Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(367,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, 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("690.367");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.j (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 367.10 | ||
Character | \(\chi\) | \(=\) | 690.367 |
Dual form | 690.2.j.a.643.10 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | + | 0.707107i | 0.500000 | + | 0.500000i | ||||
\(3\) | −0.707107 | + | 0.707107i | −0.408248 | + | 0.408248i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 0.397104 | + | 2.20052i | 0.177590 | + | 0.984105i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.66838 | − | 1.66838i | 0.630587 | − | 0.630587i | −0.317628 | − | 0.948215i | \(-0.602886\pi\) |
0.948215 | + | 0.317628i | \(0.102886\pi\) | |||||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 1.00000i | − | 0.333333i | ||||||
\(10\) | −1.27521 | + | 1.83680i | −0.403257 | + | 0.580847i | ||||
\(11\) | 3.67360i | 1.10763i | 0.832639 | + | 0.553816i | \(0.186829\pi\) | ||||
−0.832639 | + | 0.553816i | \(0.813171\pi\) | |||||||
\(12\) | −0.707107 | − | 0.707107i | −0.204124 | − | 0.204124i | ||||
\(13\) | −4.53151 | + | 4.53151i | −1.25682 | + | 1.25682i | −0.304211 | + | 0.952605i | \(0.598393\pi\) |
−0.952605 | + | 0.304211i | \(0.901607\pi\) | |||||||
\(14\) | 2.35944 | 0.630587 | ||||||||
\(15\) | −1.83680 | − | 1.27521i | −0.474260 | − | 0.329258i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.03339 | − | 4.03339i | 0.978240 | − | 0.978240i | −0.0215283 | − | 0.999768i | \(-0.506853\pi\) |
0.999768 | + | 0.0215283i | \(0.00685321\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | 0.786330 | 0.180396 | 0.0901982 | − | 0.995924i | \(-0.471250\pi\) | ||||
0.0901982 | + | 0.995924i | \(0.471250\pi\) | |||||||
\(20\) | −2.20052 | + | 0.397104i | −0.492052 | + | 0.0887951i | ||||
\(21\) | 2.35944i | 0.514872i | ||||||||
\(22\) | −2.59763 | + | 2.59763i | −0.553816 | + | 0.553816i | ||||
\(23\) | 1.01740 | + | 4.68667i | 0.212142 | + | 0.977239i | ||||
\(24\) | − | 1.00000i | − | 0.204124i | ||||||
\(25\) | −4.68462 | + | 1.74767i | −0.936923 | + | 0.349535i | ||||
\(26\) | −6.40853 | −1.25682 | ||||||||
\(27\) | 0.707107 | + | 0.707107i | 0.136083 | + | 0.136083i | ||||
\(28\) | 1.66838 | + | 1.66838i | 0.315293 | + | 0.315293i | ||||
\(29\) | − | 4.68811i | − | 0.870559i | −0.900295 | − | 0.435280i | \(-0.856649\pi\) | ||
0.900295 | − | 0.435280i | \(-0.143351\pi\) | |||||||
\(30\) | −0.397104 | − | 2.20052i | −0.0725009 | − | 0.401759i | ||||
\(31\) | −3.96306 | −0.711787 | −0.355893 | − | 0.934527i | \(-0.615823\pi\) | ||||
−0.355893 | + | 0.934527i | \(0.615823\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | −2.59763 | − | 2.59763i | −0.452189 | − | 0.452189i | ||||
\(34\) | 5.70407 | 0.978240 | ||||||||
\(35\) | 4.33382 | + | 3.00878i | 0.732549 | + | 0.508577i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −4.59728 | + | 4.59728i | −0.755789 | + | 0.755789i | −0.975553 | − | 0.219764i | \(-0.929471\pi\) |
0.219764 | + | 0.975553i | \(0.429471\pi\) | |||||||
\(38\) | 0.556019 | + | 0.556019i | 0.0901982 | + | 0.0901982i | ||||
\(39\) | − | 6.40853i | − | 1.02619i | ||||||
\(40\) | −1.83680 | − | 1.27521i | −0.290424 | − | 0.201629i | ||||
\(41\) | 6.32378 | 0.987608 | 0.493804 | − | 0.869573i | \(-0.335606\pi\) | ||||
0.493804 | + | 0.869573i | \(0.335606\pi\) | |||||||
\(42\) | −1.66838 | + | 1.66838i | −0.257436 | + | 0.257436i | ||||
\(43\) | 1.71558 | + | 1.71558i | 0.261624 | + | 0.261624i | 0.825714 | − | 0.564090i | \(-0.190773\pi\) |
−0.564090 | + | 0.825714i | \(0.690773\pi\) | |||||||
\(44\) | −3.67360 | −0.553816 | ||||||||
\(45\) | 2.20052 | − | 0.397104i | 0.328035 | − | 0.0591968i | ||||
\(46\) | −2.59457 | + | 4.03339i | −0.382548 | + | 0.594690i | ||||
\(47\) | −5.71187 | − | 5.71187i | −0.833162 | − | 0.833162i | 0.154786 | − | 0.987948i | \(-0.450531\pi\) |
−0.987948 | + | 0.154786i | \(0.950531\pi\) | |||||||
\(48\) | 0.707107 | − | 0.707107i | 0.102062 | − | 0.102062i | ||||
\(49\) | 1.43304i | 0.204720i | ||||||||
\(50\) | −4.54832 | − | 2.07673i | −0.643229 | − | 0.293694i | ||||
\(51\) | 5.70407i | 0.798730i | ||||||||
\(52\) | −4.53151 | − | 4.53151i | −0.628408 | − | 0.628408i | ||||
\(53\) | −5.93438 | − | 5.93438i | −0.815150 | − | 0.815150i | 0.170251 | − | 0.985401i | \(-0.445542\pi\) |
−0.985401 | + | 0.170251i | \(0.945542\pi\) | |||||||
\(54\) | 1.00000i | 0.136083i | ||||||||
\(55\) | −8.08385 | + | 1.45880i | −1.09003 | + | 0.196705i | ||||
\(56\) | 2.35944i | 0.315293i | ||||||||
\(57\) | −0.556019 | + | 0.556019i | −0.0736466 | + | 0.0736466i | ||||
\(58\) | 3.31499 | − | 3.31499i | 0.435280 | − | 0.435280i | ||||
\(59\) | 13.2165i | 1.72064i | 0.509754 | + | 0.860320i | \(0.329736\pi\) | ||||
−0.509754 | + | 0.860320i | \(0.670264\pi\) | |||||||
\(60\) | 1.27521 | − | 1.83680i | 0.164629 | − | 0.237130i | ||||
\(61\) | − | 3.15365i | − | 0.403783i | −0.979408 | − | 0.201892i | \(-0.935291\pi\) | ||
0.979408 | − | 0.201892i | \(-0.0647089\pi\) | |||||||
\(62\) | −2.80231 | − | 2.80231i | −0.355893 | − | 0.355893i | ||||
\(63\) | −1.66838 | − | 1.66838i | −0.210196 | − | 0.210196i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −11.7712 | − | 8.17222i | −1.46004 | − | 1.01364i | ||||
\(66\) | − | 3.67360i | − | 0.452189i | ||||||
\(67\) | 3.28081 | − | 3.28081i | 0.400815 | − | 0.400815i | −0.477705 | − | 0.878520i | \(-0.658531\pi\) |
0.878520 | + | 0.477705i | \(0.158531\pi\) | |||||||
\(68\) | 4.03339 | + | 4.03339i | 0.489120 | + | 0.489120i | ||||
\(69\) | −4.03339 | − | 2.59457i | −0.485563 | − | 0.312350i | ||||
\(70\) | 0.936943 | + | 5.19201i | 0.111986 | + | 0.620563i | ||||
\(71\) | 6.19150 | 0.734795 | 0.367398 | − | 0.930064i | \(-0.380249\pi\) | ||||
0.367398 | + | 0.930064i | \(0.380249\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 5.62505 | − | 5.62505i | 0.658362 | − | 0.658362i | −0.296630 | − | 0.954992i | \(-0.595863\pi\) |
0.954992 | + | 0.296630i | \(0.0958629\pi\) | |||||||
\(74\) | −6.50154 | −0.755789 | ||||||||
\(75\) | 2.07673 | − | 4.54832i | 0.239800 | − | 0.525194i | ||||
\(76\) | 0.786330i | 0.0901982i | ||||||||
\(77\) | 6.12895 | + | 6.12895i | 0.698459 | + | 0.698459i | ||||
\(78\) | 4.53151 | − | 4.53151i | 0.513093 | − | 0.513093i | ||||
\(79\) | 11.6580 | 1.31163 | 0.655814 | − | 0.754923i | \(-0.272326\pi\) | ||||
0.655814 | + | 0.754923i | \(0.272326\pi\) | |||||||
\(80\) | −0.397104 | − | 2.20052i | −0.0443976 | − | 0.246026i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 4.47158 | + | 4.47158i | 0.493804 | + | 0.493804i | ||||
\(83\) | 5.05048 | + | 5.05048i | 0.554362 | + | 0.554362i | 0.927697 | − | 0.373335i | \(-0.121786\pi\) |
−0.373335 | + | 0.927697i | \(0.621786\pi\) | |||||||
\(84\) | −2.35944 | −0.257436 | ||||||||
\(85\) | 10.4772 | + | 7.27389i | 1.13642 | + | 0.788964i | ||||
\(86\) | 2.42620i | 0.261624i | ||||||||
\(87\) | 3.31499 | + | 3.31499i | 0.355404 | + | 0.355404i | ||||
\(88\) | −2.59763 | − | 2.59763i | −0.276908 | − | 0.276908i | ||||
\(89\) | 16.1572 | 1.71266 | 0.856329 | − | 0.516431i | \(-0.172740\pi\) | ||||
0.856329 | + | 0.516431i | \(0.172740\pi\) | |||||||
\(90\) | 1.83680 | + | 1.27521i | 0.193616 | + | 0.134419i | ||||
\(91\) | 15.1205i | 1.58506i | ||||||||
\(92\) | −4.68667 | + | 1.01740i | −0.488619 | + | 0.106071i | ||||
\(93\) | 2.80231 | − | 2.80231i | 0.290586 | − | 0.290586i | ||||
\(94\) | − | 8.07780i | − | 0.833162i | ||||||
\(95\) | 0.312255 | + | 1.73034i | 0.0320367 | + | 0.177529i | ||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −2.18276 | + | 2.18276i | −0.221626 | + | 0.221626i | −0.809183 | − | 0.587557i | \(-0.800090\pi\) |
0.587557 | + | 0.809183i | \(0.300090\pi\) | |||||||
\(98\) | −1.01331 | + | 1.01331i | −0.102360 | + | 0.102360i | ||||
\(99\) | 3.67360 | 0.369211 | ||||||||
\(100\) | −1.74767 | − | 4.68462i | −0.174767 | − | 0.468462i | ||||
\(101\) | 17.9481 | 1.78590 | 0.892950 | − | 0.450156i | \(-0.148632\pi\) | ||||
0.892950 | + | 0.450156i | \(0.148632\pi\) | |||||||
\(102\) | −4.03339 | + | 4.03339i | −0.399365 | + | 0.399365i | ||||
\(103\) | 3.77675 | + | 3.77675i | 0.372134 | + | 0.372134i | 0.868254 | − | 0.496120i | \(-0.165242\pi\) |
−0.496120 | + | 0.868254i | \(0.665242\pi\) | |||||||
\(104\) | − | 6.40853i | − | 0.628408i | ||||||
\(105\) | −5.19201 | + | 0.936943i | −0.506688 | + | 0.0914363i | ||||
\(106\) | − | 8.39248i | − | 0.815150i | ||||||
\(107\) | 2.84433 | − | 2.84433i | 0.274972 | − | 0.274972i | −0.556126 | − | 0.831098i | \(-0.687713\pi\) |
0.831098 | + | 0.556126i | \(0.187713\pi\) | |||||||
\(108\) | −0.707107 | + | 0.707107i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | 6.76049 | 0.647537 | 0.323769 | − | 0.946136i | \(-0.395050\pi\) | ||||
0.323769 | + | 0.946136i | \(0.395050\pi\) | |||||||
\(110\) | −6.74767 | − | 4.68462i | −0.643365 | − | 0.446661i | ||||
\(111\) | − | 6.50154i | − | 0.617099i | ||||||
\(112\) | −1.66838 | + | 1.66838i | −0.157647 | + | 0.157647i | ||||
\(113\) | −12.4926 | − | 12.4926i | −1.17521 | − | 1.17521i | −0.980951 | − | 0.194257i | \(-0.937770\pi\) |
−0.194257 | − | 0.980951i | \(-0.562230\pi\) | |||||||
\(114\) | −0.786330 | −0.0736466 | ||||||||
\(115\) | −9.90913 | + | 4.09990i | −0.924031 | + | 0.382318i | ||||
