Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [12,6,Mod(11,12)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("12.11");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 12 = 2^{2} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 12.b (of order \(2\), degree \(1\), 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: | \(1.92460583776\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + 7x^{6} + 6x^{5} - 11x^{4} - 73x^{3} + 223x^{2} - 768x + 912 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.3 | ||
Root | \(0.713157 - 2.93555i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 12.11 |
Dual form | 12.6.b.a.11.4 |
$q$-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 \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91937 | − | 5.32128i | −0.339300 | − | 0.940678i | ||||
\(3\) | −14.9174 | − | 4.52459i | −0.956950 | − | 0.290253i | ||||
\(4\) | −24.6320 | + | 20.4270i | −0.769750 | + | 0.638345i | ||||
\(5\) | − | 35.2908i | − | 0.631301i | −0.948876 | − | 0.315650i | \(-0.897777\pi\) | ||
0.948876 | − | 0.315650i | \(-0.102223\pi\) | |||||||
\(6\) | 4.55538 | + | 88.0639i | 0.0516591 | + | 0.998665i | ||||
\(7\) | − | 190.564i | − | 1.46993i | −0.678107 | − | 0.734963i | \(-0.737199\pi\) | ||
0.678107 | − | 0.734963i | \(-0.262801\pi\) | |||||||
\(8\) | 155.976 | + | 91.8667i | 0.861654 | + | 0.507496i | ||||
\(9\) | 202.056 | + | 134.990i | 0.831507 | + | 0.555515i | ||||
\(10\) | −187.792 | + | 67.7362i | −0.593851 | + | 0.214201i | ||||
\(11\) | 33.3357 | 0.0830668 | 0.0415334 | − | 0.999137i | \(-0.486776\pi\) | ||||
0.0415334 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(12\) | 459.869 | − | 193.268i | 0.921894 | − | 0.387442i | ||||
\(13\) | −396.112 | −0.650070 | −0.325035 | − | 0.945702i | \(-0.605376\pi\) | ||||
−0.325035 | + | 0.945702i | \(0.605376\pi\) | |||||||
\(14\) | −1014.04 | + | 365.763i | −1.38273 | + | 0.498747i | ||||
\(15\) | −159.676 | + | 526.446i | −0.183237 | + | 0.604123i | ||||
\(16\) | 189.472 | − | 1006.32i | 0.185031 | − | 0.982733i | ||||
\(17\) | − | 1279.32i | − | 1.07364i | −0.843698 | − | 0.536818i | \(-0.819626\pi\) | ||
0.843698 | − | 0.536818i | \(-0.180374\pi\) | |||||||
\(18\) | 330.499 | − | 1334.29i | 0.240430 | − | 0.970666i | ||||
\(19\) | 1333.42i | 0.847387i | 0.905806 | + | 0.423693i | \(0.139267\pi\) | ||||
−0.905806 | + | 0.423693i | \(0.860733\pi\) | |||||||
\(20\) | 720.886 | + | 869.283i | 0.402988 | + | 0.485944i | ||||
\(21\) | −862.224 | + | 2842.71i | −0.426650 | + | 1.40665i | ||||
\(22\) | −63.9836 | − | 177.388i | −0.0281846 | − | 0.0781391i | ||||
\(23\) | 2235.78 | 0.881270 | 0.440635 | − | 0.897686i | \(-0.354753\pi\) | ||||
0.440635 | + | 0.897686i | \(0.354753\pi\) | |||||||
\(24\) | −1911.09 | − | 2076.14i | −0.677257 | − | 0.735746i | ||||
\(25\) | 1879.56 | 0.601459 | ||||||||
\(26\) | 760.287 | + | 2107.82i | 0.220569 | + | 0.611506i | ||||
\(27\) | −2403.37 | − | 2927.92i | −0.634470 | − | 0.772947i | ||||
\(28\) | 3892.66 | + | 4693.97i | 0.938320 | + | 1.13148i | ||||
\(29\) | − | 3984.36i | − | 0.879760i | −0.898057 | − | 0.439880i | \(-0.855021\pi\) | ||
0.898057 | − | 0.439880i | \(-0.144979\pi\) | |||||||
\(30\) | 3107.84 | − | 160.763i | 0.630458 | − | 0.0326124i | ||||
\(31\) | − | 3670.76i | − | 0.686044i | −0.939327 | − | 0.343022i | \(-0.888549\pi\) | ||
0.939327 | − | 0.343022i | \(-0.111451\pi\) | |||||||
\(32\) | −5718.57 | + | 923.267i | −0.987216 | + | 0.159387i | ||||
\(33\) | −497.280 | − | 150.830i | −0.0794907 | − | 0.0241104i | ||||
\(34\) | −6807.62 | + | 2455.49i | −1.00995 | + | 0.364285i | ||||
\(35\) | −6725.15 | −0.927965 | ||||||||
\(36\) | −7734.50 | + | 802.330i | −0.994663 | + | 0.103180i | ||||
\(37\) | 1216.11 | 0.146039 | 0.0730196 | − | 0.997331i | \(-0.476736\pi\) | ||||
0.0730196 | + | 0.997331i | \(0.476736\pi\) | |||||||
\(38\) | 7095.48 | − | 2559.32i | 0.797118 | − | 0.287519i | ||||
\(39\) | 5908.95 | + | 1792.25i | 0.622084 | + | 0.188685i | ||||
\(40\) | 3242.05 | − | 5504.51i | 0.320383 | − | 0.543963i | ||||
\(41\) | 9048.65i | 0.840667i | 0.907370 | + | 0.420334i | \(0.138087\pi\) | ||||
−0.907370 | + | 0.420334i | \(0.861913\pi\) | |||||||
\(42\) | 16781.8 | − | 868.092i | 1.46796 | − | 0.0759351i | ||||
\(43\) | 5349.13i | 0.441176i | 0.975367 | + | 0.220588i | \(0.0707977\pi\) | ||||
−0.975367 | + | 0.220588i | \(0.929202\pi\) | |||||||
\(44\) | −821.124 | + | 680.949i | −0.0639407 | + | 0.0530253i | ||||
\(45\) | 4763.91 | − | 7130.72i | 0.350697 | − | 0.524931i | ||||
\(46\) | −4291.29 | − | 11897.2i | −0.299015 | − | 0.828992i | ||||
\(47\) | 16413.1 | 1.08379 | 0.541895 | − | 0.840446i | \(-0.317707\pi\) | ||||
0.541895 | + | 0.840446i | \(0.317707\pi\) | |||||||
\(48\) | −7379.61 | + | 14154.3i | −0.462307 | + | 0.886720i | ||||
\(49\) | −19507.6 | −1.16068 | ||||||||
\(50\) | −3607.58 | − | 10001.7i | −0.204076 | − | 0.565780i | ||||
\(51\) | −5788.40 | + | 19084.1i | −0.311626 | + | 1.02742i | ||||
\(52\) | 9757.04 | − | 8091.40i | 0.500391 | − | 0.414969i | ||||
\(53\) | 11568.5i | 0.565702i | 0.959164 | + | 0.282851i | \(0.0912801\pi\) | ||||
−0.959164 | + | 0.282851i | \(0.908720\pi\) | |||||||
\(54\) | −10967.3 | + | 18408.8i | −0.511818 | + | 0.859094i | ||||
\(55\) | − | 1176.44i | − | 0.0524401i | ||||||
\(56\) | 17506.5 | − | 29723.4i | 0.745982 | − | 1.26657i | ||||
\(57\) | 6033.17 | − | 19891.1i | 0.245956 | − | 0.810907i | ||||
\(58\) | −21201.9 | + | 7647.48i | −0.827570 | + | 0.298503i | ||||
\(59\) | −42636.9 | −1.59461 | −0.797307 | − | 0.603574i | \(-0.793743\pi\) | ||||
−0.797307 | + | 0.603574i | \(0.793743\pi\) | |||||||
\(60\) | −6820.58 | − | 16229.1i | −0.244592 | − | 0.581992i | ||||
\(61\) | 24268.6 | 0.835065 | 0.417532 | − | 0.908662i | \(-0.362895\pi\) | ||||
0.417532 | + | 0.908662i | \(0.362895\pi\) | |||||||
\(62\) | −19533.1 | + | 7045.56i | −0.645347 | + | 0.232775i | ||||
\(63\) | 25724.2 | − | 38504.6i | 0.816566 | − | 1.22225i | ||||
\(64\) | 15889.0 | + | 28658.0i | 0.484895 | + | 0.874573i | ||||
\(65\) | 13979.1i | 0.410389i | ||||||||
\(66\) | 151.857 | + | 2935.67i | 0.00429115 | + | 0.0829559i | ||||
\(67\) | − | 19925.6i | − | 0.542280i | −0.962540 | − | 0.271140i | \(-0.912599\pi\) | ||
0.962540 | − | 0.271140i | \(-0.0874007\pi\) | |||||||
\(68\) | 26132.7 | + | 31512.2i | 0.685350 | + | 0.826431i | ||||
\(69\) | −33351.9 | − | 10116.0i | −0.843332 | − | 0.255791i | ||||
\(70\) | 12908.1 | + | 35786.4i | 0.314859 | + | 0.872917i | ||||
\(71\) | 33389.6 | 0.786078 | 0.393039 | − | 0.919522i | \(-0.371424\pi\) | ||||
0.393039 | + | 0.919522i | \(0.371424\pi\) | |||||||
\(72\) | 19114.8 | + | 39617.4i | 0.434549 | + | 0.900648i | ||||
\(73\) | 29782.6 | 0.654116 | 0.327058 | − | 0.945004i | \(-0.393943\pi\) | ||||
0.327058 | + | 0.945004i | \(0.393943\pi\) | |||||||
\(74\) | −2334.17 | − | 6471.27i | −0.0495512 | − | 0.137376i | ||||
\(75\) | −28038.1 | − | 8504.25i | −0.575567 | − | 0.174575i | ||||
\(76\) | −27237.8 | − | 32844.7i | −0.540925 | − | 0.652276i | ||||
\(77\) | − | 6352.57i | − | 0.122102i | ||||||
\(78\) | −1804.44 | − | 34883.2i | −0.0335820 | − | 0.649202i | ||||
\(79\) | 26206.1i | 0.472428i | 0.971701 | + | 0.236214i | \(0.0759066\pi\) | ||||
−0.971701 | + | 0.236214i | \(0.924093\pi\) | |||||||
\(80\) | −35513.8 | − | 6686.61i | −0.620400 | − | 0.116810i | ||||
\(81\) | 22604.3 | + | 54551.2i | 0.382806 | + | 0.923829i | ||||
\(82\) | 48150.4 | − | 17367.7i | 0.790797 | − | 0.285239i | ||||
\(83\) | −1851.74 | −0.0295042 | −0.0147521 | − | 0.999891i | \(-0.504696\pi\) | ||||
−0.0147521 | + | 0.999891i | \(0.504696\pi\) | |||||||
\(84\) | −36829.9 | − | 87634.4i | −0.569511 | − | 1.35512i | ||||
\(85\) | −45148.2 | −0.677787 | ||||||||
\(86\) | 28464.2 | − | 10267.0i | 0.415005 | − | 0.149691i | ||||
\(87\) | −18027.6 | + | 59436.2i | −0.255353 | + | 0.841886i | ||||
\(88\) | 5199.56 | + | 3062.44i | 0.0715748 | + | 0.0421561i | ||||
\(89\) | − | 120134.i | − | 1.60764i | −0.594869 | − | 0.803822i | \(-0.702796\pi\) | ||
0.594869 | − | 0.803822i | \(-0.297204\pi\) | |||||||
\(90\) | −47088.2 | − | 11663.6i | −0.612782 | − | 0.151784i | ||||
\(91\) | 75484.7i | 0.955554i | ||||||||
\(92\) | −55071.7 | + | 45670.3i | −0.678358 | + | 0.562555i | ||||
\(93\) | −16608.7 | + | 54758.1i | −0.199126 | + | 0.656510i | ||||
\(94\) | −31502.8 | − | 87338.5i | −0.367731 | − | 1.01950i | ||||
\(95\) | 47057.3 | 0.534956 | ||||||||
\(96\) | 89483.4 | + | 12101.5i | 0.990979 | + | 0.134017i | ||||
\(97\) | −75663.3 | −0.816499 | −0.408250 | − | 0.912870i | \(-0.633861\pi\) | ||||
−0.408250 | + | 0.912870i | \(0.633861\pi\) | |||||||
\(98\) | 37442.4 | + | 103805.i | 0.393820 | + | 1.09183i | ||||
\(99\) | 6735.67 | + | 4499.98i | 0.0690706 | + | 0.0461448i | ||||
\(100\) | −46297.4 | + | 38393.9i | −0.462974 | + | 0.383939i | ||||
\(101\) | 36670.8i | 0.357699i | 0.983876 | + | 0.178849i | \(0.0572375\pi\) | ||||
−0.983876 | + | 0.178849i | \(0.942763\pi\) | |||||||
\(102\) | 112662. | − | 5827.79i | 1.07220 | − | 0.0554630i | ||||
\(103\) | − | 148155.i | − | 1.37602i | −0.725702 | − | 0.688009i | \(-0.758485\pi\) | ||
0.725702 | − | 0.688009i | \(-0.241515\pi\) | |||||||
\(104\) | −61784.0 | − | 36389.5i | −0.560135 | − | 0.329908i | ||||
\(105\) | 100322. | + | 30428.6i | 0.888016 | + | 0.269345i | ||||
\(106\) | 61559.2 | − | 22204.3i | 0.532143 | − | 0.191943i | ||||
\(107\) | 35855.5 | 0.302759 | 0.151379 | − | 0.988476i | \(-0.451628\pi\) | ||||
0.151379 | + | 0.988476i | \(0.451628\pi\) | |||||||
\(108\) | 119009. | + | 23026.8i | 0.981791 | + | 0.189965i | ||||
\(109\) | 149700. | 1.20686 | 0.603429 | − | 0.797416i | \(-0.293801\pi\) | ||||
0.603429 | + | 0.797416i | \(0.293801\pi\) | |||||||
\(110\) | −6260.17 | + | 2258.03i | −0.0493293 | + | 0.0177930i | ||||
\(111\) | −18141.2 | − | 5502.41i | −0.139752 | − | 0.0423883i | ||||
\(112\) | −191768. | − | 36106.5i | −1.44454 | − | 0.271982i | ||||
