Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1560,2,Mod(781,1560)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1560, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1560.781");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1560 = 2^{3} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1560.w (of order \(2\), degree \(1\), 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: | \(12.4566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 781.3 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1560.781 |
Dual form | 1560.2.w.d.781.4 |
$q$-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 \(\left(\mathbb{Z}/1560\mathbb{Z}\right)^\times\).
\(n\) | \(391\) | \(521\) | \(781\) | \(937\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | − | 0.366025i | 0.965926 | − | 0.258819i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.73205 | − | 1.00000i | 0.866025 | − | 0.500000i | ||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.366025 | + | 1.36603i | 0.149429 | + | 0.557678i | ||||
\(7\) | 4.73205 | 1.78855 | 0.894274 | − | 0.447521i | \(-0.147693\pi\) | ||||
0.894274 | + | 0.447521i | \(0.147693\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.366025 | − | 1.36603i | −0.115747 | − | 0.431975i | ||||
\(11\) | − | 4.73205i | − | 1.42677i | −0.700774 | − | 0.713384i | \(-0.747162\pi\) | ||
0.700774 | − | 0.713384i | \(-0.252838\pi\) | |||||||
\(12\) | 1.00000 | + | 1.73205i | 0.288675 | + | 0.500000i | ||||
\(13\) | − | 1.00000i | − | 0.277350i | ||||||
\(14\) | 6.46410 | − | 1.73205i | 1.72760 | − | 0.462910i | ||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 2.00000 | − | 3.46410i | 0.500000 | − | 0.866025i | ||||
\(17\) | −4.00000 | −0.970143 | −0.485071 | − | 0.874475i | \(-0.661206\pi\) | ||||
−0.485071 | + | 0.874475i | \(0.661206\pi\) | |||||||
\(18\) | −1.36603 | + | 0.366025i | −0.321975 | + | 0.0862730i | ||||
\(19\) | − | 0.732051i | − | 0.167944i | −0.996468 | − | 0.0839720i | \(-0.973239\pi\) | ||
0.996468 | − | 0.0839720i | \(-0.0267606\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 4.73205i | 1.03262i | ||||||||
\(22\) | −1.73205 | − | 6.46410i | −0.369274 | − | 1.37815i | ||||
\(23\) | −2.00000 | −0.417029 | −0.208514 | − | 0.978019i | \(-0.566863\pi\) | ||||
−0.208514 | + | 0.978019i | \(0.566863\pi\) | |||||||
\(24\) | 2.00000 | + | 2.00000i | 0.408248 | + | 0.408248i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | −0.366025 | − | 1.36603i | −0.0717835 | − | 0.267900i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 8.19615 | − | 4.73205i | 1.54893 | − | 0.894274i | ||||
\(29\) | 4.92820i | 0.915144i | 0.889172 | + | 0.457572i | \(0.151281\pi\) | ||||
−0.889172 | + | 0.457572i | \(0.848719\pi\) | |||||||
\(30\) | 1.36603 | − | 0.366025i | 0.249401 | − | 0.0668268i | ||||
\(31\) | 0.196152 | 0.0352300 | 0.0176150 | − | 0.999845i | \(-0.494393\pi\) | ||||
0.0176150 | + | 0.999845i | \(0.494393\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | 4.73205 | 0.823744 | ||||||||
\(34\) | −5.46410 | + | 1.46410i | −0.937086 | + | 0.251091i | ||||
\(35\) | − | 4.73205i | − | 0.799863i | ||||||
\(36\) | −1.73205 | + | 1.00000i | −0.288675 | + | 0.166667i | ||||
\(37\) | − | 0.535898i | − | 0.0881012i | −0.999029 | − | 0.0440506i | \(-0.985974\pi\) | ||
0.999029 | − | 0.0440506i | \(-0.0140263\pi\) | |||||||
\(38\) | −0.267949 | − | 1.00000i | −0.0434671 | − | 0.162221i | ||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | −2.00000 | − | 2.00000i | −0.316228 | − | 0.316228i | ||||
\(41\) | −4.92820 | −0.769656 | −0.384828 | − | 0.922988i | \(-0.625739\pi\) | ||||
−0.384828 | + | 0.922988i | \(0.625739\pi\) | |||||||
\(42\) | 1.73205 | + | 6.46410i | 0.267261 | + | 0.997433i | ||||
\(43\) | 1.46410i | 0.223273i | 0.993749 | + | 0.111637i | \(0.0356093\pi\) | ||||
−0.993749 | + | 0.111637i | \(0.964391\pi\) | |||||||
\(44\) | −4.73205 | − | 8.19615i | −0.713384 | − | 1.23562i | ||||
\(45\) | 1.00000i | 0.149071i | ||||||||
\(46\) | −2.73205 | + | 0.732051i | −0.402819 | + | 0.107935i | ||||
\(47\) | −8.73205 | −1.27370 | −0.636850 | − | 0.770988i | \(-0.719763\pi\) | ||||
−0.636850 | + | 0.770988i | \(0.719763\pi\) | |||||||
\(48\) | 3.46410 | + | 2.00000i | 0.500000 | + | 0.288675i | ||||
\(49\) | 15.3923 | 2.19890 | ||||||||
\(50\) | −1.36603 | + | 0.366025i | −0.193185 | + | 0.0517638i | ||||
\(51\) | − | 4.00000i | − | 0.560112i | ||||||
\(52\) | −1.00000 | − | 1.73205i | −0.138675 | − | 0.240192i | ||||
\(53\) | 12.3923i | 1.70221i | 0.524992 | + | 0.851107i | \(0.324068\pi\) | ||||
−0.524992 | + | 0.851107i | \(0.675932\pi\) | |||||||
\(54\) | −0.366025 | − | 1.36603i | −0.0498097 | − | 0.185893i | ||||
\(55\) | −4.73205 | −0.638070 | ||||||||
\(56\) | 9.46410 | − | 9.46410i | 1.26469 | − | 1.26469i | ||||
\(57\) | 0.732051 | 0.0969625 | ||||||||
\(58\) | 1.80385 | + | 6.73205i | 0.236857 | + | 0.883962i | ||||
\(59\) | 7.66025i | 0.997280i | 0.866809 | + | 0.498640i | \(0.166167\pi\) | ||||
−0.866809 | + | 0.498640i | \(0.833833\pi\) | |||||||
\(60\) | 1.73205 | − | 1.00000i | 0.223607 | − | 0.129099i | ||||
\(61\) | − | 2.92820i | − | 0.374918i | −0.982272 | − | 0.187459i | \(-0.939975\pi\) | ||
0.982272 | − | 0.187459i | \(-0.0600252\pi\) | |||||||
\(62\) | 0.267949 | − | 0.0717968i | 0.0340296 | − | 0.00911820i | ||||
\(63\) | −4.73205 | −0.596182 | ||||||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | 6.46410 | − | 1.73205i | 0.795676 | − | 0.213201i | ||||
\(67\) | 12.1962i | 1.49000i | 0.667066 | + | 0.744999i | \(0.267550\pi\) | ||||
−0.667066 | + | 0.744999i | \(0.732450\pi\) | |||||||
\(68\) | −6.92820 | + | 4.00000i | −0.840168 | + | 0.485071i | ||||
\(69\) | − | 2.00000i | − | 0.240772i | ||||||
\(70\) | −1.73205 | − | 6.46410i | −0.207020 | − | 0.772608i | ||||
\(71\) | 13.2679 | 1.57462 | 0.787308 | − | 0.616560i | \(-0.211474\pi\) | ||||
0.787308 | + | 0.616560i | \(0.211474\pi\) | |||||||
\(72\) | −2.00000 | + | 2.00000i | −0.235702 | + | 0.235702i | ||||
\(73\) | 15.8564 | 1.85585 | 0.927926 | − | 0.372764i | \(-0.121590\pi\) | ||||
0.927926 | + | 0.372764i | \(0.121590\pi\) | |||||||
\(74\) | −0.196152 | − | 0.732051i | −0.0228023 | − | 0.0850992i | ||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | −0.732051 | − | 1.26795i | −0.0839720 | − | 0.145444i | ||||
\(77\) | − | 22.3923i | − | 2.55184i | ||||||
\(78\) | 1.36603 | − | 0.366025i | 0.154672 | − | 0.0414442i | ||||
\(79\) | 17.4641 | 1.96486 | 0.982432 | − | 0.186618i | \(-0.0597528\pi\) | ||||
0.982432 | + | 0.186618i | \(0.0597528\pi\) | |||||||
\(80\) | −3.46410 | − | 2.00000i | −0.387298 | − | 0.223607i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.73205 | + | 1.80385i | −0.743431 | + | 0.199202i | ||||
\(83\) | 5.26795i | 0.578233i | 0.957294 | + | 0.289116i | \(0.0933614\pi\) | ||||
−0.957294 | + | 0.289116i | \(0.906639\pi\) | |||||||
\(84\) | 4.73205 | + | 8.19615i | 0.516309 | + | 0.894274i | ||||
\(85\) | 4.00000i | 0.433861i | ||||||||
\(86\) | 0.535898 | + | 2.00000i | 0.0577874 | + | 0.215666i | ||||
\(87\) | −4.92820 | −0.528359 | ||||||||
\(88\) | −9.46410 | − | 9.46410i | −1.00888 | − | 1.00888i | ||||
\(89\) | 0.928203 | 0.0983893 | 0.0491947 | − | 0.998789i | \(-0.484335\pi\) | ||||
0.0491947 | + | 0.998789i | \(0.484335\pi\) | |||||||
\(90\) | 0.366025 | + | 1.36603i | 0.0385825 | + | 0.143992i | ||||
\(91\) | − | 4.73205i | − | 0.496054i | ||||||
\(92\) | −3.46410 | + | 2.00000i | −0.361158 | + | 0.208514i | ||||
\(93\) | 0.196152i | 0.0203401i | ||||||||
\(94\) | −11.9282 | + | 3.19615i | −1.23030 | + | 0.329658i | ||||
\(95\) | −0.732051 | −0.0751068 | ||||||||
\(96\) | 5.46410 | + | 1.46410i | 0.557678 | + | 0.149429i | ||||
\(97\) | −0.535898 | −0.0544122 | −0.0272061 | − | 0.999630i | \(-0.508661\pi\) | ||||
−0.0272061 | + | 0.999630i | \(0.508661\pi\) | |||||||
\(98\) | 21.0263 | − | 5.63397i | 2.12397 | − | 0.569117i | ||||
\(99\) | 4.73205i | 0.475589i | ||||||||
\(100\) | −1.73205 | + | 1.00000i | −0.173205 | + | 0.100000i | ||||
\(101\) | − | 12.0000i | − | 1.19404i | −0.802225 | − | 0.597022i | \(-0.796350\pi\) | ||
0.802225 | − | 0.597022i | \(-0.203650\pi\) | |||||||
\(102\) | −1.46410 | − | 5.46410i | −0.144968 | − | 0.541027i | ||||
\(103\) | −12.9282 | −1.27385 | −0.636927 | − | 0.770924i | \(-0.719795\pi\) | ||||
−0.636927 | + | 0.770924i | \(0.719795\pi\) | |||||||
\(104\) | −2.00000 | − | 2.00000i | −0.196116 | − | 0.196116i | ||||
\(105\) | 4.73205 | 0.461801 | ||||||||
\(106\) | 4.53590 | + | 16.9282i | 0.440565 | + | 1.64421i | ||||
\(107\) | − | 4.00000i | − | 0.386695i | −0.981130 | − | 0.193347i | \(-0.938066\pi\) | ||
0.981130 | − | 0.193347i | \(-0.0619344\pi\) | |||||||
\(108\) | −1.00000 | − | 1.73205i | −0.0962250 | − | 0.166667i | ||||
\(109\) | 15.8564i | 1.51877i | 0.650643 | + | 0.759384i | \(0.274500\pi\) | ||||
−0.650643 | + | 0.759384i | \(0.725500\pi\) | |||||||
\(110\) | −6.46410 | + | 1.73205i | −0.616328 | + | 0.165145i | ||||
\(111\) | 0.535898 | 0.0508652 | ||||||||
