Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(379,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.379");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.g (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 379.3 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.379 |
Dual form | 630.2.g.g.379.1 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.22474 | + | 0.224745i | −0.994936 | + | 0.100509i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.224745 | − | 2.22474i | −0.0710706 | − | 0.703526i | ||||
\(11\) | 4.89898 | 1.47710 | 0.738549 | − | 0.674200i | \(-0.235511\pi\) | ||||
0.738549 | + | 0.674200i | \(0.235511\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 4.44949i | − | 1.23407i | −0.786937 | − | 0.617033i | \(-0.788334\pi\) | ||
0.786937 | − | 0.617033i | \(-0.211666\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 2.00000i | − | 0.485071i | −0.970143 | − | 0.242536i | \(-0.922021\pi\) | ||
0.970143 | − | 0.242536i | \(-0.0779791\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.55051 | −0.355711 | −0.177856 | − | 0.984057i | \(-0.556916\pi\) | ||||
−0.177856 | + | 0.984057i | \(0.556916\pi\) | |||||||
\(20\) | 2.22474 | − | 0.224745i | 0.497468 | − | 0.0502545i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.89898i | 1.04447i | ||||||||
\(23\) | 2.89898i | 0.604479i | 0.953232 | + | 0.302240i | \(0.0977342\pi\) | ||||
−0.953232 | + | 0.302240i | \(0.902266\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.89898 | − | 1.00000i | 0.979796 | − | 0.200000i | ||||
\(26\) | 4.44949 | 0.872617 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 6.89898 | 1.28111 | 0.640554 | − | 0.767913i | \(-0.278705\pi\) | ||||
0.640554 | + | 0.767913i | \(0.278705\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.89898 | 1.59830 | 0.799152 | − | 0.601129i | \(-0.205282\pi\) | ||||
0.799152 | + | 0.601129i | \(0.205282\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0.224745 | + | 2.22474i | 0.0379888 | + | 0.376051i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.00000i | 0.328798i | 0.986394 | + | 0.164399i | \(0.0525685\pi\) | ||||
−0.986394 | + | 0.164399i | \(0.947432\pi\) | |||||||
\(38\) | − | 1.55051i | − | 0.251526i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0.224745 | + | 2.22474i | 0.0355353 | + | 0.351763i | ||||
\(41\) | 1.10102 | 0.171951 | 0.0859753 | − | 0.996297i | \(-0.472599\pi\) | ||||
0.0859753 | + | 0.996297i | \(0.472599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.898979i | 0.137093i | 0.997648 | + | 0.0685465i | \(0.0218362\pi\) | ||||
−0.997648 | + | 0.0685465i | \(0.978164\pi\) | |||||||
\(44\) | −4.89898 | −0.738549 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.89898 | −0.427431 | ||||||||
\(47\) | − | 8.89898i | − | 1.29805i | −0.760767 | − | 0.649025i | \(-0.775177\pi\) | ||
0.760767 | − | 0.649025i | \(-0.224823\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 1.00000 | + | 4.89898i | 0.141421 | + | 0.692820i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.44949i | 0.617033i | ||||||||
\(53\) | − | 10.8990i | − | 1.49709i | −0.663084 | − | 0.748545i | \(-0.730753\pi\) | ||
0.663084 | − | 0.748545i | \(-0.269247\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.8990 | + | 1.10102i | −1.46962 | + | 0.148462i | ||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.89898i | 0.905880i | ||||||||
\(59\) | −1.55051 | −0.201859 | −0.100930 | − | 0.994894i | \(-0.532182\pi\) | ||||
−0.100930 | + | 0.994894i | \(0.532182\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.55051 | 0.454596 | 0.227298 | − | 0.973825i | \(-0.427011\pi\) | ||||
0.227298 | + | 0.973825i | \(0.427011\pi\) | |||||||
\(62\) | 8.89898i | 1.13017i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 1.00000 | + | 9.89898i | 0.124035 | + | 1.22782i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 8.00000i | − | 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 2.00000i | 0.242536i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.22474 | + | 0.224745i | −0.265908 | + | 0.0268622i | ||||
\(71\) | 1.10102 | 0.130667 | 0.0653335 | − | 0.997863i | \(-0.479189\pi\) | ||||
0.0653335 | + | 0.997863i | \(0.479189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.89898i | − | 0.339300i | −0.985504 | − | 0.169650i | \(-0.945736\pi\) | ||
0.985504 | − | 0.169650i | \(-0.0542637\pi\) | |||||||
\(74\) | −2.00000 | −0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.55051 | 0.177856 | ||||||||
\(77\) | − | 4.89898i | − | 0.558291i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.89898 | −0.776196 | −0.388098 | − | 0.921618i | \(-0.626868\pi\) | ||||
−0.388098 | + | 0.921618i | \(0.626868\pi\) | |||||||
\(80\) | −2.22474 | + | 0.224745i | −0.248734 | + | 0.0251272i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.10102i | 0.121587i | ||||||||
\(83\) | − | 2.44949i | − | 0.268866i | −0.990923 | − | 0.134433i | \(-0.957079\pi\) | ||
0.990923 | − | 0.134433i | \(-0.0429214\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.449490 | + | 4.44949i | 0.0487540 | + | 0.482615i | ||||
\(86\) | −0.898979 | −0.0969395 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 4.89898i | − | 0.522233i | ||||||
\(89\) | −10.0000 | −1.06000 | −0.529999 | − | 0.847998i | \(-0.677808\pi\) | ||||
−0.529999 | + | 0.847998i | \(0.677808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.44949 | −0.466433 | ||||||||
\(92\) | − | 2.89898i | − | 0.302240i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 8.89898 | 0.917860 | ||||||||
\(95\) | 3.44949 | − | 0.348469i | 0.353910 | − | 0.0357522i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 15.7980i | 1.60404i | 0.597297 | + | 0.802020i | \(0.296241\pi\) | ||||
−0.597297 | + | 0.802020i | \(0.703759\pi\) | |||||||
\(98\) | − | 1.00000i | − | 0.101015i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.89898 | + | 1.00000i | −0.489898 | + | 0.100000i | ||||
\(101\) | −3.55051 | −0.353289 | −0.176644 | − | 0.984275i | \(-0.556524\pi\) | ||||
−0.176644 | + | 0.984275i | \(0.556524\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 12.8990i | − | 1.27097i | −0.772111 | − | 0.635487i | \(-0.780799\pi\) | ||
0.772111 | − | 0.635487i | \(-0.219201\pi\) | |||||||
\(104\) | −4.44949 | −0.436308 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 10.8990 | 1.05860 | ||||||||
\(107\) | 8.00000i | 0.773389i | 0.922208 | + | 0.386695i | \(0.126383\pi\) | ||||
−0.922208 | + | 0.386695i | \(0.873617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.89898 | −0.660802 | −0.330401 | − | 0.943841i | \(-0.607184\pi\) | ||||
−0.330401 | + | 0.943841i | \(0.607184\pi\) | |||||||
\(110\) | −1.10102 | − | 10.8990i | −0.104978 | − | 1.03918i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | 19.7980i | 1.86244i | 0.364464 | + | 0.931218i | \(0.381252\pi\) | ||||
−0.364464 | + | 0.931218i | \(0.618748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.651531 | − | 6.44949i | −0.0607556 | − | 0.601418i | ||||
\(116\) | −6.89898 | −0.640554 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.55051i | − | 0.142736i | ||||||
\(119\) | −2.00000 | −0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.0000 | 1.18182 | ||||||||
\(122\) | 3.55051i | 0.321448i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.89898 | −0.799152 | ||||||||
\(125\) | −10.6742 | + | 3.32577i | −0.954733 | + | 0.297465i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.8990i | − | 1.32207i | −0.750355 | − | 0.661035i | \(-0.770117\pi\) | ||
