Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,6,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.3879361069\) |
Analytic rank: | \(0\) |
Dimension: | \(92\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.2 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.6.d.b.176.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.9379 | −1.93356 | −0.966779 | − | 0.255615i | \(-0.917722\pi\) | ||||
−0.966779 | + | 0.255615i | \(0.917722\pi\) | |||||||
\(3\) | 4.58836 | − | 14.8979i | 0.294343 | − | 0.955700i | ||||
\(4\) | 87.6366 | 2.73864 | ||||||||
\(5\) | 82.7497i | 1.48027i | 0.672457 | + | 0.740136i | \(0.265239\pi\) | ||||
−0.672457 | + | 0.740136i | \(0.734761\pi\) | |||||||
\(6\) | −50.1868 | + | 162.951i | −0.569130 | + | 1.84790i | ||||
\(7\) | 211.698 | 1.63295 | 0.816473 | − | 0.577384i | \(-0.195926\pi\) | ||||
0.816473 | + | 0.577384i | \(0.195926\pi\) | |||||||
\(8\) | −608.545 | −3.36177 | ||||||||
\(9\) | −200.894 | − | 136.714i | −0.826724 | − | 0.562607i | ||||
\(10\) | − | 905.104i | − | 2.86219i | ||||||
\(11\) | 575.171 | 1.43323 | 0.716614 | − | 0.697470i | \(-0.245691\pi\) | ||||
0.716614 | + | 0.697470i | \(0.245691\pi\) | |||||||
\(12\) | 402.108 | − | 1305.60i | 0.806102 | − | 2.61732i | ||||
\(13\) | − | 586.318i | − | 0.962221i | −0.876660 | − | 0.481111i | \(-0.840234\pi\) | ||
0.876660 | − | 0.481111i | \(-0.159766\pi\) | |||||||
\(14\) | −2315.52 | −3.15739 | ||||||||
\(15\) | 1232.80 | + | 379.685i | 1.41470 | + | 0.435708i | ||||
\(16\) | 3851.81 | 3.76153 | ||||||||
\(17\) | − | 230.745i | − | 0.193647i | −0.995302 | − | 0.0968235i | \(-0.969132\pi\) | ||
0.995302 | − | 0.0968235i | \(-0.0308682\pi\) | |||||||
\(18\) | 2197.35 | + | 1495.35i | 1.59852 | + | 1.08783i | ||||
\(19\) | 39.4470 | 0.0250686 | 0.0125343 | − | 0.999921i | \(-0.496010\pi\) | ||||
0.0125343 | + | 0.999921i | \(0.496010\pi\) | |||||||
\(20\) | 7251.91i | 4.05394i | ||||||||
\(21\) | 971.346 | − | 3153.85i | 0.480646 | − | 1.56061i | ||||
\(22\) | −6291.14 | −2.77123 | ||||||||
\(23\) | 1717.40 | 0.676944 | 0.338472 | − | 0.940976i | \(-0.390090\pi\) | ||||
0.338472 | + | 0.940976i | \(0.390090\pi\) | |||||||
\(24\) | −2792.22 | + | 9066.04i | −0.989514 | + | 3.21284i | ||||
\(25\) | −3722.52 | −1.19120 | ||||||||
\(26\) | 6413.06i | 1.86051i | ||||||||
\(27\) | −2958.52 | + | 2365.60i | −0.781024 | + | 0.624500i | ||||
\(28\) | 18552.5 | 4.47206 | ||||||||
\(29\) | − | 7866.89i | − | 1.73703i | −0.495661 | − | 0.868516i | \(-0.665074\pi\) | ||
0.495661 | − | 0.868516i | \(-0.334926\pi\) | |||||||
\(30\) | −13484.1 | − | 4152.94i | −2.73540 | − | 0.842466i | ||||
\(31\) | 1806.70i | 0.337662i | 0.985645 | + | 0.168831i | \(0.0539992\pi\) | ||||
−0.985645 | + | 0.168831i | \(0.946001\pi\) | |||||||
\(32\) | −22657.1 | −3.91137 | ||||||||
\(33\) | 2639.09 | − | 8568.84i | 0.421861 | − | 1.36974i | ||||
\(34\) | 2523.86i | 0.374428i | ||||||||
\(35\) | 17517.9i | 2.41720i | ||||||||
\(36\) | −17605.7 | − | 11981.1i | −2.26410 | − | 1.54078i | ||||
\(37\) | 13241.2i | 1.59010i | 0.606546 | + | 0.795048i | \(0.292554\pi\) | ||||
−0.606546 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(38\) | −431.465 | −0.0484715 | ||||||||
\(39\) | −8734.90 | − | 2690.24i | −0.919594 | − | 0.283223i | ||||
\(40\) | − | 50357.0i | − | 4.97633i | ||||||
\(41\) | − | 282.328i | − | 0.0262298i | −0.999914 | − | 0.0131149i | \(-0.995825\pi\) | ||
0.999914 | − | 0.0131149i | \(-0.00417472\pi\) | |||||||
\(42\) | −10624.4 | + | 34496.4i | −0.929357 | + | 3.01752i | ||||
\(43\) | 7615.16i | 0.628070i | 0.949411 | + | 0.314035i | \(0.101681\pi\) | ||||
−0.949411 | + | 0.314035i | \(0.898319\pi\) | |||||||
\(44\) | 50406.1 | 3.92510 | ||||||||
\(45\) | 11313.0 | − | 16623.9i | 0.832812 | − | 1.22378i | ||||
\(46\) | −18784.7 | −1.30891 | ||||||||
\(47\) | 12556.7 | 0.829148 | 0.414574 | − | 0.910016i | \(-0.363931\pi\) | ||||
0.414574 | + | 0.910016i | \(0.363931\pi\) | |||||||
\(48\) | 17673.5 | − | 57383.8i | 1.10718 | − | 3.59489i | ||||
\(49\) | 28009.0 | 1.66651 | ||||||||
\(50\) | 40716.3 | 2.30326 | ||||||||
\(51\) | −3437.62 | − | 1058.74i | −0.185068 | − | 0.0569987i | ||||
\(52\) | − | 51382.9i | − | 2.63518i | ||||||
\(53\) | 9284.33i | 0.454005i | 0.973894 | + | 0.227003i | \(0.0728926\pi\) | ||||
−0.973894 | + | 0.227003i | \(0.927107\pi\) | |||||||
\(54\) | 32359.8 | − | 25874.6i | 1.51016 | − | 1.20751i | ||||
\(55\) | 47595.3i | 2.12157i | ||||||||
\(56\) | −128828. | −5.48959 | ||||||||
\(57\) | 180.997 | − | 587.676i | 0.00737876 | − | 0.0239580i | ||||
\(58\) | 86046.9i | 3.35865i | ||||||||
\(59\) | 5254.69 | − | 26216.6i | 0.196525 | − | 0.980499i | ||||
\(60\) | 108038. | + | 33274.3i | 3.87435 | + | 1.19325i | ||||
\(61\) | − | 17311.7i | − | 0.595683i | −0.954615 | − | 0.297842i | \(-0.903733\pi\) | ||
0.954615 | − | 0.297842i | \(-0.0962668\pi\) | |||||||
\(62\) | − | 19761.4i | − | 0.652888i | ||||||
\(63\) | −42528.8 | − | 28942.0i | −1.35000 | − | 0.918707i | ||||
\(64\) | 124562. | 3.80132 | ||||||||
\(65\) | 48517.6 | 1.42435 | ||||||||
\(66\) | −28866.0 | + | 93724.7i | −0.815693 | + | 2.64846i | ||||
\(67\) | − | 9818.20i | − | 0.267205i | −0.991035 | − | 0.133603i | \(-0.957345\pi\) | ||
0.991035 | − | 0.133603i | \(-0.0426546\pi\) | |||||||
\(68\) | − | 20221.7i | − | 0.530330i | ||||||
\(69\) | 7880.06 | − | 25585.7i | 0.199254 | − | 0.646955i | ||||
\(70\) | − | 191609.i | − | 4.67380i | ||||||
\(71\) | 12464.1i | 0.293437i | 0.989178 | + | 0.146718i | \(0.0468711\pi\) | ||||
−0.989178 | + | 0.146718i | \(0.953129\pi\) | |||||||
\(72\) | 122253. | + | 83196.4i | 2.77926 | + | 1.89136i | ||||
\(73\) | − | 59580.4i | − | 1.30857i | −0.756249 | − | 0.654284i | \(-0.772970\pi\) | ||
0.756249 | − | 0.654284i | \(-0.227030\pi\) | |||||||
\(74\) | − | 144830.i | − | 3.07454i | ||||||
\(75\) | −17080.2 | + | 55457.6i | −0.350623 | + | 1.13843i | ||||
\(76\) | 3457.00 | 0.0686539 | ||||||||
\(77\) | 121763. | 2.34038 | ||||||||
\(78\) | 95541.0 | + | 29425.4i | 1.77809 | + | 0.547628i | ||||
\(79\) | 4419.42 | 0.0796706 | 0.0398353 | − | 0.999206i | \(-0.487317\pi\) | ||||
0.0398353 | + | 0.999206i | \(0.487317\pi\) | |||||||
\(80\) | 318736.i | 5.56809i | ||||||||
\(81\) | 21667.8 | + | 54929.9i | 0.366946 | + | 0.930242i | ||||
\(82\) | 3088.07i | 0.0507168i | ||||||||
\(83\) | 39420.5 | 0.628097 | 0.314048 | − | 0.949407i | \(-0.398315\pi\) | ||||
0.314048 | + | 0.949407i | \(0.398315\pi\) | |||||||
\(84\) | 85125.5 | − | 276393.i | 1.31632 | − | 4.27394i | ||||
\(85\) | 19094.1 | 0.286650 | ||||||||
\(86\) | − | 83293.5i | − | 1.21441i | ||||||
\(87\) | −117200. | − | 36096.1i | −1.66008 | − | 0.511284i | ||||
\(88\) | −350018. | −4.81819 | ||||||||
\(89\) | −57202.6 | −0.765493 | −0.382746 | − | 0.923853i | \(-0.625022\pi\) | ||||
−0.382746 | + | 0.923853i | \(0.625022\pi\) | |||||||
\(90\) | −123740. | + | 181830.i | −1.61029 | + | 2.36624i | ||||
\(91\) | − | 124122.i | − | 1.57125i | ||||||
\(92\) | 150508. | 1.85391 | ||||||||
\(93\) | 26916.0 | + | 8289.78i | 0.322703 | + | 0.0993884i | ||||
\(94\) | −137344. | −1.60321 | ||||||||
\(95\) | 3264.22i | 0.0371083i | ||||||||
\(96\) | −103959. | + | 337542.i | −1.15128 | + | 3.73809i | ||||
\(97\) | − | 40889.7i | − | 0.441250i | −0.975359 | − | 0.220625i | \(-0.929190\pi\) | ||
0.975359 | − | 0.220625i | \(-0.0708097\pi\) | |||||||
\(98\) | −306359. | −3.22229 | ||||||||
\(99\) | −115548. | − | 78633.8i | −1.18488 | − | 0.806345i | ||||
\(100\) | −326229. | −3.26229 | ||||||||
\(101\) | −112074. | −1.09320 | −0.546601 | − | 0.837393i | \(-0.684078\pi\) | ||||
−0.546601 | + | 0.837393i | \(0.684078\pi\) | |||||||
\(102\) | 37600.2 | + | 11580.4i | 0.357840 | + | 0.110210i | ||||
\(103\) | 3686.87i | 0.0342424i | 0.999853 | + | 0.0171212i | \(0.00545012\pi\) | ||||
−0.999853 | + | 0.0171212i | \(0.994550\pi\) | |||||||
\(104\) | 356801.i | 3.23477i | ||||||||
\(105\) | 260980. | + | 80378.6i | 2.31012 | + | 0.711487i | ||||
\(106\) | − | 101551.i | − | 0.877846i | ||||||
\(107\) | 187067.i | 1.57957i | 0.613387 | + | 0.789783i | \(0.289807\pi\) | ||||
−0.613387 | + | 0.789783i | \(0.710193\pi\) | |||||||
\(108\) | −259274. | + | 207314.i | −2.13895 | + | 1.71028i | ||||
\(109\) | − | 208962.i | − | 1.68462i | −0.538994 | − | 0.842309i | \(-0.681196\pi\) | ||
0.538994 | − | 0.842309i | \(-0.318804\pi\) | |||||||
\(110\) | − | 520590.i | − | 4.10217i | ||||||
\(111\) | 197266. | + | 60755.4i | 1.51965 | + | 0.468034i | ||||
\(112\) | 815420. | 6.14237 | ||||||||
\(113\) | 171171. | 1.26105 | 0.630527 | − | 0.776167i | \(-0.282839\pi\) | ||||
0.630527 | + | 0.776167i | \(0.282839\pi\) | |||||||
\(114\) | −1979.72 | + | 6427.92i | −0.0142673 | + | 0.0463242i | ||||
