Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [735,2,Mod(178,735)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(735, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("735.178");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 735 = 3 \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 735.v (of order \(12\), degree \(4\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.86900454856\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 472.7 | ||
Character | \(\chi\) | \(=\) | 735.472 |
Dual form | 735.2.v.b.313.7 |
$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).
\(n\) | \(346\) | \(442\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.602389 | − | 2.24814i | 0.425953 | − | 1.58968i | −0.335880 | − | 0.941905i | \(-0.609034\pi\) |
0.761833 | − | 0.647774i | \(-0.224300\pi\) | |||||||
\(3\) | −0.965926 | + | 0.258819i | −0.557678 | + | 0.149429i | ||||
\(4\) | −2.95923 | − | 1.70851i | −1.47962 | − | 0.854257i | ||||
\(5\) | 1.28534 | − | 1.82973i | 0.574820 | − | 0.818280i | ||||
\(6\) | 2.32745i | 0.950178i | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.33208 | + | 2.33208i | −0.824516 | + | 0.824516i | ||||
\(9\) | 0.866025 | − | 0.500000i | 0.288675 | − | 0.166667i | ||||
\(10\) | −3.33923 | − | 3.99183i | −1.05596 | − | 1.26233i | ||||
\(11\) | −1.76389 | + | 3.05515i | −0.531834 | + | 0.921163i | 0.467476 | + | 0.884006i | \(0.345163\pi\) |
−0.999309 | + | 0.0371569i | \(0.988170\pi\) | |||||||
\(12\) | 3.30060 | + | 0.884392i | 0.952800 | + | 0.255302i | ||||
\(13\) | −4.49057 | − | 4.49057i | −1.24546 | − | 1.24546i | −0.957704 | − | 0.287756i | \(-0.907091\pi\) |
−0.287756 | − | 0.957704i | \(-0.592909\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.767970 | + | 2.10005i | −0.198289 | + | 0.542231i | ||||
\(16\) | 0.421011 | + | 0.729213i | 0.105253 | + | 0.182303i | ||||
\(17\) | −0.481759 | − | 1.79795i | −0.116844 | − | 0.436066i | 0.882575 | − | 0.470172i | \(-0.155808\pi\) |
−0.999418 | + | 0.0341060i | \(0.989142\pi\) | |||||||
\(18\) | −0.602389 | − | 2.24814i | −0.141984 | − | 0.529893i | ||||
\(19\) | 0.0699116 | + | 0.121090i | 0.0160388 | + | 0.0277800i | 0.873933 | − | 0.486046i | \(-0.161561\pi\) |
−0.857895 | + | 0.513826i | \(0.828228\pi\) | |||||||
\(20\) | −6.92973 | + | 3.21858i | −1.54953 | + | 0.719697i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.80587 | + | 5.80587i | 1.23782 | + | 1.23782i | ||||
\(23\) | −3.72112 | − | 0.997072i | −0.775908 | − | 0.207904i | −0.150928 | − | 0.988545i | \(-0.548226\pi\) |
−0.624980 | + | 0.780641i | \(0.714893\pi\) | |||||||
\(24\) | 1.64903 | − | 2.85621i | 0.336607 | − | 0.583021i | ||||
\(25\) | −1.69582 | − | 4.70364i | −0.339164 | − | 0.940727i | ||||
\(26\) | −12.8005 | + | 7.39038i | −2.51039 | + | 1.44937i | ||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.01969i | − | 0.375047i | −0.982260 | − | 0.187524i | \(-0.939954\pi\) | ||
0.982260 | − | 0.187524i | \(-0.0600462\pi\) | |||||||
\(30\) | 4.25861 | + | 2.99156i | 0.777512 | + | 0.546181i | ||||
\(31\) | 4.56612 | + | 2.63625i | 0.820100 | + | 0.473485i | 0.850451 | − | 0.526054i | \(-0.176329\pi\) |
−0.0303510 | + | 0.999539i | \(0.509663\pi\) | |||||||
\(32\) | −4.47838 | + | 1.19998i | −0.791673 | + | 0.212128i | ||||
\(33\) | 0.913058 | − | 3.40758i | 0.158943 | − | 0.593183i | ||||
\(34\) | −4.33225 | −0.742975 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.41703 | −0.569505 | ||||||||
\(37\) | −1.50406 | + | 5.61323i | −0.247266 | + | 0.922810i | 0.724965 | + | 0.688786i | \(0.241856\pi\) |
−0.972231 | + | 0.234024i | \(0.924811\pi\) | |||||||
\(38\) | 0.314343 | − | 0.0842279i | 0.0509931 | − | 0.0136636i | ||||
\(39\) | 5.49980 | + | 3.17531i | 0.880673 | + | 0.508457i | ||||
\(40\) | 1.26957 | + | 7.26459i | 0.200737 | + | 1.14863i | ||||
\(41\) | − | 0.903323i | − | 0.141075i | −0.997509 | − | 0.0705377i | \(-0.977529\pi\) | ||
0.997509 | − | 0.0705377i | \(-0.0224715\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.38469 | − | 2.38469i | 0.363663 | − | 0.363663i | −0.501497 | − | 0.865159i | \(-0.667217\pi\) |
0.865159 | + | 0.501497i | \(0.167217\pi\) | |||||||
\(44\) | 10.4395 | − | 6.02727i | 1.57382 | − | 0.908645i | ||||
\(45\) | 0.198269 | − | 2.22726i | 0.0295562 | − | 0.332020i | ||||
\(46\) | −4.48312 | + | 7.76500i | −0.661001 | + | 1.14489i | ||||
\(47\) | 2.38655 | + | 0.639474i | 0.348114 | + | 0.0932768i | 0.428639 | − | 0.903476i | \(-0.358993\pi\) |
−0.0805254 | + | 0.996753i | \(0.525660\pi\) | |||||||
\(48\) | −0.595400 | − | 0.595400i | −0.0859386 | − | 0.0859386i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −11.5960 | + | 0.979037i | −1.63992 | + | 0.138457i | ||||
\(51\) | 0.930686 | + | 1.61200i | 0.130322 | + | 0.225725i | ||||
\(52\) | 5.61644 | + | 20.9608i | 0.778860 | + | 2.90675i | ||||
\(53\) | −0.726718 | − | 2.71215i | −0.0998224 | − | 0.372542i | 0.897884 | − | 0.440232i | \(-0.145104\pi\) |
−0.997706 | + | 0.0676898i | \(0.978437\pi\) | |||||||
\(54\) | 1.16373 | + | 2.01563i | 0.158363 | + | 0.274293i | ||||
\(55\) | 3.32291 | + | 7.15434i | 0.448061 | + | 0.964691i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0988699 | − | 0.0988699i | −0.0130956 | − | 0.0130956i | ||||
\(58\) | −4.54056 | − | 1.21664i | −0.596205 | − | 0.159753i | ||||
\(59\) | −3.15338 | + | 5.46181i | −0.410535 | + | 0.711067i | −0.994948 | − | 0.100389i | \(-0.967991\pi\) |
0.584414 | + | 0.811456i | \(0.301325\pi\) | |||||||
\(60\) | 5.86057 | − | 4.90246i | 0.756597 | − | 0.632904i | ||||
\(61\) | 8.69243 | − | 5.01858i | 1.11295 | − | 0.642563i | 0.173359 | − | 0.984859i | \(-0.444538\pi\) |
0.939592 | + | 0.342296i | \(0.111205\pi\) | |||||||
\(62\) | 8.67726 | − | 8.67726i | 1.10201 | − | 1.10201i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 12.4749i | 1.55937i | ||||||||
\(65\) | −13.9884 | + | 2.44464i | −1.73505 | + | 0.303220i | ||||
\(66\) | −7.11071 | − | 4.10537i | −0.875268 | − | 0.505336i | ||||
\(67\) | 10.3615 | − | 2.77634i | 1.26585 | − | 0.339184i | 0.437412 | − | 0.899261i | \(-0.355895\pi\) |
0.828441 | + | 0.560077i | \(0.189228\pi\) | |||||||
\(68\) | −1.64618 | + | 6.14364i | −0.199629 | + | 0.745025i | ||||
\(69\) | 3.85239 | 0.463773 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.09892 | −0.605130 | −0.302565 | − | 0.953129i | \(-0.597843\pi\) | ||||
−0.302565 | + | 0.953129i | \(0.597843\pi\) | |||||||
\(72\) | −0.853601 | + | 3.18568i | −0.100598 | + | 0.375436i | ||||
\(73\) | −9.04441 | + | 2.42344i | −1.05857 | + | 0.283643i | −0.745788 | − | 0.666183i | \(-0.767927\pi\) |
−0.312780 | + | 0.949826i | \(0.601260\pi\) | |||||||
\(74\) | 11.7133 | + | 6.76269i | 1.36165 | + | 0.786147i | ||||
\(75\) | 2.85543 | + | 4.10445i | 0.329717 | + | 0.473941i | ||||
\(76\) | − | 0.477780i | − | 0.0548051i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 10.4516 | − | 10.4516i | 1.18341 | − | 1.18341i | ||||
\(79\) | 7.30150 | − | 4.21552i | 0.821483 | − | 0.474284i | −0.0294445 | − | 0.999566i | \(-0.509374\pi\) |
0.850928 | + | 0.525283i | \(0.176040\pi\) | |||||||
\(80\) | 1.87540 | + | 0.166947i | 0.209677 | + | 0.0186652i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.03080 | − | 0.544151i | −0.224264 | − | 0.0600915i | ||||
\(83\) | −7.37852 | − | 7.37852i | −0.809898 | − | 0.809898i | 0.174720 | − | 0.984618i | \(-0.444098\pi\) |
−0.984618 | + | 0.174720i | \(0.944098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.90898 | − | 1.42948i | −0.423988 | − | 0.155049i | ||||
\(86\) | −3.92463 | − | 6.79765i | −0.423203 | − | 0.733010i | ||||
\(87\) | 0.522735 | + | 1.95087i | 0.0560431 | + | 0.209156i | ||||
\(88\) | −3.01132 | − | 11.2384i | −0.321008 | − | 1.19802i | ||||
\(89\) | −1.75399 | − | 3.03799i | −0.185922 | − | 0.322027i | 0.757965 | − | 0.652296i | \(-0.226194\pi\) |
−0.943887 | + | 0.330269i | \(0.892861\pi\) | |||||||
\(90\) | −4.88777 | − | 1.78741i | −0.515216 | − | 0.188410i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 9.30816 | + | 9.30816i | 0.970443 | + | 0.970443i | ||||
\(93\) | −5.09285 | − | 1.36462i | −0.528104 | − | 0.141505i | ||||
\(94\) | 2.87526 | − | 4.98010i | 0.296560 | − | 0.513658i | ||||
\(95\) | 0.311423 | + | 0.0277226i | 0.0319513 | + | 0.00284428i | ||||
\(96\) | 4.01520 | − | 2.31818i | 0.409800 | − | 0.236598i | ||||
\(97\) | 8.70237 | − | 8.70237i | 0.883592 | − | 0.883592i | −0.110306 | − | 0.993898i | \(-0.535183\pi\) |
0.993898 | + | 0.110306i | \(0.0351831\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.52778i | 0.354556i | ||||||||
\(100\) | −3.01789 | + | 16.8165i | −0.301789 | + | 1.68165i | ||||
\(101\) | 1.24483 | + | 0.718705i | 0.123866 | + | 0.0715138i | 0.560653 | − | 0.828051i | \(-0.310550\pi\) |
−0.436787 | + | 0.899565i | \(0.643884\pi\) | |||||||
\(102\) | 4.18463 | − | 1.12127i | 0.414341 | − | 0.111022i | ||||
\(103\) | 1.60502 | − | 5.99000i | 0.158147 | − | 0.590212i | −0.840668 | − | 0.541550i | \(-0.817838\pi\) |
0.998815 | − | 0.0486620i | \(-0.0154957\pi\) | |||||||
\(104\) | 20.9448 | 2.05380 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.53507 | −0.634742 | ||||||||
\(107\) | 4.64750 | − | 17.3447i | 0.449291 | − | 1.67678i | −0.255061 | − | 0.966925i | \(-0.582095\pi\) |
0.704352 | − | 0.709851i | \(-0.251238\pi\) | |||||||
\(108\) | 3.30060 | − | 0.884392i | 0.317600 | − | 0.0851006i | ||||
\(109\) | −11.0263 | − | 6.36604i | −1.05613 | − | 0.609756i | −0.131770 | − | 0.991280i | \(-0.542066\pi\) |
−0.924359 | + | 0.381524i | \(0.875399\pi\) | |||||||
\(110\) | 18.0857 | − | 3.16068i | 1.72440 | − | 0.301359i | ||||
\(111\) | − | 5.81124i | − | 0.551579i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.1631 | − | 11.1631i | 1.05013 | − | 1.05013i | 0.0514580 | − | 0.998675i | \(-0.483613\pi\) |
