Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [390,2,Mod(307,390)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(390, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("390.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 390.t (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: | \(3.11416567883\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 6x^{10} - 24x^{9} + 18x^{8} + 40x^{7} - 82x^{6} + 12x^{5} + 228x^{4} - 284x^{3} + 124x^{2} - 16x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 343.1 | ||
Root | \(0.0572576 + 0.138232i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 390.343 |
Dual form | 390.2.t.a.307.1 |
$q$-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 \(\left(\mathbb{Z}/390\mathbb{Z}\right)^\times\).
\(n\) | \(131\) | \(157\) | \(301\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.20289 | − | 0.383740i | −0.985164 | − | 0.171614i | ||||
\(6\) | 0.707107 | − | 0.707107i | 0.288675 | − | 0.288675i | ||||
\(7\) | 1.52873 | 0.577805 | 0.288903 | − | 0.957359i | \(-0.406710\pi\) | ||||
0.288903 | + | 0.957359i | \(0.406710\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0.383740 | − | 2.20289i | 0.121349 | − | 0.696616i | ||||
\(11\) | 2.70115 | + | 2.70115i | 0.814427 | + | 0.814427i | 0.985294 | − | 0.170867i | \(-0.0546568\pi\) |
−0.170867 | + | 0.985294i | \(0.554657\pi\) | |||||||
\(12\) | 0.707107 | + | 0.707107i | 0.204124 | + | 0.204124i | ||||
\(13\) | 3.17182 | − | 1.71451i | 0.879705 | − | 0.475520i | ||||
\(14\) | 1.52873i | 0.408570i | ||||||||
\(15\) | 1.28634 | + | 1.82903i | 0.332131 | + | 0.472253i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.03439 | + | 4.03439i | 0.978483 | + | 0.978483i | 0.999773 | − | 0.0212904i | \(-0.00677744\pi\) |
−0.0212904 | + | 0.999773i | \(0.506777\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 1.06701 | + | 1.06701i | 0.244790 | + | 0.244790i | 0.818828 | − | 0.574039i | \(-0.194624\pi\) |
−0.574039 | + | 0.818828i | \(0.694624\pi\) | |||||||
\(20\) | 2.20289 | + | 0.383740i | 0.492582 | + | 0.0858069i | ||||
\(21\) | −1.08097 | − | 1.08097i | −0.235888 | − | 0.235888i | ||||
\(22\) | −2.70115 | + | 2.70115i | −0.575887 | + | 0.575887i | ||||
\(23\) | −0.485915 | + | 0.485915i | −0.101320 | + | 0.101320i | −0.755950 | − | 0.654630i | \(-0.772825\pi\) |
0.654630 | + | 0.755950i | \(0.272825\pi\) | |||||||
\(24\) | −0.707107 | + | 0.707107i | −0.144338 | + | 0.144338i | ||||
\(25\) | 4.70549 | + | 1.69068i | 0.941097 | + | 0.338136i | ||||
\(26\) | 1.71451 | + | 3.17182i | 0.336243 | + | 0.622045i | ||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −1.52873 | −0.288903 | ||||||||
\(29\) | − | 2.28429i | − | 0.424183i | −0.977250 | − | 0.212091i | \(-0.931973\pi\) | ||
0.977250 | − | 0.212091i | \(-0.0680275\pi\) | |||||||
\(30\) | −1.82903 | + | 1.28634i | −0.333933 | + | 0.234852i | ||||
\(31\) | 1.00000 | − | 1.00000i | 0.179605 | − | 0.179605i | −0.611578 | − | 0.791184i | \(-0.709465\pi\) |
0.791184 | + | 0.611578i | \(0.209465\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − | 3.82000i | − | 0.664977i | ||||||
\(34\) | −4.03439 | + | 4.03439i | −0.691892 | + | 0.691892i | ||||
\(35\) | −3.36763 | − | 0.586634i | −0.569233 | − | 0.0991593i | ||||
\(36\) | − | 1.00000i | − | 0.166667i | ||||||
\(37\) | 7.96284 | 1.30908 | 0.654541 | − | 0.756026i | \(-0.272862\pi\) | ||||
0.654541 | + | 0.756026i | \(0.272862\pi\) | |||||||
\(38\) | −1.06701 | + | 1.06701i | −0.173092 | + | 0.173092i | ||||
\(39\) | −3.45516 | − | 1.03047i | −0.553268 | − | 0.165008i | ||||
\(40\) | −0.383740 | + | 2.20289i | −0.0606746 | + | 0.348308i | ||||
\(41\) | −8.22579 | + | 8.22579i | −1.28465 | + | 1.28465i | −0.346663 | + | 0.937990i | \(0.612685\pi\) |
−0.937990 | + | 0.346663i | \(0.887315\pi\) | |||||||
\(42\) | 1.08097 | − | 1.08097i | 0.166798 | − | 0.166798i | ||||
\(43\) | 5.76210 | − | 5.76210i | 0.878711 | − | 0.878711i | −0.114690 | − | 0.993401i | \(-0.536587\pi\) |
0.993401 | + | 0.114690i | \(0.0365874\pi\) | |||||||
\(44\) | −2.70115 | − | 2.70115i | −0.407214 | − | 0.407214i | ||||
\(45\) | 0.383740 | − | 2.20289i | 0.0572046 | − | 0.328388i | ||||
\(46\) | −0.485915 | − | 0.485915i | −0.0716443 | − | 0.0716443i | ||||
\(47\) | 2.92343 | 0.426426 | 0.213213 | − | 0.977006i | \(-0.431607\pi\) | ||||
0.213213 | + | 0.977006i | \(0.431607\pi\) | |||||||
\(48\) | −0.707107 | − | 0.707107i | −0.102062 | − | 0.102062i | ||||
\(49\) | −4.66299 | −0.666141 | ||||||||
\(50\) | −1.69068 | + | 4.70549i | −0.239098 | + | 0.665456i | ||||
\(51\) | − | 5.70549i | − | 0.798928i | ||||||
\(52\) | −3.17182 | + | 1.71451i | −0.439852 | + | 0.237760i | ||||
\(53\) | −3.69068 | − | 3.69068i | −0.506954 | − | 0.506954i | 0.406636 | − | 0.913590i | \(-0.366702\pi\) |
−0.913590 | + | 0.406636i | \(0.866702\pi\) | |||||||
\(54\) | 0.707107 | + | 0.707107i | 0.0962250 | + | 0.0962250i | ||||
\(55\) | −4.91381 | − | 6.98689i | −0.662578 | − | 0.942112i | ||||
\(56\) | − | 1.52873i | − | 0.204285i | ||||||
\(57\) | − | 1.50898i | − | 0.199870i | ||||||
\(58\) | 2.28429 | 0.299943 | ||||||||
\(59\) | −4.50044 | + | 4.50044i | −0.585908 | + | 0.585908i | −0.936521 | − | 0.350613i | \(-0.885973\pi\) |
0.350613 | + | 0.936521i | \(0.385973\pi\) | |||||||
\(60\) | −1.28634 | − | 1.82903i | −0.166065 | − | 0.236126i | ||||
\(61\) | −2.43047 | −0.311190 | −0.155595 | − | 0.987821i | \(-0.549729\pi\) | ||||
−0.155595 | + | 0.987821i | \(0.549729\pi\) | |||||||
\(62\) | 1.00000 | + | 1.00000i | 0.127000 | + | 0.127000i | ||||
\(63\) | 1.52873i | 0.192602i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −7.64511 | + | 2.55973i | −0.948260 | + | 0.317496i | ||||
\(66\) | 3.82000 | 0.470210 | ||||||||
\(67\) | − | 3.79906i | − | 0.464129i | −0.972700 | − | 0.232064i | \(-0.925452\pi\) | ||
0.972700 | − | 0.232064i | \(-0.0745480\pi\) | |||||||
\(68\) | −4.03439 | − | 4.03439i | −0.489241 | − | 0.489241i | ||||
\(69\) | 0.687188 | 0.0827277 | ||||||||
\(70\) | 0.586634 | − | 3.36763i | 0.0701162 | − | 0.402509i | ||||
\(71\) | 10.7079 | − | 10.7079i | 1.27080 | − | 1.27080i | 0.325128 | − | 0.945670i | \(-0.394593\pi\) |
0.945670 | − | 0.325128i | \(-0.105407\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 10.3127i | 1.20701i | 0.797358 | + | 0.603506i | \(0.206230\pi\) | ||||
−0.797358 | + | 0.603506i | \(0.793770\pi\) | |||||||
\(74\) | 7.96284i | 0.925661i | ||||||||
\(75\) | −2.13179 | − | 4.52277i | −0.246158 | − | 0.522245i | ||||
\(76\) | −1.06701 | − | 1.06701i | −0.122395 | − | 0.122395i | ||||
\(77\) | 4.12932 | + | 4.12932i | 0.470580 | + | 0.470580i | ||||
\(78\) | 1.03047 | − | 3.45516i | 0.116678 | − | 0.391220i | ||||
\(79\) | 1.53731i | 0.172961i | 0.996254 | + | 0.0864803i | \(0.0275620\pi\) | ||||
−0.996254 | + | 0.0864803i | \(0.972438\pi\) | |||||||
\(80\) | −2.20289 | − | 0.383740i | −0.246291 | − | 0.0429034i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | −8.22579 | − | 8.22579i | −0.908387 | − | 0.908387i | ||||
\(83\) | 7.72020 | 0.847402 | 0.423701 | − | 0.905802i | \(-0.360731\pi\) | ||||
0.423701 | + | 0.905802i | \(0.360731\pi\) | |||||||
\(84\) | 1.08097 | + | 1.08097i | 0.117944 | + | 0.117944i | ||||
\(85\) | −7.33918 | − | 10.4355i | −0.796045 | − | 1.13189i | ||||
\(86\) | 5.76210 | + | 5.76210i | 0.621343 | + | 0.621343i | ||||
\(87\) | −1.61524 | + | 1.61524i | −0.173172 | + | 0.173172i | ||||
\(88\) | 2.70115 | − | 2.70115i | 0.287944 | − | 0.287944i | ||||
\(89\) | −7.21676 | + | 7.21676i | −0.764976 | + | 0.764976i | −0.977217 | − | 0.212242i | \(-0.931924\pi\) |
0.212242 | + | 0.977217i | \(0.431924\pi\) | |||||||
\(90\) | 2.20289 | + | 0.383740i | 0.232205 | + | 0.0404498i | ||||
\(91\) | 4.84885 | − | 2.62102i | 0.508298 | − | 0.274758i | ||||
\(92\) | 0.485915 | − | 0.485915i | 0.0506602 | − | 0.0506602i | ||||
\(93\) | −1.41421 | −0.146647 | ||||||||
\(94\) | 2.92343i | 0.301529i | ||||||||
\(95\) | −1.94106 | − | 2.75997i | −0.199149 | − | 0.283167i | ||||
\(96\) | 0.707107 | − | 0.707107i | 0.0721688 | − | 0.0721688i | ||||
\(97\) | − | 6.36597i | − | 0.646366i | −0.946336 | − | 0.323183i | \(-0.895247\pi\) | ||
0.946336 | − | 0.323183i | \(-0.104753\pi\) | |||||||
\(98\) | − | 4.66299i | − | 0.471033i | ||||||
\(99\) | −2.70115 | + | 2.70115i | −0.271476 | + | 0.271476i | ||||
\(100\) | −4.70549 | − | 1.69068i | −0.470549 | − | 0.169068i | ||||
\(101\) | 10.5668i | 1.05143i | 0.850660 | + | 0.525717i | \(0.176203\pi\) | ||||
−0.850660 | + | 0.525717i | \(0.823797\pi\) | |||||||
\(102\) | 5.70549 | 0.564927 | ||||||||
\(103\) | −4.86744 | + | 4.86744i | −0.479603 | + | 0.479603i | −0.905005 | − | 0.425402i | \(-0.860133\pi\) |
0.425402 | + | 0.905005i | \(0.360133\pi\) | |||||||
\(104\) | −1.71451 | − | 3.17182i | −0.168122 | − | 0.311023i | ||||
\(105\) | 1.96646 | + | 2.79609i | 0.191907 | + | 0.272870i | ||||
\(106\) | 3.69068 | − | 3.69068i | 0.358470 | − | 0.358470i | ||||
\(107\) | 13.0918 | − | 13.0918i | 1.26563 | − | 1.26563i | 0.317307 | − | 0.948323i | \(-0.397221\pi\) |
0.948323 | − | 0.317307i | \(-0.102779\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | −0.124070 | − | 0.124070i | −0.0118838 | − | 0.0118838i | 0.701140 | − | 0.713024i | \(-0.252675\pi\) |
−0.713024 | + | 0.701140i | \(0.752675\pi\) | |||||||
\(110\) | 6.98689 | − | 4.91381i | 0.666173 | − | 0.468513i | ||||
\(111\) | −5.63058 | − | 5.63058i | −0.534431 | − | 0.534431i | ||||
\(112\) | 1.52873 | 0.144451 | ||||||||
\(113\) | −3.69674 | − | 3.69674i | −0.347760 | − | 0.347760i | 0.511514 | − | 0.859275i | \(-0.329085\pi\) |
