Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 30.1 | ||
Root | \(1.77069 - 3.06693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.30 |
Dual form | 49.6.c.f.18.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.54138 | + | 6.13385i | −0.626034 | + | 1.08432i | 0.362306 | + | 0.932059i | \(0.381989\pi\) |
−0.988340 | + | 0.152263i | \(0.951344\pi\) | |||||||
\(3\) | −5.04138 | − | 8.73193i | −0.323405 | − | 0.560153i | 0.657783 | − | 0.753207i | \(-0.271494\pi\) |
−0.981188 | + | 0.193054i | \(0.938161\pi\) | |||||||
\(4\) | −9.08276 | − | 15.7318i | −0.283836 | − | 0.491619i | ||||
\(5\) | −39.9138 | + | 69.1328i | −0.714000 | + | 1.23668i | 0.249344 | + | 0.968415i | \(0.419785\pi\) |
−0.963344 | + | 0.268269i | \(0.913548\pi\) | |||||||
\(6\) | 71.4138 | 0.809849 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −97.9863 | −0.541303 | ||||||||
\(9\) | 70.6689 | − | 122.402i | 0.290819 | − | 0.503713i | ||||
\(10\) | −282.700 | − | 489.651i | −0.893976 | − | 1.54841i | ||||
\(11\) | −175.952 | − | 304.757i | −0.438442 | − | 0.759403i | 0.559128 | − | 0.829082i | \(-0.311136\pi\) |
−0.997570 | + | 0.0696781i | \(0.977803\pi\) | |||||||
\(12\) | −91.5793 | + | 158.620i | −0.183588 | + | 0.317984i | ||||
\(13\) | 291.683 | 0.478688 | 0.239344 | − | 0.970935i | \(-0.423068\pi\) | ||||
0.239344 | + | 0.970935i | \(0.423068\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 804.883 | 0.923644 | ||||||||
\(16\) | 637.655 | − | 1104.45i | 0.622710 | − | 1.07857i | ||||
\(17\) | −185.038 | − | 320.495i | −0.155288 | − | 0.268967i | 0.777876 | − | 0.628418i | \(-0.216297\pi\) |
−0.933164 | + | 0.359451i | \(0.882964\pi\) | |||||||
\(18\) | 500.531 | + | 866.946i | 0.364125 | + | 0.630682i | ||||
\(19\) | 752.463 | − | 1303.30i | 0.478190 | − | 0.828250i | −0.521497 | − | 0.853253i | \(-0.674626\pi\) |
0.999687 | + | 0.0250030i | \(0.00795952\pi\) | |||||||
\(20\) | 1450.11 | 0.810637 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2492.45 | 1.09792 | ||||||||
\(23\) | 212.855 | − | 368.676i | 0.0839006 | − | 0.145320i | −0.821022 | − | 0.570897i | \(-0.806596\pi\) |
0.904922 | + | 0.425577i | \(0.139929\pi\) | |||||||
\(24\) | 493.986 | + | 855.609i | 0.175060 | + | 0.303213i | ||||
\(25\) | −1623.72 | − | 2812.37i | −0.519592 | − | 0.899960i | ||||
\(26\) | −1032.96 | + | 1789.14i | −0.299675 | + | 0.519052i | ||||
\(27\) | −3875.19 | −1.02302 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7783.93 | −1.71872 | −0.859358 | − | 0.511374i | \(-0.829137\pi\) | ||||
−0.859358 | + | 0.511374i | \(0.829137\pi\) | |||||||
\(30\) | −2850.40 | + | 4937.03i | −0.578232 | + | 1.00153i | ||||
\(31\) | −1287.59 | − | 2230.17i | −0.240643 | − | 0.416805i | 0.720255 | − | 0.693710i | \(-0.244025\pi\) |
−0.960898 | + | 0.276904i | \(0.910692\pi\) | |||||||
\(32\) | 2948.58 | + | 5107.09i | 0.509024 | + | 0.881655i | ||||
\(33\) | −1774.08 | + | 3072.80i | −0.283588 | + | 0.491189i | ||||
\(34\) | 2621.16 | 0.388862 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2567.48 | −0.330180 | ||||||||
\(37\) | −369.809 | + | 640.528i | −0.0444092 | + | 0.0769190i | −0.887376 | − | 0.461047i | \(-0.847474\pi\) |
0.842966 | + | 0.537966i | \(0.180807\pi\) | |||||||
\(38\) | 5329.51 | + | 9230.99i | 0.598727 | + | 1.03703i | ||||
\(39\) | −1470.48 | − | 2546.95i | −0.154810 | − | 0.268139i | ||||
\(40\) | 3911.01 | − | 6774.06i | 0.386490 | − | 0.669421i | ||||
\(41\) | −7029.84 | −0.653109 | −0.326554 | − | 0.945178i | \(-0.605888\pi\) | ||||
−0.326554 | + | 0.945178i | \(0.605888\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1835.23 | 0.151363 | 0.0756816 | − | 0.997132i | \(-0.475887\pi\) | ||||
0.0756816 | + | 0.997132i | \(0.475887\pi\) | |||||||
\(44\) | −3196.26 | + | 5536.08i | −0.248891 | + | 0.431093i | ||||
\(45\) | 5641.33 | + | 9771.08i | 0.415289 | + | 0.719302i | ||||
\(46\) | 1507.60 | + | 2611.25i | 0.105049 | + | 0.181950i | ||||
\(47\) | −766.342 | + | 1327.34i | −0.0506032 | + | 0.0876473i | −0.890217 | − | 0.455536i | \(-0.849448\pi\) |
0.839614 | + | 0.543183i | \(0.182781\pi\) | |||||||
\(48\) | −12858.7 | −0.805550 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 23000.9 | 1.30113 | ||||||||
\(51\) | −1865.69 | + | 3231.47i | −0.100442 | + | 0.173970i | ||||
\(52\) | −2649.28 | − | 4588.69i | −0.135869 | − | 0.235332i | ||||
\(53\) | 4768.73 | + | 8259.68i | 0.233192 | + | 0.403900i | 0.958746 | − | 0.284265i | \(-0.0917497\pi\) |
−0.725554 | + | 0.688165i | \(0.758416\pi\) | |||||||
\(54\) | 13723.5 | − | 23769.8i | 0.640444 | − | 1.10928i | ||||
\(55\) | 28091.6 | 1.25219 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15173.8 | −0.618596 | ||||||||
\(58\) | 27565.9 | − | 47745.5i | 1.07597 | − | 1.86364i | ||||
\(59\) | −14837.0 | − | 25698.5i | −0.554903 | − | 0.961120i | −0.997911 | − | 0.0646022i | \(-0.979422\pi\) |
0.443008 | − | 0.896517i | \(-0.353911\pi\) | |||||||
\(60\) | −7310.56 | − | 12662.3i | −0.262164 | − | 0.454081i | ||||
\(61\) | −23255.4 | + | 40279.5i | −0.800201 | + | 1.38599i | 0.119282 | + | 0.992860i | \(0.461941\pi\) |
−0.919483 | + | 0.393129i | \(0.871393\pi\) | |||||||
\(62\) | 18239.4 | 0.602602 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −958.246 | −0.0292434 | ||||||||
\(65\) | −11642.2 | + | 20164.8i | −0.341783 | + | 0.591985i | ||||
\(66\) | −12565.4 | − | 21763.9i | −0.355072 | − | 0.615002i | ||||
\(67\) | −13373.0 | − | 23162.8i | −0.363951 | − | 0.630381i | 0.624656 | − | 0.780900i | \(-0.285239\pi\) |
−0.988607 | + | 0.150518i | \(0.951906\pi\) | |||||||
\(68\) | −3361.31 | + | 5821.95i | −0.0881527 | + | 0.152685i | ||||
\(69\) | −4292.34 | −0.108535 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14388.8 | −0.338748 | −0.169374 | − | 0.985552i | \(-0.554175\pi\) | ||||
−0.169374 | + | 0.985552i | \(0.554175\pi\) | |||||||
\(72\) | −6924.59 | + | 11993.7i | −0.157421 | + | 0.272661i | ||||
\(73\) | −35047.6 | − | 60704.2i | −0.769752 | − | 1.33325i | −0.937697 | − | 0.347453i | \(-0.887047\pi\) |
0.167946 | − | 0.985796i | \(-0.446287\pi\) | |||||||
\(74\) | −2619.27 | − | 4536.71i | −0.0556033 | − | 0.0963078i | ||||
\(75\) | −16371.6 | + | 28356.5i | −0.336077 | + | 0.582102i | ||||
\(76\) | −27337.8 | −0.542911 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 20830.2 | 0.387665 | ||||||||
\(79\) | 13542.9 | − | 23457.0i | 0.244143 | − | 0.422868i | −0.717748 | − | 0.696303i | \(-0.754827\pi\) |
0.961890 | + | 0.273436i | \(0.0881601\pi\) | |||||||
\(80\) | 50902.5 | + | 88165.7i | 0.889230 | + | 1.54019i | ||||
\(81\) | 2363.74 | + | 4094.13i | 0.0400302 | + | 0.0693344i | ||||
\(82\) | 24895.3 | − | 43120.0i | 0.408868 | − | 0.708181i | ||||
\(83\) | 79755.4 | 1.27076 | 0.635382 | − | 0.772198i | \(-0.280843\pi\) | ||||
0.635382 | + | 0.772198i | \(0.280843\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 29542.2 | 0.443502 | ||||||||
\(86\) | −6499.26 | + | 11257.0i | −0.0947584 | + | 0.164126i | ||||
\(87\) | 39241.8 | + | 67968.8i | 0.555841 | + | 0.962745i | ||||
\(88\) | 17240.9 | + | 29862.1i | 0.237330 | + | 0.411067i | ||||
\(89\) | 21788.7 | − | 37739.1i | 0.291579 | − | 0.505029i | −0.682605 | − | 0.730788i | \(-0.739153\pi\) |
0.974183 | + | 0.225759i | \(0.0724862\pi\) | |||||||
\(90\) | −79912.5 | −1.03994 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −7733.26 | −0.0952561 | ||||||||
\(93\) | −12982.4 | + | 22486.2i | −0.155650 | + | 0.269594i | ||||
\(94\) | −5427.82 | − | 9401.25i | −0.0633586 | − | 0.109740i | ||||
\(95\) | 60067.3 | + | 104040.i | 0.682856 | + | 1.18274i | ||||
\(96\) | 29729.8 | − | 51493.6i | 0.329241 | − | 0.570263i | ||||
\(97\) | −103374. | −1.11553 | −0.557765 | − | 0.829999i | \(-0.688341\pi\) | ||||
−0.557765 | + | 0.829999i | \(0.688341\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −49737.3 | −0.510028 | ||||||||
\(100\) | −29495.8 | + | 51088.3i | −0.294958 | + | 0.510883i | ||||
\(101\) | 14350.1 | + | 24855.1i | 0.139975 | + | 0.242444i | 0.927487 | − | 0.373855i | \(-0.121964\pi\) |
−0.787512 | + | 0.616300i | \(0.788631\pi\) | |||||||
\(102\) | −13214.2 | − | 22887.7i | −0.125760 | − | 0.217822i | ||||
\(103\) | 14614.0 | − | 25312.1i | 0.135730 | − | 0.235091i | −0.790146 | − | 0.612918i | \(-0.789995\pi\) |
0.925876 | + | 0.377828i | \(0.123329\pi\) | |||||||
\(104\) | −28580.9 | −0.259115 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −67551.6 | −0.583944 | ||||||||
\(107\) | −43929.2 | + | 76087.6i | −0.370932 | + | 0.642472i | −0.989709 | − | 0.143094i | \(-0.954295\pi\) |
0.618778 | + | 0.785566i | \(0.287628\pi\) | |||||||
\(108\) | 35197.4 | + | 60963.7i | 0.290370 | + | 0.502935i | ||||
\(109\) | −110314. | − | 191069.i | −0.889333 | − | 1.54037i | −0.840665 | − | 0.541555i | \(-0.817836\pi\) |
−0.0486678 | − | 0.998815i | \(-0.515498\pi\) | |||||||
\(110\) | −99483.2 | + | 172310.i | −0.783913 | + | 1.35778i | ||||
\(111\) | 7457.39 | 0.0574486 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 39665.6 | 0.292225 | 0.146113 | − | 0.989268i | \(-0.453324\pi\) | ||||
0.146113 | + | 0.989268i | \(0.453324\pi\) | |||||||
\(114\) | 53736.2 | − | 93073.9i | 0.387262 | − | 0.670758i | ||||
\(115\) | 16991.7 | + | 29430.5i | 0.119810 | + | 0.207517i | ||||