\(113\) | 29981.1i | 0.220877i | 0.993883 | + | 0.110439i | \(0.0352256\pi\) | ||||
−0.993883 | + | 0.110439i | \(0.964774\pi\) | |||||||
\(114\) | −117426. | + | 6074.22i | −0.846256 | + | 0.0437752i | ||||
\(115\) | − | 78902.4i | − | 0.556347i | ||||||
\(116\) | 81388.8 | + | 98142.9i | 0.561590 | + | 0.677195i | ||||
\(117\) | −80036.9 | − | 53471.2i | −0.540537 | − | 0.361123i | ||||
\(118\) | 81836.1 | + | 226883.i | 0.541053 | + | 1.50002i | ||||
\(119\) | −243792. | −1.57816 | ||||||||
\(120\) | −73268.5 | + | 67444.0i | −0.464477 | + | 0.427553i | ||||
\(121\) | −159940. | −0.993100 | ||||||||
\(122\) | −46580.5 | − | 129140.i | −0.283338 | − | 0.785527i | ||||
\(123\) | 40941.5 | − | 134982.i | 0.244006 | − | 0.804476i | ||||
\(124\) | 74982.8 | + | 90418.2i | 0.437933 | + | 0.528083i | ||||
\(125\) | − | 176615.i | − | 1.01100i | ||||||
\(126\) | −254268. | − | 62981.2i | −1.42681 | − | 0.353415i | ||||
\(127\) | 162916.i | 0.896303i | 0.893958 | + | 0.448152i | \(0.147918\pi\) | ||||
−0.893958 | + | 0.448152i | \(0.852082\pi\) | |||||||
\(128\) | 122000. | − | 139555.i | 0.658166 | − | 0.752873i | ||||
\(129\) | 24202.7 | − | 79795.0i | 0.128053 | − | 0.422184i | ||||
\(130\) | 74386.7 | − | 26831.1i | 0.386044 | − | 0.139245i | ||||
\(131\) | 244446. | 1.24453 | 0.622265 | − | 0.782807i | \(-0.286213\pi\) | ||||
0.622265 | + | 0.782807i | \(0.286213\pi\) | |||||||
\(132\) | 15330.0 | − | 6442.71i | 0.0765788 | − | 0.0321836i | ||||
\(133\) | 254101. | 1.24560 | ||||||||
\(134\) | −106030. | + | 38244.6i | −0.510111 | + | 0.183996i | ||||
\(135\) | −103329. | + | 84816.8i | −0.487962 | + | 0.400542i | ||||
\(136\) | 117527. | − | 199543.i | 0.544866 | − | 0.925102i | ||||
\(137\) | 432998.i | 1.97099i | 0.169700 | + | 0.985496i | \(0.445720\pi\) | ||||
−0.169700 | + | 0.985496i | \(0.554280\pi\) | |||||||
\(138\) | 10184.8 | + | 196891.i | 0.0455256 | + | 0.880094i | ||||
\(139\) | 102633.i | 0.450559i | 0.974294 | + | 0.225280i | \(0.0723296\pi\) | ||||
−0.974294 | + | 0.225280i | \(0.927670\pi\) | |||||||
\(140\) | 165654. | − | 137375.i | 0.714302 | − | 0.592362i | ||||
\(141\) | −244840. | − | 74262.5i | −1.03713 | − | 0.314573i | ||||
\(142\) | −64087.2 | − | 177676.i | −0.266717 | − | 0.739447i | ||||
\(143\) | −13204.7 | −0.0539992 | ||||||||
\(144\) | 174127. | − | 177756.i | 0.699777 | − | 0.714361i | ||||
\(145\) | −140611. | −0.555393 | ||||||||
\(146\) | −57163.9 | − | 158481.i | −0.221942 | − | 0.615313i | ||||
\(147\) | 291002. | + | 88264.0i | 1.11072 | + | 0.336892i | ||||
\(148\) | −29955.3 | + | 24841.6i | −0.112414 | + | 0.0932234i | ||||
\(149\) | 247074.i | 0.911721i | 0.890051 | + | 0.455860i | \(0.150668\pi\) | ||||
−0.890051 | + | 0.455860i | \(0.849332\pi\) | |||||||
\(150\) | 8562.12 | + | 165521.i | 0.0310709 | + | 0.600656i | ||||
\(151\) | 276688.i | 0.987525i | 0.869597 | + | 0.493762i | \(0.164379\pi\) | ||||
−0.869597 | + | 0.493762i | \(0.835621\pi\) | |||||||
\(152\) | −122497. | + | 207981.i | −0.430046 | + | 0.730154i | ||||
\(153\) | 172696. | − | 258494.i | 0.596421 | − | 0.892735i | ||||
\(154\) | −33803.8 | + | 12193.0i | −0.114859 | + | 0.0414293i | ||||
\(155\) | −129544. | −0.433100 | ||||||||
\(156\) | −182160. | + | 76555.8i | −0.599295 | + | 0.251864i | ||||
\(157\) | 10102.0 | 0.0327082 | 0.0163541 | − | 0.999866i | \(-0.494794\pi\) | ||||
0.0163541 | + | 0.999866i | \(0.494794\pi\) | |||||||
\(158\) | 139450. | − | 50299.4i | 0.444402 | − | 0.160295i | ||||
\(159\) | 52342.8 | − | 172572.i | 0.164197 | − | 0.541348i | ||||
\(160\) | 32582.8 | + | 201813.i | 0.100621 | + | 0.623230i | ||||
\(161\) | − | 426059.i | − | 1.29540i | ||||||
\(162\) | 246896. | − | 224988.i | 0.739139 | − | 0.673553i | ||||
\(163\) | − | 523136.i | − | 1.54222i | −0.636704 | − | 0.771108i | \(-0.719703\pi\) | ||
0.636704 | − | 0.771108i | \(-0.280297\pi\) | |||||||
\(164\) | −184837. | − | 222886.i | −0.536636 | − | 0.647104i | ||||
\(165\) | −5322.92 | + | 17549.4i | −0.0152209 | + | 0.0501826i | ||||
\(166\) | 3554.17 | + | 9853.60i | 0.0100108 | + | 0.0277540i | ||||
\(167\) | −525626. | −1.45843 | −0.729214 | − | 0.684285i | \(-0.760114\pi\) | ||||
−0.729214 | + | 0.684285i | \(0.760114\pi\) | |||||||
\(168\) | −395637. | + | 364185.i | −1.08149 | + | 0.995518i | ||||
\(169\) | −214388. | −0.577410 | ||||||||
\(170\) | 86656.2 | + | 240246.i | 0.229973 | + | 0.637579i | ||||
\(171\) | −179998. | + | 269425.i | −0.470736 | + | 0.704608i | ||||
\(172\) | −109267. | − | 131760.i | −0.281623 | − | 0.339596i | ||||
\(173\) | 168521.i | 0.428094i | 0.976823 | + | 0.214047i | \(0.0686646\pi\) | ||||
−0.976823 | + | 0.214047i | \(0.931335\pi\) | |||||||
\(174\) | 350879. | − | 18150.3i | 0.878585 | − | 0.0454476i | ||||
\(175\) | − | 358176.i | − | 0.884101i | ||||||
\(176\) | 6316.17 | − | 33546.3i | 0.0153699 | − | 0.0816324i | ||||
\(177\) | 636030. | + | 192915.i | 1.52597 | + | 0.462841i | ||||
\(178\) | −639265. | + | 230582.i | −1.51228 | + | 0.545475i | ||||
\(179\) | 688174. | 1.60534 | 0.802668 | − | 0.596427i | \(-0.203413\pi\) | ||||
0.802668 | + | 0.596427i | \(0.203413\pi\) | |||||||
\(180\) | 28314.8 | + | 272956.i | 0.0651378 | + | 0.627931i | ||||
\(181\) | 96556.0 | 0.219070 | 0.109535 | − | 0.993983i | \(-0.465064\pi\) | ||||
0.109535 | + | 0.993983i | \(0.465064\pi\) | |||||||
\(182\) | 401675. | − | 144883.i | 0.898869 | − | 0.324220i | ||||
\(183\) | −362024. | − | 109806.i | −0.799115 | − | 0.242380i | ||||
\(184\) | 348728. | + | 205394.i | 0.759350 | + | 0.447242i | ||||
\(185\) | − | 42917.5i | − | 0.0921946i | ||||||
\(186\) | 323262. | − | 16721.7i | 0.685128 | − | 0.0354404i | ||||
\(187\) | − | 42647.0i | − | 0.0891834i | ||||||
\(188\) | −404287. | + | 335271.i | −0.834248 | + | 0.691832i | ||||
\(189\) | −557956. | + | 457996.i | −1.13618 | + | 0.932625i | ||||
\(190\) | −90320.5 | − | 250405.i | −0.181511 | − | 0.503221i | ||||
\(191\) | 525163. | 1.04162 | 0.520811 | − | 0.853672i | \(-0.325630\pi\) | ||||
0.520811 | + | 0.853672i | \(0.325630\pi\) | |||||||
\(192\) | −107357. | − | 499393.i | −0.210173 | − | 0.977664i | ||||
\(193\) | 36606.6 | 0.0707402 | 0.0353701 | − | 0.999374i | \(-0.488739\pi\) | ||||
0.0353701 | + | 0.999374i | \(0.488739\pi\) | |||||||
\(194\) | 145226. | + | 402625.i | 0.277039 | + | 0.768063i | ||||
\(195\) | 63249.8 | − | 208532.i | 0.119117 | − | 0.392722i | ||||
\(196\) | 480511. | − | 398483.i | 0.893436 | − | 0.740916i | ||||
\(197\) | − | 904110.i | − | 1.65980i | −0.557912 | − | 0.829900i | \(-0.688397\pi\) | ||
0.557912 | − | 0.829900i | \(-0.311603\pi\) | |||||||
\(198\) | 11017.4 | − | 44479.5i | 0.0199718 | − | 0.0806301i | ||||
\(199\) | 520039.i | 0.930900i | 0.885074 | + | 0.465450i | \(0.154108\pi\) | ||||
−0.885074 | + | 0.465450i | \(0.845892\pi\) | |||||||
\(200\) | 293166. | + | 172669.i | 0.518250 | + | 0.305239i | ||||
\(201\) | −90155.1 | + | 297237.i | −0.157398 | + | 0.518935i | ||||
\(202\) | 195136. | − | 70385.0i | 0.336479 | − | 0.121367i | ||||
\(203\) | −759276. | −1.29318 | ||||||||
\(204\) | −247252. | − | 588320.i | −0.415971 | − | 0.989778i | ||||
\(205\) | 319334. | 0.530714 | ||||||||
\(206\) | −788375. | + | 284365.i | −1.29439 | + | 0.466883i | ||||
\(207\) | 451753. | + | 301808.i | 0.732782 | + | 0.489559i | ||||
\(208\) | −75052.1 | + | 398615.i | −0.120283 | + | 0.638845i | ||||
\(209\) | 44450.3i | 0.0703897i | ||||||||
\(210\) | −30635.6 | − | 592243.i | −0.0479379 | − | 0.926726i | ||||
\(211\) | 1.25354e6i | 1.93835i | 0.246372 | + | 0.969175i | \(0.420762\pi\) | ||||
−0.246372 | + | 0.969175i | \(0.579238\pi\) | |||||||
\(212\) | −236310. | − | 284956.i | −0.361113 | − | 0.435449i | ||||
\(213\) | −498086. | − | 151075.i | −0.752238 | − | 0.228162i | ||||
\(214\) | −68820.2 | − | 190797.i | −0.102726 | − | 0.284799i | ||||
\(215\) | 188775. | 0.278515 | ||||||||
\(216\) | −105890. | − | 677475.i | −0.154426 | − | 0.988004i | ||||
\(217\) | −699515. | −1.00843 | ||||||||
\(218\) | −287331. | − | 796597.i | −0.409488 | − | 1.13527i | ||||
\(219\) | −444278. | − | 134754.i | −0.625957 | − | 0.189859i | ||||
\(220\) | 24031.2 | + | 28978.1i | 0.0334749 | + | 0.0403658i | ||||
\(221\) | 506754.i | 0.697938i | ||||||||
\(222\) | 5539.86 | + | 107096.i | 0.00754425 | + | 0.145844i | ||||
\(223\) | − | 785292.i | − | 1.05747i | −0.848786 | − | 0.528736i | \(-0.822666\pi\) | ||
0.848786 | − | 0.528736i | \(-0.177334\pi\) | |||||||
\(224\) | 175941. | + | 1.08975e6i | 0.234287 | + | 1.45113i | ||||
\(225\) | 379777. | + | 253722.i | 0.500117 | + | 0.334120i | ||||
\(226\) | 159538. | − | 57544.9i | 0.207775 | − | 0.0749438i | ||||
\(227\) | −79311.0 | −0.102157 | −0.0510786 | − | 0.998695i | \(-0.516266\pi\) | ||||
−0.0510786 | + | 0.998695i | \(0.516266\pi\) | |||||||
\(228\) | 257707. | + | 613197.i | 0.328313 | + | 0.781201i | ||||
\(229\) | 1.19706e6 | 1.50844 | 0.754221 | − | 0.656621i | \(-0.228015\pi\) | ||||
0.754221 | + | 0.656621i | \(0.228015\pi\) | |||||||
\(230\) | −419861. | + | 151443.i | −0.523343 | + | 0.188769i | ||||
\(231\) | −28742.8 | + | 94763.7i | −0.0354405 | + | 0.116846i | ||||
\(232\) | 366030. | − | 621465.i | 0.446475 | − | 0.758048i | ||||
\(233\) | − | 683524.i | − | 0.824829i | −0.910996 | − | 0.412415i | \(-0.864686\pi\) | ||
0.910996 | − | 0.412415i | \(-0.135314\pi\) | |||||||
\(234\) | −130915. | + | 528530.i | −0.156296 | + | 0.631001i | ||||
\(235\) | − | 579230.i | − | 0.684198i | ||||||
\(236\) | 1.05023e6 | − | 870946.i | 1.22745 | − | 1.01791i | ||||
\(237\) | 118572. | − | 390927.i | 0.137124 | − | 0.452090i | ||||
\(238\) | 467928. | + | 1.29729e6i | 0.535472 | + | 1.48454i | ||||
\(239\) | 1.17006e6 | 1.32500 | 0.662498 | − | 0.749064i | \(-0.269496\pi\) | ||||
0.662498 | + | 0.749064i | \(0.269496\pi\) | |||||||
\(240\) | 499518. | + | 260432.i | 0.559787 | + | 0.291854i | ||||
