Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,6,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, 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("1045.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(167.601091705\) |
Analytic rank: | \(1\) |
Dimension: | \(36\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −7.64458 | −1.35138 | −0.675692 | − | 0.737184i | \(-0.736155\pi\) | ||||
−0.675692 | + | 0.737184i | \(0.736155\pi\) | |||||||
\(3\) | −6.22870 | −0.399572 | −0.199786 | − | 0.979840i | \(-0.564025\pi\) | ||||
−0.199786 | + | 0.979840i | \(0.564025\pi\) | |||||||
\(4\) | 26.4397 | 0.826240 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 47.6158 | 0.539975 | ||||||||
\(7\) | 101.320 | 0.781537 | 0.390769 | − | 0.920489i | \(-0.372209\pi\) | ||||
0.390769 | + | 0.920489i | \(0.372209\pi\) | |||||||
\(8\) | 42.5064 | 0.234817 | ||||||||
\(9\) | −204.203 | −0.840343 | ||||||||
\(10\) | −191.115 | −0.604357 | ||||||||
\(11\) | −121.000 | −0.301511 | ||||||||
\(12\) | −164.685 | −0.330142 | ||||||||
\(13\) | 348.722 | 0.572296 | 0.286148 | − | 0.958185i | \(-0.407625\pi\) | ||||
0.286148 | + | 0.958185i | \(0.407625\pi\) | |||||||
\(14\) | −774.549 | −1.05616 | ||||||||
\(15\) | −155.718 | −0.178694 | ||||||||
\(16\) | −1171.01 | −1.14357 | ||||||||
\(17\) | 1872.32 | 1.57129 | 0.785647 | − | 0.618675i | \(-0.212330\pi\) | ||||
0.785647 | + | 0.618675i | \(0.212330\pi\) | |||||||
\(18\) | 1561.05 | 1.13563 | ||||||||
\(19\) | 361.000 | 0.229416 | ||||||||
\(20\) | 660.992 | 0.369506 | ||||||||
\(21\) | −631.092 | −0.312280 | ||||||||
\(22\) | 924.995 | 0.407458 | ||||||||
\(23\) | −2061.94 | −0.812749 | −0.406375 | − | 0.913707i | \(-0.633207\pi\) | ||||
−0.406375 | + | 0.913707i | \(0.633207\pi\) | |||||||
\(24\) | −264.760 | −0.0938262 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −2665.83 | −0.773392 | ||||||||
\(27\) | 2785.50 | 0.735348 | ||||||||
\(28\) | 2678.87 | 0.645737 | ||||||||
\(29\) | −7892.55 | −1.74270 | −0.871350 | − | 0.490662i | \(-0.836755\pi\) | ||||
−0.871350 | + | 0.490662i | \(0.836755\pi\) | |||||||
\(30\) | 1190.40 | 0.241484 | ||||||||
\(31\) | 3271.95 | 0.611508 | 0.305754 | − | 0.952110i | \(-0.401091\pi\) | ||||
0.305754 | + | 0.952110i | \(0.401091\pi\) | |||||||
\(32\) | 7591.70 | 1.31058 | ||||||||
\(33\) | 753.673 | 0.120475 | ||||||||
\(34\) | −14313.1 | −2.12342 | ||||||||
\(35\) | 2533.00 | 0.349514 | ||||||||
\(36\) | −5399.07 | −0.694324 | ||||||||
\(37\) | 12898.6 | 1.54895 | 0.774474 | − | 0.632606i | \(-0.218015\pi\) | ||||
0.774474 | + | 0.632606i | \(0.218015\pi\) | |||||||
\(38\) | −2759.69 | −0.310029 | ||||||||
\(39\) | −2172.08 | −0.228673 | ||||||||
\(40\) | 1062.66 | 0.105013 | ||||||||
\(41\) | −12627.6 | −1.17317 | −0.586585 | − | 0.809887i | \(-0.699528\pi\) | ||||
−0.586585 | + | 0.809887i | \(0.699528\pi\) | |||||||
\(42\) | 4824.43 | 0.422010 | ||||||||
\(43\) | 14103.9 | 1.16323 | 0.581617 | − | 0.813463i | \(-0.302420\pi\) | ||||
0.581617 | + | 0.813463i | \(0.302420\pi\) | |||||||
\(44\) | −3199.20 | −0.249121 | ||||||||
\(45\) | −5105.08 | −0.375813 | ||||||||
\(46\) | 15762.7 | 1.09834 | ||||||||
\(47\) | 336.425 | 0.0222149 | 0.0111074 | − | 0.999938i | \(-0.496464\pi\) | ||||
0.0111074 | + | 0.999938i | \(0.496464\pi\) | |||||||
\(48\) | 7293.89 | 0.456937 | ||||||||
\(49\) | −6541.27 | −0.389199 | ||||||||
\(50\) | −4777.87 | −0.270277 | ||||||||
\(51\) | −11662.1 | −0.627845 | ||||||||
\(52\) | 9220.09 | 0.472854 | ||||||||
\(53\) | −19780.6 | −0.967273 | −0.483637 | − | 0.875269i | \(-0.660684\pi\) | ||||
−0.483637 | + | 0.875269i | \(0.660684\pi\) | |||||||
\(54\) | −21294.0 | −0.993738 | ||||||||
\(55\) | −3025.00 | −0.134840 | ||||||||
\(56\) | 4306.75 | 0.183518 | ||||||||
\(57\) | −2248.56 | −0.0916680 | ||||||||
\(58\) | 60335.3 | 2.35506 | ||||||||
\(59\) | −34443.1 | −1.28817 | −0.644084 | − | 0.764955i | \(-0.722761\pi\) | ||||
−0.644084 | + | 0.764955i | \(0.722761\pi\) | |||||||
\(60\) | −4117.12 | −0.147644 | ||||||||
\(61\) | −42575.8 | −1.46500 | −0.732502 | − | 0.680765i | \(-0.761647\pi\) | ||||
−0.732502 | + | 0.680765i | \(0.761647\pi\) | |||||||
\(62\) | −25012.7 | −0.826383 | ||||||||
\(63\) | −20689.9 | −0.656759 | ||||||||
\(64\) | −20563.0 | −0.627533 | ||||||||
\(65\) | 8718.04 | 0.255939 | ||||||||
\(66\) | −5761.52 | −0.162808 | ||||||||
\(67\) | −32925.8 | −0.896085 | −0.448043 | − | 0.894012i | \(-0.647879\pi\) | ||||
−0.448043 | + | 0.894012i | \(0.647879\pi\) | |||||||
\(68\) | 49503.5 | 1.29827 | ||||||||
\(69\) | 12843.2 | 0.324751 | ||||||||
\(70\) | −19363.7 | −0.472328 | ||||||||
\(71\) | 19755.3 | 0.465092 | 0.232546 | − | 0.972585i | \(-0.425294\pi\) | ||||
0.232546 | + | 0.972585i | \(0.425294\pi\) | |||||||
\(72\) | −8679.95 | −0.197327 | ||||||||
\(73\) | −2999.48 | −0.0658777 | −0.0329389 | − | 0.999457i | \(-0.510487\pi\) | ||||
−0.0329389 | + | 0.999457i | \(0.510487\pi\) | |||||||
\(74\) | −98604.1 | −2.09322 | ||||||||
\(75\) | −3892.94 | −0.0799143 | ||||||||
\(76\) | 9544.72 | 0.189552 | ||||||||
\(77\) | −12259.7 | −0.235642 | ||||||||
\(78\) | 16604.7 | 0.309025 | ||||||||
\(79\) | −59852.7 | −1.07899 | −0.539494 | − | 0.841990i | \(-0.681384\pi\) | ||||
−0.539494 | + | 0.841990i | \(0.681384\pi\) | |||||||
\(80\) | −29275.3 | −0.511419 | ||||||||
\(81\) | 32271.4 | 0.546518 | ||||||||
\(82\) | 96532.8 | 1.58540 | ||||||||
\(83\) | −65614.0 | −1.04545 | −0.522723 | − | 0.852503i | \(-0.675084\pi\) | ||||
−0.522723 | + | 0.852503i | \(0.675084\pi\) | |||||||
\(84\) | −16685.9 | −0.258018 | ||||||||
\(85\) | 46808.0 | 0.702704 | ||||||||
\(86\) | −107818. | −1.57198 | ||||||||
\(87\) | 49160.4 | 0.696333 | ||||||||
\(88\) | −5143.27 | −0.0708000 | ||||||||
\(89\) | 123011. | 1.64615 | 0.823074 | − | 0.567934i | \(-0.192257\pi\) | ||||
0.823074 | + | 0.567934i | \(0.192257\pi\) | |||||||
\(90\) | 39026.2 | 0.507867 | ||||||||
\(91\) | 35332.5 | 0.447271 | ||||||||
\(92\) | −54517.0 | −0.671526 | ||||||||
\(93\) | −20380.0 | −0.244341 | ||||||||
\(94\) | −2571.83 | −0.0300208 | ||||||||
\(95\) | 9025.00 | 0.102598 | ||||||||
\(96\) | −47286.5 | −0.523671 | ||||||||
\(97\) | −45436.7 | −0.490318 | −0.245159 | − | 0.969483i | \(-0.578840\pi\) | ||||
−0.245159 | + | 0.969483i | \(0.578840\pi\) | |||||||
\(98\) | 50005.3 | 0.525958 | ||||||||
\(99\) | 24708.6 | 0.253373 | ||||||||
\(100\) | 16524.8 | 0.165248 | ||||||||
\(101\) | −41046.0 | −0.400376 | −0.200188 | − | 0.979758i | \(-0.564155\pi\) | ||||
−0.200188 | + | 0.979758i | \(0.564155\pi\) | |||||||
\(102\) | 89152.1 | 0.848459 | ||||||||
\(103\) | −30183.1 | −0.280331 | −0.140165 | − | 0.990128i | \(-0.544763\pi\) | ||||
−0.140165 | + | 0.990128i | \(0.544763\pi\) | |||||||
\(104\) | 14822.9 | 0.134385 | ||||||||
\(105\) | −15777.3 | −0.139656 | ||||||||
\(106\) | 151214. | 1.30716 | ||||||||
\(107\) | 215833. | 1.82246 | 0.911229 | − | 0.411900i | \(-0.135135\pi\) | ||||
0.911229 | + | 0.411900i | \(0.135135\pi\) | |||||||
\(108\) | 73647.6 | 0.607574 | ||||||||
\(109\) | 63890.2 | 0.515072 | 0.257536 | − | 0.966269i | \(-0.417089\pi\) | ||||
0.257536 | + | 0.966269i | \(0.417089\pi\) | |||||||
\(110\) | 23124.9 | 0.182221 | ||||||||
\(111\) | −80341.3 | −0.618915 | ||||||||
\(112\) | −118647. | −0.893741 | ||||||||