\(116\) | 70699.6 | + | 122455.i | 0.487834 | + | 0.844953i | ||||
\(117\) | 20612.9 | − | 35702.6i | 0.139211 | − | 0.241121i | ||||
\(118\) | 210174. | 1.38955 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −78867.5 | −0.499971 | ||||||||
\(121\) | 18607.4 | − | 32229.0i | 0.115538 | − | 0.200117i | ||||
\(122\) | −164712. | − | 285290.i | −1.00191 | − | 1.73535i | ||||
\(123\) | 35440.1 | + | 61384.0i | 0.211219 | + | 0.365841i | ||||
\(124\) | −23389.7 | + | 40512.2i | −0.136606 | + | 0.236609i | ||||
\(125\) | 9774.87 | 0.0559546 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 51740.3 | 0.284655 | 0.142328 | − | 0.989820i | \(-0.454541\pi\) | ||||
0.142328 | + | 0.989820i | \(0.454541\pi\) | |||||||
\(128\) | −90961.0 | + | 157549.i | −0.490716 | + | 0.849946i | ||||
\(129\) | −9252.11 | − | 16025.1i | −0.0489515 | − | 0.0847866i | ||||
\(130\) | −82458.7 | − | 142823.i | −0.427935 | − | 0.741206i | ||||
\(131\) | −83336.9 | + | 144344.i | −0.424286 | + | 0.734885i | −0.996353 | − | 0.0853215i | \(-0.972808\pi\) |
0.572067 | + | 0.820207i | \(0.306142\pi\) | |||||||
\(132\) | 64454.2 | 0.321971 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 189436. | 0.911382 | ||||||||
\(135\) | 154674. | − | 267902.i | 0.730435 | − | 1.26515i | ||||
\(136\) | 18131.2 | + | 31404.1i | 0.0840578 | + | 0.145592i | ||||
\(137\) | −14129.7 | − | 24473.4i | −0.0643178 | − | 0.111402i | 0.832073 | − | 0.554666i | \(-0.187154\pi\) |
−0.896391 | + | 0.443264i | \(0.853820\pi\) | |||||||
\(138\) | 15200.8 | − | 26328.6i | 0.0679468 | − | 0.117687i | ||||
\(139\) | −336393. | −1.47676 | −0.738380 | − | 0.674384i | \(-0.764409\pi\) | ||||
−0.738380 | + | 0.674384i | \(0.764409\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15453.7 | 0.0654612 | ||||||||
\(142\) | 50956.1 | − | 88258.5i | 0.212068 | − | 0.367312i | ||||
\(143\) | −51322.1 | − | 88892.4i | −0.209877 | − | 0.363517i | ||||
\(144\) | −90124.9 | − | 156101.i | −0.362192 | − | 0.627334i | ||||
\(145\) | 310686. | − | 538125.i | 1.22716 | − | 2.12551i | ||||
\(146\) | 496467. | 1.92756 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13435.5 | 0.0504198 | ||||||||
\(149\) | 177691. | − | 307769.i | 0.655691 | − | 1.13569i | −0.326030 | − | 0.945360i | \(-0.605711\pi\) |
0.981720 | − | 0.190330i | \(-0.0609557\pi\) | |||||||
\(150\) | −115956. | − | 200842.i | −0.420791 | − | 0.728832i | ||||
\(151\) | 179399. | + | 310727.i | 0.640290 | + | 1.10901i | 0.985368 | + | 0.170441i | \(0.0545191\pi\) |
−0.345078 | + | 0.938574i | \(0.612148\pi\) | |||||||
\(152\) | −73731.0 | + | 127706.i | −0.258846 | + | 0.448334i | ||||
\(153\) | −52305.7 | −0.180643 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 205570. | 0.687275 | ||||||||
\(156\) | −26712.1 | + | 46266.7i | −0.0878813 | + | 0.152215i | ||||
\(157\) | 229455. | + | 397428.i | 0.742932 | + | 1.28680i | 0.951155 | + | 0.308714i | \(0.0998986\pi\) |
−0.208223 | + | 0.978081i | \(0.566768\pi\) | |||||||
\(158\) | 95921.1 | + | 166140.i | 0.305683 | + | 0.529459i | ||||
\(159\) | 48082.0 | − | 83280.4i | 0.150831 | − | 0.261246i | ||||
\(160\) | −470756. | −1.45377 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −33483.7 | −0.100241 | ||||||||
\(163\) | −251220. | + | 435126.i | −0.740603 | + | 1.28276i | 0.211618 | + | 0.977353i | \(0.432127\pi\) |
−0.952221 | + | 0.305410i | \(0.901206\pi\) | |||||||
\(164\) | 63850.3 | + | 110592.i | 0.185376 | + | 0.321081i | ||||
\(165\) | −141621. | − | 245294.i | −0.404964 | − | 0.701418i | ||||
\(166\) | −282444. | + | 489208.i | −0.795541 | + | 1.37792i | ||||
\(167\) | 676652. | 1.87748 | 0.938738 | − | 0.344632i | \(-0.111996\pi\) | ||||
0.938738 | + | 0.344632i | \(0.111996\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −286214. | −0.770858 | ||||||||
\(170\) | −104620. | + | 181208.i | −0.277647 | + | 0.480900i | ||||
\(171\) | −106351. | − | 184206.i | −0.278133 | − | 0.481741i | ||||
\(172\) | −16669.0 | − | 28871.5i | −0.0429623 | − | 0.0744130i | ||||
\(173\) | −124580. | + | 215779.i | −0.316470 | + | 0.548143i | −0.979749 | − | 0.200230i | \(-0.935831\pi\) |
0.663279 | + | 0.748373i | \(0.269164\pi\) | |||||||
\(174\) | −555880. | −1.39190 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −448786. | −1.09209 | ||||||||
\(177\) | −149598. | + | 259112.i | −0.358916 | + | 0.621661i | ||||
\(178\) | 154324. | + | 267297.i | 0.365076 | + | 0.632330i | ||||
\(179\) | −69628.9 | − | 120601.i | −0.162427 | − | 0.281331i | 0.773312 | − | 0.634026i | \(-0.218599\pi\) |
−0.935738 | + | 0.352695i | \(0.885265\pi\) | |||||||
\(180\) | 102478. | − | 177497.i | 0.235748 | − | 0.408328i | ||||
\(181\) | −306246. | −0.694823 | −0.347412 | − | 0.937713i | \(-0.612939\pi\) | ||||
−0.347412 | + | 0.937713i | \(0.612939\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 468957. | 1.03516 | ||||||||
\(184\) | −20856.9 | + | 36125.2i | −0.0454156 | + | 0.0786622i | ||||
\(185\) | −29521.0 | − | 51131.8i | −0.0634163 | − | 0.109840i | ||||
\(186\) | −91951.5 | − | 159265.i | −0.194884 | − | 0.337549i | ||||
\(187\) | −65115.4 | + | 112783.i | −0.136169 | + | 0.235852i | ||||
\(188\) | 27842.0 | 0.0574521 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −850885. | −1.70996 | ||||||||
\(191\) | −113747. | + | 197015.i | −0.225609 | + | 0.390766i | −0.956502 | − | 0.291726i | \(-0.905770\pi\) |
0.730893 | + | 0.682492i | \(0.239104\pi\) | |||||||
\(192\) | 4830.89 | + | 8367.34i | 0.00945744 | + | 0.0163808i | ||||
\(193\) | 336187. | + | 582293.i | 0.649663 | + | 1.12525i | 0.983203 | + | 0.182513i | \(0.0584231\pi\) |
−0.333541 | + | 0.942736i | \(0.608244\pi\) | |||||||
\(194\) | 366086. | − | 634079.i | 0.698359 | − | 1.20959i | ||||
\(195\) | 234770. | 0.442137 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1282.76 | −0.00235493 | −0.00117747 | − | 0.999999i | \(-0.500375\pi\) | ||||
−0.00117747 | + | 0.999999i | \(0.500375\pi\) | |||||||
\(198\) | 176139. | − | 305081.i | 0.319295 | − | 0.553035i | ||||
\(199\) | 184449. | + | 319475.i | 0.330175 | + | 0.571879i | 0.982546 | − | 0.186020i | \(-0.0595591\pi\) |
−0.652371 | + | 0.757900i | \(0.726226\pi\) | |||||||
\(200\) | 159103. | + | 275574.i | 0.281257 | + | 0.487151i | ||||
\(201\) | −134837. | + | 233545.i | −0.235407 | + | 0.407737i | ||||
\(202\) | −203277. | −0.350517 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 67782.5 | 0.114036 | ||||||||
\(205\) | 280588. | − | 485992.i | 0.466320 | − | 0.807690i | ||||
\(206\) | 103507. | + | 179280.i | 0.169943 | + | 0.294349i | ||||
\(207\) | −30084.5 | − | 52107.9i | −0.0487997 | − | 0.0845236i | ||||
\(208\) | 185993. | − | 322149.i | 0.298084 | − | 0.516296i | ||||
\(209\) | −529589. | −0.838635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 502168. | 0.776503 | 0.388251 | − | 0.921553i | \(-0.373079\pi\) | ||||
0.388251 | + | 0.921553i | \(0.373079\pi\) | |||||||
\(212\) | 86626.5 | − | 150042.i | 0.132377 | − | 0.229283i | ||||
\(213\) | 72539.2 | + | 125642.i | 0.109553 | + | 0.189751i | ||||
\(214\) | −311140. | − | 538910.i | −0.464431 | − | 0.804419i | ||||
\(215\) | −73251.1 | + | 126875.i | −0.108073 | + | 0.187188i | ||||
\(216\) | 379715. | 0.553763 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.56266e6 | 2.22701 | ||||||||
\(219\) | −353376. | + | 612066.i | −0.497883 | + | 0.862358i | ||||
\(220\) | −255150. | − | 441932.i | −0.355417 | − | 0.615600i | ||||
\(221\) | −53972.3 | − | 93482.7i | −0.0743344 | − | 0.128751i | ||||
\(222\) | −26409.5 | + | 45742.5i | −0.0359647 | + | 0.0622928i | ||||
\(223\) | 1.17328e6 | 1.57993 | 0.789967 | − | 0.613149i | \(-0.210098\pi\) | ||||
0.789967 | + | 0.613149i | \(0.210098\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −458988. | −0.604428 | ||||||||
\(226\) | −140471. | + | 243303.i | −0.182943 | + | 0.316867i | ||||
\(227\) | −455079. | − | 788220.i | −0.586168 | − | 1.01527i | −0.994729 | − | 0.102542i | \(-0.967302\pi\) |
0.408560 | − | 0.912731i | \(-0.366031\pi\) | |||||||
\(228\) | 137820. | + | 238711.i | 0.175580 | + | 0.304114i | ||||
\(229\) | 260962. | − | 452000.i | 0.328843 | − | 0.569573i | −0.653439 | − | 0.756979i | \(-0.726675\pi\) |
0.982283 | + | 0.187406i | \(0.0600079\pi\) | |||||||
\(230\) | −240697. | −0.300020 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 762719. | 0.930346 | ||||||||
\(233\) | 521394. | − | 903081.i | 0.629182 | − | 1.08977i | −0.358535 | − | 0.933516i | \(-0.616723\pi\) |
0.987716 | − | 0.156258i | \(-0.0499432\pi\) | |||||||
\(234\) | 145996. | + | 252873.i | 0.174302 | + | 0.301900i | ||||
\(235\) | −61175.2 | − | 105959.i | −0.0722613 | − | 0.125160i | ||||
\(236\) | −269522. | + | 466826.i | −0.315003 | + | 0.545601i | ||||
\(237\) | −273100. | −0.315828 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.53447e6 | −1.73766 | −0.868830 | − | 0.495110i | \(-0.835128\pi\) | ||||
−0.868830 | + | 0.495110i | \(0.835128\pi\) | |||||||
\(240\) | 513238. | − | 888954.i | 0.575163 | − | 0.996211i | ||||
\(241\) | −503789. | − | 872588.i | −0.558735 | − | 0.967758i | −0.997602 | − | 0.0692059i | \(-0.977953\pi\) |
0.438867 | − | 0.898552i | \(-0.355380\pi\) | |||||||
\(242\) | 131792. | + | 228271.i | 0.144661 | + | 0.250560i | ||||
\(243\) | −447002. | + | 774231.i | −0.485617 | + | 0.841114i | ||||
