Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.b.694.2 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.00000i | − | 0.707107i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.00000 | + | 1.00000i | −0.894427 | + | 0.447214i | ||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 3.00000i | − | 1.06066i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 1.00000 | + | 2.00000i | 0.316228 | + | 0.632456i | ||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 1.00000 | + | 2.00000i | 0.258199 | + | 0.516398i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | − | 6.00000i | − | 1.45521i | −0.685994 | − | 0.727607i | \(-0.740633\pi\) | ||
0.685994 | − | 0.727607i | \(-0.259367\pi\) | |||||||
\(18\) | 1.00000i | 0.235702i | ||||||||
\(19\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(20\) | −2.00000 | + | 1.00000i | −0.447214 | + | 0.223607i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 1.00000i | − | 0.213201i | ||||||
\(23\) | − | 6.00000i | − | 1.25109i | −0.780189 | − | 0.625543i | \(-0.784877\pi\) | ||
0.780189 | − | 0.625543i | \(-0.215123\pi\) | |||||||
\(24\) | −3.00000 | −0.612372 | ||||||||
\(25\) | 3.00000 | − | 4.00000i | 0.600000 | − | 0.800000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 1.00000i | 0.188982i | ||||||||
\(29\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(30\) | 2.00000 | − | 1.00000i | 0.365148 | − | 0.182574i | ||||
\(31\) | −6.00000 | −1.07763 | −0.538816 | − | 0.842424i | \(-0.681128\pi\) | ||||
−0.538816 | + | 0.842424i | \(0.681128\pi\) | |||||||
\(32\) | − | 5.00000i | − | 0.883883i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | −6.00000 | −1.02899 | ||||||||
\(35\) | −1.00000 | − | 2.00000i | −0.169031 | − | 0.338062i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | − | 4.00000i | − | 0.657596i | −0.944400 | − | 0.328798i | \(-0.893356\pi\) | ||
0.944400 | − | 0.328798i | \(-0.106644\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.00000 | + | 6.00000i | 0.474342 | + | 0.948683i | ||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | − | 1.00000i | − | 0.154303i | ||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 2.00000 | − | 1.00000i | 0.298142 | − | 0.149071i | ||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | − | 8.00000i | − | 1.16692i | −0.812142 | − | 0.583460i | \(-0.801699\pi\) | ||
0.812142 | − | 0.583460i | \(-0.198301\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.00000 | − | 3.00000i | −0.565685 | − | 0.424264i | ||||
\(51\) | −6.00000 | −0.840168 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2.00000i | − | 0.274721i | −0.990521 | − | 0.137361i | \(-0.956138\pi\) | ||
0.990521 | − | 0.137361i | \(-0.0438619\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.00000 | + | 1.00000i | −0.269680 | + | 0.134840i | ||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 1.00000 | + | 2.00000i | 0.129099 | + | 0.258199i | ||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 6.00000i | 0.762001i | ||||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | −7.00000 | −0.875000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.00000 | −0.123091 | ||||||||
\(67\) | − | 4.00000i | − | 0.488678i | −0.969690 | − | 0.244339i | \(-0.921429\pi\) | ||
0.969690 | − | 0.244339i | \(-0.0785709\pi\) | |||||||
\(68\) | − | 6.00000i | − | 0.727607i | ||||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | −2.00000 | + | 1.00000i | −0.239046 | + | 0.119523i | ||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 3.00000i | 0.353553i | ||||||||
\(73\) | − | 4.00000i | − | 0.468165i | −0.972217 | − | 0.234082i | \(-0.924791\pi\) | ||
0.972217 | − | 0.234082i | \(-0.0752085\pi\) | |||||||
\(74\) | −4.00000 | −0.464991 | ||||||||
\(75\) | −4.00000 | − | 3.00000i | −0.461880 | − | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.00000i | 0.113961i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.00000 | −0.225018 | −0.112509 | − | 0.993651i | \(-0.535889\pi\) | ||||
−0.112509 | + | 0.993651i | \(0.535889\pi\) | |||||||
\(80\) | 2.00000 | − | 1.00000i | 0.223607 | − | 0.111803i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 6.00000i | 0.662589i | ||||||||
\(83\) | 6.00000i | 0.658586i | 0.944228 | + | 0.329293i | \(0.106810\pi\) | ||||
−0.944228 | + | 0.329293i | \(0.893190\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 6.00000 | + | 12.0000i | 0.650791 | + | 1.30158i | ||||
\(86\) | 4.00000 | 0.431331 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 3.00000i | − | 0.319801i | ||||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | −1.00000 | − | 2.00000i | −0.105409 | − | 0.210819i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 6.00000i | − | 0.625543i | ||||||
\(93\) | 6.00000i | 0.622171i | ||||||||
\(94\) | −8.00000 | −0.825137 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.00000 | −0.510310 | ||||||||
\(97\) | 6.00000i | 0.609208i | 0.952479 | + | 0.304604i | \(0.0985241\pi\) | ||||
−0.952479 | + | 0.304604i | \(0.901476\pi\) | |||||||
\(98\) | 1.00000i | 0.101015i | ||||||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 3.00000 | − | 4.00000i | 0.300000 | − | 0.400000i | ||||
\(101\) | −14.0000 | −1.39305 | −0.696526 | − | 0.717532i | \(-0.745272\pi\) | ||||
−0.696526 | + | 0.717532i | \(0.745272\pi\) | |||||||
\(102\) | 6.00000i | 0.594089i | ||||||||
\(103\) | 8.00000i | 0.788263i | 0.919054 | + | 0.394132i | \(0.128955\pi\) | ||||
−0.919054 | + | 0.394132i | \(0.871045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | + | 1.00000i | −0.195180 | + | 0.0975900i | ||||
\(106\) | −2.00000 | −0.194257 | ||||||||
\(107\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | 1.00000 | + | 2.00000i | 0.0953463 | + | 0.190693i | ||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | − | 1.00000i | − | 0.0944911i | ||||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.00000 | + | 12.0000i | 0.559503 | + | 1.11901i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.00000 | 0.550019 | ||||||||
\(120\) | 6.00000 | − | 3.00000i | 0.547723 | − | 0.273861i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | − | 2.00000i | − | 0.181071i | ||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | −6.00000 | −0.538816 | ||||||||
\(125\) | −2.00000 | + | 11.0000i | −0.178885 | + | 0.983870i | ||||
\(126\) | −1.00000 | −0.0890871 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | − | 3.00000i | − | 0.265165i | ||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | − | 1.00000i | − | 0.0870388i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | −1.00000 | − | 2.00000i | −0.0860663 | − | 0.172133i | ||||
\(136\) | −18.0000 | −1.54349 | ||||||||
\(137\) | 14.0000i | 1.19610i | 0.801459 | + | 0.598050i | \(0.204058\pi\) | ||||
−0.801459 | + | 0.598050i | \(0.795942\pi\) | |||||||
