Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.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: | \(132.316651346\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} - 271 x^{8} + 309 x^{7} + 24456 x^{6} - 33410 x^{5} - 822204 x^{4} + 1367872 x^{3} + \cdots - 7036608 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4}\cdot 5^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Root | \(-7.65849\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 7.65849 | 1.35384 | 0.676921 | − | 0.736055i | \(-0.263314\pi\) | ||||
0.676921 | + | 0.736055i | \(0.263314\pi\) | |||||||
\(3\) | 9.00000 | 0.577350 | ||||||||
\(4\) | 26.6525 | 0.832890 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 68.9264 | 0.781641 | ||||||||
\(7\) | 112.197 | 0.865440 | 0.432720 | − | 0.901528i | \(-0.357554\pi\) | ||||
0.432720 | + | 0.901528i | \(0.357554\pi\) | |||||||
\(8\) | −40.9539 | −0.226241 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | 239.872 | 0.480869 | ||||||||
\(13\) | 849.133 | 1.39353 | 0.696767 | − | 0.717298i | \(-0.254621\pi\) | ||||
0.696767 | + | 0.717298i | \(0.254621\pi\) | |||||||
\(14\) | 859.262 | 1.17167 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1166.52 | −1.13918 | ||||||||
\(17\) | 608.382 | 0.510568 | 0.255284 | − | 0.966866i | \(-0.417831\pi\) | ||||
0.255284 | + | 0.966866i | \(0.417831\pi\) | |||||||
\(18\) | 620.338 | 0.451281 | ||||||||
\(19\) | −2245.32 | −1.42690 | −0.713452 | − | 0.700704i | \(-0.752869\pi\) | ||||
−0.713452 | + | 0.700704i | \(0.752869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1009.78 | 0.499662 | ||||||||
\(22\) | 926.677 | 0.408199 | ||||||||
\(23\) | 1287.36 | 0.507434 | 0.253717 | − | 0.967279i | \(-0.418347\pi\) | ||||
0.253717 | + | 0.967279i | \(0.418347\pi\) | |||||||
\(24\) | −368.585 | −0.130620 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6503.08 | 1.88662 | ||||||||
\(27\) | 729.000 | 0.192450 | ||||||||
\(28\) | 2990.34 | 0.720817 | ||||||||
\(29\) | 2679.38 | 0.591616 | 0.295808 | − | 0.955247i | \(-0.404411\pi\) | ||||
0.295808 | + | 0.955247i | \(0.404411\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3838.89 | 0.717467 | 0.358733 | − | 0.933440i | \(-0.383209\pi\) | ||||
0.358733 | + | 0.933440i | \(0.383209\pi\) | |||||||
\(32\) | −7623.29 | −1.31604 | ||||||||
\(33\) | 1089.00 | 0.174078 | ||||||||
\(34\) | 4659.28 | 0.691229 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2158.85 | 0.277630 | ||||||||
\(37\) | 12016.2 | 1.44299 | 0.721493 | − | 0.692422i | \(-0.243456\pi\) | ||||
0.721493 | + | 0.692422i | \(0.243456\pi\) | |||||||
\(38\) | −17195.8 | −1.93180 | ||||||||
\(39\) | 7642.20 | 0.804557 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −618.409 | −0.0574534 | −0.0287267 | − | 0.999587i | \(-0.509145\pi\) | ||||
−0.0287267 | + | 0.999587i | \(0.509145\pi\) | |||||||
\(42\) | 7733.36 | 0.676464 | ||||||||
\(43\) | 13349.9 | 1.10105 | 0.550526 | − | 0.834818i | \(-0.314427\pi\) | ||||
0.550526 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(44\) | 3224.95 | 0.251126 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 9859.21 | 0.686986 | ||||||||
\(47\) | 6897.13 | 0.455433 | 0.227716 | − | 0.973728i | \(-0.426874\pi\) | ||||
0.227716 | + | 0.973728i | \(0.426874\pi\) | |||||||
\(48\) | −10498.7 | −0.657708 | ||||||||
\(49\) | −4218.77 | −0.251013 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5475.43 | 0.294777 | ||||||||
\(52\) | 22631.5 | 1.16066 | ||||||||
\(53\) | −1982.49 | −0.0969438 | −0.0484719 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484719 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(54\) | 5583.04 | 0.260547 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4594.92 | −0.195798 | ||||||||
\(57\) | −20207.9 | −0.823824 | ||||||||
\(58\) | 20520.0 | 0.800954 | ||||||||
\(59\) | −38147.4 | −1.42671 | −0.713353 | − | 0.700805i | \(-0.752824\pi\) | ||||
−0.713353 | + | 0.700805i | \(0.752824\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5604.46 | 0.192845 | 0.0964226 | − | 0.995340i | \(-0.469260\pi\) | ||||
0.0964226 | + | 0.995340i | \(0.469260\pi\) | |||||||
\(62\) | 29400.1 | 0.971337 | ||||||||
\(63\) | 9087.98 | 0.288480 | ||||||||
\(64\) | −21054.1 | −0.642521 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 8340.10 | 0.235674 | ||||||||
\(67\) | −35672.2 | −0.970830 | −0.485415 | − | 0.874284i | \(-0.661331\pi\) | ||||
−0.485415 | + | 0.874284i | \(0.661331\pi\) | |||||||
\(68\) | 16214.9 | 0.425247 | ||||||||
\(69\) | 11586.2 | 0.292967 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 36035.5 | 0.848368 | 0.424184 | − | 0.905576i | \(-0.360561\pi\) | ||||
0.424184 | + | 0.905576i | \(0.360561\pi\) | |||||||
\(72\) | −3317.27 | −0.0754135 | ||||||||
\(73\) | 33184.8 | 0.728841 | 0.364420 | − | 0.931235i | \(-0.381267\pi\) | ||||
0.364420 | + | 0.931235i | \(0.381267\pi\) | |||||||
\(74\) | 92025.8 | 1.95358 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −59843.4 | −1.18845 | ||||||||
\(77\) | 13575.9 | 0.260940 | ||||||||
\(78\) | 58527.7 | 1.08924 | ||||||||
\(79\) | −31882.0 | −0.574749 | −0.287374 | − | 0.957818i | \(-0.592782\pi\) | ||||
−0.287374 | + | 0.957818i | \(0.592782\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −4736.08 | −0.0777829 | ||||||||
\(83\) | 91005.1 | 1.45001 | 0.725004 | − | 0.688745i | \(-0.241838\pi\) | ||||
0.725004 | + | 0.688745i | \(0.241838\pi\) | |||||||
\(84\) | 26913.0 | 0.416164 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 102240. | 1.49065 | ||||||||
\(87\) | 24114.4 | 0.341569 | ||||||||
\(88\) | −4955.42 | −0.0682141 | ||||||||
\(89\) | 50403.1 | 0.674501 | 0.337250 | − | 0.941415i | \(-0.390503\pi\) | ||||
0.337250 | + | 0.941415i | \(0.390503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 95270.4 | 1.20602 | ||||||||
\(92\) | 34311.3 | 0.422637 | ||||||||
\(93\) | 34550.0 | 0.414230 | ||||||||
\(94\) | 52821.6 | 0.616584 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −68609.6 | −0.759814 | ||||||||
\(97\) | 149344. | 1.61160 | 0.805800 | − | 0.592188i | \(-0.201736\pi\) | ||||
0.805800 | + | 0.592188i | \(0.201736\pi\) | |||||||
\(98\) | −32309.4 | −0.339832 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −55801.3 | −0.544304 | −0.272152 | − | 0.962254i | \(-0.587735\pi\) | ||||
−0.272152 | + | 0.962254i | \(0.587735\pi\) | |||||||
\(102\) | 41933.6 | 0.399081 | ||||||||
\(103\) | −41304.4 | −0.383622 | −0.191811 | − | 0.981432i | \(-0.561436\pi\) | ||||
−0.191811 | + | 0.981432i | \(0.561436\pi\) | |||||||
\(104\) | −34775.3 | −0.315274 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −15182.8 | −0.131247 | ||||||||
\(107\) | 133537. | 1.12756 | 0.563782 | − | 0.825924i | \(-0.309346\pi\) | ||||
0.563782 | + | 0.825924i | \(0.309346\pi\) | |||||||
\(108\) | 19429.7 | 0.160290 | ||||||||
\(109\) | −217266. | −1.75156 | −0.875782 | − | 0.482706i | \(-0.839654\pi\) | ||||
−0.875782 | + | 0.482706i | \(0.839654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 108146. | 0.833108 | ||||||||
