Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 331 x^{11} - 41 x^{10} + 41990 x^{9} + 7229 x^{8} - 2592364 x^{7} - 312100 x^{6} + \cdots - 6400833792 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Root | \(10.6702\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.6702 | 1.88624 | 0.943119 | − | 0.332456i | \(-0.107877\pi\) | ||||
0.943119 | + | 0.332456i | \(0.107877\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 81.8525 | 2.55789 | ||||||||
\(5\) | −61.2778 | −1.09617 | −0.548085 | − | 0.836423i | \(-0.684643\pi\) | ||||
−0.548085 | + | 0.836423i | \(0.684643\pi\) | |||||||
\(6\) | −96.0315 | −1.08902 | ||||||||
\(7\) | 186.685 | 1.44001 | 0.720004 | − | 0.693970i | \(-0.244140\pi\) | ||||
0.720004 | + | 0.693970i | \(0.244140\pi\) | |||||||
\(8\) | 531.935 | 2.93855 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | −653.844 | −2.06764 | ||||||||
\(11\) | −424.892 | −1.05876 | −0.529379 | − | 0.848385i | \(-0.677575\pi\) | ||||
−0.529379 | + | 0.848385i | \(0.677575\pi\) | |||||||
\(12\) | −736.673 | −1.47680 | ||||||||
\(13\) | 983.052 | 1.61331 | 0.806656 | − | 0.591021i | \(-0.201275\pi\) | ||||
0.806656 | + | 0.591021i | \(0.201275\pi\) | |||||||
\(14\) | 1991.96 | 2.71620 | ||||||||
\(15\) | 551.500 | 0.632874 | ||||||||
\(16\) | 3056.56 | 2.98492 | ||||||||
\(17\) | 1043.17 | 0.875455 | 0.437727 | − | 0.899108i | \(-0.355783\pi\) | ||||
0.437727 | + | 0.899108i | \(0.355783\pi\) | |||||||
\(18\) | 864.284 | 0.628746 | ||||||||
\(19\) | −302.603 | −0.192305 | −0.0961523 | − | 0.995367i | \(-0.530654\pi\) | ||||
−0.0961523 | + | 0.995367i | \(0.530654\pi\) | |||||||
\(20\) | −5015.74 | −2.80389 | ||||||||
\(21\) | −1680.17 | −0.831388 | ||||||||
\(22\) | −4533.67 | −1.99707 | ||||||||
\(23\) | 4122.49 | 1.62495 | 0.812475 | − | 0.582996i | \(-0.198120\pi\) | ||||
0.812475 | + | 0.582996i | \(0.198120\pi\) | |||||||
\(24\) | −4787.42 | −1.69658 | ||||||||
\(25\) | 629.966 | 0.201589 | ||||||||
\(26\) | 10489.3 | 3.04309 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | 15280.7 | 3.68338 | ||||||||
\(29\) | −8426.58 | −1.86061 | −0.930307 | − | 0.366782i | \(-0.880460\pi\) | ||||
−0.930307 | + | 0.366782i | \(0.880460\pi\) | |||||||
\(30\) | 5884.60 | 1.19375 | ||||||||
\(31\) | 10049.9 | 1.87827 | 0.939137 | − | 0.343544i | \(-0.111628\pi\) | ||||
0.939137 | + | 0.343544i | \(0.111628\pi\) | |||||||
\(32\) | 15592.1 | 2.69171 | ||||||||
\(33\) | 3824.03 | 0.611274 | ||||||||
\(34\) | 11130.8 | 1.65132 | ||||||||
\(35\) | −11439.6 | −1.57849 | ||||||||
\(36\) | 6630.06 | 0.852631 | ||||||||
\(37\) | 10289.5 | 1.23563 | 0.617815 | − | 0.786323i | \(-0.288018\pi\) | ||||
0.617815 | + | 0.786323i | \(0.288018\pi\) | |||||||
\(38\) | −3228.83 | −0.362732 | ||||||||
\(39\) | −8847.47 | −0.931446 | ||||||||
\(40\) | −32595.8 | −3.22116 | ||||||||
\(41\) | 1605.50 | 0.149159 | 0.0745796 | − | 0.997215i | \(-0.476239\pi\) | ||||
0.0745796 | + | 0.997215i | \(0.476239\pi\) | |||||||
\(42\) | −17927.7 | −1.56820 | ||||||||
\(43\) | −4917.05 | −0.405540 | −0.202770 | − | 0.979226i | \(-0.564994\pi\) | ||||
−0.202770 | + | 0.979226i | \(0.564994\pi\) | |||||||
\(44\) | −34778.5 | −2.70819 | ||||||||
\(45\) | −4963.50 | −0.365390 | ||||||||
\(46\) | 43987.7 | 3.06504 | ||||||||
\(47\) | −24046.6 | −1.58785 | −0.793926 | − | 0.608015i | \(-0.791966\pi\) | ||||
−0.793926 | + | 0.608015i | \(0.791966\pi\) | |||||||
\(48\) | −27509.0 | −1.72334 | ||||||||
\(49\) | 18044.3 | 1.07362 | ||||||||
\(50\) | 6721.85 | 0.380245 | ||||||||
\(51\) | −9388.55 | −0.505444 | ||||||||
\(52\) | 80465.3 | 4.12668 | ||||||||
\(53\) | −6856.60 | −0.335289 | −0.167644 | − | 0.985848i | \(-0.553616\pi\) | ||||
−0.167644 | + | 0.985848i | \(0.553616\pi\) | |||||||
\(54\) | −7778.55 | −0.363007 | ||||||||
\(55\) | 26036.4 | 1.16058 | ||||||||
\(56\) | 99304.4 | 4.23154 | ||||||||
\(57\) | 2723.43 | 0.111027 | ||||||||
\(58\) | −89913.0 | −3.50956 | ||||||||
\(59\) | 3481.00 | 0.130189 | ||||||||
\(60\) | 45141.7 | 1.61882 | ||||||||
\(61\) | −31403.4 | −1.08057 | −0.540283 | − | 0.841483i | \(-0.681683\pi\) | ||||
−0.540283 | + | 0.841483i | \(0.681683\pi\) | |||||||
\(62\) | 107234. | 3.54287 | ||||||||
\(63\) | 15121.5 | 0.480002 | ||||||||
\(64\) | 68560.1 | 2.09229 | ||||||||
\(65\) | −60239.3 | −1.76846 | ||||||||
\(66\) | 40803.0 | 1.15301 | ||||||||
\(67\) | −61147.0 | −1.66413 | −0.832066 | − | 0.554676i | \(-0.812842\pi\) | ||||
−0.832066 | + | 0.554676i | \(0.812842\pi\) | |||||||
\(68\) | 85386.3 | 2.23932 | ||||||||
\(69\) | −37102.4 | −0.938166 | ||||||||
\(70\) | −122063. | −2.97741 | ||||||||
\(71\) | −7454.90 | −0.175508 | −0.0877538 | − | 0.996142i | \(-0.527969\pi\) | ||||
−0.0877538 | + | 0.996142i | \(0.527969\pi\) | |||||||
\(72\) | 43086.7 | 0.979518 | ||||||||
\(73\) | −4324.62 | −0.0949820 | −0.0474910 | − | 0.998872i | \(-0.515123\pi\) | ||||
−0.0474910 | + | 0.998872i | \(0.515123\pi\) | |||||||
\(74\) | 109790. | 2.33069 | ||||||||
\(75\) | −5669.70 | −0.116388 | ||||||||
\(76\) | −24768.9 | −0.491894 | ||||||||
\(77\) | −79321.0 | −1.52462 | ||||||||
\(78\) | −94404.0 | −1.75693 | ||||||||
\(79\) | −30676.1 | −0.553010 | −0.276505 | − | 0.961013i | \(-0.589176\pi\) | ||||
−0.276505 | + | 0.961013i | \(0.589176\pi\) | |||||||
\(80\) | −187299. | −3.27198 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 17130.9 | 0.281350 | ||||||||
\(83\) | −29240.6 | −0.465898 | −0.232949 | − | 0.972489i | \(-0.574837\pi\) | ||||
−0.232949 | + | 0.972489i | \(0.574837\pi\) | |||||||
\(84\) | −137526. | −2.12660 | ||||||||
\(85\) | −63923.3 | −0.959648 | ||||||||
\(86\) | −52465.8 | −0.764944 | ||||||||
\(87\) | 75839.2 | 1.07423 | ||||||||
\(88\) | −226015. | −3.11122 | ||||||||
\(89\) | 23916.5 | 0.320053 | 0.160027 | − | 0.987113i | \(-0.448842\pi\) | ||||
0.160027 | + | 0.987113i | \(0.448842\pi\) | |||||||
\(90\) | −52961.4 | −0.689212 | ||||||||
\(91\) | 183521. | 2.32318 | ||||||||
\(92\) | 337436. | 4.15645 | ||||||||
\(93\) | −90449.4 | −1.08442 | ||||||||
\(94\) | −256582. | −2.99506 | ||||||||
\(95\) | 18542.9 | 0.210799 | ||||||||
\(96\) | −140329. | −1.55406 | ||||||||
\(97\) | 31653.6 | 0.341581 | 0.170790 | − | 0.985307i | \(-0.445368\pi\) | ||||
0.170790 | + | 0.985307i | \(0.445368\pi\) | |||||||
\(98\) | 192536. | 2.02510 | ||||||||
\(99\) | −34416.2 | −0.352919 | ||||||||
\(100\) | 51564.3 | 0.515643 | ||||||||
\(101\) | −90035.5 | −0.878234 | −0.439117 | − | 0.898430i | \(-0.644709\pi\) | ||||
−0.439117 | + | 0.898430i | \(0.644709\pi\) | |||||||
\(102\) | −100177. | −0.953388 | ||||||||
\(103\) | 98739.3 | 0.917059 | 0.458529 | − | 0.888679i | \(-0.348376\pi\) | ||||
0.458529 | + | 0.888679i | \(0.348376\pi\) | |||||||
\(104\) | 522920. | 4.74080 | ||||||||
\(105\) | 102957. | 0.911343 | ||||||||
\(106\) | −73161.1 | −0.632435 | ||||||||
\(107\) | −98628.3 | −0.832803 | −0.416401 | − | 0.909181i | \(-0.636709\pi\) | ||||
−0.416401 | + | 0.909181i | \(0.636709\pi\) | |||||||
\(108\) | −59670.5 | −0.492267 | ||||||||
\(109\) | 57081.3 | 0.460180 | 0.230090 | − | 0.973169i | \(-0.426098\pi\) | ||||
0.230090 | + | 0.973169i | \(0.426098\pi\) | |||||||
\(110\) | 277813. | 2.18913 | ||||||||
\(111\) | −92605.2 | −0.713392 | ||||||||
\(112\) | 570614. | 4.29830 | ||||||||
\(113\) | 70846.0 | 0.521938 | 0.260969 | − | 0.965347i | \(-0.415958\pi\) | ||||
