Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3800,2,Mod(3649,3800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3800.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3800 = 2^{3} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.3431527681\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.419904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 6x^{4} + 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.2 | ||
Root | \(-1.53209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3800.3649 |
Dual form | 3800.2.d.o.3649.5 |
$q$-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 \(\left(\mathbb{Z}/3800\mathbb{Z}\right)^\times\).
\(n\) | \(401\) | \(951\) | \(1901\) | \(1977\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 1.53209i | − 0.884552i | −0.896879 | − | 0.442276i | \(-0.854171\pi\) | ||||
0.896879 | − | 0.442276i | \(-0.145829\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.22668i | 0.841607i | 0.907152 | + | 0.420803i | \(0.138252\pi\) | ||||
−0.907152 | + | 0.420803i | \(0.861748\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.652704 | 0.217568 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.22668 | −0.972881 | −0.486441 | − | 0.873714i | \(-0.661705\pi\) | ||||
−0.486441 | + | 0.873714i | \(0.661705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.57398i | 0.436543i | 0.975888 | + | 0.218271i | \(0.0700418\pi\) | ||||
−0.975888 | + | 0.218271i | \(0.929958\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.53209i | − 0.856657i | −0.903623 | − | 0.428329i | \(-0.859103\pi\) | ||||
0.903623 | − | 0.428329i | \(-0.140897\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.41147 | 0.744445 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.47565i | 0.933238i | 0.884458 | + | 0.466619i | \(0.154528\pi\) | ||||
−0.884458 | + | 0.466619i | \(0.845472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.59627i | − 1.07700i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.92127 | −0.356772 | −0.178386 | − | 0.983961i | \(-0.557088\pi\) | ||||
−0.178386 | + | 0.983961i | \(0.557088\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.81521 | −0.685231 | −0.342616 | − | 0.939476i | \(-0.611313\pi\) | ||||
−0.342616 | + | 0.939476i | \(0.611313\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.94356i | 0.860564i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 11.3550i | − 1.86676i | −0.358894 | − | 0.933378i | \(-0.616846\pi\) | ||||
0.358894 | − | 0.933378i | \(-0.383154\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.41147 | 0.386145 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.47565 | 0.542806 | 0.271403 | − | 0.962466i | \(-0.412512\pi\) | ||||
0.271403 | + | 0.962466i | \(0.412512\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.69459i | − 0.258423i | −0.991617 | − | 0.129211i | \(-0.958755\pi\) | ||||
0.991617 | − | 0.129211i | \(-0.0412446\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 1.57398i | − 0.229588i | −0.993389 | − | 0.114794i | \(-0.963379\pi\) | ||||
0.993389 | − | 0.114794i | \(-0.0366208\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.04189 | 0.291698 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.41147 | −0.757758 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.12836i | − 0.979155i | −0.871960 | − | 0.489577i | \(-0.837151\pi\) | ||||
0.871960 | − | 0.489577i | \(-0.162849\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.53209i | 0.202930i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.88713 | 1.02682 | 0.513408 | − | 0.858145i | \(-0.328383\pi\) | ||||
0.513408 | + | 0.858145i | \(0.328383\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.79561 | −0.357941 | −0.178970 | − | 0.983854i | \(-0.557277\pi\) | ||||
−0.178970 | + | 0.983854i | \(0.557277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 1.45336i | 0.183107i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 3.22668i | − 0.394202i | −0.980383 | − | 0.197101i | \(-0.936847\pi\) | ||||
0.980383 | − | 0.197101i | \(-0.0631527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.85710 | 0.825497 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.38919 | −0.520900 | −0.260450 | − | 0.965487i | \(-0.583871\pi\) | ||||
−0.260450 | + | 0.965487i | \(0.583871\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.41147i | − 0.750406i | −0.926943 | − | 0.375203i | \(-0.877573\pi\) | ||||
0.926943 | − | 0.375203i | \(-0.122427\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.18479i | − 0.818783i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59627 | 0.967156 | 0.483578 | − | 0.875301i | \(-0.339337\pi\) | ||||
0.483578 | + | 0.875301i | \(0.339337\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.61587 | −0.735096 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 14.6236i | − 1.60515i | −0.596552 | − | 0.802575i | \(-0.703463\pi\) | ||||
0.596552 | − | 0.802575i | \(-0.296537\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.94356i | 0.315583i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.10607 | −0.647242 | −0.323621 | − | 0.946187i | \(-0.604900\pi\) | ||||
−0.323621 | + | 0.946187i | \(0.604900\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.50475 | −0.367397 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.84524i | 0.606123i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 15.7023i | − 1.59433i | −0.603761 | − | 0.797165i | \(-0.706332\pi\) | ||||
0.603761 | − | 0.797165i | \(-0.293668\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.10607 | −0.211668 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.35504 | 0.433342 | 0.216671 | − | 0.976245i | \(-0.430480\pi\) | ||||
