Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(118,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.118");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.7 | ||
Root | \(-0.517174 - 1.31626i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.307 |
Dual form | 525.2.m.b.118.7 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.86147 | + | 1.86147i | 1.31626 | + | 1.31626i | 0.916715 | + | 0.399541i | \(0.130831\pi\) |
0.399541 | + | 0.916715i | \(0.369169\pi\) | |||||||
\(3\) | −0.707107 | − | 0.707107i | −0.408248 | − | 0.408248i | ||||
\(4\) | 4.93012i | 2.46506i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.63251i | − | 1.07472i | ||||||
\(7\) | −1.46123 | + | 2.20563i | −0.552293 | + | 0.833650i | ||||
\(8\) | −5.45433 | + | 5.45433i | −1.92840 | + | 1.92840i | ||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.46279 | −0.441048 | −0.220524 | − | 0.975382i | \(-0.570777\pi\) | ||||
−0.220524 | + | 0.975382i | \(0.570777\pi\) | |||||||
\(12\) | 3.48612 | − | 3.48612i | 1.00636 | − | 1.00636i | ||||
\(13\) | 0.887844 | + | 0.887844i | 0.246244 | + | 0.246244i | 0.819427 | − | 0.573183i | \(-0.194292\pi\) |
−0.573183 | + | 0.819427i | \(0.694292\pi\) | |||||||
\(14\) | −6.82574 | + | 1.38567i | −1.82426 | + | 0.370337i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.4459 | −2.61147 | ||||||||
\(17\) | −2.10614 | + | 2.10614i | −0.510815 | + | 0.510815i | −0.914776 | − | 0.403961i | \(-0.867633\pi\) |
0.403961 | + | 0.914776i | \(0.367633\pi\) | |||||||
\(18\) | −1.86147 | + | 1.86147i | −0.438752 | + | 0.438752i | ||||
\(19\) | 3.95987 | 0.908456 | 0.454228 | − | 0.890885i | \(-0.349915\pi\) | ||||
0.454228 | + | 0.890885i | \(0.349915\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.59286 | − | 0.526369i | 0.565809 | − | 0.114863i | ||||
\(22\) | −2.72294 | − | 2.72294i | −0.580532 | − | 0.580532i | ||||
\(23\) | 4.13007 | − | 4.13007i | 0.861180 | − | 0.861180i | −0.130295 | − | 0.991475i | \(-0.541593\pi\) |
0.991475 | + | 0.130295i | \(0.0415926\pi\) | |||||||
\(24\) | 7.71359 | 1.57453 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.30539i | 0.648240i | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | −10.8740 | − | 7.20405i | −2.05500 | − | 1.36144i | ||||
\(29\) | 5.18572i | 0.962965i | 0.876456 | + | 0.481482i | \(0.159901\pi\) | ||||
−0.876456 | + | 0.481482i | \(0.840099\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.10346i | 1.09621i | 0.836408 | + | 0.548107i | \(0.184651\pi\) | ||||
−0.836408 | + | 0.548107i | \(0.815349\pi\) | |||||||
\(32\) | −8.53599 | − | 8.53599i | −1.50896 | − | 1.50896i | ||||
\(33\) | 1.03435 | + | 1.03435i | 0.180057 | + | 0.180057i | ||||
\(34\) | −7.84104 | −1.34473 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −4.93012 | −0.821687 | ||||||||
\(37\) | −2.25560 | − | 2.25560i | −0.370819 | − | 0.370819i | 0.496957 | − | 0.867775i | \(-0.334451\pi\) |
−0.867775 | + | 0.496957i | \(0.834451\pi\) | |||||||
\(38\) | 7.37117 | + | 7.37117i | 1.19576 | + | 1.19576i | ||||
\(39\) | − | 1.25560i | − | 0.201057i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 0.769968i | − | 0.120249i | −0.998191 | − | 0.0601244i | \(-0.980850\pi\) | ||
0.998191 | − | 0.0601244i | \(-0.0191497\pi\) | |||||||
\(42\) | 5.80635 | + | 3.84671i | 0.895939 | + | 0.593560i | ||||
\(43\) | 5.18572 | − | 5.18572i | 0.790816 | − | 0.790816i | −0.190811 | − | 0.981627i | \(-0.561112\pi\) |
0.981627 | + | 0.190811i | \(0.0611118\pi\) | |||||||
\(44\) | − | 7.21173i | − | 1.08721i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 15.3760 | 2.26707 | ||||||||
\(47\) | 8.57041 | − | 8.57041i | 1.25012 | − | 1.25012i | 0.294459 | − | 0.955664i | \(-0.404861\pi\) |
0.955664 | − | 0.294459i | \(-0.0951394\pi\) | |||||||
\(48\) | 7.38635 | + | 7.38635i | 1.06613 | + | 1.06613i | ||||
\(49\) | −2.72961 | − | 6.44587i | −0.389944 | − | 0.920839i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.97854 | 0.417079 | ||||||||
\(52\) | −4.37718 | + | 4.37718i | −0.607006 | + | 0.607006i | ||||
\(53\) | 0.544449 | − | 0.544449i | 0.0747859 | − | 0.0747859i | −0.668724 | − | 0.743510i | \(-0.733159\pi\) |
0.743510 | + | 0.668724i | \(0.233159\pi\) | |||||||
\(54\) | 2.63251 | 0.358240 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.06020 | − | 20.0003i | −0.542567 | − | 2.67265i | ||||
\(57\) | −2.80005 | − | 2.80005i | −0.370876 | − | 0.370876i | ||||
\(58\) | −9.65306 | + | 9.65306i | −1.26751 | + | 1.26751i | ||||
\(59\) | 3.19633 | 0.416127 | 0.208063 | − | 0.978115i | \(-0.433284\pi\) | ||||
0.208063 | + | 0.978115i | \(0.433284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 1.42064i | − | 0.181894i | −0.995856 | − | 0.0909472i | \(-0.971011\pi\) | ||
0.995856 | − | 0.0909472i | \(-0.0289894\pi\) | |||||||
\(62\) | −11.3614 | + | 11.3614i | −1.44290 | + | 1.44290i | ||||
\(63\) | −2.20563 | − | 1.46123i | −0.277883 | − | 0.184098i | ||||
\(64\) | − | 10.8872i | − | 1.36090i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.85081i | 0.474002i | ||||||||
\(67\) | 5.93012 | + | 5.93012i | 0.724480 | + | 0.724480i | 0.969514 | − | 0.245034i | \(-0.0787993\pi\) |
−0.245034 | + | 0.969514i | \(0.578799\pi\) | |||||||
\(68\) | −10.3835 | − | 10.3835i | −1.25919 | − | 1.25919i | ||||
\(69\) | −5.84081 | −0.703150 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.62611 | 0.905053 | 0.452526 | − | 0.891751i | \(-0.350523\pi\) | ||||
0.452526 | + | 0.891751i | \(0.350523\pi\) | |||||||
\(72\) | −5.45433 | − | 5.45433i | −0.642799 | − | 0.642799i | ||||
\(73\) | 6.81378 | + | 6.81378i | 0.797493 | + | 0.797493i | 0.982700 | − | 0.185207i | \(-0.0592955\pi\) |
−0.185207 | + | 0.982700i | \(0.559296\pi\) | |||||||
\(74\) | − | 8.39746i | − | 0.976185i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 19.5226i | 2.23940i | ||||||||
\(77\) | 2.13747 | − | 3.22637i | 0.243588 | − | 0.367679i | ||||
\(78\) | 2.33726 | − | 2.33726i | 0.264643 | − | 0.264643i | ||||
\(79\) | 4.52029i | 0.508573i | 0.967129 | + | 0.254286i | \(0.0818405\pi\) | ||||
−0.967129 | + | 0.254286i | \(0.918159\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 1.43327 | − | 1.43327i | 0.158278 | − | 0.158278i | ||||
\(83\) | −6.75794 | − | 6.75794i | −0.741781 | − | 0.741781i | 0.231140 | − | 0.972921i | \(-0.425754\pi\) |
−0.972921 | + | 0.231140i | \(0.925754\pi\) | |||||||
\(84\) | 2.59507 | + | 12.7831i | 0.283145 | + | 1.39475i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 19.3061 | 2.08183 | ||||||||
\(87\) | 3.66686 | − | 3.66686i | 0.393129 | − | 0.393129i | ||||
\(88\) | 7.97854 | − | 7.97854i | 0.850515 | − | 0.850515i | ||||
\(89\) | −1.19991 | −0.127190 | −0.0635950 | − | 0.997976i | \(-0.520257\pi\) | ||||
−0.0635950 | + | 0.997976i | \(0.520257\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.25560 | + | 0.660910i | −0.341280 | + | 0.0692822i | ||||
\(92\) | 20.3618 | + | 20.3618i | 2.12286 | + | 2.12286i | ||||
\(93\) | 4.31580 | − | 4.31580i | 0.447527 | − | 0.447527i | ||||
\(94\) | 31.9071 | 3.29096 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 12.0717i | 1.23206i | ||||||||
\(97\) | −8.68829 | + | 8.68829i | −0.882162 | + | 0.882162i | −0.993754 | − | 0.111592i | \(-0.964405\pi\) |
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(98\) | 6.91770 | − | 17.0799i | 0.698794 | − | 1.72533i | ||||
\(99\) | − | 1.46279i | − | 0.147016i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 15.3420i | − | 1.52659i | −0.646050 | − | 0.763295i | \(-0.723580\pi\) | ||
0.646050 | − | 0.763295i | \(-0.276420\pi\) | |||||||
\(102\) | 5.54445 | + | 5.54445i | 0.548982 | + | 0.548982i | ||||
\(103\) | 8.30776 | + | 8.30776i | 0.818588 | + | 0.818588i | 0.985903 | − | 0.167316i | \(-0.0535099\pi\) |
−0.167316 | + | 0.985903i | \(0.553510\pi\) | |||||||
\(104\) | −9.68519 | −0.949711 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.02695 | 0.196875 | ||||||||
\(107\) | −4.39022 | − | 4.39022i | −0.424418 | − | 0.424418i | 0.462303 | − | 0.886722i | \(-0.347023\pi\) |
−0.886722 | + | 0.462303i | \(0.847023\pi\) | |||||||
\(108\) | 3.48612 | + | 3.48612i | 0.335452 | + | 0.335452i | ||||
\(109\) | 7.44587i | 0.713185i | 0.934260 | + | 0.356593i | \(0.116062\pi\) | ||||
−0.934260 | + | 0.356593i | \(0.883938\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.18990i | 0.302772i | ||||||||
\(112\) | 15.2638 | − | 23.0397i | 1.44230 | − | 2.17705i | ||||
\(113\) | −2.54445 | + | 2.54445i | −0.239362 | + | 0.239362i | −0.816586 | − | 0.577224i | \(-0.804136\pi\) |
0.577224 | + | 0.816586i | \(0.304136\pi\) | |||||||
\(114\) | − | 10.4244i | − | 0.976335i | ||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −25.5663 | −2.37377 | ||||||||
\(117\) | −0.887844 | + | 0.887844i | −0.0820812 | + | 0.0820812i | ||||