0.998675 | − | 0.0514580i | \(-0.0163868\pi\) | |||||||
\(114\) | −0.281832 | + | 0.162716i | −0.0263960 | + | 0.0152397i | ||||
\(115\) | −6.60727 | + | 5.52708i | −0.616131 | + | 0.515403i | ||||
\(116\) | −3.45067 | + | 5.97674i | −0.320387 | + | 0.554926i | ||||
\(117\) | −6.13423 | − | 1.64366i | −0.567110 | − | 0.151957i | ||||
\(118\) | 10.3794 | + | 10.3794i | 0.955499 | + | 0.955499i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.10653 | − | 6.68847i | −0.283586 | − | 0.610571i | ||||
\(121\) | −0.722631 | − | 1.25163i | −0.0656938 | − | 0.113785i | ||||
\(122\) | −6.04627 | − | 22.5650i | −0.547403 | − | 2.04294i | ||||
\(123\) | 0.233797 | + | 0.872543i | 0.0210808 | + | 0.0786745i | ||||
\(124\) | −9.00815 | − | 15.6026i | −0.808955 | − | 1.40115i | ||||
\(125\) | −10.7861 | − | 2.94286i | −0.964737 | − | 0.263217i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.84282 | − | 4.84282i | −0.429731 | − | 0.429731i | 0.458806 | − | 0.888537i | \(-0.348277\pi\) |
−0.888537 | + | 0.458806i | \(0.848277\pi\) | |||||||
\(128\) | 19.0887 | + | 5.11481i | 1.68722 | + | 0.452089i | ||||
\(129\) | −1.68623 | + | 2.92064i | −0.148465 | + | 0.257148i | ||||
\(130\) | −2.93057 | + | 32.9206i | −0.257028 | + | 2.88733i | ||||
\(131\) | −2.49109 | + | 1.43823i | −0.217648 | + | 0.125659i | −0.604861 | − | 0.796331i | \(-0.706771\pi\) |
0.387213 | + | 0.921990i | \(0.373438\pi\) | |||||||
\(132\) | −8.52384 | + | 8.52384i | −0.741905 | + | 0.741905i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 24.9665i | − | 2.15678i | ||||||
\(135\) | 0.384944 | + | 2.20268i | 0.0331307 | + | 0.189577i | ||||
\(136\) | 5.31646 | + | 3.06946i | 0.455883 | + | 0.263204i | ||||
\(137\) | 19.8248 | − | 5.31203i | 1.69375 | − | 0.453838i | 0.722393 | − | 0.691482i | \(-0.243042\pi\) |
0.971352 | + | 0.237645i | \(0.0763754\pi\) | |||||||
\(138\) | 2.32064 | − | 8.66073i | 0.197546 | − | 0.737250i | ||||
\(139\) | 10.4910 | 0.889832 | 0.444916 | − | 0.895572i | \(-0.353234\pi\) | ||||
0.444916 | + | 0.895572i | \(0.353234\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.47074 | −0.208074 | ||||||||
\(142\) | −3.07153 | + | 11.4631i | −0.257757 | + | 0.961963i | ||||
\(143\) | 21.6402 | − | 5.79849i | 1.80965 | − | 0.484894i | ||||
\(144\) | 0.729213 | + | 0.421011i | 0.0607678 | + | 0.0350843i | ||||
\(145\) | −3.69549 | − | 2.59598i | −0.306894 | − | 0.215585i | ||||
\(146\) | 21.7930i | 1.80360i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 14.0411 | − | 14.0411i | 1.15418 | − | 1.15418i | ||||
\(149\) | −11.4119 | + | 6.58864i | −0.934896 | + | 0.539763i | −0.888357 | − | 0.459154i | \(-0.848153\pi\) |
−0.0465396 | + | 0.998916i | \(0.514819\pi\) | |||||||
\(150\) | 10.9475 | − | 3.94694i | 0.893858 | − | 0.322267i | ||||
\(151\) | 2.10520 | − | 3.64631i | 0.171319 | − | 0.296732i | −0.767563 | − | 0.640974i | \(-0.778531\pi\) |
0.938881 | + | 0.344242i | \(0.111864\pi\) | |||||||
\(152\) | −0.445432 | − | 0.119353i | −0.0361293 | − | 0.00968083i | ||||
\(153\) | −1.31619 | − | 1.31619i | −0.106408 | − | 0.106408i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.6926 | − | 4.96630i | 0.858853 | − | 0.398903i | ||||
\(156\) | −10.8501 | − | 18.7930i | −0.868706 | − | 1.50464i | ||||
\(157\) | 0.250229 | + | 0.933866i | 0.0199704 | + | 0.0745306i | 0.975192 | − | 0.221361i | \(-0.0710499\pi\) |
−0.955222 | + | 0.295892i | \(0.904383\pi\) | |||||||
\(158\) | −5.07877 | − | 18.9542i | −0.404045 | − | 1.50792i | ||||
\(159\) | 1.40391 | + | 2.43165i | 0.111337 | + | 0.192842i | ||||
\(160\) | −3.56059 | + | 9.73660i | −0.281489 | + | 0.769745i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.64576 | − | 1.64576i | −0.129303 | − | 0.129303i | ||||
\(163\) | 9.91429 | + | 2.65652i | 0.776547 | + | 0.208075i | 0.625262 | − | 0.780415i | \(-0.284992\pi\) |
0.151285 | + | 0.988490i | \(0.451659\pi\) | |||||||
\(164\) | −1.54334 | + | 2.67314i | −0.120515 | + | 0.208737i | ||||
\(165\) | −5.06136 | − | 6.05053i | −0.394026 | − | 0.471033i | ||||
\(166\) | −21.0327 | + | 12.1432i | −1.63246 | + | 0.942499i | ||||
\(167\) | −5.80633 | + | 5.80633i | −0.449307 | + | 0.449307i | −0.895124 | − | 0.445817i | \(-0.852913\pi\) |
0.445817 | + | 0.895124i | \(0.352913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 27.3304i | 2.10234i | ||||||||
\(170\) | −5.56840 | + | 7.92685i | −0.427077 | + | 0.607962i | ||||
\(171\) | 0.121090 | + | 0.0699116i | 0.00926001 | + | 0.00534627i | ||||
\(172\) | −11.1312 | + | 2.98258i | −0.848742 | + | 0.227420i | ||||
\(173\) | −1.16854 | + | 4.36106i | −0.0888426 | + | 0.331565i | −0.996014 | − | 0.0891961i | \(-0.971570\pi\) |
0.907172 | + | 0.420761i | \(0.138237\pi\) | |||||||
\(174\) | 4.70074 | 0.356362 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −2.97048 | −0.223908 | ||||||||
\(177\) | 1.63231 | − | 6.09186i | 0.122692 | − | 0.457892i | ||||
\(178\) | −7.88643 | + | 2.11316i | −0.591113 | + | 0.158388i | ||||
\(179\) | −12.7668 | − | 7.37089i | −0.954232 | − | 0.550926i | −0.0598390 | − | 0.998208i | \(-0.519059\pi\) |
−0.894393 | + | 0.447282i | \(0.852392\pi\) | |||||||
\(180\) | −4.39203 | + | 6.25224i | −0.327363 | + | 0.466014i | ||||
\(181\) | − | 6.11772i | − | 0.454727i | −0.973810 | − | 0.227363i | \(-0.926989\pi\) | ||
0.973810 | − | 0.227363i | \(-0.0730105\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.09734 | + | 7.09734i | −0.524650 | + | 0.524650i | ||||
\(184\) | 11.0032 | − | 6.35271i | 0.811168 | − | 0.468328i | ||||
\(185\) | 8.33747 | + | 9.96691i | 0.612983 | + | 0.732782i | ||||
\(186\) | −6.13575 | + | 10.6274i | −0.449895 | + | 0.779241i | ||||
\(187\) | 6.34277 | + | 1.69954i | 0.463829 | + | 0.124283i | ||||
\(188\) | −5.96980 | − | 5.96980i | −0.435393 | − | 0.435393i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.249922 | − | 0.683423i | 0.0181312 | − | 0.0495807i | ||||
\(191\) | 11.2238 | + | 19.4402i | 0.812124 | + | 1.40664i | 0.911375 | + | 0.411578i | \(0.135022\pi\) |
−0.0992508 | + | 0.995062i | \(0.531645\pi\) | |||||||
\(192\) | −3.22875 | − | 12.0499i | −0.233015 | − | 0.869624i | ||||
\(193\) | 4.64744 | + | 17.3445i | 0.334530 | + | 1.24848i | 0.904378 | + | 0.426733i | \(0.140336\pi\) |
−0.569848 | + | 0.821750i | \(0.692998\pi\) | |||||||
\(194\) | −14.3220 | − | 24.8064i | −1.02826 | − | 1.78100i | ||||
\(195\) | 12.8791 | − | 5.98181i | 0.922289 | − | 0.428366i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.1280 | − | 12.1280i | −0.864085 | − | 0.864085i | 0.127724 | − | 0.991810i | \(-0.459233\pi\) |
−0.991810 | + | 0.127724i | \(0.959233\pi\) | |||||||
\(198\) | 7.93097 | + | 2.12510i | 0.563630 | + | 0.151024i | ||||
\(199\) | 3.39732 | − | 5.88433i | 0.240830 | − | 0.417129i | −0.720121 | − | 0.693848i | \(-0.755914\pi\) |
0.960951 | + | 0.276719i | \(0.0892472\pi\) | |||||||
\(200\) | 14.9241 | + | 7.01447i | 1.05529 | + | 0.495998i | ||||
\(201\) | −9.28983 | + | 5.36348i | −0.655254 | + | 0.378311i | ||||
\(202\) | 2.36563 | − | 2.36563i | 0.166445 | − | 0.166445i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 6.36036i | − | 0.445314i | ||||||
\(205\) | −1.65284 | − | 1.16107i | −0.115439 | − | 0.0810929i | ||||
\(206\) | −12.4995 | − | 7.21662i | −0.870885 | − | 0.502805i | ||||
\(207\) | −3.72112 | + | 0.997072i | −0.258636 | + | 0.0693013i | ||||
\(208\) | 1.38400 | − | 5.16516i | 0.0959632 | − | 0.358140i | ||||
\(209\) | −0.493266 | −0.0341199 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.53741 | 0.174683 | 0.0873414 | − | 0.996178i | \(-0.472163\pi\) | ||||
0.0873414 | + | 0.996178i | \(0.472163\pi\) | |||||||
\(212\) | −2.48322 | + | 9.26749i | −0.170548 | + | 0.636494i | ||||
\(213\) | 4.92518 | − | 1.31970i | 0.337468 | − | 0.0904242i | ||||
\(214\) | −36.1938 | − | 20.8965i | −2.47416 | − | 1.42846i | ||||
\(215\) | −1.29821 | − | 7.42848i | −0.0885374 | − | 0.506618i | ||||
\(216\) | − | 3.29806i | − | 0.224405i | ||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −20.9539 | + | 20.9539i | −1.41918 | + | 1.41918i | ||||
\(219\) | 8.10900 | − | 4.68173i | 0.547955 | − | 0.316362i | ||||
\(220\) | 2.39004 | − | 26.8486i | 0.161136 | − | 1.81013i | ||||
\(221\) | −5.91044 | + | 10.2372i | −0.397579 | + | 0.688627i | ||||
\(222\) | −13.0645 | − | 3.50063i | −0.876833 | − | 0.234947i | ||||
\(223\) | 7.81577 | + | 7.81577i | 0.523383 | + | 0.523383i | 0.918591 | − | 0.395209i | \(-0.129328\pi\) |
−0.395209 | + | 0.918591i | \(0.629328\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.82044 | − | 3.22556i | −0.254696 | − | 0.215037i | ||||
\(226\) | −18.3717 | − | 31.8207i | −1.22207 | − | 2.11668i | ||||
\(227\) | −6.35498 | − | 23.7171i | −0.421795 | − | 1.57416i | −0.770824 | − | 0.637049i | \(-0.780155\pi\) |
0.349029 | − | 0.937112i | \(-0.386512\pi\) | |||||||
\(228\) | 0.123658 | + | 0.461500i | 0.00818948 | + | 0.0305636i | ||||
\(229\) | −3.69144 | − | 6.39377i | −0.243937 | − | 0.422512i | 0.717895 | − | 0.696151i | \(-0.245106\pi\) |
−0.961832 | + | 0.273640i | \(0.911772\pi\) | |||||||
\(230\) | 8.44553 | + | 18.1835i | 0.556882 | + | 1.19899i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.71009 | + | 4.71009i | 0.309232 | + | 0.309232i | ||||
\(233\) | −7.04458 | − | 1.88759i | −0.461505 | − | 0.123660i | 0.0205724 | − | 0.999788i | \(-0.493451\pi\) |
−0.482078 | + | 0.876128i | \(0.660118\pi\) | |||||||
\(234\) | −7.39038 | + | 12.8005i | −0.483124 | + | 0.836796i | ||||
\(235\) | 4.23758 | − | 3.54480i | 0.276429 | − | 0.231237i | ||||
\(236\) | 18.6632 | − | 10.7752i | 1.21487 | − | 0.701404i | ||||
\(237\) | −5.96165 | + | 5.96165i | −0.387251 | + | 0.387251i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.88581i | 0.639460i | 0.947509 | + | 0.319730i | \(0.103592\pi\) | ||||
−0.947509 | + | 0.319730i | \(0.896408\pi\) | |||||||
