Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,3,Mod(31,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([4, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.h (of order \(8\), 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: | \(6.97549476762\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 31.7 | ||
Character | \(\chi\) | \(=\) | 256.31 |
Dual form | 256.3.h.b.223.7 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(-1\) |
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 | 0 | ||||||||
\(3\) | 4.68670 | − | 1.94129i | 1.56223 | − | 0.647098i | 0.576758 | − | 0.816915i | \(-0.304318\pi\) |
0.985476 | + | 0.169817i | \(0.0543176\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.51028 | + | 1.86822i | 0.902055 | + | 0.373644i | 0.785010 | − | 0.619483i | \(-0.212658\pi\) |
0.117045 | + | 0.993127i | \(0.462658\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.85317 | + | 3.85317i | −0.550453 | + | 0.550453i | −0.926571 | − | 0.376119i | \(-0.877258\pi\) |
0.376119 | + | 0.926571i | \(0.377258\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 11.8326 | − | 11.8326i | 1.31473 | − | 1.31473i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.56441 | + | 1.89064i | 0.414946 | + | 0.171876i | 0.580382 | − | 0.814344i | \(-0.302903\pi\) |
−0.165436 | + | 0.986221i | \(0.552903\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.58307 | − | 2.31258i | 0.429467 | − | 0.177891i | −0.157470 | − | 0.987524i | \(-0.550334\pi\) |
0.586937 | + | 0.809633i | \(0.300334\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 24.7651 | 1.65101 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 25.0539i | 1.47376i | 0.676025 | + | 0.736879i | \(0.263701\pi\) | ||||
−0.676025 | + | 0.736879i | \(0.736299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.43433 | − | 15.5338i | −0.338649 | − | 0.817571i | −0.997846 | − | 0.0656005i | \(-0.979104\pi\) |
0.659197 | − | 0.751970i | \(-0.270896\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −10.5785 | + | 25.5388i | −0.503739 | + | 1.21613i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −26.9024 | − | 26.9024i | −1.16967 | − | 1.16967i | −0.982287 | − | 0.187381i | \(-0.940000\pi\) |
−0.187381 | − | 0.982287i | \(-0.560000\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.825315 | − | 0.825315i | −0.0330126 | − | 0.0330126i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.0136 | − | 36.2460i | 0.556058 | − | 1.34244i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.210028 | + | 0.507052i | 0.00724234 | + | 0.0174846i | 0.927459 | − | 0.373924i | \(-0.121988\pi\) |
−0.920217 | + | 0.391409i | \(0.871988\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 15.8372i | − | 0.510877i | −0.966825 | − | 0.255438i | \(-0.917780\pi\) | ||
0.966825 | − | 0.255438i | \(-0.0822198\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 25.0623 | 0.759464 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −24.5774 | + | 10.1803i | −0.702212 | + | 0.290866i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.18606 | + | 0.905498i | 0.0590828 | + | 0.0244729i | 0.412029 | − | 0.911171i | \(-0.364820\pi\) |
−0.352946 | + | 0.935644i | \(0.614820\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 21.6768 | − | 21.6768i | 0.555814 | − | 0.555814i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.1517 | + | 31.1517i | −0.759798 | + | 0.759798i | −0.976285 | − | 0.216488i | \(-0.930540\pi\) |
0.216488 | + | 0.976285i | \(0.430540\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.9078 | − | 5.34659i | −0.300182 | − | 0.124339i | 0.227509 | − | 0.973776i | \(-0.426942\pi\) |
−0.527691 | + | 0.849437i | \(0.676942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 75.4740 | − | 31.2624i | 1.67720 | − | 0.694719i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 15.0033 | 0.319220 | 0.159610 | − | 0.987180i | \(-0.448976\pi\) | ||||
0.159610 | + | 0.987180i | \(0.448976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.3062i | 0.394004i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 48.6370 | + | 117.420i | 0.953666 | + | 2.30235i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 15.4409 | − | 37.2776i | 0.291338 | − | 0.703352i | −0.708660 | − | 0.705550i | \(-0.750700\pi\) |
0.999998 | + | 0.00219873i | \(0.000699877\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.0546 | + | 17.0546i | 0.310084 | + | 0.310084i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −60.3115 | − | 60.3115i | −1.05810 | − | 1.05810i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.7242 | − | 35.5473i | 0.249562 | − | 0.602496i | −0.748605 | − | 0.663016i | \(-0.769276\pi\) |
0.998167 | + | 0.0605202i | \(0.0192760\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15.4603 | + | 37.3243i | 0.253447 | + | 0.611875i | 0.998478 | − | 0.0551552i | \(-0.0175654\pi\) |
−0.745031 | + | 0.667030i | \(0.767565\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 91.1858i | 1.44739i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 29.5016 | 0.453870 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −61.3598 | + | 25.4161i | −0.915818 | + | 0.379344i | −0.790281 | − | 0.612745i | \(-0.790065\pi\) |
−0.125537 | + | 0.992089i | \(0.540065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −178.309 | − | 73.8579i | −2.58419 | − | 1.07040i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −51.7789 | + | 51.7789i | −0.729281 | + | 0.729281i | −0.970477 | − | 0.241196i | \(-0.922460\pi\) |
0.241196 | + | 0.970477i | \(0.422460\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 64.9440 | − | 64.9440i | 0.889643 | − | 0.889643i | −0.104845 | − | 0.994489i | \(-0.533435\pi\) |
0.994489 | + | 0.104845i | \(0.0334347\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.47018 | − | 2.26582i | −0.0729358 | − | 0.0302110i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −24.8724 | + | 10.3025i | −0.323018 | + | 0.133798i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38.1202 | −0.482535 | −0.241267 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241267 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 48.4156i | − | 0.597724i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −15.9782 | − | 38.5748i | −0.192509 | − | 0.464757i | 0.797923 | − | 0.602759i | \(-0.205932\pi\) |
−0.990432 | + | 0.138002i | \(0.955932\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −46.8061 | + | 113.000i | −0.550660 | + | 1.32941i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.96868 | + | 1.96868i | 0.0226285 | + | 0.0226285i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 23.7666 | + | 23.7666i | 0.267040 | + | 0.267040i | 0.827906 | − | 0.560866i | \(-0.189532\pi\) |
−0.560866 | + | 0.827906i | \(0.689532\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.6017 | + | 30.4233i | −0.138481 | + | 0.334322i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −30.7446 | − | 74.2241i | −0.330587 | − | 0.798109i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 82.0827i | − | 0.864028i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −118.710 | −1.22382 | −0.611908 | − | 0.790929i | \(-0.709598\pi\) | ||||
−0.611908 | + | 0.790929i | \(0.709598\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 76.3798 | − | 31.6376i | 0.771514 | − | 0.319571i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 182.236 | + | 75.4846i | 1.80432 | + | 0.747372i | 0.984652 | + | 0.174529i | \(0.0558402\pi\) |
0.819665 | + | 0.572844i | \(0.194160\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −80.3171 | + | 80.3171i | −0.779777 | + | 0.779777i | −0.979793 | − | 0.200016i | \(-0.935901\pi\) |
0.200016 | + | 0.979793i | \(0.435901\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −95.4240 | + | 95.4240i | −0.908800 | + | 0.908800i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −22.6854 | − | 9.39659i | −0.212013 | − | 0.0878186i | 0.274150 | − | 0.961687i | \(-0.411604\pi\) |