0.216671 | + | 0.976245i | \(0.430480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.27126i | 0.420860i | 0.977609 | + | 0.210430i | \(0.0674863\pi\) | ||||
−0.977609 | + | 0.210430i | \(0.932514\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 0.106067i | − 0.0102539i | −0.999987 | − | 0.00512693i | \(-0.998368\pi\) | ||||
0.999987 | − | 0.00512693i | \(-0.00163196\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4115 | 1.38037 | 0.690184 | − | 0.723634i | \(-0.257529\pi\) | ||||
0.690184 | + | 0.723634i | \(0.257529\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.3969 | −1.65124 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 16.5895i | − 1.56061i | −0.625402 | − | 0.780303i | \(-0.715065\pi\) | ||||
0.625402 | − | 0.780303i | \(-0.284935\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.02734i | 0.0949777i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.86484 | 0.720968 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.588526 | −0.0535024 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.32501i | − 0.480140i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.02229i | 0.356920i | 0.983947 | + | 0.178460i | \(0.0571116\pi\) | ||||
−0.983947 | + | 0.178460i | \(0.942888\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.59627 | −0.228589 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.32770 | −0.378113 | −0.189056 | − | 0.981966i | \(-0.560543\pi\) | ||||
−0.189056 | + | 0.981966i | \(0.560543\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.22668i | − 0.193078i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 11.0223i | − 0.941698i | −0.882214 | − | 0.470849i | \(-0.843948\pi\) | ||||
0.882214 | − | 0.470849i | \(-0.156052\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.2567 | 1.46370 | 0.731848 | − | 0.681468i | \(-0.238658\pi\) | ||||
0.731848 | + | 0.681468i | \(0.238658\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.41147 | −0.203083 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 5.07873i | − 0.424704i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 3.12836i | − 0.258022i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.3824 | −1.01440 | −0.507202 | − | 0.861827i | \(-0.669320\pi\) | ||||
−0.507202 | + | 0.861827i | \(0.669320\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.8016 | 1.69281 | 0.846405 | − | 0.532540i | \(-0.178762\pi\) | ||||
0.846405 | + | 0.532540i | \(0.178762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.30541i | − 0.186381i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.25402i | 0.419317i | 0.977775 | + | 0.209658i | \(0.0672352\pi\) | ||||
−0.977775 | + | 0.209658i | \(0.932765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.9213 | −0.866113 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.96585 | −0.785419 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 6.63816i | − 0.519940i | −0.965617 | − | 0.259970i | \(-0.916287\pi\) | ||||
0.965617 | − | 0.259970i | \(-0.0837128\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.3824i | 1.26771i | 0.773453 | + | 0.633853i | \(0.218528\pi\) | ||||
−0.773453 | + | 0.633853i | \(0.781472\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5226 | 0.809430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.652704 | −0.0499135 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 4.01455i | − 0.305220i | −0.988286 | − | 0.152610i | \(-0.951232\pi\) | ||||
0.988286 | − | 0.152610i | \(-0.0487679\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 12.0838i | − 0.908272i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.2472 | −1.66283 | −0.831417 | − | 0.555648i | \(-0.812470\pi\) | ||||
−0.831417 | + | 0.555648i | \(0.812470\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.29591 | −0.542301 | −0.271150 | − | 0.962537i | \(-0.587404\pi\) | ||||
−0.271150 | + | 0.962537i | \(0.587404\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.28312i | 0.316617i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.3969i | 0.833426i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.4611 | 0.906412 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.55169 | −0.691136 | −0.345568 | − | 0.938394i | \(-0.612314\pi\) | ||||
−0.345568 | + | 0.938394i | \(0.612314\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 1.23442i | − 0.0888557i | −0.999013 | − | 0.0444278i | \(-0.985854\pi\) | ||||
0.999013 | − | 0.0444278i | \(-0.0141465\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.5672i | 0.824127i | 0.911155 | + | 0.412063i | \(0.135192\pi\) | ||||
−0.911155 | + | 0.412063i | \(0.864808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0104 | −0.851397 | −0.425698 | − | 0.904865i | \(-0.639972\pi\) | ||||
−0.425698 | + | 0.904865i | \(0.639972\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.94356 | −0.348692 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 4.27807i | − 0.300261i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.92127i | 0.203043i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.22668 | 0.223194 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.3696 | −0.782715 | −0.391357 | − | 0.920239i | \(-0.627994\pi\) | ||||
−0.391357 | + | 0.920239i | \(0.627994\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 6.72462i | 0.460764i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 8.49525i | − 0.576695i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.82295 | −0.663773 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.55943 | 0.373968 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.7493i | 0.920720i | 0.887732 | + | 0.460360i | \(0.152280\pi\) | ||||
−0.887732 | + | 0.460360i | \(0.847720\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 7.06149i | − 0.468688i | −0.972154 | − | 0.234344i | \(-0.924706\pi\) | ||||
