Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(37,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.37");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 269x^{2} + 17592 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(12.5228i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.37 |
Dual form | 76.5.c.b.37.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 12.5228i | 1.39143i | 0.718320 | + | 0.695713i | \(0.244912\pi\) | ||||
−0.718320 | + | 0.695713i | \(0.755088\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 27.8215 | 1.11286 | 0.556430 | − | 0.830894i | \(-0.312171\pi\) | ||||
0.556430 | + | 0.830894i | \(0.312171\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 50.6430 | 1.03353 | 0.516766 | − | 0.856127i | \(-0.327136\pi\) | ||||
0.516766 | + | 0.856127i | \(0.327136\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −75.8215 | −0.936068 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −26.1785 | −0.216351 | −0.108176 | − | 0.994132i | \(-0.534501\pi\) | ||||
−0.108176 | + | 0.994132i | \(0.534501\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 285.790i | 1.69107i | 0.533923 | + | 0.845533i | \(0.320717\pi\) | ||||
−0.533923 | + | 0.845533i | \(0.679283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 348.404i | 1.54846i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −447.572 | −1.54869 | −0.774346 | − | 0.632762i | \(-0.781921\pi\) | ||||
−0.774346 | + | 0.632762i | \(0.781921\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.24940 | − | 360.927i | −0.0200814 | − | 0.999798i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 634.195i | 1.43808i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 830.538 | 1.57001 | 0.785007 | − | 0.619486i | \(-0.212659\pi\) | ||||
0.785007 | + | 0.619486i | \(0.212659\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 149.037 | 0.238459 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 64.8493i | 0.0889566i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 338.117i | 0.402041i | 0.979587 | + | 0.201021i | \(0.0644258\pi\) | ||||
−0.979587 | + | 0.201021i | \(0.935574\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 669.528i | − | 0.696699i | −0.937365 | − | 0.348350i | \(-0.886742\pi\) | ||
0.937365 | − | 0.348350i | \(-0.113258\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 327.829i | − | 0.301037i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1408.97 | 1.15018 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 623.907i | − | 0.455739i | −0.973692 | − | 0.227870i | \(-0.926824\pi\) | ||
0.973692 | − | 0.227870i | \(-0.0731760\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3578.90 | −2.35299 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1721.45i | − | 1.02406i | −0.858967 | − | 0.512030i | \(-0.828893\pi\) | ||
0.858967 | − | 0.512030i | \(-0.171107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1361.32 | 0.736248 | 0.368124 | − | 0.929777i | \(-0.380000\pi\) | ||||
0.368124 | + | 0.929777i | \(0.380000\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2109.47 | −1.04171 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.46934 | −0.00157055 | −0.000785275 | − | 1.00000i | \(-0.500250\pi\) | ||||
−0.000785275 | 1.00000i | \(0.500250\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 163.716 | 0.0681867 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 5604.87i | − | 2.15489i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1178.03i | 0.419379i | 0.977768 | + | 0.209689i | \(0.0672453\pi\) | ||||
−0.977768 | + | 0.209689i | \(0.932755\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −728.325 | −0.240769 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4519.83 | − | 90.7831i | 1.39115 | − | 0.0279419i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 4437.13i | − | 1.27467i | −0.770587 | − | 0.637335i | \(-0.780037\pi\) | ||
0.770587 | − | 0.637335i | \(-0.219963\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5916.84 | 1.59012 | 0.795060 | − | 0.606530i | \(-0.207439\pi\) | ||||
0.795060 | + | 0.606530i | \(0.207439\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3839.83 | −0.967456 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7951.12i | 1.88192i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3673.66i | 0.818370i | 0.912451 | + | 0.409185i | \(0.134187\pi\) | ||||
−0.912451 | + | 0.409185i | \(0.865813\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10400.7i | 2.18456i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 7274.88i | − | 1.44314i | −0.692340 | − | 0.721571i | \(-0.743420\pi\) | ||
0.692340 | − | 0.721571i | \(-0.256580\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 616.369 | 0.115663 | 0.0578316 | − | 0.998326i | \(-0.481581\pi\) | ||||
0.0578316 | + | 0.998326i | \(0.481581\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1866.36i | 0.331798i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1325.76 | −0.223606 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 674.916i | 0.108142i | 0.998537 | + | 0.0540712i | \(0.0172198\pi\) | ||||
−0.998537 | + | 0.0540712i | \(0.982780\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6953.64 | −1.05984 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5475.95 | 0.794883 | 0.397441 | − | 0.917628i | \(-0.369898\pi\) | ||||
0.397441 | + | 0.917628i | \(0.369898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12452.1 | −1.72348 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4234.18 | −0.559411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3954.06i | − | 0.499187i | −0.968351 | − | 0.249594i | \(-0.919703\pi\) | ||
0.968351 | − | 0.249594i | \(-0.0802971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14473.3i | 1.74777i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8384.39 | 0.969406 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −201.689 | − | 10041.5i | −0.0223478 | − | 1.11264i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12827.0i | 1.36327i | 0.731693 | + | 0.681635i | \(0.238731\pi\) | ||||
−0.731693 | + | 0.681635i | \(0.761269\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1984.89 | 0.202519 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7784.44 | 0.763105 | 0.381553 | − | 0.924347i | \(-0.375390\pi\) | ||||
0.381553 | + | 0.924347i | \(0.375390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14831.5i | 1.39801i | 0.715116 | + | 0.699006i | \(0.246374\pi\) | ||||
−0.715116 | + | 0.699006i | \(0.753626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 17644.3i | 1.60039i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 13332.9i | − | 1.16454i | −0.812994 | − | 0.582272i | \(-0.802164\pi\) | ||
