Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,6,Mod(75,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, 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("76.75");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.d (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: | \(12.1891703058\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 75.18 | ||
Character | \(\chi\) | \(=\) | 76.75 |
Dual form | 76.6.d.a.75.17 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.99929 | + | 4.79628i | −0.530204 | + | 0.847870i | ||||
\(3\) | −24.6139 | −1.57898 | −0.789492 | − | 0.613760i | \(-0.789656\pi\) | ||||
−0.789492 | + | 0.613760i | \(0.789656\pi\) | |||||||
\(4\) | −14.0085 | − | 28.7708i | −0.437767 | − | 0.899089i | ||||
\(5\) | 37.3653 | 0.668411 | 0.334205 | − | 0.942500i | \(-0.391532\pi\) | ||||
0.334205 | + | 0.942500i | \(0.391532\pi\) | |||||||
\(6\) | 73.8243 | − | 118.055i | 0.837185 | − | 1.33877i | ||||
\(7\) | − | 35.5589i | − | 0.274286i | −0.990551 | − | 0.137143i | \(-0.956208\pi\) | ||
0.990551 | − | 0.137143i | \(-0.0437920\pi\) | |||||||
\(8\) | 180.009 | + | 19.1033i | 0.994416 | + | 0.105532i | ||||
\(9\) | 362.846 | 1.49319 | ||||||||
\(10\) | −112.069 | + | 179.214i | −0.354394 | + | 0.566725i | ||||
\(11\) | − | 184.937i | − | 0.460831i | −0.973092 | − | 0.230415i | \(-0.925992\pi\) | ||
0.973092 | − | 0.230415i | \(-0.0740085\pi\) | |||||||
\(12\) | 344.805 | + | 708.163i | 0.691227 | + | 1.41965i | ||||
\(13\) | − | 119.283i | − | 0.195759i | −0.995198 | − | 0.0978793i | \(-0.968794\pi\) | ||
0.995198 | − | 0.0978793i | \(-0.0312059\pi\) | |||||||
\(14\) | 170.551 | + | 106.652i | 0.232559 | + | 0.145428i | ||||
\(15\) | −919.707 | −1.05541 | ||||||||
\(16\) | −631.522 | + | 806.074i | −0.616721 | + | 0.787182i | ||||
\(17\) | 152.741 | 0.128184 | 0.0640919 | − | 0.997944i | \(-0.479585\pi\) | ||||
0.0640919 | + | 0.997944i | \(0.479585\pi\) | |||||||
\(18\) | −1088.28 | + | 1740.31i | −0.791697 | + | 1.26603i | ||||
\(19\) | −1458.65 | + | 590.280i | −0.926975 | + | 0.375123i | ||||
\(20\) | −523.433 | − | 1075.03i | −0.292608 | − | 0.600960i | ||||
\(21\) | 875.246i | 0.433093i | ||||||||
\(22\) | 887.008 | + | 554.679i | 0.390725 | + | 0.244335i | ||||
\(23\) | 1580.72i | 0.623067i | 0.950235 | + | 0.311534i | \(0.100843\pi\) | ||||
−0.950235 | + | 0.311534i | \(0.899157\pi\) | |||||||
\(24\) | −4430.72 | − | 470.206i | −1.57017 | − | 0.166633i | ||||
\(25\) | −1728.83 | −0.553227 | ||||||||
\(26\) | 572.115 | + | 357.765i | 0.165978 | + | 0.103792i | ||||
\(27\) | −2949.87 | −0.778743 | ||||||||
\(28\) | −1023.06 | + | 498.129i | −0.246607 | + | 0.120073i | ||||
\(29\) | − | 54.3855i | − | 0.0120085i | −0.999982 | − | 0.00600425i | \(-0.998089\pi\) | ||
0.999982 | − | 0.00600425i | \(-0.00191122\pi\) | |||||||
\(30\) | 2758.47 | − | 4411.17i | 0.559583 | − | 0.894850i | ||||
\(31\) | 4260.92 | 0.796342 | 0.398171 | − | 0.917311i | \(-0.369645\pi\) | ||||
0.398171 | + | 0.917311i | \(0.369645\pi\) | |||||||
\(32\) | −1972.04 | − | 5446.60i | −0.340440 | − | 0.940266i | ||||
\(33\) | 4552.02i | 0.727645i | ||||||||
\(34\) | −458.114 | + | 732.588i | −0.0679636 | + | 0.108683i | ||||
\(35\) | − | 1328.67i | − | 0.183336i | ||||||
\(36\) | −5082.94 | − | 10439.4i | −0.653670 | − | 1.34251i | ||||
\(37\) | 12169.2i | 1.46136i | 0.682722 | + | 0.730678i | \(0.260796\pi\) | ||||
−0.682722 | + | 0.730678i | \(0.739204\pi\) | |||||||
\(38\) | 1543.78 | − | 8766.52i | 0.173431 | − | 0.984846i | ||||
\(39\) | 2936.03i | 0.309100i | ||||||||
\(40\) | 6726.07 | + | 713.799i | 0.664678 | + | 0.0705385i | ||||
\(41\) | 5665.34i | 0.526340i | 0.964749 | + | 0.263170i | \(0.0847680\pi\) | ||||
−0.964749 | + | 0.263170i | \(0.915232\pi\) | |||||||
\(42\) | −4197.92 | − | 2625.11i | −0.367207 | − | 0.229628i | ||||
\(43\) | 19239.7i | 1.58682i | 0.608690 | + | 0.793408i | \(0.291695\pi\) | ||||
−0.608690 | + | 0.793408i | \(0.708305\pi\) | |||||||
\(44\) | −5320.78 | + | 2590.69i | −0.414328 | + | 0.201736i | ||||
\(45\) | 13557.8 | 0.998066 | ||||||||
\(46\) | −7581.56 | − | 4741.03i | −0.528280 | − | 0.330353i | ||||
\(47\) | 26623.3i | 1.75799i | 0.476828 | + | 0.878997i | \(0.341787\pi\) | ||||
−0.476828 | + | 0.878997i | \(0.658213\pi\) | |||||||
\(48\) | 15544.2 | − | 19840.7i | 0.973793 | − | 1.24295i | ||||
\(49\) | 15542.6 | 0.924767 | ||||||||
\(50\) | 5185.28 | − | 8291.97i | 0.293323 | − | 0.469065i | ||||
\(51\) | −3759.56 | −0.202400 | ||||||||
\(52\) | −3431.88 | + | 1670.98i | −0.176004 | + | 0.0856965i | ||||
\(53\) | − | 29445.2i | − | 1.43988i | −0.694038 | − | 0.719938i | \(-0.744170\pi\) | ||
0.694038 | − | 0.719938i | \(-0.255830\pi\) | |||||||
\(54\) | 8847.53 | − | 14148.4i | 0.412893 | − | 0.660273i | ||||
\(55\) | − | 6910.22i | − | 0.308024i | ||||||
\(56\) | 679.292 | − | 6400.91i | 0.0289459 | − | 0.272754i | ||||
\(57\) | 35903.2 | − | 14529.1i | 1.46368 | − | 0.592314i | ||||
\(58\) | 260.848 | + | 163.118i | 0.0101816 | + | 0.00636695i | ||||
\(59\) | −22874.8 | −0.855516 | −0.427758 | − | 0.903893i | \(-0.640696\pi\) | ||||
−0.427758 | + | 0.903893i | \(0.640696\pi\) | |||||||
\(60\) | 12883.7 | + | 26460.7i | 0.462023 | + | 0.948907i | ||||
\(61\) | −31754.3 | −1.09264 | −0.546320 | − | 0.837576i | \(-0.683972\pi\) | ||||
−0.546320 | + | 0.837576i | \(0.683972\pi\) | |||||||
\(62\) | −12779.7 | + | 20436.6i | −0.422224 | + | 0.675194i | ||||
\(63\) | − | 12902.4i | − | 0.409562i | ||||||
\(64\) | 32038.1 | + | 6877.50i | 0.977726 | + | 0.209885i | ||||
\(65\) | − | 4457.05i | − | 0.130847i | ||||||
\(66\) | −21832.7 | − | 13652.8i | −0.616948 | − | 0.385800i | ||||
\(67\) | 21754.5 | 0.592055 | 0.296028 | − | 0.955179i | \(-0.404338\pi\) | ||||
0.296028 | + | 0.955179i | \(0.404338\pi\) | |||||||
\(68\) | −2139.68 | − | 4394.49i | −0.0561146 | − | 0.115249i | ||||
\(69\) | − | 38907.7i | − | 0.983813i | ||||||
\(70\) | 6372.67 | + | 3985.07i | 0.155445 | + | 0.0972054i | ||||
\(71\) | −12897.9 | −0.303651 | −0.151825 | − | 0.988407i | \(-0.548515\pi\) | ||||
−0.151825 | + | 0.988407i | \(0.548515\pi\) | |||||||
\(72\) | 65315.3 | + | 6931.54i | 1.48485 | + | 0.157579i | ||||
\(73\) | 33382.4 | 0.733181 | 0.366590 | − | 0.930382i | \(-0.380525\pi\) | ||||
0.366590 | + | 0.930382i | \(0.380525\pi\) | |||||||
\(74\) | −58366.7 | − | 36498.8i | −1.23904 | − | 0.774818i | ||||
\(75\) | 42553.4 | 0.873537 | ||||||||
\(76\) | 37416.4 | + | 33697.7i | 0.743068 | + | 0.669216i | ||||
\(77\) | −6576.16 | −0.126399 | ||||||||
\(78\) | −14082.0 | − | 8805.99i | −0.262076 | − | 0.163886i | ||||
\(79\) | −57062.3 | −1.02868 | −0.514342 | − | 0.857585i | \(-0.671964\pi\) | ||||
−0.514342 | + | 0.857585i | \(0.671964\pi\) | |||||||
\(80\) | −23597.0 | + | 30119.2i | −0.412223 | + | 0.526161i | ||||
\(81\) | −15563.5 | −0.263569 | ||||||||
\(82\) | −27172.5 | − | 16992.0i | −0.446268 | − | 0.279068i | ||||
\(83\) | 14789.3i | 0.235641i | 0.993035 | + | 0.117821i | \(0.0375908\pi\) | ||||
−0.993035 | + | 0.117821i | \(0.962409\pi\) | |||||||
\(84\) | 25181.5 | − | 12260.9i | 0.389389 | − | 0.189594i | ||||
\(85\) | 5707.21 | 0.0856794 | ||||||||
\(86\) | −92278.8 | − | 57705.3i | −1.34541 | − | 0.841337i | ||||
\(87\) | 1338.64i | 0.0189612i | ||||||||
\(88\) | 3532.90 | − | 33290.2i | 0.0486322 | − | 0.458258i | ||||
\(89\) | 138076.i | 1.84775i | 0.382694 | + | 0.923875i | \(0.374996\pi\) | ||||
−0.382694 | + | 0.923875i | \(0.625004\pi\) | |||||||
\(90\) | −40663.9 | + | 65027.1i | −0.529179 | + | 0.846230i | ||||
\(91\) | −4241.58 | −0.0536938 | ||||||||
\(92\) | 45478.6 | − | 22143.5i | 0.560193 | − | 0.272758i | ||||
\(93\) | −104878. | −1.25741 | ||||||||
\(94\) | −127693. | − | 79851.0i | −1.49055 | − | 0.932096i | ||||
\(95\) | −54503.0 | + | 22056.0i | −0.619600 | + | 0.250736i | ||||
\(96\) | 48539.6 | + | 134062.i | 0.537549 | + | 1.48467i | ||||
\(97\) | − | 34257.8i | − | 0.369684i | −0.982768 | − | 0.184842i | \(-0.940823\pi\) | ||
0.982768 | − | 0.184842i | \(-0.0591773\pi\) | |||||||
\(98\) | −46616.6 | + | 74546.4i | −0.490316 | + | 0.784082i | ||||
\(99\) | − | 67103.5i | − | 0.688109i | ||||||
\(100\) | 24218.4 | + | 49740.0i | 0.242184 | + | 0.497400i | ||||
\(101\) | −112359. | −1.09598 | −0.547992 | − | 0.836483i | \(-0.684608\pi\) | ||||
−0.547992 | + | 0.836483i | \(0.684608\pi\) | |||||||
\(102\) | 11276.0 | − | 18031.9i | 0.107314 | − | 0.171609i | ||||
\(103\) | 116233. | 1.07953 | 0.539765 | − | 0.841816i | \(-0.318513\pi\) | ||||
0.539765 | + | 0.841816i | \(0.318513\pi\) | |||||||
\(104\) | 2278.70 | − | 21472.0i | 0.0206587 | − | 0.194665i | ||||
\(105\) | 32703.8i | 0.289484i | ||||||||
\(106\) | 141227. | + | 88314.7i | 1.22083 | + | 0.763429i | ||||
\(107\) | 129398. | 1.09262 | 0.546311 | − | 0.837583i | \(-0.316032\pi\) | ||||
0.546311 | + | 0.837583i | \(0.316032\pi\) | |||||||
\(108\) | 41323.4 | + | 84870.4i | 0.340908 | + | 0.700159i | ||||
\(109\) | 123459.i | 0.995303i | 0.867377 | + | 0.497652i | \(0.165804\pi\) | ||||
−0.867377 | + | 0.497652i | \(0.834196\pi\) | |||||||
\(110\) | 33143.3 | + | 20725.7i | 0.261164 | + | 0.163316i | ||||
\(111\) | − | 299531.i | − | 2.30746i | ||||||
\(112\) | 28663.2 | + | 22456.3i | 0.215913 | + | 0.169158i | ||||
\(113\) | 200568.i | 1.47763i | 0.673908 | + | 0.738815i | \(0.264614\pi\) | ||||
−0.673908 | + | 0.738815i | \(0.735386\pi\) | |||||||