\(244\) | 844893. | 0.908505 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −502028. | −0.528920 | ||||||||
\(247\) | 219480. | − | 380151.i | 0.228904 | − | 0.396473i | ||||
\(248\) | 126166. | + | 218526.i | 0.130261 | + | 0.225618i | ||||
\(249\) | −402077. | − | 696419.i | −0.410971 | − | 0.711823i | ||||
\(250\) | −34616.6 | + | 59957.6i | −0.0350295 | + | 0.0606729i | ||||
\(251\) | −8511.89 | −0.00852789 | −0.00426394 | − | 0.999991i | \(-0.501357\pi\) | ||||
−0.00426394 | + | 0.999991i | \(0.501357\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −149809. | −0.147142 | ||||||||
\(254\) | −183232. | + | 317367.i | −0.178204 | + | 0.308658i | ||||
\(255\) | −148934. | − | 257961.i | −0.143431 | − | 0.248429i | ||||
\(256\) | −659587. | − | 1.14244e6i | −0.629032 | − | 1.08951i | ||||
\(257\) | −263766. | + | 456856.i | −0.249107 | + | 0.431466i | −0.963278 | − | 0.268505i | \(-0.913470\pi\) |
0.714171 | + | 0.699971i | \(0.246804\pi\) | |||||||
\(258\) | 131061. | 0.122581 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 422972. | 0.388042 | ||||||||
\(261\) | −550082. | + | 952771.i | −0.499835 | + | 0.865739i | ||||
\(262\) | −590255. | − | 1.02235e6i | −0.531235 | − | 0.920126i | ||||
\(263\) | 176042. | + | 304914.i | 0.156938 | + | 0.271824i | 0.933763 | − | 0.357892i | \(-0.116504\pi\) |
−0.776825 | + | 0.629716i | \(0.783171\pi\) | |||||||
\(264\) | 173836. | − | 301092.i | 0.153507 | − | 0.265882i | ||||
\(265\) | −761353. | −0.665996 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −439380. | −0.377192 | ||||||||
\(268\) | −242928. | + | 420764.i | −0.206605 | + | 0.357850i | ||||
\(269\) | 239770. | + | 415294.i | 0.202029 | + | 0.349925i | 0.949182 | − | 0.314727i | \(-0.101913\pi\) |
−0.747153 | + | 0.664652i | \(0.768580\pi\) | |||||||
\(270\) | 1.09552e6 | + | 1.89749e6i | 0.914554 | + | 1.58405i | ||||
\(271\) | −488805. | + | 846636.i | −0.404308 | + | 0.700283i | −0.994241 | − | 0.107170i | \(-0.965821\pi\) |
0.589932 | + | 0.807453i | \(0.299154\pi\) | |||||||
\(272\) | −471961. | −0.386798 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 200155. | 0.161061 | ||||||||
\(275\) | −571395. | + | 989684.i | −0.455622 | + | 0.789160i | ||||
\(276\) | 38986.3 | + | 67526.2i | 0.0308063 | + | 0.0533580i | ||||
\(277\) | −484362. | − | 838939.i | −0.379289 | − | 0.656948i | 0.611670 | − | 0.791113i | \(-0.290498\pi\) |
−0.990959 | + | 0.134165i | \(0.957165\pi\) | |||||||
\(278\) | 1.19130e6 | − | 2.06339e6i | 0.924502 | − | 1.60128i | ||||
\(279\) | −363970. | −0.279934 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −318333. | −0.240501 | −0.120250 | − | 0.992744i | \(-0.538370\pi\) | ||||
−0.120250 | + | 0.992744i | \(0.538370\pi\) | |||||||
\(282\) | −54727.4 | + | 94790.6i | −0.0409809 | + | 0.0709811i | ||||
\(283\) | 886051. | + | 1.53468e6i | 0.657646 | + | 1.13908i | 0.981223 | + | 0.192875i | \(0.0617812\pi\) |
−0.323577 | + | 0.946202i | \(0.604885\pi\) | |||||||
\(284\) | 130690. | + | 226361.i | 0.0961491 | + | 0.166535i | ||||
\(285\) | 605644. | − | 1.04901e6i | 0.441678 | − | 0.765008i | ||||
\(286\) | 727004. | 0.525559 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 833492. | 0.592134 | ||||||||
\(289\) | 641451. | − | 1.11103e6i | 0.451771 | − | 0.782491i | ||||
\(290\) | 2.20052e6 | + | 3.81141e6i | 1.53649 | + | 2.66128i | ||||
\(291\) | 521147. | + | 902652.i | 0.360768 | + | 0.624868i | ||||
\(292\) | −636657. | + | 1.10272e6i | −0.436967 | + | 0.756849i | ||||
\(293\) | −1.64148e6 | −1.11703 | −0.558516 | − | 0.829494i | \(-0.688629\pi\) | ||||
−0.558516 | + | 0.829494i | \(0.688629\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.36881e6 | 1.58480 | ||||||||
\(296\) | 36236.2 | − | 62762.9i | 0.0240388 | − | 0.0416365i | ||||
\(297\) | 681846. | + | 1.18099e6i | 0.448534 | + | 0.776883i | ||||
\(298\) | 1.25854e6 | + | 2.17986e6i | 0.820969 | + | 1.42196i | ||||
\(299\) | 62086.2 | − | 107536.i | 0.0401622 | − | 0.0695629i | ||||
\(300\) | 594799. | 0.381563 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.54128e6 | −1.60337 | ||||||||
\(303\) | 144689. | − | 250608.i | 0.0905374 | − | 0.156815i | ||||
\(304\) | −959623. | − | 1.66212e6i | −0.595548 | − | 1.03152i | ||||
\(305\) | −1.85642e6 | − | 3.21542e6i | −1.14269 | − | 1.97919i | ||||
\(306\) | 185234. | − | 320835.i | 0.113088 | − | 0.195875i | ||||
\(307\) | 466930. | 0.282752 | 0.141376 | − | 0.989956i | \(-0.454847\pi\) | ||||
0.141376 | + | 0.989956i | \(0.454847\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −294698. | −0.175582 | ||||||||
\(310\) | −728002. | + | 1.26094e6i | −0.430257 | + | 0.745228i | ||||
\(311\) | −1.21898e6 | − | 2.11134e6i | −0.714654 | − | 1.23782i | −0.963093 | − | 0.269169i | \(-0.913251\pi\) |
0.248439 | − | 0.968647i | \(-0.420082\pi\) | |||||||
\(312\) | 144087. | + | 249566.i | 0.0837990 | + | 0.145144i | ||||
\(313\) | 1.21047e6 | − | 2.09659e6i | 0.698381 | − | 1.20963i | −0.270646 | − | 0.962679i | \(-0.587237\pi\) |
0.969028 | − | 0.246953i | \(-0.0794293\pi\) | |||||||
\(314\) | −3.25035e6 | −1.86040 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −492028. | −0.277186 | ||||||||
\(317\) | −938057. | + | 1.62476e6i | −0.524301 | + | 0.908116i | 0.475298 | + | 0.879825i | \(0.342340\pi\) |
−0.999600 | + | 0.0282918i | \(0.990993\pi\) | |||||||
\(318\) | 340553. | + | 589856.i | 0.188850 | + | 0.327098i | ||||
\(319\) | 1.36960e6 | + | 2.37221e6i | 0.753557 | + | 1.30520i | ||||
\(320\) | 38247.3 | − | 66246.2i | 0.0208798 | − | 0.0361648i | ||||
\(321\) | 885855. | 0.479844 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −556936. | −0.297029 | ||||||||
\(324\) | 42938.7 | − | 74371.9i | 0.0227241 | − | 0.0393592i | ||||
\(325\) | −473612. | − | 820321.i | −0.248722 | − | 0.430800i | ||||
\(326\) | −1.77933e6 | − | 3.08190e6i | −0.927285 | − | 1.60611i | ||||
\(327\) | −1.11227e6 | + | 1.92651e6i | −0.575229 | + | 0.996326i | ||||
\(328\) | 688828. | 0.353530 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.00613e6 | 1.01408 | ||||||||
\(331\) | 541549. | − | 937990.i | 0.271686 | − | 0.470575i | −0.697607 | − | 0.716480i | \(-0.745752\pi\) |
0.969294 | + | 0.245906i | \(0.0790853\pi\) | |||||||
\(332\) | −724399. | − | 1.25470e6i | −0.360689 | − | 0.624732i | ||||
\(333\) | 52268.0 | + | 90530.8i | 0.0258301 | + | 0.0447390i | ||||
\(334\) | −2.39628e6 | + | 4.15048e6i | −1.17536 | + | 2.03579i | ||||
\(335\) | 2.13507e6 | 1.03944 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.59465e6 | −1.24453 | −0.622263 | − | 0.782809i | \(-0.713786\pi\) | ||||
−0.622263 | + | 0.782809i | \(0.713786\pi\) | |||||||
\(338\) | 1.01359e6 | − | 1.75560e6i | 0.482583 | − | 0.835859i | ||||
\(339\) | −199969. | − | 346357.i | −0.0945071 | − | 0.163691i | ||||
\(340\) | −268325. | − | 464753.i | −0.125882 | − | 0.218034i | ||||
\(341\) | −453107. | + | 784804.i | −0.211016 | + | 0.365490i | ||||
\(342\) | 1.50652e6 | 0.696484 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −179828. | −0.0819333 | ||||||||
\(345\) | 171324. | − | 296741.i | 0.0774943 | − | 0.134224i | ||||
\(346\) | −882371. | − | 1.52831e6i | −0.396242 | − | 0.686312i | ||||
\(347\) | 935255. | + | 1.61991e6i | 0.416972 | + | 0.722216i | 0.995633 | − | 0.0933518i | \(-0.0297581\pi\) |
−0.578662 | + | 0.815568i | \(0.696425\pi\) | |||||||
\(348\) | 712847. | − | 1.23469e6i | 0.315536 | − | 0.546524i | ||||
\(349\) | 1.61685e6 | 0.710568 | 0.355284 | − | 0.934758i | \(-0.384384\pi\) | ||||
0.355284 | + | 0.934758i | \(0.384384\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.13033e6 | −0.489706 | ||||||||
\(352\) | 1.03762e6 | − | 1.79720e6i | 0.446354 | − | 0.773109i | ||||
\(353\) | −289153. | − | 500827.i | −0.123507 | − | 0.213920i | 0.797642 | − | 0.603132i | \(-0.206081\pi\) |
−0.921148 | + | 0.389212i | \(0.872747\pi\) | |||||||
\(354\) | −1.05957e6 | − | 1.83523e6i | −0.449387 | − | 0.778362i | ||||
\(355\) | 574310. | − | 994734.i | 0.241866 | − | 0.418925i | ||||
\(356\) | −791605. | −0.331042 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 986330. | 0.406738 | ||||||||
\(359\) | 984090. | − | 1.70449e6i | 0.402994 | − | 0.698006i | −0.591092 | − | 0.806604i | \(-0.701303\pi\) |
0.994086 | + | 0.108598i | \(0.0346362\pi\) | |||||||
\(360\) | −552773. | − | 957432.i | −0.224797 | − | 0.389360i | ||||
\(361\) | 105650. | + | 182990.i | 0.0426677 | + | 0.0739027i | ||||
\(362\) | 1.08453e6 | − | 1.87847e6i | 0.434983 | − | 0.753412i | ||||
\(363\) | −375229. | −0.149462 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.59553e6 | 2.19841 | ||||||||
\(366\) | −1.66076e6 | + | 2.87651e6i | −0.648042 | + | 1.12244i | ||||
\(367\) | 1.08726e6 | + | 1.88319e6i | 0.421375 | + | 0.729842i | 0.996074 | − | 0.0885223i | \(-0.0282144\pi\) |
−0.574700 | + | 0.818364i | \(0.694881\pi\) | |||||||
\(368\) | −271457. | − | 470177.i | −0.104491 | − | 0.180985i | ||||
\(369\) | −496791. | + | 860468.i | −0.189936 | + | 0.328979i | ||||
\(370\) | 418180. | 0.158803 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 471666. | 0.176716 | ||||||||
\(373\) | −692379. | + | 1.19924e6i | −0.257675 | + | 0.446306i | −0.965619 | − | 0.259963i | \(-0.916290\pi\) |
0.707944 | + | 0.706269i | \(0.249623\pi\) | |||||||