\(112\) | −130881. | −0.985896 | ||||||||
\(113\) | 144891. | 1.06744 | 0.533722 | − | 0.845660i | \(-0.320793\pi\) | ||||
0.533722 | + | 0.845660i | \(0.320793\pi\) | |||||||
\(114\) | −154762. | −1.11533 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 71412.2 | 0.492751 | ||||||||
\(117\) | 68779.8 | 0.464511 | ||||||||
\(118\) | −292151. | −1.93154 | ||||||||
\(119\) | 68258.7 | 0.441866 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 42921.7 | 0.261082 | ||||||||
\(123\) | −5565.68 | −0.0331707 | ||||||||
\(124\) | 102316. | 0.597571 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 69600.2 | 0.390557 | ||||||||
\(127\) | 263734. | 1.45096 | 0.725482 | − | 0.688241i | \(-0.241617\pi\) | ||||
0.725482 | + | 0.688241i | \(0.241617\pi\) | |||||||
\(128\) | 82702.5 | 0.446163 | ||||||||
\(129\) | 120149. | 0.635692 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −343441. | −1.74853 | −0.874266 | − | 0.485447i | \(-0.838657\pi\) | ||||
−0.874266 | + | 0.485447i | \(0.838657\pi\) | |||||||
\(132\) | 29024.6 | 0.144988 | ||||||||
\(133\) | −251919. | −1.23490 | ||||||||
\(134\) | −273195. | −1.31435 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −24915.6 | −0.115511 | ||||||||
\(137\) | 172845. | 0.786786 | 0.393393 | − | 0.919370i | \(-0.371301\pi\) | ||||
0.393393 | + | 0.919370i | \(0.371301\pi\) | |||||||
\(138\) | 88732.9 | 0.396631 | ||||||||
\(139\) | −79230.1 | −0.347819 | −0.173909 | − | 0.984762i | \(-0.555640\pi\) | ||||
−0.173909 | + | 0.984762i | \(0.555640\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 62074.2 | 0.262944 | ||||||||
\(142\) | 275977. | 1.14856 | ||||||||
\(143\) | 102745. | 0.420166 | ||||||||
\(144\) | −94488.5 | −0.379728 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 254146. | 0.986736 | ||||||||
\(147\) | −37969.0 | −0.144922 | ||||||||
\(148\) | 320261. | 1.20185 | ||||||||
\(149\) | −112367. | −0.414641 | −0.207321 | − | 0.978273i | \(-0.566474\pi\) | ||||
−0.207321 | + | 0.978273i | \(0.566474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 351417. | 1.25424 | 0.627119 | − | 0.778923i | \(-0.284234\pi\) | ||||
0.627119 | + | 0.778923i | \(0.284234\pi\) | |||||||
\(152\) | 91954.8 | 0.322824 | ||||||||
\(153\) | 49278.9 | 0.170189 | ||||||||
\(154\) | 103971. | 0.353272 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 203684. | 0.670107 | ||||||||
\(157\) | 202204. | 0.654696 | 0.327348 | − | 0.944904i | \(-0.393845\pi\) | ||||
0.327348 | + | 0.944904i | \(0.393845\pi\) | |||||||
\(158\) | −244168. | −0.778120 | ||||||||
\(159\) | −17842.4 | −0.0559706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 144438. | 0.439154 | ||||||||
\(162\) | 50247.4 | 0.150427 | ||||||||
\(163\) | −317741. | −0.936708 | −0.468354 | − | 0.883541i | \(-0.655153\pi\) | ||||
−0.468354 | + | 0.883541i | \(0.655153\pi\) | |||||||
\(164\) | −16482.1 | −0.0478524 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 696962. | 1.96308 | ||||||||
\(167\) | 590220. | 1.63766 | 0.818828 | − | 0.574038i | \(-0.194624\pi\) | ||||
0.818828 | + | 0.574038i | \(0.194624\pi\) | |||||||
\(168\) | −41354.2 | −0.113044 | ||||||||
\(169\) | 349734. | 0.941934 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −181871. | −0.475635 | ||||||||
\(172\) | 355809. | 0.917055 | ||||||||
\(173\) | −461802. | −1.17311 | −0.586557 | − | 0.809908i | \(-0.699517\pi\) | ||||
−0.586557 | + | 0.809908i | \(0.699517\pi\) | |||||||
\(174\) | 184680. | 0.462431 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −141149. | −0.343477 | ||||||||
\(177\) | −343326. | −0.823709 | ||||||||
\(178\) | 386012. | 0.913168 | ||||||||
\(179\) | 60459.9 | 0.141038 | 0.0705188 | − | 0.997510i | \(-0.477535\pi\) | ||||
0.0705188 | + | 0.997510i | \(0.477535\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −472232. | −1.07142 | −0.535709 | − | 0.844403i | \(-0.679955\pi\) | ||||
−0.535709 | + | 0.844403i | \(0.679955\pi\) | |||||||
\(182\) | 729627. | 1.63276 | ||||||||
\(183\) | 50440.1 | 0.111339 | ||||||||
\(184\) | −52722.3 | −0.114802 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 264601. | 0.560802 | ||||||||
\(187\) | 73614.2 | 0.153942 | ||||||||
\(188\) | 183826. | 0.379325 | ||||||||
\(189\) | 81791.8 | 0.166554 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −85661.8 | −0.169904 | −0.0849521 | − | 0.996385i | \(-0.527074\pi\) | ||||
−0.0849521 | + | 0.996385i | \(0.527074\pi\) | |||||||
\(192\) | −189487. | −0.370960 | ||||||||
\(193\) | −992251. | −1.91747 | −0.958734 | − | 0.284304i | \(-0.908237\pi\) | ||||
−0.958734 | + | 0.284304i | \(0.908237\pi\) | |||||||
\(194\) | 1.14375e6 | 2.18185 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −112441. | −0.209066 | ||||||||
\(197\) | 854973. | 1.56959 | 0.784796 | − | 0.619754i | \(-0.212767\pi\) | ||||
0.784796 | + | 0.619754i | \(0.212767\pi\) | |||||||
\(198\) | 75060.9 | 0.136066 | ||||||||
\(199\) | 77645.6 | 0.138990 | 0.0694951 | − | 0.997582i | \(-0.477861\pi\) | ||||
0.0694951 | + | 0.997582i | \(0.477861\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −321050. | −0.560509 | ||||||||
\(202\) | −427354. | −0.736902 | ||||||||
\(203\) | 300619. | 0.512008 | ||||||||
\(204\) | 145934. | 0.245517 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −316330. | −0.519364 | ||||||||
\(207\) | 104276. | 0.169145 | ||||||||
\(208\) | −990534. | −1.58749 | ||||||||
\(209\) | −271684. | −0.430228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 741653. | 1.14682 | 0.573409 | − | 0.819269i | \(-0.305621\pi\) | ||||
0.573409 | + | 0.819269i | \(0.305621\pi\) | |||||||
\(212\) | −52838.1 | −0.0807436 | ||||||||
\(213\) | 324319. | 0.489806 | ||||||||
\(214\) | 1.02269e6 | 1.52654 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −29855.4 | −0.0435400 | ||||||||
\(217\) | 430713. | 0.620925 | ||||||||
\(218\) | −1.66393e6 | −2.37134 | ||||||||
\(219\) | 298664. | 0.420796 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 516597. | 0.711494 | ||||||||
\(222\) | 828232. | 1.12790 | ||||||||
\(223\) | 278843. | 0.375490 | 0.187745 | − | 0.982218i | \(-0.439882\pi\) | ||||
0.187745 | + | 0.982218i | \(0.439882\pi\) | |||||||
\(224\) | −855313. | −1.13895 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.10965e6 | 1.44515 | ||||||||
\(227\) | −770180. | −0.992036 | −0.496018 | − | 0.868312i | \(-0.665205\pi\) | ||||
−0.496018 | + | 0.868312i | \(0.665205\pi\) | |||||||
\(228\) | −538591. | −0.686155 | ||||||||
\(229\) | −1.03700e6 | −1.30674 | −0.653370 | − | 0.757039i | \(-0.726645\pi\) | ||||
−0.653370 | + | 0.757039i | \(0.726645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 122183. | 0.150654 | ||||||||
\(232\) | −109731. | −0.133847 | ||||||||
\(233\) | −1.31100e6 | −1.58203 | −0.791014 | − | 0.611799i | \(-0.790446\pi\) | ||||
−0.791014 | + | 0.611799i | \(0.790446\pi\) | |||||||
\(234\) | 526749. | 0.628875 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.01672e6 | −1.18829 | ||||||||
\(237\) | −286938. | −0.331831 | ||||||||
