Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [40,6,Mod(29,40)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(40, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("40.29");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 40 = 2^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 40.f (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: | \(6.41535279252\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 29.17 | ||
Character | \(\chi\) | \(=\) | 40.29 |
Dual form | 40.6.f.a.29.18 |
$q$-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 \(\left(\mathbb{Z}/40\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(21\) | \(31\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.42014 | − | 5.47569i | 0.251047 | − | 0.967975i | ||||
\(3\) | −7.17847 | −0.460499 | −0.230250 | − | 0.973132i | \(-0.573954\pi\) | ||||
−0.230250 | + | 0.973132i | \(0.573954\pi\) | |||||||
\(4\) | −27.9664 | − | 15.5525i | −0.873951 | − | 0.486015i | ||||
\(5\) | −1.28331 | − | 55.8870i | −0.0229566 | − | 0.999736i | ||||
\(6\) | −10.1944 | + | 39.3071i | −0.115607 | + | 0.445751i | ||||
\(7\) | 146.905i | 1.13316i | 0.824007 | + | 0.566580i | \(0.191734\pi\) | ||||
−0.824007 | + | 0.566580i | \(0.808266\pi\) | |||||||
\(8\) | −124.877 | + | 131.049i | −0.689853 | + | 0.723950i | ||||
\(9\) | −191.470 | −0.787941 | ||||||||
\(10\) | −307.842 | − | 72.3401i | −0.973483 | − | 0.228760i | ||||
\(11\) | − | 42.4351i | − | 0.105741i | −0.998601 | − | 0.0528705i | \(-0.983163\pi\) | ||
0.998601 | − | 0.0528705i | \(-0.0168371\pi\) | |||||||
\(12\) | 200.756 | + | 111.643i | 0.402453 | + | 0.223809i | ||||
\(13\) | −605.383 | −0.993510 | −0.496755 | − | 0.867891i | \(-0.665475\pi\) | ||||
−0.496755 | + | 0.867891i | \(0.665475\pi\) | |||||||
\(14\) | 804.405 | + | 208.625i | 1.09687 | + | 0.284476i | ||||
\(15\) | 9.21223 | + | 401.183i | 0.0105715 | + | 0.460378i | ||||
\(16\) | 540.241 | + | 869.894i | 0.527579 | + | 0.849506i | ||||
\(17\) | 409.138i | 0.343359i | 0.985153 | + | 0.171679i | \(0.0549193\pi\) | ||||
−0.985153 | + | 0.171679i | \(0.945081\pi\) | |||||||
\(18\) | −271.913 | + | 1048.43i | −0.197810 | + | 0.762707i | ||||
\(19\) | − | 2096.86i | − | 1.33256i | −0.745704 | − | 0.666278i | \(-0.767886\pi\) | ||
0.745704 | − | 0.666278i | \(-0.232114\pi\) | |||||||
\(20\) | −833.291 | + | 1582.92i | −0.465824 | + | 0.884878i | ||||
\(21\) | − | 1054.55i | − | 0.521819i | ||||||
\(22\) | −232.362 | − | 60.2637i | −0.102355 | − | 0.0265460i | ||||
\(23\) | − | 3048.59i | − | 1.20166i | −0.799379 | − | 0.600828i | \(-0.794838\pi\) | ||
0.799379 | − | 0.600828i | \(-0.205162\pi\) | |||||||
\(24\) | 896.424 | − | 940.730i | 0.317677 | − | 0.333378i | ||||
\(25\) | −3121.71 | + | 143.441i | −0.998946 | + | 0.0459011i | ||||
\(26\) | −859.728 | + | 3314.89i | −0.249418 | + | 0.961693i | ||||
\(27\) | 3118.83 | 0.823345 | ||||||||
\(28\) | 2284.73 | − | 4108.40i | 0.550732 | − | 0.990325i | ||||
\(29\) | − | 4594.96i | − | 1.01458i | −0.861775 | − | 0.507290i | \(-0.830647\pi\) | ||
0.861775 | − | 0.507290i | \(-0.169353\pi\) | |||||||
\(30\) | 2209.84 | + | 519.291i | 0.448288 | + | 0.105344i | ||||
\(31\) | −5118.83 | −0.956679 | −0.478339 | − | 0.878175i | \(-0.658761\pi\) | ||||
−0.478339 | + | 0.878175i | \(0.658761\pi\) | |||||||
\(32\) | 5530.49 | − | 1722.83i | 0.954747 | − | 0.297418i | ||||
\(33\) | 304.619i | 0.0486937i | ||||||||
\(34\) | 2240.32 | + | 581.033i | 0.332363 | + | 0.0861992i | ||||
\(35\) | 8210.06 | − | 188.525i | 1.13286 | − | 0.0260135i | ||||
\(36\) | 5354.72 | + | 2977.82i | 0.688621 | + | 0.382951i | ||||
\(37\) | −11248.5 | −1.35080 | −0.675398 | − | 0.737454i | \(-0.736028\pi\) | ||||
−0.675398 | + | 0.737454i | \(0.736028\pi\) | |||||||
\(38\) | −11481.8 | − | 2977.83i | −1.28988 | − | 0.334534i | ||||
\(39\) | 4345.73 | 0.457510 | ||||||||
\(40\) | 7484.18 | + | 6810.80i | 0.739596 | + | 0.673052i | ||||
\(41\) | 11002.0 | 1.02215 | 0.511073 | − | 0.859537i | \(-0.329248\pi\) | ||||
0.511073 | + | 0.859537i | \(0.329248\pi\) | |||||||
\(42\) | −5774.40 | − | 1497.61i | −0.505107 | − | 0.131001i | ||||
\(43\) | 8413.16 | 0.693886 | 0.346943 | − | 0.937886i | \(-0.387220\pi\) | ||||
0.346943 | + | 0.937886i | \(0.387220\pi\) | |||||||
\(44\) | −659.971 | + | 1186.76i | −0.0513917 | + | 0.0924125i | ||||
\(45\) | 245.715 | + | 10700.7i | 0.0180884 | + | 0.787733i | ||||
\(46\) | −16693.2 | − | 4329.42i | −1.16317 | − | 0.301672i | ||||
\(47\) | 3975.72i | 0.262525i | 0.991348 | + | 0.131263i | \(0.0419031\pi\) | ||||
−0.991348 | + | 0.131263i | \(0.958097\pi\) | |||||||
\(48\) | −3878.11 | − | 6244.51i | −0.242950 | − | 0.391197i | ||||
\(49\) | −4774.02 | −0.284049 | ||||||||
\(50\) | −3647.81 | + | 17297.2i | −0.206351 | + | 0.978478i | ||||
\(51\) | − | 2936.99i | − | 0.158116i | ||||||
\(52\) | 16930.4 | + | 9415.21i | 0.868279 | + | 0.482860i | ||||
\(53\) | −38273.5 | −1.87158 | −0.935790 | − | 0.352558i | \(-0.885312\pi\) | ||||
−0.935790 | + | 0.352558i | \(0.885312\pi\) | |||||||
\(54\) | 4429.16 | − | 17077.7i | 0.206698 | − | 0.796977i | ||||
\(55\) | −2371.57 | + | 54.4575i | −0.105713 | + | 0.00242746i | ||||
\(56\) | −19251.7 | − | 18345.0i | −0.820350 | − | 0.781713i | ||||
\(57\) | 15052.2i | 0.613641i | ||||||||
\(58\) | −25160.6 | − | 6525.47i | −0.982088 | − | 0.254707i | ||||
\(59\) | 36611.0i | 1.36924i | 0.728898 | + | 0.684622i | \(0.240033\pi\) | ||||
−0.728898 | + | 0.684622i | \(0.759967\pi\) | |||||||
\(60\) | 5981.75 | − | 11362.9i | 0.214511 | − | 0.407485i | ||||
\(61\) | 3181.32i | 0.109467i | 0.998501 | + | 0.0547335i | \(0.0174309\pi\) | ||||
−0.998501 | + | 0.0547335i | \(0.982569\pi\) | |||||||
\(62\) | −7269.44 | + | 28029.1i | −0.240172 | + | 0.926041i | ||||
\(63\) | − | 28127.8i | − | 0.892862i | ||||||
\(64\) | −1579.62 | − | 32729.9i | −0.0482062 | − | 0.998837i | ||||
\(65\) | 776.897 | + | 33833.0i | 0.0228076 | + | 0.993248i | ||||
\(66\) | 1668.00 | + | 432.601i | 0.0471342 | + | 0.0122244i | ||||
\(67\) | 41894.6 | 1.14017 | 0.570087 | − | 0.821584i | \(-0.306909\pi\) | ||||
0.570087 | + | 0.821584i | \(0.306909\pi\) | |||||||
\(68\) | 6363.11 | − | 11442.1i | 0.166877 | − | 0.300079i | ||||
\(69\) | 21884.2i | 0.553361i | ||||||||
\(70\) | 10627.1 | − | 45223.5i | 0.259221 | − | 1.10311i | ||||
\(71\) | 72161.6 | 1.69887 | 0.849435 | − | 0.527693i | \(-0.176943\pi\) | ||||
0.849435 | + | 0.527693i | \(0.176943\pi\) | |||||||
\(72\) | 23910.1 | − | 25091.9i | 0.543563 | − | 0.570429i | ||||
\(73\) | − | 48275.5i | − | 1.06028i | −0.847911 | − | 0.530138i | \(-0.822140\pi\) | ||
0.847911 | − | 0.530138i | \(-0.177860\pi\) | |||||||
\(74\) | −15974.4 | + | 61593.2i | −0.339113 | + | 1.30754i | ||||
\(75\) | 22409.1 | − | 1029.69i | 0.460014 | − | 0.0211374i | ||||
\(76\) | −32611.3 | + | 58641.7i | −0.647642 | + | 1.16459i | ||||
\(77\) | 6233.92 | 0.119821 | ||||||||
\(78\) | 6171.53 | − | 23795.9i | 0.114857 | − | 0.442859i | ||||
\(79\) | −39428.9 | −0.710798 | −0.355399 | − | 0.934715i | \(-0.615655\pi\) | ||||
−0.355399 | + | 0.934715i | \(0.615655\pi\) | |||||||
\(80\) | 47922.4 | − | 31308.8i | 0.837170 | − | 0.546942i | ||||
\(81\) | 24138.7 | 0.408791 | ||||||||
\(82\) | 15624.4 | − | 60243.7i | 0.256607 | − | 0.989412i | ||||
\(83\) | −46504.5 | −0.740968 | −0.370484 | − | 0.928839i | \(-0.620808\pi\) | ||||
−0.370484 | + | 0.928839i | \(0.620808\pi\) | |||||||
\(84\) | −16400.9 | + | 29492.0i | −0.253612 | + | 0.456044i | ||||
\(85\) | 22865.5 | − | 525.053i | 0.343268 | − | 0.00788235i | ||||
\(86\) | 11947.8 | − | 46067.9i | 0.174198 | − | 0.671664i | ||||
\(87\) | 32984.8i | 0.467213i | ||||||||
\(88\) | 5561.07 | + | 5299.16i | 0.0765512 | + | 0.0729458i | ||||
\(89\) | −38217.3 | −0.511428 | −0.255714 | − | 0.966752i | \(-0.582311\pi\) | ||||
−0.255714 | + | 0.966752i | \(0.582311\pi\) | |||||||
\(90\) | 58942.4 | + | 13850.9i | 0.767047 | + | 0.180249i | ||||
\(91\) | − | 88933.7i | − | 1.12580i | ||||||
\(92\) | −47413.2 | + | 85258.2i | −0.584022 | + | 1.05019i | ||||
\(93\) | 36745.3 | 0.440550 | ||||||||
\(94\) | 21769.8 | + | 5646.07i | 0.254118 | + | 0.0659062i | ||||
\(95\) | −117187. | + | 2690.93i | −1.33220 | + | 0.0305910i | ||||
\(96\) | −39700.4 | + | 12367.3i | −0.439660 | + | 0.136961i | ||||
\(97\) | − | 95979.0i | − | 1.03573i | −0.855462 | − | 0.517865i | \(-0.826727\pi\) | ||
0.855462 | − | 0.517865i | \(-0.173273\pi\) | |||||||
\(98\) | −6779.76 | + | 26141.1i | −0.0713098 | + | 0.274953i | ||||
\(99\) | 8125.03i | 0.0833177i | ||||||||
\(100\) | 89533.8 | + | 44538.7i | 0.895338 | + | 0.445387i | ||||
\(101\) | − | 83900.0i | − | 0.818386i | −0.912448 | − | 0.409193i | \(-0.865810\pi\) | ||
0.912448 | − | 0.409193i | \(-0.134190\pi\) | |||||||
\(102\) | −16082.0 | − | 4170.93i | −0.153053 | − | 0.0396947i | ||||
\(103\) | 10693.4i | 0.0993165i | 0.998766 | + | 0.0496583i | \(0.0158132\pi\) | ||||
−0.998766 | + | 0.0496583i | \(0.984187\pi\) | |||||||
\(104\) | 75598.3 | − | 79334.8i | 0.685376 | − | 0.719251i | ||||
\(105\) | −58935.7 | + | 1353.32i | −0.521681 | + | 0.0119792i | ||||
\(106\) | −54353.6 | + | 209574.i | −0.469855 | + | 1.81164i | ||||
\(107\) | −109794. | −0.927081 | −0.463540 | − | 0.886076i | \(-0.653421\pi\) | ||||
−0.463540 | + | 0.886076i | \(0.653421\pi\) | |||||||
\(108\) | −87222.4 | − | 48505.5i | −0.719563 | − | 0.400158i | ||||
\(109\) | − | 135615.i | − | 1.09330i | −0.837361 | − | 0.546651i | \(-0.815903\pi\) | ||
0.837361 | − | 0.546651i | \(-0.184097\pi\) | |||||||
\(110\) | −3069.76 | + | 13063.3i | −0.0241893 | + | 0.102937i | ||||
\(111\) | 80746.9 | 0.622040 | ||||||||
\(112\) | −127792. | + | 79364.0i | −0.962625 | + | 0.597831i | ||||
\(113\) | 195440.i | 1.43985i | 0.694050 | + | 0.719927i | \(0.255825\pi\) | ||||
