Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4368,2,Mod(337,4368)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4368, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4368.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4368 = 2^{4} \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4368.h (of order \(2\), degree \(1\), 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: | \(34.8786556029\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 20x^{8} + 138x^{6} + 364x^{4} + 249x^{2} + 36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2184) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.5 | ||
Root | \(-2.69449i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4368.337 |
Dual form | 4368.2.h.r.337.6 |
$q$-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 \(\left(\mathbb{Z}/4368\mathbb{Z}\right)^\times\).
\(n\) | \(1093\) | \(1249\) | \(1457\) | \(2017\) | \(3823\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.100328i | − | 0.0448680i | −0.999748 | − | 0.0224340i | \(-0.992858\pi\) | ||
0.999748 | − | 0.0224340i | \(-0.00714157\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.72967i | 0.521514i | 0.965404 | + | 0.260757i | \(0.0839722\pi\) | ||||
−0.965404 | + | 0.260757i | \(0.916028\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.69449 | − | 2.39577i | −0.747317 | − | 0.664468i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.100328i | 0.0259046i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.15994 | −0.523862 | −0.261931 | − | 0.965087i | \(-0.584359\pi\) | ||||
−0.261931 | + | 0.965087i | \(0.584359\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.600958i | 0.137869i | 0.997621 | + | 0.0689346i | \(0.0219600\pi\) | ||||
−0.997621 | + | 0.0689346i | \(0.978040\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.00000i | 0.218218i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.58736 | −0.956531 | −0.478266 | − | 0.878215i | \(-0.658734\pi\) | ||||
−0.478266 | + | 0.878215i | \(0.658734\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98993 | 0.997987 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.17825 | 0.961578 | 0.480789 | − | 0.876836i | \(-0.340350\pi\) | ||||
0.480789 | + | 0.876836i | \(0.340350\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.01832i | 0.901316i | 0.892697 | + | 0.450658i | \(0.148811\pi\) | ||||
−0.892697 | + | 0.450658i | \(0.851189\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 1.72967i | − | 0.301096i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.100328 | −0.0169585 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.36059i | − | 0.388079i | −0.980994 | − | 0.194040i | \(-0.937841\pi\) | ||
0.980994 | − | 0.194040i | \(-0.0621591\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.69449 | + | 2.39577i | 0.431463 | + | 0.383631i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 5.02116i | − | 0.784174i | −0.919928 | − | 0.392087i | \(-0.871753\pi\) | ||
0.919928 | − | 0.392087i | \(-0.128247\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.12149 | −1.39101 | −0.695507 | − | 0.718519i | \(-0.744820\pi\) | ||||
−0.695507 | + | 0.718519i | \(0.744820\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 0.100328i | − | 0.0149560i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.59248i | 1.39921i | 0.714531 | + | 0.699603i | \(0.246640\pi\) | ||||
−0.714531 | + | 0.699603i | \(0.753360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.15994 | 0.302452 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.75964 | 0.516426 | 0.258213 | − | 0.966088i | \(-0.416866\pi\) | ||||
0.258213 | + | 0.966088i | \(0.416866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.173534 | 0.0233993 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.600958i | − | 0.0795988i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.29218i | 0.949361i | 0.880158 | + | 0.474680i | \(0.157436\pi\) | ||||
−0.880158 | + | 0.474680i | \(0.842564\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.43095 | 0.567325 | 0.283663 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283663 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.240363 | + | 0.270332i | −0.0298134 | + | 0.0335306i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 11.2985i | − | 1.38033i | −0.723652 | − | 0.690165i | \(-0.757538\pi\) | ||
0.723652 | − | 0.690165i | \(-0.242462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.58736 | 0.552254 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.0902623i | 0.0107122i | 0.999986 | + | 0.00535608i | \(0.00170490\pi\) | ||||
−0.999986 | + | 0.00535608i | \(0.998295\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.78928i | 0.911666i | 0.890065 | + | 0.455833i | \(0.150659\pi\) | ||||
−0.890065 | + | 0.455833i | \(0.849341\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.98993 | −0.576188 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.72967 | 0.197114 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.6704 | 1.65055 | 0.825275 | − | 0.564731i | \(-0.191020\pi\) | ||||
0.825275 | + | 0.564731i | \(0.191020\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.53002i | 0.387470i | 0.981054 | + | 0.193735i | \(0.0620602\pi\) | ||||
−0.981054 | + | 0.193735i | \(0.937940\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.216702i | 0.0235047i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.17825 | −0.555167 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.6369i | 1.33951i | 0.742582 | + | 0.669755i | \(0.233601\pi\) | ||||
−0.742582 | + | 0.669755i | \(0.766399\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.39577 | + | 2.69449i | −0.251145 | + | 0.282459i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 5.01832i | − | 0.520375i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.0602929 | 0.00618592 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.975148i | 0.0990113i | 0.998774 | + | 0.0495056i | \(0.0157646\pi\) | ||||
−0.998774 | + | 0.0495056i | \(0.984235\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72967i | 0.173838i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.7212 | 1.26581 | 0.632903 | − | 0.774231i | \(-0.281863\pi\) | ||||
0.632903 | + | 0.774231i | \(0.281863\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.28706 | 0.422417 | 0.211208 | − | 0.977441i | \(-0.432260\pi\) | ||||
0.211208 | + | 0.977441i | \(0.432260\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.100328 | 0.00979101 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.65209 | −0.739756 | −0.369878 | − | 0.929080i | \(-0.620600\pi\) | ||||
−0.369878 | + | 0.929080i | \(0.620600\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 5.61927i | − | 0.538229i | −0.963108 | − | 0.269114i | \(-0.913269\pi\) | ||
