Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,6,Mod(6,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, 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("43.6");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(6.89650425196\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Relative dimension: | \(17\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 6.14 | ||
Character | \(\chi\) | \(=\) | 43.6 |
Dual form | 43.6.c.a.36.14 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.70145 | 1.18466 | 0.592330 | − | 0.805695i | \(-0.298208\pi\) | ||||
0.592330 | + | 0.805695i | \(0.298208\pi\) | |||||||
\(3\) | −7.23861 | + | 12.5376i | −0.464357 | + | 0.804291i | −0.999172 | − | 0.0406787i | \(-0.987048\pi\) |
0.534815 | + | 0.844969i | \(0.320381\pi\) | |||||||
\(4\) | 12.9095 | 0.403422 | ||||||||
\(5\) | −40.0400 | + | 69.3513i | −0.716257 | + | 1.24059i | 0.246216 | + | 0.969215i | \(0.420813\pi\) |
−0.962473 | + | 0.271378i | \(0.912521\pi\) | |||||||
\(6\) | −48.5092 | + | 84.0205i | −0.550106 | + | 0.952812i | ||||
\(7\) | −74.8208 | − | 129.593i | −0.577135 | − | 0.999627i | −0.995806 | − | 0.0914889i | \(-0.970837\pi\) |
0.418671 | − | 0.908138i | \(-0.362496\pi\) | |||||||
\(8\) | −127.934 | −0.706743 | ||||||||
\(9\) | 16.7049 | + | 28.9338i | 0.0687445 | + | 0.119069i | ||||
\(10\) | −268.326 | + | 464.754i | −0.848522 | + | 1.46968i | ||||
\(11\) | 126.467 | 0.315135 | 0.157567 | − | 0.987508i | \(-0.449635\pi\) | ||||
0.157567 | + | 0.987508i | \(0.449635\pi\) | |||||||
\(12\) | −93.4468 | + | 161.855i | −0.187332 | + | 0.324468i | ||||
\(13\) | 420.937 | + | 729.085i | 0.690811 | + | 1.19652i | 0.971573 | + | 0.236742i | \(0.0760796\pi\) |
−0.280762 | + | 0.959777i | \(0.590587\pi\) | |||||||
\(14\) | −501.408 | − | 868.464i | −0.683709 | − | 1.18422i | ||||
\(15\) | −579.668 | − | 1004.01i | −0.665198 | − | 1.15216i | ||||
\(16\) | −1270.45 | −1.24067 | ||||||||
\(17\) | 1123.97 | + | 1946.77i | 0.943261 | + | 1.63378i | 0.759195 | + | 0.650863i | \(0.225593\pi\) |
0.184066 | + | 0.982914i | \(0.441074\pi\) | |||||||
\(18\) | 111.947 | + | 193.898i | 0.0814389 | + | 0.141056i | ||||
\(19\) | 1462.95 | − | 2533.91i | 0.929707 | − | 1.61030i | 0.145897 | − | 0.989300i | \(-0.453393\pi\) |
0.783810 | − | 0.621000i | \(-0.213273\pi\) | |||||||
\(20\) | −516.896 | + | 895.290i | −0.288953 | + | 0.500482i | ||||
\(21\) | 2166.40 | 1.07199 | ||||||||
\(22\) | 847.515 | 0.373328 | ||||||||
\(23\) | −1996.77 | + | 3458.50i | −0.787060 | + | 1.36323i | 0.140701 | + | 0.990052i | \(0.455064\pi\) |
−0.927761 | + | 0.373176i | \(0.878269\pi\) | |||||||
\(24\) | 926.066 | − | 1603.99i | 0.328181 | − | 0.568427i | ||||
\(25\) | −1643.90 | − | 2847.32i | −0.526048 | − | 0.911142i | ||||
\(26\) | 2820.89 | + | 4885.93i | 0.818377 | + | 1.41747i | ||||
\(27\) | −4001.65 | −1.05640 | ||||||||
\(28\) | −965.898 | − | 1672.99i | −0.232829 | − | 0.403271i | ||||
\(29\) | −1138.80 | − | 1972.46i | −0.251450 | − | 0.435524i | 0.712475 | − | 0.701697i | \(-0.247574\pi\) |
−0.963925 | + | 0.266173i | \(0.914241\pi\) | |||||||
\(30\) | −3884.62 | − | 6728.36i | −0.788034 | − | 1.36492i | ||||
\(31\) | 1142.42 | − | 1978.74i | 0.213513 | − | 0.369815i | −0.739299 | − | 0.673377i | \(-0.764843\pi\) |
0.952811 | + | 0.303563i | \(0.0981763\pi\) | |||||||
\(32\) | −4419.96 | −0.763033 | ||||||||
\(33\) | −915.448 | + | 1585.60i | −0.146335 | + | 0.253460i | ||||
\(34\) | 7532.23 | + | 13046.2i | 1.11745 | + | 1.93547i | ||||
\(35\) | 11983.3 | 1.65351 | ||||||||
\(36\) | 215.652 | + | 373.520i | 0.0277330 | + | 0.0480350i | ||||
\(37\) | 1256.01 | − | 2175.48i | 0.150831 | − | 0.261247i | −0.780702 | − | 0.624903i | \(-0.785138\pi\) |
0.931533 | + | 0.363656i | \(0.118472\pi\) | |||||||
\(38\) | 9803.91 | − | 16980.9i | 1.10139 | − | 1.90766i | ||||
\(39\) | −12188.0 | −1.28313 | ||||||||
\(40\) | 5122.48 | − | 8872.40i | 0.506210 | − | 0.876781i | ||||
\(41\) | 192.193 | 0.0178558 | 0.00892789 | − | 0.999960i | \(-0.497158\pi\) | ||||
0.00892789 | + | 0.999960i | \(0.497158\pi\) | |||||||
\(42\) | 14518.0 | 1.26994 | ||||||||
\(43\) | 12115.9 | + | 462.816i | 0.999271 | + | 0.0381713i | ||||
\(44\) | 1632.63 | 0.127132 | ||||||||
\(45\) | −2675.46 | −0.196955 | ||||||||
\(46\) | −13381.2 | + | 23177.0i | −0.932399 | + | 1.61496i | ||||
\(47\) | −6423.78 | −0.424176 | −0.212088 | − | 0.977251i | \(-0.568026\pi\) | ||||
−0.212088 | + | 0.977251i | \(0.568026\pi\) | |||||||
\(48\) | 9196.29 | − | 15928.4i | 0.576115 | − | 0.997861i | ||||
\(49\) | −2792.80 | + | 4837.28i | −0.166169 | + | 0.287813i | ||||
\(50\) | −11016.5 | − | 19081.2i | −0.623188 | − | 1.07939i | ||||
\(51\) | −32543.9 | −1.75204 | ||||||||
\(52\) | 5434.09 | + | 9412.12i | 0.278688 | + | 0.482702i | ||||
\(53\) | −11360.2 | + | 19676.4i | −0.555515 | + | 0.962180i | 0.442348 | + | 0.896843i | \(0.354145\pi\) |
−0.997863 | + | 0.0653366i | \(0.979188\pi\) | |||||||
\(54\) | −26816.9 | −1.25148 | ||||||||
\(55\) | −5063.75 | + | 8770.67i | −0.225718 | + | 0.390954i | ||||
\(56\) | 9572.14 | + | 16579.4i | 0.407886 | + | 0.706479i | ||||
\(57\) | 21179.5 | + | 36684.0i | 0.863433 | + | 1.49551i | ||||
\(58\) | −7631.60 | − | 13218.3i | −0.297883 | − | 0.515948i | ||||
\(59\) | −17318.6 | −0.647714 | −0.323857 | − | 0.946106i | \(-0.604980\pi\) | ||||
−0.323857 | + | 0.946106i | \(0.604980\pi\) | |||||||
\(60\) | −7483.22 | − | 12961.3i | −0.268355 | − | 0.464805i | ||||
\(61\) | 15021.4 | + | 26017.8i | 0.516875 | + | 0.895253i | 0.999808 | + | 0.0195959i | \(0.00623798\pi\) |
−0.482933 | + | 0.875657i | \(0.660429\pi\) | |||||||
\(62\) | 7655.91 | − | 13260.4i | 0.252940 | − | 0.438105i | ||||
\(63\) | 2499.75 | − | 4329.70i | 0.0793497 | − | 0.137438i | ||||
\(64\) | 11034.2 | 0.336737 | ||||||||
\(65\) | −67417.3 | −1.97919 | ||||||||
\(66\) | −6134.83 | + | 10625.8i | −0.173358 | + | 0.300264i | ||||
\(67\) | 726.753 | − | 1258.77i | 0.0197788 | − | 0.0342579i | −0.855967 | − | 0.517031i | \(-0.827037\pi\) |
0.875745 | + | 0.482773i | \(0.160370\pi\) | |||||||
\(68\) | 14509.9 | + | 25131.8i | 0.380532 | + | 0.659101i | ||||
\(69\) | −28907.7 | − | 50069.5i | −0.730954 | − | 1.26605i | ||||
\(70\) | 80305.5 | 1.95885 | ||||||||
\(71\) | 34539.7 | + | 59824.5i | 0.813154 | + | 1.40842i | 0.910646 | + | 0.413187i | \(0.135585\pi\) |
−0.0974922 | + | 0.995236i | \(0.531082\pi\) | |||||||
\(72\) | −2137.13 | − | 3701.62i | −0.0485847 | − | 0.0841512i | ||||
\(73\) | −6368.40 | − | 11030.4i | −0.139870 | − | 0.242261i | 0.787578 | − | 0.616216i | \(-0.211335\pi\) |
−0.927447 | + | 0.373954i | \(0.878002\pi\) | |||||||
\(74\) | 8417.12 | − | 14578.9i | 0.178683 | − | 0.309489i | ||||
\(75\) | 47598.2 | 0.977097 | ||||||||
\(76\) | 18886.0 | − | 32711.5i | 0.375064 | − | 0.649630i | ||||
\(77\) | −9462.38 | − | 16389.3i | −0.181875 | − | 0.315017i | ||||
\(78\) | −81677.4 | −1.52008 | ||||||||
\(79\) | 13220.7 | + | 22898.9i | 0.238334 | + | 0.412807i | 0.960236 | − | 0.279188i | \(-0.0900653\pi\) |
−0.721902 | + | 0.691995i | \(0.756732\pi\) | |||||||
\(80\) | 50868.7 | − | 88107.2i | 0.888640 | − | 1.53917i | ||||
\(81\) | 24907.1 | − | 43140.4i | 0.421804 | − | 0.730586i | ||||
\(82\) | 1287.98 | 0.0211530 | ||||||||
\(83\) | 14962.4 | − | 25915.6i | 0.238399 | − | 0.412920i | −0.721856 | − | 0.692044i | \(-0.756711\pi\) |
0.960255 | + | 0.279124i | \(0.0900439\pi\) | |||||||
\(84\) | 27967.1 | 0.432463 | ||||||||
\(85\) | −180015. | −2.70247 | ||||||||
\(86\) | 81193.9 | + | 3101.54i | 1.18380 | + | 0.0452201i | ||||
\(87\) | 32973.3 | 0.467051 | ||||||||
\(88\) | −16179.5 | −0.222719 | ||||||||
\(89\) | 31589.4 | − | 54714.4i | 0.422733 | − | 0.732195i | −0.573473 | − | 0.819225i | \(-0.694404\pi\) |
0.996206 | + | 0.0870298i | \(0.0277375\pi\) | |||||||
\(90\) | −17929.5 | −0.233325 | ||||||||
\(91\) | 62989.7 | − | 109101.i | 0.797382 | − | 1.38111i | ||||
\(92\) | −25777.2 | + | 44647.5i | −0.317517 | + | 0.549955i | ||||
\(93\) | 16539.1 | + | 28646.6i | 0.198292 | + | 0.343452i | ||||
\(94\) | −43048.7 | −0.502505 | ||||||||
\(95\) | 117153. | + | 202915.i | 1.33182 | + | 2.30678i | ||||
\(96\) | 31994.4 | − | 55415.9i | 0.354320 | − | 0.613700i | ||||
\(97\) | 131247. | 1.41632 | 0.708159 | − | 0.706053i | \(-0.249526\pi\) | ||||
0.708159 | + | 0.706053i | \(0.249526\pi\) | |||||||
\(98\) | −18715.9 | + | 32416.8i | −0.196854 | + | 0.340961i | ||||
\(99\) | 2112.63 | + | 3659.17i | 0.0216638 | + | 0.0375228i | ||||
\(100\) | −21221.9 | − | 36757.4i | −0.212219 | − | 0.367574i | ||||
\(101\) | −2685.19 | − | 4650.88i | −0.0261921 | − | 0.0453661i | 0.852632 | − | 0.522512i | \(-0.175005\pi\) |
−0.878824 | + | 0.477145i | \(0.841672\pi\) | |||||||
\(102\) | −218092. | −2.07558 | ||||||||
\(103\) | −19680.1 | − | 34086.9i | −0.182782 | − | 0.316588i | 0.760045 | − | 0.649871i | \(-0.225177\pi\) |
−0.942827 | + | 0.333282i | \(0.891844\pi\) | |||||||
\(104\) | −53852.3 | − | 93274.9i | −0.488226 | − | 0.845632i | ||||
\(105\) | −86742.4 | + | 150242.i | −0.767818 | + | 1.32990i | ||||
\(106\) | −76129.7 | + | 131861.i | −0.658097 | + | 1.13986i | ||||
\(107\) | −28671.5 | −0.242098 | −0.121049 | − | 0.992647i | \(-0.538626\pi\) | ||||
−0.121049 | + | 0.992647i | \(0.538626\pi\) | |||||||
\(108\) | −51659.2 | −0.426176 | ||||||||
\(109\) | 64211.8 | − | 111218.i | 0.517665 | − | 0.896621i | −0.482125 | − | 0.876103i | \(-0.660135\pi\) |
0.999789 | − | 0.0205189i | \(-0.00653183\pi\) | |||||||
\(110\) | −33934.5 | + | 58776.2i | −0.267399 | + | 0.463148i | ||||
\(111\) | 18183.6 | + | 31494.9i | 0.140079 | + | 0.242624i | ||||
\(112\) | 95056.0 | + | 164642.i | 0.716035 | + | 1.24021i | ||||
\(113\) | −20570.7 | −0.151549 | −0.0757744 | − | 0.997125i | \(-0.524143\pi\) | ||||