\(118\) | 5.94986 | + | 5.94986i | 0.547729 | + | 0.547729i | ||||
\(119\) | −1.56781 | − | 7.72294i | −0.143721 | − | 0.707960i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.86025 | −0.805477 | ||||||||
\(122\) | 2.64448 | − | 2.64448i | 0.239420 | − | 0.239420i | ||||
\(123\) | −0.544449 | + | 0.544449i | −0.0490913 | + | 0.0490913i | ||||
\(124\) | −30.0908 | −2.70223 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.38567 | − | 6.82574i | −0.123446 | − | 0.608086i | ||||
\(127\) | −7.86025 | − | 7.86025i | −0.697484 | − | 0.697484i | 0.266383 | − | 0.963867i | \(-0.414171\pi\) |
−0.963867 | + | 0.266383i | \(0.914171\pi\) | |||||||
\(128\) | 3.19418 | − | 3.19418i | 0.282329 | − | 0.282329i | ||||
\(129\) | −7.33372 | −0.645698 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 6.18216i | − | 0.540138i | −0.962841 | − | 0.270069i | \(-0.912953\pi\) | ||
0.962841 | − | 0.270069i | \(-0.0870465\pi\) | |||||||
\(132\) | −5.09947 | + | 5.09947i | −0.443851 | + | 0.443851i | ||||
\(133\) | −5.78628 | + | 8.73401i | −0.501735 | + | 0.757334i | ||||
\(134\) | 22.0775i | 1.90720i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 22.9752i | − | 1.97011i | ||||||
\(137\) | −9.05565 | − | 9.05565i | −0.773677 | − | 0.773677i | 0.205071 | − | 0.978747i | \(-0.434258\pi\) |
−0.978747 | + | 0.205071i | \(0.934258\pi\) | |||||||
\(138\) | −10.8725 | − | 10.8725i | −0.925526 | − | 0.925526i | ||||
\(139\) | 11.9913 | 1.01709 | 0.508544 | − | 0.861036i | \(-0.330184\pi\) | ||||
0.508544 | + | 0.861036i | \(0.330184\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.1204 | −1.02072 | ||||||||
\(142\) | 14.1958 | + | 14.1958i | 1.19128 | + | 1.19128i | ||||
\(143\) | −1.29873 | − | 1.29873i | −0.108605 | − | 0.108605i | ||||
\(144\) | − | 10.4459i | − | 0.870489i | ||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 25.3673i | 2.09941i | ||||||||
\(147\) | −2.62780 | + | 6.48804i | −0.216737 | + | 0.535125i | ||||
\(148\) | 11.1204 | − | 11.1204i | 0.914091 | − | 0.914091i | ||||
\(149\) | − | 0.0968261i | − | 0.00793230i | −0.999992 | − | 0.00396615i | \(-0.998738\pi\) | ||
0.999992 | − | 0.00396615i | \(-0.00126247\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4550 | −1.09495 | −0.547475 | − | 0.836822i | \(-0.684411\pi\) | ||||
−0.547475 | + | 0.836822i | \(0.684411\pi\) | |||||||
\(152\) | −21.5984 | + | 21.5984i | −1.75186 | + | 1.75186i | ||||
\(153\) | −2.10614 | − | 2.10614i | −0.170272 | − | 0.170272i | ||||
\(154\) | 9.98463 | − | 2.02695i | 0.804584 | − | 0.163336i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.19027 | 0.495618 | ||||||||
\(157\) | 1.64757 | − | 1.64757i | 0.131491 | − | 0.131491i | −0.638298 | − | 0.769789i | \(-0.720361\pi\) |
0.769789 | + | 0.638298i | \(0.220361\pi\) | |||||||
\(158\) | −8.41438 | + | 8.41438i | −0.669412 | + | 0.669412i | ||||
\(159\) | −0.769968 | −0.0610624 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.07442 | + | 15.1444i | 0.242298 | + | 1.19355i | ||||
\(162\) | −1.86147 | − | 1.86147i | −0.146251 | − | 0.146251i | ||||
\(163\) | 10.2746 | − | 10.2746i | 0.804771 | − | 0.804771i | −0.179066 | − | 0.983837i | \(-0.557308\pi\) |
0.983837 | + | 0.179066i | \(0.0573077\pi\) | |||||||
\(164\) | 3.79604 | 0.296421 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 25.1594i | − | 1.95275i | ||||||
\(167\) | 0.293008 | − | 0.293008i | 0.0226737 | − | 0.0226737i | −0.695679 | − | 0.718353i | \(-0.744896\pi\) |
0.718353 | + | 0.695679i | \(0.244896\pi\) | |||||||
\(168\) | −11.2713 | + | 17.0133i | −0.869602 | + | 1.31261i | ||||
\(169\) | − | 11.4235i | − | 0.878728i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.95987i | 0.302819i | ||||||||
\(172\) | 25.5663 | + | 25.5663i | 1.94941 | + | 1.94941i | ||||
\(173\) | −3.45189 | − | 3.45189i | −0.262442 | − | 0.262442i | 0.563603 | − | 0.826046i | \(-0.309415\pi\) |
−0.826046 | + | 0.563603i | \(0.809415\pi\) | |||||||
\(174\) | 13.6515 | 1.03492 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.2801 | 1.15178 | ||||||||
\(177\) | −2.26015 | − | 2.26015i | −0.169883 | − | 0.169883i | ||||
\(178\) | −2.23359 | − | 2.23359i | −0.167415 | − | 0.167415i | ||||
\(179\) | − | 1.99756i | − | 0.149305i | −0.997210 | − | 0.0746523i | \(-0.976215\pi\) | ||
0.997210 | − | 0.0746523i | \(-0.0237847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.48528i | 0.630706i | 0.948974 | + | 0.315353i | \(0.102123\pi\) | ||||
−0.948974 | + | 0.315353i | \(0.897877\pi\) | |||||||
\(182\) | −7.29046 | − | 4.82993i | −0.540405 | − | 0.358019i | ||||
\(183\) | −1.00454 | + | 1.00454i | −0.0742581 | + | 0.0742581i | ||||
\(184\) | 45.0536i | 3.32139i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 16.0674 | 1.17812 | ||||||||
\(187\) | 3.08084 | − | 3.08084i | 0.225294 | − | 0.225294i | ||||
\(188\) | 42.2532 | + | 42.2532i | 3.08163 | + | 3.08163i | ||||
\(189\) | 0.526369 | + | 2.59286i | 0.0382877 | + | 0.188603i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.83424 | −0.566866 | −0.283433 | − | 0.958992i | \(-0.591473\pi\) | ||||
−0.283433 | + | 0.958992i | \(0.591473\pi\) | |||||||
\(192\) | −7.69841 | + | 7.69841i | −0.555585 | + | 0.555585i | ||||
\(193\) | −13.5617 | + | 13.5617i | −0.976194 | + | 0.976194i | −0.999723 | − | 0.0235293i | \(-0.992510\pi\) |
0.0235293 | + | 0.999723i | \(0.492510\pi\) | |||||||
\(194\) | −32.3459 | −2.32230 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 31.7789 | − | 13.4573i | 2.26992 | − | 0.961236i | ||||
\(197\) | 11.4791 | + | 11.4791i | 0.817853 | + | 0.817853i | 0.985797 | − | 0.167943i | \(-0.0537126\pi\) |
−0.167943 | + | 0.985797i | \(0.553713\pi\) | |||||||
\(198\) | 2.72294 | − | 2.72294i | 0.193511 | − | 0.193511i | ||||
\(199\) | −20.1468 | −1.42817 | −0.714084 | − | 0.700061i | \(-0.753156\pi\) | ||||
−0.714084 | + | 0.700061i | \(0.753156\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 8.38646i | − | 0.591535i | ||||||
\(202\) | 28.5587 | − | 28.5587i | 2.00938 | − | 2.00938i | ||||
\(203\) | −11.4378 | − | 7.57754i | −0.802775 | − | 0.531839i | ||||
\(204\) | 14.6846i | 1.02812i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 30.9292i | 2.15494i | ||||||||
\(207\) | 4.13007 | + | 4.13007i | 0.287060 | + | 0.287060i | ||||
\(208\) | −9.27431 | − | 9.27431i | −0.643057 | − | 0.643057i | ||||
\(209\) | −5.79246 | −0.400673 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.9662 | 0.823785 | 0.411892 | − | 0.911233i | \(-0.364868\pi\) | ||||
0.411892 | + | 0.911233i | \(0.364868\pi\) | |||||||
\(212\) | 2.68420 | + | 2.68420i | 0.184352 | + | 0.184352i | ||||
\(213\) | −5.39247 | − | 5.39247i | −0.369486 | − | 0.369486i | ||||
\(214\) | − | 16.3445i | − | 1.11729i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 7.71359i | 0.524843i | ||||||||
\(217\) | −13.4620 | − | 8.91857i | −0.913858 | − | 0.605432i | ||||
\(218\) | −13.8602 | + | 13.8602i | −0.938734 | + | 0.938734i | ||||
\(219\) | − | 9.63614i | − | 0.651150i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.73985 | −0.251570 | ||||||||
\(222\) | −5.93790 | + | 5.93790i | −0.398526 | + | 0.398526i | ||||
\(223\) | −0.660910 | − | 0.660910i | −0.0442578 | − | 0.0442578i | 0.684632 | − | 0.728889i | \(-0.259963\pi\) |
−0.728889 | + | 0.684632i | \(0.759963\pi\) | |||||||
\(224\) | 31.3003 | − | 6.35418i | 2.09134 | − | 0.424557i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.47282 | −0.630123 | ||||||||
\(227\) | −17.3487 | + | 17.3487i | −1.15147 | + | 1.15147i | −0.165216 | + | 0.986257i | \(0.552832\pi\) |
−0.986257 | + | 0.165216i | \(0.947168\pi\) | |||||||
\(228\) | 13.8046 | − | 13.8046i | 0.914232 | − | 0.914232i | ||||
\(229\) | 25.0782 | 1.65721 | 0.828607 | − | 0.559831i | \(-0.189134\pi\) | ||||
0.828607 | + | 0.559831i | \(0.189134\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.79281 | + | 0.769968i | −0.249549 | + | 0.0506601i | ||||
\(232\) | −28.2847 | − | 28.2847i | −1.85698 | − | 1.85698i | ||||
\(233\) | −2.24138 | + | 2.24138i | −0.146837 | + | 0.146837i | −0.776704 | − | 0.629866i | \(-0.783110\pi\) |
0.629866 | + | 0.776704i | \(0.283110\pi\) | |||||||
\(234\) | −3.30539 | −0.216080 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 15.7583i | 1.02578i | ||||||||
\(237\) | 3.19633 | − | 3.19633i | 0.207624 | − | 0.207624i | ||||
\(238\) | 11.4576 | − | 17.2944i | 0.742684 | − | 1.12103i | ||||
\(239\) | − | 21.3769i | − | 1.38276i | −0.722492 | − | 0.691380i | \(-0.757003\pi\) | ||
0.722492 | − | 0.691380i | \(-0.242997\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.624129i | 0.0402037i | 0.999798 | + | 0.0201018i | \(0.00639905\pi\) | ||||
−0.999798 | + | 0.0201018i | \(0.993601\pi\) | |||||||
\(242\) | −16.4931 | − | 16.4931i | −1.06021 | − | 1.06021i | ||||