0.260969 | + | 0.965347i | \(0.415958\pi\) | |||||||
\(114\) | 29059.5 | 0.209424 | ||||||||
\(115\) | −252617. | −1.78122 | ||||||||
\(116\) | −689737. | −4.75925 | ||||||||
\(117\) | 79627.2 | 0.537771 | ||||||||
\(118\) | 37142.9 | 0.245567 | ||||||||
\(119\) | 194745. | 1.26066 | ||||||||
\(120\) | 293362. | 1.85974 | ||||||||
\(121\) | 19482.1 | 0.120969 | ||||||||
\(122\) | −335079. | −2.03821 | ||||||||
\(123\) | −14449.5 | −0.0861172 | ||||||||
\(124\) | 822612. | 4.80442 | ||||||||
\(125\) | 152890. | 0.875194 | ||||||||
\(126\) | 161349. | 0.905398 | ||||||||
\(127\) | −347695. | −1.91289 | −0.956444 | − | 0.291916i | \(-0.905707\pi\) | ||||
−0.956444 | + | 0.291916i | \(0.905707\pi\) | |||||||
\(128\) | 232602. | 1.25484 | ||||||||
\(129\) | 44253.4 | 0.234138 | ||||||||
\(130\) | −642763. | −3.33574 | ||||||||
\(131\) | 107422. | 0.546909 | 0.273455 | − | 0.961885i | \(-0.411834\pi\) | ||||
0.273455 | + | 0.961885i | \(0.411834\pi\) | |||||||
\(132\) | 313006. | 1.56357 | ||||||||
\(133\) | −56491.5 | −0.276920 | ||||||||
\(134\) | −652449. | −3.13895 | ||||||||
\(135\) | 44671.5 | 0.210958 | ||||||||
\(136\) | 554900. | 2.57257 | ||||||||
\(137\) | 191277. | 0.870686 | 0.435343 | − | 0.900265i | \(-0.356627\pi\) | ||||
0.435343 | + | 0.900265i | \(0.356627\pi\) | |||||||
\(138\) | −395889. | −1.76960 | ||||||||
\(139\) | 23303.1 | 0.102300 | 0.0511502 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511502 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(140\) | −936364. | −4.03761 | ||||||||
\(141\) | 216420. | 0.916746 | ||||||||
\(142\) | −79545.1 | −0.331049 | ||||||||
\(143\) | −417691. | −1.70811 | ||||||||
\(144\) | 247581. | 0.994973 | ||||||||
\(145\) | 516362. | 2.03955 | ||||||||
\(146\) | −46144.5 | −0.179159 | ||||||||
\(147\) | −162399. | −0.619855 | ||||||||
\(148\) | 842219. | 3.16061 | ||||||||
\(149\) | −16697.0 | −0.0616132 | −0.0308066 | − | 0.999525i | \(-0.509808\pi\) | ||||
−0.0308066 | + | 0.999525i | \(0.509808\pi\) | |||||||
\(150\) | −60496.6 | −0.219535 | ||||||||
\(151\) | −141376. | −0.504583 | −0.252291 | − | 0.967651i | \(-0.581184\pi\) | ||||
−0.252291 | + | 0.967651i | \(0.581184\pi\) | |||||||
\(152\) | −160965. | −0.565097 | ||||||||
\(153\) | 84497.0 | 0.291818 | ||||||||
\(154\) | −846369. | −2.87579 | ||||||||
\(155\) | −615837. | −2.05891 | ||||||||
\(156\) | −724188. | −2.38254 | ||||||||
\(157\) | −6851.37 | −0.0221834 | −0.0110917 | − | 0.999938i | \(-0.503531\pi\) | ||||
−0.0110917 | + | 0.999938i | \(0.503531\pi\) | |||||||
\(158\) | −327319. | −1.04311 | ||||||||
\(159\) | 61709.4 | 0.193579 | ||||||||
\(160\) | −955447. | −2.95057 | ||||||||
\(161\) | 769608. | 2.33994 | ||||||||
\(162\) | 70007.0 | 0.209582 | ||||||||
\(163\) | −275831. | −0.813158 | −0.406579 | − | 0.913616i | \(-0.633278\pi\) | ||||
−0.406579 | + | 0.913616i | \(0.633278\pi\) | |||||||
\(164\) | 131414. | 0.381533 | ||||||||
\(165\) | −234328. | −0.670061 | ||||||||
\(166\) | −312002. | −0.878794 | ||||||||
\(167\) | 546461. | 1.51624 | 0.758120 | − | 0.652115i | \(-0.226118\pi\) | ||||
0.758120 | + | 0.652115i | \(0.226118\pi\) | |||||||
\(168\) | −893739. | −2.44308 | ||||||||
\(169\) | 595099. | 1.60277 | ||||||||
\(170\) | −682072. | −1.81012 | ||||||||
\(171\) | −24510.9 | −0.0641015 | ||||||||
\(172\) | −402473. | −1.03733 | ||||||||
\(173\) | −563301. | −1.43095 | −0.715476 | − | 0.698637i | \(-0.753790\pi\) | ||||
−0.715476 | + | 0.698637i | \(0.753790\pi\) | |||||||
\(174\) | 809217. | 2.02625 | ||||||||
\(175\) | 117605. | 0.290290 | ||||||||
\(176\) | −1.29871e6 | −3.16031 | ||||||||
\(177\) | −31329.0 | −0.0751646 | ||||||||
\(178\) | 255193. | 0.603696 | ||||||||
\(179\) | 603180. | 1.40707 | 0.703533 | − | 0.710663i | \(-0.251605\pi\) | ||||
0.703533 | + | 0.710663i | \(0.251605\pi\) | |||||||
\(180\) | −406275. | −0.934628 | ||||||||
\(181\) | 158219. | 0.358973 | 0.179487 | − | 0.983760i | \(-0.442556\pi\) | ||||
0.179487 | + | 0.983760i | \(0.442556\pi\) | |||||||
\(182\) | 1.95820e6 | 4.38207 | ||||||||
\(183\) | 282630. | 0.623865 | ||||||||
\(184\) | 2.19290e6 | 4.77501 | ||||||||
\(185\) | −630516. | −1.35446 | ||||||||
\(186\) | −965110. | −2.04548 | ||||||||
\(187\) | −443235. | −0.926895 | ||||||||
\(188\) | −1.96828e6 | −4.06155 | ||||||||
\(189\) | −136093. | −0.277129 | ||||||||
\(190\) | 197855. | 0.397616 | ||||||||
\(191\) | −512314. | −1.01614 | −0.508070 | − | 0.861316i | \(-0.669641\pi\) | ||||
−0.508070 | + | 0.861316i | \(0.669641\pi\) | |||||||
\(192\) | −617041. | −1.20798 | ||||||||
\(193\) | −779315. | −1.50598 | −0.752991 | − | 0.658030i | \(-0.771390\pi\) | ||||
−0.752991 | + | 0.658030i | \(0.771390\pi\) | |||||||
\(194\) | 337749. | 0.644302 | ||||||||
\(195\) | 542153. | 1.02102 | ||||||||
\(196\) | 1.47697e6 | 2.74620 | ||||||||
\(197\) | −375338. | −0.689059 | −0.344530 | − | 0.938775i | \(-0.611962\pi\) | ||||
−0.344530 | + | 0.938775i | \(0.611962\pi\) | |||||||
\(198\) | −367227. | −0.665690 | ||||||||
\(199\) | 373163. | 0.667984 | 0.333992 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333992 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(200\) | 335101. | 0.592381 | ||||||||
\(201\) | 550323. | 0.960788 | ||||||||
\(202\) | −960694. | −1.65656 | ||||||||
\(203\) | −1.57312e6 | −2.67930 | ||||||||
\(204\) | −768477. | −1.29287 | ||||||||
\(205\) | −98381.4 | −0.163504 | ||||||||
\(206\) | 1.05357e6 | 1.72979 | ||||||||
\(207\) | 333922. | 0.541650 | ||||||||
\(208\) | 3.00476e6 | 4.81560 | ||||||||
\(209\) | 128574. | 0.203604 | ||||||||
\(210\) | 1.09857e6 | 1.71901 | ||||||||
\(211\) | 968282. | 1.49725 | 0.748627 | − | 0.662991i | \(-0.230713\pi\) | ||||
0.748627 | + | 0.662991i | \(0.230713\pi\) | |||||||
\(212\) | −561230. | −0.857633 | ||||||||
\(213\) | 67094.1 | 0.101329 | ||||||||
\(214\) | −1.05238e6 | −1.57086 | ||||||||
\(215\) | 301306. | 0.444541 | ||||||||
\(216\) | −387781. | −0.565525 | ||||||||
\(217\) | 1.87617e6 | 2.70473 | ||||||||
\(218\) | 609068. | 0.868009 | ||||||||
\(219\) | 38921.6 | 0.0548379 | ||||||||
\(220\) | 2.13115e6 | 2.96864 | ||||||||
\(221\) | 1.02549e6 | 1.41238 | ||||||||
\(222\) | −988113. | −1.34563 | ||||||||
\(223\) | −423194. | −0.569872 | −0.284936 | − | 0.958547i | \(-0.591972\pi\) | ||||
−0.284936 | + | 0.958547i | \(0.591972\pi\) | |||||||
\(224\) | 2.91081e6 | 3.87608 | ||||||||
\(225\) | 51027.3 | 0.0671964 | ||||||||
\(226\) | 755939. | 0.984500 | ||||||||
\(227\) | 185430. | 0.238845 | 0.119423 | − | 0.992844i | \(-0.461896\pi\) | ||||
0.119423 | + | 0.992844i | \(0.461896\pi\) | |||||||
\(228\) | 222920. | 0.283995 | ||||||||
\(229\) | 418097. | 0.526851 | 0.263426 | − | 0.964680i | \(-0.415148\pi\) | ||||
0.263426 | + | 0.964680i | \(0.415148\pi\) | |||||||
\(230\) | −2.69547e6 | −3.35981 | ||||||||
\(231\) | 713889. | 0.880239 | ||||||||
\(232\) | −4.48239e6 | −5.46751 | ||||||||
\(233\) | 137239. | 0.165611 | 0.0828055 | − | 0.996566i | \(-0.473612\pi\) | ||||
0.0828055 | + | 0.996566i | \(0.473612\pi\) | |||||||
\(234\) | 849636. | 1.01436 | ||||||||
\(235\) | 1.47352e6 | 1.74056 | ||||||||
\(236\) | 284929. | 0.333009 | ||||||||
\(237\) | 276085. | 0.319280 | ||||||||
\(238\) | 2.07796e6 | 2.37791 | ||||||||
\(239\) | −207578. | −0.235064 | −0.117532 | − | 0.993069i | \(-0.537498\pi\) | ||||