\(112\) | 9.46410 | − | 16.3923i | 0.894274 | − | 1.54893i | ||||
\(113\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(114\) | 1.00000 | − | 0.267949i | 0.0936586 | − | 0.0250957i | ||||
\(115\) | 2.00000i | 0.186501i | ||||||||
\(116\) | 4.92820 | + | 8.53590i | 0.457572 | + | 0.792538i | ||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 2.80385 | + | 10.4641i | 0.258115 | + | 0.963299i | ||||
\(119\) | −18.9282 | −1.73515 | ||||||||
\(120\) | 2.00000 | − | 2.00000i | 0.182574 | − | 0.182574i | ||||
\(121\) | −11.3923 | −1.03566 | ||||||||
\(122\) | −1.07180 | − | 4.00000i | −0.0970359 | − | 0.362143i | ||||
\(123\) | − | 4.92820i | − | 0.444361i | ||||||
\(124\) | 0.339746 | − | 0.196152i | 0.0305101 | − | 0.0176150i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −6.46410 | + | 1.73205i | −0.575868 | + | 0.154303i | ||||
\(127\) | −16.9282 | −1.50214 | −0.751068 | − | 0.660225i | \(-0.770461\pi\) | ||||
−0.751068 | + | 0.660225i | \(0.770461\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | −1.46410 | −0.128907 | ||||||||
\(130\) | −1.36603 | + | 0.366025i | −0.119808 | + | 0.0321026i | ||||
\(131\) | 7.85641i | 0.686417i | 0.939259 | + | 0.343209i | \(0.111514\pi\) | ||||
−0.939259 | + | 0.343209i | \(0.888486\pi\) | |||||||
\(132\) | 8.19615 | − | 4.73205i | 0.713384 | − | 0.411872i | ||||
\(133\) | − | 3.46410i | − | 0.300376i | ||||||
\(134\) | 4.46410 | + | 16.6603i | 0.385640 | + | 1.43923i | ||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −8.00000 | + | 8.00000i | −0.685994 | + | 0.685994i | ||||
\(137\) | 10.3923 | 0.887875 | 0.443937 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443937 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(138\) | −0.732051 | − | 2.73205i | −0.0623163 | − | 0.232568i | ||||
\(139\) | − | 2.00000i | − | 0.169638i | −0.996396 | − | 0.0848189i | \(-0.972969\pi\) | ||
0.996396 | − | 0.0848189i | \(-0.0270312\pi\) | |||||||
\(140\) | −4.73205 | − | 8.19615i | −0.399931 | − | 0.692701i | ||||
\(141\) | − | 8.73205i | − | 0.735371i | ||||||
\(142\) | 18.1244 | − | 4.85641i | 1.52096 | − | 0.407541i | ||||
\(143\) | −4.73205 | −0.395714 | ||||||||
\(144\) | −2.00000 | + | 3.46410i | −0.166667 | + | 0.288675i | ||||
\(145\) | 4.92820 | 0.409265 | ||||||||
\(146\) | 21.6603 | − | 5.80385i | 1.79262 | − | 0.480330i | ||||
\(147\) | 15.3923i | 1.26954i | ||||||||
\(148\) | −0.535898 | − | 0.928203i | −0.0440506 | − | 0.0762978i | ||||
\(149\) | − | 3.46410i | − | 0.283790i | −0.989882 | − | 0.141895i | \(-0.954680\pi\) | ||
0.989882 | − | 0.141895i | \(-0.0453196\pi\) | |||||||
\(150\) | −0.366025 | − | 1.36603i | −0.0298858 | − | 0.111536i | ||||
\(151\) | 18.7321 | 1.52439 | 0.762196 | − | 0.647346i | \(-0.224121\pi\) | ||||
0.762196 | + | 0.647346i | \(0.224121\pi\) | |||||||
\(152\) | −1.46410 | − | 1.46410i | −0.118754 | − | 0.118754i | ||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | −8.19615 | − | 30.5885i | −0.660465 | − | 2.46489i | ||||
\(155\) | − | 0.196152i | − | 0.0157553i | ||||||
\(156\) | 1.73205 | − | 1.00000i | 0.138675 | − | 0.0800641i | ||||
\(157\) | − | 22.7846i | − | 1.81841i | −0.416349 | − | 0.909205i | \(-0.636691\pi\) | ||
0.416349 | − | 0.909205i | \(-0.363309\pi\) | |||||||
\(158\) | 23.8564 | − | 6.39230i | 1.89791 | − | 0.508544i | ||||
\(159\) | −12.3923 | −0.982774 | ||||||||
\(160\) | −5.46410 | − | 1.46410i | −0.431975 | − | 0.115747i | ||||
\(161\) | −9.46410 | −0.745876 | ||||||||
\(162\) | 1.36603 | − | 0.366025i | 0.107325 | − | 0.0287577i | ||||
\(163\) | 20.1962i | 1.58188i | 0.611891 | + | 0.790942i | \(0.290409\pi\) | ||||
−0.611891 | + | 0.790942i | \(0.709591\pi\) | |||||||
\(164\) | −8.53590 | + | 4.92820i | −0.666542 | + | 0.384828i | ||||
\(165\) | − | 4.73205i | − | 0.368390i | ||||||
\(166\) | 1.92820 | + | 7.19615i | 0.149658 | + | 0.558530i | ||||
\(167\) | 9.80385 | 0.758645 | 0.379322 | − | 0.925265i | \(-0.376157\pi\) | ||||
0.379322 | + | 0.925265i | \(0.376157\pi\) | |||||||
\(168\) | 9.46410 | + | 9.46410i | 0.730171 | + | 0.730171i | ||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 1.46410 | + | 5.46410i | 0.112291 | + | 0.419077i | ||||
\(171\) | 0.732051i | 0.0559813i | ||||||||
\(172\) | 1.46410 | + | 2.53590i | 0.111637 | + | 0.193360i | ||||
\(173\) | 9.46410i | 0.719542i | 0.933041 | + | 0.359771i | \(0.117145\pi\) | ||||
−0.933041 | + | 0.359771i | \(0.882855\pi\) | |||||||
\(174\) | −6.73205 | + | 1.80385i | −0.510355 | + | 0.136749i | ||||
\(175\) | −4.73205 | −0.357709 | ||||||||
\(176\) | −16.3923 | − | 9.46410i | −1.23562 | − | 0.713384i | ||||
\(177\) | −7.66025 | −0.575780 | ||||||||
\(178\) | 1.26795 | − | 0.339746i | 0.0950368 | − | 0.0254650i | ||||
\(179\) | 10.3923i | 0.776757i | 0.921500 | + | 0.388379i | \(0.126965\pi\) | ||||
−0.921500 | + | 0.388379i | \(0.873035\pi\) | |||||||
\(180\) | 1.00000 | + | 1.73205i | 0.0745356 | + | 0.129099i | ||||
\(181\) | − | 4.92820i | − | 0.366310i | −0.983084 | − | 0.183155i | \(-0.941369\pi\) | ||
0.983084 | − | 0.183155i | \(-0.0586311\pi\) | |||||||
\(182\) | −1.73205 | − | 6.46410i | −0.128388 | − | 0.479151i | ||||
\(183\) | 2.92820 | 0.216459 | ||||||||
\(184\) | −4.00000 | + | 4.00000i | −0.294884 | + | 0.294884i | ||||
\(185\) | −0.535898 | −0.0394000 | ||||||||
\(186\) | 0.0717968 | + | 0.267949i | 0.00526439 | + | 0.0196470i | ||||
\(187\) | 18.9282i | 1.38417i | ||||||||
\(188\) | −15.1244 | + | 8.73205i | −1.10306 | + | 0.636850i | ||||
\(189\) | − | 4.73205i | − | 0.344206i | ||||||
\(190\) | −1.00000 | + | 0.267949i | −0.0725476 | + | 0.0194391i | ||||
\(191\) | −16.3923 | −1.18611 | −0.593053 | − | 0.805164i | \(-0.702077\pi\) | ||||
−0.593053 | + | 0.805164i | \(0.702077\pi\) | |||||||
\(192\) | 8.00000 | 0.577350 | ||||||||
\(193\) | −3.46410 | −0.249351 | −0.124676 | − | 0.992198i | \(-0.539789\pi\) | ||||
−0.124676 | + | 0.992198i | \(0.539789\pi\) | |||||||
\(194\) | −0.732051 | + | 0.196152i | −0.0525582 | + | 0.0140829i | ||||
\(195\) | − | 1.00000i | − | 0.0716115i | ||||||
\(196\) | 26.6603 | − | 15.3923i | 1.90430 | − | 1.09945i | ||||
\(197\) | 2.39230i | 0.170445i | 0.996362 | + | 0.0852223i | \(0.0271601\pi\) | ||||
−0.996362 | + | 0.0852223i | \(0.972840\pi\) | |||||||
\(198\) | 1.73205 | + | 6.46410i | 0.123091 | + | 0.459384i | ||||
\(199\) | −9.07180 | −0.643083 | −0.321541 | − | 0.946896i | \(-0.604201\pi\) | ||||
−0.321541 | + | 0.946896i | \(0.604201\pi\) | |||||||
\(200\) | −2.00000 | + | 2.00000i | −0.141421 | + | 0.141421i | ||||
\(201\) | −12.1962 | −0.860250 | ||||||||
\(202\) | −4.39230 | − | 16.3923i | −0.309041 | − | 1.15336i | ||||
\(203\) | 23.3205i | 1.63678i | ||||||||
\(204\) | −4.00000 | − | 6.92820i | −0.280056 | − | 0.485071i | ||||
\(205\) | 4.92820i | 0.344201i | ||||||||
\(206\) | −17.6603 | + | 4.73205i | −1.23045 | + | 0.329698i | ||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | −3.46410 | − | 2.00000i | −0.240192 | − | 0.138675i | ||||
\(209\) | −3.46410 | −0.239617 | ||||||||
\(210\) | 6.46410 | − | 1.73205i | 0.446065 | − | 0.119523i | ||||
\(211\) | − | 0.928203i | − | 0.0639001i | −0.999489 | − | 0.0319501i | \(-0.989828\pi\) | ||
0.999489 | − | 0.0319501i | \(-0.0101718\pi\) | |||||||
\(212\) | 12.3923 | + | 21.4641i | 0.851107 | + | 1.47416i | ||||
\(213\) | 13.2679i | 0.909105i | ||||||||
\(214\) | −1.46410 | − | 5.46410i | −0.100084 | − | 0.373518i | ||||
\(215\) | 1.46410 | 0.0998509 | ||||||||
\(216\) | −2.00000 | − | 2.00000i | −0.136083 | − | 0.136083i | ||||
\(217\) | 0.928203 | 0.0630105 | ||||||||
\(218\) | 5.80385 | + | 21.6603i | 0.393086 | + | 1.46702i | ||||
\(219\) | 15.8564i | 1.07148i | ||||||||
\(220\) | −8.19615 | + | 4.73205i | −0.552584 | + | 0.319035i | ||||
\(221\) | 4.00000i | 0.269069i | ||||||||
\(222\) | 0.732051 | − | 0.196152i | 0.0491320 | − | 0.0131649i | ||||
\(223\) | −26.9808 | −1.80677 | −0.903383 | − | 0.428835i | \(-0.858924\pi\) | ||||
−0.903383 | + | 0.428835i | \(0.858924\pi\) | |||||||
\(224\) | 6.92820 | − | 25.8564i | 0.462910 | − | 1.72760i | ||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.66025i | 0.375684i | 0.982199 | + | 0.187842i | \(0.0601493\pi\) | ||||
−0.982199 | + | 0.187842i | \(0.939851\pi\) | |||||||
\(228\) | 1.26795 | − | 0.732051i | 0.0839720 | − | 0.0484812i | ||||
\(229\) | − | 6.00000i | − | 0.396491i | −0.980152 | − | 0.198246i | \(-0.936476\pi\) | ||
0.980152 | − | 0.198246i | \(-0.0635244\pi\) | |||||||
\(230\) | 0.732051 | + | 2.73205i | 0.0482700 | + | 0.180146i | ||||
\(231\) | 22.3923 | 1.47331 | ||||||||
\(232\) | 9.85641 | + | 9.85641i | 0.647105 | + | 0.647105i | ||||
\(233\) | 11.8564 | 0.776739 | 0.388370 | − | 0.921504i | \(-0.373038\pi\) | ||||
0.388370 | + | 0.921504i | \(0.373038\pi\) | |||||||
\(234\) | 0.366025 | + | 1.36603i | 0.0239278 | + | 0.0892999i | ||||
\(235\) | 8.73205i | 0.569616i | ||||||||
\(236\) | 7.66025 | + | 13.2679i | 0.498640 | + | 0.863670i | ||||
\(237\) | 17.4641i | 1.13442i | ||||||||
\(238\) | −25.8564 | + | 6.92820i | −1.67602 | + | 0.449089i | ||||
