Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,2,Mod(218,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 15, 12]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.ct (of order \(20\), degree \(8\), 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: | \(6.58765816676\) |
Analytic rank: | \(0\) |
Dimension: | \(160\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{20})\) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 368.19 | ||
Character | \(\chi\) | \(=\) | 825.368 |
Dual form | 825.2.ct.b.482.19 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(e\left(\frac{2}{5}\right)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.05798 | − | 2.07639i | 0.748102 | − | 1.46823i | −0.130891 | − | 0.991397i | \(-0.541784\pi\) |
0.878993 | − | 0.476835i | \(-0.158216\pi\) | |||||||
\(3\) | −1.42761 | + | 0.980774i | −0.824233 | + | 0.566250i | ||||
\(4\) | −2.01653 | − | 2.77551i | −1.00826 | − | 1.38776i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.526092 | + | 4.00192i | 0.214776 | + | 1.63378i | ||||
\(7\) | −0.378371 | + | 2.38894i | −0.143011 | + | 0.902934i | 0.806962 | + | 0.590603i | \(0.201110\pi\) |
−0.949973 | + | 0.312332i | \(0.898890\pi\) | |||||||
\(8\) | −3.29310 | + | 0.521576i | −1.16429 | + | 0.184405i | ||||
\(9\) | 1.07616 | − | 2.80033i | 0.358721 | − | 0.933445i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.56427 | + | 2.10345i | 0.773156 | + | 0.634215i | ||||
\(12\) | 5.60098 | + | 1.98460i | 1.61686 | + | 0.572906i | ||||
\(13\) | 0.203421 | − | 0.399236i | 0.0564189 | − | 0.110728i | −0.861075 | − | 0.508477i | \(-0.830209\pi\) |
0.917494 | + | 0.397749i | \(0.130209\pi\) | |||||||
\(14\) | 4.56007 | + | 3.31309i | 1.21873 | + | 0.885460i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.280717 | + | 0.863959i | −0.0701793 | + | 0.215990i | ||||
\(17\) | 5.33912 | − | 2.72042i | 1.29493 | − | 0.659799i | 0.335576 | − | 0.942013i | \(-0.391069\pi\) |
0.959351 | + | 0.282215i | \(0.0910690\pi\) | |||||||
\(18\) | −4.67604 | − | 5.19723i | −1.10215 | − | 1.22500i | ||||
\(19\) | −1.77446 | + | 2.44234i | −0.407089 | + | 0.560310i | −0.962506 | − | 0.271262i | \(-0.912559\pi\) |
0.555416 | + | 0.831573i | \(0.312559\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.80284 | − | 3.78158i | −0.393413 | − | 0.825209i | ||||
\(22\) | 7.08053 | − | 3.09903i | 1.50958 | − | 0.660716i | ||||
\(23\) | 5.19160 | − | 5.19160i | 1.08252 | − | 1.08252i | 0.0862506 | − | 0.996273i | \(-0.472511\pi\) |
0.996273 | − | 0.0862506i | \(-0.0274886\pi\) | |||||||
\(24\) | 4.18973 | − | 3.97439i | 0.855224 | − | 0.811270i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.613758 | − | 0.844765i | −0.120368 | − | 0.165672i | ||||
\(27\) | 1.21015 | + | 5.05327i | 0.232893 | + | 0.972502i | ||||
\(28\) | 7.39353 | − | 3.76719i | 1.39725 | − | 0.711933i | ||||
\(29\) | −0.109785 | + | 0.0797634i | −0.0203865 | + | 0.0148117i | −0.597932 | − | 0.801547i | \(-0.704011\pi\) |
0.577545 | + | 0.816359i | \(0.304011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.851700 | + | 2.62126i | 0.152970 | + | 0.470793i | 0.997950 | − | 0.0640057i | \(-0.0203876\pi\) |
−0.844980 | + | 0.534798i | \(0.820388\pi\) | |||||||
\(32\) | −3.21827 | − | 3.21827i | −0.568915 | − | 0.568915i | ||||
\(33\) | −5.72380 | − | 0.487952i | −0.996386 | − | 0.0849415i | ||||
\(34\) | − | 13.9643i | − | 2.39485i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −9.94248 | + | 2.66005i | −1.65708 | + | 0.443341i | ||||
\(37\) | 0.349560 | − | 2.20704i | 0.0574674 | − | 0.362835i | −0.942150 | − | 0.335190i | \(-0.891199\pi\) |
0.999618 | − | 0.0276444i | \(-0.00880062\pi\) | |||||||
\(38\) | 3.19392 | + | 6.26841i | 0.518122 | + | 1.01687i | ||||
\(39\) | 0.101154 | + | 0.769466i | 0.0161976 | + | 0.123213i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.72375 | − | 9.25444i | 1.05007 | − | 1.44530i | 0.161327 | − | 0.986901i | \(-0.448423\pi\) |
0.888746 | − | 0.458400i | \(-0.151577\pi\) | |||||||
\(42\) | −9.75942 | − | 0.257408i | −1.50591 | − | 0.0397190i | ||||
\(43\) | 0.0892586 | + | 0.0892586i | 0.0136118 | + | 0.0136118i | 0.713880 | − | 0.700268i | \(-0.246936\pi\) |
−0.700268 | + | 0.713880i | \(0.746936\pi\) | |||||||
\(44\) | 0.667242 | − | 11.3588i | 0.100591 | − | 1.71241i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.28722 | − | 16.2724i | −0.779559 | − | 2.39923i | ||||
\(47\) | 0.0893408 | + | 0.564076i | 0.0130317 | + | 0.0822789i | 0.993347 | − | 0.115159i | \(-0.0367378\pi\) |
−0.980315 | + | 0.197438i | \(0.936738\pi\) | |||||||
\(48\) | −0.446593 | − | 1.50872i | −0.0644601 | − | 0.217765i | ||||
\(49\) | 1.09353 | + | 0.355308i | 0.156218 | + | 0.0507583i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.95409 | + | 9.12018i | −0.693712 | + | 1.27708i | ||||
\(52\) | −1.51829 | + | 0.240474i | −0.210549 | + | 0.0333477i | ||||
\(53\) | 7.16718 | + | 3.65186i | 0.984488 | + | 0.501622i | 0.870664 | − | 0.491879i | \(-0.163690\pi\) |
0.113825 | + | 0.993501i | \(0.463690\pi\) | |||||||
\(54\) | 11.7729 | + | 2.83349i | 1.60209 | + | 0.385590i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 8.06436i | − | 1.07765i | ||||||
\(57\) | 0.137866 | − | 5.22706i | 0.0182608 | − | 0.692341i | ||||
\(58\) | 0.0494705 | + | 0.312345i | 0.00649580 | + | 0.0410128i | ||||
\(59\) | −10.1795 | + | 7.39583i | −1.32526 | + | 0.962855i | −0.325406 | + | 0.945574i | \(0.605501\pi\) |
−0.999851 | + | 0.0172809i | \(0.994499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.745009 | + | 2.29290i | −0.0953886 | + | 0.293576i | −0.987355 | − | 0.158526i | \(-0.949326\pi\) |
0.891966 | + | 0.452102i | \(0.149326\pi\) | |||||||
\(62\) | 6.34385 | + | 1.00477i | 0.805670 | + | 0.127606i | ||||
\(63\) | 6.28264 | + | 3.63046i | 0.791538 | + | 0.457395i | ||||
\(64\) | −11.8152 | + | 3.83898i | −1.47690 | + | 0.479872i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.06882 | + | 11.3686i | −0.870112 | + | 1.39938i | ||||
\(67\) | 2.30927 | − | 2.30927i | 0.282122 | − | 0.282122i | −0.551833 | − | 0.833955i | \(-0.686071\pi\) |
0.833955 | + | 0.551833i | \(0.186071\pi\) | |||||||
\(68\) | −18.3171 | − | 9.33301i | −2.22127 | − | 1.13179i | ||||
\(69\) | −2.31982 | + | 12.5034i | −0.279273 | + | 1.50523i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.28175 | − | 0.741385i | −0.270794 | − | 0.0879863i | 0.170472 | − | 0.985362i | \(-0.445471\pi\) |
−0.441266 | + | 0.897376i | \(0.645471\pi\) | |||||||
\(72\) | −2.08333 | + | 9.78308i | −0.245523 | + | 1.15295i | ||||
\(73\) | 1.68786 | + | 0.267330i | 0.197549 | + | 0.0312886i | 0.254425 | − | 0.967093i | \(-0.418114\pi\) |
−0.0568759 | + | 0.998381i | \(0.518114\pi\) | |||||||
\(74\) | −4.21285 | − | 3.06082i | −0.489734 | − | 0.355813i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 10.3570 | 1.18803 | ||||||||
\(77\) | −5.99527 | + | 5.33000i | −0.683225 | + | 0.607410i | ||||
\(78\) | 1.70473 | + | 0.604041i | 0.193023 | + | 0.0683941i | ||||
\(79\) | 6.06666 | − | 1.97118i | 0.682553 | − | 0.221775i | 0.0528401 | − | 0.998603i | \(-0.483173\pi\) |
0.629713 | + | 0.776828i | \(0.283173\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.68374 | − | 6.02724i | −0.742638 | − | 0.669693i | ||||
\(82\) | −12.1023 | − | 23.7521i | −1.33648 | − | 2.62298i | ||||
\(83\) | 2.49081 | + | 4.88849i | 0.273402 | + | 0.536582i | 0.986355 | − | 0.164630i | \(-0.0526429\pi\) |
−0.712953 | + | 0.701211i | \(0.752643\pi\) | |||||||
\(84\) | −6.86035 | + | 12.6295i | −0.748525 | + | 1.37799i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.279770 | − | 0.0909026i | 0.0301683 | − | 0.00980228i | ||||
\(87\) | 0.0785006 | − | 0.221546i | 0.00841615 | − | 0.0237522i | ||||
\(88\) | −9.54150 | − | 5.58942i | −1.01713 | − | 0.595834i | ||||
\(89\) | 8.91810 | 0.945317 | 0.472658 | − | 0.881246i | \(-0.343294\pi\) | ||||
0.472658 | + | 0.881246i | \(0.343294\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.876783 | + | 0.637020i | 0.0919118 | + | 0.0667779i | ||||
\(92\) | −24.8784 | − | 3.94035i | −2.59375 | − | 0.410810i | ||||
\(93\) | −3.78676 | − | 2.90683i | −0.392669 | − | 0.301424i | ||||
\(94\) | 1.26576 | + | 0.411271i | 0.130554 | + | 0.0424194i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 7.75084 | + | 1.43805i | 0.791067 | + | 0.146771i | ||||
\(97\) | 3.35840 | + | 1.71119i | 0.340994 | + | 0.173745i | 0.616098 | − | 0.787669i | \(-0.288712\pi\) |
−0.275105 | + | 0.961414i | \(0.588712\pi\) | |||||||
\(98\) | 1.89468 | − | 1.89468i | 0.191392 | − | 0.191392i | ||||
\(99\) | 8.64995 | − | 4.91715i | 0.869353 | − | 0.494192i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.5700 | + | 4.40917i | −1.35027 | + | 0.438729i | −0.892782 | − | 0.450488i | \(-0.851250\pi\) |
−0.457486 | + | 0.889217i | \(0.651250\pi\) | |||||||
\(102\) | 13.6958 | + | 19.9356i | 1.35608 | + | 1.97392i | ||||
\(103\) | 4.21636 | + | 0.667806i | 0.415451 | + | 0.0658009i | 0.360661 | − | 0.932697i | \(-0.382551\pi\) |
0.0547897 | + | 0.998498i | \(0.482551\pi\) | |||||||
\(104\) | −0.461654 | + | 1.42082i | −0.0452689 | + | 0.139323i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 15.1654 | − | 11.0183i | 1.47299 | − | 1.07019i | ||||
\(107\) | −1.39669 | − | 8.81837i | −0.135023 | − | 0.852504i | −0.958487 | − | 0.285135i | \(-0.907961\pi\) |
0.823464 | − | 0.567369i | \(-0.192039\pi\) | |||||||
\(108\) | 11.5851 | − | 13.5488i | 1.11478 | − | 1.30374i | ||||
\(109\) | − | 9.49821i | − | 0.909763i | −0.890552 | − | 0.454882i | \(-0.849682\pi\) | ||
0.890552 | − | 0.454882i | \(-0.150318\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.66557 | + | 3.49364i | 0.158089 | + | 0.331601i | ||||
\(112\) | −1.95773 | − | 0.997514i | −0.184988 | − | 0.0942562i | ||||
