Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [19,5,Mod(8,19)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(19, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("19.8");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 19.d (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.96402929859\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 109x^{8} + 4107x^{6} + 61507x^{4} + 300520x^{2} + 108300 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 8.2 | ||
Root | \(4.58432i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 19.8 |
Dual form | 19.5.d.a.12.2 |
$q$-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 \(\left(\mathbb{Z}/19\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.97014 | − | 2.29216i | −0.992535 | − | 0.573040i | −0.0865039 | − | 0.996252i | \(-0.527570\pi\) |
−0.906031 | + | 0.423211i | \(0.860903\pi\) | |||||||
\(3\) | 10.1306 | + | 5.84893i | 1.12563 | + | 0.649881i | 0.942832 | − | 0.333270i | \(-0.108152\pi\) |
0.182796 | + | 0.983151i | \(0.441485\pi\) | |||||||
\(4\) | 2.50801 | + | 4.34400i | 0.156750 | + | 0.271500i | ||||
\(5\) | 20.8352 | − | 36.0877i | 0.833410 | − | 1.44351i | −0.0619087 | − | 0.998082i | \(-0.519719\pi\) |
0.895319 | − | 0.445426i | \(-0.146948\pi\) | |||||||
\(6\) | −26.8134 | − | 46.4422i | −0.744816 | − | 1.29006i | ||||
\(7\) | 24.1856 | 0.493583 | 0.246791 | − | 0.969069i | \(-0.420624\pi\) | ||||
0.246791 | + | 0.969069i | \(0.420624\pi\) | |||||||
\(8\) | 50.3541i | 0.786783i | ||||||||
\(9\) | 27.9200 | + | 48.3589i | 0.344692 | + | 0.597023i | ||||
\(10\) | −165.438 | + | 95.5155i | −1.65438 | + | 0.955155i | ||||
\(11\) | 62.4993 | 0.516523 | 0.258261 | − | 0.966075i | \(-0.416850\pi\) | ||||
0.258261 | + | 0.966075i | \(0.416850\pi\) | |||||||
\(12\) | 58.6767i | 0.407477i | ||||||||
\(13\) | −250.356 | + | 144.543i | −1.48139 | + | 0.855283i | −0.999777 | − | 0.0210988i | \(-0.993284\pi\) |
−0.481617 | + | 0.876382i | \(0.659950\pi\) | |||||||
\(14\) | −96.0201 | − | 55.4372i | −0.489898 | − | 0.282843i | ||||
\(15\) | 422.149 | − | 243.728i | 1.87622 | − | 1.08324i | ||||
\(16\) | 155.548 | − | 269.417i | 0.607609 | − | 1.05241i | ||||
\(17\) | −12.2538 | + | 21.2242i | −0.0424006 | + | 0.0734400i | −0.886447 | − | 0.462830i | \(-0.846834\pi\) |
0.844046 | + | 0.536270i | \(0.180167\pi\) | |||||||
\(18\) | − | 255.989i | − | 0.790089i | ||||||
\(19\) | −283.198 | + | 223.874i | −0.784483 | + | 0.620150i | ||||
\(20\) | 209.020 | 0.522550 | ||||||||
\(21\) | 245.015 | + | 141.460i | 0.555590 | + | 0.320770i | ||||
\(22\) | −248.131 | − | 143.258i | −0.512667 | − | 0.295988i | ||||