\(115\) | 142115.i | 1.00206i | ||||||||
\(116\) | − | 689428.i | − | 4.75711i | ||||||
\(117\) | −80157.7 | + | 117788.i | −0.541353 | + | 0.795491i | ||||
\(118\) | −57475.0 | + | 286754.i | −0.379992 | + | 1.89585i | ||||
\(119\) | − | 48848.3i | − | 0.316215i | ||||||
\(120\) | −750212. | − | 231056.i | −4.75588 | − | 1.46475i | ||||
\(121\) | 169771. | 1.05414 | ||||||||
\(122\) | 189353.i | 1.15179i | ||||||||
\(123\) | −4206.10 | − | 1295.42i | −0.0250678 | − | 0.00772056i | ||||
\(124\) | 158333.i | 0.924735i | ||||||||
\(125\) | − | 49444.2i | − | 0.283035i | ||||||
\(126\) | 465174. | + | 316563.i | 2.61029 | + | 1.77637i | ||||
\(127\) | −9967.86 | −0.0548394 | −0.0274197 | − | 0.999624i | \(-0.508729\pi\) | ||||
−0.0274197 | + | 0.999624i | \(0.508729\pi\) | |||||||
\(128\) | −637412. | −3.43871 | ||||||||
\(129\) | 113450. | + | 34941.1i | 0.600246 | + | 0.184868i | ||||
\(130\) | −530679. | −2.75406 | ||||||||
\(131\) | 181309. | 0.923086 | 0.461543 | − | 0.887118i | \(-0.347296\pi\) | ||||
0.461543 | + | 0.887118i | \(0.347296\pi\) | |||||||
\(132\) | 231281. | − | 750944.i | 1.15533 | − | 3.75122i | ||||
\(133\) | 8350.84 | 0.0409356 | ||||||||
\(134\) | 107390.i | 0.516656i | ||||||||
\(135\) | −195753. | − | 244816.i | −0.924430 | − | 1.15613i | ||||
\(136\) | 140419.i | 0.650997i | ||||||||
\(137\) | 24010.2i | 0.109294i | 0.998506 | + | 0.0546468i | \(0.0174033\pi\) | ||||
−0.998506 | + | 0.0546468i | \(0.982597\pi\) | |||||||
\(138\) | −86191.0 | + | 279852.i | −0.385269 | + | 1.25093i | ||||
\(139\) | 223534. | 0.981310 | 0.490655 | − | 0.871354i | \(-0.336758\pi\) | ||||
0.490655 | + | 0.871354i | \(0.336758\pi\) | |||||||
\(140\) | 1.53521e6i | 6.61986i | ||||||||
\(141\) | 57614.8 | − | 187069.i | 0.244054 | − | 0.792417i | ||||
\(142\) | − | 136330.i | − | 0.567377i | ||||||
\(143\) | − | 337233.i | − | 1.37908i | ||||||
\(144\) | −773805. | − | 526595.i | −3.10975 | − | 2.11627i | ||||
\(145\) | 650983. | 2.57128 | ||||||||
\(146\) | 651681.i | 2.53019i | ||||||||
\(147\) | 128515. | − | 417275.i | 0.490526 | − | 1.59268i | ||||
\(148\) | 1.16042e6i | 4.35471i | ||||||||
\(149\) | 342010. | 1.26204 | 0.631021 | − | 0.775766i | \(-0.282636\pi\) | ||||
0.631021 | + | 0.775766i | \(0.282636\pi\) | |||||||
\(150\) | 186821. | − | 606587.i | 0.677950 | − | 2.20123i | ||||
\(151\) | 110011.i | 0.392638i | 0.980540 | + | 0.196319i | \(0.0628987\pi\) | ||||
−0.980540 | + | 0.196319i | \(0.937101\pi\) | |||||||
\(152\) | −24005.3 | −0.0842747 | ||||||||
\(153\) | −31546.0 | + | 46355.4i | −0.108947 | + | 0.160093i | ||||
\(154\) | −1.33182e6 | −4.52527 | ||||||||
\(155\) | −149504. | −0.499831 | ||||||||
\(156\) | −765497. | − | 235763.i | −2.51844 | − | 0.775648i | ||||
\(157\) | 339957.i | 1.10071i | 0.834930 | + | 0.550357i | \(0.185508\pi\) | ||||
−0.834930 | + | 0.550357i | \(0.814492\pi\) | |||||||
\(158\) | −48339.0 | −0.154048 | ||||||||
\(159\) | 138317. | + | 42599.8i | 0.433893 | + | 0.133633i | ||||
\(160\) | − | 1.87486e6i | − | 5.78989i | ||||||
\(161\) | 363571. | 1.10541 | ||||||||
\(162\) | −236999. | − | 600815.i | −0.709511 | − | 1.79868i | ||||
\(163\) | 160683. | 0.473696 | 0.236848 | − | 0.971547i | \(-0.423886\pi\) | ||||
0.236848 | + | 0.971547i | \(0.423886\pi\) | |||||||
\(164\) | − | 24742.3i | − | 0.0718341i | ||||||
\(165\) | 709069. | + | 218384.i | 2.02758 | + | 0.624469i | ||||
\(166\) | −431175. | −1.21446 | ||||||||
\(167\) | − | 311168.i | − | 0.863383i | −0.902021 | − | 0.431692i | \(-0.857917\pi\) | ||
0.902021 | − | 0.431692i | \(-0.142083\pi\) | |||||||
\(168\) | −591108. | + | 1.91926e6i | −1.61582 | + | 5.24640i | ||||
\(169\) | 27524.2 | 0.0741307 | ||||||||
\(170\) | −208849. | −0.554255 | ||||||||
\(171\) | −7924.66 | − | 5392.94i | −0.0207248 | − | 0.0141038i | ||||
\(172\) | 667367.i | 1.72006i | ||||||||
\(173\) | −756531. | −1.92181 | −0.960907 | − | 0.276870i | \(-0.910703\pi\) | ||||
−0.960907 | + | 0.276870i | \(0.910703\pi\) | |||||||
\(174\) | 1.28192e6 | + | 394814.i | 3.20986 | + | 0.988596i | ||||
\(175\) | −788049. | −1.94517 | ||||||||
\(176\) | 2.21545e6 | 5.39113 | ||||||||
\(177\) | −366462. | − | 198575.i | −0.879217 | − | 0.476422i | ||||
\(178\) | 625674. | 1.48012 | ||||||||
\(179\) | 473943. | 1.10559 | 0.552794 | − | 0.833318i | \(-0.313562\pi\) | ||||
0.552794 | + | 0.833318i | \(0.313562\pi\) | |||||||
\(180\) | 991434. | − | 1.45686e6i | 2.28078 | − | 3.35149i | ||||
\(181\) | 209709. | 0.475795 | 0.237897 | − | 0.971290i | \(-0.423542\pi\) | ||||
0.237897 | + | 0.971290i | \(0.423542\pi\) | |||||||
\(182\) | 1.35763e6i | 3.03811i | ||||||||
\(183\) | −257908. | − | 79432.3i | −0.569295 | − | 0.175335i | ||||
\(184\) | −1.04512e6 | −2.27573 | ||||||||
\(185\) | −1.09571e6 | −2.35377 | ||||||||
\(186\) | −294403. | − | 90672.4i | −0.623965 | − | 0.192173i | ||||
\(187\) | − | 132718.i | − | 0.277540i | ||||||
\(188\) | 1.10043e6 | 2.27074 | ||||||||
\(189\) | −626312. | + | 500794.i | −1.27537 | + | 1.01977i | ||||
\(190\) | − | 35703.6i | − | 0.0717510i | ||||||
\(191\) | −194882. | −0.386534 | −0.193267 | − | 0.981146i | \(-0.561908\pi\) | ||||
−0.193267 | + | 0.981146i | \(0.561908\pi\) | |||||||
\(192\) | 571533. | − | 1.85571e6i | 1.11889 | − | 3.63292i | ||||
\(193\) | 509476. | 0.984534 | 0.492267 | − | 0.870444i | \(-0.336168\pi\) | ||||
0.492267 | + | 0.870444i | \(0.336168\pi\) | |||||||
\(194\) | 447246.i | 0.853182i | ||||||||
\(195\) | 222616. | − | 722810.i | 0.419247 | − | 1.36125i | ||||
\(196\) | 2.45462e6 | 4.56398 | ||||||||
\(197\) | 327612.i | 0.601443i | 0.953712 | + | 0.300721i | \(0.0972274\pi\) | ||||
−0.953712 | + | 0.300721i | \(0.902773\pi\) | |||||||
\(198\) | 1.26385e6 | + | 860084.i | 2.29104 | + | 1.55911i | ||||
\(199\) | −521051. | −0.932712 | −0.466356 | − | 0.884597i | \(-0.654433\pi\) | ||||
−0.466356 | + | 0.884597i | \(0.654433\pi\) | |||||||
\(200\) | 2.26532e6 | 4.00456 | ||||||||
\(201\) | −146270. | − | 45049.4i | −0.255368 | − | 0.0786500i | ||||
\(202\) | 1.22585e6 | 2.11377 | ||||||||
\(203\) | − | 1.66540e6i | − | 2.83648i | ||||||
\(204\) | −301261. | − | 92784.6i | −0.506836 | − | 0.156099i | ||||
\(205\) | 23362.6 | 0.0388272 | ||||||||
\(206\) | − | 40326.4i | − | 0.0662097i | ||||||
\(207\) | −345016. | − | 234793.i | −0.559646 | − | 0.380854i | ||||
\(208\) | − | 2.25838e6i | − | 3.61942i | ||||||
\(209\) | 22688.8 | 0.0359290 | ||||||||
\(210\) | −2.85457e6 | − | 879169.i | −4.46675 | − | 1.37570i | ||||
\(211\) | 557715.i | 0.862395i | 0.902258 | + | 0.431197i | \(0.141909\pi\) | ||||
−0.902258 | + | 0.431197i | \(0.858091\pi\) | |||||||
\(212\) | 813648.i | 1.24336i | ||||||||
\(213\) | 185688. | + | 57189.6i | 0.280437 | + | 0.0863711i | ||||
\(214\) | − | 2.04611e6i | − | 3.05418i | ||||||
\(215\) | −630152. | −0.929714 | ||||||||
\(216\) | 1.80039e6 | − | 1.43958e6i | 2.62562 | − | 2.09943i | ||||
\(217\) | 382475.i | 0.551383i | ||||||||
\(218\) | 2.28560e6i | 3.25731i | ||||||||
\(219\) | −887621. | − | 273376.i | −1.25060 | − | 0.385168i | ||||
\(220\) | 4.17109e6i | 5.81022i | ||||||||
\(221\) | −135290. | −0.186331 | ||||||||
\(222\) | −2.15767e6 | − | 664534.i | −2.93834 | − | 0.904971i | ||||
\(223\) | 123192. | 0.165890 | 0.0829450 | − | 0.996554i | \(-0.473567\pi\) | ||||
0.0829450 | + | 0.996554i | \(0.473567\pi\) | |||||||
\(224\) | −4.79645e6 | −6.38705 | ||||||||
\(225\) | 747831. | + | 508919.i | 0.984798 | + | 0.670181i | ||||
\(226\) | −1.87224e6 | −2.43832 | ||||||||
\(227\) | 668195. | 0.860673 | 0.430337 | − | 0.902668i | \(-0.358395\pi\) | ||||
0.430337 | + | 0.902668i | \(0.358395\pi\) | |||||||
\(228\) | 15861.9 | − | 51502.0i | 0.0202078 | − | 0.0656125i | ||||
\(229\) | − | 547272.i | − | 0.689627i | −0.938671 | − | 0.344813i | \(-0.887942\pi\) | ||
0.938671 | − | 0.344813i | \(-0.112058\pi\) | |||||||
\(230\) | − | 1.55443e6i | − | 1.93754i | ||||||
\(231\) | 558690. | − | 1.81401e6i | 0.688876 | − | 2.23670i | ||||
\(232\) | 4.78736e6i | 5.83950i | ||||||||
\(233\) | −978602. | −1.18091 | −0.590454 | − | 0.807071i | \(-0.701051\pi\) | ||||
−0.590454 | + | 0.807071i | \(0.701051\pi\) | |||||||
\(234\) | 876753. | − | 1.28835e6i | 1.04674 | − | 1.53813i | ||||
\(235\) | 1.03907e6i | 1.22736i | ||||||||
\(236\) | 460503. | − | 2.29754e6i | 0.538211 | − | 2.68524i | ||||
\(237\) | 20277.9 | − | 65840.1i | 0.0234505 | − | 0.0761411i | ||||
\(238\) | 534296.i | 0.611420i | ||||||||
\(239\) | − | 441167.i | − | 0.499584i | −0.968300 | − | 0.249792i | \(-0.919638\pi\) | ||
0.968300 | − | 0.249792i | \(-0.0803622\pi\) | |||||||
\(240\) | 4.74849e6 | + | 1.46247e6i | 5.32142 | + | 1.63893i | ||||
\(241\) | 457362. | 0.507244 | 0.253622 | − | 0.967303i | \(-0.418378\pi\) | ||||
