Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2520,2,Mod(361,2520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2520, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2520.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2520.bi (of order \(3\), degree \(2\), 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: | \(20.1223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 29x^{8} + 247x^{6} + 855x^{4} + 1212x^{2} + 588 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 361.5 | ||
Root | \(1.22977i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2520.361 |
Dual form | 2520.2.bi.s.1801.5 |
$q$-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 \(\left(\mathbb{Z}/2520\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(1081\) | \(1261\) | \(2017\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.87518 | + | 1.86646i | 0.708752 | + | 0.705457i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.56501 | − | 2.71069i | 0.471870 | − | 0.817302i | −0.527612 | − | 0.849485i | \(-0.676913\pi\) |
0.999482 | + | 0.0321830i | \(0.0102459\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.53916 | −0.981586 | −0.490793 | − | 0.871276i | \(-0.663293\pi\) | ||||
−0.490793 | + | 0.871276i | \(0.663293\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.76138 | + | 4.78286i | −0.669734 | + | 1.16001i | 0.308245 | + | 0.951307i | \(0.400258\pi\) |
−0.977978 | + | 0.208706i | \(0.933075\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.94839 | + | 5.10677i | 0.676408 | + | 1.17157i | 0.976055 | + | 0.217523i | \(0.0697976\pi\) |
−0.299648 | + | 0.954050i | \(0.596869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.0732100 | + | 0.126804i | 0.0152653 | + | 0.0264404i | 0.873557 | − | 0.486722i | \(-0.161807\pi\) |
−0.858292 | + | 0.513162i | \(0.828474\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.91882 | −0.542011 | −0.271006 | − | 0.962578i | \(-0.587356\pi\) | ||||
−0.271006 | + | 0.962578i | \(0.587356\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.54580 | + | 4.40946i | −0.457239 | + | 0.791962i | −0.998814 | − | 0.0486908i | \(-0.984495\pi\) |
0.541574 | + | 0.840653i | \(0.317828\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.678814 | + | 2.55719i | −0.114741 | + | 0.432244i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.321186 | − | 0.556310i | −0.0528026 | − | 0.0914568i | 0.838416 | − | 0.545031i | \(-0.183482\pi\) |
−0.891219 | + | 0.453574i | \(0.850149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.63076 | 1.34790 | 0.673949 | − | 0.738778i | \(-0.264597\pi\) | ||||
0.673949 | + | 0.738778i | \(0.264597\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.93189 | −0.904605 | −0.452303 | − | 0.891865i | \(-0.649397\pi\) | ||||
−0.452303 | + | 0.891865i | \(0.649397\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.704564 | − | 1.22034i | −0.102771 | − | 0.178005i | 0.810054 | − | 0.586355i | \(-0.199438\pi\) |
−0.912825 | + | 0.408350i | \(0.866104\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.0326205 | + | 6.99992i | 0.00466007 | + | 0.999989i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.83459 | − | 8.37376i | 0.664082 | − | 1.15022i | −0.315451 | − | 0.948942i | \(-0.602156\pi\) |
0.979533 | − | 0.201283i | \(-0.0645110\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.13003 | 0.422053 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.67062 | + | 2.89360i | −0.217496 | + | 0.376714i | −0.954042 | − | 0.299673i | \(-0.903122\pi\) |
0.736546 | + | 0.676388i | \(0.236456\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.19876 | + | 10.7366i | 0.793670 | + | 1.37468i | 0.923680 | + | 0.383164i | \(0.125165\pi\) |
−0.130011 | + | 0.991513i | \(0.541501\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.76958 | − | 3.06500i | −0.219489 | − | 0.380166i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −6.62555 | + | 11.4758i | −0.809440 | + | 1.40199i | 0.103813 | + | 0.994597i | \(0.466896\pi\) |
−0.913253 | + | 0.407394i | \(0.866438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.658762 | 0.0781807 | 0.0390903 | − | 0.999236i | \(-0.487554\pi\) | ||||
0.0390903 | + | 0.999236i | \(0.487554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.34561 | − | 4.06272i | 0.274533 | − | 0.475505i | −0.695484 | − | 0.718541i | \(-0.744810\pi\) |
0.970017 | + | 0.243036i | \(0.0781434\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.99409 | − | 2.16199i | 0.911011 | − | 0.246381i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.67499 | − | 4.63322i | −0.300960 | − | 0.521278i | 0.675394 | − | 0.737457i | \(-0.263974\pi\) |
−0.976354 | + | 0.216179i | \(0.930640\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.4787 | −1.47948 | −0.739740 | − | 0.672893i | \(-0.765051\pi\) | ||||
−0.739740 | + | 0.672893i | \(0.765051\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.52277 | −0.599028 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.20978 | + | 12.4877i | 0.764235 | + | 1.32369i | 0.940650 | + | 0.339378i | \(0.110216\pi\) |
−0.176416 | + | 0.984316i | \(0.556450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.63657 | − | 6.60571i | −0.695701 | − | 0.692467i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.94839 | + | 5.10677i | −0.302499 | + | 0.523943i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.86400 | −0.290796 | −0.145398 | − | 0.989373i | \(-0.546446\pi\) | ||||
−0.145398 | + | 0.989373i | \(0.546446\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.77861 | − | 11.7409i | 0.674497 | − | 1.16826i | −0.302118 | − | 0.953270i | \(-0.597694\pi\) |
0.976616 | − | 0.214993i | \(-0.0689729\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.93084 | + | 5.07636i | 0.288784 | + | 0.500189i | 0.973520 | − | 0.228603i | \(-0.0734157\pi\) |