\(23\) | 302.902 | + | 524.641i | 0.572593 | + | 0.991760i | 0.996299 | + | 0.0859604i | \(0.0273959\pi\) |
−0.423705 | + | 0.905800i | \(0.639271\pi\) | |||||||
\(24\) | −294.518 | + | 510.120i | −0.511316 | + | 0.885625i | ||||
\(25\) | −555.715 | − | 962.527i | −0.889144 | − | 1.54004i | ||||
\(26\) | 1325.26 | 1.96045 | ||||||||
\(27\) | − | 294.318i | − | 0.403728i | ||||||
\(28\) | 60.6576 | + | 105.062i | 0.0773693 | + | 0.134008i | ||||
\(29\) | 249.575 | − | 144.092i | 0.296760 | − | 0.171334i | −0.344227 | − | 0.938887i | \(-0.611859\pi\) |
0.640986 | + | 0.767552i | \(0.278526\pi\) | |||||||
\(30\) | −2234.65 | −2.48295 | ||||||||
\(31\) | 418.074i | 0.435040i | 0.976056 | + | 0.217520i | \(0.0697968\pi\) | ||||
−0.976056 | + | 0.217520i | \(0.930203\pi\) | |||||||
\(32\) | −537.367 | + | 310.249i | −0.524772 | + | 0.302977i | ||||
\(33\) | 633.158 | + | 365.554i | 0.581412 | + | 0.335679i | ||||
\(34\) | 97.2984 | − | 56.1752i | 0.0841681 | − | 0.0485945i | ||||
\(35\) | 503.912 | − | 872.801i | 0.411357 | − | 0.712491i | ||||
\(36\) | −140.047 | + | 242.569i | −0.108061 | + | 0.187167i | ||||
\(37\) | 2023.50i | 1.47809i | 0.673657 | + | 0.739044i | \(0.264722\pi\) | ||||
−0.673657 | + | 0.739044i | \(0.735278\pi\) | |||||||
\(38\) | 1637.49 | − | 239.675i | 1.13400 | − | 0.165980i | ||||
\(39\) | −3381.69 | −2.22333 | ||||||||
\(40\) | 1817.17 | + | 1049.14i | 1.13573 | + | 0.655713i | ||||
\(41\) | −717.741 | − | 414.388i | −0.426973 | − | 0.246513i | 0.271083 | − | 0.962556i | \(-0.412618\pi\) |
−0.698056 | + | 0.716043i | \(0.745951\pi\) | |||||||
\(42\) | −648.497 | − | 1123.23i | −0.367629 | − | 0.636752i | ||||
\(43\) | 632.930 | − | 1096.27i | 0.342310 | − | 0.592898i | −0.642552 | − | 0.766242i | \(-0.722124\pi\) |
0.984861 | + | 0.173345i | \(0.0554575\pi\) | |||||||
\(44\) | 156.749 | + | 271.497i | 0.0809652 | + | 0.140236i | ||||
\(45\) | 2326.88 | 1.14908 | ||||||||
\(46\) | − | 2777.20i | − | 1.31248i | ||||||
\(47\) | −421.122 | − | 729.404i | −0.190639 | − | 0.330196i | 0.754823 | − | 0.655928i | \(-0.227723\pi\) |
−0.945462 | + | 0.325732i | \(0.894389\pi\) | |||||||
\(48\) | 3151.60 | − | 1819.58i | 1.36788 | − | 0.789748i | ||||
\(49\) | −1816.06 | −0.756376 | ||||||||
\(50\) | 5095.15i | 2.03806i | ||||||||
\(51\) | −248.277 | + | 143.343i | −0.0954545 | + | 0.0551107i | ||||
\(52\) | −1255.79 | − | 725.029i | −0.464418 | − | 0.268132i | ||||
\(53\) | 3144.31 | − | 1815.37i | 1.11937 | − | 0.646268i | 0.178130 | − | 0.984007i | \(-0.442995\pi\) |
0.941240 | + | 0.337739i | \(0.109662\pi\) | |||||||
\(54\) | −674.624 | + | 1168.48i | −0.231353 | + | 0.400714i | ||||
