Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [124,5,Mod(35,124)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(124, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 6]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("124.35");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 124 = 2^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 124.l (of order \(10\), 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: | \(12.8178754224\) |
Analytic rank: | \(0\) |
Dimension: | \(248\) |
Relative dimension: | \(62\) over \(\Q(\zeta_{10})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 35.7 | ||
Character | \(\chi\) | \(=\) | 124.35 |
Dual form | 124.5.l.a.39.7 |
$q$-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 \(\left(\mathbb{Z}/124\mathbb{Z}\right)^\times\).
\(n\) | \(63\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.83059 | − | 1.15178i | −0.957647 | − | 0.287944i | ||||
\(3\) | 14.8017 | + | 4.80936i | 1.64463 | + | 0.534373i | 0.977567 | − | 0.210626i | \(-0.0675503\pi\) |
0.667065 | + | 0.744999i | \(0.267550\pi\) | |||||||
\(4\) | 13.3468 | + | 8.82396i | 0.834176 | + | 0.551498i | ||||
\(5\) | −27.7531 | −1.11012 | −0.555062 | − | 0.831809i | \(-0.687305\pi\) | ||||
−0.555062 | + | 0.831809i | \(0.687305\pi\) | |||||||
\(6\) | −51.1599 | − | 35.4709i | −1.42111 | − | 0.985303i | ||||
\(7\) | −6.94187 | − | 9.55467i | −0.141671 | − | 0.194993i | 0.732285 | − | 0.680998i | \(-0.238454\pi\) |
−0.873956 | + | 0.486005i | \(0.838454\pi\) | |||||||
\(8\) | −40.9630 | − | 49.1735i | −0.640046 | − | 0.768336i | ||||
\(9\) | 130.430 | + | 94.7627i | 1.61024 | + | 1.16991i | ||||
\(10\) | 106.311 | + | 31.9653i | 1.06311 | + | 0.319653i | ||||
\(11\) | 106.777 | + | 146.966i | 0.882454 | + | 1.21459i | 0.975735 | + | 0.218954i | \(0.0702645\pi\) |
−0.0932811 | + | 0.995640i | \(0.529736\pi\) | |||||||
\(12\) | 155.118 | + | 194.799i | 1.07721 | + | 1.35277i | ||||
\(13\) | 6.70197 | − | 20.6265i | 0.0396566 | − | 0.122051i | −0.929268 | − | 0.369405i | \(-0.879561\pi\) |
0.968925 | + | 0.247355i | \(0.0795614\pi\) | |||||||
\(14\) | 15.5866 | + | 44.5955i | 0.0795235 | + | 0.227528i | ||||
\(15\) | −410.792 | − | 133.475i | −1.82574 | − | 0.593220i | ||||
\(16\) | 100.275 | + | 235.544i | 0.391700 | + | 0.920093i | ||||
\(17\) | 259.665 | + | 188.658i | 0.898495 | + | 0.652795i | 0.938079 | − | 0.346421i | \(-0.112603\pi\) |
−0.0395839 | + | 0.999216i | \(0.512603\pi\) | |||||||
\(18\) | −390.477 | − | 513.223i | −1.20518 | − | 1.58402i | ||||
\(19\) | −222.161 | + | 72.1845i | −0.615404 | + | 0.199957i | −0.600099 | − | 0.799926i | \(-0.704872\pi\) |
−0.0153056 | + | 0.999883i | \(0.504872\pi\) | |||||||
\(20\) | −370.415 | − | 244.892i | −0.926039 | − | 0.612230i | ||||
\(21\) | −56.7996 | − | 174.811i | −0.128797 | − | 0.396397i | ||||
\(22\) | −239.747 | − | 685.949i | −0.495345 | − | 1.41725i | ||||
\(23\) | −377.641 | + | 519.778i | −0.713877 | + | 0.982568i | 0.285828 | + | 0.958281i | \(0.407731\pi\) |
−0.999705 | + | 0.0242867i | \(0.992269\pi\) | |||||||
\(24\) | −369.828 | − | 924.857i | −0.642062 | − | 1.60565i | ||||
\(25\) | 145.234 | 0.232374 | ||||||||
\(26\) | −49.4297 | + | 71.2926i | −0.0731208 | + | 0.105462i | ||||
\(27\) | 733.847 | + | 1010.05i | 1.00665 | + | 1.38553i | ||||
\(28\) | −8.34189 | − | 188.779i | −0.0106402 | − | 0.240790i | ||||
\(29\) | 383.845 | + | 1181.35i | 0.456415 | + | 1.40470i | 0.869466 | + | 0.493994i | \(0.164463\pi\) |
−0.413050 | + | 0.910708i | \(0.635537\pi\) | |||||||
\(30\) | 1419.84 | + | 984.427i | 1.57760 | + | 1.09381i | ||||
\(31\) | 913.603 | − | 298.079i | 0.950679 | − | 0.310176i | ||||
\(32\) | −112.820 | − | 1017.77i | −0.110176 | − | 0.993912i | ||||
\(33\) | 873.667 | + | 2688.87i | 0.802266 | + | 2.46912i | ||||
\(34\) | −777.379 | − | 1021.75i | −0.672473 | − | 0.883864i | ||||
\(35\) | 192.658 | + | 265.171i | 0.157272 | + | 0.216466i | ||||
\(36\) | 904.639 | + | 2415.69i | 0.698024 | + | 1.86396i | ||||
\(37\) | −2245.75 | −1.64043 | −0.820217 | − | 0.572052i | \(-0.806147\pi\) | ||||
−0.820217 | + | 0.572052i | \(0.806147\pi\) | |||||||
\(38\) | 934.148 | − | 20.6293i | 0.646917 | − | 0.0142862i | ||||
\(39\) | 198.401 | − | 273.075i | 0.130441 | − | 0.179537i | ||||
\(40\) | 1136.85 | + | 1364.72i | 0.710530 | + | 0.852948i | ||||
\(41\) | 507.784 | + | 1562.80i | 0.302072 | + | 0.929683i | 0.980753 | + | 0.195250i | \(0.0625519\pi\) |
−0.678681 | + | 0.734433i | \(0.737448\pi\) | |||||||
\(42\) | 16.2325 | + | 735.050i | 0.00920210 | + | 0.416695i | ||||
\(43\) | 1968.46 | − | 639.591i | 1.06461 | − | 0.345912i | 0.276222 | − | 0.961094i | \(-0.410917\pi\) |
0.788385 | + | 0.615182i | \(0.210917\pi\) | |||||||
\(44\) | 128.312 | + | 2903.72i | 0.0662766 | + | 1.49986i | ||||
\(45\) | −3619.82 | − | 2629.96i | −1.78757 | − | 1.29874i | ||||
\(46\) | 2045.26 | − | 1556.10i | 0.966567 | − | 0.735396i | ||||
\(47\) | −1617.60 | − | 525.591i | −0.732278 | − | 0.237931i | −0.0809396 | − | 0.996719i | \(-0.525792\pi\) |
−0.651338 | + | 0.758788i | \(0.725792\pi\) | |||||||
\(48\) | 351.429 | + | 3968.70i | 0.152530 | + | 1.72253i | ||||
\(49\) | 698.848 | − | 2150.83i | 0.291065 | − | 0.895807i | ||||
\(50\) | −556.330 | − | 167.277i | −0.222532 | − | 0.0669106i | ||||
\(51\) | 2936.16 | + | 4041.28i | 1.12886 | + | 1.55374i | ||||
\(52\) | 271.458 | − | 216.161i | 0.100391 | − | 0.0799412i | ||||
\(53\) | 509.911 | + | 370.472i | 0.181528 | + | 0.131888i | 0.674838 | − | 0.737966i | \(-0.264213\pi\) |
−0.493311 | + | 0.869853i | \(0.664213\pi\) | |||||||
\(54\) | −1647.71 | − | 4714.33i | −0.565058 | − | 1.61671i | ||||
\(55\) | −2963.39 | − | 4078.76i | −0.979633 | − | 1.34835i | ||||
\(56\) | −185.477 | + | 732.744i | −0.0591445 | + | 0.233656i | ||||
\(57\) | −3635.52 | −1.11897 | ||||||||
\(58\) | −109.697 | − | 4967.39i | −0.0326092 | − | 1.47663i | ||||
\(59\) | 2318.05 | + | 753.181i | 0.665916 | + | 0.216369i | 0.622419 | − | 0.782684i | \(-0.286150\pi\) |
0.0434971 | + | 0.999054i | \(0.486150\pi\) | |||||||
\(60\) | −4305.00 | − | 5406.28i | −1.19583 | − | 1.50174i | ||||
\(61\) | 2692.22 | 0.723522 | 0.361761 | − | 0.932271i | \(-0.382176\pi\) | ||||
0.361761 | + | 0.932271i | \(0.382176\pi\) | |||||||
\(62\) | −3842.96 | + | 89.5521i | −0.999729 | + | 0.0232966i | ||||
\(63\) | − | 1904.04i | − | 0.479728i | ||||||
\(64\) | −740.073 | + | 4028.59i | −0.180682 | + | 0.983542i | ||||
\(65\) | −186.000 | + | 572.450i | −0.0440238 | + | 0.135491i | ||||
\(66\) | −249.682 | − | 11306.2i | −0.0573190 | − | 2.59555i | ||||
\(67\) | − | 2951.88i | − | 0.657580i | −0.944403 | − | 0.328790i | \(-0.893359\pi\) | ||
0.944403 | − | 0.328790i | \(-0.106641\pi\) | |||||||
\(68\) | 1800.99 | + | 4809.26i | 0.389489 | + | 1.04006i | ||||
\(69\) | −8089.53 | + | 5877.38i | −1.69912 | + | 1.23449i | ||||
\(70\) | −432.577 | − | 1237.66i | −0.0882809 | − | 0.252584i | ||||
\(71\) | 4437.89 | − | 6108.23i | 0.880359 | − | 1.21171i | −0.0959626 | − | 0.995385i | \(-0.530593\pi\) |
0.976321 | − | 0.216325i | \(-0.0694071\pi\) | |||||||
\(72\) | −682.968 | − | 10295.4i | −0.131745 | − | 1.98600i | ||||
\(73\) | −1251.66 | + | 909.383i | −0.234877 | + | 0.170648i | −0.698998 | − | 0.715124i | \(-0.746370\pi\) |
0.464121 | + | 0.885772i | \(0.346370\pi\) | |||||||
\(74\) | 8602.56 | + | 2586.61i | 1.57096 | + | 0.472353i | ||||
\(75\) | 2149.70 | + | 698.480i | 0.382169 | + | 0.124174i | ||||
\(76\) | −3602.10 | − | 996.907i | −0.623632 | − | 0.172595i | ||||
\(77\) | 662.978 | − | 2040.44i | 0.111820 | − | 0.344145i | ||||
\(78\) | −1074.51 | + | 817.526i | −0.176613 | + | 0.134373i | ||||
\(79\) | −604.434 | + | 831.932i | −0.0968489 | + | 0.133301i | −0.854691 | − | 0.519137i | \(-0.826254\pi\) |
0.757842 | + | 0.652438i | \(0.226254\pi\) | |||||||
\(80\) | −2782.95 | − | 6537.06i | −0.434836 | − | 1.02142i | ||||
\(81\) | 1969.07 | + | 6060.17i | 0.300117 | + | 0.923665i | ||||
\(82\) | −145.117 | − | 6571.29i | −0.0215820 | − | 0.977288i | ||||
\(83\) | −9249.60 | + | 3005.38i | −1.34266 | + | 0.436257i | −0.890218 | − | 0.455536i | \(-0.849448\pi\) |
−0.452444 | + | 0.891793i | \(0.649448\pi\) | |||||||
\(84\) | 784.433 | − | 2834.37i | 0.111172 | − | 0.401696i | ||||
\(85\) | −7206.51 | − | 5235.83i | −0.997440 | − | 0.724683i | ||||
\(86\) | −8277.03 | + | 182.786i | −1.11912 | + | 0.0247142i | ||||
\(87\) | 19332.1i | 2.55411i | ||||||||
\(88\) | 2852.93 | − | 11270.8i | 0.368405 | − | 1.45542i | ||||
\(89\) | 7451.21 | − | 5413.62i | 0.940690 | − | 0.683451i | −0.00789670 | − | 0.999969i | \(-0.502514\pi\) |
0.948587 | + | 0.316518i | \(0.102514\pi\) | |||||||
\(90\) | 10836.9 | + | 14243.5i | 1.33789 | + | 1.75846i | ||||
\(91\) | −243.604 | + | 79.1517i | −0.0294172 | + | 0.00955823i | ||||
\(92\) | −9626.81 | + | 3605.10i | −1.13738 | + | 0.425933i | ||||
\(93\) | 14956.4 | − | 18.2283i | 1.72927 | − | 0.00210756i | ||||
\(94\) | 5591.00 | + | 3876.44i | 0.632753 | + | 0.438710i | ||||
\(95\) | 6165.65 | − | 2003.34i | 0.683175 | − | 0.221977i | ||||
\(96\) | 3224.88 | − | 15607.2i | 0.349922 | − | 1.69349i | ||||
\(97\) | −6048.22 | + | 4394.29i | −0.642812 | + | 0.467030i | −0.860815 | − | 0.508918i | \(-0.830046\pi\) |
0.218003 | + | 0.975948i | \(0.430046\pi\) | |||||||
\(98\) | −5154.28 | + | 7434.04i | −0.536680 | + | 0.774056i | ||||
\(99\) | 29287.2i | 2.98818i | ||||||||
\(100\) | 1938.41 | + | 1281.54i | 0.193841 | + | 0.128154i | ||||
\(101\) | −5615.83 | − | 4080.14i | −0.550518 | − | 0.399974i | 0.277459 | − | 0.960738i | \(-0.410508\pi\) |
−0.827976 | + | 0.560763i | \(0.810508\pi\) | |||||||
\(102\) | −6592.57 | − | 18862.3i | −0.633657 | − | 1.81298i | ||||
\(103\) | 15780.4 | − | 5127.37i | 1.48745 | − | 0.483303i | 0.551124 | − | 0.834423i | \(-0.314199\pi\) |
0.936331 | + | 0.351120i | \(0.114199\pi\) | |||||||
\(104\) | −1288.81 | + | 515.365i | −0.119158 | + | 0.0476484i | ||||
\(105\) | 1576.36 | + | 4851.55i | 0.142981 | + | 0.440050i | ||||
\(106\) | −1526.56 | − | 2006.43i | −0.135863 | − | 0.178572i | ||||
\(107\) | 5955.16 | − | 8196.58i | 0.520147 | − | 0.715921i | −0.465442 | − | 0.885078i | \(-0.654105\pi\) |
0.985589 | + | 0.169157i | \(0.0541046\pi\) | |||||||
\(108\) | 881.848 | + | 19956.4i | 0.0756042 | + | 1.71094i | ||||
\(109\) | 3987.10 | − | 12271.0i | 0.335586 | − | 1.03283i | −0.630846 | − | 0.775908i | \(-0.717292\pi\) |