−0.684736 | + | 0.728792i | \(0.740082\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.76138 | − | 6.51491i | −0.363627 | − | 0.629820i | 0.624928 | − | 0.780682i | \(-0.285128\pi\) |
−0.988555 | + | 0.150862i | \(0.951795\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.86417 | + | 4.96088i | −0.274337 | + | 0.475166i | −0.969968 | − | 0.243234i | \(-0.921792\pi\) |
0.695630 | + | 0.718400i | \(0.255125\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.50073 | −0.893754 | −0.446877 | − | 0.894596i | \(-0.647464\pi\) | ||||
−0.446877 | + | 0.894596i | \(0.647464\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0732100 | + | 0.126804i | −0.00682687 | + | 0.0118245i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −14.1051 | + | 3.81471i | −1.29302 | + | 0.349693i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.601458 | + | 1.04176i | 0.0546780 | + | 0.0947050i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5145 | 0.933009 | 0.466504 | − | 0.884519i | \(-0.345513\pi\) | ||||
0.466504 | + | 0.884519i | \(0.345513\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.105604 | − | 0.182912i | −0.00922669 | − | 0.0159811i | 0.861375 | − | 0.507969i | \(-0.169604\pi\) |
−0.870602 | + | 0.491988i | \(0.836270\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.00282 | + | 15.0792i | −0.347089 | + | 1.30753i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.57985 | − | 6.20049i | 0.305848 | − | 0.529744i | −0.671602 | − | 0.740912i | \(-0.734394\pi\) |
0.977450 | + | 0.211168i | \(0.0677268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.27313 | −0.277623 | −0.138812 | − | 0.990319i | \(-0.544328\pi\) | ||||
−0.138812 | + | 0.990319i | \(0.544328\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.53883 | + | 9.59354i | −0.463180 | + | 0.802252i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.45941 | − | 2.52777i | −0.121197 | − | 0.209920i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.50405 | − | 6.06919i | −0.287063 | − | 0.497207i | 0.686044 | − | 0.727560i | \(-0.259346\pi\) |
−0.973107 | + | 0.230352i | \(0.926012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.57842 | + | 16.5903i | −0.779481 | + | 1.35010i | 0.152760 | + | 0.988263i | \(0.451184\pi\) |
−0.932241 | + | 0.361837i | \(0.882150\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.09160 | −0.408967 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00239 | + | 5.20029i | −0.239617 | + | 0.415028i | −0.960604 | − | 0.277920i | \(-0.910355\pi\) |
0.720988 | + | 0.692948i | \(0.243688\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.0993920 | + | 0.374424i | −0.00783319 | + | 0.0295087i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.41955 | + | 11.1190i | 0.502818 | + | 0.870907i | 0.999995 | + | 0.00325713i | \(0.00103678\pi\) |
−0.497177 | + | 0.867649i | \(0.665630\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.14642 | −0.166095 | −0.0830475 | − | 0.996546i | \(-0.526465\pi\) | ||||
−0.0830475 | + | 0.996546i | \(0.526465\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.474368 | −0.0364899 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.08423 | + | 1.87794i | 0.0824323 | + | 0.142777i | 0.904294 | − | 0.426910i | \(-0.140398\pi\) |
−0.821862 | + | 0.569687i | \(0.807065\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.55400 | + | 0.690724i | −0.193064 | + | 0.0522138i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.46323 | + | 2.53439i | −0.109367 | + | 0.189429i | −0.915514 | − | 0.402286i | \(-0.868216\pi\) |
0.806147 | + | 0.591715i | \(0.201549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.4630 | 1.59533 | 0.797665 | − | 0.603101i | \(-0.206068\pi\) | ||||
0.797665 | + | 0.603101i | \(0.206068\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.321186 | − | 0.556310i | 0.0236140 | − | 0.0409007i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.64321 | + | 14.9705i | 0.632054 | + | 1.09475i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.2731 | + | 17.7936i | 0.743338 | + | 1.28750i | 0.950967 | + | 0.309291i | \(0.100092\pi\) |
−0.207630 | + | 0.978208i | \(0.566575\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.68120 | + | 15.0363i | −0.624887 | + | 1.08234i | 0.363676 | + | 0.931526i | \(0.381522\pi\) |
−0.988563 | + | 0.150810i | \(0.951812\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 24.9087 | 1.77467 | 0.887335 | − | 0.461126i | \(-0.152554\pi\) | ||||
0.887335 | + | 0.461126i | \(0.152554\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.97116 | + | 10.3424i | −0.423284 | + | 0.733150i | −0.996258 | − | 0.0864236i | \(-0.972456\pi\) |
0.572974 | + | 0.819573i | \(0.305789\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.47332 | − | 5.44788i | −0.384152 | − | 0.382366i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.31538 | + | 7.47446i | 0.301399 | + | 0.522039i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.4571 | 1.27671 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.0571436 | 0.00393393 | 0.00196696 | − | 0.999998i | \(-0.499374\pi\) | ||||
0.00196696 | + | 0.999998i | \(0.499374\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.96595 | − | 5.13717i | −0.202276 | − | 0.350352i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −13.0039 | + | 3.51689i | −0.882765 | + | 0.238742i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.77297 | − | 16.9273i | 0.657401 | − | 1.13865i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.5790 | 1.77986 | 0.889932 | − | 0.456093i | \(-0.150751\pi\) | ||||
0.889932 | + | 0.456093i | \(0.150751\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.43057 | − | 12.8701i | 0.493184 | − | 0.854220i | −0.506785 | − | 0.862073i | \(-0.669166\pi\) |
0.999969 | + | 0.00785238i | \(0.00249952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.59730 | − | 4.49866i | −0.171634 | − | 0.297280i | 0.767357 | − | 0.641220i | \(-0.221571\pi\) |
