Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (of order \(2\), degree \(1\), 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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 4 x^{13} + 77 x^{12} + 88 x^{11} - 577 x^{10} + 578 x^{9} + 1520 x^{8} + \cdots + 83521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{8}\cdot 11^{4} \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.10 | ||
Root | \(-1.43448 + 2.82504i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.m.604.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.982569i | 0.491284i | 0.969361 | + | 0.245642i | \(0.0789988\pi\) | ||||
−0.969361 | + | 0.245642i | \(0.921001\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.03456 | 0.758640 | ||||||||
\(5\) | −0.397576 | −0.0795151 | −0.0397576 | − | 0.999209i | \(-0.512659\pi\) | ||||
−0.0397576 | + | 0.999209i | \(0.512659\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 7.22681i | − 1.03240i | −0.856468 | − | 0.516201i | \(-0.827346\pi\) | ||||
0.856468 | − | 0.516201i | \(-0.172654\pi\) | |||||||
\(8\) | 6.91194i | 0.863992i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 0.390645i | − 0.0390645i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12.1597i | 0.935360i | 0.883898 | + | 0.467680i | \(0.154910\pi\) | ||||
−0.883898 | + | 0.467680i | \(0.845090\pi\) | |||||||
\(14\) | 7.10084 | 0.507203 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.34678 | 0.334174 | ||||||||
\(17\) | 20.9095i | 1.22997i | 0.788537 | + | 0.614987i | \(0.210839\pi\) | ||||
−0.788537 | + | 0.614987i | \(0.789161\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 11.1128i | − 0.584882i | −0.956284 | − | 0.292441i | \(-0.905532\pi\) | ||||
0.956284 | − | 0.292441i | \(-0.0944676\pi\) | |||||||
\(20\) | −1.20647 | −0.0603233 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.92990 | 0.257822 | 0.128911 | − | 0.991656i | \(-0.458852\pi\) | ||||
0.128911 | + | 0.991656i | \(0.458852\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −24.8419 | −0.993677 | ||||||||
\(26\) | −11.9477 | −0.459528 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − 21.9302i | − 0.783221i | ||||||||
\(29\) | 24.9546i | 0.860504i | 0.902709 | + | 0.430252i | \(0.141575\pi\) | ||||
−0.902709 | + | 0.430252i | \(0.858425\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 59.6258 | 1.92341 | 0.961707 | − | 0.274080i | \(-0.0883732\pi\) | ||||
0.961707 | + | 0.274080i | \(0.0883732\pi\) | |||||||
\(32\) | 32.9013i | 1.02817i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −20.5451 | −0.604267 | ||||||||
\(35\) | 2.87320i | 0.0820915i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.96703 | −0.161271 | −0.0806355 | − | 0.996744i | \(-0.525695\pi\) | ||||
−0.0806355 | + | 0.996744i | \(0.525695\pi\) | |||||||
\(38\) | 10.9191 | 0.287344 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 2.74802i | − 0.0687004i | ||||||||
\(41\) | 52.0396i | 1.26926i | 0.772817 | + | 0.634629i | \(0.218847\pi\) | ||||
−0.772817 | + | 0.634629i | \(0.781153\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 17.6439i | − 0.410323i | −0.978728 | − | 0.205161i | \(-0.934228\pi\) | ||||
0.978728 | − | 0.205161i | \(-0.0657719\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.82653i | 0.126664i | ||||||||
\(47\) | 55.3609 | 1.17789 | 0.588945 | − | 0.808173i | \(-0.299543\pi\) | ||||
0.588945 | + | 0.808173i | \(0.299543\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.22680 | −0.0658531 | ||||||||
\(50\) | − 24.4089i | − 0.488178i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 36.8993i | 0.709602i | ||||||||
\(53\) | 94.6520 | 1.78589 | 0.892943 | − | 0.450170i | \(-0.148636\pi\) | ||||
0.892943 | + | 0.450170i | \(0.148636\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 49.9513 | 0.891987 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −24.5196 | −0.422752 | ||||||||
\(59\) | 25.1052 | 0.425513 | 0.212756 | − | 0.977105i | \(-0.431756\pi\) | ||||
0.212756 | + | 0.977105i | \(0.431756\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 33.4062i | − 0.547642i | −0.961781 | − | 0.273821i | \(-0.911712\pi\) | ||||
0.961781 | − | 0.273821i | \(-0.0882876\pi\) | |||||||
\(62\) | 58.5865i | 0.944943i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −10.9407 | −0.170948 | ||||||||
\(65\) | − 4.83439i | − 0.0743753i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 94.6640 | 1.41290 | 0.706448 | − | 0.707765i | \(-0.250296\pi\) | ||||
0.706448 | + | 0.707765i | \(0.250296\pi\) | |||||||
\(68\) | 63.4513i | 0.933107i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.82312 | −0.0403303 | ||||||||
\(71\) | −82.7241 | −1.16513 | −0.582564 | − | 0.812785i | \(-0.697951\pi\) | ||||
−0.582564 | + | 0.812785i | \(0.697951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.5788i | 0.638065i | 0.947744 | + | 0.319033i | \(0.103358\pi\) | ||||
−0.947744 | + | 0.319033i | \(0.896642\pi\) | |||||||
\(74\) | − 5.86302i | − 0.0792299i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 33.7223i | − 0.443715i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 60.3191i | 0.763534i | 0.924259 | + | 0.381767i | \(0.124684\pi\) | ||||
−0.924259 | + | 0.381767i | \(0.875316\pi\) | |||||||
\(80\) | −2.12575 | −0.0265719 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −51.1325 | −0.623567 | ||||||||
\(83\) | − 150.673i | − 1.81534i | −0.419686 | − | 0.907670i | \(-0.637860\pi\) | ||||
0.419686 | − | 0.907670i | \(-0.362140\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 8.31313i | − 0.0978015i | ||||||||
\(86\) | 17.3363 | 0.201585 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −134.190 | −1.50775 | −0.753874 | − | 0.657019i | \(-0.771817\pi\) | ||||
−0.753874 | + | 0.657019i | \(0.771817\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 87.8758 | 0.965668 | ||||||||
\(92\) | 17.9946 | 0.195594 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 54.3959i | 0.578679i | ||||||||
\(95\) | 4.41816i | 0.0465070i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 37.6065 | 0.387696 | 0.193848 | − | 0.981032i | \(-0.437903\pi\) | ||||
0.193848 | + | 0.981032i | \(0.437903\pi\) | |||||||
\(98\) | − 3.17056i | − 0.0323526i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −75.3843 | −0.753843 | ||||||||
\(101\) | 80.8017i | 0.800017i | 0.916512 | + | 0.400008i | \(0.130993\pi\) | ||||
−0.916512 | + | 0.400008i | \(0.869007\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 99.6632 | 0.967603 | 0.483802 | − | 0.875178i | \(-0.339256\pi\) | ||||
0.483802 | + | 0.875178i | \(0.339256\pi\) | |||||||
\(104\) | −84.0470 | −0.808144 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 93.0021i | 0.877378i | ||||||||
\(107\) | − 108.254i | − 1.01172i | −0.862617 | − | 0.505858i | \(-0.831176\pi\) | ||||