\(114\) | −37998.4 | + | 215779.i | −0.273844 | + | 1.55506i | ||||
\(115\) | 59064.0i | 0.416465i | ||||||||
\(116\) | −1564.72 | + | 761.862i | −0.0107967 | + | 0.00525692i | ||||
\(117\) | − | 43281.4i | − | 0.292305i | ||||||
\(118\) | 68608.3 | − | 109714.i | 0.453598 | − | 0.725366i | ||||
\(119\) | − | 5431.31i | − | 0.0351590i | ||||||
\(120\) | −165555. | − | 17569.4i | −1.04952 | − | 0.111379i | ||||
\(121\) | 126849. | 0.787635 | ||||||||
\(122\) | 95240.2 | − | 152302.i | 0.579323 | − | 0.926417i | ||||
\(123\) | − | 139446.i | − | 0.831083i | ||||||
\(124\) | −59689.3 | − | 122590.i | −0.348612 | − | 0.715982i | ||||
\(125\) | −181365. | −1.03819 | ||||||||
\(126\) | 61883.5 | + | 38698.1i | 0.347255 | + | 0.217151i | ||||
\(127\) | 7707.66 | 0.0424046 | 0.0212023 | − | 0.999775i | \(-0.493251\pi\) | ||||
0.0212023 | + | 0.999775i | \(0.493251\pi\) | |||||||
\(128\) | −129078. | + | 133036.i | −0.696350 | + | 0.717703i | ||||
\(129\) | − | 473564.i | − | 2.50556i | ||||||
\(130\) | 21377.2 | + | 13368.0i | 0.110941 | + | 0.0693757i | ||||
\(131\) | − | 64679.8i | − | 0.329299i | −0.986352 | − | 0.164650i | \(-0.947351\pi\) | ||
0.986352 | − | 0.164650i | \(-0.0526493\pi\) | |||||||
\(132\) | 130965. | − | 63767.1i | 0.654217 | − | 0.318539i | ||||
\(133\) | 20989.7 | + | 51868.2i | 0.102891 | + | 0.254256i | ||||
\(134\) | −65248.1 | + | 104341.i | −0.313910 | + | 0.501986i | ||||
\(135\) | −110223. | −0.520520 | ||||||||
\(136\) | 27494.7 | + | 2917.85i | 0.127468 | + | 0.0135274i | ||||
\(137\) | 183622. | 0.835839 | 0.417919 | − | 0.908484i | \(-0.362759\pi\) | ||||
0.417919 | + | 0.908484i | \(0.362759\pi\) | |||||||
\(138\) | 186612. | + | 116695.i | 0.834146 | + | 0.521622i | ||||
\(139\) | 55030.4i | 0.241582i | 0.992678 | + | 0.120791i | \(0.0385432\pi\) | ||||
−0.992678 | + | 0.120791i | \(0.961457\pi\) | |||||||
\(140\) | −38227.0 | + | 18612.7i | −0.164835 | + | 0.0802583i | ||||
\(141\) | − | 655304.i | − | 2.77584i | ||||||
\(142\) | 38684.6 | − | 61862.1i | 0.160997 | − | 0.257456i | ||||
\(143\) | −22059.8 | −0.0902115 | ||||||||
\(144\) | −229145. | + | 292481.i | −0.920883 | + | 1.17541i | ||||
\(145\) | − | 2032.13i | − | 0.00802660i | ||||||
\(146\) | −100124. | + | 160111.i | −0.388736 | + | 0.621642i | ||||
\(147\) | −382564. | −1.46019 | ||||||||
\(148\) | 350117. | − | 170472.i | 1.31389 | − | 0.639733i | ||||
\(149\) | −449359. | −1.65816 | −0.829082 | − | 0.559127i | \(-0.811136\pi\) | ||||
−0.829082 | + | 0.559127i | \(0.811136\pi\) | |||||||
\(150\) | −127630. | + | 204098.i | −0.463153 | + | 0.740646i | ||||
\(151\) | 329534. | 1.17614 | 0.588069 | − | 0.808811i | \(-0.299888\pi\) | ||||
0.588069 | + | 0.808811i | \(0.299888\pi\) | |||||||
\(152\) | −273846. | + | 78390.4i | −0.961386 | + | 0.275203i | ||||
\(153\) | 55421.4 | 0.191403 | ||||||||
\(154\) | 19723.8 | − | 31541.1i | 0.0670176 | − | 0.107170i | ||||
\(155\) | 159211. | 0.532283 | ||||||||
\(156\) | 84472.0 | − | 41129.4i | 0.277908 | − | 0.135314i | ||||
\(157\) | 89868.3 | 0.290976 | 0.145488 | − | 0.989360i | \(-0.453525\pi\) | ||||
0.145488 | + | 0.989360i | \(0.453525\pi\) | |||||||
\(158\) | 171146. | − | 273687.i | 0.545412 | − | 0.872189i | ||||
\(159\) | 724763.i | 2.27354i | ||||||||
\(160\) | −73685.8 | − | 203514.i | −0.227554 | − | 0.628484i | ||||
\(161\) | 56208.7 | 0.170899 | ||||||||
\(162\) | 46679.4 | − | 74646.8i | 0.139746 | − | 0.223472i | ||||
\(163\) | − | 331481.i | − | 0.977215i | −0.872504 | − | 0.488608i | \(-0.837505\pi\) | ||
0.872504 | − | 0.488608i | \(-0.162495\pi\) | |||||||
\(164\) | 162997. | − | 79363.1i | 0.473226 | − | 0.230414i | ||||
\(165\) | 170088.i | 0.486365i | ||||||||
\(166\) | −70933.4 | − | 44357.3i | −0.199793 | − | 0.124938i | ||||
\(167\) | 345101. | 0.957535 | 0.478768 | − | 0.877942i | \(-0.341084\pi\) | ||||
0.478768 | + | 0.877942i | \(0.341084\pi\) | |||||||
\(168\) | −16720.0 | + | 157552.i | −0.0457051 | + | 0.430675i | ||||
\(169\) | 357065. | 0.961679 | ||||||||
\(170\) | −17117.6 | + | 27373.4i | −0.0454276 | + | 0.0726450i | ||||
\(171\) | −529266. | + | 214180.i | −1.38415 | + | 0.560131i | ||||
\(172\) | 553541. | − | 269520.i | 1.42669 | − | 0.694655i | ||||
\(173\) | 453340.i | 1.15162i | 0.817584 | + | 0.575810i | \(0.195313\pi\) | ||||
−0.817584 | + | 0.575810i | \(0.804687\pi\) | |||||||
\(174\) | −6420.50 | − | 4014.97i | −0.0160766 | − | 0.0100533i | ||||
\(175\) | 61475.5i | 0.151743i | ||||||||
\(176\) | 149073. | + | 116792.i | 0.362758 | + | 0.284204i | ||||
\(177\) | 563040. | 1.35085 | ||||||||
\(178\) | −662251. | − | 414130.i | −1.56665 | − | 0.979685i | ||||
\(179\) | −351268. | −0.819418 | −0.409709 | − | 0.912216i | \(-0.634370\pi\) | ||||
−0.409709 | + | 0.912216i | \(0.634370\pi\) | |||||||
\(180\) | −189925. | − | 390070.i | −0.436920 | − | 0.897349i | ||||
\(181\) | − | 328035.i | − | 0.744258i | −0.928181 | − | 0.372129i | \(-0.878628\pi\) | ||
0.928181 | − | 0.372129i | \(-0.121372\pi\) | |||||||
\(182\) | 12721.7 | − | 20343.8i | 0.0284687 | − | 0.0455254i | ||||
\(183\) | 781597. | 1.72526 | ||||||||
\(184\) | −30196.9 | + | 284543.i | −0.0657533 | + | 0.619588i | ||||
\(185\) | 454704.i | 0.976787i | ||||||||
\(186\) | 314560. | − | 503024.i | 0.666685 | − | 1.06612i | ||||
\(187\) | − | 28247.4i | − | 0.0590711i | ||||||
\(188\) | 765975. | − | 372953.i | 1.58059 | − | 0.769591i | ||||
\(189\) | 104894.i | 0.213598i | ||||||||
\(190\) | 57683.7 | − | 327564.i | 0.115923 | − | 0.658282i | ||||
\(191\) | − | 896294.i | − | 1.77774i | −0.458164 | − | 0.888868i | \(-0.651493\pi\) | ||
0.458164 | − | 0.888868i | \(-0.348507\pi\) | |||||||
\(192\) | −788584. | − | 169282.i | −1.54381 | − | 0.331405i | ||||
\(193\) | 820690.i | 1.58594i | 0.609262 | + | 0.792969i | \(0.291466\pi\) | ||||
−0.609262 | + | 0.792969i | \(0.708534\pi\) | |||||||
\(194\) | 164310. | + | 102749.i | 0.313444 | + | 0.196008i | ||||
\(195\) | 109706.i | 0.206606i | ||||||||
\(196\) | −217728. | − | 447172.i | −0.404832 | − | 0.831448i | ||||
\(197\) | −25862.2 | −0.0474788 | −0.0237394 | − | 0.999718i | \(-0.507557\pi\) | ||||
−0.0237394 | + | 0.999718i | \(0.507557\pi\) | |||||||
\(198\) | 321847. | + | 201263.i | 0.583427 | + | 0.364838i | ||||
\(199\) | 957938.i | 1.71477i | 0.514680 | + | 0.857383i | \(0.327911\pi\) | ||||
−0.514680 | + | 0.857383i | \(0.672089\pi\) | |||||||
\(200\) | −311205. | − | 33026.4i | −0.550138 | − | 0.0583830i | ||||
\(201\) | −535464. | −0.934846 | ||||||||
\(202\) | 336997. | − | 538905.i | 0.581096 | − | 0.929252i | ||||
\(203\) | −1933.89 | −0.00329376 | ||||||||
\(204\) | 52665.9 | + | 108166.i | 0.0886041 | + | 0.181976i | ||||
\(205\) | 211687.i | 0.351811i | ||||||||
\(206\) | −348615. | + | 557484.i | −0.572372 | + | 0.915301i | ||||
\(207\) | 573557.i | 0.930359i | ||||||||
\(208\) | 96151.1 | + | 75329.9i | 0.154098 | + | 0.120728i | ||||
\(209\) | 109164. | + | 269759.i | 0.172868 | + | 0.427179i | ||||
\(210\) | −156856. | − | 98088.2i | −0.245445 | − | 0.153486i | ||||
\(211\) | −365052. | −0.564479 | −0.282240 | − | 0.959344i | \(-0.591077\pi\) | ||||
−0.282240 | + | 0.959344i | \(0.591077\pi\) | |||||||
\(212\) | −847164. | + | 412484.i | −1.29458 | + | 0.630330i | ||||
\(213\) | 317469. | 0.479460 | ||||||||
\(214\) | −388103. | + | 620631.i | −0.579313 | + | 0.926401i | ||||
\(215\) | 718896.i | 1.06064i | ||||||||
\(216\) | −531003. | − | 56352.2i | −0.774394 | − | 0.0821820i | ||||
\(217\) | − | 151514.i | − | 0.218425i | ||||||
\(218\) | −592142. | − | 370288.i | −0.843888 | − | 0.527714i | ||||
\(219\) | −821673. | −1.15768 | ||||||||
\(220\) | −198813. | + | 96802.0i | −0.276941 | + | 0.134843i | ||||
\(221\) | − | 18219.4i | − | 0.0250931i | ||||||
\(222\) | 1.43663e6 | + | 898380.i | 1.95643 | + | 1.22343i | ||||
\(223\) | −390919. | −0.526411 | −0.263205 | − | 0.964740i | \(-0.584780\pi\) | ||||
−0.263205 | + | 0.964740i | \(0.584780\pi\) | |||||||
\(224\) | −193675. | + | 70123.6i | −0.257902 | + | 0.0933779i | ||||
\(225\) | −627300. | −0.826075 | ||||||||
\(226\) | −961980. | − | 601562.i | −1.25284 | − | 0.783446i | ||||
\(227\) | −1.08573e6 | −1.39848 | −0.699239 | − | 0.714888i | \(-0.746478\pi\) | ||||
−0.699239 | + | 0.714888i | \(0.746478\pi\) | |||||||
\(228\) | −920966. | − | 829433.i | −1.17329 | − | 1.05668i | ||||
\(229\) | −300421. | −0.378566 | −0.189283 | − | 0.981923i | \(-0.560616\pi\) | ||||
−0.189283 | + | 0.981923i | \(0.560616\pi\) | |||||||
\(230\) | −283287. | − | 177150.i | −0.353108 | − | 0.220811i | ||||
\(231\) | 161865. | 0.199583 | ||||||||
\(232\) | 1038.94 | − | 9789.86i | 0.00126728 | − | 0.0119414i | ||||
\(233\) | −790652. | −0.954104 | −0.477052 | − | 0.878875i | \(-0.658295\pi\) | ||||
−0.477052 | + | 0.878875i | \(0.658295\pi\) | |||||||
\(234\) | 207589. | + | 129813.i | 0.247837 | + | 0.154981i | ||||
\(235\) | 994787.i | 1.17506i | ||||||||
\(236\) | 320443. | + | 658128.i | 0.374516 | + | 0.769185i | ||||
\(237\) | 1.40453e6 | 1.62427 | ||||||||
\(238\) | 26050.1 | + | 16290.1i | 0.0298103 | + | 0.0186415i | ||||
\(239\) | − | 663704.i | − | 0.751588i | −0.926703 | − | 0.375794i | \(-0.877370\pi\) | ||
0.926703 | − | 0.375794i | \(-0.122630\pi\) | |||||||
\(240\) | 580815. | − | 741352.i | 0.650893 | − | 0.830800i | ||||
\(241\) | − | 1.16859e6i | − | 1.29604i | −0.761622 | − | 0.648021i | \(-0.775597\pi\) | ||