\(138\) | 6.00000i | 0.510754i | ||||||||
\(139\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(140\) | −1.00000 | − | 2.00000i | −0.0845154 | − | 0.169031i | ||||
\(141\) | −8.00000 | −0.673722 | ||||||||
\(142\) | − | 8.00000i | − | 0.671345i | ||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 4.00000i | − | 0.328798i | ||||||
\(149\) | −8.00000 | −0.655386 | −0.327693 | − | 0.944784i | \(-0.606271\pi\) | ||||
−0.327693 | + | 0.944784i | \(0.606271\pi\) | |||||||
\(150\) | −3.00000 | + | 4.00000i | −0.244949 | + | 0.326599i | ||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.00000i | 0.485071i | ||||||||
\(154\) | 1.00000 | 0.0805823 | ||||||||
\(155\) | 12.0000 | − | 6.00000i | 0.963863 | − | 0.481932i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000i | 1.11732i | 0.829396 | + | 0.558661i | \(0.188685\pi\) | ||||
−0.829396 | + | 0.558661i | \(0.811315\pi\) | |||||||
\(158\) | 2.00000i | 0.159111i | ||||||||
\(159\) | −2.00000 | −0.158610 | ||||||||
\(160\) | 5.00000 | + | 10.0000i | 0.395285 | + | 0.790569i | ||||
\(161\) | 6.00000 | 0.472866 | ||||||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | − | 24.0000i | − | 1.87983i | −0.341415 | − | 0.939913i | \(-0.610906\pi\) | ||
0.341415 | − | 0.939913i | \(-0.389094\pi\) | |||||||
\(164\) | −6.00000 | −0.468521 | ||||||||
\(165\) | 1.00000 | + | 2.00000i | 0.0778499 | + | 0.155700i | ||||
\(166\) | 6.00000 | 0.465690 | ||||||||
\(167\) | − | 2.00000i | − | 0.154765i | −0.997001 | − | 0.0773823i | \(-0.975344\pi\) | ||
0.997001 | − | 0.0773823i | \(-0.0246562\pi\) | |||||||
\(168\) | − | 3.00000i | − | 0.231455i | ||||||
\(169\) | 13.0000 | 1.00000 | ||||||||
\(170\) | 12.0000 | − | 6.00000i | 0.920358 | − | 0.460179i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000i | 0.304997i | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.00000 | + | 3.00000i | 0.302372 | + | 0.226779i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 12.0000i | − | 0.899438i | ||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 2.00000 | − | 1.00000i | 0.149071 | − | 0.0745356i | ||||
\(181\) | −2.00000 | −0.148659 | −0.0743294 | − | 0.997234i | \(-0.523682\pi\) | ||||
−0.0743294 | + | 0.997234i | \(0.523682\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 2.00000i | − | 0.147844i | ||||||
\(184\) | −18.0000 | −1.32698 | ||||||||
\(185\) | 4.00000 | + | 8.00000i | 0.294086 | + | 0.588172i | ||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | − | 6.00000i | − | 0.438763i | ||||||
\(188\) | − | 8.00000i | − | 0.583460i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 7.00000i | 0.505181i | ||||||||
\(193\) | − | 2.00000i | − | 0.143963i | −0.997406 | − | 0.0719816i | \(-0.977068\pi\) | ||
0.997406 | − | 0.0719816i | \(-0.0229323\pi\) | |||||||
\(194\) | 6.00000 | 0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | 18.0000i | 1.28245i | 0.767354 | + | 0.641223i | \(0.221573\pi\) | ||||
−0.767354 | + | 0.641223i | \(0.778427\pi\) | |||||||
\(198\) | 1.00000i | 0.0710669i | ||||||||
\(199\) | 14.0000 | 0.992434 | 0.496217 | − | 0.868199i | \(-0.334722\pi\) | ||||
0.496217 | + | 0.868199i | \(0.334722\pi\) | |||||||
\(200\) | −12.0000 | − | 9.00000i | −0.848528 | − | 0.636396i | ||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 14.0000i | 0.985037i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −6.00000 | −0.420084 | ||||||||
\(205\) | 12.0000 | − | 6.00000i | 0.838116 | − | 0.419058i | ||||
\(206\) | 8.00000 | 0.557386 | ||||||||
\(207\) | 6.00000i | 0.417029i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.00000 | + | 2.00000i | 0.0690066 | + | 0.138013i | ||||
\(211\) | 2.00000 | 0.137686 | 0.0688428 | − | 0.997628i | \(-0.478069\pi\) | ||||
0.0688428 | + | 0.997628i | \(0.478069\pi\) | |||||||
\(212\) | − | 2.00000i | − | 0.137361i | ||||||
\(213\) | − | 8.00000i | − | 0.548151i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | − | 8.00000i | −0.272798 | − | 0.545595i | ||||
\(216\) | 3.00000 | 0.204124 | ||||||||
\(217\) | − | 6.00000i | − | 0.407307i | ||||||
\(218\) | − | 18.0000i | − | 1.21911i | ||||||
\(219\) | −4.00000 | −0.270295 | ||||||||
\(220\) | −2.00000 | + | 1.00000i | −0.134840 | + | 0.0674200i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 4.00000i | 0.268462i | ||||||||
\(223\) | 8.00000i | 0.535720i | 0.963458 | + | 0.267860i | \(0.0863164\pi\) | ||||
−0.963458 | + | 0.267860i | \(0.913684\pi\) | |||||||
\(224\) | 5.00000 | 0.334077 | ||||||||
\(225\) | −3.00000 | + | 4.00000i | −0.200000 | + | 0.266667i | ||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | − | 22.0000i | − | 1.46019i | −0.683345 | − | 0.730096i | \(-0.739475\pi\) | ||
0.683345 | − | 0.730096i | \(-0.260525\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 12.0000 | − | 6.00000i | 0.791257 | − | 0.395628i | ||||
\(231\) | 1.00000 | 0.0657952 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 26.0000i | − | 1.70332i | −0.524097 | − | 0.851658i | \(-0.675597\pi\) | ||
0.524097 | − | 0.851658i | \(-0.324403\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | + | 16.0000i | 0.521862 | + | 1.04372i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.00000i | 0.129914i | ||||||||
\(238\) | − | 6.00000i | − | 0.388922i | ||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | −1.00000 | − | 2.00000i | −0.0645497 | − | 0.129099i | ||||
\(241\) | −14.0000 | −0.901819 | −0.450910 | − | 0.892570i | \(-0.648900\pi\) | ||||
−0.450910 | + | 0.892570i | \(0.648900\pi\) | |||||||
\(242\) | − | 1.00000i | − | 0.0642824i | ||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | 2.00000 | 0.128037 | ||||||||
\(245\) | 2.00000 | − | 1.00000i | 0.127775 | − | 0.0638877i | ||||
\(246\) | 6.00000 | 0.382546 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 18.0000i | 1.14300i | ||||||||
\(249\) | 6.00000 | 0.380235 | ||||||||
\(250\) | 11.0000 | + | 2.00000i | 0.695701 | + | 0.126491i | ||||
\(251\) | 12.0000 | 0.757433 | 0.378717 | − | 0.925513i | \(-0.376365\pi\) | ||||
0.378717 | + | 0.925513i | \(0.376365\pi\) | |||||||
\(252\) | − | 1.00000i | − | 0.0629941i | ||||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 12.0000 | − | 6.00000i | 0.751469 | − | 0.375735i | ||||
\(256\) | −17.0000 | −1.06250 | ||||||||
\(257\) | − | 14.0000i | − | 0.873296i | −0.899632 | − | 0.436648i | \(-0.856166\pi\) | ||
0.899632 | − | 0.436648i | \(-0.143834\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.0000i | 0.741362i | ||||||||
\(263\) | 28.0000i | 1.72655i | 0.504730 | + | 0.863277i | \(0.331592\pi\) | ||||
−0.504730 | + | 0.863277i | \(0.668408\pi\) | |||||||
\(264\) | −3.00000 | −0.184637 | ||||||||
\(265\) | 2.00000 | + | 4.00000i | 0.122859 | + | 0.245718i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 12.0000i | − | 0.734388i | ||||||
\(268\) | − | 4.00000i | − | 0.244339i | ||||||