0.862617 | − | 0.505858i | \(-0.168824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 175.446i | 1.60960i | 0.593546 | + | 0.804800i | \(0.297727\pi\) | ||||
−0.593546 | + | 0.804800i | \(0.702273\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − 38.6402i | − 0.345002i | ||||||||
\(113\) | −98.5234 | −0.871888 | −0.435944 | − | 0.899974i | \(-0.643586\pi\) | ||||
−0.435944 | + | 0.899974i | \(0.643586\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.35758 | −0.0205007 | ||||||||
\(116\) | 75.7262i | 0.652812i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 24.6676i | 0.209048i | ||||||||
\(119\) | 151.109 | 1.26983 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 32.8238 | 0.269048 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 180.938 | 1.45918 | ||||||||
\(125\) | 19.8159 | 0.158527 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8661i | 0.172174i | 0.996288 | + | 0.0860872i | \(0.0274364\pi\) | ||||
−0.996288 | + | 0.0860872i | \(0.972564\pi\) | |||||||
\(128\) | 120.855i | 0.944182i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.75013 | 0.0365394 | ||||||||
\(131\) | 16.3593i | 0.124880i | 0.998049 | + | 0.0624402i | \(0.0198883\pi\) | ||||
−0.998049 | + | 0.0624402i | \(0.980112\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −80.3099 | −0.603834 | ||||||||
\(134\) | 93.0139i | 0.694134i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −144.525 | −1.06269 | ||||||||
\(137\) | −30.5892 | −0.223279 | −0.111640 | − | 0.993749i | \(-0.535610\pi\) | ||||
−0.111640 | + | 0.993749i | \(0.535610\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 27.7464i | 0.199614i | 0.995007 | + | 0.0998072i | \(0.0318226\pi\) | ||||
−0.995007 | + | 0.0998072i | \(0.968177\pi\) | |||||||
\(140\) | 8.71891i | 0.0622779i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − 81.2821i | − 0.572409i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − 9.92134i | − 0.0684231i | ||||||||
\(146\) | −45.7668 | −0.313471 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −18.1073 | −0.122347 | ||||||||
\(149\) | − 198.806i | − 1.33427i | −0.744936 | − | 0.667136i | \(-0.767520\pi\) | ||||
0.744936 | − | 0.667136i | \(-0.232480\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 130.507i | 0.864287i | 0.901805 | + | 0.432144i | \(0.142243\pi\) | ||||
−0.901805 | + | 0.432144i | \(0.857757\pi\) | |||||||
\(152\) | 76.8107 | 0.505334 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −23.7058 | −0.152940 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −70.5872 | −0.449600 | −0.224800 | − | 0.974405i | \(-0.572173\pi\) | ||||
−0.224800 | + | 0.974405i | \(0.572173\pi\) | |||||||
\(158\) | −59.2677 | −0.375112 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 13.0808i | − 0.0817548i | ||||||||
\(161\) | − 42.8542i | − 0.266175i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −76.9098 | −0.471840 | −0.235920 | − | 0.971773i | \(-0.575810\pi\) | ||||
−0.235920 | + | 0.971773i | \(0.575810\pi\) | |||||||
\(164\) | 157.917i | 0.962910i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 148.047 | 0.891848 | ||||||||
\(167\) | 101.758i | 0.609328i | 0.952460 | + | 0.304664i | \(0.0985441\pi\) | ||||
−0.952460 | + | 0.304664i | \(0.901456\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.1420 | 0.125101 | ||||||||
\(170\) | 8.16822 | 0.0480483 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 53.5414i | − 0.311287i | ||||||||
\(173\) | 124.902i | 0.721979i | 0.932570 | + | 0.360989i | \(0.117561\pi\) | ||||
−0.932570 | + | 0.360989i | \(0.882439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 179.528i | 1.02587i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 131.850i | − 0.740733i | ||||||||
\(179\) | 103.230 | 0.576706 | 0.288353 | − | 0.957524i | \(-0.406892\pi\) | ||||
0.288353 | + | 0.957524i | \(0.406892\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −112.462 | −0.621335 | −0.310668 | − | 0.950519i | \(-0.600553\pi\) | ||||
−0.310668 | + | 0.950519i | \(0.600553\pi\) | |||||||
\(182\) | 86.3440i | 0.474417i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 40.9871i | 0.222756i | ||||||||
\(185\) | 2.37235 | 0.0128235 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 167.996 | 0.893595 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.34115 | −0.0228482 | ||||||||
\(191\) | −191.072 | −1.00038 | −0.500188 | − | 0.865917i | \(-0.666736\pi\) | ||||
−0.500188 | + | 0.865917i | \(0.666736\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 54.5578i | − 0.282683i | −0.989961 | − | 0.141341i | \(-0.954858\pi\) | ||||
0.989961 | − | 0.141341i | \(-0.0451415\pi\) | |||||||
\(194\) | 36.9510i | 0.190469i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −9.79193 | −0.0499588 | ||||||||
\(197\) | 75.2950i | 0.382208i | 0.981570 | + | 0.191104i | \(0.0612068\pi\) | ||||
−0.981570 | + | 0.191104i | \(0.938793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −60.7193 | −0.305122 | −0.152561 | − | 0.988294i | \(-0.548752\pi\) | ||||
−0.152561 | + | 0.988294i | \(0.548752\pi\) | |||||||
\(200\) | − 171.706i | − 0.858529i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −79.3932 | −0.393036 | ||||||||
\(203\) | 180.342 | 0.888386 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 20.6897i | − 0.100925i | ||||||||
\(206\) | 97.9259i | 0.475368i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 65.0152i | 0.312573i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 409.192i | 1.93930i | 0.244501 | + | 0.969649i | \(0.421376\pi\) | ||||
−0.244501 | + | 0.969649i | \(0.578624\pi\) | |||||||
\(212\) | 287.227 | 1.35484 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 106.367 | 0.497040 | ||||||||
\(215\) | 7.01478i | 0.0326269i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 430.905i | − 1.98574i | ||||||||
\(218\) | −172.388 | −0.790771 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −254.254 | −1.15047 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −147.312 | −0.660590 | −0.330295 | − | 0.943878i | \(-0.607148\pi\) | ||||
−0.330295 | + | 0.943878i | \(0.607148\pi\) | |||||||
\(224\) | 237.772 | 1.06148 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − 96.8060i | − 0.428345i | ||||||||
\(227\) | − 137.022i | − 0.603621i | −0.953368 | − | 0.301810i | \(-0.902409\pi\) | ||||
0.953368 | − | 0.301810i | \(-0.0975910\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 85.7061 | 0.374262 | 0.187131 | − | 0.982335i | \(-0.440081\pi\) | ||||
0.187131 | + | 0.982335i | \(0.440081\pi\) | |||||||
\(230\) | − 2.31649i | − 0.0100717i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −172.485 | −0.743469 | ||||||||
\(233\) | − 216.431i | − 0.928887i | −0.885603 | − | 0.464444i | \(-0.846254\pi\) | ||||