0.972154 | − | 0.234344i | \(-0.0752941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.05644 | 0.466302 | 0.233151 | − | 0.972440i | \(-0.425096\pi\) | ||||
0.233151 | + | 0.972440i | \(0.425096\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.0077 | −0.724256 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.9659i | 0.783909i | 0.919985 | + | 0.391955i | \(0.128201\pi\) | ||||
−0.919985 | + | 0.391955i | \(0.871799\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 13.1702i | − 0.855499i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.75103 | −0.177949 | −0.0889747 | − | 0.996034i | \(-0.528359\pi\) | ||||
−0.0889747 | + | 0.996034i | \(0.528359\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.95811 | −0.512627 | −0.256313 | − | 0.966594i | \(-0.582508\pi\) | ||||
−0.256313 | + | 0.966594i | \(0.582508\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 6.65270i | − 0.426771i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 1.57398i | − 0.100150i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22.4047 | −1.41984 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −13.6827 | −0.863646 | −0.431823 | − | 0.901958i | \(-0.642130\pi\) | ||||
−0.431823 | + | 0.901958i | \(0.642130\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 14.4415i | − 0.907930i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 10.5517i | − 0.658196i | −0.944296 | − | 0.329098i | \(-0.893255\pi\) | ||||
0.944296 | − | 0.329098i | \(-0.106745\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 25.2841 | 1.57107 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.25402 | −0.0776221 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 9.40642i | − 0.580025i | −0.957023 | − | 0.290012i | \(-0.906341\pi\) | ||||
0.957023 | − | 0.290012i | \(-0.0936594\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.35504i | 0.572519i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.02734 | −0.550407 | −0.275203 | − | 0.961386i | \(-0.588745\pi\) | ||||
−0.275203 | + | 0.961386i | \(0.588745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.3354 | −1.35678 | −0.678391 | − | 0.734701i | \(-0.737322\pi\) | ||||
−0.678391 | + | 0.734701i | \(0.737322\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.36959i | 0.324982i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 17.2959i | − 1.03921i | −0.854406 | − | 0.519605i | \(-0.826079\pi\) | ||||
0.854406 | − | 0.519605i | \(-0.173921\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.49020 | −0.149084 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.4534 | −0.623595 | −0.311798 | − | 0.950149i | \(-0.600931\pi\) | ||||
−0.311798 | + | 0.950149i | \(0.600931\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.3628i | − 1.38877i | −0.719602 | − | 0.694386i | \(-0.755676\pi\) | ||||
0.719602 | − | 0.694386i | \(-0.244324\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.73917i | 0.456829i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.52435 | 0.266138 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −24.0574 | −1.41027 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 27.9641i | − 1.63368i | −0.576864 | − | 0.816840i | \(-0.695724\pi\) | ||||
0.576864 | − | 0.816840i | \(-0.304276\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.0574i | 1.04779i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.04458 | −0.407398 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.77332 | 0.217490 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 6.67230i | − 0.383314i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.8452i | 1.30385i | 0.758285 | + | 0.651923i | \(0.226038\pi\) | ||||
−0.758285 | + | 0.651923i | \(0.773962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.54395 | 0.372272 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.8699 | −0.673080 | −0.336540 | − | 0.941669i | \(-0.609257\pi\) | ||||
−0.336540 | + | 0.941669i | \(0.609257\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.5672i | 1.44514i | 0.691297 | + | 0.722571i | \(0.257040\pi\) | ||||
−0.691297 | + | 0.722571i | \(0.742960\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 17.4020i | − 0.977392i | −0.872454 | − | 0.488696i | \(-0.837473\pi\) | ||||
0.872454 | − | 0.488696i | \(-0.162527\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.19934 | 0.347096 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.162504 | −0.00907008 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.53209i | 0.196531i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 22.0797i | − 1.22101i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.50475 | 0.193223 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.77063 | −0.372147 | −0.186074 | − | 0.982536i | \(-0.559576\pi\) | ||||
−0.186074 | + | 0.982536i | \(0.559576\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 7.41147i | − 0.406146i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.11112i | − 0.223947i | −0.993711 | − | 0.111973i | \(-0.964283\pi\) | ||||
0.993711 | − | 0.111973i | \(-0.0357172\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −25.4165 | −1.38044 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3105 | 0.666649 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.1334i | 1.08710i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 11.0247i | 0.591834i | 0.955214 | + | 0.295917i | \(0.0956252\pi\) | ||||
−0.955214 | + | 0.295917i | \(0.904375\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8307 | 1.22210 | 0.611049 | − | 0.791592i | \(-0.290748\pi\) | ||||
0.611049 | + | 0.791592i | \(0.290748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.80840 | 0.470158 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 14.6732i | 0.780978i | 0.920608 | + | 0.390489i | \(0.127694\pi\) | ||||