−0.486162 | + | 0.873868i | \(0.661604\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −181.428 | + | 75.1501i | −1.66448 | + | 0.689450i | −0.998406 | − | 0.0564360i | \(-0.982026\pi\) |
−0.666074 | + | 0.745886i | \(0.732026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0033 | 0.108138 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 32.7876i | 0.290156i | 0.989420 | + | 0.145078i | \(0.0463433\pi\) | ||||
−0.989420 | + | 0.145078i | \(0.953657\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −71.0777 | − | 171.597i | −0.618067 | − | 1.49214i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 38.6983 | − | 93.4259i | 0.330754 | − | 0.798512i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −96.5368 | − | 96.5368i | −0.811234 | − | 0.811234i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −68.3006 | − | 68.3006i | −0.564468 | − | 0.564468i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −85.5241 | + | 206.473i | −0.695318 | + | 1.67865i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −48.8860 | − | 118.021i | −0.391088 | − | 0.944169i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 130.165i | 1.02492i | 0.858710 | + | 0.512462i | \(0.171266\pi\) | ||||
−0.858710 | + | 0.512462i | \(0.828734\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −70.8744 | −0.549414 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −24.3356 | + | 10.0801i | −0.185768 | + | 0.0769476i | −0.473628 | − | 0.880725i | \(-0.657056\pi\) |
0.287861 | + | 0.957672i | \(0.407056\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 84.6471 | + | 35.0620i | 0.636444 | + | 0.263624i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 135.431 | − | 135.431i | 1.00319 | − | 1.00319i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 147.886 | − | 147.886i | 1.07946 | − | 1.07946i | 0.0829047 | − | 0.996557i | \(-0.473580\pi\) |
0.996557 | − | 0.0829047i | \(-0.0264197\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 206.929 | + | 85.7129i | 1.48870 | + | 0.616639i | 0.971033 | − | 0.238944i | \(-0.0768011\pi\) |
0.517666 | + | 0.855583i | \(0.326801\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 70.3162 | − | 29.1259i | 0.498696 | − | 0.206567i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29.8556 | 0.208781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.67932i | 0.0184781i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 37.4790 | + | 90.4823i | 0.254959 | + | 0.615526i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 20.4247 | − | 49.3095i | 0.137078 | − | 0.330936i | −0.840402 | − | 0.541964i | \(-0.817681\pi\) |
0.977480 | + | 0.211028i | \(0.0676810\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 180.137 | + | 180.137i | 1.19296 | + | 1.19296i | 0.976232 | + | 0.216726i | \(0.0695379\pi\) |
0.216726 | + | 0.976232i | \(0.430462\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 296.452 | + | 296.452i | 1.93759 | + | 1.93759i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 29.5873 | − | 71.4300i | 0.190886 | − | 0.460839i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 60.3999 | + | 145.818i | 0.384713 | + | 0.928779i | 0.991040 | + | 0.133564i | \(0.0426422\pi\) |
−0.606327 | + | 0.795215i | \(0.707358\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 204.684i | − | 1.28732i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 207.319 | 1.28769 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 152.162 | − | 63.0277i | 0.933512 | − | 0.386673i | 0.136502 | − | 0.990640i | \(-0.456414\pi\) |
0.797010 | + | 0.603966i | \(0.206414\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 113.038 | + | 46.8218i | 0.685078 | + | 0.283769i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 94.8188 | − | 94.8188i | 0.567777 | − | 0.567777i | −0.363728 | − | 0.931505i | \(-0.618496\pi\) |
0.931505 | + | 0.363728i | \(0.118496\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −93.6785 | + | 93.6785i | −0.554310 | + | 0.554310i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −259.940 | − | 107.671i | −1.52012 | − | 0.629653i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 107.416 | − | 44.4930i | 0.620900 | − | 0.257185i | −0.0499813 | − | 0.998750i | \(-0.515916\pi\) |
0.670881 | + | 0.741565i | \(0.265916\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.36016 | 0.0363437 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 195.183i | − | 1.10273i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −54.7154 | − | 132.095i | −0.305673 | − | 0.737959i | −0.999835 | − | 0.0181410i | \(-0.994225\pi\) |
0.694163 | − | 0.719818i | \(-0.255775\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 128.496 | − | 310.218i | 0.709925 | − | 1.71391i | 0.00973575 | − | 0.999953i | \(-0.496901\pi\) |
0.700189 | − | 0.713957i | \(-0.253099\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 144.915 | + | 144.915i | 0.791886 | + | 0.791886i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.16809 | + | 8.16809i | 0.0441518 | + | 0.0441518i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −47.3678 | + | 114.356i | −0.253304 | + | 0.611530i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 81.8120 | + | 197.512i | 0.432868 | + | 1.04503i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 312.806i | − | 1.63773i | −0.573986 | − | 0.818865i | \(-0.694604\pi\) | ||
0.573986 | − | 0.818865i | \(-0.305396\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −70.6708 | −0.366170 | −0.183085 | − | 0.983097i | \(-0.558608\pi\) | ||||
−0.183085 | + | 0.983097i | \(0.558608\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 138.265 | − | 57.2713i | 0.709052 | − | 0.293699i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −81.5762 | − | 33.7900i | −0.414092 | − | 0.171523i | 0.165904 | − | 0.986142i | \(-0.446946\pi\) |
−0.579996 | + | 0.814619i | \(0.696946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 102.666 | − | 102.666i | 0.515910 | − | 0.515910i | −0.400421 | − | 0.916331i | \(-0.631136\pi\) |
0.916331 | + | 0.400421i | \(0.131136\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −238.235 | + | 238.235i | −1.18525 | + | 1.18525i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.76303 | − | 1.14449i | −0.0136110 | − | 0.00563786i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −198.701 | + | 82.3046i | −0.969273 | + | 0.401486i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −636.649 | −3.07560 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 83.0678i | − | 0.397454i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.35160 | − | 20.1625i | −0.0395810 | − | 0.0955571i | 0.902853 | − | 0.429950i | \(-0.141469\pi\) |
−0.942434 | + | 0.334393i | \(0.891469\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −142.154 | + | 343.191i | −0.667391 | + | 1.61122i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −48.2292 | − | 48.2292i | −0.224322 | − | 0.224322i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 61.0233 | + | 61.0233i | 0.281213 | + | 0.281213i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 178.298 | − | 430.448i | 0.814144 | − | 1.96552i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 57.9391 | + | 139.877i | 0.262168 | + | 0.632930i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 131.685i | 0.590516i | 0.955418 | + | 0.295258i | \(0.0954056\pi\) | ||||
−0.955418 | + | 0.295258i | \(0.904594\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.5312 | −0.0868054 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −60.7552 | + | 25.1656i | −0.267644 | + | 0.110862i | −0.512470 | − | 0.858705i | \(-0.671269\pi\) |
0.244825 | + | 0.969567i | \(0.421269\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −123.210 | − | 51.0352i | −0.538035 | − | 0.222861i | 0.0970835 | − | 0.995276i | \(-0.469049\pi\) |
−0.635118 | + | 0.772415i | \(0.719049\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −96.5693 | + | 96.5693i | −0.418049 | + | 0.418049i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 110.005 | − | 110.005i | 0.472124 | − | 0.472124i | −0.430477 | − | 0.902601i | \(-0.641655\pi\) |