0.750355 | − | 0.661035i | \(-0.229883\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −9.89898 | + | 1.00000i | −0.868198 | + | 0.0877058i | ||||
\(131\) | 6.44949 | 0.563495 | 0.281747 | − | 0.959489i | \(-0.409086\pi\) | ||||
0.281747 | + | 0.959489i | \(0.409086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.55051i | 0.134446i | ||||||||
\(134\) | 8.00000 | 0.691095 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | 1.79796i | 0.153610i | 0.997046 | + | 0.0768050i | \(0.0244719\pi\) | ||||
−0.997046 | + | 0.0768050i | \(0.975528\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.55051 | −0.131513 | −0.0657563 | − | 0.997836i | \(-0.520946\pi\) | ||||
−0.0657563 | + | 0.997836i | \(0.520946\pi\) | |||||||
\(140\) | −0.224745 | − | 2.22474i | −0.0189944 | − | 0.188025i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.10102i | 0.0923956i | ||||||||
\(143\) | − | 21.7980i | − | 1.82284i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −15.3485 | + | 1.55051i | −1.27462 | + | 0.128763i | ||||
\(146\) | 2.89898 | 0.239921 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 2.00000i | − | 0.164399i | ||||||
\(149\) | −3.79796 | −0.311141 | −0.155570 | − | 0.987825i | \(-0.549722\pi\) | ||||
−0.155570 | + | 0.987825i | \(0.549722\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5959 | 1.59469 | 0.797347 | − | 0.603522i | \(-0.206236\pi\) | ||||
0.797347 | + | 0.603522i | \(0.206236\pi\) | |||||||
\(152\) | 1.55051i | 0.125763i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.89898 | 0.394771 | ||||||||
\(155\) | −19.7980 | + | 2.00000i | −1.59021 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.55051i | 0.283362i | 0.989912 | + | 0.141681i | \(0.0452507\pi\) | ||||
−0.989912 | + | 0.141681i | \(0.954749\pi\) | |||||||
\(158\) | − | 6.89898i | − | 0.548853i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.224745 | − | 2.22474i | −0.0177676 | − | 0.175882i | ||||
\(161\) | 2.89898 | 0.228472 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.10102i | 0.556195i | 0.960553 | + | 0.278097i | \(0.0897038\pi\) | ||||
−0.960553 | + | 0.278097i | \(0.910296\pi\) | |||||||
\(164\) | −1.10102 | −0.0859753 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.44949 | 0.190117 | ||||||||
\(167\) | 4.89898i | 0.379094i | 0.981872 | + | 0.189547i | \(0.0607020\pi\) | ||||
−0.981872 | + | 0.189547i | \(0.939298\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.79796 | −0.522920 | ||||||||
\(170\) | −4.44949 | + | 0.449490i | −0.341260 | + | 0.0344743i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 0.898979i | − | 0.0685465i | ||||||
\(173\) | − | 6.24745i | − | 0.474985i | −0.971389 | − | 0.237492i | \(-0.923675\pi\) | ||
0.971389 | − | 0.237492i | \(-0.0763255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 4.89898i | −0.0755929 | − | 0.370328i | ||||
\(176\) | 4.89898 | 0.369274 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 10.0000i | − | 0.749532i | ||||||
\(179\) | 13.7980 | 1.03131 | 0.515654 | − | 0.856797i | \(-0.327549\pi\) | ||||
0.515654 | + | 0.856797i | \(0.327549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2474 | −0.761687 | −0.380843 | − | 0.924640i | \(-0.624366\pi\) | ||||
−0.380843 | + | 0.924640i | \(0.624366\pi\) | |||||||
\(182\) | − | 4.44949i | − | 0.329818i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.89898 | 0.213716 | ||||||||
\(185\) | −0.449490 | − | 4.44949i | −0.0330471 | − | 0.327133i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.79796i | − | 0.716498i | ||||||
\(188\) | 8.89898i | 0.649025i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.348469 | + | 3.44949i | 0.0252806 | + | 0.250252i | ||||
\(191\) | −12.6969 | −0.918718 | −0.459359 | − | 0.888251i | \(-0.651921\pi\) | ||||
−0.459359 | + | 0.888251i | \(0.651921\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.5959i | 1.55451i | 0.629187 | + | 0.777254i | \(0.283388\pi\) | ||||
−0.629187 | + | 0.777254i | \(0.716612\pi\) | |||||||
\(194\) | −15.7980 | −1.13423 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | − | 18.8990i | − | 1.34650i | −0.739417 | − | 0.673248i | \(-0.764899\pi\) | ||
0.739417 | − | 0.673248i | \(-0.235101\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.8990 | −1.19794 | −0.598968 | − | 0.800773i | \(-0.704423\pi\) | ||||
−0.598968 | + | 0.800773i | \(0.704423\pi\) | |||||||
\(200\) | −1.00000 | − | 4.89898i | −0.0707107 | − | 0.346410i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.55051i | − | 0.249813i | ||||||
\(203\) | − | 6.89898i | − | 0.484213i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.44949 | + | 0.247449i | −0.171080 | + | 0.0172826i | ||||
\(206\) | 12.8990 | 0.898714 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 4.44949i | − | 0.308517i | ||||||
\(209\) | −7.59592 | −0.525421 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000 | 0.826114 | 0.413057 | − | 0.910705i | \(-0.364461\pi\) | ||||
0.413057 | + | 0.910705i | \(0.364461\pi\) | |||||||
\(212\) | 10.8990i | 0.748545i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.00000 | −0.546869 | ||||||||
\(215\) | −0.202041 | − | 2.00000i | −0.0137791 | − | 0.136399i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 8.89898i | − | 0.604102i | ||||||
\(218\) | − | 6.89898i | − | 0.467258i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.8990 | − | 1.10102i | 0.734809 | − | 0.0742308i | ||||
\(221\) | −8.89898 | −0.598610 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.7980 | −1.31694 | ||||||||
\(227\) | − | 7.34847i | − | 0.487735i | −0.969809 | − | 0.243868i | \(-0.921584\pi\) | ||
0.969809 | − | 0.243868i | \(-0.0784162\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.1464 | 1.26523 | 0.632616 | − | 0.774466i | \(-0.281981\pi\) | ||||
0.632616 | + | 0.774466i | \(0.281981\pi\) | |||||||
\(230\) | 6.44949 | − | 0.651531i | 0.425267 | − | 0.0429607i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − | 6.89898i | − | 0.452940i | ||||||
\(233\) | 29.7980i | 1.95213i | 0.217481 | + | 0.976065i | \(0.430216\pi\) | ||||
−0.217481 | + | 0.976065i | \(0.569784\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.00000 | + | 19.7980i | 0.130466 | + | 1.29148i | ||||
\(236\) | 1.55051 | 0.100930 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.00000i | − | 0.129641i | ||||||
\(239\) | −6.20204 | −0.401177 | −0.200588 | − | 0.979676i | \(-0.564285\pi\) | ||||
−0.200588 | + | 0.979676i | \(0.564285\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.69694 | −0.560219 | −0.280110 | − | 0.959968i | \(-0.590371\pi\) | ||||
−0.280110 | + | 0.959968i | \(0.590371\pi\) | |||||||
\(242\) | 13.0000i | 0.835672i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.55051 | −0.227298 | ||||||||
\(245\) | 2.22474 | − | 0.224745i | 0.142134 | − | 0.0143584i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.89898i | 0.438972i | ||||||||
\(248\) | − | 8.89898i | − | 0.565086i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.32577 | − | 10.6742i | −0.210340 | − | 0.675098i | ||||
\(251\) | 6.44949 | 0.407088 | 0.203544 | − | 0.979066i | \(-0.434754\pi\) | ||||
0.203544 | + | 0.979066i | \(0.434754\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2020i | 0.892875i | ||||||||
\(254\) | 14.8990 | 0.934845 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.69694i | 0.542500i | 0.962509 | + | 0.271250i | \(0.0874370\pi\) | ||||