\(238\) | 522759. | 0.598217 | ||||||||
\(239\) | 173528. | 0.196506 | 0.0982529 | − | 0.995161i | \(-0.468675\pi\) | ||||
0.0982529 | + | 0.995161i | \(0.468675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −496038. | −0.550138 | −0.275069 | − | 0.961424i | \(-0.588701\pi\) | ||||
−0.275069 | + | 0.961424i | \(0.588701\pi\) | |||||||
\(242\) | 112128. | 0.123077 | ||||||||
\(243\) | 59049.0 | 0.0641500 | ||||||||
\(244\) | 149373. | 0.160619 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −42624.7 | −0.0449080 | ||||||||
\(247\) | −1.90658e6 | −1.98844 | ||||||||
\(248\) | −157218. | −0.162320 | ||||||||
\(249\) | 819046. | 0.837162 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 831223. | 0.832785 | 0.416393 | − | 0.909185i | \(-0.363294\pi\) | ||||
0.416393 | + | 0.909185i | \(0.363294\pi\) | |||||||
\(252\) | 242217. | 0.240272 | ||||||||
\(253\) | 155770. | 0.152997 | ||||||||
\(254\) | 2.01980e6 | 1.96438 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.30711e6 | 1.24656 | ||||||||
\(257\) | −734210. | −0.693406 | −0.346703 | − | 0.937975i | \(-0.612699\pi\) | ||||
−0.346703 | + | 0.937975i | \(0.612699\pi\) | |||||||
\(258\) | 920162. | 0.860627 | ||||||||
\(259\) | 1.34818e6 | 1.24882 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 217030. | 0.197205 | ||||||||
\(262\) | −2.63024e6 | −2.36724 | ||||||||
\(263\) | −89351.2 | −0.0796547 | −0.0398273 | − | 0.999207i | \(-0.512681\pi\) | ||||
−0.0398273 | + | 0.999207i | \(0.512681\pi\) | |||||||
\(264\) | −44598.8 | −0.0393834 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.92932e6 | −1.67186 | ||||||||
\(267\) | 453628. | 0.389423 | ||||||||
\(268\) | −950753. | −0.808594 | ||||||||
\(269\) | −927745. | −0.781714 | −0.390857 | − | 0.920451i | \(-0.627821\pi\) | ||||
−0.390857 | + | 0.920451i | \(0.627821\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 494541. | 0.409052 | 0.204526 | − | 0.978861i | \(-0.434435\pi\) | ||||
0.204526 | + | 0.978861i | \(0.434435\pi\) | |||||||
\(272\) | −709692. | −0.581631 | ||||||||
\(273\) | 857434. | 0.696296 | ||||||||
\(274\) | 1.32373e6 | 1.06518 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 308801. | 0.244009 | ||||||||
\(277\) | −1.98776e6 | −1.55656 | −0.778278 | − | 0.627920i | \(-0.783907\pi\) | ||||
−0.778278 | + | 0.627920i | \(0.783907\pi\) | |||||||
\(278\) | −606783. | −0.470892 | ||||||||
\(279\) | 310950. | 0.239156 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −760827. | −0.574804 | −0.287402 | − | 0.957810i | \(-0.592792\pi\) | ||||
−0.287402 | + | 0.957810i | \(0.592792\pi\) | |||||||
\(282\) | 475395. | 0.355985 | ||||||||
\(283\) | 2.17752e6 | 1.61620 | 0.808102 | − | 0.589043i | \(-0.200495\pi\) | ||||
0.808102 | + | 0.589043i | \(0.200495\pi\) | |||||||
\(284\) | 960435. | 0.706598 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 786872. | 0.568839 | ||||||||
\(287\) | −69383.8 | −0.0497225 | ||||||||
\(288\) | −617487. | −0.438679 | ||||||||
\(289\) | −1.04973e6 | −0.739320 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.34409e6 | 0.930458 | ||||||||
\(292\) | 884458. | 0.607044 | ||||||||
\(293\) | −573498. | −0.390268 | −0.195134 | − | 0.980777i | \(-0.562514\pi\) | ||||
−0.195134 | + | 0.980777i | \(0.562514\pi\) | |||||||
\(294\) | −290785. | −0.196202 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −492109. | −0.326462 | ||||||||
\(297\) | 88209.0 | 0.0580259 | ||||||||
\(298\) | −860560. | −0.561359 | ||||||||
\(299\) | 1.09314e6 | 0.707126 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.49782e6 | 0.952894 | ||||||||
\(302\) | 2.69132e6 | 1.69804 | ||||||||
\(303\) | −502212. | −0.314254 | ||||||||
\(304\) | 2.61922e6 | 1.62551 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 377402. | 0.230410 | ||||||||
\(307\) | −784034. | −0.474776 | −0.237388 | − | 0.971415i | \(-0.576291\pi\) | ||||
−0.237388 | + | 0.971415i | \(0.576291\pi\) | |||||||
\(308\) | 361831. | 0.217334 | ||||||||
\(309\) | −371740. | −0.221484 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.20531e6 | −0.706639 | −0.353320 | − | 0.935503i | \(-0.614947\pi\) | ||||
−0.353320 | + | 0.935503i | \(0.614947\pi\) | |||||||
\(312\) | −312978. | −0.182023 | ||||||||
\(313\) | −1.46973e6 | −0.847962 | −0.423981 | − | 0.905671i | \(-0.639368\pi\) | ||||
−0.423981 | + | 0.905671i | \(0.639368\pi\) | |||||||
\(314\) | 1.54858e6 | 0.886356 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −849735. | −0.478703 | ||||||||
\(317\) | 943173. | 0.527161 | 0.263580 | − | 0.964637i | \(-0.415097\pi\) | ||||
0.263580 | + | 0.964637i | \(0.415097\pi\) | |||||||
\(318\) | −136646. | −0.0757753 | ||||||||
\(319\) | 324205. | 0.178379 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.20183e6 | 0.651000 | ||||||||
\(322\) | 1.10618e6 | 0.594545 | ||||||||
\(323\) | −1.36601e6 | −0.728532 | ||||||||
\(324\) | 174867. | 0.0925433 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.43342e6 | −1.26816 | ||||||||
\(327\) | −1.95540e6 | −1.01127 | ||||||||
\(328\) | 25326.2 | 0.0129983 | ||||||||
\(329\) | 773840. | 0.394150 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.82790e6 | −1.41871 | −0.709357 | − | 0.704850i | \(-0.751014\pi\) | ||||
−0.709357 | + | 0.704850i | \(0.751014\pi\) | |||||||
\(332\) | 2.42551e6 | 1.20770 | ||||||||
\(333\) | 973310. | 0.480995 | ||||||||
\(334\) | 4.52020e6 | 2.21713 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.17793e6 | −0.569207 | ||||||||
\(337\) | 1.66721e6 | 0.799678 | 0.399839 | − | 0.916585i | \(-0.369066\pi\) | ||||
0.399839 | + | 0.916585i | \(0.369066\pi\) | |||||||
\(338\) | 2.67843e6 | 1.27523 | ||||||||
\(339\) | 1.30402e6 | 0.616289 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 464506. | 0.216324 | ||||||||
\(342\) | −1.39286e6 | −0.643935 | ||||||||
\(343\) | −2.35903e6 | −1.08268 | ||||||||
\(344\) | −546732. | −0.249102 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.53671e6 | −1.58821 | ||||||||
\(347\) | 2.99775e6 | 1.33651 | 0.668254 | − | 0.743933i | \(-0.267042\pi\) | ||||
0.668254 | + | 0.743933i | \(0.267042\pi\) | |||||||
\(348\) | 642710. | 0.284490 | ||||||||
\(349\) | −46625.4 | −0.0204908 | −0.0102454 | − | 0.999948i | \(-0.503261\pi\) | ||||
−0.0102454 | + | 0.999948i | \(0.503261\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 619018. | 0.268186 | ||||||||
\(352\) | −922418. | −0.396800 | ||||||||
\(353\) | −1.70738e6 | −0.729280 | −0.364640 | − | 0.931149i | \(-0.618808\pi\) | ||||
−0.364640 | + | 0.931149i | \(0.618808\pi\) | |||||||
\(354\) | −2.62936e6 | −1.11517 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.34337e6 | 0.561785 | ||||||||
\(357\) | 614329. | 0.255112 | ||||||||
\(358\) | 463032. | 0.190943 | ||||||||
\(359\) | −2.51698e6 | −1.03073 | −0.515364 | − | 0.856971i | \(-0.672343\pi\) | ||||
−0.515364 | + | 0.856971i | \(0.672343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.56538e6 | 1.03606 | ||||||||
\(362\) | −3.61658e6 | −1.45053 | ||||||||
\(363\) | 131769. | 0.0524864 | ||||||||
