Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(47,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([9, 9, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bh (of order \(18\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(192\) |
Relative dimension: | \(32\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 47.15 | ||
Character | \(\chi\) | \(=\) | 864.47 |
Dual form | 864.2.bh.b.239.15 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{18}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 0.0100749 | − | 1.73202i | 0.00581674 | − | 0.999983i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.710827 | − | 4.03130i | −0.317891 | − | 1.80285i | −0.555528 | − | 0.831498i | \(-0.687484\pi\) |
0.237637 | − | 0.971354i | \(-0.423627\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.183548 | + | 0.218744i | −0.0693747 | + | 0.0826776i | −0.799616 | − | 0.600512i | \(-0.794963\pi\) |
0.730241 | + | 0.683190i | \(0.239408\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.99980 | − | 0.0348998i | −0.999932 | − | 0.0116333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.72450 | − | 0.304076i | −0.519957 | − | 0.0916824i | −0.0924901 | − | 0.995714i | \(-0.529483\pi\) |
−0.427466 | + | 0.904031i | \(0.640594\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.16532 | − | 3.20170i | 0.323203 | − | 0.887992i | −0.666583 | − | 0.745431i | \(-0.732244\pi\) |
0.989786 | − | 0.142562i | \(-0.0455339\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −6.98946 | + | 1.19055i | −1.80467 | + | 0.307399i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.91624 | − | 2.83839i | 1.19236 | − | 0.688411i | 0.233521 | − | 0.972352i | \(-0.424975\pi\) |
0.958842 | + | 0.283941i | \(0.0916419\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.46260 | + | 5.99739i | −0.794374 | + | 1.37590i | 0.128862 | + | 0.991663i | \(0.458868\pi\) |
−0.923236 | + | 0.384234i | \(0.874466\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.377021 | + | 0.320113i | 0.0822727 | + | 0.0698545i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.02493 | − | 2.53822i | 0.630742 | − | 0.529255i | −0.270417 | − | 0.962743i | \(-0.587162\pi\) |
0.901159 | + | 0.433488i | \(0.142717\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −11.0476 | + | 4.02101i | −2.20953 | + | 0.804202i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.0906699 | + | 5.19536i | −0.0174494 | + | 0.999848i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.90156 | + | 0.692110i | −0.353110 | + | 0.128522i | −0.512484 | − | 0.858697i | \(-0.671275\pi\) |
0.159374 | + | 0.987218i | \(0.449052\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.53206 | − | 3.01760i | −0.454772 | − | 0.541976i | 0.489126 | − | 0.872213i | \(-0.337316\pi\) |
−0.943898 | + | 0.330237i | \(0.892871\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.544040 | + | 2.98381i | −0.0947053 | + | 0.519414i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.01229 | + | 0.584449i | 0.171109 | + | 0.0987899i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.14294 | − | 2.96928i | 0.845494 | − | 0.488146i | −0.0136340 | − | 0.999907i | \(-0.504340\pi\) |
0.859128 | + | 0.511761i | \(0.171007\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.53368 | − | 2.05062i | −0.886097 | − | 0.328363i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.535228 | + | 1.47053i | −0.0835886 | + | 0.229658i | −0.974445 | − | 0.224628i | \(-0.927883\pi\) |
0.890856 | + | 0.454286i | \(0.150106\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0461253 | + | 0.261589i | −0.00703404 | + | 0.0398920i | −0.988123 | − | 0.153667i | \(-0.950892\pi\) |
0.981089 | + | 0.193559i | \(0.0620029\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.99164 | + | 12.1179i | 0.296897 | + | 1.80643i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.77762 | + | 4.00890i | 0.696888 | + | 0.584759i | 0.920886 | − | 0.389831i | \(-0.127467\pi\) |
−0.223998 | + | 0.974590i | \(0.571911\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.20138 | + | 6.81335i | 0.171625 | + | 0.973336i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.86662 | − | 8.54363i | −0.681464 | − | 1.19635i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.82891 | −0.800662 | −0.400331 | − | 0.916371i | \(-0.631105\pi\) | ||||
−0.400331 | + | 0.916371i | \(0.631105\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.16812i | 0.966550i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3527 | + | 6.05771i | 1.37125 | + | 0.802364i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.26158 | − | 0.751431i | 0.554810 | − | 0.0978280i | 0.110788 | − | 0.993844i | \(-0.464662\pi\) |
0.444022 | + | 0.896016i | \(0.353551\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.79887 | + | 5.71906i | −0.614432 | + | 0.732251i | −0.980102 | − | 0.198493i | \(-0.936395\pi\) |
0.365671 | + | 0.930744i | \(0.380840\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.558242 | − | 0.649783i | 0.0703318 | − | 0.0818649i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.7354 | − | 2.42191i | −1.70366 | − | 0.300402i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.743215 | + | 0.270508i | 0.0907981 | + | 0.0330478i | 0.387020 | − | 0.922071i | \(-0.373504\pi\) |
−0.296222 | + | 0.955119i | \(0.595727\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.36577 | − | 5.26482i | −0.525578 | − | 0.633810i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.39967 | − | 9.35250i | −0.640823 | − | 1.10994i | −0.985249 | − | 0.171124i | \(-0.945260\pi\) |
0.344427 | − | 0.938813i | \(-0.388073\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.194878 | + | 0.337539i | −0.0228088 | + | 0.0395060i | −0.877205 | − | 0.480117i | \(-0.840594\pi\) |
0.854396 | + | 0.519623i | \(0.173928\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.85317 | + | 19.1753i | 0.791336 | + | 2.21417i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.383044 | − | 0.321412i | 0.0436519 | − | 0.0366283i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.44109 | − | 12.2018i | −0.499661 | − | 1.37281i | −0.891603 | − | 0.452818i | \(-0.850419\pi\) |
0.391942 | − | 0.919990i | \(-0.371804\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.99756 | + | 0.209385i | 0.999729 | + | 0.0232650i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.720133 | − | 1.97855i | −0.0790448 | − | 0.217174i | 0.893875 | − | 0.448316i | \(-0.147976\pi\) |
−0.972920 | + | 0.231142i | \(0.925754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −14.9370 | − | 17.8012i | −1.62015 | − | 1.93081i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.17959 | + | 3.30051i | 0.126465 | + | 0.353852i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.61708 | − | 0.933622i | −0.171410 | − | 0.0989637i | 0.411840 | − | 0.911256i | \(-0.364886\pi\) |
−0.583251 | + | 0.812292i | \(0.698219\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.486461 | + | 0.842575i | 0.0509950 | + | 0.0883258i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.25205 | + | 4.35519i | −0.544612 | + | 0.451612i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26.6386 | + | 9.69565i | 2.73306 | + | 0.994753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.86855 | − | 16.2684i | 0.291257 | − | 1.65180i | −0.390780 | − | 0.920484i | \(-0.627795\pi\) |
0.682037 | − | 0.731318i | \(-0.261094\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.16254 | + | 0.972351i | 0.518855 | + | 0.0977250i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.0683785 | − | 0.0573764i | −0.00680391 | − | 0.00570916i | 0.639379 | − | 0.768891i | \(-0.279191\pi\) |
−0.646183 | + | 0.763182i | \(0.723636\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.0453 | + | 1.94759i | −1.08833 | + | 0.191901i | −0.688895 | − | 0.724861i | \(-0.741904\pi\) |
−0.399432 | + | 0.916763i | \(0.630793\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.02248 | − | 1.74743i | 0.0997835 | − | 0.170532i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 10.2098i | − | 0.987019i | −0.869740 | − | 0.493510i | \(-0.835714\pi\) | ||
0.869740 | − | 0.493510i | \(-0.164286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8.75424i | − | 0.838504i | −0.907870 | − | 0.419252i | \(-0.862292\pi\) | ||
