Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1470,2,Mod(97,1470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1470, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1470.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1470 = 2 \cdot 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1470.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(11.7380090971\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 32 x^{13} + 2 x^{12} + 352 x^{10} - 288 x^{9} + 2 x^{8} - 1440 x^{7} + 8800 x^{6} + \cdots + 390625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1273.2 | ||
Root | \(-1.22045 + 1.87363i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.1273 |
Dual form | 1470.2.m.c.97.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | + | 0.707107i | −0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −1.84456 | + | 1.26397i | −0.824910 | + | 0.565263i | ||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | 0.410538 | − | 2.19806i | 0.129824 | − | 0.695087i | ||||
\(11\) | 5.16148 | 1.55625 | 0.778123 | − | 0.628112i | \(-0.216172\pi\) | ||||
0.778123 | + | 0.628112i | \(0.216172\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 0.184778 | − | 0.184778i | 0.0512483 | − | 0.0512483i | −0.681018 | − | 0.732266i | \(-0.738463\pi\) |
0.732266 | + | 0.681018i | \(0.238463\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.410538 | − | 2.19806i | 0.106000 | − | 0.567536i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −0.750926 | − | 0.750926i | −0.182126 | − | 0.182126i | 0.610155 | − | 0.792282i | \(-0.291107\pi\) |
−0.792282 | + | 0.610155i | \(0.791107\pi\) | |||||||
\(18\) | 0.707107 | + | 0.707107i | 0.166667 | + | 0.166667i | ||||
\(19\) | −4.08523 | −0.937215 | −0.468608 | − | 0.883406i | \(-0.655244\pi\) | ||||
−0.468608 | + | 0.883406i | \(0.655244\pi\) | |||||||
\(20\) | 1.26397 | + | 1.84456i | 0.282632 | + | 0.412455i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.64972 | + | 3.64972i | −0.778123 | + | 0.778123i | ||||
\(23\) | −2.36811 | − | 2.36811i | −0.493785 | − | 0.493785i | 0.415712 | − | 0.909496i | \(-0.363533\pi\) |
−0.909496 | + | 0.415712i | \(0.863533\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 1.80477 | − | 4.66292i | 0.360955 | − | 0.932583i | ||||
\(26\) | 0.261316i | 0.0512483i | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 0.387531i | − | 0.0719627i | −0.999352 | − | 0.0359813i | \(-0.988544\pi\) | ||
0.999352 | − | 0.0359813i | \(-0.0114557\pi\) | |||||||
\(30\) | 1.26397 | + | 1.84456i | 0.230768 | + | 0.336768i | ||||
\(31\) | − | 10.6134i | − | 1.90623i | −0.302611 | − | 0.953114i | \(-0.597858\pi\) | ||
0.302611 | − | 0.953114i | \(-0.402142\pi\) | |||||||
\(32\) | 0.707107 | − | 0.707107i | 0.125000 | − | 0.125000i | ||||
\(33\) | −3.64972 | + | 3.64972i | −0.635335 | + | 0.635335i | ||||
\(34\) | 1.06197 | 0.182126 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 2.51162 | − | 2.51162i | 0.412907 | − | 0.412907i | −0.469843 | − | 0.882750i | \(-0.655689\pi\) |
0.882750 | + | 0.469843i | \(0.155689\pi\) | |||||||
\(38\) | 2.88869 | − | 2.88869i | 0.468608 | − | 0.468608i | ||||
\(39\) | 0.261316i | 0.0418440i | ||||||||
\(40\) | −2.19806 | − | 0.410538i | −0.347543 | − | 0.0649118i | ||||
\(41\) | − | 7.05881i | − | 1.10240i | −0.834373 | − | 0.551201i | \(-0.814170\pi\) | ||
0.834373 | − | 0.551201i | \(-0.185830\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.13217 | − | 2.13217i | −0.325153 | − | 0.325153i | 0.525587 | − | 0.850740i | \(-0.323846\pi\) |
−0.850740 | + | 0.525587i | \(0.823846\pi\) | |||||||
\(44\) | − | 5.16148i | − | 0.778123i | ||||||
\(45\) | 1.26397 | + | 1.84456i | 0.188421 | + | 0.274970i | ||||
\(46\) | 3.34901 | 0.493785 | ||||||||
\(47\) | 7.37446 | + | 7.37446i | 1.07568 | + | 1.07568i | 0.996892 | + | 0.0787836i | \(0.0251036\pi\) |
0.0787836 | + | 0.996892i | \(0.474896\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 2.02101 | + | 4.57335i | 0.285814 | + | 0.646769i | ||||
\(51\) | 1.06197 | 0.148706 | ||||||||
\(52\) | −0.184778 | − | 0.184778i | −0.0256241 | − | 0.0256241i | ||||
\(53\) | 7.15311 | + | 7.15311i | 0.982556 | + | 0.982556i | 0.999850 | − | 0.0172949i | \(-0.00550540\pi\) |
−0.0172949 | + | 0.999850i | \(0.505505\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −9.52064 | + | 6.52395i | −1.28376 | + | 0.879689i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.88869 | − | 2.88869i | 0.382617 | − | 0.382617i | ||||
\(58\) | 0.274026 | + | 0.274026i | 0.0359813 | + | 0.0359813i | ||||
\(59\) | 9.70992 | 1.26412 | 0.632062 | − | 0.774918i | \(-0.282209\pi\) | ||||
0.632062 | + | 0.774918i | \(0.282209\pi\) | |||||||
\(60\) | −2.19806 | − | 0.410538i | −0.283768 | − | 0.0530002i | ||||
\(61\) | 11.0100i | 1.40969i | 0.709361 | + | 0.704846i | \(0.248984\pi\) | ||||
−0.709361 | + | 0.704846i | \(0.751016\pi\) | |||||||
\(62\) | 7.50483 | + | 7.50483i | 0.953114 | + | 0.953114i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −0.107280 | + | 0.574387i | −0.0133065 | + | 0.0712440i | ||||
\(66\) | − | 5.16148i | − | 0.635335i | ||||||
\(67\) | −0.0355377 | + | 0.0355377i | −0.00434163 | + | 0.00434163i | −0.709274 | − | 0.704933i | \(-0.750977\pi\) |
0.704933 | + | 0.709274i | \(0.250977\pi\) | |||||||
\(68\) | −0.750926 | + | 0.750926i | −0.0910632 | + | 0.0910632i | ||||
\(69\) | 3.34901 | 0.403174 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.7253 | 1.86625 | 0.933127 | − | 0.359546i | \(-0.117068\pi\) | ||||
0.933127 | + | 0.359546i | \(0.117068\pi\) | |||||||
\(72\) | 0.707107 | − | 0.707107i | 0.0833333 | − | 0.0833333i | ||||
\(73\) | −3.22877 | + | 3.22877i | −0.377899 | + | 0.377899i | −0.870344 | − | 0.492445i | \(-0.836103\pi\) |
0.492445 | + | 0.870344i | \(0.336103\pi\) | |||||||
\(74\) | 3.55196i | 0.412907i | ||||||||
\(75\) | 2.02101 | + | 4.57335i | 0.233366 | + | 0.528085i | ||||
\(76\) | 4.08523i | 0.468608i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −0.184778 | − | 0.184778i | −0.0209220 | − | 0.0209220i | ||||
\(79\) | − | 7.46114i | − | 0.839444i | −0.907653 | − | 0.419722i | \(-0.862128\pi\) | ||
0.907653 | − | 0.419722i | \(-0.137872\pi\) | |||||||
\(80\) | 1.84456 | − | 1.26397i | 0.206228 | − | 0.141316i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.99134 | + | 4.99134i | 0.551201 | + | 0.551201i | ||||
\(83\) | −0.409165 | + | 0.409165i | −0.0449117 | + | 0.0449117i | −0.729206 | − | 0.684294i | \(-0.760110\pi\) |
0.684294 | + | 0.729206i | \(0.260110\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.33427 | + | 0.435979i | 0.253187 | + | 0.0472886i | ||||
\(86\) | 3.01534 | 0.325153 | ||||||||
\(87\) | 0.274026 | + | 0.274026i | 0.0293786 | + | 0.0293786i | ||||
\(88\) | 3.64972 | + | 3.64972i | 0.389061 | + | 0.389061i | ||||
\(89\) | 14.1264 | 1.49739 | 0.748695 | − | 0.662914i | \(-0.230681\pi\) | ||||
0.748695 | + | 0.662914i | \(0.230681\pi\) | |||||||
\(90\) | −2.19806 | − | 0.410538i | −0.231696 | − | 0.0432745i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −2.36811 | + | 2.36811i | −0.246892 | + | 0.246892i | ||||
\(93\) | 7.50483 | + | 7.50483i | 0.778215 | + | 0.778215i | ||||
\(94\) | −10.4291 | −1.07568 | ||||||||
\(95\) | 7.53543 | − | 5.16359i | 0.773119 | − | 0.529774i | ||||
\(96\) | 1.00000i | 0.102062i | ||||||||
\(97\) | 1.32497 | + | 1.32497i | 0.134530 | + | 0.134530i | 0.771165 | − | 0.636635i | \(-0.219674\pi\) |
−0.636635 | + | 0.771165i | \(0.719674\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.16148i | − | 0.518749i | ||||||
\(100\) | −4.66292 | − | 1.80477i | −0.466292 | − | 0.180477i | ||||
\(101\) | − | 2.60028i | − | 0.258737i | −0.991597 | − | 0.129369i | \(-0.958705\pi\) | ||
0.991597 | − | 0.129369i | \(-0.0412951\pi\) | |||||||
\(102\) | −0.750926 | + | 0.750926i | −0.0743528 | + | 0.0743528i | ||||
\(103\) | −6.20799 | + | 6.20799i | −0.611691 | + | 0.611691i | −0.943387 | − | 0.331695i | \(-0.892379\pi\) |
0.331695 | + | 0.943387i | \(0.392379\pi\) | |||||||
\(104\) | 0.261316 | 0.0256241 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1160 | −0.982556 | ||||||||
\(107\) | −13.6366 | + | 13.6366i | −1.31830 | + | 1.31830i | −0.403183 | + | 0.915119i | \(0.632096\pi\) |
−0.915119 | + | 0.403183i | \(0.867904\pi\) | |||||||
\(108\) | 0.707107 | − | 0.707107i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | − | 7.24117i | − | 0.693578i | −0.937943 | − | 0.346789i | \(-0.887272\pi\) | ||
0.937943 | − | 0.346789i | \(-0.112728\pi\) | |||||||
\(110\) | 2.11899 | − | 11.3452i | 0.202037 | − | 1.08173i | ||||
\(111\) | 3.55196i | 0.337137i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.46766 | − | 5.46766i | −0.514354 | − | 0.514354i | 0.401503 | − | 0.915858i | \(-0.368488\pi\) |
−0.915858 | + | 0.401503i | \(0.868488\pi\) | |||||||
\(114\) | 4.08523i | 0.382617i | ||||||||