0.253622 | + | 0.967303i | \(0.418378\pi\) | |||||||
\(242\) | −1.85693e6 | −2.03825 | ||||||||
\(243\) | 917759. | − | 70766.1i | 0.997040 | − | 0.0768794i | ||||
\(244\) | − | 1.51714e6i | − | 1.63137i | ||||||
\(245\) | 2.31774e6i | 2.46689i | ||||||||
\(246\) | 46005.7 | + | 14169.2i | 0.0484701 | + | 0.0149282i | ||||
\(247\) | − | 23128.5i | − | 0.0241215i | ||||||
\(248\) | − | 1.09946e6i | − | 1.13514i | ||||||
\(249\) | 180875. | − | 587282.i | 0.184876 | − | 0.600272i | ||||
\(250\) | 540814.i | 0.547265i | ||||||||
\(251\) | − | 928891.i | − | 0.930637i | −0.885143 | − | 0.465319i | \(-0.845940\pi\) | ||
0.885143 | − | 0.465319i | \(-0.154060\pi\) | |||||||
\(252\) | −3.72709e6 | − | 2.53638e6i | −3.69716 | − | 2.51601i | ||||
\(253\) | 987801. | 0.970216 | ||||||||
\(254\) | 109027. | 0.106035 | ||||||||
\(255\) | 87610.6 | − | 284462.i | 0.0843735 | − | 0.273951i | ||||
\(256\) | 2.98594e6 | 2.84762 | ||||||||
\(257\) | − | 641285.i | − | 0.605645i | −0.953047 | − | 0.302823i | \(-0.902071\pi\) | ||
0.953047 | − | 0.302823i | \(-0.0979289\pi\) | |||||||
\(258\) | −1.24090e6 | − | 382180.i | −1.16061 | − | 0.357453i | ||||
\(259\) | 2.80314e6i | 2.59654i | ||||||||
\(260\) | 4.25192e6 | 3.90079 | ||||||||
\(261\) | −1.07551e6 | + | 1.58041e6i | −0.977267 | + | 1.43605i | ||||
\(262\) | −1.98314e6 | −1.78484 | ||||||||
\(263\) | 1.41692e6i | 1.26316i | 0.775312 | + | 0.631578i | \(0.217593\pi\) | ||||
−0.775312 | + | 0.631578i | \(0.782407\pi\) | |||||||
\(264\) | −1.60601e6 | + | 5.21453e6i | −1.41820 | + | 4.60474i | ||||
\(265\) | −768276. | −0.672052 | ||||||||
\(266\) | −91340.3 | −0.0791513 | ||||||||
\(267\) | −262466. | + | 852198.i | −0.225318 | + | 0.731581i | ||||
\(268\) | − | 860434.i | − | 0.731780i | ||||||
\(269\) | 1.07898e6 | 0.909146 | 0.454573 | − | 0.890709i | \(-0.349792\pi\) | ||||
0.454573 | + | 0.890709i | \(0.349792\pi\) | |||||||
\(270\) | 2.14112e6 | + | 2.67777e6i | 1.78744 | + | 2.23544i | ||||
\(271\) | 1.58918e6 | 1.31447 | 0.657235 | − | 0.753685i | \(-0.271726\pi\) | ||||
0.657235 | + | 0.753685i | \(0.271726\pi\) | |||||||
\(272\) | − | 888787.i | − | 0.728409i | ||||||
\(273\) | −1.84916e6 | − | 569518.i | −1.50165 | − | 0.462488i | ||||
\(274\) | − | 262620.i | − | 0.211326i | ||||||
\(275\) | −2.14108e6 | −1.70727 | ||||||||
\(276\) | 690582. | − | 2.24224e6i | 0.545686 | − | 1.77178i | ||||
\(277\) | −1.02921e6 | −0.805942 | −0.402971 | − | 0.915213i | \(-0.632022\pi\) | ||||
−0.402971 | + | 0.915213i | \(0.632022\pi\) | |||||||
\(278\) | −2.44498e6 | −1.89742 | ||||||||
\(279\) | 247000. | − | 362955.i | 0.189971 | − | 0.279153i | ||||
\(280\) | − | 1.06605e7i | − | 8.12608i | ||||||
\(281\) | − | 677260.i | − | 0.511670i | −0.966721 | − | 0.255835i | \(-0.917650\pi\) | ||
0.966721 | − | 0.255835i | \(-0.0823503\pi\) | |||||||
\(282\) | −630182. | + | 2.04613e6i | −0.471893 | + | 1.53218i | ||||
\(283\) | 445884.i | 0.330945i | 0.986214 | + | 0.165472i | \(0.0529149\pi\) | ||||
−0.986214 | + | 0.165472i | \(0.947085\pi\) | |||||||
\(284\) | 1.09231e6i | 0.803619i | ||||||||
\(285\) | 48630.0 | + | 14977.4i | 0.0354644 | + | 0.0109226i | ||||
\(286\) | 3.68861e6i | 2.66654i | ||||||||
\(287\) | − | 59768.4i | − | 0.0428318i | ||||||
\(288\) | 4.55167e6 | + | 3.09753e6i | 3.23362 | + | 2.20056i | ||||
\(289\) | 1.36661e6 | 0.962501 | ||||||||
\(290\) | −7.12035e6 | −4.97172 | ||||||||
\(291\) | −609170. | − | 187617.i | −0.421703 | − | 0.129879i | ||||
\(292\) | − | 5.22142e6i | − | 3.58370i | ||||||
\(293\) | 968607.i | 0.659141i | 0.944131 | + | 0.329571i | \(0.106904\pi\) | ||||
−0.944131 | + | 0.329571i | \(0.893096\pi\) | |||||||
\(294\) | −1.40568e6 | + | 4.56410e6i | −0.948460 | + | 3.07955i | ||||
\(295\) | 2.16942e6 | + | 434824.i | 1.45140 | + | 0.290910i | ||||
\(296\) | − | 8.05788e6i | − | 5.34554i | ||||||
\(297\) | −1.70165e6 | + | 1.36063e6i | −1.11939 | + | 0.895052i | ||||
\(298\) | −3.74086e6 | −2.44023 | ||||||||
\(299\) | − | 1.00694e6i | − | 0.651370i | ||||||
\(300\) | −1.49685e6 | + | 4.86012e6i | −0.960232 | + | 3.11777i | ||||
\(301\) | 1.61211e6i | 1.02560i | ||||||||
\(302\) | − | 1.20328e6i | − | 0.759187i | ||||||
\(303\) | −514234. | + | 1.66966e6i | −0.321776 | + | 1.04477i | ||||
\(304\) | 151942. | 0.0942962 | ||||||||
\(305\) | 1.43254e6 | 0.881773 | ||||||||
\(306\) | 345046. | − | 507028.i | 0.210656 | − | 0.309548i | ||||
\(307\) | −942100. | −0.570494 | −0.285247 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285247 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(308\) | 1.06709e7 | 6.40948 | ||||||||
\(309\) | 54926.5 | + | 16916.7i | 0.0327255 | + | 0.0100790i | ||||
\(310\) | 1.63525e6 | 0.966452 | ||||||||
\(311\) | 2.24070e6i | 1.31366i | 0.754039 | + | 0.656830i | \(0.228103\pi\) | ||||
−0.754039 | + | 0.656830i | \(0.771897\pi\) | |||||||
\(312\) | 5.31558e6 | + | 1.63713e6i | 3.09146 | + | 0.952131i | ||||
\(313\) | − | 1.70178e6i | − | 0.981843i | −0.871204 | − | 0.490922i | \(-0.836660\pi\) | ||
0.871204 | − | 0.490922i | \(-0.163340\pi\) | |||||||
\(314\) | − | 3.71840e6i | − | 2.12829i | ||||||
\(315\) | 2.39494e6 | − | 3.51925e6i | 1.35994 | − | 1.99836i | ||||
\(316\) | 387303. | 0.218189 | ||||||||
\(317\) | 645139.i | 0.360583i | 0.983613 | + | 0.180291i | \(0.0577041\pi\) | ||||
−0.983613 | + | 0.180291i | \(0.942296\pi\) | |||||||
\(318\) | −1.51289e6 | − | 465951.i | −0.838957 | − | 0.258388i | ||||
\(319\) | − | 4.52481e6i | − | 2.48956i | ||||||
\(320\) | 1.03074e7i | 5.62699i | ||||||||
\(321\) | 2.78690e6 | + | 858330.i | 1.50959 | + | 0.464934i | ||||
\(322\) | −3.97669e6 | −2.13738 | ||||||||
\(323\) | − | 9102.20i | − | 0.00485445i | ||||||
\(324\) | 1.89889e6 | + | 4.81387e6i | 1.00493 | + | 2.54760i | ||||
\(325\) | 2.18258e6i | 1.14620i | ||||||||
\(326\) | −1.75752e6 | −0.915919 | ||||||||
\(327\) | −3.11310e6 | − | 958793.i | −1.60999 | − | 0.495856i | ||||
\(328\) | 171810.i | 0.0881786i | ||||||||
\(329\) | 2.65824e6 | 1.35395 | ||||||||
\(330\) | −7.75569e6 | − | 2.38865e6i | −3.92045 | − | 1.20745i | ||||
\(331\) | 964683. | 0.483966 | 0.241983 | − | 0.970281i | \(-0.422202\pi\) | ||||
0.241983 | + | 0.970281i | \(0.422202\pi\) | |||||||
\(332\) | 3.45468e6 | 1.72013 | ||||||||
\(333\) | 1.81025e6 | − | 2.66008e6i | 0.894600 | − | 1.31457i | ||||
\(334\) | 3.40351e6i | 1.66940i | ||||||||
\(335\) | 812453. | 0.395536 | ||||||||
\(336\) | 3.74144e6 | − | 1.21480e7i | 1.80797 | − | 5.87027i | ||||
\(337\) | − | 596925.i | − | 0.286316i | −0.989700 | − | 0.143158i | \(-0.954274\pi\) | ||
0.989700 | − | 0.143158i | \(-0.0457256\pi\) | |||||||
\(338\) | −301056. | −0.143336 | ||||||||
\(339\) | 785393. | − | 2.55008e6i | 0.371183 | − | 1.20519i | ||||
\(340\) | 1.67334e6 | 0.785033 | ||||||||
\(341\) | 1.03916e6i | 0.483946i | ||||||||
\(342\) | 86678.7 | + | 58987.1i | 0.0400726 | + | 0.0272704i | ||||
\(343\) | 2.37145e6 | 1.08837 | ||||||||
\(344\) | − | 4.63417e6i | − | 2.11143i | ||||||
\(345\) | 2.11721e6 | + | 652073.i | 0.957670 | + | 0.294950i | ||||
\(346\) | 8.27483e6 | 3.71594 | ||||||||
\(347\) | −560552. | −0.249915 | −0.124958 | − | 0.992162i | \(-0.539879\pi\) | ||||
−0.124958 | + | 0.992162i | \(0.539879\pi\) | |||||||
\(348\) | −1.02710e7 | − | 3.16334e6i | −4.54637 | − | 1.40022i | ||||
\(349\) | − | 3.18569e6i | − | 1.40004i | −0.714124 | − | 0.700019i | \(-0.753175\pi\) | ||
0.714124 | − | 0.700019i | \(-0.246825\pi\) | |||||||
\(350\) | 8.61956e6 | 3.76110 | ||||||||
\(351\) | 1.38700e6 | + | 1.73463e6i | 0.600907 | + | 0.751518i | ||||
\(352\) | −1.30317e7 | −5.60588 | ||||||||
\(353\) | −3.12050e6 | −1.33287 | −0.666435 | − | 0.745563i | \(-0.732181\pi\) | ||||
−0.666435 | + | 0.745563i | \(0.732181\pi\) | |||||||
\(354\) | 4.00831e6 | + | 2.17198e6i | 1.70002 | + | 0.921189i | ||||
\(355\) | −1.03140e6 | −0.434366 | ||||||||
\(356\) | −5.01305e6 | −2.09641 | ||||||||
\(357\) | −727737. | − | 224134.i | −0.302206 | − | 0.0930757i | ||||
\(358\) | −5.18391e6 | −2.13772 | ||||||||
\(359\) | 1.15889e6i | 0.474576i | 0.971439 | + | 0.237288i | \(0.0762586\pi\) | ||||
−0.971439 | + | 0.237288i | \(0.923741\pi\) | |||||||
\(360\) | −6.88448e6 | + | 1.01164e7i | −2.79972 | + | 4.11406i | ||||
\(361\) | −2.47454e6 | −0.999372 | ||||||||
\(362\) | −2.29376e6 | −0.919977 | ||||||||
\(363\) | 778970. | − | 2.52923e6i | 0.310280 | − | 1.00745i | ||||
\(364\) | − | 1.08777e7i | − | 4.30311i | ||||||
\(365\) | 4.93026e6 | 1.93704 | ||||||||
\(366\) | 2.82096e6 | + | 868819.i | 1.10076 | + | 0.339021i | ||||
\(367\) | 4.65500e6i | 1.80408i | 0.431657 | + | 0.902038i | \(0.357929\pi\) | ||||
−0.431657 | + | 0.902038i | \(0.642071\pi\) | |||||||
\(368\) | 6.61511e6 | 2.54635 | ||||||||