0.907870 | − | 0.419252i | \(-0.137708\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.09104 | − | 8.93760i | −0.483220 | − | 0.848319i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.0414 | − | 2.82854i | 1.50905 | − | 0.266086i | 0.642931 | − | 0.765924i | \(-0.277718\pi\) |
0.866119 | + | 0.499837i | \(0.166607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.3825 | − | 10.3902i | −1.15468 | − | 0.968889i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.60747 | + | 9.56379i | −0.333511 | + | 0.884172i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.281485 | + | 1.59638i | −0.0258037 | + | 0.146340i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.45518 | − | 2.71346i | −0.677743 | − | 0.246678i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.54159 | + | 0.941842i | 0.229168 | + | 0.0849231i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 13.8291 | + | 23.9528i | 1.23692 | + | 2.14240i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.766625 | + | 0.442611i | 0.0680270 | + | 0.0392754i | 0.533628 | − | 0.845719i | \(-0.320828\pi\) |
−0.465601 | + | 0.884995i | \(0.654162\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.452614 | + | 0.0825254i | 0.0398504 | + | 0.00726596i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.7169 | − | 15.1554i | −1.11108 | − | 1.32414i | −0.940885 | − | 0.338726i | \(-0.890004\pi\) |
−0.170197 | − | 0.985410i | \(-0.554440\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.676342 | − | 1.85823i | −0.0586463 | − | 0.161129i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 21.0085 | − | 3.32748i | 1.80812 | − | 0.286384i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.0756258 | + | 0.207780i | 0.00646115 | + | 0.0177519i | 0.942881 | − | 0.333129i | \(-0.108104\pi\) |
−0.936420 | + | 0.350881i | \(0.885882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.07052 | + | 4.25467i | −0.430076 | + | 0.360876i | −0.831980 | − | 0.554805i | \(-0.812793\pi\) |
0.401905 | + | 0.915682i | \(0.368348\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.99164 | − | 8.23456i | 0.588802 | − | 0.693475i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.98316 | + | 5.16699i | −0.249465 | + | 0.432085i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.14178 | + | 7.17377i | 0.343956 | + | 0.595749i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.8130 | − | 2.01217i | 0.974318 | − | 0.165961i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.6006 | + | 6.04213i | 1.35998 | + | 0.494991i | 0.916047 | − | 0.401071i | \(-0.131362\pi\) |
0.443929 | + | 0.896062i | \(0.353584\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.59083 | + | 1.69112i | 0.780491 | + | 0.137622i | 0.549678 | − | 0.835377i | \(-0.314750\pi\) |
0.230813 | + | 0.972998i | \(0.425862\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −14.8468 | + | 8.34302i | −1.20029 | + | 0.674493i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.3650 | + | 12.3525i | −0.832535 | + | 0.992176i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.00447 | − | 0.529770i | 0.239783 | − | 0.0422802i | −0.0524650 | − | 0.998623i | \(-0.516708\pi\) |
0.292248 | + | 0.956343i | \(0.405597\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.0587256 | + | 10.0958i | −0.00465724 | + | 0.800649i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.12757i | 0.0888652i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.38504 | 0.186811 | 0.0934053 | − | 0.995628i | \(-0.470225\pi\) | ||||
0.0934053 | + | 0.995628i | \(0.470225\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.4153 | + | 0.0722180i | 0.966533 | + | 0.00562217i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.11048 | − | 6.29787i | −0.0859319 | − | 0.487344i | −0.997152 | − | 0.0754233i | \(-0.975969\pi\) |
0.911220 | − | 0.411921i | \(-0.135142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.06566 | + | 0.894199i | 0.0819742 | + | 0.0687845i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.5964 | − | 17.8701i | 0.810326 | − | 1.36656i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.92057 | − | 10.8921i | 0.146018 | − | 0.828110i | −0.820526 | − | 0.571609i | \(-0.806319\pi\) |
0.966544 | − | 0.256501i | \(-0.0825695\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.14820 | − | 3.15466i | 0.0867959 | − | 0.238470i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.25856 | − | 7.38871i | −0.0945991 | − | 0.555370i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.8325 | − | 12.0276i | 1.55709 | − | 0.898987i | 0.559558 | − | 0.828791i | \(-0.310971\pi\) |
0.997533 | − | 0.0701962i | \(-0.0223625\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0634 | + | 9.27419i | 1.19398 | + | 0.689345i | 0.959207 | − | 0.282705i | \(-0.0912316\pi\) |
0.234774 | + | 0.972050i | \(0.424565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.85720 | + | 8.36936i | 0.728665 | + | 0.618681i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −15.6258 | − | 18.6221i | −1.14883 | − | 1.36912i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.34114 | + | 3.39990i | −0.683092 | + | 0.248625i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.11981 | − | 0.973433i | −0.0814544 | − | 0.0708068i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.74802 | + | 2.45608i | −0.488270 | + | 0.177716i | −0.574411 | − | 0.818567i | \(-0.694769\pi\) |
0.0861410 | + | 0.996283i | \(0.472546\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.83658 | + | 2.38017i | −0.204182 | + | 0.171329i | −0.739145 | − | 0.673547i | \(-0.764770\pi\) |
0.534963 | + | 0.844875i | \(0.320326\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.33319 | + | 23.7655i | −0.310306 | + | 1.70189i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.837761 | + | 1.45104i | −0.0596880 | + | 0.103383i | −0.894325 | − | 0.447417i | \(-0.852344\pi\) |
0.834637 | + | 0.550800i | \(0.185677\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.6618 | + | 7.88767i | −0.968462 | + | 0.559142i | −0.898767 | − | 0.438426i | \(-0.855536\pi\) |
−0.0696952 | + | 0.997568i | \(0.522203\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.476014 | − | 1.28454i | 0.0335754 | − | 0.0906044i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.197632 | − | 0.542990i | 0.0138711 | − | 0.0381104i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.30859 | + | 1.11237i | 0.440611 | + | 0.0776916i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.16277 | + | 7.50857i | −0.636856 | + | 0.521882i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.79491 | − | 9.28962i | 0.539185 | − | 0.642576i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.579130 | + | 3.28441i | 0.0398690 | + | 0.226108i | 0.998232 | − | 0.0594461i | \(-0.0189335\pi\) |
−0.958363 | + | 0.285554i | \(0.907822\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.2531 | + | 9.25812i | −1.11365 | + | 0.634356i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.08733 | 0.0741554 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.12484 | 0.0763590 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.582662 | + | 0.340934i | 0.0393727 | + | 0.0230382i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.35867 | − | 19.0480i | −0.225929 | − | 1.28131i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.2863 | − | 20.6010i | 1.15757 | − | 1.37954i | 0.245562 | − | 0.969381i | \(-0.421027\pi\) |
0.912012 | − | 0.410163i | \(-0.134528\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 33.2810 | − | 11.6767i | 2.21873 | − | 0.778444i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.12707 | + | 1.25669i | 0.473040 | + | 0.0834098i | 0.405086 | − | 0.914279i | \(-0.367242\pi\) |
0.0679544 | + | 0.997688i | \(0.478353\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.81653 | + | 13.2333i | −0.318286 | + | 0.874482i | 0.672628 | + | 0.739981i | \(0.265166\pi\) |
−0.990913 | + | 0.134501i | \(0.957057\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.552834 | − | 0.666679i | −0.0363738 | − | 0.0438642i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.43407 | + | 1.98266i | −0.224974 | + | 0.129889i | −0.608251 | − | 0.793745i | \(-0.708129\pi\) |