−0.920608 | + | 0.390489i | \(0.872306\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 12.0496i | − 0.637734i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.60307 | −0.190163 | −0.0950815 | − | 0.995469i | \(-0.530311\pi\) | ||||
−0.0950815 | + | 0.995469i | \(0.530311\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.901674i | 0.0473256i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 19.8007i | 1.03359i | 0.856110 | + | 0.516793i | \(0.172874\pi\) | ||||
−0.856110 | + | 0.516793i | \(0.827126\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.26857 | 0.118097 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 15.8726 | 0.824063 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 17.6631i | − 0.914562i | −0.889322 | − | 0.457281i | \(-0.848823\pi\) | ||||
0.889322 | − | 0.457281i | \(-0.151177\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.02404i | − 0.155746i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.05644 | −0.311098 | −0.155549 | − | 0.987828i | \(-0.549715\pi\) | ||||
−0.155549 | + | 0.987828i | \(0.549715\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.16250 | 0.315715 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 20.8895i | − 1.06740i | −0.845673 | − | 0.533702i | \(-0.820801\pi\) | ||||
0.845673 | − | 0.533702i | \(-0.179199\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.10607i | − 0.0562245i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.30541 | 0.116889 | 0.0584444 | − | 0.998291i | \(-0.481386\pi\) | ||||
0.0584444 | + | 0.998291i | \(0.481386\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.8084 | 0.799465 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.63041i | 0.334460i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2354i | 1.11596i | 0.829854 | + | 0.557980i | \(0.188424\pi\) | ||||
−0.829854 | + | 0.557980i | \(0.811576\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.41147 | −0.170787 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1584 | −0.707036 | −0.353518 | − | 0.935428i | \(-0.615015\pi\) | ||||
−0.353518 | + | 0.935428i | \(0.615015\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.00505i | − 0.299133i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 36.6391i | 1.81613i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.22432 | 0.208879 | 0.104440 | − | 0.994531i | \(-0.466695\pi\) | ||||
0.104440 | + | 0.994531i | \(0.466695\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.8871 | −0.832980 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.5621i | 0.864175i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − 26.4388i | − 1.29471i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 11.9632 | 0.584439 | 0.292219 | − | 0.956351i | \(-0.405606\pi\) | ||||
0.292219 | + | 0.956351i | \(0.405606\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2395 | −0.499041 | −0.249521 | − | 0.968369i | \(-0.580273\pi\) | ||||
−0.249521 | + | 0.968369i | \(0.580273\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.02734i | − 0.0499510i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.22493i | − 0.301245i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.78106 | −0.375673 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.2517 | 1.07182 | 0.535912 | − | 0.844274i | \(-0.319968\pi\) | ||||
0.535912 | + | 0.844274i | \(0.319968\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.9581i | 1.19941i | 0.800221 | + | 0.599705i | \(0.204715\pi\) | ||||
−0.800221 | + | 0.599705i | \(0.795285\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.47565i | − 0.214099i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0942 | −0.768135 | −0.384067 | − | 0.923305i | \(-0.625477\pi\) | ||||
−0.384067 | + | 0.923305i | \(0.625477\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.33275 | 0.0634642 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.7270i | 0.842235i | 0.907006 | + | 0.421117i | \(0.138362\pi\) | ||||
−0.907006 | + | 0.421117i | \(0.861638\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.9709i | 0.897293i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 37.6049 | 1.77469 | 0.887343 | − | 0.461109i | \(-0.152548\pi\) | ||||
0.887343 | + | 0.461109i | \(0.152548\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2148 | −0.528085 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 31.8699i | − 1.49738i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.1949i | 0.944677i | 0.881417 | + | 0.472339i | \(0.156590\pi\) | ||||
−0.881417 | + | 0.472339i | \(0.843410\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −19.7665 | −0.922622 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.81521 | 0.317416 | 0.158708 | − | 0.987326i | \(-0.449267\pi\) | ||||
0.158708 | + | 0.987326i | \(0.449267\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 33.7083i | − 1.56656i | −0.621670 | − | 0.783279i | \(-0.713546\pi\) | ||||
0.621670 | − | 0.783279i | \(-0.286454\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 27.5648i | − 1.27555i | −0.770224 | − | 0.637774i | \(-0.779856\pi\) | ||||
0.770224 | − | 0.637774i | \(-0.220144\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.18479 | 0.331763 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.04963 | 0.370907 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.46791i | 0.251415i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 4.65270i | − 0.213033i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −26.1438 | −1.19454 | −0.597271 | − | 0.802039i | \(-0.703748\pi\) | ||||
