | 0.784066i | \(-0.286858\pi\) |
−0.784066 | + | 0.620677i | \(0.786858\pi\) | |||||||
\(38\) | 2.67002 | + | 0.715430i | 0.0702638 | + | 0.0188271i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −7.34233 | − | 10.1817i | −0.183558 | − | 0.254542i | ||||
\(41\) | −0.348469 | + | 0.603566i | −0.00849925 | + | 0.0147211i | −0.870244 | − | 0.492621i | \(-0.836039\pi\) |
0.861744 | + | 0.507343i | \(0.169372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 36.1927 | + | 9.69781i | 0.841691 | + | 0.225530i | 0.653807 | − | 0.756661i | \(-0.273171\pi\) |
0.187883 | + | 0.982191i | \(0.439837\pi\) | |||||||
\(44\) | − | 44.2474i | − | 1.00562i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.19184 | 0.112866 | ||||||||
\(47\) | 16.1957 | − | 60.4431i | 0.344589 | − | 1.28602i | −0.548502 | − | 0.836149i | \(-0.684802\pi\) |
0.893091 | − | 0.449875i | \(-0.148532\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 21.8256 | + | 12.6010i | 0.445421 | + | 0.257164i | ||||
\(50\) | −4.37488 | + | 6.63312i | −0.0874975 | + | 0.132662i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 7.92127 | − | 29.5626i | 0.152332 | − | 0.568512i | ||||
\(53\) | −0.696938 | + | 0.696938i | −0.0131498 | + | 0.0131498i | −0.713651 | − | 0.700501i | \(-0.752960\pi\) |
0.700501 | + | 0.713651i | \(0.252960\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −53.0454 | + | 20.1464i | −0.964462 | + | 0.366299i | ||||
\(56\) | −6.12372 | − | 10.6066i | −0.109352 | − | 0.189404i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.89123 | − | 10.7902i | −0.0498487 | − | 0.186038i | ||||
\(59\) | 34.5840 | + | 19.9671i | 0.586170 | + | 0.338425i | 0.763582 | − | 0.645711i | \(-0.223439\pi\) |
−0.177412 | + | 0.984137i | \(0.556772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.95459 | − | 5.11750i | −0.0484359 | − | 0.0838935i | 0.840791 | − | 0.541360i | \(-0.182090\pi\) |
−0.889227 | + | 0.457466i | \(0.848757\pi\) | |||||||
\(62\) | 2.40408 | + | 2.40408i | 0.0387755 | + | 0.0387755i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 54.5051i | 0.851642i | ||||||||
\(65\) | −39.0473 | + | 3.96392i | −0.600728 | + | 0.0609835i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 61.6091 | − | 16.5081i | 0.919539 | − | 0.246390i | 0.232151 | − | 0.972680i | \(-0.425424\pi\) |
0.687388 | + | 0.726290i | \(0.258757\pi\) | |||||||
\(68\) | −24.7584 | − | 92.3998i | −0.364095 | − | 1.35882i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −4.90020 | + | 6.00750i | −0.0700028 | + | 0.0858215i | ||||
\(71\) | −68.0000 | −0.957746 | −0.478873 | − | 0.877884i | \(-0.658955\pi\) | ||||
−0.478873 | + | 0.877884i | \(0.658955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 77.7878 | − | 77.7878i | 1.06559 | − | 1.06559i | 0.0678931 | − | 0.997693i | \(-0.478372\pi\) |
0.997693 | − | 0.0678931i | \(-0.0216277\pi\) | |||||||
\(74\) | −2.35329 | + | 1.35867i | −0.0318013 | + | 0.0183605i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −16.9546 | + | 29.3662i | −0.223087 | + | 0.386398i | ||||
\(77\) | −53.4750 | + | 14.3286i | −0.694481 | + | 0.186086i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −21.2132 | + | 12.2474i | −0.268522 | + | 0.155031i | −0.628216 | − | 0.778039i | \(-0.716214\pi\) |
0.359694 | + | 0.933070i | \(0.382881\pi\) | |||||||
\(80\) | 69.1691 | − | 26.2702i | 0.864614 | − | 0.328377i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.156633 | + | 0.156633i | 0.00191016 | + | 0.00191016i | ||||
\(83\) | −17.9584 | − | 4.81193i | −0.216366 | − | 0.0579750i | 0.149008 | − | 0.988836i | \(-0.452392\pi\) |
−0.365373 | + | 0.930861i | \(0.619059\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −99.4993 | + | 71.7521i | −1.17058 | + | 0.844142i | ||||
\(86\) | 5.95459 | − | 10.3137i | 0.0692394 | − | 0.119926i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −27.5205 | − | 7.37410i | −0.312733 | − | 0.0837966i | ||||
\(89\) | 82.1816i | 0.923389i | 0.887039 | + | 0.461695i | \(0.152758\pi\) | ||||
−0.887039 | + | 0.461695i | \(0.847242\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −38.2929 | −0.420801 | ||||||||
\(92\) | −16.4840 | + | 61.5192i | −0.179174 | + | 0.668687i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −17.2242 | − | 9.94439i | −0.183236 | − | 0.105791i | ||||
\(95\) | 42.9249 | + | 6.95495i | 0.451841 | + | 0.0732100i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.00273 | + | 33.5986i | −0.0928117 | + | 0.346378i | −0.996679 | − | 0.0814359i | \(-0.974049\pi\) |
0.903867 | + | 0.427814i | \(0.140716\pi\) | |||||||
\(98\) | 5.66403 | − | 5.66403i | 0.0577962 | − | 0.0577962i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −64.7071 | − | 72.8990i | −0.647071 | − | 0.728990i | ||||
\(101\) | 52.8105 | + | 91.4704i | 0.522876 | + | 0.905647i | 0.999646 | + | 0.0266193i | \(0.00847419\pi\) |
−0.476770 | + | 0.879028i | \(0.658192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −32.6668 | − | 121.914i | −0.317154 | − | 1.18363i | −0.921968 | − | 0.387267i | \(-0.873419\pi\) |
0.604814 | − | 0.796367i | \(-0.293247\pi\) | |||||||
\(104\) | −17.0669 | − | 9.85357i | −0.164105 | − | 0.0947459i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.156633 | + | 0.271297i | 0.00147767 | + | 0.00255940i | ||||
\(107\) | 68.7423 | + | 68.7423i | 0.642452 | + | 0.642452i | 0.951158 | − | 0.308706i | \(-0.0998958\pi\) |
−0.308706 | + | 0.951158i | \(0.599896\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 68.6969i | 0.630247i | 0.949051 | + | 0.315124i | \(0.102046\pi\) | ||||
−0.949051 | + | 0.315124i | \(0.897954\pi\) | |||||||
\(110\) | 1.82146 | + | 17.9426i | 0.0165587 | + | 0.163115i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 69.7293 | − | 18.6839i | 0.622583 | − | 0.166821i | ||||
\(113\) | 35.7392 | + | 133.381i | 0.316276 | + | 1.18036i | 0.922796 | + | 0.385290i | \(0.125899\pi\) |
−0.606519 | + | 0.795069i | \(0.707435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 81.2568 | − | 8.24885i | 0.706581 | − | 0.0717292i | ||||
\(116\) | 137.035 | 1.18134 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.97500 | − | 8.97500i | 0.0760593 | − | 0.0760593i | ||||
\(119\) | −103.652 | + | 59.8434i | −0.871023 | + | 0.502885i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.89388 | + | 6.74439i | −0.0321808 | + | 0.0557388i | ||||
\(122\) | −1.81416 | + | 0.486103i | −0.0148702 | + | 0.00398445i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −36.1194 | + | 20.8536i | −0.291286 | + | 0.168174i | ||||
\(125\) | −57.9319 | + | 110.765i | −0.463455 | + | 0.886120i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 164.621 | + | 164.621i | 1.29623 | + | 1.29623i | 0.930865 | + | 0.365362i | \(0.119055\pi\) |
0.365362 | + | 0.930865i | \(0.380945\pi\) | |||||||
\(128\) | 73.7065 | + | 19.7496i | 0.575832 | + | 0.154294i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.99517 | + | 12.3139i | −0.0153475 | + | 0.0947223i | ||||
\(131\) | −53.0681 | + | 91.9167i | −0.405100 | + | 0.701654i | −0.994333 | − | 0.106309i | \(-0.966097\pi\) |
0.589233 | + | 0.807963i | \(0.299430\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 40.9808 | + | 10.9808i | 0.308126 | + | 0.0825621i | ||||
\(134\) | − | 20.2724i | − | 0.151287i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −61.5959 | −0.452911 | ||||||||
\(137\) | −60.9912 | + | 227.622i | −0.445191 | + | 1.66148i | 0.270239 | + | 0.962793i | \(0.412897\pi\) |
−0.715431 | + | 0.698684i | \(0.753769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 165.559 | + | 95.5857i | 1.19107 | + | 0.687667i | 0.958550 | − | 0.284924i | \(-0.0919683\pi\) |
0.232524 | + | 0.972591i | \(0.425302\pi\) | |||||||
\(140\) | −55.6262 | − | 77.1373i | −0.397330 | − | 0.550981i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.59384 | + | 20.8765i | −0.0393932 | + | 0.147018i | ||||
\(143\) | −62.9898 | + | 62.9898i | −0.440488 | + | 0.440488i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −62.3939 | − | 164.283i | −0.430303 | − | 1.13298i | ||||
\(146\) | −17.4824 | − | 30.2804i | −0.119742 | − | 0.207400i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.62756 | − | 32.1985i | −0.0582943 | − | 0.217557i | ||||
\(149\) | −73.4853 | − | 42.4268i | −0.493190 | − | 0.284744i | 0.232707 | − | 0.972547i | \(-0.425242\pi\) |
−0.725897 | + | 0.687803i | \(0.758575\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −74.4847 | − | 129.011i | −0.493276 | − | 0.854379i | 0.506694 | − | 0.862126i | \(-0.330867\pi\) |
−0.999970 | + | 0.00774676i | \(0.997534\pi\) | |||||||
\(152\) | 15.4393 | + | 15.4393i | 0.101574 | + | 0.101574i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 17.5959i | 0.114259i | ||||||||