−0.117532 | + | 0.993069i | \(0.537498\pi\) | |||||||
\(240\) | 1.68569e6 | 1.88908 | ||||||||
\(241\) | −507933. | −0.563331 | −0.281666 | − | 0.959513i | \(-0.590887\pi\) | ||||
−0.281666 | + | 0.959513i | \(0.590887\pi\) | |||||||
\(242\) | 207877. | 0.228176 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −2.57044e6 | −2.76397 | ||||||||
\(245\) | −1.10572e6 | −1.17687 | ||||||||
\(246\) | −154178. | −0.162437 | ||||||||
\(247\) | −297475. | −0.310247 | ||||||||
\(248\) | 5.34591e6 | 5.51941 | ||||||||
\(249\) | 263165. | 0.268986 | ||||||||
\(250\) | 1.63136e6 | 1.65082 | ||||||||
\(251\) | −58645.3 | −0.0587556 | −0.0293778 | − | 0.999568i | \(-0.509353\pi\) | ||||
−0.0293778 | + | 0.999568i | \(0.509353\pi\) | |||||||
\(252\) | 1.23773e6 | 1.22779 | ||||||||
\(253\) | −1.75161e6 | −1.72043 | ||||||||
\(254\) | −3.70997e6 | −3.60816 | ||||||||
\(255\) | 575310. | 0.554053 | ||||||||
\(256\) | 287983. | 0.274642 | ||||||||
\(257\) | 1586.01 | 0.00149787 | 0.000748935 | − | 1.00000i | \(-0.499762\pi\) | ||||
0.000748935 | 1.00000i | \(0.499762\pi\) | ||||||||
\(258\) | 472192. | 0.441641 | ||||||||
\(259\) | 1.92089e6 | 1.77932 | ||||||||
\(260\) | −4.93074e6 | −4.52354 | ||||||||
\(261\) | −682553. | −0.620205 | ||||||||
\(262\) | 1.14621e6 | 1.03160 | ||||||||
\(263\) | −1.39407e6 | −1.24278 | −0.621391 | − | 0.783501i | \(-0.713432\pi\) | ||||
−0.621391 | + | 0.783501i | \(0.713432\pi\) | |||||||
\(264\) | 2.03413e6 | 1.79626 | ||||||||
\(265\) | 420157. | 0.367534 | ||||||||
\(266\) | −602774. | −0.522337 | ||||||||
\(267\) | −215248. | −0.184783 | ||||||||
\(268\) | −5.00504e6 | −4.25667 | ||||||||
\(269\) | 749950. | 0.631904 | 0.315952 | − | 0.948775i | \(-0.397676\pi\) | ||||
0.315952 | + | 0.948775i | \(0.397676\pi\) | |||||||
\(270\) | 476653. | 0.397917 | ||||||||
\(271\) | 66861.0 | 0.0553031 | 0.0276516 | − | 0.999618i | \(-0.491197\pi\) | ||||
0.0276516 | + | 0.999618i | \(0.491197\pi\) | |||||||
\(272\) | 3.18852e6 | 2.61316 | ||||||||
\(273\) | −1.65169e6 | −1.34129 | ||||||||
\(274\) | 2.04096e6 | 1.64232 | ||||||||
\(275\) | −267668. | −0.213434 | ||||||||
\(276\) | −3.03693e6 | −2.39973 | ||||||||
\(277\) | −398436. | −0.312003 | −0.156002 | − | 0.987757i | \(-0.549860\pi\) | ||||
−0.156002 | + | 0.987757i | \(0.549860\pi\) | |||||||
\(278\) | 248649. | 0.192963 | ||||||||
\(279\) | 814044. | 0.626091 | ||||||||
\(280\) | −6.08515e6 | −4.63849 | ||||||||
\(281\) | 406894. | 0.307408 | 0.153704 | − | 0.988117i | \(-0.450880\pi\) | ||||
0.153704 | + | 0.988117i | \(0.450880\pi\) | |||||||
\(282\) | 2.30924e6 | 1.72920 | ||||||||
\(283\) | 2.31675e6 | 1.71954 | 0.859772 | − | 0.510678i | \(-0.170605\pi\) | ||||
0.859772 | + | 0.510678i | \(0.170605\pi\) | |||||||
\(284\) | −610203. | −0.448930 | ||||||||
\(285\) | −166886. | −0.121705 | ||||||||
\(286\) | −4.45683e6 | −3.22189 | ||||||||
\(287\) | 299723. | 0.214790 | ||||||||
\(288\) | 1.26296e6 | 0.897237 | ||||||||
\(289\) | −331649. | −0.233579 | ||||||||
\(290\) | 5.50967e6 | 3.84707 | ||||||||
\(291\) | −284882. | −0.197212 | ||||||||
\(292\) | −353981. | −0.242954 | ||||||||
\(293\) | 1.71243e6 | 1.16531 | 0.582657 | − | 0.812718i | \(-0.302013\pi\) | ||||
0.582657 | + | 0.812718i | \(0.302013\pi\) | |||||||
\(294\) | −1.73283e6 | −1.16919 | ||||||||
\(295\) | −213308. | −0.142709 | ||||||||
\(296\) | 5.47333e6 | 3.63097 | ||||||||
\(297\) | 309746. | 0.203758 | ||||||||
\(298\) | −178160. | −0.116217 | ||||||||
\(299\) | 4.05263e6 | 2.62155 | ||||||||
\(300\) | −464079. | −0.297707 | ||||||||
\(301\) | −917940. | −0.583980 | ||||||||
\(302\) | −1.50850e6 | −0.951763 | ||||||||
\(303\) | 810319. | 0.507048 | ||||||||
\(304\) | −924924. | −0.574014 | ||||||||
\(305\) | 1.92433e6 | 1.18448 | ||||||||
\(306\) | 901597. | 0.550439 | ||||||||
\(307\) | 518531. | 0.313999 | 0.157000 | − | 0.987599i | \(-0.449818\pi\) | ||||
0.157000 | + | 0.987599i | \(0.449818\pi\) | |||||||
\(308\) | −6.49262e6 | −3.89981 | ||||||||
\(309\) | −888654. | −0.529464 | ||||||||
\(310\) | −6.57109e6 | −3.88359 | ||||||||
\(311\) | −50432.7 | −0.0295673 | −0.0147836 | − | 0.999891i | \(-0.504706\pi\) | ||||
−0.0147836 | + | 0.999891i | \(0.504706\pi\) | |||||||
\(312\) | −4.70628e6 | −2.73710 | ||||||||
\(313\) | 2.84888e6 | 1.64366 | 0.821832 | − | 0.569730i | \(-0.192952\pi\) | ||||
0.821832 | + | 0.569730i | \(0.192952\pi\) | |||||||
\(314\) | −73105.2 | −0.0418432 | ||||||||
\(315\) | −926612. | −0.526164 | ||||||||
\(316\) | −2.51092e6 | −1.41454 | ||||||||
\(317\) | 1.74502e6 | 0.975331 | 0.487666 | − | 0.873031i | \(-0.337849\pi\) | ||||
0.487666 | + | 0.873031i | \(0.337849\pi\) | |||||||
\(318\) | 658450. | 0.365136 | ||||||||
\(319\) | 3.58038e6 | 1.96994 | ||||||||
\(320\) | −4.20121e6 | −2.29351 | ||||||||
\(321\) | 887655. | 0.480819 | ||||||||
\(322\) | 8.21185e6 | 4.41368 | ||||||||
\(323\) | −315667. | −0.168354 | ||||||||
\(324\) | 537035. | 0.284210 | ||||||||
\(325\) | 619290. | 0.325226 | ||||||||
\(326\) | −2.94317e6 | −1.53381 | ||||||||
\(327\) | −513732. | −0.265685 | ||||||||
\(328\) | 854021. | 0.438313 | ||||||||
\(329\) | −4.48915e6 | −2.28652 | ||||||||
\(330\) | −2.50032e6 | −1.26389 | ||||||||
\(331\) | −515970. | −0.258854 | −0.129427 | − | 0.991589i | \(-0.541314\pi\) | ||||
−0.129427 | + | 0.991589i | \(0.541314\pi\) | |||||||
\(332\) | −2.39341e6 | −1.19172 | ||||||||
\(333\) | 833447. | 0.411877 | ||||||||
\(334\) | 5.83083e6 | 2.85999 | ||||||||
\(335\) | 3.74695e6 | 1.82417 | ||||||||
\(336\) | −5.13552e6 | −2.48163 | ||||||||
\(337\) | −2.01691e6 | −0.967414 | −0.483707 | − | 0.875230i | \(-0.660710\pi\) | ||||
−0.483707 | + | 0.875230i | \(0.660710\pi\) | |||||||
\(338\) | 6.34981e6 | 3.02321 | ||||||||
\(339\) | −637614. | −0.301341 | ||||||||
\(340\) | −5.23228e6 | −2.45467 | ||||||||
\(341\) | −4.27013e6 | −1.98864 | ||||||||
\(342\) | −261535. | −0.120911 | ||||||||
\(343\) | 230992. | 0.106014 | ||||||||
\(344\) | −2.61555e6 | −1.19170 | ||||||||
\(345\) | 2.27355e6 | 1.02839 | ||||||||
\(346\) | −6.01052e6 | −2.69912 | ||||||||
\(347\) | 1.32354e6 | 0.590084 | 0.295042 | − | 0.955484i | \(-0.404666\pi\) | ||||
0.295042 | + | 0.955484i | \(0.404666\pi\) | |||||||
\(348\) | 6.20763e6 | 2.74775 | ||||||||
\(349\) | −1.20078e6 | −0.527714 | −0.263857 | − | 0.964562i | \(-0.584995\pi\) | ||||
−0.263857 | + | 0.964562i | \(0.584995\pi\) | |||||||
\(350\) | 1.25487e6 | 0.547556 | ||||||||
\(351\) | −716645. | −0.310482 | ||||||||
\(352\) | −6.62494e6 | −2.84987 | ||||||||
\(353\) | −2.56612e6 | −1.09607 | −0.548037 | − | 0.836454i | \(-0.684625\pi\) | ||||
−0.548037 | + | 0.836454i | \(0.684625\pi\) | |||||||
\(354\) | −334286. | −0.141778 | ||||||||
\(355\) | 456820. | 0.192386 | ||||||||
\(356\) | 1.95762e6 | 0.818661 | ||||||||
\(357\) | −1.75270e6 | −0.727843 | ||||||||
\(358\) | 6.43603e6 | 2.65406 | ||||||||
\(359\) | 1.98664e6 | 0.813547 | 0.406773 | − | 0.913529i | \(-0.366654\pi\) | ||||
0.406773 | + | 0.913529i | \(0.366654\pi\) | |||||||
\(360\) | −2.64026e6 | −1.07372 | ||||||||
\(361\) | −2.38453e6 | −0.963019 | ||||||||
\(362\) | 1.68822e6 | 0.677109 | ||||||||
\(363\) | −175339. | −0.0698413 | ||||||||
\(364\) | 1.50217e7 | 5.94244 | ||||||||
\(365\) | 265003. | 0.104116 | ||||||||