\(115\) | 7.36132 | + | 1.37490i | 0.686447 | + | 0.128210i | ||||
\(116\) | −0.387531 | −0.0359813 | ||||||||
\(117\) | −0.184778 | − | 0.184778i | −0.0170828 | − | 0.0170828i | ||||
\(118\) | −6.86595 | + | 6.86595i | −0.632062 | + | 0.632062i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.84456 | − | 1.26397i | 0.168384 | − | 0.115384i | ||||
\(121\) | 15.6409 | 1.42190 | ||||||||
\(122\) | −7.78528 | − | 7.78528i | −0.704846 | − | 0.704846i | ||||
\(123\) | 4.99134 | + | 4.99134i | 0.450054 | + | 0.450054i | ||||
\(124\) | −10.6134 | −0.953114 | ||||||||
\(125\) | 2.56477 | + | 10.8822i | 0.229400 | + | 0.973332i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.3115 | − | 13.3115i | 1.18120 | − | 1.18120i | 0.201770 | − | 0.979433i | \(-0.435331\pi\) |
0.979433 | − | 0.201770i | \(-0.0646693\pi\) | |||||||
\(128\) | −0.707107 | − | 0.707107i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 3.01534 | 0.265486 | ||||||||
\(130\) | −0.330295 | − | 0.482012i | −0.0289688 | − | 0.0422752i | ||||
\(131\) | − | 10.9119i | − | 0.953376i | −0.879073 | − | 0.476688i | \(-0.841837\pi\) | ||
0.879073 | − | 0.476688i | \(-0.158163\pi\) | |||||||
\(132\) | 3.64972 | + | 3.64972i | 0.317667 | + | 0.317667i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.0502580i | − | 0.00434163i | ||||||
\(135\) | −2.19806 | − | 0.410538i | −0.189179 | − | 0.0353335i | ||||
\(136\) | − | 1.06197i | − | 0.0910632i | ||||||
\(137\) | −2.89316 | + | 2.89316i | −0.247180 | + | 0.247180i | −0.819812 | − | 0.572633i | \(-0.805922\pi\) |
0.572633 | + | 0.819812i | \(0.305922\pi\) | |||||||
\(138\) | −2.36811 | + | 2.36811i | −0.201587 | + | 0.201587i | ||||
\(139\) | −10.3841 | −0.880769 | −0.440384 | − | 0.897809i | \(-0.645158\pi\) | ||||
−0.440384 | + | 0.897809i | \(0.645158\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.4291 | −0.878285 | ||||||||
\(142\) | −11.1195 | + | 11.1195i | −0.933127 | + | 0.933127i | ||||
\(143\) | 0.953730 | − | 0.953730i | 0.0797549 | − | 0.0797549i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 0.489826 | + | 0.714822i | 0.0406779 | + | 0.0593628i | ||||
\(146\) | − | 4.56617i | − | 0.377899i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.51162 | − | 2.51162i | −0.206454 | − | 0.206454i | ||||
\(149\) | − | 16.7852i | − | 1.37510i | −0.726139 | − | 0.687548i | \(-0.758687\pi\) | ||
0.726139 | − | 0.687548i | \(-0.241313\pi\) | |||||||
\(150\) | −4.66292 | − | 1.80477i | −0.380726 | − | 0.147359i | ||||
\(151\) | 9.76485 | 0.794652 | 0.397326 | − | 0.917677i | \(-0.369938\pi\) | ||||
0.397326 | + | 0.917677i | \(0.369938\pi\) | |||||||
\(152\) | −2.88869 | − | 2.88869i | −0.234304 | − | 0.234304i | ||||
\(153\) | −0.750926 | + | 0.750926i | −0.0607088 | + | 0.0607088i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.4150 | + | 19.5771i | 1.07752 | + | 1.57247i | ||||
\(156\) | 0.261316 | 0.0209220 | ||||||||
\(157\) | 8.66837 | + | 8.66837i | 0.691811 | + | 0.691811i | 0.962630 | − | 0.270819i | \(-0.0872945\pi\) |
−0.270819 | + | 0.962630i | \(0.587295\pi\) | |||||||
\(158\) | 5.27582 | + | 5.27582i | 0.419722 | + | 0.419722i | ||||
\(159\) | −10.1160 | −0.802253 | ||||||||
\(160\) | −0.410538 | + | 2.19806i | −0.0324559 | + | 0.173772i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 13.7694 | + | 13.7694i | 1.07850 | + | 1.07850i | 0.996644 | + | 0.0818553i | \(0.0260845\pi\) |
0.0818553 | + | 0.996644i | \(0.473915\pi\) | |||||||
\(164\) | −7.05881 | −0.551201 | ||||||||
\(165\) | 2.11899 | − | 11.3452i | 0.164963 | − | 0.883226i | ||||
\(166\) | − | 0.578647i | − | 0.0449117i | ||||||
\(167\) | 4.32056 | + | 4.32056i | 0.334335 | + | 0.334335i | 0.854230 | − | 0.519895i | \(-0.174029\pi\) |
−0.519895 | + | 0.854230i | \(0.674029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.9317i | 0.994747i | ||||||||
\(170\) | −1.95886 | + | 1.34230i | −0.150238 | + | 0.102949i | ||||
\(171\) | 4.08523i | 0.312405i | ||||||||
\(172\) | −2.13217 | + | 2.13217i | −0.162576 | + | 0.162576i | ||||
\(173\) | 14.3204 | − | 14.3204i | 1.08876 | − | 1.08876i | 0.0931075 | − | 0.995656i | \(-0.470320\pi\) |
0.995656 | − | 0.0931075i | \(-0.0296800\pi\) | |||||||
\(174\) | −0.387531 | −0.0293786 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.16148 | −0.389061 | ||||||||
\(177\) | −6.86595 | + | 6.86595i | −0.516076 | + | 0.516076i | ||||
\(178\) | −9.98884 | + | 9.98884i | −0.748695 | + | 0.748695i | ||||
\(179\) | 22.2204i | 1.66083i | 0.557144 | + | 0.830416i | \(0.311897\pi\) | ||||
−0.557144 | + | 0.830416i | \(0.688103\pi\) | |||||||
\(180\) | 1.84456 | − | 1.26397i | 0.137485 | − | 0.0942106i | ||||
\(181\) | − | 25.1301i | − | 1.86791i | −0.357397 | − | 0.933953i | \(-0.616336\pi\) | ||
0.357397 | − | 0.933953i | \(-0.383664\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.78528 | − | 7.78528i | −0.575504 | − | 0.575504i | ||||
\(184\) | − | 3.34901i | − | 0.246892i | ||||||
\(185\) | −1.45822 | + | 7.80742i | −0.107210 | + | 0.574013i | ||||
\(186\) | −10.6134 | −0.778215 | ||||||||
\(187\) | −3.87589 | − | 3.87589i | −0.283433 | − | 0.283433i | ||||
\(188\) | 7.37446 | − | 7.37446i | 0.537838 | − | 0.537838i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.67714 | + | 8.97957i | −0.121673 | + | 0.651446i | ||||
\(191\) | 1.53994 | 0.111426 | 0.0557130 | − | 0.998447i | \(-0.482257\pi\) | ||||
0.0557130 | + | 0.998447i | \(0.482257\pi\) | |||||||
\(192\) | −0.707107 | − | 0.707107i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | −12.7329 | − | 12.7329i | −0.916533 | − | 0.916533i | 0.0802420 | − | 0.996775i | \(-0.474431\pi\) |
−0.996775 | + | 0.0802420i | \(0.974431\pi\) | |||||||
\(194\) | −1.87379 | −0.134530 | ||||||||
\(195\) | −0.330295 | − | 0.482012i | −0.0236529 | − | 0.0345176i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.0158 | − | 12.0158i | 0.856087 | − | 0.856087i | −0.134787 | − | 0.990875i | \(-0.543035\pi\) |
0.990875 | + | 0.134787i | \(0.0430351\pi\) | |||||||
\(198\) | 3.64972 | + | 3.64972i | 0.259374 | + | 0.259374i | ||||
\(199\) | −9.42226 | −0.667926 | −0.333963 | − | 0.942586i | \(-0.608386\pi\) | ||||
−0.333963 | + | 0.942586i | \(0.608386\pi\) | |||||||
\(200\) | 4.57335 | − | 2.02101i | 0.323385 | − | 0.142907i | ||||
\(201\) | − | 0.0502580i | − | 0.00354492i | ||||||
\(202\) | 1.83867 | + | 1.83867i | 0.129369 | + | 0.129369i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 1.06197i | − | 0.0743528i | ||||||
\(205\) | 8.92211 | + | 13.0204i | 0.623147 | + | 0.909383i | ||||
\(206\) | − | 8.77942i | − | 0.611691i | ||||||
\(207\) | −2.36811 | + | 2.36811i | −0.164595 | + | 0.164595i | ||||
\(208\) | −0.184778 | + | 0.184778i | −0.0128121 | + | 0.0128121i | ||||
\(209\) | −21.0858 | −1.45854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.4641 | 0.995748 | 0.497874 | − | 0.867249i | \(-0.334114\pi\) | ||||
0.497874 | + | 0.867249i | \(0.334114\pi\) | |||||||
\(212\) | 7.15311 | − | 7.15311i | 0.491278 | − | 0.491278i | ||||
\(213\) | −11.1195 | + | 11.1195i | −0.761895 | + | 0.761895i | ||||
\(214\) | − | 19.2851i | − | 1.31830i | ||||||
\(215\) | 6.62790 | + | 1.23791i | 0.452019 | + | 0.0844250i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 5.12028 | + | 5.12028i | 0.346789 | + | 0.346789i | ||||
\(219\) | − | 4.56617i | − | 0.308553i | ||||||
\(220\) | 6.52395 | + | 9.52064i | 0.439844 | + | 0.641882i | ||||
\(221\) | −0.277510 | −0.0186673 | ||||||||
\(222\) | −2.51162 | − | 2.51162i | −0.168569 | − | 0.168569i | ||||
\(223\) | 7.80302 | − | 7.80302i | 0.522529 | − | 0.522529i | −0.395805 | − | 0.918334i | \(-0.629535\pi\) |
0.918334 | + | 0.395805i | \(0.129535\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.66292 | − | 1.80477i | −0.310861 | − | 0.120318i | ||||
\(226\) | 7.73244 | 0.514354 | ||||||||
\(227\) | 7.43269 | + | 7.43269i | 0.493325 | + | 0.493325i | 0.909352 | − | 0.416027i | \(-0.136578\pi\) |
−0.416027 | + | 0.909352i | \(0.636578\pi\) | |||||||
\(228\) | −2.88869 | − | 2.88869i | −0.191308 | − | 0.191308i | ||||
\(229\) | 10.5109 | 0.694583 | 0.347291 | − | 0.937757i | \(-0.387101\pi\) | ||||
0.347291 | + | 0.937757i | \(0.387101\pi\) | |||||||
\(230\) | −6.17744 | + | 4.23304i | −0.407328 | + | 0.279118i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.274026 | − | 0.274026i | 0.0179907 | − | 0.0179907i | ||||
\(233\) | −16.2668 | − | 16.2668i | −1.06568 | − | 1.06568i | −0.997686 | − | 0.0679900i | \(-0.978341\pi\) |
−0.0679900 | − | 0.997686i | \(-0.521659\pi\) | |||||||
\(234\) | 0.261316 | 0.0170828 | ||||||||
\(235\) | −22.9237 | − | 4.28153i | −1.49538 | − | 0.279296i | ||||
\(236\) | − | 9.70992i | − | 0.632062i | ||||||
\(237\) | 5.27582 | + | 5.27582i | 0.342702 | + | 0.342702i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.4914i | 1.26080i | 0.776272 | + | 0.630398i | \(0.217108\pi\) | ||||