\(374\) | −461197. | − | 798817.i | −0.170493 | − | 0.295303i | ||||
\(375\) | −49278.9 | − | 85353.5i | −0.0180960 | − | 0.0313432i | ||||
\(376\) | 75091.0 | − | 130061.i | 0.0273916 | − | 0.0474437i | ||||
\(377\) | −2.27044e6 | −0.822728 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.37190e6 | 1.20580 | 0.602902 | − | 0.797815i | \(-0.294011\pi\) | ||||
0.602902 | + | 0.797815i | \(0.294011\pi\) | |||||||
\(380\) | 1.09115e6 | − | 1.88993e6i | 0.387639 | − | 0.671410i | ||||
\(381\) | −260842. | − | 451792.i | −0.0920589 | − | 0.159451i | ||||
\(382\) | −805642. | − | 1.39541e6i | −0.282478 | − | 0.489265i | ||||
\(383\) | 1.64030e6 | − | 2.84108e6i | 0.571382 | − | 0.989662i | −0.425043 | − | 0.905173i | \(-0.639741\pi\) |
0.996424 | − | 0.0844886i | \(-0.0269257\pi\) | |||||||
\(384\) | 1.83428e6 | 0.634800 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.76227e6 | −1.62684 | ||||||||
\(387\) | 129694. | − | 224637.i | 0.0440192 | − | 0.0762435i | ||||
\(388\) | 938919. | + | 1.62626e6i | 0.316628 | + | 0.548415i | ||||
\(389\) | 1.47405e6 | + | 2.55313e6i | 0.493899 | + | 0.855457i | 0.999975 | − | 0.00703108i | \(-0.00223808\pi\) |
−0.506077 | + | 0.862488i | \(0.668905\pi\) | |||||||
\(390\) | −831412. | + | 1.44005e6i | −0.276793 | + | 0.479419i | ||||
\(391\) | −157545. | −0.0521150 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.68053e6 | 0.548865 | ||||||||
\(394\) | 4542.73 | − | 7868.24i | 0.00147427 | − | 0.00255351i | ||||
\(395\) | 1.08110e6 | + | 1.87251e6i | 0.348636 | + | 0.603855i | ||||
\(396\) | 451752. | + | 782458.i | 0.144765 | + | 0.250740i | ||||
\(397\) | −34635.1 | + | 59989.7i | −0.0110291 | + | 0.0191030i | −0.871487 | − | 0.490418i | \(-0.836844\pi\) |
0.860458 | + | 0.509521i | \(0.170177\pi\) | |||||||
\(398\) | −2.61282e6 | −0.826802 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.14151e6 | −1.29422 | ||||||||
\(401\) | 1.67393e6 | − | 2.89933e6i | 0.519848 | − | 0.900404i | −0.479886 | − | 0.877331i | \(-0.659322\pi\) |
0.999734 | − | 0.0230725i | \(-0.00734485\pi\) | |||||||
\(402\) | −955019. | − | 1.65414e6i | −0.294745 | − | 0.510514i | ||||
\(403\) | −375567. | − | 650501.i | −0.115193 | − | 0.199520i | ||||
\(404\) | 260677. | − | 451506.i | 0.0794602 | − | 0.137629i | ||||
\(405\) | −377384. | −0.114326 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 260274. | 0.0778834 | ||||||||
\(408\) | 182812. | − | 316640.i | 0.0543694 | − | 0.0941706i | ||||
\(409\) | 1.45608e6 | + | 2.52201e6i | 0.430406 | + | 0.745485i | 0.996908 | − | 0.0785754i | \(-0.0250371\pi\) |
−0.566502 | + | 0.824060i | \(0.691704\pi\) | |||||||
\(410\) | 1.98734e6 | + | 3.44217e6i | 0.583864 | + | 1.01128i | ||||
\(411\) | −142466. | + | 246759.i | −0.0416014 | + | 0.0720557i | ||||
\(412\) | −530940. | −0.154100 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 426163. | 0.122201 | ||||||||
\(415\) | −3.18334e6 | + | 5.51371e6i | −0.907326 | + | 1.57153i | ||||
\(416\) | 860050. | + | 1.48965e6i | 0.243663 | + | 0.422037i | ||||
\(417\) | 1.69589e6 | + | 2.93736e6i | 0.477592 | + | 0.827213i | ||||
\(418\) | 1.87547e6 | − | 3.24842e6i | 0.525014 | − | 0.909350i | ||||
\(419\) | 4.62361e6 | 1.28661 | 0.643304 | − | 0.765611i | \(-0.277563\pi\) | ||||
0.643304 | + | 0.765611i | \(0.277563\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.63042e6 | −0.723303 | −0.361652 | − | 0.932313i | \(-0.617787\pi\) | ||||
−0.361652 | + | 0.932313i | \(0.617787\pi\) | |||||||
\(422\) | −1.77837e6 | + | 3.08023e6i | −0.486117 | + | 0.841979i | ||||
\(423\) | 108313. | + | 187604.i | 0.0294327 | + | 0.0509789i | ||||
\(424\) | −467270. | − | 809336.i | −0.126227 | − | 0.218632i | ||||
\(425\) | −600901. | + | 1.04079e6i | −0.161373 | + | 0.279506i | ||||
\(426\) | −1.02756e6 | −0.274335 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.59599e6 | 0.421135 | ||||||||
\(429\) | −517468. | + | 896281.i | −0.135750 | + | 0.235126i | ||||
\(430\) | −518820. | − | 898623.i | −0.135315 | − | 0.234372i | ||||
\(431\) | −3.77064e6 | − | 6.53094e6i | −0.977736 | − | 1.69349i | −0.670592 | − | 0.741826i | \(-0.733960\pi\) |
−0.307144 | − | 0.951663i | \(-0.599373\pi\) | |||||||
\(432\) | −2.47103e6 | + | 4.27996e6i | −0.637044 | + | 1.10339i | ||||
\(433\) | −5.83558e6 | −1.49577 | −0.747883 | − | 0.663830i | \(-0.768930\pi\) | ||||
−0.747883 | + | 0.663830i | \(0.768930\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.26516e6 | −1.58748 | ||||||||
\(436\) | −2.00391e6 | + | 3.47088e6i | −0.504850 | + | 0.874426i | ||||
\(437\) | −320331. | − | 554830.i | −0.0802409 | − | 0.138981i | ||||
\(438\) | −2.50288e6 | − | 4.33512e6i | −0.623383 | − | 1.07973i | ||||
\(439\) | 84051.9 | − | 145582.i | 0.0208155 | − | 0.0360535i | −0.855430 | − | 0.517918i | \(-0.826707\pi\) |
0.876246 | + | 0.481865i | \(0.160040\pi\) | |||||||
\(440\) | −2.75259e6 | −0.677814 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 764546. | 0.186143 | ||||||||
\(443\) | 1.42076e6 | − | 2.46082e6i | 0.343962 | − | 0.595760i | −0.641203 | − | 0.767372i | \(-0.721564\pi\) |
0.985165 | + | 0.171612i | \(0.0548975\pi\) | |||||||
\(444\) | −67733.7 | − | 117318.i | −0.0163060 | − | 0.0282428i | ||||
\(445\) | 1.73934e6 | + | 3.01262e6i | 0.416374 | + | 0.721181i | ||||
\(446\) | −4.15503e6 | + | 7.19672e6i | −0.989092 | + | 1.71316i | ||||
\(447\) | −3.58323e6 | −0.848214 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41567e6 | −0.331396 | −0.165698 | − | 0.986177i | \(-0.552988\pi\) | ||||
−0.165698 | + | 0.986177i | \(0.552988\pi\) | |||||||
\(450\) | 1.62545e6 | − | 2.81536e6i | 0.378392 | − | 0.655395i | ||||
\(451\) | 1.23691e6 | + | 2.14240e6i | 0.286350 | + | 0.495973i | ||||
\(452\) | −360273. | − | 624012.i | −0.0829442 | − | 0.143664i | ||||
\(453\) | 1.80883e6 | − | 3.13299e6i | 0.414146 | − | 0.717321i | ||||
\(454\) | 6.44644e6 | 1.46784 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.48682e6 | 0.334848 | ||||||||
\(457\) | −778637. | + | 1.34864e6i | −0.174399 | + | 0.302068i | −0.939953 | − | 0.341303i | \(-0.889132\pi\) |
0.765554 | + | 0.643372i | \(0.222465\pi\) | |||||||
\(458\) | 1.84833e6 | + | 3.20141e6i | 0.411734 | + | 0.713144i | ||||
\(459\) | 717056. | + | 1.24198e6i | 0.158862 | + | 0.275158i | ||||
\(460\) | 308664. | − | 534621.i | 0.0680129 | − | 0.117802i | ||||
\(461\) | 4.45345e6 | 0.975987 | 0.487994 | − | 0.872847i | \(-0.337729\pi\) | ||||
0.487994 | + | 0.872847i | \(0.337729\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.92263e6 | 1.06720 | 0.533599 | − | 0.845738i | \(-0.320839\pi\) | ||||
0.533599 | + | 0.845738i | \(0.320839\pi\) | |||||||
\(464\) | −4.96347e6 | + | 8.59698e6i | −1.07026 | + | 1.85375i | ||||
\(465\) | −1.03636e6 | − | 1.79502e6i | −0.222268 | − | 0.384980i | ||||
\(466\) | 3.69291e6 | + | 6.39631e6i | 0.787778 | + | 1.36447i | ||||
\(467\) | 2.54545e6 | − | 4.40885e6i | 0.540098 | − | 0.935477i | −0.458800 | − | 0.888540i | \(-0.651720\pi\) |
0.998898 | − | 0.0469376i | \(-0.0149462\pi\) | |||||||
\(468\) | −748889. | −0.158053 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 866579. | 0.180952 | ||||||||
\(471\) | 2.31354e6 | − | 4.00717e6i | 0.480535 | − | 0.832312i | ||||
\(472\) | 1.45383e6 | + | 2.51810e6i | 0.300370 | + | 0.520257i | ||||
\(473\) | −322912. | − | 559301.i | −0.0663639 | − | 0.114946i | ||||
\(474\) | 967150. | − | 1.67515e6i | 0.197719 | − | 0.342459i | ||||
\(475\) | −4.88717e6 | −0.993856 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.34800e6 | 0.271266 | ||||||||
\(478\) | 5.43416e6 | − | 9.41224e6i | 1.08783 | − | 1.88418i | ||||
\(479\) | −4.15042e6 | − | 7.18874e6i | −0.826521 | − | 1.43158i | −0.900752 | − | 0.434334i | \(-0.856984\pi\) |
0.0742312 | − | 0.997241i | \(-0.476350\pi\) | |||||||
\(480\) | 2.37326e6 | + | 4.11061e6i | 0.470157 | + | 0.814335i | ||||
\(481\) | −107867. | + | 186831.i | −0.0212581 | + | 0.0368202i | ||||
\(482\) | 7.13644e6 | 1.39915 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −676028. | −0.131175 | ||||||||
\(485\) | 4.12604e6 | − | 7.14651e6i | 0.796488 | − | 1.37956i | ||||
\(486\) | −3.16601e6 | − | 5.48369e6i | −0.608025 | − | 1.05313i | ||||
\(487\) | −4.31701e6 | − | 7.47727e6i | −0.824822 | − | 1.42863i | −0.902055 | − | 0.431621i | \(-0.857942\pi\) |
0.0772330 | − | 0.997013i | \(-0.475391\pi\) | |||||||
\(488\) | 2.27871e6 | − | 3.94684e6i | 0.433151 | − | 0.750240i | ||||
\(489\) | 5.06599e6 | 0.958059 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 95039.5 | 0.0177910 | 0.00889550 | − | 0.999960i | \(-0.497168\pi\) | ||||
0.00889550 | + | 0.999960i | \(0.497168\pi\) | |||||||
\(492\) | 643788. | − | 1.11507e6i | 0.119903 | − | 0.207678i | ||||
\(493\) | 1.44032e6 | + | 2.49471e6i | 0.266896 | + | 0.462277i | ||||
\(494\) | 1.55453e6 | + | 2.69252e6i | 0.286603 | + | 0.496411i | ||||
\(495\) | 1.98521e6 | − | 3.43848e6i | 0.364160 | − | 0.630744i | ||||
\(496\) | −3.28415e6 | −0.599402 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 5.69564e6 | 1.02913 | ||||||||
\(499\) | −1.07102e6 | + | 1.85506e6i | −0.192551 | + | 0.333507i | −0.946095 | − | 0.323890i | \(-0.895009\pi\) |
0.753544 | + | 0.657397i | \(0.228343\pi\) | |||||||
\(500\) | −88782.9 | − | 153776.i | −0.0158820 | − | 0.0275084i | ||||