0.812994 | − | 0.582272i | \(-0.197836\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14552.4i | − | 1.22485i | −0.790529 | − | 0.612424i | \(-0.790194\pi\) | ||
0.790529 | − | 0.612424i | \(-0.209806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7813.09 | 0.634128 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 21313.5i | − | 1.66916i | −0.550889 | − | 0.834579i | \(-0.685711\pi\) | ||
0.550889 | − | 0.834579i | \(-0.314289\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 23106.8 | 1.74721 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 21669.0i | − | 1.58295i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −22666.4 | −1.60062 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13955.7 | −0.953192 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 21557.4 | 1.42491 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13242.0 | −0.847489 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 25075.7i | − | 1.55469i | −0.629072 | − | 0.777347i | \(-0.716565\pi\) | ||
0.629072 | − | 0.777347i | \(-0.283435\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17047.6i | 1.02444i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4832.33 | 0.281588 | 0.140794 | − | 0.990039i | \(-0.455035\pi\) | ||||
0.140794 | + | 0.990039i | \(0.455035\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −367.132 | − | 18278.4i | −0.0207548 | − | 1.03332i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1804.21i | 0.0989963i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −11246.2 | −0.599188 | −0.299594 | − | 0.954067i | \(-0.596851\pi\) | ||||
−0.299594 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −36121.0 | −1.86952 | −0.934759 | − | 0.355282i | \(-0.884385\pi\) | ||||
−0.934759 | + | 0.355282i | \(0.884385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 43.4460i | − | 0.00218530i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 7481.55i | − | 0.365864i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9406.92i | 0.447416i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2050.19i | 0.0948768i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14354.0 | −0.646549 | −0.323275 | − | 0.946305i | \(-0.604784\pi\) | ||||
−0.323275 | + | 0.946305i | \(0.604784\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 25670.1i | 1.12583i | 0.826514 | + | 0.562916i | \(0.190321\pi\) | ||||
−0.826514 | + | 0.562916i | \(0.809679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 33935.6 | 1.44968 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 18627.3i | − | 0.775329i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 35480.1 | 1.43941 | 0.719707 | − | 0.694278i | \(-0.244276\pi\) | ||||
0.719707 | + | 0.694278i | \(0.244276\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14752.3 | −0.583535 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 42061.0 | 1.62266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5740.35 | −0.216054 | −0.108027 | − | 0.994148i | \(-0.534453\pi\) | ||||
−0.108027 | + | 0.994148i | \(0.534453\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 9120.70i | − | 0.335012i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9999.93i | 0.358562i | 0.983798 | + | 0.179281i | \(0.0573771\pi\) | ||||
−0.983798 | + | 0.179281i | \(0.942623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −53115.0 | −1.85970 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 549.660 | + | 27366.0i | 0.0187976 | + | 0.935879i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 36092.8i | − | 1.20595i | −0.797761 | − | 0.602973i | \(-0.793983\pi\) | ||
0.797761 | − | 0.602973i | \(-0.206017\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7547.67 | 0.246454 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 55565.4 | 1.77361 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 35538.6i | 1.10916i | 0.832130 | + | 0.554580i | \(0.187121\pi\) | ||||
−0.832130 | + | 0.554580i | \(0.812879\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9397.52i | 0.286851i | 0.989661 | + | 0.143425i | \(0.0458117\pi\) | ||||
−0.989661 | + | 0.143425i | \(0.954188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 74095.6i | 2.21254i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 17358.0i | − | 0.507174i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11716.8 | 0.335061 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3284.17i | 0.0919394i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 39080.5 | 1.07126 | 0.535628 | − | 0.844454i | \(-0.320075\pi\) | ||||
0.535628 | + | 0.844454i | \(0.320075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 71446.1i | 1.91807i | 0.283291 | + | 0.959034i | \(0.408574\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −99570.5 | −2.61855 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −70705.6 | −1.82189 | −0.910943 | − | 0.412532i | \(-0.864645\pi\) | ||||
−0.910943 | + | 0.412532i | \(0.864645\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 40473.6 | 1.02203 | 0.511017 | − | 0.859570i | \(-0.329269\pi\) | ||||
0.511017 | + | 0.859570i | \(0.329269\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −46004.7 | −1.13870 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17123.3i | 0.415522i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 47893.2i | − | 1.13964i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −62972.6 | −1.46964 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 189.778 | + | 9448.53i | 0.00434464 | + | 0.216307i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15128.1i | 0.339798i | 0.985461 | + | 0.169899i | \(0.0543441\pi\) | ||||
−0.985461 | + | 0.169899i | \(0.945656\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 91102.2 | 2.00803 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37874.1 | 0.819341 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 33906.9i | − | 0.720060i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7718.69i | 0.160937i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 127912.i | − | 2.61894i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 54212.7i | 1.09016i | 0.838383 | + | 0.545081i | \(0.183501\pi\) | ||||
−0.838383 | + | 0.545081i | \(0.816499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −11300.2 | −0.223214 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 44673.3i | − | 0.866954i | −0.901165 | − | 0.433477i | \(-0.857287\pi\) | ||
0.901165 | − | 0.433477i | \(-0.142713\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15643.5 | 0.298307 | 0.149154 | − | 0.988814i | \(-0.452345\pi\) | ||||
0.149154 | + | 0.988814i | \(0.452345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 16602.3i | − | 0.311131i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −31912.0 | −0.587817 | −0.293909 | − | 0.955834i | \(-0.594956\pi\) | ||||