\(241\) | −790728. | −0.876969 | −0.438485 | − | 0.898739i | \(-0.644485\pi\) | ||||
−0.438485 | + | 0.898739i | \(0.644485\pi\) | |||||||
\(242\) | 306984. | + | 851084.i | 0.336959 | + | 0.934187i | ||||
\(243\) | −90375.3 | − | 916035.i | −0.0981825 | − | 0.995168i | ||||
\(244\) | −597784. | + | 495736.i | −0.642791 | + | 0.533059i | ||||
\(245\) | 688438.i | 0.732740i | ||||||||
\(246\) | −796859. | + | 41220.1i | −0.839545 | + | 0.0434281i | ||||
\(247\) | − | 528182.i | − | 0.550860i | ||||||
\(248\) | 337221. | − | 572551.i | 0.348165 | − | 0.591132i | ||||
\(249\) | 27623.0 | + | 8378.35i | 0.0282340 | + | 0.00856368i | ||||
\(250\) | −939817. | + | 338990.i | −0.951028 | + | 0.343034i | ||||
\(251\) | −1.41649e6 | −1.41915 | −0.709574 | − | 0.704631i | \(-0.751113\pi\) | ||||
−0.709574 | + | 0.704631i | \(0.751113\pi\) | |||||||
\(252\) | 152895. | + | 1.47392e6i | 0.151667 | + | 1.46208i | ||||
\(253\) | 74531.1 | 0.0732043 | ||||||||
\(254\) | 866923. | − | 312697.i | 0.843133 | − | 0.304116i | ||||
\(255\) | 673492. | + | 204277.i | 0.648608 | + | 0.196730i | ||||
\(256\) | −976777. | − | 381338.i | −0.931527 | − | 0.363672i | ||||
\(257\) | 808032.i | 0.763125i | 0.924343 | + | 0.381562i | \(0.124614\pi\) | ||||
−0.924343 | + | 0.381562i | \(0.875386\pi\) | |||||||
\(258\) | −471065. | + | 24367.4i | −0.440587 | + | 0.0227908i | ||||
\(259\) | − | 231747.i | − | 0.214667i | ||||||
\(260\) | −285552. | − | 344334.i | −0.261970 | − | 0.315897i | ||||
\(261\) | 537850. | − | 805065.i | 0.488720 | − | 0.731526i | ||||
\(262\) | −469184. | − | 1.30077e6i | −0.422269 | − | 1.17070i | ||||
\(263\) | −804766. | −0.717431 | −0.358716 | − | 0.933447i | \(-0.616785\pi\) | ||||
−0.358716 | + | 0.933447i | \(0.616785\pi\) | |||||||
\(264\) | −63707.5 | − | 69209.4i | −0.0562576 | − | 0.0611161i | ||||
\(265\) | 408261. | 0.357128 | ||||||||
\(266\) | −487715. | − | 1.35214e6i | −0.422631 | − | 1.17171i | ||||
\(267\) | −543557. | + | 1.79208e6i | −0.466623 | + | 1.53844i | ||||
\(268\) | 407021. | + | 490807.i | 0.346162 | + | 0.417420i | ||||
\(269\) | − | 432855.i | − | 0.364722i | −0.983232 | − | 0.182361i | \(-0.941626\pi\) | ||
0.983232 | − | 0.182361i | \(-0.0583739\pi\) | |||||||
\(270\) | 649660. | + | 387045.i | 0.542346 | + | 0.323111i | ||||
\(271\) | − | 207740.i | − | 0.171829i | −0.996302 | − | 0.0859147i | \(-0.972619\pi\) | ||
0.996302 | − | 0.0859147i | \(-0.0273813\pi\) | |||||||
\(272\) | −1.28740e6 | − | 242395.i | −1.05510 | − | 0.198656i | ||||
\(273\) | 341538. | − | 1.12603e6i | 0.277352 | − | 0.914418i | ||||
\(274\) | 2.30410e6 | − | 831085.i | 1.85407 | − | 0.668758i | ||||
\(275\) | 62656.4 | 0.0499613 | ||||||||
\(276\) | 1.02817e6 | − | 432104.i | 0.812438 | − | 0.341441i | ||||
\(277\) | −1.69477e6 | −1.32712 | −0.663560 | − | 0.748123i | \(-0.730955\pi\) | ||||
−0.663560 | + | 0.748123i | \(0.730955\pi\) | |||||||
\(278\) | 546141. | − | 196992.i | 0.423831 | − | 0.152875i | ||||
\(279\) | 495517. | − | 741700.i | 0.381108 | − | 0.570450i | ||||
\(280\) | −1.04896e6 | − | 617817.i | −0.799585 | − | 0.470939i | ||||
\(281\) | 1.50990e6i | 1.14073i | 0.821392 | + | 0.570364i | \(0.193198\pi\) | ||||
−0.821392 | + | 0.570364i | \(0.806802\pi\) | |||||||
\(282\) | 74767.9 | + | 1.44540e6i | 0.0559876 | + | 1.08234i | ||||
\(283\) | 1.48985e6i | 1.10580i | 0.833247 | + | 0.552901i | \(0.186479\pi\) | ||||
−0.833247 | + | 0.552901i | \(0.813521\pi\) | |||||||
\(284\) | −822454. | + | 682052.i | −0.605084 | + | 0.501789i | ||||
\(285\) | −701971. | − | 212915.i | −0.511926 | − | 0.155272i | ||||
\(286\) | 25344.7 | + | 70265.7i | 0.0183219 | + | 0.0507958i | ||||
\(287\) | 1.72435e6 | 1.23572 | ||||||||
\(288\) | −1.28010e6 | − | 585398.i | −0.909419 | − | 0.415882i | ||||
\(289\) | −216802. | −0.152693 | ||||||||
\(290\) | 269886. | + | 748232.i | 0.188445 | + | 0.522446i | ||||
\(291\) | 1.12870e6 | + | 342346.i | 0.781349 | + | 0.236991i | ||||
\(292\) | −733604. | + | 608370.i | −0.503506 | + | 0.417552i | ||||
\(293\) | 759752.i | 0.517015i | 0.966009 | + | 0.258507i | \(0.0832306\pi\) | ||||
−0.966009 | + | 0.258507i | \(0.916769\pi\) | |||||||
\(294\) | −88864.6 | − | 1.71792e6i | −0.0599598 | − | 1.15913i | ||||
\(295\) | 1.50469e6i | 1.00668i | ||||||||
\(296\) | 189684. | + | 111720.i | 0.125835 | + | 0.0741144i | ||||
\(297\) | −80117.9 | − | 97604.1i | −0.0527034 | − | 0.0642062i | ||||
\(298\) | 1.31475e6 | − | 474228.i | 0.857636 | − | 0.309347i | ||||
\(299\) | −885619. | −0.572887 | ||||||||
\(300\) | 864352. | − | 363259.i | 0.554482 | − | 0.233031i | ||||
\(301\) | 1.01935e6 | 0.648497 | ||||||||
\(302\) | 1.47233e6 | − | 531068.i | 0.928943 | − | 0.335068i | ||||
\(303\) | 165921. | − | 547033.i | 0.103823 | − | 0.342300i | ||||
\(304\) | 1.34184e6 | + | 252645.i | 0.832755 | + | 0.156793i | ||||
\(305\) | − | 856458.i | − | 0.527177i | ||||||
\(306\) | −1.70699e6 | − | 422814.i | −1.04214 | − | 0.258134i | ||||
\(307\) | − | 1.26088e6i | − | 0.763532i | −0.924259 | − | 0.381766i | \(-0.875316\pi\) | ||
0.924259 | − | 0.381766i | \(-0.124684\pi\) | |||||||
\(308\) | 129764. | + | 156477.i | 0.0779432 | + | 0.0939881i | ||||
\(309\) | −670342. | + | 2.21009e6i | −0.399393 | + | 1.31678i | ||||
\(310\) | 248643. | + | 689340.i | 0.146951 | + | 0.407408i | ||||
\(311\) | −932334. | −0.546601 | −0.273300 | − | 0.961929i | \(-0.588115\pi\) | ||||
−0.273300 | + | 0.961929i | \(0.588115\pi\) | |||||||
\(312\) | 757007. | + | 822383.i | 0.440264 | + | 0.478286i | ||||
\(313\) | 2.60743e6 | 1.50436 | 0.752179 | − | 0.658959i | \(-0.229003\pi\) | ||||
0.752179 | + | 0.658959i | \(0.229003\pi\) | |||||||
\(314\) | −19389.4 | − | 53755.4i | −0.0110979 | − | 0.0307679i | ||||
\(315\) | −1.35886e6 | − | 907829.i | −0.771609 | − | 0.515499i | ||||
\(316\) | −535314. | − | 645510.i | −0.301572 | − | 0.363651i | ||||
\(317\) | − | 1.08779e6i | − | 0.607992i | −0.952673 | − | 0.303996i | \(-0.901679\pi\) | ||
0.952673 | − | 0.303996i | \(-0.0983210\pi\) | |||||||
\(318\) | −1.01877e6 | + | 52699.0i | −0.564946 | + | 0.0292236i | ||||
\(319\) | − | 132821.i | − | 0.0730788i | ||||||
\(320\) | 1.01136e6 | − | 560736.i | 0.552118 | − | 0.306114i | ||||
\(321\) | −534870. | − | 162232.i | −0.289725 | − | 0.0878766i | ||||
\(322\) | −2.26718e6 | + | 817766.i | −1.21856 | + | 0.439531i | ||||
\(323\) | 1.70587e6 | 0.909785 | ||||||||
\(324\) | −1.67111e6 | − | 881965.i | −0.884387 | − | 0.466755i | ||||
\(325\) | −744517. | −0.390990 | ||||||||
\(326\) | −2.78375e6 | + | 1.00409e6i | −1.45073 | + | 0.523275i | ||||
\(327\) | −2.23314e6 | − | 677333.i | −1.15490 | − | 0.350294i | ||||
\(328\) | −831269. | + | 1.41137e6i | −0.426636 | + | 0.724364i | ||||
\(329\) | − | 3.12774e6i | − | 1.59309i | ||||||
\(330\) | 103602. | − | 5359.14i | 0.0523701 | − | 0.00270901i | ||||
\(331\) | − | 1.54918e6i | − | 0.777200i | −0.921406 | − | 0.388600i | \(-0.872959\pi\) | ||
0.921406 | − | 0.388600i | \(-0.127041\pi\) | |||||||
\(332\) | 45612.0 | − | 37825.5i | 0.0227109 | − | 0.0188339i | ||||
\(333\) | 245723. | + | 164163.i | 0.121433 | + | 0.0811269i | ||||
\(334\) | 1.00887e6 | + | 2.79700e6i | 0.494846 | + | 1.37191i | ||||
\(335\) | −703189. | −0.342342 | ||||||||
\(336\) | 2.69731e6 | + | 1.40629e6i | 1.30341 | + | 0.679557i | ||||
\(337\) | −1.23639e6 | −0.593035 | −0.296518 | − | 0.955027i | \(-0.595825\pi\) | ||||
−0.296518 | + | 0.955027i | \(0.595825\pi\) | |||||||
\(338\) | 411491. | + | 1.14082e6i | 0.195915 | + | 0.543157i | ||||
\(339\) | 135652. | − | 447239.i | 0.0641103 | − | 0.211369i | ||||
\(340\) | 1.11209e6 | − | 922244.i | 0.521727 | − | 0.432662i | ||||
\(341\) | − | 122367.i | − | 0.0569875i | ||||||
\(342\) | 1.77917e6 | + | 440693.i | 0.822530 | + | 0.203737i | ||||
\(343\) | 514637.i | 0.236192i | ||||||||
\(344\) | −491407. | + | 834336.i | −0.223895 | + | 0.380141i | ||||
\(345\) | −357001. | + | 1.17702e6i | −0.161481 | + | 0.532396i | ||||
\(346\) | 896748. | − | 323455.i | 0.402699 | − | 0.145253i | ||||
\(347\) | 1.35733e6 | 0.605150 | 0.302575 | − | 0.953126i | \(-0.402154\pi\) | ||||
0.302575 | + | 0.953126i | \(0.402154\pi\) | |||||||
\(348\) | −770050. | − | 1.83229e6i | −0.340856 | − | 0.811045i | ||||
\(349\) | 506931. | 0.222785 | 0.111392 | − | 0.993777i | \(-0.464469\pi\) | ||||
0.111392 | + | 0.993777i | \(0.464469\pi\) | |||||||
\(350\) | −1.90596e6 | + | 687474.i | −0.831654 | + | 0.299976i | ||||
\(351\) | 952004. | + | 1.15978e6i | 0.412450 | + | 0.502469i | ||||
\(352\) | −190632. | + | 30777.7i | −0.0820049 | + | 0.0132398i | ||||
\(353\) | 1.78557e6i | 0.762674i | 0.924436 | + | 0.381337i | \(0.124536\pi\) | ||||
−0.924436 | + | 0.381337i | \(0.875464\pi\) | |||||||
\(354\) | −194227. | − | 3.75477e6i | −0.0823763 | − | 1.59248i | ||||
\(355\) | − | 1.17835e6i | − | 0.496252i | ||||||
\(356\) | 2.45398e6 | + | 2.95914e6i | 1.02623 | + | 1.23749i | ||||
\(357\) | 3.63674e6 | + | 1.10306e6i | 1.51022 | + | 0.458067i | ||||
\(358\) | −1.32086e6 | − | 3.66197e6i | −0.544691 | − | 1.51010i | ||||
\(359\) | −1.79260e6 | −0.734087 | −0.367044 | − | 0.930204i | \(-0.619630\pi\) | ||||
−0.367044 | + | 0.930204i | \(0.619630\pi\) | |||||||
\(360\) | 1.39813e6 | − | 674576.i | 0.568580 | − | 0.274331i | ||||
\(361\) | 698100. | 0.281935 | ||||||||
\(362\) | −185327. | − | 513801.i | −0.0743305 | − | 0.206074i | ||||
\(363\) | 2.38588e6 | + | 723662.i | 0.950347 | + | 0.288250i | ||||
\(364\) | −1.54193e6 | − | 1.85934e6i | −0.609973 | − | 0.735538i | ||||
\(365\) | − | 1.05105e6i | − | 0.412944i | ||||||
\(366\) | 110553. | + | 2.13719e6i | 0.0431387 | + | 0.833950i | ||||
\(367\) | 721697.i | 0.279698i | 0.990173 | + | 0.139849i | \(0.0446617\pi\) | ||||
−0.990173 | + | 0.139849i | \(0.955338\pi\) | |||||||
\(368\) | 423617. | − | 2.24990e6i | 0.163063 | − | 0.866053i | ||||
\(369\) | −1.22148e6 | + | 1.82833e6i | −0.467003 | + | 0.699020i | ||||