−0.694050 | + | 0.719927i | \(0.744175\pi\) | |||||||
\(114\) | 82421.5 | + | 21376.3i | 0.593989 | + | 0.154053i | ||||
\(115\) | −170377. | + | 3912.30i | −1.20134 | + | 0.0275859i | ||||
\(116\) | −71462.9 | + | 128504.i | −0.493101 | + | 0.886693i | ||||
\(117\) | 115913. | 0.782827 | ||||||||
\(118\) | 200470. | + | 51992.6i | 1.32539 | + | 0.343745i | ||||
\(119\) | −60104.4 | −0.389080 | ||||||||
\(120\) | −53725.0 | − | 48891.1i | −0.340583 | − | 0.309940i | ||||
\(121\) | 159250. | 0.988819 | ||||||||
\(122\) | 17420.0 | + | 4517.92i | 0.105961 | + | 0.0274814i | ||||
\(123\) | −78977.7 | −0.470697 | ||||||||
\(124\) | 143155. | + | 79610.4i | 0.836090 | + | 0.464960i | ||||
\(125\) | 12022.6 | + | 174279.i | 0.0688214 | + | 0.997629i | ||||
\(126\) | −154019. | − | 39945.3i | −0.864268 | − | 0.224150i | ||||
\(127\) | 171245.i | 0.942126i | 0.882100 | + | 0.471063i | \(0.156130\pi\) | ||||
−0.882100 | + | 0.471063i | \(0.843870\pi\) | |||||||
\(128\) | −181462. | − | 37831.4i | −0.978952 | − | 0.204093i | ||||
\(129\) | −60393.6 | −0.319534 | ||||||||
\(130\) | 186363. | + | 43793.5i | 0.967165 | + | 0.227275i | ||||
\(131\) | − | 111420.i | − | 0.567265i | −0.958933 | − | 0.283632i | \(-0.908460\pi\) | ||
0.958933 | − | 0.283632i | \(-0.0915395\pi\) | |||||||
\(132\) | 4737.58 | − | 8519.11i | 0.0236658 | − | 0.0425559i | ||||
\(133\) | 308039. | 1.51000 | ||||||||
\(134\) | 59496.1 | − | 229402.i | 0.286238 | − | 1.10366i | ||||
\(135\) | −4002.43 | − | 174302.i | −0.0189012 | − | 0.823128i | ||||
\(136\) | −53617.1 | − | 51091.9i | −0.248574 | − | 0.236867i | ||||
\(137\) | − | 282243.i | − | 1.28476i | −0.766387 | − | 0.642379i | \(-0.777948\pi\) | ||
0.766387 | − | 0.642379i | \(-0.222052\pi\) | |||||||
\(138\) | 119831. | + | 31078.6i | 0.535640 | + | 0.138920i | ||||
\(139\) | 44060.1i | 0.193423i | 0.995312 | + | 0.0967117i | \(0.0308325\pi\) | ||||
−0.995312 | + | 0.0967117i | \(0.969168\pi\) | |||||||
\(140\) | −232538. | − | 122414.i | −1.00271 | − | 0.527852i | ||||
\(141\) | − | 28539.6i | − | 0.120893i | ||||||
\(142\) | 102479. | − | 395135.i | 0.426496 | − | 1.64446i | ||||
\(143\) | 25689.5i | 0.105055i | ||||||||
\(144\) | −103440. | − | 166558.i | −0.415701 | − | 0.669360i | ||||
\(145\) | −256798. | + | 5896.77i | −1.01431 | + | 0.0232913i | ||||
\(146\) | −264342. | − | 68557.8i | −1.02632 | − | 0.266180i | ||||
\(147\) | 34270.1 | 0.130804 | ||||||||
\(148\) | 314580. | + | 174942.i | 1.18053 | + | 0.656506i | ||||
\(149\) | 251552.i | 0.928244i | 0.885771 | + | 0.464122i | \(0.153630\pi\) | ||||
−0.885771 | + | 0.464122i | \(0.846370\pi\) | |||||||
\(150\) | 26185.7 | − | 124167.i | 0.0950246 | − | 0.450588i | ||||
\(151\) | 95790.0 | 0.341883 | 0.170942 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170942 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(152\) | 274791. | + | 261849.i | 0.964703 | + | 0.919267i | ||||
\(153\) | − | 78337.6i | − | 0.270546i | ||||||
\(154\) | 8853.02 | − | 34135.0i | 0.0300808 | − | 0.115984i | ||||
\(155\) | 6569.06 | + | 286076.i | 0.0219621 | + | 0.956427i | ||||
\(156\) | −121534. | − | 67586.8i | −0.399841 | − | 0.222357i | ||||
\(157\) | −178462. | −0.577824 | −0.288912 | − | 0.957356i | \(-0.593294\pi\) | ||||
−0.288912 | + | 0.957356i | \(0.593294\pi\) | |||||||
\(158\) | −55994.4 | + | 215900.i | −0.178444 | + | 0.688035i | ||||
\(159\) | 274745. | 0.861861 | ||||||||
\(160\) | −103381. | − | 306871.i | −0.319257 | − | 0.947668i | ||||
\(161\) | 447853. | 1.36167 | ||||||||
\(162\) | 34280.3 | − | 132176.i | 0.102626 | − | 0.395699i | ||||
\(163\) | 147330. | 0.434332 | 0.217166 | − | 0.976135i | \(-0.430319\pi\) | ||||
0.217166 | + | 0.976135i | \(0.430319\pi\) | |||||||
\(164\) | −307687. | − | 171109.i | −0.893305 | − | 0.496778i | ||||
\(165\) | 17024.2 | − | 390.922i | 0.0486808 | − | 0.00111784i | ||||
\(166\) | −66042.7 | + | 254644.i | −0.186018 | + | 0.717239i | ||||
\(167\) | 310989.i | 0.862888i | 0.902140 | + | 0.431444i | \(0.141996\pi\) | ||||
−0.902140 | + | 0.431444i | \(0.858004\pi\) | |||||||
\(168\) | 138198. | + | 131689.i | 0.377770 | + | 0.359978i | ||||
\(169\) | −4803.84 | −0.0129381 | ||||||||
\(170\) | 29597.1 | − | 125950.i | 0.0785466 | − | 0.334254i | ||||
\(171\) | 401485.i | 1.04997i | ||||||||
\(172\) | −235286. | − | 130845.i | −0.606422 | − | 0.337239i | ||||
\(173\) | −120278. | −0.305542 | −0.152771 | − | 0.988262i | \(-0.548820\pi\) | ||||
−0.152771 | + | 0.988262i | \(0.548820\pi\) | |||||||
\(174\) | 180614. | + | 46842.9i | 0.452251 | + | 0.117293i | ||||
\(175\) | −21072.2 | − | 458594.i | −0.0520133 | − | 1.13196i | ||||
\(176\) | 36914.0 | − | 22925.2i | 0.0898276 | − | 0.0557868i | ||||
\(177\) | − | 262811.i | − | 0.630536i | ||||||
\(178\) | −54273.8 | + | 209266.i | −0.128393 | + | 0.495050i | ||||
\(179\) | − | 180544.i | − | 0.421162i | −0.977576 | − | 0.210581i | \(-0.932464\pi\) | ||
0.977576 | − | 0.210581i | \(-0.0675356\pi\) | |||||||
\(180\) | 159550. | − | 303080.i | 0.367041 | − | 0.697231i | ||||
\(181\) | − | 149699.i | − | 0.339643i | −0.985475 | − | 0.169821i | \(-0.945681\pi\) | ||
0.985475 | − | 0.169821i | \(-0.0543191\pi\) | |||||||
\(182\) | −486974. | − | 126298.i | −1.08975 | − | 0.282630i | ||||
\(183\) | − | 22837.0i | − | 0.0504095i | ||||||
\(184\) | 399515. | + | 380698.i | 0.869938 | + | 0.828965i | ||||
\(185\) | 14435.3 | + | 628643.i | 0.0310097 | + | 1.35044i | ||||
\(186\) | 52183.4 | − | 201206.i | 0.110599 | − | 0.426441i | ||||
\(187\) | 17361.8 | 0.0363071 | ||||||||
\(188\) | 61832.2 | − | 111187.i | 0.127591 | − | 0.229434i | ||||
\(189\) | 458171.i | 0.932981i | ||||||||
\(190\) | −151687. | + | 645502.i | −0.304835 | + | 1.29722i | ||||
\(191\) | 213909. | 0.424273 | 0.212136 | − | 0.977240i | \(-0.431958\pi\) | ||||
0.212136 | + | 0.977240i | \(0.431958\pi\) | |||||||
\(192\) | 11339.3 | + | 234951.i | 0.0221989 | + | 0.459964i | ||||
\(193\) | 729587.i | 1.40988i | 0.709265 | + | 0.704942i | \(0.249027\pi\) | ||||
−0.709265 | + | 0.704942i | \(0.750973\pi\) | |||||||
\(194\) | −525551. | − | 136303.i | −1.00256 | − | 0.260017i | ||||
\(195\) | −5576.93 | − | 242869.i | −0.0105029 | − | 0.457390i | ||||
\(196\) | 133512. | + | 74247.8i | 0.248245 | + | 0.138052i | ||||
\(197\) | −922110. | −1.69285 | −0.846423 | − | 0.532512i | \(-0.821248\pi\) | ||||
−0.846423 | + | 0.532512i | \(0.821248\pi\) | |||||||
\(198\) | 44490.2 | + | 11538.7i | 0.0806494 | + | 0.0209167i | ||||
\(199\) | −985328. | −1.76379 | −0.881897 | − | 0.471442i | \(-0.843734\pi\) | ||||
−0.881897 | + | 0.471442i | \(0.843734\pi\) | |||||||
\(200\) | 371031. | − | 427009.i | 0.655896 | − | 0.754852i | ||||
\(201\) | −300739. | −0.525049 | ||||||||
\(202\) | −459410. | − | 119149.i | −0.792177 | − | 0.205454i | ||||
\(203\) | 675021. | 1.14968 | ||||||||
\(204\) | −45677.4 | + | 82137.0i | −0.0768469 | + | 0.138186i | ||||
\(205\) | −14119.0 | − | 614870.i | −0.0234650 | − | 1.02188i | ||||
\(206\) | 58553.6 | + | 15186.0i | 0.0961359 | + | 0.0249331i | ||||
\(207\) | 583713.i | 0.946833i | ||||||||
\(208\) | −327053. | − | 526619.i | −0.524155 | − | 0.843992i | ||||
\(209\) | −88980.5 | −0.140906 | ||||||||
\(210\) | −76286.4 | + | 324636.i | −0.119371 | + | 0.507982i | ||||
\(211\) | − | 932526.i | − | 1.44197i | −0.692953 | − | 0.720983i | \(-0.743691\pi\) | ||
0.692953 | − | 0.720983i | \(-0.256309\pi\) | |||||||
\(212\) | 1.07037e6 | + | 595247.i | 1.63567 | + | 0.909615i | ||||
\(213\) | −518010. | −0.782328 | ||||||||
\(214\) | −155922. | + | 601196.i | −0.232741 | + | 0.897391i | ||||
\(215\) | −10796.7 | − | 470186.i | −0.0159293 | − | 0.693703i | ||||
\(216\) | −389469. | + | 408719.i | −0.567987 | + | 0.596060i | ||||
\(217\) | − | 751980.i | − | 1.08407i | ||||||
\(218\) | −742584. | − | 192591.i | −1.05829 | − | 0.274470i | ||||
\(219\) | 346544.i | 0.488257i | ||||||||
\(220\) | 67171.3 | + | 35360.8i | 0.0935679 | + | 0.0492567i | ||||
\(221\) | − | 247686.i | − | 0.341130i | ||||||
\(222\) | 114672. | − | 442145.i | 0.156161 | − | 0.602119i | ||||
\(223\) | − | 748564.i | − | 1.00801i | −0.863699 | − | 0.504007i | \(-0.831858\pi\) | ||
0.863699 | − | 0.504007i | \(-0.168142\pi\) | |||||||
\(224\) | 253092. | + | 812455.i | 0.337022 | + | 1.08188i | ||||
\(225\) | 597712. | − | 27464.6i | 0.787110 | − | 0.0361674i | ||||
\(226\) | 1.07017e6 | + | 277552.i | 1.39374 | + | 0.361471i | ||||
\(227\) | 1.47117e6 | 1.89495 | 0.947475 | − | 0.319829i | \(-0.103626\pi\) | ||||
0.947475 | + | 0.319829i | \(0.103626\pi\) | |||||||
\(228\) | 234100. | − | 420957.i | 0.298238 | − | 0.536292i | ||||
\(229\) | − | 835029.i | − | 1.05223i | −0.850412 | − | 0.526117i | \(-0.823647\pi\) | ||
0.850412 | − | 0.526117i | \(-0.176353\pi\) | |||||||
\(230\) | −220536. | + | 938486.i | −0.274890 | + | 1.16979i | ||||
\(231\) | −44750.0 | −0.0551777 | ||||||||
\(232\) | 602164. | + | 573803.i | 0.734505 | + | 0.699911i | ||||
\(233\) | − | 284718.i | − | 0.343577i | −0.985134 | − | 0.171789i | \(-0.945045\pi\) | ||
0.985134 | − | 0.171789i | \(-0.0549546\pi\) | |||||||
\(234\) | 164612. | − | 634701.i | 0.196526 | − | 0.757757i | ||||
\(235\) | 222191. | − | 5102.09i | 0.262456 | − | 0.00602669i | ||||
\(236\) | 569391. | − | 1.02388e6i | 0.665473 | − | 1.19665i | ||||
\(237\) | 283039. | 0.327322 | ||||||||
\(238\) | −85356.5 | + | 329113.i | −0.0976774 | + | 0.376620i | ||||
\(239\) | 800635. | 0.906650 | 0.453325 | − | 0.891345i | \(-0.350238\pi\) | ||||
0.453325 | + | 0.891345i | \(0.350238\pi\) | |||||||
\(240\) | −344010. | + | 224749.i | −0.385516 | + | 0.251866i | ||||
\(241\) | −1.50596e6 | −1.67021 | −0.835107 | − | 0.550088i | \(-0.814594\pi\) | ||||
−0.835107 | + | 0.550088i | \(0.814594\pi\) | |||||||