0.383278 | + | 0.923633i | \(0.374795\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.7650 | − | 22.1097i | 0.832698 | − | 1.44228i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.1785 | + | 7.56913i | −1.37569 | + | 0.491668i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.58643 | + | 5.52667i | −0.426041 | + | 0.357491i | −0.830456 | − | 0.557085i | \(-0.811920\pi\) |
0.404415 | + | 0.914576i | \(0.367475\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.35562 | + | 2.31326i | −0.409401 | + | 0.149010i | −0.538507 | − | 0.842621i | \(-0.681012\pi\) |
0.129106 | + | 0.991631i | \(0.458789\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.453309 | − | 15.5819i | 0.0290798 | − | 0.999577i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26.6127 | − | 9.68623i | 1.70022 | − | 0.618831i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.1668 | + | 18.0751i | 0.965041 | + | 1.15009i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.43414 | + | 1.22735i | −0.217630 | + | 0.0777803i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.52905 | + | 5.50160i | 0.601469 | + | 0.347258i | 0.769619 | − | 0.638503i | \(-0.220446\pi\) |
−0.168151 | + | 0.985761i | \(0.553779\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.98831 | + | 3.45735i | −0.376482 | + | 0.217362i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −30.9826 | + | 25.6919i | −1.94020 | + | 1.60889i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.14513 | − | 5.89371i | 0.133810 | − | 0.367640i | −0.854633 | − | 0.519232i | \(-0.826218\pi\) |
0.988443 | + | 0.151593i | \(0.0484402\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.294465 | + | 1.66999i | −0.0182972 | + | 0.103768i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.72844 | − | 2.00982i | 0.354581 | − | 0.124405i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −18.7660 | − | 15.7466i | −1.15716 | − | 0.970975i | −0.157301 | − | 0.987551i | \(-0.550279\pi\) |
−0.999863 | + | 0.0165753i | \(0.994724\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.14335 | + | 23.4981i | 0.254524 | + | 1.44348i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.63335 | + | 2.79141i | −0.0999591 | + | 0.170832i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.2760 | 0.687508 | 0.343754 | − | 0.939060i | \(-0.388301\pi\) | ||||
0.343754 | + | 0.939060i | \(0.388301\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.04477i | − | 0.488685i | −0.969689 | − | 0.244343i | \(-0.921428\pi\) | ||
0.969689 | − | 0.244343i | \(-0.0785721\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.46426 | − | 0.834072i | 0.0886210 | − | 0.0504803i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 20.2744 | − | 3.57492i | 1.22259 | − | 0.215575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.95949 | − | 8.29400i | 0.418155 | − | 0.498338i | −0.515311 | − | 0.857003i | \(-0.672324\pi\) |
0.933466 | + | 0.358665i | \(0.116768\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.49036 | + | 9.14054i | 0.448436 | + | 0.547230i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.2657 | + | 1.81011i | 0.612399 | + | 0.107982i | 0.471241 | − | 0.882005i | \(-0.343806\pi\) |
0.141158 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.61267 | + | 2.04285i | 0.333639 | + | 0.121435i | 0.503407 | − | 0.864049i | \(-0.332080\pi\) |
−0.169768 | + | 0.985484i | \(0.554302\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.0615 | − | 46.0409i | 1.01063 | − | 2.72723i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.223429 | − | 0.386991i | −0.0131886 | − | 0.0228434i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.61293 | − | 13.1860i | 0.447819 | − | 0.775646i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −28.1482 | − | 5.13229i | −1.65008 | − | 0.300860i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −20.4054 | + | 17.1222i | −1.19210 | + | 1.00029i | −0.192275 | + | 0.981341i | \(0.561587\pi\) |
−0.999821 | + | 0.0189459i | \(0.993969\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.05849 | − | 16.6456i | −0.352739 | − | 0.969142i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.73615 | − | 8.93183i | 0.100741 | − | 0.518278i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4.60160 | − | 12.6428i | −0.266117 | − | 0.731151i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.0487550 | − | 0.0581039i | −0.00281019 | − | 0.00334905i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.100066 | + | 0.117855i | −0.00574864 | + | 0.00677059i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 26.4664 | + | 15.2804i | 1.51546 | + | 0.874953i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.60040 | + | 9.70017i | 0.319632 | + | 0.553618i | 0.980411 | − | 0.196962i | \(-0.0631075\pi\) |
−0.660780 | + | 0.750580i | \(0.729774\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.26198 | + | 19.1503i | 0.185568 | + | 1.08943i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.17205 | + | 2.61041i | 0.406690 | + | 0.148023i | 0.537261 | − | 0.843416i | \(-0.319459\pi\) |
−0.130571 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.157445 | + | 0.892917i | −0.00889933 | + | 0.0504706i | −0.988934 | − | 0.148356i | \(-0.952602\pi\) |
0.980035 | + | 0.198826i | \(0.0637130\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.01628 | − | 1.78856i | −0.169948 | − | 0.100774i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −20.1111 | − | 16.8752i | −1.12955 | − | 0.947806i | −0.130504 | − | 0.991448i | \(-0.541659\pi\) |
−0.999047 | + | 0.0436420i | \(0.986104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.48969 | − | 0.615326i | 0.195385 | − | 0.0344516i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −17.6836 | − | 0.102863i | −0.987003 | − | 0.00574123i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 39.3128i | 2.18742i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 40.0570i | 2.22196i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.1625 | − | 0.0881980i | −0.838490 | − | 0.00487736i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.75385 | + | 0.309251i | −0.0966929 | + | 0.0170496i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.2372 | + | 13.6246i | 0.892477 | + | 0.748877i | 0.968705 | − | 0.248213i | \(-0.0798434\pi\) |
−0.0762285 | + | 0.997090i | \(0.524288\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −15.5314 | + | 8.72774i | −0.851115 | + | 0.478277i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.562202 | − | 3.18841i | 0.0307164 | − | 0.174201i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.22733 | − | 0.810682i | −0.121330 | − | 0.0441606i | 0.280641 | − | 0.959813i | \(-0.409453\pi\) |
−0.401972 | + | 0.915652i | \(0.631675\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.73747 | − | 27.8126i | −0.257304 | − | 1.51057i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.44897 | + | 5.97379i | 0.186772 | + | 0.323499i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.44195 | − | 1.98721i | −0.185848 | − | 0.107299i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −18.1208 | + | 21.3421i | −0.975589 | + | 1.14902i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.7753 | − | 16.4167i | −0.739496 | − | 0.881297i | 0.256873 | − | 0.966445i | \(-0.417308\pi\) |
−0.996368 | + | 0.0851487i | \(0.972863\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.388725 | − | 1.06801i | −0.0208080 | − | 0.0571694i | 0.928854 | − | 0.370447i | \(-0.120795\pi\) |
−0.949662 | + | 0.313277i | \(0.898573\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 16.5283 | + | 6.34458i | 0.882217 | + | 0.338649i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.26744 | + | 8.97721i | 0.173908 | + | 0.477809i | 0.995770 | − | 0.0918778i | \(-0.0292869\pi\) |
−0.821862 | + | 0.569686i | \(0.807065\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −33.8645 | + | 28.4157i | −1.79734 | + | 1.50815i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.76213 | + | 0.503622i | 0.146187 | + | 0.0266545i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −14.6607 | + | 25.3930i | −0.773760 | + | 1.34019i | 0.161729 | + | 0.986835i | \(0.448293\pi\) |
−0.935489 | + | 0.353356i | \(0.885040\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.4791 | − | 25.0786i | −0.762060 | − | 1.31993i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.77489 | + | 12.8852i | −0.250617 | + | 0.676297i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.49925 | + | 0.545681i | 0.0784742 | + | 0.0285623i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.4024 | + | 3.24484i | 0.960599 | + | 0.169379i | 0.631895 | − | 0.775054i | \(-0.282277\pi\) |