\(239\) | −19.8038 | −1.28100 | −0.640502 | − | 0.767956i | \(-0.721274\pi\) | ||||
−0.640502 | + | 0.767956i | \(0.721274\pi\) | |||||||
\(240\) | 2.00000 | − | 3.46410i | 0.129099 | − | 0.223607i | ||||
\(241\) | −20.9282 | −1.34810 | −0.674052 | − | 0.738684i | \(-0.735448\pi\) | ||||
−0.674052 | + | 0.738684i | \(0.735448\pi\) | |||||||
\(242\) | −15.5622 | + | 4.16987i | −1.00037 | + | 0.268050i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −2.92820 | − | 5.07180i | −0.187459 | − | 0.324689i | ||||
\(245\) | − | 15.3923i | − | 0.983378i | ||||||
\(246\) | −1.80385 | − | 6.73205i | −0.115009 | − | 0.429220i | ||||
\(247\) | −0.732051 | −0.0465793 | ||||||||
\(248\) | 0.392305 | − | 0.392305i | 0.0249114 | − | 0.0249114i | ||||
\(249\) | −5.26795 | −0.333843 | ||||||||
\(250\) | 0.366025 | + | 1.36603i | 0.0231495 | + | 0.0863950i | ||||
\(251\) | − | 6.39230i | − | 0.403479i | −0.979439 | − | 0.201739i | \(-0.935341\pi\) | ||
0.979439 | − | 0.201739i | \(-0.0646594\pi\) | |||||||
\(252\) | −8.19615 | + | 4.73205i | −0.516309 | + | 0.298091i | ||||
\(253\) | 9.46410i | 0.595003i | ||||||||
\(254\) | −23.1244 | + | 6.19615i | −1.45095 | + | 0.388781i | ||||
\(255\) | −4.00000 | −0.250490 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −3.07180 | −0.191613 | −0.0958067 | − | 0.995400i | \(-0.530543\pi\) | ||||
−0.0958067 | + | 0.995400i | \(0.530543\pi\) | |||||||
\(258\) | −2.00000 | + | 0.535898i | −0.124515 | + | 0.0333636i | ||||
\(259\) | − | 2.53590i | − | 0.157573i | ||||||
\(260\) | −1.73205 | + | 1.00000i | −0.107417 | + | 0.0620174i | ||||
\(261\) | − | 4.92820i | − | 0.305048i | ||||||
\(262\) | 2.87564 | + | 10.7321i | 0.177658 | + | 0.663028i | ||||
\(263\) | 16.5359 | 1.01965 | 0.509824 | − | 0.860279i | \(-0.329711\pi\) | ||||
0.509824 | + | 0.860279i | \(0.329711\pi\) | |||||||
\(264\) | 9.46410 | − | 9.46410i | 0.582475 | − | 0.582475i | ||||
\(265\) | 12.3923 | 0.761253 | ||||||||
\(266\) | −1.26795 | − | 4.73205i | −0.0777430 | − | 0.290141i | ||||
\(267\) | 0.928203i | 0.0568051i | ||||||||
\(268\) | 12.1962 | + | 21.1244i | 0.744999 | + | 1.29038i | ||||
\(269\) | − | 4.14359i | − | 0.252639i | −0.991990 | − | 0.126320i | \(-0.959683\pi\) | ||
0.991990 | − | 0.126320i | \(-0.0403165\pi\) | |||||||
\(270\) | −1.36603 | + | 0.366025i | −0.0831337 | + | 0.0222756i | ||||
\(271\) | 5.66025 | 0.343836 | 0.171918 | − | 0.985111i | \(-0.445004\pi\) | ||||
0.171918 | + | 0.985111i | \(0.445004\pi\) | |||||||
\(272\) | −8.00000 | + | 13.8564i | −0.485071 | + | 0.840168i | ||||
\(273\) | 4.73205 | 0.286397 | ||||||||
\(274\) | 14.1962 | − | 3.80385i | 0.857621 | − | 0.229799i | ||||
\(275\) | 4.73205i | 0.285353i | ||||||||
\(276\) | −2.00000 | − | 3.46410i | −0.120386 | − | 0.208514i | ||||
\(277\) | 21.4641i | 1.28965i | 0.764329 | + | 0.644826i | \(0.223070\pi\) | ||||
−0.764329 | + | 0.644826i | \(0.776930\pi\) | |||||||
\(278\) | −0.732051 | − | 2.73205i | −0.0439055 | − | 0.163858i | ||||
\(279\) | −0.196152 | −0.0117433 | ||||||||
\(280\) | −9.46410 | − | 9.46410i | −0.565588 | − | 0.565588i | ||||
\(281\) | −18.3923 | −1.09719 | −0.548596 | − | 0.836087i | \(-0.684838\pi\) | ||||
−0.548596 | + | 0.836087i | \(0.684838\pi\) | |||||||
\(282\) | −3.19615 | − | 11.9282i | −0.190328 | − | 0.710314i | ||||
\(283\) | 5.46410i | 0.324807i | 0.986724 | + | 0.162404i | \(0.0519246\pi\) | ||||
−0.986724 | + | 0.162404i | \(0.948075\pi\) | |||||||
\(284\) | 22.9808 | − | 13.2679i | 1.36366 | − | 0.787308i | ||||
\(285\) | − | 0.732051i | − | 0.0433629i | ||||||
\(286\) | −6.46410 | + | 1.73205i | −0.382230 | + | 0.102418i | ||||
\(287\) | −23.3205 | −1.37657 | ||||||||
\(288\) | −1.46410 | + | 5.46410i | −0.0862730 | + | 0.321975i | ||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 6.73205 | − | 1.80385i | 0.395320 | − | 0.105926i | ||||
\(291\) | − | 0.535898i | − | 0.0314149i | ||||||
\(292\) | 27.4641 | − | 15.8564i | 1.60721 | − | 0.927926i | ||||
\(293\) | − | 22.7846i | − | 1.33109i | −0.746357 | − | 0.665546i | \(-0.768199\pi\) | ||
0.746357 | − | 0.665546i | \(-0.231801\pi\) | |||||||
\(294\) | 5.63397 | + | 21.0263i | 0.328580 | + | 1.22628i | ||||
\(295\) | 7.66025 | 0.445997 | ||||||||
\(296\) | −1.07180 | − | 1.07180i | −0.0622969 | − | 0.0622969i | ||||
\(297\) | −4.73205 | −0.274581 | ||||||||
\(298\) | −1.26795 | − | 4.73205i | −0.0734503 | − | 0.274120i | ||||
\(299\) | 2.00000i | 0.115663i | ||||||||
\(300\) | −1.00000 | − | 1.73205i | −0.0577350 | − | 0.100000i | ||||
\(301\) | 6.92820i | 0.399335i | ||||||||
\(302\) | 25.5885 | − | 6.85641i | 1.47245 | − | 0.394542i | ||||
\(303\) | 12.0000 | 0.689382 | ||||||||
\(304\) | −2.53590 | − | 1.46410i | −0.145444 | − | 0.0839720i | ||||
\(305\) | −2.92820 | −0.167668 | ||||||||
\(306\) | 5.46410 | − | 1.46410i | 0.312362 | − | 0.0836971i | ||||
\(307\) | 19.1244i | 1.09148i | 0.837953 | + | 0.545742i | \(0.183752\pi\) | ||||
−0.837953 | + | 0.545742i | \(0.816248\pi\) | |||||||
\(308\) | −22.3923 | − | 38.7846i | −1.27592 | − | 2.20996i | ||||
\(309\) | − | 12.9282i | − | 0.735460i | ||||||
\(310\) | −0.0717968 | − | 0.267949i | −0.00407778 | − | 0.0152185i | ||||
\(311\) | −31.7128 | −1.79827 | −0.899134 | − | 0.437673i | \(-0.855803\pi\) | ||||
−0.899134 | + | 0.437673i | \(0.855803\pi\) | |||||||
\(312\) | 2.00000 | − | 2.00000i | 0.113228 | − | 0.113228i | ||||
\(313\) | 8.00000 | 0.452187 | 0.226093 | − | 0.974106i | \(-0.427405\pi\) | ||||
0.226093 | + | 0.974106i | \(0.427405\pi\) | |||||||
\(314\) | −8.33975 | − | 31.1244i | −0.470639 | − | 1.75645i | ||||
\(315\) | 4.73205i | 0.266621i | ||||||||
\(316\) | 30.2487 | − | 17.4641i | 1.70162 | − | 0.982432i | ||||
\(317\) | − | 20.5359i | − | 1.15341i | −0.816952 | − | 0.576705i | \(-0.804338\pi\) | ||
0.816952 | − | 0.576705i | \(-0.195662\pi\) | |||||||
\(318\) | −16.9282 | + | 4.53590i | −0.949286 | + | 0.254361i | ||||
\(319\) | 23.3205 | 1.30570 | ||||||||
\(320\) | −8.00000 | −0.447214 | ||||||||
\(321\) | 4.00000 | 0.223258 | ||||||||
\(322\) | −12.9282 | + | 3.46410i | −0.720461 | + | 0.193047i | ||||
\(323\) | 2.92820i | 0.162930i | ||||||||
\(324\) | 1.73205 | − | 1.00000i | 0.0962250 | − | 0.0555556i | ||||
\(325\) | 1.00000i | 0.0554700i | ||||||||
\(326\) | 7.39230 | + | 27.5885i | 0.409422 | + | 1.52798i | ||||
\(327\) | −15.8564 | −0.876861 | ||||||||
\(328\) | −9.85641 | + | 9.85641i | −0.544229 | + | 0.544229i | ||||
\(329\) | −41.3205 | −2.27807 | ||||||||
\(330\) | −1.73205 | − | 6.46410i | −0.0953463 | − | 0.355837i | ||||
\(331\) | 12.0526i | 0.662469i | 0.943549 | + | 0.331234i | \(0.107465\pi\) | ||||
−0.943549 | + | 0.331234i | \(0.892535\pi\) | |||||||
\(332\) | 5.26795 | + | 9.12436i | 0.289116 | + | 0.500764i | ||||
\(333\) | 0.535898i | 0.0293671i | ||||||||
\(334\) | 13.3923 | − | 3.58846i | 0.732794 | − | 0.196352i | ||||
\(335\) | 12.1962 | 0.666347 | ||||||||
\(336\) | 16.3923 | + | 9.46410i | 0.894274 | + | 0.516309i | ||||
\(337\) | −20.0000 | −1.08947 | −0.544735 | − | 0.838608i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838608i | \(0.683370\pi\) | |||||||
\(338\) | −1.36603 | + | 0.366025i | −0.0743020 | + | 0.0199092i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.00000 | + | 6.92820i | 0.216930 | + | 0.375735i | ||||
\(341\) | − | 0.928203i | − | 0.0502650i | ||||||
\(342\) | 0.267949 | + | 1.00000i | 0.0144890 | + | 0.0540738i | ||||
\(343\) | 39.7128 | 2.14429 | ||||||||
\(344\) | 2.92820 | + | 2.92820i | 0.157878 | + | 0.157878i | ||||
\(345\) | −2.00000 | −0.107676 | ||||||||
\(346\) | 3.46410 | + | 12.9282i | 0.186231 | + | 0.695025i | ||||
\(347\) | − | 31.7128i | − | 1.70243i | −0.524815 | − | 0.851216i | \(-0.675865\pi\) | ||
0.524815 | − | 0.851216i | \(-0.324135\pi\) | |||||||
\(348\) | −8.53590 | + | 4.92820i | −0.457572 | + | 0.264179i | ||||
\(349\) | − | 34.7846i | − | 1.86198i | −0.365048 | − | 0.930989i | \(-0.618947\pi\) | ||
0.365048 | − | 0.930989i | \(-0.381053\pi\) | |||||||
\(350\) | −6.46410 | + | 1.73205i | −0.345521 | + | 0.0925820i | ||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | −25.8564 | − | 6.92820i | −1.37815 | − | 0.369274i | ||||
\(353\) | 21.7128 | 1.15566 | 0.577828 | − | 0.816158i | \(-0.303900\pi\) | ||||
0.577828 | + | 0.816158i | \(0.303900\pi\) | |||||||
\(354\) | −10.4641 | + | 2.80385i | −0.556161 | + | 0.149023i | ||||
\(355\) | − | 13.2679i | − | 0.704190i | ||||||
\(356\) | 1.60770 | − | 0.928203i | 0.0852077 | − | 0.0491947i | ||||
\(357\) | − | 18.9282i | − | 1.00179i | ||||||
\(358\) | 3.80385 | + | 14.1962i | 0.201040 | + | 0.750290i | ||||
\(359\) | 13.2679 | 0.700256 | 0.350128 | − | 0.936702i | \(-0.386138\pi\) | ||||
0.350128 | + | 0.936702i | \(0.386138\pi\) | |||||||
\(360\) | 2.00000 | + | 2.00000i | 0.105409 | + | 0.105409i | ||||
\(361\) | 18.4641 | 0.971795 | ||||||||
\(362\) | −1.80385 | − | 6.73205i | −0.0948081 | − | 0.353829i | ||||
\(363\) | − | 11.3923i | − | 0.597941i | ||||||
\(364\) | −4.73205 | − | 8.19615i | −0.248027 | − | 0.429595i | ||||
