Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(49,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.q (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 349.5 | ||
Root | \(1.98293 + 0.531325i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.349 |
Dual form | 570.2.q.b.49.5 |
$q$-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 \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | −1.37659 | − | 1.76210i | −0.615628 | − | 0.788037i | ||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | − | 0.785680i | − | 0.296959i | −0.988915 | − | 0.148480i | \(-0.952562\pi\) | ||
0.988915 | − | 0.148480i | \(-0.0474379\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −2.07321 | − | 0.837733i | −0.655607 | − | 0.264914i | ||||
\(11\) | −0.377784 | −0.113906 | −0.0569531 | − | 0.998377i | \(-0.518139\pi\) | ||||
−0.0569531 | + | 0.998377i | \(0.518139\pi\) | |||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −2.51426 | − | 1.45161i | −0.697329 | − | 0.402603i | 0.109023 | − | 0.994039i | \(-0.465228\pi\) |
−0.806352 | + | 0.591436i | \(0.798561\pi\) | |||||||
\(14\) | −0.392840 | − | 0.680419i | −0.104991 | − | 0.181850i | ||||
\(15\) | −2.07321 | − | 0.837733i | −0.535301 | − | 0.216302i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 2.45651 | − | 1.41827i | 0.595792 | − | 0.343980i | −0.171593 | − | 0.985168i | \(-0.554891\pi\) |
0.767384 | + | 0.641188i | \(0.221558\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −2.82148 | − | 3.32254i | −0.647292 | − | 0.762242i | ||||
\(20\) | −2.21432 | + | 0.311108i | −0.495137 | + | 0.0695658i | ||||
\(21\) | −0.392840 | − | 0.680419i | −0.0857247 | − | 0.148480i | ||||
\(22\) | −0.327171 | + | 0.188892i | −0.0697531 | + | 0.0402719i | ||||
\(23\) | 7.86994 | + | 4.54371i | 1.64100 | + | 0.947429i | 0.980481 | + | 0.196616i | \(0.0629952\pi\) |
0.660515 | + | 0.750813i | \(0.270338\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | −1.21002 | + | 4.85138i | −0.242003 | + | 0.970275i | ||||
\(26\) | −2.90321 | −0.569367 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | −0.680419 | − | 0.392840i | −0.128587 | − | 0.0742398i | ||||
\(29\) | 2.01037 | − | 3.48207i | 0.373317 | − | 0.646603i | −0.616757 | − | 0.787154i | \(-0.711554\pi\) |
0.990074 | + | 0.140550i | \(0.0448872\pi\) | |||||||
\(30\) | −2.21432 | + | 0.311108i | −0.404278 | + | 0.0568003i | ||||
\(31\) | −4.42864 | −0.795407 | −0.397704 | − | 0.917514i | \(-0.630193\pi\) | ||||
−0.397704 | + | 0.917514i | \(0.630193\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | −0.327171 | + | 0.188892i | −0.0569531 | + | 0.0328819i | ||||
\(34\) | 1.41827 | − | 2.45651i | 0.243231 | − | 0.421288i | ||||
\(35\) | −1.38445 | + | 1.08156i | −0.234015 | + | 0.182817i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 0.0967881i | 0.0159119i | 0.999968 | + | 0.00795593i | \(0.00253248\pi\) | ||||
−0.999968 | + | 0.00795593i | \(0.997468\pi\) | |||||||
\(38\) | −4.10474 | − | 1.46666i | −0.665877 | − | 0.237924i | ||||
\(39\) | −2.90321 | −0.464886 | ||||||||
\(40\) | −1.76210 | + | 1.37659i | −0.278613 | + | 0.217658i | ||||
\(41\) | −1.43655 | − | 2.48818i | −0.224351 | − | 0.388588i | 0.731773 | − | 0.681548i | \(-0.238693\pi\) |
−0.956125 | + | 0.292960i | \(0.905360\pi\) | |||||||
\(42\) | −0.680419 | − | 0.392840i | −0.104991 | − | 0.0606165i | ||||
\(43\) | −0.371213 | + | 0.214320i | −0.0566094 | + | 0.0326835i | −0.528038 | − | 0.849221i | \(-0.677072\pi\) |
0.471428 | + | 0.881904i | \(0.343739\pi\) | |||||||
\(44\) | −0.188892 | + | 0.327171i | −0.0284766 | + | 0.0493229i | ||||
\(45\) | −2.21432 | + | 0.311108i | −0.330091 | + | 0.0463772i | ||||
\(46\) | 9.08742 | 1.33987 | ||||||||
\(47\) | 10.4680 | + | 6.04371i | 1.52692 | + | 0.881566i | 0.999489 | + | 0.0319658i | \(0.0101768\pi\) |
0.527428 | + | 0.849600i | \(0.323157\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.125000 | − | 0.0721688i | ||||
\(49\) | 6.38271 | 0.911815 | ||||||||
\(50\) | 1.37778 | + | 4.80642i | 0.194848 | + | 0.679731i | ||||
\(51\) | 1.41827 | − | 2.45651i | 0.198597 | − | 0.343980i | ||||
\(52\) | −2.51426 | + | 1.45161i | −0.348664 | + | 0.201302i | ||||
\(53\) | 6.00443 | + | 3.46666i | 0.824772 | + | 0.476183i | 0.852059 | − | 0.523445i | \(-0.175353\pi\) |
−0.0272870 | + | 0.999628i | \(0.508687\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0.520053 | + | 0.665695i | 0.0701239 | + | 0.0897623i | ||||
\(56\) | −0.785680 | −0.104991 | ||||||||
\(57\) | −4.10474 | − | 1.46666i | −0.543686 | − | 0.194264i | ||||
\(58\) | − | 4.02074i | − | 0.527949i | ||||||
\(59\) | −4.88025 | − | 8.45283i | −0.635354 | − | 1.10047i | −0.986440 | − | 0.164122i | \(-0.947521\pi\) |
0.351086 | − | 0.936343i | \(-0.385812\pi\) | |||||||
\(60\) | −1.76210 | + | 1.37659i | −0.227487 | + | 0.177717i | ||||
\(61\) | −2.27777 | + | 3.94521i | −0.291639 | + | 0.505133i | −0.974197 | − | 0.225698i | \(-0.927534\pi\) |
0.682559 | + | 0.730831i | \(0.260867\pi\) | |||||||
\(62\) | −3.83531 | + | 2.21432i | −0.487085 | + | 0.281219i | ||||
\(63\) | −0.680419 | − | 0.392840i | −0.0857247 | − | 0.0494932i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.903212 | + | 6.42864i | 0.112030 | + | 0.797375i | ||||
\(66\) | −0.188892 | + | 0.327171i | −0.0232510 | + | 0.0402719i | ||||
\(67\) | 7.31738 | + | 4.22469i | 0.893960 | + | 0.516128i | 0.875236 | − | 0.483696i | \(-0.160706\pi\) |
0.0187245 | + | 0.999825i | \(0.494039\pi\) | |||||||
\(68\) | − | 2.83654i | − | 0.343980i | ||||||
\(69\) | 9.08742 | 1.09400 | ||||||||
\(70\) | −0.658190 | + | 1.62888i | −0.0786687 | + | 0.194689i | ||||
\(71\) | 5.86987 | + | 10.1669i | 0.696626 | + | 1.20659i | 0.969630 | + | 0.244578i | \(0.0786495\pi\) |
−0.273004 | + | 0.962013i | \(0.588017\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | −1.95744 | + | 1.13013i | −0.229101 | + | 0.132271i | −0.610157 | − | 0.792280i | \(-0.708894\pi\) |
0.381056 | + | 0.924552i | \(0.375560\pi\) | |||||||
\(74\) | 0.0483940 | + | 0.0838209i | 0.00562569 | + | 0.00974399i | ||||
\(75\) | 1.37778 | + | 4.80642i | 0.159093 | + | 0.554998i | ||||
\(76\) | −4.28814 | + | 0.782204i | −0.491884 | + | 0.0897250i | ||||
\(77\) | 0.296818i | 0.0338255i | ||||||||
\(78\) | −2.51426 | + | 1.45161i | −0.284683 | + | 0.164362i | ||||
\(79\) | −0.785680 | − | 1.36084i | −0.0883959 | − | 0.153106i | 0.818437 | − | 0.574596i | \(-0.194841\pi\) |
−0.906833 | + | 0.421490i | \(0.861507\pi\) | |||||||
\(80\) | −0.837733 | + | 2.07321i | −0.0936614 | + | 0.231792i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.48818 | − | 1.43655i | −0.274773 | − | 0.158640i | ||||
\(83\) | − | 2.75557i | − | 0.302463i | −0.988498 | − | 0.151231i | \(-0.951676\pi\) | ||
0.988498 | − | 0.151231i | \(-0.0483239\pi\) | |||||||
\(84\) | −0.785680 | −0.0857247 | ||||||||
\(85\) | −5.88074 | − | 2.37626i | −0.637855 | − | 0.257741i | ||||
\(86\) | −0.214320 | + | 0.371213i | −0.0231107 | + | 0.0400289i | ||||
\(87\) | − | 4.02074i | − | 0.431069i | ||||||
\(88\) | 0.377784i | 0.0402719i | ||||||||
\(89\) | 5.96912 | − | 10.3388i | 0.632726 | − | 1.09591i | −0.354266 | − | 0.935145i | \(-0.615269\pi\) |
0.986992 | − | 0.160769i | \(-0.0513973\pi\) | |||||||
\(90\) | −1.76210 | + | 1.37659i | −0.185742 | + | 0.145105i | ||||
\(91\) | −1.14050 | + | 1.97540i | −0.119557 | + | 0.207078i | ||||
\(92\) | 7.86994 | − | 4.54371i | 0.820498 | − | 0.473715i | ||||
\(93\) | −3.83531 | + | 2.21432i | −0.397704 | + | 0.229614i | ||||
\(94\) | 12.0874 | 1.24672 | ||||||||
\(95\) | −1.97064 | + | 9.54550i | −0.202183 | + | 0.979348i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 2.98299 | − | 1.72223i | 0.302877 | − | 0.174866i | −0.340858 | − | 0.940115i | \(-0.610717\pi\) |
0.643735 | + | 0.765249i | \(0.277384\pi\) | |||||||
\(98\) | 5.52759 | − | 3.19135i | 0.558371 | − | 0.322375i | ||||
\(99\) | −0.188892 | + | 0.327171i | −0.0189844 | + | 0.0328819i | ||||
\(100\) | 3.59641 | + | 3.47359i | 0.359641 | + | 0.347359i | ||||
\(101\) | −8.54617 | + | 14.8024i | −0.850376 | + | 1.47289i | 0.0304937 | + | 0.999535i | \(0.490292\pi\) |
−0.880870 | + | 0.473359i | \(0.843041\pi\) | |||||||
\(102\) | − | 2.83654i | − | 0.280859i | ||||||
\(103\) | 8.11753i | 0.799844i | 0.916549 | + | 0.399922i | \(0.130963\pi\) | ||||
−0.916549 | + | 0.399922i | \(0.869037\pi\) | |||||||
\(104\) | −1.45161 | + | 2.51426i | −0.142342 | + | 0.246543i | ||||
\(105\) | −0.658190 | + | 1.62888i | −0.0642328 | + | 0.158963i | ||||
\(106\) | 6.93332 | 0.673424 | ||||||||
\(107\) | − | 17.7812i | − | 1.71898i | −0.511155 | − | 0.859488i | \(-0.670782\pi\) | ||
0.511155 | − | 0.859488i | \(-0.329218\pi\) | |||||||
\(108\) | −0.866025 | − | 0.500000i | −0.0833333 | − | 0.0481125i | ||||
\(109\) | 0.722230 | + | 1.25094i | 0.0691771 | + | 0.119818i | 0.898539 | − | 0.438893i | \(-0.144629\pi\) |
−0.829362 | + | 0.558711i | \(0.811296\pi\) | |||||||
\(110\) | 0.783227 | + | 0.316482i | 0.0746777 | + | 0.0301754i | ||||
\(111\) | 0.0483940 | + | 0.0838209i | 0.00459336 | + | 0.00795593i | ||||
\(112\) | −0.680419 | + | 0.392840i | −0.0642936 | + | 0.0371199i | ||||
\(113\) | 14.3160i | 1.34674i | 0.739306 | + | 0.673369i | \(0.235154\pi\) | ||||
−0.739306 | + | 0.673369i | \(0.764846\pi\) | |||||||
\(114\) | −4.28814 | + | 0.782204i | −0.401621 | + | 0.0732602i | ||||
\(115\) | −2.82717 | − | 20.1225i | −0.263635 | − | 1.87643i | ||||
\(116\) | −2.01037 | − | 3.48207i | −0.186658 | − | 0.323302i | ||||
\(117\) | −2.51426 | + | 1.45161i | −0.232443 | + | 0.134201i | ||||
\(118\) | −8.45283 | − | 4.88025i | −0.778146 | − | 0.449263i | ||||
\(119\) | −1.11430 | − | 1.93003i | −0.102148 | − | 0.176926i | ||||
\(120\) | −0.837733 | + | 2.07321i | −0.0764742 | + | 0.189257i | ||||
\(121\) | −10.8573 | −0.987025 | ||||||||
\(122\) | 4.55554i | 0.412439i | ||||||||