−0.859275 | + | 0.511514i | \(0.829085\pi\) | |||||||
\(114\) | 1.50898 | 0.141329 | ||||||||
\(115\) | 1.25688 | − | 0.883955i | 0.117205 | − | 0.0824292i | ||||
\(116\) | 2.28429i | 0.212091i | ||||||||
\(117\) | 1.71451 | + | 3.17182i | 0.158507 | + | 0.293235i | ||||
\(118\) | −4.50044 | − | 4.50044i | −0.414299 | − | 0.414299i | ||||
\(119\) | 6.16749 | + | 6.16749i | 0.565372 | + | 0.565372i | ||||
\(120\) | 1.82903 | − | 1.28634i | 0.166967 | − | 0.117426i | ||||
\(121\) | 3.59242i | 0.326583i | ||||||||
\(122\) | − | 2.43047i | − | 0.220044i | ||||||
\(123\) | 11.6330 | 1.04891 | ||||||||
\(124\) | −1.00000 | + | 1.00000i | −0.0898027 | + | 0.0898027i | ||||
\(125\) | −9.71691 | − | 5.53007i | −0.869107 | − | 0.494624i | ||||
\(126\) | −1.52873 | −0.136190 | ||||||||
\(127\) | −10.2359 | − | 10.2359i | −0.908290 | − | 0.908290i | 0.0878440 | − | 0.996134i | \(-0.472002\pi\) |
−0.996134 | + | 0.0878440i | \(0.972002\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −8.14884 | −0.717465 | ||||||||
\(130\) | −2.55973 | − | 7.64511i | −0.224503 | − | 0.670521i | ||||
\(131\) | −11.8485 | −1.03521 | −0.517606 | − | 0.855619i | \(-0.673177\pi\) | ||||
−0.517606 | + | 0.855619i | \(0.673177\pi\) | |||||||
\(132\) | 3.82000i | 0.332489i | ||||||||
\(133\) | 1.63117 | + | 1.63117i | 0.141441 | + | 0.141441i | ||||
\(134\) | 3.79906 | 0.328189 | ||||||||
\(135\) | −1.82903 | + | 1.28634i | −0.157418 | + | 0.110710i | ||||
\(136\) | 4.03439 | − | 4.03439i | 0.345946 | − | 0.345946i | ||||
\(137\) | −11.9361 | −1.01977 | −0.509886 | − | 0.860242i | \(-0.670312\pi\) | ||||
−0.509886 | + | 0.860242i | \(0.670312\pi\) | |||||||
\(138\) | 0.687188i | 0.0584973i | ||||||||
\(139\) | − | 20.0448i | − | 1.70018i | −0.526639 | − | 0.850089i | \(-0.676548\pi\) | ||
0.526639 | − | 0.850089i | \(-0.323452\pi\) | |||||||
\(140\) | 3.36763 | + | 0.586634i | 0.284616 | + | 0.0495797i | ||||
\(141\) | −2.06718 | − | 2.06718i | −0.174088 | − | 0.174088i | ||||
\(142\) | 10.7079 | + | 10.7079i | 0.898590 | + | 0.898590i | ||||
\(143\) | 13.1987 | + | 3.93641i | 1.10373 | + | 0.329179i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | −0.876575 | + | 5.03206i | −0.0727956 | + | 0.417890i | ||||
\(146\) | −10.3127 | −0.853486 | ||||||||
\(147\) | 3.29723 | + | 3.29723i | 0.271951 | + | 0.271951i | ||||
\(148\) | −7.96284 | −0.654541 | ||||||||
\(149\) | 3.91078 | + | 3.91078i | 0.320383 | + | 0.320383i | 0.848914 | − | 0.528531i | \(-0.177257\pi\) |
−0.528531 | + | 0.848914i | \(0.677257\pi\) | |||||||
\(150\) | 4.52277 | − | 2.13179i | 0.369283 | − | 0.174060i | ||||
\(151\) | 16.6941 | + | 16.6941i | 1.35854 | + | 1.35854i | 0.875714 | + | 0.482830i | \(0.160391\pi\) |
0.482830 | + | 0.875714i | \(0.339609\pi\) | |||||||
\(152\) | 1.06701 | − | 1.06701i | 0.0865462 | − | 0.0865462i | ||||
\(153\) | −4.03439 | + | 4.03439i | −0.326161 | + | 0.326161i | ||||
\(154\) | −4.12932 | + | 4.12932i | −0.332750 | + | 0.332750i | ||||
\(155\) | −2.58663 | + | 1.81915i | −0.207763 | + | 0.146118i | ||||
\(156\) | 3.45516 | + | 1.03047i | 0.276634 | + | 0.0825039i | ||||
\(157\) | −9.39497 | + | 9.39497i | −0.749800 | + | 0.749800i | −0.974441 | − | 0.224642i | \(-0.927879\pi\) |
0.224642 | + | 0.974441i | \(0.427879\pi\) | |||||||
\(158\) | −1.53731 | −0.122302 | ||||||||
\(159\) | 5.21941i | 0.413926i | ||||||||
\(160\) | 0.383740 | − | 2.20289i | 0.0303373 | − | 0.174154i | ||||
\(161\) | −0.742832 | + | 0.742832i | −0.0585434 | + | 0.0585434i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | 14.0308i | 1.09898i | 0.835501 | + | 0.549489i | \(0.185178\pi\) | ||||
−0.835501 | + | 0.549489i | \(0.814822\pi\) | |||||||
\(164\) | 8.22579 | − | 8.22579i | 0.642326 | − | 0.642326i | ||||
\(165\) | −1.46589 | + | 8.41506i | −0.114119 | + | 0.655112i | ||||
\(166\) | 7.72020i | 0.599204i | ||||||||
\(167\) | 14.4217 | 1.11599 | 0.557993 | − | 0.829845i | \(-0.311571\pi\) | ||||
0.557993 | + | 0.829845i | \(0.311571\pi\) | |||||||
\(168\) | −1.08097 | + | 1.08097i | −0.0833990 | + | 0.0833990i | ||||
\(169\) | 7.12090 | − | 10.8762i | 0.547762 | − | 0.836635i | ||||
\(170\) | 10.4355 | − | 7.33918i | 0.800365 | − | 0.562889i | ||||
\(171\) | −1.06701 | + | 1.06701i | −0.0815965 | + | 0.0815965i | ||||
\(172\) | −5.76210 | + | 5.76210i | −0.439356 | + | 0.439356i | ||||
\(173\) | 12.0153 | − | 12.0153i | 0.913507 | − | 0.913507i | −0.0830394 | − | 0.996546i | \(-0.526463\pi\) |
0.996546 | + | 0.0830394i | \(0.0264627\pi\) | |||||||
\(174\) | −1.61524 | − | 1.61524i | −0.122451 | − | 0.122451i | ||||
\(175\) | 7.19341 | + | 2.58459i | 0.543771 | + | 0.195376i | ||||
\(176\) | 2.70115 | + | 2.70115i | 0.203607 | + | 0.203607i | ||||
\(177\) | 6.36459 | 0.478392 | ||||||||
\(178\) | −7.21676 | − | 7.21676i | −0.540919 | − | 0.540919i | ||||
\(179\) | −10.2606 | −0.766913 | −0.383456 | − | 0.923559i | \(-0.625266\pi\) | ||||
−0.383456 | + | 0.923559i | \(0.625266\pi\) | |||||||
\(180\) | −0.383740 | + | 2.20289i | −0.0286023 | + | 0.164194i | ||||
\(181\) | 22.4534i | 1.66895i | 0.551046 | + | 0.834475i | \(0.314229\pi\) | ||||
−0.551046 | + | 0.834475i | \(0.685771\pi\) | |||||||
\(182\) | 2.62102 | + | 4.84885i | 0.194283 | + | 0.359421i | ||||
\(183\) | 1.71860 | + | 1.71860i | 0.127043 | + | 0.127043i | ||||
\(184\) | 0.485915 | + | 0.485915i | 0.0358221 | + | 0.0358221i | ||||
\(185\) | −17.5413 | − | 3.05566i | −1.28966 | − | 0.224657i | ||||
\(186\) | − | 1.41421i | − | 0.103695i | ||||||
\(187\) | 21.7950i | 1.59381i | ||||||||
\(188\) | −2.92343 | −0.213213 | ||||||||
\(189\) | 1.08097 | − | 1.08097i | 0.0786293 | − | 0.0786293i | ||||
\(190\) | 2.75997 | − | 1.94106i | 0.200229 | − | 0.140819i | ||||
\(191\) | −12.2203 | −0.884229 | −0.442115 | − | 0.896959i | \(-0.645772\pi\) | ||||
−0.442115 | + | 0.896959i | \(0.645772\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 24.1428i | 1.73783i | 0.494958 | + | 0.868917i | \(0.335183\pi\) | ||||
−0.494958 | + | 0.868917i | \(0.664817\pi\) | |||||||
\(194\) | 6.36597 | 0.457050 | ||||||||
\(195\) | 7.21592 | + | 3.59591i | 0.516743 | + | 0.257508i | ||||
\(196\) | 4.66299 | 0.333071 | ||||||||
\(197\) | − | 3.53326i | − | 0.251735i | −0.992047 | − | 0.125867i | \(-0.959829\pi\) | ||
0.992047 | − | 0.125867i | \(-0.0401714\pi\) | |||||||
\(198\) | −2.70115 | − | 2.70115i | −0.191962 | − | 0.191962i | ||||
\(199\) | −12.1781 | −0.863284 | −0.431642 | − | 0.902045i | \(-0.642066\pi\) | ||||
−0.431642 | + | 0.902045i | \(0.642066\pi\) | |||||||
\(200\) | 1.69068 | − | 4.70549i | 0.119549 | − | 0.332728i | ||||
\(201\) | −2.68634 | + | 2.68634i | −0.189480 | + | 0.189480i | ||||
\(202\) | −10.5668 | −0.743476 | ||||||||
\(203\) | − | 3.49207i | − | 0.245095i | ||||||
\(204\) | 5.70549i | 0.399464i | ||||||||
\(205\) | 21.2771 | − | 14.9640i | 1.48606 | − | 1.04513i | ||||
\(206\) | −4.86744 | − | 4.86744i | −0.339130 | − | 0.339130i | ||||
\(207\) | −0.485915 | − | 0.485915i | −0.0337734 | − | 0.0337734i | ||||
\(208\) | 3.17182 | − | 1.71451i | 0.219926 | − | 0.118880i | ||||
\(209\) | 5.76432i | 0.398726i | ||||||||
\(210\) | −2.79609 | + | 1.96646i | −0.192948 | + | 0.135699i | ||||
\(211\) | −14.2670 | −0.982180 | −0.491090 | − | 0.871109i | \(-0.663401\pi\) | ||||
−0.491090 | + | 0.871109i | \(0.663401\pi\) | |||||||
\(212\) | 3.69068 | + | 3.69068i | 0.253477 | + | 0.253477i | ||||
\(213\) | −15.1433 | −1.03760 | ||||||||
\(214\) | 13.0918 | + | 13.0918i | 0.894935 | + | 0.894935i | ||||
\(215\) | −14.9044 | + | 10.4821i | −1.01647 | + | 0.714876i | ||||
\(216\) | −0.707107 | − | 0.707107i | −0.0481125 | − | 0.0481125i | ||||
\(217\) | 1.52873 | − | 1.52873i | 0.103777 | − | 0.103777i | ||||
\(218\) | 0.124070 | − | 0.124070i | 0.00840311 | − | 0.00840311i | ||||
\(219\) | 7.29219 | − | 7.29219i | 0.492761 | − | 0.492761i | ||||
\(220\) | 4.91381 | + | 6.98689i | 0.331289 | + | 0.471056i | ||||
\(221\) | 19.7134 | + | 5.87935i | 1.32606 | + | 0.395488i | ||||
\(222\) | 5.63058 | − | 5.63058i | 0.377900 | − | 0.377900i | ||||
\(223\) | −11.9632 | −0.801112 | −0.400556 | − | 0.916272i | \(-0.631183\pi\) | ||||
−0.400556 | + | 0.916272i | \(0.631183\pi\) | |||||||
\(224\) | 1.52873i | 0.102142i | ||||||||
\(225\) | −1.69068 | + | 4.70549i | −0.112712 | + | 0.313699i | ||||
\(226\) | 3.69674 | − | 3.69674i | 0.245904 | − | 0.245904i | ||||
\(227\) | − | 22.2944i | − | 1.47973i | −0.672756 | − | 0.739864i | \(-0.734890\pi\) | ||
0.672756 | − | 0.739864i | \(-0.265110\pi\) | |||||||
\(228\) | 1.50898i | 0.0999349i | ||||||||
\(229\) | 5.97023 | − | 5.97023i | 0.394524 | − | 0.394524i | −0.481772 | − | 0.876296i | \(-0.660007\pi\) |
0.876296 | + | 0.481772i | \(0.160007\pi\) | |||||||
\(230\) | 0.883955 | + | 1.25688i | 0.0582862 | + | 0.0828765i | ||||
\(231\) | − | 5.83975i | − | 0.384227i | ||||||
\(232\) | −2.28429 | −0.149971 | ||||||||
\(233\) | −13.3554 | + | 13.3554i | −0.874943 | + | 0.874943i | −0.993006 | − | 0.118063i | \(-0.962332\pi\) |
0.118063 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(234\) | −3.17182 | + | 1.71451i | −0.207348 | + | 0.112081i | ||||
\(235\) | −6.44001 | − | 1.12184i | −0.420100 | − | 0.0731806i | ||||
\(236\) | 4.50044 | − | 4.50044i | 0.292954 | − | 0.292954i | ||||
\(237\) | 1.08704 | − | 1.08704i | 0.0706108 | − | 0.0706108i | ||||
\(238\) | −6.16749 | + | 6.16749i | −0.399779 | + | 0.399779i | ||||
\(239\) | 9.78834 | + | 9.78834i | 0.633155 | + | 0.633155i | 0.948858 | − | 0.315703i | \(-0.102240\pi\) |
−0.315703 | + | 0.948858i | \(0.602240\pi\) | |||||||