−0.776272 | + | 0.630398i | \(0.782892\pi\) | |||||||
\(240\) | −0.410538 | + | 2.19806i | −0.0265001 | + | 0.141884i | ||||
\(241\) | − | 8.15049i | − | 0.525019i | −0.964929 | − | 0.262509i | \(-0.915450\pi\) | ||
0.964929 | − | 0.262509i | \(-0.0845501\pi\) | |||||||
\(242\) | −11.0598 | + | 11.0598i | −0.710950 | + | 0.710950i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 11.0100 | 0.704846 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −7.05881 | −0.450054 | ||||||||
\(247\) | −0.754861 | + | 0.754861i | −0.0480307 | + | 0.0480307i | ||||
\(248\) | 7.50483 | − | 7.50483i | 0.476557 | − | 0.476557i | ||||
\(249\) | − | 0.578647i | − | 0.0366702i | ||||||
\(250\) | −9.50843 | − | 5.88130i | −0.601366 | − | 0.371966i | ||||
\(251\) | − | 8.93480i | − | 0.563960i | −0.959420 | − | 0.281980i | \(-0.909009\pi\) | ||
0.959420 | − | 0.281980i | \(-0.0909911\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.2230 | − | 12.2230i | −0.768450 | − | 0.768450i | ||||
\(254\) | 18.8253i | 1.18120i | ||||||||
\(255\) | −1.95886 | + | 1.34230i | −0.122669 | + | 0.0840578i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 2.26445 | + | 2.26445i | 0.141253 | + | 0.141253i | 0.774197 | − | 0.632944i | \(-0.218154\pi\) |
−0.632944 | + | 0.774197i | \(0.718154\pi\) | |||||||
\(258\) | −2.13217 | + | 2.13217i | −0.132743 | + | 0.132743i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0.574387 | + | 0.107280i | 0.0356220 | + | 0.00665323i | ||||
\(261\) | −0.387531 | −0.0239876 | ||||||||
\(262\) | 7.71587 | + | 7.71587i | 0.476688 | + | 0.476688i | ||||
\(263\) | 8.87987 | + | 8.87987i | 0.547556 | + | 0.547556i | 0.925733 | − | 0.378177i | \(-0.123449\pi\) |
−0.378177 | + | 0.925733i | \(0.623449\pi\) | |||||||
\(264\) | −5.16148 | −0.317667 | ||||||||
\(265\) | −22.2356 | − | 4.15302i | −1.36592 | − | 0.255118i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.98884 | + | 9.98884i | −0.611307 | + | 0.611307i | ||||
\(268\) | 0.0355377 | + | 0.0355377i | 0.00217081 | + | 0.00217081i | ||||
\(269\) | −7.38784 | −0.450445 | −0.225222 | − | 0.974307i | \(-0.572311\pi\) | ||||
−0.225222 | + | 0.974307i | \(0.572311\pi\) | |||||||
\(270\) | 1.84456 | − | 1.26397i | 0.112256 | − | 0.0769226i | ||||
\(271\) | 2.27382i | 0.138124i | 0.997612 | + | 0.0690622i | \(0.0220007\pi\) | ||||
−0.997612 | + | 0.0690622i | \(0.977999\pi\) | |||||||
\(272\) | 0.750926 | + | 0.750926i | 0.0455316 | + | 0.0455316i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 4.09155i | − | 0.247180i | ||||||
\(275\) | 9.31531 | − | 24.0676i | 0.561734 | − | 1.45133i | ||||
\(276\) | − | 3.34901i | − | 0.201587i | ||||||
\(277\) | −17.8539 | + | 17.8539i | −1.07274 | + | 1.07274i | −0.0755979 | + | 0.997138i | \(0.524087\pi\) |
−0.997138 | + | 0.0755979i | \(0.975913\pi\) | |||||||
\(278\) | 7.34268 | − | 7.34268i | 0.440384 | − | 0.440384i | ||||
\(279\) | −10.6134 | −0.635410 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.1380 | −1.61892 | −0.809458 | − | 0.587178i | \(-0.800239\pi\) | ||||
−0.809458 | + | 0.587178i | \(0.800239\pi\) | |||||||
\(282\) | 7.37446 | − | 7.37446i | 0.439143 | − | 0.439143i | ||||
\(283\) | −2.30592 | + | 2.30592i | −0.137073 | + | 0.137073i | −0.772314 | − | 0.635241i | \(-0.780901\pi\) |
0.635241 | + | 0.772314i | \(0.280901\pi\) | |||||||
\(284\) | − | 15.7253i | − | 0.933127i | ||||||
\(285\) | −1.67714 | + | 8.97957i | −0.0993453 | + | 0.531904i | ||||
\(286\) | 1.34878i | 0.0797549i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | − | 15.8722i | − | 0.933660i | ||||||
\(290\) | −0.851815 | − | 0.159096i | −0.0500203 | − | 0.00934245i | ||||
\(291\) | −1.87379 | −0.109843 | ||||||||
\(292\) | 3.22877 | + | 3.22877i | 0.188949 | + | 0.188949i | ||||
\(293\) | 22.8732 | − | 22.8732i | 1.33627 | − | 1.33627i | 0.436625 | − | 0.899643i | \(-0.356174\pi\) |
0.899643 | − | 0.436625i | \(-0.143826\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.9105 | + | 12.2730i | −1.04279 | + | 0.714563i | ||||
\(296\) | 3.55196 | 0.206454 | ||||||||
\(297\) | 3.64972 | + | 3.64972i | 0.211778 | + | 0.211778i | ||||
\(298\) | 11.8689 | + | 11.8689i | 0.687548 | + | 0.687548i | ||||
\(299\) | −0.875150 | −0.0506112 | ||||||||
\(300\) | 4.57335 | − | 2.02101i | 0.264042 | − | 0.116683i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.90479 | + | 6.90479i | −0.397326 | + | 0.397326i | ||||
\(303\) | 1.83867 | + | 1.83867i | 0.105629 | + | 0.105629i | ||||
\(304\) | 4.08523 | 0.234304 | ||||||||
\(305\) | −13.9163 | − | 20.3086i | −0.796847 | − | 1.16287i | ||||
\(306\) | − | 1.06197i | − | 0.0607088i | ||||||
\(307\) | 2.06248 | + | 2.06248i | 0.117712 | + | 0.117712i | 0.763509 | − | 0.645797i | \(-0.223475\pi\) |
−0.645797 | + | 0.763509i | \(0.723475\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 8.77942i | − | 0.499444i | ||||||
\(310\) | −23.3289 | − | 4.35722i | −1.32499 | − | 0.247473i | ||||
\(311\) | 5.67250i | 0.321658i | 0.986982 | + | 0.160829i | \(0.0514168\pi\) | ||||
−0.986982 | + | 0.160829i | \(0.948583\pi\) | |||||||
\(312\) | −0.184778 | + | 0.184778i | −0.0104610 | + | 0.0104610i | ||||
\(313\) | 23.7286 | − | 23.7286i | 1.34122 | − | 1.34122i | 0.446374 | − | 0.894847i | \(-0.352715\pi\) |
0.894847 | − | 0.446374i | \(-0.147285\pi\) | |||||||
\(314\) | −12.2589 | −0.691811 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.46114 | −0.419722 | ||||||||
\(317\) | −7.61158 | + | 7.61158i | −0.427509 | + | 0.427509i | −0.887779 | − | 0.460270i | \(-0.847753\pi\) |
0.460270 | + | 0.887779i | \(0.347753\pi\) | |||||||
\(318\) | 7.15311 | − | 7.15311i | 0.401127 | − | 0.401127i | ||||
\(319\) | − | 2.00023i | − | 0.111992i | ||||||
\(320\) | −1.26397 | − | 1.84456i | −0.0706579 | − | 0.103114i | ||||
\(321\) | − | 19.2851i | − | 1.07639i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.06770 | + | 3.06770i | 0.170692 | + | 0.170692i | ||||
\(324\) | 1.00000i | 0.0555556i | ||||||||
\(325\) | −0.528123 | − | 1.19509i | −0.0292950 | − | 0.0662916i | ||||
\(326\) | −19.4728 | −1.07850 | ||||||||
\(327\) | 5.12028 | + | 5.12028i | 0.283152 | + | 0.283152i | ||||
\(328\) | 4.99134 | − | 4.99134i | 0.275600 | − | 0.275600i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 6.52395 | + | 9.52064i | 0.359131 | + | 0.524094i | ||||
\(331\) | −5.09546 | −0.280072 | −0.140036 | − | 0.990146i | \(-0.544722\pi\) | ||||
−0.140036 | + | 0.990146i | \(0.544722\pi\) | |||||||
\(332\) | 0.409165 | + | 0.409165i | 0.0224558 | + | 0.0224558i | ||||
\(333\) | −2.51162 | − | 2.51162i | −0.137636 | − | 0.137636i | ||||
\(334\) | −6.11020 | −0.334335 | ||||||||
\(335\) | 0.0206328 | − | 0.110470i | 0.00112729 | − | 0.00603562i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.29846 | − | 8.29846i | 0.452046 | − | 0.452046i | −0.443987 | − | 0.896033i | \(-0.646436\pi\) |
0.896033 | + | 0.443987i | \(0.146436\pi\) | |||||||
\(338\) | −9.14410 | − | 9.14410i | −0.497374 | − | 0.497374i | ||||
\(339\) | 7.73244 | 0.419969 | ||||||||
\(340\) | 0.435979 | − | 2.33427i | 0.0236443 | − | 0.126594i | ||||
\(341\) | − | 54.7810i | − | 2.96656i | ||||||
\(342\) | −2.88869 | − | 2.88869i | −0.156203 | − | 0.156203i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 3.01534i | − | 0.162576i | ||||||
\(345\) | −6.17744 | + | 4.23304i | −0.332582 | + | 0.227899i | ||||
\(346\) | 20.2522i | 1.08876i | ||||||||
\(347\) | −9.94950 | + | 9.94950i | −0.534117 | + | 0.534117i | −0.921795 | − | 0.387678i | \(-0.873277\pi\) |
0.387678 | + | 0.921795i | \(0.373277\pi\) | |||||||
\(348\) | 0.274026 | − | 0.274026i | 0.0146893 | − | 0.0146893i | ||||
\(349\) | 25.7633 | 1.37908 | 0.689540 | − | 0.724247i | \(-0.257813\pi\) | ||||
0.689540 | + | 0.724247i | \(0.257813\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.261316 | 0.0139480 | ||||||||
\(352\) | 3.64972 | − | 3.64972i | 0.194531 | − | 0.194531i | ||||
\(353\) | −0.116111 | + | 0.116111i | −0.00617997 | + | 0.00617997i | −0.710190 | − | 0.704010i | \(-0.751391\pi\) |
0.704010 | + | 0.710190i | \(0.251391\pi\) | |||||||
\(354\) | − | 9.70992i | − | 0.516076i | ||||||
\(355\) | −29.0063 | + | 19.8763i | −1.53949 | + | 1.05493i | ||||
\(356\) | − | 14.1264i | − | 0.748695i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15.7122 | − | 15.7122i | −0.830416 | − | 0.830416i | ||||
\(359\) | − | 11.3365i | − | 0.598319i | −0.954203 | − | 0.299159i | \(-0.903294\pi\) | ||
0.954203 | − | 0.299159i | \(-0.0967062\pi\) | |||||||
\(360\) | −0.410538 | + | 2.19806i | −0.0216373 | + | 0.115848i | ||||
\(361\) | −2.31092 | −0.121627 | ||||||||
\(362\) | 17.7697 | + | 17.7697i | 0.933953 | + | 0.933953i | ||||
\(363\) | −11.0598 | + | 11.0598i | −0.580488 | + | 0.580488i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.87459 | − | 10.0367i | 0.0981203 | − | 0.525345i | ||||