0.761622 | − | 0.648021i | \(-0.224403\pi\) | |||||||
\(242\) | −380458. | + | 608405.i | −0.417608 | + | 0.667812i | ||||
\(243\) | 1.09990e6 | 1.19491 | ||||||||
\(244\) | 444831. | + | 913597.i | 0.478322 | + | 0.982381i | ||||
\(245\) | 580752. | 0.618124 | ||||||||
\(246\) | 668823. | + | 418240.i | 0.704650 | + | 0.440644i | ||||
\(247\) | 70410.4 | + | 173993.i | 0.0734336 | + | 0.181463i | ||||
\(248\) | 767003. | + | 81397.6i | 0.791895 | + | 0.0840392i | ||||
\(249\) | − | 364022.i | − | 0.372074i | ||||||
\(250\) | 543966. | − | 869876.i | 0.550455 | − | 0.880253i | ||||
\(251\) | − | 789035.i | − | 0.790518i | −0.918570 | − | 0.395259i | \(-0.870655\pi\) | ||
0.918570 | − | 0.395259i | \(-0.129345\pi\) | |||||||
\(252\) | −371213. | + | 180744.i | −0.368232 | + | 0.179293i | ||||
\(253\) | 292333. | 0.287129 | ||||||||
\(254\) | −23117.5 | + | 36968.1i | −0.0224831 | + | 0.0359536i | ||||
\(255\) | −140477. | −0.135287 | ||||||||
\(256\) | −250936. | − | 1.01811e6i | −0.239311 | − | 0.970943i | ||||
\(257\) | − | 712224.i | − | 0.672642i | −0.941747 | − | 0.336321i | \(-0.890817\pi\) | ||
0.941747 | − | 0.336321i | \(-0.109183\pi\) | |||||||
\(258\) | 2.27134e6 | + | 1.42036e6i | 2.12439 | + | 1.32846i | ||||
\(259\) | 432723. | 0.400830 | ||||||||
\(260\) | −128233. | + | 62436.7i | −0.117643 | + | 0.0572805i | ||||
\(261\) | − | 19733.6i | − | 0.0179310i | ||||||
\(262\) | 310222. | + | 193993.i | 0.279203 | + | 0.174596i | ||||
\(263\) | − | 1.57887e6i | − | 1.40752i | −0.710436 | − | 0.703762i | \(-0.751502\pi\) | ||
0.710436 | − | 0.703762i | \(-0.248498\pi\) | |||||||
\(264\) | −86958.4 | + | 819403.i | −0.0767895 | + | 0.723582i | ||||
\(265\) | − | 1.10023e6i | − | 0.962428i | ||||||
\(266\) | −311728. | − | 54895.1i | −0.270130 | − | 0.0475696i | ||||
\(267\) | − | 3.39859e6i | − | 2.91757i | ||||||
\(268\) | −304749. | − | 625895.i | −0.259182 | − | 0.532310i | ||||
\(269\) | 431584.i | 0.363651i | 0.983331 | + | 0.181825i | \(0.0582005\pi\) | ||||
−0.983331 | + | 0.181825i | \(0.941799\pi\) | |||||||
\(270\) | 330590. | − | 528660.i | 0.275982 | − | 0.441333i | ||||
\(271\) | 69307.9i | 0.0573270i | 0.999589 | + | 0.0286635i | \(0.00912513\pi\) | ||||
−0.999589 | + | 0.0286635i | \(0.990875\pi\) | |||||||
\(272\) | −96459.3 | + | 123121.i | −0.0790536 | + | 0.100904i | ||||
\(273\) | 104402. | 0.0847817 | ||||||||
\(274\) | −550734. | + | 880700.i | −0.443165 | + | 0.708683i | ||||
\(275\) | 319725.i | 0.254944i | ||||||||
\(276\) | −1.11941e6 | + | 545040.i | −0.884535 | + | 0.430681i | ||||
\(277\) | −559473. | −0.438107 | −0.219053 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219053 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(278\) | −263941. | − | 165052.i | −0.204831 | − | 0.128088i | ||||
\(279\) | 1.54606e6 | 1.18909 | ||||||||
\(280\) | 25381.9 | − | 239172.i | 0.0193477 | − | 0.182312i | ||||
\(281\) | 1.35111e6i | 1.02076i | 0.859949 | + | 0.510381i | \(0.170495\pi\) | ||||
−0.859949 | + | 0.510381i | \(0.829505\pi\) | |||||||
\(282\) | 3.14302e6 | + | 1.96545e6i | 2.35356 | + | 1.47177i | ||||
\(283\) | 1.88088e6i | 1.39603i | 0.716084 | + | 0.698014i | \(0.245933\pi\) | ||||
−0.716084 | + | 0.698014i | \(0.754067\pi\) | |||||||
\(284\) | 180681. | + | 371084.i | 0.132928 | + | 0.273009i | ||||
\(285\) | 1.34153e6 | − | 542884.i | 0.978339 | − | 0.395909i | ||||
\(286\) | 66163.8 | − | 105805.i | 0.0478306 | − | 0.0764877i | ||||
\(287\) | 201454. | 0.144368 | ||||||||
\(288\) | −715546. | − | 1.97628e6i | −0.508342 | − | 1.40400i | ||||
\(289\) | −1.39653e6 | −0.983569 | ||||||||
\(290\) | 9746.66 | + | 6094.95i | 0.00680552 | + | 0.00425574i | ||||
\(291\) | 843219.i | 0.583725i | ||||||||
\(292\) | −467639. | − | 960441.i | −0.320962 | − | 0.659194i | ||||
\(293\) | 132314.i | 0.0900404i | 0.998986 | + | 0.0450202i | \(0.0143352\pi\) | ||||
−0.998986 | + | 0.0450202i | \(0.985665\pi\) | |||||||
\(294\) | 1.14742e6 | − | 1.83488e6i | 0.774201 | − | 1.23805i | ||||
\(295\) | −854725. | −0.571836 | ||||||||
\(296\) | −232471. | + | 2.19055e6i | −0.154219 | + | 1.45320i | ||||
\(297\) | 545540.i | 0.358869i | ||||||||
\(298\) | 1.34776e6 | − | 2.15525e6i | 0.879166 | − | 1.40591i | ||||
\(299\) | 188553. | 0.121971 | ||||||||
\(300\) | −596111. | − | 1.22430e6i | −0.382405 | − | 0.785387i | ||||
\(301\) | 684142. | 0.435242 | ||||||||
\(302\) | −988368. | + | 1.58054e6i | −0.623593 | + | 0.997212i | ||||
\(303\) | 2.76560e6 | 1.73054 | ||||||||
\(304\) | 445362. | − | 1.54856e6i | 0.276395 | − | 0.961044i | ||||
\(305\) | −1.18651e6 | −0.730333 | ||||||||
\(306\) | −166225. | + | 265816.i | −0.101483 | + | 0.162285i | ||||
\(307\) | 888116. | 0.537804 | 0.268902 | − | 0.963168i | \(-0.413339\pi\) | ||||
0.268902 | + | 0.963168i | \(0.413339\pi\) | |||||||
\(308\) | 92122.3 | + | 189201.i | 0.0553335 | + | 0.113644i | ||||
\(309\) | −2.86094e6 | −1.70456 | ||||||||
\(310\) | −477519. | + | 763618.i | −0.282219 | + | 0.451307i | ||||
\(311\) | 2.69154e6i | 1.57798i | 0.614409 | + | 0.788988i | \(0.289394\pi\) | ||||
−0.614409 | + | 0.788988i | \(0.710606\pi\) | |||||||
\(312\) | −56087.7 | + | 528510.i | −0.0326198 | + | 0.307374i | ||||
\(313\) | 1.10940e6 | 0.640070 | 0.320035 | − | 0.947406i | \(-0.396305\pi\) | ||||
0.320035 | + | 0.947406i | \(0.396305\pi\) | |||||||
\(314\) | −269541. | + | 431033.i | −0.154277 | + | 0.246710i | ||||
\(315\) | − | 482102.i | − | 0.273756i | ||||||
\(316\) | 799359. | + | 1.64173e6i | 0.450323 | + | 0.924877i | ||||
\(317\) | − | 1.48050e6i | − | 0.827484i | −0.910394 | − | 0.413742i | \(-0.864222\pi\) | ||
0.910394 | − | 0.413742i | \(-0.135778\pi\) | |||||||
\(318\) | −3.47616e6 | − | 2.17377e6i | −1.92767 | − | 1.20544i | ||||
\(319\) | −10057.9 | −0.00553388 | ||||||||
\(320\) | 1.19711e6 | + | 256980.i | 0.653523 | + | 0.140289i | ||||
\(321\) | −3.18500e6 | −1.72523 | ||||||||
\(322\) | −168586. | + | 269592.i | −0.0906112 | + | 0.144900i | ||||
\(323\) | −222796. | + | 90159.9i | −0.118823 | + | 0.0480847i | ||||
\(324\) | 218022. | + | 447775.i | 0.115382 | + | 0.236972i | ||||
\(325\) | 206221.i | 0.108299i | ||||||||
\(326\) | 1.58988e6 | + | 994209.i | 0.828551 | + | 0.518124i | ||||
\(327\) | − | 3.03880e6i | − | 1.57157i | ||||||
\(328\) | −108226. | + | 1.01981e6i | −0.0555455 | + | 0.523401i | ||||
\(329\) | 946697. | 0.482193 | ||||||||
\(330\) | −815787. | − | 510142.i | −0.412375 | − | 0.257873i | ||||
\(331\) | −2.75880e6 | −1.38404 | −0.692022 | − | 0.721877i | \(-0.743280\pi\) | ||||
−0.692022 | + | 0.721877i | \(0.743280\pi\) | |||||||
\(332\) | 425499. | − | 207176.i | 0.211862 | − | 0.103156i | ||||
\(333\) | 4.41553e6i | 2.18209i | ||||||||
\(334\) | −1.03506e6 | + | 1.65520e6i | −0.507690 | + | 0.811865i | ||||
\(335\) | 812864. | 0.395736 | ||||||||
\(336\) | −705513. | − | 552737.i | −0.340923 | − | 0.267098i | ||||
\(337\) | − | 2.02688e6i | − | 0.972193i | −0.873905 | − | 0.486097i | \(-0.838420\pi\) | ||
0.873905 | − | 0.486097i | \(-0.161580\pi\) | |||||||
\(338\) | −1.07094e6 | + | 1.71258e6i | −0.509886 | + | 0.815378i | ||||
\(339\) | − | 4.93677e6i | − | 2.33315i | ||||||
\(340\) | −79949.6 | − | 164201.i | −0.0375076 | − | 0.0770334i | ||||
\(341\) | − | 788001.i | − | 0.366979i | ||||||
\(342\) | 560153. | − | 3.18090e6i | 0.258965 | − | 1.47056i | ||||
\(343\) | − | 1.15032e6i | − | 0.527937i | ||||||
\(344\) | −367541. | + | 3.46330e6i | −0.167459 | + | 1.57796i | ||||
\(345\) | − | 1.45380e6i | − | 0.657591i | ||||||
\(346\) | −2.17435e6 | − | 1.35970e6i | −0.976424 | − | 0.610594i | ||||
\(347\) | − | 1.96009e6i | − | 0.873879i | −0.899491 | − | 0.436940i | \(-0.856062\pi\) | ||
0.899491 | − | 0.436940i | \(-0.143938\pi\) | |||||||
\(348\) | 38513.9 | − | 18752.4i | 0.0170478 | − | 0.00830059i | ||||
\(349\) | 2.81538e6 | 1.23730 | 0.618648 | − | 0.785668i | \(-0.287681\pi\) | ||||
0.618648 | + | 0.785668i | \(0.287681\pi\) | |||||||
\(350\) | −294854. | − | 184383.i | −0.128658 | − | 0.0804545i | ||||
\(351\) | 351870.i | 0.152446i | ||||||||
\(352\) | −1.00728e6 | + | 364702.i | −0.433304 | + | 0.156885i | ||||
\(353\) | −3.68738e6 | −1.57500 | −0.787500 | − | 0.616314i | \(-0.788625\pi\) | ||||
−0.787500 | + | 0.616314i | \(0.788625\pi\) | |||||||
\(354\) | −1.68872e6 | + | 2.70049e6i | −0.716225 | + | 1.14534i | ||||
\(355\) | −481935. | −0.202963 | ||||||||
\(356\) | 3.97256e6 | − | 1.93424e6i | 1.66129 | − | 0.808883i | ||||
\(357\) | 133686.i | 0.0555156i | ||||||||
\(358\) | 1.05355e6 | − | 1.68478e6i | 0.434459 | − | 0.694760i | ||||
\(359\) | 339534.i | 0.139042i | 0.997580 | + | 0.0695211i | \(0.0221471\pi\) | ||||
−0.997580 | + | 0.0695211i | \(0.977853\pi\) | |||||||
\(360\) | 2.44053e6 | + | 258999.i | 0.992492 | + | 0.105327i | ||||
\(361\) | 1.77924e6 | − | 1.72203e6i | 0.718565 | − | 0.695460i | ||||
\(362\) | 1.57335e6 | + | 983871.i | 0.631034 | + | 0.394609i | ||||
\(363\) | −3.12226e6 | −1.24366 | ||||||||
\(364\) | 59418.3 | + | 122034.i | 0.0235054 | + | 0.0482755i | ||||
\(365\) | 1.24734e6 | 0.490066 | ||||||||
\(366\) | −2.34424e6 | + | 3.74876e6i | −0.914742 | + | 1.46280i | ||||
\(367\) | 4.11001e6i | 1.59286i | 0.604731 | + | 0.796430i | \(0.293281\pi\) | ||||
−0.604731 | + | 0.796430i | \(0.706719\pi\) | |||||||
\(368\) | −1.27418e6 | − | 998258.i | −0.490467 | − | 0.384258i | ||||