\(269\) | 24.0000 | 1.46331 | 0.731653 | − | 0.681677i | \(-0.238749\pi\) | ||||
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | −2.00000 | + | 1.00000i | −0.121716 | + | 0.0608581i | ||||
\(271\) | 16.0000 | 0.971931 | 0.485965 | − | 0.873978i | \(-0.338468\pi\) | ||||
0.485965 | + | 0.873978i | \(0.338468\pi\) | |||||||
\(272\) | 6.00000i | 0.363803i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.0000 | 0.845771 | ||||||||
\(275\) | 3.00000 | − | 4.00000i | 0.180907 | − | 0.241209i | ||||
\(276\) | −6.00000 | −0.361158 | ||||||||
\(277\) | 10.0000i | 0.600842i | 0.953807 | + | 0.300421i | \(0.0971271\pi\) | ||||
−0.953807 | + | 0.300421i | \(0.902873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | −6.00000 | + | 3.00000i | −0.358569 | + | 0.179284i | ||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | 8.00000i | 0.476393i | ||||||||
\(283\) | − | 4.00000i | − | 0.237775i | −0.992908 | − | 0.118888i | \(-0.962067\pi\) | ||
0.992908 | − | 0.118888i | \(-0.0379328\pi\) | |||||||
\(284\) | 8.00000 | 0.474713 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 6.00000i | − | 0.354169i | ||||||
\(288\) | 5.00000i | 0.294628i | ||||||||
\(289\) | −19.0000 | −1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.00000 | 0.351726 | ||||||||
\(292\) | − | 4.00000i | − | 0.234082i | ||||||
\(293\) | 26.0000i | 1.51894i | 0.650545 | + | 0.759468i | \(0.274541\pi\) | ||||
−0.650545 | + | 0.759468i | \(0.725459\pi\) | |||||||
\(294\) | 1.00000 | 0.0583212 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −12.0000 | −0.697486 | ||||||||
\(297\) | 1.00000i | 0.0580259i | ||||||||
\(298\) | 8.00000i | 0.463428i | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −4.00000 | − | 3.00000i | −0.230940 | − | 0.173205i | ||||
\(301\) | −4.00000 | −0.230556 | ||||||||
\(302\) | − | 10.0000i | − | 0.575435i | ||||||
\(303\) | 14.0000i | 0.804279i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.00000 | + | 2.00000i | −0.229039 | + | 0.114520i | ||||
\(306\) | 6.00000 | 0.342997 | ||||||||
\(307\) | 20.0000i | 1.14146i | 0.821138 | + | 0.570730i | \(0.193340\pi\) | ||||
−0.821138 | + | 0.570730i | \(0.806660\pi\) | |||||||
\(308\) | 1.00000i | 0.0569803i | ||||||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −6.00000 | − | 12.0000i | −0.340777 | − | 0.681554i | ||||
\(311\) | 16.0000 | 0.907277 | 0.453638 | − | 0.891186i | \(-0.350126\pi\) | ||||
0.453638 | + | 0.891186i | \(0.350126\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000i | 0.113047i | 0.998401 | + | 0.0565233i | \(0.0180015\pi\) | ||||
−0.998401 | + | 0.0565233i | \(0.981998\pi\) | |||||||
\(314\) | 14.0000 | 0.790066 | ||||||||
\(315\) | 1.00000 | + | 2.00000i | 0.0563436 | + | 0.112687i | ||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 34.0000i | 1.90963i | 0.297200 | + | 0.954815i | \(0.403947\pi\) | ||||
−0.297200 | + | 0.954815i | \(0.596053\pi\) | |||||||
\(318\) | 2.00000i | 0.112154i | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 14.0000 | − | 7.00000i | 0.782624 | − | 0.391312i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 6.00000i | − | 0.334367i | ||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −24.0000 | −1.32924 | ||||||||
\(327\) | − | 18.0000i | − | 0.995402i | ||||||
\(328\) | 18.0000i | 0.993884i | ||||||||
\(329\) | 8.00000 | 0.441054 | ||||||||
\(330\) | 2.00000 | − | 1.00000i | 0.110096 | − | 0.0550482i | ||||
\(331\) | 32.0000 | 1.75888 | 0.879440 | − | 0.476011i | \(-0.157918\pi\) | ||||
0.879440 | + | 0.476011i | \(0.157918\pi\) | |||||||
\(332\) | 6.00000i | 0.329293i | ||||||||
\(333\) | 4.00000i | 0.219199i | ||||||||
\(334\) | −2.00000 | −0.109435 | ||||||||
\(335\) | 4.00000 | + | 8.00000i | 0.218543 | + | 0.437087i | ||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | − | 18.0000i | − | 0.980522i | −0.871576 | − | 0.490261i | \(-0.836901\pi\) | ||
0.871576 | − | 0.490261i | \(-0.163099\pi\) | |||||||
\(338\) | − | 13.0000i | − | 0.707107i | ||||||
\(339\) | −6.00000 | −0.325875 | ||||||||
\(340\) | 6.00000 | + | 12.0000i | 0.325396 | + | 0.650791i | ||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 12.0000 | 0.646997 | ||||||||
\(345\) | 12.0000 | − | 6.00000i | 0.646058 | − | 0.323029i | ||||
\(346\) | −6.00000 | −0.322562 | ||||||||
\(347\) | − | 16.0000i | − | 0.858925i | −0.903085 | − | 0.429463i | \(-0.858703\pi\) | ||
0.903085 | − | 0.429463i | \(-0.141297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 3.00000 | − | 4.00000i | 0.160357 | − | 0.213809i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − | 5.00000i | − | 0.266501i | ||||||
\(353\) | 10.0000i | 0.532246i | 0.963939 | + | 0.266123i | \(0.0857428\pi\) | ||||
−0.963939 | + | 0.266123i | \(0.914257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.0000 | + | 8.00000i | −0.849192 | + | 0.424596i | ||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | − | 6.00000i | − | 0.317554i | ||||||
\(358\) | − | 12.0000i | − | 0.634220i | ||||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | −3.00000 | − | 6.00000i | −0.158114 | − | 0.316228i | ||||
\(361\) | −19.0000 | −1.00000 | ||||||||
\(362\) | 2.00000i | 0.105118i | ||||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.00000 | + | 8.00000i | 0.209370 | + | 0.418739i | ||||
\(366\) | −2.00000 | −0.104542 | ||||||||
\(367\) | − | 16.0000i | − | 0.835193i | −0.908633 | − | 0.417597i | \(-0.862873\pi\) | ||
0.908633 | − | 0.417597i | \(-0.137127\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 6.00000 | 0.312348 | ||||||||
\(370\) | 8.00000 | − | 4.00000i | 0.415900 | − | 0.207950i | ||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 6.00000i | 0.311086i | ||||||||
\(373\) | 2.00000i | 0.103556i | 0.998659 | + | 0.0517780i | \(0.0164888\pi\) | ||||
−0.998659 | + | 0.0517780i | \(0.983511\pi\) | |||||||
\(374\) | −6.00000 | −0.310253 | ||||||||
\(375\) | 11.0000 | + | 2.00000i | 0.568038 | + | 0.103280i | ||||
\(376\) | −24.0000 | −1.23771 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.00000i | 0.0514344i | ||||||||
\(379\) | 24.0000 | 1.23280 | 0.616399 | − | 0.787434i | \(-0.288591\pi\) | ||||
0.616399 | + | 0.787434i | \(0.288591\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.0000i | 0.818631i | ||||||||
\(383\) | 24.0000i | 1.22634i | 0.789950 | + | 0.613171i | \(0.210106\pi\) | ||||
−0.789950 | + | 0.613171i | \(0.789894\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | −1.00000 | − | 2.00000i | −0.0509647 | − | 0.101929i | ||||
\(386\) | −2.00000 | −0.101797 | ||||||||
\(387\) | − | 4.00000i | − | 0.203331i | ||||||
\(388\) | 6.00000i | 0.304604i | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.0000 | −1.82060 | ||||||||
\(392\) | 3.00000i | 0.151523i | ||||||||
\(393\) | 12.0000i | 0.605320i | ||||||||
\(394\) | 18.0000 | 0.906827 | ||||||||
