Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 45.5 | ||
Character | \(\chi\) | \(=\) | 74.45 |
Dual form | 74.5.g.a.51.5 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{1}{12}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.73205 | − | 0.732051i | −0.683013 | − | 0.183013i | ||||
\(3\) | 6.38646 | + | 3.68723i | 0.709607 | + | 0.409692i | 0.810915 | − | 0.585163i | \(-0.198970\pi\) |
−0.101309 | + | 0.994855i | \(0.532303\pi\) | |||||||
\(4\) | 6.92820 | + | 4.00000i | 0.433013 | + | 0.250000i | ||||
\(5\) | −43.6075 | + | 11.6846i | −1.74430 | + | 0.467384i | −0.983395 | − | 0.181480i | \(-0.941911\pi\) |
−0.760905 | + | 0.648863i | \(0.775245\pi\) | |||||||
\(6\) | −14.7489 | − | 14.7489i | −0.409692 | − | 0.409692i | ||||
\(7\) | 39.7034 | − | 68.7683i | 0.810274 | − | 1.40344i | −0.102398 | − | 0.994743i | \(-0.532652\pi\) |
0.912672 | − | 0.408692i | \(-0.134015\pi\) | |||||||
\(8\) | −16.0000 | − | 16.0000i | −0.250000 | − | 0.250000i | ||||
\(9\) | −13.3087 | − | 23.0514i | −0.164305 | − | 0.284585i | ||||
\(10\) | 127.692 | 1.27692 | ||||||||
\(11\) | 23.6627i | 0.195559i | 0.995208 | + | 0.0977796i | \(0.0311740\pi\) | ||||
−0.995208 | + | 0.0977796i | \(0.968826\pi\) | |||||||
\(12\) | 29.4978 | + | 51.0917i | 0.204846 | + | 0.354803i | ||||
\(13\) | 240.572 | − | 64.4610i | 1.42350 | − | 0.381426i | 0.536776 | − | 0.843725i | \(-0.319642\pi\) |
0.886724 | + | 0.462299i | \(0.152975\pi\) | |||||||
\(14\) | −158.814 | + | 158.814i | −0.810274 | + | 0.810274i | ||||
\(15\) | −321.581 | − | 86.1675i | −1.42925 | − | 0.382966i | ||||
\(16\) | 32.0000 | + | 55.4256i | 0.125000 | + | 0.216506i | ||||
\(17\) | 122.681 | − | 457.851i | 0.424501 | − | 1.58426i | −0.340510 | − | 0.940241i | \(-0.610600\pi\) |
0.765011 | − | 0.644017i | \(-0.222734\pi\) | |||||||
\(18\) | 19.4853 | + | 72.7202i | 0.0601399 | + | 0.224445i | ||||
\(19\) | −126.519 | + | 33.9007i | −0.350469 | + | 0.0939078i | −0.429759 | − | 0.902944i | \(-0.641401\pi\) |
0.0792901 | + | 0.996852i | \(0.474735\pi\) | |||||||
\(20\) | −348.860 | − | 93.4767i | −0.872150 | − | 0.233692i | ||||
\(21\) | 507.129 | − | 292.791i | 1.14995 | − | 0.663925i | ||||
\(22\) | 17.3223 | − | 64.6476i | 0.0357898 | − | 0.133569i | ||||
\(23\) | −496.506 | − | 496.506i | −0.938574 | − | 0.938574i | 0.0596457 | − | 0.998220i | \(-0.481003\pi\) |
−0.998220 | + | 0.0596457i | \(0.981003\pi\) | |||||||
\(24\) | −43.1878 | − | 161.179i | −0.0749788 | − | 0.279825i | ||||
\(25\) | 1223.82 | − | 706.571i | 1.95811 | − | 1.13051i | ||||
\(26\) | −704.443 | −1.04207 | ||||||||
\(27\) | − | 793.620i | − | 1.08864i | ||||||
\(28\) | 550.147 | − | 317.627i | 0.701718 | − | 0.405137i | ||||
\(29\) | −503.438 | + | 503.438i | −0.598619 | + | 0.598619i | −0.939945 | − | 0.341326i | \(-0.889124\pi\) |
0.341326 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(30\) | 815.498 | + | 470.828i | 0.906108 | + | 0.523142i | ||||
\(31\) | −358.102 | + | 358.102i | −0.372635 | + | 0.372635i | −0.868436 | − | 0.495801i | \(-0.834875\pi\) |
0.495801 | + | 0.868436i | \(0.334875\pi\) | |||||||
\(32\) | −46.8513 | − | 174.851i | −0.0457532 | − | 0.170753i | ||||
\(33\) | −87.2496 | + | 151.121i | −0.0801190 | + | 0.138770i | ||||
\(34\) | −670.340 | + | 1161.06i | −0.579879 | + | 1.00438i | ||||
\(35\) | −927.837 | + | 3462.73i | −0.757418 | + | 2.82672i | ||||
\(36\) | − | 212.940i | − | 0.164305i | ||||||
\(37\) | −1348.59 | + | 235.514i | −0.985091 | + | 0.172033i | ||||
\(38\) | 370.474 | 0.256561 | ||||||||
\(39\) | 1774.08 | + | 475.364i | 1.16639 | + | 0.312534i | ||||
\(40\) | 884.673 | + | 510.766i | 0.552921 | + | 0.319229i | ||||
\(41\) | 646.276 | + | 373.127i | 0.384459 | + | 0.221968i | 0.679757 | − | 0.733438i | \(-0.262085\pi\) |
−0.295298 | + | 0.955405i | \(0.595419\pi\) | |||||||
\(42\) | −1599.84 | + | 428.676i | −0.906939 | + | 0.243013i | ||||
\(43\) | −553.213 | − | 553.213i | −0.299196 | − | 0.299196i | 0.541503 | − | 0.840699i | \(-0.317855\pi\) |
−0.840699 | + | 0.541503i | \(0.817855\pi\) | |||||||
\(44\) | −94.6506 | + | 163.940i | −0.0488898 | + | 0.0846796i | ||||
\(45\) | 849.706 | + | 849.706i | 0.419608 | + | 0.419608i | ||||
\(46\) | 993.011 | + | 1719.95i | 0.469287 | + | 0.812829i | ||||
\(47\) | 2648.46 | 1.19894 | 0.599471 | − | 0.800396i | \(-0.295378\pi\) | ||||
0.599471 | + | 0.800396i | \(0.295378\pi\) | |||||||
\(48\) | 471.965i | 0.204846i | ||||||||
\(49\) | −1952.22 | − | 3381.35i | −0.813088 | − | 1.40831i | ||||
\(50\) | −3860.78 | + | 1034.49i | −1.54431 | + | 0.413797i | ||||
\(51\) | 2471.69 | − | 2471.69i | 0.950286 | − | 0.950286i | ||||
\(52\) | 1924.57 | + | 515.688i | 0.711750 | + | 0.190713i | ||||
\(53\) | −104.046 | − | 180.213i | −0.0370401 | − | 0.0641554i | 0.846911 | − | 0.531735i | \(-0.178460\pi\) |
−0.883951 | + | 0.467579i | \(0.845126\pi\) | |||||||
\(54\) | −580.970 | + | 2168.21i | −0.199235 | + | 0.743556i | ||||
\(55\) | −276.489 | − | 1031.87i | −0.0914012 | − | 0.341114i | ||||
\(56\) | −1735.55 | + | 465.039i | −0.553427 | + | 0.148290i | ||||
\(57\) | −933.009 | − | 249.999i | −0.287168 | − | 0.0769465i | ||||
\(58\) | 1743.96 | − | 1006.88i | 0.518419 | − | 0.299309i | ||||
\(59\) | 57.1818 | − | 213.405i | 0.0164268 | − | 0.0613057i | −0.957226 | − | 0.289342i | \(-0.906564\pi\) |
0.973653 | + | 0.228036i | \(0.0732303\pi\) | |||||||
\(60\) | −1883.31 | − | 1883.31i | −0.523142 | − | 0.523142i | ||||
\(61\) | 1128.84 | + | 4212.87i | 0.303369 | + | 1.13219i | 0.934340 | + | 0.356382i | \(0.115990\pi\) |
−0.630971 | + | 0.775806i | \(0.717343\pi\) | |||||||
\(62\) | 1240.50 | − | 716.205i | 0.322712 | − | 0.186318i | ||||
\(63\) | −2113.61 | −0.532529 | ||||||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | −9737.52 | + | 5621.96i | −2.30474 | + | 1.33064i | ||||
\(66\) | 348.998 | − | 348.998i | 0.0801190 | − | 0.0801190i | ||||
\(67\) | 1832.80 | + | 1058.17i | 0.408287 | + | 0.235725i | 0.690054 | − | 0.723758i | \(-0.257587\pi\) |
−0.281766 | + | 0.959483i | \(0.590920\pi\) | |||||||
\(68\) | 2681.36 | − | 2681.36i | 0.579879 | − | 0.579879i | ||||
\(69\) | −1340.19 | − | 5001.64i | −0.281493 | − | 1.05054i | ||||
\(70\) | 5069.79 | − | 8781.14i | 1.03465 | − | 1.79207i | ||||
\(71\) | 1611.83 | − | 2791.77i | 0.319744 | − | 0.553814i | −0.660690 | − | 0.750659i | \(-0.729736\pi\) |
0.980435 | + | 0.196845i | \(0.0630696\pi\) | |||||||
\(72\) | −155.883 | + | 581.762i | −0.0300700 | + | 0.112223i | ||||
\(73\) | − | 9197.34i | − | 1.72590i | −0.505287 | − | 0.862952i | \(-0.668613\pi\) | ||
0.505287 | − | 0.862952i | \(-0.331387\pi\) | |||||||
\(74\) | 3856.82 | + | 343.801i | 0.704314 | + | 0.0627832i | ||||
\(75\) | 10421.2 | 1.85265 | ||||||||
\(76\) | −1012.15 | − | 271.206i | −0.175234 | − | 0.0469539i | ||||
\(77\) | 1627.24 | + | 939.489i | 0.274455 | + | 0.158457i | ||||
\(78\) | −4498.90 | − | 2597.44i | −0.739463 | − | 0.426929i | ||||
\(79\) | −10618.7 | + | 2845.28i | −1.70145 | + | 0.455902i | −0.973303 | − | 0.229522i | \(-0.926284\pi\) |
−0.728145 | + | 0.685424i | \(0.759617\pi\) | |||||||
\(80\) | −2043.07 | − | 2043.07i | −0.319229 | − | 0.319229i | ||||
\(81\) | 1848.25 | − | 3201.26i | 0.281702 | − | 0.487923i | ||||
\(82\) | −1492.51 | − | 1492.51i | −0.221968 | − | 0.221968i | ||||
\(83\) | 2785.13 | + | 4823.98i | 0.404286 | + | 0.700244i | 0.994238 | − | 0.107194i | \(-0.0341867\pi\) |
−0.589952 | + | 0.807438i | \(0.700853\pi\) | |||||||
\(84\) | 4684.66 | 0.663925 | ||||||||
\(85\) | 21399.2i | 2.96183i | ||||||||
\(86\) | 1106.43 | + | 1916.39i | 0.149598 | + | 0.259111i | ||||
\(87\) | −5071.48 | + | 1358.90i | −0.670033 | + | 0.179535i | ||||
\(88\) | 378.603 | − | 378.603i | 0.0488898 | − | 0.0488898i | ||||
\(89\) | 1026.15 | + | 274.955i | 0.129548 | + | 0.0347122i | 0.323010 | − | 0.946395i | \(-0.395305\pi\) |
−0.193463 | + | 0.981108i | \(0.561972\pi\) | |||||||
\(90\) | −1699.41 | − | 2943.47i | −0.209804 | − | 0.363391i | ||||
\(91\) | 5118.64 | − | 19103.0i | 0.618119 | − | 2.30685i | ||||
\(92\) | −1453.87 | − | 5425.91i | −0.171771 | − | 0.641058i | ||||
\(93\) | −3607.41 | + | 966.603i | −0.417090 | + | 0.111759i | ||||
\(94\) | −7235.74 | − | 1938.81i | −0.818893 | − | 0.219422i | ||||
\(95\) | 5121.07 | − | 2956.65i | 0.567431 | − | 0.327607i | ||||
\(96\) | 345.502 | − | 1289.43i | 0.0374894 | − | 0.139912i | ||||
\(97\) | 6808.20 | + | 6808.20i | 0.723584 | + | 0.723584i | 0.969333 | − | 0.245749i | \(-0.0790340\pi\) |
−0.245749 | + | 0.969333i | \(0.579034\pi\) | |||||||
\(98\) | 2858.25 | + | 10667.1i | 0.297611 | + | 1.11070i | ||||
\(99\) | 545.457 | − | 314.920i | 0.0556532 | − | 0.0321314i | ||||
\(100\) | 11305.1 | 1.13051 | ||||||||
\(101\) | 2577.51i | 0.252672i | 0.991987 | + | 0.126336i | \(0.0403218\pi\) | ||||
−0.991987 | + | 0.126336i | \(0.959678\pi\) | |||||||
\(102\) | −8562.20 | + | 4943.39i | −0.822972 | + | 0.475143i | ||||
\(103\) | 421.911 | − | 421.911i | 0.0397691 | − | 0.0397691i | −0.686943 | − | 0.726712i | \(-0.741048\pi\) |
0.726712 | + | 0.686943i | \(0.241048\pi\) | |||||||
\(104\) | −4880.52 | − | 2817.77i | −0.451232 | − | 0.260519i | ||||
\(105\) | −18693.5 | + | 18693.5i | −1.69555 | + | 1.69555i | ||||
\(106\) | 152.334 | + | 568.517i | 0.0135576 | + | 0.0505978i | ||||
\(107\) | 2307.80 | − | 3997.22i | 0.201572 | − | 0.349133i | −0.747463 | − | 0.664303i | \(-0.768728\pi\) |
0.949035 | + | 0.315171i | \(0.102062\pi\) | |||||||
\(108\) | 3174.48 | − | 5498.36i | 0.272160 | − | 0.471396i | ||||
\(109\) | 3403.55 | − | 12702.2i | 0.286470 | − | 1.06912i | −0.661288 | − | 0.750132i | \(-0.729990\pi\) |
0.947758 | − | 0.318990i | \(-0.103344\pi\) | |||||||
\(110\) | 3021.52i | 0.249713i | ||||||||
\(111\) | −9481.11 | − | 3468.46i | −0.769508 | − | 0.281508i | ||||
\(112\) | 5082.04 | 0.405137 | ||||||||
\(113\) | −3575.81 | − | 958.137i | −0.280039 | − | 0.0750361i | 0.116066 | − | 0.993242i | \(-0.462972\pi\) |
−0.396105 | + | 0.918205i | \(0.629638\pi\) | |||||||
\(114\) | 2366.02 | + | 1366.02i | 0.182057 | + | 0.105111i | ||||
