Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,6,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.b (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: | \(1.28307055850\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.218489.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 8x + 64 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(2.38600 + 1.51888i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.6.b.a.5.1 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.77200 | + | 3.03776i | −0.843579 | + | 0.537006i | ||||
\(3\) | 23.6095i | 1.51455i | 0.653096 | + | 0.757275i | \(0.273470\pi\) | ||||
−0.653096 | + | 0.757275i | \(0.726530\pi\) | |||||||
\(4\) | 13.5440 | − | 28.9924i | 0.423250 | − | 0.906013i | ||||
\(5\) | − | 1.38521i | − | 0.0247794i | −0.999923 | − | 0.0123897i | \(-0.996056\pi\) | ||
0.999923 | − | 0.0123897i | \(-0.00394386\pi\) | |||||||
\(6\) | −71.7200 | − | 112.665i | −0.813322 | − | 1.27764i | ||||
\(7\) | 160.704 | 1.23960 | 0.619800 | − | 0.784760i | \(-0.287214\pi\) | ||||
0.619800 | + | 0.784760i | \(0.287214\pi\) | |||||||
\(8\) | 23.4400 | + | 179.495i | 0.129489 | + | 0.991581i | ||||
\(9\) | −314.408 | −1.29386 | ||||||||
\(10\) | 4.20793 | + | 6.61022i | 0.0133067 | + | 0.0209033i | ||||
\(11\) | 129.129i | 0.321768i | 0.986973 | + | 0.160884i | \(0.0514345\pi\) | ||||
−0.986973 | + | 0.160884i | \(0.948566\pi\) | |||||||
\(12\) | 684.496 | + | 319.767i | 1.37220 | + | 0.641033i | ||||
\(13\) | − | 759.659i | − | 1.24670i | −0.781945 | − | 0.623348i | \(-0.785772\pi\) | ||
0.781945 | − | 0.623348i | \(-0.214228\pi\) | |||||||
\(14\) | −766.880 | + | 488.181i | −1.04570 | + | 0.665672i | ||||
\(15\) | 32.7041 | 0.0375296 | ||||||||
\(16\) | −657.120 | − | 785.347i | −0.641719 | − | 0.766940i | ||||
\(17\) | 323.408 | 0.271412 | 0.135706 | − | 0.990749i | \(-0.456670\pi\) | ||||
0.135706 | + | 0.990749i | \(0.456670\pi\) | |||||||
\(18\) | 1500.36 | − | 955.097i | 1.09147 | − | 0.694810i | ||||
\(19\) | − | 198.511i | − | 0.126154i | −0.998009 | − | 0.0630771i | \(-0.979909\pi\) | ||
0.998009 | − | 0.0630771i | \(-0.0200914\pi\) | |||||||
\(20\) | −40.1605 | − | 18.7613i | −0.0224504 | − | 0.0104879i | ||||
\(21\) | 3794.14i | 1.87744i | ||||||||
\(22\) | −392.264 | − | 616.204i | −0.172791 | − | 0.271436i | ||||
\(23\) | −1193.15 | −0.470302 | −0.235151 | − | 0.971959i | \(-0.575558\pi\) | ||||
−0.235151 | + | 0.971959i | \(0.575558\pi\) | |||||||
\(24\) | −4237.79 | + | 553.407i | −1.50180 | + | 0.196118i | ||||
\(25\) | 3123.08 | 0.999386 | ||||||||
\(26\) | 2307.66 | + | 3625.10i | 0.669483 | + | 1.05169i | ||||
\(27\) | − | 1685.91i | − | 0.445066i | ||||||
\(28\) | 2176.58 | − | 4659.20i | 0.524661 | − | 1.12309i | ||||
\(29\) | − | 5987.24i | − | 1.32200i | −0.750386 | − | 0.661000i | \(-0.770132\pi\) | ||
0.750386 | − | 0.661000i | \(-0.229868\pi\) | |||||||
\(30\) | −156.064 | + | 99.3472i | −0.0316591 | + | 0.0201536i | ||||
\(31\) | −4872.45 | −0.910632 | −0.455316 | − | 0.890330i | \(-0.650474\pi\) | ||||
−0.455316 | + | 0.890330i | \(0.650474\pi\) | |||||||
\(32\) | 5521.47 | + | 1751.50i | 0.953191 | + | 0.302368i | ||||
\(33\) | −3048.67 | −0.487333 | ||||||||
\(34\) | −1543.30 | + | 982.437i | −0.228957 | + | 0.145750i | ||||
\(35\) | − | 222.609i | − | 0.0307165i | ||||||
\(36\) | −4258.34 | + | 9115.45i | −0.547627 | + | 1.17225i | ||||
\(37\) | 3698.56i | 0.444149i | 0.975030 | + | 0.222074i | \(0.0712828\pi\) | ||||
−0.975030 | + | 0.222074i | \(0.928717\pi\) | |||||||
\(38\) | 603.031 | + | 947.297i | 0.0677455 | + | 0.106421i | ||||
\(39\) | 17935.2 | 1.88818 | ||||||||
\(40\) | 248.638 | − | 32.4693i | 0.0245707 | − | 0.00320866i | ||||
\(41\) | −10437.9 | −0.969734 | −0.484867 | − | 0.874588i | \(-0.661132\pi\) | ||||
−0.484867 | + | 0.874588i | \(0.661132\pi\) | |||||||
\(42\) | −11525.7 | − | 18105.6i | −1.00819 | − | 1.58377i | ||||
\(43\) | 9873.11i | 0.814297i | 0.913362 | + | 0.407148i | \(0.133477\pi\) | ||||
−0.913362 | + | 0.407148i | \(0.866523\pi\) | |||||||
\(44\) | 3743.76 | + | 1748.93i | 0.291526 | + | 0.136188i | ||||
\(45\) | 435.521i | 0.0320610i | ||||||||
\(46\) | 5693.73 | − | 3624.51i | 0.396736 | − | 0.252555i | ||||
\(47\) | −6297.98 | −0.415869 | −0.207935 | − | 0.978143i | \(-0.566674\pi\) | ||||
−0.207935 | + | 0.978143i | \(0.566674\pi\) | |||||||
\(48\) | 18541.6 | − | 15514.3i | 1.16157 | − | 0.971915i | ||||
\(49\) | 9018.79 | 0.536609 | ||||||||
\(50\) | −14903.3 | + | 9487.18i | −0.843061 | + | 0.536676i | ||||
\(51\) | 7635.50i | 0.411067i | ||||||||
\(52\) | −22024.4 | − | 10288.8i | −1.12952 | − | 0.527664i | ||||
\(53\) | − | 21728.1i | − | 1.06251i | −0.847212 | − | 0.531255i | \(-0.821721\pi\) | ||
0.847212 | − | 0.531255i | \(-0.178279\pi\) | |||||||
\(54\) | 5121.39 | + | 8045.16i | 0.239003 | + | 0.375449i | ||||
\(55\) | 178.871 | 0.00797320 | ||||||||
\(56\) | 3766.91 | + | 28845.6i | 0.160515 | + | 1.22916i | ||||
\(57\) | 4686.75 | 0.191067 | ||||||||
\(58\) | 18187.8 | + | 28571.1i | 0.709921 | + | 1.11521i | ||||
\(59\) | − | 33513.4i | − | 1.25340i | −0.779261 | − | 0.626699i | \(-0.784406\pi\) | ||
0.779261 | − | 0.626699i | \(-0.215594\pi\) | |||||||
\(60\) | 442.944 | − | 948.170i | 0.0158844 | − | 0.0340023i | ||||
\(61\) | 48506.8i | 1.66908i | 0.550944 | + | 0.834542i | \(0.314268\pi\) | ||||
−0.550944 | + | 0.834542i | \(0.685732\pi\) | |||||||
\(62\) | 23251.3 | − | 14801.3i | 0.768190 | − | 0.489015i | ||||
\(63\) | −50526.7 | −1.60387 | ||||||||
\(64\) | −31669.1 | + | 8414.75i | −0.966465 | + | 0.256798i | ||||
\(65\) | −1052.29 | −0.0308923 | ||||||||
\(66\) | 14548.3 | − | 9261.14i | 0.411104 | − | 0.261701i | ||||
\(67\) | − | 33182.4i | − | 0.903068i | −0.892254 | − | 0.451534i | \(-0.850877\pi\) | ||
0.892254 | − | 0.451534i | \(-0.149123\pi\) | |||||||
\(68\) | 4380.24 | − | 9376.38i | 0.114875 | − | 0.245903i | ||||
\(69\) | − | 28169.7i | − | 0.712295i | ||||||
\(70\) | 676.232 | + | 1062.29i | 0.0164949 | + | 0.0259118i | ||||
\(71\) | 59464.1 | 1.39994 | 0.699970 | − | 0.714173i | \(-0.253197\pi\) | ||||
0.699970 | + | 0.714173i | \(0.253197\pi\) | |||||||
\(72\) | −7369.74 | − | 56434.8i | −0.167541 | − | 1.28297i | ||||
\(73\) | 51278.6 | 1.12624 | 0.563118 | − | 0.826377i | \(-0.309602\pi\) | ||||
0.563118 | + | 0.826377i | \(0.309602\pi\) | |||||||
\(74\) | −11235.4 | − | 17649.5i | −0.238510 | − | 0.374675i | ||||
\(75\) | 73734.4i | 1.51362i | ||||||||
\(76\) | −5755.33 | − | 2688.64i | −0.114297 | − | 0.0533948i | ||||
\(77\) | 20751.6i | 0.398863i | ||||||||
\(78\) | −85586.7 | + | 54482.8i | −1.59283 | + | 1.01396i | ||||
\(79\) | −73724.5 | −1.32906 | −0.664530 | − | 0.747262i | \(-0.731368\pi\) | ||||
−0.664530 | + | 0.747262i | \(0.731368\pi\) | |||||||
\(80\) | −1087.87 | + | 910.248i | −0.0190043 | + | 0.0159014i | ||||
\(81\) | −36597.7 | −0.619785 | ||||||||
\(82\) | 49809.6 | − | 31707.8i | 0.818047 | − | 0.520752i | ||||
\(83\) | 61628.0i | 0.981935i | 0.871178 | + | 0.490967i | \(0.163357\pi\) | ||||
−0.871178 | + | 0.490967i | \(0.836643\pi\) | |||||||
\(84\) | 110001. | + | 51387.9i | 1.70098 | + | 0.794625i | ||||
\(85\) | − | 447.988i | − | 0.00672541i | ||||||
\(86\) | −29992.1 | − | 47114.5i | −0.437282 | − | 0.686923i | ||||
\(87\) | 141356. | 2.00223 | ||||||||
\(88\) | −23178.1 | + | 3026.79i | −0.319059 | + | 0.0416654i | ||||
\(89\) | −106735. | −1.42834 | −0.714169 | − | 0.699974i | \(-0.753195\pi\) | ||||
−0.714169 | + | 0.699974i | \(0.753195\pi\) | |||||||
\(90\) | −1323.01 | − | 2078.31i | −0.0172170 | − | 0.0270460i | ||||
\(91\) | − | 122080.i | − | 1.54540i | ||||||
\(92\) | −16160.1 | + | 34592.4i | −0.199055 | + | 0.426099i | ||||
\(93\) | − | 115036.i | − | 1.37920i | ||||||
\(94\) | 30054.0 | − | 19131.8i | 0.350818 | − | 0.223324i | ||||
\(95\) | −274.980 | −0.00312602 | ||||||||
\(96\) | −41352.1 | + | 130359.i | −0.457951 | + | 1.44366i | ||||
\(97\) | 12562.9 | 0.135569 | 0.0677846 | − | 0.997700i | \(-0.478407\pi\) | ||||
0.0677846 | + | 0.997700i | \(0.478407\pi\) | |||||||
\(98\) | −43037.7 | + | 27397.0i | −0.452672 | + | 0.288162i | ||||
\(99\) | − | 40599.2i | − | 0.416323i | ||||||
\(100\) | 42299.0 | − | 90545.7i | 0.422990 | − | 0.905457i | ||||
\(101\) | 64962.8i | 0.633667i | 0.948481 | + | 0.316834i | \(0.102620\pi\) | ||||
−0.948481 | + | 0.316834i | \(0.897380\pi\) | |||||||
\(102\) | −23194.8 | − | 36436.6i | −0.220745 | − | 0.346767i | ||||
\(103\) | −69035.9 | −0.641183 | −0.320591 | − | 0.947218i | \(-0.603882\pi\) | ||||
−0.320591 | + | 0.947218i | \(0.603882\pi\) | |||||||
\(104\) | 136355. | − | 17806.4i | 1.23620 | − | 0.161434i | ||||
\(105\) | 5255.68 | 0.0465217 | ||||||||
\(106\) | 66004.9 | + | 103687.i | 0.570574 | + | 0.896311i | ||||
\(107\) | 187322.i | 1.58172i | 0.612000 | + | 0.790858i | \(0.290365\pi\) | ||||
−0.612000 | + | 0.790858i | \(0.709635\pi\) | |||||||
\(108\) | −48878.6 | − | 22834.0i | −0.403236 | − | 0.188374i | ||||
\(109\) | − | 49350.5i | − | 0.397855i | −0.980014 | − | 0.198928i | \(-0.936254\pi\) | ||
0.980014 | − | 0.198928i | \(-0.0637459\pi\) | |||||||
\(110\) | −853.571 | + | 543.367i | −0.00672602 | + | 0.00428165i | ||||
\(111\) | −87321.2 | −0.672686 | ||||||||
\(112\) | −105602. | − | 126208.i | −0.795475 | − | 0.950699i | ||||
\(113\) | 171100. | 1.26053 | 0.630266 | − | 0.776379i | \(-0.282946\pi\) | ||||
0.630266 | + | 0.776379i | \(0.282946\pi\) | |||||||
\(114\) | −22365.2 | + | 14237.2i | −0.161180 | + | 0.102604i | ||||