\(113\) | 38872.1 | 0.286379 | 0.143190 | − | 0.989695i | \(-0.454264\pi\) | ||||
0.143190 | + | 0.989695i | \(0.454264\pi\) | |||||||
\(114\) | 17189.3 | 0.123879 | ||||||||
\(115\) | −51548.5 | −0.363473 | ||||||||
\(116\) | −208677. | −1.43989 | ||||||||
\(117\) | −71210.1 | −0.480925 | ||||||||
\(118\) | 263303. | 1.74081 | ||||||||
\(119\) | 189703. | 1.22803 | ||||||||
\(120\) | −6618.99 | −0.0419603 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 325475. | 1.97978 | ||||||||
\(123\) | 78653.6 | 0.468766 | ||||||||
\(124\) | 86509.3 | 0.505253 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 158165. | 0.887534 | ||||||||
\(127\) | −36546.8 | −0.201067 | −0.100533 | − | 0.994934i | \(-0.532055\pi\) | ||||
−0.100533 | + | 0.994934i | \(0.532055\pi\) | |||||||
\(128\) | −85738.9 | −0.462544 | ||||||||
\(129\) | −87848.8 | −0.464795 | ||||||||
\(130\) | −66645.8 | −0.345871 | ||||||||
\(131\) | 13416.8 | 0.0683081 | 0.0341540 | − | 0.999417i | \(-0.489126\pi\) | ||||
0.0341540 | + | 0.999417i | \(0.489126\pi\) | |||||||
\(132\) | 19926.9 | 0.0995415 | ||||||||
\(133\) | 36576.5 | 0.179297 | ||||||||
\(134\) | 251704. | 1.21096 | ||||||||
\(135\) | 69637.4 | 0.328858 | ||||||||
\(136\) | 79585.6 | 0.368967 | ||||||||
\(137\) | 287242. | 1.30752 | 0.653758 | − | 0.756704i | \(-0.273192\pi\) | ||||
0.653758 | + | 0.756704i | \(0.273192\pi\) | |||||||
\(138\) | −98181.1 | −0.438864 | ||||||||
\(139\) | 172576. | 0.757608 | 0.378804 | − | 0.925477i | \(-0.376336\pi\) | ||||
0.378804 | + | 0.925477i | \(0.376336\pi\) | |||||||
\(140\) | 66971.6 | 0.288782 | ||||||||
\(141\) | −2095.49 | −0.00887643 | ||||||||
\(142\) | −151021. | −0.628517 | ||||||||
\(143\) | −42195.3 | −0.172554 | ||||||||
\(144\) | 239125. | 0.960989 | ||||||||
\(145\) | −197314. | −0.779359 | ||||||||
\(146\) | 22929.8 | 0.0890261 | ||||||||
\(147\) | 40743.6 | 0.155513 | ||||||||
\(148\) | 341034. | 1.27980 | ||||||||
\(149\) | −422123. | −1.55766 | −0.778831 | − | 0.627234i | \(-0.784187\pi\) | ||||
−0.778831 | + | 0.627234i | \(0.784187\pi\) | |||||||
\(150\) | 29759.9 | 0.107995 | ||||||||
\(151\) | −60667.0 | −0.216526 | −0.108263 | − | 0.994122i | \(-0.534529\pi\) | ||||
−0.108263 | + | 0.994122i | \(0.534529\pi\) | |||||||
\(152\) | 15344.8 | 0.0538707 | ||||||||
\(153\) | −382334. | −1.32043 | ||||||||
\(154\) | 93720.4 | 0.318443 | ||||||||
\(155\) | 81798.7 | 0.273475 | ||||||||
\(156\) | −57429.2 | −0.188939 | ||||||||
\(157\) | −141637. | −0.458594 | −0.229297 | − | 0.973356i | \(-0.573643\pi\) | ||||
−0.229297 | + | 0.973356i | \(0.573643\pi\) | |||||||
\(158\) | 457549. | 1.45813 | ||||||||
\(159\) | 123207. | 0.386495 | ||||||||
\(160\) | 189793. | 0.586110 | ||||||||
\(161\) | −208916. | −0.635194 | ||||||||
\(162\) | −246701. | −0.738556 | ||||||||
\(163\) | 244148. | 0.719753 | 0.359877 | − | 0.933000i | \(-0.382819\pi\) | ||||
0.359877 | + | 0.933000i | \(0.382819\pi\) | |||||||
\(164\) | −333870. | −0.969320 | ||||||||
\(165\) | 18841.8 | 0.0538782 | ||||||||
\(166\) | 501592. | 1.41280 | ||||||||
\(167\) | 179805. | 0.498896 | 0.249448 | − | 0.968388i | \(-0.419751\pi\) | ||||
0.249448 | + | 0.968388i | \(0.419751\pi\) | |||||||
\(168\) | −26825.4 | −0.0733286 | ||||||||
\(169\) | −249686. | −0.672477 | ||||||||
\(170\) | −357828. | −0.949624 | ||||||||
\(171\) | −73717.4 | −0.192788 | ||||||||
\(172\) | 372901. | 0.961110 | ||||||||
\(173\) | −51815.2 | −0.131626 | −0.0658130 | − | 0.997832i | \(-0.520964\pi\) | ||||
−0.0658130 | + | 0.997832i | \(0.520964\pi\) | |||||||
\(174\) | −375811. | −0.941014 | ||||||||
\(175\) | 63325.0 | 0.156307 | ||||||||
\(176\) | 141693. | 0.344799 | ||||||||
\(177\) | 214536. | 0.514715 | ||||||||
\(178\) | −940368. | −2.22458 | ||||||||
\(179\) | −77213.0 | −0.180118 | −0.0900592 | − | 0.995936i | \(-0.528706\pi\) | ||||
−0.0900592 | + | 0.995936i | \(0.528706\pi\) | |||||||
\(180\) | −134977. | −0.310511 | ||||||||
\(181\) | −61707.1 | −0.140004 | −0.0700018 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0700018 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(182\) | −270102. | −0.604435 | ||||||||
\(183\) | 265192. | 0.585374 | ||||||||
\(184\) | −87645.7 | −0.190847 | ||||||||
\(185\) | 322464. | 0.692710 | ||||||||
\(186\) | 155797. | 0.330199 | ||||||||
\(187\) | −226551. | −0.473763 | ||||||||
\(188\) | 8894.97 | 0.0183548 | ||||||||
\(189\) | 282226. | 0.574702 | ||||||||
\(190\) | −68992.4 | −0.138649 | ||||||||
\(191\) | 834397. | 1.65497 | 0.827483 | − | 0.561491i | \(-0.189772\pi\) | ||||
0.827483 | + | 0.561491i | \(0.189772\pi\) | |||||||
\(192\) | 128081. | 0.250744 | ||||||||
\(193\) | 706298. | 1.36488 | 0.682440 | − | 0.730941i | \(-0.260919\pi\) | ||||
0.682440 | + | 0.730941i | \(0.260919\pi\) | |||||||
\(194\) | 347345. | 0.662608 | ||||||||
\(195\) | −54302.1 | −0.102266 | ||||||||
\(196\) | −172949. | −0.321572 | ||||||||
\(197\) | 644796. | 1.18374 | 0.591871 | − | 0.806033i | \(-0.298390\pi\) | ||||
0.591871 | + | 0.806033i | \(0.298390\pi\) | |||||||
\(198\) | −188887. | −0.342404 | ||||||||
\(199\) | 305920. | 0.547615 | 0.273808 | − | 0.961784i | \(-0.411717\pi\) | ||||
0.273808 | + | 0.961784i | \(0.411717\pi\) | |||||||
\(200\) | 26566.5 | 0.0469634 | ||||||||
\(201\) | 205085. | 0.358050 | ||||||||
\(202\) | 313780. | 0.541061 | ||||||||
\(203\) | −799673. | −1.36199 | ||||||||
\(204\) | −308343. | −0.518750 | ||||||||
\(205\) | −315690. | −0.524658 | ||||||||
\(206\) | 230737. | 0.378835 | ||||||||
\(207\) | 421055. | 0.682988 | ||||||||
\(208\) | −408358. | −0.654459 | ||||||||
\(209\) | −43681.0 | −0.0691714 | ||||||||
\(210\) | 120611. | 0.188729 | ||||||||
\(211\) | −868086. | −1.34232 | −0.671161 | − | 0.741311i | \(-0.734204\pi\) | ||||
−0.671161 | + | 0.741311i | \(0.734204\pi\) | |||||||
\(212\) | −522992. | −0.799199 | ||||||||
\(213\) | −123050. | −0.185837 | ||||||||
\(214\) | −1.64995e6 | −2.46284 | ||||||||
\(215\) | 352597. | 0.520214 | ||||||||
\(216\) | 118401. | 0.172672 | ||||||||
\(217\) | 331514. | 0.477917 | ||||||||
\(218\) | −488414. | −0.696060 | ||||||||
\(219\) | 18682.9 | 0.0263229 | ||||||||
\(220\) | −79980.0 | −0.111410 | ||||||||
\(221\) | 652919. | 0.899246 | ||||||||
\(222\) | 614176. | 0.836393 | ||||||||
\(223\) | 1.27660e6 | 1.71907 | 0.859535 | − | 0.511078i | \(-0.170754\pi\) | ||||
0.859535 | + | 0.511078i | \(0.170754\pi\) | |||||||
\(224\) | 769191. | 1.02427 | ||||||||
\(225\) | −127627. | −0.168069 | ||||||||
\(226\) | −297161. | −0.387008 | ||||||||
\(227\) | 73719.2 | 0.0949546 | 0.0474773 | − | 0.998872i | \(-0.484882\pi\) | ||||
0.0474773 | + | 0.998872i | \(0.484882\pi\) | |||||||
\(228\) | −59451.2 | −0.0757397 | ||||||||
\(229\) | 564598. | 0.711461 | 0.355730 | − | 0.934589i | \(-0.384232\pi\) | ||||
0.355730 | + | 0.934589i | \(0.384232\pi\) | |||||||
\(230\) | 394067. | 0.491191 | ||||||||
\(231\) | 76362.1 | 0.0941560 | ||||||||
\(232\) | −335484. | −0.409215 | ||||||||
\(233\) | −452128. | −0.545596 | −0.272798 | − | 0.962071i | \(-0.587949\pi\) | ||||
−0.272798 | + | 0.962071i | \(0.587949\pi\) | |||||||
\(234\) | 544372. | 0.649914 | ||||||||
\(235\) | 8410.63 | 0.00993479 | ||||||||
\(236\) | −910665. | −1.06434 | ||||||||
\(237\) | 372805. | 0.431133 | ||||||||
\(238\) | −1.45020e6 | −1.65953 | ||||||||