\(364\) | 2.53919e6 | 1.00448 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 386295. | 0.150736 | ||||||||
\(367\) | −2.06581e6 | −0.800616 | −0.400308 | − | 0.916381i | \(-0.631097\pi\) | ||||
−0.400308 | + | 0.916381i | \(0.631097\pi\) | |||||||
\(368\) | −1.50173e6 | −0.578061 | ||||||||
\(369\) | −50091.1 | −0.0191511 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −222429. | −0.0838991 | ||||||||
\(372\) | 920844. | 0.345008 | ||||||||
\(373\) | −3.01036e6 | −1.12033 | −0.560166 | − | 0.828380i | \(-0.689263\pi\) | ||||
−0.560166 | + | 0.828380i | \(0.689263\pi\) | |||||||
\(374\) | 563773. | 0.208413 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −282465. | −0.103037 | ||||||||
\(377\) | 2.27515e6 | 0.824436 | ||||||||
\(378\) | 626402. | 0.225488 | ||||||||
\(379\) | 510365. | 0.182508 | 0.0912541 | − | 0.995828i | \(-0.470912\pi\) | ||||
0.0912541 | + | 0.995828i | \(0.470912\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.37361e6 | 0.837715 | ||||||||
\(382\) | −656040. | −0.230024 | ||||||||
\(383\) | −3.20939e6 | −1.11796 | −0.558979 | − | 0.829182i | \(-0.688807\pi\) | ||||
−0.558979 | + | 0.829182i | \(0.688807\pi\) | |||||||
\(384\) | 744322. | 0.257592 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −7.59914e6 | −2.59595 | ||||||||
\(387\) | 1.08134e6 | 0.367017 | ||||||||
\(388\) | 3.98038e6 | 1.34229 | ||||||||
\(389\) | −4.52943e6 | −1.51764 | −0.758822 | − | 0.651298i | \(-0.774225\pi\) | ||||
−0.758822 | + | 0.651298i | \(0.774225\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 783204. | 0.259080 | ||||||||
\(392\) | 172775. | 0.0567893 | ||||||||
\(393\) | −3.09097e6 | −1.00952 | ||||||||
\(394\) | 6.54781e6 | 2.12498 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 261221. | 0.0837086 | ||||||||
\(397\) | −2.35485e6 | −0.749870 | −0.374935 | − | 0.927051i | \(-0.622335\pi\) | ||||
−0.374935 | + | 0.927051i | \(0.622335\pi\) | |||||||
\(398\) | 594648. | 0.188171 | ||||||||
\(399\) | −2.26727e6 | −0.712970 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.24320e6 | 1.00719 | 0.503597 | − | 0.863939i | \(-0.332010\pi\) | ||||
0.503597 | + | 0.863939i | \(0.332010\pi\) | |||||||
\(402\) | −2.45876e6 | −0.758841 | ||||||||
\(403\) | 3.25973e6 | 0.999814 | ||||||||
\(404\) | −1.48724e6 | −0.453345 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2.30229e6 | 0.693178 | ||||||||
\(407\) | 1.45396e6 | 0.435076 | ||||||||
\(408\) | −224240. | −0.0666904 | ||||||||
\(409\) | 2.99435e6 | 0.885103 | 0.442551 | − | 0.896743i | \(-0.354073\pi\) | ||||
0.442551 | + | 0.896743i | \(0.354073\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.55561e6 | 0.454251 | ||||||||
\(412\) | −1.10087e6 | −0.319515 | ||||||||
\(413\) | −4.28003e6 | −1.23473 | ||||||||
\(414\) | 798596. | 0.228995 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −6.47319e6 | −1.83394 | ||||||||
\(417\) | −713071. | −0.200813 | ||||||||
\(418\) | −2.08069e6 | −0.582461 | ||||||||
\(419\) | 1.09825e6 | 0.305608 | 0.152804 | − | 0.988257i | \(-0.451170\pi\) | ||||
0.152804 | + | 0.988257i | \(0.451170\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 52153.9 | 0.0143411 | 0.00717053 | − | 0.999974i | \(-0.497718\pi\) | ||||
0.00717053 | + | 0.999974i | \(0.497718\pi\) | |||||||
\(422\) | 5.67994e6 | 1.55261 | ||||||||
\(423\) | 558668. | 0.151811 | ||||||||
\(424\) | 81190.5 | 0.0219326 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 2.48380e6 | 0.663120 | ||||||||
\(427\) | 628805. | 0.166896 | ||||||||
\(428\) | 3.55909e6 | 0.939137 | ||||||||
\(429\) | 924706. | 0.242583 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 380799. | 0.0987423 | 0.0493711 | − | 0.998781i | \(-0.484278\pi\) | ||||
0.0493711 | + | 0.998781i | \(0.484278\pi\) | |||||||
\(432\) | −850396. | −0.219236 | ||||||||
\(433\) | 6.43191e6 | 1.64862 | 0.824309 | − | 0.566140i | \(-0.191564\pi\) | ||||
0.824309 | + | 0.566140i | \(0.191564\pi\) | |||||||
\(434\) | 3.29861e6 | 0.840634 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.79069e6 | −1.45886 | ||||||||
\(437\) | −2.89053e6 | −0.724060 | ||||||||
\(438\) | 2.28731e6 | 0.569692 | ||||||||
\(439\) | −2.43398e6 | −0.602776 | −0.301388 | − | 0.953502i | \(-0.597450\pi\) | ||||
−0.301388 | + | 0.953502i | \(0.597450\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −341721. | −0.0836710 | ||||||||
\(442\) | 3.95635e6 | 0.963250 | ||||||||
\(443\) | −4.37287e6 | −1.05866 | −0.529331 | − | 0.848415i | \(-0.677557\pi\) | ||||
−0.529331 | + | 0.848415i | \(0.677557\pi\) | |||||||
\(444\) | 2.88235e6 | 0.693887 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.13552e6 | 0.508354 | ||||||||
\(447\) | −1.01130e6 | −0.239393 | ||||||||
\(448\) | −2.36222e6 | −0.556064 | ||||||||
\(449\) | 6.51066e6 | 1.52409 | 0.762043 | − | 0.647527i | \(-0.224197\pi\) | ||||
0.762043 | + | 0.647527i | \(0.224197\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −74827.4 | −0.0173229 | ||||||||
\(452\) | 3.86171e6 | 0.889064 | ||||||||
\(453\) | 3.16275e6 | 0.724135 | ||||||||
\(454\) | −5.89841e6 | −1.34306 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 827593. | 0.186382 | ||||||||
\(457\) | −3.02898e6 | −0.678431 | −0.339216 | − | 0.940709i | \(-0.610162\pi\) | ||||
−0.339216 | + | 0.940709i | \(0.610162\pi\) | |||||||
\(458\) | −7.94184e6 | −1.76912 | ||||||||
\(459\) | 443510. | 0.0982589 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.31089e6 | −1.38305 | −0.691525 | − | 0.722352i | \(-0.743061\pi\) | ||||
−0.691525 | + | 0.722352i | \(0.743061\pi\) | |||||||
\(462\) | 935736. | 0.203962 | ||||||||
\(463\) | −1.33303e6 | −0.288993 | −0.144497 | − | 0.989505i | \(-0.546156\pi\) | ||||
−0.144497 | + | 0.989505i | \(0.546156\pi\) | |||||||
\(464\) | −3.12556e6 | −0.673959 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.00403e7 | −2.14182 | ||||||||
\(467\) | −2.53362e6 | −0.537587 | −0.268793 | − | 0.963198i | \(-0.586625\pi\) | ||||
−0.268793 | + | 0.963198i | \(0.586625\pi\) | |||||||
\(468\) | 1.83315e6 | 0.386887 | ||||||||
\(469\) | −4.00232e6 | −0.840195 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.81983e6 | 0.377989 | ||||||||
\(472\) | 1.56228e6 | 0.322779 | ||||||||
\(473\) | 1.61534e6 | 0.331979 | ||||||||
\(474\) | −2.19751e6 | −0.449248 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.81927e6 | 0.368026 | ||||||||
\(477\) | −160581. | −0.0323146 | ||||||||
\(478\) | 1.32896e6 | 0.266038 | ||||||||
\(479\) | −5.07626e6 | −1.01089 | −0.505447 | − | 0.862858i | \(-0.668672\pi\) | ||||
−0.505447 | + | 0.862858i | \(0.668672\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.02033e7 | 2.01085 | ||||||||
\(482\) | −3.79890e6 | −0.744801 | ||||||||
\(483\) | 1.29994e6 | 0.253546 | ||||||||
\(484\) | 390219. | 0.0757173 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 452226. | 0.0868491 | ||||||||
\(487\) | −4.42849e6 | −0.846123 | −0.423061 | − | 0.906101i | \(-0.639045\pi\) | ||||
−0.423061 | + | 0.906101i | \(0.639045\pi\) | |||||||
