Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1301,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1301");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.d (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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1301.1 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1301 |
Dual form | 2100.2.d.g.1301.2 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.61803 | − | 0.618034i | −0.934172 | − | 0.356822i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.381966 | − | 2.61803i | 0.144370 | − | 0.989524i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.23607 | + | 2.00000i | 0.745356 | + | 0.666667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.763932i | 0.230334i | 0.993346 | + | 0.115167i | \(0.0367403\pi\) | ||||
−0.993346 | + | 0.115167i | \(0.963260\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.23607i | − | 0.342824i | −0.985199 | − | 0.171412i | \(-0.945167\pi\) | ||
0.985199 | − | 0.171412i | \(-0.0548329\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.47214 | −1.08465 | −0.542326 | − | 0.840168i | \(-0.682456\pi\) | ||||
−0.542326 | + | 0.840168i | \(0.682456\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.23607i | 1.66007i | 0.557713 | + | 0.830034i | \(0.311679\pi\) | ||||
−0.557713 | + | 0.830034i | \(0.688321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.23607 | + | 4.00000i | −0.487950 | + | 0.872872i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.70820i | 1.60727i | 0.595121 | + | 0.803636i | \(0.297104\pi\) | ||||
−0.595121 | + | 0.803636i | \(0.702896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.38197 | − | 4.61803i | −0.458410 | − | 0.888741i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 4.00000i | − | 0.742781i | −0.928477 | − | 0.371391i | \(-0.878881\pi\) | ||
0.928477 | − | 0.371391i | \(-0.121119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.23607i | − | 0.581215i | −0.956842 | − | 0.290607i | \(-0.906143\pi\) | ||
0.956842 | − | 0.290607i | \(-0.0938574\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.472136 | − | 1.23607i | 0.0821883 | − | 0.215172i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.47214 | −0.735215 | −0.367607 | − | 0.929981i | \(-0.619823\pi\) | ||||
−0.367607 | + | 0.929981i | \(0.619823\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.763932 | + | 2.00000i | −0.122327 | + | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.52786 | −0.550960 | −0.275480 | − | 0.961307i | \(-0.588837\pi\) | ||||
−0.275480 | + | 0.961307i | \(0.588837\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.23607 | 1.10349 | 0.551745 | − | 0.834013i | \(-0.313962\pi\) | ||||
0.551745 | + | 0.834013i | \(0.313962\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.23607 | 0.472029 | 0.236015 | − | 0.971750i | \(-0.424159\pi\) | ||||
0.236015 | + | 0.971750i | \(0.424159\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.70820 | − | 2.00000i | −0.958315 | − | 0.285714i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.23607 | + | 2.76393i | 1.01325 | + | 0.387028i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.23607i | 1.26867i | 0.773058 | + | 0.634336i | \(0.218726\pi\) | ||||
−0.773058 | + | 0.634336i | \(0.781274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.47214 | − | 11.7082i | 0.592349 | − | 1.55079i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427 | 1.16445 | 0.582223 | − | 0.813029i | \(-0.302183\pi\) | ||||
0.582223 | + | 0.813029i | \(0.302183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 4.94427i | − | 0.633049i | −0.948584 | − | 0.316525i | \(-0.897484\pi\) | ||
0.948584 | − | 0.316525i | \(-0.102516\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.09017 | − | 5.09017i | 0.767289 | − | 0.641301i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.70820 | −1.18605 | −0.593023 | − | 0.805186i | \(-0.702066\pi\) | ||||
−0.593023 | + | 0.805186i | \(0.702066\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.76393 | − | 12.4721i | 0.573510 | − | 1.50147i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1803i | 1.44554i | 0.691088 | + | 0.722770i | \(0.257131\pi\) | ||||
−0.691088 | + | 0.722770i | \(0.742869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.76393i | 0.791658i | 0.918324 | + | 0.395829i | \(0.129543\pi\) | ||||
−0.918324 | + | 0.395829i | \(0.870457\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000 | + | 0.291796i | 0.227921 | + | 0.0332532i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4721 | 1.17821 | 0.589104 | − | 0.808057i | \(-0.299481\pi\) | ||||
0.589104 | + | 0.808057i | \(0.299481\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | + | 8.94427i | 0.111111 | + | 0.993808i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.23607 | 0.794262 | 0.397131 | − | 0.917762i | \(-0.370006\pi\) | ||||
0.397131 | + | 0.917762i | \(0.370006\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.47214 | + | 6.47214i | −0.265041 | + | 0.693886i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4721 | −1.32204 | −0.661022 | − | 0.750367i | \(-0.729877\pi\) | ||||
−0.661022 | + | 0.750367i | \(0.729877\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23607 | − | 0.472136i | −0.339232 | − | 0.0494933i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 5.23607i | −0.207390 | + | 0.542955i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.1803i | 1.43980i | 0.694080 | + | 0.719898i | \(0.255811\pi\) | ||||
−0.694080 | + | 0.719898i | \(0.744189\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.52786 | + | 1.70820i | −0.153556 | + | 0.171681i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.94427 | −0.690981 | −0.345490 | − | 0.938422i | \(-0.612287\pi\) | ||||
−0.345490 | + | 0.938422i | \(0.612287\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7639i | 1.06060i | 0.847810 | + | 0.530301i | \(0.177921\pi\) | ||||
−0.847810 | + | 0.530301i | \(0.822079\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 0.291796i | − | 0.0282090i | −0.999901 | − | 0.0141045i | \(-0.995510\pi\) | ||
0.999901 | − | 0.0141045i | \(-0.00448975\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.94427 | −0.282010 | −0.141005 | − | 0.990009i | \(-0.545033\pi\) | ||||