\(115\) | 1652.76i | 0.0116538i | ||||||||
\(116\) | −173584. | − | 81091.2i | −1.19775 | − | 0.559537i | ||||
\(117\) | 238843.i | 1.61305i | ||||||||
\(118\) | 101806. | + | 159926.i | 0.673082 | + | 1.05734i | ||||
\(119\) | 51973.0 | 0.336442 | ||||||||
\(120\) | 766.584 | + | 5870.23i | 0.00485967 | + | 0.0372136i | ||||
\(121\) | 144377. | 0.896466 | ||||||||
\(122\) | −147352. | − | 231475.i | −0.896307 | − | 1.40800i | ||||
\(123\) | − | 246433.i | − | 1.46871i | ||||||
\(124\) | −65992.5 | + | 141264.i | −0.385425 | + | 0.825045i | ||||
\(125\) | − | 8654.89i | − | 0.0495435i | ||||||
\(126\) | 241113. | − | 153488.i | 1.35299 | − | 0.861287i | ||||
\(127\) | −90479.7 | −0.497785 | −0.248892 | − | 0.968531i | \(-0.580067\pi\) | ||||
−0.248892 | + | 0.968531i | \(0.580067\pi\) | |||||||
\(128\) | 125563. | − | 136358.i | 0.677388 | − | 0.735626i | ||||
\(129\) | −233099. | −1.23329 | ||||||||
\(130\) | 5021.51 | − | 3196.60i | 0.0260601 | − | 0.0165893i | ||||
\(131\) | − | 94491.0i | − | 0.481074i | −0.970640 | − | 0.240537i | \(-0.922676\pi\) | ||
0.970640 | − | 0.240537i | \(-0.0773236\pi\) | |||||||
\(132\) | −41291.2 | + | 88388.4i | −0.206264 | + | 0.441530i | ||||
\(133\) | − | 31901.6i | − | 0.156381i | ||||||
\(134\) | 100800. | + | 158346.i | 0.484953 | + | 0.761809i | ||||
\(135\) | −2335.34 | −0.0110285 | ||||||||
\(136\) | 7580.70 | + | 58050.2i | 0.0351449 | + | 0.269127i | ||||
\(137\) | −5516.81 | −0.0251123 | −0.0125561 | − | 0.999921i | \(-0.503997\pi\) | ||||
−0.0125561 | + | 0.999921i | \(0.503997\pi\) | |||||||
\(138\) | 85572.9 | + | 134426.i | 0.382506 | + | 0.600877i | ||||
\(139\) | 164489.i | 0.722104i | 0.932546 | + | 0.361052i | \(0.117582\pi\) | ||||
−0.932546 | + | 0.361052i | \(0.882418\pi\) | |||||||
\(140\) | −6453.96 | − | 3015.01i | −0.0278295 | − | 0.0130008i | ||||
\(141\) | − | 148692.i | − | 0.629854i | ||||||
\(142\) | −283763. | + | 180638.i | −1.18096 | + | 0.751775i | ||||
\(143\) | 98094.2 | 0.401147 | ||||||||
\(144\) | 206604. | + | 246919.i | 0.830294 | + | 0.992314i | ||||
\(145\) | −8293.57 | −0.0327583 | ||||||||
\(146\) | −244702. | + | 155772.i | −0.950068 | + | 0.604795i | ||||
\(147\) | 212929.i | 0.812722i | ||||||||
\(148\) | 107230. | + | 50093.3i | 0.402405 | + | 0.187986i | ||||
\(149\) | − | 423122.i | − | 1.56135i | −0.624939 | − | 0.780674i | \(-0.714876\pi\) | ||
0.624939 | − | 0.780674i | \(-0.285124\pi\) | |||||||
\(150\) | −223987. | − | 351861.i | −0.812822 | − | 1.27686i | ||||
\(151\) | −39975.1 | −0.142675 | −0.0713373 | − | 0.997452i | \(-0.522727\pi\) | ||||
−0.0713373 | + | 0.997452i | \(0.522727\pi\) | |||||||
\(152\) | 35631.9 | − | 4653.12i | 0.125092 | − | 0.0163356i | ||||
\(153\) | −101682. | −0.351169 | ||||||||
\(154\) | −63038.3 | − | 99026.6i | −0.214192 | − | 0.336473i | ||||
\(155\) | 6749.36i | 0.0225649i | ||||||||
\(156\) | 242914. | − | 519984.i | 0.799174 | − | 1.71072i | ||||
\(157\) | 367453.i | 1.18974i | 0.803822 | + | 0.594870i | \(0.202797\pi\) | ||||
−0.803822 | + | 0.594870i | \(0.797203\pi\) | |||||||
\(158\) | 351814. | − | 223958.i | 1.12117 | − | 0.713712i | ||||
\(159\) | 512991. | 1.60922 | ||||||||
\(160\) | 2426.19 | − | 7648.39i | 0.00749248 | − | 0.0236195i | ||||
\(161\) | −191744. | −0.582986 | ||||||||
\(162\) | 174644. | − | 111175.i | 0.522838 | − | 0.332828i | ||||
\(163\) | 16030.9i | 0.0472596i | 0.999721 | + | 0.0236298i | \(0.00752230\pi\) | ||||
−0.999721 | + | 0.0236298i | \(0.992478\pi\) | |||||||
\(164\) | −141371. | + | 302619.i | −0.410440 | + | 0.878591i | ||||
\(165\) | 4223.05i | 0.0120758i | ||||||||
\(166\) | −187211. | − | 294089.i | −0.527304 | − | 0.828339i | ||||
\(167\) | −248107. | −0.688412 | −0.344206 | − | 0.938894i | \(-0.611852\pi\) | ||||
−0.344206 | + | 0.938894i | \(0.611852\pi\) | |||||||
\(168\) | −681031. | + | 88934.8i | −1.86163 | + | 0.243108i | ||||
\(169\) | −205789. | −0.554251 | ||||||||
\(170\) | 1360.88 | + | 2137.80i | 0.00361158 | + | 0.00567341i | ||||
\(171\) | 62413.6i | 0.163226i | ||||||||
\(172\) | 286245. | + | 133721.i | 0.737763 | + | 0.344651i | ||||
\(173\) | 574094.i | 1.45837i | 0.684317 | + | 0.729185i | \(0.260101\pi\) | ||||
−0.684317 | + | 0.729185i | \(0.739899\pi\) | |||||||
\(174\) | −674549. | + | 429405.i | −1.68904 | + | 1.07521i | ||||
\(175\) | 501892. | 1.23884 | ||||||||
\(176\) | 101411. | − | 84853.3i | 0.246777 | − | 0.206484i | ||||
\(177\) | 791235. | 1.89833 | ||||||||
\(178\) | 509338. | − | 324235.i | 1.20491 | − | 0.767025i | ||||
\(179\) | − | 305296.i | − | 0.712177i | −0.934452 | − | 0.356088i | \(-0.884110\pi\) | ||
0.934452 | − | 0.356088i | \(-0.115890\pi\) | |||||||
\(180\) | 12626.8 | + | 5898.69i | 0.0290477 | + | 0.0135698i | ||||
\(181\) | − | 421682.i | − | 0.956728i | −0.878162 | − | 0.478364i | \(-0.841230\pi\) | ||
0.878162 | − | 0.478364i | \(-0.158770\pi\) | |||||||
\(182\) | 370851. | + | 582568.i | 0.829891 | + | 1.30367i | ||||
\(183\) | −1.14522e6 | −2.52791 | ||||||||
\(184\) | −27967.5 | − | 214165.i | −0.0608989 | − | 0.466342i | ||||
\(185\) | 5123.28 | 0.0110057 | ||||||||
\(186\) | 349452. | + | 548952.i | 0.740637 | + | 1.16346i | ||||
\(187\) | 41761.4i | 0.0873315i | ||||||||
\(188\) | −85299.9 | + | 182594.i | −0.176017 | + | 0.376783i | ||||
\(189\) | − | 270932.i | − | 0.551705i | ||||||
\(190\) | 1312.20 | − | 835.323i | 0.00263704 | − | 0.00167869i | ||||
\(191\) | −424231. | −0.841431 | −0.420716 | − | 0.907193i | \(-0.638221\pi\) | ||||
−0.420716 | + | 0.907193i | \(0.638221\pi\) | |||||||
\(192\) | −198668. | − | 747692.i | −0.388933 | − | 1.46376i | ||||
\(193\) | −373902. | −0.722545 | −0.361272 | − | 0.932460i | \(-0.617658\pi\) | ||||
−0.361272 | + | 0.932460i | \(0.617658\pi\) | |||||||
\(194\) | −59950.2 | + | 38163.1i | −0.114363 | + | 0.0728014i | ||||
\(195\) | − | 24843.9i | − | 0.0467880i | ||||||
\(196\) | 122151. | − | 261477.i | 0.227120 | − | 0.486175i | ||||
\(197\) | − | 112848.i | − | 0.207171i | −0.994621 | − | 0.103586i | \(-0.966968\pi\) | ||
0.994621 | − | 0.103586i | \(-0.0330316\pi\) | |||||||
\(198\) | 123331. | + | 193740.i | 0.223568 | + | 0.351201i | ||||
\(199\) | 262938. | 0.470675 | 0.235338 | − | 0.971914i | \(-0.424380\pi\) | ||||
0.235338 | + | 0.971914i | \(0.424380\pi\) | |||||||
\(200\) | 73205.1 | + | 560578.i | 0.129410 | + | 0.990972i | ||||
\(201\) | 783419. | 1.36774 | ||||||||
\(202\) | −197342. | − | 310003.i | −0.340283 | − | 0.534548i | ||||
\(203\) | − | 962173.i | − | 1.63875i | ||||||
\(204\) | 221372. | + | 103415.i | 0.372432 | + | 0.173984i | ||||
\(205\) | 14458.6i | 0.0240294i | ||||||||
\(206\) | 329439. | − | 209715.i | 0.540888 | − | 0.344319i | ||||
\(207\) | 375137. | 0.608505 | ||||||||
\(208\) | −596596. | + | 499187.i | −0.956141 | + | 0.800028i | ||||
\(209\) | 25633.6 | 0.0405923 | ||||||||
\(210\) | −25080.1 | + | 15965.5i | −0.0392447 | + | 0.0249824i | ||||
\(211\) | 272968.i | 0.422090i | 0.977476 | + | 0.211045i | \(0.0676866\pi\) | ||||
−0.977476 | + | 0.211045i | \(0.932313\pi\) | |||||||
\(212\) | −629951. | − | 294286.i | −0.962648 | − | 0.449707i | ||||
\(213\) | 1.40392e6i | 2.12028i | ||||||||
\(214\) | −569039. | − | 893899.i | −0.849390 | − | 1.33430i | ||||
\(215\) | 13676.3 | 0.0201777 | ||||||||
\(216\) | 302613. | − | 39517.8i | 0.441319 | − | 0.0576313i | ||||
\(217\) | −783022. | −1.12882 | ||||||||
\(218\) | 149915. | + | 235501.i | 0.213650 | + | 0.335622i | ||||
\(219\) | 1.21066e6i | 1.70574i | ||||||||
\(220\) | 2422.63 | − | 5185.89i | 0.00337466 | − | 0.00722382i | ||||
\(221\) | − | 245680.i | − | 0.338368i | ||||||
\(222\) | 416697. | − | 265261.i | 0.567463 | − | 0.361236i | ||||
\(223\) | 1.00553e6 | 1.35405 | 0.677023 | − | 0.735962i | \(-0.263270\pi\) | ||||
0.677023 | + | 0.735962i | \(0.263270\pi\) | |||||||
\(224\) | 887323. | + | 281473.i | 1.18158 | + | 0.374815i | ||||
\(225\) | −981922. | −1.29307 | ||||||||
\(226\) | −816490. | + | 519761.i | −1.06336 | + | 0.676913i | ||||
\(227\) | 554991.i | 0.714861i | 0.933940 | + | 0.357430i | \(0.116347\pi\) | ||||
−0.933940 | + | 0.357430i | \(0.883653\pi\) | |||||||
\(228\) | 63477.4 | − | 135880.i | 0.0808690 | − | 0.173109i | ||||
\(229\) | − | 476013.i | − | 0.599832i | −0.953966 | − | 0.299916i | \(-0.903041\pi\) | ||
0.953966 | − | 0.299916i | \(-0.0969587\pi\) | |||||||
\(230\) | −5020.71 | − | 7887.00i | −0.00625814 | − | 0.00983087i | ||||
\(231\) | −489934. | −0.604098 | ||||||||
\(232\) | 1.07468e6 | − | 140341.i | 1.31087 | − | 0.171185i | ||||
\(233\) | 914141. | 1.10312 | 0.551561 | − | 0.834135i | \(-0.314032\pi\) | ||||
0.551561 | + | 0.834135i | \(0.314032\pi\) | |||||||
\(234\) | −725548. | − | 1.13976e6i | −0.866217 | − | 1.36074i | ||||
\(235\) | 8724.01i | 0.0103050i | ||||||||
\(236\) | −971635. | − | 453906.i | −1.13559 | − | 0.530501i | ||||
\(237\) | − | 1.74060e6i | − | 2.01293i | ||||||
\(238\) | −248015. | + | 157882.i | −0.283815 | + | 0.180671i | ||||
\(239\) | 375827. | 0.425592 | 0.212796 | − | 0.977097i | \(-0.431743\pi\) | ||||
0.212796 | + | 0.977097i | \(0.431743\pi\) | |||||||
\(240\) | −21490.5 | − | 25684.0i | −0.0240834 | − | 0.0287829i | ||||
\(241\) | 612110. | 0.678870 | 0.339435 | − | 0.940629i | \(-0.389764\pi\) | ||||
0.339435 | + | 0.940629i | \(0.389764\pi\) | |||||||
\(242\) | −688966. | + | 438582.i | −0.756239 | + | 0.481407i | ||||
\(243\) | − | 1.27373e6i | − | 1.38376i | ||||||
\(244\) | 1.40633e6 | + | 656977.i | 1.51221 | + | 0.706440i | ||||