−0.962509 | + | 0.271250i | \(0.912563\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.00000 | 0.124274 | ||||||||
\(260\) | −1.00000 | − | 9.89898i | −0.0620174 | − | 0.613909i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.44949i | 0.398451i | ||||||||
\(263\) | 9.79796i | 0.604168i | 0.953281 | + | 0.302084i | \(0.0976823\pi\) | ||||
−0.953281 | + | 0.302084i | \(0.902318\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.44949 | + | 24.2474i | 0.150471 | + | 1.48951i | ||||
\(266\) | −1.55051 | −0.0950679 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 8.00000i | 0.488678i | ||||||||
\(269\) | 19.1464 | 1.16738 | 0.583689 | − | 0.811977i | \(-0.301609\pi\) | ||||
0.583689 | + | 0.811977i | \(0.301609\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0000 | 0.728948 | 0.364474 | − | 0.931214i | \(-0.381249\pi\) | ||||
0.364474 | + | 0.931214i | \(0.381249\pi\) | |||||||
\(272\) | − | 2.00000i | − | 0.121268i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.79796 | −0.108619 | ||||||||
\(275\) | 24.0000 | − | 4.89898i | 1.44725 | − | 0.295420i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 14.8990i | − | 0.895193i | −0.894236 | − | 0.447596i | \(-0.852280\pi\) | ||
0.894236 | − | 0.447596i | \(-0.147720\pi\) | |||||||
\(278\) | − | 1.55051i | − | 0.0929934i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.22474 | − | 0.224745i | 0.132954 | − | 0.0134311i | ||||
\(281\) | 18.0000 | 1.07379 | 0.536895 | − | 0.843649i | \(-0.319597\pi\) | ||||
0.536895 | + | 0.843649i | \(0.319597\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 3.75255i | − | 0.223066i | −0.993761 | − | 0.111533i | \(-0.964424\pi\) | ||
0.993761 | − | 0.111533i | \(-0.0355761\pi\) | |||||||
\(284\) | −1.10102 | −0.0653335 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 21.7980 | 1.28894 | ||||||||
\(287\) | − | 1.10102i | − | 0.0649912i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | −1.55051 | − | 15.3485i | −0.0910491 | − | 0.901293i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.89898i | 0.169650i | ||||||||
\(293\) | 18.2474i | 1.06603i | 0.846107 | + | 0.533014i | \(0.178941\pi\) | ||||
−0.846107 | + | 0.533014i | \(0.821059\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44949 | − | 0.348469i | 0.200837 | − | 0.0202887i | ||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 3.79796i | − | 0.220010i | ||||||
\(299\) | 12.8990 | 0.745967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.898979 | 0.0518163 | ||||||||
\(302\) | 19.5959i | 1.12762i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.55051 | −0.0889279 | ||||||||
\(305\) | −7.89898 | + | 0.797959i | −0.452294 | + | 0.0456910i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.2474i | − | 1.15558i | −0.816184 | − | 0.577791i | \(-0.803915\pi\) | ||
0.816184 | − | 0.577791i | \(-0.196085\pi\) | |||||||
\(308\) | 4.89898i | 0.279145i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.00000 | − | 19.7980i | −0.113592 | − | 1.12445i | ||||
\(311\) | −12.0000 | −0.680458 | −0.340229 | − | 0.940343i | \(-0.610505\pi\) | ||||
−0.340229 | + | 0.940343i | \(0.610505\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.5959i | 1.22067i | 0.792142 | + | 0.610337i | \(0.208966\pi\) | ||||
−0.792142 | + | 0.610337i | \(0.791034\pi\) | |||||||
\(314\) | −3.55051 | −0.200367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.89898 | 0.388098 | ||||||||
\(317\) | 22.4949i | 1.26344i | 0.775197 | + | 0.631720i | \(0.217651\pi\) | ||||
−0.775197 | + | 0.631720i | \(0.782349\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.7980 | 1.89232 | ||||||||
\(320\) | 2.22474 | − | 0.224745i | 0.124367 | − | 0.0125636i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.89898i | 0.161554i | ||||||||
\(323\) | 3.10102i | 0.172545i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.44949 | − | 21.7980i | −0.246813 | − | 1.20913i | ||||
\(326\) | −7.10102 | −0.393289 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 1.10102i | − | 0.0607937i | ||||||
\(329\) | −8.89898 | −0.490617 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −18.6969 | −1.02768 | −0.513838 | − | 0.857887i | \(-0.671777\pi\) | ||||
−0.513838 | + | 0.857887i | \(0.671777\pi\) | |||||||
\(332\) | 2.44949i | 0.134433i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.89898 | −0.268060 | ||||||||
\(335\) | 1.79796 | + | 17.7980i | 0.0982330 | + | 0.972406i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.59592i | 0.522723i | 0.965241 | + | 0.261361i | \(0.0841715\pi\) | ||||
−0.965241 | + | 0.261361i | \(0.915829\pi\) | |||||||
\(338\) | − | 6.79796i | − | 0.369760i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.449490 | − | 4.44949i | −0.0243770 | − | 0.241307i | ||||
\(341\) | 43.5959 | 2.36085 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 0.898979 | 0.0484697 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.24745 | 0.335865 | ||||||||
\(347\) | − | 28.8990i | − | 1.55138i | −0.631115 | − | 0.775689i | \(-0.717402\pi\) | ||
0.631115 | − | 0.775689i | \(-0.282598\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.44949 | 0.452291 | 0.226145 | − | 0.974094i | \(-0.427388\pi\) | ||||
0.226145 | + | 0.974094i | \(0.427388\pi\) | |||||||
\(350\) | 4.89898 | − | 1.00000i | 0.261861 | − | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.89898i | 0.261116i | ||||||||
\(353\) | 22.8990i | 1.21879i | 0.792867 | + | 0.609395i | \(0.208588\pi\) | ||||
−0.792867 | + | 0.609395i | \(0.791412\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.44949 | + | 0.247449i | −0.130005 | + | 0.0131332i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 13.7980i | 0.729245i | ||||||||
\(359\) | −27.5959 | −1.45646 | −0.728228 | − | 0.685334i | \(-0.759656\pi\) | ||||
−0.728228 | + | 0.685334i | \(0.759656\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.5959 | −0.873469 | ||||||||
\(362\) | − | 10.2474i | − | 0.538594i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.44949 | 0.233217 | ||||||||
\(365\) | 0.651531 | + | 6.44949i | 0.0341027 | + | 0.337582i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 32.0000i | 1.67039i | 0.549957 | + | 0.835193i | \(0.314644\pi\) | ||||
−0.549957 | + | 0.835193i | \(0.685356\pi\) | |||||||
\(368\) | 2.89898i | 0.151120i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.44949 | − | 0.449490i | 0.231318 | − | 0.0233679i | ||||
\(371\) | −10.8990 | −0.565847 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.69694i | 0.243198i | 0.992579 | + | 0.121599i | \(0.0388022\pi\) | ||||
−0.992579 | + | 0.121599i | \(0.961198\pi\) | |||||||
\(374\) | 9.79796 | 0.506640 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.89898 | −0.458930 | ||||||||
\(377\) | − | 30.6969i | − | 1.58097i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −30.6969 | −1.57680 | −0.788398 | − | 0.615166i | \(-0.789089\pi\) | ||||
−0.788398 | + | 0.615166i | \(0.789089\pi\) | |||||||
\(380\) | −3.44949 | + | 0.348469i | −0.176955 | + | 0.0178761i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 12.6969i | − | 0.649632i | ||||||
\(383\) | − | 7.10102i | − | 0.362845i | −0.983405 | − | 0.181423i | \(-0.941930\pi\) | ||
0.983405 | − | 0.181423i | \(-0.0580702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.10102 | + | 10.8990i | 0.0561132 | + | 0.555463i | ||||