0.885603 | − | 0.464444i | \(-0.153746\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.0101 | −0.0936601 | ||||||||
\(236\) | 76.1833 | 0.322811 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 148.475i | 0.623846i | ||||||||
\(239\) | − 165.243i | − 0.691393i | −0.938346 | − | 0.345697i | \(-0.887643\pi\) | ||||
0.938346 | − | 0.345697i | \(-0.112357\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 233.818i | − 0.970199i | −0.874459 | − | 0.485100i | \(-0.838783\pi\) | ||||
0.874459 | − | 0.485100i | \(-0.161217\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 101.373i | − 0.415463i | ||||||||
\(245\) | 1.28290 | 0.00523632 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 135.128 | 0.547076 | ||||||||
\(248\) | 412.130i | 1.66181i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.4705i | 0.0778821i | ||||||||
\(251\) | −267.382 | −1.06527 | −0.532633 | − | 0.846346i | \(-0.678798\pi\) | ||||
−0.532633 | + | 0.846346i | \(0.678798\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −21.4850 | −0.0845866 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −162.511 | −0.634810 | ||||||||
\(257\) | −49.5133 | −0.192659 | −0.0963293 | − | 0.995350i | \(-0.530710\pi\) | ||||
−0.0963293 | + | 0.995350i | \(0.530710\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 43.1226i | 0.166496i | ||||||||
\(260\) | − 14.6703i | − 0.0564241i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.0742 | −0.0613518 | ||||||||
\(263\) | − 198.763i | − 0.755752i | −0.925856 | − | 0.377876i | \(-0.876655\pi\) | ||||
0.925856 | − | 0.377876i | \(-0.123345\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −37.6313 | −0.142005 | ||||||||
\(266\) | − 78.9100i | − 0.296654i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 287.264 | 1.07188 | ||||||||
\(269\) | −10.7729 | −0.0400480 | −0.0200240 | − | 0.999799i | \(-0.506374\pi\) | ||||
−0.0200240 | + | 0.999799i | \(0.506374\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 292.226i | − 1.07833i | −0.842202 | − | 0.539163i | \(-0.818741\pi\) | ||||
0.842202 | − | 0.539163i | \(-0.181259\pi\) | |||||||
\(272\) | 111.799i | 0.411025i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − 30.0560i | − 0.109693i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 175.365i | − 0.633088i | −0.948578 | − | 0.316544i | \(-0.897477\pi\) | ||||
0.948578 | − | 0.316544i | \(-0.102523\pi\) | |||||||
\(278\) | −27.2628 | −0.0980675 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −19.8594 | −0.0709265 | ||||||||
\(281\) | 227.381i | 0.809184i | 0.914497 | + | 0.404592i | \(0.132586\pi\) | ||||
−0.914497 | + | 0.404592i | \(0.867414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 237.446i | − 0.839032i | −0.907748 | − | 0.419516i | \(-0.862200\pi\) | ||||
0.907748 | − | 0.419516i | \(-0.137800\pi\) | |||||||
\(284\) | −251.031 | −0.883912 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 376.080 | 1.31038 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −148.209 | −0.512835 | ||||||||
\(290\) | 9.74840 | 0.0336152 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 141.346i | 0.484062i | ||||||||
\(293\) | 29.3337i | 0.100115i | 0.998746 | + | 0.0500576i | \(0.0159405\pi\) | ||||
−0.998746 | + | 0.0500576i | \(0.984060\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.98123 | −0.0338347 | ||||||||
\(296\) | − 41.2437i | − 0.139337i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 195.341 | 0.655507 | ||||||||
\(299\) | 72.1057i | 0.241156i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −127.509 | −0.423618 | ||||||||
\(302\) | −128.232 | −0.424611 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 59.4175i | − 0.195452i | ||||||||
\(305\) | 13.2815i | 0.0435458i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 347.331i | − 1.13137i | −0.824621 | − | 0.565686i | \(-0.808611\pi\) | ||||
0.824621 | − | 0.565686i | \(-0.191389\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − 23.2926i | − 0.0751373i | ||||||||
\(311\) | −440.571 | −1.41663 | −0.708314 | − | 0.705898i | \(-0.750544\pi\) | ||||
−0.708314 | + | 0.705898i | \(0.750544\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.4645 | −0.0813562 | −0.0406781 | − | 0.999172i | \(-0.512952\pi\) | ||||
−0.0406781 | + | 0.999172i | \(0.512952\pi\) | |||||||
\(314\) | − 69.3568i | − 0.220881i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 183.042i | 0.579247i | ||||||||
\(317\) | −91.3837 | −0.288277 | −0.144138 | − | 0.989558i | \(-0.546041\pi\) | ||||
−0.144138 | + | 0.989558i | \(0.546041\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 4.34975 | 0.0135930 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 42.1072 | 0.130768 | ||||||||
\(323\) | 232.363 | 0.719390 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 302.070i | − 0.929446i | ||||||||
\(326\) | − 75.5692i | − 0.231807i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −359.695 | −1.09663 | ||||||||
\(329\) | − 400.083i | − 1.21606i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −318.761 | −0.963024 | −0.481512 | − | 0.876439i | \(-0.659912\pi\) | ||||
−0.481512 | + | 0.876439i | \(0.659912\pi\) | |||||||
\(332\) | − 457.226i | − 1.37719i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −99.9840 | −0.299353 | ||||||||
\(335\) | −37.6361 | −0.112347 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 617.761i | − 1.83312i | −0.399898 | − | 0.916560i | \(-0.630954\pi\) | ||||
0.399898 | − | 0.916560i | \(-0.369046\pi\) | |||||||
\(338\) | 20.7735i | 0.0614601i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − 25.2267i | − 0.0741961i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 330.794i | − 0.964415i | ||||||||
\(344\) | 121.953 | 0.354516 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −122.725 | −0.354697 | ||||||||
\(347\) | − 201.129i | − 0.579623i | −0.957084 | − | 0.289811i | \(-0.906407\pi\) | ||||
0.957084 | − | 0.289811i | \(-0.0935925\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 484.738i | 1.38893i | 0.719525 | + | 0.694467i | \(0.244360\pi\) | ||||
−0.719525 | + | 0.694467i | \(0.755640\pi\) | |||||||
\(350\) | −176.399 | −0.503996 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −108.957 | −0.308661 | −0.154330 | − | 0.988019i | \(-0.549322\pi\) | ||||
−0.154330 | + | 0.988019i | \(0.549322\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 32.8891 | 0.0926453 | ||||||||
\(356\) | −407.206 | −1.14384 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 101.431i | 0.283327i | ||||||||
\(359\) | − 428.512i | − 1.19363i | −0.802380 | − | 0.596814i | \(-0.796433\pi\) | ||||
0.802380 | − | 0.596814i | \(-0.203567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 237.506 | 0.657913 | ||||||||
\(362\) | − 110.501i | − 0.305252i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 266.664 | 0.732594 | ||||||||
