Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.l.274.3 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 1.82843i | − 0.646447i | −0.946323 | − | 0.323223i | \(-0.895234\pi\) | ||||
0.946323 | − | 0.323223i | \(-0.104766\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 4.65685 | 0.582107 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.48528 | −0.373226 | ||||||||
\(7\) | 7.00000i | 0.377964i | ||||||||
\(8\) | − 23.1421i | − 1.02275i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −64.5685 | −1.76983 | −0.884916 | − | 0.465751i | \(-0.845784\pi\) | ||||
−0.884916 | + | 0.465751i | \(0.845784\pi\) | |||||||
\(12\) | − 13.9706i | − 0.336080i | ||||||||
\(13\) | − 32.3431i | − 0.690029i | −0.938597 | − | 0.345014i | \(-0.887874\pi\) | ||||
0.938597 | − | 0.345014i | \(-0.112126\pi\) | |||||||
\(14\) | 12.7990 | 0.244334 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.05887 | −0.0790449 | ||||||||
\(17\) | 56.3431i | 0.803836i | 0.915676 | + | 0.401918i | \(0.131656\pi\) | ||||
−0.915676 | + | 0.401918i | \(0.868344\pi\) | |||||||
\(18\) | 16.4558i | 0.215482i | ||||||||
\(19\) | 2.74517 | 0.0331465 | 0.0165733 | − | 0.999863i | \(-0.494724\pi\) | ||||
0.0165733 | + | 0.999863i | \(0.494724\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 21.0000 | 0.218218 | ||||||||
\(22\) | 118.059i | 1.14410i | ||||||||
\(23\) | 88.1665i | 0.799304i | 0.916667 | + | 0.399652i | \(0.130869\pi\) | ||||
−0.916667 | + | 0.399652i | \(0.869131\pi\) | |||||||
\(24\) | −69.4264 | −0.590484 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −59.1371 | −0.446067 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 32.5980i | 0.220016i | ||||||||
\(29\) | −246.735 | −1.57992 | −0.789958 | − | 0.613161i | \(-0.789898\pi\) | ||||
−0.789958 | + | 0.613161i | \(0.789898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −110.912 | −0.642591 | −0.321296 | − | 0.946979i | \(-0.604118\pi\) | ||||
−0.321296 | + | 0.946979i | \(0.604118\pi\) | |||||||
\(32\) | − 175.887i | − 0.971649i | ||||||||
\(33\) | 193.706i | 1.02181i | ||||||||
\(34\) | 103.019 | 0.519637 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −41.9117 | −0.194036 | ||||||||
\(37\) | − 120.676i | − 0.536190i | −0.963392 | − | 0.268095i | \(-0.913606\pi\) | ||||
0.963392 | − | 0.268095i | \(-0.0863942\pi\) | |||||||
\(38\) | − 5.01934i | − 0.0214275i | ||||||||
\(39\) | −97.0294 | −0.398388 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −176.274 | −0.671449 | −0.335724 | − | 0.941960i | \(-0.608981\pi\) | ||||
−0.335724 | + | 0.941960i | \(0.608981\pi\) | |||||||
\(42\) | − 38.3970i | − 0.141066i | ||||||||
\(43\) | − 443.362i | − 1.57238i | −0.617988 | − | 0.786188i | \(-0.712052\pi\) | ||||
0.617988 | − | 0.786188i | \(-0.287948\pi\) | |||||||
\(44\) | −300.686 | −1.03023 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 161.206 | 0.516707 | ||||||||
\(47\) | 345.206i | 1.07135i | 0.844424 | + | 0.535675i | \(0.179943\pi\) | ||||
−0.844424 | + | 0.535675i | \(0.820057\pi\) | |||||||
\(48\) | 15.1766i | 0.0456366i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 169.029 | 0.464095 | ||||||||
\(52\) | − 150.617i | − 0.401670i | ||||||||
\(53\) | 260.981i | 0.676386i | 0.941077 | + | 0.338193i | \(0.109816\pi\) | ||||
−0.941077 | + | 0.338193i | \(0.890184\pi\) | |||||||
\(54\) | 49.3675 | 0.124409 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 161.995 | 0.386562 | ||||||||
\(57\) | − 8.23550i | − 0.0191372i | ||||||||
\(58\) | 451.137i | 1.02133i | ||||||||
\(59\) | −628.999 | −1.38794 | −0.693972 | − | 0.720002i | \(-0.744141\pi\) | ||||
−0.693972 | + | 0.720002i | \(0.744141\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −115.206 | −0.241814 | −0.120907 | − | 0.992664i | \(-0.538580\pi\) | ||||
−0.120907 | + | 0.992664i | \(0.538580\pi\) | |||||||
\(62\) | 202.794i | 0.415401i | ||||||||
\(63\) | − 63.0000i | − 0.125988i | ||||||||
\(64\) | −362.068 | −0.707164 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 354.177 | 0.660547 | ||||||||
\(67\) | 951.480i | 1.73495i | 0.497479 | + | 0.867476i | \(0.334259\pi\) | ||||
−0.497479 | + | 0.867476i | \(0.665741\pi\) | |||||||
\(68\) | 262.382i | 0.467919i | ||||||||
\(69\) | 264.500 | 0.461478 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 356.264 | 0.595504 | 0.297752 | − | 0.954643i | \(-0.403763\pi\) | ||||
0.297752 | + | 0.954643i | \(0.403763\pi\) | |||||||
\(72\) | 208.279i | 0.340916i | ||||||||
\(73\) | − 656.754i | − 1.05298i | −0.850183 | − | 0.526488i | \(-0.823509\pi\) | ||||
0.850183 | − | 0.526488i | \(-0.176491\pi\) | |||||||
\(74\) | −220.648 | −0.346618 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.7838 | 0.0192948 | ||||||||
\(77\) | − 451.980i | − 0.668933i | ||||||||
\(78\) | 177.411i | 0.257537i | ||||||||
\(79\) | −440.195 | −0.626909 | −0.313455 | − | 0.949603i | \(-0.601486\pi\) | ||||
−0.313455 | + | 0.949603i | \(0.601486\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 322.304i | 0.434056i | ||||||||
\(83\) | − 54.4121i | − 0.0719579i | −0.999353 | − | 0.0359790i | \(-0.988545\pi\) | ||||
0.999353 | − | 0.0359790i | \(-0.0114549\pi\) | |||||||
\(84\) | 97.7939 | 0.127026 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −810.656 | −1.01646 | ||||||||
\(87\) | 740.205i | 0.912165i | ||||||||
\(88\) | 1494.25i | 1.81009i | ||||||||
\(89\) | 1018.78 | 1.21338 | 0.606690 | − | 0.794938i | \(-0.292497\pi\) | ||||
0.606690 | + | 0.794938i | \(0.292497\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 226.402 | 0.260806 | ||||||||
\(92\) | 410.579i | 0.465280i | ||||||||
\(93\) | 332.735i | 0.371000i | ||||||||
\(94\) | 631.184 | 0.692571 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −527.662 | −0.560982 | ||||||||
\(97\) | 724.108i | 0.757959i | 0.925405 | + | 0.378979i | \(0.123725\pi\) | ||||
−0.925405 | + | 0.378979i | \(0.876275\pi\) | |||||||
\(98\) | 89.5929i | 0.0923495i | ||||||||
\(99\) | 581.117 | 0.589944 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 268.725 | 0.264744 | 0.132372 | − | 0.991200i | \(-0.457741\pi\) | ||||
0.132372 | + | 0.991200i | \(0.457741\pi\) | |||||||
\(102\) | − 309.058i | − 0.300013i | ||||||||
\(103\) | − 1840.63i | − 1.76080i | −0.474233 | − | 0.880399i | \(-0.657275\pi\) | ||||
0.474233 | − | 0.880399i | \(-0.342725\pi\) | |||||||
\(104\) | −748.489 | −0.705725 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 477.184 | 0.437247 | ||||||||
\(107\) | 243.087i | 0.219627i | 0.993952 | + | 0.109813i | \(0.0350253\pi\) | ||||
−0.993952 | + | 0.109813i | \(0.964975\pi\) | |||||||
\(108\) | 125.735i | 0.112027i | ||||||||
\(109\) | 405.176 | 0.356044 | 0.178022 | − | 0.984027i | \(-0.443030\pi\) | ||||
0.178022 | + | 0.984027i | \(0.443030\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −362.029 | −0.309570 | ||||||||
\(112\) | − 35.4121i | − 0.0298762i | ||||||||
\(113\) | − 28.1766i | − 0.0234569i | −0.999931 | − | 0.0117285i | \(-0.996267\pi\) | ||||
0.999931 | − | 0.0117285i | \(-0.00373337\pi\) | |||||||
\(114\) | −15.0580 | −0.0123712 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1149.01 | −0.919680 | ||||||||