\(239\) | −1.18475e6 | −1.34163 | −0.670815 | − | 0.741625i | \(-0.734055\pi\) | ||||
−0.670815 | + | 0.741625i | \(0.734055\pi\) | |||||||
\(240\) | 182347. | 0.204348 | ||||||||
\(241\) | −735889. | −0.816149 | −0.408075 | − | 0.912949i | \(-0.633800\pi\) | ||||
−0.408075 | + | 0.912949i | \(0.633800\pi\) | |||||||
\(242\) | −111924. | −0.122853 | ||||||||
\(243\) | −877884. | −0.953722 | ||||||||
\(244\) | −1.12569e6 | −1.21044 | ||||||||
\(245\) | −163532. | −0.174055 | ||||||||
\(246\) | −601274. | −0.633482 | ||||||||
\(247\) | 125889. | 0.131294 | ||||||||
\(248\) | 139079. | 0.143593 | ||||||||
\(249\) | 408690. | 0.417730 | ||||||||
\(250\) | −119447. | −0.120871 | ||||||||
\(251\) | −552056. | −0.553094 | −0.276547 | − | 0.961000i | \(-0.589190\pi\) | ||||
−0.276547 | + | 0.961000i | \(0.589190\pi\) | |||||||
\(252\) | −547033. | −0.542641 | ||||||||
\(253\) | 249495. | 0.245053 | ||||||||
\(254\) | 279385. | 0.271719 | ||||||||
\(255\) | −291553. | −0.280781 | ||||||||
\(256\) | 1.31345e6 | 1.25261 | ||||||||
\(257\) | −1.75546e6 | −1.65790 | −0.828948 | − | 0.559326i | \(-0.811060\pi\) | ||||
−0.828948 | + | 0.559326i | \(0.811060\pi\) | |||||||
\(258\) | 671567. | 0.628117 | ||||||||
\(259\) | 1.30688e6 | 1.21056 | ||||||||
\(260\) | 230502. | 0.211467 | ||||||||
\(261\) | 1.61169e6 | 1.46446 | ||||||||
\(262\) | −102566. | −0.0923105 | ||||||||
\(263\) | −1.72719e6 | −1.53975 | −0.769877 | − | 0.638192i | \(-0.779682\pi\) | ||||
−0.769877 | + | 0.638192i | \(0.779682\pi\) | |||||||
\(264\) | 32035.9 | 0.0282896 | ||||||||
\(265\) | −494514. | −0.432578 | ||||||||
\(266\) | −279612. | −0.242299 | ||||||||
\(267\) | −766199. | −0.657754 | ||||||||
\(268\) | −870547. | −0.740381 | ||||||||
\(269\) | 224623. | 0.189266 | 0.0946332 | − | 0.995512i | \(-0.469832\pi\) | ||||
0.0946332 | + | 0.995512i | \(0.469832\pi\) | |||||||
\(270\) | −532349. | −0.444413 | ||||||||
\(271\) | −653975. | −0.540926 | −0.270463 | − | 0.962730i | \(-0.587177\pi\) | ||||
−0.270463 | + | 0.962730i | \(0.587177\pi\) | |||||||
\(272\) | −2.19251e6 | −1.79688 | ||||||||
\(273\) | −220075. | −0.178717 | ||||||||
\(274\) | −2.19585e6 | −1.76696 | ||||||||
\(275\) | −75625.0 | −0.0603023 | ||||||||
\(276\) | 339570. | 0.268323 | ||||||||
\(277\) | −369273. | −0.289167 | −0.144583 | − | 0.989493i | \(-0.546184\pi\) | ||||
−0.144583 | + | 0.989493i | \(0.546184\pi\) | |||||||
\(278\) | −1.31927e6 | −1.02382 | ||||||||
\(279\) | −668143. | −0.513877 | ||||||||
\(280\) | 107669. | 0.0820718 | ||||||||
\(281\) | 494947. | 0.373932 | 0.186966 | − | 0.982366i | \(-0.440135\pi\) | ||||
0.186966 | + | 0.982366i | \(0.440135\pi\) | |||||||
\(282\) | 16019.2 | 0.0119955 | ||||||||
\(283\) | 1.24510e6 | 0.924142 | 0.462071 | − | 0.886843i | \(-0.347107\pi\) | ||||
0.462071 | + | 0.886843i | \(0.347107\pi\) | |||||||
\(284\) | 522324. | 0.384277 | ||||||||
\(285\) | −56214.0 | −0.0409952 | ||||||||
\(286\) | 322566. | 0.233186 | ||||||||
\(287\) | −1.27943e6 | −0.916877 | ||||||||
\(288\) | −1.55025e6 | −1.10134 | ||||||||
\(289\) | 2.08572e6 | 1.46897 | ||||||||
\(290\) | 1.50838e6 | 1.05321 | ||||||||
\(291\) | 283012. | 0.195917 | ||||||||
\(292\) | −79305.2 | −0.0544308 | ||||||||
\(293\) | 216203. | 0.147127 | 0.0735637 | − | 0.997291i | \(-0.476563\pi\) | ||||
0.0735637 | + | 0.997291i | \(0.476563\pi\) | |||||||
\(294\) | −311468. | −0.210158 | ||||||||
\(295\) | −861078. | −0.576086 | ||||||||
\(296\) | 548271. | 0.363719 | ||||||||
\(297\) | −337045. | −0.221716 | ||||||||
\(298\) | 3.22695e6 | 2.10500 | ||||||||
\(299\) | −719044. | −0.465133 | ||||||||
\(300\) | −102928. | −0.0660284 | ||||||||
\(301\) | 1.42900e6 | 0.909110 | ||||||||
\(302\) | 463774. | 0.292610 | ||||||||
\(303\) | 255663. | 0.159979 | ||||||||
\(304\) | −422736. | −0.262352 | ||||||||
\(305\) | −1.06440e6 | −0.655169 | ||||||||
\(306\) | 2.92278e6 | 1.78440 | ||||||||
\(307\) | −3.16463e6 | −1.91636 | −0.958181 | − | 0.286163i | \(-0.907620\pi\) | ||||
−0.958181 | + | 0.286163i | \(0.907620\pi\) | |||||||
\(308\) | −324143. | −0.194697 | ||||||||
\(309\) | 188002. | 0.112012 | ||||||||
\(310\) | −625317. | −0.369570 | ||||||||
\(311\) | −366955. | −0.215135 | −0.107568 | − | 0.994198i | \(-0.534306\pi\) | ||||
−0.107568 | + | 0.994198i | \(0.534306\pi\) | |||||||
\(312\) | −92327.5 | −0.0536963 | ||||||||
\(313\) | −1.59839e6 | −0.922192 | −0.461096 | − | 0.887350i | \(-0.652544\pi\) | ||||
−0.461096 | + | 0.887350i | \(0.652544\pi\) | |||||||
\(314\) | 1.08276e6 | 0.619737 | ||||||||
\(315\) | −517246. | −0.293712 | ||||||||
\(316\) | −1.58249e6 | −0.891502 | ||||||||
\(317\) | −1.94057e6 | −1.08463 | −0.542316 | − | 0.840175i | \(-0.682452\pi\) | ||||
−0.542316 | + | 0.840175i | \(0.682452\pi\) | |||||||
\(318\) | −941869. | −0.522303 | ||||||||
\(319\) | 954999. | 0.525444 | ||||||||
\(320\) | −514075. | −0.280641 | ||||||||
\(321\) | −1.34436e6 | −0.728202 | ||||||||
\(322\) | 1.59707e6 | 0.858391 | ||||||||
\(323\) | 675907. | 0.360480 | ||||||||
\(324\) | 853244. | 0.451555 | ||||||||
\(325\) | 217951. | 0.114459 | ||||||||
\(326\) | −1.86641e6 | −0.972663 | ||||||||
\(327\) | −397953. | −0.205808 | ||||||||
\(328\) | −536754. | −0.275480 | ||||||||
\(329\) | 34086.6 | 0.0173617 | ||||||||
\(330\) | −144038. | −0.0728102 | ||||||||
\(331\) | −1.61725e6 | −0.811350 | −0.405675 | − | 0.914017i | \(-0.632963\pi\) | ||||
−0.405675 | + | 0.914017i | \(0.632963\pi\) | |||||||
\(332\) | −1.73481e6 | −0.863788 | ||||||||
\(333\) | −2.63393e6 | −1.30165 | ||||||||
\(334\) | −1.37453e6 | −0.674200 | ||||||||
\(335\) | −823145. | −0.400741 | ||||||||
\(336\) | 739017. | 0.357113 | ||||||||
\(337\) | 3.09001e6 | 1.48213 | 0.741063 | − | 0.671435i | \(-0.234322\pi\) | ||||
0.741063 | + | 0.671435i | \(0.234322\pi\) | |||||||
\(338\) | 1.90875e6 | 0.908775 | ||||||||
\(339\) | −242122. | −0.114429 | ||||||||
\(340\) | 1.23759e6 | 0.580602 | ||||||||
\(341\) | −395906. | −0.184377 | ||||||||
\(342\) | 563539. | 0.260530 | ||||||||
\(343\) | −2.36565e6 | −1.08571 | ||||||||
\(344\) | 599504. | 0.273147 | ||||||||
\(345\) | 321080. | 0.145233 | ||||||||
\(346\) | 396106. | 0.177877 | ||||||||
\(347\) | −2.14352e6 | −0.955662 | −0.477831 | − | 0.878452i | \(-0.658577\pi\) | ||||
−0.477831 | + | 0.878452i | \(0.658577\pi\) | |||||||
\(348\) | 1.29978e6 | 0.575338 | ||||||||
\(349\) | −2.48054e6 | −1.09014 | −0.545071 | − | 0.838390i | \(-0.683497\pi\) | ||||
−0.545071 | + | 0.838390i | \(0.683497\pi\) | |||||||
\(350\) | −484093. | −0.211231 | ||||||||
\(351\) | 971363. | 0.420837 | ||||||||
\(352\) | −918596. | −0.395155 | ||||||||
\(353\) | 509603. | 0.217668 | 0.108834 | − | 0.994060i | \(-0.465288\pi\) | ||||
0.108834 | + | 0.994060i | \(0.465288\pi\) | |||||||
\(354\) | −1.64004e6 | −0.695578 | ||||||||
\(355\) | 493883. | 0.207995 | ||||||||
\(356\) | 3.25237e6 | 1.36011 | ||||||||
\(357\) | −1.18161e6 | −0.490684 | ||||||||
\(358\) | 590261. | 0.243409 | ||||||||
\(359\) | 3.69814e6 | 1.51442 | 0.757212 | − | 0.653169i | \(-0.226561\pi\) | ||||
0.757212 | + | 0.653169i | \(0.226561\pi\) | |||||||
\(360\) | −216999. | −0.0882472 | ||||||||
\(361\) | 130321. | 0.0526316 | ||||||||
\(362\) | 471725. | 0.189199 | ||||||||
\(363\) | −91194.4 | −0.0363247 | ||||||||
\(364\) | 934179. | 0.369553 | ||||||||
\(365\) | −74987.0 | −0.0294614 | ||||||||