−0.0757744 | + | 0.997125i | \(0.524143\pi\) | |||||||
\(114\) | 141933. | + | 245836.i | 1.02288 | + | 1.77167i | ||||
\(115\) | −159901. | − | 276957.i | −1.12747 | − | 1.95284i | ||||
\(116\) | −14701.3 | − | 25463.4i | −0.101440 | − | 0.175700i | ||||
\(117\) | −14063.4 | + | 24358.6i | −0.0949789 | + | 0.164508i | ||||
\(118\) | −116060. | −0.767321 | ||||||||
\(119\) | 168193. | − | 291318.i | 1.08878 | − | 1.88582i | ||||
\(120\) | 74159.3 | + | 128448.i | 0.470124 | + | 0.814279i | ||||
\(121\) | −145057. | −0.900690 | ||||||||
\(122\) | 100665. | + | 174357.i | 0.612321 | + | 1.06057i | ||||
\(123\) | −1391.21 | + | 2409.65i | −0.00829146 | + | 0.0143612i | ||||
\(124\) | 14748.1 | − | 25544.5i | 0.0861356 | − | 0.149191i | ||||
\(125\) | 13037.0 | 0.0746282 | ||||||||
\(126\) | 16752.0 | − | 29015.3i | 0.0940025 | − | 0.162817i | ||||
\(127\) | 98267.2 | 0.540629 | 0.270314 | − | 0.962772i | \(-0.412872\pi\) | ||||
0.270314 | + | 0.962772i | \(0.412872\pi\) | |||||||
\(128\) | 215384. | 1.16195 | ||||||||
\(129\) | −93504.7 | + | 148554.i | −0.494720 | + | 0.785979i | ||||
\(130\) | −451794. | −2.34467 | ||||||||
\(131\) | 94616.1 | 0.481711 | 0.240856 | − | 0.970561i | \(-0.422572\pi\) | ||||
0.240856 | + | 0.970561i | \(0.422572\pi\) | |||||||
\(132\) | −11818.0 | + | 20469.3i | −0.0590348 | + | 0.102251i | ||||
\(133\) | −437837. | −2.14627 | ||||||||
\(134\) | 4870.30 | − | 8435.62i | 0.0234312 | − | 0.0405840i | ||||
\(135\) | 160226. | − | 277519.i | 0.756656 | − | 1.31057i | ||||
\(136\) | −143794. | − | 249059.i | −0.666644 | − | 1.15466i | ||||
\(137\) | 435056. | 1.98036 | 0.990180 | − | 0.139800i | \(-0.0446459\pi\) | ||||
0.990180 | + | 0.139800i | \(0.0446459\pi\) | |||||||
\(138\) | −193723. | − | 335539.i | −0.865933 | − | 1.49984i | ||||
\(139\) | −105765. | + | 183191.i | −0.464309 | + | 0.804206i | −0.999170 | − | 0.0407336i | \(-0.987031\pi\) |
0.534861 | + | 0.844940i | \(0.320364\pi\) | |||||||
\(140\) | 154698. | 0.667060 | ||||||||
\(141\) | 46499.3 | − | 80539.1i | 0.196969 | − | 0.341161i | ||||
\(142\) | 231466. | + | 400911.i | 0.963312 | + | 1.66850i | ||||
\(143\) | 53234.8 | + | 92205.4i | 0.217699 | + | 0.377065i | ||||
\(144\) | −21222.7 | − | 36758.9i | −0.0852894 | − | 0.147726i | ||||
\(145\) | 182390. | 0.720411 | ||||||||
\(146\) | −42677.6 | − | 73919.7i | −0.165698 | − | 0.286997i | ||||
\(147\) | −40432.1 | − | 70030.4i | −0.154324 | − | 0.267296i | ||||
\(148\) | 16214.5 | − | 28084.3i | 0.0608484 | − | 0.105393i | ||||
\(149\) | −141616. | + | 245287.i | −0.522574 | + | 0.905125i | 0.477081 | + | 0.878859i | \(0.341695\pi\) |
−0.999655 | + | 0.0262655i | \(0.991638\pi\) | |||||||
\(150\) | 318977. | 1.15753 | ||||||||
\(151\) | 17751.1 | 0.0633555 | 0.0316777 | − | 0.999498i | \(-0.489915\pi\) | ||||
0.0316777 | + | 0.999498i | \(0.489915\pi\) | |||||||
\(152\) | −187162. | + | 324173.i | −0.657064 | + | 1.13807i | ||||
\(153\) | −37551.6 | + | 65041.3i | −0.129688 | + | 0.224626i | ||||
\(154\) | −63411.7 | − | 109832.i | −0.215461 | − | 0.373189i | ||||
\(155\) | 91485.3 | + | 158457.i | 0.305860 | + | 0.529764i | ||||
\(156\) | −157341. | −0.517643 | ||||||||
\(157\) | 79369.5 | + | 137472.i | 0.256983 | + | 0.445107i | 0.965432 | − | 0.260654i | \(-0.0839383\pi\) |
−0.708449 | + | 0.705762i | \(0.750605\pi\) | |||||||
\(158\) | 88597.8 | + | 153456.i | 0.282345 | + | 0.489036i | ||||
\(159\) | −164464. | − | 284860.i | −0.515915 | − | 0.893591i | ||||
\(160\) | 176975. | − | 306530.i | 0.546528 | − | 0.946614i | ||||
\(161\) | 597599. | 1.81696 | ||||||||
\(162\) | 166914. | − | 289103.i | 0.499695 | − | 0.865496i | ||||
\(163\) | −104878. | − | 181653.i | −0.309182 | − | 0.535518i | 0.669002 | − | 0.743261i | \(-0.266722\pi\) |
−0.978184 | + | 0.207742i | \(0.933388\pi\) | |||||||
\(164\) | 2481.12 | 0.00720341 | ||||||||
\(165\) | −73309.0 | − | 126975.i | −0.209627 | − | 0.363085i | ||||
\(166\) | 100270. | − | 173672.i | 0.282422 | − | 0.489170i | ||||
\(167\) | 102954. | − | 178321.i | 0.285661 | − | 0.494779i | −0.687109 | − | 0.726555i | \(-0.741120\pi\) |
0.972769 | + | 0.231776i | \(0.0744537\pi\) | |||||||
\(168\) | −277156. | −0.757620 | ||||||||
\(169\) | −168730. | + | 292249.i | −0.454439 | + | 0.787112i | ||||
\(170\) | −1.20636e6 | −3.20151 | ||||||||
\(171\) | 97754.0 | 0.255649 | ||||||||
\(172\) | 156410. | + | 5974.72i | 0.403128 | + | 0.0153991i | ||||
\(173\) | 192007. | 0.487755 | 0.243877 | − | 0.969806i | \(-0.421581\pi\) | ||||
0.243877 | + | 0.969806i | \(0.421581\pi\) | |||||||
\(174\) | 220969. | 0.553296 | ||||||||
\(175\) | −245996. | + | 426077.i | −0.607201 | + | 1.05170i | ||||
\(176\) | −160670. | −0.390979 | ||||||||
\(177\) | 125363. | − | 217135.i | 0.300771 | − | 0.520950i | ||||
\(178\) | 211695. | − | 366666.i | 0.500795 | − | 0.867402i | ||||
\(179\) | −159511. | − | 276280.i | −0.372098 | − | 0.644492i | 0.617790 | − | 0.786343i | \(-0.288028\pi\) |
−0.989888 | + | 0.141851i | \(0.954695\pi\) | |||||||
\(180\) | −34538.8 | −0.0794559 | ||||||||
\(181\) | 42272.5 | + | 73218.1i | 0.0959094 | + | 0.166120i | 0.909988 | − | 0.414635i | \(-0.136091\pi\) |
−0.814078 | + | 0.580755i | \(0.802757\pi\) | |||||||
\(182\) | 422123. | − | 731138.i | 0.944627 | − | 1.63614i | ||||
\(183\) | −434936. | −0.960058 | ||||||||
\(184\) | 255455. | − | 442461.i | 0.556249 | − | 0.963452i | ||||
\(185\) | 100582. | + | 174212.i | 0.216067 | + | 0.374239i | ||||
\(186\) | 110836. | + | 191974.i | 0.234909 | + | 0.406874i | ||||
\(187\) | 142145. | + | 246203.i | 0.297255 | + | 0.514860i | ||||
\(188\) | −82927.7 | −0.171122 | ||||||||
\(189\) | 299407. | + | 518587.i | 0.609687 | + | 1.05601i | ||||
\(190\) | 785097. | + | 1.35983e6i | 1.57775 | + | 2.73275i | ||||
\(191\) | −103436. | + | 179157.i | −0.205158 | + | 0.355344i | −0.950183 | − | 0.311692i | \(-0.899104\pi\) |
0.745025 | + | 0.667037i | \(0.232438\pi\) | |||||||
\(192\) | −79872.3 | + | 138343.i | −0.156366 | + | 0.270834i | ||||
\(193\) | −860957. | −1.66375 | −0.831876 | − | 0.554962i | \(-0.812733\pi\) | ||||
−0.831876 | + | 0.554962i | \(0.812733\pi\) | |||||||
\(194\) | 879548. | 1.67786 | ||||||||
\(195\) | 488008. | − | 845254.i | 0.919052 | − | 1.59185i | ||||
\(196\) | −36053.7 | + | 62446.8i | −0.0670362 | + | 0.116110i | ||||
\(197\) | −155564. | − | 269445.i | −0.285591 | − | 0.494657i | 0.687162 | − | 0.726505i | \(-0.258856\pi\) |
−0.972752 | + | 0.231847i | \(0.925523\pi\) | |||||||
\(198\) | 14157.7 | + | 24521.8i | 0.0256643 | + | 0.0444518i | ||||
\(199\) | −109969. | −0.196851 | −0.0984254 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984254 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(200\) | 210311. | + | 364269.i | 0.371781 | + | 0.643943i | ||||
\(201\) | 10521.4 | + | 18223.6i | 0.0183689 | + | 0.0318158i | ||||
\(202\) | −17994.6 | − | 31167.6i | −0.0310288 | − | 0.0537434i | ||||
\(203\) | −170411. | + | 295161.i | −0.290241 | + | 0.502712i | ||||
\(204\) | −420125. | −0.706811 | ||||||||
\(205\) | −7695.42 | + | 13328.9i | −0.0127893 | + | 0.0221518i | ||||
\(206\) | −131885. | − | 228432.i | −0.216535 | − | 0.375050i | ||||
\(207\) | −133423. | −0.216424 | ||||||||
\(208\) | −534779. | − | 926265.i | −0.857070 | − | 1.48449i | ||||
\(209\) | 185016. | − | 320456.i | 0.292983 | − | 0.507462i | ||||
\(210\) | −581301. | + | 1.00684e6i | −0.909604 | + | 1.57548i | ||||
\(211\) | −922584. | −1.42659 | −0.713296 | − | 0.700863i | \(-0.752798\pi\) | ||||
−0.713296 | + | 0.700863i | \(0.752798\pi\) | |||||||
\(212\) | −146654. | + | 254012.i | −0.224107 | + | 0.388164i | ||||
\(213\) | −1.00008e6 | −1.51038 | ||||||||
\(214\) | −192141. | −0.286804 | ||||||||
\(215\) | −517216. | + | 821720.i | −0.763090 | + | 1.21235i | ||||
\(216\) | 511948. | 0.746605 | ||||||||
\(217\) | −341909. | −0.492902 | ||||||||
\(218\) | 430312. | − | 745323.i | 0.613257 | − | 1.06219i | ||||
\(219\) | 184394. | 0.259798 | ||||||||
\(220\) | −65370.4 | + | 113225.i | −0.0910593 | + | 0.157719i | ||||
\(221\) | −946241. | + | 1.63894e6i | −1.30323 | + | 2.25726i | ||||
\(222\) | 121857. | + | 211062.i | 0.165946 | + | 0.287427i | ||||
\(223\) | 1.06974e6 | 1.44051 | 0.720254 | − | 0.693711i | \(-0.244025\pi\) | ||||
0.720254 | + | 0.693711i | \(0.244025\pi\) | |||||||
\(224\) | 330705. | + | 572798.i | 0.440373 | + | 0.762748i | ||||
\(225\) | 54922.4 | − | 95128.4i | 0.0723258 | − | 0.125272i | ||||
\(226\) | −137853. | −0.179534 | ||||||||
\(227\) | 22321.9 | − | 38662.7i | 0.0287520 | − | 0.0497999i | −0.851291 | − | 0.524693i | \(-0.824180\pi\) |
0.880043 | + | 0.474893i | \(0.157513\pi\) | |||||||
\(228\) | 273417. | + | 473571.i | 0.348327 | + | 0.603321i | ||||
\(229\) | −45194.2 | − | 78278.6i | −0.0569500 | − | 0.0986403i | 0.836145 | − | 0.548509i | \(-0.184804\pi\) |
−0.893095 | + | 0.449868i | \(0.851471\pi\) | |||||||
\(230\) | −1.07157e6 | − | 1.85601e6i | −1.33567 | − | 2.31346i | ||||
\(231\) | 273978. | 0.337820 | ||||||||
\(232\) | 145691. | + | 252344.i | 0.177711 | + | 0.307804i | ||||
\(233\) | 357205. | + | 618696.i | 0.431050 | + | 0.746600i | 0.996964 | − | 0.0778643i | \(-0.0248101\pi\) |
−0.565914 | + | 0.824464i | \(0.691477\pi\) | |||||||
\(234\) | −94245.6 | + | 163238.i | −0.112518 | + | 0.194887i | ||||
\(235\) | 257208. | − | 445497.i | 0.303819 | − | 0.526230i | ||||
\(236\) | −223574. | −0.261302 | ||||||||
\(237\) | −382798. | −0.442689 | ||||||||
\(238\) | 1.12713e6 | − | 1.95225e6i | 1.28983 | − | 2.23406i | ||||
\(239\) | 429861. | − | 744541.i | 0.486781 | − | 0.843129i | −0.513104 | − | 0.858327i | \(-0.671504\pi\) |
0.999885 | + | 0.0151974i | \(0.00483768\pi\) | |||||||