0.963108 | − | 0.269114i | \(-0.0867310\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.36059i | 0.224058i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.95701 | −0.278172 | −0.139086 | − | 0.990280i | \(-0.544417\pi\) | ||||
−0.139086 | + | 0.990280i | \(0.544417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.460241i | 0.0429177i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.69449 | − | 2.39577i | −0.249106 | − | 0.221489i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.15994i | 0.198001i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.00825 | 0.728023 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.02116i | 0.452743i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00227i | − | 0.0896457i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.86970 | −0.343381 | −0.171690 | − | 0.985151i | \(-0.554923\pi\) | ||||
−0.171690 | + | 0.985151i | \(0.554923\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 9.12149 | 0.803103 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.9947 | −0.960607 | −0.480304 | − | 0.877102i | \(-0.659474\pi\) | ||||
−0.480304 | + | 0.877102i | \(0.659474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.600958 | 0.0521097 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.100328i | 0.00863486i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.3082i | − | 1.30787i | −0.756551 | − | 0.653935i | \(-0.773117\pi\) | ||
0.756551 | − | 0.653935i | \(-0.226883\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.45154 | 0.716850 | 0.358425 | − | 0.933558i | \(-0.383314\pi\) | ||||
0.358425 | + | 0.933558i | \(0.383314\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 9.59248i | − | 0.807833i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.14389 | − | 4.66057i | 0.346530 | − | 0.389736i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 0.519524i | − | 0.0431441i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.00000 | 0.0824786 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 0.514225i | − | 0.0421270i | −0.999778 | − | 0.0210635i | \(-0.993295\pi\) | ||
0.999778 | − | 0.0210635i | \(-0.00670521\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.01479i | 0.570855i | 0.958400 | + | 0.285428i | \(0.0921356\pi\) | ||||
−0.958400 | + | 0.285428i | \(0.907864\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.15994 | −0.174621 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.503477 | 0.0404403 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −13.3619 | −1.06639 | −0.533196 | − | 0.845992i | \(-0.679009\pi\) | ||||
−0.533196 | + | 0.845992i | \(0.679009\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.75964 | −0.298159 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.58736i | 0.361535i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.85611i | 0.145382i | 0.997355 | + | 0.0726908i | \(0.0231586\pi\) | ||||
−0.997355 | + | 0.0726908i | \(0.976841\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.173534 | −0.0135096 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 20.9884i | 1.62413i | 0.583564 | + | 0.812067i | \(0.301658\pi\) | ||||
−0.583564 | + | 0.812067i | \(0.698342\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.52053 | + | 12.9108i | 0.116964 | + | 0.993136i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.600958i | 0.0459564i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 15.1250 | 1.14993 | 0.574967 | − | 0.818177i | \(-0.305015\pi\) | ||||
0.574967 | + | 0.818177i | \(0.305015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 4.98993i | − | 0.377204i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 7.29218i | − | 0.548114i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.33040 | 0.622643 | 0.311322 | − | 0.950305i | \(-0.399228\pi\) | ||||
0.311322 | + | 0.950305i | \(0.399228\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.1024 | −1.12255 | −0.561275 | − | 0.827629i | \(-0.689689\pi\) | ||||
−0.561275 | + | 0.827629i | \(0.689689\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.43095 | −0.327545 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.236834 | −0.0174124 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.73598i | − | 0.273202i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.00000i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.9301 | 1.15266 | 0.576331 | − | 0.817217i | \(-0.304484\pi\) | ||||
0.576331 | + | 0.817217i | \(0.304484\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6341i | 0.909420i | 0.890640 | + | 0.454710i | \(0.150257\pi\) | ||||
−0.890640 | + | 0.454710i | \(0.849743\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.240363 | − | 0.270332i | 0.0172128 | − | 0.0193589i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.6935i | 0.833127i | 0.909107 | + | 0.416563i | \(0.136766\pi\) | ||||
−0.909107 | + | 0.416563i | \(0.863234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2824 | 0.799791 | 0.399895 | − | 0.916561i | \(-0.369046\pi\) | ||||
0.399895 | + | 0.916561i | \(0.369046\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 11.2985i | 0.796934i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.17825i | − | 0.363442i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.503763 | −0.0351843 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.58736 | −0.318844 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.03946 | −0.0719008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.3086 | 1.05388 | 0.526942 | − | 0.849901i | \(-0.323338\pi\) | ||||
0.526942 | + | 0.849901i | \(0.323338\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 0.0902623i | − | 0.00618467i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.915141i | 0.0624121i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.01832 | 0.340665 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 7.78928i | − | 0.526351i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.81993 | + | 5.17473i | 0.391491 | + | 0.348090i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.3168i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.98993 | 0.332662 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.32301i | 0.419673i | 0.977736 | + | 0.209836i | \(0.0672932\pi\) | ||||
−0.977736 | + | 0.209836i | \(0.932707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9153i | 0.721304i | 0.932700 | + | 0.360652i | \(0.117446\pi\) | ||||
−0.932700 | + | 0.360652i | \(0.882554\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.72967 | −0.113804 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 28.2001 | 1.84745 | 0.923725 | − | 0.383056i | \(-0.125128\pi\) | ||||