\(366\) | 3.01571e6 | 1.17676 | ||||||||
\(367\) | −1.10023e6 | −0.426400 | −0.213200 | − | 0.977009i | \(-0.568389\pi\) | ||||
−0.213200 | + | 0.977009i | \(0.568389\pi\) | |||||||
\(368\) | 1.26006e7 | 4.85035 | ||||||||
\(369\) | 130045. | 0.0497198 | ||||||||
\(370\) | −6.72771e6 | −2.55484 | ||||||||
\(371\) | −1.28003e6 | −0.482818 | ||||||||
\(372\) | −7.40351e6 | −2.77383 | ||||||||
\(373\) | −2.20944e6 | −0.822263 | −0.411131 | − | 0.911576i | \(-0.634866\pi\) | ||||
−0.411131 | + | 0.911576i | \(0.634866\pi\) | |||||||
\(374\) | −4.72940e6 | −1.74834 | ||||||||
\(375\) | −1.37601e6 | −0.505294 | ||||||||
\(376\) | −1.27913e7 | −4.66599 | ||||||||
\(377\) | −8.28377e6 | −3.00175 | ||||||||
\(378\) | −1.45214e6 | −0.522732 | ||||||||
\(379\) | −560573. | −0.200463 | −0.100231 | − | 0.994964i | \(-0.531958\pi\) | ||||
−0.100231 | + | 0.994964i | \(0.531958\pi\) | |||||||
\(380\) | 1.51778e6 | 0.539200 | ||||||||
\(381\) | 3.12926e6 | 1.10441 | ||||||||
\(382\) | −5.46648e6 | −1.91668 | ||||||||
\(383\) | −3.40354e6 | −1.18559 | −0.592795 | − | 0.805354i | \(-0.701975\pi\) | ||||
−0.592795 | + | 0.805354i | \(0.701975\pi\) | |||||||
\(384\) | −2.09342e6 | −0.724484 | ||||||||
\(385\) | 4.86061e6 | 1.67124 | ||||||||
\(386\) | −8.31543e6 | −2.84064 | ||||||||
\(387\) | −398281. | −0.135180 | ||||||||
\(388\) | 2.59092e6 | 0.873726 | ||||||||
\(389\) | −3.10419e6 | −1.04010 | −0.520048 | − | 0.854137i | \(-0.674086\pi\) | ||||
−0.520048 | + | 0.854137i | \(0.674086\pi\) | |||||||
\(390\) | 5.78487e6 | 1.92589 | ||||||||
\(391\) | 4.30047e6 | 1.42257 | ||||||||
\(392\) | 9.59842e6 | 3.15489 | ||||||||
\(393\) | −966798. | −0.315758 | ||||||||
\(394\) | −4.00492e6 | −1.29973 | ||||||||
\(395\) | 1.87976e6 | 0.606193 | ||||||||
\(396\) | −2.81706e6 | −0.902730 | ||||||||
\(397\) | −3.18351e6 | −1.01375 | −0.506875 | − | 0.862020i | \(-0.669199\pi\) | ||||
−0.506875 | + | 0.862020i | \(0.669199\pi\) | |||||||
\(398\) | 3.98171e6 | 1.25998 | ||||||||
\(399\) | 508424. | 0.159880 | ||||||||
\(400\) | 1.92553e6 | 0.601728 | ||||||||
\(401\) | 311471. | 0.0967289 | 0.0483644 | − | 0.998830i | \(-0.484599\pi\) | ||||
0.0483644 | + | 0.998830i | \(0.484599\pi\) | |||||||
\(402\) | 5.87204e6 | 1.81227 | ||||||||
\(403\) | 9.87961e6 | 3.03024 | ||||||||
\(404\) | −7.36963e6 | −2.24643 | ||||||||
\(405\) | −402044. | −0.121797 | ||||||||
\(406\) | −1.67854e7 | −5.05379 | ||||||||
\(407\) | −4.37191e6 | −1.30823 | ||||||||
\(408\) | −4.99410e6 | −1.48527 | ||||||||
\(409\) | −559438. | −0.165365 | −0.0826825 | − | 0.996576i | \(-0.526349\pi\) | ||||
−0.0826825 | + | 0.996576i | \(0.526349\pi\) | |||||||
\(410\) | −1.04975e6 | −0.308407 | ||||||||
\(411\) | −1.72149e6 | −0.502691 | ||||||||
\(412\) | 8.08206e6 | 2.34574 | ||||||||
\(413\) | 649851. | 0.187473 | ||||||||
\(414\) | 3.56300e6 | 1.02168 | ||||||||
\(415\) | 1.79180e6 | 0.510703 | ||||||||
\(416\) | 1.53278e7 | 4.34257 | ||||||||
\(417\) | −209728. | −0.0590632 | ||||||||
\(418\) | 1.37190e6 | 0.384046 | ||||||||
\(419\) | 142773. | 0.0397294 | 0.0198647 | − | 0.999803i | \(-0.493676\pi\) | ||||
0.0198647 | + | 0.999803i | \(0.493676\pi\) | |||||||
\(420\) | 8.42728e6 | 2.33112 | ||||||||
\(421\) | −3.82502e6 | −1.05179 | −0.525895 | − | 0.850550i | \(-0.676270\pi\) | ||||
−0.525895 | + | 0.850550i | \(0.676270\pi\) | |||||||
\(422\) | 1.03317e7 | 2.82418 | ||||||||
\(423\) | −1.94778e6 | −0.529284 | ||||||||
\(424\) | −3.64727e6 | −0.985265 | ||||||||
\(425\) | 657163. | 0.176482 | ||||||||
\(426\) | 715906. | 0.191131 | ||||||||
\(427\) | −5.86254e6 | −1.55602 | ||||||||
\(428\) | −8.07298e6 | −2.13022 | ||||||||
\(429\) | 3.75922e6 | 0.986176 | ||||||||
\(430\) | 3.21499e6 | 0.838509 | ||||||||
\(431\) | −4.27196e6 | −1.10773 | −0.553865 | − | 0.832606i | \(-0.686848\pi\) | ||||
−0.553865 | + | 0.832606i | \(0.686848\pi\) | |||||||
\(432\) | −2.22823e6 | −0.574448 | ||||||||
\(433\) | −3.40429e6 | −0.872583 | −0.436292 | − | 0.899805i | \(-0.643708\pi\) | ||||
−0.436292 | + | 0.899805i | \(0.643708\pi\) | |||||||
\(434\) | 2.00191e7 | 5.10176 | ||||||||
\(435\) | −4.64726e6 | −1.17753 | ||||||||
\(436\) | 4.67225e6 | 1.17709 | ||||||||
\(437\) | −1.24748e6 | −0.312486 | ||||||||
\(438\) | 415300. | 0.103437 | ||||||||
\(439\) | 6.97376e6 | 1.72705 | 0.863527 | − | 0.504303i | \(-0.168250\pi\) | ||||
0.863527 | + | 0.504303i | \(0.168250\pi\) | |||||||
\(440\) | 1.38497e7 | 3.41042 | ||||||||
\(441\) | 1.46159e6 | 0.357873 | ||||||||
\(442\) | 1.09422e7 | 2.66409 | ||||||||
\(443\) | 4.62500e6 | 1.11970 | 0.559851 | − | 0.828593i | \(-0.310858\pi\) | ||||
0.559851 | + | 0.828593i | \(0.310858\pi\) | |||||||
\(444\) | −7.57997e6 | −1.82478 | ||||||||
\(445\) | −1.46555e6 | −0.350833 | ||||||||
\(446\) | −4.51555e6 | −1.07491 | ||||||||
\(447\) | 150273. | 0.0355724 | ||||||||
\(448\) | 1.27992e7 | 3.01291 | ||||||||
\(449\) | −4.22998e6 | −0.990199 | −0.495100 | − | 0.868836i | \(-0.664868\pi\) | ||||
−0.495100 | + | 0.868836i | \(0.664868\pi\) | |||||||
\(450\) | 544470. | 0.126748 | ||||||||
\(451\) | −682163. | −0.157924 | ||||||||
\(452\) | 5.79893e6 | 1.33506 | ||||||||
\(453\) | 1.27238e6 | 0.291321 | ||||||||
\(454\) | 1.97857e6 | 0.450519 | ||||||||
\(455\) | −1.12458e7 | −2.54660 | ||||||||
\(456\) | 1.44869e6 | 0.326259 | ||||||||
\(457\) | 8.46533e6 | 1.89607 | 0.948033 | − | 0.318173i | \(-0.103069\pi\) | ||||
0.948033 | + | 0.318173i | \(0.103069\pi\) | |||||||
\(458\) | 4.46116e6 | 0.993767 | ||||||||
\(459\) | −760473. | −0.168481 | ||||||||
\(460\) | −2.06774e7 | −4.55617 | ||||||||
\(461\) | −5.61651e6 | −1.23088 | −0.615438 | − | 0.788185i | \(-0.711021\pi\) | ||||
−0.615438 | + | 0.788185i | \(0.711021\pi\) | |||||||
\(462\) | 7.61732e6 | 1.66034 | ||||||||
\(463\) | 692123. | 0.150048 | 0.0750241 | − | 0.997182i | \(-0.476097\pi\) | ||||
0.0750241 | + | 0.997182i | \(0.476097\pi\) | |||||||
\(464\) | −2.57563e7 | −5.55378 | ||||||||
\(465\) | 5.54254e6 | 1.18871 | ||||||||
\(466\) | 1.46437e6 | 0.312382 | ||||||||
\(467\) | 6.20510e6 | 1.31661 | 0.658304 | − | 0.752752i | \(-0.271274\pi\) | ||||
0.658304 | + | 0.752752i | \(0.271274\pi\) | |||||||
\(468\) | 6.51769e6 | 1.37556 | ||||||||
\(469\) | −1.14152e7 | −2.39636 | ||||||||
\(470\) | 1.57228e7 | 3.28310 | ||||||||
\(471\) | 61662.3 | 0.0128076 | ||||||||
\(472\) | 1.85167e6 | 0.382567 | ||||||||
\(473\) | 2.08921e6 | 0.429368 | ||||||||
\(474\) | 2.94588e6 | 0.602238 | ||||||||
\(475\) | −190630. | −0.0387665 | ||||||||
\(476\) | 1.59404e7 | 3.22463 | ||||||||
\(477\) | −555385. | −0.111763 | ||||||||
\(478\) | −2.21489e6 | −0.443387 | ||||||||
\(479\) | −4.54829e6 | −0.905752 | −0.452876 | − | 0.891573i | \(-0.649602\pi\) | ||||
−0.452876 | + | 0.891573i | \(0.649602\pi\) | |||||||
\(480\) | 8.59902e6 | 1.70352 | ||||||||
\(481\) | 1.01151e7 | 1.99346 | ||||||||
\(482\) | −5.41973e6 | −1.06258 | ||||||||
\(483\) | −6.92647e6 | −1.35097 | ||||||||
\(484\) | 1.59466e6 | 0.309425 | ||||||||
\(485\) | −1.93966e6 | −0.374430 | ||||||||
\(486\) | −630063. | −0.121002 | ||||||||
\(487\) | −3.94237e6 | −0.753242 | −0.376621 | − | 0.926367i | \(-0.622914\pi\) | ||||
−0.376621 | + | 0.926367i | \(0.622914\pi\) | |||||||
\(488\) | −1.67045e7 | −3.17530 | ||||||||
\(489\) | 2.48248e6 | 0.469477 | ||||||||
\(490\) | −1.17982e7 | −2.21986 | ||||||||