\(242\) | 226157. | − | 872005.i | 0.248240 | − | 0.957152i | ||||
\(243\) | −931154. | −1.01159 | ||||||||
\(244\) | 49477.4 | − | 88970.2i | 0.0532026 | − | 0.0956688i | ||||
\(245\) | 6126.56 | + | 266805.i | 0.00652081 | + | 0.283975i | ||||
\(246\) | −112159. | + | 432458.i | −0.118167 | + | 0.455623i | ||||
\(247\) | 1.26940e6i | 1.32391i | ||||||||
\(248\) | 639222. | − | 670817.i | 0.659968 | − | 0.692587i | ||||
\(249\) | 333831. | 0.341215 | ||||||||
\(250\) | 971370. | + | 181667.i | 0.982957 | + | 0.183835i | ||||
\(251\) | 1.10255e6i | 1.10463i | 0.833637 | + | 0.552313i | \(0.186255\pi\) | ||||
−0.833637 | + | 0.552313i | \(0.813745\pi\) | |||||||
\(252\) | −437457. | + | 786634.i | −0.433944 | + | 0.780317i | ||||
\(253\) | −129367. | −0.127064 | ||||||||
\(254\) | 937686. | + | 243192.i | 0.911955 | + | 0.236518i | ||||
\(255\) | −164139. | + | 3769.08i | −0.158075 | + | 0.00362981i | ||||
\(256\) | −464854. | + | 939905.i | −0.443320 | + | 0.896364i | ||||
\(257\) | − | 1.41038e6i | − | 1.33200i | −0.745953 | − | 0.665999i | \(-0.768006\pi\) | ||
0.745953 | − | 0.665999i | \(-0.231994\pi\) | |||||||
\(258\) | −85767.2 | + | 330697.i | −0.0802181 | + | 0.309301i | ||||
\(259\) | − | 1.65246e6i | − | 1.53067i | ||||||
\(260\) | 504460. | − | 958272.i | 0.462800 | − | 0.879135i | ||||
\(261\) | 879794.i | 0.799429i | ||||||||
\(262\) | −610103. | − | 158232.i | −0.549098 | − | 0.142410i | ||||
\(263\) | − | 1.68879e6i | − | 1.50552i | −0.658298 | − | 0.752758i | \(-0.728723\pi\) | ||
0.658298 | − | 0.752758i | \(-0.271277\pi\) | |||||||
\(264\) | −39920.0 | − | 38039.8i | −0.0352518 | − | 0.0335915i | ||||
\(265\) | 49116.9 | + | 2.13899e6i | 0.0429651 | + | 1.87109i | ||||
\(266\) | 437457. | − | 1.68673e6i | 0.379081 | − | 1.46164i | ||||
\(267\) | 274342. | 0.235512 | ||||||||
\(268\) | −1.17164e6 | − | 651565.i | −0.996456 | − | 0.554141i | ||||
\(269\) | 305848.i | 0.257706i | 0.991664 | + | 0.128853i | \(0.0411295\pi\) | ||||
−0.991664 | + | 0.128853i | \(0.958870\pi\) | |||||||
\(270\) | −960107. | − | 225616.i | −0.801512 | − | 0.188348i | ||||
\(271\) | −1.25325e6 | −1.03661 | −0.518306 | − | 0.855195i | \(-0.673437\pi\) | ||||
−0.518306 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(272\) | −355907. | + | 221034.i | −0.291685 | + | 0.181149i | ||||
\(273\) | 638408.i | 0.518432i | ||||||||
\(274\) | −1.54547e6 | − | 400823.i | −1.24361 | − | 0.322535i | ||||
\(275\) | 6086.93 | + | 132470.i | 0.00485363 | + | 0.105630i | ||||
\(276\) | 340354. | − | 612024.i | 0.268942 | − | 0.483610i | ||||
\(277\) | 483396. | 0.378533 | 0.189267 | − | 0.981926i | \(-0.439389\pi\) | ||||
0.189267 | + | 0.981926i | \(0.439389\pi\) | |||||||
\(278\) | 241260. | + | 62571.4i | 0.187229 | + | 0.0485584i | ||||
\(279\) | 980100. | 0.753806 | ||||||||
\(280\) | −1.00054e6 | + | 1.09946e6i | −0.762674 | + | 0.838079i | ||||
\(281\) | 88721.8 | 0.0670293 | 0.0335147 | − | 0.999438i | \(-0.489330\pi\) | ||||
0.0335147 | + | 0.999438i | \(0.489330\pi\) | |||||||
\(282\) | −156274. | − | 40530.1i | −0.117021 | − | 0.0303497i | ||||
\(283\) | −1.76445e6 | −1.30961 | −0.654807 | − | 0.755796i | \(-0.727250\pi\) | ||||
−0.654807 | + | 0.755796i | \(0.727250\pi\) | |||||||
\(284\) | −2.01810e6 | − | 1.12229e6i | −1.48473 | − | 0.825676i | ||||
\(285\) | 841224. | − | 19316.7i | 0.613479 | − | 0.0140871i | ||||
\(286\) | 140668. | + | 36482.6i | 0.101690 | + | 0.0263737i | ||||
\(287\) | 1.61625e6i | 1.15825i | ||||||||
\(288\) | −1.05892e6 | + | 329869.i | −0.752284 | + | 0.234347i | ||||
\(289\) | 1.25246e6 | 0.882105 | ||||||||
\(290\) | −332400. | + | 1.41452e6i | −0.232095 | + | 0.987677i | ||||
\(291\) | 688982.i | 0.476953i | ||||||||
\(292\) | −750803. | + | 1.35009e6i | −0.515310 | + | 0.926630i | ||||
\(293\) | −9124.96 | −0.00620957 | −0.00310479 | − | 0.999995i | \(-0.500988\pi\) | ||||
−0.00310479 | + | 0.999995i | \(0.500988\pi\) | |||||||
\(294\) | 48668.3 | − | 187653.i | 0.0328381 | − | 0.126615i | ||||
\(295\) | 2.04608e6 | − | 46983.3i | 1.36888 | − | 0.0314332i | ||||
\(296\) | 1.40467e6 | − | 1.47410e6i | 0.931850 | − | 0.977908i | ||||
\(297\) | − | 132348.i | − | 0.0870614i | ||||||
\(298\) | 1.37742e6 | + | 357238.i | 0.898517 | + | 0.233033i | ||||
\(299\) | 1.84557e6i | 1.19386i | ||||||||
\(300\) | −642716. | − | 319720.i | −0.412302 | − | 0.205100i | ||||
\(301\) | 1.23593e6i | 0.786283i | ||||||||
\(302\) | 136035. | − | 524516.i | 0.0858288 | − | 0.330934i | ||||
\(303\) | 602273.i | 0.376866i | ||||||||
\(304\) | 1.82405e6 | − | 1.13281e6i | 1.13201 | − | 0.703029i | ||||
\(305\) | 177795. | − | 4082.64i | 0.109438 | − | 0.00251299i | ||||
\(306\) | −428952. | − | 111250.i | −0.261882 | − | 0.0679199i | ||||
\(307\) | −2.64214e6 | −1.59996 | −0.799980 | − | 0.600026i | \(-0.795157\pi\) | ||||
−0.799980 | + | 0.600026i | \(0.795157\pi\) | |||||||
\(308\) | −174340. | − | 96952.9i | −0.104718 | − | 0.0582350i | ||||
\(309\) | − | 76762.0i | − | 0.0457352i | ||||||
\(310\) | 1.57579e6 | + | 370297.i | 0.931311 | + | 0.218849i | ||||
\(311\) | −1.40253e6 | −0.822262 | −0.411131 | − | 0.911576i | \(-0.634866\pi\) | ||||
−0.411131 | + | 0.911576i | \(0.634866\pi\) | |||||||
\(312\) | −542680. | + | 569503.i | −0.315615 | + | 0.331214i | ||||
\(313\) | − | 1.35907e6i | − | 0.784115i | −0.919941 | − | 0.392058i | \(-0.871763\pi\) | ||
0.919941 | − | 0.392058i | \(-0.128237\pi\) | |||||||
\(314\) | −253440. | + | 977201.i | −0.145061 | + | 0.559319i | ||||
\(315\) | −1.57198e6 | + | 36096.8i | −0.892627 | + | 0.0204971i | ||||
\(316\) | 1.10268e6 | + | 613216.i | 0.621203 | + | 0.345458i | ||||
\(317\) | 300344. | 0.167869 | 0.0839344 | − | 0.996471i | \(-0.473251\pi\) | ||||
0.0839344 | + | 0.996471i | \(0.473251\pi\) | |||||||
\(318\) | 390176. | − | 1.50442e6i | 0.216368 | − | 0.834259i | ||||
\(319\) | −194987. | −0.107283 | ||||||||
\(320\) | −1.82715e6 | + | 130283.i | −0.997468 | + | 0.0711234i | ||||
\(321\) | 788150. | 0.426920 | ||||||||
\(322\) | 636013. | − | 2.45231e6i | 0.341842 | − | 1.31806i | ||||
\(323\) | 857906. | 0.457545 | ||||||||
\(324\) | −675073. | − | 375416.i | −0.357263 | − | 0.198678i | ||||
\(325\) | 1.88983e6 | − | 86836.8i | 0.992463 | − | 0.0456032i | ||||
\(326\) | 209228. | − | 806732.i | 0.109038 | − | 0.420422i | ||||
\(327\) | 973505.i | 0.503464i | ||||||||
\(328\) | −1.37390e6 | + | 1.44180e6i | −0.705130 | + | 0.739982i | ||||
\(329\) | −584052. | −0.297483 | ||||||||
\(330\) | 22036.2 | − | 93774.7i | 0.0111391 | − | 0.0474024i | ||||
\(331\) | 2.37543e6i | 1.19172i | 0.803090 | + | 0.595858i | \(0.203188\pi\) | ||||
−0.803090 | + | 0.595858i | \(0.796812\pi\) | |||||||
\(332\) | 1.30056e6 | + | 723259.i | 0.647570 | + | 0.360121i | ||||
\(333\) | 2.15374e6 | 1.06435 | ||||||||
\(334\) | 1.70288e6 | + | 441647.i | 0.835253 | + | 0.216625i | ||||
\(335\) | −53763.9 | − | 2.34136e6i | −0.0261745 | − | 1.13987i | ||||
\(336\) | 917348. | − | 569712.i | 0.443288 | − | 0.275301i | ||||
\(337\) | − | 3.69929e6i | − | 1.77437i | −0.461416 | − | 0.887184i | \(-0.652659\pi\) | ||
0.461416 | − | 0.887184i | \(-0.347341\pi\) | |||||||
\(338\) | −6822.11 | + | 26304.4i | −0.00324808 | + | 0.0125238i | ||||
\(339\) | − | 1.40296e6i | − | 0.663051i | ||||||
\(340\) | −647632. | − | 340931.i | −0.303830 | − | 0.159945i | ||||
\(341\) | 217218.i | 0.101160i | ||||||||
\(342\) | 2.19841e6 | + | 570164.i | 1.01635 | + | 0.263593i | ||||
\(343\) | 1.76770e6i | 0.811286i | ||||||||
\(344\) | −1.05061e6 | + | 1.10254e6i | −0.478679 | + | 0.502339i | ||||
\(345\) | 1.22304e6 | − | 28084.3i | 0.553215 | − | 0.0127033i | ||||
\(346\) | −170811. | + | 658605.i | −0.0767054 | + | 0.295757i | ||||
\(347\) | 1.98355e6 | 0.884339 | 0.442170 | − | 0.896931i | \(-0.354209\pi\) | ||||
0.442170 | + | 0.896931i | \(0.354209\pi\) | |||||||
\(348\) | 512994. | − | 922466.i | 0.227072 | − | 0.408321i | ||||
\(349\) | − | 1.51829e6i | − | 0.667256i | −0.942705 | − | 0.333628i | \(-0.891727\pi\) | ||
0.942705 | − | 0.333628i | \(-0.108273\pi\) | |||||||
\(350\) | −2.54104e6 | − | 535881.i | −1.10877 | − | 0.233829i | ||||
\(351\) | −1.88809e6 | −0.818001 | ||||||||
\(352\) | −73108.4 | − | 234687.i | −0.0314493 | − | 0.100956i | ||||
\(353\) | 2.06194e6i | 0.880724i | 0.897820 | + | 0.440362i | \(0.145150\pi\) | ||||
−0.897820 | + | 0.440362i | \(0.854850\pi\) | |||||||
\(354\) | −1.43907e6 | − | 373227.i | −0.610343 | − | 0.158294i | ||||
\(355\) | −92605.9 | − | 4.03289e6i | −0.0390003 | − | 1.69842i | ||||
\(356\) | 1.06880e6 | + | 594373.i | 0.446963 | + | 0.248562i | ||||
\(357\) | 431458. | 0.179171 | ||||||||
\(358\) | −988602. | − | 256397.i | −0.407675 | − | 0.105732i | ||||
\(359\) | 1.33255e6 | 0.545691 | 0.272846 | − | 0.962058i | \(-0.412035\pi\) | ||||
0.272846 | + | 0.962058i | \(0.412035\pi\) | |||||||
\(360\) | −1.43299e6 | − | 1.30406e6i | −0.582757 | − | 0.530325i | ||||
\(361\) | −1.92072e6 | −0.775705 | ||||||||
\(362\) | −819705. | − | 212593.i | −0.328766 | − | 0.0852663i | ||||
\(363\) | −1.14317e6 | −0.455350 | ||||||||
\(364\) | −1.38314e6 | + | 2.48716e6i | −0.547158 | + | 0.983898i | ||||
\(365\) | −2.69797e6 | + | 61952.6i | −1.06000 | + | 0.0243404i | ||||
\(366\) | −125049. | − | 32431.7i | −0.0487951 | − | 0.0126552i | ||||
\(367\) | − | 313330.i | − | 0.121433i | −0.998155 | − | 0.0607166i | \(-0.980661\pi\) | ||
0.998155 | − | 0.0607166i | \(-0.0193386\pi\) | |||||||
\(368\) | 2.65195e6 | − | 1.64698e6i | 1.02081 | − | 0.633969i | ||||
\(369\) | −2.10655e6 | −0.805390 | ||||||||
\(370\) | 3.46276e6 | + | 813716.i | 1.31498 | + | 0.309007i | ||||
\(371\) | − | 5.62256e6i | − | 2.12080i | ||||||
\(372\) | −1.02764e6 | − | 571481.i | −0.385019 | − | 0.214114i | ||||
\(373\) | 2.93069e6 | 1.09068 | 0.545341 | − | 0.838215i | \(-0.316400\pi\) | ||||