\(117\) | 291.088i | 0.230010i | ||||||||
\(118\) | 1150.08i | 0.897232i | ||||||||
\(119\) | −394.402 | −0.303822 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2838.10 | 2.13230 | ||||||||
\(122\) | 210.646i | 0.156320i | ||||||||
\(123\) | 528.823i | 0.387661i | ||||||||
\(124\) | −516.500 | −0.374057 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −115.191 | −0.0814446 | ||||||||
\(127\) | 2740.90i | 1.91508i | 0.288298 | + | 0.957541i | \(0.406911\pi\) | ||||
−0.288298 | + | 0.957541i | \(0.593089\pi\) | |||||||
\(128\) | − 745.083i | − 0.514505i | ||||||||
\(129\) | −1330.09 | −0.907811 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1832.04 | −1.22188 | −0.610938 | − | 0.791678i | \(-0.709208\pi\) | ||||
−0.610938 | + | 0.791678i | \(0.709208\pi\) | |||||||
\(132\) | 902.059i | 0.594804i | ||||||||
\(133\) | 19.2162i | 0.0125282i | ||||||||
\(134\) | 1739.71 | 1.12155 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1303.90 | 0.822122 | ||||||||
\(137\) | − 382.747i | − 0.238688i | −0.992853 | − | 0.119344i | \(-0.961921\pi\) | ||||
0.992853 | − | 0.119344i | \(-0.0380792\pi\) | |||||||
\(138\) | − 483.618i | − 0.298321i | ||||||||
\(139\) | −3053.60 | −1.86333 | −0.931667 | − | 0.363314i | \(-0.881645\pi\) | ||||
−0.931667 | + | 0.363314i | \(0.881645\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1035.62 | 0.618545 | ||||||||
\(142\) | − 651.403i | − 0.384961i | ||||||||
\(143\) | 2088.35i | 1.22123i | ||||||||
\(144\) | 45.5299 | 0.0263483 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1200.83 | −0.680692 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | − 561.971i | − 0.312120i | ||||||||
\(149\) | −3560.60 | −1.95769 | −0.978843 | − | 0.204611i | \(-0.934407\pi\) | ||||
−0.978843 | + | 0.204611i | \(0.934407\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3261.80 | 1.75789 | 0.878945 | − | 0.476923i | \(-0.158248\pi\) | ||||
0.878945 | + | 0.476923i | \(0.158248\pi\) | |||||||
\(152\) | − 63.5290i | − 0.0339005i | ||||||||
\(153\) | − 507.088i | − 0.267945i | ||||||||
\(154\) | −826.412 | −0.432430 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −451.852 | −0.231905 | ||||||||
\(157\) | − 2878.46i | − 1.46322i | −0.681723 | − | 0.731611i | \(-0.738769\pi\) | ||||
0.681723 | − | 0.731611i | \(-0.261231\pi\) | |||||||
\(158\) | 804.865i | 0.405263i | ||||||||
\(159\) | 782.942 | 0.390512 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −617.166 | −0.302108 | ||||||||
\(162\) | − 148.103i | − 0.0718274i | ||||||||
\(163\) | − 927.537i | − 0.445708i | −0.974852 | − | 0.222854i | \(-0.928463\pi\) | ||||
0.974852 | − | 0.222854i | \(-0.0715373\pi\) | |||||||
\(164\) | −820.883 | −0.390855 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −99.4886 | −0.0465169 | ||||||||
\(167\) | − 1094.52i | − 0.507164i | −0.967314 | − | 0.253582i | \(-0.918391\pi\) | ||||
0.967314 | − | 0.253582i | \(-0.0816087\pi\) | |||||||
\(168\) | − 485.985i | − 0.223182i | ||||||||
\(169\) | 1150.92 | 0.523860 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.7065 | −0.0110488 | ||||||||
\(172\) | − 2064.67i | − 0.915290i | ||||||||
\(173\) | − 1713.25i | − 0.752926i | −0.926432 | − | 0.376463i | \(-0.877140\pi\) | ||||
0.926432 | − | 0.376463i | \(-0.122860\pi\) | |||||||
\(174\) | 1353.41 | 0.589666 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 326.644 | 0.139896 | ||||||||
\(177\) | 1887.00i | 0.801330i | ||||||||
\(178\) | − 1862.77i | − 0.784386i | ||||||||
\(179\) | 4065.58 | 1.69763 | 0.848816 | − | 0.528689i | \(-0.177316\pi\) | ||||
0.848816 | + | 0.528689i | \(0.177316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2791.40 | −1.14631 | −0.573157 | − | 0.819445i | \(-0.694282\pi\) | ||||
−0.573157 | + | 0.819445i | \(0.694282\pi\) | |||||||
\(182\) | − 413.960i | − 0.168597i | ||||||||
\(183\) | 345.618i | 0.139611i | ||||||||
\(184\) | 2040.36 | 0.817486 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 608.382 | 0.239832 | ||||||||
\(187\) | − 3637.99i | − 1.42266i | ||||||||
\(188\) | 1607.57i | 0.623640i | ||||||||
\(189\) | −189.000 | −0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −634.185 | −0.240251 | −0.120126 | − | 0.992759i | \(-0.538330\pi\) | ||||
−0.120126 | + | 0.992759i | \(0.538330\pi\) | |||||||
\(192\) | 1086.20i | 0.408281i | ||||||||
\(193\) | − 254.999i | − 0.0951049i | −0.998869 | − | 0.0475524i | \(-0.984858\pi\) | ||||
0.998869 | − | 0.0475524i | \(-0.0151421\pi\) | |||||||
\(194\) | 1323.98 | 0.489980 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −228.186 | −0.0831581 | ||||||||
\(197\) | − 4172.37i | − 1.50898i | −0.656311 | − | 0.754490i | \(-0.727884\pi\) | ||||
0.656311 | − | 0.754490i | \(-0.272116\pi\) | |||||||
\(198\) | − 1062.53i | − 0.381367i | ||||||||
\(199\) | 4626.48 | 1.64805 | 0.824026 | − | 0.566552i | \(-0.191723\pi\) | ||||
0.824026 | + | 0.566552i | \(0.191723\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2854.44 | 1.00168 | ||||||||
\(202\) | − 491.344i | − 0.171143i | ||||||||
\(203\) | − 1727.15i | − 0.597152i | ||||||||
\(204\) | 787.145 | 0.270153 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3365.45 | −1.13826 | ||||||||
\(207\) | − 793.499i | − 0.266435i | ||||||||
\(208\) | 163.620i | 0.0545433i | ||||||||
\(209\) | −177.251 | −0.0586638 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1562.64 | −0.509843 | −0.254921 | − | 0.966962i | \(-0.582050\pi\) | ||||
−0.254921 | + | 0.966962i | \(0.582050\pi\) | |||||||
\(212\) | 1215.35i | 0.393729i | ||||||||
\(213\) | − 1068.79i | − 0.343814i | ||||||||
\(214\) | 444.466 | 0.141977 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 624.838 | 0.196828 | ||||||||
\(217\) | − 776.382i | − 0.242877i | ||||||||
\(218\) | − 740.834i | − 0.230163i | ||||||||
\(219\) | −1970.26 | −0.607935 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1822.31 | 0.554670 | ||||||||
\(222\) | 661.943i | 0.200120i | ||||||||
\(223\) | − 1236.39i | − 0.371278i | −0.982618 | − | 0.185639i | \(-0.940564\pi\) | ||||
0.982618 | − | 0.185639i | \(-0.0594355\pi\) | |||||||
\(224\) | 1231.21 | 0.367249 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −51.5189 | −0.0151637 | ||||||||
\(227\) | − 4181.82i | − 1.22272i | −0.791353 | − | 0.611359i | \(-0.790623\pi\) | ||||
0.791353 | − | 0.611359i | \(-0.209377\pi\) | |||||||
\(228\) | − 38.3515i | − 0.0111399i | ||||||||
\(229\) | 484.774 | 0.139890 | 0.0699449 | − | 0.997551i | \(-0.477718\pi\) | ||||
0.0699449 | + | 0.997551i | \(0.477718\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1355.94 | −0.386209 | ||||||||
\(232\) | 5709.98i | 1.61585i | ||||||||
\(233\) | 2080.54i | 0.584982i | 0.956268 | + | 0.292491i | \(0.0944842\pi\) | ||||
−0.956268 | + | 0.292491i | \(0.905516\pi\) | |||||||
\(234\) | 532.234 | 0.148689 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2929.16 | −0.807932 | ||||||||
\(237\) | 1320.59i | 0.361946i | ||||||||
\(238\) | 721.135i | 0.196404i | ||||||||
\(239\) | −6814.10 | −1.84422 | −0.922108 | − | 0.386933i | \(-0.873534\pi\) | ||||