\(366\) | 11.0100 | 0.575504 | ||||||||
\(367\) | 9.84215 | + | 9.84215i | 0.513756 | + | 0.513756i | 0.915675 | − | 0.401919i | \(-0.131657\pi\) |
−0.401919 | + | 0.915675i | \(0.631657\pi\) | |||||||
\(368\) | 2.36811 | + | 2.36811i | 0.123446 | + | 0.123446i | ||||
\(369\) | −7.05881 | −0.367467 | ||||||||
\(370\) | −4.48957 | − | 6.55180i | −0.233401 | − | 0.340612i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 7.50483 | − | 7.50483i | 0.389107 | − | 0.389107i | ||||
\(373\) | −9.17514 | − | 9.17514i | −0.475071 | − | 0.475071i | 0.428480 | − | 0.903551i | \(-0.359049\pi\) |
−0.903551 | + | 0.428480i | \(0.859049\pi\) | |||||||
\(374\) | 5.48134 | 0.283433 | ||||||||
\(375\) | −9.50843 | − | 5.88130i | −0.491013 | − | 0.303709i | ||||
\(376\) | 10.4291i | 0.537838i | ||||||||
\(377\) | −0.0716073 | − | 0.0716073i | −0.00368796 | − | 0.00368796i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 24.7501i | − | 1.27133i | −0.771967 | − | 0.635663i | \(-0.780727\pi\) | ||
0.771967 | − | 0.635663i | \(-0.219273\pi\) | |||||||
\(380\) | −5.16359 | − | 7.53543i | −0.264887 | − | 0.386559i | ||||
\(381\) | 18.8253i | 0.964448i | ||||||||
\(382\) | −1.08890 | + | 1.08890i | −0.0557130 | + | 0.0557130i | ||||
\(383\) | −13.7562 | + | 13.7562i | −0.702908 | + | 0.702908i | −0.965034 | − | 0.262126i | \(-0.915577\pi\) |
0.262126 | + | 0.965034i | \(0.415577\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 18.0070 | 0.916533 | ||||||||
\(387\) | −2.13217 | + | 2.13217i | −0.108384 | + | 0.108384i | ||||
\(388\) | 1.32497 | − | 1.32497i | 0.0672650 | − | 0.0672650i | ||||
\(389\) | − | 8.60539i | − | 0.436310i | −0.975914 | − | 0.218155i | \(-0.929996\pi\) | ||
0.975914 | − | 0.218155i | \(-0.0700039\pi\) | |||||||
\(390\) | 0.574387 | + | 0.107280i | 0.0290852 | + | 0.00543234i | ||||
\(391\) | 3.55655i | 0.179862i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.71587 | + | 7.71587i | 0.389214 | + | 0.389214i | ||||
\(394\) | 16.9929i | 0.856087i | ||||||||
\(395\) | 9.43064 | + | 13.7625i | 0.474507 | + | 0.692466i | ||||
\(396\) | −5.16148 | −0.259374 | ||||||||
\(397\) | −19.1209 | − | 19.1209i | −0.959649 | − | 0.959649i | 0.0395679 | − | 0.999217i | \(-0.487402\pi\) |
−0.999217 | + | 0.0395679i | \(0.987402\pi\) | |||||||
\(398\) | 6.66254 | − | 6.66254i | 0.333963 | − | 0.333963i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.80477 | + | 4.66292i | −0.0902387 | + | 0.233146i | ||||
\(401\) | −6.66995 | −0.333082 | −0.166541 | − | 0.986035i | \(-0.553260\pi\) | ||||
−0.166541 | + | 0.986035i | \(0.553260\pi\) | |||||||
\(402\) | 0.0355377 | + | 0.0355377i | 0.00177246 | + | 0.00177246i | ||||
\(403\) | −1.96113 | − | 1.96113i | −0.0976909 | − | 0.0976909i | ||||
\(404\) | −2.60028 | −0.129369 | ||||||||
\(405\) | 1.84456 | − | 1.26397i | 0.0916567 | − | 0.0628070i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.9637 | − | 12.9637i | 0.642585 | − | 0.642585i | ||||
\(408\) | 0.750926 | + | 0.750926i | 0.0371764 | + | 0.0371764i | ||||
\(409\) | −17.0199 | −0.841579 | −0.420789 | − | 0.907158i | \(-0.638247\pi\) | ||||
−0.420789 | + | 0.907158i | \(0.638247\pi\) | |||||||
\(410\) | −15.5157 | − | 2.89791i | −0.766265 | − | 0.143118i | ||||
\(411\) | − | 4.09155i | − | 0.201821i | ||||||
\(412\) | 6.20799 | + | 6.20799i | 0.305846 | + | 0.305846i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − | 3.34901i | − | 0.164595i | ||||||
\(415\) | 0.237556 | − | 1.27190i | 0.0116612 | − | 0.0624350i | ||||
\(416\) | − | 0.261316i | − | 0.0128121i | ||||||
\(417\) | 7.34268 | − | 7.34268i | 0.359572 | − | 0.359572i | ||||
\(418\) | 14.9099 | − | 14.9099i | 0.729269 | − | 0.729269i | ||||
\(419\) | 2.00407 | 0.0979052 | 0.0489526 | − | 0.998801i | \(-0.484412\pi\) | ||||
0.0489526 | + | 0.998801i | \(0.484412\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.44745 | 0.0705444 | 0.0352722 | − | 0.999378i | \(-0.488770\pi\) | ||||
0.0352722 | + | 0.999378i | \(0.488770\pi\) | |||||||
\(422\) | −10.2276 | + | 10.2276i | −0.497874 | + | 0.497874i | ||||
\(423\) | 7.37446 | − | 7.37446i | 0.358558 | − | 0.358558i | ||||
\(424\) | 10.1160i | 0.491278i | ||||||||
\(425\) | −4.85676 | + | 2.14626i | −0.235587 | + | 0.104109i | ||||
\(426\) | − | 15.7253i | − | 0.761895i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 13.6366 | + | 13.6366i | 0.659151 | + | 0.659151i | ||||
\(429\) | 1.34878i | 0.0651196i | ||||||||
\(430\) | −5.56197 | + | 3.81129i | −0.268222 | + | 0.183797i | ||||
\(431\) | 16.8876 | 0.813447 | 0.406724 | − | 0.913551i | \(-0.366671\pi\) | ||||
0.406724 | + | 0.913551i | \(0.366671\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 20.5784 | − | 20.5784i | 0.988934 | − | 0.988934i | −0.0110055 | − | 0.999939i | \(-0.503503\pi\) |
0.999939 | + | 0.0110055i | \(0.00350324\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.851815 | − | 0.159096i | −0.0408414 | − | 0.00762808i | ||||
\(436\) | −7.24117 | −0.346789 | ||||||||
\(437\) | 9.67426 | + | 9.67426i | 0.462783 | + | 0.462783i | ||||
\(438\) | 3.22877 | + | 3.22877i | 0.154276 | + | 0.154276i | ||||
\(439\) | −2.72617 | −0.130113 | −0.0650564 | − | 0.997882i | \(-0.520723\pi\) | ||||
−0.0650564 | + | 0.997882i | \(0.520723\pi\) | |||||||
\(440\) | −11.3452 | − | 2.11899i | −0.540863 | − | 0.101019i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0.196229 | − | 0.196229i | 0.00933366 | − | 0.00933366i | ||||
\(443\) | −0.586605 | − | 0.586605i | −0.0278705 | − | 0.0278705i | 0.693034 | − | 0.720905i | \(-0.256273\pi\) |
−0.720905 | + | 0.693034i | \(0.756273\pi\) | |||||||
\(444\) | 3.55196 | 0.168569 | ||||||||
\(445\) | −26.0569 | + | 17.8553i | −1.23521 | + | 0.846420i | ||||
\(446\) | 11.0351i | 0.522529i | ||||||||
\(447\) | 11.8689 | + | 11.8689i | 0.561380 | + | 0.561380i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 26.3699i | 1.24447i | 0.782830 | + | 0.622235i | \(0.213775\pi\) | ||||
−0.782830 | + | 0.622235i | \(0.786225\pi\) | |||||||
\(450\) | 4.57335 | − | 2.02101i | 0.215590 | − | 0.0952715i | ||||
\(451\) | − | 36.4339i | − | 1.71561i | ||||||
\(452\) | −5.46766 | + | 5.46766i | −0.257177 | + | 0.257177i | ||||
\(453\) | −6.90479 | + | 6.90479i | −0.324415 | + | 0.324415i | ||||
\(454\) | −10.5114 | −0.493325 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.08523 | 0.191308 | ||||||||
\(457\) | −18.1053 | + | 18.1053i | −0.846929 | + | 0.846929i | −0.989749 | − | 0.142820i | \(-0.954383\pi\) |
0.142820 | + | 0.989749i | \(0.454383\pi\) | |||||||
\(458\) | −7.43236 | + | 7.43236i | −0.347291 | + | 0.347291i | ||||
\(459\) | − | 1.06197i | − | 0.0495685i | ||||||
\(460\) | 1.37490 | − | 7.36132i | 0.0641049 | − | 0.343223i | ||||
\(461\) | 4.45597i | 0.207535i | 0.994602 | + | 0.103768i | \(0.0330898\pi\) | ||||
−0.994602 | + | 0.103768i | \(0.966910\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4474 | − | 12.4474i | −0.578482 | − | 0.578482i | 0.356003 | − | 0.934485i | \(-0.384139\pi\) |
−0.934485 | + | 0.356003i | \(0.884139\pi\) | |||||||
\(464\) | 0.387531i | 0.0179907i | ||||||||
\(465\) | −23.3289 | − | 4.35722i | −1.08185 | − | 0.202061i | ||||
\(466\) | 23.0048 | 1.06568 | ||||||||
\(467\) | −8.34972 | − | 8.34972i | −0.386379 | − | 0.386379i | 0.487015 | − | 0.873394i | \(-0.338086\pi\) |
−0.873394 | + | 0.487015i | \(0.838086\pi\) | |||||||
\(468\) | −0.184778 | + | 0.184778i | −0.00854138 | + | 0.00854138i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 19.2370 | − | 13.1820i | 0.887336 | − | 0.608040i | ||||
\(471\) | −12.2589 | −0.564861 | ||||||||
\(472\) | 6.86595 | + | 6.86595i | 0.316031 | + | 0.316031i | ||||
\(473\) | −11.0052 | − | 11.0052i | −0.506018 | − | 0.506018i | ||||
\(474\) | −7.46114 | −0.342702 | ||||||||
\(475\) | −7.37291 | + | 19.0491i | −0.338292 | + | 0.874032i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.15311 | − | 7.15311i | 0.327519 | − | 0.327519i | ||||
\(478\) | −13.7825 | − | 13.7825i | −0.630398 | − | 0.630398i | ||||
\(479\) | −11.9092 | −0.544147 | −0.272073 | − | 0.962276i | \(-0.587709\pi\) | ||||
−0.272073 | + | 0.962276i | \(0.587709\pi\) | |||||||
\(480\) | −1.26397 | − | 1.84456i | −0.0576920 | − | 0.0841921i | ||||
\(481\) | − | 0.928184i | − | 0.0423216i | ||||||
\(482\) | 5.76326 | + | 5.76326i | 0.262509 | + | 0.262509i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 15.6409i | − | 0.710950i | ||||||
\(485\) | −4.11869 | − | 0.769261i | −0.187020 | − | 0.0349303i | ||||
\(486\) | 1.00000i | 0.0453609i | ||||||||
\(487\) | −24.0514 | + | 24.0514i | −1.08987 | + | 1.08987i | −0.0943340 | + | 0.995541i | \(0.530072\pi\) |
−0.995541 | + | 0.0943340i | \(0.969928\pi\) | |||||||
\(488\) | −7.78528 | + | 7.78528i | −0.352423 | + | 0.352423i | ||||
\(489\) | −19.4728 | −0.880591 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −32.7719 | −1.47898 | −0.739488 | − | 0.673169i | \(-0.764932\pi\) | ||||