\(155\) | 41.4456 | + | 33.8064i | 0.267391 | + | 0.218106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.0224 | + | 6.16884i | −0.146640 | + | 0.0392919i | −0.331392 | − | 0.943493i | \(-0.607518\pi\) |
0.184753 | + | 0.982785i | \(0.440852\pi\) | |||||||
\(158\) | 2.01501 | + | 7.52011i | 0.0127532 | + | 0.0475956i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −7.44634 | − | 73.3515i | −0.0465396 | − | 0.458447i | ||||
\(161\) | 79.6867 | 0.494949 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 130.606 | − | 130.606i | 0.801265 | − | 0.801265i | −0.182029 | − | 0.983293i | \(-0.558266\pi\) |
0.983293 | + | 0.182029i | \(0.0582664\pi\) | |||||||
\(164\) | −2.35329 | + | 1.35867i | −0.0143493 | + | 0.00828460i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.95459 | + | 5.11750i | −0.0177987 | + | 0.0308283i | ||||
\(167\) | 61.5192 | − | 16.4840i | 0.368379 | − | 0.0987068i | −0.0698806 | − | 0.997555i | \(-0.522262\pi\) |
0.438259 | + | 0.898849i | \(0.355595\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 92.9970 | − | 53.6918i | 0.550278 | − | 0.317703i | ||||
\(170\) | 13.8434 | + | 36.4495i | 0.0814316 | + | 0.214409i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 103.303 | + | 103.303i | 0.600599 | + | 0.600599i | ||||
\(173\) | −200.302 | − | 53.6707i | −1.15781 | − | 0.310235i | −0.371722 | − | 0.928344i | \(-0.621232\pi\) |
−0.786092 | + | 0.618109i | \(0.787899\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −67.1476 | + | 101.808i | −0.383701 | + | 0.581761i | ||||
\(176\) | 83.9671 | − | 145.435i | 0.477086 | − | 0.826337i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 25.2304 | + | 6.76045i | 0.141744 | + | 0.0379801i | ||||
\(179\) | 183.712i | 1.02632i | 0.858292 | + | 0.513161i | \(0.171526\pi\) | ||||
−0.858292 | + | 0.513161i | \(0.828474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −286.272 | −1.58162 | −0.790808 | − | 0.612064i | \(-0.790339\pi\) | ||||
−0.790808 | + | 0.612064i | \(0.790339\pi\) | |||||||
\(182\) | −3.15006 | + | 11.7562i | −0.0173080 | + | 0.0645944i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 35.5159 | + | 20.5051i | 0.193021 | + | 0.111441i | ||||
\(185\) | −34.6724 | + | 25.0034i | −0.187419 | + | 0.135153i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −72.0626 | + | 268.941i | −0.385361 | + | 1.43819i | ||||
\(188\) | 172.520 | − | 172.520i | 0.917659 | − | 0.917659i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.66632 | − | 12.6061i | 0.0298228 | − | 0.0663480i | ||||
\(191\) | −24.0454 | − | 41.6479i | −0.125892 | − | 0.218052i | 0.796189 | − | 0.605048i | \(-0.206846\pi\) |
−0.922081 | + | 0.386996i | \(0.873513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −93.5434 | − | 349.109i | −0.484681 | − | 1.80885i | −0.581494 | − | 0.813551i | \(-0.697532\pi\) |
0.0968131 | − | 0.995303i | \(-0.469135\pi\) | |||||||
\(194\) | 9.57444 | + | 5.52781i | 0.0493528 | + | 0.0284938i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 49.1311 | + | 85.0976i | 0.250669 | + | 0.434171i | ||||
\(197\) | −96.6969 | − | 96.6969i | −0.490847 | − | 0.490847i | 0.417726 | − | 0.908573i | \(-0.362827\pi\) |
−0.908573 | + | 0.417726i | \(0.862827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 192.606i | 0.967870i | 0.875104 | + | 0.483935i | \(0.160793\pi\) | ||||
−0.875104 | + | 0.483935i | \(0.839207\pi\) | |||||||
\(200\) | −56.1247 | + | 28.0968i | −0.280624 | + | 0.140484i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 32.4264 | − | 8.68862i | 0.160527 | − | 0.0430130i | ||||
\(203\) | −44.3759 | − | 165.613i | −0.218601 | − | 0.815828i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.70031 | + | 2.20259i | 0.0131723 | + | 0.0107443i | ||||
\(206\) | −40.1158 | −0.194737 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 82.1362 | − | 82.1362i | 0.394886 | − | 0.394886i | ||||
\(209\) | 85.4741 | − | 49.3485i | 0.408967 | − | 0.236117i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −73.6061 | + | 127.490i | −0.348844 | + | 0.604216i | −0.986044 | − | 0.166482i | \(-0.946759\pi\) |
0.637200 | + | 0.770698i | \(0.280092\pi\) | |||||||
\(212\) | −3.71197 | + | 0.994619i | −0.0175093 | + | 0.00469160i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 26.7593 | − | 15.4495i | 0.125043 | − | 0.0721939i | ||||
\(215\) | 76.8082 | − | 170.879i | 0.357247 | − | 0.794784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 36.8990 | + | 36.8990i | 0.170041 | + | 0.170041i | ||||
\(218\) | 21.0905 | + | 5.65117i | 0.0967452 | + | 0.0259228i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −218.389 | − | 35.3847i | −0.992678 | − | 0.160840i | ||||
\(221\) | −96.2929 | + | 166.784i | −0.435714 | + | 0.754679i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −228.712 | − | 61.2833i | −1.02562 | − | 0.274813i | −0.293475 | − | 0.955967i | \(-0.594812\pi\) |
−0.732141 | + | 0.681154i | \(0.761479\pi\) | |||||||
\(224\) | − | 71.9342i | − | 0.321135i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 43.8888 | 0.194198 | ||||||||
\(227\) | 92.6672 | − | 345.839i | 0.408225 | − | 1.52352i | −0.389803 | − | 0.920898i | \(-0.627457\pi\) |
0.798028 | − | 0.602620i | \(-0.205876\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 194.165 | + | 112.101i | 0.847881 | + | 0.489524i | 0.859935 | − | 0.510403i | \(-0.170504\pi\) |
−0.0120546 | + | 0.999927i | \(0.503837\pi\) | |||||||
\(230\) | 4.15192 | − | 25.6250i | 0.0180518 | − | 0.111413i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 22.8377 | − | 85.2316i | 0.0984386 | − | 0.367378i | ||||
\(233\) | −205.712 | + | 205.712i | −0.882883 | + | 0.882883i | −0.993827 | − | 0.110944i | \(-0.964613\pi\) |
0.110944 | + | 0.993827i | \(0.464613\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −285.373 | − | 128.272i | −1.21436 | − | 0.545840i | ||||
\(236\) | 77.8513 | + | 134.842i | 0.329878 | + | 0.571366i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.84571 | + | 36.7447i | 0.0413685 | + | 0.154389i | ||||
\(239\) | 299.470 | + | 172.899i | 1.25301 | + | 0.723427i | 0.971706 | − | 0.236192i | \(-0.0758993\pi\) |
0.281305 | + | 0.959618i | \(0.409233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −50.7878 | − | 87.9670i | −0.210738 | − | 0.365008i | 0.741208 | − | 0.671275i | \(-0.234253\pi\) |
−0.951946 | + | 0.306267i | \(0.900920\pi\) | |||||||
\(242\) | 1.75026 | + | 1.75026i | 0.00723247 | + | 0.00723247i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 23.0398i | − | 0.0944254i | ||||||
\(245\) | 79.6480 | − | 97.6461i | 0.325094 | − | 0.398556i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 65.9414 | − | 17.6689i | 0.266969 | − | 0.0715342i | ||||
\(248\) | 6.95075 | + | 25.9405i | 0.0280272 | + | 0.104599i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 29.2401 | + | 26.8973i | 0.116960 | + | 0.107589i | ||||
\(251\) | −331.258 | −1.31975 | −0.659876 | − | 0.751375i | \(-0.729391\pi\) | ||||
−0.659876 | + | 0.751375i | \(0.729391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 131.081 | − | 131.081i | 0.518105 | − | 0.518105i | ||||
\(254\) | 64.0819 | − | 36.9977i | 0.252291 | − | 0.145660i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −96.8837 | + | 167.807i | −0.378452 | + | 0.655498i | ||||
\(257\) | −45.4029 | + | 12.1657i | −0.176665 | + | 0.0473373i | −0.346067 | − | 0.938210i | \(-0.612483\pi\) |
0.169402 | + | 0.985547i | \(0.445816\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.1194 | + | 20.8536i | −0.139457 | + | 0.0805157i | ||||
\(260\) | −139.576 | − | 62.7378i | −0.536829 | − | 0.241299i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 23.8536 | + | 23.8536i | 0.0910442 | + | 0.0910442i | ||||
\(263\) | 379.969 | + | 101.812i | 1.44475 | + | 0.387119i | 0.894194 | − | 0.447679i | \(-0.147749\pi\) |
0.550555 | + | 0.834799i | \(0.314416\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.88249 | + | 3.99718i | 0.0108773 | + | 0.0150837i | ||||
\(266\) | 6.74235 | − | 11.6781i | 0.0253472 | − | 0.0439026i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 240.213 | + | 64.3648i | 0.896316 | + | 0.240167i | ||||
\(269\) | − | 488.499i | − | 1.81598i | −0.418988 | − | 0.907992i | \(-0.637615\pi\) | ||
0.418988 | − | 0.907992i | \(-0.362385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 131.576 | 0.485518 | 0.242759 | − | 0.970087i | \(-0.421947\pi\) | ||||
0.242759 | + | 0.970087i | \(0.421947\pi\) | |||||||
\(272\) | 93.9668 | − | 350.689i | 0.345466 | − | 1.28930i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 64.8644 | + | 37.4495i | 0.236731 | + | 0.136677i | ||||
\(275\) | 57.0149 | + | 277.924i | 0.207327 | + | 1.01063i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 37.1551 | − | 138.665i | 0.134134 | − | 0.500595i | −0.865866 | − | 0.500276i | \(-0.833232\pi\) |