\(365\) | − | 15.8564i | − | 0.829962i | ||||||
\(366\) | 4.00000 | − | 1.07180i | 0.209083 | − | 0.0560237i | ||||
\(367\) | −0.535898 | −0.0279737 | −0.0139868 | − | 0.999902i | \(-0.504452\pi\) | ||||
−0.0139868 | + | 0.999902i | \(0.504452\pi\) | |||||||
\(368\) | −4.00000 | + | 6.92820i | −0.208514 | + | 0.361158i | ||||
\(369\) | 4.92820 | 0.256552 | ||||||||
\(370\) | −0.732051 | + | 0.196152i | −0.0380575 | + | 0.0101975i | ||||
\(371\) | 58.6410i | 3.04449i | ||||||||
\(372\) | 0.196152 | + | 0.339746i | 0.0101700 | + | 0.0176150i | ||||
\(373\) | − | 0.928203i | − | 0.0480605i | −0.999711 | − | 0.0240303i | \(-0.992350\pi\) | ||
0.999711 | − | 0.0240303i | \(-0.00764981\pi\) | |||||||
\(374\) | 6.92820 | + | 25.8564i | 0.358249 | + | 1.33700i | ||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −17.4641 | + | 17.4641i | −0.900642 | + | 0.900642i | ||||
\(377\) | 4.92820 | 0.253815 | ||||||||
\(378\) | −1.73205 | − | 6.46410i | −0.0890871 | − | 0.332478i | ||||
\(379\) | − | 24.7321i | − | 1.27040i | −0.772348 | − | 0.635200i | \(-0.780918\pi\) | ||
0.772348 | − | 0.635200i | \(-0.219082\pi\) | |||||||
\(380\) | −1.26795 | + | 0.732051i | −0.0650444 | + | 0.0375534i | ||||
\(381\) | − | 16.9282i | − | 0.867258i | ||||||
\(382\) | −22.3923 | + | 6.00000i | −1.14569 | + | 0.306987i | ||||
\(383\) | −6.87564 | −0.351329 | −0.175665 | − | 0.984450i | \(-0.556207\pi\) | ||||
−0.175665 | + | 0.984450i | \(0.556207\pi\) | |||||||
\(384\) | 10.9282 | − | 2.92820i | 0.557678 | − | 0.149429i | ||||
\(385\) | −22.3923 | −1.14122 | ||||||||
\(386\) | −4.73205 | + | 1.26795i | −0.240855 | + | 0.0645369i | ||||
\(387\) | − | 1.46410i | − | 0.0744245i | ||||||
\(388\) | −0.928203 | + | 0.535898i | −0.0471224 | + | 0.0272061i | ||||
\(389\) | − | 8.92820i | − | 0.452678i | −0.974049 | − | 0.226339i | \(-0.927324\pi\) | ||
0.974049 | − | 0.226339i | \(-0.0726757\pi\) | |||||||
\(390\) | −0.366025 | − | 1.36603i | −0.0185344 | − | 0.0691714i | ||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | 30.7846 | − | 30.7846i | 1.55486 | − | 1.55486i | ||||
\(393\) | −7.85641 | −0.396303 | ||||||||
\(394\) | 0.875644 | + | 3.26795i | 0.0441143 | + | 0.164637i | ||||
\(395\) | − | 17.4641i | − | 0.878714i | ||||||
\(396\) | 4.73205 | + | 8.19615i | 0.237795 | + | 0.411872i | ||||
\(397\) | 15.8564i | 0.795810i | 0.917427 | + | 0.397905i | \(0.130263\pi\) | ||||
−0.917427 | + | 0.397905i | \(0.869737\pi\) | |||||||
\(398\) | −12.3923 | + | 3.32051i | −0.621170 | + | 0.166442i | ||||
\(399\) | 3.46410 | 0.173422 | ||||||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −10.0000 | −0.499376 | −0.249688 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249688 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(402\) | −16.6603 | + | 4.46410i | −0.830938 | + | 0.222649i | ||||
\(403\) | − | 0.196152i | − | 0.00977105i | ||||||
\(404\) | −12.0000 | − | 20.7846i | −0.597022 | − | 1.03407i | ||||
\(405\) | − | 1.00000i | − | 0.0496904i | ||||||
\(406\) | 8.53590 | + | 31.8564i | 0.423630 | + | 1.58101i | ||||
\(407\) | −2.53590 | −0.125700 | ||||||||
\(408\) | −8.00000 | − | 8.00000i | −0.396059 | − | 0.396059i | ||||
\(409\) | −24.2487 | −1.19902 | −0.599511 | − | 0.800367i | \(-0.704638\pi\) | ||||
−0.599511 | + | 0.800367i | \(0.704638\pi\) | |||||||
\(410\) | 1.80385 | + | 6.73205i | 0.0890857 | + | 0.332472i | ||||
\(411\) | 10.3923i | 0.512615i | ||||||||
\(412\) | −22.3923 | + | 12.9282i | −1.10319 | + | 0.636927i | ||||
\(413\) | 36.2487i | 1.78368i | ||||||||
\(414\) | 2.73205 | − | 0.732051i | 0.134273 | − | 0.0359783i | ||||
\(415\) | 5.26795 | 0.258593 | ||||||||
\(416\) | −5.46410 | − | 1.46410i | −0.267900 | − | 0.0717835i | ||||
\(417\) | 2.00000 | 0.0979404 | ||||||||
\(418\) | −4.73205 | + | 1.26795i | −0.231452 | + | 0.0620174i | ||||
\(419\) | − | 36.6410i | − | 1.79003i | −0.446035 | − | 0.895015i | \(-0.647164\pi\) | ||
0.446035 | − | 0.895015i | \(-0.352836\pi\) | |||||||
\(420\) | 8.19615 | − | 4.73205i | 0.399931 | − | 0.230900i | ||||
\(421\) | − | 5.32051i | − | 0.259306i | −0.991559 | − | 0.129653i | \(-0.958614\pi\) | ||
0.991559 | − | 0.129653i | \(-0.0413863\pi\) | |||||||
\(422\) | −0.339746 | − | 1.26795i | −0.0165386 | − | 0.0617228i | ||||
\(423\) | 8.73205 | 0.424567 | ||||||||
\(424\) | 24.7846 | + | 24.7846i | 1.20365 | + | 1.20365i | ||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 4.85641 | + | 18.1244i | 0.235294 | + | 0.878128i | ||||
\(427\) | − | 13.8564i | − | 0.670559i | ||||||
\(428\) | −4.00000 | − | 6.92820i | −0.193347 | − | 0.334887i | ||||
\(429\) | − | 4.73205i | − | 0.228466i | ||||||
\(430\) | 2.00000 | − | 0.535898i | 0.0964486 | − | 0.0258433i | ||||
\(431\) | −39.1244 | −1.88455 | −0.942277 | − | 0.334835i | \(-0.891320\pi\) | ||||
−0.942277 | + | 0.334835i | \(0.891320\pi\) | |||||||
\(432\) | −3.46410 | − | 2.00000i | −0.166667 | − | 0.0962250i | ||||
\(433\) | 17.7128 | 0.851223 | 0.425612 | − | 0.904906i | \(-0.360059\pi\) | ||||
0.425612 | + | 0.904906i | \(0.360059\pi\) | |||||||
\(434\) | 1.26795 | − | 0.339746i | 0.0608635 | − | 0.0163083i | ||||
\(435\) | 4.92820i | 0.236289i | ||||||||
\(436\) | 15.8564 | + | 27.4641i | 0.759384 | + | 1.31529i | ||||
\(437\) | 1.46410i | 0.0700375i | ||||||||
\(438\) | 5.80385 | + | 21.6603i | 0.277319 | + | 1.03497i | ||||
\(439\) | −17.8564 | −0.852240 | −0.426120 | − | 0.904667i | \(-0.640120\pi\) | ||||
−0.426120 | + | 0.904667i | \(0.640120\pi\) | |||||||
\(440\) | −9.46410 | + | 9.46410i | −0.451183 | + | 0.451183i | ||||
\(441\) | −15.3923 | −0.732967 | ||||||||
\(442\) | 1.46410 | + | 5.46410i | 0.0696402 | + | 0.259901i | ||||
\(443\) | − | 6.92820i | − | 0.329169i | −0.986363 | − | 0.164584i | \(-0.947372\pi\) | ||
0.986363 | − | 0.164584i | \(-0.0526283\pi\) | |||||||
\(444\) | 0.928203 | − | 0.535898i | 0.0440506 | − | 0.0254326i | ||||
\(445\) | − | 0.928203i | − | 0.0440011i | ||||||
\(446\) | −36.8564 | + | 9.87564i | −1.74520 | + | 0.467625i | ||||
\(447\) | 3.46410 | 0.163846 | ||||||||
\(448\) | − | 37.8564i | − | 1.78855i | ||||||
\(449\) | 26.3923 | 1.24553 | 0.622765 | − | 0.782409i | \(-0.286009\pi\) | ||||
0.622765 | + | 0.782409i | \(0.286009\pi\) | |||||||
\(450\) | 1.36603 | − | 0.366025i | 0.0643951 | − | 0.0172546i | ||||
\(451\) | 23.3205i | 1.09812i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.7321i | 0.880109i | ||||||||
\(454\) | 2.07180 | + | 7.73205i | 0.0972342 | + | 0.362883i | ||||
\(455\) | −4.73205 | −0.221842 | ||||||||
\(456\) | 1.46410 | − | 1.46410i | 0.0685628 | − | 0.0685628i | ||||
\(457\) | 15.0718 | 0.705029 | 0.352514 | − | 0.935806i | \(-0.385327\pi\) | ||||
0.352514 | + | 0.935806i | \(0.385327\pi\) | |||||||
\(458\) | −2.19615 | − | 8.19615i | −0.102619 | − | 0.382981i | ||||
\(459\) | 4.00000i | 0.186704i | ||||||||
\(460\) | 2.00000 | + | 3.46410i | 0.0932505 | + | 0.161515i | ||||
\(461\) | 3.07180i | 0.143068i | 0.997438 | + | 0.0715339i | \(0.0227894\pi\) | ||||
−0.997438 | + | 0.0715339i | \(0.977211\pi\) | |||||||
\(462\) | 30.5885 | − | 8.19615i | 1.42310 | − | 0.381320i | ||||
\(463\) | 19.6603 | 0.913689 | 0.456845 | − | 0.889546i | \(-0.348979\pi\) | ||||
0.456845 | + | 0.889546i | \(0.348979\pi\) | |||||||
\(464\) | 17.0718 | + | 9.85641i | 0.792538 | + | 0.457572i | ||||
\(465\) | 0.196152 | 0.00909635 | ||||||||
\(466\) | 16.1962 | − | 4.33975i | 0.750272 | − | 0.201035i | ||||
\(467\) | 19.6077i | 0.907336i | 0.891171 | + | 0.453668i | \(0.149885\pi\) | ||||
−0.891171 | + | 0.453668i | \(0.850115\pi\) | |||||||
\(468\) | 1.00000 | + | 1.73205i | 0.0462250 | + | 0.0800641i | ||||
\(469\) | 57.7128i | 2.66493i | ||||||||
\(470\) | 3.19615 | + | 11.9282i | 0.147428 | + | 0.550207i | ||||
\(471\) | 22.7846 | 1.04986 | ||||||||
\(472\) | 15.3205 | + | 15.3205i | 0.705184 | + | 0.705184i | ||||
\(473\) | 6.92820 | 0.318559 | ||||||||
\(474\) | 6.39230 | + | 23.8564i | 0.293608 | + | 1.09576i | ||||
\(475\) | 0.732051i | 0.0335888i | ||||||||
\(476\) | −32.7846 | + | 18.9282i | −1.50268 | + | 0.867573i | ||||
\(477\) | − | 12.3923i | − | 0.567405i | ||||||
\(478\) | −27.0526 | + | 7.24871i | −1.23736 | + | 0.331548i | ||||
\(479\) | −39.9090 | −1.82349 | −0.911744 | − | 0.410760i | \(-0.865263\pi\) | ||||
−0.911744 | + | 0.410760i | \(0.865263\pi\) | |||||||
\(480\) | 1.46410 | − | 5.46410i | 0.0668268 | − | 0.249401i | ||||
\(481\) | −0.535898 | −0.0244349 | ||||||||
\(482\) | −28.5885 | + | 7.66025i | −1.30217 | + | 0.348915i | ||||
\(483\) | − | 9.46410i | − | 0.430632i | ||||||
\(484\) | −19.7321 | + | 11.3923i | −0.896911 | + | 0.517832i | ||||
\(485\) | 0.535898i | 0.0243339i | ||||||||
\(486\) | 0.366025 | + | 1.36603i | 0.0166032 | + | 0.0619642i | ||||
\(487\) | −8.73205 | −0.395687 | −0.197843 | − | 0.980234i | \(-0.563394\pi\) | ||||
−0.197843 | + | 0.980234i | \(0.563394\pi\) | |||||||
\(488\) | −5.85641 | − | 5.85641i | −0.265107 | − | 0.265107i | ||||
\(489\) | −20.1962 | −0.913302 | ||||||||
\(490\) | −5.63397 | − | 21.0263i | −0.254517 | − | 0.949870i | ||||