−0.739488 | + | 0.673169i | \(0.764932\pi\) | |||||||
\(492\) | 4.99134 | − | 4.99134i | 0.225027 | − | 0.225027i | ||||
\(493\) | −0.291007 | + | 0.291007i | −0.0131063 | + | 0.0131063i | ||||
\(494\) | − | 1.06753i | − | 0.0480307i | ||||||
\(495\) | 6.52395 | + | 9.52064i | 0.293230 | + | 0.427921i | ||||
\(496\) | 10.6134i | 0.476557i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.409165 | + | 0.409165i | 0.0183351 | + | 0.0183351i | ||||
\(499\) | 29.0636i | 1.30107i | 0.759478 | + | 0.650533i | \(0.225454\pi\) | ||||
−0.759478 | + | 0.650533i | \(0.774546\pi\) | |||||||
\(500\) | 10.8822 | − | 2.56477i | 0.486666 | − | 0.114700i | ||||
\(501\) | −6.11020 | −0.272984 | ||||||||
\(502\) | 6.31786 | + | 6.31786i | 0.281980 | + | 0.281980i | ||||
\(503\) | 2.02797 | − | 2.02797i | 0.0904226 | − | 0.0904226i | −0.660449 | − | 0.750871i | \(-0.729634\pi\) |
0.750871 | + | 0.660449i | \(0.229634\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.28667 | + | 4.79636i | 0.146255 | + | 0.213435i | ||||
\(506\) | 17.2859 | 0.768450 | ||||||||
\(507\) | −9.14410 | − | 9.14410i | −0.406104 | − | 0.406104i | ||||
\(508\) | −13.3115 | − | 13.3115i | −0.590601 | − | 0.590601i | ||||
\(509\) | 5.18151 | 0.229666 | 0.114833 | − | 0.993385i | \(-0.463367\pi\) | ||||
0.114833 | + | 0.993385i | \(0.463367\pi\) | |||||||
\(510\) | 0.435979 | − | 2.33427i | 0.0193055 | − | 0.103363i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −2.88869 | − | 2.88869i | −0.127539 | − | 0.127539i | ||||
\(514\) | −3.20242 | −0.141253 | ||||||||
\(515\) | 3.60429 | − | 19.2977i | 0.158824 | − | 0.850357i | ||||
\(516\) | − | 3.01534i | − | 0.132743i | ||||||
\(517\) | 38.0631 | + | 38.0631i | 1.67401 | + | 1.67401i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 20.2522i | 0.888972i | ||||||||
\(520\) | −0.482012 | + | 0.330295i | −0.0211376 | + | 0.0144844i | ||||
\(521\) | 4.08595i | 0.179009i | 0.995986 | + | 0.0895044i | \(0.0285283\pi\) | ||||
−0.995986 | + | 0.0895044i | \(0.971472\pi\) | |||||||
\(522\) | 0.274026 | − | 0.274026i | 0.0119938 | − | 0.0119938i | ||||
\(523\) | 3.85548 | − | 3.85548i | 0.168588 | − | 0.168588i | −0.617770 | − | 0.786359i | \(-0.711964\pi\) |
0.786359 | + | 0.617770i | \(0.211964\pi\) | |||||||
\(524\) | −10.9119 | −0.476688 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12.5580 | −0.547556 | ||||||||
\(527\) | −7.96990 | + | 7.96990i | −0.347174 | + | 0.347174i | ||||
\(528\) | 3.64972 | − | 3.64972i | 0.158834 | − | 0.158834i | ||||
\(529\) | − | 11.7841i | − | 0.512353i | ||||||
\(530\) | 18.6596 | − | 12.7863i | 0.810520 | − | 0.555403i | ||||
\(531\) | − | 9.70992i | − | 0.421375i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.30432 | − | 1.30432i | −0.0564962 | − | 0.0564962i | ||||
\(534\) | − | 14.1264i | − | 0.611307i | ||||||
\(535\) | 7.91727 | − | 42.3898i | 0.342293 | − | 1.83267i | ||||
\(536\) | −0.0502580 | −0.00217081 | ||||||||
\(537\) | −15.7122 | − | 15.7122i | −0.678032 | − | 0.678032i | ||||
\(538\) | 5.22400 | − | 5.22400i | 0.225222 | − | 0.225222i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.410538 | + | 2.19806i | −0.0176667 | + | 0.0945894i | ||||
\(541\) | 30.1052 | 1.29432 | 0.647162 | − | 0.762353i | \(-0.275956\pi\) | ||||
0.647162 | + | 0.762353i | \(0.275956\pi\) | |||||||
\(542\) | −1.60783 | − | 1.60783i | −0.0690622 | − | 0.0690622i | ||||
\(543\) | 17.7697 | + | 17.7697i | 0.762569 | + | 0.762569i | ||||
\(544\) | −1.06197 | −0.0455316 | ||||||||
\(545\) | 9.15260 | + | 13.3567i | 0.392054 | + | 0.572140i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.00208 | + | 5.00208i | −0.213873 | + | 0.213873i | −0.805911 | − | 0.592037i | \(-0.798324\pi\) |
0.592037 | + | 0.805911i | \(0.298324\pi\) | |||||||
\(548\) | 2.89316 | + | 2.89316i | 0.123590 | + | 0.123590i | ||||
\(549\) | 11.0100 | 0.469897 | ||||||||
\(550\) | 10.4314 | + | 23.6053i | 0.444797 | + | 1.00653i | ||||
\(551\) | 1.58315i | 0.0674445i | ||||||||
\(552\) | 2.36811 | + | 2.36811i | 0.100793 | + | 0.100793i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 25.2492i | − | 1.07274i | ||||||
\(555\) | −4.48957 | − | 6.55180i | −0.190571 | − | 0.278108i | ||||
\(556\) | 10.3841i | 0.440384i | ||||||||
\(557\) | 22.4314 | − | 22.4314i | 0.950451 | − | 0.950451i | −0.0483784 | − | 0.998829i | \(-0.515405\pi\) |
0.998829 | + | 0.0483784i | \(0.0154053\pi\) | |||||||
\(558\) | 7.50483 | − | 7.50483i | 0.317705 | − | 0.317705i | ||||
\(559\) | −0.787957 | −0.0333270 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.48134 | 0.231422 | ||||||||
\(562\) | 19.1894 | − | 19.1894i | 0.809458 | − | 0.809458i | ||||
\(563\) | 15.6424 | − | 15.6424i | 0.659247 | − | 0.659247i | −0.295955 | − | 0.955202i | \(-0.595638\pi\) |
0.955202 | + | 0.295955i | \(0.0956378\pi\) | |||||||
\(564\) | 10.4291i | 0.439143i | ||||||||
\(565\) | 16.9964 | + | 3.17446i | 0.715042 | + | 0.133551i | ||||
\(566\) | − | 3.26106i | − | 0.137073i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1195 | + | 11.1195i | 0.466564 | + | 0.466564i | ||||
\(569\) | 36.8555i | 1.54506i | 0.634977 | + | 0.772531i | \(0.281010\pi\) | ||||
−0.634977 | + | 0.772531i | \(0.718990\pi\) | |||||||
\(570\) | −5.16359 | − | 7.53543i | −0.216279 | − | 0.315624i | ||||
\(571\) | 34.4042 | 1.43977 | 0.719885 | − | 0.694093i | \(-0.244194\pi\) | ||||
0.719885 | + | 0.694093i | \(0.244194\pi\) | |||||||
\(572\) | −0.953730 | − | 0.953730i | −0.0398774 | − | 0.0398774i | ||||
\(573\) | −1.08890 | + | 1.08890i | −0.0454895 | + | 0.0454895i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −15.3162 | + | 6.76839i | −0.638729 | + | 0.282262i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −32.5072 | − | 32.5072i | −1.35329 | − | 1.35329i | −0.881949 | − | 0.471346i | \(-0.843768\pi\) |
−0.471346 | − | 0.881949i | \(-0.656232\pi\) | |||||||
\(578\) | 11.2234 | + | 11.2234i | 0.466830 | + | 0.466830i | ||||
\(579\) | 18.0070 | 0.748346 | ||||||||
\(580\) | 0.714822 | − | 0.489826i | 0.0296814 | − | 0.0203389i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.32497 | − | 1.32497i | 0.0549217 | − | 0.0549217i | ||||
\(583\) | 36.9207 | + | 36.9207i | 1.52910 | + | 1.52910i | ||||
\(584\) | −4.56617 | −0.188949 | ||||||||
\(585\) | 0.574387 | + | 0.107280i | 0.0237480 | + | 0.00443549i | ||||
\(586\) | 32.3476i | 1.33627i | ||||||||
\(587\) | −6.93980 | − | 6.93980i | −0.286436 | − | 0.286436i | 0.549233 | − | 0.835669i | \(-0.314920\pi\) |
−0.835669 | + | 0.549233i | \(0.814920\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 43.3583i | 1.78655i | ||||||||
\(590\) | 3.98629 | − | 21.3430i | 0.164113 | − | 0.878676i | ||||
\(591\) | 16.9929i | 0.698992i | ||||||||
\(592\) | −2.51162 | + | 2.51162i | −0.103227 | + | 0.103227i | ||||
\(593\) | −28.8960 | + | 28.8960i | −1.18662 | + | 1.18662i | −0.208621 | + | 0.977997i | \(0.566897\pi\) |
−0.977997 | + | 0.208621i | \(0.933103\pi\) | |||||||
\(594\) | −5.16148 | −0.211778 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16.7852 | −0.687548 | ||||||||
\(597\) | 6.66254 | − | 6.66254i | 0.272680 | − | 0.272680i | ||||
\(598\) | 0.618824 | − | 0.618824i | 0.0253056 | − | 0.0253056i | ||||
\(599\) | 25.5344i | 1.04331i | 0.853157 | + | 0.521654i | \(0.174685\pi\) | ||||
−0.853157 | + | 0.521654i | \(0.825315\pi\) | |||||||
\(600\) | −1.80477 | + | 4.66292i | −0.0736796 | + | 0.190363i | ||||
\(601\) | − | 8.12886i | − | 0.331583i | −0.986161 | − | 0.165792i | \(-0.946982\pi\) | ||
0.986161 | − | 0.165792i | \(-0.0530179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.0355377 | + | 0.0355377i | 0.00144721 | + | 0.00144721i | ||||
\(604\) | − | 9.76485i | − | 0.397326i | ||||||
\(605\) | −28.8505 | + | 19.7696i | −1.17294 | + | 0.803748i | ||||
\(606\) | −2.60028 | −0.105629 | ||||||||
\(607\) | −17.5109 | − | 17.5109i | −0.710744 | − | 0.710744i | 0.255947 | − | 0.966691i | \(-0.417613\pi\) |
−0.966691 | + | 0.255947i | \(0.917613\pi\) | |||||||
\(608\) | −2.88869 | + | 2.88869i | −0.117152 | + | 0.117152i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.2007 | + | 4.52004i | 0.979858 | + | 0.183011i | ||||
\(611\) | 2.72528 | 0.110253 | ||||||||
\(612\) | 0.750926 | + | 0.750926i | 0.0303544 | + | 0.0303544i | ||||
\(613\) | −18.1428 | − | 18.1428i | −0.732780 | − | 0.732780i | 0.238389 | − | 0.971170i | \(-0.423381\pi\) |
−0.971170 | + | 0.238389i | \(0.923381\pi\) | |||||||
\(614\) | −2.91679 | −0.117712 | ||||||||
\(615\) | −15.5157 | − | 2.89791i | −0.625653 | − | 0.116855i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.6259 | − | 10.6259i | 0.427784 | − | 0.427784i | −0.460089 | − | 0.887873i | \(-0.652182\pi\) |
0.887873 | + | 0.460089i | \(0.152182\pi\) | |||||||
\(618\) | 6.20799 | + | 6.20799i | 0.249722 | + | 0.249722i | ||||
