Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [37,6,Mod(10,37)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(37, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("37.10");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 37 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 37.c (of order \(3\), degree \(2\), 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: | \(5.93420133308\) |
Analytic rank: | \(0\) |
Dimension: | \(30\) |
Relative dimension: | \(15\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.9 | ||
Character | \(\chi\) | \(=\) | 37.10 |
Dual form | 37.6.c.a.26.9 |
$q$-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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.684514 | − | 1.18561i | 0.121006 | − | 0.209589i | −0.799159 | − | 0.601120i | \(-0.794721\pi\) |
0.920165 | + | 0.391531i | \(0.128055\pi\) | |||||||
\(3\) | −2.47268 | − | 4.28281i | −0.158623 | − | 0.274743i | 0.775750 | − | 0.631041i | \(-0.217372\pi\) |
−0.934372 | + | 0.356298i | \(0.884039\pi\) | |||||||
\(4\) | 15.0629 | + | 26.0897i | 0.470715 | + | 0.815302i | ||||
\(5\) | −49.2630 | − | 85.3260i | −0.881243 | − | 1.52636i | −0.849960 | − | 0.526847i | \(-0.823374\pi\) |
−0.0312831 | − | 0.999511i | \(-0.509959\pi\) | |||||||
\(6\) | −6.77035 | −0.0767773 | ||||||||
\(7\) | −21.8515 | − | 37.8479i | −0.168553 | − | 0.291942i | 0.769358 | − | 0.638817i | \(-0.220576\pi\) |
−0.937911 | + | 0.346875i | \(0.887243\pi\) | |||||||
\(8\) | 85.0519 | 0.469850 | ||||||||
\(9\) | 109.272 | − | 189.264i | 0.449678 | − | 0.778865i | ||||
\(10\) | −134.885 | −0.426543 | ||||||||
\(11\) | −339.990 | −0.847196 | −0.423598 | − | 0.905850i | \(-0.639233\pi\) | ||||
−0.423598 | + | 0.905850i | \(0.639233\pi\) | |||||||
\(12\) | 74.4915 | − | 129.023i | 0.149332 | − | 0.258651i | ||||
\(13\) | −523.635 | − | 906.962i | −0.859350 | − | 1.48844i | −0.872550 | − | 0.488525i | \(-0.837535\pi\) |
0.0131996 | − | 0.999913i | \(-0.495798\pi\) | |||||||
\(14\) | −59.8307 | −0.0815838 | ||||||||
\(15\) | −243.624 | + | 421.968i | −0.279570 | + | 0.484230i | ||||
\(16\) | −423.793 | + | 734.031i | −0.413860 | + | 0.716827i | ||||
\(17\) | 594.708 | − | 1030.06i | 0.499093 | − | 0.864454i | −0.500907 | − | 0.865501i | \(-0.667000\pi\) |
0.999999 | + | 0.00104740i | \(0.000333399\pi\) | |||||||
\(18\) | −149.596 | − | 259.108i | −0.108828 | − | 0.188495i | ||||
\(19\) | 1357.04 | + | 2350.46i | 0.862399 | + | 1.49372i | 0.869607 | + | 0.493745i | \(0.164372\pi\) |
−0.00720776 | + | 0.999974i | \(0.502294\pi\) | |||||||
\(20\) | 1484.08 | − | 2570.51i | 0.829629 | − | 1.43696i | ||||
\(21\) | −108.064 | + | 187.172i | −0.0534727 | + | 0.0926174i | ||||
\(22\) | −232.728 | + | 403.096i | −0.102516 | + | 0.177563i | ||||
\(23\) | 1408.08 | 0.555018 | 0.277509 | − | 0.960723i | \(-0.410491\pi\) | ||||
0.277509 | + | 0.960723i | \(0.410491\pi\) | |||||||
\(24\) | −210.307 | − | 364.262i | −0.0745289 | − | 0.129088i | ||||
\(25\) | −3291.18 | + | 5700.50i | −1.05318 | + | 1.82416i | ||||
\(26\) | −1433.74 | −0.415947 | ||||||||
\(27\) | −2282.50 | −0.602562 | ||||||||
\(28\) | 658.293 | − | 1140.20i | 0.158681 | − | 0.274843i | ||||
\(29\) | 4866.38 | 1.07451 | 0.537256 | − | 0.843419i | \(-0.319461\pi\) | ||||
0.537256 | + | 0.843419i | \(0.319461\pi\) | |||||||
\(30\) | 333.528 | + | 577.687i | 0.0676595 | + | 0.117190i | ||||
\(31\) | 564.433 | 0.105489 | 0.0527446 | − | 0.998608i | \(-0.483203\pi\) | ||||
0.0527446 | + | 0.998608i | \(0.483203\pi\) | |||||||
\(32\) | 1941.02 | + | 3361.94i | 0.335084 | + | 0.580383i | ||||
\(33\) | 840.687 | + | 1456.11i | 0.134385 | + | 0.232761i | ||||
\(34\) | −814.172 | − | 1410.19i | −0.120787 | − | 0.209208i | ||||
\(35\) | −2152.94 | + | 3729.00i | −0.297072 | + | 0.514544i | ||||
\(36\) | 6583.78 | 0.846680 | ||||||||
\(37\) | 8298.91 | + | 687.024i | 0.996591 | + | 0.0825026i | ||||
\(38\) | 3715.65 | 0.417422 | ||||||||
\(39\) | −2589.57 | + | 4485.26i | −0.272625 | + | 0.472200i | ||||
\(40\) | −4189.91 | − | 7257.14i | −0.414052 | − | 0.717159i | ||||
\(41\) | −4744.67 | − | 8218.02i | −0.440805 | − | 0.763497i | 0.556944 | − | 0.830550i | \(-0.311974\pi\) |
−0.997749 | + | 0.0670528i | \(0.978640\pi\) | |||||||
\(42\) | 147.942 | + | 256.244i | 0.0129410 | + | 0.0224145i | ||||
\(43\) | −18551.2 | −1.53003 | −0.765015 | − | 0.644013i | \(-0.777268\pi\) | ||||
−0.765015 | + | 0.644013i | \(0.777268\pi\) | |||||||
\(44\) | −5121.22 | − | 8870.22i | −0.398788 | − | 0.690721i | ||||
\(45\) | −21532.2 | −1.58510 | ||||||||
\(46\) | 963.849 | − | 1669.44i | 0.0671606 | − | 0.116326i | ||||
\(47\) | 3095.29 | 0.204389 | 0.102194 | − | 0.994764i | \(-0.467414\pi\) | ||||
0.102194 | + | 0.994764i | \(0.467414\pi\) | |||||||
\(48\) | 4191.62 | 0.262591 | ||||||||
\(49\) | 7448.52 | − | 12901.2i | 0.443180 | − | 0.767610i | ||||
\(50\) | 4505.72 | + | 7804.14i | 0.254882 | + | 0.441469i | ||||
\(51\) | −5882.10 | −0.316670 | ||||||||
\(52\) | 15774.9 | − | 27322.9i | 0.809018 | − | 1.40126i | ||||
\(53\) | 2674.36 | − | 4632.13i | 0.130777 | − | 0.226512i | −0.793199 | − | 0.608962i | \(-0.791586\pi\) |
0.923976 | + | 0.382450i | \(0.124920\pi\) | |||||||
\(54\) | −1562.40 | + | 2706.16i | −0.0729137 | + | 0.126290i | ||||
\(55\) | 16748.9 | + | 29010.0i | 0.746586 | + | 1.29312i | ||||
\(56\) | −1858.51 | − | 3219.04i | −0.0791946 | − | 0.137169i | ||||
\(57\) | 6711.06 | − | 11623.9i | 0.273592 | − | 0.473876i | ||||
\(58\) | 3331.11 | − | 5769.65i | 0.130023 | − | 0.225206i | ||||
\(59\) | 9411.45 | − | 16301.1i | 0.351987 | − | 0.609659i | −0.634611 | − | 0.772832i | \(-0.718840\pi\) |
0.986597 | + | 0.163173i | \(0.0521729\pi\) | |||||||
\(60\) | −14678.7 | −0.526392 | ||||||||
\(61\) | 7339.78 | + | 12712.9i | 0.252557 | + | 0.437441i | 0.964229 | − | 0.265071i | \(-0.0853953\pi\) |
−0.711672 | + | 0.702511i | \(0.752062\pi\) | |||||||
\(62\) | 386.362 | − | 669.199i | 0.0127648 | − | 0.0221093i | ||||
\(63\) | −9551.00 | −0.303178 | ||||||||
\(64\) | −21808.1 | −0.665531 | ||||||||
\(65\) | −51591.6 | + | 89359.3i | −1.51459 | + | 2.62335i | ||||
\(66\) | 2301.85 | 0.0650455 | ||||||||
\(67\) | −27244.4 | − | 47188.6i | −0.741463 | − | 1.28425i | −0.951829 | − | 0.306629i | \(-0.900799\pi\) |
0.210366 | − | 0.977623i | \(-0.432535\pi\) | |||||||
\(68\) | 35832.0 | 0.939722 | ||||||||
\(69\) | −3481.73 | − | 6030.53i | −0.0880384 | − | 0.152487i | ||||
\(70\) | 2947.44 | + | 5105.11i | 0.0718951 | + | 0.124526i | ||||
\(71\) | 25044.2 | + | 43377.8i | 0.589605 | + | 1.02123i | 0.994284 | + | 0.106767i | \(0.0340500\pi\) |
−0.404679 | + | 0.914459i | \(0.632617\pi\) | |||||||
\(72\) | 9293.77 | − | 16097.3i | 0.211281 | − | 0.365950i | ||||
\(73\) | 39593.9 | 0.869602 | 0.434801 | − | 0.900527i | \(-0.356819\pi\) | ||||
0.434801 | + | 0.900527i | \(0.356819\pi\) | |||||||
\(74\) | 6495.27 | − | 9369.02i | 0.137885 | − | 0.198891i | ||||
\(75\) | 32552.2 | 0.668232 | ||||||||
\(76\) | −40881.8 | + | 70809.4i | −0.811888 | + | 1.40623i | ||||
\(77\) | 7429.29 | + | 12867.9i | 0.142797 | + | 0.247332i | ||||
\(78\) | 3545.19 | + | 6140.45i | 0.0659786 | + | 0.114278i | ||||
\(79\) | 29418.8 | + | 50954.9i | 0.530344 | + | 0.918583i | 0.999373 | + | 0.0354001i | \(0.0112706\pi\) |
−0.469029 | + | 0.883183i | \(0.655396\pi\) | |||||||
\(80\) | 83509.2 | 1.45885 | ||||||||
\(81\) | −20909.1 | − | 36215.6i | −0.354098 | − | 0.613315i | ||||
\(82\) | −12991.2 | −0.213361 | ||||||||
\(83\) | 43070.0 | − | 74599.4i | 0.686245 | − | 1.18861i | −0.286799 | − | 0.957991i | \(-0.592591\pi\) |
0.973044 | − | 0.230621i | \(-0.0740756\pi\) | |||||||
\(84\) | −6511.01 | −0.100682 | ||||||||
\(85\) | −117188. | −1.75929 | ||||||||
\(86\) | −12698.5 | + | 21994.5i | −0.185143 | + | 0.320677i | ||||
\(87\) | −12033.0 | − | 20841.8i | −0.170442 | − | 0.295214i | ||||
\(88\) | −28916.8 | −0.398055 | ||||||||
\(89\) | 8332.95 | − | 14433.1i | 0.111513 | − | 0.193145i | −0.804868 | − | 0.593454i | \(-0.797764\pi\) |
0.916380 | + | 0.400309i | \(0.131097\pi\) | |||||||
\(90\) | −14739.1 | + | 25528.9i | −0.191807 | + | 0.332220i | ||||
\(91\) | −22884.4 | + | 39637.0i | −0.289692 | + | 0.501761i | ||||
\(92\) | 21209.7 | + | 36736.3i | 0.261255 | + | 0.452507i | ||||
\(93\) | −1395.66 | − | 2417.36i | −0.0167330 | − | 0.0289824i | ||||
\(94\) | 2118.77 | − | 3669.82i | 0.0247323 | − | 0.0428376i | ||||
\(95\) | 133704. | − | 231581.i | 1.51997 | − | 2.63266i | ||||
\(96\) | 9599.04 | − | 16626.0i | 0.106304 | − | 0.184124i | ||||
\(97\) | −27920.3 | −0.301294 | −0.150647 | − | 0.988588i | \(-0.548136\pi\) | ||||
−0.150647 | + | 0.988588i | \(0.548136\pi\) | |||||||
\(98\) | −10197.2 | − | 17662.1i | −0.107255 | − | 0.185771i | ||||
\(99\) | −37151.2 | + | 64347.8i | −0.380965 | + | 0.659851i | ||||
\(100\) | −198299. | −1.98299 | ||||||||
\(101\) | −22177.8 | −0.216329 | −0.108165 | − | 0.994133i | \(-0.534497\pi\) | ||||
−0.108165 | + | 0.994133i | \(0.534497\pi\) | |||||||
\(102\) | −4026.38 | + | 6973.89i | −0.0383190 | + | 0.0663704i | ||||
\(103\) | 150643. | 1.39912 | 0.699559 | − | 0.714575i | \(-0.253380\pi\) | ||||
0.699559 | + | 0.714575i | \(0.253380\pi\) | |||||||
\(104\) | −44536.2 | − | 77138.9i | −0.403766 | − | 0.699343i | ||||
\(105\) | 21294.2 | 0.188490 | ||||||||
\(106\) | −3661.28 | − | 6341.52i | −0.0316496 | − | 0.0548187i | ||||
\(107\) | 39040.2 | + | 67619.6i | 0.329650 | + | 0.570970i | 0.982442 | − | 0.186567i | \(-0.0597360\pi\) |
−0.652793 | + | 0.757537i | \(0.726403\pi\) | |||||||
\(108\) | −34381.0 | − | 59549.7i | −0.283635 | − | 0.491270i | ||||
\(109\) | 36490.6 | − | 63203.6i | 0.294181 | − | 0.509537i | −0.680613 | − | 0.732643i | \(-0.738286\pi\) |
0.974794 | + | 0.223106i | \(0.0716197\pi\) | |||||||