\(491\) | 557676. | 0.104395 | 0.0521973 | − | 0.998637i | \(-0.483378\pi\) | ||||
0.0521973 | + | 0.998637i | \(0.483378\pi\) | |||||||
\(492\) | −1.18273e6 | −0.220278 | ||||||||
\(493\) | −8.79037e6 | −1.62888 | ||||||||
\(494\) | −3.17411e6 | −0.585200 | ||||||||
\(495\) | 2.10895e6 | 0.386860 | ||||||||
\(496\) | 3.07182e7 | 5.60649 | ||||||||
\(497\) | −1.39172e6 | −0.252732 | ||||||||
\(498\) | 2.80802e6 | 0.507372 | ||||||||
\(499\) | −4.02783e6 | −0.724136 | −0.362068 | − | 0.932152i | \(-0.617929\pi\) | ||||
−0.362068 | + | 0.932152i | \(0.617929\pi\) | |||||||
\(500\) | 1.25144e7 | 2.23865 | ||||||||
\(501\) | −4.91815e6 | −0.875402 | ||||||||
\(502\) | −625755. | −0.110827 | ||||||||
\(503\) | 9.17895e6 | 1.61761 | 0.808803 | − | 0.588079i | \(-0.200116\pi\) | ||||
0.808803 | + | 0.588079i | \(0.200116\pi\) | |||||||
\(504\) | 8.04365e6 | 1.41051 | ||||||||
\(505\) | 5.51717e6 | 0.962694 | ||||||||
\(506\) | −1.86900e7 | −3.24514 | ||||||||
\(507\) | −5.35589e6 | −0.925362 | ||||||||
\(508\) | −2.84597e7 | −4.89296 | ||||||||
\(509\) | −8.23834e6 | −1.40944 | −0.704718 | − | 0.709487i | \(-0.748927\pi\) | ||||
−0.704718 | + | 0.709487i | \(0.748927\pi\) | |||||||
\(510\) | 6.13865e6 | 1.04508 | ||||||||
\(511\) | −807343. | −0.136775 | ||||||||
\(512\) | −4.37045e6 | −0.736803 | ||||||||
\(513\) | 220598. | 0.0370090 | ||||||||
\(514\) | 16923.0 | 0.00282534 | ||||||||
\(515\) | −6.05053e6 | −1.00525 | ||||||||
\(516\) | 3.62226e6 | 0.598901 | ||||||||
\(517\) | 1.02172e7 | 1.68115 | ||||||||
\(518\) | 2.04962e7 | 3.35621 | ||||||||
\(519\) | 5.06971e6 | 0.826161 | ||||||||
\(520\) | −3.20434e7 | −5.19673 | ||||||||
\(521\) | −4.78219e6 | −0.771850 | −0.385925 | − | 0.922530i | \(-0.626118\pi\) | ||||
−0.385925 | + | 0.922530i | \(0.626118\pi\) | |||||||
\(522\) | −7.28296e6 | −1.16985 | ||||||||
\(523\) | −1.22841e7 | −1.96376 | −0.981881 | − | 0.189501i | \(-0.939313\pi\) | ||||
−0.981881 | + | 0.189501i | \(0.939313\pi\) | |||||||
\(524\) | 8.79277e6 | 1.39893 | ||||||||
\(525\) | −1.05845e6 | −0.167599 | ||||||||
\(526\) | −1.48749e7 | −2.34418 | ||||||||
\(527\) | 1.04838e7 | 1.64434 | ||||||||
\(528\) | 1.16884e7 | 1.82460 | ||||||||
\(529\) | 1.05586e7 | 1.64046 | ||||||||
\(530\) | 4.48315e6 | 0.693256 | ||||||||
\(531\) | 281961. | 0.0433963 | ||||||||
\(532\) | −4.62398e6 | −0.708331 | ||||||||
\(533\) | 1.57829e6 | 0.240640 | ||||||||
\(534\) | −2.29674e6 | −0.348544 | ||||||||
\(535\) | 6.04373e6 | 0.912894 | ||||||||
\(536\) | −3.25262e7 | −4.89014 | ||||||||
\(537\) | −5.42862e6 | −0.812370 | ||||||||
\(538\) | 8.00209e6 | 1.19192 | ||||||||
\(539\) | −7.66689e6 | −1.13670 | ||||||||
\(540\) | 3.65648e6 | 0.539608 | ||||||||
\(541\) | −7.08864e6 | −1.04128 | −0.520642 | − | 0.853775i | \(-0.674307\pi\) | ||||
−0.520642 | + | 0.853775i | \(0.674307\pi\) | |||||||
\(542\) | 713418. | 0.104315 | ||||||||
\(543\) | −1.42397e6 | −0.207253 | ||||||||
\(544\) | 1.62652e7 | 2.35647 | ||||||||
\(545\) | −3.49782e6 | −0.504436 | ||||||||
\(546\) | −1.76238e7 | −2.52999 | ||||||||
\(547\) | 1.55919e6 | 0.222807 | 0.111404 | − | 0.993775i | \(-0.464465\pi\) | ||||
0.111404 | + | 0.993775i | \(0.464465\pi\) | |||||||
\(548\) | 1.56565e7 | 2.22712 | ||||||||
\(549\) | −2.54367e6 | −0.360189 | ||||||||
\(550\) | −2.85606e6 | −0.402588 | ||||||||
\(551\) | 2.54991e6 | 0.357805 | ||||||||
\(552\) | −1.97361e7 | −2.75685 | ||||||||
\(553\) | −5.72678e6 | −0.796338 | ||||||||
\(554\) | −4.25138e6 | −0.588512 | ||||||||
\(555\) | 5.67464e6 | 0.781999 | ||||||||
\(556\) | 1.90742e6 | 0.261674 | ||||||||
\(557\) | 2.40850e6 | 0.328934 | 0.164467 | − | 0.986383i | \(-0.447410\pi\) | ||||
0.164467 | + | 0.986383i | \(0.447410\pi\) | |||||||
\(558\) | 8.68599e6 | 1.18096 | ||||||||
\(559\) | −4.83372e6 | −0.654262 | ||||||||
\(560\) | −3.49659e7 | −4.71167 | ||||||||
\(561\) | 3.98912e6 | 0.535143 | ||||||||
\(562\) | 4.34163e6 | 0.579845 | ||||||||
\(563\) | −1.96787e6 | −0.261652 | −0.130826 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130826 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(564\) | 1.77145e7 | 2.34494 | ||||||||
\(565\) | −4.34129e6 | −0.572133 | ||||||||
\(566\) | 2.47201e7 | 3.24347 | ||||||||
\(567\) | 1.22484e6 | 0.160001 | ||||||||
\(568\) | −3.96552e6 | −0.515739 | ||||||||
\(569\) | 5.44328e6 | 0.704823 | 0.352411 | − | 0.935845i | \(-0.385362\pi\) | ||||
0.352411 | + | 0.935845i | \(0.385362\pi\) | |||||||
\(570\) | −1.78070e6 | −0.229564 | ||||||||
\(571\) | 1.26908e7 | 1.62892 | 0.814461 | − | 0.580218i | \(-0.197033\pi\) | ||||
0.814461 | + | 0.580218i | \(0.197033\pi\) | |||||||
\(572\) | −3.41891e7 | −4.36915 | ||||||||
\(573\) | 4.61083e6 | 0.586668 | ||||||||
\(574\) | 3.19809e6 | 0.405146 | ||||||||
\(575\) | 2.59703e6 | 0.327573 | ||||||||
\(576\) | 5.55337e6 | 0.697430 | ||||||||
\(577\) | 4.17811e6 | 0.522445 | 0.261222 | − | 0.965279i | \(-0.415874\pi\) | ||||
0.261222 | + | 0.965279i | \(0.415874\pi\) | |||||||
\(578\) | −3.53875e6 | −0.440585 | ||||||||
\(579\) | 7.01384e6 | 0.869480 | ||||||||
\(580\) | 4.22655e7 | 5.21695 | ||||||||
\(581\) | −5.45878e6 | −0.670896 | ||||||||
\(582\) | −3.03974e6 | −0.371988 | ||||||||
\(583\) | 2.91331e6 | 0.354990 | ||||||||
\(584\) | −2.30042e6 | −0.279110 | ||||||||
\(585\) | −4.87938e6 | −0.589488 | ||||||||
\(586\) | 1.82719e7 | 2.19806 | ||||||||
\(587\) | 1.07114e6 | 0.128307 | 0.0641537 | − | 0.997940i | \(-0.479565\pi\) | ||||
0.0641537 | + | 0.997940i | \(0.479565\pi\) | |||||||
\(588\) | −1.32928e7 | −1.58552 | ||||||||
\(589\) | −3.04114e6 | −0.361201 | ||||||||
\(590\) | −2.27603e6 | −0.269183 | ||||||||
\(591\) | 3.37804e6 | 0.397828 | ||||||||
\(592\) | 3.14503e7 | 3.68826 | ||||||||
\(593\) | −7.74188e6 | −0.904085 | −0.452043 | − | 0.891996i | \(-0.649305\pi\) | ||||
−0.452043 | + | 0.891996i | \(0.649305\pi\) | |||||||
\(594\) | 3.30504e6 | 0.384336 | ||||||||
\(595\) | −1.19335e7 | −1.38190 | ||||||||
\(596\) | −1.36670e6 | −0.157600 | ||||||||
\(597\) | −3.35847e6 | −0.385661 | ||||||||
\(598\) | 4.32422e7 | 4.94487 | ||||||||
\(599\) | 3.00377e6 | 0.342058 | 0.171029 | − | 0.985266i | \(-0.445291\pi\) | ||||
0.171029 | + | 0.985266i | \(0.445291\pi\) | |||||||
\(600\) | −3.01591e6 | −0.342011 | ||||||||
\(601\) | 5.32845e6 | 0.601748 | 0.300874 | − | 0.953664i | \(-0.402722\pi\) | ||||
0.300874 | + | 0.953664i | \(0.402722\pi\) | |||||||
\(602\) | −9.79458e6 | −1.10153 | ||||||||
\(603\) | −4.95291e6 | −0.554711 | ||||||||
\(604\) | −1.15720e7 | −1.29067 | ||||||||
\(605\) | −1.19382e6 | −0.132602 | ||||||||
\(606\) | 8.64624e6 | 0.956414 | ||||||||
\(607\) | 1.59774e7 | 1.76009 | 0.880046 | − | 0.474888i | \(-0.157512\pi\) | ||||
0.880046 | + | 0.474888i | \(0.157512\pi\) | |||||||
\(608\) | −4.71821e6 | −0.517629 | ||||||||
\(609\) | 1.41581e7 | 1.54689 | ||||||||
\(610\) | 2.05329e7 | 2.23422 | ||||||||
\(611\) | −2.36391e7 | −2.56170 | ||||||||
\(612\) | 6.91629e6 | 0.746440 | ||||||||
\(613\) | 8.04897e6 | 0.865145 | 0.432573 | − | 0.901599i | \(-0.357606\pi\) | ||||
0.432573 | + | 0.901599i | \(0.357606\pi\) | |||||||
\(614\) | 5.53281e6 | 0.592277 | ||||||||
\(615\) | 885433. | 0.0943991 | ||||||||
\(616\) | −4.21936e7 | −4.48018 | ||||||||
\(617\) | −1.00376e7 | −1.06150 | −0.530748 | − | 0.847529i | \(-0.678089\pi\) | ||||