\(386\) | −21.5959 | −1.09920 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 15.7980i | − | 0.802020i | ||||||
\(389\) | 13.1010 | 0.664248 | 0.332124 | − | 0.943236i | \(-0.392235\pi\) | ||||
0.332124 | + | 0.943236i | \(0.392235\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.79796 | 0.293215 | ||||||||
\(392\) | 1.00000i | 0.0505076i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 18.8990 | 0.952117 | ||||||||
\(395\) | 15.3485 | − | 1.55051i | 0.772265 | − | 0.0780146i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.65153i | − | 0.133077i | −0.997784 | − | 0.0665383i | \(-0.978805\pi\) | ||
0.997784 | − | 0.0665383i | \(-0.0211954\pi\) | |||||||
\(398\) | − | 16.8990i | − | 0.847069i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.89898 | − | 1.00000i | 0.244949 | − | 0.0500000i | ||||
\(401\) | 29.3939 | 1.46786 | 0.733930 | − | 0.679225i | \(-0.237684\pi\) | ||||
0.733930 | + | 0.679225i | \(0.237684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 39.5959i | − | 1.97241i | ||||||
\(404\) | 3.55051 | 0.176644 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.89898 | 0.342391 | ||||||||
\(407\) | 9.79796i | 0.485667i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.4949 | −1.70566 | −0.852831 | − | 0.522186i | \(-0.825117\pi\) | ||||
−0.852831 | + | 0.522186i | \(0.825117\pi\) | |||||||
\(410\) | −0.247449 | − | 2.44949i | −0.0122206 | − | 0.120972i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.8990i | 0.635487i | ||||||||
\(413\) | 1.55051i | 0.0762956i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.550510 | + | 5.44949i | 0.0270235 | + | 0.267505i | ||||
\(416\) | 4.44949 | 0.218154 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 7.59592i | − | 0.371528i | ||||||
\(419\) | −1.55051 | −0.0757474 | −0.0378737 | − | 0.999283i | \(-0.512058\pi\) | ||||
−0.0378737 | + | 0.999283i | \(0.512058\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.20204 | −0.204795 | −0.102397 | − | 0.994744i | \(-0.532651\pi\) | ||||
−0.102397 | + | 0.994744i | \(0.532651\pi\) | |||||||
\(422\) | 12.0000i | 0.584151i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.8990 | −0.529301 | ||||||||
\(425\) | −2.00000 | − | 9.79796i | −0.0970143 | − | 0.475271i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.55051i | − | 0.171821i | ||||||
\(428\) | − | 8.00000i | − | 0.386695i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.00000 | − | 0.202041i | 0.0964486 | − | 0.00974328i | ||||
\(431\) | 1.79796 | 0.0866046 | 0.0433023 | − | 0.999062i | \(-0.486212\pi\) | ||||
0.0433023 | + | 0.999062i | \(0.486212\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.202041i | 0.00970947i | 0.999988 | + | 0.00485474i | \(0.00154532\pi\) | ||||
−0.999988 | + | 0.00485474i | \(0.998455\pi\) | |||||||
\(434\) | 8.89898 | 0.427165 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.89898 | 0.330401 | ||||||||
\(437\) | − | 4.49490i | − | 0.215020i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3939 | 1.02107 | 0.510537 | − | 0.859856i | \(-0.329447\pi\) | ||||
0.510537 | + | 0.859856i | \(0.329447\pi\) | |||||||
\(440\) | 1.10102 | + | 10.8990i | 0.0524891 | + | 0.519588i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 8.89898i | − | 0.423281i | ||||||
\(443\) | 9.79796i | 0.465515i | 0.972535 | + | 0.232758i | \(0.0747749\pi\) | ||||
−0.972535 | + | 0.232758i | \(0.925225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.2474 | − | 2.24745i | 1.05463 | − | 0.106539i | ||||
\(446\) | −4.00000 | −0.189405 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000i | 0.0472456i | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.39388 | 0.253988 | ||||||||
\(452\) | − | 19.7980i | − | 0.931218i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.34847 | 0.344881 | ||||||||
\(455\) | 9.89898 | − | 1.00000i | 0.464071 | − | 0.0468807i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.5959i | 1.38444i | 0.721687 | + | 0.692219i | \(0.243367\pi\) | ||||
−0.721687 | + | 0.692219i | \(0.756633\pi\) | |||||||
\(458\) | 19.1464i | 0.894654i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.651531 | + | 6.44949i | 0.0303778 | + | 0.300709i | ||||
\(461\) | −17.3485 | −0.807999 | −0.403999 | − | 0.914759i | \(-0.632380\pi\) | ||||
−0.403999 | + | 0.914759i | \(0.632380\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 3.59592i | − | 0.167116i | −0.996503 | − | 0.0835582i | \(-0.973372\pi\) | ||
0.996503 | − | 0.0835582i | \(-0.0266285\pi\) | |||||||
\(464\) | 6.89898 | 0.320277 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −29.7980 | −1.38036 | ||||||||
\(467\) | − | 10.4495i | − | 0.483545i | −0.970333 | − | 0.241772i | \(-0.922271\pi\) | ||
0.970333 | − | 0.241772i | \(-0.0777287\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.00000 | −0.369406 | ||||||||
\(470\) | −19.7980 | + | 2.00000i | −0.913212 | + | 0.0922531i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.55051i | 0.0713680i | ||||||||
\(473\) | 4.40408i | 0.202500i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.59592 | + | 1.55051i | −0.348525 | + | 0.0711423i | ||||
\(476\) | 2.00000 | 0.0916698 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 6.20204i | − | 0.283675i | ||||||
\(479\) | 9.30306 | 0.425068 | 0.212534 | − | 0.977154i | \(-0.431828\pi\) | ||||
0.212534 | + | 0.977154i | \(0.431828\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.89898 | 0.405759 | ||||||||
\(482\) | − | 8.69694i | − | 0.396135i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.0000 | −0.590909 | ||||||||
\(485\) | −3.55051 | − | 35.1464i | −0.161220 | − | 1.59592i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 7.30306i | − | 0.330933i | −0.986215 | − | 0.165467i | \(-0.947087\pi\) | ||
0.986215 | − | 0.165467i | \(-0.0529130\pi\) | |||||||
\(488\) | − | 3.55051i | − | 0.160724i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.224745 | + | 2.22474i | 0.0101529 | + | 0.100504i | ||||
\(491\) | −19.5959 | −0.884351 | −0.442176 | − | 0.896928i | \(-0.645793\pi\) | ||||
−0.442176 | + | 0.896928i | \(0.645793\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 13.7980i | − | 0.621429i | ||||||
\(494\) | −6.89898 | −0.310400 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 8.89898 | 0.399576 | ||||||||
\(497\) | − | 1.10102i | − | 0.0493875i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.20204 | −0.277641 | −0.138821 | − | 0.990318i | \(-0.544331\pi\) | ||||
−0.138821 | + | 0.990318i | \(0.544331\pi\) | |||||||
\(500\) | 10.6742 | − | 3.32577i | 0.477366 | − | 0.148733i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.44949i | 0.287855i | ||||||||
\(503\) | − | 4.00000i | − | 0.178351i | −0.996016 | − | 0.0891756i | \(-0.971577\pi\) | ||
0.996016 | − | 0.0891756i | \(-0.0284232\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.89898 | − | 0.797959i | 0.351500 | − | 0.0355087i | ||||
\(506\) | −14.2020 | −0.631358 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.8990i | 0.661035i | ||||||||
\(509\) | −31.5505 | −1.39845 | −0.699226 | − | 0.714901i | \(-0.746472\pi\) | ||||
−0.699226 | + | 0.714901i | \(0.746472\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.89898 | −0.128243 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −8.69694 | −0.383606 | ||||||||
\(515\) | 2.89898 | + | 28.6969i | 0.127744 | + | 1.26454i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43.5959i | − | 1.91735i | ||||||