0.923725 | + | 0.383056i | \(0.125128\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.962394 | 0.0627797 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.6704 | −0.952945 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 18.8481i | 1.21918i | 0.792716 | + | 0.609591i | \(0.208666\pi\) | ||||
−0.792716 | + | 0.609591i | \(0.791334\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.60921i | 0.618984i | 0.950902 | + | 0.309492i | \(0.100159\pi\) | ||||
−0.950902 | + | 0.309492i | \(0.899841\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.100328i | 0.00640972i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.43976 | − | 1.61927i | 0.0916097 | − | 0.103032i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.53002i | − | 0.223706i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.40292 | 0.530388 | 0.265194 | − | 0.964195i | \(-0.414564\pi\) | ||||
0.265194 | + | 0.964195i | \(0.414564\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 7.93461i | − | 0.498845i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 0.216702i | − | 0.0135704i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 19.6399 | 1.22510 | 0.612550 | − | 0.790432i | \(-0.290144\pi\) | ||||
0.612550 | + | 0.790432i | \(0.290144\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.36059 | −0.146680 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.17825 | 0.320526 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 25.0516 | 1.54475 | 0.772374 | − | 0.635169i | \(-0.219069\pi\) | ||||
0.772374 | + | 0.635169i | \(0.219069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.377197i | − | 0.0231710i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.6369i | − | 0.773366i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 16.8418 | 1.02686 | 0.513431 | − | 0.858131i | \(-0.328374\pi\) | ||||
0.513431 | + | 0.858131i | \(0.328374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 28.8203i | − | 1.75071i | −0.483483 | − | 0.875354i | \(-0.660629\pi\) | ||
0.483483 | − | 0.875354i | \(-0.339371\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.39577 | − | 2.69449i | 0.144999 | − | 0.163078i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.63093i | 0.520464i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.22023 | −0.253569 | −0.126785 | − | 0.991930i | \(-0.540466\pi\) | ||||
−0.126785 | + | 0.991930i | \(0.540466\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.01832i | 0.300439i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 20.1470i | 1.20187i | 0.799298 | + | 0.600935i | \(0.205205\pi\) | ||||
−0.799298 | + | 0.600935i | \(0.794795\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −14.4581 | −0.859443 | −0.429722 | − | 0.902961i | \(-0.641388\pi\) | ||||
−0.429722 | + | 0.902961i | \(0.641388\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.0602929 | −0.00357144 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.02116 | −0.296390 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3347 | −0.725568 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 0.975148i | − | 0.0571642i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.54225i | 0.206941i | 0.994633 | + | 0.103470i | \(0.0329947\pi\) | ||||
−0.994633 | + | 0.103470i | \(0.967005\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.731609 | 0.0425959 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1.72967i | − | 0.100365i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3606 | + | 10.9903i | 0.714832 | + | 0.635585i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.12149i | 0.525754i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.7212 | −0.730813 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 0.444548i | − | 0.0254548i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.2814i | 0.872157i | 0.899909 | + | 0.436079i | \(0.143633\pi\) | ||||
−0.899909 | + | 0.436079i | \(0.856367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.28706 | −0.243882 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.84178 | 0.501371 | 0.250686 | − | 0.968069i | \(-0.419344\pi\) | ||||
0.250686 | + | 0.968069i | \(0.419344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10.5838 | −0.598234 | −0.299117 | − | 0.954217i | \(-0.596692\pi\) | ||||
−0.299117 | + | 0.954217i | \(0.596692\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −0.100328 | −0.00565284 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.8435i | 1.28302i | 0.767114 | + | 0.641511i | \(0.221692\pi\) | ||||
−0.767114 | + | 0.641511i | \(0.778308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.95666i | 0.501477i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.65209 | 0.427098 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.29803i | − | 0.0722244i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.4453 | − | 11.9548i | −0.745812 | − | 0.663130i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.61927i | 0.310747i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 9.59248 | 0.528851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 24.3610i | − | 1.33900i | −0.742810 | − | 0.669502i | \(-0.766507\pi\) | ||
0.742810 | − | 0.669502i | \(-0.233493\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.36059i | − | 0.129360i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.13355 | −0.0619327 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.5047 | −0.844593 | −0.422297 | − | 0.906458i | \(-0.638776\pi\) | ||||
−0.422297 | + | 0.906458i | \(0.638776\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.95701 | 0.160603 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −8.68002 | −0.470049 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 0.460241i | − | 0.0247785i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.30754 | −0.499655 | −0.249828 | − | 0.968290i | \(-0.580374\pi\) | ||||
−0.249828 | + | 0.968290i | \(0.580374\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.43892i | 0.184081i | 0.995755 | + | 0.0920405i | \(0.0293389\pi\) | ||||
−0.995755 | + | 0.0920405i | \(0.970661\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.69449 | + | 2.39577i | 0.143821 | + | 0.127877i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.3563i | 1.18990i | 0.803761 | + | 0.594952i | \(0.202829\pi\) | ||||
−0.803761 | + | 0.594952i | \(0.797171\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.00905583 | 0.000480633 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.15994i | − | 0.114316i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9464i | 1.15829i | 0.815226 | + | 0.579143i | \(0.196613\pi\) | ||||