\(113\) | −15.7639 | + | 2.49675i | −1.48294 | + | 0.234875i | −0.844816 | − | 0.535057i | \(-0.820290\pi\) |
−0.638126 | + | 0.769932i | \(0.720290\pi\) | |||||||
\(114\) | −10.7076 | − | 5.81636i | −1.00286 | − | 0.544752i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.442769 | + | 0.143864i | 0.0411101 | + | 0.0133575i | ||||
\(117\) | −0.899081 | − | 0.999291i | −0.0831200 | − | 0.0923845i | ||||
\(118\) | 4.58701 | + | 28.9612i | 0.422268 | + | 2.66610i | ||||
\(119\) | 4.47875 | + | 13.7842i | 0.410566 | + | 1.26359i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.15096 | + | 10.7876i | 0.195542 | + | 0.980695i | ||||
\(122\) | 3.97277 | + | 3.97277i | 0.359677 | + | 0.359677i | ||||
\(123\) | −0.522398 | + | 19.8062i | −0.0471030 | + | 1.78587i | ||||
\(124\) | 5.55787 | − | 7.64976i | 0.499112 | − | 0.686968i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 14.1851 | − | 9.20430i | 1.26371 | − | 0.819984i | ||||
\(127\) | 8.33745 | + | 16.3632i | 0.739829 | + | 1.45200i | 0.886460 | + | 0.462806i | \(0.153157\pi\) |
−0.146630 | + | 0.989191i | \(0.546843\pi\) | |||||||
\(128\) | −3.10495 | + | 19.6039i | −0.274442 | + | 1.73276i | ||||
\(129\) | −0.214969 | − | 0.0398843i | −0.0189270 | − | 0.00351162i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.14091i | 0.711274i | 0.934624 | + | 0.355637i | \(0.115736\pi\) | ||||
−0.934624 | + | 0.355637i | \(0.884264\pi\) | |||||||
\(132\) | 10.1879 | + | 16.8705i | 0.886743 | + | 1.46839i | ||||
\(133\) | −5.16319 | − | 5.16319i | −0.447705 | − | 0.447705i | ||||
\(134\) | −2.35180 | − | 7.23810i | −0.203165 | − | 0.625277i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −16.1634 | + | 11.7434i | −1.38600 | + | 1.00699i | ||||
\(137\) | 1.97628 | − | 1.00697i | 0.168845 | − | 0.0860310i | −0.367525 | − | 0.930013i | \(-0.619795\pi\) |
0.536371 | + | 0.843983i | \(0.319795\pi\) | |||||||
\(138\) | 23.5077 | + | 18.0451i | 2.00111 | + | 1.53610i | ||||
\(139\) | 8.81975 | + | 12.1393i | 0.748081 | + | 1.02965i | 0.998113 | + | 0.0614079i | \(0.0195590\pi\) |
−0.250031 | + | 0.968238i | \(0.580441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.680775 | − | 0.717659i | −0.0573316 | − | 0.0604378i | ||||
\(142\) | −3.95344 | + | 3.95344i | −0.331766 | + | 0.331766i | ||||
\(143\) | 1.36140 | − | 0.595863i | 0.113846 | − | 0.0498286i | ||||
\(144\) | 2.11728 | + | 1.71586i | 0.176440 | + | 0.142989i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.34079 | − | 3.22183i | 0.193725 | − | 0.266640i | ||||
\(147\) | −1.90961 | + | 0.565259i | −0.157502 | + | 0.0466218i | ||||
\(148\) | −6.83056 | + | 3.48035i | −0.561469 | + | 0.286083i | ||||
\(149\) | 4.42291 | − | 13.6123i | 0.362339 | − | 1.11516i | −0.589292 | − | 0.807920i | \(-0.700593\pi\) |
0.951631 | − | 0.307244i | \(-0.0994067\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.03265 | − | 5.83606i | −0.653688 | − | 0.474932i | 0.210838 | − | 0.977521i | \(-0.432381\pi\) |
−0.864525 | + | 0.502589i | \(0.832381\pi\) | |||||||
\(152\) | 4.56961 | − | 8.96837i | 0.370645 | − | 0.727431i | ||||
\(153\) | −1.87231 | − | 17.8789i | −0.151367 | − | 1.44543i | ||||
\(154\) | 4.72433 | + | 18.0876i | 0.380697 | + | 1.45754i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.93168 | − | 1.83240i | 0.154658 | − | 0.146710i | ||||
\(157\) | −23.1818 | + | 3.67164i | −1.85011 | + | 0.293029i | −0.979876 | − | 0.199606i | \(-0.936034\pi\) |
−0.870236 | + | 0.492635i | \(0.836034\pi\) | |||||||
\(158\) | 2.32544 | − | 14.6822i | 0.185002 | − | 1.16806i | ||||
\(159\) | −13.8136 | + | 1.81594i | −1.09549 | + | 0.144013i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4381 | + | 14.3668i | 0.822636 | + | 1.13226i | ||||
\(162\) | −19.5862 | + | 7.50141i | −1.53883 | + | 0.589366i | ||||
\(163\) | 0.949795 | − | 1.86408i | 0.0743937 | − | 0.146006i | −0.850814 | − | 0.525467i | \(-0.823891\pi\) |
0.925208 | + | 0.379461i | \(0.123891\pi\) | |||||||
\(164\) | −39.2445 | −3.06448 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.7857 | 0.992359 | ||||||||
\(167\) | 1.25190 | − | 2.45700i | 0.0968751 | − | 0.190128i | −0.837483 | − | 0.546463i | \(-0.815974\pi\) |
0.934358 | + | 0.356335i | \(0.115974\pi\) | |||||||
\(168\) | 7.90932 | + | 11.5128i | 0.610217 | + | 0.888232i | ||||
\(169\) | 7.52320 | + | 10.3548i | 0.578708 | + | 0.796523i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.92975 | + | 7.59744i | 0.376987 | + | 0.580991i | ||||
\(172\) | 0.0677460 | − | 0.427731i | 0.00516558 | − | 0.0326142i | ||||
\(173\) | −5.98711 | + | 0.948266i | −0.455192 | + | 0.0720953i | −0.379820 | − | 0.925060i | \(-0.624014\pi\) |
−0.0753714 | + | 0.997156i | \(0.524014\pi\) | |||||||
\(174\) | −0.376964 | − | 0.397388i | −0.0285776 | − | 0.0301259i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.53713 | + | 1.62495i | −0.191244 | + | 0.122485i | ||||
\(177\) | 7.27874 | − | 20.5422i | 0.547104 | − | 1.54404i | ||||
\(178\) | 9.43513 | − | 18.5175i | 0.707193 | − | 1.38794i | ||||
\(179\) | −3.42031 | − | 2.48500i | −0.255646 | − | 0.185738i | 0.452579 | − | 0.891724i | \(-0.350504\pi\) |
−0.708225 | + | 0.705986i | \(0.750504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.65152 | − | 11.2382i | 0.271415 | − | 0.835330i | −0.718731 | − | 0.695289i | \(-0.755276\pi\) |
0.990146 | − | 0.140041i | \(-0.0447235\pi\) | |||||||
\(182\) | 2.25032 | − | 1.14660i | 0.166805 | − | 0.0849913i | ||||
\(183\) | −1.18523 | − | 4.00406i | −0.0876149 | − | 0.295989i | ||||
\(184\) | −14.3886 | + | 19.8043i | −1.06075 | + | 1.45999i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −10.0420 | + | 4.78746i | −0.736317 | + | 0.351034i | ||||
\(187\) | 19.4132 | + | 4.25471i | 1.41964 | + | 0.311135i | ||||
\(188\) | 1.38544 | − | 1.38544i | 0.101044 | − | 0.101044i | ||||
\(189\) | −12.5298 | + | 0.978959i | −0.911412 | + | 0.0712088i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.1538 | − | 19.4810i | −1.02413 | − | 1.40960i | −0.909266 | − | 0.416216i | \(-0.863356\pi\) |
−0.114866 | − | 0.993381i | \(-0.536644\pi\) | |||||||
\(192\) | 13.1023 | − | 17.0686i | 0.945579 | − | 1.23182i | ||||
\(193\) | −18.0178 | + | 9.18053i | −1.29695 | + | 0.660829i | −0.959817 | − | 0.280628i | \(-0.909457\pi\) |
−0.337133 | + | 0.941457i | \(0.609457\pi\) | |||||||
\(194\) | 7.10621 | − | 5.16296i | 0.510196 | − | 0.370679i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.21896 | − | 3.75159i | −0.0870689 | − | 0.267971i | ||||
\(197\) | 7.29534 | + | 7.29534i | 0.519772 | + | 0.519772i | 0.917502 | − | 0.397731i | \(-0.130202\pi\) |
−0.397731 | + | 0.917502i | \(0.630202\pi\) | |||||||
\(198\) | −1.05850 | − | 23.1629i | −0.0752246 | − | 1.64612i | ||||
\(199\) | 15.0255i | 1.06513i | 0.846390 | + | 0.532563i | \(0.178771\pi\) | ||||
−0.846390 | + | 0.532563i | \(0.821229\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.03187 | + | 5.56162i | −0.0727828 | + | 0.392286i | ||||
\(202\) | −5.20159 | + | 32.8415i | −0.365982 | + | 2.31072i | ||||
\(203\) | −0.149011 | − | 0.292450i | −0.0104585 | − | 0.0205259i | ||||
\(204\) | 35.3033 | − | 4.64096i | 2.47172 | − | 0.324932i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.84744 | − | 8.04831i | 0.407410 | − | 0.560752i | ||||
\(207\) | −8.95120 | − | 20.1252i | −0.622152 | − | 1.39880i | ||||
\(208\) | 0.287820 | + | 0.287820i | 0.0199567 | + | 0.0199567i | ||||
\(209\) | −9.68754 | + | 2.53031i | −0.670101 | + | 0.175025i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0208958 | + | 0.0643106i | 0.00143853 | + | 0.00442733i | 0.951773 | − | 0.306802i | \(-0.0992591\pi\) |
−0.950335 | + | 0.311230i | \(0.899259\pi\) | |||||||
\(212\) | −4.31704 | − | 27.2567i | −0.296495 | − | 1.87200i | ||||
\(213\) | 3.98459 | − | 1.17947i | 0.273020 | − | 0.0808159i | ||||
\(214\) | −19.7881 | − | 6.42954i | −1.35269 | − | 0.439514i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.62080 | − | 16.0097i | −0.450488 | − | 1.08932i | ||||
\(217\) | −6.58430 | + | 1.04285i | −0.446971 | + | 0.0707933i | ||||
\(218\) | −19.7220 | − | 10.0489i | −1.33574 | − | 0.680596i | ||||
\(219\) | −2.67180 | + | 1.27376i | −0.180543 | + | 0.0860728i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.68496i | − | 0.180610i | ||||||
\(222\) | 9.01630 | + | 0.237808i | 0.605134 | + | 0.0159607i | ||||
\(223\) | −2.78128 | − | 17.5603i | −0.186248 | − | 1.17593i | −0.886741 | − | 0.462267i | \(-0.847036\pi\) |
0.700492 | − | 0.713660i | \(-0.252964\pi\) | |||||||
\(224\) | 8.90595 | − | 6.47055i | 0.595054 | − | 0.432332i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.4936 | + | 35.3735i | −0.764540 | + | 2.35301i | ||||
\(227\) | −18.7878 | − | 2.97569i | −1.24699 | − | 0.197504i | −0.502169 | − | 0.864769i | \(-0.667465\pi\) |
−0.744820 | + | 0.667266i | \(0.767465\pi\) | |||||||
\(228\) | −14.7858 | + | 10.1579i | −0.979213 | + | 0.672721i | ||||
\(229\) | 5.69174 | − | 1.84936i | 0.376121 | − | 0.122209i | −0.114855 | − | 0.993382i | \(-0.536640\pi\) |
0.490976 | + | 0.871173i | \(0.336640\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.33141 | − | 13.4892i | 0.219190 | − | 0.887524i | ||||
\(232\) | 0.319930 | − | 0.319930i | 0.0210044 | − | 0.0210044i | ||||
\(233\) | −13.2122 | − | 6.73196i | −0.865560 | − | 0.441025i | −0.0359407 | − | 0.999354i | \(-0.511443\pi\) |
−0.829620 | + | 0.558329i | \(0.811443\pi\) | |||||||
\(234\) | −3.02613 | + | 0.809620i | −0.197824 | + | 0.0529265i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 41.0545 | + | 13.3394i | 2.67242 | + | 0.868321i | ||||
\(237\) | −6.72757 | + | 8.76410i | −0.437003 | + | 0.569290i | ||||
\(238\) | 33.3598 | + | 5.28367i | 2.16239 | + | 0.342489i | ||||
\(239\) | −13.2600 | − | 9.63393i | −0.857716 | − | 0.623167i | 0.0695465 | − | 0.997579i | \(-0.477845\pi\) |