−0.922108 | + | 0.386933i | \(0.873534\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3921.84 | −1.04825 | −0.524125 | − | 0.851642i | \(-0.675607\pi\) | ||||
−0.524125 | + | 0.851642i | \(0.675607\pi\) | |||||||
\(242\) | − 5189.25i | − 1.37842i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −536.498 | −0.140761 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 966.913 | 0.250602 | ||||||||
\(247\) | − 88.7873i | − 0.0228721i | ||||||||
\(248\) | 2566.73i | 0.657209i | ||||||||
\(249\) | −163.236 | −0.0415449 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5219.10 | −1.31246 | −0.656228 | − | 0.754562i | \(-0.727849\pi\) | ||||
−0.656228 | + | 0.754562i | \(0.727849\pi\) | |||||||
\(252\) | − 293.382i | − 0.0733386i | ||||||||
\(253\) | − 5692.78i | − 1.41463i | ||||||||
\(254\) | 5011.53 | 1.23800 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4258.88 | −1.03976 | ||||||||
\(257\) | − 6975.71i | − 1.69312i | −0.532289 | − | 0.846562i | \(-0.678668\pi\) | ||||
0.532289 | − | 0.846562i | \(-0.321332\pi\) | |||||||
\(258\) | 2431.97i | 0.586852i | ||||||||
\(259\) | 844.733 | 0.202661 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2220.62 | 0.526639 | ||||||||
\(262\) | 3349.75i | 0.789878i | ||||||||
\(263\) | − 3607.36i | − 0.845776i | −0.906182 | − | 0.422888i | \(-0.861016\pi\) | ||||
0.906182 | − | 0.422888i | \(-0.138984\pi\) | |||||||
\(264\) | 4482.76 | 1.04506 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 35.1354 | 0.00809882 | ||||||||
\(267\) | − 3056.35i | − 0.700546i | ||||||||
\(268\) | 4430.90i | 1.00993i | ||||||||
\(269\) | −5.88572 | −0.00133405 | −0.000667023 | − | 1.00000i | \(-0.500212\pi\) | ||||
−0.000667023 | 1.00000i | \(0.500212\pi\) | ||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6916.32 | 1.55032 | 0.775160 | − | 0.631765i | \(-0.217669\pi\) | ||||
0.775160 | + | 0.631765i | \(0.217669\pi\) | |||||||
\(272\) | − 285.033i | − 0.0635392i | ||||||||
\(273\) | − 679.206i | − 0.150577i | ||||||||
\(274\) | −699.825 | −0.154299 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1231.74 | 0.268630 | ||||||||
\(277\) | 2119.46i | 0.459733i | 0.973222 | + | 0.229867i | \(0.0738290\pi\) | ||||
−0.973222 | + | 0.229867i | \(0.926171\pi\) | |||||||
\(278\) | 5583.29i | 1.20455i | ||||||||
\(279\) | 998.205 | 0.214197 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −239.917 | −0.0509334 | −0.0254667 | − | 0.999676i | \(-0.508107\pi\) | ||||
−0.0254667 | + | 0.999676i | \(0.508107\pi\) | |||||||
\(282\) | − 1893.55i | − 0.399856i | ||||||||
\(283\) | − 4542.12i | − 0.954067i | −0.878885 | − | 0.477034i | \(-0.841712\pi\) | ||||
0.878885 | − | 0.477034i | \(-0.158288\pi\) | |||||||
\(284\) | 1659.07 | 0.346647 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3818.40 | 0.789463 | ||||||||
\(287\) | − 1233.92i | − 0.253784i | ||||||||
\(288\) | 1582.99i | 0.323883i | ||||||||
\(289\) | 1738.45 | 0.353847 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2172.32 | 0.437608 | ||||||||
\(292\) | − 3058.41i | − 0.612944i | ||||||||
\(293\) | − 2171.70i | − 0.433010i | −0.976281 | − | 0.216505i | \(-0.930534\pi\) | ||||
0.976281 | − | 0.216505i | \(-0.0694658\pi\) | |||||||
\(294\) | 268.779 | 0.0533180 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2792.70 | −0.548387 | ||||||||
\(297\) | − 1743.35i | − 0.340604i | ||||||||
\(298\) | 6510.29i | 1.26554i | ||||||||
\(299\) | 2851.58 | 0.551543 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3103.54 | 0.594302 | ||||||||
\(302\) | − 5963.96i | − 1.13638i | ||||||||
\(303\) | − 806.175i | − 0.152850i | ||||||||
\(304\) | −13.8875 | −0.00262007 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −927.174 | −0.173212 | ||||||||
\(307\) | 3508.64i | 0.652276i | 0.945322 | + | 0.326138i | \(0.105747\pi\) | ||||
−0.945322 | + | 0.326138i | \(0.894253\pi\) | |||||||
\(308\) | − 2104.80i | − 0.389391i | ||||||||
\(309\) | −5521.88 | −1.01660 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3133.25 | −0.571287 | −0.285643 | − | 0.958336i | \(-0.592207\pi\) | ||||
−0.285643 | + | 0.958336i | \(0.592207\pi\) | |||||||
\(312\) | 2245.47i | 0.407451i | ||||||||
\(313\) | 6389.59i | 1.15387i | 0.816790 | + | 0.576935i | \(0.195751\pi\) | ||||
−0.816790 | + | 0.576935i | \(0.804249\pi\) | |||||||
\(314\) | −5263.05 | −0.945895 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2049.92 | −0.364928 | ||||||||
\(317\) | − 1634.44i | − 0.289587i | −0.989462 | − | 0.144794i | \(-0.953748\pi\) | ||||
0.989462 | − | 0.144794i | \(-0.0462518\pi\) | |||||||
\(318\) | − 1431.55i | − 0.252445i | ||||||||
\(319\) | 15931.3 | 2.79618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 729.260 | 0.126802 | ||||||||
\(322\) | 1128.44i | 0.195297i | ||||||||
\(323\) | 154.671i | 0.0266444i | ||||||||
\(324\) | 377.205 | 0.0646785 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1695.93 | −0.288126 | ||||||||
\(327\) | − 1215.53i | − 0.205562i | ||||||||
\(328\) | 4079.36i | 0.686723i | ||||||||
\(329\) | −2416.44 | −0.404932 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4386.17 | 0.728355 | 0.364177 | − | 0.931330i | \(-0.381350\pi\) | ||||
0.364177 | + | 0.931330i | \(0.381350\pi\) | |||||||
\(332\) | − 253.389i | − 0.0418872i | ||||||||
\(333\) | 1086.09i | 0.178730i | ||||||||
\(334\) | −2001.25 | −0.327854 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −106.236 | −0.0172490 | ||||||||
\(337\) | − 1713.98i | − 0.277051i | −0.990359 | − | 0.138526i | \(-0.955764\pi\) | ||||
0.990359 | − | 0.138526i | \(-0.0442363\pi\) | |||||||
\(338\) | − 2104.38i | − 0.338648i | ||||||||
\(339\) | −84.5299 | −0.0135429 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7161.41 | 1.13728 | ||||||||
\(342\) | 45.1740i | 0.00714249i | ||||||||
\(343\) | − 343.000i | − 0.0539949i | ||||||||
\(344\) | −10260.4 | −1.60814 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3132.56 | −0.486727 | ||||||||
\(347\) | 1744.83i | 0.269935i | 0.990850 | + | 0.134967i | \(0.0430930\pi\) | ||||
−0.990850 | + | 0.134967i | \(0.956907\pi\) | |||||||
\(348\) | 3447.03i | 0.530977i | ||||||||
\(349\) | −7046.78 | −1.08082 | −0.540409 | − | 0.841403i | \(-0.681730\pi\) | ||||
−0.540409 | + | 0.841403i | \(0.681730\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 873.265 | 0.132796 | ||||||||
\(352\) | 11356.8i | 1.71966i | ||||||||
\(353\) | − 12668.5i | − 1.91013i | −0.296400 | − | 0.955064i | \(-0.595786\pi\) | ||||
0.296400 | − | 0.955064i | \(-0.404214\pi\) | |||||||
\(354\) | 3450.24 | 0.518017 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 4744.33 | 0.706317 | ||||||||
\(357\) | 1183.21i | 0.175411i | ||||||||
\(358\) | − 7433.62i | − 1.09743i | ||||||||
\(359\) | −37.7844 | −0.00555483 | −0.00277742 | − | 0.999996i | \(-0.500884\pi\) | ||||
−0.00277742 | + | 0.999996i | \(0.500884\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6851.46 | −0.998901 | ||||||||
\(362\) | 5103.87i | 0.741031i | ||||||||
\(363\) | − 8514.29i | − 1.23109i | ||||||||
\(364\) | 1054.32 | 0.151817 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 631.938 | 0.0902511 | ||||||||
\(367\) | 759.829i | 0.108073i | 0.998539 | + | 0.0540364i | \(0.0172087\pi\) | ||||