\(245\) | − | 12492.9i | − | 0.0132968i | ||||||
\(246\) | 748605. | + | 1.17598e6i | 0.788705 | + | 1.23897i | ||||
\(247\) | −150801. | −0.157276 | ||||||||
\(248\) | −114210. | − | 874582.i | −0.117917 | − | 0.902966i | ||||
\(249\) | −1.45501e6 | −1.48719 | ||||||||
\(250\) | 26291.5 | + | 41301.2i | 0.0266051 | + | 0.0417938i | ||||
\(251\) | 462623.i | 0.463493i | 0.972776 | + | 0.231746i | \(0.0744440\pi\) | ||||
−0.972776 | + | 0.231746i | \(0.925556\pi\) | |||||||
\(252\) | −684333. | + | 1.46489e6i | −0.678838 | + | 1.45313i | ||||
\(253\) | − | 154071.i | − | 0.151328i | ||||||
\(254\) | 431769. | − | 274856.i | 0.419921 | − | 0.267313i | ||||
\(255\) | 10576.8 | 0.0101860 | ||||||||
\(256\) | −184963. | + | 1.03213e6i | −0.176394 | + | 0.984320i | ||||
\(257\) | −583345. | −0.550925 | −0.275463 | − | 0.961312i | \(-0.588831\pi\) | ||||
−0.275463 | + | 0.961312i | \(0.588831\pi\) | |||||||
\(258\) | 1.11235e6 | − | 708099.i | 1.04038 | − | 0.662285i | ||||
\(259\) | 594374.i | 0.550567i | ||||||||
\(260\) | −14252.2 | + | 30508.3i | −0.0130752 | + | 0.0279888i | ||||
\(261\) | 1.88244e6i | 1.71048i | ||||||||
\(262\) | 287041. | + | 450911.i | 0.258339 | + | 0.405824i | ||||
\(263\) | −411975. | −0.367267 | −0.183633 | − | 0.982995i | \(-0.558786\pi\) | ||||
−0.183633 | + | 0.982995i | \(0.558786\pi\) | |||||||
\(264\) | −71461.0 | − | 547223.i | −0.0631044 | − | 0.483230i | ||||
\(265\) | −30098.0 | −0.0263283 | ||||||||
\(266\) | 96909.5 | + | 152234.i | 0.0839773 | + | 0.131919i | ||||
\(267\) | − | 2.51995e6i | − | 2.16329i | ||||||
\(268\) | −962037. | − | 449422.i | −0.818191 | − | 0.382224i | ||||
\(269\) | 1.14460e6i | 0.964436i | 0.876051 | + | 0.482218i | \(0.160169\pi\) | ||||
−0.876051 | + | 0.482218i | \(0.839831\pi\) | |||||||
\(270\) | 11144.2 | − | 7094.19i | 0.00930337 | − | 0.00592234i | ||||
\(271\) | −1.21607e6 | −1.00586 | −0.502928 | − | 0.864329i | \(-0.667744\pi\) | ||||
−0.502928 | + | 0.864329i | \(0.667744\pi\) | |||||||
\(272\) | −212518. | − | 253987.i | −0.174170 | − | 0.208157i | ||||
\(273\) | 2.88225e6 | 2.34059 | ||||||||
\(274\) | 26326.2 | − | 16758.7i | 0.0211842 | − | 0.0134854i | ||||
\(275\) | 403281.i | 0.321570i | ||||||||
\(276\) | −816708. | − | 381531.i | −0.645349 | − | 0.301479i | ||||
\(277\) | − | 806054.i | − | 0.631196i | −0.948893 | − | 0.315598i | \(-0.897795\pi\) | ||
0.948893 | − | 0.315598i | \(-0.102205\pi\) | |||||||
\(278\) | −499679. | − | 784942.i | −0.387774 | − | 0.609152i | ||||
\(279\) | 1.53194e6 | 1.17823 | ||||||||
\(280\) | 39957.2 | − | 5217.95i | 0.0304579 | − | 0.00397745i | ||||
\(281\) | 1.19824e6 | 0.905272 | 0.452636 | − | 0.891695i | \(-0.350484\pi\) | ||||
0.452636 | + | 0.891695i | \(0.350484\pi\) | |||||||
\(282\) | 451691. | + | 709559.i | 0.338235 | + | 0.531332i | ||||
\(283\) | 1.46287e6i | 1.08578i | 0.839805 | + | 0.542888i | \(0.182669\pi\) | ||||
−0.839805 | + | 0.542888i | \(0.817331\pi\) | |||||||
\(284\) | 805382. | − | 1.72401e6i | 0.592524 | − | 1.26836i | ||||
\(285\) | − | 6492.13i | − | 0.00473451i | ||||||
\(286\) | −468105. | + | 297987.i | −0.338399 | + | 0.215418i | ||||
\(287\) | −1.67741e6 | −1.20208 | ||||||||
\(288\) | −1.73600e6 | − | 550686.i | −1.23330 | − | 0.391222i | ||||
\(289\) | −1.31526e6 | −0.926336 | ||||||||
\(290\) | 39576.9 | − | 25193.9i | 0.0276342 | − | 0.0175914i | ||||
\(291\) | 296604.i | 0.205326i | ||||||||
\(292\) | 694518. | − | 1.48669e6i | 0.476679 | − | 1.02038i | ||||
\(293\) | − | 750723.i | − | 0.510870i | −0.966826 | − | 0.255435i | \(-0.917781\pi\) | ||
0.966826 | − | 0.255435i | \(-0.0822187\pi\) | |||||||
\(294\) | −646828. | − | 1.01610e6i | −0.436436 | − | 0.685595i | ||||
\(295\) | −46423.1 | −0.0310584 | ||||||||
\(296\) | −663874. | + | 86694.4i | −0.440410 | + | 0.0575125i | ||||
\(297\) | 217700. | 0.143208 | ||||||||
\(298\) | 1.28534e6 | + | 2.01914e6i | 0.838452 | + | 1.31712i | ||||
\(299\) | 906390.i | 0.586323i | ||||||||
\(300\) | 2.13774e6 | + | 998658.i | 1.37136 | + | 0.640640i | ||||
\(301\) | 1.58665e6i | 1.00940i | ||||||||
\(302\) | 190761. | − | 121435.i | 0.120357 | − | 0.0766170i | ||||
\(303\) | −1.53374e6 | −0.959721 | ||||||||
\(304\) | −155900. | + | 130446.i | −0.0967527 | + | 0.0809555i | ||||
\(305\) | 67192.0 | 0.0413588 | ||||||||
\(306\) | 485227. | − | 308886.i | 0.296239 | − | 0.188580i | ||||
\(307\) | − | 2.06754e6i | − | 1.25201i | −0.779819 | − | 0.626005i | \(-0.784689\pi\) | ||
0.779819 | − | 0.626005i | \(-0.215311\pi\) | |||||||
\(308\) | 601638. | + | 281059.i | 0.361375 | + | 0.168819i | ||||
\(309\) | − | 1.62990e6i | − | 0.971103i | ||||||
\(310\) | −20502.9 | − | 32207.9i | −0.0121175 | − | 0.0190353i | ||||
\(311\) | 3.06896e6 | 1.79924 | 0.899621 | − | 0.436671i | \(-0.143843\pi\) | ||||
0.899621 | + | 0.436671i | \(0.143843\pi\) | |||||||
\(312\) | 420401. | + | 3.21928e6i | 0.244499 | + | 1.87229i | ||||
\(313\) | −115148. | −0.0664345 | −0.0332173 | − | 0.999448i | \(-0.510575\pi\) | ||||
−0.0332173 | + | 0.999448i | \(0.510575\pi\) | |||||||
\(314\) | −1.11623e6 | − | 1.75348e6i | −0.638897 | − | 1.00364i | ||||
\(315\) | 69989.9i | 0.0397429i | ||||||||
\(316\) | −998526. | + | 2.13745e6i | −0.562525 | + | 1.20414i | ||||
\(317\) | 1.29930e6i | 0.726210i | 0.931748 | + | 0.363105i | \(0.118283\pi\) | ||||
−0.931748 | + | 0.363105i | \(0.881717\pi\) | |||||||
\(318\) | −2.44799e6 | + | 1.55834e6i | −1.35751 | + | 0.864162i | ||||
\(319\) | 773127. | 0.425377 | ||||||||
\(320\) | 11656.2 | + | 43868.3i | 0.00636329 | + | 0.0239484i | ||||
\(321\) | −4.42257e6 | −2.39559 | ||||||||
\(322\) | 915005. | − | 582474.i | 0.491795 | − | 0.313067i | ||||
\(323\) | − | 64200.2i | − | 0.0342397i | ||||||
\(324\) | −495679. | + | 1.06106e6i | −0.262324 | + | 0.561534i | ||||
\(325\) | − | 2.37248e6i | − | 1.24593i | ||||||
\(326\) | −48698.2 | − | 76499.7i | −0.0253787 | − | 0.0398672i | ||||
\(327\) | 1.16514e6 | 0.602571 | ||||||||
\(328\) | −244664. | − | 1.87355e6i | −0.125570 | − | 0.961569i | ||||
\(329\) | −1.01211e6 | −0.515512 | ||||||||
\(330\) | −12828.6 | − | 20152.4i | −0.00648477 | − | 0.0101869i | ||||
\(331\) | − | 2.02113e6i | − | 1.01397i | −0.861955 | − | 0.506985i | \(-0.830760\pi\) | ||
0.861955 | − | 0.506985i | \(-0.169240\pi\) | |||||||
\(332\) | 1.78674e6 | + | 834689.i | 0.889646 | + | 0.415604i | ||||
\(333\) | − | 1.16286e6i | − | 0.574667i | ||||||
\(334\) | 1.18397e6 | − | 753691.i | 0.580730 | − | 0.369681i | ||||
\(335\) | −45964.5 | −0.0223775 | ||||||||
\(336\) | 2.97972e6 | − | 2.49321e6i | 1.43988 | − | 1.20479i | ||||
\(337\) | 2.88553e6 | 1.38405 | 0.692023 | − | 0.721875i | \(-0.256719\pi\) | ||||
0.692023 | + | 0.721875i | \(0.256719\pi\) | |||||||
\(338\) | 982027. | − | 625139.i | 0.467554 | − | 0.297636i | ||||
\(339\) | 4.03958e6i | 1.90914i | ||||||||
\(340\) | −12988.2 | − | 6067.55i | −0.00609331 | − | 0.00284653i | ||||
\(341\) | − | 629175.i | − | 0.293012i | ||||||
\(342\) | −189598. | − | 297838.i | −0.0876532 | − | 0.137694i | ||||
\(343\) | −1.25160e6 | −0.574419 | ||||||||
\(344\) | −1.77218e6 | + | 231426.i | −0.807441 | + | 0.105443i | ||||
\(345\) | −39020.9 | −0.0176502 | ||||||||
\(346\) | −1.74396e6 | − | 2.73958e6i | −0.783153 | − | 1.23025i | ||||
\(347\) | 1.01894e6i | 0.454281i | 0.973862 | + | 0.227141i | \(0.0729377\pi\) | ||||
−0.973862 | + | 0.227141i | \(0.927062\pi\) | |||||||
\(348\) | 1.91452e6 | − | 4.09824e6i | 0.847446 | − | 1.81405i | ||||
\(349\) | 1.53786e6i | 0.675854i | 0.941172 | + | 0.337927i | \(0.109726\pi\) | ||||
−0.941172 | + | 0.337927i | \(0.890274\pi\) | |||||||
\(350\) | −2.39503e6 | + | 1.52463e6i | −1.04506 | + | 0.665264i | ||||
\(351\) | −1.28072e6 | −0.554862 | ||||||||
\(352\) | −226170. | + | 712983.i | −0.0972922 | + | 0.306706i | ||||
\(353\) | −490388. | −0.209461 | −0.104731 | − | 0.994501i | \(-0.533398\pi\) | ||||
−0.104731 | + | 0.994501i | \(0.533398\pi\) | |||||||
\(354\) | −3.77578e6 | + | 2.40358e6i | −1.60139 | + | 1.01942i | ||||
\(355\) | − | 82370.2i | − | 0.0346896i | ||||||
\(356\) | −1.44562e6 | + | 3.09450e6i | −0.604544 | + | 1.29409i | ||||
\(357\) | 1.22706e6i | 0.509558i | ||||||||
\(358\) | 927415. | + | 1.45687e6i | 0.382443 | + | 0.600777i | ||||
\(359\) | 3.19930e6 | 1.31014 | 0.655072 | − | 0.755567i | \(-0.272638\pi\) | ||||
0.655072 | + | 0.755567i | \(0.272638\pi\) | |||||||
\(360\) | −78173.9 | + | 10208.6i | −0.0317911 | + | 0.00415156i | ||||
\(361\) | 2.43669e6 | 0.984085 | ||||||||
\(362\) | 1.28097e6 | + | 2.01227e6i | 0.513768 | + | 0.807075i | ||||
\(363\) | 3.40866e6i | 1.35774i | ||||||||
\(364\) | −3.53940e6 | − | 1.65346e6i | −1.40016 | − | 0.654093i | ||||
\(365\) | − | 71031.6i | − | 0.0279074i | ||||||
\(366\) | 5.46500e6 | − | 3.47891e6i | 2.13249 | − | 1.35750i | ||||
\(367\) | −2.06745e6 | −0.801252 | −0.400626 | − | 0.916242i | \(-0.631207\pi\) | ||||
−0.400626 | + | 0.916242i | \(0.631207\pi\) | |||||||
\(368\) | 784044. | + | 937039.i | 0.301801 | + | 0.360693i | ||||
\(369\) | 3.28175e6 | 1.25470 | ||||||||
\(370\) | −24448.3 | + | 15563.3i | −0.00928419 | + | 0.00591013i | ||||
\(371\) | − | 3.49180e6i | − | 1.31709i | ||||||
\(372\) | −3.33517e6 | − | 1.55805e6i | −1.24957 | − | 0.583746i | ||||
\(373\) | 4.93913e6i | 1.83814i | 0.394095 | + | 0.919070i | \(0.371058\pi\) | ||||
−0.394095 | + | 0.919070i | \(0.628942\pi\) | |||||||
\(374\) | −126861. | − | 199286.i | −0.0468975 | − | 0.0736710i | ||||
\(375\) | 204338. | 0.0750361 | ||||||||