\(366\) | −2.02728e6 | −0.791065 | ||||||||
\(367\) | −2.49046e6 | −0.965192 | −0.482596 | − | 0.875843i | \(-0.660306\pi\) | ||||
−0.482596 | + | 0.875843i | \(0.660306\pi\) | |||||||
\(368\) | 2.41456e6 | 0.929434 | ||||||||
\(369\) | 2.57860e6 | 0.985865 | ||||||||
\(370\) | −2.46510e6 | −0.936118 | ||||||||
\(371\) | −2.00417e6 | −0.755960 | ||||||||
\(372\) | −538841. | −0.201885 | ||||||||
\(373\) | 1.40770e6 | 0.523887 | 0.261943 | − | 0.965083i | \(-0.415637\pi\) | ||||
0.261943 | + | 0.965083i | \(0.415637\pi\) | |||||||
\(374\) | 1.73189e6 | 0.640236 | ||||||||
\(375\) | −97323.5 | −0.0357388 | ||||||||
\(376\) | 14300.2 | 0.00521643 | ||||||||
\(377\) | −2.75231e6 | −0.997340 | ||||||||
\(378\) | −2.15750e6 | −0.776644 | ||||||||
\(379\) | 4.31778e6 | 1.54405 | 0.772026 | − | 0.635591i | \(-0.219243\pi\) | ||||
0.772026 | + | 0.635591i | \(0.219243\pi\) | |||||||
\(380\) | 238618. | 0.0847704 | ||||||||
\(381\) | 227639. | 0.0803406 | ||||||||
\(382\) | −6.37862e6 | −2.23650 | ||||||||
\(383\) | −3.58709e6 | −1.24952 | −0.624762 | − | 0.780815i | \(-0.714804\pi\) | ||||
−0.624762 | + | 0.780815i | \(0.714804\pi\) | |||||||
\(384\) | 534042. | 0.184819 | ||||||||
\(385\) | −306493. | −0.105382 | ||||||||
\(386\) | −5.39935e6 | −1.84448 | ||||||||
\(387\) | −2.88005e6 | −0.977515 | ||||||||
\(388\) | −1.20133e6 | −0.405120 | ||||||||
\(389\) | −1.93585e6 | −0.648631 | −0.324316 | − | 0.945949i | \(-0.605134\pi\) | ||||
−0.324316 | + | 0.945949i | \(0.605134\pi\) | |||||||
\(390\) | 415117. | 0.138200 | ||||||||
\(391\) | −3.86061e6 | −1.27707 | ||||||||
\(392\) | −278046. | −0.0913906 | ||||||||
\(393\) | −83569.6 | −0.0272940 | ||||||||
\(394\) | −4.92920e6 | −1.59969 | ||||||||
\(395\) | −1.49632e6 | −0.482538 | ||||||||
\(396\) | 653287. | 0.209347 | ||||||||
\(397\) | 2.43980e6 | 0.776923 | 0.388461 | − | 0.921465i | \(-0.373007\pi\) | ||||
0.388461 | + | 0.921465i | \(0.373007\pi\) | |||||||
\(398\) | −2.33863e6 | −0.740039 | ||||||||
\(399\) | −227824. | −0.0716420 | ||||||||
\(400\) | −731883. | −0.228714 | ||||||||
\(401\) | −3.29385e6 | −1.02292 | −0.511462 | − | 0.859306i | \(-0.670896\pi\) | ||||
−0.511462 | + | 0.859306i | \(0.670896\pi\) | |||||||
\(402\) | −1.56779e6 | −0.483863 | ||||||||
\(403\) | 1.14100e6 | 0.349964 | ||||||||
\(404\) | −1.08524e6 | −0.330806 | ||||||||
\(405\) | 806784. | 0.244410 | ||||||||
\(406\) | 6.11317e6 | 1.84057 | ||||||||
\(407\) | −1.56073e6 | −0.467025 | ||||||||
\(408\) | −495715. | −0.147429 | ||||||||
\(409\) | −1.76138e6 | −0.520649 | −0.260325 | − | 0.965521i | \(-0.583830\pi\) | ||||
−0.260325 | + | 0.965521i | \(0.583830\pi\) | |||||||
\(410\) | 2.41332e6 | 0.709014 | ||||||||
\(411\) | −1.78915e6 | −0.522446 | ||||||||
\(412\) | −798031. | −0.231620 | ||||||||
\(413\) | −3.48978e6 | −1.00675 | ||||||||
\(414\) | −3.21879e6 | −0.922979 | ||||||||
\(415\) | −1.64035e6 | −0.467537 | ||||||||
\(416\) | 2.64739e6 | 0.750041 | ||||||||
\(417\) | −1.07493e6 | −0.302718 | ||||||||
\(418\) | 333923. | 0.0934772 | ||||||||
\(419\) | −5.36494e6 | −1.49290 | −0.746448 | − | 0.665444i | \(-0.768242\pi\) | ||||
−0.746448 | + | 0.665444i | \(0.768242\pi\) | |||||||
\(420\) | −417146. | −0.115389 | ||||||||
\(421\) | −4.11271e6 | −1.13090 | −0.565448 | − | 0.824784i | \(-0.691297\pi\) | ||||
−0.565448 | + | 0.824784i | \(0.691297\pi\) | |||||||
\(422\) | 6.63616e6 | 1.81399 | ||||||||
\(423\) | −68699.1 | −0.0186681 | ||||||||
\(424\) | −840801. | −0.227132 | ||||||||
\(425\) | 1.17020e6 | 0.314259 | ||||||||
\(426\) | 940667. | 0.251138 | ||||||||
\(427\) | −4.31378e6 | −1.14495 | ||||||||
\(428\) | 5.70654e6 | 1.50579 | ||||||||
\(429\) | 262822. | 0.0689476 | ||||||||
\(430\) | −2.69545e6 | −0.703009 | ||||||||
\(431\) | −2.96777e6 | −0.769551 | −0.384775 | − | 0.923010i | \(-0.625721\pi\) | ||||
−0.384775 | + | 0.923010i | \(0.625721\pi\) | |||||||
\(432\) | −3.26185e6 | −0.840921 | ||||||||
\(433\) | −714434. | −0.183123 | −0.0915614 | − | 0.995799i | \(-0.529186\pi\) | ||||
−0.0915614 | + | 0.995799i | \(0.529186\pi\) | |||||||
\(434\) | −2.53428e6 | −0.645849 | ||||||||
\(435\) | 1.22901e6 | 0.311410 | ||||||||
\(436\) | 1.68923e6 | 0.425573 | ||||||||
\(437\) | −744361. | −0.186457 | ||||||||
\(438\) | −142823. | −0.0355723 | ||||||||
\(439\) | 4.89099e6 | 1.21125 | 0.605627 | − | 0.795748i | \(-0.292922\pi\) | ||||
0.605627 | + | 0.795748i | \(0.292922\pi\) | |||||||
\(440\) | −128582. | −0.0316627 | ||||||||
\(441\) | 1.33575e6 | 0.327061 | ||||||||
\(442\) | −4.99129e6 | −1.21523 | ||||||||
\(443\) | −2.61257e6 | −0.632497 | −0.316249 | − | 0.948676i | \(-0.602423\pi\) | ||||
−0.316249 | + | 0.948676i | \(0.602423\pi\) | |||||||
\(444\) | −2.12420e6 | −0.511372 | ||||||||
\(445\) | 3.07527e6 | 0.736180 | ||||||||
\(446\) | −9.75909e6 | −2.32312 | ||||||||
\(447\) | 2.62928e6 | 0.622397 | ||||||||
\(448\) | −2.08344e6 | −0.490441 | ||||||||
\(449\) | 1.31679e6 | 0.308249 | 0.154124 | − | 0.988051i | \(-0.450744\pi\) | ||||
0.154124 | + | 0.988051i | \(0.450744\pi\) | |||||||
\(450\) | 975656. | 0.227125 | ||||||||
\(451\) | 1.52794e6 | 0.353724 | ||||||||
\(452\) | 1.02776e6 | 0.236618 | ||||||||
\(453\) | 377877. | 0.0865177 | ||||||||
\(454\) | −563552. | −0.128320 | ||||||||
\(455\) | 883312. | 0.200026 | ||||||||
\(456\) | −95578.3 | −0.0215252 | ||||||||
\(457\) | 5.96805e6 | 1.33672 | 0.668362 | − | 0.743836i | \(-0.266996\pi\) | ||||
0.668362 | + | 0.743836i | \(0.266996\pi\) | |||||||
\(458\) | −4.31612e6 | −0.961457 | ||||||||
\(459\) | 5.21534e6 | 1.15545 | ||||||||
\(460\) | −1.36293e6 | −0.300315 | ||||||||
\(461\) | −7.32928e6 | −1.60623 | −0.803117 | − | 0.595821i | \(-0.796827\pi\) | ||||
−0.803117 | + | 0.595821i | \(0.796827\pi\) | |||||||
\(462\) | −583757. | −0.127241 | ||||||||
\(463\) | 5.01351e6 | 1.08690 | 0.543450 | − | 0.839442i | \(-0.317118\pi\) | ||||
0.543450 | + | 0.839442i | \(0.317118\pi\) | |||||||
\(464\) | 9.24229e6 | 1.99290 | ||||||||
\(465\) | −509500. | −0.109273 | ||||||||
\(466\) | 3.45633e6 | 0.737310 | ||||||||
\(467\) | −1.63096e6 | −0.346059 | −0.173029 | − | 0.984917i | \(-0.555356\pi\) | ||||
−0.173029 | + | 0.984917i | \(0.555356\pi\) | |||||||
\(468\) | −1.88277e6 | −0.397359 | ||||||||
\(469\) | −3.33604e6 | −0.700324 | ||||||||
\(470\) | −64295.7 | −0.0134257 | ||||||||
\(471\) | 882217. | 0.183241 | ||||||||
\(472\) | −1.46405e6 | −0.302484 | ||||||||
\(473\) | −1.70657e6 | −0.350728 | ||||||||
\(474\) | −2.84994e6 | −0.582626 | ||||||||
\(475\) | 225625. | 0.0458831 | ||||||||
\(476\) | 5.01569e6 | 1.01464 | ||||||||
\(477\) | 4.03926e6 | 0.812841 | ||||||||
\(478\) | 9.05693e6 | 1.81306 | ||||||||
\(479\) | −6.11130e6 | −1.21701 | −0.608506 | − | 0.793549i | \(-0.708231\pi\) | ||||
−0.608506 | + | 0.793549i | \(0.708231\pi\) | |||||||
\(480\) | −1.18216e6 | −0.234193 | ||||||||
\(481\) | 4.49801e6 | 0.886457 | ||||||||
\(482\) | 5.62556e6 | 1.10293 | ||||||||
\(483\) | 1.30127e6 | 0.253805 | ||||||||
\(484\) | 387103. | 0.0751127 | ||||||||
\(485\) | −1.13592e6 | −0.219277 | ||||||||
\(486\) | 6.71106e6 | 1.28884 | ||||||||
\(487\) | 2.10585e6 | 0.402351 | 0.201176 | − | 0.979555i | \(-0.435524\pi\) | ||||
0.201176 | + | 0.979555i | \(0.435524\pi\) | |||||||
\(488\) | −1.80975e6 | −0.344008 | ||||||||
\(489\) | −1.52072e6 | −0.287593 | ||||||||
