Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7,6,Mod(1,7)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("7.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 7.a (trivial) |
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: | yes |
Analytic conductor: | \(1.12268673869\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.725083 | 0.128178 | 0.0640889 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640889 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(3\) | 19.6495 | 1.26052 | 0.630258 | − | 0.776386i | \(-0.282949\pi\) | ||||
0.630258 | + | 0.776386i | \(0.282949\pi\) | |||||||
\(4\) | −31.4743 | −0.983570 | ||||||||
\(5\) | −46.7492 | −0.836275 | −0.418137 | − | 0.908384i | \(-0.637317\pi\) | ||||
−0.418137 | + | 0.908384i | \(0.637317\pi\) | |||||||
\(6\) | 14.2475 | 0.161570 | ||||||||
\(7\) | 49.0000 | 0.377964 | ||||||||
\(8\) | −46.0241 | −0.254250 | ||||||||
\(9\) | 143.103 | 0.588901 | ||||||||
\(10\) | −33.8970 | −0.107192 | ||||||||
\(11\) | 666.090 | 1.65978 | 0.829891 | − | 0.557926i | \(-0.188403\pi\) | ||||
0.829891 | + | 0.557926i | \(0.188403\pi\) | |||||||
\(12\) | −618.453 | −1.23981 | ||||||||
\(13\) | −650.640 | −1.06778 | −0.533890 | − | 0.845554i | \(-0.679271\pi\) | ||||
−0.533890 | + | 0.845554i | \(0.679271\pi\) | |||||||
\(14\) | 35.5291 | 0.0484466 | ||||||||
\(15\) | −918.598 | −1.05414 | ||||||||
\(16\) | 973.805 | 0.950981 | ||||||||
\(17\) | 1186.89 | 0.996069 | 0.498035 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498035 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(18\) | 103.762 | 0.0754840 | ||||||||
\(19\) | −1565.05 | −0.994591 | −0.497296 | − | 0.867581i | \(-0.665674\pi\) | ||||
−0.497296 | + | 0.867581i | \(0.665674\pi\) | |||||||
\(20\) | 1471.40 | 0.822535 | ||||||||
\(21\) | 962.826 | 0.476430 | ||||||||
\(22\) | 482.970 | 0.212747 | ||||||||
\(23\) | −1100.15 | −0.433644 | −0.216822 | − | 0.976211i | \(-0.569569\pi\) | ||||
−0.216822 | + | 0.976211i | \(0.569569\pi\) | |||||||
\(24\) | −904.350 | −0.320486 | ||||||||
\(25\) | −939.515 | −0.300645 | ||||||||
\(26\) | −471.768 | −0.136866 | ||||||||
\(27\) | −1962.93 | −0.518197 | ||||||||
\(28\) | −1542.24 | −0.371755 | ||||||||
\(29\) | 2396.72 | 0.529203 | 0.264602 | − | 0.964358i | \(-0.414760\pi\) | ||||
0.264602 | + | 0.964358i | \(0.414760\pi\) | |||||||
\(30\) | −666.060 | −0.135117 | ||||||||
\(31\) | −2048.46 | −0.382844 | −0.191422 | − | 0.981508i | \(-0.561310\pi\) | ||||
−0.191422 | + | 0.981508i | \(0.561310\pi\) | |||||||
\(32\) | 2178.86 | 0.376144 | ||||||||
\(33\) | 13088.3 | 2.09218 | ||||||||
\(34\) | 860.596 | 0.127674 | ||||||||
\(35\) | −2290.71 | −0.316082 | ||||||||
\(36\) | −4504.06 | −0.579226 | ||||||||
\(37\) | 1077.54 | 0.129399 | 0.0646995 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0646995 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(38\) | −1134.79 | −0.127484 | ||||||||
\(39\) | −12784.7 | −1.34595 | ||||||||
\(40\) | 2151.59 | 0.212622 | ||||||||
\(41\) | 1098.21 | 0.102029 | 0.0510147 | − | 0.998698i | \(-0.483754\pi\) | ||||
0.0510147 | + | 0.998698i | \(0.483754\pi\) | |||||||
\(42\) | 698.128 | 0.0610678 | ||||||||
\(43\) | 16564.3 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(44\) | −20964.7 | −1.63251 | ||||||||
\(45\) | −6689.95 | −0.492483 | ||||||||
\(46\) | −797.702 | −0.0555835 | ||||||||
\(47\) | −8298.39 | −0.547960 | −0.273980 | − | 0.961735i | \(-0.588340\pi\) | ||||
−0.273980 | + | 0.961735i | \(0.588340\pi\) | |||||||
\(48\) | 19134.8 | 1.19873 | ||||||||
\(49\) | 2401.00 | 0.142857 | ||||||||
\(50\) | −681.226 | −0.0385360 | ||||||||
\(51\) | 23321.9 | 1.25556 | ||||||||
\(52\) | 20478.4 | 1.05024 | ||||||||
\(53\) | 5519.18 | 0.269889 | 0.134944 | − | 0.990853i | \(-0.456914\pi\) | ||||
0.134944 | + | 0.990853i | \(0.456914\pi\) | |||||||
\(54\) | −1423.28 | −0.0664213 | ||||||||
\(55\) | −31139.1 | −1.38803 | ||||||||
\(56\) | −2255.18 | −0.0960973 | ||||||||
\(57\) | −30752.5 | −1.25370 | ||||||||
\(58\) | 1737.82 | 0.0678321 | ||||||||
\(59\) | −14230.4 | −0.532216 | −0.266108 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266108 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(60\) | 28912.2 | 1.03682 | ||||||||
\(61\) | −14234.7 | −0.489807 | −0.244904 | − | 0.969547i | \(-0.578756\pi\) | ||||
−0.244904 | + | 0.969547i | \(0.578756\pi\) | |||||||
\(62\) | −1485.30 | −0.0490721 | ||||||||
\(63\) | 7012.05 | 0.222584 | ||||||||
\(64\) | −29581.9 | −0.902768 | ||||||||
\(65\) | 30416.9 | 0.892958 | ||||||||
\(66\) | 9490.12 | 0.268171 | ||||||||
\(67\) | 19730.4 | 0.536970 | 0.268485 | − | 0.963284i | \(-0.413477\pi\) | ||||
0.268485 | + | 0.963284i | \(0.413477\pi\) | |||||||
\(68\) | −37356.6 | −0.979704 | ||||||||
\(69\) | −21617.5 | −0.546615 | ||||||||
\(70\) | −1660.95 | −0.0405147 | ||||||||
\(71\) | 64562.7 | 1.51997 | 0.759986 | − | 0.649940i | \(-0.225206\pi\) | ||||
0.759986 | + | 0.649940i | \(0.225206\pi\) | |||||||
\(72\) | −6586.18 | −0.149728 | ||||||||
\(73\) | 28567.0 | 0.627418 | 0.313709 | − | 0.949519i | \(-0.398428\pi\) | ||||
0.313709 | + | 0.949519i | \(0.398428\pi\) | |||||||
\(74\) | 781.309 | 0.0165861 | ||||||||
\(75\) | −18461.0 | −0.378968 | ||||||||
\(76\) | 49258.8 | 0.978251 | ||||||||
\(77\) | 32638.4 | 0.627339 | ||||||||
\(78\) | −9270.00 | −0.172521 | ||||||||
\(79\) | −30633.4 | −0.552239 | −0.276119 | − | 0.961123i | \(-0.589049\pi\) | ||||
−0.276119 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(80\) | −45524.6 | −0.795282 | ||||||||
\(81\) | −73344.6 | −1.24210 | ||||||||
\(82\) | 796.293 | 0.0130779 | ||||||||
\(83\) | −675.946 | −0.0107700 | −0.00538501 | − | 0.999986i | \(-0.501714\pi\) | ||||
−0.00538501 | + | 0.999986i | \(0.501714\pi\) | |||||||
\(84\) | −30304.2 | −0.468603 | ||||||||
\(85\) | −55486.3 | −0.832987 | ||||||||
\(86\) | 12010.5 | 0.175111 | ||||||||
\(87\) | 47094.4 | 0.667069 | ||||||||
\(88\) | −30656.2 | −0.421999 | ||||||||
\(89\) | 125971. | 1.68576 | 0.842882 | − | 0.538098i | \(-0.180857\pi\) | ||||
0.842882 | + | 0.538098i | \(0.180857\pi\) | |||||||
\(90\) | −4850.76 | −0.0631254 | ||||||||
\(91\) | −31881.3 | −0.403583 | ||||||||
\(92\) | 34626.5 | 0.426520 | ||||||||
\(93\) | −40251.1 | −0.482582 | ||||||||
\(94\) | −6017.02 | −0.0702363 | ||||||||
\(95\) | 73164.9 | 0.831751 | ||||||||
\(96\) | 42813.5 | 0.474136 | ||||||||
\(97\) | −22906.8 | −0.247192 | −0.123596 | − | 0.992333i | \(-0.539443\pi\) | ||||
−0.123596 | + | 0.992333i | \(0.539443\pi\) | |||||||
\(98\) | 1740.92 | 0.0183111 | ||||||||
\(99\) | 95319.4 | 0.977447 | ||||||||
\(100\) | 29570.5 | 0.295705 | ||||||||
\(101\) | −181474. | −1.77015 | −0.885077 | − | 0.465444i | \(-0.845895\pi\) | ||||
−0.885077 | + | 0.465444i | \(0.845895\pi\) | |||||||
\(102\) | 16910.3 | 0.160935 | ||||||||
\(103\) | 64772.0 | 0.601581 | 0.300791 | − | 0.953690i | \(-0.402749\pi\) | ||||
0.300791 | + | 0.953690i | \(0.402749\pi\) | |||||||
\(104\) | 29945.1 | 0.271483 | ||||||||
\(105\) | −45011.3 | −0.398427 | ||||||||
\(106\) | 4001.86 | 0.0345938 | ||||||||
\(107\) | −148170. | −1.25112 | −0.625562 | − | 0.780175i | \(-0.715130\pi\) | ||||
−0.625562 | + | 0.780175i | \(0.715130\pi\) | |||||||
\(108\) | 61781.7 | 0.509683 | ||||||||
\(109\) | −111294. | −0.897237 | −0.448618 | − | 0.893723i | \(-0.648084\pi\) | ||||
−0.448618 | + | 0.893723i | \(0.648084\pi\) | |||||||
\(110\) | −22578.5 | −0.177915 | ||||||||
\(111\) | 21173.2 | 0.163110 | ||||||||
\(112\) | 47716.4 | 0.359437 | ||||||||