\(518\) | 2.00000i | 0.0878750i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.89898 | − | 1.00000i | 0.434099 | − | 0.0438529i | ||||
\(521\) | −32.6969 | −1.43248 | −0.716239 | − | 0.697855i | \(-0.754138\pi\) | ||||
−0.716239 | + | 0.697855i | \(0.754138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 33.1464i | 1.44939i | 0.689069 | + | 0.724696i | \(0.258020\pi\) | ||||
−0.689069 | + | 0.724696i | \(0.741980\pi\) | |||||||
\(524\) | −6.44949 | −0.281747 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9.79796 | −0.427211 | ||||||||
\(527\) | − | 17.7980i | − | 0.775291i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 14.5959 | 0.634605 | ||||||||
\(530\) | −24.2474 | + | 2.44949i | −1.05324 | + | 0.106399i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 1.55051i | − | 0.0672231i | ||||||
\(533\) | − | 4.89898i | − | 0.212198i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.79796 | − | 17.7980i | −0.0777325 | − | 0.769473i | ||||
\(536\) | −8.00000 | −0.345547 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 19.1464i | 0.825461i | ||||||||
\(539\) | −4.89898 | −0.211014 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.59592 | 0.412561 | 0.206280 | − | 0.978493i | \(-0.433864\pi\) | ||||
0.206280 | + | 0.978493i | \(0.433864\pi\) | |||||||
\(542\) | 12.0000i | 0.515444i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.00000 | 0.0857493 | ||||||||
\(545\) | 15.3485 | − | 1.55051i | 0.657456 | − | 0.0664166i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.6969i | − | 0.799423i | −0.916641 | − | 0.399712i | \(-0.869110\pi\) | ||
0.916641 | − | 0.399712i | \(-0.130890\pi\) | |||||||
\(548\) | − | 1.79796i | − | 0.0768050i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.89898 | + | 24.0000i | 0.208893 | + | 1.02336i | ||||
\(551\) | −10.6969 | −0.455705 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.89898i | 0.293374i | ||||||||
\(554\) | 14.8990 | 0.632997 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.55051 | 0.0657563 | ||||||||
\(557\) | − | 12.6969i | − | 0.537987i | −0.963142 | − | 0.268993i | \(-0.913309\pi\) | ||
0.963142 | − | 0.268993i | \(-0.0866909\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0.224745 | + | 2.22474i | 0.00949720 | + | 0.0940126i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 18.0000i | 0.759284i | ||||||||
\(563\) | − | 30.0454i | − | 1.26626i | −0.774044 | − | 0.633131i | \(-0.781769\pi\) | ||
0.774044 | − | 0.633131i | \(-0.218231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.44949 | − | 44.0454i | −0.187191 | − | 1.85300i | ||||
\(566\) | 3.75255 | 0.157731 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.10102i | − | 0.0461978i | ||||||
\(569\) | 33.7980 | 1.41688 | 0.708442 | − | 0.705769i | \(-0.249398\pi\) | ||||
0.708442 | + | 0.705769i | \(0.249398\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1010 | −0.464563 | −0.232282 | − | 0.972649i | \(-0.574619\pi\) | ||||
−0.232282 | + | 0.972649i | \(0.574619\pi\) | |||||||
\(572\) | 21.7980i | 0.911418i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.10102 | 0.0459557 | ||||||||
\(575\) | 2.89898 | + | 14.2020i | 0.120896 | + | 0.592266i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 2.49490i | − | 0.103864i | −0.998651 | − | 0.0519320i | \(-0.983462\pi\) | ||
0.998651 | − | 0.0519320i | \(-0.0165379\pi\) | |||||||
\(578\) | 13.0000i | 0.540729i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 15.3485 | − | 1.55051i | 0.637310 | − | 0.0643814i | ||||
\(581\) | −2.44949 | −0.101622 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 53.3939i | − | 2.21135i | ||||||
\(584\) | −2.89898 | −0.119961 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −18.2474 | −0.753795 | ||||||||
\(587\) | − | 1.14643i | − | 0.0473182i | −0.999720 | − | 0.0236591i | \(-0.992468\pi\) | ||
0.999720 | − | 0.0236591i | \(-0.00753162\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.7980 | −0.568535 | ||||||||
\(590\) | 0.348469 | + | 3.44949i | 0.0143463 | + | 0.142013i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.00000i | 0.0821995i | ||||||||
\(593\) | − | 10.8990i | − | 0.447567i | −0.974639 | − | 0.223784i | \(-0.928159\pi\) | ||
0.974639 | − | 0.223784i | \(-0.0718409\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.44949 | − | 0.449490i | 0.182411 | − | 0.0184273i | ||||
\(596\) | 3.79796 | 0.155570 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.8990i | 0.527478i | ||||||||
\(599\) | −13.1010 | −0.535293 | −0.267647 | − | 0.963517i | \(-0.586246\pi\) | ||||
−0.267647 | + | 0.963517i | \(0.586246\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.3939 | −1.60691 | −0.803455 | − | 0.595366i | \(-0.797007\pi\) | ||||
−0.803455 | + | 0.595366i | \(0.797007\pi\) | |||||||
\(602\) | 0.898979i | 0.0366397i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.5959 | −0.797347 | ||||||||
\(605\) | −28.9217 | + | 2.92168i | −1.17583 | + | 0.118783i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.3939i | 1.35542i | 0.735331 | + | 0.677708i | \(0.237027\pi\) | ||||
−0.735331 | + | 0.677708i | \(0.762973\pi\) | |||||||
\(608\) | − | 1.55051i | − | 0.0628815i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.797959 | − | 7.89898i | −0.0323084 | − | 0.319820i | ||||
\(611\) | −39.5959 | −1.60188 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 27.7980i | 1.12275i | 0.827562 | + | 0.561374i | \(0.189727\pi\) | ||||
−0.827562 | + | 0.561374i | \(0.810273\pi\) | |||||||
\(614\) | 20.2474 | 0.817121 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.89898 | −0.197386 | ||||||||
\(617\) | − | 29.5959i | − | 1.19149i | −0.803175 | − | 0.595743i | \(-0.796858\pi\) | ||
0.803175 | − | 0.595743i | \(-0.203142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.5505 | 1.67006 | 0.835028 | − | 0.550207i | \(-0.185451\pi\) | ||||
0.835028 | + | 0.550207i | \(0.185451\pi\) | |||||||
\(620\) | 19.7980 | − | 2.00000i | 0.795105 | − | 0.0803219i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 12.0000i | − | 0.481156i | ||||||
\(623\) | 10.0000i | 0.400642i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.0000 | − | 9.79796i | 0.920000 | − | 0.391918i | ||||
\(626\) | −21.5959 | −0.863146 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 3.55051i | − | 0.141681i | ||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −42.4949 | −1.69170 | −0.845848 | − | 0.533425i | \(-0.820905\pi\) | ||||
−0.845848 | + | 0.533425i | \(0.820905\pi\) | |||||||
\(632\) | 6.89898i | 0.274427i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −22.4949 | −0.893387 | ||||||||
\(635\) | 3.34847 | + | 33.1464i | 0.132880 | + | 1.31538i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.44949i | 0.176295i | ||||||||
\(638\) | 33.7980i | 1.33807i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.224745 | + | 2.22474i | 0.00888382 | + | 0.0879408i | ||||
\(641\) | −25.7980 | −1.01896 | −0.509479 | − | 0.860483i | \(-0.670162\pi\) | ||||
−0.509479 | + | 0.860483i | \(0.670162\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 25.1464i | − | 0.991678i | −0.868414 | − | 0.495839i | \(-0.834861\pi\) | ||
0.868414 | − | 0.495839i | \(-0.165139\pi\) | |||||||
\(644\) | −2.89898 | −0.114236 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.10102 | −0.122008 | ||||||||
\(647\) | 46.2929i | 1.81996i | 0.414652 | + | 0.909980i | \(0.363903\pi\) | ||||
−0.414652 | + | 0.909980i | \(0.636097\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7.59592 | −0.298166 | ||||||||