\(123\) | −2.48818 | − | 1.43655i | −0.224351 | − | 0.129529i | ||||
\(124\) | −2.21432 | + | 3.83531i | −0.198852 | + | 0.344421i | ||||
\(125\) | 10.2143 | − | 4.54617i | 0.913597 | − | 0.406622i | ||||
\(126\) | −0.785680 | −0.0699940 | ||||||||
\(127\) | −3.14252 | − | 1.81433i | −0.278854 | − | 0.160996i | 0.354051 | − | 0.935226i | \(-0.384804\pi\) |
−0.632904 | + | 0.774230i | \(0.718137\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | −0.214320 | + | 0.371213i | −0.0188698 | + | 0.0326835i | ||||
\(130\) | 3.99652 | + | 5.11576i | 0.350518 | + | 0.448682i | ||||
\(131\) | 8.40321 | + | 14.5548i | 0.734192 | + | 1.27166i | 0.955077 | + | 0.296358i | \(0.0957722\pi\) |
−0.220885 | + | 0.975300i | \(0.570895\pi\) | |||||||
\(132\) | 0.377784i | 0.0328819i | ||||||||
\(133\) | −2.61045 | + | 2.21678i | −0.226355 | + | 0.192219i | ||||
\(134\) | 8.44938 | 0.729916 | ||||||||
\(135\) | −1.76210 | + | 1.37659i | −0.151658 | + | 0.118478i | ||||
\(136\) | −1.41827 | − | 2.45651i | −0.121615 | − | 0.210644i | ||||
\(137\) | −1.89969 | − | 1.09679i | −0.162302 | − | 0.0937049i | 0.416649 | − | 0.909067i | \(-0.363204\pi\) |
−0.578951 | + | 0.815362i | \(0.696538\pi\) | |||||||
\(138\) | 7.86994 | − | 4.54371i | 0.669934 | − | 0.386786i | ||||
\(139\) | 0.836535 | − | 1.44892i | 0.0709540 | − | 0.122896i | −0.828366 | − | 0.560188i | \(-0.810729\pi\) |
0.899320 | + | 0.437292i | \(0.144062\pi\) | |||||||
\(140\) | 0.244431 | + | 1.73975i | 0.0206582 | + | 0.147035i | ||||
\(141\) | 12.0874 | 1.01794 | ||||||||
\(142\) | 10.1669 | + | 5.86987i | 0.853189 | + | 0.492589i | ||||
\(143\) | 0.949846 | + | 0.548394i | 0.0794301 | + | 0.0458590i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | −8.90321 | + | 1.25088i | −0.739372 | + | 0.103880i | ||||
\(146\) | −1.13013 | + | 1.95744i | −0.0935299 | + | 0.161999i | ||||
\(147\) | 5.52759 | − | 3.19135i | 0.455908 | − | 0.263218i | ||||
\(148\) | 0.0838209 | + | 0.0483940i | 0.00689004 | + | 0.00397797i | ||||
\(149\) | 2.69926 | + | 4.67526i | 0.221132 | + | 0.383012i | 0.955152 | − | 0.296116i | \(-0.0956914\pi\) |
−0.734020 | + | 0.679128i | \(0.762358\pi\) | |||||||
\(150\) | 3.59641 | + | 3.47359i | 0.293645 | + | 0.283618i | ||||
\(151\) | 9.07160 | 0.738236 | 0.369118 | − | 0.929382i | \(-0.379660\pi\) | ||||
0.369118 | + | 0.929382i | \(0.379660\pi\) | |||||||
\(152\) | −3.32254 | + | 2.82148i | −0.269493 | + | 0.228852i | ||||
\(153\) | − | 2.83654i | − | 0.229320i | ||||||
\(154\) | 0.148409 | + | 0.257052i | 0.0119591 | + | 0.0207138i | ||||
\(155\) | 6.09641 | + | 7.80372i | 0.489675 | + | 0.626810i | ||||
\(156\) | −1.45161 | + | 2.51426i | −0.116221 | + | 0.201302i | ||||
\(157\) | −13.3094 | + | 7.68421i | −1.06221 | + | 0.613267i | −0.926042 | − | 0.377419i | \(-0.876812\pi\) |
−0.136166 | + | 0.990686i | \(0.543478\pi\) | |||||||
\(158\) | −1.36084 | − | 0.785680i | −0.108262 | − | 0.0625054i | ||||
\(159\) | 6.93332 | 0.549848 | ||||||||
\(160\) | 0.311108 | + | 2.21432i | 0.0245952 | + | 0.175057i | ||||
\(161\) | 3.56990 | − | 6.18325i | 0.281348 | − | 0.487309i | ||||
\(162\) | −0.866025 | − | 0.500000i | −0.0680414 | − | 0.0392837i | ||||
\(163\) | − | 7.31756i | − | 0.573156i | −0.958057 | − | 0.286578i | \(-0.907482\pi\) | ||
0.958057 | − | 0.286578i | \(-0.0925177\pi\) | |||||||
\(164\) | −2.87310 | −0.224351 | ||||||||
\(165\) | 0.783227 | + | 0.316482i | 0.0609741 | + | 0.0246381i | ||||
\(166\) | −1.37778 | − | 2.38639i | −0.106937 | − | 0.185220i | ||||
\(167\) | 5.03277 | + | 2.90567i | 0.389448 | + | 0.224848i | 0.681921 | − | 0.731426i | \(-0.261145\pi\) |
−0.292473 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(168\) | −0.680419 | + | 0.392840i | −0.0524955 | + | 0.0303083i | ||||
\(169\) | −2.28568 | − | 3.95891i | −0.175822 | − | 0.304532i | ||||
\(170\) | −6.28100 | + | 0.882468i | −0.481730 | + | 0.0676822i | ||||
\(171\) | −4.28814 | + | 0.782204i | −0.327922 | + | 0.0598167i | ||||
\(172\) | 0.428639i | 0.0326835i | ||||||||
\(173\) | −7.55647 | + | 4.36273i | −0.574508 | + | 0.331692i | −0.758948 | − | 0.651152i | \(-0.774286\pi\) |
0.184440 | + | 0.982844i | \(0.440953\pi\) | |||||||
\(174\) | −2.01037 | − | 3.48207i | −0.152406 | − | 0.263975i | ||||
\(175\) | 3.81163 | + | 0.950685i | 0.288132 | + | 0.0718651i | ||||
\(176\) | 0.188892 | + | 0.327171i | 0.0142383 | + | 0.0246614i | ||||
\(177\) | −8.45283 | − | 4.88025i | −0.635354 | − | 0.366822i | ||||
\(178\) | − | 11.9382i | − | 0.894809i | ||||||
\(179\) | 23.2306 | 1.73634 | 0.868169 | − | 0.496269i | \(-0.165297\pi\) | ||||
0.868169 | + | 0.496269i | \(0.165297\pi\) | |||||||
\(180\) | −0.837733 | + | 2.07321i | −0.0624409 | + | 0.154528i | ||||
\(181\) | −3.77309 | + | 6.53518i | −0.280451 | + | 0.485756i | −0.971496 | − | 0.237056i | \(-0.923817\pi\) |
0.691045 | + | 0.722812i | \(0.257151\pi\) | |||||||
\(182\) | 2.28100i | 0.169079i | ||||||||
\(183\) | 4.55554i | 0.336755i | ||||||||
\(184\) | 4.54371 | − | 7.86994i | 0.334967 | − | 0.580179i | ||||
\(185\) | 0.170551 | − | 0.133237i | 0.0125391 | − | 0.00979580i | ||||
\(186\) | −2.21432 | + | 3.83531i | −0.162362 | + | 0.281219i | ||||
\(187\) | −0.928032 | + | 0.535799i | −0.0678644 | + | 0.0391815i | ||||
\(188\) | 10.4680 | − | 6.04371i | 0.763458 | − | 0.440783i | ||||
\(189\) | −0.785680 | −0.0571498 | ||||||||
\(190\) | 3.06613 | + | 9.25197i | 0.222440 | + | 0.671208i | ||||
\(191\) | −20.4701 | −1.48117 | −0.740583 | − | 0.671965i | \(-0.765451\pi\) | ||||
−0.740583 | + | 0.671965i | \(0.765451\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | −16.3886 | + | 9.46198i | −1.17968 | + | 0.681088i | −0.955940 | − | 0.293561i | \(-0.905160\pi\) |
−0.223739 | + | 0.974649i | \(0.571826\pi\) | |||||||
\(194\) | 1.72223 | − | 2.98299i | 0.123649 | − | 0.214166i | ||||
\(195\) | 3.99652 | + | 5.11576i | 0.286197 | + | 0.366347i | ||||
\(196\) | 3.19135 | − | 5.52759i | 0.227954 | − | 0.394828i | ||||
\(197\) | − | 1.73038i | − | 0.123284i | −0.998098 | − | 0.0616422i | \(-0.980366\pi\) | ||
0.998098 | − | 0.0616422i | \(-0.0196338\pi\) | |||||||
\(198\) | 0.377784i | 0.0268480i | ||||||||
\(199\) | 7.53580 | − | 13.0524i | 0.534199 | − | 0.925259i | −0.465003 | − | 0.885309i | \(-0.653947\pi\) |
0.999202 | − | 0.0399501i | \(-0.0127199\pi\) | |||||||
\(200\) | 4.85138 | + | 1.21002i | 0.343044 | + | 0.0855610i | ||||
\(201\) | 8.44938 | 0.595974 | ||||||||
\(202\) | 17.0923i | 1.20261i | ||||||||
\(203\) | −2.73579 | − | 1.57951i | −0.192015 | − | 0.110860i | ||||
\(204\) | −1.41827 | − | 2.45651i | −0.0992986 | − | 0.171990i | ||||
\(205\) | −2.40689 | + | 5.95654i | −0.168104 | + | 0.416023i | ||||
\(206\) | 4.05877 | + | 7.02999i | 0.282788 | + | 0.489803i | ||||
\(207\) | 7.86994 | − | 4.54371i | 0.546998 | − | 0.315810i | ||||
\(208\) | 2.90321i | 0.201302i | ||||||||
\(209\) | 1.06591 | + | 1.25520i | 0.0737306 | + | 0.0868242i | ||||
\(210\) | 0.244431 | + | 1.73975i | 0.0168674 | + | 0.120054i | ||||
\(211\) | −6.65801 | − | 11.5320i | −0.458357 | − | 0.793897i | 0.540518 | − | 0.841333i | \(-0.318228\pi\) |
−0.998874 | + | 0.0474357i | \(0.984895\pi\) | |||||||
\(212\) | 6.00443 | − | 3.46666i | 0.412386 | − | 0.238091i | ||||
\(213\) | 10.1669 | + | 5.86987i | 0.696626 | + | 0.402197i | ||||
\(214\) | −8.89062 | − | 15.3990i | −0.607750 | − | 1.05265i | ||||
\(215\) | 0.888660 | + | 0.359085i | 0.0606061 | + | 0.0244894i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 3.47949i | 0.236203i | ||||||||
\(218\) | 1.25094 | + | 0.722230i | 0.0847243 | + | 0.0489156i | ||||
\(219\) | −1.13013 | + | 1.95744i | −0.0763669 | + | 0.132271i | ||||
\(220\) | 0.836535 | − | 0.117532i | 0.0563992 | − | 0.00792398i | ||||
\(221\) | −8.23506 | −0.553950 | ||||||||
\(222\) | 0.0838209 | + | 0.0483940i | 0.00562569 | + | 0.00324800i | ||||
\(223\) | 16.6003 | − | 9.58419i | 1.11164 | − | 0.641805i | 0.172386 | − | 0.985030i | \(-0.444852\pi\) |
0.939253 | + | 0.343224i | \(0.111519\pi\) | |||||||
\(224\) | −0.392840 | + | 0.680419i | −0.0262477 | + | 0.0454624i | ||||
\(225\) | 3.59641 | + | 3.47359i | 0.239761 | + | 0.231573i | ||||
\(226\) | 7.15801 | + | 12.3980i | 0.476144 | + | 0.824706i | ||||
\(227\) | − | 6.88247i | − | 0.456805i | −0.973567 | − | 0.228403i | \(-0.926650\pi\) | ||
0.973567 | − | 0.228403i | \(-0.0733503\pi\) | |||||||
\(228\) | −3.32254 | + | 2.82148i | −0.220040 | + | 0.186857i | ||||
\(229\) | −13.7462 | −0.908375 | −0.454187 | − | 0.890906i | \(-0.650070\pi\) | ||||
−0.454187 | + | 0.890906i | \(0.650070\pi\) | |||||||
\(230\) | −12.5096 | − | 16.0130i | −0.824860 | − | 1.05586i | ||||
\(231\) | 0.148409 | + | 0.257052i | 0.00976459 | + | 0.0169128i | ||||
\(232\) | −3.48207 | − | 2.01037i | −0.228609 | − | 0.131987i | ||||
\(233\) | −5.88642 | + | 3.39853i | −0.385632 | + | 0.222645i | −0.680266 | − | 0.732965i | \(-0.738136\pi\) |
0.294634 | + | 0.955610i | \(0.404802\pi\) | |||||||
\(234\) | −1.45161 | + | 2.51426i | −0.0948945 | + | 0.164362i | ||||
\(235\) | −3.76049 | − | 26.7654i | −0.245307 | − | 1.74598i | ||||
\(236\) | −9.76049 | −0.635354 | ||||||||
\(237\) | −1.36084 | − | 0.785680i | −0.0883959 | − | 0.0510354i | ||||
\(238\) | −1.93003 | − | 1.11430i | −0.125105 | − | 0.0722297i | ||||
\(239\) | 10.8573 | 0.702299 | 0.351149 | − | 0.936319i | \(-0.385791\pi\) | ||||
0.351149 | + | 0.936319i | \(0.385791\pi\) | |||||||
\(240\) | 0.311108 | + | 2.21432i | 0.0200819 | + | 0.142934i | ||||
\(241\) | 4.84368 | − | 8.38950i | 0.312009 | − | 0.540415i | −0.666788 | − | 0.745247i | \(-0.732331\pi\) |
0.978797 | + | 0.204832i | \(0.0656648\pi\) | |||||||
\(242\) | −9.40268 | + | 5.42864i | −0.604427 | + | 0.348966i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 2.27777 | + | 3.94521i | 0.145819 | + | 0.252566i | ||||
\(245\) | −8.78635 | − | 11.2470i | −0.561339 | − | 0.718544i | ||||