\(113\) | −43175.5 | −0.318084 | −0.159042 | − | 0.987272i | \(-0.550840\pi\) | ||||
−0.159042 | + | 0.987272i | \(0.550840\pi\) | |||||||
\(114\) | −22298.1 | −0.160696 | ||||||||
\(115\) | 51431.2 | 0.362646 | ||||||||
\(116\) | −75435.0 | −0.520509 | ||||||||
\(117\) | −93108.5 | −0.628817 | ||||||||
\(118\) | −10318.2 | −0.0682182 | ||||||||
\(119\) | 58157.8 | 0.376479 | ||||||||
\(120\) | 42277.6 | 0.268014 | ||||||||
\(121\) | 282625. | 1.75488 | ||||||||
\(122\) | −10321.4 | −0.0627824 | ||||||||
\(123\) | 21579.3 | 0.128610 | ||||||||
\(124\) | 64473.6 | 0.376554 | ||||||||
\(125\) | 190013. | 1.08770 | ||||||||
\(126\) | 5084.31 | 0.0285303 | ||||||||
\(127\) | −131449. | −0.723182 | −0.361591 | − | 0.932337i | \(-0.617766\pi\) | ||||
−0.361591 | + | 0.932337i | \(0.617766\pi\) | |||||||
\(128\) | −91172.8 | −0.491859 | ||||||||
\(129\) | 325480. | 1.72207 | ||||||||
\(130\) | 22054.7 | 0.114457 | ||||||||
\(131\) | −349458. | −1.77916 | −0.889582 | − | 0.456775i | \(-0.849005\pi\) | ||||
−0.889582 | + | 0.456775i | \(0.849005\pi\) | |||||||
\(132\) | −411946. | −2.05781 | ||||||||
\(133\) | −76687.5 | −0.375920 | ||||||||
\(134\) | 14306.2 | 0.0688276 | ||||||||
\(135\) | 91765.2 | 0.433355 | ||||||||
\(136\) | −54625.7 | −0.253250 | ||||||||
\(137\) | 386434. | 1.75903 | 0.879516 | − | 0.475869i | \(-0.157866\pi\) | ||||
0.879516 | + | 0.475869i | \(0.157866\pi\) | |||||||
\(138\) | −15674.4 | −0.0700639 | ||||||||
\(139\) | 17289.3 | 0.0758997 | 0.0379498 | − | 0.999280i | \(-0.487917\pi\) | ||||
0.0379498 | + | 0.999280i | \(0.487917\pi\) | |||||||
\(140\) | 72098.4 | 0.310889 | ||||||||
\(141\) | −163059. | −0.690713 | ||||||||
\(142\) | 46813.3 | 0.194827 | ||||||||
\(143\) | −433384. | −1.77228 | ||||||||
\(144\) | 139354. | 0.560034 | ||||||||
\(145\) | −112045. | −0.442559 | ||||||||
\(146\) | 20713.4 | 0.0804210 | ||||||||
\(147\) | 47178.5 | 0.180074 | ||||||||
\(148\) | −33914.9 | −0.127273 | ||||||||
\(149\) | −112171. | −0.413917 | −0.206959 | − | 0.978350i | \(-0.566357\pi\) | ||||
−0.206959 | + | 0.978350i | \(0.566357\pi\) | |||||||
\(150\) | −13385.8 | −0.0485752 | ||||||||
\(151\) | 30495.4 | 0.108841 | 0.0544205 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544205 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(152\) | 72030.1 | 0.252874 | ||||||||
\(153\) | 169848. | 0.586586 | ||||||||
\(154\) | 23665.5 | 0.0804108 | ||||||||
\(155\) | 95763.6 | 0.320163 | ||||||||
\(156\) | 402390. | 1.32384 | ||||||||
\(157\) | 523509. | 1.69502 | 0.847510 | − | 0.530780i | \(-0.178101\pi\) | ||||
0.847510 | + | 0.530780i | \(0.178101\pi\) | |||||||
\(158\) | −22211.7 | −0.0707847 | ||||||||
\(159\) | 108449. | 0.340199 | ||||||||
\(160\) | −101860. | −0.314560 | ||||||||
\(161\) | −53907.5 | −0.163902 | ||||||||
\(162\) | −53180.9 | −0.159209 | ||||||||
\(163\) | −439646. | −1.29609 | −0.648043 | − | 0.761604i | \(-0.724412\pi\) | ||||
−0.648043 | + | 0.761604i | \(0.724412\pi\) | |||||||
\(164\) | −34565.3 | −0.100353 | ||||||||
\(165\) | −611869. | −1.74964 | ||||||||
\(166\) | −490.117 | −0.00138048 | ||||||||
\(167\) | 279353. | 0.775107 | 0.387554 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387554 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(168\) | −44313.2 | −0.121132 | ||||||||
\(169\) | 52038.8 | 0.140156 | ||||||||
\(170\) | −40232.2 | −0.106770 | ||||||||
\(171\) | −223964. | −0.585716 | ||||||||
\(172\) | −521349. | −1.34372 | ||||||||
\(173\) | 99699.4 | 0.253266 | 0.126633 | − | 0.991950i | \(-0.459583\pi\) | ||||
0.126633 | + | 0.991950i | \(0.459583\pi\) | |||||||
\(174\) | 34147.3 | 0.0855034 | ||||||||
\(175\) | −46036.2 | −0.113633 | ||||||||
\(176\) | 648641. | 1.57842 | ||||||||
\(177\) | −279621. | −0.670867 | ||||||||
\(178\) | 91339.7 | 0.216077 | ||||||||
\(179\) | 329980. | 0.769760 | 0.384880 | − | 0.922967i | \(-0.374243\pi\) | ||||
0.384880 | + | 0.922967i | \(0.374243\pi\) | |||||||
\(180\) | 210561. | 0.484392 | ||||||||
\(181\) | −505810. | −1.14760 | −0.573800 | − | 0.818995i | \(-0.694531\pi\) | ||||
−0.573800 | + | 0.818995i | \(0.694531\pi\) | |||||||
\(182\) | −23116.6 | −0.0517304 | ||||||||
\(183\) | −279706. | −0.617410 | ||||||||
\(184\) | 50633.5 | 0.110254 | ||||||||
\(185\) | −50374.3 | −0.108213 | ||||||||
\(186\) | −29185.4 | −0.0618562 | ||||||||
\(187\) | 790578. | 1.65326 | ||||||||
\(188\) | 261186. | 0.538958 | ||||||||
\(189\) | −96183.4 | −0.195860 | ||||||||
\(190\) | 53050.6 | 0.106612 | ||||||||
\(191\) | −63835.6 | −0.126613 | −0.0633067 | − | 0.997994i | \(-0.520165\pi\) | ||||
−0.0633067 | + | 0.997994i | \(0.520165\pi\) | |||||||
\(192\) | −581270. | −1.13795 | ||||||||
\(193\) | 469355. | 0.907001 | 0.453501 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453501 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(194\) | −16609.3 | −0.0316845 | ||||||||
\(195\) | 597676. | 1.12559 | ||||||||
\(196\) | −75569.7 | −0.140510 | ||||||||
\(197\) | 268021. | 0.492043 | 0.246021 | − | 0.969264i | \(-0.420877\pi\) | ||||
0.246021 | + | 0.969264i | \(0.420877\pi\) | |||||||
\(198\) | 69114.5 | 0.125287 | ||||||||
\(199\) | −605167. | −1.08328 | −0.541642 | − | 0.840609i | \(-0.682197\pi\) | ||||
−0.541642 | + | 0.840609i | \(0.682197\pi\) | |||||||
\(200\) | 43240.3 | 0.0764388 | ||||||||
\(201\) | 387693. | 0.676859 | ||||||||
\(202\) | −131584. | −0.226894 | ||||||||
\(203\) | 117439. | 0.200020 | ||||||||
\(204\) | −734039. | −1.23493 | ||||||||
\(205\) | −51340.4 | −0.0853246 | ||||||||
\(206\) | 46965.1 | 0.0771094 | ||||||||
\(207\) | −157435. | −0.255374 | ||||||||
\(208\) | −633596. | −1.01544 | ||||||||
\(209\) | −1.04246e6 | −1.65080 | ||||||||
\(210\) | −32636.9 | −0.0510694 | ||||||||
\(211\) | 335389. | 0.518612 | 0.259306 | − | 0.965795i | \(-0.416506\pi\) | ||||
0.259306 | + | 0.965795i | \(0.416506\pi\) | |||||||
\(212\) | −173712. | −0.265455 | ||||||||
\(213\) | 1.26862e6 | 1.91595 | ||||||||
\(214\) | −107435. | −0.160366 | ||||||||
\(215\) | −774367. | −1.14249 | ||||||||
\(216\) | 90341.9 | 0.131751 | ||||||||
\(217\) | −100374. | −0.144702 | ||||||||
\(218\) | −80697.7 | −0.115006 | ||||||||
\(219\) | 561327. | 0.790871 | ||||||||
\(220\) | 980081. | 1.36523 | ||||||||
\(221\) | −772240. | −1.06358 | ||||||||
\(222\) | 15352.3 | 0.0209070 | ||||||||
\(223\) | 1.02526e6 | 1.38061 | 0.690305 | − | 0.723518i | \(-0.257476\pi\) | ||||
0.690305 | + | 0.723518i | \(0.257476\pi\) | |||||||
\(224\) | 106764. | 0.142169 | ||||||||
\(225\) | −134447. | −0.177050 | ||||||||
\(226\) | −31305.8 | −0.0407713 | ||||||||
\(227\) | −504226. | −0.649473 | −0.324736 | − | 0.945805i | \(-0.605276\pi\) | ||||
−0.324736 | + | 0.945805i | \(0.605276\pi\) | |||||||
\(228\) | 967912. | 1.23310 | ||||||||
\(229\) | −1.11939e6 | −1.41057 | −0.705283 | − | 0.708925i | \(-0.749180\pi\) | ||||
−0.705283 | + | 0.708925i | \(0.749180\pi\) | |||||||
\(230\) | 37291.9 | 0.0464831 | ||||||||
\(231\) | 641328. | 0.790770 | ||||||||
\(232\) | −110307. | −0.134550 | ||||||||
\(233\) | 770703. | 0.930031 | 0.465015 | − | 0.885303i | \(-0.346049\pi\) | ||||
0.465015 | + | 0.885303i | \(0.346049\pi\) | |||||||
\(234\) | −67511.3 | −0.0806004 | ||||||||
\(235\) | 387943. | 0.458245 | ||||||||
\(236\) | 447892. | 0.523472 | ||||||||
\(237\) | −601930. | −0.696106 | ||||||||
\(238\) | 42169.2 | 0.0482562 | ||||||||
\(239\) | −171646. | −0.194374 | −0.0971871 | − | 0.995266i | \(-0.530985\pi\) | ||||
−0.0971871 | + | 0.995266i | \(0.530985\pi\) | |||||||