\(115\) | 27452.8 | + | 15849.9i | 2.07583 | + | 1.19848i | ||||
\(116\) | −5501.68 | + | 1474.17i | −0.408864 | + | 0.109555i | ||||
\(117\) | −4687.62 | − | 4687.62i | −0.342437 | − | 0.342437i | ||||
\(118\) | −312.447 | + | 541.174i | −0.0224395 | + | 0.0388663i | ||||
\(119\) | −26614.8 | − | 26614.8i | −1.87944 | − | 1.87944i | ||||
\(120\) | 3766.62 | + | 6523.98i | 0.261571 | + | 0.453054i | ||||
\(121\) | 14081.1 | 0.961757 | ||||||||
\(122\) | − | 12336.1i | − | 0.828819i | ||||||
\(123\) | 2751.61 | + | 4765.93i | 0.181877 | + | 0.315019i | ||||
\(124\) | −3913.42 | + | 1048.60i | −0.254515 | + | 0.0681970i | ||||
\(125\) | −25159.8 | + | 25159.8i | −1.61023 | + | 1.61023i | ||||
\(126\) | 5774.49 | + | 1547.27i | 0.363724 | + | 0.0974596i | ||||
\(127\) | −6402.95 | − | 11090.2i | −0.396984 | − | 0.687596i | 0.596368 | − | 0.802711i | \(-0.296610\pi\) |
−0.993352 | + | 0.115115i | \(0.963276\pi\) | |||||||
\(128\) | 374.810 | − | 1398.81i | 0.0228766 | − | 0.0853766i | ||||
\(129\) | −1493.25 | − | 5572.89i | −0.0897333 | − | 0.334889i | ||||
\(130\) | 30719.0 | − | 8231.12i | 1.81769 | − | 0.487049i | ||||
\(131\) | 13341.2 | + | 3574.77i | 0.777416 | + | 0.208308i | 0.625645 | − | 0.780108i | \(-0.284836\pi\) |
0.151771 | + | 0.988416i | \(0.451502\pi\) | |||||||
\(132\) | −1208.97 | + | 697.997i | −0.0693851 | + | 0.0400595i | ||||
\(133\) | −2691.95 | + | 10046.5i | −0.152182 | + | 0.567951i | ||||
\(134\) | −4232.68 | − | 4232.68i | −0.235725 | − | 0.235725i | ||||
\(135\) | 9273.12 | + | 34607.8i | 0.508813 | + | 1.89892i | ||||
\(136\) | −9288.50 | + | 5362.72i | −0.502190 | + | 0.289939i | ||||
\(137\) | 8360.31 | 0.445432 | 0.222716 | − | 0.974883i | \(-0.428508\pi\) | ||||
0.222716 | + | 0.974883i | \(0.428508\pi\) | |||||||
\(138\) | 14645.8i | 0.769052i | ||||||||
\(139\) | −17897.4 | + | 10333.1i | −0.926317 | + | 0.534810i | −0.885645 | − | 0.464363i | \(-0.846283\pi\) |
−0.0406724 | + | 0.999173i | \(0.512950\pi\) | |||||||
\(140\) | −20279.2 | + | 20279.2i | −1.03465 | + | 1.03465i | ||||
\(141\) | 16914.3 | + | 9765.48i | 0.850778 | + | 0.491197i | ||||
\(142\) | −6447.33 | + | 6447.33i | −0.319744 | + | 0.319744i | ||||
\(143\) | 1525.32 | + | 5692.56i | 0.0745913 | + | 0.278379i | ||||
\(144\) | 851.759 | − | 1475.29i | 0.0410763 | − | 0.0711463i | ||||
\(145\) | 16071.2 | − | 27836.1i | 0.764386 | − | 1.32395i | ||||
\(146\) | −6732.92 | + | 25127.6i | −0.315862 | + | 1.17881i | ||||
\(147\) | − | 28793.2i | − | 1.33246i | ||||||
\(148\) | −10285.4 | − | 3762.67i | −0.469565 | − | 0.171780i | ||||
\(149\) | 7002.63 | 0.315420 | 0.157710 | − | 0.987485i | \(-0.449589\pi\) | ||||
0.157710 | + | 0.987485i | \(0.449589\pi\) | |||||||
\(150\) | −28471.1 | − | 7628.81i | −1.26538 | − | 0.339058i | ||||
\(151\) | 30099.1 | + | 17377.7i | 1.32008 | + | 0.762148i | 0.983741 | − | 0.179593i | \(-0.0574779\pi\) |
0.336339 | + | 0.941741i | \(0.390811\pi\) | |||||||
\(152\) | 2566.72 | + | 1481.89i | 0.111094 | + | 0.0641402i | ||||
\(153\) | −12186.8 | + | 3265.45i | −0.520604 | + | 0.139495i | ||||
\(154\) | −3757.95 | − | 3757.95i | −0.158457 | − | 0.158457i | ||||
\(155\) | 11431.7 | − | 19800.2i | 0.475824 | − | 0.824151i | ||||
\(156\) | 10389.8 | + | 10389.8i | 0.426929 | + | 0.426929i | ||||
\(157\) | −17524.5 | − | 30353.2i | −0.710960 | − | 1.23142i | −0.964497 | − | 0.264093i | \(-0.914927\pi\) |
0.253537 | − | 0.967326i | \(-0.418406\pi\) | |||||||
\(158\) | 31093.8 | 1.24555 | ||||||||
\(159\) | − | 1534.56i | − | 0.0607002i | ||||||
\(160\) | 4086.13 | + | 7077.39i | 0.159614 | + | 0.276460i | ||||
\(161\) | −53856.8 | + | 14430.9i | −2.07773 | + | 0.556726i | ||||
\(162\) | −7392.99 | + | 7392.99i | −0.281702 | + | 0.281702i | ||||
\(163\) | 24350.9 | + | 6524.80i | 0.916515 | + | 0.245579i | 0.686095 | − | 0.727512i | \(-0.259323\pi\) |
0.230420 | + | 0.973091i | \(0.425990\pi\) | |||||||
\(164\) | 2985.02 | + | 5170.20i | 0.110984 | + | 0.192230i | ||||
\(165\) | 2038.95 | − | 7609.47i | 0.0748926 | − | 0.279503i | ||||
\(166\) | −4077.71 | − | 15218.2i | −0.147979 | − | 0.552265i | ||||
\(167\) | −1342.48 | + | 359.716i | −0.0481365 | + | 0.0128981i | −0.282807 | − | 0.959177i | \(-0.591266\pi\) |
0.234670 | + | 0.972075i | \(0.424599\pi\) | |||||||
\(168\) | −12798.7 | − | 3429.41i | −0.453469 | − | 0.121507i | ||||
\(169\) | 28984.9 | − | 16734.5i | 1.01484 | − | 0.585920i | ||||
\(170\) | 15665.3 | − | 58463.7i | 0.542052 | − | 2.02296i | ||||
\(171\) | 2465.27 | + | 2465.27i | 0.0843086 | + | 0.0843086i | ||||
\(172\) | −1619.92 | − | 6045.62i | −0.0547566 | − | 0.204354i | ||||
\(173\) | −33415.9 | + | 19292.7i | −1.11651 | + | 0.644614i | −0.940506 | − | 0.339776i | \(-0.889649\pi\) |
−0.175999 | + | 0.984390i | \(0.556315\pi\) | |||||||
\(174\) | 14850.3 | 0.490498 | ||||||||
\(175\) | − | 112213.i | − | 3.66410i | ||||||
\(176\) | −1311.52 | + | 757.205i | −0.0423398 | + | 0.0244449i | ||||
\(177\) | 1152.06 | − | 1152.06i | 0.0367730 | − | 0.0367730i | ||||
\(178\) | −2602.20 | − | 1502.38i | −0.0821298 | − | 0.0474177i | ||||
\(179\) | 41819.1 | − | 41819.1i | 1.30517 | − | 1.30517i | 0.380318 | − | 0.924856i | \(-0.375815\pi\) |
0.924856 | − | 0.380318i | \(-0.124185\pi\) | |||||||
\(180\) | 2488.11 | + | 9285.76i | 0.0767936 | + | 0.286598i | ||||
\(181\) | −18497.1 | + | 32038.0i | −0.564608 | + | 0.977930i | 0.432478 | + | 0.901645i | \(0.357639\pi\) |
−0.997086 | + | 0.0762857i | \(0.975694\pi\) | |||||||
\(182\) | −27968.8 | + | 48443.3i | −0.844366 | + | 1.46248i | ||||
\(183\) | −8324.55 | + | 31067.6i | −0.248576 | + | 0.927696i | ||||
\(184\) | 15888.2i | 0.469287i | ||||||||
\(185\) | 56056.7 | − | 26027.9i | 1.63789 | − | 0.760493i | ||||
\(186\) | 10563.2 | 0.305331 | ||||||||
\(187\) | 10834.0 | + | 2902.95i | 0.309816 | + | 0.0830150i | ||||
\(188\) | 18349.1 | + | 10593.9i | 0.519157 | + | 0.299736i | ||||
\(189\) | −54575.9 | − | 31509.4i | −1.52784 | − | 0.882098i | ||||
\(190\) | −16155.4 | + | 4328.83i | −0.447519 | + | 0.119912i | ||||
\(191\) | −6845.27 | − | 6845.27i | −0.187639 | − | 0.187639i | 0.607035 | − | 0.794675i | \(-0.292359\pi\) |
−0.794675 | + | 0.607035i | \(0.792359\pi\) | |||||||
\(192\) | −1887.86 | + | 3269.87i | −0.0512115 | + | 0.0887009i | ||||
\(193\) | 46468.5 | + | 46468.5i | 1.24751 | + | 1.24751i | 0.956816 | + | 0.290696i | \(0.0938867\pi\) |
0.290696 | + | 0.956816i | \(0.406113\pi\) | |||||||
\(194\) | −13616.4 | − | 23584.3i | −0.361792 | − | 0.626642i | ||||
\(195\) | −82917.8 | −2.18061 | ||||||||
\(196\) | − | 31235.6i | − | 0.813088i | ||||||
\(197\) | 2911.48 | + | 5042.82i | 0.0750206 | + | 0.129940i | 0.901095 | − | 0.433621i | \(-0.142764\pi\) |
−0.826075 | + | 0.563561i | \(0.809431\pi\) | |||||||
\(198\) | −1720.75 | + | 461.075i | −0.0438923 | + | 0.0117609i | ||||
\(199\) | 7387.55 | − | 7387.55i | 0.186550 | − | 0.186550i | −0.607653 | − | 0.794203i | \(-0.707889\pi\) |
0.794203 | + | 0.607653i | \(0.207889\pi\) | |||||||
\(200\) | −30886.2 | − | 8275.94i | −0.772156 | − | 0.206898i | ||||
\(201\) | 7803.42 | + | 13515.9i | 0.193149 | + | 0.334544i | ||||
\(202\) | 1886.87 | − | 7041.89i | 0.0462422 | − | 0.172578i | ||||
\(203\) | 14632.4 | + | 54608.8i | 0.355078 | + | 1.32517i | ||||
\(204\) | 27011.2 | − | 7237.62i | 0.649058 | − | 0.173914i | ||||
\(205\) | −32542.3 | − | 8719.68i | −0.774356 | − | 0.207488i | ||||
\(206\) | −1461.54 | + | 843.821i | −0.0344411 | + | 0.0198846i | ||||
\(207\) | −4837.29 | + | 18053.0i | −0.112892 | + | 0.421317i | ||||
\(208\) | 11271.1 | + | 11271.1i | 0.260519 | + | 0.260519i | ||||
\(209\) | −802.181 | − | 2993.78i | −0.0183645 | − | 0.0685373i | ||||
\(210\) | 64756.1 | − | 37386.9i | 1.46839 | − | 0.847777i | ||||
\(211\) | −165.278 | −0.00371236 | −0.00185618 | − | 0.999998i | \(-0.500591\pi\) | ||||
−0.00185618 | + | 0.999998i | \(0.500591\pi\) | |||||||
\(212\) | − | 1664.73i | − | 0.0370401i | ||||||
\(213\) | 20587.8 | − | 11886.4i | 0.453786 | − | 0.261993i | ||||
\(214\) | −9231.18 | + | 9231.18i | −0.201572 | + | 0.201572i | ||||
\(215\) | 30588.3 | + | 17660.2i | 0.661726 | + | 0.382048i | ||||
\(216\) | −12697.9 | + | 12697.9i | −0.272160 | + | 0.272160i | ||||
\(217\) | 10408.2 | + | 38844.0i | 0.221033 | + | 0.824906i | ||||
\(218\) | −18597.4 | + | 32211.6i | −0.391326 | + | 0.677796i | ||||
\(219\) | 33912.7 | − | 58738.5i | 0.707088 | − | 1.22471i | ||||
\(220\) | 2211.91 | − | 8254.95i | 0.0457006 | − | 0.170557i | ||||
\(221\) | − | 118054.i | − | 2.41711i | ||||||
\(222\) | 23363.8 | + | 16416.7i | 0.474064 | + | 0.333103i | ||||
\(223\) | 17804.5 | 0.358030 | 0.179015 | − | 0.983846i | \(-0.442709\pi\) | ||||
0.179015 | + | 0.983846i | \(0.442709\pi\) | |||||||
\(224\) | −13884.4 | − | 3720.31i | −0.276714 | − | 0.0741452i | ||||
\(225\) | −32574.9 | − | 18807.1i | −0.643455 | − | 0.371499i | ||||
\(226\) | 9067.90 | + | 5235.36i | 0.177537 | + | 0.102501i | ||||
\(227\) | 44745.1 | − | 11989.4i | 0.868348 | − | 0.232673i | 0.202974 | − | 0.979184i | \(-0.434939\pi\) |
0.665373 | + | 0.746511i | \(0.268272\pi\) | |||||||
\(228\) | −5464.08 | − | 5464.08i | −0.105111 | − | 0.105111i | ||||
\(229\) | −25747.3 | + | 44595.7i | −0.490977 | + | 0.850397i | −0.999946 | − | 0.0103877i | \(-0.996693\pi\) |
0.508969 | + | 0.860785i | \(0.330027\pi\) | |||||||
\(230\) | −63399.6 | − | 63399.6i | −1.19848 | − | 1.19848i | ||||
\(231\) | 6928.21 | + | 12000.0i | 0.129837 | + | 0.224884i | ||||
\(232\) | 16110.0 | 0.299309 | ||||||||
\(233\) | 24235.7i | 0.446419i | 0.974770 | + | 0.223210i | \(0.0716534\pi\) | ||||
−0.974770 | + | 0.223210i | \(0.928347\pi\) | |||||||
\(234\) | 9375.23 | + | 16238.4i | 0.171218 | + | 0.296559i | ||||
\(235\) | −115493. | + | 30946.2i | −2.09131 | + | 0.560366i | ||||
\(236\) | 1249.79 | − | 1249.79i | 0.0224395 | − | 0.0224395i | ||||
\(237\) | −78307.4 | − | 20982.4i | −1.39414 | − | 0.373558i | ||||
\(238\) | 53229.6 | + | 92196.3i | 0.939721 | + | 1.62765i | ||||
\(239\) | −12582.0 | + | 46956.6i | −0.220269 | + | 0.822055i | 0.763976 | + | 0.645245i | \(0.223245\pi\) |
