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 | 97.2 | ||
Root | \(-1.22045 - 1.87363i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1470.97 |
Dual form | 1470.2.m.c.1273.2 |
$q$-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 \(\left(\mathbb{Z}/1470\mathbb{Z}\right)^\times\).
\(n\) | \(491\) | \(1081\) | \(1177\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | 0.732266 | − | 0.681018i | \(-0.238463\pi\) |
−0.681018 | + | 0.732266i | \(0.738463\pi\) | |||||||
\(14\) | 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 | −0.792282 | − | 0.610155i | \(-0.791107\pi\) |
0.610155 | + | 0.792282i | \(0.291107\pi\) | |||||||
\(18\) | 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 | −0.909496 | − | 0.415712i | \(-0.863533\pi\) |
0.415712 | + | 0.909496i | \(0.363533\pi\) | |||||||
\(24\) | −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 | \(0.0114557\pi\) | ||||
−0.999352 | + | 0.0359813i | \(0.988544\pi\) | |||||||
\(30\) | 1.26397 | − | 1.84456i | 0.230768 | − | 0.336768i | ||||
\(31\) | 10.6134i | 1.90623i | 0.302611 | + | 0.953114i | \(0.402142\pi\) | ||||
−0.302611 | + | 0.953114i | \(0.597858\pi\) | |||||||
\(32\) | 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 | 0.882750 | − | 0.469843i | \(-0.155689\pi\) |
−0.469843 | + | 0.882750i | \(0.655689\pi\) | |||||||
\(38\) | 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 | \(0.185830\pi\) | ||||
−0.834373 | + | 0.551201i | \(0.814170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.13217 | + | 2.13217i | −0.325153 | + | 0.325153i | −0.850740 | − | 0.525587i | \(-0.823846\pi\) |
0.525587 | + | 0.850740i | \(0.323846\pi\) | |||||||
\(44\) | 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 | 0.0787836 | − | 0.996892i | \(-0.474896\pi\) |
0.996892 | − | 0.0787836i | \(-0.0251036\pi\) | |||||||
\(48\) | 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 | −0.0172949 | − | 0.999850i | \(-0.505505\pi\) |
0.999850 | + | 0.0172949i | \(0.00550540\pi\) | |||||||
\(54\) | −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 | \(-0.751016\pi\) | ||
0.709361 | − | 0.704846i | \(-0.248984\pi\) | |||||||
\(62\) | 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 | 0.704933 | − | 0.709274i | \(-0.250977\pi\) |
−0.709274 | + | 0.704933i | \(0.750977\pi\) | |||||||
\(68\) | −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 | 0.492445 | − | 0.870344i | \(-0.336103\pi\) |
−0.870344 | + | 0.492445i | \(0.836103\pi\) | |||||||
\(74\) | − | 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 | \(0.137872\pi\) | ||||
−0.907653 | + | 0.419722i | \(0.862128\pi\) | |||||||
\(80\) | 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 | 0.684294 | − | 0.729206i | \(-0.260110\pi\) |
−0.729206 | + | 0.684294i | \(0.760110\pi\) | |||||||
\(84\) | 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 | −0.636635 | − | 0.771165i | \(-0.719674\pi\) |
0.771165 | + | 0.636635i | \(0.219674\pi\) | |||||||
\(98\) | 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 | \(0.0412951\pi\) | ||||
−0.991597 | + | 0.129369i | \(0.958705\pi\) | |||||||
\(102\) | −0.750926 | − | 0.750926i | −0.0743528 | − | 0.0743528i | ||||
\(103\) | −6.20799 | − | 6.20799i | −0.611691 | − | 0.611691i | 0.331695 | − | 0.943387i | \(-0.392379\pi\) |
−0.943387 | + | 0.331695i | \(0.892379\pi\) | |||||||
\(104\) | 0.261316 | 0.0256241 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −10.1160 | −0.982556 | ||||||||
\(107\) | −13.6366 | − | 13.6366i | −1.31830 | − | 1.31830i | −0.915119 | − | 0.403183i | \(-0.867904\pi\) |
