Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(247,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.247");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.k (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: | \(7.42608738798\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 247.2 | ||
Character | \(\chi\) | \(=\) | 930.247 |
Dual form | 930.2.k.b.433.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | −2.14949 | + | 0.616200i | −0.961280 | + | 0.275573i | ||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 0.0344550 | + | 0.0344550i | 0.0130228 | + | 0.0130228i | 0.713588 | − | 0.700565i | \(-0.247069\pi\) |
−0.700565 | + | 0.713588i | \(0.747069\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 1.95564 | + | 1.08420i | 0.618427 | + | 0.342853i | ||||
\(11\) | − | 0.241934i | − | 0.0729458i | −0.999335 | − | 0.0364729i | \(-0.988388\pi\) | ||
0.999335 | − | 0.0364729i | \(-0.0116123\pi\) | |||||||
\(12\) | 0.707107 | − | 0.707107i | 0.204124 | − | 0.204124i | ||||
\(13\) | 3.88473 | + | 3.88473i | 1.07743 | + | 1.07743i | 0.996739 | + | 0.0806917i | \(0.0257129\pi\) |
0.0806917 | + | 0.996739i | \(0.474287\pi\) | |||||||
\(14\) | − | 0.0487267i | − | 0.0130228i | ||||||
\(15\) | 1.95564 | + | 1.08420i | 0.504943 | + | 0.279939i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 1.35699 | − | 1.35699i | 0.329118 | − | 0.329118i | −0.523133 | − | 0.852251i | \(-0.675237\pi\) |
0.852251 | + | 0.523133i | \(0.175237\pi\) | |||||||
\(18\) | 0.707107 | − | 0.707107i | 0.166667 | − | 0.166667i | ||||
\(19\) | − | 8.10639i | − | 1.85973i | −0.367898 | − | 0.929866i | \(-0.619922\pi\) | ||
0.367898 | − | 0.929866i | \(-0.380078\pi\) | |||||||
\(20\) | −0.616200 | − | 2.14949i | −0.137787 | − | 0.480640i | ||||
\(21\) | − | 0.0487267i | − | 0.0106330i | ||||||
\(22\) | −0.171073 | + | 0.171073i | −0.0364729 | + | 0.0364729i | ||||
\(23\) | −2.64257 | − | 2.64257i | −0.551015 | − | 0.551015i | 0.375719 | − | 0.926734i | \(-0.377396\pi\) |
−0.926734 | + | 0.375719i | \(0.877396\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 4.24059 | − | 2.64903i | 0.848119 | − | 0.529806i | ||||
\(26\) | − | 5.49384i | − | 1.07743i | ||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −0.0344550 | + | 0.0344550i | −0.00651138 | + | 0.00651138i | ||||
\(29\) | −8.54385 | −1.58655 | −0.793277 | − | 0.608862i | \(-0.791626\pi\) | ||||
−0.793277 | + | 0.608862i | \(0.791626\pi\) | |||||||
\(30\) | −0.616200 | − | 2.14949i | −0.112502 | − | 0.392441i | ||||
\(31\) | −3.04494 | + | 4.66137i | −0.546887 | + | 0.837207i | ||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | −0.171073 | + | 0.171073i | −0.0297800 | + | 0.0297800i | ||||
\(34\) | −1.91907 | −0.329118 | ||||||||
\(35\) | −0.0952917 | − | 0.0528294i | −0.0161072 | − | 0.00892980i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −4.54476 | + | 4.54476i | −0.747154 | + | 0.747154i | −0.973944 | − | 0.226790i | \(-0.927177\pi\) |
0.226790 | + | 0.973944i | \(0.427177\pi\) | |||||||
\(38\) | −5.73208 | + | 5.73208i | −0.929866 | + | 0.929866i | ||||
\(39\) | − | 5.49384i | − | 0.879719i | ||||||
\(40\) | −1.08420 | + | 1.95564i | −0.171427 | + | 0.309213i | ||||
\(41\) | −1.46546 | −0.228866 | −0.114433 | − | 0.993431i | \(-0.536505\pi\) | ||||
−0.114433 | + | 0.993431i | \(0.536505\pi\) | |||||||
\(42\) | −0.0344550 | + | 0.0344550i | −0.00531652 | + | 0.00531652i | ||||
\(43\) | −0.329923 | − | 0.329923i | −0.0503128 | − | 0.0503128i | 0.681503 | − | 0.731816i | \(-0.261327\pi\) |
−0.731816 | + | 0.681503i | \(0.761327\pi\) | |||||||
\(44\) | 0.241934 | 0.0364729 | ||||||||
\(45\) | −0.616200 | − | 2.14949i | −0.0918577 | − | 0.320427i | ||||
\(46\) | 3.73716i | 0.551015i | ||||||||
\(47\) | −2.81146 | − | 2.81146i | −0.410093 | − | 0.410093i | 0.471678 | − | 0.881771i | \(-0.343649\pi\) |
−0.881771 | + | 0.471678i | \(0.843649\pi\) | |||||||
\(48\) | 0.707107 | + | 0.707107i | 0.102062 | + | 0.102062i | ||||
\(49\) | − | 6.99763i | − | 0.999661i | ||||||
\(50\) | −4.87170 | − | 1.12541i | −0.688962 | − | 0.159156i | ||||
\(51\) | −1.91907 | −0.268724 | ||||||||
\(52\) | −3.88473 | + | 3.88473i | −0.538715 | + | 0.538715i | ||||
\(53\) | 0.597357 | + | 0.597357i | 0.0820533 | + | 0.0820533i | 0.746942 | − | 0.664889i | \(-0.231521\pi\) |
−0.664889 | + | 0.746942i | \(0.731521\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.149080 | + | 0.520034i | 0.0201019 | + | 0.0701214i | ||||
\(56\) | 0.0487267 | 0.00651138 | ||||||||
\(57\) | −5.73208 | + | 5.73208i | −0.759233 | + | 0.759233i | ||||
\(58\) | 6.04141 | + | 6.04141i | 0.793277 | + | 0.793277i | ||||
\(59\) | − | 13.6979i | − | 1.78332i | −0.452705 | − | 0.891660i | \(-0.649541\pi\) | ||
0.452705 | − | 0.891660i | \(-0.350459\pi\) | |||||||
\(60\) | −1.08420 | + | 1.95564i | −0.139969 | + | 0.252472i | ||||
\(61\) | − | 11.6907i | − | 1.49684i | −0.663223 | − | 0.748421i | \(-0.730812\pi\) | ||
0.663223 | − | 0.748421i | \(-0.269188\pi\) | |||||||
\(62\) | 5.44918 | − | 1.14299i | 0.692047 | − | 0.145160i | ||||
\(63\) | −0.0344550 | + | 0.0344550i | −0.00434092 | + | 0.00434092i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −10.7440 | − | 5.95641i | −1.33262 | − | 0.738802i | ||||
\(66\) | 0.241934 | 0.0297800 | ||||||||
\(67\) | −0.653315 | − | 0.653315i | −0.0798151 | − | 0.0798151i | 0.666072 | − | 0.745887i | \(-0.267974\pi\) |
−0.745887 | + | 0.666072i | \(0.767974\pi\) | |||||||
\(68\) | 1.35699 | + | 1.35699i | 0.164559 | + | 0.164559i | ||||
\(69\) | 3.73716i | 0.449902i | ||||||||
\(70\) | 0.0300254 | + | 0.104737i | 0.00358872 | + | 0.0125185i | ||||
\(71\) | −4.44096 | −0.527045 | −0.263522 | − | 0.964653i | \(-0.584884\pi\) | ||||
−0.263522 | + | 0.964653i | \(0.584884\pi\) | |||||||
\(72\) | 0.707107 | + | 0.707107i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 8.64429 | + | 8.64429i | 1.01174 | + | 1.01174i | 0.999930 | + | 0.0118067i | \(0.00375829\pi\) |
0.0118067 | + | 0.999930i | \(0.496242\pi\) | |||||||
\(74\) | 6.42726 | 0.747154 | ||||||||
\(75\) | −4.87170 | − | 1.12541i | −0.562535 | − | 0.129951i | ||||
\(76\) | 8.10639 | 0.929866 | ||||||||
\(77\) | 0.00833583 | − | 0.00833583i | 0.000949956 | − | 0.000949956i | ||||
\(78\) | −3.88473 | + | 3.88473i | −0.439859 | + | 0.439859i | ||||
\(79\) | −12.9046 | −1.45188 | −0.725939 | − | 0.687759i | \(-0.758595\pi\) | ||||
−0.725939 | + | 0.687759i | \(0.758595\pi\) | |||||||
\(80\) | 2.14949 | − | 0.616200i | 0.240320 | − | 0.0688933i | ||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.03624 | + | 1.03624i | 0.114433 | + | 0.114433i | ||||
\(83\) | −0.681471 | − | 0.681471i | −0.0748011 | − | 0.0748011i | 0.668716 | − | 0.743518i | \(-0.266844\pi\) |
−0.743518 | + | 0.668716i | \(0.766844\pi\) | |||||||
\(84\) | 0.0487267 | 0.00531652 | ||||||||
\(85\) | −2.08065 | + | 3.75301i | −0.225679 | + | 0.407071i | ||||
\(86\) | 0.466581i | 0.0503128i | ||||||||
\(87\) | 6.04141 | + | 6.04141i | 0.647708 | + | 0.647708i | ||||
\(88\) | −0.171073 | − | 0.171073i | −0.0182365 | − | 0.0182365i | ||||
\(89\) | −2.20446 | −0.233672 | −0.116836 | − | 0.993151i | \(-0.537275\pi\) | ||||
−0.116836 | + | 0.993151i | \(0.537275\pi\) | |||||||
\(90\) | −1.08420 | + | 1.95564i | −0.114284 | + | 0.206142i | ||||
\(91\) | 0.267697i | 0.0280622i | ||||||||
\(92\) | 2.64257 | − | 2.64257i | 0.275507 | − | 0.275507i | ||||
\(93\) | 5.44918 | − | 1.14299i | 0.565054 | − | 0.118523i | ||||
\(94\) | 3.97600i | 0.410093i | ||||||||
\(95\) | 4.99516 | + | 17.4246i | 0.512493 | + | 1.78772i | ||||
\(96\) | − | 1.00000i | − | 0.102062i | ||||||
\(97\) | −5.06944 | − | 5.06944i | −0.514724 | − | 0.514724i | 0.401246 | − | 0.915970i | \(-0.368577\pi\) |
−0.915970 | + | 0.401246i | \(0.868577\pi\) | |||||||
\(98\) | −4.94807 | + | 4.94807i | −0.499830 | + | 0.499830i | ||||
\(99\) | 0.241934 | 0.0243153 | ||||||||
\(100\) | 2.64903 | + | 4.24059i | 0.264903 | + | 0.424059i | ||||
\(101\) | −11.8507 | −1.17919 | −0.589593 | − | 0.807700i | \(-0.700712\pi\) | ||||
−0.589593 | + | 0.807700i | \(0.700712\pi\) | |||||||
\(102\) | 1.35699 | + | 1.35699i | 0.134362 | + | 0.134362i | ||||
\(103\) | −8.10157 | + | 8.10157i | −0.798272 | + | 0.798272i | −0.982823 | − | 0.184551i | \(-0.940917\pi\) |
0.184551 | + | 0.982823i | \(0.440917\pi\) | |||||||
\(104\) | 5.49384 | 0.538715 | ||||||||
\(105\) | 0.0300254 | + | 0.104737i | 0.00293018 | + | 0.0102213i | ||||
\(106\) | − | 0.844790i | − | 0.0820533i | ||||||
\(107\) | −10.2618 | − | 10.2618i | −0.992044 | − | 0.992044i | 0.00792440 | − | 0.999969i | \(-0.497478\pi\) |
−0.999969 | + | 0.00792440i | \(0.997478\pi\) | |||||||
\(108\) | 0.707107 | + | 0.707107i | 0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 6.81387i | − | 0.652651i | −0.945258 | − | 0.326325i | \(-0.894190\pi\) | ||
0.945258 | − | 0.326325i | \(-0.105810\pi\) | |||||||
\(110\) | 0.262304 | − | 0.473135i | 0.0250097 | − | 0.0451116i | ||||
\(111\) | 6.42726 | 0.610049 | ||||||||
\(112\) | −0.0344550 | − | 0.0344550i | −0.00325569 | − | 0.00325569i | ||||
\(113\) | 0.808734 | − | 0.808734i | 0.0760793 | − | 0.0760793i | −0.668043 | − | 0.744123i | \(-0.732868\pi\) |
0.744123 | + | 0.668043i | \(0.232868\pi\) | |||||||
\(114\) | 8.10639 | 0.759233 | ||||||||
\(115\) | 7.30854 | + | 4.05183i | 0.681525 | + | 0.377835i | ||||
\(116\) | − | 8.54385i | − | 0.793277i | ||||||
\(117\) | −3.88473 | + | 3.88473i | −0.359144 | + | 0.359144i | ||||