−0.938991 | + | 0.343941i | \(0.888238\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.25441 | + | 10.8330i | 0.409740 | + | 0.709691i | 0.994860 | − | 0.101256i | \(-0.0322860\pi\) |
−0.585120 | + | 0.810947i | \(0.698953\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.704564 | − | 1.22034i | 0.0459607 | − | 0.0796062i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 14.5201 | 0.939228 | 0.469614 | − | 0.882872i | \(-0.344393\pi\) | ||||
0.469614 | + | 0.882872i | \(0.344393\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.31809 | + | 10.9433i | −0.406984 | + | 0.704917i | −0.994550 | − | 0.104259i | \(-0.966753\pi\) |
0.587566 | + | 0.809176i | \(0.300086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.04580 | + | 3.52821i | −0.386252 | + | 0.225409i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10.4348 | − | 18.0736i | −0.663952 | − | 1.15000i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.7531 | −1.62552 | −0.812762 | − | 0.582596i | \(-0.802037\pi\) | ||||
−0.812762 | + | 0.582596i | \(0.802037\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.458299 | 0.0288130 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.82662 | − | 8.35996i | −0.301077 | − | 0.521480i | 0.675304 | − | 0.737540i | \(-0.264013\pi\) |
−0.976380 | + | 0.216060i | \(0.930679\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.436051 | − | 1.64266i | 0.0270949 | − | 0.102070i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.8069 | + | 20.4501i | −0.728042 | + | 1.26101i | 0.229667 | + | 0.973269i | \(0.426236\pi\) |
−0.957709 | + | 0.287737i | \(0.907097\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.66919 | 0.593973 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.44923 | − | 12.9024i | 0.454188 | − | 0.786676i | −0.544453 | − | 0.838791i | \(-0.683263\pi\) |
0.998641 | + | 0.0521149i | \(0.0165962\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.2256 | − | 19.4433i | −0.681905 | − | 1.18109i | −0.974399 | − | 0.224827i | \(-0.927818\pi\) |
0.292494 | − | 0.956267i | \(-0.405515\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.56501 | + | 2.71069i | 0.0943739 | + | 0.163460i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.33400 | − | 16.1670i | 0.560826 | − | 0.971379i | −0.436599 | − | 0.899656i | \(-0.643817\pi\) |
0.997425 | − | 0.0717224i | \(-0.0228496\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.9279 | 1.18880 | 0.594400 | − | 0.804169i | \(-0.297390\pi\) | ||||
0.594400 | + | 0.804169i | \(0.297390\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.73835 | − | 16.8673i | 0.578885 | − | 1.00266i | −0.416723 | − | 0.909034i | \(-0.636821\pi\) |
0.995608 | − | 0.0936241i | \(-0.0298452\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 16.1843 | + | 16.1090i | 0.955326 | + | 0.950885i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.75047 | − | 11.6922i | −0.397087 | − | 0.687774i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.4381 | −1.42769 | −0.713844 | − | 0.700305i | \(-0.753047\pi\) | ||||
−0.713844 | + | 0.700305i | \(0.753047\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.34124 | −0.194534 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.259102 | − | 0.448778i | −0.0149842 | − | 0.0259535i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.1234 | − | 11.0717i | −0.641141 | − | 0.638160i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.19876 | + | 10.7366i | −0.354940 | + | 0.614774i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.63208 | −0.207294 | −0.103647 | − | 0.994614i | \(-0.533051\pi\) | ||||
−0.103647 | + | 0.994614i | \(0.533051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.89822 | − | 11.9481i | 0.391162 | − | 0.677513i | −0.601441 | − | 0.798917i | \(-0.705407\pi\) |
0.992603 | + | 0.121405i | \(0.0387399\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.45360 | − | 12.9100i | −0.421303 | − | 0.729718i | 0.574765 | − | 0.818319i | \(-0.305094\pi\) |
−0.996067 | + | 0.0886012i | \(0.971760\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.17616 | + | 2.03716i | 0.0660595 | + | 0.114418i | 0.897163 | − | 0.441699i | \(-0.145624\pi\) |
−0.831104 | + | 0.556117i | \(0.812291\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.56800 | + | 7.91200i | −0.255759 | + | 0.442987i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −32.5666 | −1.81205 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.76958 | − | 3.06500i | 0.0981586 | − | 0.170016i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.956536 | − | 3.60340i | 0.0527355 | − | 0.198662i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3584 | − | 28.3335i | −0.899137 | − | 1.55735i | −0.828600 | − | 0.559841i | \(-0.810862\pi\) |
−0.0705370 | − | 0.997509i | \(-0.522471\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2511 | −0.723985 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.65676 | 0.144723 | 0.0723615 | − | 0.997378i | \(-0.476946\pi\) | ||||
0.0723615 | + | 0.997378i | \(0.476946\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.96843 | + | 13.8017i | 0.431515 | + | 0.747406i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0039 | + | 13.1870i | −0.702147 | + | 0.712032i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −17.7311 | + | 30.7112i | −0.951856 | + | 1.64866i | −0.210451 | + | 0.977604i | \(0.567493\pi\) |
−0.741405 | + | 0.671058i | \(0.765840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.8638 | 1.06328 | 0.531642 | − | 0.846969i | \(-0.321575\pi\) | ||||
0.531642 | + | 0.846969i | \(0.321575\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −14.8473 | + | 25.7164i | −0.790244 | + | 1.36874i | 0.135571 | + | 0.990768i | \(0.456713\pi\) |