\(369\) | −38598.1 | + | 56718.1i | −0.0147571 | + | 0.0216848i | ||||
\(370\) | 1.19847e7 | 4.55116 | ||||||||
\(371\) | 1.96547e6i | 0.741366i | ||||||||
\(372\) | 2.35883e6 | + | 726489.i | 0.883769 | + | 0.272190i | ||||
\(373\) | −4.30976e6 | −1.60391 | −0.801956 | − | 0.597383i | \(-0.796207\pi\) | ||||
−0.801956 | + | 0.597383i | \(0.796207\pi\) | |||||||
\(374\) | 1.45165e6i | 0.536640i | ||||||||
\(375\) | −736614. | − | 226868.i | −0.270497 | − | 0.0833095i | ||||
\(376\) | −7.64134e6 | −2.78741 | ||||||||
\(377\) | −4.61250e6 | −1.67141 | ||||||||
\(378\) | 6.85051e6 | − | 5.47761e6i | 2.46600 | − | 1.97179i | ||||
\(379\) | −4.75138e6 | −1.69911 | −0.849556 | − | 0.527499i | \(-0.823130\pi\) | ||||
−0.849556 | + | 0.527499i | \(0.823130\pi\) | |||||||
\(380\) | 286066.i | 0.101626i | ||||||||
\(381\) | −45736.1 | + | 148500.i | −0.0161416 | + | 0.0524100i | ||||
\(382\) | 2.13159e6 | 0.747385 | ||||||||
\(383\) | 681890.i | 0.237529i | 0.992922 | + | 0.118765i | \(0.0378934\pi\) | ||||
−0.992922 | + | 0.118765i | \(0.962107\pi\) | |||||||
\(384\) | −2.92467e6 | + | 9.49609e6i | −1.01216 | + | 3.28637i | ||||
\(385\) | 1.00758e7i | 3.46440i | ||||||||
\(386\) | −5.57257e6 | −1.90365 | ||||||||
\(387\) | 1.04110e6 | − | 1.52984e6i | 0.353357 | − | 0.519241i | ||||
\(388\) | − | 3.58344e6i | − | 1.20843i | ||||||
\(389\) | − | 4.06334e6i | − | 1.36147i | −0.732529 | − | 0.680736i | \(-0.761660\pi\) | ||
0.732529 | − | 0.680736i | \(-0.238340\pi\) | |||||||
\(390\) | −2.43494e6 | + | 7.90599e6i | −0.810639 | + | 2.63205i | ||||
\(391\) | − | 396283.i | − | 0.131088i | ||||||
\(392\) | −1.70448e7 | −5.60242 | ||||||||
\(393\) | 831912. | − | 2.70113e6i | 0.271704 | − | 0.882193i | ||||
\(394\) | − | 3.58337e6i | − | 1.16292i | ||||||
\(395\) | 365706.i | 0.117934i | ||||||||
\(396\) | −1.01263e7 | − | 6.89120e6i | −3.24498 | − | 2.20829i | ||||
\(397\) | 3.10911e6i | 0.990058i | 0.868877 | + | 0.495029i | \(0.164843\pi\) | ||||
−0.868877 | + | 0.495029i | \(0.835157\pi\) | |||||||
\(398\) | 5.69918e6 | 1.80345 | ||||||||
\(399\) | 38316.6 | − | 124410.i | 0.0120491 | − | 0.0391221i | ||||
\(400\) | −1.43384e7 | −4.48075 | ||||||||
\(401\) | −1.83192e6 | −0.568913 | −0.284456 | − | 0.958689i | \(-0.591813\pi\) | ||||
−0.284456 | + | 0.958689i | \(0.591813\pi\) | |||||||
\(402\) | 1.59988e6 | + | 492744.i | 0.493768 | + | 0.152074i | ||||
\(403\) | 1.05930e6 | 0.324905 | ||||||||
\(404\) | −9.82176e6 | −2.99389 | ||||||||
\(405\) | −4.54543e6 | + | 1.79300e6i | −1.37701 | + | 0.543179i | ||||
\(406\) | 1.82159e7i | 5.48450i | ||||||||
\(407\) | 7.61597e6i | 2.27897i | ||||||||
\(408\) | 2.09195e6 | + | 644293.i | 0.622157 | + | 0.191616i | ||||
\(409\) | − | 3.65587e6i | − | 1.08064i | −0.841458 | − | 0.540322i | \(-0.818302\pi\) | ||
0.841458 | − | 0.540322i | \(-0.181698\pi\) | |||||||
\(410\) | −255537. | −0.0750747 | ||||||||
\(411\) | 357702. | + | 110168.i | 0.104452 | + | 0.0321699i | ||||
\(412\) | 323105.i | 0.0937778i | ||||||||
\(413\) | 1.11241e6 | − | 5.55001e6i | 0.320914 | − | 1.60110i | ||||
\(414\) | 3.77374e6 | + | 2.56813e6i | 1.08211 | + | 0.736403i | ||||
\(415\) | 3.26203e6i | 0.929754i | ||||||||
\(416\) | 1.32842e7i | 3.76360i | ||||||||
\(417\) | 1.02565e6 | − | 3.33018e6i | 0.288842 | − | 0.937837i | ||||
\(418\) | −248166. | −0.0694708 | ||||||||
\(419\) | 5.27692e6 | 1.46840 | 0.734202 | − | 0.678931i | \(-0.237556\pi\) | ||||
0.734202 | + | 0.678931i | \(0.237556\pi\) | |||||||
\(420\) | 2.28714e7 | + | 7.04411e6i | 6.32660 | + | 1.94851i | ||||
\(421\) | − | 1.31301e6i | − | 0.361046i | −0.983571 | − | 0.180523i | \(-0.942221\pi\) | ||
0.983571 | − | 0.180523i | \(-0.0577790\pi\) | |||||||
\(422\) | − | 6.10020e6i | − | 1.66749i | ||||||
\(423\) | −2.52257e6 | − | 1.71668e6i | −0.685477 | − | 0.466485i | ||||
\(424\) | − | 5.64994e6i | − | 1.52626i | ||||||
\(425\) | 858953.i | 0.230673i | ||||||||
\(426\) | −2.03103e6 | − | 625532.i | −0.542242 | − | 0.167003i | ||||
\(427\) | − | 3.66486e6i | − | 0.972718i | ||||||
\(428\) | 1.63939e7i | 4.32587i | ||||||||
\(429\) | −5.02406e6 | − | 1.54735e6i | −1.31799 | − | 0.405924i | ||||
\(430\) | 6.89251e6 | 1.79766 | ||||||||
\(431\) | −2.94982e6 | −0.764896 | −0.382448 | − | 0.923977i | \(-0.624919\pi\) | ||||
−0.382448 | + | 0.923977i | \(0.624919\pi\) | |||||||
\(432\) | −1.13956e7 | + | 9.11185e6i | −2.93785 | + | 2.34908i | ||||
\(433\) | 4.16711e6 | 1.06811 | 0.534054 | − | 0.845450i | \(-0.320668\pi\) | ||||
0.534054 | + | 0.845450i | \(0.320668\pi\) | |||||||
\(434\) | − | 4.18345e6i | − | 1.06613i | ||||||
\(435\) | 2.98694e6 | − | 9.69827e6i | 0.756839 | − | 2.45737i | ||||
\(436\) | − | 1.83127e7i | − | 4.61357i | ||||||
\(437\) | 67746.4 | 0.0169700 | ||||||||
\(438\) | 9.70867e6 | + | 2.99015e6i | 2.41810 | + | 0.744744i | ||||
\(439\) | 1.65701e6 | 0.410359 | 0.205180 | − | 0.978724i | \(-0.434222\pi\) | ||||
0.205180 | + | 0.978724i | \(0.434222\pi\) | |||||||
\(440\) | − | 2.89639e7i | − | 7.13222i | ||||||
\(441\) | −5.62685e6 | − | 3.82922e6i | −1.37774 | − | 0.937591i | ||||
\(442\) | 1.47978e6 | 0.360282 | ||||||||
\(443\) | −4.88064e6 | −1.18159 | −0.590796 | − | 0.806821i | \(-0.701186\pi\) | ||||
−0.590796 | + | 0.806821i | \(0.701186\pi\) | |||||||
\(444\) | 1.72877e7 | + | 5.32440e6i | 4.16179 | + | 1.28178i | ||||
\(445\) | − | 4.73350e6i | − | 1.13314i | ||||||
\(446\) | −1.34746e6 | −0.320758 | ||||||||
\(447\) | 1.56927e6 | − | 5.09523e6i | 0.371473 | − | 1.20613i | ||||
\(448\) | 2.63695e7 | 6.20735 | ||||||||
\(449\) | 4.26247e6i | 0.997803i | 0.866659 | + | 0.498902i | \(0.166263\pi\) | ||||
−0.866659 | + | 0.498902i | \(0.833737\pi\) | |||||||
\(450\) | −8.17966e6 | − | 5.56648e6i | −1.90416 | − | 1.29583i | ||||
\(451\) | − | 162387.i | − | 0.0375933i | ||||||
\(452\) | 1.50008e7 | 3.45358 | ||||||||
\(453\) | 1.63892e6 | + | 504767.i | 0.375244 | + | 0.115570i | ||||
\(454\) | −7.30861e6 | −1.66416 | ||||||||
\(455\) | 1.02711e7 | 2.32588 | ||||||||
\(456\) | −110145. | + | 357628.i | −0.0248057 | + | 0.0805414i | ||||
\(457\) | 3.75535e6i | 0.841123i | 0.907264 | + | 0.420561i | \(0.138167\pi\) | ||||
−0.907264 | + | 0.420561i | \(0.861833\pi\) | |||||||
\(458\) | 5.98598e6i | 1.33343i | ||||||||
\(459\) | 545852. | + | 682664.i | 0.120933 | + | 0.151243i | ||||
\(460\) | 1.24545e7i | 2.74429i | ||||||||
\(461\) | − | 4.23096e6i | − | 0.927229i | −0.886037 | − | 0.463614i | \(-0.846552\pi\) | ||
0.886037 | − | 0.463614i | \(-0.153448\pi\) | |||||||
\(462\) | −6.11087e6 | + | 1.98413e7i | −1.33198 | + | 4.32480i | ||||
\(463\) | 8.02997e6i | 1.74085i | 0.492301 | + | 0.870425i | \(0.336156\pi\) | ||||
−0.492301 | + | 0.870425i | \(0.663844\pi\) | |||||||
\(464\) | − | 3.03017e7i | − | 6.53390i | ||||||
\(465\) | −685977. | + | 2.22729e6i | −0.147122 | + | 0.477688i | ||||
\(466\) | 1.07038e7 | 2.28335 | ||||||||
\(467\) | −6.56680e6 | −1.39336 | −0.696678 | − | 0.717384i | \(-0.745339\pi\) | ||||
−0.696678 | + | 0.717384i | \(0.745339\pi\) | |||||||
\(468\) | −7.02475e6 | + | 1.03225e7i | −1.48257 | + | 2.17857i | ||||
\(469\) | − | 2.07849e6i | − | 0.436331i | ||||||
\(470\) | − | 1.13652e7i | − | 2.37318i | ||||||
\(471\) | 5.06463e6 | + | 1.55984e6i | 1.05195 | + | 0.323988i | ||||
\(472\) | −3.19772e6 | + | 1.59540e7i | −0.660670 | + | 3.29621i | ||||
\(473\) | 4.38002e6i | 0.900168i | ||||||||
\(474\) | −221797. | + | 720149.i | −0.0453429 | + | 0.147223i | ||||
\(475\) | −146842. | −0.0298618 | ||||||||
\(476\) | − | 4.28090e6i | − | 0.866000i | ||||||
\(477\) | 1.26929e6 | − | 1.86517e6i | 0.255427 | − | 0.375337i | ||||
\(478\) | 4.82542e6i | 0.965974i | ||||||||
\(479\) | 8.13362e6i | 1.61974i | 0.586610 | + | 0.809870i | \(0.300462\pi\) | ||||
−0.586610 | + | 0.809870i | \(0.699538\pi\) | |||||||
\(480\) | −2.79315e7 | − | 8.60255e6i | −5.53339 | − | 1.70421i | ||||
\(481\) | 7.76356e6 | 1.53002 | ||||||||
\(482\) | −5.00255e6 | −0.980786 | ||||||||
\(483\) | 1.66819e6 | − | 5.41644e6i | 0.325371 | − | 1.05644i | ||||
\(484\) | 1.48782e7 | 2.88693 | ||||||||
\(485\) | 3.38361e6 | 0.653170 | ||||||||
\(486\) | −1.00383e7 | + | 774030.i | −1.92784 | + | 0.148651i | ||||
\(487\) | −5.76281e6 | −1.10106 | −0.550532 | − | 0.834814i | \(-0.685575\pi\) | ||||
−0.550532 | + | 0.834814i | \(0.685575\pi\) | |||||||
\(488\) | 1.05350e7i | 2.00255i | ||||||||
\(489\) | 737269. | − | 2.39383e6i | 0.139429 | − | 0.452711i | ||||
\(490\) | − | 2.53511e7i | − | 4.76987i | ||||||
\(491\) | 29783.7i | 0.00557538i | 0.999996 | + | 0.00278769i | \(0.000887351\pi\) | ||||
−0.999996 | + | 0.00278769i | \(0.999113\pi\) | |||||||
\(492\) | −368608. | − | 113527.i | −0.0686518 | − | 0.0211439i | ||||
\(493\) | −1.81525e6 | −0.336371 | ||||||||