−0.815226 | + | 0.579143i | \(0.803387\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.6388 | 0.980992 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.00825 | −0.420324 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.781482 | 0.0409047 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.2817 | 1.00650 | 0.503249 | − | 0.864142i | \(-0.332138\pi\) | ||||
0.503249 | + | 0.864142i | \(0.332138\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 5.02116i | − | 0.261391i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 3.75964i | − | 0.195191i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.9095 | 0.720207 | 0.360104 | − | 0.932912i | \(-0.382741\pi\) | ||||
0.360104 | + | 0.932912i | \(0.382741\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00227i | 0.0517570i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.9527 | − | 12.4059i | −0.718603 | − | 0.638938i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.95974i | − | 0.408864i | −0.978881 | − | 0.204432i | \(-0.934465\pi\) | ||
0.978881 | − | 0.204432i | \(-0.0655348\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.86970 | 0.198251 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 5.90565i | − | 0.301765i | −0.988552 | − | 0.150882i | \(-0.951789\pi\) | ||
0.988552 | − | 0.150882i | \(-0.0482115\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.173534i | − | 0.00884411i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.12149 | −0.463671 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.14072 | −0.311347 | −0.155673 | − | 0.987809i | \(-0.549755\pi\) | ||||
−0.155673 | + | 0.987809i | \(0.549755\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.90842 | 0.501090 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 10.9947 | 0.554607 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.47185i | − | 0.0740569i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.7330i | 1.19112i | 0.803309 | + | 0.595562i | \(0.203071\pi\) | ||||
−0.803309 | + | 0.595562i | \(0.796929\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.600958 | −0.0300855 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 17.3288i | − | 0.865359i | −0.901548 | − | 0.432680i | \(-0.857568\pi\) | ||
0.901548 | − | 0.432680i | \(-0.142432\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.0228 | − | 13.5218i | 0.598896 | − | 0.673569i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 0.100328i | − | 0.00498534i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.08304 | 0.202389 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 12.9697i | − | 0.641310i | −0.947196 | − | 0.320655i | \(-0.896097\pi\) | ||
0.947196 | − | 0.320655i | \(-0.103903\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 15.3082i | 0.755099i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.29218 | 0.358825 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.354160 | 0.0173850 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.45154 | −0.413874 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 15.0831 | 0.736860 | 0.368430 | − | 0.929655i | \(-0.379895\pi\) | ||||
0.368430 | + | 0.929655i | \(0.379895\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.38118i | 0.408474i | 0.978921 | + | 0.204237i | \(0.0654713\pi\) | ||||
−0.978921 | + | 0.204237i | \(0.934529\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.59248i | 0.466402i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −10.7780 | −0.522808 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 4.43095i | − | 0.214429i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.14389 | + | 4.66057i | −0.200069 | + | 0.225014i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.6630i | 0.995303i | 0.867377 | + | 0.497651i | \(0.165804\pi\) | ||||
−0.867377 | + | 0.497651i | \(0.834196\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.3286 | −1.21721 | −0.608607 | − | 0.793472i | \(-0.708271\pi\) | ||||
−0.608607 | + | 0.793472i | \(0.708271\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.519524i | 0.0249093i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.75681i | − | 0.131876i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.8537 | −0.565744 | −0.282872 | − | 0.959158i | \(-0.591287\pi\) | ||||
−0.282872 | + | 0.959158i | \(0.591287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | −0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9.60467 | 0.456332 | 0.228166 | − | 0.973622i | \(-0.426727\pi\) | ||||
0.228166 | + | 0.973622i | \(0.426727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.26784 | 0.0601011 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.514225i | 0.0243220i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 20.0907i | 0.948140i | 0.880487 | + | 0.474070i | \(0.157216\pi\) | ||||
−0.880487 | + | 0.474070i | \(0.842784\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.68494 | 0.408958 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 7.01479i | − | 0.329583i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.270332 | + | 0.240363i | 0.0126734 | + | 0.0112684i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.2985i | 1.08986i | 0.838482 | + | 0.544929i | \(0.183443\pi\) | ||||
−0.838482 | + | 0.544929i | \(0.816557\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.15994 | 0.100817 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 12.6580i | − | 0.589544i | −0.955568 | − | 0.294772i | \(-0.904756\pi\) | ||
0.955568 | − | 0.294772i | \(-0.0952437\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 0.838801i | − | 0.0389824i | −0.999810 | − | 0.0194912i | \(-0.993795\pi\) | ||
0.999810 | − | 0.0194912i | \(-0.00620464\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.503477 | −0.0233482 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 5.81287 | 0.268988 | 0.134494 | − | 0.990914i | \(-0.457059\pi\) | ||||
0.134494 | + | 0.990914i | \(0.457059\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.2985 | −0.521716 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.3619 | 0.615682 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 15.7771i | − | 0.725434i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.99874i | 0.137592i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.75964 | 0.172142 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 7.73229i | − | 0.353297i | −0.984274 | − | 0.176649i | \(-0.943474\pi\) | ||
0.984274 | − | 0.176649i | \(-0.0565256\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65545 | + | 6.36059i | −0.257866 | + | 0.290018i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 4.58736i | − | 0.208732i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0978346 | 0.00444244 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 41.4021i | − | 1.87611i | −0.346488 | − | 0.938054i | \(-0.612626\pi\) | ||