\(240\) | 736438. | + | 1.27555e6i | 0.825293 | + | 1.42945i | ||||
\(241\) | −160818. | − | 278546.i | −0.178358 | − | 0.308926i | 0.762960 | − | 0.646446i | \(-0.223745\pi\) |
−0.941318 | + | 0.337520i | \(0.890412\pi\) | |||||||
\(242\) | −972093. | −1.06701 | ||||||||
\(243\) | −125615. | − | 217571.i | −0.136466 | − | 0.236366i | ||||
\(244\) | 193918. | + | 335876.i | 0.208518 | + | 0.361164i | ||||
\(245\) | −223648. | − | 387369.i | −0.238040 | − | 0.412297i | ||||
\(246\) | −9323.16 | + | 16148.2i | −0.00982257 | + | 0.0170132i | ||||
\(247\) | 2.46325e6 | 2.56901 | ||||||||
\(248\) | −146155. | + | 253148.i | −0.150899 | + | 0.261364i | ||||
\(249\) | 216614. | + | 375186.i | 0.221405 | + | 0.383485i | ||||
\(250\) | 87366.9 | 0.0884091 | ||||||||
\(251\) | −710851. | − | 1.23123e6i | −0.712187 | − | 1.23354i | −0.964035 | − | 0.265777i | \(-0.914372\pi\) |
0.251848 | − | 0.967767i | \(-0.418962\pi\) | |||||||
\(252\) | 32270.5 | − | 55894.2i | 0.0320114 | − | 0.0554453i | ||||
\(253\) | −252526. | + | 437387.i | −0.248030 | + | 0.429601i | ||||
\(254\) | 658533. | 0.640462 | ||||||||
\(255\) | 1.30306e6 | − | 2.25696e6i | 1.25491 | − | 2.17357i | ||||
\(256\) | 1.09029e6 | 1.03978 | ||||||||
\(257\) | 1.11378e6 | 1.05188 | 0.525942 | − | 0.850520i | \(-0.323713\pi\) | ||||
0.525942 | + | 0.850520i | \(0.323713\pi\) | |||||||
\(258\) | −626618. | + | 995530.i | −0.586075 | + | 0.931119i | ||||
\(259\) | −375904. | −0.348199 | ||||||||
\(260\) | −870323. | −0.798449 | ||||||||
\(261\) | 38047.0 | − | 65899.4i | 0.0345716 | − | 0.0598798i | ||||
\(262\) | 634066. | 0.570665 | ||||||||
\(263\) | −137625. | + | 238373.i | −0.122689 | + | 0.212504i | −0.920827 | − | 0.389971i | \(-0.872485\pi\) |
0.798138 | + | 0.602475i | \(0.205819\pi\) | |||||||
\(264\) | 117117. | − | 202853.i | 0.103421 | − | 0.179131i | ||||
\(265\) | −909723. | − | 1.57569e6i | −0.795783 | − | 1.37834i | ||||
\(266\) | −2.93415e6 | −2.54260 | ||||||||
\(267\) | 457327. | + | 792113.i | 0.392598 | + | 0.680000i | ||||
\(268\) | 9382.02 | − | 16250.1i | 0.00797920 | − | 0.0138204i | ||||
\(269\) | 1.40639e6 | 1.18502 | 0.592509 | − | 0.805564i | \(-0.298137\pi\) | ||||
0.592509 | + | 0.805564i | \(0.298137\pi\) | |||||||
\(270\) | 1.07375e6 | − | 1.85978e6i | 0.896381 | − | 1.55258i | ||||
\(271\) | 970874. | + | 1.68160e6i | 0.803044 | + | 1.39091i | 0.917603 | + | 0.397497i | \(0.130121\pi\) |
−0.114559 | + | 0.993416i | \(0.536545\pi\) | |||||||
\(272\) | −1.42795e6 | − | 2.47327e6i | −1.17028 | − | 2.02698i | ||||
\(273\) | 911917. | + | 1.57949e6i | 0.740540 | + | 1.28265i | ||||
\(274\) | 2.91551e6 | 2.34605 | ||||||||
\(275\) | −207900. | − | 360093.i | −0.165776 | − | 0.287133i | ||||
\(276\) | −373183. | − | 646372.i | −0.294883 | − | 0.510752i | ||||
\(277\) | 31373.2 | − | 54340.0i | 0.0245674 | − | 0.0425521i | −0.853480 | − | 0.521125i | \(-0.825512\pi\) |
0.878048 | + | 0.478573i | \(0.158846\pi\) | |||||||
\(278\) | −708782. | + | 1.22765e6i | −0.550048 | + | 0.952712i | ||||
\(279\) | 76336.4 | 0.0587113 | ||||||||
\(280\) | −1.53307e6 | −1.16860 | ||||||||
\(281\) | 713099. | − | 1.23512e6i | 0.538746 | − | 0.933136i | −0.460226 | − | 0.887802i | \(-0.652232\pi\) |
0.998972 | − | 0.0453337i | \(-0.0144351\pi\) | |||||||
\(282\) | 311613. | − | 539729.i | 0.233342 | − | 0.404160i | ||||
\(283\) | 653541. | + | 1.13197e6i | 0.485073 | + | 0.840170i | 0.999853 | − | 0.0171517i | \(-0.00545984\pi\) |
−0.514780 | + | 0.857322i | \(0.672127\pi\) | |||||||
\(284\) | 445890. | + | 772304.i | 0.328044 | + | 0.568188i | ||||
\(285\) | −3.39211e6 | −2.47376 | ||||||||
\(286\) | 356751. | + | 617910.i | 0.257899 | + | 0.446694i | ||||
\(287\) | −14380.1 | − | 24907.0i | −0.0103052 | − | 0.0178491i | ||||
\(288\) | −73835.1 | − | 127886.i | −0.0524544 | − | 0.0908536i | ||||
\(289\) | −1.81668e6 | + | 3.14659e6i | −1.27948 | + | 2.21613i | ||||
\(290\) | 1.22228e6 | 0.853443 | ||||||||
\(291\) | −950049. | + | 1.64553e6i | −0.657678 | + | 1.13913i | ||||
\(292\) | −82212.8 | − | 142397.i | −0.0564264 | − | 0.0977334i | ||||
\(293\) | 154259. | 0.104974 | 0.0524870 | − | 0.998622i | \(-0.483285\pi\) | ||||
0.0524870 | + | 0.998622i | \(0.483285\pi\) | |||||||
\(294\) | −270954. | − | 469306.i | −0.182821 | − | 0.316656i | ||||
\(295\) | 693437. | − | 1.20107e6i | 0.463929 | − | 0.803549i | ||||
\(296\) | −160687. | + | 278318.i | −0.106599 | + | 0.184634i | ||||
\(297\) | −506078. | −0.332909 | ||||||||
\(298\) | −949036. | + | 1.64378e6i | −0.619073 | + | 1.07227i | ||||
\(299\) | −3.36206e6 | −2.17484 | ||||||||
\(300\) | 614469. | 0.394182 | ||||||||
\(301\) | −846541. | − | 1.60477e6i | −0.538557 | − | 1.02093i | ||||
\(302\) | 118959. | 0.0750548 | ||||||||
\(303\) | 77748.1 | 0.0486500 | ||||||||
\(304\) | −1.85861e6 | + | 3.21920e6i | −1.15346 | + | 1.99786i | ||||
\(305\) | −2.40582e6 | −1.48086 | ||||||||
\(306\) | −251651. | + | 435871.i | −0.153636 | + | 0.266106i | ||||
\(307\) | 914488. | − | 1.58394e6i | 0.553773 | − | 0.959163i | −0.444225 | − | 0.895915i | \(-0.646521\pi\) |
0.997998 | − | 0.0632479i | \(-0.0201459\pi\) | |||||||
\(308\) | −122155. | − | 211578.i | −0.0733724 | − | 0.127085i | ||||
\(309\) | 569827. | 0.339505 | ||||||||
\(310\) | 613085. | + | 1.06189e6i | 0.362340 | + | 0.627591i | ||||
\(311\) | 515362. | − | 892633.i | 0.302142 | − | 0.523326i | −0.674479 | − | 0.738294i | \(-0.735632\pi\) |
0.976621 | + | 0.214969i | \(0.0689649\pi\) | |||||||
\(312\) | 1.55926e6 | 0.906845 | ||||||||
\(313\) | −906617. | + | 1.57031e6i | −0.523074 | + | 0.905990i | 0.476566 | + | 0.879139i | \(0.341881\pi\) |
−0.999639 | + | 0.0268513i | \(0.991452\pi\) | |||||||
\(314\) | 531891. | + | 921262.i | 0.304438 | + | 0.527301i | ||||
\(315\) | 200180. | + | 346722.i | 0.113670 | + | 0.196881i | ||||
\(316\) | 170672. | + | 295613.i | 0.0961491 | + | 0.166535i | ||||
\(317\) | −3.17573e6 | −1.77499 | −0.887495 | − | 0.460818i | \(-0.847556\pi\) | ||||
−0.887495 | + | 0.460818i | \(0.847556\pi\) | |||||||
\(318\) | −1.10215e6 | − | 1.90898e6i | −0.611184 | − | 1.05860i | ||||
\(319\) | −144021. | − | 249451.i | −0.0792406 | − | 0.137249i | ||||
\(320\) | −441809. | + | 765236.i | −0.241190 | + | 0.417754i | ||||
\(321\) | 207542. | − | 359474.i | 0.112420 | − | 0.194717i | ||||
\(322\) | 4.00478e6 | 2.15248 | ||||||||
\(323\) | 6.57725e6 | 3.50783 | ||||||||
\(324\) | 321538. | − | 556920.i | 0.170165 | − | 0.294734i | ||||
\(325\) | 1.38396e6 | − | 2.39709e6i | 0.726799 | − | 1.25885i | ||||
\(326\) | −702832. | − | 1.21734e6i | −0.366275 | − | 0.634407i | ||||
\(327\) | 929609. | + | 1.61013e6i | 0.480763 | + | 0.832706i | ||||
\(328\) | −24588.1 | −0.0126194 | ||||||||
\(329\) | 480632. | + | 832480.i | 0.244807 | + | 0.424018i | ||||
\(330\) | −491277. | − | 850917.i | −0.248337 | − | 0.430133i | ||||
\(331\) | 231514. | + | 400994.i | 0.116147 | + | 0.201172i | 0.918238 | − | 0.396030i | \(-0.129612\pi\) |
−0.802091 | + | 0.597202i | \(0.796279\pi\) | |||||||
\(332\) | 193157. | − | 334557.i | 0.0961755 | − | 0.166581i | ||||
\(333\) | 83926.4 | 0.0414752 | ||||||||
\(334\) | 689939. | − | 1.19501e6i | 0.338411 | − | 0.586145i | ||||
\(335\) | 58198.4 | + | 100803.i | 0.0283334 | + | 0.0490749i | ||||
\(336\) | −2.75229e6 | −1.32999 | ||||||||
\(337\) | 510042. | + | 883419.i | 0.244642 | + | 0.423733i | 0.962031 | − | 0.272940i | \(-0.0879962\pi\) |
−0.717389 | + | 0.696673i | \(0.754663\pi\) | |||||||
\(338\) | −1.13074e6 | + | 1.95849e6i | −0.538356 | + | 0.932461i | ||||
\(339\) | 148903. | − | 257908.i | 0.0703728 | − | 0.121889i | ||||
\(340\) | −2.32390e6 | −1.09023 | ||||||||
\(341\) | 144479. | − | 250246.i | 0.0672852 | − | 0.116541i | ||||
\(342\) | 655094. | 0.302858 | ||||||||
\(343\) | −1.67919e6 | −0.770662 | ||||||||
\(344\) | −1.55003e6 | − | 59210.0i | −0.706228 | − | 0.0269773i | ||||
\(345\) | 4.62985e6 | 2.09420 | ||||||||
\(346\) | 1.28673e6 | 0.577824 | ||||||||
\(347\) | −879171. | + | 1.52277e6i | −0.391967 | + | 0.678907i | −0.992709 | − | 0.120536i | \(-0.961539\pi\) |
0.600742 | + | 0.799443i | \(0.294872\pi\) | |||||||
\(348\) | 425668. | 0.188418 | ||||||||
\(349\) | 1.53484e6 | − | 2.65843e6i | 0.674529 | − | 1.16832i | −0.302077 | − | 0.953284i | \(-0.597680\pi\) |
0.976606 | − | 0.215036i | \(-0.0689868\pi\) | |||||||
\(350\) | −1.64853e6 | + | 2.85534e6i | −0.719328 | + | 1.24591i | ||||
\(351\) | −1.68444e6 | − | 2.91754e6i | −0.729774 | − | 1.26401i | ||||
\(352\) | −558980. | −0.240458 | ||||||||
\(353\) | −999829. | − | 1.73175e6i | −0.427060 | − | 0.739689i | 0.569550 | − | 0.821956i | \(-0.307117\pi\) |
−0.996610 | + | 0.0822669i | \(0.973784\pi\) | |||||||
\(354\) | 840113. | − | 1.45512e6i | 0.356311 | − | 0.617149i | ||||
\(355\) | −5.53188e6 | −2.32971 | ||||||||
\(356\) | 407803. | − | 706335.i | 0.170540 | − | 0.295383i | ||||
\(357\) | 2.43496e6 | + | 4.21748e6i | 1.01116 | + | 1.75139i | ||||
\(358\) | −1.06895e6 | − | 1.85148e6i | −0.440809 | − | 0.763504i | ||||
\(359\) | 451611. | + | 782214.i | 0.184939 | + | 0.320324i | 0.943556 | − | 0.331213i | \(-0.107458\pi\) |
−0.758617 | + | 0.651537i | \(0.774125\pi\) | |||||||
\(360\) | 342283. | 0.139197 | ||||||||
\(361\) | −3.04241e6 | − | 5.26961e6i | −1.22871 | − | 2.12819i | ||||
\(362\) | 283287. | + | 490668.i | 0.113620 | + | 0.196796i | ||||
\(363\) | 1.05001e6 | − | 1.81867e6i | 0.418242 | − | 0.724416i | ||||
\(364\) | 813166. | − | 1.40844e6i | 0.321681 | − | 0.557168i | ||||
\(365\) | 1.01996e6 | 0.400730 | ||||||||
\(366\) | −2.91470e6 | −1.13734 | ||||||||
\(367\) | −841055. | + | 1.45675e6i | −0.325956 | + | 0.564573i | −0.981705 | − | 0.190406i | \(-0.939020\pi\) |
0.655749 | + | 0.754979i | \(0.272353\pi\) | |||||||