\(116\) | 4.68811 | 0.435280 | ||||||||
\(117\) | 4.53151 | + | 4.53151i | 0.418939 | + | 0.418939i | ||||
\(118\) | −9.34547 | + | 9.34547i | −0.860320 | + | 0.860320i | ||||
\(119\) | − | 13.4584i | − | 1.23373i | ||||||
\(120\) | 2.20052 | − | 0.397104i | 0.200879 | − | 0.0362505i | ||||
\(121\) | −2.49535 | −0.226850 | ||||||||
\(122\) | 2.22997 | − | 2.22997i | 0.201892 | − | 0.201892i | ||||
\(123\) | −4.47158 | + | 4.47158i | −0.403189 | + | 0.403189i | ||||
\(124\) | − | 3.96306i | − | 0.355893i | ||||||
\(125\) | −5.70608 | − | 9.61461i | −0.510367 | − | 0.859957i | ||||
\(126\) | − | 2.35944i | − | 0.210196i | ||||||
\(127\) | −1.27645 | − | 1.27645i | −0.113267 | − | 0.113267i | 0.648202 | − | 0.761469i | \(-0.275521\pi\) |
−0.761469 | + | 0.648202i | \(0.775521\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −2.42620 | −0.213615 | ||||||||
\(130\) | −2.54485 | − | 14.1021i | −0.223198 | − | 1.23684i | ||||
\(131\) | 7.96128 | 0.695580 | 0.347790 | − | 0.937572i | \(-0.386932\pi\) | ||||
0.347790 | + | 0.937572i | \(0.386932\pi\) | |||||||
\(132\) | 2.59763 | − | 2.59763i | 0.226095 | − | 0.226095i | ||||
\(133\) | 1.31189 | − | 1.31189i | 0.113756 | − | 0.113756i | ||||
\(134\) | 4.63977 | 0.400815 | ||||||||
\(135\) | −1.27521 | + | 1.83680i | −0.109753 | + | 0.158087i | ||||
\(136\) | 5.70407i | 0.489120i | ||||||||
\(137\) | 9.80005 | − | 9.80005i | 0.837275 | − | 0.837275i | −0.151225 | − | 0.988499i | \(-0.548322\pi\) |
0.988499 | + | 0.151225i | \(0.0483216\pi\) | |||||||
\(138\) | −1.01740 | − | 4.68667i | −0.0866066 | − | 0.398956i | ||||
\(139\) | 17.2801i | 1.46568i | 0.680404 | + | 0.732838i | \(0.261805\pi\) | ||||
−0.680404 | + | 0.732838i | \(0.738195\pi\) | |||||||
\(140\) | −3.00878 | + | 4.33382i | −0.254289 | + | 0.366275i | ||||
\(141\) | 8.07780 | 0.680274 | ||||||||
\(142\) | 4.37805 | + | 4.37805i | 0.367398 | + | 0.367398i | ||||
\(143\) | −16.6470 | − | 16.6470i | −1.39209 | − | 1.39209i | ||||
\(144\) | 1.00000i | 0.0833333i | ||||||||
\(145\) | 10.3163 | − | 1.86167i | 0.856721 | − | 0.154603i | ||||
\(146\) | 7.95502 | 0.658362 | ||||||||
\(147\) | −1.01331 | − | 1.01331i | −0.0835768 | − | 0.0835768i | ||||
\(148\) | −4.59728 | − | 4.59728i | −0.377894 | − | 0.377894i | ||||
\(149\) | 6.63038 | 0.543182 | 0.271591 | − | 0.962413i | \(-0.412450\pi\) | ||||
0.271591 | + | 0.962413i | \(0.412450\pi\) | |||||||
\(150\) | 4.68462 | − | 1.74767i | 0.382497 | − | 0.142697i | ||||
\(151\) | −5.31700 | −0.432691 | −0.216345 | − | 0.976317i | \(-0.569414\pi\) | ||||
−0.216345 | + | 0.976317i | \(0.569414\pi\) | |||||||
\(152\) | −0.556019 | + | 0.556019i | −0.0450991 | + | 0.0450991i | ||||
\(153\) | −4.03339 | − | 4.03339i | −0.326080 | − | 0.326080i | ||||
\(154\) | 8.66764i | 0.698459i | ||||||||
\(155\) | −1.57375 | − | 8.72082i | −0.126406 | − | 0.700473i | ||||
\(156\) | 6.40853 | 0.513093 | ||||||||
\(157\) | −4.64687 | + | 4.64687i | −0.370860 | + | 0.370860i | −0.867791 | − | 0.496930i | \(-0.834461\pi\) |
0.496930 | + | 0.867791i | \(0.334461\pi\) | |||||||
\(158\) | 8.24345 | + | 8.24345i | 0.655814 | + | 0.655814i | ||||
\(159\) | 8.39248 | 0.665567 | ||||||||
\(160\) | 1.27521 | − | 1.83680i | 0.100814 | − | 0.145212i | ||||
\(161\) | 9.51653 | + | 6.12173i | 0.750008 | + | 0.482460i | ||||
\(162\) | −0.707107 | − | 0.707107i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | −11.0630 | + | 11.0630i | −0.866523 | + | 0.866523i | −0.992086 | − | 0.125563i | \(-0.959926\pi\) |
0.125563 | + | 0.992086i | \(0.459926\pi\) | |||||||
\(164\) | 6.32378i | 0.493804i | ||||||||
\(165\) | 4.68462 | − | 6.74767i | 0.364697 | − | 0.525306i | ||||
\(166\) | 7.14245i | 0.554362i | ||||||||
\(167\) | 6.27676 | + | 6.27676i | 0.485710 | + | 0.485710i | 0.906949 | − | 0.421239i | \(-0.138405\pi\) |
−0.421239 | + | 0.906949i | \(0.638405\pi\) | |||||||
\(168\) | −1.66838 | − | 1.66838i | −0.128718 | − | 0.128718i | ||||
\(169\) | − | 28.0692i | − | 2.15917i | ||||||
\(170\) | 2.26511 | + | 12.5519i | 0.173726 | + | 0.962690i | ||||
\(171\) | − | 0.786330i | − | 0.0601322i | ||||||
\(172\) | −1.71558 | + | 1.71558i | −0.130812 | + | 0.130812i | ||||
\(173\) | 3.53407 | − | 3.53407i | 0.268690 | − | 0.268690i | −0.559882 | − | 0.828572i | \(-0.689154\pi\) |
0.828572 | + | 0.559882i | \(0.189154\pi\) | |||||||
\(174\) | 4.68811i | 0.355404i | ||||||||
\(175\) | −4.89993 | + | 10.7315i | −0.370400 | + | 0.811224i | ||||
\(176\) | − | 3.67360i | − | 0.276908i | ||||||
\(177\) | −9.34547 | − | 9.34547i | −0.702449 | − | 0.702449i | ||||
\(178\) | 11.4249 | + | 11.4249i | 0.856329 | + | 0.856329i | ||||
\(179\) | − | 9.16746i | − | 0.685208i | −0.939480 | − | 0.342604i | \(-0.888691\pi\) | ||
0.939480 | − | 0.342604i | \(-0.111309\pi\) | |||||||
\(180\) | 0.397104 | + | 2.20052i | 0.0295984 | + | 0.164017i | ||||
\(181\) | − | 20.5860i | − | 1.53015i | −0.643942 | − | 0.765074i | \(-0.722702\pi\) | ||
0.643942 | − | 0.765074i | \(-0.277298\pi\) | |||||||
\(182\) | −10.6918 | + | 10.6918i | −0.792531 | + | 0.792531i | ||||
\(183\) | 2.22997 | + | 2.22997i | 0.164844 | + | 0.164844i | ||||
\(184\) | −4.03339 | − | 2.59457i | −0.297345 | − | 0.191274i | ||||
\(185\) | −11.9420 | − | 8.29084i | −0.877996 | − | 0.609554i | ||||
\(186\) | 3.96306 | 0.290586 | ||||||||
\(187\) | 14.8171 | + | 14.8171i | 1.08353 | + | 1.08353i | ||||
\(188\) | 5.71187 | − | 5.71187i | 0.416581 | − | 0.416581i | ||||
\(189\) | 2.35944 | 0.171624 | ||||||||
\(190\) | −1.00274 | + | 1.44433i | −0.0727462 | + | 0.104783i | ||||
\(191\) | 15.4598i | 1.11864i | 0.828953 | + | 0.559318i | \(0.188937\pi\) | ||||
−0.828953 | + | 0.559318i | \(0.811063\pi\) | |||||||
\(192\) | 0.707107 | + | 0.707107i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 1.12895 | − | 1.12895i | 0.0812635 | − | 0.0812635i | −0.665307 | − | 0.746570i | \(-0.731699\pi\) |
0.746570 | + | 0.665307i | \(0.231699\pi\) | |||||||
\(194\) | −3.08689 | −0.221626 | ||||||||
\(195\) | 14.1021 | − | 2.54485i | 1.00987 | − | 0.182241i | ||||
\(196\) | −1.43304 | −0.102360 | ||||||||
\(197\) | −14.7323 | − | 14.7323i | −1.04963 | − | 1.04963i | −0.998702 | − | 0.0509309i | \(-0.983781\pi\) |
−0.0509309 | − | 0.998702i | \(-0.516219\pi\) | |||||||
\(198\) | 2.59763 | + | 2.59763i | 0.184605 | + | 0.184605i | ||||
\(199\) | −16.9393 | −1.20080 | −0.600399 | − | 0.799700i | \(-0.704992\pi\) | ||||
−0.600399 | + | 0.799700i | \(0.704992\pi\) | |||||||
\(200\) | 2.07673 | − | 4.54832i | 0.146847 | − | 0.321615i | ||||
\(201\) | 4.63977i | 0.327264i | ||||||||
\(202\) | 12.6912 | + | 12.6912i | 0.892950 | + | 0.892950i | ||||
\(203\) | −7.82152 | − | 7.82152i | −0.548963 | − | 0.548963i | ||||
\(204\) | −5.70407 | −0.399365 | ||||||||
\(205\) | 2.51120 | + | 13.9156i | 0.175390 | + | 0.971909i | ||||
\(206\) | 5.34112i | 0.372134i | ||||||||
\(207\) | 4.68667 | − | 1.01740i | 0.325746 | − | 0.0707140i | ||||
\(208\) | 4.53151 | − | 4.53151i | 0.314204 | − | 0.314204i | ||||
\(209\) | 2.88866i | 0.199813i | ||||||||
\(210\) | −4.33382 | − | 3.00878i | −0.299062 | − | 0.207626i | ||||
\(211\) | 1.79018 | 0.123241 | 0.0616206 | − | 0.998100i | \(-0.480373\pi\) | ||||
0.0616206 | + | 0.998100i | \(0.480373\pi\) | |||||||
\(212\) | 5.93438 | − | 5.93438i | 0.407575 | − | 0.407575i | ||||
\(213\) | −4.37805 | + | 4.37805i | −0.299979 | + | 0.299979i | ||||
\(214\) | 4.02249 | 0.274972 | ||||||||
\(215\) | −3.09392 | + | 4.45645i | −0.211003 | + | 0.303927i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −6.61188 | + | 6.61188i | −0.448843 | + | 0.448843i | ||||
\(218\) | 4.78039 | + | 4.78039i | 0.323769 | + | 0.323769i | ||||
\(219\) | 7.95502i | 0.537550i | ||||||||
\(220\) | −1.45880 | − | 8.08385i | −0.0983524 | − | 0.545013i | ||||
\(221\) | 36.5547i | 2.45893i | ||||||||
\(222\) | 4.59728 | − | 4.59728i | 0.308549 | − | 0.308549i | ||||
\(223\) | −5.34860 | + | 5.34860i | −0.358169 | + | 0.358169i | −0.863138 | − | 0.504969i | \(-0.831504\pi\) |
0.504969 | + | 0.863138i | \(0.331504\pi\) | |||||||
\(224\) | −2.35944 | −0.157647 | ||||||||
\(225\) | 1.74767 | + | 4.68462i | 0.116512 | + | 0.312308i | ||||
\(226\) | − | 17.6672i | − | 1.17521i | ||||||
\(227\) | −3.63528 | + | 3.63528i | −0.241282 | + | 0.241282i | −0.817380 | − | 0.576098i | \(-0.804574\pi\) |
0.576098 | + | 0.817380i | \(0.304574\pi\) | |||||||
\(228\) | −0.556019 | − | 0.556019i | −0.0368233 | − | 0.0368233i | ||||
\(229\) | 19.7330 | 1.30399 | 0.651995 | − | 0.758223i | \(-0.273932\pi\) | ||||
0.651995 | + | 0.758223i | \(0.273932\pi\) | |||||||
\(230\) | −9.90588 | − | 4.10774i | −0.653174 | − | 0.270856i | ||||
\(231\) | −8.66764 | −0.570289 | ||||||||
\(232\) | 3.31499 | + | 3.31499i | 0.217640 | + | 0.217640i | ||||
\(233\) | 11.0336 | − | 11.0336i | 0.722834 | − | 0.722834i | −0.246348 | − | 0.969181i | \(-0.579231\pi\) |
0.969181 | + | 0.246348i | \(0.0792306\pi\) | |||||||
\(234\) | 6.40853i | 0.418939i | ||||||||
\(235\) | 10.3009 | − | 14.8373i | 0.671957 | − | 0.967880i | ||||
\(236\) | −13.2165 | −0.860320 | ||||||||
\(237\) | −8.24345 | + | 8.24345i | −0.535470 | + | 0.535470i | ||||
\(238\) | 9.51653 | − | 9.51653i | 0.616865 | − | 0.616865i | ||||
\(239\) | − | 29.2176i | − | 1.88993i | −0.327174 | − | 0.944964i | \(-0.606096\pi\) | ||
0.327174 | − | 0.944964i | \(-0.393904\pi\) | |||||||
\(240\) | 1.83680 | + | 1.27521i | 0.118565 | + | 0.0823145i | ||||