−0.597271 | + | 0.802039i | \(0.703748\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 17.8726 | 0.814919 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.2686i | 0.694744i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 5.63310i | 0.255260i | 0.991822 | + | 0.127630i | \(0.0407370\pi\) | ||||
−0.991822 | + | 0.127630i | \(0.959263\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.1702 | −0.459914 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.6682 | 0.661966 | 0.330983 | − | 0.943637i | \(-0.392620\pi\) | ||||
0.330983 | + | 0.943637i | \(0.392620\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.78611i | 0.305631i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 9.77332i | − 0.438393i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.7793 | −0.751145 | −0.375572 | − | 0.926793i | \(-0.622554\pi\) | ||||
−0.375572 | + | 0.926793i | \(0.622554\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 25.0993 | 1.12135 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 3.12330i | 0.139261i | 0.997573 | + | 0.0696306i | \(0.0221821\pi\) | ||||
−0.997573 | + | 0.0696306i | \(0.977818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 16.1215i | − 0.715983i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 40.1566 | 1.77991 | 0.889956 | − | 0.456047i | \(-0.150735\pi\) | ||||
0.889956 | + | 0.456047i | \(0.150735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.2763 | 0.631547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.59627i | 0.247081i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.07873i | 0.223362i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.15064 | −0.269983 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.75465 | −0.383548 | −0.191774 | − | 0.981439i | \(-0.561424\pi\) | ||||
−0.191774 | + | 0.981439i | \(0.561424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 26.9522i | − 1.17854i | −0.807937 | − | 0.589270i | \(-0.799416\pi\) | ||||
0.807937 | − | 0.589270i | \(-0.200584\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.4757i | 0.587009i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.96854 | 0.129067 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.14796 | 0.223402 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.47060i | 0.236958i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.0847i | 1.47086i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.58853 | −0.283788 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.48751 | 0.364907 | 0.182453 | − | 0.983215i | \(-0.441596\pi\) | ||||
0.182453 | + | 0.983215i | \(0.441596\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.1780i | 0.479693i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.62267i | 0.154894i | 0.996996 | + | 0.0774472i | \(0.0246769\pi\) | ||||
−0.996996 | + | 0.0774472i | \(0.975323\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.82470 | −0.0778764 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.92127 | 0.0818490 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.1411i | 0.813964i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.01455i | 0.0853591i | 0.999089 | + | 0.0426796i | \(0.0135895\pi\) | ||||
−0.999089 | + | 0.0426796i | \(0.986411\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.66725 | 0.112813 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 17.4611 | 0.737208 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 16.5185i | − 0.696171i | −0.937463 | − | 0.348085i | \(-0.886832\pi\) | ||||
0.937463 | − | 0.348085i | \(-0.113168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 14.7314i | − 0.618662i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.18304 | 0.343051 | 0.171525 | − | 0.985180i | \(-0.445130\pi\) | ||||
0.171525 | + | 0.985180i | \(0.445130\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −36.9796 | −1.54755 | −0.773774 | − | 0.633462i | \(-0.781633\pi\) | ||||
−0.773774 | + | 0.633462i | \(0.781633\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6340i | 0.611346i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.7347i | 0.779937i | 0.920828 | + | 0.389968i | \(0.127514\pi\) | ||||
−0.920828 | + | 0.389968i | \(0.872486\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.89124 | −0.0785975 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 32.5621 | 1.35090 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 23.0009i | 0.952601i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 29.2968i | − 1.20921i | −0.796525 | − | 0.604605i | \(-0.793331\pi\) | ||||
0.796525 | − | 0.604605i | \(-0.206669\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.81521 | 0.157203 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 17.7219 | 0.728983 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.4260i | 0.920926i | 0.887679 | + | 0.460463i | \(0.152317\pi\) | ||||
−0.887679 | + | 0.460463i | \(0.847683\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 18.4010i | 0.753105i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 33.1002 | 1.35244 | 0.676219 | − | 0.736701i | \(-0.263617\pi\) | ||||
0.676219 | + | 0.736701i | \(0.263617\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.5613 | 1.77690 | 0.888451 | − | 0.458971i | \(-0.151782\pi\) | ||||
0.888451 | + | 0.458971i | \(0.151782\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 2.10607i | − 0.0857657i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.03178i | 0.0824676i | 0.999150 | + | 0.0412338i | \(0.0131288\pi\) | ||||
−0.999150 | + | 0.0412338i | \(0.986871\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.55438 | −0.265597 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.47741 | 0.100225 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 25.1266i | 1.01485i | 0.861695 | + | 0.507427i | \(0.169403\pi\) | ||||