\(118\) | −9.68591 | + | 9.68591i | −0.891660 | + | 0.891660i | ||||
\(119\) | 0.0935101 | 0.00857205 | ||||||||
\(120\) | 2.14949 | − | 0.616200i | 0.196220 | − | 0.0562511i | ||||
\(121\) | 10.9415 | 0.994679 | ||||||||
\(122\) | −8.26659 | + | 8.26659i | −0.748421 | + | 0.748421i | ||||
\(123\) | 1.03624 | + | 1.03624i | 0.0934342 | + | 0.0934342i | ||||
\(124\) | −4.66137 | − | 3.04494i | −0.418603 | − | 0.273443i | ||||
\(125\) | −7.48277 | + | 8.30711i | −0.669279 | + | 0.743011i | ||||
\(126\) | 0.0487267 | 0.00434092 | ||||||||
\(127\) | 10.1076 | − | 10.1076i | 0.896907 | − | 0.896907i | −0.0982539 | − | 0.995161i | \(-0.531326\pi\) |
0.995161 | + | 0.0982539i | \(0.0313257\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 0.466581i | 0.0410802i | ||||||||
\(130\) | 3.38531 | + | 11.8089i | 0.296911 | + | 1.03571i | ||||
\(131\) | 7.31940 | 0.639499 | 0.319749 | − | 0.947502i | \(-0.396401\pi\) | ||||
0.319749 | + | 0.947502i | \(0.396401\pi\) | |||||||
\(132\) | −0.171073 | − | 0.171073i | −0.0148900 | − | 0.0148900i | ||||
\(133\) | 0.279305 | − | 0.279305i | 0.0242189 | − | 0.0242189i | ||||
\(134\) | 0.923926i | 0.0798151i | ||||||||
\(135\) | −1.08420 | + | 1.95564i | −0.0933129 | + | 0.168314i | ||||
\(136\) | − | 1.91907i | − | 0.164559i | ||||||
\(137\) | −0.736104 | + | 0.736104i | −0.0628896 | + | 0.0628896i | −0.737852 | − | 0.674962i | \(-0.764160\pi\) |
0.674962 | + | 0.737852i | \(0.264160\pi\) | |||||||
\(138\) | 2.64257 | − | 2.64257i | 0.224951 | − | 0.224951i | ||||
\(139\) | 4.32252 | 0.366631 | 0.183316 | − | 0.983054i | \(-0.441317\pi\) | ||||
0.183316 | + | 0.983054i | \(0.441317\pi\) | |||||||
\(140\) | 0.0528294 | − | 0.0952917i | 0.00446490 | − | 0.00805362i | ||||
\(141\) | 3.97600i | 0.334840i | ||||||||
\(142\) | 3.14023 | + | 3.14023i | 0.263522 | + | 0.263522i | ||||
\(143\) | 0.939849 | − | 0.939849i | 0.0785941 | − | 0.0785941i | ||||
\(144\) | − | 1.00000i | − | 0.0833333i | ||||||
\(145\) | 18.3649 | − | 5.26472i | 1.52512 | − | 0.437212i | ||||
\(146\) | − | 12.2249i | − | 1.01174i | ||||||
\(147\) | −4.94807 | + | 4.94807i | −0.408110 | + | 0.408110i | ||||
\(148\) | −4.54476 | − | 4.54476i | −0.373577 | − | 0.373577i | ||||
\(149\) | − | 15.8034i | − | 1.29467i | −0.762206 | − | 0.647334i | \(-0.775884\pi\) | ||
0.762206 | − | 0.647334i | \(-0.224116\pi\) | |||||||
\(150\) | 2.64903 | + | 4.24059i | 0.216292 | + | 0.346243i | ||||
\(151\) | − | 3.30031i | − | 0.268575i | −0.990942 | − | 0.134288i | \(-0.957125\pi\) | ||
0.990942 | − | 0.134288i | \(-0.0428746\pi\) | |||||||
\(152\) | −5.73208 | − | 5.73208i | −0.464933 | − | 0.464933i | ||||
\(153\) | 1.35699 | + | 1.35699i | 0.109706 | + | 0.109706i | ||||
\(154\) | −0.0117886 | −0.000949956 | ||||||||
\(155\) | 3.67271 | − | 11.8958i | 0.294999 | − | 0.955497i | ||||
\(156\) | 5.49384 | 0.439859 | ||||||||
\(157\) | −4.79524 | − | 4.79524i | −0.382702 | − | 0.382702i | 0.489373 | − | 0.872075i | \(-0.337226\pi\) |
−0.872075 | + | 0.489373i | \(0.837226\pi\) | |||||||
\(158\) | 9.12491 | + | 9.12491i | 0.725939 | + | 0.725939i | ||||
\(159\) | − | 0.844790i | − | 0.0669962i | ||||||
\(160\) | −1.95564 | − | 1.08420i | −0.154607 | − | 0.0857134i | ||||
\(161\) | − | 0.182100i | − | 0.0143515i | ||||||
\(162\) | 0.707107 | + | 0.707107i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 12.0108 | − | 12.0108i | 0.940756 | − | 0.940756i | −0.0575847 | − | 0.998341i | \(-0.518340\pi\) |
0.998341 | + | 0.0575847i | \(0.0183399\pi\) | |||||||
\(164\) | − | 1.46546i | − | 0.114433i | ||||||
\(165\) | 0.262304 | − | 0.473135i | 0.0204204 | − | 0.0368335i | ||||
\(166\) | 0.963745i | 0.0748011i | ||||||||
\(167\) | 12.9307 | − | 12.9307i | 1.00060 | − | 1.00060i | 0.000604752 | − | 1.00000i | \(-0.499808\pi\) |
1.00000 | 0.000604752i | \(-0.000192499\pi\) | ||||||||
\(168\) | −0.0344550 | − | 0.0344550i | −0.00265826 | − | 0.00265826i | ||||
\(169\) | 17.1823i | 1.32171i | ||||||||
\(170\) | 4.12502 | − | 1.18253i | 0.316375 | − | 0.0906961i | ||||
\(171\) | 8.10639 | 0.619911 | ||||||||
\(172\) | 0.329923 | − | 0.329923i | 0.0251564 | − | 0.0251564i | ||||
\(173\) | −17.7387 | + | 17.7387i | −1.34865 | + | 1.34865i | −0.461511 | + | 0.887135i | \(0.652692\pi\) |
−0.887135 | + | 0.461511i | \(0.847308\pi\) | |||||||
\(174\) | − | 8.54385i | − | 0.647708i | ||||||
\(175\) | 0.237382 | + | 0.0548373i | 0.0179444 | + | 0.00414531i | ||||
\(176\) | 0.241934i | 0.0182365i | ||||||||
\(177\) | −9.68591 | + | 9.68591i | −0.728037 | + | 0.728037i | ||||
\(178\) | 1.55879 | + | 1.55879i | 0.116836 | + | 0.116836i | ||||
\(179\) | −7.57644 | −0.566290 | −0.283145 | − | 0.959077i | \(-0.591378\pi\) | ||||
−0.283145 | + | 0.959077i | \(0.591378\pi\) | |||||||
\(180\) | 2.14949 | − | 0.616200i | 0.160213 | − | 0.0459289i | ||||
\(181\) | 4.86746i | 0.361795i | 0.983502 | + | 0.180898i | \(0.0579003\pi\) | ||||
−0.983502 | + | 0.180898i | \(0.942100\pi\) | |||||||
\(182\) | 0.189290 | − | 0.189290i | 0.0140311 | − | 0.0140311i | ||||
\(183\) | −8.26659 | + | 8.26659i | −0.611084 | + | 0.611084i | ||||
\(184\) | −3.73716 | −0.275507 | ||||||||
\(185\) | 6.96842 | − | 12.5694i | 0.512329 | − | 0.924120i | ||||
\(186\) | −4.66137 | − | 3.04494i | −0.341788 | − | 0.223265i | ||||
\(187\) | −0.328302 | − | 0.328302i | −0.0240078 | − | 0.0240078i | ||||
\(188\) | 2.81146 | − | 2.81146i | 0.205047 | − | 0.205047i | ||||
\(189\) | 0.0487267 | 0.00354435 | ||||||||
\(190\) | 8.78893 | − | 15.8531i | 0.637616 | − | 1.15011i | ||||
\(191\) | 18.8465 | 1.36368 | 0.681841 | − | 0.731500i | \(-0.261180\pi\) | ||||
0.681841 | + | 0.731500i | \(0.261180\pi\) | |||||||
\(192\) | −0.707107 | + | 0.707107i | −0.0510310 | + | 0.0510310i | ||||
\(193\) | −6.30444 | + | 6.30444i | −0.453803 | + | 0.453803i | −0.896615 | − | 0.442811i | \(-0.853981\pi\) |
0.442811 | + | 0.896615i | \(0.353981\pi\) | |||||||
\(194\) | 7.16927i | 0.514724i | ||||||||
\(195\) | 3.38531 | + | 11.8089i | 0.242427 | + | 0.845656i | ||||
\(196\) | 6.99763 | 0.499830 | ||||||||
\(197\) | 12.4152 | − | 12.4152i | 0.884545 | − | 0.884545i | −0.109448 | − | 0.993993i | \(-0.534908\pi\) |
0.993993 | + | 0.109448i | \(0.0349082\pi\) | |||||||
\(198\) | −0.171073 | − | 0.171073i | −0.0121576 | − | 0.0121576i | ||||
\(199\) | −7.08879 | −0.502511 | −0.251255 | − | 0.967921i | \(-0.580843\pi\) | ||||
−0.251255 | + | 0.967921i | \(0.580843\pi\) | |||||||
\(200\) | 1.12541 | − | 4.87170i | 0.0795782 | − | 0.344481i | ||||
\(201\) | 0.923926i | 0.0651687i | ||||||||
\(202\) | 8.37970 | + | 8.37970i | 0.589593 | + | 0.589593i | ||||
\(203\) | −0.294378 | − | 0.294378i | −0.0206613 | − | 0.0206613i | ||||
\(204\) | − | 1.91907i | − | 0.134362i | ||||||
\(205\) | 3.14998 | − | 0.903016i | 0.220004 | − | 0.0630694i | ||||
\(206\) | 11.4574 | 0.798272 | ||||||||
\(207\) | 2.64257 | − | 2.64257i | 0.183672 | − | 0.183672i | ||||
\(208\) | −3.88473 | − | 3.88473i | −0.269358 | − | 0.269358i | ||||
\(209\) | −1.96121 | −0.135660 | ||||||||
\(210\) | 0.0528294 | − | 0.0952917i | 0.00364557 | − | 0.00657576i | ||||
\(211\) | 2.44965 | 0.168641 | 0.0843205 | − | 0.996439i | \(-0.473128\pi\) | ||||
0.0843205 | + | 0.996439i | \(0.473128\pi\) | |||||||
\(212\) | −0.597357 | + | 0.597357i | −0.0410266 | + | 0.0410266i | ||||
\(213\) | 3.14023 | + | 3.14023i | 0.215165 | + | 0.215165i | ||||
\(214\) | 14.5124i | 0.992044i | ||||||||
\(215\) | 0.912464 | + | 0.505866i | 0.0622295 | + | 0.0344998i | ||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −0.265521 | + | 0.0556942i | −0.0180247 | + | 0.00378077i | ||||
\(218\) | −4.81814 | + | 4.81814i | −0.326325 | + | 0.326325i | ||||
\(219\) | − | 12.2249i | − | 0.826080i | ||||||
\(220\) | −0.520034 | + | 0.149080i | −0.0350607 | + | 0.0100510i | ||||
\(221\) | 10.5431 | 0.709204 | ||||||||
\(222\) | −4.54476 | − | 4.54476i | −0.305024 | − | 0.305024i | ||||
\(223\) | −15.8119 | − | 15.8119i | −1.05884 | − | 1.05884i | −0.998157 | − | 0.0606828i | \(-0.980672\pi\) |
−0.0606828 | − | 0.998157i | \(-0.519328\pi\) | |||||||
\(224\) | 0.0487267i | 0.00325569i | ||||||||
\(225\) | 2.64903 | + | 4.24059i | 0.176602 | + | 0.282706i | ||||
\(226\) | −1.14372 | −0.0760793 | ||||||||
\(227\) | 19.2620 | + | 19.2620i | 1.27847 | + | 1.27847i | 0.941526 | + | 0.336940i | \(0.109392\pi\) |
0.336940 | + | 0.941526i | \(0.390608\pi\) | |||||||
\(228\) | −5.73208 | − | 5.73208i | −0.379616 | − | 0.379616i | ||||
\(229\) | −27.0642 | −1.78845 | −0.894226 | − | 0.447617i | \(-0.852273\pi\) | ||||
−0.894226 | + | 0.447617i | \(0.852273\pi\) | |||||||
\(230\) | −2.30284 | − | 8.03299i | −0.151845 | − | 0.529680i | ||||
\(231\) | −0.0117886 | −0.000775636 | ||||||||
\(232\) | −6.04141 | + | 6.04141i | −0.396638 | + | 0.396638i | ||||
\(233\) | 9.02104 | − | 9.02104i | 0.590988 | − | 0.590988i | −0.346910 | − | 0.937898i | \(-0.612769\pi\) |
0.937898 | + | 0.346910i | \(0.112769\pi\) | |||||||
\(234\) | 5.49384 | 0.359144 | ||||||||
\(235\) | 7.77561 | + | 4.31077i | 0.507225 | + | 0.281204i | ||||
\(236\) | 13.6979 | 0.891660 | ||||||||
\(237\) | 9.12491 | + | 9.12491i | 0.592727 | + | 0.592727i | ||||
\(238\) | −0.0661216 | − | 0.0661216i | −0.00428603 | − | 0.00428603i | ||||
\(239\) | 18.6644 | 1.20730 | 0.603651 | − | 0.797249i | \(-0.293712\pi\) | ||||
0.603651 | + | 0.797249i | \(0.293712\pi\) | |||||||
\(240\) | −1.95564 | − | 1.08420i | −0.126236 | − | 0.0699847i | ||||
\(241\) | 17.5955i | 1.13343i | 0.823915 | + | 0.566713i | \(0.191785\pi\) | ||||