\(241\) | − | 0.443590i | − | 0.0285742i | −0.999898 | − | 0.0142871i | \(-0.995452\pi\) | ||
0.999898 | − | 0.0142871i | \(-0.00454788\pi\) | |||||||
\(242\) | −1.76448 | − | 1.76448i | −0.113425 | − | 0.113425i | ||||
\(243\) | 0.707107 | − | 0.707107i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 3.15365 | 0.201892 | ||||||||
\(245\) | −3.15345 | + | 0.569067i | −0.201466 | + | 0.0363564i | ||||
\(246\) | −6.32378 | −0.403189 | ||||||||
\(247\) | −3.56326 | + | 3.56326i | −0.226725 | + | 0.226725i | ||||
\(248\) | 2.80231 | − | 2.80231i | 0.177947 | − | 0.177947i | ||||
\(249\) | −7.14245 | −0.452635 | ||||||||
\(250\) | 2.76375 | − | 10.8334i | 0.174795 | − | 0.685162i | ||||
\(251\) | 16.1442i | 1.01901i | 0.860467 | + | 0.509505i | \(0.170172\pi\) | ||||
−0.860467 | + | 0.509505i | \(0.829828\pi\) | |||||||
\(252\) | 1.66838 | − | 1.66838i | 0.105098 | − | 0.105098i | ||||
\(253\) | −17.2170 | + | 3.73751i | −1.08242 | + | 0.234975i | ||||
\(254\) | − | 1.80517i | − | 0.113267i | ||||||
\(255\) | −12.5519 | + | 2.26511i | −0.786033 | + | 0.141847i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 11.2370 | + | 11.2370i | 0.700942 | + | 0.700942i | 0.964613 | − | 0.263671i | \(-0.0849333\pi\) |
−0.263671 | + | 0.964613i | \(0.584933\pi\) | |||||||
\(258\) | −1.71558 | − | 1.71558i | −0.106808 | − | 0.106808i | ||||
\(259\) | 15.3400i | 0.953181i | ||||||||
\(260\) | 8.17222 | − | 11.7712i | 0.506820 | − | 0.730018i | ||||
\(261\) | −4.68811 | −0.290186 | ||||||||
\(262\) | 5.62947 | + | 5.62947i | 0.347790 | + | 0.347790i | ||||
\(263\) | 14.6564 | + | 14.6564i | 0.903750 | + | 0.903750i | 0.995758 | − | 0.0920079i | \(-0.0293285\pi\) |
−0.0920079 | + | 0.995758i | \(0.529329\pi\) | |||||||
\(264\) | 3.67360 | 0.226095 | ||||||||
\(265\) | 10.7022 | − | 15.4153i | 0.657430 | − | 0.946955i | ||||
\(266\) | 1.85530 | 0.113756 | ||||||||
\(267\) | −11.4249 | + | 11.4249i | −0.699190 | + | 0.699190i | ||||
\(268\) | 3.28081 | + | 3.28081i | 0.200408 | + | 0.200408i | ||||
\(269\) | 29.0834i | 1.77325i | 0.462491 | + | 0.886624i | \(0.346956\pi\) | ||||
−0.462491 | + | 0.886624i | \(0.653044\pi\) | |||||||
\(270\) | −2.20052 | + | 0.397104i | −0.133920 | + | 0.0241670i | ||||
\(271\) | −13.4284 | −0.815720 | −0.407860 | − | 0.913044i | \(-0.633725\pi\) | ||||
−0.407860 | + | 0.913044i | \(0.633725\pi\) | |||||||
\(272\) | −4.03339 | + | 4.03339i | −0.244560 | + | 0.244560i | ||||
\(273\) | −10.6918 | − | 10.6918i | −0.647099 | − | 0.647099i | ||||
\(274\) | 13.8594 | 0.837275 | ||||||||
\(275\) | −6.42026 | − | 17.2094i | −0.387156 | − | 1.03777i | ||||
\(276\) | 2.59457 | − | 4.03339i | 0.156175 | − | 0.242781i | ||||
\(277\) | −5.20205 | − | 5.20205i | −0.312561 | − | 0.312561i | 0.533340 | − | 0.845901i | \(-0.320937\pi\) |
−0.845901 | + | 0.533340i | \(0.820937\pi\) | |||||||
\(278\) | −12.2188 | + | 12.2188i | −0.732838 | + | 0.732838i | ||||
\(279\) | 3.96306i | 0.237262i | ||||||||
\(280\) | −5.19201 | + | 0.936943i | −0.310282 | + | 0.0559930i | ||||
\(281\) | − | 12.8316i | − | 0.765467i | −0.923859 | − | 0.382734i | \(-0.874983\pi\) | ||
0.923859 | − | 0.382734i | \(-0.125017\pi\) | |||||||
\(282\) | 5.71187 | + | 5.71187i | 0.340137 | + | 0.340137i | ||||
\(283\) | −15.0828 | − | 15.0828i | −0.896580 | − | 0.896580i | 0.0985516 | − | 0.995132i | \(-0.468579\pi\) |
−0.995132 | + | 0.0985516i | \(0.968579\pi\) | |||||||
\(284\) | 6.19150i | 0.367398i | ||||||||
\(285\) | −1.44433 | − | 1.00274i | −0.0855548 | − | 0.0593970i | ||||
\(286\) | − | 23.5424i | − | 1.39209i | ||||||
\(287\) | 10.5504 | − | 10.5504i | 0.622772 | − | 0.622772i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | − | 15.5364i | − | 0.913907i | ||||||
\(290\) | 8.61112 | + | 5.97832i | 0.505662 | + | 0.351059i | ||||
\(291\) | − | 3.08689i | − | 0.180957i | ||||||
\(292\) | 5.62505 | + | 5.62505i | 0.329181 | + | 0.329181i | ||||
\(293\) | 10.7905 | + | 10.7905i | 0.630387 | + | 0.630387i | 0.948165 | − | 0.317778i | \(-0.102937\pi\) |
−0.317778 | + | 0.948165i | \(0.602937\pi\) | |||||||
\(294\) | − | 1.43304i | − | 0.0835768i | ||||||
\(295\) | −29.0832 | + | 5.24832i | −1.69329 | + | 0.305569i | ||||
\(296\) | − | 6.50154i | − | 0.377894i | ||||||
\(297\) | −2.59763 | + | 2.59763i | −0.150730 | + | 0.150730i | ||||
\(298\) | 4.68838 | + | 4.68838i | 0.271591 | + | 0.271591i | ||||
\(299\) | −25.8481 | − | 16.6274i | −1.49483 | − | 0.961586i | ||||
\(300\) | 4.54832 | + | 2.07673i | 0.262597 | + | 0.119900i | ||||
\(301\) | 5.72447 | 0.329953 | ||||||||
\(302\) | −3.75968 | − | 3.75968i | −0.216345 | − | 0.216345i | ||||
\(303\) | −12.6912 | + | 12.6912i | −0.729091 | + | 0.729091i | ||||
\(304\) | −0.786330 | −0.0450991 | ||||||||
\(305\) | 6.93968 | − | 1.25233i | 0.397365 | − | 0.0717080i | ||||
\(306\) | − | 5.70407i | − | 0.326080i | ||||||
\(307\) | −13.6279 | − | 13.6279i | −0.777786 | − | 0.777786i | 0.201668 | − | 0.979454i | \(-0.435364\pi\) |
−0.979454 | + | 0.201668i | \(0.935364\pi\) | |||||||
\(308\) | −6.12895 | + | 6.12895i | −0.349229 | + | 0.349229i | ||||
\(309\) | −5.34112 | −0.303846 | ||||||||
\(310\) | 5.05374 | − | 7.27936i | 0.287033 | − | 0.413440i | ||||
\(311\) | −17.5183 | −0.993373 | −0.496686 | − | 0.867930i | \(-0.665450\pi\) | ||||
−0.496686 | + | 0.867930i | \(0.665450\pi\) | |||||||
\(312\) | 4.53151 | + | 4.53151i | 0.256546 | + | 0.256546i | ||||
\(313\) | 14.1927 | + | 14.1927i | 0.802219 | + | 0.802219i | 0.983442 | − | 0.181223i | \(-0.0580056\pi\) |
−0.181223 | + | 0.983442i | \(0.558006\pi\) | |||||||
\(314\) | −6.57166 | −0.370860 | ||||||||
\(315\) | 3.00878 | − | 4.33382i | 0.169526 | − | 0.244183i | ||||
\(316\) | 11.6580i | 0.655814i | ||||||||
\(317\) | −16.2313 | − | 16.2313i | −0.911639 | − | 0.911639i | 0.0847624 | − | 0.996401i | \(-0.472987\pi\) |
−0.996401 | + | 0.0847624i | \(0.972987\pi\) | |||||||
\(318\) | 5.93438 | + | 5.93438i | 0.332784 | + | 0.332784i | ||||
\(319\) | 17.2222 | 0.964260 | ||||||||
\(320\) | 2.20052 | − | 0.397104i | 0.123013 | − | 0.0221988i | ||||
\(321\) | 4.02249i | 0.224514i | ||||||||
\(322\) | 2.40049 | + | 11.0579i | 0.133774 | + | 0.616234i | ||||
\(323\) | 3.17157 | − | 3.17157i | 0.176471 | − | 0.176471i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 13.3088 | − | 29.1480i | 0.738239 | − | 1.61684i | ||||
\(326\) | −15.6455 | −0.866523 | ||||||||
\(327\) | −4.78039 | + | 4.78039i | −0.264356 | + | 0.264356i | ||||
\(328\) | −4.47158 | + | 4.47158i | −0.246902 | + | 0.246902i | ||||
\(329\) | −19.0591 | −1.05076 | ||||||||
\(330\) | 8.08385 | − | 1.45880i | 0.445001 | − | 0.0803044i | ||||
\(331\) | −3.14011 | −0.172596 | −0.0862980 | − | 0.996269i | \(-0.527504\pi\) | ||||
−0.0862980 | + | 0.996269i | \(0.527504\pi\) | |||||||
\(332\) | −5.05048 | + | 5.05048i | −0.277181 | + | 0.277181i | ||||
\(333\) | 4.59728 | + | 4.59728i | 0.251930 | + | 0.251930i | ||||
\(334\) | 8.87668i | 0.485710i | ||||||||
\(335\) | 8.52234 | + | 5.91669i | 0.465625 | + | 0.323263i | ||||
\(336\) | − | 2.35944i | − | 0.128718i | ||||||
\(337\) | −20.1525 | + | 20.1525i | −1.09778 | + | 1.09778i | −0.103108 | + | 0.994670i | \(0.532879\pi\) |
−0.994670 | + | 0.103108i | \(0.967121\pi\) | |||||||
\(338\) | 19.8479 | − | 19.8479i | 1.07959 | − | 1.07959i | ||||
\(339\) | 17.6672 | 0.959553 | ||||||||
\(340\) | −7.27389 | + | 10.4772i | −0.394482 | + | 0.568208i | ||||
\(341\) | − | 14.5587i | − | 0.788398i | ||||||
\(342\) | 0.556019 | − | 0.556019i | 0.0300661 | − | 0.0300661i | ||||
\(343\) | 14.0695 | + | 14.0695i | 0.759681 | + | 0.759681i | ||||
\(344\) | −2.42620 | −0.130812 | ||||||||
\(345\) | 4.10774 | − | 9.90588i | 0.221153 | − | 0.533315i | ||||
\(346\) | 4.99793 | 0.268690 | ||||||||
\(347\) | −7.73799 | − | 7.73799i | −0.415397 | − | 0.415397i | 0.468217 | − | 0.883614i | \(-0.344897\pi\) |
−0.883614 | + | 0.468217i | \(0.844897\pi\) | |||||||
\(348\) | −3.31499 | + | 3.31499i | −0.177702 | + | 0.177702i | ||||
\(349\) | − | 16.2770i | − | 0.871286i | −0.900119 | − | 0.435643i | \(-0.856521\pi\) | ||
0.900119 | − | 0.435643i | \(-0.143479\pi\) | |||||||
\(350\) | −11.0531 | + | 4.12353i | −0.590812 | + | 0.220412i | ||||
\(351\) | −6.40853 | −0.342062 | ||||||||
\(352\) | 2.59763 | − | 2.59763i | 0.138454 | − | 0.138454i | ||||
\(353\) | −15.7516 | + | 15.7516i | −0.838375 | + | 0.838375i | −0.988645 | − | 0.150270i | \(-0.951986\pi\) |
0.150270 | + | 0.988645i | \(0.451986\pi\) | |||||||
\(354\) | − | 13.2165i | − | 0.702449i | ||||||
\(355\) | 2.45867 | + | 13.6245i | 0.130493 | + | 0.723115i | ||||
\(356\) | 16.1572i | 0.856329i | ||||||||
\(357\) | 9.51653 | + | 9.51653i | 0.503668 | + | 0.503668i | ||||
\(358\) | 6.48237 | − | 6.48237i | 0.342604 | − | 0.342604i | ||||
\(359\) | 21.4828 | 1.13382 | 0.566910 | − | 0.823780i | \(-0.308139\pi\) | ||||
0.566910 | + | 0.823780i | \(0.308139\pi\) | |||||||
\(360\) | −1.27521 | + | 1.83680i | −0.0672095 | + | 0.0968079i | ||||
\(361\) | −18.3817 | −0.967457 | ||||||||
\(362\) | 14.5565 | − | 14.5565i | 0.765074 | − | 0.765074i | ||||
\(363\) | 1.76448 | − | 1.76448i | 0.0926111 | − | 0.0926111i | ||||
\(364\) | −15.1205 | −0.792531 | ||||||||
\(365\) | 14.6118 | + | 10.1443i | 0.764816 | + | 0.530978i | ||||
\(366\) | 3.15365i | 0.164844i | ||||||||
\(367\) | 15.6149 | − | 15.6149i | 0.815091 | − | 0.815091i | −0.170301 | − | 0.985392i | \(-0.554474\pi\) |