−0.984245 | + | 0.176810i | \(0.943422\pi\) | |||||||
\(240\) | −5514.72 | − | 20581.2i | −0.0957416 | − | 0.357313i | ||||
\(241\) | −8229.58 | + | 2205.11i | −0.141691 | + | 0.0379661i | −0.328968 | − | 0.944341i | \(-0.606701\pi\) |
0.187276 | + | 0.982307i | \(0.440034\pi\) | |||||||
\(242\) | −38470.2 | − | 10308.1i | −0.656892 | − | 0.176014i | ||||
\(243\) | −32063.3 | + | 18511.8i | −0.542996 | + | 0.313499i | ||||
\(244\) | −9030.69 | + | 33703.0i | −0.151684 | + | 0.566094i | ||||
\(245\) | 124641. | + | 124641.i | 2.07649 | + | 2.07649i | ||||
\(246\) | −4028.64 | − | 15035.1i | −0.0665714 | − | 0.248448i | ||||
\(247\) | −28251.6 | + | 16311.1i | −0.463073 | + | 0.267355i | ||||
\(248\) | 11459.3 | 0.186318 | ||||||||
\(249\) | 41077.6i | 0.662531i | ||||||||
\(250\) | 87156.1 | − | 50319.6i | 1.39450 | − | 0.805114i | ||||
\(251\) | 26642.1 | − | 26642.1i | 0.422884 | − | 0.422884i | −0.463312 | − | 0.886195i | \(-0.653339\pi\) |
0.886195 | + | 0.463312i | \(0.153339\pi\) | |||||||
\(252\) | −14643.5 | − | 8454.43i | −0.230592 | − | 0.133132i | ||||
\(253\) | 11748.6 | − | 11748.6i | 0.183547 | − | 0.183547i | ||||
\(254\) | 9374.57 | + | 34986.4i | 0.145306 | + | 0.542290i | ||||
\(255\) | −78903.7 | + | 136665.i | −1.21344 | + | 2.10173i | ||||
\(256\) | −2048.00 | + | 3547.24i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −1821.16 | + | 6796.68i | −0.0275729 | + | 0.102904i | −0.978341 | − | 0.207000i | \(-0.933630\pi\) |
0.950768 | + | 0.309903i | \(0.100297\pi\) | |||||||
\(258\) | 16318.6i | 0.245156i | ||||||||
\(259\) | −37347.7 | + | 102091.i | −0.556756 | + | 1.52191i | ||||
\(260\) | −89951.4 | −1.33064 | ||||||||
\(261\) | 18305.1 | + | 4904.83i | 0.268714 | + | 0.0720017i | ||||
\(262\) | −33832.0 | − | 19532.9i | −0.492862 | − | 0.284554i | ||||
\(263\) | 97555.0 | + | 56323.4i | 1.41039 | + | 0.814287i | 0.995424 | − | 0.0955522i | \(-0.0304617\pi\) |
0.414962 | + | 0.909839i | \(0.363795\pi\) | |||||||
\(264\) | 3813.92 | − | 1021.94i | 0.0547223 | − | 0.0146628i | ||||
\(265\) | 6642.88 | + | 6642.88i | 0.0945943 | + | 0.0945943i | ||||
\(266\) | 14709.1 | − | 25476.9i | 0.207884 | − | 0.360067i | ||||
\(267\) | 5539.62 | + | 5539.62i | 0.0777065 | + | 0.0777065i | ||||
\(268\) | 8465.35 | + | 14662.4i | 0.117862 | + | 0.204144i | ||||
\(269\) | −19015.0 | −0.262780 | −0.131390 | − | 0.991331i | \(-0.541944\pi\) | ||||
−0.131390 | + | 0.991331i | \(0.541944\pi\) | |||||||
\(270\) | − | 101339.i | − | 1.39010i | ||||||
\(271\) | −39396.4 | − | 68236.6i | −0.536437 | − | 0.929135i | −0.999092 | − | 0.0425974i | \(-0.986437\pi\) |
0.462656 | − | 0.886538i | \(-0.346897\pi\) | |||||||
\(272\) | 29302.4 | − | 7851.57i | 0.396065 | − | 0.106125i | ||||
\(273\) | 103127. | − | 103127.i | 1.38372 | − | 1.38372i | ||||
\(274\) | −22840.8 | − | 6120.17i | −0.304235 | − | 0.0815197i | ||||
\(275\) | 16719.4 | + | 28958.8i | 0.221082 | + | 0.382926i | ||||
\(276\) | 10721.5 | − | 40013.1i | 0.140746 | − | 0.525272i | ||||
\(277\) | 23042.4 | + | 85995.3i | 0.300309 | + | 1.12077i | 0.936909 | + | 0.349573i | \(0.113673\pi\) |
−0.636601 | + | 0.771194i | \(0.719660\pi\) | |||||||
\(278\) | 56460.9 | − | 15128.6i | 0.730563 | − | 0.195754i | ||||
\(279\) | 13020.7 | + | 3488.87i | 0.167272 | + | 0.0448205i | ||||
\(280\) | 70249.1 | − | 40558.3i | 0.896035 | − | 0.517326i | ||||
\(281\) | −3171.64 | + | 11836.7i | −0.0401672 | + | 0.149906i | −0.983097 | − | 0.183086i | \(-0.941391\pi\) |
0.942930 | + | 0.332992i | \(0.108058\pi\) | |||||||
\(282\) | −39061.9 | − | 39061.9i | −0.491197 | − | 0.491197i | ||||
\(283\) | −24519.3 | − | 91507.1i | −0.306150 | − | 1.14257i | −0.931951 | − | 0.362585i | \(-0.881894\pi\) |
0.625801 | − | 0.779983i | \(-0.284772\pi\) | |||||||
\(284\) | 22334.2 | − | 12894.7i | 0.276907 | − | 0.159872i | ||||
\(285\) | 43607.3 | 0.536871 | ||||||||
\(286\) | − | 16669.0i | − | 0.203787i | ||||||
\(287\) | 51318.7 | − | 29628.9i | 0.623034 | − | 0.359709i | ||||
\(288\) | −3407.03 | + | 3407.03i | −0.0410763 | + | 0.0410763i | ||||
\(289\) | −122245. | − | 70578.4i | −1.46365 | − | 0.845038i | ||||
\(290\) | −64284.8 | + | 64284.8i | −0.764386 | + | 0.764386i | ||||
\(291\) | 18377.0 | + | 68583.7i | 0.217014 | + | 0.809907i | ||||
\(292\) | 36789.4 | − | 63721.0i | 0.431476 | − | 0.747338i | ||||
\(293\) | 30435.0 | − | 52715.0i | 0.354518 | − | 0.614043i | −0.632517 | − | 0.774546i | \(-0.717978\pi\) |
0.987035 | + | 0.160503i | \(0.0513116\pi\) | |||||||
\(294\) | −21078.1 | + | 78664.4i | −0.243857 | + | 0.910088i | ||||
\(295\) | 9974.21i | 0.114613i | ||||||||
\(296\) | 25345.7 | + | 17809.2i | 0.289281 | + | 0.203264i | ||||
\(297\) | 18779.2 | 0.212894 | ||||||||
\(298\) | −19131.5 | − | 5126.28i | −0.215436 | − | 0.0577258i | ||||
\(299\) | −151450. | − | 87439.9i | −1.69406 | − | 0.978064i | ||||
\(300\) | 72199.9 | + | 41684.6i | 0.802221 | + | 0.463162i | ||||
\(301\) | −60008.0 | + | 16079.1i | −0.662332 | + | 0.177471i | ||||
\(302\) | −69511.0 | − | 69511.0i | −0.762148 | − | 0.762148i | ||||
\(303\) | −9503.86 | + | 16461.2i | −0.103518 | + | 0.179298i | ||||
\(304\) | −5927.58 | − | 5927.58i | −0.0641402 | − | 0.0641402i | ||||
\(305\) | −98451.4 | − | 170523.i | −1.05833 | − | 1.83309i | ||||
\(306\) | 35685.5 | 0.381109 | ||||||||
\(307\) | 8323.80i | 0.0883171i | 0.999025 | + | 0.0441586i | \(0.0140607\pi\) | ||||
−0.999025 | + | 0.0441586i | \(0.985939\pi\) | |||||||
\(308\) | 7515.91 | + | 13017.9i | 0.0792283 | + | 0.137227i | ||||
\(309\) | 4250.20 | − | 1138.84i | 0.0445135 | − | 0.0119274i | ||||
\(310\) | −45726.7 | + | 45726.7i | −0.475824 | + | 0.475824i | ||||
\(311\) | −108541. | − | 29083.6i | −1.12221 | − | 0.300695i | −0.350433 | − | 0.936588i | \(-0.613966\pi\) |
−0.771778 | + | 0.635892i | \(0.780632\pi\) | |||||||
\(312\) | −20779.5 | − | 35991.2i | −0.213465 | − | 0.369732i | ||||
\(313\) | −18785.4 | + | 70107.9i | −0.191748 | + | 0.715614i | 0.801337 | + | 0.598214i | \(0.204123\pi\) |
−0.993085 | + | 0.117400i | \(0.962544\pi\) | |||||||
\(314\) | 25657.6 | + | 95755.4i | 0.260229 | + | 0.971190i | ||||
\(315\) | 92169.2 | − | 24696.7i | 0.928890 | − | 0.248895i | ||||
\(316\) | −84949.9 | − | 22762.3i | −0.850724 | − | 0.227951i | ||||
\(317\) | −17647.3 | + | 10188.7i | −0.175615 | + | 0.101391i | −0.585231 | − | 0.810867i | \(-0.698996\pi\) |
0.409616 | + | 0.912258i | \(0.365663\pi\) | |||||||
\(318\) | −1123.38 | + | 4192.50i | −0.0111089 | + | 0.0414590i | ||||
\(319\) | −11912.7 | − | 11912.7i | −0.117065 | − | 0.117065i | ||||
\(320\) | −5982.51 | − | 22327.0i | −0.0584230 | − | 0.218037i | ||||
\(321\) | 29477.3 | − | 17018.7i | 0.286074 | − | 0.165165i | ||||
\(322\) | 157704. | 1.52100 | ||||||||
\(323\) | 62085.8i | 0.595097i | ||||||||
\(324\) | 25610.1 | − | 14786.0i | 0.243961 | − | 0.140851i | ||||
\(325\) | 248869. | − | 248869.i | 2.35616 | − | 2.35616i | ||||
\(326\) | −61751.4 | − | 35652.2i | −0.581047 | − | 0.335468i | ||||
\(327\) | 68572.7 | − | 68572.7i | 0.641292 | − | 0.641292i | ||||
\(328\) | −4370.37 | − | 16310.4i | −0.0406229 | − | 0.151607i | ||||
\(329\) | 105153. | − | 182130.i | 0.971471 | − | 1.68264i | ||||
\(330\) | −11141.0 | + | 19296.8i | −0.102305 | + | 0.177198i | ||||
\(331\) | 27718.0 | − | 103445.i | 0.252992 | − | 0.944178i | −0.716205 | − | 0.697890i | \(-0.754122\pi\) |
0.969197 | − | 0.246288i | \(-0.0792108\pi\) | |||||||
\(332\) | 44562.0i | 0.404286i | ||||||||
\(333\) | 23376.9 | + | 27952.5i | 0.210814 | + | 0.252076i | ||||
\(334\) | 3931.05 | 0.0352383 | ||||||||
\(335\) | −92288.2 | − | 24728.5i | −0.822350 | − | 0.220348i | ||||
\(336\) | 32456.2 | + | 18738.6i | 0.287488 | + | 0.165981i | ||||
\(337\) | −7047.82 | − | 4069.06i | −0.0620576 | − | 0.0358290i | 0.468650 | − | 0.883384i | \(-0.344740\pi\) |
−0.530708 | + | 0.847555i | \(0.678074\pi\) | |||||||
\(338\) | −91438.8 | + | 24500.9i | −0.800381 | + | 0.214461i | ||||
\(339\) | −19303.9 | − | 19303.9i | −0.167976 | − | 0.167976i | ||||
\(340\) | −85596.8 | + | 148258.i | −0.740456 | + | 1.28251i | ||||
\(341\) | −8473.66 | − | 8473.66i | −0.0728723 | − | 0.0728723i | ||||
\(342\) | −4930.53 | − | 8539.94i | −0.0421543 | − | 0.0730134i | ||||
\(343\) | −119384. | −1.01475 | ||||||||
\(344\) | 17702.8i | 0.149598i | ||||||||
\(345\) | 116884. | + | 202450.i | 0.982015 | + | 1.70090i | ||||
\(346\) | 105417. | − | 28246.4i | 0.880560 | − | 0.235945i | ||||
\(347\) | 11850.1 | − | 11850.1i | 0.0984150 | − | 0.0984150i | −0.656185 | − | 0.754600i | \(-0.727831\pi\) |
0.754600 | + | 0.656185i | \(0.227831\pi\) | |||||||
\(348\) | −40571.8 | − | 10871.2i | −0.335017 | − | 0.0897674i | ||||
\(349\) | 21225.1 | + | 36762.9i | 0.174260 | + | 0.301827i | 0.939905 | − | 0.341436i | \(-0.110913\pi\) |
−0.765645 | + | 0.643264i | \(0.777580\pi\) | |||||||
\(350\) | −82145.8 | + | 306572.i | −0.670578 | + | 2.50263i | ||||
\(351\) | −51157.5 | − | 190922.i | −0.415236 | − | 1.54968i | ||||
\(352\) | 4137.45 | − | 1108.63i | 0.0333924 | − | 0.00894745i | ||||
\(353\) | 55303.5 | + | 14818.5i | 0.443816 | + | 0.118920i | 0.473805 | − | 0.880630i | \(-0.342880\pi\) |
−0.0299882 | + | 0.999550i | \(0.509547\pi\) | |||||||
\(354\) | −3990.86 | + | 2304.12i | −0.0318464 | + | 0.0183865i | ||||
\(355\) | −37667.2 | + | 140576.i | −0.298887 | + | 1.11546i | ||||
\(356\) | 6009.53 | + | 6009.53i | 0.0474177 | + | 0.0474177i | ||||
\(357\) | −71839.6 | − | 268109.i | −0.563673 | − | 2.10366i | ||||
\(358\) | −144866. | + | 83638.1i | −1.13031 | + | 0.652587i | ||||
\(359\) | 250770. | 1.94575 | 0.972876 | − | 0.231329i | \(-0.0743074\pi\) | ||||
0.972876 | + | 0.231329i | \(0.0743074\pi\) | |||||||
\(360\) | − | 27190.6i | − | 0.209804i | ||||||
\(361\) | −98003.5 | + | 56582.3i | −0.752016 | + | 0.434177i | ||||
\(362\) | 73988.5 | − | 73988.5i | 0.564608 | − | 0.564608i | ||||
\(363\) | 89928.3 | + | 51920.1i | 0.682469 | + | 0.394024i | ||||
\(364\) | 111875. | − | 111875.i | 0.844366 | − | 0.844366i | ||||
\(365\) | 107467. | + | 401073.i | 0.806659 | + | 3.01049i | ||||