1.00000 | 0.000318873i | \(-0.000101500\pi\) | ||||||||
\(278\) | 42.9648 | − | 42.9648i | 0.154550 | − | 0.154550i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −57.2474 | + | 21.7423i | −0.204455 | + | 0.0776512i | ||||
\(281\) | −171.652 | − | 297.309i | −0.610860 | − | 1.05804i | −0.991096 | − | 0.133150i | \(-0.957491\pi\) |
0.380236 | − | 0.924889i | \(-0.375843\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.436242 | + | 1.62808i | 0.00154149 | + | 0.00575293i | 0.966692 | − | 0.255941i | \(-0.0823854\pi\) |
−0.965151 | + | 0.261694i | \(0.915719\pi\) | |||||||
\(284\) | −229.610 | − | 132.565i | −0.808485 | − | 0.466779i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 14.1566 | + | 24.5200i | 0.0494987 | + | 0.0857343i | ||||
\(287\) | 2.40408 | + | 2.40408i | 0.00837659 | + | 0.00837659i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 312.939i | 1.08283i | ||||||||
\(290\) | −55.5686 | + | 5.64110i | −0.191616 | + | 0.0194521i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 414.306 | − | 111.013i | 1.41886 | − | 0.380181i | ||||
\(293\) | 35.3454 | + | 131.911i | 0.120633 | + | 0.450207i | 0.999646 | − | 0.0265892i | \(-0.00846462\pi\) |
−0.879014 | + | 0.476796i | \(0.841798\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 126.207 | − | 154.726i | 0.427821 | − | 0.524496i | ||||
\(296\) | −21.4643 | −0.0725145 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −19.0704 | + | 19.0704i | −0.0639946 | + | 0.0639946i | ||||
\(299\) | 111.044 | − | 64.1112i | 0.371384 | − | 0.214419i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 91.3939 | − | 158.299i | 0.303634 | − | 0.525910i | ||||
\(302\) | −45.7347 | + | 12.2546i | −0.151439 | + | 0.0405780i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −111.455 | + | 64.3485i | −0.366628 | + | 0.211673i | ||||
\(305\) | −27.6209 | + | 10.4903i | −0.0905604 | + | 0.0343945i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −124.969 | − | 124.969i | −0.407066 | − | 0.407066i | 0.473648 | − | 0.880714i | \(-0.342937\pi\) |
−0.880714 | + | 0.473648i | \(0.842937\pi\) | |||||||
\(308\) | −208.498 | − | 55.8669i | −0.676942 | − | 0.181386i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.7882 | − | 9.94312i | 0.0444781 | − | 0.0320746i | ||||
\(311\) | 293.151 | − | 507.752i | 0.942608 | − | 1.63264i | 0.182136 | − | 0.983273i | \(-0.441699\pi\) |
0.760472 | − | 0.649371i | \(-0.224968\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 139.845 | + | 37.4713i | 0.446788 | + | 0.119717i | 0.475196 | − | 0.879880i | \(-0.342377\pi\) |
−0.0284079 | + | 0.999596i | \(0.509044\pi\) | |||||||
\(314\) | 7.57551i | 0.0241258i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −95.5051 | −0.302231 | ||||||||
\(317\) | −39.8174 | + | 148.601i | −0.125607 | + | 0.468772i | −0.999861 | − | 0.0166979i | \(-0.994685\pi\) |
0.874254 | + | 0.485469i | \(0.161351\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −345.421 | − | 199.429i | −1.08283 | − | 0.625170i | ||||
\(320\) | 269.017 | + | 43.5878i | 0.840679 | + | 0.136212i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.55522 | − | 24.4644i | 0.0203578 | − | 0.0759764i | ||||
\(323\) | 150.879 | − | 150.879i | 0.467116 | − | 0.467116i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.6617 | + | 195.893i | −0.0358823 | + | 0.602749i | ||||
\(326\) | −29.3531 | − | 50.8410i | −0.0900401 | − | 0.155954i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.452863 | + | 1.69011i | 0.00138068 | + | 0.00515276i | ||||
\(329\) | −264.365 | − | 152.631i | −0.803541 | − | 0.463924i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 122.712 | + | 212.543i | 0.370730 | + | 0.642124i | 0.989678 | − | 0.143308i | \(-0.0457741\pi\) |
−0.618948 | + | 0.785432i | \(0.712441\pi\) | |||||||
\(332\) | −51.2577 | − | 51.2577i | −0.154391 | − | 0.154391i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 20.2429i | − | 0.0606074i | ||||||
\(335\) | −32.2091 | − | 317.282i | −0.0961466 | − | 0.947110i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −292.067 | + | 78.2592i | −0.866669 | + | 0.232223i | −0.664647 | − | 0.747158i | \(-0.731418\pi\) |
−0.202022 | + | 0.979381i | \(0.564751\pi\) | |||||||
\(338\) | −8.83363 | − | 32.9676i | −0.0261350 | − | 0.0975372i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −475.851 | + | 48.3064i | −1.39956 | + | 0.142078i | ||||
\(341\) | 121.394 | 0.355994 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 255.959 | − | 255.959i | 0.746237 | − | 0.746237i | ||||
\(344\) | 81.4674 | − | 47.0352i | 0.236824 | − | 0.136730i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −32.9546 | + | 57.0790i | −0.0952445 | + | 0.164968i | ||||
\(347\) | 218.632 | − | 58.5824i | 0.630064 | − | 0.168825i | 0.0703655 | − | 0.997521i | \(-0.477583\pi\) |
0.559699 | + | 0.828696i | \(0.310917\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −258.084 | + | 149.005i | −0.739494 | + | 0.426947i | −0.821885 | − | 0.569653i | \(-0.807078\pi\) |
0.0823911 | + | 0.996600i | \(0.473744\pi\) | |||||||
\(350\) | 25.7321 | + | 28.9898i | 0.0735204 | + | 0.0828280i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −118.328 | − | 118.328i | −0.336159 | − | 0.336159i | ||||
\(353\) | 30.7627 | + | 8.24285i | 0.0871466 | + | 0.0233509i | 0.302129 | − | 0.953267i | \(-0.402303\pi\) |
−0.214982 | + | 0.976618i | \(0.568969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −54.3797 | + | 335.623i | −0.153182 | + | 0.945417i | ||||
\(356\) | −160.212 | + | 277.496i | −0.450034 | + | 0.779482i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 56.4008 | + | 15.1126i | 0.157544 | + | 0.0422138i | ||||
\(359\) | 48.2724i | 0.134464i | 0.997737 | + | 0.0672318i | \(0.0214167\pi\) | ||||
−0.997737 | + | 0.0672318i | \(0.978583\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 285.363 | 0.790480 | ||||||||
\(362\) | −23.5494 | + | 87.8877i | −0.0650537 | + | 0.242784i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −129.300 | − | 74.6515i | −0.355220 | − | 0.205087i | ||||
\(365\) | −321.725 | − | 446.139i | −0.881438 | − | 1.22230i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 53.6263 | − | 200.136i | 0.146121 | − | 0.545330i | −0.853582 | − | 0.520958i | \(-0.825575\pi\) |
0.999703 | − | 0.0243716i | \(-0.00775850\pi\) | |||||||
\(368\) | −170.924 | + | 170.924i | −0.464467 | + | 0.464467i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.82399 | + | 12.7015i | 0.0130378 | + | 0.0343284i | ||||
\(371\) | 2.40408 | + | 4.16399i | 0.00648001 | + | 0.0112237i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 31.5538 | + | 117.760i | 0.0845947 | + | 0.315712i | 0.995237 | − | 0.0974836i | \(-0.0310794\pi\) |
−0.910642 | + | 0.413195i | \(0.864413\pi\) | |||||||
\(374\) | 76.6388 | + | 44.2474i | 0.204917 | + | 0.118309i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −78.5505 | − | 136.053i | −0.208911 | − | 0.361844i | ||||
\(377\) | −195.081 | − | 195.081i | −0.517455 | − | 0.517455i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 210.000i | − | 0.554090i | −0.960857 | − | 0.277045i | \(-0.910645\pi\) | ||
0.960857 | − | 0.277045i | \(-0.0893551\pi\) | |||||||
\(380\) | 131.382 | + | 107.166i | 0.345743 | + | 0.282015i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −14.7642 | + | 3.95606i | −0.0386498 | + | 0.0103562i | ||||
\(383\) | −3.89126 | − | 14.5224i | −0.0101599 | − | 0.0379174i | 0.960660 | − | 0.277728i | \(-0.0895814\pi\) |
−0.970820 | + | 0.239810i | \(0.922915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 27.9566 | + | 275.392i | 0.0726146 | + | 0.715303i | ||||
\(386\) | −114.874 | −0.297601 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −95.8990 | + | 95.8990i | −0.247162 | + | 0.247162i | ||||
\(389\) | −463.616 | + | 267.669i | −1.19181 | + | 0.688094i | −0.958718 | − | 0.284360i | \(-0.908219\pi\) |
−0.233096 | + | 0.972454i | \(0.574886\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 200.384 | − | 347.075i | 0.512490 | − | 0.887659i | ||||
\(392\) | 61.1160 | − | 16.3760i | 0.155908 | − | 0.0417755i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −37.6412 | + | 21.7321i | −0.0955360 | + | 0.0551577i | ||||
\(395\) | 43.4847 | + | 114.495i | 0.110088 | + | 0.289860i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 118.742 | + | 118.742i | 0.299099 | + | 0.299099i | 0.840661 | − | 0.541562i | \(-0.182167\pi\) |
−0.541562 | + | 0.840661i | \(0.682167\pi\) | |||||||
\(398\) | 59.1315 | + | 15.8442i | 0.148572 | + | 0.0398096i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −74.3452 | − | 362.402i | −0.185863 | − | 0.906004i | ||||