−0.927263 | + | 0.374411i | \(0.877845\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6613 | −1.07325 | −0.536626 | − | 0.843820i | \(-0.680301\pi\) | ||||
−0.536626 | + | 0.843820i | \(0.680301\pi\) | |||||||
\(242\) | 24.6751 | + | 6.94683i | 1.58617 | + | 0.446559i | ||||
\(243\) | 15.4532 | + | 2.04933i | 0.991321 | + | 0.131465i | ||||
\(244\) | 7.86631 | − | 2.55592i | 0.503589 | − | 0.163626i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 40.5729 | + | 22.0392i | 2.58683 | + | 1.40517i | ||||
\(247\) | 0.614107 | + | 1.20525i | 0.0390747 | + | 0.0766884i | ||||
\(248\) | −4.17192 | − | 8.18785i | −0.264917 | − | 0.519929i | ||||
\(249\) | −8.35042 | − | 4.53596i | −0.529187 | − | 0.287455i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.4903 | − | 5.03310i | 0.977739 | − | 0.317687i | 0.223803 | − | 0.974634i | \(-0.428153\pi\) |
0.753936 | + | 0.656948i | \(0.228153\pi\) | |||||||
\(252\) | −2.59274 | − | 24.7585i | −0.163327 | − | 1.55964i | ||||
\(253\) | 24.2330 | − | 2.39237i | 1.52351 | − | 0.150407i | ||||
\(254\) | 42.7972 | 2.68534 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 17.3193 | + | 12.5832i | 1.08246 | + | 0.786451i | ||||
\(257\) | 6.18423 | + | 0.979486i | 0.385762 | + | 0.0610986i | 0.346303 | − | 0.938123i | \(-0.387437\pi\) |
0.0394582 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(258\) | −0.310248 | + | 0.404165i | −0.0193152 | + | 0.0251622i | ||||
\(259\) | 5.14022 | + | 1.67016i | 0.319398 | + | 0.103779i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.105218 | + | 0.393273i | 0.00651280 | + | 0.0243430i | ||||
\(262\) | 16.9037 | + | 8.61288i | 1.04432 | + | 0.532105i | ||||
\(263\) | −0.0420929 | + | 0.0420929i | −0.00259556 | + | 0.00259556i | −0.708403 | − | 0.705808i | \(-0.750584\pi\) |
0.705808 | + | 0.708403i | \(0.250584\pi\) | |||||||
\(264\) | 19.1035 | − | 1.37852i | 1.17574 | − | 0.0848422i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −16.1833 | + | 5.25829i | −0.992265 | + | 0.322406i | ||||
\(267\) | −12.7316 | + | 8.74664i | −0.779162 | + | 0.535286i | ||||
\(268\) | −11.0661 | − | 1.75270i | −0.675971 | − | 0.107063i | ||||
\(269\) | −1.14760 | + | 3.53195i | −0.0699704 | + | 0.215347i | −0.979927 | − | 0.199357i | \(-0.936115\pi\) |
0.909957 | + | 0.414704i | \(0.136115\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.7140 | + | 7.78419i | −0.650830 | + | 0.472856i | −0.863554 | − | 0.504257i | \(-0.831767\pi\) |
0.212724 | + | 0.977112i | \(0.431767\pi\) | |||||||
\(272\) | 0.851546 | + | 5.37645i | 0.0516326 | + | 0.325995i | ||||
\(273\) | −1.87648 | − | 0.0494929i | −0.113570 | − | 0.00299545i | ||||
\(274\) | − | 5.16889i | − | 0.312264i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 39.3813 | − | 18.7748i | 2.37048 | − | 1.13011i | ||||
\(277\) | −7.94417 | − | 4.04776i | −0.477319 | − | 0.243206i | 0.198742 | − | 0.980052i | \(-0.436314\pi\) |
−0.676061 | + | 0.736846i | \(0.736314\pi\) | |||||||
\(278\) | 34.5371 | − | 5.47015i | 2.07140 | − | 0.328078i | ||||
\(279\) | 8.25698 | + | 0.435865i | 0.494332 | + | 0.0260946i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3133 | − | 4.00084i | −0.734552 | − | 0.238670i | −0.0822308 | − | 0.996613i | \(-0.526204\pi\) |
−0.652321 | + | 0.757943i | \(0.726204\pi\) | |||||||
\(282\) | −2.21039 | + | 0.654291i | −0.131627 | + | 0.0389625i | ||||
\(283\) | −0.809544 | − | 5.11126i | −0.0481224 | − | 0.303833i | 0.951874 | − | 0.306489i | \(-0.0991544\pi\) |
−0.999996 | + | 0.00265657i | \(0.999154\pi\) | |||||||
\(284\) | 2.54349 | + | 7.82805i | 0.150928 | + | 0.464510i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.203084 | − | 3.45722i | 0.0120086 | − | 0.204429i | ||||
\(287\) | 19.5642 | + | 19.5642i | 1.15484 | + | 1.15484i | ||||
\(288\) | −12.4756 | + | 5.54884i | −0.735133 | + | 0.326969i | ||||
\(289\) | 11.1132 | − | 15.2960i | 0.653718 | − | 0.899766i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.47279 | + | 0.850912i | −0.379441 | + | 0.0498813i | ||||
\(292\) | −2.66163 | − | 5.22375i | −0.155760 | − | 0.305697i | ||||
\(293\) | −2.47003 | + | 15.5951i | −0.144301 | + | 0.911078i | 0.804213 | + | 0.594341i | \(0.202587\pi\) |
−0.948513 | + | 0.316737i | \(0.897413\pi\) | |||||||
\(294\) | −0.846621 | + | 4.56313i | −0.0493759 | + | 0.266127i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.45032i | 0.433041i | ||||||||
\(297\) | −7.52618 | + | 15.5034i | −0.436713 | + | 0.899601i | ||||
\(298\) | −23.5852 | − | 23.5852i | −1.36625 | − | 1.36625i | ||||
\(299\) | −1.01660 | − | 3.12876i | −0.0587912 | − | 0.180941i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.247006 | + | 0.179461i | −0.0142372 | + | 0.0103439i | ||||
\(302\) | −20.6163 | + | 10.5045i | −1.18634 | + | 0.604468i | ||||
\(303\) | 15.0484 | − | 19.6037i | 0.864506 | − | 1.12620i | ||||
\(304\) | −1.61196 | − | 2.21867i | −0.0924521 | − | 0.127249i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −39.1046 | − | 15.0278i | −2.23546 | − | 0.859084i | ||||
\(307\) | 5.43877 | − | 5.43877i | 0.310407 | − | 0.310407i | −0.534660 | − | 0.845067i | \(-0.679560\pi\) |
0.845067 | + | 0.534660i | \(0.179560\pi\) | |||||||
\(308\) | 26.8831 | + | 5.89186i | 1.53181 | + | 0.335720i | ||||
\(309\) | −6.67431 | + | 3.18193i | −0.379688 | + | 0.181014i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.3642 | − | 14.2651i | 0.587699 | − | 0.808898i | −0.406814 | − | 0.913511i | \(-0.633360\pi\) |
0.994513 | + | 0.104613i | \(0.0333603\pi\) | |||||||
\(312\) | −0.734444 | − | 2.48117i | −0.0415797 | − | 0.140468i | ||||
\(313\) | −12.8408 | + | 6.54272i | −0.725805 | + | 0.369816i | −0.777531 | − | 0.628845i | \(-0.783528\pi\) |
0.0517253 | + | 0.998661i | \(0.483528\pi\) | |||||||
\(314\) | −16.9020 | + | 52.0191i | −0.953838 | + | 2.93561i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −17.7046 | − | 12.8632i | −0.995963 | − | 0.723610i | ||||
\(317\) | 4.90253 | − | 9.62175i | 0.275353 | − | 0.540411i | −0.711371 | − | 0.702817i | \(-0.751925\pi\) |
0.986724 | + | 0.162406i | \(0.0519253\pi\) | |||||||
\(318\) | −10.8439 | + | 30.6037i | −0.608094 | + | 1.71617i | ||||
\(319\) | −0.449297 | − | 0.0263926i | −0.0251558 | − | 0.00147770i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6428 | + | 11.2194i | 0.594021 | + | 0.626205i | ||||
\(322\) | 40.8743 | − | 6.47386i | 2.27784 | − | 0.360774i | ||||
\(323\) | −2.82989 | + | 17.8672i | −0.157459 | + | 0.994158i | ||||
\(324\) | −3.25073 | + | 30.7049i | −0.180596 | + | 1.70583i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.86570 | − | 3.94430i | −0.158716 | − | 0.218454i | ||||
\(327\) | 9.31560 | + | 13.5598i | 0.515154 | + | 0.749857i | ||||
\(328\) | −17.3151 | + | 33.9827i | −0.956065 | + | 1.87638i | ||||
\(329\) | −1.38135 | −0.0761561 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.77976 | −0.0978245 | −0.0489123 | − | 0.998803i | \(-0.515575\pi\) | ||||
−0.0489123 | + | 0.998803i | \(0.515575\pi\) | |||||||
\(332\) | 8.54529 | − | 16.7711i | 0.468983 | − | 0.920432i | ||||
\(333\) | −5.80426 | − | 3.35402i | −0.318071 | − | 0.183799i | ||||
\(334\) | −3.77721 | − | 5.19888i | −0.206680 | − | 0.284470i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.77322 | − | 0.496027i | 0.205846 | − | 0.0270605i | ||||
\(337\) | 0.311391 | − | 1.96604i | 0.0169625 | − | 0.107097i | −0.977754 | − | 0.209753i | \(-0.932734\pi\) |
0.994717 | + | 0.102656i | \(0.0327340\pi\) | |||||||
\(338\) | 29.4600 | − | 4.66600i | 1.60241 | − | 0.253797i | ||||
\(339\) | 20.0560 | − | 19.0252i | 1.08929 | − | 1.03331i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.32972 | + | 8.51314i | −0.180314 | + | 0.461012i | ||||
\(342\) | 20.9908 | − | 2.19819i | 1.13505 | − | 0.118864i | ||||
\(343\) | −8.94909 | + | 17.5636i | −0.483206 | + | 0.948345i | ||||
\(344\) | −0.340493 | − | 0.247382i | −0.0183581 | − | 0.0133380i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.36525 | + | 13.4349i | −0.234677 | + | 0.722262i | ||||
\(347\) | −24.1209 | + | 12.2902i | −1.29488 | + | 0.659774i | −0.959340 | − | 0.282253i | \(-0.908918\pi\) |
−0.335538 | + | 0.942027i | \(0.608918\pi\) | |||||||
\(348\) | −0.773202 | + | 0.228874i | −0.0414480 | + | 0.0122689i | ||||
\(349\) | 3.10685 | − | 4.27621i | 0.166306 | − | 0.228900i | −0.717728 | − | 0.696324i | \(-0.754818\pi\) |
0.884033 | + | 0.467424i | \(0.154818\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.26362 | + | 0.544807i | 0.120823 | + | 0.0290796i | ||||
\(352\) | −1.48303 | − | 15.0220i | −0.0790457 | − | 0.800675i | ||||
\(353\) | −4.81168 | + | 4.81168i | −0.256100 | + | 0.256100i | −0.823466 | − | 0.567366i | \(-0.807963\pi\) |
0.567366 | + | 0.823466i | \(0.307963\pi\) | |||||||
\(354\) | −34.9529 | − | 36.8467i | −1.85773 | − | 1.95838i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.9836 | − | 24.7523i | −0.953129 | − | 1.31187i | ||||
\(357\) | −19.9131 | − | 15.2858i | −1.05391 | − | 0.809012i | ||||
\(358\) | −8.77845 | + | 4.47284i | −0.463955 | + | 0.236397i | ||||
\(359\) | 5.32038 | − | 3.86548i | 0.280799 | − | 0.204012i | −0.438467 | − | 0.898747i | \(-0.644478\pi\) |
0.719266 | + | 0.694735i | \(0.244478\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.05503 | + | 9.40241i | 0.160791 | + | 0.494864i | ||||
\(362\) | −19.4717 | − | 19.4717i | −1.02341 | − | 1.02341i | ||||
\(363\) | −13.6510 | − | 13.2910i | −0.716491 | − | 0.697596i | ||||
\(364\) | − | 3.71809i | − | 0.194881i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −9.56796 | − | 1.77519i | −0.500125 | − | 0.0927907i | ||||
\(367\) | −0.235142 | + | 1.48463i | −0.0122743 | + | 0.0774968i | −0.993065 | − | 0.117566i | \(-0.962491\pi\) |