0.902601 | + | 0.430477i | \(0.141655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 67.6692 | + | 28.0295i | 0.287954 | + | 0.119274i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −178.658 | + | 74.0026i | −0.753832 | + | 0.312247i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 277.831 | 1.16247 | 0.581236 | − | 0.813735i | \(-0.302569\pi\) | ||||
0.581236 | + | 0.813735i | \(0.302569\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 52.0006i | − | 0.215770i | −0.994163 | − | 0.107885i | \(-0.965592\pi\) | ||
0.994163 | − | 0.107885i | \(-0.0344079\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 41.1331 | + | 99.3041i | 0.169272 | + | 0.408659i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −36.0681 | + | 87.0762i | −0.147217 | + | 0.355413i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −71.8466 | − | 71.8466i | −0.290877 | − | 0.290877i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −149.770 | − | 149.770i | −0.601487 | − | 0.601487i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −28.7912 | + | 69.5080i | −0.114706 | + | 0.276924i | −0.970798 | − | 0.239899i | \(-0.922886\pi\) |
0.856092 | + | 0.516823i | \(0.172886\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −71.9307 | − | 173.656i | −0.284311 | − | 0.686388i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 620.461i | 2.43318i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 241.501 | 0.939692 | 0.469846 | − | 0.882748i | \(-0.344309\pi\) | ||||
0.469846 | + | 0.882748i | \(0.344309\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9123 | + | 4.93424i | −0.0459935 | + | 0.0190511i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.48491 | + | 3.51456i | 0.0325092 | + | 0.0134658i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −118.637 | + | 118.637i | −0.451090 | + | 0.451090i | −0.895716 | − | 0.444626i | \(-0.853336\pi\) |
0.444626 | + | 0.895716i | \(0.353336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 139.285 | − | 139.285i | 0.525606 | − | 0.525606i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 157.525 | + | 65.2489i | 0.589981 | + | 0.244378i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 231.194 | − | 95.7638i | 0.859459 | − | 0.355999i | 0.0909629 | − | 0.995854i | \(-0.471006\pi\) |
0.768496 | + | 0.639855i | \(0.221006\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.13724 | −0.00788650 | −0.00394325 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394325 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 167.048i | 0.611899i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.20670 | − | 5.32745i | −0.00802437 | − | 0.0193725i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 177.679 | − | 428.955i | 0.641441 | − | 1.54857i | −0.183296 | − | 0.983058i | \(-0.558677\pi\) |
0.824737 | − | 0.565517i | \(-0.191323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −187.395 | − | 187.395i | −0.671665 | − | 0.671665i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −261.664 | − | 261.664i | −0.931188 | − | 0.931188i | 0.0665922 | − | 0.997780i | \(-0.478787\pi\) |
−0.997780 | + | 0.0665922i | \(0.978787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −160.904 | + | 388.456i | −0.568564 | + | 1.37264i | 0.334201 | + | 0.942502i | \(0.391534\pi\) |
−0.902765 | + | 0.430134i | \(0.858466\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −159.347 | − | 384.697i | −0.559111 | − | 1.34981i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 240.066i | − | 0.836465i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −338.697 | −1.17196 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −556.359 | + | 230.452i | −1.91189 | + | 0.791930i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 141.895 | + | 58.7749i | 0.484284 | + | 0.200597i | 0.611448 | − | 0.791285i | \(-0.290587\pi\) |
−0.127164 | + | 0.991882i | \(0.540587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 132.820 | − | 132.820i | 0.450238 | − | 0.450238i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 137.056 | − | 137.056i | 0.461468 | − | 0.461468i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −212.412 | − | 87.9838i | −0.710407 | − | 0.294260i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 70.3373 | − | 29.1347i | 0.233679 | − | 0.0967929i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1000.62 | 3.30239 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 197.226i | 0.646643i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 36.1806 | + | 87.3476i | 0.117852 | + | 0.284520i | 0.971787 | − | 0.235860i | \(-0.0757905\pi\) |
−0.853935 | + | 0.520379i | \(0.825791\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −220.503 | + | 532.341i | −0.713602 | + | 1.72279i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 221.462 | + | 221.462i | 0.712098 | + | 0.712098i | 0.966974 | − | 0.254876i | \(-0.0820346\pi\) |
−0.254876 | + | 0.966974i | \(0.582035\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 280.384 | + | 280.384i | 0.895795 | + | 0.895795i | 0.995061 | − | 0.0992662i | \(-0.0316495\pi\) |
−0.0992662 | + | 0.995061i | \(0.531650\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −170.355 | + | 411.273i | −0.540809 | + | 1.30563i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −155.972 | − | 376.549i | −0.492024 | − | 1.18785i | −0.953688 | − | 0.300796i | \(-0.902748\pi\) |
0.461665 | − | 0.887055i | \(-0.347252\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.71148i | 0.00849994i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −124.561 | −0.388041 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 389.183 | − | 161.205i | 1.20490 | − | 0.499086i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.51640 | − | 2.69918i | −0.0200505 | − | 0.00830517i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −704.412 | + | 704.412i | −2.15416 | + | 2.15416i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −57.8104 | + | 57.8104i | −0.175715 | + | 0.175715i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 418.148 | + | 173.202i | 1.26329 | + | 0.523270i | 0.910917 | − | 0.412591i | \(-0.135376\pi\) |
0.352370 | + | 0.935861i | \(0.385376\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.5812 | − | 15.1524i | 0.109853 | − | 0.0455027i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −324.232 | −0.967857 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 38.1203i | 0.113116i | 0.998399 | + | 0.0565582i | \(0.0180127\pi\) | ||||
−0.998399 | + | 0.0565582i | \(0.981987\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 63.6504 | + | 153.666i | 0.187759 | + | 0.453291i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 29.9424 | − | 72.2873i | 0.0878076 | − | 0.211986i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −263.195 | − | 263.195i | −0.767333 | − | 0.767333i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −666.239 | − | 666.239i | −1.93113 | − | 1.93113i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 201.452 | − | 486.348i | 0.580553 | − | 1.40158i | −0.311760 | − | 0.950161i | \(-0.600918\pi\) |
0.892313 | − | 0.451418i | \(-0.149082\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 53.2160 | + | 128.475i | 0.152481 | + | 0.368122i | 0.981600 | − | 0.190951i | \(-0.0611571\pi\) |
−0.829118 | + | 0.559073i | \(0.811157\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 237.084i | − | 0.675452i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −223.875 | −0.634208 | −0.317104 | − | 0.948391i | \(-0.602710\pi\) | ||||
−0.317104 | + | 0.948391i | \(0.602710\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −330.272 | + | 136.803i | −0.930343 | + | 0.385361i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −639.846 | − | 265.033i | −1.79228 | − | 0.742389i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −44.5652 | + | 44.5652i | −0.124137 | + | 0.124137i | −0.766446 | − | 0.642309i | \(-0.777977\pi\) |