\(401\) | −210.151 | + | 363.992i | −0.524067 | + | 0.907711i | 0.475540 | + | 0.879694i | \(0.342253\pi\) |
−0.999607 | + | 0.0280172i | \(0.991081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 81.1057 | + | 21.7322i | 0.201255 | + | 0.0539260i | ||||
\(404\) | 411.814i | 1.01934i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −54.4949 | −0.134224 | ||||||||
\(407\) | −25.1116 | + | 93.7177i | −0.0616992 | + | 0.230265i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 446.099 | + | 257.555i | 1.09071 | + | 0.629719i | 0.933764 | − | 0.357889i | \(-0.116503\pi\) |
0.156941 | + | 0.987608i | \(0.449837\pi\) | |||||||
\(410\) | 0.898345 | − | 0.647825i | 0.00219108 | − | 0.00158006i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 127.367 | − | 475.341i | 0.309144 | − | 1.15374i | ||||
\(413\) | 137.753 | − | 137.753i | 0.333541 | − | 0.333541i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.1112 | + | 84.7878i | −0.0918343 | + | 0.204308i | ||||
\(416\) | −57.8740 | − | 100.241i | −0.139120 | − | 0.240963i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.11904 | − | 30.3007i | −0.0194235 | − | 0.0724896i | ||||
\(419\) | 76.7312 | + | 44.3008i | 0.183129 | + | 0.105730i | 0.588762 | − | 0.808306i | \(-0.299615\pi\) |
−0.405633 | + | 0.914036i | \(0.632949\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 128.576 | + | 222.699i | 0.305405 | + | 0.528977i | 0.977351 | − | 0.211623i | \(-0.0678748\pi\) |
−0.671946 | + | 0.740600i | \(0.734541\pi\) | |||||||
\(422\) | 33.0852 | + | 33.0852i | 0.0784009 | + | 0.0784009i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.47449i | 0.00583605i | ||||||||
\(425\) | 274.572 | + | 548.472i | 0.646053 | + | 1.29052i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.8446 | + | 7.46094i | −0.0652099 | + | 0.0174729i | ||||
\(428\) | 98.1040 | + | 366.129i | 0.229215 | + | 0.855441i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −46.1425 | − | 37.6375i | −0.107308 | − | 0.0875291i | ||||
\(431\) | 804.636 | 1.86690 | 0.933452 | − | 0.358702i | \(-0.116781\pi\) | ||||
0.933452 | + | 0.358702i | \(0.116781\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −344.848 | + | 344.848i | −0.796416 | + | 0.796416i | −0.982528 | − | 0.186113i | \(-0.940411\pi\) |
0.186113 | + | 0.982528i | \(0.440411\pi\) | |||||||
\(434\) | 14.3636 | − | 8.29286i | 0.0330960 | − | 0.0191080i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −133.924 | + | 231.963i | −0.307165 | + | 0.532026i | ||||
\(437\) | −137.223 | + | 36.7687i | −0.314011 | + | 0.0841390i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 374.927 | − | 216.464i | 0.854048 | − | 0.493085i | −0.00796652 | − | 0.999968i | \(-0.502536\pi\) |
0.862015 | + | 0.506883i | \(0.169203\pi\) | |||||||
\(440\) | −58.4041 | + | 129.934i | −0.132737 | + | 0.295305i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 43.2827 | + | 43.2827i | 0.0979246 | + | 0.0979246i | ||||
\(443\) | −334.855 | − | 89.7240i | −0.755880 | − | 0.202537i | −0.139755 | − | 0.990186i | \(-0.544632\pi\) |
−0.616124 | + | 0.787649i | \(0.711298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 405.618 | + | 65.7208i | 0.911502 | + | 0.147687i | ||||
\(446\) | −37.6288 | + | 65.1750i | −0.0843696 | + | 0.146132i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 256.833 | + | 68.8182i | 0.573288 | + | 0.153612i | ||||
\(449\) | 386.091i | 0.859890i | 0.902855 | + | 0.429945i | \(0.141467\pi\) | ||||
−0.902855 | + | 0.429945i | \(0.858533\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.90918 | 0.0175370 | ||||||||
\(452\) | −139.346 | + | 520.048i | −0.308289 | + | 1.15055i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −98.5519 | − | 56.8990i | −0.217075 | − | 0.125328i | ||||
\(455\) | −30.6228 | + | 189.000i | −0.0673030 | + | 0.415384i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −81.8971 | + | 305.644i | −0.179206 | + | 0.668805i | 0.816591 | + | 0.577217i | \(0.195861\pi\) |
−0.995797 | + | 0.0915887i | \(0.970806\pi\) | |||||||
\(458\) | 50.3883 | − | 50.3883i | 0.110018 | − | 0.110018i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 290.454 | + | 130.556i | 0.631422 | + | 0.283818i | ||||
\(461\) | 361.310 | + | 625.807i | 0.783753 | + | 1.35750i | 0.929741 | + | 0.368213i | \(0.120030\pi\) |
−0.145989 | + | 0.989286i | \(0.546636\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −47.4741 | − | 177.176i | −0.102536 | − | 0.382669i | 0.895518 | − | 0.445025i | \(-0.146805\pi\) |
−0.998054 | + | 0.0623562i | \(0.980139\pi\) | |||||||
\(464\) | 450.416 | + | 260.048i | 0.970724 | + | 0.560448i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 46.2327 | + | 80.0773i | 0.0992117 | + | 0.171840i | ||||
\(467\) | 415.258 | + | 415.258i | 0.889203 | + | 0.889203i | 0.994446 | − | 0.105244i | \(-0.0335623\pi\) |
−0.105244 | + | 0.994446i | \(0.533562\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 311.151i | − | 0.663435i | ||||||
\(470\) | −62.8561 | + | 77.0597i | −0.133736 | + | 0.163957i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 96.8421 | − | 25.9488i | 0.205174 | − | 0.0549762i | ||||
\(473\) | −110.055 | − | 410.732i | −0.232675 | − | 0.868355i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 68.6542 | − | 206.300i | 0.144535 | − | 0.434315i | ||||
\(476\) | −466.656 | −0.980370 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 77.7163 | − | 77.7163i | 0.162586 | − | 0.162586i | ||||
\(479\) | 264.094 | − | 152.474i | 0.551344 | − | 0.318318i | −0.198320 | − | 0.980137i | \(-0.563549\pi\) |
0.749664 | + | 0.661819i | \(0.230215\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −33.5551 | + | 58.1191i | −0.0697611 | + | 0.120830i | ||||
\(482\) | −31.1844 | + | 8.35584i | −0.0646980 | + | 0.0173358i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −26.2962 | + | 15.1821i | −0.0543311 | + | 0.0313681i | ||||
\(485\) | 158.631 | + | 71.3031i | 0.327074 | + | 0.147017i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −429.318 | − | 429.318i | −0.881556 | − | 0.881556i | 0.112137 | − | 0.993693i | \(-0.464231\pi\) |
−0.993693 | + | 0.112137i | \(0.964231\pi\) | |||||||
\(488\) | −14.3300 | − | 3.83972i | −0.0293648 | − | 0.00786828i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −23.4260 | − | 32.4851i | −0.0478082 | − | 0.0662961i | ||||
\(491\) | 207.159 | − | 358.810i | 0.421912 | − | 0.730773i | −0.574214 | − | 0.818705i | \(-0.694692\pi\) |
0.996127 | + | 0.0879316i | \(0.0280257\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −832.916 | − | 223.179i | −1.68948 | − | 0.452696i | ||||
\(494\) | − | 21.6980i | − | 0.0439230i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −158.293 | −0.319139 | ||||||||
\(497\) | −85.8569 | + | 320.422i | −0.172750 | + | 0.644713i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −318.338 | − | 183.792i | −0.637951 | − | 0.368321i | 0.145874 | − | 0.989303i | \(-0.453401\pi\) |
−0.783825 | + | 0.620982i | \(0.786734\pi\) | |||||||
\(500\) | −411.549 | + | 261.073i | −0.823098 | + | 0.522147i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −27.2500 | + | 101.698i | −0.0542829 | + | 0.202587i | ||||
\(503\) | −9.59133 | + | 9.59133i | −0.0190683 | + | 0.0190683i | −0.716577 | − | 0.697508i | \(-0.754292\pi\) |
0.697508 | + | 0.716577i | \(0.254292\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 493.697 | − | 187.504i | 0.977618 | − | 0.371295i | ||||
\(506\) | −29.4597 | − | 51.0257i | −0.0582207 | − | 0.100841i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 234.935 | + | 876.788i | 0.462470 | + | 1.72596i | ||||
\(509\) | −673.325 | − | 388.745i | −1.32284 | − | 0.763742i | −0.338659 | − | 0.940909i | \(-0.609973\pi\) |
−0.984181 | + | 0.177167i | \(0.943307\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −268.328 | − | 464.758i | −0.525104 | − | 0.909507i | ||||
\(512\) | 259.376 | + | 259.376i | 0.506593 | + | 0.506593i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 14.9398i | 0.0290658i | ||||||||
\(515\) | −627.848 | + | 63.7365i | −1.21912 | + | 0.123760i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −685.937 | + | 183.796i | −1.32676 | + | 0.355505i | ||||
\(518\) | 3.43093 | + | 12.8044i | 0.00662341 | + | 0.0247189i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −62.2820 | + | 76.3560i | −0.119773 | + | 0.146838i | ||||
\(521\) | 321.605 | 0.617284 | 0.308642 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308642 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −582.454 | + | 582.454i | −1.11368 | + | 1.11368i | −0.121030 | + | 0.992649i | \(0.538620\pi\) |
−0.992649 | + | 0.121030i | \(0.961380\pi\) | |||||||
\(524\) | −358.381 | + | 206.911i | −0.683934 | + | 0.394869i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 62.5143 | − | 108.278i | 0.118848 | − | 0.205852i | ||||