−0.823915 | + | 0.566713i | \(0.808215\pi\) | |||||||
\(242\) | −7.73679 | − | 7.73679i | −0.497339 | − | 0.497339i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 11.6907 | 0.748421 | ||||||||
\(245\) | 4.31194 | + | 15.0413i | 0.275480 | + | 0.960954i | ||||
\(246\) | − | 1.46546i | − | 0.0934342i | ||||||
\(247\) | 31.4911 | − | 31.4911i | 2.00373 | − | 2.00373i | ||||
\(248\) | 1.14299 | + | 5.44918i | 0.0725800 | + | 0.346023i | ||||
\(249\) | 0.963745i | 0.0610749i | ||||||||
\(250\) | 11.1651 | − | 0.582899i | 0.706145 | − | 0.0368658i | ||||
\(251\) | 1.15940i | 0.0731808i | 0.999330 | + | 0.0365904i | \(0.0116497\pi\) | ||||
−0.999330 | + | 0.0365904i | \(0.988350\pi\) | |||||||
\(252\) | −0.0344550 | − | 0.0344550i | −0.00217046 | − | 0.00217046i | ||||
\(253\) | −0.639328 | + | 0.639328i | −0.0401942 | + | 0.0401942i | ||||
\(254\) | −14.2944 | −0.896907 | ||||||||
\(255\) | 4.12502 | − | 1.18253i | 0.258319 | − | 0.0740531i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.36262 | − | 3.36262i | −0.209754 | − | 0.209754i | 0.594409 | − | 0.804163i | \(-0.297386\pi\) |
−0.804163 | + | 0.594409i | \(0.797386\pi\) | |||||||
\(258\) | 0.329923 | − | 0.329923i | 0.0205401 | − | 0.0205401i | ||||
\(259\) | −0.313179 | −0.0194600 | ||||||||
\(260\) | 5.95641 | − | 10.7440i | 0.369401 | − | 0.666312i | ||||
\(261\) | − | 8.54385i | − | 0.528851i | ||||||
\(262\) | −5.17559 | − | 5.17559i | −0.319749 | − | 0.319749i | ||||
\(263\) | 16.2256 | + | 16.2256i | 1.00051 | + | 1.00051i | 1.00000 | 0.000512751i | \(0.000163214\pi\) | |
0.000512751 | 1.00000i | \(0.499837\pi\) | ||||||||
\(264\) | 0.241934i | 0.0148900i | ||||||||
\(265\) | −1.65210 | − | 0.915920i | −0.101488 | − | 0.0562645i | ||||
\(266\) | −0.394998 | −0.0242189 | ||||||||
\(267\) | 1.55879 | + | 1.55879i | 0.0953962 | + | 0.0953962i | ||||
\(268\) | 0.653315 | − | 0.653315i | 0.0399075 | − | 0.0399075i | ||||
\(269\) | 0.853836 | 0.0520593 | 0.0260296 | − | 0.999661i | \(-0.491714\pi\) | ||||
0.0260296 | + | 0.999661i | \(0.491714\pi\) | |||||||
\(270\) | 2.14949 | − | 0.616200i | 0.130814 | − | 0.0375008i | ||||
\(271\) | − | 15.1304i | − | 0.919103i | −0.888151 | − | 0.459552i | \(-0.848010\pi\) | ||
0.888151 | − | 0.459552i | \(-0.151990\pi\) | |||||||
\(272\) | −1.35699 | + | 1.35699i | −0.0822795 | + | 0.0822795i | ||||
\(273\) | 0.189290 | − | 0.189290i | 0.0114564 | − | 0.0114564i | ||||
\(274\) | 1.04101 | 0.0628896 | ||||||||
\(275\) | −0.640890 | − | 1.02594i | −0.0386471 | − | 0.0618667i | ||||
\(276\) | −3.73716 | −0.224951 | ||||||||
\(277\) | −11.1206 | + | 11.1206i | −0.668173 | + | 0.668173i | −0.957293 | − | 0.289120i | \(-0.906637\pi\) |
0.289120 | + | 0.957293i | \(0.406637\pi\) | |||||||
\(278\) | −3.05648 | − | 3.05648i | −0.183316 | − | 0.183316i | ||||
\(279\) | −4.66137 | − | 3.04494i | −0.279069 | − | 0.182296i | ||||
\(280\) | −0.104737 | + | 0.0300254i | −0.00625926 | + | 0.00179436i | ||||
\(281\) | −11.2075 | −0.668581 | −0.334290 | − | 0.942470i | \(-0.608497\pi\) | ||||
−0.334290 | + | 0.942470i | \(0.608497\pi\) | |||||||
\(282\) | 2.81146 | − | 2.81146i | 0.167420 | − | 0.167420i | ||||
\(283\) | 2.06960 | − | 2.06960i | 0.123025 | − | 0.123025i | −0.642914 | − | 0.765939i | \(-0.722275\pi\) |
0.765939 | + | 0.642914i | \(0.222275\pi\) | |||||||
\(284\) | − | 4.44096i | − | 0.263522i | ||||||
\(285\) | 8.78893 | − | 15.8531i | 0.520611 | − | 0.939059i | ||||
\(286\) | −1.32915 | −0.0785941 | ||||||||
\(287\) | −0.0504923 | − | 0.0504923i | −0.00298047 | − | 0.00298047i | ||||
\(288\) | −0.707107 | + | 0.707107i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 13.3172i | 0.783362i | ||||||||
\(290\) | −16.7087 | − | 9.26322i | −0.981167 | − | 0.543955i | ||||
\(291\) | 7.16927i | 0.420270i | ||||||||
\(292\) | −8.64429 | + | 8.64429i | −0.505869 | + | 0.505869i | ||||
\(293\) | −15.8821 | + | 15.8821i | −0.927841 | + | 0.927841i | −0.997566 | − | 0.0697252i | \(-0.977788\pi\) |
0.0697252 | + | 0.997566i | \(0.477788\pi\) | |||||||
\(294\) | 6.99763 | 0.408110 | ||||||||
\(295\) | 8.44068 | + | 29.4436i | 0.491435 | + | 1.71427i | ||||
\(296\) | 6.42726i | 0.373577i | ||||||||
\(297\) | −0.171073 | − | 0.171073i | −0.00992667 | − | 0.00992667i | ||||
\(298\) | −11.1747 | + | 11.1747i | −0.647334 | + | 0.647334i | ||||
\(299\) | − | 20.5314i | − | 1.18736i | ||||||
\(300\) | 1.12541 | − | 4.87170i | 0.0649753 | − | 0.281268i | ||||
\(301\) | − | 0.0227350i | − | 0.00131042i | ||||||
\(302\) | −2.33367 | + | 2.33367i | −0.134288 | + | 0.134288i | ||||
\(303\) | 8.37970 | + | 8.37970i | 0.481401 | + | 0.481401i | ||||
\(304\) | 8.10639i | 0.464933i | ||||||||
\(305\) | 7.20382 | + | 25.1291i | 0.412490 | + | 1.43889i | ||||
\(306\) | − | 1.91907i | − | 0.109706i | ||||||
\(307\) | 6.44243 | + | 6.44243i | 0.367689 | + | 0.367689i | 0.866634 | − | 0.498945i | \(-0.166279\pi\) |
−0.498945 | + | 0.866634i | \(0.666279\pi\) | |||||||
\(308\) | 0.00833583 | + | 0.00833583i | 0.000474978 | + | 0.000474978i | ||||
\(309\) | 11.4574 | 0.651786 | ||||||||
\(310\) | −11.0086 | + | 5.81463i | −0.625248 | + | 0.330249i | ||||
\(311\) | 10.1552 | 0.575850 | 0.287925 | − | 0.957653i | \(-0.407035\pi\) | ||||
0.287925 | + | 0.957653i | \(0.407035\pi\) | |||||||
\(312\) | −3.88473 | − | 3.88473i | −0.219930 | − | 0.219930i | ||||
\(313\) | 15.3235 | + | 15.3235i | 0.866136 | + | 0.866136i | 0.992042 | − | 0.125906i | \(-0.0401838\pi\) |
−0.125906 | + | 0.992042i | \(0.540184\pi\) | |||||||
\(314\) | 6.78150i | 0.382702i | ||||||||
\(315\) | 0.0528294 | − | 0.0952917i | 0.00297660 | − | 0.00536908i | ||||
\(316\) | − | 12.9046i | − | 0.725939i | ||||||
\(317\) | 0.905319 | + | 0.905319i | 0.0508478 | + | 0.0508478i | 0.732073 | − | 0.681226i | \(-0.238553\pi\) |
−0.681226 | + | 0.732073i | \(0.738553\pi\) | |||||||
\(318\) | −0.597357 | + | 0.597357i | −0.0334981 | + | 0.0334981i | ||||
\(319\) | 2.06705i | 0.115732i | ||||||||
\(320\) | 0.616200 | + | 2.14949i | 0.0344467 | + | 0.120160i | ||||
\(321\) | 14.5124i | 0.810001i | ||||||||
\(322\) | −0.128764 | + | 0.128764i | −0.00717573 | + | 0.00717573i | ||||
\(323\) | −11.0003 | − | 11.0003i | −0.612072 | − | 0.612072i | ||||
\(324\) | − | 1.00000i | − | 0.0555556i | ||||||
\(325\) | 26.7643 | + | 6.18280i | 1.48462 | + | 0.342960i | ||||
\(326\) | −16.9858 | −0.940756 | ||||||||
\(327\) | −4.81814 | + | 4.81814i | −0.266444 | + | 0.266444i | ||||
\(328\) | −1.03624 | + | 1.03624i | −0.0572165 | + | 0.0572165i | ||||
\(329\) | − | 0.193737i | − | 0.0106811i | ||||||
\(330\) | −0.520034 | + | 0.149080i | −0.0286269 | + | 0.00820657i | ||||
\(331\) | − | 35.2620i | − | 1.93818i | −0.246715 | − | 0.969088i | \(-0.579351\pi\) | ||
0.246715 | − | 0.969088i | \(-0.420649\pi\) | |||||||
\(332\) | 0.681471 | − | 0.681471i | 0.0374006 | − | 0.0374006i | ||||
\(333\) | −4.54476 | − | 4.54476i | −0.249051 | − | 0.249051i | ||||
\(334\) | −18.2867 | −1.00060 | ||||||||
\(335\) | 1.80686 | + | 1.00172i | 0.0987196 | + | 0.0547298i | ||||
\(336\) | 0.0487267i | 0.00265826i | ||||||||
\(337\) | −5.38072 | + | 5.38072i | −0.293107 | + | 0.293107i | −0.838306 | − | 0.545200i | \(-0.816454\pi\) |
0.545200 | + | 0.838306i | \(0.316454\pi\) | |||||||
\(338\) | 12.1497 | − | 12.1497i | 0.660857 | − | 0.660857i | ||||
\(339\) | −1.14372 | −0.0621185 | ||||||||
\(340\) | −3.75301 | − | 2.08065i | −0.203535 | − | 0.112839i | ||||
\(341\) | 1.12774 | + | 0.736673i | 0.0610707 | + | 0.0398931i | ||||
\(342\) | −5.73208 | − | 5.73208i | −0.309955 | − | 0.309955i | ||||
\(343\) | 0.482288 | − | 0.482288i | 0.0260411 | − | 0.0260411i | ||||
\(344\) | −0.466581 | −0.0251564 | ||||||||
\(345\) | −2.30284 | − | 8.03299i | −0.123981 | − | 0.432482i | ||||
\(346\) | 25.0863 | 1.34865 | ||||||||
\(347\) | −24.2354 | + | 24.2354i | −1.30102 | + | 1.30102i | −0.373320 | + | 0.927703i | \(0.621781\pi\) |
−0.927703 | + | 0.373320i | \(0.878219\pi\) | |||||||
\(348\) | −6.04141 | + | 6.04141i | −0.323854 | + | 0.323854i | ||||
\(349\) | − | 10.3438i | − | 0.553692i | −0.960914 | − | 0.276846i | \(-0.910711\pi\) | ||
0.960914 | − | 0.276846i | \(-0.0892892\pi\) | |||||||
\(350\) | −0.129079 | − | 0.206630i | −0.00689954 | − | 0.0110448i | ||||
\(351\) | 5.49384 | 0.293240 | ||||||||
\(352\) | 0.171073 | − | 0.171073i | 0.00911823 | − | 0.00911823i | ||||
\(353\) | −17.9124 | − | 17.9124i | −0.953381 | − | 0.953381i | 0.0455794 | − | 0.998961i | \(-0.485487\pi\) |
−0.998961 | + | 0.0455794i | \(0.985487\pi\) | |||||||
\(354\) | 13.6979 | 0.728037 | ||||||||
\(355\) | 9.54578 | − | 2.73652i | 0.506637 | − | 0.145239i | ||||
\(356\) | − | 2.20446i | − | 0.116836i | ||||||
\(357\) | −0.0661216 | − | 0.0661216i | −0.00349953 | − | 0.00349953i | ||||
\(358\) | 5.35735 | + | 5.35735i | 0.283145 | + | 0.283145i | ||||
\(359\) | 20.7844i | 1.09696i | 0.836165 | + | 0.548478i | \(0.184793\pi\) | ||||
−0.836165 | + | 0.548478i | \(0.815207\pi\) | |||||||
\(360\) | −1.95564 | − | 1.08420i | −0.103071 | − | 0.0571422i | ||||
\(361\) | −46.7135 | −2.45861 | ||||||||
\(362\) | 3.44181 | − | 3.44181i | 0.180898 | − | 0.180898i | ||||
\(363\) | −7.73679 | − | 7.73679i | −0.406076 | − | 0.406076i | ||||
\(364\) | −0.267697 | −0.0140311 | ||||||||
\(365\) | −23.9074 | − | 13.2542i | −1.25137 | − | 0.693755i | ||||
\(366\) | 11.6907 | 0.611084 | ||||||||
\(367\) | −18.3540 | + | 18.3540i | −0.958073 | + | 0.958073i | −0.999156 | − | 0.0410828i | \(-0.986919\pi\) |