−0.998539 | + | 0.0540364i | \(0.982791\pi\) | |||||||
\(368\) | − 446.023i | − 0.0631809i | ||||||||
\(369\) | 1586.47 | 0.223816 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1826.86 | −0.255650 | ||||||||
\(372\) | 1549.50i | 0.215962i | ||||||||
\(373\) | 719.320i | 0.0998525i | 0.998753 | + | 0.0499263i | \(0.0158986\pi\) | ||||
−0.998753 | + | 0.0499263i | \(0.984101\pi\) | |||||||
\(374\) | −6651.81 | −0.919671 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7988.81 | 1.09572 | ||||||||
\(377\) | 7980.19i | 1.09019i | ||||||||
\(378\) | 345.573i | 0.0470221i | ||||||||
\(379\) | −572.559 | −0.0775999 | −0.0388000 | − | 0.999247i | \(-0.512354\pi\) | ||||
−0.0388000 | + | 0.999247i | \(0.512354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8222.69 | 1.10567 | ||||||||
\(382\) | 1159.56i | 0.155310i | ||||||||
\(383\) | 4513.18i | 0.602122i | 0.953605 | + | 0.301061i | \(0.0973408\pi\) | ||||
−0.953605 | + | 0.301061i | \(0.902659\pi\) | |||||||
\(384\) | −2235.25 | −0.297050 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −466.247 | −0.0614802 | ||||||||
\(387\) | 3990.26i | 0.524125i | ||||||||
\(388\) | 3372.06i | 0.441213i | ||||||||
\(389\) | 6902.13 | 0.899619 | 0.449810 | − | 0.893124i | \(-0.351492\pi\) | ||||
0.449810 | + | 0.893124i | \(0.351492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4967.58 | −0.642510 | ||||||||
\(392\) | 1133.96i | 0.146107i | ||||||||
\(393\) | 5496.11i | 0.705451i | ||||||||
\(394\) | −7628.88 | −0.975475 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2706.18 | 0.343410 | ||||||||
\(397\) | − 4124.58i | − 0.521427i | −0.965416 | − | 0.260714i | \(-0.916042\pi\) | ||||
0.965416 | − | 0.260714i | \(-0.0839579\pi\) | |||||||
\(398\) | − 8459.18i | − 1.06538i | ||||||||
\(399\) | 57.6485 | 0.00723317 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1002.50 | −0.124844 | −0.0624219 | − | 0.998050i | \(-0.519882\pi\) | ||||
−0.0624219 | + | 0.998050i | \(0.519882\pi\) | |||||||
\(402\) | − 5219.14i | − 0.647530i | ||||||||
\(403\) | 3587.23i | 0.443406i | ||||||||
\(404\) | 1251.41 | 0.154109 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3157.96 | −0.386027 | ||||||||
\(407\) | 7791.89i | 0.948967i | ||||||||
\(408\) | − 3911.70i | − 0.474652i | ||||||||
\(409\) | −10335.0 | −1.24947 | −0.624736 | − | 0.780836i | \(-0.714794\pi\) | ||||
−0.624736 | + | 0.780836i | \(0.714794\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1148.24 | −0.137807 | ||||||||
\(412\) | − 8571.53i | − 1.02497i | ||||||||
\(413\) | − 4402.99i | − 0.524594i | ||||||||
\(414\) | −1450.85 | −0.172236 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5688.75 | −0.670466 | ||||||||
\(417\) | 9160.81i | 1.07580i | ||||||||
\(418\) | 324.091i | 0.0379230i | ||||||||
\(419\) | −3183.21 | −0.371145 | −0.185573 | − | 0.982631i | \(-0.559414\pi\) | ||||
−0.185573 | + | 0.982631i | \(0.559414\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6944.34 | −0.803911 | −0.401956 | − | 0.915659i | \(-0.631669\pi\) | ||||
−0.401956 | + | 0.915659i | \(0.631669\pi\) | |||||||
\(422\) | 2857.18i | 0.329586i | ||||||||
\(423\) | − 3106.85i | − 0.357117i | ||||||||
\(424\) | 6039.65 | 0.691772 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1954.21 | −0.222258 | ||||||||
\(427\) | − 806.442i | − 0.0913969i | ||||||||
\(428\) | 1132.02i | 0.127846i | ||||||||
\(429\) | 6265.05 | 0.705080 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3868.41 | 0.432331 | 0.216166 | − | 0.976357i | \(-0.430645\pi\) | ||||
0.216166 | + | 0.976357i | \(0.430645\pi\) | |||||||
\(432\) | − 136.590i | − 0.0152122i | ||||||||
\(433\) | − 6132.96i | − 0.680673i | −0.940304 | − | 0.340336i | \(-0.889459\pi\) | ||||
0.940304 | − | 0.340336i | \(-0.110541\pi\) | |||||||
\(434\) | −1419.56 | −0.157007 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1886.84 | 0.207256 | ||||||||
\(437\) | 242.032i | 0.0264942i | ||||||||
\(438\) | 3602.48i | 0.392998i | ||||||||
\(439\) | 4090.14 | 0.444673 | 0.222337 | − | 0.974970i | \(-0.428632\pi\) | ||||
0.222337 | + | 0.974970i | \(0.428632\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | − 3331.97i | − 0.358565i | ||||||||
\(443\) | 12434.5i | 1.33359i | 0.745241 | + | 0.666795i | \(0.232334\pi\) | ||||
−0.745241 | + | 0.666795i | \(0.767666\pi\) | |||||||
\(444\) | −1685.91 | −0.180203 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2260.66 | −0.240012 | ||||||||
\(447\) | 10681.8i | 1.13027i | ||||||||
\(448\) | − 2534.48i | − 0.267283i | ||||||||
\(449\) | −883.046 | −0.0928141 | −0.0464071 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464071 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11381.8 | 1.18835 | ||||||||
\(452\) | − 131.214i | − 0.0136544i | ||||||||
\(453\) | − 9785.40i | − 1.01492i | ||||||||
\(454\) | −7646.15 | −0.790422 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −190.587 | −0.0195725 | ||||||||
\(457\) | 9068.44i | 0.928235i | 0.885774 | + | 0.464118i | \(0.153629\pi\) | ||||
−0.885774 | + | 0.464118i | \(0.846371\pi\) | |||||||
\(458\) | − 886.373i | − 0.0904312i | ||||||||
\(459\) | −1521.26 | −0.154698 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12508.9 | 1.26377 | 0.631885 | − | 0.775063i | \(-0.282282\pi\) | ||||
0.631885 | + | 0.775063i | \(0.282282\pi\) | |||||||
\(462\) | 2479.24i | 0.249663i | ||||||||
\(463\) | 12688.7i | 1.27363i | 0.771015 | + | 0.636817i | \(0.219749\pi\) | ||||
−0.771015 | + | 0.636817i | \(0.780251\pi\) | |||||||
\(464\) | 1248.20 | 0.124884 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3804.12 | 0.378160 | ||||||||
\(467\) | 10136.5i | 1.00442i | 0.864747 | + | 0.502208i | \(0.167479\pi\) | ||||
−0.864747 | + | 0.502208i | \(0.832521\pi\) | |||||||
\(468\) | 1355.56i | 0.133890i | ||||||||
\(469\) | −6660.36 | −0.655750 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −8635.37 | −0.844791 | ||||||||
\(472\) | 14556.4i | 1.41952i | ||||||||
\(473\) | 28627.3i | 2.78284i | ||||||||
\(474\) | 2414.59 | 0.233979 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1836.67 | −0.176857 | ||||||||
\(477\) | − 2348.83i | − 0.225462i | ||||||||
\(478\) | 12459.1i | 1.19219i | ||||||||
\(479\) | 11361.1 | 1.08372 | 0.541861 | − | 0.840468i | \(-0.317720\pi\) | ||||
0.541861 | + | 0.840468i | \(0.317720\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3903.05 | −0.369987 | ||||||||
\(482\) | 7170.80i | 0.677637i | ||||||||
\(483\) | 1851.50i | 0.174422i | ||||||||
\(484\) | 13216.6 | 1.24123 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −444.308 | −0.0414696 | ||||||||
\(487\) | − 7929.53i | − 0.737826i | −0.929464 | − | 0.368913i | \(-0.879730\pi\) | ||||
0.929464 | − | 0.368913i | \(-0.120270\pi\) | |||||||
\(488\) | 2666.11i | 0.247314i | ||||||||
\(489\) | −2782.61 | −0.257329 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8111.51 | 0.745555 | 0.372777 | − | 0.927921i | \(-0.378405\pi\) | ||||
0.372777 | + | 0.927921i | \(0.378405\pi\) | |||||||
\(492\) | 2462.65i | 0.225660i | ||||||||
\(493\) | − 13901.8i | − 1.26999i | ||||||||