0.545341 | + | 0.838215i | \(0.316400\pi\) | |||||||
\(374\) | 24656.2 | − | 95068.1i | 0.00911480 | − | 0.0351444i | ||||
\(375\) | −86303.9 | − | 1.25105e6i | −0.0316922 | − | 0.459407i | ||||
\(376\) | −521014. | − | 496475.i | −0.190055 | − | 0.181104i | ||||
\(377\) | 2.78171e6i | 1.00800i | ||||||||
\(378\) | 2.50880e6 | + | 650665.i | 0.903102 | + | 0.234222i | ||||
\(379\) | 4.10811e6i | 1.46907i | 0.678569 | + | 0.734537i | \(0.262601\pi\) | ||||
−0.678569 | + | 0.734537i | \(0.737399\pi\) | |||||||
\(380\) | 3.31916e6 | + | 1.74729e6i | 1.17915 | + | 0.620736i | ||||
\(381\) | − | 1.22928e6i | − | 0.433848i | ||||||
\(382\) | 303780. | − | 1.17130e6i | 0.106512 | − | 0.410685i | ||||
\(383\) | − | 958991.i | − | 0.334055i | −0.985952 | − | 0.167027i | \(-0.946583\pi\) | ||
0.985952 | − | 0.167027i | \(-0.0534168\pi\) | |||||||
\(384\) | 1.30262e6 | + | 271572.i | 0.450806 | + | 0.0939846i | ||||
\(385\) | −8000.07 | − | 348395.i | −0.00275069 | − | 0.119790i | ||||
\(386\) | 3.99499e6 | + | 1.03611e6i | 1.36473 | + | 0.353948i | ||||
\(387\) | −1.61086e6 | −0.546741 | ||||||||
\(388\) | −1.49271e6 | + | 2.68419e6i | −0.503380 | + | 0.905178i | ||||
\(389\) | − | 647634.i | − | 0.216998i | −0.994097 | − | 0.108499i | \(-0.965396\pi\) | ||
0.994097 | − | 0.108499i | \(-0.0346044\pi\) | |||||||
\(390\) | −1.33780e6 | − | 314370.i | −0.445379 | − | 0.104660i | ||||
\(391\) | 1.24730e6 | 0.412599 | ||||||||
\(392\) | 596164. | − | 625630.i | 0.195952 | − | 0.205637i | ||||
\(393\) | 799827.i | 0.261225i | ||||||||
\(394\) | −1.30952e6 | + | 5.04919e6i | −0.424984 | + | 1.63863i | ||||
\(395\) | 50599.6 | + | 2.20356e6i | 0.0163175 | + | 0.710611i | ||||
\(396\) | 126364. | − | 227228.i | 0.0404936 | − | 0.0728155i | ||||
\(397\) | −2.06284e6 | −0.656885 | −0.328443 | − | 0.944524i | \(-0.606524\pi\) | ||||
−0.328443 | + | 0.944524i | \(0.606524\pi\) | |||||||
\(398\) | −1.39930e6 | + | 5.39535e6i | −0.442796 | + | 1.70731i | ||||
\(399\) | −2.21125e6 | −0.695352 | ||||||||
\(400\) | −1.81125e6 | − | 2.63806e6i | −0.566017 | − | 0.824394i | ||||
\(401\) | −1.92225e6 | −0.596964 | −0.298482 | − | 0.954415i | \(-0.596480\pi\) | ||||
−0.298482 | + | 0.954415i | \(0.596480\pi\) | |||||||
\(402\) | −427091. | + | 1.64676e6i | −0.131812 | + | 0.508234i | ||||
\(403\) | 3.09885e6 | 0.950470 | ||||||||
\(404\) | −1.30485e6 | + | 2.34638e6i | −0.397748 | + | 0.715229i | ||||
\(405\) | −30977.5 | − | 1.34904e6i | −0.00938446 | − | 0.408683i | ||||
\(406\) | 958623. | − | 3.69621e6i | 0.288624 | − | 1.11286i | ||||
\(407\) | 477330.i | 0.142834i | ||||||||
\(408\) | 384889. | + | 366761.i | 0.114468 | + | 0.109077i | ||||
\(409\) | 1.40471e6 | 0.415221 | 0.207610 | − | 0.978212i | \(-0.433431\pi\) | ||||
0.207610 | + | 0.978212i | \(0.433431\pi\) | |||||||
\(410\) | −3.38689e6 | − | 795888.i | −0.995042 | − | 0.233826i | ||||
\(411\) | 2.02607e6i | 0.591630i | ||||||||
\(412\) | 166308. | − | 299055.i | 0.0482693 | − | 0.0867977i | ||||
\(413\) | −5.37833e6 | −1.55157 | ||||||||
\(414\) | 3.19623e6 | + | 828952.i | 0.916511 | + | 0.237700i | ||||
\(415\) | 59679.8 | + | 2.59899e6i | 0.0170101 | + | 0.740773i | ||||
\(416\) | −3.34807e6 | + | 1.04297e6i | −0.948551 | + | 0.295487i | ||||
\(417\) | − | 316284.i | − | 0.0890712i | ||||||
\(418\) | −126364. | + | 487230.i | −0.0353740 | + | 0.136393i | ||||
\(419\) | − | 4.03594e6i | − | 1.12308i | −0.827451 | − | 0.561538i | \(-0.810210\pi\) | ||
0.827451 | − | 0.561538i | \(-0.189790\pi\) | |||||||
\(420\) | 1.66927e6 | + | 878748.i | 0.461746 | + | 0.243075i | ||||
\(421\) | − | 594910.i | − | 0.163586i | −0.996649 | − | 0.0817929i | \(-0.973935\pi\) | ||
0.996649 | − | 0.0817929i | \(-0.0260646\pi\) | |||||||
\(422\) | −5.10623e6 | − | 1.32432e6i | −1.39579 | − | 0.362001i | ||||
\(423\) | − | 761229.i | − | 0.206854i | ||||||
\(424\) | 4.77947e6 | − | 5.01570e6i | 1.29111 | − | 1.35493i | ||||
\(425\) | −58687.2 | − | 1.27721e6i | −0.0157605 | − | 0.342997i | ||||
\(426\) | −735645. | + | 2.83646e6i | −0.196401 | + | 0.757274i | ||||
\(427\) | −467352. | −0.124044 | ||||||||
\(428\) | 3.07053e6 | + | 1.70756e6i | 0.810223 | + | 0.450575i | ||||
\(429\) | − | 184411.i | − | 0.0483776i | ||||||
\(430\) | −2.58993e6 | − | 608609.i | −0.675486 | − | 0.158733i | ||||
\(431\) | 4.15801e6 | 1.07818 | 0.539091 | − | 0.842247i | \(-0.318768\pi\) | ||||
0.539091 | + | 0.842247i | \(0.318768\pi\) | |||||||
\(432\) | 1.68492e6 | + | 2.71305e6i | 0.434380 | + | 0.699436i | ||||
\(433\) | 2.27636e6i | 0.583474i | 0.956499 | + | 0.291737i | \(0.0942333\pi\) | ||||
−0.956499 | + | 0.291737i | \(0.905767\pi\) | |||||||
\(434\) | −4.11761e6 | − | 1.06792e6i | −1.04935 | − | 0.272153i | ||||
\(435\) | 1.84342e6 | − | 42329.8i | 0.467090 | − | 0.0107256i | ||||
\(436\) | −2.10914e6 | + | 3.79265e6i | −0.531361 | + | 0.955492i | ||||
\(437\) | −6.39247e6 | −1.60127 | ||||||||
\(438\) | 1.89757e6 | + | 492140.i | 0.472620 | + | 0.122575i | ||||
\(439\) | −1.28126e6 | −0.317305 | −0.158653 | − | 0.987334i | \(-0.550715\pi\) | ||||
−0.158653 | + | 0.987334i | \(0.550715\pi\) | |||||||
\(440\) | 289017. | − | 317592.i | 0.0711692 | − | 0.0782056i | ||||
\(441\) | 914079. | 0.223814 | ||||||||
\(442\) | −1.35625e6 | − | 351748.i | −0.330205 | − | 0.0856398i | ||||
\(443\) | 6.01266e6 | 1.45565 | 0.727825 | − | 0.685763i | \(-0.240531\pi\) | ||||
0.727825 | + | 0.685763i | \(0.240531\pi\) | |||||||
\(444\) | −2.25820e6 | − | 1.25581e6i | −0.543632 | − | 0.302320i | ||||
\(445\) | 49044.7 | + | 2.13585e6i | 0.0117407 | + | 0.511294i | ||||
\(446\) | −4.09891e6 | − | 1.06306e6i | −0.975733 | − | 0.253059i | ||||
\(447\) | − | 1.80576e6i | − | 0.427455i | ||||||
\(448\) | 4.80818e6 | − | 232054.i | 1.13184 | − | 0.0546253i | ||||
\(449\) | 2.11543e6 | 0.495202 | 0.247601 | − | 0.968862i | \(-0.420358\pi\) | ||||
0.247601 | + | 0.968862i | \(0.420358\pi\) | |||||||
\(450\) | 698445. | − | 3.31189e6i | 0.162593 | − | 0.770983i | ||||
\(451\) | − | 466872.i | − | 0.108083i | ||||||
\(452\) | 3.03958e6 | − | 5.46577e6i | 0.699790 | − | 1.25836i | ||||
\(453\) | −687625. | −0.157437 | ||||||||
\(454\) | 2.08926e6 | − | 8.05567e6i | 0.475722 | − | 1.83426i | ||||
\(455\) | −4.97024e6 | + | 114130.i | −1.12551 | + | 0.0258447i | ||||
\(456\) | −1.97258e6 | − | 1.87967e6i | −0.444245 | − | 0.423322i | ||||
\(457\) | − | 1.35964e6i | − | 0.304533i | −0.988339 | − | 0.152267i | \(-0.951343\pi\) | ||
0.988339 | − | 0.152267i | \(-0.0486573\pi\) | |||||||
\(458\) | −4.57236e6 | − | 1.18586e6i | −1.01854 | − | 0.264161i | ||||
\(459\) | 1.27603e6i | 0.282703i | ||||||||
\(460\) | 4.82567e6 | + | 2.54036e6i | 1.06332 | + | 0.559759i | ||||
\(461\) | 2.06438e6i | 0.452415i | 0.974079 | + | 0.226208i | \(0.0726328\pi\) | ||||
−0.974079 | + | 0.226208i | \(0.927367\pi\) | |||||||
\(462\) | −63551.2 | + | 245037.i | −0.0138522 | + | 0.0534106i | ||||
\(463\) | 1.48917e6i | 0.322843i | 0.986886 | + | 0.161421i | \(0.0516078\pi\) | ||||
−0.986886 | + | 0.161421i | \(0.948392\pi\) | |||||||
\(464\) | 3.99712e6 | − | 2.48239e6i | 0.861892 | − | 0.535272i | ||||
\(465\) | −47155.8 | − | 2.05359e6i | −0.0101135 | − | 0.440434i | ||||
\(466\) | −1.55903e6 | − | 404338.i | −0.332574 | − | 0.0862541i | ||||
\(467\) | 7.05856e6 | 1.49770 | 0.748849 | − | 0.662741i | \(-0.230607\pi\) | ||||
0.748849 | + | 0.662741i | \(0.230607\pi\) | |||||||
\(468\) | −3.24166e6 | − | 1.80273e6i | −0.684152 | − | 0.380465i | ||||
\(469\) | 6.15452e6i | 1.29200i | ||||||||
\(470\) | 287604. | − | 1.22389e6i | 0.0600552 | − | 0.255564i | ||||
\(471\) | 1.28108e6 | 0.266087 | ||||||||
\(472\) | −4.79783e6 | − | 4.57186e6i | −0.991264 | − | 0.944577i | ||||
\(473\) | − | 357014.i | − | 0.0733722i | ||||||
\(474\) | 401954. | − | 1.54983e6i | 0.0821732 | − | 0.316839i | ||||
\(475\) | 300776. | + | 6.54578e6i | 0.0611658 | + | 1.33115i | ||||
\(476\) | 1.68090e6 | + | 934772.i | 0.340037 | + | 0.189099i | ||||
\(477\) | 7.32821e6 | 1.47469 | ||||||||
\(478\) | 1.13701e6 | − | 4.38403e6i | 0.227612 | − | 0.877614i | ||||
\(479\) | 1.47482e6 | 0.293697 | 0.146849 | − | 0.989159i | \(-0.453087\pi\) | ||||
0.146849 | + | 0.989159i | \(0.453087\pi\) | |||||||
\(480\) | 742117. | + | 2.20287e6i | 0.147018 | + | 0.436400i | ||||
\(481\) | 6.80964e6 | 1.34203 | ||||||||
\(482\) | −2.13867e6 | + | 8.24619e6i | −0.419302 | + | 1.61672i | ||||
\(483\) | −3.21490e6 | −0.627046 | ||||||||
\(484\) | −4.45366e6 | − | 2.47673e6i | −0.864179 | − | 0.480580i | ||||
\(485\) | −5.36397e6 | + | 123171.i | −1.03546 | + | 0.0237769i | ||||
\(486\) | −1.32237e6 | + | 5.09871e6i | −0.253958 | + | 0.979196i | ||||
\(487\) | − | 9.13416e6i | − | 1.74520i | −0.488433 | − | 0.872602i | \(-0.662431\pi\) | ||
0.488433 | − | 0.872602i | \(-0.337569\pi\) | |||||||
\(488\) | −416909. | − | 397273.i | −0.0792486 | − | 0.0755161i | ||||
\(489\) | −1.05760e6 | −0.200009 | ||||||||
\(490\) | 1.46964e6 | + | 345353.i | 0.276517 | + | 0.0649790i | ||||
\(491\) | 4.74188e6i | 0.887660i | 0.896111 | + | 0.443830i | \(0.146381\pi\) | ||||
−0.896111 | + | 0.443830i | \(0.853619\pi\) | |||||||
\(492\) | 2.20872e6 | + | 1.22830e6i | 0.411366 | + | 0.228766i | ||||
\(493\) | 1.87997e6 | 0.348365 | ||||||||
\(494\) | 6.95087e6 | + | 1.80273e6i | 1.28151 | + | 0.332363i | ||||
\(495\) | 454083. | − | 10427.0i | 0.0832957 | − | 0.00191269i | ||||
\(496\) | −2.76540e6 | − | 4.45284e6i | −0.504724 | − | 0.812704i | ||||
\(497\) | 1.06009e7i | 1.92509i | ||||||||
\(498\) | 474086. | − | 1.82796e6i | 0.0856611 | − | 0.330288i | ||||
\(499\) | − | 539009.i | − | 0.0969046i | −0.998825 | − | 0.0484523i | \(-0.984571\pi\) | ||
0.998825 | − | 0.0484523i | \(-0.0154289\pi\) | |||||||
\(500\) | 2.37423e6 | − | 5.06093e6i | 0.424716 | − | 0.905327i | ||||