0.642309 | + | 0.766446i | \(0.277977\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 55.3658 | − | 55.3658i | 0.153368 | − | 0.153368i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −452.696 | − | 187.513i | −1.24710 | − | 0.516565i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 414.245 | − | 171.586i | 1.13492 | − | 0.470098i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −294.972 | −0.803739 | −0.401869 | − | 0.915697i | \(-0.631639\pi\) | ||||
−0.401869 | + | 0.915697i | \(0.631639\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 737.210i | 1.99786i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 84.1406 | + | 203.133i | 0.226794 | + | 0.547529i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −96.5187 | + | 233.017i | −0.258763 | + | 0.624710i | −0.998857 | − | 0.0477936i | \(-0.984781\pi\) |
0.740094 | + | 0.672504i | \(0.234781\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −458.228 | − | 458.228i | −1.22194 | − | 1.22194i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.34520 | + | 2.34520i | 0.00622069 | + | 0.00622069i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 70.2002 | − | 169.478i | 0.185225 | − | 0.447172i | −0.803804 | − | 0.594894i | \(-0.797194\pi\) |
0.989029 | + | 0.147722i | \(0.0471941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 252.689 | + | 610.046i | 0.663227 | + | 1.60117i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 519.043i | 1.35520i | 0.735429 | + | 0.677602i | \(0.236981\pi\) | ||||
−0.735429 | + | 0.677602i | \(0.763019\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −131.429 | −0.341373 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −215.997 | + | 89.4688i | −0.558131 | + | 0.231185i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −52.0121 | − | 21.5441i | −0.133707 | − | 0.0553834i | 0.314827 | − | 0.949149i | \(-0.398054\pi\) |
−0.448534 | + | 0.893766i | \(0.648054\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 674.009 | − | 674.009i | 1.72381 | − | 1.72381i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −94.4851 | + | 94.4851i | −0.240420 | + | 0.240420i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −171.933 | − | 71.2169i | −0.435273 | − | 0.180296i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −138.533 | + | 57.3823i | −0.348950 | + | 0.144540i | −0.550272 | − | 0.834985i | \(-0.685476\pi\) |
0.201322 | + | 0.979525i | \(0.435476\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 464.781 | 1.16487 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3014i | 0.0281830i | 0.999901 | + | 0.0140915i | \(0.00448560\pi\) | ||||
−0.999901 | + | 0.0140915i | \(0.995514\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −36.6248 | − | 88.4200i | −0.0908803 | − | 0.219404i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 90.4509 | − | 218.368i | 0.223336 | − | 0.539180i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.26612 | + | 8.26612i | 0.0203099 | + | 0.0203099i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 188.958 | + | 188.958i | 0.462001 | + | 0.462001i | 0.899311 | − | 0.437310i | \(-0.144069\pi\) |
−0.437310 | + | 0.899311i | \(0.644069\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 406.008 | − | 980.190i | 0.987854 | − | 2.38489i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 80.2350 | + | 193.704i | 0.194274 | + | 0.469018i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 203.834i | − | 0.491166i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1136.21 | 2.72472 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 238.026 | − | 98.5936i | 0.568081 | − | 0.235307i | −0.0801080 | − | 0.996786i | \(-0.525527\pi\) |
0.648189 | + | 0.761479i | \(0.275527\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −324.923 | − | 134.588i | −0.771790 | − | 0.319686i | −0.0381925 | − | 0.999270i | \(-0.512160\pi\) |
−0.733597 | + | 0.679585i | \(0.762160\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 177.528 | − | 177.528i | 0.419688 | − | 0.419688i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6773 | − | 20.6773i | 0.0486526 | − | 0.0486526i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −203.388 | − | 84.2461i | −0.476318 | − | 0.197298i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 139.924 | − | 57.9586i | 0.326164 | − | 0.135102i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.1400 | −0.0374479 | −0.0187239 | − | 0.999825i | \(-0.505960\pi\) | ||||
−0.0187239 | + | 0.999825i | \(0.505960\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 732.781i | − | 1.69233i | −0.532918 | − | 0.846167i | \(-0.678905\pi\) | ||
0.532918 | − | 0.846167i | \(-0.321095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.20136 | + | 12.5572i | 0.0119571 | + | 0.0288671i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −244.799 | + | 590.996i | −0.560180 | + | 1.35239i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 460.630 | + | 460.630i | 1.04927 | + | 1.04927i | 0.998722 | + | 0.0505487i | \(0.0160970\pi\) |
0.0505487 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 228.442 | + | 228.442i | 0.518009 | + | 0.518009i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 55.5453 | − | 134.098i | 0.125384 | − | 0.302705i | −0.848705 | − | 0.528866i | \(-0.822618\pi\) |
0.974090 | + | 0.226161i | \(0.0726175\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 62.7927 | + | 151.595i | 0.141107 | + | 0.340663i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 270.749i | − | 0.605703i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 731.262 | 1.62865 | 0.814323 | − | 0.580412i | \(-0.197108\pi\) | ||||
0.814323 | + | 0.580412i | \(0.197108\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −201.086 | + | 83.2924i | −0.445866 | + | 0.184684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1193.95 | + | 494.549i | 2.63564 | + | 1.09172i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −113.675 | + | 113.675i | −0.249834 | + | 0.249834i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −332.873 | + | 332.873i | −0.728388 | + | 0.728388i | −0.970298 | − | 0.241911i | \(-0.922226\pi\) |
0.241911 | + | 0.970298i | \(0.422226\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 908.102 | + | 376.148i | 1.97844 | + | 0.819495i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 132.650 | − | 54.9455i | 0.287744 | − | 0.119188i | −0.234143 | − | 0.972202i | \(-0.575228\pi\) |
0.521887 | + | 0.853015i | \(0.325228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −873.591 | −1.88680 | −0.943402 | − | 0.331650i | \(-0.892395\pi\) | ||||
−0.943402 | + | 0.331650i | \(0.892395\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 392.209i | − | 0.843460i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 135.550 | + | 327.247i | 0.290258 | + | 0.700744i | 0.999993 | − | 0.00372448i | \(-0.00118554\pi\) |
−0.709735 | + | 0.704468i | \(0.751186\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 138.497 | − | 334.362i | 0.295303 | − | 0.712925i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 566.153 | + | 566.153i | 1.20202 | + | 1.20202i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −48.8081 | − | 48.8081i | −0.103188 | − | 0.103188i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.50997 | + | 18.1307i | −0.0158105 | + | 0.0381698i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −258.385 | − | 623.796i | −0.541687 | − | 1.30775i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 296.032i | 0.618021i | 0.951059 | + | 0.309011i | \(0.0999979\pi\) | ||||
−0.951059 | + | 0.309011i | \(0.900002\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2990 | 0.0297276 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 971.641 | − | 402.467i | 2.01168 | − | 0.833265i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −535.416 | − | 221.777i | −1.10395 | − | 0.457271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −232.632 | + | 232.632i | −0.477683 | + | 0.477683i | −0.904390 | − | 0.426707i | \(-0.859674\pi\) |
0.426707 | + | 0.904390i | \(0.359674\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 590.784 | − | 590.784i | 1.20815 | − | 1.20815i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −217.435 | − | 90.0644i | −0.442840 | − | 0.183430i | 0.150110 | − | 0.988669i | \(-0.452037\pi\) |