\(110\) | 45859.5 | 0.361366 | ||||||||
\(111\) | −17578.2 | − | 37241.5i | −0.135415 | − | 0.286893i | ||||
\(112\) | 37042.1 | 0.279029 | ||||||||
\(113\) | −42713.2 | + | 73981.5i | −0.314678 | + | 0.545038i | −0.979369 | − | 0.202080i | \(-0.935230\pi\) |
0.664691 | + | 0.747118i | \(0.268563\pi\) | |||||||
\(114\) | −9187.63 | − | 15913.4i | −0.0662127 | − | 0.114684i | ||||
\(115\) | −69366.1 | − | 120146.i | −0.489106 | − | 0.847156i | ||||
\(116\) | 73301.8 | + | 126962.i | 0.505789 | + | 0.876052i | ||||
\(117\) | −228874. | −1.54572 | ||||||||
\(118\) | −12884.5 | − | 22316.7i | −0.0851851 | − | 0.147545i | ||||
\(119\) | −51981.0 | −0.336494 | ||||||||
\(120\) | −20720.7 | + | 35889.2i | −0.131356 | + | 0.227516i | ||||
\(121\) | −45458.0 | −0.282258 | ||||||||
\(122\) | 20096.7 | 0.122244 | ||||||||
\(123\) | −23464.2 | + | 40641.1i | −0.139843 | + | 0.242216i | ||||
\(124\) | 8501.98 | + | 14725.9i | 0.0496553 | + | 0.0860056i | ||||
\(125\) | 340640. | 1.94994 | ||||||||
\(126\) | −6537.80 | + | 11323.8i | −0.0366864 | + | 0.0635427i | ||||
\(127\) | 48085.4 | − | 83286.4i | 0.264548 | − | 0.458210i | −0.702897 | − | 0.711291i | \(-0.748111\pi\) |
0.967445 | + | 0.253081i | \(0.0814440\pi\) | |||||||
\(128\) | −77040.5 | + | 133438.i | −0.415618 | + | 0.719871i | ||||
\(129\) | 45871.1 | + | 79451.1i | 0.242697 | + | 0.420364i | ||||
\(130\) | 70630.4 | + | 122335.i | 0.366550 | + | 0.634883i | ||||
\(131\) | 64950.2 | − | 112497.i | 0.330675 | − | 0.572747i | −0.651969 | − | 0.758246i | \(-0.726057\pi\) |
0.982644 | + | 0.185499i | \(0.0593901\pi\) | |||||||
\(132\) | −25326.3 | + | 43866.5i | −0.126514 | + | 0.219128i | ||||
\(133\) | 59306.7 | − | 102722.i | 0.290720 | − | 0.503541i | ||||
\(134\) | −74596.6 | −0.358886 | ||||||||
\(135\) | 112443. | + | 194757.i | 0.531004 | + | 0.919725i | ||||
\(136\) | 50581.0 | − | 87608.9i | 0.234499 | − | 0.406164i | ||||
\(137\) | 163292. | 0.743300 | 0.371650 | − | 0.928373i | \(-0.378792\pi\) | ||||
0.371650 | + | 0.928373i | \(0.378792\pi\) | |||||||
\(138\) | −9533.17 | −0.0426128 | ||||||||
\(139\) | −94437.2 | + | 163570.i | −0.414578 | + | 0.718070i | −0.995384 | − | 0.0959722i | \(-0.969404\pi\) |
0.580806 | + | 0.814042i | \(0.302737\pi\) | |||||||
\(140\) | −129718. | −0.559345 | ||||||||
\(141\) | −7653.67 | − | 13256.5i | −0.0324207 | − | 0.0561543i | ||||
\(142\) | 68572.4 | 0.285383 | ||||||||
\(143\) | 178030. | + | 308358.i | 0.728038 | + | 1.26100i | ||||
\(144\) | 92617.1 | + | 160418.i | 0.372207 | + | 0.644682i | ||||
\(145\) | −239733. | − | 415229.i | −0.946907 | − | 1.64009i | ||||
\(146\) | 27102.6 | − | 46943.0i | 0.105227 | − | 0.182259i | ||||
\(147\) | −73671.4 | −0.281194 | ||||||||
\(148\) | 107081. | + | 226864.i | 0.401846 | + | 0.851358i | ||||
\(149\) | −307061. | −1.13308 | −0.566539 | − | 0.824035i | \(-0.691718\pi\) | ||||
−0.566539 | + | 0.824035i | \(0.691718\pi\) | |||||||
\(150\) | 22282.5 | − | 38594.4i | 0.0808602 | − | 0.140054i | ||||
\(151\) | 41841.5 | + | 72471.7i | 0.149336 | + | 0.258658i | 0.930982 | − | 0.365064i | \(-0.118953\pi\) |
−0.781646 | + | 0.623722i | \(0.785620\pi\) | |||||||
\(152\) | 115419. | + | 199911.i | 0.405198 | + | 0.701824i | ||||
\(153\) | −129969. | − | 225114.i | −0.448862 | − | 0.777451i | ||||
\(154\) | 20341.8 | 0.0691175 | ||||||||
\(155\) | −27805.6 | − | 48160.8i | −0.0929616 | − | 0.161014i | ||||
\(156\) | −156025. | −0.513315 | ||||||||
\(157\) | −54261.5 | + | 93983.7i | −0.175688 | + | 0.304301i | −0.940399 | − | 0.340072i | \(-0.889548\pi\) |
0.764711 | + | 0.644373i | \(0.222882\pi\) | |||||||
\(158\) | 80550.4 | 0.256700 | ||||||||
\(159\) | −26451.4 | −0.0829767 | ||||||||
\(160\) | 191240. | − | 331238.i | 0.590581 | − | 1.02292i | ||||
\(161\) | −30768.6 | − | 53292.8i | −0.0935499 | − | 0.162033i | ||||
\(162\) | −57250.3 | −0.171392 | ||||||||
\(163\) | −43054.7 | + | 74572.8i | −0.126926 | + | 0.219843i | −0.922484 | − | 0.386035i | \(-0.873844\pi\) |
0.795558 | + | 0.605877i | \(0.207178\pi\) | |||||||
\(164\) | 142937. | − | 247574.i | 0.414987 | − | 0.718779i | ||||
\(165\) | 82829.5 | − | 143465.i | 0.236851 | − | 0.410238i | ||||
\(166\) | −58964.0 | − | 102129.i | −0.166080 | − | 0.287659i | ||||
\(167\) | 32440.0 | + | 56187.7i | 0.0900097 | + | 0.155901i | 0.907515 | − | 0.420020i | \(-0.137977\pi\) |
−0.817505 | + | 0.575921i | \(0.804644\pi\) | |||||||
\(168\) | −9191.03 | + | 15919.3i | −0.0251241 | + | 0.0435163i | ||||
\(169\) | −362740. | + | 628285.i | −0.976965 | + | 1.69215i | ||||
\(170\) | −80217.0 | + | 138940.i | −0.212885 | + | 0.368727i | ||||
\(171\) | 593144. | 1.55121 | ||||||||
\(172\) | −279434. | − | 483994.i | −0.720208 | − | 1.24744i | ||||
\(173\) | 44966.8 | − | 77884.8i | 0.114229 | − | 0.197851i | −0.803242 | − | 0.595653i | \(-0.796894\pi\) |
0.917471 | + | 0.397802i | \(0.130227\pi\) | |||||||
\(174\) | −32947.1 | −0.0824982 | ||||||||
\(175\) | 287669. | 0.710066 | ||||||||
\(176\) | 144085. | − | 249563.i | 0.350621 | − | 0.607293i | ||||
\(177\) | −93086.1 | −0.223332 | ||||||||
\(178\) | −11408.0 | − | 19759.3i | −0.0269874 | − | 0.0467436i | ||||
\(179\) | −790485. | −1.84400 | −0.922000 | − | 0.387190i | \(-0.873446\pi\) | ||||
−0.922000 | + | 0.387190i | \(0.873446\pi\) | |||||||
\(180\) | −324337. | − | 561768.i | −0.746131 | − | 1.29234i | ||||
\(181\) | 27592.6 | + | 47791.9i | 0.0626032 | + | 0.108432i | 0.895628 | − | 0.444803i | \(-0.146726\pi\) |
−0.833025 | + | 0.553235i | \(0.813393\pi\) | |||||||
\(182\) | 31329.4 | + | 54264.2i | 0.0701090 | + | 0.121432i | ||||
\(183\) | 36297.9 | − | 62869.9i | 0.0801224 | − | 0.138776i | ||||
\(184\) | 119760. | 0.260775 | ||||||||
\(185\) | −350208. | − | 741958.i | −0.752310 | − | 1.59386i | ||||
\(186\) | −3821.41 | −0.00809917 | ||||||||
\(187\) | −202194. | + | 350211.i | −0.422829 | + | 0.732362i | ||||
\(188\) | 46624.0 | + | 80755.1i | 0.0962088 | + | 0.166638i | ||||
\(189\) | 49876.1 | + | 86388.0i | 0.101564 | + | 0.175913i | ||||
\(190\) | −183044. | − | 317041.i | −0.367851 | − | 0.637136i | ||||
\(191\) | 529061. | 1.04935 | 0.524677 | − | 0.851301i | \(-0.324186\pi\) | ||||
0.524677 | + | 0.851301i | \(0.324186\pi\) | |||||||
\(192\) | 53924.6 | + | 93400.2i | 0.105568 | + | 0.182850i | ||||
\(193\) | 408009. | 0.788454 | 0.394227 | − | 0.919013i | \(-0.371012\pi\) | ||||
0.394227 | + | 0.919013i | \(0.371012\pi\) | |||||||
\(194\) | −19111.8 | + | 33102.6i | −0.0364584 | + | 0.0631478i | ||||
\(195\) | 510279. | 0.960995 | ||||||||
\(196\) | 448785. | 0.834446 | ||||||||
\(197\) | −194132. | + | 336246.i | −0.356394 | + | 0.617293i | −0.987356 | − | 0.158521i | \(-0.949327\pi\) |
0.630961 | + | 0.775814i | \(0.282661\pi\) | |||||||
\(198\) | 50861.1 | + | 88094.0i | 0.0921983 | + | 0.159692i | ||||
\(199\) | −427354. | −0.764989 | −0.382495 | − | 0.923958i | \(-0.624935\pi\) | ||||
−0.382495 | + | 0.923958i | \(0.624935\pi\) | |||||||
\(200\) | −279922. | + | 484838.i | −0.494836 | + | 0.857081i | ||||
\(201\) | −134733. | + | 233365.i | −0.235226 | + | 0.407423i | ||||
\(202\) | −15181.0 | + | 26294.3i | −0.0261772 | + | 0.0453402i | ||||
\(203\) | −106338. | − | 184183.i | −0.181112 | − | 0.313696i | ||||
\(204\) | −88601.3 | − | 153462.i | −0.149061 | − | 0.258182i | ||||
\(205\) | −467474. | + | 809688.i | −0.776913 | + | 1.34565i | ||||
\(206\) | 103117. | − | 178604.i | 0.169302 | − | 0.293240i | ||||
\(207\) | 153863. | − | 266498.i | 0.249579 | − | 0.432284i | ||||
\(208\) | 887651. | 1.42260 | ||||||||
\(209\) | −461379. | − | 799132.i | −0.730621 | − | 1.26547i | ||||
\(210\) | 14576.2 | − | 25246.7i | 0.0228084 | − | 0.0395053i | ||||
\(211\) | 74721.7 | 0.115542 | 0.0577711 | − | 0.998330i | \(-0.481601\pi\) | ||||
0.0577711 | + | 0.998330i | \(0.481601\pi\) | |||||||
\(212\) | 161134. | 0.246234 | ||||||||
\(213\) | 123853. | − | 214519.i | 0.187050 | − | 0.323979i | ||||
\(214\) | 106894. | 0.159559 | ||||||||
\(215\) | 913885. | + | 1.58290e6i | 1.34833 | + | 2.33537i | ||||
\(216\) | −194131. | −0.283114 | ||||||||
\(217\) | −12333.7 | − | 21362.6i | −0.0177805 | − | 0.0307967i | ||||
\(218\) | −49956.7 | − | 86527.5i | −0.0711955 | − | 0.123314i | ||||
\(219\) | −97903.1 | − | 169573.i | −0.137939 | − | 0.238917i | ||||
\(220\) | −504574. | + | 873947.i | −0.702858 | + | 1.21739i | ||||
\(221\) | −1.24564e6 | −1.71558 | ||||||||
\(222\) | −56186.5 | − | 4651.39i | −0.0765156 | − | 0.00633433i | ||||
\(223\) | 177377. | 0.238856 | 0.119428 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119428 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(224\) | 84828.2 | − | 146927.i | 0.112959 | − | 0.195651i | ||||
\(225\) | 719266. | + | 1.24581e6i | 0.947182 | + | 1.64057i | ||||
\(226\) | 58475.6 | + | 101283.i | 0.0761560 | + | 0.131906i | ||||
\(227\) | −258214. | − | 447240.i | −0.332595 | − | 0.576071i | 0.650425 | − | 0.759570i | \(-0.274591\pi\) |
−0.983020 | + | 0.183500i | \(0.941257\pi\) | |||||||
\(228\) | 404351. | 0.515136 | ||||||||
\(229\) | 111008. | + | 192272.i | 0.139883 | + | 0.242285i | 0.927452 | − | 0.373941i | \(-0.121994\pi\) |
−0.787569 | + | 0.616227i | \(0.788661\pi\) | |||||||
\(230\) | −189928. | −0.236739 | ||||||||
\(231\) | 36740.6 | − | 63636.5i | 0.0453018 | − | 0.0784651i | ||||
\(232\) | 413895. | 0.504860 | ||||||||
\(233\) | 530582. | 0.640269 | 0.320134 | − | 0.947372i | \(-0.396272\pi\) | ||||
0.320134 | + | 0.947372i | \(0.396272\pi\) | |||||||
\(234\) | −156667. | + | 271356.i | −0.187042 | + | 0.323966i | ||||
\(235\) | −152483. | − | 264109.i | −0.180116 | − | 0.311970i | ||||
\(236\) | 567054. | 0.662742 | ||||||||
\(237\) | 145487. | − | 251991.i | 0.168249 | − | 0.291416i | ||||
\(238\) | −35581.8 | + | 61629.4i | −0.0407179 | + | 0.0705254i | ||||