0.0410828 | + | 0.999156i | \(0.486919\pi\) | |||||||
\(368\) | 2.64257 | + | 2.64257i | 0.137754 | + | 0.137754i | ||||
\(369\) | − | 1.46546i | − | 0.0762887i | ||||||
\(370\) | −13.8153 | + | 3.96048i | −0.718224 | + | 0.205896i | ||||
\(371\) | 0.0411639i | 0.00213712i | ||||||||
\(372\) | 1.14299 | + | 5.44918i | 0.0592614 | + | 0.282527i | ||||
\(373\) | 21.9349 | − | 21.9349i | 1.13575 | − | 1.13575i | 0.146542 | − | 0.989204i | \(-0.453186\pi\) |
0.989204 | − | 0.146542i | \(-0.0468143\pi\) | |||||||
\(374\) | 0.464289i | 0.0240078i | ||||||||
\(375\) | 11.1651 | − | 0.582899i | 0.576565 | − | 0.0301008i | ||||
\(376\) | −3.97600 | −0.205047 | ||||||||
\(377\) | −33.1906 | − | 33.1906i | −1.70940 | − | 1.70940i | ||||
\(378\) | −0.0344550 | − | 0.0344550i | −0.00177217 | − | 0.00177217i | ||||
\(379\) | − | 16.6229i | − | 0.853861i | −0.904284 | − | 0.426931i | \(-0.859595\pi\) | ||
0.904284 | − | 0.426931i | \(-0.140405\pi\) | |||||||
\(380\) | −17.4246 | + | 4.99516i | −0.893862 | + | 0.256246i | ||||
\(381\) | −14.2944 | −0.732322 | ||||||||
\(382\) | −13.3265 | − | 13.3265i | −0.681841 | − | 0.681841i | ||||
\(383\) | 12.1354 | + | 12.1354i | 0.620088 | + | 0.620088i | 0.945554 | − | 0.325466i | \(-0.105521\pi\) |
−0.325466 | + | 0.945554i | \(0.605521\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −0.0127812 | + | 0.0230543i | −0.000651391 | + | 0.00117496i | ||||
\(386\) | 8.91582 | 0.453803 | ||||||||
\(387\) | 0.329923 | − | 0.329923i | 0.0167709 | − | 0.0167709i | ||||
\(388\) | 5.06944 | − | 5.06944i | 0.257362 | − | 0.257362i | ||||
\(389\) | 4.95801 | 0.251381 | 0.125691 | − | 0.992069i | \(-0.459885\pi\) | ||||
0.125691 | + | 0.992069i | \(0.459885\pi\) | |||||||
\(390\) | 5.95641 | − | 10.7440i | 0.301615 | − | 0.544041i | ||||
\(391\) | −7.17189 | −0.362698 | ||||||||
\(392\) | −4.94807 | − | 4.94807i | −0.249915 | − | 0.249915i | ||||
\(393\) | −5.17559 | − | 5.17559i | −0.261074 | − | 0.261074i | ||||
\(394\) | −17.5577 | −0.884545 | ||||||||
\(395\) | 27.7382 | − | 7.95181i | 1.39566 | − | 0.400099i | ||||
\(396\) | 0.241934i | 0.0121576i | ||||||||
\(397\) | −14.1182 | − | 14.1182i | −0.708573 | − | 0.708573i | 0.257662 | − | 0.966235i | \(-0.417048\pi\) |
−0.966235 | + | 0.257662i | \(0.917048\pi\) | |||||||
\(398\) | 5.01253 | + | 5.01253i | 0.251255 | + | 0.251255i | ||||
\(399\) | −0.394998 | −0.0197746 | ||||||||
\(400\) | −4.24059 | + | 2.64903i | −0.212030 | + | 0.132452i | ||||
\(401\) | 39.3985i | 1.96747i | 0.179637 | + | 0.983733i | \(0.442508\pi\) | ||||
−0.179637 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(402\) | 0.653315 | − | 0.653315i | 0.0325844 | − | 0.0325844i | ||||
\(403\) | −29.9369 | + | 6.27941i | −1.49126 | + | 0.312800i | ||||
\(404\) | − | 11.8507i | − | 0.589593i | ||||||
\(405\) | 2.14949 | − | 0.616200i | 0.106809 | − | 0.0306192i | ||||
\(406\) | 0.416314i | 0.0206613i | ||||||||
\(407\) | 1.09953 | + | 1.09953i | 0.0545018 | + | 0.0545018i | ||||
\(408\) | −1.35699 | + | 1.35699i | −0.0671810 | + | 0.0671810i | ||||
\(409\) | 10.0302 | 0.495959 | 0.247980 | − | 0.968765i | \(-0.420233\pi\) | ||||
0.247980 | + | 0.968765i | \(0.420233\pi\) | |||||||
\(410\) | −2.86590 | − | 1.58885i | −0.141537 | − | 0.0784675i | ||||
\(411\) | 1.04101 | 0.0513492 | ||||||||
\(412\) | −8.10157 | − | 8.10157i | −0.399136 | − | 0.399136i | ||||
\(413\) | 0.471962 | − | 0.471962i | 0.0232238 | − | 0.0232238i | ||||
\(414\) | −3.73716 | −0.183672 | ||||||||
\(415\) | 1.88474 | + | 1.04489i | 0.0925180 | + | 0.0512916i | ||||
\(416\) | 5.49384i | 0.269358i | ||||||||
\(417\) | −3.05648 | − | 3.05648i | −0.149677 | − | 0.149677i | ||||
\(418\) | 1.38678 | + | 1.38678i | 0.0678299 | + | 0.0678299i | ||||
\(419\) | 8.39979i | 0.410356i | 0.978725 | + | 0.205178i | \(0.0657774\pi\) | ||||
−0.978725 | + | 0.205178i | \(0.934223\pi\) | |||||||
\(420\) | −0.104737 | + | 0.0300254i | −0.00511066 | + | 0.00146509i | ||||
\(421\) | −22.3492 | −1.08923 | −0.544616 | − | 0.838685i | \(-0.683325\pi\) | ||||
−0.544616 | + | 0.838685i | \(0.683325\pi\) | |||||||
\(422\) | −1.73217 | − | 1.73217i | −0.0843205 | − | 0.0843205i | ||||
\(423\) | 2.81146 | − | 2.81146i | 0.136698 | − | 0.136698i | ||||
\(424\) | 0.844790 | 0.0410266 | ||||||||
\(425\) | 2.15973 | − | 9.34914i | 0.104762 | − | 0.453500i | ||||
\(426\) | − | 4.44096i | − | 0.215165i | ||||||
\(427\) | 0.402803 | − | 0.402803i | 0.0194930 | − | 0.0194930i | ||||
\(428\) | 10.2618 | − | 10.2618i | 0.496022 | − | 0.496022i | ||||
\(429\) | −1.32915 | −0.0641718 | ||||||||
\(430\) | −0.287508 | − | 1.00291i | −0.0138649 | − | 0.0483647i | ||||
\(431\) | 0.528344 | 0.0254494 | 0.0127247 | − | 0.999919i | \(-0.495949\pi\) | ||||
0.0127247 | + | 0.999919i | \(0.495949\pi\) | |||||||
\(432\) | −0.707107 | + | 0.707107i | −0.0340207 | + | 0.0340207i | ||||
\(433\) | 21.1562 | + | 21.1562i | 1.01670 | + | 1.01670i | 0.999858 | + | 0.0168458i | \(0.00536245\pi\) |
0.0168458 | + | 0.999858i | \(0.494638\pi\) | |||||||
\(434\) | 0.227133 | + | 0.148370i | 0.0109027 | + | 0.00712197i | ||||
\(435\) | −16.7087 | − | 9.26322i | −0.801119 | − | 0.444138i | ||||
\(436\) | 6.81387 | 0.326325 | ||||||||
\(437\) | −21.4217 | + | 21.4217i | −1.02474 | + | 1.02474i | ||||
\(438\) | −8.64429 | + | 8.64429i | −0.413040 | + | 0.413040i | ||||
\(439\) | 23.1210i | 1.10351i | 0.834008 | + | 0.551753i | \(0.186041\pi\) | ||||
−0.834008 | + | 0.551753i | \(0.813959\pi\) | |||||||
\(440\) | 0.473135 | + | 0.262304i | 0.0225558 | + | 0.0125049i | ||||
\(441\) | 6.99763 | 0.333220 | ||||||||
\(442\) | −7.45508 | − | 7.45508i | −0.354602 | − | 0.354602i | ||||
\(443\) | 12.5636 | − | 12.5636i | 0.596913 | − | 0.596913i | −0.342577 | − | 0.939490i | \(-0.611300\pi\) |
0.939490 | + | 0.342577i | \(0.111300\pi\) | |||||||
\(444\) | 6.42726i | 0.305024i | ||||||||
\(445\) | 4.73845 | − | 1.35839i | 0.224624 | − | 0.0643937i | ||||
\(446\) | 22.3613i | 1.05884i | ||||||||
\(447\) | −11.1747 | + | 11.1747i | −0.528546 | + | 0.528546i | ||||
\(448\) | 0.0344550 | − | 0.0344550i | 0.00162785 | − | 0.00162785i | ||||
\(449\) | 1.12394 | 0.0530420 | 0.0265210 | − | 0.999648i | \(-0.491557\pi\) | ||||
0.0265210 | + | 0.999648i | \(0.491557\pi\) | |||||||
\(450\) | 1.12541 | − | 4.87170i | 0.0530521 | − | 0.229654i | ||||
\(451\) | 0.354544i | 0.0166948i | ||||||||
\(452\) | 0.808734 | + | 0.808734i | 0.0380397 | + | 0.0380397i | ||||
\(453\) | −2.33367 | + | 2.33367i | −0.109645 | + | 0.109645i | ||||
\(454\) | − | 27.2406i | − | 1.27847i | ||||||
\(455\) | −0.164955 | − | 0.575411i | −0.00773320 | − | 0.0269757i | ||||
\(456\) | 8.10639i | 0.379616i | ||||||||
\(457\) | 12.7413 | − | 12.7413i | 0.596013 | − | 0.596013i | −0.343236 | − | 0.939249i | \(-0.611523\pi\) |
0.939249 | + | 0.343236i | \(0.111523\pi\) | |||||||
\(458\) | 19.1373 | + | 19.1373i | 0.894226 | + | 0.894226i | ||||
\(459\) | − | 1.91907i | − | 0.0895746i | ||||||
\(460\) | −4.05183 | + | 7.30854i | −0.188917 | + | 0.340762i | ||||
\(461\) | 31.9605i | 1.48855i | 0.667875 | + | 0.744273i | \(0.267204\pi\) | ||||
−0.667875 | + | 0.744273i | \(0.732796\pi\) | |||||||
\(462\) | 0.00833583 | + | 0.00833583i | 0.000387818 | + | 0.000387818i | ||||
\(463\) | 6.70781 | + | 6.70781i | 0.311738 | + | 0.311738i | 0.845583 | − | 0.533844i | \(-0.179253\pi\) |
−0.533844 | + | 0.845583i | \(0.679253\pi\) | |||||||
\(464\) | 8.54385 | 0.396638 | ||||||||
\(465\) | −11.0086 | + | 5.81463i | −0.510513 | + | 0.269647i | ||||
\(466\) | −12.7577 | −0.590988 | ||||||||
\(467\) | 10.0801 | + | 10.0801i | 0.466449 | + | 0.466449i | 0.900762 | − | 0.434313i | \(-0.143009\pi\) |
−0.434313 | + | 0.900762i | \(0.643009\pi\) | |||||||
\(468\) | −3.88473 | − | 3.88473i | −0.179572 | − | 0.179572i | ||||
\(469\) | − | 0.0450199i | − | 0.00207883i | ||||||
\(470\) | −2.45001 | − | 8.54636i | −0.113011 | − | 0.394214i | ||||
\(471\) | 6.78150i | 0.312475i | ||||||||
\(472\) | −9.68591 | − | 9.68591i | −0.445830 | − | 0.445830i | ||||
\(473\) | −0.0798195 | + | 0.0798195i | −0.00367011 | + | 0.00367011i | ||||
\(474\) | − | 12.9046i | − | 0.592727i | ||||||
\(475\) | −21.4741 | − | 34.3759i | −0.985298 | − | 1.57727i | ||||
\(476\) | 0.0935101i | 0.00428603i | ||||||||
\(477\) | −0.597357 | + | 0.597357i | −0.0273511 | + | 0.0273511i | ||||
\(478\) | −13.1978 | − | 13.1978i | −0.603651 | − | 0.603651i | ||||
\(479\) | 9.22871i | 0.421671i | 0.977522 | + | 0.210835i | \(0.0676184\pi\) | ||||
−0.977522 | + | 0.210835i | \(0.932382\pi\) | |||||||
\(480\) | 0.616200 | + | 2.14949i | 0.0281256 | + | 0.0981102i | ||||
\(481\) | −35.3104 | −1.61001 | ||||||||
\(482\) | 12.4419 | − | 12.4419i | 0.566713 | − | 0.566713i | ||||
\(483\) | −0.128764 | + | 0.128764i | −0.00585896 | + | 0.00585896i | ||||
\(484\) | 10.9415i | 0.497339i | ||||||||
\(485\) | 14.0205 | + | 7.77291i | 0.636638 | + | 0.352950i | ||||
\(486\) | − | 1.00000i | − | 0.0453609i | ||||||
\(487\) | 19.6425 | − | 19.6425i | 0.890086 | − | 0.890086i | −0.104444 | − | 0.994531i | \(-0.533306\pi\) |
0.994531 | + | 0.104444i | \(0.0333064\pi\) | |||||||
\(488\) | −8.26659 | − | 8.26659i | −0.374211 | − | 0.374211i | ||||
\(489\) | −16.9858 | −0.768124 | ||||||||
\(490\) | 7.58681 | − | 13.6848i | 0.342737 | − | 0.618217i | ||||
\(491\) | − | 1.10627i | − | 0.0499255i | −0.999688 | − | 0.0249627i | \(-0.992053\pi\) | ||
0.999688 | − | 0.0249627i | \(-0.00794671\pi\) | |||||||