\(240\) | −894535. | −1.00247 | ||||||||
\(241\) | −383779. | −0.425637 | −0.212818 | − | 0.977092i | \(-0.568264\pi\) | ||||
−0.212818 | + | 0.977092i | \(0.568264\pi\) | |||||||
\(242\) | 204926. | 0.224936 | ||||||||
\(243\) | −964193. | −1.04749 | ||||||||
\(244\) | 448028. | 0.481760 | ||||||||
\(245\) | −112245. | −0.119468 | ||||||||
\(246\) | 15646.8 | 0.0164849 | ||||||||
\(247\) | 1.01828e6 | 1.06201 | ||||||||
\(248\) | 94278.3 | 0.0973380 | ||||||||
\(249\) | −13282.0 | −0.0135758 | ||||||||
\(250\) | 137775. | 0.139418 | ||||||||
\(251\) | −1.57046e6 | −1.57342 | −0.786708 | − | 0.617325i | \(-0.788216\pi\) | ||||
−0.786708 | + | 0.617325i | \(0.788216\pi\) | |||||||
\(252\) | −220699. | −0.218927 | ||||||||
\(253\) | −732801. | −0.719755 | ||||||||
\(254\) | −95311.4 | −0.0926959 | ||||||||
\(255\) | −1.09028e6 | −1.04999 | ||||||||
\(256\) | 880513. | 0.839723 | ||||||||
\(257\) | 790656. | 0.746715 | 0.373357 | − | 0.927688i | \(-0.378207\pi\) | ||||
0.373357 | + | 0.927688i | \(0.378207\pi\) | |||||||
\(258\) | 236000. | 0.220731 | ||||||||
\(259\) | 52799.7 | 0.0489082 | ||||||||
\(260\) | −957348. | −0.878287 | ||||||||
\(261\) | 342978. | 0.311648 | ||||||||
\(262\) | −253386. | −0.228049 | ||||||||
\(263\) | 464416. | 0.414017 | 0.207008 | − | 0.978339i | \(-0.433627\pi\) | ||||
0.207008 | + | 0.978339i | \(0.433627\pi\) | |||||||
\(264\) | −602379. | −0.531936 | ||||||||
\(265\) | −258017. | −0.225701 | ||||||||
\(266\) | −55604.8 | −0.0481846 | ||||||||
\(267\) | 2.47527e6 | 2.12493 | ||||||||
\(268\) | −621001. | −0.528147 | ||||||||
\(269\) | 1.99959e6 | 1.68484 | 0.842422 | − | 0.538818i | \(-0.181129\pi\) | ||||
0.842422 | + | 0.538818i | \(0.181129\pi\) | |||||||
\(270\) | 66537.4 | 0.0555464 | ||||||||
\(271\) | 1.61296e6 | 1.33414 | 0.667070 | − | 0.744995i | \(-0.267548\pi\) | ||||
0.667070 | + | 0.744995i | \(0.267548\pi\) | |||||||
\(272\) | 1.15580e6 | 0.947243 | ||||||||
\(273\) | −626452. | −0.508723 | ||||||||
\(274\) | 280197. | 0.225469 | ||||||||
\(275\) | −625801. | −0.499005 | ||||||||
\(276\) | 680393. | 0.537635 | ||||||||
\(277\) | −2.08119e6 | −1.62972 | −0.814860 | − | 0.579658i | \(-0.803186\pi\) | ||||
−0.814860 | + | 0.579658i | \(0.803186\pi\) | |||||||
\(278\) | 12536.2 | 0.00972865 | ||||||||
\(279\) | −293140. | −0.225457 | ||||||||
\(280\) | 105428. | 0.0803637 | ||||||||
\(281\) | −982035. | −0.741927 | −0.370964 | − | 0.928647i | \(-0.620973\pi\) | ||||
−0.370964 | + | 0.928647i | \(0.620973\pi\) | |||||||
\(282\) | −118231. | −0.0885340 | ||||||||
\(283\) | −1.39622e6 | −1.03630 | −0.518152 | − | 0.855289i | \(-0.673380\pi\) | ||||
−0.518152 | + | 0.855289i | \(0.673380\pi\) | |||||||
\(284\) | −2.03206e6 | −1.49500 | ||||||||
\(285\) | 1.43765e6 | 1.04844 | ||||||||
\(286\) | −314240. | −0.227167 | ||||||||
\(287\) | 53812.3 | 0.0385635 | ||||||||
\(288\) | 311801. | 0.221512 | ||||||||
\(289\) | −11140.3 | −0.00784609 | ||||||||
\(290\) | −81241.7 | −0.0567262 | ||||||||
\(291\) | −450107. | −0.311590 | ||||||||
\(292\) | −899124. | −0.617110 | ||||||||
\(293\) | 2.56205e6 | 1.74348 | 0.871742 | − | 0.489965i | \(-0.162990\pi\) | ||||
0.871742 | + | 0.489965i | \(0.162990\pi\) | |||||||
\(294\) | 34208.3 | 0.0230814 | ||||||||
\(295\) | 665260. | 0.445078 | ||||||||
\(296\) | −49593.0 | −0.0328996 | ||||||||
\(297\) | −1.30749e6 | −0.860094 | ||||||||
\(298\) | −81333.0 | −0.0530550 | ||||||||
\(299\) | 715803. | 0.463037 | ||||||||
\(300\) | 581046. | 0.372741 | ||||||||
\(301\) | 811651. | 0.516361 | ||||||||
\(302\) | 22111.7 | 0.0139510 | ||||||||
\(303\) | −3.56588e6 | −2.23131 | ||||||||
\(304\) | −1.52405e6 | −0.945838 | ||||||||
\(305\) | 665463. | 0.409613 | ||||||||
\(306\) | 123154. | 0.0751873 | ||||||||
\(307\) | −884855. | −0.535829 | −0.267915 | − | 0.963443i | \(-0.586334\pi\) | ||||
−0.267915 | + | 0.963443i | \(0.586334\pi\) | |||||||
\(308\) | −1.02727e6 | −0.617032 | ||||||||
\(309\) | 1.27274e6 | 0.758303 | ||||||||
\(310\) | 69436.5 | 0.0410378 | ||||||||
\(311\) | 1.80120e6 | 1.05599 | 0.527997 | − | 0.849246i | \(-0.322943\pi\) | ||||
0.527997 | + | 0.849246i | \(0.322943\pi\) | |||||||
\(312\) | 588406. | 0.342208 | ||||||||
\(313\) | 950366. | 0.548315 | 0.274158 | − | 0.961685i | \(-0.411601\pi\) | ||||
0.274158 | + | 0.961685i | \(0.411601\pi\) | |||||||
\(314\) | 379587. | 0.217264 | ||||||||
\(315\) | −327807. | −0.186141 | ||||||||
\(316\) | 964162. | 0.543166 | ||||||||
\(317\) | 3.04277e6 | 1.70068 | 0.850338 | − | 0.526237i | \(-0.176398\pi\) | ||||
0.850338 | + | 0.526237i | \(0.176398\pi\) | |||||||
\(318\) | 78634.6 | 0.0436060 | ||||||||
\(319\) | 1.59643e6 | 0.878362 | ||||||||
\(320\) | 1.38293e6 | 0.754962 | ||||||||
\(321\) | −2.91146e6 | −1.57706 | ||||||||
\(322\) | −39087.4 | −0.0210086 | ||||||||
\(323\) | −1.85755e6 | −0.990682 | ||||||||
\(324\) | 2.30847e6 | 1.22169 | ||||||||
\(325\) | 611286. | 0.321023 | ||||||||
\(326\) | −318780. | −0.166129 | ||||||||
\(327\) | −2.18688e6 | −1.13098 | ||||||||
\(328\) | −50544.1 | −0.0259409 | ||||||||
\(329\) | −406621. | −0.207110 | ||||||||
\(330\) | −443655. | −0.224265 | ||||||||
\(331\) | −2.19616e6 | −1.10178 | −0.550889 | − | 0.834579i | \(-0.685711\pi\) | ||||
−0.550889 | + | 0.834579i | \(0.685711\pi\) | |||||||
\(332\) | 21274.9 | 0.0105931 | ||||||||
\(333\) | 154200. | 0.0762032 | ||||||||
\(334\) | 202554. | 0.0993515 | ||||||||
\(335\) | −922382. | −0.449054 | ||||||||
\(336\) | 937604. | 0.453076 | ||||||||
\(337\) | −2.41491e6 | −1.15832 | −0.579158 | − | 0.815216i | \(-0.696618\pi\) | ||||
−0.579158 | + | 0.815216i | \(0.696618\pi\) | |||||||
\(338\) | 37732.5 | 0.0179648 | ||||||||
\(339\) | −848377. | −0.400950 | ||||||||
\(340\) | 1.74639e6 | 0.819302 | ||||||||
\(341\) | −1.36446e6 | −0.635438 | ||||||||
\(342\) | −162392. | −0.0750757 | ||||||||
\(343\) | 117649. | 0.0539949 | ||||||||
\(344\) | −762357. | −0.347346 | ||||||||
\(345\) | 1.01060e6 | 0.457121 | ||||||||
\(346\) | 72290.3 | 0.0324631 | ||||||||
\(347\) | −1.08833e6 | −0.485219 | −0.242609 | − | 0.970124i | \(-0.578003\pi\) | ||||
−0.242609 | + | 0.970124i | \(0.578003\pi\) | |||||||
\(348\) | −1.48226e6 | −0.656110 | ||||||||
\(349\) | 2.79267e6 | 1.22731 | 0.613657 | − | 0.789573i | \(-0.289698\pi\) | ||||
0.613657 | + | 0.789573i | \(0.289698\pi\) | |||||||
\(350\) | −33380.1 | −0.0145652 | ||||||||
\(351\) | 1.27716e6 | 0.553321 | ||||||||
\(352\) | 1.45132e6 | 0.624317 | ||||||||
\(353\) | 2.53134e6 | 1.08122 | 0.540610 | − | 0.841273i | \(-0.318193\pi\) | ||||
0.540610 | + | 0.841273i | \(0.318193\pi\) | |||||||
\(354\) | −202748. | −0.0859902 | ||||||||
\(355\) | −3.01825e6 | −1.27111 | ||||||||
\(356\) | −3.96485e6 | −1.65807 | ||||||||
\(357\) | 1.14277e6 | 0.474558 | ||||||||
\(358\) | 239263. | 0.0986661 | ||||||||
\(359\) | 1.09028e6 | 0.446480 | 0.223240 | − | 0.974763i | \(-0.428337\pi\) | ||||
0.223240 | + | 0.974763i | \(0.428337\pi\) | |||||||
\(360\) | 307899. | 0.125214 | ||||||||
\(361\) | −26712.8 | −0.0107883 | ||||||||
\(362\) | −366754. | −0.147097 | ||||||||
\(363\) | 5.55343e6 | 2.21205 | ||||||||
\(364\) | 1.00344e6 | 0.396953 | ||||||||
\(365\) | −1.33548e6 | −0.524694 | ||||||||
\(366\) | −202810. | −0.0791382 | ||||||||
\(367\) | 188070. | 0.0728879 | 0.0364439 | − | 0.999336i | \(-0.488397\pi\) | ||||
0.0364439 | + | 0.999336i | \(0.488397\pi\) | |||||||
\(368\) | −1.07133e6 | −0.412387 | ||||||||
\(369\) | 157157. | 0.0600853 | ||||||||
\(370\) | −36525.6 | −0.0138705 | ||||||||