\(243\) | 0.707107 | + | 0.707107i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 7.00393 | 0.448381 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.02695 | −0.129234 | ||||||||
\(247\) | 3.51575 | + | 3.51575i | 0.223702 | + | 0.223702i | ||||
\(248\) | −33.2903 | − | 33.2903i | −2.11394 | − | 2.11394i | ||||
\(249\) | 9.55717i | 0.605661i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 16.3443i | − | 1.03164i | −0.856696 | − | 0.515822i | \(-0.827487\pi\) | ||
0.856696 | − | 0.515822i | \(-0.172513\pi\) | |||||||
\(252\) | 7.20405 | − | 10.8740i | 0.453813 | − | 0.684999i | ||||
\(253\) | −6.04143 | + | 6.04143i | −0.379821 | + | 0.379821i | ||||
\(254\) | − | 29.2632i | − | 1.83614i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.88265 | −0.617666 | ||||||||
\(257\) | 21.3054 | − | 21.3054i | 1.32900 | − | 1.32900i | 0.422749 | − | 0.906247i | \(-0.361065\pi\) |
0.906247 | − | 0.422749i | \(-0.138935\pi\) | |||||||
\(258\) | −13.6515 | − | 13.6515i | −0.849904 | − | 0.849904i | ||||
\(259\) | 8.27098 | − | 1.67907i | 0.513933 | − | 0.104332i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.18572 | −0.320988 | ||||||||
\(262\) | 11.5079 | − | 11.5079i | 0.710960 | − | 0.710960i | ||||
\(263\) | 16.3449 | − | 16.3449i | 1.00787 | − | 1.00787i | 0.00789784 | − | 0.999969i | \(-0.497486\pi\) |
0.999969 | − | 0.00789784i | \(-0.00251399\pi\) | |||||||
\(264\) | −11.2834 | −0.694442 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −27.0291 | + | 5.48709i | −1.65726 | + | 0.336435i | ||||
\(267\) | 0.848464 | + | 0.848464i | 0.0519251 | + | 0.0519251i | ||||
\(268\) | −29.2362 | + | 29.2362i | −1.78589 | + | 1.78589i | ||||
\(269\) | 16.5903 | 1.01153 | 0.505764 | − | 0.862672i | \(-0.331211\pi\) | ||||
0.505764 | + | 0.862672i | \(0.331211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.78033i | − | 0.472621i | −0.971678 | − | 0.236311i | \(-0.924062\pi\) | ||
0.971678 | − | 0.236311i | \(-0.0759383\pi\) | |||||||
\(272\) | 22.0005 | − | 22.0005i | 1.33398 | − | 1.33398i | ||||
\(273\) | 2.76939 | + | 1.83472i | 0.167611 | + | 0.111043i | ||||
\(274\) | − | 33.7136i | − | 2.03671i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 28.7959i | − | 1.73331i | ||||||
\(277\) | −21.3107 | − | 21.3107i | −1.28043 | − | 1.28043i | −0.940421 | − | 0.340013i | \(-0.889569\pi\) |
−0.340013 | − | 0.940421i | \(-0.610431\pi\) | |||||||
\(278\) | 22.3214 | + | 22.3214i | 1.33875 | + | 1.33875i | ||||
\(279\) | −6.10346 | −0.365405 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.1519 | −1.26182 | −0.630908 | − | 0.775858i | \(-0.717317\pi\) | ||||
−0.630908 | + | 0.775858i | \(0.717317\pi\) | |||||||
\(282\) | −22.5617 | − | 22.5617i | −1.34353 | − | 1.34353i | ||||
\(283\) | 2.65471 | + | 2.65471i | 0.157806 | + | 0.157806i | 0.781594 | − | 0.623788i | \(-0.214407\pi\) |
−0.623788 | + | 0.781594i | \(0.714407\pi\) | |||||||
\(284\) | 37.5977i | 2.23101i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.83508i | − | 0.285905i | ||||||
\(287\) | 1.69826 | + | 1.12510i | 0.100245 | + | 0.0664126i | ||||
\(288\) | 8.53599 | − | 8.53599i | 0.502988 | − | 0.502988i | ||||
\(289\) | 8.12832i | 0.478136i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.2871 | 0.720282 | ||||||||
\(292\) | −33.5928 | + | 33.5928i | −1.96587 | + | 1.96587i | ||||
\(293\) | −1.56714 | − | 1.56714i | −0.0915536 | − | 0.0915536i | 0.659847 | − | 0.751400i | \(-0.270621\pi\) |
−0.751400 | + | 0.659847i | \(0.770621\pi\) | |||||||
\(294\) | −16.9688 | + | 7.18572i | −0.989643 | + | 0.419080i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 24.6056 | 1.43017 | ||||||||
\(297\) | −1.03435 | + | 1.03435i | −0.0600190 | + | 0.0600190i | ||||
\(298\) | 0.180239 | − | 0.180239i | 0.0104409 | − | 0.0104409i | ||||
\(299\) | 7.33372 | 0.424120 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.86025 | + | 19.0153i | 0.222501 | + | 1.09603i | ||||
\(302\) | −25.0460 | − | 25.0460i | −1.44123 | − | 1.44123i | ||||
\(303\) | −10.8485 | + | 10.8485i | −0.623228 | + | 0.623228i | ||||
\(304\) | −41.3643 | −2.37240 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 7.84104i | − | 0.448242i | ||||||
\(307\) | −17.3551 | + | 17.3551i | −0.990510 | + | 0.990510i | −0.999955 | − | 0.00944588i | \(-0.996993\pi\) |
0.00944588 | + | 0.999955i | \(0.496993\pi\) | |||||||
\(308\) | 15.9064 | + | 10.5380i | 0.906352 | + | 0.600459i | ||||
\(309\) | − | 11.7489i | − | 0.668374i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 31.0648i | − | 1.76153i | −0.473558 | − | 0.880763i | \(-0.657030\pi\) | ||
0.473558 | − | 0.880763i | \(-0.342970\pi\) | |||||||
\(312\) | 6.84846 | + | 6.84846i | 0.387718 | + | 0.387718i | ||||
\(313\) | 5.72426 | + | 5.72426i | 0.323554 | + | 0.323554i | 0.850129 | − | 0.526575i | \(-0.176524\pi\) |
−0.526575 | + | 0.850129i | \(0.676524\pi\) | |||||||
\(314\) | 6.13381 | 0.346151 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −22.2856 | −1.25366 | ||||||||
\(317\) | −0.752579 | − | 0.752579i | −0.0422691 | − | 0.0422691i | 0.685656 | − | 0.727925i | \(-0.259515\pi\) |
−0.727925 | + | 0.685656i | \(0.759515\pi\) | |||||||
\(318\) | −1.43327 | − | 1.43327i | −0.0803738 | − | 0.0803738i | ||||
\(319\) | − | 7.58562i | − | 0.424713i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.20871i | 0.346536i | ||||||||
\(322\) | −22.4679 | + | 33.9138i | −1.25209 | + | 1.88994i | ||||
\(323\) | −8.34005 | + | 8.34005i | −0.464053 | + | 0.464053i | ||||
\(324\) | − | 4.93012i | − | 0.273896i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 38.2518 | 2.11857 | ||||||||
\(327\) | 5.26503 | − | 5.26503i | 0.291157 | − | 0.291157i | ||||
\(328\) | 4.19966 | + | 4.19966i | 0.231887 | + | 0.231887i | ||||
\(329\) | 6.37980 | + | 31.4265i | 0.351730 | + | 1.73260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.8082 | 0.868899 | 0.434449 | − | 0.900696i | \(-0.356943\pi\) | ||||
0.434449 | + | 0.900696i | \(0.356943\pi\) | |||||||
\(332\) | 33.3175 | − | 33.3175i | 1.82853 | − | 1.82853i | ||||
\(333\) | 2.25560 | − | 2.25560i | 0.123606 | − | 0.123606i | ||||
\(334\) | 1.09085 | 0.0596887 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −27.0847 | + | 5.49839i | −1.47759 | + | 0.299962i | ||||
\(337\) | 20.0460 | + | 20.0460i | 1.09197 | + | 1.09197i | 0.995318 | + | 0.0966558i | \(0.0308146\pi\) |
0.0966558 | + | 0.995318i | \(0.469185\pi\) | |||||||
\(338\) | 21.2644 | − | 21.2644i | 1.15663 | − | 1.15663i | ||||
\(339\) | 3.59839 | 0.195438 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 8.92808i | − | 0.483482i | ||||||
\(342\) | −7.37117 | + | 7.37117i | −0.398587 | + | 0.398587i | ||||
\(343\) | 18.2058 | + | 3.39840i | 0.983020 | + | 0.183497i | ||||
\(344\) | 56.5693i | 3.05001i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 12.8512i | − | 0.690883i | ||||||
\(347\) | 20.0847 | + | 20.0847i | 1.07820 | + | 1.07820i | 0.996671 | + | 0.0815328i | \(0.0259815\pi\) |
0.0815328 | + | 0.996671i | \(0.474018\pi\) | |||||||
\(348\) | 18.0781 | + | 18.0781i | 0.969087 | + | 0.969087i | ||||
\(349\) | −14.7663 | −0.790420 | −0.395210 | − | 0.918591i | \(-0.629328\pi\) | ||||
−0.395210 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.25560 | 0.0670190 | ||||||||
\(352\) | 12.4864 | + | 12.4864i | 0.665525 | + | 0.665525i | ||||
\(353\) | −12.4890 | − | 12.4890i | −0.664724 | − | 0.664724i | 0.291766 | − | 0.956490i | \(-0.405757\pi\) |
−0.956490 | + | 0.291766i | \(0.905757\pi\) | |||||||
\(354\) | − | 8.41438i | − | 0.447219i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 5.91570i | − | 0.313531i | ||||||
\(357\) | −4.35233 | + | 6.56955i | −0.230350 | + | 0.347697i | ||||
\(358\) | 3.71839 | − | 3.71839i | 0.196523 | − | 0.196523i | ||||
\(359\) | − | 10.5372i | − | 0.556133i | −0.960562 | − | 0.278066i | \(-0.910306\pi\) | ||
0.960562 | − | 0.278066i | \(-0.0896935\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.31943 | −0.174707 | ||||||||
\(362\) | −15.7951 | + | 15.7951i | −0.830171 | + | 0.830171i | ||||
\(363\) | 6.26514 | + | 6.26514i | 0.328835 | + | 0.328835i | ||||
\(364\) | −3.25837 | − | 16.0505i | −0.170785 | − | 0.841276i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.73985 | −0.195485 | ||||||||
\(367\) | 11.1910 | − | 11.1910i | 0.584163 | − | 0.584163i | −0.351881 | − | 0.936045i | \(-0.614458\pi\) |
0.936045 | + | 0.351881i | \(0.114458\pi\) | |||||||
\(368\) | −43.1422 | + | 43.1422i | −2.24894 | + | 2.24894i | ||||
\(369\) | 0.769968 | 0.0400829 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.405287 | + | 1.99642i | 0.0210415 | + | 0.103649i | ||||
\(372\) | 21.2774 | + | 21.2774i | 1.10318 | + | 1.10318i | ||||
\(373\) | −17.2746 | + | 17.2746i | −0.894446 | + | 0.894446i | −0.994938 | − | 0.100492i | \(-0.967958\pi\) |