\(240\) | −1.85471 | + | 0.324132i | −0.119721 | + | 0.0209226i | ||||
\(241\) | 2.91713 | + | 1.68420i | 0.187909 | + | 0.108489i | 0.591003 | − | 0.806669i | \(-0.298732\pi\) |
−0.403095 | + | 0.915158i | \(0.632065\pi\) | |||||||
\(242\) | −3.24916 | + | 0.870610i | −0.208864 | + | 0.0559649i | ||||
\(243\) | −0.258819 | + | 0.965926i | −0.0166032 | + | 0.0619642i | ||||
\(244\) | −34.2972 | −2.19565 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.10244 | 0.134047 | ||||||||
\(247\) | 0.229822 | − | 0.857708i | 0.0146232 | − | 0.0545746i | ||||
\(248\) | −16.7965 | + | 4.50062i | −1.06658 | + | 0.285789i | ||||
\(249\) | 9.03681 | + | 5.21740i | 0.572684 | + | 0.330639i | ||||
\(250\) | −13.1134 | + | 22.4759i | −0.829363 | + | 1.42150i | ||||
\(251\) | − | 4.93770i | − | 0.311665i | −0.987784 | − | 0.155832i | \(-0.950194\pi\) | ||
0.987784 | − | 0.155832i | \(-0.0498060\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.60986 | − | 9.60986i | 0.604167 | − | 0.604167i | ||||
\(254\) | −13.8046 | + | 7.97010i | −0.866179 | + | 0.500089i | ||||
\(255\) | 4.14576 | + | 0.369052i | 0.259618 | + | 0.0231109i | ||||
\(256\) | 10.5227 | − | 18.2259i | 0.657670 | − | 1.13912i | ||||
\(257\) | 19.8010 | + | 5.30566i | 1.23515 | + | 0.330958i | 0.816584 | − | 0.577227i | \(-0.195865\pi\) |
0.418569 | + | 0.908185i | \(0.362532\pi\) | |||||||
\(258\) | 5.55026 | + | 5.55026i | 0.345544 | + | 0.345544i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 45.5717 | + | 16.6652i | 2.82624 | + | 1.03353i | ||||
\(261\) | −1.00985 | − | 1.74910i | −0.0625079 | − | 0.108267i | ||||
\(262\) | 1.73275 | + | 6.46671i | 0.107050 | + | 0.399515i | ||||
\(263\) | −0.900371 | − | 3.36023i | −0.0555192 | − | 0.207201i | 0.932594 | − | 0.360926i | \(-0.117539\pi\) |
−0.988114 | + | 0.153726i | \(0.950873\pi\) | |||||||
\(264\) | 5.81743 | + | 10.0761i | 0.358038 | + | 0.620140i | ||||
\(265\) | −5.89658 | − | 2.15632i | −0.362224 | − | 0.132462i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.48051 | + | 2.48051i | 0.151805 | + | 0.151805i | ||||
\(268\) | −35.4054 | − | 9.48684i | −2.16273 | − | 0.579501i | ||||
\(269\) | −9.35542 | + | 16.2041i | −0.570410 | + | 0.987979i | 0.426114 | + | 0.904670i | \(0.359882\pi\) |
−0.996524 | + | 0.0833095i | \(0.973451\pi\) | |||||||
\(270\) | 5.18384 | + | 0.461461i | 0.315478 | + | 0.0280836i | ||||
\(271\) | −6.07958 | + | 3.51005i | −0.369308 | + | 0.213220i | −0.673156 | − | 0.739500i | \(-0.735062\pi\) |
0.303848 | + | 0.952721i | \(0.401728\pi\) | |||||||
\(272\) | 1.10826 | − | 1.10826i | 0.0671982 | − | 0.0671982i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 47.7689i | − | 2.88582i | ||||||
\(275\) | 17.3616 | + | 3.11571i | 1.04694 | + | 0.187885i | ||||
\(276\) | −11.4001 | − | 6.58186i | −0.686206 | − | 0.396181i | ||||
\(277\) | 7.53340 | − | 2.01857i | 0.452638 | − | 0.121284i | −0.0252953 | − | 0.999680i | \(-0.508053\pi\) |
0.477934 | + | 0.878396i | \(0.341386\pi\) | |||||||
\(278\) | 6.31964 | − | 23.5852i | 0.379027 | − | 1.41455i | ||||
\(279\) | 5.27250 | 0.315657 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.11841 | −0.186029 | −0.0930143 | − | 0.995665i | \(-0.529650\pi\) | ||||
−0.0930143 | + | 0.995665i | \(0.529650\pi\) | |||||||
\(282\) | −1.48834 | + | 5.55457i | −0.0886296 | + | 0.330770i | ||||
\(283\) | 30.3411 | − | 8.12988i | 1.80359 | − | 0.483271i | 0.809063 | − | 0.587721i | \(-0.199975\pi\) |
0.994530 | + | 0.104450i | \(0.0333082\pi\) | |||||||
\(284\) | 15.0889 | + | 8.71157i | 0.895361 | + | 0.516937i | ||||
\(285\) | −0.307986 | + | 0.0538241i | −0.0182435 | + | 0.00318827i | ||||
\(286\) | − | 52.1434i | − | 3.08330i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.27840 | + | 3.27840i | −0.193182 | + | 0.193182i | ||||
\(289\) | 11.7219 | − | 6.76765i | 0.689524 | − | 0.398097i | ||||
\(290\) | −8.06227 | + | 6.74421i | −0.473433 | + | 0.396034i | ||||
\(291\) | −6.15350 | + | 10.6582i | −0.360725 | + | 0.624794i | ||||
\(292\) | 30.9050 | + | 8.28097i | 1.80858 | + | 0.484607i | ||||
\(293\) | 1.77405 | + | 1.77405i | 0.103641 | + | 0.103641i | 0.757026 | − | 0.653385i | \(-0.226652\pi\) |
−0.653385 | + | 0.757026i | \(0.726652\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.94049 | + | 12.7901i | 0.345868 | + | 0.744668i | ||||
\(296\) | −9.58292 | − | 16.5981i | −0.556996 | − | 0.964746i | ||||
\(297\) | −0.913058 | − | 3.40758i | −0.0529810 | − | 0.197728i | ||||
\(298\) | 7.93785 | + | 29.6245i | 0.459827 | + | 1.71610i | ||||
\(299\) | 12.2325 | + | 21.1874i | 0.707426 | + | 1.22530i | ||||
\(300\) | −1.43737 | − | 17.0246i | −0.0829863 | − | 0.982914i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.92929 | − | 6.92929i | −0.398736 | − | 0.398736i | ||||
\(303\) | −1.38843 | − | 0.372029i | −0.0797633 | − | 0.0213725i | ||||
\(304\) | −0.0588671 | + | 0.101961i | −0.00337626 | + | 0.00584786i | ||||
\(305\) | 1.99005 | − | 22.3553i | 0.113950 | − | 1.28006i | ||||
\(306\) | −3.75184 | + | 2.16613i | −0.214478 | + | 0.123829i | ||||
\(307\) | −10.6518 | + | 10.6518i | −0.607929 | + | 0.607929i | −0.942404 | − | 0.334476i | \(-0.891441\pi\) |
0.334476 | + | 0.942404i | \(0.391441\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.20130i | 0.352780i | ||||||||
\(310\) | −4.72384 | − | 27.0302i | −0.268296 | − | 1.53521i | ||||
\(311\) | 16.1465 | + | 9.32219i | 0.915584 | + | 0.528613i | 0.882224 | − | 0.470831i | \(-0.156046\pi\) |
0.0333607 | + | 0.999443i | \(0.489379\pi\) | |||||||
\(312\) | −20.2311 | + | 5.42090i | −1.14536 | + | 0.306898i | ||||
\(313\) | 5.31635 | − | 19.8409i | 0.300498 | − | 1.12147i | −0.636254 | − | 0.771479i | \(-0.719517\pi\) |
0.936752 | − | 0.349994i | \(-0.113816\pi\) | |||||||
\(314\) | 2.25020 | 0.126986 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −28.8091 | −1.62064 | ||||||||
\(317\) | −7.55924 | + | 28.2115i | −0.424569 | + | 1.58451i | 0.340292 | + | 0.940320i | \(0.389474\pi\) |
−0.764862 | + | 0.644195i | \(0.777193\pi\) | |||||||
\(318\) | 6.31239 | − | 1.69140i | 0.353981 | − | 0.0948490i | ||||
\(319\) | 6.17047 | + | 3.56252i | 0.345480 | + | 0.199463i | ||||
\(320\) | 22.8258 | + | 16.0345i | 1.27600 | + | 0.896355i | ||||
\(321\) | 17.9566i | 1.00224i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.184034 | − | 0.184034i | 0.0102399 | − | 0.0102399i | ||||
\(324\) | −2.95923 | + | 1.70851i | −0.164402 | + | 0.0949174i | ||||
\(325\) | −13.5068 | + | 28.7372i | −0.749222 | + | 1.59405i | ||||
\(326\) | 11.9445 | − | 20.6885i | 0.661545 | − | 1.14583i | ||||
\(327\) | 12.2983 | + | 3.29531i | 0.680095 | + | 0.182231i | ||||
\(328\) | 2.10662 | + | 2.10662i | 0.116319 | + | 0.116319i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −16.6514 | + | 7.73390i | −0.916628 | + | 0.425737i | ||||
\(331\) | 11.8275 | + | 20.4858i | 0.650098 | + | 1.12600i | 0.983099 | + | 0.183076i | \(0.0586054\pi\) |
−0.333001 | + | 0.942926i | \(0.608061\pi\) | |||||||
\(332\) | 9.22846 | + | 34.4411i | 0.506477 | + | 1.89020i | ||||
\(333\) | 1.50406 | + | 5.61323i | 0.0824220 | + | 0.307603i | ||||
\(334\) | 9.55580 | + | 16.5511i | 0.522870 | + | 0.905638i | ||||
\(335\) | 8.23799 | − | 22.5272i | 0.450090 | − | 1.23079i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.38731 | − | 8.38731i | −0.456886 | − | 0.456886i | 0.440746 | − | 0.897632i | \(-0.354714\pi\) |
−0.897632 | + | 0.440746i | \(0.854714\pi\) | |||||||
\(338\) | 61.4428 | + | 16.4635i | 3.34205 | + | 0.895499i | ||||
\(339\) | −7.89348 | + | 13.6719i | −0.428715 | + | 0.742556i | ||||
\(340\) | 9.12530 | + | 10.9087i | 0.494889 | + | 0.591608i | ||||
\(341\) | −16.1083 | + | 9.30013i | −0.872313 | + | 0.503630i | ||||
\(342\) | 0.230115 | − | 0.230115i | 0.0124432 | − | 0.0124432i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 11.1226i | 0.599691i | ||||||||
\(345\) | 4.95162 | − | 7.04883i | 0.266586 | − | 0.379496i | ||||
\(346\) | 9.10037 | + | 5.25410i | 0.489239 | + | 0.282462i | ||||
\(347\) | −10.5150 | + | 2.81748i | −0.564473 | + | 0.151250i | −0.529761 | − | 0.848147i | \(-0.677718\pi\) |
−0.0347126 | + | 0.999397i | \(0.511052\pi\) | |||||||
\(348\) | 1.78620 | − | 6.66619i | 0.0957503 | − | 0.357345i | ||||
\(349\) | 5.13321 | 0.274775 | 0.137387 | − | 0.990517i | \(-0.456130\pi\) | ||||
0.137387 | + | 0.990517i | \(0.456130\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.35062 | 0.338971 | ||||||||
\(352\) | 4.23326 | − | 15.7988i | 0.225634 | − | 0.842076i | ||||
\(353\) | −20.8591 | + | 5.58918i | −1.11022 | + | 0.297482i | −0.766919 | − | 0.641744i | \(-0.778211\pi\) |
−0.343299 | + | 0.939226i | \(0.611544\pi\) | |||||||
\(354\) | −12.7121 | − | 7.33933i | −0.675640 | − | 0.390081i | ||||
\(355\) | −6.55382 | + | 9.32964i | −0.347841 | + | 0.495166i | ||||
\(356\) | 11.9868i | 0.635301i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −24.2614 | + | 24.2614i | −1.28225 | + | 1.28225i | ||||
\(359\) | −3.58984 | + | 2.07260i | −0.189465 | + | 0.109388i | −0.591732 | − | 0.806135i | \(-0.701556\pi\) |
0.402267 | + | 0.915522i | \(0.368222\pi\) | |||||||
\(360\) | 4.73178 | + | 5.65653i | 0.249386 | + | 0.298126i | ||||
\(361\) | 9.49022 | − | 16.4376i | 0.499486 | − | 0.865134i | ||||
\(362\) | −13.7535 | − | 3.68525i | −0.722869 | − | 0.193692i | ||||
\(363\) | 1.02196 | + | 1.02196i | 0.0536387 | + | 0.0536387i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.19086 | + | 19.6638i | −0.376387 | + | 1.02925i | ||||
\(366\) | 11.6805 | + | 20.2312i | 0.610549 | + | 1.05750i | ||||
\(367\) | −0.879473 | − | 3.28224i | −0.0459081 | − | 0.171331i | 0.939166 | − | 0.343465i | \(-0.111601\pi\) |
−0.985074 | + | 0.172133i | \(0.944934\pi\) | |||||||
\(368\) | −0.839557 | − | 3.13327i | −0.0437650 | − | 0.163333i | ||||