\(55\) | 1302.19 | − | 2255.46i | 0.430475 | − | 0.745605i | ||||
\(56\) | 1217.84i | 0.388343i | ||||||||
\(57\) | −4178.41 | + | 611.581i | −1.28606 | + | 0.188237i | ||||
\(58\) | −1321.13 | −0.392726 | ||||||||
\(59\) | −4625.90 | − | 2670.77i | −1.32890 | − | 0.767241i | −0.343771 | − | 0.939053i | \(-0.611704\pi\) |
−0.985130 | + | 0.171812i | \(0.945038\pi\) | |||||||
\(60\) | 2117.51 | + | 1222.54i | 0.588196 | + | 0.339595i | ||||
\(61\) | 1471.85 | + | 2549.32i | 0.395552 | + | 0.685116i | 0.993171 | − | 0.116664i | \(-0.0372201\pi\) |
−0.597620 | + | 0.801780i | \(0.703887\pi\) | |||||||
\(62\) | 958.292 | − | 1659.81i | 0.249296 | − | 0.431793i | ||||
\(63\) | 675.261 | + | 1169.59i | 0.170134 | + | 0.294680i | ||||
\(64\) | −2132.97 | −0.520745 | ||||||||
\(65\) | 12046.3i | 2.85121i | ||||||||
\(66\) | −1675.82 | − | 2902.60i | −0.384715 | − | 0.666346i | ||||
\(67\) | 4194.98 | − | 2421.97i | 0.934501 | − | 0.539534i | 0.0462688 | − | 0.998929i | \(-0.485267\pi\) |
0.888232 | + | 0.459395i | \(0.151934\pi\) | |||||||
\(68\) | −122.930 | −0.0265853 | ||||||||
\(69\) | 7086.61i | 1.48847i | ||||||||
\(70\) | −4001.20 | + | 2310.10i | −0.816572 | + | 0.471448i | ||||
\(71\) | −4788.02 | − | 2764.37i | −0.949816 | − | 0.548377i | −0.0567923 | − | 0.998386i | \(-0.518087\pi\) |
−0.893024 | + | 0.450009i | \(0.851421\pi\) | |||||||
\(72\) | −2435.07 | + | 1405.89i | −0.469728 | + | 0.271198i | ||||
\(73\) | 792.717 | − | 1373.03i | 0.148755 | − | 0.257652i | −0.782012 | − | 0.623263i | \(-0.785807\pi\) |
0.930768 | + | 0.365611i | \(0.119140\pi\) | |||||||
\(74\) | 4638.19 | − | 8033.59i | 0.847004 | − | 1.46705i | ||||
\(75\) | − | 13001.4i | − | 2.31135i | ||||||
\(76\) | −1682.77 | − | 668.735i | −0.291339 | − | 0.115778i | ||||
\(77\) | 1511.58 | 0.254947 | ||||||||
\(78\) | 13425.8 | + | 7751.37i | 2.20673 | + | 1.27406i | ||||
\(79\) | 4627.33 | + | 2671.59i | 0.741440 | + | 0.428071i | 0.822593 | − | 0.568631i | \(-0.192527\pi\) |
−0.0811524 | + | 0.996702i | \(0.525860\pi\) | |||||||
\(80\) | −6481.76 | − | 11226.7i | −1.01277 | − | 1.75418i | ||||
\(81\) | 3982.97 | − | 6898.70i | 0.607067 | − | 1.05147i | ||||
\(82\) | 1899.69 | + | 3290.36i | 0.282524 | + | 0.489345i | ||||
\(83\) | −740.501 | −0.107490 | −0.0537452 | − | 0.998555i | \(-0.517116\pi\) | ||||
−0.0537452 | + | 0.998555i | \(0.517116\pi\) | |||||||
\(84\) | 1419.13i | 0.201124i | ||||||||
\(85\) | 510.621 | + | 884.421i | 0.0706741 | + | 0.122411i | ||||
\(86\) | −5025.64 | + | 2901.56i | −0.679508 | + | 0.392314i | ||||
\(87\) | 3371.14 | 0.445388 | ||||||||