0.100492 | + | 0.994938i | \(0.467958\pi\) | |||||||
\(374\) | 11.4698 | 0.593088 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 93.4917i | 4.82147i | ||||||||
\(377\) | −4.60412 | + | 4.60412i | −0.237124 | + | 0.237124i | ||||
\(378\) | −3.84671 | + | 5.80635i | −0.197853 | + | 0.298646i | ||||
\(379\) | 17.6237i | 0.905267i | 0.891697 | + | 0.452634i | \(0.149515\pi\) | ||||
−0.891697 | + | 0.452634i | \(0.850485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.1161i | 0.569493i | ||||||||
\(382\) | −14.5832 | − | 14.5832i | −0.746141 | − | 0.746141i | ||||
\(383\) | 16.1249 | + | 16.1249i | 0.823942 | + | 0.823942i | 0.986671 | − | 0.162729i | \(-0.0520295\pi\) |
−0.162729 | + | 0.986671i | \(0.552030\pi\) | |||||||
\(384\) | −4.51726 | −0.230520 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −50.4894 | −2.56984 | ||||||||
\(387\) | 5.18572 | + | 5.18572i | 0.263605 | + | 0.263605i | ||||
\(388\) | −42.8343 | − | 42.8343i | −2.17458 | − | 2.17458i | ||||
\(389\) | 15.4011i | 0.780865i | 0.920632 | + | 0.390432i | \(0.127674\pi\) | ||||
−0.920632 | + | 0.390432i | \(0.872326\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.3971i | 0.879807i | ||||||||
\(392\) | 50.0461 | + | 20.2697i | 2.52771 | + | 1.02378i | ||||
\(393\) | −4.37145 | + | 4.37145i | −0.220510 | + | 0.220510i | ||||
\(394\) | 42.7360i | 2.15301i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 7.21173 | 0.362403 | ||||||||
\(397\) | 16.1781 | − | 16.1781i | 0.811955 | − | 0.811955i | −0.172972 | − | 0.984927i | \(-0.555337\pi\) |
0.984927 | + | 0.172972i | \(0.0553370\pi\) | |||||||
\(398\) | −37.5026 | − | 37.5026i | −1.87983 | − | 1.87983i | ||||
\(399\) | 10.2674 | − | 2.08435i | 0.514013 | − | 0.104348i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.977595 | −0.0488188 | −0.0244094 | − | 0.999702i | \(-0.507771\pi\) | ||||
−0.0244094 | + | 0.999702i | \(0.507771\pi\) | |||||||
\(402\) | 15.6111 | − | 15.6111i | 0.778612 | − | 0.778612i | ||||
\(403\) | −5.41892 | + | 5.41892i | −0.269936 | + | 0.269936i | ||||
\(404\) | 75.6382 | 3.76314 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.18572 | − | 35.3964i | −0.356622 | − | 1.75670i | ||||
\(407\) | 3.29947 | + | 3.29947i | 0.163549 | + | 0.163549i | ||||
\(408\) | −16.2459 | + | 16.2459i | −0.804293 | + | 0.804293i | ||||
\(409\) | −24.3171 | −1.20241 | −0.601203 | − | 0.799097i | \(-0.705312\pi\) | ||||
−0.601203 | + | 0.799097i | \(0.705312\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.8066i | 0.631704i | ||||||||
\(412\) | −40.9583 | + | 40.9583i | −2.01787 | + | 2.01787i | ||||
\(413\) | −4.67058 | + | 7.04992i | −0.229824 | + | 0.346904i | ||||
\(414\) | 15.3760i | 0.755689i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 15.1573i | − | 0.743146i | ||||||
\(417\) | −8.47912 | − | 8.47912i | −0.415224 | − | 0.415224i | ||||
\(418\) | −10.7825 | − | 10.7825i | −0.527388 | − | 0.527388i | ||||
\(419\) | −15.9893 | −0.781127 | −0.390563 | − | 0.920576i | \(-0.627720\pi\) | ||||
−0.390563 | + | 0.920576i | \(0.627720\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.7000 | 0.716433 | 0.358216 | − | 0.933639i | \(-0.383385\pi\) | ||||
0.358216 | + | 0.933639i | \(0.383385\pi\) | |||||||
\(422\) | 22.2746 | + | 22.2746i | 1.08431 | + | 1.08431i | ||||
\(423\) | 8.57041 | + | 8.57041i | 0.416708 | + | 0.416708i | ||||
\(424\) | 5.93921i | 0.288434i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 20.0758i | − | 0.972677i | ||||||
\(427\) | 3.13341 | + | 2.07588i | 0.151636 | + | 0.100459i | ||||
\(428\) | 21.6443 | − | 21.6443i | 1.04622 | − | 1.04622i | ||||
\(429\) | 1.83668i | 0.0886758i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2722 | 1.07281 | 0.536407 | − | 0.843960i | \(-0.319781\pi\) | ||||
0.536407 | + | 0.843960i | \(0.319781\pi\) | |||||||
\(432\) | −7.38635 | + | 7.38635i | −0.355376 | + | 0.355376i | ||||
\(433\) | −28.0171 | − | 28.0171i | −1.34642 | − | 1.34642i | −0.889520 | − | 0.456896i | \(-0.848961\pi\) |
−0.456896 | − | 0.889520i | \(-0.651039\pi\) | |||||||
\(434\) | −8.45741 | − | 41.6606i | −0.405968 | − | 1.99978i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −36.7091 | −1.75805 | ||||||||
\(437\) | 16.3545 | − | 16.3545i | 0.782344 | − | 0.782344i | ||||
\(438\) | 17.9374 | − | 17.9374i | 0.857080 | − | 0.857080i | ||||
\(439\) | 2.35656 | 0.112473 | 0.0562363 | − | 0.998417i | \(-0.482090\pi\) | ||||
0.0562363 | + | 0.998417i | \(0.482090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.44587 | − | 2.72961i | 0.306946 | − | 0.129981i | ||||
\(442\) | −6.96162 | − | 6.96162i | −0.331130 | − | 0.331130i | ||||
\(443\) | 5.47247 | − | 5.47247i | 0.260005 | − | 0.260005i | −0.565051 | − | 0.825056i | \(-0.691144\pi\) |
0.825056 | + | 0.565051i | \(0.191144\pi\) | |||||||
\(444\) | −15.7266 | −0.746352 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 2.46053i | − | 0.116509i | ||||||
\(447\) | −0.0684664 | + | 0.0684664i | −0.00323835 | + | 0.00323835i | ||||
\(448\) | 24.0131 | + | 15.9087i | 1.13451 | + | 0.751616i | ||||
\(449\) | − | 1.20020i | − | 0.0566410i | −0.999599 | − | 0.0283205i | \(-0.990984\pi\) | ||
0.999599 | − | 0.0283205i | \(-0.00901591\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.12630i | 0.0530354i | ||||||||
\(452\) | −12.5444 | − | 12.5444i | −0.590041 | − | 0.590041i | ||||
\(453\) | 9.51409 | + | 9.51409i | 0.447011 | + | 0.447011i | ||||
\(454\) | −64.5881 | −3.03127 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 30.5448 | 1.43039 | ||||||||
\(457\) | 21.0775 | + | 21.0775i | 0.985962 | + | 0.985962i | 0.999903 | − | 0.0139406i | \(-0.00443756\pi\) |
−0.0139406 | + | 0.999903i | \(0.504438\pi\) | |||||||
\(458\) | 46.6823 | + | 46.6823i | 2.18132 | + | 2.18132i | ||||
\(459\) | 2.97854i | 0.139026i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.9670i | 1.02311i | 0.859252 | + | 0.511553i | \(0.170929\pi\) | ||||
−0.859252 | + | 0.511553i | \(0.829071\pi\) | |||||||
\(462\) | −8.49347 | − | 5.62693i | −0.395152 | − | 0.261788i | ||||
\(463\) | 21.6776 | − | 21.6776i | 1.00744 | − | 1.00744i | 0.00746987 | − | 0.999972i | \(-0.497622\pi\) |
0.999972 | − | 0.00746987i | \(-0.00237776\pi\) | |||||||
\(464\) | − | 54.1694i | − | 2.51475i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.34450 | −0.386551 | ||||||||
\(467\) | 7.11299 | − | 7.11299i | 0.329150 | − | 0.329150i | −0.523113 | − | 0.852263i | \(-0.675230\pi\) |
0.852263 | + | 0.523113i | \(0.175230\pi\) | |||||||
\(468\) | −4.37718 | − | 4.37718i | −0.202335 | − | 0.202335i | ||||
\(469\) | −21.7449 | + | 4.41438i | −1.00409 | + | 0.203837i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.33002 | −0.107362 | ||||||||
\(472\) | −17.4338 | + | 17.4338i | −0.802457 | + | 0.802457i | ||||
\(473\) | −7.58562 | + | 7.58562i | −0.348787 | + | 0.348787i | ||||
\(474\) | 11.8997 | 0.546572 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 38.0750 | − | 7.72950i | 1.74517 | − | 0.354281i | ||||
\(477\) | 0.544449 | + | 0.544449i | 0.0249286 | + | 0.0249286i | ||||
\(478\) | 39.7925 | − | 39.7925i | 1.82007 | − | 1.82007i | ||||
\(479\) | −31.7749 | −1.45183 | −0.725917 | − | 0.687782i | \(-0.758584\pi\) | ||||
−0.725917 | + | 0.687782i | \(0.758584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 4.00524i | − | 0.182623i | ||||||
\(482\) | −1.16180 | + | 1.16180i | −0.0529184 | + | 0.0529184i | ||||
\(483\) | 8.53477 | − | 12.8827i | 0.388345 | − | 0.586181i | ||||
\(484\) | − | 43.6821i | − | 1.98555i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.63251i | 0.119413i | ||||||||
\(487\) | 4.81428 | + | 4.81428i | 0.218156 | + | 0.218156i | 0.807721 | − | 0.589565i | \(-0.200701\pi\) |
−0.589565 | + | 0.807721i | \(0.700701\pi\) | |||||||
\(488\) | 7.74864 | + | 7.74864i | 0.350765 | + | 0.350765i | ||||
\(489\) | −14.5305 | −0.657092 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.3401 | 1.27897 | 0.639484 | − | 0.768804i | \(-0.279148\pi\) | ||||
0.639484 | + | 0.768804i | \(0.279148\pi\) | |||||||
\(492\) | −2.68420 | − | 2.68420i | −0.121013 | − | 0.121013i | ||||
\(493\) | −10.9219 | − | 10.9219i | −0.491897 | − | 0.491897i | ||||
\(494\) | 13.0889i | 0.588897i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 63.7559i | − | 2.86273i | ||||||
\(497\) | −11.1435 | + | 16.8204i | −0.499855 | + | 0.754497i | ||||
\(498\) | −17.7904 | + | 17.7904i | −0.797206 | + | 0.797206i | ||||
\(499\) | 3.39197i | 0.151845i | 0.997114 | + | 0.0759227i | \(0.0241902\pi\) | ||||
−0.997114 | + | 0.0759227i | \(0.975810\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −0.414376 | −0.0185130 | ||||||||
\(502\) | 30.4244 | − | 30.4244i | 1.35791 | − | 1.35791i | ||||
\(503\) | −8.32921 | − | 8.32921i | −0.371381 | − | 0.371381i | 0.496599 | − | 0.867980i | \(-0.334582\pi\) |