\(650\) | 21.7980 | − | 4.44949i | 0.854986 | − | 0.174523i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 7.10102i | − | 0.278097i | ||||||
\(653\) | − | 20.2020i | − | 0.790567i | −0.918559 | − | 0.395283i | \(-0.870646\pi\) | ||
0.918559 | − | 0.395283i | \(-0.129354\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −14.3485 | + | 1.44949i | −0.560641 | + | 0.0566363i | ||||
\(656\) | 1.10102 | 0.0429876 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 8.89898i | − | 0.346918i | ||||||
\(659\) | 16.8990 | 0.658291 | 0.329145 | − | 0.944279i | \(-0.393239\pi\) | ||||
0.329145 | + | 0.944279i | \(0.393239\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.9444 | −1.59255 | −0.796276 | − | 0.604933i | \(-0.793200\pi\) | ||||
−0.796276 | + | 0.604933i | \(0.793200\pi\) | |||||||
\(662\) | − | 18.6969i | − | 0.726677i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.44949 | −0.0950586 | ||||||||
\(665\) | −0.348469 | − | 3.44949i | −0.0135131 | − | 0.133765i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20.0000i | 0.774403i | ||||||||
\(668\) | − | 4.89898i | − | 0.189547i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −17.7980 | + | 1.79796i | −0.687595 | + | 0.0694612i | ||||
\(671\) | 17.3939 | 0.671483 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 17.7980i | 0.686061i | 0.939324 | + | 0.343030i | \(0.111453\pi\) | ||||
−0.939324 | + | 0.343030i | \(0.888547\pi\) | |||||||
\(674\) | −9.59592 | −0.369621 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.79796 | 0.261460 | ||||||||
\(677\) | 36.4495i | 1.40087i | 0.713717 | + | 0.700434i | \(0.247010\pi\) | ||||
−0.713717 | + | 0.700434i | \(0.752990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7980 | 0.606270 | ||||||||
\(680\) | 4.44949 | − | 0.449490i | 0.170630 | − | 0.0172371i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 43.5959i | 1.66937i | ||||||||
\(683\) | 3.59592i | 0.137594i | 0.997631 | + | 0.0687970i | \(0.0219161\pi\) | ||||
−0.997631 | + | 0.0687970i | \(0.978084\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.404082 | − | 4.00000i | −0.0154392 | − | 0.152832i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0.898979i | 0.0342733i | ||||||||
\(689\) | −48.4949 | −1.84751 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.1464 | 0.804448 | 0.402224 | − | 0.915541i | \(-0.368237\pi\) | ||||
0.402224 | + | 0.915541i | \(0.368237\pi\) | |||||||
\(692\) | 6.24745i | 0.237492i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.8990 | 1.09699 | ||||||||
\(695\) | 3.44949 | − | 0.348469i | 0.130847 | − | 0.0132182i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 2.20204i | − | 0.0834083i | ||||||
\(698\) | 8.44949i | 0.319818i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | + | 4.89898i | 0.0377964 | + | 0.185164i | ||||
\(701\) | −11.3031 | −0.426911 | −0.213455 | − | 0.976953i | \(-0.568472\pi\) | ||||
−0.213455 | + | 0.976953i | \(0.568472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.10102i | − | 0.116957i | ||||||
\(704\) | −4.89898 | −0.184637 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.8990 | −0.861814 | ||||||||
\(707\) | 3.55051i | 0.133531i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.2929 | 1.06256 | 0.531280 | − | 0.847196i | \(-0.321711\pi\) | ||||
0.531280 | + | 0.847196i | \(0.321711\pi\) | |||||||
\(710\) | −0.247449 | − | 2.44949i | −0.00928658 | − | 0.0919277i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 25.7980i | 0.966141i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.89898 | + | 48.4949i | 0.183211 | + | 1.81361i | ||||
\(716\) | −13.7980 | −0.515654 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 27.5959i | − | 1.02987i | ||||||
\(719\) | −4.49490 | −0.167631 | −0.0838157 | − | 0.996481i | \(-0.526711\pi\) | ||||
−0.0838157 | + | 0.996481i | \(0.526711\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.8990 | −0.480383 | ||||||||
\(722\) | − | 16.5959i | − | 0.617636i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 10.2474 | 0.380843 | ||||||||
\(725\) | 33.7980 | − | 6.89898i | 1.25522 | − | 0.256222i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 22.6969i | 0.841783i | 0.907111 | + | 0.420891i | \(0.138283\pi\) | ||||
−0.907111 | + | 0.420891i | \(0.861717\pi\) | |||||||
\(728\) | 4.44949i | 0.164909i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.44949 | + | 0.651531i | −0.238706 | + | 0.0241142i | ||||
\(731\) | 1.79796 | 0.0664999 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.6413i | − | 1.46419i | −0.681205 | − | 0.732093i | \(-0.738544\pi\) | ||
0.681205 | − | 0.732093i | \(-0.261456\pi\) | |||||||
\(734\) | −32.0000 | −1.18114 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.89898 | −0.106858 | ||||||||
\(737\) | − | 39.1918i | − | 1.44365i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.49490 | −0.165347 | −0.0826737 | − | 0.996577i | \(-0.526346\pi\) | ||||
−0.0826737 | + | 0.996577i | \(0.526346\pi\) | |||||||
\(740\) | 0.449490 | + | 4.44949i | 0.0165236 | + | 0.163566i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 10.8990i | − | 0.400114i | ||||||
\(743\) | − | 44.6969i | − | 1.63977i | −0.572527 | − | 0.819886i | \(-0.694037\pi\) | ||
0.572527 | − | 0.819886i | \(-0.305963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.44949 | − | 0.853572i | 0.309565 | − | 0.0312725i | ||||
\(746\) | −4.69694 | −0.171967 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.79796i | 0.358249i | ||||||||
\(749\) | 8.00000 | 0.292314 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −41.7980 | −1.52523 | −0.762615 | − | 0.646853i | \(-0.776085\pi\) | ||||
−0.762615 | + | 0.646853i | \(0.776085\pi\) | |||||||
\(752\) | − | 8.89898i | − | 0.324512i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 30.6969 | 1.11792 | ||||||||
\(755\) | −43.5959 | + | 4.40408i | −1.58662 | + | 0.160281i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 51.7980i | − | 1.88263i | −0.337531 | − | 0.941314i | \(-0.609592\pi\) | ||
0.337531 | − | 0.941314i | \(-0.390408\pi\) | |||||||
\(758\) | − | 30.6969i | − | 1.11496i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.348469 | − | 3.44949i | −0.0126403 | − | 0.125126i | ||||
\(761\) | 21.1010 | 0.764911 | 0.382456 | − | 0.923974i | \(-0.375078\pi\) | ||||
0.382456 | + | 0.923974i | \(0.375078\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.89898i | 0.249760i | ||||||||
\(764\) | 12.6969 | 0.459359 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.10102 | 0.256570 | ||||||||
\(767\) | 6.89898i | 0.249108i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 40.6969 | 1.46757 | 0.733785 | − | 0.679382i | \(-0.237752\pi\) | ||||
0.733785 | + | 0.679382i | \(0.237752\pi\) | |||||||
\(770\) | −10.8990 | + | 1.10102i | −0.392772 | + | 0.0396780i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 21.5959i | − | 0.777254i | ||||||
\(773\) | 1.34847i | 0.0485011i | 0.999706 | + | 0.0242505i | \(0.00771994\pi\) | ||||
−0.999706 | + | 0.0242505i | \(0.992280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 43.5959 | − | 8.89898i | 1.56601 | − | 0.319661i | ||||
\(776\) | 15.7980 | 0.567114 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.1010i | 0.469694i | ||||||||
\(779\) | −1.70714 | −0.0611648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.39388 | 0.193008 | ||||||||