0.328703 | + | 0.944433i | \(0.393388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.65690 | − | 4.39260i | 0.0862546 | − | 0.228670i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.06989 | − | 1.27504i | 0.0555457 | − | 0.0661968i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −31.6158 | + | 5.57471i | −1.63700 | + | 0.288648i | −0.915063 | − | 0.403310i | \(-0.867860\pi\) |
−0.721938 | + | 0.691958i | \(0.756748\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 41.6260 | − | 23.7110i | 2.14956 | − | 1.22443i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.89475i | 0.355097i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.2516 | 1.14299 | 0.571494 | − | 0.820606i | \(-0.306364\pi\) | ||||
0.571494 | + | 0.820606i | \(0.306364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.774336 | − | 1.32335i | 0.0396704 | − | 0.0677974i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.21165 | − | 12.5429i | −0.113010 | − | 0.640911i | −0.987716 | − | 0.156258i | \(-0.950057\pi\) |
0.874706 | − | 0.484653i | \(-0.161054\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.56799 | − | 1.31570i | −0.0799120 | − | 0.0670541i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.147496 | − | 0.783105i | 0.00749763 | − | 0.0398075i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.88879 | − | 27.7257i | 0.247872 | − | 1.40575i | −0.565856 | − | 0.824504i | \(-0.691454\pi\) |
0.813728 | − | 0.581246i | \(-0.197435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.66683 | − | 21.0644i | 0.387728 | − | 1.06527i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −26.3777 | + | 21.8733i | −1.33058 | + | 1.10336i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −46.0322 | + | 26.5767i | −2.31613 | + | 1.33722i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −18.6821 | − | 10.7861i | −0.937626 | − | 0.541339i | −0.0484110 | − | 0.998828i | \(-0.515416\pi\) |
−0.889215 | + | 0.457489i | \(0.848749\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.22532 | + | 1.15272i | −0.161468 | + | 0.0577080i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.6424 | − | 19.8336i | −0.831079 | − | 0.990442i | −0.999988 | − | 0.00481031i | \(-0.998469\pi\) |
0.168909 | − | 0.985632i | \(-0.445976\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.6121 | + | 4.59043i | −0.628254 | + | 0.228666i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.55162 | − | 36.4207i | −0.275862 | − | 1.80976i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −9.77189 | + | 3.55668i | −0.484374 | + | 0.176298i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.7032 | + | 16.5330i | −0.974262 | + | 0.817502i | −0.983214 | − | 0.182457i | \(-0.941595\pi\) |
0.00895224 | + | 0.999960i | \(0.497150\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.360642 | − | 0.128892i | 0.0177891 | − | 0.00635778i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.617834 | + | 1.07012i | −0.0304016 | + | 0.0526571i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.46423 | + | 4.30948i | −0.366405 | + | 0.211544i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.31809 | + | 8.82511i | 0.358369 | + | 0.432168i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.71802 | − | 4.72021i | 0.0839305 | − | 0.230597i | −0.890627 | − | 0.454734i | \(-0.849734\pi\) |
0.974558 | + | 0.224137i | \(0.0719564\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.5017 | + | 5.20195i | 1.43783 | + | 0.253528i | 0.837592 | − | 0.546296i | \(-0.183963\pi\) |
0.600235 | + | 0.799824i | \(0.295074\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −14.1920 | − | 12.1926i | −0.690038 | − | 0.592826i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −42.8996 | + | 51.1258i | −2.08094 | + | 2.47996i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.370190 | − | 2.09945i | −0.0179147 | − | 0.101599i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.91928 | + | 5.21896i | 0.430627 | + | 0.251974i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.3440 | 1.36528 | 0.682640 | − | 0.730754i | \(-0.260832\pi\) | ||||
0.682640 | + | 0.730754i | \(0.260832\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 37.9757 | 1.82499 | 0.912497 | − | 0.409083i | \(-0.134151\pi\) | ||||
0.912497 | + | 0.409083i | \(0.134151\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.4669 | − | 7.10137i | 0.597740 | − | 0.340485i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.74858 | + | 26.9305i | 0.227155 | + | 1.28826i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.33133 | + | 8.73714i | −0.349905 | + | 0.417001i | −0.912077 | − | 0.410020i | \(-0.865522\pi\) |
0.562171 | + | 0.827021i | \(0.309966\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.36611 | − | 20.4806i | −0.160291 | − | 0.975267i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.1408 | − | 3.37504i | −0.909406 | − | 0.160353i | −0.300672 | − | 0.953728i | \(-0.597211\pi\) |
−0.608734 | + | 0.793375i | \(0.708322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.61425 | + | 7.18258i | −0.123927 | + | 0.340487i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.6324 | − | 28.6918i | 0.502893 | − | 1.35707i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.4365 | − | 8.91229i | 0.728495 | − | 0.420597i | −0.0893764 | − | 0.995998i | \(-0.528487\pi\) |
0.817871 | + | 0.575401i | \(0.195154\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37015 | − | 2.37318i | 0.0645180 | − | 0.111748i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.02569 | − | 16.5945i | 0.142159 | − | 0.779677i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.05088 | − | 2.55999i | 0.143028 | − | 0.120014i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.7281 | − | 5.36059i | 0.688952 | − | 0.250758i | 0.0262653 | − | 0.999655i | \(-0.491639\pi\) |
0.662686 | + | 0.748897i | \(0.269416\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.3007 | + | 25.7990i | 0.667500 | + | 1.20419i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.7308 | + | 9.72920i | −1.24498 | + | 0.453134i | −0.878701 | − | 0.477373i | \(-0.841589\pi\) |
−0.366274 | + | 0.930507i | \(0.619367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.52477 | − | 5.39241i | −0.210284 | − | 0.250606i | 0.650585 | − | 0.759433i | \(-0.274524\pi\) |
−0.860869 | + | 0.508827i | \(0.830079\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 21.2904 | + | 18.0768i | 0.987317 | + | 0.838292i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.49779 | + | 5.48355i | 0.439505 | + | 0.253749i | 0.703388 | − | 0.710806i | \(-0.251670\pi\) |
−0.263882 | + | 0.964555i | \(0.585003\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.195588 | + | 0.112923i | −0.00903141 | + | 0.00521429i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.887303 | − | 5.20915i | −0.0408847 | − | 0.240025i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.159086 | − | 0.437085i | 0.00731479 | − | 0.0200972i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 14.1379 | − | 80.1801i | 0.648692 | − | 3.67892i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 17.4855 | + | 0.203428i | 0.800608 | + | 0.00931433i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.9431 | − | 15.8951i | −0.865530 | − | 0.726266i | 0.0976217 | − | 0.995224i | \(-0.468876\pi\) |
−0.963152 | + | 0.268957i | \(0.913321\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.51355 | − | 19.9263i | −0.160204 | − | 0.908562i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.95298 | + | 0.0113602i | 0.0888637 | + | 0.000516905i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −67.6217 | −3.07054 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.8260i | 0.943714i | 0.881675 | + | 0.471857i | \(0.156416\pi\) | ||||
−0.881675 | + | 0.471857i | \(0.843584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.0240290 | − | 4.13094i | 0.00108663 | − | 0.186808i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3028 | + | 3.05095i | −0.780865 | + | 0.137687i | −0.549851 | − | 0.835263i | \(-0.685315\pi\) |