−0.925816 | + | 0.377976i | \(0.876620\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.329381 | + | 0.570505i | 0.0174817 | + | 0.0302792i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −17.5641 | − | 30.4219i | −0.926997 | − | 1.60561i | −0.788317 | − | 0.615269i | \(-0.789048\pi\) |
−0.138680 | − | 0.990337i | \(-0.544286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.88604 | + | 13.6590i | −0.415055 | + | 0.718896i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.69122 | 0.245550 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.94568 | − | 10.2982i | 0.310362 | − | 0.537563i | −0.668079 | − | 0.744091i | \(-0.732883\pi\) |
0.978441 | + | 0.206528i | \(0.0662164\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.6951 | − | 6.67874i | 1.28210 | − | 0.346743i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −12.7884 | − | 22.1501i | −0.662156 | − | 1.14689i | −0.980048 | − | 0.198761i | \(-0.936308\pi\) |
0.317892 | − | 0.948127i | \(-0.397025\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3302 | 0.532031 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.9174 | 1.38265 | 0.691327 | − | 0.722542i | \(-0.257026\pi\) | ||||
0.691327 | + | 0.722542i | \(0.257026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.99973 | − | 17.3200i | −0.510962 | − | 0.885013i | −0.999919 | − | 0.0127049i | \(-0.995956\pi\) |
0.488957 | − | 0.872308i | \(-0.337378\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.86938 | + | 5.84209i | 0.299131 | + | 0.297740i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.7269 | − | 28.9718i | 0.848087 | − | 1.46893i | −0.0348254 | − | 0.999393i | \(-0.511088\pi\) |
0.882913 | − | 0.469537i | \(-0.155579\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.808644 | −0.0408949 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.67499 | − | 4.63322i | 0.134593 | − | 0.233123i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.36765 | + | 2.36883i | 0.0686402 | + | 0.118888i | 0.898303 | − | 0.439377i | \(-0.144801\pi\) |
−0.829663 | + | 0.558265i | \(0.811467\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.53112 | + | 9.58018i | 0.276211 | + | 0.478412i | 0.970440 | − | 0.241343i | \(-0.0775878\pi\) |
−0.694229 | + | 0.719754i | \(0.744254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.00999 | − | 15.6058i | 0.448820 | − | 0.777378i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.01064 | −0.0996638 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.6241 | − | 23.5977i | 0.673669 | − | 1.16683i | −0.303187 | − | 0.952931i | \(-0.598051\pi\) |
0.976856 | − | 0.213898i | \(-0.0686160\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.53351 | + | 2.30787i | −0.419907 | + | 0.113563i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.73935 | − | 11.6729i | −0.330822 | − | 0.573000i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 17.9126 | 0.875090 | 0.437545 | − | 0.899197i | \(-0.355848\pi\) | ||||
0.437545 | + | 0.899197i | \(0.355848\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.4906 | 1.77844 | 0.889221 | − | 0.457478i | \(-0.151247\pi\) | ||||
0.889221 | + | 0.457478i | \(0.151247\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.76138 | − | 4.78286i | −0.133947 | − | 0.232003i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.41561 | + | 31.7028i | −0.407260 | + | 1.53421i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.52755 | − | 7.84194i | 0.218084 | − | 0.377733i | −0.736138 | − | 0.676831i | \(-0.763353\pi\) |
0.954222 | + | 0.299099i | \(0.0966859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.24154 | 0.155778 | 0.0778892 | − | 0.996962i | \(-0.475182\pi\) | ||||
0.0778892 | + | 0.996962i | \(0.475182\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −0.431704 | + | 0.747733i | −0.0206512 | + | 0.0357689i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.61353 | + | 16.6511i | 0.458829 | + | 0.794715i | 0.998899 | − | 0.0469050i | \(-0.0149358\pi\) |
−0.540071 | + | 0.841620i | \(0.681602\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.57427 | − | 2.72671i | −0.0747956 | − | 0.129550i | 0.826202 | − | 0.563374i | \(-0.190497\pi\) |
−0.900997 | + | 0.433825i | \(0.857164\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.20978 | + | 12.4877i | −0.341776 | + | 0.591974i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −20.8343 | −0.983233 | −0.491616 | − | 0.870812i | \(-0.663594\pi\) | ||||
−0.491616 | + | 0.870812i | \(0.663594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.5073 | − | 23.3953i | 0.636032 | − | 1.10164i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.40243 | − | 9.05029i | 0.112628 | − | 0.424284i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.4872 | − | 30.2888i | −0.818018 | − | 1.41685i | −0.907140 | − | 0.420828i | \(-0.861740\pi\) |
0.0891226 | − | 0.996021i | \(-0.471594\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 36.4665 | 1.69842 | 0.849208 | − | 0.528058i | \(-0.177080\pi\) | ||||
0.849208 | + | 0.528058i | \(0.177080\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −28.6711 | −1.33246 | −0.666230 | − | 0.745747i | \(-0.732093\pi\) | ||||
−0.666230 | + | 0.745747i | \(0.732093\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −0.0975696 | − | 0.168996i | −0.00451498 | − | 0.00782018i | 0.863759 | − | 0.503905i | \(-0.168104\pi\) |
−0.868274 | + | 0.496085i | \(0.834771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.8433 | + | 9.15285i | −1.56274 | + | 0.422639i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.28350 | + | 16.0795i | −0.426856 | + | 0.739336i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.89679 | −0.270563 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.78547 | + | 10.0207i | −0.264345 | + | 0.457859i | −0.967392 | − | 0.253285i | \(-0.918489\pi\) |