\(240\) | 1.28634 | + | 1.82903i | 0.0830327 | + | 0.118063i | ||||
\(241\) | −4.18100 | − | 4.18100i | −0.269322 | − | 0.269322i | 0.559505 | − | 0.828827i | \(-0.310991\pi\) |
−0.828827 | + | 0.559505i | \(0.810991\pi\) | |||||||
\(242\) | −3.59242 | −0.230929 | ||||||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 2.43047 | 0.155595 | ||||||||
\(245\) | 10.2721 | + | 1.78938i | 0.656259 | + | 0.114319i | ||||
\(246\) | 11.6330i | 0.741695i | ||||||||
\(247\) | 5.21378 | + | 1.55497i | 0.331745 | + | 0.0989402i | ||||
\(248\) | −1.00000 | − | 1.00000i | −0.0635001 | − | 0.0635001i | ||||
\(249\) | −5.45901 | − | 5.45901i | −0.345950 | − | 0.345950i | ||||
\(250\) | 5.53007 | − | 9.71691i | 0.349752 | − | 0.614551i | ||||
\(251\) | − | 16.6015i | − | 1.04788i | −0.851755 | − | 0.523940i | \(-0.824462\pi\) | ||
0.851755 | − | 0.523940i | \(-0.175538\pi\) | |||||||
\(252\) | − | 1.52873i | − | 0.0963009i | ||||||
\(253\) | −2.62506 | −0.165036 | ||||||||
\(254\) | 10.2359 | − | 10.2359i | 0.642258 | − | 0.642258i | ||||
\(255\) | −2.18942 | + | 12.5686i | −0.137107 | + | 0.787075i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.6326 | − | 11.6326i | −0.725624 | − | 0.725624i | 0.244121 | − | 0.969745i | \(-0.421501\pi\) |
−0.969745 | + | 0.244121i | \(0.921501\pi\) | |||||||
\(258\) | − | 8.14884i | − | 0.507324i | ||||||
\(259\) | 12.1730 | 0.756395 | ||||||||
\(260\) | 7.64511 | − | 2.55973i | 0.474130 | − | 0.158748i | ||||
\(261\) | 2.28429 | 0.141394 | ||||||||
\(262\) | − | 11.8485i | − | 0.732005i | ||||||
\(263\) | 1.07114 | + | 1.07114i | 0.0660491 | + | 0.0660491i | 0.739360 | − | 0.673311i | \(-0.235128\pi\) |
−0.673311 | + | 0.739360i | \(0.735128\pi\) | |||||||
\(264\) | −3.82000 | −0.235105 | ||||||||
\(265\) | 6.71391 | + | 9.54643i | 0.412432 | + | 0.586433i | ||||
\(266\) | −1.63117 | + | 1.63117i | −0.100014 | + | 0.100014i | ||||
\(267\) | 10.2060 | 0.624600 | ||||||||
\(268\) | 3.79906i | 0.232064i | ||||||||
\(269\) | − | 16.8729i | − | 1.02876i | −0.857562 | − | 0.514380i | \(-0.828022\pi\) | ||
0.857562 | − | 0.514380i | \(-0.171978\pi\) | |||||||
\(270\) | −1.28634 | − | 1.82903i | −0.0782839 | − | 0.111311i | ||||
\(271\) | 4.55193 | + | 4.55193i | 0.276510 | + | 0.276510i | 0.831714 | − | 0.555204i | \(-0.187360\pi\) |
−0.555204 | + | 0.831714i | \(0.687360\pi\) | |||||||
\(272\) | 4.03439 | + | 4.03439i | 0.244621 | + | 0.244621i | ||||
\(273\) | −5.28200 | − | 1.57531i | −0.319681 | − | 0.0953424i | ||||
\(274\) | − | 11.9361i | − | 0.721087i | ||||||
\(275\) | 8.14345 | + | 17.2770i | 0.491069 | + | 1.04184i | ||||
\(276\) | −0.687188 | −0.0413638 | ||||||||
\(277\) | 3.22540 | + | 3.22540i | 0.193796 | + | 0.193796i | 0.797334 | − | 0.603538i | \(-0.206243\pi\) |
−0.603538 | + | 0.797334i | \(0.706243\pi\) | |||||||
\(278\) | 20.0448 | 1.20221 | ||||||||
\(279\) | 1.00000 | + | 1.00000i | 0.0598684 | + | 0.0598684i | ||||
\(280\) | −0.586634 | + | 3.36763i | −0.0350581 | + | 0.201254i | ||||
\(281\) | 4.05048 | + | 4.05048i | 0.241631 | + | 0.241631i | 0.817525 | − | 0.575894i | \(-0.195346\pi\) |
−0.575894 | + | 0.817525i | \(0.695346\pi\) | |||||||
\(282\) | 2.06718 | − | 2.06718i | 0.123099 | − | 0.123099i | ||||
\(283\) | 14.1280 | − | 14.1280i | 0.839825 | − | 0.839825i | −0.149010 | − | 0.988836i | \(-0.547609\pi\) |
0.988836 | + | 0.149010i | \(0.0476088\pi\) | |||||||
\(284\) | −10.7079 | + | 10.7079i | −0.635399 | + | 0.635399i | ||||
\(285\) | −0.579058 | + | 3.32413i | −0.0343004 | + | 0.196905i | ||||
\(286\) | −3.93641 | + | 13.1987i | −0.232765 | + | 0.780456i | ||||
\(287\) | −12.5750 | + | 12.5750i | −0.742279 | + | 0.742279i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 15.5526i | 0.914858i | ||||||||
\(290\) | −5.03206 | − | 0.876575i | −0.295493 | − | 0.0514743i | ||||
\(291\) | −4.50142 | + | 4.50142i | −0.263878 | + | 0.263878i | ||||
\(292\) | − | 10.3127i | − | 0.603506i | ||||||
\(293\) | − | 29.4674i | − | 1.72150i | −0.509027 | − | 0.860751i | \(-0.669995\pi\) | ||
0.509027 | − | 0.860751i | \(-0.330005\pi\) | |||||||
\(294\) | −3.29723 | + | 3.29723i | −0.192298 | + | 0.192298i | ||||
\(295\) | 11.6410 | − | 8.18700i | 0.677765 | − | 0.476666i | ||||
\(296\) | − | 7.96284i | − | 0.462831i | ||||||
\(297\) | 3.82000 | 0.221659 | ||||||||
\(298\) | −3.91078 | + | 3.91078i | −0.226545 | + | 0.226545i | ||||
\(299\) | −0.708129 | + | 2.37434i | −0.0409522 | + | 0.137312i | ||||
\(300\) | 2.13179 | + | 4.52277i | 0.123079 | + | 0.261122i | ||||
\(301\) | 8.80868 | − | 8.80868i | 0.507724 | − | 0.507724i | ||||
\(302\) | −16.6941 | + | 16.6941i | −0.960636 | + | 0.960636i | ||||
\(303\) | 7.47184 | − | 7.47184i | 0.429246 | − | 0.429246i | ||||
\(304\) | 1.06701 | + | 1.06701i | 0.0611974 | + | 0.0611974i | ||||
\(305\) | 5.35407 | + | 0.932668i | 0.306573 | + | 0.0534044i | ||||
\(306\) | −4.03439 | − | 4.03439i | −0.230631 | − | 0.230631i | ||||
\(307\) | −20.8097 | −1.18767 | −0.593835 | − | 0.804587i | \(-0.702387\pi\) | ||||
−0.593835 | + | 0.804587i | \(0.702387\pi\) | |||||||
\(308\) | −4.12932 | − | 4.12932i | −0.235290 | − | 0.235290i | ||||
\(309\) | 6.88359 | 0.391594 | ||||||||
\(310\) | −1.81915 | − | 2.58663i | −0.103321 | − | 0.146911i | ||||
\(311\) | − | 31.1763i | − | 1.76785i | −0.467631 | − | 0.883924i | \(-0.654892\pi\) | ||
0.467631 | − | 0.883924i | \(-0.345108\pi\) | |||||||
\(312\) | −1.03047 | + | 3.45516i | −0.0583391 | + | 0.195610i | ||||
\(313\) | 10.7473 | + | 10.7473i | 0.607475 | + | 0.607475i | 0.942285 | − | 0.334811i | \(-0.108672\pi\) |
−0.334811 | + | 0.942285i | \(0.608672\pi\) | |||||||
\(314\) | −9.39497 | − | 9.39497i | −0.530189 | − | 0.530189i | ||||
\(315\) | 0.586634 | − | 3.36763i | 0.0330531 | − | 0.189744i | ||||
\(316\) | − | 1.53731i | − | 0.0864803i | ||||||
\(317\) | − | 19.2205i | − | 1.07953i | −0.841816 | − | 0.539764i | \(-0.818513\pi\) | ||
0.841816 | − | 0.539764i | \(-0.181487\pi\) | |||||||
\(318\) | −5.21941 | −0.292690 | ||||||||
\(319\) | 6.17022 | − | 6.17022i | 0.345466 | − | 0.345466i | ||||
\(320\) | 2.20289 | + | 0.383740i | 0.123146 | + | 0.0214517i | ||||
\(321\) | −18.5146 | −1.03338 | ||||||||
\(322\) | −0.742832 | − | 0.742832i | −0.0413964 | − | 0.0413964i | ||||
\(323\) | 8.60949i | 0.479045i | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 17.8237 | − | 2.70509i | 0.988678 | − | 0.150051i | ||||
\(326\) | −14.0308 | −0.777095 | ||||||||
\(327\) | 0.175462i | 0.00970308i | ||||||||
\(328\) | 8.22579 | + | 8.22579i | 0.454193 | + | 0.454193i | ||||
\(329\) | 4.46913 | 0.246391 | ||||||||
\(330\) | −8.41506 | − | 1.46589i | −0.463234 | − | 0.0806945i | ||||
\(331\) | 12.9738 | − | 12.9738i | 0.713107 | − | 0.713107i | −0.254077 | − | 0.967184i | \(-0.581772\pi\) |
0.967184 | + | 0.254077i | \(0.0817717\pi\) | |||||||
\(332\) | −7.72020 | −0.423701 | ||||||||
\(333\) | 7.96284i | 0.436361i | ||||||||
\(334\) | 14.4217i | 0.789122i | ||||||||
\(335\) | −1.45785 | + | 8.36892i | −0.0796509 | + | 0.457243i | ||||
\(336\) | −1.08097 | − | 1.08097i | −0.0589720 | − | 0.0589720i | ||||
\(337\) | −19.7453 | − | 19.7453i | −1.07560 | − | 1.07560i | −0.996898 | − | 0.0786992i | \(-0.974923\pi\) |
−0.0786992 | − | 0.996898i | \(-0.525077\pi\) | |||||||
\(338\) | 10.8762 | + | 7.12090i | 0.591590 | + | 0.387326i | ||||
\(339\) | 5.22798i | 0.283945i | ||||||||
\(340\) | 7.33918 | + | 10.4355i | 0.398023 | + | 0.565944i | ||||
\(341\) | 5.40230 | 0.292551 | ||||||||
\(342\) | −1.06701 | − | 1.06701i | −0.0576974 | − | 0.0576974i | ||||
\(343\) | −17.8295 | −0.962705 | ||||||||
\(344\) | −5.76210 | − | 5.76210i | −0.310671 | − | 0.310671i | ||||
\(345\) | −1.51380 | − | 0.263701i | −0.0815004 | − | 0.0141972i | ||||
\(346\) | 12.0153 | + | 12.0153i | 0.645947 | + | 0.645947i | ||||
\(347\) | −0.843939 | + | 0.843939i | −0.0453050 | + | 0.0453050i | −0.729396 | − | 0.684091i | \(-0.760199\pi\) |
0.684091 | + | 0.729396i | \(0.260199\pi\) | |||||||
\(348\) | 1.61524 | − | 1.61524i | 0.0865859 | − | 0.0865859i | ||||
\(349\) | 17.0343 | − | 17.0343i | 0.911828 | − | 0.911828i | −0.0845883 | − | 0.996416i | \(-0.526958\pi\) |
0.996416 | + | 0.0845883i | \(0.0269575\pi\) | |||||||
\(350\) | −2.58459 | + | 7.19341i | −0.138152 | + | 0.384504i | ||||
\(351\) | 1.03047 | − | 3.45516i | 0.0550026 | − | 0.184423i | ||||
\(352\) | −2.70115 | + | 2.70115i | −0.143972 | + | 0.143972i | ||||
\(353\) | −6.51257 | −0.346629 | −0.173314 | − | 0.984867i | \(-0.555448\pi\) | ||||
−0.173314 | + | 0.984867i | \(0.555448\pi\) | |||||||
\(354\) | 6.36459i | 0.338274i | ||||||||
\(355\) | −27.6975 | + | 19.4794i | −1.47003 | + | 1.03386i | ||||
\(356\) | 7.21676 | − | 7.21676i | 0.382488 | − | 0.382488i | ||||
\(357\) | − | 8.72214i | − | 0.461625i | ||||||
\(358\) | − | 10.2606i | − | 0.542289i | ||||||
\(359\) | 17.5895 | − | 17.5895i | 0.928337 | − | 0.928337i | −0.0692614 | − | 0.997599i | \(-0.522064\pi\) |
0.997599 | + | 0.0692614i | \(0.0220643\pi\) | |||||||
\(360\) | −2.20289 | − | 0.383740i | −0.116103 | − | 0.0202249i | ||||
\(361\) | − | 16.7230i | − | 0.880156i | ||||||
\(362\) | −22.4534 | −1.18013 | ||||||||
\(363\) | 2.54022 | − | 2.54022i | 0.133327 | − | 0.133327i | ||||
\(364\) | −4.84885 | + | 2.62102i | −0.254149 | + | 0.137379i | ||||
\(365\) | 3.95740 | − | 22.7178i | 0.207140 | − | 1.18911i | ||||
\(366\) | −1.71860 | + | 1.71860i | −0.0898327 | + | 0.0898327i | ||||
\(367\) | −10.9276 | + | 10.9276i | −0.570418 | + | 0.570418i | −0.932245 | − | 0.361827i | \(-0.882153\pi\) |
0.361827 | + | 0.932245i | \(0.382153\pi\) | |||||||