0.985392 | + | 0.170301i | \(0.0544741\pi\) | |||||||
\(368\) | −1.01740 | − | 4.68667i | −0.0530355 | − | 0.244310i | ||||
\(369\) | − | 6.32378i | − | 0.329203i | ||||||
\(370\) | −2.58179 | − | 14.3068i | −0.134221 | − | 0.743775i | ||||
\(371\) | −19.8016 | −1.02805 | ||||||||
\(372\) | 2.80231 | + | 2.80231i | 0.145293 | + | 0.145293i | ||||
\(373\) | −24.9972 | − | 24.9972i | −1.29430 | − | 1.29430i | −0.932098 | − | 0.362205i | \(-0.882024\pi\) |
−0.362205 | − | 0.932098i | \(-0.617976\pi\) | |||||||
\(374\) | 20.9545i | 1.08353i | ||||||||
\(375\) | 10.8334 | + | 2.76375i | 0.559432 | + | 0.142719i | ||||
\(376\) | 8.07780 | 0.416581 | ||||||||
\(377\) | 21.2442 | + | 21.2442i | 1.09413 | + | 1.09413i | ||||
\(378\) | 1.66838 | + | 1.66838i | 0.0858120 | + | 0.0858120i | ||||
\(379\) | 17.4047 | 0.894022 | 0.447011 | − | 0.894528i | \(-0.352489\pi\) | ||||
0.447011 | + | 0.894528i | \(0.352489\pi\) | |||||||
\(380\) | −1.73034 | + | 0.312255i | −0.0887645 | + | 0.0160183i | ||||
\(381\) | 1.80517 | 0.0924818 | ||||||||
\(382\) | −10.9318 | + | 10.9318i | −0.559318 | + | 0.559318i | ||||
\(383\) | −16.8119 | − | 16.8119i | −0.859046 | − | 0.859046i | 0.132180 | − | 0.991226i | \(-0.457802\pi\) |
−0.991226 | + | 0.132180i | \(0.957802\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −11.0531 | + | 15.9207i | −0.563317 | + | 0.811396i | ||||
\(386\) | 1.59657 | 0.0812635 | ||||||||
\(387\) | 1.71558 | − | 1.71558i | 0.0872080 | − | 0.0872080i | ||||
\(388\) | −2.18276 | − | 2.18276i | −0.110813 | − | 0.110813i | ||||
\(389\) | −18.5763 | −0.941855 | −0.470927 | − | 0.882172i | \(-0.656081\pi\) | ||||
−0.470927 | + | 0.882172i | \(0.656081\pi\) | |||||||
\(390\) | 11.7712 | + | 8.17222i | 0.596057 | + | 0.413817i | ||||
\(391\) | 23.0067 | + | 14.7996i | 1.16350 | + | 0.748448i | ||||
\(392\) | −1.01331 | − | 1.01331i | −0.0511801 | − | 0.0511801i | ||||
\(393\) | −5.62947 | + | 5.62947i | −0.283969 | + | 0.283969i | ||||
\(394\) | − | 20.8346i | − | 1.04963i | ||||||
\(395\) | 4.62944 | + | 25.6537i | 0.232932 | + | 1.29078i | ||||
\(396\) | 3.67360i | 0.184605i | ||||||||
\(397\) | −10.1799 | − | 10.1799i | −0.510914 | − | 0.510914i | 0.403892 | − | 0.914806i | \(-0.367657\pi\) |
−0.914806 | + | 0.403892i | \(0.867657\pi\) | |||||||
\(398\) | −11.9779 | − | 11.9779i | −0.600399 | − | 0.600399i | ||||
\(399\) | 1.85530i | 0.0928811i | ||||||||
\(400\) | 4.68462 | − | 1.74767i | 0.234231 | − | 0.0873837i | ||||
\(401\) | − | 26.3514i | − | 1.31593i | −0.753049 | − | 0.657964i | \(-0.771418\pi\) | ||
0.753049 | − | 0.657964i | \(-0.228582\pi\) | |||||||
\(402\) | −3.28081 | + | 3.28081i | −0.163632 | + | 0.163632i | ||||
\(403\) | 17.9587 | − | 17.9587i | 0.894585 | − | 0.894585i | ||||
\(404\) | 17.9481i | 0.892950i | ||||||||
\(405\) | −0.397104 | − | 2.20052i | −0.0197323 | − | 0.109345i | ||||
\(406\) | − | 11.0613i | − | 0.548963i | ||||||
\(407\) | −16.8886 | − | 16.8886i | −0.837136 | − | 0.837136i | ||||
\(408\) | −4.03339 | − | 4.03339i | −0.199682 | − | 0.199682i | ||||
\(409\) | 9.66258i | 0.477784i | 0.971046 | + | 0.238892i | \(0.0767842\pi\) | ||||
−0.971046 | + | 0.238892i | \(0.923216\pi\) | |||||||
\(410\) | −8.06415 | + | 11.6155i | −0.398260 | + | 0.573649i | ||||
\(411\) | 13.8594i | 0.683632i | ||||||||
\(412\) | −3.77675 | + | 3.77675i | −0.186067 | + | 0.186067i | ||||
\(413\) | 22.0501 | + | 22.0501i | 1.08501 | + | 1.08501i | ||||
\(414\) | 4.03339 | + | 2.59457i | 0.198230 | + | 0.127516i | ||||
\(415\) | −9.10813 | + | 13.1193i | −0.447101 | + | 0.643999i | ||||
\(416\) | 6.40853 | 0.314204 | ||||||||
\(417\) | −12.2188 | − | 12.2188i | −0.598359 | − | 0.598359i | ||||
\(418\) | −2.04259 | + | 2.04259i | −0.0999065 | + | 0.0999065i | ||||
\(419\) | 6.10226 | 0.298115 | 0.149057 | − | 0.988829i | \(-0.452376\pi\) | ||||
0.149057 | + | 0.988829i | \(0.452376\pi\) | |||||||
\(420\) | −0.936943 | − | 5.19201i | −0.0457181 | − | 0.253344i | ||||
\(421\) | − | 36.0060i | − | 1.75483i | −0.479736 | − | 0.877413i | \(-0.659268\pi\) | ||
0.479736 | − | 0.877413i | \(-0.340732\pi\) | |||||||
\(422\) | 1.26585 | + | 1.26585i | 0.0616206 | + | 0.0616206i | ||||
\(423\) | −5.71187 | + | 5.71187i | −0.277721 | + | 0.277721i | ||||
\(424\) | 8.39248 | 0.407575 | ||||||||
\(425\) | −11.8458 | + | 25.9439i | −0.574607 | + | 1.25846i | ||||
\(426\) | −6.19150 | −0.299979 | ||||||||
\(427\) | −5.26147 | − | 5.26147i | −0.254620 | − | 0.254620i | ||||
\(428\) | 2.84433 | + | 2.84433i | 0.137486 | + | 0.137486i | ||||
\(429\) | 23.5424 | 1.13664 | ||||||||
\(430\) | −5.33891 | + | 0.963454i | −0.257465 | + | 0.0464619i | ||||
\(431\) | 18.9507i | 0.912823i | 0.889769 | + | 0.456411i | \(0.150865\pi\) | ||||
−0.889769 | + | 0.456411i | \(0.849135\pi\) | |||||||
\(432\) | −0.707107 | − | 0.707107i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | −6.63048 | − | 6.63048i | −0.318641 | − | 0.318641i | 0.529604 | − | 0.848245i | \(-0.322340\pi\) |
−0.848245 | + | 0.529604i | \(0.822340\pi\) | |||||||
\(434\) | −9.35061 | −0.448843 | ||||||||
\(435\) | −5.97832 | + | 8.61112i | −0.286639 | + | 0.412871i | ||||
\(436\) | 6.76049i | 0.323769i | ||||||||
\(437\) | 0.800010 | + | 3.68527i | 0.0382697 | + | 0.176290i | ||||
\(438\) | −5.62505 | + | 5.62505i | −0.268775 | + | 0.268775i | ||||
\(439\) | − | 13.5147i | − | 0.645019i | −0.946566 | − | 0.322510i | \(-0.895474\pi\) | ||
0.946566 | − | 0.322510i | \(-0.104526\pi\) | |||||||
\(440\) | 4.68462 | − | 6.74767i | 0.223330 | − | 0.321683i | ||||
\(441\) | 1.43304 | 0.0682402 | ||||||||
\(442\) | −25.8481 | + | 25.8481i | −1.22947 | + | 1.22947i | ||||
\(443\) | −0.351909 | + | 0.351909i | −0.0167197 | + | 0.0167197i | −0.715417 | − | 0.698698i | \(-0.753763\pi\) |
0.698698 | + | 0.715417i | \(0.253763\pi\) | |||||||
\(444\) | 6.50154 | 0.308549 | ||||||||
\(445\) | 6.41608 | + | 35.5543i | 0.304151 | + | 1.68543i | ||||
\(446\) | −7.56406 | −0.358169 | ||||||||
\(447\) | −4.68838 | + | 4.68838i | −0.221753 | + | 0.221753i | ||||
\(448\) | −1.66838 | − | 1.66838i | −0.0788234 | − | 0.0788234i | ||||
\(449\) | 16.0808i | 0.758899i | 0.925212 | + | 0.379450i | \(0.123887\pi\) | ||||
−0.925212 | + | 0.379450i | \(0.876113\pi\) | |||||||
\(450\) | −2.07673 | + | 4.54832i | −0.0978981 | + | 0.214410i | ||||
\(451\) | 23.2310i | 1.09391i | ||||||||
\(452\) | 12.4926 | − | 12.4926i | 0.587604 | − | 0.587604i | ||||
\(453\) | 3.75968 | − | 3.75968i | 0.176645 | − | 0.176645i | ||||
\(454\) | −5.14106 | −0.241282 | ||||||||
\(455\) | −33.2731 | + | 6.00442i | −1.55987 | + | 0.281492i | ||||
\(456\) | − | 0.786330i | − | 0.0368233i | ||||||
\(457\) | −16.4841 | + | 16.4841i | −0.771092 | + | 0.771092i | −0.978297 | − | 0.207206i | \(-0.933563\pi\) |
0.207206 | + | 0.978297i | \(0.433563\pi\) | |||||||
\(458\) | 13.9533 | + | 13.9533i | 0.651995 | + | 0.651995i | ||||
\(459\) | 5.70407 | 0.266243 | ||||||||
\(460\) | −4.09990 | − | 9.90913i | −0.191159 | − | 0.462015i | ||||
\(461\) | −19.0085 | −0.885314 | −0.442657 | − | 0.896691i | \(-0.645964\pi\) | ||||
−0.442657 | + | 0.896691i | \(0.645964\pi\) | |||||||
\(462\) | −6.12895 | − | 6.12895i | −0.285144 | − | 0.285144i | ||||
\(463\) | −5.51731 | + | 5.51731i | −0.256411 | + | 0.256411i | −0.823593 | − | 0.567182i | \(-0.808034\pi\) |
0.567182 | + | 0.823593i | \(0.308034\pi\) | |||||||
\(464\) | 4.68811i | 0.217640i | ||||||||
\(465\) | 7.27936 | + | 5.05374i | 0.337572 | + | 0.234362i | ||||
\(466\) | 15.6038 | 0.722834 | ||||||||
\(467\) | 7.96465 | − | 7.96465i | 0.368560 | − | 0.368560i | −0.498392 | − | 0.866952i | \(-0.666076\pi\) |
0.866952 | + | 0.498392i | \(0.166076\pi\) | |||||||
\(468\) | −4.53151 | + | 4.53151i | −0.209469 | + | 0.209469i | ||||
\(469\) | − | 10.9473i | − | 0.505498i | ||||||
\(470\) | 17.7754 | − | 3.20773i | 0.819918 | − | 0.147961i | ||||
\(471\) | − | 6.57166i | − | 0.302806i | ||||||
\(472\) | −9.34547 | − | 9.34547i | −0.430160 | − | 0.430160i | ||||
\(473\) | −6.30237 | + | 6.30237i | −0.289783 | + | 0.289783i | ||||
\(474\) | −11.6580 | −0.535470 | ||||||||
\(475\) | −3.68365 | + | 1.37425i | −0.169018 | + | 0.0630548i | ||||
\(476\) | 13.4584 | 0.616865 | ||||||||
\(477\) | −5.93438 | + | 5.93438i | −0.271717 | + | 0.271717i | ||||
\(478\) | 20.6600 | − | 20.6600i | 0.944964 | − | 0.944964i | ||||
\(479\) | 20.8212 | 0.951345 | 0.475673 | − | 0.879622i | \(-0.342205\pi\) | ||||
0.475673 | + | 0.879622i | \(0.342205\pi\) | |||||||
\(480\) | 0.397104 | + | 2.20052i | 0.0181252 | + | 0.100440i | ||||
\(481\) | − | 41.6653i | − | 1.89977i | ||||||
\(482\) | 0.313666 | − | 0.313666i | 0.0142871 | − | 0.0142871i | ||||
\(483\) | −11.0579 | + | 2.40049i | −0.503153 | + | 0.109226i | ||||
\(484\) | − | 2.49535i | − | 0.113425i | ||||||
\(485\) | −5.67000 | − | 3.93643i | −0.257461 | − | 0.178744i | ||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −1.77520 | − | 1.77520i | −0.0804421 | − | 0.0804421i | 0.665741 | − | 0.746183i | \(-0.268116\pi\) |
−0.746183 | + | 0.665741i | \(0.768116\pi\) | |||||||
\(488\) | 2.22997 | + | 2.22997i | 0.100946 | + | 0.100946i | ||||
\(489\) | − | 15.6455i | − | 0.707513i | ||||||
\(490\) | −2.63221 | − | 1.82743i | −0.118911 | − | 0.0825550i | ||||
\(491\) | 18.6403 | 0.841225 | 0.420612 | − | 0.907240i | \(-0.361815\pi\) | ||||
0.420612 | + | 0.907240i | \(0.361815\pi\) | |||||||
