Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,5,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(18.2964834658\) |
Analytic rank: | \(0\) |
Dimension: | \(78\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.6 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.5.b.a.119.73 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 7.08630i | − | 1.77157i | −0.464092 | − | 0.885787i | \(-0.653619\pi\) | ||
0.464092 | − | 0.885787i | \(-0.346381\pi\) | |||||||
\(3\) | −1.58963 | − | 8.85850i | −0.176625 | − | 0.984278i | ||||
\(4\) | −34.2156 | −2.13848 | ||||||||
\(5\) | − | 8.65783i | − | 0.346313i | −0.984894 | − | 0.173157i | \(-0.944603\pi\) | ||
0.984894 | − | 0.173157i | \(-0.0553967\pi\) | |||||||
\(6\) | −62.7740 | + | 11.2646i | −1.74372 | + | 0.312905i | ||||
\(7\) | −70.0243 | −1.42907 | −0.714534 | − | 0.699601i | \(-0.753361\pi\) | ||||
−0.714534 | + | 0.699601i | \(0.753361\pi\) | |||||||
\(8\) | 129.081i | 2.01690i | ||||||||
\(9\) | −75.9462 | + | 28.1634i | −0.937607 | + | 0.347697i | ||||
\(10\) | −61.3520 | −0.613520 | ||||||||
\(11\) | − | 225.973i | − | 1.86754i | −0.357871 | − | 0.933771i | \(-0.616497\pi\) | ||
0.357871 | − | 0.933771i | \(-0.383503\pi\) | |||||||
\(12\) | 54.3901 | + | 303.099i | 0.377709 | + | 2.10486i | ||||
\(13\) | 156.064 | 0.923455 | 0.461727 | − | 0.887022i | \(-0.347230\pi\) | ||||
0.461727 | + | 0.887022i | \(0.347230\pi\) | |||||||
\(14\) | 496.213i | 2.53170i | ||||||||
\(15\) | −76.6954 | + | 13.7627i | −0.340869 | + | 0.0611677i | ||||
\(16\) | 367.259 | 1.43460 | ||||||||
\(17\) | 15.4786i | 0.0535591i | 0.999641 | + | 0.0267795i | \(0.00852521\pi\) | ||||
−0.999641 | + | 0.0267795i | \(0.991475\pi\) | |||||||
\(18\) | 199.575 | + | 538.177i | 0.615971 | + | 1.66104i | ||||
\(19\) | 179.462 | 0.497125 | 0.248563 | − | 0.968616i | \(-0.420042\pi\) | ||||
0.248563 | + | 0.968616i | \(0.420042\pi\) | |||||||
\(20\) | 296.233i | 0.740583i | ||||||||
\(21\) | 111.313 | + | 620.310i | 0.252409 | + | 1.40660i | ||||
\(22\) | −1601.31 | −3.30849 | ||||||||
\(23\) | − | 621.607i | − | 1.17506i | −0.809202 | − | 0.587530i | \(-0.800100\pi\) | ||
0.809202 | − | 0.587530i | \(-0.199900\pi\) | |||||||
\(24\) | 1143.47 | − | 205.191i | 1.98519 | − | 0.356235i | ||||
\(25\) | 550.042 | 0.880067 | ||||||||
\(26\) | − | 1105.91i | − | 1.63597i | ||||||
\(27\) | 370.212 | + | 628.000i | 0.507835 | + | 0.861454i | ||||
\(28\) | 2395.92 | 3.05603 | ||||||||
\(29\) | 442.113i | 0.525699i | 0.964837 | + | 0.262850i | \(0.0846623\pi\) | ||||
−0.964837 | + | 0.262850i | \(0.915338\pi\) | |||||||
\(30\) | 97.5268 | + | 543.487i | 0.108363 | + | 0.603874i | ||||
\(31\) | −258.752 | −0.269252 | −0.134626 | − | 0.990896i | \(-0.542983\pi\) | ||||
−0.134626 | + | 0.990896i | \(0.542983\pi\) | |||||||
\(32\) | − | 537.204i | − | 0.524613i | ||||||
\(33\) | −2001.78 | + | 359.212i | −1.83818 | + | 0.329855i | ||||
\(34\) | 109.686 | 0.0948838 | ||||||||
\(35\) | 606.259i | 0.494905i | ||||||||
\(36\) | 2598.55 | − | 963.629i | 2.00505 | − | 0.743541i | ||||
\(37\) | −2503.21 | −1.82850 | −0.914248 | − | 0.405154i | \(-0.867218\pi\) | ||||
−0.914248 | + | 0.405154i | \(0.867218\pi\) | |||||||
\(38\) | − | 1271.72i | − | 0.880694i | ||||||
\(39\) | −248.083 | − | 1382.49i | −0.163105 | − | 0.908936i | ||||
\(40\) | 1117.56 | 0.698478 | ||||||||
\(41\) | 241.937i | 0.143925i | 0.997407 | + | 0.0719623i | \(0.0229261\pi\) | ||||
−0.997407 | + | 0.0719623i | \(0.977074\pi\) | |||||||
\(42\) | 4395.70 | − | 788.794i | 2.49190 | − | 0.447162i | ||||
\(43\) | 2192.78 | 1.18593 | 0.592964 | − | 0.805229i | \(-0.297958\pi\) | ||||
0.592964 | + | 0.805229i | \(0.297958\pi\) | |||||||
\(44\) | 7731.79i | 3.99369i | ||||||||
\(45\) | 243.834 | + | 657.529i | 0.120412 | + | 0.324706i | ||||
\(46\) | −4404.89 | −2.08171 | ||||||||
\(47\) | − | 2940.86i | − | 1.33131i | −0.746261 | − | 0.665654i | \(-0.768153\pi\) | ||
0.746261 | − | 0.665654i | \(-0.231847\pi\) | |||||||
\(48\) | −583.804 | − | 3253.36i | −0.253387 | − | 1.41205i | ||||
\(49\) | 2502.40 | 1.04223 | ||||||||
\(50\) | − | 3897.76i | − | 1.55910i | ||||||
\(51\) | 137.117 | − | 24.6052i | 0.0527170 | − | 0.00945988i | ||||
\(52\) | −5339.82 | −1.97479 | ||||||||
\(53\) | 289.041i | 0.102898i | 0.998676 | + | 0.0514491i | \(0.0163840\pi\) | ||||
−0.998676 | + | 0.0514491i | \(0.983616\pi\) | |||||||
\(54\) | 4450.20 | − | 2623.43i | 1.52613 | − | 0.899668i | ||||
\(55\) | −1956.43 | −0.646755 | ||||||||
\(56\) | − | 9038.83i | − | 2.88228i | ||||||
\(57\) | −285.278 | − | 1589.77i | −0.0878049 | − | 0.489310i | ||||
\(58\) | 3132.94 | 0.931315 | ||||||||
\(59\) | 453.188i | 0.130189i | ||||||||
\(60\) | 2624.18 | − | 470.900i | 0.728939 | − | 0.130806i | ||||
\(61\) | −4432.23 | −1.19114 | −0.595570 | − | 0.803304i | \(-0.703074\pi\) | ||||
−0.595570 | + | 0.803304i | \(0.703074\pi\) | |||||||
\(62\) | 1833.59i | 0.477001i | ||||||||
\(63\) | 5318.08 | − | 1972.12i | 1.33990 | − | 0.496882i | ||||
\(64\) | 2069.35 | 0.505213 | ||||||||
\(65\) | − | 1351.17i | − | 0.319805i | ||||||
\(66\) | 2545.48 | + | 14185.2i | 0.584363 | + | 3.25647i | ||||
\(67\) | −1621.56 | −0.361229 | −0.180615 | − | 0.983554i | \(-0.557809\pi\) | ||||
−0.180615 | + | 0.983554i | \(0.557809\pi\) | |||||||
\(68\) | − | 529.609i | − | 0.114535i | ||||||
\(69\) | −5506.51 | + | 988.123i | −1.15659 | + | 0.207545i | ||||
\(70\) | 4296.13 | 0.876761 | ||||||||
\(71\) | 7336.07i | 1.45528i | 0.685958 | + | 0.727641i | \(0.259383\pi\) | ||||
−0.685958 | + | 0.727641i | \(0.740617\pi\) | |||||||
\(72\) | −3635.37 | − | 9803.23i | −0.701268 | − | 1.89106i | ||||
\(73\) | −1743.91 | −0.327250 | −0.163625 | − | 0.986523i | \(-0.552319\pi\) | ||||
−0.163625 | + | 0.986523i | \(0.552319\pi\) | |||||||
\(74\) | 17738.5i | 3.23932i | ||||||||
\(75\) | −874.362 | − | 4872.55i | −0.155442 | − | 0.866231i | ||||
\(76\) | −6140.41 | −1.06309 | ||||||||
\(77\) | 15823.6i | 2.66884i | ||||||||
\(78\) | −9796.75 | + | 1757.99i | −1.61025 | + | 0.288953i | ||||
\(79\) | 2560.10 | 0.410206 | 0.205103 | − | 0.978740i | \(-0.434247\pi\) | ||||
0.205103 | + | 0.978740i | \(0.434247\pi\) | |||||||
\(80\) | − | 3179.66i | − | 0.496823i | ||||||
\(81\) | 4974.64 | − | 4277.81i | 0.758214 | − | 0.652006i | ||||
\(82\) | 1714.44 | 0.254973 | ||||||||
\(83\) | 4640.76i | 0.673648i | 0.941568 | + | 0.336824i | \(0.109353\pi\) | ||||
−0.941568 | + | 0.336824i | \(0.890647\pi\) | |||||||
\(84\) | −3808.63 | − | 21224.3i | −0.539771 | − | 3.00798i | ||||
\(85\) | 134.011 | 0.0185482 | ||||||||
\(86\) | − | 15538.7i | − | 2.10096i | ||||||
\(87\) | 3916.46 | − | 702.795i | 0.517434 | − | 0.0928518i | ||||
\(88\) | 29168.8 | 3.76664 | ||||||||
\(89\) | 8720.43i | 1.10093i | 0.834860 | + | 0.550463i | \(0.185549\pi\) | ||||
−0.834860 | + | 0.550463i | \(0.814451\pi\) | |||||||
\(90\) | 4659.45 | − | 1727.88i | 0.575241 | − | 0.213319i | ||||
\(91\) | −10928.3 | −1.31968 | ||||||||
\(92\) | 21268.7i | 2.51284i | ||||||||
\(93\) | 411.319 | + | 2292.15i | 0.0475568 | + | 0.265019i | ||||
\(94\) | −20839.8 | −2.35851 | ||||||||
\(95\) | − | 1553.75i | − | 0.172161i | ||||||
\(96\) | −4758.82 | + | 853.953i | −0.516365 | + | 0.0926599i | ||||
\(97\) | 12826.5 | 1.36322 | 0.681610 | − | 0.731715i | \(-0.261280\pi\) | ||||
0.681610 | + | 0.731715i | \(0.261280\pi\) | |||||||
\(98\) | − | 17732.8i | − | 1.84639i | ||||||
\(99\) | 6364.16 | + | 17161.8i | 0.649338 | + | 1.75102i | ||||
\(100\) | −18820.0 | −1.88200 | ||||||||
\(101\) | − | 9691.64i | − | 0.950067i | −0.879968 | − | 0.475034i | \(-0.842436\pi\) | ||
0.879968 | − | 0.475034i | \(-0.157564\pi\) | |||||||
\(102\) | −174.359 | − | 971.651i | −0.0167589 | − | 0.0933921i | ||||
\(103\) | −19054.9 | −1.79610 | −0.898052 | − | 0.439889i | \(-0.855018\pi\) | ||||
−0.898052 | + | 0.439889i | \(0.855018\pi\) | |||||||
\(104\) | 20144.9i | 1.86251i | ||||||||
\(105\) | 5370.54 | − | 963.725i | 0.487124 | − | 0.0874127i | ||||
\(106\) | 2048.23 | 0.182292 | ||||||||
\(107\) | − | 13776.4i | − | 1.20329i | −0.798764 | − | 0.601644i | \(-0.794513\pi\) | ||
0.798764 | − | 0.601644i | \(-0.205487\pi\) | |||||||
\(108\) | −12667.0 | − | 21487.4i | −1.08599 | − | 1.84220i | ||||
\(109\) | −5789.04 | −0.487252 | −0.243626 | − | 0.969869i | \(-0.578337\pi\) | ||||
−0.243626 | + | 0.969869i | \(0.578337\pi\) | |||||||
\(110\) | 13863.9i | 1.14577i | ||||||||
\(111\) | 3979.17 | + | 22174.7i | 0.322959 | + | 1.79975i | ||||
\(112\) | −25717.0 | −2.05015 | ||||||||