0.966433 | − | 0.256920i | \(-0.0827078\pi\) | |||||||
\(110\) | 6653.71 | + | 19037.2i | 0.549894 | + | 1.57332i | ||||
\(111\) | −33241.0 | − | 10800.6i | −2.69791 | − | 0.876604i | ||||
\(112\) | 1554.44 | − | 2593.21i | 0.123919 | − | 0.206729i | ||||
\(113\) | −1145.40 | + | 832.183i | −0.0897017 | + | 0.0651721i | −0.631732 | − | 0.775187i | \(-0.717656\pi\) |
0.542030 | + | 0.840359i | \(0.317656\pi\) | |||||||
\(114\) | 13926.2 | + | 4187.31i | 1.07157 | + | 0.322200i | ||||
\(115\) | 10480.7 | − | 14425.4i | 0.792492 | − | 1.09077i | ||||
\(116\) | −5301.11 | + | 19154.4i | −0.393959 | + | 1.42348i | ||||
\(117\) | 2828.76 | − | 2055.22i | 0.206645 | − | 0.150136i | ||||
\(118\) | −8012.01 | − | 5555.01i | −0.575410 | − | 0.398952i | ||||
\(119\) | − | 3790.65i | − | 0.267682i | ||||||
\(120\) | 10263.9 | + | 25667.6i | 0.712768 | + | 1.78247i | ||||
\(121\) | −5673.33 | + | 17460.7i | −0.387496 | + | 1.19259i | ||||
\(122\) | −10312.8 | − | 3100.84i | −0.692878 | − | 0.208334i | ||||
\(123\) | 25574.2i | 1.69041i | ||||||||
\(124\) | 14823.9 | + | 4083.19i | 0.964095 | + | 0.265556i | ||||
\(125\) | 13315.0 | 0.852160 | ||||||||
\(126\) | −2193.03 | + | 7293.60i | −0.138135 | + | 0.459410i | ||||
\(127\) | 7377.80 | + | 2397.19i | 0.457425 | + | 0.148626i | 0.528661 | − | 0.848833i | \(-0.322694\pi\) |
−0.0712361 | + | 0.997459i | \(0.522694\pi\) | |||||||
\(128\) | 7474.94 | − | 14579.5i | 0.456234 | − | 0.889860i | ||||
\(129\) | 32212.5 | 1.93573 | ||||||||
\(130\) | 1371.83 | − | 1978.59i | 0.0811731 | − | 0.117076i | ||||
\(131\) | −17639.7 | − | 24278.9i | −1.02789 | − | 1.41477i | −0.906518 | − | 0.422166i | \(-0.861270\pi\) |
−0.121375 | − | 0.992607i | \(-0.538730\pi\) | |||||||
\(132\) | −12065.8 | + | 43597.1i | −0.692483 | + | 2.50213i | ||||
\(133\) | 2231.91 | + | 1621.58i | 0.126175 | + | 0.0916716i | ||||
\(134\) | −3399.90 | + | 11307.4i | −0.189346 | + | 0.629730i | ||||
\(135\) | −20366.5 | − | 28032.1i | −1.11750 | − | 1.53811i | ||||
\(136\) | −1359.68 | − | 20496.6i | −0.0735123 | − | 1.10817i | ||||
\(137\) | 3565.51 | − | 10973.5i | 0.189968 | − | 0.584662i | −0.810030 | − | 0.586388i | \(-0.800549\pi\) |
0.999999 | + | 0.00172596i | \(0.000549391\pi\) | |||||||
\(138\) | 37757.1 | − | 13196.5i | 1.98262 | − | 0.692949i | ||||
\(139\) | −27046.0 | − | 8787.77i | −1.39982 | − | 0.454830i | −0.490689 | − | 0.871335i | \(-0.663255\pi\) |
−0.909133 | + | 0.416505i | \(0.863255\pi\) | |||||||
\(140\) | 231.513 | + | 5239.21i | 0.0118119 | + | 0.267306i | ||||
\(141\) | −21415.5 | − | 15559.3i | −1.07718 | − | 0.782619i | ||||
\(142\) | −24035.0 | + | 18286.7i | −1.19198 | + | 0.906896i | ||||
\(143\) | 3747.01 | − | 1217.48i | 0.183237 | − | 0.0595373i | ||||
\(144\) | −9241.88 | + | 40224.2i | −0.445693 | + | 1.93983i | ||||
\(145\) | −10652.9 | − | 32786.2i | −0.506677 | − | 1.55939i | ||||
\(146\) | 5841.99 | − | 2041.84i | 0.274066 | − | 0.0957892i | ||||
\(147\) | 20688.3 | − | 28474.9i | 0.957390 | − | 1.31773i | ||||
\(148\) | −29973.7 | − | 19816.5i | −1.36841 | − | 0.904696i | ||||
\(149\) | −15455.5 | −0.696161 | −0.348080 | − | 0.937465i | \(-0.613166\pi\) | ||||
−0.348080 | + | 0.937465i | \(0.613166\pi\) | |||||||
\(150\) | −7430.13 | − | 5151.57i | −0.330228 | − | 0.228958i | ||||
\(151\) | 1252.63 | + | 1724.10i | 0.0549375 | + | 0.0756149i | 0.835602 | − | 0.549336i | \(-0.185119\pi\) |
−0.780664 | + | 0.624951i | \(0.785119\pi\) | |||||||
\(152\) | 12649.9 | + | 7967.55i | 0.547522 | + | 0.344856i | ||||
\(153\) | 15990.3 | + | 49213.1i | 0.683084 | + | 2.10232i | ||||
\(154\) | −4889.72 | + | 7052.47i | −0.206178 | + | 0.297372i | ||||
\(155\) | −25355.3 | + | 8272.61i | −1.05537 | + | 0.344333i | ||||
\(156\) | 5057.63 | − | 1894.01i | 0.207825 | − | 0.0778274i | ||||
\(157\) | −5873.54 | − | 18076.9i | −0.238287 | − | 0.733373i | −0.996668 | − | 0.0815613i | \(-0.974009\pi\) |
0.758381 | − | 0.651811i | \(-0.225991\pi\) | |||||||
\(158\) | 3273.54 | − | 2490.62i | 0.131130 | − | 0.0997683i | ||||
\(159\) | 5765.81 | + | 7935.96i | 0.228069 | + | 0.313910i | ||||
\(160\) | 3131.10 | + | 28246.1i | 0.122309 | + | 1.10336i | ||||
\(161\) | 7587.84 | 0.292730 | ||||||||
\(162\) | −562.731 | − | 25481.9i | −0.0214423 | − | 0.970962i | ||||
\(163\) | 14666.0 | − | 20186.1i | 0.551998 | − | 0.759760i | −0.438283 | − | 0.898837i | \(-0.644413\pi\) |
0.990282 | + | 0.139076i | \(0.0444134\pi\) | |||||||
\(164\) | −7012.77 | + | 25339.0i | −0.260737 | + | 0.942112i | ||||
\(165\) | −24247.0 | − | 74624.5i | −0.890614 | − | 2.74103i | ||||
\(166\) | 38892.9 | − | 858.893i | 1.41141 | − | 0.0311690i | ||||
\(167\) | 5729.92 | − | 1861.76i | 0.205455 | − | 0.0667562i | −0.204482 | − | 0.978870i | \(-0.565551\pi\) |
0.409936 | + | 0.912114i | \(0.365551\pi\) | |||||||
\(168\) | −6269.40 | + | 9953.82i | −0.222130 | + | 0.352672i | ||||
\(169\) | 22725.8 | + | 16511.3i | 0.795693 | + | 0.578105i | ||||
\(170\) | 21574.7 | + | 28356.6i | 0.746528 | + | 0.981198i | ||||
\(171\) | −35816.8 | − | 11637.6i | −1.22488 | − | 0.397988i | ||||
\(172\) | 31916.4 | + | 8833.11i | 1.07884 | + | 0.298577i | ||||
\(173\) | −15993.1 | + | 49221.8i | −0.534369 | + | 1.64462i | 0.210640 | + | 0.977564i | \(0.432445\pi\) |
−0.745009 | + | 0.667054i | \(0.767555\pi\) | |||||||
\(174\) | 22266.2 | − | 74053.3i | 0.735442 | − | 2.44594i | ||||
\(175\) | −1008.19 | − | 1387.66i | −0.0329206 | − | 0.0453113i | ||||
\(176\) | −23909.8 | + | 39887.7i | −0.771881 | + | 1.28770i | ||||
\(177\) | 30688.8 | + | 22296.7i | 0.979565 | + | 0.711695i | ||||
\(178\) | −34777.8 | + | 12155.2i | −1.09764 | + | 0.383639i | ||||
\(179\) | 27024.3 | + | 37195.7i | 0.843428 | + | 1.16088i | 0.985273 | + | 0.170990i | \(0.0546965\pi\) |
−0.141845 | + | 0.989889i | \(0.545303\pi\) | |||||||
\(180\) | −25106.5 | − | 67042.7i | −0.774892 | − | 2.06922i | ||||
\(181\) | −11381.8 | −0.347419 | −0.173710 | − | 0.984797i | \(-0.555575\pi\) | ||||
−0.173710 | + | 0.984797i | \(0.555575\pi\) | |||||||
\(182\) | 1024.31 | − | 22.6204i | 0.0309236 | − | 0.000682901i | ||||
\(183\) | 39849.5 | + | 12947.9i | 1.18993 | + | 0.386631i | ||||
\(184\) | 41028.6 | − | 2721.71i | 1.21186 | − | 0.0803908i | ||||
\(185\) | 62326.6 | 1.82108 | ||||||||
\(186\) | −57312.9 | − | 17156.6i | −1.65663 | − | 0.495914i | ||||
\(187\) | 58306.2i | 1.66737i | ||||||||
\(188\) | −16952.0 | − | 21288.6i | −0.479630 | − | 0.602326i | ||||
\(189\) | 4556.45 | − | 14023.3i | 0.127557 | − | 0.392579i | ||||
\(190\) | −25925.5 | + | 572.526i | −0.718157 | + | 0.0158595i | ||||
\(191\) | − | 11799.7i | − | 0.323447i | −0.986836 | − | 0.161724i | \(-0.948295\pi\) | ||
0.986836 | − | 0.161724i | \(-0.0517053\pi\) | |||||||
\(192\) | −30329.2 | + | 56070.6i | −0.822733 | + | 1.52101i | ||||
\(193\) | −57426.9 | + | 41723.1i | −1.54170 | + | 1.12011i | −0.592448 | + | 0.805609i | \(0.701838\pi\) |
−0.949256 | + | 0.314504i | \(0.898162\pi\) | |||||||
\(194\) | 28229.5 | − | 9866.51i | 0.750066 | − | 0.262156i | ||||
\(195\) | −5506.24 | + | 7578.69i | −0.144806 | + | 0.199308i | ||||
\(196\) | 28306.3 | − | 22540.2i | 0.736835 | − | 0.586739i | ||||
\(197\) | −14561.4 | + | 10579.5i | −0.375208 | + | 0.272605i | −0.759367 | − | 0.650662i | \(-0.774491\pi\) |
0.384159 | + | 0.923267i | \(0.374491\pi\) | |||||||
\(198\) | 33732.3 | − | 112187.i | 0.860429 | − | 2.86162i | ||||
\(199\) | 58191.8 | + | 18907.7i | 1.46945 | + | 0.477454i | 0.930943 | − | 0.365165i | \(-0.118987\pi\) |
0.538510 | + | 0.842619i | \(0.318987\pi\) | |||||||
\(200\) | −5949.19 | − | 7141.64i | −0.148730 | − | 0.178541i | ||||
\(201\) | 14196.6 | − | 43692.7i | 0.351393 | − | 1.08148i | ||||
\(202\) | 16812.5 | + | 22097.5i | 0.412031 | + | 0.541553i | ||||
\(203\) | 8622.84 | − | 11868.3i | 0.209247 | − | 0.288003i | ||||
\(204\) | 3528.32 | + | 79846.7i | 0.0847827 | + | 1.91866i | ||||
\(205\) | −14092.6 | − | 43372.4i | −0.335338 | − | 1.03206i | ||||
\(206\) | −66353.8 | + | 1465.33i | −1.56362 | + | 0.0345303i | ||||
\(207\) | −98511.2 | + | 32008.2i | −2.29903 | + | 0.747000i | ||||
\(208\) | 5530.50 | − | 489.726i | 0.127831 | − | 0.0113195i | ||||
\(209\) | −34330.3 | − | 24942.4i | −0.785933 | − | 0.571014i | ||||
\(210\) | −450.502 | − | 20399.9i | −0.0102155 | − | 0.462583i | ||||
\(211\) | 12269.6i | 0.275592i | 0.990461 | + | 0.137796i | \(0.0440018\pi\) | ||||
−0.990461 | + | 0.137796i | \(0.955998\pi\) | |||||||
\(212\) | 3536.66 | + | 9444.06i | 0.0786904 | + | 0.210130i | ||||
\(213\) | 95064.9 | − | 69068.7i | 2.09537 | − | 1.52238i | ||||
\(214\) | −32252.4 | + | 24538.7i | −0.704263 | + | 0.535826i | ||||
\(215\) | −54630.8 | + | 17750.6i | −1.18185 | + | 0.384005i | ||||
\(216\) | 19607.4 | − | 77460.6i | 0.420254 | − | 1.66025i | ||||
\(217\) | −9190.16 | − | 6659.94i | −0.195166 | − | 0.141433i | ||||
\(218\) | −29406.4 | + | 42413.0i | −0.618770 | + | 0.892455i | ||||
\(219\) | −22900.2 | + | 7440.73i | −0.477476 | + | 0.155141i | ||||
\(220\) | −3561.04 | − | 80587.3i | −0.0735752 | − | 1.66503i | ||||
\(221\) | 5631.63 | − | 4091.62i | 0.115305 | − | 0.0837742i | ||||
\(222\) | 114893. | + | 79659.0i | 2.33123 | + | 1.61633i | ||||
\(223\) | − | 58403.3i | − | 1.17443i | −0.809431 | − | 0.587215i | \(-0.800224\pi\) | ||
0.809431 | − | 0.587215i | \(-0.199776\pi\) | |||||||
\(224\) | −8941.23 | + | 8143.16i | −0.178197 | + | 0.162292i | ||||
\(225\) | 18942.8 | + | 13762.7i | 0.374178 | + | 0.271856i | ||||
\(226\) | 5346.05 | − | 1868.50i | 0.104669 | − | 0.0365828i | ||||
\(227\) | 65555.6 | − | 21300.3i | 1.27221 | − | 0.413365i | 0.406378 | − | 0.913705i | \(-0.366792\pi\) |
0.865829 | + | 0.500340i | \(0.166792\pi\) | |||||||
\(228\) | −48522.6 | − | 32079.7i | −0.933415 | − | 0.617107i | ||||
\(229\) | 6129.04 | + | 18863.2i | 0.116875 | + | 0.359704i | 0.992333 | − | 0.123589i | \(-0.0394405\pi\) |
−0.875459 | + | 0.483293i | \(0.839441\pi\) | |||||||
\(230\) | −56762.2 | + | 43186.5i | −1.07301 | + | 0.816381i | ||||
\(231\) | 19626.4 | − | 27013.4i | 0.367804 | − | 0.506239i | ||||
\(232\) | 42367.9 | − | 67266.8i | 0.787157 | − | 1.24975i | ||||
\(233\) | −14058.4 | + | 43267.4i | −0.258956 | + | 0.796983i | 0.734069 | + | 0.679075i | \(0.237619\pi\) |
−0.993024 | + | 0.117908i | \(0.962381\pi\) | |||||||