\(371\) | 270440. | 0.102008 | ||||||||
\(372\) | 1.26687e6 | 0.474653 | ||||||||
\(373\) | −1.79371e6 | −0.667545 | −0.333772 | − | 0.942654i | \(-0.608322\pi\) | ||||
−0.333772 | + | 0.942654i | \(0.608322\pi\) | |||||||
\(374\) | 573234. | 0.211911 | ||||||||
\(375\) | 3.73366e6 | 1.37106 | ||||||||
\(376\) | 381926. | 0.139319 | ||||||||
\(377\) | −1.55940e6 | −0.565073 | ||||||||
\(378\) | −69740.9 | −0.0251049 | ||||||||
\(379\) | 3.58806e6 | 1.28310 | 0.641551 | − | 0.767080i | \(-0.278291\pi\) | ||||
0.641551 | + | 0.767080i | \(0.278291\pi\) | |||||||
\(380\) | −2.30281e6 | −0.818086 | ||||||||
\(381\) | −2.58291e6 | −0.911583 | ||||||||
\(382\) | −46286.1 | −0.0162290 | ||||||||
\(383\) | −3.42457e6 | −1.19291 | −0.596457 | − | 0.802645i | \(-0.703425\pi\) | ||||
−0.596457 | + | 0.802645i | \(0.703425\pi\) | |||||||
\(384\) | −1.79150e6 | −0.619996 | ||||||||
\(385\) | −1.52582e6 | −0.524627 | ||||||||
\(386\) | 340321. | 0.116257 | ||||||||
\(387\) | 2.37040e6 | 0.804534 | ||||||||
\(388\) | 720974. | 0.243131 | ||||||||
\(389\) | 8625.27 | 0.00289001 | 0.00144500 | − | 0.999999i | \(-0.499540\pi\) | ||||
0.00144500 | + | 0.999999i | \(0.499540\pi\) | |||||||
\(390\) | 433365. | 0.144275 | ||||||||
\(391\) | −1.30576e6 | −0.431940 | ||||||||
\(392\) | −110504. | −0.0363214 | ||||||||
\(393\) | −6.86667e6 | −2.24267 | ||||||||
\(394\) | 194337. | 0.0630690 | ||||||||
\(395\) | 1.43208e6 | 0.461823 | ||||||||
\(396\) | −3.00011e6 | −0.961388 | ||||||||
\(397\) | 1.25709e6 | 0.400306 | 0.200153 | − | 0.979765i | \(-0.435856\pi\) | ||||
0.200153 | + | 0.979765i | \(0.435856\pi\) | |||||||
\(398\) | −438796. | −0.138853 | ||||||||
\(399\) | −1.50687e6 | −0.473853 | ||||||||
\(400\) | −914904. | −0.285908 | ||||||||
\(401\) | 1.42670e6 | 0.443070 | 0.221535 | − | 0.975152i | \(-0.428893\pi\) | ||||
0.221535 | + | 0.975152i | \(0.428893\pi\) | |||||||
\(402\) | 281110. | 0.0867583 | ||||||||
\(403\) | 1.33281e6 | 0.408794 | ||||||||
\(404\) | 5.71176e6 | 1.74107 | ||||||||
\(405\) | 3.42880e6 | 1.03873 | ||||||||
\(406\) | 85153.2 | 0.0256381 | ||||||||
\(407\) | 717741. | 0.214774 | ||||||||
\(408\) | −1.07337e6 | −0.319226 | ||||||||
\(409\) | −3.06529e6 | −0.906073 | −0.453036 | − | 0.891492i | \(-0.649659\pi\) | ||||
−0.453036 | + | 0.891492i | \(0.649659\pi\) | |||||||
\(410\) | −37226.0 | −0.0109367 | ||||||||
\(411\) | 7.59324e6 | 2.21729 | ||||||||
\(412\) | −2.03865e6 | −0.591698 | ||||||||
\(413\) | −697291. | −0.201159 | ||||||||
\(414\) | −114154. | −0.0327332 | ||||||||
\(415\) | 31599.9 | 0.00900670 | ||||||||
\(416\) | −1.41765e6 | −0.401640 | ||||||||
\(417\) | 339726. | 0.0956728 | ||||||||
\(418\) | −755873. | −0.211596 | ||||||||
\(419\) | −248240. | −0.0690776 | −0.0345388 | − | 0.999403i | \(-0.510996\pi\) | ||||
−0.0345388 | + | 0.999403i | \(0.510996\pi\) | |||||||
\(420\) | 1.41670e6 | 0.391881 | ||||||||
\(421\) | 5.96280e6 | 1.63963 | 0.819814 | − | 0.572630i | \(-0.194077\pi\) | ||||
0.819814 | + | 0.572630i | \(0.194077\pi\) | |||||||
\(422\) | 243185. | 0.0664746 | ||||||||
\(423\) | −1.18752e6 | −0.322695 | ||||||||
\(424\) | −254015. | −0.0686192 | ||||||||
\(425\) | −1.11510e6 | −0.299463 | ||||||||
\(426\) | 919857. | 0.245582 | ||||||||
\(427\) | −697503. | −0.185130 | ||||||||
\(428\) | 4.66353e6 | 1.23057 | ||||||||
\(429\) | −8.51579e6 | −2.23399 | ||||||||
\(430\) | −561481. | −0.146441 | ||||||||
\(431\) | −4.93538e6 | −1.27976 | −0.639879 | − | 0.768476i | \(-0.721015\pi\) | ||||
−0.639879 | + | 0.768476i | \(0.721015\pi\) | |||||||
\(432\) | −1.91151e6 | −0.492795 | ||||||||
\(433\) | 4.15513e6 | 1.06504 | 0.532519 | − | 0.846418i | \(-0.321245\pi\) | ||||
0.532519 | + | 0.846418i | \(0.321245\pi\) | |||||||
\(434\) | −72779.7 | −0.0185475 | ||||||||
\(435\) | −2.20162e6 | −0.557853 | ||||||||
\(436\) | 3.50291e6 | 0.882496 | ||||||||
\(437\) | 1.72180e6 | 0.431299 | ||||||||
\(438\) | 407008. | 0.101372 | ||||||||
\(439\) | −227955. | −0.0564531 | −0.0282265 | − | 0.999602i | \(-0.508986\pi\) | ||||
−0.0282265 | + | 0.999602i | \(0.508986\pi\) | |||||||
\(440\) | 1.43315e6 | 0.352907 | ||||||||
\(441\) | 343590. | 0.0841287 | ||||||||
\(442\) | −559938. | −0.136328 | ||||||||
\(443\) | −1.98462e6 | −0.480472 | −0.240236 | − | 0.970715i | \(-0.577225\pi\) | ||||
−0.240236 | + | 0.970715i | \(0.577225\pi\) | |||||||
\(444\) | −666411. | −0.160430 | ||||||||
\(445\) | −5.88906e6 | −1.40976 | ||||||||
\(446\) | 743397. | 0.176963 | ||||||||
\(447\) | −2.20410e6 | −0.521749 | ||||||||
\(448\) | −1.44951e6 | −0.341214 | ||||||||
\(449\) | 2.61077e6 | 0.611157 | 0.305579 | − | 0.952167i | \(-0.401150\pi\) | ||||
0.305579 | + | 0.952167i | \(0.401150\pi\) | |||||||
\(450\) | −97485.5 | −0.0226939 | ||||||||
\(451\) | 731506. | 0.169347 | ||||||||
\(452\) | 1.35892e6 | 0.312858 | ||||||||
\(453\) | 599220. | 0.137196 | ||||||||
\(454\) | −365606. | −0.0832480 | ||||||||
\(455\) | 1.49043e6 | 0.337506 | ||||||||
\(456\) | 1.41536e6 | 0.318752 | ||||||||
\(457\) | −4.09917e6 | −0.918132 | −0.459066 | − | 0.888402i | \(-0.651816\pi\) | ||||
−0.459066 | + | 0.888402i | \(0.651816\pi\) | |||||||
\(458\) | −811652. | −0.180803 | ||||||||
\(459\) | −2.32979e6 | −0.516160 | ||||||||
\(460\) | −1.61876e6 | −0.356687 | ||||||||
\(461\) | −2.62378e6 | −0.575009 | −0.287505 | − | 0.957779i | \(-0.592826\pi\) | ||||
−0.287505 | + | 0.957779i | \(0.592826\pi\) | |||||||
\(462\) | 465016. | 0.101359 | ||||||||
\(463\) | −4.28563e6 | −0.929100 | −0.464550 | − | 0.885547i | \(-0.653784\pi\) | ||||
−0.464550 | + | 0.885547i | \(0.653784\pi\) | |||||||
\(464\) | 2.33394e6 | 0.503262 | ||||||||
\(465\) | 1.88171e6 | 0.403571 | ||||||||
\(466\) | 558824. | 0.119209 | ||||||||
\(467\) | 990118. | 0.210085 | 0.105042 | − | 0.994468i | \(-0.466502\pi\) | ||||
0.105042 | + | 0.994468i | \(0.466502\pi\) | |||||||
\(468\) | 2.93052e6 | 0.618486 | ||||||||
\(469\) | 966792. | 0.202955 | ||||||||
\(470\) | 281291. | 0.0587369 | ||||||||
\(471\) | 1.02867e7 | 2.13660 | ||||||||
\(472\) | 654942. | 0.135316 | ||||||||
\(473\) | 1.10333e7 | 2.26753 | ||||||||
\(474\) | −436449. | −0.0892253 | ||||||||
\(475\) | 1.47039e6 | 0.299019 | ||||||||
\(476\) | −1.83047e6 | −0.370293 | ||||||||
\(477\) | 789812. | 0.158938 | ||||||||
\(478\) | −124457. | −0.0249144 | ||||||||
\(479\) | 2.57976e6 | 0.513737 | 0.256868 | − | 0.966446i | \(-0.417309\pi\) | ||||
0.256868 | + | 0.966446i | \(0.417309\pi\) | |||||||
\(480\) | −2.00150e6 | −0.396508 | ||||||||
\(481\) | −701093. | −0.138170 | ||||||||
\(482\) | −278272. | −0.0545571 | ||||||||
\(483\) | −1.05926e6 | −0.206601 | ||||||||
\(484\) | −8.89540e6 | −1.72604 | ||||||||
\(485\) | 1.07087e6 | 0.206720 | ||||||||
\(486\) | −699120. | −0.134264 | ||||||||
\(487\) | 3.21474e6 | 0.614219 | 0.307109 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307109 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(488\) | 655141. | 0.124533 | ||||||||
\(489\) | −8.63882e6 | −1.63374 | ||||||||
\(490\) | −81386.7 | −0.0153131 | ||||||||
\(491\) | −7.86108e6 | −1.47156 | −0.735781 | − | 0.677220i | \(-0.763185\pi\) | ||||
−0.735781 | + | 0.677220i | \(0.763185\pi\) | |||||||
\(492\) | −679192. | −0.126497 | ||||||||
\(493\) | 2.84465e6 | 0.527123 | ||||||||
\(494\) | 738341. | 0.136125 | ||||||||
\(495\) | −4.45610e6 | −0.817415 | ||||||||
\(496\) | −1.99480e6 | −0.364078 | ||||||||
\(497\) | 3.16357e6 | 0.574495 | ||||||||
\(498\) | −9630.55 | −0.00174011 | ||||||||