−0.141005 | + | 0.990009i | \(0.545033\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.23607 | + | 2.76393i | 0.686817 | + | 0.262341i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.2361i | 1.62143i | 0.585439 | + | 0.810716i | \(0.300922\pi\) | ||||
−0.585439 | + | 0.810716i | \(0.699078\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.47214 | − | 2.76393i | 0.228549 | − | 0.255526i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.70820 | + | 11.7082i | −0.156591 | + | 1.07329i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4164 | 0.946946 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.70820 | + | 2.18034i | 0.514691 | + | 0.196595i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.1246 | 1.87451 | 0.937253 | − | 0.348650i | \(-0.113360\pi\) | ||||
0.937253 | + | 0.348650i | \(0.113360\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −11.7082 | − | 4.47214i | −1.03085 | − | 0.393750i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.4164 | 1.34694 | 0.673469 | − | 0.739216i | \(-0.264804\pi\) | ||||
0.673469 | + | 0.739216i | \(0.264804\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.9443 | + | 2.76393i | 1.64268 | + | 0.239663i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 1.23607i | − | 0.105604i | −0.998605 | − | 0.0528022i | \(-0.983185\pi\) | ||
0.998605 | − | 0.0528022i | \(-0.0168153\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.2361i | 1.29231i | 0.763208 | + | 0.646153i | \(0.223623\pi\) | ||||
−0.763208 | + | 0.646153i | \(0.776377\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.23607 | − | 2.00000i | −0.440956 | − | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.944272 | 0.0789640 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.61803 | + | 7.38197i | 0.793282 | + | 0.608854i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 15.4164i | − | 1.26296i | −0.775392 | − | 0.631481i | \(-0.782448\pi\) | ||
0.775392 | − | 0.631481i | \(-0.217552\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.94427 | 0.727875 | 0.363937 | − | 0.931423i | \(-0.381432\pi\) | ||||
0.363937 | + | 0.931423i | \(0.381432\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −10.0000 | − | 8.94427i | −0.808452 | − | 0.723102i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1.81966i | − | 0.145225i | −0.997360 | − | 0.0726123i | \(-0.976866\pi\) | ||
0.997360 | − | 0.0726123i | \(-0.0231336\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.70820 | − | 14.9443i | 0.452690 | − | 1.18516i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.1803 | + | 2.94427i | 1.59043 | + | 0.232041i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.6525 | −1.46097 | −0.730487 | − | 0.682926i | \(-0.760707\pi\) | ||||
−0.730487 | + | 0.682926i | \(0.760707\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.76393 | 0.678173 | 0.339087 | − | 0.940755i | \(-0.389882\pi\) | ||||
0.339087 | + | 0.940755i | \(0.389882\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.4721 | 0.882472 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.4721 | + | 16.1803i | −1.10671 | + | 1.23734i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −14.4721 | − | 5.52786i | −1.08779 | − | 0.415500i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7639i | 0.954021i | 0.878898 | + | 0.477011i | \(0.158280\pi\) | ||||
−0.878898 | + | 0.477011i | \(0.841720\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.47214i | 0.481070i | 0.970640 | + | 0.240535i | \(0.0773229\pi\) | ||||
−0.970640 | + | 0.240535i | \(0.922677\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.05573 | + | 8.00000i | −0.225886 | + | 0.591377i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 3.41641i | − | 0.249832i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0000 | + | 4.47214i | −0.945611 | + | 0.325300i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.23607i | 0.523584i | 0.965124 | + | 0.261792i | \(0.0843134\pi\) | ||||
−0.965124 | + | 0.261792i | \(0.915687\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.00000 | 0.431889 | 0.215945 | − | 0.976406i | \(-0.430717\pi\) | ||||
0.215945 | + | 0.976406i | \(0.430717\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 25.2361i | − | 1.79800i | −0.437953 | − | 0.898998i | \(-0.644296\pi\) | ||
0.437953 | − | 0.898998i | \(-0.355704\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.76393i | 0.621259i | 0.950531 | + | 0.310629i | \(0.100540\pi\) | ||||
−0.950531 | + | 0.310629i | \(0.899460\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.7082 | + | 6.00000i | 1.10797 | + | 0.423207i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.4721 | − | 1.52786i | −0.735000 | − | 0.107235i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −15.4164 | + | 17.2361i | −1.07151 | + | 1.19799i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.52786 | −0.382370 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | −0.550743 | −0.275371 | − | 0.961338i | \(-0.588801\pi\) | ||||
−0.275371 | + | 0.961338i | \(0.588801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.52786 | − | 19.7082i | 0.515801 | − | 1.35038i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.47214 | − | 1.23607i | −0.575126 | − | 0.0839098i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.18034 | − | 10.9443i | 0.282481 | − | 0.739545i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.52786i | 0.371844i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.7082i | 0.784039i | 0.919957 | + | 0.392020i | \(0.128223\pi\) | ||||
−0.919957 | + | 0.392020i | \(0.871777\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.2361 | −1.54223 | −0.771116 | − | 0.636695i | \(-0.780301\pi\) | ||||
−0.771116 | + | 0.636695i | \(0.780301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8885i | 0.917781i | 0.888493 | + | 0.458890i | \(0.151753\pi\) | ||||
−0.888493 | + | 0.458890i | \(0.848247\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.05573 | − | 1.70820i | −0.201052 | − | 0.112392i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 1.81966i | − | 0.119210i | −0.998222 | − | 0.0596049i | \(-0.981016\pi\) | ||
0.998222 | − | 0.0596049i | \(-0.0189841\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −16.9443 | − | 6.47214i | −1.10065 | − | 0.420410i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.180340i | 0.0116652i | 0.999983 | + | 0.00583261i | \(0.00185659\pi\) | ||||
−0.999983 | + | 0.00583261i | \(0.998143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.3607i | 1.05388i | 0.849901 | + | 0.526942i | \(0.176662\pi\) | ||||