−0.861695 | + | 0.507427i | \(0.830597\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 24.4979i | − 0.986250i | −0.869958 | − | 0.493125i | \(-0.835855\pi\) | ||||
0.869958 | − | 0.493125i | \(-0.164145\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.05138 | −0.363806 | −0.181903 | − | 0.983316i | \(-0.558226\pi\) | ||||
−0.181903 | + | 0.983316i | \(0.558226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 25.0469 | 1.00510 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 13.5963i | − 0.544723i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 4.94356i | − 0.197427i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −40.1070 | −1.59917 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.7324 | 0.944770 | 0.472385 | − | 0.881392i | \(-0.343393\pi\) | ||||
0.472385 | + | 0.881392i | \(0.343393\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 17.4192i | 0.692352i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.21389i | 0.127339i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.86484 | −0.113331 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.6067 | 0.418939 | 0.209470 | − | 0.977815i | \(-0.432826\pi\) | ||||
0.209470 | + | 0.977815i | \(0.432826\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.1634i | 1.22897i | 0.788930 | + | 0.614483i | \(0.210635\pi\) | ||||
−0.788930 | + | 0.614483i | \(0.789365\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 12.9154i | − 0.507757i | −0.967236 | − | 0.253878i | \(-0.918294\pi\) | ||||
0.967236 | − | 0.253878i | \(-0.0817063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.4492 | −0.998970 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.0155 | −0.510117 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 10.8060i | − 0.422873i | −0.977392 | − | 0.211436i | \(-0.932186\pi\) | ||||
0.977392 | − | 0.211436i | \(-0.0678141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 4.18479i | − 0.163264i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.3583 | 1.10468 | 0.552342 | − | 0.833618i | \(-0.313734\pi\) | ||||
0.552342 | + | 0.833618i | \(0.313734\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −28.9691 | −1.12677 | −0.563385 | − | 0.826195i | \(-0.690501\pi\) | ||||
−0.563385 | + | 0.826195i | \(0.690501\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 8.51754i | − 0.330794i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 8.59896i | − 0.332953i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 21.0651 | 0.814424 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 9.02053 | 0.348234 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.6973i | 0.605086i | 0.953136 | + | 0.302543i | \(0.0978355\pi\) | ||||
−0.953136 | + | 0.302543i | \(0.902164\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3.25578i | 0.125130i | 0.998041 | + | 0.0625648i | \(0.0199280\pi\) | ||||
−0.998041 | + | 0.0625648i | \(0.980072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.9641 | 1.34180 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.8188 | −0.414578 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 33.1834i | − 1.26973i | −0.772625 | − | 0.634863i | \(-0.781057\pi\) | ||||
0.772625 | − | 0.634863i | \(-0.218943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 10.8111i | − 0.412469i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.2199 | 0.427443 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 41.1242 | 1.56444 | 0.782220 | − | 0.623002i | \(-0.214087\pi\) | ||||
0.782220 | + | 0.623002i | \(0.214087\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 4.68954i | − 0.178141i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 12.2763i | − 0.464998i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.3327 | 0.693408 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 44.9198 | 1.69660 | 0.848300 | − | 0.529517i | \(-0.177627\pi\) | ||||
0.848300 | + | 0.529517i | \(0.177627\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3550i | 0.428263i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.69728i | 0.364704i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 34.9240 | 1.31160 | 0.655798 | − | 0.754936i | \(-0.272332\pi\) | ||||
0.655798 | + | 0.754936i | \(0.272332\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.61081 | 0.210422 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 17.0755i | − 0.639484i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.21482i | 0.157405i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −29.0077 | −1.08181 | −0.540903 | − | 0.841085i | \(-0.681917\pi\) | ||||
−0.540903 | + | 0.841085i | \(0.681917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.51073 | −0.354198 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 12.1925i | 0.453445i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 8.27126i | − 0.306764i | −0.988167 | − | 0.153382i | \(-0.950983\pi\) | ||||
0.988167 | − | 0.153382i | \(-0.0490165\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0401 | −1.11260 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.98545 | −0.221380 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 12.6696i | − 0.467963i | −0.972241 | − | 0.233981i | \(-0.924824\pi\) | ||||
0.972241 | − | 0.233981i | \(-0.0751755\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4115i | 0.383512i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.9733 | −0.661157 | −0.330579 | − | 0.943778i | \(-0.607244\pi\) | ||||
−0.330579 | + | 0.943778i | \(0.607244\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.41147 | −0.0885877 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.47977i | − 0.201033i | −0.994935 | − | 0.100517i | \(-0.967950\pi\) | ||||