−0.403183 | − | 0.915119i | \(-0.632096\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | 7.24117i | 0.693578i | 0.937943 | + | 0.346789i | \(0.112728\pi\) | ||||
−0.937943 | + | 0.346789i | \(0.887272\pi\) | |||||||
\(110\) | 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 | −0.915858 | − | 0.401503i | \(-0.868488\pi\) |
0.401503 | + | 0.915858i | \(0.368488\pi\) | |||||||
\(114\) | − | 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 | 0.979433 | + | 0.201770i | \(0.0646693\pi\) |
0.201770 | + | 0.979433i | \(0.435331\pi\) | |||||||
\(128\) | −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 | \(0.158163\pi\) | ||||
−0.879073 | + | 0.476688i | \(0.841837\pi\) | |||||||
\(132\) | 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 | 0.572633 | − | 0.819812i | \(-0.305922\pi\) |
−0.819812 | + | 0.572633i | \(0.805922\pi\) | |||||||
\(138\) | −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 | \(0.241313\pi\) | ||||
−0.726139 | + | 0.687548i | \(0.758687\pi\) | |||||||
\(150\) | −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 | −0.270819 | − | 0.962630i | \(-0.587295\pi\) |
0.962630 | + | 0.270819i | \(0.0872945\pi\) | |||||||
\(158\) | 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 | 0.0818553 | − | 0.996644i | \(-0.473915\pi\) |
0.996644 | − | 0.0818553i | \(-0.0260845\pi\) | |||||||
\(164\) | −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 | −0.519895 | − | 0.854230i | \(-0.674029\pi\) |
0.854230 | + | 0.519895i | \(0.174029\pi\) | |||||||
\(168\) | 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 | 0.995656 | + | 0.0931075i | \(0.0296800\pi\) |
0.0931075 | + | 0.995656i | \(0.470320\pi\) | |||||||
\(174\) | −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 | \(-0.688103\pi\) | ||
0.557144 | − | 0.830416i | \(-0.311897\pi\) | |||||||
\(180\) | 1.84456 | + | 1.26397i | 0.137485 | + | 0.0942106i | ||||
\(181\) | 25.1301i | 1.86791i | 0.357397 | + | 0.933953i | \(0.383664\pi\) | ||||
−0.357397 | + | 0.933953i | \(0.616336\pi\) | |||||||
\(182\) | 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 | −0.996775 | − | 0.0802420i | \(-0.974431\pi\) |
0.0802420 | + | 0.996775i | \(0.474431\pi\) | |||||||
\(194\) | −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 | 0.990875 | − | 0.134787i | \(-0.0430351\pi\) |
−0.134787 | + | 0.990875i | \(0.543035\pi\) | |||||||
\(198\) | 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 | 0.918334 | − | 0.395805i | \(-0.129535\pi\) |
−0.395805 | + | 0.918334i | \(0.629535\pi\) | |||||||
\(224\) | 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 | −0.416027 | − | 0.909352i | \(-0.636578\pi\) |
0.909352 | + | 0.416027i | \(0.136578\pi\) | |||||||
\(228\) | −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 | −0.0679900 | + | 0.997686i | \(0.521659\pi\) |
−0.997686 | + | 0.0679900i | \(0.978341\pi\) | |||||||
\(234\) | 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 | \(-0.782892\pi\) | ||
0.776272 | − | 0.630398i | \(-0.217108\pi\) | |||||||
\(240\) | −0.410538 | − | 2.19806i | −0.0265001 | − | 0.141884i | ||||
\(241\) | 8.15049i | 0.525019i | 0.964929 | + | 0.262509i | \(0.0845501\pi\) | ||||
−0.964929 | + | 0.262509i | \(0.915450\pi\) | |||||||
\(242\) | −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 | \(0.0909911\pi\) | ||||
−0.959420 | + | 0.281980i | \(0.909009\pi\) | |||||||
\(252\) | 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 | −0.632944 | − | 0.774197i | \(-0.718154\pi\) |
0.774197 | + | 0.632944i | \(0.218154\pi\) | |||||||
\(258\) | −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 | −0.378177 | − | 0.925733i | \(-0.623449\pi\) |