\(239\) | 501940. | − | 869386.i | 0.568404 | − | 0.984505i | −0.428320 | − | 0.903627i | \(-0.640894\pi\) |
0.996724 | − | 0.0808775i | \(-0.0257723\pi\) | |||||||
\(240\) | −206492. | − | 357654.i | −0.231406 | − | 0.400807i | ||||
\(241\) | 551083. | + | 954504.i | 0.611187 | + | 1.05861i | 0.991041 | + | 0.133561i | \(0.0426411\pi\) |
−0.379853 | + | 0.925047i | \(0.624026\pi\) | |||||||
\(242\) | −31116.6 | + | 53895.6i | −0.0341550 | + | 0.0591582i | ||||
\(243\) | −380727. | + | 659439.i | −0.413617 | + | 0.716405i | ||||
\(244\) | −221117. | + | 382985.i | −0.237764 | + | 0.411820i | ||||
\(245\) | −1.46775e6 | −1.56220 | ||||||||
\(246\) | 32123.1 | + | 55638.8i | 0.0338438 | + | 0.0586193i | ||||
\(247\) | 1.42119e6 | − | 2.46157e6i | 1.48221 | − | 2.56726i | ||||
\(248\) | 48006.1 | 0.0495641 | ||||||||
\(249\) | −425994. | −0.435416 | ||||||||
\(250\) | 233173. | − | 403868.i | 0.235955 | − | 0.408686i | ||||
\(251\) | −243215. | −0.243672 | −0.121836 | − | 0.992550i | \(-0.538878\pi\) | ||||
−0.121836 | + | 0.992550i | \(0.538878\pi\) | |||||||
\(252\) | −143866. | − | 249183.i | −0.142710 | − | 0.247182i | ||||
\(253\) | −478732. | −0.470209 | ||||||||
\(254\) | −65830.3 | − | 114021.i | −0.0640238 | − | 0.110892i | ||||
\(255\) | 289770. | + | 501896.i | 0.279063 | + | 0.483351i | ||||
\(256\) | −243460. | − | 421684.i | −0.232181 | − | 0.402150i | ||||
\(257\) | −668377. | + | 1.15766e6i | −0.631232 | + | 1.09333i | 0.356068 | + | 0.934460i | \(0.384117\pi\) |
−0.987300 | + | 0.158866i | \(0.949216\pi\) | |||||||
\(258\) | 125598. | 0.117472 | ||||||||
\(259\) | −155341. | − | 329109.i | −0.143892 | − | 0.304853i | ||||
\(260\) | −3.10847e6 | −2.85177 | ||||||||
\(261\) | 531758. | − | 921032.i | 0.483184 | − | 0.836900i | ||||
\(262\) | −88918.6 | − | 154012.i | −0.0800275 | − | 0.138612i | ||||
\(263\) | 247329. | + | 428387.i | 0.220489 | + | 0.381897i | 0.954956 | − | 0.296746i | \(-0.0959015\pi\) |
−0.734468 | + | 0.678643i | \(0.762568\pi\) | |||||||
\(264\) | 71502.1 | + | 123845.i | 0.0631406 | + | 0.109363i | ||||
\(265\) | −526988. | −0.460985 | ||||||||
\(266\) | −81192.6 | − | 140630.i | −0.0703578 | − | 0.121863i | ||||
\(267\) | −82419.0 | −0.0707537 | ||||||||
\(268\) | 820757. | − | 1.42159e6i | 0.698036 | − | 1.20903i | ||||
\(269\) | −764022. | −0.643762 | −0.321881 | − | 0.946780i | \(-0.604315\pi\) | ||||
−0.321881 | + | 0.946780i | \(0.604315\pi\) | |||||||
\(270\) | 307875. | 0.257019 | ||||||||
\(271\) | 649285. | − | 1.12459e6i | 0.537047 | − | 0.930192i | −0.462015 | − | 0.886872i | \(-0.652873\pi\) |
0.999061 | − | 0.0433197i | \(-0.0137934\pi\) | |||||||
\(272\) | 504066. | + | 873067.i | 0.413109 | + | 0.715526i | ||||
\(273\) | 226344. | 0.183807 | ||||||||
\(274\) | 111776. | − | 193601.i | 0.0899438 | − | 0.155787i | ||||
\(275\) | 1.11897e6 | − | 1.93811e6i | 0.892249 | − | 1.54542i | ||||
\(276\) | 104890. | − | 181674.i | 0.0828820 | − | 0.143556i | ||||
\(277\) | 124682. | + | 215956.i | 0.0976351 | + | 0.169109i | 0.910705 | − | 0.413057i | \(-0.135539\pi\) |
−0.813070 | + | 0.582166i | \(0.802206\pi\) | |||||||
\(278\) | 129287. | + | 223932.i | 0.100333 | + | 0.173782i | ||||
\(279\) | 61676.5 | − | 106827.i | 0.0474361 | − | 0.0821618i | ||||
\(280\) | −183112. | + | 317159.i | −0.139579 | + | 0.241759i | ||||
\(281\) | 808604. | − | 1.40054e6i | 0.610900 | − | 1.05811i | −0.380189 | − | 0.924909i | \(-0.624141\pi\) |
0.991089 | − | 0.133201i | \(-0.0425256\pi\) | |||||||
\(282\) | −20956.2 | −0.0156924 | ||||||||
\(283\) | 1.11212e6 | + | 1.92624e6i | 0.825438 | + | 1.42970i | 0.901584 | + | 0.432604i | \(0.142405\pi\) |
−0.0761461 | + | 0.997097i | \(0.524262\pi\) | |||||||
\(284\) | −754476. | + | 1.30679e6i | −0.555072 | + | 0.961413i | ||||
\(285\) | −1.32243e6 | −0.964405 | ||||||||
\(286\) | 487458. | 0.352388 | ||||||||
\(287\) | −207357. | + | 359152.i | −0.148598 | + | 0.257379i | ||||
\(288\) | 848392. | 0.602720 | ||||||||
\(289\) | 2574.28 | + | 4458.79i | 0.00181306 | + | 0.00314031i | ||||
\(290\) | −656402. | −0.458326 | ||||||||
\(291\) | 69038.0 | + | 119577.i | 0.0477920 | + | 0.0827782i | ||||
\(292\) | 596397. | + | 1.03299e6i | 0.409335 | + | 0.708989i | ||||
\(293\) | −716059. | − | 1.24025e6i | −0.487282 | − | 0.843996i | 0.512612 | − | 0.858621i | \(-0.328678\pi\) |
−0.999893 | + | 0.0146243i | \(0.995345\pi\) | |||||||
\(294\) | −50429.1 | + | 87345.8i | −0.0340262 | + | 0.0589350i | ||||
\(295\) | −1.85454e6 | −1.24074 | ||||||||
\(296\) | 705839. | + | 58432.7i | 0.468248 | + | 0.0387638i | ||||
\(297\) | 776027. | 0.510488 | ||||||||
\(298\) | −210188. | + | 364056.i | −0.137109 | + | 0.237480i | ||||
\(299\) | −737318. | − | 1.27707e6i | −0.476955 | − | 0.826110i | ||||
\(300\) | 490330. | + | 849277.i | 0.314547 | + | 0.544811i | ||||
\(301\) | 405371. | + | 702123.i | 0.257891 | + | 0.446680i | ||||
\(302\) | 114565. | 0.0722824 | ||||||||
\(303\) | 54838.8 | + | 94983.5i | 0.0343148 | + | 0.0594349i | ||||
\(304\) | −2.30041e6 | −1.42765 | ||||||||
\(305\) | 723159. | − | 1.25255e6i | 0.445127 | − | 0.770983i | ||||
\(306\) | −355864. | −0.217260 | ||||||||
\(307\) | −263641. | −0.159649 | −0.0798245 | − | 0.996809i | \(-0.525436\pi\) | ||||
−0.0798245 | + | 0.996809i | \(0.525436\pi\) | |||||||
\(308\) | −223813. | + | 387655.i | −0.134434 | + | 0.232846i | ||||
\(309\) | −372491. | − | 645174.i | −0.221932 | − | 0.384398i | ||||
\(310\) | −76133.4 | −0.0449957 | ||||||||
\(311\) | −1.26348e6 | + | 2.18841e6i | −0.740743 | + | 1.28300i | 0.211415 | + | 0.977396i | \(0.432193\pi\) |
−0.952158 | + | 0.305607i | \(0.901141\pi\) | |||||||
\(312\) | −220248. | + | 381480.i | −0.128093 | + | 0.221863i | ||||
\(313\) | 139059. | − | 240857.i | 0.0802301 | − | 0.138963i | −0.823119 | − | 0.567869i | \(-0.807768\pi\) |
0.903349 | + | 0.428907i | \(0.141101\pi\) | |||||||
\(314\) | 74285.6 | + | 128666.i | 0.0425187 | + | 0.0736446i | ||||
\(315\) | 470511. | + | 814949.i | 0.267174 | + | 0.462758i | ||||
\(316\) | −886265. | + | 1.53506e6i | −0.499282 | + | 0.864781i | ||||
\(317\) | 411987. | − | 713582.i | 0.230269 | − | 0.398838i | −0.727618 | − | 0.685982i | \(-0.759373\pi\) |
0.957887 | + | 0.287145i | \(0.0927061\pi\) | |||||||
\(318\) | −18106.4 | + | 31361.2i | −0.0100407 | + | 0.0173910i | ||||
\(319\) | −1.65452e6 | −0.910323 | ||||||||
\(320\) | 1.07433e6 | + | 1.86080e6i | 0.586495 | + | 1.01584i | ||||
\(321\) | 193068. | − | 334404.i | 0.104580 | − | 0.181138i | ||||
\(322\) | −84246.2 | −0.0452804 | ||||||||
\(323\) | 3.22817e6 | 1.72167 | ||||||||
\(324\) | 629903. | − | 1.09102e6i | 0.333358 | − | 0.577393i | ||||
\(325\) | 6.89351e6 | 3.62020 | ||||||||
\(326\) | 58943.0 | + | 102092.i | 0.0307177 | + | 0.0532046i | ||||
\(327\) | −360919. | −0.186655 | ||||||||
\(328\) | −403544. | − | 698958.i | −0.207112 | − | 0.358729i | ||||
\(329\) | −67636.7 | − | 117150.i | −0.0344503 | − | 0.0596697i | ||||
\(330\) | −113396. | − | 196408.i | −0.0573209 | − | 0.0992826i | ||||
\(331\) | −554501. | + | 960423.i | −0.278184 | + | 0.481829i | −0.970933 | − | 0.239350i | \(-0.923066\pi\) |
0.692750 | + | 0.721178i | \(0.256399\pi\) | |||||||
\(332\) | 2.59503e6 | 1.29210 | ||||||||
\(333\) | 1.03687e6 | − | 1.49561e6i | 0.512403 | − | 0.739110i | ||||
\(334\) | 88822.5 | 0.0435669 | ||||||||
\(335\) | −2.68428e6 | + | 4.64930e6i | −1.30682 | + | 2.26348i | ||||
\(336\) | −91593.3 | − | 158644.i | −0.0442604 | − | 0.0766613i | ||||
\(337\) | 956999. | + | 1.65757e6i | 0.459025 | + | 0.795055i | 0.998910 | − | 0.0466839i | \(-0.0148654\pi\) |
−0.539884 | + | 0.841739i | \(0.681532\pi\) | |||||||
\(338\) | 496602. | + | 860140.i | 0.236438 | + | 0.409522i | ||||
\(339\) | 422465. | 0.199660 | ||||||||
\(340\) | −1.76519e6 | − | 3.05740e6i | −0.828123 | − | 1.43435i | ||||
\(341\) | −191901. | −0.0893700 | ||||||||
\(342\) | 406015. | − | 703239.i | 0.187706 | − | 0.325115i | ||||
\(343\) | −1.38556e6 | −0.635903 | ||||||||
\(344\) | −1.57781e6 | −0.718884 | ||||||||
\(345\) | −343041. | + | 594164.i | −0.155167 | + | 0.268756i | ||||
\(346\) | −61560.8 | − | 106626.i | −0.0276448 | − | 0.0478823i | ||||
\(347\) | −1.32025e6 | −0.588615 | −0.294308 | − | 0.955711i | \(-0.595089\pi\) | ||||
−0.294308 | + | 0.955711i | \(0.595089\pi\) | |||||||
\(348\) | 362504. | − | 627876.i | 0.160459 | − | 0.277924i | ||||
\(349\) | −258449. | + | 447647.i | −0.113583 | + | 0.196731i | −0.917212 | − | 0.398399i | \(-0.869566\pi\) |
0.803630 | + | 0.595130i | \(0.202899\pi\) | |||||||
\(350\) | 196914. | − | 341065.i | 0.0859223 | − | 0.148822i | ||||
\(351\) | 1.19520e6 | + | 2.07014e6i | 0.517812 | + | 0.896876i | ||||
\(352\) | −659925. | − | 1.14302e6i | −0.283882 | − | 0.491698i | ||||
\(353\) | 1.95078e6 | − | 3.37884e6i | 0.833241 | − | 1.44322i | −0.0622140 | − | 0.998063i | \(-0.519816\pi\) |
0.895455 | − | 0.445153i | \(-0.146851\pi\) | |||||||
\(354\) | −63718.8 | + | 110364.i | −0.0270246 | + | 0.0468080i | ||||
\(355\) | 2.46750e6 | − | 4.27384e6i | 1.03917 | − | 1.79990i | ||||
\(356\) | 502073. | 0.209963 | ||||||||
\(357\) | 128533. | + | 222625.i | 0.0533756 | + | 0.0924493i | ||||
\(358\) | −541098. | + | 937209.i | −0.223135 | + | 0.386482i | ||||
\(359\) | −4.78385e6 | −1.95903 | −0.979515 | − | 0.201370i | \(-0.935461\pi\) | ||||
−0.979515 | + | 0.201370i | \(0.935461\pi\) | |||||||
\(360\) | −1.83135e6 | −0.744760 | ||||||||
\(361\) | −2.44506e6 | + | 4.23497e6i | −0.987464 | + | 1.71034i | ||||
\(362\) | 75550.2 | 0.0303015 | ||||||||
\(363\) | 112403. | + | 194688.i | 0.0447726 | + | 0.0775484i | ||||
\(364\) | −1.37882e6 | −0.545450 | ||||||||
\(365\) | −1.95051e6 | − | 3.37838e6i | −0.766331 | − | 1.32732i | ||||
\(366\) | −49692.9 | − | 86070.6i | −0.0193906 | − | 0.0335855i | ||||