\(494\) | −162.341 | −0.0147856 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 561.088 | 0.0507936 | ||||||||
\(497\) | 2493.85i | 0.225079i | ||||||||
\(498\) | 298.466i | 0.0268566i | ||||||||
\(499\) | −16816.6 | −1.50865 | −0.754324 | − | 0.656502i | \(-0.772035\pi\) | ||||
−0.754324 | + | 0.656502i | \(0.772035\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3283.55 | −0.292811 | ||||||||
\(502\) | 9542.74i | 0.848433i | ||||||||
\(503\) | − 17764.6i | − 1.57472i | −0.616491 | − | 0.787362i | \(-0.711446\pi\) | ||||
0.616491 | − | 0.787362i | \(-0.288554\pi\) | |||||||
\(504\) | −1457.95 | −0.128854 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −10408.8 | −0.914485 | ||||||||
\(507\) | − 3452.76i | − 0.302451i | ||||||||
\(508\) | 12764.0i | 1.11478i | ||||||||
\(509\) | −13908.8 | −1.21120 | −0.605598 | − | 0.795771i | \(-0.707066\pi\) | ||||
−0.605598 | + | 0.795771i | \(0.707066\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4597.27 | 0.397987 | ||||||||
\(512\) | 1826.38i | 0.157647i | ||||||||
\(513\) | 74.1195i | 0.00637905i | ||||||||
\(514\) | −12754.6 | −1.09451 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −6194.02 | −0.528443 | ||||||||
\(517\) | − 22289.5i | − 1.89611i | ||||||||
\(518\) | − 1544.53i | − 0.131009i | ||||||||
\(519\) | −5139.76 | −0.434702 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8639.68 | −0.726510 | −0.363255 | − | 0.931690i | \(-0.618335\pi\) | ||||
−0.363255 | + | 0.931690i | \(0.618335\pi\) | |||||||
\(522\) | − 4060.23i | − 0.340444i | ||||||||
\(523\) | 23242.2i | 1.94323i | 0.236561 | + | 0.971617i | \(0.423980\pi\) | ||||
−0.236561 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(524\) | −8531.53 | −0.711263 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6595.79 | −0.546749 | ||||||||
\(527\) | − 6249.11i | − 0.516538i | ||||||||
\(528\) | − 979.932i | − 0.0807691i | ||||||||
\(529\) | 4393.66 | 0.361113 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5660.99 | 0.462648 | ||||||||
\(532\) | 89.4869i | 0.00729276i | ||||||||
\(533\) | 5701.26i | 0.463319i | ||||||||
\(534\) | −5588.32 | −0.452865 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 22019.3 | 1.77442 | ||||||||
\(537\) | − 12196.8i | − 0.980128i | ||||||||
\(538\) | 10.7616i | 0 0.000862390i | ||||||||
\(539\) | 3163.86 | 0.252833 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11395.2 | 0.905577 | 0.452789 | − | 0.891618i | \(-0.350429\pi\) | ||||
0.452789 | + | 0.891618i | \(0.350429\pi\) | |||||||
\(542\) | − 12646.0i | − 1.00220i | ||||||||
\(543\) | 8374.19i | 0.661825i | ||||||||
\(544\) | 9910.04 | 0.781047 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1241.88 | −0.0973398 | ||||||||
\(547\) | 7870.21i | 0.615184i | 0.951518 | + | 0.307592i | \(0.0995232\pi\) | ||||
−0.951518 | + | 0.307592i | \(0.900477\pi\) | |||||||
\(548\) | − 1782.40i | − 0.138942i | ||||||||
\(549\) | 1036.85 | 0.0806045 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −677.329 | −0.0523687 | ||||||||
\(552\) | − 6121.08i | − 0.471976i | ||||||||
\(553\) | − 3081.37i | − 0.236949i | ||||||||
\(554\) | 3875.28 | 0.297193 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −14220.2 | −1.08466 | ||||||||
\(557\) | − 17769.8i | − 1.35176i | −0.737012 | − | 0.675880i | \(-0.763764\pi\) | ||||
0.737012 | − | 0.675880i | \(-0.236236\pi\) | |||||||
\(558\) | − 1825.15i | − 0.138467i | ||||||||
\(559\) | −14339.7 | −1.08498 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10914.0 | −0.821370 | ||||||||
\(562\) | 438.672i | 0.0329257i | ||||||||
\(563\) | 15192.8i | 1.13730i | 0.822579 | + | 0.568651i | \(0.192534\pi\) | ||||
−0.822579 | + | 0.568651i | \(0.807466\pi\) | |||||||
\(564\) | 4822.72 | 0.360059 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −8304.93 | −0.616753 | ||||||||
\(567\) | 567.000i | 0.0419961i | ||||||||
\(568\) | − 8244.71i | − 0.609050i | ||||||||
\(569\) | 23300.0 | 1.71667 | 0.858335 | − | 0.513090i | \(-0.171499\pi\) | ||||
0.858335 | + | 0.513090i | \(0.171499\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10638.2 | 0.779673 | 0.389837 | − | 0.920884i | \(-0.372531\pi\) | ||||
0.389837 | + | 0.920884i | \(0.372531\pi\) | |||||||
\(572\) | 9725.14i | 0.710889i | ||||||||
\(573\) | 1902.55i | 0.138709i | ||||||||
\(574\) | −2256.13 | −0.164058 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3258.61 | 0.235721 | ||||||||
\(577\) | 897.258i | 0.0647372i | 0.999476 | + | 0.0323686i | \(0.0103050\pi\) | ||||
−0.999476 | + | 0.0323686i | \(0.989695\pi\) | |||||||
\(578\) | − 3178.63i | − 0.228743i | ||||||||
\(579\) | −764.997 | −0.0549088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 380.885 | 0.0271975 | ||||||||
\(582\) | − 3971.93i | − 0.282890i | ||||||||
\(583\) | − 16851.1i | − 1.19709i | ||||||||
\(584\) | −15198.7 | −1.07693 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −3970.79 | −0.279918 | ||||||||
\(587\) | 14712.9i | 1.03452i | 0.855828 | + | 0.517261i | \(0.173048\pi\) | ||||
−0.855828 | + | 0.517261i | \(0.826952\pi\) | |||||||
\(588\) | 684.558i | 0.0480114i | ||||||||
\(589\) | −304.471 | −0.0212997 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12517.1 | −0.871210 | ||||||||
\(592\) | 610.486i | 0.0423831i | ||||||||
\(593\) | − 7216.29i | − 0.499726i | −0.968281 | − | 0.249863i | \(-0.919614\pi\) | ||||
0.968281 | − | 0.249863i | \(-0.0803856\pi\) | |||||||
\(594\) | −3187.59 | −0.220182 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −16581.2 | −1.13958 | ||||||||
\(597\) | − 13879.4i | − 0.951503i | ||||||||
\(598\) | − 5213.91i | − 0.356543i | ||||||||
\(599\) | 20885.5 | 1.42464 | 0.712320 | − | 0.701855i | \(-0.247645\pi\) | ||||
0.712320 | + | 0.701855i | \(0.247645\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11047.7 | −0.749823 | −0.374911 | − | 0.927061i | \(-0.622327\pi\) | ||||
−0.374911 | + | 0.927061i | \(0.622327\pi\) | |||||||
\(602\) | − 5674.59i | − 0.384185i | ||||||||
\(603\) | − 8563.32i | − 0.578317i | ||||||||
\(604\) | 15189.7 | 1.02328 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1474.03 | −0.0988093 | ||||||||
\(607\) | 9434.94i | 0.630894i | 0.948943 | + | 0.315447i | \(0.102154\pi\) | ||||
−0.948943 | + | 0.315447i | \(0.897846\pi\) | |||||||
\(608\) | − 482.840i | − 0.0322068i | ||||||||
\(609\) | −5181.44 | −0.344766 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11165.0 | 0.739263 | ||||||||
\(612\) | − 2361.44i | − 0.155973i | ||||||||
\(613\) | − 17662.6i | − 1.16376i | −0.813274 | − | 0.581881i | \(-0.802317\pi\) | ||||
0.813274 | − | 0.581881i | \(-0.197683\pi\) | |||||||
\(614\) | 6415.30 | 0.421662 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10459.8 | −0.684150 | ||||||||
\(617\) | 10817.4i | 0.705820i | 0.935657 | + | 0.352910i | \(0.114808\pi\) | ||||
−0.935657 | + | 0.352910i | \(0.885192\pi\) | |||||||
\(618\) | 10096.3i | 0.657176i | ||||||||
\(619\) | −29073.9 | −1.88785 | −0.943926 | − | 0.330158i | \(-0.892898\pi\) | ||||
−0.943926 | + | 0.330158i | \(0.892898\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2380.50 | −0.153826 | ||||||||
\(622\) | 5728.92i | 0.369306i | ||||||||