\(369\) | −0.451661 | − | 0.782300i | −0.0235126 | − | 0.0407249i | ||||
\(370\) | 27.4295 | − | 12.7399i | 1.42599 | − | 0.662315i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.7394 | + | 12.7394i | 0.660509 | + | 0.660509i | ||||
\(373\) | 34.6439 | + | 9.28280i | 1.79379 | + | 0.480645i | 0.992981 | − | 0.118271i | \(-0.0377352\pi\) |
0.800812 | + | 0.598916i | \(0.204402\pi\) | |||||||
\(374\) | 7.64163 | − | 13.2357i | 0.395139 | − | 0.684401i | ||||
\(375\) | 11.1802 | + | 0.0509371i | 0.577344 | + | 0.00263038i | ||||
\(376\) | −7.05693 | + | 4.07432i | −0.363934 | + | 0.210117i | ||||
\(377\) | −9.06957 | + | 9.06957i | −0.467107 | + | 0.467107i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.02575i | − | 0.412255i | −0.978525 | − | 0.206128i | \(-0.933914\pi\) | ||
0.978525 | − | 0.206128i | \(-0.0660862\pi\) | |||||||
\(380\) | −0.874208 | − | 0.614107i | −0.0448459 | − | 0.0315030i | ||||
\(381\) | 5.93122 | + | 3.42439i | 0.303866 | + | 0.175437i | ||||
\(382\) | 50.4654 | − | 13.5222i | 2.58203 | − | 0.691853i | ||||
\(383\) | −8.49599 | + | 31.7075i | −0.434125 | + | 1.62018i | 0.309028 | + | 0.951053i | \(0.399996\pi\) |
−0.743152 | + | 0.669122i | \(0.766670\pi\) | |||||||
\(384\) | −19.7621 | −1.00848 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 41.7925 | 2.12718 | ||||||||
\(387\) | 0.872859 | − | 3.25755i | 0.0443699 | − | 0.165591i | ||||
\(388\) | −40.6205 | + | 10.8842i | −2.06219 | + | 0.552562i | ||||
\(389\) | 13.4380 | + | 7.75844i | 0.681334 | + | 0.393369i | 0.800358 | − | 0.599523i | \(-0.204643\pi\) |
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(390\) | −5.68977 | − | 32.5574i | −0.288113 | − | 1.64861i | ||||
\(391\) | 7.17073i | 0.362640i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.03397 | − | 2.03397i | 0.102600 | − | 0.102600i | ||||
\(394\) | −34.5713 | + | 19.9598i | −1.74168 | + | 1.00556i | ||||
\(395\) | 1.67161 | − | 18.7781i | 0.0841080 | − | 0.944831i | ||||
\(396\) | 6.02727 | − | 10.4395i | 0.302882 | − | 0.524606i | ||||
\(397\) | −20.3268 | − | 5.44656i | −1.02017 | − | 0.273355i | −0.290299 | − | 0.956936i | \(-0.593755\pi\) |
−0.729875 | + | 0.683581i | \(0.760422\pi\) | |||||||
\(398\) | −11.1823 | − | 11.1823i | −0.560519 | − | 0.560519i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.71599 | − | 3.21690i | 0.135800 | − | 0.160845i | ||||
\(401\) | −9.34890 | − | 16.1928i | −0.466862 | − | 0.808628i | 0.532422 | − | 0.846479i | \(-0.321282\pi\) |
−0.999283 | + | 0.0378510i | \(0.987949\pi\) | |||||||
\(402\) | 6.46180 | + | 24.1158i | 0.322285 | + | 1.20279i | ||||
\(403\) | −8.66622 | − | 32.3428i | −0.431695 | − | 1.61111i | ||||
\(404\) | −2.45584 | − | 4.25363i | −0.122182 | − | 0.211626i | ||||
\(405\) | −0.941924 | − | 2.02800i | −0.0468046 | − | 0.100772i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.4963 | − | 14.4963i | −0.718553 | − | 0.718553i | ||||
\(408\) | −5.92974 | − | 1.58887i | −0.293566 | − | 0.0786608i | ||||
\(409\) | 11.9001 | − | 20.6115i | 0.588421 | − | 1.01918i | −0.406018 | − | 0.913865i | \(-0.633083\pi\) |
0.994439 | − | 0.105310i | \(-0.0335836\pi\) | |||||||
\(410\) | −3.60591 | + | 3.01640i | −0.178083 | + | 0.148969i | ||||
\(411\) | −17.7744 | + | 10.2621i | −0.876747 | + | 0.506190i | ||||
\(412\) | −14.9836 | + | 14.9836i | −0.738190 | + | 0.738190i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8.96625i | 0.440667i | ||||||||
\(415\) | −22.9846 | + | 4.01682i | −1.12827 | + | 0.197178i | ||||
\(416\) | 25.4991 | + | 14.7219i | 1.25019 | + | 0.721800i | ||||
\(417\) | −10.1335 | + | 2.71526i | −0.496239 | + | 0.132967i | ||||
\(418\) | −0.297138 | + | 1.10893i | −0.0145335 | + | 0.0542397i | ||||
\(419\) | 9.72005 | 0.474856 | 0.237428 | − | 0.971405i | \(-0.423696\pi\) | ||||
0.237428 | + | 0.971405i | \(0.423696\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.0095 | 0.634043 | 0.317022 | − | 0.948418i | \(-0.397317\pi\) | ||||
0.317022 | + | 0.948418i | \(0.397317\pi\) | |||||||
\(422\) | 1.52851 | − | 5.70448i | 0.0744067 | − | 0.277690i | ||||
\(423\) | 2.38655 | − | 0.639474i | 0.116038 | − | 0.0310923i | ||||
\(424\) | 8.01972 | + | 4.63019i | 0.389472 | + | 0.224862i | ||||
\(425\) | −7.63991 | + | 5.31502i | −0.370590 | + | 0.257816i | ||||
\(426\) | − | 11.8675i | − | 0.574981i | ||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −43.3867 | + | 43.3867i | −2.09718 | + | 2.09718i | ||||
\(429\) | −19.4021 | + | 11.2018i | −0.936743 | + | 0.540829i | ||||
\(430\) | −17.4823 | − | 1.55626i | −0.843073 | − | 0.0750496i | ||||
\(431\) | −6.60239 | + | 11.4357i | −0.318026 | + | 0.550837i | −0.980076 | − | 0.198622i | \(-0.936353\pi\) |
0.662050 | + | 0.749460i | \(0.269687\pi\) | |||||||
\(432\) | −0.813332 | − | 0.217932i | −0.0391314 | − | 0.0104852i | ||||
\(433\) | 13.9321 | + | 13.9321i | 0.669535 | + | 0.669535i | 0.957608 | − | 0.288074i | \(-0.0930148\pi\) |
−0.288074 | + | 0.957608i | \(0.593015\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.24146 | + | 1.55106i | 0.203362 | + | 0.0743678i | ||||
\(436\) | 21.7529 | + | 37.6772i | 1.04178 | + | 1.80441i | ||||
\(437\) | −0.139414 | − | 0.520299i | −0.00666906 | − | 0.0248893i | ||||
\(438\) | −5.64044 | − | 21.0504i | −0.269511 | − | 1.00583i | ||||
\(439\) | 6.30838 | + | 10.9264i | 0.301083 | + | 0.521490i | 0.976381 | − | 0.216054i | \(-0.0693187\pi\) |
−0.675299 | + | 0.737544i | \(0.735985\pi\) | |||||||
\(440\) | −24.4338 | − | 8.93522i | −1.16484 | − | 0.425970i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 19.4543 | + | 19.4543i | 0.925346 | + | 0.925346i | ||||
\(443\) | −18.4828 | − | 4.95246i | −0.878146 | − | 0.235299i | −0.208539 | − | 0.978014i | \(-0.566871\pi\) |
−0.669607 | + | 0.742716i | \(0.733537\pi\) | |||||||
\(444\) | −9.92859 | + | 17.1968i | −0.471190 | + | 0.816125i | ||||
\(445\) | −7.81317 | − | 0.695521i | −0.370380 | − | 0.0329709i | ||||
\(446\) | 22.2791 | − | 12.8629i | 1.05495 | − | 0.609074i | ||||
\(447\) | 9.31775 | − | 9.31775i | 0.440714 | − | 0.440714i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 22.2412i | − | 1.04963i | −0.851217 | − | 0.524814i | \(-0.824135\pi\) | ||
0.851217 | − | 0.524814i | \(-0.175865\pi\) | |||||||
\(450\) | −9.55291 | + | 6.64587i | −0.450329 | + | 0.313289i | ||||
\(451\) | 2.75979 | + | 1.59336i | 0.129953 | + | 0.0750286i | ||||
\(452\) | −52.1064 | + | 13.9619i | −2.45088 | + | 0.656711i | ||||
\(453\) | −1.08973 | + | 4.06693i | −0.0512000 | + | 0.191081i | ||||
\(454\) | −57.1477 | −2.68207 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.461145 | 0.0215951 | ||||||||
\(457\) | −2.74748 | + | 10.2537i | −0.128522 | + | 0.479650i | −0.999941 | − | 0.0108896i | \(-0.996534\pi\) |
0.871419 | + | 0.490540i | \(0.163200\pi\) | |||||||
\(458\) | −16.5978 | + | 4.44737i | −0.775564 | + | 0.207812i | ||||
\(459\) | 1.61200 | + | 0.930686i | 0.0752415 | + | 0.0434407i | ||||
\(460\) | 28.9955 | − | 5.06730i | 1.35192 | − | 0.236264i | ||||
\(461\) | 6.43806i | 0.299851i | 0.988697 | + | 0.149925i | \(0.0479033\pi\) | ||||
−0.988697 | + | 0.149925i | \(0.952097\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.4584 | + | 10.4584i | −0.486041 | + | 0.486041i | −0.907054 | − | 0.421014i | \(-0.861674\pi\) |
0.421014 | + | 0.907054i | \(0.361674\pi\) | |||||||
\(464\) | 1.47279 | − | 0.850314i | 0.0683724 | − | 0.0394748i | ||||
\(465\) | −9.04292 | + | 7.56453i | −0.419355 | + | 0.350797i | ||||
\(466\) | −8.48714 | + | 14.7002i | −0.393159 | + | 0.680972i | ||||
\(467\) | −10.0867 | − | 2.70272i | −0.466756 | − | 0.125067i | 0.0177729 | − | 0.999842i | \(-0.494342\pi\) |
−0.484529 | + | 0.874775i | \(0.661009\pi\) | |||||||
\(468\) | 15.3444 | + | 15.3444i | 0.709295 | + | 0.709295i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −5.41655 | − | 11.6620i | −0.249847 | − | 0.537930i | ||||
\(471\) | −0.483404 | − | 0.837281i | −0.0222741 | − | 0.0385799i | ||||
\(472\) | −5.38345 | − | 20.0913i | −0.247794 | − | 0.924778i | ||||
\(473\) | 3.07926 | + | 11.4919i | 0.141584 | + | 0.528400i | ||||
\(474\) | 9.81143 | + | 16.9939i | 0.450654 | + | 0.780555i | ||||
\(475\) | 0.451008 | − | 0.534186i | 0.0206936 | − | 0.0245102i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.98543 | − | 1.98543i | −0.0909066 | − | 0.0909066i | ||||
\(478\) | 22.2247 | + | 5.95510i | 1.01654 | + | 0.272380i | ||||
\(479\) | 15.3074 | − | 26.5132i | 0.699412 | − | 1.21142i | −0.269258 | − | 0.963068i | \(-0.586778\pi\) |
0.968670 | − | 0.248350i | \(-0.0798883\pi\) | |||||||
\(480\) | 0.919245 | − | 10.3264i | 0.0419576 | − | 0.471332i | ||||
\(481\) | 31.9607 | − | 18.4525i | 1.45728 | − | 0.841362i | ||||
\(482\) | 5.54358 | − | 5.54358i | 0.252503 | − | 0.252503i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.93850i | 0.224477i | ||||||||
\(485\) | −4.73751 | − | 27.1085i | −0.215119 | − | 1.23093i | ||||
\(486\) | 2.01563 | + | 1.16373i | 0.0914309 | + | 0.0527877i | ||||
\(487\) | −17.3396 | + | 4.64613i | −0.785733 | + | 0.210536i | −0.629311 | − | 0.777154i | \(-0.716663\pi\) |
−0.156422 | + | 0.987690i | \(0.549996\pi\) | |||||||
\(488\) | −8.56773 | + | 31.9752i | −0.387843 | + | 1.44745i | ||||
\(489\) | −10.2640 | −0.464155 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.26968 | 0.237817 | 0.118909 | − | 0.992905i | \(-0.462060\pi\) | ||||
0.118909 | + | 0.992905i | \(0.462060\pi\) | |||||||
\(492\) | 0.798891 | − | 2.98150i | 0.0360168 | − | 0.134417i | ||||
\(493\) | −3.63130 | + | 0.973004i | −0.163546 | + | 0.0438219i | ||||
\(494\) | −1.78981 | − | 1.03335i | −0.0805273 | − | 0.0464925i | ||||
\(495\) | 6.45489 | + | 4.53439i | 0.290126 | + | 0.203806i | ||||
\(496\) | 4.43957i | 0.199343i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 17.1731 | − | 17.1731i | 0.769547 | − | 0.769547i | ||||