\(490\) | 1.25013e6 | 0.235216 | ||||||||
\(491\) | 1.34844e6 | 0.252422 | 0.126211 | − | 0.992003i | \(-0.459718\pi\) | ||||
0.126211 | + | 0.992003i | \(0.459718\pi\) | |||||||
\(492\) | 2.07957e6 | 0.387313 | ||||||||
\(493\) | −1.47774e7 | −2.73829 | ||||||||
\(494\) | −962366. | −0.177428 | ||||||||
\(495\) | 617715. | 0.113312 | ||||||||
\(496\) | −3.83150e6 | −0.699301 | ||||||||
\(497\) | 2.00161e6 | 0.363486 | ||||||||
\(498\) | −3.12427e6 | −0.564514 | ||||||||
\(499\) | −208526. | −0.0374894 | −0.0187447 | − | 0.999824i | \(-0.505967\pi\) | ||||
−0.0187447 | + | 0.999824i | \(0.505967\pi\) | |||||||
\(500\) | 413120. | 0.0739011 | ||||||||
\(501\) | −1.11995e6 | −0.199345 | ||||||||
\(502\) | 4.22024e6 | 0.747442 | ||||||||
\(503\) | −1.27893e6 | −0.225386 | −0.112693 | − | 0.993630i | \(-0.535948\pi\) | ||||
−0.112693 | + | 0.993630i | \(0.535948\pi\) | |||||||
\(504\) | −879451. | −0.154218 | ||||||||
\(505\) | −1.02615e6 | −0.179053 | ||||||||
\(506\) | −1.90728e6 | −0.331161 | ||||||||
\(507\) | 1.55522e6 | 0.268703 | ||||||||
\(508\) | −966286. | −0.166129 | ||||||||
\(509\) | 5.59640e6 | 0.957446 | 0.478723 | − | 0.877966i | \(-0.341100\pi\) | ||||
0.478723 | + | 0.877966i | \(0.341100\pi\) | |||||||
\(510\) | 2.22880e6 | 0.379443 | ||||||||
\(511\) | −303907. | −0.0514859 | ||||||||
\(512\) | −7.29717e6 | −1.23021 | ||||||||
\(513\) | 1.00556e6 | 0.168701 | ||||||||
\(514\) | 1.34197e7 | 2.24045 | ||||||||
\(515\) | −754577. | −0.125368 | ||||||||
\(516\) | −2.32269e6 | −0.384032 | ||||||||
\(517\) | −40707.4 | −0.00669803 | ||||||||
\(518\) | −9.99056e6 | −1.63593 | ||||||||
\(519\) | 322741. | 0.0525940 | ||||||||
\(520\) | 370573. | 0.0600987 | ||||||||
\(521\) | −3.65769e6 | −0.590353 | −0.295177 | − | 0.955443i | \(-0.595379\pi\) | ||||
−0.295177 | + | 0.955443i | \(0.595379\pi\) | |||||||
\(522\) | −1.23207e7 | −1.97906 | ||||||||
\(523\) | 9.45457e6 | 1.51143 | 0.755714 | − | 0.654902i | \(-0.227290\pi\) | ||||
0.755714 | + | 0.654902i | \(0.227290\pi\) | |||||||
\(524\) | 354737. | 0.0564389 | ||||||||
\(525\) | −394432. | −0.0624560 | ||||||||
\(526\) | 1.32037e7 | 2.08080 | ||||||||
\(527\) | 6.12614e6 | 0.960860 | ||||||||
\(528\) | −882561. | −0.137772 | ||||||||
\(529\) | −2.18474e6 | −0.339439 | ||||||||
\(530\) | 3.78036e6 | 0.584579 | ||||||||
\(531\) | 7.03340e6 | 1.08250 | ||||||||
\(532\) | 967070. | 0.148142 | ||||||||
\(533\) | −4.40352e6 | −0.671401 | ||||||||
\(534\) | 5.85727e6 | 0.888878 | ||||||||
\(535\) | 5.39581e6 | 0.815028 | ||||||||
\(536\) | −1.39956e6 | −0.210416 | ||||||||
\(537\) | 480937. | 0.0719701 | ||||||||
\(538\) | −1.71715e6 | −0.255772 | ||||||||
\(539\) | 791494. | 0.117348 | ||||||||
\(540\) | 1.84119e6 | 0.271715 | ||||||||
\(541\) | 1.16104e7 | 1.70550 | 0.852752 | − | 0.522316i | \(-0.174932\pi\) | ||||
0.852752 | + | 0.522316i | \(0.174932\pi\) | |||||||
\(542\) | 4.99937e6 | 0.730999 | ||||||||
\(543\) | 384355. | 0.0559414 | ||||||||
\(544\) | 1.42141e7 | 2.05931 | ||||||||
\(545\) | 1.59725e6 | 0.230347 | ||||||||
\(546\) | 1.68239e6 | 0.241515 | ||||||||
\(547\) | −1.85732e6 | −0.265411 | −0.132706 | − | 0.991155i | \(-0.542366\pi\) | ||||
−0.132706 | + | 0.991155i | \(0.542366\pi\) | |||||||
\(548\) | 7.59459e6 | 1.08032 | ||||||||
\(549\) | 8.69412e6 | 1.23110 | ||||||||
\(550\) | 578122. | 0.0814915 | ||||||||
\(551\) | −2.84921e6 | −0.399803 | ||||||||
\(552\) | 545919. | 0.0762571 | ||||||||
\(553\) | −6.06428e6 | −0.843269 | ||||||||
\(554\) | 2.82294e6 | 0.390776 | ||||||||
\(555\) | −2.00853e6 | −0.276787 | ||||||||
\(556\) | 4.56286e6 | 0.625966 | ||||||||
\(557\) | 8.06391e6 | 1.10131 | 0.550653 | − | 0.834734i | \(-0.314379\pi\) | ||||
0.550653 | + | 0.834734i | \(0.314379\pi\) | |||||||
\(558\) | 5.10767e6 | 0.694445 | ||||||||
\(559\) | 4.91832e6 | 0.665714 | ||||||||
\(560\) | −2.96617e6 | −0.399693 | ||||||||
\(561\) | 1.41112e6 | 0.189302 | ||||||||
\(562\) | −3.78367e6 | −0.505326 | ||||||||
\(563\) | −1.43323e7 | −1.90566 | −0.952828 | − | 0.303510i | \(-0.901841\pi\) | ||||
−0.952828 | + | 0.303510i | \(0.901841\pi\) | |||||||
\(564\) | −55404.1 | −0.00733406 | ||||||||
\(565\) | 971801. | 0.128073 | ||||||||
\(566\) | −9.51828e6 | −1.24887 | ||||||||
\(567\) | 3.26973e6 | 0.427125 | ||||||||
\(568\) | 839728. | 0.109211 | ||||||||
\(569\) | 1.28139e7 | 1.65921 | 0.829604 | − | 0.558352i | \(-0.188566\pi\) | ||||
0.829604 | + | 0.558352i | \(0.188566\pi\) | |||||||
\(570\) | 429733. | 0.0554002 | ||||||||
\(571\) | −1.17442e7 | −1.50742 | −0.753709 | − | 0.657208i | \(-0.771737\pi\) | ||||
−0.753709 | + | 0.657208i | \(0.771737\pi\) | |||||||
\(572\) | −1.11563e6 | −0.142571 | ||||||||
\(573\) | −5.19721e6 | −0.661277 | ||||||||
\(574\) | 9.78069e6 | 1.23905 | ||||||||
\(575\) | −1.28871e6 | −0.162550 | ||||||||
\(576\) | 4.19903e6 | 0.527343 | ||||||||
\(577\) | −9.09404e6 | −1.13715 | −0.568575 | − | 0.822632i | \(-0.692505\pi\) | ||||
−0.568575 | + | 0.822632i | \(0.692505\pi\) | |||||||
\(578\) | −1.59445e7 | −1.98514 | ||||||||
\(579\) | −4.39932e6 | −0.545367 | ||||||||
\(580\) | −5.21691e6 | −0.643937 | ||||||||
\(581\) | −6.64801e6 | −0.817055 | ||||||||
\(582\) | −2.16351e6 | −0.264759 | ||||||||
\(583\) | 2.39345e6 | 0.291644 | ||||||||
\(584\) | −127497. | −0.0154692 | ||||||||
\(585\) | −1.78025e6 | −0.215076 | ||||||||
\(586\) | −1.65279e6 | −0.198826 | ||||||||
\(587\) | 6.76839e6 | 0.810756 | 0.405378 | − | 0.914149i | \(-0.367140\pi\) | ||||
0.405378 | + | 0.914149i | \(0.367140\pi\) | |||||||
\(588\) | 1.07725e6 | 0.128491 | ||||||||
\(589\) | 1.18117e6 | 0.140290 | ||||||||
\(590\) | 6.58259e6 | 0.778514 | ||||||||
\(591\) | −4.01625e6 | −0.472990 | ||||||||
\(592\) | −1.51044e7 | −1.77133 | ||||||||
\(593\) | −7.70951e6 | −0.900306 | −0.450153 | − | 0.892951i | \(-0.648631\pi\) | ||||
−0.450153 | + | 0.892951i | \(0.648631\pi\) | |||||||
\(594\) | 2.57657e6 | 0.299623 | ||||||||
\(595\) | 4.74258e6 | 0.549190 | ||||||||
\(596\) | −1.11608e7 | −1.28700 | ||||||||
\(597\) | −1.90549e6 | −0.218812 | ||||||||
\(598\) | 5.49679e6 | 0.628574 | ||||||||
\(599\) | −9.86863e6 | −1.12380 | −0.561901 | − | 0.827205i | \(-0.689930\pi\) | ||||
−0.561901 | + | 0.827205i | \(0.689930\pi\) | |||||||
\(600\) | −165475. | −0.0187652 | ||||||||
\(601\) | −5.17221e6 | −0.584104 | −0.292052 | − | 0.956402i | \(-0.594338\pi\) | ||||
−0.292052 | + | 0.956402i | \(0.594338\pi\) | |||||||
\(602\) | −1.09241e7 | −1.22856 | ||||||||
\(603\) | 6.72355e6 | 0.753018 | ||||||||
\(604\) | −1.60402e6 | −0.178903 | ||||||||
\(605\) | 366025. | 0.0406558 | ||||||||
\(606\) | −1.95444e6 | −0.216193 | ||||||||
\(607\) | −3.58821e6 | −0.395282 | −0.197641 | − | 0.980275i | \(-0.563328\pi\) | ||||
−0.197641 | + | 0.980275i | \(0.563328\pi\) | |||||||
\(608\) | 2.74061e6 | 0.300668 | ||||||||
\(609\) | 4.98093e6 | 0.544210 | ||||||||
\(610\) | 8.13686e6 | 0.885386 | ||||||||
\(611\) | 117319. | 0.0127135 | ||||||||
\(612\) | −1.01088e7 | −1.09099 | ||||||||
\(613\) | 1.23143e7 | 1.32360 | 0.661801 | − | 0.749680i | \(-0.269793\pi\) | ||||
0.661801 | + | 0.749680i | \(0.269793\pi\) | |||||||
\(614\) | 2.41923e7 | 2.58974 | ||||||||
\(615\) | 1.96634e6 | 0.209638 | ||||||||
\(616\) | −521116. | −0.0553328 | ||||||||
\(617\) | −1.87011e7 | −1.97767 | −0.988836 | − | 0.149007i | \(-0.952392\pi\) | ||||