\(488\) | −229524. | −0.0436294 | ||||||||
\(489\) | −2.85967e6 | −0.540809 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.27064e6 | 0.612250 | 0.306125 | − | 0.951991i | \(-0.400967\pi\) | ||||
0.306125 | + | 0.951991i | \(0.400967\pi\) | |||||||
\(492\) | −148339. | −0.0276276 | ||||||||
\(493\) | 1.63009e6 | 0.302060 | ||||||||
\(494\) | −1.46015e7 | −2.69203 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.47816e6 | −0.817327 | ||||||||
\(497\) | 4.04308e6 | 0.734212 | ||||||||
\(498\) | 6.27265e6 | 1.13339 | ||||||||
\(499\) | −160223. | −0.0288053 | −0.0144027 | − | 0.999896i | \(-0.504585\pi\) | ||||
−0.0144027 | + | 0.999896i | \(0.504585\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.31198e6 | 0.945502 | ||||||||
\(502\) | 6.36591e6 | 1.12746 | ||||||||
\(503\) | 4.82699e6 | 0.850661 | 0.425330 | − | 0.905038i | \(-0.360158\pi\) | ||||
0.425330 | + | 0.905038i | \(0.360158\pi\) | |||||||
\(504\) | −372188. | −0.0652659 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.19296e6 | 0.207134 | ||||||||
\(507\) | 3.14760e6 | 0.543826 | ||||||||
\(508\) | 7.02917e6 | 1.20849 | ||||||||
\(509\) | −3.12997e6 | −0.535483 | −0.267741 | − | 0.963491i | \(-0.586277\pi\) | ||||
−0.267741 | + | 0.963491i | \(0.586277\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.72325e6 | 0.630768 | ||||||||
\(512\) | 7.36400e6 | 1.24148 | ||||||||
\(513\) | −1.63684e6 | −0.274608 | ||||||||
\(514\) | −5.62294e6 | −0.938763 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 3.20228e6 | 0.529462 | ||||||||
\(517\) | 834553. | 0.137318 | ||||||||
\(518\) | 1.03250e7 | 1.69070 | ||||||||
\(519\) | −4.15622e6 | −0.677298 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.30204e6 | 1.17856 | 0.589278 | − | 0.807930i | \(-0.299412\pi\) | ||||
0.589278 | + | 0.807930i | \(0.299412\pi\) | |||||||
\(522\) | 1.66212e6 | 0.266985 | ||||||||
\(523\) | 3.34673e6 | 0.535016 | 0.267508 | − | 0.963556i | \(-0.413800\pi\) | ||||
0.267508 | + | 0.963556i | \(0.413800\pi\) | |||||||
\(524\) | −9.15355e6 | −1.45634 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −684296. | −0.107840 | ||||||||
\(527\) | 2.33551e6 | 0.366316 | ||||||||
\(528\) | −1.27035e6 | −0.198307 | ||||||||
\(529\) | −4.77905e6 | −0.742511 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.08994e6 | −0.475569 | ||||||||
\(532\) | −6.71427e6 | −1.02854 | ||||||||
\(533\) | −525111. | −0.0800632 | ||||||||
\(534\) | 3.47411e6 | 0.527218 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.46092e6 | 0.219641 | ||||||||
\(537\) | 544139. | 0.0814281 | ||||||||
\(538\) | −7.10513e6 | −1.05832 | ||||||||
\(539\) | −510472. | −0.0756832 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.74690e6 | −0.697296 | −0.348648 | − | 0.937254i | \(-0.613359\pi\) | ||||
−0.348648 | + | 0.937254i | \(0.613359\pi\) | |||||||
\(542\) | 3.78744e6 | 0.553793 | ||||||||
\(543\) | −4.25008e6 | −0.618583 | ||||||||
\(544\) | −4.63787e6 | −0.671926 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 6.56665e6 | 0.942675 | ||||||||
\(547\) | −9.86753e6 | −1.41007 | −0.705034 | − | 0.709173i | \(-0.749068\pi\) | ||||
−0.705034 | + | 0.709173i | \(0.749068\pi\) | |||||||
\(548\) | 4.60676e6 | 0.655306 | ||||||||
\(549\) | 453961. | 0.0642818 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.01608e6 | −0.844179 | ||||||||
\(552\) | −474501. | −0.0662810 | ||||||||
\(553\) | −3.57708e6 | −0.497411 | ||||||||
\(554\) | −1.52232e7 | −2.10733 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.11168e6 | −0.289695 | ||||||||
\(557\) | 799590. | 0.109202 | 0.0546008 | − | 0.998508i | \(-0.482611\pi\) | ||||
0.0546008 | + | 0.998508i | \(0.482611\pi\) | |||||||
\(558\) | 2.38141e6 | 0.323779 | ||||||||
\(559\) | 1.13359e7 | 1.53435 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 662527. | 0.0888785 | ||||||||
\(562\) | −5.82678e6 | −0.778194 | ||||||||
\(563\) | −1.95313e6 | −0.259693 | −0.129847 | − | 0.991534i | \(-0.541448\pi\) | ||||
−0.129847 | + | 0.991534i | \(0.541448\pi\) | |||||||
\(564\) | 1.65443e6 | 0.219004 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1.66765e7 | 2.18809 | ||||||||
\(567\) | 736126. | 0.0961600 | ||||||||
\(568\) | −1.47579e6 | −0.191935 | ||||||||
\(569\) | −1.55722e6 | −0.201637 | −0.100819 | − | 0.994905i | \(-0.532146\pi\) | ||||
−0.100819 | + | 0.994905i | \(0.532146\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.77525e6 | 0.227861 | 0.113930 | − | 0.993489i | \(-0.463656\pi\) | ||||
0.113930 | + | 0.993489i | \(0.463656\pi\) | |||||||
\(572\) | 2.73841e6 | 0.349952 | ||||||||
\(573\) | −770957. | −0.0980942 | ||||||||
\(574\) | −531375. | −0.0673165 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.70538e6 | −0.214174 | ||||||||
\(577\) | −7.49718e6 | −0.937472 | −0.468736 | − | 0.883338i | \(-0.655290\pi\) | ||||
−0.468736 | + | 0.883338i | \(0.655290\pi\) | |||||||
\(578\) | −8.03934e6 | −1.00092 | ||||||||
\(579\) | −8.93026e6 | −1.10705 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.02105e7 | 1.25490 | ||||||||
\(582\) | 1.02937e7 | 1.25969 | ||||||||
\(583\) | −239881. | −0.0292297 | ||||||||
\(584\) | −1.35905e6 | −0.164893 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.39213e6 | −0.528361 | ||||||||
\(587\) | −8.46392e6 | −1.01386 | −0.506928 | − | 0.861988i | \(-0.669219\pi\) | ||||
−0.506928 | + | 0.861988i | \(0.669219\pi\) | |||||||
\(588\) | −1.01197e6 | −0.120704 | ||||||||
\(589\) | −8.61956e6 | −1.02376 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.69476e6 | 0.906205 | ||||||||
\(592\) | −1.40172e7 | −1.64383 | ||||||||
\(593\) | −6.09896e6 | −0.712228 | −0.356114 | − | 0.934442i | \(-0.615899\pi\) | ||||
−0.356114 | + | 0.934442i | \(0.615899\pi\) | |||||||
\(594\) | 675548. | 0.0785579 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.99486e6 | −0.345351 | ||||||||
\(597\) | 698811. | 0.0802461 | ||||||||
\(598\) | 8.37178e6 | 0.957337 | ||||||||
\(599\) | −4.91865e6 | −0.560118 | −0.280059 | − | 0.959983i | \(-0.590354\pi\) | ||||
−0.280059 | + | 0.959983i | \(0.590354\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.00491e7 | 1.13486 | 0.567431 | − | 0.823421i | \(-0.307937\pi\) | ||||
0.567431 | + | 0.823421i | \(0.307937\pi\) | |||||||
\(602\) | 1.14711e7 | 1.29007 | ||||||||
\(603\) | −2.88945e6 | −0.323610 | ||||||||
\(604\) | 9.36613e6 | 1.04464 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.84619e6 | −0.425450 | ||||||||
\(607\) | 1.26381e7 | 1.39222 | 0.696112 | − | 0.717933i | \(-0.254912\pi\) | ||||
0.696112 | + | 0.717933i | \(0.254912\pi\) | |||||||
\(608\) | 1.71168e7 | 1.87786 | ||||||||
\(609\) | 2.70557e6 | 0.295608 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.85658e6 | 0.634660 | ||||||||
\(612\) | 1.31341e6 | 0.141749 | ||||||||
\(613\) | 1.14049e7 | 1.22586 | 0.612932 | − | 0.790136i | \(-0.289990\pi\) | ||||
0.612932 | + | 0.790136i | \(0.289990\pi\) | |||||||
\(614\) | −6.00452e6 | −0.642772 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −555985. | −0.0590352 | ||||||||