0.925733 | + | 0.378177i | \(0.123449\pi\) | |||||||
\(264\) | −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 | \(-0.977999\pi\) | ||
0.997612 | − | 0.0690622i | \(-0.0220007\pi\) | |||||||
\(272\) | 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 | −0.997138 | − | 0.0755979i | \(-0.975913\pi\) |
−0.0755979 | − | 0.997138i | \(-0.524087\pi\) | |||||||
\(278\) | 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 | 0.635241 | − | 0.772314i | \(-0.280901\pi\) |
−0.772314 | + | 0.635241i | \(0.780901\pi\) | |||||||
\(284\) | 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 | 0.899643 | + | 0.436625i | \(0.143826\pi\) |
0.436625 | + | 0.899643i | \(0.356174\pi\) | |||||||
\(294\) | 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 | −0.645797 | − | 0.763509i | \(-0.723475\pi\) |
0.763509 | + | 0.645797i | \(0.223475\pi\) | |||||||
\(308\) | 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 | \(-0.948583\pi\) | ||
0.986982 | − | 0.160829i | \(-0.0514168\pi\) | |||||||
\(312\) | −0.184778 | − | 0.184778i | −0.0104610 | − | 0.0104610i | ||||
\(313\) | 23.7286 | + | 23.7286i | 1.34122 | + | 1.34122i | 0.894847 | + | 0.446374i | \(0.147285\pi\) |
0.446374 | + | 0.894847i | \(0.352715\pi\) | |||||||
\(314\) | −12.2589 | −0.691811 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.46114 | −0.419722 | ||||||||
\(317\) | −7.61158 | − | 7.61158i | −0.427509 | − | 0.427509i | 0.460270 | − | 0.887779i | \(-0.347753\pi\) |
−0.887779 | + | 0.460270i | \(0.847753\pi\) | |||||||
\(318\) | 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 | 0.896033 | − | 0.443987i | \(-0.146436\pi\) |
−0.443987 | + | 0.896033i | \(0.646436\pi\) | |||||||
\(338\) | −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 | 0.387678 | − | 0.921795i | \(-0.373277\pi\) |
−0.921795 | + | 0.387678i | \(0.873277\pi\) | |||||||
\(348\) | 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 | 0.704010 | − | 0.710190i | \(-0.251391\pi\) |
−0.710190 | + | 0.704010i | \(0.751391\pi\) | |||||||
\(354\) | 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 | \(0.0967062\pi\) | ||||
−0.954203 | + | 0.299159i | \(0.903294\pi\) | |||||||
\(360\) | −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 | −0.401919 | − | 0.915675i | \(-0.631657\pi\) |
0.915675 | + | 0.401919i | \(0.131657\pi\) | |||||||
\(368\) | 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 | −0.903551 | − | 0.428480i | \(-0.859049\pi\) |
0.428480 | + | 0.903551i | \(0.359049\pi\) | |||||||
\(374\) | 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 | \(0.219273\pi\) | ||||
−0.771967 | + | 0.635663i | \(0.780727\pi\) | |||||||
\(380\) | −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 | 0.262126 | − | 0.965034i | \(-0.415577\pi\) |
−0.965034 | + | 0.262126i | \(0.915577\pi\) | |||||||
\(384\) | 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 | \(0.0700039\pi\) | ||||
−0.975914 | + | 0.218155i | \(0.929996\pi\) | |||||||
\(390\) | 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 | −0.999217 | − | 0.0395679i | \(-0.987402\pi\) |
0.0395679 | + | 0.999217i | \(0.487402\pi\) | |||||||
\(398\) | 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 | 0.999939 | − | 0.0110055i | \(-0.00350324\pi\) |
−0.0110055 | + | 0.999939i | \(0.503503\pi\) | |||||||
\(434\) | 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 | −0.720905 | − | 0.693034i | \(-0.756273\pi\) |
0.693034 | + | 0.720905i | \(0.256273\pi\) | |||||||
\(444\) | 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 | \(-0.786225\pi\) | ||
0.782830 | − | 0.622235i | \(-0.213775\pi\) | |||||||