−0.592951 | + | 0.805239i | \(0.702037\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.7036 | + | 5.26201i | −0.0257680 | + | 0.0106735i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 403.600 | 0.815354 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 399.026i | − | 0.802869i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −64.7699 | − | 156.368i | −0.129799 | − | 0.313364i | 0.845597 | − | 0.533822i | \(-0.179245\pi\) |
−0.975396 | + | 0.220458i | \(0.929245\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 260.316 | − | 628.458i | 0.519593 | − | 1.25441i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −612.203 | − | 612.203i | −1.21710 | − | 1.21710i | −0.968642 | − | 0.248460i | \(-0.920075\pi\) |
−0.248460 | − | 0.968642i | \(-0.579925\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 680.913 | + | 680.913i | 1.34834 | + | 1.34834i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −257.185 | + | 620.900i | −0.507269 | + | 1.22466i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 273.870 | + | 661.182i | 0.538056 | + | 1.29898i | 0.926078 | + | 0.377332i | \(0.123158\pi\) |
−0.388022 | + | 0.921650i | \(0.626842\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 500.480i | 0.979413i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −659.641 | −1.28585 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −512.302 | + | 212.202i | −0.994761 | + | 0.412043i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 68.4813 | + | 28.3659i | 0.132459 | + | 0.0548663i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 417.051 | − | 417.051i | 0.803566 | − | 0.803566i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −527.816 | + | 527.816i | −1.01308 | + | 1.01308i | −0.0131690 | + | 0.999913i | \(0.504192\pi\) |
−0.999913 | + | 0.0131690i | \(0.995808\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.01268 | − | 2.07632i | −0.00958447 | − | 0.00397002i | 0.377886 | − | 0.925852i | \(-0.376651\pi\) |
−0.387471 | + | 0.921882i | \(0.626651\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 29.8081 | − | 12.3469i | 0.0567774 | − | 0.0235180i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 396.783 | 0.752908 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 918.476i | 1.73625i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −246.391 | − | 594.841i | −0.464013 | − | 1.12023i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −101.881 | + | 245.963i | −0.191147 | + | 0.461469i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −84.7624 | − | 84.7624i | −0.158434 | − | 0.158434i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −512.869 | − | 512.869i | −0.955064 | − | 0.955064i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.5010 | + | 88.1213i | −0.0677199 | + | 0.163490i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 229.279 | + | 553.528i | 0.423806 | + | 1.02316i | 0.981215 | + | 0.192919i | \(0.0617955\pi\) |
−0.557409 | + | 0.830238i | \(0.688204\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1703.35i | − | 3.13692i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −958.688 | −1.75906 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 391.381 | − | 162.115i | 0.715504 | − | 0.296371i | 0.00492387 | − | 0.999988i | \(-0.498433\pi\) |
0.710580 | + | 0.703617i | \(0.248433\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 624.578 | + | 258.709i | 1.13766 | + | 0.471236i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.52508 | − | 6.52508i | 0.0118423 | − | 0.0118423i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 146.884 | − | 146.884i | 0.265613 | − | 0.265613i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 54.1381 | + | 22.4247i | 0.0975461 | + | 0.0404049i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −364.486 | + | 150.975i | −0.654374 | + | 0.271050i | −0.685069 | − | 0.728478i | \(-0.740228\pi\) |
0.0306953 | + | 0.999529i | \(0.490228\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −84.4296 | −0.151037 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 627.908i | 1.11927i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −114.762 | − | 277.059i | −0.203840 | − | 0.492113i | 0.788591 | − | 0.614918i | \(-0.210811\pi\) |
−0.992431 | + | 0.122805i | \(0.960811\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −61.2544 | + | 147.881i | −0.108415 | + | 0.261736i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 186.554 | + | 186.554i | 0.329019 | + | 0.329019i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 172.424 | + | 172.424i | 0.303029 | + | 0.303029i | 0.842198 | − | 0.539169i | \(-0.181261\pi\) |
−0.539169 | + | 0.842198i | \(0.681261\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −295.206 | + | 712.690i | −0.516998 | + | 1.24814i | 0.422740 | + | 0.906251i | \(0.361068\pi\) |
−0.939739 | + | 0.341894i | \(0.888932\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −607.250 | − | 1466.03i | −1.05977 | − | 2.55852i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 44.4059i | 0.0772276i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −756.330 | −1.31080 | −0.655398 | − | 0.755283i | \(-0.727499\pi\) | ||||
−0.655398 | + | 0.755283i | \(0.727499\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −331.213 | + | 137.193i | −0.572043 | + | 0.236948i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 210.202 | + | 87.0686i | 0.361794 | + | 0.149860i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 140.957 | − | 140.957i | 0.241779 | − | 0.241779i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 349.080 | − | 349.080i | 0.596717 | − | 0.596717i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −736.720 | − | 305.159i | −1.25506 | − | 0.519863i | −0.346670 | − | 0.937987i | \(-0.612688\pi\) |
−0.908390 | + | 0.418125i | \(0.862688\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −246.012 | + | 101.902i | −0.417678 | + | 0.173008i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −447.919 | −0.757901 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 76.7003i | − | 0.129343i | −0.997907 | − | 0.0646714i | \(-0.979400\pi\) | ||
0.997907 | − | 0.0646714i | \(-0.0205999\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −255.056 | − | 615.759i | −0.428665 | − | 1.03489i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 281.860 | − | 680.470i | 0.472127 | − | 1.13982i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.1251 | + | 34.1251i | 0.0569702 | + | 0.0569702i | 0.735018 | − | 0.678048i | \(-0.237174\pi\) |
−0.678048 | + | 0.735018i | \(0.737174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 212.552 | + | 212.552i | 0.353664 | + | 0.353664i | 0.861471 | − | 0.507807i | \(-0.169544\pi\) |
−0.507807 | + | 0.861471i | \(0.669544\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −425.307 | + | 1026.78i | −0.705318 | + | 1.70279i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −180.454 | − | 435.655i | −0.298271 | − | 0.720091i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 56.8377i | − | 0.0936371i | −0.998903 | − | 0.0468186i | \(-0.985092\pi\) | ||
0.998903 | − | 0.0468186i | \(-0.0149083\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1713 | −0.0249118 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 83.7646 | − | 34.6964i | 0.137094 | − | 0.0567863i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.45320 | + | 3.08722i | 0.0121586 | + | 0.00503624i | 0.388754 | − | 0.921341i | \(-0.372905\pi\) |
−0.376596 | + | 0.926378i | \(0.622905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −771.474 | + | 771.474i | −1.25443 | + | 1.25443i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −325.733 | + | 325.733i | −0.527931 | + | 0.527931i | −0.919955 | − | 0.392024i | \(-0.871775\pi\) |
0.392024 | + | 0.919955i | \(0.371775\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −76.1643 | − | 31.5483i | −0.123044 | − | 0.0509665i | 0.320312 | − | 0.947312i | \(-0.396212\pi\) |