0.346488 | − | 0.938054i | \(-0.387374\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.85611i | − | 0.0839361i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.6958 | −1.34015 | −0.670076 | − | 0.742293i | \(-0.733738\pi\) | ||||
−0.670076 | + | 0.742293i | \(0.733738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.1847 | −0.503734 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.173534 | 0.00779977 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.0902623 | 0.00404882 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 32.4816i | − | 1.45408i | −0.686596 | − | 0.727039i | \(-0.740896\pi\) | ||
0.686596 | − | 0.727039i | \(-0.259104\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 20.9884i | − | 0.937695i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.0437 | 0.626177 | 0.313089 | − | 0.949724i | \(-0.398636\pi\) | ||||
0.313089 | + | 0.949724i | \(0.398636\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.27629i | − | 0.0567942i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.52053 | − | 12.9108i | −0.0675293 | − | 0.573387i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 18.4985i | 0.819930i | 0.912101 | + | 0.409965i | \(0.134459\pi\) | ||||
−0.912101 | + | 0.409965i | \(0.865541\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.78928 | 0.344577 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 0.600958i | − | 0.0265329i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 0.430112i | − | 0.0189530i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −16.5918 | −0.729707 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.1250 | −0.663915 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.96065 | −0.261141 | −0.130570 | − | 0.991439i | \(-0.541681\pi\) | ||||
−0.130570 | + | 0.991439i | \(0.541681\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.7879 | −1.34626 | −0.673131 | − | 0.739523i | \(-0.735051\pi\) | ||||
−0.673131 | + | 0.739523i | \(0.735051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.98993i | 0.217779i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10.8393i | − | 0.472165i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.95610 | −0.0850480 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.29218i | 0.316454i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0296 | + | 13.5295i | −0.521059 | + | 0.586026i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.767719i | 0.0331914i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.33040 | −0.359483 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 1.72967i | − | 0.0745021i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.3216i | 1.34662i | 0.739360 | + | 0.673310i | \(0.235128\pi\) | ||||
−0.739360 | + | 0.673310i | \(0.764872\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.1024 | 0.648105 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.563770 | −0.0241493 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.69833 | 0.414671 | 0.207335 | − | 0.978270i | \(-0.433521\pi\) | ||||
0.207335 | + | 0.978270i | \(0.433521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.43095 | 0.189108 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.11191i | 0.132572i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 14.6704i | − | 0.623849i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.236834 | 0.0100530 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 16.5268i | − | 0.700265i | −0.936700 | − | 0.350132i | \(-0.886137\pi\) | ||
0.936700 | − | 0.350132i | \(-0.113863\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 24.5778 | + | 21.8530i | 1.03953 | + | 0.924285i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.73598i | 0.157733i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −40.2421 | −1.69600 | −0.848001 | − | 0.529995i | \(-0.822194\pi\) | ||||
−0.848001 | + | 0.529995i | \(0.822194\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.296671i | 0.0124810i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.00000i | − | 0.0419961i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.77987 | 0.116538 | 0.0582692 | − | 0.998301i | \(-0.481442\pi\) | ||||
0.0582692 | + | 0.998301i | \(0.481442\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0993 | 1.38516 | 0.692581 | − | 0.721340i | \(-0.256474\pi\) | ||||
0.692581 | + | 0.721340i | \(0.256474\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.9301 | −0.665489 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.8906 | −0.954606 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 12.0432i | − | 0.501364i | −0.968070 | − | 0.250682i | \(-0.919345\pi\) | ||
0.968070 | − | 0.250682i | \(-0.0806548\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 12.6341i | − | 0.525054i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.53002 | 0.146450 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.50292i | 0.269324i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.240363 | + | 0.270332i | −0.00993779 | + | 0.0111769i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16.7989i | − | 0.693366i | −0.937982 | − | 0.346683i | \(-0.887308\pi\) | ||
0.937982 | − | 0.346683i | \(-0.112692\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.01580 | −0.124264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 11.6935i | − | 0.481006i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 24.2969i | 0.997754i | 0.866673 | + | 0.498877i | \(0.166254\pi\) | ||||
−0.866673 | + | 0.498877i | \(0.833746\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.216702 | 0.00888393 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.2824 | −0.461760 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 42.7379 | 1.74622 | 0.873111 | − | 0.487522i | \(-0.162099\pi\) | ||||
0.873111 | + | 0.487522i | \(0.162099\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.7948 | −0.970611 | −0.485306 | − | 0.874345i | \(-0.661292\pi\) | ||||
−0.485306 | + | 0.874345i | \(0.661292\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 11.2985i | − | 0.460110i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 0.803451i | − | 0.0326649i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.2740 | −0.985251 | −0.492625 | − | 0.870241i | \(-0.663963\pi\) | ||||
−0.492625 | + | 0.870241i | \(0.663963\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5.17825i | 0.209833i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.9814 | − | 25.8468i | 0.929728 | − | 1.04565i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 22.0876i | − | 0.892109i | −0.895006 | − | 0.446055i | \(-0.852829\pi\) | ||
0.895006 | − | 0.446055i | \(-0.147171\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.503763 | 0.0203137 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.89122i | 0.398205i | 0.979979 | + | 0.199103i | \(0.0638027\pi\) | ||||