\(368\) | 2.53679e6 | − | 4.39385e6i | 0.976484 | − | 1.69132i | ||||
\(369\) | 3210.57 | + | 5560.88i | 0.00122749 | + | 0.00212607i | ||||
\(370\) | 674043. | + | 1.16748e6i | 0.255966 | + | 0.443347i | ||||
\(371\) | 3.39991e6 | 1.28243 | ||||||||
\(372\) | 213512. | + | 369813.i | 0.0799954 | + | 0.138556i | ||||
\(373\) | 1.39183e6 | + | 2.41071e6i | 0.517980 | + | 0.897167i | 0.999782 | + | 0.0208873i | \(0.00664912\pi\) |
−0.481802 | + | 0.876280i | \(0.660018\pi\) | |||||||
\(374\) | 952580. | + | 1.64992e6i | 0.352146 | + | 0.609935i | ||||
\(375\) | −94369.9 | + | 163453.i | −0.0346541 | + | 0.0600227i | ||||
\(376\) | 821821. | 0.299783 | ||||||||
\(377\) | 958725. | − | 1.66056e6i | 0.347409 | − | 0.601729i | ||||
\(378\) | 2.00646e6 | + | 3.47529e6i | 0.722272 | + | 1.25101i | ||||
\(379\) | 1.42785e6 | 0.510603 | 0.255302 | − | 0.966861i | \(-0.417825\pi\) | ||||
0.255302 | + | 0.966861i | \(0.417825\pi\) | |||||||
\(380\) | 1.51239e6 | + | 2.61953e6i | 0.537284 | + | 0.930604i | ||||
\(381\) | −711318. | + | 1.23204e6i | −0.251045 | + | 0.434823i | ||||
\(382\) | −693172. | + | 1.20061e6i | −0.243043 | + | 0.420962i | ||||
\(383\) | 1.85487e6 | 0.646124 | 0.323062 | − | 0.946378i | \(-0.395288\pi\) | ||||
0.323062 | + | 0.946378i | \(0.395288\pi\) | |||||||
\(384\) | −1.55908e6 | + | 2.70041e6i | −0.539561 | + | 0.934547i | ||||
\(385\) | 1.51549e6 | 0.521078 | ||||||||
\(386\) | −5.76967e6 | −1.97098 | ||||||||
\(387\) | 189004. | + | 358289.i | 0.0641494 | + | 0.121606i | ||||
\(388\) | 1.69434e6 | 0.571374 | ||||||||
\(389\) | 2.61813e6 | 0.877238 | 0.438619 | − | 0.898673i | \(-0.355468\pi\) | ||||
0.438619 | + | 0.898673i | \(0.355468\pi\) | |||||||
\(390\) | 3.27036e6 | − | 5.66443e6i | 1.08877 | − | 1.88580i | ||||
\(391\) | −8.97722e6 | −2.96961 | ||||||||
\(392\) | 357295. | − | 618853.i | 0.117439 | − | 0.203410i | ||||
\(393\) | −684890. | + | 1.18626e6i | −0.223686 | + | 0.387436i | ||||
\(394\) | −1.04251e6 | − | 1.80567e6i | −0.338328 | − | 0.586001i | ||||
\(395\) | −2.11742e6 | −0.682834 | ||||||||
\(396\) | 27272.9 | + | 47238.1i | 0.00873964 | + | 0.0151375i | ||||
\(397\) | 2.05810e6 | − | 3.56473e6i | 0.655374 | − | 1.13514i | −0.326425 | − | 0.945223i | \(-0.605844\pi\) |
0.981800 | − | 0.189919i | \(-0.0608225\pi\) | |||||||
\(398\) | −736952. | −0.233201 | ||||||||
\(399\) | 3.16933e6 | − | 5.48945e6i | 0.996634 | − | 1.72622i | ||||
\(400\) | 2.08849e6 | + | 3.61737e6i | 0.652653 | + | 1.13043i | ||||
\(401\) | 267212. | + | 462825.i | 0.0829842 | + | 0.143733i | 0.904530 | − | 0.426409i | \(-0.140222\pi\) |
−0.821546 | + | 0.570142i | \(0.806888\pi\) | |||||||
\(402\) | 70508.5 | + | 122124.i | 0.0217609 | + | 0.0376909i | ||||
\(403\) | 1.92356e6 | 0.589987 | ||||||||
\(404\) | −34664.4 | − | 60040.5i | −0.0105665 | − | 0.0183017i | ||||
\(405\) | 1.99456e6 | + | 3.45468e6i | 0.604240 | + | 1.04657i | ||||
\(406\) | −1.14200e6 | + | 1.97801e6i | −0.343837 | + | 0.595543i | ||||
\(407\) | 158845. | − | 275127.i | 0.0475321 | − | 0.0823279i | ||||
\(408\) | 4.16348e6 | 1.23824 | ||||||||
\(409\) | −2.78895e6 | −0.824389 | −0.412195 | − | 0.911096i | \(-0.635238\pi\) | ||||
−0.412195 | + | 0.911096i | \(0.635238\pi\) | |||||||
\(410\) | −51570.5 | + | 89322.7i | −0.0151510 | + | 0.0262423i | ||||
\(411\) | −3.14920e6 | + | 5.45458e6i | −0.919595 | + | 1.59278i | ||||
\(412\) | −254060. | − | 440045.i | −0.0737384 | − | 0.127719i | ||||
\(413\) | 1.29579e6 | + | 2.24438e6i | 0.373818 | + | 0.647472i | ||||
\(414\) | −894130. | −0.256389 | ||||||||
\(415\) | 1.19819e6 | + | 2.07532e6i | 0.341510 | + | 0.591513i | ||||
\(416\) | −1.86053e6 | − | 3.22253e6i | −0.527112 | − | 0.912984i | ||||
\(417\) | −1.53119e6 | − | 2.65210e6i | −0.431210 | − | 0.746878i | ||||
\(418\) | 1.23987e6 | − | 2.14752e6i | 0.347086 | − | 0.601170i | ||||
\(419\) | −4.86995e6 | −1.35516 | −0.677578 | − | 0.735451i | \(-0.736970\pi\) | ||||
−0.677578 | + | 0.735451i | \(0.736970\pi\) | |||||||
\(420\) | −1.11980e6 | + | 1.93955e6i | −0.309754 | + | 0.536510i | ||||
\(421\) | −2.26694e6 | − | 3.92645e6i | −0.623354 | − | 1.07968i | −0.988857 | − | 0.148870i | \(-0.952436\pi\) |
0.365503 | − | 0.930810i | \(-0.380897\pi\) | |||||||
\(422\) | −6.18265e6 | −1.69003 | ||||||||
\(423\) | −107309. | − | 185864.i | −0.0291598 | − | 0.0505062i | ||||
\(424\) | 1.45336e6 | − | 2.51729e6i | 0.392606 | − | 0.680014i | ||||
\(425\) | 3.69539e6 | − | 6.40060e6i | 0.992402 | − | 1.71889i | ||||
\(426\) | −6.70198e6 | −1.78928 | ||||||||
\(427\) | 2.24782e6 | − | 3.89334e6i | 0.596613 | − | 1.03336i | ||||
\(428\) | −370135. | −0.0976676 | ||||||||
\(429\) | −1.54138e6 | −0.404360 | ||||||||
\(430\) | −3.46610e6 | + | 5.50672e6i | −0.904003 | + | 1.43622i | ||||
\(431\) | 1.87803e6 | 0.486977 | 0.243489 | − | 0.969904i | \(-0.421708\pi\) | ||||
0.243489 | + | 0.969904i | \(0.421708\pi\) | |||||||
\(432\) | 5.08389e6 | 1.31065 | ||||||||
\(433\) | 2.05652e6 | − | 3.56199e6i | 0.527124 | − | 0.913006i | −0.472376 | − | 0.881397i | \(-0.656604\pi\) |
0.999500 | − | 0.0316087i | \(-0.0100630\pi\) | |||||||
\(434\) | −2.29128e6 | −0.583922 | ||||||||
\(435\) | −1.32025e6 | + | 2.28674e6i | −0.334528 | + | 0.579420i | ||||
\(436\) | 828941. | − | 1.43577e6i | 0.208837 | − | 0.361716i | ||||
\(437\) | 5.84235e6 | + | 1.01192e7i | 1.46347 | + | 2.53481i | ||||
\(438\) | 1.23571e6 | 0.307772 | ||||||||
\(439\) | 579055. | + | 1.00295e6i | 0.143403 | + | 0.248382i | 0.928776 | − | 0.370641i | \(-0.120862\pi\) |
−0.785373 | + | 0.619023i | \(0.787529\pi\) | |||||||
\(440\) | 647826. | − | 1.12207e6i | 0.159524 | − | 0.276304i | ||||
\(441\) | −186614. | −0.0456929 | ||||||||
\(442\) | −6.34119e6 | + | 1.09833e7i | −1.54389 | + | 2.67409i | ||||
\(443\) | −33352.8 | − | 57768.7i | −0.00807463 | − | 0.0139857i | 0.861960 | − | 0.506977i | \(-0.169237\pi\) |
−0.870034 | + | 0.492991i | \(0.835904\pi\) | |||||||
\(444\) | 234741. | + | 406583.i | 0.0565108 | + | 0.0978796i | ||||
\(445\) | 2.52968e6 | + | 4.38153e6i | 0.605571 | + | 1.04888i | ||||
\(446\) | 7.16881e6 | 1.70651 | ||||||||
\(447\) | −2.05021e6 | − | 3.55107e6i | −0.485322 | − | 0.840603i | ||||
\(448\) | −825587. | − | 1.42996e6i | −0.194343 | − | 0.336611i | ||||
\(449\) | 988357. | − | 1.71188e6i | 0.231365 | − | 0.400736i | −0.726845 | − | 0.686802i | \(-0.759014\pi\) |
0.958210 | + | 0.286065i | \(0.0923475\pi\) | |||||||
\(450\) | 368060. | − | 637499.i | 0.0856816 | − | 0.148405i | ||||
\(451\) | 24306.2 | 0.00562698 | ||||||||
\(452\) | −265557. | −0.0611381 | ||||||||
\(453\) | −128494. | + | 222558.i | −0.0294196 | + | 0.0509562i | ||||
\(454\) | 149590. | − | 259097.i | 0.0340613 | − | 0.0589959i | ||||
\(455\) | 5.04422e6 | + | 8.73684e6i | 1.14226 | + | 1.97845i | ||||
\(456\) | −2.70958e6 | − | 4.69313e6i | −0.610225 | − | 1.05694i | ||||
\(457\) | −5.08786e6 | −1.13958 | −0.569790 | − | 0.821790i | \(-0.692976\pi\) | ||||
−0.569790 | + | 0.821790i | \(0.692976\pi\) | |||||||
\(458\) | −302867. | − | 524581.i | −0.0674665 | − | 0.116855i | ||||
\(459\) | −4.49773e6 | − | 7.79030e6i | −0.996464 | − | 1.72593i | ||||
\(460\) | −2.06424e6 | − | 3.57537e6i | −0.454847 | − | 0.787819i | ||||
\(461\) | −881697. | + | 1.52714e6i | −0.193227 | + | 0.334678i | −0.946318 | − | 0.323238i | \(-0.895229\pi\) |
0.753091 | + | 0.657916i | \(0.228562\pi\) | |||||||
\(462\) | 1.83605e6 | 0.400203 | ||||||||
\(463\) | −1.07000e6 | + | 1.85330e6i | −0.231970 | + | 0.401784i | −0.958388 | − | 0.285469i | \(-0.907851\pi\) |
0.726418 | + | 0.687254i | \(0.241184\pi\) | |||||||
\(464\) | 1.44678e6 | + | 2.50590e6i | 0.311967 | + | 0.540343i | ||||
\(465\) | −2.64891e6 | −0.568113 | ||||||||
\(466\) | 2.39379e6 | + | 4.14617e6i | 0.510648 | + | 0.884467i | ||||
\(467\) | 1.55319e6 | − | 2.69020e6i | 0.329558 | − | 0.570811i | −0.652866 | − | 0.757473i | \(-0.726434\pi\) |
0.982424 | + | 0.186662i | \(0.0597671\pi\) | |||||||
\(468\) | −181552. | + | 314457.i | −0.0383165 | + | 0.0663662i | ||||
\(469\) | −217505. | −0.0456601 | ||||||||
\(470\) | 1.72367e6 | − | 2.98548e6i | 0.359922 | − | 0.623404i | ||||
\(471\) | −2.29810e6 | −0.477328 | ||||||||
\(472\) | 2.21564e6 | 0.457767 | ||||||||
\(473\) | 1.53226e6 | + | 58531.1i | 0.314905 | + | 0.0120291i | ||||
\(474\) | −2.56530e6 | −0.524436 | ||||||||
\(475\) | −9.61979e6 | −1.95628 | ||||||||
\(476\) | 2.17128e6 | − | 3.76077e6i | 0.439237 | − | 0.760780i | ||||
\(477\) | −759084. | −0.152754 | ||||||||
\(478\) | 2.88070e6 | − | 4.98951e6i | 0.576670 | − | 0.998822i | ||||
\(479\) | −4.43049e6 | + | 7.67384e6i | −0.882294 | + | 1.52818i | −0.0335093 | + | 0.999438i | \(0.510668\pi\) |
−0.848784 | + | 0.528739i | \(0.822665\pi\) | |||||||
\(480\) | 2.56211e6 | + | 4.43770e6i | 0.507568 | + | 0.879134i | ||||
\(481\) | 2.11481e6 | 0.416782 | ||||||||
\(482\) | −1.07772e6 | − | 1.86666e6i | −0.211294 | − | 0.365972i | ||||
\(483\) | −4.32579e6 | + | 7.49248e6i | −0.843718 | + | 1.46136i | ||||
\(484\) | −1.87261e6 | −0.363358 | ||||||||
\(485\) | −5.25514e6 | + | 9.10217e6i | −1.01445 | + | 1.75708i | ||||
\(486\) | −841800. | − | 1.45804e6i | −0.161666 | − | 0.280014i | ||||
\(487\) | 4.51371e6 | + | 7.81797e6i | 0.862405 | + | 1.49373i | 0.869601 | + | 0.493754i | \(0.164376\pi\) |
−0.00719675 | + | 0.999974i | \(0.502291\pi\) | |||||||
\(488\) | −1.92175e6 | − | 3.32856e6i | −0.365298 | − | 0.632714i | ||||
\(489\) | 3.03667e6 | 0.574283 | ||||||||
\(490\) | −1.49876e6 | − | 2.59594e6i | −0.281996 | − | 0.488432i | ||||
\(491\) | −1.09845e6 | − | 1.90256e6i | −0.205625 | − | 0.356152i | 0.744707 | − | 0.667392i | \(-0.232589\pi\) |
−0.950332 | + | 0.311239i | \(0.899256\pi\) | |||||||
\(492\) | −17959.9 | + | 31107.4i | −0.00334495 | + | 0.00579363i | ||||