\(499\) | 31.1135 | − | 17.9634i | 1.39283 | − | 0.804150i | 0.399202 | − | 0.916863i | \(-0.369287\pi\) |
0.993628 | + | 0.112713i | \(0.0359540\pi\) | |||||||
\(500\) | 26.8906 | + | 27.1368i | 1.20259 | + | 1.21359i | ||||
\(501\) | 4.10569 | − | 7.11127i | 0.183429 | − | 0.317708i | ||||
\(502\) | −11.1007 | − | 2.97441i | −0.495447 | − | 0.132755i | ||||
\(503\) | −2.39146 | − | 2.39146i | −0.106630 | − | 0.106630i | 0.651779 | − | 0.758409i | \(-0.274023\pi\) |
−0.758409 | + | 0.651779i | \(0.774023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91507 | − | 1.35393i | 0.129719 | − | 0.0602492i | ||||
\(506\) | −15.8155 | − | 27.3932i | −0.703085 | − | 1.21778i | ||||
\(507\) | −7.07364 | − | 26.3992i | −0.314151 | − | 1.17243i | ||||
\(508\) | 6.05701 | + | 22.6051i | 0.268736 | + | 1.00294i | ||||
\(509\) | −16.3136 | − | 28.2560i | −0.723087 | − | 1.25242i | −0.959756 | − | 0.280834i | \(-0.909389\pi\) |
0.236669 | − | 0.971590i | \(-0.423944\pi\) | |||||||
\(510\) | 3.32704 | − | 9.09796i | 0.147324 | − | 0.402864i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.68782 | − | 6.68782i | −0.295563 | − | 0.295563i | ||||
\(513\) | −0.135059 | − | 0.0361889i | −0.00596299 | − | 0.00159778i | ||||
\(514\) | 23.8558 | − | 41.3194i | 1.05223 | − | 1.82252i | ||||
\(515\) | −8.89710 | − | 10.6359i | −0.392053 | − | 0.468674i | ||||
\(516\) | 9.97992 | − | 5.76191i | 0.439341 | − | 0.253654i | ||||
\(517\) | −6.16330 | + | 6.16330i | −0.271062 | + | 0.271062i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 4.51490i | − | 0.198182i | ||||||
\(520\) | 26.9211 | − | 38.3232i | 1.18057 | − | 1.68059i | ||||
\(521\) | −5.77709 | − | 3.33540i | −0.253099 | − | 0.146127i | 0.368084 | − | 0.929793i | \(-0.380014\pi\) |
−0.621182 | + | 0.783666i | \(0.713347\pi\) | |||||||
\(522\) | −4.54056 | + | 1.21664i | −0.198735 | + | 0.0532509i | ||||
\(523\) | −5.72338 | + | 21.3599i | −0.250266 | + | 0.934005i | 0.720397 | + | 0.693562i | \(0.243960\pi\) |
−0.970663 | + | 0.240444i | \(0.922707\pi\) | |||||||
\(524\) | 9.82896 | 0.429380 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.09666 | −0.353031 | ||||||||
\(527\) | 2.54007 | − | 9.47969i | 0.110647 | − | 0.412942i | ||||
\(528\) | 2.86926 | − | 0.768816i | 0.124868 | − | 0.0334584i | ||||
\(529\) | −7.06598 | − | 4.07955i | −0.307217 | − | 0.177372i | ||||
\(530\) | −8.39976 | + | 11.9574i | −0.364862 | + | 0.519397i | ||||
\(531\) | 6.30675i | 0.273690i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.05643 | + | 4.05643i | −0.175704 | + | 0.175704i | ||||
\(534\) | 7.07078 | − | 4.08232i | 0.305983 | − | 0.176659i | ||||
\(535\) | −25.7625 | − | 30.7975i | −1.11381 | − | 1.33149i | ||||
\(536\) | −17.6891 | + | 30.6384i | −0.764053 | + | 1.32338i | ||||
\(537\) | 14.2395 | + | 3.81545i | 0.614478 | + | 0.164649i | ||||
\(538\) | 30.7935 | + | 30.7935i | 1.32760 | + | 1.32760i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.62418 | − | 7.17594i | 0.112927 | − | 0.308803i | ||||
\(541\) | −7.12948 | − | 12.3486i | −0.306520 | − | 0.530909i | 0.671078 | − | 0.741386i | \(-0.265831\pi\) |
−0.977599 | + | 0.210478i | \(0.932498\pi\) | |||||||
\(542\) | 4.22882 | + | 15.7822i | 0.181644 | + | 0.677903i | ||||
\(543\) | 1.58338 | + | 5.90927i | 0.0679495 | + | 0.253591i | ||||
\(544\) | 4.31499 | + | 7.47379i | 0.185004 | + | 0.320436i | ||||
\(545\) | −25.8207 | + | 11.9927i | −1.10604 | + | 0.513709i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2527 | − | 11.2527i | −0.481132 | − | 0.481132i | 0.424361 | − | 0.905493i | \(-0.360499\pi\) |
−0.905493 | + | 0.424361i | \(0.860499\pi\) | |||||||
\(548\) | −67.7418 | − | 18.1514i | −2.89379 | − | 0.775388i | ||||
\(549\) | 5.01858 | − | 8.69243i | 0.214188 | − | 0.370984i | ||||
\(550\) | 17.4630 | − | 37.1544i | 0.744624 | − | 1.58427i | ||||
\(551\) | 0.244565 | − | 0.141200i | 0.0104188 | − | 0.00601532i | ||||
\(552\) | −8.98409 | + | 8.98409i | −0.382388 | + | 0.382388i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 18.1521i | − | 0.771211i | ||||||
\(555\) | −10.6330 | − | 7.46940i | −0.451346 | − | 0.317058i | ||||
\(556\) | −31.0452 | − | 17.9240i | −1.31661 | − | 0.760145i | ||||
\(557\) | −13.5980 | + | 3.64356i | −0.576164 | + | 0.154383i | −0.535122 | − | 0.844775i | \(-0.679734\pi\) |
−0.0410418 | + | 0.999157i | \(0.513068\pi\) | |||||||
\(558\) | 3.17610 | − | 11.8534i | 0.134455 | − | 0.501793i | ||||
\(559\) | −21.4173 | −0.905854 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.56652 | −0.277239 | ||||||||
\(562\) | −1.87849 | + | 7.01063i | −0.0792395 | + | 0.295726i | ||||
\(563\) | −33.9375 | + | 9.09354i | −1.43030 | + | 0.383247i | −0.889125 | − | 0.457665i | \(-0.848686\pi\) |
−0.541172 | + | 0.840912i | \(0.682019\pi\) | |||||||
\(564\) | 7.31149 | + | 4.22129i | 0.307869 | + | 0.177748i | ||||
\(565\) | −6.07710 | − | 34.7737i | −0.255666 | − | 1.46294i | ||||
\(566\) | − | 73.1086i | − | 3.07299i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.8911 | − | 11.8911i | 0.498939 | − | 0.498939i | ||||
\(569\) | 22.1757 | − | 12.8031i | 0.929652 | − | 0.536735i | 0.0429507 | − | 0.999077i | \(-0.486324\pi\) |
0.886702 | + | 0.462342i | \(0.152991\pi\) | |||||||
\(570\) | −0.0645229 | + | 0.724821i | −0.00270257 | + | 0.0303594i | ||||
\(571\) | −15.1850 | + | 26.3013i | −0.635474 | + | 1.10067i | 0.350941 | + | 0.936398i | \(0.385862\pi\) |
−0.986415 | + | 0.164275i | \(0.947471\pi\) | |||||||
\(572\) | −73.9453 | − | 19.8136i | −3.09181 | − | 0.828448i | ||||
\(573\) | −15.8728 | − | 15.8728i | −0.663096 | − | 0.663096i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.62050 | + | 19.1937i | 0.0675795 | + | 0.800431i | ||||
\(576\) | 6.23747 | + | 10.8036i | 0.259895 | + | 0.450151i | ||||
\(577\) | −5.93273 | − | 22.1412i | −0.246983 | − | 0.921752i | −0.972376 | − | 0.233418i | \(-0.925009\pi\) |
0.725394 | − | 0.688334i | \(-0.241658\pi\) | |||||||
\(578\) | −8.15351 | − | 30.4293i | −0.339141 | − | 1.26569i | ||||
\(579\) | −8.97817 | − | 15.5506i | −0.373120 | − | 0.646263i | ||||
\(580\) | 6.50055 | + | 13.9959i | 0.269920 | + | 0.581149i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 20.2543 | + | 20.2543i | 0.839569 | + | 0.839569i | ||||
\(583\) | 9.56788 | + | 2.56370i | 0.396261 | + | 0.106178i | ||||
\(584\) | 15.4406 | − | 26.7440i | 0.638938 | − | 1.10667i | ||||
\(585\) | −10.8920 | + | 9.11133i | −0.450329 | + | 0.376707i | ||||
\(586\) | 5.05699 | − | 2.91966i | 0.208902 | − | 0.120610i | ||||
\(587\) | −3.26809 | + | 3.26809i | −0.134888 | + | 0.134888i | −0.771327 | − | 0.636439i | \(-0.780407\pi\) |
0.636439 | + | 0.771327i | \(0.280407\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.737218i | 0.0303765i | ||||||||
\(590\) | 32.3325 | − | 5.65047i | 1.33111 | − | 0.232626i | ||||
\(591\) | 14.8537 | + | 8.57580i | 0.611001 | + | 0.352761i | ||||
\(592\) | −4.72647 | + | 1.26645i | −0.194257 | + | 0.0520509i | ||||
\(593\) | 3.38581 | − | 12.6360i | 0.139038 | − | 0.518899i | −0.860910 | − | 0.508757i | \(-0.830105\pi\) |
0.999949 | − | 0.0101415i | \(-0.00322821\pi\) | |||||||
\(594\) | −8.21074 | −0.336891 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 45.0272 | 1.84438 | ||||||||
\(597\) | −1.75858 | + | 6.56312i | −0.0719740 | + | 0.268610i | ||||
\(598\) | 55.0011 | − | 14.7375i | 2.24916 | − | 0.602661i | ||||
\(599\) | 1.72270 | + | 0.994603i | 0.0703877 | + | 0.0406384i | 0.534781 | − | 0.844991i | \(-0.320394\pi\) |
−0.464393 | + | 0.885629i | \(0.653728\pi\) | |||||||
\(600\) | −16.2310 | − | 2.91282i | −0.662628 | − | 0.118916i | ||||
\(601\) | 28.1436i | 1.14800i | 0.818855 | + | 0.574001i | \(0.194609\pi\) | ||||
−0.818855 | + | 0.574001i | \(0.805391\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.58511 | − | 7.58511i | 0.308890 | − | 0.308890i | ||||
\(604\) | −12.4595 | + | 7.19352i | −0.506972 | + | 0.292700i | ||||
\(605\) | −3.21898 | − | 0.286551i | −0.130870 | − | 0.0116499i | ||||
\(606\) | −1.67275 | + | 2.89729i | −0.0679509 | + | 0.117694i | ||||
\(607\) | 42.8022 | + | 11.4688i | 1.73729 | + | 0.465505i | 0.981841 | − | 0.189706i | \(-0.0607535\pi\) |
0.755446 | + | 0.655211i | \(0.227420\pi\) | |||||||
\(608\) | −0.458396 | − | 0.458396i | −0.0185904 | − | 0.0185904i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −49.0593 | − | 17.9405i | −1.98635 | − | 0.726391i | ||||
\(611\) | −7.84536 | − | 13.5886i | −0.317389 | − | 0.549734i | ||||
\(612\) | 1.64618 | + | 6.14364i | 0.0665430 | + | 0.248342i | ||||
\(613\) | 4.91551 | + | 18.3450i | 0.198536 | + | 0.740946i | 0.991323 | + | 0.131447i | \(0.0419624\pi\) |
−0.792787 | + | 0.609498i | \(0.791371\pi\) | |||||||
\(614\) | 17.5302 | + | 30.3632i | 0.707462 | + | 1.22536i | ||||
\(615\) | 1.89703 | + | 0.693725i | 0.0764954 | + | 0.0279737i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.02128 | + | 8.02128i | 0.322924 | + | 0.322924i | 0.849888 | − | 0.526963i | \(-0.176670\pi\) |
−0.526963 | + | 0.849888i | \(0.676670\pi\) | |||||||
\(618\) | 13.9414 | + | 3.73560i | 0.560807 | + | 0.150268i | ||||
\(619\) | −15.2997 | + | 26.4998i | −0.614945 | + | 1.06512i | 0.375449 | + | 0.926843i | \(0.377488\pi\) |
−0.990394 | + | 0.138273i | \(0.955845\pi\) | |||||||
\(620\) | −40.1270 | − | 3.57207i | −1.61154 | − | 0.143458i | ||||
\(621\) | 3.33627 | − | 1.92619i | 0.133880 | − | 0.0772955i | ||||
\(622\) | 30.6841 | − | 30.6841i | 1.23032 | − | 1.23032i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 5.34737i | 0.214066i | ||||||||
\(625\) | −19.2484 | + | 15.9531i | −0.769935 | + | 0.638122i | ||||
\(626\) | −41.4027 | − | 23.9038i | −1.65478 | − | 0.955390i | ||||
\(627\) | 0.476458 | − | 0.127667i | 0.0190279 | − | 0.00509851i | ||||
\(628\) | 0.855038 | − | 3.19105i | 0.0341197 | − | 0.127337i | ||||