\(365\) | − 18.5186i | − 0.0507358i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 427.936 | 1.16604 | 0.583019 | − | 0.812459i | \(-0.301871\pi\) | ||||
0.583019 | + | 0.812459i | \(0.301871\pi\) | |||||||
\(368\) | 31.7059 | 0.0861572 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.33099i | 0.00629998i | ||||||||
\(371\) | − 684.032i | − 1.84375i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 104.312i | 0.279656i | 0.990176 | + | 0.139828i | \(0.0446549\pi\) | ||||
−0.990176 | + | 0.139828i | \(0.955345\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 382.651i | 1.01769i | ||||||||
\(377\) | −303.440 | −0.804881 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 224.659 | 0.592767 | 0.296383 | − | 0.955069i | \(-0.404219\pi\) | ||||
0.296383 | + | 0.955069i | \(0.404219\pi\) | |||||||
\(380\) | 13.4072i | 0.0352820i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 187.741i | − 0.491469i | ||||||||
\(383\) | −59.2675 | −0.154745 | −0.0773727 | − | 0.997002i | \(-0.524653\pi\) | ||||
−0.0773727 | + | 0.997002i | \(0.524653\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.6068 | 0.138878 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 114.119 | 0.294122 | ||||||||
\(389\) | 412.174 | 1.05957 | 0.529786 | − | 0.848131i | \(-0.322272\pi\) | ||||
0.529786 | + | 0.848131i | \(0.322272\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 123.991i | 0.317114i | ||||||||
\(392\) | − 22.3035i | − 0.0568966i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −73.9825 | −0.187773 | ||||||||
\(395\) | − 23.9814i | − 0.0607125i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 619.925 | 1.56152 | 0.780762 | − | 0.624829i | \(-0.214831\pi\) | ||||
0.780762 | + | 0.624829i | \(0.214831\pi\) | |||||||
\(398\) | − 59.6609i | − 0.149902i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −132.824 | −0.332061 | ||||||||
\(401\) | 672.081 | 1.67601 | 0.838006 | − | 0.545661i | \(-0.183721\pi\) | ||||
0.838006 | + | 0.545661i | \(0.183721\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 725.031i | 1.79909i | ||||||||
\(404\) | 245.197i | 0.606924i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 177.199i | 0.436450i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 614.345i | − 1.50207i | −0.660264 | − | 0.751034i | \(-0.729556\pi\) | ||||
0.660264 | − | 0.751034i | \(-0.270444\pi\) | |||||||
\(410\) | 20.3290 | 0.0495830 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 302.434 | 0.734062 | ||||||||
\(413\) | − 181.431i | − 0.439300i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 59.9040i | 0.144347i | ||||||||
\(416\) | −400.070 | −0.961706 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 60.9488 | 0.145462 | 0.0727312 | − | 0.997352i | \(-0.476828\pi\) | ||||
0.0727312 | + | 0.997352i | \(0.476828\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 208.608 | 0.495506 | 0.247753 | − | 0.968823i | \(-0.420308\pi\) | ||||
0.247753 | + | 0.968823i | \(0.420308\pi\) | |||||||
\(422\) | −402.059 | −0.952747 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 654.229i | 1.54299i | ||||||||
\(425\) | − 519.434i | − 1.22220i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −241.420 | −0.565386 | ||||||||
\(428\) | − 328.502i | − 0.767528i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.89250 | −0.0160291 | ||||||||
\(431\) | − 270.722i | − 0.628124i | −0.949402 | − | 0.314062i | \(-0.898310\pi\) | ||||
0.949402 | − | 0.314062i | \(-0.101690\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −627.302 | −1.44873 | −0.724367 | − | 0.689414i | \(-0.757868\pi\) | ||||
−0.724367 | + | 0.689414i | \(0.757868\pi\) | |||||||
\(434\) | 423.393 | 0.975561 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 532.402i | 1.22111i | ||||||||
\(437\) | − 65.8976i | − 0.150795i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 495.244i | − 1.12812i | −0.825734 | − | 0.564060i | \(-0.809239\pi\) | ||||
0.825734 | − | 0.564060i | \(-0.190761\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 249.822i | − 0.565207i | ||||||||
\(443\) | −742.004 | −1.67495 | −0.837477 | − | 0.546473i | \(-0.815970\pi\) | ||||
−0.837477 | + | 0.546473i | \(0.815970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 53.3505 | 0.119889 | ||||||||
\(446\) | − 144.744i | − 0.324537i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 79.0664i | 0.176487i | ||||||||
\(449\) | 713.566 | 1.58923 | 0.794617 | − | 0.607111i | \(-0.207672\pi\) | ||||
0.794617 | + | 0.607111i | \(0.207672\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −298.975 | −0.661449 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 134.633 | 0.296549 | ||||||||
\(455\) | −34.9373 | −0.0767852 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 282.514i | 0.618192i | 0.951031 | + | 0.309096i | \(0.100027\pi\) | ||||
−0.951031 | + | 0.309096i | \(0.899973\pi\) | |||||||
\(458\) | 84.2121i | 0.183869i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.15422 | −0.0155527 | ||||||||
\(461\) | − 198.186i | − 0.429905i | −0.976624 | − | 0.214953i | \(-0.931040\pi\) | ||||
0.976624 | − | 0.214953i | \(-0.0689597\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −226.915 | −0.490097 | −0.245049 | − | 0.969511i | \(-0.578804\pi\) | ||||
−0.245049 | + | 0.969511i | \(0.578804\pi\) | |||||||
\(464\) | 133.427i | 0.287558i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 212.658 | 0.456348 | ||||||||
\(467\) | −149.659 | −0.320468 | −0.160234 | − | 0.987079i | \(-0.551225\pi\) | ||||
−0.160234 | + | 0.987079i | \(0.551225\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 684.119i | − 1.45868i | ||||||||
\(470\) | − 21.6265i | − 0.0460138i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 173.526i | 0.367640i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 276.063i | 0.581184i | ||||||||
\(476\) | 458.550 | 0.963341 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 162.363 | 0.339671 | ||||||||
\(479\) | 325.770i | 0.680105i | 0.940407 | + | 0.340052i | \(0.110445\pi\) | ||||
−0.940407 | + | 0.340052i | \(0.889555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 72.5572i | − 0.150847i | ||||||||
\(482\) | 229.742 | 0.476644 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.9514 | −0.0308277 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −306.924 | −0.630234 | −0.315117 | − | 0.949053i | \(-0.602044\pi\) | ||||
−0.315117 | + | 0.949053i | \(0.602044\pi\) | |||||||
\(488\) | 230.901 | 0.473158 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.26054i | 0.00257252i | ||||||||
\(491\) | − 613.874i | − 1.25025i | −0.780524 | − | 0.625126i | \(-0.785047\pi\) | ||||
0.780524 | − | 0.625126i | \(-0.214953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −521.790 | −1.05840 | ||||||||