\(623\) | 7131.49i | 0.458615i | ||||||||
\(624\) | 490.860 | 0.0314906 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 11682.9 | 0.745915 | ||||||||
\(627\) | 531.754i | 0.0338696i | ||||||||
\(628\) | − 13404.5i | − 0.851751i | ||||||||
\(629\) | 6799.28 | 0.431009 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2203.17 | −0.138996 | −0.0694981 | − | 0.997582i | \(-0.522140\pi\) | ||||
−0.0694981 | + | 0.997582i | \(0.522140\pi\) | |||||||
\(632\) | 10187.1i | 0.641170i | ||||||||
\(633\) | 4687.93i | 0.294358i | ||||||||
\(634\) | −2988.45 | −0.187203 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3646.05 | 0.227319 | ||||||||
\(637\) | 1584.81i | 0.0985755i | ||||||||
\(638\) | − 29129.3i | − 1.80758i | ||||||||
\(639\) | −3206.38 | −0.198501 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 22466.5 | 1.38436 | 0.692180 | − | 0.721725i | \(-0.256651\pi\) | ||||
0.692180 | + | 0.721725i | \(0.256651\pi\) | |||||||
\(642\) | − 1333.40i | − 0.0819705i | ||||||||
\(643\) | − 12347.0i | − 0.757257i | −0.925549 | − | 0.378629i | \(-0.876396\pi\) | ||||
0.925549 | − | 0.378629i | \(-0.123604\pi\) | |||||||
\(644\) | −2874.05 | −0.175859 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 282.805 | 0.0172242 | ||||||||
\(647\) | 24114.0i | 1.46525i | 0.680631 | + | 0.732626i | \(0.261706\pi\) | ||||
−0.680631 | + | 0.732626i | \(0.738294\pi\) | |||||||
\(648\) | − 1874.51i | − 0.113639i | ||||||||
\(649\) | 40613.6 | 2.45643 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2329.15 | −0.140225 | ||||||||
\(652\) | − 4319.41i | − 0.259449i | ||||||||
\(653\) | 7843.33i | 0.470035i | 0.971991 | + | 0.235018i | \(0.0755148\pi\) | ||||
−0.971991 | + | 0.235018i | \(0.924485\pi\) | |||||||
\(654\) | −2222.50 | −0.132885 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 891.749 | 0.0530746 | ||||||||
\(657\) | 5910.78i | 0.350992i | ||||||||
\(658\) | 4418.29i | 0.261767i | ||||||||
\(659\) | −21242.8 | −1.25569 | −0.627846 | − | 0.778338i | \(-0.716063\pi\) | ||||
−0.627846 | + | 0.778338i | \(0.716063\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22221.7 | −1.30760 | −0.653801 | − | 0.756667i | \(-0.726827\pi\) | ||||
−0.653801 | + | 0.756667i | \(0.726827\pi\) | |||||||
\(662\) | − 8019.79i | − 0.470843i | ||||||||
\(663\) | − 5466.94i | − 0.320239i | ||||||||
\(664\) | −1259.21 | −0.0735948 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1985.83 | 0.115539 | ||||||||
\(667\) | − 21753.8i | − 1.26283i | ||||||||
\(668\) | − 5097.01i | − 0.295223i | ||||||||
\(669\) | −3709.18 | −0.214358 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7438.69 | 0.427969 | ||||||||
\(672\) | − 3693.63i | − 0.212031i | ||||||||
\(673\) | − 3787.85i | − 0.216955i | −0.994099 | − | 0.108478i | \(-0.965402\pi\) | ||||
0.994099 | − | 0.108478i | \(-0.0345976\pi\) | |||||||
\(674\) | −3133.88 | −0.179099 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5359.67 | 0.304943 | ||||||||
\(677\) | 11296.8i | 0.641314i | 0.947195 | + | 0.320657i | \(0.103904\pi\) | ||||
−0.947195 | + | 0.320657i | \(0.896096\pi\) | |||||||
\(678\) | 154.557i | 0.00875474i | ||||||||
\(679\) | −5068.75 | −0.286481 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12545.5 | −0.705937 | ||||||||
\(682\) | − 13094.1i | − 0.735190i | ||||||||
\(683\) | 4807.14i | 0.269312i | 0.990892 | + | 0.134656i | \(0.0429929\pi\) | ||||
−0.990892 | + | 0.134656i | \(0.957007\pi\) | |||||||
\(684\) | −115.055 | −0.00643161 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −627.151 | −0.0349048 | ||||||||
\(687\) | − 1454.32i | − 0.0807654i | ||||||||
\(688\) | 2242.92i | 0.124288i | ||||||||
\(689\) | 8440.94 | 0.466726 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5393.47 | 0.296928 | 0.148464 | − | 0.988918i | \(-0.452567\pi\) | ||||
0.148464 | + | 0.988918i | \(0.452567\pi\) | |||||||
\(692\) | − 7978.37i | − 0.438283i | ||||||||
\(693\) | 4067.82i | 0.222978i | ||||||||
\(694\) | 3190.29 | 0.174498 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 17129.9 | 0.932914 | ||||||||
\(697\) | − 9931.84i | − 0.539735i | ||||||||
\(698\) | 12884.5i | 0.698691i | ||||||||
\(699\) | 6241.63 | 0.337740 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2404.77 | 0.129568 | 0.0647838 | − | 0.997899i | \(-0.479364\pi\) | ||||
0.0647838 | + | 0.997899i | \(0.479364\pi\) | |||||||
\(702\) | − 1596.70i | − 0.0858456i | ||||||||
\(703\) | − 331.276i | − 0.0177729i | ||||||||
\(704\) | 23378.2 | 1.25156 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23163.4 | −1.23480 | ||||||||
\(707\) | 1881.07i | 0.100064i | ||||||||
\(708\) | 8787.47i | 0.466460i | ||||||||
\(709\) | 21617.3 | 1.14507 | 0.572535 | − | 0.819881i | \(-0.305960\pi\) | ||||
0.572535 | + | 0.819881i | \(0.305960\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3961.76 | 0.208970 | ||||||||
\(712\) | − 23576.8i | − 1.24098i | ||||||||
\(713\) | − 9778.70i | − 0.513626i | ||||||||
\(714\) | 2163.41 | 0.113394 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 18932.8 | 0.988203 | ||||||||
\(717\) | 20442.3i | 1.06476i | ||||||||
\(718\) | 69.0860i | 0.00359090i | ||||||||
\(719\) | 18228.6 | 0.945498 | 0.472749 | − | 0.881197i | \(-0.343262\pi\) | ||||
0.472749 | + | 0.881197i | \(0.343262\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12884.4 | 0.665519 | ||||||||
\(722\) | 12527.4i | 0.645736i | ||||||||
\(723\) | 11765.5i | 0.605207i | ||||||||
\(724\) | −12999.1 | −0.667278 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −15567.8 | −0.795832 | ||||||||
\(727\) | − 20196.5i | − 1.03033i | −0.857092 | − | 0.515164i | \(-0.827731\pi\) | ||||
0.857092 | − | 0.515164i | \(-0.172269\pi\) | |||||||
\(728\) | − 5239.43i | − 0.266739i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24980.4 | 1.26393 | ||||||||
\(732\) | 1609.49i | 0.0812686i | ||||||||
\(733\) | − 15264.9i | − 0.769196i | −0.923084 | − | 0.384598i | \(-0.874340\pi\) | ||||
0.923084 | − | 0.384598i | \(-0.125660\pi\) | |||||||
\(734\) | 1389.29 | 0.0698633 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 15507.4 | 0.776643 | ||||||||
\(737\) | − 61435.7i | − 3.07057i | ||||||||
\(738\) | − 2900.74i | − 0.144685i | ||||||||
\(739\) | −13906.0 | −0.692207 | −0.346103 | − | 0.938196i | \(-0.612495\pi\) | ||||
−0.346103 | + | 0.938196i | \(0.612495\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −266.362 | −0.0132052 | ||||||||
\(742\) | 3340.29i | 0.165264i | ||||||||
\(743\) | 4592.87i | 0.226778i | 0.993551 | + | 0.113389i | \(0.0361706\pi\) | ||||
−0.993551 | + | 0.113389i | \(0.963829\pi\) | |||||||
\(744\) | 7700.20 | 0.379440 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1315.22 | 0.0645493 | ||||||||
\(747\) | 489.709i | 0.0239860i | ||||||||
\(748\) | − 16941.6i | − 0.828137i | ||||||||
\(749\) | −1701.61 | −0.0830111 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8390.80 | −0.407702 | −0.203851 | − | 0.979002i | \(-0.565346\pi\) | ||||
−0.203851 | + | 0.979002i | \(0.565346\pi\) | |||||||
\(752\) | − 1746.35i | − 0.0846848i | ||||||||
\(753\) | 15657.3i | 0.757747i | ||||||||