0.994935 | − | 0.100517i | \(-0.0320496\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 9.54488i | − 0.349229i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.236177 | 0.00862972 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.5803 | 1.18887 | 0.594436 | − | 0.804143i | \(-0.297375\pi\) | ||||
0.594436 | + | 0.804143i | \(0.297375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 20.9632i | 0.763940i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.97359i | − 0.180768i | −0.995907 | − | 0.0903841i | \(-0.971191\pi\) | ||||
0.995907 | − | 0.0903841i | \(-0.0288095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.1257 | −0.803111 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.5262 | 0.889075 | 0.444537 | − | 0.895760i | \(-0.353368\pi\) | ||||
0.444537 | + | 0.895760i | \(0.353368\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.0898i | 1.16173i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.4142i | 0.448249i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.4688 | 0.882369 | 0.441185 | − | 0.897416i | \(-0.354558\pi\) | ||||
0.441185 | + | 0.897416i | \(0.354558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −16.1661 | −0.582209 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.43645i | 0.159568i | 0.996812 | + | 0.0797840i | \(0.0254231\pi\) | ||||
−0.996812 | + | 0.0797840i | \(0.974577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 38.7374i | − 1.38970i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.47565 | −0.124528 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 14.1625 | 0.506774 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.7520i | 0.384244i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 1.73143i | − 0.0617188i | −0.999524 | − | 0.0308594i | \(-0.990176\pi\) | ||||
0.999524 | − | 0.0308594i | \(-0.00982441\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −14.4115 | −0.513062 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.9394 | 1.31342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 4.40022i | − 0.156257i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 48.3979i | 1.71434i | 0.515033 | + | 0.857170i | \(0.327779\pi\) | ||||
−0.515033 | + | 0.857170i | \(0.672221\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.55943 | −0.196678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.98545 | −0.140819 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.6878i | 0.730056i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 13.8307i | 0.486863i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −45.7861 | −1.60975 | −0.804877 | − | 0.593442i | \(-0.797769\pi\) | ||||
−0.804877 | + | 0.593442i | \(0.797769\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.0779 | −1.40733 | −0.703663 | − | 0.710534i | \(-0.748453\pi\) | ||||
−0.703663 | + | 0.710534i | \(0.748453\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 34.2199i | 1.20014i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.69459i | 0.0592863i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.28756 | −0.0799339 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −51.9208 | −1.81205 | −0.906024 | − | 0.423227i | \(-0.860897\pi\) | ||||
−0.906024 | + | 0.423227i | \(0.860897\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 18.0779i | − 0.630156i | −0.949066 | − | 0.315078i | \(-0.897969\pi\) | ||||
0.949066 | − | 0.315078i | \(-0.102031\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.5022i | 1.61704i | 0.588469 | + | 0.808519i | \(0.299731\pi\) | ||||
−0.588469 | + | 0.808519i | \(0.700269\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 44.6946 | 1.55231 | 0.776154 | − | 0.630544i | \(-0.217168\pi\) | ||||
0.776154 | + | 0.630544i | \(0.217168\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.4989 | −0.919236 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 7.21213i | − 0.249886i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 21.3509i | 0.737996i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.37134 | 0.219963 | 0.109982 | − | 0.993934i | \(-0.464921\pi\) | ||||
0.109982 | + | 0.993934i | \(0.464921\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.3087 | −0.872714 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.0155i | 0.551602i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 1.31046i | − 0.0450279i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −35.7939 | −1.22844 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 50.8212 | 1.74213 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 37.9813i | − 1.30046i | −0.759739 | − | 0.650228i | \(-0.774673\pi\) | ||||
0.759739 | − | 0.650228i | \(-0.225327\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 47.2104i | − 1.61268i | −0.591455 | − | 0.806338i | \(-0.701446\pi\) | ||||
0.591455 | − | 0.806338i | \(-0.298554\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.6587 | −0.534268 | −0.267134 | − | 0.963659i | \(-0.586077\pi\) | ||||
−0.267134 | + | 0.963659i | \(0.586077\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11.8571 | 0.404089 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 54.9026i | 1.86891i | 0.356086 | + | 0.934453i | \(0.384111\pi\) | ||||
−0.356086 | + | 0.934453i | \(0.615889\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 6.93170i | − 0.235413i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.7374 | −0.940927 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.07873 | 0.172086 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 10.2490i | − 0.346875i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.74329i | 0.261472i | 0.991417 | + | 0.130736i | \(0.0417341\pi\) | ||||