\(494\) | 132.772i | 0.268770i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 318.806 | 0.642754 | ||||||||
\(497\) | 597.832i | 1.20288i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 409.466 | 0.820573 | 0.410287 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410287 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(500\) | 60.1326 | 0.120265 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 262.721i | − 0.523349i | ||||||||
\(503\) | − 707.795i | − 1.40715i | −0.710623 | − | 0.703573i | \(-0.751587\pi\) | ||||
0.710623 | − | 0.703573i | \(-0.248413\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 32.1248i | − 0.0636134i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 66.3541i | 0.130618i | ||||||||
\(509\) | −205.948 | −0.404613 | −0.202306 | − | 0.979322i | \(-0.564844\pi\) | ||||
−0.202306 | + | 0.979322i | \(0.564844\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 336.616 | 0.658740 | ||||||||
\(512\) | 323.743i | 0.632310i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − 48.6502i | − 0.0946502i | ||||||||
\(515\) | −39.6236 | −0.0769391 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −42.3709 | −0.0817971 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 33.4150 | 0.0642597 | ||||||||
\(521\) | 332.454 | 0.638108 | 0.319054 | − | 0.947737i | \(-0.396635\pi\) | ||||
0.319054 | + | 0.947737i | \(0.396635\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 312.797i | − 0.598082i | −0.954240 | − | 0.299041i | \(-0.903333\pi\) | ||||
0.954240 | − | 0.299041i | \(-0.0966668\pi\) | |||||||
\(524\) | 49.6434i | 0.0947393i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 195.298 | 0.371289 | ||||||||
\(527\) | 1246.75i | 2.36575i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −493.836 | −0.933528 | ||||||||
\(530\) | − 36.9754i | − 0.0697648i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −243.705 | −0.458092 | ||||||||
\(533\) | −632.785 | −1.18721 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 43.0390i | 0.0804467i | ||||||||
\(536\) | 654.312i | 1.22073i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 10.5851i | − 0.0196750i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 61.0698i | 0.112883i | 0.998406 | + | 0.0564416i | \(0.0179755\pi\) | ||||
−0.998406 | + | 0.0564416i | \(0.982025\pi\) | |||||||
\(542\) | 287.132 | 0.529764 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −687.952 | −1.26462 | ||||||||
\(545\) | − 69.7532i | − 0.127988i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 571.085i | 1.04403i | 0.852936 | + | 0.522016i | \(0.174820\pi\) | ||||
−0.852936 | + | 0.522016i | \(0.825180\pi\) | |||||||
\(548\) | −92.8248 | −0.169388 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 277.315 | 0.503294 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 435.915 | 0.788273 | ||||||||
\(554\) | 172.309 | 0.311026 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 84.1981i | 0.151435i | ||||||||
\(557\) | 704.122i | 1.26413i | 0.774914 | + | 0.632066i | \(0.217793\pi\) | ||||
−0.774914 | + | 0.632066i | \(0.782207\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 214.544 | 0.383800 | ||||||||
\(560\) | 15.3624i | 0.0274328i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −223.417 | −0.397539 | ||||||||
\(563\) | 505.018i | 0.897013i | 0.893780 | + | 0.448506i | \(0.148044\pi\) | ||||
−0.893780 | + | 0.448506i | \(0.851956\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 39.1705 | 0.0693283 | ||||||||
\(566\) | 233.307 | 0.412204 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 571.784i | − 1.00666i | ||||||||
\(569\) | 673.489i | 1.18364i | 0.806072 | + | 0.591818i | \(0.201590\pi\) | ||||
−0.806072 | + | 0.591818i | \(0.798410\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 446.598i | 0.782134i | 0.920362 | + | 0.391067i | \(0.127894\pi\) | ||||
−0.920362 | + | 0.391067i | \(0.872106\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 369.525i | 0.643772i | ||||||||
\(575\) | −147.310 | −0.256191 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −576.690 | −0.999463 | −0.499732 | − | 0.866180i | \(-0.666568\pi\) | ||||
−0.499732 | + | 0.866180i | \(0.666568\pi\) | |||||||
\(578\) | − 145.626i | − 0.251948i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 30.1069i | − 0.0519085i | ||||||||
\(581\) | −1088.89 | −1.87416 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −321.949 | −0.551283 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.8224 | −0.0491850 | ||||||||
\(587\) | −906.327 | −1.54400 | −0.771999 | − | 0.635624i | \(-0.780743\pi\) | ||||
−0.771999 | + | 0.635624i | \(0.780743\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 662.608i | − 1.12497i | ||||||||
\(590\) | − 9.80725i | − 0.0166225i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −31.9044 | −0.0538926 | ||||||||
\(593\) | − 724.877i | − 1.22239i | −0.791480 | − | 0.611195i | \(-0.790689\pi\) | ||||
0.791480 | − | 0.611195i | \(-0.209311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −60.0774 | −0.100970 | ||||||||
\(596\) | − 603.290i | − 1.01223i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −70.8488 | −0.118476 | ||||||||
\(599\) | −398.301 | −0.664944 | −0.332472 | − | 0.943113i | \(-0.607883\pi\) | ||||
−0.332472 | + | 0.943113i | \(0.607883\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 985.468i | 1.63971i | 0.572568 | + | 0.819857i | \(0.305947\pi\) | ||||
−0.572568 | + | 0.819857i | \(0.694053\pi\) | |||||||
\(602\) | − 125.286i | − 0.208117i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 396.032i | 0.655682i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 178.969i | − 0.294842i | −0.989074 | − | 0.147421i | \(-0.952903\pi\) | ||||
0.989074 | − | 0.147421i | \(-0.0470972\pi\) | |||||||
\(608\) | 365.625 | 0.601357 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −13.0500 | −0.0213934 | ||||||||
\(611\) | 673.171i | 1.10175i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 1060.89i | − 1.73065i | −0.501211 | − | 0.865325i | \(-0.667112\pi\) | ||||
0.501211 | − | 0.865325i | \(-0.332888\pi\) | |||||||
\(614\) | 341.277 | 0.555825 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −55.3570 | −0.0897196 | −0.0448598 | − | 0.998993i | \(-0.514284\pi\) | ||||
−0.0448598 | + | 0.998993i | \(0.514284\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −752.536 | −1.21573 | −0.607864 | − | 0.794041i | \(-0.707973\pi\) | ||||
−0.607864 | + | 0.794041i | \(0.707973\pi\) | |||||||
\(620\) | −71.9366 | −0.116027 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 432.892i | − 0.695967i | ||||||||
\(623\) | 969.762i | 1.55660i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 613.170 | 0.981072 | ||||||||