\(246\) | −2.87310 | −0.183182 | ||||||||
\(247\) | 2.27091 | + | 12.4494i | 0.144494 | + | 0.792135i | ||||
\(248\) | 4.42864i | 0.281219i | ||||||||
\(249\) | −1.37778 | − | 2.38639i | −0.0873135 | − | 0.151231i | ||||
\(250\) | 6.57277 | − | 9.04426i | 0.415699 | − | 0.572009i | ||||
\(251\) | −7.54617 | + | 13.0704i | −0.476310 | + | 0.824993i | −0.999632 | − | 0.0271420i | \(-0.991359\pi\) |
0.523321 | + | 0.852135i | \(0.324693\pi\) | |||||||
\(252\) | −0.680419 | + | 0.392840i | −0.0428624 | + | 0.0247466i | ||||
\(253\) | −2.97314 | − | 1.71654i | −0.186920 | − | 0.107918i | ||||
\(254\) | −3.62867 | −0.227683 | ||||||||
\(255\) | −6.28100 | + | 0.882468i | −0.393331 | + | 0.0552623i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −19.7676 | − | 11.4128i | −1.23307 | − | 0.711912i | −0.265400 | − | 0.964139i | \(-0.585504\pi\) |
−0.967668 | + | 0.252226i | \(0.918837\pi\) | |||||||
\(258\) | 0.428639i | 0.0266859i | ||||||||
\(259\) | 0.0760445 | 0.00472517 | ||||||||
\(260\) | 6.01897 | + | 2.43212i | 0.373281 | + | 0.150833i | ||||
\(261\) | −2.01037 | − | 3.48207i | −0.124439 | − | 0.215534i | ||||
\(262\) | 14.5548 | + | 8.40321i | 0.899198 | + | 0.519152i | ||||
\(263\) | −10.4885 | + | 6.05554i | −0.646749 | + | 0.373401i | −0.787209 | − | 0.616686i | \(-0.788475\pi\) |
0.140461 | + | 0.990086i | \(0.455142\pi\) | |||||||
\(264\) | 0.188892 | + | 0.327171i | 0.0116255 | + | 0.0201360i | ||||
\(265\) | −2.15701 | − | 15.3526i | −0.132504 | − | 0.943102i | ||||
\(266\) | −1.15233 | + | 3.22501i | −0.0706537 | + | 0.197738i | ||||
\(267\) | − | 11.9382i | − | 0.730609i | ||||||
\(268\) | 7.31738 | − | 4.22469i | 0.446980 | − | 0.258064i | ||||
\(269\) | −12.6168 | − | 21.8529i | −0.769258 | − | 1.33239i | −0.937966 | − | 0.346728i | \(-0.887293\pi\) |
0.168708 | − | 0.985666i | \(-0.446040\pi\) | |||||||
\(270\) | −0.837733 | + | 2.07321i | −0.0509828 | + | 0.126172i | ||||
\(271\) | −15.4652 | − | 26.7865i | −0.939444 | − | 1.62717i | −0.766511 | − | 0.642232i | \(-0.778009\pi\) |
−0.172934 | − | 0.984933i | \(-0.555325\pi\) | |||||||
\(272\) | −2.45651 | − | 1.41827i | −0.148948 | − | 0.0859951i | ||||
\(273\) | 2.28100i | 0.138052i | ||||||||
\(274\) | −2.19358 | −0.132519 | ||||||||
\(275\) | 0.457125 | − | 1.83277i | 0.0275657 | − | 0.110520i | ||||
\(276\) | 4.54371 | − | 7.86994i | 0.273499 | − | 0.473715i | ||||
\(277\) | 19.4938i | 1.17127i | 0.810576 | + | 0.585634i | \(0.199154\pi\) | ||||
−0.810576 | + | 0.585634i | \(0.800846\pi\) | |||||||
\(278\) | − | 1.67307i | − | 0.100344i | ||||||
\(279\) | −2.21432 | + | 3.83531i | −0.132568 | + | 0.229614i | ||||
\(280\) | 1.08156 | + | 1.38445i | 0.0646354 | + | 0.0827367i | ||||
\(281\) | 3.71755 | − | 6.43898i | 0.221770 | − | 0.384117i | −0.733575 | − | 0.679608i | \(-0.762150\pi\) |
0.955346 | + | 0.295491i | \(0.0954832\pi\) | |||||||
\(282\) | 10.4680 | − | 6.04371i | 0.623361 | − | 0.359898i | ||||
\(283\) | −1.48485 | + | 0.857279i | −0.0882652 | + | 0.0509599i | −0.543483 | − | 0.839420i | \(-0.682895\pi\) |
0.455218 | + | 0.890380i | \(0.349561\pi\) | |||||||
\(284\) | 11.7397 | 0.696626 | ||||||||
\(285\) | 3.06613 | + | 9.25197i | 0.181622 | + | 0.548039i | ||||
\(286\) | 1.09679 | 0.0648544 | ||||||||
\(287\) | −1.95491 | + | 1.12867i | −0.115395 | + | 0.0666232i | ||||
\(288\) | −0.866025 | + | 0.500000i | −0.0510310 | + | 0.0294628i | ||||
\(289\) | −4.47703 | + | 7.75445i | −0.263355 | + | 0.456144i | ||||
\(290\) | −7.08497 | + | 5.53490i | −0.416043 | + | 0.325021i | ||||
\(291\) | 1.72223 | − | 2.98299i | 0.100959 | − | 0.174866i | ||||
\(292\) | 2.26025i | 0.132271i | ||||||||
\(293\) | 7.93825i | 0.463757i | 0.972745 | + | 0.231879i | \(0.0744872\pi\) | ||||
−0.972745 | + | 0.231879i | \(0.925513\pi\) | |||||||
\(294\) | 3.19135 | − | 5.52759i | 0.186124 | − | 0.322375i | ||||
\(295\) | −8.17668 | + | 20.2356i | −0.476065 | + | 1.17816i | ||||
\(296\) | 0.0967881 | 0.00562569 | ||||||||
\(297\) | 0.377784i | 0.0219213i | ||||||||
\(298\) | 4.67526 | + | 2.69926i | 0.270831 | + | 0.156364i | ||||
\(299\) | −13.1914 | − | 22.8481i | −0.762876 | − | 1.32134i | ||||
\(300\) | 4.85138 | + | 1.21002i | 0.280094 | + | 0.0698603i | ||||
\(301\) | 0.168387 | + | 0.291654i | 0.00970565 | + | 0.0168107i | ||||
\(302\) | 7.85623 | − | 4.53580i | 0.452076 | − | 0.261006i | ||||
\(303\) | 17.0923i | 0.981929i | ||||||||
\(304\) | −1.46666 | + | 4.10474i | −0.0841188 | + | 0.235423i | ||||
\(305\) | 10.0874 | − | 1.41726i | 0.577604 | − | 0.0811523i | ||||
\(306\) | −1.41827 | − | 2.45651i | −0.0810770 | − | 0.140429i | ||||
\(307\) | 0.919506 | − | 0.530877i | 0.0524790 | − | 0.0302988i | −0.473531 | − | 0.880777i | \(-0.657021\pi\) |
0.526010 | + | 0.850478i | \(0.323687\pi\) | |||||||
\(308\) | 0.257052 | + | 0.148409i | 0.0146469 | + | 0.00845638i | ||||
\(309\) | 4.05877 | + | 7.02999i | 0.230895 | + | 0.399922i | ||||
\(310\) | 9.18150 | + | 3.71002i | 0.521474 | + | 0.210715i | ||||
\(311\) | 17.5210 | 0.993524 | 0.496762 | − | 0.867887i | \(-0.334522\pi\) | ||||
0.496762 | + | 0.867887i | \(0.334522\pi\) | |||||||
\(312\) | 2.90321i | 0.164362i | ||||||||
\(313\) | 10.6480 | + | 6.14764i | 0.601862 | + | 0.347485i | 0.769774 | − | 0.638317i | \(-0.220369\pi\) |
−0.167912 | + | 0.985802i | \(0.553702\pi\) | |||||||
\(314\) | −7.68421 | + | 13.3094i | −0.433645 | + | 0.751095i | ||||
\(315\) | 0.244431 | + | 1.73975i | 0.0137721 | + | 0.0980237i | ||||
\(316\) | −1.57136 | −0.0883959 | ||||||||
\(317\) | −20.7188 | − | 11.9620i | −1.16368 | − | 0.671852i | −0.211498 | − | 0.977379i | \(-0.567834\pi\) |
−0.952183 | + | 0.305527i | \(0.901167\pi\) | |||||||
\(318\) | 6.00443 | − | 3.46666i | 0.336712 | − | 0.194401i | ||||
\(319\) | −0.759487 | + | 1.31547i | −0.0425231 | + | 0.0736522i | ||||
\(320\) | 1.37659 | + | 1.76210i | 0.0769536 | + | 0.0985046i | ||||
\(321\) | −8.89062 | − | 15.3990i | −0.496226 | − | 0.859488i | ||||
\(322\) | − | 7.13981i | − | 0.397886i | ||||||
\(323\) | −11.6432 | − | 4.16024i | −0.647847 | − | 0.231482i | ||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | 10.0846 | − | 10.4411i | 0.559392 | − | 0.579170i | ||||
\(326\) | −3.65878 | − | 6.33719i | −0.202641 | − | 0.350985i | ||||
\(327\) | 1.25094 | + | 0.722230i | 0.0691771 | + | 0.0399394i | ||||
\(328\) | −2.48818 | + | 1.43655i | −0.137387 | + | 0.0793202i | ||||
\(329\) | 4.74842 | − | 8.22451i | 0.261789 | − | 0.453432i | ||||
\(330\) | 0.836535 | − | 0.117532i | 0.0460498 | − | 0.00646991i | ||||
\(331\) | 13.0810 | 0.718995 | 0.359497 | − | 0.933146i | \(-0.382948\pi\) | ||||
0.359497 | + | 0.933146i | \(0.382948\pi\) | |||||||
\(332\) | −2.38639 | − | 1.37778i | −0.130970 | − | 0.0756157i | ||||
\(333\) | 0.0838209 | + | 0.0483940i | 0.00459336 | + | 0.00265198i | ||||
\(334\) | 5.81135 | 0.317983 | ||||||||
\(335\) | −2.62867 | − | 18.7096i | −0.143620 | − | 1.02222i | ||||
\(336\) | −0.392840 | + | 0.680419i | −0.0214312 | + | 0.0371199i | ||||
\(337\) | −14.3953 | + | 8.31111i | −0.784160 | + | 0.452735i | −0.837903 | − | 0.545820i | \(-0.816218\pi\) |
0.0537427 | + | 0.998555i | \(0.482885\pi\) | |||||||
\(338\) | −3.95891 | − | 2.28568i | −0.215337 | − | 0.124325i | ||||
\(339\) | 7.15801 | + | 12.3980i | 0.388770 | + | 0.673369i | ||||
\(340\) | −4.99827 | + | 3.90474i | −0.271069 | + | 0.211764i | ||||
\(341\) | 1.67307 | 0.0906019 | ||||||||
\(342\) | −3.32254 | + | 2.82148i | −0.179662 | + | 0.152568i | ||||
\(343\) | − | 10.5145i | − | 0.567731i | ||||||
\(344\) | 0.214320 | + | 0.371213i | 0.0115553 | + | 0.0200144i | ||||
\(345\) | −12.5096 | − | 16.0130i | −0.673496 | − | 0.862109i | ||||
\(346\) | −4.36273 | + | 7.55647i | −0.234542 | + | 0.406238i | ||||
\(347\) | −4.62989 | + | 2.67307i | −0.248546 | + | 0.143498i | −0.619098 | − | 0.785314i | \(-0.712502\pi\) |
0.370552 | + | 0.928812i | \(0.379168\pi\) | |||||||
\(348\) | −3.48207 | − | 2.01037i | −0.186658 | − | 0.107767i | ||||
\(349\) | −0.882468 | −0.0472374 | −0.0236187 | − | 0.999721i | \(-0.507519\pi\) | ||||
−0.0236187 | + | 0.999721i | \(0.507519\pi\) | |||||||
\(350\) | 3.77631 | − | 1.08250i | 0.201852 | − | 0.0578620i | ||||
\(351\) | −1.45161 | + | 2.51426i | −0.0774810 | + | 0.134201i | ||||
\(352\) | 0.327171 | + | 0.188892i | 0.0174383 | + | 0.0100680i | ||||
\(353\) | − | 15.1032i | − | 0.803864i | −0.915669 | − | 0.401932i | \(-0.868339\pi\) | ||
0.915669 | − | 0.401932i | \(-0.131661\pi\) | |||||||
\(354\) | −9.76049 | −0.518764 | ||||||||
\(355\) | 9.83477 | − | 24.3390i | 0.521975 | − | 1.29178i | ||||
\(356\) | −5.96912 | − | 10.3388i | −0.316363 | − | 0.547957i | ||||
\(357\) | −1.93003 | − | 1.11430i | −0.102148 | − | 0.0589753i | ||||
\(358\) | 20.1183 | − | 11.6153i | 1.06329 | − | 0.613888i | ||||
\(359\) | −7.82394 | − | 13.5515i | −0.412932 | − | 0.715219i | 0.582277 | − | 0.812990i | \(-0.302162\pi\) |
−0.995209 | + | 0.0977715i | \(0.968829\pi\) | |||||||
\(360\) | 0.311108 | + | 2.21432i | 0.0163968 | + | 0.116705i | ||||
\(361\) | −3.07851 | + | 18.7489i | −0.162027 | + | 0.986786i | ||||
\(362\) | 7.54617i | 0.396618i | ||||||||
\(363\) | −9.40268 | + | 5.42864i | −0.493513 | + | 0.284930i | ||||
\(364\) | 1.14050 | + | 1.97540i | 0.0597783 | + | 0.103539i | ||||
\(365\) | 4.68598 | + | 1.89349i | 0.245275 | + | 0.0991097i | ||||
\(366\) | 2.27777 | + | 3.94521i | 0.119061 | + | 0.206220i | ||||
\(367\) | 27.8642 | + | 16.0874i | 1.45450 | + | 0.839756i | 0.998732 | − | 0.0503417i | \(-0.0160310\pi\) |
0.455769 | + | 0.890098i | \(0.349364\pi\) | |||||||
\(368\) | − | 9.08742i | − | 0.473715i | ||||||
\(369\) | −2.87310 | −0.149568 | ||||||||
\(370\) | 0.0810825 | − | 0.200662i | 0.00421528 | − | 0.0104319i | ||||
\(371\) | 2.72369 | − | 4.71757i | 0.141407 | − | 0.244924i | ||||
\(372\) | 4.42864i | 0.229614i | ||||||||