\(527\) | 253.501 | − | 67.9254i | 0.481026 | − | 0.128891i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 227.047 | − | 131.086i | 0.429201 | − | 0.247799i | ||||
\(530\) | 1.46428 | − | 0.556128i | 0.00276280 | − | 0.00104930i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 116.969 | + | 116.969i | 0.219867 | + | 0.219867i | ||||
\(533\) | 5.28428 | + | 1.41592i | 0.00991423 | + | 0.00265651i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 394.260 | − | 284.314i | 0.736935 | − | 0.531427i | ||||
\(536\) | 80.0658 | − | 138.678i | 0.149377 | − | 0.258728i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −149.973 | − | 40.1851i | −0.278760 | − | 0.0746935i | ||||
\(539\) | − | 286.005i | − | 0.530621i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 460.697 | 0.851566 | 0.425783 | − | 0.904825i | \(-0.359999\pi\) | ||||
0.425783 | + | 0.904825i | \(0.359999\pi\) | |||||||
\(542\) | 10.8237 | − | 40.3946i | 0.0199699 | − | 0.0745288i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −313.309 | − | 180.889i | −0.575935 | − | 0.332516i | ||||
\(545\) | 339.063 | + | 54.9370i | 0.622134 | + | 0.100802i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −242.227 | + | 904.005i | −0.442829 | + | 1.65266i | 0.278777 | + | 0.960356i | \(0.410071\pi\) |
−0.721606 | + | 0.692304i | \(0.756596\pi\) | |||||||
\(548\) | −649.691 | + | 649.691i | −1.18557 | + | 1.18557i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 90.0148 | + | 5.35867i | 0.163663 | + | 0.00974304i | ||||
\(551\) | 152.833 | + | 264.715i | 0.277374 | + | 0.480426i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 30.9273 | + | 115.422i | 0.0559264 | + | 0.208720i | ||||
\(554\) | −39.5146 | − | 22.8138i | −0.0713260 | − | 0.0411801i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 372.687 | + | 645.512i | 0.670300 | + | 1.16099i | ||||
\(557\) | 125.909 | + | 125.909i | 0.226049 | + | 0.226049i | 0.811040 | − | 0.584991i | \(-0.198902\pi\) |
−0.584991 | + | 0.811040i | \(0.698902\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 294.120i | − | 0.526155i | ||||||
\(560\) | −36.4543 | − | 359.100i | −0.0650970 | − | 0.641250i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −105.397 | + | 28.2409i | −0.187538 | + | 0.0502507i | ||||
\(563\) | −73.2084 | − | 273.218i | −0.130033 | − | 0.485289i | 0.869936 | − | 0.493164i | \(-0.164160\pi\) |
−0.999969 | + | 0.00787538i | \(0.997493\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 686.898 | − | 69.7310i | 1.21575 | − | 0.123418i | ||||
\(566\) | 0.535718 | 0.000946498 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −120.717 | + | 120.717i | −0.212531 | + | 0.212531i | ||||
\(569\) | −519.476 | + | 299.919i | −0.912962 | + | 0.527099i | −0.881383 | − | 0.472402i | \(-0.843387\pi\) |
−0.0315793 | + | 0.999501i | \(0.510054\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 123.985 | − | 214.749i | 0.217137 | − | 0.376092i | −0.736795 | − | 0.676117i | \(-0.763662\pi\) |
0.953932 | + | 0.300024i | \(0.0969948\pi\) | |||||||
\(572\) | −335.490 | + | 89.8943i | −0.586521 | + | 0.157158i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.935836 | − | 0.540305i | 0.00163038 | − | 0.000941298i | ||||
\(575\) | 24.2679 | − | 407.650i | 0.0422050 | − | 0.708957i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −292.121 | − | 292.121i | −0.506276 | − | 0.506276i | 0.407105 | − | 0.913381i | \(-0.366538\pi\) |
−0.913381 | + | 0.407105i | \(0.866538\pi\) | |||||||
\(578\) | 96.0745 | + | 25.7431i | 0.166219 | + | 0.0445382i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 109.587 | − | 676.356i | 0.188943 | − | 1.16613i | ||||
\(581\) | −45.3485 | + | 78.5459i | −0.0780524 | + | 0.135191i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.8041 | + | 2.89496i | 0.0185320 | + | 0.00496563i | ||||
\(584\) | − | 276.186i | − | 0.472922i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 43.4051 | 0.0740702 | ||||||||
\(587\) | 223.721 | − | 834.938i | 0.381126 | − | 1.42238i | −0.463058 | − | 0.886328i | \(-0.653248\pi\) |
0.844184 | − | 0.536053i | \(-0.180085\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −80.5669 | − | 46.5153i | −0.136786 | − | 0.0789734i | ||||
\(590\) | −37.1200 | − | 51.4746i | −0.0629153 | − | 0.0872452i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 32.7445 | − | 122.204i | 0.0553117 | − | 0.206426i | ||||
\(593\) | 524.742 | − | 524.742i | 0.884894 | − | 0.884894i | −0.109133 | − | 0.994027i | \(-0.534807\pi\) |
0.994027 | + | 0.109133i | \(0.0348074\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 212.474 | + | 559.444i | 0.357100 | + | 0.940242i | ||||
\(596\) | −165.421 | − | 286.518i | −0.277552 | − | 0.480735i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10.5479 | − | 39.3652i | −0.0176386 | − | 0.0658281i | ||||
\(599\) | 319.441 | + | 184.429i | 0.533290 | + | 0.307895i | 0.742355 | − | 0.670007i | \(-0.233709\pi\) |
−0.209065 | + | 0.977902i | \(0.567042\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −466.242 | − | 807.555i | −0.775777 | − | 1.34368i | −0.934357 | − | 0.356339i | \(-0.884025\pi\) |
0.158580 | − | 0.987346i | \(-0.449308\pi\) | |||||||
\(602\) | −41.0806 | − | 41.0806i | −0.0682402 | − | 0.0682402i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 580.829i | − | 0.961637i | ||||||
\(605\) | 30.1739 | + | 24.6122i | 0.0498742 | + | 0.0406814i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −701.605 | + | 187.995i | −1.15586 | + | 0.309711i | −0.785310 | − | 0.619103i | \(-0.787496\pi\) |
−0.370547 | + | 0.928814i | \(0.620830\pi\) | |||||||
\(608\) | 33.1916 | + | 123.873i | 0.0545914 | + | 0.203738i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.948440 | + | 9.34278i | 0.00155482 | + | 0.0153160i | ||||
\(611\) | −491.192 | −0.803915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −615.287 | + | 615.287i | −1.00373 | + | 1.00373i | −0.00373821 | + | 0.999993i | \(0.501190\pi\) |
−0.999993 | + | 0.00373821i | \(0.998810\pi\) | |||||||
\(614\) | −48.6468 | + | 28.0862i | −0.0792293 | + | 0.0457430i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −69.4949 | + | 120.369i | −0.112816 | + | 0.195404i | ||||
\(617\) | −746.876 | + | 200.125i | −1.21050 | + | 0.324352i | −0.806957 | − | 0.590610i | \(-0.798887\pi\) |
−0.403540 | + | 0.914962i | \(0.632220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 132.389 | − | 76.4347i | 0.213875 | − | 0.123481i | −0.389236 | − | 0.921138i | \(-0.627261\pi\) |
0.603111 | + | 0.797657i | \(0.293928\pi\) | |||||||
\(620\) | 74.0408 | + | 194.949i | 0.119421 | + | 0.314434i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −131.768 | − | 131.768i | −0.211846 | − | 0.211846i | ||||
\(623\) | 387.247 | + | 103.763i | 0.621585 | + | 0.166553i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 500.367 | + | 374.510i | 0.800588 | + | 0.599215i | ||||
\(626\) | 23.0079 | − | 39.8509i | 0.0367539 | − | 0.0636595i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −89.7639 | − | 24.0522i | −0.142936 | − | 0.0382996i | ||||
\(629\) | 209.757i | 0.333477i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.4847 | −0.0657444 | −0.0328722 | − | 0.999460i | \(-0.510465\pi\) | ||||
−0.0328722 | + | 0.999460i | \(0.510465\pi\) | |||||||
\(632\) | −15.9165 | + | 59.4012i | −0.0251843 | + | 0.0939892i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 42.3460 | + | 24.4485i | 0.0667918 | + | 0.0385622i | ||||
\(635\) | 944.156 | − | 680.861i | 1.48686 | − | 1.07222i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 51.2012 | − | 191.085i | 0.0803786 | − | 0.299977i | ||||
\(638\) | −89.6413 | + | 89.6413i | −0.140504 | + | 0.140504i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 156.420 | − | 347.994i | 0.244406 | − | 0.543741i | ||||
\(641\) | −23.6061 | − | 40.8870i | −0.0368270 | − | 0.0637863i | 0.847024 | − | 0.531554i | \(-0.178392\pi\) |
−0.883851 | + | 0.467768i | \(0.845058\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 168.508 | + | 628.880i | 0.262065 | + | 0.978041i | 0.964022 | + | 0.265822i | \(0.0856432\pi\) |
−0.701957 | + | 0.712219i | \(0.747690\pi\) | |||||||
\(644\) | 269.071 | + | 155.348i | 0.417813 | + | 0.241224i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −33.9092 | − | 58.7324i | −0.0524910 | − | 0.0909171i | ||||
\(647\) | −281.287 | − | 281.287i | −0.434756 | − | 0.434756i | 0.455487 | − | 0.890243i | \(-0.349465\pi\) |
−0.890243 | + | 0.455487i | \(0.849465\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 453.192i | − | 0.698293i | ||||||
\(650\) | 59.1814 | + | 19.6949i | 0.0910482 | + | 0.0302998i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 695.622 | − | 186.391i | 1.06690 | − | 0.285876i | ||||