−0.293909 | + | 0.955834i | \(0.594956\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −96.5224 | −0.00174780 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8451.87 | −0.150472 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 63704.3 | 1.11525 | 0.557626 | − | 0.830092i | \(-0.311712\pi\) | ||||
0.557626 | + | 0.830092i | \(0.311712\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 87289.1i | 1.50288i | 0.659799 | + | 0.751442i | \(0.270642\pi\) | ||||
−0.659799 | + | 0.751442i | \(0.729358\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 81826.5i | − | 1.38574i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4554.84 | 0.0758823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 103149. | − | 2071.81i | 1.69073 | − | 0.0339590i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 68574.4i | 1.10602i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14230.5 | 0.225878 | 0.112939 | − | 0.993602i | \(-0.463974\pi\) | ||||
0.112939 | + | 0.993602i | \(0.463974\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −21742.2 | −0.339674 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 155936.i | − | 2.39809i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 89311.3i | − | 1.35220i | −0.736811 | − | 0.676099i | \(-0.763669\pi\) | ||
0.736811 | − | 0.676099i | \(-0.236331\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 31596.5i | − | 0.471021i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 25636.5i | − | 0.376338i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3477.95 | −0.0502820 | −0.0251410 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251410 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 32774.7i | 0.466710i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 49516.1 | 0.694583 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 39297.9i | 0.543081i | 0.962427 | + | 0.271540i | \(0.0875331\pi\) | ||||
−0.962427 | + | 0.271540i | \(0.912467\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −61483.1 | −0.837177 | −0.418589 | − | 0.908176i | \(-0.637475\pi\) | ||||
−0.418589 | + | 0.908176i | \(0.637475\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −181247. | −2.43189 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3901.55 | −0.0515908 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −134140. | −1.74823 | −0.874115 | − | 0.485718i | \(-0.838558\pi\) | ||||
−0.874115 | + | 0.485718i | \(0.838558\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 50764.6i | 0.652158i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 43582.6i | 0.551951i | 0.961165 | + | 0.275975i | \(0.0890009\pi\) | ||||
−0.961165 | + | 0.275975i | \(0.910999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8204.37 | 0.102441 | 0.0512203 | − | 0.998687i | \(-0.483689\pi\) | ||||
0.0512203 | + | 0.998687i | \(0.483689\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 125749. | − | 2525.72i | 1.54815 | − | 0.0310954i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 87179.3i | − | 1.05840i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 116800. | 1.39845 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −160630. | −1.89689 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 17438.2i | − | 0.203127i | −0.994829 | − | 0.101563i | \(-0.967616\pi\) | ||
0.994829 | − | 0.101563i | \(-0.0323845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 123448.i | − | 1.41853i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 1697.66i | − | 0.0192459i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 237360.i | 2.65500i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 68941.5 | 0.760935 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 97483.2i | 1.06180i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 164615. | 1.76958 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 102263.i | − | 1.08503i | −0.840046 | − | 0.542515i | \(-0.817472\pi\) | ||
0.840046 | − | 0.542515i | \(-0.182528\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −185733. | −1.94523 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −30122.3 | −0.311435 | −0.155717 | − | 0.987802i | \(-0.549769\pi\) | ||||
−0.155717 | + | 0.987802i | \(0.549769\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 30961.5 | 0.316033 | 0.158017 | − | 0.987436i | \(-0.449490\pi\) | ||||
0.158017 | + | 0.987436i | \(0.449490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −106830. | −1.07664 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 162737.i | 1.61946i | 0.586806 | + | 0.809728i | \(0.300385\pi\) | ||||
−0.586806 | + | 0.809728i | \(0.699615\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8851.38i | − | 0.0869821i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 166965. | 1.62038 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3244.63 | + | 161541.i | 0.0311000 | + | 1.54838i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 42593.2i | 0.403249i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 182238. | 1.70429 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −175.698 | −0.00162321 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 94272.9i | − | 0.860460i | −0.902719 | − | 0.430230i | \(-0.858432\pi\) | ||
0.902719 | − | 0.430230i | \(-0.141568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 47305.6i | 0.426603i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 102207.i | 0.910732i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 46995.7i | 0.413807i | 0.978361 | + | 0.206904i | \(0.0663387\pi\) | ||||
−0.978361 | + | 0.206904i | \(0.933661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 266905. | 2.32251 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17527.2i | 0.150732i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −113303. | −0.963058 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 289363.i | 2.43111i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −143263. | −1.18980 | −0.594902 | − | 0.803798i | \(-0.702809\pi\) | ||||
−0.594902 | + | 0.803798i | \(0.702809\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 50339.8 | 0.413296 | 0.206648 | − | 0.978415i | \(-0.433745\pi\) | ||||
0.206648 | + | 0.978415i | \(0.433745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18533.3 | −0.150431 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −111315. | −0.893318 | −0.446659 | − | 0.894704i | \(-0.647386\pi\) | ||||
−0.446659 | + | 0.894704i | \(0.647386\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 202398.i | − | 1.60602i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 283848.i | − | 2.22715i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −198233. | −1.53811 | −0.769053 | − | 0.639184i | \(-0.779272\pi\) | ||||