\(234\) | −13203.0 | + | 4614.59i | −0.241124 | + | 0.0842754i | ||||
\(235\) | 44893.4 | + | 14586.8i | 0.812919 | + | 0.264133i | ||||
\(236\) | 24292.6 | + | 30507.0i | 0.436164 | + | 0.547741i | ||||
\(237\) | −12947.7 | + | 9407.05i | −0.230513 | + | 0.167478i | ||||
\(238\) | −4365.98 | + | 14520.4i | −0.0770776 | + | 0.256345i | ||||
\(239\) | −27787.6 | + | 38246.4i | −0.486470 | + | 0.669568i | −0.979732 | − | 0.200312i | \(-0.935804\pi\) |
0.493262 | + | 0.869881i | \(0.335804\pi\) | |||||||
\(240\) | −9753.25 | − | 110144.i | −0.169327 | − | 1.91222i | ||||
\(241\) | 73488.0 | − | 53392.1i | 1.26527 | − | 0.919270i | 0.266263 | − | 0.963900i | \(-0.414211\pi\) |
0.999004 | + | 0.0446302i | \(0.0142110\pi\) | |||||||
\(242\) | 41843.0 | − | 60350.4i | 0.714484 | − | 1.03050i | ||||
\(243\) | − | 1957.45i | − | 0.0331495i | ||||||
\(244\) | 35932.6 | + | 23756.1i | 0.603545 | + | 0.399021i | ||||
\(245\) | −19395.2 | + | 59692.2i | −0.323118 | + | 0.994456i | ||||
\(246\) | 29455.7 | − | 97964.1i | 0.486742 | − | 1.61881i | ||||
\(247\) | 5066.19i | 0.0830401i | ||||||||
\(248\) | −52081.5 | − | 32714.9i | −0.846798 | − | 0.531915i | ||||
\(249\) | −151364. | −2.44131 | ||||||||
\(250\) | −51004.3 | − | 15335.9i | −0.816069 | − | 0.245374i | ||||
\(251\) | −2877.15 | − | 934.842i | −0.0456683 | − | 0.0148385i | 0.286094 | − | 0.958202i | \(-0.407643\pi\) |
−0.331762 | + | 0.943363i | \(0.607643\pi\) | |||||||
\(252\) | 16801.2 | − | 25412.9i | 0.264569 | − | 0.400178i | ||||
\(253\) | −116713. | −1.82338 | ||||||||
\(254\) | −25500.3 | − | 17680.2i | −0.395255 | − | 0.274044i | ||||
\(255\) | −81487.5 | − | 112158.i | −1.25317 | − | 1.72484i | ||||
\(256\) | −45425.7 | + | 47238.5i | −0.693141 | + | 0.720802i | ||||
\(257\) | −32027.3 | − | 23269.2i | −0.484902 | − | 0.352302i | 0.318319 | − | 0.947984i | \(-0.396882\pi\) |
−0.803220 | + | 0.595682i | \(0.796882\pi\) | |||||||
\(258\) | −123393. | − | 37101.7i | −1.85375 | − | 0.557383i | ||||
\(259\) | 15589.7 | + | 21457.4i | 0.232402 | + | 0.319874i | ||||
\(260\) | −7533.79 | + | 5999.13i | −0.111447 | + | 0.0887445i | ||||
\(261\) | −61883.5 | + | 190458.i | −0.908435 | + | 2.79587i | ||||
\(262\) | 39606.4 | + | 113320.i | 0.576983 | + | 1.65083i | ||||
\(263\) | 20167.0 | + | 6552.64i | 0.291561 | + | 0.0947338i | 0.451145 | − | 0.892450i | \(-0.351016\pi\) |
−0.159585 | + | 0.987184i | \(0.551016\pi\) | |||||||
\(264\) | 96433.3 | − | 153105.i | 1.38363 | − | 2.19676i | ||||
\(265\) | −14151.6 | − | 10281.7i | −0.201518 | − | 0.146411i | ||||
\(266\) | −6681.84 | − | 8782.27i | −0.0944350 | − | 0.124120i | ||||
\(267\) | 136326. | − | 44295.1i | 1.91231 | − | 0.621346i | ||||
\(268\) | 26047.2 | − | 39398.2i | 0.362654 | − | 0.548538i | ||||
\(269\) | 13733.7 | + | 42267.9i | 0.189794 | + | 0.584125i | 0.999998 | − | 0.00202259i | \(-0.000643811\pi\) |
−0.810204 | + | 0.586148i | \(0.800644\pi\) | |||||||
\(270\) | 45729.0 | + | 130837.i | 0.627284 | + | 1.79475i | ||||
\(271\) | 52069.5 | − | 71667.5i | 0.708997 | − | 0.975851i | −0.290821 | − | 0.956778i | \(-0.593928\pi\) |
0.999818 | − | 0.0190734i | \(-0.00607162\pi\) | |||||||
\(272\) | −18399.1 | + | 80080.2i | −0.248691 | + | 1.08240i | ||||
\(273\) | −3986.42 | −0.0534882 | ||||||||
\(274\) | −26297.1 | + | 37928.4i | −0.350273 | + | 0.505200i | ||||
\(275\) | 15507.6 | + | 21344.4i | 0.205059 | + | 0.282240i | ||||
\(276\) | −159831. | + | 7062.72i | −2.09818 | + | 0.0927159i | ||||
\(277\) | −2276.00 | − | 7004.80i | −0.0296628 | − | 0.0912927i | 0.935129 | − | 0.354307i | \(-0.115283\pi\) |
−0.964792 | + | 0.263015i | \(0.915283\pi\) | |||||||
\(278\) | 93480.4 | + | 64813.2i | 1.20957 | + | 0.838637i | ||||
\(279\) | 147408. | + | 47697.1i | 1.89370 | + | 0.612750i | ||||
\(280\) | 5147.56 | − | 20335.9i | 0.0656577 | − | 0.259386i | ||||
\(281\) | 12810.1 | + | 39425.5i | 0.162234 | + | 0.499303i | 0.998822 | − | 0.0485287i | \(-0.0154533\pi\) |
−0.836588 | + | 0.547832i | \(0.815453\pi\) | |||||||
\(282\) | 64113.1 | + | 84267.0i | 0.806211 | + | 1.05964i | ||||
\(283\) | 70355.3 | + | 96835.7i | 0.878464 | + | 1.20910i | 0.976844 | + | 0.213953i | \(0.0686339\pi\) |
−0.0983802 | + | 0.995149i | \(0.531366\pi\) | |||||||
\(284\) | 113131. | − | 42365.7i | 1.40263 | − | 0.525264i | ||||
\(285\) | 100897. | 1.24219 | ||||||||
\(286\) | −15755.5 | + | 347.938i | −0.192620 | + | 0.00425373i | ||||
\(287\) | 11407.0 | − | 15700.4i | 0.138487 | − | 0.190611i | ||||
\(288\) | 81731.2 | − | 143438.i | 0.985378 | − | 1.72933i | ||||
\(289\) | 6024.82 | + | 18542.5i | 0.0721353 | + | 0.222010i | ||||
\(290\) | 3044.44 | + | 137860.i | 0.0362003 | + | 1.63924i | ||||
\(291\) | −110658. | + | 35954.8i | −1.30676 | + | 0.424591i | ||||
\(292\) | −24730.0 | + | 1092.79i | −0.290041 | + | 0.0128165i | ||||
\(293\) | 7567.74 | + | 5498.29i | 0.0881518 | + | 0.0640460i | 0.630988 | − | 0.775792i | \(-0.282650\pi\) |
−0.542836 | + | 0.839838i | \(0.682650\pi\) | |||||||
\(294\) | −112045. | + | 85247.5i | −1.29628 | + | 0.986250i | ||||
\(295\) | −64333.1 | − | 20903.1i | −0.739249 | − | 0.240196i | ||||
\(296\) | 91992.8 | + | 110432.i | 1.04995 | + | 1.26041i | ||||
\(297\) | −70085.5 | + | 215701.i | −0.794539 | + | 2.44534i | ||||
\(298\) | 59203.5 | + | 17801.2i | 0.666677 | + | 0.200455i | ||||
\(299\) | 8190.29 | + | 11273.0i | 0.0916130 | + | 0.126094i | ||||
\(300\) | 22528.3 | + | 28291.4i | 0.250315 | + | 0.314349i | ||||
\(301\) | −19775.9 | − | 14368.0i | −0.218274 | − | 0.158586i | ||||
\(302\) | −2812.53 | − | 8047.05i | −0.0308378 | − | 0.0882313i | ||||
\(303\) | −63500.9 | − | 87401.5i | −0.691663 | − | 0.951993i | ||||
\(304\) | −39279.9 | − | 45090.3i | −0.425033 | − | 0.487906i | ||||
\(305\) | −74717.5 | −0.803198 | ||||||||
\(306\) | −4569.80 | − | 206932.i | −0.0488039 | − | 2.20997i | ||||
\(307\) | 8212.73 | + | 2668.48i | 0.0871386 | + | 0.0283131i | 0.352262 | − | 0.935901i | \(-0.385413\pi\) |
−0.265123 | + | 0.964215i | \(0.585413\pi\) | |||||||
\(308\) | 26853.4 | − | 21383.2i | 0.283072 | − | 0.225409i | ||||
\(309\) | 258236. | 2.70458 | ||||||||
\(310\) | 106654. | − | 2485.35i | 1.10982 | − | 0.0258621i | ||||
\(311\) | 18315.3i | 0.189363i | 0.995508 | + | 0.0946813i | \(0.0301832\pi\) | ||||
−0.995508 | + | 0.0946813i | \(0.969817\pi\) | |||||||
\(312\) | −21555.2 | + | 1429.90i | −0.221433 | + | 0.0146892i | ||||
\(313\) | 48333.4 | − | 148755.i | 0.493354 | − | 1.51839i | −0.326153 | − | 0.945317i | \(-0.605753\pi\) |
0.819507 | − | 0.573069i | \(-0.194247\pi\) | |||||||
\(314\) | 1678.57 | + | 76010.2i | 0.0170248 | + | 0.770926i | ||||
\(315\) | 52843.0i | 0.532558i | ||||||||
\(316\) | −15408.2 | + | 5770.14i | −0.154304 | + | 0.0577846i | ||||
\(317\) | −85920.4 | + | 62424.8i | −0.855022 | + | 0.621210i | −0.926526 | − | 0.376230i | \(-0.877220\pi\) |
0.0715038 | + | 0.997440i | \(0.477220\pi\) | |||||||
\(318\) | −12946.0 | − | 37040.3i | −0.128021 | − | 0.366286i | ||||
\(319\) | −132633. | + | 182554.i | −1.30338 | + | 1.79394i | ||||
\(320\) | 20539.3 | − | 111806.i | 0.200579 | − | 1.09185i | ||||
\(321\) | 127567. | − | 92682.7i | 1.23802 | − | 0.899474i | ||||
\(322\) | −29065.9 | − | 8739.50i | −0.280332 | − | 0.0842898i | ||||
\(323\) | −71305.6 | − | 23168.6i | −0.683469 | − | 0.222073i | ||||
\(324\) | −27193.9 | + | 98259.0i | −0.259049 | + | 0.936014i | ||||
\(325\) | 973.351 | − | 2995.67i | 0.00921516 | − | 0.0283613i | ||||
\(326\) | −79429.4 | + | 60432.6i | −0.747388 | + | 0.568638i | ||||
\(327\) | 118032. | − | 162457.i | 1.10383 | − | 1.51929i | ||||
\(328\) | 56048.0 | − | 88986.3i | 0.520969 | − | 0.827133i | ||||
\(329\) | 6207.34 | + | 19104.2i | 0.0573474 | + | 0.176497i | ||||
\(330\) | 6929.43 | + | 313783.i | 0.0636311 | + | 2.88138i | ||||
\(331\) | −60708.5 | + | 19725.4i | −0.554107 | + | 0.180040i | −0.572668 | − | 0.819788i | \(-0.694092\pi\) |
0.0185610 | + | 0.999828i | \(0.494092\pi\) | |||||||
\(332\) | −149972. | − | 41505.9i | −1.36061 | − | 0.376559i | ||||
\(333\) | −292913. | − | 212814.i | −2.64150 | − | 1.91916i | ||||
\(334\) | −24093.3 | + | 532.066i | −0.215975 | + | 0.00476949i | ||||
\(335\) | 81923.7i | 0.729995i | ||||||||
\(336\) | 35480.1 | − | 30908.0i | 0.314272 | − | 0.273774i | ||||
\(337\) | −90951.1 | + | 66079.9i | −0.800845 | + | 0.581848i | −0.911162 | − | 0.412049i | \(-0.864813\pi\) |
0.110317 | + | 0.993896i | \(0.464813\pi\) | |||||||
\(338\) | −68035.9 | − | 89422.9i | −0.595532 | − | 0.782736i | ||||
\(339\) | −20956.1 | + | 6809.06i | −0.182353 | + | 0.0592499i | ||||
\(340\) | −49983.2 | − | 133472.i | −0.432380 | − | 1.15460i | ||||
\(341\) | 141359. | + | 102440.i | 1.21567 | + | 0.880973i | ||||
\(342\) | 123795. | + | 85831.7i | 1.05841 | + | 0.733830i | ||||
\(343\) | −52370.3 | + | 17016.1i | −0.445140 | + | 0.144635i | ||||
\(344\) | −112085. | − | 70596.6i | −0.947175 | − | 0.596577i | ||||
\(345\) | 224509. | − | 163116.i | 1.88624 | − | 1.37043i | ||||
\(346\) | 117956. | − | 170128.i | 0.985295 | − | 1.42110i | ||||
\(347\) | − | 176281.i | − | 1.46402i | −0.681293 | − | 0.732011i | \(-0.738582\pi\) | ||
0.681293 | − | 0.732011i | \(-0.261418\pi\) | |||||||
\(348\) | −170586. | + | 258022.i | −1.40859 | + | 2.13058i | ||||
\(349\) | 103464. | + | 75170.8i | 0.849449 | + | 0.617161i | 0.924994 | − | 0.379981i | \(-0.124070\pi\) |
−0.0755448 | + | 0.997142i | \(0.524070\pi\) | |||||||
\(350\) | 2263.70 | + | 6476.76i | 0.0184792 | + | 0.0528715i | ||||
\(351\) | 25752.1 | − | 8367.38i | 0.209025 | − | 0.0679165i | ||||
\(352\) | 137530. | − | 125255.i | 1.10997 | − | 1.01090i | ||||
\(353\) | −6944.79 | − | 21373.9i | −0.0557327 | − | 0.171527i | 0.919315 | − | 0.393522i | \(-0.128743\pi\) |
−0.975048 | + | 0.221994i | \(0.928743\pi\) | |||||||
\(354\) | −91875.3 | − | 120756.i | −0.733149 | − | 0.963613i | ||||
\(355\) | −123165. | + | 169522.i | −0.977307 | + | 1.34515i | ||||
\(356\) | 147219. | − | 6505.43i | 1.16162 | − | 0.0513305i | ||||
\(357\) | 18230.6 | − | 56108.0i | 0.143042 | − | 0.440239i | ||||
\(358\) | −60677.7 | − | 173607.i | −0.473438 | − | 1.35457i | ||||
\(359\) | 53882.8 | + | 17507.6i | 0.418082 | + | 0.135843i | 0.510501 | − | 0.859877i | \(-0.329460\pi\) |
−0.0924190 | + | 0.995720i | \(0.529460\pi\) | |||||||
\(360\) | 18954.5 | + | 285730.i | 0.146254 | + | 2.20471i | ||||