\(653\) | 32.8775 | + | 122.700i | 0.0503484 | + | 0.187903i | 0.986520 | − | 0.163641i | \(-0.0523237\pi\) |
−0.936172 | + | 0.351543i | \(0.885657\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 411.228 | + | 335.431i | 0.627830 | + | 0.512108i | ||||
\(656\) | −10.3133 | −0.0157214 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −68.6061 | + | 68.6061i | −0.104265 | + | 0.104265i | ||||
\(659\) | 936.379 | − | 540.619i | 1.42091 | − | 0.820362i | 0.424532 | − | 0.905413i | \(-0.360439\pi\) |
0.996377 | + | 0.0850507i | \(0.0271052\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 316.196 | − | 547.668i | 0.478361 | − | 0.828545i | −0.521332 | − | 0.853354i | \(-0.674564\pi\) |
0.999692 | + | 0.0248092i | \(0.00789783\pi\) | |||||||
\(662\) | 75.3468 | − | 20.1891i | 0.113817 | − | 0.0304971i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −40.4231 | + | 23.3383i | −0.0608781 | + | 0.0351480i | ||||
\(665\) | 86.9694 | − | 193.485i | 0.130781 | − | 0.290954i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 405.959 | + | 405.959i | 0.608634 | + | 0.608634i | ||||
\(668\) | 239.862 | + | 64.2709i | 0.359075 | + | 0.0962139i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −100.057 | − | 16.2119i | −0.149339 | − | 0.0241969i | ||||
\(671\) | −33.5301 | + | 58.0758i | −0.0499703 | + | 0.0865512i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −318.684 | − | 85.3911i | −0.473527 | − | 0.126881i | 0.0141597 | − | 0.999900i | \(-0.495493\pi\) |
−0.487687 | + | 0.873018i | \(0.662159\pi\) | |||||||
\(674\) | 96.1046i | 0.142588i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 418.687 | 0.619359 | ||||||||
\(677\) | −17.7113 | + | 66.0996i | −0.0261615 | + | 0.0976360i | −0.977772 | − | 0.209670i | \(-0.932761\pi\) |
0.951611 | + | 0.307306i | \(0.0994276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 146.953 | + | 84.8434i | 0.216426 | + | 0.124953i | ||||
\(680\) | −49.2583 | + | 304.015i | −0.0724387 | + | 0.447081i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.98614 | − | 37.2688i | 0.0146424 | − | 0.0546463i | ||||
\(683\) | 213.410 | − | 213.410i | 0.312459 | − | 0.312459i | −0.533402 | − | 0.845862i | \(-0.679087\pi\) |
0.845862 | + | 0.533402i | \(0.179087\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1074.69 | + | 483.060i | 1.56888 | + | 0.705197i | ||||
\(686\) | −57.5255 | − | 99.6371i | −0.0838564 | − | 0.145244i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 143.508 | + | 535.578i | 0.208587 | + | 0.778457i | ||||
\(689\) | 6.70020 | + | 3.86836i | 0.00972453 | + | 0.00561446i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −75.5607 | − | 130.875i | −0.109350 | − | 0.189399i | 0.806157 | − | 0.591701i | \(-0.201544\pi\) |
−0.915507 | + | 0.402302i | \(0.868210\pi\) | |||||||
\(692\) | −571.712 | − | 571.712i | −0.826173 | − | 0.826173i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 71.9408i | − | 0.103661i | ||||||
\(695\) | 604.174 | − | 740.700i | 0.869315 | − | 1.06576i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5164 | − | 4.42555i | 0.0236964 | − | 0.00634942i | ||||
\(698\) | 24.5149 | + | 91.4910i | 0.0351217 | + | 0.131076i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −425.206 | + | 212.864i | −0.607437 | + | 0.304091i | ||||
\(701\) | −745.680 | −1.06374 | −0.531869 | − | 0.846827i | \(-0.678510\pi\) | ||||
−0.531869 | + | 0.846827i | \(0.678510\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.5765 | − | 52.5765i | 0.0747888 | − | 0.0747888i | ||||
\(704\) | 535.680 | − | 309.275i | 0.760908 | − | 0.439311i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.06123 | − | 8.76631i | 0.00716888 | − | 0.0124169i | ||||
\(707\) | 497.695 | − | 133.357i | 0.703954 | − | 0.188624i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 622.715 | − | 359.524i | 0.878300 | − | 0.507087i | 0.00820246 | − | 0.999966i | \(-0.497389\pi\) |
0.870097 | + | 0.492880i | \(0.164056\pi\) | |||||||
\(710\) | 98.5653 | + | 44.3041i | 0.138824 | + | 0.0624001i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 145.893 | + | 145.893i | 0.204906 | + | 0.204906i | ||||
\(713\) | −168.779 | − | 45.2243i | −0.236717 | − | 0.0634282i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 260.522 | + | 361.268i | 0.364366 | + | 0.505269i | ||||
\(716\) | −358.144 | + | 620.324i | −0.500201 | + | 0.866374i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.8200 | + | 3.97100i | 0.0206407 | + | 0.00553065i | ||||
\(719\) | − | 605.271i | − | 0.841824i | −0.907101 | − | 0.420912i | \(-0.861710\pi\) | ||
0.907101 | − | 0.420912i | \(-0.138290\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −615.716 | −0.853975 | ||||||||
\(722\) | 23.4746 | − | 87.6086i | 0.0325134 | − | 0.121342i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −966.632 | − | 558.085i | −1.33513 | − | 0.770836i | ||||
\(725\) | −860.735 | + | 176.576i | −1.18722 | + | 0.243553i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −90.0884 | + | 336.214i | −0.123918 | + | 0.462468i | −0.999799 | − | 0.0200593i | \(-0.993614\pi\) |
0.875881 | + | 0.482528i | \(0.160281\pi\) | |||||||
\(728\) | −67.9796 | + | 67.9796i | −0.0933786 | + | 0.0933786i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −163.434 | + | 62.0714i | −0.223882 | + | 0.0850294i | ||||
\(731\) | −459.646 | − | 796.130i | −0.628791 | − | 1.08910i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −99.1060 | − | 369.869i | −0.135206 | − | 0.504596i | −0.999997 | − | 0.00246376i | \(-0.999216\pi\) |
0.864791 | − | 0.502132i | \(-0.167451\pi\) | |||||||
\(734\) | −57.0318 | − | 32.9273i | −0.0776999 | − | 0.0448601i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 120.435 | + | 208.599i | 0.163634 | + | 0.283423i | ||||
\(737\) | −511.828 | − | 511.828i | −0.694474 | − | 0.694474i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 515.666i | − | 0.697789i | −0.937162 | − | 0.348895i | \(-0.886557\pi\) | ||
0.937162 | − | 0.348895i | \(-0.113443\pi\) | |||||||
\(740\) | −165.819 | + | 16.8333i | −0.224080 | + | 0.0227477i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.47614 | − | 0.395531i | 0.00198941 | − | 0.000533060i | ||||
\(743\) | 153.987 | + | 574.689i | 0.207251 | + | 0.773471i | 0.988752 | + | 0.149567i | \(0.0477879\pi\) |
−0.781501 | + | 0.623904i | \(0.785545\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −268.169 | + | 328.768i | −0.359959 | + | 0.441299i | ||||
\(746\) | 38.7490 | 0.0519424 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −767.626 | + | 767.626i | −1.02624 | + | 1.02624i | ||||
\(749\) | 410.714 | − | 237.126i | 0.548350 | − | 0.316590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 429.893 | − | 744.597i | 0.572428 | − | 0.991474i | −0.423888 | − | 0.905715i | \(-0.639335\pi\) |
0.996316 | − | 0.0857596i | \(-0.0273317\pi\) | |||||||
\(752\) | 894.435 | − | 239.663i | 1.18941 | − | 0.318701i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −75.9389 | + | 43.8434i | −0.100715 | + | 0.0581477i | ||||
\(755\) | −696.318 | + | 264.459i | −0.922275 | + | 0.350276i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −956.075 | − | 956.075i | −1.26298 | − | 1.26298i | −0.949642 | − | 0.313337i | \(-0.898553\pi\) |
−0.313337 | − | 0.949642i | \(-0.601447\pi\) | |||||||
\(758\) | −64.4715 | − | 17.2751i | −0.0850548 | − | 0.0227904i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 88.5495 | − | 63.8558i | 0.116512 | − | 0.0840208i | ||||
\(761\) | 161.379 | − | 279.517i | 0.212062 | − | 0.367302i | −0.740298 | − | 0.672279i | \(-0.765315\pi\) |
0.952360 | + | 0.304977i | \(0.0986488\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 323.706 | + | 86.7368i | 0.424255 | + | 0.113679i | ||||
\(764\) | − | 187.505i | − | 0.245426i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.77858 | −0.00623835 | ||||||||
\(767\) | 81.1314 | − | 302.786i | 0.105778 | − | 0.394767i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −599.638 | − | 346.201i | −0.779763 | − | 0.450196i | 0.0565833 | − | 0.998398i | \(-0.481979\pi\) |
−0.836346 | + | 0.548202i | \(0.815313\pi\) | |||||||
\(770\) | 86.8470 | + | 14.0715i | 0.112788 | + | 0.0182746i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 364.724 | − | 1361.17i | 0.472440 | − | 1.76317i | ||||
\(773\) | 375.226 | − | 375.226i | 0.485415 | − | 0.485415i | −0.421441 | − | 0.906856i | \(-0.638475\pi\) |
0.906856 | + | 0.421441i | \(0.138475\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 200.000 | − | 177.526i | 0.258065 | − | 0.229065i | ||||
\(776\) | 43.6640 | + | 75.6283i | 0.0562681 | + | 0.0974592i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 44.0381 | + | 164.352i | 0.0566042 | + | 0.211250i | ||||