\(501\) | − | 2.23243e6i | − | 0.397359i | ||||||
\(502\) | 6.03724e6 | + | 1.56578e6i | 1.06925 | + | 0.277313i | ||||
\(503\) | 2.21657e6i | 0.390627i | 0.980741 | + | 0.195313i | \(0.0625724\pi\) | ||||
−0.980741 | + | 0.195313i | \(0.937428\pi\) | |||||||
\(504\) | 3.68612e6 | + | 3.51251e6i | 0.646387 | + | 0.615943i | ||||
\(505\) | −4.68891e6 | + | 107670.i | −0.818171 | + | 0.0187874i | ||||
\(506\) | −183719. | + | 708376.i | −0.0318991 | + | 0.122995i | ||||
\(507\) | 34484.2 | 0.00595800 | ||||||||
\(508\) | 2.66329e6 | − | 4.78912e6i | 0.457887 | − | 0.823372i | ||||
\(509\) | − | 3.35132e6i | − | 0.573352i | −0.958028 | − | 0.286676i | \(-0.907450\pi\) | ||
0.958028 | − | 0.286676i | \(-0.0925503\pi\) | |||||||
\(510\) | −212462. | + | 904129.i | −0.0361706 | + | 0.153924i | ||||
\(511\) | 7.09190e6 | 1.20146 | ||||||||
\(512\) | 4.48648e6 | + | 3.88019e6i | 0.756363 | + | 0.654152i | ||||
\(513\) | − | 6.53974e6i | − | 1.09715i | ||||||
\(514\) | −7.72281e6 | − | 2.00293e6i | −1.28934 | − | 0.334394i | ||||
\(515\) | 597620. | − | 13722.9i | 0.0992903 | − | 0.00227997i | ||||
\(516\) | 1.68899e6 | + | 939270.i | 0.279257 | + | 0.155298i | ||||
\(517\) | 168710. | 0.0277597 | ||||||||
\(518\) | −9.04834e6 | − | 2.34671e6i | −1.48165 | − | 0.384269i | ||||
\(519\) | 863411. | 0.140702 | ||||||||
\(520\) | −4.53080e6 | − | 4.12315e6i | −0.734795 | − | 0.668683i | ||||
\(521\) | 5.01924e6 | 0.810109 | 0.405054 | − | 0.914293i | \(-0.367253\pi\) | ||||
0.405054 | + | 0.914293i | \(0.367253\pi\) | |||||||
\(522\) | 4.81748e6 | + | 1.24943e6i | 0.773827 | + | 0.200694i | ||||
\(523\) | −3.44581e6 | −0.550855 | −0.275428 | − | 0.961322i | \(-0.588819\pi\) | ||||
−0.275428 | + | 0.961322i | \(0.588819\pi\) | |||||||
\(524\) | −1.73286e6 | + | 3.11602e6i | −0.275699 | + | 0.495761i | ||||
\(525\) | 151266. | + | 3.29200e6i | 0.0239521 | + | 0.521269i | ||||
\(526\) | −9.24727e6 | − | 2.39831e6i | −1.45730 | − | 0.377955i | ||||
\(527\) | − | 2.09431e6i | − | 0.328484i | ||||||
\(528\) | −264986. | + | 164568.i | −0.0413655 | + | 0.0256898i | ||||
\(529\) | −2.85758e6 | −0.443975 | ||||||||
\(530\) | 1.17822e7 | + | 2.76871e6i | 1.82195 | + | 0.428142i | ||||
\(531\) | − | 7.00988e6i | − | 1.07888i | ||||||
\(532\) | −8.61474e6 | − | 4.79076e6i | −1.31966 | − | 0.733881i | ||||
\(533\) | −6.66044e6 | −1.01551 | ||||||||
\(534\) | 389603. | − | 1.50221e6i | 0.0591247 | − | 0.227970i | ||||
\(535\) | 140900. | + | 6.13603e6i | 0.0212826 | + | 0.926836i | ||||
\(536\) | −5.23166e6 | + | 5.49024e6i | −0.786552 | + | 0.825429i | ||||
\(537\) | 1.29603e6i | 0.193945i | ||||||||
\(538\) | 1.67473e6 | + | 434346.i | 0.249453 | + | 0.0646963i | ||||
\(539\) | 202586.i | 0.0300357i | ||||||||
\(540\) | −2.59889e6 | + | 4.93684e6i | −0.383534 | + | 0.728559i | ||||
\(541\) | − | 3.97667e6i | − | 0.584153i | −0.956395 | − | 0.292076i | \(-0.905654\pi\) | ||
0.956395 | − | 0.292076i | \(-0.0943461\pi\) | |||||||
\(542\) | −1.77979e6 | + | 6.86244e6i | −0.260238 | + | 1.00341i | ||||
\(543\) | 1.07461e6i | 0.156405i | ||||||||
\(544\) | 704875. | + | 2.26274e6i | 0.102121 | + | 0.327821i | ||||
\(545\) | −7.57908e6 | + | 174036.i | −1.09301 | + | 0.0250985i | ||||
\(546\) | 3.49573e6 | + | 906627.i | 0.501829 | + | 0.130151i | ||||
\(547\) | −9.20664e6 | −1.31563 | −0.657814 | − | 0.753181i | \(-0.728519\pi\) | ||||
−0.657814 | + | 0.753181i | \(0.728519\pi\) | |||||||
\(548\) | −4.38957e6 | + | 7.89332e6i | −0.624411 | + | 1.12281i | ||||
\(549\) | − | 609127.i | − | 0.0862535i | ||||||
\(550\) | 734009. | + | 154795.i | 0.103465 | + | 0.0218198i | ||||
\(551\) | −9.63498e6 | −1.35198 | ||||||||
\(552\) | −2.86790e6 | − | 2.73283e6i | −0.400606 | − | 0.381738i | ||||
\(553\) | − | 5.79229e6i | − | 0.805448i | ||||||
\(554\) | 686489. | − | 2.64693e6i | 0.0950296 | − | 0.366410i | ||||
\(555\) | −103624. | − | 4.51270e6i | −0.0142799 | − | 0.621876i | ||||
\(556\) | 685244. | − | 1.23220e6i | 0.0940066 | − | 0.169042i | ||||
\(557\) | 6.00805e6 | 0.820531 | 0.410266 | − | 0.911966i | \(-0.365436\pi\) | ||||
0.410266 | + | 0.911966i | \(0.365436\pi\) | |||||||
\(558\) | 1.39188e6 | − | 5.36672e6i | 0.189241 | − | 0.729665i | ||||
\(559\) | −5.09319e6 | −0.689383 | ||||||||
\(560\) | 4.59941e6 | + | 7.04003e6i | 0.619773 | + | 0.948647i | ||||
\(561\) | −124631. | −0.0167194 | ||||||||
\(562\) | 125997. | − | 485814.i | 0.0168275 | − | 0.0648827i | ||||
\(563\) | −3.22469e6 | −0.428763 | −0.214381 | − | 0.976750i | \(-0.568774\pi\) | ||||
−0.214381 | + | 0.976750i | \(0.568774\pi\) | |||||||
\(564\) | −443861. | + | 798150.i | −0.0587556 | + | 0.105654i | ||||
\(565\) | 1.09226e7 | − | 250811.i | 1.43947 | − | 0.0330542i | ||||
\(566\) | −2.50576e6 | + | 9.66158e6i | −0.328775 | + | 1.26767i | ||||
\(567\) | 3.54609e6i | 0.463225i | ||||||||
\(568\) | −9.01130e6 | + | 9.45669e6i | −1.17197 | + | 1.22990i | ||||
\(569\) | −3.74802e6 | −0.485312 | −0.242656 | − | 0.970112i | \(-0.578019\pi\) | ||||
−0.242656 | + | 0.970112i | \(0.578019\pi\) | |||||||
\(570\) | 1.08888e6 | − | 4.63372e6i | 0.140376 | − | 0.597369i | ||||
\(571\) | − | 4.37966e6i | − | 0.562148i | −0.959686 | − | 0.281074i | \(-0.909309\pi\) | ||
0.959686 | − | 0.281074i | \(-0.0906906\pi\) | |||||||
\(572\) | 399535. | − | 718444.i | 0.0510582 | − | 0.0918127i | ||||
\(573\) | −1.53554e6 | −0.195377 | ||||||||
\(574\) | 8.85009e6 | + | 2.29530e6i | 1.12116 | + | 0.290776i | ||||
\(575\) | 437293. | + | 9.51681e6i | 0.0551573 | + | 1.20039i | ||||
\(576\) | 302449. | + | 6.26678e6i | 0.0379836 | + | 0.787025i | ||||
\(577\) | 1.03145e7i | 1.28976i | 0.764284 | + | 0.644880i | \(0.223093\pi\) | ||||
−0.764284 | + | 0.644880i | \(0.776907\pi\) | |||||||
\(578\) | 1.77867e6 | − | 6.85810e6i | 0.221450 | − | 0.853855i | ||||
\(579\) | − | 5.23732e6i | − | 0.649251i | ||||||
\(580\) | 7.27344e6 | + | 3.82893e6i | 0.897779 | + | 0.472615i | ||||
\(581\) | − | 6.83173e6i | − | 0.839635i | ||||||
\(582\) | 3.77266e6 | + | 978449.i | 0.461679 | + | 0.119738i | ||||
\(583\) | 1.62414e6i | 0.197903i | ||||||||
\(584\) | 6.32645e6 | + | 6.02848e6i | 0.767587 | + | 0.731435i | ||||
\(585\) | −148752. | − | 6.47800e6i | −0.0179710 | − | 0.782620i | ||||
\(586\) | −12958.7 | + | 49965.5i | −0.00155890 | + | 0.00601071i | ||||
\(587\) | −5.88489e6 | −0.704925 | −0.352463 | − | 0.935826i | \(-0.614656\pi\) | ||||
−0.352463 | + | 0.935826i | \(0.614656\pi\) | |||||||
\(588\) | −958413. | − | 532985.i | −0.114317 | − | 0.0635729i | ||||
\(589\) | 1.07335e7i | 1.27483i | ||||||||
\(590\) | 2.64844e6 | − | 1.12704e7i | 0.313228 | − | 1.33294i | ||||
\(591\) | 6.61934e6 | 0.779554 | ||||||||
\(592\) | −6.07689e6 | − | 9.78498e6i | −0.712652 | − | 1.14751i | ||||
\(593\) | − | 1.07458e7i | − | 1.25488i | −0.778664 | − | 0.627442i | \(-0.784102\pi\) | ||
0.778664 | − | 0.627442i | \(-0.215898\pi\) | |||||||
\(594\) | −724696. | − | 187952.i | −0.0842732 | − | 0.0218565i | ||||
\(595\) | 77132.8 | + | 3.35905e6i | 0.00893196 | + | 0.388977i | ||||
\(596\) | 3.91226e6 | − | 7.03501e6i | 0.451140 | − | 0.811239i | ||||
\(597\) | 7.07314e6 | 0.812226 | ||||||||
\(598\) | 1.01058e7 | + | 2.62096e6i | 1.15562 | + | 0.299714i | ||||
\(599\) | 1.01249e6 | 0.115299 | 0.0576493 | − | 0.998337i | \(-0.481639\pi\) | ||||
0.0576493 | + | 0.998337i | \(0.481639\pi\) | |||||||
\(600\) | −2.66343e6 | + | 3.06527e6i | −0.302039 | + | 0.347608i | ||||
\(601\) | 7.16049e6 | 0.808643 | 0.404321 | − | 0.914617i | \(-0.367508\pi\) | ||||
0.404321 | + | 0.914617i | \(0.367508\pi\) | |||||||
\(602\) | 6.76759e6 | + | 1.75520e6i | 0.761102 | + | 0.197394i | ||||
\(603\) | −8.02154e6 | −0.898390 | ||||||||
\(604\) | −2.67890e6 | − | 1.48977e6i | −0.298789 | − | 0.166160i | ||||
\(605\) | −204368. | − | 8.90001e6i | −0.0226999 | − | 0.988558i | ||||
\(606\) | 3.29786e6 | + | 855311.i | 0.364797 | + | 0.0946112i | ||||
\(607\) | − | 1.22036e7i | − | 1.34437i | −0.740385 | − | 0.672183i | \(-0.765357\pi\) | ||
0.740385 | − | 0.672183i | \(-0.234643\pi\) | |||||||
\(608\) | −3.61253e6 | − | 1.15967e7i | −0.396326 | − | 1.27225i | ||||
\(609\) | −4.84562e6 | −0.529427 | ||||||||
\(610\) | 230137. | − | 979346.i | 0.0250416 | − | 0.106564i | ||||
\(611\) | − | 2.40683e6i | − | 0.260821i | ||||||
\(612\) | −1.21834e6 | + | 2.19082e6i | −0.131489 | + | 0.236444i | ||||
\(613\) | 1.15888e7 | 1.24563 | 0.622815 | − | 0.782369i | \(-0.285989\pi\) | ||||
0.622815 | + | 0.782369i | \(0.285989\pi\) | |||||||
\(614\) | −3.75220e6 | + | 1.44675e7i | −0.401666 | + | 1.54872i | ||||
\(615\) | 101353. | + | 4.41382e6i | 0.0108056 | + | 0.470573i | ||||
\(616\) | −778471. | + | 816948.i | −0.0826591 | + | 0.0867447i | ||||
\(617\) | 1.47499e6i | 0.155983i | 0.996954 | + | 0.0779915i | \(0.0248507\pi\) | ||||
−0.996954 | + | 0.0779915i | \(0.975149\pi\) | |||||||
\(618\) | −420325. | − | 109013.i | −0.0442705 | − | 0.0114817i | ||||
\(619\) | 6.94510e6i | 0.728537i | 0.931294 | + | 0.364269i | \(0.118681\pi\) | ||||
−0.931294 | + | 0.364269i | \(0.881319\pi\) | |||||||
\(620\) | 4.26547e6 | − | 8.10268e6i | 0.445644 | − | 0.846544i | ||||
\(621\) | − | 9.50803e6i | − | 0.989377i | ||||||
\(622\) | −1.99178e6 | + | 7.67981e6i | −0.206427 | + | 0.795929i | ||||
\(623\) | − | 5.61430e6i | − | 0.579530i | ||||||
\(624\) | 2.34774e6 | + | 3.78032e6i | 0.241373 | + | 0.388658i | ||||
\(625\) | 9.72447e6 | − | 895561.i | 0.995786 | − | 0.0917055i | ||||
\(626\) | −7.44183e6 | − | 1.93006e6i | −0.759004 | − | 0.196850i | ||||
\(627\) | 638744. | 0.0648870 | ||||||||
\(628\) | 4.99093e6 | + | 2.77552e6i | 0.504990 | + | 0.280831i | ||||
\(629\) | − | 4.60218e6i | − | 0.463807i | ||||||
\(630\) | −2.03477e6 | + | 8.65893e6i | −0.204251 | + | 0.869186i | ||||