\(626\) | − 25.0206i | − 0.0399690i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −214.201 | −0.341084 | ||||||||
\(629\) | − 124.768i | − 0.198359i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −335.720 | −0.532045 | −0.266022 | − | 0.963967i | \(-0.585709\pi\) | ||||
−0.266022 | + | 0.963967i | \(0.585709\pi\) | |||||||
\(632\) | −416.922 | −0.659687 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 89.7908i | − 0.141626i | ||||||||
\(635\) | − 8.69344i | − 0.0136905i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 39.2369i | − 0.0615964i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 48.0491i | − 0.0750768i | ||||||||
\(641\) | 552.092 | 0.861299 | 0.430649 | − | 0.902519i | \(-0.358285\pi\) | ||||
0.430649 | + | 0.902519i | \(0.358285\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −138.358 | −0.215176 | −0.107588 | − | 0.994196i | \(-0.534313\pi\) | ||||
−0.107588 | + | 0.994196i | \(0.534313\pi\) | |||||||
\(644\) | − 130.044i | − 0.201931i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 228.313i | 0.353425i | ||||||||
\(647\) | 1012.85 | 1.56546 | 0.782730 | − | 0.622362i | \(-0.213827\pi\) | ||||
0.782730 | + | 0.622362i | \(0.213827\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 296.805 | 0.456623 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −233.387 | −0.357956 | ||||||||
\(653\) | 7.70732 | 0.0118029 | 0.00590147 | − | 0.999983i | \(-0.498121\pi\) | ||||
0.00590147 | + | 0.999983i | \(0.498121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 6.50407i | − 0.00992988i | ||||||||
\(656\) | 278.244i | 0.424153i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 393.109 | 0.597430 | ||||||||
\(659\) | 736.073i | 1.11695i | 0.829520 | + | 0.558477i | \(0.188614\pi\) | ||||
−0.829520 | + | 0.558477i | \(0.811386\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −471.170 | −0.712813 | −0.356407 | − | 0.934331i | \(-0.615998\pi\) | ||||
−0.356407 | + | 0.934331i | \(0.615998\pi\) | |||||||
\(662\) | − 313.205i | − 0.473119i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1041.44 | 1.56844 | ||||||||
\(665\) | 31.9292 | 0.0480139 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 147.978i | 0.221856i | ||||||||
\(668\) | 308.790i | 0.462260i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 36.9801i | − 0.0551941i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1150.46i | 1.70946i | 0.519077 | + | 0.854728i | \(0.326276\pi\) | ||||
−0.519077 | + | 0.854728i | \(0.673724\pi\) | |||||||
\(674\) | 606.993 | 0.900583 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 64.1568 | 0.0949065 | ||||||||
\(677\) | − 1172.40i | − 1.73176i | −0.500252 | − | 0.865880i | \(-0.666759\pi\) | ||||
0.500252 | − | 0.865880i | \(-0.333241\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 271.775i | − 0.400258i | ||||||||
\(680\) | 57.4598 | 0.0844997 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 329.083 | 0.481820 | 0.240910 | − | 0.970547i | \(-0.422554\pi\) | ||||
0.240910 | + | 0.970547i | \(0.422554\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.1615 | 0.0177541 | ||||||||
\(686\) | 325.028 | 0.473802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 94.3380i | − 0.137119i | ||||||||
\(689\) | 1150.94i | 1.67045i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 719.083 | 1.04064 | 0.520321 | − | 0.853971i | \(-0.325812\pi\) | ||||
0.520321 | + | 0.853971i | \(0.325812\pi\) | |||||||
\(692\) | 379.023i | 0.547722i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 197.623 | 0.284760 | ||||||||
\(695\) | − 11.0313i | − 0.0158724i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1088.12 | −1.56115 | ||||||||
\(698\) | −476.288 | −0.682361 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 544.788i | 0.778269i | ||||||||
\(701\) | − 100.688i | − 0.143635i | −0.997418 | − | 0.0718175i | \(-0.977120\pi\) | ||||
0.997418 | − | 0.0718175i | \(-0.0228799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 66.3102i | 0.0943246i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 107.058i | − 0.151640i | ||||||||
\(707\) | 583.938 | 0.825938 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 275.579 | 0.388687 | 0.194343 | − | 0.980934i | \(-0.437742\pi\) | ||||
0.194343 | + | 0.980934i | \(0.437742\pi\) | |||||||
\(710\) | 32.3158i | 0.0455152i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 927.510i | − 1.30268i | ||||||||
\(713\) | 353.575 | 0.495898 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 313.258 | 0.437512 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 421.043 | 0.586411 | ||||||||
\(719\) | −92.7087 | −0.128941 | −0.0644706 | − | 0.997920i | \(-0.520536\pi\) | ||||
−0.0644706 | + | 0.997920i | \(0.520536\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 720.247i | − 0.998955i | ||||||||
\(722\) | 233.366i | 0.323222i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −341.272 | −0.471370 | ||||||||
\(725\) | − 619.921i | − 0.855063i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 40.4150 | 0.0555915 | 0.0277958 | − | 0.999614i | \(-0.491151\pi\) | ||||
0.0277958 | + | 0.999614i | \(0.491151\pi\) | |||||||
\(728\) | 607.392i | 0.834329i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.1958 | 0.0249257 | ||||||||
\(731\) | 368.926 | 0.504686 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 714.364i | − 0.974575i | −0.873241 | − | 0.487288i | \(-0.837986\pi\) | ||||
0.873241 | − | 0.487288i | \(-0.162014\pi\) | |||||||
\(734\) | 420.476i | 0.572856i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 195.102i | 0.265084i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 51.5783i | − 0.0697947i | −0.999391 | − | 0.0348974i | \(-0.988890\pi\) | ||||
0.999391 | − | 0.0348974i | \(-0.0111104\pi\) | |||||||
\(740\) | 7.19902 | 0.00972841 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 672.108 | 0.905807 | ||||||||
\(743\) | − 898.577i | − 1.20939i | −0.796457 | − | 0.604695i | \(-0.793295\pi\) | ||||
0.796457 | − | 0.604695i | \(-0.206705\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 79.0406i | 0.106095i | ||||||||
\(746\) | −102.493 | −0.137391 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −782.328 | −1.04450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 342.057 | 0.455469 | 0.227734 | − | 0.973723i | \(-0.426868\pi\) | ||||
0.227734 | + | 0.973723i | \(0.426868\pi\) | |||||||
\(752\) | 296.002 | 0.393620 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 298.151i | − 0.395426i | ||||||||
\(755\) | − 51.8865i | − 0.0687239i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −807.960 | −1.06732 | −0.533659 | − | 0.845700i | \(-0.679184\pi\) | ||||
−0.533659 | + | 0.845700i | \(0.679184\pi\) | |||||||