\(501\) | −3.41126e6 | − | 5.90848e6i | −0.607185 | − | 1.05167i | ||||
\(502\) | 30143.8 | − | 52210.7i | 0.00533875 | − | 0.00924698i | ||||
\(503\) | −5.24794e6 | −0.924844 | −0.462422 | − | 0.886660i | \(-0.653019\pi\) | ||||
−0.462422 | + | 0.886660i | \(0.653019\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.29107e6 | −0.399769 | ||||||||
\(506\) | 530531. | − | 918907.i | 0.0921159 | − | 0.159549i | ||||
\(507\) | 1.44292e6 | + | 2.49920e6i | 0.249299 | + | 0.431799i | ||||
\(508\) | −469945. | − | 813968.i | −0.0807956 | − | 0.139942i | ||||
\(509\) | −5.29453e6 | + | 9.17040e6i | −0.905802 | + | 1.56889i | −0.0859643 | + | 0.996298i | \(0.527397\pi\) |
−0.819837 | + | 0.572596i | \(0.805936\pi\) | |||||||
\(510\) | 2.10972e6 | 0.359170 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.52190e6 | 0.593747 | ||||||||
\(513\) | −2.91593e6 | + | 5.05055e6i | −0.489198 | + | 0.847315i | ||||
\(514\) | −1.86819e6 | − | 3.23580e6i | −0.311899 | − | 0.540225i | ||||
\(515\) | 1.16660e6 | + | 2.02061e6i | 0.193822 | + | 0.335709i | ||||
\(516\) | −168069. | + | 291105.i | −0.0277885 | + | 0.0481310i | ||||
\(517\) | 539357. | 0.0887462 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.51222e6 | 0.409392 | ||||||||
\(520\) | 1.14077e6 | − | 1.97588e6i | 0.185008 | − | 0.320443i | ||||
\(521\) | −2.27232e6 | − | 3.93578e6i | −0.366755 | − | 0.635238i | 0.622301 | − | 0.782778i | \(-0.286198\pi\) |
−0.989056 | + | 0.147540i | \(0.952865\pi\) | |||||||
\(522\) | −3.89610e6 | − | 6.74825e6i | −0.625827 | − | 1.08396i | ||||
\(523\) | −2.63599e6 | + | 4.56566e6i | −0.421394 | + | 0.729877i | −0.996076 | − | 0.0885004i | \(-0.971793\pi\) |
0.574682 | + | 0.818377i | \(0.305126\pi\) | |||||||
\(524\) | 3.02772e6 | 0.481711 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.49373e6 | −0.392993 | ||||||||
\(527\) | −476504. | + | 825330.i | −0.0747378 | + | 0.129450i | ||||
\(528\) | 2.26250e6 | + | 3.91877e6i | 0.353187 | + | 0.611737i | ||||
\(529\) | 3.12756e6 | + | 5.41709e6i | 0.485921 | + | 0.841641i | ||||
\(530\) | 2.69624e6 | − | 4.67003e6i | 0.416936 | − | 0.722154i | ||||
\(531\) | −4.19407e6 | −0.645504 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.05048e6 | −0.312635 | ||||||||
\(534\) | 1.55601e6 | − | 2.69509e6i | 0.236135 | − | 0.408997i | ||||
\(535\) | −3.50676e6 | − | 6.07389e6i | −0.529690 | − | 0.917451i | ||||
\(536\) | 1.31037e6 | + | 2.26963e6i | 0.197008 | + | 0.341227i | ||||
\(537\) | −702052. | + | 1.21599e6i | −0.105059 | + | 0.181968i | ||||
\(538\) | −3.39647e6 | −0.505908 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −5.61945e6 | −0.829296 | ||||||||
\(541\) | −2.96723e6 | + | 5.13939e6i | −0.435871 | + | 0.754950i | −0.997366 | − | 0.0725298i | \(-0.976893\pi\) |
0.561496 | + | 0.827480i | \(0.310226\pi\) | |||||||
\(542\) | −3.46209e6 | − | 5.99652e6i | −0.506221 | − | 0.876801i | ||||
\(543\) | 1.54390e6 | + | 2.67412e6i | 0.224709 | + | 0.389208i | ||||
\(544\) | 1.09120e6 | − | 1.89001e6i | 0.158091 | − | 0.273821i | ||||
\(545\) | 1.76122e7 | 2.53994 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.82017e6 | −1.26040 | −0.630200 | − | 0.776433i | \(-0.717027\pi\) | ||||
−0.630200 | + | 0.776433i | \(0.717027\pi\) | |||||||
\(548\) | −256673. | + | 444571.i | −0.0365115 | + | 0.0632397i | ||||
\(549\) | 3.28687e6 | + | 5.69302e6i | 0.465427 | + | 0.806143i | ||||
\(550\) | −4.04705e6 | − | 7.00970e6i | −0.570469 | − | 0.988081i | ||||
\(551\) | −5.85712e6 | + | 1.01448e7i | −0.821874 | + | 1.42353i | ||||
\(552\) | 420590. | 0.0587505 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.86124e6 | 0.949791 | ||||||||
\(555\) | −297653. | + | 515550.i | −0.0410183 | + | 0.0710458i | ||||
\(556\) | 3.05538e6 | + | 5.29207e6i | 0.419158 | + | 0.726004i | ||||
\(557\) | 591120. | + | 1.02385e6i | 0.0807304 | + | 0.139829i | 0.903564 | − | 0.428453i | \(-0.140941\pi\) |
−0.822833 | + | 0.568283i | \(0.807608\pi\) | |||||||
\(558\) | 1.28896e6 | − | 2.23254e6i | 0.175248 | − | 0.303538i | ||||
\(559\) | 535306. | 0.0724556 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.31309e6 | 0.176151 | ||||||||
\(562\) | 1.12734e6 | − | 1.95261e6i | 0.150561 | − | 0.260780i | ||||
\(563\) | 2.03870e6 | + | 3.53114e6i | 0.271071 | + | 0.469509i | 0.969136 | − | 0.246525i | \(-0.0792888\pi\) |
−0.698065 | + | 0.716034i | \(0.745955\pi\) | |||||||
\(564\) | −140362. | − | 243114.i | −0.0185803 | − | 0.0321820i | ||||
\(565\) | −1.58321e6 | + | 2.74219e6i | −0.208649 | + | 0.361391i | ||||
\(566\) | −1.25514e7 | −1.64684 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.40990e6 | 0.183366 | ||||||||
\(569\) | −4.08807e6 | + | 7.08075e6i | −0.529344 | + | 0.916851i | 0.470070 | + | 0.882629i | \(0.344229\pi\) |
−0.999414 | + | 0.0342216i | \(0.989105\pi\) | |||||||
\(570\) | 4.28964e6 | + | 7.42987e6i | 0.553010 | + | 0.957842i | ||||
\(571\) | −1.65307e6 | − | 2.86321e6i | −0.212179 | − | 0.367504i | 0.740217 | − | 0.672368i | \(-0.234723\pi\) |
−0.952396 | + | 0.304863i | \(0.901389\pi\) | |||||||
\(572\) | −932292. | + | 1.61478e6i | −0.119141 | + | 0.206359i | ||||
\(573\) | 2.29377e6 | 0.291852 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.38247e6 | −0.174376 | ||||||||
\(576\) | −67718.3 | + | 117291.i | −0.00850452 | + | 0.0147303i | ||||
\(577\) | −3.57497e6 | − | 6.19203e6i | −0.447026 | − | 0.774272i | 0.551165 | − | 0.834396i | \(-0.314184\pi\) |
−0.998191 | + | 0.0601245i | \(0.980850\pi\) | |||||||
\(578\) | 4.54324e6 | + | 7.86913e6i | 0.565648 | + | 0.979731i | ||||
\(579\) | 3.38970e6 | − | 5.87112e6i | 0.420208 | − | 0.727821i | ||||
\(580\) | −1.12876e7 | −1.39325 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −7.38232e6 | −0.903411 | ||||||||
\(583\) | 1.67813e6 | − | 2.90661e6i | 0.204482 | − | 0.354173i | ||||
\(584\) | 3.43418e6 | + | 5.94818e6i | 0.416669 | + | 0.721692i | ||||
\(585\) | 1.64548e6 | + | 2.85005e6i | 0.198794 | + | 0.344321i | ||||
\(586\) | 5.81309e6 | − | 1.00686e7i | 0.699300 | − | 1.21122i | ||||
\(587\) | −9.69191e6 | −1.16095 | −0.580476 | − | 0.814277i | \(-0.697133\pi\) | ||||
−0.580476 | + | 0.814277i | \(0.697133\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.87545e6 | −0.460292 | ||||||||
\(590\) | −8.38886e6 | + | 1.45299e7i | −0.992139 | + | 1.71844i | ||||
\(591\) | 6466.87 | + | 11200.9i | 0.000761597 | + | 0.00131912i | ||||
\(592\) | 471621. | + | 816872.i | 0.0553081 | + | 0.0957965i | ||||
\(593\) | 3.31980e6 | − | 5.75006e6i | 0.387682 | − | 0.671484i | −0.604456 | − | 0.796639i | \(-0.706609\pi\) |
0.992137 | + | 0.125154i | \(0.0399426\pi\) | |||||||
\(594\) | −9.65871e6 | −1.12319 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −6.45569e6 | −0.744435 | ||||||||
\(597\) | 1.85976e6 | − | 3.22119e6i | 0.213560 | − | 0.369897i | ||||
\(598\) | 439742. | + | 761655.i | 0.0502857 | + | 0.0870974i | ||||
\(599\) | 1.62096e6 | + | 2.80758e6i | 0.184588 | + | 0.319716i | 0.943438 | − | 0.331550i | \(-0.107572\pi\) |
−0.758849 | + | 0.651266i | \(0.774238\pi\) | |||||||
\(600\) | 1.60420e6 | − | 2.77855e6i | 0.181919 | − | 0.315094i | ||||
\(601\) | 5.65076e6 | 0.638147 | 0.319074 | − | 0.947730i | \(-0.396628\pi\) | ||||
0.319074 | + | 0.947730i | \(0.396628\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.78023e6 | −0.423375 | ||||||||
\(604\) | 3.25887e6 | − | 5.64453e6i | 0.363475 | − | 0.629557i | ||||
\(605\) | 1.48539e6 | + | 2.57277e6i | 0.164988 | + | 0.285767i | ||||
\(606\) | 1.02480e6 | + | 1.77500e6i | 0.113359 | + | 0.196343i | ||||
\(607\) | 117837. | − | 204100.i | 0.0129811 | − | 0.0224839i | −0.859462 | − | 0.511200i | \(-0.829201\pi\) |
0.872443 | + | 0.488716i | \(0.162535\pi\) | |||||||
\(608\) | 8.87478e6 | 0.973641 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.62972e7 | 2.86144 | ||||||||
\(611\) | −223529. | + | 387163.i | −0.0242231 | + | 0.0419557i | ||||
\(612\) | 475080. | + | 822863.i | 0.0512729 | + | 0.0888073i | ||||
\(613\) | −394438. | − | 683187.i | −0.0423963 | − | 0.0734325i | 0.844049 | − | 0.536267i | \(-0.180166\pi\) |
−0.886445 | + | 0.462834i | \(0.846833\pi\) | |||||||
\(614\) | −1.65358e6 | + | 2.86408e6i | −0.177012 | + | 0.306595i | ||||
\(615\) | −5.65820e6 | −0.603240 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.67739e7 | 1.77387 | 0.886935 | − | 0.461894i | \(-0.152830\pi\) | ||||
0.886935 | + | 0.461894i | \(0.152830\pi\) | |||||||
\(618\) | 1.04364e6 | − | 1.80763e6i | 0.109921 | − | 0.190388i | ||||
\(619\) | 4.11150e6 | + | 7.12132e6i | 0.431294 | + | 0.747023i | 0.996985 | − | 0.0775941i | \(-0.0247238\pi\) |
−0.565691 | + | 0.824617i | \(0.691390\pi\) | |||||||
\(620\) | −1.86714e6 | − | 3.23399e6i | −0.195074 | − | 0.337878i | ||||
\(621\) | −824854. | + | 1.42869e6i | −0.0858318 | + | 0.148665i | ||||
\(622\) | 1.72675e7 | 1.78959 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.75065e6 | −0.385607 | ||||||||
\(625\) | 4.68399e6 | − | 8.11290e6i | 0.479640 | − | 0.830761i | ||||
\(626\) | 8.57346e6 | + | 1.48497e7i | 0.874420 | + | 1.51454i | ||||
\(627\) | 2.66986e6 | + | 4.62433e6i | 0.271218 | + | 0.469764i | ||||
\(628\) | 4.16818e6 | − | 7.21949e6i | 0.421742 | − | 0.730479i | ||||