−0.769053 | + | 0.639184i | \(0.779272\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −130216. | + | 5233.01i | −0.999193 | + | 0.0401548i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 174765.i | − | 1.32630i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 17148.3 | 0.128717 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 50895.1 | 0.377871 | 0.188936 | − | 0.981989i | \(-0.439496\pi\) | ||||
0.188936 | + | 0.981989i | \(0.439496\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 130523.i | 0.958591i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 59659.3i | 0.433441i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 55481.8i | − | 0.398779i | −0.979920 | − | 0.199390i | \(-0.936104\pi\) | ||
0.979920 | − | 0.199390i | \(-0.0638959\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 165828.i | − | 1.17922i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −96630.4 | −0.679878 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20996.6i | 0.146174i | 0.997326 | + | 0.0730869i | \(0.0232850\pi\) | ||||
−0.997326 | + | 0.0730869i | \(0.976715\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 314018. | 2.16324 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 34553.2i | − | 0.235554i | −0.993040 | − | 0.117777i | \(-0.962423\pi\) | ||
0.993040 | − | 0.117777i | \(-0.0375768\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −36884.6 | −0.248842 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −103218. | −0.689178 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 103703. | 0.685315 | 0.342657 | − | 0.939460i | \(-0.388673\pi\) | ||||
0.342657 | + | 0.939460i | \(0.388673\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −371726. | −2.43147 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 60514.4i | 0.391809i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 18777.2i | 0.120347i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −99884.3 | −0.633748 | −0.316874 | − | 0.948468i | \(-0.602633\pi\) | ||||
−0.316874 | + | 0.948468i | \(0.602633\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 228898. | − | 4597.53i | 1.43779 | − | 0.0288788i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 211625.i | 1.31607i | 0.752989 | + | 0.658034i | \(0.228612\pi\) | ||||
−0.752989 | + | 0.658034i | \(0.771388\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 191344. | 1.17816 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −193461. | −1.17946 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16332.9i | 0.0985997i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 59115.4i | 0.353390i | 0.984266 | + | 0.176695i | \(0.0565406\pi\) | ||||
−0.984266 | + | 0.176695i | \(0.943459\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 140834.i | − | 0.833726i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 224710.i | − | 1.31741i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 152349. | 0.884593 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 452337.i | − | 2.60130i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 266956. | 1.52059 | 0.760294 | − | 0.649579i | \(-0.225055\pi\) | ||||
0.760294 | + | 0.649579i | \(0.225055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 136181.i | − | 0.768338i | −0.923263 | − | 0.384169i | \(-0.874488\pi\) | ||
0.923263 | − | 0.384169i | \(-0.125512\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 263.051 | 0.00147014 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −66704.7 | −0.369299 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 299647. | 1.64344 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 93690.3 | 0.509073 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 62111.0i | − | 0.334360i | −0.985926 | − | 0.167180i | \(-0.946534\pi\) | ||
0.985926 | − | 0.167180i | \(-0.0534660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 175495.i | 0.936027i | 0.883721 | + | 0.468014i | \(0.155030\pi\) | ||||
−0.883721 | + | 0.468014i | \(0.844970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −117801. | −0.622546 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6020.90 | − | 299764.i | −0.0315282 | − | 1.56970i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 46581.0i | − | 0.241702i | −0.992671 | − | 0.120851i | \(-0.961438\pi\) | ||
0.992671 | − | 0.120851i | \(-0.0385623\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12413.2 | −0.0638274 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 97027.2 | 0.494408 | 0.247204 | − | 0.968963i | \(-0.420488\pi\) | ||||
0.247204 | + | 0.968963i | \(0.420488\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 110008.i | − | 0.555526i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 179753.i | − | 0.899626i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 151069.i | 0.749346i | 0.927157 | + | 0.374673i | \(0.122245\pi\) | ||||
−0.927157 | + | 0.374673i | \(0.877755\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 45064.9i | 0.221557i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −321463. | −1.56651 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 402669.i | 1.94502i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −220171. | −1.05421 | −0.527107 | − | 0.849799i | \(-0.676723\pi\) | ||||
−0.527107 | + | 0.849799i | \(0.676723\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 29024.8i | − | 0.137766i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −70055.5 | −0.329640 | −0.164820 | − | 0.986324i | \(-0.552704\pi\) | ||||
−0.164820 | + | 0.986324i | \(0.552704\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −405846. | −1.89321 | −0.946606 | − | 0.322393i | \(-0.895513\pi\) | ||||
−0.946606 | + | 0.322393i | \(0.895513\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 233266. | 1.07881 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 293552. | 1.34602 | 0.673010 | − | 0.739633i | \(-0.265001\pi\) | ||||
0.673010 | + | 0.739633i | \(0.265001\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 186045.i | 0.845811i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 444312.i | 2.00284i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −35637.4 | −0.159288 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1080.43 | − | 53791.4i | −0.00478859 | − | 0.238411i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 89320.4i | − | 0.392567i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −299532. | −1.30548 | −0.652742 | − | 0.757580i | \(-0.726382\pi\) | ||||
−0.652742 | + | 0.757580i | \(0.726382\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 178306. | 0.770685 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 526723.i | 2.25781i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 356867.i | 1.51713i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 103571.i | 0.436697i | 0.975871 | + | 0.218349i | \(0.0700670\pi\) | ||||