\(113\) | 16701.6i | 1.30798i | 0.756502 | + | 0.653992i | \(0.226907\pi\) | ||||
−0.756502 | + | 0.653992i | \(0.773093\pi\) | |||||||
\(114\) | −11265.6 | + | 2021.57i | −0.866848 | + | 0.155553i | ||||
\(115\) | −5381.77 | −0.406939 | ||||||||
\(116\) | − | 15127.2i | − | 1.12420i | ||||||
\(117\) | −11852.5 | + | 4395.29i | −0.865838 | + | 0.321082i | ||||
\(118\) | 3211.42 | 0.230639 | ||||||||
\(119\) | − | 1083.88i | − | 0.0765395i | ||||||
\(120\) | −1776.51 | − | 9899.95i | −0.123369 | − | 0.687496i | ||||
\(121\) | −36422.6 | −2.48771 | ||||||||
\(122\) | 31408.1i | 2.11019i | ||||||||
\(123\) | 2143.20 | − | 384.590i | 0.141662 | − | 0.0254207i | ||||
\(124\) | 8853.35 | 0.575790 | ||||||||
\(125\) | − | 10173.3i | − | 0.651092i | ||||||
\(126\) | −13975.1 | − | 37685.5i | −0.880264 | − | 2.37374i | ||||
\(127\) | 30521.6 | 1.89234 | 0.946170 | − | 0.323670i | \(-0.104917\pi\) | ||||
0.946170 | + | 0.323670i | \(0.104917\pi\) | |||||||
\(128\) | − | 23259.3i | − | 1.41964i | ||||||
\(129\) | −3485.70 | − | 19424.8i | −0.209465 | − | 1.16728i | ||||
\(130\) | −9574.83 | −0.566558 | ||||||||
\(131\) | 9964.10i | 0.580625i | 0.956932 | + | 0.290312i | \(0.0937592\pi\) | ||||
−0.956932 | + | 0.290312i | \(0.906241\pi\) | |||||||
\(132\) | 68492.1 | − | 12290.7i | 3.93091 | − | 0.705387i | ||||
\(133\) | −12566.7 | −0.710425 | ||||||||
\(134\) | 11490.9i | 0.639945i | ||||||||
\(135\) | 5437.12 | − | 3205.23i | 0.298333 | − | 0.175870i | ||||
\(136\) | −1997.99 | −0.108023 | ||||||||
\(137\) | 8591.87i | 0.457769i | 0.973454 | + | 0.228885i | \(0.0735079\pi\) | ||||
−0.973454 | + | 0.228885i | \(0.926492\pi\) | |||||||
\(138\) | 7002.14 | + | 39020.8i | 0.367682 | + | 2.04898i | ||||
\(139\) | −33423.9 | −1.72992 | −0.864962 | − | 0.501837i | \(-0.832658\pi\) | ||||
−0.864962 | + | 0.501837i | \(0.832658\pi\) | |||||||
\(140\) | − | 20743.5i | − | 1.05834i | ||||||
\(141\) | −26051.6 | + | 4674.87i | −1.31038 | + | 0.235142i | ||||
\(142\) | 51985.6 | 2.57814 | ||||||||
\(143\) | − | 35266.2i | − | 1.72459i | ||||||
\(144\) | −27891.9 | + | 10343.3i | −1.34510 | + | 0.498807i | ||||
\(145\) | 3827.74 | 0.182057 | ||||||||
\(146\) | 12357.9i | 0.579747i | ||||||||
\(147\) | −3977.89 | − | 22167.5i | −0.184085 | − | 1.02585i | ||||
\(148\) | 85648.9 | 3.91020 | ||||||||
\(149\) | − | 38544.7i | − | 1.73617i | −0.496418 | − | 0.868084i | \(-0.665352\pi\) | ||
0.496418 | − | 0.868084i | \(-0.334648\pi\) | |||||||
\(150\) | −34528.3 | + | 6195.99i | −1.53459 | + | 0.275377i | ||||
\(151\) | 13143.4 | 0.576441 | 0.288221 | − | 0.957564i | \(-0.406936\pi\) | ||||
0.288221 | + | 0.957564i | \(0.406936\pi\) | |||||||
\(152\) | 23165.2i | 1.00265i | ||||||||
\(153\) | −435.930 | − | 1175.54i | −0.0186223 | − | 0.0502173i | ||||
\(154\) | 112131. | 4.72805 | ||||||||
\(155\) | 2240.23i | 0.0932457i | ||||||||
\(156\) | 8488.33 | + | 47302.8i | 0.348797 | + | 1.94374i | ||||
\(157\) | 1902.76 | 0.0771942 | 0.0385971 | − | 0.999255i | \(-0.487711\pi\) | ||||
0.0385971 | + | 0.999255i | \(0.487711\pi\) | |||||||
\(158\) | − | 18141.6i | − | 0.726711i | ||||||
\(159\) | 2560.47 | − | 459.467i | 0.101280 | − | 0.0181744i | ||||
\(160\) | −4651.02 | −0.181680 | ||||||||
\(161\) | 43527.6i | 1.67924i | ||||||||
\(162\) | −30313.8 | − | 35251.8i | −1.15508 | − | 1.34323i | ||||
\(163\) | 16415.8 | 0.617854 | 0.308927 | − | 0.951086i | \(-0.400030\pi\) | ||||
0.308927 | + | 0.951086i | \(0.400030\pi\) | |||||||
\(164\) | − | 8278.04i | − | 0.307779i | ||||||
\(165\) | 3110.00 | + | 17331.1i | 0.114233 | + | 0.636586i | ||||
\(166\) | 32885.8 | 1.19342 | ||||||||
\(167\) | − | 25416.2i | − | 0.911333i | −0.890151 | − | 0.455667i | \(-0.849401\pi\) | ||
0.890151 | − | 0.455667i | \(-0.150599\pi\) | |||||||
\(168\) | −80070.5 | + | 14368.4i | −2.83696 | + | 0.509083i | ||||
\(169\) | −4205.07 | −0.147231 | ||||||||
\(170\) | − | 949.641i | − | 0.0328595i | ||||||
\(171\) | −13629.5 | + | 5054.27i | −0.466108 | + | 0.172849i | ||||
\(172\) | −75027.4 | −2.53608 | ||||||||
\(173\) | − | 23861.0i | − | 0.797252i | −0.917114 | − | 0.398626i | \(-0.869487\pi\) | ||
0.917114 | − | 0.398626i | \(-0.130513\pi\) | |||||||
\(174\) | −4980.21 | − | 27753.2i | −0.164494 | − | 0.916673i | ||||
\(175\) | −38516.3 | −1.25767 | ||||||||
\(176\) | − | 82990.4i | − | 2.67918i | ||||||
\(177\) | 4014.56 | − | 720.399i | 0.128142 | − | 0.0229946i | ||||
\(178\) | 61795.6 | 1.95037 | ||||||||
\(179\) | 21390.9i | 0.667610i | 0.942642 | + | 0.333805i | \(0.108333\pi\) | ||||
−0.942642 | + | 0.333805i | \(0.891667\pi\) | |||||||
\(180\) | −8342.94 | − | 22497.8i | −0.257498 | − | 0.694376i | ||||
\(181\) | 36138.0 | 1.10308 | 0.551540 | − | 0.834148i | \(-0.314040\pi\) | ||||
0.551540 | + | 0.834148i | \(0.314040\pi\) | |||||||
\(182\) | 77440.9i | 2.33791i | ||||||||
\(183\) | 7045.59 | + | 39262.9i | 0.210385 | + | 1.17241i | ||||
\(184\) | 80237.8 | 2.36997 | ||||||||
\(185\) | 21672.4i | 0.633233i | ||||||||
\(186\) | 16242.9 | − | 2914.73i | 0.469501 | − | 0.0842504i | ||||
\(187\) | 3497.73 | 0.100024 | ||||||||
\(188\) | 100623.i | 2.84697i | ||||||||
\(189\) | −25923.8 | − | 43975.3i | −0.725731 | − | 1.23108i | ||||
\(190\) | −11010.4 | −0.304996 | ||||||||
\(191\) | − | 38862.2i | − | 1.06527i | −0.846344 | − | 0.532636i | \(-0.821201\pi\) | ||
0.846344 | − | 0.532636i | \(-0.178799\pi\) | |||||||
\(192\) | −3289.50 | − | 18331.4i | −0.0892335 | − | 0.497271i | ||||
\(193\) | −32884.5 | −0.882830 | −0.441415 | − | 0.897303i | \(-0.645523\pi\) | ||||
−0.441415 | + | 0.897303i | \(0.645523\pi\) | |||||||
\(194\) | − | 90892.7i | − | 2.41505i | ||||||
\(195\) | −11969.4 | + | 2147.86i | −0.314777 | + | 0.0564856i | ||||
\(196\) | −85621.2 | −2.22879 | ||||||||
\(197\) | − | 40794.8i | − | 1.05117i | −0.850742 | − | 0.525584i | \(-0.823847\pi\) | ||
0.850742 | − | 0.525584i | \(-0.176153\pi\) | |||||||
\(198\) | 121613. | − | 45098.4i | 3.10206 | − | 1.15035i | ||||
\(199\) | −22665.5 | −0.572346 | −0.286173 | − | 0.958178i | \(-0.592383\pi\) | ||||
−0.286173 | + | 0.958178i | \(0.592383\pi\) | |||||||
\(200\) | 71000.1i | 1.77500i | ||||||||
\(201\) | 2577.67 | + | 14364.6i | 0.0638023 | + | 0.355550i | ||||
\(202\) | −68677.8 | −1.68312 | ||||||||
\(203\) | − | 30958.7i | − | 0.751260i | ||||||
\(204\) | −4691.54 | + | 841.880i | −0.112734 | + | 0.0202297i | ||||
\(205\) | 2094.65 | 0.0498430 | ||||||||
\(206\) | 135028.i | 3.18193i | ||||||||
\(207\) | 17506.6 | + | 47208.7i | 0.408565 | + | 1.10174i | ||||
\(208\) | 57315.8 | 1.32479 | ||||||||
\(209\) | − | 40553.5i | − | 0.928402i | ||||||
\(210\) | −6829.24 | − | 38057.3i | −0.154858 | − | 0.862977i | ||||
\(211\) | −29824.6 | −0.669899 | −0.334949 | − | 0.942236i | \(-0.608719\pi\) | ||||
−0.334949 | + | 0.942236i | \(0.608719\pi\) | |||||||
\(212\) | − | 9889.71i | − | 0.220045i | ||||||
\(213\) | 64986.6 | − | 11661.6i | 1.43240 | − | 0.257039i | ||||
\(214\) | −97624.0 | −2.13171 | ||||||||
\(215\) | − | 18984.7i | − | 0.410703i | ||||||
\(216\) | −81063.1 | + | 47787.5i | −1.73746 | + | 1.02425i | ||||
\(217\) | 18118.9 | 0.384780 | ||||||||
\(218\) | 41022.9i | 0.863203i | ||||||||
\(219\) | 2772.17 | + | 15448.5i | 0.0578006 | + | 0.322105i | ||||
\(220\) | 66940.6 | 1.38307 | ||||||||
\(221\) | 2415.64i | 0.0494594i | ||||||||
\(222\) | 157137. | − | 28197.6i | 3.18839 | − | 0.572145i | ||||
\(223\) | 15909.7 | 0.319927 | 0.159964 | − | 0.987123i | \(-0.448862\pi\) | ||||
0.159964 | + | 0.987123i | \(0.448862\pi\) | |||||||
\(224\) | 37617.3i | 0.749707i | ||||||||
\(225\) | −41773.6 | + | 15491.1i | −0.825157 | + | 0.305996i | ||||
\(226\) | 118353. | 2.31719 | ||||||||
\(227\) | − | 26000.0i | − | 0.504570i | −0.967653 | − | 0.252285i | \(-0.918818\pi\) | ||
0.967653 | − | 0.252285i | \(-0.0811820\pi\) | |||||||
\(228\) | 9760.97 | + | 54394.9i | 0.187769 | + | 1.04638i | ||||
\(229\) | −27370.1 | −0.521922 | −0.260961 | − | 0.965349i | \(-0.584039\pi\) | ||||
−0.260961 | + | 0.965349i | \(0.584039\pi\) | |||||||
\(230\) | 38136.8i | 0.720923i | ||||||||
\(231\) | 140173. | − | 25153.6i | 2.62688 | − | 0.471385i | ||||
\(232\) | −57068.5 | −1.06028 | ||||||||
\(233\) | 87779.4i | 1.61689i | 0.588571 | + | 0.808446i | \(0.299691\pi\) | ||||
−0.588571 | + | 0.808446i | \(0.700309\pi\) | |||||||
\(234\) | 31146.4 | + | 83990.0i | 0.568821 | + | 1.53390i | ||||
\(235\) | −25461.5 | −0.461049 | ||||||||
\(236\) | − | 15506.1i | − | 0.278406i | ||||||