\(491\) | − | 41.3205i | − | 1.86477i | −0.361469 | − | 0.932384i | \(-0.617725\pi\) | ||
0.361469 | − | 0.932384i | \(-0.382275\pi\) | |||||||
\(492\) | −4.92820 | − | 8.53590i | −0.222181 | − | 0.384828i | ||||
\(493\) | − | 19.7128i | − | 0.887820i | ||||||
\(494\) | −1.00000 | + | 0.267949i | −0.0449921 | + | 0.0120556i | ||||
\(495\) | 4.73205 | 0.212690 | ||||||||
\(496\) | 0.392305 | − | 0.679492i | 0.0176150 | − | 0.0305101i | ||||
\(497\) | 62.7846 | 2.81627 | ||||||||
\(498\) | −7.19615 | + | 1.92820i | −0.322467 | + | 0.0864049i | ||||
\(499\) | 2.19615i | 0.0983133i | 0.998791 | + | 0.0491566i | \(0.0156534\pi\) | ||||
−0.998791 | + | 0.0491566i | \(0.984347\pi\) | |||||||
\(500\) | 1.00000 | + | 1.73205i | 0.0447214 | + | 0.0774597i | ||||
\(501\) | 9.80385i | 0.438004i | ||||||||
\(502\) | −2.33975 | − | 8.73205i | −0.104428 | − | 0.389731i | ||||
\(503\) | 35.1769 | 1.56846 | 0.784231 | − | 0.620470i | \(-0.213058\pi\) | ||||
0.784231 | + | 0.620470i | \(0.213058\pi\) | |||||||
\(504\) | −9.46410 | + | 9.46410i | −0.421565 | + | 0.421565i | ||||
\(505\) | −12.0000 | −0.533993 | ||||||||
\(506\) | 3.46410 | + | 12.9282i | 0.153998 | + | 0.574729i | ||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | −29.3205 | + | 16.9282i | −1.30089 | + | 0.751068i | ||||
\(509\) | − | 5.60770i | − | 0.248557i | −0.992247 | − | 0.124278i | \(-0.960338\pi\) | ||
0.992247 | − | 0.124278i | \(-0.0396616\pi\) | |||||||
\(510\) | −5.46410 | + | 1.46410i | −0.241954 | + | 0.0648315i | ||||
\(511\) | 75.0333 | 3.31928 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | −0.732051 | −0.0323208 | ||||||||
\(514\) | −4.19615 | + | 1.12436i | −0.185084 | + | 0.0495932i | ||||
\(515\) | 12.9282i | 0.569685i | ||||||||
\(516\) | −2.53590 | + | 1.46410i | −0.111637 | + | 0.0644535i | ||||
\(517\) | 41.3205i | 1.81727i | ||||||||
\(518\) | −0.928203 | − | 3.46410i | −0.0407829 | − | 0.152204i | ||||
\(519\) | −9.46410 | −0.415428 | ||||||||
\(520\) | −2.00000 | + | 2.00000i | −0.0877058 | + | 0.0877058i | ||||
\(521\) | 9.46410 | 0.414630 | 0.207315 | − | 0.978274i | \(-0.433528\pi\) | ||||
0.207315 | + | 0.978274i | \(0.433528\pi\) | |||||||
\(522\) | −1.80385 | − | 6.73205i | −0.0789523 | − | 0.294654i | ||||
\(523\) | 16.0000i | 0.699631i | 0.936819 | + | 0.349816i | \(0.113756\pi\) | ||||
−0.936819 | + | 0.349816i | \(0.886244\pi\) | |||||||
\(524\) | 7.85641 | + | 13.6077i | 0.343209 | + | 0.594455i | ||||
\(525\) | − | 4.73205i | − | 0.206524i | ||||||
\(526\) | 22.5885 | − | 6.05256i | 0.984904 | − | 0.263904i | ||||
\(527\) | −0.784610 | −0.0341781 | ||||||||
\(528\) | 9.46410 | − | 16.3923i | 0.411872 | − | 0.713384i | ||||
\(529\) | −19.0000 | −0.826087 | ||||||||
\(530\) | 16.9282 | − | 4.53590i | 0.735314 | − | 0.197027i | ||||
\(531\) | − | 7.66025i | − | 0.332427i | ||||||
\(532\) | −3.46410 | − | 6.00000i | −0.150188 | − | 0.260133i | ||||
\(533\) | 4.92820i | 0.213464i | ||||||||
\(534\) | 0.339746 | + | 1.26795i | 0.0147022 | + | 0.0548695i | ||||
\(535\) | −4.00000 | −0.172935 | ||||||||
\(536\) | 24.3923 | + | 24.3923i | 1.05359 | + | 1.05359i | ||||
\(537\) | −10.3923 | −0.448461 | ||||||||
\(538\) | −1.51666 | − | 5.66025i | −0.0653879 | − | 0.244031i | ||||
\(539\) | − | 72.8372i | − | 3.13732i | ||||||
\(540\) | −1.73205 | + | 1.00000i | −0.0745356 | + | 0.0430331i | ||||
\(541\) | − | 32.2487i | − | 1.38648i | −0.720707 | − | 0.693240i | \(-0.756183\pi\) | ||
0.720707 | − | 0.693240i | \(-0.243817\pi\) | |||||||
\(542\) | 7.73205 | − | 2.07180i | 0.332120 | − | 0.0889913i | ||||
\(543\) | 4.92820 | 0.211489 | ||||||||
\(544\) | −5.85641 | + | 21.8564i | −0.251091 | + | 0.937086i | ||||
\(545\) | 15.8564 | 0.679214 | ||||||||
\(546\) | 6.46410 | − | 1.73205i | 0.276638 | − | 0.0741249i | ||||
\(547\) | − | 16.7846i | − | 0.717658i | −0.933403 | − | 0.358829i | \(-0.883176\pi\) | ||
0.933403 | − | 0.358829i | \(-0.116824\pi\) | |||||||
\(548\) | 18.0000 | − | 10.3923i | 0.768922 | − | 0.443937i | ||||
\(549\) | 2.92820i | 0.124973i | ||||||||
\(550\) | 1.73205 | + | 6.46410i | 0.0738549 | + | 0.275630i | ||||
\(551\) | 3.60770 | 0.153693 | ||||||||
\(552\) | −4.00000 | − | 4.00000i | −0.170251 | − | 0.170251i | ||||
\(553\) | 82.6410 | 3.51425 | ||||||||
\(554\) | 7.85641 | + | 29.3205i | 0.333787 | + | 1.24571i | ||||
\(555\) | − | 0.535898i | − | 0.0227476i | ||||||
\(556\) | −2.00000 | − | 3.46410i | −0.0848189 | − | 0.146911i | ||||
\(557\) | − | 34.7846i | − | 1.47387i | −0.675963 | − | 0.736936i | \(-0.736272\pi\) | ||
0.675963 | − | 0.736936i | \(-0.263728\pi\) | |||||||
\(558\) | −0.267949 | + | 0.0717968i | −0.0113432 | + | 0.00303940i | ||||
\(559\) | 1.46410 | 0.0619249 | ||||||||
\(560\) | −16.3923 | − | 9.46410i | −0.692701 | − | 0.399931i | ||||
\(561\) | −18.9282 | −0.799149 | ||||||||
\(562\) | −25.1244 | + | 6.73205i | −1.05981 | + | 0.283974i | ||||
\(563\) | 4.67949i | 0.197217i | 0.995126 | + | 0.0986085i | \(0.0314392\pi\) | ||||
−0.995126 | + | 0.0986085i | \(0.968561\pi\) | |||||||
\(564\) | −8.73205 | − | 15.1244i | −0.367686 | − | 0.636850i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 2.00000 | + | 7.46410i | 0.0840663 | + | 0.313740i | ||||
\(567\) | 4.73205 | 0.198727 | ||||||||
\(568\) | 26.5359 | − | 26.5359i | 1.11342 | − | 1.11342i | ||||
\(569\) | 35.8564 | 1.50318 | 0.751589 | − | 0.659631i | \(-0.229288\pi\) | ||||
0.751589 | + | 0.659631i | \(0.229288\pi\) | |||||||
\(570\) | −0.267949 | − | 1.00000i | −0.0112232 | − | 0.0418854i | ||||
\(571\) | 26.3923i | 1.10448i | 0.833684 | + | 0.552242i | \(0.186227\pi\) | ||||
−0.833684 | + | 0.552242i | \(0.813773\pi\) | |||||||
\(572\) | −8.19615 | + | 4.73205i | −0.342698 | + | 0.197857i | ||||
\(573\) | − | 16.3923i | − | 0.684798i | ||||||
\(574\) | −31.8564 | + | 8.53590i | −1.32966 | + | 0.356282i | ||||
\(575\) | 2.00000 | 0.0834058 | ||||||||
\(576\) | 8.00000i | 0.333333i | ||||||||
\(577\) | −42.3923 | −1.76481 | −0.882407 | − | 0.470486i | \(-0.844079\pi\) | ||||
−0.882407 | + | 0.470486i | \(0.844079\pi\) | |||||||
\(578\) | −1.36603 | + | 0.366025i | −0.0568192 | + | 0.0152246i | ||||
\(579\) | − | 3.46410i | − | 0.143963i | ||||||
\(580\) | 8.53590 | − | 4.92820i | 0.354434 | − | 0.204633i | ||||
\(581\) | 24.9282i | 1.03420i | ||||||||
\(582\) | −0.196152 | − | 0.732051i | −0.00813078 | − | 0.0303445i | ||||
\(583\) | 58.6410 | 2.42866 | ||||||||
\(584\) | 31.7128 | − | 31.7128i | 1.31229 | − | 1.31229i | ||||
\(585\) | 1.00000 | 0.0413449 | ||||||||
\(586\) | −8.33975 | − | 31.1244i | −0.344512 | − | 1.28574i | ||||
\(587\) | − | 2.33975i | − | 0.0965717i | −0.998834 | − | 0.0482858i | \(-0.984624\pi\) | ||
0.998834 | − | 0.0482858i | \(-0.0153758\pi\) | |||||||
\(588\) | 15.3923 | + | 26.6603i | 0.634768 | + | 1.09945i | ||||
\(589\) | − | 0.143594i | − | 0.00591667i | ||||||
\(590\) | 10.4641 | − | 2.80385i | 0.430800 | − | 0.115433i | ||||
\(591\) | −2.39230 | −0.0984063 | ||||||||
\(592\) | −1.85641 | − | 1.07180i | −0.0762978 | − | 0.0440506i | ||||
\(593\) | −5.32051 | −0.218487 | −0.109244 | − | 0.994015i | \(-0.534843\pi\) | ||||
−0.109244 | + | 0.994015i | \(0.534843\pi\) | |||||||
\(594\) | −6.46410 | + | 1.73205i | −0.265225 | + | 0.0710669i | ||||
\(595\) | 18.9282i | 0.775981i | ||||||||
\(596\) | −3.46410 | − | 6.00000i | −0.141895 | − | 0.245770i | ||||
\(597\) | − | 9.07180i | − | 0.371284i | ||||||
\(598\) | 0.732051 | + | 2.73205i | 0.0299358 | + | 0.111722i | ||||
\(599\) | −38.2487 | −1.56280 | −0.781400 | − | 0.624030i | \(-0.785494\pi\) | ||||
−0.781400 | + | 0.624030i | \(0.785494\pi\) | |||||||
\(600\) | −2.00000 | − | 2.00000i | −0.0816497 | − | 0.0816497i | ||||
\(601\) | 40.3923 | 1.64764 | 0.823818 | − | 0.566854i | \(-0.191840\pi\) | ||||
0.823818 | + | 0.566854i | \(0.191840\pi\) | |||||||
\(602\) | 2.53590 | + | 9.46410i | 0.103356 | + | 0.385728i | ||||
\(603\) | − | 12.1962i | − | 0.496666i | ||||||
\(604\) | 32.4449 | − | 18.7321i | 1.32016 | − | 0.762196i | ||||
\(605\) | 11.3923i | 0.463163i | ||||||||
\(606\) | 16.3923 | − | 4.39230i | 0.665892 | − | 0.178425i | ||||
\(607\) | 16.5359 | 0.671171 | 0.335586 | − | 0.942010i | \(-0.391066\pi\) | ||||
0.335586 | + | 0.942010i | \(0.391066\pi\) | |||||||
\(608\) | −4.00000 | − | 1.07180i | −0.162221 | − | 0.0434671i | ||||
\(609\) | −23.3205 | −0.944995 | ||||||||
\(610\) | −4.00000 | + | 1.07180i | −0.161955 | + | 0.0433958i | ||||
\(611\) | 8.73205i | 0.353261i | ||||||||
\(612\) | 6.92820 | − | 4.00000i | 0.280056 | − | 0.161690i | ||||
\(613\) | − | 26.0000i | − | 1.05013i | −0.851062 | − | 0.525065i | \(-0.824041\pi\) | ||
0.851062 | − | 0.525065i | \(-0.175959\pi\) | |||||||
\(614\) | 7.00000 | + | 26.1244i | 0.282497 | + | 1.05429i | ||||
\(615\) | −4.92820 | −0.198724 | ||||||||
\(616\) | −44.7846 | − | 44.7846i | −1.80442 | − | 1.80442i | ||||
\(617\) | −0.928203 | −0.0373681 | −0.0186840 | − | 0.999825i | \(-0.505948\pi\) | ||||
−0.0186840 | + | 0.999825i | \(0.505948\pi\) | |||||||