\(368\) | −0.485915 | + | 0.485915i | −0.0253301 | + | 0.0253301i | ||||
\(369\) | −8.22579 | − | 8.22579i | −0.428218 | − | 0.428218i | ||||
\(370\) | 3.05566 | − | 17.5413i | 0.158856 | − | 0.911929i | ||||
\(371\) | −5.64204 | − | 5.64204i | −0.292920 | − | 0.292920i | ||||
\(372\) | 1.41421 | 0.0733236 | ||||||||
\(373\) | 6.56604 | + | 6.56604i | 0.339977 | + | 0.339977i | 0.856359 | − | 0.516382i | \(-0.172721\pi\) |
−0.516382 | + | 0.856359i | \(0.672721\pi\) | |||||||
\(374\) | −21.7950 | −1.12699 | ||||||||
\(375\) | 2.96054 | + | 10.7812i | 0.152882 | + | 0.556741i | ||||
\(376\) | − | 2.92343i | − | 0.150764i | ||||||
\(377\) | −3.91645 | − | 7.24537i | −0.201707 | − | 0.373156i | ||||
\(378\) | 1.08097 | + | 1.08097i | 0.0555993 | + | 0.0555993i | ||||
\(379\) | −23.1557 | − | 23.1557i | −1.18943 | − | 1.18943i | −0.977226 | − | 0.212203i | \(-0.931936\pi\) |
−0.212203 | − | 0.977226i | \(-0.568064\pi\) | |||||||
\(380\) | 1.94106 | + | 2.75997i | 0.0995743 | + | 0.141584i | ||||
\(381\) | 14.4758i | 0.741616i | ||||||||
\(382\) | − | 12.2203i | − | 0.625244i | ||||||
\(383\) | 1.38206 | 0.0706198 | 0.0353099 | − | 0.999376i | \(-0.488758\pi\) | ||||
0.0353099 | + | 0.999376i | \(0.488758\pi\) | |||||||
\(384\) | −0.707107 | + | 0.707107i | −0.0360844 | + | 0.0360844i | ||||
\(385\) | −7.51188 | − | 10.6811i | −0.382841 | − | 0.544357i | ||||
\(386\) | −24.1428 | −1.22883 | ||||||||
\(387\) | 5.76210 | + | 5.76210i | 0.292904 | + | 0.292904i | ||||
\(388\) | 6.36597i | 0.323183i | ||||||||
\(389\) | −19.6760 | −0.997614 | −0.498807 | − | 0.866713i | \(-0.666228\pi\) | ||||
−0.498807 | + | 0.866713i | \(0.666228\pi\) | |||||||
\(390\) | −3.59591 | + | 7.21592i | −0.182086 | + | 0.365392i | ||||
\(391\) | −3.92074 | −0.198280 | ||||||||
\(392\) | 4.66299i | 0.235516i | ||||||||
\(393\) | 8.37818 | + | 8.37818i | 0.422624 | + | 0.422624i | ||||
\(394\) | 3.53326 | 0.178003 | ||||||||
\(395\) | 0.589926 | − | 3.38652i | 0.0296824 | − | 0.170395i | ||||
\(396\) | 2.70115 | − | 2.70115i | 0.135738 | − | 0.135738i | ||||
\(397\) | −35.9373 | −1.80364 | −0.901819 | − | 0.432113i | \(-0.857768\pi\) | ||||
−0.901819 | + | 0.432113i | \(0.857768\pi\) | |||||||
\(398\) | − | 12.1781i | − | 0.610434i | ||||||
\(399\) | − | 2.30683i | − | 0.115486i | ||||||
\(400\) | 4.70549 | + | 1.69068i | 0.235274 | + | 0.0845339i | ||||
\(401\) | −1.64796 | − | 1.64796i | −0.0822953 | − | 0.0822953i | 0.664761 | − | 0.747056i | \(-0.268533\pi\) |
−0.747056 | + | 0.664761i | \(0.768533\pi\) | |||||||
\(402\) | −2.68634 | − | 2.68634i | −0.133982 | − | 0.133982i | ||||
\(403\) | 1.45731 | − | 4.88633i | 0.0725938 | − | 0.243406i | ||||
\(404\) | − | 10.5668i | − | 0.525717i | ||||||
\(405\) | 2.20289 | + | 0.383740i | 0.109463 | + | 0.0190682i | ||||
\(406\) | 3.49207 | 0.173308 | ||||||||
\(407\) | 21.5088 | + | 21.5088i | 1.06615 | + | 1.06615i | ||||
\(408\) | −5.70549 | −0.282464 | ||||||||
\(409\) | 12.3833 | + | 12.3833i | 0.612314 | + | 0.612314i | 0.943548 | − | 0.331234i | \(-0.107465\pi\) |
−0.331234 | + | 0.943548i | \(0.607465\pi\) | |||||||
\(410\) | 14.9640 | + | 21.2771i | 0.739018 | + | 1.05080i | ||||
\(411\) | 8.44011 | + | 8.44011i | 0.416320 | + | 0.416320i | ||||
\(412\) | 4.86744 | − | 4.86744i | 0.239801 | − | 0.239801i | ||||
\(413\) | −6.87996 | + | 6.87996i | −0.338540 | + | 0.338540i | ||||
\(414\) | 0.485915 | − | 0.485915i | 0.0238814 | − | 0.0238814i | ||||
\(415\) | −17.0068 | − | 2.96255i | −0.834830 | − | 0.145426i | ||||
\(416\) | 1.71451 | + | 3.17182i | 0.0840608 | + | 0.155511i | ||||
\(417\) | −14.1738 | + | 14.1738i | −0.694095 | + | 0.694095i | ||||
\(418\) | −5.76432 | −0.281942 | ||||||||
\(419\) | 8.21451i | 0.401305i | 0.979662 | + | 0.200652i | \(0.0643062\pi\) | ||||
−0.979662 | + | 0.200652i | \(0.935694\pi\) | |||||||
\(420\) | −1.96646 | − | 2.79609i | −0.0959534 | − | 0.136435i | ||||
\(421\) | −10.9922 | + | 10.9922i | −0.535725 | + | 0.535725i | −0.922270 | − | 0.386545i | \(-0.873668\pi\) |
0.386545 | + | 0.922270i | \(0.373668\pi\) | |||||||
\(422\) | − | 14.2670i | − | 0.694506i | ||||||
\(423\) | 2.92343i | 0.142142i | ||||||||
\(424\) | −3.69068 | + | 3.69068i | −0.179235 | + | 0.179235i | ||||
\(425\) | 12.1629 | + | 25.8046i | 0.589988 | + | 1.25171i | ||||
\(426\) | − | 15.1433i | − | 0.733696i | ||||||
\(427\) | −3.71553 | −0.179807 | ||||||||
\(428\) | −13.0918 | + | 13.0918i | −0.632815 | + | 0.632815i | ||||
\(429\) | −6.54944 | − | 12.1164i | −0.316210 | − | 0.584984i | ||||
\(430\) | −10.4821 | − | 14.9044i | −0.505494 | − | 0.718756i | ||||
\(431\) | 15.4246 | − | 15.4246i | 0.742976 | − | 0.742976i | −0.230174 | − | 0.973150i | \(-0.573929\pi\) |
0.973150 | + | 0.230174i | \(0.0739294\pi\) | |||||||
\(432\) | 0.707107 | − | 0.707107i | 0.0340207 | − | 0.0340207i | ||||
\(433\) | −3.28016 | + | 3.28016i | −0.157634 | + | 0.157634i | −0.781518 | − | 0.623883i | \(-0.785554\pi\) |
0.623883 | + | 0.781518i | \(0.285554\pi\) | |||||||
\(434\) | 1.52873 | + | 1.52873i | 0.0733813 | + | 0.0733813i | ||||
\(435\) | 4.17804 | − | 2.93837i | 0.200321 | − | 0.140884i | ||||
\(436\) | 0.124070 | + | 0.124070i | 0.00594190 | + | 0.00594190i | ||||
\(437\) | −1.03696 | −0.0496043 | ||||||||
\(438\) | 7.29219 | + | 7.29219i | 0.348434 | + | 0.348434i | ||||
\(439\) | 12.4347 | 0.593477 | 0.296739 | − | 0.954959i | \(-0.404101\pi\) | ||||
0.296739 | + | 0.954959i | \(0.404101\pi\) | |||||||
\(440\) | −6.98689 | + | 4.91381i | −0.333087 | + | 0.234257i | ||||
\(441\) | − | 4.66299i | − | 0.222047i | ||||||
\(442\) | −5.87935 | + | 19.7134i | −0.279652 | + | 0.937669i | ||||
\(443\) | −12.5904 | − | 12.5904i | −0.598187 | − | 0.598187i | 0.341643 | − | 0.939830i | \(-0.389017\pi\) |
−0.939830 | + | 0.341643i | \(0.889017\pi\) | |||||||
\(444\) | 5.63058 | + | 5.63058i | 0.267215 | + | 0.267215i | ||||
\(445\) | 18.6671 | − | 13.1284i | 0.884907 | − | 0.622346i | ||||
\(446\) | − | 11.9632i | − | 0.566472i | ||||||
\(447\) | − | 5.53068i | − | 0.261592i | ||||||
\(448\) | −1.52873 | −0.0722256 | ||||||||
\(449\) | 15.4853 | − | 15.4853i | 0.730796 | − | 0.730796i | −0.239982 | − | 0.970777i | \(-0.577141\pi\) |
0.970777 | + | 0.239982i | \(0.0771414\pi\) | |||||||
\(450\) | −4.70549 | − | 1.69068i | −0.221819 | − | 0.0796993i | ||||
\(451\) | −44.4382 | −2.09251 | ||||||||
\(452\) | 3.69674 | + | 3.69674i | 0.173880 | + | 0.173880i | ||||
\(453\) | − | 23.6090i | − | 1.10925i | ||||||
\(454\) | 22.2944 | 1.04633 | ||||||||
\(455\) | −11.6873 | + | 3.91314i | −0.547909 | + | 0.183451i | ||||
\(456\) | −1.50898 | −0.0706646 | ||||||||
\(457\) | 15.3846i | 0.719660i | 0.933018 | + | 0.359830i | \(0.117165\pi\) | ||||
−0.933018 | + | 0.359830i | \(0.882835\pi\) | |||||||
\(458\) | 5.97023 | + | 5.97023i | 0.278971 | + | 0.278971i | ||||
\(459\) | 5.70549 | 0.266309 | ||||||||
\(460\) | −1.25688 | + | 0.883955i | −0.0586026 | + | 0.0412146i | ||||
\(461\) | −26.1557 | + | 26.1557i | −1.21819 | + | 1.21819i | −0.249925 | + | 0.968265i | \(0.580406\pi\) |
−0.968265 | + | 0.249925i | \(0.919594\pi\) | |||||||
\(462\) | 5.83975 | 0.271690 | ||||||||
\(463\) | 5.65611i | 0.262862i | 0.991325 | + | 0.131431i | \(0.0419571\pi\) | ||||
−0.991325 | + | 0.131431i | \(0.958043\pi\) | |||||||
\(464\) | − | 2.28429i | − | 0.106046i | ||||||
\(465\) | 3.11536 | + | 0.542690i | 0.144472 | + | 0.0251667i | ||||
\(466\) | −13.3554 | − | 13.3554i | −0.618678 | − | 0.618678i | ||||
\(467\) | 23.4369 | + | 23.4369i | 1.08453 | + | 1.08453i | 0.996081 | + | 0.0884497i | \(0.0281913\pi\) |
0.0884497 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(468\) | −1.71451 | − | 3.17182i | −0.0792533 | − | 0.146617i | ||||
\(469\) | − | 5.80773i | − | 0.268176i | ||||||
\(470\) | 1.12184 | − | 6.44001i | 0.0517465 | − | 0.297056i | ||||
\(471\) | 13.2865 | 0.612209 | ||||||||
\(472\) | 4.50044 | + | 4.50044i | 0.207150 | + | 0.207150i | ||||
\(473\) | 31.1286 | 1.43129 | ||||||||
\(474\) | 1.08704 | + | 1.08704i | 0.0499294 | + | 0.0499294i | ||||
\(475\) | 3.21684 | + | 6.82479i | 0.147599 | + | 0.313143i | ||||
\(476\) | −6.16749 | − | 6.16749i | −0.282686 | − | 0.282686i | ||||
\(477\) | 3.69068 | − | 3.69068i | 0.168985 | − | 0.168985i | ||||
\(478\) | −9.78834 | + | 9.78834i | −0.447708 | + | 0.447708i | ||||
\(479\) | −3.55522 | + | 3.55522i | −0.162442 | + | 0.162442i | −0.783648 | − | 0.621206i | \(-0.786643\pi\) |
0.621206 | + | 0.783648i | \(0.286643\pi\) | |||||||
\(480\) | −1.82903 | + | 1.28634i | −0.0834833 | + | 0.0587130i | ||||
\(481\) | 25.2567 | − | 13.6524i | 1.15161 | − | 0.622495i | ||||
\(482\) | 4.18100 | − | 4.18100i | 0.190439 | − | 0.190439i | ||||
\(483\) | 1.05052 | 0.0478005 | ||||||||
\(484\) | − | 3.59242i | − | 0.163292i | ||||||
\(485\) | −2.44288 | + | 14.0236i | −0.110925 | + | 0.636777i | ||||
\(486\) | −0.707107 | + | 0.707107i | −0.0320750 | + | 0.0320750i | ||||
\(487\) | − | 6.62780i | − | 0.300334i | −0.988661 | − | 0.150167i | \(-0.952019\pi\) | ||
0.988661 | − | 0.150167i | \(-0.0479812\pi\) | |||||||
\(488\) | 2.43047i | 0.110022i | ||||||||
\(489\) | 9.92129 | − | 9.92129i | 0.448656 | − | 0.448656i | ||||
\(490\) | −1.78938 | + | 10.2721i | −0.0808357 | + | 0.464045i | ||||
\(491\) | 15.5268i | 0.700713i | 0.936616 | + | 0.350357i | \(0.113940\pi\) | ||||
−0.936616 | + | 0.350357i | \(0.886060\pi\) | |||||||
\(492\) | −11.6330 | −0.524457 | ||||||||
\(493\) | 9.21573 | − | 9.21573i | 0.415056 | − | 0.415056i | ||||
\(494\) | −1.55497 | + | 5.21378i | −0.0699613 | + | 0.234579i | ||||