\(367\) | 123879. | + | 214565.i | 0.0480102 | + | 0.0831562i | 0.889032 | − | 0.457845i | \(-0.151379\pi\) |
−0.841022 | + | 0.541002i | \(0.818045\pi\) | |||||||
\(368\) | −596733. | + | 1.03357e6i | −0.229700 | + | 0.397852i | ||||
\(369\) | −2.07383e6 | −0.792881 | ||||||||
\(370\) | −1.11940e6 | − | 92669.1i | −0.425089 | − | 0.0351909i | ||||
\(371\) | −233755. | −0.0881712 | ||||||||
\(372\) | 42045.4 | − | 72824.8i | 0.0157529 | − | 0.0272849i | ||||
\(373\) | 917087. | + | 1.58844e6i | 0.341302 | + | 0.591152i | 0.984675 | − | 0.174401i | \(-0.0557989\pi\) |
−0.643373 | + | 0.765553i | \(0.722466\pi\) | |||||||
\(374\) | 276810. | + | 479449.i | 0.102330 | + | 0.177241i | ||||
\(375\) | −842296. | − | 1.45890e6i | −0.309305 | − | 0.535732i | ||||
\(376\) | 263260. | 0.0960320 | ||||||||
\(377\) | −2.54821e6 | − | 4.41363e6i | −0.923382 | − | 1.59935i | ||||
\(378\) | 136564. | 0.0491593 | ||||||||
\(379\) | 2.35307e6 | − | 4.07564e6i | 0.841468 | − | 1.45746i | −0.0471860 | − | 0.998886i | \(-0.515025\pi\) |
0.888654 | − | 0.458579i | \(-0.151641\pi\) | |||||||
\(380\) | 8.05584e6 | 2.86188 | ||||||||
\(381\) | −475600. | −0.167853 | ||||||||
\(382\) | 362150. | − | 627262.i | 0.126978 | − | 0.219933i | ||||
\(383\) | 1.24088e6 | + | 2.14927e6i | 0.432248 | + | 0.748675i | 0.997067 | − | 0.0765401i | \(-0.0243873\pi\) |
−0.564819 | + | 0.825215i | \(0.691054\pi\) | |||||||
\(384\) | 761987. | 0.263706 | ||||||||
\(385\) | 731978. | − | 1.26782e6i | 0.251679 | − | 0.435920i | ||||
\(386\) | 279288. | − | 483741.i | 0.0954078 | − | 0.165251i | ||||
\(387\) | −2.02712e6 | + | 3.51107e6i | −0.688020 | + | 1.19169i | ||||
\(388\) | −420559. | − | 728430.i | −0.141823 | − | 0.245645i | ||||
\(389\) | 2.93239e6 | + | 5.07904e6i | 0.982533 | + | 1.70180i | 0.652424 | + | 0.757854i | \(0.273752\pi\) |
0.330109 | + | 0.943943i | \(0.392914\pi\) | |||||||
\(390\) | 349293. | − | 604994.i | 0.116286 | − | 0.201414i | ||||
\(391\) | 837394. | − | 1.45041e6i | 0.277005 | − | 0.479787i | ||||
\(392\) | 633511. | − | 1.09727e6i | 0.208228 | − | 0.360662i | ||||
\(393\) | −642405. | −0.209811 | ||||||||
\(394\) | 265772. | + | 460330.i | 0.0862518 | + | 0.149392i | ||||
\(395\) | 2.89852e6 | − | 5.02038e6i | 0.934724 | − | 1.61899i | ||||
\(396\) | −2.23842e6 | −0.717304 | ||||||||
\(397\) | −1.93079e6 | −0.614837 | −0.307418 | − | 0.951574i | \(-0.599465\pi\) | ||||
−0.307418 | + | 0.951574i | \(0.599465\pi\) | |||||||
\(398\) | −292530. | + | 506677.i | −0.0925684 | + | 0.160333i | ||||
\(399\) | −586587. | −0.184459 | ||||||||
\(400\) | −2.78956e6 | − | 4.83166e6i | −0.871738 | − | 1.50989i | ||||
\(401\) | 4.04409e6 | 1.25591 | 0.627957 | − | 0.778248i | \(-0.283892\pi\) | ||||
0.627957 | + | 0.778248i | \(0.283892\pi\) | |||||||
\(402\) | 184454. | + | 319483.i | 0.0569276 | + | 0.0986014i | ||||
\(403\) | −295557. | − | 511919.i | −0.0906521 | − | 0.157014i | ||||
\(404\) | −334062. | − | 578612.i | −0.101830 | − | 0.176374i | ||||
\(405\) | −2.06009e6 | + | 3.56818e6i | −0.624092 | + | 1.08096i | ||||
\(406\) | −291159. | −0.0876628 | ||||||||
\(407\) | −2.82155e6 | − | 233581.i | −0.844308 | − | 0.0698959i | ||||
\(408\) | −500284. | −0.148787 | ||||||||
\(409\) | −1.72521e6 | + | 2.98816e6i | −0.509958 | + | 0.883273i | 0.489976 | + | 0.871736i | \(0.337006\pi\) |
−0.999933 | + | 0.0115369i | \(0.996328\pi\) | |||||||
\(410\) | 639985. | + | 1.10849e6i | 0.188023 | + | 0.325665i | ||||
\(411\) | −403770. | − | 699350.i | −0.117904 | − | 0.204216i | ||||
\(412\) | 2.26911e6 | + | 3.93021e6i | 0.658586 | + | 1.14070i | ||||
\(413\) | −822617. | −0.237314 | ||||||||
\(414\) | −210643. | − | 364844.i | −0.0604012 | − | 0.104618i | ||||
\(415\) | −8.48702e6 | −2.41900 | ||||||||
\(416\) | 2.03277e6 | − | 3.52086e6i | 0.575909 | − | 0.997504i | ||||
\(417\) | 934053. | 0.263046 | ||||||||
\(418\) | −1.26328e6 | −0.353639 | ||||||||
\(419\) | −380573. | + | 659172.i | −0.105902 | + | 0.183427i | −0.914106 | − | 0.405475i | \(-0.867106\pi\) |
0.808204 | + | 0.588902i | \(0.200440\pi\) | |||||||
\(420\) | 320752. | + | 555558.i | 0.0887249 | + | 0.153676i | ||||
\(421\) | 2.94008e6 | 0.808451 | 0.404226 | − | 0.914659i | \(-0.367541\pi\) | ||||
0.404226 | + | 0.914659i | \(0.367541\pi\) | |||||||
\(422\) | 51148.0 | − | 88591.0i | 0.0139813 | − | 0.0242163i | ||||
\(423\) | 338227. | − | 585827.i | 0.0919090 | − | 0.159191i | ||||
\(424\) | 227460. | − | 393972.i | 0.0614455 | − | 0.106427i | ||||
\(425\) | 3.91458e6 | + | 6.78026e6i | 1.05127 | + | 1.82085i | ||||
\(426\) | −169558. | − | 293683.i | −0.0452683 | − | 0.0784070i | ||||
\(427\) | 320771. | − | 555591.i | 0.0851383 | − | 0.147464i | ||||
\(428\) | −1.17612e6 | + | 2.03709e6i | −0.310342 | + | 0.537528i | ||||
\(429\) | 880426. | − | 1.52494e6i | 0.230967 | − | 0.400046i | ||||
\(430\) | 2.50227e6 | 0.652624 | ||||||||
\(431\) | −1.31893e6 | − | 2.28445e6i | −0.342001 | − | 0.592363i | 0.642803 | − | 0.766031i | \(-0.277771\pi\) |
−0.984804 | + | 0.173668i | \(0.944438\pi\) | |||||||
\(432\) | 967308. | − | 1.67543e6i | 0.249376 | − | 0.431933i | ||||
\(433\) | 1.16452e6 | 0.298487 | 0.149244 | − | 0.988800i | \(-0.452316\pi\) | ||||
0.149244 | + | 0.988800i | \(0.452316\pi\) | |||||||
\(434\) | −33770.4 | −0.00860620 | ||||||||
\(435\) | −1.18557e6 | + | 2.05346e6i | −0.300402 | + | 0.520311i | ||||
\(436\) | 2.19862e6 | 0.553902 | ||||||||
\(437\) | 1.91082e6 | + | 3.30963e6i | 0.478647 | + | 0.829040i | ||||
\(438\) | −268064. | −0.0667657 | ||||||||
\(439\) | 2.34381e6 | + | 4.05960e6i | 0.580445 | + | 1.00536i | 0.995427 | + | 0.0955302i | \(0.0304547\pi\) |
−0.414982 | + | 0.909830i | \(0.636212\pi\) | |||||||
\(440\) | 1.42453e6 | + | 2.46735e6i | 0.350783 | + | 0.607575i | ||||
\(441\) | −1.62783e6 | − | 2.81948e6i | −0.398576 | − | 0.690354i | ||||
\(442\) | −852657. | + | 1.47685e6i | −0.207596 | + | 0.359567i | ||||
\(443\) | 1.37568e6 | 0.333049 | 0.166524 | − | 0.986037i | \(-0.446746\pi\) | ||||
0.166524 | + | 0.986037i | \(0.446746\pi\) | |||||||
\(444\) | 706840. | − | 1.01957e6i | 0.170163 | − | 0.245449i | ||||
\(445\) | −1.64202e6 | −0.393079 | ||||||||
\(446\) | 121417. | − | 210301.i | 0.0289031 | − | 0.0500616i | ||||
\(447\) | 759266. | + | 1.31509e6i | 0.179732 | + | 0.311305i | ||||
\(448\) | 476541. | + | 825393.i | 0.112177 | + | 0.194297i | ||||
\(449\) | −2.77963e6 | − | 4.81445e6i | −0.650684 | − | 1.12702i | −0.982957 | − | 0.183835i | \(-0.941149\pi\) |
0.332273 | − | 0.943183i | \(-0.392185\pi\) | |||||||
\(450\) | 1.96939e6 | 0.458459 | ||||||||
\(451\) | 1.61314e6 | + | 2.79404e6i | 0.373449 | + | 0.646832i | ||||
\(452\) | −2.57354e6 | −0.592495 | ||||||||
\(453\) | 206922. | − | 358399.i | 0.0473763 | − | 0.0820581i | ||||
\(454\) | −707005. | −0.160984 | ||||||||
\(455\) | 4.50942e6 | 1.02116 | ||||||||
\(456\) | 570788. | − | 988634.i | 0.128547 | − | 0.222650i | ||||
\(457\) | 3.65756e6 | + | 6.33508e6i | 0.819221 | + | 1.41893i | 0.906257 | + | 0.422727i | \(0.138927\pi\) |
−0.0870357 | + | 0.996205i | \(0.527739\pi\) | |||||||
\(458\) | 303947. | 0.0677071 | ||||||||
\(459\) | −1.35742e6 | + | 2.35112e6i | −0.300734 | + | 0.520887i | ||||
\(460\) | 2.08971e6 | − | 3.61948e6i | 0.460459 | − | 0.797538i | ||||
\(461\) | −1.23171e6 | + | 2.13339e6i | −0.269934 | + | 0.467539i | −0.968844 | − | 0.247670i | \(-0.920335\pi\) |
0.698911 | + | 0.715209i | \(0.253668\pi\) | |||||||
\(462\) | −50298.9 | − | 87120.2i | −0.0109636 | − | 0.0189895i | ||||
\(463\) | 2.58424e6 | + | 4.47603e6i | 0.560248 | + | 0.970377i | 0.997474 | + | 0.0710260i | \(0.0226273\pi\) |
−0.437227 | + | 0.899351i | \(0.644039\pi\) | |||||||
\(464\) | −2.06234e6 | + | 3.57208e6i | −0.444698 | + | 0.770240i | ||||
\(465\) | −137509. | + | 238173.i | −0.0294916 | + | 0.0510810i | ||||
\(466\) | 363191. | − | 629065.i | 0.0774765 | − | 0.134193i | ||||
\(467\) | −4.13950e6 | −0.878325 | −0.439163 | − | 0.898408i | \(-0.644725\pi\) | ||||
−0.439163 | + | 0.898408i | \(0.644725\pi\) | |||||||
\(468\) | −3.44750e6 | − | 5.97124e6i | −0.727595 | − | 1.26023i | ||||
\(469\) | −1.19066e6 | + | 2.06229e6i | −0.249952 | + | 0.432929i | ||||
\(470\) | −417508. | −0.0871806 | ||||||||
\(471\) | 536686. | 0.111473 | ||||||||
\(472\) | 800462. | − | 1.38644e6i | 0.165381 | − | 0.286448i | ||||
\(473\) | 6.30720e6 | 1.29624 | ||||||||
\(474\) | −199176. | − | 344983.i | −0.0407184 | − | 0.0705263i | ||||
\(475\) | −1.78651e7 | −3.63304 | ||||||||
\(476\) | −782984. | − | 1.35617e6i | −0.158393 | − | 0.274344i | ||||
\(477\) | −584464. | − | 1.01232e6i | −0.117615 | − | 0.203715i | ||||
\(478\) | −687170. | − | 1.19021e6i | −0.137561 | − | 0.238262i | ||||
\(479\) | 3.40359e6 | − | 5.89520e6i | 0.677796 | − | 1.17398i | −0.297847 | − | 0.954614i | \(-0.596269\pi\) |
0.975643 | − | 0.219363i | \(-0.0703980\pi\) | |||||||
\(480\) | −1.89151e6 | −0.374719 | ||||||||
\(481\) | −3.72250e6 | − | 7.88655e6i | −0.733620 | − | 1.55426i | ||||
\(482\) | 1.50890e6 | 0.295830 | ||||||||
\(483\) | −152162. | + | 263553.i | −0.0296783 | + | 0.0514043i | ||||
\(484\) | −684728. | − | 1.18598e6i | −0.132863 | − | 0.230126i | ||||
\(485\) | 1.37543e6 | + | 2.38232e6i | 0.265513 | + | 0.459882i | ||||
\(486\) | 521226. | + | 902791.i | 0.100100 | + | 0.173379i | ||||
\(487\) | 313113. | 0.0598244 | 0.0299122 | − | 0.999553i | \(-0.490477\pi\) | ||||
0.0299122 | + | 0.999553i | \(0.490477\pi\) | |||||||
\(488\) | 624263. | + | 1.08125e6i | 0.118664 | + | 0.205532i | ||||
\(489\) | 425842. | 0.0805335 | ||||||||
\(490\) | −1.00469e6 | + | 1.74018e6i | −0.189035 | + | 0.327419i | ||||
\(491\) | −453024. | −0.0848042 | −0.0424021 | − | 0.999101i | \(-0.513501\pi\) | ||||
−0.0424021 | + | 0.999101i | \(0.513501\pi\) | |||||||