\(629\) | 10.8169 | 0.431298 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.68706 | 0.266207 | 0.133104 | − | 0.991102i | \(-0.457506\pi\) | ||||
0.133104 | + | 0.991102i | \(0.457506\pi\) | |||||||
\(632\) | −7.19675 | + | 26.8587i | −0.286272 | + | 1.06838i | ||||
\(633\) | −2.45095 | + | 0.656731i | −0.0974167 | + | 0.0261027i | ||||
\(634\) | 58.8699 | + | 33.9885i | 2.33802 | + | 1.34986i | ||||
\(635\) | −15.0857 | + | 2.63640i | −0.598658 | + | 0.104622i | ||||
\(636\) | − | 9.59441i | − | 0.380443i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 11.7261 | − | 11.7261i | 0.464240 | − | 0.464240i | ||||
\(639\) | −4.41579 | + | 2.54946i | −0.174686 | + | 0.100855i | ||||
\(640\) | 33.8941 | − | 28.3530i | 1.33978 | − | 1.12075i | ||||
\(641\) | −24.4639 | + | 42.3726i | −0.966264 | + | 1.67362i | −0.260085 | + | 0.965586i | \(0.583751\pi\) |
−0.706179 | + | 0.708033i | \(0.749583\pi\) | |||||||
\(642\) | 40.3690 | + | 10.8168i | 1.59324 | + | 0.426906i | ||||
\(643\) | −3.55117 | − | 3.55117i | −0.140044 | − | 0.140044i | 0.633609 | − | 0.773653i | \(-0.281573\pi\) |
−0.773653 | + | 0.633609i | \(0.781573\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.17661 | + | 6.83936i | 0.125079 | + | 0.269300i | ||||
\(646\) | −0.302875 | − | 0.524594i | −0.0119164 | − | 0.0206399i | ||||
\(647\) | 7.51337 | + | 28.0403i | 0.295381 | + | 1.10238i | 0.940914 | + | 0.338645i | \(0.109969\pi\) |
−0.645533 | + | 0.763732i | \(0.723365\pi\) | |||||||
\(648\) | 0.853601 | + | 3.18568i | 0.0335326 | + | 0.125145i | ||||
\(649\) | −11.1244 | − | 19.2681i | −0.436672 | − | 0.756338i | ||||
\(650\) | 56.4691 | + | 47.6762i | 2.21490 | + | 1.87001i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.8000 | − | 24.8000i | −0.971242 | − | 0.971242i | ||||
\(653\) | −9.80085 | − | 2.62613i | −0.383537 | − | 0.102768i | 0.0618985 | − | 0.998082i | \(-0.480284\pi\) |
−0.445436 | + | 0.895314i | \(0.646951\pi\) | |||||||
\(654\) | 14.8167 | − | 25.6632i | 0.579377 | − | 1.00351i | ||||
\(655\) | −0.570313 | + | 6.40664i | −0.0222840 | + | 0.250328i | ||||
\(656\) | 0.658715 | − | 0.380309i | 0.0257185 | − | 0.0148486i | ||||
\(657\) | −6.62097 | + | 6.62097i | −0.258309 | + | 0.258309i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.2380i | 0.749405i | 0.927145 | + | 0.374703i | \(0.122255\pi\) | ||||
−0.927145 | + | 0.374703i | \(0.877745\pi\) | |||||||
\(660\) | 4.64033 | + | 26.5523i | 0.180624 | + | 1.03355i | ||||
\(661\) | −16.0842 | − | 9.28623i | −0.625604 | − | 0.361193i | 0.153444 | − | 0.988157i | \(-0.450964\pi\) |
−0.779048 | + | 0.626965i | \(0.784297\pi\) | |||||||
\(662\) | 53.1798 | − | 14.2495i | 2.06689 | − | 0.553822i | ||||
\(663\) | 3.05947 | − | 11.4181i | 0.118820 | − | 0.443442i | ||||
\(664\) | 34.4146 | 1.33555 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 13.5254 | 0.524098 | ||||||||
\(667\) | −2.01378 | + | 7.51552i | −0.0779738 | + | 0.291002i | ||||
\(668\) | 27.1025 | − | 7.26209i | 1.04863 | − | 0.280979i | ||||
\(669\) | −9.57233 | − | 5.52659i | −0.370088 | − | 0.213670i | ||||
\(670\) | −45.6819 | − | 32.0903i | −1.76485 | − | 1.23976i | ||||
\(671\) | 35.4089i | 1.36695i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.7627 | − | 11.7627i | 0.453420 | − | 0.453420i | −0.443068 | − | 0.896488i | \(-0.646110\pi\) |
0.896488 | + | 0.443068i | \(0.146110\pi\) | |||||||
\(674\) | −23.9083 | + | 13.8035i | −0.920913 | + | 0.531690i | ||||
\(675\) | 4.52510 | + | 2.12685i | 0.174171 | + | 0.0818623i | ||||
\(676\) | 46.6944 | − | 80.8771i | 1.79594 | − | 3.11066i | ||||
\(677\) | −48.0456 | − | 12.8738i | −1.84654 | − | 0.494780i | −0.847209 | − | 0.531259i | \(-0.821719\pi\) |
−0.999334 | + | 0.0364792i | \(0.988386\pi\) | |||||||
\(678\) | 25.9815 | + | 25.9815i | 0.997813 | + | 0.997813i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 12.4497 | − | 5.78240i | 0.477425 | − | 0.221745i | ||||
\(681\) | 12.2769 | + | 21.2642i | 0.470451 | + | 0.814846i | ||||
\(682\) | 11.2046 | + | 41.8161i | 0.429046 | + | 1.60122i | ||||
\(683\) | 11.7226 | + | 43.7494i | 0.448553 | + | 1.67402i | 0.706380 | + | 0.707833i | \(0.250327\pi\) |
−0.257827 | + | 0.966191i | \(0.583006\pi\) | |||||||
\(684\) | −0.238890 | − | 0.413769i | −0.00913418 | − | 0.0158209i | ||||
\(685\) | 15.7619 | − | 43.1017i | 0.602232 | − | 1.64683i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.22049 | + | 5.22049i | 0.199174 | + | 0.199174i | ||||
\(688\) | 2.74293 | + | 0.734967i | 0.104573 | + | 0.0280204i | ||||
\(689\) | −8.91571 | + | 15.4425i | −0.339662 | + | 0.588311i | ||||
\(690\) | −12.8640 | − | 15.3781i | −0.489724 | − | 0.585434i | ||||
\(691\) | 17.7216 | − | 10.2316i | 0.674161 | − | 0.389227i | −0.123490 | − | 0.992346i | \(-0.539409\pi\) |
0.797652 | + | 0.603119i | \(0.206075\pi\) | |||||||
\(692\) | 10.9089 | − | 10.9089i | 0.414695 | − | 0.414695i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.3364i | 0.961756i | ||||||||
\(695\) | 13.4844 | − | 19.1956i | 0.511493 | − | 0.728132i | ||||
\(696\) | −5.76866 | − | 3.33054i | −0.218660 | − | 0.126244i | ||||
\(697\) | −1.62413 | + | 0.435184i | −0.0615182 | + | 0.0164838i | ||||
\(698\) | 3.09219 | − | 11.5402i | 0.117041 | − | 0.436803i | ||||
\(699\) | 7.29308 | 0.275850 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.5198 | −0.926099 | −0.463049 | − | 0.886332i | \(-0.653245\pi\) | ||||
−0.463049 | + | 0.886332i | \(0.653245\pi\) | |||||||
\(702\) | 3.82554 | − | 14.2771i | 0.144386 | − | 0.538855i | ||||
\(703\) | −0.784860 | + | 0.210303i | −0.0296015 | + | 0.00793171i | ||||
\(704\) | −38.1128 | − | 22.0045i | −1.43643 | − | 0.829324i | ||||
\(705\) | −3.17573 | + | 4.52078i | −0.119605 | + | 0.170262i | ||||
\(706\) | 50.2611i | 1.89160i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −15.2384 | + | 15.2384i | −0.572694 | + | 0.572694i | ||||
\(709\) | −8.72879 | + | 5.03957i | −0.327817 | + | 0.189265i | −0.654871 | − | 0.755740i | \(-0.727277\pi\) |
0.327055 | + | 0.945005i | \(0.393944\pi\) | |||||||
\(710\) | 17.0264 | + | 20.3540i | 0.638991 | + | 0.763873i | ||||
\(711\) | 4.21552 | − | 7.30150i | 0.158095 | − | 0.273828i | ||||
\(712\) | 11.1753 | + | 2.99441i | 0.418812 | + | 0.112220i | ||||
\(713\) | −14.3626 | − | 14.3626i | −0.537883 | − | 0.537883i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 17.2053 | − | 47.0488i | 0.643443 | − | 1.75953i | ||||
\(716\) | 25.1865 | + | 43.6244i | 0.941265 | + | 1.63032i | ||||
\(717\) | −2.55864 | − | 9.54896i | −0.0955540 | − | 0.356612i | ||||
\(718\) | 2.49702 | + | 9.31900i | 0.0931879 | + | 0.347782i | ||||
\(719\) | −1.67817 | − | 2.90667i | −0.0625851 | − | 0.108401i | 0.833035 | − | 0.553220i | \(-0.186601\pi\) |
−0.895620 | + | 0.444820i | \(0.853268\pi\) | |||||||
\(720\) | 1.70762 | − | 0.793122i | 0.0636393 | − | 0.0295579i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −31.2372 | − | 31.2372i | −1.16253 | − | 1.16253i | ||||
\(723\) | −3.25363 | − | 0.871808i | −0.121004 | − | 0.0324229i | ||||
\(724\) | −10.4522 | + | 18.1038i | −0.388454 | + | 0.672821i | ||||
\(725\) | −9.49990 | + | 3.42504i | −0.352817 | + | 0.127203i | ||||
\(726\) | 2.91312 | − | 1.68189i | 0.108116 | − | 0.0624208i | ||||
\(727\) | −23.0330 | + | 23.0330i | −0.854247 | + | 0.854247i | −0.990653 | − | 0.136406i | \(-0.956445\pi\) |
0.136406 | + | 0.990653i | \(0.456445\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 39.8753 | + | 28.0113i | 1.47585 | + | 1.03675i | ||||
\(731\) | −5.43640 | − | 3.13871i | −0.201073 | − | 0.116089i | ||||
\(732\) | 33.1286 | − | 8.87677i | 1.22447 | − | 0.328095i | ||||
\(733\) | −12.4202 | + | 46.3528i | −0.458751 | + | 1.71208i | 0.218071 | + | 0.975933i | \(0.430024\pi\) |
−0.676821 | + | 0.736147i | \(0.736643\pi\) | |||||||
\(734\) | −7.90873 | −0.291917 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 17.8611 | 0.658367 | ||||||||
\(737\) | −9.79434 | + | 36.5530i | −0.360779 | + | 1.34645i | ||||
\(738\) | −2.03080 | + | 0.544151i | −0.0747548 | + | 0.0200305i | ||||
\(739\) | −16.4664 | − | 9.50689i | −0.605727 | − | 0.349717i | 0.165564 | − | 0.986199i | \(-0.447055\pi\) |
−0.771291 | + | 0.636482i | \(0.780389\pi\) | |||||||
\(740\) | −7.64391 | − | 43.7391i | −0.280996 | − | 1.60788i | ||||
\(741\) | 0.887964i | 0.0326202i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.50371 | + | 2.50371i | −0.0918524 | + | 0.0918524i | −0.751540 | − | 0.659688i | \(-0.770689\pi\) |
0.659688 | + | 0.751540i | \(0.270689\pi\) | |||||||
\(744\) | 15.0594 | − | 8.69452i | 0.552103 | − | 0.318757i | ||||
\(745\) | −2.61265 | + | 29.3493i | −0.0957199 | + | 1.07527i | ||||
\(746\) | 41.7382 | − | 72.2926i | 1.52814 | − | 2.64682i | ||||
\(747\) | −10.0792 | − | 2.70073i | −0.368780 | − | 0.0988144i | ||||
\(748\) | −15.8660 | − | 15.8660i | −0.580120 | − | 0.580120i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 6.84935 | − | 25.1041i | 0.250103 | − | 0.916671i | ||||
\(751\) | −12.4684 | − | 21.5959i | −0.454978 | − | 0.788046i | 0.543708 | − | 0.839274i | \(-0.317020\pi\) |
−0.998687 | + | 0.0512283i | \(0.983686\pi\) | |||||||
\(752\) | 0.538452 | + | 2.00953i | 0.0196353 | + | 0.0732800i | ||||
\(753\) | 1.27797 | + | 4.76945i | 0.0465718 | + | 0.173808i | ||||
\(754\) | 14.9263 | + | 25.8531i | 0.543584 | + | 0.941515i | ||||
\(755\) | −3.96587 | − | 8.53868i | −0.144333 | − | 0.310754i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.224148 | − | 0.224148i | −0.00814681 | − | 0.00814681i | 0.703022 | − | 0.711168i | \(-0.251834\pi\) |
−0.711168 | + | 0.703022i | \(0.751834\pi\) | |||||||
\(758\) | −18.0431 | − | 4.83462i | −0.655353 | − | 0.175601i | ||||
\(759\) | −6.79520 | + | 11.7696i | −0.246650 | + | 0.427211i | ||||
\(760\) | −0.790914 | + | 0.661612i | −0.0286895 | + | 0.0239992i | ||||