\(782\) | 5.79796i | 0.207335i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.00000 | −0.0357143 | ||||||||
\(785\) | −0.797959 | − | 7.89898i | −0.0284804 | − | 0.281927i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 50.4495i | 1.79833i | 0.437610 | + | 0.899165i | \(0.355825\pi\) | ||||
−0.437610 | + | 0.899165i | \(0.644175\pi\) | |||||||
\(788\) | 18.8990i | 0.673248i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.55051 | + | 15.3485i | 0.0551647 | + | 0.546074i | ||||
\(791\) | 19.7980 | 0.703934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 15.7980i | − | 0.561002i | ||||||
\(794\) | 2.65153 | 0.0940993 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.8990 | 0.598968 | ||||||||
\(797\) | 0.944387i | 0.0334519i | 0.999860 | + | 0.0167260i | \(0.00532429\pi\) | ||||
−0.999860 | + | 0.0167260i | \(0.994676\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17.7980 | −0.629647 | ||||||||
\(800\) | 1.00000 | + | 4.89898i | 0.0353553 | + | 0.173205i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.3939i | 1.03793i | ||||||||
\(803\) | − | 14.2020i | − | 0.501179i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.44949 | + | 0.651531i | −0.227315 | + | 0.0229634i | ||||
\(806\) | 39.5959 | 1.39471 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.55051i | 0.124907i | ||||||||
\(809\) | 47.5959 | 1.67338 | 0.836692 | − | 0.547674i | \(-0.184487\pi\) | ||||
0.836692 | + | 0.547674i | \(0.184487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.9444 | 0.524768 | 0.262384 | − | 0.964963i | \(-0.415491\pi\) | ||||
0.262384 | + | 0.964963i | \(0.415491\pi\) | |||||||
\(812\) | 6.89898i | 0.242107i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −9.79796 | −0.343418 | ||||||||
\(815\) | −1.59592 | − | 15.7980i | −0.0559026 | − | 0.553378i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 1.39388i | − | 0.0487656i | ||||||
\(818\) | − | 34.4949i | − | 1.20609i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.44949 | − | 0.247449i | 0.0855399 | − | 0.00864128i | ||||
\(821\) | −8.20204 | −0.286253 | −0.143127 | − | 0.989704i | \(-0.545716\pi\) | ||||
−0.143127 | + | 0.989704i | \(0.545716\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.1918i | 1.36614i | 0.730352 | + | 0.683071i | \(0.239356\pi\) | ||||
−0.730352 | + | 0.683071i | \(0.760644\pi\) | |||||||
\(824\) | −12.8990 | −0.449357 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.55051 | −0.0539492 | ||||||||
\(827\) | 15.5959i | 0.542323i | 0.962534 | + | 0.271162i | \(0.0874078\pi\) | ||||
−0.962534 | + | 0.271162i | \(0.912592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.6413 | 1.51573 | 0.757863 | − | 0.652414i | \(-0.226244\pi\) | ||||
0.757863 | + | 0.652414i | \(0.226244\pi\) | |||||||
\(830\) | −5.44949 | + | 0.550510i | −0.189155 | + | 0.0191085i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.44949i | 0.154258i | ||||||||
\(833\) | 2.00000i | 0.0692959i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.10102 | − | 10.8990i | −0.0381024 | − | 0.377175i | ||||
\(836\) | 7.59592 | 0.262710 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 1.55051i | − | 0.0535615i | ||||||
\(839\) | 36.8990 | 1.27389 | 0.636947 | − | 0.770907i | \(-0.280197\pi\) | ||||
0.636947 | + | 0.770907i | \(0.280197\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 18.5959 | 0.641239 | ||||||||
\(842\) | − | 4.20204i | − | 0.144812i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −12.0000 | −0.413057 | ||||||||
\(845\) | 15.1237 | − | 1.52781i | 0.520272 | − | 0.0525581i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 13.0000i | − | 0.446685i | ||||||
\(848\) | − | 10.8990i | − | 0.374272i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.79796 | − | 2.00000i | 0.336067 | − | 0.0685994i | ||||
\(851\) | −5.79796 | −0.198751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.8434i | 1.15877i | 0.815052 | + | 0.579387i | \(0.196708\pi\) | ||||
−0.815052 | + | 0.579387i | \(0.803292\pi\) | |||||||
\(854\) | 3.55051 | 0.121496 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 8.00000 | 0.273434 | ||||||||
\(857\) | 53.1918i | 1.81700i | 0.417886 | + | 0.908499i | \(0.362771\pi\) | ||||
−0.417886 | + | 0.908499i | \(0.637229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −53.6413 | −1.83022 | −0.915109 | − | 0.403206i | \(-0.867896\pi\) | ||||
−0.915109 | + | 0.403206i | \(0.867896\pi\) | |||||||
\(860\) | 0.202041 | + | 2.00000i | 0.00688954 | + | 0.0681994i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.79796i | 0.0612387i | ||||||||
\(863\) | − | 45.3939i | − | 1.54523i | −0.634878 | − | 0.772613i | \(-0.718949\pi\) | ||
0.634878 | − | 0.772613i | \(-0.281051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40408 | + | 13.8990i | 0.0477402 | + | 0.472579i | ||||
\(866\) | −0.202041 | −0.00686563 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.89898i | 0.302051i | ||||||||
\(869\) | −33.7980 | −1.14652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −35.5959 | −1.20612 | ||||||||
\(872\) | 6.89898i | 0.233629i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.49490 | 0.152042 | ||||||||
\(875\) | 3.32577 | + | 10.6742i | 0.112431 | + | 0.360855i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 39.3939i | − | 1.33024i | −0.746738 | − | 0.665118i | \(-0.768381\pi\) | ||
0.746738 | − | 0.665118i | \(-0.231619\pi\) | |||||||
\(878\) | 21.3939i | 0.722008i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.8990 | + | 1.10102i | −0.367405 | + | 0.0371154i | ||||
\(881\) | −8.20204 | −0.276334 | −0.138167 | − | 0.990409i | \(-0.544121\pi\) | ||||
−0.138167 | + | 0.990409i | \(0.544121\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 22.2020i | − | 0.747158i | −0.927598 | − | 0.373579i | \(-0.878130\pi\) | ||
0.927598 | − | 0.373579i | \(-0.121870\pi\) | |||||||
\(884\) | 8.89898 | 0.299305 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.79796 | −0.329169 | ||||||||
\(887\) | − | 2.69694i | − | 0.0905543i | −0.998974 | − | 0.0452772i | \(-0.985583\pi\) | ||
0.998974 | − | 0.0452772i | \(-0.0144171\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.8990 | −0.499696 | ||||||||
\(890\) | 2.24745 | + | 22.2474i | 0.0753347 | + | 0.745736i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 4.00000i | − | 0.133930i | ||||||
\(893\) | 13.7980i | 0.461731i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −30.6969 | + | 3.10102i | −1.02609 | + | 0.103656i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 10.0000i | − | 0.333704i | ||||||
\(899\) | 61.3939 | 2.04760 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21.7980 | −0.726195 | ||||||||
\(902\) | 5.39388i | 0.179596i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.7980 | 0.658470 | ||||||||
\(905\) | 22.7980 | − | 2.30306i | 0.757830 | − | 0.0765564i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 41.7980i | − | 1.38788i | −0.720034 | − | 0.693939i | \(-0.755874\pi\) | ||
0.720034 | − | 0.693939i | \(-0.244126\pi\) | |||||||
\(908\) | 7.34847i | 0.243868i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00000 | + | 9.89898i | 0.0331497 | + | 0.328148i | ||||
\(911\) | 35.5959 | 1.17935 | 0.589673 | − | 0.807642i | \(-0.299257\pi\) | ||||
0.589673 | + | 0.807642i | \(0.299257\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 12.0000i | − | 0.397142i | ||||||
\(914\) | −29.5959 | −0.978946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −19.1464 | −0.632616 | ||||||||