\(376\) | −147625. | − | 1.13046e6i | −0.0538505 | − | 0.412368i | ||||
\(377\) | −4.54826e6 | −1.64813 | ||||||||
\(378\) | 823028. | + | 1.29289e6i | 0.296268 | + | 0.465406i | ||||
\(379\) | − | 5.21670e6i | − | 1.86551i | −0.360510 | − | 0.932755i | \(-0.617397\pi\) | ||
0.360510 | − | 0.932755i | \(-0.382603\pi\) | |||||||
\(380\) | −3724.33 | + | 7972.32i | −0.00132309 | + | 0.00283221i | ||||
\(381\) | − | 2.13618e6i | − | 0.753920i | ||||||
\(382\) | 2.02443e6 | − | 1.28871e6i | 0.709814 | − | 0.451853i | ||||
\(383\) | −4.22327e6 | −1.47113 | −0.735566 | − | 0.677453i | \(-0.763084\pi\) | ||||
−0.735566 | + | 0.677453i | \(0.763084\pi\) | |||||||
\(384\) | 3.21935e6 | + | 2.96448e6i | 1.11414 | + | 1.02594i | ||||
\(385\) | 28745.2 | 0.00988358 | ||||||||
\(386\) | 1.78426e6 | − | 1.13583e6i | 0.609523 | − | 0.388010i | ||||
\(387\) | − | 3.10418e6i | − | 1.05359i | ||||||
\(388\) | 170152. | − | 364229.i | 0.0573797 | − | 0.122827i | ||||
\(389\) | − | 615402.i | − | 0.206198i | −0.994671 | − | 0.103099i | \(-0.967124\pi\) | ||
0.994671 | − | 0.103099i | \(-0.0328759\pi\) | |||||||
\(390\) | 75470.0 | + | 118555.i | 0.0251254 | + | 0.0394693i | ||||
\(391\) | −385875. | −0.127645 | ||||||||
\(392\) | 211401. | + | 1.61883e6i | 0.0694851 | + | 0.532092i | ||||
\(393\) | 2.23088e6 | 0.728611 | ||||||||
\(394\) | 342807. | + | 538513.i | 0.111252 | + | 0.174765i | ||||
\(395\) | 102124.i | 0.0329332i | ||||||||
\(396\) | −1.17707e6 | − | 549876.i | −0.377194 | − | 0.176209i | ||||
\(397\) | − | 1.60554e6i | − | 0.511263i | −0.966774 | − | 0.255632i | \(-0.917717\pi\) | ||
0.966774 | − | 0.255632i | \(-0.0822835\pi\) | |||||||
\(398\) | −1.25474e6 | + | 798744.i | −0.397051 | + | 0.252755i | ||||
\(399\) | 753180. | 0.236846 | ||||||||
\(400\) | −2.05224e6 | − | 2.45270e6i | −0.641325 | − | 0.766469i | ||||
\(401\) | 1.47973e6 | 0.459539 | 0.229769 | − | 0.973245i | \(-0.426203\pi\) | ||||
0.229769 | + | 0.973245i | \(0.426203\pi\) | |||||||
\(402\) | −3.73848e6 | + | 2.37984e6i | −1.15380 | + | 0.734485i | ||||
\(403\) | 3.70140e6i | 1.13528i | ||||||||
\(404\) | 1.88343e6 | + | 879856.i | 0.574111 | + | 0.268200i | ||||
\(405\) | 50695.4i | 0.0153579i | ||||||||
\(406\) | 2.92285e6 | + | 4.59149e6i | 0.880019 | + | 1.38242i | ||||
\(407\) | −477592. | −0.142913 | ||||||||
\(408\) | −1.37054e6 | + | 178976.i | −0.407606 | + | 0.0532287i | ||||
\(409\) | 1.15560e6 | 0.341584 | 0.170792 | − | 0.985307i | \(-0.445367\pi\) | ||||
0.170792 | + | 0.985307i | \(0.445367\pi\) | |||||||
\(410\) | −43921.9 | − | 68996.6i | −0.0129039 | − | 0.0202707i | ||||
\(411\) | − | 130249.i | − | 0.0380338i | ||||||
\(412\) | −935022. | + | 2.00152e6i | −0.271381 | + | 0.580920i | ||||
\(413\) | − | 5.38575e6i | − | 1.55371i | ||||||
\(414\) | −1.79015e6 | + | 1.13958e6i | −0.513322 | + | 0.326770i | ||||
\(415\) | 85367.6 | 0.0243317 | ||||||||
\(416\) | 1.33054e6 | − | 4.19444e6i | 0.376961 | − | 1.18834i | ||||
\(417\) | −3.88350e6 | −1.09366 | ||||||||
\(418\) | −122324. | + | 77868.8i | −0.0342428 | + | 0.0217983i | ||||
\(419\) | 1.84397e6i | 0.513121i | 0.966528 | + | 0.256560i | \(0.0825893\pi\) | ||||
−0.966528 | + | 0.256560i | \(0.917411\pi\) | |||||||
\(420\) | 71182.9 | − | 152375.i | 0.0196903 | − | 0.0421492i | ||||
\(421\) | 4.13061e6i | 1.13582i | 0.823091 | + | 0.567909i | \(0.192248\pi\) | ||||
−0.823091 | + | 0.567909i | \(0.807752\pi\) | |||||||
\(422\) | −829211. | − | 1.30260e6i | −0.226665 | − | 0.356066i | ||||
\(423\) | 1.98014e6 | 0.538077 | ||||||||
\(424\) | 3.90010e6 | − | 509309.i | 1.05356 | − | 0.137583i | ||||
\(425\) | 1.01003e6 | 0.271245 | ||||||||
\(426\) | −4.26477e6 | − | 6.69950e6i | −1.13860 | − | 1.78862i | ||||
\(427\) | 7.79524e6i | 2.06900i | ||||||||
\(428\) | 5.43091e6 | + | 2.53708e6i | 1.43305 | + | 0.669461i | ||||
\(429\) | 2.31595e6i | 0.607556i | ||||||||
\(430\) | −65263.4 | + | 41545.4i | −0.0170215 | + | 0.0108356i | ||||
\(431\) | 3.44366e6 | 0.892950 | 0.446475 | − | 0.894796i | \(-0.352679\pi\) | ||||
0.446475 | + | 0.894796i | \(0.352679\pi\) | |||||||
\(432\) | −1.32402e6 | + | 1.10784e6i | −0.341339 | + | 0.285607i | ||||
\(433\) | −2.41696e6 | −0.619511 | −0.309755 | − | 0.950816i | \(-0.600247\pi\) | ||||
−0.309755 | + | 0.950816i | \(0.600247\pi\) | |||||||
\(434\) | 3.73658e6 | − | 2.37864e6i | 0.952249 | − | 0.606183i | ||||
\(435\) | − | 195807.i | − | 0.0496141i | ||||||
\(436\) | −1.43079e6 | − | 668403.i | −0.360462 | − | 0.168392i | ||||
\(437\) | 236854.i | 0.0593305i | ||||||||
\(438\) | −3.67770e6 | − | 5.77728e6i | −0.915992 | − | 1.43893i | ||||
\(439\) | −3.22639e6 | −0.799015 | −0.399507 | − | 0.916730i | \(-0.630819\pi\) | ||||
−0.399507 | + | 0.916730i | \(0.630819\pi\) | |||||||
\(440\) | 4192.74 | + | 32106.5i | 0.00103244 | + | 0.00790607i | ||||
\(441\) | −2.83558e6 | −0.694298 | ||||||||
\(442\) | 746317. | + | 1.17239e6i | 0.181705 | + | 0.285440i | ||||
\(443\) | − | 6.44624e6i | − | 1.56062i | −0.625393 | − | 0.780310i | \(-0.715061\pi\) | ||
0.625393 | − | 0.780310i | \(-0.284939\pi\) | |||||||
\(444\) | −1.18268e6 | + | 2.53165e6i | −0.284714 | + | 0.609462i | ||||
\(445\) | 147850.i | 0.0353933i | ||||||||
\(446\) | −4.79840e6 | + | 3.05457e6i | −1.14224 | + | 0.727130i | ||||
\(447\) | 9.98969e6 | 2.36474 | ||||||||
\(448\) | −5.08936e6 | + | 1.35229e6i | −1.19803 | + | 0.318327i | ||||
\(449\) | −1.82600e6 | −0.427450 | −0.213725 | − | 0.976894i | \(-0.568560\pi\) | ||||
−0.213725 | + | 0.976894i | \(0.568560\pi\) | |||||||
\(450\) | 4.68573e6 | − | 2.98285e6i | 1.09080 | − | 0.694384i | ||||
\(451\) | − | 1.34783e6i | − | 0.312029i | ||||||
\(452\) | 2.31738e6 | − | 4.96060e6i | 0.533520 | − | 1.14206i | ||||
\(453\) | − | 943791.i | − | 0.216088i | ||||||
\(454\) | −1.68593e6 | − | 2.64842e6i | −0.383884 | − | 0.603041i | ||||
\(455\) | −169107. | −0.0382941 | ||||||||
\(456\) | 109858. | + | 841250.i | 0.0247411 | + | 0.189458i | ||||
\(457\) | 2.26865e6 | 0.508132 | 0.254066 | − | 0.967187i | \(-0.418232\pi\) | ||||
0.254066 | + | 0.967187i | \(0.418232\pi\) | |||||||
\(458\) | 1.44601e6 | + | 2.27153e6i | 0.322113 | + | 0.506006i | ||||
\(459\) | − | 545237.i | − | 0.120796i | ||||||
\(460\) | 47917.6 | + | 22385.1i | 0.0105585 | + | 0.00493246i | ||||
\(461\) | − | 2.82378e6i | − | 0.618840i | −0.950925 | − | 0.309420i | \(-0.899865\pi\) | ||
0.950925 | − | 0.309420i | \(-0.100135\pi\) | |||||||
\(462\) | 2.33797e6 | − | 1.48830e6i | 0.509605 | − | 0.324404i | ||||
\(463\) | 3.05836e6 | 0.663035 | 0.331517 | − | 0.943449i | \(-0.392439\pi\) | ||||
0.331517 | + | 0.943449i | \(0.392439\pi\) | |||||||
\(464\) | −4.70206e6 | + | 3.93433e6i | −1.01389 | + | 0.848352i | ||||
\(465\) | −159349. | −0.0341756 | ||||||||
\(466\) | −4.36228e6 | + | 2.77694e6i | −0.930570 | + | 0.592383i | ||||
\(467\) | 5.19478e6i | 1.10224i | 0.834427 | + | 0.551119i | \(0.185799\pi\) | ||||
−0.834427 | + | 0.551119i | \(0.814201\pi\) | |||||||
\(468\) | 6.92464e6 | + | 3.23489e6i | 1.46144 | + | 0.682724i | ||||
\(469\) | − | 5.33254e6i | − | 1.11944i | ||||||
\(470\) | −26501.5 | − | 41631.0i | −0.00553383 | − | 0.00869305i | ||||
\(471\) | −8.67537e6 | −1.80192 | ||||||||
\(472\) | 6.01550e6 | − | 785556.i | 1.24285 | − | 0.162301i | ||||
\(473\) | −1.27491e6 | −0.262014 | ||||||||
\(474\) | 5.28753e6 | + | 8.30614e6i | 1.08095 | + | 1.69806i | ||||
\(475\) | − | 619967.i | − | 0.126077i | ||||||
\(476\) | 703922. | − | 1.50682e6i | 0.142399 | − | 0.304821i | ||||
\(477\) | 6.83151e6i | 1.37474i | ||||||||
\(478\) | −1.79345e6 | + | 1.14167e6i | −0.359020 | + | 0.228545i | ||||
\(479\) | −8.27094e6 | −1.64708 | −0.823542 | − | 0.567255i | \(-0.808006\pi\) | ||||
−0.823542 | + | 0.567255i | \(0.808006\pi\) | |||||||
\(480\) | 180575. | + | 57281.2i | 0.0357729 | + | 0.0113477i | ||||
\(481\) | 2.80965e6 | 0.553719 | ||||||||
\(482\) | −2.92099e6 | + | 1.85944e6i | −0.572680 | + | 0.364557i | ||||
\(483\) | − | 4.52699e6i | − | 0.882961i | ||||||
\(484\) | 1.95544e6 | − | 4.18583e6i | 0.379429 | − | 0.812209i | ||||
\(485\) | − | 17402.2i | − | 0.00335932i | ||||||
\(486\) | 3.86929e6 | + | 6.07824e6i | 0.743088 | + | 1.16731i | ||||
\(487\) | −4.95663e6 | −0.947031 | −0.473515 | − | 0.880786i | \(-0.657015\pi\) | ||||
−0.473515 | + | 0.880786i | \(0.657015\pi\) | |||||||
\(488\) | −8.70675e6 | + | 1.13700e6i | −1.65503 | + | 0.216128i | ||||
\(489\) | −378482. | −0.0715770 | ||||||||
\(490\) | 37950.5 | + | 59616.2i | 0.00714047 | + | 0.0112169i | ||||
\(491\) | 6.01801e6i | 1.12655i | 0.826271 | + | 0.563273i | \(0.190458\pi\) | ||||
−0.826271 | + | 0.563273i | \(0.809542\pi\) | |||||||
\(492\) | −7.14469e6 | − | 3.33769e6i | −1.33067 | − | 0.621632i | ||||
\(493\) | − | 1.93632e6i | − | 0.358806i | ||||||
\(494\) | 719623. | − | 458098.i | 0.132675 | − | 0.0844580i | ||||
\(495\) | −56238.4 | −0.0103162 | ||||||||
\(496\) | 3.20178e6 | + | 3.82656e6i | 0.584370 | + | 0.698400i | ||||
\(497\) | 9.55613e6 | 1.73537 | ||||||||
\(498\) | 6.94329e6 | − | 4.41996e6i | 1.25456 | − | 0.798629i | ||||
\(499\) | − | 7.87834e6i | − | 1.41639i | −0.706016 | − | 0.708196i | \(-0.749509\pi\) | ||
0.706016 | − | 0.708196i | \(-0.250491\pi\) | |||||||
\(500\) | −250926. | − | 117222.i | −0.0448870 | − | 0.0209693i | ||||
\(501\) | − | 5.85769e6i | − | 1.04263i | ||||||
\(502\) | −1.40534e6 | − | 2.20764e6i | −0.248898 | − | 0.390993i | ||||
\(503\) | 9.09472e6 | 1.60276 | 0.801382 | − | 0.598153i | \(-0.204099\pi\) | ||||