\(761\) | 12.1337 | − | 7.00541i | 0.439847 | − | 0.253946i | −0.263685 | − | 0.964609i | \(-0.584938\pi\) |
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(762\) | 11.2714 | − | 11.2714i | 0.408321 | − | 0.408321i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 76.7039i | − | 2.77505i | ||||||
\(765\) | −4.10002 | + | 0.716525i | −0.148236 | + | 0.0259060i | ||||
\(766\) | 66.1651 | + | 38.2004i | 2.39064 | + | 1.38024i | ||||
\(767\) | 38.6871 | − | 10.3662i | 1.39691 | − | 0.374301i | ||||
\(768\) | −5.44696 | + | 20.3283i | −0.196550 | + | 0.733535i | ||||
\(769\) | 49.1264 | 1.77154 | 0.885772 | − | 0.464120i | \(-0.153629\pi\) | ||||
0.885772 | + | 0.464120i | \(0.153629\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.4995 | −0.738272 | ||||||||
\(772\) | 15.8804 | − | 59.2666i | 0.571549 | − | 2.13305i | ||||
\(773\) | 22.4052 | − | 6.00345i | 0.805858 | − | 0.215929i | 0.167704 | − | 0.985837i | \(-0.446365\pi\) |
0.638154 | + | 0.769908i | \(0.279698\pi\) | |||||||
\(774\) | −6.79765 | − | 3.92463i | −0.244337 | − | 0.141068i | ||||
\(775\) | 4.65664 | − | 25.9480i | 0.167271 | − | 0.932079i | ||||
\(776\) | 40.5893i | 1.45707i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 25.5370 | − | 25.5370i | 0.915546 | − | 0.915546i | ||||
\(779\) | 0.109384 | − | 0.0631527i | 0.00391908 | − | 0.00226268i | ||||
\(780\) | −48.3321 | − | 4.30249i | −1.73057 | − | 0.154054i | ||||
\(781\) | 8.99394 | − | 15.5780i | 0.321829 | − | 0.557423i | ||||
\(782\) | 16.1208 | + | 4.31957i | 0.576480 | + | 0.154467i | ||||
\(783\) | 1.42814 | + | 1.42814i | 0.0510375 | + | 0.0510375i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.03035 | + | 0.742481i | 0.0724663 | + | 0.0265003i | ||||
\(786\) | −3.34742 | − | 5.79789i | −0.119398 | − | 0.206804i | ||||
\(787\) | −3.76964 | − | 14.0685i | −0.134373 | − | 0.501488i | −1.00000 | 0.000797382i | \(-0.999746\pi\) | |
0.865626 | − | 0.500690i | \(-0.166920\pi\) | |||||||
\(788\) | 15.1687 | + | 56.6105i | 0.540364 | + | 2.01667i | ||||
\(789\) | 1.73938 | + | 3.01270i | 0.0619237 | + | 0.107255i | ||||
\(790\) | −41.2090 | − | 15.0698i | −1.46615 | − | 0.536158i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −8.22708 | − | 8.22708i | −0.292337 | − | 0.292337i | ||||
\(793\) | −61.5702 | − | 16.4977i | −2.18642 | − | 0.585850i | ||||
\(794\) | −24.4893 | + | 42.4167i | −0.869093 | + | 1.50531i | ||||
\(795\) | 6.25375 | + | 0.556704i | 0.221798 | + | 0.0197442i | ||||
\(796\) | −20.1069 | + | 11.6087i | −0.712671 | + | 0.411461i | ||||
\(797\) | 38.0535 | − | 38.0535i | 1.34792 | − | 1.34792i | 0.460013 | − | 0.887912i | \(-0.347845\pi\) |
0.887912 | − | 0.460013i | \(-0.152155\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.59896i | − | 0.162700i | ||||||
\(800\) | 13.2388 | + | 19.0297i | 0.468062 | + | 0.672802i | ||||
\(801\) | −3.03799 | − | 1.75399i | −0.107342 | − | 0.0619740i | ||||
\(802\) | −42.0354 | + | 11.2633i | −1.48432 | + | 0.397722i | ||||
\(803\) | 8.54938 | − | 31.9067i | 0.301701 | − | 1.12596i | ||||
\(804\) | 36.6543 | 1.29270 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −77.9317 | −2.74503 | ||||||||
\(807\) | 4.84272 | − | 18.0733i | 0.170472 | − | 0.636210i | ||||
\(808\) | −4.57913 | + | 1.22698i | −0.161093 | + | 0.0431648i | ||||
\(809\) | 15.3437 | + | 8.85869i | 0.539456 | + | 0.311455i | 0.744858 | − | 0.667222i | \(-0.232517\pi\) |
−0.205402 | + | 0.978678i | \(0.565850\pi\) | |||||||
\(810\) | −5.12664 | + | 0.895939i | −0.180132 | + | 0.0314801i | ||||
\(811\) | − | 27.9256i | − | 0.980600i | −0.871554 | − | 0.490300i | \(-0.836887\pi\) | ||
0.871554 | − | 0.490300i | \(-0.163113\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.96396 | − | 4.96396i | 0.174094 | − | 0.174094i | ||||
\(814\) | −41.3221 | + | 23.8573i | −1.44834 | + | 0.836199i | ||||
\(815\) | 17.6039 | − | 14.7259i | 0.616638 | − | 0.515827i | ||||
\(816\) | −0.783659 | + | 1.35734i | −0.0274336 | + | 0.0475163i | ||||
\(817\) | 0.455481 | + | 0.122046i | 0.0159353 | + | 0.00426984i | ||||
\(818\) | −39.1693 | − | 39.1693i | −1.36952 | − | 1.36952i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.90742 | + | 6.25978i | 0.101531 | + | 0.218601i | ||||
\(821\) | 9.80771 | + | 16.9874i | 0.342291 | + | 0.592866i | 0.984858 | − | 0.173364i | \(-0.0554637\pi\) |
−0.642566 | + | 0.766230i | \(0.722130\pi\) | |||||||
\(822\) | 12.3635 | + | 46.1412i | 0.431227 | + | 1.60936i | ||||
\(823\) | −13.0933 | − | 48.8650i | −0.456405 | − | 1.70333i | −0.683924 | − | 0.729553i | \(-0.739728\pi\) |
0.227519 | − | 0.973774i | \(-0.426939\pi\) | |||||||
\(824\) | 10.2261 | + | 17.7122i | 0.356245 | + | 0.617034i | ||||
\(825\) | −17.5764 | + | 1.48396i | −0.611931 | + | 0.0516647i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.2487 | + | 18.2487i | 0.634570 | + | 0.634570i | 0.949211 | − | 0.314641i | \(-0.101884\pi\) |
−0.314641 | + | 0.949211i | \(0.601884\pi\) | |||||||
\(828\) | 12.7152 | + | 3.40702i | 0.441883 | + | 0.118402i | ||||
\(829\) | −20.5574 | + | 35.6064i | −0.713988 | + | 1.23666i | 0.249361 | + | 0.968411i | \(0.419779\pi\) |
−0.963349 | + | 0.268252i | \(0.913554\pi\) | |||||||
\(830\) | −4.81526 | + | 54.0924i | −0.167140 | + | 1.87757i | ||||
\(831\) | −6.75426 | + | 3.89958i | −0.234303 | + | 0.135275i | ||||
\(832\) | 56.0196 | − | 56.0196i | 1.94213 | − | 1.94213i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 24.4172i | 0.845499i | ||||||||
\(835\) | 3.16093 | + | 18.0871i | 0.109388 | + | 0.625930i | ||||
\(836\) | 1.45969 | + | 0.842752i | 0.0504844 | + | 0.0291472i | ||||
\(837\) | −5.09285 | + | 1.36462i | −0.176035 | + | 0.0471683i | ||||
\(838\) | 5.85525 | − | 21.8521i | 0.202266 | − | 0.754868i | ||||
\(839\) | 46.0286 | 1.58908 | 0.794541 | − | 0.607210i | \(-0.207711\pi\) | ||||
0.794541 | + | 0.607210i | \(0.207711\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.9208 | 0.859339 | ||||||||
\(842\) | 7.83676 | − | 29.2472i | 0.270073 | − | 1.00793i | ||||
\(843\) | 3.01215 | − | 0.807103i | 0.103744 | − | 0.0277981i | ||||
\(844\) | −7.50880 | − | 4.33521i | −0.258464 | − | 0.149224i | ||||
\(845\) | 50.0073 | + | 35.1288i | 1.72030 | + | 1.20847i | ||||
\(846\) | − | 5.75052i | − | 0.197707i | ||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.67178 | − | 1.67178i | 0.0574091 | − | 0.0574091i | ||||
\(849\) | −27.2031 | + | 15.7057i | −0.933609 | + | 0.539019i | ||||
\(850\) | 7.34673 | + | 20.3773i | 0.251991 | + | 0.698937i | ||||
\(851\) | 11.1936 | − | 19.3879i | 0.383711 | − | 0.664608i | ||||
\(852\) | −16.8295 | − | 4.50944i | −0.576568 | − | 0.154491i | ||||
\(853\) | −22.9994 | − | 22.9994i | −0.787484 | − | 0.787484i | 0.193597 | − | 0.981081i | \(-0.437984\pi\) |
−0.981081 | + | 0.193597i | \(0.937984\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.283561 | − | 0.131703i | 0.00969759 | − | 0.00450414i | ||||
\(856\) | 29.6109 | + | 51.2876i | 1.01208 | + | 1.75298i | ||||
\(857\) | −2.22400 | − | 8.30009i | −0.0759705 | − | 0.283526i | 0.917481 | − | 0.397779i | \(-0.130219\pi\) |
−0.993452 | + | 0.114254i | \(0.963552\pi\) | |||||||
\(858\) | 13.4957 | + | 50.3666i | 0.460735 | + | 1.71949i | ||||
\(859\) | −1.33433 | − | 2.31112i | −0.0455266 | − | 0.0788544i | 0.842364 | − | 0.538909i | \(-0.181163\pi\) |
−0.887891 | + | 0.460054i | \(0.847830\pi\) | |||||||
\(860\) | −8.84995 | + | 24.2006i | −0.301781 | + | 0.825234i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 21.7319 | + | 21.7319i | 0.740190 | + | 0.740190i | ||||
\(863\) | −0.515877 | − | 0.138229i | −0.0175607 | − | 0.00470537i | 0.250028 | − | 0.968239i | \(-0.419560\pi\) |
−0.267589 | + | 0.963533i | \(0.586227\pi\) | |||||||
\(864\) | 2.31818 | − | 4.01520i | 0.0788660 | − | 0.136600i | ||||
\(865\) | 6.47758 | + | 7.74354i | 0.220244 | + | 0.263288i | ||||
\(866\) | 39.7140 | − | 22.9289i | 1.34954 | − | 0.779155i | ||||
\(867\) | −9.57090 | + | 9.57090i | −0.325045 | + | 0.325045i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 29.7429i | 1.00896i | ||||||||
\(870\) | 6.04202 | − | 8.60107i | 0.204844 | − | 0.291604i | ||||
\(871\) | −58.9962 | − | 34.0615i | −1.99901 | − | 1.15413i | ||||
\(872\) | 40.5604 | − | 10.8681i | 1.37355 | − | 0.368041i | ||||
\(873\) | 3.18529 | − | 11.8877i | 0.107806 | − | 0.402336i | ||||
\(874\) | −1.25369 | −0.0424067 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.9952 | −1.08102 | ||||||||
\(877\) | 10.7066 | − | 39.9574i | 0.361535 | − | 1.34927i | −0.510523 | − | 0.859864i | \(-0.670548\pi\) |
0.872058 | − | 0.489402i | \(-0.162785\pi\) | |||||||
\(878\) | 28.3643 | − | 7.60019i | 0.957249 | − | 0.256494i | ||||
\(879\) | −2.17276 | − | 1.25444i | −0.0732854 | − | 0.0423113i | ||||
\(880\) | −3.81806 | + | 5.43517i | −0.128707 | + | 0.183219i | ||||
\(881\) | 23.0542i | 0.776715i | 0.921509 | + | 0.388358i | \(0.126957\pi\) | ||||
−0.921509 | + | 0.388358i | \(0.873043\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.73430 | + | 7.73430i | −0.260280 | + | 0.260280i | −0.825168 | − | 0.564888i | \(-0.808919\pi\) |
0.564888 | + | 0.825168i | \(0.308919\pi\) | |||||||
\(884\) | 34.9807 | − | 20.1961i | 1.17653 | − | 0.679269i | ||||
\(885\) | −9.04839 | − | 10.8168i | −0.304158 | − | 0.363602i | ||||
\(886\) | −22.2677 | + | 38.5688i | −0.748098 | + | 1.29574i | ||||
\(887\) | 49.6024 | + | 13.2909i | 1.66549 | + | 0.446265i | 0.963888 | − | 0.266308i | \(-0.0858039\pi\) |
0.701597 | + | 0.712574i | \(0.252471\pi\) | |||||||
\(888\) | 13.5523 | + | 13.5523i | 0.454785 | + | 0.454785i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −6.27020 | + | 17.1462i | −0.210177 | + | 0.574740i | ||||
\(891\) | 1.76389 | + | 3.05515i | 0.0590926 | + | 0.102351i | ||||
\(892\) | −9.77533 | − | 36.4820i | −0.327302 | − | 1.22151i | ||||