−0.849901 | + | 0.526942i | \(0.823338\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3.90983 | − | 15.0902i | 0.250816 | − | 0.968035i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.94427 | 0.569110 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −11.7082 | − | 4.47214i | −0.741977 | − | 0.283410i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.3607 | −1.28515 | −0.642577 | − | 0.766221i | \(-0.722135\pi\) | ||||
−0.642577 | + | 0.766221i | \(0.722135\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.88854 | −0.370210 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.4721 | 1.02750 | 0.513752 | − | 0.857939i | \(-0.328255\pi\) | ||||
0.513752 | + | 0.857939i | \(0.328255\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.70820 | + | 11.7082i | −0.106143 | + | 0.727512i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | − | 8.94427i | 0.495188 | − | 0.553637i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 22.1803i | − | 1.36770i | −0.729623 | − | 0.683849i | \(-0.760305\pi\) | ||
0.729623 | − | 0.683849i | \(-0.239695\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 20.1803 | + | 7.70820i | 1.23502 | + | 0.471734i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.5279 | 1.19063 | 0.595317 | − | 0.803491i | \(-0.297026\pi\) | ||||
0.595317 | + | 0.803491i | \(0.297026\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 21.1246i | − | 1.28323i | −0.767027 | − | 0.641614i | \(-0.778265\pi\) | ||
0.767027 | − | 0.641614i | \(-0.221735\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.94427 | + | 2.76393i | 0.299241 | + | 0.167281i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.41641 | −0.0851037 | −0.0425519 | − | 0.999094i | \(-0.513549\pi\) | ||||
−0.0425519 | + | 0.999094i | \(0.513549\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.47214 | − | 7.23607i | 0.387477 | − | 0.433212i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 11.4164i | − | 0.681046i | −0.940236 | − | 0.340523i | \(-0.889396\pi\) | ||
0.940236 | − | 0.340523i | \(-0.110604\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.65248i | 0.514336i | 0.966367 | + | 0.257168i | \(0.0827894\pi\) | ||||
−0.966367 | + | 0.257168i | \(0.917211\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.34752 | + | 9.23607i | −0.0795418 | + | 0.545188i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.76393 | − | 22.9443i | 0.513751 | − | 1.34502i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000 | 0.817889 | 0.408944 | − | 0.912559i | \(-0.365897\pi\) | ||||
0.408944 | + | 0.912559i | \(0.365897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.52786 | − | 1.81966i | 0.204707 | − | 0.105587i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 9.52786 | 0.551011 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.76393 | − | 18.9443i | 0.159310 | − | 1.09193i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.2361 | + | 4.29180i | 0.645495 | + | 0.246557i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 18.1803i | − | 1.03761i | −0.854894 | − | 0.518803i | \(-0.826378\pi\) | ||
0.854894 | − | 0.518803i | \(-0.173622\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.65248 | − | 17.4164i | 0.378446 | − | 0.990785i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −32.3607 | −1.83501 | −0.917503 | − | 0.397729i | \(-0.869798\pi\) | ||||
−0.917503 | + | 0.397729i | \(0.869798\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.29180i | − | 0.242587i | −0.992617 | − | 0.121293i | \(-0.961296\pi\) | ||
0.992617 | − | 0.121293i | \(-0.0387042\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.18034i | − | 0.347122i | −0.984823 | − | 0.173561i | \(-0.944473\pi\) | ||
0.984823 | − | 0.173561i | \(-0.0555275\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.05573 | 0.171088 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.180340 | + | 0.472136i | −0.0100656 | + | 0.0263521i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 32.3607i | − | 1.80060i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.76393 | + | 1.81966i | 0.263446 | + | 0.100627i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.23607 | − | 8.47214i | 0.0681466 | − | 0.467084i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.9443 | −1.15120 | −0.575601 | − | 0.817731i | \(-0.695232\pi\) | ||||
−0.575601 | + | 0.817731i | \(0.695232\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −10.0000 | − | 8.94427i | −0.547997 | − | 0.490143i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.00000 | −0.108947 | −0.0544735 | − | 0.998515i | \(-0.517348\pi\) | ||||
−0.0544735 | + | 0.998515i | \(0.517348\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 10.6525 | − | 27.8885i | 0.578563 | − | 1.51470i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.47214 | 0.133874 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.79837 | + | 16.7984i | −0.421073 | + | 0.907027i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 32.6525i | 1.75288i | 0.481514 | + | 0.876438i | \(0.340087\pi\) | ||||
−0.481514 | + | 0.876438i | \(0.659913\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.94427i | 0.478776i | 0.970924 | + | 0.239388i | \(0.0769468\pi\) | ||||
−0.970924 | + | 0.239388i | \(0.923053\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.70820 | + | 2.94427i | −0.304681 | + | 0.157154i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.4164 | −1.35278 | −0.676389 | − | 0.736544i | \(-0.736456\pi\) | ||||
−0.676389 | + | 0.736544i | \(0.736456\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.0000 | − | 17.8885i | 0.529256 | − | 0.946762i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 34.0689i | 1.79809i | 0.437859 | + | 0.899043i | \(0.355737\pi\) | ||||
−0.437859 | + | 0.899043i | \(0.644263\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −33.3607 | −1.75583 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −16.8541 | − | 6.43769i | −0.884611 | − | 0.337891i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 24.6525i | 1.28685i | 0.765510 | + | 0.643424i | \(0.222487\pi\) | ||||
−0.765510 | + | 0.643424i | \(0.777513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.88854 | − | 7.05573i | −0.410661 | − | 0.367307i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 24.1803 | + | 3.52786i | 1.25538 | + | 0.183158i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.52786 | −0.389778 | −0.194889 | − | 0.980825i | \(-0.562435\pi\) | ||||