−0.975871 | + | 0.218349i | \(0.929933\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 71885.5i | − | 0.300624i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −317179. | −1.31565 | −0.657827 | − | 0.753169i | \(-0.728524\pi\) | ||||
−0.657827 | + | 0.753169i | \(0.728524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 151332.i | − | 0.622638i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 55222.7 | 0.225376 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 368422.i | − | 1.49153i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −816.803 | −0.00328032 | −0.00164016 | − | 0.999999i | \(-0.500522\pi\) | ||||
−0.00164016 | + | 0.999999i | \(0.500522\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −125228. | −0.498913 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −174475. | −0.689601 | −0.344800 | − | 0.938676i | \(-0.612053\pi\) | ||||
−0.344800 | + | 0.938676i | \(0.612053\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 216575. | 0.849230 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 665151.i | − | 2.58764i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 345595.i | 1.33393i | 0.745090 | + | 0.666964i | \(0.232407\pi\) | ||||
−0.745090 | + | 0.666964i | \(0.767593\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 31214.8 | 0.119541 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 23405.9 | − | 470.119i | 0.0889386 | − | 0.00178638i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 412635.i | 1.55579i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 90.8221 | 0.000339790 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 451984. | 1.67799 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 64679.5i | − | 0.238282i | −0.992877 | − | 0.119141i | \(-0.961986\pi\) | ||
0.992877 | − | 0.119141i | \(-0.0380140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 187404.i | 0.685135i | 0.939493 | + | 0.342567i | \(0.111296\pi\) | ||||
−0.939493 | + | 0.342567i | \(0.888704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 94518.2i | 0.342923i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 299662.i | 1.07897i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 409952. | 1.46495 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 336430.i | 1.19318i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 491972. | 1.73175 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 370941.i | − | 1.29598i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −445044. | −1.54332 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4285.85 | −0.0147523 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 217204. | 0.742119 | 0.371060 | − | 0.928609i | \(-0.378995\pi\) | ||||
0.371060 | + | 0.928609i | \(0.378995\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −117684. | −0.399132 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 404871.i | − | 1.36309i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 136963.i | 0.457751i | 0.973456 | + | 0.228875i | \(0.0735049\pi\) | ||||
−0.973456 | + | 0.228875i | \(0.926495\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −448624. | −1.48846 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 122036. | − | 2451.14i | 0.401960 | − | 0.00807357i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 34179.8i | 0.111768i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 217372. | 0.705696 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 213586. | 0.688435 | 0.344218 | − | 0.938890i | \(-0.388144\pi\) | ||||
0.344218 | + | 0.938890i | \(0.388144\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 389053.i | 1.24504i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 146727.i | 0.466213i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 220639.i | 0.696091i | 0.937478 | + | 0.348045i | \(0.113154\pi\) | ||||
−0.937478 | + | 0.348045i | \(0.886846\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 592973.i | − | 1.85754i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −352153. | −1.09538 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 335154.i | − | 1.03519i | −0.855626 | − | 0.517595i | \(-0.826827\pi\) | ||
0.855626 | − | 0.517595i | \(-0.173173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −124545. | −0.381991 | −0.190996 | − | 0.981591i | \(-0.561172\pi\) | ||||
−0.190996 | + | 0.981591i | \(0.561172\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 489398.i | 1.49057i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 123781. | 0.374384 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 215350. | 0.646834 | 0.323417 | − | 0.946257i | \(-0.395168\pi\) | ||||
0.323417 | + | 0.946257i | \(0.395168\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −894708. | −2.66885 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 277318. | 0.821536 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 30839.2i | − | 0.0907331i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 602866.i | − | 1.76161i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 396441. | 1.15054 | 0.575271 | − | 0.817963i | \(-0.304897\pi\) | ||||
0.575271 | + | 0.817963i | \(0.304897\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −241651. | + | 4853.68i | −0.696559 | + | 0.0139907i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 885435.i | − | 2.53502i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −160553. | −0.456573 | −0.228286 | − | 0.973594i | \(-0.573312\pi\) | ||||
−0.228286 | + | 0.973594i | \(0.573312\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −630614. | −1.78127 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 506844.i | 1.42209i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 39005.8i | − | 0.108711i | −0.998522 | − | 0.0543557i | \(-0.982690\pi\) | ||
0.998522 | − | 0.0543557i | \(-0.0173105\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 297294.i | − | 0.823071i | −0.911394 | − | 0.411535i | \(-0.864993\pi\) | ||
0.911394 | − | 0.411535i | \(-0.135007\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 278543.i | − | 0.766050i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −388268. | −1.06077 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 638986.i | − | 1.73426i | −0.498082 | − | 0.867130i | \(-0.665962\pi\) | ||
0.498082 | − | 0.867130i | \(-0.334038\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −214432. | −0.578169 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 991.504i | − | 0.00265590i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 620859. | 1.65224 | 0.826118 | − | 0.563497i | \(-0.190544\pi\) | ||||
0.826118 | + | 0.563497i | \(0.190544\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 599759. | 1.58572 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 264977. | 0.696045 | 0.348022 | − | 0.937486i | \(-0.386853\pi\) | ||||