−0.231014 | + | 0.972950i | \(0.574204\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.38402 | + | 8.79993i | −0.332560 | + | 0.396329i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.250166 | − | 21.5029i | 0.0112441 | − | 0.966484i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.03691 | + | 0.535489i | 0.136224 | + | 0.0240199i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.48450 | + | 3.08810i | 0.379818 | + | 0.138243i | 0.524872 | − | 0.851181i | \(-0.324113\pi\) |
−0.145054 | + | 0.989424i | \(0.546335\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10.9192 | + | 1.85993i | −0.487835 | + | 0.0830957i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.43613 | − | 7.68360i | −0.197797 | − | 0.342595i | 0.750017 | − | 0.661419i | \(-0.230045\pi\) |
−0.947814 | + | 0.318824i | \(0.896712\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.182696 | + | 0.316439i | −0.00812987 | + | 0.0140813i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.55951 | − | 1.83674i | 0.0692602 | − | 0.0815727i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 15.9153 | − | 13.3546i | 0.705435 | − | 0.591930i | −0.217879 | − | 0.975976i | \(-0.569914\pi\) |
0.923314 | + | 0.384046i | \(0.125469\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0380652 | − | 0.104583i | −0.00168391 | − | 0.00462649i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −30.8447 | − | 18.5332i | −1.36183 | − | 0.818262i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 15.7026 | + | 43.1426i | 0.691940 | + | 1.90109i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −7.02001 | − | 8.36612i | −0.308740 | − | 0.367941i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8460 | − | 3.43620i | −0.827246 | − | 0.150833i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0938 | − | 5.82764i | −0.442216 | − | 0.255314i | 0.262321 | − | 0.964981i | \(-0.415512\pi\) |
−0.704537 | + | 0.709667i | \(0.748845\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.0754 | − | 20.9151i | −0.528019 | − | 0.914555i | −0.999466 | − | 0.0326613i | \(-0.989602\pi\) |
0.471448 | − | 0.881894i | \(-0.343732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.45237 | − | 2.02049i | −0.237961 | − | 0.0881815i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −21.0133 | − | 7.64823i | −0.915356 | − | 0.333162i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.28625 | + | 7.29469i | −0.0559240 | + | 0.317161i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −12.8101 | + | 2.10541i | −0.555910 | + | 0.0913671i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.08448 | + | 3.42728i | 0.176918 | + | 0.148452i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.1588 | + | 7.25740i | −1.77945 | + | 0.313765i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −20.6222 | − | 36.2035i | −0.889915 | − | 1.56229i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 12.1149i | − | 0.521828i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.65438i | − | 0.0711274i | −0.999367 | − | 0.0355637i | \(-0.988677\pi\) | ||
0.999367 | − | 0.0355637i | \(-0.0113227\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 16.2249 | − | 27.7287i | 0.696279 | − | 1.18995i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.2910 | + | 6.22275i | −1.51170 | + | 0.266553i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.7235 | + | 18.2281i | 0.928828 | + | 0.779379i | 0.975607 | − | 0.219526i | \(-0.0704511\pi\) |
−0.0467786 | + | 0.998905i | \(0.514896\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 14.5952 | − | 16.9886i | 0.622909 | − | 0.725054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.43347 | − | 13.8009i | 0.103669 | − | 0.587937i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.48423 | + | 1.26815i | 0.148164 | + | 0.0539274i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −32.4113 | + | 26.8766i | −1.37578 | + | 1.14085i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.50566 | + | 16.4643i | 0.402768 | + | 0.697614i | 0.994059 | − | 0.108844i | \(-0.0347149\pi\) |
−0.591291 | + | 0.806458i | \(0.701382\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.783780 | + | 0.452516i | 0.0331504 | + | 0.0191394i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.79459 | + | 16.2133i | 0.244648 | + | 0.684527i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.8594 | + | 27.2427i | 0.963408 | + | 1.14814i | 0.988917 | + | 0.148470i | \(0.0474349\pi\) |
−0.0255091 | + | 0.999675i | \(0.508121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −22.8054 | − | 62.6572i | −0.959429 | − | 2.63601i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.69729 | + | 1.92973i | −0.0712794 | + | 0.0810412i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.493250 | + | 1.35519i | 0.0206781 | + | 0.0568127i | 0.949602 | − | 0.313457i | \(-0.101487\pi\) |
−0.928924 | + | 0.370270i | \(0.879265\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.1309 | − | 17.7309i | 0.884300 | − | 0.742016i | −0.0827583 | − | 0.996570i | \(-0.526373\pi\) |
0.967059 | + | 0.254554i | \(0.0819285\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.18599 | + | 11.7125i | 0.174872 | + | 0.489295i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.2121 | + | 40.2046i | −0.968013 | + | 1.67665i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.6302 | + | 28.8044i | 0.692325 | + | 1.19914i | 0.971074 | + | 0.238778i | \(0.0767468\pi\) |
−0.278749 | + | 0.960364i | \(0.589920\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.09393 | + | 4.93700i | 0.170138 | + | 0.205175i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.564975 | + | 0.205634i | 0.0234391 | + | 0.00853115i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0520 | + | 1.77243i | 0.416310 | + | 0.0734066i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 41.1188 | + | 7.74461i | 1.70005 | + | 0.320200i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.57594 | − | 3.06988i | 0.106320 | − | 0.126708i | −0.710260 | − | 0.703939i | \(-0.751423\pi\) |
0.816580 | + | 0.577232i | \(0.195867\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 26.8652 | − | 4.73706i | 1.10696 | − | 0.195187i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.50480 | + | 1.46564i | 0.103034 | + | 0.0602883i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 21.2442i | 0.872395i | 0.899851 | + | 0.436198i | \(0.143675\pi\) | ||||
−0.899851 | + | 0.436198i | \(0.856325\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.63558 | 0.272032 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 13.5240 | + | 23.7421i | 0.553499 | + | 0.971698i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 2.69240 | + | 15.2693i | 0.110008 | + | 0.623888i | 0.989101 | + | 0.147238i | \(0.0470382\pi\) |
−0.879093 | + | 0.476651i | \(0.841851\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.35047 | + | 7.00688i | 0.340623 | + | 0.285817i | 0.797012 | − | 0.603964i | \(-0.206413\pi\) |
−0.456389 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.22005 | − | 0.837407i | −0.0904075 | − | 0.0341019i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −5.63944 | + | 31.9829i | −0.229276 | + | 1.30029i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.2605 | + | 41.9279i | −0.619405 | + | 1.70180i | 0.0890338 | + | 0.996029i | \(0.471622\pi\) |
−0.708439 | + | 0.705772i | \(0.750600\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.938479 | − | 0.347774i | −0.0380291 | − | 0.0140925i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.4028 | − | 10.6249i | 0.744497 | − | 0.429836i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 31.4233 | + | 18.1422i | 1.26918 | + | 0.732759i | 0.974832 | − | 0.222941i | \(-0.0715658\pi\) |
0.294343 | + | 0.955700i | \(0.404899\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.99022 | − | 10.9154i | 0.0802532 | − | 0.440152i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.1074 | + | 34.6889i | 1.17182 | + | 1.39652i | 0.900959 | + | 0.433904i | \(0.142864\pi\) |
0.270862 | + | 0.962618i | \(0.412691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −41.0905 | + | 14.9557i | −1.65157 | + | 0.601121i | −0.989005 | − | 0.147885i | \(-0.952753\pi\) |