\(492\) | −4.47158 | − | 4.47158i | −0.201595 | − | 0.201595i | ||||
\(493\) | −18.9089 | − | 18.9089i | −0.851616 | − | 0.851616i | ||||
\(494\) | −5.03922 | −0.226725 | ||||||||
\(495\) | 1.45880 | + | 8.08385i | 0.0655683 | + | 0.363342i | ||||
\(496\) | 3.96306 | 0.177947 | ||||||||
\(497\) | 10.3297 | − | 10.3297i | 0.463352 | − | 0.463352i | ||||
\(498\) | −5.05048 | − | 5.05048i | −0.226317 | − | 0.226317i | ||||
\(499\) | − | 17.8392i | − | 0.798593i | −0.916822 | − | 0.399296i | \(-0.869254\pi\) | ||
0.916822 | − | 0.399296i | \(-0.130746\pi\) | |||||||
\(500\) | 9.61461 | − | 5.70608i | 0.429978 | − | 0.255184i | ||||
\(501\) | −8.87668 | −0.396581 | ||||||||
\(502\) | −11.4157 | + | 11.4157i | −0.509505 | + | 0.509505i | ||||
\(503\) | 28.8127 | + | 28.8127i | 1.28470 | + | 1.28470i | 0.937965 | + | 0.346731i | \(0.112708\pi\) |
0.346731 | + | 0.937965i | \(0.387292\pi\) | |||||||
\(504\) | 2.35944 | 0.105098 | ||||||||
\(505\) | 7.12725 | + | 39.4952i | 0.317158 | + | 1.75751i | ||||
\(506\) | −14.8171 | − | 9.53142i | −0.658698 | − | 0.423723i | ||||
\(507\) | 19.8479 | + | 19.8479i | 0.881478 | + | 0.881478i | ||||
\(508\) | 1.27645 | − | 1.27645i | 0.0566333 | − | 0.0566333i | ||||
\(509\) | − | 5.84360i | − | 0.259013i | −0.991579 | − | 0.129506i | \(-0.958661\pi\) | ||
0.991579 | − | 0.129506i | \(-0.0413393\pi\) | |||||||
\(510\) | −10.4772 | − | 7.27389i | −0.463940 | − | 0.322093i | ||||
\(511\) | − | 18.7694i | − | 0.830309i | ||||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0.556019 | + | 0.556019i | 0.0245489 | + | 0.0245489i | ||||
\(514\) | 15.8915i | 0.700942i | ||||||||
\(515\) | −6.81106 | + | 9.81058i | −0.300131 | + | 0.432306i | ||||
\(516\) | − | 2.42620i | − | 0.106808i | ||||||
\(517\) | 20.9831 | − | 20.9831i | 0.922837 | − | 0.922837i | ||||
\(518\) | −10.8470 | + | 10.8470i | −0.476590 | + | 0.476590i | ||||
\(519\) | 4.99793i | 0.219385i | ||||||||
\(520\) | 14.1021 | − | 2.54485i | 0.618419 | − | 0.111599i | ||||
\(521\) | 3.19214i | 0.139850i | 0.997552 | + | 0.0699250i | \(0.0222760\pi\) | ||||
−0.997552 | + | 0.0699250i | \(0.977724\pi\) | |||||||
\(522\) | −3.31499 | − | 3.31499i | −0.145093 | − | 0.145093i | ||||
\(523\) | −26.8233 | − | 26.8233i | −1.17290 | − | 1.17290i | −0.981514 | − | 0.191388i | \(-0.938701\pi\) |
−0.191388 | − | 0.981514i | \(-0.561299\pi\) | |||||||
\(524\) | 7.96128i | 0.347790i | ||||||||
\(525\) | −4.12353 | − | 11.0531i | −0.179966 | − | 0.482396i | ||||
\(526\) | 20.7272i | 0.903750i | ||||||||
\(527\) | −15.9846 | + | 15.9846i | −0.696298 | + | 0.696298i | ||||
\(528\) | 2.59763 | + | 2.59763i | 0.113047 | + | 0.113047i | ||||
\(529\) | −20.9298 | + | 9.53641i | −0.909992 | + | 0.414627i | ||||
\(530\) | 18.4679 | − | 3.33269i | 0.802193 | − | 0.144763i | ||||
\(531\) | 13.2165 | 0.573547 | ||||||||
\(532\) | 1.31189 | + | 1.31189i | 0.0568778 | + | 0.0568778i | ||||
\(533\) | −28.6563 | + | 28.6563i | −1.24124 | + | 1.24124i | ||||
\(534\) | −16.1572 | −0.699190 | ||||||||
\(535\) | 7.38852 | + | 5.12953i | 0.319434 | + | 0.221769i | ||||
\(536\) | 4.63977i | 0.200408i | ||||||||
\(537\) | 6.48237 | + | 6.48237i | 0.279735 | + | 0.279735i | ||||
\(538\) | −20.5651 | + | 20.5651i | −0.886624 | + | 0.886624i | ||||
\(539\) | −5.26443 | −0.226755 | ||||||||
\(540\) | −1.83680 | − | 1.27521i | −0.0790433 | − | 0.0548763i | ||||
\(541\) | −22.2667 | −0.957322 | −0.478661 | − | 0.878000i | \(-0.658878\pi\) | ||||
−0.478661 | + | 0.878000i | \(0.658878\pi\) | |||||||
\(542\) | −9.49535 | − | 9.49535i | −0.407860 | − | 0.407860i | ||||
\(543\) | 14.5565 | + | 14.5565i | 0.624681 | + | 0.624681i | ||||
\(544\) | −5.70407 | −0.244560 | ||||||||
\(545\) | 2.68462 | + | 14.8766i | 0.114996 | + | 0.637244i | ||||
\(546\) | − | 15.1205i | − | 0.647099i | ||||||
\(547\) | 2.91934 | + | 2.91934i | 0.124822 | + | 0.124822i | 0.766758 | − | 0.641936i | \(-0.221869\pi\) |
−0.641936 | + | 0.766758i | \(0.721869\pi\) | |||||||
\(548\) | 9.80005 | + | 9.80005i | 0.418637 | + | 0.418637i | ||||
\(549\) | −3.15365 | −0.134594 | ||||||||
\(550\) | 7.62909 | − | 16.7087i | 0.325305 | − | 0.712461i | ||||
\(551\) | − | 3.68640i | − | 0.157046i | ||||||
\(552\) | 4.68667 | − | 1.01740i | 0.199478 | − | 0.0433033i | ||||
\(553\) | 19.4499 | − | 19.4499i | 0.827095 | − | 0.827095i | ||||
\(554\) | − | 7.35681i | − | 0.312561i | ||||||
\(555\) | 14.3068 | − | 2.58179i | 0.607290 | − | 0.109591i | ||||
\(556\) | −17.2801 | −0.732838 | ||||||||
\(557\) | 16.2953 | − | 16.2953i | 0.690452 | − | 0.690452i | −0.271879 | − | 0.962331i | \(-0.587645\pi\) |
0.962331 | + | 0.271879i | \(0.0876451\pi\) | |||||||
\(558\) | −2.80231 | + | 2.80231i | −0.118631 | + | 0.118631i | ||||
\(559\) | −15.5484 | −0.657626 | ||||||||
\(560\) | −4.33382 | − | 3.00878i | −0.183137 | − | 0.127144i | ||||
\(561\) | −20.9545 | −0.884699 | ||||||||
\(562\) | 9.07329 | − | 9.07329i | 0.382734 | − | 0.382734i | ||||
\(563\) | 13.7932 | + | 13.7932i | 0.581316 | + | 0.581316i | 0.935265 | − | 0.353949i | \(-0.115161\pi\) |
−0.353949 | + | 0.935265i | \(0.615161\pi\) | |||||||
\(564\) | 8.07780i | 0.340137i | ||||||||
\(565\) | 22.5295 | − | 32.4512i | 0.947822 | − | 1.36523i | ||||
\(566\) | − | 21.3303i | − | 0.896580i | ||||||
\(567\) | −1.66838 | + | 1.66838i | −0.0700652 | + | 0.0700652i | ||||
\(568\) | −4.37805 | + | 4.37805i | −0.183699 | + | 0.183699i | ||||
\(569\) | −8.31567 | −0.348611 | −0.174305 | − | 0.984692i | \(-0.555768\pi\) | ||||
−0.174305 | + | 0.984692i | \(0.555768\pi\) | |||||||
\(570\) | −0.312255 | − | 1.73034i | −0.0130789 | − | 0.0724759i | ||||
\(571\) | − | 32.9103i | − | 1.37725i | −0.725116 | − | 0.688627i | \(-0.758214\pi\) | ||
0.725116 | − | 0.688627i | \(-0.241786\pi\) | |||||||
\(572\) | 16.6470 | − | 16.6470i | 0.696045 | − | 0.696045i | ||||
\(573\) | −10.9318 | − | 10.9318i | −0.456681 | − | 0.456681i | ||||
\(574\) | 14.9206 | 0.622772 | ||||||||
\(575\) | −12.9569 | − | 20.1772i | −0.540340 | − | 0.841447i | ||||
\(576\) | −1.00000 | −0.0416667 | ||||||||
\(577\) | 28.4271 | + | 28.4271i | 1.18344 | + | 1.18344i | 0.978848 | + | 0.204588i | \(0.0655855\pi\) |
0.204588 | + | 0.978848i | \(0.434415\pi\) | |||||||
\(578\) | 10.9859 | − | 10.9859i | 0.456953 | − | 0.456953i | ||||
\(579\) | 1.59657i | 0.0663514i | ||||||||
\(580\) | 1.86167 | + | 10.3163i | 0.0773014 | + | 0.428361i | ||||
\(581\) | 16.8522 | 0.699147 | ||||||||
\(582\) | 2.18276 | − | 2.18276i | 0.0904783 | − | 0.0904783i | ||||
\(583\) | 21.8005 | − | 21.8005i | 0.902886 | − | 0.902886i | ||||
\(584\) | 7.95502i | 0.329181i | ||||||||
\(585\) | −8.17222 | + | 11.7712i | −0.337880 | + | 0.486679i | ||||
\(586\) | 15.2601i | 0.630387i | ||||||||
\(587\) | 5.63929 | + | 5.63929i | 0.232758 | + | 0.232758i | 0.813843 | − | 0.581085i | \(-0.197372\pi\) |
−0.581085 | + | 0.813843i | \(0.697372\pi\) | |||||||
\(588\) | 1.01331 | − | 1.01331i | 0.0417884 | − | 0.0417884i | ||||
\(589\) | −3.11627 | −0.128404 | ||||||||
\(590\) | −24.2761 | − | 16.8538i | −0.999430 | − | 0.693861i | ||||
\(591\) | 20.8346 | 0.857022 | ||||||||
\(592\) | 4.59728 | − | 4.59728i | 0.188947 | − | 0.188947i | ||||
\(593\) | 23.5246 | − | 23.5246i | 0.966038 | − | 0.966038i | −0.0334034 | − | 0.999442i | \(-0.510635\pi\) |
0.999442 | + | 0.0334034i | \(0.0106346\pi\) | |||||||
\(594\) | −3.67360 | −0.150730 | ||||||||
\(595\) | 29.6156 | − | 5.34439i | 1.21412 | − | 0.219099i | ||||
\(596\) | 6.63038i | 0.271591i | ||||||||
\(597\) | 11.9779 | − | 11.9779i | 0.490224 | − | 0.490224i | ||||
\(598\) | −6.52001 | − | 30.0347i | −0.266623 | − | 1.22821i | ||||
\(599\) | 31.5446i | 1.28888i | 0.764655 | + | 0.644440i | \(0.222909\pi\) | ||||
−0.764655 | + | 0.644440i | \(0.777091\pi\) | |||||||
\(600\) | 1.74767 | + | 4.68462i | 0.0713485 | + | 0.191249i | ||||
\(601\) | −31.2717 | −1.27560 | −0.637799 | − | 0.770203i | \(-0.720155\pi\) | ||||
−0.637799 | + | 0.770203i | \(0.720155\pi\) | |||||||
\(602\) | 4.04781 | + | 4.04781i | 0.164977 | + | 0.164977i | ||||
\(603\) | −3.28081 | − | 3.28081i | −0.133605 | − | 0.133605i | ||||
\(604\) | − | 5.31700i | − | 0.216345i | ||||||
\(605\) | −0.990913 | − | 5.49107i | −0.0402863 | − | 0.223244i | ||||
\(606\) | −17.9481 | −0.729091 | ||||||||
\(607\) | −1.12613 | − | 1.12613i | −0.0457084 | − | 0.0457084i | 0.683883 | − | 0.729592i | \(-0.260290\pi\) |
−0.729592 | + | 0.683883i | \(0.760290\pi\) | |||||||
\(608\) | −0.556019 | − | 0.556019i | −0.0225496 | − | 0.0225496i | ||||
\(609\) | 11.0613 | 0.448227 | ||||||||
\(610\) | 5.79262 | + | 4.02157i | 0.234536 | + | 0.162828i | ||||
\(611\) | 51.7668 | 2.09426 | ||||||||
\(612\) | 4.03339 | − | 4.03339i | 0.163040 | − | 0.163040i | ||||
\(613\) | 26.5829 | + | 26.5829i | 1.07367 | + | 1.07367i | 0.997061 | + | 0.0766132i | \(0.0244107\pi\) |
0.0766132 | + | 0.997061i | \(0.475589\pi\) | |||||||
\(614\) | − | 19.2728i | − | 0.777786i | ||||||
\(615\) | −11.6155 | − | 8.06415i | −0.468383 | − | 0.325178i | ||||
\(616\) | −8.66764 | −0.349229 | ||||||||
\(617\) | 27.2723 | − | 27.2723i | 1.09794 | − | 1.09794i | 0.103290 | − | 0.994651i | \(-0.467063\pi\) |
0.994651 | − | 0.103290i | \(-0.0329369\pi\) | |||||||
\(618\) | −3.77675 | − | 3.77675i | −0.151923 | − | 0.151923i | ||||
\(619\) | 13.9863 | 0.562157 | 0.281078 | − | 0.959685i | \(-0.409308\pi\) | ||||