\(492\) | −1.41375e6 | −0.263306 | ||||||||
\(493\) | 2.89408e6 | − | 5.01269e6i | 0.536281 | − | 0.928866i | ||||
\(494\) | −1.94564e6 | − | 3.36995e6i | −0.358712 | − | 0.621307i | ||||
\(495\) | 7.32072e6 | 1.34289 | ||||||||
\(496\) | −239203. | + | 414311.i | −0.0436578 | + | 0.0756175i | ||||
\(497\) | 1.09451e6 | − | 1.89574e6i | 0.198759 | − | 0.344261i | ||||
\(498\) | −291599. | + | 505064.i | −0.0526881 | + | 0.0912584i | ||||
\(499\) | 113855. | + | 197203.i | 0.0204693 | + | 0.0354538i | 0.876079 | − | 0.482168i | \(-0.160151\pi\) |
−0.855609 | + | 0.517622i | \(0.826817\pi\) | |||||||
\(500\) | 5.13103e6 | + | 8.88720e6i | 0.917866 | + | 1.58979i | ||||
\(501\) | 160428. | − | 277869.i | 0.0285552 | − | 0.0494590i | ||||
\(502\) | −166484. | + | 288359.i | −0.0294859 | + | 0.0510710i | ||||
\(503\) | 469421. | − | 813061.i | 0.0827261 | − | 0.143286i | −0.821694 | − | 0.569929i | \(-0.806971\pi\) |
0.904420 | + | 0.426643i | \(0.140304\pi\) | |||||||
\(504\) | −812331. | −0.142448 | ||||||||
\(505\) | 1.09255e6 | + | 1.89235e6i | 0.190639 | + | 0.330196i | ||||
\(506\) | −327699. | + | 567591.i | −0.0568982 | + | 0.0985505i | ||||
\(507\) | 3.58777e6 | 0.619876 | ||||||||
\(508\) | 2.89722e6 | 0.498106 | ||||||||
\(509\) | 5.35276e6 | − | 9.27126e6i | 0.915764 | − | 1.58615i | 0.109986 | − | 0.993933i | \(-0.464919\pi\) |
0.805778 | − | 0.592217i | \(-0.201747\pi\) | |||||||
\(510\) | 793406. | 0.135073 | ||||||||
\(511\) | −865185. | − | 1.49855e6i | −0.146574 | − | 0.253874i | ||||
\(512\) | −5.59720e6 | −0.943617 | ||||||||
\(513\) | −3.09744e6 | − | 5.36493e6i | −0.519649 | − | 0.900058i | ||||
\(514\) | 915028. | + | 1.58487e6i | 0.152766 | + | 0.264598i | ||||
\(515\) | −7.42110e6 | − | 1.28537e7i | −1.23296 | − | 2.13556i | ||||
\(516\) | −1.38190e6 | + | 2.39353e6i | −0.228483 | + | 0.395744i | ||||
\(517\) | −1.05237e6 | −0.173157 | ||||||||
\(518\) | −496530. | − | 41105.1i | −0.0813057 | − | 0.00673087i | ||||
\(519\) | −444755. | −0.0724773 | ||||||||
\(520\) | −4.38797e6 | + | 7.60018e6i | −0.711631 | + | 1.23258i | ||||
\(521\) | 2.32178e6 | + | 4.02143e6i | 0.374737 | + | 0.649063i | 0.990288 | − | 0.139034i | \(-0.0443998\pi\) |
−0.615551 | + | 0.788097i | \(0.711067\pi\) | |||||||
\(522\) | −727992. | − | 1.26092e6i | −0.116937 | − | 0.202540i | ||||
\(523\) | −4.16878e6 | − | 7.22054e6i | −0.666431 | − | 1.15429i | −0.978895 | − | 0.204363i | \(-0.934488\pi\) |
0.312464 | − | 0.949929i | \(-0.398846\pi\) | |||||||
\(524\) | 3.91335e6 | 0.622616 | ||||||||
\(525\) | −711315. | − | 1.23203e6i | −0.112633 | − | 0.195085i | ||||
\(526\) | 677202. | 0.106722 | ||||||||
\(527\) | 335672. | − | 581401.i | 0.0526489 | − | 0.0911905i | ||||
\(528\) | −1.42511e6 | −0.222466 | ||||||||
\(529\) | −4.45366e6 | −0.691955 | ||||||||
\(530\) | −360731. | + | 624804.i | −0.0557820 | + | 0.0966172i | ||||
\(531\) | −2.05681e6 | − | 3.56250e6i | −0.316561 | − | 0.548300i | ||||
\(532\) | 3.57332e6 | 0.547385 | ||||||||
\(533\) | −4.96895e6 | + | 8.60648e6i | −0.757612 | + | 1.31222i | ||||
\(534\) | −56417.0 | + | 97717.1i | −0.00856163 | + | 0.0148292i | ||||
\(535\) | 3.84647e6 | − | 6.66229e6i | 0.581003 | − | 1.00633i | ||||
\(536\) | −2.31719e6 | − | 4.01348e6i | −0.348377 | − | 0.603406i | ||||
\(537\) | 1.95462e6 | + | 3.38550e6i | 0.292500 | + | 0.506626i | ||||
\(538\) | −522984. | + | 905835.i | −0.0778991 | + | 0.134925i | ||||
\(539\) | −2.53242e6 | + | 4.38628e6i | −0.375460 | + | 0.650316i | ||||
\(540\) | −3.38743e6 | + | 5.86719e6i | −0.499903 | + | 0.865857i | ||||
\(541\) | 5.06199e6 | 0.743581 | 0.371790 | − | 0.928317i | \(-0.378744\pi\) | ||||
0.371790 | + | 0.928317i | \(0.378744\pi\) | |||||||
\(542\) | −888889. | − | 1.53960e6i | −0.129972 | − | 0.225118i | ||||
\(543\) | 136456. | − | 236348.i | 0.0198606 | − | 0.0343996i | ||||
\(544\) | 4.61735e6 | 0.668952 | ||||||||
\(545\) | −7.19055e6 | −1.03698 | ||||||||
\(546\) | 154936. | − | 268356.i | 0.0222418 | − | 0.0385239i | ||||
\(547\) | −6.80524e6 | −0.972467 | −0.486234 | − | 0.873829i | \(-0.661630\pi\) | ||||
−0.486234 | + | 0.873829i | \(0.661630\pi\) | |||||||
\(548\) | 2.45965e6 | + | 4.26024e6i | 0.349882 | + | 0.606014i | ||||
\(549\) | 3.20812e6 | 0.454276 | ||||||||
\(550\) | −1.53190e6 | − | 2.65333e6i | −0.215935 | − | 0.374011i | ||||
\(551\) | 6.60387e6 | + | 1.14382e7i | 0.926658 | + | 1.60502i | ||||
\(552\) | −296128. | − | 512908.i | −0.0413649 | − | 0.0716460i | ||||
\(553\) | 1.28569e6 | − | 2.22688e6i | 0.178782 | − | 0.309660i | ||||
\(554\) | 341388. | 0.0472578 | ||||||||
\(555\) | −2.31171e6 | + | 3.33450e6i | −0.318568 | + | 0.459514i | ||||
\(556\) | −5.68998e6 | −0.780592 | ||||||||
\(557\) | 6.68795e6 | − | 1.15839e7i | 0.913388 | − | 1.58203i | 0.104143 | − | 0.994562i | \(-0.466790\pi\) |
0.809245 | − | 0.587472i | \(-0.199877\pi\) | |||||||
\(558\) | −84436.9 | − | 146249.i | −0.0114801 | − | 0.0198842i | ||||
\(559\) | 9.71403e6 | + | 1.68252e7i | 1.31483 | + | 2.27735i | ||||
\(560\) | −1.82480e6 | − | 3.16065e6i | −0.245893 | − | 0.425899i | ||||
\(561\) | 1.99985e6 | 0.268281 | ||||||||
\(562\) | −1.10700e6 | − | 1.91738e6i | −0.147845 | − | 0.256076i | ||||
\(563\) | 2.78302e6 | 0.370037 | 0.185018 | − | 0.982735i | \(-0.440766\pi\) | ||||
0.185018 | + | 0.982735i | \(0.440766\pi\) | |||||||
\(564\) | 230573. | − | 399364.i | 0.0305218 | − | 0.0528653i | ||||
\(565\) | 8.41673e6 | 1.10923 | ||||||||
\(566\) | 3.04504e6 | 0.399532 | ||||||||
\(567\) | −913791. | + | 1.58273e6i | −0.119368 | + | 0.206752i | ||||
\(568\) | 2.13006e6 | + | 3.68937e6i | 0.277026 | + | 0.479823i | ||||
\(569\) | 2.97313e6 | 0.384975 | 0.192488 | − | 0.981299i | \(-0.438344\pi\) | ||||
0.192488 | + | 0.981299i | \(0.438344\pi\) | |||||||
\(570\) | −905220. | + | 1.56789e6i | −0.116699 | + | 0.202128i | ||||
\(571\) | 4.26817e6 | − | 7.39269e6i | 0.547837 | − | 0.948882i | −0.450585 | − | 0.892733i | \(-0.648785\pi\) |
0.998422 | − | 0.0561486i | \(-0.0178820\pi\) | |||||||
\(572\) | −5.36330e6 | + | 9.28951e6i | −0.685397 | + | 1.18714i | ||||
\(573\) | −1.30820e6 | − | 2.26587e6i | −0.166452 | − | 0.288303i | ||||
\(574\) | 283877. | + | 491690.i | 0.0359626 | + | 0.0622890i | ||||
\(575\) | −4.63424e6 | + | 8.02674e6i | −0.584533 | + | 1.01244i | ||||
\(576\) | −2.38301e6 | + | 4.12750e6i | −0.299275 | + | 0.518359i | ||||
\(577\) | 2.70917e6 | − | 4.69243e6i | 0.338764 | − | 0.586757i | −0.645436 | − | 0.763814i | \(-0.723324\pi\) |
0.984201 | + | 0.177057i | \(0.0566578\pi\) | |||||||
\(578\) | 7048.54 | 0.000877565 | ||||||||
\(579\) | −1.00888e6 | − | 1.74743e6i | −0.125067 | − | 0.216622i | ||||
\(580\) | 7.22213e6 | − | 1.25091e7i | 0.891446 | − | 1.54403i | ||||
\(581\) | −3.76458e6 | −0.462675 | ||||||||
\(582\) | 189030. | 0.0231325 | ||||||||
\(583\) | −909256. | + | 1.57488e6i | −0.110794 | + | 0.191900i | ||||
\(584\) | 3.36753e6 | 0.408583 | ||||||||
\(585\) | 1.12750e7 | + | 1.95289e7i | 1.36216 | + | 2.35933i | ||||
\(586\) | −1.96061e6 | −0.235856 | ||||||||
\(587\) | −2.08780e6 | − | 3.61617e6i | −0.250088 | − | 0.433166i | 0.713462 | − | 0.700694i | \(-0.247126\pi\) |
−0.963550 | + | 0.267529i | \(0.913793\pi\) | |||||||
\(588\) | −1.10970e6 | − | 1.92206e6i | −0.132362 | − | 0.229258i | ||||
\(589\) | 765957. | + | 1.32668e6i | 0.0909737 | + | 0.157571i | ||||
\(590\) | −1.26946e6 | + | 2.19877e6i | −0.150138 | + | 0.260046i | ||||
\(591\) | 1.92010e6 | 0.226129 | ||||||||
\(592\) | −4.02132e6 | + | 5.80050e6i | −0.471589 | + | 0.680239i | ||||
\(593\) | −1.20172e7 | −1.40335 | −0.701676 | − | 0.712496i | \(-0.747565\pi\) | ||||
−0.701676 | + | 0.712496i | \(0.747565\pi\) | |||||||
\(594\) | 531202. | − | 920068.i | 0.0617722 | − | 0.106993i | ||||
\(595\) | 2.56074e6 | + | 4.43533e6i | 0.296533 | + | 0.513610i | ||||
\(596\) | −4.62523e6 | − | 8.01113e6i | −0.533356 | − | 0.923801i | ||||
\(597\) | 1.05671e6 | + | 1.83028e6i | 0.121345 | + | 0.210175i | ||||
\(598\) | −2.01882e6 | −0.230858 | ||||||||
\(599\) | −387917. | − | 671891.i | −0.0441745 | − | 0.0765124i | 0.843093 | − | 0.537768i | \(-0.180732\pi\) |
−0.887267 | + | 0.461256i | \(0.847399\pi\) | |||||||
\(600\) | 2.76863e6 | 0.313969 | ||||||||
\(601\) | 73097.2 | − | 126608.i | 0.00825495 | − | 0.0142980i | −0.861868 | − | 0.507132i | \(-0.830706\pi\) |
0.870123 | + | 0.492834i | \(0.164039\pi\) | |||||||
\(602\) | 1.10993e6 | 0.124826 | ||||||||
\(603\) | −1.19081e7 | −1.33368 | ||||||||
\(604\) | −1.26051e6 | + | 2.18326e6i | −0.140590 | + | 0.243508i | ||||
\(605\) | 2.23940e6 | + | 3.87875e6i | 0.248738 | + | 0.430827i | ||||
\(606\) | 150152. | 0.0166092 | ||||||||
\(607\) | 6.62670e6 | − | 1.14778e7i | 0.730005 | − | 1.26441i | −0.226875 | − | 0.973924i | \(-0.572851\pi\) |
0.956880 | − | 0.290482i | \(-0.0938157\pi\) | |||||||
\(608\) | −5.26807e6 | + | 9.12456e6i | −0.577953 | + | 1.00104i | ||||
\(609\) | −525880. | + | 910851.i | −0.0574570 | + | 0.0995185i | ||||
\(610\) | −990026. | − | 1.71477e6i | −0.107726 | − | 0.186587i | ||||
\(611\) | −1.62080e6 | − | 2.80731e6i | −0.175641 | − | 0.304220i | ||||
\(612\) | 3.91543e6 | − | 6.78172e6i | 0.422572 | − | 0.731916i | ||||
\(613\) | −3.53183e6 | + | 6.11731e6i | −0.379619 | + | 0.657520i | −0.991007 | − | 0.133811i | \(-0.957278\pi\) |
0.611387 | + | 0.791331i | \(0.290612\pi\) | |||||||
\(614\) | −180466. | + | 312576.i | −0.0193185 | + | 0.0334606i | ||||
\(615\) | 4.62366e6 | 0.492944 | ||||||||
\(616\) | 631875. | + | 1.09444e6i | 0.0670934 | + | 0.116209i | ||||
\(617\) | 8.33613e6 | − | 1.44386e7i | 0.881560 | − | 1.52691i | 0.0319528 | − | 0.999489i | \(-0.489827\pi\) |
0.849607 | − | 0.527417i | \(-0.176839\pi\) | |||||||
\(618\) | −1.01990e6 | −0.107421 | ||||||||
\(619\) | 1.76322e7 | 1.84961 | 0.924803 | − | 0.380447i | \(-0.124230\pi\) | ||||