\(370\) | −228376. | + | 82374.8i | −0.0867255 | + | 0.0312817i | ||||
\(371\) | 2.20454e6 | 0.831540 | ||||||||
\(372\) | −709441. | − | 1.68807e6i | −0.265802 | − | 0.632460i | ||||
\(373\) | −4.93336e6 | −1.83599 | −0.917996 | − | 0.396591i | \(-0.870193\pi\) | ||||
−0.917996 | + | 0.396591i | \(0.870193\pi\) | |||||||
\(374\) | −226936. | + | 81855.5i | −0.0838929 | + | 0.0302600i | ||||
\(375\) | −799111. | + | 2.63463e6i | −0.293446 | + | 0.967479i | ||||
\(376\) | 2.56005e6 | + | 1.50781e6i | 0.933852 | + | 0.550020i | ||||
\(377\) | 1.57826e6i | 0.571905i | ||||||||
\(378\) | 3.50805e6 | + | 2.08997e6i | 1.26280 | + | 0.752335i | ||||
\(379\) | 3.76403e6i | 1.34603i | 0.739629 | + | 0.673015i | \(0.235001\pi\) | ||||
−0.739629 | + | 0.673015i | \(0.764999\pi\) | |||||||
\(380\) | −1.15912e6 | + | 961241.i | −0.411783 | + | 0.341486i | ||||
\(381\) | 737130. | − | 2.43028e6i | 0.260155 | − | 0.857717i | ||||
\(382\) | −1.00798e6 | − | 2.79454e6i | −0.353423 | − | 0.979831i | ||||
\(383\) | −1.15231e6 | −0.401394 | −0.200697 | − | 0.979653i | \(-0.564321\pi\) | ||||
−0.200697 | + | 0.979653i | \(0.564321\pi\) | |||||||
\(384\) | −2.45135e6 | + | 1.52980e6i | −0.848356 | + | 0.529427i | ||||
\(385\) | −224187. | −0.0770831 | ||||||||
\(386\) | −70261.7 | − | 194794.i | −0.0240022 | − | 0.0665437i | ||||
\(387\) | −722080. | + | 1.08082e6i | −0.245080 | + | 0.366841i | ||||
\(388\) | 1.86374e6 | − | 1.54558e6i | 0.628501 | − | 0.521208i | ||||
\(389\) | − | 4.29070e6i | − | 1.43765i | −0.695189 | − | 0.718827i | \(-0.744679\pi\) | ||
0.695189 | − | 0.718827i | \(-0.255321\pi\) | |||||||
\(390\) | −1.23105e6 | + | 63680.2i | −0.409841 | + | 0.0212003i | ||||
\(391\) | − | 2.86028e6i | − | 0.946163i | ||||||
\(392\) | −3.04272e6 | − | 1.79210e6i | −1.00011 | − | 0.589043i | ||||
\(393\) | −3.64650e6 | − | 1.10602e6i | −1.19095 | − | 0.361228i | ||||
\(394\) | −4.81102e6 | + | 1.73532e6i | −1.56134 | + | 0.563171i | ||||
\(395\) | 924835. | 0.298244 | ||||||||
\(396\) | −257835. | + | 26746.2i | −0.0826234 | + | 0.00857085i | ||||
\(397\) | 2.49061e6 | 0.793102 | 0.396551 | − | 0.918013i | \(-0.370207\pi\) | ||||
0.396551 | + | 0.918013i | \(0.370207\pi\) | |||||||
\(398\) | 2.76727e6 | − | 998149.i | 0.875678 | − | 0.315855i | ||||
\(399\) | −3.79052e6 | − | 1.14970e6i | −1.19197 | − | 0.361538i | ||||
\(400\) | 356124. | − | 1.89144e6i | 0.111289 | − | 0.591074i | ||||
\(401\) | 1.01615e6i | 0.315569i | 0.987474 | + | 0.157785i | \(0.0504352\pi\) | ||||
−0.987474 | + | 0.157785i | \(0.949565\pi\) | |||||||
\(402\) | 1.75472e6 | − | 90768.6i | 0.541556 | − | 0.0280137i | ||||
\(403\) | 1.45403e6i | 0.445976i | ||||||||
\(404\) | −749077. | − | 903277.i | −0.228335 | − | 0.275339i | ||||
\(405\) | 1.92515e6 | − | 797724.i | 0.583214 | − | 0.241666i | ||||
\(406\) | 1.45733e6 | + | 4.04032e6i | 0.438777 | + | 1.21647i | ||||
\(407\) | 40539.9 | 0.0121310 | ||||||||
\(408\) | −2.65604e6 | + | 2.44490e6i | −0.789923 | + | 0.727127i | ||||
\(409\) | 2.55994e6 | 0.756697 | 0.378349 | − | 0.925663i | \(-0.376492\pi\) | ||||
0.378349 | + | 0.925663i | \(0.376492\pi\) | |||||||
\(410\) | −612921. | − | 1.69926e6i | −0.180071 | − | 0.499231i | ||||
\(411\) | 1.95914e6 | − | 6.45920e6i | 0.572086 | − | 1.88614i | ||||
\(412\) | 3.02637e6 | + | 3.64936e6i | 0.878374 | + | 1.05919i | ||||
\(413\) | 8.12505e6i | 2.34396i | ||||||||
\(414\) | 738923. | − | 2.98318e6i | 0.211884 | − | 0.855420i | ||||
\(415\) | 65349.2i | 0.0186260i | ||||||||
\(416\) | 2.26519e6 | − | 365717.i | 0.641759 | − | 0.103613i | ||||
\(417\) | 464375. | − | 1.53102e6i | 0.130776 | − | 0.431163i | ||||
\(418\) | 236532. | − | 85316.7i | 0.0662140 | − | 0.0238833i | ||||
\(419\) | −140154. | −0.0390006 | −0.0195003 | − | 0.999810i | \(-0.506208\pi\) | ||||
−0.0195003 | + | 0.999810i | \(0.506208\pi\) | |||||||
\(420\) | −3.09269e6 | + | 1.29976e6i | −0.855486 | + | 0.359533i | ||||
\(421\) | −143774. | −0.0395344 | −0.0197672 | − | 0.999805i | \(-0.506292\pi\) | ||||
−0.0197672 | + | 0.999805i | \(0.506292\pi\) | |||||||
\(422\) | 6.67044e6 | − | 2.40601e6i | 1.82336 | − | 0.657683i | ||||
\(423\) | 3.31636e6 | + | 2.21560e6i | 0.901179 | + | 0.602062i | ||||
\(424\) | −1.06276e6 | + | 1.80441e6i | −0.287092 | + | 0.487439i | ||||
\(425\) | − | 2.40456e6i | − | 0.645748i | ||||||
\(426\) | 152103. | + | 2.94042e6i | 0.0406081 | + | 0.785029i | ||||
\(427\) | − | 4.62472e6i | − | 1.22748i | ||||||
\(428\) | −883194. | + | 732422.i | −0.233049 | + | 0.193265i | ||||
\(429\) | 196979. | + | 59745.7i | 0.0516745 | + | 0.0156734i | ||||
\(430\) | −362330. | − | 1.00452e6i | −0.0945002 | − | 0.261993i | ||||
\(431\) | −6.33735e6 | −1.64329 | −0.821646 | − | 0.569998i | \(-0.806944\pi\) | ||||
−0.821646 | + | 0.569998i | \(0.806944\pi\) | |||||||
\(432\) | −3.40179e6 | + | 1.86380e6i | −0.876997 | + | 0.480495i | ||||
\(433\) | 3.23311e6 | 0.828707 | 0.414353 | − | 0.910116i | \(-0.364008\pi\) | ||||
0.414353 | + | 0.910116i | \(0.364008\pi\) | |||||||
\(434\) | 1.34263e6 | + | 3.72231e6i | 0.342162 | + | 0.948612i | ||||
\(435\) | 2.09755e6 | + | 636209.i | 0.531483 | + | 0.161204i | ||||
\(436\) | −3.68742e6 | + | 3.05793e6i | −0.928980 | + | 0.770392i | ||||
\(437\) | 2.98122e6i | 0.746777i | ||||||||
\(438\) | 135671. | + | 2.62277e6i | 0.0337911 | + | 0.653243i | ||||
\(439\) | − | 431210.i | − | 0.106789i | −0.998573 | − | 0.0533947i | \(-0.982996\pi\) | ||
0.998573 | − | 0.0533947i | \(-0.0170041\pi\) | |||||||
\(440\) | 108076. | − | 183497.i | 0.0266132 | − | 0.0451852i | ||||
\(441\) | −3.94163e6 | − | 2.63333e6i | −0.965116 | − | 0.644777i | ||||
\(442\) | 2.69658e6 | − | 972650.i | 0.656535 | − | 0.236811i | ||||
\(443\) | 1.62011e6 | 0.392225 | 0.196112 | − | 0.980581i | \(-0.437168\pi\) | ||||
0.196112 | + | 0.980581i | \(0.437168\pi\) | |||||||
\(444\) | 559252. | − | 235036.i | 0.134633 | − | 0.0565817i | ||||
\(445\) | −4.23961e6 | −1.01491 | ||||||||
\(446\) | −4.17876e6 | + | 1.50727e6i | −0.994741 | + | 0.358801i | ||||
\(447\) | 1.11791e6 | − | 3.68570e6i | 0.264630 | − | 0.872471i | ||||
\(448\) | 5.46118e6 | − | 3.02788e6i | 1.28556 | − | 0.712759i | ||||
\(449\) | 782536.i | 0.183184i | 0.995797 | + | 0.0915922i | \(0.0291956\pi\) | ||||
−0.995797 | + | 0.0915922i | \(0.970804\pi\) | |||||||
\(450\) | 621193. | − | 2.50789e6i | 0.144609 | − | 0.583817i | ||||
\(451\) | 301643.i | 0.0698315i | ||||||||
\(452\) | −612425. | − | 738494.i | −0.140996 | − | 0.170020i | ||||
\(453\) | 1.25190e6 | − | 4.12746e6i | 0.286632 | − | 0.945012i | ||||
\(454\) | 152227. | + | 422036.i | 0.0346620 | + | 0.0960970i | ||||
\(455\) | 2.66391e6 | 0.603242 | ||||||||
\(456\) | 2.76836e6 | − | 2.54828e6i | 0.623462 | − | 0.573899i | ||||
\(457\) | 3.85018e6 | 0.862365 | 0.431182 | − | 0.902265i | \(-0.358097\pi\) | ||||
0.431182 | + | 0.902265i | \(0.358097\pi\) | |||||||
\(458\) | −2.29761e6 | − | 6.36991e6i | −0.511815 | − | 1.41896i | ||||
\(459\) | −3.74575e6 | + | 3.07468e6i | −0.829863 | + | 0.681190i | ||||
\(460\) | 1.61174e6 | + | 1.94352e6i | 0.355141 | + | 0.428248i | ||||
\(461\) | − | 2.26341e6i | − | 0.496032i | −0.968756 | − | 0.248016i | \(-0.920221\pi\) | ||
0.968756 | − | 0.248016i | \(-0.0797786\pi\) | |||||||
\(462\) | 559432. | − | 28938.4i | 0.121939 | − | 0.00630768i | ||||
\(463\) | 7.51046e6i | 1.62822i | 0.580708 | + | 0.814112i | \(0.302776\pi\) | ||||
−0.580708 | + | 0.814112i | \(0.697224\pi\) | |||||||
\(464\) | −4.00954e6 | − | 754925.i | −0.864568 | − | 0.162783i | ||||
\(465\) | 1.93246e6 | + | 586134.i | 0.414455 | + | 0.125709i | ||||
\(466\) | −3.63722e6 | + | 1.31194e6i | −0.775899 | + | 0.279865i | ||||
\(467\) | −5.74296e6 | −1.21855 | −0.609275 | − | 0.792959i | \(-0.708539\pi\) | ||||
−0.609275 | + | 0.792959i | \(0.708539\pi\) | |||||||
\(468\) | 3.06373e6 | − | 317813.i | 0.646600 | − | 0.0670743i | ||||
\(469\) | −3.79709e6 | −0.797112 | ||||||||
\(470\) | −3.08225e6 | + | 1.11176e6i | −0.643610 | + | 0.232149i | ||||
\(471\) | −150695. | − | 45707.3i | −0.0313001 | − | 0.00949365i | ||||
\(472\) | −6.65033e6 | − | 3.91691e6i | −1.37401 | − | 0.809261i | ||||
\(473\) | 178317.i | 0.0366471i | ||||||||
\(474\) | −2.30782e6 | + | 119379.i | −0.471797 | + | 0.0244052i | ||||
\(475\) | 2.50624e6i | 0.509669i | ||||||||
\(476\) | 6.00509e6 | − | 4.97995e6i | 1.21479 | − | 1.00741i | ||||
\(477\) | −1.56163e6 | + | 2.33749e6i | −0.314256 | + | 0.470385i | ||||
\(478\) | −2.24579e6 | − | 6.22623e6i | −0.449572 | − | 1.24639i | ||||
\(479\) | 6.71306e6 | 1.33685 | 0.668424 | − | 0.743781i | \(-0.266969\pi\) | ||||
0.668424 | + | 0.743781i | \(0.266969\pi\) | |||||||
\(480\) | 427070. | − | 3.15794e6i | 0.0846051 | − | 0.625606i | ||||
\(481\) | −481717. | −0.0949356 | ||||||||
\(482\) | 1.51770e6 | + | 4.20768e6i | 0.297556 | + | 0.824945i | ||||
\(483\) | −1.92774e6 | + | 6.35568e6i | −0.375994 | + | 1.23964i | ||||
\(484\) | 3.93964e6 | − | 3.26710e6i | 0.764439 | − | 0.633940i | ||||
\(485\) | 2.67022e6i | 0.515457i | ||||||||
\(486\) | −4.70102e6 | + | 2.23913e6i | −0.902820 | + | 0.430019i | ||||
\(487\) | − | 1.39245e6i | − | 0.266047i | −0.991113 | − | 0.133024i | \(-0.957531\pi\) | ||
0.991113 | − | 0.133024i | \(-0.0424686\pi\) | |||||||
\(488\) | 3.78532e6 | + | 2.22948e6i | 0.719537 | + | 0.423792i | ||||
\(489\) | −2.36698e6 | + | 7.80381e6i | −0.447633 | + | 1.47582i | ||||
\(490\) | 3.66337e6 | − | 1.32137e6i | 0.689272 | − | 0.248619i | ||||
\(491\) | 1.82030e6 | 0.340753 | 0.170376 | − | 0.985379i | \(-0.445502\pi\) | ||||
0.170376 | + | 0.985379i | \(0.445502\pi\) | |||||||
\(492\) | 1.74881e6 | + | 4.16119e6i | 0.325710 | + | 0.775006i | ||||
\(493\) | −5.09728e6 | −0.944541 | ||||||||
\(494\) | −2.81061e6 | + | 1.01378e6i | −0.518182 | + | 0.186907i | ||||
\(495\) | 158808. | − | 237707.i | 0.0291313 | − | 0.0436043i | ||||
\(496\) | −3.69395e6 | − | 695506.i | −0.674198 | − | 0.126940i | ||||