\(629\) | 273714. | 0.0275849 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.94507e6 | −0.594406 | −0.297203 | − | 0.954814i | \(-0.596054\pi\) | ||||
−0.297203 | + | 0.954814i | \(0.596054\pi\) | |||||||
\(632\) | −1.32702e6 | + | 2.29846e6i | −0.132155 | + | 0.228899i | ||||
\(633\) | −2.53162e6 | − | 4.38490e6i | −0.251125 | − | 0.434961i | ||||
\(634\) | −6.64403e6 | − | 1.15078e7i | −0.656460 | − | 1.13702i | ||||
\(635\) | −2.06515e6 | + | 3.57695e6i | −0.203244 | + | 0.352029i | ||||
\(636\) | −1.74687e6 | −0.171245 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.94011e7 | −1.88701 | ||||||||
\(639\) | −1.01684e6 | + | 1.76122e6i | −0.0985144 | + | 0.170632i | ||||
\(640\) | −7.26120e6 | − | 1.25768e7i | −0.700743 | − | 1.21372i | ||||
\(641\) | 5.33804e6 | + | 9.24576e6i | 0.513141 | + | 0.888786i | 0.999884 | + | 0.0152411i | \(0.00485157\pi\) |
−0.486743 | + | 0.873545i | \(0.661815\pi\) | |||||||
\(642\) | −3.13715e6 | + | 5.43371e6i | −0.300399 | + | 0.520306i | ||||
\(643\) | 3.13159e6 | 0.298701 | 0.149351 | − | 0.988784i | \(-0.452282\pi\) | ||||
0.149351 | + | 0.988784i | \(0.452282\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.47715e6 | 0.139806 | ||||||||
\(646\) | 1.97232e6 | − | 3.41616e6i | 0.185950 | − | 0.322075i | ||||
\(647\) | −2.46728e6 | − | 4.27346e6i | −0.231717 | − | 0.401346i | 0.726596 | − | 0.687065i | \(-0.241101\pi\) |
−0.958314 | + | 0.285719i | \(0.907768\pi\) | |||||||
\(648\) | −231615. | − | 401168.i | −0.0216685 | − | 0.0375309i | ||||
\(649\) | −5.22120e6 | + | 9.04339e6i | −0.486585 | + | 0.842790i | ||||
\(650\) | 6.70897e6 | 0.622834 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 9.12710e6 | 0.840841 | ||||||||
\(653\) | −2.86112e6 | + | 4.95561e6i | −0.262575 | + | 0.454793i | −0.966925 | − | 0.255059i | \(-0.917905\pi\) |
0.704351 | + | 0.709852i | \(0.251238\pi\) | |||||||
\(654\) | −7.87794e6 | − | 1.36450e7i | −0.720226 | − | 1.24747i | ||||
\(655\) | −6.65258e6 | − | 1.15226e7i | −0.605881 | − | 1.04942i | ||||
\(656\) | −4.48261e6 | + | 7.76411e6i | −0.406698 | + | 0.704421i | ||||
\(657\) | −9.90710e6 | −0.895433 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 362477. | 0.0325137 | 0.0162569 | − | 0.999868i | \(-0.494825\pi\) | ||||
0.0162569 | + | 0.999868i | \(0.494825\pi\) | |||||||
\(660\) | −2.57261e6 | + | 4.45590e6i | −0.229887 | + | 0.398176i | ||||
\(661\) | −9.56053e6 | − | 1.65593e7i | −0.851096 | − | 1.47414i | −0.880220 | − | 0.474565i | \(-0.842605\pi\) |
0.0291249 | − | 0.999576i | \(-0.490728\pi\) | |||||||
\(662\) | 3.83566e6 | + | 6.64356e6i | 0.340170 | + | 0.589191i | ||||
\(663\) | −544190. | + | 942564.i | −0.0480802 | + | 0.0832774i | ||||
\(664\) | −7.81494e6 | −0.687868 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −740404. | −0.0646819 | ||||||||
\(667\) | −1.65685e6 | + | 2.86975e6i | −0.144201 | + | 0.249764i | ||||
\(668\) | −6.14587e6 | − | 1.06450e7i | −0.532896 | − | 0.923003i | ||||
\(669\) | −5.91495e6 | − | 1.02450e7i | −0.510958 | − | 0.885006i | ||||
\(670\) | −7.56111e6 | + | 1.30962e7i | −0.650727 | + | 1.12709i | ||||
\(671\) | 1.63673e7 | 1.40337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −573374. | −0.0487978 | −0.0243989 | − | 0.999702i | \(-0.507767\pi\) | ||||
−0.0243989 | + | 0.999702i | \(0.507767\pi\) | |||||||
\(674\) | 9.18864e6 | − | 1.59152e7i | 0.779115 | − | 1.34947i | ||||
\(675\) | 6.29224e6 | + | 1.08985e7i | 0.531552 | + | 0.920675i | ||||
\(676\) | 2.59962e6 | + | 4.50267e6i | 0.218798 | + | 0.378968i | ||||
\(677\) | 5.84516e6 | − | 1.01241e7i | 0.490146 | − | 0.848957i | −0.509790 | − | 0.860299i | \(-0.670277\pi\) |
0.999936 | + | 0.0113419i | \(0.00361030\pi\) | |||||||
\(678\) | 2.83267e6 | 0.236659 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.89473e6 | −0.240069 | ||||||||
\(681\) | −4.58846e6 | + | 7.94744e6i | −0.379139 | + | 0.656689i | ||||
\(682\) | −3.20925e6 | − | 5.55858e6i | −0.264206 | − | 0.457618i | ||||
\(683\) | −9.18370e6 | − | 1.59066e7i | −0.753297 | − | 1.30475i | −0.946217 | − | 0.323534i | \(-0.895129\pi\) |
0.192920 | − | 0.981214i | \(-0.438204\pi\) | |||||||
\(684\) | −1.93193e6 | + | 3.34620e6i | −0.157889 | + | 0.273471i | ||||
\(685\) | 2.25588e6 | 0.183692 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.26244e6 | −0.425398 | ||||||||
\(688\) | 1.17025e6 | − | 2.02693e6i | 0.0942554 | − | 0.163255i | ||||
\(689\) | 1.39096e6 | + | 2.40921e6i | 0.111626 | + | 0.193342i | ||||
\(690\) | 1.21344e6 | + | 2.10175e6i | 0.0970280 | + | 0.168057i | ||||
\(691\) | 1.17806e7 | − | 2.04045e7i | 0.938579 | − | 1.62567i | 0.170454 | − | 0.985366i | \(-0.445477\pi\) |
0.768125 | − | 0.640300i | \(-0.221190\pi\) | |||||||
\(692\) | 4.52612e6 | 0.359303 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.32484e7 | −1.04415 | ||||||||
\(695\) | 1.34267e7 | − | 2.32558e7i | 1.05441 | − | 1.82629i | ||||
\(696\) | −3.84516e6 | − | 6.66001e6i | −0.300878 | − | 0.521137i | ||||
\(697\) | 1.30078e6 | + | 2.25303e6i | 0.101420 | + | 0.175665i | ||||
\(698\) | −5.72587e6 | + | 9.91750e6i | −0.444839 | + | 0.770484i | ||||
\(699\) | −1.05142e7 | −0.813921 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.32980e7 | 1.02210 | 0.511048 | − | 0.859552i | \(-0.329257\pi\) | ||||
0.511048 | + | 0.859552i | \(0.329257\pi\) | |||||||
\(702\) | 4.00291e6 | − | 6.93325e6i | 0.306573 | − | 0.530999i | ||||
\(703\) | 556535. | + | 963946.i | 0.0424721 | + | 0.0735639i | ||||
\(704\) | 168605. | + | 292033.i | 0.0128215 | + | 0.0222075i | ||||
\(705\) | −616815. | + | 1.06836e6i | −0.0467393 | + | 0.0809549i | ||||
\(706\) | 4.09600e6 | 0.309277 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 5.43506e6 | 0.407494 | ||||||||
\(709\) | 3.42677e6 | − | 5.93533e6i | 0.256017 | − | 0.443434i | −0.709154 | − | 0.705053i | \(-0.750923\pi\) |
0.965171 | + | 0.261619i | \(0.0842564\pi\) | |||||||
\(710\) | 4.06770e6 | + | 7.04547e6i | 0.302833 | + | 0.524522i | ||||
\(711\) | −1.91412e6 | − | 3.31536e6i | −0.142003 | − | 0.245956i | ||||
\(712\) | −2.13499e6 | + | 3.69791e6i | −0.157832 | + | 0.273374i | ||||
\(713\) | −1.09628e6 | −0.0807602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.19384e6 | 0.599408 | ||||||||
\(716\) | −1.26485e6 | + | 2.19078e6i | −0.0922051 | + | 0.159704i | ||||
\(717\) | 7.73587e6 | + | 1.33989e7i | 0.561968 | + | 0.973357i | ||||
\(718\) | 6.97008e6 | + | 1.20725e7i | 0.504576 | + | 0.873951i | ||||
\(719\) | 1.32865e7 | − | 2.30128e7i | 0.958490 | − | 1.66015i | 0.232318 | − | 0.972640i | \(-0.425369\pi\) |
0.726172 | − | 0.687513i | \(-0.241298\pi\) | |||||||
\(720\) | 1.43889e7 | 1.03442 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −1.49658e6 | −0.106846 | ||||||||
\(723\) | −5.07958e6 | + | 8.79810e6i | −0.361395 | + | 0.625955i | ||||
\(724\) | 2.78156e6 | + | 4.81781e6i | 0.197216 | + | 0.341588i | ||||
\(725\) | 1.26390e7 | + | 2.18913e7i | 0.893031 | + | 1.54678i | ||||
\(726\) | 1.32883e6 | − | 2.30160e6i | 0.0935680 | − | 0.162065i | ||||
\(727\) | −2.16991e6 | −0.152267 | −0.0761335 | − | 0.997098i | \(-0.524258\pi\) | ||||
−0.0761335 | + | 0.997098i | \(0.524258\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.01628e7 | 0.708264 | ||||||||
\(730\) | −1.98159e7 | + | 3.43221e7i | −1.37628 | + | 2.38379i | ||||
\(731\) | −339587. | − | 588182.i | −0.0235049 | − | 0.0407116i | ||||
\(732\) | −4.25943e6 | − | 7.37755e6i | −0.293815 | − | 0.508902i | ||||
\(733\) | −8.73265e6 | + | 1.51254e7i | −0.600324 | + | 1.03979i | 0.392447 | + | 0.919774i | \(0.371628\pi\) |
−0.992772 | + | 0.120018i | \(0.961705\pi\) | |||||||
\(734\) | −1.54016e7 | −1.05518 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.51048e6 | 0.170829 | ||||||||
\(737\) | −4.70602e6 | + | 8.15106e6i | −0.319143 | + | 0.552771i | ||||
\(738\) | −3.51865e6 | − | 6.09449e6i | −0.237813 | − | 0.411904i | ||||
\(739\) | 6.82304e6 | + | 1.18178e7i | 0.459586 | + | 0.796026i | 0.998939 | − | 0.0460536i | \(-0.0146645\pi\) |
−0.539353 | + | 0.842080i | \(0.681331\pi\) | |||||||
\(740\) | −536264. | + | 928836.i | −0.0359997 | + | 0.0623533i | ||||
\(741\) | −4.42594e6 | −0.296114 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.48965e7 | 0.989944 | 0.494972 | − | 0.868909i | \(-0.335178\pi\) | ||||
0.494972 | + | 0.868909i | \(0.335178\pi\) | |||||||
\(744\) | 1.27210e6 | − | 2.20334e6i | 0.0842538 | − | 0.145932i | ||||
\(745\) | 1.41846e7 | + | 2.45685e7i | 0.936326 | + | 1.62176i | ||||
\(746\) | −4.90396e6 | − | 8.49390e6i | −0.322626 | − | 0.558805i | ||||
\(747\) | 5.63623e6 | − | 9.76224e6i | 0.369562 | − | 0.640100i | ||||
\(748\) | 2.36571e6 | 0.154599 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 698061. | 0.0453148 | ||||||||
\(751\) | 1.26731e7 | − | 2.19505e7i | 0.819944 | − | 1.42019i | −0.0857783 | − | 0.996314i | \(-0.527338\pi\) |
0.905723 | − | 0.423871i | \(-0.139329\pi\) | |||||||
\(752\) | 977324. | + | 1.69277e6i | 0.0630222 | + | 0.109158i | ||||
\(753\) | 42911.7 | + | 74325.2i | 0.00275796 | + | 0.00477693i | ||||
\(754\) | 8.04049e6 | − | 1.39265e7i | 0.515056 | − | 0.892102i | ||||
\(755\) | −2.86419e7 | −1.82867 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.66725e7 | −1.69170 | −0.845852 | − | 0.533417i | \(-0.820908\pi\) | ||||
−0.845852 | + | 0.533417i | \(0.820908\pi\) | |||||||