−0.194889 | + | 0.980825i | \(0.562435\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.94427 | −0.254643 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.52786 | 0.0784811 | 0.0392406 | − | 0.999230i | \(-0.487506\pi\) | ||||
0.0392406 | + | 0.999230i | \(0.487506\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −34.1803 | − | 13.0557i | −1.75111 | − | 0.668865i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.2361 | 0.778527 | 0.389263 | − | 0.921127i | \(-0.372730\pi\) | ||||
0.389263 | + | 0.921127i | \(0.372730\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 16.1803 | + | 14.4721i | 0.822493 | + | 0.735660i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.47214i | 0.125342i | 0.998034 | + | 0.0626711i | \(0.0199619\pi\) | ||||
−0.998034 | + | 0.0626711i | \(0.980038\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 34.4721i | − | 1.74333i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −24.9443 | − | 9.52786i | −1.25827 | − | 0.480617i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.70820i | − | 0.186109i | −0.995661 | − | 0.0930547i | \(-0.970337\pi\) | ||
0.995661 | − | 0.0930547i | \(-0.0296631\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −28.9443 | − | 16.1803i | −1.44903 | − | 0.810030i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 28.9443i | − | 1.44541i | −0.691158 | − | 0.722704i | \(-0.742899\pi\) | ||
0.691158 | − | 0.722704i | \(-0.257101\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.00000 | −0.199254 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 3.41641i | − | 0.169345i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.0000i | 0.593362i | 0.954977 | + | 0.296681i | \(0.0958798\pi\) | ||||
−0.954977 | + | 0.296681i | \(0.904120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.763932 | + | 2.00000i | −0.0376820 | + | 0.0986527i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.41641 | − | 23.4164i | 0.168110 | − | 1.15225i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.41641 | − | 24.6525i | 0.461123 | − | 1.20724i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 32.4721 | 1.58260 | 0.791298 | − | 0.611431i | \(-0.209406\pi\) | ||||
0.791298 | + | 0.611431i | \(0.209406\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.23607 | + | 6.47214i | 0.351830 | + | 0.314686i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.9443 | − | 1.88854i | −0.626417 | − | 0.0913930i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.52786 | − | 0.583592i | −0.0737660 | − | 0.0281761i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 0.763932i | − | 0.0367973i | −0.999831 | − | 0.0183987i | \(-0.994143\pi\) | ||
0.999831 | − | 0.0183987i | \(-0.00585680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 32.6525i | 1.56918i | 0.620016 | + | 0.784589i | \(0.287126\pi\) | ||||
−0.620016 | + | 0.784589i | \(0.712874\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −55.7771 | −2.66818 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.18034i | − | 0.199517i | −0.995012 | − | 0.0997584i | \(-0.968193\pi\) | ||
0.995012 | − | 0.0997584i | \(-0.0318070\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.0000 | − | 17.8885i | −0.523810 | − | 0.851835i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 24.0689i | − | 1.14355i | −0.820411 | − | 0.571774i | \(-0.806256\pi\) | ||
0.820411 | − | 0.571774i | \(-0.193744\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.52786 | + | 24.9443i | −0.450653 | + | 1.17982i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 29.8885i | − | 1.41053i | −0.708945 | − | 0.705264i | \(-0.750829\pi\) | ||
0.708945 | − | 0.705264i | \(-0.249171\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.69505i | − | 0.126905i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.4721 | − | 5.52786i | −0.679960 | − | 0.259722i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.05573 | 0.423609 | 0.211805 | − | 0.977312i | \(-0.432066\pi\) | ||||
0.211805 | + | 0.977312i | \(0.432066\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 10.6525 | + | 20.6525i | 0.497215 | + | 0.963975i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.4721 | −1.13978 | −0.569891 | − | 0.821721i | \(-0.693014\pi\) | ||||
−0.569891 | + | 0.821721i | \(0.693014\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.7639 | 0.964982 | 0.482491 | − | 0.875901i | \(-0.339732\pi\) | ||||
0.482491 | + | 0.875901i | \(0.339732\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 36.5410 | 1.69092 | 0.845458 | − | 0.534041i | \(-0.179327\pi\) | ||||
0.845458 | + | 0.534041i | \(0.179327\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.70820 | + | 25.4164i | −0.171229 | + | 1.17362i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.12461 | + | 2.94427i | −0.0518194 | + | 0.135665i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.52786i | 0.254171i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −18.4721 | + | 20.6525i | −0.845781 | + | 0.945612i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.9443 | 0.591439 | 0.295719 | − | 0.955275i | \(-0.404441\pi\) | ||||
0.295719 | + | 0.955275i | \(0.404441\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.52786i | 0.252049i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −30.8328 | − | 17.2361i | −1.40294 | − | 0.784268i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.23607 | 0.146640 | 0.0733201 | − | 0.997308i | \(-0.476641\pi\) | ||||
0.0733201 | + | 0.997308i | \(0.476641\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 30.1803 | + | 11.5279i | 1.36480 | + | 0.521308i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 41.1246i | − | 1.85593i | −0.372670 | − | 0.927964i | \(-0.621558\pi\) | ||
0.372670 | − | 0.927964i | \(-0.378442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 17.8885i | 0.805659i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 31.8885 | + | 4.65248i | 1.43040 | + | 0.208692i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.3607 | −0.732405 | −0.366202 | − | 0.930535i | \(-0.619342\pi\) | ||||
−0.366202 | + | 0.930535i | \(0.619342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −14.1803 | − | 5.41641i | −0.633531 | − | 0.241987i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.6525 | −0.831673 | −0.415836 | − | 0.909439i | \(-0.636511\pi\) | ||||