0.801382 | + | 0.598153i | \(0.204099\pi\) | |||||||
\(504\) | −1.18435e6 | − | 9.06930e6i | −0.207684 | − | 1.59037i | ||||
\(505\) | 89987.0 | 0.0157019 | ||||||||
\(506\) | 468030. | + | 735226.i | 0.0812639 | + | 0.127657i | ||||
\(507\) | − | 4.85858e6i | − | 0.839440i | ||||||
\(508\) | −1.22546e6 | + | 2.62322e6i | −0.210687 | + | 0.450999i | ||||
\(509\) | 1.07691e7i | 1.84241i | 0.389076 | + | 0.921206i | \(0.372794\pi\) | ||||
−0.389076 | + | 0.921206i | \(0.627206\pi\) | |||||||
\(510\) | −50472.3 | + | 32129.7i | −0.00859266 | + | 0.00546992i | ||||
\(511\) | 8.24068e6 | 1.39608 | ||||||||
\(512\) | −2.25273e6 | − | 5.48722e6i | −0.379783 | − | 0.925076i | ||||
\(513\) | −334672. | −0.0561470 | ||||||||
\(514\) | 2.78372e6 | − | 1.77206e6i | 0.464749 | − | 0.295850i | ||||
\(515\) | 95629.1i | 0.0158881i | ||||||||
\(516\) | −3.15709e6 | + | 6.75810e6i | −0.521991 | + | 1.11738i | ||||
\(517\) | − | 813253.i | − | 0.133813i | ||||||
\(518\) | −1.80557e6 | − | 2.83635e6i | −0.295658 | − | 0.464447i | ||||
\(519\) | −1.35541e7 | −2.20877 | ||||||||
\(520\) | −24665.6 | − | 188880.i | −0.00400022 | − | 0.0306322i | ||||
\(521\) | −1.88429e6 | −0.304126 | −0.152063 | − | 0.988371i | \(-0.548592\pi\) | ||||
−0.152063 | + | 0.988371i | \(0.548592\pi\) | |||||||
\(522\) | −5.71839e6 | − | 8.98299e6i | −0.918539 | − | 1.44293i | ||||
\(523\) | − | 2.14270e6i | − | 0.342537i | −0.985224 | − | 0.171269i | \(-0.945213\pi\) | ||
0.985224 | − | 0.171269i | \(-0.0547866\pi\) | |||||||
\(524\) | −2.73952e6 | − | 1.27979e6i | −0.435859 | − | 0.203615i | ||||
\(525\) | 1.18494e7i | 1.87628i | ||||||||
\(526\) | 1.96595e6 | − | 1.25148e6i | 0.309818 | − | 0.197224i | ||||
\(527\) | −1.57579e6 | −0.247156 | ||||||||
\(528\) | 2.00334e6 | + | 2.39427e6i | 0.312731 | + | 0.373755i | ||||
\(529\) | −5.01273e6 | −0.778816 | ||||||||
\(530\) | 143628. | − | 91430.6i | 0.0222100 | − | 0.0141384i | ||||
\(531\) | 1.05369e7i | 1.62172i | ||||||||
\(532\) | −924904. | − | 432075.i | −0.141683 | − | 0.0661882i | ||||
\(533\) | 7.92923e6i | 1.20896i | ||||||||
\(534\) | 7.65502e6 | + | 1.20252e7i | 1.16170 | + | 1.82490i | ||||
\(535\) | 259479. | 0.0391939 | ||||||||
\(536\) | 5.95608e6 | − | 777796.i | 0.895465 | − | 0.116938i | ||||
\(537\) | 7.20787e6 | 1.07863 | ||||||||
\(538\) | −3.47703e6 | − | 5.46204e6i | −0.517908 | − | 0.813578i | ||||
\(539\) | 1.16459e6i | 0.172664i | ||||||||
\(540\) | −31629.8 | + | 67707.0i | −0.00466780 | + | 0.00999193i | ||||
\(541\) | − | 9.23309e6i | − | 1.35629i | −0.734926 | − | 0.678147i | \(-0.762783\pi\) | ||
0.734926 | − | 0.678147i | \(-0.237217\pi\) | |||||||
\(542\) | 5.80309e6 | − | 3.69413e6i | 0.848518 | − | 0.540150i | ||||
\(543\) | 9.95569e6 | 1.44901 | ||||||||
\(544\) | 1.78569e6 | + | 566450.i | 0.258707 | + | 0.0820662i | ||||
\(545\) | −68360.7 | −0.00985859 | ||||||||
\(546\) | −1.37541e7 | + | 8.75560e6i | −1.97447 | + | 1.25691i | ||||
\(547\) | 6.30413e6i | 0.900858i | 0.892812 | + | 0.450429i | \(0.148729\pi\) | ||||
−0.892812 | + | 0.450429i | \(0.851271\pi\) | |||||||
\(548\) | −74719.7 | + | 159946.i | −0.0106288 | + | 0.0227521i | ||||
\(549\) | − | 1.52509e7i | − | 2.15956i | ||||||
\(550\) | −1.22507e6 | − | 1.92446e6i | −0.172685 | − | 0.271270i | ||||
\(551\) | −1.18853e6 | −0.166776 | ||||||||
\(552\) | 5.05633e6 | − | 660300.i | 0.706298 | − | 0.0922345i | ||||
\(553\) | −1.18478e7 | −1.64750 | ||||||||
\(554\) | 2.44860e6 | + | 3.84649e6i | 0.338956 | + | 0.532464i | ||||
\(555\) | 120958.i | 0.0166687i | ||||||||
\(556\) | 4.76893e6 | + | 2.22784e6i | 0.654236 | + | 0.305631i | ||||
\(557\) | − | 6.50282e6i | − | 0.888104i | −0.896001 | − | 0.444052i | \(-0.853540\pi\) | ||
0.896001 | − | 0.444052i | \(-0.146460\pi\) | |||||||
\(558\) | −7.31041e6 | + | 4.65366e6i | −0.993931 | + | 0.632717i | ||||
\(559\) | 7.50020e6 | 1.01518 | ||||||||
\(560\) | −174825. | + | 146281.i | −0.0235577 | + | 0.0197114i | ||||
\(561\) | −985966. | −0.132268 | ||||||||
\(562\) | −5.71802e6 | + | 3.63998e6i | −0.763668 | + | 0.486136i | ||||
\(563\) | − | 6.06434e6i | − | 0.806329i | −0.915127 | − | 0.403165i | \(-0.867910\pi\) | ||
0.915127 | − | 0.403165i | \(-0.132090\pi\) | |||||||
\(564\) | −4.31094e6 | − | 2.01389e6i | −0.570656 | − | 0.266586i | ||||
\(565\) | − | 237009.i | − | 0.0312352i | ||||||
\(566\) | −4.44385e6 | − | 6.98082e6i | −0.583067 | − | 0.915937i | ||||
\(567\) | −5.88140e6 | −0.768286 | ||||||||
\(568\) | 1.39384e6 | + | 1.06735e7i | 0.181277 | + | 1.38815i | ||||
\(569\) | 8.67931e6 | 1.12384 | 0.561920 | − | 0.827191i | \(-0.310063\pi\) | ||||
0.561920 | + | 0.827191i | \(0.310063\pi\) | |||||||
\(570\) | 19721.5 | + | 30980.5i | 0.00254246 | + | 0.00399393i | ||||
\(571\) | 5.13091e6i | 0.658573i | 0.944230 | + | 0.329287i | \(0.106808\pi\) | ||||
−0.944230 | + | 0.329287i | \(0.893192\pi\) | |||||||
\(572\) | 1.32859e6 | − | 2.84399e6i | 0.169785 | − | 0.363444i | ||||
\(573\) | − | 1.00159e7i | − | 1.27439i | ||||||
\(574\) | 8.00460e6 | − | 5.09557e6i | 1.01405 | − | 0.645525i | ||||
\(575\) | −3.72631e6 | −0.470013 | ||||||||
\(576\) | 9.95703e6 | − | 2.64567e6i | 1.25047 | − | 0.332261i | ||||
\(577\) | −1.05397e7 | −1.31792 | −0.658962 | − | 0.752176i | \(-0.729004\pi\) | ||||
−0.658962 | + | 0.752176i | \(0.729004\pi\) | |||||||
\(578\) | 6.27644e6 | − | 3.99546e6i | 0.781437 | − | 0.497447i | ||||
\(579\) | − | 8.82764e6i | − | 1.09433i | ||||||
\(580\) | −112328. | + | 240451.i | −0.0138650 | + | 0.0296794i | ||||
\(581\) | 9.90387e6i | 1.21721i | ||||||||
\(582\) | −901012. | − | 1.41539e6i | −0.110261 | − | 0.173209i | ||||
\(583\) | 2.80574e6 | 0.341881 | ||||||||
\(584\) | 1.20197e6 | + | 9.20427e6i | 0.145835 | + | 1.11675i | ||||
\(585\) | 330847. | 0.0399704 | ||||||||
\(586\) | 2.28052e6 | + | 3.58245e6i | 0.274340 | + | 0.430959i | ||||
\(587\) | − | 5.07345e6i | − | 0.607727i | −0.952716 | − | 0.303863i | \(-0.901723\pi\) | ||
0.952716 | − | 0.303863i | \(-0.0982767\pi\) | |||||||
\(588\) | 6.17333e6 | + | 2.88391e6i | 0.736336 | + | 0.343985i | ||||
\(589\) | 967237.i | 0.114880i | ||||||||
\(590\) | 221531. | − | 141022.i | 0.0262002 | − | 0.0166785i | ||||
\(591\) | 2.66429e6 | 0.313771 | ||||||||
\(592\) | 2.90465e6 | − | 2.43040e6i | 0.340636 | − | 0.285019i | ||||
\(593\) | −1.41356e7 | −1.65073 | −0.825366 | − | 0.564599i | \(-0.809031\pi\) | ||||
−0.825366 | + | 0.564599i | \(0.809031\pi\) | |||||||
\(594\) | −1.03886e6 | + | 661321.i | −0.120807 | + | 0.0769035i | ||||
\(595\) | − | 71993.4i | − | 0.00833682i | ||||||
\(596\) | −1.22673e7 | − | 5.73076e6i | −1.41460 | − | 0.660841i | ||||
\(597\) | 6.20784e6i | 0.712861i | ||||||||
\(598\) | −2.75340e6 | − | 4.32529e6i | −0.314859 | − | 0.494610i | ||||
\(599\) | 7.17896e6 | 0.817512 | 0.408756 | − | 0.912644i | \(-0.365963\pi\) | ||||
0.408756 | + | 0.912644i | \(0.365963\pi\) | |||||||
\(600\) | −1.32350e7 | + | 1.72834e6i | −1.50088 | + | 0.195997i | ||||
\(601\) | −3.61001e6 | −0.407683 | −0.203841 | − | 0.979004i | \(-0.565343\pi\) | ||||
−0.203841 | + | 0.979004i | \(0.565343\pi\) | |||||||
\(602\) | −4.81986e6 | − | 7.57149e6i | −0.542055 | − | 0.851511i | ||||
\(603\) | 1.04328e7i | 1.16844i | ||||||||
\(604\) | −541422. | + | 1.15897e6i | −0.0603870 | + | 0.129265i | ||||
\(605\) | − | 199992.i | − | 0.0222138i | ||||||
\(606\) | 7.31900e6 | − | 4.65913e6i | 0.809600 | − | 0.515375i | ||||
\(607\) | 4.03263e6 | 0.444239 | 0.222119 | − | 0.975020i | \(-0.428703\pi\) | ||||
0.222119 | + | 0.975020i | \(0.428703\pi\) | |||||||
\(608\) | 347693. | − | 1.09608e6i | 0.0381450 | − | 0.120249i | ||||
\(609\) | 2.27164e7 | 2.48197 | ||||||||
\(610\) | −320641. | + | 204113.i | −0.0348894 | + | 0.0222099i | ||||
\(611\) | 4.78432e6i | 0.518462i | ||||||||
\(612\) | −1.37718e6 | + | 2.94801e6i | −0.148632 | + | 0.318164i | ||||
\(613\) | 1.31815e7i | 1.41682i | 0.705801 | + | 0.708410i | \(0.250587\pi\) | ||||
−0.705801 | + | 0.708410i | \(0.749413\pi\) | |||||||
\(614\) | 6.28069e6 | + | 9.86630e6i | 0.672336 | + | 1.05617i | ||||
\(615\) | −341361. | −0.0363937 | ||||||||
\(616\) | −3.72481e6 | + | 486418.i | −0.395505 | + | 0.0516485i | ||||
\(617\) | 7.04507e6 | 0.745027 | 0.372514 | − | 0.928027i | \(-0.378496\pi\) | ||||
0.372514 | + | 0.928027i | \(0.378496\pi\) | |||||||
\(618\) | 4.95126e6 | + | 7.77790e6i | 0.521488 | + | 0.819202i | ||||
\(619\) | − | 6.48539e6i | − | 0.680314i | −0.940369 | − | 0.340157i | \(-0.889520\pi\) | ||
0.940369 | − | 0.340157i | \(-0.110480\pi\) | |||||||
\(620\) | 195680. | + | 91413.3i | 0.0204441 | + | 0.00955059i | ||||
\(621\) | 2.01155e6i | 0.209315i | ||||||||
\(622\) | −1.46451e7 | + | 9.32276e6i | −1.51780 | + | 0.966203i | ||||
\(623\) | −1.71527e7 | −1.77057 | ||||||||
\(624\) | −1.17856e7 | − | 1.40853e7i | −1.21168 | − | 1.44812i | ||||
\(625\) | 9.74764e6 | 0.998158 | ||||||||
\(626\) | 549484. | − | 349791.i | 0.0560428 | − | 0.0356757i | ||||
\(627\) | 605196.i | 0.0614791i | ||||||||
\(628\) | 1.06533e7 | + | 4.97678e6i | 1.07792 | + | 0.503558i | ||||
\(629\) | 1.19614e6i | 0.120547i | ||||||||
\(630\) | −212613. | − | 333992.i | −0.0213421 | − | 0.0335262i | ||||
\(631\) | −4.09103e6 | −0.409034 | −0.204517 | − | 0.978863i | \(-0.565562\pi\) | ||||
−0.204517 | + | 0.978863i | \(0.565562\pi\) | |||||||
\(632\) | −1.72811e6 | − | 1.32332e7i | −0.172099 | − | 1.31787i | ||||
\(633\) | −6.44463e6 | −0.639276 | ||||||||
\(634\) | −3.94698e6 | − | 6.20028e6i | −0.389979 | − | 0.612616i | ||||
\(635\) | 125333.i | 0.0123348i | ||||||||