\(779\) | −5.24918 | − | 3.03062i | −0.00673836 | − | 0.00389039i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 385.848 | + | 668.308i | 0.494043 | + | 0.855708i | ||||
\(782\) | −90.0704 | − | 90.0704i | −0.115180 | − | 0.115180i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 372.939i | 0.475687i | ||||||||
\(785\) | 12.0361 | + | 118.563i | 0.0153326 | + | 0.151036i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1244.44 | + | 333.445i | −1.58124 | + | 0.423692i | −0.939309 | − | 0.343072i | \(-0.888533\pi\) |
−0.641930 | + | 0.766763i | \(0.721866\pi\) | |||||||
\(788\) | −137.999 | − | 515.018i | −0.175125 | − | 0.653576i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 38.7279 | − | 3.93150i | 0.0490227 | − | 0.00497658i | ||||
\(791\) | 673.626 | 0.851613 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.7990 | + | 32.7990i | −0.0413606 | + | 0.0413606i | ||||
\(794\) | 46.2228 | − | 26.6867i | 0.0582151 | − | 0.0336105i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −375.484 | + | 650.357i | −0.471713 | + | 0.817031i | ||||
\(797\) | 9.85838 | − | 2.64154i | 0.0123694 | − | 0.00331436i | −0.252629 | − | 0.967563i | \(-0.581295\pi\) |
0.264998 | + | 0.964249i | \(0.414629\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1329.57 | + | 767.626i | −1.66404 | + | 0.960733i | ||||
\(800\) | −367.991 | − | 21.9069i | −0.459989 | − | 0.0273836i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 94.4607 | + | 94.4607i | 0.117781 | + | 0.117781i | ||||
\(803\) | −1205.89 | − | 323.117i | −1.50173 | − | 0.402387i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 63.7256 | − | 393.305i | 0.0791622 | − | 0.488577i | ||||
\(806\) | 13.3439 | − | 23.1123i | 0.0165557 | − | 0.0286753i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 256.135 | + | 68.6313i | 0.316999 | + | 0.0849397i | ||||
\(809\) | − | 150.000i | − | 0.185414i | −0.995693 | − | 0.0927070i | \(-0.970448\pi\) | ||
0.995693 | − | 0.0927070i | \(-0.0295520\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1336.85 | 1.64839 | 0.824197 | − | 0.566304i | \(-0.191627\pi\) | ||||
0.824197 | + | 0.566304i | \(0.191627\pi\) | |||||||
\(812\) | 173.021 | − | 645.722i | 0.213080 | − | 0.795224i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 26.7063 | + | 15.4189i | 0.0328087 | + | 0.0189421i | ||||
\(815\) | −540.178 | − | 749.070i | −0.662795 | − | 0.919104i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −84.3412 | + | 314.766i | −0.103233 | + | 0.385270i | ||||
\(818\) | 115.768 | − | 115.768i | 0.141526 | − | 0.141526i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.82399 | + | 12.7015i | 0.00588291 | + | 0.0154897i | ||||
\(821\) | 16.9467 | + | 29.3525i | 0.0206415 | + | 0.0357521i | 0.876162 | − | 0.482017i | \(-0.160096\pi\) |
−0.855520 | + | 0.517770i | \(0.826762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 176.289 | + | 657.920i | 0.214203 | + | 0.799417i | 0.986446 | + | 0.164089i | \(0.0524685\pi\) |
−0.772242 | + | 0.635328i | \(0.780865\pi\) | |||||||
\(824\) | −274.421 | − | 158.437i | −0.333035 | − | 0.192278i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.9592 | − | 53.6229i | −0.0374808 | − | 0.0649187i | ||||
\(827\) | 350.756 | + | 350.756i | 0.424131 | + | 0.424131i | 0.886623 | − | 0.462492i | \(-0.153045\pi\) |
−0.462492 | + | 0.886623i | \(0.653045\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 697.423i | − | 0.841283i | −0.907227 | − | 0.420641i | \(-0.861805\pi\) | ||
0.907227 | − | 0.420641i | \(-0.138195\pi\) | |||||||
\(830\) | 22.8953 | + | 18.6753i | 0.0275847 | + | 0.0225003i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 413.265 | − | 110.734i | 0.496713 | − | 0.133094i | ||||
\(833\) | −160.032 | − | 597.249i | −0.192116 | − | 0.716986i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.1621 | − | 316.819i | −0.0385175 | − | 0.379424i | ||||
\(836\) | 384.817 | 0.460308 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 19.9127 | − | 19.9127i | 0.0237622 | − | 0.0237622i | ||||
\(839\) | 62.6764 | − | 36.1862i | 0.0747037 | − | 0.0431302i | −0.462183 | − | 0.886785i | \(-0.652934\pi\) |
0.536887 | + | 0.843654i | \(0.319600\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 197.136 | − | 341.449i | 0.234406 | − | 0.406004i | ||||
\(842\) | 78.9472 | − | 21.1538i | 0.0937615 | − | 0.0251233i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −497.079 | + | 286.989i | −0.588956 | + | 0.340034i | ||||
\(845\) | −190.633 | − | 501.936i | −0.225602 | − | 0.594008i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.8638 | + | 26.8638i | 0.0317164 | + | 0.0317164i | ||||
\(848\) | −14.0882 | − | 3.77492i | −0.0166134 | − | 0.00445155i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 190.972 | − | 39.1771i | 0.224673 | − | 0.0460907i | ||||
\(851\) | 69.8275 | − | 120.945i | 0.0820535 | − | 0.142121i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 101.864 | + | 27.2945i | 0.119419 | + | 0.0319982i | 0.318034 | − | 0.948079i | \(-0.396978\pi\) |
−0.198615 | + | 0.980078i | \(0.563644\pi\) | |||||||
\(854\) | 9.16225i | 0.0107286i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 244.070 | 0.285129 | ||||||||
\(857\) | −107.310 | + | 400.486i | −0.125216 | + | 0.467311i | −0.999847 | − | 0.0174768i | \(-0.994437\pi\) |
0.874632 | + | 0.484788i | \(0.161103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 681.447 | + | 393.434i | 0.793303 | + | 0.458014i | 0.841124 | − | 0.540842i | \(-0.181894\pi\) |
−0.0478212 | + | 0.998856i | \(0.515228\pi\) | |||||||
\(860\) | 592.478 | − | 427.254i | 0.688927 | − | 0.496808i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 66.1912 | − | 247.029i | 0.0767879 | − | 0.286577i | ||||
\(863\) | −1072.68 | + | 1072.68i | −1.24297 | + | 1.24297i | −0.284204 | + | 0.958764i | \(0.591729\pi\) |
−0.958764 | + | 0.284204i | \(0.908271\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −425.081 | + | 945.696i | −0.491423 | + | 1.09329i | ||||
\(866\) | 77.5028 | + | 134.239i | 0.0894952 | + | 0.155010i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 52.6595 | + | 196.528i | 0.0606676 | + | 0.226415i | ||||
\(869\) | 240.737 | + | 138.990i | 0.277028 | + | 0.159942i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −250.334 | − | 433.591i | −0.287410 | − | 0.497808i | ||||
\(872\) | 121.955 | + | 121.955i | 0.139856 | + | 0.139856i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 45.1531i | 0.0516626i | ||||||||
\(875\) | 448.790 | + | 412.832i | 0.512903 | + | 0.471808i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −327.108 | + | 87.6483i | −0.372985 | + | 0.0999411i | −0.440442 | − | 0.897781i | \(-0.645178\pi\) |
0.0674567 | + | 0.997722i | \(0.478512\pi\) | |||||||
\(878\) | −35.6137 | − | 132.912i | −0.0405623 | − | 0.151381i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −650.667 | − | 530.736i | −0.739394 | − | 0.603109i | ||||
\(881\) | 62.8490 | 0.0713382 | 0.0356691 | − | 0.999364i | \(-0.488644\pi\) | ||||
0.0356691 | + | 0.999364i | \(0.488644\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −158.061 | + | 158.061i | −0.179005 | + | 0.179005i | −0.790922 | − | 0.611917i | \(-0.790399\pi\) |
0.611917 | + | 0.790922i | \(0.290399\pi\) | |||||||
\(884\) | −650.288 | + | 375.444i | −0.735620 | + | 0.424710i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −55.0918 | + | 95.4219i | −0.0621804 | + | 0.107700i | ||||
\(887\) | −41.2630 | + | 11.0564i | −0.0465198 | + | 0.0124649i | −0.282004 | − | 0.959413i | \(-0.590999\pi\) |
0.235484 | + | 0.971878i | \(0.424332\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 983.559 | − | 567.858i | 1.10637 | − | 0.638761i | ||||
\(890\) | 53.5439 | − | 119.121i | 0.0601616 | − | 0.133844i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −652.803 | − | 652.803i | −0.731841 | − | 0.731841i | ||||
\(893\) | 525.670 | + | 140.853i | 0.588657 | + | 0.157730i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 906.734 | + | 146.915i | 1.01311 | + | 0.164150i | ||||
\(896\) | 186.124 | − | 322.376i | 0.207727 | − | 0.359794i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 118.533 | + | 31.7607i | 0.131996 | + | 0.0353683i | ||||
\(899\) | 375.959i | 0.418197i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.1816 | 0.0268387 | ||||||||
\(902\) | 0.650628 | − | 2.42818i | 0.000721317 | − | 0.00269199i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 300.231 | + | 173.338i | 0.332114 | + | 0.191746i | ||||
\(905\) | −228.932 | + | 1412.94i | −0.252964 | + | 1.56126i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 209.126 | − | 780.467i | 0.230568 | − | 0.860493i | −0.749528 | − | 0.661972i | \(-0.769720\pi\) |