\(373\) | − | 15.1160i | − | 0.782677i | −0.920247 | − | 0.391338i | \(-0.872012\pi\) | ||
0.920247 | − | 0.391338i | \(-0.127988\pi\) | |||||||
\(374\) | −0.535799 | + | 0.928032i | −0.0277055 | + | 0.0479874i | ||||
\(375\) | 6.57277 | − | 9.04426i | 0.339417 | − | 0.467044i | ||||
\(376\) | 6.04371 | − | 10.4680i | 0.311681 | − | 0.539847i | ||||
\(377\) | −10.1092 | + | 5.83654i | −0.520649 | + | 0.300597i | ||||
\(378\) | −0.680419 | + | 0.392840i | −0.0349970 | + | 0.0202055i | ||||
\(379\) | 0.907658 | 0.0466232 | 0.0233116 | − | 0.999728i | \(-0.492579\pi\) | ||||
0.0233116 | + | 0.999728i | \(0.492579\pi\) | |||||||
\(380\) | 7.28133 | + | 6.47938i | 0.373524 | + | 0.332385i | ||||
\(381\) | −3.62867 | −0.185902 | ||||||||
\(382\) | −17.7276 | + | 10.2351i | −0.907025 | + | 0.523671i | ||||
\(383\) | −0.526479 | + | 0.303963i | −0.0269018 | + | 0.0155318i | −0.513391 | − | 0.858155i | \(-0.671611\pi\) |
0.486489 | + | 0.873687i | \(0.338277\pi\) | |||||||
\(384\) | −0.500000 | + | 0.866025i | −0.0255155 | + | 0.0441942i | ||||
\(385\) | 0.523023 | − | 0.408595i | 0.0266557 | − | 0.0208240i | ||||
\(386\) | −9.46198 | + | 16.3886i | −0.481602 | + | 0.834159i | ||||
\(387\) | 0.428639i | 0.0217890i | ||||||||
\(388\) | − | 3.44446i | − | 0.174866i | ||||||
\(389\) | −6.04048 | + | 10.4624i | −0.306265 | + | 0.530466i | −0.977542 | − | 0.210740i | \(-0.932413\pi\) |
0.671277 | + | 0.741206i | \(0.265746\pi\) | |||||||
\(390\) | 6.01897 | + | 2.43212i | 0.304782 | + | 0.123155i | ||||
\(391\) | 25.7768 | 1.30359 | ||||||||
\(392\) | − | 6.38271i | − | 0.322375i | ||||||
\(393\) | 14.5548 | + | 8.40321i | 0.734192 | + | 0.423886i | ||||
\(394\) | −0.865190 | − | 1.49855i | −0.0435876 | − | 0.0754960i | ||||
\(395\) | −1.31638 | + | 3.25776i | −0.0662343 | + | 0.163916i | ||||
\(396\) | 0.188892 | + | 0.327171i | 0.00949219 | + | 0.0164410i | ||||
\(397\) | −16.3351 | + | 9.43110i | −0.819837 | + | 0.473333i | −0.850360 | − | 0.526201i | \(-0.823616\pi\) |
0.0305230 | + | 0.999534i | \(0.490283\pi\) | |||||||
\(398\) | − | 15.0716i | − | 0.755471i | ||||||
\(399\) | −1.15233 | + | 3.22501i | −0.0576885 | + | 0.161453i | ||||
\(400\) | 4.80642 | − | 1.37778i | 0.240321 | − | 0.0688892i | ||||
\(401\) | −4.88739 | − | 8.46521i | −0.244065 | − | 0.422732i | 0.717804 | − | 0.696246i | \(-0.245148\pi\) |
−0.961868 | + | 0.273513i | \(0.911814\pi\) | |||||||
\(402\) | 7.31738 | − | 4.22469i | 0.364958 | − | 0.210708i | ||||
\(403\) | 11.1347 | + | 6.42864i | 0.554660 | + | 0.320233i | ||||
\(404\) | 8.54617 | + | 14.8024i | 0.425188 | + | 0.736447i | ||||
\(405\) | −0.837733 | + | 2.07321i | −0.0416273 | + | 0.103019i | ||||
\(406\) | −3.15902 | −0.156779 | ||||||||
\(407\) | − | 0.0365650i | − | 0.00181246i | ||||||
\(408\) | −2.45651 | − | 1.41827i | −0.121615 | − | 0.0702147i | ||||
\(409\) | −19.1916 | + | 33.2408i | −0.948963 | + | 1.64365i | −0.201348 | + | 0.979520i | \(0.564532\pi\) |
−0.747615 | + | 0.664133i | \(0.768801\pi\) | |||||||
\(410\) | 0.893844 | + | 6.36196i | 0.0441438 | + | 0.314195i | ||||
\(411\) | −2.19358 | −0.108201 | ||||||||
\(412\) | 7.02999 | + | 4.05877i | 0.346343 | + | 0.199961i | ||||
\(413\) | −6.64122 | + | 3.83431i | −0.326793 | + | 0.188674i | ||||
\(414\) | 4.54371 | − | 7.86994i | 0.223311 | − | 0.386786i | ||||
\(415\) | −4.85560 | + | 3.79328i | −0.238352 | + | 0.186205i | ||||
\(416\) | 1.45161 | + | 2.51426i | 0.0711708 | + | 0.123272i | ||||
\(417\) | − | 1.67307i | − | 0.0819306i | ||||||
\(418\) | 1.55071 | + | 0.554082i | 0.0758476 | + | 0.0271010i | ||||
\(419\) | −30.7560 | −1.50253 | −0.751266 | − | 0.660000i | \(-0.770556\pi\) | ||||
−0.751266 | + | 0.660000i | \(0.770556\pi\) | |||||||
\(420\) | 1.08156 | + | 1.38445i | 0.0527746 | + | 0.0675542i | ||||
\(421\) | 6.31433 | + | 10.9367i | 0.307742 | + | 0.533024i | 0.977868 | − | 0.209223i | \(-0.0670934\pi\) |
−0.670126 | + | 0.742247i | \(0.733760\pi\) | |||||||
\(422\) | −11.5320 | − | 6.65801i | −0.561370 | − | 0.324107i | ||||
\(423\) | 10.4680 | − | 6.04371i | 0.508972 | − | 0.293855i | ||||
\(424\) | 3.46666 | − | 6.00443i | 0.168356 | − | 0.291601i | ||||
\(425\) | 3.90813 | + | 13.6336i | 0.189572 | + | 0.661326i | ||||
\(426\) | 11.7397 | 0.568793 | ||||||||
\(427\) | 3.09968 | + | 1.78960i | 0.150004 | + | 0.0866047i | ||||
\(428\) | −15.3990 | − | 8.89062i | −0.744339 | − | 0.429744i | ||||
\(429\) | 1.09679 | 0.0529534 | ||||||||
\(430\) | 0.949145 | − | 0.133353i | 0.0457718 | − | 0.00643086i | ||||
\(431\) | 17.6763 | − | 30.6162i | 0.851437 | − | 1.47473i | −0.0284739 | − | 0.999595i | \(-0.509065\pi\) |
0.879911 | − | 0.475138i | \(-0.157602\pi\) | |||||||
\(432\) | −0.866025 | + | 0.500000i | −0.0416667 | + | 0.0240563i | ||||
\(433\) | 18.0052 | + | 10.3953i | 0.865274 | + | 0.499566i | 0.865775 | − | 0.500434i | \(-0.166826\pi\) |
−0.000500727 | 1.00000i | \(0.500159\pi\) | ||||||||
\(434\) | 1.73975 | + | 3.01333i | 0.0835105 | + | 0.144645i | ||||
\(435\) | −7.08497 | + | 5.53490i | −0.339698 | + | 0.265378i | ||||
\(436\) | 1.44446 | 0.0691771 | ||||||||
\(437\) | −7.10822 | − | 38.9681i | −0.340032 | − | 1.86410i | ||||
\(438\) | 2.26025i | 0.107999i | ||||||||
\(439\) | −1.96444 | − | 3.40251i | −0.0937576 | − | 0.162393i | 0.815332 | − | 0.578994i | \(-0.196555\pi\) |
−0.909089 | + | 0.416601i | \(0.863221\pi\) | |||||||
\(440\) | 0.665695 | − | 0.520053i | 0.0317358 | − | 0.0247926i | ||||
\(441\) | 3.19135 | − | 5.52759i | 0.151969 | − | 0.263218i | ||||
\(442\) | −7.13177 | + | 4.11753i | −0.339224 | + | 0.195851i | ||||
\(443\) | −1.38265 | − | 0.798275i | −0.0656918 | − | 0.0379272i | 0.466794 | − | 0.884366i | \(-0.345409\pi\) |
−0.532486 | + | 0.846439i | \(0.678742\pi\) | |||||||
\(444\) | 0.0967881 | 0.00459336 | ||||||||
\(445\) | −26.4351 | + | 3.71408i | −1.25314 | + | 0.176064i | ||||
\(446\) | 9.58419 | − | 16.6003i | 0.453825 | − | 0.786047i | ||||
\(447\) | 4.67526 | + | 2.69926i | 0.221132 | + | 0.127671i | ||||
\(448\) | 0.785680i | 0.0371199i | ||||||||
\(449\) | 14.4588 | 0.682351 | 0.341175 | − | 0.940000i | \(-0.389175\pi\) | ||||
0.341175 | + | 0.940000i | \(0.389175\pi\) | |||||||
\(450\) | 4.85138 | + | 1.21002i | 0.228696 | + | 0.0570407i | ||||
\(451\) | 0.542706 | + | 0.939995i | 0.0255550 | + | 0.0442626i | ||||
\(452\) | 12.3980 | + | 7.15801i | 0.583155 | + | 0.336685i | ||||
\(453\) | 7.85623 | − | 4.53580i | 0.369118 | − | 0.213110i | ||||
\(454\) | −3.44123 | − | 5.96039i | −0.161505 | − | 0.279735i | ||||
\(455\) | 5.05086 | − | 0.709636i | 0.236788 | − | 0.0332682i | ||||
\(456\) | −1.46666 | + | 4.10474i | −0.0686827 | + | 0.192222i | ||||
\(457\) | − | 28.9052i | − | 1.35213i | −0.736842 | − | 0.676065i | \(-0.763684\pi\) | ||
0.736842 | − | 0.676065i | \(-0.236316\pi\) | |||||||
\(458\) | −11.9046 | + | 6.87310i | −0.556264 | + | 0.321159i | ||||
\(459\) | −1.41827 | − | 2.45651i | −0.0661991 | − | 0.114660i | ||||
\(460\) | −18.8401 | − | 7.61283i | −0.878426 | − | 0.354950i | ||||
\(461\) | −1.22369 | − | 2.11949i | −0.0569928 | − | 0.0987145i | 0.836121 | − | 0.548545i | \(-0.184818\pi\) |
−0.893114 | + | 0.449830i | \(0.851485\pi\) | |||||||
\(462\) | 0.257052 | + | 0.148409i | 0.0119591 | + | 0.00690460i | ||||
\(463\) | 7.67460i | 0.356669i | 0.983970 | + | 0.178335i | \(0.0570709\pi\) | ||||
−0.983970 | + | 0.178335i | \(0.942929\pi\) | |||||||
\(464\) | −4.02074 | −0.186658 | ||||||||
\(465\) | 9.18150 | + | 3.71002i | 0.425782 | + | 0.172048i | ||||
\(466\) | −3.39853 | + | 5.88642i | −0.157434 | + | 0.272683i | ||||
\(467\) | − | 9.78123i | − | 0.452622i | −0.974055 | − | 0.226311i | \(-0.927334\pi\) | ||
0.974055 | − | 0.226311i | \(-0.0726665\pi\) | |||||||
\(468\) | 2.90321i | 0.134201i | ||||||||
\(469\) | 3.31926 | − | 5.74912i | 0.153269 | − | 0.265470i | ||||
\(470\) | −16.6394 | − | 21.2993i | −0.767518 | − | 0.982463i | ||||
\(471\) | −7.68421 | + | 13.3094i | −0.354070 | + | 0.613267i | ||||
\(472\) | −8.45283 | + | 4.88025i | −0.389073 | + | 0.224632i | ||||
\(473\) | 0.140238 | − | 0.0809666i | 0.00644817 | − | 0.00372285i | ||||
\(474\) | −1.57136 | −0.0721750 | ||||||||
\(475\) | 19.5329 | − | 9.66774i | 0.896232 | − | 0.443586i | ||||
\(476\) | −2.22861 | −0.102148 | ||||||||
\(477\) | 6.00443 | − | 3.46666i | 0.274924 | − | 0.158728i | ||||
\(478\) | 9.40268 | − | 5.42864i | 0.430069 | − | 0.248300i | ||||
\(479\) | −16.9716 | + | 29.3956i | −0.775451 | + | 1.34312i | 0.159089 | + | 0.987264i | \(0.449144\pi\) |
−0.934540 | + | 0.355857i | \(0.884189\pi\) | |||||||
\(480\) | 1.37659 | + | 1.76210i | 0.0628323 | + | 0.0804286i | ||||
\(481\) | 0.140498 | − | 0.243350i | 0.00640616 | − | 0.0110958i | ||||
\(482\) | − | 9.68736i | − | 0.441247i | ||||||
\(483\) | − | 7.13981i | − | 0.324872i | ||||||
\(484\) | −5.42864 | + | 9.40268i | −0.246756 | + | 0.427395i | ||||
\(485\) | −7.14109 | − | 2.88554i | −0.324260 | − | 0.131025i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 33.8780i | 1.53516i | 0.640953 | + | 0.767580i | \(0.278539\pi\) | ||||
−0.640953 | + | 0.767580i | \(0.721461\pi\) | |||||||
\(488\) | 3.94521 | + | 2.27777i | 0.178591 | + | 0.103110i | ||||
\(489\) | −3.65878 | − | 6.33719i | −0.165456 | − | 0.286578i | ||||
\(490\) | −13.2327 | − | 5.34700i | −0.597792 | − | 0.241553i | ||||
\(491\) | 20.5622 | + | 35.6148i | 0.927960 | + | 1.60727i | 0.786729 | + | 0.617298i | \(0.211773\pi\) |
0.141231 | + | 0.989977i | \(0.454894\pi\) | |||||||
\(492\) | −2.48818 | + | 1.43655i | −0.112176 | + | 0.0647647i | ||||
\(493\) | − | 11.4050i | − | 0.513655i | ||||||
\(494\) | 8.19135 | + | 9.64603i | 0.368546 | + | 0.433995i | ||||
\(495\) | 0.836535 | − | 0.117532i | 0.0375995 | − | 0.00528266i | ||||
\(496\) | 2.21432 | + | 3.83531i | 0.0994259 | + | 0.172211i | ||||
\(497\) | 7.98795 | − | 4.61184i | 0.358308 | − | 0.206869i | ||||