\(494\) | 252976.i | 0.0466403i | ||||||||
\(495\) | 6.50692e6 | − | 9.56160e6i | 1.19361 | − | 1.75395i | ||||
\(496\) | 6.95906e6i | 1.27012i | ||||||||
\(497\) | 2.63862e6i | 0.479166i | ||||||||
\(498\) | −1.97839e6 | + | 6.42360e6i | −0.357468 | + | 1.16066i | ||||
\(499\) | −6.44186e6 | −1.15814 | −0.579068 | − | 0.815279i | \(-0.696584\pi\) | ||||
−0.579068 | + | 0.815279i | \(0.696584\pi\) | |||||||
\(500\) | − | 4.33313e6i | − | 0.775133i | ||||||
\(501\) | −4.63574e6 | − | 1.42775e6i | −0.825135 | − | 0.254131i | ||||
\(502\) | 1.01601e7i | 1.79944i | ||||||||
\(503\) | 8.29145e6 | 1.46120 | 0.730601 | − | 0.682805i | \(-0.239240\pi\) | ||||
0.730601 | + | 0.682805i | \(0.239240\pi\) | |||||||
\(504\) | 2.58807e7 | + | 1.76125e7i | 4.53837 | + | 3.08848i | ||||
\(505\) | − | 9.27406e6i | − | 1.61823i | ||||||
\(506\) | −1.08044e7 | −1.87597 | ||||||||
\(507\) | 126291. | − | 410052.i | 0.0218199 | − | 0.0708467i | ||||
\(508\) | −873550. | −0.150186 | ||||||||
\(509\) | −8.34624e6 | −1.42789 | −0.713947 | − | 0.700199i | \(-0.753094\pi\) | ||||
−0.713947 | + | 0.700199i | \(0.753094\pi\) | |||||||
\(510\) | −958272. | + | 3.11140e6i | −0.163141 | + | 0.529701i | ||||
\(511\) | − | 1.26130e7i | − | 2.13682i | ||||||
\(512\) | −1.22626e7 | −2.06732 | ||||||||
\(513\) | −116704. | + | 93315.9i | −0.0195792 | + | 0.0156553i | ||||
\(514\) | 7.01428e6i | 1.17105i | ||||||||
\(515\) | −305087. | −0.0506881 | ||||||||
\(516\) | 9.94236e6 | + | 3.06212e6i | 1.64386 | + | 0.506288i | ||||
\(517\) | 7.22228e6 | 1.18836 | ||||||||
\(518\) | − | 3.06603e7i | − | 5.02056i | ||||||
\(519\) | −3.47123e6 | + | 1.12707e7i | −0.565673 | + | 1.83668i | ||||
\(520\) | −2.95252e7 | −4.78833 | ||||||||
\(521\) | − | 9.84429e6i | − | 1.58888i | −0.607345 | − | 0.794438i | \(-0.707765\pi\) | ||
0.607345 | − | 0.794438i | \(-0.292235\pi\) | |||||||
\(522\) | 1.17638e7 | − | 1.72863e7i | 1.88960 | − | 2.77668i | ||||
\(523\) | −5.24419e6 | −0.838348 | −0.419174 | − | 0.907906i | \(-0.637680\pi\) | ||||
−0.419174 | + | 0.907906i | \(0.637680\pi\) | |||||||
\(524\) | 1.58893e7 | 2.52800 | ||||||||
\(525\) | −3.61585e6 | + | 1.17403e7i | −0.572548 | + | 1.85900i | ||||
\(526\) | − | 1.54981e7i | − | 2.44239i | ||||||
\(527\) | 416888. | 0.0653872 | ||||||||
\(528\) | 1.01653e7 | − | 3.30055e7i | 1.58684 | − | 5.15231i | ||||
\(529\) | −3.48687e6 | −0.541747 | ||||||||
\(530\) | 8.40329e6 | 1.29945 | ||||||||
\(531\) | −4.63981e6 | + | 4.54838e6i | −0.714108 | + | 0.700036i | ||||
\(532\) | 731840. | 0.112108 | ||||||||
\(533\) | −165534. | −0.0252389 | ||||||||
\(534\) | 2.87082e6 | − | 9.32122e6i | 0.435664 | − | 1.41455i | ||||
\(535\) | −1.54797e7 | −2.33819 | ||||||||
\(536\) | 5.97482e6i | 0.898282i | ||||||||
\(537\) | 2.17462e6 | − | 7.06074e6i | 0.325422 | − | 1.05661i | ||||
\(538\) | −1.18017e7 | −1.75789 | ||||||||
\(539\) | 1.61100e7 | 2.38849 | ||||||||
\(540\) | −1.71551e7 | − | 2.14549e7i | −2.53169 | − | 3.16623i | ||||
\(541\) | 1.21868e7i | 1.79018i | 0.445881 | + | 0.895092i | \(0.352890\pi\) | ||||
−0.445881 | + | 0.895092i | \(0.647110\pi\) | |||||||
\(542\) | −1.73823e7 | −2.54161 | ||||||||
\(543\) | 962218. | − | 3.12421e6i | 0.140047 | − | 0.454717i | ||||
\(544\) | 5.22801e6i | 0.757424i | ||||||||
\(545\) | 1.72916e7 | 2.49369 | ||||||||
\(546\) | 2.02258e7 | + | 6.22930e6i | 2.90352 | + | 0.894247i | ||||
\(547\) | 750385. | 0.107230 | 0.0536149 | − | 0.998562i | \(-0.482926\pi\) | ||||
0.0536149 | + | 0.998562i | \(0.482926\pi\) | |||||||
\(548\) | 2.10418e6i | 0.299317i | ||||||||
\(549\) | −2.36675e6 | + | 3.47782e6i | −0.335136 | + | 0.492466i | ||||
\(550\) | 2.34189e7 | 3.30110 | ||||||||
\(551\) | − | 310325.i | − | 0.0435449i | ||||||
\(552\) | −4.79537e6 | + | 1.55701e7i | −0.669846 | + | 2.17492i | ||||
\(553\) | 935583. | 0.130098 | ||||||||
\(554\) | 1.12573e7 | 1.55833 | ||||||||
\(555\) | −5.02749e6 | + | 1.63237e7i | −0.692818 | + | 2.24950i | ||||
\(556\) | 1.95897e7 | 2.68746 | ||||||||
\(557\) | − | 984038.i | − | 0.134392i | −0.997740 | − | 0.0671961i | \(-0.978595\pi\) | ||
0.997740 | − | 0.0671961i | \(-0.0214053\pi\) | |||||||
\(558\) | −2.70165e6 | + | 3.96995e6i | −0.367320 | + | 0.539758i | ||||
\(559\) | 4.46491e6 | 0.604342 | ||||||||
\(560\) | 6.74758e7i | 9.09238i | ||||||||
\(561\) | −1.97722e6 | − | 608958.i | −0.265245 | − | 0.0816921i | ||||
\(562\) | 7.40777e6i | 0.989343i | ||||||||
\(563\) | 1.88523e6 | 0.250664 | 0.125332 | − | 0.992115i | \(-0.460000\pi\) | ||||
0.125332 | + | 0.992115i | \(0.460000\pi\) | |||||||
\(564\) | 5.04917e6 | − | 1.63941e7i | 0.668378 | − | 2.17015i | ||||
\(565\) | 1.41643e7i | 1.86670i | ||||||||
\(566\) | − | 4.87701e6i | − | 0.639901i | ||||||
\(567\) | 4.58702e6 | + | 1.16285e7i | 0.599202 | + | 1.51903i | ||||
\(568\) | − | 7.58496e6i | − | 0.986466i | ||||||
\(569\) | −9.06285e6 | −1.17350 | −0.586751 | − | 0.809767i | \(-0.699593\pi\) | ||||
−0.586751 | + | 0.809767i | \(0.699593\pi\) | |||||||
\(570\) | −531908. | − | 163821.i | −0.0685724 | − | 0.0211194i | ||||
\(571\) | − | 2.73395e6i | − | 0.350914i | −0.984487 | − | 0.175457i | \(-0.943860\pi\) | ||
0.984487 | − | 0.175457i | \(-0.0561403\pi\) | |||||||
\(572\) | − | 2.95540e7i | − | 3.77682i | ||||||
\(573\) | −894186. | + | 2.90332e6i | −0.113774 | + | 0.369410i | ||||
\(574\) | 653738.i | 0.0828178i | ||||||||
\(575\) | −6.39306e6 | −0.806379 | ||||||||
\(576\) | −2.50237e7 | − | 1.70293e7i | −3.14264 | − | 2.13865i | ||||
\(577\) | −1.88079e6 | −0.235181 | −0.117590 | − | 0.993062i | \(-0.537517\pi\) | ||||
−0.117590 | + | 0.993062i | \(0.537517\pi\) | |||||||
\(578\) | −1.49478e7 | −1.86105 | ||||||||
\(579\) | 2.33766e6 | − | 7.59012e6i | 0.289791 | − | 0.940918i | ||||
\(580\) | 5.70499e7 | 7.04182 | ||||||||
\(581\) | 8.34523e6 | 1.02565 | ||||||||
\(582\) | 6.66301e6 | + | 2.05212e6i | 0.815386 | + | 0.251128i | ||||
\(583\) | 5.34008e6i | 0.650694i | ||||||||
\(584\) | 3.62574e7i | 4.39910i | ||||||||
\(585\) | −9.74690e6 | − | 6.63302e6i | −1.17754 | − | 0.801349i | ||||
\(586\) | − | 1.05945e7i | − | 1.27449i | ||||||
\(587\) | −9.02658e6 | −1.08125 | −0.540627 | − | 0.841262i | \(-0.681813\pi\) | ||||
−0.540627 | + | 0.841262i | \(0.681813\pi\) | |||||||
\(588\) | 1.12627e7 | − | 3.65686e7i | 1.34338 | − | 4.36179i | ||||
\(589\) | 71268.8i | 0.00846469i | ||||||||
\(590\) | −2.37288e7 | − | 4.75604e6i | −2.80638 | − | 0.562491i | ||||
\(591\) | 4.88073e6 | + | 1.50320e6i | 0.574799 | + | 0.177031i | ||||
\(592\) | 5.10026e7i | 5.98120i | ||||||||
\(593\) | − | 3.53803e6i | − | 0.413166i | −0.978429 | − | 0.206583i | \(-0.933766\pi\) | ||
0.978429 | − | 0.206583i | \(-0.0662343\pi\) | |||||||
\(594\) | 1.86124e7 | − | 1.48823e7i | 2.16440 | − | 1.73063i | ||||
\(595\) | 4.04219e6 | 0.468084 | ||||||||
\(596\) | 2.99726e7 | 3.45628 | ||||||||
\(597\) | −2.39077e6 | + | 7.76256e6i | −0.274537 | + | 0.891393i | ||||
\(598\) | 1.10138e7i | 1.25946i | ||||||||
\(599\) | 1.42114e7i | 1.61834i | 0.587574 | + | 0.809170i | \(0.300083\pi\) | ||||
−0.587574 | + | 0.809170i | \(0.699917\pi\) | |||||||
\(600\) | 1.03941e7 | − | 3.37485e7i | 1.17871 | − | 3.82715i | ||||
\(601\) | 1.35365e7i | 1.52869i | 0.644806 | + | 0.764346i | \(0.276938\pi\) | ||||
−0.644806 | + | 0.764346i | \(0.723062\pi\) | |||||||
\(602\) | − | 1.76331e7i | − | 1.98306i | ||||||
\(603\) | −1.34228e6 | + | 1.97242e6i | −0.150332 | + | 0.220905i | ||||
\(604\) | 9.64095e6i | 1.07529i | ||||||||
\(605\) | 1.40485e7i | 1.56042i | ||||||||
\(606\) | 5.62461e6 | − | 1.82625e7i | 0.622173 | − | 2.02013i | ||||
\(607\) | −5004.17 | −0.000551265 | −0.000275633 | − | 1.00000i | \(-0.500088\pi\) | ||||
−0.000275633 | 1.00000i | \(0.500088\pi\) | ||||||||
\(608\) | −893752. | −0.0980523 | ||||||||
\(609\) | −2.48110e7 | − | 7.64147e6i | −2.71082 | − | 0.834898i | ||||
\(610\) | −1.56689e7 | −1.70496 | ||||||||
\(611\) | − | 7.36224e6i | − | 0.797824i | ||||||
\(612\) | −2.76459e6 | + | 4.06243e6i | −0.298368 | + | 0.438437i | ||||
\(613\) | − | 9.45865e6i | − | 1.01667i | −0.861161 | − | 0.508333i | \(-0.830262\pi\) | ||
0.861161 | − | 0.508333i | \(-0.169738\pi\) | |||||||
\(614\) | 1.03045e7 | 1.10308 | ||||||||
\(615\) | 107196. | − | 348053.i | 0.0114285 | − | 0.0371072i | ||||
\(616\) | −7.40981e7 | −7.86783 | ||||||||
\(617\) | 1.35592e7i | 1.43391i | 0.697120 | + | 0.716954i | \(0.254464\pi\) | ||||
−0.697120 | + | 0.716954i | \(0.745536\pi\) | |||||||
\(618\) | −600778. | − | 185032.i | −0.0632766 | − | 0.0194884i | ||||
\(619\) | 6.13962e6 | 0.644043 | 0.322022 | − | 0.946732i | \(-0.395638\pi\) | ||||
0.322022 | + | 0.946732i | \(0.395638\pi\) | |||||||
\(620\) | −1.31020e7 | −1.36886 | ||||||||
\(621\) | −5.08097e6 | + | 4.06270e6i | −0.528710 | + | 0.422752i | ||||