\(366\) | 45486.2 | − | 78784.3i | 0.339560 | − | 0.588136i | ||||
\(367\) | −3655.93 | + | 6332.26i | −0.0271435 | + | 0.0470139i | −0.879278 | − | 0.476309i | \(-0.841974\pi\) |
0.852135 | + | 0.523323i | \(0.175308\pi\) | |||||||
\(368\) | 11631.0 | − | 43407.3i | 0.0858855 | − | 0.320529i | ||||
\(369\) | − | 19863.4i | − | 0.145882i | ||||||
\(370\) | −172204. | + | 30073.1i | −1.25788 | + | 0.219672i | ||||
\(371\) | −16523.9 | −0.120051 | ||||||||
\(372\) | −28859.3 | − | 7732.83i | −0.208545 | − | 0.0558795i | ||||
\(373\) | 82552.3 | + | 47661.6i | 0.593351 | + | 0.342571i | 0.766421 | − | 0.642338i | \(-0.222035\pi\) |
−0.173070 | + | 0.984909i | \(0.555369\pi\) | |||||||
\(374\) | −27473.8 | − | 15862.0i | −0.196416 | − | 0.113401i | ||||
\(375\) | −253452. | + | 67912.3i | −1.80233 | + | 0.482932i | ||||
\(376\) | −42375.4 | − | 42375.4i | −0.299736 | − | 0.299736i | ||||
\(377\) | −88660.8 | + | 153565.i | −0.623805 | + | 1.08046i | ||||
\(378\) | 126038. | + | 126038.i | 0.882098 | + | 0.882098i | ||||
\(379\) | 46750.0 | + | 80973.4i | 0.325464 | + | 0.563721i | 0.981606 | − | 0.190917i | \(-0.0611460\pi\) |
−0.656142 | + | 0.754638i | \(0.727813\pi\) | |||||||
\(380\) | 47306.4 | 0.327607 | ||||||||
\(381\) | − | 94436.5i | − | 0.650564i | ||||||
\(382\) | 13690.5 | + | 23712.7i | 0.0938196 | + | 0.162500i | ||||
\(383\) | −49257.8 | + | 13198.6i | −0.335797 | + | 0.0899766i | −0.422778 | − | 0.906233i | \(-0.638945\pi\) |
0.0869804 | + | 0.996210i | \(0.472278\pi\) | |||||||
\(384\) | 7551.44 | − | 7551.44i | 0.0512115 | − | 0.0512115i | ||||
\(385\) | −81937.5 | − | 21955.1i | −0.552791 | − | 0.148120i | ||||
\(386\) | −92937.1 | − | 160972.i | −0.623756 | − | 1.08038i | ||||
\(387\) | −5389.77 | + | 20114.9i | −0.0359872 | + | 0.134306i | ||||
\(388\) | 19935.8 | + | 74401.4i | 0.132425 | + | 0.494217i | ||||
\(389\) | −133806. | + | 35853.3i | −0.884256 | + | 0.236936i | −0.672242 | − | 0.740331i | \(-0.734669\pi\) |
−0.212013 | + | 0.977267i | \(0.568002\pi\) | |||||||
\(390\) | 226536. | + | 60700.0i | 1.48939 | + | 0.399080i | ||||
\(391\) | −288237. | + | 166414.i | −1.88537 | + | 1.08852i | ||||
\(392\) | −22866.0 | + | 85337.2i | −0.148805 | + | 0.555349i | ||||
\(393\) | 72022.3 | + | 72022.3i | 0.466318 | + | 0.466318i | ||||
\(394\) | −4262.70 | − | 15908.6i | −0.0274595 | − | 0.102480i | ||||
\(395\) | 429811. | − | 248151.i | 2.75475 | − | 1.59046i | ||||
\(396\) | 5038.72 | 0.0321314 | ||||||||
\(397\) | − | 125916.i | − | 0.798914i | −0.916752 | − | 0.399457i | \(-0.869199\pi\) | ||
0.916752 | − | 0.399457i | \(-0.130801\pi\) | |||||||
\(398\) | −25591.2 | + | 14775.1i | −0.161557 | + | 0.0932748i | ||||
\(399\) | −54235.7 | + | 54235.7i | −0.340674 | + | 0.340674i | ||||
\(400\) | 78324.3 | + | 45220.6i | 0.489527 | + | 0.282629i | ||||
\(401\) | 6608.59 | − | 6608.59i | 0.0410979 | − | 0.0410979i | −0.686259 | − | 0.727357i | \(-0.740748\pi\) |
0.727357 | + | 0.686259i | \(0.240748\pi\) | |||||||
\(402\) | −11425.0 | − | 42638.7i | −0.0706975 | − | 0.263847i | ||||
\(403\) | −63065.7 | + | 109233.i | −0.388314 | + | 0.672579i | ||||
\(404\) | −10310.0 | + | 17857.5i | −0.0631681 | + | 0.109410i | ||||
\(405\) | −43192.1 | + | 161195.i | −0.263326 | + | 0.982746i | ||||
\(406\) | − | 159906.i | − | 0.970090i | ||||||
\(407\) | −5572.88 | − | 31911.2i | −0.0336427 | − | 0.192644i | ||||
\(408\) | −79094.2 | −0.475143 | ||||||||
\(409\) | 201785. | + | 54068.2i | 1.20627 | + | 0.323218i | 0.805296 | − | 0.592873i | \(-0.202007\pi\) |
0.400970 | + | 0.916091i | \(0.368673\pi\) | |||||||
\(410\) | 82524.0 | + | 47645.2i | 0.490922 | + | 0.283434i | ||||
\(411\) | 53392.8 | + | 30826.3i | 0.316081 | + | 0.182490i | ||||
\(412\) | 4610.72 | − | 1235.44i | 0.0271628 | − | 0.00727825i | ||||
\(413\) | −12405.2 | − | 12405.2i | −0.0727284 | − | 0.0727284i | ||||
\(414\) | 26431.4 | − | 45780.6i | 0.154213 | − | 0.267104i | ||||
\(415\) | −177819. | − | 177819.i | −1.03248 | − | 1.03248i | ||||
\(416\) | −22542.2 | − | 39044.2i | −0.130259 | − | 0.225616i | ||||
\(417\) | −152401. | −0.876428 | ||||||||
\(418\) | 8766.40i | 0.0501728i | ||||||||
\(419\) | −88582.6 | − | 153430.i | −0.504569 | − | 0.873939i | −0.999986 | − | 0.00528379i | \(-0.998318\pi\) |
0.495417 | − | 0.868655i | \(-0.335015\pi\) | |||||||
\(420\) | −204286. | + | 54738.3i | −1.15808 | + | 0.310308i | ||||
\(421\) | 15323.1 | − | 15323.1i | 0.0864536 | − | 0.0864536i | −0.662557 | − | 0.749011i | \(-0.730529\pi\) |
0.749011 | + | 0.662557i | \(0.230529\pi\) | |||||||
\(422\) | 451.548 | + | 120.992i | 0.00253559 | + | 0.000679410i | ||||
\(423\) | −35247.7 | − | 61050.8i | −0.196993 | − | 0.341201i | ||||
\(424\) | −1218.67 | + | 4548.13i | −0.00677882 | + | 0.0252989i | ||||
\(425\) | −173365. | − | 647008.i | −0.959808 | − | 3.58205i | ||||
\(426\) | −64948.4 | + | 17402.9i | −0.357890 | + | 0.0958962i | ||||
\(427\) | 334531. | + | 89637.3i | 1.83477 | + | 0.491624i | ||||
\(428\) | 31977.8 | − | 18462.4i | 0.174566 | − | 0.100786i | ||||
\(429\) | −11248.4 | + | 41979.5i | −0.0611189 | + | 0.228099i | ||||
\(430\) | −70640.6 | − | 70640.6i | −0.382048 | − | 0.382048i | ||||
\(431\) | 71479.1 | + | 266764.i | 0.384791 | + | 1.43606i | 0.838496 | + | 0.544907i | \(0.183435\pi\) |
−0.453705 | + | 0.891152i | \(0.649898\pi\) | |||||||
\(432\) | 43986.9 | − | 25395.8i | 0.235698 | − | 0.136080i | ||||
\(433\) | −54416.2 | −0.290237 | −0.145118 | − | 0.989414i | \(-0.546356\pi\) | ||||
−0.145118 | + | 0.989414i | \(0.546356\pi\) | |||||||
\(434\) | − | 113743.i | − | 0.603873i | ||||||
\(435\) | 205276. | − | 118516.i | 1.08483 | − | 0.626325i | ||||
\(436\) | 74389.5 | − | 74389.5i | 0.391326 | − | 0.391326i | ||||
\(437\) | 79649.3 | + | 45985.6i | 0.417080 | + | 0.240801i | ||||
\(438\) | −135651. | + | 135651.i | −0.707088 | + | 0.707088i | ||||
\(439\) | −23033.9 | − | 85963.5i | −0.119519 | − | 0.446052i | 0.880066 | − | 0.474851i | \(-0.157498\pi\) |
−0.999585 | + | 0.0287997i | \(0.990831\pi\) | |||||||
\(440\) | −12086.1 | + | 20933.7i | −0.0624282 | + | 0.108129i | ||||
\(441\) | −51963.2 | + | 90002.9i | −0.267189 | + | 0.462785i | ||||
\(442\) | −86421.5 | + | 322529.i | −0.442361 | + | 1.65092i | ||||
\(443\) | 124255.i | 0.633149i | 0.948568 | + | 0.316574i | \(0.102533\pi\) | ||||
−0.948568 | + | 0.316574i | \(0.897467\pi\) | |||||||
\(444\) | −51813.2 | − | 61954.6i | −0.262830 | − | 0.314273i | ||||
\(445\) | −47960.4 | −0.242194 | ||||||||
\(446\) | −48642.7 | − | 13033.8i | −0.244539 | − | 0.0655240i | ||||
\(447\) | 44722.1 | + | 25820.3i | 0.223824 | + | 0.129225i | ||||
\(448\) | 35209.4 | + | 20328.2i | 0.175429 | + | 0.101284i | ||||
\(449\) | 265772. | − | 71213.4i | 1.31831 | − | 0.353240i | 0.469964 | − | 0.882685i | \(-0.344267\pi\) |
0.848344 | + | 0.529446i | \(0.177600\pi\) | |||||||
\(450\) | 75228.5 | + | 75228.5i | 0.371499 | + | 0.371499i | ||||
\(451\) | −8829.19 | + | 15292.6i | −0.0434078 | + | 0.0751845i | ||||
\(452\) | −20941.4 | − | 20941.4i | −0.102501 | − | 0.102501i | ||||
\(453\) | 128151. | + | 221965.i | 0.624492 | + | 1.08165i | ||||
\(454\) | −131023. | −0.635674 | ||||||||
\(455\) | 892844.i | 4.31274i | ||||||||
\(456\) | 10928.2 | + | 18928.1i | 0.0525554 | + | 0.0910287i | ||||
\(457\) | −257063. | + | 68879.9i | −1.23086 | + | 0.329807i | −0.814913 | − | 0.579583i | \(-0.803215\pi\) |
−0.415944 | + | 0.909390i | \(0.636549\pi\) | |||||||
\(458\) | 102989. | − | 102989.i | 0.490977 | − | 0.490977i | ||||
\(459\) | −363359. | − | 97361.8i | −1.72469 | − | 0.462129i | ||||
\(460\) | 126799. | + | 219623.i | 0.599240 | + | 1.03791i | ||||
\(461\) | 91736.8 | − | 342366.i | 0.431660 | − | 1.61098i | −0.317276 | − | 0.948333i | \(-0.602768\pi\) |
0.748936 | − | 0.662643i | \(-0.230565\pi\) | |||||||
\(462\) | −10143.6 | − | 37856.5i | −0.0475235 | − | 0.177360i | ||||
\(463\) | 305237. | − | 81788.0i | 1.42389 | − | 0.381529i | 0.537026 | − | 0.843566i | \(-0.319548\pi\) |
0.886861 | + | 0.462037i | \(0.152881\pi\) | |||||||
\(464\) | −44013.4 | − | 11793.4i | −0.204432 | − | 0.0547774i | ||||
\(465\) | 146016. | − | 84302.3i | 0.675296 | − | 0.389882i | ||||
\(466\) | 17741.7 | − | 66213.0i | 0.0817004 | − | 0.304910i | ||||
\(467\) | 22323.5 | + | 22323.5i | 0.102359 | + | 0.102359i | 0.756432 | − | 0.654072i | \(-0.226941\pi\) |
−0.654072 | + | 0.756432i | \(0.726941\pi\) | |||||||
\(468\) | −13726.3 | − | 51227.2i | −0.0626703 | − | 0.233889i | ||||
\(469\) | 145537. | − | 84025.9i | 0.661649 | − | 0.382003i | ||||
\(470\) | 338186. | 1.53095 | ||||||||
\(471\) | − | 258467.i | − | 1.16510i | ||||||
\(472\) | −4329.39 | + | 2499.58i | −0.0194331 | + | 0.0112197i | ||||
\(473\) | 13090.5 | − | 13090.5i | 0.0585105 | − | 0.0585105i | ||||
\(474\) | 198580. | + | 114650.i | 0.883848 | + | 0.510290i | ||||
\(475\) | −130883. | + | 130883.i | −0.580091 | + | 0.580091i | ||||
\(476\) | −77933.5 | − | 290852.i | −0.343962 | − | 1.28368i | ||||
\(477\) | −2769.43 | + | 4796.80i | −0.0121718 | + | 0.0210821i | ||||
\(478\) | 68749.3 | − | 119077.i | 0.300893 | − | 0.521162i | ||||
\(479\) | −55066.6 | + | 205511.i | −0.240003 | + | 0.895705i | 0.735826 | + | 0.677171i | \(0.236794\pi\) |
−0.975829 | + | 0.218534i | \(0.929873\pi\) | |||||||
\(480\) | 60266.0i | 0.261571i | ||||||||
\(481\) | −309251. | + | 143589.i | −1.33666 | + | 0.620629i | ||||
\(482\) | 24097.9 | 0.103725 | ||||||||
\(483\) | −397165. | − | 106420.i | −1.70246 | − | 0.456172i | ||||
\(484\) | 97556.6 | + | 56324.3i | 0.416453 | + | 0.240439i | ||||
\(485\) | −376440. | − | 217338.i | −1.60034 | − | 0.923956i | ||||
\(486\) | 101150. | − | 27103.1i | 0.428247 | − | 0.114748i | ||||
\(487\) | −180349. | − | 180349.i | −0.760422 | − | 0.760422i | 0.215976 | − | 0.976399i | \(-0.430707\pi\) |
−0.976399 | + | 0.215976i | \(0.930707\pi\) | |||||||
\(488\) | 49344.6 | − | 85467.3i | 0.207205 | − | 0.358889i | ||||
\(489\) | 131458. | + | 131458.i | 0.549753 | + | 0.549753i | ||||
\(490\) | −249283. | − | 431770.i | −1.03824 | − | 1.79829i | ||||