\(498\) | −2.38639 | − | 1.37778i | −0.106937 | − | 0.0617400i | ||||
\(499\) | 9.98987 | + | 17.3030i | 0.447208 | + | 0.774587i | 0.998203 | − | 0.0599217i | \(-0.0190851\pi\) |
−0.550995 | + | 0.834508i | \(0.685752\pi\) | |||||||
\(500\) | 1.17006 | − | 11.1189i | 0.0523267 | − | 0.497254i | ||||
\(501\) | 5.81135 | 0.259632 | ||||||||
\(502\) | 15.0923i | 0.673604i | ||||||||
\(503\) | 18.2708 | + | 10.5486i | 0.814653 | + | 0.470340i | 0.848569 | − | 0.529084i | \(-0.177465\pi\) |
−0.0339160 | + | 0.999425i | \(0.510798\pi\) | |||||||
\(504\) | −0.392840 | + | 0.680419i | −0.0174985 | + | 0.0303083i | ||||
\(505\) | 37.8479 | − | 5.31756i | 1.68421 | − | 0.236628i | ||||
\(506\) | −3.43309 | −0.152619 | ||||||||
\(507\) | −3.95891 | − | 2.28568i | −0.175822 | − | 0.101511i | ||||
\(508\) | −3.14252 | + | 1.81433i | −0.139427 | + | 0.0804981i | ||||
\(509\) | −11.3620 | + | 19.6795i | −0.503610 | + | 0.872278i | 0.496381 | + | 0.868105i | \(0.334662\pi\) |
−0.999991 | + | 0.00417367i | \(0.998671\pi\) | |||||||
\(510\) | −4.99827 | + | 3.90474i | −0.221327 | + | 0.172905i | ||||
\(511\) | 0.887918 | + | 1.53792i | 0.0392792 | + | 0.0680335i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −3.32254 | + | 2.82148i | −0.146694 | + | 0.124571i | ||||
\(514\) | −22.8256 | −1.00680 | ||||||||
\(515\) | 14.3039 | − | 11.1745i | 0.630306 | − | 0.492407i | ||||
\(516\) | 0.214320 | + | 0.371213i | 0.00943490 | + | 0.0163417i | ||||
\(517\) | −3.95465 | − | 2.28322i | −0.173925 | − | 0.100416i | ||||
\(518\) | 0.0658565 | − | 0.0380222i | 0.00289357 | − | 0.00167060i | ||||
\(519\) | −4.36273 | + | 7.55647i | −0.191503 | + | 0.331692i | ||||
\(520\) | 6.42864 | − | 0.903212i | 0.281914 | − | 0.0396085i | ||||
\(521\) | 29.0923 | 1.27456 | 0.637279 | − | 0.770633i | \(-0.280060\pi\) | ||||
0.637279 | + | 0.770633i | \(0.280060\pi\) | |||||||
\(522\) | −3.48207 | − | 2.01037i | −0.152406 | − | 0.0879916i | ||||
\(523\) | 6.84186 | + | 3.95015i | 0.299174 | + | 0.172728i | 0.642072 | − | 0.766645i | \(-0.278075\pi\) |
−0.342898 | + | 0.939373i | \(0.611409\pi\) | |||||||
\(524\) | 16.8064 | 0.734192 | ||||||||
\(525\) | 3.77631 | − | 1.08250i | 0.164812 | − | 0.0472441i | ||||
\(526\) | −6.05554 | + | 10.4885i | −0.264034 | + | 0.457320i | ||||
\(527\) | −10.8790 | + | 6.28100i | −0.473897 | + | 0.273604i | ||||
\(528\) | 0.327171 | + | 0.188892i | 0.0142383 | + | 0.00822048i | ||||
\(529\) | 29.7906 | + | 51.5988i | 1.29524 | + | 2.24343i | ||||
\(530\) | −9.54432 | − | 12.2172i | −0.414579 | − | 0.530683i | ||||
\(531\) | −9.76049 | −0.423569 | ||||||||
\(532\) | 0.614563 | + | 3.36911i | 0.0266447 | + | 0.146069i | ||||
\(533\) | 8.34122i | 0.361298i | ||||||||
\(534\) | −5.96912 | − | 10.3388i | −0.258309 | − | 0.447405i | ||||
\(535\) | −31.3324 | + | 24.4774i | −1.35462 | + | 1.05825i | ||||
\(536\) | 4.22469 | − | 7.31738i | 0.182479 | − | 0.316063i | ||||
\(537\) | 20.1183 | − | 11.6153i | 0.868169 | − | 0.501238i | ||||
\(538\) | −21.8529 | − | 12.6168i | −0.942145 | − | 0.543947i | ||||
\(539\) | −2.41129 | −0.103861 | ||||||||
\(540\) | 0.311108 | + | 2.21432i | 0.0133879 | + | 0.0952891i | ||||
\(541\) | 10.3160 | − | 17.8679i | 0.443521 | − | 0.768201i | −0.554427 | − | 0.832232i | \(-0.687063\pi\) |
0.997948 | + | 0.0640318i | \(0.0203959\pi\) | |||||||
\(542\) | −26.7865 | − | 15.4652i | −1.15058 | − | 0.664287i | ||||
\(543\) | 7.54617i | 0.323837i | ||||||||
\(544\) | −2.83654 | −0.121615 | ||||||||
\(545\) | 1.21007 | − | 2.99467i | 0.0518338 | − | 0.128278i | ||||
\(546\) | 1.14050 | + | 1.97540i | 0.0488088 | + | 0.0845393i | ||||
\(547\) | 7.43965 | + | 4.29529i | 0.318097 | + | 0.183653i | 0.650544 | − | 0.759469i | \(-0.274541\pi\) |
−0.332447 | + | 0.943122i | \(0.607874\pi\) | |||||||
\(548\) | −1.89969 | + | 1.09679i | −0.0811508 | + | 0.0468525i | ||||
\(549\) | 2.27777 | + | 3.94521i | 0.0972128 | + | 0.168378i | ||||
\(550\) | −0.520505 | − | 1.81579i | −0.0221944 | − | 0.0774256i | ||||
\(551\) | −17.2415 | + | 3.14504i | −0.734513 | + | 0.133983i | ||||
\(552\) | − | 9.08742i | − | 0.386786i | ||||||
\(553\) | −1.06918 | + | 0.617293i | −0.0454663 | + | 0.0262500i | ||||
\(554\) | 9.74689 | + | 16.8821i | 0.414106 | + | 0.717252i | ||||
\(555\) | 0.0810825 | − | 0.200662i | 0.00344176 | − | 0.00851763i | ||||
\(556\) | −0.836535 | − | 1.44892i | −0.0354770 | − | 0.0614480i | ||||
\(557\) | 21.3209 | + | 12.3097i | 0.903397 | + | 0.521577i | 0.878301 | − | 0.478108i | \(-0.158677\pi\) |
0.0250964 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(558\) | 4.42864i | 0.187479i | ||||||||
\(559\) | 1.24443 | 0.0526338 | ||||||||
\(560\) | 1.62888 | + | 0.658190i | 0.0688328 | + | 0.0278136i | ||||
\(561\) | −0.535799 | + | 0.928032i | −0.0226215 | + | 0.0391815i | ||||
\(562\) | − | 7.43509i | − | 0.313630i | ||||||
\(563\) | − | 33.6958i | − | 1.42011i | −0.704146 | − | 0.710055i | \(-0.748670\pi\) | ||
0.704146 | − | 0.710055i | \(-0.251330\pi\) | |||||||
\(564\) | 6.04371 | − | 10.4680i | 0.254486 | − | 0.440783i | ||||
\(565\) | 25.2263 | − | 19.7073i | 1.06128 | − | 0.829091i | ||||
\(566\) | −0.857279 | + | 1.48485i | −0.0360341 | + | 0.0624129i | ||||
\(567\) | −0.680419 | + | 0.392840i | −0.0285749 | + | 0.0164977i | ||||
\(568\) | 10.1669 | − | 5.86987i | 0.426594 | − | 0.246294i | ||||
\(569\) | 3.59703 | 0.150795 | 0.0753976 | − | 0.997154i | \(-0.475977\pi\) | ||||
0.0753976 | + | 0.997154i | \(0.475977\pi\) | |||||||
\(570\) | 7.28133 | + | 6.47938i | 0.304981 | + | 0.271391i | ||||
\(571\) | 22.2623 | 0.931647 | 0.465823 | − | 0.884878i | \(-0.345758\pi\) | ||||
0.465823 | + | 0.884878i | \(0.345758\pi\) | |||||||
\(572\) | 0.949846 | − | 0.548394i | 0.0397151 | − | 0.0229295i | ||||
\(573\) | −17.7276 | + | 10.2351i | −0.740583 | + | 0.427576i | ||||
\(574\) | −1.12867 | + | 1.95491i | −0.0471097 | + | 0.0815965i | ||||
\(575\) | −31.5660 | + | 32.6821i | −1.31639 | + | 1.36294i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 34.7719i | 1.44757i | 0.690025 | + | 0.723786i | \(0.257600\pi\) | ||||
−0.690025 | + | 0.723786i | \(0.742400\pi\) | |||||||
\(578\) | 8.95407i | 0.372440i | ||||||||
\(579\) | −9.46198 | + | 16.3886i | −0.393226 | + | 0.681088i | ||||
\(580\) | −3.36831 | + | 8.33585i | −0.139861 | + | 0.346127i | ||||
\(581\) | −2.16500 | −0.0898192 | ||||||||
\(582\) | − | 3.44446i | − | 0.142777i | ||||||
\(583\) | −2.26838 | − | 1.30965i | −0.0939468 | − | 0.0542402i | ||||
\(584\) | 1.13013 | + | 1.95744i | 0.0467650 | + | 0.0809993i | ||||
\(585\) | 6.01897 | + | 2.43212i | 0.248854 | + | 0.100556i | ||||
\(586\) | 3.96912 | + | 6.87472i | 0.163963 | + | 0.283992i | ||||
\(587\) | 21.7306 | − | 12.5462i | 0.896918 | − | 0.517836i | 0.0207191 | − | 0.999785i | \(-0.493404\pi\) |
0.876199 | + | 0.481949i | \(0.160071\pi\) | |||||||
\(588\) | − | 6.38271i | − | 0.263218i | ||||||
\(589\) | 12.4953 | + | 14.7143i | 0.514861 | + | 0.606293i | ||||
\(590\) | 3.03657 | + | 21.6128i | 0.125013 | + | 0.889787i | ||||
\(591\) | −0.865190 | − | 1.49855i | −0.0355891 | − | 0.0616422i | ||||
\(592\) | 0.0838209 | − | 0.0483940i | 0.00344502 | − | 0.00198898i | ||||
\(593\) | 36.9025 | + | 21.3057i | 1.51540 | + | 0.874919i | 0.999837 | + | 0.0180690i | \(0.00575185\pi\) |
0.515567 | + | 0.856850i | \(0.327581\pi\) | |||||||
\(594\) | 0.188892 | + | 0.327171i | 0.00775034 | + | 0.0134240i | ||||
\(595\) | −1.86698 | + | 4.62038i | −0.0765387 | + | 0.189417i | ||||
\(596\) | 5.39853 | 0.221132 | ||||||||
\(597\) | − | 15.0716i | − | 0.616839i | ||||||
\(598\) | −22.8481 | − | 13.1914i | −0.934328 | − | 0.539435i | ||||
\(599\) | −21.3652 | + | 37.0056i | −0.872958 | + | 1.51201i | −0.0140358 | + | 0.999901i | \(0.504468\pi\) |
−0.858922 | + | 0.512106i | \(0.828865\pi\) | |||||||
\(600\) | 4.80642 | − | 1.37778i | 0.196221 | − | 0.0562478i | ||||
\(601\) | −40.1481 | −1.63768 | −0.818838 | − | 0.574025i | \(-0.805381\pi\) | ||||
−0.818838 | + | 0.574025i | \(0.805381\pi\) | |||||||
\(602\) | 0.291654 | + | 0.168387i | 0.0118869 | + | 0.00686293i | ||||
\(603\) | 7.31738 | − | 4.22469i | 0.297987 | − | 0.172043i | ||||
\(604\) | 4.53580 | − | 7.85623i | 0.184559 | − | 0.319666i | ||||
\(605\) | 14.9460 | + | 19.1316i | 0.607641 | + | 0.777812i | ||||
\(606\) | 8.54617 | + | 14.8024i | 0.347164 | + | 0.601307i | ||||
\(607\) | 36.0988i | 1.46520i | 0.680657 | + | 0.732602i | \(0.261695\pi\) | ||||
−0.680657 | + | 0.732602i | \(0.738305\pi\) | |||||||
\(608\) | 0.782204 | + | 4.28814i | 0.0317226 | + | 0.173907i | ||||
\(609\) | −3.15902 | −0.128010 | ||||||||
\(610\) | 8.02733 | − | 6.27110i | 0.325017 | − | 0.253909i | ||||
\(611\) | −17.5462 | − | 30.3909i | −0.709842 | − | 1.22948i | ||||
\(612\) | −2.45651 | − | 1.41827i | −0.0992986 | − | 0.0573301i | ||||
\(613\) | 21.8144 | − | 12.5946i | 0.881076 | − | 0.508690i | 0.0100632 | − | 0.999949i | \(-0.496797\pi\) |
0.871013 | + | 0.491260i | \(0.163463\pi\) | |||||||
\(614\) | 0.530877 | − | 0.919506i | 0.0214245 | − | 0.0371083i | ||||
\(615\) | 0.893844 | + | 6.36196i | 0.0360433 | + | 0.256539i | ||||
\(616\) | 0.296818 | 0.0119591 | ||||||||
\(617\) | 2.97740 | + | 1.71900i | 0.119866 | + | 0.0692045i | 0.558734 | − | 0.829347i | \(-0.311287\pi\) |
−0.438868 | + | 0.898551i | \(0.644621\pi\) | |||||||
\(618\) | 7.02999 | + | 4.05877i | 0.282788 | + | 0.163268i | ||||
\(619\) | 20.7397 | 0.833601 | 0.416800 | − | 0.908998i | \(-0.363151\pi\) | ||||
0.416800 | + | 0.908998i | \(0.363151\pi\) | |||||||
\(620\) | 9.80642 | − | 1.37778i | 0.393835 | − | 0.0553332i | ||||
\(621\) | 4.54371 | − | 7.86994i | 0.182333 | − | 0.315810i | ||||
\(622\) | 15.1736 | − | 8.76049i | 0.608407 | − | 0.351264i | ||||
\(623\) | −8.12301 | − | 4.68982i | −0.325442 | − | 0.187894i | ||||
\(624\) | 1.45161 | + | 2.51426i | 0.0581107 | + | 0.100651i | ||||