−0.530748 | + | 0.847529i | \(0.678089\pi\) | |||||||
\(618\) | −9.48209e6 | −0.998695 | ||||||||
\(619\) | −3.31323e6 | −0.347556 | −0.173778 | − | 0.984785i | \(-0.555598\pi\) | ||||
−0.173778 | + | 0.984785i | \(0.555598\pi\) | |||||||
\(620\) | −5.04078e7 | −5.26646 | ||||||||
\(621\) | −3.00530e6 | −0.312722 | ||||||||
\(622\) | −538126. | −0.0557709 | ||||||||
\(623\) | 4.46485e6 | 0.460879 | ||||||||
\(624\) | −2.70428e7 | −2.78029 | ||||||||
\(625\) | −1.13374e7 | −1.16095 | ||||||||
\(626\) | 3.03980e7 | 3.10034 | ||||||||
\(627\) | −1.15716e6 | −0.117551 | ||||||||
\(628\) | −560802. | −0.0567427 | ||||||||
\(629\) | 1.07337e7 | 1.08174 | ||||||||
\(630\) | −9.88710e6 | −0.992471 | ||||||||
\(631\) | 1.30632e7 | 1.30610 | 0.653048 | − | 0.757316i | \(-0.273490\pi\) | ||||
0.653048 | + | 0.757316i | \(0.273490\pi\) | |||||||
\(632\) | −1.63177e7 | −1.62505 | ||||||||
\(633\) | −8.71454e6 | −0.864441 | ||||||||
\(634\) | 1.86197e7 | 1.83971 | ||||||||
\(635\) | 2.13060e7 | 2.09685 | ||||||||
\(636\) | 5.05107e6 | 0.495155 | ||||||||
\(637\) | 1.77385e7 | 1.73208 | ||||||||
\(638\) | 3.82033e7 | 3.71577 | ||||||||
\(639\) | −603847. | −0.0585025 | ||||||||
\(640\) | −1.42534e7 | −1.37552 | ||||||||
\(641\) | −3.24010e6 | −0.311468 | −0.155734 | − | 0.987799i | \(-0.549774\pi\) | ||||
−0.155734 | + | 0.987799i | \(0.549774\pi\) | |||||||
\(642\) | 9.47143e6 | 0.906939 | ||||||||
\(643\) | −1.43038e7 | −1.36435 | −0.682174 | − | 0.731189i | \(-0.738966\pi\) | ||||
−0.682174 | + | 0.731189i | \(0.738966\pi\) | |||||||
\(644\) | 6.29944e7 | 5.98531 | ||||||||
\(645\) | −2.71175e6 | −0.256656 | ||||||||
\(646\) | −3.36823e6 | −0.317556 | ||||||||
\(647\) | −1.69491e7 | −1.59179 | −0.795896 | − | 0.605434i | \(-0.793000\pi\) | ||||
−0.795896 | + | 0.605434i | \(0.793000\pi\) | |||||||
\(648\) | 3.49003e6 | 0.326506 | ||||||||
\(649\) | −1.47905e6 | −0.137839 | ||||||||
\(650\) | 6.60793e6 | 0.613454 | ||||||||
\(651\) | −1.68855e7 | −1.56157 | ||||||||
\(652\) | −2.25775e7 | −2.07997 | ||||||||
\(653\) | 4.66123e6 | 0.427777 | 0.213889 | − | 0.976858i | \(-0.431387\pi\) | ||||
0.213889 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(654\) | −5.48161e6 | −0.501145 | ||||||||
\(655\) | −6.58258e6 | −0.599506 | ||||||||
\(656\) | 4.90730e6 | 0.445228 | ||||||||
\(657\) | −350295. | −0.0316607 | ||||||||
\(658\) | −4.79000e7 | −4.31291 | ||||||||
\(659\) | 1.84395e7 | 1.65400 | 0.827001 | − | 0.562201i | \(-0.190045\pi\) | ||||
0.827001 | + | 0.562201i | \(0.190045\pi\) | |||||||
\(660\) | −1.91803e7 | −1.71394 | ||||||||
\(661\) | −1.59041e6 | −0.141581 | −0.0707905 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707905 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(662\) | −5.50549e6 | −0.488260 | ||||||||
\(663\) | −9.22944e6 | −0.815439 | ||||||||
\(664\) | −1.55541e7 | −1.36907 | ||||||||
\(665\) | 3.46168e6 | 0.303551 | ||||||||
\(666\) | 8.89302e6 | 0.776897 | ||||||||
\(667\) | −3.47385e7 | −3.02341 | ||||||||
\(668\) | 4.47292e7 | 3.87838 | ||||||||
\(669\) | 3.80875e6 | 0.329016 | ||||||||
\(670\) | 3.99806e7 | 3.44082 | ||||||||
\(671\) | 1.33430e7 | 1.14406 | ||||||||
\(672\) | −2.61973e7 | −2.23786 | ||||||||
\(673\) | −1.37250e7 | −1.16809 | −0.584044 | − | 0.811722i | \(-0.698530\pi\) | ||||
−0.584044 | + | 0.811722i | \(0.698530\pi\) | |||||||
\(674\) | −2.15208e7 | −1.82477 | ||||||||
\(675\) | −459245. | −0.0387959 | ||||||||
\(676\) | 4.87104e7 | 4.09972 | ||||||||
\(677\) | 1.55559e7 | 1.30444 | 0.652219 | − | 0.758031i | \(-0.273838\pi\) | ||||
0.652219 | + | 0.758031i | \(0.273838\pi\) | |||||||
\(678\) | −6.80345e6 | −0.568401 | ||||||||
\(679\) | 5.90925e6 | 0.491878 | ||||||||
\(680\) | −3.40030e7 | −2.81998 | ||||||||
\(681\) | −1.66887e6 | −0.137897 | ||||||||
\(682\) | −4.55630e7 | −3.75104 | ||||||||
\(683\) | −1.03021e7 | −0.845033 | −0.422517 | − | 0.906355i | \(-0.638853\pi\) | ||||
−0.422517 | + | 0.906355i | \(0.638853\pi\) | |||||||
\(684\) | −2.00628e6 | −0.163965 | ||||||||
\(685\) | −1.17210e7 | −0.954420 | ||||||||
\(686\) | 2.46472e6 | 0.199967 | ||||||||
\(687\) | −3.76287e6 | −0.304178 | ||||||||
\(688\) | −1.50292e7 | −1.21050 | ||||||||
\(689\) | −6.74040e6 | −0.540926 | ||||||||
\(690\) | 2.42592e7 | 1.93979 | ||||||||
\(691\) | 5.02324e6 | 0.400211 | 0.200106 | − | 0.979774i | \(-0.435871\pi\) | ||||
0.200106 | + | 0.979774i | \(0.435871\pi\) | |||||||
\(692\) | −4.61076e7 | −3.66022 | ||||||||
\(693\) | −6.42500e6 | −0.508206 | ||||||||
\(694\) | 1.41224e7 | 1.11304 | ||||||||
\(695\) | −1.42797e6 | −0.112139 | ||||||||
\(696\) | 4.03415e7 | 3.15667 | ||||||||
\(697\) | 1.67481e6 | 0.130582 | ||||||||
\(698\) | −1.28125e7 | −0.995393 | ||||||||
\(699\) | −1.23515e6 | −0.0956155 | ||||||||
\(700\) | 9.62630e6 | 0.742530 | ||||||||
\(701\) | −1.22395e7 | −0.940739 | −0.470370 | − | 0.882469i | \(-0.655879\pi\) | ||||
−0.470370 | + | 0.882469i | \(0.655879\pi\) | |||||||
\(702\) | −7.64673e6 | −0.585643 | ||||||||
\(703\) | −3.11363e6 | −0.237617 | ||||||||
\(704\) | −2.91306e7 | −2.21523 | ||||||||
\(705\) | −1.32617e7 | −1.00491 | ||||||||
\(706\) | −2.73809e7 | −2.06745 | ||||||||
\(707\) | −1.68083e7 | −1.26466 | ||||||||
\(708\) | −2.56436e6 | −0.192263 | ||||||||
\(709\) | 3.66774e6 | 0.274021 | 0.137010 | − | 0.990570i | \(-0.456251\pi\) | ||||
0.137010 | + | 0.990570i | \(0.456251\pi\) | |||||||
\(710\) | 4.87435e6 | 0.362886 | ||||||||
\(711\) | −2.48477e6 | −0.184337 | ||||||||
\(712\) | 1.27220e7 | 0.940493 | ||||||||
\(713\) | 4.14307e7 | 3.05210 | ||||||||
\(714\) | −1.87016e7 | −1.37288 | ||||||||
\(715\) | 2.55952e7 | 1.87238 | ||||||||
\(716\) | 4.93718e7 | 3.59912 | ||||||||
\(717\) | 1.86820e6 | 0.135714 | ||||||||
\(718\) | 2.11978e7 | 1.53454 | ||||||||
\(719\) | 1.96481e7 | 1.41742 | 0.708709 | − | 0.705501i | \(-0.249278\pi\) | ||||
0.708709 | + | 0.705501i | \(0.249278\pi\) | |||||||
\(720\) | −1.51712e7 | −1.09066 | ||||||||
\(721\) | 1.84332e7 | 1.32057 | ||||||||
\(722\) | −2.54433e7 | −1.81648 | ||||||||
\(723\) | 4.57140e6 | 0.325240 | ||||||||
\(724\) | 1.29506e7 | 0.918215 | ||||||||
\(725\) | −5.30846e6 | −0.375080 | ||||||||
\(726\) | −1.87090e6 | −0.131737 | ||||||||
\(727\) | 1.64307e6 | 0.115297 | 0.0576486 | − | 0.998337i | \(-0.481640\pi\) | ||||
0.0576486 | + | 0.998337i | \(0.481640\pi\) | |||||||
\(728\) | 9.76214e7 | 6.82679 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 2.82763e6 | 0.196388 | ||||||||
\(731\) | −5.12933e6 | −0.355032 | ||||||||
\(732\) | 2.31340e7 | 1.59578 | ||||||||
\(733\) | −4.63590e6 | −0.318694 | −0.159347 | − | 0.987223i | \(-0.550939\pi\) | ||||
−0.159347 | + | 0.987223i | \(0.550939\pi\) | |||||||
\(734\) | −1.17396e7 | −0.804291 | ||||||||
\(735\) | 9.95145e6 | 0.679467 | ||||||||
\(736\) | 6.42781e7 | 4.37390 | ||||||||
\(737\) | 2.59809e7 | 1.76191 | ||||||||
\(738\) | 1.38761e6 | 0.0937833 | ||||||||
\(739\) | 2.52043e7 | 1.69771 | 0.848855 | − | 0.528625i | \(-0.177292\pi\) | ||||
0.848855 | + | 0.528625i | \(0.177292\pi\) | |||||||
\(740\) | −5.16093e7 | −3.46457 | ||||||||
\(741\) | 2.67727e6 | 0.179121 | ||||||||
\(742\) | −1.36581e7 | −0.910710 | ||||||||
\(743\) | 2.59323e7 | 1.72333 | 0.861666 | − | 0.507475i | \(-0.169421\pi\) | ||||
0.861666 | + | 0.507475i | \(0.169421\pi\) | |||||||