−0.867980 | + | 0.496599i | \(0.834582\pi\) | |||||||
\(504\) | 20.0003 | − | 4.06020i | 0.890883 | − | 0.180856i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.4918 | −0.999884 | ||||||||
\(507\) | −8.07761 | + | 8.07761i | −0.358739 | + | 0.358739i | ||||
\(508\) | 38.7520 | − | 38.7520i | 1.71934 | − | 1.71934i | ||||
\(509\) | 38.9452 | 1.72622 | 0.863108 | − | 0.505020i | \(-0.168515\pi\) | ||||
0.863108 | + | 0.505020i | \(0.168515\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.9852 | + | 5.07217i | −1.10528 | + | 0.224380i | ||||
\(512\) | −24.7846 | − | 24.7846i | −1.09534 | − | 1.09534i | ||||
\(513\) | 2.80005 | − | 2.80005i | 0.123625 | − | 0.123625i | ||||
\(514\) | 79.3187 | 3.49860 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 36.1562i | − | 1.59169i | ||||||
\(517\) | −12.5367 | + | 12.5367i | −0.551364 | + | 0.551364i | ||||
\(518\) | 18.5217 | + | 12.2706i | 0.813796 | + | 0.539140i | ||||
\(519\) | 4.88171i | 0.214283i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.06726i | 0.309622i | 0.987944 | + | 0.154811i | \(0.0494769\pi\) | ||||
−0.987944 | + | 0.154811i | \(0.950523\pi\) | |||||||
\(522\) | −9.65306 | − | 9.65306i | −0.422503 | − | 0.422503i | ||||
\(523\) | 14.5887 | + | 14.5887i | 0.637921 | + | 0.637921i | 0.950042 | − | 0.312121i | \(-0.101040\pi\) |
−0.312121 | + | 0.950042i | \(0.601040\pi\) | |||||||
\(524\) | 30.4788 | 1.33147 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 60.8508 | 2.65322 | ||||||||
\(527\) | −12.8548 | − | 12.8548i | −0.559962 | − | 0.559962i | ||||
\(528\) | −10.8047 | − | 10.8047i | −0.470213 | − | 0.470213i | ||||
\(529\) | − | 11.1150i | − | 0.483261i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.19633i | 0.138709i | ||||||||
\(532\) | −43.0597 | − | 28.5271i | −1.86688 | − | 1.23681i | ||||
\(533\) | 0.683611 | − | 0.683611i | 0.0296105 | − | 0.0296105i | ||||
\(534\) | 3.15878i | 0.136694i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −64.6897 | −2.79417 | ||||||||
\(537\) | −1.41249 | + | 1.41249i | −0.0609533 | + | 0.0609533i | ||||
\(538\) | 30.8823 | + | 30.8823i | 1.33143 | + | 1.33143i | ||||
\(539\) | 3.99284 | + | 9.42895i | 0.171984 | + | 0.406134i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18.6013 | 0.799731 | 0.399865 | − | 0.916574i | \(-0.369057\pi\) | ||||
0.399865 | + | 0.916574i | \(0.369057\pi\) | |||||||
\(542\) | 14.4828 | − | 14.4828i | 0.622091 | − | 0.622091i | ||||
\(543\) | 6.00000 | − | 6.00000i | 0.257485 | − | 0.257485i | ||||
\(544\) | 35.9560 | 1.54160 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.73985 | + | 8.57041i | 0.0744589 | + | 0.366780i | ||||
\(547\) | 7.22715 | + | 7.22715i | 0.309011 | + | 0.309011i | 0.844526 | − | 0.535515i | \(-0.179882\pi\) |
−0.535515 | + | 0.844526i | \(0.679882\pi\) | |||||||
\(548\) | 44.6455 | − | 44.6455i | 1.90716 | − | 1.90716i | ||||
\(549\) | 1.42064 | 0.0606315 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.5348i | 0.874812i | ||||||||
\(552\) | 31.8577 | − | 31.8577i | 1.35595 | − | 1.35595i | ||||
\(553\) | −9.97009 | − | 6.60519i | −0.423971 | − | 0.280881i | ||||
\(554\) | − | 79.3382i | − | 3.37076i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 59.1185i | 2.50718i | ||||||||
\(557\) | 0.558927 | + | 0.558927i | 0.0236825 | + | 0.0236825i | 0.718849 | − | 0.695166i | \(-0.244669\pi\) |
−0.695166 | + | 0.718849i | \(0.744669\pi\) | |||||||
\(558\) | −11.3614 | − | 11.3614i | −0.480966 | − | 0.480966i | ||||
\(559\) | 9.20823 | 0.389467 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.35697 | −0.183951 | ||||||||
\(562\) | −39.3736 | − | 39.3736i | −1.66087 | − | 1.66087i | ||||
\(563\) | 0.702475 | + | 0.702475i | 0.0296058 | + | 0.0296058i | 0.721755 | − | 0.692149i | \(-0.243336\pi\) |
−0.692149 | + | 0.721755i | \(0.743336\pi\) | |||||||
\(564\) | − | 59.7550i | − | 2.51614i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.88333i | 0.415427i | ||||||||
\(567\) | 1.46123 | − | 2.20563i | 0.0613659 | − | 0.0926278i | ||||
\(568\) | −41.5953 | + | 41.5953i | −1.74530 | + | 1.74530i | ||||
\(569\) | 9.72049i | 0.407504i | 0.979023 | + | 0.203752i | \(0.0653137\pi\) | ||||
−0.979023 | + | 0.203752i | \(0.934686\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.986684 | −0.0412914 | −0.0206457 | − | 0.999787i | \(-0.506572\pi\) | ||||
−0.0206457 | + | 0.999787i | \(0.506572\pi\) | |||||||
\(572\) | 6.40289 | − | 6.40289i | 0.267718 | − | 0.267718i | ||||
\(573\) | 5.53964 | + | 5.53964i | 0.231422 | + | 0.231422i | ||||
\(574\) | 1.06692 | + | 5.25560i | 0.0445326 | + | 0.219365i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 10.8872 | 0.453633 | ||||||||
\(577\) | −10.3510 | + | 10.3510i | −0.430917 | + | 0.430917i | −0.888940 | − | 0.458024i | \(-0.848558\pi\) |
0.458024 | + | 0.888940i | \(0.348558\pi\) | |||||||
\(578\) | −15.1306 | + | 15.1306i | −0.629350 | + | 0.629350i | ||||
\(579\) | 19.1792 | 0.797059 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.7804 | − | 5.03060i | 1.02807 | − | 0.208705i | ||||
\(582\) | 22.8720 | + | 22.8720i | 0.948076 | + | 0.948076i | ||||
\(583\) | −0.796415 | + | 0.796415i | −0.0329841 | + | 0.0329841i | ||||
\(584\) | −74.3292 | −3.07576 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 5.83438i | − | 0.241016i | ||||||
\(587\) | −21.1413 | + | 21.1413i | −0.872594 | + | 0.872594i | −0.992755 | − | 0.120160i | \(-0.961659\pi\) |
0.120160 | + | 0.992755i | \(0.461659\pi\) | |||||||
\(588\) | −31.9868 | − | 12.9554i | −1.31912 | − | 0.534270i | ||||
\(589\) | 24.1689i | 0.995862i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 16.2339i | − | 0.667774i | ||||||
\(592\) | 23.5617 | + | 23.5617i | 0.968381 | + | 0.968381i | ||||
\(593\) | 7.07816 | + | 7.07816i | 0.290665 | + | 0.290665i | 0.837343 | − | 0.546678i | \(-0.184108\pi\) |
−0.546678 | + | 0.837343i | \(0.684108\pi\) | |||||||
\(594\) | −3.85081 | −0.158001 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.477365 | 0.0195536 | ||||||||
\(597\) | 14.2459 | + | 14.2459i | 0.583047 | + | 0.583047i | ||||
\(598\) | 13.6515 | + | 13.6515i | 0.558251 | + | 0.558251i | ||||
\(599\) | − | 7.13847i | − | 0.291670i | −0.989309 | − | 0.145835i | \(-0.953413\pi\) | ||
0.989309 | − | 0.145835i | \(-0.0465869\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 35.0829i | − | 1.43106i | −0.698580 | − | 0.715532i | \(-0.746185\pi\) | ||
0.698580 | − | 0.715532i | \(-0.253815\pi\) | |||||||
\(602\) | −28.2107 | + | 42.5822i | −1.14978 | + | 1.73552i | ||||
\(603\) | −5.93012 | + | 5.93012i | −0.241493 | + | 0.241493i | ||||
\(604\) | − | 66.3346i | − | 2.69912i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −40.3881 | −1.64066 | ||||||||
\(607\) | −5.36385 | + | 5.36385i | −0.217712 | + | 0.217712i | −0.807533 | − | 0.589822i | \(-0.799198\pi\) |
0.589822 | + | 0.807533i | \(0.299198\pi\) | |||||||
\(608\) | −33.8014 | − | 33.8014i | −1.37083 | − | 1.37083i | ||||
\(609\) | 2.72961 | + | 13.4459i | 0.110609 | + | 0.544854i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.2184 | 0.615670 | ||||||||
\(612\) | 10.3835 | − | 10.3835i | 0.419730 | − | 0.419730i | ||||
\(613\) | 10.4888 | − | 10.4888i | 0.423639 | − | 0.423639i | −0.462816 | − | 0.886454i | \(-0.653161\pi\) |
0.886454 | + | 0.462816i | \(0.153161\pi\) | |||||||
\(614\) | −64.6120 | −2.60753 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.93921 | + | 29.2562i | 0.239298 | + | 1.17877i | ||||
\(617\) | −19.7986 | − | 19.7986i | −0.797060 | − | 0.797060i | 0.185571 | − | 0.982631i | \(-0.440586\pi\) |
−0.982631 | + | 0.185571i | \(0.940586\pi\) | |||||||
\(618\) | 21.8703 | − | 21.8703i | 0.879752 | − | 0.879752i | ||||
\(619\) | 12.0675 | 0.485034 | 0.242517 | − | 0.970147i | \(-0.422027\pi\) | ||||
0.242517 | + | 0.970147i | \(0.422027\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 5.84081i | − | 0.234383i | ||||||
\(622\) | 57.8262 | − | 57.8262i | 2.31862 | − | 2.31862i | ||||
\(623\) | 1.75334 | − | 2.64655i | 0.0702462 | − | 0.106032i | ||||
\(624\) | 13.1158i | 0.525054i | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 21.3110i | 0.851761i | ||||||||
\(627\) | 4.09588 | + | 4.09588i | 0.163574 | + | 0.163574i | ||||
\(628\) | 8.12275 | + | 8.12275i | 0.324133 | + | 0.324133i | ||||
\(629\) | 9.50124 | 0.378839 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.4435 | 1.21194 | 0.605969 | − | 0.795488i | \(-0.292786\pi\) | ||||
0.605969 | + | 0.795488i | \(0.292786\pi\) | |||||||
\(632\) | −24.6552 | − | 24.6552i | −0.980730 | − | 0.980730i | ||||
\(633\) | −8.46135 | − | 8.46135i | −0.336309 | − | 0.336309i | ||||
\(634\) | − | 2.80180i | − | 0.111274i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 3.79604i | − | 0.150523i | ||||||