\(617\) | 1.57880e7 | 1.66961 | 0.834804 | − | 0.550547i | \(-0.185581\pi\) | ||||
0.834804 | + | 0.550547i | \(0.185581\pi\) | |||||||
\(618\) | −2.84697e6 | −0.299855 | ||||||||
\(619\) | −3.22994e6 | −0.338819 | −0.169409 | − | 0.985546i | \(-0.554186\pi\) | ||||
−0.169409 | + | 0.985546i | \(0.554186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 938483. | 0.0976557 | ||||||||
\(622\) | −9.23086e6 | −0.956679 | ||||||||
\(623\) | 5.65509e6 | 0.583740 | ||||||||
\(624\) | −8.91481e6 | −0.916538 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.12559e7 | −1.14801 | ||||||||
\(627\) | −2.44516e6 | −0.248392 | ||||||||
\(628\) | 5.38923e6 | 0.545290 | ||||||||
\(629\) | 7.31042e6 | 0.736742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.46803e7 | −1.46778 | −0.733890 | − | 0.679268i | \(-0.762297\pi\) | ||||
−0.733890 | + | 0.679268i | \(0.762297\pi\) | |||||||
\(632\) | 1.30569e6 | 0.130031 | ||||||||
\(633\) | 6.67488e6 | 0.662116 | ||||||||
\(634\) | 7.22328e6 | 0.713693 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −475543. | −0.0466173 | ||||||||
\(637\) | −3.58230e6 | −0.349795 | ||||||||
\(638\) | 2.48292e6 | 0.241497 | ||||||||
\(639\) | 2.91887e6 | 0.282789 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.89836e6 | −0.374746 | −0.187373 | − | 0.982289i | \(-0.559997\pi\) | ||||
−0.187373 | + | 0.982289i | \(0.559997\pi\) | |||||||
\(642\) | 9.20421e6 | 0.881351 | ||||||||
\(643\) | 1.22406e7 | 1.16754 | 0.583772 | − | 0.811917i | \(-0.301576\pi\) | ||||
0.583772 | + | 0.811917i | \(0.301576\pi\) | |||||||
\(644\) | 3.84963e6 | 0.365767 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.04616e7 | −0.986318 | ||||||||
\(647\) | −1.57395e7 | −1.47819 | −0.739095 | − | 0.673601i | \(-0.764746\pi\) | ||||
−0.739095 | + | 0.673601i | \(0.764746\pi\) | |||||||
\(648\) | −268699. | −0.0251378 | ||||||||
\(649\) | −4.61583e6 | −0.430168 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.87642e6 | 0.358491 | ||||||||
\(652\) | −8.46859e6 | −0.780175 | ||||||||
\(653\) | 5.37711e6 | 0.493476 | 0.246738 | − | 0.969082i | \(-0.420641\pi\) | ||||
0.246738 | + | 0.969082i | \(0.420641\pi\) | |||||||
\(654\) | −1.49754e7 | −1.36910 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 721389. | 0.0654500 | ||||||||
\(657\) | 2.68797e6 | 0.242947 | ||||||||
\(658\) | 5.92644e6 | 0.533617 | ||||||||
\(659\) | −5.58169e6 | −0.500671 | −0.250335 | − | 0.968159i | \(-0.580541\pi\) | ||||
−0.250335 | + | 0.968159i | \(0.580541\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.97463e6 | 0.264807 | 0.132403 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132403 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(662\) | −2.16575e7 | −1.92071 | ||||||||
\(663\) | 4.64937e6 | 0.410781 | ||||||||
\(664\) | −3.72701e6 | −0.328051 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.45409e6 | 0.651192 | ||||||||
\(667\) | 3.44932e6 | 0.300206 | ||||||||
\(668\) | 1.57308e7 | 1.36399 | ||||||||
\(669\) | 2.50959e6 | 0.216789 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 678139. | 0.0581450 | ||||||||
\(672\) | −7.69781e6 | −0.657573 | ||||||||
\(673\) | −4.89911e6 | −0.416946 | −0.208473 | − | 0.978028i | \(-0.566849\pi\) | ||||
−0.208473 | + | 0.978028i | \(0.566849\pi\) | |||||||
\(674\) | 1.27683e7 | 1.08264 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 9.32127e6 | 0.784528 | ||||||||
\(677\) | 2.13572e7 | 1.79091 | 0.895453 | − | 0.445156i | \(-0.146852\pi\) | ||||
0.895453 | + | 0.445156i | \(0.146852\pi\) | |||||||
\(678\) | 9.98682e6 | 0.834359 | ||||||||
\(679\) | 1.67559e7 | 1.39474 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.93162e6 | −0.572752 | ||||||||
\(682\) | 3.55741e6 | 0.292869 | ||||||||
\(683\) | −1.39735e7 | −1.14618 | −0.573089 | − | 0.819493i | \(-0.694255\pi\) | ||||
−0.573089 | + | 0.819493i | \(0.694255\pi\) | |||||||
\(684\) | −4.84732e6 | −0.396152 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.80666e7 | −1.46577 | ||||||||
\(687\) | −9.33298e6 | −0.754446 | ||||||||
\(688\) | −1.55730e7 | −1.25430 | ||||||||
\(689\) | −1.68339e6 | −0.135094 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.97099e7 | 1.57033 | 0.785164 | − | 0.619288i | \(-0.212579\pi\) | ||||
0.785164 | + | 0.619288i | \(0.212579\pi\) | |||||||
\(692\) | −1.23082e7 | −0.977076 | ||||||||
\(693\) | 1.09965e6 | 0.0869800 | ||||||||
\(694\) | 2.29582e7 | 1.80942 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −987580. | −0.0772768 | ||||||||
\(697\) | −376228. | −0.0293339 | ||||||||
\(698\) | −357080. | −0.0277413 | ||||||||
\(699\) | −1.17990e7 | −0.913384 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.31790e7 | −1.01295 | −0.506473 | − | 0.862256i | \(-0.669051\pi\) | ||||
−0.506473 | + | 0.862256i | \(0.669051\pi\) | |||||||
\(702\) | 4.74074e6 | 0.363081 | ||||||||
\(703\) | −2.69802e7 | −2.05900 | ||||||||
\(704\) | −2.54755e6 | −0.193727 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.30760e7 | −0.987330 | ||||||||
\(707\) | −6.26076e6 | −0.471062 | ||||||||
\(708\) | −9.15050e6 | −0.686059 | ||||||||
\(709\) | −2.28382e7 | −1.70626 | −0.853131 | − | 0.521697i | \(-0.825299\pi\) | ||||
−0.853131 | + | 0.521697i | \(0.825299\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.58244e6 | −0.191583 | ||||||||
\(712\) | −2.06420e6 | −0.152599 | ||||||||
\(713\) | 4.94203e6 | 0.364067 | ||||||||
\(714\) | 4.70483e6 | 0.345381 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.61141e6 | 0.117469 | ||||||||
\(717\) | 1.56175e6 | 0.113453 | ||||||||
\(718\) | −1.92763e7 | −1.39544 | ||||||||
\(719\) | −3.78947e6 | −0.273373 | −0.136687 | − | 0.990614i | \(-0.543645\pi\) | ||||
−0.136687 | + | 0.990614i | \(0.543645\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.63424e6 | −0.332002 | ||||||||
\(722\) | 1.96469e7 | 1.40266 | ||||||||
\(723\) | −4.46434e6 | −0.317623 | ||||||||
\(724\) | −1.25861e7 | −0.892373 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.00915e6 | 0.0710583 | ||||||||
\(727\) | −2.52016e7 | −1.76845 | −0.884223 | − | 0.467065i | \(-0.845312\pi\) | ||||
−0.884223 | + | 0.467065i | \(0.845312\pi\) | |||||||
\(728\) | −3.90169e6 | −0.272851 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 8.12185e6 | 0.562162 | ||||||||
\(732\) | 1.34435e6 | 0.0927334 | ||||||||
\(733\) | 1.83693e7 | 1.26279 | 0.631397 | − | 0.775460i | \(-0.282482\pi\) | ||||
0.631397 | + | 0.775460i | \(0.282482\pi\) | |||||||
\(734\) | −1.58210e7 | −1.08391 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.81390e6 | −0.667801 | ||||||||
\(737\) | −4.31634e6 | −0.292716 | ||||||||
\(738\) | −383622. | −0.0259276 | ||||||||
\(739\) | 4.22050e6 | 0.284284 | 0.142142 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142142 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.71592e7 | −1.14803 | ||||||||
\(742\) | −1.70347e6 | −0.113586 | ||||||||
\(743\) | −6.24107e6 | −0.414750 | −0.207375 | − | 0.978261i | \(-0.566492\pi\) | ||||
−0.207375 | + | 0.978261i | \(0.566492\pi\) | |||||||