\(495\) | 6.98689 | − | 4.91381i | 0.314037 | − | 0.220859i | ||||
\(496\) | 1.00000 | − | 1.00000i | 0.0449013 | − | 0.0449013i | ||||
\(497\) | 16.3695 | − | 16.3695i | 0.734274 | − | 0.734274i | ||||
\(498\) | 5.45901 | − | 5.45901i | 0.244624 | − | 0.244624i | ||||
\(499\) | 3.06206 | + | 3.06206i | 0.137077 | + | 0.137077i | 0.772316 | − | 0.635239i | \(-0.219098\pi\) |
−0.635239 | + | 0.772316i | \(0.719098\pi\) | |||||||
\(500\) | 9.71691 | + | 5.53007i | 0.434553 | + | 0.247312i | ||||
\(501\) | −10.1977 | − | 10.1977i | −0.455600 | − | 0.455600i | ||||
\(502\) | 16.6015 | 0.740963 | ||||||||
\(503\) | −21.0989 | − | 21.0989i | −0.940753 | − | 0.940753i | 0.0575878 | − | 0.998340i | \(-0.481659\pi\) |
−0.998340 | + | 0.0575878i | \(0.981659\pi\) | |||||||
\(504\) | 1.52873 | 0.0680950 | ||||||||
\(505\) | 4.05489 | − | 23.2775i | 0.180440 | − | 1.03583i | ||||
\(506\) | − | 2.62506i | − | 0.116698i | ||||||
\(507\) | −12.7259 | + | 2.65543i | −0.565177 | + | 0.117932i | ||||
\(508\) | 10.2359 | + | 10.2359i | 0.454145 | + | 0.454145i | ||||
\(509\) | 23.9745 | + | 23.9745i | 1.06265 | + | 1.06265i | 0.997901 | + | 0.0647506i | \(0.0206252\pi\) |
0.0647506 | + | 0.997901i | \(0.479375\pi\) | |||||||
\(510\) | −12.5686 | − | 2.18942i | −0.556546 | − | 0.0969493i | ||||
\(511\) | 15.7653i | 0.697418i | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 1.50898 | 0.0666233 | ||||||||
\(514\) | 11.6326 | − | 11.6326i | 0.513094 | − | 0.513094i | ||||
\(515\) | 12.5903 | − | 8.85462i | 0.554794 | − | 0.390181i | ||||
\(516\) | 8.14884 | 0.358732 | ||||||||
\(517\) | 7.89663 | + | 7.89663i | 0.347293 | + | 0.347293i | ||||
\(518\) | 12.1730i | 0.534852i | ||||||||
\(519\) | −16.9922 | −0.745875 | ||||||||
\(520\) | 2.55973 | + | 7.64511i | 0.112252 | + | 0.335260i | ||||
\(521\) | −17.4440 | −0.764238 | −0.382119 | − | 0.924113i | \(-0.624806\pi\) | ||||
−0.382119 | + | 0.924113i | \(0.624806\pi\) | |||||||
\(522\) | 2.28429i | 0.0999808i | ||||||||
\(523\) | 20.2159 | + | 20.2159i | 0.883980 | + | 0.883980i | 0.993936 | − | 0.109957i | \(-0.0350712\pi\) |
−0.109957 | + | 0.993936i | \(0.535071\pi\) | |||||||
\(524\) | 11.8485 | 0.517606 | ||||||||
\(525\) | −3.25893 | − | 6.91409i | −0.142231 | − | 0.301756i | ||||
\(526\) | −1.07114 | + | 1.07114i | −0.0467038 | + | 0.0467038i | ||||
\(527\) | 8.06878 | 0.351481 | ||||||||
\(528\) | − | 3.82000i | − | 0.166244i | ||||||
\(529\) | 22.5278i | 0.979468i | ||||||||
\(530\) | −9.54643 | + | 6.71391i | −0.414671 | + | 0.291634i | ||||
\(531\) | −4.50044 | − | 4.50044i | −0.195303 | − | 0.195303i | ||||
\(532\) | −1.63117 | − | 1.63117i | −0.0707203 | − | 0.0707203i | ||||
\(533\) | −11.9875 | + | 40.1940i | −0.519237 | + | 1.74099i | ||||
\(534\) | 10.2060i | 0.441659i | ||||||||
\(535\) | −33.8636 | + | 23.8160i | −1.46405 | + | 1.02965i | ||||
\(536\) | −3.79906 | −0.164094 | ||||||||
\(537\) | 7.25534 | + | 7.25534i | 0.313091 | + | 0.313091i | ||||
\(538\) | 16.8729 | 0.727443 | ||||||||
\(539\) | −12.5954 | − | 12.5954i | −0.542524 | − | 0.542524i | ||||
\(540\) | 1.82903 | − | 1.28634i | 0.0787088 | − | 0.0553551i | ||||
\(541\) | −0.554543 | − | 0.554543i | −0.0238417 | − | 0.0238417i | 0.695085 | − | 0.718927i | \(-0.255367\pi\) |
−0.718927 | + | 0.695085i | \(0.755367\pi\) | |||||||
\(542\) | −4.55193 | + | 4.55193i | −0.195522 | + | 0.195522i | ||||
\(543\) | 15.8770 | − | 15.8770i | 0.681346 | − | 0.681346i | ||||
\(544\) | −4.03439 | + | 4.03439i | −0.172973 | + | 0.172973i | ||||
\(545\) | 0.225703 | + | 0.320925i | 0.00966807 | + | 0.0137469i | ||||
\(546\) | 1.57531 | − | 5.28200i | 0.0674172 | − | 0.226049i | ||||
\(547\) | −9.17919 | + | 9.17919i | −0.392474 | + | 0.392474i | −0.875568 | − | 0.483095i | \(-0.839513\pi\) |
0.483095 | + | 0.875568i | \(0.339513\pi\) | |||||||
\(548\) | 11.9361 | 0.509886 | ||||||||
\(549\) | − | 2.43047i | − | 0.103730i | ||||||
\(550\) | −17.2770 | + | 8.14345i | −0.736694 | + | 0.347238i | ||||
\(551\) | 2.43737 | − | 2.43737i | 0.103835 | − | 0.103835i | ||||
\(552\) | − | 0.687188i | − | 0.0292487i | ||||||
\(553\) | 2.35013i | 0.0999375i | ||||||||
\(554\) | −3.22540 | + | 3.22540i | −0.137034 | + | 0.137034i | ||||
\(555\) | 10.2429 | + | 14.5642i | 0.434787 | + | 0.618218i | ||||
\(556\) | 20.0448i | 0.850089i | ||||||||
\(557\) | 37.1733 | 1.57508 | 0.787541 | − | 0.616262i | \(-0.211354\pi\) | ||||
0.787541 | + | 0.616262i | \(0.211354\pi\) | |||||||
\(558\) | −1.00000 | + | 1.00000i | −0.0423334 | + | 0.0423334i | ||||
\(559\) | 8.39716 | − | 28.1555i | 0.355162 | − | 1.19085i | ||||
\(560\) | −3.36763 | − | 0.586634i | −0.142308 | − | 0.0247898i | ||||
\(561\) | 15.4114 | − | 15.4114i | 0.650669 | − | 0.650669i | ||||
\(562\) | −4.05048 | + | 4.05048i | −0.170859 | + | 0.170859i | ||||
\(563\) | 19.8005 | − | 19.8005i | 0.834493 | − | 0.834493i | −0.153635 | − | 0.988128i | \(-0.549098\pi\) |
0.988128 | + | 0.153635i | \(0.0490979\pi\) | |||||||
\(564\) | 2.06718 | + | 2.06718i | 0.0870439 | + | 0.0870439i | ||||
\(565\) | 6.72495 | + | 9.56212i | 0.282921 | + | 0.402282i | ||||
\(566\) | 14.1280 | + | 14.1280i | 0.593846 | + | 0.593846i | ||||
\(567\) | −1.52873 | −0.0642006 | ||||||||
\(568\) | −10.7079 | − | 10.7079i | −0.449295 | − | 0.449295i | ||||
\(569\) | −22.5105 | −0.943689 | −0.471844 | − | 0.881682i | \(-0.656412\pi\) | ||||
−0.471844 | + | 0.881682i | \(0.656412\pi\) | |||||||
\(570\) | −3.32413 | − | 0.579058i | −0.139233 | − | 0.0242541i | ||||
\(571\) | − | 17.9308i | − | 0.750379i | −0.926948 | − | 0.375190i | \(-0.877578\pi\) | ||
0.926948 | − | 0.375190i | \(-0.122422\pi\) | |||||||
\(572\) | −13.1987 | − | 3.93641i | −0.551866 | − | 0.164590i | ||||
\(573\) | 8.64105 | + | 8.64105i | 0.360985 | + | 0.360985i | ||||
\(574\) | −12.5750 | − | 12.5750i | −0.524870 | − | 0.524870i | ||||
\(575\) | −3.10799 | + | 1.46494i | −0.129612 | + | 0.0610923i | ||||
\(576\) | − | 1.00000i | − | 0.0416667i | ||||||
\(577\) | − | 12.5758i | − | 0.523535i | −0.965131 | − | 0.261768i | \(-0.915695\pi\) | ||
0.965131 | − | 0.261768i | \(-0.0843054\pi\) | |||||||
\(578\) | −15.5526 | −0.646902 | ||||||||
\(579\) | 17.0715 | − | 17.0715i | 0.709467 | − | 0.709467i | ||||
\(580\) | 0.876575 | − | 5.03206i | 0.0363978 | − | 0.208945i | ||||
\(581\) | 11.8021 | 0.489633 | ||||||||
\(582\) | −4.50142 | − | 4.50142i | −0.186590 | − | 0.186590i | ||||
\(583\) | − | 19.9381i | − | 0.825754i | ||||||
\(584\) | 10.3127 | 0.426743 | ||||||||
\(585\) | −2.55973 | − | 7.64511i | −0.105832 | − | 0.316087i | ||||
\(586\) | 29.4674 | 1.21729 | ||||||||
\(587\) | 9.73305i | 0.401726i | 0.979619 | + | 0.200863i | \(0.0643746\pi\) | ||||
−0.979619 | + | 0.200863i | \(0.935625\pi\) | |||||||
\(588\) | −3.29723 | − | 3.29723i | −0.135976 | − | 0.135976i | ||||
\(589\) | 2.13403 | 0.0879310 | ||||||||
\(590\) | 8.18700 | + | 11.6410i | 0.337053 | + | 0.479252i | ||||
\(591\) | −2.49840 | + | 2.49840i | −0.102770 | + | 0.102770i | ||||
\(592\) | 7.96284 | 0.327271 | ||||||||
\(593\) | 29.3940i | 1.20707i | 0.797337 | + | 0.603534i | \(0.206241\pi\) | ||||
−0.797337 | + | 0.603534i | \(0.793759\pi\) | |||||||
\(594\) | 3.82000i | 0.156737i | ||||||||
\(595\) | −11.2196 | − | 15.9530i | −0.459959 | − | 0.654010i | ||||
\(596\) | −3.91078 | − | 3.91078i | −0.160192 | − | 0.160192i | ||||
\(597\) | 8.61123 | + | 8.61123i | 0.352434 | + | 0.352434i | ||||
\(598\) | −2.37434 | − | 0.708129i | −0.0970941 | − | 0.0289575i | ||||
\(599\) | − | 7.65108i | − | 0.312615i | −0.987708 | − | 0.156307i | \(-0.950041\pi\) | ||
0.987708 | − | 0.156307i | \(-0.0499590\pi\) | |||||||
\(600\) | −4.52277 | + | 2.13179i | −0.184641 | + | 0.0870301i | ||||
\(601\) | −8.65440 | −0.353020 | −0.176510 | − | 0.984299i | \(-0.556481\pi\) | ||||
−0.176510 | + | 0.984299i | \(0.556481\pi\) | |||||||
\(602\) | 8.80868 | + | 8.80868i | 0.359015 | + | 0.359015i | ||||
\(603\) | 3.79906 | 0.154710 | ||||||||
\(604\) | −16.6941 | − | 16.6941i | −0.679272 | − | 0.679272i | ||||
\(605\) | 1.37855 | − | 7.91372i | 0.0560462 | − | 0.321738i | ||||
\(606\) | 7.47184 | + | 7.47184i | 0.303523 | + | 0.303523i | ||||
\(607\) | 19.6391 | − | 19.6391i | 0.797125 | − | 0.797125i | −0.185516 | − | 0.982641i | \(-0.559396\pi\) |
0.982641 | + | 0.185516i | \(0.0593958\pi\) | |||||||
\(608\) | −1.06701 | + | 1.06701i | −0.0432731 | + | 0.0432731i | ||||
\(609\) | −2.46926 | + | 2.46926i | −0.100060 | + | 0.100060i | ||||
\(610\) | −0.932668 | + | 5.35407i | −0.0377626 | + | 0.216780i | ||||
\(611\) | 9.27260 | − | 5.01226i | 0.375129 | − | 0.202774i | ||||
\(612\) | 4.03439 | − | 4.03439i | 0.163080 | − | 0.163080i | ||||
\(613\) | 5.05853 | 0.204312 | 0.102156 | − | 0.994768i | \(-0.467426\pi\) | ||||
0.102156 | + | 0.994768i | \(0.467426\pi\) | |||||||
\(614\) | − | 20.8097i | − | 0.839810i | ||||||
\(615\) | −25.6263 | − | 4.46406i | −1.03335 | − | 0.180008i | ||||
\(616\) | 4.12932 | − | 4.12932i | 0.166375 | − | 0.166375i | ||||
\(617\) | 3.30694i | 0.133132i | 0.997782 | + | 0.0665662i | \(0.0212044\pi\) | ||||
−0.997782 | + | 0.0665662i | \(0.978796\pi\) | |||||||
\(618\) | 6.88359i | 0.276899i | ||||||||
\(619\) | −2.89470 | + | 2.89470i | −0.116348 | + | 0.116348i | −0.762884 | − | 0.646536i | \(-0.776217\pi\) |
0.646536 | + | 0.762884i | \(0.276217\pi\) | |||||||
\(620\) | 2.58663 | − | 1.81915i | 0.103882 | − | 0.0730590i | ||||
\(621\) | 0.687188i | 0.0275759i | ||||||||
\(622\) | 31.1763 | 1.25006 | ||||||||
\(623\) | −11.0325 | + | 11.0325i | −0.442007 | + | 0.442007i | ||||