\(637\) | 3.29946 | − | 8.14639i | 0.130729 | − | 0.322772i | ||||
\(638\) | 14.1204 | − | 14.1204i | 0.559032 | − | 0.559032i | ||||
\(639\) | 7.62611i | 0.301684i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 36.5929 | 1.44533 | 0.722666 | − | 0.691198i | \(-0.242917\pi\) | ||||
0.722666 | + | 0.691198i | \(0.242917\pi\) | |||||||
\(642\) | −11.5573 | + | 11.5573i | −0.456131 | + | 0.456131i | ||||
\(643\) | −12.1140 | − | 12.1140i | −0.477731 | − | 0.477731i | 0.426675 | − | 0.904405i | \(-0.359685\pi\) |
−0.904405 | + | 0.426675i | \(0.859685\pi\) | |||||||
\(644\) | −74.6638 | + | 15.1573i | −2.94217 | + | 0.597280i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.0495 | −1.22163 | ||||||||
\(647\) | −19.0978 | + | 19.0978i | −0.750814 | + | 0.750814i | −0.974631 | − | 0.223817i | \(-0.928148\pi\) |
0.223817 | + | 0.974631i | \(0.428148\pi\) | |||||||
\(648\) | 5.45433 | − | 5.45433i | 0.214266 | − | 0.214266i | ||||
\(649\) | −4.67556 | −0.183532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.21267 | + | 15.8254i | 0.125915 | + | 0.620248i | ||||
\(652\) | 50.6552 | + | 50.6552i | 1.98381 | + | 1.98381i | ||||
\(653\) | −20.3709 | + | 20.3709i | −0.797173 | + | 0.797173i | −0.982649 | − | 0.185476i | \(-0.940617\pi\) |
0.185476 | + | 0.982649i | \(0.440617\pi\) | |||||||
\(654\) | 19.6013 | 0.766473 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.04298i | 0.314026i | ||||||||
\(657\) | −6.81378 | + | 6.81378i | −0.265831 | + | 0.265831i | ||||
\(658\) | −46.6236 | + | 70.3752i | −1.81758 | + | 2.74351i | ||||
\(659\) | 31.4882i | 1.22661i | 0.789847 | + | 0.613304i | \(0.210160\pi\) | ||||
−0.789847 | + | 0.613304i | \(0.789840\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 48.1880i | − | 1.87430i | −0.348931 | − | 0.937149i | \(-0.613455\pi\) | ||
0.348931 | − | 0.937149i | \(-0.386545\pi\) | |||||||
\(662\) | 29.4265 | + | 29.4265i | 1.14369 | + | 1.14369i | ||||
\(663\) | 2.64448 | + | 2.64448i | 0.102703 | + | 0.102703i | ||||
\(664\) | 73.7201 | 2.86089 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 8.39746 | 0.325395 | ||||||||
\(667\) | 21.4174 | + | 21.4174i | 0.829286 | + | 0.829286i | ||||
\(668\) | 1.44457 | + | 1.44457i | 0.0558920 | + | 0.0558920i | ||||
\(669\) | 0.934668i | 0.0361364i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.07810i | 0.0802241i | ||||||||
\(672\) | −26.6257 | − | 17.6396i | −1.02711 | − | 0.680461i | ||||
\(673\) | 30.6900 | − | 30.6900i | 1.18301 | − | 1.18301i | 0.204055 | − | 0.978960i | \(-0.434588\pi\) |
0.978960 | − | 0.204055i | \(-0.0654120\pi\) | |||||||
\(674\) | 74.6299i | 2.87463i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 56.3191 | 2.16612 | ||||||||
\(677\) | −1.54060 | + | 1.54060i | −0.0592101 | + | 0.0592101i | −0.736092 | − | 0.676882i | \(-0.763331\pi\) |
0.676882 | + | 0.736092i | \(0.263331\pi\) | |||||||
\(678\) | 6.69830 | + | 6.69830i | 0.257246 | + | 0.257246i | ||||
\(679\) | −6.46755 | − | 31.8587i | −0.248202 | − | 1.22263i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.5348 | 0.940174 | ||||||||
\(682\) | 16.6193 | − | 16.6193i | 0.636387 | − | 0.636387i | ||||
\(683\) | −14.2154 | + | 14.2154i | −0.543936 | + | 0.543936i | −0.924680 | − | 0.380744i | \(-0.875668\pi\) |
0.380744 | + | 0.924680i | \(0.375668\pi\) | |||||||
\(684\) | −19.5226 | −0.746467 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.5635 | + | 40.2155i | 1.05238 | + | 1.53544i | ||||
\(687\) | −17.7330 | − | 17.7330i | −0.676555 | − | 0.676555i | ||||
\(688\) | −54.1694 | + | 54.1694i | −2.06519 | + | 2.06519i | ||||
\(689\) | 0.966772 | 0.0368311 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 10.2887i | 0.391401i | 0.980664 | + | 0.195700i | \(0.0626980\pi\) | ||||
−0.980664 | + | 0.195700i | \(0.937302\pi\) | |||||||
\(692\) | 17.0182 | − | 17.0182i | 0.646937 | − | 0.646937i | ||||
\(693\) | 3.22637 | + | 2.13747i | 0.122560 | + | 0.0811959i | ||||
\(694\) | 74.7741i | 2.83838i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 40.0005i | 1.51622i | ||||||||
\(697\) | 1.62166 | + | 1.62166i | 0.0614248 | + | 0.0614248i | ||||
\(698\) | −27.4869 | − | 27.4869i | −1.04040 | − | 1.04040i | ||||
\(699\) | 3.16979 | 0.119892 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −44.3183 | −1.67388 | −0.836939 | − | 0.547297i | \(-0.815657\pi\) | ||||
−0.836939 | + | 0.547297i | \(0.815657\pi\) | |||||||
\(702\) | 2.33726 | + | 2.33726i | 0.0882142 | + | 0.0882142i | ||||
\(703\) | −8.93189 | − | 8.93189i | −0.336872 | − | 0.336872i | ||||
\(704\) | 15.9257i | 0.600222i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 46.4958i | − | 1.74989i | ||||||
\(707\) | 33.8389 | + | 22.4183i | 1.27264 | + | 0.843126i | ||||
\(708\) | 11.1428 | − | 11.1428i | 0.418772 | − | 0.418772i | ||||
\(709\) | − | 0.817976i | − | 0.0307197i | −0.999882 | − | 0.0153599i | \(-0.995111\pi\) | ||
0.999882 | − | 0.0153599i | \(-0.00488939\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.52029 | −0.169524 | ||||||||
\(712\) | 6.54470 | − | 6.54470i | 0.245273 | − | 0.245273i | ||||
\(713\) | 25.2077 | + | 25.2077i | 0.944037 | + | 0.944037i | ||||
\(714\) | −20.3307 | + | 4.12728i | −0.760858 | + | 0.154460i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.84821 | 0.368045 | ||||||||
\(717\) | −15.1158 | + | 15.1158i | −0.564509 | + | 0.564509i | ||||
\(718\) | 19.6147 | − | 19.6147i | 0.732013 | − | 0.732013i | ||||
\(719\) | −0.00762056 | −0.000284199 | −0.000142099 | − | 1.00000i | \(-0.500045\pi\) | ||||
−0.000142099 | 1.00000i | \(0.500045\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −30.4634 | + | 6.18428i | −1.13452 | + | 0.230315i | ||||
\(722\) | −6.17902 | − | 6.17902i | −0.229959 | − | 0.229959i | ||||
\(723\) | 0.441326 | − | 0.441326i | 0.0164131 | − | 0.0164131i | ||||
\(724\) | −41.8335 | −1.55473 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 23.3247i | 0.865661i | ||||||||
\(727\) | 28.5738 | − | 28.5738i | 1.05974 | − | 1.05974i | 0.0616465 | − | 0.998098i | \(-0.480365\pi\) |
0.998098 | − | 0.0616465i | \(-0.0196352\pi\) | |||||||
\(728\) | 14.1523 | − | 21.3619i | 0.524519 | − | 0.791726i | ||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 21.8438i | 0.807921i | ||||||||
\(732\) | −4.95253 | − | 4.95253i | −0.183051 | − | 0.183051i | ||||
\(733\) | −24.1522 | − | 24.1522i | −0.892083 | − | 0.892083i | 0.102636 | − | 0.994719i | \(-0.467272\pi\) |
−0.994719 | + | 0.102636i | \(0.967272\pi\) | |||||||
\(734\) | 41.6632 | 1.53782 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −70.5085 | −2.59898 | ||||||||
\(737\) | −8.67452 | − | 8.67452i | −0.319530 | − | 0.319530i | ||||
\(738\) | 1.43327 | + | 1.43327i | 0.0527594 | + | 0.0527594i | ||||
\(739\) | − | 37.9522i | − | 1.39609i | −0.716052 | − | 0.698047i | \(-0.754053\pi\) | ||
0.716052 | − | 0.698047i | \(-0.245947\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.97202i | − | 0.182652i | ||||||
\(742\) | −2.96184 | + | 4.47070i | −0.108733 | + | 0.164125i | ||||
\(743\) | 18.8022 | − | 18.8022i | 0.689784 | − | 0.689784i | −0.272400 | − | 0.962184i | \(-0.587817\pi\) |
0.962184 | + | 0.272400i | \(0.0878174\pi\) | |||||||
\(744\) | 47.0796i | 1.72602i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −64.3123 | −2.35464 | ||||||||
\(747\) | 6.75794 | − | 6.75794i | 0.247260 | − | 0.247260i | ||||
\(748\) | 15.1889 | + | 15.1889i | 0.555363 | + | 0.555363i | ||||
\(749\) | 16.0983 | − | 3.26807i | 0.588220 | − | 0.119413i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.105915 | 0.00386490 | 0.00193245 | − | 0.999998i | \(-0.499385\pi\) | ||||
0.00193245 | + | 0.999998i | \(0.499385\pi\) | |||||||
\(752\) | −89.5254 | + | 89.5254i | −3.26466 | + | 3.26466i | ||||
\(753\) | −11.5572 | + | 11.5572i | −0.421167 | + | 0.421167i | ||||
\(754\) | −17.1408 | −0.624232 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.7831 | + | 2.59507i | −0.464918 | + | 0.0943816i | ||||
\(757\) | −3.14514 | − | 3.14514i | −0.114312 | − | 0.114312i | 0.647637 | − | 0.761949i | \(-0.275757\pi\) |
−0.761949 | + | 0.647637i | \(0.775757\pi\) | |||||||
\(758\) | −32.8059 | + | 32.8059i | −1.19156 | + | 1.19156i | ||||
\(759\) | 8.54387 | 0.310123 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 35.1123i | − | 1.27282i | −0.771351 | − | 0.636410i | \(-0.780419\pi\) | ||
0.771351 | − | 0.636410i | \(-0.219581\pi\) | |||||||
\(762\) | −20.6922 | + | 20.6922i | −0.749599 | + | 0.749599i | ||||
\(763\) | −16.4228 | − | 10.8801i | −0.594547 | − | 0.393887i | ||||
\(764\) | − | 38.6238i | − | 1.39736i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 60.0318i | 2.16904i | ||||||||
\(767\) | 2.83784 | + | 2.83784i | 0.102469 | + | 0.102469i | ||||