−0.415836 | + | 0.909439i | \(0.636511\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.5623 | − | 7.09017i | −0.824381 | − | 0.314886i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.9443 | −1.01699 | −0.508493 | − | 0.861066i | \(-0.669797\pi\) | ||||
−0.508493 | + | 0.861066i | \(0.669797\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.7082 | + | 2.58359i | 0.783365 | + | 0.114291i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 33.4164 | − | 17.2361i | 1.47537 | − | 0.760991i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.47214i | 0.108724i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.23607 | + | 1.23607i | 0.142048 | + | 0.0542574i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.88854 | −0.345603 | −0.172802 | − | 0.984957i | \(-0.555282\pi\) | ||||
−0.172802 | + | 0.984957i | \(0.555282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 8.29180i | − | 0.362575i | −0.983430 | − | 0.181287i | \(-0.941974\pi\) | ||
0.983430 | − | 0.181287i | \(-0.0580264\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 14.4721i | 0.630416i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −36.4164 | −1.58332 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 20.0000 | + | 17.8885i | 0.867926 | + | 0.776297i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.36068i | 0.188882i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.88854 | − | 20.6525i | 0.340416 | − | 0.891220i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.52786 | − | 5.12461i | 0.0658098 | − | 0.220733i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −43.8885 | −1.88692 | −0.943458 | − | 0.331492i | \(-0.892448\pi\) | ||||
−0.943458 | + | 0.331492i | \(0.892448\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.00000 | − | 10.4721i | 0.171656 | − | 0.449402i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.7082 | −0.757148 | −0.378574 | − | 0.925571i | \(-0.623585\pi\) | ||||
−0.378574 | + | 0.925571i | \(0.623585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 9.88854 | − | 11.0557i | 0.422033 | − | 0.471847i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.9443 | 1.23307 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.00000 | − | 27.4164i | 0.170097 | − | 1.16586i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14.1803i | − | 0.600840i | −0.953807 | − | 0.300420i | \(-0.902873\pi\) | ||
0.953807 | − | 0.300420i | \(-0.0971269\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.94427i | − | 0.378302i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.11146 | + | 5.52786i | −0.0891457 | + | 0.233387i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −18.0689 | −0.761513 | −0.380756 | − | 0.924675i | \(-0.624336\pi\) | ||||
−0.380756 | + | 0.924675i | \(0.624336\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.7984 | + | 0.798374i | 0.999438 | + | 0.0335286i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 21.8885i | − | 0.917615i | −0.888536 | − | 0.458808i | \(-0.848277\pi\) | ||
0.888536 | − | 0.458808i | \(-0.151723\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.83282 | 0.285944 | 0.142972 | − | 0.989727i | \(-0.454334\pi\) | ||||
0.142972 | + | 0.989727i | \(0.454334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.47214 | − | 11.7082i | 0.186826 | − | 0.489117i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.0689i | 1.33505i | 0.744590 | + | 0.667523i | \(0.232645\pi\) | ||||
−0.744590 | + | 0.667523i | \(0.767355\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.70820 | − | 3.70820i | −0.403459 | − | 0.154108i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.76393 | − | 18.9443i | 0.114667 | − | 0.785941i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.05573 | −0.292218 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.29180 | 0.259690 | 0.129845 | − | 0.991534i | \(-0.458552\pi\) | ||||
0.129845 | + | 0.991534i | \(0.458552\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.4164 | 0.964856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −15.5967 | + | 40.8328i | −0.641564 | + | 1.67964i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.5279 | 0.801913 | 0.400957 | − | 0.916097i | \(-0.368678\pi\) | ||||
0.400957 | + | 0.916097i | \(0.368678\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 5.41641 | − | 14.1803i | 0.221679 | − | 0.580363i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 30.6525i | − | 1.25243i | −0.779652 | − | 0.626213i | \(-0.784604\pi\) | ||
0.779652 | − | 0.626213i | \(-0.215396\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.3050i | 1.84803i | 0.382359 | + | 0.924014i | \(0.375112\pi\) | ||||
−0.382359 | + | 0.924014i | \(0.624888\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.7082 | − | 19.4164i | −0.884026 | − | 0.790697i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 40.0689i | − | 1.62635i | −0.582022 | − | 0.813173i | \(-0.697738\pi\) | ||
0.582022 | − | 0.813173i | \(-0.302262\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 16.0000 | + | 8.94427i | 0.648353 | + | 0.362440i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 4.00000i | − | 0.161823i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −22.3607 | −0.903139 | −0.451570 | − | 0.892236i | \(-0.649136\pi\) | ||||
−0.451570 | + | 0.892236i | \(0.649136\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 26.5410i | 1.06850i | 0.845326 | + | 0.534251i | \(0.179406\pi\) | ||||
−0.845326 | + | 0.534251i | \(0.820594\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 5.70820i | − | 0.229432i | −0.993398 | − | 0.114716i | \(-0.963404\pi\) | ||
0.993398 | − | 0.114716i | \(-0.0365958\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 35.5967 | − | 18.3607i | 1.42845 | − | 0.736789i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −4.76393 | + | 32.6525i | −0.190863 | + | 1.30819i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.94427 | + | 3.41641i | 0.357200 | + | 0.136438i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000 | 0.797452 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.94427 | 0.356066 | 0.178033 | − | 0.984025i | \(-0.443027\pi\) | ||||
0.178033 | + | 0.984025i | \(0.443027\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.9443 | + | 4.94427i | 0.514489 | + | 0.196517i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.47214 | + | 8.29180i | −0.0979496 | + | 0.328533i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.3607 | + | 27.2361i | −0.963694 | + | 1.07744i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.5836i | − | 0.497022i | −0.968629 | − | 0.248511i | \(-0.920059\pi\) | ||