0.924803 | + | 0.380447i | \(0.124230\pi\) | |||||||
\(620\) | 837666. | − | 1.45088e6i | 0.0875168 | − | 0.151584i | ||||
\(621\) | −3.21394e6 | −0.334433 | ||||||||
\(622\) | 1.72974e6 | + | 2.99600e6i | 0.179269 | + | 0.310503i | ||||
\(623\) | −728350. | −0.0751831 | ||||||||
\(624\) | −2.19488e6 | − | 3.80164e6i | −0.225657 | − | 0.390850i | ||||
\(625\) | −6.49602e6 | − | 1.12514e7i | −0.665192 | − | 1.15215i | ||||
\(626\) | −190375. | − | 329740.i | −0.0194167 | − | 0.0336307i | ||||
\(627\) | −2.28169e6 | + | 3.95200e6i | −0.231786 | + | 0.401466i | ||||
\(628\) | −3.26934e6 | −0.330796 | ||||||||
\(629\) | 5.64311e6 | − | 8.13983e6i | 0.568711 | − | 0.820330i | ||||
\(630\) | 1.28829e6 | 0.129319 | ||||||||
\(631\) | −4.14758e6 | + | 7.18381e6i | −0.414688 | + | 0.718260i | −0.995396 | − | 0.0958520i | \(-0.969442\pi\) |
0.580708 | + | 0.814112i | \(0.302776\pi\) | |||||||
\(632\) | 2.50213e6 | + | 4.33381e6i | 0.249182 | + | 0.431596i | ||||
\(633\) | −184763. | − | 320019.i | −0.0183276 | − | 0.0317444i | ||||
\(634\) | −564022. | − | 976915.i | −0.0557279 | − | 0.0965236i | ||||
\(635\) | −9.47532e6 | −0.932523 | ||||||||
\(636\) | −398434. | − | 690109.i | −0.0390584 | − | 0.0676511i | ||||
\(637\) | −1.56012e7 | −1.52339 | ||||||||
\(638\) | −1.13254e6 | + | 1.96162e6i | −0.110155 | + | 0.190794i | ||||
\(639\) | 1.09465e7 | 1.06053 | ||||||||
\(640\) | 1.51810e7 | 1.46504 | ||||||||
\(641\) | −8.13948e6 | + | 1.40980e7i | −0.782441 | + | 1.35523i | 0.148075 | + | 0.988976i | \(0.452692\pi\) |
−0.930516 | + | 0.366251i | \(0.880641\pi\) | |||||||
\(642\) | −264316. | − | 457808.i | −0.0253096 | − | 0.0438375i | ||||
\(643\) | −1.06133e7 | −1.01233 | −0.506166 | − | 0.862436i | \(-0.668938\pi\) | ||||
−0.506166 | + | 0.862436i | \(0.668938\pi\) | |||||||
\(644\) | 926928. | − | 1.60549e6i | 0.0880707 | − | 0.152543i | ||||
\(645\) | 4.51950e6 | − | 7.82800e6i | 0.427751 | − | 0.740886i | ||||
\(646\) | 2.20972e6 | − | 3.82736e6i | 0.208332 | − | 0.360842i | ||||
\(647\) | −2.66970e6 | − | 4.62405e6i | −0.250727 | − | 0.434272i | 0.712999 | − | 0.701165i | \(-0.247336\pi\) |
−0.963726 | + | 0.266893i | \(0.914003\pi\) | |||||||
\(648\) | −1.77836e6 | − | 3.08021e6i | −0.166373 | − | 0.288166i | ||||
\(649\) | −3.19979e6 | + | 5.54221e6i | −0.298202 | + | 0.516501i | ||||
\(650\) | 4.71871e6 | − | 8.17304e6i | 0.438066 | − | 0.758753i | ||||
\(651\) | −60994.7 | + | 105646.i | −0.00564079 | + | 0.00977013i | ||||
\(652\) | −2.59411e6 | −0.238984 | ||||||||
\(653\) | −3.50495e6 | − | 6.07075e6i | −0.321661 | − | 0.557134i | 0.659170 | − | 0.751994i | \(-0.270908\pi\) |
−0.980831 | + | 0.194861i | \(0.937575\pi\) | |||||||
\(654\) | −247054. | + | 427910.i | −0.0225864 | + | 0.0391209i | ||||
\(655\) | −1.27986e7 | −1.16562 | ||||||||
\(656\) | 8.04304e6 | 0.729727 | ||||||||
\(657\) | 4.32649e6 | − | 7.49369e6i | 0.391041 | − | 0.677302i | ||||
\(658\) | −185193. | −0.0166748 | ||||||||
\(659\) | −7.80237e6 | − | 1.35141e7i | −0.699863 | − | 1.21220i | −0.968514 | − | 0.248961i | \(-0.919911\pi\) |
0.268651 | − | 0.963238i | \(-0.413422\pi\) | |||||||
\(660\) | 4.99060e6 | 0.445957 | ||||||||
\(661\) | 6.86671e6 | + | 1.18935e7i | 0.611287 | + | 1.05878i | 0.991024 | + | 0.133686i | \(0.0426812\pi\) |
−0.379737 | + | 0.925095i | \(0.623985\pi\) | |||||||
\(662\) | 759127. | + | 1.31485e6i | 0.0673239 | + | 0.116608i | ||||
\(663\) | 3.08007e6 | + | 5.33484e6i | 0.272130 | + | 0.471343i | ||||
\(664\) | 3.66318e6 | − | 6.34482e6i | 0.322432 | − | 0.558469i | ||||
\(665\) | −1.16865e7 | −1.02478 | ||||||||
\(666\) | −1.06347e6 | − | 2.25309e6i | −0.0929052 | − | 0.196831i | ||||
\(667\) | 6.85225e6 | 0.596373 | ||||||||
\(668\) | −977279. | + | 1.69270e6i | −0.0847378 | + | 0.146770i | ||||
\(669\) | −438598. | − | 759675.i | −0.0378880 | − | 0.0656239i | ||||
\(670\) | 3.67485e6 | + | 6.36503e6i | 0.316266 | + | 0.547789i | ||||
\(671\) | −2.49545e6 | − | 4.32225e6i | −0.213965 | − | 0.370598i | ||||
\(672\) | −839014. | −0.0716714 | ||||||||
\(673\) | 1.51040e6 | + | 2.61609e6i | 0.128545 | + | 0.222646i | 0.923113 | − | 0.384529i | \(-0.125636\pi\) |
−0.794568 | + | 0.607175i | \(0.792303\pi\) | |||||||
\(674\) | 2.62032e6 | 0.222180 | ||||||||
\(675\) | 7.51213e6 | − | 1.30114e7i | 0.634605 | − | 1.09917i | ||||
\(676\) | −2.18557e7 | −1.83949 | ||||||||
\(677\) | −5.63262e6 | −0.472323 | −0.236162 | − | 0.971714i | \(-0.575889\pi\) | ||||
−0.236162 | + | 0.971714i | \(0.575889\pi\) | |||||||
\(678\) | 289184. | − | 500881.i | 0.0241601 | − | 0.0418466i | ||||
\(679\) | 610100. | + | 1.05672e6i | 0.0507839 | + | 0.0879604i | ||||
\(680\) | −9.96709e6 | −0.826601 | ||||||||
\(681\) | −1.27696e6 | + | 2.21176e6i | −0.105514 | + | 0.182756i | ||||
\(682\) | −131359. | + | 227521.i | −0.0108143 | + | 0.0187310i | ||||
\(683\) | 1.06483e6 | − | 1.84434e6i | 0.0873429 | − | 0.151282i | −0.819044 | − | 0.573730i | \(-0.805496\pi\) |
0.906387 | + | 0.422448i | \(0.138829\pi\) | |||||||
\(684\) | 8.93445e6 | + | 1.54749e7i | 0.730176 | + | 1.26470i | ||||
\(685\) | −8.04426e6 | − | 1.39331e7i | −0.655028 | − | 1.13454i | ||||
\(686\) | −948437. | + | 1.64274e6i | −0.0769482 | + | 0.133278i | ||||
\(687\) | 548976. | − | 950855.i | 0.0443774 | − | 0.0768639i | ||||
\(688\) | 7.86185e6 | − | 1.36171e7i | 0.633218 | − | 1.09677i | ||||
\(689\) | −5.60156e6 | −0.449532 | ||||||||
\(690\) | 469633. | + | 813428.i | 0.0375522 | + | 0.0650423i | ||||
\(691\) | −6.31430e6 | + | 1.09367e7i | −0.503072 | + | 0.871347i | 0.496922 | + | 0.867795i | \(0.334464\pi\) |
−0.999994 | + | 0.00355105i | \(0.998870\pi\) | |||||||
\(692\) | 2.70932e6 | 0.215077 | ||||||||
\(693\) | 3.24724e6 | 0.256851 | ||||||||
\(694\) | −903728. | + | 1.56530e6i | −0.0712261 | + | 0.123367i | ||||
\(695\) | 1.86090e7 | 1.46137 | ||||||||
\(696\) | −1.02343e6 | − | 1.77264e6i | −0.0800822 | − | 0.138706i | ||||
\(697\) | −1.12868e7 | −0.880011 | ||||||||
\(698\) | 353824. | + | 612842.i | 0.0274884 | + | 0.0476113i | ||||
\(699\) | −1.31196e6 | − | 2.27238e6i | −0.101561 | − | 0.175909i | ||||
\(700\) | 4.33313e6 | + | 7.50520e6i | 0.334239 | + | 0.578918i | ||||
\(701\) | −1.07790e7 | + | 1.86698e7i | −0.828483 | + | 1.43497i | 0.0707453 | + | 0.997494i | \(0.477462\pi\) |
−0.899228 | + | 0.437480i | \(0.855871\pi\) | |||||||
\(702\) | 3.27252e6 | 0.250634 | ||||||||
\(703\) | 9.64712e6 | + | 2.04386e7i | 0.736223 | + | 1.55978i | ||||
\(704\) | 7.41454e6 | 0.563836 | ||||||||
\(705\) | −754085. | + | 1.30611e6i | −0.0571410 | + | 0.0989711i | ||||
\(706\) | −2.67067e6 | − | 4.62573e6i | −0.201655 | − | 0.349276i | ||||
\(707\) | 484619. | + | 839385.i | 0.0364630 | + | 0.0631557i | ||||
\(708\) | −1.40215e6 | − | 2.42859e6i | −0.105126 | − | 0.182083i | ||||
\(709\) | 1.75735e7 | 1.31293 | 0.656465 | − | 0.754356i | \(-0.272051\pi\) | ||||
0.656465 | + | 0.754356i | \(0.272051\pi\) | |||||||
\(710\) | −3.37808e6 | − | 5.85101e6i | −0.251492 | − | 0.435597i | ||||
\(711\) | 1.28586e7 | 0.953935 | ||||||||
\(712\) | 708733. | − | 1.22756e6i | 0.0523942 | − | 0.0907494i | ||||
\(713\) | 794765. | 0.0585484 | ||||||||
\(714\) | 351930. | 0.0258351 | ||||||||
\(715\) | 1.75406e7 | − | 3.03813e7i | 1.28316 | − | 2.22249i | ||||
\(716\) | −1.19070e7 | − | 2.06235e7i | −0.867999 | − | 1.50342i | ||||
\(717\) | −4.96456e6 | −0.360647 | ||||||||
\(718\) | −3.27461e6 | + | 5.67179e6i | −0.237055 | + | 0.410591i | ||||
\(719\) | −1.16001e7 | + | 2.00919e7i | −0.836833 | + | 1.44944i | 0.0556958 | + | 0.998448i | \(0.482262\pi\) |
−0.892529 | + | 0.450990i | \(0.851071\pi\) | |||||||
\(720\) | 9.12519e6 | − | 1.58053e7i | 0.656010 | − | 1.13624i | ||||
\(721\) | −3.29177e6 | − | 5.70151e6i | −0.235826 | − | 0.408462i | ||||
\(722\) | 3.34736e6 | + | 5.79779e6i | 0.238978 | + | 0.413923i | ||||
\(723\) | 2.72531e6 | − | 4.72037e6i | 0.193896 | − | 0.335838i | ||||
\(724\) | −831249. | + | 1.43977e6i | −0.0589366 | + | 0.102081i | ||||
\(725\) | −1.60162e7 | + | 2.77408e7i | −1.13165 | + | 1.96008i | ||||
\(726\) | 307766. | 0.0216710 | ||||||||
\(727\) | 1.36924e7 | + | 2.37159e7i | 0.960820 | + | 1.66419i | 0.720449 | + | 0.693508i | \(0.243936\pi\) |
0.240371 | + | 0.970681i | \(0.422731\pi\) | |||||||
\(728\) | −1.94636e6 | + | 3.37120e6i | −0.136112 | + | 0.235753i | ||||
\(729\) | −6.39616e6 | −0.445759 | ||||||||
\(730\) | −5.34061e6 | −0.370923 | ||||||||
\(731\) | −1.10325e7 | + | 1.91089e7i | −0.763627 | + | 1.32264i | ||||
\(732\) | 2.18701e6 | 0.150859 | ||||||||
\(733\) | −6.70320e6 | − | 1.16103e7i | −0.460810 | − | 0.798146i | 0.538191 | − | 0.842823i | \(-0.319108\pi\) |
−0.999002 | + | 0.0446762i | \(0.985774\pi\) | |||||||
\(734\) | 339189. | 0.0232381 | ||||||||
\(735\) | 3.62927e6 | + | 6.28608e6i | 0.247800 | + | 0.429202i | ||||
\(736\) | 2.73310e6 | + | 4.73387e6i | 0.185978 | + | 0.322123i | ||||
\(737\) | 9.26280e6 | + | 1.60436e7i | 0.628165 | + | 1.08801i | ||||
\(738\) | −1.41957e6 | + | 2.45877e6i | −0.0959435 | + | 0.166179i | ||||
\(739\) | 1.76268e7 | 1.18730 | 0.593651 | − | 0.804723i | \(-0.297686\pi\) | ||||
0.593651 | + | 0.804723i | \(0.297686\pi\) | |||||||
\(740\) | 1.40823e7 | − | 2.03128e7i | 0.945353 | − | 1.36361i | ||||
\(741\) | −1.40566e7 | −0.940446 | ||||||||
\(742\) | −160009. | + | 277144.i | −0.0106693 | + | 0.0184797i | ||||
\(743\) | −1.12976e6 | − | 1.95681e6i | −0.0750785 | − | 0.130040i | 0.826042 | − | 0.563609i | \(-0.190587\pi\) |
−0.901120 | + | 0.433569i | \(0.857254\pi\) | |||||||
\(744\) | −118704. | − | 205601.i | −0.00786199 | − | 0.0136174i | ||||
\(745\) | 1.51268e7 | + | 2.62003e7i | 0.998517 | + | 1.72948i | ||||
\(746\) | 2.51104e6 | 0.165198 | ||||||||
\(747\) | −9.41265e6 | − | 1.63032e7i | −0.617178 | − | 1.06898i | ||||