−0.443356 | + | 0.896346i | \(0.646212\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1379.00 | + | 571.202i | −2.22062 | + | 0.919810i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −183.153 | −0.293986 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 594.458i | − | 0.951133i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −161.259 | − | 389.314i | −0.257192 | − | 0.620915i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −22.6862 | + | 54.7694i | −0.0360671 | + | 0.0870738i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 70.1301 | + | 70.1301i | 0.111141 | + | 0.111141i | 0.760490 | − | 0.649349i | \(-0.224959\pi\) |
−0.649349 | + | 0.760490i | \(0.724959\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −78.2829 | − | 78.2829i | −0.123670 | − | 0.123670i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −243.177 | + | 587.082i | −0.382956 | + | 0.924538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 44.6471 | + | 107.788i | 0.0700897 | + | 0.169211i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1225.36i | 1.91762i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 458.396 | 0.715126 | 0.357563 | − | 0.933889i | \(-0.383608\pi\) | ||||
0.357563 | + | 0.933889i | \(0.383608\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 882.443 | − | 365.520i | 1.37238 | − | 0.568460i | 0.429950 | − | 0.902853i | \(-0.358531\pi\) |
0.942434 | + | 0.334393i | \(0.108531\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −319.663 | − | 132.409i | −0.495602 | − | 0.205285i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −130.433 | + | 130.433i | −0.201597 | + | 0.201597i | −0.800684 | − | 0.599087i | \(-0.795530\pi\) |
0.599087 | + | 0.800684i | \(0.295530\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 134.414 | − | 134.414i | 0.207110 | − | 0.207110i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 404.462 | + | 167.534i | 0.621294 | + | 0.257348i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −989.811 | + | 409.993i | −1.51579 | + | 0.627861i | −0.976743 | − | 0.214415i | \(-0.931216\pi\) |
−0.539047 | + | 0.842275i | \(0.681216\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −128.592 | −0.196324 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 1536.91i | − | 2.33928i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 457.745 | + | 1105.09i | 0.694605 | + | 1.67693i | 0.735289 | + | 0.677753i | \(0.237046\pi\) |
−0.0406841 | + | 0.999172i | \(0.512954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 96.2729 | − | 232.423i | 0.145647 | − | 0.351624i | −0.834173 | − | 0.551502i | \(-0.814055\pi\) |
0.979821 | + | 0.199879i | \(0.0640548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 543.087 | + | 543.087i | 0.819135 | + | 0.819135i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 316.278 | + | 316.278i | 0.475607 | + | 0.475607i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.99066 | − | 19.2912i | 0.0119800 | − | 0.0289223i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 255.640 | + | 617.168i | 0.382122 | + | 0.922524i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 199.593i | 0.297456i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −135.640 | −0.201545 | −0.100772 | − | 0.994910i | \(-0.532131\pi\) | ||||
−0.100772 | + | 0.994910i | \(0.532131\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −42.3053 | + | 17.5234i | −0.0626745 | + | 0.0259606i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 348.196 | + | 144.228i | 0.514322 | + | 0.213039i | 0.624721 | − | 0.780848i | \(-0.285213\pi\) |
−0.110399 | + | 0.993887i | \(0.535213\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 457.411 | − | 457.411i | 0.673653 | − | 0.673653i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −235.888 | + | 235.888i | −0.346384 | + | 0.346384i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 812.940 | + | 336.731i | 1.19025 | + | 0.493017i | 0.887836 | − | 0.460159i | \(-0.152208\pi\) |
0.302413 | + | 0.953177i | \(0.402208\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 943.292 | − | 390.724i | 1.37707 | − | 0.570400i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −676.523 | −0.984749 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 243.832i | − | 0.353892i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 78.3893 | + | 189.249i | 0.113443 | + | 0.273876i | 0.970396 | − | 0.241518i | \(-0.0776454\pi\) |
−0.856953 | + | 0.515395i | \(0.827645\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −172.400 | + | 416.209i | −0.248773 | + | 0.600591i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 773.177 | + | 773.177i | 1.11249 | + | 1.11249i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −780.471 | − | 780.471i | −1.11976 | − | 1.11976i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 302.008 | − | 729.112i | 0.432057 | − | 1.04308i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −432.140 | − | 1043.28i | −0.616463 | − | 1.48827i | −0.855785 | − | 0.517332i | \(-0.826925\pi\) |
0.239322 | − | 0.970940i | \(-0.423075\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 39.7843i | − | 0.0565921i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 371.559 | 0.527034 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −993.041 | + | 411.331i | −1.40458 | + | 0.581798i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −367.507 | − | 152.226i | −0.518345 | − | 0.214706i | 0.108145 | − | 0.994135i | \(-0.465509\pi\) |
−0.626490 | + | 0.779430i | \(0.715509\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −451.061 | + | 451.061i | −0.634403 | + | 0.634403i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −426.058 | + | 426.058i | −0.597556 | + | 0.597556i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 134.657 | + | 55.7768i | 0.188332 | + | 0.0780096i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1302.11 | − | 539.352i | 1.81605 | − | 0.752234i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −100.566 | −0.139869 | −0.0699344 | − | 0.997552i | \(-0.522279\pi\) | ||||
−0.0699344 | + | 0.997552i | \(0.522279\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 618.950i | − | 0.858461i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −100.949 | − | 243.711i | −0.139625 | − | 0.337084i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.245139 | − | 0.591817i | 0.000338122 | − | 0.000816300i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −332.402 | − | 332.402i | −0.457224 | − | 0.457224i | 0.440519 | − | 0.897743i | \(-0.354794\pi\) |
−0.897743 | + | 0.440519i | \(0.854794\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 693.672 | + | 693.672i | 0.951540 | + | 0.951540i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 133.953 | − | 323.391i | 0.183246 | − | 0.442395i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 166.189 | + | 401.215i | 0.226724 | + | 0.547360i | 0.995775 | − | 0.0918276i | \(-0.0292709\pi\) |
−0.769051 | + | 0.639187i | \(0.779271\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 478.119i | 0.650502i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −328.124 | −0.445215 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1011.25 | + | 418.874i | −1.36840 | + | 0.566812i | −0.941355 | − | 0.337417i | \(-0.890447\pi\) |
−0.427049 | + | 0.904229i | \(0.640447\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −476.199 | − | 197.248i | −0.642643 | − | 0.266192i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 458.897 | − | 458.897i | 0.617627 | − | 0.617627i | −0.327295 | − | 0.944922i | \(-0.606137\pi\) |
0.944922 | + | 0.327295i | \(0.106137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 184.242 | − | 184.242i | 0.247304 | − | 0.247304i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −645.503 | − | 267.376i | −0.864128 | − | 0.357933i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 123.617 | − | 51.2039i | 0.165043 | − | 0.0683630i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −636.920 | −0.848096 | −0.424048 | − | 0.905640i | \(-0.639391\pi\) | ||||