\(395\) | 4.00000 | − | 2.00000i | 0.201262 | − | 0.100631i | ||||
\(396\) | −1.00000 | −0.0502519 | ||||||||
\(397\) | − | 14.0000i | − | 0.702640i | −0.936255 | − | 0.351320i | \(-0.885733\pi\) | ||
0.936255 | − | 0.351320i | \(-0.114267\pi\) | |||||||
\(398\) | − | 14.0000i | − | 0.701757i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | + | 4.00000i | −0.150000 | + | 0.200000i | ||||
\(401\) | 34.0000 | 1.69788 | 0.848939 | − | 0.528490i | \(-0.177242\pi\) | ||||
0.848939 | + | 0.528490i | \(0.177242\pi\) | |||||||
\(402\) | 4.00000i | 0.199502i | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | −2.00000 | + | 1.00000i | −0.0993808 | + | 0.0496904i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 4.00000i | − | 0.198273i | ||||||
\(408\) | 18.0000i | 0.891133i | ||||||||
\(409\) | −26.0000 | −1.28562 | −0.642809 | − | 0.766027i | \(-0.722231\pi\) | ||||
−0.642809 | + | 0.766027i | \(0.722231\pi\) | |||||||
\(410\) | −6.00000 | − | 12.0000i | −0.296319 | − | 0.592638i | ||||
\(411\) | 14.0000 | 0.690569 | ||||||||
\(412\) | 8.00000i | 0.394132i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 6.00000 | 0.294884 | ||||||||
\(415\) | −6.00000 | − | 12.0000i | −0.294528 | − | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.0000 | 1.75872 | 0.879358 | − | 0.476162i | \(-0.157972\pi\) | ||||
0.879358 | + | 0.476162i | \(0.157972\pi\) | |||||||
\(420\) | −2.00000 | + | 1.00000i | −0.0975900 | + | 0.0487950i | ||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | − | 2.00000i | − | 0.0973585i | ||||||
\(423\) | 8.00000i | 0.388973i | ||||||||
\(424\) | −6.00000 | −0.291386 | ||||||||
\(425\) | −24.0000 | − | 18.0000i | −1.16417 | − | 0.873128i | ||||
\(426\) | −8.00000 | −0.387601 | ||||||||
\(427\) | 2.00000i | 0.0967868i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −8.00000 | + | 4.00000i | −0.385794 | + | 0.192897i | ||||
\(431\) | −24.0000 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 34.0000i | − | 1.63394i | −0.576683 | − | 0.816968i | \(-0.695653\pi\) | ||
0.576683 | − | 0.816968i | \(-0.304347\pi\) | |||||||
\(434\) | −6.00000 | −0.288009 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 18.0000 | 0.862044 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 4.00000i | 0.191127i | ||||||||
\(439\) | −28.0000 | −1.33637 | −0.668184 | − | 0.743996i | \(-0.732928\pi\) | ||||
−0.668184 | + | 0.743996i | \(0.732928\pi\) | |||||||
\(440\) | 3.00000 | + | 6.00000i | 0.143019 | + | 0.286039i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 22.0000i | 1.04525i | 0.852562 | + | 0.522626i | \(0.175047\pi\) | ||||
−0.852562 | + | 0.522626i | \(0.824953\pi\) | |||||||
\(444\) | −4.00000 | −0.189832 | ||||||||
\(445\) | −24.0000 | + | 12.0000i | −1.13771 | + | 0.568855i | ||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 8.00000i | 0.378387i | ||||||||
\(448\) | − | 7.00000i | − | 0.330719i | ||||||
\(449\) | 6.00000 | 0.283158 | 0.141579 | − | 0.989927i | \(-0.454782\pi\) | ||||
0.141579 | + | 0.989927i | \(0.454782\pi\) | |||||||
\(450\) | 4.00000 | + | 3.00000i | 0.188562 | + | 0.141421i | ||||
\(451\) | −6.00000 | −0.282529 | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | − | 10.0000i | − | 0.469841i | ||||||
\(454\) | −22.0000 | −1.03251 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 10.0000i | − | 0.467780i | −0.972263 | − | 0.233890i | \(-0.924854\pi\) | ||
0.972263 | − | 0.233890i | \(-0.0751456\pi\) | |||||||
\(458\) | − | 22.0000i | − | 1.02799i | ||||||
\(459\) | 6.00000 | 0.280056 | ||||||||
\(460\) | 6.00000 | + | 12.0000i | 0.279751 | + | 0.559503i | ||||
\(461\) | −2.00000 | −0.0931493 | −0.0465746 | − | 0.998915i | \(-0.514831\pi\) | ||||
−0.0465746 | + | 0.998915i | \(0.514831\pi\) | |||||||
\(462\) | − | 1.00000i | − | 0.0465242i | ||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.00000 | − | 12.0000i | −0.278243 | − | 0.556487i | ||||
\(466\) | −26.0000 | −1.20443 | ||||||||
\(467\) | − | 36.0000i | − | 1.66588i | −0.553362 | − | 0.832941i | \(-0.686655\pi\) | ||
0.553362 | − | 0.832941i | \(-0.313345\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 16.0000 | − | 8.00000i | 0.738025 | − | 0.369012i | ||||
\(471\) | 14.0000 | 0.645086 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.00000i | 0.183920i | ||||||||
\(474\) | 2.00000 | 0.0918630 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 6.00000 | 0.275010 | ||||||||
\(477\) | 2.00000i | 0.0915737i | ||||||||
\(478\) | − | 24.0000i | − | 1.09773i | ||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 10.0000 | − | 5.00000i | 0.456435 | − | 0.228218i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 14.0000i | 0.637683i | ||||||||
\(483\) | − | 6.00000i | − | 0.273009i | ||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −6.00000 | − | 12.0000i | −0.272446 | − | 0.544892i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 4.00000i | 0.181257i | 0.995885 | + | 0.0906287i | \(0.0288876\pi\) | ||||
−0.995885 | + | 0.0906287i | \(0.971112\pi\) | |||||||
\(488\) | − | 6.00000i | − | 0.271607i | ||||||
\(489\) | −24.0000 | −1.08532 | ||||||||
\(490\) | −1.00000 | − | 2.00000i | −0.0451754 | − | 0.0903508i | ||||
\(491\) | −36.0000 | −1.62466 | −0.812329 | − | 0.583200i | \(-0.801800\pi\) | ||||
−0.812329 | + | 0.583200i | \(0.801800\pi\) | |||||||
\(492\) | 6.00000i | 0.270501i | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.00000 | − | 1.00000i | 0.0898933 | − | 0.0449467i | ||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 8.00000i | 0.358849i | ||||||||
\(498\) | − | 6.00000i | − | 0.268866i | ||||||
\(499\) | 12.0000 | 0.537194 | 0.268597 | − | 0.963253i | \(-0.413440\pi\) | ||||
0.268597 | + | 0.963253i | \(0.413440\pi\) | |||||||
\(500\) | −2.00000 | + | 11.0000i | −0.0894427 | + | 0.491935i | ||||
\(501\) | −2.00000 | −0.0893534 | ||||||||
\(502\) | − | 12.0000i | − | 0.535586i | ||||||
\(503\) | 30.0000i | 1.33763i | 0.743427 | + | 0.668817i | \(0.233199\pi\) | ||||
−0.743427 | + | 0.668817i | \(0.766801\pi\) | |||||||
\(504\) | −3.00000 | −0.133631 | ||||||||
\(505\) | 28.0000 | − | 14.0000i | 1.24598 | − | 0.622992i | ||||
\(506\) | −6.00000 | −0.266733 | ||||||||
\(507\) | − | 13.0000i | − | 0.577350i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | −6.00000 | − | 12.0000i | −0.265684 | − | 0.531369i | ||||
\(511\) | 4.00000 | 0.176950 | ||||||||
\(512\) | 11.0000i | 0.486136i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.0000 | −0.617514 | ||||||||
\(515\) | −8.00000 | − | 16.0000i | −0.352522 | − | 0.705044i | ||||
\(516\) | 4.00000 | 0.176090 | ||||||||
\(517\) | − | 8.00000i | − | 0.351840i | ||||||
\(518\) | − | 4.00000i | − | 0.175750i | ||||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −36.0000 | −1.57719 | −0.788594 | − | 0.614914i | \(-0.789191\pi\) | ||||