0.980097 | − | 0.198521i | \(-0.0636138\pi\) | |||||||
\(908\) | 987.110 | − | 987.110i | 1.08713 | − | 1.08713i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 55.5051 | + | 24.9490i | 0.0609946 | + | 0.0274165i | ||||
\(911\) | −86.6811 | − | 150.136i | −0.0951494 | − | 0.164804i | 0.814522 | − | 0.580133i | \(-0.197000\pi\) |
−0.909671 | + | 0.415330i | \(0.863666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 54.6080 | + | 203.800i | 0.0598116 | + | 0.223220i | ||||
\(914\) | 87.0979 | + | 50.2860i | 0.0952931 | + | 0.0550175i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 437.080 | + | 757.044i | 0.477161 | + | 0.826467i | ||||
\(917\) | 366.116 | + | 366.116i | 0.399254 | + | 0.399254i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1147.42i | 1.24856i | 0.781202 | + | 0.624278i | \(0.214607\pi\) | ||||
−0.781202 | + | 0.624278i | \(0.785393\pi\) | |||||||
\(920\) | 129.608 | − | 158.895i | 0.140878 | − | 0.172712i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 221.850 | − | 59.4444i | 0.240618 | − | 0.0644733i | ||||
\(923\) | 138.151 | + | 515.585i | 0.149676 | + | 0.558597i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 95.6800 | + | 191.126i | 0.103438 | + | 0.206622i | ||||
\(926\) | −58.2995 | −0.0629584 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 366.464 | − | 366.464i | 0.394897 | − | 0.394897i | ||||
\(929\) | −190.779 | + | 110.146i | −0.205360 | + | 0.118565i | −0.599153 | − | 0.800635i | \(-0.704496\pi\) |
0.393793 | + | 0.919199i | \(0.371163\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −109.590 | + | 189.816i | −0.117712 | + | 0.203884i | ||||
\(932\) | −1095.64 | + | 293.576i | −1.17558 | + | 0.314996i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 161.647 | − | 93.3270i | 0.173070 | − | 0.0999219i | ||||
\(935\) | 1269.77 | + | 570.747i | 1.35804 | + | 0.610425i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −396.090 | − | 396.090i | −0.422721 | − | 0.422721i | 0.463418 | − | 0.886140i | \(-0.346623\pi\) |
−0.886140 | + | 0.463418i | \(0.846623\pi\) | |||||||
\(938\) | −95.5256 | − | 25.5960i | −0.101840 | − | 0.0272879i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −713.531 | − | 989.459i | −0.759075 | − | 1.05262i | ||||
\(941\) | −92.8854 | + | 160.882i | −0.0987093 | + | 0.170970i | −0.911151 | − | 0.412073i | \(-0.864805\pi\) |
0.812441 | + | 0.583043i | \(0.198138\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.9965 | − | 2.94650i | −0.0116612 | − | 0.00312461i | ||||
\(944\) | 590.944i | 0.626000i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −135.151 | −0.142866 | ||||||||
\(947\) | −309.361 | + | 1154.55i | −0.326675 | + | 1.21917i | 0.585943 | + | 0.810352i | \(0.300724\pi\) |
−0.912618 | + | 0.408814i | \(0.865942\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −747.833 | − | 431.762i | −0.788022 | − | 0.454965i | ||||
\(950\) | −57.6878 | − | 38.0480i | −0.0607240 | − | 0.0400506i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −77.7711 | + | 290.246i | −0.0816923 | + | 0.304880i | ||||
\(953\) | −630.499 | + | 630.499i | −0.661594 | + | 0.661594i | −0.955756 | − | 0.294161i | \(-0.904960\pi\) |
0.294161 | + | 0.955756i | \(0.404960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −224.788 | + | 85.3735i | −0.235380 | + | 0.0893963i | ||||
\(956\) | 674.130 | + | 1167.63i | 0.705156 | + | 1.22137i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −25.0858 | − | 93.6215i | −0.0261856 | − | 0.0977260i | ||||
\(959\) | 995.570 | + | 574.792i | 1.03813 | + | 0.599366i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 423.288 | + | 733.156i | 0.440466 | + | 0.762909i | ||||
\(962\) | 15.0827 | + | 15.0827i | 0.0156785 | + | 0.0156785i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 396.041i | − | 0.410831i | ||||||
\(965\) | −1797.88 | + | 182.513i | −1.86309 | + | 0.189133i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 521.399 | − | 139.708i | 0.539192 | − | 0.144476i | 0.0210624 | − | 0.999778i | \(-0.493295\pi\) |
0.518130 | + | 0.855302i | \(0.326628\pi\) | |||||||
\(968\) | 5.06039 | + | 18.8856i | 0.00522768 | + | 0.0195100i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 34.9399 | − | 42.8353i | 0.0360205 | − | 0.0441601i | ||||
\(971\) | −1000.44 | −1.03032 | −0.515159 | − | 0.857095i | \(-0.672267\pi\) | ||||
−0.515159 | + | 0.857095i | \(0.672267\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 659.444 | − | 659.444i | 0.677743 | − | 0.677743i | ||||
\(974\) | −167.120 | + | 96.4870i | −0.171581 | + | 0.0990626i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 43.7219 | − | 75.7286i | 0.0447971 | − | 0.0775908i | ||||
\(977\) | −810.957 | + | 217.295i | −0.830048 | + | 0.222411i | −0.648735 | − | 0.761015i | \(-0.724702\pi\) |
−0.181313 | + | 0.983425i | \(0.558035\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 807.686 | − | 466.318i | 0.825011 | − | 0.476321i | ||||
\(980\) | 459.301 | − | 174.441i | 0.468674 | − | 0.178001i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −93.1158 | − | 93.1158i | −0.0948226 | − | 0.0948226i | ||||
\(983\) | 1662.91 | + | 445.576i | 1.69167 | + | 0.453282i | 0.970820 | − | 0.239807i | \(-0.0770843\pi\) |
0.720852 | + | 0.693090i | \(0.243751\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −554.589 | + | 399.932i | −0.563035 | + | 0.406022i | ||||
\(986\) | −137.035 | + | 237.352i | −0.138981 | + | 0.240722i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 257.104 | + | 68.8908i | 0.260227 | + | 0.0697276i | ||||
\(989\) | 612.059i | 0.618867i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −544.061 | −0.549002 | −0.274501 | − | 0.961587i | \(-0.588513\pi\) | ||||
−0.274501 | + | 0.961587i | \(0.588513\pi\) | |||||||
\(992\) | −40.8245 | + | 152.359i | −0.0411538 | + | 0.153588i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 91.3091 | + | 52.7173i | 0.0918603 | + | 0.0530356i | ||||
\(995\) | 950.633 | + | 154.027i | 0.955410 | + | 0.154801i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −115.932 | + | 432.666i | −0.116281 | + | 0.433967i | −0.999380 | − | 0.0352205i | \(-0.988787\pi\) |
0.883098 | + | 0.469188i | \(0.155453\pi\) | |||||||
\(998\) | −82.6128 | + | 82.6128i | −0.0827783 | + | 0.0827783i | ||||
\(999\) | 0 | 0 |
(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 | 405.3.l.h.352.2 | 8 | ||
3.2 | odd | 2 | 405.3.l.f.352.1 | 8 | |||
5.3 | odd | 4 | inner | 405.3.l.h.28.1 | 8 | ||
9.2 | odd | 6 | 405.3.l.f.217.2 | 8 | |||
9.4 | even | 3 | 15.3.f.a.7.2 | ✓ | 4 | ||
9.5 | odd | 6 | 45.3.g.b.37.1 | 4 | |||
9.7 | even | 3 | inner | 405.3.l.h.217.1 | 8 | ||
15.8 | even | 4 | 405.3.l.f.28.2 | 8 | |||
36.23 | even | 6 | 720.3.bh.k.577.2 | 4 | |||
36.31 | odd | 6 | 240.3.bg.a.97.2 | 4 | |||
45.4 | even | 6 | 75.3.f.c.7.1 | 4 | |||
45.13 | odd | 12 | 15.3.f.a.13.2 | yes | 4 | ||
45.14 | odd | 6 | 225.3.g.a.82.2 | 4 | |||
45.22 | odd | 12 | 75.3.f.c.43.1 | 4 | |||
45.23 | even | 12 | 45.3.g.b.28.1 | 4 | |||
45.32 | even | 12 | 225.3.g.a.118.2 | 4 | |||
45.38 | even | 12 | 405.3.l.f.298.1 | 8 | |||
45.43 | odd | 12 | inner | 405.3.l.h.298.2 | 8 | ||
72.13 | even | 6 | 960.3.bg.i.577.2 | 4 | |||
72.67 | odd | 6 | 960.3.bg.h.577.1 | 4 | |||
180.23 | odd | 12 | 720.3.bh.k.433.2 | 4 | |||
180.67 | even | 12 | 1200.3.bg.k.193.1 | 4 | |||
180.103 | even | 12 | 240.3.bg.a.193.2 | 4 | |||
180.139 | odd | 6 | 1200.3.bg.k.1057.1 | 4 | |||
360.13 | odd | 12 | 960.3.bg.i.193.2 | 4 | |||
360.283 | even | 12 | 960.3.bg.h.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.3.f.a.7.2 | ✓ | 4 | 9.4 | even | 3 | ||
15.3.f.a.13.2 | yes | 4 | 45.13 | odd | 12 | ||
45.3.g.b.28.1 | 4 | 45.23 | even | 12 | |||
45.3.g.b.37.1 | 4 | 9.5 | odd | 6 | |||
75.3.f.c.7.1 | 4 | 45.4 | even | 6 | |||
75.3.f.c.43.1 | 4 | 45.22 | odd | 12 | |||
225.3.g.a.82.2 | 4 | 45.14 | odd | 6 | |||
225.3.g.a.118.2 | 4 | 45.32 | even | 12 | |||
240.3.bg.a.97.2 | 4 | 36.31 | odd | 6 | |||
240.3.bg.a.193.2 | 4 | 180.103 | even | 12 | |||
405.3.l.f.28.2 | 8 | 15.8 | even | 4 | |||
405.3.l.f.217.2 | 8 | 9.2 | odd | 6 | |||
405.3.l.f.298.1 | 8 | 45.38 | even | 12 | |||
405.3.l.f.352.1 | 8 | 3.2 | odd | 2 | |||
405.3.l.h.28.1 | 8 | 5.3 | odd | 4 | inner | ||
405.3.l.h.217.1 | 8 | 9.7 | even | 3 | inner | ||
405.3.l.h.298.2 | 8 | 45.43 | odd | 12 | inner | ||
405.3.l.h.352.2 | 8 | 1.1 | even | 1 | trivial | ||
720.3.bh.k.433.2 | 4 | 180.23 | odd | 12 | |||
720.3.bh.k.577.2 | 4 | 36.23 | even | 6 | |||
960.3.bg.h.193.1 | 4 | 360.283 | even | 12 | |||
960.3.bg.h.577.1 | 4 | 72.67 | odd | 6 | |||
960.3.bg.i.193.2 | 4 | 360.13 | odd | 12 | |||
960.3.bg.i.577.2 | 4 | 72.13 | even | 6 | |||
1200.3.bg.k.193.1 | 4 | 180.67 | even | 12 | |||
1200.3.bg.k.1057.1 | 4 | 180.139 | odd | 6 |