\(619\) | 35.7243 | 1.43588 | 0.717940 | − | 0.696105i | \(-0.245085\pi\) | ||||
0.717940 | + | 0.696105i | \(0.245085\pi\) | |||||||
\(620\) | 19.5771 | − | 13.4150i | 0.786234 | − | 0.538761i | ||||
\(621\) | − | 3.34901i | − | 0.134391i | ||||||
\(622\) | −4.01106 | − | 4.01106i | −0.160829 | − | 0.160829i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 0.261316i | − | 0.0104610i | ||||||
\(625\) | −18.4856 | − | 16.8310i | −0.739423 | − | 0.673241i | ||||
\(626\) | 33.5573i | 1.34122i | ||||||||
\(627\) | 14.9099 | − | 14.9099i | 0.595445 | − | 0.595445i | ||||
\(628\) | 8.66837 | − | 8.66837i | 0.345906 | − | 0.345906i | ||||
\(629\) | −3.77208 | −0.150403 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 11.8871 | 0.473220 | 0.236610 | − | 0.971605i | \(-0.423964\pi\) | ||||
0.236610 | + | 0.971605i | \(0.423964\pi\) | |||||||
\(632\) | 5.27582 | − | 5.27582i | 0.209861 | − | 0.209861i | ||||
\(633\) | −10.2276 | + | 10.2276i | −0.406512 | + | 0.406512i | ||||
\(634\) | − | 10.7644i | − | 0.427509i | ||||||
\(635\) | −7.72849 | + | 41.3790i | −0.306696 | + | 1.64208i | ||||
\(636\) | 10.1160i | 0.401127i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.41438 | + | 1.41438i | 0.0559958 | + | 0.0559958i | ||||
\(639\) | − | 15.7253i | − | 0.622085i | ||||||
\(640\) | 2.19806 | + | 0.410538i | 0.0868859 | + | 0.0162279i | ||||
\(641\) | 4.10018 | 0.161947 | 0.0809736 | − | 0.996716i | \(-0.474197\pi\) | ||||
0.0809736 | + | 0.996716i | \(0.474197\pi\) | |||||||
\(642\) | 13.6366 | + | 13.6366i | 0.538195 | + | 0.538195i | ||||
\(643\) | 0.865126 | − | 0.865126i | 0.0341173 | − | 0.0341173i | −0.689842 | − | 0.723960i | \(-0.742320\pi\) |
0.723960 | + | 0.689842i | \(0.242320\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.56197 | + | 3.81129i | −0.219002 | + | 0.150070i | ||||
\(646\) | −4.33839 | −0.170692 | ||||||||
\(647\) | −21.6196 | − | 21.6196i | −0.849956 | − | 0.849956i | 0.140171 | − | 0.990127i | \(-0.455235\pi\) |
−0.990127 | + | 0.140171i | \(0.955235\pi\) | |||||||
\(648\) | −0.707107 | − | 0.707107i | −0.0277778 | − | 0.0277778i | ||||
\(649\) | 50.1176 | 1.96729 | ||||||||
\(650\) | 1.21849 | + | 0.471616i | 0.0477933 | + | 0.0184983i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.7694 | − | 13.7694i | 0.539250 | − | 0.539250i | ||||
\(653\) | 13.9720 | + | 13.9720i | 0.546768 | + | 0.546768i | 0.925505 | − | 0.378736i | \(-0.123641\pi\) |
−0.378736 | + | 0.925505i | \(0.623641\pi\) | |||||||
\(654\) | −7.24117 | −0.283152 | ||||||||
\(655\) | 13.7923 | + | 20.1276i | 0.538909 | + | 0.786450i | ||||
\(656\) | 7.05881i | 0.275600i | ||||||||
\(657\) | 3.22877 | + | 3.22877i | 0.125966 | + | 0.125966i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 37.7204i | 1.46938i | 0.678403 | + | 0.734690i | \(0.262672\pi\) | ||||
−0.678403 | + | 0.734690i | \(0.737328\pi\) | |||||||
\(660\) | −11.3452 | − | 2.11899i | −0.441613 | − | 0.0824814i | ||||
\(661\) | − | 9.49534i | − | 0.369326i | −0.982802 | − | 0.184663i | \(-0.940881\pi\) | ||
0.982802 | − | 0.184663i | \(-0.0591193\pi\) | |||||||
\(662\) | 3.60303 | − | 3.60303i | 0.140036 | − | 0.140036i | ||||
\(663\) | 0.196229 | − | 0.196229i | 0.00762090 | − | 0.00762090i | ||||
\(664\) | −0.578647 | −0.0224558 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.55196 | 0.137636 | ||||||||
\(667\) | −0.917715 | + | 0.917715i | −0.0355341 | + | 0.0355341i | ||||
\(668\) | 4.32056 | − | 4.32056i | 0.167168 | − | 0.167168i | ||||
\(669\) | 11.0351i | 0.426643i | ||||||||
\(670\) | 0.0635244 | + | 0.0927036i | 0.00245416 | + | 0.00358145i | ||||
\(671\) | 56.8281i | 2.19383i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.09653 | + | 8.09653i | 0.312098 | + | 0.312098i | 0.845722 | − | 0.533624i | \(-0.179170\pi\) |
−0.533624 | + | 0.845722i | \(0.679170\pi\) | |||||||
\(674\) | 11.7358i | 0.452046i | ||||||||
\(675\) | 4.57335 | − | 2.02101i | 0.176028 | − | 0.0777888i | ||||
\(676\) | 12.9317 | 0.497374 | ||||||||
\(677\) | 3.17891 | + | 3.17891i | 0.122176 | + | 0.122176i | 0.765551 | − | 0.643375i | \(-0.222467\pi\) |
−0.643375 | + | 0.765551i | \(0.722467\pi\) | |||||||
\(678\) | −5.46766 | + | 5.46766i | −0.209984 | + | 0.209984i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.34230 | + | 1.95886i | 0.0514747 | + | 0.0751190i | ||||
\(681\) | −10.5114 | −0.402798 | ||||||||
\(682\) | 38.7360 | + | 38.7360i | 1.48328 | + | 1.48328i | ||||
\(683\) | 22.6023 | + | 22.6023i | 0.864852 | + | 0.864852i | 0.991897 | − | 0.127045i | \(-0.0405494\pi\) |
−0.127045 | + | 0.991897i | \(0.540549\pi\) | |||||||
\(684\) | 4.08523 | 0.156203 | ||||||||
\(685\) | 1.67974 | − | 8.99346i | 0.0641795 | − | 0.343622i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.43236 | + | 7.43236i | −0.283562 | + | 0.283562i | ||||
\(688\) | 2.13217 | + | 2.13217i | 0.0812882 | + | 0.0812882i | ||||
\(689\) | 2.64348 | 0.100709 | ||||||||
\(690\) | 1.37490 | − | 7.36132i | 0.0523414 | − | 0.280241i | ||||
\(691\) | 29.0533i | 1.10524i | 0.833434 | + | 0.552620i | \(0.186372\pi\) | ||||
−0.833434 | + | 0.552620i | \(0.813628\pi\) | |||||||
\(692\) | −14.3204 | − | 14.3204i | −0.544382 | − | 0.544382i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 14.0707i | − | 0.534117i | ||||||
\(695\) | 19.1541 | − | 13.1252i | 0.726555 | − | 0.497866i | ||||
\(696\) | 0.387531i | 0.0146893i | ||||||||
\(697\) | −5.30065 | + | 5.30065i | −0.200776 | + | 0.200776i | ||||
\(698\) | −18.2174 | + | 18.2174i | −0.689540 | + | 0.689540i | ||||
\(699\) | 23.0048 | 0.870121 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.75353 | −0.141769 | −0.0708844 | − | 0.997485i | \(-0.522582\pi\) | ||||
−0.0708844 | + | 0.997485i | \(0.522582\pi\) | |||||||
\(702\) | −0.184778 | + | 0.184778i | −0.00697400 | + | 0.00697400i | ||||
\(703\) | −10.2605 | + | 10.2605i | −0.386983 | + | 0.386983i | ||||
\(704\) | 5.16148i | 0.194531i | ||||||||
\(705\) | 19.2370 | − | 13.1820i | 0.724507 | − | 0.496462i | ||||
\(706\) | − | 0.164206i | − | 0.00617997i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 6.86595 | + | 6.86595i | 0.258038 | + | 0.258038i | ||||
\(709\) | − | 30.2423i | − | 1.13577i | −0.823106 | − | 0.567887i | \(-0.807761\pi\) | ||
0.823106 | − | 0.567887i | \(-0.192239\pi\) | |||||||
\(710\) | 6.45585 | − | 34.5652i | 0.242284 | − | 1.29721i | ||||
\(711\) | −7.46114 | −0.279815 | ||||||||
\(712\) | 9.98884 | + | 9.98884i | 0.374348 | + | 0.374348i | ||||
\(713\) | −25.1338 | + | 25.1338i | −0.941267 | + | 0.941267i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.553725 | + | 2.96469i | −0.0207081 | + | 0.110873i | ||||
\(716\) | 22.2204 | 0.830416 | ||||||||
\(717\) | −13.7825 | − | 13.7825i | −0.514718 | − | 0.514718i | ||||
\(718\) | 8.01613 | + | 8.01613i | 0.299159 | + | 0.299159i | ||||
\(719\) | −2.97972 | −0.111125 | −0.0555624 | − | 0.998455i | \(-0.517695\pi\) | ||||
−0.0555624 | + | 0.998455i | \(0.517695\pi\) | |||||||
\(720\) | −1.26397 | − | 1.84456i | −0.0471053 | − | 0.0687425i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1.63406 | − | 1.63406i | 0.0608136 | − | 0.0608136i | ||||
\(723\) | 5.76326 | + | 5.76326i | 0.214338 | + | 0.214338i | ||||
\(724\) | −25.1301 | −0.933953 | ||||||||
\(725\) | −1.80702 | − | 0.699405i | −0.0671112 | − | 0.0259753i | ||||
\(726\) | − | 15.6409i | − | 0.580488i | ||||||
\(727\) | −18.0738 | − | 18.0738i | −0.670321 | − | 0.670321i | 0.287469 | − | 0.957790i | \(-0.407186\pi\) |
−0.957790 | + | 0.287469i | \(0.907186\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 5.77149 | + | 8.42255i | 0.213612 | + | 0.311733i | ||||
\(731\) | 3.20220i | 0.118438i | ||||||||
\(732\) | −7.78528 | + | 7.78528i | −0.287752 | + | 0.287752i | ||||
\(733\) | 14.5519 | − | 14.5519i | 0.537486 | − | 0.537486i | −0.385304 | − | 0.922790i | \(-0.625903\pi\) |
0.922790 | + | 0.385304i | \(0.125903\pi\) | |||||||
\(734\) | −13.9189 | −0.513756 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.34901 | −0.123446 | ||||||||
\(737\) | −0.183427 | + | 0.183427i | −0.00675664 | + | 0.00675664i | ||||
\(738\) | 4.99134 | − | 4.99134i | 0.183734 | − | 0.183734i | ||||
\(739\) | − | 15.1843i | − | 0.558562i | −0.960209 | − | 0.279281i | \(-0.909904\pi\) | ||
0.960209 | − | 0.279281i | \(-0.0900961\pi\) | |||||||
\(740\) | 7.80742 | + | 1.45822i | 0.287007 | + | 0.0536051i | ||||
\(741\) | − | 1.06753i | − | 0.0392169i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.7267 | − | 26.7267i | −0.980509 | − | 0.980509i | 0.0193046 | − | 0.999814i | \(-0.493855\pi\) |
−0.999814 | + | 0.0193046i | \(0.993855\pi\) | |||||||
\(744\) | 10.6134i | 0.389107i | ||||||||
\(745\) | 21.2159 | + | 30.9612i | 0.777291 | + | 1.13433i | ||||
\(746\) | 12.9756 | 0.475071 | ||||||||
\(747\) | 0.409165 | + | 0.409165i | 0.0149706 | + | 0.0149706i | ||||