\(492\) | −1.03624 | + | 1.03624i | −0.0467171 | + | 0.0467171i | ||||
\(493\) | −11.5939 | + | 11.5939i | −0.522163 | + | 0.522163i | ||||
\(494\) | −44.5352 | −2.00373 | ||||||||
\(495\) | −0.520034 | + | 0.149080i | −0.0233738 | + | 0.00670064i | ||||
\(496\) | 3.04494 | − | 4.66137i | 0.136722 | − | 0.209302i | ||||
\(497\) | −0.153013 | − | 0.153013i | −0.00686358 | − | 0.00686358i | ||||
\(498\) | 0.681471 | − | 0.681471i | 0.0305374 | − | 0.0305374i | ||||
\(499\) | −30.7515 | −1.37663 | −0.688313 | − | 0.725414i | \(-0.741648\pi\) | ||||
−0.688313 | + | 0.725414i | \(0.741648\pi\) | |||||||
\(500\) | −8.30711 | − | 7.48277i | −0.371505 | − | 0.334640i | ||||
\(501\) | −18.2867 | −0.816990 | ||||||||
\(502\) | 0.819821 | − | 0.819821i | 0.0365904 | − | 0.0365904i | ||||
\(503\) | 8.46280 | − | 8.46280i | 0.377337 | − | 0.377337i | −0.492803 | − | 0.870141i | \(-0.664028\pi\) |
0.870141 | + | 0.492803i | \(0.164028\pi\) | |||||||
\(504\) | 0.0487267i | 0.00217046i | ||||||||
\(505\) | 25.4729 | − | 7.30240i | 1.13353 | − | 0.324952i | ||||
\(506\) | 0.904147 | 0.0401942 | ||||||||
\(507\) | 12.1497 | − | 12.1497i | 0.539588 | − | 0.539588i | ||||
\(508\) | 10.1076 | + | 10.1076i | 0.448454 | + | 0.448454i | ||||
\(509\) | −20.4726 | −0.907431 | −0.453716 | − | 0.891147i | \(-0.649902\pi\) | ||||
−0.453716 | + | 0.891147i | \(0.649902\pi\) | |||||||
\(510\) | −3.75301 | − | 2.08065i | −0.166186 | − | 0.0921329i | ||||
\(511\) | 0.595677i | 0.0263512i | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −5.73208 | − | 5.73208i | −0.253078 | − | 0.253078i | ||||
\(514\) | 4.75546i | 0.209754i | ||||||||
\(515\) | 12.4220 | − | 22.4064i | 0.547380 | − | 0.987345i | ||||
\(516\) | −0.466581 | −0.0205401 | ||||||||
\(517\) | −0.680187 | + | 0.680187i | −0.0299146 | + | 0.0299146i | ||||
\(518\) | 0.221451 | + | 0.221451i | 0.00973001 | + | 0.00973001i | ||||
\(519\) | 25.0863 | 1.10116 | ||||||||
\(520\) | −11.8089 | + | 3.38531i | −0.517856 | + | 0.148456i | ||||
\(521\) | −3.57424 | −0.156590 | −0.0782951 | − | 0.996930i | \(-0.524948\pi\) | ||||
−0.0782951 | + | 0.996930i | \(0.524948\pi\) | |||||||
\(522\) | −6.04141 | + | 6.04141i | −0.264426 | + | 0.264426i | ||||
\(523\) | −11.4759 | − | 11.4759i | −0.501805 | − | 0.501805i | 0.410194 | − | 0.911998i | \(-0.365461\pi\) |
−0.911998 | + | 0.410194i | \(0.865461\pi\) | |||||||
\(524\) | 7.31940i | 0.319749i | ||||||||
\(525\) | −0.129079 | − | 0.206630i | −0.00563345 | − | 0.00901808i | ||||
\(526\) | − | 22.9464i | − | 1.00051i | ||||||
\(527\) | 2.19348 | + | 10.4574i | 0.0955496 | + | 0.455530i | ||||
\(528\) | 0.171073 | − | 0.171073i | 0.00744500 | − | 0.00744500i | ||||
\(529\) | − | 9.03360i | − | 0.392765i | ||||||
\(530\) | 0.520560 | + | 1.81587i | 0.0226117 | + | 0.0788762i | ||||
\(531\) | 13.6979 | 0.594440 | ||||||||
\(532\) | 0.279305 | + | 0.279305i | 0.0121094 | + | 0.0121094i | ||||
\(533\) | −5.69291 | − | 5.69291i | −0.246587 | − | 0.246587i | ||||
\(534\) | − | 2.20446i | − | 0.0953962i | ||||||
\(535\) | 28.3809 | + | 15.7343i | 1.22701 | + | 0.680252i | ||||
\(536\) | −0.923926 | −0.0399075 | ||||||||
\(537\) | 5.35735 | + | 5.35735i | 0.231187 | + | 0.231187i | ||||
\(538\) | −0.603753 | − | 0.603753i | −0.0260296 | − | 0.0260296i | ||||
\(539\) | −1.69296 | −0.0729211 | ||||||||
\(540\) | −1.95564 | − | 1.08420i | −0.0841572 | − | 0.0466564i | ||||
\(541\) | 2.91694 | 0.125409 | 0.0627046 | − | 0.998032i | \(-0.480027\pi\) | ||||
0.0627046 | + | 0.998032i | \(0.480027\pi\) | |||||||
\(542\) | −10.6988 | + | 10.6988i | −0.459552 | + | 0.459552i | ||||
\(543\) | 3.44181 | − | 3.44181i | 0.147702 | − | 0.147702i | ||||
\(544\) | 1.91907 | 0.0822795 | ||||||||
\(545\) | 4.19871 | + | 14.6463i | 0.179853 | + | 0.627380i | ||||
\(546\) | −0.267697 | −0.0114564 | ||||||||
\(547\) | −17.5259 | − | 17.5259i | −0.749353 | − | 0.749353i | 0.225005 | − | 0.974358i | \(-0.427760\pi\) |
−0.974358 | + | 0.225005i | \(0.927760\pi\) | |||||||
\(548\) | −0.736104 | − | 0.736104i | −0.0314448 | − | 0.0314448i | ||||
\(549\) | 11.6907 | 0.498948 | ||||||||
\(550\) | −0.272274 | + | 1.17863i | −0.0116098 | + | 0.0502569i | ||||
\(551\) | 69.2597i | 2.95056i | ||||||||
\(552\) | 2.64257 | + | 2.64257i | 0.112475 | + | 0.112475i | ||||
\(553\) | −0.444627 | − | 0.444627i | −0.0189075 | − | 0.0189075i | ||||
\(554\) | 15.7269 | 0.668173 | ||||||||
\(555\) | −13.8153 | + | 3.96048i | −0.586428 | + | 0.168113i | ||||
\(556\) | 4.32252i | 0.183316i | ||||||||
\(557\) | 21.0848 | − | 21.0848i | 0.893390 | − | 0.893390i | −0.101451 | − | 0.994841i | \(-0.532348\pi\) |
0.994841 | + | 0.101451i | \(0.0323484\pi\) | |||||||
\(558\) | 1.14299 | + | 5.44918i | 0.0483867 | + | 0.230682i | ||||
\(559\) | − | 2.56332i | − | 0.108417i | ||||||
\(560\) | 0.0952917 | + | 0.0528294i | 0.00402681 | + | 0.00223245i | ||||
\(561\) | 0.464289i | 0.0196023i | ||||||||
\(562\) | 7.92487 | + | 7.92487i | 0.334290 | + | 0.334290i | ||||
\(563\) | −18.6518 | + | 18.6518i | −0.786080 | + | 0.786080i | −0.980849 | − | 0.194769i | \(-0.937604\pi\) |
0.194769 | + | 0.980849i | \(0.437604\pi\) | |||||||
\(564\) | −3.97600 | −0.167420 | ||||||||
\(565\) | −1.24002 | + | 2.23671i | −0.0521681 | + | 0.0940990i | ||||
\(566\) | −2.92685 | −0.123025 | ||||||||
\(567\) | −0.0344550 | − | 0.0344550i | −0.00144697 | − | 0.00144697i | ||||
\(568\) | −3.14023 | + | 3.14023i | −0.131761 | + | 0.131761i | ||||
\(569\) | 44.2050 | 1.85317 | 0.926586 | − | 0.376084i | \(-0.122730\pi\) | ||||
0.926586 | + | 0.376084i | \(0.122730\pi\) | |||||||
\(570\) | −17.4246 | + | 4.99516i | −0.729835 | + | 0.209224i | ||||
\(571\) | − | 25.3388i | − | 1.06040i | −0.847874 | − | 0.530198i | \(-0.822117\pi\) | ||
0.847874 | − | 0.530198i | \(-0.177883\pi\) | |||||||
\(572\) | 0.939849 | + | 0.939849i | 0.0392970 | + | 0.0392970i | ||||
\(573\) | −13.3265 | − | 13.3265i | −0.556721 | − | 0.556721i | ||||
\(574\) | 0.0714069i | 0.00298047i | ||||||||
\(575\) | −18.2063 | − | 4.20582i | −0.759257 | − | 0.175395i | ||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −15.7492 | − | 15.7492i | −0.655648 | − | 0.655648i | 0.298699 | − | 0.954347i | \(-0.403447\pi\) |
−0.954347 | + | 0.298699i | \(0.903447\pi\) | |||||||
\(578\) | 9.41666 | − | 9.41666i | 0.391681 | − | 0.391681i | ||||
\(579\) | 8.91582 | 0.370529 | ||||||||
\(580\) | 5.26472 | + | 18.3649i | 0.218606 | + | 0.762561i | ||||
\(581\) | − | 0.0469601i | − | 0.00194823i | ||||||
\(582\) | 5.06944 | − | 5.06944i | 0.210135 | − | 0.210135i | ||||
\(583\) | 0.144521 | − | 0.144521i | 0.00598545 | − | 0.00598545i | ||||
\(584\) | 12.2249 | 0.505869 | ||||||||
\(585\) | 5.95641 | − | 10.7440i | 0.246267 | − | 0.444208i | ||||
\(586\) | 22.4607 | 0.927841 | ||||||||
\(587\) | −22.8549 | + | 22.8549i | −0.943325 | + | 0.943325i | −0.998478 | − | 0.0551533i | \(-0.982435\pi\) |
0.0551533 | + | 0.998478i | \(0.482435\pi\) | |||||||
\(588\) | −4.94807 | − | 4.94807i | −0.204055 | − | 0.204055i | ||||
\(589\) | 37.7869 | + | 24.6834i | 1.55698 | + | 1.01706i | ||||
\(590\) | 14.8513 | − | 26.7882i | 0.611418 | − | 1.10285i | ||||
\(591\) | −17.5577 | −0.722228 | ||||||||
\(592\) | 4.54476 | − | 4.54476i | 0.186789 | − | 0.186789i | ||||
\(593\) | −9.77033 | + | 9.77033i | −0.401219 | + | 0.401219i | −0.878663 | − | 0.477443i | \(-0.841564\pi\) |
0.477443 | + | 0.878663i | \(0.341564\pi\) | |||||||
\(594\) | 0.241934i | 0.00992667i | ||||||||
\(595\) | −0.200999 | + | 0.0576209i | −0.00824014 | + | 0.00236223i | ||||
\(596\) | 15.8034 | 0.647334 | ||||||||
\(597\) | 5.01253 | + | 5.01253i | 0.205149 | + | 0.205149i | ||||
\(598\) | −14.5179 | + | 14.5179i | −0.593680 | + | 0.593680i | ||||
\(599\) | − | 0.724583i | − | 0.0296057i | −0.999890 | − | 0.0148028i | \(-0.995288\pi\) | ||
0.999890 | − | 0.0148028i | \(-0.00471206\pi\) | |||||||
\(600\) | −4.24059 | + | 2.64903i | −0.173122 | + | 0.108146i | ||||
\(601\) | − | 12.8455i | − | 0.523978i | −0.965071 | − | 0.261989i | \(-0.915622\pi\) | ||
0.965071 | − | 0.261989i | \(-0.0843784\pi\) | |||||||
\(602\) | −0.0160761 | + | 0.0160761i | −0.000655211 | + | 0.000655211i | ||||
\(603\) | 0.653315 | − | 0.653315i | 0.0266050 | − | 0.0266050i | ||||
\(604\) | 3.30031 | 0.134288 | ||||||||
\(605\) | −23.5185 | + | 6.74214i | −0.956165 | + | 0.274107i | ||||
\(606\) | − | 11.8507i | − | 0.481401i | ||||||
\(607\) | −7.27742 | − | 7.27742i | −0.295381 | − | 0.295381i | 0.543820 | − | 0.839202i | \(-0.316977\pi\) |
−0.839202 | + | 0.543820i | \(0.816977\pi\) | |||||||
\(608\) | 5.73208 | − | 5.73208i | 0.232467 | − | 0.232467i | ||||
\(609\) | 0.416314i | 0.0168699i | ||||||||
\(610\) | 12.6750 | − | 22.8628i | 0.513198 | − | 0.925688i | ||||
\(611\) | − | 21.8435i | − | 0.883694i | ||||||
\(612\) | −1.35699 | + | 1.35699i | −0.0548530 | + | 0.0548530i | ||||
\(613\) | 10.9037 | + | 10.9037i | 0.440396 | + | 0.440396i | 0.892145 | − | 0.451749i | \(-0.149200\pi\) |
−0.451749 | + | 0.892145i | \(0.649200\pi\) | |||||||
\(614\) | − | 9.11097i | − | 0.367689i | ||||||
\(615\) | −2.86590 | − | 1.58885i | −0.115564 | − | 0.0640685i | ||||
\(616\) | − | 0.0117886i | − | 0.000474978i | ||||||
\(617\) | 20.7282 | + | 20.7282i | 0.834486 | + | 0.834486i | 0.988127 | − | 0.153641i | \(-0.0490998\pi\) |
−0.153641 | + | 0.988127i | \(0.549100\pi\) | |||||||
\(618\) | −8.10157 | − | 8.10157i | −0.325893 | − | 0.325893i | ||||
\(619\) | −32.6126 | −1.31081 | −0.655406 | − | 0.755277i | \(-0.727502\pi\) | ||||