\(237\) | −4069.60 | − | 22678.6i | −0.0724528 | − | 0.403757i | ||||
\(238\) | −7680.67 | −0.135595 | ||||||||
\(239\) | 27127.4i | 0.474911i | 0.971398 | + | 0.237455i | \(0.0763134\pi\) | ||||
−0.971398 | + | 0.237455i | \(0.923687\pi\) | |||||||
\(240\) | −28167.1 | + | 5054.48i | −0.489012 | + | 0.0877514i | ||||
\(241\) | 13743.6 | 0.236628 | 0.118314 | − | 0.992976i | \(-0.462251\pi\) | ||||
0.118314 | + | 0.992976i | \(0.462251\pi\) | |||||||
\(242\) | 258101.i | 4.40717i | ||||||||
\(243\) | −45802.8 | − | 37267.8i | −0.775675 | − | 0.631133i | ||||
\(244\) | 151652. | 2.54722 | ||||||||
\(245\) | − | 21665.4i | − | 0.360939i | ||||||
\(246\) | −2725.32 | − | 15187.4i | −0.0450347 | − | 0.250965i | ||||
\(247\) | 28007.6 | 0.459073 | ||||||||
\(248\) | − | 33400.0i | − | 0.543054i | ||||||
\(249\) | 41110.2 | − | 7377.08i | 0.663057 | − | 0.118983i | ||||
\(250\) | −72091.2 | −1.15346 | ||||||||
\(251\) | − | 78056.8i | − | 1.23898i | −0.785006 | − | 0.619488i | \(-0.787340\pi\) | ||
0.785006 | − | 0.619488i | \(-0.212660\pi\) | |||||||
\(252\) | −181961. | + | 67477.5i | −2.86535 | + | 1.06257i | ||||
\(253\) | −140466. | −2.19447 | ||||||||
\(254\) | − | 216285.i | − | 3.35242i | ||||||
\(255\) | −213.027 | − | 1187.14i | −0.00327608 | − | 0.0182566i | ||||
\(256\) | −131713. | −2.00978 | ||||||||
\(257\) | 78115.9i | 1.18270i | 0.806416 | + | 0.591348i | \(0.201404\pi\) | ||||
−0.806416 | + | 0.591348i | \(0.798596\pi\) | |||||||
\(258\) | −137650. | + | 24700.7i | −2.06793 | + | 0.371083i | ||||
\(259\) | 175286. | 2.61304 | ||||||||
\(260\) | 46231.3i | 0.683895i | ||||||||
\(261\) | −12451.4 | − | 33576.8i | −0.182784 | − | 0.492899i | ||||
\(262\) | 70608.6 | 1.02862 | ||||||||
\(263\) | 17157.0i | 0.248045i | 0.992279 | + | 0.124022i | \(0.0395795\pi\) | ||||
−0.992279 | + | 0.124022i | \(0.960421\pi\) | |||||||
\(264\) | −46367.6 | − | 258392.i | −0.665283 | − | 3.70742i | ||||
\(265\) | 2502.47 | 0.0356350 | ||||||||
\(266\) | 89051.5i | 1.25857i | ||||||||
\(267\) | 77249.9 | − | 13862.2i | 1.08362 | − | 0.194451i | ||||
\(268\) | 55482.7 | 0.772481 | ||||||||
\(269\) | − | 111286.i | − | 1.53792i | −0.639295 | − | 0.768961i | \(-0.720774\pi\) | ||
0.639295 | − | 0.768961i | \(-0.279226\pi\) | |||||||
\(270\) | −22713.2 | − | 38529.0i | −0.311567 | − | 0.528519i | ||||
\(271\) | −86909.3 | −1.18339 | −0.591695 | − | 0.806162i | \(-0.701541\pi\) | ||||
−0.591695 | + | 0.806162i | \(0.701541\pi\) | |||||||
\(272\) | 5684.64i | 0.0768360i | ||||||||
\(273\) | 17371.9 | + | 96808.0i | 0.233089 | + | 1.29893i | ||||
\(274\) | 60884.6 | 0.810972 | ||||||||
\(275\) | − | 124294.i | − | 1.64356i | ||||||
\(276\) | 188409. | − | 33809.3i | 2.47333 | − | 0.443831i | ||||
\(277\) | −96252.5 | −1.25445 | −0.627224 | − | 0.778839i | \(-0.715809\pi\) | ||||
−0.627224 | + | 0.778839i | \(0.715809\pi\) | |||||||
\(278\) | 236851.i | 3.06469i | ||||||||
\(279\) | 19651.2 | − | 7287.34i | 0.252453 | − | 0.0936182i | ||||
\(280\) | −78256.7 | −0.998172 | ||||||||
\(281\) | − | 39522.8i | − | 0.500535i | −0.968177 | − | 0.250268i | \(-0.919481\pi\) | ||
0.968177 | − | 0.250268i | \(-0.0805186\pi\) | |||||||
\(282\) | 33127.5 | + | 184609.i | 0.416572 | + | 2.32143i | ||||
\(283\) | −100369. | −1.25322 | −0.626611 | − | 0.779333i | \(-0.715558\pi\) | ||||
−0.626611 | + | 0.779333i | \(0.715558\pi\) | |||||||
\(284\) | − | 251008.i | − | 3.11208i | ||||||
\(285\) | −13763.9 | + | 2469.89i | −0.169454 | + | 0.0304080i | ||||
\(286\) | −249906. | −3.05524 | ||||||||
\(287\) | − | 16941.5i | − | 0.205678i | ||||||
\(288\) | 15129.5 | + | 40798.6i | 0.182406 | + | 0.491881i | ||||
\(289\) | 83281.4 | 0.997131 | ||||||||
\(290\) | − | 27124.5i | − | 0.322527i | ||||||
\(291\) | −20389.4 | − | 113624.i | −0.240779 | − | 1.34179i | ||||
\(292\) | 59669.1 | 0.699816 | ||||||||
\(293\) | 44745.7i | 0.521214i | 0.965445 | + | 0.260607i | \(0.0839227\pi\) | ||||
−0.965445 | + | 0.260607i | \(0.916077\pi\) | |||||||
\(294\) | −157086. | + | 28188.5i | −1.81736 | + | 0.326120i | ||||
\(295\) | 3923.62 | 0.0450862 | ||||||||
\(296\) | − | 323118.i | − | 3.68789i | ||||||
\(297\) | 141911. | − | 83657.8i | 1.60880 | − | 0.948404i | ||||
\(298\) | −273139. | −3.07575 | ||||||||
\(299\) | − | 97010.4i | − | 1.08512i | ||||||
\(300\) | 29916.8 | + | 166717.i | 0.332409 | + | 1.85241i | ||||
\(301\) | −153548. | −1.69477 | ||||||||
\(302\) | − | 93138.3i | − | 1.02121i | ||||||
\(303\) | −85853.4 | + | 15406.1i | −0.935131 | + | 0.167806i | ||||
\(304\) | 65909.1 | 0.713178 | ||||||||
\(305\) | 38373.5i | 0.412507i | ||||||||
\(306\) | −8330.21 | + | 3089.13i | −0.0889638 | + | 0.0329908i | ||||
\(307\) | −125274. | −1.32918 | −0.664589 | − | 0.747209i | \(-0.731393\pi\) | ||||
−0.664589 | + | 0.747209i | \(0.731393\pi\) | |||||||
\(308\) | − | 541413.i | − | 5.70726i | ||||||
\(309\) | 30290.1 | + | 168798.i | 0.317237 | + | 1.76787i | ||||
\(310\) | 15874.9 | 0.165192 | ||||||||
\(311\) | − | 23197.4i | − | 0.239839i | −0.992784 | − | 0.119919i | \(-0.961736\pi\) | ||
0.992784 | − | 0.119919i | \(-0.0382636\pi\) | |||||||
\(312\) | 178454. | − | 32022.9i | 1.83323 | − | 0.328967i | ||||
\(313\) | −43815.3 | −0.447236 | −0.223618 | − | 0.974677i | \(-0.571787\pi\) | ||||
−0.223618 | + | 0.974677i | \(0.571787\pi\) | |||||||
\(314\) | − | 13483.5i | − | 0.136755i | ||||||
\(315\) | −17074.3 | − | 46043.0i | −0.172077 | − | 0.464026i | ||||
\(316\) | −87595.3 | −0.877216 | ||||||||
\(317\) | 49751.8i | 0.495096i | 0.968876 | + | 0.247548i | \(0.0796249\pi\) | ||||
−0.968876 | + | 0.247548i | \(0.920375\pi\) | |||||||
\(318\) | −3255.92 | − | 18144.2i | −0.0321973 | − | 0.179426i | ||||
\(319\) | 99905.4 | 0.981765 | ||||||||
\(320\) | − | 17916.1i | − | 0.174962i | ||||||
\(321\) | −122039. | + | 21899.4i | −1.18437 | + | 0.212531i | ||||
\(322\) | 308449. | 2.97490 | ||||||||
\(323\) | 2777.82i | 0.0266256i | ||||||||
\(324\) | −170210. | + | 146368.i | −1.62142 | + | 1.39430i | ||||
\(325\) | 85841.7 | 0.812702 | ||||||||
\(326\) | − | 116327.i | − | 1.09457i | ||||||
\(327\) | 9202.42 | + | 51282.2i | 0.0860610 | + | 0.479591i | ||||
\(328\) | −31229.6 | −0.290281 | ||||||||
\(329\) | 205931.i | 1.90253i | ||||||||
\(330\) | 122813. | − | 22038.4i | 1.12776 | − | 0.202373i | ||||
\(331\) | −61831.6 | −0.564358 | −0.282179 | − | 0.959362i | \(-0.591057\pi\) | ||||
−0.282179 | + | 0.959362i | \(0.591057\pi\) | |||||||
\(332\) | − | 158787.i | − | 1.44058i | ||||||
\(333\) | 190109. | − | 70499.1i | 1.71441 | − | 0.635762i | ||||
\(334\) | −180107. | −1.61449 | ||||||||
\(335\) | 14039.2i | 0.125099i | ||||||||
\(336\) | 40880.5 | + | 227814.i | 0.362108 | + | 2.01791i | ||||
\(337\) | −59090.1 | −0.520302 | −0.260151 | − | 0.965568i | \(-0.583772\pi\) | ||||
−0.260151 | + | 0.965568i | \(0.583772\pi\) | |||||||
\(338\) | 29798.4i | 0.260831i | ||||||||
\(339\) | 147952. | − | 26549.4i | 1.28742 | − | 0.231023i | ||||
\(340\) | −4585.26 | −0.0396649 | ||||||||
\(341\) | 58470.8i | 0.502840i | ||||||||
\(342\) | 35816.1 | + | 96582.5i | 0.306215 | + | 0.825745i | ||||
\(343\) | −7100.56 | −0.0603538 | ||||||||
\(344\) | 283047.i | 2.39189i | ||||||||
\(345\) | 8555.01 | + | 47674.4i | 0.0718757 | + | 0.400541i | ||||
\(346\) | −169086. | −1.41239 | ||||||||
\(347\) | 98499.7i | 0.818043i | 0.912525 | + | 0.409021i | \(0.134130\pi\) | ||||
−0.912525 | + | 0.409021i | \(0.865870\pi\) | |||||||
\(348\) | −134004. | + | 24046.6i | −1.10652 | + | 0.198561i | ||||
\(349\) | −47248.8 | −0.387918 | −0.193959 | − | 0.981010i | \(-0.562133\pi\) | ||||
−0.193959 | + | 0.981010i | \(0.562133\pi\) | |||||||
\(350\) | 272938.i | 2.22806i | ||||||||
\(351\) | 57776.7 | + | 98008.1i | 0.468963 | + | 0.795514i | ||||
\(352\) | −121393. | −0.979737 | ||||||||
\(353\) | 115826.i | 0.929513i | 0.885438 | + | 0.464757i | \(0.153858\pi\) | ||||
−0.885438 | + | 0.464757i | \(0.846142\pi\) | |||||||
\(354\) | −5104.96 | − | 28448.4i | −0.0407367 | − | 0.227013i | ||||
\(355\) | 63514.5 | 0.503983 | ||||||||
\(356\) | − | 298375.i | − | 2.35430i | ||||||
\(357\) | −9601.52 | + | 1722.96i | −0.0753361 | + | 0.0135188i | ||||
\(358\) | 151582. | 1.18272 | ||||||||
\(359\) | − | 66309.4i | − | 0.514501i | −0.966345 | − | 0.257250i | \(-0.917184\pi\) | ||
0.966345 | − | 0.257250i | \(-0.0828165\pi\) | |||||||
\(360\) | −84874.7 | + | 31474.5i | −0.654898 | + | 0.242858i | ||||
\(361\) | −98114.3 | −0.752866 | ||||||||
\(362\) | − | 256085.i | − | 1.95419i | ||||||