\(497\) | − | 6.36286e6i | − | 1.15548i | ||||||
\(498\) | −8435.37 | − | 163071.i | −0.00152416 | − | 0.0294648i | ||||
\(499\) | − | 5.00674e6i | − | 0.900126i | −0.892997 | − | 0.450063i | \(-0.851401\pi\) | ||
0.892997 | − | 0.450063i | \(-0.148599\pi\) | |||||||
\(500\) | 3.60772e6 | + | 4.35038e6i | 0.645368 | + | 0.778219i | ||||
\(501\) | 7.84095e6 | + | 2.37824e6i | 1.39564 | + | 0.423313i | ||||
\(502\) | 2.71876e6 | + | 7.53751e6i | 0.481518 | + | 1.33496i | ||||
\(503\) | 6.04240e6 | 1.06485 | 0.532426 | − | 0.846477i | \(-0.321280\pi\) | ||||
0.532426 | + | 0.846477i | \(0.321280\pi\) | |||||||
\(504\) | 7.54965e6 | − | 3.64259e6i | 1.32389 | − | 0.638755i | ||||
\(505\) | 1.29414e6 | 0.225815 | ||||||||
\(506\) | −143053. | − | 396601.i | −0.0248382 | − | 0.0688617i | ||||
\(507\) | 3.19811e6 | + | 970019.i | 0.552552 | + | 0.167595i | ||||
\(508\) | −3.32790e6 | − | 4.01295e6i | −0.572151 | − | 0.689930i | ||||
\(509\) | − | 9.24427e6i | − | 1.58153i | −0.612118 | − | 0.790767i | \(-0.709682\pi\) | ||
0.612118 | − | 0.790767i | \(-0.290318\pi\) | |||||||
\(510\) | −205667. | − | 3.97593e6i | −0.0350139 | − | 0.676882i | ||||
\(511\) | − | 5.67548e6i | − | 0.961503i | ||||||
\(512\) | −154407. | + | 5.92963e6i | −0.0260311 | + | 0.999661i | ||||
\(513\) | 3.90414e6 | − | 3.20469e6i | 0.654985 | − | 0.537642i | ||||
\(514\) | 4.29976e6 | − | 1.55091e6i | 0.717855 | − | 0.258929i | ||||
\(515\) | −5.22851e6 | −0.868681 | ||||||||
\(516\) | 1.03382e6 | + | 2.45990e6i | 0.170930 | + | 0.406718i | ||||
\(517\) | 547141. | 0.0900270 | ||||||||
\(518\) | −1.23319e6 | + | 444809.i | −0.201932 | + | 0.0728365i | ||||
\(519\) | 762490. | − | 2.51389e6i | 0.124256 | − | 0.409665i | ||||
\(520\) | −1.28421e6 | + | 2.18041e6i | −0.208271 | + | 0.353614i | ||||
\(521\) | 7.94882e6i | 1.28295i | 0.767146 | + | 0.641473i | \(0.221676\pi\) | ||||
−0.767146 | + | 0.641473i | \(0.778324\pi\) | |||||||
\(522\) | −5.31631e6 | − | 1.31683e6i | −0.853953 | − | 0.211521i | ||||
\(523\) | − | 182966.i | − | 0.0292494i | −0.999893 | − | 0.0146247i | \(-0.995345\pi\) | ||
0.999893 | − | 0.0146247i | \(-0.00465535\pi\) | |||||||
\(524\) | −6.02120e6 | + | 4.99331e6i | −0.957977 | + | 0.794439i | ||||
\(525\) | −1.62060e6 | + | 5.34305e6i | −0.256613 | + | 0.846040i | ||||
\(526\) | 1.54465e6 | + | 4.28238e6i | 0.243425 | + | 0.674872i | ||||
\(527\) | −4.69608e6 | −0.736561 | ||||||||
\(528\) | −246004. | + | 471844.i | −0.0384023 | + | 0.0736570i | ||||
\(529\) | −1.43764e6 | −0.223362 | ||||||||
\(530\) | −783606. | − | 2.17247e6i | −0.121174 | − | 0.335942i | ||||
\(531\) | −8.61504e6 | − | 5.75556e6i | −1.32593 | − | 0.885832i | ||||
\(532\) | −6.25902e6 | + | 5.19053e6i | −0.958798 | + | 0.795120i | ||||
\(533\) | − | 3.58428e6i | − | 0.546492i | ||||||
\(534\) | 1.05794e7 | − | 547255.i | 1.60550 | − | 0.0830495i | ||||
\(535\) | − | 1.26537e6i | − | 0.191132i | ||||||
\(536\) | 1.83050e6 | − | 3.10791e6i | 0.275205 | − | 0.467258i | ||||
\(537\) | −1.02658e7 | − | 3.11371e6i | −1.53623 | − | 0.465953i | ||||
\(538\) | −2.30334e6 | + | 830811.i | −0.343086 | + | 0.123750i | ||||
\(539\) | −650299. | −0.0964142 | ||||||||
\(540\) | 812634. | − | 4.19991e6i | 0.119925 | − | 0.619805i | ||||
\(541\) | 7.40533e6 | 1.08781 | 0.543903 | − | 0.839148i | \(-0.316946\pi\) | ||||
0.543903 | + | 0.839148i | \(0.316946\pi\) | |||||||
\(542\) | −1.10544e6 | + | 398731.i | −0.161636 | + | 0.0583018i | ||||
\(543\) | −1.44036e6 | − | 436877.i | −0.209639 | − | 0.0635857i | ||||
\(544\) | 1.18115e6 | + | 7.31588e6i | 0.171123 | + | 1.05991i | ||||
\(545\) | − | 5.28304e6i | − | 0.761891i | ||||||
\(546\) | −6.64747e6 | + | 343862.i | −0.954278 | + | 0.0493631i | ||||
\(547\) | 5.88557e6i | 0.841047i | 0.907282 | + | 0.420523i | \(0.138154\pi\) | ||||
−0.907282 | + | 0.420523i | \(0.861846\pi\) | |||||||
\(548\) | −8.84487e6 | − | 1.06656e7i | −1.25817 | − | 1.51717i | ||||
\(549\) | 4.90362e6 | + | 3.27602e6i | 0.694362 | + | 0.463891i | ||||
\(550\) | −120261. | − | 333412.i | −0.0169519 | − | 0.0469975i | ||||
\(551\) | 5.31282e6 | 0.745497 | ||||||||
\(552\) | −4.27278e6 | − | 4.64178e6i | −0.596847 | − | 0.648391i | ||||
\(553\) | 4.99395e6 | 0.694434 | ||||||||
\(554\) | 3.25289e6 | + | 9.01832e6i | 0.450293 | + | 1.24839i | ||||
\(555\) | −194184. | + | 640217.i | −0.0267598 | + | 0.0882256i | ||||
\(556\) | −2.09650e6 | − | 2.52807e6i | −0.287612 | − | 0.346818i | ||||
\(557\) | 730413.i | 0.0997540i | 0.998755 | + | 0.0498770i | \(0.0158829\pi\) | ||||
−0.998755 | + | 0.0498770i | \(0.984117\pi\) | |||||||
\(558\) | −4.89787e6 | − | 1.21318e6i | −0.665920 | − | 0.164946i | ||||
\(559\) | − | 2.11886e6i | − | 0.286795i | ||||||
\(560\) | −1.27423e6 | + | 6.76764e6i | −0.171703 | + | 0.911942i | ||||
\(561\) | −192960. | + | 636181.i | −0.0258857 | + | 0.0853441i | ||||
\(562\) | 8.03460e6 | − | 2.89806e6i | 1.07306 | − | 0.387050i | ||||
\(563\) | −7.31154e6 | −0.972160 | −0.486080 | − | 0.873914i | \(-0.661574\pi\) | ||||
−0.486080 | + | 0.873914i | \(0.661574\pi\) | |||||||
\(564\) | 7.54786e6 | − | 3.17212e6i | 0.999140 | − | 0.419906i | ||||
\(565\) | 1.05806e6 | 0.139440 | ||||||||
\(566\) | 7.92793e6 | − | 2.85959e6i | 1.04020 | − | 0.375199i | ||||
\(567\) | 1.03955e7 | − | 4.30757e6i | 1.35796 | − | 0.562697i | ||||
\(568\) | 5.20798e6 | + | 3.06740e6i | 0.677327 | + | 0.398932i | ||||
\(569\) | 363173.i | 0.0470254i | 0.999724 | + | 0.0235127i | \(0.00748502\pi\) | ||||
−0.999724 | + | 0.0235127i | \(0.992515\pi\) | |||||||
\(570\) | 214364. | + | 4.14405e6i | 0.0276353 | + | 0.534242i | ||||
\(571\) | 4.63421e6i | 0.594820i | 0.954750 | + | 0.297410i | \(0.0961228\pi\) | ||||
−0.954750 | + | 0.297410i | \(0.903877\pi\) | |||||||
\(572\) | 325257. | − | 269732.i | 0.0415659 | − | 0.0344701i | ||||
\(573\) | −7.83405e6 | − | 2.37615e6i | −0.996781 | − | 0.302334i | ||||
\(574\) | −3.30966e6 | − | 9.17572e6i | −0.419280 | − | 1.16241i | ||||
\(575\) | 4.20228e6 | 0.530048 | ||||||||
\(576\) | −658071. | + | 7.93538e6i | −0.0826450 | + | 0.996579i | ||||
\(577\) | −9.36102e6 | −1.17053 | −0.585267 | − | 0.810841i | \(-0.699010\pi\) | ||||
−0.585267 | + | 0.810841i | \(0.699010\pi\) | |||||||
\(578\) | 416124. | + | 1.15366e6i | 0.0518088 | + | 0.143635i | ||||
\(579\) | −546074. | − | 165630.i | −0.0676948 | − | 0.0205325i | ||||
\(580\) | 3.46354e6 | − | 2.87227e6i | 0.427514 | − | 0.354532i | ||||
\(581\) | 352874.i | 0.0433690i | ||||||||
\(582\) | −344675. | − | 6.66320e6i | −0.0421796 | − | 0.815409i | ||||
\(583\) | 385644.i | 0.0469910i | ||||||||
\(584\) | 4.64537e6 | + | 2.73603e6i | 0.563622 | + | 0.331962i | ||||
\(585\) | −1.88704e6 | + | 2.82456e6i | −0.227977 | + | 0.341241i | ||||
\(586\) | 4.04285e6 | − | 1.45825e6i | 0.486344 | − | 0.175423i | ||||
\(587\) | 4.07722e6 | 0.488393 | 0.244196 | − | 0.969726i | \(-0.421476\pi\) | ||||
0.244196 | + | 0.969726i | \(0.421476\pi\) | |||||||
\(588\) | −8.97094e6 | + | 3.77019e6i | −1.07003 | + | 0.449697i | ||||
\(589\) | 4.89465e6 | 0.581345 | ||||||||
\(590\) | 8.00687e6 | − | 2.88806e6i | 0.946962 | − | 0.341567i | ||||
\(591\) | −4.09073e6 | + | 1.34869e7i | −0.481762 | + | 1.58835i | ||||
\(592\) | 230419. | − | 1.22380e6i | 0.0270218 | − | 0.143517i | ||||
\(593\) | 9.55091e6i | 1.11534i | 0.830062 | + | 0.557671i | \(0.188305\pi\) | ||||
−0.830062 | + | 0.557671i | \(0.811695\pi\) | |||||||
\(594\) | −365603. | + | 613669.i | −0.0425151 | + | 0.0713621i | ||||
\(595\) | 8.60362e6i | 0.996296i | ||||||||
\(596\) | −5.04700e6 | − | 6.08594e6i | −0.581992 | − | 0.701797i | ||||
\(597\) | 2.35297e6 | − | 7.75762e6i | 0.270196 | − | 0.890825i | ||||
\(598\) | 1.69983e6 | + | 4.71263e6i | 0.194381 | + | 0.538902i | ||||
\(599\) | 1.32333e7 | 1.50695 | 0.753477 | − | 0.657475i | \(-0.228375\pi\) | ||||
0.753477 | + | 0.657475i | \(0.228375\pi\) | |||||||
\(600\) | −3.59202e6 | − | 3.90223e6i | −0.407343 | − | 0.442522i | ||||
\(601\) | 275735. | 0.0311391 | 0.0155696 | − | 0.999879i | \(-0.495044\pi\) | ||||
0.0155696 | + | 0.999879i | \(0.495044\pi\) | |||||||
\(602\) | −1.95652e6 | − | 5.42425e6i | −0.220035 | − | 0.610027i | ||||
\(603\) | 2.68976e6 | − | 4.02608e6i | 0.301245 | − | 0.450910i | ||||
\(604\) | −5.65192e6 | − | 6.81538e6i | −0.630382 | − | 0.760147i | ||||
\(605\) | 5.64440e6i | 0.626945i | ||||||||
\(606\) | −3.22938e6 | + | 167050.i | −0.357221 | + | 0.0184784i | ||||
\(607\) | 7.63408e6i | 0.840978i | 0.907298 | + | 0.420489i | \(0.138141\pi\) | ||||
−0.907298 | + | 0.420489i | \(0.861859\pi\) | |||||||
\(608\) | −1.23110e6 | − | 7.62523e6i | −0.135062 | − | 0.836554i | ||||
\(609\) | 1.13264e7 | + | 3.43542e6i | 1.23751 | + | 0.375350i | ||||
\(610\) | −4.55745e6 | + | 1.64386e6i | −0.495904 | + | 0.178871i | ||||
\(611\) | −6.50142e6 | −0.704539 | ||||||||
\(612\) | 1.02644e6 | + | 9.89490e6i | 0.110778 | + | 1.06791i | ||||
\(613\) | −1.16844e7 | −1.25590 | −0.627952 | − | 0.778252i | \(-0.716107\pi\) | ||||
−0.627952 | + | 0.778252i | \(0.716107\pi\) | |||||||
\(614\) | −6.70948e6 | + | 2.42010e6i | −0.718237 | + | 0.259067i | ||||
\(615\) | −4.76362e6 | − | 1.44486e6i | −0.507866 | − | 0.154041i | ||||
\(616\) | 583590. | − | 990849.i | 0.0619663 | − | 0.105210i | ||||
\(617\) | 1.81938e6i | 0.192402i | 0.995362 | + | 0.0962011i | \(0.0306692\pi\) | ||||
−0.995362 | + | 0.0962011i | \(0.969331\pi\) | |||||||
\(618\) | 1.30471e7 | − | 674904.i | 1.37418 | − | 0.0710838i | ||||
\(619\) | − | 1.02220e7i | − | 1.07228i | −0.844129 | − | 0.536140i | \(-0.819882\pi\) | ||
0.844129 | − | 0.536140i | \(-0.180118\pi\) | |||||||
\(620\) | 3.19093e6 | − | 2.64620e6i | 0.333379 | − | 0.276467i | ||||
\(621\) | −5.37340e6 | − | 6.54618e6i | −0.559140 | − | 0.681176i | ||||
\(622\) | 1.78950e6 | + | 4.96121e6i | 0.185462 | + | 0.514176i | ||||
\(623\) | −2.28932e7 | −2.36312 | ||||||||
\(624\) | 2.92315e6 | − | 5.60671e6i | 0.300531 | − | 0.576430i | ||||