\(768\) | 6.98809 | + | 6.98809i | 0.252161 | + | 0.252161i | ||||
\(769\) | −8.16835 | −0.294558 | −0.147279 | − | 0.989095i | \(-0.547052\pi\) | ||||
−0.147279 | + | 0.989095i | \(0.547052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.1304 | −1.08512 | ||||||||
\(772\) | −66.8609 | − | 66.8609i | −2.40638 | − | 2.40638i | ||||
\(773\) | −2.51166 | − | 2.51166i | −0.0903382 | − | 0.0903382i | 0.660494 | − | 0.750832i | \(-0.270347\pi\) |
−0.750832 | + | 0.660494i | \(0.770347\pi\) | |||||||
\(774\) | 19.3061i | 0.693944i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 94.7776i | − | 3.40232i | ||||||
\(777\) | −7.03574 | − | 4.66118i | −0.252406 | − | 0.167219i | ||||
\(778\) | −28.6686 | + | 28.6686i | −1.02782 | + | 1.02782i | ||||
\(779\) | − | 3.04897i | − | 0.109241i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11.1554 | −0.399171 | ||||||||
\(782\) | −32.3840 | + | 32.3840i | −1.15805 | + | 1.15805i | ||||
\(783\) | 3.66686 | + | 3.66686i | 0.131043 | + | 0.131043i | ||||
\(784\) | 28.5131 | + | 67.3327i | 1.01833 | + | 2.40474i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −16.2746 | −0.580497 | ||||||||
\(787\) | 12.7347 | − | 12.7347i | 0.453943 | − | 0.453943i | −0.442718 | − | 0.896661i | \(-0.645986\pi\) |
0.896661 | + | 0.442718i | \(0.145986\pi\) | |||||||
\(788\) | −56.5935 | + | 56.5935i | −2.01606 | + | 2.01606i | ||||
\(789\) | −23.1151 | −0.822920 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.89408 | − | 9.33014i | −0.0673459 | − | 0.331742i | ||||
\(792\) | 7.97854 | + | 7.97854i | 0.283505 | + | 0.283505i | ||||
\(793\) | 1.26131 | − | 1.26131i | 0.0447903 | − | 0.0447903i | ||||
\(794\) | 60.2300 | 2.13748 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 99.3261i | − | 3.52052i | ||||||
\(797\) | 23.3462 | − | 23.3462i | 0.826967 | − | 0.826967i | −0.160129 | − | 0.987096i | \(-0.551191\pi\) |
0.987096 | + | 0.160129i | \(0.0511912\pi\) | |||||||
\(798\) | 22.9924 | + | 15.2325i | 0.813922 | + | 0.539224i | ||||
\(799\) | 36.1010i | 1.27716i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 1.19991i | − | 0.0423967i | ||||||
\(802\) | −1.81976 | − | 1.81976i | −0.0642580 | − | 0.0642580i | ||||
\(803\) | −9.96713 | − | 9.96713i | −0.351732 | − | 0.351732i | ||||
\(804\) | 41.3463 | 1.45817 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20.1743 | −0.710609 | ||||||||
\(807\) | −11.7311 | − | 11.7311i | −0.412955 | − | 0.412955i | ||||
\(808\) | 83.6806 | + | 83.6806i | 2.94387 | + | 2.94387i | ||||
\(809\) | − | 27.8210i | − | 0.978135i | −0.872246 | − | 0.489067i | \(-0.837337\pi\) | ||
0.872246 | − | 0.489067i | \(-0.162663\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.12216i | 0.179863i | 0.995948 | + | 0.0899317i | \(0.0286649\pi\) | ||||
−0.995948 | + | 0.0899317i | \(0.971335\pi\) | |||||||
\(812\) | 37.3582 | − | 56.3897i | 1.31102 | − | 1.97889i | ||||
\(813\) | −5.50152 | + | 5.50152i | −0.192947 | + | 0.192947i | ||||
\(814\) | 12.2837i | 0.430544i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −31.1134 | −1.08919 | ||||||||
\(817\) | 20.5348 | − | 20.5348i | 0.718421 | − | 0.718421i | ||||
\(818\) | −45.2656 | − | 45.2656i | −1.58267 | − | 1.58267i | ||||
\(819\) | −0.660910 | − | 3.25560i | −0.0230941 | − | 0.113760i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −26.1405 | −0.912308 | −0.456154 | − | 0.889901i | \(-0.650773\pi\) | ||||
−0.456154 | + | 0.889901i | \(0.650773\pi\) | |||||||
\(822\) | −23.8391 | + | 23.8391i | −0.831485 | + | 0.831485i | ||||
\(823\) | −13.7296 | + | 13.7296i | −0.478583 | + | 0.478583i | −0.904678 | − | 0.426095i | \(-0.859889\pi\) |
0.426095 | + | 0.904678i | \(0.359889\pi\) | |||||||
\(824\) | −90.6265 | −3.15712 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −21.8173 | + | 4.42907i | −0.759122 | + | 0.154107i | ||||
\(827\) | −15.7484 | − | 15.7484i | −0.547624 | − | 0.547624i | 0.378129 | − | 0.925753i | \(-0.376568\pi\) |
−0.925753 | + | 0.378129i | \(0.876568\pi\) | |||||||
\(828\) | −20.3618 | + | 20.3618i | −0.707620 | + | 0.707620i | ||||
\(829\) | −47.2996 | −1.64278 | −0.821392 | − | 0.570365i | \(-0.806802\pi\) | ||||
−0.821392 | + | 0.570365i | \(0.806802\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.1378i | 1.04547i | ||||||||
\(832\) | 9.66613 | − | 9.66613i | 0.335113 | − | 0.335113i | ||||
\(833\) | 19.3249 | + | 7.82698i | 0.669567 | + | 0.271189i | ||||
\(834\) | − | 31.5672i | − | 1.09308i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 28.5575i | − | 0.987683i | ||||||
\(837\) | 4.31580 | + | 4.31580i | 0.149176 | + | 0.149176i | ||||
\(838\) | −29.7635 | − | 29.7635i | −1.02816 | − | 1.02816i | ||||
\(839\) | −10.8244 | −0.373699 | −0.186850 | − | 0.982389i | \(-0.559828\pi\) | ||||
−0.186850 | + | 0.982389i | \(0.559828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.10826 | 0.0726986 | ||||||||
\(842\) | 27.3635 | + | 27.3635i | 0.943009 | + | 0.943009i | ||||
\(843\) | 14.9566 | + | 14.9566i | 0.515134 | + | 0.515134i | ||||
\(844\) | 58.9947i | 2.03068i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 31.9071i | 1.09699i | ||||||||
\(847\) | 12.9469 | − | 19.5424i | 0.444860 | − | 0.671486i | ||||
\(848\) | −5.68725 | + | 5.68725i | −0.195301 | + | 0.195301i | ||||
\(849\) | − | 3.75433i | − | 0.128848i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −18.6316 | −0.638683 | ||||||||
\(852\) | 26.5856 | − | 26.5856i | 0.910806 | − | 0.910806i | ||||
\(853\) | 33.5751 | + | 33.5751i | 1.14959 | + | 1.14959i | 0.986633 | + | 0.162958i | \(0.0521034\pi\) |
0.162958 | + | 0.986633i | \(0.447897\pi\) | |||||||
\(854\) | 1.96854 | + | 9.69693i | 0.0673622 | + | 0.331822i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 47.8914 | 1.63689 | ||||||||
\(857\) | 8.92479 | − | 8.92479i | 0.304865 | − | 0.304865i | −0.538049 | − | 0.842914i | \(-0.680838\pi\) |
0.842914 | + | 0.538049i | \(0.180838\pi\) | |||||||
\(858\) | −3.41892 | + | 3.41892i | −0.116720 | + | 0.116720i | ||||
\(859\) | −20.3701 | −0.695020 | −0.347510 | − | 0.937676i | \(-0.612973\pi\) | ||||
−0.347510 | + | 0.937676i | \(0.612973\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.405287 | − | 1.99642i | −0.0138122 | − | 0.0680378i | ||||
\(862\) | 41.4589 | + | 41.4589i | 1.41210 | + | 1.41210i | ||||
\(863\) | 14.9014 | − | 14.9014i | 0.507250 | − | 0.507250i | −0.406431 | − | 0.913681i | \(-0.633227\pi\) |
0.913681 | + | 0.406431i | \(0.133227\pi\) | |||||||
\(864\) | −12.0717 | −0.410688 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 104.306i | − | 3.54446i | ||||||
\(867\) | 5.74759 | − | 5.74759i | 0.195198 | − | 0.195198i | ||||
\(868\) | 43.9696 | − | 66.3692i | 1.49243 | − | 2.25272i | ||||
\(869\) | − | 6.61223i | − | 0.224305i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5301i | 0.356797i | ||||||||
\(872\) | −40.6122 | − | 40.6122i | −1.37530 | − | 1.37530i | ||||
\(873\) | −8.68829 | − | 8.68829i | −0.294054 | − | 0.294054i | ||||
\(874\) | 60.8869 | 2.05953 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 47.5074 | 1.60512 | ||||||||
\(877\) | −23.4634 | − | 23.4634i | −0.792302 | − | 0.792302i | 0.189566 | − | 0.981868i | \(-0.439292\pi\) |
−0.981868 | + | 0.189566i | \(0.939292\pi\) | |||||||
\(878\) | 4.38667 | + | 4.38667i | 0.148043 | + | 0.148043i | ||||
\(879\) | 2.21628i | 0.0747532i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34.9639i | 1.17796i | 0.808147 | + | 0.588981i | \(0.200471\pi\) | ||||
−0.808147 | + | 0.588981i | \(0.799529\pi\) | |||||||
\(882\) | 17.0799 | + | 6.91770i | 0.575109 | + | 0.232931i | ||||
\(883\) | −19.3814 | + | 19.3814i | −0.652235 | + | 0.652235i | −0.953531 | − | 0.301295i | \(-0.902581\pi\) |
0.301295 | + | 0.953531i | \(0.402581\pi\) | |||||||
\(884\) | − | 18.4379i | − | 0.620135i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.3737 | 0.684466 | ||||||||
\(887\) | −19.2450 | + | 19.2450i | −0.646184 | + | 0.646184i | −0.952069 | − | 0.305884i | \(-0.901048\pi\) |
0.305884 | + | 0.952069i | \(0.401048\pi\) | |||||||
\(888\) | −17.3988 | − | 17.3988i | −0.583865 | − | 0.583865i | ||||
\(889\) | 28.8224 | − | 5.85116i | 0.966673 | − | 0.196242i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.46279 | 0.0490053 | ||||||||
\(892\) | 3.25837 | − | 3.25837i | 0.109098 | − | 0.109098i | ||||
\(893\) | 33.9377 | − | 33.9377i | 1.13568 | − | 1.13568i | ||||
\(894\) | −0.254896 | −0.00852500 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.37775 | + | 11.7126i | 0.0794349 | + | 0.391292i | ||||
\(897\) | −5.18572 | − | 5.18572i | −0.173146 | − | 0.173146i | ||||
\(898\) | 2.23414 | − | 2.23414i | 0.0745541 | − | 0.0745541i | ||||
\(899\) | −31.6509 | −1.05562 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.29338i | 0.0764035i | ||||||||