\(636\) | 6.94795e6 | − | 1.48728e7i | 0.681104 | − | 1.45798i | ||||
\(637\) | − | 6.85121e6i | − | 0.668989i | ||||||
\(638\) | −3.68936e6 | + | 2.34857e6i | −0.358839 | + | 0.228430i | ||||
\(639\) | −1.86960e7 | −1.81133 | ||||||||
\(640\) | −188885. | − | 173931.i | −0.0182283 | − | 0.0167852i | ||||
\(641\) | 8.17877e6 | 0.786218 | 0.393109 | − | 0.919492i | \(-0.371400\pi\) | ||||
0.393109 | + | 0.919492i | \(0.371400\pi\) | |||||||
\(642\) | 2.11045e7 | − | 1.34347e7i | 2.02087 | − | 1.28644i | ||||
\(643\) | 1.41619e7i | 1.35081i | 0.737448 | + | 0.675404i | \(0.236031\pi\) | ||||
−0.737448 | + | 0.675404i | \(0.763969\pi\) | |||||||
\(644\) | −2.59699e6 | + | 5.55914e6i | −0.246749 | + | 0.528193i | ||||
\(645\) | 322891.i | 0.0305602i | ||||||||
\(646\) | 195025. | + | 306364.i | 0.0183869 | + | 0.0288839i | ||||
\(647\) | 1.23662e7 | 1.16138 | 0.580690 | − | 0.814124i | \(-0.302783\pi\) | ||||
0.580690 | + | 0.814124i | \(0.302783\pi\) | |||||||
\(648\) | −857852. | − | 6.56912e6i | −0.0802555 | − | 0.614567i | ||||
\(649\) | 4.32756e6 | 0.403303 | ||||||||
\(650\) | 7.20702e6 | + | 1.13215e7i | 0.669072 | + | 1.05104i | ||||
\(651\) | − | 1.84868e7i | − | 1.70965i | ||||||
\(652\) | 464776. | + | 217123.i | 0.0428178 | + | 0.0200026i | ||||
\(653\) | − | 1.99967e7i | − | 1.83517i | −0.397543 | − | 0.917584i | \(-0.630137\pi\) | ||
0.397543 | − | 0.917584i | \(-0.369863\pi\) | |||||||
\(654\) | −5.56005e6 | + | 3.53942e6i | −0.508316 | + | 0.323584i | ||||
\(655\) | −130890. | −0.0119207 | ||||||||
\(656\) | 6.85894e6 | + | 8.19735e6i | 0.622296 | + | 0.743728i | ||||
\(657\) | −1.61224e7 | −1.45719 | ||||||||
\(658\) | 4.82980e6 | − | 3.07455e6i | 0.434875 | − | 0.276833i | ||||
\(659\) | − | 1.68566e7i | − | 1.51202i | −0.654562 | − | 0.756009i | \(-0.727147\pi\) | ||
0.654562 | − | 0.756009i | \(-0.272853\pi\) | |||||||
\(660\) | 122436. | + | 57197.0i | 0.0109408 | + | 0.00511109i | ||||
\(661\) | 1.65602e6i | 0.147422i | 0.997280 | + | 0.0737111i | \(0.0234843\pi\) | ||||
−0.997280 | + | 0.0737111i | \(0.976516\pi\) | |||||||
\(662\) | 6.13972e6 | + | 9.64485e6i | 0.544507 | + | 0.855363i | ||||
\(663\) | 5.80038e6 | 0.512475 | ||||||||
\(664\) | −1.10619e7 | + | 1.44456e6i | −0.973668 | + | 0.127150i | ||||
\(665\) | −44190.3 | −0.00387501 | ||||||||
\(666\) | 3.53249e6 | + | 5.54916e6i | 0.308599 | + | 0.484777i | ||||
\(667\) | 7.14369e6i | 0.621739i | ||||||||
\(668\) | −3.36037e6 | + | 7.19323e6i | −0.291370 | + | 0.623710i | ||||
\(669\) | 2.37401e7i | 2.05077i | ||||||||
\(670\) | 219343. | − | 139629.i | 0.0188771 | − | 0.0120168i | ||||
\(671\) | −6.26364e6 | −0.537057 | ||||||||
\(672\) | −6.64545e6 | + | 2.09493e7i | −0.567676 | + | 1.78956i | ||||
\(673\) | 1.37081e7 | 1.16665 | 0.583324 | − | 0.812240i | \(-0.301752\pi\) | ||||
0.583324 | + | 0.812240i | \(0.301752\pi\) | |||||||
\(674\) | −1.37698e7 | + | 8.76555e6i | −1.16755 | + | 0.743241i | ||||
\(675\) | − | 5.26523e6i | − | 0.444793i | ||||||
\(676\) | −2.78721e6 | + | 5.96633e6i | −0.234587 | + | 0.502158i | ||||
\(677\) | − | 2.21494e6i | − | 0.185734i | −0.995679 | − | 0.0928669i | \(-0.970397\pi\) | ||
0.995679 | − | 0.0928669i | \(-0.0296031\pi\) | |||||||
\(678\) | −1.22713e7 | − | 1.92769e7i | −1.02522 | − | 1.61051i | ||||
\(679\) | 2.01891e6 | 0.168052 | ||||||||
\(680\) | 80411.7 | − | 10500.8i | 0.00666879 | − | 0.000870867i | ||||
\(681\) | −1.31031e7 | −1.08269 | ||||||||
\(682\) | 1.91128e6 | + | 3.00242e6i | 0.157349 | + | 0.247179i | ||||
\(683\) | 532823.i | 0.0437050i | 0.999761 | + | 0.0218525i | \(0.00695643\pi\) | ||||
−0.999761 | + | 0.0218525i | \(0.993044\pi\) | |||||||
\(684\) | 1.80952e6 | + | 845330.i | 0.147885 | + | 0.0690854i | ||||
\(685\) | 7641.93i | 0.000622267i | ||||||||
\(686\) | 5.97262e6 | − | 3.80205e6i | 0.484568 | − | 0.308466i | ||||
\(687\) | 1.12384e7 | 0.908476 | ||||||||
\(688\) | 7.75381e6 | − | 6.48781e6i | 0.624517 | − | 0.522549i | ||||
\(689\) | −1.65060e7 | −1.32463 | ||||||||
\(690\) | 186208. | − | 118536.i | 0.0148893 | − | 0.00947826i | ||||
\(691\) | − | 5.63330e6i | − | 0.448816i | −0.974495 | − | 0.224408i | \(-0.927955\pi\) | ||
0.974495 | − | 0.224408i | \(-0.0720448\pi\) | |||||||
\(692\) | 1.66444e7 | + | 7.77553e6i | 1.32130 | + | 0.617255i | ||||
\(693\) | − | 6.52446e6i | − | 0.516074i | ||||||
\(694\) | −3.09530e6 | − | 4.86238e6i | −0.243952 | − | 0.383222i | ||||
\(695\) | 227852. | 0.0178933 | ||||||||
\(696\) | 3.31338e6 | + | 2.53727e7i | 0.259268 | + | 1.98538i | ||||
\(697\) | −3.37569e6 | −0.263197 | ||||||||
\(698\) | −4.67165e6 | − | 7.33866e6i | −0.362937 | − | 0.570136i | ||||
\(699\) | 2.15824e7i | 1.67073i | ||||||||
\(700\) | 6.79762e6 | − | 1.45511e7i | 0.524339 | − | 1.12240i | ||||
\(701\) | − | 5.94926e6i | − | 0.457265i | −0.973513 | − | 0.228633i | \(-0.926575\pi\) | ||
0.973513 | − | 0.228633i | \(-0.0734254\pi\) | |||||||
\(702\) | 6.11158e6 | − | 3.89051e6i | 0.468070 | − | 0.297964i | ||||
\(703\) | 734207. | 0.0560312 | ||||||||
\(704\) | −1.08659e6 | − | 4.08941e6i | −0.0826293 | − | 0.310977i | ||||
\(705\) | −205970. | −0.0156074 | ||||||||
\(706\) | 2.34013e6 | − | 1.48968e6i | 0.176697 | − | 0.112482i | ||||
\(707\) | 1.04398e7i | 0.785494i | ||||||||
\(708\) | 1.07165e7 | − | 2.29398e7i | 0.803470 | − | 1.71991i | ||||
\(709\) | − | 8.89034e6i | − | 0.664206i | −0.943243 | − | 0.332103i | \(-0.892242\pi\) | ||
0.943243 | − | 0.332103i | \(-0.107758\pi\) | |||||||
\(710\) | 250221. | + | 393071.i | 0.0186285 | + | 0.0292634i | ||||
\(711\) | 2.31796e7 | 1.71962 | ||||||||
\(712\) | −2.50187e6 | − | 1.91584e7i | −0.184954 | − | 1.41631i | ||||
\(713\) | 5.81358e6 | 0.428272 | ||||||||
\(714\) | −3.72750e6 | − | 5.85551e6i | −0.273636 | − | 0.429853i | ||||
\(715\) | − | 135881.i | − | 0.00994015i | ||||||
\(716\) | −8.85125e6 | − | 4.13492e6i | −0.645241 | − | 0.301429i | ||||
\(717\) | 8.87308e6i | 0.644579i | ||||||||
\(718\) | −1.52671e7 | + | 9.71871e6i | −1.10521 | + | 0.703554i | ||||
\(719\) | −1.23030e7 | −0.887539 | −0.443769 | − | 0.896141i | \(-0.646359\pi\) | ||||
−0.443769 | + | 0.896141i | \(0.646359\pi\) | |||||||
\(720\) | 342035. | − | 286189.i | 0.0245889 | − | 0.0205742i | ||||
\(721\) | −1.10943e7 | −0.794811 | ||||||||
\(722\) | −1.16279e7 | + | 7.40209e6i | −0.830153 | + | 0.528459i | ||||
\(723\) | 1.44516e7i | 1.02818i | ||||||||
\(724\) | −1.22256e7 | − | 5.71126e6i | −0.866807 | − | 0.404935i | ||||
\(725\) | − | 1.86986e7i | − | 1.32119i | ||||||
\(726\) | −1.03547e7 | − | 1.62661e7i | −0.729115 | − | 1.14536i | ||||
\(727\) | −4.81217e6 | −0.337679 | −0.168840 | − | 0.985644i | \(-0.554002\pi\) | ||||
−0.168840 | + | 0.985644i | \(0.554002\pi\) | |||||||
\(728\) | 2.19128e7 | − | 2.86157e6i | 1.53239 | − | 0.200113i | ||||
\(729\) | 2.11789e7 | 1.47599 | ||||||||
\(730\) | 215777. | + | 338963.i | 0.0149864 | + | 0.0235421i | ||||
\(731\) | 3.19304e6i | 0.221010i | ||||||||
\(732\) | −1.55109e7 | + | 3.32027e7i | −1.06994 | + | 2.29032i | ||||
\(733\) | 2.11550e6i | 0.145430i | 0.997353 | + | 0.0727148i | \(0.0231663\pi\) | ||||
−0.997353 | + | 0.0727148i | \(0.976834\pi\) | |||||||
\(734\) | 9.86585e6 | − | 6.28041e6i | 0.675919 | − | 0.430277i | ||||
\(735\) | 294951. | 0.0201387 | ||||||||
\(736\) | −6.58796e6 | − | 2.08981e6i | −0.448287 | − | 0.142204i | ||||
\(737\) | 4.28481e6 | 0.290578 | ||||||||
\(738\) | −1.56605e7 | + | 9.96918e6i | −1.05844 | + | 0.673781i | ||||
\(739\) | 3.53365e6i | 0.238019i | 0.992893 | + | 0.119010i | \(0.0379719\pi\) | ||||
−0.992893 | + | 0.119010i | \(0.962028\pi\) | |||||||
\(740\) | 69389.7 | − | 148536.i | 0.00465817 | − | 0.00997133i | ||||
\(741\) | − | 3.56034e6i | − | 0.238202i | ||||||
\(742\) | 1.06073e7 | + | 1.66629e7i | 0.707283 | + | 1.11107i | ||||
\(743\) | 2.10515e7 | 1.39898 | 0.699489 | − | 0.714643i | \(-0.253411\pi\) | ||||
0.699489 | + | 0.714643i | \(0.253411\pi\) | |||||||
\(744\) | 2.06484e7 | − | 2.69645e6i | 1.36759 | − | 0.178591i | ||||
\(745\) | −586112. | −0.0386892 | ||||||||
\(746\) | −1.50039e7 | − | 2.35695e7i | −0.987091 | − | 1.55062i | ||||
\(747\) | − | 1.93763e7i | − | 1.27049i | ||||||
\(748\) | 1.21076e6 | + | 565617.i | 0.0791235 | + | 0.0369631i | ||||
\(749\) | 3.01033e7i | 1.96070i | ||||||||
\(750\) | −975100. | + | 620729.i | −0.0632988 | + | 0.0402948i | ||||
\(751\) | −9.76794e6 | −0.631980 | −0.315990 | − | 0.948763i | \(-0.602337\pi\) | ||||
−0.315990 | + | 0.948763i | \(0.602337\pi\) | |||||||
\(752\) | 4.13853e6 | + | 4.94610e6i | 0.266871 | + | 0.318947i | ||||
\(753\) | −1.09223e7 | −0.701983 | ||||||||
\(754\) | 2.17043e7 | − | 1.38165e7i | 1.39033 | − | 0.885056i | ||||
\(755\) | 55373.8i | 0.00353538i | ||||||||
\(756\) | −7.85499e6 | − | 3.66951e6i | −0.499851 | − | 0.233509i | ||||
\(757\) | 3.90009e6i | 0.247363i | 0.992322 | + | 0.123682i | \(0.0394701\pi\) | ||||
−0.992322 | + | 0.123682i | \(0.960530\pi\) | |||||||
\(758\) | 1.58471e7 | + | 2.48941e7i | 1.00179 | + | 1.57370i | ||||
\(759\) | 3.63753e6 | 0.229194 | ||||||||
\(760\) | −6445.53 | − | 49357.6i | −0.000404785 | − | 0.00309970i | ||||
\(761\) | −1.28261e7 | −0.802845 | −0.401422 | − | 0.915893i | \(-0.631484\pi\) | ||||
−0.401422 | + | 0.915893i | \(0.631484\pi\) | |||||||
\(762\) | 6.48920e6 | + | 1.01938e7i | 0.404859 | + | 0.635991i | ||||
\(763\) | − | 7.93082e6i | − | 0.493181i | ||||||
\(764\) | −5.74578e6 | + | 1.22995e7i | −0.356136 | + | 0.762348i | ||||
\(765\) | 140851.i | 0.00870174i | ||||||||