\(369\) | 2.05564e6i | 0.785927i | ||||||||
\(370\) | −2.18089e6 | − | 1.36379e6i | −0.828188 | − | 0.517897i | ||||
\(371\) | −1.04704e6 | −0.394938 | ||||||||
\(372\) | 1.46919e6 | + | 3.01743e6i | 0.550453 | + | 1.13052i | ||||
\(373\) | 1.45363e6i | 0.540981i | 0.962723 | + | 0.270491i | \(0.0871859\pi\) | ||||
−0.962723 | + | 0.270491i | \(0.912814\pi\) | |||||||
\(374\) | 135482. | + | 84722.2i | 0.0500846 | + | 0.0313197i | ||||
\(375\) | 4.46411e6 | 1.63929 | ||||||||
\(376\) | −508592. | + | 4.79242e6i | −0.185524 | + | 1.74818i | ||||
\(377\) | −6487.28 | −0.00235076 | ||||||||
\(378\) | −503103. | − | 314609.i | −0.181104 | − | 0.113251i | ||||
\(379\) | −2.73757e6 | −0.978964 | −0.489482 | − | 0.872013i | \(-0.662814\pi\) | ||||
−0.489482 | + | 0.872013i | \(0.662814\pi\) | |||||||
\(380\) | 1.39808e6 | + | 1.25912e6i | 0.496674 | + | 0.447311i | ||||
\(381\) | −189716. | −0.0669563 | ||||||||
\(382\) | 4.29887e6 | + | 2.68825e6i | 1.50729 | + | 0.942563i | ||||
\(383\) | −754121. | −0.262690 | −0.131345 | − | 0.991337i | \(-0.541930\pi\) | ||||
−0.131345 | + | 0.991337i | \(0.541930\pi\) | |||||||
\(384\) | 3.17712e6 | − | 3.27454e6i | 1.09953 | − | 1.13324i | ||||
\(385\) | −245720. | −0.0844868 | ||||||||
\(386\) | −3.93626e6 | − | 2.46149e6i | −1.34467 | − | 0.840871i | ||||
\(387\) | 6.98103e6i | 2.36942i | ||||||||
\(388\) | −985626. | + | 479901.i | −0.332378 | + | 0.161835i | ||||
\(389\) | 2.55373e6 | 0.855660 | 0.427830 | − | 0.903859i | \(-0.359278\pi\) | ||||
0.427830 | + | 0.903859i | \(0.359278\pi\) | |||||||
\(390\) | −526178. | − | 329039.i | −0.175175 | − | 0.109543i | ||||
\(391\) | 241440.i | 0.0798671i | ||||||||
\(392\) | 2.79779e6 | + | 296914.i | 0.919603 | + | 0.0975922i | ||||
\(393\) | 1.59202e6i | 0.519958i | ||||||||
\(394\) | 77568.1 | − | 124042.i | 0.0251735 | − | 0.0402558i | ||||
\(395\) | −2.13215e6 | −0.687583 | ||||||||
\(396\) | −1.93062e6 | + | 940022.i | −0.618671 | + | 0.301231i | ||||
\(397\) | 3.10038e6 | 0.987275 | 0.493638 | − | 0.869668i | \(-0.335667\pi\) | ||||
0.493638 | + | 0.869668i | \(0.335667\pi\) | |||||||
\(398\) | −4.59453e6 | − | 2.87313e6i | −1.45390 | − | 0.909176i | ||||
\(399\) | −516640. | − | 1.27668e6i | −0.162463 | − | 0.401467i | ||||
\(400\) | 1.09180e6 | − | 1.39357e6i | 0.341187 | − | 0.435490i | ||||
\(401\) | − | 4.01172e6i | − | 1.24586i | −0.782277 | − | 0.622931i | \(-0.785942\pi\) | ||
0.782277 | − | 0.622931i | \(-0.214058\pi\) | |||||||
\(402\) | 1.60601e6 | − | 2.56823e6i | 0.495660 | − | 0.792628i | ||||
\(403\) | − | 508256.i | − | 0.155891i | ||||||
\(404\) | 1.57398e6 | + | 3.23266e6i | 0.479785 | + | 0.985387i | ||||
\(405\) | −581535. | −0.176172 | ||||||||
\(406\) | 5800.30 | − | 9275.48i | 0.00174637 | − | 0.00279268i | ||||
\(407\) | 2.25053e6 | 0.673438 | ||||||||
\(408\) | −676752. | − | 71819.8i | −0.201270 | − | 0.0213596i | ||||
\(409\) | 5.50569e6i | 1.62743i | 0.581261 | + | 0.813717i | \(0.302560\pi\) | ||||
−0.581261 | + | 0.813717i | \(0.697440\pi\) | |||||||
\(410\) | −1.01531e6 | − | 634911.i | −0.298290 | − | 0.186532i | ||||
\(411\) | −4.51965e6 | −1.31978 | ||||||||
\(412\) | −1.62825e6 | − | 3.34411e6i | −0.472582 | − | 0.970594i | ||||
\(413\) | 813405.i | 0.234656i | ||||||||
\(414\) | −2.75094e6 | − | 1.72026e6i | −0.788823 | − | 0.493280i | ||||
\(415\) | 552605.i | 0.157505i | ||||||||
\(416\) | −649688. | + | 235231.i | −0.184065 | + | 0.0666440i | ||||
\(417\) | − | 1.35451e6i | − | 0.381455i | ||||||
\(418\) | −1.62125e6 | − | 285501.i | −0.453847 | − | 0.0799221i | ||||
\(419\) | − | 3.74656e6i | − | 1.04255i | −0.853388 | − | 0.521276i | \(-0.825456\pi\) | ||
0.853388 | − | 0.521276i | \(-0.174544\pi\) | |||||||
\(420\) | 940916. | − | 458132.i | 0.260272 | − | 0.126727i | ||||
\(421\) | − | 2.72843e6i | − | 0.750254i | −0.926974 | − | 0.375127i | \(-0.877599\pi\) | ||
0.926974 | − | 0.375127i | \(-0.122401\pi\) | |||||||
\(422\) | 1.09490e6 | − | 1.75089e6i | 0.299289 | − | 0.478605i | ||||
\(423\) | 9.66015e6i | 2.62502i | ||||||||
\(424\) | 562500. | − | 5.30039e6i | 0.151952 | − | 1.43184i | ||||
\(425\) | −264064. | −0.0709148 | ||||||||
\(426\) | −952181. | + | 1.52267e6i | −0.254212 | + | 0.406519i | ||||
\(427\) | 1.12915e6i | 0.299696i | ||||||||
\(428\) | −1.81268e6 | − | 3.72290e6i | −0.478313 | − | 0.982363i | ||||
\(429\) | 542979. | 0.142443 | ||||||||
\(430\) | −3.44802e6 | − | 2.15618e6i | −0.899289 | − | 0.562358i | ||||
\(431\) | 3.80201e6 | 0.985870 | 0.492935 | − | 0.870066i | \(-0.335924\pi\) | ||||
0.492935 | + | 0.870066i | \(0.335924\pi\) | |||||||
\(432\) | 1.86291e6 | − | 2.37782e6i | 0.480267 | − | 0.613012i | ||||
\(433\) | 4.66140e6i | 1.19480i | 0.801942 | + | 0.597401i | \(0.203800\pi\) | ||||
−0.801942 | + | 0.597401i | \(0.796200\pi\) | |||||||
\(434\) | 726703. | + | 454434.i | 0.185196 | + | 0.115810i | ||||
\(435\) | 50018.8i | 0.0126739i | ||||||||
\(436\) | 3.55201e6 | − | 1.72947e6i | 0.894866 | − | 0.435711i | ||||
\(437\) | −933066. | − | 2.30572e6i | −0.233727 | − | 0.577568i | ||||
\(438\) | 2.46444e6 | − | 3.94097e6i | 0.613807 | − | 0.981563i | ||||
\(439\) | −2.23839e6 | −0.554338 | −0.277169 | − | 0.960821i | \(-0.589396\pi\) | ||||
−0.277169 | + | 0.960821i | \(0.589396\pi\) | |||||||
\(440\) | 132008. | − | 1.24390e6i | 0.0325063 | − | 0.306304i | ||||
\(441\) | 5.63955e6 | 1.38086 | ||||||||
\(442\) | 87385.4 | + | 54645.3i | 0.0212757 | + | 0.0133045i | ||||
\(443\) | − | 354337.i | − | 0.0857842i | −0.999080 | − | 0.0428921i | \(-0.986343\pi\) | ||
0.999080 | − | 0.0428921i | \(-0.0136572\pi\) | |||||||
\(444\) | −8.61775e6 | + | 4.19599e6i | −2.07461 | + | 1.01013i | ||||
\(445\) | 5.15925e6i | 1.23506i | ||||||||
\(446\) | 1.17248e6 | − | 1.87496e6i | 0.279105 | − | 0.446328i | ||||
\(447\) | 1.10605e7 | 2.61822 | ||||||||
\(448\) | 244557. | − | 1.13924e6i | 0.0575684 | − | 0.268177i | ||||
\(449\) | − | 3.20959e6i | − | 0.751335i | −0.926755 | − | 0.375667i | \(-0.877413\pi\) | ||
0.926755 | − | 0.375667i | \(-0.122587\pi\) | |||||||
\(450\) | 1.88146e6 | − | 3.00871e6i | 0.437988 | − | 0.700404i | ||||
\(451\) | 1.04773e6 | 0.242554 | ||||||||
\(452\) | 5.77051e6 | − | 2.80966e6i | 1.32852 | − | 0.646857i | ||||
\(453\) | −8.11113e6 | −1.85710 | ||||||||
\(454\) | 3.25641e6 | − | 5.20744e6i | 0.741479 | − | 1.18573i | ||||
\(455\) | −158488. | −0.0358895 | ||||||||
\(456\) | 6.74043e6 | − | 1.92949e6i | 1.51801 | − | 0.434542i | ||||
\(457\) | 7.37437e6 | 1.65171 | 0.825857 | − | 0.563880i | \(-0.190692\pi\) | ||||
0.825857 | + | 0.563880i | \(0.190692\pi\) | |||||||
\(458\) | 901050. | − | 1.44090e6i | 0.200718 | − | 0.320975i | ||||
\(459\) | −450567. | −0.0998222 | ||||||||
\(460\) | 1.69932e6 | − | 827400.i | 0.374439 | − | 0.182314i | ||||
\(461\) | −1.81438e6 | −0.397626 | −0.198813 | − | 0.980037i | \(-0.563709\pi\) | ||||
−0.198813 | + | 0.980037i | \(0.563709\pi\) | |||||||
\(462\) | −485480. | + | 776350.i | −0.105820 | + | 0.169220i | ||||
\(463\) | 4.76937e6i | 1.03397i | 0.855994 | + | 0.516985i | \(0.172946\pi\) | ||||
−0.855994 | + | 0.516985i | \(0.827054\pi\) | |||||||
\(464\) | 43838.8 | + | 34345.7i | 0.00945287 | + | 0.00740589i | ||||
\(465\) | −3.91880e6 | −0.840467 | ||||||||
\(466\) | 2.37139e6 | − | 3.79218e6i | 0.505870 | − | 0.808956i | ||||
\(467\) | 545828.i | 0.115815i | 0.998322 | + | 0.0579073i | \(0.0184428\pi\) | ||||
−0.998322 | + | 0.0579073i | \(0.981557\pi\) | |||||||
\(468\) | −1.24524e6 | + | 606308.i | −0.262808 | + | 0.127961i | ||||
\(469\) | − | 773567.i | − | 0.162393i | ||||||
\(470\) | −4.77128e6 | − | 2.98365e6i | −0.996299 | − | 0.623023i | ||||
\(471\) | −2.21201e6 | −0.459447 | ||||||||
\(472\) | −4.11767e6 | − | 436984.i | −0.850739 | − | 0.0902840i | ||||
\(473\) | 3.55812e6 | 0.731254 | ||||||||
\(474\) | −4.21259e6 | + | 6.73650e6i | −0.861198 | + | 1.37717i | ||||
\(475\) | 2.52177e6 | − | 1.02050e6i | 0.512828 | − | 0.207528i | ||||
\(476\) | −156263. | + | 76084.6i | −0.0316111 | + | 0.0153915i | ||||
\(477\) | − | 1.06841e7i | − | 2.15001i | ||||||
\(478\) | 3.18331e6 | + | 1.99064e6i | 0.637249 | + | 0.398495i | ||||
\(479\) | − | 1.80069e6i | − | 0.358591i | −0.983795 | − | 0.179296i | \(-0.942618\pi\) | ||
0.983795 | − | 0.179296i | \(-0.0573819\pi\) | |||||||
\(480\) | 1.81370e6 | + | 5.00928e6i | 0.359304 | + | 0.992367i | ||||
\(481\) | 1.45158e6 | 0.286073 | ||||||||
\(482\) | 5.60488e6 | + | 3.50494e6i | 1.09888 | + | 0.687168i | ||||
\(483\) | −1.38352e6 | −0.269846 | ||||||||
\(484\) | −1.77697e6 | − | 3.64956e6i | −0.344800 | − | 0.708154i | ||||
\(485\) | − | 1.28005e6i | − | 0.247100i | ||||||
\(486\) | −3.29891e6 | + | 5.27542e6i | −0.633549 | + | 1.01313i | ||||
\(487\) | −5.50150e6 | −1.05113 | −0.525567 | − | 0.850752i | \(-0.676147\pi\) | ||||
−0.525567 | + | 0.850752i | \(0.676147\pi\) | |||||||
\(488\) | −5.71604e6 | − | 606610.i | −1.08654 | − | 0.115308i | ||||
\(489\) | 8.15906e6i | 1.54301i | ||||||||
\(490\) | −1.74184e6 | + | 2.78545e6i | −0.327732 | + | 0.524089i | ||||
\(491\) | − | 3.27324e6i | − | 0.612737i | −0.951913 | − | 0.306369i | \(-0.900886\pi\) | ||
0.951913 | − | 0.306369i | \(-0.0991140\pi\) | |||||||
\(492\) | −4.01199e6 | + | 1.95344e6i | −0.747217 | + | 0.363820i | ||||
\(493\) | − | 8306.90i | − | 0.00153929i | ||||||
\(494\) | −1.04570e6 | − | 184147.i | −0.192792 | − | 0.0339505i | ||||