\(625\) | −22.0717 | − | 11.7405i | −0.882869 | − | 0.469619i | ||||
\(626\) | 12.2953 | 0.491418 | ||||||||
\(627\) | 1.55071 | + | 0.554082i | 0.0619293 | + | 0.0221279i | ||||
\(628\) | 15.3684i | 0.613267i | ||||||||
\(629\) | 0.137271 | + | 0.237761i | 0.00547337 | + | 0.00948015i | ||||
\(630\) | 1.08156 | + | 1.38445i | 0.0430903 | + | 0.0551578i | ||||
\(631\) | −17.1629 | + | 29.7271i | −0.683246 | + | 1.18342i | 0.290739 | + | 0.956802i | \(0.406099\pi\) |
−0.973985 | + | 0.226614i | \(0.927234\pi\) | |||||||
\(632\) | −1.36084 | + | 0.785680i | −0.0541312 | + | 0.0312527i | ||||
\(633\) | −11.5320 | − | 6.65801i | −0.458357 | − | 0.264632i | ||||
\(634\) | −23.9240 | −0.950142 | ||||||||
\(635\) | 1.12891 | + | 8.03503i | 0.0447993 | + | 0.318861i | ||||
\(636\) | 3.46666 | − | 6.00443i | 0.137462 | − | 0.238091i | ||||
\(637\) | −16.0478 | − | 9.26517i | −0.635835 | − | 0.367100i | ||||
\(638\) | 1.51897i | 0.0601368i | ||||||||
\(639\) | 11.7397 | 0.464417 | ||||||||
\(640\) | 2.07321 | + | 0.837733i | 0.0819509 | + | 0.0331143i | ||||
\(641\) | 1.54125 | + | 2.66952i | 0.0608757 | + | 0.105440i | 0.894857 | − | 0.446353i | \(-0.147277\pi\) |
−0.833981 | + | 0.551793i | \(0.813944\pi\) | |||||||
\(642\) | −15.3990 | − | 8.89062i | −0.607750 | − | 0.350885i | ||||
\(643\) | −27.9069 | + | 16.1121i | −1.10054 | + | 0.635398i | −0.936363 | − | 0.351032i | \(-0.885831\pi\) |
−0.164179 | + | 0.986431i | \(0.552497\pi\) | |||||||
\(644\) | −3.56990 | − | 6.18325i | −0.140674 | − | 0.243654i | ||||
\(645\) | 0.949145 | − | 0.133353i | 0.0373725 | − | 0.00525077i | ||||
\(646\) | −12.1635 | + | 2.21875i | −0.478565 | + | 0.0872956i | ||||
\(647\) | 4.90813i | 0.192959i | 0.995335 | + | 0.0964793i | \(0.0307582\pi\) | ||||
−0.995335 | + | 0.0964793i | \(0.969242\pi\) | |||||||
\(648\) | −0.866025 | + | 0.500000i | −0.0340207 | + | 0.0196419i | ||||
\(649\) | 1.84368 | + | 3.19335i | 0.0723708 | + | 0.125350i | ||||
\(650\) | 3.51293 | − | 14.0846i | 0.137789 | − | 0.552443i | ||||
\(651\) | 1.73975 | + | 3.01333i | 0.0681861 | + | 0.118102i | ||||
\(652\) | −6.33719 | − | 3.65878i | −0.248184 | − | 0.143289i | ||||
\(653\) | 41.4405i | 1.62169i | 0.585260 | + | 0.810846i | \(0.300993\pi\) | ||||
−0.585260 | + | 0.810846i | \(0.699007\pi\) | |||||||
\(654\) | 1.44446 | 0.0564829 | ||||||||
\(655\) | 14.0793 | − | 34.8433i | 0.550123 | − | 1.36144i | ||||
\(656\) | −1.43655 | + | 2.48818i | −0.0560879 | + | 0.0971470i | ||||
\(657\) | 2.26025i | 0.0881809i | ||||||||
\(658\) | − | 9.49685i | − | 0.370226i | ||||||
\(659\) | −0.665688 | + | 1.15300i | −0.0259315 | + | 0.0449147i | −0.878700 | − | 0.477375i | \(-0.841589\pi\) |
0.852768 | + | 0.522289i | \(0.174922\pi\) | |||||||
\(660\) | 0.665695 | − | 0.520053i | 0.0259121 | − | 0.0202430i | ||||
\(661\) | 18.1891 | − | 31.5045i | 0.707475 | − | 1.22538i | −0.258316 | − | 0.966061i | \(-0.583167\pi\) |
0.965791 | − | 0.259322i | \(-0.0834992\pi\) | |||||||
\(662\) | 11.3284 | − | 6.54048i | 0.440293 | − | 0.254203i | ||||
\(663\) | −7.13177 | + | 4.11753i | −0.276975 | + | 0.159912i | ||||
\(664\) | −2.75557 | −0.106937 | ||||||||
\(665\) | 7.49971 | + | 1.54829i | 0.290826 | + | 0.0600403i | ||||
\(666\) | 0.0967881 | 0.00375046 | ||||||||
\(667\) | 31.6430 | − | 18.2691i | 1.22522 | − | 0.707382i | ||||
\(668\) | 5.03277 | − | 2.90567i | 0.194724 | − | 0.112424i | ||||
\(669\) | 9.58419 | − | 16.6003i | 0.370546 | − | 0.641805i | ||||
\(670\) | −11.6313 | − | 14.8887i | −0.449357 | − | 0.575200i | ||||
\(671\) | 0.860506 | − | 1.49044i | 0.0332195 | − | 0.0575378i | ||||
\(672\) | 0.785680i | 0.0303083i | ||||||||
\(673\) | − | 38.8069i | − | 1.49590i | −0.663757 | − | 0.747948i | \(-0.731039\pi\) | ||
0.663757 | − | 0.747948i | \(-0.268961\pi\) | |||||||
\(674\) | −8.31111 | + | 14.3953i | −0.320132 | + | 0.554485i | ||||
\(675\) | 4.85138 | + | 1.21002i | 0.186730 | + | 0.0465735i | ||||
\(676\) | −4.57136 | −0.175822 | ||||||||
\(677\) | 31.6242i | 1.21542i | 0.794160 | + | 0.607709i | \(0.207911\pi\) | ||||
−0.794160 | + | 0.607709i | \(0.792089\pi\) | |||||||
\(678\) | 12.3980 | + | 7.15801i | 0.476144 | + | 0.274902i | ||||
\(679\) | −1.35312 | − | 2.34368i | −0.0519281 | − | 0.0899421i | ||||
\(680\) | −2.37626 | + | 5.88074i | −0.0911253 | + | 0.225516i | ||||
\(681\) | −3.44123 | − | 5.96039i | −0.131868 | − | 0.228403i | ||||
\(682\) | 1.44892 | − | 0.836535i | 0.0554821 | − | 0.0320326i | ||||
\(683\) | 24.2000i | 0.925988i | 0.886361 | + | 0.462994i | \(0.153225\pi\) | ||||
−0.886361 | + | 0.462994i | \(0.846775\pi\) | |||||||
\(684\) | −1.46666 | + | 4.10474i | −0.0560792 | + | 0.156949i | ||||
\(685\) | 0.682439 | + | 4.85728i | 0.0260746 | + | 0.185587i | ||||
\(686\) | −5.25726 | − | 9.10585i | −0.200723 | − | 0.347663i | ||||
\(687\) | −11.9046 | + | 6.87310i | −0.454187 | + | 0.262225i | ||||
\(688\) | 0.371213 | + | 0.214320i | 0.0141524 | + | 0.00817086i | ||||
\(689\) | −10.0645 | − | 17.4321i | −0.383425 | − | 0.664112i | ||||
\(690\) | −18.8401 | − | 7.61283i | −0.717232 | − | 0.289815i | ||||
\(691\) | −21.1782 | −0.805658 | −0.402829 | − | 0.915275i | \(-0.631973\pi\) | ||||
−0.402829 | + | 0.915275i | \(0.631973\pi\) | |||||||
\(692\) | 8.72546i | 0.331692i | ||||||||
\(693\) | 0.257052 | + | 0.148409i | 0.00976459 | + | 0.00563759i | ||||
\(694\) | −2.67307 | + | 4.62989i | −0.101468 | + | 0.175748i | ||||
\(695\) | −3.70471 | + | 0.520505i | −0.140528 | + | 0.0197439i | ||||
\(696\) | −4.02074 | −0.152406 | ||||||||
\(697\) | −7.05780 | − | 4.07483i | −0.267333 | − | 0.154345i | ||||
\(698\) | −0.764240 | + | 0.441234i | −0.0289269 | + | 0.0167010i | ||||
\(699\) | −3.39853 | + | 5.88642i | −0.128544 | + | 0.222645i | ||||
\(700\) | 2.72913 | − | 2.82563i | 0.103152 | − | 0.106799i | ||||
\(701\) | 11.1635 | + | 19.3357i | 0.421638 | + | 0.730299i | 0.996100 | − | 0.0882326i | \(-0.0281219\pi\) |
−0.574462 | + | 0.818531i | \(0.694789\pi\) | |||||||
\(702\) | 2.90321i | 0.109575i | ||||||||
\(703\) | 0.321582 | − | 0.273086i | 0.0121287 | − | 0.0102996i | ||||
\(704\) | 0.377784 | 0.0142383 | ||||||||
\(705\) | −16.6394 | − | 21.2993i | −0.626676 | − | 0.802177i | ||||
\(706\) | −7.55162 | − | 13.0798i | −0.284209 | − | 0.492264i | ||||
\(707\) | 11.6300 | + | 6.71456i | 0.437389 | + | 0.252527i | ||||
\(708\) | −8.45283 | + | 4.88025i | −0.317677 | + | 0.183411i | ||||
\(709\) | −11.2733 | + | 19.5260i | −0.423379 | + | 0.733313i | −0.996267 | − | 0.0863198i | \(-0.972489\pi\) |
0.572889 | + | 0.819633i | \(0.305823\pi\) | |||||||
\(710\) | −3.65233 | − | 25.9956i | −0.137069 | − | 0.975596i | ||||
\(711\) | −1.57136 | −0.0589306 | ||||||||
\(712\) | −10.3388 | − | 5.96912i | −0.387464 | − | 0.223702i | ||||
\(713\) | −34.8531 | − | 20.1225i | −1.30526 | − | 0.753592i | ||||
\(714\) | −2.22861 | −0.0834036 | ||||||||
\(715\) | −0.341219 | − | 2.42864i | −0.0127609 | − | 0.0908260i | ||||
\(716\) | 11.6153 | − | 20.1183i | 0.434084 | − | 0.751856i | ||||
\(717\) | 9.40268 | − | 5.42864i | 0.351149 | − | 0.202736i | ||||
\(718\) | −13.5515 | − | 7.82394i | −0.505736 | − | 0.291987i | ||||
\(719\) | −16.3111 | − | 28.2517i | −0.608302 | − | 1.05361i | −0.991520 | − | 0.129952i | \(-0.958518\pi\) |
0.383219 | − | 0.923658i | \(-0.374816\pi\) | |||||||
\(720\) | 1.37659 | + | 1.76210i | 0.0513024 | + | 0.0656697i | ||||
\(721\) | 6.37778 | 0.237521 | ||||||||
\(722\) | 6.70841 | + | 17.7763i | 0.249661 | + | 0.661566i | ||||
\(723\) | − | 9.68736i | − | 0.360277i | ||||||
\(724\) | 3.77309 | + | 6.53518i | 0.140226 | + | 0.242878i | ||||
\(725\) | 14.4602 | + | 13.9664i | 0.537040 | + | 0.518700i | ||||
\(726\) | −5.42864 | + | 9.40268i | −0.201476 | + | 0.348966i | ||||
\(727\) | 32.6741 | − | 18.8644i | 1.21182 | − | 0.699643i | 0.248662 | − | 0.968590i | \(-0.420009\pi\) |
0.963155 | + | 0.268948i | \(0.0866758\pi\) | |||||||
\(728\) | 1.97540 | + | 1.14050i | 0.0732132 | + | 0.0422697i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 5.00492 | − | 0.703182i | 0.185240 | − | 0.0260259i | ||||
\(731\) | −0.607926 | + | 1.05296i | −0.0224849 | + | 0.0389451i | ||||
\(732\) | 3.94521 | + | 2.27777i | 0.145819 | + | 0.0841888i | ||||
\(733\) | 47.5531i | 1.75641i | 0.478281 | + | 0.878207i | \(0.341260\pi\) | ||||
−0.478281 | + | 0.878207i | \(0.658740\pi\) | |||||||
\(734\) | 32.1748 | 1.18760 | ||||||||
\(735\) | −13.2327 | − | 5.34700i | −0.488095 | − | 0.197227i | ||||
\(736\) | −4.54371 | − | 7.86994i | −0.167483 | − | 0.290090i | ||||
\(737\) | −2.76439 | − | 1.59602i | −0.101828 | − | 0.0587902i | ||||
\(738\) | −2.48818 | + | 1.43655i | −0.0915911 | + | 0.0528801i | ||||
\(739\) | −14.6602 | − | 25.3923i | −0.539286 | − | 0.934070i | −0.998943 | − | 0.0459735i | \(-0.985361\pi\) |
0.459657 | − | 0.888096i | \(-0.347972\pi\) | |||||||
\(740\) | −0.0301115 | − | 0.214320i | −0.00110692 | − | 0.00787855i | ||||
\(741\) | 8.19135 | + | 9.64603i | 0.300917 | + | 0.354356i | ||||
\(742\) | − | 5.44738i | − | 0.199979i | ||||||
\(743\) | 7.39176 | − | 4.26764i | 0.271177 | − | 0.156564i | −0.358245 | − | 0.933628i | \(-0.616625\pi\) |
0.629423 | + | 0.777063i | \(0.283291\pi\) | |||||||
\(744\) | 2.21432 | + | 3.83531i | 0.0811809 | + | 0.140609i | ||||
\(745\) | 4.52252 | − | 11.1923i | 0.165692 | − | 0.410054i | ||||
\(746\) | −7.55800 | − | 13.0908i | −0.276718 | − | 0.479290i | ||||
\(747\) | −2.38639 | − | 1.37778i | −0.0873135 | − | 0.0504105i | ||||
\(748\) | 1.07160i | 0.0391815i | ||||||||
\(749\) | −13.9704 | −0.510466 | ||||||||
\(750\) | 1.17006 | − | 11.1189i | 0.0427246 | − | 0.406007i | ||||
\(751\) | 3.79213 | − | 6.56817i | 0.138377 | − | 0.239676i | −0.788505 | − | 0.615028i | \(-0.789145\pi\) |
0.926882 | + | 0.375352i | \(0.122478\pi\) | |||||||
\(752\) | − | 12.0874i | − | 0.440783i | ||||||