\(361\) | −61287.0 | + | 44527.6i | −0.470277 | + | 0.341676i | ||||
\(362\) | 43599.0 | + | 13109.3i | 0.332705 | + | 0.100037i | ||||
\(363\) | −167950. | + | 231163.i | −1.27458 | + | 1.75430i | ||||
\(364\) | −3949.77 | − | 1093.13i | −0.0298105 | − | 0.00825028i | ||||
\(365\) | 34737.4 | − | 25238.2i | 0.260742 | − | 0.189440i | ||||
\(366\) | −137734. | − | 95495.6i | −1.02820 | − | 0.712888i | ||||
\(367\) | − | 158238.i | − | 1.17484i | −0.809283 | − | 0.587419i | \(-0.800144\pi\) | ||
0.809283 | − | 0.587419i | \(-0.199856\pi\) | |||||||
\(368\) | −160299. | − | 36830.0i | −1.18368 | − | 0.271961i | ||||
\(369\) | −81864.8 | + | 251954.i | −0.601235 | + | 1.85041i | ||||
\(370\) | −238748. | − | 71786.3i | −1.74396 | − | 0.524371i | ||||
\(371\) | − | 7443.80i | − | 0.0540813i | ||||||
\(372\) | 199782. | + | 131732.i | 1.44368 | + | 0.951929i | ||||
\(373\) | 241670. | 1.73702 | 0.868512 | − | 0.495669i | \(-0.165077\pi\) | ||||
0.868512 | + | 0.495669i | \(0.165077\pi\) | |||||||
\(374\) | 67155.7 | − | 223347.i | 0.480109 | − | 1.59675i | ||||
\(375\) | 197084. | + | 64036.6i | 1.40149 | + | 0.455371i | ||||
\(376\) | 40416.6 | + | 101073.i | 0.285880 | + | 0.714923i | ||||
\(377\) | 26939.8 | 0.189545 | ||||||||
\(378\) | −33605.6 | + | 48469.6i | −0.235195 | + | 0.339223i | ||||
\(379\) | 150095. | + | 206588.i | 1.04493 | + | 1.43823i | 0.893121 | + | 0.449816i | \(0.148510\pi\) |
0.151810 | + | 0.988410i | \(0.451490\pi\) | |||||||
\(380\) | 99969.3 | + | 27667.2i | 0.692308 | + | 0.191601i | ||||
\(381\) | 97674.9 | + | 70965.0i | 0.672873 | + | 0.488871i | ||||
\(382\) | −13590.6 | + | 45199.7i | −0.0931347 | + | 0.309748i | ||||
\(383\) | −54272.0 | − | 74699.0i | −0.369980 | − | 0.509234i | 0.582916 | − | 0.812533i | \(-0.301912\pi\) |
−0.952895 | + | 0.303299i | \(0.901912\pi\) | |||||||
\(384\) | 180760. | − | 179851.i | 1.22585 | − | 1.21969i | ||||
\(385\) | −18399.7 | + | 56628.4i | −0.124133 | + | 0.382043i | ||||
\(386\) | 268035. | − | 93681.1i | 1.79894 | − | 0.628749i | ||||
\(387\) | 317355. | + | 103115.i | 2.11896 | + | 0.688492i | ||||
\(388\) | −119500. | + | 5280.52i | −0.793785 | + | 0.0350763i | ||||
\(389\) | 212586. | + | 154453.i | 1.40487 | + | 1.02070i | 0.994044 | + | 0.108982i | \(0.0347589\pi\) |
0.410824 | + | 0.911715i | \(0.365241\pi\) | |||||||
\(390\) | 29821.1 | − | 22688.9i | 0.196062 | − | 0.149171i | ||||
\(391\) | −196120. | + | 63723.4i | −1.28283 | + | 0.416817i | ||||
\(392\) | −134391. | + | 53739.6i | −0.874576 | + | 0.349722i | ||||
\(393\) | −144331. | − | 444205.i | −0.934488 | − | 2.87606i | ||||
\(394\) | 67964.1 | − | 23754.2i | 0.437812 | − | 0.153020i | ||||
\(395\) | 16774.9 | − | 23088.7i | 0.107514 | − | 0.147981i | ||||
\(396\) | −258429. | + | 390891.i | −1.64798 | + | 2.49267i | ||||
\(397\) | −282588. | −1.79297 | −0.896485 | − | 0.443074i | \(-0.853888\pi\) | ||||
−0.896485 | + | 0.443074i | \(0.853888\pi\) | |||||||
\(398\) | −201132. | − | 139451.i | −1.26974 | − | 0.880353i | ||||
\(399\) | 25237.3 | + | 34736.2i | 0.158525 | + | 0.218191i | ||||
\(400\) | 14563.3 | + | 34208.8i | 0.0910209 | + | 0.213805i | ||||
\(401\) | −81255.1 | − | 250078.i | −0.505315 | − | 1.55520i | −0.800241 | − | 0.599679i | \(-0.795295\pi\) |
0.294926 | − | 0.955520i | \(-0.404705\pi\) | |||||||
\(402\) | −104706. | + | 151018.i | −0.647916 | + | 0.934492i | ||||
\(403\) | −25.4016 | − | 20842.2i | −0.000156405 | − | 0.128331i | ||||
\(404\) | −38950.5 | − | 104011.i | −0.238644 | − | 0.637258i | ||||
\(405\) | −54647.7 | − | 168188.i | −0.333167 | − | 1.02538i | ||||
\(406\) | −46700.2 | + | 35531.1i | −0.283313 | + | 0.215554i | ||||
\(407\) | −239795. | − | 330049.i | −1.44761 | − | 1.99246i | ||||
\(408\) | 78450.1 | − | 309924.i | 0.471273 | − | 1.86181i | ||||
\(409\) | −85518.7 | −0.511228 | −0.255614 | − | 0.966779i | \(-0.582278\pi\) | ||||
−0.255614 | + | 0.966779i | \(0.582278\pi\) | |||||||
\(410\) | 4027.45 | + | 182373.i | 0.0239587 | + | 1.08491i | ||||
\(411\) | 105551. | − | 145279.i | 0.624856 | − | 0.860040i | ||||
\(412\) | 255862. | + | 70811.7i | 1.50734 | + | 0.417168i | ||||
\(413\) | −8895.23 | − | 27376.7i | −0.0521503 | − | 0.160502i | ||||
\(414\) | 414222. | − | 9147.49i | 2.41675 | − | 0.0533705i | ||||
\(415\) | 256705. | − | 83408.4i | 1.49052 | − | 0.484299i | ||||
\(416\) | −21749.1 | − | 4493.96i | −0.125677 | − | 0.0259682i | ||||
\(417\) | −358062. | − | 260148.i | −2.05914 | − | 1.49606i | ||||
\(418\) | 102777. | + | 135085.i | 0.588226 | + | 0.773134i | ||||
\(419\) | −179295. | − | 58256.6i | −1.02127 | − | 0.331831i | −0.249937 | − | 0.968262i | \(-0.580410\pi\) |
−0.771334 | + | 0.636431i | \(0.780410\pi\) | |||||||
\(420\) | −21770.4 | + | 78662.5i | −0.123415 | + | 0.445933i | ||||
\(421\) | −69854.2 | + | 214989.i | −0.394120 | + | 1.21298i | 0.535525 | + | 0.844519i | \(0.320114\pi\) |
−0.929645 | + | 0.368456i | \(0.879886\pi\) | |||||||
\(422\) | 14131.9 | − | 46999.9i | 0.0793550 | − | 0.263920i | ||||
\(423\) | −161177. | − | 221841.i | −0.900786 | − | 1.23983i | ||||
\(424\) | −2670.04 | − | 40249.8i | −0.0148521 | − | 0.223888i | ||||
\(425\) | 37712.1 | + | 27399.4i | 0.208787 | + | 0.151692i | ||||
\(426\) | −443706. | + | 155080.i | −2.44499 | + | 0.854550i | ||||
\(427\) | −18689.1 | − | 25723.3i | −0.102502 | − | 0.141082i | ||||
\(428\) | 151809. | − | 56850.1i | 0.828723 | − | 0.310344i | ||||
\(429\) | 61317.4 | 0.333173 | ||||||||
\(430\) | 229713. | − | 5072.87i | 1.24236 | − | 0.0274358i | ||||
\(431\) | 18329.0 | + | 5955.44i | 0.0986696 | + | 0.0320597i | 0.357936 | − | 0.933746i | \(-0.383481\pi\) |
−0.259266 | + | 0.965806i | \(0.583481\pi\) | |||||||
\(432\) | −164325. | + | 274137.i | −0.880514 | + | 1.46892i | ||||
\(433\) | −16712.0 | −0.0891359 | −0.0445679 | − | 0.999006i | \(-0.514191\pi\) | ||||
−0.0445679 | + | 0.999006i | \(0.514191\pi\) | |||||||
\(434\) | 27533.0 | + | 36096.5i | 0.146175 | + | 0.191640i | ||||
\(435\) | − | 536525.i | − | 2.83538i | ||||||
\(436\) | 161494. | − | 128597.i | 0.849541 | − | 0.676486i | ||||
\(437\) | 46377.2 | − | 142734.i | 0.242852 | − | 0.747421i | ||||
\(438\) | 96291.3 | − | 2126.45i | 0.501925 | − | 0.0110843i | ||||
\(439\) | − | 71036.1i | − | 0.368595i | −0.982870 | − | 0.184298i | \(-0.940999\pi\) | ||
0.982870 | − | 0.184298i | \(-0.0590011\pi\) | |||||||
\(440\) | −79177.6 | + | 312798.i | −0.408975 | + | 1.61569i | ||||
\(441\) | 294969. | − | 214308.i | 1.51670 | − | 1.10195i | ||||
\(442\) | −26285.1 | + | 9186.92i | −0.134544 | + | 0.0470246i | ||||
\(443\) | 68270.8 | − | 93966.6i | 0.347878 | − | 0.478813i | −0.598843 | − | 0.800866i | \(-0.704373\pi\) |
0.946722 | + | 0.322053i | \(0.104373\pi\) | |||||||
\(444\) | −348357. | − | 437471.i | −1.76709 | − | 2.21913i | ||||
\(445\) | −206794. | + | 150245.i | −1.04428 | + | 0.758715i | ||||
\(446\) | −67267.5 | + | 223719.i | −0.338170 | + | 1.12469i | ||||
\(447\) | −228767. | − | 74330.9i | −1.14493 | − | 0.372010i | ||||
\(448\) | 43629.3 | − | 20894.8i | 0.217381 | − | 0.104107i | ||||
\(449\) | 102823. | − | 316456.i | 0.510032 | − | 1.56972i | −0.282112 | − | 0.959381i | \(-0.591035\pi\) |
0.792144 | − | 0.610335i | \(-0.208965\pi\) | |||||||
\(450\) | −56710.3 | − | 74537.1i | −0.280051 | − | 0.368085i | ||||
\(451\) | −175458. | + | 241498.i | −0.862622 | + | 1.18730i | ||||
\(452\) | −22630.6 | + | 1000.02i | −0.110769 | + | 0.00489474i | ||||
\(453\) | 10249.2 | + | 31543.9i | 0.0499453 | + | 0.153716i | ||||
\(454\) | −275650. | + | 6087.32i | −1.33735 | + | 0.0295334i | ||||
\(455\) | 6760.76 | − | 2196.70i | 0.0326567 | − | 0.0106108i | ||||
\(456\) | 148922. | + | 178771.i | 0.716190 | + | 0.859742i | ||||
\(457\) | 54891.7 | + | 39881.2i | 0.262830 | + | 0.190957i | 0.711394 | − | 0.702794i | \(-0.248064\pi\) |
−0.448564 | + | 0.893751i | \(0.648064\pi\) | |||||||
\(458\) | −1751.59 | − | 79316.6i | −0.00835029 | − | 0.378123i | ||||
\(459\) | 400722.i | 1.90203i | ||||||||
\(460\) | 267174. | − | 100053.i | 1.26264 | − | 0.472838i | ||||
\(461\) | 251912. | − | 183024.i | 1.18535 | − | 0.861206i | 0.192584 | − | 0.981281i | \(-0.438313\pi\) |
0.992765 | + | 0.120074i | \(0.0383132\pi\) | |||||||
\(462\) | −106294. | + | 80872.0i | −0.497995 | + | 0.378891i | ||||
\(463\) | 65773.1 | − | 21371.0i | 0.306822 | − | 0.0996925i | −0.151559 | − | 0.988448i | \(-0.548429\pi\) |
0.458381 | + | 0.888756i | \(0.348429\pi\) | |||||||
\(464\) | −239770. | + | 208873.i | −1.11368 | + | 0.970167i | ||||
\(465\) | −415087. | + | 505.891i | −1.91970 | + | 0.00233965i | ||||
\(466\) | 103687. | − | 149548.i | 0.477475 | − | 0.688664i | ||||
\(467\) | −199136. | + | 64703.1i | −0.913094 | + | 0.296682i | −0.727631 | − | 0.685969i | \(-0.759379\pi\) |
−0.185463 | + | 0.982651i | \(0.559379\pi\) | |||||||
\(468\) | 55890.1 | − | 2469.71i | 0.255178 | − | 0.0112760i | ||||
\(469\) | −28204.2 | + | 20491.5i | −0.128224 | + | 0.0931599i | ||||
\(470\) | −155168. | − | 107583.i | −0.702434 | − | 0.487022i | ||||
\(471\) | − | 295817.i | − | 1.33346i | ||||||
\(472\) | −57917.7 | − | 144839.i | −0.259973 | − | 0.650134i | ||||
\(473\) | 304184. | + | 221003.i | 1.35961 | + | 0.987815i | ||||
\(474\) | 60432.1 | − | 21121.7i | 0.268975 | − | 0.0940096i | ||||
\(475\) | −32265.2 | + | 10483.6i | −0.143004 | + | 0.0464647i | ||||
\(476\) | 33448.6 | − | 50593.1i | 0.147626 | − | 0.223294i | ||||
\(477\) | 31400.6 | + | 96641.1i | 0.138007 | + | 0.424742i | ||||
\(478\) | 150494. | − | 114501.i | 0.658665 | − | 0.501134i | ||||
\(479\) | −4277.99 | + | 5888.14i | −0.0186453 | + | 0.0256630i | −0.818238 | − | 0.574880i | \(-0.805049\pi\) |
0.799593 | + | 0.600543i | \(0.205049\pi\) | |||||||
\(480\) | −89500.3 | + | 433149.i | −0.388456 | + | 1.87999i | ||||
\(481\) | −15051.0 | + | 46322.2i | −0.0650541 | + | 0.200216i | ||||
\(482\) | −342998. | + | 119882.i | −1.47638 | + | 0.516010i | ||||
\(483\) | 112313. | + | 36492.7i | 0.481432 | + | 0.156427i | ||||
\(484\) | −229794. | + | 182984.i | −0.980951 | + | 0.781127i | ||||
\(485\) | 167857. | − | 121955.i | 0.713601 | − | 0.518461i | ||||
\(486\) | −2254.54 | + | 7498.17i | −0.00954521 | + | 0.0317456i | ||||
\(487\) | 11409.8 | − | 15704.2i | 0.0481081 | − | 0.0662152i | −0.784285 | − | 0.620400i | \(-0.786970\pi\) |
0.832393 | + | 0.554185i | \(0.186970\pi\) | |||||||