\(499\) | −1.35382e6 | −0.243395 | −0.121697 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121697 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(500\) | −5.98051e6 | −1.06983 | ||||||||
\(501\) | 5.48914e6 | 0.977035 | ||||||||
\(502\) | −1.13872e6 | −0.201677 | ||||||||
\(503\) | 3.85775e6 | 0.679851 | 0.339926 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339926 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(504\) | −322723. | −0.0565918 | ||||||||
\(505\) | 8.48376e6 | 1.48034 | ||||||||
\(506\) | −531341. | −0.0922565 | ||||||||
\(507\) | 1.02254e6 | 0.176669 | ||||||||
\(508\) | 4.13726e6 | 0.711301 | ||||||||
\(509\) | −1.06060e7 | −1.81451 | −0.907253 | − | 0.420585i | \(-0.861825\pi\) | ||||
−0.907253 | + | 0.420585i | \(0.861825\pi\) | |||||||
\(510\) | −790542. | −0.134586 | ||||||||
\(511\) | 1.39978e6 | 0.237142 | ||||||||
\(512\) | 3.55598e6 | 0.599493 | ||||||||
\(513\) | 3.07208e6 | 0.515394 | ||||||||
\(514\) | 573291. | 0.0957122 | ||||||||
\(515\) | −3.02804e6 | −0.503087 | ||||||||
\(516\) | −1.02443e7 | −1.69378 | ||||||||
\(517\) | −5.52747e6 | −0.909495 | ||||||||
\(518\) | 38284.1 | 0.00626895 | ||||||||
\(519\) | 1.95904e6 | 0.319246 | ||||||||
\(520\) | −1.39991e6 | −0.227034 | ||||||||
\(521\) | −9.17989e6 | −1.48164 | −0.740821 | − | 0.671703i | \(-0.765563\pi\) | ||||
−0.740821 | + | 0.671703i | \(0.765563\pi\) | |||||||
\(522\) | 248687. | 0.0399464 | ||||||||
\(523\) | 9.05585e6 | 1.44769 | 0.723844 | − | 0.689964i | \(-0.242373\pi\) | ||||
0.723844 | + | 0.689964i | \(0.242373\pi\) | |||||||
\(524\) | 1.09989e7 | 1.74993 | ||||||||
\(525\) | −904589. | −0.143236 | ||||||||
\(526\) | 336740. | 0.0530677 | ||||||||
\(527\) | −2.43130e6 | −0.381339 | ||||||||
\(528\) | 1.27455e7 | 1.98963 | ||||||||
\(529\) | −5.22601e6 | −0.811953 | ||||||||
\(530\) | −187084. | −0.0289299 | ||||||||
\(531\) | −2.03642e6 | −0.313422 | ||||||||
\(532\) | 2.41368e6 | 0.369744 | ||||||||
\(533\) | −714539. | −0.108945 | ||||||||
\(534\) | 1.79478e6 | 0.272369 | ||||||||
\(535\) | 6.92681e6 | 1.04628 | ||||||||
\(536\) | −908075. | −0.136524 | ||||||||
\(537\) | 6.48394e6 | 0.970295 | ||||||||
\(538\) | 1.44987e6 | 0.215960 | ||||||||
\(539\) | 1.59928e6 | 0.237112 | ||||||||
\(540\) | −2.88824e6 | −0.426235 | ||||||||
\(541\) | 1.21783e7 | 1.78894 | 0.894468 | − | 0.447132i | \(-0.147555\pi\) | ||||
0.894468 | + | 0.447132i | \(0.147555\pi\) | |||||||
\(542\) | 1.16953e6 | 0.171007 | ||||||||
\(543\) | −9.93891e6 | −1.44657 | ||||||||
\(544\) | 2.58608e6 | 0.374666 | ||||||||
\(545\) | 5.20292e6 | 0.750336 | ||||||||
\(546\) | −454230. | −0.0652070 | ||||||||
\(547\) | −9.00451e6 | −1.28674 | −0.643372 | − | 0.765554i | \(-0.722465\pi\) | ||||
−0.643372 | + | 0.765554i | \(0.722465\pi\) | |||||||
\(548\) | −1.21627e7 | −1.73013 | ||||||||
\(549\) | −2.03703e6 | −0.288448 | ||||||||
\(550\) | −453758. | −0.0639613 | ||||||||
\(551\) | −3.75099e6 | −0.526341 | ||||||||
\(552\) | 994924. | 0.138977 | ||||||||
\(553\) | −1.50103e6 | −0.208727 | ||||||||
\(554\) | −1.50904e6 | −0.208894 | ||||||||
\(555\) | −989830. | −0.136404 | ||||||||
\(556\) | −544167. | −0.0746527 | ||||||||
\(557\) | 1.54461e6 | 0.210950 | 0.105475 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105475 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(558\) | −212551. | −0.0288986 | ||||||||
\(559\) | −1.07774e7 | −1.45876 | ||||||||
\(560\) | −2.23070e6 | −0.300588 | ||||||||
\(561\) | 1.55345e7 | 2.08396 | ||||||||
\(562\) | −712057. | −0.0950986 | ||||||||
\(563\) | −1.18748e7 | −1.57890 | −0.789449 | − | 0.613816i | \(-0.789634\pi\) | ||||
−0.789449 | + | 0.613816i | \(0.789634\pi\) | |||||||
\(564\) | 5.13217e6 | 0.679365 | ||||||||
\(565\) | 2.01842e6 | 0.266005 | ||||||||
\(566\) | −1.01237e6 | −0.132831 | ||||||||
\(567\) | −3.59388e6 | −0.469468 | ||||||||
\(568\) | −2.97144e6 | −0.386452 | ||||||||
\(569\) | −1.54308e6 | −0.199806 | −0.0999031 | − | 0.994997i | \(-0.531853\pi\) | ||||
−0.0999031 | + | 0.994997i | \(0.531853\pi\) | |||||||
\(570\) | 1.04242e6 | 0.134386 | ||||||||
\(571\) | −7.01812e6 | −0.900804 | −0.450402 | − | 0.892826i | \(-0.648719\pi\) | ||||
−0.450402 | + | 0.892826i | \(0.648719\pi\) | |||||||
\(572\) | 1.36404e7 | 1.74317 | ||||||||
\(573\) | −1.25434e6 | −0.159598 | ||||||||
\(574\) | 39018.4 | 0.00494298 | ||||||||
\(575\) | 1.03361e6 | 0.130373 | ||||||||
\(576\) | −4.23326e6 | −0.531641 | ||||||||
\(577\) | −5.37543e6 | −0.672162 | −0.336081 | − | 0.941833i | \(-0.609102\pi\) | ||||
−0.336081 | + | 0.941833i | \(0.609102\pi\) | |||||||
\(578\) | −8077.66 | −0.00100569 | ||||||||
\(579\) | 9.22259e6 | 1.14329 | ||||||||
\(580\) | 3.52652e6 | 0.435288 | ||||||||
\(581\) | −33121.4 | −0.00407069 | ||||||||
\(582\) | −326365. | −0.0399389 | ||||||||
\(583\) | 3.67627e6 | 0.447957 | ||||||||
\(584\) | −1.31477e6 | −0.159521 | ||||||||
\(585\) | 4.35274e6 | 0.525864 | ||||||||
\(586\) | 1.85770e6 | 0.223476 | ||||||||
\(587\) | −2.06682e6 | −0.247575 | −0.123788 | − | 0.992309i | \(-0.539504\pi\) | ||||
−0.123788 | + | 0.992309i | \(0.539504\pi\) | |||||||
\(588\) | −1.48491e6 | −0.177115 | ||||||||
\(589\) | 3.20594e6 | 0.380774 | ||||||||
\(590\) | 482369. | 0.0570492 | ||||||||
\(591\) | 5.26648e6 | 0.620228 | ||||||||
\(592\) | 1.04932e6 | 0.123056 | ||||||||
\(593\) | −5.46947e6 | −0.638717 | −0.319358 | − | 0.947634i | \(-0.603467\pi\) | ||||
−0.319358 | + | 0.947634i | \(0.603467\pi\) | |||||||
\(594\) | −948035. | −0.110245 | ||||||||
\(595\) | −2.71883e6 | −0.314840 | ||||||||
\(596\) | 3.53049e6 | 0.407117 | ||||||||
\(597\) | −1.18912e7 | −1.36550 | ||||||||
\(598\) | 519016. | 0.0593510 | ||||||||
\(599\) | 1.09943e7 | 1.25199 | 0.625996 | − | 0.779826i | \(-0.284693\pi\) | ||||
0.625996 | + | 0.779826i | \(0.284693\pi\) | |||||||
\(600\) | 849651. | 0.0963524 | ||||||||
\(601\) | 1.58788e7 | 1.79322 | 0.896608 | − | 0.442826i | \(-0.146024\pi\) | ||||
0.896608 | + | 0.442826i | \(0.146024\pi\) | |||||||
\(602\) | 588514. | 0.0661859 | ||||||||
\(603\) | 2.82348e6 | 0.316222 | ||||||||
\(604\) | −959820. | −0.107053 | ||||||||
\(605\) | −1.32125e7 | −1.46756 | ||||||||
\(606\) | −2.58555e6 | −0.286004 | ||||||||
\(607\) | 5.33262e6 | 0.587447 | 0.293724 | − | 0.955890i | \(-0.405105\pi\) | ||||
0.293724 | + | 0.955890i | \(0.405105\pi\) | |||||||
\(608\) | −3.41003e6 | −0.374110 | ||||||||
\(609\) | 2.30762e6 | 0.252128 | ||||||||
\(610\) | 482516. | 0.0525033 | ||||||||
\(611\) | 5.39926e6 | 0.585102 | ||||||||
\(612\) | −5.34584e6 | −0.576949 | ||||||||
\(613\) | −8.91838e6 | −0.958594 | −0.479297 | − | 0.877653i | \(-0.659108\pi\) | ||||
−0.479297 | + | 0.877653i | \(0.659108\pi\) | |||||||
\(614\) | −641593. | −0.0686814 | ||||||||
\(615\) | −1.00881e6 | −0.107553 | ||||||||
\(616\) | −1.50215e6 | −0.159501 | ||||||||
\(617\) | 9.63586e6 | 1.01901 | 0.509504 | − | 0.860468i | \(-0.329829\pi\) | ||||
0.509504 | + | 0.860468i | \(0.329829\pi\) | |||||||
\(618\) | 922841. | 0.0971976 | ||||||||
\(619\) | 1.21747e7 | 1.27712 | 0.638560 | − | 0.769572i | \(-0.279530\pi\) | ||||
0.638560 | + | 0.769572i | \(0.279530\pi\) | |||||||
\(620\) | −3.01409e6 | −0.314903 | ||||||||
\(621\) | 2.15952e6 | 0.224713 | ||||||||
\(622\) | 1.30602e6 | 0.135355 | ||||||||
\(623\) | 6.17260e6 | 0.637159 | ||||||||
\(624\) | −1.24498e7 | −1.27998 | ||||||||
\(625\) | −5.94695e6 | −0.608968 | ||||||||
\(626\) | 689094. | 0.0702818 | ||||||||
\(627\) | −2.04839e7 | −2.08087 | ||||||||
\(628\) | −1.64770e7 | −1.66717 | ||||||||