0.980791 | + | 0.195062i | \(0.0624910\pi\) | |||||||
\(368\) | 3.02796 | + | 5.94271i | 0.157843 | + | 0.309785i | ||||
\(369\) | −18.6797 | − | 28.7880i | −0.972425 | − | 1.49865i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −11.4359 | + | 15.7402i | −0.593724 | + | 0.817191i | ||||
\(372\) | −0.431816 | + | 16.3719i | −0.0223886 | + | 0.848844i | ||||
\(373\) | −7.58222 | − | 7.58222i | −0.392593 | − | 0.392593i | 0.483018 | − | 0.875610i | \(-0.339541\pi\) |
−0.875610 | + | 0.483018i | \(0.839541\pi\) | |||||||
\(374\) | 29.3732 | − | 35.8081i | 1.51885 | − | 1.85159i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.588416 | − | 1.81096i | −0.0303452 | − | 0.0933931i | ||||
\(377\) | 0.00951189 | + | 0.0600557i | 0.000489887 | + | 0.00309303i | ||||
\(378\) | −11.2236 | + | 27.0526i | −0.577278 | + | 1.39144i | ||||
\(379\) | −2.10943 | − | 0.685394i | −0.108354 | − | 0.0352063i | 0.254338 | − | 0.967115i | \(-0.418142\pi\) |
−0.362692 | + | 0.931909i | \(0.618142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −27.9512 | − | 15.1831i | −1.43199 | − | 0.777856i | ||||
\(382\) | −55.4246 | + | 8.77840i | −2.83577 | + | 0.449142i | ||||
\(383\) | 13.0657 | + | 6.65732i | 0.667627 | + | 0.340173i | 0.754739 | − | 0.656025i | \(-0.227764\pi\) |
−0.0871115 | + | 0.996199i | \(0.527764\pi\) | |||||||
\(384\) | −14.7943 | − | 31.0321i | −0.754970 | − | 1.58360i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 47.1248i | 2.39859i | ||||||||
\(387\) | 0.346011 | − | 0.153897i | 0.0175887 | − | 0.00782303i | ||||
\(388\) | −2.02288 | − | 12.7719i | −0.102696 | − | 0.648397i | ||||
\(389\) | −8.25648 | + | 5.99868i | −0.418620 | + | 0.304145i | −0.777082 | − | 0.629399i | \(-0.783301\pi\) |
0.358462 | + | 0.933544i | \(0.383301\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.5953 | − | 41.8419i | 0.687542 | − | 2.11604i | ||||
\(392\) | −3.78641 | − | 0.599708i | −0.191243 | − | 0.0302898i | ||||
\(393\) | −7.98439 | − | 11.6221i | −0.402759 | − | 0.586256i | ||||
\(394\) | 22.8663 | − | 7.42971i | 1.15199 | − | 0.374303i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −31.0905 | − | 14.0925i | −1.56236 | − | 0.708174i | ||||
\(397\) | −2.17909 | + | 2.17909i | −0.109365 | + | 0.109365i | −0.759672 | − | 0.650307i | \(-0.774640\pi\) |
0.650307 | + | 0.759672i | \(0.274640\pi\) | |||||||
\(398\) | 31.1988 | + | 15.8966i | 1.56385 | + | 0.796823i | ||||
\(399\) | 12.4350 | + | 2.30712i | 0.622527 | + | 0.115500i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −19.2181 | − | 6.24433i | −0.959704 | − | 0.311827i | −0.213052 | − | 0.977041i | \(-0.568340\pi\) |
−0.746653 | + | 0.665214i | \(0.768340\pi\) | |||||||
\(402\) | 10.4564 | + | 8.02663i | 0.521518 | + | 0.400332i | ||||
\(403\) | 1.21976 | + | 0.193191i | 0.0607604 | + | 0.00962351i | ||||
\(404\) | 39.6021 | + | 28.7726i | 1.97028 | + | 1.43149i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.764890 | −0.0379609 | ||||||||
\(407\) | 5.53877 | − | 4.92416i | 0.274547 | − | 0.244081i | ||||
\(408\) | 11.5574 | − | 32.6176i | 0.572179 | − | 1.61481i | ||||
\(409\) | −17.9054 | + | 5.81781i | −0.885364 | + | 0.287672i | −0.716183 | − | 0.697913i | \(-0.754112\pi\) |
−0.169181 | + | 0.985585i | \(0.554112\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.83376 | + | 3.37585i | −0.0904529 | + | 0.166518i | ||||
\(412\) | −6.64891 | − | 13.0492i | −0.327568 | − | 0.642889i | ||||
\(413\) | −13.8166 | − | 27.1166i | −0.679869 | − | 1.33432i | ||||
\(414\) | −51.2581 | − | 2.70579i | −2.51920 | − | 0.132982i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.93951 | + | 0.630186i | −0.0950925 | + | 0.0308974i | ||||
\(417\) | −24.4972 | − | 8.68012i | −1.19963 | − | 0.425067i | ||||
\(418\) | −4.99526 | + | 22.7922i | −0.244326 | + | 1.11480i | ||||
\(419\) | −9.78216 | −0.477890 | −0.238945 | − | 0.971033i | \(-0.576802\pi\) | ||||
−0.238945 | + | 0.971033i | \(0.576802\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.4907 | − | 14.1608i | −0.949919 | − | 0.690157i | 0.000868744 | − | 1.00000i | \(-0.499723\pi\) |
−0.950788 | + | 0.309843i | \(0.899723\pi\) | |||||||
\(422\) | 0.155641 | + | 0.0246512i | 0.00757651 | + | 0.00120000i | ||||
\(423\) | 1.67575 | + | 0.356854i | 0.0814775 | + | 0.0173508i | ||||
\(424\) | −25.5070 | − | 8.28771i | −1.23873 | − | 0.402487i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.76656 | − | 9.52143i | 0.0855900 | − | 0.461315i | ||||
\(427\) | −5.19571 | − | 2.64735i | −0.251438 | − | 0.128114i | ||||
\(428\) | −21.6590 | + | 21.6590i | −1.04693 | + | 1.04693i | ||||
\(429\) | −1.35915 | + | 2.18589i | −0.0656204 | + | 0.105536i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.67958 | − | 0.545728i | 0.0809025 | − | 0.0262868i | −0.268286 | − | 0.963339i | \(-0.586457\pi\) |
0.349189 | + | 0.937052i | \(0.386457\pi\) | |||||||
\(432\) | −4.70553 | − | 0.373023i | −0.226395 | − | 0.0179471i | ||||
\(433\) | 35.4809 | + | 5.61962i | 1.70510 | + | 0.270062i | 0.931534 | − | 0.363653i | \(-0.118471\pi\) |
0.773567 | + | 0.633715i | \(0.218471\pi\) | |||||||
\(434\) | −4.80066 | + | 14.7749i | −0.230439 | + | 0.709218i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.3624 | + | 19.1534i | −1.26253 | + | 0.917282i | ||||
\(437\) | 3.46734 | + | 21.8919i | 0.165865 | + | 1.04723i | ||||
\(438\) | −0.181867 | + | 6.89531i | −0.00868993 | + | 0.329471i | ||||
\(439\) | − | 19.7378i | − | 0.942032i | −0.882125 | − | 0.471016i | \(-0.843887\pi\) | ||
0.882125 | − | 0.471016i | \(-0.156113\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.17180 | − | 2.67987i | 0.103419 | − | 0.127613i | ||||
\(442\) | −5.57504 | − | 2.84063i | −0.265178 | − | 0.135115i | ||||
\(443\) | 5.41218 | − | 0.857205i | 0.257140 | − | 0.0407270i | −0.0265332 | − | 0.999648i | \(-0.508447\pi\) |
0.283674 | + | 0.958921i | \(0.408447\pi\) | |||||||
\(444\) | 6.33798 | − | 11.6678i | 0.300787 | − | 0.553731i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −39.4047 | − | 12.8034i | −1.86587 | − | 0.606257i | ||||
\(447\) | 7.03639 | + | 23.7710i | 0.332810 | + | 1.12433i | ||||
\(448\) | −4.70058 | − | 29.6783i | −0.222081 | − | 1.40217i | ||||
\(449\) | −12.0577 | − | 37.1097i | −0.569037 | − | 1.75132i | −0.655641 | − | 0.755073i | \(-0.727602\pi\) |
0.0866042 | − | 0.996243i | \(-0.472398\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 36.7078 | − | 9.58780i | 1.72850 | − | 0.451472i | ||||
\(452\) | 38.7181 | + | 38.7181i | 1.82115 | + | 1.82115i | ||||
\(453\) | 17.1914 | + | 0.453429i | 0.807721 | + | 0.0213040i | ||||
\(454\) | −26.0557 | + | 35.8626i | −1.22286 | + | 1.68312i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.27230 | + | 17.2851i | 0.106410 | + | 0.809450i | ||||
\(457\) | 0.801431 | + | 1.57290i | 0.0374893 | + | 0.0735770i | 0.908991 | − | 0.416815i | \(-0.136854\pi\) |
−0.871502 | + | 0.490392i | \(0.836854\pi\) | |||||||
\(458\) | 2.18173 | − | 13.7749i | 0.101945 | − | 0.643658i | ||||
\(459\) | 20.2081 | + | 23.6879i | 0.943235 | + | 1.10566i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.4498i | 0.952441i | 0.879326 | + | 0.476221i | \(0.157994\pi\) | ||||
−0.879326 | + | 0.476221i | \(0.842006\pi\) | |||||||
\(462\) | −24.4843 | − | 21.1885i | −1.13911 | − | 0.985780i | ||||
\(463\) | −22.0819 | − | 22.0819i | −1.02623 | − | 1.02623i | −0.999646 | − | 0.0265876i | \(-0.991536\pi\) |
−0.0265876 | − | 0.999646i | \(-0.508464\pi\) | |||||||
\(464\) | −0.0380938 | − | 0.117241i | −0.00176846 | − | 0.00544276i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.9564 | + | 20.3115i | −1.29505 | + | 0.940912i | ||||
\(467\) | −13.5336 | + | 6.89569i | −0.626258 | + | 0.319094i | −0.738161 | − | 0.674625i | \(-0.764305\pi\) |
0.111903 | + | 0.993719i | \(0.464305\pi\) | |||||||
\(468\) | −0.960524 | + | 4.51051i | −0.0444002 | + | 0.208498i | ||||
\(469\) | 4.64294 | + | 6.39046i | 0.214391 | + | 0.295084i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.4937 | − | 27.9778i | 1.35900 | − | 1.28915i | ||||
\(472\) | 29.6646 | − | 29.6646i | 1.36542 | − | 1.36542i | ||||
\(473\) | 0.0411318 | + | 0.416635i | 0.00189124 | + | 0.0191569i | ||||
\(474\) | 11.0801 | + | 23.2413i | 0.508927 | + | 1.06751i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 29.2266 | − | 40.2270i | 1.33960 | − | 1.84380i | ||||
\(477\) | 17.9395 | − | 16.1405i | 0.821393 | − | 0.739023i | ||||
\(478\) | −34.0326 | + | 17.3405i | −1.55661 | + | 0.793134i | ||||
\(479\) | −11.6789 | + | 35.9441i | −0.533624 | + | 1.64233i | 0.212980 | + | 0.977057i | \(0.431683\pi\) |
−0.746604 | + | 0.665269i | \(0.768317\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.810022 | − | 0.588515i | −0.0369338 | − | 0.0268340i | ||||
\(482\) | −17.6273 | + | 34.5955i | −0.802901 | + | 1.57578i | ||||
\(483\) | −28.9921 | − | 10.2728i | −1.31919 | − | 0.467430i | ||||
\(484\) | 25.6038 | − | 27.7236i | 1.16381 | − | 1.26016i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 20.6043 | − | 29.9187i | 0.934630 | − | 1.35714i | ||||
\(487\) | 17.6946 | − | 2.80255i | 0.801818 | − | 0.126996i | 0.257941 | − | 0.966161i | \(-0.416956\pi\) |
0.543877 | + | 0.839165i | \(0.316956\pi\) | |||||||
\(488\) | 1.25747 | − | 7.93933i | 0.0569228 | − | 0.359397i | ||||
\(489\) | 0.472298 | + | 3.59272i | 0.0213581 | + | 0.162468i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.4010 | + | 17.0685i | 0.559648 | + | 0.770289i | 0.991282 | − | 0.131760i | \(-0.0420628\pi\) |
−0.431634 | + | 0.902049i | \(0.642063\pi\) | |||||||
\(492\) | 56.0260 | − | 38.4900i | 2.52585 | − | 1.73526i | ||||
\(493\) | −0.369165 | + | 0.724528i | −0.0166264 | + | 0.0326311i | ||||
\(494\) | 3.15229 | 0.141828 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.50375 | −0.112422 | ||||||||