\(618\) | −4.73205 | − | 17.6603i | −0.190351 | − | 0.710400i | ||||
\(619\) | − | 28.0526i | − | 1.12753i | −0.825936 | − | 0.563764i | \(-0.809353\pi\) | ||
0.825936 | − | 0.563764i | \(-0.190647\pi\) | |||||||
\(620\) | −0.196152 | − | 0.339746i | −0.00787767 | − | 0.0136445i | ||||
\(621\) | 2.00000i | 0.0802572i | ||||||||
\(622\) | −43.3205 | + | 11.6077i | −1.73699 | + | 0.465426i | ||||
\(623\) | 4.39230 | 0.175974 | ||||||||
\(624\) | 2.00000 | − | 3.46410i | 0.0800641 | − | 0.138675i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 10.9282 | − | 2.92820i | 0.436779 | − | 0.117035i | ||||
\(627\) | − | 3.46410i | − | 0.138343i | ||||||
\(628\) | −22.7846 | − | 39.4641i | −0.909205 | − | 1.57479i | ||||
\(629\) | 2.14359i | 0.0854707i | ||||||||
\(630\) | 1.73205 | + | 6.46410i | 0.0690066 | + | 0.257536i | ||||
\(631\) | 7.80385 | 0.310666 | 0.155333 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155333 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(632\) | 34.9282 | − | 34.9282i | 1.38937 | − | 1.38937i | ||||
\(633\) | 0.928203 | 0.0368928 | ||||||||
\(634\) | −7.51666 | − | 28.0526i | −0.298525 | − | 1.11411i | ||||
\(635\) | 16.9282i | 0.671775i | ||||||||
\(636\) | −21.4641 | + | 12.3923i | −0.851107 | + | 0.491387i | ||||
\(637\) | − | 15.3923i | − | 0.609865i | ||||||
\(638\) | 31.8564 | − | 8.53590i | 1.26121 | − | 0.337939i | ||||
\(639\) | −13.2679 | −0.524872 | ||||||||
\(640\) | −10.9282 | + | 2.92820i | −0.431975 | + | 0.115747i | ||||
\(641\) | 29.4641 | 1.16376 | 0.581881 | − | 0.813274i | \(-0.302317\pi\) | ||||
0.581881 | + | 0.813274i | \(0.302317\pi\) | |||||||
\(642\) | 5.46410 | − | 1.46410i | 0.215651 | − | 0.0577835i | ||||
\(643\) | 34.4449i | 1.35837i | 0.733966 | + | 0.679186i | \(0.237667\pi\) | ||||
−0.733966 | + | 0.679186i | \(0.762333\pi\) | |||||||
\(644\) | −16.3923 | + | 9.46410i | −0.645947 | + | 0.372938i | ||||
\(645\) | 1.46410i | 0.0576489i | ||||||||
\(646\) | 1.07180 | + | 4.00000i | 0.0421693 | + | 0.157378i | ||||
\(647\) | −38.7846 | −1.52478 | −0.762390 | − | 0.647118i | \(-0.775974\pi\) | ||||
−0.762390 | + | 0.647118i | \(0.775974\pi\) | |||||||
\(648\) | 2.00000 | − | 2.00000i | 0.0785674 | − | 0.0785674i | ||||
\(649\) | 36.2487 | 1.42289 | ||||||||
\(650\) | 0.366025 | + | 1.36603i | 0.0143567 | + | 0.0535799i | ||||
\(651\) | 0.928203i | 0.0363792i | ||||||||
\(652\) | 20.1962 | + | 34.9808i | 0.790942 | + | 1.36995i | ||||
\(653\) | 16.9282i | 0.662452i | 0.943551 | + | 0.331226i | \(0.107462\pi\) | ||||
−0.943551 | + | 0.331226i | \(0.892538\pi\) | |||||||
\(654\) | −21.6603 | + | 5.80385i | −0.846983 | + | 0.226948i | ||||
\(655\) | 7.85641 | 0.306975 | ||||||||
\(656\) | −9.85641 | + | 17.0718i | −0.384828 | + | 0.666542i | ||||
\(657\) | −15.8564 | −0.618617 | ||||||||
\(658\) | −56.4449 | + | 15.1244i | −2.20045 | + | 0.589609i | ||||
\(659\) | 34.0000i | 1.32445i | 0.749304 | + | 0.662226i | \(0.230388\pi\) | ||||
−0.749304 | + | 0.662226i | \(0.769612\pi\) | |||||||
\(660\) | −4.73205 | − | 8.19615i | −0.184195 | − | 0.319035i | ||||
\(661\) | 10.3923i | 0.404214i | 0.979363 | + | 0.202107i | \(0.0647788\pi\) | ||||
−0.979363 | + | 0.202107i | \(0.935221\pi\) | |||||||
\(662\) | 4.41154 | + | 16.4641i | 0.171459 | + | 0.639895i | ||||
\(663\) | −4.00000 | −0.155347 | ||||||||
\(664\) | 10.5359 | + | 10.5359i | 0.408872 | + | 0.408872i | ||||
\(665\) | −3.46410 | −0.134332 | ||||||||
\(666\) | 0.196152 | + | 0.732051i | 0.00760075 | + | 0.0283664i | ||||
\(667\) | − | 9.85641i | − | 0.381642i | ||||||
\(668\) | 16.9808 | − | 9.80385i | 0.657005 | − | 0.379322i | ||||
\(669\) | − | 26.9808i | − | 1.04314i | ||||||
\(670\) | 16.6603 | − | 4.46410i | 0.643642 | − | 0.172463i | ||||
\(671\) | −13.8564 | −0.534921 | ||||||||
\(672\) | 25.8564 | + | 6.92820i | 0.997433 | + | 0.267261i | ||||
\(673\) | −9.07180 | −0.349692 | −0.174846 | − | 0.984596i | \(-0.555943\pi\) | ||||
−0.174846 | + | 0.984596i | \(0.555943\pi\) | |||||||
\(674\) | −27.3205 | + | 7.32051i | −1.05235 | + | 0.281975i | ||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | −1.73205 | + | 1.00000i | −0.0666173 | + | 0.0384615i | ||||
\(677\) | − | 6.53590i | − | 0.251195i | −0.992081 | − | 0.125597i | \(-0.959915\pi\) | ||
0.992081 | − | 0.125597i | \(-0.0400848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.53590 | −0.0973188 | ||||||||
\(680\) | 8.00000 | + | 8.00000i | 0.306786 | + | 0.306786i | ||||
\(681\) | −5.66025 | −0.216901 | ||||||||
\(682\) | −0.339746 | − | 1.26795i | −0.0130095 | − | 0.0485523i | ||||
\(683\) | 33.2679i | 1.27296i | 0.771292 | + | 0.636481i | \(0.219611\pi\) | ||||
−0.771292 | + | 0.636481i | \(0.780389\pi\) | |||||||
\(684\) | 0.732051 | + | 1.26795i | 0.0279907 | + | 0.0484812i | ||||
\(685\) | − | 10.3923i | − | 0.397070i | ||||||
\(686\) | 54.2487 | − | 14.5359i | 2.07123 | − | 0.554983i | ||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | 5.07180 | + | 2.92820i | 0.193360 | + | 0.111637i | ||||
\(689\) | 12.3923 | 0.472109 | ||||||||
\(690\) | −2.73205 | + | 0.732051i | −0.104007 | + | 0.0278687i | ||||
\(691\) | − | 34.5885i | − | 1.31581i | −0.753102 | − | 0.657903i | \(-0.771443\pi\) | ||
0.753102 | − | 0.657903i | \(-0.228557\pi\) | |||||||
\(692\) | 9.46410 | + | 16.3923i | 0.359771 | + | 0.623142i | ||||
\(693\) | 22.3923i | 0.850613i | ||||||||
\(694\) | −11.6077 | − | 43.3205i | −0.440622 | − | 1.64442i | ||||
\(695\) | −2.00000 | −0.0758643 | ||||||||
\(696\) | −9.85641 | + | 9.85641i | −0.373606 | + | 0.373606i | ||||
\(697\) | 19.7128 | 0.746676 | ||||||||
\(698\) | −12.7321 | − | 47.5167i | −0.481915 | − | 1.79853i | ||||
\(699\) | 11.8564i | 0.448450i | ||||||||
\(700\) | −8.19615 | + | 4.73205i | −0.309785 | + | 0.178855i | ||||
\(701\) | − | 18.0000i | − | 0.679851i | −0.940452 | − | 0.339925i | \(-0.889598\pi\) | ||
0.940452 | − | 0.339925i | \(-0.110402\pi\) | |||||||
\(702\) | −1.36603 | + | 0.366025i | −0.0515573 | + | 0.0138147i | ||||
\(703\) | −0.392305 | −0.0147961 | ||||||||
\(704\) | −37.8564 | −1.42677 | ||||||||
\(705\) | −8.73205 | −0.328868 | ||||||||
\(706\) | 29.6603 | − | 7.94744i | 1.11628 | − | 0.299106i | ||||
\(707\) | − | 56.7846i | − | 2.13561i | ||||||
\(708\) | −13.2679 | + | 7.66025i | −0.498640 | + | 0.287890i | ||||
\(709\) | 35.0718i | 1.31715i | 0.752516 | + | 0.658574i | \(0.228840\pi\) | ||||
−0.752516 | + | 0.658574i | \(0.771160\pi\) | |||||||
\(710\) | −4.85641 | − | 18.1244i | −0.182258 | − | 0.680195i | ||||
\(711\) | −17.4641 | −0.654955 | ||||||||
\(712\) | 1.85641 | − | 1.85641i | 0.0695718 | − | 0.0695718i | ||||
\(713\) | −0.392305 | −0.0146919 | ||||||||
\(714\) | −6.92820 | − | 25.8564i | −0.259281 | − | 0.967652i | ||||
\(715\) | 4.73205i | 0.176969i | ||||||||
\(716\) | 10.3923 | + | 18.0000i | 0.388379 | + | 0.672692i | ||||
\(717\) | − | 19.8038i | − | 0.739588i | ||||||
\(718\) | 18.1244 | − | 4.85641i | 0.676395 | − | 0.181239i | ||||
\(719\) | −1.85641 | −0.0692323 | −0.0346161 | − | 0.999401i | \(-0.511021\pi\) | ||||
−0.0346161 | + | 0.999401i | \(0.511021\pi\) | |||||||
\(720\) | 3.46410 | + | 2.00000i | 0.129099 | + | 0.0745356i | ||||
\(721\) | −61.1769 | −2.27835 | ||||||||
\(722\) | 25.2224 | − | 6.75833i | 0.938682 | − | 0.251519i | ||||
\(723\) | − | 20.9282i | − | 0.778328i | ||||||
\(724\) | −4.92820 | − | 8.53590i | −0.183155 | − | 0.317234i | ||||
\(725\) | − | 4.92820i | − | 0.183029i | ||||||
\(726\) | −4.16987 | − | 15.5622i | −0.154759 | − | 0.577567i | ||||
\(727\) | −4.92820 | −0.182777 | −0.0913885 | − | 0.995815i | \(-0.529130\pi\) | ||||
−0.0913885 | + | 0.995815i | \(0.529130\pi\) | |||||||
\(728\) | −9.46410 | − | 9.46410i | −0.350763 | − | 0.350763i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −5.80385 | − | 21.6603i | −0.214810 | − | 0.801682i | ||||
\(731\) | − | 5.85641i | − | 0.216607i | ||||||
\(732\) | 5.07180 | − | 2.92820i | 0.187459 | − | 0.108230i | ||||
\(733\) | − | 6.39230i | − | 0.236105i | −0.993007 | − | 0.118053i | \(-0.962335\pi\) | ||
0.993007 | − | 0.118053i | \(-0.0376651\pi\) | |||||||
\(734\) | −0.732051 | + | 0.196152i | −0.0270205 | + | 0.00724012i | ||||
\(735\) | 15.3923 | 0.567754 | ||||||||
\(736\) | −2.92820 | + | 10.9282i | −0.107935 | + | 0.402819i | ||||
\(737\) | 57.7128 | 2.12588 | ||||||||
\(738\) | 6.73205 | − | 1.80385i | 0.247810 | − | 0.0664005i | ||||
\(739\) | − | 13.4115i | − | 0.493352i | −0.969098 | − | 0.246676i | \(-0.920662\pi\) | ||
0.969098 | − | 0.246676i | \(-0.0793383\pi\) | |||||||
\(740\) | −0.928203 | + | 0.535898i | −0.0341214 | + | 0.0197000i | ||||
\(741\) | − | 0.732051i | − | 0.0268926i | ||||||
\(742\) | 21.4641 | + | 80.1051i | 0.787972 | + | 2.94075i | ||||
\(743\) | −32.4449 | −1.19029 | −0.595143 | − | 0.803620i | \(-0.702905\pi\) | ||||
−0.595143 | + | 0.803620i | \(0.702905\pi\) | |||||||
\(744\) | 0.392305 | + | 0.392305i | 0.0143826 | + | 0.0143826i | ||||
\(745\) | −3.46410 | −0.126915 | ||||||||
\(746\) | −0.339746 | − | 1.26795i | −0.0124390 | − | 0.0464229i | ||||