0.703047 | + | 0.711144i | \(0.251822\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.13673 | + | 1.96887i | 0.0518303 | + | 0.0897727i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.43200 | − | 2.48030i | −0.0650239 | − | 0.112625i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7824 | − | 25.6039i | 0.669854 | − | 1.16022i | −0.308090 | − | 0.951357i | \(-0.599690\pi\) |
0.977945 | − | 0.208864i | \(-0.0669767\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 39.0817 | 1.76373 | 0.881866 | − | 0.471501i | \(-0.156288\pi\) | ||||
0.881866 | + | 0.471501i | \(0.156288\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.05998 | − | 13.9603i | 0.363003 | − | 0.628740i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.23530 | + | 1.22956i | 0.0554107 | + | 0.0551531i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −8.43216 | − | 14.6049i | −0.377475 | − | 0.653807i | 0.613219 | − | 0.789913i | \(-0.289874\pi\) |
−0.990694 | + | 0.136106i | \(0.956541\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −17.2768 | −0.770335 | −0.385167 | − | 0.922847i | \(-0.625856\pi\) | ||||
−0.385167 | + | 0.922847i | \(0.625856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5572 | 0.603289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.189173 | − | 0.327657i | −0.00838495 | − | 0.0145232i | 0.861802 | − | 0.507244i | \(-0.169336\pi\) |
−0.870187 | + | 0.492721i | \(0.836002\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9814 | − | 3.24034i | 0.530024 | − | 0.143344i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.93084 | + | 5.07636i | −0.129148 | + | 0.223691i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.41061 | −0.193978 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.39844 | − | 16.2786i | 0.411753 | − | 0.713178i | −0.583328 | − | 0.812237i | \(-0.698250\pi\) |
0.995082 | + | 0.0990588i | \(0.0315832\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.76719 | + | 6.52496i | 0.164728 | + | 0.285317i | 0.936559 | − | 0.350511i | \(-0.113992\pi\) |
−0.771831 | + | 0.635828i | \(0.780659\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.0599 | − | 24.3524i | −0.612457 | − | 1.06081i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4893 | − | 19.9000i | 0.499534 | − | 0.865218i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −30.5456 | −1.32308 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.76138 | − | 6.51491i | 0.162619 | − | 0.281664i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 19.0256 | + | 10.8666i | 0.819492 | + | 0.468056i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.347666 | + | 0.602175i | 0.0149473 | + | 0.0258895i | 0.873402 | − | 0.486999i | \(-0.161909\pi\) |
−0.858455 | + | 0.512889i | \(0.828575\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.72833 | −0.245375 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.8791 | 0.935482 | 0.467741 | − | 0.883866i | \(-0.345068\pi\) | ||||
0.467741 | + | 0.883866i | \(0.345068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.60583 | − | 14.9057i | −0.366621 | − | 0.635006i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.63165 | − | 13.6809i | 0.154433 | − | 0.581772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.4950 | − | 32.0343i | 0.783660 | − | 1.35734i | −0.146137 | − | 0.989264i | \(-0.546684\pi\) |
0.929796 | − | 0.368074i | \(-0.119983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20.9939 | 0.887947 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −20.8040 | + | 36.0336i | −0.876784 | + | 1.51863i | −0.0219336 | + | 0.999759i | \(0.506982\pi\) |
−0.854850 | + | 0.518875i | \(0.826351\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.75037 | − | 8.22787i | −0.199849 | − | 0.346149i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.42337 | + | 16.3218i | 0.395048 | + | 0.684244i | 0.993107 | − | 0.117208i | \(-0.0373945\pi\) |
−0.598059 | + | 0.801452i | \(0.704061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.33875 | + | 16.1752i | −0.390815 | + | 0.676911i | −0.992557 | − | 0.121779i | \(-0.961140\pi\) |
0.601743 | + | 0.798690i | \(0.294473\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −0.146420 | −0.00610614 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 13.9151 | − | 24.1016i | 0.579292 | − | 1.00336i | −0.416269 | − | 0.909242i | \(-0.636662\pi\) |
0.995561 | − | 0.0941215i | \(-0.0300042\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.2750 | − | 25.1575i | −1.04858 | − | 1.04371i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −15.1324 | − | 26.2101i | −0.626721 | − | 1.08551i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.4459 | 0.720070 | 0.360035 | − | 0.932939i | \(-0.382765\pi\) | ||||
0.360035 | + | 0.932939i | \(0.382765\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −30.0241 | −1.23712 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.44153 | + | 14.6212i | 0.346652 | + | 0.600419i | 0.985653 | − | 0.168787i | \(-0.0539851\pi\) |
−0.639000 | + | 0.769206i | \(0.720652\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.3562 | − | 10.3080i | −0.424563 | − | 0.422589i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.76198 | + | 4.78388i | −0.112851 | + | 0.195464i | −0.916919 | − | 0.399074i | \(-0.869332\pi\) |
0.804067 | + | 0.594538i | \(0.202665\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.7051 | 1.70119 | 0.850593 | − | 0.525824i | \(-0.176243\pi\) | ||||
0.850593 | + | 0.525824i | \(0.176243\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.601458 | + | 1.04176i | −0.0244527 | + | 0.0423534i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.3356 | + | 24.8299i | 0.581862 | + | 1.00781i | 0.995259 | + | 0.0972636i | \(0.0310090\pi\) |
−0.413397 | + | 0.910551i | \(0.635658\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.49356 | + | 4.31898i | 0.100879 | + | 0.174727i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.10644 | − | 5.38052i | 0.125468 | − | 0.217317i | −0.796448 | − | 0.604707i | \(-0.793290\pi\) |