\(88\) | 3147.10i | 0.406392i | ||||||||
\(89\) | 4789.36 | − | 2765.14i | 0.604641 | − | 0.349089i | −0.166224 | − | 0.986088i | \(-0.553158\pi\) |
0.770865 | + | 0.636998i | \(0.219824\pi\) | |||||||
\(90\) | −9238.05 | − | 5333.59i | −1.14050 | − | 0.658468i | ||||
\(91\) | −6054.99 | + | 3495.85i | −0.731191 | + | 0.422153i | ||||
\(92\) | −1519.36 | + | 2631.61i | −0.179509 | + | 0.310918i | ||||
\(93\) | −2445.28 | + | 4235.36i | −0.282725 | + | 0.489693i | ||||
\(94\) | 3861.11i | 0.436975i | ||||||||
\(95\) | 2178.59 | + | 14884.5i | 0.241395 | + | 1.64925i | ||||
\(96\) | −7258.50 | −0.787597 | ||||||||
\(97\) | 2969.63 | + | 1714.52i | 0.315616 | + | 0.182221i | 0.649437 | − | 0.760415i | \(-0.275005\pi\) |
−0.333821 | + | 0.942637i | \(0.608338\pi\) | |||||||
\(98\) | 7210.01 | + | 4162.70i | 0.750730 | + | 0.433434i | ||||
\(99\) | 1744.98 | + | 3022.40i | 0.178041 | + | 0.308376i | ||||
\(100\) | 2787.47 | − | 4828.05i | 0.278747 | − | 0.482805i | ||||
\(101\) | −702.204 | − | 1216.25i | −0.0688368 | − | 0.119229i | 0.829553 | − | 0.558428i | \(-0.188595\pi\) |
−0.898390 | + | 0.439200i | \(0.855262\pi\) | |||||||
\(102\) | 1314.26 | 0.126323 | ||||||||
\(103\) | − | 8424.53i | − | 0.794093i | −0.917798 | − | 0.397047i | \(-0.870035\pi\) | ||
0.917798 | − | 0.397047i | \(-0.129965\pi\) | |||||||
\(104\) | −7278.33 | − | 12606.4i | −0.672923 | − | 1.16554i | ||||
\(105\) | 10209.9 | − | 5894.70i | 0.926069 | − | 0.534666i | ||||
\(106\) | −16644.5 | −1.48135 | ||||||||
\(107\) | − | 8311.74i | − | 0.725980i | −0.931793 | − | 0.362990i | \(-0.881756\pi\) | ||
0.931793 | − | 0.362990i | \(-0.118244\pi\) | |||||||
\(108\) | 1278.52 | − | 738.151i | 0.109612 | − | 0.0632846i | ||||
\(109\) | −8045.29 | − | 4644.95i | −0.677156 | − | 0.390956i | 0.121627 | − | 0.992576i | \(-0.461189\pi\) |
−0.798783 | + | 0.601620i | \(0.794522\pi\) | |||||||
\(110\) | −10339.7 | + | 5969.65i | −0.854524 | + | 0.493359i | ||||
\(111\) | −11835.3 | + | 20499.4i | −0.960582 | + | 1.66378i | ||||
\(112\) | 3762.01 | − | 6516.00i | 0.299905 | − | 0.519451i | ||||
\(113\) | − | 4056.19i | − | 0.317659i | −0.987306 | − | 0.158830i | \(-0.949228\pi\) | ||
0.987306 | − | 0.158830i | \(-0.0507721\pi\) | |||||||
\(114\) | 17990.7 | + | 7149.52i | 1.38433 | + | 0.550133i | ||||
\(115\) | 25244.1 | 1.90882 | ||||||||
\(116\) | 1251.87 | + | 722.768i | 0.0930344 | + | 0.0537134i | ||||
\(117\) | −13979.9 | − | 8071.28i | −1.02125 | − | 0.589618i | ||||
\(118\) | 12243.7 | + | 21206.6i | 0.879320 | + | 1.52303i | ||||
\(119\) | −296.364 | + | 513.318i | −0.0209282 | + | 0.0362487i | ||||