\(625\) | −359248. | −0.0367870 | ||||||||
\(626\) | −5.00462e6 | − | 1.38748e7i | −0.510429 | − | 1.41512i | ||||
\(627\) | 201120. | − | 663082.i | 0.0204308 | − | 0.0673594i | ||||
\(628\) | −248832. | + | 206353.i | −0.0251772 | + | 0.0208791i | ||||
\(629\) | − | 1.55580e6i | − | 0.156793i | ||||||
\(630\) | −2.22265e6 | + | 8.97332e6i | −0.223111 | + | 0.900745i | ||||
\(631\) | − | 1.08527e7i | − | 1.08509i | −0.840027 | − | 0.542545i | \(-0.817461\pi\) | ||
0.840027 | − | 0.542545i | \(-0.182539\pi\) | |||||||
\(632\) | −2.40747e6 | + | 4.08753e6i | −0.239755 | + | 0.407069i | ||||
\(633\) | 5.67176e6 | − | 1.86995e7i | 0.562612 | − | 1.85490i | ||||
\(634\) | −5.78845e6 | + | 2.08788e6i | −0.571925 | + | 0.206292i | ||||
\(635\) | 5.74944e6 | 0.565837 | ||||||||
\(636\) | 2.23582e6 | + | 5.32000e6i | 0.219177 | + | 0.521517i | ||||
\(637\) | 7.72720e6 | 0.754525 | ||||||||
\(638\) | −706780. | + | 254934.i | −0.0687436 | + | 0.0247957i | ||||
\(639\) | 6.74658e6 | + | 4.50727e6i | 0.653629 | + | 0.436678i | ||||
\(640\) | −4.92502e6 | − | 4.30548e6i | −0.475289 | − | 0.415501i | ||||
\(641\) | − | 397330.i | − | 0.0381949i | −0.999818 | − | 0.0190975i | \(-0.993921\pi\) | ||
0.999818 | − | 0.0190975i | \(-0.00607928\pi\) | |||||||
\(642\) | 163336. | + | 3.15758e6i | 0.0156402 | + | 0.302355i | ||||
\(643\) | − | 5.25770e6i | − | 0.501497i | −0.968052 | − | 0.250748i | \(-0.919323\pi\) | ||
0.968052 | − | 0.250748i | \(-0.0806767\pi\) | |||||||
\(644\) | 8.70312e6 | + | 1.04947e7i | 0.826914 | + | 0.997137i | ||||
\(645\) | −2.81603e6 | − | 854131.i | −0.266525 | − | 0.0808398i | ||||
\(646\) | −3.27419e6 | − | 9.07739e6i | −0.308690 | − | 0.855814i | ||||
\(647\) | −7.78890e6 | −0.731502 | −0.365751 | − | 0.930713i | \(-0.619188\pi\) | ||||
−0.365751 | + | 0.930713i | \(0.619188\pi\) | |||||||
\(648\) | −1.48570e6 | + | 1.05853e7i | −0.138993 | + | 0.990293i | ||||
\(649\) | −1.42133e6 | −0.132459 | ||||||||
\(650\) | 1.42901e6 | + | 3.96178e6i | 0.132663 | + | 0.367796i | ||||
\(651\) | 1.04349e7 | + | 3.16502e6i | 0.965021 | + | 0.292701i | ||||
\(652\) | 1.06861e7 | + | 1.28859e7i | 0.984466 | + | 1.18712i | ||||
\(653\) | 1.12506e7i | 1.03251i | 0.856435 | + | 0.516255i | \(0.172674\pi\) | ||||
−0.856435 | + | 0.516255i | \(0.827326\pi\) | |||||||
\(654\) | 681942. | + | 1.31832e7i | 0.0623452 | + | 1.20525i | ||||
\(655\) | − | 8.62670e6i | − | 0.785672i | ||||||
\(656\) | 9.10582e6 | + | 1.71447e6i | 0.826151 | + | 0.155550i | ||||
\(657\) | 6.01775e6 | + | 4.02035e6i | 0.543902 | + | 0.363371i | ||||
\(658\) | −1.66436e7 | + | 6.00330e6i | −1.49859 | + | 0.540537i | ||||
\(659\) | 437221. | 0.0392182 | 0.0196091 | − | 0.999808i | \(-0.493758\pi\) | ||||
0.0196091 | + | 0.999808i | \(0.493758\pi\) | |||||||
\(660\) | −227368. | − | 541009.i | −0.0203175 | − | 0.0483442i | ||||
\(661\) | −2.76418e6 | −0.246072 | −0.123036 | − | 0.992402i | \(-0.539263\pi\) | ||||
−0.123036 | + | 0.992402i | \(0.539263\pi\) | |||||||
\(662\) | −8.24364e6 | + | 2.97346e6i | −0.731095 | + | 0.263704i | ||||
\(663\) | 2.29286e6 | − | 7.55944e6i | 0.202578 | − | 0.667891i | ||||
\(664\) | −288826. | − | 170113.i | −0.0254224 | − | 0.0149733i | ||||
\(665\) | − | 8.96742e6i | − | 0.786346i | ||||||
\(666\) | 401924. | − | 1.62265e6i | 0.0351122 | − | 0.141755i | ||||
\(667\) | − | 8.90816e6i | − | 0.775306i | ||||||
\(668\) | 1.29472e7 | − | 1.07370e7i | 1.12263 | − | 0.930981i | ||||
\(669\) | −3.55313e6 | + | 1.17145e7i | −0.306934 | + | 1.01195i | ||||
\(670\) | 1.34968e6 | + | 3.74186e6i | 0.116157 | + | 0.322033i | ||||
\(671\) | 809010. | 0.0693661 | ||||||||
\(672\) | 2.30610e6 | − | 1.70523e7i | 0.196995 | − | 1.45667i | ||||
\(673\) | −4.40364e6 | −0.374778 | −0.187389 | − | 0.982286i | \(-0.560003\pi\) | ||||
−0.187389 | + | 0.982286i | \(0.560003\pi\) | |||||||
\(674\) | 2.37309e6 | + | 6.57917e6i | 0.201217 | + | 0.557855i | ||||
\(675\) | −4.51728e6 | − | 5.50320e6i | −0.381608 | − | 0.464896i | ||||
\(676\) | 5.28081e6 | − | 4.37932e6i | 0.444461 | − | 0.368587i | ||||
\(677\) | 1.33389e7i | 1.11853i | 0.828988 | + | 0.559267i | \(0.188917\pi\) | ||||
−0.828988 | + | 0.559267i | \(0.811083\pi\) | |||||||
\(678\) | −2.64025e6 | + | 136575.i | −0.220582 | + | 0.0114103i | ||||
\(679\) | 1.44187e7i | 1.20019i | ||||||||
\(680\) | −7.04203e6 | − | 4.14761e6i | −0.584018 | − | 0.343974i | ||||
\(681\) | 1.18311e6 | + | 358850.i | 0.0977593 | + | 0.0296514i | ||||
\(682\) | −651150. | + | 234868.i | −0.0536068 | + | 0.0193359i | ||||
\(683\) | 1.54515e7 | 1.26742 | 0.633709 | − | 0.773571i | \(-0.281532\pi\) | ||||
0.633709 | + | 0.773571i | \(0.281532\pi\) | |||||||
\(684\) | −1.06984e6 | − | 1.03133e7i | −0.0874336 | − | 0.842864i | ||||
\(685\) | 1.52808e7 | 1.24429 | ||||||||
\(686\) | 2.73853e6 | − | 987780.i | 0.222181 | − | 0.0801401i | ||||
\(687\) | −1.78571e7 | − | 5.41623e6i | −1.44350 | − | 0.437830i | ||||
\(688\) | 5.38293e6 | + | 1.01351e6i | 0.433558 | + | 0.0816314i | ||||
\(689\) | − | 4.58243e6i | − | 0.367745i | ||||||
\(690\) | 6.94845e6 | − | 359431.i | 0.555604 | − | 0.0287404i | ||||
\(691\) | 1.41207e7i | 1.12503i | 0.826789 | + | 0.562513i | \(0.190165\pi\) | ||||
−0.826789 | + | 0.562513i | \(0.809835\pi\) | |||||||
\(692\) | −3.44239e6 | − | 4.15101e6i | −0.273272 | − | 0.329525i | ||||
\(693\) | 857535. | − | 1.28358e6i | 0.0678295 | − | 0.101529i | ||||
\(694\) | −2.60523e6 | − | 7.22276e6i | −0.205328 | − | 0.569252i | ||||
\(695\) | 3.62202e6 | 0.284438 | ||||||||
\(696\) | −8.27209e6 | + | 7.61449e6i | −0.647280 | + | 0.595824i | ||||
\(697\) | 1.15761e7 | 0.902570 | ||||||||
\(698\) | −972990. | − | 2.69752e6i | −0.0755909 | − | 0.209569i | ||||
\(699\) | −3.09267e6 | + | 1.01964e7i | −0.239409 | + | 0.789320i | ||||
\(700\) | 7.31649e6 | + | 8.82261e6i | 0.564362 | + | 0.680537i | ||||
\(701\) | − | 1.80511e7i | − | 1.38743i | −0.720252 | − | 0.693713i | \(-0.755974\pi\) | ||
0.720252 | − | 0.693713i | \(-0.244026\pi\) | |||||||
\(702\) | 4.34429e6 | − | 7.29194e6i | 0.332718 | − | 0.558471i | ||||
\(703\) | 1.62158e6i | 0.123752i | ||||||||
\(704\) | 529671. | + | 955333.i | 0.0402786 | + | 0.0726479i | ||||
\(705\) | −2.62078e6 | + | 8.64059e6i | −0.198590 | + | 0.654743i | ||||
\(706\) | 9.50150e6 | − | 3.42717e6i | 0.717431 | − | 0.258776i | ||||
\(707\) | 6.98814e6 | 0.525791 | ||||||||
\(708\) | −1.96074e7 | + | 8.24035e6i | −1.47007 | + | 0.617820i | ||||
\(709\) | −1.76046e7 | −1.31526 | −0.657628 | − | 0.753343i | \(-0.728440\pi\) | ||||
−0.657628 | + | 0.753343i | \(0.728440\pi\) | |||||||
\(710\) | −6.27031e6 | + | 2.26169e6i | −0.466813 | + | 0.168378i | ||||
\(711\) | −3.53757e6 | + | 5.29511e6i | −0.262441 | + | 0.392827i | ||||
\(712\) | 1.10363e7 | − | 1.87380e7i | 0.815874 | − | 1.38523i | ||||
\(713\) | − | 8.20701e6i | − | 0.604590i | ||||||
\(714\) | −1.11057e6 | − | 2.14693e7i | −0.0815266 | − | 1.57606i | ||||
\(715\) | 466003.i | 0.0340897i | ||||||||
\(716\) | −1.69511e7 | + | 1.40574e7i | −1.23571 | + | 1.02476i | ||||
\(717\) | −1.74543e7 | − | 5.29406e6i | −1.26795 | − | 0.384584i | ||||
\(718\) | 3.44067e6 | + | 9.53893e6i | 0.249076 | + | 0.690540i | ||||
\(719\) | −1.00812e7 | −0.727259 | −0.363630 | − | 0.931544i | \(-0.618463\pi\) | ||||
−0.363630 | + | 0.931544i | \(0.618463\pi\) | |||||||
\(720\) | −6.27314e6 | − | 6.14508e6i | −0.450977 | − | 0.441770i | ||||
\(721\) | −2.82330e7 | −2.02264 | ||||||||
\(722\) | −1.33991e6 | − | 3.71478e6i | −0.0956608 | − | 0.265210i | ||||
\(723\) | 1.17956e7 | + | 3.57772e6i | 0.839215 | + | 0.254543i | ||||
\(724\) | −2.37837e6 | + | 1.97235e6i | −0.168629 | + | 0.139842i | ||||
\(725\) | − | 7.48885e6i | − | 0.529140i | ||||||
\(726\) | −728587. | − | 1.40849e7i | −0.0513026 | − | 0.991774i | ||||
\(727\) | 2.32781e7i | 1.63347i | 0.577013 | + | 0.816735i | \(0.304218\pi\) | ||||
−0.577013 | + | 0.816735i | \(0.695782\pi\) | |||||||
\(728\) | −6.93453e6 | + | 1.17738e7i | −0.484940 | + | 0.823357i | ||||
\(729\) | −2.79653e6 | + | 1.40738e7i | −0.194895 | + | 0.980824i | ||||
\(730\) | −5.59293e6 | + | 2.01736e6i | −0.388447 | + | 0.140112i | ||||
\(731\) | 6.84325e6 | 0.473663 | ||||||||
\(732\) | 1.11604e7 | − | 4.69034e6i | 0.769841 | − | 0.323539i | ||||
\(733\) | 2.69297e7 | 1.85128 | 0.925640 | − | 0.378405i | \(-0.123527\pi\) | ||||
0.925640 | + | 0.378405i | \(0.123527\pi\) | |||||||
\(734\) | 3.84035e6 | − | 1.38521e6i | 0.263106 | − | 0.0949017i | ||||
\(735\) | 3.11490e6 | − | 1.02697e7i | 0.212680 | − | 0.701195i | ||||
\(736\) | −1.27854e7 | + | 2.06422e6i | −0.870004 | + | 0.140463i | ||||
\(737\) | − | 664232.i | − | 0.0450455i | ||||||
\(738\) | 1.20736e7 | + | 2.99057e6i | 0.816007 | + | 0.202122i | ||||
\(739\) | − | 6.71268e6i | − | 0.452152i | −0.974110 | − | 0.226076i | \(-0.927410\pi\) | ||
0.974110 | − | 0.226076i | \(-0.0725898\pi\) | |||||||
\(740\) | 876679. | + | 1.05715e6i | 0.0588520 | + | 0.0709668i | ||||
\(741\) | −2.38981e6 | + | 7.87910e6i | −0.159889 | + | 0.527146i | ||||
\(742\) | −4.23133e6 | − | 1.17310e7i | −0.282142 | − | 0.782211i | ||||
\(743\) | −1.95647e7 | −1.30017 | −0.650087 | − | 0.759860i | \(-0.725268\pi\) | ||||
−0.650087 | + | 0.759860i | \(0.725268\pi\) | |||||||
\(744\) | −7.62101e6 | + | 7.01517e6i | −0.504754 | + | 0.464628i | ||||
\(745\) | 8.71944e6 | 0.575570 | ||||||||
\(746\) | 9.46896e6 | + | 2.62518e7i | 0.622953 | + | 1.72708i | ||||
\(747\) | −374155. | − | 249966.i | −0.0245329 | − | 0.0163900i | ||||
\(748\) | 871151. | + | 1.05048e6i | 0.0569298 | + | 0.0686490i | ||||
\(749\) | − | 6.83277e6i | − | 0.445033i | ||||||
\(750\) | 1.55534e7 | − | 804548.i | 1.00965 | − | 0.0522275i | ||||
\(751\) | 6.08953e6i | 0.393989i | 0.980405 | + | 0.196994i | \(0.0631180\pi\) | ||||
−0.980405 | + | 0.196994i | \(0.936882\pi\) | |||||||
\(752\) | 3.10982e6 | − | 1.65168e7i | 0.200535 | − | 1.06508i | ||||