\(753\) | 15.0923i | 0.549996i | ||||||||
\(754\) | −5.83654 | + | 10.1092i | −0.212554 | + | 0.368154i | ||||
\(755\) | −12.4878 | − | 15.9851i | −0.454479 | − | 0.581757i | ||||
\(756\) | −0.392840 | + | 0.680419i | −0.0142875 | + | 0.0247466i | ||||
\(757\) | 26.1600 | − | 15.1035i | 0.950801 | − | 0.548945i | 0.0574714 | − | 0.998347i | \(-0.481696\pi\) |
0.893330 | + | 0.449402i | \(0.148363\pi\) | |||||||
\(758\) | 0.786055 | − | 0.453829i | 0.0285508 | − | 0.0164838i | ||||
\(759\) | −3.43309 | −0.124613 | ||||||||
\(760\) | 9.54550 | + | 1.97064i | 0.346252 | + | 0.0714827i | ||||
\(761\) | −46.3526 | −1.68028 | −0.840140 | − | 0.542369i | \(-0.817527\pi\) | ||||
−0.840140 | + | 0.542369i | \(0.817527\pi\) | |||||||
\(762\) | −3.14252 | + | 1.81433i | −0.113841 | + | 0.0657264i | ||||
\(763\) | 0.982839 | − | 0.567442i | 0.0355812 | − | 0.0205428i | ||||
\(764\) | −10.2351 | + | 17.7276i | −0.370292 | + | 0.641364i | ||||
\(765\) | −4.99827 | + | 3.90474i | −0.180713 | + | 0.141176i | ||||
\(766\) | −0.303963 | + | 0.526479i | −0.0109826 | + | 0.0190225i | ||||
\(767\) | 28.3368i | 1.02318i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | 3.85950 | − | 6.68485i | 0.139177 | − | 0.241062i | −0.788008 | − | 0.615665i | \(-0.788888\pi\) |
0.927185 | + | 0.374603i | \(0.122221\pi\) | |||||||
\(770\) | 0.248654 | − | 0.615366i | 0.00896086 | − | 0.0221762i | ||||
\(771\) | −22.8256 | −0.822045 | ||||||||
\(772\) | 18.9240i | 0.681088i | ||||||||
\(773\) | 18.0095 | + | 10.3978i | 0.647755 | + | 0.373982i | 0.787596 | − | 0.616193i | \(-0.211326\pi\) |
−0.139841 | + | 0.990174i | \(0.544659\pi\) | |||||||
\(774\) | 0.214320 | + | 0.371213i | 0.00770356 | + | 0.0133430i | ||||
\(775\) | 5.35872 | − | 21.4850i | 0.192491 | − | 0.771764i | ||||
\(776\) | −1.72223 | − | 2.98299i | −0.0618245 | − | 0.107083i | ||||
\(777\) | 0.0658565 | − | 0.0380222i | 0.00236259 | − | 0.00136404i | ||||
\(778\) | 12.0810i | 0.433124i | ||||||||
\(779\) | −4.21387 | + | 11.7933i | −0.150977 | + | 0.422540i | ||||
\(780\) | 6.42864 | − | 0.903212i | 0.230182 | − | 0.0323402i | ||||
\(781\) | −2.21755 | − | 3.84090i | −0.0793501 | − | 0.137438i | ||||
\(782\) | 22.3234 | − | 12.8884i | 0.798282 | − | 0.460888i | ||||
\(783\) | −3.48207 | − | 2.01037i | −0.124439 | − | 0.0718448i | ||||
\(784\) | −3.19135 | − | 5.52759i | −0.113977 | − | 0.197414i | ||||
\(785\) | 31.8620 | + | 12.8746i | 1.13720 | + | 0.459515i | ||||
\(786\) | 16.8064 | 0.599465 | ||||||||
\(787\) | − | 31.7255i | − | 1.13089i | −0.824786 | − | 0.565445i | \(-0.808704\pi\) | ||
0.824786 | − | 0.565445i | \(-0.191296\pi\) | |||||||
\(788\) | −1.49855 | − | 0.865190i | −0.0533837 | − | 0.0308211i | ||||
\(789\) | −6.05554 | + | 10.4885i | −0.215583 | + | 0.373401i | ||||
\(790\) | 0.488863 | + | 3.47949i | 0.0173929 | + | 0.123795i | ||||
\(791\) | 11.2478 | 0.399927 | ||||||||
\(792\) | 0.327171 | + | 0.188892i | 0.0116255 | + | 0.00671199i | ||||
\(793\) | 11.4538 | − | 6.61285i | 0.406736 | − | 0.234829i | ||||
\(794\) | −9.43110 | + | 16.3351i | −0.334697 | + | 0.579713i | ||||
\(795\) | −9.54432 | − | 12.2172i | −0.338502 | − | 0.433301i | ||||
\(796\) | −7.53580 | − | 13.0524i | −0.267099 | − | 0.462630i | ||||
\(797\) | − | 54.5417i | − | 1.93197i | −0.258604 | − | 0.965984i | \(-0.583262\pi\) | ||
0.258604 | − | 0.965984i | \(-0.416738\pi\) | |||||||
\(798\) | 0.614563 | + | 3.36911i | 0.0217553 | + | 0.119265i | ||||
\(799\) | 34.2864 | 1.21297 | ||||||||
\(800\) | 3.47359 | − | 3.59641i | 0.122810 | − | 0.127152i | ||||
\(801\) | −5.96912 | − | 10.3388i | −0.210909 | − | 0.365304i | ||||
\(802\) | −8.46521 | − | 4.88739i | −0.298917 | − | 0.172580i | ||||
\(803\) | 0.739489 | − | 0.426944i | 0.0260960 | − | 0.0150665i | ||||
\(804\) | 4.22469 | − | 7.31738i | 0.148993 | − | 0.258064i | ||||
\(805\) | −15.8098 | + | 2.22125i | −0.557223 | + | 0.0782888i | ||||
\(806\) | 12.8573 | 0.452878 | ||||||||
\(807\) | −21.8529 | − | 12.6168i | −0.769258 | − | 0.444131i | ||||
\(808\) | 14.8024 | + | 8.54617i | 0.520747 | + | 0.300653i | ||||
\(809\) | 14.4429 | 0.507786 | 0.253893 | − | 0.967232i | \(-0.418289\pi\) | ||||
0.253893 | + | 0.967232i | \(0.418289\pi\) | |||||||
\(810\) | 0.311108 | + | 2.21432i | 0.0109312 | + | 0.0778033i | ||||
\(811\) | 16.0079 | − | 27.7265i | 0.562114 | − | 0.973610i | −0.435198 | − | 0.900335i | \(-0.643322\pi\) |
0.997312 | − | 0.0732748i | \(-0.0233450\pi\) | |||||||
\(812\) | −2.73579 | + | 1.57951i | −0.0960074 | + | 0.0554299i | ||||
\(813\) | −26.7865 | − | 15.4652i | −0.939444 | − | 0.542388i | ||||
\(814\) | −0.0182825 | − | 0.0316662i | −0.000640802 | − | 0.00110990i | ||||
\(815\) | −12.8943 | + | 10.0733i | −0.451668 | + | 0.352851i | ||||
\(816\) | −2.83654 | −0.0992986 | ||||||||
\(817\) | 1.75945 | + | 0.628669i | 0.0615555 | + | 0.0219943i | ||||
\(818\) | 38.3832i | 1.34204i | ||||||||
\(819\) | 1.14050 | + | 1.97540i | 0.0398522 | + | 0.0690261i | ||||
\(820\) | 3.95507 | + | 5.06270i | 0.138117 | + | 0.176797i | ||||
\(821\) | 2.73038 | − | 4.72916i | 0.0952909 | − | 0.165049i | −0.814439 | − | 0.580249i | \(-0.802955\pi\) |
0.909730 | + | 0.415200i | \(0.136289\pi\) | |||||||
\(822\) | −1.89969 | + | 1.09679i | −0.0662594 | + | 0.0382549i | ||||
\(823\) | −45.4901 | − | 26.2637i | −1.58568 | − | 0.915496i | −0.994006 | − | 0.109322i | \(-0.965132\pi\) |
−0.591679 | − | 0.806174i | \(-0.701535\pi\) | |||||||
\(824\) | 8.11753 | 0.282788 | ||||||||
\(825\) | −0.520505 | − | 1.81579i | −0.0181217 | − | 0.0632178i | ||||
\(826\) | −3.83431 | + | 6.64122i | −0.133413 | + | 0.231078i | ||||
\(827\) | 18.7229 | + | 10.8097i | 0.651058 | + | 0.375888i | 0.788861 | − | 0.614571i | \(-0.210671\pi\) |
−0.137804 | + | 0.990460i | \(0.544004\pi\) | |||||||
\(828\) | − | 9.08742i | − | 0.315810i | ||||||
\(829\) | −22.1432 | −0.769065 | −0.384533 | − | 0.923111i | \(-0.625637\pi\) | ||||
−0.384533 | + | 0.923111i | \(0.625637\pi\) | |||||||
\(830\) | −2.30843 | + | 5.71288i | −0.0801268 | + | 0.198297i | ||||
\(831\) | 9.74689 | + | 16.8821i | 0.338116 | + | 0.585634i | ||||
\(832\) | 2.51426 | + | 1.45161i | 0.0871661 | + | 0.0503254i | ||||
\(833\) | 15.6792 | − | 9.05239i | 0.543252 | − | 0.313647i | ||||
\(834\) | −0.836535 | − | 1.44892i | −0.0289669 | − | 0.0501721i | ||||
\(835\) | −1.80796 | − | 12.8682i | −0.0625669 | − | 0.445322i | ||||
\(836\) | 1.61999 | − | 0.295505i | 0.0560286 | − | 0.0102202i | ||||
\(837\) | 4.42864i | 0.153076i | ||||||||
\(838\) | −26.6355 | + | 15.3780i | −0.920109 | + | 0.531225i | ||||
\(839\) | −15.0622 | − | 26.0885i | −0.520006 | − | 0.900677i | −0.999730 | − | 0.0232570i | \(-0.992596\pi\) |
0.479724 | − | 0.877420i | \(-0.340737\pi\) | |||||||
\(840\) | 1.62888 | + | 0.658190i | 0.0562017 | + | 0.0227097i | ||||
\(841\) | 6.41681 | + | 11.1142i | 0.221269 | + | 0.383250i | ||||
\(842\) | 10.9367 | + | 6.31433i | 0.376905 | + | 0.217606i | ||||
\(843\) | − | 7.43509i | − | 0.256078i | ||||||
\(844\) | −13.3160 | −0.458357 | ||||||||
\(845\) | −3.82958 | + | 9.47740i | −0.131741 | + | 0.326032i | ||||
\(846\) | 6.04371 | − | 10.4680i | 0.207787 | − | 0.359898i | ||||
\(847\) | 8.53035i | 0.293106i | ||||||||
\(848\) | − | 6.93332i | − | 0.238091i | ||||||
\(849\) | −0.857279 | + | 1.48485i | −0.0294217 | + | 0.0509599i | ||||
\(850\) | 10.2013 | + | 9.85297i | 0.349903 | + | 0.337954i | ||||
\(851\) | −0.439777 | + | 0.761716i | −0.0150754 | + | 0.0261113i | ||||
\(852\) | 10.1669 | − | 5.86987i | 0.348313 | − | 0.201099i | ||||
\(853\) | 20.1303 | − | 11.6222i | 0.689247 | − | 0.397937i | −0.114083 | − | 0.993471i | \(-0.536393\pi\) |
0.803330 | + | 0.595534i | \(0.203060\pi\) | |||||||
\(854\) | 3.57920 | 0.122478 | ||||||||
\(855\) | 7.28133 | + | 6.47938i | 0.249016 | + | 0.221590i | ||||
\(856\) | −17.7812 | −0.607750 | ||||||||
\(857\) | 31.9390 | − | 18.4400i | 1.09102 | − | 0.629899i | 0.157170 | − | 0.987572i | \(-0.449763\pi\) |
0.933847 | + | 0.357673i | \(0.116430\pi\) | |||||||
\(858\) | 0.949846 | − | 0.548394i | 0.0324272 | − | 0.0187219i | ||||
\(859\) | 14.2057 | − | 24.6050i | 0.484693 | − | 0.839513i | −0.515153 | − | 0.857099i | \(-0.672265\pi\) |
0.999845 | + | 0.0175859i | \(0.00559806\pi\) | |||||||
\(860\) | 0.755307 | − | 0.590060i | 0.0257558 | − | 0.0201209i | ||||
\(861\) | −1.12867 | + | 1.95491i | −0.0384649 | + | 0.0666232i | ||||
\(862\) | − | 35.3526i | − | 1.20411i | ||||||
\(863\) | 15.3082i | 0.521097i | 0.965461 | + | 0.260548i | \(0.0839034\pi\) | ||||
−0.965461 | + | 0.260548i | \(0.916097\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 18.0897 | + | 7.30960i | 0.615069 | + | 0.248534i | ||||
\(866\) | 20.7906 | 0.706493 | ||||||||
\(867\) | 8.95407i | 0.304096i | ||||||||
\(868\) | 3.01333 | + | 1.73975i | 0.102279 | + | 0.0590509i | ||||
\(869\) | 0.296818 | + | 0.514103i | 0.0100689 | + | 0.0174398i | ||||
\(870\) | −3.36831 | + | 8.33585i | −0.114196 | + | 0.282612i | ||||
\(871\) | −12.2652 | − | 21.2439i | −0.415590 | − | 0.719822i | ||||
\(872\) | 1.25094 | − | 0.722230i | 0.0423622 | − | 0.0244578i | ||||
\(873\) | − | 3.44446i | − | 0.116577i | ||||||
\(874\) | −25.6400 | − | 30.1933i | −0.867285 | − | 1.02130i | ||||
\(875\) | −3.57184 | − | 8.02519i | −0.120750 | − | 0.271301i | ||||
\(876\) | 1.13013 | + | 1.95744i | 0.0381834 | + | 0.0661356i | ||||
\(877\) | −23.8022 | + | 13.7422i | −0.803743 | + | 0.464041i | −0.844778 | − | 0.535116i | \(-0.820268\pi\) |
0.0410351 | + | 0.999158i | \(0.486934\pi\) | |||||||
\(878\) | −3.40251 | − | 1.96444i | −0.114829 | − | 0.0662966i | ||||
\(879\) | 3.96912 | + | 6.87472i | 0.133875 | + | 0.231879i | ||||
\(880\) | 0.316482 | − | 0.783227i | 0.0106686 | − | 0.0264026i | ||||
\(881\) | −20.3210 | −0.684630 | −0.342315 | − | 0.939585i | \(-0.611211\pi\) | ||||
−0.342315 | + | 0.939585i | \(0.611211\pi\) | |||||||