\(758\) | −1.19412e7 | + | 2.06828e7i | −0.754875 | + | 1.30748i | ||||
\(759\) | 755245. | + | 1.30812e6i | 0.0475864 | + | 0.0824221i | ||||
\(760\) | −5.88577e6 | − | 1.01945e7i | −0.369632 | − | 0.640221i | ||||
\(761\) | 289914. | − | 502146.i | 0.0181471 | − | 0.0314318i | −0.856809 | − | 0.515634i | \(-0.827557\pi\) |
0.874956 | + | 0.484202i | \(0.160890\pi\) | |||||||
\(762\) | 3.69497e6 | 0.230528 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.13255e6 | 0.256144 | ||||||||
\(765\) | 2.08772e6 | − | 3.61604e6i | 0.128979 | − | 0.223398i | ||||
\(766\) | 1.16179e7 | + | 2.01227e7i | 0.715408 | + | 1.23912i | ||||
\(767\) | −4.32770e6 | − | 7.49580e6i | −0.265625 | − | 0.460076i | ||||
\(768\) | −6.65046e6 | + | 1.15189e7i | −0.406864 | + | 0.704708i | ||||
\(769\) | −1.52438e7 | −0.929562 | −0.464781 | − | 0.885426i | \(-0.653867\pi\) | ||||
−0.464781 | + | 0.885426i | \(0.653867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.31898e6 | 0.322250 | ||||||||
\(772\) | 6.10702e6 | − | 1.05777e7i | 0.368796 | − | 0.638773i | ||||
\(773\) | −9.74628e6 | − | 1.68810e7i | −0.586665 | − | 1.01613i | −0.994666 | − | 0.103152i | \(-0.967107\pi\) |
0.408001 | − | 0.912982i | \(-0.366226\pi\) | |||||||
\(774\) | 918592. | + | 1.59105e6i | 0.0551150 | + | 0.0954620i | ||||
\(775\) | −4.18138e6 | + | 7.24236e6i | −0.250072 | + | 0.433137i | ||||
\(776\) | 1.01292e7 | 0.603839 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.08807e7 | −1.23679 | ||||||||
\(779\) | −5.28969e6 | + | 9.16201e6i | −0.312311 | + | 0.540938i | ||||
\(780\) | −2.13236e6 | − | 3.69336e6i | −0.125495 | − | 0.217363i | ||||
\(781\) | 2.53173e6 | + | 4.38508e6i | 0.148521 | + | 0.257247i | ||||
\(782\) | 557927. | − | 966358.i | 0.0326257 | − | 0.0565094i | ||||
\(783\) | 3.01642e7 | 1.75828 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.66337e7 | −2.12181 | ||||||||
\(786\) | −5.95140e6 | + | 1.03081e7i | −0.343608 | + | 0.595146i | ||||
\(787\) | 6.81384e6 | + | 1.18019e7i | 0.392153 | + | 0.679228i | 0.992733 | − | 0.120336i | \(-0.0383971\pi\) |
−0.600580 | + | 0.799564i | \(0.705064\pi\) | |||||||
\(788\) | 11651.0 | + | 20180.1i | 0.000668416 | + | 0.00115773i | ||||
\(789\) | 1.77499e6 | − | 3.07438e6i | 0.101509 | − | 0.175819i | ||||
\(790\) | −1.53143e7 | −0.873031 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 4.87357e6 | 0.276080 | ||||||||
\(793\) | −6.78320e6 | + | 1.17488e7i | −0.383046 | + | 0.663456i | ||||
\(794\) | −245312. | − | 424893.i | −0.0138092 | − | 0.0239182i | ||||
\(795\) | 3.83827e6 | + | 6.64808e6i | 0.215386 | + | 0.373060i | ||||
\(796\) | 3.35061e6 | − | 5.80343e6i | 0.187431 | − | 0.324640i | ||||
\(797\) | −3.62853e6 | −0.202341 | −0.101171 | − | 0.994869i | \(-0.532259\pi\) | ||||
−0.101171 | + | 0.994869i | \(0.532259\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 567208. | 0.0314323 | ||||||||
\(800\) | 9.57537e6 | − | 1.65850e7i | 0.528969 | − | 0.916202i | ||||
\(801\) | −3.07956e6 | − | 5.33396e6i | −0.169593 | − | 0.293744i | ||||
\(802\) | 1.18561e7 | + | 2.05353e7i | 0.650885 | + | 1.12737i | ||||
\(803\) | −1.23334e7 | + | 2.13620e7i | −0.674983 | + | 1.16910i | ||||
\(804\) | 4.89877e6 | 0.267268 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.32010e6 | 0.288458 | ||||||||
\(807\) | 2.41754e6 | − | 4.18731e6i | 0.130674 | − | 0.226335i | ||||
\(808\) | −1.40611e6 | − | 2.43546e6i | −0.0757691 | − | 0.131236i | ||||
\(809\) | −1.49390e7 | − | 2.58751e7i | −0.802509 | − | 1.38999i | −0.917960 | − | 0.396673i | \(-0.870165\pi\) |
0.115451 | − | 0.993313i | \(-0.463169\pi\) | |||||||
\(810\) | 1.33646e6 | − | 2.31482e6i | 0.0715721 | − | 0.123967i | ||||
\(811\) | 1.02643e6 | 0.0547995 | 0.0273998 | − | 0.999625i | \(-0.491277\pi\) | ||||
0.0273998 | + | 0.999625i | \(0.491277\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.85702e6 | 0.523021 | ||||||||
\(814\) | −921730. | + | 1.59648e6i | −0.0487576 | + | 0.0844507i | ||||
\(815\) | −2.00543e7 | − | 3.47351e7i | −1.05758 | − | 1.83178i | ||||
\(816\) | 2.37934e6 | + | 4.12113e6i | 0.125092 | + | 0.216666i | ||||
\(817\) | 1.38094e6 | − | 2.39187e6i | 0.0723804 | − | 0.125367i | ||||
\(818\) | −2.06262e7 | −1.07779 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.01940e7 | −0.529434 | ||||||||
\(821\) | 5.75312e6 | − | 9.96470e6i | 0.297883 | − | 0.515948i | −0.677768 | − | 0.735275i | \(-0.737053\pi\) |
0.975651 | + | 0.219327i | \(0.0703861\pi\) | |||||||
\(822\) | −1.00906e6 | − | 1.74774e6i | −0.0520877 | − | 0.0902186i | ||||
\(823\) | 1.25605e7 | + | 2.17554e7i | 0.646408 | + | 1.11961i | 0.983974 | + | 0.178310i | \(0.0570630\pi\) |
−0.337566 | + | 0.941302i | \(0.609604\pi\) | |||||||
\(824\) | −1.43197e6 | + | 2.48024e6i | −0.0734708 | + | 0.127255i | ||||
\(825\) | 1.15225e7 | 0.589401 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.14447e6 | −0.109032 | −0.0545162 | − | 0.998513i | \(-0.517362\pi\) | ||||
−0.0545162 | + | 0.998513i | \(0.517362\pi\) | |||||||
\(828\) | −546501. | + | 946568.i | −0.0277023 | + | 0.0479817i | ||||
\(829\) | 409033. | + | 708465.i | 0.0206715 | + | 0.0358041i | 0.876176 | − | 0.481991i | \(-0.160086\pi\) |
−0.855505 | + | 0.517795i | \(0.826753\pi\) | |||||||
\(830\) | −2.25469e7 | − | 3.90523e7i | −1.13603 | − | 1.96767i | ||||
\(831\) | −4.88370e6 | + | 8.45882e6i | −0.245328 | + | 0.424920i | ||||
\(832\) | −279504. | −0.0139984 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.40231e7 | −1.19595 | ||||||||
\(835\) | −2.70078e7 | + | 4.67788e7i | −1.34052 | + | 2.32184i | ||||
\(836\) | 4.81013e6 | + | 8.33138e6i | 0.238035 | + | 0.412289i | ||||
\(837\) | 4.98964e6 | + | 8.64232e6i | 0.246182 | + | 0.426399i | ||||
\(838\) | −1.63740e7 | + | 2.83606e7i | −0.805460 | + | 1.39510i | ||||
\(839\) | 2.11279e7 | 1.03622 | 0.518110 | − | 0.855314i | \(-0.326636\pi\) | ||||
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.00785e7 | 1.95398 | ||||||||
\(842\) | 9.31533e6 | − | 1.61346e7i | 0.452812 | − | 0.784294i | ||||
\(843\) | 1.60484e6 | + | 2.77966e6i | 0.0777790 | + | 0.134717i | ||||
\(844\) | −4.56107e6 | − | 7.90001e6i | −0.220400 | − | 0.381743i | ||||
\(845\) | 1.14239e7 | − | 1.97868e7i | 0.550393 | − | 0.953308i | ||||
\(846\) | −1.53431e6 | −0.0737035 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 1.21632e7 | 0.580844 | ||||||||
\(849\) | 8.93384e6 | − | 1.54739e7i | 0.425372 | − | 0.736766i | ||||
\(850\) | −4.25604e6 | − | 7.37167e6i | −0.202050 | − | 0.349960i | ||||
\(851\) | 157432. | + | 272679.i | 0.00745191 | + | 0.0129071i | ||||
\(852\) | 1.31771e6 | − | 2.28235e6i | 0.0621902 | − | 0.107717i | ||||
\(853\) | 1.89000e7 | 0.889386 | 0.444693 | − | 0.895683i | \(-0.353313\pi\) | ||||
0.444693 | + | 0.895683i | \(0.353313\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.69796e7 | 0.794349 | ||||||||
\(856\) | 4.30446e6 | − | 7.45554e6i | 0.200786 | − | 0.347772i | ||||
\(857\) | 1.86143e7 | + | 3.22409e7i | 0.865753 | + | 1.49953i | 0.866297 | + | 0.499529i | \(0.166493\pi\) |
−0.000544054 | 1.00000i | \(0.500173\pi\) | ||||||||
\(858\) | −3.66511e6 | − | 6.34815e6i | −0.169968 | − | 0.294394i | ||||
\(859\) | 1.51032e6 | − | 2.61595e6i | 0.0698371 | − | 0.120961i | −0.828992 | − | 0.559260i | \(-0.811085\pi\) |
0.898829 | + | 0.438298i | \(0.144419\pi\) | |||||||
\(860\) | 2.66129e6 | 0.122700 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.34131e7 | 2.44838 | ||||||||
\(863\) | 1.35921e7 | − | 2.35423e7i | 0.621242 | − | 1.07602i | −0.368013 | − | 0.929821i | \(-0.619962\pi\) |
0.989255 | − | 0.146202i | \(-0.0467048\pi\) | |||||||
\(864\) | −1.14263e7 | − | 1.97909e7i | −0.520740 | − | 0.901949i | ||||
\(865\) | −9.94493e6 | − | 1.72251e7i | −0.451920 | − | 0.782748i | ||||
\(866\) | 2.06660e7 | − | 3.57946e7i | 0.936400 | − | 1.62189i | ||||
\(867\) | −1.29352e7 | −0.584420 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.53158e6 | −0.428169 | ||||||||
\(870\) | 2.21873e7 | − | 3.84295e7i | 0.993817 | − | 1.72134i | ||||
\(871\) | −3.90068e6 | − | 6.75618e6i | −0.174219 | − | 0.301756i | ||||
\(872\) | 1.08093e7 | + | 1.87222e7i | 0.481399 | + | 0.833807i | ||||
\(873\) | −7.30532e6 | + | 1.26532e7i | −0.324417 | + | 0.561906i | ||||
\(874\) | 4.53766e6 | 0.200934 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.28385e7 | 0.565269 | ||||||||
\(877\) | −8.69339e6 | + | 1.50574e7i | −0.381672 | + | 0.661075i | −0.991301 | − | 0.131611i | \(-0.957985\pi\) |
0.609629 | + | 0.792687i | \(0.291318\pi\) | |||||||
\(878\) | 595320. | + | 1.03112e6i | 0.0260624 | + | 0.0451414i | ||||
\(879\) | 8.27531e6 | + | 1.43333e7i | 0.361253 | + | 0.625709i | ||||
\(880\) | 1.79128e7 | − | 3.10258e7i | 0.779751 | − | 1.35057i | ||||
\(881\) | 8.14472e6 | 0.353538 | 0.176769 | − | 0.984252i | \(-0.443435\pi\) | ||||
0.176769 | + | 0.984252i | \(0.443435\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.10298e7 | −1.33930 | −0.669649 | − | 0.742678i | \(-0.733555\pi\) | ||||
−0.669649 | + | 0.742678i | \(0.733555\pi\) | |||||||
\(884\) | −980435. | + | 1.69816e6i | −0.0421976 | + | 0.0730884i | ||||
\(885\) | −1.19421e7 | − | 2.06843e7i | −0.512533 | − | 0.887732i | ||||
\(886\) | 1.00629e7 | + | 1.74294e7i | 0.430664 | + | 0.745931i | ||||