\(495\) | − | 2.50734e6i | − | 0.459939i | ||||||
\(496\) | −2.69087e6 | + | 3.43462e6i | −0.491121 | + | 0.626866i | ||||
\(497\) | 458637.i | 0.0832872i | ||||||||
\(498\) | 1.74595e6 | + | 1.09181e6i | 0.315470 | + | 0.197275i | ||||
\(499\) | 7.04077e6i | 1.26581i | 0.774229 | + | 0.632905i | \(0.218138\pi\) | ||||
−0.774229 | + | 0.632905i | \(0.781862\pi\) | |||||||
\(500\) | 2.54066e6 | + | 5.21802e6i | 0.454487 | + | 0.933428i | ||||
\(501\) | −8.49429e6 | −1.51193 | ||||||||
\(502\) | 3.78443e6 | + | 2.36654e6i | 0.670257 | + | 0.419136i | ||||
\(503\) | − | 2.17610e6i | − | 0.383494i | −0.981444 | − | 0.191747i | \(-0.938585\pi\) | ||
0.981444 | − | 0.191747i | \(-0.0614153\pi\) | |||||||
\(504\) | 246478. | − | 2.32254e6i | 0.0432217 | − | 0.407275i | ||||
\(505\) | −4.19833e6 | −0.732568 | ||||||||
\(506\) | −876791. | + | 1.40211e6i | −0.152237 | + | 0.243448i | ||||
\(507\) | −8.78876e6 | −1.51848 | ||||||||
\(508\) | −107973. | − | 221756.i | −0.0185633 | − | 0.0381255i | ||||
\(509\) | − | 1.87029e6i | − | 0.319974i | −0.987119 | − | 0.159987i | \(-0.948855\pi\) | ||
0.987119 | − | 0.159987i | \(-0.0511453\pi\) | |||||||
\(510\) | 421331. | − | 673766.i | 0.0717295 | − | 0.114705i | ||||
\(511\) | − | 1.18704e6i | − | 0.201101i | ||||||
\(512\) | 5.63575e6 | + | 1.85004e6i | 0.950117 | + | 0.311894i | ||||
\(513\) | 4.30284e6 | − | 1.74125e6i | 0.721875 | − | 0.292125i | ||||
\(514\) | 3.41602e6 | + | 2.13617e6i | 0.570313 | + | 0.356638i | ||||
\(515\) | 4.34307e6 | 0.721570 | ||||||||
\(516\) | −1.36248e7 | + | 6.63394e6i | −2.25272 | + | 1.09685i | ||||
\(517\) | 4.92363e6 | 0.810138 | ||||||||
\(518\) | −1.29786e6 | + | 2.07546e6i | −0.212522 | + | 0.339852i | ||||
\(519\) | − | 1.11585e7i | − | 1.81839i | ||||||
\(520\) | 85144.2 | − | 802307.i | 0.0138085 | − | 0.130116i | ||||
\(521\) | − | 8.14120e6i | − | 1.31400i | −0.753892 | − | 0.656998i | \(-0.771826\pi\) | ||
0.753892 | − | 0.656998i | \(-0.228174\pi\) | |||||||
\(522\) | 94647.6 | + | 59186.6i | 0.0152031 | + | 0.00950709i | ||||
\(523\) | 465737. | 0.0744538 | 0.0372269 | − | 0.999307i | \(-0.488148\pi\) | ||||
0.0372269 | + | 0.999307i | \(0.488148\pi\) | |||||||
\(524\) | −1.86089e6 | + | 906069.i | −0.296069 | + | 0.144156i | ||||
\(525\) | − | 1.51316e6i | − | 0.239599i | ||||||
\(526\) | 7.57267e6 | + | 4.73547e6i | 1.19340 | + | 0.746275i | ||||
\(527\) | 650818. | 0.102078 | ||||||||
\(528\) | −3.66927e6 | − | 2.87470e6i | −0.572789 | − | 0.448754i | ||||
\(529\) | 3.93767e6 | 0.611787 | ||||||||
\(530\) | 5.27700e6 | + | 3.29990e6i | 0.816014 | + | 0.510284i | ||||
\(531\) | −8.30004e6 | −1.27745 | ||||||||
\(532\) | 1.19826e6 | − | 1.33049e6i | 0.183557 | − | 0.203813i | ||||
\(533\) | 675780. | 0.103036 | ||||||||
\(534\) | 1.63006e7 | + | 1.01934e7i | 2.47372 | + | 1.54691i | ||||
\(535\) | 4.83501e6 | 0.730320 | ||||||||
\(536\) | 3.91600e6 | + | 415582.i | 0.588749 | + | 0.0624806i | ||||
\(537\) | 8.64608e6 | 1.29385 | ||||||||
\(538\) | −2.06999e6 | − | 1.29444e6i | −0.308328 | − | 0.192809i | ||||
\(539\) | − | 2.87439e6i | − | 0.426161i | ||||||
\(540\) | 1.54406e6 | + | 3.17121e6i | 0.227866 | + | 0.467994i | ||||
\(541\) | 4.56771e6 | 0.670974 | 0.335487 | − | 0.942045i | \(-0.391099\pi\) | ||||
0.335487 | + | 0.942045i | \(0.391099\pi\) | |||||||
\(542\) | −332420. | − | 207874.i | −0.0486058 | − | 0.0303950i | ||||
\(543\) | 8.07423e6i | 1.17517i | ||||||||
\(544\) | −301211. | − | 831920.i | −0.0436389 | − | 0.120527i | ||||
\(545\) | 4.61307e6i | 0.665271i | ||||||||
\(546\) | −313132. | + | 500741.i | −0.0449516 | + | 0.0718839i | ||||
\(547\) | −499953. | −0.0714431 | −0.0357216 | − | 0.999362i | \(-0.511373\pi\) | ||||
−0.0357216 | + | 0.999362i | \(0.511373\pi\) | |||||||
\(548\) | −2.57227e6 | − | 5.28295e6i | −0.365902 | − | 0.751493i | ||||
\(549\) | −1.15219e7 | −1.63152 | ||||||||
\(550\) | −1.53349e6 | − | 958948.i | −0.216159 | − | 0.135172i | ||||
\(551\) | 32102.7 | + | 79329.6i | 0.00450466 | + | 0.0111316i | ||||
\(552\) | 743264. | − | 7.00372e6i | 0.103823 | − | 0.978320i | ||||
\(553\) | 2.02908e6i | 0.282153i | ||||||||
\(554\) | 1.67802e6 | − | 2.68339e6i | 0.232286 | − | 0.371458i | ||||
\(555\) | − | 1.11921e7i | − | 1.54233i | ||||||
\(556\) | 1.58327e6 | − | 770895.i | 0.217204 | − | 0.105757i | ||||
\(557\) | −9.53980e6 | −1.30287 | −0.651435 | − | 0.758704i | \(-0.725833\pi\) | ||||
−0.651435 | + | 0.758704i | \(0.725833\pi\) | |||||||
\(558\) | −4.63707e6 | + | 7.41532e6i | −0.630462 | + | 1.00819i | ||||
\(559\) | 2.29497e6 | 0.310633 | ||||||||
\(560\) | 1.07101e6 | + | 839085.i | 0.144319 | + | 0.113067i | ||||
\(561\) | 695280.i | 0.0932723i | ||||||||
\(562\) | −6.48028e6 | − | 4.05236e6i | −0.865473 | − | 0.541212i | ||||
\(563\) | 5.85980e6 | 0.779133 | 0.389567 | − | 0.920998i | \(-0.372625\pi\) | ||||
0.389567 | + | 0.920998i | \(0.372625\pi\) | |||||||
\(564\) | −1.88536e7 | + | 9.17985e6i | −2.49573 | + | 1.21517i | ||||
\(565\) | 7.49428e6i | 0.987664i | ||||||||
\(566\) | −9.02120e6 | − | 5.64129e6i | −1.18365 | − | 0.740180i | ||||
\(567\) | 553421.i | 0.0722933i | ||||||||
\(568\) | −2.32174e6 | − | 246393.i | −0.301955 | − | 0.0320447i | ||||
\(569\) | − | 1.27882e6i | − | 0.165588i | −0.996567 | − | 0.0827940i | \(-0.973616\pi\) | ||
0.996567 | − | 0.0827940i | \(-0.0263844\pi\) | |||||||
\(570\) | −1.41982e6 | + | 8.06263e6i | −0.183040 | + | 1.03942i | ||||
\(571\) | − | 3.42245e6i | − | 0.439285i | −0.975580 | − | 0.219642i | \(-0.929511\pi\) | ||
0.975580 | − | 0.219642i | \(-0.0704891\pi\) | |||||||
\(572\) | 309026. | + | 634680.i | 0.0394916 | + | 0.0811082i | ||||
\(573\) | 2.20613e7i | 2.80702i | ||||||||
\(574\) | −604217. | + | 966227.i | −0.0765444 | + | 0.122405i | ||||
\(575\) | − | 2.73280e6i | − | 0.344698i | ||||||
\(576\) | 1.16249e7 | + | 2.49547e6i | 1.45993 | + | 0.313398i | ||||
\(577\) | −9.67549e6 | −1.20985 | −0.604927 | − | 0.796281i | \(-0.706798\pi\) | ||||
−0.604927 | + | 0.796281i | \(0.706798\pi\) | |||||||
\(578\) | 4.18859e6 | − | 6.69813e6i | 0.521493 | − | 0.833938i | ||||
\(579\) | − | 2.02004e7i | − | 2.50417i | ||||||
\(580\) | −58466.1 | + | 28467.2i | −0.00721663 | + | 0.00351378i | ||||
\(581\) | 525891. | 0.0646331 | ||||||||
\(582\) | −4.04431e6 | − | 2.52906e6i | −0.494923 | − | 0.309493i | ||||
\(583\) | −5.44550e6 | −0.663539 | ||||||||
\(584\) | 6.00912e6 | + | 637714.i | 0.729086 | + | 0.0773737i | ||||
\(585\) | − | 1.61722e6i | − | 0.195380i | ||||||
\(586\) | −634616. | − | 396849.i | −0.0763426 | − | 0.0477398i | ||||
\(587\) | 8.70606e6i | 1.04286i | 0.853294 | + | 0.521430i | \(0.174601\pi\) | ||||
−0.853294 | + | 0.521430i | \(0.825399\pi\) | |||||||
\(588\) | 5.35915e6 | + | 1.10067e7i | 0.639224 | + | 1.31284i | ||||
\(589\) | −6.21521e6 | + | 2.51514e6i | −0.738189 | + | 0.298726i | ||||
\(590\) | 2.56357e6 | − | 4.09950e6i | 0.303190 | − | 0.484843i | ||||
\(591\) | 636570. | 0.0749683 | ||||||||
\(592\) | −9.80925e6 | − | 7.68509e6i | −1.15035 | − | 0.901249i | ||||
\(593\) | −1.31815e7 | −1.53932 | −0.769660 | − | 0.638453i | \(-0.779574\pi\) | ||||
−0.769660 | + | 0.638453i | \(0.779574\pi\) | |||||||
\(594\) | −2.61656e6 | − | 1.63623e6i | −0.304274 | − | 0.190274i | ||||
\(595\) | − | 202942.i | − | 0.0235007i | ||||||
\(596\) | 6.29486e6 | + | 1.29284e7i | 0.725889 | + | 1.49084i | ||||
\(597\) | − | 2.35786e7i | − | 2.70759i | ||||||
\(598\) | −565525. | + | 904352.i | −0.0646694 | + | 0.103415i | ||||
\(599\) | 1.39991e7 | 1.59416 | 0.797082 | − | 0.603871i | \(-0.206376\pi\) | ||||
0.797082 | + | 0.603871i | \(0.206376\pi\) | |||||||
\(600\) | 7.65998e6 | + | 812909.i | 0.868659 | + | 0.0921858i | ||||
\(601\) | 3.23278e6i | 0.365081i | 0.983198 | + | 0.182541i | \(0.0584321\pi\) | ||||
−0.983198 | + | 0.182541i | \(0.941568\pi\) | |||||||
\(602\) | −2.05194e6 | + | 3.28134e6i | −0.230767 | + | 0.369028i | ||||
\(603\) | 7.89353e6 | 0.884053 | ||||||||
\(604\) | −4.61629e6 | − | 9.48098e6i | −0.514874 | − | 1.05745i | ||||
\(605\) | 4.73976e6 | 0.526464 | ||||||||
\(606\) | −8.29482e6 | + | 1.32646e7i | −0.917541 | + | 1.46728i | ||||
\(607\) | −3.71893e6 | −0.409681 | −0.204841 | − | 0.978795i | \(-0.565668\pi\) | ||||
−0.204841 | + | 0.978795i | \(0.565668\pi\) | |||||||
\(608\) | 6.09154e6 | + | 6.78065e6i | 0.668295 | + | 0.743896i | ||||
\(609\) | 47600.7 | 0.00520080 | ||||||||
\(610\) | 3.55868e6 | − | 5.69082e6i | 0.387226 | − | 0.619227i | ||||
\(611\) | 3.17571e6 | 0.344142 | ||||||||
\(612\) | −776373. | − | 1.59452e6i | −0.0837899 | − | 0.172088i | ||||
\(613\) | −1.26975e7 | −1.36479 | −0.682395 | − | 0.730984i | \(-0.739061\pi\) | ||||
−0.682395 | + | 0.730984i | \(0.739061\pi\) | |||||||
\(614\) | −2.66372e6 | + | 4.25965e6i | −0.285146 | + | 0.455988i | ||||
\(615\) | − | 5.21045e6i | − | 0.555505i | ||||||
\(616\) | −1.18376e6 | − | 125626.i | −0.125694 | − | 0.0133391i | ||||
\(617\) | −1.09244e6 | −0.115527 | −0.0577635 | − | 0.998330i | \(-0.518397\pi\) | ||||
−0.0577635 | + | 0.998330i | \(0.518397\pi\) | |||||||
\(618\) | 8.58079e6 | − | 1.37219e7i | 0.903766 | − | 1.44525i | ||||
\(619\) | 1.38672e7i | 1.45466i | 0.686285 | + | 0.727332i | \(0.259240\pi\) | ||||
−0.686285 | + | 0.727332i | \(0.740760\pi\) | |||||||
\(620\) | −2.23031e6 | − | 4.58062e6i | −0.233016 | − | 0.478570i | ||||