0.281078 | + | 0.959685i | \(0.409308\pi\) | |||||||
\(620\) | 8.72082 | − | 1.57375i | 0.350236 | − | 0.0632032i | ||||
\(621\) | −2.59457 | + | 4.03339i | −0.104117 | + | 0.161854i | ||||
\(622\) | −12.3873 | − | 12.3873i | −0.496686 | − | 0.496686i | ||||
\(623\) | 26.9562 | − | 26.9562i | 1.07998 | − | 1.07998i | ||||
\(624\) | 6.40853i | 0.256546i | ||||||||
\(625\) | 18.8913 | − | 16.3744i | 0.755651 | − | 0.654975i | ||||
\(626\) | 20.0715i | 0.802219i | ||||||||
\(627\) | −2.04259 | − | 2.04259i | −0.0815733 | − | 0.0815733i | ||||
\(628\) | −4.64687 | − | 4.64687i | −0.185430 | − | 0.185430i | ||||
\(629\) | 37.0852i | 1.47869i | ||||||||
\(630\) | 5.19201 | − | 0.936943i | 0.206854 | − | 0.0373287i | ||||
\(631\) | − | 0.0291909i | − | 0.00116207i | −1.00000 | 0.000581037i | \(-0.999815\pi\) | |||
1.00000 | 0.000581037i | \(-0.000184950\pi\) | ||||||||
\(632\) | −8.24345 | + | 8.24345i | −0.327907 | + | 0.327907i | ||||
\(633\) | −1.26585 | + | 1.26585i | −0.0503130 | + | 0.0503130i | ||||
\(634\) | − | 22.9545i | − | 0.911639i | ||||||
\(635\) | 2.30198 | − | 3.31574i | 0.0913512 | − | 0.131581i | ||||
\(636\) | 8.39248i | 0.332784i | ||||||||
\(637\) | −6.49385 | − | 6.49385i | −0.257296 | − | 0.257296i | ||||
\(638\) | 12.1780 | + | 12.1780i | 0.482130 | + | 0.482130i | ||||
\(639\) | − | 6.19150i | − | 0.244932i | ||||||
\(640\) | 1.83680 | + | 1.27521i | 0.0726059 | + | 0.0504071i | ||||
\(641\) | 35.5918i | 1.40579i | 0.711292 | + | 0.702897i | \(0.248110\pi\) | ||||
−0.711292 | + | 0.702897i | \(0.751890\pi\) | |||||||
\(642\) | −2.84433 | + | 2.84433i | −0.112257 | + | 0.112257i | ||||
\(643\) | 21.0238 | + | 21.0238i | 0.829097 | + | 0.829097i | 0.987392 | − | 0.158295i | \(-0.0505996\pi\) |
−0.158295 | + | 0.987392i | \(0.550600\pi\) | |||||||
\(644\) | −6.12173 | + | 9.51653i | −0.241230 | + | 0.375004i | ||||
\(645\) | −0.963454 | − | 5.33891i | −0.0379360 | − | 0.210219i | ||||
\(646\) | 4.48528 | 0.176471 | ||||||||
\(647\) | 5.39555 | + | 5.39555i | 0.212121 | + | 0.212121i | 0.805168 | − | 0.593047i | \(-0.202075\pi\) |
−0.593047 | + | 0.805168i | \(0.702075\pi\) | |||||||
\(648\) | 0.707107 | − | 0.707107i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | −48.5521 | −1.90584 | ||||||||
\(650\) | 30.0215 | − | 11.2000i | 1.17754 | − | 0.439301i | ||||
\(651\) | − | 9.35061i | − | 0.366479i | ||||||
\(652\) | −11.0630 | − | 11.0630i | −0.433262 | − | 0.433262i | ||||
\(653\) | −6.27260 | + | 6.27260i | −0.245466 | + | 0.245466i | −0.819107 | − | 0.573641i | \(-0.805530\pi\) |
0.573641 | + | 0.819107i | \(0.305530\pi\) | |||||||
\(654\) | −6.76049 | −0.264356 | ||||||||
\(655\) | 3.16145 | + | 17.5190i | 0.123528 | + | 0.684523i | ||||
\(656\) | −6.32378 | −0.246902 | ||||||||
\(657\) | −5.62505 | − | 5.62505i | −0.219454 | − | 0.219454i | ||||
\(658\) | −13.4768 | − | 13.4768i | −0.525381 | − | 0.525381i | ||||
\(659\) | −24.4164 | −0.951126 | −0.475563 | − | 0.879682i | \(-0.657756\pi\) | ||||
−0.475563 | + | 0.879682i | \(0.657756\pi\) | |||||||
\(660\) | 6.74767 | + | 4.68462i | 0.262653 | + | 0.182348i | ||||
\(661\) | − | 5.36247i | − | 0.208576i | −0.994547 | − | 0.104288i | \(-0.966744\pi\) | ||
0.994547 | − | 0.104288i | \(-0.0332563\pi\) | |||||||
\(662\) | −2.22039 | − | 2.22039i | −0.0862980 | − | 0.0862980i | ||||
\(663\) | −25.8481 | − | 25.8481i | −1.00386 | − | 1.00386i | ||||
\(664\) | −7.14245 | −0.277181 | ||||||||
\(665\) | 3.40781 | + | 2.36590i | 0.132149 | + | 0.0917455i | ||||
\(666\) | 6.50154i | 0.251930i | ||||||||
\(667\) | 21.9716 | − | 4.76966i | 0.850744 | − | 0.184682i | ||||
\(668\) | −6.27676 | + | 6.27676i | −0.242855 | + | 0.242855i | ||||
\(669\) | − | 7.56406i | − | 0.292443i | ||||||
\(670\) | 1.84247 | + | 10.2099i | 0.0711809 | + | 0.394444i | ||||
\(671\) | 11.5852 | 0.447243 | ||||||||
\(672\) | 1.66838 | − | 1.66838i | 0.0643590 | − | 0.0643590i | ||||
\(673\) | −7.83125 | + | 7.83125i | −0.301872 | + | 0.301872i | −0.841746 | − | 0.539874i | \(-0.818472\pi\) |
0.539874 | + | 0.841746i | \(0.318472\pi\) | |||||||
\(674\) | −28.5000 | −1.09778 | ||||||||
\(675\) | −4.54832 | − | 2.07673i | −0.175065 | − | 0.0799335i | ||||
\(676\) | 28.0692 | 1.07959 | ||||||||
\(677\) | −17.8901 | + | 17.8901i | −0.687573 | + | 0.687573i | −0.961695 | − | 0.274122i | \(-0.911613\pi\) |
0.274122 | + | 0.961695i | \(0.411613\pi\) | |||||||
\(678\) | 12.4926 | + | 12.4926i | 0.479776 | + | 0.479776i | ||||
\(679\) | 7.28333i | 0.279508i | ||||||||
\(680\) | −12.5519 | + | 2.26511i | −0.481345 | + | 0.0868630i | ||||
\(681\) | − | 5.14106i | − | 0.197006i | ||||||
\(682\) | 10.2946 | − | 10.2946i | 0.394199 | − | 0.394199i | ||||
\(683\) | −12.3778 | + | 12.3778i | −0.473622 | + | 0.473622i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) |
0.429463 | + | 0.903085i | \(0.358703\pi\) | |||||||
\(684\) | 0.786330 | 0.0300661 | ||||||||
\(685\) | 25.4569 | + | 17.6736i | 0.972658 | + | 0.675274i | ||||
\(686\) | 19.8973i | 0.759681i | ||||||||
\(687\) | −13.9533 | + | 13.9533i | −0.532352 | + | 0.532352i | ||||
\(688\) | −1.71558 | − | 1.71558i | −0.0654060 | − | 0.0654060i | ||||
\(689\) | 53.7834 | 2.04899 | ||||||||
\(690\) | 9.90913 | − | 4.09990i | 0.377234 | − | 0.156081i | ||||
\(691\) | 40.8522 | 1.55409 | 0.777045 | − | 0.629445i | \(-0.216718\pi\) | ||||
0.777045 | + | 0.629445i | \(0.216718\pi\) | |||||||
\(692\) | 3.53407 | + | 3.53407i | 0.134345 | + | 0.134345i | ||||
\(693\) | 6.12895 | − | 6.12895i | 0.232820 | − | 0.232820i | ||||
\(694\) | − | 10.9432i | − | 0.415397i | ||||||
\(695\) | −38.0252 | + | 6.86198i | −1.44238 | + | 0.260290i | ||||
\(696\) | −4.68811 | −0.177702 | ||||||||
\(697\) | 25.5062 | − | 25.5062i | 0.966117 | − | 0.966117i | ||||
\(698\) | 11.5096 | − | 11.5096i | 0.435643 | − | 0.435643i | ||||
\(699\) | 15.6038i | 0.590191i | ||||||||
\(700\) | −10.7315 | − | 4.89993i | −0.405612 | − | 0.185200i | ||||
\(701\) | − | 17.8753i | − | 0.675139i | −0.941301 | − | 0.337570i | \(-0.890395\pi\) | ||
0.941301 | − | 0.337570i | \(-0.109605\pi\) | |||||||
\(702\) | −4.53151 | − | 4.53151i | −0.171031 | − | 0.171031i | ||||
\(703\) | −3.61498 | + | 3.61498i | −0.136342 | + | 0.136342i | ||||
\(704\) | 3.67360 | 0.138454 | ||||||||
\(705\) | 3.20773 | + | 17.7754i | 0.120810 | + | 0.669460i | ||||
\(706\) | −22.2762 | −0.838375 | ||||||||
\(707\) | 29.9441 | − | 29.9441i | 1.12616 | − | 1.12616i | ||||
\(708\) | 9.34547 | − | 9.34547i | 0.351224 | − | 0.351224i | ||||
\(709\) | −41.7130 | −1.56656 | −0.783282 | − | 0.621667i | \(-0.786456\pi\) | ||||
−0.783282 | + | 0.621667i | \(0.786456\pi\) | |||||||
\(710\) | −7.89546 | + | 11.3725i | −0.296311 | + | 0.426804i | ||||
\(711\) | − | 11.6580i | − | 0.437209i | ||||||
\(712\) | −11.4249 | + | 11.4249i | −0.428164 | + | 0.428164i | ||||
\(713\) | −4.03201 | − | 18.5736i | −0.151000 | − | 0.695586i | ||||
\(714\) | 13.4584i | 0.503668i | ||||||||
\(715\) | 30.0215 | − | 43.2427i | 1.12274 | − | 1.61718i | ||||
\(716\) | 9.16746 | 0.342604 | ||||||||
\(717\) | 20.6600 | + | 20.6600i | 0.771560 | + | 0.771560i | ||||
\(718\) | 15.1907 | + | 15.1907i | 0.566910 | + | 0.566910i | ||||
\(719\) | − | 0.928560i | − | 0.0346295i | −0.999850 | − | 0.0173147i | \(-0.994488\pi\) | ||
0.999850 | − | 0.0173147i | \(-0.00551172\pi\) | |||||||
\(720\) | −2.20052 | + | 0.397104i | −0.0820087 | + | 0.0147992i | ||||
\(721\) | 12.6021 | 0.469325 | ||||||||
\(722\) | −12.9978 | − | 12.9978i | −0.483729 | − | 0.483729i | ||||
\(723\) | 0.313666 | + | 0.313666i | 0.0116654 | + | 0.0116654i | ||||
\(724\) | 20.5860 | 0.765074 | ||||||||
\(725\) | 8.19328 | + | 21.9620i | 0.304291 | + | 0.815647i | ||||
\(726\) | 2.49535 | 0.0926111 | ||||||||
\(727\) | 17.7713 | − | 17.7713i | 0.659101 | − | 0.659101i | −0.296066 | − | 0.955167i | \(-0.595675\pi\) |
0.955167 | + | 0.296066i | \(0.0956749\pi\) | |||||||
\(728\) | −10.6918 | − | 10.6918i | −0.396266 | − | 0.396266i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 3.15897 | + | 17.5052i | 0.116919 | + | 0.647897i | ||||
\(731\) | 13.8392 | 0.511862 | ||||||||
\(732\) | −2.22997 | + | 2.22997i | −0.0824219 | + | 0.0824219i | ||||
\(733\) | −14.2968 | − | 14.2968i | −0.528065 | − | 0.528065i | 0.391930 | − | 0.919995i | \(-0.371807\pi\) |
−0.919995 | + | 0.391930i | \(0.871807\pi\) | |||||||
\(734\) | 22.0828 | 0.815091 | ||||||||
\(735\) | 1.82743 | − | 2.63221i | 0.0674059 | − | 0.0970907i | ||||
\(736\) | 2.59457 | − | 4.03339i | 0.0956371 | − | 0.148673i | ||||
\(737\) | 12.0524 | + | 12.0524i | 0.443956 | + | 0.443956i | ||||
\(738\) | 4.47158 | − | 4.47158i | 0.164601 | − | 0.164601i | ||||
\(739\) | 43.2771i | 1.59197i | 0.605315 | + | 0.795986i | \(0.293047\pi\) | ||||
−0.605315 | + | 0.795986i | \(0.706953\pi\) | |||||||
\(740\) | 8.29084 | − | 11.9420i | 0.304777 | − | 0.438998i | ||||
\(741\) | − | 5.03922i | − | 0.185120i | ||||||
\(742\) | −14.0018 | − | 14.0018i | −0.514023 | − | 0.514023i | ||||
\(743\) | −34.4467 | − | 34.4467i | −1.26373 | − | 1.26373i | −0.949273 | − | 0.314452i | \(-0.898179\pi\) |
−0.314452 | − | 0.949273i | \(-0.601821\pi\) | |||||||
\(744\) | 3.96306i | 0.145293i | ||||||||
\(745\) | 2.63295 | + | 14.5903i | 0.0964638 | + | 0.534548i | ||||
\(746\) | − | 35.3513i | − | 1.29430i | ||||||
\(747\) | 5.05048 | − | 5.05048i | 0.184787 | − | 0.184787i | ||||
\(748\) | −14.8171 | + | 14.8171i | −0.541765 | + | 0.541765i | ||||