\(748\) | −3.87589 | + | 3.87589i | −0.141717 | + | 0.141717i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 10.8822 | − | 2.56477i | 0.397361 | − | 0.0936521i | ||||
\(751\) | 15.8471 | 0.578268 | 0.289134 | − | 0.957289i | \(-0.406633\pi\) | ||||
0.289134 | + | 0.957289i | \(0.406633\pi\) | |||||||
\(752\) | −7.37446 | − | 7.37446i | −0.268919 | − | 0.268919i | ||||
\(753\) | 6.31786 | + | 6.31786i | 0.230236 | + | 0.230236i | ||||
\(754\) | 0.101268 | 0.00368796 | ||||||||
\(755\) | −18.0118 | + | 12.3425i | −0.655517 | + | 0.449188i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.96309 | − | 3.96309i | 0.144041 | − | 0.144041i | −0.631409 | − | 0.775450i | \(-0.717523\pi\) |
0.775450 | + | 0.631409i | \(0.217523\pi\) | |||||||
\(758\) | 17.5009 | + | 17.5009i | 0.635663 | + | 0.635663i | ||||
\(759\) | 17.2859 | 0.627437 | ||||||||
\(760\) | 8.97957 | + | 1.67714i | 0.325723 | + | 0.0608363i | ||||
\(761\) | 13.6146i | 0.493529i | 0.969075 | + | 0.246765i | \(0.0793675\pi\) | ||||
−0.969075 | + | 0.246765i | \(0.920633\pi\) | |||||||
\(762\) | −13.3115 | − | 13.3115i | −0.482224 | − | 0.482224i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 1.53994i | − | 0.0557130i | ||||||
\(765\) | 0.435979 | − | 2.33427i | 0.0157629 | − | 0.0843958i | ||||
\(766\) | − | 19.4542i | − | 0.702908i | ||||||
\(767\) | 1.79418 | − | 1.79418i | 0.0647841 | − | 0.0647841i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | −6.93519 | −0.250089 | −0.125045 | − | 0.992151i | \(-0.539907\pi\) | ||||
−0.125045 | + | 0.992151i | \(0.539907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.20242 | −0.115332 | ||||||||
\(772\) | −12.7329 | + | 12.7329i | −0.458267 | + | 0.458267i | ||||
\(773\) | 26.7038 | − | 26.7038i | 0.960469 | − | 0.960469i | −0.0387784 | − | 0.999248i | \(-0.512347\pi\) |
0.999248 | + | 0.0387784i | \(0.0123466\pi\) | |||||||
\(774\) | − | 3.01534i | − | 0.108384i | ||||||
\(775\) | −49.4895 | − | 19.1548i | −1.77772 | − | 0.688062i | ||||
\(776\) | 1.87379i | 0.0672650i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6.08493 | + | 6.08493i | 0.218155 | + | 0.218155i | ||||
\(779\) | 28.8369i | 1.03319i | ||||||||
\(780\) | −0.482012 | + | 0.330295i | −0.0172588 | + | 0.0118264i | ||||
\(781\) | 81.1661 | 2.90435 | ||||||||
\(782\) | −2.51486 | − | 2.51486i | −0.0899312 | − | 0.0899312i | ||||
\(783\) | 0.274026 | − | 0.274026i | 0.00979288 | − | 0.00979288i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −26.9458 | − | 5.03276i | −0.961738 | − | 0.179627i | ||||
\(786\) | −10.9119 | −0.389214 | ||||||||
\(787\) | −26.9827 | − | 26.9827i | −0.961828 | − | 0.961828i | 0.0374699 | − | 0.999298i | \(-0.488070\pi\) |
−0.999298 | + | 0.0374699i | \(0.988070\pi\) | |||||||
\(788\) | −12.0158 | − | 12.0158i | −0.428044 | − | 0.428044i | ||||
\(789\) | −12.5580 | −0.447078 | ||||||||
\(790\) | −16.4000 | − | 3.06308i | −0.583487 | − | 0.108980i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.64972 | − | 3.64972i | 0.129687 | − | 0.129687i | ||||
\(793\) | 2.03442 | + | 2.03442i | 0.0722442 | + | 0.0722442i | ||||
\(794\) | 27.0410 | 0.959649 | ||||||||
\(795\) | 18.6596 | − | 12.7863i | 0.661787 | − | 0.453484i | ||||
\(796\) | 9.42226i | 0.333963i | ||||||||
\(797\) | 27.7007 | + | 27.7007i | 0.981208 | + | 0.981208i | 0.999827 | − | 0.0186189i | \(-0.00592691\pi\) |
−0.0186189 | + | 0.999827i | \(0.505927\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.0753i | − | 0.391818i | ||||||
\(800\) | −2.02101 | − | 4.57335i | −0.0714536 | − | 0.161692i | ||||
\(801\) | − | 14.1264i | − | 0.499130i | ||||||
\(802\) | 4.71637 | − | 4.71637i | 0.166541 | − | 0.166541i | ||||
\(803\) | −16.6652 | + | 16.6652i | −0.588103 | + | 0.588103i | ||||
\(804\) | −0.0502580 | −0.00177246 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.77346 | 0.0976909 | ||||||||
\(807\) | 5.22400 | − | 5.22400i | 0.183893 | − | 0.183893i | ||||
\(808\) | 1.83867 | − | 1.83867i | 0.0646843 | − | 0.0646843i | ||||
\(809\) | − | 37.1345i | − | 1.30558i | −0.757540 | − | 0.652789i | \(-0.773599\pi\) | ||
0.757540 | − | 0.652789i | \(-0.226401\pi\) | |||||||
\(810\) | −0.410538 | + | 2.19806i | −0.0144248 | + | 0.0772319i | ||||
\(811\) | 50.9815i | 1.79020i | 0.445863 | + | 0.895101i | \(0.352897\pi\) | ||||
−0.445863 | + | 0.895101i | \(0.647103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.60783 | − | 1.60783i | −0.0563891 | − | 0.0563891i | ||||
\(814\) | 18.3334i | 0.642585i | ||||||||
\(815\) | −42.8024 | − | 7.99433i | −1.49930 | − | 0.280029i | ||||
\(816\) | −1.06197 | −0.0371764 | ||||||||
\(817\) | 8.71040 | + | 8.71040i | 0.304738 | + | 0.304738i | ||||
\(818\) | 12.0349 | − | 12.0349i | 0.420789 | − | 0.420789i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 13.0204 | − | 8.92211i | 0.454691 | − | 0.311574i | ||||
\(821\) | −27.8441 | −0.971765 | −0.485882 | − | 0.874024i | \(-0.661502\pi\) | ||||
−0.485882 | + | 0.874024i | \(0.661502\pi\) | |||||||
\(822\) | 2.89316 | + | 2.89316i | 0.100911 | + | 0.100911i | ||||
\(823\) | 22.0442 | + | 22.0442i | 0.768412 | + | 0.768412i | 0.977827 | − | 0.209415i | \(-0.0671560\pi\) |
−0.209415 | + | 0.977827i | \(0.567156\pi\) | |||||||
\(824\) | −8.77942 | −0.305846 | ||||||||
\(825\) | 10.4314 | + | 23.6053i | 0.363175 | + | 0.821829i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.46031 | + | 2.46031i | −0.0855533 | + | 0.0855533i | −0.748588 | − | 0.663035i | \(-0.769268\pi\) |
0.663035 | + | 0.748588i | \(0.269268\pi\) | |||||||
\(828\) | 2.36811 | + | 2.36811i | 0.0822975 | + | 0.0822975i | ||||
\(829\) | −23.1065 | −0.802523 | −0.401262 | − | 0.915964i | \(-0.631428\pi\) | ||||
−0.401262 | + | 0.915964i | \(0.631428\pi\) | |||||||
\(830\) | 0.731390 | + | 1.06735i | 0.0253869 | + | 0.0370481i | ||||
\(831\) | − | 25.2492i | − | 0.875885i | ||||||
\(832\) | 0.184778 | + | 0.184778i | 0.00640603 | + | 0.00640603i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.3841i | 0.359572i | ||||||||
\(835\) | −13.4306 | − | 2.50847i | −0.464784 | − | 0.0868092i | ||||
\(836\) | 21.0858i | 0.729269i | ||||||||
\(837\) | 7.50483 | − | 7.50483i | 0.259405 | − | 0.259405i | ||||
\(838\) | −1.41709 | + | 1.41709i | −0.0489526 | + | 0.0489526i | ||||
\(839\) | −17.5563 | −0.606112 | −0.303056 | − | 0.952973i | \(-0.598007\pi\) | ||||
−0.303056 | + | 0.952973i | \(0.598007\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.8498 | 0.994821 | ||||||||
\(842\) | −1.02350 | + | 1.02350i | −0.0352722 | + | 0.0352722i | ||||
\(843\) | 19.1894 | − | 19.1894i | 0.660920 | − | 0.660920i | ||||
\(844\) | − | 14.4641i | − | 0.497874i | ||||||
\(845\) | −16.3453 | − | 23.8533i | −0.562294 | − | 0.820577i | ||||
\(846\) | 10.4291i | 0.358558i | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.15311 | − | 7.15311i | −0.245639 | − | 0.245639i | ||||
\(849\) | − | 3.26106i | − | 0.111919i | ||||||
\(850\) | 1.91662 | − | 4.95188i | 0.0657394 | − | 0.169848i | ||||
\(851\) | −11.8956 | −0.407775 | ||||||||
\(852\) | 11.1195 | + | 11.1195i | 0.380948 | + | 0.380948i | ||||
\(853\) | −16.6127 | + | 16.6127i | −0.568806 | + | 0.568806i | −0.931794 | − | 0.362988i | \(-0.881757\pi\) |
0.362988 | + | 0.931794i | \(0.381757\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.16359 | − | 7.53543i | −0.176591 | − | 0.257706i | ||||
\(856\) | −19.2851 | −0.659151 | ||||||||
\(857\) | −13.2049 | − | 13.2049i | −0.451071 | − | 0.451071i | 0.444639 | − | 0.895710i | \(-0.353332\pi\) |
−0.895710 | + | 0.444639i | \(0.853332\pi\) | |||||||
\(858\) | −0.953730 | − | 0.953730i | −0.0325598 | − | 0.0325598i | ||||
\(859\) | 21.2126 | 0.723764 | 0.361882 | − | 0.932224i | \(-0.382134\pi\) | ||||
0.361882 | + | 0.932224i | \(0.382134\pi\) | |||||||
\(860\) | 1.23791 | − | 6.62790i | 0.0422125 | − | 0.226009i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −11.9413 | + | 11.9413i | −0.406724 | + | 0.406724i | ||||
\(863\) | −0.653661 | − | 0.653661i | −0.0222509 | − | 0.0222509i | 0.695894 | − | 0.718145i | \(-0.255008\pi\) |
−0.718145 | + | 0.695894i | \(0.755008\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −8.31429 | + | 44.5154i | −0.282694 | + | 1.51357i | ||||
\(866\) | 29.1022i | 0.988934i | ||||||||
\(867\) | 11.2234 | + | 11.2234i | 0.381165 | + | 0.381165i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 38.5106i | − | 1.30638i | ||||||
\(870\) | 0.714822 | − | 0.489826i | 0.0242347 | − | 0.0166067i | ||||
\(871\) | 0.0131332i | 0.000445002i | ||||||||
\(872\) | 5.12028 | − | 5.12028i | 0.173395 | − | 0.173395i | ||||
\(873\) | 1.32497 | − | 1.32497i | 0.0448433 | − | 0.0448433i | ||||
\(874\) | −13.6815 | −0.462783 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.56617 | −0.154276 | ||||||||
\(877\) | 32.5505 | − | 32.5505i | 1.09915 | − | 1.09915i | 0.104641 | − | 0.994510i | \(-0.466631\pi\) |