\(622\) | − | 2.45085e7i | − | 2.54004i | ||||||
\(623\) | −1.21097e7 | −1.25001 | ||||||||
\(624\) | −3.36451e7 | − | 1.03623e7i | −3.45908 | − | 1.06535i | ||||
\(625\) | −7.54136e6 | −0.772236 | ||||||||
\(626\) | 1.86138e7i | 1.89845i | ||||||||
\(627\) | 104104. | − | 338015.i | 0.0105755 | − | 0.0343373i | ||||
\(628\) | 2.97927e7i | 3.01446i | ||||||||
\(629\) | 3.05535e6 | 0.307917 | ||||||||
\(630\) | −2.61955e7 | + | 3.84930e7i | −2.62952 | + | 3.86394i | ||||
\(631\) | 1.01365e7 | 1.01348 | 0.506739 | − | 0.862099i | \(-0.330851\pi\) | ||||
0.506739 | + | 0.862099i | \(0.330851\pi\) | |||||||
\(632\) | −2.68942e6 | −0.267834 | ||||||||
\(633\) | 8.30877e6 | + | 2.55900e6i | 0.824191 | + | 0.253840i | ||||
\(634\) | − | 7.05644e6i | − | 0.697208i | ||||||
\(635\) | − | 824837.i | − | 0.0811772i | ||||||
\(636\) | 1.21216e7 | + | 3.73331e6i | 1.18828 | + | 0.365974i | ||||
\(637\) | − | 1.64222e7i | − | 1.60355i | ||||||
\(638\) | 4.94917e7i | 4.81372i | ||||||||
\(639\) | 1.70401e6 | − | 2.50396e6i | 0.165090 | − | 0.242591i | ||||
\(640\) | − | 5.27456e7i | − | 5.09022i | ||||||
\(641\) | − | 1.31805e7i | − | 1.26703i | −0.773731 | − | 0.633514i | \(-0.781612\pi\) | ||
0.773731 | − | 0.633514i | \(-0.218388\pi\) | |||||||
\(642\) | −3.04827e7 | − | 9.38828e6i | −2.91888 | − | 0.898977i | ||||
\(643\) | 1.28000e7 | 1.22091 | 0.610453 | − | 0.792053i | \(-0.290988\pi\) | ||||
0.610453 | + | 0.792053i | \(0.290988\pi\) | |||||||
\(644\) | 3.18621e7 | 3.02733 | ||||||||
\(645\) | −2.89136e6 | + | 9.38794e6i | −0.273655 | + | 0.888528i | ||||
\(646\) | 99558.6i | 0.00938636i | ||||||||
\(647\) | − | 1.22343e7i | − | 1.14900i | −0.818506 | − | 0.574498i | \(-0.805197\pi\) | ||
0.818506 | − | 0.574498i | \(-0.194803\pi\) | |||||||
\(648\) | −1.31858e7 | − | 3.34273e7i | −1.23359 | − | 3.12726i | ||||
\(649\) | 3.02235e6 | − | 1.50791e7i | 0.281665 | − | 1.40528i | ||||
\(650\) | − | 2.38727e7i | − | 2.21625i | ||||||
\(651\) | 5.69806e6 | + | 1.75493e6i | 0.526957 | + | 0.162296i | ||||
\(652\) | 1.40817e7 | 1.29729 | ||||||||
\(653\) | 6.66464e6i | 0.611637i | 0.952090 | + | 0.305818i | \(0.0989300\pi\) | ||||
−0.952090 | + | 0.305818i | \(0.901070\pi\) | |||||||
\(654\) | 3.40506e7 | + | 1.04871e7i | 3.11301 | + | 0.958766i | ||||
\(655\) | 1.50033e7i | 1.36642i | ||||||||
\(656\) | − | 1.08747e6i | − | 0.0986642i | ||||||
\(657\) | −8.14545e6 | + | 1.19693e7i | −0.736210 | + | 1.08182i | ||||
\(658\) | −2.90754e7 | −2.61795 | ||||||||
\(659\) | 7.72743e6 | 0.693141 | 0.346570 | − | 0.938024i | \(-0.387346\pi\) | ||||
0.346570 | + | 0.938024i | \(0.387346\pi\) | |||||||
\(660\) | 6.21404e7 | + | 1.91384e7i | 5.55283 | + | 1.71020i | ||||
\(661\) | −1.82927e7 | −1.62845 | −0.814227 | − | 0.580547i | \(-0.802839\pi\) | ||||
−0.814227 | + | 0.580547i | \(0.802839\pi\) | |||||||
\(662\) | −1.05516e7 | −0.935775 | ||||||||
\(663\) | −620759. | + | 2.01554e6i | −0.0548453 | + | 0.178077i | ||||
\(664\) | −2.39891e7 | −2.11152 | ||||||||
\(665\) | 691030.i | 0.0605958i | ||||||||
\(666\) | −1.98003e7 | + | 2.90956e7i | −1.72976 | + | 2.54180i | ||||
\(667\) | − | 1.35106e7i | − | 1.17587i | ||||||
\(668\) | − | 2.72697e7i | − | 2.36450i | ||||||
\(669\) | 565249. | − | 1.83530e6i | 0.0488286 | − | 0.158541i | ||||
\(670\) | −8.88649e6 | −0.764792 | ||||||||
\(671\) | − | 9.95720e6i | − | 0.853751i | ||||||
\(672\) | −2.20078e7 | + | 7.14570e7i | −1.87998 | + | 6.10410i | ||||
\(673\) | − | 5.36267e6i | − | 0.456398i | −0.973615 | − | 0.228199i | \(-0.926716\pi\) | ||
0.973615 | − | 0.228199i | \(-0.0732836\pi\) | |||||||
\(674\) | 6.52908e6i | 0.553608i | ||||||||
\(675\) | 1.10131e7 | − | 8.80600e6i | 0.930360 | − | 0.743908i | ||||
\(676\) | 2.41213e6 | 0.203018 | ||||||||
\(677\) | − | 7.82835e6i | − | 0.656445i | −0.944600 | − | 0.328222i | \(-0.893550\pi\) | ||
0.944600 | − | 0.328222i | \(-0.106450\pi\) | |||||||
\(678\) | −8.59051e6 | + | 2.78924e7i | −0.717703 | + | 2.33030i | ||||
\(679\) | − | 8.65627e6i | − | 0.720537i | ||||||
\(680\) | −1.16196e7 | −0.963652 | ||||||||
\(681\) | 3.06591e6 | − | 9.95469e6i | 0.253333 | − | 0.822545i | ||||
\(682\) | − | 1.13662e7i | − | 0.935738i | ||||||
\(683\) | 1.11818e6 | 0.0917191 | 0.0458596 | − | 0.998948i | \(-0.485397\pi\) | ||||
0.0458596 | + | 0.998948i | \(0.485397\pi\) | |||||||
\(684\) | −694490. | − | 472619.i | −0.0567578 | − | 0.0386252i | ||||
\(685\) | −1.98684e6 | −0.161784 | ||||||||
\(686\) | −2.59386e7 | −2.10444 | ||||||||
\(687\) | −8.15319e6 | − | 2.51108e6i | −0.659076 | − | 0.202987i | ||||
\(688\) | 2.93321e7i | 2.36250i | ||||||||
\(689\) | 5.44357e6 | 0.436854 | ||||||||
\(690\) | −2.31577e7 | − | 7.13228e6i | −1.85171 | − | 0.570303i | ||||
\(691\) | − | 2.04795e6i | − | 0.163164i | −0.996667 | − | 0.0815818i | \(-0.974003\pi\) | ||
0.996667 | − | 0.0815818i | \(-0.0259972\pi\) | |||||||
\(692\) | −6.62998e7 | −5.26317 | ||||||||
\(693\) | −2.44614e7 | − | 1.66466e7i | −1.93485 | − | 1.31672i | ||||
\(694\) | 6.13124e6 | 0.483225 | ||||||||
\(695\) | 1.84974e7i | 1.45261i | ||||||||
\(696\) | 7.13215e7 | + | 2.19661e7i | 5.58081 | + | 1.71882i | ||||
\(697\) | −65146.0 | −0.00507932 | ||||||||
\(698\) | 3.48446e7i | 2.70706i | ||||||||
\(699\) | −4.49017e6 | + | 1.45791e7i | −0.347592 | + | 1.12859i | ||||
\(700\) | −6.90620e7 | −5.32714 | ||||||||
\(701\) | −8.72479e6 | −0.670594 | −0.335297 | − | 0.942112i | \(-0.608837\pi\) | ||||
−0.335297 | + | 0.942112i | \(0.608837\pi\) | |||||||
\(702\) | −1.51708e7 | − | 1.89731e7i | −1.16189 | − | 1.45310i | ||||
\(703\) | 522326.i | 0.0398614i | ||||||||
\(704\) | 7.16443e7 | 5.44816 | ||||||||
\(705\) | 1.54799e7 | + | 4.76761e6i | 1.17299 | + | 0.361267i | ||||
\(706\) | 3.41316e7 | 2.57718 | ||||||||
\(707\) | −2.37258e7 | −1.78514 | ||||||||
\(708\) | −3.21155e7 | − | 1.74024e7i | −2.40786 | − | 1.30475i | ||||
\(709\) | −2.37271e7 | −1.77268 | −0.886338 | − | 0.463038i | \(-0.846759\pi\) | ||||
−0.886338 | + | 0.463038i | \(0.846759\pi\) | |||||||
\(710\) | 1.12813e7 | 0.839872 | ||||||||
\(711\) | −887835. | − | 604195.i | −0.0658656 | − | 0.0448233i | ||||
\(712\) | 3.48104e7 | 2.57341 | ||||||||
\(713\) | 3.10283e6i | 0.228578i | ||||||||
\(714\) | 7.95988e6 | + | 2.45154e6i | 0.584334 | + | 0.179967i | ||||
\(715\) | 2.79060e7 | 2.04142 | ||||||||
\(716\) | 4.15347e7 | 3.02781 | ||||||||
\(717\) | −6.57245e6 | − | 2.02423e6i | −0.477452 | − | 0.147049i | ||||
\(718\) | − | 1.26758e7i | − | 0.917621i | ||||||
\(719\) | −1.98910e7 | −1.43495 | −0.717473 | − | 0.696586i | \(-0.754701\pi\) | ||||
−0.717473 | + | 0.696586i | \(0.754701\pi\) | |||||||
\(720\) | 4.35755e7 | − | 6.40321e7i | 3.13265 | − | 4.60327i | ||||
\(721\) | 780502.i | 0.0559160i | ||||||||
\(722\) | 2.70662e7 | 1.93234 | ||||||||
\(723\) | 2.09854e6 | − | 6.81372e6i | 0.149304 | − | 0.484773i | ||||
\(724\) | 1.83782e7 | 1.30303 | ||||||||
\(725\) | 2.92846e7i | 2.06916i | ||||||||
\(726\) | −8.52026e6 | + | 2.76643e7i | −0.599945 | + | 1.94795i | ||||
\(727\) | 1.36021e7 | 0.954489 | 0.477244 | − | 0.878771i | \(-0.341636\pi\) | ||||
0.477244 | + | 0.878771i | \(0.341636\pi\) | |||||||
\(728\) | 7.55341e7i | 5.28220i | ||||||||
\(729\) | 3.15674e6 | − | 1.39974e7i | 0.219998 | − | 0.975500i | ||||
\(730\) | −5.39264e7 | −3.74537 | ||||||||
\(731\) | 1.75716e6 | 0.121624 | ||||||||
\(732\) | −2.26022e7 | − | 6.96118e6i | −1.55910 | − | 0.480181i | ||||
\(733\) | 1.37934e7 | 0.948224 | 0.474112 | − | 0.880465i | \(-0.342769\pi\) | ||||
0.474112 | + | 0.880465i | \(0.342769\pi\) | |||||||
\(734\) | − | 5.09157e7i | − | 3.48828i | ||||||
\(735\) | 3.45294e7 | + | 1.06346e7i | 2.35760 | + | 0.726112i | ||||
\(736\) | −3.89113e7 | −2.64778 | ||||||||
\(737\) | − | 5.64714e6i | − | 0.382966i | ||||||
\(738\) | 422181. | − | 620374.i | 0.0285337 | − | 0.0419288i | ||||
\(739\) | − | 8.43574e6i | − | 0.568214i | −0.958793 | − | 0.284107i | \(-0.908303\pi\) | ||
0.958793 | − | 0.284107i | \(-0.0916971\pi\) | |||||||
\(740\) | −9.60240e7 | −6.44615 | ||||||||
\(741\) | −344565. | − | 106122.i | −0.0230529 | − | 0.00710000i | ||||
\(742\) | − | 2.14981e7i | − | 1.43347i | ||||||
\(743\) | − | 2.88582e7i | − | 1.91777i | −0.283794 | − | 0.958885i | \(-0.591593\pi\) | ||
0.283794 | − | 0.958885i | \(-0.408407\pi\) | |||||||
\(744\) | −1.63796e7 | − | 5.04471e6i | −1.08485 | − | 0.334121i | ||||
\(745\) | 2.83013e7i | 1.86816i | ||||||||
\(746\) | 4.71395e7 | 3.10126 | ||||||||
\(747\) | −7.91933e6 | − | 5.38931e6i | −0.519263 | − | 0.353372i | ||||
\(748\) | − | 1.16310e7i | − | 0.760085i | ||||||
\(749\) | 3.96017e7i | 2.57934i | ||||||||
\(750\) | 8.05698e6 | + | 2.48145e6i | 0.523021 | + | 0.161084i | ||||