−0.662563 | + | 0.749006i | \(0.730531\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.9127 | + | 15.9458i | 0.518169 | + | 0.639881i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.501037 | − | 0.182363i | 0.0200736 | − | 0.00730620i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 41.7001 | − | 34.9905i | 1.66800 | − | 1.39962i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.0113 | − | 13.5945i | −0.639429 | − | 0.542914i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.8559 | − | 29.1953i | 0.672090 | − | 1.16409i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.6964 | − | 18.2999i | 1.26181 | − | 0.728509i | 0.288389 | − | 0.957513i | \(-0.406880\pi\) |
0.973425 | + | 0.229004i | \(0.0735470\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.69450 | − | 0.969975i | 0.226336 | − | 0.0385531i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.23936 | − | 3.40512i | 0.0491825 | − | 0.135128i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 23.2143 | + | 4.09331i | 0.919785 | + | 0.162183i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 15.8715 | + | 28.2440i | 0.627867 | + | 1.11732i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.5704 | − | 19.7478i | 0.654490 | − | 0.779990i | −0.332094 | − | 0.943246i | \(-0.607755\pi\) |
0.986584 | + | 0.163256i | \(0.0521996\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.30668 | + | 30.0957i | 0.209275 | + | 1.18686i | 0.890569 | + | 0.454848i | \(0.150306\pi\) |
−0.681294 | + | 0.732010i | \(0.738583\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.0109547 | − | 1.88328i | 0.000431343 | − | 0.0741542i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.9596 | 0.824008 | 0.412004 | − | 0.911182i | \(-0.364829\pi\) | ||||
0.412004 | + | 0.911182i | \(0.364829\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.57758 | −0.297446 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.0113326 | − | 1.94824i | 0.000444160 | − | 0.0763577i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.21883 | − | 6.91233i | −0.0476965 | − | 0.270500i | 0.951628 | − | 0.307253i | \(-0.0994098\pi\) |
−0.999324 | + | 0.0367525i | \(0.988299\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −52.0566 | + | 62.0386i | −2.03402 | + | 2.42405i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.596376 | − | 1.00575i | 0.0232668 | − | 0.0392380i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −24.6203 | − | 4.34123i | −0.959072 | − | 0.169110i | −0.327865 | − | 0.944725i | \(-0.606329\pi\) |
−0.631207 | + | 0.775614i | \(0.717440\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.17476 | + | 5.97510i | −0.0845883 | + | 0.232404i | −0.974774 | − | 0.223193i | \(-0.928352\pi\) |
0.890186 | + | 0.455597i | \(0.150574\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −33.0253 | + | 5.62539i | −1.28260 | + | 0.218472i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.01034 | + | 4.04742i | −0.271849 | + | 0.156952i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.99535 | + | 6.92015i | −0.154701 | + | 0.267949i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −35.5072 | − | 30.1478i | −1.37279 | − | 1.16558i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 10.0147 | − | 8.40331i | 0.386612 | − | 0.324406i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.0990 | + | 11.3191i | −1.19878 | + | 0.436320i | −0.862798 | − | 0.505549i | \(-0.831290\pi\) |
−0.335981 | + | 0.941869i | \(0.609068\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −19.8889 | − | 57.7611i | −0.765525 | − | 2.22322i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.7565 | + | 7.91874i | −0.836172 | + | 0.304342i | −0.724389 | − | 0.689391i | \(-0.757878\pi\) |
−0.111783 | + | 0.993733i | \(0.535656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.03209 | + | 3.61351i | 0.116361 | + | 0.138674i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.24843 | − | 12.3316i | 0.0861599 | − | 0.472547i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.4976 | + | 12.4116i | 0.822583 | + | 0.474918i | 0.851306 | − | 0.524669i | \(-0.175811\pi\) |
−0.0287236 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.783867 | − | 0.452566i | 0.0299500 | − | 0.0172917i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 22.8719 | + | 8.47567i | 0.872616 | + | 0.323367i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.79257 | + | 18.6624i | −0.258776 | + | 0.710982i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.875636 | + | 4.96598i | −0.0333108 | + | 0.188915i | −0.996923 | − | 0.0783902i | \(-0.975022\pi\) |
0.963612 | + | 0.267305i | \(0.0861331\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.16027 | + | 0.950803i | −0.0440751 | + | 0.0361180i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.7561 | + | 17.4164i | 0.787324 | + | 0.660643i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.54262 | + | 8.74865i | 0.0584310 | + | 0.331379i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.39942 | + | 5.96786i | 0.128578 | + | 0.225725i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.1723 | −0.875207 | −0.437604 | − | 0.899168i | \(-0.644173\pi\) | ||||
−0.437604 | + | 0.899168i | \(0.644173\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.1256i | 1.55108i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −38.1658 | − | 22.3320i | −1.43741 | − | 0.841074i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.0251015 | − | 0.00442607i | 0.000944039 | − | 0.000166460i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0337 | − | 11.9577i | 0.376823 | − | 0.449081i | −0.543986 | − | 0.839095i | \(-0.683085\pi\) |
0.920809 | + | 0.390014i | \(0.127530\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.8965 | + | 36.7579i | 0.483657 | + | 1.37853i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −15.3186 | − | 2.70109i | −0.573688 | − | 0.101157i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 22.9502 | + | 8.35319i | 0.858289 | + | 0.312392i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.50596 | + | 11.4635i | 0.355007 | + | 0.428113i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.4776 | − | 32.0041i | −0.689096 | − | 1.19355i | −0.972131 | − | 0.234440i | \(-0.924674\pi\) |
0.283034 | − | 0.959110i | \(-0.408659\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.60132 | − | 2.77358i | 0.0596365 | − | 0.103293i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.94258 | + | 11.0314i | 0.146626 | + | 0.410261i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 18.2247 | − | 15.2924i | 0.676849 | − | 0.567944i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.03567 | + | 11.0879i | 0.149675 | + | 0.411228i | 0.991759 | − | 0.128118i | \(-0.0408937\pi\) |
−0.842084 | + | 0.539346i | \(0.818671\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.9836 | − | 0.942126i | −0.999391 | − | 0.0348935i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.515730 | + | 1.41696i | 0.0190750 | + | 0.0524080i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22.2989 | + | 26.5748i | 0.823629 | + | 0.981562i | 0.999996 | − | 0.00276204i | \(-0.000879186\pi\) |
−0.176368 | + | 0.984324i | \(0.556435\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −16.5086 | − | 46.1914i | −0.608930 | − | 1.70379i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.19942 | − | 0.692485i | −0.0441812 | − | 0.0255080i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.86442 | + | 17.0857i | 0.362868 | + | 0.628507i | 0.988432 | − | 0.151667i | \(-0.0484641\pi\) |
−0.625563 | + | 0.780173i | \(0.715131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 31.4593 | − | 26.0871i | 1.15569 | − | 0.958335i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.0759 | − | 4.75924i | −0.479709 | − | 0.174600i | 0.0908366 | − | 0.995866i | \(-0.471046\pi\) |
−0.570545 | + | 0.821266i | \(0.693268\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.5575 | − | 71.2170i | 0.460070 | − | 2.60919i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.09120 | + | 5.96038i | 0.0765131 | + | 0.218079i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.23334 | + | 1.87399i | 0.0816044 | + | 0.0684742i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.4163 | − | 6.59750i | 1.36534 | − | 0.240746i | 0.557514 | − | 0.830168i | \(-0.311755\pi\) |
0.807826 | + | 0.589421i | \(0.200644\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 9.62490 | − | 16.4491i | 0.350751 | − | 0.599438i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 39.8656i | − | 1.45086i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 13.2372i | − | 0.481113i | −0.970635 | − | 0.240556i | \(-0.922670\pi\) | ||