\(753\) | 2.11302e7 | + | 6.40902e6i | 1.35805 | + | 0.411912i | ||||
\(754\) | 8.39833e6 | − | 3.02926e6i | 0.537978 | − | 0.194048i | ||||
\(755\) | 9.76454e6 | 0.623425 | ||||||||
\(756\) | 4.38808e6 | − | 2.26787e7i | 0.279235 | − | 1.44316i | ||||
\(757\) | 2.24957e7 | 1.42679 | 0.713396 | − | 0.700761i | \(-0.247156\pi\) | ||||
0.713396 | + | 0.700761i | \(0.247156\pi\) | |||||||
\(758\) | 2.00294e7 | − | 7.22457e6i | 1.26618 | − | 0.456708i | ||||
\(759\) | −1.11181e6 | − | 337223.i | −0.0700528 | − | 0.0212478i | ||||
\(760\) | 7.33981e6 | + | 4.32300e6i | 0.460947 | + | 0.271488i | ||||
\(761\) | 1.94840e7i | 1.21960i | 0.792555 | + | 0.609800i | \(0.208750\pi\) | ||||
−0.792555 | + | 0.609800i | \(0.791250\pi\) | |||||||
\(762\) | −1.43470e7 | + | 742146.i | −0.895107 | + | 0.0463022i | ||||
\(763\) | − | 2.85275e7i | − | 1.77399i | ||||||
\(764\) | −1.29358e7 | + | 1.07275e7i | −0.801789 | + | 0.664915i | ||||
\(765\) | −9.12247e6 | − | 6.09456e6i | −0.563584 | − | 0.376521i | ||||
\(766\) | 2.21171e6 | + | 6.13175e6i | 0.136193 | + | 0.377583i | ||||
\(767\) | 1.68890e7 | 1.03661 | ||||||||
\(768\) | 1.28455e7 | + | 1.01081e7i | 0.785868 | + | 0.618395i | ||||
\(769\) | −2.49302e7 | −1.52023 | −0.760117 | − | 0.649786i | \(-0.774858\pi\) | ||||
−0.760117 | + | 0.649786i | \(0.774858\pi\) | |||||||
\(770\) | 430299. | + | 1.19296e6i | 0.0261543 | + | 0.0725104i | ||||
\(771\) | 3.65602e6 | − | 1.20537e7i | 0.221499 | − | 0.730272i | ||||
\(772\) | −901694. | + | 747764.i | −0.0544523 | + | 0.0451566i | ||||
\(773\) | − | 3.44505e6i | − | 0.207370i | −0.994610 | − | 0.103685i | \(-0.966937\pi\) | ||
0.994610 | − | 0.103685i | \(-0.0330634\pi\) | |||||||
\(774\) | 7.13731e6 | + | 1.76788e6i | 0.428235 | + | 0.106072i | ||||
\(775\) | − | 6.89942e6i | − | 0.412628i | ||||||
\(776\) | −1.18017e7 | − | 6.95093e6i | −0.703540 | − | 0.414371i | ||||
\(777\) | −1.04856e6 | + | 3.45706e6i | −0.0623077 | + | 0.205425i | ||||
\(778\) | −2.28320e7 | + | 8.23546e6i | −1.35237 | + | 0.487797i | ||||
\(779\) | −1.20656e7 | −0.712370 | ||||||||
\(780\) | 2.70171e6 | + | 6.42856e6i | 0.159002 | + | 0.378335i | ||||
\(781\) | 1.11307e6 | 0.0652970 | ||||||||
\(782\) | −1.52203e7 | + | 5.48994e6i | −0.890035 | + | 0.321034i | ||||
\(783\) | −1.16659e7 | + | 9.57590e6i | −0.680008 | + | 0.558181i | ||||
\(784\) | −3.69614e6 | + | 1.96309e7i | −0.214763 | + | 1.14064i | ||||
\(785\) | − | 356506.i | − | 0.0206487i | ||||||
\(786\) | 1.11355e6 | + | 2.15269e7i | 0.0642913 | + | 1.24287i | ||||
\(787\) | − | 9.04481e6i | − | 0.520550i | −0.965534 | − | 0.260275i | \(-0.916187\pi\) | ||
0.965534 | − | 0.260275i | \(-0.0838133\pi\) | |||||||
\(788\) | 1.84683e7 | + | 2.22700e7i | 1.05952 | + | 1.27763i | ||||
\(789\) | 1.20050e7 | + | 3.64124e6i | 0.686546 | + | 0.208236i | ||||
\(790\) | −1.77510e6 | − | 4.92131e6i | −0.101194 | − | 0.280552i | ||||
\(791\) | 5.71331e6 | 0.324673 | ||||||||
\(792\) | 637205. | + | 1.32067e6i | 0.0360966 | + | 0.0748139i | ||||
\(793\) | −9.61309e6 | −0.542850 | ||||||||
\(794\) | −4.78041e6 | − | 1.32532e7i | −0.269100 | − | 0.746054i | ||||
\(795\) | −6.09019e6 | − | 1.84722e6i | −0.341754 | − | 0.103657i | ||||
\(796\) | −1.06229e7 | − | 1.28096e7i | −0.594236 | − | 0.716561i | ||||
\(797\) | − | 8.73525e6i | − | 0.487113i | −0.969887 | − | 0.243556i | \(-0.921686\pi\) | ||
0.969887 | − | 0.243556i | \(-0.0783141\pi\) | |||||||
\(798\) | 1.15753e6 | + | 2.23771e7i | 0.0643464 | + | 1.24393i | ||||
\(799\) | − | 2.09976e7i | − | 1.16360i | ||||||
\(800\) | −1.07484e7 | + | 1.73534e6i | −0.593771 | + | 0.0958648i | ||||
\(801\) | 1.62169e7 | − | 2.42738e7i | 0.893071 | − | 1.33677i | ||||
\(802\) | 5.40719e6 | − | 1.95036e6i | 0.296849 | − | 0.107073i | ||||
\(803\) | 992821. | 0.0543353 | ||||||||
\(804\) | −3.85097e6 | − | 9.16315e6i | −0.210102 | − | 0.499925i | ||||
\(805\) | −1.50359e7 | −0.817788 | ||||||||
\(806\) | 7.73732e6 | − | 2.79083e6i | 0.419520 | − | 0.151320i | ||||
\(807\) | −1.95849e6 | + | 6.45706e6i | −0.105862 | + | 0.349021i | ||||
\(808\) | −3.36883e6 | + | 5.71977e6i | −0.181531 | + | 0.308213i | ||||
\(809\) | − | 2.81254e7i | − | 1.51087i | −0.655222 | − | 0.755437i | \(-0.727425\pi\) | ||
0.655222 | − | 0.755437i | \(-0.272575\pi\) | |||||||
\(810\) | −7.94000e6 | − | 8.71314e6i | −0.425214 | − | 0.466619i | ||||
\(811\) | 3.13595e7i | 1.67424i | 0.547020 | + | 0.837119i | \(0.315762\pi\) | ||||
−0.547020 | + | 0.837119i | \(0.684238\pi\) | |||||||
\(812\) | 1.87025e7 | − | 1.55098e7i | 0.995427 | − | 0.825496i | ||||
\(813\) | −939941. | + | 3.09894e6i | −0.0498740 | + | 0.164432i | ||||
\(814\) | −77811.2 | − | 215724.i | −0.00411605 | − | 0.0114114i | ||||
\(815\) | −1.84619e7 | −0.973602 | ||||||||
\(816\) | 1.81079e7 | + | 9.44088e6i | 0.952014 | + | 0.496349i | ||||
\(817\) | −7.13262e6 | −0.373847 | ||||||||
\(818\) | −4.91349e6 | − | 1.36222e7i | −0.256748 | − | 0.711809i | ||||
\(819\) | −1.01897e7 | + | 1.52521e7i | −0.530825 | + | 0.794550i | ||||
\(820\) | −7.86584e6 | + | 6.52305e6i | −0.408517 | + | 0.338778i | ||||
\(821\) | 2.15360e7i | 1.11508i | 0.830149 | + | 0.557541i | \(0.188255\pi\) | ||||
−0.830149 | + | 0.557541i | \(0.811745\pi\) | |||||||
\(822\) | −3.81315e7 | + | 1.97247e6i | −1.96836 | + | 0.101820i | ||||
\(823\) | − | 3.44819e7i | − | 1.77456i | −0.461228 | − | 0.887282i | \(-0.652591\pi\) | ||
0.461228 | − | 0.887282i | \(-0.347409\pi\) | |||||||
\(824\) | 1.36105e7 | − | 2.31087e7i | 0.698324 | − | 1.18565i | ||||
\(825\) | −934669. | − | 283495.i | −0.0478105 | − | 0.0145014i | ||||
\(826\) | 4.32357e7 | − | 1.55950e7i | 2.20492 | − | 0.795308i | ||||
\(827\) | −4.02453e6 | −0.204622 | −0.102311 | − | 0.994752i | \(-0.532624\pi\) | ||||
−0.102311 | + | 0.994752i | \(0.532624\pi\) | |||||||
\(828\) | −1.72926e7 | + | 1.79383e6i | −0.876567 | + | 0.0909297i | ||||
\(829\) | 2.00981e7 | 1.01571 | 0.507855 | − | 0.861443i | \(-0.330439\pi\) | ||||
0.507855 | + | 0.861443i | \(0.330439\pi\) | |||||||
\(830\) | 347741. | − | 125430.i | 0.0175211 | − | 0.00631982i | ||||
\(831\) | 2.52815e7 | + | 7.66813e6i | 1.26999 | + | 0.385201i | ||||
\(832\) | −6.29384e6 | − | 1.13518e7i | −0.315215 | − | 0.568533i | ||||
\(833\) | 2.49565e7i | 1.24615i | ||||||||
\(834\) | −9.03830e6 | + | 467535.i | −0.449958 | + | 0.0232755i | ||||
\(835\) | 1.85497e7i | 0.920707i | ||||||||
\(836\) | −907988. | − | 1.09490e6i | −0.0449329 | − | 0.0541825i | ||||
\(837\) | −1.07477e7 | + | 8.82220e6i | −0.530276 | + | 0.435275i | ||||
\(838\) | 269008. | + | 745800.i | 0.0132329 | + | 0.0366870i | ||||
\(839\) | −870459. | −0.0426917 | −0.0213458 | − | 0.999772i | \(-0.506795\pi\) | ||||
−0.0213458 | + | 0.999772i | \(0.506795\pi\) | |||||||
\(840\) | 1.28524e7 | + | 1.39623e7i | 0.628471 | + | 0.682747i | ||||
\(841\) | 4.63599e6 | 0.226023 | ||||||||
\(842\) | 275956. | + | 765061.i | 0.0134140 | + | 0.0371891i | ||||
\(843\) | 6.83168e6 | − | 2.25237e7i | 0.331100 | − | 1.09162i | ||||
\(844\) | −2.56061e7 | − | 3.08772e7i | −1.23734 | − | 1.49205i | ||||
\(845\) | 7.56592e6i | 0.364519i | ||||||||
\(846\) | 5.42451e6 | − | 2.18999e7i | 0.260576 | − | 1.05200i | ||||
\(847\) | 3.04787e7i | 1.45978i | ||||||||
\(848\) | 1.16416e7 | + | 2.19191e6i | 0.555934 | + | 0.104672i | ||||
\(849\) | 6.74098e6 | − | 2.22247e7i | 0.320962 | − | 1.05820i | ||||
\(850\) | −1.27953e7 | + | 4.61525e6i | −0.607441 | + | 0.219103i | ||||
\(851\) | 2.71896e6 | 0.128700 | ||||||||
\(852\) | 1.53549e7 | − | 6.45315e6i | 0.724681 | − | 0.304560i | ||||
\(853\) | −2.81846e6 | −0.132629 | −0.0663145 | − | 0.997799i | \(-0.521124\pi\) | ||||
−0.0663145 | + | 0.997799i | \(0.521124\pi\) | |||||||
\(854\) | −2.46094e7 | + | 8.87656e6i | −1.15467 | + | 0.416486i | ||||
\(855\) | 9.50821e6 | + | 6.35227e6i | 0.444819 | + | 0.297176i | ||||
\(856\) | 5.59260e6 | + | 3.29393e6i | 0.260873 | + | 0.153649i | ||||
\(857\) | 3.15864e7i | 1.46909i | 0.678559 | + | 0.734545i | \(0.262605\pi\) | ||||
−0.678559 | + | 0.734545i | \(0.737395\pi\) | |||||||
\(858\) | −60152.3 | − | 1.16285e6i | −0.00278955 | − | 0.0539271i | ||||
\(859\) | 3.28617e7i | 1.51952i | 0.650202 | + | 0.759762i | \(0.274684\pi\) | ||||
−0.650202 | + | 0.759762i | \(0.725316\pi\) | |||||||
\(860\) | −4.64991e6 | + | 3.85612e6i | −0.214387 | + | 0.177789i | ||||
\(861\) | −2.57227e7 | − | 7.80197e6i | −1.18252 | − | 0.358671i | ||||
\(862\) | 1.21638e7 | + | 3.37228e7i | 0.557570 | + | 1.54581i | ||||
\(863\) | 3.88977e7 | 1.77786 | 0.888928 | − | 0.458047i | \(-0.151451\pi\) | ||||
0.888928 | + | 0.458047i | \(0.151451\pi\) | |||||||
\(864\) | 1.64471e7 | + | 1.45246e7i | 0.749557 | + | 0.661940i | ||||
\(865\) | 5.94724e6 | 0.270256 | ||||||||
\(866\) | −6.20555e6 | − | 1.72043e7i | −0.281181 | − | 0.779546i | ||||
\(867\) | 3.23412e6 | + | 980942.i | 0.146119 | + | 0.0443196i | ||||
\(868\) | 1.72305e7 | − | 1.42890e7i | 0.776242 | − | 0.643729i | ||||
\(869\) | 873599.i | 0.0392430i | ||||||||
\(870\) | −640538. | − | 1.23828e7i | −0.0286911 | − | 0.554651i | ||||
\(871\) | 7.89276e6i | 0.352520i | ||||||||
\(872\) | 2.33497e7 | + | 1.37525e7i | 1.03989 | + | 0.612477i | ||||
\(873\) | −1.52882e7 | − | 1.02138e7i | −0.678925 | − | 0.453578i | ||||
\(874\) | 1.58639e7 | − | 5.72208e6i | 0.702477 | − | 0.253382i | ||||
\(875\) | −3.36564e7 | −1.48610 | ||||||||
\(876\) | 1.36961e7 | − | 5.75602e6i | 0.603026 | − | 0.253432i | ||||
\(877\) | −2.60310e7 | −1.14286 | −0.571428 | − | 0.820652i | \(-0.693610\pi\) | ||||
−0.571428 | + | 0.820652i | \(0.693610\pi\) | |||||||
\(878\) | −2.29459e6 | + | 827654.i | −0.100454 | + | 0.0362337i | ||||
\(879\) | 3.43757e6 | − | 1.13335e7i | 0.150065 | − | 0.494757i | ||||
\(880\) | −1.18387e6 | − | 222903.i | −0.0515346 | − | 0.00970306i | ||||
\(881\) | − | 1.20174e7i | − | 0.521638i | −0.965388 | − | 0.260819i | \(-0.916007\pi\) | ||
0.965388 | − | 0.260819i | \(-0.0839926\pi\) | |||||||