\(882\) | − | 6.38271i | − | 0.214917i | ||||||
\(883\) | −27.8026 | − | 16.0519i | −0.935633 | − | 0.540188i | −0.0470444 | − | 0.998893i | \(-0.514980\pi\) |
−0.888589 | + | 0.458705i | \(0.848314\pi\) | |||||||
\(884\) | −4.11753 | + | 7.13177i | −0.138488 | + | 0.239868i | ||||
\(885\) | 3.03657 | + | 21.6128i | 0.102073 | + | 0.726508i | ||||
\(886\) | −1.59655 | −0.0536371 | ||||||||
\(887\) | 21.1520 | + | 12.2121i | 0.710214 | + | 0.410042i | 0.811140 | − | 0.584852i | \(-0.198847\pi\) |
−0.100926 | + | 0.994894i | \(0.532181\pi\) | |||||||
\(888\) | 0.0838209 | − | 0.0483940i | 0.00281285 | − | 0.00162400i | ||||
\(889\) | −1.42549 | + | 2.46902i | −0.0478093 | + | 0.0828081i | ||||
\(890\) | −21.0364 | + | 16.4340i | −0.705142 | + | 0.550870i | ||||
\(891\) | 0.188892 | + | 0.327171i | 0.00632813 | + | 0.0109606i | ||||
\(892\) | − | 19.1684i | − | 0.641805i | ||||||
\(893\) | −9.45483 | − | 51.8326i | −0.316394 | − | 1.73451i | ||||
\(894\) | 5.39853 | 0.180554 | ||||||||
\(895\) | −31.9790 | − | 40.9347i | −1.06894 | − | 1.36830i | ||||
\(896\) | 0.392840 | + | 0.680419i | 0.0131239 | + | 0.0227312i | ||||
\(897\) | −22.8481 | − | 13.1914i | −0.762876 | − | 0.440446i | ||||
\(898\) | 12.5216 | − | 7.22938i | 0.417853 | − | 0.241247i | ||||
\(899\) | −8.90321 | + | 15.4208i | −0.296939 | + | 0.514313i | ||||
\(900\) | 4.80642 | − | 1.37778i | 0.160214 | − | 0.0459261i | ||||
\(901\) | 19.6666 | 0.655190 | ||||||||
\(902\) | 0.939995 | + | 0.542706i | 0.0312984 | + | 0.0180701i | ||||
\(903\) | 0.291654 | + | 0.168387i | 0.00970565 | + | 0.00560356i | ||||
\(904\) | 14.3160 | 0.476144 | ||||||||
\(905\) | 16.7096 | − | 2.34767i | 0.555447 | − | 0.0780393i | ||||
\(906\) | 4.53580 | − | 7.85623i | 0.150692 | − | 0.261006i | ||||
\(907\) | −0.681745 | + | 0.393606i | −0.0226370 | + | 0.0130695i | −0.511276 | − | 0.859417i | \(-0.670827\pi\) |
0.488639 | + | 0.872486i | \(0.337494\pi\) | |||||||
\(908\) | −5.96039 | − | 3.44123i | −0.197803 | − | 0.114201i | ||||
\(909\) | 8.54617 | + | 14.8024i | 0.283459 | + | 0.490965i | ||||
\(910\) | 4.01935 | − | 3.13999i | 0.133240 | − | 0.104090i | ||||
\(911\) | 5.93978 | 0.196794 | 0.0983968 | − | 0.995147i | \(-0.468629\pi\) | ||||
0.0983968 | + | 0.995147i | \(0.468629\pi\) | |||||||
\(912\) | 0.782204 | + | 4.28814i | 0.0259014 | + | 0.141995i | ||||
\(913\) | 1.04101i | 0.0344524i | ||||||||
\(914\) | −14.4526 | − | 25.0327i | −0.478050 | − | 0.828007i | ||||
\(915\) | 8.02733 | − | 6.27110i | 0.265375 | − | 0.207316i | ||||
\(916\) | −6.87310 | + | 11.9046i | −0.227094 | + | 0.393338i | ||||
\(917\) | 11.4354 | − | 6.60224i | 0.377631 | − | 0.218025i | ||||
\(918\) | −2.45651 | − | 1.41827i | −0.0810770 | − | 0.0468098i | ||||
\(919\) | −28.5096 | −0.940445 | −0.470223 | − | 0.882548i | \(-0.655826\pi\) | ||||
−0.470223 | + | 0.882548i | \(0.655826\pi\) | |||||||
\(920\) | −20.1225 | + | 2.82717i | −0.663418 | + | 0.0932090i | ||||
\(921\) | 0.530877 | − | 0.919506i | 0.0174930 | − | 0.0302988i | ||||
\(922\) | −2.11949 | − | 1.22369i | −0.0698017 | − | 0.0403000i | ||||
\(923\) | − | 34.0830i | − | 1.12185i | ||||||
\(924\) | 0.296818 | 0.00976459 | ||||||||
\(925\) | −0.469555 | − | 0.117115i | −0.0154389 | − | 0.00385072i | ||||
\(926\) | 3.83730 | + | 6.64640i | 0.126102 | + | 0.218414i | ||||
\(927\) | 7.02999 | + | 4.05877i | 0.230895 | + | 0.133307i | ||||
\(928\) | −3.48207 | + | 2.01037i | −0.114304 | + | 0.0659937i | ||||
\(929\) | −1.34199 | − | 2.32439i | −0.0440291 | − | 0.0762606i | 0.843171 | − | 0.537645i | \(-0.180686\pi\) |
−0.887200 | + | 0.461385i | \(0.847353\pi\) | |||||||
\(930\) | 9.80642 | − | 1.37778i | 0.321565 | − | 0.0451793i | ||||
\(931\) | −18.0087 | − | 21.2068i | −0.590211 | − | 0.695024i | ||||
\(932\) | 6.79706i | 0.222645i | ||||||||
\(933\) | 15.1736 | − | 8.76049i | 0.496762 | − | 0.286806i | ||||
\(934\) | −4.89062 | − | 8.47080i | −0.160026 | − | 0.277173i | ||||
\(935\) | 2.22165 | + | 0.897713i | 0.0726557 | + | 0.0293584i | ||||
\(936\) | 1.45161 | + | 2.51426i | 0.0474472 | + | 0.0821810i | ||||
\(937\) | −42.3258 | − | 24.4368i | −1.38272 | − | 0.798315i | −0.390241 | − | 0.920713i | \(-0.627608\pi\) |
−0.992481 | + | 0.122398i | \(0.960942\pi\) | |||||||
\(938\) | − | 6.63851i | − | 0.216755i | ||||||
\(939\) | 12.2953 | 0.401242 | ||||||||
\(940\) | −25.0598 | − | 10.1260i | −0.817360 | − | 0.330275i | ||||
\(941\) | 28.7961 | − | 49.8762i | 0.938724 | − | 1.62592i | 0.170871 | − | 0.985293i | \(-0.445342\pi\) |
0.767854 | − | 0.640625i | \(-0.221325\pi\) | |||||||
\(942\) | 15.3684i | 0.500730i | ||||||||
\(943\) | − | 26.1091i | − | 0.850228i | ||||||
\(944\) | −4.88025 | + | 8.45283i | −0.158838 | + | 0.275116i | ||||
\(945\) | 1.08156 | + | 1.38445i | 0.0351831 | + | 0.0450362i | ||||
\(946\) | 0.0809666 | − | 0.140238i | 0.00263245 | − | 0.00455954i | ||||
\(947\) | −24.0430 | + | 13.8812i | −0.781293 | + | 0.451080i | −0.836888 | − | 0.547373i | \(-0.815628\pi\) |
0.0555950 | + | 0.998453i | \(0.482294\pi\) | |||||||
\(948\) | −1.36084 | + | 0.785680i | −0.0441980 | + | 0.0255177i | ||||
\(949\) | 6.56199 | 0.213011 | ||||||||
\(950\) | 12.0821 | − | 18.1390i | 0.391996 | − | 0.588506i | ||||
\(951\) | −23.9240 | −0.775787 | ||||||||
\(952\) | −1.93003 | + | 1.11430i | −0.0625527 | + | 0.0361148i | ||||
\(953\) | 23.3993 | − | 13.5096i | 0.757978 | − | 0.437619i | −0.0705910 | − | 0.997505i | \(-0.522489\pi\) |
0.828569 | + | 0.559886i | \(0.189155\pi\) | |||||||
\(954\) | 3.46666 | − | 6.00443i | 0.112237 | − | 0.194401i | ||||
\(955\) | 28.1789 | + | 36.0705i | 0.911848 | + | 1.16721i | ||||
\(956\) | 5.42864 | − | 9.40268i | 0.175575 | − | 0.304104i | ||||
\(957\) | 1.51897i | 0.0491015i | ||||||||
\(958\) | 33.9432i | 1.09665i | ||||||||
\(959\) | −0.861725 | + | 1.49255i | −0.0278265 | + | 0.0481970i | ||||
\(960\) | 2.07321 | + | 0.837733i | 0.0669126 | + | 0.0270377i | ||||
\(961\) | −11.3872 | −0.367327 | ||||||||
\(962\) | − | 0.280996i | − | 0.00905968i | ||||||
\(963\) | −15.3990 | − | 8.89062i | −0.496226 | − | 0.286496i | ||||
\(964\) | −4.84368 | − | 8.38950i | −0.156004 | − | 0.270208i | ||||
\(965\) | 39.2334 | + | 15.8532i | 1.26297 | + | 0.510333i | ||||
\(966\) | −3.56990 | − | 6.18325i | −0.114860 | − | 0.198943i | ||||
\(967\) | −47.4916 | + | 27.4193i | −1.52723 | + | 0.881744i | −0.527749 | + | 0.849400i | \(0.676964\pi\) |
−0.999477 | + | 0.0323441i | \(0.989703\pi\) | |||||||
\(968\) | 10.8573i | 0.348966i | ||||||||
\(969\) | −12.1635 | + | 2.21875i | −0.390747 | + | 0.0712765i | ||||
\(970\) | −7.62714 | + | 1.07160i | −0.244893 | + | 0.0344070i | ||||
\(971\) | 9.23575 | + | 15.9968i | 0.296389 | + | 0.513362i | 0.975307 | − | 0.220853i | \(-0.0708840\pi\) |
−0.678918 | + | 0.734214i | \(0.737551\pi\) | |||||||
\(972\) | −0.866025 | + | 0.500000i | −0.0277778 | + | 0.0160375i | ||||
\(973\) | −1.13839 | − | 0.657249i | −0.0364951 | − | 0.0210704i | ||||
\(974\) | 16.9390 | + | 29.3392i | 0.542761 | + | 0.940090i | ||||
\(975\) | 3.51293 | − | 14.0846i | 0.112504 | − | 0.451067i | ||||
\(976\) | 4.55554 | 0.145819 | ||||||||
\(977\) | − | 21.1131i | − | 0.675467i | −0.941242 | − | 0.337734i | \(-0.890340\pi\) | ||
0.941242 | − | 0.337734i | \(-0.109660\pi\) | |||||||
\(978\) | −6.33719 | − | 3.65878i | −0.202641 | − | 0.116995i | ||||
\(979\) | −2.25504 | + | 3.90585i | −0.0720714 | + | 0.124831i | ||||
\(980\) | −14.1334 | + | 1.98571i | −0.451473 | + | 0.0634312i | ||||
\(981\) | 1.44446 | 0.0461181 | ||||||||
\(982\) | 35.6148 | + | 20.5622i | 1.13651 | + | 0.656167i | ||||
\(983\) | −29.0617 | + | 16.7788i | −0.926924 | + | 0.535160i | −0.885837 | − | 0.463996i | \(-0.846415\pi\) |
−0.0410865 | + | 0.999156i | \(0.513082\pi\) | |||||||
\(984\) | −1.43655 | + | 2.48818i | −0.0457955 | + | 0.0793202i | ||||
\(985\) | −3.04911 | + | 2.38202i | −0.0971526 | + | 0.0758974i | ||||
\(986\) | −5.70249 | − | 9.87700i | −0.181604 | − | 0.314548i | ||||
\(987\) | − | 9.49685i | − | 0.302288i | ||||||
\(988\) | 11.9169 | + | 4.25803i | 0.379128 | + | 0.135466i | ||||
\(989\) | −3.89523 | −0.123861 | ||||||||
\(990\) | 0.665695 | − | 0.520053i | 0.0211572 | − | 0.0165284i | ||||
\(991\) | 7.88347 | + | 13.6546i | 0.250427 | + | 0.433752i | 0.963643 | − | 0.267192i | \(-0.0860957\pi\) |
−0.713217 | + | 0.700944i | \(0.752762\pi\) | |||||||
\(992\) | 3.83531 | + | 2.21432i | 0.121771 | + | 0.0703047i | ||||
\(993\) | 11.3284 | − | 6.54048i | 0.359497 | − | 0.207556i | ||||
\(994\) | 4.61184 | − | 7.98795i | 0.146279 | − | 0.253362i | ||||
\(995\) | −33.3733 | + | 4.68889i | −1.05801 | + | 0.148648i | ||||
\(996\) | −2.75557 | −0.0873135 | ||||||||
\(997\) | 29.9992 | + | 17.3200i | 0.950083 | + | 0.548531i | 0.893107 | − | 0.449845i | \(-0.148521\pi\) |
0.0569762 | + | 0.998376i | \(0.481854\pi\) | |||||||
\(998\) | 17.3030 | + | 9.98987i | 0.547716 | + | 0.316224i | ||||
\(999\) | 0.0967881 | 0.00306224 |
(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 | 570.2.q.b.349.5 | yes | 12 | |
3.2 | odd | 2 | 1710.2.t.b.919.2 | 12 | |||
5.4 | even | 2 | inner | 570.2.q.b.349.1 | yes | 12 | |
15.14 | odd | 2 | 1710.2.t.b.919.6 | 12 | |||
19.11 | even | 3 | inner | 570.2.q.b.49.1 | ✓ | 12 | |
57.11 | odd | 6 | 1710.2.t.b.1189.6 | 12 | |||
95.49 | even | 6 | inner | 570.2.q.b.49.5 | yes | 12 | |
285.239 | odd | 6 | 1710.2.t.b.1189.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.q.b.49.1 | ✓ | 12 | 19.11 | even | 3 | inner | |
570.2.q.b.49.5 | yes | 12 | 95.49 | even | 6 | inner | |
570.2.q.b.349.1 | yes | 12 | 5.4 | even | 2 | inner | |
570.2.q.b.349.5 | yes | 12 | 1.1 | even | 1 | trivial | |
1710.2.t.b.919.2 | 12 | 3.2 | odd | 2 | |||
1710.2.t.b.919.6 | 12 | 15.14 | odd | 2 | |||
1710.2.t.b.1189.2 | 12 | 285.239 | odd | 6 | |||
1710.2.t.b.1189.6 | 12 | 57.11 | odd | 6 |