\(488\) | −110281. | − | 132386.i | −0.463087 | − | 0.555908i | ||||
\(489\) | 314164. | − | 228254.i | 1.31383 | − | 0.954553i | ||||
\(490\) | 143047. | − | 206317.i | 0.595781 | − | 0.859298i | ||||
\(491\) | 411544.i | 1.70708i | 0.521031 | + | 0.853538i | \(0.325548\pi\) | ||||
−0.521031 | + | 0.853538i | \(0.674452\pi\) | |||||||
\(492\) | −225665. | + | 341334.i | −0.932255 | + | 1.41010i | ||||
\(493\) | −123200. | + | 379172.i | −0.506895 | + | 1.56006i | ||||
\(494\) | 5835.12 | − | 19406.5i | 0.0239109 | − | 0.0795231i | ||||
\(495\) | − | 812809.i | − | 3.31725i | ||||||
\(496\) | 161822. | + | 185303.i | 0.657772 | + | 0.753217i | ||||
\(497\) | −89169.3 | −0.360996 | ||||||||
\(498\) | 579812. | + | 174337.i | 2.33791 | + | 0.702960i | ||||
\(499\) | 343414. | + | 111582.i | 1.37917 | + | 0.448119i | 0.902396 | − | 0.430908i | \(-0.141806\pi\) |
0.476773 | + | 0.879027i | \(0.341806\pi\) | |||||||
\(500\) | 177713. | + | 117491.i | 0.710852 | + | 0.469964i | ||||
\(501\) | 93766.4 | 0.373570 | ||||||||
\(502\) | 9944.44 | + | 6894.83i | 0.0394614 | + | 0.0273600i | ||||
\(503\) | −49085.8 | − | 67560.8i | −0.194008 | − | 0.267029i | 0.700920 | − | 0.713240i | \(-0.252773\pi\) |
−0.894928 | + | 0.446211i | \(0.852773\pi\) | |||||||
\(504\) | −93628.4 | + | 77995.2i | −0.368593 | + | 0.307048i | ||||
\(505\) | 155857. | + | 113236.i | 0.611142 | + | 0.444021i | ||||
\(506\) | 447080. | + | 134427.i | 1.74616 | + | 0.525033i | ||||
\(507\) | 256972. | + | 353691.i | 0.999699 | + | 1.37597i | ||||
\(508\) | 77317.5 | + | 97096.4i | 0.299606 | + | 0.376249i | ||||
\(509\) | −99949.6 | + | 307613.i | −0.385785 | + | 1.18732i | 0.550124 | + | 0.835083i | \(0.314581\pi\) |
−0.935909 | + | 0.352242i | \(0.885419\pi\) | |||||||
\(510\) | 182964. | + | 523486.i | 0.703438 | + | 2.01263i | ||||
\(511\) | 17377.7 | + | 5646.36i | 0.0665504 | + | 0.0216235i | ||||
\(512\) | 228415. | − | 128631.i | 0.871336 | − | 0.490688i | ||||
\(513\) | −235942. | − | 171422.i | −0.896543 | − | 0.651377i | ||||
\(514\) | 95882.4 | + | 126023.i | 0.362922 | + | 0.477005i | ||||
\(515\) | −437955. | + | 142300.i | −1.65126 | + | 0.536526i | ||||
\(516\) | 429935. | + | 284242.i | 1.61474 | + | 1.06755i | ||||
\(517\) | −95478.7 | − | 293853.i | −0.357211 | − | 1.09938i | ||||
\(518\) | −35003.7 | − | 100151.i | −0.130453 | − | 0.373245i | ||||
\(519\) | −473450. | + | 651648.i | −1.75768 | + | 2.41924i | ||||
\(520\) | 35768.5 | − | 14303.0i | 0.132280 | − | 0.0528956i | ||||
\(521\) | 234443. | 0.863698 | 0.431849 | − | 0.901946i | \(-0.357861\pi\) | ||||
0.431849 | + | 0.901946i | \(0.357861\pi\) | |||||||
\(522\) | 456415. | − | 658289.i | 1.67502 | − | 2.41588i | ||||
\(523\) | 111042. | + | 152836.i | 0.405961 | + | 0.558757i | 0.962227 | − | 0.272247i | \(-0.0877668\pi\) |
−0.556267 | + | 0.831004i | \(0.687767\pi\) | |||||||
\(524\) | −21197.2 | − | 479698.i | −0.0771998 | − | 1.74705i | ||||
\(525\) | −8249.20 | − | 25388.4i | −0.0299291 | − | 0.0921122i | ||||
\(526\) | −69704.1 | − | 48328.3i | −0.251934 | − | 0.174675i | ||||
\(527\) | 293466. | + | 94957.5i | 1.05666 | + | 0.341907i | ||||
\(528\) | −545740. | + | 475414.i | −1.95757 | + | 1.70531i | ||||
\(529\) | −41081.1 | − | 126435.i | −0.146802 | − | 0.451809i | ||||
\(530\) | 42366.7 | + | 55684.6i | 0.150825 | + | 0.198236i | ||||
\(531\) | 230969. | + | 317902.i | 0.819153 | + | 1.12747i | ||||
\(532\) | 15480.2 | + | 41337.2i | 0.0546956 | + | 0.146056i | ||||
\(533\) | 35638.3 | 0.125448 | ||||||||
\(534\) | −573229. | + | 12658.9i | −2.01023 | + | 0.0443929i | ||||
\(535\) | −165274. | + | 227480.i | −0.577427 | + | 0.794760i | ||||
\(536\) | −145154. | + | 120918.i | −0.505243 | + | 0.420881i | ||||
\(537\) | 221117. | + | 680529.i | 0.766786 | + | 2.35992i | ||||
\(538\) | −3924.88 | − | 177729.i | −0.0135601 | − | 0.614036i | ||||
\(539\) | 390720. | − | 126953.i | 1.34489 | − | 0.436982i | ||||
\(540\) | −24474.0 | − | 553853.i | −0.0839300 | − | 1.89936i | ||||
\(541\) | −401507. | − | 291712.i | −1.37183 | − | 0.996690i | −0.997592 | − | 0.0693553i | \(-0.977906\pi\) |
−0.374234 | − | 0.927334i | \(-0.622094\pi\) | |||||||
\(542\) | −282002. | + | 214556.i | −0.959960 | + | 0.730369i | ||||
\(543\) | −168470. | − | 54739.2i | −0.571377 | − | 0.185652i | ||||
\(544\) | 162714. | − | 285563.i | 0.549829 | − | 0.964947i | ||||
\(545\) | −110654. | + | 340559.i | −0.372542 | + | 1.14657i | ||||
\(546\) | 15270.3 | + | 4591.46i | 0.0512228 | + | 0.0154016i | ||||
\(547\) | −137767. | − | 189620.i | −0.460437 | − | 0.633737i | 0.514162 | − | 0.857693i | \(-0.328103\pi\) |
−0.974599 | + | 0.223956i | \(0.928103\pi\) | |||||||
\(548\) | 144418. | − | 115000.i | 0.480907 | − | 0.382944i | ||||
\(549\) | 351146. | + | 255122.i | 1.16504 | + | 0.846455i | ||||
\(550\) | −34819.3 | − | 99622.8i | −0.115105 | − | 0.329331i | ||||
\(551\) | −170551. | − | 234743.i | −0.561760 | − | 0.773196i | ||||
\(552\) | 620383. | + | 157036.i | 2.03602 | + | 0.515371i | ||||
\(553\) | 12144.7 | 0.0397134 | ||||||||
\(554\) | 650.447 | + | 29453.9i | 0.00211930 | + | 0.0959674i | ||||
\(555\) | 922539. | + | 299751.i | 2.99501 | + | 0.973139i | ||||
\(556\) | −283435. | − | 355941.i | −0.916861 | − | 1.15141i | ||||
\(557\) | 203756. | 0.656750 | 0.328375 | − | 0.944548i | \(-0.393499\pi\) | ||||
0.328375 | + | 0.944548i | \(0.393499\pi\) | |||||||
\(558\) | −509722. | − | 352489.i | −1.63706 | − | 1.13208i | ||||
\(559\) | − | 44889.0i | − | 0.143654i | ||||||
\(560\) | −43140.6 | + | 71969.6i | −0.137566 | + | 0.229495i | ||||
\(561\) | −280415. | + | 863030.i | −0.890997 | + | 2.74221i | ||||
\(562\) | −3660.95 | − | 165777.i | −0.0115910 | − | 0.524871i | ||||
\(563\) | 171014.i | 0.539528i | 0.962926 | + | 0.269764i | \(0.0869457\pi\) | ||||
−0.962926 | + | 0.269764i | \(0.913054\pi\) | |||||||
\(564\) | −148534. | − | 396636.i | −0.466948 | − | 1.24691i | ||||
\(565\) | 31788.4 | − | 23095.6i | 0.0995800 | − | 0.0723491i | ||||
\(566\) | −157969. | − | 451971.i | −0.493105 | − | 1.41084i | ||||
\(567\) | 44233.9 | − | 60882.7i | 0.137591 | − | 0.189377i | ||||
\(568\) | −482152. | + | 31984.5i | −1.49447 | + | 0.0991386i | ||||
\(569\) | −259571. | + | 188589.i | −0.801736 | + | 0.582495i | −0.911423 | − | 0.411471i | \(-0.865015\pi\) |
0.109687 | + | 0.993966i | \(0.465015\pi\) | |||||||
\(570\) | −386494. | − | 116211.i | −1.18958 | − | 0.357681i | ||||
\(571\) | 52453.0 | + | 17043.0i | 0.160879 | + | 0.0522726i | 0.388349 | − | 0.921512i | \(-0.373046\pi\) |
−0.227470 | + | 0.973785i | \(0.573046\pi\) | |||||||
\(572\) | 60753.7 | + | 16814.0i | 0.185687 | + | 0.0513902i | ||||
\(573\) | 56748.9 | − | 174655.i | 0.172841 | − | 0.531951i | ||||
\(574\) | −61779.1 | + | 47003.6i | −0.187507 | + | 0.142662i | ||||
\(575\) | −54846.1 | + | 75489.2i | −0.165886 | + | 0.228323i | ||||
\(576\) | −478287. | + | 455316.i | −1.44160 | + | 1.37236i | ||||
\(577\) | 339.529 | + | 1044.96i | 0.00101982 | + | 0.00313869i | 0.951565 | − | 0.307447i | \(-0.0994748\pi\) |
−0.950545 | + | 0.310586i | \(0.899475\pi\) | |||||||
\(578\) | −1721.81 | − | 77967.9i | −0.00515381 | − | 0.233378i | ||||
\(579\) | −1.05068e6 | + | 341386.i | −3.13409 | + | 1.01833i | ||||
\(580\) | 147122. | − | 531593.i | 0.437343 | − | 1.58024i | ||||
\(581\) | 92924.9 | + | 67513.9i | 0.275283 | + | 0.200005i | ||||
\(582\) | 465295. | − | 10275.4i | 1.37367 | − | 0.0303355i | ||||
\(583\) | 114497.i | 0.336867i | ||||||||
\(584\) | 95989.2 | + | 24297.4i | 0.281447 | + | 0.0712418i | ||||
\(585\) | −78506.9 | + | 57038.6i | −0.229401 | + | 0.166670i | ||||
\(586\) | −22656.1 | − | 29778.0i | −0.0659767 | − | 0.0867163i | ||||
\(587\) | 597595. | − | 194170.i | 1.73433 | − | 0.563517i | 0.740262 | − | 0.672318i | \(-0.234701\pi\) |
0.994063 | + | 0.108802i | \(0.0347013\pi\) | |||||||
\(588\) | 527384. | − | 197498.i | 1.52536 | − | 0.571225i | ||||
\(589\) | −181450. | + | 132169.i | −0.523030 | + | 0.380979i | ||||
\(590\) | 222358. | + | 154169.i | 0.638776 | + | 0.442886i | ||||
\(591\) | −266415. | + | 86563.4i | −0.762752 | + | 0.247833i | ||||
\(592\) | −225194. | − | 528974.i | −0.642559 | − | 1.50935i | ||||
\(593\) | 66833.1 | − | 48557.1i | 0.190056 | − | 0.138084i | −0.488688 | − | 0.872459i | \(-0.662524\pi\) |
0.678744 | + | 0.734375i | \(0.262524\pi\) | |||||||
\(594\) | 516908. | − | 745539.i | 1.46501 | − | 2.11299i | ||||
\(595\) | 105202.i | 0.297161i | ||||||||
\(596\) | −206281. | − | 136378.i | −0.580721 | − | 0.383931i | ||||
\(597\) | 770403. | + | 559731.i | 2.16157 | + | 1.57047i | ||||
\(598\) | −18389.7 | − | 52615.5i | −0.0514248 | − | 0.147133i | ||||
\(599\) | −402470. | + | 130770.i | −1.12171 | + | 0.364465i | −0.810419 | − | 0.585851i | \(-0.800760\pi\) |
−0.311288 | + | 0.950316i | \(0.600760\pi\) | |||||||
\(600\) | −53711.4 | − | 134320.i | −0.149198 | − | 0.373112i | ||||
\(601\) | 48243.0 | + | 148477.i | 0.133563 | + | 0.411064i | 0.995364 | − | 0.0961826i | \(-0.0306633\pi\) |
−0.861801 | + | 0.507247i | \(0.830663\pi\) | |||||||
\(602\) | 59204.5 | + | 77815.3i | 0.163366 | + | 0.214720i | ||||
\(603\) | 279728. | − | 385012.i | 0.769309 | − | 1.05886i | ||||
\(604\) | 1505.26 | + | 34064.4i | 0.00412607 | + | 0.0933741i | ||||
\(605\) | 157452. | − | 484589.i | 0.430168 | − | 1.32392i | ||||
\(606\) | 142579. | + | 407938.i | 0.388249 | + | 1.11083i | ||||
\(607\) | 186636. | + | 60641.8i | 0.506546 | + | 0.164587i | 0.551131 | − | 0.834419i | \(-0.314197\pi\) |
−0.0445849 | + | 0.999006i | \(0.514197\pi\) | |||||||
\(608\) | 98531.1 | + | 217964.i | 0.266542 | + | 0.589628i | ||||
\(609\) | 184712. | − | 134201.i | 0.498035 | − | 0.361843i | ||||
\(610\) | 286212. | + | 86057.9i | 0.769180 | + | 0.231276i | ||||
\(611\) | −21682.2 | + | 29843.0i | −0.0580793 | + | 0.0799394i | ||||
\(612\) | −220835. | + | 797937.i | −0.589610 | + | 2.13042i | ||||
\(613\) | 10679.6 | − | 7759.18i | 0.0284206 | − | 0.0206488i | −0.573484 | − | 0.819217i | \(-0.694409\pi\) |
0.601905 | + | 0.798568i | \(0.294409\pi\) | |||||||
\(614\) | −28386.1 | − | 19681.1i | −0.0752955 | − | 0.0522050i | ||||
\(615\) | − | 709762.i | − | 1.87656i | ||||||
\(616\) | −127493. | + | 50981.3i | −0.335989 | + | 0.134354i | ||||
\(617\) | 156174. | − | 480655.i | 0.410241 | − | 1.26259i | −0.506197 | − | 0.862418i | \(-0.668949\pi\) |