\(629\) | 1.27893e6 | 0.128890 | ||||||||
\(630\) | −237687. | −0.0238591 | ||||||||
\(631\) | −1.30854e7 | −1.30832 | −0.654161 | − | 0.756356i | \(-0.726978\pi\) | ||||
−0.654161 | + | 0.756356i | \(0.726978\pi\) | |||||||
\(632\) | 1.40987e6 | 0.140407 | ||||||||
\(633\) | 6.59023e6 | 0.653719 | ||||||||
\(634\) | 2.20626e6 | 0.217989 | ||||||||
\(635\) | 6.14513e6 | 0.604779 | ||||||||
\(636\) | −3.41336e6 | −0.334610 | ||||||||
\(637\) | −1.56219e6 | −0.152540 | ||||||||
\(638\) | 1.15754e6 | 0.112586 | ||||||||
\(639\) | 9.23911e6 | 0.895113 | ||||||||
\(640\) | 4.26226e6 | 0.411329 | ||||||||
\(641\) | −441107. | −0.0424032 | −0.0212016 | − | 0.999775i | \(-0.506749\pi\) | ||||
−0.0212016 | + | 0.999775i | \(0.506749\pi\) | |||||||
\(642\) | −2.11105e6 | −0.202144 | ||||||||
\(643\) | −4.18888e6 | −0.399550 | −0.199775 | − | 0.979842i | \(-0.564021\pi\) | ||||
−0.199775 | + | 0.979842i | \(0.564021\pi\) | |||||||
\(644\) | 1.69670e6 | 0.161209 | ||||||||
\(645\) | −1.52159e7 | −1.44012 | ||||||||
\(646\) | −1.34688e6 | −0.126983 | ||||||||
\(647\) | 1.87822e7 | 1.76395 | 0.881973 | − | 0.471300i | \(-0.156215\pi\) | ||||
0.881973 | + | 0.471300i | \(0.156215\pi\) | |||||||
\(648\) | 3.37562e6 | 0.315803 | ||||||||
\(649\) | −9.47874e6 | −0.883362 | ||||||||
\(650\) | 443233. | 0.0411480 | ||||||||
\(651\) | −1.97231e6 | −0.182399 | ||||||||
\(652\) | 1.38375e7 | 1.27479 | ||||||||
\(653\) | −1.51733e6 | −0.139251 | −0.0696254 | − | 0.997573i | \(-0.522180\pi\) | ||||
−0.0696254 | + | 0.997573i | \(0.522180\pi\) | |||||||
\(654\) | −1.58567e6 | −0.144967 | ||||||||
\(655\) | 1.63368e7 | 1.48787 | ||||||||
\(656\) | 1.06944e6 | 0.0970281 | ||||||||
\(657\) | 4.08802e6 | 0.369487 | ||||||||
\(658\) | −294834. | −0.0265468 | ||||||||
\(659\) | 1.84809e7 | 1.65772 | 0.828859 | − | 0.559458i | \(-0.188991\pi\) | ||||
0.828859 | + | 0.559458i | \(0.188991\pi\) | |||||||
\(660\) | 1.92581e7 | 1.72089 | ||||||||
\(661\) | −1.03952e7 | −0.925403 | −0.462702 | − | 0.886514i | \(-0.653120\pi\) | ||||
−0.462702 | + | 0.886514i | \(0.653120\pi\) | |||||||
\(662\) | −1.59240e6 | −0.141223 | ||||||||
\(663\) | −1.51741e7 | −1.34066 | ||||||||
\(664\) | 31109.8 | 0.00273828 | ||||||||
\(665\) | 3.58508e6 | 0.314372 | ||||||||
\(666\) | 111808. | 0.00976756 | ||||||||
\(667\) | −2.63676e6 | −0.229486 | ||||||||
\(668\) | −8.79242e6 | −0.762372 | ||||||||
\(669\) | 2.01458e7 | 1.74028 | ||||||||
\(670\) | −668803. | −0.0575587 | ||||||||
\(671\) | −9.48162e6 | −0.812973 | ||||||||
\(672\) | 2.09786e6 | 0.179207 | ||||||||
\(673\) | −1.10398e7 | −0.939556 | −0.469778 | − | 0.882785i | \(-0.655666\pi\) | ||||
−0.469778 | + | 0.882785i | \(0.655666\pi\) | |||||||
\(674\) | −1.75101e6 | −0.148470 | ||||||||
\(675\) | 1.84420e6 | 0.155793 | ||||||||
\(676\) | −1.63788e6 | −0.137853 | ||||||||
\(677\) | −8.23485e6 | −0.690532 | −0.345266 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345266 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(678\) | −615144. | −0.0513928 | ||||||||
\(679\) | −1.12243e6 | −0.0934298 | ||||||||
\(680\) | 2.55371e6 | 0.211787 | ||||||||
\(681\) | −9.90780e6 | −0.818671 | ||||||||
\(682\) | −989343. | −0.0814490 | ||||||||
\(683\) | 1.98437e7 | 1.62768 | 0.813842 | − | 0.581086i | \(-0.197372\pi\) | ||||
0.813842 | + | 0.581086i | \(0.197372\pi\) | |||||||
\(684\) | 7.04909e6 | 0.576093 | ||||||||
\(685\) | −1.80655e7 | −1.47103 | ||||||||
\(686\) | 85305.3 | 0.00692095 | ||||||||
\(687\) | −2.19955e7 | −1.77804 | ||||||||
\(688\) | 1.61304e7 | 1.29919 | ||||||||
\(689\) | −3.59100e6 | −0.288182 | ||||||||
\(690\) | 732767. | 0.0585927 | ||||||||
\(691\) | −2.37019e6 | −0.188837 | −0.0944185 | − | 0.995533i | \(-0.530099\pi\) | ||||
−0.0944185 | + | 0.995533i | \(0.530099\pi\) | |||||||
\(692\) | −3.13796e6 | −0.249105 | ||||||||
\(693\) | 4.67065e6 | 0.369440 | ||||||||
\(694\) | −789131. | −0.0621943 | ||||||||
\(695\) | −808259. | −0.0634730 | ||||||||
\(696\) | −2.16748e6 | −0.169602 | ||||||||
\(697\) | 1.30346e6 | 0.101628 | ||||||||
\(698\) | 2.02491e6 | 0.157314 | ||||||||
\(699\) | 1.51439e7 | 1.17232 | ||||||||
\(700\) | 1.44896e6 | 0.111766 | ||||||||
\(701\) | −1.56833e7 | −1.20543 | −0.602714 | − | 0.797957i | \(-0.705914\pi\) | ||||
−0.602714 | + | 0.797957i | \(0.705914\pi\) | |||||||
\(702\) | 926045. | 0.0709234 | ||||||||
\(703\) | −1.68641e6 | −0.128699 | ||||||||
\(704\) | −1.97042e7 | −1.49840 | ||||||||
\(705\) | 7.62288e6 | 0.577626 | ||||||||
\(706\) | 1.83543e6 | 0.138588 | ||||||||
\(707\) | −8.89223e6 | −0.669056 | ||||||||
\(708\) | 8.80085e6 | 0.659844 | ||||||||
\(709\) | 3.68544e6 | 0.275343 | 0.137671 | − | 0.990478i | \(-0.456038\pi\) | ||||
0.137671 | + | 0.990478i | \(0.456038\pi\) | |||||||
\(710\) | −2.18848e6 | −0.162928 | ||||||||
\(711\) | −4.38373e6 | −0.325214 | ||||||||
\(712\) | −5.79772e6 | −0.428605 | ||||||||
\(713\) | 2.25361e6 | 0.166018 | ||||||||
\(714\) | 828604. | 0.0608277 | ||||||||
\(715\) | 2.02604e7 | 1.48212 | ||||||||
\(716\) | −1.03859e7 | −0.757113 | ||||||||
\(717\) | −3.37276e6 | −0.245012 | ||||||||
\(718\) | 790544. | 0.0572289 | ||||||||
\(719\) | −1.56427e7 | −1.12847 | −0.564233 | − | 0.825615i | \(-0.690828\pi\) | ||||
−0.564233 | + | 0.825615i | \(0.690828\pi\) | |||||||
\(720\) | −6.51470e6 | −0.468342 | ||||||||
\(721\) | 3.17383e6 | 0.227376 | ||||||||
\(722\) | −19369.0 | −0.00138282 | ||||||||
\(723\) | −7.54107e6 | −0.536522 | ||||||||
\(724\) | 1.59200e7 | 1.12875 | ||||||||
\(725\) | −2.25175e6 | −0.159102 | ||||||||
\(726\) | 4.02670e6 | 0.283536 | ||||||||
\(727\) | 1.85908e7 | 1.30456 | 0.652279 | − | 0.757979i | \(-0.273813\pi\) | ||||
0.652279 | + | 0.757979i | \(0.273813\pi\) | |||||||
\(728\) | 1.46731e6 | 0.102611 | ||||||||
\(729\) | −1.12318e6 | −0.0782767 | ||||||||
\(730\) | −968335. | −0.0672541 | ||||||||
\(731\) | 1.96601e7 | 1.36079 | ||||||||
\(732\) | 8.80353e6 | 0.607266 | ||||||||
\(733\) | 2.49466e7 | 1.71495 | 0.857476 | − | 0.514524i | \(-0.172031\pi\) | ||||
0.857476 | + | 0.514524i | \(0.172031\pi\) | |||||||
\(734\) | 136367. | 0.00934260 | ||||||||
\(735\) | −2.20555e6 | −0.150591 | ||||||||
\(736\) | −2.39708e6 | −0.163113 | ||||||||
\(737\) | 1.31422e7 | 0.891253 | ||||||||
\(738\) | 113952. | 0.00770159 | ||||||||
\(739\) | −2.42944e7 | −1.63642 | −0.818211 | − | 0.574918i | \(-0.805034\pi\) | ||||
−0.818211 | + | 0.574918i | \(0.805034\pi\) | |||||||
\(740\) | 1.58549e6 | 0.106435 | ||||||||
\(741\) | 2.00088e7 | 1.33868 | ||||||||
\(742\) | 196091. | 0.0130752 | ||||||||
\(743\) | 4.16541e6 | 0.276812 | 0.138406 | − | 0.990376i | \(-0.455802\pi\) | ||||
0.138406 | + | 0.990376i | \(0.455802\pi\) | |||||||
\(744\) | 1.85252e6 | 0.122696 | ||||||||
\(745\) | 5.24388e6 | 0.346148 | ||||||||
\(746\) | −1.30059e6 | −0.0855644 | ||||||||
\(747\) | −96729.9 | −0.00634248 | ||||||||
\(748\) | −2.48828e7 | −1.62610 | ||||||||
\(749\) | −7.26032e6 | −0.472880 | ||||||||
\(750\) | 2.70721e6 | 0.175739 | ||||||||
\(751\) | −2.36434e7 | −1.52972 | −0.764858 | − | 0.644199i | \(-0.777191\pi\) | ||||
−0.764858 | + | 0.644199i | \(0.777191\pi\) | |||||||
\(752\) | −8.08101e6 | −0.521100 | ||||||||
\(753\) | −3.08588e7 | −1.98332 | ||||||||
\(754\) | −1.13070e6 | −0.0724298 | ||||||||
\(755\) | −1.42564e6 | −0.0910209 | ||||||||
\(756\) | 3.02730e6 | 0.192642 | ||||||||
\(757\) | 1.50108e7 | 0.952062 | 0.476031 | − | 0.879429i | \(-0.342075\pi\) | ||||
0.476031 | + | 0.879429i | \(0.342075\pi\) | |||||||
\(758\) | 2.60164e6 | 0.164465 | ||||||||