\(120\) | 12272.7 | + | 21257.0i | 0.852271 | + | 1.47618i | ||||
\(121\) | −10734.8 | −0.733204 | ||||||||
\(122\) | − | 13494.9i | − | 0.906668i | ||||||
\(123\) | −4847.45 | − | 8396.04i | −0.320408 | − | 0.554963i | ||||
\(124\) | −1816.11 | + | 1048.53i | −0.118113 | + | 0.0681928i | ||||
\(125\) | −20269.8 | −1.29727 | ||||||||
\(126\) | − | 6191.23i | − | 0.389974i | ||||||
\(127\) | −9729.41 | + | 5617.28i | −0.603225 | + | 0.348272i | −0.770309 | − | 0.637671i | \(-0.779898\pi\) |
0.167084 | + | 0.985943i | \(0.446565\pi\) | |||||||
\(128\) | 17066.1 | + | 9853.10i | 1.04163 | + | 0.601385i | ||||
\(129\) | 12824.0 | − | 7403.93i | 0.770626 | − | 0.444921i | ||||
\(130\) | 27612.2 | − | 47825.7i | 1.63386 | − | 2.82992i | ||||
\(131\) | 3002.45 | − | 5200.40i | 0.174958 | − | 0.303036i | −0.765189 | − | 0.643806i | \(-0.777354\pi\) |
0.940147 | + | 0.340770i | \(0.110688\pi\) | |||||||
\(132\) | 3667.25i | 0.210471i | ||||||||
\(133\) | −6849.31 | + | 5414.52i | −0.387208 | + | 0.306095i | ||||
\(134\) | −22206.2 | −1.23670 | ||||||||
\(135\) | −10621.3 | − | 6132.18i | −0.582785 | − | 0.336471i | ||||
\(136\) | −1068.72 | − | 617.028i | −0.0577813 | − | 0.0333601i | ||||
\(137\) | 8783.25 | + | 15213.0i | 0.467966 | + | 0.810540i | 0.999330 | − | 0.0366031i | \(-0.0116537\pi\) |
−0.531364 | + | 0.847144i | \(0.678320\pi\) | |||||||
\(138\) | 16243.6 | − | 28134.8i | 0.852954 | − | 1.47736i | ||||
\(139\) | 5697.89 | + | 9869.03i | 0.294906 | + | 0.510793i | 0.974963 | − | 0.222367i | \(-0.0713782\pi\) |
−0.680057 | + | 0.733160i | \(0.738045\pi\) | |||||||
\(140\) | 5055.26 | 0.257922 | ||||||||
\(141\) | − | 9852.45i | − | 0.495571i | ||||||
\(142\) | 12672.7 | + | 21949.8i | 0.628484 | + | 1.08857i | ||||
\(143\) | −15647.0 | + | 9033.82i | −0.765174 | + | 0.441773i | ||||
\(144\) | 17371.6 | 0.837751 | ||||||||
\(145\) | − | 12008.8i | − | 0.571167i | ||||||
\(146\) | −6294.40 | + | 3634.07i | −0.295290 | + | 0.170486i | ||||
\(147\) | −18397.9 | − | 10622.0i | −0.851398 | − | 0.491555i | ||||
\(148\) | −8790.09 | + | 5074.96i | −0.401301 | + | 0.231691i | ||||
\(149\) | −8963.63 | + | 15525.5i | −0.403749 | + | 0.699314i | −0.994175 | − | 0.107778i | \(-0.965626\pi\) |
0.590426 | + | 0.807092i | \(0.298960\pi\) | |||||||
\(150\) | −29801.2 | + | 51617.2i | −1.32450 | + | 2.29410i | ||||
\(151\) | − | 2550.85i | − | 0.111874i | −0.998434 | − | 0.0559372i | \(-0.982185\pi\) | ||
0.998434 | − | 0.0559372i | \(-0.0178147\pi\) | |||||||
\(152\) | −11273.0 | − | 14260.2i | −0.487924 | − | 0.617218i | ||||
\(153\) | −1368.50 | −0.0584605 | ||||||||
\(154\) | −6001.18 | − | 3464.79i | −0.253044 | − | 0.146095i | ||||