0.916439 | − | 0.400175i | \(-0.131051\pi\) | |||||||
\(618\) | −989196. | − | 297430.i | −2.59003 | − | 0.778768i | ||||
\(619\) | − | 425683.i | − | 1.11098i | −0.831524 | − | 0.555489i | \(-0.812531\pi\) | ||
0.831524 | − | 0.555489i | \(-0.187469\pi\) | |||||||
\(620\) | −411410. | − | 113321.i | −1.07026 | − | 0.294800i | ||||
\(621\) | −802135. | −2.08000 | ||||||||
\(622\) | 21095.2 | − | 70158.5i | 0.0545258 | − | 0.181343i | ||||
\(623\) | −103451. | − | 33613.1i | −0.266537 | − | 0.0866030i | ||||
\(624\) | 84215.9 | + | 19349.4i | 0.216284 | + | 0.0496933i | ||||
\(625\) | −460303. | −1.17838 | ||||||||
\(626\) | −356478. | + | 514149.i | −0.909669 | + | 1.31202i | ||||
\(627\) | −388190. | − | 534297.i | −0.987436 | − | 1.35909i | ||||
\(628\) | 81116.8 | − | 293097.i | 0.205680 | − | 0.743177i | ||||
\(629\) | −583144. | − | 423679.i | −1.47392 | − | 1.07087i | ||||
\(630\) | 60863.3 | − | 202420.i | 0.153347 | − | 0.510002i | ||||
\(631\) | −37556.1 | − | 51691.6i | −0.0943240 | − | 0.129826i | 0.759247 | − | 0.650803i | \(-0.225568\pi\) |
−0.853571 | + | 0.520977i | \(0.825568\pi\) | |||||||
\(632\) | 65668.4 | − | 4356.24i | 0.164408 | − | 0.0109063i | ||||
\(633\) | −59009.0 | + | 181611.i | −0.147269 | + | 0.453247i | ||||
\(634\) | 401025. | − | 140163.i | 0.997684 | − | 0.348702i | ||||
\(635\) | −204757. | − | 66529.5i | −0.507798 | − | 0.164993i | ||||
\(636\) | 6928.65 | + | 156797.i | 0.0171291 | + | 0.387636i | ||||
\(637\) | −39680.6 | − | 28829.6i | −0.0977911 | − | 0.0710494i | ||||
\(638\) | 718323. | − | 546524.i | 1.76473 | − | 1.34267i | ||||
\(639\) | 1.15766e6 | − | 376148.i | 2.83518 | − | 0.921206i | ||||
\(640\) | −207453. | + | 404625.i | −0.506476 | + | 0.987854i | ||||
\(641\) | −232002. | − | 714030.i | −0.564646 | − | 1.73780i | −0.669001 | − | 0.743262i | \(-0.733278\pi\) |
0.104355 | − | 0.994540i | \(-0.466722\pi\) | |||||||
\(642\) | −595405. | + | 208101.i | −1.44458 | + | 0.504898i | ||||
\(643\) | −192621. | + | 265120.i | −0.465887 | + | 0.641239i | −0.975717 | − | 0.219037i | \(-0.929709\pi\) |
0.509829 | + | 0.860276i | \(0.329709\pi\) | |||||||
\(644\) | 101274. | + | 66954.9i | 0.244188 | + | 0.161440i | ||||
\(645\) | −893997. | −2.14890 | ||||||||
\(646\) | 246458. | + | 170878.i | 0.590578 | + | 0.409468i | ||||
\(647\) | 73882.8 | + | 101691.i | 0.176496 | + | 0.242926i | 0.888095 | − | 0.459660i | \(-0.152029\pi\) |
−0.711599 | + | 0.702586i | \(0.752029\pi\) | |||||||
\(648\) | 217341. | − | 345068.i | 0.517597 | − | 0.821779i | ||||
\(649\) | 136823. | + | 421097.i | 0.324839 | + | 0.999753i | ||||
\(650\) | −7178.84 | + | 10354.1i | −0.0169913 | + | 0.0245067i | ||||
\(651\) | −104000. | − | 142777.i | −0.245398 | − | 0.336897i | ||||
\(652\) | 373866. | − | 140007.i | 0.879470 | − | 0.329348i | ||||
\(653\) | −32007.2 | − | 98508.0i | −0.0750622 | − | 0.231018i | 0.906485 | − | 0.422238i | \(-0.138755\pi\) |
−0.981547 | + | 0.191221i | \(0.938755\pi\) | |||||||
\(654\) | −639244. | + | 486358.i | −1.49455 | + | 1.13711i | ||||
\(655\) | 489555. | + | 673815.i | 1.14109 | + | 1.57057i | ||||
\(656\) | −317189. | + | 276315.i | −0.737073 | + | 0.642092i | ||||
\(657\) | −249429. | −0.577851 | ||||||||
\(658\) | −1773.97 | − | 80329.9i | −0.00409726 | − | 0.185535i | ||||
\(659\) | 324012. | − | 445965.i | 0.746089 | − | 1.02690i | −0.252156 | − | 0.967687i | \(-0.581140\pi\) |
0.998245 | − | 0.0592168i | \(-0.0188603\pi\) | |||||||
\(660\) | 334864. | − | 1.20995e6i | 0.768741 | − | 2.77767i | ||||
\(661\) | 32657.3 | + | 100509.i | 0.0747443 | + | 0.230039i | 0.981448 | − | 0.191729i | \(-0.0614095\pi\) |
−0.906704 | + | 0.421768i | \(0.861410\pi\) | |||||||
\(662\) | 255269. | − | 5637.23i | 0.582480 | − | 0.0128632i | ||||
\(663\) | 103036. | − | 33478.3i | 0.234401 | − | 0.0761616i | ||||
\(664\) | 526676. | + | 331726.i | 1.19456 | + | 0.752391i | ||||
\(665\) | −61942.4 | − | 45003.8i | −0.140070 | − | 0.101767i | ||||
\(666\) | 876915. | + | 1.15257e6i | 1.97701 | + | 2.59848i | ||||
\(667\) | −758998. | − | 246613.i | −1.70604 | − | 0.554326i | ||||
\(668\) | 92904.4 | + | 25712.0i | 0.208201 | + | 0.0576213i | ||||
\(669\) | 280882. | − | 864467.i | 0.627584 | − | 1.93151i | ||||
\(670\) | 94357.7 | − | 313816.i | 0.210198 | − | 0.699077i | ||||
\(671\) | 287467. | + | 395665.i | 0.638475 | + | 0.878785i | ||||
\(672\) | −171509. | + | 77530.8i | −0.379794 | + | 0.171686i | ||||
\(673\) | −368333. | − | 267610.i | −0.813225 | − | 0.590842i | 0.101539 | − | 0.994832i | \(-0.467623\pi\) |
−0.914764 | + | 0.403989i | \(0.867623\pi\) | |||||||
\(674\) | 424506. | − | 148369.i | 0.934466 | − | 0.326606i | ||||
\(675\) | 106579. | + | 146694.i | 0.233919 | + | 0.321961i | ||||
\(676\) | 157622. | + | 420904.i | 0.344925 | + | 0.921065i | ||||
\(677\) | −395475. | −0.862863 | −0.431432 | − | 0.902146i | \(-0.641991\pi\) | ||||
−0.431432 | + | 0.902146i | \(0.641991\pi\) | |||||||
\(678\) | 88116.9 | − | 1945.93i | 0.191690 | − | 0.00423320i | ||||
\(679\) | 83971.9 | + | 27284.1i | 0.182135 | + | 0.0591794i | ||||
\(680\) | 37735.4 | + | 568845.i | 0.0816077 | + | 1.23020i | ||||
\(681\) | 1.07277e6 | 2.31320 | ||||||||
\(682\) | −423500. | − | 555221.i | −0.910510 | − | 1.19371i | ||||
\(683\) | 234403.i | 0.502483i | 0.967924 | + | 0.251241i | \(0.0808388\pi\) | ||||
−0.967924 | + | 0.251241i | \(0.919161\pi\) | |||||||
\(684\) | −375351. | − | 471371.i | −0.802278 | − | 1.00751i | ||||
\(685\) | −98954.0 | + | 304549.i | −0.210888 | + | 0.649047i | ||||
\(686\) | 220208. | − | 4862.97i | 0.467934 | − | 0.0103336i | ||||
\(687\) | 308685.i | 0.654036i | ||||||||
\(688\) | 348040. | + | 399523.i | 0.735279 | + | 0.844044i | ||||
\(689\) | 11059.0 | − | 8034.81i | 0.0232957 | − | 0.0169253i | ||||
\(690\) | −1.04788e6 | + | 366244.i | −2.20096 | + | 0.769259i | ||||
\(691\) | 155137. | − | 213528.i | 0.324907 | − | 0.447197i | −0.615050 | − | 0.788488i | \(-0.710864\pi\) |
0.939958 | + | 0.341291i | \(0.110864\pi\) | |||||||
\(692\) | −647788. | + | 515831.i | −1.35276 | + | 1.07720i | ||||
\(693\) | 279829. | − | 203308.i | 0.582675 | − | 0.423338i | ||||
\(694\) | −203037. | + | 675262.i | −0.421556 | + | 1.40202i | ||||
\(695\) | 750609. | + | 243888.i | 1.55398 | + | 0.504917i | ||||
\(696\) | 950627. | − | 791899.i | 1.96242 | − | 1.63475i | ||||
\(697\) | −162980. | + | 501601.i | −0.335482 | + | 1.03251i | ||||
\(698\) | −309747. | − | 407116.i | −0.635765 | − | 0.835616i | ||||
\(699\) | −416177. | + | 572819.i | −0.851773 | + | 1.17237i | ||||
\(700\) | −1211.52 | − | 27417.1i | −0.00247250 | − | 0.0559532i | ||||
\(701\) | 74431.5 | + | 229077.i | 0.151468 | + | 0.466170i | 0.997786 | − | 0.0665077i | \(-0.0211857\pi\) |
−0.846318 | + | 0.532678i | \(0.821186\pi\) | |||||||
\(702\) | −108283. | + | 2391.28i | −0.219729 | + | 0.00485239i | ||||
\(703\) | 498919. | − | 162109.i | 1.00953 | − | 0.328016i | ||||
\(704\) | −671087. | + | 321395.i | −1.35405 | + | 0.648475i | ||||
\(705\) | 594346. | + | 431817.i | 1.19581 | + | 0.868804i | ||||
\(706\) | 1984.72 | + | 89873.4i | 0.00398190 | + | 0.180311i | ||||
\(707\) | 81981.2i | 0.164012i | ||||||||
\(708\) | 212852. | + | 568387.i | 0.424631 | + | 1.13391i | ||||
\(709\) | −110288. | + | 80128.9i | −0.219399 | + | 0.159403i | −0.692056 | − | 0.721844i | \(-0.743295\pi\) |
0.472657 | + | 0.881247i | \(0.343295\pi\) | |||||||
\(710\) | 667046. | − | 507511.i | 1.32324 | − | 1.00677i | ||||
\(711\) | −157672. | + | 51230.8i | −0.311900 | + | 0.101343i | ||||
\(712\) | −571430. | − | 144644.i | −1.12721 | − | 0.285326i | ||||
\(713\) | −190079. | + | 587438.i | −0.373899 | + | 1.15553i | ||||
\(714\) | −134458. | + | 193929.i | −0.263748 | + | 0.380406i | ||||
\(715\) | −103991. | + | 33788.8i | −0.203416 | + | 0.0660938i | ||||
\(716\) | 32474.5 | + | 734906.i | 0.0633455 | + | 1.43353i | ||||
\(717\) | −595245. | + | 432471.i | −1.15786 | + | 0.841237i | ||||
\(718\) | −186238. | − | 129125.i | −0.361260 | − | 0.250474i | ||||
\(719\) | − | 541790.i | − | 1.04803i | −0.851710 | − | 0.524014i | \(-0.824434\pi\) | ||
0.851710 | − | 0.524014i | \(-0.175566\pi\) | |||||||
\(720\) | 256491. | − | 1.11635e6i | 0.494774 | − | 2.15345i | ||||
\(721\) | −158536. | − | 115183.i | −0.304970 | − | 0.221574i | ||||
\(722\) | 286051. | − | 99978.0i | 0.548743 | − | 0.191792i | ||||
\(723\) | 1.34453e6 | − | 436864.i | 2.57213 | − | 0.835736i | ||||
\(724\) | −151911. | − | 100433.i | −0.289809 | − | 0.191601i | ||||
\(725\) | 55747.2 | + | 171572.i | 0.106059 | + | 0.326416i | ||||
\(726\) | 909594. | − | 692050.i | 1.72574 | − | 1.31300i | ||||
\(727\) | 171573. | − | 236150.i | 0.324623 | − | 0.446806i | −0.615248 | − | 0.788333i | \(-0.710944\pi\) |
0.939872 | + | 0.341528i | \(0.110944\pi\) | |||||||
\(728\) | 13870.9 | + | 8736.58i | 0.0261723 | + | 0.0164846i | ||||
\(729\) | 168909. | − | 519847.i | 0.317831 | − | 0.978184i | ||||
\(730\) | −162133. | + | 56667.4i | −0.304247 | + | 0.106338i | ||||
\(731\) | 631804. | + | 205286.i | 1.18235 | + | 0.384170i | ||||
\(732\) | 417612. | + | 524443.i | 0.779383 | + | 0.978760i | ||||
\(733\) | −395401. | + | 287276.i | −0.735918 | + | 0.534676i | −0.891430 | − | 0.453158i | \(-0.850297\pi\) |
0.155512 | + | 0.987834i | \(0.450297\pi\) | |||||||
\(734\) | −182254. | + | 606143.i | −0.338287 | + | 1.12508i | ||||
\(735\) | −574163. | + | 790267.i | −1.06282 | + | 1.46285i | ||||
\(736\) | 571618. | + | 325709.i | 1.05524 | + | 0.601276i | ||||
\(737\) | 433825. | − | 315192.i | 0.798692 | − | 0.580284i | ||||
\(738\) | 603785. | − | 870842.i | 1.10859 | − | 1.59892i | ||||
\(739\) | 529726.i | 0.969980i | 0.874520 | + | 0.484990i | \(0.161177\pi\) | ||||
−0.874520 | + | 0.484990i | \(0.838823\pi\) | |||||||
\(740\) | 831862. | + | 549968.i | 1.51911 | + | 1.00432i | ||||
\(741\) | −24365.1 | + | 74988.2i | −0.0443744 | + | 0.136570i | ||||
\(742\) | −8573.60 | + | 28514.1i | −0.0155724 | + | 0.0517908i | ||||
\(743\) | 146434.i | 0.265256i | 0.991166 | + | 0.132628i | \(0.0423415\pi\) | ||||
−0.991166 | + | 0.132628i | \(0.957658\pi\) | |||||||
\(744\) | −613556. | − | 734714.i | −1.10843 | − | 1.32731i | ||||
\(745\) | 428937. | 0.772824 | ||||||||
\(746\) | −925740. | − | 278350.i | −1.66346 | − | 0.500166i | ||||