−0.979979 | + | 0.199103i | \(0.936197\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 34.8194i | − | 1.39951i | −0.714384 | − | 0.699754i | \(-0.753293\pi\) | ||
0.714384 | − | 0.699754i | \(-0.246707\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 4.58736 | 0.184085 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 12.6369 | 0.506287 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.8491 | 0.993965 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.03946 | 0.0415119 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.09874i | 0.203300i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 12.5965i | − | 0.501459i | −0.968057 | − | 0.250730i | \(-0.919329\pi\) | ||
0.968057 | − | 0.250730i | \(-0.0806705\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3086 | −0.608460 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.388239i | 0.0154068i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.69449 | + | 2.39577i | 0.106760 | + | 0.0949240i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.0902623i | 0.00357072i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.2769 | 0.919382 | 0.459691 | − | 0.888079i | \(-0.347960\pi\) | ||||
0.459691 | + | 0.888079i | \(0.347960\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 19.6817i | 0.776172i | 0.921623 | + | 0.388086i | \(0.126864\pi\) | ||||
−0.921623 | + | 0.388086i | \(0.873136\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 0.915141i | − | 0.0360336i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.7578 | 0.737446 | 0.368723 | − | 0.929539i | \(-0.379795\pi\) | ||||
0.368723 | + | 0.929539i | \(0.379795\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.6130 | −0.495105 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.01832 | −0.196683 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.61599 | −0.258904 | −0.129452 | − | 0.991586i | \(-0.541322\pi\) | ||||
−0.129452 | + | 0.991586i | \(0.541322\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.10307i | 0.0431006i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.78928i | 0.303889i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.3670 | −1.18293 | −0.591466 | − | 0.806330i | \(-0.701451\pi\) | ||||
−0.591466 | + | 0.806330i | \(0.701451\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 43.6458i | − | 1.69763i | −0.528693 | − | 0.848813i | \(-0.677318\pi\) | ||
0.528693 | − | 0.848813i | \(-0.322682\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.81993 | − | 5.17473i | −0.226027 | − | 0.200970i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 0.0602929i | − | 0.00233806i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −23.7545 | −0.919779 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 20.3168i | − | 0.785493i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.66408i | 0.295868i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 33.9517 | 1.30874 | 0.654370 | − | 0.756174i | \(-0.272934\pi\) | ||||
0.654370 | + | 0.756174i | \(0.272934\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.98993 | −0.192063 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −33.8557 | −1.30118 | −0.650589 | − | 0.759430i | \(-0.725478\pi\) | ||||
−0.650589 | + | 0.759430i | \(0.725478\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.975148 | 0.0374227 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6.32301i | − | 0.242298i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.24440i | 0.277199i | 0.990348 | + | 0.138600i | \(0.0442601\pi\) | ||||
−0.990348 | + | 0.138600i | \(0.955740\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.53584 | −0.0586815 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 10.9153i | − | 0.416445i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −10.1303 | − | 9.00724i | −0.385934 | − | 0.343149i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 6.57468i | − | 0.250113i | −0.992150 | − | 0.125056i | \(-0.960089\pi\) | ||
0.992150 | − | 0.125056i | \(-0.0399111\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.72967 | 0.0657046 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 0.847926i | − | 0.0321637i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.8454i | 0.410799i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −28.2001 | −1.06663 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5.00672 | −0.189101 | −0.0945506 | − | 0.995520i | \(-0.530141\pi\) | ||||
−0.0945506 | + | 0.995520i | \(0.530141\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.41862 | 0.0535042 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.962394 | −0.0362459 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 12.7212i | − | 0.478430i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 9.72245i | − | 0.365134i | −0.983193 | − | 0.182567i | \(-0.941559\pi\) | ||
0.983193 | − | 0.182567i | \(-0.0584407\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 14.6704 | 0.550183 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 23.0208i | − | 0.862137i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.467585 | − | 0.415748i | −0.0174867 | − | 0.0155481i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 18.8481i | − | 0.703895i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.3786 | −0.424349 | −0.212174 | − | 0.977232i | \(-0.568054\pi\) | ||||
−0.212174 | + | 0.977232i | \(0.568054\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 4.28706i | − | 0.159658i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 9.60921i | − | 0.357370i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.8392 | 0.959642 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.9815 | 1.48283 | 0.741415 | − | 0.671046i | \(-0.234155\pi\) | ||||
0.741415 | + | 0.671046i | \(0.234155\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 19.7019 | 0.728700 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 16.4073i | 0.606017i | 0.952988 | + | 0.303009i | \(0.0979911\pi\) | ||||
−0.952988 | + | 0.303009i | \(0.902009\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 0.100328i | − | 0.00370065i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.5426 | 0.719862 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 40.5818i | − | 1.49283i | −0.665482 | − | 0.746413i | \(-0.731774\pi\) | ||
0.665482 | − | 0.746413i | \(-0.268226\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.43976 | + | 1.61927i | −0.0528909 | + | 0.0594855i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.9435i | 1.02515i | 0.858643 | + | 0.512574i | \(0.171308\pi\) | ||||