\(902\) | −2.09657 | + | 2.09657i | −0.0698082 | + | 0.0698082i | ||||
\(903\) | 10.7163 | − | 16.1755i | 0.356615 | − | 0.538286i | ||||
\(904\) | − | 27.7565i | − | 0.923169i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 35.4204i | 1.17676i | ||||||||
\(907\) | 14.8842 | + | 14.8842i | 0.494220 | + | 0.494220i | 0.909633 | − | 0.415413i | \(-0.136363\pi\) |
−0.415413 | + | 0.909633i | \(0.636363\pi\) | |||||||
\(908\) | −85.5312 | − | 85.5312i | −2.83845 | − | 2.83845i | ||||
\(909\) | 15.3420 | 0.508863 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.7484 | −0.786819 | −0.393410 | − | 0.919363i | \(-0.628705\pi\) | ||||
−0.393410 | + | 0.919363i | \(0.628705\pi\) | |||||||
\(912\) | 29.2490 | + | 29.2490i | 0.968530 | + | 0.968530i | ||||
\(913\) | 9.88545 | + | 9.88545i | 0.327161 | + | 0.327161i | ||||
\(914\) | 78.4700i | 2.59556i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 123.639i | 4.08514i | ||||||||
\(917\) | 13.6356 | + | 9.03357i | 0.450286 | + | 0.298315i | ||||
\(918\) | −5.54445 | + | 5.54445i | −0.182994 | + | 0.182994i | ||||
\(919\) | − | 35.7695i | − | 1.17993i | −0.807430 | − | 0.589964i | \(-0.799142\pi\) | ||
0.807430 | − | 0.589964i | \(-0.200858\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 24.5439 | 0.808748 | ||||||||
\(922\) | −40.8909 | + | 40.8909i | −1.34667 | + | 1.34667i | ||||
\(923\) | 6.77080 | + | 6.77080i | 0.222863 | + | 0.222863i | ||||
\(924\) | −3.79604 | − | 18.6990i | −0.124880 | − | 0.615153i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 80.7042 | 2.65210 | ||||||||
\(927\) | −8.30776 | + | 8.30776i | −0.272863 | + | 0.272863i | ||||
\(928\) | 44.2653 | − | 44.2653i | 1.45308 | − | 1.45308i | ||||
\(929\) | 5.58936 | 0.183381 | 0.0916905 | − | 0.995788i | \(-0.470773\pi\) | ||||
0.0916905 | + | 0.995788i | \(0.470773\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −10.8089 | − | 25.5248i | −0.354247 | − | 0.836542i | ||||
\(932\) | −11.0503 | − | 11.0503i | −0.361963 | − | 0.361963i | ||||
\(933\) | −21.9662 | + | 21.9662i | −0.719140 | + | 0.719140i | ||||
\(934\) | 26.4812 | 0.866491 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 9.68519i | − | 0.316570i | ||||||
\(937\) | −20.4143 | + | 20.4143i | −0.666906 | + | 0.666906i | −0.956999 | − | 0.290092i | \(-0.906314\pi\) |
0.290092 | + | 0.956999i | \(0.406314\pi\) | |||||||
\(938\) | −48.6947 | − | 32.2603i | −1.58994 | − | 1.05334i | ||||
\(939\) | − | 8.09533i | − | 0.264181i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.1143i | 0.557910i | 0.960304 | + | 0.278955i | \(0.0899880\pi\) | ||||
−0.960304 | + | 0.278955i | \(0.910012\pi\) | |||||||
\(942\) | −4.33726 | − | 4.33726i | −0.141316 | − | 0.141316i | ||||
\(943\) | −3.18002 | − | 3.18002i | −0.103556 | − | 0.103556i | ||||
\(944\) | −33.3884 | −1.08670 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −28.2408 | −0.918187 | ||||||||
\(947\) | −6.82151 | − | 6.82151i | −0.221669 | − | 0.221669i | 0.587532 | − | 0.809201i | \(-0.300100\pi\) |
−0.809201 | + | 0.587532i | \(0.800100\pi\) | |||||||
\(948\) | 15.7583 | + | 15.7583i | 0.511806 | + | 0.511806i | ||||
\(949\) | 12.0991i | 0.392755i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.06431i | 0.0345125i | ||||||||
\(952\) | 50.6748 | + | 33.5721i | 1.64238 | + | 1.08808i | ||||
\(953\) | −30.7169 | + | 30.7169i | −0.995017 | + | 0.995017i | −0.999988 | − | 0.00497101i | \(-0.998418\pi\) |
0.00497101 | + | 0.999988i | \(0.498418\pi\) | |||||||
\(954\) | 2.02695i | 0.0656249i | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 105.391 | 3.40859 | ||||||||
\(957\) | −5.36385 | + | 5.36385i | −0.173389 | + | 0.173389i | ||||
\(958\) | −59.1480 | − | 59.1480i | −1.91099 | − | 1.91099i | ||||
\(959\) | 33.2058 | − | 6.74102i | 1.07227 | − | 0.217679i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.25222 | −0.201684 | ||||||||
\(962\) | 7.45563 | − | 7.45563i | 0.240379 | − | 0.240379i | ||||
\(963\) | 4.39022 | − | 4.39022i | 0.141473 | − | 0.141473i | ||||
\(964\) | −3.07703 | −0.0991046 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 39.8678 | − | 8.09345i | 1.28273 | − | 0.260403i | ||||
\(967\) | −24.6730 | − | 24.6730i | −0.793431 | − | 0.793431i | 0.188619 | − | 0.982050i | \(-0.439599\pi\) |
−0.982050 | + | 0.188619i | \(0.939599\pi\) | |||||||
\(968\) | 48.3267 | − | 48.3267i | 1.55328 | − | 1.55328i | ||||
\(969\) | 11.7946 | 0.378898 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.2020i | 0.680404i | 0.940352 | + | 0.340202i | \(0.110496\pi\) | ||||
−0.940352 | + | 0.340202i | \(0.889504\pi\) | |||||||
\(972\) | −3.48612 | + | 3.48612i | −0.111817 | + | 0.111817i | ||||
\(973\) | −17.5220 | + | 26.4483i | −0.561731 | + | 0.847895i | ||||
\(974\) | 17.9232i | 0.574297i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 14.8398i | 0.475011i | ||||||||
\(977\) | −8.19657 | − | 8.19657i | −0.262231 | − | 0.262231i | 0.563729 | − | 0.825960i | \(-0.309366\pi\) |
−0.825960 | + | 0.563729i | \(0.809366\pi\) | |||||||
\(978\) | −27.0481 | − | 27.0481i | −0.864902 | − | 0.864902i | ||||
\(979\) | 1.75521 | 0.0560969 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.44587 | −0.237728 | ||||||||
\(982\) | 52.7541 | + | 52.7541i | 1.68345 | + | 1.68345i | ||||
\(983\) | −1.74914 | − | 1.74914i | −0.0557891 | − | 0.0557891i | 0.678662 | − | 0.734451i | \(-0.262560\pi\) |
−0.734451 | + | 0.678662i | \(0.762560\pi\) | |||||||
\(984\) | − | 5.93921i | − | 0.189335i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 40.6615i | − | 1.29492i | ||||||
\(987\) | 17.7107 | − | 26.7331i | 0.563738 | − | 0.850924i | ||||
\(988\) | −17.3331 | + | 17.3331i | −0.551438 | + | 0.551438i | ||||
\(989\) | − | 42.8348i | − | 1.36207i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37.1253 | −1.17932 | −0.589662 | − | 0.807650i | \(-0.700739\pi\) | ||||
−0.589662 | + | 0.807650i | \(0.700739\pi\) | |||||||
\(992\) | 52.0991 | − | 52.0991i | 1.65415 | − | 1.65415i | ||||
\(993\) | −11.1781 | − | 11.1781i | −0.354727 | − | 0.354727i | ||||
\(994\) | −52.0539 | + | 10.5673i | −1.65105 | + | 0.335174i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −47.1180 | −1.49299 | ||||||||
\(997\) | −40.5538 | + | 40.5538i | −1.28435 | + | 1.28435i | −0.346186 | + | 0.938166i | \(0.612524\pi\) |
−0.938166 | + | 0.346186i | \(0.887476\pi\) | |||||||
\(998\) | −6.31404 | + | 6.31404i | −0.199868 | + | 0.199868i | ||||
\(999\) | −3.18990 | −0.100924 |
(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 | 525.2.m.b.307.7 | 16 | ||
5.2 | odd | 4 | 105.2.m.a.13.1 | ✓ | 16 | ||
5.3 | odd | 4 | inner | 525.2.m.b.118.8 | 16 | ||
5.4 | even | 2 | 105.2.m.a.97.2 | yes | 16 | ||
7.6 | odd | 2 | inner | 525.2.m.b.307.8 | 16 | ||
15.2 | even | 4 | 315.2.p.e.118.8 | 16 | |||
15.14 | odd | 2 | 315.2.p.e.307.7 | 16 | |||
20.7 | even | 4 | 1680.2.cz.d.433.6 | 16 | |||
20.19 | odd | 2 | 1680.2.cz.d.97.3 | 16 | |||
35.2 | odd | 12 | 735.2.v.a.178.7 | 32 | |||
35.4 | even | 6 | 735.2.v.a.607.8 | 32 | |||
35.9 | even | 6 | 735.2.v.a.472.1 | 32 | |||
35.12 | even | 12 | 735.2.v.a.178.8 | 32 | |||
35.13 | even | 4 | inner | 525.2.m.b.118.7 | 16 | ||
35.17 | even | 12 | 735.2.v.a.313.1 | 32 | |||
35.19 | odd | 6 | 735.2.v.a.472.2 | 32 | |||
35.24 | odd | 6 | 735.2.v.a.607.7 | 32 | |||
35.27 | even | 4 | 105.2.m.a.13.2 | yes | 16 | ||
35.32 | odd | 12 | 735.2.v.a.313.2 | 32 | |||
35.34 | odd | 2 | 105.2.m.a.97.1 | yes | 16 | ||
105.62 | odd | 4 | 315.2.p.e.118.7 | 16 | |||
105.104 | even | 2 | 315.2.p.e.307.8 | 16 | |||
140.27 | odd | 4 | 1680.2.cz.d.433.3 | 16 | |||
140.139 | even | 2 | 1680.2.cz.d.97.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.m.a.13.1 | ✓ | 16 | 5.2 | odd | 4 | ||
105.2.m.a.13.2 | yes | 16 | 35.27 | even | 4 | ||
105.2.m.a.97.1 | yes | 16 | 35.34 | odd | 2 | ||
105.2.m.a.97.2 | yes | 16 | 5.4 | even | 2 | ||
315.2.p.e.118.7 | 16 | 105.62 | odd | 4 | |||
315.2.p.e.118.8 | 16 | 15.2 | even | 4 | |||
315.2.p.e.307.7 | 16 | 15.14 | odd | 2 | |||
315.2.p.e.307.8 | 16 | 105.104 | even | 2 | |||
525.2.m.b.118.7 | 16 | 35.13 | even | 4 | inner | ||
525.2.m.b.118.8 | 16 | 5.3 | odd | 4 | inner | ||
525.2.m.b.307.7 | 16 | 1.1 | even | 1 | trivial | ||
525.2.m.b.307.8 | 16 | 7.6 | odd | 2 | inner | ||
735.2.v.a.178.7 | 32 | 35.2 | odd | 12 | |||
735.2.v.a.178.8 | 32 | 35.12 | even | 12 | |||
735.2.v.a.313.1 | 32 | 35.17 | even | 12 | |||
735.2.v.a.313.2 | 32 | 35.32 | odd | 12 | |||
735.2.v.a.472.1 | 32 | 35.9 | even | 6 | |||
735.2.v.a.472.2 | 32 | 35.19 | odd | 6 | |||
735.2.v.a.607.7 | 32 | 35.24 | odd | 6 | |||
735.2.v.a.607.8 | 32 | 35.4 | even | 6 | |||
1680.2.cz.d.97.3 | 16 | 20.19 | odd | 2 | |||
1680.2.cz.d.97.6 | 16 | 140.139 | even | 2 | |||
1680.2.cz.d.433.3 | 16 | 140.27 | odd | 4 | |||
1680.2.cz.d.433.6 | 16 | 20.7 | even | 4 |