0.970635 | − | 0.240556i | \(-0.0773299\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.92788 | + | 10.4067i | 0.215168 | + | 0.377740i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.5700 | − | 8.21155i | 1.68816 | − | 0.297668i | 0.754626 | − | 0.656155i | \(-0.227818\pi\) |
0.933535 | + | 0.358486i | \(0.116707\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.91494 | + | 1.60683i | 0.0693255 | + | 0.0581710i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 44.1867 | + | 53.9214i | 1.59757 | + | 1.94953i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.56026 | − | 14.5200i | 0.0924456 | − | 0.524285i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.2190 | + | 4.81132i | 0.476689 | + | 0.173501i | 0.569180 | − | 0.822213i | \(-0.307261\pi\) |
−0.0924911 | + | 0.995714i | \(0.529483\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.1864 | − | 3.77480i | −0.366855 | − | 0.135946i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −17.6365 | − | 30.5473i | −0.634341 | − | 1.09871i | −0.986654 | − | 0.162829i | \(-0.947938\pi\) |
0.352313 | − | 0.935882i | \(-0.385395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.1071 | + | 23.1558i | 1.44069 | + | 0.831783i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.88950 | + | 0.526845i | 0.103660 | + | 0.0189005i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.96605 | − | 8.30182i | −0.249585 | − | 0.297443i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.46786 | + | 17.7703i | 0.231438 | + | 0.635871i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.42335 | − | 9.94202i | −0.122340 | − | 0.355299i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.27132 | − | 11.7354i | −0.152450 | − | 0.418853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.1892 | − | 18.6190i | 0.790961 | − | 0.663695i | −0.155022 | − | 0.987911i | \(-0.549545\pi\) |
0.945983 | + | 0.324216i | \(0.105100\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −27.4625 | + | 32.3445i | −0.977690 | + | 1.15150i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.32565 | + | 4.02814i | −0.0826906 | + | 0.143224i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.7185 | + | 22.0291i | 0.451647 | + | 0.782276i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 40.7409 | − | 6.93962i | 1.44493 | − | 0.246123i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.52330 | − | 3.10223i | −0.301911 | − | 0.109887i | 0.186623 | − | 0.982432i | \(-0.440246\pi\) |
−0.488534 | + | 0.872545i | \(0.662468\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.8668 | + | 6.14795i | 1.23350 | + | 0.217499i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.81833 | + | 2.85711i | 0.170247 | + | 0.100951i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.438706 | − | 0.522829i | 0.0154816 | − | 0.0184502i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.54558 | − | 0.801509i | 0.160211 | − | 0.0282495i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.113604 | − | 19.5302i | 0.00399906 | − | 0.687497i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 9.61585i | − | 0.338075i | −0.985610 | − | 0.169038i | \(-0.945934\pi\) | ||
0.985610 | − | 0.169038i | \(-0.0540660\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.5031 | 0.474156 | 0.237078 | − | 0.971491i | \(-0.423810\pi\) | ||||
0.237078 | + | 0.971491i | \(0.423810\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.9337 | − | 0.0810502i | −0.488677 | − | 0.00284255i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.69535 | − | 9.61481i | −0.0593855 | − | 0.336792i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.40914 | − | 1.18241i | −0.0492996 | − | 0.0413673i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.42988 | − | 2.54453i | −0.0499640 | − | 0.0889131i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.09003 | + | 6.18187i | −0.0380423 | + | 0.215749i | −0.997903 | − | 0.0647288i | \(-0.979382\pi\) |
0.959861 | + | 0.280478i | \(0.0904929\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.0239 | − | 38.5302i | 0.488841 | − | 1.34308i | −0.412890 | − | 0.910781i | \(-0.635480\pi\) |
0.901731 | − | 0.432298i | \(-0.142297\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.98757 | − | 35.1516i | −0.208460 | − | 1.22382i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 36.5263 | − | 21.0885i | 1.27014 | − | 0.733318i | 0.295129 | − | 0.955457i | \(-0.404637\pi\) |
0.975015 | + | 0.222139i | \(0.0713040\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.97893 | + | 2.29724i | 0.138194 | + | 0.0797864i | 0.567503 | − | 0.823371i | \(-0.307910\pi\) |
−0.429309 | + | 0.903158i | \(0.641243\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.2953 | − | 12.1375i | −0.495897 | − | 0.421047i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 25.2452 | + | 30.0861i | 0.874695 | + | 1.04242i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.5992 | + | 8.95339i | −0.851292 | + | 0.309845i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.9071 | − | 12.8814i | 0.549829 | − | 0.445246i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 29.1595 | − | 10.6132i | 1.00670 | − | 0.366408i | 0.214533 | − | 0.976717i | \(-0.431177\pi\) |
0.792163 | + | 0.610309i | \(0.208955\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0784 | + | 16.0087i | −0.657876 | + | 0.552023i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.23858 | − | 17.7621i | 0.111543 | − | 0.611760i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.84728 | − | 4.93163i | 0.0979494 | − | 0.169653i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.96194 | − | 1.13273i | 0.0674130 | − | 0.0389209i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.59480 | − | 9.70069i | 0.123373 | − | 0.332927i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.02036 | − | 22.0358i | 0.274935 | − | 0.755376i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.5512 | + | 5.03434i | 0.977573 | + | 0.172373i | 0.639537 | − | 0.768761i | \(-0.279126\pi\) |
0.338036 | + | 0.941133i | \(0.390237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −79.5720 | − | 30.0147i | −2.72130 | − | 1.02648i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.00052 | − | 4.76763i | 0.136655 | − | 0.162859i | −0.693377 | − | 0.720575i | \(-0.743878\pi\) |
0.830032 | + | 0.557716i | \(0.188322\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.56731 | − | 25.9025i | −0.155835 | − | 0.883782i | −0.958019 | − | 0.286705i | \(-0.907440\pi\) |
0.802184 | − | 0.597076i | \(-0.203671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.672528 | + | 0.383086i | −0.0229197 | + | 0.0130555i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −21.6556 | −0.737166 | −0.368583 | − | 0.929595i | \(-0.620157\pi\) | ||||
−0.368583 | + | 0.929595i | \(0.620157\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −45.2744 | −1.53938 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −22.7617 | − | 13.3186i | −0.773028 | − | 0.452324i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.94839 | + | 22.3924i | 0.133940 | + | 0.759611i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.73217 | − | 2.06432i | 0.0586924 | − | 0.0699469i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −9.17283 | + | 48.7017i | −0.310453 | + | 1.64830i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −7.77785 | − | 1.37144i | −0.262939 | − | 0.0463633i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.3125 | − | 44.8181i | 0.550833 | − | 1.51340i | −0.281744 | − | 0.959490i | \(-0.590913\pi\) |
0.832576 | − | 0.553910i | \(-0.186865\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 29.4504 | + | 35.5151i | 0.993336 | + | 1.19789i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 10.2022 | − | 5.89026i | 0.343722 | − | 0.198448i | −0.318195 | − | 0.948025i | \(-0.603077\pi\) |
0.661917 | + | 0.749578i | \(0.269743\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.94659 | − | 8.56774i | 0.166466 | − | 0.288327i | −0.770709 | − | 0.637187i | \(-0.780098\pi\) |
0.937175 | + | 0.348860i | \(0.113431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −28.8915 | + | 10.3257i | −0.971177 | + | 0.347095i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.2674 | − | 23.7192i | 0.949127 | − | 0.796412i | −0.0300236 | − | 0.999549i | \(-0.509558\pi\) |