\(363\) | 57898.4 | + | 322650.i | 0.439393 | + | 2.44860i | ||||
\(364\) | 373917. | 2.82210 | ||||||||
\(365\) | 15098.5i | 0.113331i | ||||||||
\(366\) | 278229. | − | 49927.2i | 2.07702 | − | 0.372713i | ||||
\(367\) | 227240. | 1.68714 | 0.843572 | − | 0.537016i | \(-0.180449\pi\) | ||||
0.843572 | + | 0.537016i | \(0.180449\pi\) | |||||||
\(368\) | − | 228291.i | − | 1.68575i | ||||||
\(369\) | −6813.79 | − | 18374.2i | −0.0500421 | − | 0.134945i | ||||
\(370\) | 153577. | 1.12182 | ||||||||
\(371\) | − | 20239.9i | − | 0.147048i | ||||||
\(372\) | −14073.5 | − | 78427.4i | −0.101699 | − | 0.566738i | ||||
\(373\) | 252202. | 1.81272 | 0.906361 | − | 0.422504i | \(-0.138849\pi\) | ||||
0.906361 | + | 0.422504i | \(0.138849\pi\) | |||||||
\(374\) | − | 24786.0i | − | 0.177200i | ||||||
\(375\) | −90120.4 | + | 16171.8i | −0.640856 | + | 0.114999i | ||||
\(376\) | 379610. | 2.68511 | ||||||||
\(377\) | 68997.9i | 0.485459i | ||||||||
\(378\) | −311622. | + | 183704.i | −2.18094 | + | 1.28569i | ||||
\(379\) | −20628.3 | −0.143610 | −0.0718049 | − | 0.997419i | \(-0.522876\pi\) | ||||
−0.0718049 | + | 0.997419i | \(0.522876\pi\) | |||||||
\(380\) | 53162.7i | 0.368162i | ||||||||
\(381\) | −48517.9 | − | 270375.i | −0.334235 | − | 1.86259i | ||||
\(382\) | −275389. | −1.88721 | ||||||||
\(383\) | − | 269587.i | − | 1.83781i | −0.394474 | − | 0.918907i | \(-0.629073\pi\) | ||
0.394474 | − | 0.918907i | \(-0.370927\pi\) | |||||||
\(384\) | −206043. | + | 36973.6i | −1.39732 | + | 0.250744i | ||||
\(385\) | 136998. | 0.924256 | ||||||||
\(386\) | 233030.i | 1.56400i | ||||||||
\(387\) | −166533. | + | 61756.3i | −1.11193 | + | 0.412343i | ||||
\(388\) | −438868. | −2.91522 | ||||||||
\(389\) | 151849.i | 1.00349i | 0.865015 | + | 0.501746i | \(0.167309\pi\) | ||||
−0.865015 | + | 0.501746i | \(0.832691\pi\) | |||||||
\(390\) | 15220.4 | + | 84818.6i | 0.100068 | + | 0.557650i | ||||
\(391\) | 9621.58 | 0.0629351 | ||||||||
\(392\) | 323013.i | 2.10207i | ||||||||
\(393\) | 88267.0 | − | 15839.2i | 0.571496 | − | 0.102553i | ||||
\(394\) | −289084. | −1.86222 | ||||||||
\(395\) | − | 22164.9i | − | 0.142060i | ||||||
\(396\) | −217754. | − | 587200.i | −1.38859 | − | 3.74452i | ||||
\(397\) | −116775. | −0.740919 | −0.370459 | − | 0.928849i | \(-0.620800\pi\) | ||||
−0.370459 | + | 0.928849i | \(0.620800\pi\) | |||||||
\(398\) | 160614.i | 1.01395i | ||||||||
\(399\) | 19976.4 | + | 111322.i | 0.125479 | + | 0.699256i | ||||
\(400\) | 202008. | 1.26255 | ||||||||
\(401\) | − | 131648.i | − | 0.818700i | −0.912377 | − | 0.409350i | \(-0.865755\pi\) | ||
0.912377 | − | 0.409350i | \(-0.134245\pi\) | |||||||
\(402\) | 101792. | − | 18266.2i | 0.629884 | − | 0.113030i | ||||
\(403\) | −40381.8 | −0.248642 | ||||||||
\(404\) | 331605.i | 2.03170i | ||||||||
\(405\) | −37036.6 | − | 43069.6i | −0.225798 | − | 0.262580i | ||||
\(406\) | −219382. | −1.33091 | ||||||||
\(407\) | 565657.i | 3.41479i | ||||||||
\(408\) | 3176.06 | + | 17699.2i | 0.0190796 | + | 0.106325i | ||||
\(409\) | −130585. | −0.780630 | −0.390315 | − | 0.920681i | \(-0.627634\pi\) | ||||
−0.390315 | + | 0.920681i | \(0.627634\pi\) | |||||||
\(410\) | − | 14843.3i | − | 0.0883006i | ||||||
\(411\) | 76111.1 | − | 13657.9i | 0.450572 | − | 0.0808536i | ||||
\(412\) | 651974. | 3.84093 | ||||||||
\(413\) | − | 31734.1i | − | 0.186049i | ||||||
\(414\) | 334535. | − | 124057.i | 1.95182 | − | 0.723803i | ||||
\(415\) | 40178.9 | 0.233293 | ||||||||
\(416\) | − | 83838.1i | − | 0.484456i | ||||||
\(417\) | 53131.5 | + | 296085.i | 0.305548 | + | 1.70273i | ||||
\(418\) | −287374. | −1.64473 | ||||||||
\(419\) | 21577.2i | 0.122904i | 0.998110 | + | 0.0614522i | \(0.0195732\pi\) | ||||
−0.998110 | + | 0.0614522i | \(0.980427\pi\) | |||||||
\(420\) | −183756. | + | 32974.5i | −1.04170 | + | 0.186930i | ||||
\(421\) | −115411. | −0.651152 | −0.325576 | − | 0.945516i | \(-0.605558\pi\) | ||||
−0.325576 | + | 0.945516i | \(0.605558\pi\) | |||||||
\(422\) | 211346.i | 1.18678i | ||||||||
\(423\) | 82824.7 | + | 223347.i | 0.462891 | + | 1.24824i | ||||
\(424\) | −37309.8 | −0.207535 | ||||||||
\(425\) | 8513.86i | 0.0471356i | ||||||||
\(426\) | −82637.7 | − | 460515.i | −0.455365 | − | 2.53761i | ||||
\(427\) | 310364. | 1.70222 | ||||||||
\(428\) | 471369.i | 2.57320i | ||||||||
\(429\) | −312405. | + | 56060.0i | −1.69748 | + | 0.304606i | ||||
\(430\) | −134531. | −0.727590 | ||||||||
\(431\) | 17024.2i | 0.0916459i | 0.998950 | + | 0.0458229i | \(0.0145910\pi\) | ||||
−0.998950 | + | 0.0458229i | \(0.985409\pi\) | |||||||
\(432\) | 135964. | + | 230638.i | 0.728543 | + | 1.23585i | ||||
\(433\) | 125401. | 0.668844 | 0.334422 | − | 0.942423i | \(-0.391459\pi\) | ||||
0.334422 | + | 0.942423i | \(0.391459\pi\) | |||||||
\(434\) | − | 128396.i | − | 0.681666i | ||||||
\(435\) | −6084.68 | − | 33908.1i | −0.0321558 | − | 0.179194i | ||||
\(436\) | 198076. | 1.04198 | ||||||||
\(437\) | − | 111555.i | − | 0.584152i | ||||||
\(438\) | 109472. | − | 19644.4i | 0.570633 | − | 0.102398i | ||||
\(439\) | 277022. | 1.43743 | 0.718713 | − | 0.695307i | \(-0.244732\pi\) | ||||
0.718713 | + | 0.695307i | \(0.244732\pi\) | |||||||
\(440\) | − | 252539.i | − | 1.30444i | ||||||
\(441\) | −190048. | + | 70476.2i | −0.977205 | + | 0.362381i | ||||
\(442\) | 17118.0 | 0.0876209 | ||||||||
\(443\) | 241189.i | 1.22900i | 0.788918 | + | 0.614499i | \(0.210642\pi\) | ||||
−0.788918 | + | 0.614499i | \(0.789358\pi\) | |||||||
\(444\) | −136150. | − | 758722.i | −0.690639 | − | 3.84872i | ||||
\(445\) | 75500.0 | 0.381265 | ||||||||
\(446\) | − | 112741.i | − | 0.566775i | ||||||
\(447\) | −341448. | + | 61271.6i | −1.70887 | + | 0.306651i | ||||
\(448\) | −144905. | −0.721984 | ||||||||
\(449\) | − | 58868.2i | − | 0.292004i | −0.989284 | − | 0.146002i | \(-0.953359\pi\) | ||
0.989284 | − | 0.146002i | \(-0.0466405\pi\) | |||||||
\(450\) | 109774. | + | 296020.i | 0.542096 | + | 1.46183i | ||||
\(451\) | 54671.2 | 0.268785 | ||||||||
\(452\) | − | 571457.i | − | 2.79709i | ||||||
\(453\) | −20893.2 | − | 116431.i | −0.101814 | − | 0.567378i | ||||
\(454\) | −184244. | −0.893883 | ||||||||
\(455\) | 94615.1i | 0.457022i | ||||||||
\(456\) | 205209. | − | 36824.1i | 0.986886 | − | 0.177093i | ||||
\(457\) | 198349. | 0.949726 | 0.474863 | − | 0.880060i | \(-0.342498\pi\) | ||||
0.474863 | + | 0.880060i | \(0.342498\pi\) | |||||||
\(458\) | 193953.i | 0.924624i | ||||||||
\(459\) | −9720.54 | + | 5730.35i | −0.0461387 | + | 0.0271992i | ||||
\(460\) | 184141. | 0.870230 | ||||||||
\(461\) | − | 368156.i | − | 1.73233i | −0.499761 | − | 0.866163i | \(-0.666579\pi\) | ||
0.499761 | − | 0.866163i | \(-0.333421\pi\) | |||||||
\(462\) | −178246. | − | 993309.i | −0.835094 | − | 4.65372i | ||||
\(463\) | 258187. | 1.20441 | 0.602203 | − | 0.798343i | \(-0.294290\pi\) | ||||
0.602203 | + | 0.798343i | \(0.294290\pi\) | |||||||
\(464\) | 162370.i | 0.754170i | ||||||||
\(465\) | 19845.1 | − | 3561.13i | 0.0917797 | − | 0.0164695i | ||||
\(466\) | 622031. | 2.86444 | ||||||||
\(467\) | 78827.9i | 0.361448i | 0.983534 | + | 0.180724i | \(0.0578441\pi\) | ||||
−0.983534 | + | 0.180724i | \(0.942156\pi\) | |||||||
\(468\) | 405539. | − | 150388.i | 1.85157 | − | 0.686627i | ||||
\(469\) | 113549. | 0.516221 | ||||||||
\(470\) | 180427.i | 0.816783i | ||||||||
\(471\) | −3024.68 | − | 16855.6i | −0.0136344 | − | 0.0759806i | ||||
\(472\) | −58498.0 | −0.262577 | ||||||||
\(473\) | − | 495508.i | − | 2.21477i | ||||||
\(474\) | −160708. | + | 28838.4i | −0.715286 | + | 0.128355i | ||||
\(475\) | 98711.7 | 0.437504 | ||||||||
\(476\) | 37085.5i | 0.163678i | ||||||||
\(477\) | −8140.38 | − | 21951.5i | −0.0357773 | − | 0.0964780i | ||||
\(478\) | 192233. | 0.841340 | ||||||||
\(479\) | − | 240842.i | − | 1.04969i | −0.851197 | − | 0.524846i | \(-0.824123\pi\) | ||
0.851197 | − | 0.524846i | \(-0.175877\pi\) | |||||||
\(480\) | 7393.39 | + | 41201.1i | 0.0320894 | + | 0.178824i | ||||
\(481\) | −390661. | −1.68853 | ||||||||
\(482\) | − | 97391.2i | − | 0.419204i | ||||||
\(483\) | 385589. | − | 69192.6i | 1.65284 | − | 0.296596i | ||||
\(484\) | 1.24622e6 | 5.31991 | ||||||||
\(485\) | − | 111050.i | − | 0.472102i | ||||||
\(486\) | −264090. | + | 324572.i | −1.11810 | + | 1.37417i | ||||
\(487\) | −132259. | −0.557656 | −0.278828 | − | 0.960341i | \(-0.589946\pi\) | ||||
−0.278828 | + | 0.960341i | \(0.589946\pi\) | |||||||
\(488\) | − | 572118.i | − | 2.40240i | ||||||