\(744\) | −1.41496e6 | −0.0937155 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.30548e7 | −1.51675 | ||||||||
\(747\) | 7.37141e6 | 0.483336 | ||||||||
\(748\) | 1.96200e6 | 0.128217 | ||||||||
\(749\) | 1.49825e7 | 0.975840 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −542004. | −0.0350673 | −0.0175337 | − | 0.999846i | \(-0.505581\pi\) | ||||
−0.0175337 | + | 0.999846i | \(0.505581\pi\) | |||||||
\(752\) | −8.04568e6 | −0.518822 | ||||||||
\(753\) | 7.48100e6 | 0.480809 | ||||||||
\(754\) | 1.74242e7 | 1.11616 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.17995e6 | 0.138721 | ||||||||
\(757\) | −1.63709e7 | −1.03833 | −0.519164 | − | 0.854675i | \(-0.673756\pi\) | ||||
−0.519164 | + | 0.854675i | \(0.673756\pi\) | |||||||
\(758\) | 3.90862e6 | 0.247087 | ||||||||
\(759\) | 1.40193e6 | 0.0883329 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.17890e7 | −0.737931 | −0.368966 | − | 0.929443i | \(-0.620288\pi\) | ||||
−0.368966 | + | 0.929443i | \(0.620288\pi\) | |||||||
\(762\) | 1.81782e7 | 1.13413 | ||||||||
\(763\) | −2.43767e7 | −1.51587 | ||||||||
\(764\) | −2.28310e6 | −0.141511 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.45791e7 | −1.51354 | ||||||||
\(767\) | −3.23922e7 | −1.98816 | ||||||||
\(768\) | 1.17640e7 | 0.719699 | ||||||||
\(769\) | −2.22979e7 | −1.35972 | −0.679858 | − | 0.733344i | \(-0.737958\pi\) | ||||
−0.679858 | + | 0.733344i | \(0.737958\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.60789e6 | −0.400338 | ||||||||
\(772\) | −2.64459e7 | −1.59704 | ||||||||
\(773\) | 2.38341e7 | 1.43467 | 0.717333 | − | 0.696730i | \(-0.245363\pi\) | ||||
0.717333 | + | 0.696730i | \(0.245363\pi\) | |||||||
\(774\) | 8.28146e6 | 0.496883 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.11620e6 | −0.364609 | ||||||||
\(777\) | 1.21336e7 | 0.721005 | ||||||||
\(778\) | −3.46886e7 | −2.05465 | ||||||||
\(779\) | 1.38853e6 | 0.0819805 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.36029e6 | 0.255793 | ||||||||
\(782\) | 5.99816e6 | 0.350753 | ||||||||
\(783\) | 1.95327e6 | 0.113856 | ||||||||
\(784\) | 4.92130e6 | 0.285950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −2.36721e7 | −1.36673 | ||||||||
\(787\) | −6.85248e6 | −0.394376 | −0.197188 | − | 0.980366i | \(-0.563181\pi\) | ||||
−0.197188 | + | 0.980366i | \(0.563181\pi\) | |||||||
\(788\) | 2.27872e7 | 1.30730 | ||||||||
\(789\) | −804161. | −0.0459886 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.62564e7 | 0.923810 | ||||||||
\(792\) | −401389. | −0.0227380 | ||||||||
\(793\) | 4.75893e6 | 0.268736 | ||||||||
\(794\) | −1.80346e7 | −1.01521 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.06945e6 | 0.115764 | ||||||||
\(797\) | −4.96228e6 | −0.276717 | −0.138358 | − | 0.990382i | \(-0.544183\pi\) | ||||
−0.138358 | + | 0.990382i | \(0.544183\pi\) | |||||||
\(798\) | −1.73639e7 | −0.965250 | ||||||||
\(799\) | 4.19609e6 | 0.232529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.08265e6 | 0.224834 | ||||||||
\(802\) | 2.48380e7 | 1.36358 | ||||||||
\(803\) | 4.01537e6 | 0.219754 | ||||||||
\(804\) | −8.55678e6 | −0.466842 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.49646e7 | 1.35359 | ||||||||
\(807\) | −8.34971e6 | −0.451323 | ||||||||
\(808\) | 2.28528e6 | 0.123144 | ||||||||
\(809\) | −1.48303e6 | −0.0796669 | −0.0398335 | − | 0.999206i | \(-0.512683\pi\) | ||||
−0.0398335 | + | 0.999206i | \(0.512683\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.26617e6 | −0.441319 | −0.220659 | − | 0.975351i | \(-0.570821\pi\) | ||||
−0.220659 | + | 0.975351i | \(0.570821\pi\) | |||||||
\(812\) | 8.01225e6 | 0.426446 | ||||||||
\(813\) | 4.45087e6 | 0.236167 | ||||||||
\(814\) | 1.11351e7 | 0.589025 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −6.38723e6 | −0.335805 | ||||||||
\(817\) | −2.99749e7 | −1.57110 | ||||||||
\(818\) | 2.29322e7 | 1.19829 | ||||||||
\(819\) | 7.71690e6 | 0.402007 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.39516e7 | 1.24016 | 0.620078 | − | 0.784540i | \(-0.287101\pi\) | ||||
0.620078 | + | 0.784540i | \(0.287101\pi\) | |||||||
\(822\) | 1.19136e7 | 0.614984 | ||||||||
\(823\) | −1.11177e7 | −0.572156 | −0.286078 | − | 0.958206i | \(-0.592352\pi\) | ||||
−0.286078 | + | 0.958206i | \(0.592352\pi\) | |||||||
\(824\) | 1.69158e6 | 0.0867908 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.27786e7 | −1.67163 | ||||||||
\(827\) | −1.84798e7 | −0.939580 | −0.469790 | − | 0.882778i | \(-0.655670\pi\) | ||||
−0.469790 | + | 0.882778i | \(0.655670\pi\) | |||||||
\(828\) | 2.77921e6 | 0.140879 | ||||||||
\(829\) | 1.97075e7 | 0.995969 | 0.497984 | − | 0.867186i | \(-0.334074\pi\) | ||||
0.497984 | + | 0.867186i | \(0.334074\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.78898e7 | −0.898678 | ||||||||
\(832\) | −1.78778e7 | −0.895374 | ||||||||
\(833\) | −2.56662e6 | −0.128159 | ||||||||
\(834\) | −5.46105e6 | −0.271870 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −7.24106e6 | −0.358333 | ||||||||
\(837\) | 2.79855e6 | 0.138077 | ||||||||
\(838\) | 8.41090e6 | 0.413745 | ||||||||
\(839\) | 3.06964e7 | 1.50550 | 0.752752 | − | 0.658304i | \(-0.228726\pi\) | ||||
0.752752 | + | 0.658304i | \(0.228726\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.33321e7 | −0.649991 | ||||||||
\(842\) | 399420. | 0.0194155 | ||||||||
\(843\) | −6.84744e6 | −0.331863 | ||||||||
\(844\) | 1.97669e7 | 0.955173 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.27855e6 | 0.205528 | ||||||||
\(847\) | 1.64268e6 | 0.0786764 | ||||||||
\(848\) | 2.31262e6 | 0.110437 | ||||||||
\(849\) | 1.95977e7 | 0.933116 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.54691e7 | 0.732220 | ||||||||
\(852\) | 8.64392e6 | 0.407954 | ||||||||
\(853\) | −1.45171e7 | −0.683137 | −0.341569 | − | 0.939857i | \(-0.610958\pi\) | ||||
−0.341569 | + | 0.939857i | \(0.610958\pi\) | |||||||
\(854\) | 4.81570e6 | 0.225951 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.46885e6 | −0.255101 | ||||||||
\(857\) | 2.63178e7 | 1.22405 | 0.612024 | − | 0.790840i | \(-0.290356\pi\) | ||||
0.612024 | + | 0.790840i | \(0.290356\pi\) | |||||||
\(858\) | 7.08185e6 | 0.328419 | ||||||||
\(859\) | −7.00715e6 | −0.324010 | −0.162005 | − | 0.986790i | \(-0.551796\pi\) | ||||
−0.162005 | + | 0.986790i | \(0.551796\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −624454. | −0.0287073 | ||||||||
\(862\) | 2.91635e6 | 0.133681 | ||||||||
\(863\) | 1.80082e6 | 0.0823084 | 0.0411542 | − | 0.999153i | \(-0.486897\pi\) | ||||
0.0411542 | + | 0.999153i | \(0.486897\pi\) | |||||||
\(864\) | −5.55738e6 | −0.253271 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.92587e7 | 2.23197 | ||||||||
\(867\) | −9.44756e6 | −0.426847 | ||||||||
\(868\) | 1.14796e7 | 0.517162 | ||||||||
\(869\) | −3.85772e6 | −0.173293 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.02904e7 | −1.35288 | ||||||||
\(872\) | 8.89790e6 | 0.396275 | ||||||||
\(873\) | 1.20968e7 | 0.537200 | ||||||||