\(754\) | 14591.2 | 0.704748 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −880.145 | −0.0423420 | ||||||||
\(757\) | 1368.89i | 0.0657240i | 0.999460 | + | 0.0328620i | \(0.0104622\pi\) | ||||
−0.999460 | + | 0.0328620i | \(0.989538\pi\) | |||||||
\(758\) | 1046.88i | 0.0501642i | ||||||||
\(759\) | −17078.4 | −0.816739 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1623.77 | −0.0773478 | −0.0386739 | − | 0.999252i | \(-0.512313\pi\) | ||||
−0.0386739 | + | 0.999252i | \(0.512313\pi\) | |||||||
\(762\) | − 15034.6i | − 0.714759i | ||||||||
\(763\) | 2836.23i | 0.134572i | ||||||||
\(764\) | −2953.31 | −0.139852 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8252.03 | 0.389240 | ||||||||
\(767\) | 20343.8i | 0.957722i | ||||||||
\(768\) | 12776.6i | 0.600308i | ||||||||
\(769\) | 26842.5 | 1.25873 | 0.629366 | − | 0.777109i | \(-0.283315\pi\) | ||||
0.629366 | + | 0.777109i | \(0.283315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20927.1 | −0.977526 | ||||||||
\(772\) | − 1187.49i | − 0.0553612i | ||||||||
\(773\) | − 20961.4i | − 0.975330i | −0.873031 | − | 0.487665i | \(-0.837849\pi\) | ||||
0.873031 | − | 0.487665i | \(-0.162151\pi\) | |||||||
\(774\) | 7295.90 | 0.338819 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 16757.4 | 0.775200 | ||||||||
\(777\) | − 2534.20i | − 0.117006i | ||||||||
\(778\) | − 12620.0i | − 0.581556i | ||||||||
\(779\) | −483.902 | −0.0222562 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23003.5 | −1.05394 | ||||||||
\(782\) | 9082.86i | 0.415348i | ||||||||
\(783\) | − 6661.85i | − 0.304055i | ||||||||
\(784\) | 247.885 | 0.0112921 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10049.2 | 0.456036 | ||||||||
\(787\) | − 35333.2i | − 1.60037i | −0.599751 | − | 0.800187i | \(-0.704734\pi\) | ||||
0.599751 | − | 0.800187i | \(-0.295266\pi\) | |||||||
\(788\) | − 19430.1i | − 0.878388i | ||||||||
\(789\) | −10822.1 | −0.488309 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 197.236 | 0.00886589 | ||||||||
\(792\) | − 13448.3i | − 0.603364i | ||||||||
\(793\) | 3726.13i | 0.166858i | ||||||||
\(794\) | −7541.49 | −0.337075 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21544.8 | 0.959342 | ||||||||
\(797\) | 8137.04i | 0.361642i | 0.983516 | + | 0.180821i | \(0.0578755\pi\) | ||||
−0.983516 | + | 0.180821i | \(0.942125\pi\) | |||||||
\(798\) | − 105.406i | − 0.00467586i | ||||||||
\(799\) | −19450.0 | −0.861191 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9169.05 | −0.404460 | ||||||||
\(802\) | 1832.99i | 0.0807049i | ||||||||
\(803\) | 42405.6i | 1.86359i | ||||||||
\(804\) | 13292.7 | 0.583082 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6558.99 | 0.286639 | ||||||||
\(807\) | 17.6572i | 0 0.000770212i | ||||||||
\(808\) | − 6218.87i | − 0.270766i | ||||||||
\(809\) | 36281.0 | 1.57673 | 0.788364 | − | 0.615209i | \(-0.210928\pi\) | ||||
0.788364 | + | 0.615209i | \(0.210928\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34237.2 | −1.48240 | −0.741202 | − | 0.671282i | \(-0.765744\pi\) | ||||
−0.741202 | + | 0.671282i | \(0.765744\pi\) | |||||||
\(812\) | − 8043.06i | − 0.347606i | ||||||||
\(813\) | − 20749.0i | − 0.895077i | ||||||||
\(814\) | 14246.9 | 0.613456 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −855.099 | −0.0366844 | ||||||||
\(817\) | − 1217.10i | − 0.0521188i | ||||||||
\(818\) | 18896.8i | 0.807717i | ||||||||
\(819\) | −2037.62 | −0.0869355 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23247.8 | −0.988250 | −0.494125 | − | 0.869391i | \(-0.664511\pi\) | ||||
−0.494125 | + | 0.869391i | \(0.664511\pi\) | |||||||
\(822\) | 2099.47i | 0.0890846i | ||||||||
\(823\) | 42934.0i | 1.81845i | 0.416306 | + | 0.909225i | \(0.363325\pi\) | ||||
−0.416306 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(824\) | −42596.0 | −1.80085 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8050.55 | −0.339122 | ||||||||
\(827\) | 781.391i | 0.0328557i | 0.999865 | + | 0.0164278i | \(0.00522938\pi\) | ||||
−0.999865 | + | 0.0164278i | \(0.994771\pi\) | |||||||
\(828\) | − 3695.21i | − 0.155093i | ||||||||
\(829\) | 33493.3 | 1.40322 | 0.701611 | − | 0.712561i | \(-0.252465\pi\) | ||||
0.701611 | + | 0.712561i | \(0.252465\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6358.39 | 0.265427 | ||||||||
\(832\) | 11710.4i | 0.487964i | ||||||||
\(833\) | − 2760.81i | − 0.114834i | ||||||||
\(834\) | 16749.9 | 0.695445 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −825.434 | −0.0341486 | ||||||||
\(837\) | − 2994.62i | − 0.123667i | ||||||||
\(838\) | 5820.27i | 0.239926i | ||||||||
\(839\) | −15155.7 | −0.623639 | −0.311819 | − | 0.950141i | \(-0.600938\pi\) | ||||
−0.311819 | + | 0.950141i | \(0.600938\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 36489.2 | 1.49613 | ||||||||
\(842\) | 12697.2i | 0.519686i | ||||||||
\(843\) | 719.752i | 0.0294064i | ||||||||
\(844\) | −7277.01 | −0.296783 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5680.66 | −0.230857 | ||||||||
\(847\) | 19866.7i | 0.805935i | ||||||||
\(848\) | − 1320.27i | − 0.0534649i | ||||||||
\(849\) | −13626.4 | −0.550831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10639.6 | 0.428579 | ||||||||
\(852\) | − 4977.21i | − 0.200137i | ||||||||
\(853\) | − 2917.48i | − 0.117107i | −0.998284 | − | 0.0585537i | \(-0.981351\pi\) | ||||
0.998284 | − | 0.0585537i | \(-0.0186489\pi\) | |||||||
\(854\) | −1474.52 | −0.0590832 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5625.54 | 0.224623 | ||||||||
\(857\) | 31560.7i | 1.25799i | 0.777411 | + | 0.628993i | \(0.216532\pi\) | ||||
−0.777411 | + | 0.628993i | \(0.783468\pi\) | |||||||
\(858\) | − 11455.2i | − 0.455797i | ||||||||
\(859\) | 1404.81 | 0.0557991 | 0.0278995 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0278995 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3701.76 | −0.146522 | ||||||||
\(862\) | − 7073.11i | − 0.279479i | ||||||||
\(863\) | − 9808.24i | − 0.386879i | −0.981112 | − | 0.193439i | \(-0.938036\pi\) | ||||
0.981112 | − | 0.193439i | \(-0.0619643\pi\) | |||||||
\(864\) | 4748.96 | 0.186994 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −11213.7 | −0.440018 | ||||||||
\(867\) | − 5215.35i | − 0.204294i | ||||||||
\(868\) | − 3615.50i | − 0.141380i | ||||||||
\(869\) | 28422.8 | 1.10952 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30773.9 | 1.19717 | ||||||||
\(872\) | − 9376.63i | − 0.364143i | ||||||||
\(873\) | − 6516.97i | − 0.252653i | ||||||||
\(874\) | 442.537 | 0.0171271 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9175.22 | −0.353883 | ||||||||
\(877\) | 7196.05i | 0.277073i | 0.990357 | + | 0.138537i | \(0.0442399\pi\) | ||||
−0.990357 | + | 0.138537i | \(0.955760\pi\) | |||||||
\(878\) | − 7478.52i | − 0.287458i | ||||||||
\(879\) | −6515.10 | −0.249999 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3183.27 | −0.121733 | −0.0608667 | − | 0.998146i | \(-0.519386\pi\) | ||||
−0.0608667 | + | 0.998146i | \(0.519386\pi\) | |||||||
\(882\) | − 806.336i | − 0.0307832i | ||||||||
\(883\) | 25392.5i | 0.967751i | 0.875137 | + | 0.483876i | \(0.160771\pi\) | ||||