−0.988836 | + | 0.149007i | \(0.952392\pi\) | |||||||
\(618\) | −1.43719e6 | −0.151371 | ||||||||
\(619\) | −5.99899e6 | −0.629291 | −0.314646 | − | 0.949209i | \(-0.601886\pi\) | ||||
−0.314646 | + | 0.949209i | \(0.601886\pi\) | |||||||
\(620\) | 2.16273e6 | 0.225956 | ||||||||
\(621\) | −5.74353e6 | −0.597654 | ||||||||
\(622\) | 2.80522e6 | 0.290730 | ||||||||
\(623\) | 1.24635e7 | 1.28653 | ||||||||
\(624\) | 2.54354e6 | 0.261503 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | 1.22190e7 | 1.24624 | ||||||||
\(627\) | 272076. | 0.0276389 | ||||||||
\(628\) | −3.74485e6 | −0.378909 | ||||||||
\(629\) | 2.41502e7 | 2.43385 | ||||||||
\(630\) | 3.95413e6 | 0.396917 | ||||||||
\(631\) | −2.74704e6 | −0.274657 | −0.137329 | − | 0.990526i | \(-0.543852\pi\) | ||||
−0.137329 | + | 0.990526i | \(0.543852\pi\) | |||||||
\(632\) | −2.54413e6 | −0.253364 | ||||||||
\(633\) | 5.40705e6 | 0.536354 | ||||||||
\(634\) | 1.48349e7 | 1.46575 | ||||||||
\(635\) | −913671. | −0.0899198 | ||||||||
\(636\) | 3.25756e6 | 0.319337 | ||||||||
\(637\) | −2.28108e6 | −0.222737 | ||||||||
\(638\) | −7.30057e6 | −0.710076 | ||||||||
\(639\) | −4.03410e6 | −0.390836 | ||||||||
\(640\) | −2.14347e6 | −0.206856 | ||||||||
\(641\) | −3.34150e6 | −0.321216 | −0.160608 | − | 0.987018i | \(-0.551345\pi\) | ||||
−0.160608 | + | 0.987018i | \(0.551345\pi\) | |||||||
\(642\) | 1.02770e7 | 0.984081 | ||||||||
\(643\) | −1.30231e7 | −1.24219 | −0.621095 | − | 0.783735i | \(-0.713312\pi\) | ||||
−0.621095 | + | 0.783735i | \(0.713312\pi\) | |||||||
\(644\) | −5.52366e6 | −0.524822 | ||||||||
\(645\) | −2.19622e6 | −0.207863 | ||||||||
\(646\) | −5.16703e6 | −0.487147 | ||||||||
\(647\) | −2.76130e6 | −0.259330 | −0.129665 | − | 0.991558i | \(-0.541390\pi\) | ||||
−0.129665 | + | 0.991558i | \(0.541390\pi\) | |||||||
\(648\) | 1.37174e6 | 0.128332 | ||||||||
\(649\) | 4.16762e6 | 0.388397 | ||||||||
\(650\) | −1.66615e6 | −0.154678 | ||||||||
\(651\) | −2.06490e6 | −0.190962 | ||||||||
\(652\) | 6.45519e6 | 0.594689 | ||||||||
\(653\) | −2.42480e6 | −0.222532 | −0.111266 | − | 0.993791i | \(-0.535491\pi\) | ||||
−0.111266 | + | 0.993791i | \(0.535491\pi\) | |||||||
\(654\) | 3.04218e6 | 0.278126 | ||||||||
\(655\) | 335421. | 0.0305483 | ||||||||
\(656\) | 1.47871e7 | 1.34160 | ||||||||
\(657\) | 612503. | 0.0553599 | ||||||||
\(658\) | −260578. | −0.0234624 | ||||||||
\(659\) | −981659. | −0.0880536 | −0.0440268 | − | 0.999030i | \(-0.514019\pi\) | ||||
−0.0440268 | + | 0.999030i | \(0.514019\pi\) | |||||||
\(660\) | 498172. | 0.0445163 | ||||||||
\(661\) | 1.08141e7 | 0.962691 | 0.481345 | − | 0.876531i | \(-0.340148\pi\) | ||||
0.481345 | + | 0.876531i | \(0.340148\pi\) | |||||||
\(662\) | 1.23632e7 | 1.09645 | ||||||||
\(663\) | −4.06684e6 | −0.359313 | ||||||||
\(664\) | −2.78902e6 | −0.245488 | ||||||||
\(665\) | 914412. | 0.0801840 | ||||||||
\(666\) | 2.01353e7 | 1.75903 | ||||||||
\(667\) | 1.62740e7 | 1.41638 | ||||||||
\(668\) | 4.75398e6 | 0.412208 | ||||||||
\(669\) | −7.95157e6 | −0.686891 | ||||||||
\(670\) | 6.29260e6 | 0.541556 | ||||||||
\(671\) | 5.15168e6 | 0.441715 | ||||||||
\(672\) | −4.79106e6 | −0.409269 | ||||||||
\(673\) | −1.91232e7 | −1.62750 | −0.813752 | − | 0.581213i | \(-0.802578\pi\) | ||||
−0.813752 | + | 0.581213i | \(0.802578\pi\) | |||||||
\(674\) | −2.36218e7 | −2.00292 | ||||||||
\(675\) | 1.74094e6 | 0.147070 | ||||||||
\(676\) | −6.60162e6 | −0.555627 | ||||||||
\(677\) | 1.92361e7 | 1.61304 | 0.806520 | − | 0.591206i | \(-0.201348\pi\) | ||||
0.806520 | + | 0.591206i | \(0.201348\pi\) | |||||||
\(678\) | 1.85093e6 | 0.154637 | ||||||||
\(679\) | −4.60365e6 | −0.383202 | ||||||||
\(680\) | 1.98964e6 | 0.165007 | ||||||||
\(681\) | −459175. | −0.0379411 | ||||||||
\(682\) | 3.02654e6 | 0.249164 | ||||||||
\(683\) | 1.55899e7 | 1.27876 | 0.639382 | − | 0.768889i | \(-0.279190\pi\) | ||||
0.639382 | + | 0.768889i | \(0.279190\pi\) | |||||||
\(684\) | −1.94906e6 | −0.159289 | ||||||||
\(685\) | 7.18105e6 | 0.584739 | ||||||||
\(686\) | 1.80844e7 | 1.46721 | ||||||||
\(687\) | −3.51672e6 | −0.284279 | ||||||||
\(688\) | −1.65158e7 | −1.33024 | ||||||||
\(689\) | −6.89792e6 | −0.553566 | ||||||||
\(690\) | −2.45453e6 | −0.196266 | ||||||||
\(691\) | 278716. | 0.0222058 | 0.0111029 | − | 0.999938i | \(-0.496466\pi\) | ||||
0.0111029 | + | 0.999938i | \(0.496466\pi\) | |||||||
\(692\) | −1.36998e6 | −0.108755 | ||||||||
\(693\) | 2.50347e6 | 0.198020 | ||||||||
\(694\) | 1.63863e7 | 1.29147 | ||||||||
\(695\) | 4.31441e6 | 0.338812 | ||||||||
\(696\) | 2.08963e6 | 0.163511 | ||||||||
\(697\) | −2.36429e7 | −1.84340 | ||||||||
\(698\) | 1.89627e7 | 1.47320 | ||||||||
\(699\) | 2.81617e6 | 0.218005 | ||||||||
\(700\) | 1.67429e6 | 0.129147 | ||||||||
\(701\) | 3.38089e6 | 0.259858 | 0.129929 | − | 0.991523i | \(-0.458525\pi\) | ||||
0.129929 | + | 0.991523i | \(0.458525\pi\) | |||||||
\(702\) | −7.42567e6 | −0.568713 | ||||||||
\(703\) | 4.65638e6 | 0.355353 | ||||||||
\(704\) | 2.48812e6 | 0.189208 | ||||||||
\(705\) | −52387.3 | −0.00396966 | ||||||||
\(706\) | −3.89570e6 | −0.294153 | ||||||||
\(707\) | −4.15878e6 | −0.312908 | ||||||||
\(708\) | 5.67226e6 | 0.425278 | ||||||||
\(709\) | −7.04913e6 | −0.526647 | −0.263324 | − | 0.964708i | \(-0.584819\pi\) | ||||
−0.263324 | + | 0.964708i | \(0.584819\pi\) | |||||||
\(710\) | −3.77553e6 | −0.281082 | ||||||||
\(711\) | 1.22221e7 | 0.906719 | ||||||||
\(712\) | 5.22875e6 | 0.386543 | ||||||||
\(713\) | −6.74657e6 | −0.497003 | ||||||||
\(714\) | 9.03288e6 | 0.663103 | ||||||||
\(715\) | −1.05488e6 | −0.0771684 | ||||||||
\(716\) | −2.04149e6 | −0.148821 | ||||||||
\(717\) | 7.37947e6 | 0.536077 | ||||||||
\(718\) | −2.82708e7 | −2.04657 | ||||||||
\(719\) | −5.49405e6 | −0.396343 | −0.198171 | − | 0.980167i | \(-0.563500\pi\) | ||||
−0.198171 | + | 0.980167i | \(0.563500\pi\) | |||||||
\(720\) | 5.97812e6 | 0.429767 | ||||||||
\(721\) | −3.05815e6 | −0.219089 | ||||||||
\(722\) | −996250. | −0.0711255 | ||||||||
\(723\) | 4.58363e6 | 0.326110 | ||||||||
\(724\) | −1.63152e6 | −0.115676 | ||||||||
\(725\) | −4.93285e6 | −0.348540 | ||||||||
\(726\) | 697144. | 0.0490886 | ||||||||
\(727\) | 1.84759e7 | 1.29649 | 0.648246 | − | 0.761431i | \(-0.275503\pi\) | ||||
0.648246 | + | 0.761431i | \(0.275503\pi\) | |||||||
\(728\) | 1.50186e6 | 0.105027 | ||||||||
\(729\) | −2.37386e6 | −0.165438 | ||||||||
\(730\) | 573244. | 0.0398137 | ||||||||
\(731\) | 2.64069e7 | 1.82778 | ||||||||
\(732\) | 7.01160e6 | 0.483659 | ||||||||
\(733\) | −3.68370e6 | −0.253235 | −0.126618 | − | 0.991952i | \(-0.540412\pi\) | ||||
−0.126618 | + | 0.991952i | \(0.540412\pi\) | |||||||
\(734\) | 1.90385e7 | 1.30435 | ||||||||
\(735\) | 1.01859e6 | 0.0695475 | ||||||||
\(736\) | −1.56536e7 | −1.06517 | ||||||||
\(737\) | 3.98402e6 | 0.270180 | ||||||||
\(738\) | −1.97123e7 | −1.33228 | ||||||||
\(739\) | −1.68856e7 | −1.13738 | −0.568689 | − | 0.822553i | \(-0.692549\pi\) | ||||
−0.568689 | + | 0.822553i | \(0.692549\pi\) | |||||||
\(740\) | 8.52584e6 | 0.572345 | ||||||||
\(741\) | −784123. | −0.0524612 | ||||||||
\(742\) | 1.53210e7 | 1.02159 | ||||||||
\(743\) | 6.60639e6 | 0.439028 | 0.219514 | − | 0.975609i | \(-0.429553\pi\) | ||||
0.219514 | + | 0.975609i | \(0.429553\pi\) | |||||||