\(747\) | −1.49122e6 | − | 484526.i | −2.67239 | − | 0.868313i | ||||
\(748\) | −514492. | + | 778203.i | −0.919550 | + | 1.39088i | ||||
\(749\) | −119656. | −0.213289 | ||||||||
\(750\) | −681194. | − | 472295.i | −1.21101 | − | 0.839636i | ||||
\(751\) | −123399. | − | 169845.i | −0.218793 | − | 0.301143i | 0.685485 | − | 0.728087i | \(-0.259590\pi\) |
−0.904278 | + | 0.426944i | \(0.859590\pi\) | |||||||
\(752\) | −38405.9 | − | 433720.i | −0.0679145 | − | 0.766961i | ||||
\(753\) | −38090.6 | − | 27674.5i | −0.0671782 | − | 0.0488078i | ||||
\(754\) | −103195. | − | 31028.6i | −0.181517 | − | 0.0545782i | ||||
\(755\) | −34764.3 | − | 47849.0i | −0.0609874 | − | 0.0839419i | ||||
\(756\) | 184556. | − | 146961.i | 0.322911 | − | 0.257133i | ||||
\(757\) | 253596. | − | 780487.i | 0.442537 | − | 1.36199i | −0.442625 | − | 0.896707i | \(-0.645953\pi\) |
0.885162 | − | 0.465283i | \(-0.154047\pi\) | |||||||
\(758\) | −337009. | − | 964230.i | −0.586548 | − | 1.67819i | ||||
\(759\) | −1.72755e6 | − | 561315.i | −2.99880 | − | 0.974368i | ||||
\(760\) | −351075. | − | 221124.i | −0.607816 | − | 0.382833i | ||||
\(761\) | 60016.9 | + | 43604.8i | 0.103634 | + | 0.0752949i | 0.638396 | − | 0.769708i | \(-0.279598\pi\) |
−0.534761 | + | 0.845003i | \(0.679598\pi\) | |||||||
\(762\) | −292417. | − | 384337.i | −0.503608 | − | 0.661916i | ||||
\(763\) | −144924. | + | 47088.5i | −0.248937 | + | 0.0808846i | ||||
\(764\) | 104120. | − | 157488.i | 0.178380 | − | 0.269812i | ||||
\(765\) | −443780. | − | 1.36582e6i | −0.758307 | − | 2.33383i | ||||
\(766\) | 121857. | + | 348650.i | 0.207679 | + | 0.594200i | ||||
\(767\) | 31071.0 | − | 42765.6i | 0.0528160 | − | 0.0726949i | ||||
\(768\) | −899564. | + | 480740.i | −1.52514 | + | 0.815057i | ||||
\(769\) | 455.371 | 0.000770040 | 0.000385020 | − | 1.00000i | \(-0.499877\pi\) | ||||
0.000385020 | 1.00000i | \(0.499877\pi\) | ||||||||
\(770\) | 135705. | − | 195728.i | 0.228883 | − | 0.330119i | ||||
\(771\) | −362148. | − | 498454.i | −0.609224 | − | 0.838525i | ||||
\(772\) | −1.13463e6 | + | 50137.7i | −1.90379 | + | 0.0841260i | ||||
\(773\) | −156291. | − | 481015.i | −0.261562 | − | 0.805006i | −0.992465 | − | 0.122525i | \(-0.960901\pi\) |
0.730903 | − | 0.682481i | \(-0.239099\pi\) | |||||||
\(774\) | −1.09689e6 | − | 760512.i | −1.83097 | − | 1.26948i | ||||
\(775\) | 132686. | − | 43291.1i | 0.220913 | − | 0.0720767i | ||||
\(776\) | 463836. | + | 117409.i | 0.770266 | + | 0.194975i | ||||
\(777\) | 127558. | + | 392583.i | 0.211283 | + | 0.650263i | ||||
\(778\) | −636435. | − | 836497.i | −1.05146 | − | 1.38199i | ||||
\(779\) | −225619. | − | 310539.i | −0.371793 | − | 0.511730i | ||||
\(780\) | −140365. | + | 52564.5i | −0.230711 | + | 0.0863980i | ||||
\(781\) | 1.37157e6 | 2.24861 | ||||||||
\(782\) | 824652. | − | 18211.2i | 1.34852 | − | 0.0297801i | ||||
\(783\) | −911548. | + | 1.25464e6i | −1.48681 | + | 2.04642i | ||||
\(784\) | 576692. | − | 51066.2i | 0.938236 | − | 0.0830809i | ||||
\(785\) | 163009. | + | 501690.i | 0.264528 | + | 0.814134i | ||||
\(786\) | 41247.7 | + | 1.86780e6i | 0.0667658 | + | 3.02333i | ||||
\(787\) | 362754. | − | 117866.i | 0.585684 | − | 0.190300i | −0.00116145 | − | 0.999999i | \(-0.500370\pi\) |
0.586845 | + | 0.809699i | \(0.300370\pi\) | |||||||
\(788\) | −287702. | + | 12713.2i | −0.463330 | + | 0.0204739i | ||||
\(789\) | 266991. | + | 193980.i | 0.428887 | + | 0.311604i | ||||
\(790\) | −90850.7 | + | 69122.3i | −0.145571 | + | 0.110755i | ||||
\(791\) | 15902.5 | + | 5167.02i | 0.0254162 | + | 0.00825824i | ||||
\(792\) | 1.44015e6 | − | 1.19969e6i | 2.29593 | − | 1.91257i | ||||
\(793\) | 18043.2 | − | 55531.3i | 0.0286924 | − | 0.0883062i | ||||
\(794\) | 1.08248e6 | + | 325478.i | 1.71703 | + | 0.516275i | ||||
\(795\) | −160019. | − | 220247.i | −0.253185 | − | 0.348479i | ||||
\(796\) | 609835. | + | 765840.i | 0.962468 | + | 1.20868i | ||||
\(797\) | −967168. | − | 702688.i | −1.52260 | − | 1.10623i | −0.960181 | − | 0.279377i | \(-0.909872\pi\) |
−0.562416 | − | 0.826855i | \(-0.690128\pi\) | |||||||
\(798\) | −56665.4 | − | 162128.i | −0.0889841 | − | 0.254596i | ||||
\(799\) | −320878. | − | 441651.i | −0.502628 | − | 0.691808i | ||||
\(800\) | −16385.2 | − | 147814.i | −0.0256019 | − | 0.230959i | ||||
\(801\) | 1.48487e6 | 2.31431 | ||||||||
\(802\) | 23221.5 | + | 1.05153e6i | 0.0361029 | + | 1.63483i | ||||
\(803\) | −267297. | − | 86849.9i | −0.414536 | − | 0.134691i | ||||
\(804\) | 575023. | − | 457889.i | 0.889556 | − | 0.708350i | ||||
\(805\) | −210586. | −0.324966 | ||||||||
\(806\) | −23908.2 | + | 79867.1i | −0.0368025 | + | 0.122941i | ||||
\(807\) | 691686.i | 1.06209i | ||||||||
\(808\) | 29406.1 | + | 443285.i | 0.0450417 | + | 0.678985i | ||||
\(809\) | 126725. | − | 390019.i | 0.193627 | − | 0.595921i | −0.806363 | − | 0.591420i | \(-0.798567\pi\) |
0.999990 | − | 0.00450070i | \(-0.00143262\pi\) | |||||||
\(810\) | 15617.5 | + | 707202.i | 0.0238036 | + | 1.07789i | ||||
\(811\) | − | 135474.i | − | 0.205975i | −0.994683 | − | 0.102987i | \(-0.967160\pi\) | ||
0.994683 | − | 0.102987i | \(-0.0328401\pi\) | |||||||
\(812\) | 219813. | − | 82316.7i | 0.333382 | − | 0.124846i | ||||
\(813\) | 1.11539e6 | − | 810379.i | 1.68751 | − | 1.22605i | ||||
\(814\) | 538412. | + | 1.54047e6i | 0.812580 | + | 2.32491i | ||||
\(815\) | −407028. | + | 560226.i | −0.612786 | + | 0.843428i | ||||
\(816\) | −657473. | + | 1.09683e6i | −0.987410 | + | 1.64725i | ||||
\(817\) | −391146. | + | 284185.i | −0.585997 | + | 0.425752i | ||||
\(818\) | 327587. | + | 98498.4i | 0.489576 | + | 0.147205i | ||||
\(819\) | −39273.8 | − | 12760.8i | −0.0585511 | − | 0.0190244i | ||||
\(820\) | 194626. | − | 703237.i | 0.289450 | − | 1.04586i | ||||
\(821\) | −211278. | + | 650247.i | −0.313450 | + | 0.964699i | 0.662938 | + | 0.748674i | \(0.269309\pi\) |
−0.976388 | + | 0.216025i | \(0.930691\pi\) | |||||||
\(822\) | −571652. | + | 434932.i | −0.846035 | + | 0.643691i | ||||
\(823\) | 660412. | − | 908978.i | 0.975023 | − | 1.34200i | 0.0355553 | − | 0.999368i | \(-0.488680\pi\) |
0.939468 | − | 0.342637i | \(-0.111320\pi\) | |||||||
\(824\) | −898543. | − | 565946.i | −1.32338 | − | 0.833529i | ||||
\(825\) | 126886. | + | 390514.i | 0.186425 | + | 0.573758i | ||||
\(826\) | 2542.13 | + | 115114.i | 0.00372595 | + | 0.168721i | ||||
\(827\) | −644597. | + | 209442.i | −0.942492 | + | 0.306234i | −0.739661 | − | 0.672980i | \(-0.765014\pi\) |
−0.202831 | + | 0.979214i | \(0.565014\pi\) | |||||||
\(828\) | −1.59725e6 | − | 442051.i | −2.32977 | − | 0.644780i | ||||
\(829\) | 917751. | + | 666785.i | 1.33541 | + | 0.970235i | 0.999599 | + | 0.0283068i | \(0.00901155\pi\) |
0.335815 | + | 0.941928i | \(0.390988\pi\) | |||||||
\(830\) | −1.07940e6 | + | 23836.9i | −1.56684 | + | 0.0346014i | ||||
\(831\) | − | 114629.i | − | 0.165994i | ||||||
\(832\) | 78135.9 | + | 42264.6i | 0.112877 | + | 0.0610563i | ||||
\(833\) | 587238. | − | 426653.i | 0.846299 | − | 0.614872i | ||||
\(834\) | 1.07196e6 | + | 1.40893e6i | 1.54115 | + | 2.02561i | ||||
\(835\) | −159023. | + | 51669.7i | −0.228080 | + | 0.0741077i | ||||
\(836\) | −238110. | − | 635832.i | −0.340694 | − | 0.909766i | ||||
\(837\) | 971520. | + | 704043.i | 1.38676 | + | 1.00496i | ||||
\(838\) | 619708. | + | 429665.i | 0.882469 | + | 0.611846i | ||||
\(839\) | 470515. | − | 152880.i | 0.668420 | − | 0.217183i | 0.0449015 | − | 0.998991i | \(-0.485703\pi\) |
0.623519 | + | 0.781809i | \(0.285703\pi\) | |||||||
\(840\) | 173995. | − | 276249.i | 0.246592 | − | 0.391509i | ||||
\(841\) | −676058. | + | 491185.i | −0.955855 | + | 0.694469i | ||||
\(842\) | 515202. | − | 743078.i | 0.726697 | − | 1.04812i | ||||
\(843\) | 645172.i | 0.907864i | ||||||||
\(844\) | −108267. | + | 163760.i | −0.151988 | + | 0.229892i | ||||
\(845\) | −630711. | − | 458238.i | −0.883318 | − | 0.641768i | ||||
\(846\) | 361891. | + | 1.03542e6i | 0.505635 | + | 1.44669i | ||||
\(847\) | 206215. | − | 67003.2i | 0.287444 | − | 0.0933962i | ||||
\(848\) | −36130.9 | + | 157256.i | −0.0502443 | + | 0.218683i | ||||
\(849\) | 575659. | + | 1.77170e6i | 0.798638 | + | 2.45795i | ||||
\(850\) | −112901. | − | 148392.i | −0.156265 | − | 0.205387i | ||||
\(851\) | 848089. | − | 1.16729e6i | 1.17107 | − | 1.61184i | ||||
\(852\) | 1.87827e6 | − | 82998.3i | 2.58750 | − | 0.114338i | ||||
\(853\) | −108469. | + | 333833.i | −0.149076 | + | 0.458809i | −0.997513 | − | 0.0704883i | \(-0.977544\pi\) |
0.848437 | + | 0.529297i | \(0.177544\pi\) | |||||||
\(854\) | 41962.7 | + | 120061.i | 0.0575370 | + | 0.164621i | ||||
\(855\) | 994026. | + | 322979.i | 1.35977 | + | 0.441816i | ||||
\(856\) | −646996. | + | 42919.7i | −0.882986 | + | 0.0585746i | ||||
\(857\) | 724715. | − | 526536.i | 0.986747 | − | 0.716913i | 0.0275403 | − | 0.999621i | \(-0.491233\pi\) |
0.959206 | + | 0.282707i | \(0.0912325\pi\) | |||||||
\(858\) | −234882. | − | 70624.0i | −0.319062 | − | 0.0959351i | ||||
\(859\) | −479943. | + | 660585.i | −0.650434 | + | 0.895245i | −0.999118 | − | 0.0419950i | \(-0.986629\pi\) |
0.348684 | + | 0.937240i | \(0.386629\pi\) | |||||||
\(860\) | −885779. | − | 245146.i | −1.19765 | − | 0.331457i | ||||
\(861\) | 244352. | − | 177532.i | 0.329618 | − | 0.239481i | ||||
\(862\) | −63351.4 | − | 43923.7i | −0.0852593 | − | 0.0591132i | ||||
\(863\) | − | 356357.i | − | 0.478480i | −0.970960 | − | 0.239240i | \(-0.923102\pi\) | ||
0.970960 | − | 0.239240i | \(-0.0768983\pi\) | |||||||
\(864\) | 945206. | − | 860839.i | 1.26619 | − | 1.15317i | ||||
\(865\) | 443858. | − | 1.36606e6i | 0.593215 | − | 1.82573i | ||||
\(866\) | 64016.8 | + | 19248.5i | 0.0853607 | + | 0.0256661i | ||||
\(867\) | 303435.i | 0.403672i | ||||||||
\(868\) | −63892.3 | − | 169983.i | −0.0848026 | − | 0.225614i | ||||
\(869\) | −186805. | −0.247371 | ||||||||
\(870\) | −617957. | + | 2.05521e6i | −0.816431 | + | 2.71529i | ||||
\(871\) | −60887.0 | − | 19783.4i | −0.0802580 | − | 0.0260774i | ||||
\(872\) | −766733. | + | 306598.i | −1.00835 | + | 0.403215i | ||||
\(873\) | −1.20528e6 | −1.58147 | ||||||||
\(874\) | −342050. | + | 493340.i | −0.447782 | + | 0.645838i | ||||
\(875\) | −92431.0 | − | 127220.i | −0.120726 | − | 0.166165i | ||||
\(876\) | −371302. | − | 102761.i | −0.483859 | − | 0.133912i | ||||
\(877\) | −834353. | − | 606193.i | −1.08480 | − | 0.788155i | −0.106288 | − | 0.994335i | \(-0.533897\pi\) |