\(766\) | 2.01534e7 | − | 1.28293e7i | 1.24102 | − | 0.790006i | ||||
\(767\) | −2.54588e7 | −1.56261 | ||||||||
\(768\) | −2.43682e7 | − | 4.36688e6i | −1.49080 | − | 0.267158i | ||||
\(769\) | 1.15731e7 | 0.705724 | 0.352862 | − | 0.935675i | \(-0.385208\pi\) | ||||
0.352862 | + | 0.935675i | \(0.385208\pi\) | |||||||
\(770\) | −137172. | + | 87321.2i | −0.00833758 | + | 0.00530754i | ||||
\(771\) | − | 1.37725e7i | − | 0.834404i | ||||||
\(772\) | −5.06413e6 | + | 1.08403e7i | −0.305817 | + | 0.654635i | ||||
\(773\) | − | 3.69152e6i | − | 0.222206i | −0.993809 | − | 0.111103i | \(-0.964562\pi\) | ||
0.993809 | − | 0.111103i | \(-0.0354384\pi\) | |||||||
\(774\) | 9.42977e6 | + | 1.48132e7i | 0.565782 | + | 0.888783i | ||||
\(775\) | −1.52171e7 | −0.910073 | ||||||||
\(776\) | 294475. | + | 2.25498e6i | 0.0175547 | + | 0.134428i | ||||
\(777\) | −1.40329e7 | −0.833861 | ||||||||
\(778\) | 1.86944e6 | + | 2.93670e6i | 0.110730 | + | 0.173944i | ||||
\(779\) | 2.07204e6i | 0.122336i | ||||||||
\(780\) | −720286. | − | 336486.i | −0.0423905 | − | 0.0198030i | ||||
\(781\) | 7.67855e6i | 0.450455i | ||||||||
\(782\) | 1.84140e6 | − | 1.17220e6i | 0.107679 | − | 0.0685463i | ||||
\(783\) | −1.00939e7 | −0.588378 | ||||||||
\(784\) | −5.92643e6 | − | 7.08288e6i | −0.344352 | − | 0.411547i | ||||
\(785\) | 508998. | 0.0294810 | ||||||||
\(786\) | −1.06458e7 | + | 6.77689e6i | −0.614640 | + | 0.391268i | ||||
\(787\) | − | 3.15075e7i | − | 1.81333i | −0.421851 | − | 0.906665i | \(-0.638619\pi\) | ||
0.421851 | − | 0.906665i | \(-0.361381\pi\) | |||||||
\(788\) | −3.27175e6 | − | 1.52842e6i | −0.187700 | − | 0.0876853i | ||||
\(789\) | − | 9.72652e6i | − | 0.556244i | ||||||
\(790\) | −310228. | − | 487335.i | −0.0176853 | − | 0.0277818i | ||||
\(791\) | 2.74965e7 | 1.56256 | ||||||||
\(792\) | 7.28737e6 | − | 951648.i | 0.412818 | − | 0.0539093i | ||||
\(793\) | 3.68487e7 | 2.08084 | ||||||||
\(794\) | 4.87725e6 | + | 7.66164e6i | 0.274551 | + | 0.431291i | ||||
\(795\) | − | 710599.i | − | 0.0398755i | ||||||
\(796\) | 3.56124e6 | − | 7.62322e6i | 0.199213 | − | 0.426438i | ||||
\(797\) | − | 1.13115e7i | − | 0.630775i | −0.948963 | − | 0.315387i | \(-0.897866\pi\) | ||
0.948963 | − | 0.315387i | \(-0.102134\pi\) | |||||||
\(798\) | −3.59418e6 | + | 2.28798e6i | −0.199799 | + | 0.127188i | ||||
\(799\) | −2.03682e6 | −0.112872 | ||||||||
\(800\) | 1.72440e7 | + | 5.47008e6i | 0.952606 | + | 0.302182i | ||||
\(801\) | 3.35583e7 | 1.84807 | ||||||||
\(802\) | −7.06128e6 | + | 4.49507e6i | −0.387657 | + | 0.246775i | ||||
\(803\) | 6.62156e6i | 0.362386i | ||||||||
\(804\) | 1.06106e7 | − | 2.27132e7i | 0.578897 | − | 1.23919i | ||||
\(805\) | 265606.i | 0.0144460i | ||||||||
\(806\) | −1.12440e7 | − | 1.76631e7i | −0.609652 | − | 0.957699i | ||||
\(807\) | −2.70235e7 | −1.46069 | ||||||||
\(808\) | −1.16605e7 | + | 1.52273e6i | −0.628332 | + | 0.0820530i | ||||
\(809\) | −1.87371e7 | −1.00654 | −0.503271 | − | 0.864128i | \(-0.667870\pi\) | ||||
−0.503271 | + | 0.864128i | \(0.667870\pi\) | |||||||
\(810\) | −154001. | − | 241919.i | −0.00824727 | − | 0.0129556i | ||||
\(811\) | 1.04019e6i | 0.0555341i | 0.999614 | + | 0.0277671i | \(0.00883967\pi\) | ||||
−0.999614 | + | 0.0277671i | \(0.991160\pi\) | |||||||
\(812\) | −2.78957e7 | − | 1.30317e7i | −1.48473 | − | 0.693602i | ||||
\(813\) | − | 2.87108e7i | − | 1.52342i | ||||||
\(814\) | 2.27907e6 | − | 1.45081e6i | 0.120558 | − | 0.0767450i | ||||
\(815\) | 22206.2 | 0.00117106 | ||||||||
\(816\) | 5.99652e6 | − | 5.01744e6i | 0.315263 | − | 0.263789i | ||||
\(817\) | 1.95992e6 | 0.102727 | ||||||||
\(818\) | −5.51451e6 | + | 3.51043e6i | −0.288153 | + | 0.183433i | ||||
\(819\) | 3.83831e7i | 1.99954i | ||||||||
\(820\) | 419191. | + | 195828.i | 0.0217709 | + | 0.0101704i | ||||
\(821\) | 2.89521e7i | 1.49907i | 0.661965 | + | 0.749535i | \(0.269723\pi\) | ||||
−0.661965 | + | 0.749535i | \(0.730277\pi\) | |||||||
\(822\) | 395666. | + | 621549.i | 0.0204244 | + | 0.0320845i | ||||
\(823\) | −1.73232e7 | −0.891517 | −0.445758 | − | 0.895153i | \(-0.647066\pi\) | ||||
−0.445758 | + | 0.895153i | \(0.647066\pi\) | |||||||
\(824\) | −1.61820e6 | − | 1.23916e7i | −0.0830262 | − | 0.635785i | ||||
\(825\) | −9.52125e6 | −0.487034 | ||||||||
\(826\) | 1.63606e7 | + | 2.57008e7i | 0.834352 | + | 1.31068i | ||||
\(827\) | 7.19436e6i | 0.365787i | 0.983133 | + | 0.182893i | \(0.0585463\pi\) | ||||
−0.983133 | + | 0.182893i | \(0.941454\pi\) | |||||||
\(828\) | 5.08086e6 | − | 1.08761e7i | 0.257550 | − | 0.551313i | ||||
\(829\) | 2.28187e7i | 1.15320i | 0.817026 | + | 0.576600i | \(0.195621\pi\) | ||||
−0.817026 | + | 0.576600i | \(0.804379\pi\) | |||||||
\(830\) | −407374. | + | 259326.i | −0.0205257 | + | 0.0130663i | ||||
\(831\) | 1.90305e7 | 0.955978 | ||||||||
\(832\) | 6.39235e6 | + | 2.40578e7i | 0.320149 | + | 1.20489i | ||||
\(833\) | 2.91675e6 | 0.145642 | ||||||||
\(834\) | 1.85321e7 | − | 1.17972e7i | 0.922591 | − | 0.587303i | ||||
\(835\) | 343680.i | 0.0170584i | ||||||||
\(836\) | 347182. | − | 743180.i | 0.0171807 | − | 0.0367772i | ||||
\(837\) | 8.21451e6i | 0.405292i | ||||||||
\(838\) | −5.60155e6 | − | 8.79945e6i | −0.275549 | − | 0.432858i | ||||
\(839\) | 1.81694e7 | 0.891121 | 0.445560 | − | 0.895252i | \(-0.353004\pi\) | ||||
0.445560 | + | 0.895252i | \(0.353004\pi\) | |||||||
\(840\) | 123193. | + | 943369.i | 0.00602405 | + | 0.0461300i | ||||
\(841\) | −1.53359e7 | −0.747684 | ||||||||
\(842\) | −1.25478e7 | − | 1.97113e7i | −0.609941 | − | 0.958152i | ||||
\(843\) | 2.82899e7i | 1.37108i | ||||||||
\(844\) | 7.91399e6 | + | 3.69707e6i | 0.382419 | + | 0.178650i | ||||
\(845\) | 285061.i | 0.0137340i | ||||||||
\(846\) | −9.44921e6 | + | 6.01518e6i | −0.453910 | + | 0.288950i | ||||
\(847\) | 2.32019e7 | 1.11126 | ||||||||
\(848\) | −1.70641e7 | + | 1.42780e7i | −0.814882 | + | 0.681832i | ||||
\(849\) | −3.45376e7 | −1.64446 | ||||||||
\(850\) | −4.81986e6 | + | 3.06823e6i | −0.228817 | + | 0.145660i | ||||
\(851\) | − | 4.41295e6i | − | 0.208884i | ||||||
\(852\) | 4.07030e7 | + | 1.90147e7i | 1.92100 | + | 0.897408i | ||||
\(853\) | 2.58313e7i | 1.21555i | 0.794108 | + | 0.607776i | \(0.207938\pi\) | ||||
−0.794108 | + | 0.607776i | \(0.792062\pi\) | |||||||
\(854\) | −2.36801e7 | − | 3.71989e7i | −1.11106 | − | 1.74536i | ||||
\(855\) | 86455.8 | 0.00404463 | ||||||||
\(856\) | −3.36234e7 | + | 4.39083e6i | −1.56840 | + | 0.204815i | ||||
\(857\) | 1.83988e7 | 0.855731 | 0.427866 | − | 0.903842i | \(-0.359266\pi\) | ||||
0.427866 | + | 0.903842i | \(0.359266\pi\) | |||||||
\(858\) | −7.03531e6 | − | 1.10517e7i | −0.326261 | − | 0.512522i | ||||
\(859\) | − | 2.69993e7i | − | 1.24845i | −0.781246 | − | 0.624224i | \(-0.785415\pi\) | ||
0.781246 | − | 0.624224i | \(-0.214585\pi\) | |||||||
\(860\) | 185232. | − | 396509.i | 0.00854023 | − | 0.0182813i | ||||
\(861\) | − | 3.96028e7i | − | 1.82061i | ||||||
\(862\) | −1.64332e7 | + | 1.04610e7i | −0.753274 | + | 0.479519i | ||||
\(863\) | 3.05160e7 | 1.39477 | 0.697383 | − | 0.716699i | \(-0.254348\pi\) | ||||
0.697383 | + | 0.716699i | \(0.254348\pi\) | |||||||
\(864\) | 2.95287e6 | − | 9.30870e6i | 0.134574 | − | 0.424233i | ||||
\(865\) | 795240. | 0.0361375 | ||||||||
\(866\) | 1.15337e7 | − | 7.34214e6i | 0.522606 | − | 0.332681i | ||||
\(867\) | − | 3.10527e7i | − | 1.40298i | ||||||
\(868\) | −1.06053e7 | + | 2.27017e7i | −0.477773 | + | 1.02273i | ||||
\(869\) | − | 9.51999e6i | − | 0.427648i | ||||||
\(870\) | 594815. | + | 934391.i | 0.0266430 | + | 0.0418534i | ||||
\(871\) | −2.52073e7 | −1.12585 | ||||||||
\(872\) | 8.85818e6 | − | 1.15678e6i | 0.394506 | − | 0.0515179i | ||||
\(873\) | −3.94988e6 | −0.175408 | ||||||||
\(874\) | −719508. | − | 1.13027e6i | −0.0318608 | − | 0.0500499i | ||||
\(875\) | − | 1.39088e6i | − | 0.0614141i | ||||||
\(876\) | 3.51000e7 | + | 1.63972e7i | 1.54542 | + | 0.721954i | ||||
\(877\) | − | 2.80238e7i | − | 1.23035i | −0.788391 | − | 0.615174i | \(-0.789086\pi\) | ||
0.788391 | − | 0.615174i | \(-0.210914\pi\) | |||||||
\(878\) | 1.53963e7 | − | 9.80099e6i | 0.674032 | − | 0.429075i | ||||
\(879\) | 1.77242e7 | 0.773738 | ||||||||
\(880\) | −117540. | − | 140476.i | −0.00511655 | − | 0.00611496i | ||||
\(881\) | −8.04971e6 | −0.349414 | −0.174707 | − | 0.984620i | \(-0.555898\pi\) | ||||
−0.174707 | + | 0.984620i | \(0.555898\pi\) | |||||||
\(882\) | 1.35314e7 | − | 8.61382e6i | 0.585695 | − | 0.372842i | ||||
\(883\) | 8.61922e6i | 0.372020i | 0.982548 | + | 0.186010i | \(0.0595556\pi\) | ||||
−0.982548 | + | 0.186010i | \(0.940444\pi\) | |||||||
\(884\) | −7.12286e6 | − | 3.32749e6i | −0.306566 | − | 0.143214i | ||||
\(885\) | − | 1.09603e6i | − | 0.0470395i | ||||||
\(886\) | 1.95821e7 | + | 3.07615e7i | 0.838061 | + | 1.31651i | ||||
\(887\) | 6.77038e6 | 0.288937 | 0.144469 | − | 0.989509i | \(-0.453853\pi\) | ||||
0.144469 | + | 0.989509i | \(0.453853\pi\) | |||||||
\(888\) | −2.04681e6 | − | 1.56737e7i | −0.0871055 | − | 0.667022i | ||||
\(889\) | −1.45404e7 | −0.617054 | ||||||||
\(890\) | −449133. | − | 705540.i | −0.0190064 | − | 0.0298570i | ||||
\(891\) | − | 4.72583e6i | − | 0.199427i | ||||||
\(892\) | 1.36189e7 | − | 2.91528e7i | 0.573100 | − | 1.22678i | ||||
\(893\) | 1.25022e6i | 0.0524636i | ||||||||
\(894\) | −4.76708e7 | + | 3.03463e7i | −1.99484 | + | 1.26988i | ||||
\(895\) | −422898. | −0.0176473 | ||||||||
\(896\) | 2.01785e7 | − | 2.19134e7i | 0.839690 | − | 0.911883i | ||||