\(491\) | 440636. | 1.82775 | 0.913876 | − | 0.405994i | \(-0.133075\pi\) | ||||
0.913876 | + | 0.405994i | \(0.133075\pi\) | |||||||
\(492\) | 44025.8i | 0.181877i | ||||||||
\(493\) | 168737. | + | 292262.i | 0.694252 | + | 1.20248i | ||||
\(494\) | 89125.5 | − | 23881.1i | 0.365214 | − | 0.0978589i | ||||
\(495\) | −20106.3 | + | 20106.3i | −0.0820582 | + | 0.0820582i | ||||
\(496\) | −31307.3 | − | 8388.78i | −0.127257 | − | 0.0340985i | ||||
\(497\) | −127990. | − | 221686.i | −0.518161 | − | 0.897481i | ||||
\(498\) | 30070.9 | − | 112226.i | 0.121252 | − | 0.452517i | ||||
\(499\) | −10387.3 | − | 38765.9i | −0.0417158 | − | 0.155686i | 0.941926 | − | 0.335820i | \(-0.109013\pi\) |
−0.983642 | + | 0.180134i | \(0.942347\pi\) | |||||||
\(500\) | −274951. | + | 73673.0i | −1.09981 | + | 0.294692i | ||||
\(501\) | −9900.04 | − | 2652.71i | −0.0394422 | − | 0.0105685i | ||||
\(502\) | −92290.9 | + | 53284.2i | −0.366228 | + | 0.211442i | ||||
\(503\) | −7896.18 | + | 29469.0i | −0.0312091 | + | 0.116474i | −0.979773 | − | 0.200111i | \(-0.935870\pi\) |
0.948564 | + | 0.316585i | \(0.102536\pi\) | |||||||
\(504\) | 33817.7 | + | 33817.7i | 0.133132 | + | 0.133132i | ||||
\(505\) | −30117.1 | − | 112399.i | −0.118095 | − | 0.440736i | ||||
\(506\) | −40698.5 | + | 23497.3i | −0.158956 | + | 0.0917734i | ||||
\(507\) | 246815. | 0.960186 | ||||||||
\(508\) | − | 102447.i | − | 0.396984i | ||||||
\(509\) | 110400. | − | 63739.7i | 0.426123 | − | 0.246022i | −0.271570 | − | 0.962419i | \(-0.587543\pi\) |
0.697694 | + | 0.716396i | \(0.254210\pi\) | |||||||
\(510\) | 315615. | − | 315615.i | 1.21344 | − | 1.21344i | ||||
\(511\) | −632486. | − | 365166.i | −2.42219 | − | 1.39845i | ||||
\(512\) | 8192.00 | − | 8192.00i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 26904.3 | + | 100408.i | 0.102232 | + | 0.381535i | ||||
\(514\) | 9951.03 | − | 17235.7i | 0.0376653 | − | 0.0652383i | ||||
\(515\) | −13468.6 | + | 23328.3i | −0.0507818 | + | 0.0879567i | ||||
\(516\) | 11946.0 | − | 44583.1i | 0.0448667 | − | 0.167445i | ||||
\(517\) | 62669.7i | 0.234464i | ||||||||
\(518\) | 176772. | − | 251577.i | 0.658799 | − | 0.937588i | ||||
\(519\) | −284546. | −1.05637 | ||||||||
\(520\) | 245752. | + | 65849.0i | 0.908845 | + | 0.243524i | ||||
\(521\) | 63176.1 | + | 36474.8i | 0.232744 | + | 0.134375i | 0.611837 | − | 0.790984i | \(-0.290431\pi\) |
−0.379094 | + | 0.925358i | \(0.623764\pi\) | |||||||
\(522\) | −46419.8 | − | 26800.5i | −0.170358 | − | 0.0983562i | ||||
\(523\) | −8057.10 | + | 2158.89i | −0.0294561 | + | 0.00789274i | −0.273517 | − | 0.961867i | \(-0.588187\pi\) |
0.244061 | + | 0.969760i | \(0.421520\pi\) | |||||||
\(524\) | 78131.7 | + | 78131.7i | 0.284554 | + | 0.284554i | ||||
\(525\) | 413755. | − | 716646.i | 1.50115 | − | 2.60007i | ||||
\(526\) | −225294. | − | 225294.i | −0.814287 | − | 0.814287i | ||||
\(527\) | 120025. | + | 207890.i | 0.432167 | + | 0.748534i | ||||
\(528\) | −11167.9 | −0.0400595 | ||||||||
\(529\) | 213195.i | 0.761842i | ||||||||
\(530\) | −13285.8 | − | 23011.6i | −0.0472971 | − | 0.0819211i | ||||
\(531\) | −5680.30 | + | 1522.03i | −0.0201457 | + | 0.00539803i | ||||
\(532\) | −58836.3 | + | 58836.3i | −0.207884 | + | 0.207884i | ||||
\(533\) | 179528. | + | 48104.3i | 0.631942 | + | 0.169328i | ||||
\(534\) | −11079.2 | − | 19189.8i | −0.0388533 | − | 0.0672958i | ||||
\(535\) | −53931.3 | + | 201274.i | −0.188423 | + | 0.703203i | ||||
\(536\) | −12394.1 | − | 46255.5i | −0.0431406 | − | 0.161003i | ||||
\(537\) | 421272. | − | 112880.i | 1.46088 | − | 0.391441i | ||||
\(538\) | 51950.1 | + | 13920.0i | 0.179482 | + | 0.0480921i | ||||
\(539\) | 80011.7 | − | 46194.8i | 0.275408 | − | 0.159007i | ||||
\(540\) | −74185.0 | + | 276862.i | −0.254407 | + | 0.949459i | ||||
\(541\) | −124056. | − | 124056.i | −0.423862 | − | 0.423862i | 0.462669 | − | 0.886531i | \(-0.346892\pi\) |
−0.886531 | + | 0.462669i | \(0.846892\pi\) | |||||||
\(542\) | 57680.4 | + | 215266.i | 0.196349 | + | 0.732786i | ||||
\(543\) | −236263. | + | 136406.i | −0.801300 | + | 0.462631i | ||||
\(544\) | −85803.5 | −0.289939 | ||||||||
\(545\) | 593682.i | 1.99876i | ||||||||
\(546\) | −357243. | + | 206254.i | −1.19834 | + | 0.691860i | ||||
\(547\) | 357891. | − | 357891.i | 1.19612 | − | 1.19612i | 0.220806 | − | 0.975318i | \(-0.429131\pi\) |
0.975318 | − | 0.220806i | \(-0.0708687\pi\) | |||||||
\(548\) | 57921.9 | + | 33441.2i | 0.192878 | + | 0.111358i | ||||
\(549\) | 82089.2 | − | 82089.2i | 0.272359 | − | 0.272359i | ||||
\(550\) | −24478.8 | − | 91356.3i | −0.0809218 | − | 0.302004i | ||||
\(551\) | 46627.7 | − | 80761.5i | 0.153582 | − | 0.266012i | ||||
\(552\) | −58583.3 | + | 101469.i | −0.192263 | + | 0.333009i | ||||
\(553\) | −225935. | + | 843200.i | −0.738810 | + | 2.75728i | ||||
\(554\) | − | 251812.i | − | 0.820458i | ||||||
\(555\) | 453975. | + | 40467.7i | 1.47382 | + | 0.131378i | ||||
\(556\) | −165329. | −0.534810 | ||||||||
\(557\) | −536150. | − | 143661.i | −1.72813 | − | 0.463051i | −0.748378 | − | 0.663272i | \(-0.769167\pi\) |
−0.979751 | + | 0.200221i | \(0.935834\pi\) | |||||||
\(558\) | −33019.0 | − | 19063.6i | −0.106046 | − | 0.0612259i | ||||
\(559\) | −168748. | − | 97426.6i | −0.540026 | − | 0.311784i | ||||
\(560\) | −221615. | + | 59381.5i | −0.706680 | + | 0.189354i | ||||
\(561\) | 58486.9 | + | 58486.9i | 0.185837 | + | 0.185837i | ||||
\(562\) | 17330.2 | − | 30016.7i | 0.0548694 | − | 0.0950366i | ||||
\(563\) | −102838. | − | 102838.i | −0.324442 | − | 0.324442i | 0.526026 | − | 0.850468i | \(-0.323681\pi\) |
−0.850468 | + | 0.526026i | \(0.823681\pi\) | |||||||
\(564\) | 78123.9 | + | 135314.i | 0.245598 | + | 0.425389i | ||||
\(565\) | 167128. | 0.523542 | ||||||||
\(566\) | 267951.i | 0.836418i | ||||||||
\(567\) | −146764. | − | 254202.i | −0.456512 | − | 0.790702i | ||||
\(568\) | −70457.7 | + | 18879.1i | −0.218389 | + | 0.0585173i | ||||
\(569\) | 100260. | − | 100260.i | 0.309674 | − | 0.309674i | −0.535109 | − | 0.844783i | \(-0.679730\pi\) |
0.844783 | + | 0.535109i | \(0.179730\pi\) | |||||||
\(570\) | −119137. | − | 31922.8i | −0.366690 | − | 0.0982542i | ||||
\(571\) | 126878. | + | 219760.i | 0.389148 | + | 0.674025i | 0.992335 | − | 0.123575i | \(-0.0394360\pi\) |
−0.603187 | + | 0.797600i | \(0.706103\pi\) | |||||||
\(572\) | −12202.5 | + | 45540.5i | −0.0372957 | + | 0.139189i | ||||
\(573\) | −18477.0 | − | 68957.1i | −0.0562759 | − | 0.210024i | ||||
\(574\) | −161895. | + | 43379.7i | −0.491372 | + | 0.131663i | ||||
\(575\) | −958449. | − | 256816.i | −2.89890 | − | 0.776758i | ||||
\(576\) | 11802.3 | − | 6814.07i | 0.0355731 | − | 0.0205382i | ||||
\(577\) | −48666.0 | + | 181624.i | −0.146175 | + | 0.545533i | 0.853525 | + | 0.521052i | \(0.174460\pi\) |
−0.999700 | + | 0.0244816i | \(0.992206\pi\) | |||||||
\(578\) | 282314. | + | 282314.i | 0.845038 | + | 0.845038i | ||||
\(579\) | 125430. | + | 468110.i | 0.374148 | + | 1.39634i | ||||
\(580\) | 222689. | − | 128570.i | 0.661977 | − | 0.382193i | ||||
\(581\) | 442316. | 1.31033 | ||||||||
\(582\) | − | 200827.i | − | 0.592893i | ||||||
\(583\) | 4264.31 | − | 2462.00i | 0.0125462 | − | 0.00724354i | ||||
\(584\) | −147157. | + | 147157.i | −0.431476 | + | 0.431476i | ||||
\(585\) | 259188. | + | 149642.i | 0.757362 | + | 0.437263i | ||||
\(586\) | −121740. | + | 121740.i | −0.354518 | + | 0.354518i | ||||
\(587\) | −143947. | − | 537216.i | −0.417759 | − | 1.55910i | −0.779245 | − | 0.626719i | \(-0.784397\pi\) |
0.361486 | − | 0.932377i | \(-0.382269\pi\) | |||||||
\(588\) | 115173. | − | 199485.i | 0.333115 | − | 0.576973i | ||||
\(589\) | 33166.9 | − | 57446.7i | 0.0956036 | − | 0.165590i | ||||
\(590\) | 7301.63 | − | 27250.1i | 0.0209757 | − | 0.0782823i | ||||
\(591\) | 42941.1i | 0.122941i | ||||||||
\(592\) | −56208.4 | − | 67210.0i | −0.160383 | − | 0.191774i | ||||
\(593\) | −674610. | −1.91842 | −0.959210 | − | 0.282695i | \(-0.908772\pi\) | ||||
−0.959210 | + | 0.282695i | \(0.908772\pi\) | |||||||
\(594\) | −51305.6 | − | 13747.3i | −0.145409 | − | 0.0389623i | ||||
\(595\) | 1.47159e6 | + | 849621.i | 4.15673 | + | 2.39989i | ||||
\(596\) | 48515.7 | + | 28010.5i | 0.136581 | + | 0.0788549i | ||||
\(597\) | 74419.9 | − | 19940.7i | 0.208805 | − | 0.0559491i | ||||
\(598\) | 349760. | + | 349760.i | 0.978064 | + | 0.978064i | ||||
\(599\) | 144517. | − | 250311.i | 0.402777 | − | 0.697631i | −0.591283 | − | 0.806464i | \(-0.701378\pi\) |
0.994060 | + | 0.108834i | \(0.0347116\pi\) | |||||||
\(600\) | −166738. | − | 166738.i | −0.463162 | − | 0.463162i | ||||
\(601\) | −295558. | − | 511922.i | −0.818265 | − | 1.41728i | −0.906959 | − | 0.421218i | \(-0.861603\pi\) |
0.0886941 | − | 0.996059i | \(-0.471731\pi\) | |||||||
\(602\) | 175716. | 0.484861 | ||||||||
\(603\) | − | 56331.5i | − | 0.154923i | ||||||
\(604\) | 139022. | + | 240793.i | 0.381074 | + | 0.660040i | ||||
\(605\) | −614040. | + | 164532.i | −1.67759 | + | 0.449509i | ||||
\(606\) | 38015.4 | − | 38015.4i | 0.103518 | − | 0.103518i | ||||
\(607\) | 292148. | + | 78280.9i | 0.792914 | + | 0.212461i | 0.632470 | − | 0.774585i | \(-0.282041\pi\) |
0.160443 | + | 0.987045i | \(0.448708\pi\) | |||||||
\(608\) | 11855.2 | + | 20533.7i | 0.0320701 | + | 0.0555470i | ||||
\(609\) | −107906. | + | 402710.i | −0.290945 | + | 1.08582i | ||||
\(610\) | 144143. | + | 537948.i | 0.387377 | + | 1.44571i | ||||
\(611\) | 637145. | − | 170722.i | 1.70669 | − | 0.457307i | ||||
\(612\) | −97494.6 | − | 26123.6i | −0.260302 | − | 0.0697477i | ||||
\(613\) | −457797. | + | 264309.i | −1.21829 | + | 0.703382i | −0.964553 | − | 0.263890i | \(-0.914994\pi\) |
−0.253741 | + | 0.967272i | \(0.581661\pi\) | |||||||
\(614\) | 6093.44 | − | 22741.0i | 0.0161632 | − | 0.0603217i | ||||
\(615\) | −175679. | − | 175679.i | −0.464482 | − | 0.464482i | ||||
\(616\) | −11004.1 | − | 41067.7i | −0.0289996 | − | 0.108228i | ||||
\(617\) | −445642. | + | 257292.i | −1.17062 | + | 0.675858i | −0.953826 | − | 0.300359i | \(-0.902893\pi\) |