\(631\) | 3.38551e6 | 0.338494 | 0.169247 | − | 0.985574i | \(-0.445867\pi\) | ||||
0.169247 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(632\) | 4.92374e6 | − | 5.16711e6i | 0.490346 | − | 0.514582i | ||||
\(633\) | 6.69411e6i | 0.664024i | ||||||||
\(634\) | 426529. | − | 1.64459e6i | 0.0421430 | − | 0.162493i | ||||
\(635\) | 9.57037e6 | − | 219761.i | 0.941878 | − | 0.0216280i | ||||
\(636\) | −7.68364e6 | − | 4.27296e6i | −0.753224 | − | 0.418877i | ||||
\(637\) | 2.89011e6 | 0.282206 | ||||||||
\(638\) | −276909. | + | 1.06769e6i | −0.0269330 | + | 0.103847i | ||||
\(639\) | −1.38167e7 | −1.33861 | ||||||||
\(640\) | −1.88141e6 | + | 1.01899e7i | −0.181566 | + | 0.983379i | ||||
\(641\) | −6.43478e6 | −0.618570 | −0.309285 | − | 0.950969i | \(-0.600090\pi\) | ||||
−0.309285 | + | 0.950969i | \(0.600090\pi\) | |||||||
\(642\) | 1.11928e6 | − | 4.31567e6i | 0.107177 | − | 0.413248i | ||||
\(643\) | 819506. | 0.0781672 | 0.0390836 | − | 0.999236i | \(-0.487556\pi\) | ||||
0.0390836 | + | 0.999236i | \(0.487556\pi\) | |||||||
\(644\) | −1.25248e7 | − | 6.96522e6i | −1.19003 | − | 0.661790i | ||||
\(645\) | 77504.0 | + | 3.37522e6i | 0.00733541 | + | 0.319450i | ||||
\(646\) | 1.21834e6 | − | 4.69763e6i | 0.114865 | − | 0.442892i | ||||
\(647\) | − | 1.00673e7i | − | 0.945482i | −0.881201 | − | 0.472741i | \(-0.843265\pi\) | ||
0.881201 | − | 0.472741i | \(-0.156735\pi\) | |||||||
\(648\) | −3.01436e6 | + | 3.16335e6i | −0.282006 | + | 0.295944i | ||||
\(649\) | 1.55359e6 | 0.144785 | ||||||||
\(650\) | 2.20833e6 | − | 1.04714e7i | 0.205012 | − | 0.972127i | ||||
\(651\) | 5.39807e6i | 0.499213i | ||||||||
\(652\) | −4.12029e6 | − | 2.29134e6i | −0.379584 | − | 0.211092i | ||||
\(653\) | 3.73524e6 | 0.342796 | 0.171398 | − | 0.985202i | \(-0.445172\pi\) | ||||
0.171398 | + | 0.985202i | \(0.445172\pi\) | |||||||
\(654\) | 5.33061e6 | + | 1.38251e6i | 0.487341 | + | 0.126393i | ||||
\(655\) | −6.22694e6 | + | 142987.i | −0.567115 | + | 0.0130225i | ||||
\(656\) | 5.94375e6 | + | 9.57059e6i | 0.539263 | + | 0.868319i | ||||
\(657\) | 9.24328e6i | 0.835435i | ||||||||
\(658\) | −829434. | + | 3.19809e6i | −0.0746822 | + | 0.287956i | ||||
\(659\) | − | 2.11585e6i | − | 0.189789i | −0.995487 | − | 0.0948947i | \(-0.969749\pi\) | ||
0.995487 | − | 0.0948947i | \(-0.0302514\pi\) | |||||||
\(660\) | −482187. | − | 253836.i | −0.0430879 | − | 0.0226827i | ||||
\(661\) | 1.89096e7i | 1.68337i | 0.539970 | + | 0.841684i | \(0.318435\pi\) | ||||
−0.539970 | + | 0.841684i | \(0.681565\pi\) | |||||||
\(662\) | 1.30071e7 | + | 3.37344e6i | 1.15355 | + | 0.299177i | ||||
\(663\) | 1.77800e6i | 0.157090i | ||||||||
\(664\) | 5.80733e6 | − | 6.09436e6i | 0.511159 | − | 0.536424i | ||||
\(665\) | −395310. | − | 1.72154e7i | −0.0346644 | − | 1.50960i | ||||
\(666\) | 3.05861e6 | − | 1.17932e7i | 0.267201 | − | 1.03026i | ||||
\(667\) | −1.40082e7 | −1.21918 | ||||||||
\(668\) | 4.83665e6 | − | 8.69726e6i | 0.419376 | − | 0.754121i | ||||
\(669\) | 5.37355e6i | 0.464190i | ||||||||
\(670\) | −1.28969e7 | − | 3.03066e6i | −1.10994 | − | 0.260826i | ||||
\(671\) | 135000. | 0.0115752 | ||||||||
\(672\) | −1.81681e6 | − | 5.83218e6i | −0.155198 | − | 0.498205i | ||||
\(673\) | − | 2.10683e6i | − | 0.179304i | −0.995973 | − | 0.0896522i | \(-0.971424\pi\) | ||
0.995973 | − | 0.0896522i | \(-0.0285755\pi\) | |||||||
\(674\) | −2.02562e7 | − | 5.25350e6i | −1.71754 | − | 0.445450i | ||||
\(675\) | −9.73606e6 | + | 447368.i | −0.822477 | + | 0.0377925i | ||||
\(676\) | 134346. | + | 74711.6i | 0.0113073 | + | 0.00628813i | ||||
\(677\) | −5.17934e6 | −0.434313 | −0.217156 | − | 0.976137i | \(-0.569678\pi\) | ||||
−0.217156 | + | 0.976137i | \(0.569678\pi\) | |||||||
\(678\) | −7.68220e6 | − | 1.99240e6i | −0.641817 | − | 0.166457i | ||||
\(679\) | 1.40998e7 | 1.17365 | ||||||||
\(680\) | −2.78656e6 | + | 3.06207e6i | −0.231098 | + | 0.253947i | ||||
\(681\) | −1.05607e7 | −0.872623 | ||||||||
\(682\) | 1.18942e6 | + | 308479.i | 0.0979206 | + | 0.0253960i | ||||
\(683\) | 8.80956e6 | 0.722608 | 0.361304 | − | 0.932448i | \(-0.382332\pi\) | ||||
0.361304 | + | 0.932448i | \(0.382332\pi\) | |||||||
\(684\) | 6.24408e6 | − | 1.12281e7i | 0.510303 | − | 0.917626i | ||||
\(685\) | −1.57737e7 | + | 362206.i | −1.28442 | + | 0.0294937i | ||||
\(686\) | 9.67940e6 | + | 2.51038e6i | 0.785304 | + | 0.203671i | ||||
\(687\) | 5.99423e6i | 0.484553i | ||||||||
\(688\) | 4.54514e6 | + | 7.31856e6i | 0.366080 | + | 0.589460i | ||||
\(689\) | 2.31701e7 | 1.85943 | ||||||||
\(690\) | 1.58311e6 | − | 6.73689e6i | 0.126587 | − | 0.538688i | ||||
\(691\) | 5.78539e6i | 0.460933i | 0.973080 | + | 0.230466i | \(0.0740252\pi\) | ||||
−0.973080 | + | 0.230466i | \(0.925975\pi\) | |||||||
\(692\) | 3.36374e6 | + | 1.87062e6i | 0.267028 | + | 0.148498i | ||||
\(693\) | −1.19361e6 | −0.0944122 | ||||||||
\(694\) | 2.81691e6 | − | 1.08613e7i | 0.222011 | − | 0.856018i | ||||
\(695\) | 2.46239e6 | − | 56543.0i | 0.193372 | − | 0.00444034i | ||||
\(696\) | −4.32262e6 | − | 4.11903e6i | −0.338239 | − | 0.322308i | ||||
\(697\) | 4.50135e6i | 0.350963i | ||||||||
\(698\) | −8.31371e6 | − | 2.15619e6i | −0.645887 | − | 0.167513i | ||||
\(699\) | 2.04384e6i | 0.158217i | ||||||||
\(700\) | −6.54295e6 | + | 1.31529e7i | −0.504694 | + | 1.01456i | ||||
\(701\) | 2.01716e7i | 1.55041i | 0.631711 | + | 0.775204i | \(0.282353\pi\) | ||||
−0.631711 | + | 0.775204i | \(0.717647\pi\) | |||||||
\(702\) | −2.68134e6 | + | 1.03386e7i | −0.205357 | + | 0.791805i | ||||
\(703\) | 2.35865e7i | 1.80001i | ||||||||
\(704\) | −1.38890e6 | + | 67031.4i | −0.105618 | + | 0.00509738i | ||||
\(705\) | −1.59499e6 | + | 36625.2i | −0.120861 | + | 0.00277528i | ||||
\(706\) | 1.12906e7 | + | 2.92824e6i | 0.852519 | + | 0.221103i | ||||
\(707\) | 1.23253e7 | 0.927362 | ||||||||
\(708\) | −4.08735e6 | + | 7.34987e6i | −0.306450 | + | 0.551057i | ||||
\(709\) | − | 1.71661e7i | − | 1.28250i | −0.767334 | − | 0.641248i | \(-0.778417\pi\) | ||
0.767334 | − | 0.641248i | \(-0.221583\pi\) | |||||||
\(710\) | −2.22144e7 | − | 5.22018e6i | −1.65382 | − | 0.388633i | ||||
\(711\) | 7.54943e6 | 0.560067 | ||||||||
\(712\) | 4.77245e6 | − | 5.00833e6i | 0.352810 | − | 0.370248i | ||||
\(713\) | 1.56052e7i | 1.14960i | ||||||||
\(714\) | 612729. | − | 2.36253e6i | 0.0449804 | − | 0.173433i | ||||
\(715\) | 1.43571e6 | − | 32967.7i | 0.105027 | − | 0.00241170i | ||||
\(716\) | −2.80790e6 | + | 5.04916e6i | −0.204691 | + | 0.368075i | ||||
\(717\) | −5.74733e6 | −0.417511 | ||||||||
\(718\) | 1.89240e6 | − | 7.29663e6i | 0.136994 | − | 0.528215i | ||||
\(719\) | 1.37927e7 | 0.995009 | 0.497505 | − | 0.867461i | \(-0.334250\pi\) | ||||
0.497505 | + | 0.867461i | \(0.334250\pi\) | |||||||
\(720\) | −9.17569e6 | + | 5.99468e6i | −0.659641 | + | 0.430958i | ||||
\(721\) | −1.57091e6 | −0.112541 | ||||||||
\(722\) | −2.72769e6 | + | 1.05173e7i | −0.194739 | + | 0.750863i | ||||
\(723\) | 1.08105e7 | 0.769132 | ||||||||
\(724\) | −2.32819e6 | + | 4.18654e6i | −0.165071 | + | 0.296831i | ||||
\(725\) | 659105. | + | 1.43441e7i | 0.0465704 | + | 1.01351i | ||||
\(726\) | −1.62346e6 | + | 6.25966e6i | −0.114314 | + | 0.440767i | ||||
\(727\) | − | 9.10175e6i | − | 0.638688i | −0.947639 | − | 0.319344i | \(-0.896537\pi\) | ||
0.947639 | − | 0.319344i | \(-0.103463\pi\) | |||||||
\(728\) | 1.16547e7 | + | 1.11058e7i | 0.815026 | + | 0.776640i | ||||
\(729\) | 818554. | 0.0570465 | ||||||||
\(730\) | −3.49225e6 | + | 1.48612e7i | −0.242549 | + | 1.03216i | ||||
\(731\) | 3.44215e6i | 0.238252i | ||||||||
\(732\) | −355172. | + | 638670.i | −0.0244997 | + | 0.0440554i | ||||
\(733\) | −1.79637e7 | −1.23491 | −0.617456 | − | 0.786605i | \(-0.711837\pi\) | ||||
−0.617456 | + | 0.786605i | \(0.711837\pi\) | |||||||
\(734\) | −1.71570e6 | − | 444972.i | −0.117544 | − | 0.0304855i | ||||
\(735\) | −43979.3 | − | 1.91525e6i | −0.00300283 | − | 0.130770i | ||||
\(736\) | −5.25220e6 | − | 1.68602e7i | −0.357394 | − | 1.14728i | ||||
\(737\) | − | 1.77780e6i | − | 0.120563i | ||||||
\(738\) | −2.99159e6 | + | 1.15348e7i | −0.202191 | + | 0.779598i | ||||
\(739\) | 1.38839e7i | 0.935192i | 0.883942 | + | 0.467596i | \(0.154880\pi\) | ||||
−0.883942 | + | 0.467596i | \(0.845120\pi\) | |||||||
\(740\) | 9.37325e6 | − | 1.78054e7i | 0.629232 | − | 1.19529i | ||||
\(741\) | − | 9.11238e6i | − | 0.609658i | ||||||
\(742\) | −3.07874e7 | − | 7.98480e6i | −2.05288 | − | 0.532420i | ||||
\(743\) | 2.37521e6i | 0.157845i | 0.996881 | + | 0.0789225i | \(0.0251480\pi\) | ||||
−0.996881 | + | 0.0789225i | \(0.974852\pi\) | |||||||
\(744\) | −4.58864e6 | + | 4.81544e6i | −0.303914 | + | 0.318936i | ||||
\(745\) | 1.40585e7 | − | 322820.i | 0.927999 | − | 0.0213093i | ||||
\(746\) | 4.16198e6 | − | 1.60476e7i | 0.273812 | − | 1.05575i | ||||
\(747\) | 8.90419e6 | 0.583839 | ||||||||
\(748\) | −485548. | − | 270019.i | −0.0317306 | − | 0.0176458i | ||||
\(749\) | − | 1.61292e7i | − | 1.05053i | ||||||
\(750\) | −6.97295e6 | − | 1.30409e6i | −0.452651 | − | 0.0846556i | ||||
\(751\) | −1.99260e7 | −1.28920 | −0.644600 | − | 0.764520i | \(-0.722976\pi\) | ||||
−0.644600 | + | 0.764520i | \(0.722976\pi\) | |||||||
\(752\) | −3.45845e6 | + | 2.14785e6i | −0.223017 | + | 0.138503i | ||||
\(753\) | − | 7.91465e6i | − | 0.508679i | ||||||
\(754\) | 1.52318e7 | + | 3.95041e6i | 0.975714 | + | 0.253054i | ||||
\(755\) | −122929. | − | 5.35341e6i | −0.00784848 | − | 0.341793i | ||||
\(756\) | 7.12568e6 | − | 1.28134e7i | 0.453442 | − | 0.815379i | ||||
\(757\) | −1.30771e7 | −0.829413 | −0.414707 | − | 0.909955i | \(-0.636116\pi\) | ||||
−0.414707 | + | 0.909955i | \(0.636116\pi\) | |||||||
\(758\) | 2.24947e7 | + | 5.83407e6i | 1.42203 | + | 0.368807i | ||||
\(759\) | 928660. | 0.0585130 | ||||||||