−0.875137 | + | 0.483876i | \(0.839229\pi\) | |||||||
\(884\) | 8486.25 | 0.322877 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 22735.6 | 0.862095 | ||||||||
\(887\) | 30634.2i | 1.15964i | 0.814746 | + | 0.579818i | \(0.196876\pi\) | ||||
−0.814746 | + | 0.579818i | \(0.803124\pi\) | |||||||
\(888\) | 8378.11i | 0.316612i | ||||||||
\(889\) | −19186.3 | −0.723833 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5230.05 | −0.196648 | ||||||||
\(892\) | − 5757.71i | − 0.216124i | ||||||||
\(893\) | 947.648i | 0.0355116i | ||||||||
\(894\) | 19530.9 | 0.730660 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 5215.58 | 0.194465 | ||||||||
\(897\) | − 8554.75i | − 0.318433i | ||||||||
\(898\) | 1614.59i | 0.0599994i | ||||||||
\(899\) | 27365.8 | 1.01524 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14704.5 | −0.543704 | ||||||||
\(902\) | − 20810.7i | − 0.768206i | ||||||||
\(903\) | − 9310.61i | − 0.343120i | ||||||||
\(904\) | −652.067 | −0.0239905 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −17891.9 | −0.656091 | ||||||||
\(907\) | 28089.9i | 1.02834i | 0.857687 | + | 0.514172i | \(0.171901\pi\) | ||||
−0.857687 | + | 0.514172i | \(0.828099\pi\) | |||||||
\(908\) | − 19474.1i | − 0.711753i | ||||||||
\(909\) | −2418.52 | −0.0882480 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36102.7 | −1.31299 | −0.656495 | − | 0.754330i | \(-0.727962\pi\) | ||||
−0.656495 | + | 0.754330i | \(0.727962\pi\) | |||||||
\(912\) | 41.6624i | 0.00151270i | ||||||||
\(913\) | 3513.31i | 0.127353i | ||||||||
\(914\) | 16581.0 | 0.600055 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2257.52 | 0.0814308 | ||||||||
\(917\) | − 12824.3i | − 0.461826i | ||||||||
\(918\) | 2781.52i | 0.100004i | ||||||||
\(919\) | 14533.8 | 0.521682 | 0.260841 | − | 0.965382i | \(-0.416000\pi\) | ||||
0.260841 | + | 0.965382i | \(0.416000\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10525.9 | 0.376592 | ||||||||
\(922\) | − 22871.6i | − 0.816959i | ||||||||
\(923\) | − 11522.7i | − 0.410915i | ||||||||
\(924\) | −6314.41 | −0.224815 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 23200.3 | 0.823336 | ||||||||
\(927\) | 16565.6i | 0.586933i | ||||||||
\(928\) | 43397.6i | 1.53512i | ||||||||
\(929\) | −16539.6 | −0.584118 | −0.292059 | − | 0.956400i | \(-0.594340\pi\) | ||||
−0.292059 | + | 0.956400i | \(0.594340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −134.513 | −0.00473522 | ||||||||
\(932\) | 9688.79i | 0.340522i | ||||||||
\(933\) | 9399.74i | 0.329833i | ||||||||
\(934\) | 18533.9 | 0.649301 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6736.41 | 0.235242 | ||||||||
\(937\) | − 30212.3i | − 1.05335i | −0.850065 | − | 0.526677i | \(-0.823438\pi\) | ||||
0.850065 | − | 0.526677i | \(-0.176562\pi\) | |||||||
\(938\) | 12178.0i | 0.423908i | ||||||||
\(939\) | 19168.8 | 0.666187 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26414.4 | −0.915074 | −0.457537 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457537 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(942\) | 15789.1i | 0.546112i | ||||||||
\(943\) | − 15541.5i | − 0.536692i | ||||||||
\(944\) | 3182.03 | 0.109710 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 52342.9 | 1.79896 | ||||||||
\(947\) | − 10187.3i | − 0.349570i | −0.984607 | − | 0.174785i | \(-0.944077\pi\) | ||||
0.984607 | − | 0.174785i | \(-0.0559231\pi\) | |||||||
\(948\) | 6149.77i | 0.210691i | ||||||||
\(949\) | −21241.5 | −0.726583 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4903.31 | −0.167193 | ||||||||
\(952\) | 9127.31i | 0.310733i | ||||||||
\(953\) | 2211.39i | 0.0751669i | 0.999293 | + | 0.0375834i | \(0.0119660\pi\) | ||||
−0.999293 | + | 0.0375834i | \(0.988034\pi\) | |||||||
\(954\) | −4294.66 | −0.145749 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −31732.3 | −1.07353 | ||||||||
\(957\) | − 47794.0i | − 1.61438i | ||||||||
\(958\) | − 20773.0i | − 0.700569i | ||||||||
\(959\) | 2679.23 | 0.0902156 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17489.6 | −0.587077 | ||||||||
\(962\) | 7136.44i | 0.239177i | ||||||||
\(963\) | − 2187.78i | − 0.0732089i | ||||||||
\(964\) | −18263.4 | −0.610193 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3385.33 | 0.112755 | ||||||||
\(967\) | − 7955.89i | − 0.264575i | −0.991211 | − | 0.132287i | \(-0.957768\pi\) | ||||
0.991211 | − | 0.132287i | \(-0.0422322\pi\) | |||||||
\(968\) | − 65679.6i | − 2.18081i | ||||||||
\(969\) | 464.014 | 0.0153832 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 53071.2 | 1.75400 | 0.877001 | − | 0.480488i | \(-0.159541\pi\) | ||||
0.877001 | + | 0.480488i | \(0.159541\pi\) | |||||||
\(972\) | − 1131.62i | − 0.0373422i | ||||||||
\(973\) | − 21375.2i | − 0.704274i | ||||||||
\(974\) | −14498.6 | −0.476965 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 582.813 | 0.0191141 | ||||||||
\(977\) | 22448.2i | 0.735089i | 0.930006 | + | 0.367545i | \(0.119801\pi\) | ||||
−0.930006 | + | 0.367545i | \(0.880199\pi\) | |||||||
\(978\) | 5087.80i | 0.166350i | ||||||||
\(979\) | −65781.4 | −2.14748 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3646.58 | −0.118681 | ||||||||
\(982\) | − 14831.3i | − 0.481961i | ||||||||
\(983\) | 21712.8i | 0.704509i | 0.935904 | + | 0.352254i | \(0.114585\pi\) | ||||
−0.935904 | + | 0.352254i | \(0.885415\pi\) | |||||||
\(984\) | 12238.1 | 0.396479 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −25418.5 | −0.820983 | ||||||||
\(987\) | 7249.33i | 0.233788i | ||||||||
\(988\) | − 413.470i | − 0.0133140i | ||||||||
\(989\) | 39089.7 | 1.25681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −37849.2 | −1.21324 | −0.606620 | − | 0.794992i | \(-0.707475\pi\) | ||||
−0.606620 | + | 0.794992i | \(0.707475\pi\) | |||||||
\(992\) | 19508.0i | 0.624373i | ||||||||
\(993\) | − 13158.5i | − 0.420516i | ||||||||
\(994\) | 4559.82 | 0.145502 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −760.168 | −0.0241836 | ||||||||
\(997\) | 39573.1i | 1.25707i | 0.777783 | + | 0.628533i | \(0.216344\pi\) | ||||
−0.777783 | + | 0.628533i | \(0.783656\pi\) | |||||||
\(998\) | 30748.0i | 0.975261i | ||||||||
\(999\) | 3258.26 | 0.103190 |
(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 | 525.4.d.l.274.2 | 4 | ||
5.2 | odd | 4 | 105.4.a.e.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 525.4.a.l.1.1 | 2 | |||
5.4 | even | 2 | inner | 525.4.d.l.274.3 | 4 | ||
15.2 | even | 4 | 315.4.a.k.1.1 | 2 | |||
15.8 | even | 4 | 1575.4.a.q.1.2 | 2 | |||
20.7 | even | 4 | 1680.4.a.bo.1.2 | 2 | |||
35.27 | even | 4 | 735.4.a.o.1.2 | 2 | |||
105.62 | odd | 4 | 2205.4.a.bb.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.a.e.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
315.4.a.k.1.1 | 2 | 15.2 | even | 4 | |||
525.4.a.l.1.1 | 2 | 5.3 | odd | 4 | |||
525.4.d.l.274.2 | 4 | 1.1 | even | 1 | trivial | ||
525.4.d.l.274.3 | 4 | 5.4 | even | 2 | inner | ||
735.4.a.o.1.2 | 2 | 35.27 | even | 4 | |||
1575.4.a.q.1.2 | 2 | 15.8 | even | 4 | |||
1680.4.a.bo.1.2 | 2 | 20.7 | even | 4 | |||
2205.4.a.bb.1.1 | 2 | 105.62 | odd | 4 |