\(744\) | −866281. | −0.0573755 | ||||||||
\(745\) | −1.05531e7 | −0.696607 | ||||||||
\(746\) | −1.07613e7 | −0.707972 | ||||||||
\(747\) | 1.33986e7 | 0.878532 | ||||||||
\(748\) | −5.98992e6 | −0.391442 | ||||||||
\(749\) | 2.18681e7 | 1.42432 | ||||||||
\(750\) | 743998. | 0.0482968 | ||||||||
\(751\) | −1.89853e6 | −0.122834 | −0.0614169 | − | 0.998112i | \(-0.519562\pi\) | ||||
−0.0614169 | + | 0.998112i | \(0.519562\pi\) | |||||||
\(752\) | −393958. | −0.0254042 | ||||||||
\(753\) | 3.43859e6 | 0.221001 | ||||||||
\(754\) | 2.10402e7 | 1.34779 | ||||||||
\(755\) | −1.51668e6 | −0.0968334 | ||||||||
\(756\) | 7.46197e6 | 0.474842 | ||||||||
\(757\) | −1.71645e7 | −1.08866 | −0.544328 | − | 0.838873i | \(-0.683215\pi\) | ||||
−0.544328 | + | 0.838873i | \(0.683215\pi\) | |||||||
\(758\) | −3.30076e7 | −2.08661 | ||||||||
\(759\) | −1.55403e6 | −0.0979162 | ||||||||
\(760\) | 383620. | 0.0240917 | ||||||||
\(761\) | −2.24988e7 | −1.40831 | −0.704154 | − | 0.710048i | \(-0.748673\pi\) | ||||
−0.704154 | + | 0.710048i | \(0.748673\pi\) | |||||||
\(762\) | −1.74021e6 | −0.108571 | ||||||||
\(763\) | 6.47335e6 | 0.402548 | ||||||||
\(764\) | 2.20612e7 | 1.36740 | ||||||||
\(765\) | −9.55834e6 | −0.590512 | ||||||||
\(766\) | 2.74218e7 | 1.68859 | ||||||||
\(767\) | −1.20111e7 | −0.737214 | ||||||||
\(768\) | −8.18112e6 | −0.500506 | ||||||||
\(769\) | 9.49198e6 | 0.578816 | 0.289408 | − | 0.957206i | \(-0.406542\pi\) | ||||
0.289408 | + | 0.957206i | \(0.406542\pi\) | |||||||
\(770\) | 2.34301e6 | 0.142412 | ||||||||
\(771\) | 1.09342e7 | 0.662448 | ||||||||
\(772\) | 1.86743e7 | 1.12772 | ||||||||
\(773\) | −2.21086e6 | −0.133080 | −0.0665399 | − | 0.997784i | \(-0.521196\pi\) | ||||
−0.0665399 | + | 0.997784i | \(0.521196\pi\) | |||||||
\(774\) | 2.20168e7 | 1.32100 | ||||||||
\(775\) | 2.04497e6 | 0.122302 | ||||||||
\(776\) | −1.93135e6 | −0.115135 | ||||||||
\(777\) | −8.14017e6 | −0.483705 | ||||||||
\(778\) | 1.47988e7 | 0.876550 | ||||||||
\(779\) | −4.55856e6 | −0.269144 | ||||||||
\(780\) | −1.43573e6 | −0.0844960 | ||||||||
\(781\) | −2.39039e6 | −0.140230 | ||||||||
\(782\) | 2.95128e7 | 1.72581 | ||||||||
\(783\) | −2.19847e7 | −1.28149 | ||||||||
\(784\) | 7.65992e6 | 0.445076 | ||||||||
\(785\) | −3.54093e6 | −0.205090 | ||||||||
\(786\) | 638854. | 0.0368846 | ||||||||
\(787\) | 8.03367e6 | 0.462357 | 0.231178 | − | 0.972911i | \(-0.425742\pi\) | ||||
0.231178 | + | 0.972911i | \(0.425742\pi\) | |||||||
\(788\) | 1.70482e7 | 0.978055 | ||||||||
\(789\) | 1.07582e7 | 0.615242 | ||||||||
\(790\) | 1.14387e7 | 0.652094 | ||||||||
\(791\) | 3.93851e6 | 0.223816 | ||||||||
\(792\) | 1.05027e6 | 0.0594962 | ||||||||
\(793\) | −1.48471e7 | −0.838415 | ||||||||
\(794\) | −1.86512e7 | −1.04992 | ||||||||
\(795\) | 3.08018e6 | 0.172846 | ||||||||
\(796\) | 8.08843e6 | 0.452462 | ||||||||
\(797\) | −3.24452e7 | −1.80928 | −0.904638 | − | 0.426181i | \(-0.859859\pi\) | ||||
−0.904638 | + | 0.426181i | \(0.859859\pi\) | |||||||
\(798\) | 1.74162e6 | 0.0968158 | ||||||||
\(799\) | 629895. | 0.0349061 | ||||||||
\(800\) | 4.74482e6 | 0.262117 | ||||||||
\(801\) | −2.51192e7 | −1.38333 | ||||||||
\(802\) | 2.51801e7 | 1.38236 | ||||||||
\(803\) | 362937. | 0.0198629 | ||||||||
\(804\) | 5.42238e6 | 0.295835 | ||||||||
\(805\) | −5.22289e6 | −0.284067 | ||||||||
\(806\) | −8.72247e6 | −0.472936 | ||||||||
\(807\) | −1.39911e6 | −0.0756254 | ||||||||
\(808\) | −1.74472e6 | −0.0940150 | ||||||||
\(809\) | −3.17402e7 | −1.70506 | −0.852529 | − | 0.522680i | \(-0.824932\pi\) | ||||
−0.852529 | + | 0.522680i | \(0.824932\pi\) | |||||||
\(810\) | −6.16753e6 | −0.330292 | ||||||||
\(811\) | −1.73321e7 | −0.925333 | −0.462667 | − | 0.886532i | \(-0.653107\pi\) | ||||
−0.462667 | + | 0.886532i | \(0.653107\pi\) | |||||||
\(812\) | −2.11431e7 | −1.12533 | ||||||||
\(813\) | 4.07342e6 | 0.216139 | ||||||||
\(814\) | 1.19311e7 | 0.631131 | ||||||||
\(815\) | 6.10369e6 | 0.321883 | ||||||||
\(816\) | 1.36565e7 | 0.717983 | ||||||||
\(817\) | 5.09149e6 | 0.266864 | ||||||||
\(818\) | 1.34650e7 | 0.703597 | ||||||||
\(819\) | −7.21500e6 | −0.375861 | ||||||||
\(820\) | −8.34674e6 | −0.433493 | ||||||||
\(821\) | −2.70198e7 | −1.39902 | −0.699511 | − | 0.714621i | \(-0.746599\pi\) | ||||
−0.699511 | + | 0.714621i | \(0.746599\pi\) | |||||||
\(822\) | 1.36773e7 | 0.706025 | ||||||||
\(823\) | −2.69624e7 | −1.38758 | −0.693790 | − | 0.720177i | \(-0.744061\pi\) | ||||
−0.693790 | + | 0.720177i | \(0.744061\pi\) | |||||||
\(824\) | −1.28297e6 | −0.0658264 | ||||||||
\(825\) | 471046. | 0.0240951 | ||||||||
\(826\) | 2.66779e7 | 1.36051 | ||||||||
\(827\) | 4.94483e6 | 0.251413 | 0.125706 | − | 0.992067i | \(-0.459880\pi\) | ||||
0.125706 | + | 0.992067i | \(0.459880\pi\) | |||||||
\(828\) | 1.11326e7 | 0.564312 | ||||||||
\(829\) | 1.19548e7 | 0.604167 | 0.302083 | − | 0.953281i | \(-0.402318\pi\) | ||||
0.302083 | + | 0.953281i | \(0.402318\pi\) | |||||||
\(830\) | 1.25398e7 | 0.631823 | ||||||||
\(831\) | 2.30009e6 | 0.115543 | ||||||||
\(832\) | −7.17077e6 | −0.359135 | ||||||||
\(833\) | −1.22474e7 | −0.611547 | ||||||||
\(834\) | 8.21737e6 | 0.409089 | ||||||||
\(835\) | 4.49512e6 | 0.223113 | ||||||||
\(836\) | −1.15491e6 | −0.0571522 | ||||||||
\(837\) | 9.11400e6 | 0.449672 | ||||||||
\(838\) | 4.10127e7 | 2.01748 | ||||||||
\(839\) | −1.29369e7 | −0.634489 | −0.317245 | − | 0.948344i | \(-0.602758\pi\) | ||||
−0.317245 | + | 0.948344i | \(0.602758\pi\) | |||||||
\(840\) | −670636. | −0.0327936 | ||||||||
\(841\) | 4.17813e7 | 2.03700 | ||||||||
\(842\) | 3.14400e7 | 1.52828 | ||||||||
\(843\) | −3.08288e6 | −0.149413 | ||||||||
\(844\) | −2.29519e7 | −1.10908 | ||||||||
\(845\) | −6.24215e6 | −0.300741 | ||||||||
\(846\) | 525176. | 0.0252278 | ||||||||
\(847\) | 1.48343e6 | 0.0710489 | ||||||||
\(848\) | 2.31633e7 | 1.10614 | ||||||||
\(849\) | −7.75537e6 | −0.369261 | ||||||||
\(850\) | −8.94569e6 | −0.424685 | ||||||||
\(851\) | −2.65961e7 | −1.25891 | ||||||||
\(852\) | −3.25340e6 | −0.153546 | ||||||||
\(853\) | −2.58592e7 | −1.21687 | −0.608433 | − | 0.793606i | \(-0.708201\pi\) | ||||
−0.608433 | + | 0.793606i | \(0.708201\pi\) | |||||||
\(854\) | 3.29771e7 | 1.54727 | ||||||||
\(855\) | −1.84293e6 | −0.0862173 | ||||||||
\(856\) | 9.17426e6 | 0.427944 | ||||||||
\(857\) | −8.71458e6 | −0.405317 | −0.202658 | − | 0.979249i | \(-0.564958\pi\) | ||||
−0.202658 | + | 0.979249i | \(0.564958\pi\) | |||||||
\(858\) | −2.00917e6 | −0.0931746 | ||||||||
\(859\) | −7.82669e6 | −0.361905 | −0.180953 | − | 0.983492i | \(-0.557918\pi\) | ||||
−0.180953 | + | 0.983492i | \(0.557918\pi\) | |||||||
\(860\) | 9.32254e6 | 0.429821 | ||||||||
\(861\) | 7.96917e6 | 0.366358 | ||||||||
\(862\) | 2.26874e7 | 1.03996 | ||||||||
\(863\) | 3.03821e7 | 1.38865 | 0.694323 | − | 0.719664i | \(-0.255704\pi\) | ||||
0.694323 | + | 0.719664i | \(0.255704\pi\) | |||||||
\(864\) | 2.11467e7 | 0.963735 | ||||||||
\(865\) | −1.29538e6 | −0.0588649 | ||||||||
\(866\) | 5.46155e6 | 0.247469 | ||||||||
\(867\) | −1.29913e7 | −0.586957 | ||||||||
\(868\) | 8.76511e6 | 0.394874 | ||||||||
\(869\) | 7.24218e6 | 0.325327 | ||||||||
\(870\) | −9.39527e6 | −0.420834 | ||||||||
\(871\) | −1.14819e7 | −0.512826 | ||||||||
\(872\) | 2.71574e6 | 0.120948 | ||||||||
\(873\) | 9.27833e6 | 0.412035 | ||||||||