\(749\) | − | 9.49083i | − | 0.346787i | ||||||
\(750\) | 5.70608 | + | 9.61461i | 0.208357 | + | 0.351076i | ||||
\(751\) | − | 6.81223i | − | 0.248582i | −0.992246 | − | 0.124291i | \(-0.960334\pi\) | ||
0.992246 | − | 0.124291i | \(-0.0396656\pi\) | |||||||
\(752\) | 5.71187 | + | 5.71187i | 0.208290 | + | 0.208290i | ||||
\(753\) | −11.4157 | − | 11.4157i | −0.416009 | − | 0.416009i | ||||
\(754\) | 30.0439i | 1.09413i | ||||||||
\(755\) | −2.11140 | − | 11.7002i | −0.0768417 | − | 0.425813i | ||||
\(756\) | 2.35944i | 0.0858120i | ||||||||
\(757\) | 9.32141 | − | 9.32141i | 0.338793 | − | 0.338793i | −0.517120 | − | 0.855913i | \(-0.672996\pi\) |
0.855913 | + | 0.517120i | \(0.172996\pi\) | |||||||
\(758\) | 12.3070 | + | 12.3070i | 0.447011 | + | 0.447011i | ||||
\(759\) | 9.53142 | − | 14.8171i | 0.345969 | − | 0.537825i | ||||
\(760\) | −1.44433 | − | 1.00274i | −0.0523914 | − | 0.0363731i | ||||
\(761\) | 12.3215 | 0.446654 | 0.223327 | − | 0.974744i | \(-0.428308\pi\) | ||||
0.223327 | + | 0.974744i | \(0.428308\pi\) | |||||||
\(762\) | 1.27645 | + | 1.27645i | 0.0462409 | + | 0.0462409i | ||||
\(763\) | 11.2790 | − | 11.2790i | 0.408329 | − | 0.408329i | ||||
\(764\) | −15.4598 | −0.559318 | ||||||||
\(765\) | 7.27389 | − | 10.4772i | 0.262988 | − | 0.378805i | ||||
\(766\) | − | 23.7756i | − | 0.859046i | ||||||
\(767\) | −59.8907 | − | 59.8907i | −2.16253 | − | 2.16253i | ||||
\(768\) | −0.707107 | + | 0.707107i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 10.6748 | 0.384944 | 0.192472 | − | 0.981302i | \(-0.438350\pi\) | ||||
0.192472 | + | 0.981302i | \(0.438350\pi\) | |||||||
\(770\) | −19.0734 | + | 3.44195i | −0.687356 | + | 0.124039i | ||||
\(771\) | −15.8915 | −0.572317 | ||||||||
\(772\) | 1.12895 | + | 1.12895i | 0.0406317 | + | 0.0406317i | ||||
\(773\) | −7.08827 | − | 7.08827i | −0.254947 | − | 0.254947i | 0.568048 | − | 0.822995i | \(-0.307699\pi\) |
−0.822995 | + | 0.568048i | \(0.807699\pi\) | |||||||
\(774\) | 2.42620 | 0.0872080 | ||||||||
\(775\) | 18.5654 | − | 6.92614i | 0.666890 | − | 0.248794i | ||||
\(776\) | − | 3.08689i | − | 0.110813i | ||||||
\(777\) | −10.8470 | − | 10.8470i | −0.389134 | − | 0.389134i | ||||
\(778\) | −13.1354 | − | 13.1354i | −0.470927 | − | 0.470927i | ||||
\(779\) | 4.97257 | 0.178161 | ||||||||
\(780\) | 2.54485 | + | 14.1021i | 0.0911203 | + | 0.504937i | ||||
\(781\) | 22.7451i | 0.813883i | ||||||||
\(782\) | 5.80330 | + | 26.7331i | 0.207526 | + | 0.955974i | ||||
\(783\) | 3.31499 | − | 3.31499i | 0.118468 | − | 0.118468i | ||||
\(784\) | − | 1.43304i | − | 0.0511801i | ||||||
\(785\) | −12.0708 | − | 8.38026i | −0.430827 | − | 0.299104i | ||||
\(786\) | −7.96128 | −0.283969 | ||||||||
\(787\) | 27.3724 | − | 27.3724i | 0.975719 | − | 0.975719i | −0.0239928 | − | 0.999712i | \(-0.507638\pi\) |
0.999712 | + | 0.0239928i | \(0.00763787\pi\) | |||||||
\(788\) | 14.7323 | − | 14.7323i | 0.524817 | − | 0.524817i | ||||
\(789\) | −20.7272 | −0.737909 | ||||||||
\(790\) | −14.8664 | + | 21.4134i | −0.528923 | + | 0.761856i | ||||
\(791\) | −41.6848 | −1.48214 | ||||||||
\(792\) | −2.59763 | + | 2.59763i | −0.0923027 | + | 0.0923027i | ||||
\(793\) | 14.2908 | + | 14.2908i | 0.507481 | + | 0.507481i | ||||
\(794\) | − | 14.3965i | − | 0.510914i | ||||||
\(795\) | 3.33269 | + | 18.4679i | 0.118198 | + | 0.654988i | ||||
\(796\) | − | 16.9393i | − | 0.600399i | ||||||
\(797\) | −5.88390 | + | 5.88390i | −0.208418 | + | 0.208418i | −0.803595 | − | 0.595177i | \(-0.797082\pi\) |
0.595177 | + | 0.803595i | \(0.297082\pi\) | |||||||
\(798\) | −1.31189 | + | 1.31189i | −0.0464405 | + | 0.0464405i | ||||
\(799\) | −46.0764 | −1.63006 | ||||||||
\(800\) | 4.54832 | + | 2.07673i | 0.160807 | + | 0.0734236i | ||||
\(801\) | − | 16.1572i | − | 0.570886i | ||||||
\(802\) | 18.6333 | − | 18.6333i | 0.657964 | − | 0.657964i | ||||
\(803\) | 20.6642 | + | 20.6642i | 0.729223 | + | 0.729223i | ||||
\(804\) | −4.63977 | −0.163632 | ||||||||
\(805\) | −9.69197 | + | 23.3723i | −0.341597 | + | 0.823766i | ||||
\(806\) | 25.3974 | 0.894585 | ||||||||
\(807\) | −20.5651 | − | 20.5651i | −0.723925 | − | 0.723925i | ||||
\(808\) | −12.6912 | + | 12.6912i | −0.446475 | + | 0.446475i | ||||
\(809\) | − | 38.4367i | − | 1.35136i | −0.737194 | − | 0.675681i | \(-0.763850\pi\) | ||
0.737194 | − | 0.675681i | \(-0.236150\pi\) | |||||||
\(810\) | 1.27521 | − | 1.83680i | 0.0448063 | − | 0.0645386i | ||||
\(811\) | 28.6160 | 1.00485 | 0.502423 | − | 0.864622i | \(-0.332442\pi\) | ||||
0.502423 | + | 0.864622i | \(0.332442\pi\) | |||||||
\(812\) | 7.82152 | − | 7.82152i | 0.274482 | − | 0.274482i | ||||
\(813\) | 9.49535 | − | 9.49535i | 0.333016 | − | 0.333016i | ||||
\(814\) | − | 23.8841i | − | 0.837136i | ||||||
\(815\) | −28.7376 | − | 19.9513i | −1.00664 | − | 0.698863i | ||||
\(816\) | − | 5.70407i | − | 0.199682i | ||||||
\(817\) | 1.34901 | + | 1.34901i | 0.0471960 | + | 0.0471960i | ||||
\(818\) | −6.83248 | + | 6.83248i | −0.238892 | + | 0.238892i | ||||
\(819\) | 15.1205 | 0.528354 | ||||||||
\(820\) | −13.9156 | + | 2.51120i | −0.485955 | + | 0.0876948i | ||||
\(821\) | −1.99566 | −0.0696491 | −0.0348245 | − | 0.999393i | \(-0.511087\pi\) | ||||
−0.0348245 | + | 0.999393i | \(0.511087\pi\) | |||||||
\(822\) | −9.80005 | + | 9.80005i | −0.341816 | + | 0.341816i | ||||
\(823\) | −22.5450 | + | 22.5450i | −0.785868 | + | 0.785868i | −0.980814 | − | 0.194946i | \(-0.937547\pi\) |
0.194946 | + | 0.980814i | \(0.437547\pi\) | |||||||
\(824\) | −5.34112 | −0.186067 | ||||||||
\(825\) | 16.7087 | + | 7.62909i | 0.581722 | + | 0.265611i | ||||
\(826\) | 31.1835i | 1.08501i | ||||||||
\(827\) | −7.70100 | + | 7.70100i | −0.267790 | + | 0.267790i | −0.828209 | − | 0.560419i | \(-0.810640\pi\) |
0.560419 | + | 0.828209i | \(0.310640\pi\) | |||||||
\(828\) | 1.01740 | + | 4.68667i | 0.0353570 | + | 0.162873i | ||||
\(829\) | − | 7.15906i | − | 0.248644i | −0.992242 | − | 0.124322i | \(-0.960324\pi\) | ||
0.992242 | − | 0.124322i | \(-0.0396756\pi\) | |||||||
\(830\) | −15.7171 | + | 2.83630i | −0.545550 | + | 0.0984493i | ||||
\(831\) | 7.35681 | 0.255205 | ||||||||
\(832\) | 4.53151 | + | 4.53151i | 0.157102 | + | 0.157102i | ||||
\(833\) | 5.78002 | + | 5.78002i | 0.200266 | + | 0.200266i | ||||
\(834\) | − | 17.2801i | − | 0.598359i | ||||||
\(835\) | −11.3196 | + | 16.3047i | −0.391732 | + | 0.564247i | ||||
\(836\) | −2.88866 | −0.0999065 | ||||||||
\(837\) | −2.80231 | − | 2.80231i | −0.0968619 | − | 0.0968619i | ||||
\(838\) | 4.31495 | + | 4.31495i | 0.149057 | + | 0.149057i | ||||
\(839\) | −23.3383 | −0.805727 | −0.402864 | − | 0.915260i | \(-0.631985\pi\) | ||||
−0.402864 | + | 0.915260i | \(0.631985\pi\) | |||||||
\(840\) | 3.00878 | − | 4.33382i | 0.103813 | − | 0.149531i | ||||
\(841\) | 7.02166 | 0.242126 | ||||||||
\(842\) | 25.4601 | − | 25.4601i | 0.877413 | − | 0.877413i | ||||
\(843\) | 9.07329 | + | 9.07329i | 0.312501 | + | 0.312501i | ||||
\(844\) | 1.79018i | 0.0616206i | ||||||||
\(845\) | 61.7670 | − | 11.1464i | 2.12485 | − | 0.383448i | ||||
\(846\) | −8.07780 | −0.277721 | ||||||||
\(847\) | −4.16318 | + | 4.16318i | −0.143049 | + | 0.143049i | ||||
\(848\) | 5.93438 | + | 5.93438i | 0.203787 | + | 0.203787i | ||||
\(849\) | 21.3303 | 0.732055 | ||||||||
\(850\) | −26.7214 | + | 9.96885i | −0.916536 | + | 0.341929i | ||||
\(851\) | −26.2232 | − | 16.8687i | −0.898921 | − | 0.578252i | ||||
\(852\) | −4.37805 | − | 4.37805i | −0.149989 | − | 0.149989i | ||||
\(853\) | 8.37110 | − | 8.37110i | 0.286621 | − | 0.286621i | −0.549122 | − | 0.835743i | \(-0.685038\pi\) |
0.835743 | + | 0.549122i | \(0.185038\pi\) | |||||||
\(854\) | − | 7.44084i | − | 0.254620i | ||||||
\(855\) | 1.73034 | − | 0.312255i | 0.0591763 | − | 0.0106789i | ||||
\(856\) | 4.02249i | 0.137486i | ||||||||
\(857\) | −13.0178 | − | 13.0178i | −0.444680 | − | 0.444680i | 0.448901 | − | 0.893581i | \(-0.351816\pi\) |
−0.893581 | + | 0.448901i | \(0.851816\pi\) | |||||||
\(858\) | 16.6470 | + | 16.6470i | 0.568318 | + | 0.568318i | ||||
\(859\) | 37.9996i | 1.29653i | 0.761415 | + | 0.648264i | \(0.224505\pi\) | ||||
−0.761415 | + | 0.648264i | \(0.775495\pi\) | |||||||
\(860\) | −4.45645 | − | 3.09392i | −0.151964 | − | 0.105502i | ||||
\(861\) | 14.9206i | 0.508492i | ||||||||
\(862\) | −13.4002 | + | 13.4002i | −0.456411 | + | 0.456411i | ||||
\(863\) | 33.0016 | − | 33.0016i | 1.12339 | − | 1.12339i | 0.132159 | − | 0.991229i | \(-0.457809\pi\) |
0.991229 | − | 0.132159i | \(-0.0421910\pi\) | |||||||
\(864\) | − | 1.00000i | − | 0.0340207i | ||||||
\(865\) | 9.18020 | + | 6.37342i | 0.312136 | + | 0.216703i | ||||
\(866\) | − | 9.37691i | − | 0.318641i | ||||||
\(867\) | 10.9859 | + | 10.9859i | 0.373101 | + | 0.373101i | ||||
\(868\) | −6.61188 | − | 6.61188i | −0.224422 | − | 0.224422i | ||||
\(869\) | 42.8269i | 1.45280i | ||||||||
\(870\) | −10.3163 | + | 1.86167i | −0.349755 | + | 0.0631164i | ||||
\(871\) | 29.7341i | 1.00750i | ||||||||
\(872\) | −4.78039 | + | 4.78039i | −0.161884 | + | 0.161884i | ||||
\(873\) | 2.18276 | + | 2.18276i | 0.0738752 | + | 0.0738752i | ||||
\(874\) | −2.04019 | + | 3.17157i | −0.0690104 | + | 0.107280i | ||||
\(875\) | −25.5607 | − | 6.52089i | −0.864108 | − | 0.220446i | ||||
\(876\) | −7.95502 | −0.268775 | ||||||||
\(877\) | 21.6889 | + | 21.6889i | 0.732381 | + | 0.732381i | 0.971091 | − | 0.238710i | \(-0.0767244\pi\) |