−0.978514 | + | 0.206181i | \(0.933897\pi\) | |||||||
\(878\) | −81817.7 | + | 272110.i | −0.106135 | + | 0.352984i | ||||
\(879\) | 85572.1 | + | 117780.i | 0.110753 | + | 0.152438i | ||||
\(880\) | 663571. | − | 1.10701e6i | 0.856883 | − | 1.42950i | ||||
\(881\) | −207537. | + | 638734.i | −0.267389 | + | 0.822940i | 0.723744 | + | 0.690069i | \(0.242420\pi\) |
−0.991133 | + | 0.132871i | \(0.957580\pi\) | |||||||
\(882\) | −1.37674e6 | + | 481186.i | −1.76976 | + | 0.618551i | ||||
\(883\) | 117811. | + | 38279.1i | 0.151100 | + | 0.0490953i | 0.383590 | − | 0.923503i | \(-0.374687\pi\) |
−0.232491 | + | 0.972599i | \(0.574687\pi\) | |||||||
\(884\) | 111269. | − | 4916.80i | 0.142386 | − | 0.00629185i | ||||
\(885\) | −851708. | − | 618802.i | −1.08744 | − | 0.790069i | ||||
\(886\) | −369746. | + | 281315.i | −0.471016 | + | 0.358365i | ||||
\(887\) | 117221. | − | 38087.6i | 0.148991 | − | 0.0484101i | −0.233572 | − | 0.972339i | \(-0.575041\pi\) |
0.382563 | + | 0.923929i | \(0.375041\pi\) | |||||||
\(888\) | 830542. | + | 2.07700e6i | 1.05326 | + | 2.63397i | ||||
\(889\) | −28311.4 | − | 87133.4i | −0.0358226 | − | 0.110251i | ||||
\(890\) | 965191. | − | 337345.i | 1.21852 | − | 0.425887i | ||||
\(891\) | −680387. | + | 936472.i | −0.857039 | + | 1.17961i | ||||
\(892\) | 515348. | − | 779498.i | 0.647696 | − | 0.979682i | ||||
\(893\) | 397308. | 0.498223 | ||||||||
\(894\) | 790700. | + | 548220.i | 0.989319 | + | 0.685929i | ||||
\(895\) | −750007. | − | 1.03230e6i | −0.936309 | − | 1.28872i | ||||
\(896\) | −191192. | + | 29788.1i | −0.238152 | + | 0.0371046i | ||||
\(897\) | 67014.4 | + | 206249.i | 0.0832881 | + | 0.256334i | ||||
\(898\) | −758359. | + | 1.09379e6i | −0.940421 | + | 1.35637i | ||||
\(899\) | 702819. | + | 964872.i | 0.869609 | + | 1.19385i | ||||
\(900\) | 131384. | + | 350839.i | 0.162202 | + | 0.433134i | ||||
\(901\) | 62513.7 | + | 192397.i | 0.0770062 | + | 0.237001i | ||||
\(902\) | 950260. | − | 722989.i | 1.16796 | − | 0.888626i | ||||
\(903\) | −223615. | − | 307780.i | −0.274237 | − | 0.377455i | ||||
\(904\) | 87840.4 | + | 22234.8i | 0.107487 | + | 0.0272079i | ||||
\(905\) | 315880. | 0.385678 | ||||||||
\(906\) | −2929.08 | − | 132636.i | −0.00356841 | − | 0.161587i | ||||
\(907\) | 418426. | − | 575914.i | 0.508632 | − | 0.700072i | −0.475056 | − | 0.879956i | \(-0.657572\pi\) |
0.983688 | + | 0.179884i | \(0.0575721\pi\) | |||||||
\(908\) | 1.06291e6 | + | 294169.i | 1.28921 | + | 0.356800i | ||||
\(909\) | −345826. | − | 1.06434e6i | −0.418533 | − | 1.28811i | ||||
\(910\) | −28427.8 | + | 627.786i | −0.0343290 | + | 0.000758105i | ||||
\(911\) | −453836. | + | 147460.i | −0.546843 | + | 0.177680i | −0.569393 | − | 0.822066i | \(-0.692822\pi\) |
0.0225499 | + | 0.999746i | \(0.492822\pi\) | |||||||
\(912\) | −364553. | − | 856324.i | −0.438299 | − | 1.02955i | ||||
\(913\) | −1.42933e6 | − | 1.03847e6i | −1.71471 | − | 1.24581i | ||||
\(914\) | −164333. | − | 215991.i | −0.196713 | − | 0.258550i | ||||
\(915\) | −1.10595e6 | − | 359343.i | −1.32097 | − | 0.429208i | ||||
\(916\) | −84645.4 | + | 305847.i | −0.100882 | + | 0.364513i | ||||
\(917\) | −109525. | + | 337082.i | −0.130249 | + | 0.400864i | ||||
\(918\) | 461542. | − | 1.53500e6i | 0.547678 | − | 1.82147i | ||||
\(919\) | −27311.6 | − | 37591.2i | −0.0323382 | − | 0.0445097i | 0.792542 | − | 0.609818i | \(-0.208757\pi\) |
−0.824880 | + | 0.565308i | \(0.808757\pi\) | |||||||
\(920\) | −1.13867e6 | + | 75535.9i | −1.34531 | + | 0.0892437i | ||||
\(921\) | 108729. | + | 78995.9i | 0.128181 | + | 0.0931291i | ||||
\(922\) | −1.17577e6 | + | 410946.i | −1.38313 | + | 0.483418i | ||||
\(923\) | −96249.1 | − | 132475.i | −0.112978 | − | 0.155501i | ||||
\(924\) | 500315. | − | 187361.i | 0.586003 | − | 0.219449i | ||||
\(925\) | −326159. | −0.381194 | ||||||||
\(926\) | −276564. | + | 6107.52i | −0.322533 | + | 0.00712267i | ||||
\(927\) | 2.54412e6 | + | 826633.i | 2.96058 | + | 0.961952i | ||||
\(928\) | 1.15904e6 | − | 523945.i | 1.34586 | − | 0.608401i | ||||
\(929\) | −419398. | −0.485954 | −0.242977 | − | 0.970032i | \(-0.578124\pi\) | ||||
−0.242977 | + | 0.970032i | \(0.578124\pi\) | |||||||
\(930\) | 1.59061e6 | + | 476150.i | 1.83907 | + | 0.550526i | ||||
\(931\) | 528277.i | 0.609484i | ||||||||
\(932\) | −569426. | + | 453432.i | −0.655549 | + | 0.522011i | ||||
\(933\) | −88085.0 | + | 271098.i | −0.101190 | + | 0.311432i | ||||
\(934\) | 837331. | − | 18491.2i | 0.959850 | − | 0.0211969i | ||||
\(935\) | − | 1.61818e6i | − | 1.85098i | ||||||
\(936\) | −216937. | − | 54912.5i | −0.247617 | − | 0.0626786i | ||||
\(937\) | 306963. | − | 223022.i | 0.349628 | − | 0.254020i | −0.399085 | − | 0.916914i | \(-0.630672\pi\) |
0.748713 | + | 0.662894i | \(0.230672\pi\) | |||||||
\(938\) | 131640. | − | 46009.8i | 0.149618 | − | 0.0522931i | ||||
\(939\) | 1.43083e6 | − | 1.96937e6i | 1.62277 | − | 2.23355i | ||||
\(940\) | 470472. | + | 590825.i | 0.532449 | + | 0.668657i | ||||
\(941\) | 579179. | − | 420798.i | 0.654084 | − | 0.475220i | −0.210576 | − | 0.977578i | \(-0.567534\pi\) |
0.864660 | + | 0.502358i | \(0.167534\pi\) | |||||||
\(942\) | −340715. | + | 1.13315e6i | −0.383963 | + | 1.27699i | ||||
\(943\) | −1.00407e6 | − | 326242.i | −1.12912 | − | 0.366873i | ||||
\(944\) | 55036.4 | + | 621528.i | 0.0617599 | + | 0.697456i | ||||
\(945\) | −126456. | + | 389190.i | −0.141604 | + | 0.435811i | ||||
\(946\) | −910659. | − | 1.19692e6i | −1.01759 | − | 1.33747i | ||||
\(947\) | 145096. | − | 199707.i | 0.161791 | − | 0.222686i | −0.720423 | − | 0.693535i | \(-0.756052\pi\) |
0.882214 | + | 0.470849i | \(0.156052\pi\) | |||||||
\(948\) | −255818. | + | 11304.2i | −0.284652 | + | 0.0125784i | ||||
\(949\) | 10368.9 | + | 31912.0i | 0.0115133 | + | 0.0354342i | ||||
\(950\) | 135670. | − | 2996.06i | 0.150326 | − | 0.00331974i | ||||
\(951\) | −1.57199e6 | + | 510770.i | −1.73816 | + | 0.564761i | ||||
\(952\) | −186400. | + | 155276.i | −0.205670 | + | 0.171329i | ||||
\(953\) | −769211. | − | 558864.i | −0.846954 | − | 0.615348i | 0.0773507 | − | 0.997004i | \(-0.475354\pi\) |
−0.924304 | + | 0.381656i | \(0.875354\pi\) | |||||||
\(954\) | −8973.84 | − | 406359.i | −0.00986010 | − | 0.446491i | ||||
\(955\) | 327477.i | 0.359066i | ||||||||
\(956\) | −708362. | + | 265271.i | −0.775067 | + | 0.290251i | ||||
\(957\) | −2.84116e6 | + | 2.06422e6i | −3.10221 | + | 2.25389i | ||||
\(958\) | 23169.0 | − | 17627.8i | 0.0252451 | − | 0.0192073i | ||||
\(959\) | −129600. | + | 42109.5i | −0.140918 | + | 0.0457871i | ||||
\(960\) | 841730. | − | 1.55613e6i | 0.913335 | − | 1.68851i | ||||
\(961\) | 745819. | − | 544652.i | 0.807582 | − | 0.589755i | ||||
\(962\) | 111007. | − | 160106.i | 0.119950 | − | 0.173004i | ||||
\(963\) | 1.55346e6 | − | 504750.i | 1.67513 | − | 0.544281i | ||||
\(964\) | 1.45196e6 | − | 64160.2i | 1.56243 | − | 0.0690417i | ||||
\(965\) | 1.59377e6 | − | 1.15794e6i | 1.71148 | − | 1.24346i | ||||
\(966\) | −388193. | − | 269148.i | −0.416000 | − | 0.288427i | ||||
\(967\) | 936125.i | 1.00111i | 0.865705 | + | 0.500554i | \(0.166870\pi\) | ||||
−0.865705 | + | 0.500554i | \(0.833130\pi\) | |||||||
\(968\) | 1.09100e6 | − | 436265.i | 1.16433 | − | 0.465585i | ||||
\(969\) | −944017. | − | 685869.i | −1.00539 | − | 0.730455i | ||||
\(970\) | −783455. | + | 273826.i | −0.832665 | + | 0.291026i | ||||
\(971\) | 360244. | − | 117050.i | 0.382084 | − | 0.124147i | −0.111676 | − | 0.993745i | \(-0.535622\pi\) |
0.493760 | + | 0.869598i | \(0.335622\pi\) | |||||||
\(972\) | 17272.4 | − | 26125.7i | 0.0182819 | − | 0.0276526i | ||||
\(973\) | 103785. | + | 319419.i | 0.109625 | + | 0.337392i | ||||
\(974\) | −61793.8 | + | 47014.8i | −0.0651369 | + | 0.0495583i | ||||
\(975\) | 28814.5 | − | 39659.7i | 0.0303111 | − | 0.0417196i | ||||
\(976\) | 269964. | + | 634137.i | 0.283404 | + | 0.665707i | ||||
\(977\) | −417846. | + | 1.28600e6i | −0.437751 | + | 1.34726i | 0.452490 | + | 0.891769i | \(0.350536\pi\) |
−0.890241 | + | 0.455489i | \(0.849464\pi\) | |||||||
\(978\) | −1.46633e6 | + | 512499.i | −1.53304 | + | 0.535816i | ||||
\(979\) | 1.59123e6 | + | 517023.i | 1.66023 | + | 0.539442i | ||||
\(980\) | −785586. | + | 625559.i | −0.817978 | + | 0.651353i | ||||
\(981\) | 1.68287e6 | − | 1.22268e6i | 1.74869 | − | 1.27050i | ||||
\(982\) | 474006. | − | 1.57645e6i | 0.491542 | − | 1.63478i | ||||
\(983\) | 249586. | − | 343526.i | 0.258293 | − | 0.355510i | −0.660101 | − | 0.751177i | \(-0.729486\pi\) |
0.918394 | + | 0.395667i | \(0.129486\pi\) | |||||||
\(984\) | 1.25757e6 | − | 1.04759e6i | 1.29880 | − | 1.08194i | ||||
\(985\) | 404125. | − | 293614.i | 0.416527 | − | 0.302625i | ||||
\(986\) | 908651. | − | 1.31055e6i | 0.934638 | − | 1.34803i | ||||
\(987\) | 312628.i | 0.320918i | ||||||||
\(988\) | −44703.9 | + | 67617.6i | −0.0457964 | + | 0.0692701i | ||||
\(989\) | −410925. | + | 1.26470e6i | −0.420117 | + | 1.29299i | ||||
\(990\) | −936174. | + | 3.11354e6i | −0.955183 | + | 3.17676i | ||||
\(991\) | 308365.i | 0.313992i | 0.987599 | + | 0.156996i | \(0.0501809\pi\) | ||||
−0.987599 | + | 0.156996i | \(0.949819\pi\) | |||||||
\(992\) | −406447. | − | 896205.i | −0.413029 | − | 0.910718i | ||||
\(993\) | −993455. | −1.00751 | ||||||||
\(994\) | 341571. | + | 102703.i | 0.345707 | + | 0.103947i | ||||
\(995\) | −1.61500e6 | − | 524746.i | −1.63127 | − | 0.530033i | ||||
\(996\) | −2.02022e6 | − | 1.33563e6i | −2.03648 | − | 1.34638i | ||||
\(997\) | 1.45110e6 | 1.45985 | 0.729923 | − | 0.683529i | \(-0.239556\pi\) | ||||
0.729923 | + | 0.683529i | \(0.239556\pi\) | |||||||
\(998\) | −1.18696e6 | − | 822962.i | −1.19172 | − | 0.826264i | ||||
\(999\) | −1.64804e6 | − | 2.26833e6i | −1.65134 | − | 2.27288i |
(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 | 124.5.l.a.35.7 | ✓ | 248 | |
4.3 | odd | 2 | inner | 124.5.l.a.35.44 | yes | 248 | |
31.8 | even | 5 | inner | 124.5.l.a.39.44 | yes | 248 | |
124.39 | odd | 10 | inner | 124.5.l.a.39.7 | yes | 248 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
124.5.l.a.35.7 | ✓ | 248 | 1.1 | even | 1 | trivial | |
124.5.l.a.35.44 | yes | 248 | 4.3 | odd | 2 | inner | |
124.5.l.a.39.7 | yes | 248 | 124.39 | odd | 10 | inner | |
124.5.l.a.39.44 | yes | 248 | 31.8 | even | 5 | inner |