\(450\) | 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 | 0.142820 | − | 0.989749i | \(-0.454383\pi\) |
−0.989749 | + | 0.142820i | \(0.954383\pi\) | |||||||
\(458\) | −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 | \(-0.966910\pi\) | ||
0.994602 | − | 0.103768i | \(-0.0330898\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.4474 | + | 12.4474i | −0.578482 | + | 0.578482i | −0.934485 | − | 0.356003i | \(-0.884139\pi\) |
0.356003 | + | 0.934485i | \(0.384139\pi\) | |||||||
\(464\) | − | 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 | −0.873394 | − | 0.487015i | \(-0.838086\pi\) |
0.487015 | + | 0.873394i | \(0.338086\pi\) | |||||||
\(468\) | −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 | −0.995541 | − | 0.0943340i | \(-0.969928\pi\) |
−0.0943340 | − | 0.995541i | \(-0.530072\pi\) | |||||||
\(488\) | −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 | \(-0.774546\pi\) | ||
0.759478 | − | 0.650533i | \(-0.225454\pi\) | |||||||
\(500\) | 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 | 0.750871 | − | 0.660449i | \(-0.229634\pi\) |
−0.660449 | + | 0.750871i | \(0.729634\pi\) | |||||||
\(504\) | 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 | \(-0.971472\pi\) | ||
0.995986 | − | 0.0895044i | \(-0.0285283\pi\) | |||||||
\(522\) | 0.274026 | + | 0.274026i | 0.0119938 | + | 0.0119938i | ||||
\(523\) | 3.85548 | + | 3.85548i | 0.168588 | + | 0.168588i | 0.786359 | − | 0.617770i | \(-0.211964\pi\) |
−0.617770 | + | 0.786359i | \(0.711964\pi\) | |||||||
\(524\) | −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 | 0.592037 | − | 0.805911i | \(-0.298324\pi\) |
−0.805911 | + | 0.592037i | \(0.798324\pi\) | |||||||
\(548\) | 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 | 0.998829 | − | 0.0483784i | \(-0.0154053\pi\) |
−0.0483784 | + | 0.998829i | \(0.515405\pi\) | |||||||
\(558\) | 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 | 0.955202 | − | 0.295955i | \(-0.0956378\pi\) |
−0.295955 | + | 0.955202i | \(0.595638\pi\) | |||||||
\(564\) | − | 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 | \(-0.718990\pi\) | ||
0.634977 | − | 0.772531i | \(-0.281010\pi\) | |||||||
\(570\) | −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 | −0.471346 | + | 0.881949i | \(0.656232\pi\) |
−0.881949 | + | 0.471346i | \(0.843768\pi\) | |||||||
\(578\) | 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 | −0.835669 | − | 0.549233i | \(-0.814920\pi\) |
0.549233 | + | 0.835669i | \(0.314920\pi\) | |||||||
\(588\) | 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 | −0.977997 | − | 0.208621i | \(-0.933103\pi\) |
−0.208621 | − | 0.977997i | \(-0.566897\pi\) | |||||||
\(594\) | −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 | \(-0.825315\pi\) | ||
0.853157 | − | 0.521654i | \(-0.174685\pi\) | |||||||
\(600\) | −1.80477 | − | 4.66292i | −0.0736796 | − | 0.190363i | ||||
\(601\) | 8.12886i | 0.331583i | 0.986161 | + | 0.165792i | \(0.0530179\pi\) | ||||
−0.986161 | + | 0.165792i | \(0.946982\pi\) | |||||||
\(602\) | 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 | −0.966691 | − | 0.255947i | \(-0.917613\pi\) |
0.255947 | + | 0.966691i | \(0.417613\pi\) | |||||||
\(608\) | −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 | −0.971170 | − | 0.238389i | \(-0.923381\pi\) |
0.238389 | + | 0.971170i | \(0.423381\pi\) | |||||||
\(614\) | −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 | 0.887873 | − | 0.460089i | \(-0.152182\pi\) |
−0.460089 | + | 0.887873i | \(0.652182\pi\) | |||||||