\(155\) | 15087.3 | + | 8710.67i | 0.627984 | + | 0.362567i | ||||
\(156\) | −8481.29 | − | 14690.0i | −0.348508 | − | 0.603634i | ||||
\(157\) | −20083.8 | + | 34786.2i | −0.814793 | + | 1.41126i | 0.0946826 | + | 0.995508i | \(0.469816\pi\) |
−0.909476 | + | 0.415756i | \(0.863517\pi\) | |||||||
\(158\) | −12247.4 | − | 21213.2i | −0.490604 | − | 0.849751i | ||||
\(159\) | 42471.9 | 1.67999 | ||||||||
\(160\) | 25856.4i | 1.01002i | ||||||||
\(161\) | 7325.85 | + | 12688.7i | 0.282622 | + | 0.489516i | ||||
\(162\) | −31625.9 | + | 18259.2i | −1.20507 | + | 0.695748i | ||||
\(163\) | 8363.32 | 0.314777 | 0.157389 | − | 0.987537i | \(-0.449692\pi\) | ||||
0.157389 | + | 0.987537i | \(0.449692\pi\) | |||||||
\(164\) | − | 4157.15i | − | 0.154564i | ||||||
\(165\) | 26384.0 | − | 15232.8i | 0.969110 | − | 0.559516i | ||||
\(166\) | 2939.89 | + | 1697.35i | 0.106688 | + | 0.0615963i | ||||
\(167\) | 25860.0 | − | 14930.3i | 0.927246 | − | 0.535346i | 0.0413065 | − | 0.999147i | \(-0.486848\pi\) |
0.885940 | + | 0.463801i | \(0.153515\pi\) | |||||||
\(168\) | −7123.08 | + | 12337.5i | −0.252377 | + | 0.437129i | ||||
\(169\) | 27504.8 | − | 47639.7i | 0.963019 | − | 1.66800i | ||||
\(170\) | − | 4681.70i | − | 0.161997i | ||||||
\(171\) | −18733.2 | − | 7444.59i | −0.640649 | − | 0.254594i | ||||
\(172\) | 6349.58 | 0.214629 | ||||||||
\(173\) | 12746.0 | + | 7358.89i | 0.425874 | + | 0.245878i | 0.697587 | − | 0.716500i | \(-0.254257\pi\) |
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(174\) | −13383.9 | − | 7727.20i | −0.442063 | − | 0.255225i | ||||
\(175\) | −13440.3 | − | 23279.2i | −0.438866 | − | 0.760139i | ||||
\(176\) | 9721.63 | − | 16838.4i | 0.313844 | − | 0.543594i | ||||
\(177\) | −31242.3 | − | 54113.2i | −0.997232 | − | 1.72726i | ||||
\(178\) | −25352.6 | −0.800169 | ||||||||
\(179\) | 16538.4i | 0.516163i | 0.966123 | + | 0.258082i | \(0.0830903\pi\) | ||||
−0.966123 | + | 0.258082i | \(0.916910\pi\) | |||||||
\(180\) | 5835.84 | + | 10108.0i | 0.180118 | + | 0.311974i | ||||
\(181\) | 10274.9 | − | 5932.22i | 0.313632 | − | 0.181076i | −0.334919 | − | 0.942247i | \(-0.608709\pi\) |
0.648551 | + | 0.761171i | \(0.275375\pi\) | |||||||
\(182\) | 32052.2 | 0.967643 | ||||||||
\(183\) | 34435.0i | 1.02825i | ||||||||
\(184\) | −26417.9 | + | 15252.4i | −0.780301 | + | 0.450507i | ||||
\(185\) | 73023.6 | + | 42160.2i | 2.13363 | + | 1.23185i | ||||
\(186\) | 19416.2 | − | 11210.0i | 0.561228 | − | 0.324025i | ||||
\(187\) | −765.852 | + | 1326.49i | −0.0219009 | + | 0.0379334i | ||||
\(188\) | 2112.35 | − | 3658.70i | 0.0597655 | − | 0.103517i | ||||