−0.655406 | + | 0.755277i | \(0.727502\pi\) | |||||||
\(620\) | 11.8958 | + | 3.67271i | 0.477749 | + | 0.147500i | ||||
\(621\) | −3.73716 | −0.149967 | ||||||||
\(622\) | −7.18083 | − | 7.18083i | −0.287925 | − | 0.287925i | ||||
\(623\) | −0.0759545 | − | 0.0759545i | −0.00304305 | − | 0.00304305i | ||||
\(624\) | 5.49384i | 0.219930i | ||||||||
\(625\) | 10.9653 | − | 22.4669i | 0.438611 | − | 0.898677i | ||||
\(626\) | − | 21.6707i | − | 0.866136i | ||||||
\(627\) | 1.38678 | + | 1.38678i | 0.0553829 | + | 0.0553829i | ||||
\(628\) | 4.79524 | − | 4.79524i | 0.191351 | − | 0.191351i | ||||
\(629\) | 12.3344i | 0.491804i | ||||||||
\(630\) | −0.104737 | + | 0.0300254i | −0.00417284 | + | 0.00119624i | ||||
\(631\) | 8.88412i | 0.353671i | 0.984240 | + | 0.176836i | \(0.0565861\pi\) | ||||
−0.984240 | + | 0.176836i | \(0.943414\pi\) | |||||||
\(632\) | −9.12491 | + | 9.12491i | −0.362970 | + | 0.362970i | ||||
\(633\) | −1.73217 | − | 1.73217i | −0.0688474 | − | 0.0688474i | ||||
\(634\) | − | 1.28031i | − | 0.0508478i | ||||||
\(635\) | −15.4979 | + | 27.9546i | −0.615016 | + | 1.10934i | ||||
\(636\) | 0.844790 | 0.0334981 | ||||||||
\(637\) | 27.1839 | − | 27.1839i | 1.07707 | − | 1.07707i | ||||
\(638\) | 1.46162 | − | 1.46162i | 0.0578662 | − | 0.0578662i | ||||
\(639\) | − | 4.44096i | − | 0.175682i | ||||||
\(640\) | 1.08420 | − | 1.95564i | 0.0428567 | − | 0.0773033i | ||||
\(641\) | 10.7525i | 0.424697i | 0.977194 | + | 0.212348i | \(0.0681111\pi\) | ||||
−0.977194 | + | 0.212348i | \(0.931889\pi\) | |||||||
\(642\) | 10.2618 | − | 10.2618i | 0.405000 | − | 0.405000i | ||||
\(643\) | −11.7446 | − | 11.7446i | −0.463162 | − | 0.463162i | 0.436529 | − | 0.899690i | \(-0.356208\pi\) |
−0.899690 | + | 0.436529i | \(0.856208\pi\) | |||||||
\(644\) | 0.182100 | 0.00717573 | ||||||||
\(645\) | −0.287508 | − | 1.00291i | −0.0113206 | − | 0.0394896i | ||||
\(646\) | 15.5567i | 0.612072i | ||||||||
\(647\) | −5.34144 | + | 5.34144i | −0.209994 | + | 0.209994i | −0.804265 | − | 0.594271i | \(-0.797441\pi\) |
0.594271 | + | 0.804265i | \(0.297441\pi\) | |||||||
\(648\) | −0.707107 | + | 0.707107i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | −3.31400 | −0.130086 | ||||||||
\(650\) | −14.5534 | − | 23.2971i | −0.570829 | − | 0.913789i | ||||
\(651\) | 0.227133 | + | 0.148370i | 0.00890205 | + | 0.00581507i | ||||
\(652\) | 12.0108 | + | 12.0108i | 0.470378 | + | 0.470378i | ||||
\(653\) | 25.5474 | − | 25.5474i | 0.999745 | − | 0.999745i | −0.000254663 | − | 1.00000i | \(-0.500081\pi\) |
1.00000 | 0.000254663i | \(8.10619e-5\pi\) | ||||||||
\(654\) | 6.81387 | 0.266444 | ||||||||
\(655\) | −15.7330 | + | 4.51022i | −0.614737 | + | 0.176229i | ||||
\(656\) | 1.46546 | 0.0572165 | ||||||||
\(657\) | −8.64429 | + | 8.64429i | −0.337246 | + | 0.337246i | ||||
\(658\) | −0.136993 | + | 0.136993i | −0.00534054 | + | 0.00534054i | ||||
\(659\) | − | 31.8901i | − | 1.24226i | −0.783706 | − | 0.621132i | \(-0.786673\pi\) | ||
0.783706 | − | 0.621132i | \(-0.213327\pi\) | |||||||
\(660\) | 0.473135 | + | 0.262304i | 0.0184168 | + | 0.0102102i | ||||
\(661\) | −13.1832 | −0.512767 | −0.256383 | − | 0.966575i | \(-0.582531\pi\) | ||||
−0.256383 | + | 0.966575i | \(0.582531\pi\) | |||||||
\(662\) | −24.9340 | + | 24.9340i | −0.969088 | + | 0.969088i | ||||
\(663\) | −7.45508 | − | 7.45508i | −0.289531 | − | 0.289531i | ||||
\(664\) | −0.963745 | −0.0374006 | ||||||||
\(665\) | −0.428255 | + | 0.772472i | −0.0166070 | + | 0.0299552i | ||||
\(666\) | 6.42726i | 0.249051i | ||||||||
\(667\) | 22.5778 | + | 22.5778i | 0.874214 | + | 0.874214i | ||||
\(668\) | 12.9307 | + | 12.9307i | 0.500302 | + | 0.500302i | ||||
\(669\) | 22.3613i | 0.864539i | ||||||||
\(670\) | −0.569324 | − | 1.98597i | −0.0219949 | − | 0.0767247i | ||||
\(671\) | −2.82838 | −0.109188 | ||||||||
\(672\) | 0.0344550 | − | 0.0344550i | 0.00132913 | − | 0.00132913i | ||||
\(673\) | −25.9900 | − | 25.9900i | −1.00184 | − | 1.00184i | −0.999998 | − | 0.00184286i | \(-0.999413\pi\) |
−0.00184286 | − | 0.999998i | \(-0.500587\pi\) | |||||||
\(674\) | 7.60949 | 0.293107 | ||||||||
\(675\) | 1.12541 | − | 4.87170i | 0.0433169 | − | 0.187512i | ||||
\(676\) | −17.1823 | −0.660857 | ||||||||
\(677\) | −8.51300 | + | 8.51300i | −0.327181 | + | 0.327181i | −0.851514 | − | 0.524333i | \(-0.824315\pi\) |
0.524333 | + | 0.851514i | \(0.324315\pi\) | |||||||
\(678\) | 0.808734 | + | 0.808734i | 0.0310593 | + | 0.0310593i | ||||
\(679\) | − | 0.349335i | − | 0.0134063i | ||||||
\(680\) | 1.18253 | + | 4.12502i | 0.0453481 | + | 0.158187i | ||||
\(681\) | − | 27.2406i | − | 1.04386i | ||||||
\(682\) | −0.276529 | − | 1.31834i | −0.0105888 | − | 0.0504819i | ||||
\(683\) | 7.75769 | − | 7.75769i | 0.296840 | − | 0.296840i | −0.542935 | − | 0.839775i | \(-0.682687\pi\) |
0.839775 | + | 0.542935i | \(0.182687\pi\) | |||||||
\(684\) | 8.10639i | 0.309955i | ||||||||
\(685\) | 1.12866 | − | 2.03583i | 0.0431239 | − | 0.0777852i | ||||
\(686\) | −0.682058 | −0.0260411 | ||||||||
\(687\) | 19.1373 | + | 19.1373i | 0.730132 | + | 0.730132i | ||||
\(688\) | 0.329923 | + | 0.329923i | 0.0125782 | + | 0.0125782i | ||||
\(689\) | 4.64114i | 0.176813i | ||||||||
\(690\) | −4.05183 | + | 7.30854i | −0.154250 | + | 0.278231i | ||||
\(691\) | 8.98563 | 0.341829 | 0.170915 | − | 0.985286i | \(-0.445328\pi\) | ||||
0.170915 | + | 0.985286i | \(0.445328\pi\) | |||||||
\(692\) | −17.7387 | − | 17.7387i | −0.674323 | − | 0.674323i | ||||
\(693\) | 0.00833583 | + | 0.00833583i | 0.000316652 | + | 0.000316652i | ||||
\(694\) | 34.2740 | 1.30102 | ||||||||
\(695\) | −9.29120 | + | 2.66354i | −0.352435 | + | 0.101034i | ||||
\(696\) | 8.54385 | 0.323854 | ||||||||
\(697\) | −1.98861 | + | 1.98861i | −0.0753240 | + | 0.0753240i | ||||
\(698\) | −7.31418 | + | 7.31418i | −0.276846 | + | 0.276846i | ||||
\(699\) | −12.7577 | −0.482540 | ||||||||
\(700\) | −0.0548373 | + | 0.237382i | −0.00207266 | + | 0.00897219i | ||||
\(701\) | 21.0088 | 0.793491 | 0.396745 | − | 0.917929i | \(-0.370140\pi\) | ||||
0.396745 | + | 0.917929i | \(0.370140\pi\) | |||||||
\(702\) | −3.88473 | − | 3.88473i | −0.146620 | − | 0.146620i | ||||
\(703\) | 36.8416 | + | 36.8416i | 1.38951 | + | 1.38951i | ||||
\(704\) | −0.241934 | −0.00911823 | ||||||||
\(705\) | −2.45001 | − | 8.54636i | −0.0922728 | − | 0.321875i | ||||
\(706\) | 25.3320i | 0.953381i | ||||||||
\(707\) | −0.408315 | − | 0.408315i | −0.0153563 | − | 0.0153563i | ||||
\(708\) | −9.68591 | − | 9.68591i | −0.364019 | − | 0.364019i | ||||
\(709\) | −28.8232 | −1.08248 | −0.541239 | − | 0.840869i | \(-0.682045\pi\) | ||||
−0.541239 | + | 0.840869i | \(0.682045\pi\) | |||||||
\(710\) | −8.68490 | − | 4.81488i | −0.325938 | − | 0.180699i | ||||
\(711\) | − | 12.9046i | − | 0.483959i | ||||||
\(712\) | −1.55879 | + | 1.55879i | −0.0584180 | + | 0.0584180i | ||||
\(713\) | 20.3645 | − | 4.27155i | 0.762656 | − | 0.159971i | ||||
\(714\) | 0.0935101i | 0.00349953i | ||||||||
\(715\) | −1.44106 | + | 2.59933i | −0.0538925 | + | 0.0972094i | ||||
\(716\) | − | 7.57644i | − | 0.283145i | ||||||
\(717\) | −13.1978 | − | 13.1978i | −0.492879 | − | 0.492879i | ||||
\(718\) | 14.6968 | − | 14.6968i | 0.548478 | − | 0.548478i | ||||
\(719\) | 19.4702 | 0.726116 | 0.363058 | − | 0.931767i | \(-0.381733\pi\) | ||||
0.363058 | + | 0.931767i | \(0.381733\pi\) | |||||||
\(720\) | 0.616200 | + | 2.14949i | 0.0229644 | + | 0.0801067i | ||||
\(721\) | −0.558279 | −0.0207914 | ||||||||
\(722\) | 33.0314 | + | 33.0314i | 1.22930 | + | 1.22930i | ||||
\(723\) | 12.4419 | − | 12.4419i | 0.462719 | − | 0.462719i | ||||
\(724\) | −4.86746 | −0.180898 | ||||||||
\(725\) | −36.2310 | + | 22.6329i | −1.34559 | + | 0.840565i | ||||
\(726\) | 10.9415i | 0.406076i | ||||||||
\(727\) | 23.8912 | + | 23.8912i | 0.886075 | + | 0.886075i | 0.994143 | − | 0.108068i | \(-0.0344666\pi\) |
−0.108068 | + | 0.994143i | \(0.534467\pi\) | |||||||
\(728\) | 0.189290 | + | 0.189290i | 0.00701556 | + | 0.00701556i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 7.53297 | + | 26.2772i | 0.278808 | + | 0.972563i | ||||
\(731\) | −0.895403 | −0.0331177 | ||||||||
\(732\) | −8.26659 | − | 8.26659i | −0.305542 | − | 0.305542i | ||||
\(733\) | 27.0190 | − | 27.0190i | 0.997968 | − | 0.997968i | −0.00202986 | − | 0.999998i | \(-0.500646\pi\) |
0.999998 | + | 0.00202986i | \(0.000646125\pi\) | |||||||
\(734\) | 25.9565 | 0.958073 | ||||||||
\(735\) | 7.58681 | − | 13.6848i | 0.279844 | − | 0.504772i | ||||
\(736\) | − | 3.73716i | − | 0.137754i | ||||||
\(737\) | −0.158059 | + | 0.158059i | −0.00582218 | + | 0.00582218i | ||||
\(738\) | −1.03624 | + | 1.03624i | −0.0381443 | + | 0.0381443i | ||||
\(739\) | −35.9676 | −1.32309 | −0.661544 | − | 0.749906i | \(-0.730099\pi\) | ||||
−0.661544 | + | 0.749906i | \(0.730099\pi\) | |||||||
\(740\) | 12.5694 | + | 6.96842i | 0.462060 | + | 0.256164i | ||||
\(741\) | −44.5352 | −1.63604 | ||||||||
\(742\) | 0.0291072 | − | 0.0291072i | 0.00106856 | − | 0.00106856i | ||||
\(743\) | −17.1623 | − | 17.1623i | −0.629624 | − | 0.629624i | 0.318349 | − | 0.947973i | \(-0.396871\pi\) |
−0.947973 | + | 0.318349i | \(0.896871\pi\) | |||||||
\(744\) | 3.04494 | − | 4.66137i | 0.111633 | − | 0.170894i | ||||
\(745\) | 9.73809 | + | 33.9693i | 0.356776 | + | 1.24454i | ||||
\(746\) | −31.0206 | −1.13575 | ||||||||
\(747\) | 0.681471 | − | 0.681471i | 0.0249337 | − | 0.0249337i | ||||