−0.238710 | + | 0.971091i | \(0.576724\pi\) | |||||||
\(878\) | 9.55631 | − | 9.55631i | 0.322510 | − | 0.322510i | ||||
\(879\) | −15.2601 | −0.514709 | ||||||||
\(880\) | 8.08385 | − | 1.45880i | 0.272507 | − | 0.0491762i | ||||
\(881\) | − | 15.1907i | − | 0.511787i | −0.966705 | − | 0.255893i | \(-0.917630\pi\) | ||
0.966705 | − | 0.255893i | \(-0.0823696\pi\) | |||||||
\(882\) | 1.01331 | + | 1.01331i | 0.0341201 | + | 0.0341201i | ||||
\(883\) | −6.02330 | + | 6.02330i | −0.202700 | + | 0.202700i | −0.801156 | − | 0.598456i | \(-0.795781\pi\) |
0.598456 | + | 0.801156i | \(0.295781\pi\) | |||||||
\(884\) | −36.5547 | −1.22947 | ||||||||
\(885\) | 16.8538 | − | 24.2761i | 0.566535 | − | 0.816031i | ||||
\(886\) | −0.497674 | −0.0167197 | ||||||||
\(887\) | −26.0842 | − | 26.0842i | −0.875823 | − | 0.875823i | 0.117276 | − | 0.993099i | \(-0.462584\pi\) |
−0.993099 | + | 0.117276i | \(0.962584\pi\) | |||||||
\(888\) | 4.59728 | + | 4.59728i | 0.154275 | + | 0.154275i | ||||
\(889\) | −4.25920 | −0.142849 | ||||||||
\(890\) | −20.6038 | + | 29.6775i | −0.690641 | + | 0.994793i | ||||
\(891\) | − | 3.67360i | − | 0.123070i | ||||||
\(892\) | −5.34860 | − | 5.34860i | −0.179084 | − | 0.179084i | ||||
\(893\) | −4.49141 | − | 4.49141i | −0.150299 | − | 0.150299i | ||||
\(894\) | −6.63038 | −0.221753 | ||||||||
\(895\) | 20.1732 | − | 3.64043i | 0.674316 | − | 0.121686i | ||||
\(896\) | − | 2.35944i | − | 0.0788234i | ||||||
\(897\) | 30.0347 | − | 6.52001i | 1.00283 | − | 0.217697i | ||||
\(898\) | −11.3708 | + | 11.3708i | −0.379450 | + | 0.379450i | ||||
\(899\) | 18.5793i | 0.619653i | ||||||||
\(900\) | −4.68462 | + | 1.74767i | −0.156154 | + | 0.0582558i | ||||
\(901\) | −47.8713 | −1.59482 | ||||||||
\(902\) | −16.4268 | + | 16.4268i | −0.546953 | + | 0.546953i | ||||
\(903\) | −4.04781 | + | 4.04781i | −0.134703 | + | 0.134703i | ||||
\(904\) | 17.6672 | 0.587604 | ||||||||
\(905\) | 45.3001 | − | 8.17480i | 1.50583 | − | 0.271740i | ||||
\(906\) | 5.31700 | 0.176645 | ||||||||
\(907\) | 34.1419 | − | 34.1419i | 1.13366 | − | 1.13366i | 0.144101 | − | 0.989563i | \(-0.453971\pi\) |
0.989563 | − | 0.144101i | \(-0.0460292\pi\) | |||||||
\(908\) | −3.63528 | − | 3.63528i | −0.120641 | − | 0.120641i | ||||
\(909\) | − | 17.9481i | − | 0.595300i | ||||||
\(910\) | −27.7734 | − | 19.2819i | −0.920680 | − | 0.639188i | ||||
\(911\) | 51.3620i | 1.70170i | 0.525408 | + | 0.850850i | \(0.323913\pi\) | ||||
−0.525408 | + | 0.850850i | \(0.676087\pi\) | |||||||
\(912\) | 0.556019 | − | 0.556019i | 0.0184116 | − | 0.0184116i | ||||
\(913\) | −18.5534 | + | 18.5534i | −0.614029 | + | 0.614029i | ||||
\(914\) | −23.3120 | −0.771092 | ||||||||
\(915\) | −4.02157 | + | 5.79262i | −0.132949 | + | 0.191498i | ||||
\(916\) | 19.7330i | 0.651995i | ||||||||
\(917\) | 13.2824 | − | 13.2824i | 0.438624 | − | 0.438624i | ||||
\(918\) | 4.03339 | + | 4.03339i | 0.133122 | + | 0.133122i | ||||
\(919\) | −32.8817 | −1.08467 | −0.542334 | − | 0.840163i | \(-0.682459\pi\) | ||||
−0.542334 | + | 0.840163i | \(0.682459\pi\) | |||||||
\(920\) | 4.10774 | − | 9.90588i | 0.135428 | − | 0.326587i | ||||
\(921\) | 19.2728 | 0.635060 | ||||||||
\(922\) | −13.4410 | − | 13.4410i | −0.442657 | − | 0.442657i | ||||
\(923\) | −28.0568 | + | 28.0568i | −0.923502 | + | 0.923502i | ||||
\(924\) | − | 8.66764i | − | 0.285144i | ||||||
\(925\) | 13.5020 | − | 29.5711i | 0.443942 | − | 0.972291i | ||||
\(926\) | −7.80265 | −0.256411 | ||||||||
\(927\) | 3.77675 | − | 3.77675i | 0.124045 | − | 0.124045i | ||||
\(928\) | −3.31499 | + | 3.31499i | −0.108820 | + | 0.108820i | ||||
\(929\) | 5.45556i | 0.178991i | 0.995987 | + | 0.0894956i | \(0.0285255\pi\) | ||||
−0.995987 | + | 0.0894956i | \(0.971475\pi\) | |||||||
\(930\) | 1.57375 | + | 8.72082i | 0.0516052 | + | 0.285967i | ||||
\(931\) | 1.12684i | 0.0369308i | ||||||||
\(932\) | 11.0336 | + | 11.0336i | 0.361417 | + | 0.361417i | ||||
\(933\) | 12.3873 | − | 12.3873i | 0.405543 | − | 0.405543i | ||||
\(934\) | 11.2637 | 0.368560 | ||||||||
\(935\) | −26.7214 | + | 38.4892i | −0.873883 | + | 1.25873i | ||||
\(936\) | −6.40853 | −0.209469 | ||||||||
\(937\) | −21.1697 | + | 21.1697i | −0.691585 | + | 0.691585i | −0.962581 | − | 0.270996i | \(-0.912647\pi\) |
0.270996 | + | 0.962581i | \(0.412647\pi\) | |||||||
\(938\) | 7.74089 | − | 7.74089i | 0.252749 | − | 0.252749i | ||||
\(939\) | −20.0715 | −0.655009 | ||||||||
\(940\) | 14.8373 | + | 10.3009i | 0.483940 | + | 0.335978i | ||||
\(941\) | 36.5837i | 1.19259i | 0.802764 | + | 0.596297i | \(0.203362\pi\) | ||||
−0.802764 | + | 0.596297i | \(0.796638\pi\) | |||||||
\(942\) | 4.64687 | − | 4.64687i | 0.151403 | − | 0.151403i | ||||
\(943\) | 6.43379 | + | 29.6375i | 0.209513 | + | 0.965129i | ||||
\(944\) | − | 13.2165i | − | 0.430160i | ||||||
\(945\) | 0.936943 | + | 5.19201i | 0.0304788 | + | 0.168896i | ||||
\(946\) | −8.91289 | −0.289783 | ||||||||
\(947\) | 15.4336 | + | 15.4336i | 0.501524 | + | 0.501524i | 0.911911 | − | 0.410388i | \(-0.134607\pi\) |
−0.410388 | + | 0.911911i | \(0.634607\pi\) | |||||||
\(948\) | −8.24345 | − | 8.24345i | −0.267735 | − | 0.267735i | ||||
\(949\) | 50.9800i | 1.65488i | ||||||||
\(950\) | −3.57648 | − | 1.63300i | −0.116036 | − | 0.0529814i | ||||
\(951\) | 22.9545 | 0.744350 | ||||||||
\(952\) | 9.51653 | + | 9.51653i | 0.308433 | + | 0.308433i | ||||
\(953\) | 11.4422 | + | 11.4422i | 0.370650 | + | 0.370650i | 0.867714 | − | 0.497064i | \(-0.165589\pi\) |
−0.497064 | + | 0.867714i | \(0.665589\pi\) | |||||||
\(954\) | −8.39248 | −0.271717 | ||||||||
\(955\) | −34.0198 | + | 6.13917i | −1.10085 | + | 0.198659i | ||||
\(956\) | 29.2176 | 0.944964 | ||||||||
\(957\) | −12.1780 | + | 12.1780i | −0.393657 | + | 0.393657i | ||||
\(958\) | 14.7228 | + | 14.7228i | 0.475673 | + | 0.475673i | ||||
\(959\) | − | 32.7003i | − | 1.05595i | ||||||
\(960\) | −1.27521 | + | 1.83680i | −0.0411573 | + | 0.0592825i | ||||
\(961\) | −15.2941 | −0.493359 | ||||||||
\(962\) | 29.4618 | − | 29.4618i | 0.949887 | − | 0.949887i | ||||
\(963\) | −2.84433 | − | 2.84433i | −0.0916573 | − | 0.0916573i | ||||
\(964\) | 0.443590 | 0.0142871 | ||||||||
\(965\) | 2.93259 | + | 2.03597i | 0.0944034 | + | 0.0655402i | ||||
\(966\) | −9.51653 | − | 6.12173i | −0.306189 | − | 0.196964i | ||||
\(967\) | −36.7778 | − | 36.7778i | −1.18269 | − | 1.18269i | −0.979044 | − | 0.203651i | \(-0.934719\pi\) |
−0.203651 | − | 0.979044i | \(-0.565281\pi\) | |||||||
\(968\) | 1.76448 | − | 1.76448i | 0.0567125 | − | 0.0567125i | ||||
\(969\) | 4.48528i | 0.144088i | ||||||||
\(970\) | −1.22582 | − | 6.79277i | −0.0393586 | − | 0.218103i | ||||
\(971\) | − | 28.5026i | − | 0.914694i | −0.889288 | − | 0.457347i | \(-0.848800\pi\) | ||
0.889288 | − | 0.457347i | \(-0.151200\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 28.8296 | + | 28.8296i | 0.924236 | + | 0.924236i | ||||
\(974\) | − | 2.51052i | − | 0.0804421i | ||||||
\(975\) | 11.2000 | + | 30.0215i | 0.358688 | + | 0.961457i | ||||
\(976\) | 3.15365i | 0.100946i | ||||||||
\(977\) | −32.4577 | + | 32.4577i | −1.03841 | + | 1.03841i | −0.0391805 | + | 0.999232i | \(0.512475\pi\) |
−0.999232 | + | 0.0391805i | \(0.987525\pi\) | |||||||
\(978\) | 11.0630 | − | 11.0630i | 0.353757 | − | 0.353757i | ||||
\(979\) | 59.3550i | 1.89700i | ||||||||
\(980\) | −0.569067 | − | 3.15345i | −0.0181782 | − | 0.100733i | ||||
\(981\) | − | 6.76049i | − | 0.215846i | ||||||
\(982\) | 13.1807 | + | 13.1807i | 0.420612 | + | 0.420612i | ||||
\(983\) | 24.1997 | + | 24.1997i | 0.771850 | + | 0.771850i | 0.978430 | − | 0.206580i | \(-0.0662333\pi\) |
−0.206580 | + | 0.978430i | \(0.566233\pi\) | |||||||
\(984\) | − | 6.32378i | − | 0.201595i | ||||||
\(985\) | 26.5685 | − | 38.2690i | 0.846544 | − | 1.21935i | ||||
\(986\) | − | 26.7413i | − | 0.851616i | ||||||
\(987\) | 13.4768 | − | 13.4768i | 0.428972 | − | 0.428972i | ||||
\(988\) | −3.56326 | − | 3.56326i | −0.113363 | − | 0.113363i | ||||
\(989\) | −6.29495 | + | 9.78580i | −0.200168 | + | 0.311170i | ||||
\(990\) | −4.68462 | + | 6.74767i | −0.148887 | + | 0.214455i | ||||
\(991\) | −58.8787 | −1.87034 | −0.935171 | − | 0.354196i | \(-0.884755\pi\) | ||||
−0.935171 | + | 0.354196i | \(0.884755\pi\) | |||||||
\(992\) | 2.80231 | + | 2.80231i | 0.0889734 | + | 0.0889734i | ||||
\(993\) | 2.22039 | − | 2.22039i | 0.0704620 | − | 0.0704620i | ||||
\(994\) | 14.6085 | 0.463352 | ||||||||
\(995\) | −6.72668 | − | 37.2754i | −0.213250 | − | 1.18171i | ||||
\(996\) | − | 7.14245i | − | 0.226317i | ||||||
\(997\) | −10.0163 | − | 10.0163i | −0.317219 | − | 0.317219i | 0.530479 | − | 0.847698i | \(-0.322012\pi\) |
−0.847698 | + | 0.530479i | \(0.822012\pi\) | |||||||
\(998\) | 12.6142 | − | 12.6142i | 0.399296 | − | 0.399296i | ||||
\(999\) | −6.50154 | −0.205700 |
(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 | 690.2.j.a.367.10 | yes | 24 | |
5.3 | odd | 4 | inner | 690.2.j.a.643.9 | yes | 24 | |
23.22 | odd | 2 | inner | 690.2.j.a.367.9 | ✓ | 24 | |
115.68 | even | 4 | inner | 690.2.j.a.643.10 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.j.a.367.9 | ✓ | 24 | 23.22 | odd | 2 | inner | |
690.2.j.a.367.10 | yes | 24 | 1.1 | even | 1 | trivial | |
690.2.j.a.643.9 | yes | 24 | 5.3 | odd | 4 | inner | |
690.2.j.a.643.10 | yes | 24 | 115.68 | even | 4 | inner |