−0.991417 | + | 0.130736i | \(0.958266\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −42.8435 | −1.44507 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −48.6005 | −1.63739 | −0.818696 | − | 0.574227i | \(-0.805303\pi\) | ||||
−0.818696 | + | 0.574227i | \(0.805303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 31.1625i | 1.04870i | 0.851502 | + | 0.524351i | \(0.175692\pi\) | ||||
−0.851502 | + | 0.524351i | \(0.824308\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.52259i | 0.151854i | 0.997113 | + | 0.0759269i | \(0.0241916\pi\) | ||||
−0.997113 | + | 0.0759269i | \(0.975808\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.95636 | −0.300387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 21.3473 | 0.715161 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.57398i | 0.0526712i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 10.7929i | 0.360365i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.33006 | 0.244471 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −25.1780 | −0.838800 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 5.78106i | − 0.192382i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.9777i | 0.928985i | 0.885577 | + | 0.464492i | \(0.153763\pi\) | ||||
−0.885577 | + | 0.464492i | \(0.846237\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.84255 | 0.0942814 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5895 | 1.17913 | 0.589566 | − | 0.807720i | \(-0.299299\pi\) | ||||
0.589566 | + | 0.807720i | \(0.299299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.1857i | 1.56162i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 9.63640i | − 0.318222i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.8854 | −0.688945 | −0.344472 | − | 0.938796i | \(-0.611942\pi\) | ||||
−0.344472 | + | 0.938796i | \(0.611942\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 35.0009 | 1.15332 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 6.90848i | − 0.227395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.78787i | 0.0915655i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −45.5885 | −1.49571 | −0.747856 | − | 0.663862i | \(-0.768916\pi\) | ||||
−0.747856 | + | 0.663862i | \(0.768916\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.04189 | −0.0669202 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.1857i | 0.595374i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.7638i | 1.13568i | 0.823137 | + | 0.567842i | \(0.192222\pi\) | ||||
−0.823137 | + | 0.567842i | \(0.807778\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 39.1712 | 1.27830 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.80066 | 0.189096 | 0.0945480 | − | 0.995520i | \(-0.469859\pi\) | ||||
0.0945480 | + | 0.995520i | \(0.469859\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.5558i | 0.506567i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.4466i | 0.599433i | 0.954028 | + | 0.299716i | \(0.0968920\pi\) | ||||
−0.954028 | + | 0.299716i | \(0.903108\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.0915 | 0.327585 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −26.6614 | −0.864554 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.6568i | 0.507174i | 0.967313 | + | 0.253587i | \(0.0816105\pi\) | ||||
−0.967313 | + | 0.253587i | \(0.918390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 9.49794i | − 0.307025i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.5431 | 0.792539 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.4442 | −0.530458 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 0.0692302i | − 0.00223091i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 13.9923i | − 0.449961i | −0.974363 | − | 0.224980i | \(-0.927768\pi\) | ||||
0.974363 | − | 0.224980i | \(-0.0722318\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.41147 | 0.173842 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.0487 | 0.418753 | 0.209376 | − | 0.977835i | \(-0.432857\pi\) | ||||
0.209376 | + | 0.977835i | \(0.432857\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 38.4252i | 1.23186i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 17.3327i | − 0.554524i | −0.960794 | − | 0.277262i | \(-0.910573\pi\) | ||||
0.960794 | − | 0.277262i | \(-0.0894270\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.7023 | 0.629689 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.40642 | 0.300324 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 25.3114i | 0.807308i | 0.914912 | + | 0.403654i | \(0.132260\pi\) | ||||
−0.914912 | + | 0.403654i | \(0.867740\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 5.36959i | − 0.170916i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 7.58441 | 0.241170 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.1762 | 1.18094 | 0.590471 | − | 0.807059i | \(-0.298942\pi\) | ||||
0.590471 | + | 0.807059i | \(0.298942\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.3732i | 0.329184i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.3865i | 0.835669i | 0.908523 | + | 0.417834i | \(0.137211\pi\) | ||||
−0.908523 | + | 0.417834i | \(0.862789\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −63.5458 | −2.01050 |
(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 | 3800.2.d.o.3649.2 | 6 | ||
5.2 | odd | 4 | 3800.2.a.s.1.1 | ✓ | 3 | ||
5.3 | odd | 4 | 3800.2.a.t.1.3 | yes | 3 | ||
5.4 | even | 2 | inner | 3800.2.d.o.3649.5 | 6 | ||
20.3 | even | 4 | 7600.2.a.bs.1.1 | 3 | |||
20.7 | even | 4 | 7600.2.a.br.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3800.2.a.s.1.1 | ✓ | 3 | 5.2 | odd | 4 | ||
3800.2.a.t.1.3 | yes | 3 | 5.3 | odd | 4 | ||
3800.2.d.o.3649.2 | 6 | 1.1 | even | 1 | trivial | ||
3800.2.d.o.3649.5 | 6 | 5.4 | even | 2 | inner | ||
7600.2.a.br.1.3 | 3 | 20.7 | even | 4 | |||
7600.2.a.bs.1.1 | 3 | 20.3 | even | 4 |