\(887\) | −7.35138e6 | + | 1.27330e7i | −0.313733 | + | 0.543401i | −0.979167 | − | 0.203055i | \(-0.934913\pi\) |
0.665435 | + | 0.746456i | \(0.268246\pi\) | |||||||
\(888\) | −730722. | −0.0310971 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −2.46386e7 | −1.04266 | ||||||||
\(891\) | 831810. | − | 1.44074e6i | 0.0351018 | − | 0.0607982i | ||||
\(892\) | −1.06566e7 | − | 1.84578e7i | −0.448443 | − | 0.776726i | ||||
\(893\) | 1.15329e6 | + | 1.99755e6i | 0.0483959 | + | 0.0838242i | ||||
\(894\) | 1.26896e7 | − | 2.19790e7i | 0.531010 | − | 0.919737i | ||||
\(895\) | 1.11166e7 | 0.463890 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.25200e6 | −0.0519545 | ||||||||
\(898\) | 5.01344e6 | − | 8.68354e6i | 0.207465 | − | 0.359340i | ||||
\(899\) | 1.00225e7 | + | 1.73595e7i | 0.413596 | + | 0.716370i | ||||
\(900\) | 4.16888e6 | + | 7.22071e6i | 0.171559 | + | 0.297148i | ||||
\(901\) | 1.76479e6 | − | 3.05671e6i | 0.0724238 | − | 0.125442i | ||||
\(902\) | −1.75215e7 | −0.717060 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.88669e6 | −0.158183 | ||||||||
\(905\) | 1.22235e7 | − | 2.11716e7i | 0.496104 | − | 0.859277i | ||||
\(906\) | 1.28115e7 | + | 2.21902e7i | 0.518538 | + | 0.898135i | ||||
\(907\) | −6.54701e6 | − | 1.13398e7i | −0.264256 | − | 0.457705i | 0.703112 | − | 0.711079i | \(-0.251793\pi\) |
−0.967368 | + | 0.253374i | \(0.918460\pi\) | |||||||
\(908\) | −8.26675e6 | + | 1.43184e7i | −0.332752 | + | 0.576343i | ||||
\(909\) | 4.05643e6 | 0.162830 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.68695e7 | 1.07266 | 0.536332 | − | 0.844007i | \(-0.319809\pi\) | ||||
0.536332 | + | 0.844007i | \(0.319809\pi\) | |||||||
\(912\) | −9.67566e6 | + | 1.67587e7i | −0.385206 | + | 0.667197i | ||||
\(913\) | −1.40331e7 | − | 2.43061e7i | −0.557156 | − | 0.965023i | ||||
\(914\) | −5.51490e6 | − | 9.55209e6i | −0.218360 | − | 0.378210i | ||||
\(915\) | −1.87179e7 | + | 3.24203e7i | −0.739101 | + | 1.28016i | ||||
\(916\) | −9.48103e6 | −0.373351 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −1.01575e7 | −0.397813 | ||||||||
\(919\) | −636586. | + | 1.10260e6i | −0.0248638 | + | 0.0430654i | −0.878190 | − | 0.478313i | \(-0.841249\pi\) |
0.853326 | + | 0.521378i | \(0.174582\pi\) | |||||||
\(920\) | −1.66496e6 | − | 2.88379e6i | −0.0648535 | − | 0.112330i | ||||
\(921\) | −2.35397e6 | − | 4.07720e6i | −0.0914435 | − | 0.158385i | ||||
\(922\) | −1.57714e7 | + | 2.73168e7i | −0.611001 | + | 1.05828i | ||||
\(923\) | −4.19695e6 | −0.162155 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.40187e6 | 0.0922986 | ||||||||
\(926\) | −1.74329e7 | + | 3.01947e7i | −0.668102 | + | 1.15719i | ||||
\(927\) | −2.06551e6 | − | 3.57756e6i | −0.0789454 | − | 0.136737i | ||||
\(928\) | −2.29516e7 | − | 3.97533e7i | −0.874867 | − | 1.51531i | ||||
\(929\) | −4.65852e6 | + | 8.06880e6i | −0.177096 | + | 0.306740i | −0.940885 | − | 0.338727i | \(-0.890004\pi\) |
0.763789 | + | 0.645467i | \(0.223337\pi\) | |||||||
\(930\) | 1.46805e7 | 0.556589 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −1.89428e7 | −0.714338 | ||||||||
\(933\) | −1.22907e7 | + | 2.12881e7i | −0.462245 | + | 0.800631i | ||||
\(934\) | 1.80288e7 | + | 3.12268e7i | 0.676239 | + | 1.17128i | ||||
\(935\) | −5.19801e6 | − | 9.00322e6i | −0.194450 | − | 0.336797i | ||||
\(936\) | −2.01978e6 | + | 3.49837e6i | −0.0753555 | + | 0.130520i | ||||
\(937\) | −1.18158e7 | −0.439657 | −0.219829 | − | 0.975539i | \(-0.570550\pi\) | ||||
−0.219829 | + | 0.975539i | \(0.570550\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.44097e7 | −0.903439 | ||||||||
\(940\) | −1.11128e6 | + | 1.92479e6i | −0.0410208 | + | 0.0710501i | ||||
\(941\) | −1.26765e7 | − | 2.19563e7i | −0.466685 | − | 0.808323i | 0.532591 | − | 0.846373i | \(-0.321219\pi\) |
−0.999276 | + | 0.0380504i | \(0.987885\pi\) | |||||||
\(942\) | 1.63863e7 | + | 2.83819e7i | 0.601663 | + | 1.04211i | ||||
\(943\) | −1.49634e6 | + | 2.59173e6i | −0.0547962 | + | 0.0949098i | ||||
\(944\) | −3.78436e7 | −1.38217 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.57422e6 | 0.166184 | ||||||||
\(947\) | −1.32471e7 | + | 2.29446e7i | −0.480004 | + | 0.831391i | −0.999737 | − | 0.0229375i | \(-0.992698\pi\) |
0.519733 | + | 0.854329i | \(0.326031\pi\) | |||||||
\(948\) | 2.48050e6 | + | 4.29635e6i | 0.0896434 | + | 0.155267i | ||||
\(949\) | −1.02228e7 | − | 1.77063e7i | −0.368471 | − | 0.638210i | ||||
\(950\) | 1.73073e7 | − | 2.99772e7i | 0.622187 | − | 1.07766i | ||||
\(951\) | 1.89164e7 | 0.678246 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.88335e7 | −0.671735 | −0.335868 | − | 0.941909i | \(-0.609030\pi\) | ||||
−0.335868 | + | 0.941909i | \(0.609030\pi\) | |||||||
\(954\) | −4.77380e6 | + | 8.26846e6i | −0.169822 | + | 0.294140i | ||||
\(955\) | −9.08015e6 | − | 1.57273e7i | −0.322170 | − | 0.558014i | ||||
\(956\) | 1.39373e7 | + | 2.41401e7i | 0.493211 | + | 0.854267i | ||||
\(957\) | 1.38093e7 | − | 2.39184e7i | 0.487408 | − | 0.844215i | ||||
\(958\) | 5.87929e7 | 2.06972 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −771276. | −0.0270105 | ||||||||
\(961\) | 1.09988e7 | − | 1.90505e7i | 0.384182 | − | 0.665423i | ||||
\(962\) | −763995. | − | 1.32328e6i | −0.0266166 | − | 0.0461013i | ||||
\(963\) | 6.20886e6 | + | 1.07541e7i | 0.215748 | + | 0.373686i | ||||
\(964\) | −9.15159e6 | + | 1.58510e7i | −0.317179 | + | 0.549370i | ||||
\(965\) | −5.36740e7 | −1.85544 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.14956e7 | −1.08314 | −0.541569 | − | 0.840656i | \(-0.682169\pi\) | ||||
−0.541569 | + | 0.840656i | \(0.682169\pi\) | |||||||
\(968\) | −1.82328e6 | + | 3.15801e6i | −0.0625409 | + | 0.108324i | ||||
\(969\) | 2.80773e6 | + | 4.86312e6i | 0.0960606 | + | 0.166382i | ||||
\(970\) | 2.92238e7 | + | 5.06171e7i | 0.997257 | + | 1.72730i | ||||
\(971\) | −3.42834e6 | + | 5.93806e6i | −0.116691 | + | 0.202114i | −0.918454 | − | 0.395527i | \(-0.870562\pi\) |
0.801764 | + | 0.597641i | \(0.203895\pi\) | |||||||
\(972\) | 1.62401e7 | 0.551343 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 6.11527e7 | 2.06547 | ||||||||
\(975\) | −4.77532e6 | + | 8.27110e6i | −0.160876 | + | 0.278645i | ||||
\(976\) | 2.96579e7 | + | 5.13689e7i | 0.996587 | + | 1.72614i | ||||
\(977\) | −1.40735e7 | − | 2.43761e7i | −0.471701 | − | 0.817010i | 0.527775 | − | 0.849384i | \(-0.323027\pi\) |
−0.999476 | + | 0.0323741i | \(0.989693\pi\) | |||||||
\(978\) | −1.79406e7 | + | 3.10740e7i | −0.599777 | + | 1.03884i | ||||
\(979\) | −1.53350e7 | −0.511361 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.11831e7 | −1.03454 | ||||||||
\(982\) | −336571. | + | 582958.i | −0.0111378 | + | 0.0192912i | ||||
\(983\) | 1.17458e7 | + | 2.03443e7i | 0.387703 | + | 0.671521i | 0.992140 | − | 0.125132i | \(-0.0399354\pi\) |
−0.604437 | + | 0.796653i | \(0.706602\pi\) | |||||||
\(984\) | −3.47264e6 | − | 6.01480e6i | −0.114333 | − | 0.198031i | ||||
\(985\) | 51199.7 | − | 88680.5i | 0.00168142 | − | 0.00291231i | ||||
\(986\) | −2.04029e7 | −0.668343 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.97395e6 | −0.259885 | ||||||||
\(989\) | 390639. | − | 676607.i | 0.0126995 | − | 0.0219961i | ||||
\(990\) | 1.40607e7 | + | 2.43539e7i | 0.455953 | + | 0.789734i | ||||
\(991\) | 1.07206e6 | + | 1.85686e6i | 0.0346765 | + | 0.0600615i | 0.882843 | − | 0.469669i | \(-0.155627\pi\) |
−0.848166 | + | 0.529730i | \(0.822293\pi\) | |||||||
\(992\) | 7.59311e6 | − | 1.31517e7i | 0.244986 | − | 0.424327i | ||||
\(993\) | −1.09206e7 | −0.351459 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.94483e7 | −0.942979 | ||||||||
\(996\) | −7.30395e6 | + | 1.26508e7i | −0.233297 | + | 0.404082i | ||||
\(997\) | 1.25436e7 | + | 2.17261e7i | 0.399654 | + | 0.692220i | 0.993683 | − | 0.112223i | \(-0.0357971\pi\) |
−0.594029 | + | 0.804443i | \(0.702464\pi\) | |||||||
\(998\) | −7.58576e6 | − | 1.31389e7i | −0.241086 | − | 0.417574i | ||||
\(999\) | 1.43308e6 | − | 2.48216e6i | 0.0454314 | − | 0.0786895i |
(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 | 49.6.c.f.30.1 | 4 | ||
7.2 | even | 3 | 49.6.a.e.1.2 | 2 | |||
7.3 | odd | 6 | 7.6.c.a.4.1 | yes | 4 | ||
7.4 | even | 3 | inner | 49.6.c.f.18.1 | 4 | ||
7.5 | odd | 6 | 49.6.a.d.1.2 | 2 | |||
7.6 | odd | 2 | 7.6.c.a.2.1 | ✓ | 4 | ||
21.2 | odd | 6 | 441.6.a.m.1.1 | 2 | |||
21.5 | even | 6 | 441.6.a.n.1.1 | 2 | |||
21.17 | even | 6 | 63.6.e.d.46.2 | 4 | |||
21.20 | even | 2 | 63.6.e.d.37.2 | 4 | |||
28.3 | even | 6 | 112.6.i.c.81.1 | 4 | |||
28.19 | even | 6 | 784.6.a.ba.1.2 | 2 | |||
28.23 | odd | 6 | 784.6.a.t.1.1 | 2 | |||
28.27 | even | 2 | 112.6.i.c.65.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.c.a.2.1 | ✓ | 4 | 7.6 | odd | 2 | ||
7.6.c.a.4.1 | yes | 4 | 7.3 | odd | 6 | ||
49.6.a.d.1.2 | 2 | 7.5 | odd | 6 | |||
49.6.a.e.1.2 | 2 | 7.2 | even | 3 | |||
49.6.c.f.18.1 | 4 | 7.4 | even | 3 | inner | ||
49.6.c.f.30.1 | 4 | 1.1 | even | 1 | trivial | ||
63.6.e.d.37.2 | 4 | 21.20 | even | 2 | |||
63.6.e.d.46.2 | 4 | 21.17 | even | 6 | |||
112.6.i.c.65.1 | 4 | 28.27 | even | 2 | |||
112.6.i.c.81.1 | 4 | 28.3 | even | 6 | |||
441.6.a.m.1.1 | 2 | 21.2 | odd | 6 | |||
441.6.a.n.1.1 | 2 | 21.5 | even | 6 | |||
784.6.a.t.1.1 | 2 | 28.23 | odd | 6 | |||
784.6.a.ba.1.2 | 2 | 28.19 | even | 6 |