0.348022 | + | 0.937486i | \(0.386853\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −105833. | −0.276210 | −0.138105 | − | 0.990418i | \(-0.544101\pi\) | ||||
−0.138105 | + | 0.990418i | \(0.544101\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 53859.8i | 0.139663i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 200246.i | − | 0.515926i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −461561. | −1.18160 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −118322. | + | 2376.56i | −0.300976 | + | 0.00604525i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 279243.i | 0.705800i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 108947. | 0.273626 | 0.136813 | − | 0.990597i | \(-0.456314\pi\) | ||||
0.136813 | + | 0.990597i | \(0.456314\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −189447. | −0.472804 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 697643.i | − | 1.73016i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 46788.5i | 0.115308i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 551593.i | 1.35088i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 711723.i | − | 1.73219i | −0.499882 | − | 0.866093i | \(-0.666623\pi\) | ||
0.499882 | − | 0.866093i | \(-0.333377\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 712239. | 1.72268 | 0.861338 | − | 0.508032i | \(-0.169627\pi\) | ||||
0.861338 | + | 0.508032i | \(0.169627\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 474291.i | 1.14005i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −498438. | −1.19070 | −0.595350 | − | 0.803467i | \(-0.702987\pi\) | ||||
−0.595350 | + | 0.803467i | \(0.702987\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 116157.i | 0.275776i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 424611. | 1.00191 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 130175. | 0.305281 | 0.152641 | − | 0.988282i | \(-0.451222\pi\) | ||||
0.152641 | + | 0.988282i | \(0.451222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 134443. | 0.313368 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −46734.0 | −0.108269 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 258996.i | 0.596379i | 0.954507 | + | 0.298190i | \(0.0963828\pi\) | ||||
−0.954507 | + | 0.298190i | \(0.903617\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 767174.i | 1.75586i | 0.478785 | + | 0.877932i | \(0.341077\pi\) | ||||
−0.478785 | + | 0.877932i | \(0.658923\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.60182e6 | 3.64406 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10214.2 | − | 508534.i | −0.0230972 | − | 1.14994i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 280819.i | 0.631211i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −678896. | −1.51688 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −154894. | −0.344024 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 63926.3i | 0.141140i | 0.997507 | + | 0.0705699i | \(0.0224818\pi\) | ||||
−0.997507 | + | 0.0705699i | \(0.977518\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9664.93i | 0.0212125i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 466563.i | − | 1.01797i | −0.860777 | − | 0.508983i | \(-0.830022\pi\) | ||
0.860777 | − | 0.508983i | \(-0.169978\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 649598.i | 1.40898i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 559436. | 1.20630 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 133694.i | − | 0.286595i | −0.989680 | − | 0.143298i | \(-0.954229\pi\) | ||
0.989680 | − | 0.143298i | \(-0.0457706\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −312885. | −0.666813 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 195901.i | 0.415073i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −336671. | −0.709197 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −185512. | −0.388522 | −0.194261 | − | 0.980950i | \(-0.562231\pi\) | ||||
−0.194261 | + | 0.980950i | \(0.562231\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 100521. | 0.209310 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.00494e6 | −2.08051 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 770471.i | 1.58596i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 399629.i | − | 0.817905i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 77805.2 | 0.158333 | 0.0791667 | − | 0.996861i | \(-0.474774\pi\) | ||||
0.0791667 | + | 0.996861i | \(0.474774\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −225185. | + | 4522.95i | −0.455647 | + | 0.00915190i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 1208.73i | − | 0.00243194i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 394227. | 0.788693 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −425698. | −0.846856 | −0.423428 | − | 0.905930i | \(-0.639173\pi\) | ||||
−0.423428 | + | 0.905930i | \(0.639173\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 51173.2i | − | 0.101229i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 556068.i | − | 1.09383i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 208148.i | − | 0.407156i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 797759.i | 1.55179i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 434230. | 0.839967 | 0.419984 | − | 0.907532i | \(-0.362036\pi\) | ||||
0.419984 | + | 0.907532i | \(0.362036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 751113.i | 1.44489i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.09311e6 | −2.09115 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 50391.8i | 0.0958702i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 571303. | 1.08093 | 0.540465 | − | 0.841366i | \(-0.318248\pi\) | ||||
0.540465 | + | 0.841366i | \(0.318248\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 461456. | 0.868310 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −609290. | −1.14022 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 257404. | 0.479079 | 0.239540 | − | 0.970887i | \(-0.423003\pi\) | ||||
0.239540 | + | 0.970887i | \(0.423003\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 57039.5i | 0.105585i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 96170.9i | − | 0.177055i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −239337. | −0.438248 | −0.219124 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219124 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 25944.9 | + | 1.29172e6i | 0.0472515 | + | 2.35252i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 591739.i | 1.07190i | 0.844251 | + | 0.535948i | \(0.180046\pi\) | ||||
−0.844251 | + | 0.535948i | \(0.819954\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −399351. | −0.719519 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −415195. | −0.744064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 675217.i | − | 1.20359i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 89204.9i | − | 0.158164i | −0.996868 | − | 0.0790822i | \(-0.974801\pi\) | ||