\(489\) | −26094.9 | − | 145419.i | −0.109129 | − | 0.608140i | ||||
\(490\) | −153527. | −0.639431 | ||||||||
\(491\) | 159708.i | 0.662467i | 0.943549 | + | 0.331233i | \(0.107465\pi\) | ||||
−0.943549 | + | 0.331233i | \(0.892535\pi\) | |||||||
\(492\) | −73331.0 | + | 13159.0i | −0.302941 | + | 0.0543616i | ||||
\(493\) | −6843.28 | −0.0281560 | ||||||||
\(494\) | − | 198470.i | − | 0.813281i | ||||||
\(495\) | 148584. | − | 55099.9i | 0.606402 | − | 0.224874i | ||||
\(496\) | −95028.8 | −0.386271 | ||||||||
\(497\) | − | 513703.i | − | 2.07970i | ||||||
\(498\) | −52276.2 | − | 291319.i | −0.210788 | − | 1.17466i | ||||
\(499\) | 438821. | 1.76233 | 0.881163 | − | 0.472813i | \(-0.156761\pi\) | ||||
0.881163 | + | 0.472813i | \(0.156761\pi\) | |||||||
\(500\) | 348086.i | 1.39235i | ||||||||
\(501\) | −225149. | + | 40402.2i | −0.897005 | + | 0.160964i | ||||
\(502\) | −553134. | −2.19494 | ||||||||
\(503\) | 231337.i | 0.914343i | 0.889379 | + | 0.457171i | \(0.151137\pi\) | ||||
−0.889379 | + | 0.457171i | \(0.848863\pi\) | |||||||
\(504\) | 254564. | + | 686464.i | 1.00216 | + | 2.70245i | ||||
\(505\) | −83908.6 | −0.329021 | ||||||||
\(506\) | 995385.i | 3.88768i | ||||||||
\(507\) | 6684.50 | + | 37250.7i | 0.0260048 | + | 0.144917i | ||||
\(508\) | −1.04431e6 | −4.04672 | ||||||||
\(509\) | 317545.i | 1.22566i | 0.790215 | + | 0.612830i | \(0.209969\pi\) | ||||
−0.790215 | + | 0.612830i | \(0.790031\pi\) | |||||||
\(510\) | −8412.40 | + | 1509.57i | −0.0323429 | + | 0.00580382i | ||||
\(511\) | 122116. | 0.467662 | ||||||||
\(512\) | 561207.i | 2.14083i | ||||||||
\(513\) | 66439.1 | + | 112702.i | 0.252458 | + | 0.428251i | ||||
\(514\) | 553553. | 2.09523 | ||||||||
\(515\) | 164974.i | 0.622015i | ||||||||
\(516\) | 119266. | + | 664630.i | 0.447936 | + | 2.49621i | ||||
\(517\) | −664553. | −2.48627 | ||||||||
\(518\) | − | 1.24213e6i | − | 4.62920i | ||||||
\(519\) | −211372. | + | 37930.0i | −0.784718 | + | 0.140815i | ||||
\(520\) | 174411. | 0.645013 | ||||||||
\(521\) | − | 203095.i | − | 0.748210i | −0.927386 | − | 0.374105i | \(-0.877950\pi\) | ||
0.927386 | − | 0.374105i | \(-0.122050\pi\) | |||||||
\(522\) | −237935. | + | 88234.5i | −0.873208 | + | 0.323815i | ||||
\(523\) | 188696. | 0.689858 | 0.344929 | − | 0.938629i | \(-0.387903\pi\) | ||||
0.344929 | + | 0.938629i | \(0.387903\pi\) | |||||||
\(524\) | − | 340928.i | − | 1.24165i | ||||||
\(525\) | 61226.6 | + | 341197.i | 0.222137 | + | 1.23790i | ||||
\(526\) | 121580. | 0.439430 | ||||||||
\(527\) | − | 4005.10i | − | 0.0144209i | ||||||
\(528\) | −735171. | + | 131924.i | −2.63706 | + | 0.473211i | ||||
\(529\) | −106554. | −0.380767 | ||||||||
\(530\) | − | 17733.2i | − | 0.0631300i | ||||||
\(531\) | −12763.3 | − | 34417.9i | −0.0452663 | − | 0.122066i | ||||
\(532\) | 429978. | 1.51923 | ||||||||
\(533\) | 37757.7i | 0.132908i | ||||||||
\(534\) | −98231.9 | − | 547416.i | −0.344485 | − | 1.91971i | ||||
\(535\) | −119274. | −0.416715 | ||||||||
\(536\) | − | 209313.i | − | 0.728562i | ||||||
\(537\) | 189491. | − | 34003.6i | 0.657114 | − | 0.117917i | ||||
\(538\) | −788603. | −2.72454 | ||||||||
\(539\) | − | 565474.i | − | 1.94641i | ||||||
\(540\) | −186034. | + | 109669.i | −0.637978 | + | 0.376094i | ||||
\(541\) | −424126. | −1.44911 | −0.724553 | − | 0.689219i | \(-0.757954\pi\) | ||||
−0.724553 | + | 0.689219i | \(0.757954\pi\) | |||||||
\(542\) | 615865.i | 2.09646i | ||||||||
\(543\) | −57446.0 | − | 320129.i | −0.194832 | − | 1.08574i | ||||
\(544\) | 8315.14 | 0.0280978 | ||||||||
\(545\) | 50120.5i | 0.168742i | ||||||||
\(546\) | 686011. | − | 123102.i | 2.30115 | − | 0.412934i | ||||
\(547\) | −133095. | −0.444823 | −0.222412 | − | 0.974953i | \(-0.571393\pi\) | ||||
−0.222412 | + | 0.974953i | \(0.571393\pi\) | |||||||
\(548\) | − | 293976.i | − | 0.978929i | ||||||
\(549\) | 336611. | − | 124827.i | 1.11682 | − | 0.414155i | ||||
\(550\) | −880787. | −2.91169 | ||||||||
\(551\) | 79342.6i | 0.261338i | ||||||||
\(552\) | −127548. | − | 710787.i | −0.418597 | − | 2.33271i | ||||
\(553\) | −179269. | −0.586212 | ||||||||
\(554\) | 682074.i | 2.22235i | ||||||||
\(555\) | 191985. | − | 34451.0i | 0.623277 | − | 0.111845i | ||||
\(556\) | 1.14362e6 | 3.69940 | ||||||||
\(557\) | 23822.6i | 0.0767854i | 0.999263 | + | 0.0383927i | \(0.0122238\pi\) | ||||
−0.999263 | + | 0.0383927i | \(0.987776\pi\) | |||||||
\(558\) | −51640.2 | − | 139254.i | −0.165852 | − | 0.447239i | ||||
\(559\) | 342214. | 1.09515 | ||||||||
\(560\) | 222654.i | 0.709993i | ||||||||
\(561\) | −5560.09 | − | 30984.7i | −0.0176667 | − | 0.0984512i | ||||
\(562\) | −280070. | −0.886736 | ||||||||
\(563\) | 225139.i | 0.710286i | 0.934812 | + | 0.355143i | \(0.115568\pi\) | ||||
−0.934812 | + | 0.355143i | \(0.884432\pi\) | |||||||
\(564\) | 891372. | − | 159953.i | 2.80221 | − | 0.502847i | ||||
\(565\) | 144600. | 0.452972 | ||||||||
\(566\) | 711246.i | 2.22017i | ||||||||
\(567\) | −348346. | + | 299551.i | −1.08354 | + | 0.931760i | ||||
\(568\) | −946950. | −2.93515 | ||||||||
\(569\) | − | 356315.i | − | 1.10055i | −0.834983 | − | 0.550275i | \(-0.814523\pi\) | ||
0.834983 | − | 0.550275i | \(-0.185477\pi\) | |||||||
\(570\) | 17502.4 | + | 97535.3i | 0.0538700 | + | 0.300201i | ||||
\(571\) | 50591.2 | 0.155168 | 0.0775841 | − | 0.996986i | \(-0.475279\pi\) | ||||
0.0775841 | + | 0.996986i | \(0.475279\pi\) | |||||||
\(572\) | 1.20665e6i | 3.68800i | ||||||||
\(573\) | −344261. | + | 61776.4i | −1.04852 | + | 0.188154i | ||||
\(574\) | −120052. | −0.364374 | ||||||||
\(575\) | − | 341910.i | − | 1.03413i | ||||||
\(576\) | −157160. | + | 58280.1i | −0.473692 | + | 0.175661i | ||||
\(577\) | 25449.4 | 0.0764409 | 0.0382205 | − | 0.999269i | \(-0.487831\pi\) | ||||
0.0382205 | + | 0.999269i | \(0.487831\pi\) | |||||||
\(578\) | − | 590157.i | − | 1.76649i | ||||||
\(579\) | 52274.2 | + | 291308.i | 0.155930 | + | 0.868951i | ||||
\(580\) | −130969. | −0.389324 | ||||||||
\(581\) | − | 324966.i | − | 0.962688i | ||||||
\(582\) | −805174. | + | 144486.i | −2.37708 | + | 0.426558i | ||||
\(583\) | 65315.3 | 0.192167 | ||||||||
\(584\) | − | 225107.i | − | 0.660029i | ||||||
\(585\) | 38053.7 | + | 102617.i | 0.111195 | + | 0.299851i | ||||
\(586\) | 317081. | 0.923370 | ||||||||
\(587\) | 479696.i | 1.39216i | 0.717963 | + | 0.696081i | \(0.245075\pi\) | ||||
−0.717963 | + | 0.696081i | \(0.754925\pi\) | |||||||
\(588\) | 136106. | + | 758476.i | 0.393661 | + | 2.19375i | ||||
\(589\) | −46436.1 | −0.133852 | ||||||||
\(590\) | − | 27804.0i | − | 0.0798735i | ||||||
\(591\) | −361381. | + | 64848.5i | −1.03464 | + | 0.185663i | ||||
\(592\) | −919326. | −2.62317 | ||||||||
\(593\) | 84236.0i | 0.239546i | 0.992801 | + | 0.119773i | \(0.0382166\pi\) | ||||
−0.992801 | + | 0.119773i | \(0.961783\pi\) | |||||||
\(594\) | −592824. | − | 1.00562e6i | −1.68017 | − | 2.85011i | ||||
\(595\) | −9384.01 | −0.0265066 | ||||||||
\(596\) | 1.31883e6i | 3.71275i | ||||||||
\(597\) | 36029.7 | + | 200782.i | 0.101091 | + | 0.563348i | ||||
\(598\) | −687444. | −1.92236 | ||||||||
\(599\) | − | 505826.i | − | 1.40977i | −0.709323 | − | 0.704883i | \(-0.750999\pi\) | ||
0.709323 | − | 0.704883i | \(-0.249001\pi\) | |||||||
\(600\) | 628955. | − | 112864.i | 1.74710 | − | 0.313510i | ||||
\(601\) | −4842.12 | −0.0134056 | −0.00670281 | − | 0.999978i | \(-0.502134\pi\) | ||||
−0.00670281 | + | 0.999978i | \(0.502134\pi\) | |||||||
\(602\) | 1.08809e6i | 3.00241i | ||||||||
\(603\) | 123151. | − | 45668.7i | 0.338691 | − | 0.125598i | ||||
\(604\) | −449711. | −1.23271 | ||||||||
\(605\) | 315341.i | 0.861528i | ||||||||
\(606\) | 109172. | + | 608383.i | 0.297281 | + | 1.65665i | ||||
\(607\) | 535910. | 1.45450 | 0.727252 | − | 0.686371i | \(-0.240797\pi\) | ||||
0.727252 | + | 0.686371i | \(0.240797\pi\) | |||||||
\(608\) | − | 96407.8i | − | 0.260798i | ||||||
\(609\) | −274247. | + | 49212.7i | −0.739448 | + | 0.132691i | ||||
\(610\) | 271926. | 0.730788 | ||||||||
\(611\) | − | 458962.i | − | 1.22940i | ||||||
\(612\) | 14915.6 | + | 40221.8i | 0.0398234 | + | 0.107389i | ||||
\(613\) | 341628. | 0.909143 | 0.454571 | − | 0.890710i | \(-0.349792\pi\) | ||||
0.454571 | + | 0.890710i | \(0.349792\pi\) | |||||||
\(614\) | 887727.i | 2.35474i | ||||||||
\(615\) | −3329.72 | − | 18555.5i | −0.00880354 | − | 0.0490594i | ||||
\(616\) | −2.04253e6 | −5.38278 | ||||||||
\(617\) | − | 374929.i | − | 0.984870i | −0.870349 | − | 0.492435i | \(-0.836107\pi\) | ||