\(618\) | 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 | 0.723960 | − | 0.689842i | \(-0.242320\pi\) |
−0.689842 | + | 0.723960i | \(0.742320\pi\) | |||||||
\(644\) | 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 | −0.990127 | − | 0.140171i | \(-0.955235\pi\) |
0.140171 | + | 0.990127i | \(0.455235\pi\) | |||||||
\(648\) | −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 | −0.378736 | − | 0.925505i | \(-0.623641\pi\) |
0.925505 | + | 0.378736i | \(0.123641\pi\) | |||||||
\(654\) | −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 | \(-0.737328\pi\) | ||
0.678403 | − | 0.734690i | \(-0.262672\pi\) | |||||||
\(660\) | −11.3452 | + | 2.11899i | −0.441613 | + | 0.0824814i | ||||
\(661\) | 9.49534i | 0.369326i | 0.982802 | + | 0.184663i | \(0.0591193\pi\) | ||||
−0.982802 | + | 0.184663i | \(0.940881\pi\) | |||||||
\(662\) | 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 | −0.533624 | − | 0.845722i | \(-0.679170\pi\) |
0.845722 | + | 0.533624i | \(0.179170\pi\) | |||||||
\(674\) | − | 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 | −0.643375 | − | 0.765551i | \(-0.722467\pi\) |
0.765551 | + | 0.643375i | \(0.222467\pi\) | |||||||
\(678\) | −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 | −0.127045 | − | 0.991897i | \(-0.540549\pi\) |
0.991897 | + | 0.127045i | \(0.0405494\pi\) | |||||||
\(684\) | 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 | \(-0.813628\pi\) | ||
0.833434 | − | 0.552620i | \(-0.186372\pi\) | |||||||
\(692\) | −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 | \(0.192239\pi\) | ||||
−0.823106 | + | 0.567887i | \(0.807761\pi\) | |||||||
\(710\) | 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 | −0.957790 | − | 0.287469i | \(-0.907186\pi\) |
0.287469 | + | 0.957790i | \(0.407186\pi\) | |||||||
\(728\) | 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 | 0.922790 | − | 0.385304i | \(-0.125903\pi\) |
−0.385304 | + | 0.922790i | \(0.625903\pi\) | |||||||
\(734\) | −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 | \(0.0900961\pi\) | ||||
−0.960209 | + | 0.279281i | \(0.909904\pi\) | |||||||
\(740\) | 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 | −0.999814 | − | 0.0193046i | \(-0.993855\pi\) |
0.0193046 | + | 0.999814i | \(0.493855\pi\) | |||||||
\(744\) | − | 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 | 0.775450 | − | 0.631409i | \(-0.217523\pi\) |
−0.631409 | + | 0.775450i | \(0.717523\pi\) | |||||||
\(758\) | 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 | \(-0.920633\pi\) | ||
0.969075 | − | 0.246765i | \(-0.0793675\pi\) | |||||||
\(762\) | −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 | 0.999248 | − | 0.0387784i | \(-0.0123466\pi\) |
−0.0387784 | + | 0.999248i | \(0.512347\pi\) | |||||||
\(774\) | 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 | −0.999298 | − | 0.0374699i | \(-0.988070\pi\) |
0.0374699 | + | 0.999298i | \(0.488070\pi\) | |||||||
\(788\) | −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 | −0.0186189 | − | 0.999827i | \(-0.505927\pi\) |
0.999827 | + | 0.0186189i | \(0.00592691\pi\) | |||||||
\(798\) | 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 | \(0.226401\pi\) | ||||
−0.757540 | + | 0.652789i | \(0.773599\pi\) | |||||||
\(810\) | −0.410538 | − | 2.19806i | −0.0144248 | − | 0.0772319i | ||||
\(811\) | − | 50.9815i | − | 1.79020i | −0.445863 | − | 0.895101i | \(-0.647103\pi\) | ||
0.445863 | − | 0.895101i | \(-0.352897\pi\) | |||||||
\(812\) | 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 | −0.209415 | − | 0.977827i | \(-0.567156\pi\) |
0.977827 | + | 0.209415i | \(0.0671560\pi\) | |||||||