\(747\) | − | 5.26795i | − | 0.192744i | ||||||
\(748\) | 18.9282 | + | 32.7846i | 0.692084 | + | 1.19872i | ||||
\(749\) | − | 18.9282i | − | 0.691621i | ||||||
\(750\) | −1.36603 | + | 0.366025i | −0.0498802 | + | 0.0133654i | ||||
\(751\) | −16.0000 | −0.583848 | −0.291924 | − | 0.956441i | \(-0.594295\pi\) | ||||
−0.291924 | + | 0.956441i | \(0.594295\pi\) | |||||||
\(752\) | −17.4641 | + | 30.2487i | −0.636850 | + | 1.10306i | ||||
\(753\) | 6.39230 | 0.232949 | ||||||||
\(754\) | 6.73205 | − | 1.80385i | 0.245167 | − | 0.0656923i | ||||
\(755\) | − | 18.7321i | − | 0.681729i | ||||||
\(756\) | −4.73205 | − | 8.19615i | −0.172103 | − | 0.298091i | ||||
\(757\) | 11.6077i | 0.421889i | 0.977498 | + | 0.210944i | \(0.0676539\pi\) | ||||
−0.977498 | + | 0.210944i | \(0.932346\pi\) | |||||||
\(758\) | −9.05256 | − | 33.7846i | −0.328804 | − | 1.22711i | ||||
\(759\) | −9.46410 | −0.343525 | ||||||||
\(760\) | −1.46410 | + | 1.46410i | −0.0531085 | + | 0.0531085i | ||||
\(761\) | −18.3923 | −0.666721 | −0.333360 | − | 0.942800i | \(-0.608183\pi\) | ||||
−0.333360 | + | 0.942800i | \(0.608183\pi\) | |||||||
\(762\) | −6.19615 | − | 23.1244i | −0.224463 | − | 0.837707i | ||||
\(763\) | 75.0333i | 2.71639i | ||||||||
\(764\) | −28.3923 | + | 16.3923i | −1.02720 | + | 0.593053i | ||||
\(765\) | − | 4.00000i | − | 0.144620i | ||||||
\(766\) | −9.39230 | + | 2.51666i | −0.339358 | + | 0.0909306i | ||||
\(767\) | 7.66025 | 0.276596 | ||||||||
\(768\) | 13.8564 | − | 8.00000i | 0.500000 | − | 0.288675i | ||||
\(769\) | −1.32051 | −0.0476187 | −0.0238094 | − | 0.999717i | \(-0.507579\pi\) | ||||
−0.0238094 | + | 0.999717i | \(0.507579\pi\) | |||||||
\(770\) | −30.5885 | + | 8.19615i | −1.10233 | + | 0.295369i | ||||
\(771\) | − | 3.07180i | − | 0.110628i | ||||||
\(772\) | −6.00000 | + | 3.46410i | −0.215945 | + | 0.124676i | ||||
\(773\) | 31.1769i | 1.12136i | 0.828034 | + | 0.560678i | \(0.189459\pi\) | ||||
−0.828034 | + | 0.560678i | \(0.810541\pi\) | |||||||
\(774\) | −0.535898 | − | 2.00000i | −0.0192625 | − | 0.0718885i | ||||
\(775\) | −0.196152 | −0.00704600 | ||||||||
\(776\) | −1.07180 | + | 1.07180i | −0.0384753 | + | 0.0384753i | ||||
\(777\) | 2.53590 | 0.0909748 | ||||||||
\(778\) | −3.26795 | − | 12.1962i | −0.117162 | − | 0.437253i | ||||
\(779\) | 3.60770i | 0.129259i | ||||||||
\(780\) | −1.00000 | − | 1.73205i | −0.0358057 | − | 0.0620174i | ||||
\(781\) | − | 62.7846i | − | 2.24661i | ||||||
\(782\) | 10.9282 | − | 2.92820i | 0.390792 | − | 0.104712i | ||||
\(783\) | 4.92820 | 0.176120 | ||||||||
\(784\) | 30.7846 | − | 53.3205i | 1.09945 | − | 1.90430i | ||||
\(785\) | −22.7846 | −0.813218 | ||||||||
\(786\) | −10.7321 | + | 2.87564i | −0.382800 | + | 0.102571i | ||||
\(787\) | 48.9808i | 1.74598i | 0.487742 | + | 0.872988i | \(0.337821\pi\) | ||||
−0.487742 | + | 0.872988i | \(0.662179\pi\) | |||||||
\(788\) | 2.39230 | + | 4.14359i | 0.0852223 | + | 0.147609i | ||||
\(789\) | 16.5359i | 0.588694i | ||||||||
\(790\) | −6.39230 | − | 23.8564i | −0.227428 | − | 0.848773i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 9.46410 | + | 9.46410i | 0.336292 | + | 0.336292i | ||||
\(793\) | −2.92820 | −0.103984 | ||||||||
\(794\) | 5.80385 | + | 21.6603i | 0.205971 | + | 0.768694i | ||||
\(795\) | 12.3923i | 0.439510i | ||||||||
\(796\) | −15.7128 | + | 9.07180i | −0.556926 | + | 0.321541i | ||||
\(797\) | 33.7128i | 1.19417i | 0.802178 | + | 0.597085i | \(0.203674\pi\) | ||||
−0.802178 | + | 0.597085i | \(0.796326\pi\) | |||||||
\(798\) | 4.73205 | − | 1.26795i | 0.167513 | − | 0.0448849i | ||||
\(799\) | 34.9282 | 1.23567 | ||||||||
\(800\) | −1.46410 | + | 5.46410i | −0.0517638 | + | 0.193185i | ||||
\(801\) | −0.928203 | −0.0327964 | ||||||||
\(802\) | −13.6603 | + | 3.66025i | −0.482360 | + | 0.129248i | ||||
\(803\) | − | 75.0333i | − | 2.64787i | ||||||
\(804\) | −21.1244 | + | 12.1962i | −0.744999 | + | 0.430125i | ||||
\(805\) | 9.46410i | 0.333566i | ||||||||
\(806\) | −0.0717968 | − | 0.267949i | −0.00252893 | − | 0.00943811i | ||||
\(807\) | 4.14359 | 0.145861 | ||||||||
\(808\) | −24.0000 | − | 24.0000i | −0.844317 | − | 0.844317i | ||||
\(809\) | 20.3923 | 0.716955 | 0.358478 | − | 0.933538i | \(-0.383296\pi\) | ||||
0.358478 | + | 0.933538i | \(0.383296\pi\) | |||||||
\(810\) | −0.366025 | − | 1.36603i | −0.0128608 | − | 0.0479972i | ||||
\(811\) | − | 23.2679i | − | 0.817048i | −0.912748 | − | 0.408524i | \(-0.866044\pi\) | ||
0.912748 | − | 0.408524i | \(-0.133956\pi\) | |||||||
\(812\) | 23.3205 | + | 40.3923i | 0.818389 | + | 1.41749i | ||||
\(813\) | 5.66025i | 0.198514i | ||||||||
\(814\) | −3.46410 | + | 0.928203i | −0.121417 | + | 0.0325335i | ||||
\(815\) | 20.1962 | 0.707440 | ||||||||
\(816\) | −13.8564 | − | 8.00000i | −0.485071 | − | 0.280056i | ||||
\(817\) | 1.07180 | 0.0374974 | ||||||||
\(818\) | −33.1244 | + | 8.87564i | −1.15817 | + | 0.310330i | ||||
\(819\) | 4.73205i | 0.165351i | ||||||||
\(820\) | 4.92820 | + | 8.53590i | 0.172100 | + | 0.298087i | ||||
\(821\) | − | 24.9282i | − | 0.870000i | −0.900430 | − | 0.435000i | \(-0.856748\pi\) | ||
0.900430 | − | 0.435000i | \(-0.143252\pi\) | |||||||
\(822\) | 3.80385 | + | 14.1962i | 0.132674 | + | 0.495148i | ||||
\(823\) | 14.0000 | 0.488009 | 0.244005 | − | 0.969774i | \(-0.421539\pi\) | ||||
0.244005 | + | 0.969774i | \(0.421539\pi\) | |||||||
\(824\) | −25.8564 | + | 25.8564i | −0.900751 | + | 0.900751i | ||||
\(825\) | −4.73205 | −0.164749 | ||||||||
\(826\) | 13.2679 | + | 49.5167i | 0.461651 | + | 1.72290i | ||||
\(827\) | − | 22.3397i | − | 0.776829i | −0.921485 | − | 0.388415i | \(-0.873023\pi\) | ||
0.921485 | − | 0.388415i | \(-0.126977\pi\) | |||||||
\(828\) | 3.46410 | − | 2.00000i | 0.120386 | − | 0.0695048i | ||||
\(829\) | − | 28.0000i | − | 0.972480i | −0.873825 | − | 0.486240i | \(-0.838368\pi\) | ||
0.873825 | − | 0.486240i | \(-0.161632\pi\) | |||||||
\(830\) | 7.19615 | − | 1.92820i | 0.249782 | − | 0.0669289i | ||||
\(831\) | −21.4641 | −0.744581 | ||||||||
\(832\) | −8.00000 | −0.277350 | ||||||||
\(833\) | −61.5692 | −2.13325 | ||||||||
\(834\) | 2.73205 | − | 0.732051i | 0.0946032 | − | 0.0253488i | ||||
\(835\) | − | 9.80385i | − | 0.339276i | ||||||
\(836\) | −6.00000 | + | 3.46410i | −0.207514 | + | 0.119808i | ||||
\(837\) | − | 0.196152i | − | 0.00678002i | ||||||
\(838\) | −13.4115 | − | 50.0526i | −0.463294 | − | 1.72904i | ||||
\(839\) | 30.0526 | 1.03753 | 0.518765 | − | 0.854917i | \(-0.326392\pi\) | ||||
0.518765 | + | 0.854917i | \(0.326392\pi\) | |||||||
\(840\) | 9.46410 | − | 9.46410i | 0.326543 | − | 0.326543i | ||||
\(841\) | 4.71281 | 0.162511 | ||||||||
\(842\) | −1.94744 | − | 7.26795i | −0.0671133 | − | 0.250470i | ||||
\(843\) | − | 18.3923i | − | 0.633465i | ||||||
\(844\) | −0.928203 | − | 1.60770i | −0.0319501 | − | 0.0553391i | ||||
\(845\) | 1.00000i | 0.0344010i | ||||||||
\(846\) | 11.9282 | − | 3.19615i | 0.410100 | − | 0.109886i | ||||
\(847\) | −53.9090 | −1.85233 | ||||||||
\(848\) | 42.9282 | + | 24.7846i | 1.47416 | + | 0.851107i | ||||
\(849\) | −5.46410 | −0.187527 | ||||||||
\(850\) | 5.46410 | − | 1.46410i | 0.187417 | − | 0.0502183i | ||||
\(851\) | 1.07180i | 0.0367407i | ||||||||
\(852\) | 13.2679 | + | 22.9808i | 0.454552 | + | 0.787308i | ||||
\(853\) | − | 26.7846i | − | 0.917088i | −0.888672 | − | 0.458544i | \(-0.848371\pi\) | ||
0.888672 | − | 0.458544i | \(-0.151629\pi\) | |||||||
\(854\) | −5.07180 | − | 18.9282i | −0.173553 | − | 0.647710i | ||||
\(855\) | 0.732051 | 0.0250356 | ||||||||
\(856\) | −8.00000 | − | 8.00000i | −0.273434 | − | 0.273434i | ||||
\(857\) | 45.7128 | 1.56152 | 0.780760 | − | 0.624831i | \(-0.214832\pi\) | ||||
0.780760 | + | 0.624831i | \(0.214832\pi\) | |||||||
\(858\) | −1.73205 | − | 6.46410i | −0.0591312 | − | 0.220681i | ||||
\(859\) | − | 0.928203i | − | 0.0316699i | −0.999875 | − | 0.0158349i | \(-0.994959\pi\) | ||
0.999875 | − | 0.0158349i | \(-0.00504063\pi\) | |||||||
\(860\) | 2.53590 | − | 1.46410i | 0.0864734 | − | 0.0499255i | ||||
\(861\) | − | 23.3205i | − | 0.794761i | ||||||
\(862\) | −53.4449 | + | 14.3205i | −1.82034 | + | 0.487758i | ||||
\(863\) | −45.1244 | −1.53605 | −0.768025 | − | 0.640419i | \(-0.778761\pi\) | ||||
−0.768025 | + | 0.640419i | \(0.778761\pi\) | |||||||
\(864\) | −5.46410 | − | 1.46410i | −0.185893 | − | 0.0498097i | ||||
\(865\) | 9.46410 | 0.321789 | ||||||||
\(866\) | 24.1962 | − | 6.48334i | 0.822219 | − | 0.220313i | ||||
\(867\) | − | 1.00000i | − | 0.0339618i | ||||||
\(868\) | 1.60770 | − | 0.928203i | 0.0545687 | − | 0.0315053i | ||||
\(869\) | − | 82.6410i | − | 2.80340i | ||||||
\(870\) | 1.80385 | + | 6.73205i | 0.0611562 | + | 0.228238i | ||||
\(871\) | 12.1962 | 0.413251 | ||||||||
\(872\) | 31.7128 | + | 31.7128i | 1.07393 | + | 1.07393i | ||||
\(873\) | 0.535898 | 0.0181374 | ||||||||
\(874\) | 0.535898 | + | 2.00000i | 0.0181270 | + | 0.0676510i | ||||
\(875\) | 4.73205i | 0.159973i | ||||||||
\(876\) | 15.8564 | + | 27.4641i | 0.535738 | + | 0.927926i | ||||