\(497\) | 2.63447 | − | 5.17044i | 0.118172 | − | 0.231926i | ||||
\(498\) | −18.2530 | + | 12.5398i | −0.817935 | + | 0.561923i | ||||
\(499\) | 22.0825 | + | 30.3939i | 0.988547 | + | 1.36062i | 0.932096 | + | 0.362212i | \(0.117978\pi\) |
0.0564511 | + | 0.998405i | \(0.482022\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.622525 | + | 4.73548i | 0.0278124 | + | 0.211565i | ||||
\(502\) | 5.93765 | − | 37.4889i | 0.265010 | − | 1.67321i | ||||
\(503\) | −16.2460 | + | 2.57311i | −0.724373 | + | 0.114729i | −0.507724 | − | 0.861520i | \(-0.669513\pi\) |
−0.216650 | + | 0.976249i | \(0.569513\pi\) | |||||||
\(504\) | −22.5829 | − | 8.67858i | −1.00592 | − | 0.386575i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.6704 | − | 52.8483i | 0.918911 | − | 2.34939i | ||||
\(507\) | −20.8959 | − | 7.40409i | −0.928021 | − | 0.328827i | ||||
\(508\) | 28.6035 | − | 56.1375i | 1.26908 | − | 2.49070i | ||||
\(509\) | −4.83733 | − | 3.51452i | −0.214411 | − | 0.155779i | 0.475396 | − | 0.879772i | \(-0.342305\pi\) |
−0.689807 | + | 0.723993i | \(0.742305\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.27727 | + | 3.93104i | −0.0565032 | + | 0.173899i | ||||
\(512\) | 9.08125 | − | 4.62713i | 0.401338 | − | 0.204492i | ||||
\(513\) | −14.4891 | − | 6.01125i | −0.639711 | − | 0.265403i | ||||
\(514\) | 8.57656 | − | 11.8046i | 0.378296 | − | 0.520680i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.322793 | + | 0.677079i | 0.0142102 | + | 0.0298067i | ||||
\(517\) | −0.957413 | + | 1.63437i | −0.0421070 | + | 0.0718793i | ||||
\(518\) | 8.90613 | − | 8.90613i | 0.391313 | − | 0.391313i | ||||
\(519\) | 7.61725 | − | 7.22576i | 0.334360 | − | 0.317176i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.7454 | + | 35.4354i | 1.12792 | + | 1.55246i | 0.791952 | + | 0.610583i | \(0.209065\pi\) |
0.335972 | + | 0.941872i | \(0.390935\pi\) | |||||||
\(522\) | 0.927907 | + | 0.197600i | 0.0406134 | + | 0.00864872i | ||||
\(523\) | 7.72545 | − | 3.93631i | 0.337810 | − | 0.172123i | −0.276853 | − | 0.960912i | \(-0.589292\pi\) |
0.614664 | + | 0.788789i | \(0.289292\pi\) | |||||||
\(524\) | 22.5952 | − | 16.4164i | 0.987076 | − | 0.717153i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0428682 | + | 0.131935i | 0.00186914 | + | 0.00575262i | ||||
\(527\) | 11.6783 | + | 11.6783i | 0.508713 | + | 0.508713i | ||||
\(528\) | 2.02834 | − | 4.80815i | 0.0882722 | − | 0.209248i | ||||
\(529\) | − | 30.9055i | − | 1.34372i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.75600 | + | 36.4651i | 0.423374 | + | 1.58245i | ||||
\(532\) | −3.91878 | + | 24.7422i | −0.169901 | + | 1.07271i | ||||
\(533\) | −2.32696 | − | 4.56691i | −0.100792 | − | 0.197815i | ||||
\(534\) | 4.69175 | + | 35.6896i | 0.203032 | + | 1.54444i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.40019 | + | 8.80911i | −0.276446 | + | 0.380496i | ||||
\(537\) | 7.32011 | + | 0.193071i | 0.315886 | + | 0.00833162i | ||||
\(538\) | 6.11958 | + | 6.11958i | 0.263834 | + | 0.263834i | ||||
\(539\) | 2.05672 | + | 3.21129i | 0.0885893 | + | 0.138320i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.87737 | + | 18.0887i | 0.252688 | + | 0.777694i | 0.994276 | + | 0.106839i | \(0.0340728\pi\) |
−0.741588 | + | 0.670855i | \(0.765927\pi\) | |||||||
\(542\) | 4.82788 | + | 30.4820i | 0.207375 | + | 1.30931i | ||||
\(543\) | 5.80919 | + | 19.6251i | 0.249296 | + | 0.842196i | ||||
\(544\) | −25.9378 | − | 8.42769i | −1.11207 | − | 0.361334i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.08804 | + | 3.84395i | −0.0893598 | + | 0.164506i | ||||
\(547\) | 7.31231 | − | 1.15816i | 0.312652 | − | 0.0495192i | 0.00186328 | − | 0.999998i | \(-0.499407\pi\) |
0.310789 | + | 0.950479i | \(0.399407\pi\) | |||||||
\(548\) | −6.78008 | − | 3.45463i | −0.289631 | − | 0.147574i | ||||
\(549\) | 5.61914 | + | 4.55381i | 0.239819 | + | 0.194352i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 0.409669i | − | 0.0174525i | ||||||
\(552\) | 1.11792 | − | 42.3849i | 0.0475818 | − | 1.80402i | ||||
\(553\) | 2.41358 | + | 15.2387i | 0.102636 | + | 0.648016i | ||||
\(554\) | −16.8095 | + | 12.2128i | −0.714166 | + | 0.518872i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.9076 | − | 48.9587i | 0.674634 | − | 2.07631i | ||||
\(557\) | 25.1380 | + | 3.98146i | 1.06513 | + | 0.168700i | 0.664310 | − | 0.747457i | \(-0.268725\pi\) |
0.400820 | + | 0.916157i | \(0.368725\pi\) | |||||||
\(558\) | 9.64071 | − | 16.6836i | 0.408124 | − | 0.706273i | ||||
\(559\) | 0.0537924 | − | 0.0174782i | 0.00227518 | − | 0.000739249i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −31.8875 | + | 12.9659i | −1.34629 | + | 0.547421i | ||||
\(562\) | −21.3345 | + | 21.3345i | −0.899943 | + | 0.899943i | ||||
\(563\) | −33.8735 | − | 17.2594i | −1.42760 | − | 0.727397i | −0.442081 | − | 0.896975i | \(-0.645760\pi\) |
−0.985517 | + | 0.169578i | \(0.945760\pi\) | |||||||
\(564\) | −0.619071 | + | 3.33668i | −0.0260676 | + | 0.140500i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −11.4695 | − | 3.72665i | −0.482098 | − | 0.156643i | ||||
\(567\) | 16.9276 | − | 13.6865i | 0.710894 | − | 0.574780i | ||||
\(568\) | 7.90072 | + | 1.25135i | 0.331507 | + | 0.0525055i | ||||
\(569\) | 10.0734 | + | 7.31872i | 0.422297 | + | 0.306817i | 0.778561 | − | 0.627569i | \(-0.215950\pi\) |
−0.356264 | + | 0.934385i | \(0.615950\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.18213 | −0.300563 | −0.150281 | − | 0.988643i | \(-0.548018\pi\) | ||||
−0.150281 | + | 0.988643i | \(0.548018\pi\) | |||||||
\(572\) | −4.39913 | − | 2.57702i | −0.183937 | − | 0.107750i | ||||
\(573\) | 39.3126 | + | 13.9297i | 1.64231 | + | 0.581922i | ||||
\(574\) | 61.3215 | − | 19.9246i | 2.55951 | − | 0.831636i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.96463 | + | 37.2178i | −0.0818598 | + | 1.55074i | ||||
\(577\) | 13.5832 | + | 26.6585i | 0.565475 | + | 1.10981i | 0.979856 | + | 0.199704i | \(0.0639981\pi\) |
−0.414381 | + | 0.910104i | \(0.636002\pi\) | |||||||
\(578\) | −20.0031 | − | 39.2582i | −0.832017 | − | 1.63293i | ||||
\(579\) | 16.7185 | − | 30.7777i | 0.694795 | − | 1.27908i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −12.6208 | + | 4.10073i | −0.523597 | + | 0.170127i | ||||
\(582\) | −5.08122 | + | 14.3403i | −0.210623 | + | 0.594425i | ||||
\(583\) | 10.6971 | + | 24.4402i | 0.443027 | + | 1.01221i | ||||
\(584\) | −5.69771 | −0.235773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 29.7684 | + | 21.6280i | 1.22972 | + | 0.893446i | ||||
\(587\) | −14.9049 | − | 2.36071i | −0.615192 | − | 0.0974369i | −0.158941 | − | 0.987288i | \(-0.550808\pi\) |
−0.456251 | + | 0.889851i | \(0.650808\pi\) | |||||||
\(588\) | 5.41967 | + | 4.16029i | 0.223503 | + | 0.171567i | ||||
\(589\) | −7.91331 | − | 2.57119i | −0.326062 | − | 0.105944i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.5700 | − | 3.25985i | −0.722734 | − | 0.134092i | ||||
\(592\) | 1.80866 | + | 0.921560i | 0.0743356 | + | 0.0378759i | ||||
\(593\) | 17.4933 | − | 17.4933i | 0.718363 | − | 0.718363i | −0.249907 | − | 0.968270i | \(-0.580400\pi\) |
0.968270 | + | 0.249907i | \(0.0803999\pi\) | |||||||
\(594\) | 24.2287 | + | 32.0296i | 0.994117 | + | 1.31419i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −46.7001 | + | 15.1738i | −1.91291 | + | 0.621542i | ||||
\(597\) | −14.7366 | − | 21.4506i | −0.603128 | − | 0.877913i | ||||
\(598\) | −7.57207 | − | 1.19930i | −0.309645 | − | 0.0490429i | ||||
\(599\) | 9.89221 | − | 30.4451i | 0.404185 | − | 1.24395i | −0.517390 | − | 0.855750i | \(-0.673096\pi\) |
0.921574 | − | 0.388202i | \(-0.126904\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6718 | − | 8.48005i | 0.476102 | − | 0.345908i | −0.323713 | − | 0.946155i | \(-0.604931\pi\) |
0.799815 | + | 0.600247i | \(0.204931\pi\) | |||||||
\(602\) | 0.111304 | + | 0.702748i | 0.00453642 | + | 0.0286419i | ||||
\(603\) | −3.98157 | − | 8.95188i | −0.162142 | − | 0.364549i | ||||
\(604\) | 34.0633i | 1.38602i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −24.7843 | − | 51.9866i | −1.00679 | − | 2.11181i | ||||
\(607\) | 19.7642 | + | 10.0704i | 0.802203 | + | 0.408743i | 0.806490 | − | 0.591248i | \(-0.201365\pi\) |
−0.00428676 | + | 0.999991i | \(0.501365\pi\) | |||||||
\(608\) | 13.5708 | − | 2.14940i | 0.550368 | − | 0.0871698i | ||||
\(609\) | 0.499557 | + | 0.271360i | 0.0202431 | + | 0.0109960i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.243373 | + | 0.0790768i | 0.00984583 | + | 0.00319910i | ||||
\(612\) | −45.8477 | + | 41.2500i | −1.85328 | + | 1.66743i | ||||
\(613\) | 3.88920 | + | 24.5554i | 0.157083 | + | 0.991784i | 0.932719 | + | 0.360604i | \(0.117429\pi\) |
−0.775636 | + | 0.631180i | \(0.782571\pi\) | |||||||
\(614\) | −5.53895 | − | 17.0471i | −0.223534 | − | 0.687966i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 16.9630 | − | 20.6792i | 0.683460 | − | 0.833189i | ||||
\(617\) | −0.787744 | − | 0.787744i | −0.0317134 | − | 0.0317134i | 0.691072 | − | 0.722786i | \(-0.257139\pi\) |
−0.722786 | + | 0.691072i | \(0.757139\pi\) | |||||||
\(618\) | −0.454313 | + | 17.2249i | −0.0182752 | + | 0.692887i | ||||
\(619\) | 11.7187 | − | 16.1294i | 0.471014 | − | 0.648295i | −0.505733 | − | 0.862690i | \(-0.668778\pi\) |
0.976747 | + | 0.214395i | \(0.0687780\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 32.5172 | + | 19.9520i | 1.30487 | + | 0.800645i | ||||
\(622\) | −18.6549 | − | 36.6122i | −0.747992 | − | 1.46802i | ||||
\(623\) | −3.37435 | + | 21.3048i | −0.135190 | + | 0.853559i | ||||
\(624\) | −0.693183 | − | 0.128610i | −0.0277495 | − | 0.00514850i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 33.5846i | 1.34231i | ||||||||
\(627\) | 11.3484 | − | 13.1136i | 0.453212 | − | 0.523707i | ||||