−0.424048 | + | 0.905640i | \(0.639391\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 381.656i | 0.506847i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 475.932 | + | 1149.00i | 0.630373 | + | 1.52186i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 414.804 | − | 1001.43i | 0.547958 | − | 1.32289i | −0.371038 | − | 0.928618i | \(-0.620998\pi\) |
0.918995 | − | 0.394269i | \(-0.129002\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −674.236 | − | 674.236i | −0.888321 | − | 0.888321i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −520.779 | − | 520.779i | −0.684334 | − | 0.684334i | 0.276639 | − | 0.960974i | \(-0.410779\pi\) |
−0.960974 | + | 0.276639i | \(0.910779\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 409.508 | − | 988.640i | 0.536708 | − | 1.29573i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 783.243 | + | 1890.92i | 1.02385 | + | 2.47179i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 232.514i | − | 0.303147i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 973.035 | 1.26533 | 0.632663 | − | 0.774427i | \(-0.281962\pi\) | ||||
0.632663 | + | 0.774427i | \(0.281962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1131.84 | − | 468.825i | 1.46802 | − | 0.608073i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −959.578 | − | 397.470i | −1.24137 | − | 0.514192i | −0.337227 | − | 0.941423i | \(-0.609489\pi\) |
−0.904142 | + | 0.427232i | \(0.859489\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.0707 | + | 13.0707i | −0.0168654 | + | 0.0168654i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −46.2506 | + | 46.2506i | −0.0595246 | + | 0.0595246i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 684.346 | + | 283.465i | 0.878493 | + | 0.363884i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −334.236 | + | 138.445i | −0.427958 | + | 0.177266i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.5319 | 0.0274992 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 770.521i | 0.981556i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −412.612 | − | 996.133i | −0.524284 | − | 1.26573i | −0.935219 | − | 0.354070i | \(-0.884798\pi\) |
0.410935 | − | 0.911665i | \(-0.365202\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −325.706 | + | 786.323i | −0.412808 | + | 0.996607i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −126.336 | − | 126.336i | −0.159717 | − | 0.159717i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 172.631 | + | 172.631i | 0.217694 | + | 0.217694i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 382.395 | − | 923.183i | 0.481000 | − | 1.16124i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.5600 | + | 112.406i | 0.0584191 | + | 0.141036i | 0.950394 | − | 0.311049i | \(-0.100680\pi\) |
−0.891975 | + | 0.452085i | \(0.850680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 375.892i | 0.470453i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 562.440 | 0.702172 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 419.216 | − | 173.645i | 0.522063 | − | 0.216245i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 935.065 | + | 387.317i | 1.16157 | + | 0.481139i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 897.633 | − | 897.633i | 1.11231 | − | 1.11231i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −80.8371 | + | 80.8371i | −0.0999222 | + | 0.0999222i | −0.755301 | − | 0.655378i | \(-0.772509\pi\) |
0.655378 | + | 0.755301i | \(0.272509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1277.99 | − | 529.360i | −1.57582 | − | 0.652725i | −0.588074 | − | 0.808807i | \(-0.700114\pi\) |
−0.987744 | + | 0.156082i | \(0.950114\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0166 | + | 4.14902i | −0.0123206 | + | 0.00510334i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 804.044 | 0.986557 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 234.910i | 0.287527i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 210.875 | + | 509.096i | 0.257478 | + | 0.621607i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −83.7084 | + | 202.090i | −0.101959 | + | 0.246151i | −0.966625 | − | 0.256197i | \(-0.917530\pi\) |
0.864666 | + | 0.502348i | \(0.167530\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 588.539 | + | 588.539i | 0.715114 | + | 0.715114i | 0.967601 | − | 0.252486i | \(-0.0812482\pi\) |
−0.252486 | + | 0.967601i | \(0.581248\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.6843 | − | 20.6843i | −0.0250719 | − | 0.0250719i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −281.470 | + | 679.529i | −0.340351 | + | 0.821679i | 0.657329 | + | 0.753603i | \(0.271686\pi\) |
−0.997680 | + | 0.0680759i | \(0.978314\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.83745 | − | 16.5071i | −0.00824783 | − | 0.0199120i | 0.919702 | − | 0.392617i | \(-0.128430\pi\) |
−0.927950 | + | 0.372705i | \(0.878430\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 2355.31i | − | 2.83431i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −483.695 | −0.580666 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 604.801 | − | 250.517i | 0.724313 | − | 0.300020i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −574.034 | − | 237.773i | −0.685823 | − | 0.284077i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −358.991 | + | 358.991i | −0.427879 | + | 0.427879i | −0.887905 | − | 0.460026i | \(-0.847840\pi\) |
0.460026 | + | 0.887905i | \(0.347840\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 594.464 | − | 594.464i | 0.706854 | − | 0.706854i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1734.31 | − | 718.373i | −2.05730 | − | 0.852163i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −597.527 | + | 247.504i | −0.707133 | + | 0.292904i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 526.348 | 0.621426 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2132.94i | 2.51229i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −34.4503 | − | 83.1704i | −0.0404821 | − | 0.0977325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −545.396 | + | 1316.70i | −0.639386 | + | 1.54361i | 0.188114 | + | 0.982147i | \(0.439763\pi\) |
−0.827499 | + | 0.561467i | \(0.810237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −971.249 | − | 971.249i | −1.13596 | − | 1.13596i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 157.052 | + | 157.052i | 0.183258 | + | 0.183258i | 0.792774 | − | 0.609516i | \(-0.208636\pi\) |
−0.609516 | + | 0.792774i | \(0.708636\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17.7307 | + | 42.8057i | −0.0206411 | + | 0.0498321i | −0.933864 | − | 0.357628i | \(-0.883586\pi\) |
0.913223 | + | 0.407460i | \(0.133586\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −466.038 | − | 1125.12i | −0.541275 | − | 1.30675i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 186.088i | − | 0.215629i | −0.994171 | − | 0.107815i | \(-0.965615\pi\) | ||
0.994171 | − | 0.107815i | \(-0.0343853\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 567.597 | 0.656181 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1587.37 | + | 657.510i | −1.83088 | + | 0.758374i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −173.996 | − | 72.0716i | −0.200226 | − | 0.0829363i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −283.799 | + | 283.799i | −0.325831 | + | 0.325831i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1404.65 | + | 1404.65i | −1.60899 | + | 1.60899i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 643.121 | + | 266.390i | 0.734996 | + | 0.304445i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 216.654 | − | 89.7412i | 0.247040 | − | 0.102328i | −0.255728 | − | 0.966749i | \(-0.582315\pi\) |
0.502768 | + | 0.864421i | \(0.332315\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 779.119 | 0.886370 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47.9671i | − | 0.0544462i | −0.999629 | − | 0.0272231i | \(-0.991334\pi\) | ||