−0.216794 | + | 0.976217i | \(0.569560\pi\) | |||||||
\(618\) | −12445.4 | −0.0325862 | ||||||||
\(619\) | − | 208300.i | − | 0.543635i | −0.962349 | − | 0.271817i | \(-0.912375\pi\) | ||
0.962349 | − | 0.271817i | \(-0.0876247\pi\) | |||||||
\(620\) | 158402. | − | 91453.4i | 0.412076 | − | 0.237912i | ||||
\(621\) | −394037. | + | 394037.i | −1.02177 | + | 1.02177i | ||||
\(622\) | 275250. | + | 158916.i | 0.711453 | + | 0.410758i | ||||
\(623\) | 59649.7 | − | 59649.7i | 0.153685 | − | 0.153685i | ||||
\(624\) | 30423.3 | + | 113541.i | 0.0781335 | + | 0.291598i | ||||
\(625\) | 361567. | − | 626252.i | 0.925611 | − | 1.60320i | ||||
\(626\) | 102645. | − | 177787.i | 0.261933 | − | 0.453681i | ||||
\(627\) | 5915.64 | − | 22077.5i | 0.0150476 | − | 0.0561584i | ||||
\(628\) | − | 280391.i | − | 0.710960i | ||||||
\(629\) | −57615.9 | + | 646346.i | −0.145627 | + | 1.63367i | ||||
\(630\) | −269890. | −0.679995 | ||||||||
\(631\) | 85248.6 | + | 22842.3i | 0.214106 | + | 0.0573695i | 0.364277 | − | 0.931290i | \(-0.381316\pi\) |
−0.150172 | + | 0.988660i | \(0.547983\pi\) | |||||||
\(632\) | 215424. | + | 124375.i | 0.539337 | + | 0.311387i | ||||
\(633\) | −1055.54 | − | 609.418i | −0.00263432 | − | 0.00152092i | ||||
\(634\) | 55672.1 | − | 14917.3i | 0.138503 | − | 0.0371117i | ||||
\(635\) | 408801. | + | 408801.i | 1.01383 | + | 1.01383i | ||||
\(636\) | 6138.24 | − | 10631.8i | 0.0151750 | − | 0.0262839i | ||||
\(637\) | −687615. | − | 687615.i | −1.69460 | − | 1.69460i | ||||
\(638\) | 23825.4 | + | 41266.8i | 0.0585327 | + | 0.101382i | ||||
\(639\) | −85805.7 | −0.210143 | ||||||||
\(640\) | 65378.1i | 0.159614i | ||||||||
\(641\) | 361270. | + | 625738.i | 0.879257 | + | 1.52292i | 0.852158 | + | 0.523285i | \(0.175294\pi\) |
0.0270995 | + | 0.999633i | \(0.491373\pi\) | |||||||
\(642\) | −92992.1 | + | 24917.2i | −0.225619 | + | 0.0604545i | ||||
\(643\) | 370460. | − | 370460.i | 0.896023 | − | 0.896023i | −0.0990586 | − | 0.995082i | \(-0.531583\pi\) |
0.995082 | + | 0.0990586i | \(0.0315831\pi\) | |||||||
\(644\) | −430855. | − | 115447.i | −1.03887 | − | 0.278363i | ||||
\(645\) | 130234. | + | 225572.i | 0.313044 | + | 0.542207i | ||||
\(646\) | 45450.0 | − | 169622.i | 0.108910 | − | 0.406459i | ||||
\(647\) | −141741. | − | 528986.i | −0.338601 | − | 1.26368i | −0.899912 | − | 0.436071i | \(-0.856370\pi\) |
0.561311 | − | 0.827605i | \(-0.310297\pi\) | |||||||
\(648\) | −80792.1 | + | 21648.2i | −0.192406 | + | 0.0515551i | ||||
\(649\) | 5049.74 | + | 1353.07i | 0.0119889 | + | 0.00321242i | ||||
\(650\) | −862109. | + | 497739.i | −2.04050 | + | 1.17808i | ||||
\(651\) | −76754.9 | + | 286453.i | −0.181111 | + | 0.675915i | ||||
\(652\) | 142609. | + | 142609.i | 0.335468 | + | 0.335468i | ||||
\(653\) | 23021.3 | + | 85916.5i | 0.0539887 | + | 0.201488i | 0.987652 | − | 0.156663i | \(-0.0500737\pi\) |
−0.933663 | + | 0.358152i | \(0.883407\pi\) | |||||||
\(654\) | −237543. | + | 137145.i | −0.555375 | + | 0.320646i | ||||
\(655\) | −623548. | −1.45341 | ||||||||
\(656\) | 47760.3i | 0.110984i | ||||||||
\(657\) | −212011. | + | 122405.i | −0.491166 | + | 0.283575i | ||||
\(658\) | −420612. | + | 420612.i | −0.971471 | + | 0.971471i | ||||
\(659\) | −411803. | − | 237755.i | −0.948242 | − | 0.547468i | −0.0557074 | − | 0.998447i | \(-0.517741\pi\) |
−0.892534 | + | 0.450980i | \(0.851075\pi\) | |||||||
\(660\) | 44564.2 | − | 44564.2i | 0.102305 | − | 0.102305i | ||||
\(661\) | 138046. | + | 515193.i | 0.315951 | + | 1.17914i | 0.923101 | + | 0.384558i | \(0.125646\pi\) |
−0.607150 | + | 0.794587i | \(0.707687\pi\) | |||||||
\(662\) | −151454. | + | 262326.i | −0.345593 | + | 0.598585i | ||||
\(663\) | 435292. | − | 753947.i | 0.990269 | − | 1.71520i | ||||
\(664\) | 32621.7 | − | 121746.i | 0.0739895 | − | 0.276132i | ||||
\(665\) | − | 469556.i | − | 1.06180i | ||||||
\(666\) | −43404.3 | − | 93480.7i | −0.0978554 | − | 0.210753i | ||||
\(667\) | 499920. | 1.12370 | ||||||||
\(668\) | −10739.8 | − | 2877.73i | −0.0240682 | − | 0.00644906i | ||||
\(669\) | 113708. | + | 65649.1i | 0.254061 | + | 0.146682i | ||||
\(670\) | 234033. | + | 135119.i | 0.521349 | + | 0.301001i | ||||
\(671\) | −99687.8 | + | 26711.3i | −0.221410 | + | 0.0593266i | ||||
\(672\) | −74954.5 | − | 74954.5i | −0.165981 | − | 0.165981i | ||||
\(673\) | 409341. | − | 708999.i | 0.903764 | − | 1.56536i | 0.0811959 | − | 0.996698i | \(-0.474126\pi\) |
0.822568 | − | 0.568667i | \(-0.192541\pi\) | |||||||
\(674\) | 16276.2 | + | 16276.2i | 0.0358290 | + | 0.0358290i | ||||
\(675\) | −560749. | − | 971246.i | −1.23072 | − | 2.13168i | ||||
\(676\) | 267751. | 0.585920 | ||||||||
\(677\) | − | 451334.i | − | 0.984738i | −0.870386 | − | 0.492369i | \(-0.836131\pi\) | ||
0.870386 | − | 0.492369i | \(-0.163869\pi\) | |||||||
\(678\) | 38607.9 | + | 66870.8i | 0.0839879 | + | 0.145471i | ||||
\(679\) | 738498. | − | 197880.i | 1.60181 | − | 0.429202i | ||||
\(680\) | 342387. | − | 342387.i | 0.740456 | − | 0.740456i | ||||
\(681\) | 329970. | + | 88415.3i | 0.711510 | + | 0.190648i | ||||
\(682\) | 16947.3 | + | 29353.6i | 0.0364361 | + | 0.0631092i | ||||
\(683\) | 151823. | − | 566611.i | 0.325459 | − | 1.21463i | −0.588391 | − | 0.808577i | \(-0.700238\pi\) |
0.913850 | − | 0.406052i | \(-0.133095\pi\) | |||||||
\(684\) | 7218.80 | + | 26940.9i | 0.0154295 | + | 0.0575838i | ||||
\(685\) | −364572. | + | 97686.8i | −0.776966 | + | 0.208187i | ||||
\(686\) | 326163. | + | 87395.1i | 0.693085 | + | 0.185712i | ||||
\(687\) | −328869. | + | 189872.i | −0.696801 | + | 0.402298i | ||||
\(688\) | 12959.4 | − | 48365.0i | 0.0273783 | − | 0.102177i | ||||
\(689\) | −36647.1 | − | 36647.1i | −0.0771972 | − | 0.0771972i | ||||
\(690\) | −171131. | − | 638668.i | −0.359442 | − | 1.34146i | ||||
\(691\) | 294693. | − | 170141.i | 0.617182 | − | 0.356330i | −0.158589 | − | 0.987345i | \(-0.550694\pi\) |
0.775771 | + | 0.631014i | \(0.217361\pi\) | |||||||
\(692\) | −308683. | −0.644614 | ||||||||
\(693\) | − | 50013.6i | − | 0.104141i | ||||||
\(694\) | −41049.8 | + | 23700.1i | −0.0852299 | + | 0.0492075i | ||||
\(695\) | 659722. | − | 659722.i | 1.36581 | − | 1.36581i | ||||
\(696\) | 102886. | + | 59401.3i | 0.212392 | + | 0.122625i | ||||
\(697\) | 250122. | − | 250122.i | 0.514857 | − | 0.514857i | ||||
\(698\) | −31075.6 | − | 115976.i | −0.0637836 | − | 0.238044i | ||||
\(699\) | −89362.3 | + | 154780.i | −0.182894 | + | 0.316782i | ||||
\(700\) | 448853. | − | 777436.i | 0.916026 | − | 1.58660i | ||||
\(701\) | 78737.6 | − | 293853.i | 0.160231 | − | 0.597989i | −0.838370 | − | 0.545102i | \(-0.816491\pi\) |
0.998600 | − | 0.0528874i | \(-0.0168424\pi\) | |||||||
\(702\) | 559060.i | 1.13445i | ||||||||
\(703\) | 162638. | − | 75515.1i | 0.329088 | − | 0.152800i | ||||
\(704\) | −12115.3 | −0.0244449 | ||||||||
\(705\) | −851696. | − | 228211.i | −1.71359 | − | 0.459155i | ||||
\(706\) | −140244. | − | 80970.0i | −0.281368 | − | 0.162448i | ||||
\(707\) | 177251. | + | 102336.i | 0.354609 | + | 0.204734i | ||||
\(708\) | 12590.0 | − | 3373.47i | 0.0251165 | − | 0.00672993i | ||||
\(709\) | −139680. | − | 139680.i | −0.277869 | − | 0.277869i | 0.554389 | − | 0.832258i | \(-0.312952\pi\) |
−0.832258 | + | 0.554389i | \(0.812952\pi\) | |||||||
\(710\) | 205817. | − | 356486.i | 0.408287 | − | 0.707173i | ||||
\(711\) | 206910. | + | 206910.i | 0.409300 | + | 0.409300i | ||||
\(712\) | −12019.1 | − | 20817.6i | −0.0237088 | − | 0.0410649i | ||||
\(713\) | 355600. | 0.699492 | ||||||||
\(714\) | 785078.i | 1.53998i | ||||||||
\(715\) | −133031. | − | 230416.i | −0.260219 | − | 0.450713i | ||||
\(716\) | 457007. | − | 122455.i | 0.891450 | − | 0.238863i | ||||
\(717\) | −253494. | + | 253494.i | −0.493094 | + | 0.493094i | ||||
\(718\) | −685117. | − | 183577.i | −1.32897 | − | 0.356097i | ||||
\(719\) | 279522. | + | 484147.i | 0.540703 | + | 0.936525i | 0.998864 | + | 0.0476560i | \(0.0151751\pi\) |
−0.458161 | + | 0.888869i | \(0.651492\pi\) | |||||||
\(720\) | −19904.9 | + | 74286.1i | −0.0383968 | + | 0.143299i | ||||
\(721\) | −12262.8 | − | 45765.4i | −0.0235895 | − | 0.0880373i | ||||
\(722\) | 309172. | − | 82842.3i | 0.593096 | − | 0.158920i | ||||
\(723\) | −60688.6 | − | 16261.5i | −0.116100 | − | 0.0311088i | ||||
\(724\) | −256304. | + | 147977.i | −0.488965 | + | 0.282304i | ||||
\(725\) | −260402. | + | 971832.i | −0.495413 | + | 1.84891i | ||||
\(726\) | −207680. | − | 207680.i | −0.394024 | − | 0.394024i | ||||
\(727\) | 96328.9 | + | 359504.i | 0.182259 | + | 0.680198i | 0.995201 | + | 0.0978538i | \(0.0311977\pi\) |
−0.812942 | + | 0.582344i | \(0.802136\pi\) | |||||||
\(728\) | −387547. | + | 223750.i | −0.731242 | + | 0.422183i | ||||
\(729\) | −572445. | −1.07716 | ||||||||
\(730\) | − | 1.17442e6i | − | 2.20383i | ||||||
\(731\) | −321157. | + | 185420.i | −0.601012 | + | 0.346994i | ||||
\(732\) | −181945. | + | 181945.i | −0.339560 | + | 0.339560i | ||||
\(733\) | −218052. | − | 125893.i | −0.405838 | − | 0.234311i | 0.283162 | − | 0.959072i | \(-0.408617\pi\) |
−0.689000 | + | 0.724761i | \(0.741950\pi\) | |||||||
\(734\) | 14623.7 | − | 14623.7i | 0.0271435 | − | 0.0271435i | ||||
\(735\) | 336436. | + | 1.25560e6i | 0.622771 | + | 2.32421i | ||||
\(736\) | −63552.7 | + | 110077.i | −0.117322 | + | 0.203207i | ||||
\(737\) | −25039.1 | + | 43369.0i | −0.0460982 | + | 0.0798444i | ||||
\(738\) | −14541.0 | + | 54267.8i | −0.0266982 | + | 0.0996391i | ||||
\(739\) | 473919.i | 0.867792i | 0.900963 | + | 0.433896i | \(0.142861\pi\) | ||||
−0.900963 | + | 0.433896i | \(0.857139\pi\) | |||||||
\(740\) | 492484. | + | 43900.5i | 0.899350 | + | 0.0801689i | ||||
\(741\) | −240571. | −0.438133 | ||||||||
\(742\) | 45144.1 | + | 12096.3i | 0.0819961 | + | 0.0219708i | ||||
\(743\) | 610593. | + | 352526.i | 1.10605 | + | 0.638578i | 0.937803 | − | 0.347168i | \(-0.112856\pi\) |
0.168246 | + | 0.985745i | \(0.446190\pi\) | |||||||
\(744\) | 73184.3 | + | 42253.0i | 0.132212 | + | 0.0763328i | ||||
\(745\) | −305367. | + | 81822.9i | −0.550186 | + | 0.147422i | ||||