\(628\) | 56.9376 | + | 56.9376i | 2.27206 | + | 2.27206i | ||||
\(629\) | −4.13772 | − | 12.7346i | −0.164982 | − | 0.507762i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.8897 | − | 10.0914i | 0.552939 | − | 0.401734i | −0.275929 | − | 0.961178i | \(-0.588985\pi\) |
0.828868 | + | 0.559444i | \(0.188985\pi\) | |||||||
\(632\) | −18.9500 | + | 9.65550i | −0.753790 | + | 0.384075i | ||||
\(633\) | −0.0929053 | − | 0.0713167i | −0.00369265 | − | 0.00283458i | ||||
\(634\) | −14.7918 | − | 20.3592i | −0.587457 | − | 0.808565i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 32.8957 | + | 34.6780i | 1.30440 | + | 1.37507i | ||||
\(637\) | 0.364298 | − | 0.364298i | 0.0144340 | − | 0.0144340i | ||||
\(638\) | −0.530147 | + | 0.904995i | −0.0209887 | + | 0.0358291i | ||||
\(639\) | −4.53166 | + | 5.59181i | −0.179270 | + | 0.221209i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.94225 | − | 4.04965i | 0.116212 | − | 0.159952i | −0.746948 | − | 0.664882i | \(-0.768482\pi\) |
0.863160 | + | 0.504930i | \(0.168482\pi\) | |||||||
\(642\) | 34.5557 | − | 10.2287i | 1.36380 | − | 0.403696i | ||||
\(643\) | 30.5223 | − | 15.5519i | 1.20368 | − | 0.613307i | 0.267071 | − | 0.963677i | \(-0.413944\pi\) |
0.936611 | + | 0.350370i | \(0.113944\pi\) | |||||||
\(644\) | 18.8265 | − | 57.9421i | 0.741869 | − | 2.28324i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 34.1054 | + | 24.7790i | 1.34186 | + | 0.974918i | ||||
\(647\) | 13.3415 | − | 26.1841i | 0.524507 | − | 1.02940i | −0.465053 | − | 0.885283i | \(-0.653965\pi\) |
0.989560 | − | 0.144120i | \(-0.0460352\pi\) | |||||||
\(648\) | 25.1539 | + | 16.3622i | 0.988138 | + | 0.642769i | ||||
\(649\) | −41.6598 | − | 2.44718i | −1.63529 | − | 0.0960602i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.37703 | − | 7.94650i | 0.328322 | − | 0.311448i | ||||
\(652\) | −7.08906 | + | 1.12280i | −0.277629 | + | 0.0439721i | ||||
\(653\) | 2.94202 | − | 18.5752i | 0.115130 | − | 0.726903i | −0.860820 | − | 0.508910i | \(-0.830049\pi\) |
0.975950 | − | 0.217994i | \(-0.0699512\pi\) | |||||||
\(654\) | 38.0111 | − | 4.99694i | 1.48635 | − | 0.195396i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.10799 | + | 8.40692i | 0.238477 | + | 0.328235i | ||||
\(657\) | 2.56502 | − | 4.43887i | 0.100071 | − | 0.173177i | ||||
\(658\) | −1.46143 | + | 2.86822i | −0.0569725 | + | 0.111815i | ||||
\(659\) | 26.1551 | 1.01886 | 0.509429 | − | 0.860513i | \(-0.329857\pi\) | ||||
0.509429 | + | 0.860513i | \(0.329857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.51293 | −0.136637 | −0.0683185 | − | 0.997664i | \(-0.521763\pi\) | ||||
−0.0683185 | + | 0.997664i | \(0.521763\pi\) | |||||||
\(662\) | −1.88294 | + | 3.69549i | −0.0731827 | + | 0.143629i | ||||
\(663\) | 2.63334 | + | 3.83309i | 0.102271 | + | 0.148865i | ||||
\(664\) | −10.7522 | − | 14.7991i | −0.417266 | − | 0.574318i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −13.1050 | + | 8.50345i | −0.507810 | + | 0.329502i | ||||
\(667\) | −0.155860 | + | 0.984060i | −0.00603491 | + | 0.0381029i | ||||
\(668\) | −9.34392 | + | 1.47993i | −0.361527 | + | 0.0572603i | ||||
\(669\) | 21.1933 | + | 22.3416i | 0.819381 | + | 0.863775i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.73342 | + | 4.31253i | −0.259941 | + | 0.166483i | ||||
\(672\) | −6.36811 | + | 17.9722i | −0.245655 | + | 0.693292i | ||||
\(673\) | 9.48021 | − | 18.6060i | 0.365435 | − | 0.717207i | −0.632939 | − | 0.774201i | \(-0.718152\pi\) |
0.998374 | + | 0.0569946i | \(0.0181518\pi\) | |||||||
\(674\) | −3.75284 | − | 2.72660i | −0.144554 | − | 0.105025i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.5691 | − | 41.7615i | 0.521890 | − | 1.60621i | ||||
\(677\) | 26.0529 | − | 13.2746i | 1.00130 | − | 0.510185i | 0.125101 | − | 0.992144i | \(-0.460074\pi\) |
0.876194 | + | 0.481959i | \(0.160074\pi\) | |||||||
\(678\) | −18.2851 | − | 61.7723i | −0.702234 | − | 2.37235i | ||||
\(679\) | −5.35865 | + | 7.37555i | −0.205646 | + | 0.283048i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.7402 | − | 14.1784i | 1.13965 | − | 0.543319i | ||||
\(682\) | 14.1539 | + | 15.9205i | 0.541979 | + | 0.609627i | ||||
\(683\) | −27.5049 | + | 27.5049i | −1.05245 | + | 1.05245i | −0.0539001 | + | 0.998546i | \(0.517165\pi\) |
−0.998546 | + | 0.0539001i | \(0.982835\pi\) | |||||||
\(684\) | 11.1458 | − | 29.0030i | 0.426171 | − | 1.10896i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.0010 | + | 37.1637i | 1.03090 | + | 1.41892i | ||||
\(687\) | −6.31181 | + | 8.22249i | −0.240811 | + | 0.313707i | ||||
\(688\) | −0.102172 | + | 0.0520594i | −0.00389528 | + | 0.00198474i | ||||
\(689\) | 2.91591 | − | 2.11853i | 0.111087 | − | 0.0807097i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.64332 | + | 11.2130i | 0.138599 | + | 0.426563i | 0.996132 | − | 0.0878650i | \(-0.0280044\pi\) |
−0.857534 | + | 0.514428i | \(0.828004\pi\) | |||||||
\(692\) | 14.7051 | + | 14.7051i | 0.559005 | + | 0.559005i | ||||
\(693\) | 8.47389 | + | 22.5247i | 0.321896 | + | 0.855643i | ||||
\(694\) | 63.0873i | 2.39476i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.142958 | + | 0.770516i | −0.00541879 | + | 0.0292063i | ||||
\(697\) | 10.7229 | − | 67.7020i | 0.406161 | − | 2.56440i | ||||
\(698\) | −5.59212 | − | 10.9752i | −0.211665 | − | 0.415416i | ||||
\(699\) | 25.4645 | − | 3.34755i | 0.963154 | − | 0.126616i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.34624 | − | 5.98209i | 0.164155 | − | 0.225940i | −0.719013 | − | 0.694997i | \(-0.755406\pi\) |
0.883168 | + | 0.469056i | \(0.155406\pi\) | |||||||
\(702\) | 3.52609 | − | 4.12377i | 0.133084 | − | 0.155642i | ||||
\(703\) | 4.77005 | + | 4.77005i | 0.179906 | + | 0.179906i | ||||
\(704\) | −38.3724 | − | 15.0085i | −1.44621 | − | 0.565653i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.90030 | + | 15.0816i | 0.184425 | + | 0.567603i | ||||
\(707\) | −5.39874 | − | 34.0863i | −0.203040 | − | 1.28195i | ||||
\(708\) | −71.6929 | + | 21.2216i | −2.69438 | + | 0.797558i | ||||
\(709\) | −20.7627 | − | 6.74621i | −0.779759 | − | 0.253359i | −0.108022 | − | 0.994149i | \(-0.534452\pi\) |
−0.671737 | + | 0.740789i | \(0.734452\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.00877 | − | 19.1100i | 0.0378318 | − | 0.716681i | ||||
\(712\) | −29.3682 | + | 4.65146i | −1.10062 | + | 0.174321i | ||||
\(713\) | 18.0302 | + | 9.18687i | 0.675238 | + | 0.344051i | ||||
\(714\) | −52.8070 | + | 25.1754i | −1.97625 | + | 0.942164i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 14.5042i | 0.542047i | ||||||||
\(717\) | 28.3788 | + | 0.748503i | 1.05983 | + | 0.0279534i | ||||
\(718\) | −2.39743 | − | 15.1368i | −0.0894714 | − | 0.564900i | ||||
\(719\) | −28.9990 | + | 21.0690i | −1.08148 | + | 0.785742i | −0.977941 | − | 0.208884i | \(-0.933017\pi\) |
−0.103540 | + | 0.994625i | \(0.533017\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.19070 | + | 9.81996i | −0.118828 | + | 0.365714i | ||||
\(722\) | 22.7553 | + | 3.60408i | 0.846863 | + | 0.134130i | ||||
\(723\) | 23.7860 | − | 16.3410i | 0.884610 | − | 0.607729i | ||||
\(724\) | −38.5552 | + | 12.5273i | −1.43289 | + | 0.465575i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −42.0398 | + | 14.2833i | −1.56024 | + | 0.530102i | ||||
\(727\) | −8.71680 | + | 8.71680i | −0.323288 | + | 0.323288i | −0.850027 | − | 0.526739i | \(-0.823415\pi\) |
0.526739 | + | 0.850027i | \(0.323415\pi\) | |||||||
\(728\) | −3.21959 | − | 1.64046i | −0.119326 | − | 0.0607996i | ||||
\(729\) | −24.0711 | + | 12.2304i | −0.891522 | + | 0.452978i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.719384 | + | 0.233742i | 0.0266074 | + | 0.00864526i | ||||
\(732\) | −8.72328 | + | 11.3639i | −0.322422 | + | 0.420023i | ||||
\(733\) | −11.9816 | − | 1.89770i | −0.442552 | − | 0.0700933i | −0.0688176 | − | 0.997629i | \(-0.521923\pi\) |
−0.373734 | + | 0.927536i | \(0.621923\pi\) | |||||||
\(734\) | 2.83389 | + | 2.05894i | 0.104601 | + | 0.0759970i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −33.4160 | −1.23173 | ||||||||
\(737\) | 10.7790 | − | 1.06415i | 0.397051 | − | 0.0391984i | ||||
\(738\) | −79.5379 | + | 8.32932i | −2.92783 | + | 0.306607i | ||||
\(739\) | 6.57866 | − | 2.13754i | 0.242000 | − | 0.0786306i | −0.185506 | − | 0.982643i | \(-0.559392\pi\) |
0.427506 | + | 0.904013i | \(0.359392\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.05879 | − | 1.11834i | −0.0756315 | − | 0.0410831i | ||||
\(742\) | 20.5839 | + | 40.3983i | 0.755660 | + | 1.48307i | ||||
\(743\) | 17.3378 | + | 34.0274i | 0.636064 | + | 1.24835i | 0.953879 | + | 0.300192i | \(0.0970509\pi\) |
−0.317815 | + | 0.948153i | \(0.602949\pi\) | |||||||
\(744\) | 13.9863 | + | 7.59738i | 0.512763 | + | 0.278534i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −23.7655 | + | 7.72187i | −0.870116 | + | 0.282718i | ||||
\(747\) | 16.3699 | − | 1.71428i | 0.598944 | − | 0.0627223i | ||||
\(748\) | −27.3383 | − | 62.4614i | −0.999588 | − | 2.28382i | ||||
\(749\) | 21.5950 | 0.789065 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8683 | − | 7.89626i | −0.396589 | − | 0.288139i | 0.371561 | − | 0.928408i | \(-0.378823\pi\) |
−0.768150 | + | 0.640270i | \(0.778823\pi\) | |||||||
\(752\) | −0.512418 | − | 0.0811590i | −0.0186860 | − | 0.00295956i | ||||
\(753\) | −17.1778 | + | 22.3778i | −0.625995 | + | 0.815493i | ||||
\(754\) | 0.134763 | + | 0.0437870i | 0.00490777 | + | 0.00159463i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 27.9839 | + | 32.8027i | 1.01776 | + | 1.19302i | ||||
\(757\) | −18.9821 | − | 9.67185i | −0.689915 | − | 0.351529i | 0.0736284 | − | 0.997286i | \(-0.476542\pi\) |
−0.763543 | + | 0.645756i | \(0.776542\pi\) | |||||||