0.996868 | − | 0.0790822i | \(-0.0251990\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 178207.i | 0.314292i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 714181.i | 1.25289i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −673763. | −1.17575 | −0.587875 | − | 0.808952i | \(-0.700035\pi\) | ||||
−0.587875 | + | 0.808952i | \(0.700035\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 272274.i | − | 0.472632i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −490950. | −0.847750 | −0.423875 | − | 0.905721i | \(-0.639330\pi\) | ||||
−0.423875 | + | 0.905721i | \(0.639330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 736979.i | − | 1.26592i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 944140. | 1.61329 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.26809e6 | 2.15555 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −572323. | −0.967807 | −0.483904 | − | 0.875121i | \(-0.660781\pi\) | ||||
−0.483904 | + | 0.875121i | \(0.660781\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.11843e6 | 1.88148 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 233033.i | − | 0.389995i | −0.980804 | − | 0.194997i | \(-0.937530\pi\) | ||
0.980804 | − | 0.194997i | \(-0.0624698\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 99784.2i | − | 0.166134i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 395678. | 0.655391 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −621317. | + | 12479.5i | −1.02385 | + | 0.0205646i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 190445.i | 0.312226i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21926.6 | −0.0357642 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 987111. | 1.60187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 876845.i | − | 1.41571i | −0.706359 | − | 0.707854i | \(-0.749664\pi\) | ||
0.706359 | − | 0.707854i | \(-0.250336\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 43553.8i | − | 0.0699636i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.07938e6i | − | 1.72513i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.69097e6i | 2.68900i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −410433. | −0.649393 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 376141.i | 0.592153i | 0.955164 | + | 0.296076i | \(0.0956783\pi\) | ||||
−0.955164 | + | 0.296076i | \(0.904322\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1552.78 | 0.00243230 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 299803.i | 0.467273i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −16135.6 | −0.0250239 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.17020e6 | 1.80579 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −492121. | −0.755657 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 979635. | 1.49681 | 0.748406 | − | 0.663241i | \(-0.230820\pi\) | ||||
0.748406 | + | 0.663241i | \(0.230820\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 583716.i | 0.887483i | 0.896155 | + | 0.443741i | \(0.146349\pi\) | ||||
−0.896155 | + | 0.443741i | \(0.853651\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 769943.i | − | 1.16487i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −159705. | −0.240438 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9868.77 | − | 491338.i | −0.0147849 | − | 0.736100i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 1.09739e6i | − | 1.63603i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −702550. | −1.04230 | −0.521148 | − | 0.853466i | \(-0.674496\pi\) | ||||
−0.521148 | + | 0.853466i | \(0.674496\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −366360. | −0.540889 | −0.270444 | − | 0.962736i | \(-0.587171\pi\) | ||||
−0.270444 | + | 0.962736i | \(0.587171\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 48858.5i | − | 0.0717848i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 718634.i | − | 1.05074i | −0.850873 | − | 0.525372i | \(-0.823926\pi\) | ||
0.850873 | − | 0.525372i | \(-0.176074\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 421812.i | − | 0.613775i | −0.951746 | − | 0.306888i | \(-0.900712\pi\) | ||
0.951746 | − | 0.306888i | \(-0.0992876\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.67981e6i | − | 2.43253i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −73274.9 | −0.105600 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 278213.i | 0.399029i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 43418.4 | 0.0619760 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 172794.i | 0.245473i | 0.992439 | + | 0.122737i | \(0.0391671\pi\) | ||||
−0.992439 | + | 0.122737i | \(0.960833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 592958. | 0.838363 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −545778. | −0.767999 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.47774e6 | −2.06959 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −706758. | −0.985154 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 102742.i | 0.142539i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 518178.i | − | 0.715517i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −395245. | −0.543211 | −0.271606 | − | 0.962409i | \(-0.587555\pi\) | ||||
−0.271606 | + | 0.962409i | \(0.587555\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 15292.4 | + | 761365.i | 0.0209191 | + | 1.04150i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.07871e6i | − | 1.46874i | −0.678750 | − | 0.734370i | \(-0.737478\pi\) | ||
0.678750 | − | 0.734370i | \(-0.262522\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 888609. | 1.20427 | 0.602136 | − | 0.798393i | \(-0.294316\pi\) | ||||
0.602136 | + | 0.798393i | \(0.294316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.09173e6 | 1.47268 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 510125.i | − | 0.684944i | −0.939528 | − | 0.342472i | \(-0.888736\pi\) | ||
0.939528 | − | 0.342472i | \(-0.111264\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − | 1.00416e6i | − | 1.34205i | ||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.46267e6i | 1.94584i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 17668.3i | − | 0.0233967i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.04990e6 | −1.38392 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 972563.i | − | 1.27611i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −670616. | −0.875907 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.24926e6i | 1.62425i | 0.583485 | + | 0.812124i | \(0.301689\pi\) | ||||