\(751\) | − | 1.56331e7i | − | 1.01145i | −0.862694 | − | 0.505726i | \(-0.831225\pi\) | ||
0.862694 | − | 0.505726i | \(-0.168775\pi\) | |||||||
\(752\) | 4.83661e7 | 3.11887 | ||||||||
\(753\) | −1.38385e7 | − | 4.26208e6i | −0.889410 | − | 0.273927i | ||||
\(754\) | 5.04508e7 | 3.23177 | ||||||||
\(755\) | −9.10334e6 | −0.581210 | ||||||||
\(756\) | −5.48879e7 | + | 4.38879e7i | −3.49279 | + | 2.79280i | ||||
\(757\) | −2.27834e7 | −1.44504 | −0.722518 | − | 0.691352i | \(-0.757015\pi\) | ||||
−0.722518 | + | 0.691352i | \(0.757015\pi\) | |||||||
\(758\) | 5.19699e7 | 3.28533 | ||||||||
\(759\) | 4.53239e6 | − | 1.47162e7i | 0.285576 | − | 0.927235i | ||||
\(760\) | − | 1.98643e6i | − | 0.124750i | ||||||
\(761\) | 1.72608e7i | 1.08044i | 0.841524 | + | 0.540220i | \(0.181659\pi\) | ||||
−0.841524 | + | 0.540220i | \(0.818341\pi\) | |||||||
\(762\) | 500255. | − | 1.62427e6i | 0.0312107 | − | 0.101338i | ||||
\(763\) | − | 4.42369e7i | − | 2.75089i | ||||||
\(764\) | −1.70788e7 | −1.05858 | ||||||||
\(765\) | −3.83589e6 | − | 2.61043e6i | −0.236981 | − | 0.161272i | ||||
\(766\) | − | 7.45841e6i | − | 0.459277i | ||||||
\(767\) | −1.53713e7 | − | 3.08092e6i | −0.943457 | − | 0.189100i | ||||
\(768\) | 1.37006e7 | − | 4.44842e7i | 0.838177 | − | 2.72147i | ||||
\(769\) | − | 5.09443e6i | − | 0.310656i | −0.987863 | − | 0.155328i | \(-0.950357\pi\) | ||
0.987863 | − | 0.155328i | \(-0.0496434\pi\) | |||||||
\(770\) | − | 1.10208e8i | − | 6.69863i | ||||||
\(771\) | −9.55379e6 | − | 2.94244e6i | −0.578815 | − | 0.178267i | ||||
\(772\) | 4.46488e7 | 2.69629 | ||||||||
\(773\) | −2.45291e7 | −1.47650 | −0.738250 | − | 0.674527i | \(-0.764348\pi\) | ||||
−0.738250 | + | 0.674527i | \(0.764348\pi\) | |||||||
\(774\) | −1.13874e7 | + | 1.67332e7i | −0.683236 | + | 1.00398i | ||||
\(775\) | − | 6.72547e6i | − | 0.402224i | ||||||
\(776\) | 2.48832e7i | 1.48338i | ||||||||
\(777\) | 4.17608e7 | + | 1.28618e7i | 2.48151 | + | 0.764274i | ||||
\(778\) | 4.44442e7i | 2.63248i | ||||||||
\(779\) | − | 11137.0i | − | 0.000657543i | ||||||
\(780\) | 1.95093e7 | − | 6.33447e7i | 1.14817 | − | 3.72798i | ||||
\(781\) | 7.16898e6i | 0.420562i | ||||||||
\(782\) | 4.33449e6i | 0.253467i | ||||||||
\(783\) | 1.86099e7 | + | 2.32743e7i | 1.08478 | + | 1.35666i | ||||
\(784\) | 1.07885e8 | 6.26863 | ||||||||
\(785\) | −2.81313e7 | −1.62936 | ||||||||
\(786\) | −9.09933e6 | + | 2.95445e7i | −0.525355 | + | 1.70577i | ||||
\(787\) | −2.15653e7 | −1.24114 | −0.620568 | − | 0.784153i | \(-0.713098\pi\) | ||||
−0.620568 | + | 0.784153i | \(0.713098\pi\) | |||||||
\(788\) | 2.87108e7i | 1.64714i | ||||||||
\(789\) | 2.11092e7 | + | 6.50135e6i | 1.20720 | + | 0.371802i | ||||
\(790\) | − | 4.00004e6i | − | 0.228032i | ||||||
\(791\) | 3.62365e7 | 2.05923 | ||||||||
\(792\) | 7.03165e7 | + | 4.78522e7i | 3.98331 | + | 2.71075i | ||||
\(793\) | −1.01502e7 | −0.573179 | ||||||||
\(794\) | − | 3.40070e7i | − | 1.91433i | ||||||
\(795\) | −3.52512e6 | + | 1.14457e7i | −0.197814 | + | 0.642280i | ||||
\(796\) | −4.56632e7 | −2.55437 | ||||||||
\(797\) | 7.29413e6 | 0.406750 | 0.203375 | − | 0.979101i | \(-0.434809\pi\) | ||||
0.203375 | + | 0.979101i | \(0.434809\pi\) | |||||||
\(798\) | −419102. | + | 1.36078e6i | −0.0232977 | + | 0.0756449i | ||||
\(799\) | − | 2.89741e6i | − | 0.160562i | ||||||
\(800\) | 8.43412e7 | 4.65924 | ||||||||
\(801\) | 1.14917e7 | + | 7.82038e6i | 0.632851 | + | 0.430672i | ||||
\(802\) | 2.00373e7 | 1.10003 | ||||||||
\(803\) | − | 3.42689e7i | − | 1.87548i | ||||||
\(804\) | −1.28186e7 | − | 3.94798e6i | −0.699362 | − | 0.215394i | ||||
\(805\) | 3.00854e7i | 1.63631i | ||||||||
\(806\) | −1.15865e7 | −0.628223 | ||||||||
\(807\) | 4.95076e6 | − | 1.60746e7i | 0.267601 | − | 0.868871i | ||||
\(808\) | 6.82019e7 | 3.67509 | ||||||||
\(809\) | −1.51435e7 | −0.813498 | −0.406749 | − | 0.913540i | \(-0.633338\pi\) | ||||
−0.406749 | + | 0.913540i | \(0.633338\pi\) | |||||||
\(810\) | 4.97173e7 | − | 1.96116e7i | 2.66253 | − | 1.05027i | ||||
\(811\) | 2.36256e7i | 1.26134i | 0.776052 | + | 0.630669i | \(0.217219\pi\) | ||||
−0.776052 | + | 0.630669i | \(0.782781\pi\) | |||||||
\(812\) | − | 1.45950e8i | − | 7.76811i | ||||||
\(813\) | 7.29174e6 | − | 2.36755e7i | 0.386906 | − | 1.25624i | ||||
\(814\) | − | 8.33023e7i | − | 4.40652i | ||||||
\(815\) | 1.32964e7i | 0.701199i | ||||||||
\(816\) | −1.32410e7 | − | 4.07807e6i | −0.696140 | − | 0.214402i | ||||
\(817\) | 300395.i | 0.0157448i | ||||||||
\(818\) | 3.99874e7i | 2.08949i | ||||||||
\(819\) | −1.69692e7 | + | 2.49354e7i | −0.883999 | + | 1.29899i | ||||
\(820\) | 2.04742e6 | 0.106334 | ||||||||
\(821\) | 2.39412e7 | 1.23962 | 0.619809 | − | 0.784753i | \(-0.287210\pi\) | ||||
0.619809 | + | 0.784753i | \(0.287210\pi\) | |||||||
\(822\) | −3.91249e6 | − | 1.20500e6i | −0.201964 | − | 0.0622023i | ||||
\(823\) | 2.79178e7i | 1.43675i | 0.695656 | + | 0.718375i | \(0.255114\pi\) | ||||
−0.695656 | + | 0.718375i | \(0.744886\pi\) | |||||||
\(824\) | − | 2.24363e6i | − | 0.115115i | ||||||
\(825\) | −9.82406e6 | + | 3.18976e7i | −0.502523 | + | 1.63164i | ||||
\(826\) | −1.21673e7 | + | 6.07052e7i | −0.620506 | + | 3.09582i | ||||
\(827\) | − | 8.74192e6i | − | 0.444471i | −0.974993 | − | 0.222235i | \(-0.928665\pi\) | ||
0.974993 | − | 0.222235i | \(-0.0713353\pi\) | |||||||
\(828\) | −3.02360e7 | − | 2.05764e7i | −1.53267 | − | 1.04302i | ||||
\(829\) | 5.84445e6 | 0.295364 | 0.147682 | − | 0.989035i | \(-0.452819\pi\) | ||||
0.147682 | + | 0.989035i | \(0.452819\pi\) | |||||||
\(830\) | − | 3.56796e7i | − | 1.79773i | ||||||
\(831\) | −4.72237e6 | + | 1.53330e7i | −0.237223 | + | 0.770238i | ||||
\(832\) | − | 7.30328e7i | − | 3.65771i | ||||||
\(833\) | − | 6.46296e6i | − | 0.322715i | ||||||
\(834\) | −1.12184e7 | + | 3.64250e7i | −0.558492 | + | 1.81336i | ||||
\(835\) | 2.57491e7 | 1.27804 | ||||||||
\(836\) | 1.98837e6 | 0.0983967 | ||||||||
\(837\) | −4.27394e6 | − | 5.34515e6i | −0.210870 | − | 0.263722i | ||||
\(838\) | −5.77182e7 | −2.83924 | ||||||||
\(839\) | −3.40866e7 | −1.67178 | −0.835890 | − | 0.548896i | \(-0.815048\pi\) | ||||
−0.835890 | + | 0.548896i | \(0.815048\pi\) | |||||||
\(840\) | −1.58818e8 | − | 4.89140e7i | −7.76609 | − | 2.39186i | ||||
\(841\) | −4.13768e7 | −2.01728 | ||||||||
\(842\) | 1.43615e7i | 0.698103i | ||||||||
\(843\) | −1.00897e7 | − | 3.10751e6i | −0.489002 | − | 0.150606i | ||||
\(844\) | 4.88763e7i | 2.36179i | ||||||||
\(845\) | 2.27762e6i | 0.109734i | ||||||||
\(846\) | 2.75915e7 | + | 1.87768e7i | 1.32541 | + | 0.901976i | ||||
\(847\) | 3.59402e7 | 1.72136 | ||||||||
\(848\) | 3.57615e7i | 1.70776i | ||||||||
\(849\) | 6.64272e6 | + | 2.04587e6i | 0.316284 | + | 0.0974113i | ||||
\(850\) | − | 9.39510e6i | − | 0.446020i | ||||||
\(851\) | 2.27405e7i | 1.07641i | ||||||||
\(852\) | 1.62731e7 | + | 5.01191e6i | 0.768018 | + | 0.236540i | ||||
\(853\) | −1.73172e7 | −0.814901 | −0.407451 | − | 0.913227i | \(-0.633582\pi\) | ||||
−0.407451 | + | 0.913227i | \(0.633582\pi\) | |||||||
\(854\) | 4.00857e7i | 1.88081i | ||||||||
\(855\) | 446264. | − | 655763.i | 0.0208774 | − | 0.0306783i | ||||
\(856\) | − | 1.13839e8i | − | 5.31013i | ||||||
\(857\) | 2.47376e7 | 1.15055 | 0.575275 | − | 0.817960i | \(-0.304895\pi\) | ||||
0.575275 | + | 0.817960i | \(0.304895\pi\) | |||||||
\(858\) | 5.49525e7 | + | 1.69247e7i | 2.54841 | + | 0.784877i | ||||
\(859\) | − | 1.32435e7i | − | 0.612380i | −0.951970 | − | 0.306190i | \(-0.900946\pi\) | ||
0.951970 | − | 0.306190i | \(-0.0990542\pi\) | |||||||
\(860\) | −5.52244e7 | −2.54616 | ||||||||
\(861\) | −890422. | − | 274239.i | −0.0409344 | − | 0.0126073i | ||||
\(862\) | 3.22647e7 | 1.47897 | ||||||||
\(863\) | 1.95133e7 | 0.891874 | 0.445937 | − | 0.895064i | \(-0.352871\pi\) | ||||
0.445937 | + | 0.895064i | \(0.352871\pi\) | |||||||
\(864\) | 6.70313e7 | − | 5.35976e7i | 3.05487 | − | 2.44265i | ||||
\(865\) | − | 6.26027e7i | − | 2.84481i | ||||||
\(866\) | −4.55793e7 | −2.06525 | ||||||||
\(867\) | 6.27051e6 | − | 2.03597e7i | 0.283306 | − | 0.919862i | ||||
\(868\) | 3.35188e7i | 1.51004i | ||||||||
\(869\) | 2.54193e6 | 0.114186 | ||||||||
\(870\) | −3.26707e7 | + | 1.06078e8i | −1.46339 | + | 4.75147i | ||||
\(871\) | −5.75659e6 | −0.257110 | ||||||||
\(872\) | 1.27163e8i | 5.66330i | ||||||||
\(873\) | −5.59018e6 | + | 8.21450e6i | −0.248251 | + | 0.364792i | ||||
\(874\) | −741000. | −0.0328125 | ||||||||
\(875\) | − | 1.04672e7i | − | 0.462181i | ||||||
\(876\) | −7.77882e7 | − | 2.39577e7i | −3.42494 | − | 1.05484i | ||||
\(877\) | 7.91204e6 | 0.347368 | 0.173684 | − | 0.984801i | \(-0.444433\pi\) | ||||
0.173684 | + | 0.984801i | \(0.444433\pi\) | |||||||
\(878\) | −1.81241e7 | −0.793453 | ||||||||