0.968629 | − | 0.248511i | \(-0.0799412\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 24.2918i | − | 0.957975i | −0.877822 | − | 0.478987i | \(-0.841004\pi\) | ||
0.877822 | − | 0.478987i | \(-0.158996\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.12461 | −0.358726 | −0.179363 | − | 0.983783i | \(-0.557404\pi\) | ||||
−0.179363 | + | 0.983783i | \(0.557404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.83282i | 0.268211i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9443 | + | 7.23607i | 0.507326 | + | 0.283604i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 21.5967i | − | 0.845146i | −0.906329 | − | 0.422573i | \(-0.861127\pi\) | ||
0.906329 | − | 0.422573i | \(-0.138873\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −13.5279 | + | 15.1246i | −0.527772 | + | 0.590067i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.7639i | 1.43212i | 0.698039 | + | 0.716060i | \(0.254056\pi\) | ||||
−0.698039 | + | 0.716060i | \(0.745944\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.8328i | 0.888094i | 0.896004 | + | 0.444047i | \(0.146458\pi\) | ||||
−0.896004 | + | 0.444047i | \(0.853542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.41641 | − | 8.94427i | 0.132682 | − | 0.347367i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.8328 | 1.19385 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 7.23607 | − | 18.9443i | 0.279763 | − | 0.732428i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.77709 | 0.145813 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.9443 | −0.576059 | −0.288030 | − | 0.957621i | \(-0.593000\pi\) | ||||
−0.288030 | + | 0.957621i | \(0.593000\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.00000 | 0.230599 | 0.115299 | − | 0.993331i | \(-0.463217\pi\) | ||||
0.115299 | + | 0.993331i | \(0.463217\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.1246 | + | 5.41641i | 1.42471 | + | 0.207863i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 37.5967 | + | 14.3607i | 1.44071 | + | 0.550302i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.2918i | − | 0.776444i | −0.921566 | − | 0.388222i | \(-0.873089\pi\) | ||
0.921566 | − | 0.388222i | \(-0.126911\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.58359 | − | 22.4721i | 0.327484 | − | 0.857365i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.4164 | 0.434931 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.18034i | 0.311195i | 0.987821 | + | 0.155597i | \(0.0497302\pi\) | ||||
−0.987821 | + | 0.155597i | \(0.950270\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.88854 | + | 4.65248i | 0.147714 | + | 0.176733i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7771 | 0.597600 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.12461 | + | 2.94427i | −0.0425367 | + | 0.111363i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.05573i | 0.115413i | 0.998334 | + | 0.0577066i | \(0.0183788\pi\) | ||||
−0.998334 | + | 0.0577066i | \(0.981621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 32.3607i | − | 1.22051i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.65248 | + | 18.1803i | −0.0997566 | + | 0.683742i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.9443 | −0.861690 | −0.430845 | − | 0.902426i | \(-0.641784\pi\) | ||||
−0.430845 | + | 0.902426i | \(0.641784\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 23.4164 | + | 20.9443i | 0.878184 | + | 0.785472i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 24.9443 | 0.934170 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.111456 | − | 0.291796i | 0.00416241 | − | 0.0108973i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.11146 | −0.227919 | −0.113959 | − | 0.993485i | \(-0.536353\pi\) | ||||
−0.113959 | + | 0.993485i | \(0.536353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.1803 | + | 4.11146i | 1.04949 | + | 0.153119i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 10.1115 | − | 26.4721i | 0.376049 | − | 0.984509i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.70820i | 0.137530i | 0.997633 | + | 0.0687648i | \(0.0219058\pi\) | ||||
−0.997633 | + | 0.0687648i | \(0.978094\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −15.6525 | + | 22.0000i | −0.579721 | + | 0.814815i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −32.3607 | −1.19690 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 48.6525i | 1.79702i | 0.438953 | + | 0.898510i | \(0.355350\pi\) | ||||
−0.438953 | + | 0.898510i | \(0.644650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.41641i | − | 0.273187i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 40.3607 | 1.48469 | 0.742346 | − | 0.670017i | \(-0.233713\pi\) | ||||
0.742346 | + | 0.670017i | \(0.233713\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −14.4721 | − | 5.52786i | −0.531647 | − | 0.203071i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24.6525i | 0.904412i | 0.891914 | + | 0.452206i | \(0.149363\pi\) | ||||
−0.891914 | + | 0.452206i | \(0.850637\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.1803 | + | 14.4721i | 0.592008 | + | 0.529508i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.763932 | − | 0.111456i | −0.0279135 | − | 0.00407252i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.0000 | −1.60558 | −0.802791 | − | 0.596260i | \(-0.796653\pi\) | ||||
−0.802791 | + | 0.596260i | \(0.796653\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 32.9443 | + | 12.5836i | 1.20056 | + | 0.458572i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3050 | −1.28318 | −0.641590 | − | 0.767048i | \(-0.721725\pi\) | ||||
−0.641590 | + | 0.767048i | \(0.721725\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.52786 | + | 3.63932i | 0.345840 | + | 0.132099i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3050 | 1.13480 | 0.567402 | − | 0.823441i | \(-0.307949\pi\) | ||||
0.567402 | + | 0.823441i | \(0.307949\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.12461 | + | 7.70820i | −0.0407137 | + | 0.279056i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 11.0557i | − | 0.399199i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 31.4164i | − | 1.13290i | −0.824095 | − | 0.566452i | \(-0.808316\pi\) | ||