−0.788594 | + | 0.614914i | \(0.789191\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.00000i | − | 0.349816i | −0.984585 | − | 0.174908i | \(-0.944037\pi\) | ||
0.984585 | − | 0.174908i | \(-0.0559627\pi\) | |||||||
\(524\) | −12.0000 | −0.524222 | ||||||||
\(525\) | 3.00000 | − | 4.00000i | 0.130931 | − | 0.174574i | ||||
\(526\) | 28.0000 | 1.22086 | ||||||||
\(527\) | 36.0000i | 1.56818i | ||||||||
\(528\) | 1.00000i | 0.0435194i | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | 4.00000 | − | 2.00000i | 0.173749 | − | 0.0868744i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.0000 | −0.519291 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −12.0000 | −0.518321 | ||||||||
\(537\) | − | 12.0000i | − | 0.517838i | ||||||
\(538\) | − | 24.0000i | − | 1.03471i | ||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | −1.00000 | − | 2.00000i | −0.0430331 | − | 0.0860663i | ||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | − | 16.0000i | − | 0.687259i | ||||||
\(543\) | 2.00000i | 0.0858282i | ||||||||
\(544\) | −30.0000 | −1.28624 | ||||||||
\(545\) | −36.0000 | + | 18.0000i | −1.54207 | + | 0.771035i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 20.0000i | 0.855138i | 0.903983 | + | 0.427569i | \(0.140630\pi\) | ||||
−0.903983 | + | 0.427569i | \(0.859370\pi\) | |||||||
\(548\) | 14.0000i | 0.598050i | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | −4.00000 | − | 3.00000i | −0.170561 | − | 0.127920i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 18.0000i | 0.766131i | ||||||||
\(553\) | − | 2.00000i | − | 0.0850487i | ||||||
\(554\) | 10.0000 | 0.424859 | ||||||||
\(555\) | 8.00000 | − | 4.00000i | 0.339581 | − | 0.169791i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 18.0000i | − | 0.762684i | −0.924434 | − | 0.381342i | \(-0.875462\pi\) | ||
0.924434 | − | 0.381342i | \(-0.124538\pi\) | |||||||
\(558\) | − | 6.00000i | − | 0.254000i | ||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.00000 | + | 2.00000i | 0.0422577 | + | 0.0845154i | ||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 24.0000i | 1.01238i | ||||||||
\(563\) | 6.00000i | 0.252870i | 0.991975 | + | 0.126435i | \(0.0403535\pi\) | ||||
−0.991975 | + | 0.126435i | \(0.959647\pi\) | |||||||
\(564\) | −8.00000 | −0.336861 | ||||||||
\(565\) | 6.00000 | + | 12.0000i | 0.252422 | + | 0.504844i | ||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | − | 24.0000i | − | 1.00702i | ||||||
\(569\) | −28.0000 | −1.17382 | −0.586911 | − | 0.809652i | \(-0.699656\pi\) | ||||
−0.586911 | + | 0.809652i | \(0.699656\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.00000 | 0.0836974 | 0.0418487 | − | 0.999124i | \(-0.486675\pi\) | ||||
0.0418487 | + | 0.999124i | \(0.486675\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000i | 0.668410i | ||||||||
\(574\) | −6.00000 | −0.250435 | ||||||||
\(575\) | −24.0000 | − | 18.0000i | −1.00087 | − | 0.750652i | ||||
\(576\) | 7.00000 | 0.291667 | ||||||||
\(577\) | 2.00000i | 0.0832611i | 0.999133 | + | 0.0416305i | \(0.0132552\pi\) | ||||
−0.999133 | + | 0.0416305i | \(0.986745\pi\) | |||||||
\(578\) | 19.0000i | 0.790296i | ||||||||
\(579\) | −2.00000 | −0.0831172 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.00000 | −0.248922 | ||||||||
\(582\) | − | 6.00000i | − | 0.248708i | ||||||
\(583\) | − | 2.00000i | − | 0.0828315i | ||||||
\(584\) | −12.0000 | −0.496564 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.0000 | 1.07405 | ||||||||
\(587\) | 24.0000i | 0.990586i | 0.868726 | + | 0.495293i | \(0.164939\pi\) | ||||
−0.868726 | + | 0.495293i | \(0.835061\pi\) | |||||||
\(588\) | 1.00000i | 0.0412393i | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.0000 | 0.740421 | ||||||||
\(592\) | 4.00000i | 0.164399i | ||||||||
\(593\) | 10.0000i | 0.410651i | 0.978694 | + | 0.205325i | \(0.0658253\pi\) | ||||
−0.978694 | + | 0.205325i | \(0.934175\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | −12.0000 | + | 6.00000i | −0.491952 | + | 0.245976i | ||||
\(596\) | −8.00000 | −0.327693 | ||||||||
\(597\) | − | 14.0000i | − | 0.572982i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | −9.00000 | + | 12.0000i | −0.367423 | + | 0.489898i | ||||
\(601\) | −10.0000 | −0.407909 | −0.203954 | − | 0.978980i | \(-0.565379\pi\) | ||||
−0.203954 | + | 0.978980i | \(0.565379\pi\) | |||||||
\(602\) | 4.00000i | 0.163028i | ||||||||
\(603\) | 4.00000i | 0.162893i | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | −2.00000 | + | 1.00000i | −0.0813116 | + | 0.0406558i | ||||
\(606\) | 14.0000 | 0.568711 | ||||||||
\(607\) | 40.0000i | 1.62355i | 0.583970 | + | 0.811775i | \(0.301498\pi\) | ||||
−0.583970 | + | 0.811775i | \(0.698502\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | + | 4.00000i | 0.0809776 | + | 0.161955i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 6.00000i | 0.242536i | ||||||||
\(613\) | 38.0000i | 1.53481i | 0.641165 | + | 0.767403i | \(0.278451\pi\) | ||||
−0.641165 | + | 0.767403i | \(0.721549\pi\) | |||||||
\(614\) | 20.0000 | 0.807134 | ||||||||
\(615\) | −6.00000 | − | 12.0000i | −0.241943 | − | 0.483887i | ||||
\(616\) | 3.00000 | 0.120873 | ||||||||
\(617\) | 18.0000i | 0.724653i | 0.932051 | + | 0.362326i | \(0.118017\pi\) | ||||
−0.932051 | + | 0.362326i | \(0.881983\pi\) | |||||||
\(618\) | − | 8.00000i | − | 0.321807i | ||||||
\(619\) | −18.0000 | −0.723481 | −0.361741 | − | 0.932279i | \(-0.617817\pi\) | ||||
−0.361741 | + | 0.932279i | \(0.617817\pi\) | |||||||
\(620\) | 12.0000 | − | 6.00000i | 0.481932 | − | 0.240966i | ||||
\(621\) | 6.00000 | 0.240772 | ||||||||
\(622\) | − | 16.0000i | − | 0.641542i | ||||||
\(623\) | 12.0000i | 0.480770i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.00000 | − | 24.0000i | −0.280000 | − | 0.960000i | ||||
\(626\) | 2.00000 | 0.0799361 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.0000i | 0.558661i | ||||||||
\(629\) | −24.0000 | −0.956943 | ||||||||
\(630\) | 2.00000 | − | 1.00000i | 0.0796819 | − | 0.0398410i | ||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 6.00000i | 0.238667i | ||||||||
\(633\) | − | 2.00000i | − | 0.0794929i | ||||||
\(634\) | 34.0000 | 1.35031 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.00000 | −0.0793052 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.00000 | −0.316475 | ||||||||
\(640\) | 3.00000 | + | 6.00000i | 0.118585 | + | 0.237171i | ||||
\(641\) | −30.0000 | −1.18493 | −0.592464 | − | 0.805597i | \(-0.701845\pi\) | ||||
−0.592464 | + | 0.805597i | \(0.701845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 12.0000i | − | 0.473234i | −0.971603 | − | 0.236617i | \(-0.923961\pi\) | ||
0.971603 | − | 0.236617i | \(-0.0760386\pi\) | |||||||
\(644\) | 6.00000 | 0.236433 | ||||||||