\(624\) | −3.45516 | − | 1.03047i | −0.138317 | − | 0.0412520i | ||||
\(625\) | 19.2832 | + | 15.9109i | 0.771329 | + | 0.636437i | ||||
\(626\) | −10.7473 | + | 10.7473i | −0.429549 | + | 0.429549i | ||||
\(627\) | 4.07599 | − | 4.07599i | 0.162779 | − | 0.162779i | ||||
\(628\) | 9.39497 | − | 9.39497i | 0.374900 | − | 0.374900i | ||||
\(629\) | 32.1252 | + | 32.1252i | 1.28092 | + | 1.28092i | ||||
\(630\) | 3.36763 | + | 0.586634i | 0.134170 | + | 0.0233721i | ||||
\(631\) | 6.05694 | + | 6.05694i | 0.241123 | + | 0.241123i | 0.817315 | − | 0.576192i | \(-0.195462\pi\) |
−0.576192 | + | 0.817315i | \(0.695462\pi\) | |||||||
\(632\) | 1.53731 | 0.0611508 | ||||||||
\(633\) | 10.0883 | + | 10.0883i | 0.400973 | + | 0.400973i | ||||
\(634\) | 19.2205 | 0.763342 | ||||||||
\(635\) | 18.6207 | + | 26.4766i | 0.738940 | + | 1.05069i | ||||
\(636\) | − | 5.21941i | − | 0.206963i | ||||||
\(637\) | −14.7902 | + | 7.99475i | −0.586008 | + | 0.316763i | ||||
\(638\) | 6.17022 | + | 6.17022i | 0.244281 | + | 0.244281i | ||||
\(639\) | 10.7079 | + | 10.7079i | 0.423599 | + | 0.423599i | ||||
\(640\) | −0.383740 | + | 2.20289i | −0.0151687 | + | 0.0870770i | ||||
\(641\) | 6.88364i | 0.271887i | 0.990717 | + | 0.135944i | \(0.0434066\pi\) | ||||
−0.990717 | + | 0.135944i | \(0.956593\pi\) | |||||||
\(642\) | − | 18.5146i | − | 0.730712i | ||||||
\(643\) | −44.0145 | −1.73576 | −0.867882 | − | 0.496771i | \(-0.834519\pi\) | ||||
−0.867882 | + | 0.496771i | \(0.834519\pi\) | |||||||
\(644\) | 0.742832 | − | 0.742832i | 0.0292717 | − | 0.0292717i | ||||
\(645\) | 17.9510 | + | 3.12703i | 0.706821 | + | 0.123127i | ||||
\(646\) | −8.60949 | −0.338736 | ||||||||
\(647\) | 6.25687 | + | 6.25687i | 0.245983 | + | 0.245983i | 0.819320 | − | 0.573337i | \(-0.194351\pi\) |
−0.573337 | + | 0.819320i | \(0.694351\pi\) | |||||||
\(648\) | 1.00000i | 0.0392837i | ||||||||
\(649\) | −24.3127 | −0.954358 | ||||||||
\(650\) | 2.70509 | + | 17.8237i | 0.106102 | + | 0.699101i | ||||
\(651\) | −2.16195 | −0.0847335 | ||||||||
\(652\) | − | 14.0308i | − | 0.549489i | ||||||
\(653\) | −29.1179 | − | 29.1179i | −1.13947 | − | 1.13947i | −0.988545 | − | 0.150926i | \(-0.951774\pi\) |
−0.150926 | − | 0.988545i | \(-0.548226\pi\) | |||||||
\(654\) | −0.175462 | −0.00686111 | ||||||||
\(655\) | 26.1011 | + | 4.54676i | 1.01985 | + | 0.177657i | ||||
\(656\) | −8.22579 | + | 8.22579i | −0.321163 | + | 0.321163i | ||||
\(657\) | −10.3127 | −0.402337 | ||||||||
\(658\) | 4.46913i | 0.174225i | ||||||||
\(659\) | 41.2913i | 1.60848i | 0.594304 | + | 0.804241i | \(0.297428\pi\) | ||||
−0.594304 | + | 0.804241i | \(0.702572\pi\) | |||||||
\(660\) | 1.46589 | − | 8.41506i | 0.0570596 | − | 0.327556i | ||||
\(661\) | −27.4575 | − | 27.4575i | −1.06797 | − | 1.06797i | −0.997515 | − | 0.0704594i | \(-0.977553\pi\) |
−0.0704594 | − | 0.997515i | \(-0.522447\pi\) | |||||||
\(662\) | 12.9738 | + | 12.9738i | 0.504243 | + | 0.504243i | ||||
\(663\) | −9.78212 | − | 18.0968i | −0.379906 | − | 0.702821i | ||||
\(664\) | − | 7.72020i | − | 0.299602i | ||||||
\(665\) | −2.96736 | − | 4.21925i | −0.115069 | − | 0.163615i | ||||
\(666\) | −7.96284 | −0.308554 | ||||||||
\(667\) | 1.10997 | + | 1.10997i | 0.0429783 | + | 0.0429783i | ||||
\(668\) | −14.4217 | −0.557993 | ||||||||
\(669\) | 8.45923 | + | 8.45923i | 0.327053 | + | 0.327053i | ||||
\(670\) | −8.36892 | − | 1.45785i | −0.323320 | − | 0.0563217i | ||||
\(671\) | −6.56506 | − | 6.56506i | −0.253441 | − | 0.253441i | ||||
\(672\) | 1.08097 | − | 1.08097i | 0.0416995 | − | 0.0416995i | ||||
\(673\) | 27.6552 | − | 27.6552i | 1.06603 | − | 1.06603i | 0.0683689 | − | 0.997660i | \(-0.478221\pi\) |
0.997660 | − | 0.0683689i | \(-0.0217795\pi\) | |||||||
\(674\) | 19.7453 | − | 19.7453i | 0.760562 | − | 0.760562i | ||||
\(675\) | 4.52277 | − | 2.13179i | 0.174082 | − | 0.0820527i | ||||
\(676\) | −7.12090 | + | 10.8762i | −0.273881 | + | 0.418317i | ||||
\(677\) | −16.1493 | + | 16.1493i | −0.620669 | + | 0.620669i | −0.945703 | − | 0.325033i | \(-0.894624\pi\) |
0.325033 | + | 0.945703i | \(0.394624\pi\) | |||||||
\(678\) | −5.22798 | −0.200780 | ||||||||
\(679\) | − | 9.73184i | − | 0.373474i | ||||||
\(680\) | −10.4355 | + | 7.33918i | −0.400183 | + | 0.281445i | ||||
\(681\) | −15.7645 | + | 15.7645i | −0.604096 | + | 0.604096i | ||||
\(682\) | 5.40230i | 0.206865i | ||||||||
\(683\) | 45.8440i | 1.75417i | 0.480333 | + | 0.877086i | \(0.340516\pi\) | ||||
−0.480333 | + | 0.877086i | \(0.659484\pi\) | |||||||
\(684\) | 1.06701 | − | 1.06701i | 0.0407983 | − | 0.0407983i | ||||
\(685\) | 26.2940 | + | 4.58037i | 1.00464 | + | 0.175007i | ||||
\(686\) | − | 17.8295i | − | 0.680735i | ||||||
\(687\) | −8.44318 | −0.322128 | ||||||||
\(688\) | 5.76210 | − | 5.76210i | 0.219678 | − | 0.219678i | ||||
\(689\) | −18.0339 | − | 5.37846i | −0.687036 | − | 0.204903i | ||||
\(690\) | 0.263701 | − | 1.51380i | 0.0100389 | − | 0.0576295i | ||||
\(691\) | −17.8144 | + | 17.8144i | −0.677692 | + | 0.677692i | −0.959477 | − | 0.281786i | \(-0.909073\pi\) |
0.281786 | + | 0.959477i | \(0.409073\pi\) | |||||||
\(692\) | −12.0153 | + | 12.0153i | −0.456753 | + | 0.456753i | ||||
\(693\) | −4.12932 | + | 4.12932i | −0.156860 | + | 0.156860i | ||||
\(694\) | −0.843939 | − | 0.843939i | −0.0320355 | − | 0.0320355i | ||||
\(695\) | −7.69200 | + | 44.1566i | −0.291774 | + | 1.67496i | ||||
\(696\) | 1.61524 | + | 1.61524i | 0.0612255 | + | 0.0612255i | ||||
\(697\) | −66.3721 | −2.51402 | ||||||||
\(698\) | 17.0343 | + | 17.0343i | 0.644760 | + | 0.644760i | ||||
\(699\) | 18.8874 | 0.714388 | ||||||||
\(700\) | −7.19341 | − | 2.58459i | −0.271885 | − | 0.0976882i | ||||
\(701\) | − | 21.1219i | − | 0.797763i | −0.917003 | − | 0.398881i | \(-0.869399\pi\) | ||
0.917003 | − | 0.398881i | \(-0.130601\pi\) | |||||||
\(702\) | 3.45516 | + | 1.03047i | 0.130407 | + | 0.0388927i | ||||
\(703\) | 8.49645 | + | 8.49645i | 0.320450 | + | 0.320450i | ||||
\(704\) | −2.70115 | − | 2.70115i | −0.101803 | − | 0.101803i | ||||
\(705\) | 3.76052 | + | 5.34704i | 0.141629 | + | 0.201381i | ||||
\(706\) | − | 6.51257i | − | 0.245104i | ||||||
\(707\) | 16.1537i | 0.607523i | ||||||||
\(708\) | −6.36459 | −0.239196 | ||||||||
\(709\) | 9.51410 | − | 9.51410i | 0.357310 | − | 0.357310i | −0.505511 | − | 0.862820i | \(-0.668696\pi\) |
0.862820 | + | 0.505511i | \(0.168696\pi\) | |||||||
\(710\) | −19.4794 | − | 27.6975i | −0.731048 | − | 1.03947i | ||||
\(711\) | −1.53731 | −0.0576535 | ||||||||
\(712\) | 7.21676 | + | 7.21676i | 0.270460 | + | 0.270460i | ||||
\(713\) | 0.971830i | 0.0363953i | ||||||||
\(714\) | 8.72214 | 0.326418 | ||||||||
\(715\) | −27.5648 | − | 13.7364i | −1.03087 | − | 0.513711i | ||||
\(716\) | 10.2606 | 0.383456 | ||||||||
\(717\) | − | 13.8428i | − | 0.516969i | ||||||
\(718\) | 17.5895 | + | 17.5895i | 0.656433 | + | 0.656433i | ||||
\(719\) | −33.0993 | −1.23440 | −0.617198 | − | 0.786808i | \(-0.711732\pi\) | ||||
−0.617198 | + | 0.786808i | \(0.711732\pi\) | |||||||
\(720\) | 0.383740 | − | 2.20289i | 0.0143011 | − | 0.0820970i | ||||
\(721\) | −7.44099 | + | 7.44099i | −0.277117 | + | 0.277117i | ||||
\(722\) | 16.7230 | 0.622364 | ||||||||
\(723\) | 5.91283i | 0.219901i | ||||||||
\(724\) | − | 22.4534i | − | 0.834475i | ||||||
\(725\) | 3.86200 | − | 10.7487i | 0.143431 | − | 0.399197i | ||||
\(726\) | 2.54022 | + | 2.54022i | 0.0942765 | + | 0.0942765i | ||||
\(727\) | 3.32729 | + | 3.32729i | 0.123402 | + | 0.123402i | 0.766111 | − | 0.642708i | \(-0.222189\pi\) |
−0.642708 | + | 0.766111i | \(0.722189\pi\) | |||||||
\(728\) | −2.62102 | − | 4.84885i | −0.0971416 | − | 0.179710i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 22.7178 | + | 3.95740i | 0.840824 | + | 0.146470i | ||||
\(731\) | 46.4931 | 1.71961 | ||||||||
\(732\) | −1.71860 | − | 1.71860i | −0.0635213 | − | 0.0635213i | ||||
\(733\) | −33.4623 | −1.23596 | −0.617980 | − | 0.786194i | \(-0.712049\pi\) | ||||
−0.617980 | + | 0.786194i | \(0.712049\pi\) | |||||||
\(734\) | −10.9276 | − | 10.9276i | −0.403346 | − | 0.403346i | ||||
\(735\) | −5.99817 | − | 8.52873i | −0.221246 | − | 0.314587i | ||||
\(736\) | −0.485915 | − | 0.485915i | −0.0179111 | − | 0.0179111i | ||||
\(737\) | 10.2618 | − | 10.2618i | 0.377999 | − | 0.377999i | ||||
\(738\) | 8.22579 | − | 8.22579i | 0.302796 | − | 0.302796i | ||||
\(739\) | −34.2147 | + | 34.2147i | −1.25861 | + | 1.25861i | −0.306850 | + | 0.951758i | \(0.599275\pi\) |
−0.951758 | + | 0.306850i | \(0.900725\pi\) | |||||||
\(740\) | 17.5413 | + | 3.05566i | 0.644831 | + | 0.112328i | ||||
\(741\) | −2.58717 | − | 4.78623i | −0.0950421 | − | 0.175826i | ||||
\(742\) | 5.64204 | − | 5.64204i | 0.207126 | − | 0.207126i | ||||
\(743\) | −39.0384 | −1.43218 | −0.716091 | − | 0.698007i | \(-0.754070\pi\) | ||||
−0.716091 | + | 0.698007i | \(0.754070\pi\) | |||||||
\(744\) | 1.41421i | 0.0518476i | ||||||||
\(745\) | −7.11431 | − | 10.1158i | −0.260648 | − | 0.370613i | ||||
\(746\) | −6.56604 | + | 6.56604i | −0.240400 | + | 0.240400i | ||||
\(747\) | 7.72020i | 0.282467i | ||||||||
\(748\) | − | 21.7950i | − | 0.796903i | ||||||
\(749\) | 20.0138 | − | 20.0138i | 0.731287 | − | 0.731287i | ||||
\(750\) | −10.7812 | + | 2.96054i | −0.393675 | + | 0.108104i | ||||
\(751\) | 4.17727i | 0.152431i | 0.997091 | + | 0.0762154i | \(0.0242837\pi\) | ||||
−0.997091 | + | 0.0762154i | \(0.975716\pi\) | |||||||
\(752\) | 2.92343 | 0.106607 | ||||||||
\(753\) | −11.7391 | + | 11.7391i | −0.427795 | + | 0.427795i | ||||
\(754\) | 7.24537 | − | 3.91645i | 0.263861 | − | 0.142629i | ||||