\(748\) | −1.21825e7 | −0.796129 | ||||||||
\(749\) | 1.70618e6 | − | 2.95518e6i | 0.111127 | − | 0.192477i | ||||
\(750\) | −2.30625e6 | −0.149711 | ||||||||
\(751\) | 2.50338e7 | 1.61967 | 0.809837 | − | 0.586655i | \(-0.199555\pi\) | ||||
0.809837 | + | 0.586655i | \(0.199555\pi\) | |||||||
\(752\) | −1.31176e6 | + | 2.27204e6i | −0.0845883 | + | 0.146511i | ||||
\(753\) | 601394. | + | 1.04165e6i | 0.0386520 | + | 0.0669472i | ||||
\(754\) | −6.97714e6 | −0.446940 | ||||||||
\(755\) | 4.12248e6 | − | 7.14034e6i | 0.263203 | − | 0.455881i | ||||
\(756\) | −1.50256e6 | + | 2.60250e6i | −0.0956150 | + | 0.165610i | ||||
\(757\) | −4.89896e6 | + | 8.48525e6i | −0.310716 | + | 0.538177i | −0.978518 | − | 0.206163i | \(-0.933902\pi\) |
0.667801 | + | 0.744340i | \(0.267236\pi\) | |||||||
\(758\) | −3.22142e6 | − | 5.57967e6i | −0.203646 | − | 0.352724i | ||||
\(759\) | 1.18375e6 | + | 2.05032e6i | 0.0745858 | + | 0.129186i | ||||
\(760\) | 1.13717e7 | − | 1.96964e7i | 0.714156 | − | 1.23695i | ||||
\(761\) | 9.05189e6 | − | 1.56783e7i | 0.566601 | − | 0.981382i | −0.430298 | − | 0.902687i | \(-0.641591\pi\) |
0.996899 | − | 0.0786949i | \(-0.0250753\pi\) | |||||||
\(762\) | −325555. | + | 563878.i | −0.0203113 | + | 0.0351801i | ||||
\(763\) | −3.18950e6 | −0.198340 | ||||||||
\(764\) | 7.96918e6 | + | 1.38030e7i | 0.493947 | + | 0.855541i | ||||
\(765\) | −1.28054e7 | + | 2.21795e7i | −0.791112 | + | 1.37025i | ||||
\(766\) | 3.39760e6 | 0.209218 | ||||||||
\(767\) | −1.97126e7 | −1.20992 | ||||||||
\(768\) | −1.20400e6 | + | 2.08538e6i | −0.0736584 | + | 0.127580i | ||||
\(769\) | −2.72742e6 | −0.166317 | −0.0831584 | − | 0.996536i | \(-0.526501\pi\) | ||||
−0.0831584 | + | 0.996536i | \(0.526501\pi\) | |||||||
\(770\) | −1.00210e6 | − | 1.73569e6i | −0.0609093 | − | 0.105498i | ||||
\(771\) | 6.61074e6 | 0.400511 | ||||||||
\(772\) | 6.14579e6 | + | 1.06448e7i | 0.371137 | + | 0.642828i | ||||
\(773\) | −1.61246e6 | − | 2.79286e6i | −0.0970598 | − | 0.168112i | 0.813407 | − | 0.581695i | \(-0.197610\pi\) |
−0.910466 | + | 0.413583i | \(0.864277\pi\) | |||||||
\(774\) | 2.77518e6 | + | 4.80675e6i | 0.166509 | + | 0.288403i | ||||
\(775\) | −1.85765e6 | + | 3.21755e6i | −0.111099 | + | 0.192429i | ||||
\(776\) | −2.37467e6 | −0.141563 | ||||||||
\(777\) | −1.02540e6 | + | 1.47908e6i | −0.0609315 | + | 0.0878900i | ||||
\(778\) | 8.02904e6 | 0.475570 | ||||||||
\(779\) | 1.28774e7 | − | 2.23043e7i | 0.760300 | − | 1.31688i | ||||
\(780\) | 7.68627e6 | + | 1.33130e7i | 0.452355 | + | 0.783502i | ||||
\(781\) | −8.51477e6 | − | 1.47480e7i | −0.499511 | − | 0.865179i | ||||
\(782\) | −1.14642e6 | − | 1.98565e6i | −0.0670387 | − | 0.116114i | ||||
\(783\) | −1.11075e7 | −0.647460 | ||||||||
\(784\) | 6.31326e6 | + | 1.09349e7i | 0.366829 | + | 0.635367i | ||||
\(785\) | 1.06923e7 | 0.619296 | ||||||||
\(786\) | −439735. | + | 761644.i | −0.0253884 | + | 0.0439740i | ||||
\(787\) | −2.49843e7 | −1.43790 | −0.718952 | − | 0.695060i | \(-0.755378\pi\) | ||||
−0.718952 | + | 0.695060i | \(0.755378\pi\) | |||||||
\(788\) | −1.16967e7 | −0.671040 | ||||||||
\(789\) | 1.22313e6 | − | 2.11853e6i | 0.0699490 | − | 0.121155i | ||||
\(790\) | −3.96815e6 | − | 6.87305e6i | −0.226215 | − | 0.391815i | ||||
\(791\) | 3.73340e6 | 0.212160 | ||||||||
\(792\) | −3.15979e6 | + | 5.47291e6i | −0.178997 | + | 0.310031i | ||||
\(793\) | 7.68673e6 | − | 1.33138e7i | 0.434069 | − | 0.751830i | ||||
\(794\) | −1.32166e6 | + | 2.28918e6i | −0.0743990 | + | 0.128863i | ||||
\(795\) | 1.30308e6 | + | 2.25699e6i | 0.0731226 | + | 0.126652i | ||||
\(796\) | −6.43719e6 | − | 1.11495e7i | −0.360092 | − | 0.623698i | ||||
\(797\) | 7.78733e6 | − | 1.34881e7i | 0.434253 | − | 0.752148i | −0.562981 | − | 0.826470i | \(-0.690346\pi\) |
0.997234 | + | 0.0743214i | \(0.0236791\pi\) | |||||||
\(798\) | −401527. | + | 695465.i | −0.0223207 | + | 0.0386606i | ||||
\(799\) | 1.84079e6 | − | 3.18835e6i | 0.102009 | − | 0.176684i | ||||
\(800\) | −2.55530e7 | −1.41161 | ||||||||
\(801\) | −1.82111e6 | − | 3.15426e6i | −0.100289 | − | 0.173706i | ||||
\(802\) | 2.76824e6 | − | 4.79473e6i | 0.151973 | − | 0.263225i | ||||
\(803\) | −1.34615e7 | −0.736724 | ||||||||
\(804\) | −8.11789e6 | −0.442897 | ||||||||
\(805\) | −3.03151e6 | + | 5.25073e6i | −0.164880 | + | 0.285581i | ||||
\(806\) | −809251. | −0.0438779 | ||||||||
\(807\) | 1.88919e6 | + | 3.27216e6i | 0.102115 | + | 0.176869i | ||||
\(808\) | −1.88627e6 | −0.101642 | ||||||||
\(809\) | 695396. | + | 1.20446e6i | 0.0373560 | + | 0.0647026i | 0.884099 | − | 0.467300i | \(-0.154773\pi\) |
−0.846743 | + | 0.532002i | \(0.821440\pi\) | |||||||
\(810\) | 2.82032e6 | + | 4.88494e6i | 0.151038 | + | 0.261605i | ||||
\(811\) | −5.34587e6 | − | 9.25931e6i | −0.285408 | − | 0.494341i | 0.687300 | − | 0.726374i | \(-0.258796\pi\) |
−0.972708 | + | 0.232033i | \(0.925462\pi\) | |||||||
\(812\) | 3.20351e6 | − | 5.54864e6i | 0.170505 | − | 0.295322i | ||||
\(813\) | −6.42190e6 | −0.340751 | ||||||||
\(814\) | −2.20832e6 | + | 3.18537e6i | −0.116816 | + | 0.168500i | ||||
\(815\) | 8.48400e6 | 0.447411 | ||||||||
\(816\) | 2.49279e6 | − | 4.31764e6i | 0.131057 | − | 0.226997i | ||||
\(817\) | −2.51746e7 | − | 4.36038e7i | −1.31950 | − | 2.28543i | ||||
\(818\) | 2.36187e6 | + | 4.09087e6i | 0.123416 | + | 0.213763i | ||||
\(819\) | 5.00124e6 | + | 8.66240e6i | 0.260536 | + | 0.451262i | ||||
\(820\) | −2.81660e7 | −1.46282 | ||||||||
\(821\) | −6.09794e6 | − | 1.05619e7i | −0.315737 | − | 0.546872i | 0.663857 | − | 0.747859i | \(-0.268918\pi\) |
−0.979594 | + | 0.200987i | \(0.935585\pi\) | |||||||
\(822\) | −1.10554e6 | −0.0570686 | ||||||||
\(823\) | 7.85586e6 | − | 1.36068e7i | 0.404291 | − | 0.700253i | −0.589948 | − | 0.807442i | \(-0.700852\pi\) |
0.994239 | + | 0.107189i | \(0.0341849\pi\) | |||||||
\(824\) | 1.28124e7 | 0.657376 | ||||||||
\(825\) | −1.10674e7 | −0.566124 | ||||||||
\(826\) | −563093. | + | 975306.i | −0.0287164 | + | 0.0497383i | ||||
\(827\) | 1.88268e7 | + | 3.26090e7i | 0.957222 | + | 1.65796i | 0.729199 | + | 0.684302i | \(0.239893\pi\) |
0.228023 | + | 0.973656i | \(0.426774\pi\) | |||||||
\(828\) | 9.27048e6 | 0.469922 | ||||||||
\(829\) | 1.34171e7 | − | 2.32391e7i | 0.678067 | − | 1.17445i | −0.297495 | − | 0.954723i | \(-0.596151\pi\) |
0.975562 | − | 0.219723i | \(-0.0705153\pi\) | |||||||
\(830\) | −5.80949e6 | + | 1.00623e7i | −0.292713 | + | 0.506994i | ||||
\(831\) | 616600. | − | 1.06798e6i | 0.0309743 | − | 0.0536490i | ||||
\(832\) | 1.14195e7 | + | 1.97792e7i | 0.571925 | + | 0.990602i | ||||
\(833\) | −8.85939e6 | − | 1.53449e7i | −0.442376 | − | 0.766217i | ||||
\(834\) | 639373. | − | 1.10743e6i | 0.0318302 | − | 0.0551315i | ||||
\(835\) | 3.19618e6 | − | 5.53594e6i | 0.158641 | − | 0.274774i | ||||
\(836\) | 1.38994e7 | − | 2.40745e7i | 0.687829 | − | 1.19135i | ||||
\(837\) | −1.28832e6 | −0.0635637 | ||||||||
\(838\) | 521016. | + | 902426.i | 0.0256295 | + | 0.0443917i | ||||
\(839\) | −3.39576e6 | + | 5.88163e6i | −0.166545 | + | 0.288465i | −0.937203 | − | 0.348785i | \(-0.886594\pi\) |
0.770658 | + | 0.637249i | \(0.219928\pi\) | |||||||
\(840\) | 1.81111e6 | 0.0885619 | ||||||||
\(841\) | 3.17055e6 | 0.154577 | ||||||||
\(842\) | 2.01253e6 | − | 3.48580e6i | 0.0978276 | − | 0.169442i | ||||
\(843\) | −7.99769e6 | −0.387611 | ||||||||
\(844\) | 1.12552e6 | + | 1.94946e6i | 0.0543874 | + | 0.0942018i | ||||
\(845\) | 7.14787e7 | 3.44378 | ||||||||
\(846\) | −463043. | − | 802014.i | −0.0222431 | − | 0.0385262i | ||||
\(847\) | 993326. | + | 1.72049e6i | 0.0475755 | + | 0.0824032i | ||||
\(848\) | 2.26675e6 | + | 3.92613e6i | 0.108247 | + | 0.187489i | ||||
\(849\) | 5.49983e6 | − | 9.52598e6i | 0.261866 | − | 0.453566i | ||||
\(850\) | 1.07184e7 | 0.508839 | ||||||||
\(851\) | 1.16855e7 | + | 967383.i | 0.553126 | + | 0.0457904i | ||||
\(852\) | 7.46232e6 | 0.352188 | ||||||||
\(853\) | −1.46354e7 | + | 2.53492e7i | −0.688702 | + | 1.19287i | 0.283556 | + | 0.958956i | \(0.408486\pi\) |
−0.972258 | + | 0.233911i | \(0.924848\pi\) | |||||||
\(854\) | −439144. | − | 760620.i | −0.0206045 | − | 0.0356881i | ||||
\(855\) | −2.92200e7 | − | 5.06106e7i | −1.36699 | − | 2.36770i | ||||
\(856\) | 3.32045e6 | + | 5.75118e6i | 0.154886 | + | 0.268270i | ||||
\(857\) | −6.84774e6 | −0.318489 | −0.159245 | − | 0.987239i | \(-0.550906\pi\) | ||||
−0.159245 | + | 0.987239i | \(0.550906\pi\) | |||||||
\(858\) | −1.20533e6 | − | 2.08769e6i | −0.0558968 | − | 0.0968161i | ||||
\(859\) | 1.46671e7 | 0.678207 | 0.339103 | − | 0.940749i | \(-0.389876\pi\) | ||||
0.339103 | + | 0.940749i | \(0.389876\pi\) | |||||||
\(860\) | −2.75315e7 | + | 4.76859e7i | −1.26936 | + | 2.19859i | ||||
\(861\) | 2.05091e6 | 0.0942841 | ||||||||
\(862\) | −3.61129e6 | −0.165537 | ||||||||
\(863\) | −7.84326e6 | + | 1.35849e7i | −0.358484 | + | 0.620912i | −0.987708 | − | 0.156312i | \(-0.950040\pi\) |
0.629224 | + | 0.777224i | \(0.283373\pi\) | |||||||
\(864\) | −4.43037e6 | − | 7.67363e6i | −0.201909 | − | 0.349717i | ||||
\(865\) | −8.86079e6 | −0.402654 | ||||||||
\(866\) | 797128. | − | 1.38067e6i | 0.0361188 | − | 0.0625596i | ||||
\(867\) | 12730.8 | − | 22050.4i | 0.000575185 | − | 0.000996249i | ||||
\(868\) | 371562. | − | 643565.i | 0.0167391 | − | 0.0289930i | ||||
\(869\) | −1.00021e7 | − | 1.73241e7i | −0.449306 | − | 0.778220i | ||||
\(870\) | 1.62307e6 | + | 2.81125e6i | 0.0727010 | + | 0.125922i | ||||
\(871\) | −2.85322e7 | + | 4.94192e7i | −1.27435 | + | 2.20724i | ||||
\(872\) | 3.10360e6 | − | 5.37559e6i | 0.138221 | − | 0.239406i | ||||
\(873\) | −3.05089e6 | + | 5.28430e6i | −0.135485 | + | 0.234667i | ||||
\(874\) | 5.23192e6 | 0.231677 | ||||||||
\(875\) | −7.44351e6 | − | 1.28925e7i | −0.328668 | − | 0.569270i | ||||