\(621\) | − | 4.66292e6i | − | 0.485209i | ||||||
\(622\) | −1.29094e7 | − | 8.07271e6i | −1.33792 | − | 0.836649i | ||||
\(623\) | 4.90984e6 | 0.506812 | ||||||||
\(624\) | −2.36666e6 | − | 1.85417e6i | −0.243318 | − | 0.190628i | ||||
\(625\) | −1.37415e6 | −0.140712 | ||||||||
\(626\) | −3.32741e6 | + | 5.32099e6i | −0.339368 | + | 0.542696i | ||||
\(627\) | −2.68697e6 | − | 6.63982e6i | −0.272956 | − | 0.674508i | ||||
\(628\) | −1.25892e6 | − | 2.58558e6i | −0.127380 | − | 0.261613i | ||||
\(629\) | 1.85873e6i | 0.187322i | ||||||||
\(630\) | 2.31230e6 | + | 1.44596e6i | 0.232109 | + | 0.145146i | ||||
\(631\) | 8.68724e6i | 0.868577i | 0.900774 | + | 0.434289i | \(0.143000\pi\) | ||||
−0.900774 | + | 0.434289i | \(0.857000\pi\) | |||||||
\(632\) | −1.02717e7 | − | 1.09008e6i | −1.02294 | − | 0.108559i | ||||
\(633\) | 8.98536e6 | 0.891304 | ||||||||
\(634\) | 7.10087e6 | + | 4.44044e6i | 0.701599 | + | 0.438736i | ||||
\(635\) | 287999. | 0.0283437 | ||||||||
\(636\) | 2.08520e7 | − | 1.01529e7i | 2.04412 | − | 0.995281i | ||||
\(637\) | − | 1.85397e6i | − | 0.181031i | ||||||
\(638\) | 30166.5 | − | 48240.4i | 0.00293409 | − | 0.00469201i | ||||
\(639\) | −4.67996e6 | −0.453409 | ||||||||
\(640\) | −4.82304e6 | + | 4.97093e6i | −0.465447 | + | 0.479720i | ||||
\(641\) | 1.02590e7i | 0.986187i | 0.869976 | + | 0.493094i | \(0.164134\pi\) | ||||
−0.869976 | + | 0.493094i | \(0.835866\pi\) | |||||||
\(642\) | 9.55275e6 | − | 1.52762e7i | 0.914726 | − | 1.46277i | ||||
\(643\) | 1.81124e7i | 1.72762i | 0.503816 | + | 0.863811i | \(0.331929\pi\) | ||||
−0.503816 | + | 0.863811i | \(0.668071\pi\) | |||||||
\(644\) | −787401. | − | 1.61717e6i | −0.0748137 | − | 0.153653i | ||||
\(645\) | − | 1.76949e7i | − | 1.67474i | ||||||
\(646\) | 235798. | − | 1.33901e6i | 0.0222310 | − | 0.126241i | ||||
\(647\) | − | 4.32480e6i | − | 0.406167i | −0.979161 | − | 0.203084i | \(-0.934904\pi\) | ||
0.979161 | − | 0.203084i | \(-0.0650964\pi\) | |||||||
\(648\) | −2.80156e6 | − | 297314.i | −0.262097 | − | 0.0278149i | ||||
\(649\) | 4.23040e6i | 0.394248i | ||||||||
\(650\) | −989092. | − | 618516.i | −0.0918234 | − | 0.0574206i | ||||
\(651\) | 3.72935e6i | 0.344890i | ||||||||
\(652\) | −9.53700e6 | + | 4.64357e6i | −0.878603 | + | 0.427792i | ||||
\(653\) | 1.62050e7 | 1.48719 | 0.743594 | − | 0.668631i | \(-0.233120\pi\) | ||||
0.743594 | + | 0.668631i | \(0.233120\pi\) | |||||||
\(654\) | 1.45749e7 | + | 9.11425e6i | 1.33249 | + | 0.833252i | ||||
\(655\) | − | 2.41678e6i | − | 0.220107i | ||||||
\(656\) | −4.56669e6 | − | 3.57779e6i | −0.414325 | − | 0.324605i | ||||
\(657\) | 1.21127e7 | 1.09478 | ||||||||
\(658\) | −2.83942e6 | + | 4.54062e6i | −0.255661 | + | 0.408837i | ||||
\(659\) | −1.58461e7 | −1.42137 | −0.710687 | − | 0.703508i | \(-0.751616\pi\) | ||||
−0.710687 | + | 0.703508i | \(0.751616\pi\) | |||||||
\(660\) | 4.89356e6 | − | 2.38268e6i | 0.437286 | − | 0.212915i | ||||
\(661\) | 9.57271e6i | 0.852180i | 0.904681 | + | 0.426090i | \(0.140109\pi\) | ||||
−0.904681 | + | 0.426090i | \(0.859891\pi\) | |||||||
\(662\) | 8.27443e6 | − | 1.32320e7i | 0.733826 | − | 1.17349i | ||||
\(663\) | 448452.i | 0.0396216i | ||||||||
\(664\) | −282523. | + | 2.66219e6i | −0.0248676 | + | 0.234325i | ||||
\(665\) | 784287. | + | 1.93807e6i | 0.0687735 | + | 0.169948i | ||||
\(666\) | −2.11781e7 | − | 1.32434e7i | −1.85013 | − | 1.15695i | ||||
\(667\) | 85968.2 | 0.00748210 | ||||||||
\(668\) | −4.83436e6 | − | 9.92884e6i | −0.419177 | − | 0.860909i | ||||
\(669\) | 9.62206e6 | 0.831195 | ||||||||
\(670\) | −2.43801e6 | + | 3.89872e6i | −0.209821 | + | 0.335533i | ||||
\(671\) | 5.87253e6i | 0.503523i | ||||||||
\(672\) | 4.76712e6 | − | 1.72602e6i | 0.407223 | − | 0.147442i | ||||
\(673\) | − | 1.94503e7i | − | 1.65535i | −0.561208 | − | 0.827675i | \(-0.689663\pi\) | ||
0.561208 | − | 0.827675i | \(-0.310337\pi\) | |||||||
\(674\) | 9.72146e6 | + | 6.07919e6i | 0.824293 | + | 0.515461i | ||||
\(675\) | 5.09985e6 | 0.430822 | ||||||||
\(676\) | −5.00195e6 | − | 1.02730e7i | −0.420991 | − | 0.864634i | ||||
\(677\) | − | 2.59599e6i | − | 0.217686i | −0.994059 | − | 0.108843i | \(-0.965285\pi\) | ||
0.994059 | − | 0.108843i | \(-0.0347146\pi\) | |||||||
\(678\) | 2.36781e7 | + | 1.48068e7i | 1.97821 | + | 1.23705i | ||||
\(679\) | −1.21817e6 | −0.101399 | ||||||||
\(680\) | 1.02735e6 | + | 109026.i | 0.0852010 | + | 0.00904189i | ||||
\(681\) | 2.67240e7 | 2.20818 | ||||||||
\(682\) | 3.77947e6 | + | 2.36344e6i | 0.311150 | + | 0.194574i | ||||
\(683\) | −5.32769e6 | −0.437006 | −0.218503 | − | 0.975836i | \(-0.570117\pi\) | ||||
−0.218503 | + | 0.975836i | \(0.570117\pi\) | |||||||
\(684\) | 1.35764e7 | + | 1.22271e7i | 1.10954 | + | 0.999269i | ||||
\(685\) | 6.86108e6 | 0.558684 | ||||||||
\(686\) | 5.51723e6 | + | 3.45013e6i | 0.447622 | + | 0.279914i | ||||
\(687\) | 7.39455e6 | 0.597751 | ||||||||
\(688\) | −1.55086e7 | − | 1.21503e7i | −1.24911 | − | 0.978622i | ||||
\(689\) | −3.51232e6 | −0.281868 | ||||||||
\(690\) | 6.97281e6 | + | 4.36036e6i | 0.557552 | + | 0.348658i | ||||
\(691\) | − | 1.58455e7i | − | 1.26244i | −0.775604 | − | 0.631220i | \(-0.782554\pi\) | ||
0.775604 | − | 0.631220i | \(-0.217446\pi\) | |||||||
\(692\) | 1.30430e7 | − | 6.35063e6i | 1.03541 | − | 0.504141i | ||||
\(693\) | −2.38613e6 | −0.188739 | ||||||||
\(694\) | 9.40111e6 | + | 5.87886e6i | 0.740936 | + | 0.463335i | ||||
\(695\) | 2.05623e6i | 0.161476i | ||||||||
\(696\) | −25572.4 | + | 240967.i | −0.00200101 | + | 0.0188553i | ||||
\(697\) | 865330.i | 0.0674683i | ||||||||
\(698\) | −8.44415e6 | + | 1.35034e7i | −0.656020 | + | 1.04907i | ||||
\(699\) | 1.94611e7 | 1.50651 | ||||||||
\(700\) | 1.76870e6 | − | 861182.i | 0.136430 | − | 0.0664278i | ||||
\(701\) | 2.64710e6 | 0.203458 | 0.101729 | − | 0.994812i | \(-0.467563\pi\) | ||||
0.101729 | + | 0.994812i | \(0.467563\pi\) | |||||||
\(702\) | −1.68767e6 | − | 1.05536e6i | −0.129254 | − | 0.0808273i | ||||
\(703\) | −7.18321e6 | − | 1.77506e7i | −0.548189 | − | 1.35464i | ||||
\(704\) | 1.27190e6 | − | 5.92503e6i | 0.0967213 | − | 0.450566i | ||||
\(705\) | − | 2.44856e7i | − | 1.85540i | ||||||
\(706\) | 1.10595e7 | − | 1.76857e7i | 0.835072 | − | 1.33540i | ||||
\(707\) | 3.99537e6i | 0.300613i | ||||||||
\(708\) | −7.88736e6 | − | 1.61991e7i | −0.591356 | − | 1.21453i | ||||
\(709\) | −9.79778e6 | −0.732001 | −0.366001 | − | 0.930615i | \(-0.619273\pi\) | ||||
−0.366001 | + | 0.930615i | \(0.619273\pi\) | |||||||
\(710\) | 1.44546e6 | − | 2.31149e6i | 0.107612 | − | 0.172087i | ||||
\(711\) | −2.07048e7 | −1.53602 | ||||||||
\(712\) | −2.63770e6 | + | 2.48549e7i | −0.194996 | + | 1.83743i | ||||
\(713\) | 6.73532e6i | 0.496174i | ||||||||
\(714\) | −641194. | − | 400962.i | −0.0470700 | − | 0.0294346i | ||||
\(715\) | −824272. | −0.0602984 | ||||||||
\(716\) | 4.92075e6 | + | 1.01063e7i | 0.358714 | + | 0.736730i | ||||
\(717\) | 1.63364e7i | 1.18675i | ||||||||
\(718\) | −1.62850e6 | − | 1.01836e6i | −0.117890 | − | 0.0737208i | ||||
\(719\) | 1.44832e7i | 1.04483i | 0.852693 | + | 0.522413i | \(0.174968\pi\) | ||||
−0.852693 | + | 0.522413i | \(0.825032\pi\) | |||||||
\(720\) | −8.56207e6 | + | 1.09286e7i | −0.615528 | + | 0.785659i | ||||
\(721\) | − | 4.13311e6i | − | 0.296100i | ||||||
\(722\) | 2.92287e6 | + | 1.36986e7i | 0.208673 | + | 0.977986i | ||||
\(723\) | 2.87636e7i | 2.04643i | ||||||||
\(724\) | −9.43784e6 | + | 4.59529e6i | −0.669154 | + | 0.325811i | ||||
\(725\) | 94023.6i | 0.00664342i | ||||||||
\(726\) | 9.36457e6 | − | 1.49752e7i | 0.659396 | − | 1.05446i | ||||
\(727\) | 1.11083e7i | 0.779489i | 0.920923 | + | 0.389745i | \(0.127437\pi\) | ||||
−0.920923 | + | 0.389745i | \(0.872563\pi\) | |||||||
\(728\) | −763521. | − | 81028.1i | −0.0533940 | − | 0.00566640i | ||||
\(729\) | −2.32909e7 | −1.62318 | ||||||||
\(730\) | −3.74115e6 | + | 5.98261e6i | −0.259835 | + | 0.415512i | ||||
\(731\) | 2.93869e6i | 0.203404i | ||||||||
\(732\) | −1.09490e7 | − | 2.24872e7i | −0.755262 | − | 1.55116i | ||||
\(733\) | 2.26383e7 | 1.55627 | 0.778133 | − | 0.628099i | \(-0.216167\pi\) | ||||
0.778133 | + | 0.628099i | \(0.216167\pi\) | |||||||
\(734\) | −1.97127e7 | − | 1.23271e7i | −1.35054 | − | 0.844541i | ||||
\(735\) | −1.42946e7 | −0.976009 | ||||||||
\(736\) | 8.60955e6 | − | 3.11724e6i | 0.585849 | − | 0.212117i | ||||
\(737\) | − | 4.02321e6i | − | 0.272837i | ||||||
\(738\) | −9.85944e6 | − | 6.16547e6i | −0.666364 | − | 0.416702i | ||||
\(739\) | − | 1.18449e7i | − | 0.797850i | −0.916983 | − | 0.398925i | \(-0.869383\pi\) | ||
0.916983 | − | 0.398925i | \(-0.130617\pi\) | |||||||
\(740\) | 1.30822e7 | − | 6.36974e6i | 0.878218 | − | 0.427605i | ||||
\(741\) | −1.73308e6 | − | 4.28264e6i | −0.115950 | − | 0.286528i | ||||
\(742\) | 3.14038e6 | − | 5.02190e6i | 0.209398 | − | 0.334856i | ||||
\(743\) | −2.25253e7 | −1.49692 | −0.748461 | − | 0.663179i | \(-0.769207\pi\) | ||||
−0.748461 | + | 0.663179i | \(0.769207\pi\) | |||||||
\(744\) | −1.88790e7 | − | 2.00351e6i | −1.25039 | − | 0.132697i | ||||
\(745\) | −1.67904e7 | −1.10833 | ||||||||
\(746\) | −6.97202e6 | − | 4.35986e6i | −0.458682 | − | 0.286831i | ||||
\(747\) | 5.36622e6i | 0.351858i | ||||||||
\(748\) | −812702. | + | 395705.i | −0.0531101 | + | 0.0258593i | ||||
\(749\) | − | 4.60127e6i | − | 0.299691i | ||||||