\(824\) | −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 | 0.663035 | − | 0.748588i | \(-0.269268\pi\) |
−0.748588 | + | 0.663035i | \(0.769268\pi\) | |||||||
\(828\) | 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 | 0.362988 | − | 0.931794i | \(-0.381757\pi\) |
−0.931794 | + | 0.362988i | \(0.881757\pi\) | |||||||
\(854\) | 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 | −0.895710 | − | 0.444639i | \(-0.853332\pi\) |
0.444639 | + | 0.895710i | \(0.353332\pi\) | |||||||
\(858\) | −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 | −0.718145 | − | 0.695894i | \(-0.755008\pi\) |
0.695894 | + | 0.718145i | \(0.255008\pi\) | |||||||
\(864\) | 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 | 0.994510 | + | 0.104641i | \(0.0333694\pi\) |
0.104641 | + | 0.994510i | \(0.466631\pi\) | |||||||
\(878\) | 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 | \(0.253706\pi\) | ||||
−0.698826 | + | 0.715291i | \(0.746294\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.4976 | − | 31.4976i | 1.05998 | − | 1.05998i | 0.0618962 | − | 0.998083i | \(-0.480285\pi\) |
0.998083 | − | 0.0618962i | \(-0.0197148\pi\) | |||||||
\(884\) | − | 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 | −0.312388 | − | 0.949955i | \(-0.601129\pi\) |
0.949955 | + | 0.312388i | \(0.101129\pi\) | |||||||
\(888\) | −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 | 0.907549 | + | 0.419947i | \(0.137951\pi\) |
0.419947 | + | 0.907549i | \(0.362049\pi\) | |||||||
\(908\) | 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 | \(0.214754\pi\) | ||||
−0.780914 | + | 0.624638i | \(0.785246\pi\) | |||||||
\(920\) | 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 | −0.923151 | − | 0.384438i | \(-0.874395\pi\) |
0.384438 | + | 0.923151i | \(0.374395\pi\) | |||||||
\(938\) | 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 | \(-0.975145\pi\) | ||
0.996953 | − | 0.0780060i | \(-0.0248553\pi\) | |||||||
\(942\) | 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 | 0.944405 | − | 0.328785i | \(-0.106639\pi\) |
−0.328785 | + | 0.944405i | \(0.606639\pi\) | |||||||
\(948\) | 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 | −0.896325 | − | 0.443398i | \(-0.853773\pi\) |
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(954\) | − | 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 | 0.695412 | − | 0.718612i | \(-0.255222\pi\) |
−0.718612 | + | 0.695412i | \(0.755222\pi\) | |||||||
\(968\) | 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 | \(-0.957917\pi\) | ||
0.991273 | − | 0.131823i | \(-0.0420830\pi\) | |||||||
\(972\) | −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 | 0.147286 | − | 0.989094i | \(-0.452946\pi\) |
−0.989094 | + | 0.147286i | \(0.952946\pi\) | |||||||
\(978\) | 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 | 0.942462 | − | 0.334312i | \(-0.108504\pi\) |
−0.334312 | + | 0.942462i | \(0.608504\pi\) | |||||||
\(984\) | − | 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 | 0.0129095 | − | 0.999917i | \(-0.495891\pi\) |
0.999917 | − | 0.0129095i | \(-0.00410933\pi\) | |||||||
\(998\) | −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.97.2 | ✓ | 16 | |
5.3 | odd | 4 | 1470.2.m.f.1273.3 | yes | 16 | ||
7.6 | odd | 2 | 1470.2.m.f.97.3 | yes | 16 | ||
35.13 | even | 4 | inner | 1470.2.m.c.1273.2 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1470.2.m.c.97.2 | ✓ | 16 | 1.1 | even | 1 | trivial | |
1470.2.m.c.1273.2 | yes | 16 | 35.13 | even | 4 | inner | |
1470.2.m.f.97.3 | yes | 16 | 7.6 | odd | 2 | ||
1470.2.m.f.1273.3 | yes | 16 | 5.3 | odd | 4 |