\(760\) | 1.42813e7 | − | 1.56933e7i | 0.896879 | − | 0.985552i | ||||
\(761\) | −1.75251e7 | −1.09698 | −0.548492 | − | 0.836156i | \(-0.684798\pi\) | ||||
−0.548492 | + | 0.836156i | \(0.684798\pi\) | |||||||
\(762\) | −6.73115e6 | − | 1.74574e6i | −0.419954 | − | 0.108916i | ||||
\(763\) | 1.99224e7 | 1.23888 | ||||||||
\(764\) | −5.98226e6 | − | 3.32681e6i | −0.370794 | − | 0.206203i | ||||
\(765\) | −4.37805e6 | + | 100532.i | −0.270475 | + | 0.00621082i | ||||
\(766\) | −5.25114e6 | − | 1.36190e6i | −0.323356 | − | 0.0838634i | ||||
\(767\) | − | 2.21637e7i | − | 1.36036i | ||||||
\(768\) | 3.33694e6 | − | 6.74708e6i | 0.204148 | − | 0.412775i | ||||
\(769\) | −3.13820e7 | −1.91366 | −0.956830 | − | 0.290647i | \(-0.906129\pi\) | ||||
−0.956830 | + | 0.290647i | \(0.906129\pi\) | |||||||
\(770\) | −1.91906e6 | − | 450963.i | −0.116644 | − | 0.0274103i | ||||
\(771\) | 1.01244e7i | 0.613384i | ||||||||
\(772\) | 1.13469e7 | − | 2.04039e7i | 0.685225 | − | 1.23217i | ||||
\(773\) | 103265. | 0.00621590 | 0.00310795 | − | 0.999995i | \(-0.499011\pi\) | ||||
0.00310795 | + | 0.999995i | \(0.499011\pi\) | |||||||
\(774\) | −2.28765e6 | + | 8.82060e6i | −0.137258 | + | 0.529232i | ||||
\(775\) | 1.59795e7 | − | 734250.i | 0.955671 | − | 0.0439126i | ||||
\(776\) | 1.25779e7 | + | 1.19855e7i | 0.749817 | + | 0.714502i | ||||
\(777\) | 1.18621e7i | 0.704870i | ||||||||
\(778\) | −3.54625e6 | − | 919729.i | −0.210049 | − | 0.0544767i | ||||
\(779\) | − | 2.30697e7i | − | 1.36207i | ||||||
\(780\) | −3.62125e6 | + | 6.87893e6i | −0.213119 | + | 0.404841i | ||||
\(781\) | − | 3.06218e6i | − | 0.179640i | ||||||
\(782\) | 1.77133e6 | − | 6.82981e6i | 0.103582 | − | 0.399385i | ||||
\(783\) | − | 1.43309e7i | − | 0.835350i | ||||||
\(784\) | −2.57912e6 | − | 4.15289e6i | −0.149859 | − | 0.241302i | ||||
\(785\) | 229022. | + | 9.97368e6i | 0.0132649 | + | 0.577672i | ||||
\(786\) | 4.37960e6 | + | 1.13586e6i | 0.252859 | + | 0.0655798i | ||||
\(787\) | 5.01823e6 | 0.288811 | 0.144405 | − | 0.989519i | \(-0.453873\pi\) | ||||
0.144405 | + | 0.989519i | \(0.453873\pi\) | |||||||
\(788\) | 2.57881e7 | + | 1.43411e7i | 1.47946 | + | 0.822748i | ||||
\(789\) | 1.21229e7i | 0.693288i | ||||||||
\(790\) | 1.21379e7 | + | 2.85229e6i | 0.691950 | + | 0.162602i | ||||
\(791\) | −2.87111e7 | −1.63158 | ||||||||
\(792\) | −1.06478e6 | − | 1.01463e6i | −0.0603178 | − | 0.0574769i | ||||
\(793\) | − | 1.92592e6i | − | 0.108757i | ||||||
\(794\) | −2.92952e6 | + | 1.12955e7i | −0.164909 | + | 0.635849i | ||||
\(795\) | −352584. | − | 1.53547e7i | −0.0197854 | − | 0.861634i | ||||
\(796\) | 2.75561e7 | + | 1.53243e7i | 1.54147 | + | 0.857230i | ||||
\(797\) | 9.61578e6 | 0.536215 | 0.268107 | − | 0.963389i | \(-0.413602\pi\) | ||||
0.268107 | + | 0.963389i | \(0.413602\pi\) | |||||||
\(798\) | −3.14027e6 | + | 1.21081e7i | −0.174566 | + | 0.673084i | ||||
\(799\) | −1.62662e6 | −0.0901403 | ||||||||
\(800\) | −1.70174e7 | + | 6.17146e6i | −0.940089 | + | 0.340928i | ||||
\(801\) | 7.31745e6 | 0.402975 | ||||||||
\(802\) | −2.72985e6 | + | 1.05256e7i | −0.149866 | + | 0.577846i | ||||
\(803\) | −2.04857e6 | −0.112115 | ||||||||
\(804\) | 8.41060e6 | + | 4.67724e6i | 0.458867 | + | 0.255182i | ||||
\(805\) | −574736. | − | 2.50291e7i | −0.0312592 | − | 1.36131i | ||||
\(806\) | 4.40080e6 | − | 1.69684e7i | 0.238613 | − | 0.920031i | ||||
\(807\) | − | 2.19552e6i | − | 0.118673i | ||||||
\(808\) | 1.09950e7 | + | 1.04771e7i | 0.592470 | + | 0.564566i | ||||
\(809\) | 2.06325e7 | 1.10836 | 0.554181 | − | 0.832396i | \(-0.313032\pi\) | ||||
0.554181 | + | 0.832396i | \(0.313032\pi\) | |||||||
\(810\) | −7.43092e6 | − | 1.74620e6i | −0.397951 | − | 0.0935149i | ||||
\(811\) | − | 3.18795e7i | − | 1.70200i | −0.525164 | − | 0.851001i | \(-0.675996\pi\) | ||
0.525164 | − | 0.851001i | \(-0.324004\pi\) | |||||||
\(812\) | −1.88779e7 | − | 1.04982e7i | −1.00476 | − | 0.558762i | ||||
\(813\) | 8.99645e6 | 0.477359 | ||||||||
\(814\) | 2.61371e6 | + | 677875.i | 0.138260 | + | 0.0358582i | ||||
\(815\) | −189070. | − | 8.23381e6i | −0.00997078 | − | 0.434217i | ||||
\(816\) | 2.55487e6 | − | 1.58668e6i | 0.134321 | − | 0.0834189i | ||||
\(817\) | − | 1.76412e7i | − | 0.924642i | ||||||
\(818\) | 1.99488e6 | − | 7.69177e6i | 0.104240 | − | 0.401923i | ||||
\(819\) | 1.70281e7i | 0.887067i | ||||||||
\(820\) | −9.16788e6 | + | 1.74153e7i | −0.476140 | + | 0.904474i | ||||
\(821\) | 7.88522e6i | 0.408278i | 0.978942 | + | 0.204139i | \(0.0654394\pi\) | ||||
−0.978942 | + | 0.204139i | \(0.934561\pi\) | |||||||
\(822\) | 1.10941e7 | + | 2.87730e6i | 0.572683 | + | 0.148527i | ||||
\(823\) | 51764.9i | 0.00266401i | 0.999999 | + | 0.00133200i | \(0.000423990\pi\) | ||||
−0.999999 | + | 0.00133200i | \(0.999576\pi\) | |||||||
\(824\) | −1.40135e6 | − | 1.33535e6i | −0.0719002 | − | 0.0685138i | ||||
\(825\) | −43694.9 | − | 950932.i | −0.00223509 | − | 0.0486423i | ||||
\(826\) | −7.63796e6 | + | 2.94501e7i | −0.389518 | + | 1.50188i | ||||
\(827\) | 5.24793e6 | 0.266824 | 0.133412 | − | 0.991061i | \(-0.457407\pi\) | ||||
0.133412 | + | 0.991061i | \(0.457407\pi\) | |||||||
\(828\) | 9.07818e6 | − | 1.63244e7i | 0.460175 | − | 0.827485i | ||||
\(829\) | − | 6.76109e6i | − | 0.341689i | −0.985298 | − | 0.170844i | \(-0.945350\pi\) | ||
0.985298 | − | 0.170844i | \(-0.0546495\pi\) | |||||||
\(830\) | 1.43160e7 | + | 3.36414e6i | 0.721320 | + | 0.169504i | ||||
\(831\) | −3.47004e6 | −0.174314 | ||||||||
\(832\) | 956277. | + | 1.98141e7i | 0.0478934 | + | 0.992355i | ||||
\(833\) | − | 1.95323e6i | − | 0.0975308i | ||||||
\(834\) | −1.73188e6 | − | 449167.i | −0.0862187 | − | 0.0223611i | ||||
\(835\) | 1.73802e7 | − | 399097.i | 0.862660 | − | 0.0198090i | ||||
\(836\) | 2.48847e6 | + | 1.38387e6i | 0.123145 | + | 0.0684823i | ||||
\(837\) | −1.59647e7 | −0.787677 | ||||||||
\(838\) | −2.20995e7 | − | 5.73158e6i | −1.08711 | − | 0.281945i | ||||
\(839\) | −5.32681e6 | −0.261254 | −0.130627 | − | 0.991432i | \(-0.541699\pi\) | ||||
−0.130627 | + | 0.991432i | \(0.541699\pi\) | |||||||
\(840\) | 7.18234e6 | − | 7.89245e6i | 0.351211 | − | 0.385935i | ||||
\(841\) | −602476. | −0.0293731 | ||||||||
\(842\) | −3.25754e6 | − | 844853.i | −0.158347 | − | 0.0410678i | ||||
\(843\) | −636887. | −0.0308669 | ||||||||
\(844\) | −1.45031e7 | + | 2.60794e7i | −0.700816 | + | 1.26021i | ||||
\(845\) | 6164.83 | + | 268472.i | 0.000297016 | + | 0.0129347i | ||||
\(846\) | −4.16826e6 | − | 1.08105e6i | −0.200230 | − | 0.0519302i | ||||
\(847\) | 2.33946e7i | 1.12049i | ||||||||
\(848\) | −2.06769e7 | − | 3.32939e7i | −0.987407 | − | 1.58992i | ||||
\(849\) | 1.26660e7 | 0.603076 | ||||||||
\(850\) | −7.07695e6 | − | 1.49246e6i | −0.335969 | − | 0.0708525i | ||||
\(851\) | 3.42920e7i | 1.62319i | ||||||||
\(852\) | 1.44869e7 | + | 8.05633e6i | 0.683716 | + | 0.380223i | ||||
\(853\) | −8.20548e6 | −0.386128 | −0.193064 | − | 0.981186i | \(-0.561843\pi\) | ||||
−0.193064 | + | 0.981186i | \(0.561843\pi\) | |||||||
\(854\) | −663704. | + | 2.55907e6i | −0.0311408 | + | 0.120071i | ||||
\(855\) | 2.24378e7 | − | 515231.i | 1.04970 | − | 0.0241039i | ||||
\(856\) | 1.37107e7 | − | 1.43883e7i | 0.639549 | − | 0.671160i | ||||
\(857\) | − | 5.45868e6i | − | 0.253884i | −0.991910 | − | 0.126942i | \(-0.959484\pi\) | ||
0.991910 | − | 0.126942i | \(-0.0405162\pi\) | |||||||
\(858\) | −1.00978e6 | − | 261889.i | −0.0468283 | − | 0.0121451i | ||||
\(859\) | − | 3.18230e7i | − | 1.47149i | −0.677257 | − | 0.735747i | \(-0.736831\pi\) | ||
0.677257 | − | 0.735747i | \(-0.263169\pi\) | |||||||
\(860\) | −7.01061e6 | + | 1.33173e7i | −0.323229 | + | 0.614004i | ||||
\(861\) | − | 1.16022e7i | − | 0.533375i | ||||||
\(862\) | 5.90494e6 | − | 2.27680e7i | 0.270675 | − | 1.04365i | ||||
\(863\) | 9.28914e6i | 0.424569i | 0.977208 | + | 0.212285i | \(0.0680904\pi\) | ||||
−0.977208 | + | 0.212285i | \(0.931910\pi\) | |||||||
\(864\) | 1.72486e7 | − | 5.37320e6i | 0.786086 | − | 0.244877i | ||||
\(865\) | 154354. | + | 6.72196e6i | 0.00701420 | + | 0.305461i | ||||
\(866\) | 1.24647e7 | + | 3.23275e6i | 0.564789 | + | 0.146480i | ||||
\(867\) | −8.99077e6 | −0.406208 | ||||||||
\(868\) | −1.16951e7 | + | 2.10302e7i | −0.526874 | + | 0.947423i | ||||
\(869\) | 1.67317e6i | 0.0751606i | ||||||||
\(870\) | 2.38612e6 | − | 1.01541e7i | 0.106880 | − | 0.454824i | ||||
\(871\) | −2.53623e7 | −1.13277 | ||||||||
\(872\) | 1.77721e7 | + | 1.69351e7i | 0.791495 | + | 0.754217i | ||||
\(873\) | 1.83771e7i | 0.816094i | ||||||||
\(874\) | −9.07819e6 | + | 3.50032e7i | −0.401995 | + | 1.54999i | ||||
\(875\) | −2.56024e7 | + | 1.76618e6i | −1.13047 | + | 0.0779856i | ||||
\(876\) | 5.38961e6 | − | 9.69159e6i | 0.237300 | − | 0.426712i | ||||
\(877\) | 1.60806e7 | 0.705997 | 0.352999 | − | 0.935624i | \(-0.385162\pi\) | ||||
0.352999 | + | 0.935624i | \(0.385162\pi\) | |||||||
\(878\) | −1.81957e6 | + | 7.01580e6i | −0.0796585 | + | 0.307143i | ||||
\(879\) | 65503.2 | 0.00285950 | ||||||||
\(880\) | −1.32859e6 | − | 2.03359e6i | −0.0578342 | − | 0.0885233i | ||||
\(881\) | −1.74471e7 | −0.757327 | −0.378663 | − | 0.925535i | \(-0.623616\pi\) | ||||
−0.378663 | + | 0.925535i | \(0.623616\pi\) | |||||||
\(882\) | 1.29812e6 | − | 5.00522e6i | 0.0561879 | − | 0.216646i | ||||
\(883\) | −2.18862e7 | −0.944645 | −0.472323 | − | 0.881426i | \(-0.656584\pi\) | ||||
−0.472323 | + | 0.881426i | \(0.656584\pi\) | |||||||
\(884\) | −3.85212e6 | + | 6.92688e6i | −0.165794 | + | 0.298131i | ||||
\(885\) | −1.46877e7 | + | 337268.i | −0.630370 | + | 0.0144750i | ||||
\(886\) | 8.53880e6 | − | 3.29235e7i | 0.365437 | − | 1.40903i | ||||
\(887\) | 4.00556e7i | 1.70944i | 0.519088 | + | 0.854721i | \(0.326272\pi\) | ||||
−0.519088 | + | 0.854721i | \(0.673728\pi\) | |||||||