\(493\) | 2.55995e6 | − | 4.43396e6i | 0.474366 | − | 0.821626i | ||||
\(494\) | 1.65073e7 | 3.04340 | ||||||||
\(495\) | −338358. | −0.0620674 | ||||||||
\(496\) | −1.45139e6 | + | 2.51388e6i | −0.264899 | + | 0.458819i | ||||
\(497\) | 5.16858e6 | − | 8.95224e6i | 0.938599 | − | 1.62570i | ||||
\(498\) | 1.45163e6 | + | 2.51429e6i | 0.262290 | + | 0.454299i | ||||
\(499\) | 3.02136e6 | + | 5.23315e6i | 0.543189 | + | 0.940832i | 0.998718 | + | 0.0506108i | \(0.0161168\pi\) |
−0.455529 | + | 0.890221i | \(0.650550\pi\) | |||||||
\(500\) | 168301. | 0.0301066 | ||||||||
\(501\) | 1.49048e6 | + | 2.58159e6i | 0.265297 | + | 0.459508i | ||||
\(502\) | −4.76373e6 | − | 8.25103e6i | −0.843700 | − | 1.46133i | ||||
\(503\) | −5.26666e6 | − | 9.12213e6i | −0.928145 | − | 1.60759i | −0.786424 | − | 0.617687i | \(-0.788070\pi\) |
−0.141720 | − | 0.989907i | \(-0.545263\pi\) | |||||||
\(504\) | −319804. | + | 553916.i | −0.0560799 | + | 0.0971332i | ||||
\(505\) | 430059. | 0.0750412 | ||||||||
\(506\) | −1.69229e6 | + | 2.93113e6i | −0.293831 | + | 0.508931i | ||||
\(507\) | −2.44274e6 | − | 4.23096e6i | −0.422044 | − | 0.731002i | ||||
\(508\) | 1.26858e6 | 0.218101 | ||||||||
\(509\) | −3.64087e6 | − | 6.30617e6i | −0.622889 | − | 1.07887i | −0.988945 | − | 0.148282i | \(-0.952626\pi\) |
0.366056 | − | 0.930593i | \(-0.380708\pi\) | |||||||
\(510\) | 8.73238e6 | − | 1.51249e7i | 1.48665 | − | 2.57494i | ||||
\(511\) | −952978. | + | 1.65061e6i | −0.161447 | + | 0.279635i | ||||
\(512\) | 414251. | 0.0698375 | ||||||||
\(513\) | −5.85422e6 | + | 1.01398e7i | −0.982145 | + | 1.70113i | ||||
\(514\) | 7.46397e6 | 1.24613 | ||||||||
\(515\) | 3.15196e6 | 0.523677 | ||||||||
\(516\) | −1.20710e6 | + | 1.91776e6i | −0.199581 | + | 0.317081i | ||||
\(517\) | −812398. | −0.133673 | ||||||||
\(518\) | −2.51910e6 | −0.412498 | ||||||||
\(519\) | −1.38986e6 | + | 2.40731e6i | −0.226492 | + | 0.392296i | ||||
\(520\) | 8.62498e6 | 1.39878 | ||||||||
\(521\) | 4.07788e6 | − | 7.06309e6i | 0.658172 | − | 1.13999i | −0.322916 | − | 0.946428i | \(-0.604663\pi\) |
0.981088 | − | 0.193560i | \(-0.0620036\pi\) | |||||||
\(522\) | 254971. | − | 441622.i | 0.0409556 | − | 0.0709372i | ||||
\(523\) | 1.09579e6 | + | 1.89797e6i | 0.175176 | + | 0.303414i | 0.940222 | − | 0.340562i | \(-0.110617\pi\) |
−0.765046 | + | 0.643975i | \(0.777284\pi\) | |||||||
\(524\) | 1.22145e6 | 0.194333 | ||||||||
\(525\) | −3.56134e6 | − | 6.16842e6i | −0.563917 | − | 0.976732i | ||||
\(526\) | −922285. | + | 1.59744e6i | −0.145345 | + | 0.251745i | ||||
\(527\) | 5.13620e6 | 0.805593 | ||||||||
\(528\) | 1.16303e6 | − | 2.01443e6i | 0.181554 | − | 0.314461i | ||||
\(529\) | −4.75598e6 | − | 8.23761e6i | −0.738926 | − | 1.27986i | ||||
\(530\) | −6.09647e6 | − | 1.05594e7i | −0.942733 | − | 1.63286i | ||||
\(531\) | −289306. | − | 501093.i | −0.0445268 | − | 0.0771226i | ||||
\(532\) | −5.65225e6 | −0.865850 | ||||||||
\(533\) | 80901.4 | + | 140125.i | 0.0123350 | + | 0.0213648i | ||||
\(534\) | 3.06475e6 | + | 5.30831e6i | 0.465096 | + | 0.805569i | ||||
\(535\) | 1.14801e6 | − | 1.98841e6i | 0.173405 | − | 0.300345i | ||||
\(536\) | −92976.6 | + | 161040.i | −0.0139785 | + | 0.0242115i | ||||
\(537\) | 4.61854e6 | 0.691145 | ||||||||
\(538\) | 9.42486e6 | 1.40384 | ||||||||
\(539\) | −353198. | + | 611757.i | −0.0523657 | + | 0.0907000i | ||||
\(540\) | 2.06844e6 | − | 3.58263e6i | 0.305251 | − | 0.528711i | ||||
\(541\) | 326611. | + | 565707.i | 0.0479776 | + | 0.0830996i | 0.889017 | − | 0.457874i | \(-0.151389\pi\) |
−0.841039 | + | 0.540974i | \(0.818056\pi\) | |||||||
\(542\) | 6.50627e6 | + | 1.12692e7i | 0.951335 | + | 1.64776i | ||||
\(543\) | −1.22398e6 | −0.178145 | ||||||||
\(544\) | −4.96790e6 | − | 8.60465e6i | −0.719740 | − | 1.24663i | ||||
\(545\) | 5.14208e6 | + | 8.90634e6i | 0.741562 | + | 1.28442i | ||||
\(546\) | 6.11117e6 | + | 1.05849e7i | 0.877289 | + | 1.51951i | ||||
\(547\) | −345049. | + | 597643.i | −0.0493075 | + | 0.0854031i | −0.889626 | − | 0.456690i | \(-0.849035\pi\) |
0.840318 | + | 0.542093i | \(0.182368\pi\) | |||||||
\(548\) | 5.61636e6 | 0.798920 | ||||||||
\(549\) | −501862. | + | 869250.i | −0.0710646 | + | 0.123087i | ||||
\(550\) | −1.39323e6 | − | 2.41314e6i | −0.196388 | − | 0.340155i | ||||
\(551\) | −6.66403e6 | −0.935099 | ||||||||
\(552\) | 3.69828e6 | + | 6.40560e6i | 0.516597 | + | 0.894772i | ||||
\(553\) | 1.97836e6 | − | 3.42663e6i | 0.275102 | − | 0.476490i | ||||
\(554\) | 210246. | − | 364157.i | 0.0291041 | − | 0.0504098i | ||||
\(555\) | −2.91228e6 | −0.401330 | ||||||||
\(556\) | −1.36538e6 | + | 2.36490e6i | −0.187312 | + | 0.324434i | ||||
\(557\) | −8.71526e6 | −1.19026 | −0.595131 | − | 0.803629i | \(-0.702900\pi\) | ||||
−0.595131 | + | 0.803629i | \(0.702900\pi\) | |||||||
\(558\) | 511565. | 0.0695529 | ||||||||
\(559\) | 4.76259e6 | + | 9.02831e6i | 0.644635 | + | 1.22202i | ||||
\(560\) | −1.52242e7 | −2.05146 | ||||||||
\(561\) | −4.11574e6 | −0.552129 | ||||||||
\(562\) | 4.77880e6 | − | 8.27713e6i | 0.638231 | − | 1.10545i | ||||
\(563\) | 3.56075e6 | 0.473447 | 0.236723 | − | 0.971577i | \(-0.423927\pi\) | ||||
0.236723 | + | 0.971577i | \(0.423927\pi\) | |||||||
\(564\) | 600282. | − | 1.03972e6i | 0.0794616 | − | 0.137632i | ||||
\(565\) | 823650. | − | 1.42660e6i | 0.108548 | − | 0.188010i | ||||
\(566\) | 4.37968e6 | + | 7.58582e6i | 0.574647 | + | 0.995317i | ||||
\(567\) | −7.45428e6 | −0.973751 | ||||||||
\(568\) | −4.41881e6 | − | 7.65360e6i | −0.574691 | − | 0.995394i | ||||
\(569\) | −2.72714e6 | + | 4.72354e6i | −0.353123 | + | 0.611628i | −0.986795 | − | 0.161975i | \(-0.948214\pi\) |
0.633672 | + | 0.773602i | \(0.281547\pi\) | |||||||
\(570\) | −2.27320e7 | −2.93057 | ||||||||
\(571\) | 2.43360e6 | − | 4.21512e6i | 0.312362 | − | 0.541027i | −0.666511 | − | 0.745495i | \(-0.732213\pi\) |
0.978873 | + | 0.204468i | \(0.0655464\pi\) | |||||||
\(572\) | 687234. | + | 1.19032e6i | 0.0878243 | + | 0.152116i | ||||
\(573\) | −1.49747e6 | − | 2.59369e6i | −0.190533 | − | 0.330013i | ||||
\(574\) | −96367.3 | − | 166913.i | −0.0122082 | − | 0.0211451i | ||||
\(575\) | 1.31299e7 | 1.65612 | ||||||||
\(576\) | 184325. | + | 319261.i | 0.0231488 | + | 0.0400949i | ||||
\(577\) | 5.49945e6 | + | 9.52532e6i | 0.687669 | + | 1.19108i | 0.972590 | + | 0.232527i | \(0.0746993\pi\) |
−0.284921 | + | 0.958551i | \(0.591967\pi\) | |||||||
\(578\) | −1.21744e7 | + | 2.10867e7i | −1.51576 | + | 2.62537i | ||||
\(579\) | 6.23214e6 | − | 1.07944e7i | 0.772575 | − | 1.33814i | ||||
\(580\) | 2.35456e6 | 0.290629 | ||||||||
\(581\) | −4.47799e6 | −0.550354 | ||||||||
\(582\) | −6.36671e6 | + | 1.10275e7i | −0.779125 | + | 1.34948i | ||||
\(583\) | −1.43669e6 | + | 2.48842e6i | −0.175062 | + | 0.303216i | ||||
\(584\) | 814736. | + | 1.41116e6i | 0.0988519 | + | 0.171216i | ||||
\(585\) | −1.12620e6 | − | 1.95064e6i | −0.136059 | − | 0.235660i | ||||
\(586\) | 1.03376e6 | 0.124358 | ||||||||
\(587\) | −5.21729e6 | − | 9.03661e6i | −0.624956 | − | 1.08246i | −0.988549 | − | 0.150898i | \(-0.951783\pi\) |
0.363593 | − | 0.931558i | \(-0.381550\pi\) | |||||||
\(588\) | −521957. | − | 904057.i | −0.0622575 | − | 0.107833i | ||||
\(589\) | −3.34263e6 | − | 5.78960e6i | −0.397008 | − | 0.687638i | ||||
\(590\) | 4.64704e6 | − | 8.04890e6i | 0.549599 | − | 0.951933i | ||||
\(591\) | 4.50428e6 | 0.530464 | ||||||||
\(592\) | −1.59570e6 | + | 2.76384e6i | −0.187132 | + | 0.324122i | ||||
\(593\) | 3.21382e6 | + | 5.56651e6i | 0.375306 | + | 0.650049i | 0.990373 | − | 0.138426i | \(-0.0442044\pi\) |
−0.615067 | + | 0.788475i | \(0.710871\pi\) | |||||||
\(594\) | −3.39146e6 | −0.394385 | ||||||||
\(595\) | 1.34689e7 | + | 2.33287e7i | 1.55969 | + | 2.70146i | ||||
\(596\) | −1.82820e6 | + | 3.16653e6i | −0.210818 | + | 0.365147i | ||||
\(597\) | 796022. | − | 1.37875e6i | 0.0914091 | − | 0.158325i | ||||
\(598\) | −2.25307e7 | −2.57645 | ||||||||
\(599\) | −6.80546e6 | + | 1.17874e7i | −0.774980 | + | 1.34231i | 0.159825 | + | 0.987145i | \(0.448907\pi\) |
−0.934806 | + | 0.355160i | \(0.884426\pi\) | |||||||
\(600\) | −6.08944e6 | −0.690557 | ||||||||
\(601\) | 7.75878e6 | 0.876209 | 0.438104 | − | 0.898924i | \(-0.355650\pi\) | ||||
0.438104 | + | 0.898924i | \(0.355650\pi\) | |||||||
\(602\) | −5.67306e6 | − | 1.07543e7i | −0.638008 | − | 1.20945i | ||||
\(603\) | 48561.4 | 0.00543874 | ||||||||
\(604\) | 229158. | 0.0255590 | ||||||||
\(605\) | 5.80808e6 | − | 1.00599e7i | 0.645125 | − | 1.11739i | ||||
\(606\) | 521025. | 0.0576338 | ||||||||
\(607\) | −2.10666e6 | + | 3.64884e6i | −0.232072 | + | 0.401961i | −0.958418 | − | 0.285369i | \(-0.907884\pi\) |
0.726346 | + | 0.687330i | \(0.241217\pi\) | |||||||
\(608\) | −6.46619e6 | + | 1.11998e7i | −0.709397 | + | 1.22871i | ||||
\(609\) | −2.46709e6 | − | 4.27312e6i | −0.269551 | − | 0.466876i | ||||
\(610\) | −1.61225e7 | −1.75432 | ||||||||
\(611\) | −2.70401e6 | − | 4.68348e6i | −0.293025 | − | 0.507535i | ||||
\(612\) | −484772. | + | 839650.i | −0.0523190 | + | 0.0906191i | ||||
\(613\) | 5.01051e6 | 0.538556 | 0.269278 | − | 0.963062i | \(-0.413215\pi\) | ||||
0.269278 | + | 0.963062i | \(0.413215\pi\) | |||||||
\(614\) | 6.12840e6 | − | 1.06147e7i | 0.656033 | − | 1.13628i | ||||
\(615\) | −111408. | − | 192965.i | −0.0118776 | − | 0.0205727i | ||||
\(616\) | 1.21056e6 | + | 2.09676e6i | 0.128539 | + | 0.222636i | ||||
\(617\) | 4.47750e6 | + | 7.75526e6i | 0.473503 | + | 0.820131i | 0.999540 | − | 0.0303305i | \(-0.00965597\pi\) |
−0.526037 | + | 0.850462i | \(0.676323\pi\) | |||||||
\(618\) | 3.81867e6 | 0.402199 | ||||||||
\(619\) | 1.73192e6 | + | 2.99977e6i | 0.181677 | + | 0.314674i | 0.942452 | − | 0.334342i | \(-0.108514\pi\) |