\(758\) | −3.65487 | + | 3.65487i | −0.132751 | + | 0.132751i | ||||
\(759\) | −32.2490 | + | 27.1825i | −1.17056 | + | 0.986661i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.2126 | − | 6.89240i | 0.768957 | − | 0.249849i | 0.101839 | − | 0.994801i | \(-0.467527\pi\) |
0.667118 | + | 0.744952i | \(0.267527\pi\) | |||||||
\(762\) | −61.0979 | + | 41.9744i | −2.21334 | + | 1.52057i | ||||
\(763\) | 22.6907 | + | 3.59385i | 0.821457 | + | 0.130106i | ||||
\(764\) | −25.5283 | + | 78.5681i | −0.923582 | + | 2.84249i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27.6464 | − | 20.0863i | 0.998906 | − | 0.725748i | ||||
\(767\) | 0.881962 | + | 5.56849i | 0.0318458 | + | 0.201067i | ||||
\(768\) | −37.0666 | − | 0.977646i | −1.33753 | − | 0.0352778i | ||||
\(769\) | 15.4925i | 0.558675i | 0.960193 | + | 0.279337i | \(0.0901148\pi\) | ||||
−0.960193 | + | 0.279337i | \(0.909885\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.78935 | + | 4.66700i | −0.352555 | + | 0.168078i | ||||
\(772\) | 61.8141 | + | 31.4959i | 2.22474 | + | 1.13356i | ||||
\(773\) | 53.9386 | − | 8.54304i | 1.94004 | − | 0.307272i | 0.940561 | − | 0.339625i | \(-0.110300\pi\) |
0.999477 | + | 0.0323528i | \(0.0103000\pi\) | |||||||
\(774\) | 0.0465203 | − | 0.881274i | 0.00167214 | − | 0.0316768i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −11.9521 | − | 3.88346i | −0.429054 | − | 0.139408i | ||||
\(777\) | −8.97629 | + | 2.65705i | −0.322023 | + | 0.0953212i | ||||
\(778\) | 3.72048 | + | 23.4902i | 0.133386 | + | 0.842163i | ||||
\(779\) | 10.6714 | + | 32.8433i | 0.382344 | + | 1.17673i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.29155 | − | 6.70067i | −0.153564 | − | 0.239769i | ||||
\(782\) | −72.4969 | − | 72.4969i | −2.59248 | − | 2.59248i | ||||
\(783\) | −0.535922 | − | 0.458247i | −0.0191523 | − | 0.0163764i | ||||
\(784\) | −0.613944 | + | 0.845021i | −0.0219266 | + | 0.0301793i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −32.5793 | + | 4.28287i | −1.16206 | + | 0.152765i | ||||
\(787\) | −10.5992 | − | 20.8021i | −0.377821 | − | 0.741516i | 0.621294 | − | 0.783578i | \(-0.286607\pi\) |
−0.999115 | + | 0.0420620i | \(0.986607\pi\) | |||||||
\(788\) | 5.53706 | − | 34.9596i | 0.197249 | − | 1.24538i | ||||
\(789\) | 0.0188088 | − | 0.101376i | 0.000669610 | − | 0.00360908i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 38.6037i | − | 1.37259i | ||||||
\(792\) | −25.9205 | + | 20.7043i | −0.921044 | + | 0.735694i | ||||
\(793\) | 0.763859 | + | 0.763859i | 0.0271254 | + | 0.0271254i | ||||
\(794\) | 2.21922 | + | 6.83006i | 0.0787573 | + | 0.242390i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 41.7034 | − | 30.2993i | 1.47814 | − | 1.07393i | ||||
\(797\) | 11.0470 | − | 5.62875i | 0.391306 | − | 0.199380i | −0.247257 | − | 0.968950i | \(-0.579529\pi\) |
0.638563 | + | 0.769570i | \(0.279529\pi\) | |||||||
\(798\) | 17.9464 | − | 23.3790i | 0.635295 | − | 0.827608i | ||||
\(799\) | 2.01152 | + | 2.76862i | 0.0711626 | + | 0.0979469i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.59734 | − | 24.9737i | 0.339105 | − | 0.882401i | ||||
\(802\) | −33.2979 | + | 33.2979i | −1.17579 | + | 1.17579i | ||||
\(803\) | 3.76580 | + | 4.23584i | 0.132892 | + | 0.149479i | ||||
\(804\) | 17.5171 | − | 8.35118i | 0.617782 | − | 0.294523i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.69161 | − | 2.32831i | 0.0595845 | − | 0.0820111i | ||||
\(807\) | −1.82571 | − | 6.16779i | −0.0642682 | − | 0.217117i | ||||
\(808\) | 42.3877 | − | 21.5976i | 1.49120 | − | 0.759802i | ||||
\(809\) | −1.24636 | + | 3.83591i | −0.0438198 | + | 0.134864i | −0.970573 | − | 0.240808i | \(-0.922588\pi\) |
0.926753 | + | 0.375671i | \(0.122588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.6248 | − | 9.89899i | −0.478431 | − | 0.347601i | 0.322287 | − | 0.946642i | \(-0.395548\pi\) |
−0.800718 | + | 0.599041i | \(0.795548\pi\) | |||||||
\(812\) | −0.511214 | + | 1.00331i | −0.0179401 | + | 0.0352094i | ||||
\(813\) | 7.66095 | − | 21.6209i | 0.268681 | − | 0.758276i | ||||
\(814\) | −4.36460 | − | 16.7103i | −0.152979 | − | 0.585696i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.48877 | − | 6.84033i | −0.227152 | − | 0.239459i | ||||
\(817\) | −0.376386 | + | 0.0596136i | −0.0131681 | + | 0.00208562i | ||||
\(818\) | −6.86339 | + | 43.3337i | −0.239973 | + | 1.51513i | ||||
\(819\) | 2.72743 | − | 1.76975i | 0.0953042 | − | 0.0618400i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.8846 | + | 21.8632i | 0.554375 | + | 0.763032i | 0.990598 | − | 0.136807i | \(-0.0436839\pi\) |
−0.436222 | + | 0.899839i | \(0.643684\pi\) | |||||||
\(822\) | 5.06951 | + | 7.37918i | 0.176820 | + | 0.257378i | ||||
\(823\) | 21.4431 | − | 42.0844i | 0.747458 | − | 1.46697i | −0.132130 | − | 0.991232i | \(-0.542182\pi\) |
0.879588 | − | 0.475736i | \(-0.157818\pi\) | |||||||
\(824\) | −14.2332 | −0.495837 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −70.9223 | −2.46770 | ||||||||
\(827\) | −22.6800 | + | 44.5120i | −0.788661 | + | 1.54783i | 0.0471960 | + | 0.998886i | \(0.484971\pi\) |
−0.835857 | + | 0.548948i | \(0.815029\pi\) | |||||||
\(828\) | −37.8075 | + | 65.4273i | −1.31390 | + | 2.27376i | ||||
\(829\) | −19.9942 | − | 27.5196i | −0.694426 | − | 0.955795i | −0.999993 | − | 0.00362489i | \(-0.998846\pi\) |
0.305567 | − | 0.952170i | \(-0.401154\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.3112 | − | 2.01280i | 0.531138 | − | 0.0698233i | ||||
\(832\) | −0.870793 | + | 5.49797i | −0.0301893 | + | 0.190608i | ||||
\(833\) | 6.80506 | − | 1.07782i | 0.235781 | − | 0.0373441i | ||||
\(834\) | −43.9407 | + | 41.6824i | −1.52154 | + | 1.44334i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.5581 | + | 21.7855i | 0.918532 | + | 0.753466i | ||||
\(837\) | −12.2153 | + | 7.47598i | −0.422221 | + | 0.258408i | ||||
\(838\) | −10.3493 | + | 20.3116i | −0.357510 | + | 0.701653i | ||||
\(839\) | 5.55047 | + | 4.03266i | 0.191624 | + | 0.139223i | 0.679460 | − | 0.733712i | \(-0.262214\pi\) |
−0.487837 | + | 0.872935i | \(0.662214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.95580 | + | 27.5631i | −0.308821 | + | 0.950453i | ||||
\(842\) | −50.0242 | + | 25.4886i | −1.72395 | + | 0.878394i | ||||
\(843\) | 21.5026 | − | 6.36493i | 0.740589 | − | 0.219220i | ||||
\(844\) | 0.136358 | − | 0.187681i | 0.00469364 | − | 0.00646024i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.51387 | − | 3.10196i | 0.0864285 | − | 0.106648i | ||||
\(847\) | −26.5849 | + | 1.05678i | −0.913468 | + | 0.0363115i | ||||
\(848\) | −5.16701 | + | 5.16701i | −0.177436 | + | 0.177436i | ||||
\(849\) | 6.16871 | + | 6.50293i | 0.211709 | + | 0.223180i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.64329 | − | 13.2728i | −0.330568 | − | 0.454987i | ||||
\(852\) | −11.3087 | − | 8.68085i | −0.387429 | − | 0.297401i | ||||
\(853\) | −43.5974 | + | 22.2140i | −1.49275 | + | 0.760592i | −0.994329 | − | 0.106345i | \(-0.966085\pi\) |
−0.498417 | + | 0.866937i | \(0.666085\pi\) | |||||||
\(854\) | −10.9939 | + | 7.98752i | −0.376203 | + | 0.273327i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.19889 | + | 28.3113i | 0.314412 | + | 0.967660i | ||||
\(857\) | 4.13097 | + | 4.13097i | 0.141111 | + | 0.141111i | 0.774134 | − | 0.633022i | \(-0.218186\pi\) |
−0.633022 | + | 0.774134i | \(0.718186\pi\) | |||||||
\(858\) | 3.10082 | + | 5.13475i | 0.105860 | + | 0.175297i | ||||
\(859\) | 23.1741i | 0.790689i | 0.918533 | + | 0.395345i | \(0.129375\pi\) | ||||
−0.918533 | + | 0.395345i | \(0.870625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −47.1183 | − | 8.74208i | −1.60579 | − | 0.297929i | ||||
\(862\) | 0.643807 | − | 4.06484i | 0.0219281 | − | 0.138449i | ||||
\(863\) | 16.3796 | + | 32.1468i | 0.557568 | + | 1.09429i | 0.982009 | + | 0.188833i | \(0.0604705\pi\) |
−0.424441 | + | 0.905455i | \(0.639530\pi\) | |||||||
\(864\) | 12.3682 | − | 20.1574i | 0.420775 | − | 0.685767i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 49.2064 | − | 67.7268i | 1.67210 | − | 2.30145i | ||||
\(867\) | −0.863434 | + | 32.7364i | −0.0293238 | + | 1.11178i | ||||
\(868\) | 16.1719 | + | 16.1719i | 0.548909 | + | 0.548909i | ||||
\(869\) | 19.7028 | + | 7.70631i | 0.668373 | + | 0.261419i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.452190 | − | 1.39170i | −0.0153219 | − | 0.0471559i | ||||
\(872\) | 4.95403 | + | 31.2785i | 0.167765 | + | 1.05923i | ||||
\(873\) | 8.40609 | − | 7.56311i | 0.284503 | − | 0.255973i | ||||
\(874\) | 49.1247 | + | 15.9616i | 1.66167 | + | 0.539908i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 8.92310 | + | 4.84704i | 0.301484 | + | 0.163766i | ||||
\(877\) | −25.8384 | + | 4.09240i | −0.872500 | + | 0.138190i | −0.576598 | − | 0.817028i | \(-0.695620\pi\) |
−0.295902 | + | 0.955218i | \(0.595620\pi\) | |||||||
\(878\) | −40.9834 | − | 20.8821i | −1.38312 | − | 0.704736i | ||||
\(879\) | −11.7691 | − | 24.6864i | −0.396961 | − | 0.832652i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 38.3802i | − | 1.29306i | −0.762888 | − | 0.646530i | \(-0.776219\pi\) | ||
0.762888 | − | 0.646530i | \(-0.223781\pi\) | |||||||
\(882\) | −3.26676 | − | 7.34474i | −0.109997 | − | 0.247310i | ||||
\(883\) | 3.91659 | + | 24.7284i | 0.131804 | + | 0.832175i | 0.961669 | + | 0.274212i | \(0.0884170\pi\) |
−0.829866 | + | 0.557963i | \(0.811583\pi\) | |||||||
\(884\) | −7.45215 | + | 5.41431i | −0.250643 | + | 0.182103i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.94606 | − | 12.1447i | 0.132570 | − | 0.408010i | ||||
\(887\) | −11.5562 | − | 1.83033i | −0.388021 | − | 0.0614564i | −0.0406235 | − | 0.999175i | \(-0.512934\pi\) |
−0.347397 | + | 0.937718i | \(0.612934\pi\) | |||||||
\(888\) | −7.30708 | − | 10.6362i | −0.245209 | − | 0.356927i | ||||