\(645\) | −8.00000 | + | 4.00000i | −0.315000 | + | 0.157500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.0000i | 0.471769i | 0.971781 | + | 0.235884i | \(0.0757987\pi\) | ||||
−0.971781 | + | 0.235884i | \(0.924201\pi\) | |||||||
\(648\) | − | 3.00000i | − | 0.117851i | ||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −6.00000 | −0.235159 | ||||||||
\(652\) | − | 24.0000i | − | 0.939913i | ||||||
\(653\) | 6.00000i | 0.234798i | 0.993085 | + | 0.117399i | \(0.0374557\pi\) | ||||
−0.993085 | + | 0.117399i | \(0.962544\pi\) | |||||||
\(654\) | −18.0000 | −0.703856 | ||||||||
\(655\) | 24.0000 | − | 12.0000i | 0.937758 | − | 0.468879i | ||||
\(656\) | 6.00000 | 0.234261 | ||||||||
\(657\) | 4.00000i | 0.156055i | ||||||||
\(658\) | − | 8.00000i | − | 0.311872i | ||||||
\(659\) | 48.0000 | 1.86981 | 0.934907 | − | 0.354892i | \(-0.115482\pi\) | ||||
0.934907 | + | 0.354892i | \(0.115482\pi\) | |||||||
\(660\) | 1.00000 | + | 2.00000i | 0.0389249 | + | 0.0778499i | ||||
\(661\) | 46.0000 | 1.78919 | 0.894596 | − | 0.446875i | \(-0.147463\pi\) | ||||
0.894596 | + | 0.446875i | \(0.147463\pi\) | |||||||
\(662\) | − | 32.0000i | − | 1.24372i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 18.0000 | 0.698535 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | − | 2.00000i | − | 0.0773823i | ||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | 8.00000 | − | 4.00000i | 0.309067 | − | 0.154533i | ||||
\(671\) | 2.00000 | 0.0772091 | ||||||||
\(672\) | − | 5.00000i | − | 0.192879i | ||||||
\(673\) | − | 46.0000i | − | 1.77317i | −0.462566 | − | 0.886585i | \(-0.653071\pi\) | ||
0.462566 | − | 0.886585i | \(-0.346929\pi\) | |||||||
\(674\) | −18.0000 | −0.693334 | ||||||||
\(675\) | 4.00000 | + | 3.00000i | 0.153960 | + | 0.115470i | ||||
\(676\) | 13.0000 | 0.500000 | ||||||||
\(677\) | − | 30.0000i | − | 1.15299i | −0.817099 | − | 0.576497i | \(-0.804419\pi\) | ||
0.817099 | − | 0.576497i | \(-0.195581\pi\) | |||||||
\(678\) | 6.00000i | 0.230429i | ||||||||
\(679\) | −6.00000 | −0.230259 | ||||||||
\(680\) | 36.0000 | − | 18.0000i | 1.38054 | − | 0.690268i | ||||
\(681\) | −22.0000 | −0.843042 | ||||||||
\(682\) | 6.00000i | 0.229752i | ||||||||
\(683\) | − | 10.0000i | − | 0.382639i | −0.981528 | − | 0.191320i | \(-0.938723\pi\) | ||
0.981528 | − | 0.191320i | \(-0.0612767\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | − | 28.0000i | −0.534913 | − | 1.06983i | ||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | − | 22.0000i | − | 0.839352i | ||||||
\(688\) | − | 4.00000i | − | 0.152499i | ||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | −6.00000 | − | 12.0000i | −0.228416 | − | 0.456832i | ||||
\(691\) | 34.0000 | 1.29342 | 0.646710 | − | 0.762736i | \(-0.276144\pi\) | ||||
0.646710 | + | 0.762736i | \(0.276144\pi\) | |||||||
\(692\) | − | 6.00000i | − | 0.228086i | ||||||
\(693\) | − | 1.00000i | − | 0.0379869i | ||||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 36.0000i | 1.36360i | ||||||||
\(698\) | 14.0000i | 0.529908i | ||||||||
\(699\) | −26.0000 | −0.983410 | ||||||||
\(700\) | 4.00000 | + | 3.00000i | 0.151186 | + | 0.113389i | ||||
\(701\) | −36.0000 | −1.35970 | −0.679851 | − | 0.733351i | \(-0.737955\pi\) | ||||
−0.679851 | + | 0.733351i | \(0.737955\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −7.00000 | −0.263822 | ||||||||
\(705\) | 16.0000 | − | 8.00000i | 0.602595 | − | 0.301297i | ||||
\(706\) | 10.0000 | 0.376355 | ||||||||
\(707\) | − | 14.0000i | − | 0.526524i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0000 | 1.42712 | 0.713560 | − | 0.700594i | \(-0.247082\pi\) | ||||
0.713560 | + | 0.700594i | \(0.247082\pi\) | |||||||
\(710\) | 8.00000 | + | 16.0000i | 0.300235 | + | 0.600469i | ||||
\(711\) | 2.00000 | 0.0750059 | ||||||||
\(712\) | − | 36.0000i | − | 1.34916i | ||||||
\(713\) | 36.0000i | 1.34821i | ||||||||
\(714\) | −6.00000 | −0.224544 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.0000 | 0.448461 | ||||||||
\(717\) | − | 24.0000i | − | 0.896296i | ||||||
\(718\) | − | 12.0000i | − | 0.447836i | ||||||
\(719\) | −24.0000 | −0.895049 | −0.447524 | − | 0.894272i | \(-0.647694\pi\) | ||||
−0.447524 | + | 0.894272i | \(0.647694\pi\) | |||||||
\(720\) | −2.00000 | + | 1.00000i | −0.0745356 | + | 0.0372678i | ||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 19.0000i | 0.707107i | ||||||||
\(723\) | 14.0000i | 0.520666i | ||||||||
\(724\) | −2.00000 | −0.0743294 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.00000 | −0.0371135 | ||||||||
\(727\) | 16.0000i | 0.593407i | 0.954970 | + | 0.296704i | \(0.0958873\pi\) | ||||
−0.954970 | + | 0.296704i | \(0.904113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 8.00000 | − | 4.00000i | 0.296093 | − | 0.148047i | ||||
\(731\) | 24.0000 | 0.887672 | ||||||||
\(732\) | − | 2.00000i | − | 0.0739221i | ||||||
\(733\) | − | 20.0000i | − | 0.738717i | −0.929287 | − | 0.369358i | \(-0.879577\pi\) | ||
0.929287 | − | 0.369358i | \(-0.120423\pi\) | |||||||
\(734\) | −16.0000 | −0.590571 | ||||||||
\(735\) | −1.00000 | − | 2.00000i | −0.0368856 | − | 0.0737711i | ||||
\(736\) | −30.0000 | −1.10581 | ||||||||
\(737\) | − | 4.00000i | − | 0.147342i | ||||||
\(738\) | − | 6.00000i | − | 0.220863i | ||||||
\(739\) | 14.0000 | 0.514998 | 0.257499 | − | 0.966279i | \(-0.417102\pi\) | ||||
0.257499 | + | 0.966279i | \(0.417102\pi\) | |||||||
\(740\) | 4.00000 | + | 8.00000i | 0.147043 | + | 0.294086i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 2.00000i | − | 0.0734223i | ||||||
\(743\) | 36.0000i | 1.32071i | 0.750953 | + | 0.660356i | \(0.229595\pi\) | ||||
−0.750953 | + | 0.660356i | \(0.770405\pi\) | |||||||
\(744\) | 18.0000 | 0.659912 | ||||||||
\(745\) | 16.0000 | − | 8.00000i | 0.586195 | − | 0.293097i | ||||
\(746\) | 2.00000 | 0.0732252 | ||||||||
\(747\) | − | 6.00000i | − | 0.219529i | ||||||
\(748\) | − | 6.00000i | − | 0.219382i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 2.00000 | − | 11.0000i | 0.0730297 | − | 0.401663i | ||||
\(751\) | −20.0000 | −0.729810 | −0.364905 | − | 0.931045i | \(-0.618899\pi\) | ||||
−0.364905 | + | 0.931045i | \(0.618899\pi\) | |||||||
\(752\) | 8.00000i | 0.291730i | ||||||||
\(753\) | − | 12.0000i | − | 0.437304i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20.0000 | + | 10.0000i | −0.727875 | + | 0.363937i | ||||
\(756\) | −1.00000 | −0.0363696 | ||||||||
\(757\) | − | 12.0000i | − | 0.436147i | −0.975932 | − | 0.218074i | \(-0.930023\pi\) | ||
0.975932 | − | 0.218074i | \(-0.0699773\pi\) | |||||||
\(758\) | − | 24.0000i | − | 0.871719i | ||||||
\(759\) | −6.00000 | −0.217786 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.0000 | −1.08750 | −0.543750 | − | 0.839248i | \(-0.682996\pi\) | ||||
−0.543750 | + | 0.839248i | \(0.682996\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.0000i | 0.651644i | ||||||||