−0.760775 | + | 0.649016i | \(0.775181\pi\) | |||||||
\(620\) | 1.18103e6 | + | 2.04560e6i | 0.123390 | + | 0.213718i | ||||
\(621\) | 7.99036e6 | − | 1.38397e7i | 0.831452 | − | 1.44012i | ||||
\(622\) | 3.45367e6 | − | 5.98194e6i | 0.357936 | − | 0.619963i | ||||
\(623\) | −9.45417e6 | −0.975895 | ||||||||
\(624\) | 1.54842e7 | 1.59195 | ||||||||
\(625\) | 4.61519e6 | − | 7.99374e6i | 0.472595 | − | 0.818559i | ||||
\(626\) | −6.07565e6 | + | 1.05233e7i | −0.619665 | + | 1.07329i | ||||
\(627\) | 2.67851e6 | + | 4.63932e6i | 0.272098 | + | 0.471287i | ||||
\(628\) | 1.02462e6 | + | 1.77469e6i | 0.103672 | + | 0.179566i | ||||
\(629\) | 5.64688e6 | 0.569092 | ||||||||
\(630\) | 1.34150e6 | + | 2.32354e6i | 0.134660 | + | 0.233238i | ||||
\(631\) | −9.19741e6 | − | 1.59304e7i | −0.919586 | − | 1.59277i | −0.800045 | − | 0.599940i | \(-0.795191\pi\) |
−0.119540 | − | 0.992829i | \(-0.538142\pi\) | |||||||
\(632\) | −1.69138e6 | − | 2.92955e6i | −0.168441 | − | 0.291748i | ||||
\(633\) | 6.67823e6 | − | 1.15670e7i | 0.662448 | − | 1.14739i | ||||
\(634\) | −2.12820e7 | −2.10276 | ||||||||
\(635\) | −3.93462e6 | + | 6.81495e6i | −0.387229 | + | 0.670701i | ||||
\(636\) | −2.12315e6 | − | 3.67740e6i | −0.208131 | − | 0.360494i | ||||
\(637\) | −4.70238e6 | −0.459166 | ||||||||
\(638\) | −965148. | − | 1.67168e6i | −0.0938733 | − | 0.162593i | ||||
\(639\) | −1.15397e6 | + | 1.99873e6i | −0.111800 | + | 0.193643i | ||||
\(640\) | −8.62397e6 | + | 1.49371e7i | −0.832256 | + | 1.44151i | ||||
\(641\) | 1.82412e7 | 1.75351 | 0.876756 | − | 0.480936i | \(-0.159703\pi\) | ||||
0.876756 | + | 0.480936i | \(0.159703\pi\) | |||||||
\(642\) | 1.39083e6 | − | 2.40900e6i | 0.133180 | − | 0.230674i | ||||
\(643\) | 7.75417e6 | 0.739619 | 0.369809 | − | 0.929108i | \(-0.379423\pi\) | ||||
0.369809 | + | 0.929108i | \(0.379423\pi\) | |||||||
\(644\) | 7.71470e6 | 0.733000 | ||||||||
\(645\) | −6.55851e6 | − | 1.24328e7i | −0.620734 | − | 1.17671i | ||||
\(646\) | 4.40772e7 | 4.15559 | ||||||||
\(647\) | 1.50603e7 | 1.41440 | 0.707199 | − | 0.707014i | \(-0.249958\pi\) | ||||
0.707199 | + | 0.707014i | \(0.249958\pi\) | |||||||
\(648\) | −3.18647e6 | + | 5.51913e6i | −0.298107 | + | 0.516336i | ||||
\(649\) | −2.19024e6 | −0.204117 | ||||||||
\(650\) | 9.27453e6 | − | 1.60640e7i | 0.861011 | − | 1.49131i | ||||
\(651\) | 2.47494e6 | − | 4.28673e6i | 0.228883 | − | 0.396436i | ||||
\(652\) | −1.35392e6 | − | 2.34505e6i | −0.124730 | − | 0.216040i | ||||
\(653\) | −1.72831e7 | −1.58613 | −0.793064 | − | 0.609138i | \(-0.791515\pi\) | ||||
−0.793064 | + | 0.609138i | \(0.791515\pi\) | |||||||
\(654\) | 6.22973e6 | + | 1.07902e7i | 0.569541 | + | 0.986474i | ||||
\(655\) | −3.78843e6 | + | 6.56175e6i | −0.345029 | + | 0.597608i | ||||
\(656\) | −244172. | −0.0221532 | ||||||||
\(657\) | 212767. | − | 368524.i | 0.0192305 | − | 0.0333083i | ||||
\(658\) | 3.22094e6 | + | 5.57882e6i | 0.290013 | + | 0.502317i | ||||
\(659\) | −122541. | − | 212248.i | −0.0109918 | − | 0.0190384i | 0.860477 | − | 0.509489i | \(-0.170166\pi\) |
−0.871469 | + | 0.490451i | \(0.836832\pi\) | |||||||
\(660\) | −946382. | − | 1.63918e6i | −0.0845681 | − | 0.146476i | ||||
\(661\) | 1.24794e7 | 1.11093 | 0.555467 | − | 0.831538i | \(-0.312539\pi\) | ||||
0.555467 | + | 0.831538i | \(0.312539\pi\) | |||||||
\(662\) | 1.55148e6 | + | 2.68724e6i | 0.137594 | + | 0.238321i | ||||
\(663\) | −1.36990e7 | − | 2.37273e7i | −1.21033 | − | 2.09635i | ||||
\(664\) | −1.91420e6 | + | 3.31549e6i | −0.168487 | + | 0.291828i | ||||
\(665\) | 1.75310e7 | − | 3.03646e7i | 1.53728 | − | 2.66264i | ||||
\(666\) | 562429. | 0.0491340 | ||||||||
\(667\) | 9.09565e6 | 0.791625 | ||||||||
\(668\) | 1.32908e6 | − | 2.30203e6i | 0.115242 | − | 0.199604i | ||||
\(669\) | −7.74343e6 | + | 1.34120e7i | −0.668910 | + | 1.15859i | ||||
\(670\) | 390014. | + | 675524.i | 0.0335655 | + | 0.0581371i | ||||
\(671\) | 1.89971e6 | + | 3.29040e6i | 0.162885 | + | 0.282125i | ||||
\(672\) | −9.57538e6 | −0.817962 | ||||||||
\(673\) | 1.52145e6 | + | 2.63523e6i | 0.129485 | + | 0.224275i | 0.923477 | − | 0.383653i | \(-0.125334\pi\) |
−0.793992 | + | 0.607928i | \(0.792001\pi\) | |||||||
\(674\) | 3.41802e6 | + | 5.92019e6i | 0.289818 | + | 0.501979i | ||||
\(675\) | 6.57831e6 | + | 1.13940e7i | 0.555719 | + | 0.962533i | ||||
\(676\) | −2.17822e6 | + | 3.77279e6i | −0.183331 | + | 0.317538i | ||||
\(677\) | −9.51921e6 | −0.798233 | −0.399116 | − | 0.916900i | \(-0.630683\pi\) | ||||
−0.399116 | + | 0.916900i | \(0.630683\pi\) | |||||||
\(678\) | 997868. | − | 1.72836e6i | 0.0833679 | − | 0.144397i | ||||
\(679\) | −9.82003e6 | − | 1.70088e7i | −0.817407 | − | 1.41579i | ||||
\(680\) | 2.30300e7 | 1.90995 | ||||||||
\(681\) | 323160. | + | 559729.i | 0.0267024 | + | 0.0462499i | ||||
\(682\) | 968222. | − | 1.67701e6i | 0.0797102 | − | 0.138062i | ||||
\(683\) | 1.94066e6 | − | 3.36132e6i | 0.159183 | − | 0.275714i | −0.775391 | − | 0.631481i | \(-0.782447\pi\) |
0.934574 | + | 0.355768i | \(0.115781\pi\) | |||||||
\(684\) | 1.26195e6 | 0.103134 | ||||||||
\(685\) | −1.74196e7 | + | 3.01717e7i | −1.41845 | + | 2.45682i | ||||
\(686\) | −1.12530e7 | −0.912973 | ||||||||
\(687\) | 1.30857e6 | 0.105781 | ||||||||
\(688\) | −1.53926e7 | − | 587984.i | −1.23977 | − | 0.0473581i | ||||
\(689\) | −1.91277e7 | −1.53502 | ||||||||
\(690\) | 3.10267e7 | 2.48092 | ||||||||
\(691\) | 6.28227e6 | − | 1.08812e7i | 0.500520 | − | 0.866926i | −0.499480 | − | 0.866325i | \(-0.666476\pi\) |
1.00000 | 0.000600381i | \(-0.000191107\pi\) | ||||||||
\(692\) | 2.47871e6 | 0.196771 | ||||||||
\(693\) | 316137. | − | 547565.i | 0.0250059 | − | 0.0433114i | ||||
\(694\) | −5.89173e6 | + | 1.02048e7i | −0.464348 | + | 0.804275i | ||||
\(695\) | −8.46969e6 | − | 1.46699e7i | −0.665129 | − | 1.15204i | ||||
\(696\) | −4.21841e6 | −0.330085 | ||||||||
\(697\) | 216019. | + | 374157.i | 0.0168427 | + | 0.0291724i | ||||
\(698\) | 1.02857e7 | − | 1.78153e7i | 0.799089 | − | 1.38406i | ||||
\(699\) | −1.03427e7 | −0.800644 | ||||||||
\(700\) | −3.17568e6 | + | 5.50044e6i | −0.244958 | + | 0.424280i | ||||
\(701\) | 5.57285e6 | + | 9.65246e6i | 0.428334 | + | 0.741896i | 0.996725 | − | 0.0808625i | \(-0.0257675\pi\) |
−0.568392 | + | 0.822758i | \(0.692434\pi\) | |||||||
\(702\) | −1.12882e7 | − | 1.95518e7i | −0.864535 | − | 1.49742i | ||||
\(703\) | −3.67498e6 | − | 6.36525e6i | −0.280457 | − | 0.485766i | ||||
\(704\) | 1.39546e6 | 0.106118 | ||||||||
\(705\) | 3.72366e6 | + | 6.44957e6i | 0.282161 | + | 0.488717i | ||||
\(706\) | −6.70031e6 | − | 1.16053e7i | −0.505921 | − | 0.876281i | ||||
\(707\) | −401815. | + | 695965.i | −0.0302328 | + | 0.0523647i | ||||
\(708\) | 1.61837e6 | − | 2.80310e6i | 0.121337 | − | 0.210162i | ||||
\(709\) | −1.12600e7 | −0.841243 | −0.420622 | − | 0.907236i | \(-0.638188\pi\) | ||||
−0.420622 | + | 0.907236i | \(0.638188\pi\) | |||||||
\(710\) | −3.70716e7 | −2.75991 | ||||||||
\(711\) | −441701. | + | 765049.i | −0.0327683 | + | 0.0567564i | ||||
\(712\) | −4.04136e6 | + | 6.99984e6i | −0.298764 | + | 0.517474i | ||||
\(713\) | 4.56231e6 | + | 7.90215e6i | 0.336094 | + | 0.582132i | ||||
\(714\) | 1.63178e7 | + | 2.82632e7i | 1.19789 | + | 2.07480i | ||||
\(715\) | −8.52608e6 | −0.623712 | ||||||||
\(716\) | −2.05920e6 | − | 3.56664e6i | −0.150112 | − | 0.260002i | ||||
\(717\) | 6.22320e6 | + | 1.07789e7i | 0.452081 | + | 0.783027i | ||||
\(718\) | 3.02645e6 | + | 5.24197e6i | 0.219090 | + | 0.379475i | ||||
\(719\) | −6.24554e6 | + | 1.08176e7i | −0.450555 | + | 0.780384i | −0.998421 | − | 0.0561824i | \(-0.982107\pi\) |
0.547866 | + | 0.836566i | \(0.315441\pi\) | |||||||
\(720\) | 3.39903e6 | 0.244357 | ||||||||
\(721\) | −2.94496e6 | + | 5.10082e6i | −0.210980 | + | 0.365428i | ||||
\(722\) | −2.03886e7 | − | 3.53140e7i | −1.45561 | − | 2.52118i | ||||
\(723\) | 4.65641e6 | 0.331288 | ||||||||
\(724\) | 545716. | + | 945208.i | 0.0386919 | + | 0.0670164i | ||||
\(725\) | −3.74414e6 | + | 6.48504e6i | −0.264549 | + | 0.458213i | ||||
\(726\) | 7.03661e6 | − | 1.21878e7i | 0.495475 | − | 0.858188i | ||||
\(727\) | 1.74704e7 | 1.22594 | 0.612968 | − | 0.790108i | \(-0.289975\pi\) | ||||
0.612968 | + | 0.790108i | \(0.289975\pi\) | |||||||
\(728\) | −8.05854e6 | + | 1.39578e7i | −0.563544 | + | 0.976087i | ||||
\(729\) | 1.57420e7 | 1.09708 | ||||||||
\(730\) | 6.83523e6 | 0.474729 | ||||||||
\(731\) | 1.27169e7 | + | 2.41070e7i | 0.880211 | + | 1.66859i | ||||
\(732\) | −5.61480e6 | −0.387308 | ||||||||
\(733\) | 2.31567e6 | 0.159190 | 0.0795952 | − | 0.996827i | \(-0.474637\pi\) | ||||
0.0795952 | + | 0.996827i | \(0.474637\pi\) | |||||||
\(734\) | −5.63629e6 | + | 9.76234e6i | −0.386148 | + | 0.668827i | ||||
\(735\) | 6.47560e6 | 0.442142 | ||||||||
\(736\) | 8.82563e6 | − | 1.52864e7i | 0.600553 | − | 1.04019i | ||||
\(737\) | 91910.5 | − | 159194.i | 0.00623299 | − | 0.0107959i | ||||
\(738\) | 21515.5 | + | 37266.0i | 0.00145416 | + | 0.00251867i | ||||
\(739\) | 3.84040e6 | 0.258682 | 0.129341 | − | 0.991600i | \(-0.458714\pi\) | ||||
0.129341 | + | 0.991600i | \(0.458714\pi\) | |||||||
\(740\) | 1.29846e6 | + | 2.24899e6i | 0.0871662 | + | 0.150976i | ||||
\(741\) | −1.78305e7 | + | 3.08833e7i | −1.19294 | + | 2.06623i | ||||
\(742\) | 2.27844e7 | 1.51924 | ||||||||
\(743\) | 6.41374e6 | − | 1.11089e7i | 0.426225 | − | 0.738244i | −0.570309 | − | 0.821431i | \(-0.693176\pi\) |
0.996534 | + | 0.0831865i | \(0.0265097\pi\) | |||||||
\(744\) | −2.11592e6 | − | 3.66488e6i | −0.140142 | − | 0.242732i | ||||
\(745\) | −1.13406e7 | − | 1.96426e7i | −0.748595 | − | 1.29660i | ||||
\(746\) | 9.32726e6 | + | 1.61553e7i | 0.613631 | + | 1.06284i | ||||
\(747\) | 999781. | 0.0655546 | ||||||||