−0.583485 | + | 0.812124i | \(0.698311\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 218376. | 0.282636 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −977935. | −1.25996 | −0.629982 | − | 0.776610i | \(-0.716938\pi\) | ||||
−0.629982 | + | 0.776610i | \(0.716938\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 465114. | 0.596538 | 0.298269 | − | 0.954482i | \(-0.403591\pi\) | ||||
0.298269 | + | 0.954482i | \(0.403591\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.54591e6 | 1.97378 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.12281e6i | 1.42711i | 0.700599 | + | 0.713555i | \(0.252916\pi\) | ||||
−0.700599 | + | 0.713555i | \(0.747084\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.26991e6i | − | 1.60682i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 182036. | 0.229299 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.1507 | + | 1252.18i | 3.15389e−5 | + | 0.00157023i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 988738.i | 1.23434i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.97242e6 | −3.69424 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 226379. | 0.280102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 527256.i | − | 0.649489i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 863343.i | 1.05879i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 261453.i | 0.319225i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 637072.i | − | 0.774415i | −0.921993 | − | 0.387207i | \(-0.873440\pi\) | ||
0.921993 | − | 0.387207i | \(-0.126560\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −590228. | −0.714318 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 311275.i | 0.375066i | 0.982258 | + | 0.187533i | \(0.0600491\pi\) | ||||
−0.982258 | + | 0.187533i | \(0.939951\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −143352. | −0.171974 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.06145e6i | 2.46224i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 244724. | 0.291030 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 444591. | 0.526416 | 0.263208 | − | 0.964739i | \(-0.415219\pi\) | ||||
0.263208 | + | 0.964739i | \(0.415219\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.28062e6 | 1.50974 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.07909e6 | 2.44045 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 92985.0i | − | 0.108675i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 1.12455e6i | − | 1.30863i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 526124. | 0.609617 | 0.304808 | − | 0.952414i | \(-0.401408\pi\) | ||||
0.304808 | + | 0.952414i | \(0.401408\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1186.85 | − | 59089.7i | −0.00136929 | − | 0.0681730i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 377216.i | − | 0.433338i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 325978. | 0.372877 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.26151e6 | 1.43685 | 0.718426 | − | 0.695603i | \(-0.244863\pi\) | ||||
0.718426 | + | 0.695603i | \(0.244863\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 387725.i | 0.439737i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 243694.i | − | 0.275211i | −0.990487 | − | 0.137605i | \(-0.956059\pi\) | ||
0.990487 | − | 0.137605i | \(-0.0439405\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.42973e6i | − | 1.60779i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 91370.5i | 0.102316i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.01262e6 | 1.12914 | 0.564569 | − | 0.825386i | \(-0.309042\pi\) | ||||
0.564569 | + | 0.825386i | \(0.309042\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 176152.i | 0.195594i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.03794e6 | −2.25335 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.58910e6i | − | 1.74971i | −0.484386 | − | 0.874854i | \(-0.660957\pi\) | ||
0.484386 | − | 0.874854i | \(-0.339043\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.08728e6 | 1.19216 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 110844. | 0.121029 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −569540. | −0.619280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 475253. | 0.514610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.01092e6i | 1.09009i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.98774e6i | 2.13454i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 854289. | 0.913591 | 0.456795 | − | 0.889572i | \(-0.348997\pi\) | ||||
0.456795 | + | 0.889572i | \(0.348997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.02295e6 | + | 40632.0i | −2.15446 | + | 0.0432733i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 800970.i | 0.849528i | 0.905304 | + | 0.424764i | \(0.139643\pi\) | ||||
−0.905304 | + | 0.424764i | \(0.860357\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.82928e6 | −1.93221 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −533388. | −0.561092 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.32952e6i | 1.39286i | 0.717627 | + | 0.696428i | \(0.245228\pi\) | ||||
−0.717627 | + | 0.696428i | \(0.754772\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 103511.i | 0.108000i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.10339e6i | 1.14654i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.40685e6i | 1.45593i | 0.685615 | + | 0.727964i | \(0.259533\pi\) | ||||
−0.685615 | + | 0.727964i | \(0.740467\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.96714e6 | −2.02751 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 2200.24i | − | 0.00225858i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.13063e6 | 1.15592 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4828.18i | 0.00491627i | 0.999997 | + | 0.00245814i | \(0.000782450\pi\) | ||||
−0.999997 | + | 0.00245814i | \(0.999218\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.18056e6 | 1.19727 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.12604e6 | 1.13738 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.85065e6 | 1.86180 | 0.930900 | − | 0.365274i | \(-0.119025\pi\) | ||||
0.930900 | + | 0.365274i | \(0.119025\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 40460.0 | 0.0405410 |
(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 | 76.5.c.b.37.4 | yes | 4 | |
3.2 | odd | 2 | 684.5.h.c.37.2 | 4 | |||
4.3 | odd | 2 | 304.5.e.d.113.1 | 4 | |||
19.18 | odd | 2 | inner | 76.5.c.b.37.1 | ✓ | 4 | |
57.56 | even | 2 | 684.5.h.c.37.1 | 4 | |||
76.75 | even | 2 | 304.5.e.d.113.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.c.b.37.1 | ✓ | 4 | 19.18 | odd | 2 | inner | |
76.5.c.b.37.4 | yes | 4 | 1.1 | even | 1 | trivial | |
304.5.e.d.113.1 | 4 | 4.3 | odd | 2 | |||
304.5.e.d.113.4 | 4 | 76.75 | even | 2 | |||
684.5.h.c.37.1 | 4 | 57.56 | even | 2 | |||
684.5.h.c.37.2 | 4 | 3.2 | odd | 2 |