0.870349 | − | 0.492435i | \(-0.163893\pi\) | |||||||
\(618\) | 1.19615e6 | − | 214645.i | 3.13191 | − | 0.562010i | ||||
\(619\) | 176698. | 0.461158 | 0.230579 | − | 0.973054i | \(-0.425938\pi\) | ||||
0.230579 | + | 0.973054i | \(0.425938\pi\) | |||||||
\(620\) | − | 76650.8i | − | 0.199404i | ||||||
\(621\) | 390369. | − | 230126.i | 1.01226 | − | 0.596737i | ||||
\(622\) | −164384. | −0.424892 | ||||||||
\(623\) | − | 610642.i | − | 1.57330i | ||||||
\(624\) | −91110.8 | − | 507732.i | −0.233992 | − | 1.30396i | ||||
\(625\) | 255697. | 0.654585 | ||||||||
\(626\) | 310488.i | 0.792313i | ||||||||
\(627\) | −359244. | + | 64465.0i | −0.913806 | + | 0.163979i | ||||
\(628\) | −65104.1 | −0.165078 | ||||||||
\(629\) | − | 38746.1i | − | 0.0979325i | ||||||
\(630\) | −326275. | + | 120994.i | −0.822057 | + | 0.304847i | ||||
\(631\) | 414056. | 1.03992 | 0.519960 | − | 0.854190i | \(-0.325947\pi\) | ||||
0.519960 | + | 0.854190i | \(0.325947\pi\) | |||||||
\(632\) | 330461.i | 0.827343i | ||||||||
\(633\) | 47409.9 | + | 264201.i | 0.118321 | + | 0.659367i | ||||
\(634\) | 352556. | 0.877100 | ||||||||
\(635\) | − | 264251.i | − | 0.655343i | ||||||
\(636\) | −87608.0 | + | 15721.0i | −0.216586 | + | 0.0388655i | ||||
\(637\) | 390534. | 0.962455 | ||||||||
\(638\) | − | 707960.i | − | 1.73927i | ||||||
\(639\) | −206609. | − | 557147.i | −0.505997 | − | 1.36448i | ||||
\(640\) | −201375. | −0.491639 | ||||||||
\(641\) | − | 275394.i | − | 0.670252i | −0.942173 | − | 0.335126i | \(-0.891221\pi\) | ||
0.942173 | − | 0.335126i | \(-0.108779\pi\) | |||||||
\(642\) | 155186. | + | 864802.i | 0.376514 | + | 2.09820i | ||||
\(643\) | 267744. | 0.647586 | 0.323793 | − | 0.946128i | \(-0.395042\pi\) | ||||
0.323793 | + | 0.946128i | \(0.395042\pi\) | |||||||
\(644\) | − | 1.48932e6i | − | 3.59102i | ||||||
\(645\) | −168176. | + | 30178.6i | −0.404246 | + | 0.0725405i | ||||
\(646\) | 19684.4 | 0.0471692 | ||||||||
\(647\) | − | 680208.i | − | 1.62493i | −0.583013 | − | 0.812463i | \(-0.698126\pi\) | ||
0.583013 | − | 0.812463i | \(-0.301874\pi\) | |||||||
\(648\) | 552185. | + | 642133.i | 1.31503 | + | 1.52924i | ||||
\(649\) | 102408. | 0.243133 | ||||||||
\(650\) | − | 608300.i | − | 1.43976i | ||||||
\(651\) | −28802.3 | − | 160506.i | −0.0679618 | − | 0.378730i | ||||
\(652\) | −561675. | −1.32127 | ||||||||
\(653\) | − | 714728.i | − | 1.67616i | −0.545550 | − | 0.838078i | \(-0.683679\pi\) | ||
0.545550 | − | 0.838078i | \(-0.316321\pi\) | |||||||
\(654\) | 363401. | − | 65211.1i | 0.849632 | − | 0.152463i | ||||
\(655\) | 86267.5 | 0.201078 | ||||||||
\(656\) | 88853.6i | 0.206475i | ||||||||
\(657\) | 132444. | − | 49114.6i | 0.306832 | − | 0.113784i | ||||
\(658\) | 1.45929e6 | 3.37047 | ||||||||
\(659\) | 257886.i | 0.593824i | 0.954905 | + | 0.296912i | \(0.0959568\pi\) | ||||
−0.954905 | + | 0.296912i | \(0.904043\pi\) | |||||||
\(660\) | −106411. | − | 592993.i | −0.244285 | − | 1.36133i | ||||
\(661\) | −157805. | −0.361174 | −0.180587 | − | 0.983559i | \(-0.557800\pi\) | ||||
−0.180587 | + | 0.983559i | \(0.557800\pi\) | |||||||
\(662\) | 438157.i | 0.999802i | ||||||||
\(663\) | 21399.0 | − | 3839.97i | 0.0486818 | − | 0.00873577i | ||||
\(664\) | −599036. | −1.35868 | ||||||||
\(665\) | 108801.i | 0.246030i | ||||||||
\(666\) | −499577. | − | 1.34717e6i | −1.12630 | − | 3.03721i | ||||
\(667\) | 274821. | 0.617728 | ||||||||
\(668\) | 869630.i | 1.94886i | ||||||||
\(669\) | −25290.4 | − | 140936.i | −0.0565072 | − | 0.314897i | ||||
\(670\) | 99485.9 | 0.221621 | ||||||||
\(671\) | 1.00156e6i | 2.22450i | ||||||||
\(672\) | 333233. | − | 59797.5i | 0.737920 | − | 0.132417i | ||||
\(673\) | −160084. | −0.353441 | −0.176720 | − | 0.984261i | \(-0.556549\pi\) | ||||
−0.176720 | + | 0.984261i | \(0.556549\pi\) | |||||||
\(674\) | 418730.i | 0.921753i | ||||||||
\(675\) | 203632. | + | 345426.i | 0.446929 | + | 0.758137i | ||||
\(676\) | 143879. | 0.314851 | ||||||||
\(677\) | 402856.i | 0.878968i | 0.898251 | + | 0.439484i | \(0.144839\pi\) | ||||
−0.898251 | + | 0.439484i | \(0.855161\pi\) | |||||||
\(678\) | −188137. | − | 1.04843e6i | −0.409274 | − | 2.28076i | ||||
\(679\) | −898170. | −1.94813 | ||||||||
\(680\) | 17298.3i | 0.0374098i | ||||||||
\(681\) | −230321. | + | 41330.3i | −0.496637 | + | 0.0891198i | ||||
\(682\) | 414341. | 0.890819 | ||||||||
\(683\) | − | 37881.8i | − | 0.0812061i | −0.999175 | − | 0.0406031i | \(-0.987072\pi\) | ||
0.999175 | − | 0.0406031i | \(-0.0129279\pi\) | |||||||
\(684\) | 466341. | − | 172935.i | 0.996761 | − | 0.369633i | ||||
\(685\) | 74387.0 | 0.158532 | ||||||||
\(686\) | 50316.7i | 0.106921i | ||||||||
\(687\) | 43508.3 | + | 242458.i | 0.0921847 | + | 0.513717i | ||||
\(688\) | 805318. | 1.70134 | ||||||||
\(689\) | 45108.8i | 0.0950218i | ||||||||
\(690\) | 337835. | − | 60623.3i | 0.709589 | − | 0.127333i | ||||
\(691\) | −559150. | −1.17104 | −0.585521 | − | 0.810658i | \(-0.699110\pi\) | ||||
−0.585521 | + | 0.810658i | \(0.699110\pi\) | |||||||
\(692\) | 816418.i | 1.70490i | ||||||||
\(693\) | −445646. | − | 1.20174e6i | −0.927948 | − | 2.50233i | ||||
\(694\) | 697998. | 1.44922 | ||||||||
\(695\) | 289378.i | 0.599096i | ||||||||
\(696\) | 90717.7 | + | 505542.i | 0.187272 | + | 1.04361i | ||||
\(697\) | −3744.84 | −0.00770847 | ||||||||
\(698\) | 334819.i | 0.687225i | ||||||||
\(699\) | 777594. | − | 139537.i | 1.59147 | − | 0.285584i | ||||
\(700\) | 1.31786e6 | 2.68951 | ||||||||
\(701\) | − | 628916.i | − | 1.27984i | −0.768440 | − | 0.639921i | \(-0.778967\pi\) | ||
0.768440 | − | 0.639921i | \(-0.221033\pi\) | |||||||
\(702\) | 694515. | − | 409423.i | 1.40931 | − | 0.830803i | ||||
\(703\) | −449232. | −0.908992 | ||||||||
\(704\) | − | 467617.i | − | 0.943507i | ||||||
\(705\) | 40474.2 | + | 225550.i | 0.0814330 | + | 0.453801i | ||||
\(706\) | 820775. | 1.64670 | ||||||||
\(707\) | 678650.i | 1.35771i | ||||||||
\(708\) | −137361. | + | 24648.9i | −0.274029 | + | 0.0491735i | ||||
\(709\) | −244960. | −0.487307 | −0.243653 | − | 0.969862i | \(-0.578346\pi\) | ||||
−0.243653 | + | 0.969862i | \(0.578346\pi\) | |||||||
\(710\) | − | 450083.i | − | 0.892844i | ||||||
\(711\) | −194430. | + | 72101.1i | −0.384612 | + | 0.142627i | ||||
\(712\) | −1.12564e6 | −2.22045 | ||||||||
\(713\) | 160842.i | 0.316388i | ||||||||
\(714\) | 12209.4 | + | 68039.2i | 0.0239496 | + | 0.133464i | ||||
\(715\) | −305328. | −0.597249 | ||||||||
\(716\) | − | 731903.i | − | 1.42767i | ||||||
\(717\) | 240308. | − | 43122.4i | 0.467445 | − | 0.0838813i | ||||
\(718\) | −469888. | −0.911476 | ||||||||
\(719\) | 689940.i | 1.33461i | 0.744785 | + | 0.667304i | \(0.232552\pi\) | ||||
−0.744785 | + | 0.667304i | \(0.767448\pi\) | |||||||
\(720\) | 89550.3 | + | 241483.i | 0.172744 | + | 0.465824i | ||||
\(721\) | 1.33430e6 | 2.56675 | ||||||||
\(722\) | 695267.i | 1.33376i | ||||||||
\(723\) | −21847.2 | − | 121748.i | −0.0417945 | − | 0.232908i | ||||
\(724\) | −1.23648e6 | −2.35891 | ||||||||
\(725\) | 243181.i | 0.462651i | ||||||||
\(726\) | 2.28639e6 | − | 410285.i | 4.33788 | − | 0.778417i | ||||
\(727\) | −35938.5 | −0.0679973 | −0.0339986 | − | 0.999422i | \(-0.510824\pi\) | ||||
−0.0339986 | + | 0.999422i | \(0.510824\pi\) | |||||||
\(728\) | − | 1.41063e6i | − | 2.66165i | ||||||
\(729\) | −257327. | + | 464986.i | −0.484206 | + | 0.874954i | ||||
\(730\) | 106993. | 0.200774 | ||||||||
\(731\) | 33941.1i | 0.0635172i | ||||||||
\(732\) | −241069. | − | 1.34341e6i | −0.449904 | − | 2.50718i | ||||
\(733\) | −165921. | −0.308811 | −0.154406 | − | 0.988008i | \(-0.549346\pi\) | ||||
−0.154406 | + | 0.988008i | \(0.549346\pi\) | |||||||
\(734\) | − | 1.61029e6i | − | 2.98890i | ||||||
\(735\) | −191923. | + | 34439.9i | −0.355265 | + | 0.0637510i | ||||
\(736\) | −333929. | −0.616452 | ||||||||
\(737\) | 366428.i | 0.674611i | ||||||||
\(738\) | −130205. | + | 48284.5i | −0.239065 | + | 0.0886534i | ||||
\(739\) | −748038. | −1.36973 | −0.684865 | − | 0.728670i | \(-0.740139\pi\) | ||||
−0.684865 | + | 0.728670i | \(0.740139\pi\) | |||||||
\(740\) | − | 741534.i | − | 1.35415i | ||||||
\(741\) | −44521.6 | − | 248105.i | −0.0810838 | − | 0.451855i | ||||
\(742\) | −143426. | −0.260507 | ||||||||
\(743\) | − | 534864.i | − | 0.968871i | −0.874827 | − | 0.484435i | \(-0.839025\pi\) | ||
0.874827 | − | 0.484435i | \(-0.160975\pi\) | |||||||
\(744\) | −295874. | + | 53093.5i | −0.534516 | + | 0.0959171i | ||||
\(745\) | −333713. | −0.601258 | ||||||||