\(748\) | 0.328302 | − | 0.328302i | 0.0120039 | − | 0.0120039i | ||||
\(749\) | − | 0.707139i | − | 0.0258383i | ||||||
\(750\) | −8.30711 | − | 7.48277i | −0.303333 | − | 0.273232i | ||||
\(751\) | −37.8302 | −1.38044 | −0.690222 | − | 0.723598i | \(-0.742487\pi\) | ||||
−0.690222 | + | 0.723598i | \(0.742487\pi\) | |||||||
\(752\) | 2.81146 | + | 2.81146i | 0.102523 | + | 0.102523i | ||||
\(753\) | 0.819821 | − | 0.819821i | 0.0298759 | − | 0.0298759i | ||||
\(754\) | 46.9385i | 1.70940i | ||||||||
\(755\) | 2.03365 | + | 7.09398i | 0.0740122 | + | 0.258176i | ||||
\(756\) | 0.0487267i | 0.00177217i | ||||||||
\(757\) | −15.9320 | + | 15.9320i | −0.579059 | + | 0.579059i | −0.934644 | − | 0.355585i | \(-0.884282\pi\) |
0.355585 | + | 0.934644i | \(0.384282\pi\) | |||||||
\(758\) | −11.7542 | + | 11.7542i | −0.426931 | + | 0.426931i | ||||
\(759\) | 0.904147 | 0.0328185 | ||||||||
\(760\) | 15.8531 | + | 8.78893i | 0.575054 | + | 0.318808i | ||||
\(761\) | − | 46.0885i | − | 1.67071i | −0.549713 | − | 0.835354i | \(-0.685263\pi\) | ||
0.549713 | − | 0.835354i | \(-0.314737\pi\) | |||||||
\(762\) | 10.1076 | + | 10.1076i | 0.366161 | + | 0.366161i | ||||
\(763\) | 0.234772 | − | 0.234772i | 0.00849931 | − | 0.00849931i | ||||
\(764\) | 18.8465i | 0.681841i | ||||||||
\(765\) | −3.75301 | − | 2.08065i | −0.135690 | − | 0.0752262i | ||||
\(766\) | − | 17.1620i | − | 0.620088i | ||||||
\(767\) | 53.2128 | − | 53.2128i | 1.92140 | − | 1.92140i | ||||
\(768\) | −0.707107 | − | 0.707107i | −0.0255155 | − | 0.0255155i | ||||
\(769\) | 11.2917i | 0.407189i | 0.979055 | + | 0.203594i | \(0.0652624\pi\) | ||||
−0.979055 | + | 0.203594i | \(0.934738\pi\) | |||||||
\(770\) | 0.0253395 | − | 0.00726417i | 0.000913174 | − | 0.000261782i | ||||
\(771\) | 4.75546i | 0.171264i | ||||||||
\(772\) | −6.30444 | − | 6.30444i | −0.226902 | − | 0.226902i | ||||
\(773\) | 5.24463 | + | 5.24463i | 0.188636 | + | 0.188636i | 0.795106 | − | 0.606470i | \(-0.207415\pi\) |
−0.606470 | + | 0.795106i | \(0.707415\pi\) | |||||||
\(774\) | −0.466581 | −0.0167709 | ||||||||
\(775\) | −0.564224 | + | 27.8331i | −0.0202675 | + | 0.999795i | ||||
\(776\) | −7.16927 | −0.257362 | ||||||||
\(777\) | 0.221451 | + | 0.221451i | 0.00794452 | + | 0.00794452i | ||||
\(778\) | −3.50584 | − | 3.50584i | −0.125691 | − | 0.125691i | ||||
\(779\) | 11.8796i | 0.425630i | ||||||||
\(780\) | −11.8089 | + | 3.38531i | −0.422828 | + | 0.121213i | ||||
\(781\) | 1.07442i | 0.0384457i | ||||||||
\(782\) | 5.07129 | + | 5.07129i | 0.181349 | + | 0.181349i | ||||
\(783\) | −6.04141 | + | 6.04141i | −0.215903 | + | 0.215903i | ||||
\(784\) | 6.99763i | 0.249915i | ||||||||
\(785\) | 13.2621 | + | 7.35249i | 0.473346 | + | 0.262421i | ||||
\(786\) | 7.31940i | 0.261074i | ||||||||
\(787\) | −13.5398 | + | 13.5398i | −0.482641 | + | 0.482641i | −0.905974 | − | 0.423333i | \(-0.860860\pi\) |
0.423333 | + | 0.905974i | \(0.360860\pi\) | |||||||
\(788\) | 12.4152 | + | 12.4152i | 0.442273 | + | 0.442273i | ||||
\(789\) | − | 22.9464i | − | 0.816915i | ||||||
\(790\) | −25.2367 | − | 13.9911i | −0.897880 | − | 0.497781i | ||||
\(791\) | 0.0557299 | 0.00198153 | ||||||||
\(792\) | 0.171073 | − | 0.171073i | 0.00607882 | − | 0.00607882i | ||||
\(793\) | 45.4153 | − | 45.4153i | 1.61274 | − | 1.61274i | ||||
\(794\) | 19.9662i | 0.708573i | ||||||||
\(795\) | 0.520560 | + | 1.81587i | 0.0184624 | + | 0.0644021i | ||||
\(796\) | − | 7.08879i | − | 0.251255i | ||||||
\(797\) | 9.78542 | − | 9.78542i | 0.346618 | − | 0.346618i | −0.512231 | − | 0.858848i | \(-0.671181\pi\) |
0.858848 | + | 0.512231i | \(0.171181\pi\) | |||||||
\(798\) | 0.279305 | + | 0.279305i | 0.00988731 | + | 0.00988731i | ||||
\(799\) | −7.63023 | −0.269938 | ||||||||
\(800\) | 4.87170 | + | 1.12541i | 0.172241 | + | 0.0397891i | ||||
\(801\) | − | 2.20446i | − | 0.0778906i | ||||||
\(802\) | 27.8589 | − | 27.8589i | 0.983733 | − | 0.983733i | ||||
\(803\) | 2.09135 | − | 2.09135i | 0.0738020 | − | 0.0738020i | ||||
\(804\) | −0.923926 | −0.0325844 | ||||||||
\(805\) | 0.112210 | + | 0.391421i | 0.00395488 | + | 0.0137958i | ||||
\(806\) | 25.6088 | + | 16.7284i | 0.902032 | + | 0.589232i | ||||
\(807\) | −0.603753 | − | 0.603753i | −0.0212531 | − | 0.0212531i | ||||
\(808\) | −8.37970 | + | 8.37970i | −0.294797 | + | 0.294797i | ||||
\(809\) | 13.6119 | 0.478568 | 0.239284 | − | 0.970950i | \(-0.423087\pi\) | ||||
0.239284 | + | 0.970950i | \(0.423087\pi\) | |||||||
\(810\) | −1.95564 | − | 1.08420i | −0.0687141 | − | 0.0380948i | ||||
\(811\) | 33.5786 | 1.17910 | 0.589551 | − | 0.807731i | \(-0.299305\pi\) | ||||
0.589551 | + | 0.807731i | \(0.299305\pi\) | |||||||
\(812\) | 0.294378 | − | 0.294378i | 0.0103307 | − | 0.0103307i | ||||
\(813\) | −10.6988 | + | 10.6988i | −0.375222 | + | 0.375222i | ||||
\(814\) | − | 1.55497i | − | 0.0545018i | ||||||
\(815\) | −18.4160 | + | 33.2180i | −0.645083 | + | 1.16358i | ||||
\(816\) | 1.91907 | 0.0671810 | ||||||||
\(817\) | −2.67448 | + | 2.67448i | −0.0935683 | + | 0.0935683i | ||||
\(818\) | −7.09239 | − | 7.09239i | −0.247980 | − | 0.247980i | ||||
\(819\) | −0.267697 | −0.00935408 | ||||||||
\(820\) | 0.903016 | + | 3.14998i | 0.0315347 | + | 0.110002i | ||||
\(821\) | − | 14.7572i | − | 0.515031i | −0.966274 | − | 0.257516i | \(-0.917096\pi\) | ||
0.966274 | − | 0.257516i | \(-0.0829039\pi\) | |||||||
\(822\) | −0.736104 | − | 0.736104i | −0.0256746 | − | 0.0256746i | ||||
\(823\) | −9.22666 | − | 9.22666i | −0.321621 | − | 0.321621i | 0.527768 | − | 0.849389i | \(-0.323029\pi\) |
−0.849389 | + | 0.527768i | \(0.823029\pi\) | |||||||
\(824\) | 11.4574i | 0.399136i | ||||||||
\(825\) | −0.272274 | + | 1.17863i | −0.00947936 | + | 0.0410346i | ||||
\(826\) | −0.667456 | −0.0232238 | ||||||||
\(827\) | 19.7186 | − | 19.7186i | 0.685683 | − | 0.685683i | −0.275592 | − | 0.961275i | \(-0.588874\pi\) |
0.961275 | + | 0.275592i | \(0.0888739\pi\) | |||||||
\(828\) | 2.64257 | + | 2.64257i | 0.0918358 | + | 0.0918358i | ||||
\(829\) | 30.2439 | 1.05041 | 0.525207 | − | 0.850974i | \(-0.323988\pi\) | ||||
0.525207 | + | 0.850974i | \(0.323988\pi\) | |||||||
\(830\) | −0.593860 | − | 2.07156i | −0.0206132 | − | 0.0719048i | ||||
\(831\) | 15.7269 | 0.545561 | ||||||||
\(832\) | 3.88473 | − | 3.88473i | 0.134679 | − | 0.134679i | ||||
\(833\) | −9.49570 | − | 9.49570i | −0.329007 | − | 0.329007i | ||||
\(834\) | 4.32252i | 0.149677i | ||||||||
\(835\) | −19.8264 | + | 35.7622i | −0.686121 | + | 1.23760i | ||||
\(836\) | − | 1.96121i | − | 0.0678299i | ||||||
\(837\) | 1.14299 | + | 5.44918i | 0.0395076 | + | 0.188351i | ||||
\(838\) | 5.93955 | − | 5.93955i | 0.205178 | − | 0.205178i | ||||
\(839\) | − | 33.3839i | − | 1.15254i | −0.817260 | − | 0.576269i | \(-0.804508\pi\) | ||
0.817260 | − | 0.576269i | \(-0.195492\pi\) | |||||||
\(840\) | 0.0952917 | + | 0.0528294i | 0.00328788 | + | 0.00182279i | ||||
\(841\) | 43.9974 | 1.51715 | ||||||||
\(842\) | 15.8033 | + | 15.8033i | 0.544616 | + | 0.544616i | ||||
\(843\) | 7.92487 | + | 7.92487i | 0.272947 | + | 0.272947i | ||||
\(844\) | 2.44965i | 0.0843205i | ||||||||
\(845\) | −10.5877 | − | 36.9331i | −0.364229 | − | 1.27054i | ||||
\(846\) | −3.97600 | −0.136698 | ||||||||
\(847\) | 0.376988 | + | 0.376988i | 0.0129535 | + | 0.0129535i | ||||
\(848\) | −0.597357 | − | 0.597357i | −0.0205133 | − | 0.0205133i | ||||
\(849\) | −2.92685 | −0.100449 | ||||||||
\(850\) | −8.13801 | + | 5.08368i | −0.279131 | + | 0.174369i | ||||
\(851\) | 24.0197 | 0.823386 | ||||||||
\(852\) | −3.14023 | + | 3.14023i | −0.107583 | + | 0.107583i | ||||
\(853\) | 28.2893 | − | 28.2893i | 0.968608 | − | 0.968608i | −0.0309136 | − | 0.999522i | \(-0.509842\pi\) |
0.999522 | + | 0.0309136i | \(0.00984168\pi\) | |||||||
\(854\) | −0.569650 | −0.0194930 | ||||||||
\(855\) | −17.4246 | + | 4.99516i | −0.595908 | + | 0.170831i | ||||
\(856\) | −14.5124 | −0.496022 | ||||||||
\(857\) | 34.0629 | + | 34.0629i | 1.16357 | + | 1.16357i | 0.983689 | + | 0.179876i | \(0.0575696\pi\) |
0.179876 | + | 0.983689i | \(0.442430\pi\) | |||||||
\(858\) | 0.939849 | + | 0.939849i | 0.0320859 | + | 0.0320859i | ||||
\(859\) | 31.7668 | 1.08387 | 0.541934 | − | 0.840421i | \(-0.317692\pi\) | ||||
0.541934 | + | 0.840421i | \(0.317692\pi\) | |||||||
\(860\) | −0.505866 | + | 0.912464i | −0.0172499 | + | 0.0311148i | ||||
\(861\) | 0.0714069i | 0.00243354i | ||||||||
\(862\) | −0.373596 | − | 0.373596i | −0.0127247 | − | 0.0127247i | ||||
\(863\) | −36.5834 | − | 36.5834i | −1.24531 | − | 1.24531i | −0.957767 | − | 0.287544i | \(-0.907161\pi\) |
−0.287544 | − | 0.957767i | \(-0.592839\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 27.1985 | − | 49.0596i | 0.924775 | − | 1.66808i | ||||
\(866\) | − | 29.9194i | − | 1.01670i | ||||||
\(867\) | 9.41666 | − | 9.41666i | 0.319806 | − | 0.319806i | ||||
\(868\) | −0.0556942 | − | 0.265521i | −0.00189039 | − | 0.00901236i | ||||
\(869\) | 3.12206i | 0.105908i | ||||||||
\(870\) | 5.26472 | + | 18.3649i | 0.178491 | + | 0.622628i | ||||
\(871\) | − | 5.07590i | − | 0.171990i | ||||||
\(872\) | −4.81814 | − | 4.81814i | −0.163163 | − | 0.163163i | ||||
\(873\) | 5.06944 | − | 5.06944i | 0.171575 | − | 0.171575i | ||||
\(874\) | 30.2949 | 1.02474 | ||||||||
\(875\) | −0.544040 | + | 0.0284027i | −0.0183919 | + | 0.000960188i | ||||
\(876\) | 12.2249 | 0.413040 | ||||||||
\(877\) | −13.7222 | − | 13.7222i | −0.463367 | − | 0.463367i | 0.436390 | − | 0.899757i | \(-0.356257\pi\) |