0.824095 | − | 0.566452i | \(-0.191684\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −26.6525 | − | 10.1803i | −0.959865 | − | 0.366636i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −18.0000 | −0.647415 | −0.323708 | − | 0.946157i | \(-0.604929\pi\) | ||||
−0.323708 | + | 0.946157i | \(0.604929\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.0000 | − | 17.8885i | 0.358748 | − | 0.641748i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 25.5279i | − | 0.914631i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.30495 | −0.332957 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −18.4721 | + | 9.52786i | −0.660140 | + | 0.340498i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 16.2918i | − | 0.580740i | −0.956914 | − | 0.290370i | \(-0.906222\pi\) | ||
0.956914 | − | 0.290370i | \(-0.0937784\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.7082 | + | 35.8885i | −0.488025 | + | 1.27767i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 45.1246 | + | 6.58359i | 1.60445 | + | 0.234086i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.11146 | −0.217024 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 28.8328 | 1.02131 | 0.510655 | − | 0.859785i | \(-0.329403\pi\) | ||||
0.510655 | + | 0.859785i | \(0.329403\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.4721 | −0.511987 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −27.8885 | − | 24.9443i | −0.985393 | − | 0.881363i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.16718 | −0.182346 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.5967 | − | 12.0689i | −1.11226 | − | 0.424845i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.3607i | 0.434578i | 0.976107 | + | 0.217289i | \(0.0697215\pi\) | ||||
−0.976107 | + | 0.217289i | \(0.930279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.70820i | − | 0.0599832i | −0.999550 | − | 0.0299916i | \(-0.990452\pi\) | ||
0.999550 | − | 0.0299916i | \(-0.00954805\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −13.0557 | + | 34.1803i | −0.457884 | + | 1.19876i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 52.3607i | 1.83187i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.29180 | − | 7.52786i | −0.219853 | − | 0.263045i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.8328i | 1.63448i | 0.576300 | + | 0.817238i | \(0.304496\pi\) | ||||
−0.576300 | + | 0.817238i | \(0.695504\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.5967 | 0.404237 | 0.202119 | − | 0.979361i | \(-0.435217\pi\) | ||||
0.202119 | + | 0.979361i | \(0.435217\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.7082i | 1.38079i | 0.723433 | + | 0.690395i | \(0.242563\pi\) | ||||
−0.723433 | + | 0.690395i | \(0.757437\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 20.3607i | − | 0.707156i | −0.935405 | − | 0.353578i | \(-0.884965\pi\) | ||
0.935405 | − | 0.353578i | \(-0.115035\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.29180 | + | 0.875388i | 0.0795015 | + | 0.0303669i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.0000 | + | 8.94427i | 1.03944 | + | 0.309901i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −14.9443 | + | 7.70820i | −0.516550 | + | 0.266435i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.9443 | −0.446886 | −0.223443 | − | 0.974717i | \(-0.571730\pi\) | ||||
−0.223443 | + | 0.974717i | \(0.571730\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0000 | 0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.05573 | + | 18.4721i | −0.243012 | + | 0.636214i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.97871 | − | 27.2705i | 0.136710 | − | 0.937026i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 5.34752 | − | 14.0000i | 0.183527 | − | 0.480479i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 34.4721i | − | 1.18169i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 19.1246i | − | 0.654814i | −0.944883 | − | 0.327407i | \(-0.893825\pi\) | ||
0.944883 | − | 0.327407i | \(-0.106175\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −28.4721 | −0.972590 | −0.486295 | − | 0.873795i | \(-0.661652\pi\) | ||||
−0.486295 | + | 0.873795i | \(0.661652\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.3475i | 0.455412i | 0.973730 | + | 0.227706i | \(0.0731225\pi\) | ||||
−0.973730 | + | 0.227706i | \(0.926878\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.88854 | − | 14.1115i | 0.268841 | − | 0.480917i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 52.6525i | 1.79231i | 0.443740 | + | 0.896156i | \(0.353651\pi\) | ||||
−0.443740 | + | 0.896156i | \(0.646349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −4.85410 | − | 1.85410i | −0.164854 | − | 0.0629686i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0000i | 0.406604i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −28.3607 | + | 31.7082i | −0.959864 | + | 1.07316i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 32.4721 | 1.09651 | 0.548253 | − | 0.836312i | \(-0.315293\pi\) | ||||
0.548253 | + | 0.836312i | \(0.315293\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −22.6525 | − | 8.65248i | −0.764049 | − | 0.291841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −16.8328 | −0.567112 | −0.283556 | − | 0.958956i | \(-0.591514\pi\) | ||||
−0.283556 | + | 0.958956i | \(0.591514\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.5967 | 1.19793 | 0.598963 | − | 0.800777i | \(-0.295580\pi\) | ||||
0.598963 | + | 0.800777i | \(0.295580\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.1803 | 0.543283 | 0.271641 | − | 0.962399i | \(-0.412434\pi\) | ||||
0.271641 | + | 0.962399i | \(0.412434\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.06888 | − | 55.3050i | 0.270622 | − | 1.85487i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.83282 | + | 0.763932i | −0.228908 | + | 0.0255927i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 23.4164i | 0.783600i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −15.4164 | − | 5.88854i | −0.514739 | − | 0.196613i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.9443 | −0.431716 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.3050i | − | 1.37607i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −16.1803 | + | 28.9443i | −0.538448 | + | 0.963205i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 27.2361 | 0.904359 | 0.452179 | − | 0.891927i | \(-0.350647\pi\) | ||||