\(750\) | −1.33891e7 | + | 2.14111e7i | −0.869160 | + | 1.38991i | ||||
\(751\) | 4.38866e6 | 0.283944 | 0.141972 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141972 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(752\) | −2.14604e7 | − | 1.68132e7i | −1.38386 | − | 1.08419i | ||||
\(753\) | 1.94213e7i | 1.24822i | ||||||||
\(754\) | 19457.2 | − | 31114.8i | 0.00124639 | − | 0.00199314i | ||||
\(755\) | 1.23131e7 | 0.786143 | ||||||||
\(756\) | 3.01790e6 | − | 1.46942e6i | 0.192044 | − | 0.0935062i | ||||
\(757\) | 7.77022e6 | 0.492826 | 0.246413 | − | 0.969165i | \(-0.420748\pi\) | ||||
0.246413 | + | 0.969165i | \(0.420748\pi\) | |||||||
\(758\) | 8.21075e6 | − | 1.31301e7i | 0.519051 | − | 0.830034i | ||||
\(759\) | −7.19546e6 | −0.453371 | ||||||||
\(760\) | −1.02323e7 | + | 2.92908e6i | −0.642601 | + | 0.183949i | ||||
\(761\) | 1.04389e7 | 0.653418 | 0.326709 | − | 0.945125i | \(-0.394060\pi\) | ||||
0.326709 | + | 0.945125i | \(0.394060\pi\) | |||||||
\(762\) | 569013. | − | 909930.i | 0.0355005 | − | 0.0567702i | ||||
\(763\) | 4.39006e6 | 0.272998 | ||||||||
\(764\) | −2.57871e7 | + | 1.25558e7i | −1.59834 | + | 0.778233i | ||||
\(765\) | 2.07084e6 | 0.127936 | ||||||||
\(766\) | 2.26183e6 | − | 3.61697e6i | 0.139280 | − | 0.222727i | ||||
\(767\) | 2.72858e6i | 0.167475i | ||||||||
\(768\) | 6.17652e6 | + | 2.50596e7i | 0.377868 | + | 1.53310i | ||||
\(769\) | −2.70798e7 | −1.65131 | −0.825656 | − | 0.564174i | \(-0.809195\pi\) | ||||
−0.825656 | + | 0.564174i | \(0.809195\pi\) | |||||||
\(770\) | 736985. | − | 1.17854e6i | 0.0447952 | − | 0.0716338i | ||||
\(771\) | 1.75306e7i | 1.06209i | ||||||||
\(772\) | 2.36120e7 | − | 1.14967e7i | 1.42590 | − | 0.694271i | ||||
\(773\) | 1.19968e7i | 0.722134i | 0.932540 | + | 0.361067i | \(0.117587\pi\) | ||||
−0.932540 | + | 0.361067i | \(0.882413\pi\) | |||||||
\(774\) | −3.34830e7 | − | 2.09381e7i | −2.00896 | − | 1.25628i | ||||
\(775\) | −7.36643e6 | −0.440558 | ||||||||
\(776\) | 654436. | − | 6.16670e6i | 0.0390133 | − | 0.367619i | ||||
\(777\) | −1.06510e7 | −0.632904 | ||||||||
\(778\) | −7.65938e6 | + | 1.22484e7i | −0.453675 | + | 0.725488i | ||||
\(779\) | −3.34414e6 | − | 8.26377e6i | −0.197442 | − | 0.487904i | ||||
\(780\) | 3.15632e6 | − | 1.53681e6i | 0.185757 | − | 0.0904450i | ||||
\(781\) | 2.38530e6i | 0.139932i | ||||||||
\(782\) | −1.15801e6 | − | 724149.i | −0.0677169 | − | 0.0423459i | ||||
\(783\) | 160431.i | 0.00935153i | ||||||||
\(784\) | −9.81547e6 | + | 1.25285e7i | −0.570323 | + | 0.727960i | ||||
\(785\) | 3.35795e6 | 0.194491 | ||||||||
\(786\) | −7.63579e6 | − | 4.77494e6i | −0.440857 | − | 0.275684i | ||||
\(787\) | 8.04857e6 | 0.463214 | 0.231607 | − | 0.972809i | \(-0.425602\pi\) | ||||
0.231607 | + | 0.972809i | \(0.425602\pi\) | |||||||
\(788\) | 362291. | + | 744076.i | 0.0207846 | + | 0.0426876i | ||||
\(789\) | 3.88621e7i | 2.22246i | ||||||||
\(790\) | 6.39493e6 | − | 1.02264e7i | 0.364559 | − | 0.582981i | ||||
\(791\) | 7.13199e6 | 0.405293 | ||||||||
\(792\) | 1.28190e6 | − | 1.20792e7i | 0.0726173 | − | 0.684267i | ||||
\(793\) | 3.78775e6i | 0.213894i | ||||||||
\(794\) | −9.29893e6 | + | 1.48703e7i | −0.523458 | + | 0.837081i | ||||
\(795\) | 2.70810e7i | 1.51966i | ||||||||
\(796\) | 2.75607e7 | − | 1.34193e7i | 1.54173 | − | 0.750667i | ||||
\(797\) | 1.67184e7i | 0.932286i | 0.884709 | + | 0.466143i | \(0.154357\pi\) | ||||
−0.884709 | + | 0.466143i | \(0.845643\pi\) | |||||||
\(798\) | 7.67286e6 | + | 1.35118e6i | 0.426530 | + | 0.0751116i | ||||
\(799\) | 4.06647e6i | 0.225346i | ||||||||
\(800\) | 3.40933e6 | + | 9.41628e6i | 0.188341 | + | 0.520181i | ||||
\(801\) | 5.01003e7i | 2.75905i | ||||||||
\(802\) | 1.92413e7 | + | 1.20323e7i | 1.05633 | + | 0.660562i | ||||
\(803\) | − | 6.17364e6i | − | 0.337872i | ||||||
\(804\) | 7.50107e6 | + | 1.54058e7i | 0.409245 | + | 0.840510i | ||||
\(805\) | 2.10025e6 | 0.114230 | ||||||||
\(806\) | 2.43774e6 | + | 1.52441e6i | 0.132175 | + | 0.0826539i | ||||
\(807\) | − | 1.06230e7i | − | 0.574199i | ||||||
\(808\) | −2.02256e7 | − | 2.14642e6i | −1.08986 | − | 0.115661i | ||||
\(809\) | −2.25763e7 | −1.21278 | −0.606390 | − | 0.795167i | \(-0.707383\pi\) | ||||
−0.606390 | + | 0.795167i | \(0.707383\pi\) | |||||||
\(810\) | 1.74419e6 | − | 2.78920e6i | 0.0934074 | − | 0.149371i | ||||
\(811\) | 3.15131e7 | 1.68244 | 0.841219 | − | 0.540694i | \(-0.181838\pi\) | ||||
0.841219 | + | 0.540694i | \(0.181838\pi\) | |||||||
\(812\) | 27091.0 | + | 55639.7i | 0.00144190 | + | 0.00296138i | ||||
\(813\) | − | 1.70594e6i | − | 0.0905185i | ||||||
\(814\) | −6.74997e6 | + | 1.07941e7i | −0.357060 | + | 0.570988i | ||||
\(815\) | − | 1.23859e7i | − | 0.653181i | ||||||
\(816\) | 2.37424e6 | − | 3.03048e6i | 0.124824 | − | 0.159326i | ||||
\(817\) | −1.13568e7 | − | 2.80640e7i | −0.595251 | − | 1.47094i | ||||
\(818\) | −2.64068e7 | − | 1.65132e7i | −1.37985 | − | 0.862873i | ||||
\(819\) | −1.53904e6 | −0.0801752 | ||||||||
\(820\) | 6.09041e6 | − | 2.96543e6i | 0.316310 | − | 0.154011i | ||||
\(821\) | 2.59036e7 | 1.34123 | 0.670614 | − | 0.741807i | \(-0.266031\pi\) | ||||
0.670614 | + | 0.741807i | \(0.266031\pi\) | |||||||
\(822\) | 1.35557e7 | − | 2.16775e7i | 0.699751 | − | 1.11900i | ||||
\(823\) | − | 2.62980e7i | − | 1.35339i | −0.736262 | − | 0.676696i | \(-0.763411\pi\) | ||
0.736262 | − | 0.676696i | \(-0.236589\pi\) | |||||||
\(824\) | 2.09229e7 | + | 2.22042e6i | 1.07350 | + | 0.113925i | ||||
\(825\) | − | 7.86969e6i | − | 0.402553i | ||||||
\(826\) | −3.90132e6 | − | 2.43964e6i | −0.198958 | − | 0.124416i | ||||
\(827\) | 6.67461e6 | 0.339361 | 0.169681 | − | 0.985499i | \(-0.445726\pi\) | ||||
0.169681 | + | 0.985499i | \(0.445726\pi\) | |||||||
\(828\) | 1.65017e7 | − | 8.03469e6i | 0.836475 | − | 0.407280i | ||||
\(829\) | − | 1.20700e7i | − | 0.609985i | −0.952355 | − | 0.304993i | \(-0.901346\pi\) | ||
0.952355 | − | 0.304993i | \(-0.0986540\pi\) | |||||||
\(830\) | −2.65045e6 | − | 1.65742e6i | −0.133544 | − | 0.0835099i | ||||
\(831\) | 1.37708e7 | 0.691764 | ||||||||
\(832\) | 820370. | − | 3.82161e6i | 0.0410867 | − | 0.191398i | ||||
\(833\) | 2.37399e6 | 0.118540 | ||||||||
\(834\) | 6.49662e6 | + | 4.06258e6i | 0.323424 | + | 0.202249i | ||||
\(835\) | 1.28948e7 | 0.640027 | ||||||||
\(836\) | 6.23195e6 | − | 6.91967e6i | 0.308395 | − | 0.342428i | ||||
\(837\) | −1.25692e7 | −0.620146 | ||||||||
\(838\) | 1.79695e7 | + | 1.12370e7i | 0.883949 | + | 0.552766i | ||||
\(839\) | −1.45567e7 | −0.713935 | −0.356967 | − | 0.934117i | \(-0.616189\pi\) | ||||
−0.356967 | + | 0.934117i | \(0.616189\pi\) | |||||||
\(840\) | −624749. | + | 5.88696e6i | −0.0305497 | + | 0.287868i | ||||
\(841\) | 2.05082e7 | 0.999856 | ||||||||
\(842\) | 1.30863e7 | + | 8.18336e6i | 0.636117 | + | 0.397788i | ||||
\(843\) | − | 3.32561e7i | − | 1.61177i | ||||||
\(844\) | 5.11384e6 | + | 1.05028e7i | 0.247110 | + | 0.507517i | ||||
\(845\) | 1.33418e7 | 0.642796 | ||||||||
\(846\) | −4.63328e7 | − | 2.89736e7i | −2.22568 | − | 1.39180i | ||||
\(847\) | − | 4.51063e6i | − | 0.216037i | ||||||
\(848\) | 2.37350e7 | + | 1.85953e7i | 1.13344 | + | 0.888001i | ||||
\(849\) | − | 4.62958e7i | − | 2.20431i | ||||||
\(850\) | 792004. | − | 1.26652e6i | 0.0375993 | − | 0.0601265i | ||||
\(851\) | −1.92360e7 | −0.910523 | ||||||||
\(852\) | −4.44727e6 | − | 9.13385e6i | −0.209891 | − | 0.431077i | ||||
\(853\) | 2.79860e7 | 1.31695 | 0.658474 | − | 0.752604i | \(-0.271202\pi\) | ||||
0.658474 | + | 0.752604i | \(0.271202\pi\) | |||||||
\(854\) | −5.41571e6 | − | 3.38664e6i | −0.254103 | − | 0.158900i | ||||
\(855\) | −1.97762e7 | + | 8.00292e6i | −0.925182 | + | 0.374398i | ||||
\(856\) | 2.32928e7 | + | 2.47193e6i | 1.08652 | + | 0.115306i | ||||
\(857\) | − | 6.77607e6i | − | 0.315156i | −0.987507 | − | 0.157578i | \(-0.949631\pi\) | ||
0.987507 | − | 0.157578i | \(-0.0503686\pi\) | |||||||
\(858\) | −1.62855e6 | + | 2.60428e6i | −0.0755237 | + | 0.120773i | ||||
\(859\) | − | 7.42658e6i | − | 0.343405i | −0.985149 | − | 0.171702i | \(-0.945073\pi\) | ||
0.985149 | − | 0.171702i | \(-0.0549267\pi\) | |||||||
\(860\) | 2.06832e7 | − | 1.00707e7i | 0.953614 | − | 0.464315i | ||||
\(861\) | −4.95856e6 | −0.227954 | ||||||||
\(862\) | −1.14033e7 | + | 1.82355e7i | −0.522713 | + | 0.835890i | ||||
\(863\) | −3.81986e7 | −1.74591 | −0.872953 | − | 0.487805i | \(-0.837798\pi\) | ||||
−0.872953 | + | 0.487805i | \(0.837798\pi\) | |||||||
\(864\) | 5.81727e6 | + | 1.60668e7i | 0.265115 | + | 0.732226i | ||||
\(865\) | 1.69392e7i | 0.769755i | ||||||||
\(866\) | −2.23573e7 | − | 1.39809e7i | −1.01304 | − | 0.633490i | ||||
\(867\) | 3.43740e7 | 1.55304 | ||||||||
\(868\) | −4.35918e6 | + | 2.12249e6i | −0.196384 | + | 0.0956194i | ||||
\(869\) | 1.05529e7i | 0.474049i | ||||||||
\(870\) | −239904. | − | 150021.i | −0.0107458 | − | 0.00671975i | ||||
\(871\) | − | 2.59495e6i | − | 0.115900i | ||||||
\(872\) | −2.35846e6 | + | 2.22236e7i | −0.105036 | + | 0.989745i | ||||
\(873\) | − | 1.24303e7i | − | 0.552009i | ||||||
\(874\) | 1.38574e7 | + | 2.44028e6i | 0.613625 | + | 0.108059i | ||||
\(875\) | 6.44915e6i | 0.284762i | ||||||||
\(876\) | 1.15104e7 | + | 2.36402e7i | 0.506794 | + | 1.04086i | ||||
\(877\) | − | 2.75655e7i | − | 1.21023i | −0.796139 | − | 0.605114i | \(-0.793128\pi\) | ||
0.796139 | − | 0.605114i | \(-0.206872\pi\) | |||||||