0.921916 | + | 0.387390i | \(0.126623\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −14.6550 | −0.589988 | −0.294994 | − | 0.955499i | \(-0.595318\pi\) | ||||
−0.294994 | + | 0.955499i | \(0.595318\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.4589 | − | 26.7756i | 0.621347 | − | 1.07620i | −0.367889 | − | 0.929870i | \(-0.619919\pi\) |
0.989235 | − | 0.146334i | \(-0.0467475\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.78820 | + | 36.8735i | −0.392156 | + | 1.47731i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.54767 | 0.141455 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.4514 | −0.933584 | −0.466792 | − | 0.884367i | \(-0.654590\pi\) | ||||
−0.466792 | + | 0.884367i | \(0.654590\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.25724 | + | 9.10580i | 0.208627 | + | 0.361353i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.115449 | − | 24.7738i | −0.00457426 | − | 0.981575i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.6564 | + | 18.4574i | −0.420903 | + | 0.729025i | −0.996028 | − | 0.0890406i | \(-0.971620\pi\) |
0.575125 | + | 0.818065i | \(0.304953\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.958256 | −0.0377899 | −0.0188950 | − | 0.999821i | \(-0.506015\pi\) | ||||
−0.0188950 | + | 0.999821i | \(0.506015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0.836865 | − | 1.44949i | 0.0329006 | − | 0.0569855i | −0.849106 | − | 0.528222i | \(-0.822859\pi\) |
0.882007 | + | 0.471237i | \(0.156192\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.22909 | + | 9.05704i | 0.205260 | + | 0.355520i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.2047 | − | 31.5315i | −0.712405 | − | 1.23392i | −0.963952 | − | 0.266077i | \(-0.914273\pi\) |
0.251547 | − | 0.967845i | \(-0.419061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.105604 | − | 0.182912i | 0.00412630 | − | 0.00714696i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.6686 | −0.688273 | −0.344136 | − | 0.938920i | \(-0.611828\pi\) | ||||
−0.344136 | + | 0.938920i | \(0.611828\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.772562 | − | 1.33812i | 0.0300492 | − | 0.0520467i | −0.850610 | − | 0.525798i | \(-0.823767\pi\) |
0.880659 | + | 0.473751i | \(0.157100\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −15.0604 | + | 4.07305i | −0.584016 | + | 0.157946i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.213687 | − | 0.370117i | −0.00827399 | − | 0.0143310i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.8046 | 1.49803 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.0768 | 1.73758 | 0.868792 | − | 0.495178i | \(-0.164897\pi\) | ||||
0.868792 | + | 0.495178i | \(0.164897\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −15.3864 | − | 26.6501i | −0.591349 | − | 1.02425i | −0.994051 | − | 0.108916i | \(-0.965262\pi\) |
0.402702 | − | 0.915331i | \(-0.368071\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.37053 | − | 5.34556i | −0.206102 | − | 0.205144i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.48261 | + | 4.30000i | −0.0949943 | + | 0.164535i | −0.909606 | − | 0.415471i | \(-0.863617\pi\) |
0.814612 | + | 0.580006i | \(0.196950\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.15971 | 0.273558 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −17.1104 | + | 29.6361i | −0.651854 | + | 1.12904i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.58026 | − | 13.1294i | −0.288367 | − | 0.499466i | 0.685053 | − | 0.728493i | \(-0.259779\pi\) |
−0.973420 | + | 0.229027i | \(0.926446\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.63657 | − | 2.83462i | −0.0620785 | − | 0.107523i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23.8328 | + | 41.2797i | −0.902733 | + | 1.56358i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9545 | 0.640364 | 0.320182 | − | 0.947356i | \(-0.396256\pi\) | ||||
0.320182 | + | 0.947356i | \(0.396256\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.89396 | − | 3.28044i | 0.0714322 | − | 0.123724i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 34.6251 | − | 9.36430i | 1.30221 | − | 0.352181i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1603 | − | 40.1149i | −0.869805 | − | 1.50655i | −0.862196 | − | 0.506575i | \(-0.830911\pi\) |
−0.00760839 | − | 0.999971i | \(-0.502422\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.745513 | −0.0279197 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.0777 | −0.414281 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −10.2544 | − | 17.7612i | −0.382425 | − | 0.662380i | 0.608983 | − | 0.793183i | \(-0.291578\pi\) |
−0.991408 | + | 0.130803i | \(0.958244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.97899 | + | 14.9894i | −0.148185 | + | 0.558235i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.45941 | − | 2.52777i | 0.0542011 | − | 0.0938791i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 42.7056 | 1.58386 | 0.791931 | − | 0.610611i | \(-0.209076\pi\) | ||||
0.791931 | + | 0.610611i | \(0.209076\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 16.3802 | − | 28.3714i | 0.605845 | − | 1.04935i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.31438 | + | 16.1330i | 0.344034 | + | 0.595885i | 0.985178 | − | 0.171536i | \(-0.0548730\pi\) |
−0.641143 | + | 0.767421i | \(0.721540\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.7382 | + | 35.9195i | 0.763900 | + | 1.32311i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.39263 | + | 12.8044i | −0.271942 | + | 0.471018i | −0.969359 | − | 0.245648i | \(-0.920999\pi\) |
0.697417 | + | 0.716666i | \(0.254333\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.3016 | 0.487988 | 0.243994 | − | 0.969777i | \(-0.421542\pi\) | ||||