\(764\) | −16.0000 | −0.578860 | ||||||||
\(765\) | −6.00000 | − | 12.0000i | −0.216930 | − | 0.433861i | ||||
\(766\) | 24.0000 | 0.867155 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 17.0000i | 0.613435i | ||||||||
\(769\) | 22.0000 | 0.793340 | 0.396670 | − | 0.917961i | \(-0.370166\pi\) | ||||
0.396670 | + | 0.917961i | \(0.370166\pi\) | |||||||
\(770\) | −2.00000 | + | 1.00000i | −0.0720750 | + | 0.0360375i | ||||
\(771\) | −14.0000 | −0.504198 | ||||||||
\(772\) | − | 2.00000i | − | 0.0719816i | ||||||
\(773\) | 18.0000i | 0.647415i | 0.946157 | + | 0.323708i | \(0.104929\pi\) | ||||
−0.946157 | + | 0.323708i | \(0.895071\pi\) | |||||||
\(774\) | −4.00000 | −0.143777 | ||||||||
\(775\) | −18.0000 | + | 24.0000i | −0.646579 | + | 0.862105i | ||||
\(776\) | 18.0000 | 0.646162 | ||||||||
\(777\) | − | 4.00000i | − | 0.143499i | ||||||
\(778\) | 14.0000i | 0.501924i | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 36.0000i | 1.28736i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −14.0000 | − | 28.0000i | −0.499681 | − | 0.999363i | ||||
\(786\) | 12.0000 | 0.428026 | ||||||||
\(787\) | − | 20.0000i | − | 0.712923i | −0.934310 | − | 0.356462i | \(-0.883983\pi\) | ||
0.934310 | − | 0.356462i | \(-0.116017\pi\) | |||||||
\(788\) | 18.0000i | 0.641223i | ||||||||
\(789\) | 28.0000 | 0.996826 | ||||||||
\(790\) | −2.00000 | − | 4.00000i | −0.0711568 | − | 0.142314i | ||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 3.00000i | 0.106600i | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −14.0000 | −0.496841 | ||||||||
\(795\) | 4.00000 | − | 2.00000i | 0.141865 | − | 0.0709327i | ||||
\(796\) | 14.0000 | 0.496217 | ||||||||
\(797\) | − | 2.00000i | − | 0.0708436i | −0.999372 | − | 0.0354218i | \(-0.988723\pi\) | ||
0.999372 | − | 0.0354218i | \(-0.0112775\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −48.0000 | −1.69812 | ||||||||
\(800\) | −20.0000 | − | 15.0000i | −0.707107 | − | 0.530330i | ||||
\(801\) | −12.0000 | −0.423999 | ||||||||
\(802\) | − | 34.0000i | − | 1.20058i | ||||||
\(803\) | − | 4.00000i | − | 0.141157i | ||||||
\(804\) | −4.00000 | −0.141069 | ||||||||
\(805\) | −12.0000 | + | 6.00000i | −0.422944 | + | 0.211472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 24.0000i | − | 0.844840i | ||||||
\(808\) | 42.0000i | 1.47755i | ||||||||
\(809\) | −40.0000 | −1.40633 | −0.703163 | − | 0.711029i | \(-0.748229\pi\) | ||||
−0.703163 | + | 0.711029i | \(0.748229\pi\) | |||||||
\(810\) | 1.00000 | + | 2.00000i | 0.0351364 | + | 0.0702728i | ||||
\(811\) | −32.0000 | −1.12367 | −0.561836 | − | 0.827249i | \(-0.689905\pi\) | ||||
−0.561836 | + | 0.827249i | \(0.689905\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 16.0000i | − | 0.561144i | ||||||
\(814\) | −4.00000 | −0.140200 | ||||||||
\(815\) | 24.0000 | + | 48.0000i | 0.840683 | + | 1.68137i | ||||
\(816\) | 6.00000 | 0.210042 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 26.0000i | 0.909069i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | − | 6.00000i | 0.419058 | − | 0.209529i | ||||
\(821\) | −28.0000 | −0.977207 | −0.488603 | − | 0.872506i | \(-0.662493\pi\) | ||||
−0.488603 | + | 0.872506i | \(0.662493\pi\) | |||||||
\(822\) | − | 14.0000i | − | 0.488306i | ||||||
\(823\) | − | 16.0000i | − | 0.557725i | −0.960331 | − | 0.278862i | \(-0.910043\pi\) | ||
0.960331 | − | 0.278862i | \(-0.0899574\pi\) | |||||||
\(824\) | 24.0000 | 0.836080 | ||||||||
\(825\) | −4.00000 | − | 3.00000i | −0.139262 | − | 0.104447i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.0000i | 0.834562i | 0.908778 | + | 0.417281i | \(0.137017\pi\) | ||||
−0.908778 | + | 0.417281i | \(0.862983\pi\) | |||||||
\(828\) | 6.00000i | 0.208514i | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | −12.0000 | + | 6.00000i | −0.416526 | + | 0.208263i | ||||
\(831\) | 10.0000 | 0.346896 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.00000i | 0.207888i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.00000 | + | 4.00000i | 0.0692129 | + | 0.138426i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 6.00000i | − | 0.207390i | ||||||
\(838\) | − | 36.0000i | − | 1.24360i | ||||||
\(839\) | 4.00000 | 0.138095 | 0.0690477 | − | 0.997613i | \(-0.478004\pi\) | ||||
0.0690477 | + | 0.997613i | \(0.478004\pi\) | |||||||
\(840\) | 3.00000 | + | 6.00000i | 0.103510 | + | 0.207020i | ||||
\(841\) | −29.0000 | −1.00000 | ||||||||
\(842\) | 22.0000i | 0.758170i | ||||||||
\(843\) | 24.0000i | 0.826604i | ||||||||
\(844\) | 2.00000 | 0.0688428 | ||||||||
\(845\) | −26.0000 | + | 13.0000i | −0.894427 | + | 0.447214i | ||||
\(846\) | 8.00000 | 0.275046 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 2.00000i | 0.0686803i | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | −18.0000 | + | 24.0000i | −0.617395 | + | 0.823193i | ||||
\(851\) | −24.0000 | −0.822709 | ||||||||
\(852\) | − | 8.00000i | − | 0.274075i | ||||||
\(853\) | − | 44.0000i | − | 1.50653i | −0.657716 | − | 0.753266i | \(-0.728477\pi\) | ||
0.657716 | − | 0.753266i | \(-0.271523\pi\) | |||||||
\(854\) | 2.00000 | 0.0684386 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.0000i | 0.341593i | 0.985306 | + | 0.170797i | \(0.0546341\pi\) | ||||
−0.985306 | + | 0.170797i | \(0.945366\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.0000 | 0.477674 | 0.238837 | − | 0.971060i | \(-0.423234\pi\) | ||||
0.238837 | + | 0.971060i | \(0.423234\pi\) | |||||||
\(860\) | −4.00000 | − | 8.00000i | −0.136399 | − | 0.272798i | ||||
\(861\) | −6.00000 | −0.204479 | ||||||||
\(862\) | 24.0000i | 0.817443i | ||||||||
\(863\) | − | 42.0000i | − | 1.42970i | −0.699280 | − | 0.714848i | \(-0.746496\pi\) | ||
0.699280 | − | 0.714848i | \(-0.253504\pi\) | |||||||
\(864\) | 5.00000 | 0.170103 | ||||||||
\(865\) | 6.00000 | + | 12.0000i | 0.204006 | + | 0.408012i | ||||
\(866\) | −34.0000 | −1.15537 | ||||||||
\(867\) | 19.0000i | 0.645274i | ||||||||
\(868\) | − | 6.00000i | − | 0.203653i | ||||||
\(869\) | −2.00000 | −0.0678454 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | − | 54.0000i | − | 1.82867i | ||||||
\(873\) | − | 6.00000i | − | 0.203069i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −11.0000 | − | 2.00000i | −0.371868 | − | 0.0676123i | ||||
\(876\) | −4.00000 | −0.135147 | ||||||||
\(877\) | 26.0000i | 0.877958i | 0.898497 | + | 0.438979i | \(0.144660\pi\) | ||||
−0.898497 | + | 0.438979i | \(0.855340\pi\) | |||||||
\(878\) | 28.0000i | 0.944954i | ||||||||
\(879\) | 26.0000 | 0.876958 | ||||||||
\(880\) | 2.00000 | − | 1.00000i | 0.0674200 | − | 0.0337100i | ||||
\(881\) | 52.0000 | 1.75192 | 0.875962 | − | 0.482380i | \(-0.160227\pi\) | ||||
0.875962 | + | 0.482380i | \(0.160227\pi\) | |||||||
\(882\) | − | 1.00000i | − | 0.0336718i | ||||||
\(883\) | − | 44.0000i | − | 1.48072i | −0.672212 | − | 0.740359i | \(-0.734656\pi\) | ||