\(759\) | −1.43992e7 | −0.907262 | ||||||||
\(760\) | −3.36735e6 | −0.211472 | ||||||||
\(761\) | 2.92191e6 | 0.182897 | 0.0914483 | − | 0.995810i | \(-0.470850\pi\) | ||||
0.0914483 | + | 0.995810i | \(0.470850\pi\) | |||||||
\(762\) | −1.87282e6 | −0.116845 | ||||||||
\(763\) | −5.45343e6 | −0.339124 | ||||||||
\(764\) | 2.00918e6 | 0.124533 | ||||||||
\(765\) | −7.94025e6 | −0.490547 | ||||||||
\(766\) | −2.48310e6 | −0.152905 | ||||||||
\(767\) | 9.25887e6 | 0.568290 | ||||||||
\(768\) | 1.73016e7 | 1.05848 | ||||||||
\(769\) | 1.42847e7 | 0.871073 | 0.435536 | − | 0.900171i | \(-0.356559\pi\) | ||||
0.435536 | + | 0.900171i | \(0.356559\pi\) | |||||||
\(770\) | −1.10634e6 | −0.0672455 | ||||||||
\(771\) | 1.55360e7 | 0.941246 | ||||||||
\(772\) | −1.47726e7 | −0.892100 | ||||||||
\(773\) | −1.09012e7 | −0.656186 | −0.328093 | − | 0.944645i | \(-0.606406\pi\) | ||||
−0.328093 | + | 0.944645i | \(0.606406\pi\) | |||||||
\(774\) | 1.71874e6 | 0.103123 | ||||||||
\(775\) | 1.92455e6 | 0.115100 | ||||||||
\(776\) | 1.05426e6 | 0.0628485 | ||||||||
\(777\) | 1.03749e6 | 0.0616496 | ||||||||
\(778\) | 6254.04 | 0.000370434 0 | ||||||||
\(779\) | −1.71875e6 | −0.101478 | ||||||||
\(780\) | −1.88114e7 | −1.10710 | ||||||||
\(781\) | 4.30045e7 | 2.52282 | ||||||||
\(782\) | −946787. | −0.0553650 | ||||||||
\(783\) | −4.70459e6 | −0.274231 | ||||||||
\(784\) | 2.33811e6 | 0.135854 | ||||||||
\(785\) | −2.44736e7 | −1.41750 | ||||||||
\(786\) | −4.97890e6 | −0.287460 | ||||||||
\(787\) | −2.56449e7 | −1.47593 | −0.737963 | − | 0.674841i | \(-0.764212\pi\) | ||||
−0.737963 | + | 0.674841i | \(0.764212\pi\) | |||||||
\(788\) | −8.43576e6 | −0.483959 | ||||||||
\(789\) | 9.12555e6 | 0.521875 | ||||||||
\(790\) | 1.03838e6 | 0.0591955 | ||||||||
\(791\) | −2.11560e6 | −0.120224 | ||||||||
\(792\) | −4.38699e6 | −0.248516 | ||||||||
\(793\) | 9.26169e6 | 0.523007 | ||||||||
\(794\) | 911498. | 0.0513103 | ||||||||
\(795\) | −5.06991e6 | −0.284500 | ||||||||
\(796\) | 1.90472e7 | 1.06549 | ||||||||
\(797\) | 7.73086e6 | 0.431104 | 0.215552 | − | 0.976492i | \(-0.430845\pi\) | ||||
0.215552 | + | 0.976492i | \(0.430845\pi\) | |||||||
\(798\) | −1.09261e6 | −0.0607375 | ||||||||
\(799\) | −9.84931e6 | −0.545807 | ||||||||
\(800\) | −2.04707e6 | −0.113086 | ||||||||
\(801\) | 1.80269e7 | 0.992748 | ||||||||
\(802\) | 1.03448e6 | 0.0567917 | ||||||||
\(803\) | 1.90282e7 | 1.04138 | ||||||||
\(804\) | −1.22024e7 | −0.665738 | ||||||||
\(805\) | 2.52013e6 | 0.137067 | ||||||||
\(806\) | 966395. | 0.0523983 | ||||||||
\(807\) | 3.92909e7 | 2.12377 | ||||||||
\(808\) | 8.35218e6 | 0.450061 | ||||||||
\(809\) | −1.87811e7 | −1.00890 | −0.504452 | − | 0.863440i | \(-0.668305\pi\) | ||||
−0.504452 | + | 0.863440i | \(0.668305\pi\) | |||||||
\(810\) | 2.48616e6 | 0.133143 | ||||||||
\(811\) | −9.00729e6 | −0.480886 | −0.240443 | − | 0.970663i | \(-0.577293\pi\) | ||||
−0.240443 | + | 0.970663i | \(0.577293\pi\) | |||||||
\(812\) | −3.69632e6 | −0.196734 | ||||||||
\(813\) | 3.16939e7 | 1.68170 | ||||||||
\(814\) | 520422. | 0.0275293 | ||||||||
\(815\) | 2.05531e7 | 1.08388 | ||||||||
\(816\) | 2.27110e7 | 1.19402 | ||||||||
\(817\) | −2.59240e7 | −1.35877 | ||||||||
\(818\) | −2.22259e6 | −0.116138 | ||||||||
\(819\) | −4.56231e6 | −0.237671 | ||||||||
\(820\) | 1.61590e6 | 0.0839228 | ||||||||
\(821\) | −9.27965e6 | −0.480478 | −0.240239 | − | 0.970714i | \(-0.577226\pi\) | ||||
−0.240239 | + | 0.970714i | \(0.577226\pi\) | |||||||
\(822\) | 5.50572e6 | 0.284207 | ||||||||
\(823\) | −1.08308e7 | −0.557393 | −0.278697 | − | 0.960379i | \(-0.589902\pi\) | ||||
−0.278697 | + | 0.960379i | \(0.589902\pi\) | |||||||
\(824\) | −2.98107e6 | −0.152952 | ||||||||
\(825\) | −1.22967e7 | −0.629004 | ||||||||
\(826\) | −505593. | −0.0257841 | ||||||||
\(827\) | −2.05230e7 | −1.04346 | −0.521731 | − | 0.853110i | \(-0.674714\pi\) | ||||
−0.521731 | + | 0.853110i | \(0.674714\pi\) | |||||||
\(828\) | 4.95515e6 | 0.251178 | ||||||||
\(829\) | −1.42216e7 | −0.718724 | −0.359362 | − | 0.933198i | \(-0.617006\pi\) | ||||
−0.359362 | + | 0.933198i | \(0.617006\pi\) | |||||||
\(830\) | 22912.6 | 0.00115446 | ||||||||
\(831\) | −4.08944e7 | −2.05429 | ||||||||
\(832\) | 1.92472e7 | 0.963958 | ||||||||
\(833\) | 2.84973e6 | 0.142296 | ||||||||
\(834\) | 246329. | 0.0122631 | ||||||||
\(835\) | −1.30595e7 | −0.648202 | ||||||||
\(836\) | 3.28108e7 | 1.62368 | ||||||||
\(837\) | 4.02097e6 | 0.198389 | ||||||||
\(838\) | −179995. | −0.00885421 | ||||||||
\(839\) | −9.29934e6 | −0.456087 | −0.228043 | − | 0.973651i | \(-0.573233\pi\) | ||||
−0.228043 | + | 0.973651i | \(0.573233\pi\) | |||||||
\(840\) | 2.07160e6 | 0.101300 | ||||||||
\(841\) | −1.47669e7 | −0.719944 | ||||||||
\(842\) | 4.32353e6 | 0.210164 | ||||||||
\(843\) | −1.92965e7 | −0.935211 | ||||||||
\(844\) | −1.05561e7 | −0.510092 | ||||||||
\(845\) | −2.43277e6 | −0.117209 | ||||||||
\(846\) | −861053. | −0.0413623 | ||||||||
\(847\) | 1.38486e7 | 0.663281 | ||||||||
\(848\) | 5.37461e6 | 0.256659 | ||||||||
\(849\) | −2.74350e7 | −1.30628 | ||||||||
\(850\) | −808543. | −0.0383845 | ||||||||
\(851\) | −1.18546e6 | −0.0561131 | ||||||||
\(852\) | −3.99290e7 | −1.88447 | ||||||||
\(853\) | −3.07436e6 | −0.144671 | −0.0723357 | − | 0.997380i | \(-0.523045\pi\) | ||||
−0.0723357 | + | 0.997380i | \(0.523045\pi\) | |||||||
\(854\) | −505747. | −0.0237295 | ||||||||
\(855\) | 1.04701e7 | 0.489819 | ||||||||
\(856\) | 6.81938e6 | 0.318098 | ||||||||
\(857\) | 3.45835e7 | 1.60848 | 0.804242 | − | 0.594302i | \(-0.202572\pi\) | ||||
0.804242 | + | 0.594302i | \(0.202572\pi\) | |||||||
\(858\) | −6.17465e6 | −0.286348 | ||||||||
\(859\) | 1.63022e7 | 0.753814 | 0.376907 | − | 0.926251i | \(-0.376988\pi\) | ||||
0.376907 | + | 0.926251i | \(0.376988\pi\) | |||||||
\(860\) | 2.43726e7 | 1.12372 | ||||||||
\(861\) | 1.05738e6 | 0.0486099 | ||||||||
\(862\) | −3.57856e6 | −0.164036 | ||||||||
\(863\) | 2.56962e7 | 1.17447 | 0.587235 | − | 0.809416i | \(-0.300216\pi\) | ||||
0.587235 | + | 0.809416i | \(0.300216\pi\) | |||||||
\(864\) | −4.27694e6 | −0.194917 | ||||||||
\(865\) | −4.66087e6 | −0.211800 | ||||||||
\(866\) | 3.01281e6 | 0.136514 | ||||||||
\(867\) | −218902. | −0.00989012 | ||||||||
\(868\) | 3.15921e6 | 0.142324 | ||||||||
\(869\) | −2.04046e7 | −0.916596 | ||||||||
\(870\) | −1.59636e6 | −0.0715043 | ||||||||
\(871\) | −1.28374e7 | −0.573366 | ||||||||
\(872\) | 5.12222e6 | 0.228122 | ||||||||
\(873\) | −3.27803e6 | −0.145572 | ||||||||
\(874\) | 1.24844e6 | 0.0552829 | ||||||||
\(875\) | 9.31062e6 | 0.411111 | ||||||||
\(876\) | −1.76673e7 | −0.777877 | ||||||||
\(877\) | 3.30060e7 | 1.44908 | 0.724542 | − | 0.689230i | \(-0.242051\pi\) | ||||
0.724542 | + | 0.689230i | \(0.242051\pi\) | |||||||
\(878\) | −165286. | −0.00723603 | ||||||||
\(879\) | 5.03429e7 | 2.19769 | ||||||||
\(880\) | −3.03235e7 | −1.31999 | ||||||||
\(881\) | 2.26705e6 | 0.0984060 | 0.0492030 | − | 0.998789i | \(-0.484332\pi\) | ||||
0.0492030 | + | 0.998789i | \(0.484332\pi\) | |||||||
\(882\) | 249131. | 0.0107834 | ||||||||
\(883\) | 1.97779e7 | 0.853649 | 0.426825 | − | 0.904334i | \(-0.359632\pi\) | ||||
0.426825 | + | 0.904334i | \(0.359632\pi\) | |||||||
\(884\) | 2.43057e7 | 1.04611 | ||||||||
\(885\) | 1.30720e7 | 0.561029 | ||||||||
\(886\) | −1.43901e6 | −0.0615858 | ||||||||
\(887\) | −36468.3 | −0.00155635 | −0.000778173 | − | 1.00000i | \(-0.500248\pi\) | ||||
−0.000778173 | 1.00000i | \(0.500248\pi\) | ||||||||