0.994510 | − | 0.104641i | \(-0.0333694\pi\) | |||||||
\(878\) | 1.92769 | − | 1.92769i | 0.0650564 | − | 0.0650564i | ||||
\(879\) | 32.3476i | 1.09106i | ||||||||
\(880\) | 9.52064 | − | 6.52395i | 0.320941 | − | 0.219922i | ||||
\(881\) | − | 42.4620i | − | 1.43058i | −0.698826 | − | 0.715291i | \(-0.746294\pi\) | ||
0.698826 | − | 0.715291i | \(-0.253706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.4976 | + | 31.4976i | 1.05998 | + | 1.05998i | 0.998083 | + | 0.0618962i | \(0.0197148\pi\) |
0.0618962 | + | 0.998083i | \(0.480285\pi\) | |||||||
\(884\) | 0.277510i | 0.00933366i | ||||||||
\(885\) | 3.98629 | − | 21.3430i | 0.133998 | − | 0.717436i | ||||
\(886\) | 0.829585 | 0.0278705 | ||||||||
\(887\) | 18.9884 | + | 18.9884i | 0.637567 | + | 0.637567i | 0.949955 | − | 0.312388i | \(-0.101129\pi\) |
−0.312388 | + | 0.949955i | \(0.601129\pi\) | |||||||
\(888\) | −2.51162 | + | 2.51162i | −0.0842844 | + | 0.0842844i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.79941 | − | 31.0505i | 0.194397 | − | 1.04082i | ||||
\(891\) | −5.16148 | −0.172916 | ||||||||
\(892\) | −7.80302 | − | 7.80302i | −0.261264 | − | 0.261264i | ||||
\(893\) | −30.1263 | − | 30.1263i | −1.00814 | − | 1.00814i | ||||
\(894\) | −16.7852 | −0.561380 | ||||||||
\(895\) | −28.0859 | − | 40.9868i | −0.938807 | − | 1.37004i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.618824 | − | 0.618824i | 0.0206619 | − | 0.0206619i | ||||
\(898\) | −18.6463 | − | 18.6463i | −0.622235 | − | 0.622235i | ||||
\(899\) | −4.11303 | −0.137177 | ||||||||
\(900\) | −1.80477 | + | 4.66292i | −0.0601591 | + | 0.155431i | ||||
\(901\) | − | 10.7429i | − | 0.357899i | ||||||
\(902\) | 25.7627 | + | 25.7627i | 0.857804 | + | 0.857804i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7.73244i | − | 0.257177i | ||||||
\(905\) | 31.7636 | + | 46.3539i | 1.05586 | + | 1.54085i | ||||
\(906\) | − | 9.76485i | − | 0.324415i | ||||||
\(907\) | 39.9794 | − | 39.9794i | 1.32750 | − | 1.32750i | 0.419947 | − | 0.907549i | \(-0.362049\pi\) |
0.907549 | − | 0.419947i | \(-0.137951\pi\) | |||||||
\(908\) | 7.43269 | − | 7.43269i | 0.246663 | − | 0.246663i | ||||
\(909\) | −2.60028 | −0.0862457 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 16.7618 | 0.555342 | 0.277671 | − | 0.960676i | \(-0.410437\pi\) | ||||
0.277671 | + | 0.960676i | \(0.410437\pi\) | |||||||
\(912\) | −2.88869 | + | 2.88869i | −0.0956542 | + | 0.0956542i | ||||
\(913\) | −2.11190 | + | 2.11190i | −0.0698936 | + | 0.0698936i | ||||
\(914\) | − | 25.6047i | − | 0.846929i | ||||||
\(915\) | 24.2007 | + | 4.52004i | 0.800051 | + | 0.149428i | ||||
\(916\) | − | 10.5109i | − | 0.347291i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.750926 | + | 0.750926i | 0.0247843 | + | 0.0247843i | ||||
\(919\) | − | 37.8718i | − | 1.24928i | −0.780914 | − | 0.624638i | \(-0.785246\pi\) | ||
0.780914 | − | 0.624638i | \(-0.214754\pi\) | |||||||
\(920\) | 4.23304 | + | 6.17744i | 0.139559 | + | 0.203664i | ||||
\(921\) | −2.91679 | −0.0961114 | ||||||||
\(922\) | −3.15084 | − | 3.15084i | −0.103768 | − | 0.103768i | ||||
\(923\) | 2.90570 | − | 2.90570i | 0.0956423 | − | 0.0956423i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.17856 | − | 16.2444i | −0.236030 | − | 0.534111i | ||||
\(926\) | 17.6033 | 0.578482 | ||||||||
\(927\) | 6.20799 | + | 6.20799i | 0.203897 | + | 0.203897i | ||||
\(928\) | −0.274026 | − | 0.274026i | −0.00899533 | − | 0.00899533i | ||||
\(929\) | −1.03579 | −0.0339832 | −0.0169916 | − | 0.999856i | \(-0.505409\pi\) | ||||
−0.0169916 | + | 0.999856i | \(0.505409\pi\) | |||||||
\(930\) | 19.5771 | − | 13.4150i | 0.641957 | − | 0.439896i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.2668 | + | 16.2668i | −0.532838 | + | 0.532838i | ||||
\(933\) | −4.01106 | − | 4.01106i | −0.131316 | − | 0.131316i | ||||
\(934\) | 11.8083 | 0.386379 | ||||||||
\(935\) | 12.0483 | + | 2.25030i | 0.394022 | + | 0.0735927i | ||||
\(936\) | − | 0.261316i | − | 0.00854138i | ||||||
\(937\) | −16.4902 | − | 16.4902i | −0.538713 | − | 0.538713i | 0.384438 | − | 0.923151i | \(-0.374395\pi\) |
−0.923151 | + | 0.384438i | \(0.874395\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.5573i | 1.09510i | ||||||||
\(940\) | −4.28153 | + | 22.9237i | −0.139648 | + | 0.747688i | ||||
\(941\) | 4.78578i | 0.156012i | 0.996953 | + | 0.0780060i | \(0.0248553\pi\) | ||||
−0.996953 | + | 0.0780060i | \(0.975145\pi\) | |||||||
\(942\) | 8.66837 | − | 8.66837i | 0.282431 | − | 0.282431i | ||||
\(943\) | −16.7160 | + | 16.7160i | −0.544349 | + | 0.544349i | ||||
\(944\) | −9.70992 | −0.316031 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 15.5636 | 0.506018 | ||||||||
\(947\) | 18.9447 | − | 18.9447i | 0.615620 | − | 0.615620i | −0.328785 | − | 0.944405i | \(-0.606639\pi\) |
0.944405 | + | 0.328785i | \(0.106639\pi\) | |||||||
\(948\) | 5.27582 | − | 5.27582i | 0.171351 | − | 0.171351i | ||||
\(949\) | 1.19321i | 0.0387333i | ||||||||
\(950\) | −8.25630 | − | 18.6832i | −0.267870 | − | 0.606162i | ||||
\(951\) | − | 10.7644i | − | 0.349060i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.9822 | − | 13.9822i | −0.452927 | − | 0.452927i | 0.443398 | − | 0.896325i | \(-0.353773\pi\) |
−0.896325 | + | 0.443398i | \(0.853773\pi\) | |||||||
\(954\) | 10.1160i | 0.327519i | ||||||||
\(955\) | −2.84050 | + | 1.94643i | −0.0919165 | + | 0.0629850i | ||||
\(956\) | 19.4914 | 0.630398 | ||||||||
\(957\) | 1.41438 | + | 1.41438i | 0.0457204 | + | 0.0457204i | ||||
\(958\) | 8.42110 | − | 8.42110i | 0.272073 | − | 0.272073i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 2.19806 | + | 0.410538i | 0.0709420 | + | 0.0132501i | ||||
\(961\) | −81.6449 | −2.63371 | ||||||||
\(962\) | 0.656326 | + | 0.656326i | 0.0211608 | + | 0.0211608i | ||||
\(963\) | 13.6366 | + | 13.6366i | 0.439434 | + | 0.439434i | ||||
\(964\) | −8.15049 | −0.262509 | ||||||||
\(965\) | 39.5805 | + | 7.39257i | 1.27414 | + | 0.237975i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −0.721442 | + | 0.721442i | −0.0232000 | + | 0.0232000i | −0.718612 | − | 0.695412i | \(-0.755222\pi\) |
0.695412 | + | 0.718612i | \(0.255222\pi\) | |||||||
\(968\) | 11.0598 | + | 11.0598i | 0.355475 | + | 0.355475i | ||||
\(969\) | −4.33839 | −0.139369 | ||||||||
\(970\) | 3.45630 | − | 2.36841i | 0.110975 | − | 0.0760449i | ||||
\(971\) | 8.21543i | 0.263646i | 0.991273 | + | 0.131823i | \(0.0420830\pi\) | ||||
−0.991273 | + | 0.131823i | \(0.957917\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 34.0139i | − | 1.08987i | ||||||
\(975\) | 1.21849 | + | 0.471616i | 0.0390230 | + | 0.0151038i | ||||
\(976\) | − | 11.0100i | − | 0.352423i | ||||||
\(977\) | −26.3124 | + | 26.3124i | −0.841808 | + | 0.841808i | −0.989094 | − | 0.147286i | \(-0.952946\pi\) |
0.147286 | + | 0.989094i | \(0.452946\pi\) | |||||||
\(978\) | 13.7694 | − | 13.7694i | 0.440296 | − | 0.440296i | ||||
\(979\) | 72.9129 | 2.33031 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.24117 | −0.231193 | ||||||||
\(982\) | 23.1733 | − | 23.1733i | 0.739488 | − | 0.739488i | ||||
\(983\) | 19.0672 | − | 19.0672i | 0.608150 | − | 0.608150i | −0.334312 | − | 0.942462i | \(-0.608504\pi\) |
0.942462 | + | 0.334312i | \(0.108504\pi\) | |||||||
\(984\) | 7.05881i | 0.225027i | ||||||||
\(985\) | −6.97621 | + | 37.3513i | −0.222281 | + | 1.19011i | ||||
\(986\) | − | 0.411546i | − | 0.0131063i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0.754861 | + | 0.754861i | 0.0240153 | + | 0.0240153i | ||||
\(989\) | 10.0984i | 0.321111i | ||||||||
\(990\) | −11.3452 | − | 2.11899i | −0.360575 | − | 0.0673458i | ||||
\(991\) | −3.65897 | −0.116231 | −0.0581155 | − | 0.998310i | \(-0.518509\pi\) | ||||
−0.0581155 | + | 0.998310i | \(0.518509\pi\) | |||||||
\(992\) | −7.50483 | − | 7.50483i | −0.238279 | − | 0.238279i | ||||
\(993\) | 3.60303 | − | 3.60303i | 0.114339 | − | 0.114339i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.3799 | − | 11.9094i | 0.550980 | − | 0.377554i | ||||
\(996\) | −0.578647 | −0.0183351 | ||||||||
\(997\) | 31.9803 | + | 31.9803i | 1.01283 | + | 1.01283i | 0.999917 | + | 0.0129095i | \(0.00410933\pi\) |
0.0129095 | + | 0.999917i | \(0.495891\pi\) | |||||||
\(998\) | −20.5511 | − | 20.5511i | −0.650533 | − | 0.650533i | ||||
\(999\) | 3.55196 | 0.112379 |
(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 | 1470.2.m.c.1273.2 | yes | 16 | |
5.2 | odd | 4 | 1470.2.m.f.97.3 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.f.1273.3 | yes | 16 | ||
35.27 | even | 4 | inner | 1470.2.m.c.97.2 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.c.97.2 | ✓ | 16 | 35.27 | even | 4 | inner | |
1470.2.m.c.1273.2 | yes | 16 | 1.1 | even | 1 | trivial | |
1470.2.m.f.97.3 | yes | 16 | 5.2 | odd | 4 | ||
1470.2.m.f.1273.3 | yes | 16 | 7.6 | odd | 2 |