−0.899757 | + | 0.436390i | \(0.856257\pi\) | |||||||
\(878\) | 16.3490 | − | 16.3490i | 0.551753 | − | 0.551753i | ||||
\(879\) | 22.4607 | 0.757579 | ||||||||
\(880\) | −0.149080 | − | 0.520034i | −0.00502548 | − | 0.0175303i | ||||
\(881\) | 43.5538i | 1.46736i | 0.679493 | + | 0.733682i | \(0.262200\pi\) | ||||
−0.679493 | + | 0.733682i | \(0.737800\pi\) | |||||||
\(882\) | −4.94807 | − | 4.94807i | −0.166610 | − | 0.166610i | ||||
\(883\) | 30.3612 | + | 30.3612i | 1.02174 | + | 1.02174i | 0.999758 | + | 0.0219787i | \(0.00699661\pi\) |
0.0219787 | + | 0.999758i | \(0.493003\pi\) | |||||||
\(884\) | 10.5431i | 0.354602i | ||||||||
\(885\) | 14.8513 | − | 26.7882i | 0.499220 | − | 0.900476i | ||||
\(886\) | −17.7676 | −0.596913 | ||||||||
\(887\) | 15.7102 | + | 15.7102i | 0.527498 | + | 0.527498i | 0.919826 | − | 0.392327i | \(-0.128330\pi\) |
−0.392327 | + | 0.919826i | \(0.628330\pi\) | |||||||
\(888\) | 4.54476 | − | 4.54476i | 0.152512 | − | 0.152512i | ||||
\(889\) | 0.696517 | 0.0233604 | ||||||||
\(890\) | −4.31112 | − | 2.39007i | −0.144509 | − | 0.0801152i | ||||
\(891\) | 0.241934i | 0.00810509i | ||||||||
\(892\) | 15.8119 | − | 15.8119i | 0.529420 | − | 0.529420i | ||||
\(893\) | −22.7908 | + | 22.7908i | −0.762663 | + | 0.762663i | ||||
\(894\) | 15.8034 | 0.528546 | ||||||||
\(895\) | 16.2855 | − | 4.66861i | 0.544363 | − | 0.156054i | ||||
\(896\) | −0.0487267 | −0.00162785 | ||||||||
\(897\) | −14.5179 | + | 14.5179i | −0.484738 | + | 0.484738i | ||||
\(898\) | −0.794746 | − | 0.794746i | −0.0265210 | − | 0.0265210i | ||||
\(899\) | 26.0155 | − | 39.8260i | 0.867664 | − | 1.32827i | ||||
\(900\) | −4.24059 | + | 2.64903i | −0.141353 | + | 0.0883010i | ||||
\(901\) | 1.62121 | 0.0540105 | ||||||||
\(902\) | 0.250701 | − | 0.250701i | 0.00834741 | − | 0.00834741i | ||||
\(903\) | −0.0160761 | + | 0.0160761i | −0.000534978 | + | 0.000534978i | ||||
\(904\) | − | 1.14372i | − | 0.0380397i | ||||||
\(905\) | −2.99933 | − | 10.4625i | −0.0997011 | − | 0.347787i | ||||
\(906\) | 3.30031 | 0.109645 | ||||||||
\(907\) | 22.6786 | + | 22.6786i | 0.753032 | + | 0.753032i | 0.975044 | − | 0.222012i | \(-0.0712624\pi\) |
−0.222012 | + | 0.975044i | \(0.571262\pi\) | |||||||
\(908\) | −19.2620 | + | 19.2620i | −0.639233 | + | 0.639233i | ||||
\(909\) | − | 11.8507i | − | 0.393062i | ||||||
\(910\) | −0.290236 | + | 0.523518i | −0.00962124 | + | 0.0173544i | ||||
\(911\) | 35.9909i | 1.19243i | 0.802824 | + | 0.596216i | \(0.203330\pi\) | ||||
−0.802824 | + | 0.596216i | \(0.796670\pi\) | |||||||
\(912\) | 5.73208 | − | 5.73208i | 0.189808 | − | 0.189808i | ||||
\(913\) | −0.164871 | + | 0.164871i | −0.00545643 | + | 0.00545643i | ||||
\(914\) | −18.0189 | −0.596013 | ||||||||
\(915\) | 12.6750 | − | 22.8628i | 0.419024 | − | 0.755821i | ||||
\(916\) | − | 27.0642i | − | 0.894226i | ||||||
\(917\) | 0.252190 | + | 0.252190i | 0.00832804 | + | 0.00832804i | ||||
\(918\) | −1.35699 | + | 1.35699i | −0.0447873 | + | 0.0447873i | ||||
\(919\) | − | 1.89965i | − | 0.0626635i | −0.999509 | − | 0.0313318i | \(-0.990025\pi\) | ||
0.999509 | − | 0.0313318i | \(-0.00997484\pi\) | |||||||
\(920\) | 8.03299 | − | 2.30284i | 0.264840 | − | 0.0759225i | ||||
\(921\) | − | 9.11097i | − | 0.300217i | ||||||
\(922\) | 22.5995 | − | 22.5995i | 0.744273 | − | 0.744273i | ||||
\(923\) | −17.2519 | − | 17.2519i | −0.567854 | − | 0.567854i | ||||
\(924\) | − | 0.0117886i | − | 0.000387818i | ||||||
\(925\) | −7.23328 | + | 31.3117i | −0.237829 | + | 1.02952i | ||||
\(926\) | − | 9.48627i | − | 0.311738i | ||||||
\(927\) | −8.10157 | − | 8.10157i | −0.266091 | − | 0.266091i | ||||
\(928\) | −6.04141 | − | 6.04141i | −0.198319 | − | 0.198319i | ||||
\(929\) | 23.8623 | 0.782896 | 0.391448 | − | 0.920200i | \(-0.371974\pi\) | ||||
0.391448 | + | 0.920200i | \(0.371974\pi\) | |||||||
\(930\) | 11.8958 | + | 3.67271i | 0.390080 | + | 0.120433i | ||||
\(931\) | −56.7255 | −1.85910 | ||||||||
\(932\) | 9.02104 | + | 9.02104i | 0.295494 | + | 0.295494i | ||||
\(933\) | −7.18083 | − | 7.18083i | −0.235090 | − | 0.235090i | ||||
\(934\) | − | 14.2554i | − | 0.466449i | ||||||
\(935\) | 0.907980 | + | 0.503381i | 0.0296941 | + | 0.0164623i | ||||
\(936\) | 5.49384i | 0.179572i | ||||||||
\(937\) | 32.3207 | + | 32.3207i | 1.05587 | + | 1.05587i | 0.998344 | + | 0.0575269i | \(0.0183215\pi\) |
0.0575269 | + | 0.998344i | \(0.481678\pi\) | |||||||
\(938\) | −0.0318339 | + | 0.0318339i | −0.00103941 | + | 0.00103941i | ||||
\(939\) | − | 21.6707i | − | 0.707197i | ||||||
\(940\) | −4.31077 | + | 7.77561i | −0.140602 | + | 0.253612i | ||||
\(941\) | 15.5412i | 0.506627i | 0.967384 | + | 0.253314i | \(0.0815205\pi\) | ||||
−0.967384 | + | 0.253314i | \(0.918480\pi\) | |||||||
\(942\) | 4.79524 | − | 4.79524i | 0.156237 | − | 0.156237i | ||||
\(943\) | 3.87258 | + | 3.87258i | 0.126109 | + | 0.126109i | ||||
\(944\) | 13.6979i | 0.445830i | ||||||||
\(945\) | −0.104737 | + | 0.0300254i | −0.00340711 | + | 0.000976727i | ||||
\(946\) | 0.112882 | 0.00367011 | ||||||||
\(947\) | 1.24213 | − | 1.24213i | 0.0403639 | − | 0.0403639i | −0.686637 | − | 0.727001i | \(-0.740914\pi\) |
0.727001 | + | 0.686637i | \(0.240914\pi\) | |||||||
\(948\) | −9.12491 | + | 9.12491i | −0.296363 | + | 0.296363i | ||||
\(949\) | 67.1615i | 2.18015i | ||||||||
\(950\) | −9.12297 | + | 39.4919i | −0.295988 | + | 1.28129i | ||||
\(951\) | − | 1.28031i | − | 0.0415170i | ||||||
\(952\) | 0.0661216 | − | 0.0661216i | 0.00214301 | − | 0.00214301i | ||||
\(953\) | 4.65276 | + | 4.65276i | 0.150718 | + | 0.150718i | 0.778439 | − | 0.627721i | \(-0.216012\pi\) |
−0.627721 | + | 0.778439i | \(0.716012\pi\) | |||||||
\(954\) | 0.844790 | 0.0273511 | ||||||||
\(955\) | −40.5102 | + | 11.6132i | −1.31088 | + | 0.375794i | ||||
\(956\) | 18.6644i | 0.603651i | ||||||||
\(957\) | 1.46162 | − | 1.46162i | 0.0472476 | − | 0.0472476i | ||||
\(958\) | 6.52569 | − | 6.52569i | 0.210835 | − | 0.210835i | ||||
\(959\) | −0.0507249 | −0.00163799 | ||||||||
\(960\) | 1.08420 | − | 1.95564i | 0.0349923 | − | 0.0631179i | ||||
\(961\) | −12.4567 | − | 28.3871i | −0.401830 | − | 0.915714i | ||||
\(962\) | 24.9682 | + | 24.9682i | 0.805007 | + | 0.805007i | ||||
\(963\) | 10.2618 | − | 10.2618i | 0.330681 | − | 0.330681i | ||||
\(964\) | −17.5955 | −0.566713 | ||||||||
\(965\) | 9.66652 | − | 17.4361i | 0.311176 | − | 0.561288i | ||||
\(966\) | 0.182100 | 0.00585896 | ||||||||
\(967\) | −2.16898 | + | 2.16898i | −0.0697498 | + | 0.0697498i | −0.741121 | − | 0.671371i | \(-0.765706\pi\) |
0.671371 | + | 0.741121i | \(0.265706\pi\) | |||||||
\(968\) | 7.73679 | − | 7.73679i | 0.248670 | − | 0.248670i | ||||
\(969\) | 15.5567i | 0.499755i | ||||||||
\(970\) | −4.41771 | − | 15.4103i | −0.141844 | − | 0.494794i | ||||
\(971\) | −20.3741 | −0.653835 | −0.326918 | − | 0.945053i | \(-0.606010\pi\) | ||||
−0.326918 | + | 0.945053i | \(0.606010\pi\) | |||||||
\(972\) | −0.707107 | + | 0.707107i | −0.0226805 | + | 0.0226805i | ||||
\(973\) | 0.148932 | + | 0.148932i | 0.00477455 | + | 0.00477455i | ||||
\(974\) | −27.7787 | −0.890086 | ||||||||
\(975\) | −14.5534 | − | 23.2971i | −0.466080 | − | 0.746106i | ||||
\(976\) | 11.6907i | 0.374211i | ||||||||
\(977\) | −18.2867 | − | 18.2867i | −0.585043 | − | 0.585043i | 0.351242 | − | 0.936285i | \(-0.385760\pi\) |
−0.936285 | + | 0.351242i | \(0.885760\pi\) | |||||||
\(978\) | 12.0108 | + | 12.0108i | 0.384062 | + | 0.384062i | ||||
\(979\) | 0.533333i | 0.0170454i | ||||||||
\(980\) | −15.0413 | + | 4.31194i | −0.480477 | + | 0.137740i | ||||
\(981\) | 6.81387 | 0.217550 | ||||||||
\(982\) | −0.782254 | + | 0.782254i | −0.0249627 | + | 0.0249627i | ||||
\(983\) | −15.5673 | − | 15.5673i | −0.496519 | − | 0.496519i | 0.413833 | − | 0.910353i | \(-0.364190\pi\) |
−0.910353 | + | 0.413833i | \(0.864190\pi\) | |||||||
\(984\) | 1.46546 | 0.0467171 | ||||||||
\(985\) | −19.0360 | + | 34.3365i | −0.606539 | + | 1.09405i | ||||
\(986\) | 16.3963 | 0.522163 | ||||||||
\(987\) | −0.136993 | + | 0.136993i | −0.00436054 | + | 0.00436054i | ||||
\(988\) | 31.4911 | + | 31.4911i | 1.00187 | + | 1.00187i | ||||
\(989\) | 1.74369i | 0.0554462i | ||||||||
\(990\) | 0.473135 | + | 0.262304i | 0.0150372 | + | 0.00833658i | ||||
\(991\) | − | 45.9481i | − | 1.45959i | −0.683666 | − | 0.729795i | \(-0.739615\pi\) | ||
0.683666 | − | 0.729795i | \(-0.260385\pi\) | |||||||
\(992\) | −5.44918 | + | 1.14299i | −0.173012 | + | 0.0362900i | ||||
\(993\) | −24.9340 | + | 24.9340i | −0.791257 | + | 0.791257i | ||||
\(994\) | 0.216393i | 0.00686358i | ||||||||
\(995\) | 15.2373 | − | 4.36811i | 0.483054 | − | 0.138478i | ||||
\(996\) | −0.963745 | −0.0305374 | ||||||||
\(997\) | 43.3516 | + | 43.3516i | 1.37296 | + | 1.37296i | 0.856025 | + | 0.516935i | \(0.172927\pi\) |
0.516935 | + | 0.856025i | \(0.327073\pi\) | |||||||
\(998\) | 21.7446 | + | 21.7446i | 0.688313 | + | 0.688313i | ||||
\(999\) | 6.42726i | 0.203350i |
(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 | 930.2.k.b.247.2 | yes | 32 | |
5.3 | odd | 4 | 930.2.k.a.433.2 | yes | 32 | ||
31.30 | odd | 2 | 930.2.k.a.247.2 | ✓ | 32 | ||
155.123 | even | 4 | inner | 930.2.k.b.433.2 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.k.a.247.2 | ✓ | 32 | 31.30 | odd | 2 | ||
930.2.k.a.433.2 | yes | 32 | 5.3 | odd | 4 | ||
930.2.k.b.247.2 | yes | 32 | 1.1 | even | 1 | trivial | |
930.2.k.b.433.2 | yes | 32 | 155.123 | even | 4 | inner |