\(744\) | −4.81132e7 | −3.18663 | ||||||||
\(745\) | 1.02316e6 | 0.0675386 | ||||||||
\(746\) | −2.35751e7 | −1.55098 | ||||||||
\(747\) | −2.36849e6 | −0.155299 | ||||||||
\(748\) | −3.62799e7 | −2.37090 | ||||||||
\(749\) | −1.84124e7 | −1.19924 | ||||||||
\(750\) | −1.46823e7 | −0.953104 | ||||||||
\(751\) | 2.11649e7 | 1.36936 | 0.684678 | − | 0.728846i | \(-0.259943\pi\) | ||||
0.684678 | + | 0.728846i | \(0.259943\pi\) | |||||||
\(752\) | −7.34999e7 | −4.73961 | ||||||||
\(753\) | 527808. | 0.0339225 | ||||||||
\(754\) | −8.83892e7 | −5.66201 | ||||||||
\(755\) | 8.66319e6 | 0.553109 | ||||||||
\(756\) | −1.11396e7 | −0.708867 | ||||||||
\(757\) | 1.49940e7 | 0.950992 | 0.475496 | − | 0.879718i | \(-0.342269\pi\) | ||||
0.475496 | + | 0.879718i | \(0.342269\pi\) | |||||||
\(758\) | −5.98140e6 | −0.378120 | ||||||||
\(759\) | 1.57645e7 | 0.993291 | ||||||||
\(760\) | 9.86360e6 | 0.619443 | ||||||||
\(761\) | −2.32932e7 | −1.45803 | −0.729015 | − | 0.684497i | \(-0.760022\pi\) | ||||
−0.729015 | + | 0.684497i | \(0.760022\pi\) | |||||||
\(762\) | 3.33897e7 | 2.08317 | ||||||||
\(763\) | 1.06562e7 | 0.662663 | ||||||||
\(764\) | −4.19342e7 | −2.59917 | ||||||||
\(765\) | −5.17779e6 | −0.319883 | ||||||||
\(766\) | −3.63164e7 | −2.23630 | ||||||||
\(767\) | 3.42201e6 | 0.210035 | ||||||||
\(768\) | −2.59185e6 | −0.158565 | ||||||||
\(769\) | −5.03552e6 | −0.307064 | −0.153532 | − | 0.988144i | \(-0.549065\pi\) | ||||
−0.153532 | + | 0.988144i | \(0.549065\pi\) | |||||||
\(770\) | 5.18636e7 | 3.15236 | ||||||||
\(771\) | −14274.1 | −0.000864795 0 | ||||||||
\(772\) | −6.37890e7 | −3.85214 | ||||||||
\(773\) | −1.34665e7 | −0.810599 | −0.405300 | − | 0.914184i | \(-0.632833\pi\) | ||||
−0.405300 | + | 0.914184i | \(0.632833\pi\) | |||||||
\(774\) | −4.24973e6 | −0.254981 | ||||||||
\(775\) | 6.33112e6 | 0.378640 | ||||||||
\(776\) | 1.68376e7 | 1.00375 | ||||||||
\(777\) | −1.72880e7 | −1.02729 | ||||||||
\(778\) | −3.31222e7 | −1.96187 | ||||||||
\(779\) | −485829. | −0.0286840 | ||||||||
\(780\) | 4.43766e7 | 2.61167 | ||||||||
\(781\) | 3.16753e6 | 0.185820 | ||||||||
\(782\) | 4.58867e7 | 2.68331 | ||||||||
\(783\) | 6.14298e6 | 0.358075 | ||||||||
\(784\) | 5.51535e7 | 3.20467 | ||||||||
\(785\) | 419837. | 0.0243168 | ||||||||
\(786\) | −1.03159e7 | −0.595595 | ||||||||
\(787\) | 6.43085e6 | 0.370111 | 0.185055 | − | 0.982728i | \(-0.440754\pi\) | ||||
0.185055 | + | 0.982728i | \(0.440754\pi\) | |||||||
\(788\) | −3.07223e7 | −1.76254 | ||||||||
\(789\) | 1.25466e7 | 0.717520 | ||||||||
\(790\) | 2.00574e7 | 1.14342 | ||||||||
\(791\) | 1.32259e7 | 0.751595 | ||||||||
\(792\) | −1.83072e7 | −1.03707 | ||||||||
\(793\) | −3.08711e7 | −1.74329 | ||||||||
\(794\) | −3.39686e7 | −1.91217 | ||||||||
\(795\) | −3.78142e6 | −0.212196 | ||||||||
\(796\) | 3.05444e7 | 1.70863 | ||||||||
\(797\) | 2.19054e7 | 1.22153 | 0.610765 | − | 0.791812i | \(-0.290862\pi\) | ||||
0.610765 | + | 0.791812i | \(0.290862\pi\) | |||||||
\(798\) | 5.42497e6 | 0.301571 | ||||||||
\(799\) | −2.50848e7 | −1.39009 | ||||||||
\(800\) | 9.82247e6 | 0.542620 | ||||||||
\(801\) | 1.93723e6 | 0.106684 | ||||||||
\(802\) | 3.32344e6 | 0.182454 | ||||||||
\(803\) | 1.83750e6 | 0.100563 | ||||||||
\(804\) | 4.50453e7 | 2.45759 | ||||||||
\(805\) | −4.71599e7 | −2.56497 | ||||||||
\(806\) | 1.05417e8 | 5.71575 | ||||||||
\(807\) | −6.74955e6 | −0.364830 | ||||||||
\(808\) | −4.78930e7 | −2.58074 | ||||||||
\(809\) | −3.19147e7 | −1.71443 | −0.857214 | − | 0.514961i | \(-0.827806\pi\) | ||||
−0.857214 | + | 0.514961i | \(0.827806\pi\) | |||||||
\(810\) | −4.28987e6 | −0.229737 | ||||||||
\(811\) | 7.21928e6 | 0.385426 | 0.192713 | − | 0.981255i | \(-0.438271\pi\) | ||||
0.192713 | + | 0.981255i | \(0.438271\pi\) | |||||||
\(812\) | −1.28764e8 | −6.85335 | ||||||||
\(813\) | −601749. | −0.0319293 | ||||||||
\(814\) | −4.66490e7 | −2.46764 | ||||||||
\(815\) | 1.69023e7 | 0.891359 | ||||||||
\(816\) | −2.86966e7 | −1.50871 | ||||||||
\(817\) | 1.48792e6 | 0.0779872 | ||||||||
\(818\) | −5.96930e6 | −0.311918 | ||||||||
\(819\) | 1.48652e7 | 0.774393 | ||||||||
\(820\) | −8.05277e6 | −0.418225 | ||||||||
\(821\) | 1.80572e7 | 0.934958 | 0.467479 | − | 0.884004i | \(-0.345162\pi\) | ||||
0.467479 | + | 0.884004i | \(0.345162\pi\) | |||||||
\(822\) | −1.83686e7 | −0.948194 | ||||||||
\(823\) | −4.54084e6 | −0.233688 | −0.116844 | − | 0.993150i | \(-0.537278\pi\) | ||||
−0.116844 | + | 0.993150i | \(0.537278\pi\) | |||||||
\(824\) | 5.25229e7 | 2.69483 | ||||||||
\(825\) | 2.40901e6 | 0.123226 | ||||||||
\(826\) | 6.93402e6 | 0.353619 | ||||||||
\(827\) | 2.72523e7 | 1.38561 | 0.692803 | − | 0.721127i | \(-0.256376\pi\) | ||||
0.692803 | + | 0.721127i | \(0.256376\pi\) | |||||||
\(828\) | 2.73323e7 | 1.38548 | ||||||||
\(829\) | 1.54051e7 | 0.778537 | 0.389269 | − | 0.921124i | \(-0.372728\pi\) | ||||
0.389269 | + | 0.921124i | \(0.372728\pi\) | |||||||
\(830\) | 1.91188e7 | 0.963308 | ||||||||
\(831\) | 3.58592e6 | 0.180135 | ||||||||
\(832\) | 6.73982e7 | 3.37552 | ||||||||
\(833\) | 1.88234e7 | 0.939906 | ||||||||
\(834\) | −2.23784e6 | −0.111407 | ||||||||
\(835\) | −3.34859e7 | −1.66206 | ||||||||
\(836\) | 1.05241e7 | 0.520797 | ||||||||
\(837\) | −7.32640e6 | −0.361474 | ||||||||
\(838\) | 1.52341e6 | 0.0749390 | ||||||||
\(839\) | 1.50266e7 | 0.736979 | 0.368489 | − | 0.929632i | \(-0.379875\pi\) | ||||
0.368489 | + | 0.929632i | \(0.379875\pi\) | |||||||
\(840\) | 5.47664e7 | 2.67803 | ||||||||
\(841\) | 5.04961e7 | 2.46188 | ||||||||
\(842\) | −4.08137e7 | −1.98393 | ||||||||
\(843\) | −3.66204e6 | −0.177482 | ||||||||
\(844\) | 7.92564e7 | 3.82982 | ||||||||
\(845\) | −3.64663e7 | −1.75691 | ||||||||
\(846\) | −2.07831e7 | −0.998355 | ||||||||
\(847\) | 3.63702e6 | 0.174196 | ||||||||
\(848\) | −2.09576e7 | −1.00081 | ||||||||
\(849\) | −2.08508e7 | −0.992780 | ||||||||
\(850\) | 7.01205e6 | 0.332887 | ||||||||
\(851\) | 4.24182e7 | 2.00784 | ||||||||
\(852\) | 5.49182e6 | 0.259190 | ||||||||
\(853\) | 3.68547e7 | 1.73428 | 0.867142 | − | 0.498060i | \(-0.165954\pi\) | ||||
0.867142 | + | 0.498060i | \(0.165954\pi\) | |||||||
\(854\) | −6.25543e7 | −2.93503 | ||||||||
\(855\) | 1.50197e6 | 0.0702662 | ||||||||
\(856\) | −5.24639e7 | −2.44724 | ||||||||
\(857\) | −3.27506e7 | −1.52324 | −0.761618 | − | 0.648026i | \(-0.775595\pi\) | ||||
−0.761618 | + | 0.648026i | \(0.775595\pi\) | |||||||
\(858\) | 4.01115e7 | 1.86016 | ||||||||
\(859\) | 3.34950e7 | 1.54881 | 0.774403 | − | 0.632693i | \(-0.218050\pi\) | ||||
0.774403 | + | 0.632693i | \(0.218050\pi\) | |||||||
\(860\) | 2.46627e7 | 1.13709 | ||||||||
\(861\) | −2.69750e6 | −0.124009 | ||||||||
\(862\) | −4.55826e7 | −2.08944 | ||||||||
\(863\) | 1.12755e7 | 0.515358 | 0.257679 | − | 0.966231i | \(-0.417042\pi\) | ||||
0.257679 | + | 0.966231i | \(0.417042\pi\) | |||||||
\(864\) | −1.13666e7 | −0.518020 | ||||||||
\(865\) | 3.45178e7 | 1.56857 | ||||||||
\(866\) | −3.63244e7 | −1.64590 | ||||||||
\(867\) | 2.98484e6 | 0.134857 | ||||||||
\(868\) | 1.53569e8 | 6.91840 | ||||||||
\(869\) | 1.30340e7 | 0.585503 | ||||||||
\(870\) | −4.95870e7 | −2.22111 | ||||||||
\(871\) | −6.01107e7 | −2.68476 | ||||||||
\(872\) | 3.03636e7 | 1.35226 | ||||||||
\(873\) | 2.56394e6 | 0.113860 | ||||||||
\(874\) | −1.33108e7 | −0.589422 | ||||||||