\(874\) | −2.21371e7 | −0.980263 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.96013e6 | 0.350477 | ||||||||
\(877\) | −4.22779e7 | −1.85615 | −0.928077 | − | 0.372388i | \(-0.878539\pi\) | ||||
−0.928077 | + | 0.372388i | \(0.878539\pi\) | |||||||
\(878\) | −1.86406e7 | −0.816064 | ||||||||
\(879\) | −5.16148e6 | −0.225321 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.29766e6 | 0.403584 | 0.201792 | − | 0.979428i | \(-0.435323\pi\) | ||||
0.201792 | + | 0.979428i | \(0.435323\pi\) | |||||||
\(882\) | −2.61706e6 | −0.113277 | ||||||||
\(883\) | −3.50752e7 | −1.51390 | −0.756951 | − | 0.653472i | \(-0.773312\pi\) | ||||
−0.756951 | + | 0.653472i | \(0.773312\pi\) | |||||||
\(884\) | 1.37686e7 | 0.592596 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.34896e7 | −1.43326 | ||||||||
\(887\) | 3.66149e7 | 1.56260 | 0.781302 | − | 0.624153i | \(-0.214556\pi\) | ||||
0.781302 | + | 0.624153i | \(0.214556\pi\) | |||||||
\(888\) | −4.42898e6 | −0.188483 | ||||||||
\(889\) | 2.95902e7 | 1.25572 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 7.43186e6 | 0.312742 | ||||||||
\(893\) | −1.54863e7 | −0.649859 | ||||||||
\(894\) | −7.74504e6 | −0.324101 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9.27899e6 | 0.386128 | ||||||||
\(897\) | 9.83823e6 | 0.408259 | ||||||||
\(898\) | 4.98618e7 | 2.06337 | ||||||||
\(899\) | 1.02859e7 | 0.424464 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.20611e6 | −0.0494964 | ||||||||
\(902\) | −573065. | −0.0234524 | ||||||||
\(903\) | 1.34804e7 | 0.550154 | ||||||||
\(904\) | −5.93385e6 | −0.241499 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.42219e7 | 0.980365 | ||||||||
\(907\) | 4.65461e7 | 1.87873 | 0.939366 | − | 0.342916i | \(-0.111415\pi\) | ||||
0.939366 | + | 0.342916i | \(0.111415\pi\) | |||||||
\(908\) | −2.05272e7 | −0.826257 | ||||||||
\(909\) | −4.51991e6 | −0.181435 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.05339e7 | 1.21895 | 0.609476 | − | 0.792805i | \(-0.291380\pi\) | ||||
0.609476 | + | 0.792805i | \(0.291380\pi\) | |||||||
\(912\) | 2.35730e7 | 0.938487 | ||||||||
\(913\) | 1.10116e7 | 0.437194 | ||||||||
\(914\) | −2.31974e7 | −0.918490 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.76386e7 | −1.08837 | ||||||||
\(917\) | −3.85331e7 | −1.51325 | ||||||||
\(918\) | 3.39662e6 | 0.133027 | ||||||||
\(919\) | −2.39764e7 | −0.936472 | −0.468236 | − | 0.883603i | \(-0.655110\pi\) | ||||
−0.468236 | + | 0.883603i | \(0.655110\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.05630e6 | −0.274112 | ||||||||
\(922\) | −4.83319e7 | −1.87243 | ||||||||
\(923\) | 3.05989e7 | 1.18223 | ||||||||
\(924\) | 3.25648e6 | 0.125478 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.02090e7 | −0.391251 | ||||||||
\(927\) | −3.34566e6 | −0.127874 | ||||||||
\(928\) | −2.04257e7 | −0.778587 | ||||||||
\(929\) | 3.60560e7 | 1.37069 | 0.685343 | − | 0.728221i | \(-0.259652\pi\) | ||||
0.685343 | + | 0.728221i | \(0.259652\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.47251e6 | 0.358171 | ||||||||
\(932\) | −3.49415e7 | −1.31765 | ||||||||
\(933\) | −1.08478e7 | −0.407978 | ||||||||
\(934\) | −1.94037e7 | −0.727808 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.81680e6 | −0.105091 | ||||||||
\(937\) | −2.89459e7 | −1.07706 | −0.538528 | − | 0.842608i | \(-0.681019\pi\) | ||||
−0.538528 | + | 0.842608i | \(0.681019\pi\) | |||||||
\(938\) | −3.06518e7 | −1.13749 | ||||||||
\(939\) | −1.32276e7 | −0.489571 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.26496e7 | −0.833849 | −0.416924 | − | 0.908941i | \(-0.636892\pi\) | ||||
−0.416924 | + | 0.908941i | \(0.636892\pi\) | |||||||
\(942\) | 1.39372e7 | 0.511738 | ||||||||
\(943\) | −796113. | −0.0291538 | ||||||||
\(944\) | 4.44998e7 | 1.62528 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.23711e7 | 0.449448 | ||||||||
\(947\) | −3.01070e7 | −1.09092 | −0.545460 | − | 0.838137i | \(-0.683645\pi\) | ||||
−0.545460 | + | 0.838137i | \(0.683645\pi\) | |||||||
\(948\) | −7.64762e6 | −0.276379 | ||||||||
\(949\) | 2.81783e7 | 1.01566 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.48855e6 | 0.304356 | ||||||||
\(952\) | −2.79546e6 | −0.0999681 | ||||||||
\(953\) | 3.69781e7 | 1.31890 | 0.659450 | − | 0.751748i | \(-0.270789\pi\) | ||||
0.659450 | + | 0.751748i | \(0.270789\pi\) | |||||||
\(954\) | −1.22981e6 | −0.0437489 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.62496e6 | 0.163668 | ||||||||
\(957\) | 2.91785e6 | 0.102987 | ||||||||
\(958\) | −3.88765e7 | −1.36859 | ||||||||
\(959\) | 1.93928e7 | 0.680916 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.38921e7 | −0.485242 | ||||||||
\(962\) | 7.81421e7 | 2.72237 | ||||||||
\(963\) | 1.08165e7 | 0.375855 | ||||||||
\(964\) | −1.32206e7 | −0.458205 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.95559e6 | 0.343261 | ||||||||
\(967\) | −5.23212e6 | −0.179933 | −0.0899666 | − | 0.995945i | \(-0.528676\pi\) | ||||
−0.0899666 | + | 0.995945i | \(0.528676\pi\) | |||||||
\(968\) | −599606. | −0.0205673 | ||||||||
\(969\) | −1.22941e7 | −0.420618 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.23574e7 | 1.78209 | 0.891046 | − | 0.453913i | \(-0.149972\pi\) | ||||
0.891046 | + | 0.453913i | \(0.149972\pi\) | |||||||
\(972\) | 1.57380e6 | 0.0534299 | ||||||||
\(973\) | −8.88940e6 | −0.301017 | ||||||||
\(974\) | −3.39156e7 | −1.14552 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.53774e6 | −0.219686 | ||||||||
\(977\) | −3.76035e7 | −1.26035 | −0.630176 | − | 0.776452i | \(-0.717017\pi\) | ||||
−0.630176 | + | 0.776452i | \(0.717017\pi\) | |||||||
\(978\) | −2.19007e7 | −0.732170 | ||||||||
\(979\) | 6.09878e6 | 0.203370 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.75986e7 | −0.583855 | ||||||||
\(982\) | 2.50482e7 | 0.828890 | ||||||||
\(983\) | −4.17452e6 | −0.137791 | −0.0688957 | − | 0.997624i | \(-0.521948\pi\) | ||||
−0.0688957 | + | 0.997624i | \(0.521948\pi\) | |||||||
\(984\) | 227936. | 0.00750457 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.24840e7 | 0.408942 | ||||||||
\(987\) | 6.96456e6 | 0.227562 | ||||||||
\(988\) | −5.08150e7 | −1.65615 | ||||||||
\(989\) | 1.71861e7 | 0.558711 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.89607e6 | −0.255404 | −0.127702 | − | 0.991813i | \(-0.540760\pi\) | ||||
−0.127702 | + | 0.991813i | \(0.540760\pi\) | |||||||
\(992\) | −2.92650e7 | −0.944212 | ||||||||
\(993\) | −2.54511e7 | −0.819095 | ||||||||
\(994\) | 3.09639e7 | 0.994008 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 2.18296e7 | 0.697264 | ||||||||
\(997\) | 9.45089e6 | 0.301117 | 0.150558 | − | 0.988601i | \(-0.451893\pi\) | ||||
0.150558 | + | 0.988601i | \(0.451893\pi\) | |||||||
\(998\) | −1.22706e6 | −0.0389979 | ||||||||
\(999\) | 8.75979e6 | 0.277703 |
(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 | 825.6.a.t.1.8 | ✓ | 10 | |
5.4 | even | 2 | 825.6.a.u.1.3 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
825.6.a.t.1.8 | ✓ | 10 | 1.1 | even | 1 | trivial | |
825.6.a.u.1.3 | yes | 10 | 5.4 | even | 2 |