\(893\) | 0.0894132 | + | 0.333695i | 0.00299210 | + | 0.0111667i | ||||
\(894\) | −15.3347 | − | 26.5606i | −0.512871 | − | 0.888318i | ||||
\(895\) | −29.8963 | + | 13.8856i | −0.999323 | + | 0.464146i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −17.2994 | − | 17.2994i | −0.577611 | − | 0.577611i | ||||
\(898\) | −50.0015 | − | 13.3979i | −1.66857 | − | 0.447092i | ||||
\(899\) | 5.32442 | − | 9.22216i | 0.177579 | − | 0.307576i | ||||
\(900\) | 5.79467 | + | 16.0725i | 0.193156 | + | 0.535748i | ||||
\(901\) | −4.52620 | + | 2.61320i | −0.150790 | + | 0.0870584i | ||||
\(902\) | 5.24458 | − | 5.24458i | 0.174625 | − | 0.174625i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 52.0664i | 1.73170i | ||||||||
\(905\) | −11.1938 | − | 7.86333i | −0.372094 | − | 0.261386i | ||||
\(906\) | 8.48661 | + | 4.89974i | 0.281949 | + | 0.162783i | ||||
\(907\) | 13.5581 | − | 3.63289i | 0.450191 | − | 0.120628i | −0.0265979 | − | 0.999646i | \(-0.508467\pi\) |
0.476789 | + | 0.879018i | \(0.341801\pi\) | |||||||
\(908\) | −21.7152 | + | 81.0421i | −0.720643 | + | 2.68948i | ||||
\(909\) | 1.43741 | 0.0476759 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 42.2471 | 1.39971 | 0.699854 | − | 0.714286i | \(-0.253248\pi\) | ||||
0.699854 | + | 0.714286i | \(0.253248\pi\) | |||||||
\(912\) | 0.0304719 | − | 0.113723i | 0.00100902 | − | 0.00376573i | ||||
\(913\) | 35.5574 | − | 9.52758i | 1.17678 | − | 0.315317i | ||||
\(914\) | 21.3969 | + | 12.3535i | 0.707745 | + | 0.408617i | ||||
\(915\) | 3.86375 | + | 22.1087i | 0.127731 | + | 0.730890i | ||||
\(916\) | 25.2275i | 0.833541i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 3.06337 | − | 3.06337i | 0.101106 | − | 0.101106i | ||||
\(919\) | 3.66062 | − | 2.11346i | 0.120753 | − | 0.0697166i | −0.438407 | − | 0.898777i | \(-0.644457\pi\) |
0.559160 | + | 0.829060i | \(0.311124\pi\) | |||||||
\(920\) | 2.51909 | − | 28.2983i | 0.0830519 | − | 0.932967i | ||||
\(921\) | 7.53194 | − | 13.0457i | 0.248186 | − | 0.429870i | ||||
\(922\) | 14.4737 | + | 3.87822i | 0.476666 | + | 0.127722i | ||||
\(923\) | 22.8970 | + | 22.8970i | 0.753665 | + | 0.753665i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.9532 | − | 2.44449i | 0.951976 | − | 0.0803743i | ||||
\(926\) | 17.2119 | + | 29.8119i | 0.565618 | + | 0.979679i | ||||
\(927\) | −1.60502 | − | 5.99000i | −0.0527156 | − | 0.196737i | ||||
\(928\) | 2.42359 | + | 9.04495i | 0.0795581 | + | 0.296915i | ||||
\(929\) | −3.81103 | − | 6.60089i | −0.125036 | − | 0.216568i | 0.796711 | − | 0.604360i | \(-0.206571\pi\) |
−0.921747 | + | 0.387792i | \(0.873238\pi\) | |||||||
\(930\) | 11.5588 | + | 24.8866i | 0.379029 | + | 0.816063i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17.6216 | + | 17.6216i | 0.577214 | + | 0.577214i | ||||
\(933\) | −18.0091 | − | 4.82552i | −0.589591 | − | 0.157980i | ||||
\(934\) | −12.1522 | + | 21.0483i | −0.397633 | + | 0.688720i | ||||
\(935\) | 11.2623 | − | 9.42108i | 0.368316 | − | 0.308102i | ||||
\(936\) | 18.1387 | − | 10.4724i | 0.592882 | − | 0.342300i | ||||
\(937\) | −31.1453 | + | 31.1453i | −1.01747 | + | 1.01747i | −0.0176276 | + | 0.999845i | \(0.505611\pi\) |
−0.999845 | + | 0.0176276i | \(0.994389\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 20.5408i | 0.670324i | ||||||||
\(940\) | −18.5963 | + | 3.24992i | −0.606545 | + | 0.106001i | ||||
\(941\) | −35.5296 | − | 20.5130i | −1.15823 | − | 0.668706i | −0.207352 | − | 0.978266i | \(-0.566485\pi\) |
−0.950880 | + | 0.309561i | \(0.899818\pi\) | |||||||
\(942\) | −2.17353 | + | 0.582395i | −0.0708173 | + | 0.0189754i | ||||
\(943\) | −0.900678 | + | 3.36137i | −0.0293301 | + | 0.109461i | ||||
\(944\) | −5.31043 | −0.172840 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.6905 | 0.900295 | ||||||||
\(947\) | 13.8565 | − | 51.7131i | 0.450276 | − | 1.68045i | −0.251343 | − | 0.967898i | \(-0.580872\pi\) |
0.701618 | − | 0.712553i | \(-0.252461\pi\) | |||||||
\(948\) | 27.8275 | − | 7.45635i | 0.903795 | − | 0.242171i | ||||
\(949\) | 51.4972 | + | 29.7319i | 1.67167 | + | 0.965139i | ||||
\(950\) | −0.929247 | − | 1.33572i | −0.0301487 | − | 0.0433364i | ||||
\(951\) | − | 29.2067i | − | 0.947091i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.5644 | − | 35.5644i | 1.15204 | − | 1.15204i | 0.165900 | − | 0.986143i | \(-0.446947\pi\) |
0.986143 | − | 0.165900i | \(-0.0530528\pi\) | |||||||
\(954\) | −5.65954 | + | 3.26753i | −0.183234 | + | 0.105790i | ||||
\(955\) | 49.9965 | + | 4.45065i | 1.61785 | + | 0.144020i | ||||
\(956\) | 16.8900 | − | 29.2544i | 0.546263 | − | 0.946155i | ||||
\(957\) | −6.88226 | − | 1.84410i | −0.222472 | − | 0.0596112i | ||||
\(958\) | −50.3845 | − | 50.3845i | −1.62785 | − | 1.62785i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −26.1980 | − | 9.58039i | −0.845538 | − | 0.309206i | ||||
\(961\) | −1.60035 | − | 2.77188i | −0.0516241 | − | 0.0894156i | ||||
\(962\) | −22.2312 | − | 82.9679i | −0.716762 | − | 2.67499i | ||||
\(963\) | −4.64750 | − | 17.3447i | −0.149764 | − | 0.558925i | ||||
\(964\) | −5.75497 | − | 9.96790i | −0.185355 | − | 0.321044i | ||||
\(965\) | 37.7092 | + | 13.7899i | 1.21390 | + | 0.443914i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.89078 | − | 5.89078i | −0.189435 | − | 0.189435i | 0.606017 | − | 0.795452i | \(-0.292766\pi\) |
−0.795452 | + | 0.606017i | \(0.792766\pi\) | |||||||
\(968\) | 4.60415 | + | 1.23368i | 0.147983 | + | 0.0396519i | ||||
\(969\) | −0.130131 | + | 0.225394i | −0.00418043 | + | 0.00724071i | ||||
\(970\) | −63.7976 | − | 5.67920i | −2.04842 | − | 0.182348i | ||||
\(971\) | 2.71844 | − | 1.56949i | 0.0872389 | − | 0.0503674i | −0.455746 | − | 0.890110i | \(-0.650627\pi\) |
0.542985 | + | 0.839742i | \(0.317294\pi\) | |||||||
\(972\) | 2.41620 | − | 2.41620i | 0.0774998 | − | 0.0774998i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 41.7807i | 1.33874i | ||||||||
\(975\) | 5.60883 | − | 31.2538i | 0.179626 | − | 1.00092i | ||||
\(976\) | 7.31922 | + | 4.22576i | 0.234283 | + | 0.135263i | ||||
\(977\) | −28.5027 | + | 7.63727i | −0.911882 | + | 0.244338i | −0.684112 | − | 0.729377i | \(-0.739810\pi\) |
−0.227770 | + | 0.973715i | \(0.573143\pi\) | |||||||
\(978\) | −6.18293 | + | 23.0750i | −0.197708 | + | 0.737858i | ||||
\(979\) | 12.3754 | 0.395518 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.7321 | −0.406504 | ||||||||
\(982\) | 3.17439 | − | 11.8470i | 0.101299 | − | 0.378053i | ||||
\(983\) | −52.8361 | + | 14.1574i | −1.68521 | + | 0.451551i | −0.969147 | − | 0.246484i | \(-0.920725\pi\) |
−0.716064 | + | 0.698035i | \(0.754058\pi\) | |||||||
\(984\) | −2.58008 | − | 1.48961i | −0.0822498 | − | 0.0474869i | ||||
\(985\) | −37.7796 | + | 6.60241i | −1.20376 | + | 0.210370i | ||||
\(986\) | 8.74982i | 0.278651i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.14550 | + | 2.14550i | −0.0682575 | + | 0.0682575i | ||||
\(989\) | −11.2515 | + | 6.49603i | −0.357775 | + | 0.206562i | ||||
\(990\) | 14.0823 | − | 11.7801i | 0.447565 | − | 0.374395i | ||||
\(991\) | −24.3059 | + | 42.0991i | −0.772104 | + | 1.33732i | 0.164304 | + | 0.986410i | \(0.447462\pi\) |
−0.936408 | + | 0.350913i | \(0.885871\pi\) | |||||||
\(992\) | −23.6123 | − | 6.32689i | −0.749690 | − | 0.200879i | ||||
\(993\) | −16.7266 | − | 16.7266i | −0.530803 | − | 0.530803i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.40004 | − | 13.7795i | −0.202895 | − | 0.436840i | ||||
\(996\) | −17.8280 | − | 30.8790i | −0.564902 | − | 0.978439i | ||||
\(997\) | 2.81774 | + | 10.5159i | 0.0892387 | + | 0.333043i | 0.996083 | − | 0.0884222i | \(-0.0281825\pi\) |
−0.906844 | + | 0.421466i | \(0.861516\pi\) | |||||||
\(998\) | −21.6418 | − | 80.7685i | −0.685061 | − | 2.55668i | ||||
\(999\) | −2.90562 | − | 5.03269i | −0.0919298 | − | 0.159227i |
(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 | 735.2.v.b.472.7 | 32 | ||
5.3 | odd | 4 | inner | 735.2.v.b.178.2 | 32 | ||
7.2 | even | 3 | 105.2.u.a.82.2 | yes | 32 | ||
7.3 | odd | 6 | 735.2.m.c.97.13 | 32 | |||
7.4 | even | 3 | 735.2.m.c.97.14 | 32 | |||
7.5 | odd | 6 | inner | 735.2.v.b.607.2 | 32 | ||
7.6 | odd | 2 | 105.2.u.a.52.7 | ✓ | 32 | ||
21.2 | odd | 6 | 315.2.bz.d.82.7 | 32 | |||
21.20 | even | 2 | 315.2.bz.d.262.2 | 32 | |||
35.2 | odd | 12 | 525.2.bc.e.418.2 | 32 | |||
35.3 | even | 12 | 735.2.m.c.538.14 | 32 | |||
35.9 | even | 6 | 525.2.bc.e.82.7 | 32 | |||
35.13 | even | 4 | 105.2.u.a.73.2 | yes | 32 | ||
35.18 | odd | 12 | 735.2.m.c.538.13 | 32 | |||
35.23 | odd | 12 | 105.2.u.a.103.7 | yes | 32 | ||
35.27 | even | 4 | 525.2.bc.e.493.7 | 32 | |||
35.33 | even | 12 | inner | 735.2.v.b.313.7 | 32 | ||
35.34 | odd | 2 | 525.2.bc.e.157.2 | 32 | |||
105.23 | even | 12 | 315.2.bz.d.208.2 | 32 | |||
105.83 | odd | 4 | 315.2.bz.d.73.7 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.u.a.52.7 | ✓ | 32 | 7.6 | odd | 2 | ||
105.2.u.a.73.2 | yes | 32 | 35.13 | even | 4 | ||
105.2.u.a.82.2 | yes | 32 | 7.2 | even | 3 | ||
105.2.u.a.103.7 | yes | 32 | 35.23 | odd | 12 | ||
315.2.bz.d.73.7 | 32 | 105.83 | odd | 4 | |||
315.2.bz.d.82.7 | 32 | 21.2 | odd | 6 | |||
315.2.bz.d.208.2 | 32 | 105.23 | even | 12 | |||
315.2.bz.d.262.2 | 32 | 21.20 | even | 2 | |||
525.2.bc.e.82.7 | 32 | 35.9 | even | 6 | |||
525.2.bc.e.157.2 | 32 | 35.34 | odd | 2 | |||
525.2.bc.e.418.2 | 32 | 35.2 | odd | 12 | |||
525.2.bc.e.493.7 | 32 | 35.27 | even | 4 | |||
735.2.m.c.97.13 | 32 | 7.3 | odd | 6 | |||
735.2.m.c.97.14 | 32 | 7.4 | even | 3 | |||
735.2.m.c.538.13 | 32 | 35.18 | odd | 12 | |||
735.2.m.c.538.14 | 32 | 35.3 | even | 12 | |||
735.2.v.b.178.2 | 32 | 5.3 | odd | 4 | inner | ||
735.2.v.b.313.7 | 32 | 35.33 | even | 12 | inner | ||
735.2.v.b.472.7 | 32 | 1.1 | even | 1 | trivial | ||
735.2.v.b.607.2 | 32 | 7.5 | odd | 6 | inner |