\(748\) | 1.83502e6 | + | 3.17835e6i | 0.119919 | + | 0.207706i | ||||
\(749\) | 2.14523e6 | + | 3.71564e6i | 0.139723 | + | 0.242008i | ||||
\(750\) | −632415. | + | 1.09538e6i | −0.0410534 | + | 0.0711066i | ||||
\(751\) | −4.50277e6 | + | 7.79902e6i | −0.291326 | + | 0.504592i | −0.974124 | − | 0.226016i | \(-0.927430\pi\) |
0.682797 | + | 0.730608i | \(0.260763\pi\) | |||||||
\(752\) | 8.16108e6 | 0.526263 | ||||||||
\(753\) | 2.05823e7 | 1.32284 | ||||||||
\(754\) | 6.42485e6 | − | 1.11282e7i | 0.411562 | − | 0.712845i | ||||
\(755\) | −710756. | + | 1.23106e6i | −0.0453788 | + | 0.0785984i | ||||
\(756\) | 3.86519e6 | + | 6.69470e6i | 0.245961 | + | 0.426017i | ||||
\(757\) | −7.22813e6 | − | 1.25195e7i | −0.458444 | − | 0.794049i | 0.540435 | − | 0.841386i | \(-0.318260\pi\) |
−0.998879 | + | 0.0473372i | \(0.984926\pi\) | |||||||
\(758\) | 9.56865e6 | 0.604892 | ||||||||
\(759\) | −3.65587e6 | − | 6.33216e6i | −0.230349 | − | 0.398976i | ||||
\(760\) | −1.49879e7 | − | 2.59598e7i | −0.941254 | − | 1.63030i | ||||
\(761\) | 6.95980e6 | + | 1.20547e7i | 0.435647 | + | 0.754563i | 0.997348 | − | 0.0727771i | \(-0.0231862\pi\) |
−0.561701 | + | 0.827340i | \(0.689853\pi\) | |||||||
\(762\) | −4.76687e6 | + | 8.25646e6i | −0.297403 | + | 0.515117i | ||||
\(763\) | −1.92175e7 | −1.19505 | ||||||||
\(764\) | −1.33531e6 | + | 2.31282e6i | −0.0827652 | + | 0.143354i | ||||
\(765\) | −3.00713e6 | − | 5.20851e6i | −0.185780 | − | 0.321780i | ||||
\(766\) | 1.24303e7 | 0.765438 | ||||||||
\(767\) | −7.29005e6 | − | 1.26267e7i | −0.447448 | − | 0.775002i | ||||
\(768\) | −7.89220e6 | + | 1.36697e7i | −0.482831 | + | 0.836287i | ||||
\(769\) | 1.31773e7 | − | 2.28237e7i | 0.803545 | − | 1.39178i | −0.113724 | − | 0.993512i | \(-0.536278\pi\) |
0.917269 | − | 0.398268i | \(-0.130389\pi\) | |||||||
\(770\) | 1.01560e7 | 0.617300 | ||||||||
\(771\) | −8.06225e6 | + | 1.39642e7i | −0.488450 | + | 0.846020i | ||||
\(772\) | −1.11145e7 | −0.671193 | ||||||||
\(773\) | −2.13712e7 | −1.28641 | −0.643205 | − | 0.765694i | \(-0.722396\pi\) | ||||
−0.643205 | + | 0.765694i | \(0.722396\pi\) | |||||||
\(774\) | 1.26660e6 | + | 2.40106e6i | 0.0759953 | + | 0.144062i | ||||
\(775\) | −7.51213e6 | −0.449271 | ||||||||
\(776\) | −1.67910e7 | −1.00097 | ||||||||
\(777\) | 2.72102e6 | − | 4.71295e6i | 0.161689 | − | 0.280053i | ||||
\(778\) | 1.75453e7 | 1.03923 | ||||||||
\(779\) | 281170. | − | 487000.i | 0.0166006 | − | 0.0287532i | ||||
\(780\) | 6.29993e6 | − | 1.09118e7i | 0.370766 | − | 0.642185i | ||||
\(781\) | 4.36814e6 | + | 7.56584e6i | 0.256253 | + | 0.443843i | ||||
\(782\) | −6.01604e7 | −3.51798 | ||||||||
\(783\) | 4.55707e6 | + | 7.89307e6i | 0.265632 | + | 0.460089i | ||||
\(784\) | 3.54811e6 | − | 6.14552e6i | 0.206161 | − | 0.357082i | ||||
\(785\) | −1.27118e7 | −0.736263 | ||||||||
\(786\) | −4.58976e6 | + | 7.94969e6i | −0.264992 | + | 0.458980i | ||||
\(787\) | 2.45063e6 | + | 4.24461e6i | 0.141039 | + | 0.244287i | 0.927888 | − | 0.372858i | \(-0.121622\pi\) |
−0.786849 | + | 0.617146i | \(0.788289\pi\) | |||||||
\(788\) | −2.00825e6 | − | 3.47840e6i | −0.115213 | − | 0.199555i | ||||
\(789\) | −1.99242e6 | − | 3.45098e6i | −0.113943 | − | 0.197356i | ||||
\(790\) | −1.41898e7 | −0.808927 | ||||||||
\(791\) | 1.53911e6 | + | 2.66582e6i | 0.0874641 | + | 0.151492i | ||||
\(792\) | −270277. | − | 468133.i | −0.0153107 | − | 0.0265190i | ||||
\(793\) | −1.26461e7 | + | 2.19037e7i | −0.714125 | + | 1.23690i | ||||
\(794\) | 1.37922e7 | − | 2.38889e7i | 0.776396 | − | 1.34476i | ||||
\(795\) | 2.63405e7 | 1.47811 | ||||||||
\(796\) | −1.41964e6 | −0.0794139 | ||||||||
\(797\) | 357156. | − | 618612.i | 0.0199164 | − | 0.0344963i | −0.855895 | − | 0.517149i | \(-0.826993\pi\) |
0.875812 | + | 0.482653i | \(0.160327\pi\) | |||||||
\(798\) | 2.12391e7 | − | 3.67873e7i | 1.18067 | − | 2.04499i | ||||
\(799\) | −7.22013e6 | − | 1.25056e7i | −0.400109 | − | 0.693009i | ||||
\(800\) | 7.26597e6 | + | 1.25850e7i | 0.401392 | + | 0.695231i | ||||
\(801\) | 2.11079e6 | 0.116242 | ||||||||
\(802\) | 1.79071e6 | + | 3.10160e6i | 0.0983081 | + | 0.170275i | ||||
\(803\) | −805394. | − | 1.39498e6i | −0.0440778 | − | 0.0763450i | ||||
\(804\) | 135826. | + | 235257.i | 0.00741040 | + | 0.0128352i | ||||
\(805\) | −2.39278e7 | + | 4.14442e7i | −1.30141 | + | 2.25411i | ||||
\(806\) | 1.28906e7 | 0.698935 | ||||||||
\(807\) | −1.01803e7 | + | 1.76328e7i | −0.550272 | + | 0.953099i | ||||
\(808\) | 343527. | + | 595006.i | 0.0185111 | + | 0.0320622i | ||||
\(809\) | −1.35024e7 | −0.725337 | −0.362669 | − | 0.931918i | \(-0.618134\pi\) | ||||
−0.362669 | + | 0.931918i | \(0.618134\pi\) | |||||||
\(810\) | 1.33664e7 | + | 2.31514e7i | 0.715819 | + | 1.23984i | ||||
\(811\) | 1.65308e7 | − | 2.86322e7i | 0.882556 | − | 1.52863i | 0.0340660 | − | 0.999420i | \(-0.489154\pi\) |
0.848490 | − | 0.529212i | \(-0.177512\pi\) | |||||||
\(812\) | −2.19993e6 | + | 3.81038e6i | −0.117089 | + | 0.202805i | ||||
\(813\) | −2.81111e7 | −1.49160 | ||||||||
\(814\) | 1.06449e6 | − | 1.84375e6i | 0.0563094 | − | 0.0975307i | ||||
\(815\) | 1.67972e7 | 0.885814 | ||||||||
\(816\) | 4.13454e7 | 2.17371 | ||||||||
\(817\) | 1.88977e7 | − | 3.00234e7i | 0.990497 | − | 1.57364i | ||||
\(818\) | −1.86900e7 | −0.976622 | ||||||||
\(819\) | 4.20895e6 | 0.219263 | ||||||||
\(820\) | −99343.9 | + | 172069.i | −0.00515949 | + | 0.00893650i | ||||
\(821\) | 2.51338e7 | 1.30137 | 0.650685 | − | 0.759348i | \(-0.274482\pi\) | ||||
0.650685 | + | 0.759348i | \(0.274482\pi\) | |||||||
\(822\) | −2.11043e7 | + | 3.65536e7i | −1.08941 | + | 1.88691i | ||||
\(823\) | 70044.8 | − | 121321.i | 0.00360476 | − | 0.00624362i | −0.864217 | − | 0.503119i | \(-0.832186\pi\) |
0.867822 | + | 0.496875i | \(0.165519\pi\) | |||||||
\(824\) | 2.51776e6 | + | 4.36089e6i | 0.129180 | + | 0.223747i | ||||
\(825\) | 6.01962e6 | 0.307917 | ||||||||
\(826\) | 8.68369e6 | + | 1.50406e7i | 0.442848 | + | 0.767035i | ||||
\(827\) | −3.93111e6 | + | 6.80889e6i | −0.199872 | + | 0.346188i | −0.948487 | − | 0.316817i | \(-0.897386\pi\) |
0.748615 | + | 0.663005i | \(0.230719\pi\) | |||||||
\(828\) | −1.72243e6 | −0.0873102 | ||||||||
\(829\) | −1.38930e6 | + | 2.40634e6i | −0.0702119 | + | 0.121610i | −0.898994 | − | 0.437961i | \(-0.855701\pi\) |
0.828782 | + | 0.559571i | \(0.189034\pi\) | |||||||
\(830\) | 8.02959e6 | + | 1.39077e7i | 0.404574 | + | 0.700743i | ||||
\(831\) | 454198. | + | 786693.i | 0.0228161 | + | 0.0395187i | ||||
\(832\) | 4.64471e6 | + | 8.04487e6i | 0.232622 | + | 0.402912i | ||||
\(833\) | −1.25561e7 | −0.626964 | ||||||||
\(834\) | −1.02612e7 | − | 1.77729e7i | −0.510838 | − | 0.884797i | ||||
\(835\) | 8.24452e6 | + | 1.42799e7i | 0.409213 | + | 0.708777i | ||||
\(836\) | 2.38846e6 | − | 4.13693e6i | 0.118196 | − | 0.204721i | ||||
\(837\) | −4.57158e6 | + | 7.91821e6i | −0.225555 | + | 0.390673i | ||||
\(838\) | −3.26357e7 | −1.60540 | ||||||||
\(839\) | −3.13532e7 | −1.53772 | −0.768860 | − | 0.639417i | \(-0.779176\pi\) | ||||
−0.768860 | + | 0.639417i | \(0.779176\pi\) | |||||||
\(840\) | 1.10973e7 | − | 1.92211e7i | 0.542650 | − | 0.939898i | ||||
\(841\) | 7.66185e6 | − | 1.32707e7i | 0.373546 | − | 0.647000i | ||||
\(842\) | −1.51918e7 | − | 2.63130e7i | −0.738463 | − | 1.27906i | ||||
\(843\) | 1.03237e7 | + | 1.78812e7i | 0.500341 | + | 0.866617i | ||||
\(844\) | −1.19101e7 | −0.575518 | ||||||||
\(845\) | −1.35119e7 | − | 2.34033e7i | −0.650990 | − | 1.12755i | ||||
\(846\) | −719124. | − | 1.24556e6i | −0.0345444 | − | 0.0598327i | ||||
\(847\) | 1.08533e7 | + | 1.87984e7i | 0.519820 | + | 0.900354i | ||||
\(848\) | 1.44325e7 | − | 2.49979e7i | 0.689212 | − | 1.19375i | ||||
\(849\) | −1.89229e7 | −0.900988 | ||||||||
\(850\) | 2.47645e7 | − | 4.28933e7i | 1.17566 | − | 2.03630i | ||||
\(851\) | 5.01593e6 | + | 8.68785e6i | 0.237426 | + | 0.411234i | ||||
\(852\) | −1.29105e7 | −0.609318 | ||||||||
\(853\) | 1.14610e7 | + | 1.98511e7i | 0.539326 | + | 0.934140i | 0.998940 | + | 0.0460215i | \(0.0146543\pi\) |
−0.459614 | + | 0.888119i | \(0.652012\pi\) | |||||||
\(854\) | 1.50637e7 | − | 2.60911e7i | 0.706784 | − | 1.22419i | ||||
\(855\) | −3.91407e6 | + | 6.77936e6i | −0.183110 | + | 0.317157i | ||||
\(856\) | 3.66807e6 | 0.171101 | ||||||||
\(857\) | 1.21459e7 | − | 2.10372e7i | 0.564906 | − | 0.978445i | −0.432153 | − | 0.901800i | \(-0.642246\pi\) |
0.997058 | − | 0.0766449i | \(-0.0244208\pi\) | |||||||
\(858\) | −1.03295e7 | −0.479029 | ||||||||
\(859\) | 6.79860e6 | 0.314367 | 0.157183 | − | 0.987569i | \(-0.449759\pi\) | ||||
0.157183 | + | 0.987569i | \(0.449759\pi\) | |||||||
\(860\) | −6.67699e6 | + | 1.06080e7i | −0.307847 | + | 0.489088i | ||||
\(861\) | 416367. | 0.0191412 | ||||||||
\(862\) | 1.25855e7 | 0.576903 | ||||||||
\(863\) | 1.31013e7 | − | 2.26922e7i | 0.598809 | − | 1.03717i | −0.394189 | − | 0.919030i | \(-0.628974\pi\) |
0.992997 | − | 0.118138i | \(-0.0376924\pi\) | |||||||
\(864\) | 1.76871e7 | 0.806070 | ||||||||
\(865\) | −7.68795e6 | + | 1.33159e7i | −0.349358 | + | 0.605105i | ||||
\(866\) | 1.37817e7 | − | 2.38705e7i | 0.624463 | − | 1.08160i | ||||
\(867\) | −2.63006e7 | − | 4.55539e7i | −1.18828 | − | 2.05815i | ||||
\(868\) | −4.41386e6 | −0.198847 | ||||||||
\(869\) | 1.67198e6 | + | 2.89596e6i | 0.0751074 | + | 0.130090i | ||||
\(870\) | −8.84759e6 | + | 1.53245e7i | −0.396302 | + | 0.686416i | ||||
\(871\) | 1.22367e6 | 0.0546537 | ||||||||
\(872\) | −8.21488e6 | + | 1.42286e7i | −0.365856 | + | 0.633681i | ||||
\(873\) | 2.19248e6 | + | 3.79748e6i | 0.0973642 | + | 0.168640i | ||||
\(874\) | 3.91522e7 | + | 6.78137e7i | 1.73372 | + | 3.00288i | ||||
\(875\) | −975439. | − | 1.68951e6i | −0.0430705 | − | 0.0746003i | ||||