\(746\) | − | 1.78718e6i | − | 3.21137i | ||||||
\(747\) | −130700. | − | 352448.i | −0.234225 | − | 0.631617i | ||||
\(748\) | −119677. | −0.213898 | ||||||||
\(749\) | 964686.i | 1.71958i | ||||||||
\(750\) | 114598. | + | 638620.i | 0.203730 | + | 1.13532i | ||||
\(751\) | −911644. | −1.61639 | −0.808194 | − | 0.588917i | \(-0.799555\pi\) | ||||
−0.808194 | + | 0.588917i | \(0.799555\pi\) | |||||||
\(752\) | − | 1.08006e6i | − | 1.90990i | ||||||
\(753\) | −691466. | + | 124081.i | −1.21950 | + | 0.218835i | ||||
\(754\) | 488939. | 0.860028 | ||||||||
\(755\) | − | 113794.i | − | 0.199629i | ||||||
\(756\) | 887000. | + | 1.50464e6i | 1.55196 | + | 2.63263i | ||||
\(757\) | −738108. | −1.28804 | −0.644019 | − | 0.765010i | \(-0.722734\pi\) | ||||
−0.644019 | + | 0.765010i | \(0.722734\pi\) | |||||||
\(758\) | 146178.i | 0.254416i | ||||||||
\(759\) | 223289. | + | 1.24432e6i | 0.387600 | + | 2.15997i | ||||
\(760\) | 200561. | 0.347231 | ||||||||
\(761\) | 931700.i | 1.60882i | 0.594076 | + | 0.804409i | \(0.297518\pi\) | ||||
−0.594076 | + | 0.804409i | \(0.702482\pi\) | |||||||
\(762\) | −1.91596e6 | + | 343812.i | −3.29972 | + | 0.592122i | ||||
\(763\) | 405373. | 0.696316 | ||||||||
\(764\) | 1.32969e6i | 2.27806i | ||||||||
\(765\) | −10177.6 | + | 3774.21i | −0.0173909 | + | 0.00644915i | ||||
\(766\) | −1.91037e6 | −3.25582 | ||||||||
\(767\) | 70726.2i | 0.120224i | ||||||||
\(768\) | 209374. | + | 1.16678e6i | 0.354977 | + | 1.97818i | ||||
\(769\) | −1.09188e6 | −1.84639 | −0.923193 | − | 0.384336i | \(-0.874430\pi\) | ||||
−0.923193 | + | 0.384336i | \(0.874430\pi\) | |||||||
\(770\) | − | 970807.i | − | 1.63739i | ||||||
\(771\) | 691990. | − | 124175.i | 1.16410 | − | 0.208894i | ||||
\(772\) | 1.12517e6 | 1.88791 | ||||||||
\(773\) | 641269.i | 1.07320i | 0.843836 | + | 0.536601i | \(0.180292\pi\) | ||||
−0.843836 | + | 0.536601i | \(0.819708\pi\) | |||||||
\(774\) | 437623. | + | 1.18010e6i | 0.730497 | + | 1.96987i | ||||
\(775\) | −142324. | −0.236960 | ||||||||
\(776\) | 1.65567e6i | 2.74947i | ||||||||
\(777\) | −278639. | − | 1.55277e6i | −0.461530 | − | 2.57196i | ||||
\(778\) | 1.07605e6 | 1.77776 | ||||||||
\(779\) | 43418.6i | 0.0715486i | ||||||||
\(780\) | 409540. | − | 73490.5i | 0.673143 | − | 0.120793i | ||||
\(781\) | 1.65775e6 | 2.71780 | ||||||||
\(782\) | − | 68181.4i | − | 0.111494i | ||||||
\(783\) | −277647. | + | 163676.i | −0.452866 | + | 0.266969i | ||||
\(784\) | 919029. | 1.49519 | ||||||||
\(785\) | − | 16473.8i | − | 0.0267334i | ||||||
\(786\) | −112241. | − | 625486.i | −0.181680 | − | 1.01245i | ||||
\(787\) | 402369. | 0.649643 | 0.324822 | − | 0.945775i | \(-0.394696\pi\) | ||||
0.324822 | + | 0.945775i | \(0.394696\pi\) | |||||||
\(788\) | 1.39582e6i | 2.24790i | ||||||||
\(789\) | 151985. | − | 27273.2i | 0.244145 | − | 0.0438110i | ||||
\(790\) | −157067. | −0.251670 | ||||||||
\(791\) | − | 1.16952e6i | − | 1.86920i | ||||||
\(792\) | −2.21526e6 | + | 821495.i | −3.53163 | + | 1.30965i | ||||
\(793\) | −691711. | −1.09996 | ||||||||
\(794\) | 827506.i | 1.31259i | ||||||||
\(795\) | −3977.99 | − | 22168.1i | −0.00629404 | − | 0.0350747i | ||||
\(796\) | 775513. | 1.22395 | ||||||||
\(797\) | − | 338721.i | − | 0.533243i | −0.963801 | − | 0.266622i | \(-0.914093\pi\) | ||
0.963801 | − | 0.266622i | \(-0.0859074\pi\) | |||||||
\(798\) | 788863. | − | 141559.i | 1.23878 | − | 0.222296i | ||||
\(799\) | 45520.3 | 0.0713035 | ||||||||
\(800\) | − | 295484.i | − | 0.461695i | ||||||
\(801\) | −245597. | − | 662283.i | −0.382788 | − | 1.03224i | ||||
\(802\) | −932896. | −1.45039 | ||||||||
\(803\) | 394077.i | 0.611153i | ||||||||
\(804\) | −88196.7 | − | 491493.i | −0.136440 | − | 0.760336i | ||||
\(805\) | 376855. | 0.581543 | ||||||||
\(806\) | 286157.i | 0.440489i | ||||||||
\(807\) | −985824. | + | 176903.i | −1.51374 | + | 0.271636i | ||||
\(808\) | 1.25101e6 | 1.91619 | ||||||||
\(809\) | 444127.i | 0.678594i | 0.940679 | + | 0.339297i | \(0.110189\pi\) | ||||
−0.940679 | + | 0.339297i | \(0.889811\pi\) | |||||||
\(810\) | −305204. | + | 262452.i | −0.465179 | + | 0.400019i | ||||
\(811\) | −961721. | −1.46220 | −0.731101 | − | 0.682269i | \(-0.760993\pi\) | ||||
−0.731101 | + | 0.682269i | \(0.760993\pi\) | |||||||
\(812\) | 1.05927e6i | 1.60655i | ||||||||
\(813\) | 138153. | + | 769886.i | 0.209016 | + | 1.16478i | ||||
\(814\) | 4.00842e6 | 6.04956 | ||||||||
\(815\) | − | 142125.i | − | 0.213971i | ||||||
\(816\) | 50357.4 | − | 9036.46i | 0.0756280 | − | 0.0135712i | ||||
\(817\) | 393521. | 0.589555 | ||||||||
\(818\) | 925361.i | 1.38294i | ||||||||
\(819\) | 829960. | − | 307777.i | 1.23734 | − | 0.458848i | ||||
\(820\) | −71669.9 | −0.106588 | ||||||||
\(821\) | − | 65970.3i | − | 0.0978728i | −0.998802 | − | 0.0489364i | \(-0.984417\pi\) | ||
0.998802 | − | 0.0489364i | \(-0.0155832\pi\) | |||||||
\(822\) | −96783.8 | − | 539346.i | −0.143238 | − | 0.798222i | ||||
\(823\) | −228850. | −0.337871 | −0.168935 | − | 0.985627i | \(-0.554033\pi\) | ||||
−0.168935 | + | 0.985627i | \(0.554033\pi\) | |||||||
\(824\) | − | 2.45963e6i | − | 3.62255i | ||||||
\(825\) | −1.10106e6 | + | 197582.i | −1.61772 | + | 0.290295i | ||||
\(826\) | −224878. | −0.329599 | ||||||||
\(827\) | − | 824936.i | − | 1.20617i | −0.797676 | − | 0.603086i | \(-0.793938\pi\) | ||
0.797676 | − | 0.603086i | \(-0.206062\pi\) | |||||||
\(828\) | −598999. | − | 1.61527e6i | −0.873706 | − | 2.35606i | ||||
\(829\) | −557367. | −0.811022 | −0.405511 | − | 0.914090i | \(-0.632906\pi\) | ||||
−0.405511 | + | 0.914090i | \(0.632906\pi\) | |||||||
\(830\) | − | 284720.i | − | 0.413297i | ||||||
\(831\) | 153006. | + | 852653.i | 0.221567 | + | 1.23473i | ||||
\(832\) | 322951. | 0.466542 | ||||||||
\(833\) | 38733.6i | 0.0558210i | ||||||||
\(834\) | 2.09815e6 | − | 376506.i | 3.01651 | − | 0.541302i | ||||
\(835\) | −220049. | −0.315607 | ||||||||
\(836\) | 1.38756e6i | 1.98537i | ||||||||
\(837\) | −95793.0 | − | 162496.i | −0.136736 | − | 0.231949i | ||||
\(838\) | 152903. | 0.217734 | ||||||||
\(839\) | − | 361932.i | − | 0.514165i | −0.966389 | − | 0.257083i | \(-0.917239\pi\) | ||
0.966389 | − | 0.257083i | \(-0.0827613\pi\) | |||||||
\(840\) | 124399. | + | 693237.i | 0.176302 | + | 0.982479i | ||||
\(841\) | 511817. | 0.723640 | ||||||||
\(842\) | 817835.i | 1.15356i | ||||||||
\(843\) | −350113. | + | 62826.5i | −0.492666 | + | 0.0884072i | ||||
\(844\) | 1.02047e6 | 1.43256 | ||||||||
\(845\) | 36406.8i | 0.0509882i | ||||||||
\(846\) | 1.58270e6 | − | 586920.i | 2.21136 | − | 0.820046i | ||||
\(847\) | 2.55047e6 | 3.55511 | ||||||||
\(848\) | 106153.i | 0.147618i | ||||||||
\(849\) | 159550. | + | 889121.i | 0.221351 | + | 1.23352i | ||||
\(850\) | 60331.7 | 0.0835042 | ||||||||
\(851\) | 1.55601e6i | 2.14859i | ||||||||
\(852\) | −2.22356e6 | + | 399010.i | −3.06316 | + | 0.549673i | ||||
\(853\) | −443032. | −0.608888 | −0.304444 | − | 0.952530i | \(-0.598471\pi\) | ||||
−0.304444 | + | 0.952530i | \(0.598471\pi\) | |||||||
\(854\) | − | 2.19933e6i | − | 3.01561i | ||||||
\(855\) | 43759.1 | + | 118002.i | 0.0598599 | + | 0.161419i | ||||
\(856\) | 1.77828e6 | 2.42691 | ||||||||
\(857\) | − | 1.05613e6i | − | 1.43799i | −0.695014 | − | 0.718996i | \(-0.744602\pi\) | ||
0.695014 | − | 0.718996i | \(-0.255398\pi\) | |||||||
\(858\) | 397258. | + | 2.21380e6i | 0.539633 | + | 3.00721i | ||||
\(859\) | −434895. | −0.589384 | −0.294692 | − | 0.955592i | \(-0.595217\pi\) | ||||
−0.294692 | + | 0.955592i | \(0.595217\pi\) | |||||||
\(860\) | 649574.i | 0.878278i | ||||||||
\(861\) | −150076. | + | 26930.7i | −0.202444 | + | 0.0363279i | ||||
\(862\) | 120639. | 0.162357 | ||||||||
\(863\) | 19733.9i | 0.0264967i | 0.999912 | + | 0.0132483i | \(0.00421720\pi\) | ||||
−0.999912 | + | 0.0132483i | \(0.995783\pi\) | |||||||
\(864\) | 337364. | − | 198879.i | 0.451930 | − | 0.266417i | ||||
\(865\) | −206584. | −0.276099 | ||||||||
\(866\) | − | 888628.i | − | 1.18491i | ||||||
\(867\) | −132386. | − | 737749.i | −0.176119 | − | 0.981455i | ||||
\(868\) | −619949. | −0.822843 | ||||||||
\(869\) | − | 578512.i | − | 0.766077i | ||||||
\(870\) | −240283. | + | 43117.9i | −0.317456 | + | 0.0569664i | ||||
\(871\) | −253067. | −0.333579 | ||||||||
\(872\) | − | 747257.i | − | 0.982736i | ||||||
\(873\) | −974127. | + | 361240.i | −1.27817 | + | 0.473988i | ||||
\(874\) | −790512. | −1.03487 | ||||||||
\(875\) | 712379.i | 0.930455i | ||||||||
\(876\) | −94851.6 | − | 528579.i | −0.123605 | − | 0.688813i | ||||