\(917\) | − | 6.44949i | − | 0.212981i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.8990 | 0.887315 | 0.443658 | − | 0.896196i | \(-0.353681\pi\) | ||||
0.443658 | + | 0.896196i | \(0.353681\pi\) | |||||||
\(920\) | −6.44949 | + | 0.651531i | −0.212633 | + | 0.0214803i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 17.3485i | − | 0.571341i | ||||||
\(923\) | − | 4.89898i | − | 0.161252i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.00000 | + | 9.79796i | 0.0657596 | + | 0.322155i | ||||
\(926\) | 3.59592 | 0.118169 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.89898i | 0.226470i | ||||||||
\(929\) | −28.2929 | −0.928259 | −0.464129 | − | 0.885767i | \(-0.653633\pi\) | ||||
−0.464129 | + | 0.885767i | \(0.653633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.55051 | 0.0508159 | ||||||||
\(932\) | − | 29.7980i | − | 0.976065i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.4495 | 0.341918 | ||||||||
\(935\) | 2.20204 | + | 21.7980i | 0.0720144 | + | 0.712869i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 41.1010i | − | 1.34271i | −0.741135 | − | 0.671356i | \(-0.765712\pi\) | ||
0.741135 | − | 0.671356i | \(-0.234288\pi\) | |||||||
\(938\) | − | 8.00000i | − | 0.261209i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.00000 | − | 19.7980i | −0.0652328 | − | 0.645738i | ||||
\(941\) | 19.5505 | 0.637328 | 0.318664 | − | 0.947868i | \(-0.396766\pi\) | ||||
0.318664 | + | 0.947868i | \(0.396766\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.19184i | 0.103940i | ||||||||
\(944\) | −1.55051 | −0.0504648 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −4.40408 | −0.143189 | ||||||||
\(947\) | − | 44.0908i | − | 1.43276i | −0.697711 | − | 0.716379i | \(-0.745798\pi\) | ||
0.697711 | − | 0.716379i | \(-0.254202\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.8990 | −0.418719 | ||||||||
\(950\) | −1.55051 | − | 7.59592i | −0.0503052 | − | 0.246444i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.00000i | 0.0648204i | ||||||||
\(953\) | 2.20204i | 0.0713311i | 0.999364 | + | 0.0356656i | \(0.0113551\pi\) | ||||
−0.999364 | + | 0.0356656i | \(0.988645\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 28.2474 | − | 2.85357i | 0.914066 | − | 0.0923394i | ||||
\(956\) | 6.20204 | 0.200588 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.30306i | 0.300568i | ||||||||
\(959\) | 1.79796 | 0.0580591 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 48.1918 | 1.55458 | ||||||||
\(962\) | 8.89898i | 0.286915i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.69694 | 0.280110 | ||||||||
\(965\) | −4.85357 | − | 48.0454i | −0.156242 | − | 1.54664i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 36.2929i | − | 1.16710i | −0.812077 | − | 0.583550i | \(-0.801663\pi\) | ||
0.812077 | − | 0.583550i | \(-0.198337\pi\) | |||||||
\(968\) | − | 13.0000i | − | 0.417836i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 35.1464 | − | 3.55051i | 1.12848 | − | 0.114000i | ||||
\(971\) | 9.55051 | 0.306490 | 0.153245 | − | 0.988188i | \(-0.451028\pi\) | ||||
0.153245 | + | 0.988188i | \(0.451028\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.55051i | 0.0497071i | ||||||||
\(974\) | 7.30306 | 0.234005 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.55051 | 0.113649 | ||||||||
\(977\) | 29.3939i | 0.940393i | 0.882562 | + | 0.470197i | \(0.155817\pi\) | ||||
−0.882562 | + | 0.470197i | \(0.844183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −48.9898 | −1.56572 | ||||||||
\(980\) | −2.22474 | + | 0.224745i | −0.0710669 | + | 0.00717921i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 19.5959i | − | 0.625331i | ||||||
\(983\) | − | 13.3031i | − | 0.424302i | −0.977237 | − | 0.212151i | \(-0.931953\pi\) | ||
0.977237 | − | 0.212151i | \(-0.0680468\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.24745 | + | 42.0454i | 0.135335 | + | 1.33968i | ||||
\(986\) | 13.7980 | 0.439417 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 6.89898i | − | 0.219486i | ||||||
\(989\) | −2.60612 | −0.0828699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.3031 | 0.994375 | 0.497187 | − | 0.867643i | \(-0.334366\pi\) | ||||
0.497187 | + | 0.867643i | \(0.334366\pi\) | |||||||
\(992\) | 8.89898i | 0.282543i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.10102 | 0.0349223 | ||||||||
\(995\) | 37.5959 | − | 3.79796i | 1.19187 | − | 0.120403i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 57.3485i | 1.81624i | 0.418705 | + | 0.908122i | \(0.362484\pi\) | ||||
−0.418705 | + | 0.908122i | \(0.637516\pi\) | |||||||
\(998\) | − | 6.20204i | − | 0.196322i | ||||||
\(999\) | 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 | 630.2.g.g.379.3 | 4 | ||
3.2 | odd | 2 | 70.2.c.a.29.2 | ✓ | 4 | ||
4.3 | odd | 2 | 5040.2.t.t.1009.2 | 4 | |||
5.2 | odd | 4 | 3150.2.a.bs.1.2 | 2 | |||
5.3 | odd | 4 | 3150.2.a.bt.1.2 | 2 | |||
5.4 | even | 2 | inner | 630.2.g.g.379.1 | 4 | ||
12.11 | even | 2 | 560.2.g.e.449.2 | 4 | |||
15.2 | even | 4 | 350.2.a.h.1.2 | 2 | |||
15.8 | even | 4 | 350.2.a.g.1.1 | 2 | |||
15.14 | odd | 2 | 70.2.c.a.29.3 | yes | 4 | ||
20.19 | odd | 2 | 5040.2.t.t.1009.1 | 4 | |||
21.2 | odd | 6 | 490.2.i.c.459.1 | 8 | |||
21.5 | even | 6 | 490.2.i.f.459.2 | 8 | |||
21.11 | odd | 6 | 490.2.i.c.79.4 | 8 | |||
21.17 | even | 6 | 490.2.i.f.79.3 | 8 | |||
21.20 | even | 2 | 490.2.c.e.99.1 | 4 | |||
24.5 | odd | 2 | 2240.2.g.j.449.1 | 4 | |||
24.11 | even | 2 | 2240.2.g.i.449.3 | 4 | |||
60.23 | odd | 4 | 2800.2.a.bm.1.2 | 2 | |||
60.47 | odd | 4 | 2800.2.a.bl.1.1 | 2 | |||
60.59 | even | 2 | 560.2.g.e.449.4 | 4 | |||
105.44 | odd | 6 | 490.2.i.c.459.4 | 8 | |||
105.59 | even | 6 | 490.2.i.f.79.2 | 8 | |||
105.62 | odd | 4 | 2450.2.a.bq.1.1 | 2 | |||
105.74 | odd | 6 | 490.2.i.c.79.1 | 8 | |||
105.83 | odd | 4 | 2450.2.a.bl.1.2 | 2 | |||
105.89 | even | 6 | 490.2.i.f.459.3 | 8 | |||
105.104 | even | 2 | 490.2.c.e.99.4 | 4 | |||
120.29 | odd | 2 | 2240.2.g.j.449.3 | 4 | |||
120.59 | even | 2 | 2240.2.g.i.449.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.c.a.29.2 | ✓ | 4 | 3.2 | odd | 2 | ||
70.2.c.a.29.3 | yes | 4 | 15.14 | odd | 2 | ||
350.2.a.g.1.1 | 2 | 15.8 | even | 4 | |||
350.2.a.h.1.2 | 2 | 15.2 | even | 4 | |||
490.2.c.e.99.1 | 4 | 21.20 | even | 2 | |||
490.2.c.e.99.4 | 4 | 105.104 | even | 2 | |||
490.2.i.c.79.1 | 8 | 105.74 | odd | 6 | |||
490.2.i.c.79.4 | 8 | 21.11 | odd | 6 | |||
490.2.i.c.459.1 | 8 | 21.2 | odd | 6 | |||
490.2.i.c.459.4 | 8 | 105.44 | odd | 6 | |||
490.2.i.f.79.2 | 8 | 105.59 | even | 6 | |||
490.2.i.f.79.3 | 8 | 21.17 | even | 6 | |||
490.2.i.f.459.2 | 8 | 21.5 | even | 6 | |||
490.2.i.f.459.3 | 8 | 105.89 | even | 6 | |||
560.2.g.e.449.2 | 4 | 12.11 | even | 2 | |||
560.2.g.e.449.4 | 4 | 60.59 | even | 2 | |||
630.2.g.g.379.1 | 4 | 5.4 | even | 2 | inner | ||
630.2.g.g.379.3 | 4 | 1.1 | even | 1 | trivial | ||
2240.2.g.i.449.1 | 4 | 120.59 | even | 2 | |||
2240.2.g.i.449.3 | 4 | 24.11 | even | 2 | |||
2240.2.g.j.449.1 | 4 | 24.5 | odd | 2 | |||
2240.2.g.j.449.3 | 4 | 120.29 | odd | 2 | |||
2450.2.a.bl.1.2 | 2 | 105.83 | odd | 4 | |||
2450.2.a.bq.1.1 | 2 | 105.62 | odd | 4 | |||
2800.2.a.bl.1.1 | 2 | 60.47 | odd | 4 | |||
2800.2.a.bm.1.2 | 2 | 60.23 | odd | 4 | |||
3150.2.a.bs.1.2 | 2 | 5.2 | odd | 4 | |||
3150.2.a.bt.1.2 | 2 | 5.3 | odd | 4 | |||
5040.2.t.t.1009.1 | 4 | 20.19 | odd | 2 | |||
5040.2.t.t.1009.2 | 4 | 4.3 | odd | 2 |