\(878\) | 6.71358e6 | − | 1.07359e7i | 0.293912 | − | 0.470007i | ||||
\(879\) | − | 3.25677e6i | − | 0.142172i | ||||||
\(880\) | 5.57015e6 | + | 4.36395e6i | 0.242471 | + | 0.189965i | ||||
\(881\) | −2.02187e7 | −0.877635 | −0.438818 | − | 0.898576i | \(-0.644603\pi\) | ||||
−0.438818 | + | 0.898576i | \(0.644603\pi\) | |||||||
\(882\) | −1.69146e7 | + | 2.70488e7i | −0.732135 | + | 1.17079i | ||||
\(883\) | 9.86623e6i | 0.425843i | 0.977069 | + | 0.212922i | \(0.0682979\pi\) | ||||
−0.977069 | + | 0.212922i | \(0.931702\pi\) | |||||||
\(884\) | −524188. | + | 255227.i | −0.0225609 | + | 0.0109849i | ||||
\(885\) | 2.10381e7 | 0.902920 | ||||||||
\(886\) | 1.69950e6 | + | 1.06276e6i | 0.0727338 | + | 0.0454832i | ||||
\(887\) | 1.02588e7 | 0.437812 | 0.218906 | − | 0.975746i | \(-0.429751\pi\) | ||||
0.218906 | + | 0.975746i | \(0.429751\pi\) | |||||||
\(888\) | 5.72202e6 | − | 5.39181e7i | 0.243510 | − | 2.29458i | ||||
\(889\) | − | 274076.i | − | 0.0116310i | ||||||
\(890\) | −2.47452e7 | − | 1.54741e7i | −1.04717 | − | 0.654832i | ||||
\(891\) | 2.87826e6i | 0.121461i | ||||||||
\(892\) | 5.47620e6 | + | 1.12471e7i | 0.230445 | + | 0.473290i | ||||
\(893\) | −1.57152e7 | − | 3.88342e7i | −0.659464 | − | 1.62962i | ||||
\(894\) | −3.31736e7 | + | 5.30492e7i | −1.38819 | + | 2.21991i | ||||
\(895\) | −1.31252e7 | −0.547708 | ||||||||
\(896\) | 4.73062e6 | + | 4.58988e6i | 0.196856 | + | 0.190999i | ||||
\(897\) | −4.64103e6 | −0.192590 | ||||||||
\(898\) | 1.53941e7 | + | 9.62648e6i | 0.637034 | + | 0.398361i | ||||
\(899\) | − | 231733.i | − | 0.00956287i | ||||||
\(900\) | 8.78756e6 | + | 1.80480e7i | 0.361628 | + | 0.742714i | ||||
\(901\) | − | 4.49749e6i | − | 0.184569i | ||||||
\(902\) | −3.14244e6 | + | 5.02520e6i | −0.128603 | + | 0.205654i | ||||
\(903\) | −1.68394e7 | −0.687240 | ||||||||
\(904\) | −3.83150e6 | + | 3.61040e7i | −0.155937 | + | 1.46938i | ||||
\(905\) | − | 1.22571e7i | − | 0.497470i | ||||||
\(906\) | 2.43276e7 | − | 3.89032e7i | 0.984644 | − | 1.57458i | ||||
\(907\) | 3.62275e6 | 0.146224 | 0.0731122 | − | 0.997324i | \(-0.476707\pi\) | ||||
0.0731122 | + | 0.997324i | \(0.476707\pi\) | |||||||
\(908\) | 1.52094e7 | + | 3.12373e7i | 0.612207 | + | 1.25736i | ||||
\(909\) | −4.07690e7 | −1.63652 | ||||||||
\(910\) | 475351. | − | 760152.i | 0.0190288 | − | 0.0304297i | ||||
\(911\) | 3.77977e7 | 1.50893 | 0.754465 | − | 0.656340i | \(-0.227896\pi\) | ||||
0.754465 | + | 0.656340i | \(0.227896\pi\) | |||||||
\(912\) | −1.09621e7 | + | 3.81161e7i | −0.436423 | + | 1.51747i | ||||
\(913\) | 2.73508e6 | 0.108591 | ||||||||
\(914\) | −2.21179e7 | + | 3.53695e7i | −0.875746 | + | 1.40044i | ||||
\(915\) | 2.92046e7 | 1.15318 | ||||||||
\(916\) | 4.20846e6 | + | 8.64337e6i | 0.165724 | + | 0.340365i | ||||
\(917\) | −2.29995e6 | −0.0903222 | ||||||||
\(918\) | 1.35138e6 | − | 2.16104e6i | 0.0529262 | − | 0.0846363i | ||||
\(919\) | − | 4.62054e7i | − | 1.80469i | −0.431010 | − | 0.902347i | \(-0.641843\pi\) | ||
0.431010 | − | 0.902347i | \(-0.358157\pi\) | |||||||
\(920\) | −1.12831e6 | + | 1.06320e7i | −0.0439502 | + | 0.414139i | ||||
\(921\) | −2.18600e7 | −0.849184 | ||||||||
\(922\) | 5.44184e6 | − | 8.70225e6i | 0.210823 | − | 0.337135i | ||||
\(923\) | 1.53851e6i | 0.0594422i | ||||||||
\(924\) | −2.26749e6 | − | 4.65699e6i | −0.0873707 | − | 0.179443i | ||||
\(925\) | − | 2.10385e7i | − | 0.808462i | ||||||
\(926\) | −2.28752e7 | − | 1.43047e7i | −0.876673 | − | 0.548216i | ||||
\(927\) | 4.21745e7 | 1.61195 | ||||||||
\(928\) | −296217. | + | 107250.i | −0.0112912 | + | 0.00408817i | ||||
\(929\) | 1.29869e7 | 0.493702 | 0.246851 | − | 0.969053i | \(-0.420604\pi\) | ||||
0.246851 | + | 0.969053i | \(0.420604\pi\) | |||||||
\(930\) | 1.17536e7 | − | 1.87957e7i | 0.445619 | − | 0.712607i | ||||
\(931\) | −2.26712e7 | + | 9.17446e6i | −0.857236 | + | 0.346902i | ||||
\(932\) | 1.10759e7 | + | 2.27477e7i | 0.417675 | + | 0.857824i | ||||
\(933\) | − | 6.62494e7i | − | 2.49160i | ||||||
\(934\) | −2.61794e6 | − | 1.63709e6i | −0.0981957 | − | 0.0614054i | ||||
\(935\) | − | 1.05547e6i | − | 0.0394837i | ||||||
\(936\) | 826815. | − | 7.79102e6i | 0.0308474 | − | 0.290673i | ||||
\(937\) | −1.95487e7 | −0.727392 | −0.363696 | − | 0.931518i | \(-0.618485\pi\) | ||||
−0.363696 | + | 0.931518i | \(0.618485\pi\) | |||||||
\(938\) | 3.71024e6 | + | 2.32015e6i | 0.137688 | + | 0.0861012i | ||||
\(939\) | −2.73067e7 | −1.01066 | ||||||||
\(940\) | 2.86209e7 | − | 1.39355e7i | 1.05648 | − | 0.514403i | ||||
\(941\) | 4.73488e7i | 1.74315i | 0.490263 | + | 0.871575i | \(0.336901\pi\) | ||||
−0.490263 | + | 0.871575i | \(0.663099\pi\) | |||||||
\(942\) | 6.63446e6 | − | 1.06094e7i | 0.243601 | − | 0.389551i | ||||
\(943\) | −8.95531e6 | −0.327945 | ||||||||
\(944\) | 1.44460e7 | − | 1.84388e7i | 0.527614 | − | 0.673447i | ||||
\(945\) | 3.91941e6i | 0.142771i | ||||||||
\(946\) | −1.06718e7 | + | 1.70657e7i | −0.387714 | + | 0.620008i | ||||
\(947\) | − | 4.33759e7i | − | 1.57172i | −0.618407 | − | 0.785858i | \(-0.712222\pi\) | ||
0.618407 | − | 0.785858i | \(-0.287778\pi\) | |||||||
\(948\) | −1.96754e7 | − | 4.04094e7i | −0.711053 | − | 1.46037i | ||||
\(949\) | − | 3.98196e6i | − | 0.143526i | ||||||
\(950\) | −2.66894e6 | + | 1.51559e7i | −0.0959465 | + | 0.544844i | ||||
\(951\) | 3.64409e7i | 1.30658i | ||||||||
\(952\) | 103756. | − | 977682.i | 0.00371039 | − | 0.0349627i | ||||
\(953\) | − | 2.83056e7i | − | 1.00958i | −0.863242 | − | 0.504790i | \(-0.831570\pi\) | ||
0.863242 | − | 0.504790i | \(-0.168430\pi\) | |||||||
\(954\) | 5.12438e7 | + | 3.20446e7i | 1.82293 | + | 1.13995i | ||||
\(955\) | − | 3.34903e7i | − | 1.18826i | ||||||
\(956\) | −1.90953e7 | + | 9.29752e6i | −0.675744 | + | 0.329020i | ||||
\(957\) | 247564. | 0.00873792 | ||||||||
\(958\) | 8.63660e6 | + | 5.40078e6i | 0.304039 | + | 0.190127i | ||||
\(959\) | − | 6.52939e6i | − | 0.229259i | ||||||
\(960\) | −2.94657e7 | − | 6.32528e6i | −1.03190 | − | 0.221514i | ||||
\(961\) | −1.04737e7 | −0.365840 | ||||||||
\(962\) | −4.35369e6 | + | 6.96216e6i | −0.151677 | + | 0.242553i | ||||
\(963\) | 4.69517e7 | 1.63149 | ||||||||
\(964\) | −3.36213e7 | + | 1.63702e7i | −1.16526 | + | 0.567364i | ||||
\(965\) | 3.06653e7i | 1.06006i | ||||||||
\(966\) | 4.14957e6 | − | 6.63573e6i | 0.143074 | − | 0.228795i | ||||
\(967\) | − | 1.08700e7i | − | 0.373821i | −0.982377 | − | 0.186911i | \(-0.940153\pi\) | ||
0.982377 | − | 0.186911i | \(-0.0598475\pi\) | |||||||
\(968\) | 2.28340e7 | + | 2.42324e6i | 0.783237 | + | 0.0831204i | ||||
\(969\) | 5.48389e6 | − | 2.21919e6i | 0.187620 | − | 0.0759250i | ||||
\(970\) | 6.13949e6 | + | 3.83925e6i | 0.209509 | + | 0.131014i | ||||
\(971\) | −3.87606e7 | −1.31929 | −0.659647 | − | 0.751575i | \(-0.729294\pi\) | ||||
−0.659647 | + | 0.751575i | \(0.729294\pi\) | |||||||
\(972\) | −1.54080e7 | − | 3.16450e7i | −0.523094 | − | 1.07433i | ||||
\(973\) | 1.95682e6 | 0.0662627 | ||||||||
\(974\) | 1.65006e7 | − | 2.63867e7i | 0.557316 | − | 0.891225i | ||||
\(975\) | − | 5.07591e6i | − | 0.171002i | ||||||
\(976\) | 2.00535e7 | − | 2.55963e7i | 0.673854 | − | 0.860107i | ||||
\(977\) | 3.23311e7i | 1.08364i | 0.840496 | + | 0.541818i | \(0.182264\pi\) | ||||
−0.840496 | + | 0.541818i | \(0.817736\pi\) | |||||||
\(978\) | −3.91331e7 | − | 2.44714e7i | −1.30827 | − | 0.818110i | ||||
\(979\) | 2.55353e7 | 0.851500 | ||||||||
\(980\) | −8.13549e6 | − | 1.67087e7i | −0.270594 | − | 0.555748i | ||||
\(981\) | 4.47965e7i | 1.48618i | ||||||||
\(982\) | 1.56994e7 | + | 9.81739e6i | 0.519521 | + | 0.324876i | ||||
\(983\) | −2.85807e7 | −0.943386 | −0.471693 | − | 0.881763i | \(-0.656357\pi\) | ||||
−0.471693 | + | 0.881763i | \(0.656357\pi\) | |||||||
\(984\) | 2.66388e6 | − | 2.51015e7i | 0.0877055 | − | 0.826442i | ||||
\(985\) | −966348. | −0.0317353 | ||||||||
\(986\) | 39842.2 | + | 24914.8i | 0.00130512 | + | 0.000816141i | ||||
\(987\) | −2.33019e7 | −0.761376 | ||||||||
\(988\) | 4.01957e6 | − | 4.46315e6i | 0.131005 | − | 0.145462i | ||||
\(989\) | −3.04125e7 | −0.988693 | ||||||||
\(990\) | 1.20259e7 | + | 7.52024e6i | 0.389969 | + | 0.243862i | ||||
\(991\) | 3.55974e7 | 1.15142 | 0.575711 | − | 0.817653i | \(-0.304725\pi\) | ||||
0.575711 | + | 0.817653i | \(0.304725\pi\) | |||||||
\(992\) | −8.40271e6 | − | 2.32076e7i | −0.271107 | − | 0.748773i | ||||
\(993\) | 6.79048e7 | 2.18538 | ||||||||
\(994\) | −2.19975e6 | − | 1.37558e6i | −0.0706167 | − | 0.0441592i | ||||
\(995\) | 3.57936e7i | 1.14617i | ||||||||
\(996\) | −1.04732e7 | + | 5.09941e6i | −0.334527 | + | 0.162882i | ||||
\(997\) | 1.29194e7 | 0.411627 | 0.205814 | − | 0.978591i | \(-0.434016\pi\) | ||||
0.205814 | + | 0.978591i | \(0.434016\pi\) | |||||||
\(998\) | −3.37695e7 | − | 2.11173e7i | −1.07324 | − | 0.671138i | ||||
\(999\) | − | 3.58975e7i | − | 1.13802i |
(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 | 76.6.d.a.75.18 | yes | 48 | |
4.3 | odd | 2 | inner | 76.6.d.a.75.32 | yes | 48 | |
19.18 | odd | 2 | inner | 76.6.d.a.75.31 | yes | 48 | |
76.75 | even | 2 | inner | 76.6.d.a.75.17 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.6.d.a.75.17 | ✓ | 48 | 76.75 | even | 2 | inner | |
76.6.d.a.75.18 | yes | 48 | 1.1 | even | 1 | trivial | |
76.6.d.a.75.31 | yes | 48 | 19.18 | odd | 2 | inner | |
76.6.d.a.75.32 | yes | 48 | 4.3 | odd | 2 | inner |