\(877\) | 412672. | 0.536545 | 0.268273 | − | 0.963343i | \(-0.413547\pi\) | ||||
0.268273 | + | 0.963343i | \(0.413547\pi\) | |||||||
\(878\) | − | 1.96306e6i | − | 2.54651i | ||||||
\(879\) | 396380. | − | 71129.0i | 0.513020 | − | 0.0920596i | ||||
\(880\) | −718517. | −0.927837 | ||||||||
\(881\) | 1.25288e6i | 1.61420i | 0.590414 | + | 0.807101i | \(0.298965\pi\) | ||||
−0.590414 | + | 0.807101i | \(0.701035\pi\) | |||||||
\(882\) | 499416. | + | 1.34674e6i | 0.641985 | + | 1.73119i | ||||
\(883\) | 261200. | 0.335006 | 0.167503 | − | 0.985872i | \(-0.446430\pi\) | ||||
0.167503 | + | 0.985872i | \(0.446430\pi\) | |||||||
\(884\) | − | 82652.8i | − | 0.105768i | ||||||
\(885\) | −6237.10 | − | 34757.4i | −0.00796335 | − | 0.0443773i | ||||
\(886\) | 1.70914e6 | 2.17726 | ||||||||
\(887\) | 804200.i | 1.02216i | 0.859534 | + | 0.511078i | \(0.170754\pi\) | ||||
−0.859534 | + | 0.511078i | \(0.829246\pi\) | |||||||
\(888\) | −2.86234e6 | + | 513637.i | −3.62991 | + | 0.651374i | ||||
\(889\) | −2.13725e6 | −2.70428 | ||||||||
\(890\) | − | 535016.i | − | 0.675439i | ||||||
\(891\) | −966668. | − | 1.12413e6i | −1.21765 | − | 1.41600i | ||||
\(892\) | −544359. | −0.684157 | ||||||||
\(893\) | − | 527773.i | − | 0.661826i | ||||||
\(894\) | 434189. | + | 2.41960e6i | 0.543255 | + | 3.02739i | ||||
\(895\) | 185199. | 0.231202 | ||||||||
\(896\) | 1.62872e6i | 2.02876i | ||||||||
\(897\) | −859367. | + | 154210.i | −1.06806 | + | 0.191659i | ||||
\(898\) | −417158. | −0.517306 | ||||||||
\(899\) | − | 114397.i | − | 0.141546i | ||||||
\(900\) | 1.42931e6 | − | 530037.i | 1.76458 | − | 0.654366i | ||||
\(901\) | −4473.94 | −0.00551113 | ||||||||
\(902\) | − | 387416.i | − | 0.476173i | ||||||
\(903\) | 244084. | + | 1.36020e6i | 0.299339 | + | 1.66813i | ||||
\(904\) | −2.15587e6 | −2.63807 | ||||||||
\(905\) | − | 312877.i | − | 0.382012i | ||||||
\(906\) | −825066. | + | 148055.i | −1.00515 | + | 0.180371i | ||||
\(907\) | 109017. | 0.132519 | 0.0662596 | − | 0.997802i | \(-0.478893\pi\) | ||||
0.0662596 | + | 0.997802i | \(0.478893\pi\) | |||||||
\(908\) | 889605.i | 1.07901i | ||||||||
\(909\) | 272950. | + | 736043.i | 0.330335 | + | 0.890790i | ||||
\(910\) | 670470. | 0.809649 | ||||||||
\(911\) | − | 453728.i | − | 0.546712i | −0.961913 | − | 0.273356i | \(-0.911866\pi\) | ||
0.961913 | − | 0.273356i | \(-0.0881338\pi\) | |||||||
\(912\) | −104771. | − | 583856.i | −0.125965 | − | 0.701966i | ||||
\(913\) | 1.04868e6 | 1.25807 | ||||||||
\(914\) | − | 1.40556e6i | − | 1.68251i | ||||||
\(915\) | 339932. | − | 60999.6i | 0.406022 | − | 0.0728592i | ||||
\(916\) | 936486. | 1.11612 | ||||||||
\(917\) | − | 697729.i | − | 0.829752i | ||||||
\(918\) | 40607.0 | + | 68882.6i | 0.0481854 | + | 0.0817381i | ||||
\(919\) | −330226. | −0.391003 | −0.195502 | − | 0.980703i | \(-0.562634\pi\) | ||||
−0.195502 | + | 0.980703i | \(0.562634\pi\) | |||||||
\(920\) | − | 694686.i | − | 0.820754i | ||||||
\(921\) | 199138. | + | 1.10974e6i | 0.234766 | + | 1.30828i | ||||
\(922\) | −2.60886e6 | −3.06895 | ||||||||
\(923\) | 1.14490e6i | 1.34389i | ||||||||
\(924\) | −4.79611e6 | + | 860645.i | −5.61753 | + | 1.00805i | ||||
\(925\) | −1.37687e6 | −1.60920 | ||||||||
\(926\) | − | 1.82959e6i | − | 2.13369i | ||||||
\(927\) | 1.44714e6 | − | 536651.i | 1.68404 | − | 0.624500i | ||||
\(928\) | 237505. | 0.275789 | ||||||||
\(929\) | 1.48562e6i | 1.72138i | 0.509131 | + | 0.860689i | \(0.329967\pi\) | ||||
−0.509131 | + | 0.860689i | \(0.670033\pi\) | |||||||
\(930\) | −25235.2 | − | 140628.i | −0.0291770 | − | 0.162595i | ||||
\(931\) | 449087. | 0.518120 | ||||||||
\(932\) | − | 3.00343e6i | − | 3.45768i | ||||||
\(933\) | −205495. | + | 36875.3i | −0.236068 | + | 0.0423616i | ||||
\(934\) | 558598. | 0.640332 | ||||||||
\(935\) | − | 30282.8i | − | 0.0346396i | ||||||
\(936\) | −567350. | − | 1.52993e6i | −0.647589 | − | 1.74630i | ||||
\(937\) | 544687. | 0.620395 | 0.310197 | − | 0.950672i | \(-0.399605\pi\) | ||||
0.310197 | + | 0.950672i | \(0.399605\pi\) | |||||||
\(938\) | − | 804639.i | − | 0.914524i | ||||||
\(939\) | 69650.0 | + | 388138.i | 0.0789933 | + | 0.440205i | ||||
\(940\) | 871179. | 0.985943 | ||||||||
\(941\) | − | 269431.i | − | 0.304277i | −0.988359 | − | 0.152138i | \(-0.951384\pi\) | ||
0.988359 | − | 0.152138i | \(-0.0486159\pi\) | |||||||
\(942\) | −119444. | + | 21433.8i | −0.134605 | + | 0.0241544i | ||||
\(943\) | 150390. | 0.169120 | ||||||||
\(944\) | 166437.i | 0.186770i | ||||||||
\(945\) | −380730. | + | 224444.i | −0.426338 | + | 0.251330i | ||||
\(946\) | −3.51132e6 | −3.92363 | ||||||||
\(947\) | − | 775388.i | − | 0.864608i | −0.901728 | − | 0.432304i | \(-0.857701\pi\) | ||
0.901728 | − | 0.432304i | \(-0.142299\pi\) | |||||||
\(948\) | 139244. | + | 775963.i | 0.154939 | + | 0.863425i | ||||
\(949\) | −272162. | −0.302200 | ||||||||
\(950\) | − | 699501.i | − | 0.775070i | ||||||
\(951\) | 440726. | − | 79086.7i | 0.487313 | − | 0.0874465i | ||||
\(952\) | 139908. | 0.154372 | ||||||||
\(953\) | − | 16310.0i | − | 0.0179584i | −0.999960 | − | 0.00897920i | \(-0.997142\pi\) | ||
0.999960 | − | 0.00897920i | \(-0.00285821\pi\) | |||||||
\(954\) | −155555. | + | 57685.2i | −0.170918 | + | 0.0633822i | ||||
\(955\) | −336462. | −0.368918 | ||||||||
\(956\) | − | 928180.i | − | 1.01559i | ||||||
\(957\) | −158812. | − | 885013.i | −0.173405 | − | 0.966330i | ||||
\(958\) | −1.70668e6 | −1.85961 | ||||||||
\(959\) | − | 601640.i | − | 0.654183i | ||||||
\(960\) | −158710. | + | 28480.0i | −0.172211 | + | 0.0309027i | ||||
\(961\) | −856569. | −0.927503 | ||||||||
\(962\) | 2.76834e6i | 2.99136i | ||||||||
\(963\) | 387992. | + | 1.04627e6i | 0.418379 | + | 1.12821i | ||||
\(964\) | −470245. | −0.506023 | ||||||||
\(965\) | 284709.i | 0.305736i | ||||||||
\(966\) | −490320. | − | 2.73240e6i | −0.525442 | − | 2.92813i | ||||
\(967\) | 1.64756e6 | 1.76193 | 0.880967 | − | 0.473178i | \(-0.156893\pi\) | ||||
0.880967 | + | 0.473178i | \(0.156893\pi\) | |||||||
\(968\) | − | 4.70148e6i | − | 5.01746i | ||||||
\(969\) | 24607.3 | − | 4415.70i | 0.0262070 | − | 0.00470275i | ||||
\(970\) | −786934. | −0.836363 | ||||||||
\(971\) | − | 1.68663e6i | − | 1.78888i | −0.447186 | − | 0.894441i | \(-0.647574\pi\) | ||
0.447186 | − | 0.894441i | \(-0.352426\pi\) | |||||||
\(972\) | 1.56717e6 | + | 1.27514e6i | 1.65876 | + | 1.34966i | ||||
\(973\) | 2.34048e6 | 2.47218 | ||||||||
\(974\) | 937224.i | 0.987929i | ||||||||
\(975\) | −136456. | − | 760429.i | −0.143544 | − | 0.799925i | ||||
\(976\) | −1.62778e6 | −1.70881 | ||||||||
\(977\) | 211107.i | 0.221163i | 0.993867 | + | 0.110582i | \(0.0352714\pi\) | ||||
−0.993867 | + | 0.110582i | \(0.964729\pi\) | |||||||
\(978\) | −1.03048e6 | + | 184916.i | −1.07737 | + | 0.193329i | ||||
\(979\) | 1.97058e6 | 2.05602 | ||||||||
\(980\) | 741294.i | 0.771860i | ||||||||
\(981\) | 439655. | − | 163039.i | 0.456851 | − | 0.169416i | ||||
\(982\) | 1.13174e6 | 1.17361 | ||||||||
\(983\) | 164036.i | 0.169759i | 0.996391 | + | 0.0848796i | \(0.0270506\pi\) | ||||
−0.996391 | + | 0.0848796i | \(0.972949\pi\) | |||||||
\(984\) | 49643.4 | + | 276647.i | 0.0512710 | + | 0.285717i | ||||
\(985\) | −353194. | −0.364033 | ||||||||
\(986\) | 48493.5i | 0.0498804i | ||||||||
\(987\) | 1.82424e6 | − | 327354.i | 1.87262 | − | 0.336034i | ||||
\(988\) | −958296. | −0.981716 | ||||||||
\(989\) | − | 1.36305e6i | − | 1.39354i | ||||||
\(990\) | −390454. | − | 1.05291e6i | −0.398382 | − | 1.07429i | ||||
\(991\) | −1.71373e6 | −1.74500 | −0.872501 | − | 0.488613i | \(-0.837503\pi\) | ||||
−0.872501 | + | 0.488613i | \(0.837503\pi\) | |||||||
\(992\) | 139002.i | 0.141253i | ||||||||
\(993\) | 98289.2 | + | 547736.i | 0.0996798 | + | 0.555485i | ||||
\(994\) | −3.64026e6 | −3.68433 | ||||||||
\(995\) | 196234.i | 0.198211i | ||||||||
\(996\) | −1.40661e6 | + | 252411.i | −1.41793 | + | 0.254443i | ||||
\(997\) | −677731. | −0.681816 | −0.340908 | − | 0.940097i | \(-0.610734\pi\) | ||||
−0.340908 | + | 0.940097i | \(0.610734\pi\) | |||||||
\(998\) | − | 3.10962e6i | − | 3.12209i | ||||||
\(999\) | −926719. | − | 1.57202e6i | −0.928575 | − | 1.57517i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.5.b.a.119.6 | ✓ | 78 | |
3.2 | odd | 2 | inner | 177.5.b.a.119.73 | yes | 78 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.5.b.a.119.6 | ✓ | 78 | 1.1 | even | 1 | trivial | |
177.5.b.a.119.73 | yes | 78 | 3.2 | odd | 2 | inner |