\(746\) | −190646. | − | 190646.i | −0.342571 | − | 0.342571i | ||||
\(747\) | 74133.0 | − | 128402.i | 0.132853 | − | 0.230108i | ||||
\(748\) | 63448.1 | + | 63448.1i | 0.113401 | + | 0.113401i | ||||
\(749\) | −183255. | − | 317407.i | −0.326657 | − | 0.565786i | ||||
\(750\) | 742159. | 1.31939 | ||||||||
\(751\) | 197292.i | 0.349808i | 0.984585 | + | 0.174904i | \(0.0559616\pi\) | ||||
−0.984585 | + | 0.174904i | \(0.944038\pi\) | |||||||
\(752\) | 84750.8 | + | 146793.i | 0.149868 | + | 0.259579i | ||||
\(753\) | 268384. | − | 71913.3i | 0.473333 | − | 0.126829i | ||||
\(754\) | 354643. | − | 354643.i | 0.623805 | − | 0.623805i | ||||
\(755\) | −1.51560e6 | − | 406104.i | −2.65883 | − | 0.712432i | ||||
\(756\) | −252075. | − | 436607.i | −0.441049 | − | 0.763919i | ||||
\(757\) | 79572.7 | − | 296969.i | 0.138858 | − | 0.518227i | −0.861094 | − | 0.508446i | \(-0.830220\pi\) |
0.999952 | − | 0.00978045i | \(-0.00311326\pi\) | |||||||
\(758\) | −68446.8 | − | 255447.i | −0.119128 | − | 0.444593i | ||||
\(759\) | 118352. | − | 31712.4i | 0.205444 | − | 0.0550485i | ||||
\(760\) | −129243. | − | 34630.7i | −0.223759 | − | 0.0599562i | ||||
\(761\) | 562405. | − | 324705.i | 0.971135 | − | 0.560685i | 0.0715531 | − | 0.997437i | \(-0.477204\pi\) |
0.899582 | + | 0.436752i | \(0.143871\pi\) | |||||||
\(762\) | −69132.3 | + | 258005.i | −0.119061 | + | 0.444343i | ||||
\(763\) | −738379. | − | 738379.i | −1.26832 | − | 1.26832i | ||||
\(764\) | −20044.3 | − | 74806.5i | −0.0343404 | − | 0.128160i | ||||
\(765\) | 493281. | − | 284796.i | 0.842892 | − | 0.486644i | ||||
\(766\) | 144237. | 0.245821 | ||||||||
\(767\) | − | 55025.2i | − | 0.0935343i | ||||||
\(768\) | −26159.0 | + | 15102.9i | −0.0443504 | + | 0.0256057i | ||||
\(769\) | 405138. | − | 405138.i | 0.685094 | − | 0.685094i | −0.276049 | − | 0.961143i | \(-0.589025\pi\) |
0.961143 | + | 0.276049i | \(0.0890253\pi\) | |||||||
\(770\) | 207785. | + | 119965.i | 0.350456 | + | 0.202336i | ||||
\(771\) | −36691.7 | + | 36691.7i | −0.0617247 | + | 0.0617247i | ||||
\(772\) | 136069. | + | 507818.i | 0.228310 | + | 0.852066i | ||||
\(773\) | −499650. | + | 865420.i | −0.836194 | + | 1.44833i | 0.0568605 | + | 0.998382i | \(0.481891\pi\) |
−0.893055 | + | 0.449948i | \(0.851442\pi\) | |||||||
\(774\) | 29450.2 | − | 51009.3i | 0.0491594 | − | 0.0851466i | ||||
\(775\) | −185227. | + | 691277.i | −0.308391 | + | 1.15093i | ||||
\(776\) | − | 217863.i | − | 0.361792i | ||||||
\(777\) | −614952. | + | 514291.i | −1.01859 | + | 0.851857i | ||||
\(778\) | 391812. | 0.647320 | ||||||||
\(779\) | −94415.5 | − | 25298.6i | −0.155585 | − | 0.0416889i | ||||
\(780\) | −574471. | − | 331671.i | −0.944233 | − | 0.545153i | ||||
\(781\) | 66060.8 | + | 38140.2i | 0.108303 | + | 0.0625290i | ||||
\(782\) | 909302. | − | 243647.i | 1.48694 | − | 0.398425i | ||||
\(783\) | 399539. | + | 399539.i | 0.651681 | + | 0.651681i | ||||
\(784\) | 124942. | − | 216406.i | 0.203272 | − | 0.352077i | ||||
\(785\) | 1.11886e6 | + | 1.11886e6i | 1.81567 | + | 1.81567i | ||||
\(786\) | −144045. | − | 249493.i | −0.233159 | − | 0.403843i | ||||
\(787\) | −1.13706e6 | −1.83584 | −0.917920 | − | 0.396765i | \(-0.870133\pi\) | ||||
−0.917920 | + | 0.396765i | \(0.870133\pi\) | |||||||
\(788\) | 46583.6i | 0.0750206i | ||||||||
\(789\) | 415354. | + | 719415.i | 0.667213 | + | 1.15565i | ||||
\(790\) | −1.35592e6 | + | 363319.i | −2.17261 | + | 0.582148i | ||||
\(791\) | −207862. | + | 207862.i | −0.332216 | + | 0.332216i | ||||
\(792\) | −13766.0 | − | 3688.60i | −0.0219462 | − | 0.00588046i | ||||
\(793\) | 543132. | + | 940732.i | 0.863692 | + | 1.49596i | ||||
\(794\) | −92177.0 | + | 344009.i | −0.146211 | + | 0.545669i | ||||
\(795\) | 17930.7 | + | 66918.4i | 0.0283703 | + | 0.105879i | ||||
\(796\) | 80732.7 | − | 21632.3i | 0.127416 | − | 0.0341409i | ||||
\(797\) | 256458. | + | 68717.6i | 0.403737 | + | 0.108181i | 0.454972 | − | 0.890506i | \(-0.349649\pi\) |
−0.0512350 | + | 0.998687i | \(0.516316\pi\) | |||||||
\(798\) | 187878. | − | 108471.i | 0.295033 | − | 0.170337i | ||||
\(799\) | 324915. | − | 1.21260e6i | 0.508952 | − | 1.89943i | ||||
\(800\) | −180882. | − | 180882.i | −0.282629 | − | 0.282629i | ||||
\(801\) | −7318.60 | − | 27313.4i | −0.0114068 | − | 0.0425707i | ||||
\(802\) | −22892.8 | + | 13217.2i | −0.0355919 | + | 0.0205490i | ||||
\(803\) | 217634. | 0.337516 | ||||||||
\(804\) | 124855.i | 0.193149i | ||||||||
\(805\) | 2.17994e6 | − | 1.25859e6i | 3.36398 | − | 1.94219i | ||||
\(806\) | 252263. | − | 252263.i | 0.388314 | − | 0.388314i | ||||
\(807\) | −121439. | − | 70112.8i | −0.186471 | − | 0.107659i | ||||
\(808\) | 41240.2 | − | 41240.2i | 0.0631681 | − | 0.0631681i | ||||
\(809\) | −274732. | − | 1.02531e6i | −0.419771 | − | 1.56661i | −0.775084 | − | 0.631858i | \(-0.782292\pi\) |
0.355313 | − | 0.934747i | \(-0.384374\pi\) | |||||||
\(810\) | 236006. | − | 408774.i | 0.359710 | − | 0.623036i | ||||
\(811\) | −491948. | + | 852079.i | −0.747959 | + | 1.29550i | 0.200841 | + | 0.979624i | \(0.435633\pi\) |
−0.948800 | + | 0.315878i | \(0.897701\pi\) | |||||||
\(812\) | −117059. | + | 436871.i | −0.177539 | + | 0.662584i | ||||
\(813\) | − | 581054.i | − | 0.879095i | ||||||
\(814\) | −8135.24 | + | 91262.7i | −0.0122778 | + | 0.137735i | ||||
\(815\) | −1.13812e6 | −1.71346 | ||||||||
\(816\) | 216089. | + | 57901.0i | 0.324529 | + | 0.0869572i | ||||
\(817\) | 88746.3 | + | 51237.7i | 0.132955 | + | 0.0767619i | ||||
\(818\) | −511707. | − | 295434.i | −0.764742 | − | 0.441524i | ||||
\(819\) | −508474. | + | 136245.i | −0.758056 | + | 0.203120i | ||||
\(820\) | −190581. | − | 190581.i | −0.283434 | − | 0.283434i | ||||
\(821\) | −341399. | + | 591320.i | −0.506496 | + | 0.877276i | 0.493476 | + | 0.869759i | \(0.335726\pi\) |
−0.999972 | + | 0.00751686i | \(0.997607\pi\) | |||||||
\(822\) | −123305. | − | 123305.i | −0.182490 | − | 0.182490i | ||||
\(823\) | 161297. | + | 279374.i | 0.238137 | + | 0.412465i | 0.960180 | − | 0.279384i | \(-0.0901301\pi\) |
−0.722043 | + | 0.691848i | \(0.756797\pi\) | |||||||
\(824\) | −13501.1 | −0.0198846 | ||||||||
\(825\) | 246592.i | 0.362303i | ||||||||
\(826\) | 24810.4 | + | 42972.9i | 0.0363642 | + | 0.0629847i | ||||
\(827\) | −729319. | + | 195421.i | −1.06637 | + | 0.285732i | −0.749000 | − | 0.662570i | \(-0.769466\pi\) |
−0.317367 | + | 0.948303i | \(0.602799\pi\) | |||||||
\(828\) | −105726. | + | 105726.i | −0.154213 | + | 0.154213i | ||||
\(829\) | 922914. | + | 247294.i | 1.34293 | + | 0.359836i | 0.857519 | − | 0.514452i | \(-0.172005\pi\) |
0.485407 | + | 0.874288i | \(0.338671\pi\) | |||||||
\(830\) | 355637. | + | 615982.i | 0.516239 | + | 0.894152i | ||||
\(831\) | −169925. | + | 634168.i | −0.246068 | + | 0.918338i | ||||
\(832\) | 33004.0 | + | 123173.i | 0.0476782 | + | 0.177938i | ||||
\(833\) | −1.78765e6 | + | 479000.i | −2.57628 | + | 0.690313i | ||||
\(834\) | 416368. | + | 111565.i | 0.598612 | + | 0.160398i | ||||
\(835\) | 54339.0 | − | 31372.6i | 0.0779360 | − | 0.0449964i | ||||
\(836\) | 6417.45 | − | 23950.2i | 0.00918226 | − | 0.0342687i | ||||
\(837\) | 284197. | + | 284197.i | 0.405666 | + | 0.405666i | ||||
\(838\) | 129694. | + | 484024.i | 0.184685 | + | 0.689254i | ||||
\(839\) | −603772. | + | 348588.i | −0.857727 | + | 0.495209i | −0.863250 | − | 0.504776i | \(-0.831575\pi\) |
0.00552358 | + | 0.999985i | \(0.498242\pi\) | |||||||
\(840\) | 598191. | 0.847777 | ||||||||
\(841\) | 200381.i | 0.283312i | ||||||||
\(842\) | −53080.9 | + | 30646.2i | −0.0748710 | + | 0.0432268i | ||||
\(843\) | −63900.3 | + | 63900.3i | −0.0899182 | + | 0.0899182i | ||||
\(844\) | −1145.08 | − | 661.113i | −0.00160750 | − | 0.000928091i | ||||
\(845\) | −1.06842e6 | + | 1.06842e6i | −1.49634 | + | 1.49634i | ||||
\(846\) | 51606.2 | + | 192597.i | 0.0721043 | + | 0.269097i | ||||
\(847\) | 559067. | − | 968332.i | 0.779286 | − | 1.34976i | ||||
\(848\) | 6658.93 | − | 11533.6i | 0.00926004 | − | 0.0160389i | ||||
\(849\) | 180816. | − | 674815.i | 0.250854 | − | 0.936201i | ||||
\(850\) | 1.89457e6i | 2.62225i | ||||||||
\(851\) | 786516. | + | 552649.i | 1.08605 | + | 0.763115i | ||||
\(852\) | 190182. | 0.261993 | ||||||||
\(853\) | 142224. | + | 38108.7i | 0.195467 | + | 0.0523753i | 0.355224 | − | 0.934781i | \(-0.384404\pi\) |
−0.159757 | + | 0.987156i | \(0.551071\pi\) | |||||||
\(854\) | −848336. | − | 489787.i | −1.16319 | − | 0.671571i | ||||
\(855\) | −136310. | − | 78698.5i | −0.186464 | − | 0.107655i | ||||
\(856\) | −100880. | + | 27030.8i | −0.137676 | + | 0.0368902i | ||||
\(857\) | −521580. | − | 521580.i | −0.710165 | − | 0.710165i | 0.256405 | − | 0.966570i | \(-0.417462\pi\) |
−0.966570 | + | 0.256405i | \(0.917462\pi\) | |||||||
\(858\) | 61462.3 | − | 106456.i | 0.0834900 | − | 0.144609i | ||||
\(859\) | 737920. | + | 737920.i | 1.00005 | + | 1.00005i | 1.00000 | 5.34024e-5i | \(1.69985e-5\pi\) | |
5.34024e−5 | 1.00000i | \(0.499983\pi\) | ||||||||
\(860\) | 141281. | + | 244706.i | 0.191024 | + | 0.330863i | ||||
\(861\) | 436993. | 0.589479 | ||||||||
\(862\) | − | 781139.i | − | 1.05127i | ||||||
\(863\) | −121321. | − | 210135.i | −0.162898 | − | 0.282148i | 0.773009 | − | 0.634395i | \(-0.218751\pi\) |
−0.935907 | + | 0.352248i | \(0.885418\pi\) | |||||||
\(864\) | −138765. | + | 37182.1i | −0.185889 | + | 0.0498088i | ||||
\(865\) | 1.23176e6 | − | 1.23176e6i | 1.64624 | − | 1.64624i | ||||
\(866\) | 148668. | + | 39835.4i | 0.198235 | + | 0.0531170i | ||||
\(867\) | −520477. | − | 901493.i | −0.692410 | − | 1.19929i | ||||
\(868\) | −83265.8 | + | 310752.i | −0.110516 | + | 0.412453i | ||||
\(869\) | −67326.9 | − | 251268.i | −0.0891558 | − | 0.332734i | ||||
\(870\) | −647585. | + | 173520.i | −0.855576 | + | 0.229251i | ||||
\(871\) | 509131. | + | 136421.i | 0.671109 | + | 0.179823i | ||||
\(872\) | −257693. | + | 148779.i | −0.338898 | + | 0.195663i | ||||
\(873\) | 66330.1 | − | 247547.i | 0.0870326 | − | 0.324810i | ||||
\(874\) | −183942. | − | 183942.i | −0.240801 | − | 0.240801i | ||||