0.243994 | + | 0.969777i | \(0.421542\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.50405 | − | 6.06919i | 0.128378 | − | 0.222358i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.10656 | − | 19.2371i | 0.186590 | − | 0.702909i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.1441 | − | 24.4983i | −0.516126 | − | 0.893956i | −0.999825 | − | 0.0187215i | \(-0.994040\pi\) |
0.483699 | − | 0.875234i | \(-0.339293\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −19.1568 | −0.697189 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.8800 | −1.08601 | −0.543003 | − | 0.839731i | \(-0.682713\pi\) | ||||
−0.543003 | + | 0.839731i | \(0.682713\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.7487 | + | 44.5980i | 0.933389 | + | 1.61668i | 0.777482 | + | 0.628905i | \(0.216497\pi\) |
0.155906 | + | 0.987772i | \(0.450170\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.6301 | + | 3.95669i | −0.529647 | + | 0.143242i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.91258 | − | 10.2409i | 0.213491 | − | 0.369777i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.9959 | −1.18986 | −0.594932 | − | 0.803776i | \(-0.702821\pi\) | ||||
−0.594932 | + | 0.803776i | \(0.702821\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7.56630 | − | 13.1052i | 0.272141 | − | 0.471362i | −0.697269 | − | 0.716810i | \(-0.745602\pi\) |
0.969410 | + | 0.245448i | \(0.0789350\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.54580 | − | 4.40946i | −0.0914479 | − | 0.158392i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 25.4469 | + | 44.0753i | 0.911729 | + | 1.57916i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.03097 | − | 1.78570i | 0.0368911 | − | 0.0638972i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.00478 | −0.214320 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.70761 | − | 11.6179i | 0.239101 | − | 0.414134i | −0.721356 | − | 0.692565i | \(-0.756481\pi\) |
0.960456 | + | 0.278430i | \(0.0898141\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −17.8156 | − | 17.7328i | −0.633450 | − | 0.630505i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.9384 | − | 37.9984i | −0.779055 | − | 1.34936i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 26.8075 | 0.949571 | 0.474785 | − | 0.880102i | \(-0.342526\pi\) | ||||
0.474785 | + | 0.880102i | \(0.342526\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.78228 | 0.275317 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.34183 | − | 12.7164i | −0.259088 | − | 0.448753i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.373956 | + | 0.101136i | −0.0131802 | + | 0.00356457i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0360362 | − | 0.0624165i | 0.00126697 | − | 0.00219445i | −0.865391 | − | 0.501097i | \(-0.832930\pi\) |
0.866658 | + | 0.498902i | \(0.166263\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.2578 | 0.922038 | 0.461019 | − | 0.887390i | \(-0.347484\pi\) | ||||
0.461019 | + | 0.887390i | \(0.347484\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.41955 | + | 11.1190i | −0.224867 | + | 0.389481i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17.4896 | − | 30.2928i | −0.611882 | − | 1.05981i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.29573 | − | 3.97633i | −0.0801217 | − | 0.138775i | 0.823180 | − | 0.567780i | \(-0.192198\pi\) |
−0.903302 | + | 0.429005i | \(0.858864\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.2120 | + | 29.8121i | −0.599974 | + | 1.03919i | 0.392850 | + | 0.919603i | \(0.371489\pi\) |
−0.992824 | + | 0.119583i | \(0.961844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.9574 | 0.589666 | 0.294833 | − | 0.955549i | \(-0.404736\pi\) | ||||
0.294833 | + | 0.955549i | \(0.404736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.36886 | − | 7.56709i | 0.151737 | − | 0.262816i | −0.780129 | − | 0.625618i | \(-0.784847\pi\) |
0.931866 | + | 0.362802i | \(0.118180\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.5697 | − | 19.1735i | −1.16312 | − | 0.664321i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.07321 | − | 1.85885i | −0.0371400 | − | 0.0643283i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.15230 | −0.108830 | −0.0544148 | − | 0.998518i | \(-0.517329\pi\) | ||||
−0.0544148 | + | 0.998518i | \(0.517329\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.4805 | −0.706224 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.237184 | − | 0.410815i | −0.00815938 | − | 0.0141325i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.816556 | + | 3.07608i | −0.0280572 | + | 0.105695i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.0470280 | − | 0.0814549i | 0.00161210 | − | 0.00279224i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 34.9120 | 1.19536 | 0.597682 | − | 0.801733i | \(-0.296089\pi\) | ||||
0.597682 | + | 0.801733i | \(0.296089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.0322 | + | 38.1609i | −0.752605 | + | 1.30355i | 0.193951 | + | 0.981011i | \(0.437870\pi\) |
−0.946556 | + | 0.322539i | \(0.895464\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.61353 | − | 16.6511i | −0.328009 | − | 0.568129i | 0.654107 | − | 0.756402i | \(-0.273044\pi\) |
−0.982117 | + | 0.188273i | \(0.939711\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −4.40940 | − | 7.63730i | −0.150098 | − | 0.259977i | 0.781166 | − | 0.624324i | \(-0.214625\pi\) |
−0.931263 | + | 0.364347i | \(0.881292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.08423 | + | 1.87794i | −0.0368648 | + | 0.0638518i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.7456 | −0.568056 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 23.4489 | − | 40.6146i | 0.794534 | − | 1.37617i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.87518 | − | 1.86646i | −0.0633927 | − | 0.0630980i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.8631 | − | 36.1359i | −0.704496 | − | 1.22022i | −0.966873 | − | 0.255257i | \(-0.917840\pi\) |