\(755\) | −30.3691 | − | 43.1815i | −1.10524 | − | 1.57153i | ||||
\(756\) | −1.08097 | + | 1.08097i | −0.0393147 | + | 0.0393147i | ||||
\(757\) | 12.0444 | − | 12.0444i | 0.437763 | − | 0.437763i | −0.453496 | − | 0.891258i | \(-0.649823\pi\) |
0.891258 | + | 0.453496i | \(0.149823\pi\) | |||||||
\(758\) | 23.1557 | − | 23.1557i | 0.841053 | − | 0.841053i | ||||
\(759\) | 1.85620 | + | 1.85620i | 0.0673757 | + | 0.0673757i | ||||
\(760\) | −2.75997 | + | 1.94106i | −0.100115 | + | 0.0704097i | ||||
\(761\) | 15.0242 | + | 15.0242i | 0.544628 | + | 0.544628i | 0.924882 | − | 0.380254i | \(-0.124163\pi\) |
−0.380254 | + | 0.924882i | \(0.624163\pi\) | |||||||
\(762\) | −14.4758 | −0.524402 | ||||||||
\(763\) | −0.189670 | − | 0.189670i | −0.00686652 | − | 0.00686652i | ||||
\(764\) | 12.2203 | 0.442115 | ||||||||
\(765\) | 10.4355 | − | 7.33918i | 0.377296 | − | 0.265348i | ||||
\(766\) | 1.38206i | 0.0499358i | ||||||||
\(767\) | −6.55854 | + | 21.9907i | −0.236815 | + | 0.794037i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 17.0100 | + | 17.0100i | 0.613397 | + | 0.613397i | 0.943830 | − | 0.330432i | \(-0.107195\pi\) |
−0.330432 | + | 0.943830i | \(0.607195\pi\) | |||||||
\(770\) | 10.6811 | − | 7.51188i | 0.384918 | − | 0.270709i | ||||
\(771\) | 16.4510i | 0.592470i | ||||||||
\(772\) | − | 24.1428i | − | 0.868917i | ||||||
\(773\) | −20.2751 | −0.729246 | −0.364623 | − | 0.931155i | \(-0.618802\pi\) | ||||
−0.364623 | + | 0.931155i | \(0.618802\pi\) | |||||||
\(774\) | −5.76210 | + | 5.76210i | −0.207114 | + | 0.207114i | ||||
\(775\) | 6.39616 | − | 3.01481i | 0.229757 | − | 0.108295i | ||||
\(776\) | −6.36597 | −0.228525 | ||||||||
\(777\) | −8.60763 | − | 8.60763i | −0.308797 | − | 0.308797i | ||||
\(778\) | − | 19.6760i | − | 0.705420i | ||||||
\(779\) | −17.5540 | −0.628939 | ||||||||
\(780\) | −7.21592 | − | 3.59591i | −0.258371 | − | 0.128754i | ||||
\(781\) | 57.8475 | 2.06994 | ||||||||
\(782\) | − | 3.92074i | − | 0.140205i | ||||||
\(783\) | −1.61524 | − | 1.61524i | −0.0577240 | − | 0.0577240i | ||||
\(784\) | −4.66299 | −0.166535 | ||||||||
\(785\) | 24.3013 | − | 17.0909i | 0.867352 | − | 0.610000i | ||||
\(786\) | −8.37818 | + | 8.37818i | −0.298840 | + | 0.298840i | ||||
\(787\) | 20.9508 | 0.746815 | 0.373408 | − | 0.927667i | \(-0.378189\pi\) | ||||
0.373408 | + | 0.927667i | \(0.378189\pi\) | |||||||
\(788\) | 3.53326i | 0.125867i | ||||||||
\(789\) | − | 1.51482i | − | 0.0539289i | ||||||
\(790\) | 3.38652 | + | 0.589926i | 0.120487 | + | 0.0209886i | ||||
\(791\) | −5.65132 | − | 5.65132i | −0.200938 | − | 0.200938i | ||||
\(792\) | 2.70115 | + | 2.70115i | 0.0959812 | + | 0.0959812i | ||||
\(793\) | −7.70901 | + | 4.16707i | −0.273755 | + | 0.147977i | ||||
\(794\) | − | 35.9373i | − | 1.27537i | ||||||
\(795\) | 2.00290 | − | 11.4978i | 0.0710354 | − | 0.407785i | ||||
\(796\) | 12.1781 | 0.431642 | ||||||||
\(797\) | −20.7876 | − | 20.7876i | −0.736334 | − | 0.736334i | 0.235532 | − | 0.971866i | \(-0.424317\pi\) |
−0.971866 | + | 0.235532i | \(0.924317\pi\) | |||||||
\(798\) | 2.30683 | 0.0816608 | ||||||||
\(799\) | 11.7943 | + | 11.7943i | 0.417251 | + | 0.417251i | ||||
\(800\) | −1.69068 | + | 4.70549i | −0.0597745 | + | 0.166364i | ||||
\(801\) | −7.21676 | − | 7.21676i | −0.254992 | − | 0.254992i | ||||
\(802\) | 1.64796 | − | 1.64796i | 0.0581916 | − | 0.0581916i | ||||
\(803\) | −27.8562 | + | 27.8562i | −0.983023 | + | 0.983023i | ||||
\(804\) | 2.68634 | − | 2.68634i | 0.0947399 | − | 0.0947399i | ||||
\(805\) | 1.92144 | − | 1.35133i | 0.0677217 | − | 0.0476280i | ||||
\(806\) | 4.88633 | + | 1.45731i | 0.172114 | + | 0.0513315i | ||||
\(807\) | −11.9310 | + | 11.9310i | −0.419990 | + | 0.419990i | ||||
\(808\) | 10.5668 | 0.371738 | ||||||||
\(809\) | 33.1948i | 1.16707i | 0.812090 | + | 0.583533i | \(0.198330\pi\) | ||||
−0.812090 | + | 0.583533i | \(0.801670\pi\) | |||||||
\(810\) | −0.383740 | + | 2.20289i | −0.0134833 | + | 0.0774018i | ||||
\(811\) | −18.7578 | + | 18.7578i | −0.658674 | + | 0.658674i | −0.955066 | − | 0.296392i | \(-0.904217\pi\) |
0.296392 | + | 0.955066i | \(0.404217\pi\) | |||||||
\(812\) | 3.49207i | 0.122547i | ||||||||
\(813\) | − | 6.43741i | − | 0.225770i | ||||||
\(814\) | −21.5088 | + | 21.5088i | −0.753884 | + | 0.753884i | ||||
\(815\) | 5.38419 | − | 30.9084i | 0.188600 | − | 1.08267i | ||||
\(816\) | − | 5.70549i | − | 0.199732i | ||||||
\(817\) | 12.2965 | 0.430199 | ||||||||
\(818\) | −12.3833 | + | 12.3833i | −0.432971 | + | 0.432971i | ||||
\(819\) | 2.62102 | + | 4.84885i | 0.0915860 | + | 0.169433i | ||||
\(820\) | −21.2771 | + | 14.9640i | −0.743029 | + | 0.522565i | ||||
\(821\) | 35.9136 | − | 35.9136i | 1.25339 | − | 1.25339i | 0.299203 | − | 0.954189i | \(-0.403279\pi\) |
0.954189 | − | 0.299203i | \(-0.0967208\pi\) | |||||||
\(822\) | −8.44011 | + | 8.44011i | −0.294383 | + | 0.294383i | ||||
\(823\) | 19.7562 | − | 19.7562i | 0.688659 | − | 0.688659i | −0.273276 | − | 0.961936i | \(-0.588107\pi\) |
0.961936 | + | 0.273276i | \(0.0881073\pi\) | |||||||
\(824\) | 4.86744 | + | 4.86744i | 0.169565 | + | 0.169565i | ||||
\(825\) | 6.45839 | − | 17.9750i | 0.224852 | − | 0.625808i | ||||
\(826\) | −6.87996 | − | 6.87996i | −0.239384 | − | 0.239384i | ||||
\(827\) | −25.7405 | −0.895086 | −0.447543 | − | 0.894262i | \(-0.647701\pi\) | ||||
−0.447543 | + | 0.894262i | \(0.647701\pi\) | |||||||
\(828\) | 0.485915 | + | 0.485915i | 0.0168867 | + | 0.0168867i | ||||
\(829\) | −20.1531 | −0.699946 | −0.349973 | − | 0.936760i | \(-0.613809\pi\) | ||||
−0.349973 | + | 0.936760i | \(0.613809\pi\) | |||||||
\(830\) | 2.96255 | − | 17.0068i | 0.102832 | − | 0.590314i | ||||
\(831\) | − | 4.56141i | − | 0.158234i | ||||||
\(832\) | −3.17182 | + | 1.71451i | −0.109963 | + | 0.0594400i | ||||
\(833\) | −18.8123 | − | 18.8123i | −0.651808 | − | 0.651808i | ||||
\(834\) | −14.1738 | − | 14.1738i | −0.490799 | − | 0.490799i | ||||
\(835\) | −31.7695 | − | 5.53419i | −1.09943 | − | 0.191519i | ||||
\(836\) | − | 5.76432i | − | 0.199363i | ||||||
\(837\) | − | 1.41421i | − | 0.0488824i | ||||||
\(838\) | −8.21451 | −0.283765 | ||||||||
\(839\) | −39.6805 | + | 39.6805i | −1.36992 | + | 1.36992i | −0.509384 | + | 0.860539i | \(0.670127\pi\) |
−0.860539 | + | 0.509384i | \(0.829873\pi\) | |||||||
\(840\) | 2.79609 | − | 1.96646i | 0.0964741 | − | 0.0678493i | ||||
\(841\) | 23.7820 | 0.820069 | ||||||||
\(842\) | −10.9922 | − | 10.9922i | −0.378815 | − | 0.378815i | ||||
\(843\) | − | 5.72824i | − | 0.197291i | ||||||
\(844\) | 14.2670 | 0.491090 | ||||||||
\(845\) | −19.8602 | + | 21.2267i | −0.683213 | + | 0.730219i | ||||
\(846\) | −2.92343 | −0.100510 | ||||||||
\(847\) | 5.49183i | 0.188702i | ||||||||
\(848\) | −3.69068 | − | 3.69068i | −0.126738 | − | 0.126738i | ||||
\(849\) | −19.9801 | −0.685714 | ||||||||
\(850\) | −25.8046 | + | 12.1629i | −0.885091 | + | 0.417185i | ||||
\(851\) | −3.86927 | + | 3.86927i | −0.132637 | + | 0.132637i | ||||
\(852\) | 15.1433 | 0.518801 | ||||||||
\(853\) | − | 1.09187i | − | 0.0373849i | −0.999825 | − | 0.0186924i | \(-0.994050\pi\) | ||
0.999825 | − | 0.0186924i | \(-0.00595034\pi\) | |||||||
\(854\) | − | 3.71553i | − | 0.127143i | ||||||
\(855\) | 2.75997 | − | 1.94106i | 0.0943890 | − | 0.0663829i | ||||
\(856\) | −13.0918 | − | 13.0918i | −0.447468 | − | 0.447468i | ||||
\(857\) | −22.5338 | − | 22.5338i | −0.769740 | − | 0.769740i | 0.208321 | − | 0.978061i | \(-0.433200\pi\) |
−0.978061 | + | 0.208321i | \(0.933200\pi\) | |||||||
\(858\) | 12.1164 | − | 6.54944i | 0.413646 | − | 0.223594i | ||||
\(859\) | 23.9381i | 0.816758i | 0.912812 | + | 0.408379i | \(0.133906\pi\) | ||||
−0.912812 | + | 0.408379i | \(0.866094\pi\) | |||||||
\(860\) | 14.9044 | − | 10.4821i | 0.508237 | − | 0.357438i | ||||
\(861\) | 17.7837 | 0.606068 | ||||||||
\(862\) | 15.4246 | + | 15.4246i | 0.525363 | + | 0.525363i | ||||
\(863\) | 36.6009 | 1.24591 | 0.622955 | − | 0.782258i | \(-0.285932\pi\) | ||||
0.622955 | + | 0.782258i | \(0.285932\pi\) | |||||||
\(864\) | 0.707107 | + | 0.707107i | 0.0240563 | + | 0.0240563i | ||||
\(865\) | −31.0792 | + | 21.8577i | −1.05672 | + | 0.743184i | ||||
\(866\) | −3.28016 | − | 3.28016i | −0.111464 | − | 0.111464i | ||||
\(867\) | 10.9973 | − | 10.9973i | 0.373489 | − | 0.373489i | ||||
\(868\) | −1.52873 | + | 1.52873i | −0.0518884 | + | 0.0518884i | ||||
\(869\) | −4.15250 | + | 4.15250i | −0.140864 | + | 0.140864i | ||||
\(870\) | 2.93837 | + | 4.17804i | 0.0996201 | + | 0.141649i | ||||
\(871\) | −6.51353 | − | 12.0499i | −0.220703 | − | 0.408296i | ||||
\(872\) | −0.124070 | + | 0.124070i | −0.00420156 | + | 0.00420156i | ||||
\(873\) | 6.36597 | 0.215455 | ||||||||
\(874\) | − | 1.03696i | − | 0.0350755i | ||||||
\(875\) | −14.8545 | − | 8.45397i | −0.502174 | − | 0.285796i | ||||
\(876\) | −7.29219 | + | 7.29219i | −0.246380 | + | 0.246380i | ||||
\(877\) | − | 27.6527i | − | 0.933765i | −0.884319 | − | 0.466883i | \(-0.845377\pi\) | ||
0.884319 | − | 0.466883i | \(-0.154623\pi\) | |||||||
\(878\) | 12.4347i | 0.419652i | ||||||||
\(879\) | −20.8366 | + | 20.8366i | −0.702800 | + | 0.702800i | ||||
\(880\) | −4.91381 | − | 6.98689i | −0.165644 | − | 0.235528i | ||||
\(881\) | 42.6267i | 1.43613i | 0.695976 | + | 0.718065i | \(0.254972\pi\) | ||||
−0.695976 | + | 0.718065i | \(0.745028\pi\) | |||||||
\(882\) | 4.66299 | 0.157011 | ||||||||
\(883\) | 32.2845 | − | 32.2845i | 1.08646 | − | 1.08646i | 0.0905713 | − | 0.995890i | \(-0.471131\pi\) |
0.995890 | − | 0.0905713i | \(-0.0288693\pi\) | |||||||