0.452179 | + | 0.891927i | \(0.350647\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −15.5279 | − | 13.8885i | −0.515027 | − | 0.460654i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 46.0689i | 1.52633i | 0.646204 | + | 0.763165i | \(0.276356\pi\) | ||||
−0.646204 | + | 0.763165i | \(0.723644\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.52786i | 0.182946i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.88854 | − | 40.3607i | 0.194457 | − | 1.33283i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.4721 | −1.13713 | −0.568565 | − | 0.822638i | \(-0.692501\pi\) | ||||
−0.568565 | + | 0.822638i | \(0.692501\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.2361 | + | 29.4164i | −0.370241 | + | 0.969304i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.0557 | 0.495565 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −21.5279 | + | 24.0689i | −0.707068 | + | 0.790526i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.8885 | −0.652522 | −0.326261 | − | 0.945280i | \(-0.605789\pi\) | ||||
−0.326261 | + | 0.945280i | \(0.605789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14.4721 | − | 48.5410i | 0.474305 | − | 1.59087i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 52.3607 | + | 20.0000i | 1.71421 | + | 0.654771i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 14.7639i | − | 0.482317i | −0.970486 | − | 0.241158i | \(-0.922473\pi\) | ||
0.970486 | − | 0.241158i | \(-0.0775273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.65248 | + | 6.94427i | −0.0865603 | + | 0.226618i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.2492 | −1.44248 | −0.721242 | − | 0.692683i | \(-0.756428\pi\) | ||||
−0.721242 | + | 0.692683i | \(0.756428\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 27.1935i | − | 0.885542i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 25.2361i | − | 0.820062i | −0.912072 | − | 0.410031i | \(-0.865518\pi\) | ||
0.912072 | − | 0.410031i | \(-0.134482\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.36068 | 0.271399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.81966 | + | 10.0000i | −0.123861 | + | 0.324272i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.70820i | − | 0.120121i | −0.998195 | − | 0.0600603i | \(-0.980871\pi\) | ||
0.998195 | − | 0.0600603i | \(-0.0191293\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.94427 | − | 1.88854i | −0.159826 | − | 0.0610480i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.23607 | − | 0.472136i | −0.104498 | − | 0.0152461i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.5279 | 0.662189 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.583592 | − | 0.652476i | 0.0188060 | − | 0.0210257i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −44.1803 | −1.42074 | −0.710372 | − | 0.703826i | \(-0.751473\pi\) | ||||
−0.710372 | + | 0.703826i | \(0.751473\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.0000 | + | 52.3607i | −0.642493 | + | 1.68207i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −0.583592 | −0.0187284 | −0.00936418 | − | 0.999956i | \(-0.502981\pi\) | ||||
−0.00936418 | + | 0.999956i | \(0.502981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.8885 | + | 5.81966i | 1.27877 | + | 0.186570i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 49.9574i | − | 1.59828i | −0.601145 | − | 0.799140i | \(-0.705289\pi\) | ||
0.601145 | − | 0.799140i | \(-0.294711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 9.52786i | − | 0.304512i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.58359 | − | 5.88854i | −0.210198 | − | 0.188007i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.5410 | 1.29306 | 0.646529 | − | 0.762890i | \(-0.276220\pi\) | ||||
0.646529 | + | 0.762890i | \(0.276220\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −7.23607 | + | 12.9443i | −0.230327 | + | 0.412021i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 55.7771i | 1.77361i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39.7771 | 1.26356 | 0.631780 | − | 0.775147i | \(-0.282324\pi\) | ||||
0.631780 | + | 0.775147i | \(0.282324\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.8885 | + | 12.9443i | 1.07542 | + | 0.410774i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16.0689i | 0.508907i | 0.967085 | + | 0.254453i | \(0.0818955\pi\) | ||||
−0.967085 | + | 0.254453i | \(0.918104\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.6525 | + | 20.6525i | 0.337029 | + | 0.653415i |
(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 | 2100.2.d.g.1301.1 | 4 | ||
3.2 | odd | 2 | 2100.2.d.h.1301.3 | 4 | |||
5.2 | odd | 4 | 2100.2.f.h.1049.2 | 4 | |||
5.3 | odd | 4 | 2100.2.f.b.1049.3 | 4 | |||
5.4 | even | 2 | 420.2.d.d.41.4 | yes | 4 | ||
7.6 | odd | 2 | 2100.2.d.h.1301.4 | 4 | |||
15.2 | even | 4 | 2100.2.f.g.1049.1 | 4 | |||
15.8 | even | 4 | 2100.2.f.a.1049.4 | 4 | |||
15.14 | odd | 2 | 420.2.d.c.41.2 | yes | 4 | ||
20.19 | odd | 2 | 1680.2.f.f.881.1 | 4 | |||
21.20 | even | 2 | inner | 2100.2.d.g.1301.2 | 4 | ||
35.13 | even | 4 | 2100.2.f.g.1049.2 | 4 | |||
35.27 | even | 4 | 2100.2.f.a.1049.3 | 4 | |||
35.34 | odd | 2 | 420.2.d.c.41.1 | ✓ | 4 | ||
60.59 | even | 2 | 1680.2.f.j.881.3 | 4 | |||
105.62 | odd | 4 | 2100.2.f.b.1049.4 | 4 | |||
105.83 | odd | 4 | 2100.2.f.h.1049.1 | 4 | |||
105.104 | even | 2 | 420.2.d.d.41.3 | yes | 4 | ||
140.139 | even | 2 | 1680.2.f.j.881.4 | 4 | |||
420.419 | odd | 2 | 1680.2.f.f.881.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.d.c.41.1 | ✓ | 4 | 35.34 | odd | 2 | ||
420.2.d.c.41.2 | yes | 4 | 15.14 | odd | 2 | ||
420.2.d.d.41.3 | yes | 4 | 105.104 | even | 2 | ||
420.2.d.d.41.4 | yes | 4 | 5.4 | even | 2 | ||
1680.2.f.f.881.1 | 4 | 20.19 | odd | 2 | |||
1680.2.f.f.881.2 | 4 | 420.419 | odd | 2 | |||
1680.2.f.j.881.3 | 4 | 60.59 | even | 2 | |||
1680.2.f.j.881.4 | 4 | 140.139 | even | 2 | |||
2100.2.d.g.1301.1 | 4 | 1.1 | even | 1 | trivial | ||
2100.2.d.g.1301.2 | 4 | 21.20 | even | 2 | inner | ||
2100.2.d.h.1301.3 | 4 | 3.2 | odd | 2 | |||
2100.2.d.h.1301.4 | 4 | 7.6 | odd | 2 | |||
2100.2.f.a.1049.3 | 4 | 35.27 | even | 4 | |||
2100.2.f.a.1049.4 | 4 | 15.8 | even | 4 | |||
2100.2.f.b.1049.3 | 4 | 5.3 | odd | 4 | |||
2100.2.f.b.1049.4 | 4 | 105.62 | odd | 4 | |||
2100.2.f.g.1049.1 | 4 | 15.2 | even | 4 | |||
2100.2.f.g.1049.2 | 4 | 35.13 | even | 4 | |||
2100.2.f.h.1049.1 | 4 | 105.83 | odd | 4 | |||
2100.2.f.h.1049.2 | 4 | 5.2 | odd | 4 |