−0.858643 | + | 0.512574i | \(0.828692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.0515911 | −0.00189015 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.53002i | 0.129157i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.65209i | 0.279601i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.0228 | −0.876603 | −0.438301 | − | 0.898828i | \(-0.644420\pi\) | ||||
−0.438301 | + | 0.898828i | \(0.644420\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −8.40292 | −0.306219 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.703779 | 0.0256131 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.8309 | −1.30230 | −0.651148 | − | 0.758951i | \(-0.725712\pi\) | ||||
−0.651148 | + | 0.758951i | \(0.725712\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.93461i | 0.288008i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.91320i | − | 0.0693534i | −0.999399 | − | 0.0346767i | \(-0.988960\pi\) | ||
0.999399 | − | 0.0346767i | \(-0.0110402\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.61927 | −0.203431 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.216702i | 0.00783489i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.4704 | − | 19.6487i | 0.630820 | − | 0.709473i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 17.8802i | − | 0.644775i | −0.946608 | − | 0.322387i | \(-0.895515\pi\) | ||
0.946608 | − | 0.322387i | \(-0.104485\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.6399 | −0.707312 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.5791i | 0.380505i | 0.981735 | + | 0.190253i | \(0.0609307\pi\) | ||||
−0.981735 | + | 0.190253i | \(0.939069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 25.0411i | 0.899502i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.36059 | 0.0846859 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.01751 | 0.108113 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.156124 | −0.00558654 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.17825 | −0.185056 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.34057i | 0.0478469i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 20.0459i | − | 0.714558i | −0.933998 | − | 0.357279i | \(-0.883705\pi\) | ||
0.933998 | − | 0.357279i | \(-0.116295\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −25.0516 | −0.891860 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.95701i | 0.105139i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −11.9392 | − | 10.6156i | −0.423972 | − | 0.376970i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.377197i | 0.0133778i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 35.2505 | 1.24864 | 0.624319 | − | 0.781170i | \(-0.285377\pi\) | ||||
0.624319 | + | 0.781170i | \(0.285377\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 20.7192i | − | 0.732992i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 12.6369i | 0.446503i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.4729 | −0.475447 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.460241 | 0.0162214 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.8418 | −0.592859 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −31.2729 | −1.09950 | −0.549748 | − | 0.835330i | \(-0.685276\pi\) | ||||
−0.549748 | + | 0.835330i | \(0.685276\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6818i | 0.515549i | 0.966205 | + | 0.257775i | \(0.0829892\pi\) | ||||
−0.966205 | + | 0.257775i | \(0.917011\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.8203i | 1.01077i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.186219 | 0.00652298 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 5.48163i | − | 0.191778i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.39577 | + | 2.69449i | −0.0837151 | + | 0.0941530i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.5314i | 0.646750i | 0.946271 | + | 0.323375i | \(0.104817\pi\) | ||||
−0.946271 | + | 0.323375i | \(0.895183\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.08133 | 0.0376928 | 0.0188464 | − | 0.999822i | \(-0.494001\pi\) | ||||
0.0188464 | + | 0.999822i | \(0.494001\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 8.63093i | − | 0.300490i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.5392i | 0.540353i | 0.962811 | + | 0.270176i | \(0.0870820\pi\) | ||||
−0.962811 | + | 0.270176i | \(0.912918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1608 | 0.352898 | 0.176449 | − | 0.984310i | \(-0.443539\pi\) | ||||
0.176449 | + | 0.984310i | \(0.443539\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.22023 | 0.146398 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.15994 | 0.0748374 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.10573 | 0.0728717 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 5.01832i | − | 0.173458i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.2082i | 0.455999i | 0.973661 | + | 0.227999i | \(0.0732184\pi\) | ||||
−0.973661 | + | 0.227999i | \(0.926782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.18568 | −0.0753682 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 20.1470i | − | 0.693900i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.29531 | − | 0.152552i | 0.0445601 | − | 0.00524795i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 8.00825i | − | 0.275167i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.4581 | 0.496200 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.8289i | 0.371210i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 52.8473i | − | 1.80946i | −0.425989 | − | 0.904729i | \(-0.640074\pi\) | ||
0.425989 | − | 0.904729i | \(-0.359926\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0602929 | 0.00206197 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.5246 | −1.58925 | −0.794625 | − | 0.607100i | \(-0.792333\pi\) | ||||
−0.794625 | + | 0.607100i | \(0.792333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.4633 | −1.03939 | −0.519697 | − | 0.854350i | \(-0.673955\pi\) | ||||
−0.519697 | + | 0.854350i | \(0.673955\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.02116 | 0.171121 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 30.6461i | − | 1.04320i | −0.853189 | − | 0.521602i | \(-0.825335\pi\) | ||
0.853189 | − | 0.521602i | \(-0.174665\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.51746i | − | 0.0515953i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12.3347 | 0.418907 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.3749i | 0.860785i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −27.0686 | + | 30.4436i | −0.917185 | + | 1.03154i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.975148i | 0.0330038i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.00227 | −0.0338829 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 19.8663i | − | 0.670839i | −0.942069 | − | 0.335419i | \(-0.891122\pi\) | ||