\(758\) | 220.743i | 0.291217i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −30.5381 | −0.0401817 | ||||||||
\(761\) | 782.358i | 1.02807i | 0.857771 | + | 0.514033i | \(0.171849\pi\) | ||||
−0.857771 | + | 0.514033i | \(0.828151\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1267.92 | 1.66175 | ||||||||
\(764\) | −579.818 | −0.758925 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 58.2344i | − 0.0760240i | ||||||||
\(767\) | 305.272i | 0.398008i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 652.678i | − 0.848736i | −0.905490 | − | 0.424368i | \(-0.860496\pi\) | ||||
0.905490 | − | 0.424368i | \(-0.139504\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − 165.559i | − 0.214454i | ||||||||
\(773\) | 864.726 | 1.11866 | 0.559331 | − | 0.828944i | \(-0.311058\pi\) | ||||
0.559331 | + | 0.828944i | \(0.311058\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1481.22 | −1.91125 | ||||||||
\(776\) | 259.934i | 0.334967i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 404.989i | 0.520551i | ||||||||
\(779\) | 578.304 | 0.742367 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −121.830 | −0.155793 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −17.2530 | −0.0220064 | ||||||||
\(785\) | 28.0637 | 0.0357500 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 436.626i | 0.554798i | 0.960755 | + | 0.277399i | \(0.0894724\pi\) | ||||
−0.960755 | + | 0.277399i | \(0.910528\pi\) | |||||||
\(788\) | 228.487i | 0.289958i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 23.5634 | 0.0298271 | ||||||||
\(791\) | 712.010i | 0.900139i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 406.208 | 0.512243 | ||||||||
\(794\) | 609.119i | 0.767152i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −184.256 | −0.231478 | ||||||||
\(797\) | −453.109 | −0.568519 | −0.284259 | − | 0.958747i | \(-0.591748\pi\) | ||||
−0.284259 | + | 0.958747i | \(0.591748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1157.57i | 1.44877i | ||||||||
\(800\) | − 817.333i | − 1.02167i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 660.366i | 0.823399i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 17.0378i | 0.0211650i | ||||||||
\(806\) | −712.393 | −0.883863 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −558.496 | −0.691208 | ||||||||
\(809\) | 115.243i | 0.142451i | 0.997460 | + | 0.0712256i | \(0.0226910\pi\) | ||||
−0.997460 | + | 0.0712256i | \(0.977309\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.2681i | 0.0410211i | 0.999790 | + | 0.0205105i | \(0.00652917\pi\) | ||||
−0.999790 | + | 0.0205105i | \(0.993471\pi\) | |||||||
\(812\) | 547.259 | 0.673965 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 30.5775 | 0.0375184 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −196.072 | −0.239991 | ||||||||
\(818\) | 603.637 | 0.737942 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 62.7840i | − 0.0765659i | ||||||||
\(821\) | − 715.058i | − 0.870960i | −0.900198 | − | 0.435480i | \(-0.856579\pi\) | ||||
0.900198 | − | 0.435480i | \(-0.143421\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −157.039 | −0.190813 | −0.0954066 | − | 0.995438i | \(-0.530415\pi\) | ||||
−0.0954066 | + | 0.995438i | \(0.530415\pi\) | |||||||
\(824\) | 688.866i | 0.836002i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 178.268 | 0.215821 | ||||||||
\(827\) | 854.310i | 1.03302i | 0.856280 | + | 0.516511i | \(0.172770\pi\) | ||||
−0.856280 | + | 0.516511i | \(0.827230\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1374.17 | −1.65763 | −0.828813 | − | 0.559526i | \(-0.810983\pi\) | ||||
−0.828813 | + | 0.559526i | \(0.810983\pi\) | |||||||
\(830\) | −58.8598 | −0.0709154 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 133.035i | − 0.159898i | ||||||||
\(833\) | − 67.4710i | − 0.0809976i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 40.4564i | − 0.0484508i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 59.8864i | 0.0714634i | ||||||||
\(839\) | −652.536 | −0.777755 | −0.388877 | − | 0.921290i | \(-0.627137\pi\) | ||||
−0.388877 | + | 0.921290i | \(0.627137\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 218.267 | 0.259533 | ||||||||
\(842\) | 204.972i | 0.243435i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1241.72i | 1.47123i | ||||||||
\(845\) | −8.40556 | −0.00994741 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 506.083 | 0.596796 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 510.379 | 0.600446 | ||||||||
\(851\) | −35.3839 | −0.0415792 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1323.71i | 1.55183i | 0.630835 | + | 0.775917i | \(0.282712\pi\) | ||||
−0.630835 | + | 0.775917i | \(0.717288\pi\) | |||||||
\(854\) | − 237.212i | − 0.277765i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 748.242 | 0.874114 | ||||||||
\(857\) | 38.8452i | 0.0453269i | 0.999743 | + | 0.0226634i | \(0.00721462\pi\) | ||||
−0.999743 | + | 0.0226634i | \(0.992785\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 227.261 | 0.264564 | 0.132282 | − | 0.991212i | \(-0.457770\pi\) | ||||
0.132282 | + | 0.991212i | \(0.457770\pi\) | |||||||
\(860\) | 21.2868i | 0.0247520i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 266.003 | 0.308588 | ||||||||
\(863\) | −957.225 | −1.10918 | −0.554592 | − | 0.832123i | \(-0.687126\pi\) | ||||
−0.554592 | + | 0.832123i | \(0.687126\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 49.6581i | − 0.0574082i | ||||||||
\(866\) | − 616.367i | − 0.711741i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 1307.61i | − 1.50646i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1151.08i | 1.32157i | ||||||||
\(872\) | −1212.67 | −1.39068 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 64.7489 | 0.0740834 | ||||||||
\(875\) | − 143.206i | − 0.163664i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1203.94i | 1.37280i | 0.727225 | + | 0.686399i | \(0.240810\pi\) | ||||
−0.727225 | + | 0.686399i | \(0.759190\pi\) | |||||||
\(878\) | 486.612 | 0.554228 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1170.77 | −1.32892 | −0.664458 | − | 0.747326i | \(-0.731337\pi\) | ||||
−0.664458 | + | 0.747326i | \(0.731337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 364.218 | 0.412478 | 0.206239 | − | 0.978502i | \(-0.433878\pi\) | ||||
0.206239 | + | 0.978502i | \(0.433878\pi\) | |||||||
\(884\) | −771.547 | −0.872791 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − 729.070i | − 0.822878i | ||||||||
\(887\) | − 284.728i | − 0.321001i | −0.987036 | − | 0.160501i | \(-0.948689\pi\) | ||||
0.987036 | − | 0.160501i | \(-0.0513108\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 158.022 | 0.177753 | ||||||||
\(890\) | 52.4205i | 0.0588995i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −447.025 | −0.501150 | ||||||||