\(874\) | 5.69033e6 | 0.251976 | ||||||||
\(875\) | 1.58312e6 | 0.0699028 | ||||||||
\(876\) | 493969. | 0.0217490 | ||||||||
\(877\) | −1.35330e7 | −0.594151 | −0.297075 | − | 0.954854i | \(-0.596011\pi\) | ||||
−0.297075 | + | 0.954854i | \(0.596011\pi\) | |||||||
\(878\) | −3.73896e7 | −1.63687 | ||||||||
\(879\) | −1.34667e6 | −0.0587879 | ||||||||
\(880\) | 3.54232e6 | 0.154199 | ||||||||
\(881\) | −1.37016e7 | −0.594748 | −0.297374 | − | 0.954761i | \(-0.596111\pi\) | ||||
−0.297374 | + | 0.954761i | \(0.596111\pi\) | |||||||
\(882\) | −1.02112e7 | −0.441985 | ||||||||
\(883\) | −1.99152e7 | −0.859572 | −0.429786 | − | 0.902931i | \(-0.641411\pi\) | ||||
−0.429786 | + | 0.902931i | \(0.641411\pi\) | |||||||
\(884\) | 1.72630e7 | 0.742992 | ||||||||
\(885\) | 5.36340e6 | 0.230188 | ||||||||
\(886\) | 1.99720e7 | 0.854747 | ||||||||
\(887\) | 2.92450e7 | 1.24808 | 0.624039 | − | 0.781393i | \(-0.285490\pi\) | ||||
0.624039 | + | 0.781393i | \(0.285490\pi\) | |||||||
\(888\) | −3.41502e6 | −0.145332 | ||||||||
\(889\) | −3.70292e6 | −0.157141 | ||||||||
\(890\) | −2.35092e7 | −0.994862 | ||||||||
\(891\) | −3.90483e6 | −0.164781 | ||||||||
\(892\) | 3.37529e7 | 1.42036 | ||||||||
\(893\) | 121449. | 0.00509644 | ||||||||
\(894\) | −2.00997e7 | −0.841098 | ||||||||
\(895\) | −1.93032e6 | −0.0805514 | ||||||||
\(896\) | −8.68706e6 | −0.361496 | ||||||||
\(897\) | 4.47871e6 | 0.185854 | ||||||||
\(898\) | −1.00663e7 | −0.416562 | ||||||||
\(899\) | −2.58240e7 | −1.06568 | ||||||||
\(900\) | −3.37442e6 | −0.138865 | ||||||||
\(901\) | −3.70355e7 | −1.51987 | ||||||||
\(902\) | −1.16805e7 | −0.478017 | ||||||||
\(903\) | −8.90083e6 | −0.363255 | ||||||||
\(904\) | 1.65231e6 | 0.0672467 | ||||||||
\(905\) | −1.54268e6 | −0.0626115 | ||||||||
\(906\) | −2.88871e6 | −0.116919 | ||||||||
\(907\) | 4.19188e7 | 1.69196 | 0.845981 | − | 0.533212i | \(-0.179015\pi\) | ||||
0.845981 | + | 0.533212i | \(0.179015\pi\) | |||||||
\(908\) | 1.94911e6 | 0.0784552 | ||||||||
\(909\) | 8.38173e6 | 0.336453 | ||||||||
\(910\) | −6.75255e6 | −0.270311 | ||||||||
\(911\) | 743586. | 0.0296849 | 0.0148424 | − | 0.999890i | \(-0.495275\pi\) | ||||
0.0148424 | + | 0.999890i | \(0.495275\pi\) | |||||||
\(912\) | 2.63310e6 | 0.104829 | ||||||||
\(913\) | 7.93929e6 | 0.315214 | ||||||||
\(914\) | −4.56232e7 | −1.80643 | ||||||||
\(915\) | 6.62981e6 | 0.261787 | ||||||||
\(916\) | 1.49278e7 | 0.587837 | ||||||||
\(917\) | 1.35939e6 | 0.0533853 | ||||||||
\(918\) | −3.98691e7 | −1.56146 | ||||||||
\(919\) | −7.06851e6 | −0.276083 | −0.138041 | − | 0.990426i | \(-0.544081\pi\) | ||||
−0.138041 | + | 0.990426i | \(0.544081\pi\) | |||||||
\(920\) | −2.19114e6 | −0.0853495 | ||||||||
\(921\) | 1.97116e7 | 0.765724 | ||||||||
\(922\) | 5.60293e7 | 2.17064 | ||||||||
\(923\) | 6.88911e6 | 0.266170 | ||||||||
\(924\) | 2.01899e6 | 0.0777954 | ||||||||
\(925\) | 8.06160e6 | 0.309790 | ||||||||
\(926\) | −3.83262e7 | −1.46882 | ||||||||
\(927\) | 6.16349e6 | 0.235574 | ||||||||
\(928\) | −5.99179e7 | −2.28395 | ||||||||
\(929\) | 2.22626e7 | 0.846322 | 0.423161 | − | 0.906054i | \(-0.360920\pi\) | ||||
0.423161 | + | 0.906054i | \(0.360920\pi\) | |||||||
\(930\) | 3.89492e6 | 0.147670 | ||||||||
\(931\) | −2.36140e6 | −0.0892884 | ||||||||
\(932\) | −1.19541e7 | −0.450793 | ||||||||
\(933\) | 2.28565e6 | 0.0859619 | ||||||||
\(934\) | 1.24680e7 | 0.467658 | ||||||||
\(935\) | −5.66377e6 | −0.211873 | ||||||||
\(936\) | −3.02689e6 | −0.112929 | ||||||||
\(937\) | 2.60019e7 | 0.967513 | 0.483757 | − | 0.875203i | \(-0.339272\pi\) | ||||
0.483757 | + | 0.875203i | \(0.339272\pi\) | |||||||
\(938\) | 2.55026e7 | 0.946407 | ||||||||
\(939\) | 9.95589e6 | 0.368482 | ||||||||
\(940\) | 222374. | 0.00820852 | ||||||||
\(941\) | 1.00670e7 | 0.370617 | 0.185309 | − | 0.982680i | \(-0.440672\pi\) | ||||
0.185309 | + | 0.982680i | \(0.440672\pi\) | |||||||
\(942\) | −6.74418e6 | −0.247629 | ||||||||
\(943\) | 2.60374e7 | 0.953494 | ||||||||
\(944\) | 4.03334e7 | 1.47311 | ||||||||
\(945\) | 7.05566e6 | 0.257015 | ||||||||
\(946\) | 1.30460e7 | 0.473968 | ||||||||
\(947\) | 1.49217e7 | 0.540684 | 0.270342 | − | 0.962764i | \(-0.412863\pi\) | ||||
0.270342 | + | 0.962764i | \(0.412863\pi\) | |||||||
\(948\) | 9.85684e6 | 0.356219 | ||||||||
\(949\) | −1.04598e6 | −0.0377016 | ||||||||
\(950\) | −1.72481e6 | −0.0620058 | ||||||||
\(951\) | 1.20873e7 | 0.433388 | ||||||||
\(952\) | 8.06360e6 | 0.288361 | ||||||||
\(953\) | 1.67029e7 | 0.595744 | 0.297872 | − | 0.954606i | \(-0.403723\pi\) | ||||
0.297872 | + | 0.954606i | \(0.403723\pi\) | |||||||
\(954\) | −3.08784e7 | −1.09846 | ||||||||
\(955\) | 2.08599e7 | 0.740123 | ||||||||
\(956\) | −3.13244e7 | −1.10851 | ||||||||
\(957\) | −5.94841e6 | −0.209952 | ||||||||
\(958\) | 4.67184e7 | 1.64465 | ||||||||
\(959\) | 2.91034e7 | 1.02187 | ||||||||
\(960\) | 3.20202e6 | 0.112136 | ||||||||
\(961\) | −1.79235e7 | −0.626057 | ||||||||
\(962\) | −3.43854e7 | −1.19794 | ||||||||
\(963\) | −4.40737e7 | −1.53149 | ||||||||
\(964\) | −1.94567e7 | −0.674335 | ||||||||
\(965\) | 1.76574e7 | 0.610393 | ||||||||
\(966\) | −9.94770e6 | −0.342989 | ||||||||
\(967\) | 1.70186e7 | 0.585271 | 0.292636 | − | 0.956224i | \(-0.405468\pi\) | ||||
0.292636 | + | 0.956224i | \(0.405468\pi\) | |||||||
\(968\) | 622336. | 0.0213470 | ||||||||
\(969\) | −4.21003e6 | −0.144037 | ||||||||
\(970\) | 8.68362e6 | 0.296327 | ||||||||
\(971\) | −4.93436e7 | −1.67951 | −0.839755 | − | 0.542965i | \(-0.817302\pi\) | ||||
−0.839755 | + | 0.542965i | \(0.817302\pi\) | |||||||
\(972\) | −2.32110e7 | −0.788003 | ||||||||
\(973\) | 1.74854e7 | 0.592099 | ||||||||
\(974\) | −1.60984e7 | −0.543731 | ||||||||
\(975\) | −1.35755e6 | −0.0457346 | ||||||||
\(976\) | 4.98569e7 | 1.67533 | ||||||||
\(977\) | −1.06785e7 | −0.357909 | −0.178955 | − | 0.983857i | \(-0.557272\pi\) | ||||
−0.178955 | + | 0.983857i | \(0.557272\pi\) | |||||||
\(978\) | 1.16253e7 | 0.388649 | ||||||||
\(979\) | −1.48843e7 | −0.496332 | ||||||||
\(980\) | −4.32373e6 | −0.143811 | ||||||||
\(981\) | −1.30466e7 | −0.432837 | ||||||||
\(982\) | −1.03082e7 | −0.341119 | ||||||||
\(983\) | −3.12100e6 | −0.103017 | −0.0515086 | − | 0.998673i | \(-0.516403\pi\) | ||||
−0.0515086 | + | 0.998673i | \(0.516403\pi\) | |||||||
\(984\) | 3.34328e6 | 0.110074 | ||||||||
\(985\) | 1.61199e7 | 0.529385 | ||||||||
\(986\) | 1.12967e8 | 3.70049 | ||||||||
\(987\) | −212315. | −0.00693726 | ||||||||
\(988\) | 3.32845e6 | 0.108480 | ||||||||
\(989\) | −2.90813e7 | −0.945417 | ||||||||
\(990\) | −4.72217e6 | −0.153128 | ||||||||
\(991\) | −1.50879e7 | −0.488027 | −0.244014 | − | 0.969772i | \(-0.578464\pi\) | ||||
−0.244014 | + | 0.969772i | \(0.578464\pi\) | |||||||
\(992\) | 2.48397e7 | 0.801432 | ||||||||
\(993\) | 1.00734e7 | 0.324192 | ||||||||
\(994\) | −1.53015e7 | −0.491210 | ||||||||
\(995\) | 7.64801e6 | 0.244901 | ||||||||
\(996\) | 1.08056e7 | 0.345145 | ||||||||
\(997\) | 1.70096e7 | 0.541945 | 0.270973 | − | 0.962587i | \(-0.412655\pi\) | ||||
0.270973 | + | 0.962587i | \(0.412655\pi\) | |||||||
\(998\) | 1.59409e6 | 0.0506626 | ||||||||
\(999\) | 3.59289e7 | 1.13902 |
(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 | 1045.6.a.b.1.7 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.6.a.b.1.7 | ✓ | 36 | 1.1 | even | 1 | trivial |