0.942069 | − | 0.335419i | \(-0.108878\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 3.54225i | − | 0.119477i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.5688 | −0.659289 | −0.329644 | − | 0.944105i | \(-0.606929\pi\) | ||||
−0.329644 | + | 0.944105i | \(0.606929\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.0463 | −1.34767 | −0.673833 | − | 0.738883i | \(-0.735353\pi\) | ||||
−0.673833 | + | 0.738883i | \(0.735353\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.731609 | −0.0245928 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.8417 | 0.464758 | 0.232379 | − | 0.972625i | \(-0.425349\pi\) | ||||
0.232379 | + | 0.972625i | \(0.425349\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.86970i | 0.129786i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.72967i | 0.0579460i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.76468 | −0.192908 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 0.835772i | − | 0.0279368i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −12.3606 | − | 10.9903i | −0.412708 | − | 0.366955i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 25.9861i | 0.866686i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.12059 | −0.270536 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 9.12149i | − | 0.303544i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.51519i | 0.0503666i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −34.2782 | −1.13819 | −0.569094 | − | 0.822272i | \(-0.692706\pi\) | ||||
−0.569094 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.7212 | 0.421935 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.32005 | −0.275655 | −0.137828 | − | 0.990456i | \(-0.544012\pi\) | ||||
−0.137828 | + | 0.990456i | \(0.544012\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.10576 | −0.202071 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.444548i | 0.0146963i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.9947i | 0.363075i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.3211 | −1.13215 | −0.566074 | − | 0.824355i | \(-0.691538\pi\) | ||||
−0.566074 | + | 0.824355i | \(0.691538\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 15.2814i | − | 0.503540i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.216248 | − | 0.243211i | 0.00711789 | − | 0.00800537i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 11.7792i | − | 0.387298i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.28706 | 0.140806 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 41.9922i | − | 1.37772i | −0.724895 | − | 0.688859i | \(-0.758112\pi\) | ||
0.724895 | − | 0.688859i | \(-0.241888\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 0.600958i | − | 0.0196956i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.84178 | −0.289467 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.374823 | −0.0122580 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −50.0568 | −1.63529 | −0.817643 | − | 0.575726i | \(-0.804719\pi\) | ||||
−0.817643 | + | 0.575726i | \(0.804719\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10.5838 | 0.345390 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.63237i | 0.216209i | 0.994140 | + | 0.108105i | \(0.0344781\pi\) | ||||
−0.994140 | + | 0.108105i | \(0.965522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 23.0339i | 0.750087i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.100328 | 0.00326367 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 48.0550i | − | 1.56158i | −0.624795 | − | 0.780789i | \(-0.714818\pi\) | ||
0.624795 | − | 0.780789i | \(-0.285182\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.6614 | − | 20.9881i | 0.605773 | − | 0.681303i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 22.8435i | − | 0.740753i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.5129 | 0.794051 | 0.397026 | − | 0.917808i | \(-0.370042\pi\) | ||||
0.397026 | + | 0.917808i | \(0.370042\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 1.59823i | − | 0.0517176i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 8.95666i | − | 0.289528i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.3082 | −0.494328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.81650 | 0.187629 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.65209 | −0.246585 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.26755 | 0.0408039 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.0407i | 1.09468i | 0.836912 | + | 0.547338i | \(0.184359\pi\) | ||||
−0.836912 | + | 0.547338i | \(0.815641\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.29803i | 0.0416988i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −32.0733 | −1.02928 | −0.514640 | − | 0.857406i | \(-0.672074\pi\) | ||||
−0.514640 | + | 0.857406i | \(0.672074\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 8.45154i | − | 0.270944i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.4453 | + | 11.9548i | 0.430595 | + | 0.382859i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 15.4439i | − | 0.494094i | −0.969003 | − | 0.247047i | \(-0.920540\pi\) | ||
0.969003 | − | 0.247047i | \(-0.0794602\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −21.8576 | −0.698573 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 5.61927i | − | 0.179410i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.2099i | 1.37818i | 0.724674 | + | 0.689091i | \(0.241990\pi\) | ||||
−0.724674 | + | 0.689091i | \(0.758010\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.17318 | 0.0373807 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.59248 | −0.305332 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.8436 | 1.33055 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.153790 | 0.00488529 | 0.00244264 | − | 0.999997i | \(-0.499222\pi\) | ||||
0.00244264 | + | 0.999997i | \(0.499222\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 24.3610i | 0.773075i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 1.13194i | − | 0.0358850i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.2907 | 1.21268 | 0.606339 | − | 0.795206i | \(-0.292638\pi\) | ||||
0.606339 | + | 0.795206i | \(0.292638\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.36059i | 0.0746859i |
(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 | 4368.2.h.r.337.5 | 10 | ||
4.3 | odd | 2 | 2184.2.h.f.337.5 | ✓ | 10 | ||
13.12 | even | 2 | inner | 4368.2.h.r.337.6 | 10 | ||
52.51 | odd | 2 | 2184.2.h.f.337.6 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2184.2.h.f.337.5 | ✓ | 10 | 4.3 | odd | 2 | ||
2184.2.h.f.337.6 | yes | 10 | 52.51 | odd | 2 | ||
4368.2.h.r.337.5 | 10 | 1.1 | even | 1 | trivial | ||
4368.2.h.r.337.6 | 10 | 13.12 | even | 2 | inner |