0.979150 | + | 0.203137i | \(0.0651138\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.237531 | + | 0.0864544i | −0.00796655 | + | 0.00289959i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.4526 | − | 3.09703i | −0.517683 | − | 0.103754i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.5859 | + | 14.7721i | −1.35816 | + | 0.494329i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −63.2952 | − | 75.4323i | −2.11573 | − | 2.52143i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.9439 | + | 7.84269i | −0.732686 | + | 0.261860i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.90337 | + | 3.98566i | 0.230240 | + | 0.132929i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −28.6563 | + | 16.5447i | −0.954680 | + | 0.551185i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.101128 | + | 0.0838593i | −0.00336534 | + | 0.00279066i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.9688 | − | 71.3486i | 0.863231 | − | 2.37171i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.93067 | − | 16.6207i | 0.0973113 | − | 0.551880i | −0.896703 | − | 0.442632i | \(-0.854045\pi\) |
0.994015 | − | 0.109248i | \(-0.0348441\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.203119 | + | 0.174504i | 0.00673704 | + | 0.00578793i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15.2762 | + | 12.8182i | 0.506122 | + | 0.424687i | 0.859762 | − | 0.510695i | \(-0.170612\pi\) |
−0.353640 | + | 0.935382i | \(0.615056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.640240 | + | 3.63098i | 0.0211889 | + | 0.120168i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 26.7326 | − | 45.6865i | 0.883753 | − | 1.51035i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.64933 | 0.186557 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 52.4126i | − | 1.72893i | −0.502690 | − | 0.864467i | \(-0.667656\pi\) | ||
0.502690 | − | 0.864467i | \(-0.332344\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.8573 | − | 9.60228i | 0.555468 | − | 0.316406i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −36.2363 | + | 6.38943i | −1.19273 | + | 0.210311i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −44.8778 | + | 53.4833i | −1.47557 | + | 1.75852i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 33.2017 | − | 5.45689i | 1.09049 | − | 0.179228i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −16.3482 | − | 2.88262i | −0.536366 | − | 0.0945757i | −0.101097 | − | 0.994877i | \(-0.532235\pi\) |
−0.435268 | + | 0.900301i | \(0.643346\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.0222 | − | 16.3868i | −1.47554 | − | 0.537054i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.59355 | − | 12.3958i | 0.150386 | − | 0.405822i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.3459 | + | 35.2402i | 0.665383 | + | 1.15248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.11716 | − | 3.66703i | 0.0691647 | − | 0.119797i | −0.829369 | − | 0.558701i | \(-0.811300\pi\) |
0.898534 | + | 0.438904i | \(0.144633\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.54496 | + | 0.281695i | 0.0504180 | + | 0.00919276i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.5192 | − | 39.0342i | 1.51648 | − | 1.27248i | 0.666727 | − | 0.745302i | \(-0.267695\pi\) |
0.849755 | − | 0.527178i | \(-0.176750\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.11349 | + | 5.80677i | 0.0688248 | + | 0.189095i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.12821 | + | 5.20625i | −0.101761 | + | 0.169359i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −2.60051 | − | 7.14483i | −0.0845051 | − | 0.232176i | 0.890242 | − | 0.455488i | \(-0.150535\pi\) |
−0.974747 | + | 0.223312i | \(0.928313\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.853604 | + | 1.01729i | 0.0277092 | + | 0.0330225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29.4308 | + | 34.6628i | −0.954360 | + | 1.12402i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.40608 | − | 3.12120i | −0.175120 | − | 0.101106i | 0.409878 | − | 0.912140i | \(-0.365571\pi\) |
−0.584998 | + | 0.811035i | \(0.698905\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.6979 | + | 25.4574i | 0.475612 | + | 0.823783i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.03060 | − | 6.05041i | −0.0333146 | − | 0.195582i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.0593317 | − | 0.0215950i | −0.00191592 | − | 0.000697338i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.68856 | − | 15.2476i | 0.0867276 | − | 0.491857i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.356321 | + | 30.6273i | −0.0114823 | + | 0.986952i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.6115 | + | 9.74321i | 0.373788 | + | 0.313645i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.55187 | + | 1.50792i | −0.275009 | + | 0.0484916i | −0.309452 | − | 0.950915i | \(-0.600146\pi\) |
0.0344424 | + | 0.999407i | \(0.489034\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 68.0906 | + | 0.396072i | 2.18739 | + | 0.0127237i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.6838i | 0.920507i | 0.887787 | + | 0.460254i | \(0.152242\pi\) | ||||
−0.887787 | + | 0.460254i | \(0.847758\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.89008i | − | 0.0605933i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 69.3796 | + | 0.403570i | 2.22193 | + | 0.0129246i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.0242 | + | 4.23611i | −0.768601 | + | 0.135525i | −0.544182 | − | 0.838967i | \(-0.683160\pi\) |
−0.224420 | + | 0.974493i | \(0.572049\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.50476 | + | 2.10175i | 0.0800526 | + | 0.0671721i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.305522 | + | 26.2609i | −0.00975456 | + | 0.838448i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.90983 | + | 10.8312i | −0.0609141 | + | 0.345461i | 0.939084 | + | 0.343687i | \(0.111676\pi\) |
−0.999998 | + | 0.00177427i | \(0.999435\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.44509 | + | 2.34582i | 0.205358 | + | 0.0747441i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.517960 | + | 3.04082i | 0.0164868 | + | 0.0967904i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.524445 | + | 0.908366i | 0.0166764 | + | 0.0288844i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 32.0529 | + | 18.5057i | 1.01819 | + | 0.587854i | 0.913580 | − | 0.406659i | \(-0.133306\pi\) |
0.104613 | + | 0.994513i | \(0.466640\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 23.7617 | − | 27.9859i | 0.754056 | − | 0.888106i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 41.5088 | + | 49.4682i | 1.31592 | + | 1.56825i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24777 | + | 11.6706i | 0.134528 | + | 0.369613i | 0.988605 | − | 0.150534i | \(-0.0480993\pi\) |
−0.854077 | + | 0.520147i | \(0.825877\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.9602 | + | 26.9886i | 0.473318 | + | 0.853883i |
(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 | 864.2.bh.b.47.15 | 192 | ||
4.3 | odd | 2 | 216.2.v.b.155.6 | yes | 192 | ||
8.3 | odd | 2 | inner | 864.2.bh.b.47.16 | 192 | ||
8.5 | even | 2 | 216.2.v.b.155.20 | yes | 192 | ||
12.11 | even | 2 | 648.2.v.b.467.27 | 192 | |||
24.5 | odd | 2 | 648.2.v.b.467.13 | 192 | |||
27.23 | odd | 18 | inner | 864.2.bh.b.239.16 | 192 | ||
108.23 | even | 18 | 216.2.v.b.131.20 | yes | 192 | ||
108.31 | odd | 18 | 648.2.v.b.179.13 | 192 | |||
216.77 | odd | 18 | 216.2.v.b.131.6 | ✓ | 192 | ||
216.85 | even | 18 | 648.2.v.b.179.27 | 192 | |||
216.131 | even | 18 | inner | 864.2.bh.b.239.15 | 192 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.v.b.131.6 | ✓ | 192 | 216.77 | odd | 18 | ||
216.2.v.b.131.20 | yes | 192 | 108.23 | even | 18 | ||
216.2.v.b.155.6 | yes | 192 | 4.3 | odd | 2 | ||
216.2.v.b.155.20 | yes | 192 | 8.5 | even | 2 | ||
648.2.v.b.179.13 | 192 | 108.31 | odd | 18 | |||
648.2.v.b.179.27 | 192 | 216.85 | even | 18 | |||
648.2.v.b.467.13 | 192 | 24.5 | odd | 2 | |||
648.2.v.b.467.27 | 192 | 12.11 | even | 2 | |||
864.2.bh.b.47.15 | 192 | 1.1 | even | 1 | trivial | ||
864.2.bh.b.47.16 | 192 | 8.3 | odd | 2 | inner | ||
864.2.bh.b.239.15 | 192 | 216.131 | even | 18 | inner | ||
864.2.bh.b.239.16 | 192 | 27.23 | odd | 18 | inner |