\(875\) | 2.85423e7 | 1.26029 | ||||||||
\(876\) | 3.18583e6 | 0.140269 | ||||||||
\(877\) | −3.74225e6 | −0.164299 | −0.0821493 | − | 0.996620i | \(-0.526178\pi\) | ||||
−0.0821493 | + | 0.996620i | \(0.526178\pi\) | |||||||
\(878\) | 7.44112e7 | 3.25763 | ||||||||
\(879\) | −1.54118e7 | −0.672794 | ||||||||
\(880\) | 7.95818e7 | 3.46423 | ||||||||
\(881\) | 1.20043e7 | 0.521073 | 0.260537 | − | 0.965464i | \(-0.416101\pi\) | ||||
0.260537 | + | 0.965464i | \(0.416101\pi\) | |||||||
\(882\) | 1.55954e7 | 0.675034 | ||||||||
\(883\) | −1.38235e7 | −0.596647 | −0.298324 | − | 0.954465i | \(-0.596427\pi\) | ||||
−0.298324 | + | 0.954465i | \(0.596427\pi\) | |||||||
\(884\) | 8.39392e7 | 3.61272 | ||||||||
\(885\) | 1.91977e6 | 0.0823932 | ||||||||
\(886\) | 4.93495e7 | 2.11202 | ||||||||
\(887\) | 1.58414e7 | 0.676059 | 0.338030 | − | 0.941135i | \(-0.390240\pi\) | ||||
0.338030 | + | 0.941135i | \(0.390240\pi\) | |||||||
\(888\) | −4.92600e7 | −2.09634 | ||||||||
\(889\) | −6.49095e7 | −2.75457 | ||||||||
\(890\) | −1.56376e7 | −0.661754 | ||||||||
\(891\) | −2.78772e6 | −0.117640 | ||||||||
\(892\) | −3.46395e7 | −1.45767 | ||||||||
\(893\) | 7.27659e6 | 0.305351 | ||||||||
\(894\) | 1.60344e6 | 0.0670980 | ||||||||
\(895\) | −3.69615e7 | −1.54238 | ||||||||
\(896\) | 4.34234e7 | 1.80698 | ||||||||
\(897\) | −3.64736e7 | −1.51355 | ||||||||
\(898\) | −4.51346e7 | −1.86775 | ||||||||
\(899\) | −8.46865e7 | −3.49474 | ||||||||
\(900\) | 4.17671e6 | 0.171881 | ||||||||
\(901\) | −7.15262e6 | −0.293530 | ||||||||
\(902\) | −7.27880e6 | −0.297881 | ||||||||
\(903\) | 8.26146e6 | 0.337161 | ||||||||
\(904\) | 3.76855e7 | 1.53374 | ||||||||
\(905\) | −9.69531e6 | −0.393496 | ||||||||
\(906\) | 1.35765e7 | 0.549501 | ||||||||
\(907\) | −3.64791e7 | −1.47240 | −0.736200 | − | 0.676764i | \(-0.763382\pi\) | ||||
−0.736200 | + | 0.676764i | \(0.763382\pi\) | |||||||
\(908\) | 1.51780e7 | 0.610940 | ||||||||
\(909\) | −7.29287e6 | −0.292745 | ||||||||
\(910\) | −1.19994e8 | −4.80349 | ||||||||
\(911\) | −3.55848e7 | −1.42059 | −0.710294 | − | 0.703905i | \(-0.751438\pi\) | ||||
−0.710294 | + | 0.703905i | \(0.751438\pi\) | |||||||
\(912\) | 8.32432e6 | 0.331407 | ||||||||
\(913\) | 1.24241e7 | 0.493273 | ||||||||
\(914\) | 9.03265e7 | 3.57643 | ||||||||
\(915\) | −1.73190e7 | −0.683863 | ||||||||
\(916\) | 3.42223e7 | 1.34763 | ||||||||
\(917\) | 2.00541e7 | 0.787553 | ||||||||
\(918\) | −8.11437e6 | −0.317796 | ||||||||
\(919\) | 3.19136e7 | 1.24649 | 0.623243 | − | 0.782028i | \(-0.285815\pi\) | ||||
0.623243 | + | 0.782028i | \(0.285815\pi\) | |||||||
\(920\) | −1.34376e8 | −5.23422 | ||||||||
\(921\) | −4.66678e6 | −0.181288 | ||||||||
\(922\) | −5.99291e7 | −2.32172 | ||||||||
\(923\) | −7.32856e6 | −0.283149 | ||||||||
\(924\) | 5.84336e7 | 2.25156 | ||||||||
\(925\) | 6.48202e6 | 0.249090 | ||||||||
\(926\) | 7.38507e6 | 0.283026 | ||||||||
\(927\) | 7.99788e6 | 0.305686 | ||||||||
\(928\) | −1.31388e8 | −5.00824 | ||||||||
\(929\) | −3.37958e6 | −0.128477 | −0.0642383 | − | 0.997935i | \(-0.520462\pi\) | ||||
−0.0642383 | + | 0.997935i | \(0.520462\pi\) | |||||||
\(930\) | 5.91398e7 | 2.24219 | ||||||||
\(931\) | −5.46028e6 | −0.206462 | ||||||||
\(932\) | 1.12334e7 | 0.423615 | ||||||||
\(933\) | 453894. | 0.0170707 | ||||||||
\(934\) | 6.62095e7 | 2.48344 | ||||||||
\(935\) | 2.71605e7 | 1.01603 | ||||||||
\(936\) | 4.23565e7 | 1.58027 | ||||||||
\(937\) | 3.48856e7 | 1.29807 | 0.649034 | − | 0.760760i | \(-0.275173\pi\) | ||||
0.649034 | + | 0.760760i | \(0.275173\pi\) | |||||||
\(938\) | −1.21802e8 | −4.52011 | ||||||||
\(939\) | −2.56399e7 | −0.948970 | ||||||||
\(940\) | 1.20612e8 | 4.45215 | ||||||||
\(941\) | −4.74186e7 | −1.74572 | −0.872859 | − | 0.487972i | \(-0.837737\pi\) | ||||
−0.872859 | + | 0.487972i | \(0.837737\pi\) | |||||||
\(942\) | 657947. | 0.0241582 | ||||||||
\(943\) | 6.61865e6 | 0.242376 | ||||||||
\(944\) | 1.06399e7 | 0.388603 | ||||||||
\(945\) | 8.33950e6 | 0.303781 | ||||||||
\(946\) | 2.22923e7 | 0.809891 | ||||||||
\(947\) | 3.31556e7 | 1.20139 | 0.600693 | − | 0.799480i | \(-0.294892\pi\) | ||||
0.600693 | + | 0.799480i | \(0.294892\pi\) | |||||||
\(948\) | 2.25983e7 | 0.816684 | ||||||||
\(949\) | −4.25133e6 | −0.153236 | ||||||||
\(950\) | −2.03405e6 | −0.0731229 | ||||||||
\(951\) | −1.57052e7 | −0.563108 | ||||||||
\(952\) | 1.03592e8 | 3.70452 | ||||||||
\(953\) | 4.68158e7 | 1.66978 | 0.834892 | − | 0.550413i | \(-0.185530\pi\) | ||||
0.834892 | + | 0.550413i | \(0.185530\pi\) | |||||||
\(954\) | −5.92605e6 | −0.210812 | ||||||||
\(955\) | 3.13935e7 | 1.11386 | ||||||||
\(956\) | −1.69908e7 | −0.601269 | ||||||||
\(957\) | −3.22235e7 | −1.13735 | ||||||||
\(958\) | −4.85310e7 | −1.70846 | ||||||||
\(959\) | 3.57086e7 | 1.25379 | ||||||||
\(960\) | 3.78109e7 | 1.32416 | ||||||||
\(961\) | 7.23719e7 | 2.52791 | ||||||||
\(962\) | 1.07930e8 | 3.76013 | ||||||||
\(963\) | −7.98890e6 | −0.277601 | ||||||||
\(964\) | −4.15756e7 | −1.44094 | ||||||||
\(965\) | 4.77547e7 | 1.65081 | ||||||||
\(966\) | −7.39066e7 | −2.54824 | ||||||||
\(967\) | −3.49546e7 | −1.20209 | −0.601047 | − | 0.799214i | \(-0.705250\pi\) | ||||
−0.601047 | + | 0.799214i | \(0.705250\pi\) | |||||||
\(968\) | 1.03632e7 | 0.355473 | ||||||||
\(969\) | 2.84101e6 | 0.0971992 | ||||||||
\(970\) | −2.06965e7 | −0.706265 | ||||||||
\(971\) | 5.44571e6 | 0.185356 | 0.0926780 | − | 0.995696i | \(-0.470457\pi\) | ||||
0.0926780 | + | 0.995696i | \(0.470457\pi\) | |||||||
\(972\) | −4.83331e6 | −0.164089 | ||||||||
\(973\) | 4.35035e6 | 0.147313 | ||||||||
\(974\) | −4.20657e7 | −1.42079 | ||||||||
\(975\) | −5.57361e6 | −0.187769 | ||||||||
\(976\) | −9.59862e7 | −3.22540 | ||||||||
\(977\) | 2.76151e7 | 0.925573 | 0.462786 | − | 0.886470i | \(-0.346850\pi\) | ||||
0.462786 | + | 0.886470i | \(0.346850\pi\) | |||||||
\(978\) | 2.64885e7 | 0.885545 | ||||||||
\(979\) | −1.01619e7 | −0.338859 | ||||||||
\(980\) | −9.05057e7 | −3.01031 | ||||||||
\(981\) | 4.62359e6 | 0.153393 | ||||||||
\(982\) | 5.95050e6 | 0.196913 | ||||||||
\(983\) | −8.85517e6 | −0.292289 | −0.146145 | − | 0.989263i | \(-0.546687\pi\) | ||||
−0.146145 | + | 0.989263i | \(0.546687\pi\) | |||||||
\(984\) | −7.68619e6 | −0.253060 | ||||||||
\(985\) | 2.29999e7 | 0.755326 | ||||||||
\(986\) | −9.37948e7 | −3.07246 | ||||||||
\(987\) | 4.04024e7 | 1.32012 | ||||||||
\(988\) | −2.43491e7 | −0.793579 | ||||||||
\(989\) | −2.02705e7 | −0.658982 | ||||||||
\(990\) | 2.25029e7 | 0.729709 | ||||||||
\(991\) | 3.63535e7 | 1.17588 | 0.587938 | − | 0.808906i | \(-0.299940\pi\) | ||||
0.587938 | + | 0.808906i | \(0.299940\pi\) | |||||||
\(992\) | 1.56699e8 | 5.05577 | ||||||||
\(993\) | 4.64373e6 | 0.149449 | ||||||||
\(994\) | −1.48499e7 | −0.476713 | ||||||||
\(995\) | −2.28666e7 | −0.732224 | ||||||||
\(996\) | 2.15407e7 | 0.688038 | ||||||||
\(997\) | 3.59054e6 | 0.114399 | 0.0571994 | − | 0.998363i | \(-0.481783\pi\) | ||||
0.0571994 | + | 0.998363i | \(0.481783\pi\) | |||||||
\(998\) | −4.29777e7 | −1.36589 | ||||||||
\(999\) | −7.50102e6 | −0.237797 |
(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 | 177.6.a.d.1.13 | ✓ | 13 | |
3.2 | odd | 2 | 531.6.a.e.1.1 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.a.d.1.13 | ✓ | 13 | 1.1 | even | 1 | trivial | |
531.6.a.e.1.1 | 13 | 3.2 | odd | 2 |