\(875\) | 731268. | + | 2.72913e6i | 0.955125 | + | 3.56458i | ||||
\(876\) | 469908. | − | 271301.i | 0.612356 | − | 0.353544i | ||||
\(877\) | 977479. | 1.27089 | 0.635446 | − | 0.772146i | \(-0.280816\pi\) | ||||
0.635446 | + | 0.772146i | \(0.280816\pi\) | |||||||
\(878\) | 251719.i | 0.326532i | ||||||||
\(879\) | 388744. | − | 224442.i | 0.503137 | − | 0.290486i | ||||
\(880\) | 48344.4 | − | 48344.4i | 0.0624282 | − | 0.0624282i | ||||
\(881\) | −983731. | − | 567957.i | −1.26743 | − | 0.731752i | −0.292930 | − | 0.956134i | \(-0.594630\pi\) |
−0.974501 | + | 0.224382i | \(0.927964\pi\) | |||||||
\(882\) | 207853. | − | 207853.i | 0.267189 | − | 0.267189i | ||||
\(883\) | −192599. | − | 718790.i | −0.247020 | − | 0.921893i | −0.972357 | − | 0.233499i | \(-0.924983\pi\) |
0.725337 | − | 0.688394i | \(-0.241684\pi\) | |||||||
\(884\) | 472216. | − | 817902.i | 0.604277 | − | 1.04664i | ||||
\(885\) | −36777.2 | + | 63699.9i | −0.0469561 | + | 0.0813303i | ||||
\(886\) | 90960.8 | − | 339470.i | 0.115874 | − | 0.432449i | ||||
\(887\) | − | 668201.i | − | 0.849298i | −0.905358 | − | 0.424649i | \(-0.860398\pi\) | ||
0.905358 | − | 0.424649i | \(-0.139602\pi\) | |||||||
\(888\) | 96202.5 | + | 207193.i | 0.122000 | + | 0.262754i | ||||
\(889\) | −1.01688e6 | −1.28666 | ||||||||
\(890\) | 131030. | + | 35109.4i | 0.165421 | + | 0.0443245i | ||||
\(891\) | 75750.3 | + | 43734.5i | 0.0954177 | + | 0.0550895i | ||||
\(892\) | 123353. | + | 71217.9i | 0.155032 | + | 0.0895075i | ||||
\(893\) | −335081. | + | 89784.8i | −0.420191 | + | 0.112590i | ||||
\(894\) | −103281. | − | 103281.i | −0.129225 | − | 0.129225i | ||||
\(895\) | −1.33499e6 | + | 2.31226e6i | −1.66660 | + | 2.88663i | ||||
\(896\) | −81312.6 | − | 81312.6i | −0.101284 | − | 0.101284i | ||||
\(897\) | −644821. | − | 1.11686e6i | −0.801410 | − | 1.38808i | ||||
\(898\) | −778235. | −0.965068 | ||||||||
\(899\) | − | 360565.i | − | 0.446133i | ||||||
\(900\) | −150457. | − | 260599.i | −0.185749 | − | 0.321728i | ||||
\(901\) | −95274.8 | + | 25528.8i | −0.117362 | + | 0.0314471i | ||||
\(902\) | 35316.8 | − | 35316.8i | 0.0434078 | − | 0.0434078i | ||||
\(903\) | −442526. | − | 118574.i | −0.542704 | − | 0.145417i | ||||
\(904\) | 41882.8 | + | 72543.2i | 0.0512506 | + | 0.0887687i | ||||
\(905\) | 432263. | − | 1.61323e6i | 0.527777 | − | 1.96969i | ||||
\(906\) | −187627. | − | 700232.i | −0.228580 | − | 0.853072i | ||||
\(907\) | 1.31389e6 | − | 352054.i | 1.59714 | − | 0.427952i | 0.652962 | − | 0.757390i | \(-0.273526\pi\) |
0.944177 | + | 0.329438i | \(0.106859\pi\) | |||||||
\(908\) | 357961. | + | 95915.3i | 0.434174 | + | 0.116337i | ||||
\(909\) | 59415.2 | − | 34303.4i | 0.0719068 | − | 0.0415154i | ||||
\(910\) | 653608. | − | 2.43930e6i | 0.789286 | − | 2.94565i | ||||
\(911\) | 265206. | + | 265206.i | 0.319556 | + | 0.319556i | 0.848597 | − | 0.529040i | \(-0.177448\pi\) |
−0.529040 | + | 0.848597i | \(0.677448\pi\) | |||||||
\(912\) | −15999.9 | − | 59712.6i | −0.0192366 | − | 0.0717920i | ||||
\(913\) | −114148. | + | 65903.5i | −0.136939 | + | 0.0790618i | ||||
\(914\) | 752734. | 0.901050 | ||||||||
\(915\) | − | 1.45205e6i | − | 1.73436i | ||||||
\(916\) | −356765. | + | 205979.i | −0.425199 | + | 0.245489i | ||||
\(917\) | 775524. | − | 775524.i | 0.922267 | − | 0.922267i | ||||
\(918\) | 921442. | + | 531995.i | 1.09341 | + | 0.631280i | ||||
\(919\) | 740422. | − | 740422.i | 0.876694 | − | 0.876694i | −0.116497 | − | 0.993191i | \(-0.537166\pi\) |
0.993191 | + | 0.116497i | \(0.0371664\pi\) | |||||||
\(920\) | −185647. | − | 692844.i | −0.219337 | − | 0.818577i | ||||
\(921\) | −30691.7 | + | 53159.6i | −0.0361828 | + | 0.0626704i | ||||
\(922\) | −501259. | + | 868206.i | −0.589658 | + | 1.02132i | ||||
\(923\) | 207800. | − | 775522.i | 0.243918 | − | 0.910313i | ||||
\(924\) | 110851.i | 0.129837i | ||||||||
\(925\) | −1.48402e6 | + | 1.24110e6i | −1.73443 | + | 1.45052i | ||||
\(926\) | −893796. | −1.04236 | ||||||||
\(927\) | −15340.7 | − | 4110.53i | −0.0178520 | − | 0.00478342i | ||||
\(928\) | 111614. | + | 64440.1i | 0.129605 | + | 0.0748273i | ||||
\(929\) | −357768. | − | 206558.i | −0.414544 | − | 0.239337i | 0.278196 | − | 0.960524i | \(-0.410263\pi\) |
−0.692740 | + | 0.721187i | \(0.743597\pi\) | |||||||
\(930\) | −460636. | + | 123427.i | −0.532589 | + | 0.142707i | ||||
\(931\) | 361624. | + | 361624.i | 0.417213 | + | 0.417213i | ||||
\(932\) | −96942.6 | + | 167910.i | −0.111605 | + | 0.193305i | ||||
\(933\) | −585958. | − | 585958.i | −0.673136 | − | 0.673136i | ||||
\(934\) | −44646.9 | − | 77330.7i | −0.0511797 | − | 0.0886458i | ||||
\(935\) | −506362. | −0.579212 | ||||||||
\(936\) | 150004.i | 0.171218i | ||||||||
\(937\) | 607759. | + | 1.05267e6i | 0.692233 | + | 1.19898i | 0.971105 | + | 0.238655i | \(0.0767064\pi\) |
−0.278871 | + | 0.960328i | \(0.589960\pi\) | |||||||
\(938\) | −459126. | + | 123022.i | −0.521826 | + | 0.139823i | ||||
\(939\) | −378476. | + | 378476.i | −0.429247 | + | 0.429247i | ||||
\(940\) | −923943. | − | 247570.i | −1.04566 | − | 0.280183i | ||||
\(941\) | 738032. | + | 1.27831e6i | 0.833481 | + | 1.44363i | 0.895261 | + | 0.445542i | \(0.146989\pi\) |
−0.0617802 | + | 0.998090i | \(0.519678\pi\) | |||||||
\(942\) | −189211. | + | 706144.i | −0.213228 | + | 0.795777i | ||||
\(943\) | −135620. | − | 506139.i | −0.152510 | − | 0.569176i | ||||
\(944\) | 13657.9 | − | 3659.63i | 0.0153264 | − | 0.00410670i | ||||
\(945\) | 2.74809e6 | + | 736349.i | 3.07729 | + | 0.824556i | ||||
\(946\) | −45346.8 | + | 26181.0i | −0.0506715 | + | 0.0292552i | ||||
\(947\) | −240252. | + | 896634.i | −0.267897 | + | 0.999805i | 0.692556 | + | 0.721364i | \(0.256484\pi\) |
−0.960453 | + | 0.278441i | \(0.910182\pi\) | |||||||
\(948\) | −458600. | − | 458600.i | −0.510290 | − | 0.510290i | ||||
\(949\) | −592869. | − | 2.21262e6i | −0.658304 | − | 2.45682i | ||||
\(950\) | 453392. | − | 261766.i | 0.502374 | − | 0.290046i | ||||
\(951\) | −150272. | −0.166156 | ||||||||
\(952\) | 851673.i | 0.939721i | ||||||||
\(953\) | 788093. | − | 455006.i | 0.867744 | − | 0.500992i | 0.00114632 | − | 0.999999i | \(-0.499635\pi\) |
0.866598 | + | 0.499007i | \(0.166302\pi\) | |||||||
\(954\) | 11077.7 | − | 11077.7i | 0.0121718 | − | 0.0121718i | ||||
\(955\) | 378489. | + | 218521.i | 0.414999 | + | 0.239600i | ||||
\(956\) | −274997. | + | 274997.i | −0.300893 | + | 0.300893i | ||||
\(957\) | −32155.2 | − | 120005.i | −0.0351097 | − | 0.131031i | ||||
\(958\) | 300889. | − | 521156.i | 0.327851 | − | 0.567854i | ||||
\(959\) | 331933. | − | 574924.i | 0.360922 | − | 0.625135i | ||||
\(960\) | 44117.7 | − | 164650.i | 0.0478708 | − | 0.178656i | ||||
\(961\) | 667046.i | 0.722286i | ||||||||
\(962\) | 950004. | − | 165906.i | 1.02654 | − | 0.179272i | ||||
\(963\) | −122855. | −0.132477 | ||||||||
\(964\) | −65836.6 | − | 17640.9i | −0.0708457 | − | 0.0189830i | ||||
\(965\) | −2.56934e6 | − | 1.48341e6i | −2.75910 | − | 1.59297i | ||||
\(966\) | 1.00717e6 | + | 581489.i | 1.07932 | + | 0.623143i | ||||
\(967\) | −1.40705e6 | + | 377019.i | −1.50473 | + | 0.403190i | −0.914680 | − | 0.404180i | \(-0.867557\pi\) |
−0.590046 | + | 0.807370i | \(0.700890\pi\) | |||||||
\(968\) | −225297. | − | 225297.i | −0.240439 | − | 0.240439i | ||||
\(969\) | −228924. | + | 396509.i | −0.243806 | + | 0.422285i | ||||
\(970\) | 869350. | + | 869350.i | 0.923956 | + | 0.923956i | ||||
\(971\) | −393371. | − | 681338.i | −0.417219 | − | 0.722644i | 0.578440 | − | 0.815725i | \(-0.303662\pi\) |
−0.995659 | + | 0.0930811i | \(0.970328\pi\) | |||||||
\(972\) | −296189. | −0.313499 | ||||||||
\(973\) | 1.64103e6i | 1.73337i | ||||||||
\(974\) | 360697. | + | 624746.i | 0.380211 | + | 0.658545i | ||||
\(975\) | 2.50703e6 | − | 671758.i | 2.63725 | − | 0.706648i | ||||
\(976\) | −197378. | + | 197378.i | −0.207205 | + | 0.207205i | ||||
\(977\) | −695361. | − | 186321.i | −0.728486 | − | 0.195197i | −0.124531 | − | 0.992216i | \(-0.539743\pi\) |
−0.603955 | + | 0.797018i | \(0.706409\pi\) | |||||||
\(978\) | −262915. | − | 455382.i | −0.274877 | − | 0.476100i | ||||
\(979\) | −6506.17 | + | 24281.3i | −0.00678828 | + | 0.0253342i | ||||
\(980\) | 364975. | + | 1.36211e6i | 0.380024 | + | 1.41827i | ||||
\(981\) | −338101. | + | 90594.0i | −0.351325 | + | 0.0941372i | ||||
\(982\) | −1.20384e6 | − | 322568.i | −1.24838 | − | 0.334502i | ||||
\(983\) | 1.09781e6 | − | 633818.i | 1.13610 | − | 0.655930i | 0.190641 | − | 0.981660i | \(-0.438943\pi\) |
0.945463 | + | 0.325730i | \(0.105610\pi\) | |||||||
\(984\) | 32229.1 | − | 120281.i | 0.0332857 | − | 0.124224i | ||||
\(985\) | −185886. | − | 185886.i | −0.191590 | − | 0.191590i | ||||
\(986\) | −247049. | − | 921998.i | −0.254114 | − | 0.948366i | ||||
\(987\) | 1.34311e6 | − | 775446.i | 1.37873 | − | 0.796008i | ||||
\(988\) | −260977. | −0.267355 | ||||||||
\(989\) | 549346.i | 0.561634i | ||||||||
\(990\) | 69650.3 | − | 40212.6i | 0.0710645 | − | 0.0410291i | ||||
\(991\) | −575248. | + | 575248.i | −0.585744 | + | 0.585744i | −0.936476 | − | 0.350732i | \(-0.885933\pi\) |
0.350732 | + | 0.936476i | \(0.385933\pi\) | |||||||
\(992\) | 79392.2 | + | 45837.1i | 0.0806779 | + | 0.0465794i | ||||
\(993\) | 558445. | − | 558445.i | 0.566346 | − | 0.566346i | ||||
\(994\) | 187391. | + | 699353.i | 0.189660 | + | 0.707821i | ||||
\(995\) | −235832. | + | 408473.i | −0.238208 | + | 0.412589i | ||||
\(996\) | −164310. | + | 284594.i | −0.165633 | + | 0.286884i | ||||
\(997\) | −126440. | + | 471882.i | −0.127203 | + | 0.474726i | −0.999909 | − | 0.0135196i | \(-0.995696\pi\) |
0.872706 | + | 0.488246i | \(0.162363\pi\) | |||||||
\(998\) | 113514.i | 0.113970i | ||||||||
\(999\) | 186908. | + | 1.07027e6i | 0.187283 | + | 1.07241i |
(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 | 74.5.g.a.45.5 | ✓ | 28 | |
37.14 | odd | 12 | inner | 74.5.g.a.51.5 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.g.a.45.5 | ✓ | 28 | 1.1 | even | 1 | trivial | |
74.5.g.a.51.5 | yes | 28 | 37.14 | odd | 12 | inner |