\(888\) | −974478. | −0.0414705 | ||||||||
\(889\) | −6.44100e6 | −0.273337 | ||||||||
\(890\) | −4.27005e6 | −0.180700 | ||||||||
\(891\) | −4.88541e7 | −2.06161 | ||||||||
\(892\) | −3.22692e7 | −1.35793 | ||||||||
\(893\) | 1.29874e7 | 0.544997 | ||||||||
\(894\) | −1.59815e6 | −0.0668767 | ||||||||
\(895\) | −1.54263e7 | −0.643730 | ||||||||
\(896\) | −4.46747e6 | −0.185905 | ||||||||
\(897\) | 1.40652e7 | 0.583665 | ||||||||
\(898\) | 1.89303e6 | 0.0783367 | ||||||||
\(899\) | −4.90958e6 | −0.202602 | ||||||||
\(900\) | 4.23163e6 | 0.174141 | ||||||||
\(901\) | 6.55068e6 | 0.268828 | ||||||||
\(902\) | 530403. | 0.0217065 | ||||||||
\(903\) | 1.59485e7 | 0.650881 | ||||||||
\(904\) | 1.98711e6 | 0.0808727 | ||||||||
\(905\) | 2.36462e7 | 0.959709 | ||||||||
\(906\) | 434484. | 0.0175854 | ||||||||
\(907\) | 1.62298e7 | 0.655079 | 0.327540 | − | 0.944837i | \(-0.393781\pi\) | ||||
0.327540 | + | 0.944837i | \(0.393781\pi\) | |||||||
\(908\) | 1.58702e7 | 0.638802 | ||||||||
\(909\) | −2.59695e7 | −1.04245 | ||||||||
\(910\) | 1.08068e6 | 0.0432608 | ||||||||
\(911\) | −2.61699e7 | −1.04474 | −0.522368 | − | 0.852720i | \(-0.674951\pi\) | ||||
−0.522368 | + | 0.852720i | \(0.674951\pi\) | |||||||
\(912\) | −2.99469e7 | −1.19224 | ||||||||
\(913\) | −450241. | −0.0178759 | ||||||||
\(914\) | −2.97224e6 | −0.117684 | ||||||||
\(915\) | 1.30760e7 | 0.516324 | ||||||||
\(916\) | 3.52320e7 | 1.38739 | ||||||||
\(917\) | −1.71234e7 | −0.672461 | ||||||||
\(918\) | −1.68929e6 | −0.0661602 | ||||||||
\(919\) | 4.05973e6 | 0.158565 | 0.0792826 | − | 0.996852i | \(-0.474737\pi\) | ||||
0.0792826 | + | 0.996852i | \(0.474737\pi\) | |||||||
\(920\) | −2.36708e6 | −0.0922025 | ||||||||
\(921\) | −1.73870e7 | −0.675421 | ||||||||
\(922\) | −1.90246e6 | −0.0737034 | ||||||||
\(923\) | −4.20070e7 | −1.62300 | ||||||||
\(924\) | −2.01853e7 | −0.777778 | ||||||||
\(925\) | −1.01237e6 | −0.0389031 | ||||||||
\(926\) | −3.10744e6 | −0.119090 | ||||||||
\(927\) | 9.26907e6 | 0.354272 | ||||||||
\(928\) | 5.22212e6 | 0.199057 | ||||||||
\(929\) | 3.69518e6 | 0.140474 | 0.0702370 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702370 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(930\) | 1.36439e6 | 0.0517288 | ||||||||
\(931\) | −3.75769e6 | −0.142084 | ||||||||
\(932\) | −2.42573e7 | −0.914751 | ||||||||
\(933\) | 3.53927e7 | 1.33110 | ||||||||
\(934\) | 717918. | 0.0269282 | ||||||||
\(935\) | −3.69589e7 | −1.38258 | ||||||||
\(936\) | 4.28523e6 | 0.159877 | ||||||||
\(937\) | −1.91384e7 | −0.712126 | −0.356063 | − | 0.934462i | \(-0.615881\pi\) | ||||
−0.356063 | + | 0.934462i | \(0.615881\pi\) | |||||||
\(938\) | 701004. | 0.0260144 | ||||||||
\(939\) | 1.86742e7 | 0.691160 | ||||||||
\(940\) | −1.22102e7 | −0.450717 | ||||||||
\(941\) | 1.20954e7 | 0.445294 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(942\) | 7.45870e6 | 0.273865 | ||||||||
\(943\) | −1.20820e6 | −0.0442445 | ||||||||
\(944\) | −1.38577e7 | −0.506127 | ||||||||
\(945\) | 4.49649e6 | 0.163793 | ||||||||
\(946\) | 8.00007e6 | 0.290647 | ||||||||
\(947\) | −1.95969e7 | −0.710087 | −0.355044 | − | 0.934850i | \(-0.615534\pi\) | ||||
−0.355044 | + | 0.934850i | \(0.615534\pi\) | |||||||
\(948\) | 1.89453e7 | 0.684669 | ||||||||
\(949\) | −1.85868e7 | −0.669945 | ||||||||
\(950\) | 1.06615e6 | 0.0383275 | ||||||||
\(951\) | 5.97890e7 | 2.14373 | ||||||||
\(952\) | −2.67666e6 | −0.0957196 | ||||||||
\(953\) | 4.23265e7 | 1.50966 | 0.754832 | − | 0.655918i | \(-0.227718\pi\) | ||||
0.754832 | + | 0.655918i | \(0.227718\pi\) | |||||||
\(954\) | 572679. | 0.0203723 | ||||||||
\(955\) | 2.98426e6 | 0.105884 | ||||||||
\(956\) | 5.40243e6 | 0.191181 | ||||||||
\(957\) | 3.13691e7 | 1.10719 | ||||||||
\(958\) | 1.87054e6 | 0.0658496 | ||||||||
\(959\) | 1.89353e7 | 0.664852 | ||||||||
\(960\) | 2.71739e7 | 0.951642 | ||||||||
\(961\) | −2.44330e7 | −0.853430 | ||||||||
\(962\) | −508351. | −0.0177103 | ||||||||
\(963\) | −2.12035e7 | −0.736788 | ||||||||
\(964\) | 1.20792e7 | 0.418644 | ||||||||
\(965\) | −2.19419e7 | −0.758502 | ||||||||
\(966\) | −768048. | −0.0264817 | ||||||||
\(967\) | 1.39211e6 | 0.0478749 | 0.0239375 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239375 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(968\) | −1.30075e7 | −0.446176 | ||||||||
\(969\) | −3.64999e7 | −1.24877 | ||||||||
\(970\) | 776471. | 0.0264970 | ||||||||
\(971\) | 4.41877e7 | 1.50402 | 0.752009 | − | 0.659153i | \(-0.229085\pi\) | ||||
0.752009 | + | 0.659153i | \(0.229085\pi\) | |||||||
\(972\) | 3.03473e7 | 1.03028 | ||||||||
\(973\) | 847175. | 0.0286874 | ||||||||
\(974\) | 2.33095e6 | 0.0787292 | ||||||||
\(975\) | 1.20115e7 | 0.404654 | ||||||||
\(976\) | −1.38619e7 | −0.465798 | ||||||||
\(977\) | −5.60457e7 | −1.87848 | −0.939239 | − | 0.343264i | \(-0.888467\pi\) | ||||
−0.939239 | + | 0.343264i | \(0.888467\pi\) | |||||||
\(978\) | −6.26386e6 | −0.209409 | ||||||||
\(979\) | 8.39082e7 | 2.79800 | ||||||||
\(980\) | 3.53282e6 | 0.117505 | ||||||||
\(981\) | −1.59266e7 | −0.528384 | ||||||||
\(982\) | −5.69993e6 | −0.188621 | ||||||||
\(983\) | −5.00560e7 | −1.65224 | −0.826118 | − | 0.563497i | \(-0.809456\pi\) | ||||
−0.826118 | + | 0.563497i | \(0.809456\pi\) | |||||||
\(984\) | −993166. | −0.0326990 | ||||||||
\(985\) | −1.25298e7 | −0.411483 | ||||||||
\(986\) | 2.06261e6 | 0.0675654 | ||||||||
\(987\) | −7.98990e6 | −0.261065 | ||||||||
\(988\) | −3.20497e7 | −1.04456 | ||||||||
\(989\) | −1.82233e7 | −0.592428 | ||||||||
\(990\) | −3.23104e6 | −0.104774 | ||||||||
\(991\) | 1.59116e7 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(992\) | −4.46330e6 | −0.144005 | ||||||||
\(993\) | −4.31534e7 | −1.38881 | ||||||||
\(994\) | 2.29385e6 | 0.0736375 | ||||||||
\(995\) | 2.82911e7 | 0.905924 | ||||||||
\(996\) | 418041. | 0.0133528 | ||||||||
\(997\) | 4.25995e7 | 1.35727 | 0.678635 | − | 0.734476i | \(-0.262572\pi\) | ||||
0.678635 | + | 0.734476i | \(0.262572\pi\) | |||||||
\(998\) | −981634. | −0.0311978 | ||||||||
\(999\) | −2.11514e6 | −0.0670542 |
(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 | 7.6.a.b.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 63.6.a.f.1.2 | 2 | |||
4.3 | odd | 2 | 112.6.a.h.1.1 | 2 | |||
5.2 | odd | 4 | 175.6.b.c.99.3 | 4 | |||
5.3 | odd | 4 | 175.6.b.c.99.2 | 4 | |||
5.4 | even | 2 | 175.6.a.c.1.2 | 2 | |||
7.2 | even | 3 | 49.6.c.e.18.2 | 4 | |||
7.3 | odd | 6 | 49.6.c.d.30.2 | 4 | |||
7.4 | even | 3 | 49.6.c.e.30.2 | 4 | |||
7.5 | odd | 6 | 49.6.c.d.18.2 | 4 | |||
7.6 | odd | 2 | 49.6.a.f.1.1 | 2 | |||
8.3 | odd | 2 | 448.6.a.u.1.2 | 2 | |||
8.5 | even | 2 | 448.6.a.w.1.1 | 2 | |||
11.10 | odd | 2 | 847.6.a.c.1.2 | 2 | |||
12.11 | even | 2 | 1008.6.a.bq.1.2 | 2 | |||
21.20 | even | 2 | 441.6.a.l.1.2 | 2 | |||
28.27 | even | 2 | 784.6.a.v.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
49.6.a.f.1.1 | 2 | 7.6 | odd | 2 | |||
49.6.c.d.18.2 | 4 | 7.5 | odd | 6 | |||
49.6.c.d.30.2 | 4 | 7.3 | odd | 6 | |||
49.6.c.e.18.2 | 4 | 7.2 | even | 3 | |||
49.6.c.e.30.2 | 4 | 7.4 | even | 3 | |||
63.6.a.f.1.2 | 2 | 3.2 | odd | 2 | |||
112.6.a.h.1.1 | 2 | 4.3 | odd | 2 | |||
175.6.a.c.1.2 | 2 | 5.4 | even | 2 | |||
175.6.b.c.99.2 | 4 | 5.3 | odd | 4 | |||
175.6.b.c.99.3 | 4 | 5.2 | odd | 4 | |||
441.6.a.l.1.2 | 2 | 21.20 | even | 2 | |||
448.6.a.u.1.2 | 2 | 8.3 | odd | 2 | |||
448.6.a.w.1.1 | 2 | 8.5 | even | 2 | |||
784.6.a.v.1.2 | 2 | 28.27 | even | 2 | |||
847.6.a.c.1.2 | 2 | 11.10 | odd | 2 | |||
1008.6.a.bq.1.2 | 2 | 12.11 | even | 2 |