\(893\) | − 615.212i | − 0.688928i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −41.0419 | −0.0458568 | ||||||||
\(896\) | 873.399 | 0.974775 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 701.127i | 0.780766i | ||||||||
\(899\) | 1487.94i | 1.65511i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1979.13i | 2.19659i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 680.988i | − 0.753305i | ||||||||
\(905\) | 44.7120 | 0.0494056 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 756.730 | 0.834322 | 0.417161 | − | 0.908833i | \(-0.363025\pi\) | ||||
0.417161 | + | 0.908833i | \(0.363025\pi\) | |||||||
\(908\) | − 415.801i | − 0.457931i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 34.3283i | − 0.0377234i | ||||||||
\(911\) | 659.343 | 0.723757 | 0.361879 | − | 0.932225i | \(-0.382135\pi\) | ||||
0.361879 | + | 0.932225i | \(0.382135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −277.589 | −0.303708 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 260.080 | 0.283930 | ||||||||
\(917\) | 118.226 | 0.128927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 746.936i | 0.812771i | 0.913702 | + | 0.406385i | \(0.133211\pi\) | ||||
−0.913702 | + | 0.406385i | \(0.866789\pi\) | |||||||
\(920\) | − 16.2955i | − 0.0177125i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 194.732 | 0.211206 | ||||||||
\(923\) | − 1005.90i | − 1.08981i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 148.233 | 0.160251 | ||||||||
\(926\) | − 222.960i | − 0.240777i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −821.040 | −0.884741 | ||||||||
\(929\) | 1212.62 | 1.30529 | 0.652647 | − | 0.757662i | \(-0.273658\pi\) | ||||
0.652647 | + | 0.757662i | \(0.273658\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.8587i | 0.0385163i | ||||||||
\(932\) | − 656.772i | − 0.704691i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 147.050i | − 0.157441i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1591.84i | − 1.69887i | −0.527697 | − | 0.849433i | \(-0.676944\pi\) | ||||
0.527697 | − | 0.849433i | \(-0.323056\pi\) | |||||||
\(938\) | 672.194 | 0.716625 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −66.7910 | −0.0710543 | ||||||||
\(941\) | 596.807i | 0.634226i | 0.948388 | + | 0.317113i | \(0.102713\pi\) | ||||
−0.948388 | + | 0.317113i | \(0.897287\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 308.590i | 0.327242i | ||||||||
\(944\) | 134.232 | 0.142195 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 883.411 | 0.932852 | 0.466426 | − | 0.884560i | \(-0.345541\pi\) | ||||
0.466426 | + | 0.884560i | \(0.345541\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −566.383 | −0.596821 | ||||||||
\(950\) | −271.250 | −0.285527 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1044.46i | 1.09712i | ||||||||
\(953\) | − 282.867i | − 0.296817i | −0.988926 | − | 0.148409i | \(-0.952585\pi\) | ||||
0.988926 | − | 0.148409i | \(-0.0474151\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 75.9655 | 0.0795450 | ||||||||
\(956\) | − 501.440i | − 0.524518i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −320.091 | −0.334125 | ||||||||
\(959\) | 221.063i | 0.230514i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2594.24 | 2.69952 | ||||||||
\(962\) | 71.2924 | 0.0741086 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 709.535i | − 0.736032i | ||||||||
\(965\) | 21.6908i | 0.0224776i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 335.731i | 0.347188i | 0.984817 | + | 0.173594i | \(0.0555381\pi\) | ||||
−0.984817 | + | 0.173594i | \(0.944462\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 14.6908i | − 0.0151452i | ||||||||
\(971\) | −1395.34 | −1.43701 | −0.718505 | − | 0.695522i | \(-0.755173\pi\) | ||||
−0.718505 | + | 0.695522i | \(0.755173\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 200.518 | 0.206082 | ||||||||
\(974\) | − 301.574i | − 0.309624i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 178.615i | − 0.183008i | ||||||||
\(977\) | 1163.83 | 1.19123 | 0.595614 | − | 0.803271i | \(-0.296909\pi\) | ||||
0.595614 | + | 0.803271i | \(0.296909\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 3.89303 | 0.00397248 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 603.173 | 0.614230 | ||||||||
\(983\) | 409.788 | 0.416875 | 0.208438 | − | 0.978036i | \(-0.433162\pi\) | ||||
0.208438 | + | 0.978036i | \(0.433162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 29.9354i | − 0.0303913i | ||||||||
\(986\) | − 512.694i | − 0.519974i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 410.053 | 0.415033 | ||||||||
\(989\) | − 104.626i | − 0.105790i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1604.17 | 1.61874 | 0.809372 | − | 0.587297i | \(-0.199808\pi\) | ||||
0.809372 | + | 0.587297i | \(0.199808\pi\) | |||||||
\(992\) | 1961.77i | 1.97759i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −587.411 | −0.590956 | ||||||||
\(995\) | 24.1405 | 0.0242618 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 72.3843i | − 0.0726021i | −0.999341 | − | 0.0363010i | \(-0.988442\pi\) | ||||
0.999341 | − | 0.0363010i | \(-0.0115575\pi\) | |||||||
\(998\) | 402.329i | 0.403135i | ||||||||
\(999\) | 0 | 0 |
(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 | 1089.3.c.m.604.10 | 16 | ||
3.2 | odd | 2 | 363.3.c.e.241.7 | 16 | |||
11.6 | odd | 10 | 99.3.k.c.19.4 | 16 | |||
11.9 | even | 5 | 99.3.k.c.73.4 | 16 | |||
11.10 | odd | 2 | inner | 1089.3.c.m.604.7 | 16 | ||
33.2 | even | 10 | 363.3.g.f.40.4 | 16 | |||
33.5 | odd | 10 | 363.3.g.f.118.4 | 16 | |||
33.8 | even | 10 | 363.3.g.a.112.4 | 16 | |||
33.14 | odd | 10 | 363.3.g.g.112.1 | 16 | |||
33.17 | even | 10 | 33.3.g.a.19.1 | yes | 16 | ||
33.20 | odd | 10 | 33.3.g.a.7.1 | ✓ | 16 | ||
33.26 | odd | 10 | 363.3.g.a.94.4 | 16 | |||
33.29 | even | 10 | 363.3.g.g.94.1 | 16 | |||
33.32 | even | 2 | 363.3.c.e.241.10 | 16 | |||
132.83 | odd | 10 | 528.3.bf.b.481.3 | 16 | |||
132.119 | even | 10 | 528.3.bf.b.337.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.g.a.7.1 | ✓ | 16 | 33.20 | odd | 10 | ||
33.3.g.a.19.1 | yes | 16 | 33.17 | even | 10 | ||
99.3.k.c.19.4 | 16 | 11.6 | odd | 10 | |||
99.3.k.c.73.4 | 16 | 11.9 | even | 5 | |||
363.3.c.e.241.7 | 16 | 3.2 | odd | 2 | |||
363.3.c.e.241.10 | 16 | 33.32 | even | 2 | |||
363.3.g.a.94.4 | 16 | 33.26 | odd | 10 | |||
363.3.g.a.112.4 | 16 | 33.8 | even | 10 | |||
363.3.g.f.40.4 | 16 | 33.2 | even | 10 | |||
363.3.g.f.118.4 | 16 | 33.5 | odd | 10 | |||
363.3.g.g.94.1 | 16 | 33.29 | even | 10 | |||
363.3.g.g.112.1 | 16 | 33.14 | odd | 10 | |||
528.3.bf.b.337.3 | 16 | 132.119 | even | 10 | |||
528.3.bf.b.481.3 | 16 | 132.83 | odd | 10 | |||
1089.3.c.m.604.7 | 16 | 11.10 | odd | 2 | inner | ||
1089.3.c.m.604.10 | 16 | 1.1 | even | 1 | trivial |