\(876\) | 2.38043e6 | 0.104808 | ||||||||
\(877\) | −668743. | − | 1.15830e6i | −0.0293603 | − | 0.0508535i | 0.850972 | − | 0.525211i | \(-0.176014\pi\) |
−0.880332 | + | 0.474358i | \(0.842680\pi\) | |||||||
\(878\) | 3.88051e6 | + | 6.72124e6i | 0.169884 | + | 0.294248i | ||||
\(879\) | −1.11662e6 | + | 1.93404e6i | −0.0487454 | + | 0.0844295i | ||||
\(880\) | 6.43323e6 | − | 1.11427e7i | 0.280042 | − | 0.485046i | ||||
\(881\) | 2.55902e7 | 1.11079 | 0.555397 | − | 0.831585i | \(-0.312566\pi\) | ||||
0.555397 | + | 0.831585i | \(0.312566\pi\) | |||||||
\(882\) | −1.25059e6 | −0.0541306 | ||||||||
\(883\) | 1.79489e7 | − | 3.10883e7i | 0.774703 | − | 1.34182i | −0.160259 | − | 0.987075i | \(-0.551233\pi\) |
0.934961 | − | 0.354749i | \(-0.115434\pi\) | |||||||
\(884\) | −1.22155e7 | + | 2.11579e7i | −0.525751 | + | 0.910628i | ||||
\(885\) | 1.00390e7 | + | 1.73881e7i | 0.430858 | + | 0.746268i | ||||
\(886\) | −223512. | − | 387134.i | −0.00956570 | − | 0.0165683i | ||||
\(887\) | 1.39773e7 | 0.596505 | 0.298253 | − | 0.954487i | \(-0.403596\pi\) | ||||
0.298253 | + | 0.954487i | \(0.403596\pi\) | |||||||
\(888\) | −2.32630e6 | − | 4.02928e6i | −0.0989997 | − | 0.171473i | ||||
\(889\) | −7.35243e6 | − | 1.27348e7i | −0.312016 | − | 0.540427i | ||||
\(890\) | 1.69525e7 | + | 2.93626e7i | 0.717396 | + | 1.24257i | ||||
\(891\) | 3.14993e6 | − | 5.45584e6i | 0.132925 | − | 0.230233i | ||||
\(892\) | 1.38098e7 | 0.581132 | ||||||||
\(893\) | −9.39768e6 | + | 1.62773e7i | −0.394359 | + | 0.683050i | ||||
\(894\) | −1.37394e7 | − | 2.37974e7i | −0.574942 | − | 0.995829i | ||||
\(895\) | 2.55472e7 | 1.06607 | ||||||||
\(896\) | −1.61152e7 | − | 2.79123e7i | −0.670603 | − | 1.16152i | ||||
\(897\) | 2.43366e7 | − | 4.21523e7i | 1.00990 | − | 1.74920i | ||||
\(898\) | 6.62343e6 | − | 1.14721e7i | 0.274089 | − | 0.474736i | ||||
\(899\) | −5.20396e6 | −0.214751 | ||||||||
\(900\) | 709021. | − | 1.22806e6i | 0.0291778 | − | 0.0505374i | ||||
\(901\) | −5.10740e7 | −2.09598 | ||||||||
\(902\) | 162887. | 0.00666606 | ||||||||
\(903\) | 2.62478e7 | + | 1.00264e6i | 1.07121 | + | 0.0409192i | ||||
\(904\) | 2.63169e6 | 0.107106 | ||||||||
\(905\) | −6.77036e6 | −0.274783 | ||||||||
\(906\) | −861095. | + | 1.49146e6i | −0.0348522 | + | 0.0603658i | ||||
\(907\) | −3.51929e7 | −1.42049 | −0.710244 | − | 0.703956i | \(-0.751415\pi\) | ||||
−0.710244 | + | 0.703956i | \(0.751415\pi\) | |||||||
\(908\) | 288165. | − | 499116.i | 0.0115992 | − | 0.0200903i | ||||
\(909\) | 89711.6 | − | 155385.i | 0.00360113 | − | 0.00623734i | ||||
\(910\) | 3.38036e7 | + | 5.85495e7i | 1.35319 | + | 2.34380i | ||||
\(911\) | −9.27200e6 | −0.370150 | −0.185075 | − | 0.982724i | \(-0.559253\pi\) | ||||
−0.185075 | + | 0.982724i | \(0.559253\pi\) | |||||||
\(912\) | −2.69075e7 | − | 4.66051e7i | −1.07124 | − | 1.85544i | ||||
\(913\) | 1.89225e6 | − | 3.27747e6i | 0.0751280 | − | 0.130125i | ||||
\(914\) | −3.40961e7 | −1.35002 | ||||||||
\(915\) | 1.74148e7 | − | 3.01634e7i | 0.687648 | − | 1.19104i | ||||
\(916\) | −583434. | − | 1.01054e6i | −0.0229749 | − | 0.0397936i | ||||
\(917\) | −7.07925e6 | − | 1.22616e7i | −0.278012 | − | 0.481532i | ||||
\(918\) | −3.01413e7 | − | 5.22063e7i | −1.18047 | − | 2.04464i | ||||
\(919\) | 482262. | 0.0188362 | 0.00941811 | − | 0.999956i | \(-0.497002\pi\) | ||||
0.00941811 | + | 0.999956i | \(0.497002\pi\) | |||||||
\(920\) | 2.04568e7 | + | 3.54322e7i | 0.796835 | + | 1.38016i | ||||
\(921\) | 1.32392e7 | + | 2.29311e7i | 0.514297 | + | 0.890789i | ||||
\(922\) | −5.90865e6 | + | 1.02341e7i | −0.228908 | + | 0.396481i | ||||
\(923\) | −2.90781e7 | + | 5.03648e7i | −1.12347 | + | 1.94591i | ||||
\(924\) | 3.53692e6 | 0.136284 | ||||||||
\(925\) | −8.25904e6 | −0.317377 | ||||||||
\(926\) | −7.17058e6 | + | 1.24198e7i | −0.274806 | + | 0.475978i | ||||
\(927\) | 657509. | − | 1.13884e6i | 0.0251306 | − | 0.0435274i | ||||
\(928\) | 5.03344e6 | + | 8.71817e6i | 0.191865 | + | 0.332319i | ||||
\(929\) | 5.37891e6 | + | 9.31654e6i | 0.204482 | + | 0.354173i | 0.949968 | − | 0.312349i | \(-0.101116\pi\) |
−0.745486 | + | 0.666522i | \(0.767782\pi\) | |||||||
\(930\) | −1.77515e7 | −0.673021 | ||||||||
\(931\) | 8.17148e6 | + | 1.41534e7i | 0.308977 | + | 0.535164i | ||||
\(932\) | 4.61133e6 | + | 7.98706e6i | 0.173895 | + | 0.301194i | ||||
\(933\) | 7.46101e6 | + | 1.29229e7i | 0.280604 | + | 0.486020i | ||||
\(934\) | 1.04086e7 | − | 1.80282e7i | 0.390414 | − | 0.676217i | ||||
\(935\) | −2.27660e7 | −0.851643 | ||||||||
\(936\) | 1.79920e6 | − | 3.11630e6i | 0.0671257 | − | 0.116265i | ||||
\(937\) | 2.44181e7 | + | 4.22934e7i | 0.908581 | + | 1.57371i | 0.816037 | + | 0.577999i | \(0.196166\pi\) |
0.0925431 | + | 0.995709i | \(0.470500\pi\) | |||||||
\(938\) | −1.45760e6 | −0.0540918 | ||||||||
\(939\) | −1.31253e7 | − | 2.27337e7i | −0.485786 | − | 0.841406i | ||||
\(940\) | 3.32042e6 | − | 5.75114e6i | 0.122567 | − | 0.212292i | ||||
\(941\) | −6.15307e6 | + | 1.06574e7i | −0.226526 | + | 0.392354i | −0.956776 | − | 0.290825i | \(-0.906070\pi\) |
0.730250 | + | 0.683180i | \(0.239403\pi\) | |||||||
\(942\) | −1.54006e7 | −0.565471 | ||||||||
\(943\) | −383765. | + | 664701.i | −0.0140536 | + | 0.0243415i | ||||
\(944\) | 2.20024e7 | 0.803601 | ||||||||
\(945\) | −4.79529e7 | −1.74677 | ||||||||
\(946\) | 1.02684e7 | + | 392244.i | 0.373056 | + | 0.0142504i | ||||
\(947\) | 2.36458e7 | 0.856799 | 0.428400 | − | 0.903589i | \(-0.359078\pi\) | ||||
0.428400 | + | 0.903589i | \(0.359078\pi\) | |||||||
\(948\) | −4.94172e6 | −0.178590 | ||||||||
\(949\) | 5.36140e6 | − | 9.28621e6i | 0.193247 | − | 0.334713i | ||||
\(950\) | −6.44666e7 | −2.31753 | ||||||||
\(951\) | 2.29879e7 | − | 3.98162e7i | 0.824230 | − | 1.42761i | ||||
\(952\) | −2.15176e7 | + | 3.72695e7i | −0.769486 | + | 1.33279i | ||||
\(953\) | −1.58773e6 | − | 2.75002e6i | −0.0566296 | − | 0.0980854i | 0.836321 | − | 0.548240i | \(-0.184702\pi\) |
−0.892950 | + | 0.450155i | \(0.851369\pi\) | |||||||
\(954\) | −5.08696e6 | −0.180962 | ||||||||
\(955\) | −8.28316e6 | − | 1.43469e7i | −0.293892 | − | 0.509036i | ||||
\(956\) | 5.54929e6 | − | 9.61165e6i | 0.196378 | − | 0.340137i | ||||
\(957\) | 4.17004e6 | 0.147184 | ||||||||
\(958\) | −2.96907e7 | + | 5.14259e7i | −1.04522 | + | 1.81037i | ||||
\(959\) | −3.25513e7 | − | 5.63804e7i | −1.14293 | − | 1.97962i | ||||
\(960\) | −6.39617e6 | − | 1.10785e7i | −0.223997 | − | 0.387974i | ||||
\(961\) | 1.17043e7 | + | 2.02725e7i | 0.408825 | + | 0.708105i | ||||
\(962\) | 1.41723e7 | 0.493746 | ||||||||
\(963\) | −478956. | − | 829576.i | −0.0166429 | − | 0.0288264i | ||||
\(964\) | −2.07608e6 | − | 3.59588e6i | −0.0719536 | − | 0.124627i | ||||
\(965\) | 3.44727e7 | − | 5.97085e7i | 1.19167 | − | 2.06404i | ||||
\(966\) | −2.89891e7 | + | 5.02105e7i | −0.999520 | + | 1.73122i | ||||
\(967\) | −2.30138e7 | −0.791447 | −0.395724 | − | 0.918370i | \(-0.629506\pi\) | ||||
−0.395724 | + | 0.918370i | \(0.629506\pi\) | |||||||
\(968\) | 1.85578e7 | 0.636557 | ||||||||
\(969\) | −4.76102e7 | + | 8.24633e7i | −1.62889 | + | 2.82131i | ||||
\(970\) | −3.52171e7 | + | 6.09978e7i | −1.20178 | + | 2.08154i | ||||
\(971\) | 1.48150e7 | + | 2.56603e7i | 0.504258 | + | 0.873401i | 0.999988 | + | 0.00492403i | \(0.00156737\pi\) |
−0.495730 | + | 0.868477i | \(0.665099\pi\) | |||||||
\(972\) | −1.62162e6 | − | 2.80873e6i | −0.0550533 | − | 0.0953551i | ||||
\(973\) | 3.16538e7 | 1.07187 | ||||||||
\(974\) | 3.02484e7 | + | 5.23918e7i | 1.02166 | + | 1.76956i | ||||
\(975\) | 2.00359e7 | + | 3.47032e7i | 0.674989 | + | 1.16912i | ||||
\(976\) | −1.90839e7 | − | 3.30543e7i | −0.641272 | − | 1.11072i | ||||
\(977\) | 1.57030e6 | − | 2.71983e6i | 0.0526315 | − | 0.0911604i | −0.838509 | − | 0.544887i | \(-0.816572\pi\) |
0.891141 | + | 0.453727i | \(0.149906\pi\) | |||||||
\(978\) | 2.03501e7 | 0.680330 | ||||||||
\(979\) | 3.99502e6 | − | 6.91958e6i | 0.133218 | − | 0.230740i | ||||
\(980\) | −2.88718e6 | − | 5.00074e6i | −0.0960303 | − | 0.166329i | ||||
\(981\) | 4.29061e6 | 0.142346 | ||||||||
\(982\) | −7.36118e6 | − | 1.27499e7i | −0.243595 | − | 0.421919i | ||||
\(983\) | −959179. | + | 1.66135e6i | −0.0316604 | + | 0.0548374i | −0.881421 | − | 0.472331i | \(-0.843413\pi\) |
0.849761 | + | 0.527168i | \(0.176746\pi\) | |||||||
\(984\) | 177984. | − | 308277.i | 0.00585993 | − | 0.0101497i | ||||
\(985\) | 2.49151e7 | 0.818225 | ||||||||
\(986\) | 1.71554e7 | − | 2.97140e7i | 0.561963 | − | 0.973348i | ||||
\(987\) | −1.39164e7 | −0.454711 | ||||||||
\(988\) | 3.17992e7 | 1.03639 | ||||||||
\(989\) | −2.57932e7 | + | 4.09786e7i | −0.838522 | + | 1.33219i | ||||
\(990\) | −2.26749e6 | −0.0735288 | ||||||||
\(991\) | 3.01657e7 | 0.975728 | 0.487864 | − | 0.872920i | \(-0.337776\pi\) | ||||
0.487864 | + | 0.872920i | \(0.337776\pi\) | |||||||
\(992\) | −5.04947e6 | + | 8.74594e6i | −0.162917 | + | 0.282181i | ||||
\(993\) | −6.70336e6 | −0.215734 | ||||||||
\(994\) | 3.46370e7 | − | 5.99930e7i | 1.11192 | − | 1.92590i | ||||
\(995\) | 4.40315e6 | − | 7.62648e6i | 0.140996 | − | 0.244212i | ||||
\(996\) | 2.79637e6 | + | 4.84346e6i | 0.0893196 | + | 0.154706i | ||||
\(997\) | 3.82271e7 | 1.21796 | 0.608980 | − | 0.793185i | \(-0.291579\pi\) | ||||
0.608980 | + | 0.793185i | \(0.291579\pi\) | |||||||
\(998\) | 2.02475e7 | + | 3.50697e7i | 0.643495 | + | 1.11457i | ||||
\(999\) | −5.02613e6 | + | 8.70551e6i | −0.159338 | + | 0.275982i |
(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 | 43.6.c.a.6.14 | ✓ | 34 | |
43.36 | even | 3 | inner | 43.6.c.a.36.14 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.6.c.a.6.14 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.6.c.a.36.14 | yes | 34 | 43.36 | even | 3 | inner |