\(889\) | −42.2453 | + | 13.7263i | −1.41686 | + | 0.460366i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.46089 | − | 29.5144i | −0.149446 | − | 0.988770i | ||||
\(892\) | −43.1304 | + | 43.1304i | −1.44411 | + | 1.44411i | ||||
\(893\) | −1.53619 | − | 0.782730i | −0.0514068 | − | 0.0261931i | ||||
\(894\) | 56.8023 | + | 10.5388i | 1.89975 | + | 0.352470i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −45.6577 | − | 14.8351i | −1.52532 | − | 0.495606i | ||||
\(897\) | 4.51991 | + | 3.46961i | 0.150915 | + | 0.115847i | ||||
\(898\) | −89.8111 | − | 14.2247i | −2.99704 | − | 0.474684i | ||||
\(899\) | −0.302585 | − | 0.219841i | −0.0100918 | − | 0.00733210i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.2011 | 1.60581 | ||||||||
\(902\) | 18.9279 | − | 86.3635i | 0.630230 | − | 2.87559i | ||||
\(903\) | 0.176619 | − | 0.498458i | 0.00587753 | − | 0.0165876i | ||||
\(904\) | 50.6098 | − | 16.4441i | 1.68326 | − | 0.546923i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 19.1296 | − | 35.2164i | 0.635537 | − | 1.16999i | ||||
\(907\) | 7.08553 | + | 13.9061i | 0.235271 | + | 0.461745i | 0.978211 | − | 0.207612i | \(-0.0665693\pi\) |
−0.742940 | + | 0.669358i | \(0.766569\pi\) | |||||||
\(908\) | 29.6270 | + | 58.1463i | 0.983208 | + | 1.92965i | ||||
\(909\) | −2.25643 | + | 42.7456i | −0.0748412 | + | 1.41778i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.91910 | + | 1.92323i | −0.196109 | + | 0.0637195i | −0.405425 | − | 0.914129i | \(-0.632876\pi\) |
0.209316 | + | 0.977848i | \(0.432876\pi\) | |||||||
\(912\) | 4.47726 | + | 1.58644i | 0.148257 | + | 0.0525322i | ||||
\(913\) | −3.89561 | + | 17.7747i | −0.128926 | + | 0.588257i | ||||
\(914\) | 4.11385 | 0.136074 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.6105 | − | 12.0682i | −0.548826 | − | 0.398745i | ||||
\(917\) | −19.4481 | − | 3.08028i | −0.642234 | − | 0.101720i | ||||
\(918\) | 70.5652 | − | 16.8988i | 2.32900 | − | 0.557744i | ||||
\(919\) | −46.2031 | − | 15.0123i | −1.52410 | − | 0.495210i | −0.577163 | − | 0.816629i | \(-0.695840\pi\) |
−0.946937 | + | 0.321419i | \(0.895840\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.43026 | + | 13.0987i | −0.0800799 | + | 0.431616i | ||||
\(922\) | 42.4618 | + | 21.6354i | 1.39841 | + | 0.712523i | ||||
\(923\) | −0.760144 | + | 0.760144i | −0.0250204 | + | 0.0250204i | ||||
\(924\) | −44.1573 | + | 17.9550i | −1.45267 | + | 0.590675i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −69.2129 | + | 22.4886i | −2.27448 | + | 0.739023i | ||||
\(927\) | 6.40758 | − | 11.0886i | 0.210453 | − | 0.364196i | ||||
\(928\) | 0.610018 | + | 0.0966173i | 0.0200248 | + | 0.00317162i | ||||
\(929\) | −1.60697 | + | 4.94575i | −0.0527230 | + | 0.162265i | −0.973951 | − | 0.226758i | \(-0.927187\pi\) |
0.921228 | + | 0.389023i | \(0.127187\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.80820 | + | 2.04028i | −0.0920351 | + | 0.0668674i | ||||
\(932\) | 7.95816 | + | 50.2458i | 0.260678 | + | 1.64586i | ||||
\(933\) | −0.805240 | + | 30.5300i | −0.0263624 | + | 0.999506i | ||||
\(934\) | 35.3965i | 1.15821i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.48197 | + | 2.82183i | 0.113812 | + | 0.0922343i | ||||
\(937\) | −3.49458 | − | 1.78058i | −0.114163 | − | 0.0581690i | 0.395976 | − | 0.918261i | \(-0.370406\pi\) |
−0.510139 | + | 0.860092i | \(0.670406\pi\) | |||||||
\(938\) | 18.1812 | − | 2.87963i | 0.593639 | − | 0.0940231i | ||||
\(939\) | 11.9148 | − | 21.9344i | 0.388825 | − | 0.715802i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.1878 | + | 17.6067i | 1.76647 | + | 0.573961i | 0.997838 | − | 0.0657275i | \(-0.0209368\pi\) |
0.768634 | + | 0.639689i | \(0.220937\pi\) | |||||||
\(942\) | −26.8894 | − | 90.8404i | −0.876105 | − | 2.95974i | ||||
\(943\) | −13.1384 | − | 82.9524i | −0.427844 | − | 2.70130i | ||||
\(944\) | −3.53214 | − | 10.8708i | −0.114961 | − | 0.353814i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.908614 | + | 0.355384i | 0.0295416 | + | 0.0115545i | ||||
\(947\) | 22.0350 | + | 22.0350i | 0.716041 | + | 0.716041i | 0.967792 | − | 0.251751i | \(-0.0810063\pi\) |
−0.251751 | + | 0.967792i | \(0.581006\pi\) | |||||||
\(948\) | 37.8912 | + | 0.999397i | 1.23065 | + | 0.0324589i | ||||
\(949\) | 0.450074 | − | 0.619473i | 0.0146100 | − | 0.0201089i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.43785 | + | 18.5444i | 0.0790526 | + | 0.601344i | ||||
\(952\) | −21.9384 | − | 43.0566i | −0.711029 | − | 1.39547i | ||||
\(953\) | −7.15190 | + | 45.1553i | −0.231673 | + | 1.46272i | 0.547969 | + | 0.836499i | \(0.315401\pi\) |
−0.779642 | + | 0.626226i | \(0.784599\pi\) | |||||||
\(954\) | −14.5345 | − | 54.3257i | −0.470571 | − | 1.75886i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 56.2303i | 1.81862i | ||||||||
\(957\) | 0.667308 | − | 0.402980i | 0.0215710 | − | 0.0130265i | ||||
\(958\) | 62.2780 | + | 62.2780i | 2.01211 | + | 2.01211i | ||||
\(959\) | 1.65782 | + | 5.10223i | 0.0535336 | + | 0.164760i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.9339 | − | 13.7563i | 0.610771 | − | 0.443751i | ||||
\(962\) | −2.07897 | + | 1.05929i | −0.0670288 | + | 0.0341529i | ||||
\(963\) | −26.1975 | − | 5.57881i | −0.844201 | − | 0.179775i | ||||
\(964\) | 33.5981 | + | 46.2438i | 1.08212 | + | 1.48941i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −52.0034 | + | 49.3306i | −1.67318 | + | 1.58719i | ||||
\(967\) | −28.3939 | + | 28.3939i | −0.913085 | + | 0.913085i | −0.996514 | − | 0.0834284i | \(-0.973413\pi\) |
0.0834284 | + | 0.996514i | \(0.473413\pi\) | |||||||
\(968\) | −12.7099 | − | 34.4029i | −0.408512 | − | 1.10575i | ||||
\(969\) | −13.4837 | − | 28.2830i | −0.433159 | − | 0.908580i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.2400 | − | 22.3525i | 0.521167 | − | 0.717325i | −0.464585 | − | 0.885529i | \(-0.653797\pi\) |
0.985752 | + | 0.168203i | \(0.0537965\pi\) | |||||||
\(972\) | −25.4738 | − | 47.0230i | −0.817073 | − | 1.50826i | ||||
\(973\) | −32.3373 | + | 16.4767i | −1.03669 | + | 0.528218i | ||||
\(974\) | 12.9012 | − | 39.7060i | 0.413383 | − | 1.27226i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.77184 | − | 1.28731i | −0.0567151 | − | 0.0412059i | ||||
\(977\) | 7.74253 | − | 15.1956i | 0.247705 | − | 0.486149i | −0.733356 | − | 0.679844i | \(-0.762047\pi\) |
0.981062 | + | 0.193695i | \(0.0620473\pi\) | |||||||
\(978\) | 7.95958 | + | 2.82033i | 0.254519 | + | 0.0901842i | ||||
\(979\) | 22.8684 | + | 18.7588i | 0.730878 | + | 0.599534i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −26.5982 | − | 10.2216i | −0.849214 | − | 0.326352i | ||||
\(982\) | 48.5608 | − | 7.69127i | 1.54964 | − | 0.245438i | ||||
\(983\) | 4.00807 | − | 25.3059i | 0.127837 | − | 0.807134i | −0.837559 | − | 0.546347i | \(-0.816018\pi\) |
0.965396 | − | 0.260787i | \(-0.0839820\pi\) | |||||||
\(984\) | −8.61015 | − | 65.4964i | −0.274482 | − | 2.08795i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.11384 | + | 1.53307i | 0.0354718 | + | 0.0488227i | ||||
\(987\) | 1.97203 | − | 1.35479i | 0.0627704 | − | 0.0431234i | ||||
\(988\) | 2.10683 | − | 4.13489i | 0.0670272 | − | 0.131548i | ||||
\(989\) | 0.926791 | 0.0294702 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 55.5676 | 1.76516 | 0.882581 | − | 0.470160i | \(-0.155804\pi\) | ||||
0.882581 | + | 0.470160i | \(0.155804\pi\) | |||||||
\(992\) | 5.69493 | − | 11.1769i | 0.180814 | − | 0.354868i | ||||
\(993\) | 2.54081 | − | 1.74554i | 0.0806302 | − | 0.0553932i | ||||
\(994\) | −7.94867 | − | 10.9404i | −0.252117 | − | 0.347009i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 4.24926 | + | 32.3236i | 0.134643 | + | 1.02421i | ||||
\(997\) | 5.04903 | − | 31.8783i | 0.159904 | − | 1.00960i | −0.768992 | − | 0.639258i | \(-0.779242\pi\) |
0.928897 | − | 0.370339i | \(-0.120758\pi\) | |||||||
\(998\) | 86.4724 | − | 13.6959i | 2.73724 | − | 0.433536i | ||||
\(999\) | 11.5758 | − | 0.904418i | 0.366241 | − | 0.0286145i |
(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 | 825.2.ct.b.368.19 | 160 | ||
3.2 | odd | 2 | inner | 825.2.ct.b.368.2 | 160 | ||
5.2 | odd | 4 | inner | 825.2.ct.b.632.19 | 160 | ||
5.3 | odd | 4 | 165.2.v.a.137.2 | yes | 160 | ||
5.4 | even | 2 | 165.2.v.a.38.2 | ✓ | 160 | ||
11.9 | even | 5 | inner | 825.2.ct.b.218.2 | 160 | ||
15.2 | even | 4 | inner | 825.2.ct.b.632.2 | 160 | ||
15.8 | even | 4 | 165.2.v.a.137.19 | yes | 160 | ||
15.14 | odd | 2 | 165.2.v.a.38.19 | yes | 160 | ||
33.20 | odd | 10 | inner | 825.2.ct.b.218.19 | 160 | ||
55.9 | even | 10 | 165.2.v.a.53.19 | yes | 160 | ||
55.42 | odd | 20 | inner | 825.2.ct.b.482.2 | 160 | ||
55.53 | odd | 20 | 165.2.v.a.152.19 | yes | 160 | ||
165.53 | even | 20 | 165.2.v.a.152.2 | yes | 160 | ||
165.119 | odd | 10 | 165.2.v.a.53.2 | yes | 160 | ||
165.152 | even | 20 | inner | 825.2.ct.b.482.19 | 160 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.2.v.a.38.2 | ✓ | 160 | 5.4 | even | 2 | ||
165.2.v.a.38.19 | yes | 160 | 15.14 | odd | 2 | ||
165.2.v.a.53.2 | yes | 160 | 165.119 | odd | 10 | ||
165.2.v.a.53.19 | yes | 160 | 55.9 | even | 10 | ||
165.2.v.a.137.2 | yes | 160 | 5.3 | odd | 4 | ||
165.2.v.a.137.19 | yes | 160 | 15.8 | even | 4 | ||
165.2.v.a.152.2 | yes | 160 | 165.53 | even | 20 | ||
165.2.v.a.152.19 | yes | 160 | 55.53 | odd | 20 | ||
825.2.ct.b.218.2 | 160 | 11.9 | even | 5 | inner | ||
825.2.ct.b.218.19 | 160 | 33.20 | odd | 10 | inner | ||
825.2.ct.b.368.2 | 160 | 3.2 | odd | 2 | inner | ||
825.2.ct.b.368.19 | 160 | 1.1 | even | 1 | trivial | ||
825.2.ct.b.482.2 | 160 | 55.42 | odd | 20 | inner | ||
825.2.ct.b.482.19 | 160 | 165.152 | even | 20 | inner | ||
825.2.ct.b.632.2 | 160 | 15.2 | even | 4 | inner | ||
825.2.ct.b.632.19 | 160 | 5.2 | odd | 4 | inner |