\(879\) | 1.44302e7 | + | 4.44432e6i | 0.629941 | + | 0.194014i | ||||
\(880\) | 1.83328e8i | 7.98034i | ||||||||
\(881\) | −1.24157e7 | −0.538928 | −0.269464 | − | 0.963010i | \(-0.586846\pi\) | ||||
−0.269464 | + | 0.963010i | \(0.586846\pi\) | |||||||
\(882\) | 6.15456e7 | + | 4.18834e7i | 2.66395 | + | 1.81289i | ||||
\(883\) | −2.25517e7 | −0.973369 | −0.486685 | − | 0.873578i | \(-0.661794\pi\) | ||||
−0.486685 | + | 0.873578i | \(0.661794\pi\) | |||||||
\(884\) | −1.18564e7 | −0.510295 | ||||||||
\(885\) | 1.64320e7 | − | 3.03246e7i | 0.705234 | − | 1.30148i | ||||
\(886\) | 5.33838e7 | 2.28468 | ||||||||
\(887\) | 4.65113e7 | 1.98495 | 0.992475 | − | 0.122448i | \(-0.0390745\pi\) | ||||
0.992475 | + | 0.122448i | \(0.0390745\pi\) | |||||||
\(888\) | −1.20045e8 | − | 3.69724e7i | −5.10873 | − | 1.57342i | ||||
\(889\) | −2.11018e6 | −0.0895497 | ||||||||
\(890\) | 5.17744e7i | 2.19099i | ||||||||
\(891\) | 1.24627e7 | + | 3.15941e7i | 0.525917 | + | 1.33325i | ||||
\(892\) | 1.07961e7 | 0.454314 | ||||||||
\(893\) | 495325. | 0.0207856 | ||||||||
\(894\) | −1.71644e7 | + | 5.57309e7i | −0.718265 | + | 2.33213i | ||||
\(895\) | 3.92186e7i | 1.63657i | ||||||||
\(896\) | −1.34939e8 | −5.61522 | ||||||||
\(897\) | −1.50013e7 | − | 4.62022e6i | −0.622514 | − | 0.191726i | ||||
\(898\) | − | 4.66222e7i | − | 1.92931i | ||||||
\(899\) | 1.42131e7 | 0.586529 | ||||||||
\(900\) | 6.55374e7 | + | 4.45999e7i | 2.69701 | + | 1.83539i | ||||
\(901\) | 2.14232e6 | 0.0879168 | ||||||||
\(902\) | 1.77617e6i | 0.0726888i | ||||||||
\(903\) | 2.40171e7 | + | 7.39695e6i | 0.980169 | + | 0.301879i | ||||
\(904\) | −1.04165e8 | −4.23937 | ||||||||
\(905\) | 1.73533e7i | 0.704306i | ||||||||
\(906\) | −1.79263e7 | − | 5.52107e6i | −0.725555 | − | 0.223462i | ||||
\(907\) | 350883. | 0.0141626 | 0.00708132 | − | 0.999975i | \(-0.497746\pi\) | ||||
0.00708132 | + | 0.999975i | \(0.497746\pi\) | |||||||
\(908\) | 5.85583e7 | 2.35708 | ||||||||
\(909\) | 2.25149e7 | + | 1.53220e7i | 0.903776 | + | 0.615043i | ||||
\(910\) | −1.12344e8 | −4.49723 | ||||||||
\(911\) | − | 9.21882e6i | − | 0.368027i | −0.982924 | − | 0.184013i | \(-0.941091\pi\) | ||
0.982924 | − | 0.184013i | \(-0.0589090\pi\) | |||||||
\(912\) | 697164. | − | 2.26362e6i | 0.0277554 | − | 0.0901188i | ||||
\(913\) | 2.26735e7 | 0.900206 | ||||||||
\(914\) | − | 4.10754e7i | − | 1.62636i | ||||||
\(915\) | 6.57300e6 | − | 2.13418e7i | 0.259544 | − | 0.842711i | ||||
\(916\) | − | 4.79610e7i | − | 1.88864i | ||||||
\(917\) | 3.83828e7 | 1.50735 | ||||||||
\(918\) | −5.97045e6 | − | 7.46688e6i | −0.233830 | − | 0.292437i | ||||
\(919\) | − | 2.74490e7i | − | 1.07210i | −0.844185 | − | 0.536052i | \(-0.819915\pi\) | ||
0.844185 | − | 0.536052i | \(-0.180085\pi\) | |||||||
\(920\) | − | 8.64832e7i | − | 3.36870i | ||||||
\(921\) | −4.32269e6 | + | 1.40353e7i | −0.167921 | + | 0.545221i | ||||
\(922\) | 4.62777e7i | 1.79285i | ||||||||
\(923\) | 7.30791e6 | 0.282351 | ||||||||
\(924\) | 4.89617e7 | − | 1.58973e8i | 1.88659 | − | 6.12554i | ||||
\(925\) | − | 4.92906e7i | − | 1.89413i | ||||||
\(926\) | − | 8.78306e7i | − | 3.36603i | ||||||
\(927\) | 504045. | − | 740669.i | 0.0192650 | − | 0.0283090i | ||||
\(928\) | 1.78240e8i | 6.79417i | ||||||||
\(929\) | 4.06836e6 | 0.154661 | 0.0773303 | − | 0.997006i | \(-0.475360\pi\) | ||||
0.0773303 | + | 0.997006i | \(0.475360\pi\) | |||||||
\(930\) | 7.50312e6 | − | 2.43618e7i | 0.284469 | − | 0.923638i | ||||
\(931\) | 1.10487e6 | 0.0417770 | ||||||||
\(932\) | −8.57614e7 | −3.23409 | ||||||||
\(933\) | 3.33817e7 | + | 1.02811e7i | 1.25546 | + | 0.386667i | ||||
\(934\) | 7.18267e7 | 2.69413 | ||||||||
\(935\) | 1.09824e7 | 0.410835 | ||||||||
\(936\) | 4.87796e7 | − | 7.16792e7i | 1.81990 | − | 2.67426i | ||||
\(937\) | − | 1.26365e7i | − | 0.470196i | −0.971972 | − | 0.235098i | \(-0.924459\pi\) | ||
0.971972 | − | 0.235098i | \(-0.0755411\pi\) | |||||||
\(938\) | 2.27342e7i | 0.843672i | ||||||||
\(939\) | −2.53529e7 | − | 7.80837e6i | −0.938347 | − | 0.288999i | ||||
\(940\) | 9.10603e7i | 3.36132i | ||||||||
\(941\) | 6.96792e6 | 0.256525 | 0.128262 | − | 0.991740i | \(-0.459060\pi\) | ||||
0.128262 | + | 0.991740i | \(0.459060\pi\) | |||||||
\(942\) | −5.53962e7 | − | 1.70613e7i | −2.03401 | − | 0.626449i | ||||
\(943\) | − | 484872.i | − | 0.0177561i | ||||||
\(944\) | 2.02400e7 | − | 1.00981e8i | 0.739233 | − | 3.68818i | ||||
\(945\) | −4.14405e7 | − | 5.18271e7i | −1.50954 | − | 1.88789i | ||||
\(946\) | − | 4.79080e7i | − | 1.74053i | ||||||
\(947\) | 2.68052e7i | 0.971280i | 0.874159 | + | 0.485640i | \(0.161413\pi\) | ||||
−0.874159 | + | 0.485640i | \(0.838587\pi\) | |||||||
\(948\) | 1.77709e6 | − | 5.77000e6i | 0.0642226 | − | 0.208524i | ||||
\(949\) | −3.49330e7 | −1.25913 | ||||||||
\(950\) | 1.60614e6 | 0.0577395 | ||||||||
\(951\) | 9.61121e6 | + | 2.96013e6i | 0.344609 | + | 0.106135i | ||||
\(952\) | 2.97264e7i | 1.06304i | ||||||||
\(953\) | 7.74354e6i | 0.276190i | 0.990419 | + | 0.138095i | \(0.0440979\pi\) | ||||
−0.990419 | + | 0.138095i | \(0.955902\pi\) | |||||||
\(954\) | −1.38834e7 | + | 2.04009e7i | −0.493883 | + | 0.725736i | ||||
\(955\) | − | 1.61264e7i | − | 0.572175i | ||||||
\(956\) | − | 3.86624e7i | − | 1.36818i | ||||||
\(957\) | −6.74101e7 | − | 2.07614e7i | −2.37928 | − | 0.732786i | ||||
\(958\) | − | 8.89643e7i | − | 3.13186i | ||||||
\(959\) | 5.08292e6i | 0.178471i | ||||||||
\(960\) | 1.53559e8 | + | 4.72942e7i | 5.37771 | + | 1.65627i | ||||
\(961\) | 2.53650e7 | 0.885985 | ||||||||
\(962\) | −8.49167e7 | −2.95839 | ||||||||
\(963\) | 2.55746e7 | − | 3.75806e7i | 0.888675 | − | 1.30586i | ||||
\(964\) | 4.00816e7 | 1.38916 | ||||||||
\(965\) | 4.21590e7i | 1.45738i | ||||||||
\(966\) | −1.82465e7 | + | 5.92442e7i | −0.629123 | + | 2.04269i | ||||
\(967\) | − | 2.62473e6i | − | 0.0902648i | −0.998981 | − | 0.0451324i | \(-0.985629\pi\) | ||
0.998981 | − | 0.0451324i | \(-0.0143710\pi\) | |||||||
\(968\) | −1.03313e8 | −3.54379 | ||||||||
\(969\) | −135604. | − | 41764.1i | −0.00463940 | − | 0.00142887i | ||||
\(970\) | −3.70095e7 | −1.26294 | ||||||||
\(971\) | − | 1.70673e6i | − | 0.0580921i | −0.999578 | − | 0.0290460i | \(-0.990753\pi\) | ||
0.999578 | − | 0.0290460i | \(-0.00924695\pi\) | |||||||
\(972\) | 8.04293e7 | − | 6.20171e6i | 2.73054 | − | 0.210545i | ||||
\(973\) | 4.73216e7 | 1.60243 | ||||||||
\(974\) | 6.30328e7 | 2.12897 | ||||||||
\(975\) | 3.25158e7 | + | 1.00144e7i | 1.09543 | + | 0.337377i | ||||
\(976\) | − | 6.66814e7i | − | 2.24068i | ||||||
\(977\) | −5.62239e7 | −1.88445 | −0.942225 | − | 0.334981i | \(-0.891270\pi\) | ||||
−0.942225 | + | 0.334981i | \(0.891270\pi\) | |||||||
\(978\) | −8.06414e6 | + | 2.61834e7i | −0.269595 | + | 0.875344i | ||||
\(979\) | −3.29013e7 | −1.09713 | ||||||||
\(980\) | 2.03119e8i | 6.75593i | ||||||||
\(981\) | −2.85680e7 | + | 4.19793e7i | −0.947779 | + | 1.39271i | ||||
\(982\) | − | 325769.i | − | 0.0107803i | ||||||
\(983\) | 3.71158e6 | 0.122511 | 0.0612555 | − | 0.998122i | \(-0.480490\pi\) | ||||
0.0612555 | + | 0.998122i | \(0.480490\pi\) | |||||||
\(984\) | 2.55960e6 | + | 788324.i | 0.0842722 | + | 0.0259548i | ||||
\(985\) | −2.71098e7 | −0.890299 | ||||||||
\(986\) | 1.98549e7 | 0.650393 | ||||||||
\(987\) | 1.21969e7 | − | 3.96021e7i | 0.398527 | − | 1.29397i | ||||
\(988\) | − | 2.02690e6i | − | 0.0660602i | ||||||
\(989\) | 1.30783e7i | 0.425168i | ||||||||
\(990\) | −7.11717e7 | + | 1.04583e8i | −2.30791 | + | 3.39137i | ||||
\(991\) | − | 2.89699e7i | − | 0.937051i | −0.883450 | − | 0.468525i | \(-0.844785\pi\) | ||
0.883450 | − | 0.468525i | \(-0.155215\pi\) | |||||||
\(992\) | − | 4.09345e7i | − | 1.32072i | ||||||
\(993\) | 4.42631e6 | − | 1.43717e7i | 0.142452 | − | 0.462526i | ||||
\(994\) | − | 2.88608e7i | − | 0.926495i | ||||||
\(995\) | − | 4.31168e7i | − | 1.38067i | ||||||
\(996\) | 1.58513e7 | − | 5.14674e7i | 0.506310 | − | 1.64393i | ||||
\(997\) | −3.80182e7 | −1.21131 | −0.605653 | − | 0.795729i | \(-0.707088\pi\) | ||||
−0.605653 | + | 0.795729i | \(0.707088\pi\) | |||||||
\(998\) | 7.04601e7 | 2.23932 | ||||||||
\(999\) | −3.13235e7 | − | 3.91743e7i | −0.993016 | − | 1.24190i |
(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 | 177.6.d.b.176.2 | yes | 92 | |
3.2 | odd | 2 | inner | 177.6.d.b.176.91 | yes | 92 | |
59.58 | odd | 2 | inner | 177.6.d.b.176.92 | yes | 92 | |
177.176 | even | 2 | inner | 177.6.d.b.176.1 | ✓ | 92 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.6.d.b.176.1 | ✓ | 92 | 177.176 | even | 2 | inner | |
177.6.d.b.176.2 | yes | 92 | 1.1 | even | 1 | trivial | |
177.6.d.b.176.91 | yes | 92 | 3.2 | odd | 2 | inner | |
177.6.d.b.176.92 | yes | 92 | 59.58 | odd | 2 | inner |