\(897\) | −2.13994e7 | −0.888015 | ||||||||
\(898\) | 8.71369e6 | − | 5.54696e6i | 0.360588 | − | 0.229543i | ||||
\(899\) | 2.91725e7i | 1.20386i | ||||||||
\(900\) | −1.32992e7 | + | 2.84683e7i | −0.547290 | + | 1.17153i | ||||
\(901\) | − | 7.02706e6i | − | 0.288378i | ||||||
\(902\) | 4.09440e6 | + | 6.43187e6i | 0.167561 | + | 0.263221i | ||||
\(903\) | −3.74600e7 | −1.52879 | ||||||||
\(904\) | 4.01059e6 | + | 3.07117e7i | 0.163225 | + | 1.24992i | ||||
\(905\) | −584117. | −0.0237071 | ||||||||
\(906\) | 2.86701e6 | + | 4.50377e6i | 0.116040 | + | 0.182287i | ||||
\(907\) | 3.35760e7i | 1.35522i | 0.735421 | + | 0.677611i | \(0.236985\pi\) | ||||
−0.735421 | + | 0.677611i | \(0.763015\pi\) | |||||||
\(908\) | 1.60905e7 | + | 7.51680e6i | 0.647673 | + | 0.302565i | ||||
\(909\) | − | 2.04248e7i | − | 0.819877i | ||||||
\(910\) | 806977. | − | 513706.i | 0.0323041 | − | 0.0205642i | ||||
\(911\) | −3.92094e7 | −1.56529 | −0.782645 | − | 0.622469i | \(-0.786130\pi\) | ||||
−0.782645 | + | 0.622469i | \(0.786130\pi\) | |||||||
\(912\) | −3.07976e6 | − | 3.68073e6i | −0.122611 | − | 0.146537i | ||||
\(913\) | −7.95797e6 | −0.315955 | ||||||||
\(914\) | −1.08260e7 | + | 6.89161e6i | −0.428649 | + | 0.272869i | ||||
\(915\) | 1.58637e6i | 0.0626400i | ||||||||
\(916\) | −1.38008e7 | − | 6.44712e6i | −0.543456 | − | 0.253879i | ||||
\(917\) | − | 1.51851e7i | − | 0.596340i | ||||||
\(918\) | 1.65630e6 | + | 2.60187e6i | 0.0648683 | + | 0.101901i | ||||
\(919\) | 1.65806e7 | 0.647609 | 0.323804 | − | 0.946124i | \(-0.395038\pi\) | ||||
0.323804 | + | 0.946124i | \(0.395038\pi\) | |||||||
\(920\) | −296664. | + | 38740.9i | −0.0115557 | + | 0.00150904i | ||||
\(921\) | 4.88136e7 | 1.89623 | ||||||||
\(922\) | 8.57797e6 | + | 1.34751e7i | 0.332321 | + | 0.522040i | ||||
\(923\) | − | 4.51725e7i | − | 1.74530i | ||||||
\(924\) | −6.63567e6 | + | 1.42044e7i | −0.255685 | + | 0.547321i | ||||
\(925\) | 1.15509e7i | 0.443876i | ||||||||
\(926\) | −1.45945e7 | + | 9.29057e6i | −0.559322 | + | 0.356053i | ||||
\(927\) | 2.17054e7 | 0.829601 | ||||||||
\(928\) | 1.04867e7 | − | 3.30584e7i | 0.399730 | − | 1.26012i | ||||
\(929\) | 3.97202e7 | 1.50998 | 0.754992 | − | 0.655734i | \(-0.227641\pi\) | ||||
0.754992 | + | 0.655734i | \(0.227641\pi\) | |||||||
\(930\) | 760413. | − | 484064.i | 0.0288298 | − | 0.0183525i | ||||
\(931\) | − | 1.79033e6i | − | 0.0676955i | ||||||
\(932\) | 1.23811e7 | − | 2.65032e7i | 0.466897 | − | 0.999443i | ||||
\(933\) | 7.24565e7i | 2.72504i | ||||||||
\(934\) | −1.57805e7 | − | 2.47895e7i | −0.591907 | − | 0.929824i | ||||
\(935\) | 57848.2 | 0.00216402 | ||||||||
\(936\) | −4.28712e7 | + | 5.59849e6i | −1.59947 | + | 0.208873i | ||||
\(937\) | 2.47490e7 | 0.920891 | 0.460446 | − | 0.887688i | \(-0.347690\pi\) | ||||
0.460446 | + | 0.887688i | \(0.347690\pi\) | |||||||
\(938\) | 1.61990e7 | + | 2.54469e7i | 0.601148 | + | 0.944339i | ||||
\(939\) | − | 2.71858e6i | − | 0.100618i | ||||||
\(940\) | 252930. | + | 118158.i | 0.00933643 | + | 0.00436158i | ||||
\(941\) | 3.63378e7i | 1.33778i | 0.743361 | + | 0.668890i | \(0.233230\pi\) | ||||
−0.743361 | + | 0.668890i | \(0.766770\pi\) | |||||||
\(942\) | 4.13989e7 | − | 2.63537e7i | 1.52006 | − | 0.967641i | ||||
\(943\) | 1.24540e7 | 0.456067 | ||||||||
\(944\) | −2.63197e7 | + | 2.20223e7i | −0.961281 | + | 0.804329i | ||||
\(945\) | −375298. | −0.0136709 | ||||||||
\(946\) | 6.08385e6 | − | 3.87286e6i | 0.221030 | − | 0.140703i | ||||
\(947\) | 5.78262e6i | 0.209532i | 0.994497 | + | 0.104766i | \(0.0334093\pi\) | ||||
−0.994497 | + | 0.104766i | \(0.966591\pi\) | |||||||
\(948\) | −5.04642e7 | − | 2.35747e7i | −1.82374 | − | 0.851971i | ||||
\(949\) | − | 3.89543e7i | − | 1.40407i | ||||||
\(950\) | 1.88331e6 | + | 2.95849e6i | 0.0677039 | + | 0.106356i | ||||
\(951\) | −3.06759e7 | −1.09988 | ||||||||
\(952\) | 1.21825e6 | + | 9.32891e6i | 0.0435656 | + | 0.333610i | ||||
\(953\) | −4.95180e7 | −1.76616 | −0.883081 | − | 0.469220i | \(-0.844535\pi\) | ||||
−0.883081 | + | 0.469220i | \(0.844535\pi\) | |||||||
\(954\) | −2.07525e7 | − | 3.26000e7i | −0.738243 | − | 1.15970i | ||||
\(955\) | 587648.i | 0.0208501i | ||||||||
\(956\) | 5.09020e6 | − | 1.08961e7i | 0.180132 | − | 0.385591i | ||||
\(957\) | 1.82531e7i | 0.644254i | ||||||||
\(958\) | 3.94689e7 | − | 2.51251e7i | 1.38945 | − | 0.884494i | ||||
\(959\) | −886573. | −0.0311292 | ||||||||
\(960\) | −1.03571e6 | + | 275197.i | −0.0362710 | + | 0.00963751i | ||||
\(961\) | −4.88839e6 | −0.170749 | ||||||||
\(962\) | −1.34076e7 | + | 8.53504e6i | −0.467105 | + | 0.297350i | ||||
\(963\) | − | 5.88954e7i | − | 2.04652i | ||||||
\(964\) | 8.29042e6 | − | 1.77465e7i | 0.287332 | − | 0.615065i | ||||
\(965\) | 517932.i | 0.0179042i | ||||||||
\(966\) | 1.37519e7 | + | 2.16028e7i | 0.474155 | + | 0.744847i | ||||
\(967\) | −1.73855e7 | −0.597891 | −0.298945 | − | 0.954270i | \(-0.596635\pi\) | ||||
−0.298945 | + | 0.954270i | \(0.596635\pi\) | |||||||
\(968\) | 3.38419e6 | + | 2.59149e7i | 0.116083 | + | 0.888918i | ||||
\(969\) | 1.51573e6 | 0.0518577 | ||||||||
\(970\) | 52863.9 | + | 83043.6i | 0.00180397 | + | 0.00283385i | ||||
\(971\) | 5.82121e7i | 1.98137i | 0.136186 | + | 0.990683i | \(0.456516\pi\) | ||||
−0.136186 | + | 0.990683i | \(0.543484\pi\) | |||||||
\(972\) | −3.69285e7 | − | 1.72514e7i | −1.25371 | − | 0.585677i | ||||
\(973\) | 2.64341e7i | 0.895121i | ||||||||
\(974\) | 2.36530e7 | − | 1.50571e7i | 0.798895 | − | 0.508561i | ||||
\(975\) | 5.60130e7 | 1.88702 | ||||||||
\(976\) | 3.80947e7 | − | 3.18748e7i | 1.28009 | − | 1.07108i | ||||
\(977\) | 2.03137e7 | 0.680853 | 0.340426 | − | 0.940271i | \(-0.389429\pi\) | ||||
0.340426 | + | 0.940271i | \(0.389429\pi\) | |||||||
\(978\) | 1.80612e6 | − | 1.14974e6i | 0.0603809 | − | 0.0384373i | ||||
\(979\) | − | 1.37826e7i | − | 0.459593i | ||||||
\(980\) | −362200. | − | 169204.i | −0.0120471 | − | 0.00562789i | ||||
\(981\) | 1.55162e7i | 0.514769i | ||||||||
\(982\) | −1.82813e7 | − | 2.87180e7i | −0.604962 | − | 0.950331i | ||||
\(983\) | −5.54003e7 | −1.82864 | −0.914321 | − | 0.404991i | \(-0.867275\pi\) | ||||
−0.914321 | + | 0.404991i | \(0.867275\pi\) | |||||||
\(984\) | 4.42336e7 | − | 5.77640e6i | 1.45634 | − | 0.190182i | ||||
\(985\) | −156319. | −0.00513357 | ||||||||
\(986\) | 5.88208e6 | + | 9.24013e6i | 0.192681 | + | 0.302681i | ||||
\(987\) | − | 2.38954e7i | − | 0.780768i | ||||||
\(988\) | −2.04245e6 | + | 4.37209e6i | −0.0665670 | + | 0.142494i | ||||
\(989\) | − | 1.17801e7i | − | 0.382965i | ||||||
\(990\) | 268370. | − | 170839.i | 0.00870253 | − | 0.00553986i | ||||
\(991\) | −9.26753e6 | −0.299764 | −0.149882 | − | 0.988704i | \(-0.547889\pi\) | ||||
−0.149882 | + | 0.988704i | \(0.547889\pi\) | |||||||
\(992\) | −2.69031e7 | − | 8.53410e6i | −0.868007 | − | 0.275346i | ||||
\(993\) | 4.77179e7 | 1.53571 | ||||||||
\(994\) | −4.56019e7 | + | 2.90292e7i | −1.46392 | + | 0.931901i | ||||
\(995\) | − | 364224.i | − | 0.0116630i | ||||||
\(996\) | −1.97066e7 | + | 4.21841e7i | −0.629453 | + | 1.34741i | ||||
\(997\) | − | 5.53912e7i | − | 1.76483i | −0.470471 | − | 0.882415i | \(-0.655916\pi\) | ||
0.470471 | − | 0.882415i | \(-0.344084\pi\) | |||||||
\(998\) | 2.39325e7 | + | 3.75955e7i | 0.760611 | + | 1.19484i | ||||
\(999\) | 6.23544e6 | 0.197676 |
(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 | 8.6.b.a.5.2 | yes | 4 | |
3.2 | odd | 2 | 72.6.d.b.37.3 | 4 | |||
4.3 | odd | 2 | 32.6.b.a.17.1 | 4 | |||
5.2 | odd | 4 | 200.6.f.a.149.3 | 8 | |||
5.3 | odd | 4 | 200.6.f.a.149.6 | 8 | |||
5.4 | even | 2 | 200.6.d.a.101.3 | 4 | |||
8.3 | odd | 2 | 32.6.b.a.17.4 | 4 | |||
8.5 | even | 2 | inner | 8.6.b.a.5.1 | ✓ | 4 | |
12.11 | even | 2 | 288.6.d.b.145.3 | 4 | |||
16.3 | odd | 4 | 256.6.a.n.1.4 | 4 | |||
16.5 | even | 4 | 256.6.a.k.1.4 | 4 | |||
16.11 | odd | 4 | 256.6.a.n.1.1 | 4 | |||
16.13 | even | 4 | 256.6.a.k.1.1 | 4 | |||
20.3 | even | 4 | 800.6.f.a.49.8 | 8 | |||
20.7 | even | 4 | 800.6.f.a.49.1 | 8 | |||
20.19 | odd | 2 | 800.6.d.a.401.4 | 4 | |||
24.5 | odd | 2 | 72.6.d.b.37.4 | 4 | |||
24.11 | even | 2 | 288.6.d.b.145.2 | 4 | |||
40.3 | even | 4 | 800.6.f.a.49.2 | 8 | |||
40.13 | odd | 4 | 200.6.f.a.149.4 | 8 | |||
40.19 | odd | 2 | 800.6.d.a.401.1 | 4 | |||
40.27 | even | 4 | 800.6.f.a.49.7 | 8 | |||
40.29 | even | 2 | 200.6.d.a.101.4 | 4 | |||
40.37 | odd | 4 | 200.6.f.a.149.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.6.b.a.5.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
8.6.b.a.5.2 | yes | 4 | 1.1 | even | 1 | trivial | |
32.6.b.a.17.1 | 4 | 4.3 | odd | 2 | |||
32.6.b.a.17.4 | 4 | 8.3 | odd | 2 | |||
72.6.d.b.37.3 | 4 | 3.2 | odd | 2 | |||
72.6.d.b.37.4 | 4 | 24.5 | odd | 2 | |||
200.6.d.a.101.3 | 4 | 5.4 | even | 2 | |||
200.6.d.a.101.4 | 4 | 40.29 | even | 2 | |||
200.6.f.a.149.3 | 8 | 5.2 | odd | 4 | |||
200.6.f.a.149.4 | 8 | 40.13 | odd | 4 | |||
200.6.f.a.149.5 | 8 | 40.37 | odd | 4 | |||
200.6.f.a.149.6 | 8 | 5.3 | odd | 4 | |||
256.6.a.k.1.1 | 4 | 16.13 | even | 4 | |||
256.6.a.k.1.4 | 4 | 16.5 | even | 4 | |||
256.6.a.n.1.1 | 4 | 16.11 | odd | 4 | |||
256.6.a.n.1.4 | 4 | 16.3 | odd | 4 | |||
288.6.d.b.145.2 | 4 | 24.11 | even | 2 | |||
288.6.d.b.145.3 | 4 | 12.11 | even | 2 | |||
800.6.d.a.401.1 | 4 | 40.19 | odd | 2 | |||
800.6.d.a.401.4 | 4 | 20.19 | odd | 2 | |||
800.6.f.a.49.1 | 8 | 20.7 | even | 4 | |||
800.6.f.a.49.2 | 8 | 40.3 | even | 4 | |||
800.6.f.a.49.7 | 8 | 40.27 | even | 4 | |||
800.6.f.a.49.8 | 8 | 20.3 | even | 4 |