\(876\) | 2.94940e6 | − | 5.10852e6i | 0.129860 | − | 0.224923i | ||||
\(877\) | 1.30627e7 | 0.573500 | 0.286750 | − | 0.958005i | \(-0.407425\pi\) | ||||
0.286750 | + | 0.958005i | \(0.407425\pi\) | |||||||
\(878\) | 6.41748e6 | 0.280950 | ||||||||
\(879\) | −3.54118e6 | + | 6.13350e6i | −0.154588 | + | 0.267754i | ||||
\(880\) | −2.83923e7 | −1.23593 | ||||||||
\(881\) | −3.51299e6 | − | 6.08467e6i | −0.152488 | − | 0.264118i | 0.779653 | − | 0.626211i | \(-0.215395\pi\) |
−0.932142 | + | 0.362094i | \(0.882062\pi\) | |||||||
\(882\) | −4.45708e6 | −0.192921 | ||||||||
\(883\) | −1.30909e7 | − | 2.26741e7i | −0.565025 | − | 0.978652i | −0.997047 | − | 0.0767894i | \(-0.975533\pi\) |
0.432022 | − | 0.901863i | \(-0.357800\pi\) | |||||||
\(884\) | −1.87629e7 | − | 3.24983e7i | −0.807550 | − | 1.39872i | ||||
\(885\) | 4.58570e6 | + | 7.94267e6i | 0.196810 | + | 0.340885i | ||||
\(886\) | 941672. | − | 1.63102e6i | 0.0403009 | − | 0.0698033i | ||||
\(887\) | 1.67972e7 | 0.716848 | 0.358424 | − | 0.933559i | \(-0.383314\pi\) | ||||
0.358424 | + | 0.933559i | \(0.383314\pi\) | |||||||
\(888\) | −1.49506e6 | − | 3.16746e6i | −0.0636247 | − | 0.134797i | ||||
\(889\) | −4.20295e6 | −0.178361 | ||||||||
\(890\) | −1.12399e6 | + | 1.94681e6i | −0.0475649 | + | 0.0823849i | ||||
\(891\) | 7.10888e6 | + | 1.23129e7i | 0.299990 | + | 0.519598i | ||||
\(892\) | 2.67182e6 | + | 4.62772e6i | 0.112433 | + | 0.194740i | ||||
\(893\) | 4.20043e6 | + | 7.27535e6i | 0.176264 | + | 0.305299i | ||||
\(894\) | 2.07891e6 | 0.0869946 | ||||||||
\(895\) | 3.89416e7 | + | 6.74489e7i | 1.62501 | + | 2.81460i | ||||
\(896\) | 6.73380e6 | 0.280214 | ||||||||
\(897\) | −3.64631e6 | + | 6.31559e6i | −0.151312 | + | 0.262080i | ||||
\(898\) | −7.61077e6 | −0.314947 | ||||||||
\(899\) | 2.74675e6 | 0.113349 | ||||||||
\(900\) | −2.16684e7 | + | 3.75308e7i | −0.891705 | + | 1.54448i | ||||
\(901\) | −3.18093e6 | − | 5.50953e6i | −0.130539 | − | 0.226101i | ||||
\(902\) | 4.41687e6 | 0.180758 | ||||||||
\(903\) | 2.00471e6 | − | 3.47226e6i | 0.0818148 | − | 0.141707i | ||||
\(904\) | −3.63284e6 | + | 6.29227e6i | −0.147851 | + | 0.256086i | ||||
\(905\) | 2.71859e6 | − | 4.70874e6i | 0.110337 | − | 0.191110i | ||||
\(906\) | −283282. | − | 490659.i | −0.0114656 | − | 0.0198591i | ||||
\(907\) | −8.12855e6 | − | 1.40791e7i | −0.328091 | − | 0.568271i | 0.654042 | − | 0.756459i | \(-0.273072\pi\) |
−0.982133 | + | 0.188187i | \(0.939739\pi\) | |||||||
\(908\) | 7.77889e6 | − | 1.34734e7i | 0.313114 | − | 0.542330i | ||||
\(909\) | −2.42341e6 | + | 4.19747e6i | −0.0972785 | + | 0.168491i | ||||
\(910\) | 3.08676e6 | − | 5.34643e6i | 0.123566 | − | 0.214023i | ||||
\(911\) | 3.99805e7 | 1.59607 | 0.798036 | − | 0.602610i | \(-0.205873\pi\) | ||||
0.798036 | + | 0.602610i | \(0.205873\pi\) | |||||||
\(912\) | 5.68820e6 | + | 9.85224e6i | 0.226458 | + | 0.392237i | ||||
\(913\) | −1.46433e7 | + | 2.53630e7i | −0.581384 | + | 1.00699i | ||||
\(914\) | 1.00146e7 | 0.396523 | ||||||||
\(915\) | −7.15258e6 | −0.282429 | ||||||||
\(916\) | −3.34421e6 | + | 5.79234e6i | −0.131691 | + | 0.228095i | ||||
\(917\) | −5.67704e6 | −0.222945 | ||||||||
\(918\) | 1.85835e6 | + | 3.21875e6i | 0.0727814 | + | 0.126061i | ||||
\(919\) | −2.99128e6 | −0.116834 | −0.0584168 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584168 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(920\) | −5.89972e6 | − | 1.02186e7i | −0.229806 | − | 0.398036i | ||||
\(921\) | 651900. | + | 1.12912e6i | 0.0253240 | + | 0.0438624i | ||||
\(922\) | 1.68625e6 | + | 2.92067e6i | 0.0653273 | + | 0.113150i | ||||
\(923\) | 2.62280e7 | − | 4.54283e7i | 1.01335 | − | 1.75518i | ||||
\(924\) | 2.21368e6 | 0.0852970 | ||||||||
\(925\) | −3.12296e7 | + | 4.50468e7i | −1.20009 | + | 1.73105i | ||||
\(926\) | 7.07579e6 | 0.271174 | ||||||||
\(927\) | 1.64610e7 | − | 2.85112e7i | 0.629152 | − | 1.08972i | ||||
\(928\) | 9.44573e6 | + | 1.63605e7i | 0.360052 | + | 0.623629i | ||||
\(929\) | 2.11401e7 | + | 3.66158e7i | 0.803652 | + | 1.39197i | 0.917197 | + | 0.398433i | \(0.130446\pi\) |
−0.113545 | + | 0.993533i | \(0.536221\pi\) | |||||||
\(930\) | 188254. | + | 326065.i | 0.00713734 | + | 0.0123622i | ||||
\(931\) | 4.04317e7 | 1.52879 | ||||||||
\(932\) | 7.99209e6 | + | 1.38427e7i | 0.301384 | + | 0.522013i | ||||
\(933\) | 1.24967e7 | 0.469994 | ||||||||
\(934\) | −2.83354e6 | + | 4.90784e6i | −0.106283 | + | 0.184087i | ||||
\(935\) | 3.98428e7 | 1.49046 | ||||||||
\(936\) | −1.94662e7 | −0.726258 | ||||||||
\(937\) | 5.97758e6 | − | 1.03535e7i | 0.222421 | − | 0.385245i | −0.733121 | − | 0.680098i | \(-0.761937\pi\) |
0.955543 | + | 0.294853i | \(0.0952706\pi\) | |||||||
\(938\) | 1.63005e6 | + | 2.82333e6i | 0.0604914 | + | 0.104774i | ||||
\(939\) | −1.37539e6 | −0.0509053 | ||||||||
\(940\) | 4.59367e6 | − | 7.95647e6i | 0.169567 | − | 0.293698i | ||||
\(941\) | 1.07858e7 | − | 1.86816e7i | 0.397082 | − | 0.687765i | −0.596283 | − | 0.802774i | \(-0.703356\pi\) |
0.993364 | + | 0.115009i | \(0.0366897\pi\) | |||||||
\(942\) | 367369. | − | 636303.i | 0.0134889 | − | 0.0233634i | ||||
\(943\) | −6.68087e6 | − | 1.15716e7i | −0.244655 | − | 0.423754i | ||||
\(944\) | 7.97701e6 | + | 1.38166e7i | 0.291347 | + | 0.504627i | ||||
\(945\) | 4.91409e6 | − | 8.51146e6i | 0.179004 | − | 0.310045i | ||||
\(946\) | 4.31737e6 | − | 7.47790e6i | 0.156852 | − | 0.271676i | ||||
\(947\) | −2.67679e7 | + | 4.63634e7i | −0.969929 | + | 1.67997i | −0.274183 | + | 0.961678i | \(0.588407\pi\) |
−0.695746 | + | 0.718288i | \(0.744926\pi\) | |||||||
\(948\) | 8.76581e6 | 0.316790 | ||||||||
\(949\) | −2.07327e7 | − | 3.59101e7i | −0.747293 | − | 1.29435i | ||||
\(950\) | −1.22289e7 | + | 2.11810e7i | −0.439620 | + | 0.761445i | ||||
\(951\) | −4.07485e6 | −0.146104 | ||||||||
\(952\) | −4.42109e6 | −0.158102 | ||||||||
\(953\) | −1.48390e6 | + | 2.57020e6i | −0.0529266 | + | 0.0916715i | −0.891275 | − | 0.453463i | \(-0.850188\pi\) |
0.838348 | + | 0.545135i | \(0.183522\pi\) | |||||||
\(954\) | −1.60030e6 | −0.0569285 | ||||||||
\(955\) | −2.60631e7 | − | 4.51427e7i | −0.924737 | − | 1.60169i | ||||
\(956\) | 3.02427e7 | 1.07023 | ||||||||
\(957\) | 4.09111e6 | + | 7.08600e6i | 0.144398 | + | 0.250105i | ||||
\(958\) | −4.65962e6 | − | 8.07069e6i | −0.164035 | − | 0.284117i | ||||
\(959\) | −3.56818e6 | − | 6.18027e6i | −0.125285 | − | 0.217001i | ||||
\(960\) | 5.31298e6 | − | 9.20234e6i | 0.186063 | − | 0.322270i | ||||
\(961\) | −2.83106e7 | −0.988872 | ||||||||
\(962\) | −1.18985e7 | − | 985015.i | −0.414529 | − | 0.0343167i | ||||
\(963\) | 1.70640e7 | 0.592944 | ||||||||
\(964\) | −1.66018e7 | + | 2.87551e7i | −0.575390 | + | 0.996605i | ||||
\(965\) | −2.00997e7 | − | 3.48138e7i | −0.694819 | − | 1.20346i | ||||
\(966\) | 208314. | + | 360811.i | 0.00718251 | + | 0.0124405i | ||||
\(967\) | −1.83136e7 | − | 3.17201e7i | −0.629807 | − | 1.09086i | −0.987590 | − | 0.157053i | \(-0.949801\pi\) |
0.357783 | − | 0.933805i | \(-0.383533\pi\) | |||||||
\(968\) | −3.86629e6 | −0.132619 | ||||||||
\(969\) | −7.98223e6 | − | 1.38256e7i | −0.273096 | − | 0.473016i | ||||
\(970\) | 3.76602e6 | 0.128515 | ||||||||
\(971\) | −2.33925e7 | + | 4.05170e7i | −0.796212 | + | 1.37908i | 0.125855 | + | 0.992049i | \(0.459833\pi\) |
−0.922067 | + | 0.387031i | \(0.873501\pi\) | |||||||
\(972\) | −2.29394e7 | −0.778783 | ||||||||
\(973\) | 8.25438e6 | 0.279513 | ||||||||
\(974\) | 214330. | − | 371230.i | 0.00723912 | − | 0.0125385i | ||||
\(975\) | −1.70455e7 | − | 2.95236e7i | −0.574246 | − | 0.994623i | ||||
\(976\) | −1.24422e7 | −0.418093 | ||||||||
\(977\) | −2.64643e7 | + | 4.58375e7i | −0.887001 | + | 1.53633i | −0.0435982 | + | 0.999049i | \(0.513882\pi\) |
−0.843403 | + | 0.537282i | \(0.819451\pi\) | |||||||
\(978\) | 291495. | − | 504884.i | 0.00974505 | − | 0.0168789i | ||||
\(979\) | −2.83312e6 | + | 4.90710e6i | −0.0944730 | + | 0.163632i | ||||
\(980\) | −2.21085e7 | − | 3.82930e7i | −0.735349 | − | 1.27366i | ||||
\(981\) | −7.97478e6 | − | 1.38127e7i | −0.264573 | − | 0.458255i | ||||
\(982\) | −310101. | + | 537111.i | −0.0102618 | + | 0.0177740i | ||||
\(983\) | −1.30178e6 | + | 2.25475e6i | −0.0429689 | + | 0.0744243i | −0.886710 | − | 0.462326i | \(-0.847015\pi\) |
0.843741 | + | 0.536750i | \(0.180348\pi\) | |||||||
\(984\) | −1.99567e6 | + | 3.45661e6i | −0.0657055 | + | 0.113805i | ||||
\(985\) | 3.82540e7 | 1.25628 | ||||||||
\(986\) | −3.96207e6 | − | 6.86251e6i | −0.129787 | − | 0.224797i | ||||
\(987\) | −334489. | + | 579351.i | −0.0109292 | + | 0.0189299i | ||||
\(988\) | 8.56286e7 | 2.79079 | ||||||||
\(989\) | −2.61215e7 | −0.849194 | ||||||||
\(990\) | 5.01114e6 | − | 8.67955e6i | 0.162498 | − | 0.281455i | ||||
\(991\) | −5.40729e7 | −1.74902 | −0.874511 | − | 0.485005i | \(-0.838818\pi\) | ||||
−0.874511 | + | 0.485005i | \(0.838818\pi\) | |||||||
\(992\) | 1.09557e6 | + | 1.89759e6i | 0.0353478 | + | 0.0612241i | ||||
\(993\) | 5.48442e6 | 0.176505 | ||||||||
\(994\) | −1.49841e6 | − | 2.59533e6i | −0.0481022 | − | 0.0833155i | ||||
\(995\) | 2.10527e7 | + | 3.64644e7i | 0.674142 | + | 1.16765i | ||||
\(996\) | −6.41669e6 | − | 1.11140e7i | −0.204957 | − | 0.354996i | ||||
\(997\) | 1.56517e7 | − | 2.71095e7i | 0.498681 | − | 0.863742i | −0.501317 | − | 0.865263i | \(-0.667151\pi\) |
0.999999 | + | 0.00152182i | \(0.000484410\pi\) | |||||||
\(998\) | 311743. | 0.00990763 | ||||||||
\(999\) | −1.89423e7 | − | 1.56813e6i | −0.600508 | − | 0.0497129i |
(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 | 37.6.c.a.10.9 | ✓ | 30 | |
37.26 | even | 3 | inner | 37.6.c.a.26.9 | yes | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
37.6.c.a.10.9 | ✓ | 30 | 1.1 | even | 1 | trivial | |
37.6.c.a.26.9 | yes | 30 | 37.26 | even | 3 | inner |