\(888\) | −1.00834e7 | + | 1.05818e7i | −0.429116 | + | 0.450326i | ||||
\(889\) | −2.51567e7 | −1.06758 | ||||||||
\(890\) | 1.17649e7 | + | 2.76464e6i | 0.497867 | + | 0.116994i | ||||
\(891\) | − | 1.02433e6i | − | 0.0432260i | ||||||
\(892\) | −1.16420e7 | + | 2.09347e7i | −0.489910 | + | 0.880955i | ||||
\(893\) | 8.33653e6 | 0.349830 | ||||||||
\(894\) | −9.88778e6 | − | 2.56442e6i | −0.413766 | − | 0.107311i | ||||
\(895\) | −1.00900e7 | + | 231694.i | −0.421051 | + | 0.00966846i | ||||
\(896\) | 5.55762e6 | − | 2.66577e7i | 0.231270 | − | 1.10931i | ||||
\(897\) | − | 1.32484e7i | − | 0.549770i | ||||||
\(898\) | 3.00420e6 | − | 1.15834e7i | 0.124319 | − | 0.479343i | ||||
\(899\) | 2.35208e7i | 0.970628i | ||||||||
\(900\) | −1.71430e7 | − | 8.52781e6i | −0.705473 | − | 0.350939i | ||||
\(901\) | − | 1.56592e7i | − | 0.642623i | ||||||
\(902\) | −2.55645e6 | − | 663022.i | −0.104621 | − | 0.0271339i | ||||
\(903\) | − | 8.87211e6i | − | 0.362083i | ||||||
\(904\) | −2.56123e7 | − | 2.44060e7i | −1.04238 | − | 0.993287i | ||||
\(905\) | −8.36622e6 | + | 192111.i | −0.339553 | + | 0.00779704i | ||||
\(906\) | −976522. | + | 3.76523e6i | −0.0395241 | + | 0.152395i | ||||
\(907\) | 1.61797e7 | 0.653060 | 0.326530 | − | 0.945187i | \(-0.394121\pi\) | ||||
0.326530 | + | 0.945187i | \(0.394121\pi\) | |||||||
\(908\) | −4.11433e7 | − | 2.28803e7i | −1.65609 | − | 0.920974i | ||||
\(909\) | 1.60643e7i | 0.644840i | ||||||||
\(910\) | −6.43348e6 | + | 2.73776e7i | −0.257539 | + | 1.09595i | ||||
\(911\) | 3.81429e7 | 1.52271 | 0.761356 | − | 0.648334i | \(-0.224534\pi\) | ||||
0.761356 | + | 0.648334i | \(0.224534\pi\) | |||||||
\(912\) | −1.30939e7 | + | 8.13185e6i | −0.521291 | + | 0.323744i | ||||
\(913\) | 1.97342e6i | 0.0783508i | ||||||||
\(914\) | −7.44500e6 | − | 1.93088e6i | −0.294781 | − | 0.0764523i | ||||
\(915\) | −1.27629e6 | + | 29307.1i | −0.0503962 | + | 0.00115723i | ||||
\(916\) | −1.29868e7 | + | 2.33528e7i | −0.511402 | + | 0.919601i | ||||
\(917\) | 1.63682e7 | 0.642801 | ||||||||
\(918\) | 6.98716e6 | + | 1.81214e6i | 0.273649 | + | 0.0709717i | ||||
\(919\) | −5.75041e6 | −0.224600 | −0.112300 | − | 0.993674i | \(-0.535822\pi\) | ||||
−0.112300 | + | 0.993674i | \(0.535822\pi\) | |||||||
\(920\) | 2.07634e7 | − | 2.28162e7i | 0.808776 | − | 0.888739i | ||||
\(921\) | 1.89665e7 | 0.736780 | ||||||||
\(922\) | 1.13039e7 | + | 2.93170e6i | 0.437927 | + | 0.113578i | ||||
\(923\) | −4.36854e7 | −1.68784 | ||||||||
\(924\) | 1.25150e6 | + | 695973.i | 0.0482225 | + | 0.0268171i | ||||
\(925\) | 3.51144e7 | − | 1.61349e6i | 1.34937 | − | 0.0620030i | ||||
\(926\) | 8.15422e6 | + | 2.11482e6i | 0.312504 | + | 0.0810487i | ||||
\(927\) | − | 2.04745e6i | − | 0.0782555i | ||||||
\(928\) | −7.91632e6 | − | 2.54124e7i | −0.301754 | − | 0.968668i | ||||
\(929\) | 1.58033e7 | 0.600771 | 0.300386 | − | 0.953818i | \(-0.402885\pi\) | ||||
0.300386 | + | 0.953818i | \(0.402885\pi\) | |||||||
\(930\) | −1.13118e7 | − | 2.65816e6i | −0.428868 | − | 0.100780i | ||||
\(931\) | 1.00104e7i | 0.378512i | ||||||||
\(932\) | −4.42806e6 | + | 7.96254e6i | −0.166984 | + | 0.300270i | ||||
\(933\) | 1.00680e7 | 0.378651 | ||||||||
\(934\) | 1.00241e7 | − | 3.86505e7i | 0.375993 | − | 1.44973i | ||||
\(935\) | −22280.7 | − | 970300.i | −0.000833488 | − | 0.0362975i | ||||
\(936\) | −1.44748e7 | + | 1.51902e7i | −0.540035 | + | 0.566727i | ||||
\(937\) | − | 1.61564e7i | − | 0.601167i | −0.953756 | − | 0.300583i | \(-0.902819\pi\) | ||
0.953756 | − | 0.300583i | \(-0.0971814\pi\) | |||||||
\(938\) | 3.37003e7 | + | 8.74026e6i | 1.25062 | + | 0.324353i | ||||
\(939\) | 9.75602e6i | 0.361084i | ||||||||
\(940\) | −6.29323e6 | − | 3.31293e6i | −0.232303 | − | 0.122290i | ||||
\(941\) | 4.39614e7i | 1.61844i | 0.587504 | + | 0.809221i | \(0.300111\pi\) | ||||
−0.587504 | + | 0.809221i | \(0.699889\pi\) | |||||||
\(942\) | 1.81931e6 | − | 7.01481e6i | 0.0668005 | − | 0.257566i | ||||
\(943\) | − | 3.35407e7i | − | 1.22827i | ||||||
\(944\) | −3.18476e7 | + | 1.97788e7i | −1.16318 | + | 0.722385i | ||||
\(945\) | 2.56058e7 | − | 587976.i | 0.932735 | − | 0.0214181i | ||||
\(946\) | −1.95490e6 | − | 507008.i | −0.0710225 | − | 0.0184199i | ||||
\(947\) | −4.52665e7 | −1.64022 | −0.820111 | − | 0.572205i | \(-0.806088\pi\) | ||||
−0.820111 | + | 0.572205i | \(0.806088\pi\) | |||||||
\(948\) | −7.91558e6 | − | 4.40195e6i | −0.286063 | − | 0.159083i | ||||
\(949\) | 2.92252e7i | 1.05340i | ||||||||
\(950\) | 3.62698e7 | + | 7.64895e6i | 1.30388 | + | 0.274975i | ||||
\(951\) | −2.15601e6 | −0.0773035 | ||||||||
\(952\) | 7.50564e6 | − | 7.87661e6i | 0.268408 | − | 0.281674i | ||||
\(953\) | − | 3.21216e6i | − | 0.114569i | −0.998358 | − | 0.0572843i | \(-0.981756\pi\) | ||
0.998358 | − | 0.0572843i | \(-0.0182441\pi\) | |||||||
\(954\) | 1.04071e7 | − | 4.01270e7i | 0.370218 | − | 1.42747i | ||||
\(955\) | −274512. | − | 1.19547e7i | −0.00973986 | − | 0.424161i | ||||
\(956\) | −2.23909e7 | − | 1.24518e7i | −0.792367 | − | 0.440645i | ||||
\(957\) | 1.39971e6 | 0.0494036 | ||||||||
\(958\) | 2.09444e6 | − | 8.07565e6i | 0.0737318 | − | 0.284292i | ||||
\(959\) | 4.14628e7 | 1.45583 | ||||||||
\(960\) | 1.31161e7 | − | 935232.i | 0.459333 | − | 0.0327523i | ||||
\(961\) | −2.42676e6 | −0.0847654 | ||||||||
\(962\) | 9.67063e6 | − | 3.72875e7i | 0.336912 | − | 1.29905i | ||||
\(963\) | 2.10221e7 | 0.730485 | ||||||||
\(964\) | 4.21164e7 | + | 2.34215e7i | 1.45968 | + | 0.811748i | ||||
\(965\) | 4.07744e7 | − | 936288.i | 1.40951 | − | 0.0323662i | ||||
\(966\) | −4.56560e6 | + | 1.76038e7i | −0.157418 | + | 0.606965i | ||||
\(967\) | 4.06241e6i | 0.139707i | 0.997557 | + | 0.0698533i | \(0.0222531\pi\) | ||||
−0.997557 | + | 0.0698533i | \(0.977747\pi\) | |||||||
\(968\) | −1.98866e7 | + | 2.08696e7i | −0.682139 | + | 0.715855i | ||||
\(969\) | −6.15845e6 | −0.210699 | ||||||||
\(970\) | −6.94313e6 | + | 2.95464e7i | −0.236933 | + | 1.00827i | ||||
\(971\) | − | 2.41409e7i | − | 0.821685i | −0.911706 | − | 0.410842i | \(-0.865235\pi\) | ||
0.911706 | − | 0.410842i | \(-0.134765\pi\) | |||||||
\(972\) | 2.60410e7 | + | 1.44817e7i | 0.884082 | + | 0.491649i | ||||
\(973\) | −6.47264e6 | −0.219179 | ||||||||
\(974\) | −5.00158e7 | − | 1.29718e7i | −1.68931 | − | 0.438128i | ||||
\(975\) | −1.35661e7 | + | 623355.i | −0.457028 | + | 0.0210002i | ||||
\(976\) | −2.76741e6 | + | 1.71868e6i | −0.0929928 | + | 0.0577526i | ||||
\(977\) | − | 1.48416e7i | − | 0.497443i | −0.968575 | − | 0.248722i | \(-0.919990\pi\) | ||
0.968575 | − | 0.248722i | \(-0.0800104\pi\) | |||||||
\(978\) | −1.50194e6 | + | 5.79110e6i | −0.0502118 | + | 0.193604i | ||||
\(979\) | 1.62175e6i | 0.0540790i | ||||||||
\(980\) | 3.97814e6 | − | 7.55687e6i | 0.132317 | − | 0.251349i | ||||
\(981\) | 2.59661e7i | 0.861457i | ||||||||
\(982\) | 2.59651e7 | + | 6.73412e6i | 0.859233 | + | 0.222845i | ||||
\(983\) | − | 3.34107e7i | − | 1.10281i | −0.834237 | − | 0.551406i | \(-0.814092\pi\) | ||
0.834237 | − | 0.551406i | \(-0.185908\pi\) | |||||||
\(984\) | 9.86247e6 | − | 1.03499e7i | 0.324712 | − | 0.340761i | ||||
\(985\) | 1.18336e6 | + | 5.15339e7i | 0.0388620 | + | 1.69240i | ||||
\(986\) | 2.66982e6 | − | 1.02942e7i | 0.0874560 | − | 0.337208i | ||||
\(987\) | 4.19260e6 | 0.136991 | ||||||||
\(988\) | 1.97424e7 | − | 3.55007e7i | 0.643438 | − | 1.15703i | ||||
\(989\) | − | 2.56483e7i | − | 0.833812i | ||||||
\(990\) | 587766. | − | 2.50123e6i | 0.0190597 | − | 0.0811083i | ||||
\(991\) | 5.15057e7 | 1.66599 | 0.832993 | − | 0.553284i | \(-0.186626\pi\) | ||||
0.832993 | + | 0.553284i | \(0.186626\pi\) | |||||||
\(992\) | −2.83096e7 | + | 8.81886e6i | −0.913387 | + | 0.284533i | ||||
\(993\) | − | 1.70520e7i | − | 0.548784i | ||||||
\(994\) | 5.80472e7 | + | 1.50547e7i | 1.86344 | + | 0.483288i | ||||
\(995\) | 1.26448e6 | + | 5.50670e7i | 0.0404907 | + | 1.76333i | ||||
\(996\) | −9.33606e6 | − | 5.19190e6i | −0.298205 | − | 0.165836i | ||||
\(997\) | −1.18985e7 | −0.379102 | −0.189551 | − | 0.981871i | \(-0.560703\pi\) | ||||
−0.189551 | + | 0.981871i | \(0.560703\pi\) | |||||||
\(998\) | −2.95144e6 | − | 765466.i | −0.0938012 | − | 0.0243276i | ||||
\(999\) | −3.50821e7 | −1.11217 |
(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 | 40.6.f.a.29.17 | yes | 28 | |
4.3 | odd | 2 | 160.6.f.a.49.17 | 28 | |||
5.2 | odd | 4 | 200.6.d.e.101.26 | 28 | |||
5.3 | odd | 4 | 200.6.d.e.101.3 | 28 | |||
5.4 | even | 2 | inner | 40.6.f.a.29.12 | yes | 28 | |
8.3 | odd | 2 | 160.6.f.a.49.11 | 28 | |||
8.5 | even | 2 | inner | 40.6.f.a.29.11 | ✓ | 28 | |
20.3 | even | 4 | 800.6.d.e.401.8 | 28 | |||
20.7 | even | 4 | 800.6.d.e.401.21 | 28 | |||
20.19 | odd | 2 | 160.6.f.a.49.12 | 28 | |||
40.3 | even | 4 | 800.6.d.e.401.7 | 28 | |||
40.13 | odd | 4 | 200.6.d.e.101.4 | 28 | |||
40.19 | odd | 2 | 160.6.f.a.49.18 | 28 | |||
40.27 | even | 4 | 800.6.d.e.401.22 | 28 | |||
40.29 | even | 2 | inner | 40.6.f.a.29.18 | yes | 28 | |
40.37 | odd | 4 | 200.6.d.e.101.25 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.f.a.29.11 | ✓ | 28 | 8.5 | even | 2 | inner | |
40.6.f.a.29.12 | yes | 28 | 5.4 | even | 2 | inner | |
40.6.f.a.29.17 | yes | 28 | 1.1 | even | 1 | trivial | |
40.6.f.a.29.18 | yes | 28 | 40.29 | even | 2 | inner | |
160.6.f.a.49.11 | 28 | 8.3 | odd | 2 | |||
160.6.f.a.49.12 | 28 | 20.19 | odd | 2 | |||
160.6.f.a.49.17 | 28 | 4.3 | odd | 2 | |||
160.6.f.a.49.18 | 28 | 40.19 | odd | 2 | |||
200.6.d.e.101.3 | 28 | 5.3 | odd | 4 | |||
200.6.d.e.101.4 | 28 | 40.13 | odd | 4 | |||
200.6.d.e.101.25 | 28 | 40.37 | odd | 4 | |||
200.6.d.e.101.26 | 28 | 5.2 | odd | 4 | |||
800.6.d.e.401.7 | 28 | 40.3 | even | 4 | |||
800.6.d.e.401.8 | 28 | 20.3 | even | 4 | |||
800.6.d.e.401.21 | 28 | 20.7 | even | 4 | |||
800.6.d.e.401.22 | 28 | 40.27 | even | 4 |