\(884\) | −19.7134 | − | 5.87935i | −0.663032 | − | 0.197744i | ||||
\(885\) | −14.0205 | − | 2.44235i | −0.471294 | − | 0.0820986i | ||||
\(886\) | 12.5904 | − | 12.5904i | 0.422982 | − | 0.422982i | ||||
\(887\) | −14.7620 | + | 14.7620i | −0.495658 | + | 0.495658i | −0.910083 | − | 0.414425i | \(-0.863983\pi\) |
0.414425 | + | 0.910083i | \(0.363983\pi\) | |||||||
\(888\) | −5.63058 | + | 5.63058i | −0.188950 | + | 0.188950i | ||||
\(889\) | −15.6479 | − | 15.6479i | −0.524815 | − | 0.524815i | ||||
\(890\) | 13.1284 | + | 18.6671i | 0.440065 | + | 0.625724i | ||||
\(891\) | −2.70115 | − | 2.70115i | −0.0904919 | − | 0.0904919i | ||||
\(892\) | 11.9632 | 0.400556 | ||||||||
\(893\) | 3.11934 | + | 3.11934i | 0.104385 | + | 0.104385i | ||||
\(894\) | 5.53068 | 0.184973 | ||||||||
\(895\) | 22.6030 | + | 3.93740i | 0.755535 | + | 0.131613i | ||||
\(896\) | − | 1.52873i | − | 0.0510712i | ||||||
\(897\) | 2.17964 | − | 1.17819i | 0.0727760 | − | 0.0393387i | ||||
\(898\) | 15.4853 | + | 15.4853i | 0.516751 | + | 0.516751i | ||||
\(899\) | −2.28429 | − | 2.28429i | −0.0761855 | − | 0.0761855i | ||||
\(900\) | 1.69068 | − | 4.70549i | 0.0563559 | − | 0.156850i | ||||
\(901\) | − | 29.7793i | − | 0.992091i | ||||||
\(902\) | − | 44.4382i | − | 1.47963i | ||||||
\(903\) | −12.4574 | −0.414555 | ||||||||
\(904\) | −3.69674 | + | 3.69674i | −0.122952 | + | 0.122952i | ||||
\(905\) | 8.61627 | − | 49.4625i | 0.286415 | − | 1.64419i | ||||
\(906\) | 23.6090 | 0.784356 | ||||||||
\(907\) | 21.1516 | + | 21.1516i | 0.702328 | + | 0.702328i | 0.964910 | − | 0.262581i | \(-0.0845738\pi\) |
−0.262581 | + | 0.964910i | \(0.584574\pi\) | |||||||
\(908\) | 22.2944i | 0.739864i | ||||||||
\(909\) | −10.5668 | −0.350478 | ||||||||
\(910\) | −3.91314 | − | 11.6873i | −0.129719 | − | 0.387430i | ||||
\(911\) | 9.72304 | 0.322139 | 0.161069 | − | 0.986943i | \(-0.448506\pi\) | ||||
0.161069 | + | 0.986943i | \(0.448506\pi\) | |||||||
\(912\) | − | 1.50898i | − | 0.0499674i | ||||||
\(913\) | 20.8534 | + | 20.8534i | 0.690147 | + | 0.690147i | ||||
\(914\) | −15.3846 | −0.508876 | ||||||||
\(915\) | −3.12640 | − | 4.44539i | −0.103356 | − | 0.146960i | ||||
\(916\) | −5.97023 | + | 5.97023i | −0.197262 | + | 0.197262i | ||||
\(917\) | −18.1132 | −0.598151 | ||||||||
\(918\) | 5.70549i | 0.188309i | ||||||||
\(919\) | 8.88839i | 0.293201i | 0.989196 | + | 0.146600i | \(0.0468331\pi\) | ||||
−0.989196 | + | 0.146600i | \(0.953167\pi\) | |||||||
\(920\) | −0.883955 | − | 1.25688i | −0.0291431 | − | 0.0414383i | ||||
\(921\) | 14.7147 | + | 14.7147i | 0.484865 | + | 0.484865i | ||||
\(922\) | −26.1557 | − | 26.1557i | −0.861391 | − | 0.861391i | ||||
\(923\) | 15.6048 | − | 52.3225i | 0.513637 | − | 1.72222i | ||||
\(924\) | 5.83975i | 0.192114i | ||||||||
\(925\) | 37.4690 | + | 13.4626i | 1.23197 | + | 0.442647i | ||||
\(926\) | −5.65611 | −0.185871 | ||||||||
\(927\) | −4.86744 | − | 4.86744i | −0.159868 | − | 0.159868i | ||||
\(928\) | 2.28429 | 0.0749856 | ||||||||
\(929\) | −2.93787 | − | 2.93787i | −0.0963885 | − | 0.0963885i | 0.657268 | − | 0.753657i | \(-0.271712\pi\) |
−0.753657 | + | 0.657268i | \(0.771712\pi\) | |||||||
\(930\) | −0.542690 | + | 3.11536i | −0.0177955 | + | 0.102157i | ||||
\(931\) | −4.97547 | − | 4.97547i | −0.163064 | − | 0.163064i | ||||
\(932\) | 13.3554 | − | 13.3554i | 0.437472 | − | 0.437472i | ||||
\(933\) | −22.0450 | + | 22.0450i | −0.721721 | + | 0.721721i | ||||
\(934\) | −23.4369 | + | 23.4369i | −0.766879 | + | 0.766879i | ||||
\(935\) | 8.36360 | − | 48.0120i | 0.273519 | − | 1.57016i | ||||
\(936\) | 3.17182 | − | 1.71451i | 0.103674 | − | 0.0560406i | ||||
\(937\) | 8.97253 | − | 8.97253i | 0.293120 | − | 0.293120i | −0.545192 | − | 0.838311i | \(-0.683543\pi\) |
0.838311 | + | 0.545192i | \(0.183543\pi\) | |||||||
\(938\) | 5.80773 | 0.189629 | ||||||||
\(939\) | − | 15.1990i | − | 0.496001i | ||||||
\(940\) | 6.44001 | + | 1.12184i | 0.210050 | + | 0.0365903i | ||||
\(941\) | −17.2320 | + | 17.2320i | −0.561746 | + | 0.561746i | −0.929803 | − | 0.368057i | \(-0.880023\pi\) |
0.368057 | + | 0.929803i | \(0.380023\pi\) | |||||||
\(942\) | 13.2865i | 0.432897i | ||||||||
\(943\) | − | 7.99407i | − | 0.260323i | ||||||
\(944\) | −4.50044 | + | 4.50044i | −0.146477 | + | 0.146477i | ||||
\(945\) | −2.79609 | + | 1.96646i | −0.0909567 | + | 0.0639689i | ||||
\(946\) | 31.1286i | 1.01208i | ||||||||
\(947\) | 12.7574 | 0.414559 | 0.207280 | − | 0.978282i | \(-0.433539\pi\) | ||||
0.207280 | + | 0.978282i | \(0.433539\pi\) | |||||||
\(948\) | −1.08704 | + | 1.08704i | −0.0353054 | + | 0.0353054i | ||||
\(949\) | 17.6813 | + | 32.7101i | 0.573958 | + | 1.06181i | ||||
\(950\) | −6.82479 | + | 3.21684i | −0.221425 | + | 0.104368i | ||||
\(951\) | −13.5909 | + | 13.5909i | −0.440716 | + | 0.440716i | ||||
\(952\) | 6.16749 | − | 6.16749i | 0.199889 | − | 0.199889i | ||||
\(953\) | 26.8078 | − | 26.8078i | 0.868391 | − | 0.868391i | −0.123904 | − | 0.992294i | \(-0.539541\pi\) |
0.992294 | + | 0.123904i | \(0.0395414\pi\) | |||||||
\(954\) | 3.69068 | + | 3.69068i | 0.119490 | + | 0.119490i | ||||
\(955\) | 26.9200 | + | 4.68941i | 0.871111 | + | 0.151746i | ||||
\(956\) | −9.78834 | − | 9.78834i | −0.316578 | − | 0.316578i | ||||
\(957\) | −8.72601 | −0.282072 | ||||||||
\(958\) | −3.55522 | − | 3.55522i | −0.114864 | − | 0.114864i | ||||
\(959\) | −18.2471 | −0.589229 | ||||||||
\(960\) | −1.28634 | − | 1.82903i | −0.0415163 | − | 0.0590316i | ||||
\(961\) | 29.0000i | 0.935484i | ||||||||
\(962\) | 13.6524 | + | 25.2567i | 0.440170 | + | 0.814309i | ||||
\(963\) | 13.0918 | + | 13.0918i | 0.421877 | + | 0.421877i | ||||
\(964\) | 4.18100 | + | 4.18100i | 0.134661 | + | 0.134661i | ||||
\(965\) | 9.26454 | − | 53.1839i | 0.298236 | − | 1.71205i | ||||
\(966\) | 1.05052i | 0.0338000i | ||||||||
\(967\) | 31.5490i | 1.01455i | 0.861785 | + | 0.507275i | \(0.169347\pi\) | ||||
−0.861785 | + | 0.507275i | \(0.830653\pi\) | |||||||
\(968\) | 3.59242 | 0.115465 | ||||||||
\(969\) | 6.08783 | − | 6.08783i | 0.195569 | − | 0.195569i | ||||
\(970\) | −14.0236 | − | 2.44288i | −0.450269 | − | 0.0784361i | ||||
\(971\) | 0.406721 | 0.0130523 | 0.00652616 | − | 0.999979i | \(-0.497923\pi\) | ||||
0.00652616 | + | 0.999979i | \(0.497923\pi\) | |||||||
\(972\) | −0.707107 | − | 0.707107i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | − | 30.6431i | − | 0.982372i | ||||||
\(974\) | 6.62780 | 0.212368 | ||||||||
\(975\) | −14.5160 | − | 10.6904i | −0.464884 | − | 0.342368i | ||||
\(976\) | −2.43047 | −0.0777974 | ||||||||
\(977\) | − | 50.8543i | − | 1.62697i | −0.581584 | − | 0.813486i | \(-0.697567\pi\) | ||
0.581584 | − | 0.813486i | \(-0.302433\pi\) | |||||||
\(978\) | 9.92129 | + | 9.92129i | 0.317248 | + | 0.317248i | ||||
\(979\) | −38.9871 | −1.24603 | ||||||||
\(980\) | −10.2721 | − | 1.78938i | −0.328129 | − | 0.0571595i | ||||
\(981\) | 0.124070 | − | 0.124070i | 0.00396127 | − | 0.00396127i | ||||
\(982\) | −15.5268 | −0.495479 | ||||||||
\(983\) | − | 22.0015i | − | 0.701738i | −0.936425 | − | 0.350869i | \(-0.885886\pi\) | ||
0.936425 | − | 0.350869i | \(-0.114114\pi\) | |||||||
\(984\) | − | 11.6330i | − | 0.370847i | ||||||
\(985\) | −1.35585 | + | 7.78341i | −0.0432011 | + | 0.248000i | ||||
\(986\) | 9.21573 | + | 9.21573i | 0.293489 | + | 0.293489i | ||||
\(987\) | −3.16016 | − | 3.16016i | −0.100589 | − | 0.100589i | ||||
\(988\) | −5.21378 | − | 1.55497i | −0.165872 | − | 0.0494701i | ||||
\(989\) | 5.59978i | 0.178063i | ||||||||
\(990\) | 4.91381 | + | 6.98689i | 0.156171 | + | 0.222058i | ||||
\(991\) | 5.60675 | 0.178104 | 0.0890521 | − | 0.996027i | \(-0.471616\pi\) | ||||
0.0890521 | + | 0.996027i | \(0.471616\pi\) | |||||||
\(992\) | 1.00000 | + | 1.00000i | 0.0317500 | + | 0.0317500i | ||||
\(993\) | −18.3478 | −0.582249 | ||||||||
\(994\) | 16.3695 | + | 16.3695i | 0.519210 | + | 0.519210i | ||||
\(995\) | 26.8271 | + | 4.67323i | 0.850477 | + | 0.148151i | ||||
\(996\) | 5.45901 | + | 5.45901i | 0.172975 | + | 0.172975i | ||||
\(997\) | 37.6139 | − | 37.6139i | 1.19124 | − | 1.19124i | 0.214526 | − | 0.976718i | \(-0.431179\pi\) |
0.976718 | − | 0.214526i | \(-0.0688206\pi\) | |||||||
\(998\) | −3.06206 | + | 3.06206i | −0.0969278 | + | 0.0969278i | ||||
\(999\) | 5.63058 | − | 5.63058i | 0.178144 | − | 0.178144i |
(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 | 390.2.t.a.343.1 | yes | 12 | |
3.2 | odd | 2 | 1170.2.w.f.343.5 | 12 | |||
5.2 | odd | 4 | 390.2.j.a.187.2 | yes | 12 | ||
5.3 | odd | 4 | 1950.2.j.c.1357.5 | 12 | |||
5.4 | even | 2 | 1950.2.t.b.343.5 | 12 | |||
13.8 | odd | 4 | 390.2.j.a.73.2 | ✓ | 12 | ||
15.2 | even | 4 | 1170.2.m.f.577.3 | 12 | |||
39.8 | even | 4 | 1170.2.m.f.73.3 | 12 | |||
65.8 | even | 4 | 1950.2.t.b.307.5 | 12 | |||
65.34 | odd | 4 | 1950.2.j.c.1243.5 | 12 | |||
65.47 | even | 4 | inner | 390.2.t.a.307.1 | yes | 12 | |
195.47 | odd | 4 | 1170.2.w.f.307.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.j.a.73.2 | ✓ | 12 | 13.8 | odd | 4 | ||
390.2.j.a.187.2 | yes | 12 | 5.2 | odd | 4 | ||
390.2.t.a.307.1 | yes | 12 | 65.47 | even | 4 | inner | |
390.2.t.a.343.1 | yes | 12 | 1.1 | even | 1 | trivial | |
1170.2.m.f.73.3 | 12 | 39.8 | even | 4 | |||
1170.2.m.f.577.3 | 12 | 15.2 | even | 4 | |||
1170.2.w.f.307.5 | 12 | 195.47 | odd | 4 | |||
1170.2.w.f.343.5 | 12 | 3.2 | odd | 2 | |||
1950.2.j.c.1243.5 | 12 | 65.34 | odd | 4 | |||
1950.2.j.c.1357.5 | 12 | 5.3 | odd | 4 | |||
1950.2.t.b.307.5 | 12 | 65.8 | even | 4 | |||
1950.2.t.b.343.5 | 12 | 5.4 | even | 2 |