0.262377 | − | 0.964965i | \(-0.415494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.3791 | −0.686590 | −0.343295 | − | 0.939228i | \(-0.611543\pi\) | ||||
−0.343295 | + | 0.939228i | \(0.611543\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.35431 | 0.213840 | 0.106920 | − | 0.994268i | \(-0.465901\pi\) | ||||
0.106920 | + | 0.994268i | \(0.465901\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.75542 | + | 9.96867i | 0.193248 | + | 0.334715i | 0.946325 | − | 0.323217i | \(-0.104764\pi\) |
−0.753077 | + | 0.657933i | \(0.771431\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 19.7166 | + | 19.6249i | 0.661272 | + | 0.658198i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.15466 | − | 7.19608i | 0.139030 | − | 0.240808i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.92647 | −0.0978210 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7.43074 | − | 12.8704i | 0.247829 | − | 0.429252i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.7003 | + | 46.2463i | 0.889517 | + | 1.54069i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.7315 | + | 18.5875i | 0.356727 | + | 0.617869i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.7519 | + | 22.0869i | −0.423419 | + | 0.733383i | −0.996271 | − | 0.0862754i | \(-0.972504\pi\) |
0.572852 | + | 0.819659i | \(0.305837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.5459 | 1.24395 | 0.621976 | − | 0.783036i | \(-0.286330\pi\) | ||||
0.621976 | + | 0.783036i | \(0.286330\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −21.0944 | + | 36.5365i | −0.698121 | + | 1.20918i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.143371 | − | 0.540100i | 0.00473454 | − | 0.0178357i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.69222 | + | 8.12717i | 0.154782 | + | 0.268090i | 0.932980 | − | 0.359929i | \(-0.117199\pi\) |
−0.778198 | + | 0.628020i | \(0.783866\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.33146 | −0.0767410 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.642371 | 0.0211210 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.7943 | + | 29.0886i | 0.551003 | + | 0.954365i | 0.998203 | + | 0.0599308i | \(0.0190880\pi\) |
−0.447200 | + | 0.894434i | \(0.647579\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −35.6508 | + | 20.8051i | −1.16841 | + | 0.681860i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.64321 | + | 14.9705i | −0.282663 | + | 0.489587i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.4312 | 1.12482 | 0.562409 | − | 0.826860i | \(-0.309875\pi\) | ||||
0.562409 | + | 0.826860i | \(0.309875\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.9732 | − | 43.2549i | 0.814104 | − | 1.41007i | −0.0958663 | − | 0.995394i | \(-0.530562\pi\) |
0.909970 | − | 0.414674i | \(-0.136105\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.631858 | + | 1.09441i | 0.0205761 | + | 0.0356389i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −11.0586 | − | 19.1540i | −0.359355 | − | 0.622420i | 0.628499 | − | 0.777811i | \(-0.283670\pi\) |
−0.987853 | + | 0.155390i | \(0.950336\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.30149 | + | 14.3786i | −0.269478 | + | 0.466749i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.8406 | −1.93843 | −0.969213 | − | 0.246224i | \(-0.920810\pi\) | ||||
−0.969213 | + | 0.246224i | \(0.920810\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −10.2731 | + | 17.7936i | −0.332431 | + | 0.575787i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.2859 | − | 4.94538i | 0.590482 | − | 0.159695i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.53779 | + | 4.39558i | 0.0818641 | + | 0.141793i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17.3624 | −0.558916 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.70505 | 0.119146 | 0.0595732 | − | 0.998224i | \(-0.481026\pi\) | ||||
0.0595732 | + | 0.998224i | \(0.481026\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.66137 | − | 4.60963i | −0.0854074 | − | 0.147930i | 0.820157 | − | 0.572138i | \(-0.193886\pi\) |
−0.905565 | + | 0.424208i | \(0.860553\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.13772 | − | 6.10918i | −0.196766 | − | 0.195851i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.6726 | − | 27.1457i | 0.501410 | − | 0.868467i | −0.498589 | − | 0.866838i | \(-0.666148\pi\) |
0.999999 | − | 0.00162842i | \(-0.000518343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45.1336 | 1.44248 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26.6847 | − | 46.2193i | 0.851110 | − | 1.47417i | −0.0290970 | − | 0.999577i | \(-0.509263\pi\) |
0.880207 | − | 0.474590i | \(-0.157403\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.4543 | + | 21.5715i | 0.396828 | + | 0.687326i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.434274 | − | 0.752185i | −0.0138091 | − | 0.0239181i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.81499 | − | 6.60776i | 0.121187 | − | 0.209902i | −0.799049 | − | 0.601266i | \(-0.794663\pi\) |
0.920236 | + | 0.391364i | \(0.127997\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −11.9423 | −0.378597 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.09598 | + | 12.2906i | −0.224732 | + | 0.389247i | −0.956239 | − | 0.292587i | \(-0.905484\pi\) |
0.731507 | + | 0.681834i | \(0.238817\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 2520.2.bi.s.361.5 | yes | 10 | |
3.2 | odd | 2 | 2520.2.bi.r.361.5 | ✓ | 10 | ||
7.2 | even | 3 | inner | 2520.2.bi.s.1801.5 | yes | 10 | |
21.2 | odd | 6 | 2520.2.bi.r.1801.5 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2520.2.bi.r.361.5 | ✓ | 10 | 3.2 | odd | 2 | ||
2520.2.bi.r.1801.5 | yes | 10 | 21.2 | odd | 6 | ||
2520.2.bi.s.361.5 | yes | 10 | 1.1 | even | 1 | trivial | |
2520.2.bi.s.1801.5 | yes | 10 | 7.2 | even | 3 | inner |