0.999629 | − | 0.0272231i | \(-0.00866645\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −115.380 | − | 278.551i | −0.130668 | − | 0.315460i | 0.844982 | − | 0.534795i | \(-0.179611\pi\) |
−0.975650 | + | 0.219335i | \(0.929611\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 364.645 | − | 880.331i | 0.412028 | − | 0.994724i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 233.227 | + | 233.227i | 0.262939 | + | 0.262939i | 0.826247 | − | 0.563308i | \(-0.190472\pi\) |
−0.563308 | + | 0.826247i | \(0.690472\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −501.549 | − | 501.549i | −0.564172 | − | 0.564172i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 91.5365 | − | 220.989i | 0.102735 | − | 0.248023i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −96.5364 | − | 233.059i | −0.108103 | − | 0.260985i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 698.004i | − | 0.779892i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1166.31 | −1.30024 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.03028 | − | 3.32625i | 0.00893246 | − | 0.00369994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 933.949 | + | 386.854i | 1.03657 | + | 0.429361i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 273.091 | − | 273.091i | 0.302426 | − | 0.302426i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1159.11 | − | 1159.11i | 1.28078 | − | 1.28078i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 827.946 | + | 342.947i | 0.912841 | + | 0.378111i | 0.789143 | − | 0.614209i | \(-0.210525\pi\) |
0.123697 | + | 0.992320i | \(0.460525\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3049.50 | − | 1263.14i | 3.35478 | − | 1.38960i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1321.92 | 1.45107 | 0.725534 | − | 0.688186i | \(-0.241593\pi\) | ||||
0.725534 | + | 0.688186i | \(0.241593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 206.280i | − | 0.225937i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 382.874 | + | 924.340i | 0.418442 | + | 1.01021i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 54.9287 | − | 132.610i | 0.0599004 | − | 0.144612i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −717.026 | − | 717.026i | −0.780224 | − | 0.780224i | 0.199645 | − | 0.979868i | \(-0.436021\pi\) |
−0.979868 | + | 0.199645i | \(0.936021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 339.135 | + | 339.135i | 0.368225 | + | 0.368225i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −169.342 | + | 408.828i | −0.183469 | + | 0.442934i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05687 | − | 2.55151i | −0.00114256 | − | 0.00275839i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1900.72i | 2.05039i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −430.578 | −0.463485 | −0.231743 | − | 0.972777i | \(-0.574443\pi\) | ||||
−0.231743 | + | 0.972777i | \(0.574443\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 299.899 | − | 124.222i | 0.322126 | − | 0.133429i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1467.85 | + | 608.004i | 1.57326 | + | 0.651666i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −427.284 | + | 427.284i | −0.456988 | + | 0.456988i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 752.850 | − | 752.850i | 0.803469 | − | 0.803469i | −0.180167 | − | 0.983636i | \(-0.557664\pi\) |
0.983636 | + | 0.180167i | \(0.0576639\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1858.38 | + | 769.767i | 1.97911 | + | 0.819773i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1482.20 | − | 613.948i | 1.57513 | − | 0.652442i | 0.587501 | − | 0.809223i | \(-0.300112\pi\) |
0.987633 | + | 0.156781i | \(0.0501118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1676.11 | 1.77742 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1043.67i | 1.10442i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −528.730 | − | 1276.47i | −0.558321 | − | 1.34791i | −0.911094 | − | 0.412198i | \(-0.864761\pi\) |
0.352773 | − | 0.935709i | \(-0.385239\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 212.398 | − | 512.775i | 0.223813 | − | 0.540332i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1461.98 | − | 1461.98i | −1.53731 | − | 1.53731i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −538.112 | − | 538.112i | −0.564650 | − | 0.564650i | 0.365975 | − | 0.930625i | \(-0.380736\pi\) |
−0.930625 | + | 0.365975i | \(0.880736\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 584.391 | − | 1410.84i | 0.611927 | − | 1.47732i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.26378 | + | 12.7079i | 0.00550030 | + | 0.0132789i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1139.66i | 1.18839i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 710.184 | 0.739005 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −379.612 | + | 157.240i | −0.394197 | + | 0.163282i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −318.745 | − | 132.028i | −0.330306 | − | 0.136817i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −380.769 | + | 380.769i | −0.393763 | + | 0.393763i | −0.876026 | − | 0.482263i | \(-0.839815\pi\) |
0.482263 | + | 0.876026i | \(0.339815\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1511.04 | − | 1511.04i | 1.55938 | − | 1.55938i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1000.67 | + | 414.490i | 1.03055 | + | 0.426869i | 0.832912 | − | 0.553405i | \(-0.186672\pi\) |
0.197642 | + | 0.980274i | \(0.436672\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1127.60 | + | 467.067i | −1.15889 | + | 0.480028i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −35.7803 | −0.0366977 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 920.476i | 0.942145i | 0.882095 | + | 0.471072i | \(0.156133\pi\) | ||||
−0.882095 | + | 0.471072i | \(0.843867\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 63.5463 | + | 153.414i | 0.0649094 | + | 0.156705i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1257.55 | + | 3035.98i | −1.28190 | + | 3.09478i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 465.265 | + | 465.265i | 0.473312 | + | 0.473312i | 0.902985 | − | 0.429673i | \(-0.141371\pi\) |
−0.429673 | + | 0.902985i | \(0.641371\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −304.804 | − | 304.804i | −0.309446 | − | 0.309446i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −158.713 | + | 383.167i | −0.160803 | + | 0.388214i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 203.415 | + | 491.087i | 0.205677 | + | 0.496549i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 365.984i | 0.369307i | 0.982804 | + | 0.184654i | \(0.0591164\pi\) | ||||
−0.982804 | + | 0.184654i | \(0.940884\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2295.97 | 2.31216 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 654.855 | − | 271.250i | 0.658146 | − | 0.272613i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 77.3922 | + | 32.0569i | 0.0776251 | + | 0.0321534i | 0.421158 | − | 0.906987i | \(-0.361624\pi\) |
−0.343533 | + | 0.939141i | \(0.611624\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 65.6413 | − | 65.6413i | 0.0657070 | − | 0.0657070i |
(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 | 256.3.h.b.31.7 | 28 | ||
4.3 | odd | 2 | 256.3.h.a.31.1 | 28 | |||
8.3 | odd | 2 | 128.3.h.a.15.7 | 28 | |||
8.5 | even | 2 | 32.3.h.a.27.2 | yes | 28 | ||
24.5 | odd | 2 | 288.3.u.a.91.6 | 28 | |||
32.3 | odd | 8 | 32.3.h.a.19.2 | ✓ | 28 | ||
32.13 | even | 8 | 256.3.h.a.223.1 | 28 | |||
32.19 | odd | 8 | inner | 256.3.h.b.223.7 | 28 | ||
32.29 | even | 8 | 128.3.h.a.111.7 | 28 | |||
96.35 | even | 8 | 288.3.u.a.19.6 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.3.h.a.19.2 | ✓ | 28 | 32.3 | odd | 8 | ||
32.3.h.a.27.2 | yes | 28 | 8.5 | even | 2 | ||
128.3.h.a.15.7 | 28 | 8.3 | odd | 2 | |||
128.3.h.a.111.7 | 28 | 32.29 | even | 8 | |||
256.3.h.a.31.1 | 28 | 4.3 | odd | 2 | |||
256.3.h.a.223.1 | 28 | 32.13 | even | 8 | |||
256.3.h.b.31.7 | 28 | 1.1 | even | 1 | trivial | ||
256.3.h.b.223.7 | 28 | 32.19 | odd | 8 | inner | ||
288.3.u.a.19.6 | 28 | 96.35 | even | 8 | |||
288.3.u.a.91.6 | 28 | 24.5 | odd | 2 |