\(882\) | −6.44724e6 | + | 2.60289e7i | −0.279063 | + | 1.12664i | ||||
\(883\) | − | 2.58606e7i | − | 1.11619i | −0.829778 | − | 0.558094i | \(-0.811533\pi\) | ||
0.829778 | − | 0.558094i | \(-0.188467\pi\) | |||||||
\(884\) | −1.03515e7 | − | 1.24824e7i | −0.445525 | − | 0.537238i | ||||
\(885\) | 6.80811e6 | − | 2.24460e7i | 0.292192 | − | 0.963343i | ||||
\(886\) | −3.10960e6 | − | 8.62106e6i | −0.133082 | − | 0.368957i | ||||
\(887\) | 7.77528e6 | 0.331824 | 0.165912 | − | 0.986141i | \(-0.446943\pi\) | ||||
0.165912 | + | 0.986141i | \(0.446943\pi\) | |||||||
\(888\) | −2.32410e6 | − | 2.52482e6i | −0.0989061 | − | 0.107448i | ||||
\(889\) | 3.10459e7 | 1.31750 | ||||||||
\(890\) | 8.13740e6 | + | 2.25602e7i | 0.344358 | + | 0.954701i | ||||
\(891\) | 753530. | + | 1.81850e6i | 0.0317985 | + | 0.0767395i | ||||
\(892\) | 1.60412e7 | + | 1.93433e7i | 0.675032 | + | 0.813990i | ||||
\(893\) | 2.18855e7i | 0.918390i | ||||||||
\(894\) | −2.17583e7 | + | 1.12552e6i | −0.910503 | + | 0.0470987i | ||||
\(895\) | − | 2.42862e7i | − | 1.01345i | ||||||
\(896\) | −2.65942e7 | − | 2.32488e7i | −1.10667 | − | 0.967456i | ||||
\(897\) | 1.32111e7 | + | 4.00707e6i | 0.548224 | + | 0.166282i | ||||
\(898\) | 4.16409e6 | − | 1.50198e6i | 0.172318 | − | 0.0621546i | ||||
\(899\) | −1.46257e7 | −0.603554 | ||||||||
\(900\) | −1.45375e7 | + | 1.50803e6i | −0.598249 | + | 0.0620587i | ||||
\(901\) | 1.47998e7 | 0.607357 | ||||||||
\(902\) | 1.60512e6 | − | 578965.i | 0.0656890 | − | 0.0236939i | ||||
\(903\) | −1.52060e7 | − | 4.61215e6i | −0.620579 | − | 0.188228i | ||||
\(904\) | −2.75426e6 | + | 4.67633e6i | −0.112094 | + | 0.190320i | ||||
\(905\) | − | 3.40753e6i | − | 0.138299i | ||||||
\(906\) | −2.43662e7 | + | 1.26042e6i | −0.986206 | + | 0.0510146i | ||||
\(907\) | 7.84270e6i | 0.316554i | 0.987395 | + | 0.158277i | \(0.0505938\pi\) | ||||
−0.987395 | + | 0.158277i | \(0.949406\pi\) | |||||||
\(908\) | 1.95359e6 | − | 1.62009e6i | 0.0786355 | − | 0.0652115i | ||||
\(909\) | −4.95020e6 | + | 7.40957e6i | −0.198707 | + | 0.297429i | ||||
\(910\) | −5.11304e6 | − | 1.41754e7i | −0.204680 | − | 0.567457i | ||||
\(911\) | −1.38954e7 | −0.554721 | −0.277360 | − | 0.960766i | \(-0.589460\pi\) | ||||
−0.277360 | + | 0.960766i | \(0.589460\pi\) | |||||||
\(912\) | −1.88736e7 | − | 9.84009e6i | −0.751395 | − | 0.391753i | ||||
\(913\) | −61728.8 | −0.00245082 | ||||||||
\(914\) | −7.38994e6 | − | 2.04879e7i | −0.292601 | − | 0.811208i | ||||
\(915\) | −3.87512e6 | + | 1.27761e7i | −0.153015 | + | 0.504482i | ||||
\(916\) | −2.94861e7 | + | 2.44525e7i | −1.16112 | + | 0.962907i | ||||
\(917\) | − | 4.65826e7i | − | 1.82937i | ||||||
\(918\) | 2.35507e7 | + | 1.40307e7i | 0.922353 | + | 0.549506i | ||||
\(919\) | 1.73363e6i | 0.0677124i | 0.999427 | + | 0.0338562i | \(0.0107788\pi\) | ||||
−0.999427 | + | 0.0338562i | \(0.989221\pi\) | |||||||
\(920\) | 7.24850e6 | − | 1.23069e7i | 0.282344 | − | 0.479378i | ||||
\(921\) | −5.70496e6 | + | 1.88090e7i | −0.221617 | + | 0.730662i | ||||
\(922\) | −1.20442e7 | + | 4.34432e6i | −0.466607 | + | 0.168304i | ||||
\(923\) | −1.32260e7 | −0.511006 | ||||||||
\(924\) | −1.22775e6 | − | 2.92135e6i | −0.0473075 | − | 0.112565i | ||||
\(925\) | 2.28576e6 | 0.0878366 | ||||||||
\(926\) | 3.99652e7 | − | 1.44154e7i | 1.53163 | − | 0.552457i | ||||
\(927\) | 1.99995e7 | − | 2.99357e7i | 0.764398 | − | 1.14417i | ||||
\(928\) | 3.67863e6 | + | 2.27849e7i | 0.140222 | + | 0.868513i | ||||
\(929\) | − | 2.75393e6i | − | 0.104692i | −0.998629 | − | 0.0523460i | \(-0.983330\pi\) | ||
0.998629 | − | 0.0523460i | \(-0.0166699\pi\) | |||||||
\(930\) | −590123. | − | 1.14082e7i | −0.0223736 | − | 0.432522i | ||||
\(931\) | − | 2.60118e7i | − | 0.983548i | ||||||
\(932\) | 1.39624e7 | + | 1.68366e7i | 0.526526 | + | 0.634913i | ||||
\(933\) | 1.39080e7 | + | 4.21843e6i | 0.523070 | + | 0.158653i | ||||
\(934\) | 1.10229e7 | + | 3.05599e7i | 0.413455 | + | 1.14626i | ||||
\(935\) | −1.50504e6 | −0.0563015 | ||||||||
\(936\) | −7.57161e6 | − | 1.56930e7i | −0.282487 | − | 0.585484i | ||||
\(937\) | −2.15099e7 | −0.800367 | −0.400183 | − | 0.916435i | \(-0.631054\pi\) | ||||
−0.400183 | + | 0.916435i | \(0.631054\pi\) | |||||||
\(938\) | 7.28804e6 | + | 2.02054e7i | 0.270460 | + | 0.749826i | ||||
\(939\) | −3.88960e7 | − | 1.17975e7i | −1.43960 | − | 0.436644i | ||||
\(940\) | 1.18320e7 | + | 1.42676e7i | 0.436754 | + | 0.526661i | ||||
\(941\) | 2.36563e7i | 0.870907i | 0.900211 | + | 0.435454i | \(0.143412\pi\) | ||||
−0.900211 | + | 0.435454i | \(0.856588\pi\) | |||||||
\(942\) | 46018.3 | + | 889618.i | 0.00168968 | + | 0.0326645i | ||||
\(943\) | 2.02308e7i | 0.740855i | ||||||||
\(944\) | −8.07850e6 | + | 4.29063e7i | −0.295053 | + | 1.56708i | ||||
\(945\) | 1.61630e7 | + | 1.96907e7i | 0.588767 | + | 0.717268i | ||||
\(946\) | 948874. | − | 342257.i | 0.0344731 | − | 0.0124344i | ||||
\(947\) | 3.42431e6 | 0.124079 | 0.0620396 | − | 0.998074i | \(-0.480240\pi\) | ||||
0.0620396 | + | 0.998074i | \(0.480240\pi\) | |||||||
\(948\) | 5.06481e6 | + | 1.20514e7i | 0.183038 | + | 0.435528i | ||||
\(949\) | −1.17972e7 | −0.425221 | ||||||||
\(950\) | 1.33364e7 | − | 4.81041e6i | 0.479434 | − | 0.172931i | ||||
\(951\) | −4.92182e6 | + | 1.62270e7i | −0.176471 | + | 0.581818i | ||||
\(952\) | −3.80257e7 | − | 2.23964e7i | −1.35983 | − | 0.800913i | ||||
\(953\) | − | 3.22434e7i | − | 1.15003i | −0.818143 | − | 0.575014i | \(-0.804996\pi\) | ||
0.818143 | − | 0.575014i | \(-0.195004\pi\) | |||||||
\(954\) | 1.54358e7 | + | 3.82338e6i | 0.549108 | + | 0.136012i | ||||
\(955\) | − | 1.85334e7i | − | 0.657577i | ||||||
\(956\) | −2.88210e7 | + | 2.39009e7i | −1.01992 | + | 0.845804i | ||||
\(957\) | −600963. | + | 1.98135e6i | −0.0212113 | + | 0.0699327i | ||||
\(958\) | −1.28849e7 | − | 3.57221e7i | −0.453593 | − | 1.25754i | ||||
\(959\) | 8.25138e7 | 2.89721 | ||||||||
\(960\) | −1.76240e7 | + | 3.78870e6i | −0.617200 | + | 0.132682i | ||||
\(961\) | 1.51547e7 | 0.529344 | ||||||||
\(962\) | 924595. | + | 2.56335e6i | 0.0322117 | + | 0.0893038i | ||||
\(963\) | 7.24483e6 | + | 4.84014e6i | 0.251746 | + | 0.168187i | ||||
\(964\) | 1.94772e7 | − | 1.61522e7i | 0.675047 | − | 0.559809i | ||||
\(965\) | − | 1.29188e6i | − | 0.0446583i | ||||||
\(966\) | 3.75204e7 | − | 1.94086e6i | 1.29367 | − | 0.0669193i | ||||
\(967\) | − | 2.68972e7i | − | 0.924998i | −0.886620 | − | 0.462499i | \(-0.846953\pi\) | ||
0.886620 | − | 0.462499i | \(-0.153047\pi\) | |||||||
\(968\) | −2.49468e7 | − | 1.46931e7i | −0.855708 | − | 0.503995i | ||||
\(969\) | −2.54470e7 | − | 7.71835e6i | −0.870618 | − | 0.264068i | ||||
\(970\) | 1.42090e7 | − | 5.12514e6i | 0.484879 | − | 0.174895i | ||||
\(971\) | −4.53191e6 | −0.154253 | −0.0771264 | − | 0.997021i | \(-0.524574\pi\) | ||||
−0.0771264 | + | 0.997021i | \(0.524574\pi\) | |||||||
\(972\) | 2.09380e7 | + | 2.07177e7i | 0.710837 | + | 0.703357i | ||||
\(973\) | 1.95582e7 | 0.662289 | ||||||||
\(974\) | −7.40964e6 | + | 2.67264e6i | −0.250265 | + | 0.0902699i | ||||
\(975\) | 1.11062e7 | + | 3.36864e6i | 0.374158 | + | 0.113486i | ||||
\(976\) | 4.59822e6 | − | 2.44219e7i | 0.154513 | − | 0.820645i | ||||
\(977\) | − | 1.54207e7i | − | 0.516853i | −0.966031 | − | 0.258426i | \(-0.916796\pi\) | ||
0.966031 | − | 0.258426i | \(-0.0832039\pi\) | |||||||
\(978\) | 4.60694e7 | − | 2.38308e6i | 1.54016 | − | 0.0796695i | ||||
\(979\) | − | 4.00474e6i | − | 0.133542i | ||||||
\(980\) | −1.40628e7 | − | 1.69576e7i | −0.467741 | − | 0.564027i | ||||
\(981\) | 3.02479e7 | + | 2.02081e7i | 1.00351 | + | 0.670428i | ||||
\(982\) | −3.49384e6 | − | 9.68632e6i | −0.115618 | − | 0.320539i | ||||
\(983\) | −2.15180e7 | −0.710263 | −0.355131 | − | 0.934816i | \(-0.615564\pi\) | ||||
−0.355131 | + | 0.934816i | \(0.615564\pi\) | |||||||
\(984\) | 1.87862e7 | − | 1.72928e7i | 0.618518 | − | 0.569348i | ||||
\(985\) | −3.19067e7 | −1.04783 | ||||||||
\(986\) | 9.78358e6 | + | 2.71240e7i | 0.320483 | + | 0.888509i | ||||
\(987\) | −1.41518e7 | + | 4.66577e7i | −0.462399 | + | 1.52451i | ||||
\(988\) | 1.07892e7 | + | 1.30102e7i | 0.351639 | + | 0.424025i | ||||
\(989\) | 1.19595e7i | 0.388796i | ||||||||
\(990\) | −1.56972e6 | − | 388813.i | −0.0509018 | − | 0.0126082i | ||||
\(991\) | 1.65100e7i | 0.534028i | 0.963693 | + | 0.267014i | \(0.0860370\pi\) | ||||
−0.963693 | + | 0.267014i | \(0.913963\pi\) | |||||||
\(992\) | 3.38909e6 | + | 2.09915e7i | 0.109346 | + | 0.677274i | ||||
\(993\) | −7.00943e6 | + | 2.31098e7i | −0.225585 | + | 0.743742i | ||||
\(994\) | −3.38586e7 | + | 1.22127e7i | −1.08693 | + | 0.392054i | ||||
\(995\) | 1.83526e7 | 0.587678 | ||||||||
\(996\) | −851556. | + | 357881.i | −0.0271997 | + | 0.0114312i | ||||
\(997\) | −1.65409e7 | −0.527012 | −0.263506 | − | 0.964658i | \(-0.584879\pi\) | ||||
−0.263506 | + | 0.964658i | \(0.584879\pi\) | |||||||
\(998\) | −2.66422e7 | + | 9.60980e6i | −0.846729 | + | 0.305413i | ||||
\(999\) | −2.92277e6 | − | 3.56068e6i | −0.0926575 | − | 0.112881i |
(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 | 12.6.b.a.11.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 12.6.b.a.11.6 | yes | 8 | |
4.3 | odd | 2 | inner | 12.6.b.a.11.5 | yes | 8 | |
8.3 | odd | 2 | 192.6.c.e.191.1 | 8 | |||
8.5 | even | 2 | 192.6.c.e.191.8 | 8 | |||
12.11 | even | 2 | inner | 12.6.b.a.11.4 | yes | 8 | |
24.5 | odd | 2 | 192.6.c.e.191.2 | 8 | |||
24.11 | even | 2 | 192.6.c.e.191.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
12.6.b.a.11.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
12.6.b.a.11.4 | yes | 8 | 12.11 | even | 2 | inner | |
12.6.b.a.11.5 | yes | 8 | 4.3 | odd | 2 | inner | |
12.6.b.a.11.6 | yes | 8 | 3.2 | odd | 2 | inner | |
192.6.c.e.191.1 | 8 | 8.3 | odd | 2 | |||
192.6.c.e.191.2 | 8 | 24.5 | odd | 2 | |||
192.6.c.e.191.7 | 8 | 24.11 | even | 2 | |||
192.6.c.e.191.8 | 8 | 8.5 | even | 2 |