0.672212 | − | 0.740359i | \(-0.265344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22.0000 | 0.739104 | ||||||||
\(887\) | − | 26.0000i | − | 0.872995i | −0.899706 | − | 0.436497i | \(-0.856219\pi\) | ||
0.899706 | − | 0.436497i | \(-0.143781\pi\) | |||||||
\(888\) | 12.0000i | 0.402694i | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | + | 24.0000i | 0.402241 | + | 0.804482i | ||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | 8.00000i | 0.267860i | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 8.00000 | 0.267560 | ||||||||
\(895\) | −24.0000 | + | 12.0000i | −0.802232 | + | 0.401116i | ||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 6.00000i | − | 0.200223i | ||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −3.00000 | + | 4.00000i | −0.100000 | + | 0.133333i | ||||
\(901\) | −12.0000 | −0.399778 | ||||||||
\(902\) | 6.00000i | 0.199778i | ||||||||
\(903\) | 4.00000i | 0.133112i | ||||||||
\(904\) | −18.0000 | −0.598671 | ||||||||
\(905\) | 4.00000 | − | 2.00000i | 0.132964 | − | 0.0664822i | ||||
\(906\) | −10.0000 | −0.332228 | ||||||||
\(907\) | 20.0000i | 0.664089i | 0.943264 | + | 0.332045i | \(0.107738\pi\) | ||||
−0.943264 | + | 0.332045i | \(0.892262\pi\) | |||||||
\(908\) | − | 22.0000i | − | 0.730096i | ||||||
\(909\) | 14.0000 | 0.464351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.0000 | 1.32526 | 0.662630 | − | 0.748947i | \(-0.269440\pi\) | ||||
0.662630 | + | 0.748947i | \(0.269440\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.00000i | 0.198571i | ||||||||
\(914\) | −10.0000 | −0.330771 | ||||||||
\(915\) | 2.00000 | + | 4.00000i | 0.0661180 | + | 0.132236i | ||||
\(916\) | 22.0000 | 0.726900 | ||||||||
\(917\) | − | 12.0000i | − | 0.396275i | ||||||
\(918\) | − | 6.00000i | − | 0.198030i | ||||||
\(919\) | 34.0000 | 1.12156 | 0.560778 | − | 0.827966i | \(-0.310502\pi\) | ||||
0.560778 | + | 0.827966i | \(0.310502\pi\) | |||||||
\(920\) | 36.0000 | − | 18.0000i | 1.18688 | − | 0.593442i | ||||
\(921\) | 20.0000 | 0.659022 | ||||||||
\(922\) | 2.00000i | 0.0658665i | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 1.00000 | 0.0328976 | ||||||||
\(925\) | −16.0000 | − | 12.0000i | −0.526077 | − | 0.394558i | ||||
\(926\) | 4.00000 | 0.131448 | ||||||||
\(927\) | − | 8.00000i | − | 0.262754i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −56.0000 | −1.83730 | −0.918650 | − | 0.395072i | \(-0.870720\pi\) | ||||
−0.918650 | + | 0.395072i | \(0.870720\pi\) | |||||||
\(930\) | −12.0000 | + | 6.00000i | −0.393496 | + | 0.196748i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 26.0000i | − | 0.851658i | ||||||
\(933\) | − | 16.0000i | − | 0.523816i | ||||||
\(934\) | −36.0000 | −1.17796 | ||||||||
\(935\) | 6.00000 | + | 12.0000i | 0.196221 | + | 0.392442i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.00000i | 0.261349i | 0.991425 | + | 0.130674i | \(0.0417142\pi\) | ||||
−0.991425 | + | 0.130674i | \(0.958286\pi\) | |||||||
\(938\) | − | 4.00000i | − | 0.130605i | ||||||
\(939\) | 2.00000 | 0.0652675 | ||||||||
\(940\) | 8.00000 | + | 16.0000i | 0.260931 | + | 0.521862i | ||||
\(941\) | 38.0000 | 1.23876 | 0.619382 | − | 0.785090i | \(-0.287383\pi\) | ||||
0.619382 | + | 0.785090i | \(0.287383\pi\) | |||||||
\(942\) | − | 14.0000i | − | 0.456145i | ||||||
\(943\) | 36.0000i | 1.17232i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.00000 | − | 1.00000i | 0.0650600 | − | 0.0325300i | ||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 14.0000i | 0.454939i | 0.973785 | + | 0.227469i | \(0.0730452\pi\) | ||||
−0.973785 | + | 0.227469i | \(0.926955\pi\) | |||||||
\(948\) | 2.00000i | 0.0649570i | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.0000 | 1.10253 | ||||||||
\(952\) | − | 18.0000i | − | 0.583383i | ||||||
\(953\) | 58.0000i | 1.87880i | 0.342817 | + | 0.939402i | \(0.388619\pi\) | ||||
−0.342817 | + | 0.939402i | \(0.611381\pi\) | |||||||
\(954\) | 2.00000 | 0.0647524 | ||||||||
\(955\) | 32.0000 | − | 16.0000i | 1.03550 | − | 0.517748i | ||||
\(956\) | 24.0000 | 0.776215 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 16.0000i | − | 0.516937i | ||||||
\(959\) | −14.0000 | −0.452084 | ||||||||
\(960\) | −7.00000 | − | 14.0000i | −0.225924 | − | 0.451848i | ||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.0000 | −0.450910 | ||||||||
\(965\) | 2.00000 | + | 4.00000i | 0.0643823 | + | 0.128765i | ||||
\(966\) | −6.00000 | −0.193047 | ||||||||
\(967\) | 8.00000i | 0.257263i | 0.991692 | + | 0.128631i | \(0.0410584\pi\) | ||||
−0.991692 | + | 0.128631i | \(0.958942\pi\) | |||||||
\(968\) | − | 3.00000i | − | 0.0964237i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −12.0000 | + | 6.00000i | −0.385297 | + | 0.192648i | ||||
\(971\) | 48.0000 | 1.54039 | 0.770197 | − | 0.637806i | \(-0.220158\pi\) | ||||
0.770197 | + | 0.637806i | \(0.220158\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 4.00000 | 0.128168 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | − | 22.0000i | − | 0.703842i | −0.936030 | − | 0.351921i | \(-0.885529\pi\) | ||
0.936030 | − | 0.351921i | \(-0.114471\pi\) | |||||||
\(978\) | 24.0000i | 0.767435i | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 2.00000 | − | 1.00000i | 0.0638877 | − | 0.0319438i | ||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | 36.0000i | 1.14881i | ||||||||
\(983\) | − | 60.0000i | − | 1.91370i | −0.290578 | − | 0.956851i | \(-0.593847\pi\) | ||
0.290578 | − | 0.956851i | \(-0.406153\pi\) | |||||||
\(984\) | 18.0000 | 0.573819 | ||||||||
\(985\) | −18.0000 | − | 36.0000i | −0.573528 | − | 1.14706i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 8.00000i | − | 0.254643i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.0000 | 0.763156 | ||||||||
\(990\) | −1.00000 | − | 2.00000i | −0.0317821 | − | 0.0635642i | ||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | 30.0000i | 0.952501i | ||||||||
\(993\) | − | 32.0000i | − | 1.01549i | ||||||
\(994\) | 8.00000 | 0.253745 | ||||||||
\(995\) | −28.0000 | + | 14.0000i | −0.887660 | + | 0.443830i | ||||
\(996\) | 6.00000 | 0.190117 | ||||||||
\(997\) | − | 44.0000i | − | 1.39349i | −0.717317 | − | 0.696747i | \(-0.754630\pi\) | ||
0.717317 | − | 0.696747i | \(-0.245370\pi\) | |||||||
\(998\) | − | 12.0000i | − | 0.379853i | ||||||
\(999\) | 4.00000 | 0.126554 |
(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 | 1155.2.c.b.694.1 | ✓ | 2 | |
5.2 | odd | 4 | 5775.2.a.r.1.1 | 1 | |||
5.3 | odd | 4 | 5775.2.a.i.1.1 | 1 | |||
5.4 | even | 2 | inner | 1155.2.c.b.694.2 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.b.694.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1155.2.c.b.694.2 | yes | 2 | 5.4 | even | 2 | inner | |
5775.2.a.i.1.1 | 1 | 5.3 | odd | 4 | |||
5775.2.a.r.1.1 | 1 | 5.2 | odd | 4 |