\(877\) | − | 17.6077i | − | 0.594570i | −0.954789 | − | 0.297285i | \(-0.903919\pi\) | ||
0.954789 | − | 0.297285i | \(-0.0960811\pi\) | |||||||
\(878\) | −24.3923 | + | 6.53590i | −0.823200 | + | 0.220576i | ||||
\(879\) | 22.7846 | 0.768506 | ||||||||
\(880\) | −9.46410 | + | 16.3923i | −0.319035 | + | 0.552584i | ||||
\(881\) | −35.5692 | −1.19836 | −0.599179 | − | 0.800615i | \(-0.704506\pi\) | ||||
−0.599179 | + | 0.800615i | \(0.704506\pi\) | |||||||
\(882\) | −21.0263 | + | 5.63397i | −0.707992 | + | 0.189706i | ||||
\(883\) | − | 3.32051i | − | 0.111744i | −0.998438 | − | 0.0558720i | \(-0.982206\pi\) | ||
0.998438 | − | 0.0558720i | \(-0.0177939\pi\) | |||||||
\(884\) | 4.00000 | + | 6.92820i | 0.134535 | + | 0.233021i | ||||
\(885\) | 7.66025i | 0.257497i | ||||||||
\(886\) | −2.53590 | − | 9.46410i | −0.0851952 | − | 0.317953i | ||||
\(887\) | −43.1769 | −1.44974 | −0.724869 | − | 0.688886i | \(-0.758100\pi\) | ||||
−0.724869 | + | 0.688886i | \(0.758100\pi\) | |||||||
\(888\) | 1.07180 | − | 1.07180i | 0.0359671 | − | 0.0359671i | ||||
\(889\) | −80.1051 | −2.68664 | ||||||||
\(890\) | −0.339746 | − | 1.26795i | −0.0113883 | − | 0.0425018i | ||||
\(891\) | − | 4.73205i | − | 0.158530i | ||||||
\(892\) | −46.7321 | + | 26.9808i | −1.56470 | + | 0.903383i | ||||
\(893\) | 6.39230i | 0.213910i | ||||||||
\(894\) | 4.73205 | − | 1.26795i | 0.158263 | − | 0.0424066i | ||||
\(895\) | 10.3923 | 0.347376 | ||||||||
\(896\) | −13.8564 | − | 51.7128i | −0.462910 | − | 1.72760i | ||||
\(897\) | −2.00000 | −0.0667781 | ||||||||
\(898\) | 36.0526 | − | 9.66025i | 1.20309 | − | 0.322367i | ||||
\(899\) | 0.966679i | 0.0322405i | ||||||||
\(900\) | 1.73205 | − | 1.00000i | 0.0577350 | − | 0.0333333i | ||||
\(901\) | − | 49.5692i | − | 1.65139i | ||||||
\(902\) | 8.53590 | + | 31.8564i | 0.284214 | + | 1.06070i | ||||
\(903\) | −6.92820 | −0.230556 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.92820 | −0.163819 | ||||||||
\(906\) | 6.85641 | + | 25.5885i | 0.227789 | + | 0.850120i | ||||
\(907\) | 39.3205i | 1.30562i | 0.757523 | + | 0.652808i | \(0.226409\pi\) | ||||
−0.757523 | + | 0.652808i | \(0.773591\pi\) | |||||||
\(908\) | 5.66025 | + | 9.80385i | 0.187842 | + | 0.325352i | ||||
\(909\) | 12.0000i | 0.398015i | ||||||||
\(910\) | −6.46410 | + | 1.73205i | −0.214283 | + | 0.0574169i | ||||
\(911\) | −28.1051 | −0.931164 | −0.465582 | − | 0.885005i | \(-0.654155\pi\) | ||||
−0.465582 | + | 0.885005i | \(0.654155\pi\) | |||||||
\(912\) | 1.46410 | − | 2.53590i | 0.0484812 | − | 0.0839720i | ||||
\(913\) | 24.9282 | 0.825003 | ||||||||
\(914\) | 20.5885 | − | 5.51666i | 0.681006 | − | 0.182475i | ||||
\(915\) | − | 2.92820i | − | 0.0968034i | ||||||
\(916\) | −6.00000 | − | 10.3923i | −0.198246 | − | 0.343371i | ||||
\(917\) | 37.1769i | 1.22769i | ||||||||
\(918\) | 1.46410 | + | 5.46410i | 0.0483226 | + | 0.180342i | ||||
\(919\) | −33.4641 | −1.10388 | −0.551939 | − | 0.833884i | \(-0.686112\pi\) | ||||
−0.551939 | + | 0.833884i | \(0.686112\pi\) | |||||||
\(920\) | 4.00000 | + | 4.00000i | 0.131876 | + | 0.131876i | ||||
\(921\) | −19.1244 | −0.630169 | ||||||||
\(922\) | 1.12436 | + | 4.19615i | 0.0370287 | + | 0.138193i | ||||
\(923\) | − | 13.2679i | − | 0.436720i | ||||||
\(924\) | 38.7846 | − | 22.3923i | 1.27592 | − | 0.736653i | ||||
\(925\) | 0.535898i | 0.0176202i | ||||||||
\(926\) | 26.8564 | − | 7.19615i | 0.882556 | − | 0.236480i | ||||
\(927\) | 12.9282 | 0.424618 | ||||||||
\(928\) | 26.9282 | + | 7.21539i | 0.883962 | + | 0.236857i | ||||
\(929\) | 10.3923 | 0.340960 | 0.170480 | − | 0.985361i | \(-0.445468\pi\) | ||||
0.170480 | + | 0.985361i | \(0.445468\pi\) | |||||||
\(930\) | 0.267949 | − | 0.0717968i | 0.00878640 | − | 0.00235431i | ||||
\(931\) | − | 11.2679i | − | 0.369292i | ||||||
\(932\) | 20.5359 | − | 11.8564i | 0.672676 | − | 0.388370i | ||||
\(933\) | − | 31.7128i | − | 1.03823i | ||||||
\(934\) | 7.17691 | + | 26.7846i | 0.234836 | + | 0.876419i | ||||
\(935\) | 18.9282 | 0.619018 | ||||||||
\(936\) | 2.00000 | + | 2.00000i | 0.0653720 | + | 0.0653720i | ||||
\(937\) | −20.6410 | −0.674313 | −0.337156 | − | 0.941449i | \(-0.609465\pi\) | ||||
−0.337156 | + | 0.941449i | \(0.609465\pi\) | |||||||
\(938\) | 21.1244 | + | 78.8372i | 0.689735 | + | 2.57412i | ||||
\(939\) | 8.00000i | 0.261070i | ||||||||
\(940\) | 8.73205 | + | 15.1244i | 0.284808 | + | 0.493302i | ||||
\(941\) | − | 4.53590i | − | 0.147866i | −0.997263 | − | 0.0739330i | \(-0.976445\pi\) | ||
0.997263 | − | 0.0739330i | \(-0.0235551\pi\) | |||||||
\(942\) | 31.1244 | − | 8.33975i | 1.01409 | − | 0.271724i | ||||
\(943\) | 9.85641 | 0.320969 | ||||||||
\(944\) | 26.5359 | + | 15.3205i | 0.863670 | + | 0.498640i | ||||
\(945\) | −4.73205 | −0.153934 | ||||||||
\(946\) | 9.46410 | − | 2.53590i | 0.307704 | − | 0.0824492i | ||||
\(947\) | 24.1962i | 0.786269i | 0.919481 | + | 0.393135i | \(0.128609\pi\) | ||||
−0.919481 | + | 0.393135i | \(0.871391\pi\) | |||||||
\(948\) | 17.4641 | + | 30.2487i | 0.567208 | + | 0.982432i | ||||
\(949\) | − | 15.8564i | − | 0.514721i | ||||||
\(950\) | 0.267949 | + | 1.00000i | 0.00869342 | + | 0.0324443i | ||||
\(951\) | 20.5359 | 0.665922 | ||||||||
\(952\) | −37.8564 | + | 37.8564i | −1.22693 | + | 1.22693i | ||||
\(953\) | 12.9282 | 0.418786 | 0.209393 | − | 0.977832i | \(-0.432851\pi\) | ||||
0.209393 | + | 0.977832i | \(0.432851\pi\) | |||||||
\(954\) | −4.53590 | − | 16.9282i | −0.146855 | − | 0.548071i | ||||
\(955\) | 16.3923i | 0.530443i | ||||||||
\(956\) | −34.3013 | + | 19.8038i | −1.10938 | + | 0.640502i | ||||
\(957\) | 23.3205i | 0.753845i | ||||||||
\(958\) | −54.5167 | + | 14.6077i | −1.76135 | + | 0.471953i | ||||
\(959\) | 49.1769 | 1.58801 | ||||||||
\(960\) | − | 8.00000i | − | 0.258199i | ||||||
\(961\) | −30.9615 | −0.998759 | ||||||||
\(962\) | −0.732051 | + | 0.196152i | −0.0236023 | + | 0.00632421i | ||||
\(963\) | 4.00000i | 0.128898i | ||||||||
\(964\) | −36.2487 | + | 20.9282i | −1.16749 | + | 0.674052i | ||||
\(965\) | 3.46410i | 0.111513i | ||||||||
\(966\) | −3.46410 | − | 12.9282i | −0.111456 | − | 0.415958i | ||||
\(967\) | 12.7321 | 0.409435 | 0.204718 | − | 0.978821i | \(-0.434372\pi\) | ||||
0.204718 | + | 0.978821i | \(0.434372\pi\) | |||||||
\(968\) | −22.7846 | + | 22.7846i | −0.732325 | + | 0.732325i | ||||
\(969\) | −2.92820 | −0.0940674 | ||||||||
\(970\) | 0.196152 | + | 0.732051i | 0.00629807 | + | 0.0235047i | ||||
\(971\) | − | 30.0000i | − | 0.962746i | −0.876516 | − | 0.481373i | \(-0.840138\pi\) | ||
0.876516 | − | 0.481373i | \(-0.159862\pi\) | |||||||
\(972\) | 1.00000 | + | 1.73205i | 0.0320750 | + | 0.0555556i | ||||
\(973\) | − | 9.46410i | − | 0.303405i | ||||||
\(974\) | −11.9282 | + | 3.19615i | −0.382204 | + | 0.102411i | ||||
\(975\) | −1.00000 | −0.0320256 | ||||||||
\(976\) | −10.1436 | − | 5.85641i | −0.324689 | − | 0.187459i | ||||
\(977\) | 38.1051 | 1.21909 | 0.609545 | − | 0.792751i | \(-0.291352\pi\) | ||||
0.609545 | + | 0.792751i | \(0.291352\pi\) | |||||||
\(978\) | −27.5885 | + | 7.39230i | −0.882182 | + | 0.236380i | ||||
\(979\) | − | 4.39230i | − | 0.140379i | ||||||
\(980\) | −15.3923 | − | 26.6603i | −0.491689 | − | 0.851631i | ||||
\(981\) | − | 15.8564i | − | 0.506256i | ||||||
\(982\) | −15.1244 | − | 56.4449i | −0.482638 | − | 1.80123i | ||||
\(983\) | 57.5167 | 1.83450 | 0.917248 | − | 0.398316i | \(-0.130405\pi\) | ||||
0.917248 | + | 0.398316i | \(0.130405\pi\) | |||||||
\(984\) | −9.85641 | − | 9.85641i | −0.314211 | − | 0.314211i | ||||
\(985\) | 2.39230 | 0.0762252 | ||||||||
\(986\) | −7.21539 | − | 26.9282i | −0.229785 | − | 0.857569i | ||||
\(987\) | − | 41.3205i | − | 1.31525i | ||||||
\(988\) | −1.26795 | + | 0.732051i | −0.0403388 | + | 0.0232896i | ||||
\(989\) | − | 2.92820i | − | 0.0931114i | ||||||
\(990\) | 6.46410 | − | 1.73205i | 0.205443 | − | 0.0550482i | ||||
\(991\) | −33.1769 | −1.05390 | −0.526950 | − | 0.849896i | \(-0.676664\pi\) | ||||
−0.526950 | + | 0.849896i | \(0.676664\pi\) | |||||||
\(992\) | 0.287187 | − | 1.07180i | 0.00911820 | − | 0.0340296i | ||||
\(993\) | −12.0526 | −0.382476 | ||||||||
\(994\) | 85.7654 | − | 22.9808i | 2.72031 | − | 0.728906i | ||||
\(995\) | 9.07180i | 0.287595i | ||||||||
\(996\) | −9.12436 | + | 5.26795i | −0.289116 | + | 0.166921i | ||||
\(997\) | − | 60.1051i | − | 1.90355i | −0.306800 | − | 0.951774i | \(-0.599258\pi\) | ||
0.306800 | − | 0.951774i | \(-0.400742\pi\) | |||||||
\(998\) | 0.803848 | + | 3.00000i | 0.0254454 | + | 0.0949633i | ||||
\(999\) | −0.535898 | −0.0169551 |
(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 | 1560.2.w.d.781.3 | ✓ | 4 | |
4.3 | odd | 2 | 6240.2.w.c.3121.1 | 4 | |||
8.3 | odd | 2 | 6240.2.w.c.3121.3 | 4 | |||
8.5 | even | 2 | inner | 1560.2.w.d.781.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.w.d.781.3 | ✓ | 4 | 1.1 | even | 1 | trivial | |
1560.2.w.d.781.4 | yes | 4 | 8.5 | even | 2 | inner | |
6240.2.w.c.3121.1 | 4 | 4.3 | odd | 2 | |||
6240.2.w.c.3121.3 | 4 | 8.3 | odd | 2 |