\(189\) | − | 7118.24i | − | 0.199273i | ||||||
\(190\) | 25468.3 | − | 64087.1i | 0.705492 | − | 1.77526i | ||||
\(191\) | 50556.6 | 1.38583 | 0.692917 | − | 0.721017i | \(-0.256325\pi\) | ||||
0.692917 | + | 0.721017i | \(0.256325\pi\) | |||||||
\(192\) | −21608.4 | − | 12475.6i | −0.586165 | − | 0.338423i | ||||
\(193\) | −41764.2 | − | 24112.6i | −1.12122 | − | 0.647335i | −0.179506 | − | 0.983757i | \(-0.557450\pi\) |
−0.941711 | + | 0.336422i | \(0.890783\pi\) | |||||||
\(194\) | −7859.91 | − | 13613.8i | −0.208840 | − | 0.361722i | ||||
\(195\) | −70458.3 | + | 122037.i | −1.85295 | + | 3.20940i | ||||
\(196\) | −4554.69 | − | 7888.95i | −0.118562 | − | 0.205356i | ||||
\(197\) | −39065.4 | −1.00661 | −0.503303 | − | 0.864110i | \(-0.667882\pi\) | ||||
−0.503303 | + | 0.864110i | \(0.667882\pi\) | |||||||
\(198\) | − | 15999.1i | − | 0.408099i | ||||||
\(199\) | −12907.6 | − | 22356.6i | −0.325941 | − | 0.564546i | 0.655761 | − | 0.754968i | \(-0.272348\pi\) |
−0.981702 | + | 0.190422i | \(0.939014\pi\) | |||||||
\(200\) | 48467.2 | − | 27982.5i | 1.21168 | − | 0.699564i | ||||
\(201\) | 56663.8 | 1.40253 | ||||||||
\(202\) | 6438.26i | 0.157785i | ||||||||
\(203\) | 6036.11 | − | 3484.95i | 0.146475 | − | 0.0845676i | ||||
\(204\) | −1245.36 | − | 719.010i | −0.0299251 | − | 0.0172773i | ||||
\(205\) | −29908.6 | + | 17267.7i | −0.711686 | + | 0.410892i | ||||
\(206\) | −19310.4 | + | 33446.6i | −0.455047 | + | 0.788165i | ||||
\(207\) | −16914.0 | + | 29296.0i | −0.394736 | + | 0.683703i | ||||
\(208\) | 89933.4i | 2.07871i | ||||||||
\(209\) | −17699.7 | + | 13992.0i | −0.405204 | + | 0.320322i | ||||
\(210\) | −54046.4 | −1.22554 | ||||||||
\(211\) | 5877.77 | + | 3393.53i | 0.132023 | + | 0.0762232i | 0.564557 | − | 0.825394i | \(-0.309047\pi\) |
−0.432534 | + | 0.901618i | \(0.642381\pi\) | |||||||
\(212\) | 15771.9 | + | 9105.91i | 0.350923 | + | 0.202606i | ||||
\(213\) | −32337.2 | − | 56009.6i | −0.712759 | − | 1.23454i | ||||
\(214\) | −19051.9 | + | 32998.8i | −0.416016 | + | 0.720560i | ||||
\(215\) | −26374.5 | − | 45682.0i | −0.570568 | − | 0.988253i | ||||
\(216\) | 14820.1 | 0.317647 | ||||||||
\(217\) | 10111.3i | 0.214728i | ||||||||
\(218\) | 21293.9 | + | 36882.2i | 0.448067 | + | 0.776075i | ||||
\(219\) | 16061.5 | − | 9273.10i | 0.334886 | − | 0.193347i | ||||
\(220\) | 13063.6 | 0.269909 | ||||||||
\(221\) | − | 7084.78i | − | 0.145058i | ||||||
\(222\) | 93975.8 | − | 54257.0i | 1.90682 | − | 1.10090i | ||||
\(223\) | 8103.55 | + | 4678.58i | 0.162954 | + | 0.0940816i | 0.579259 | − | 0.815143i | \(-0.303342\pi\) |
−0.416305 | + | 0.909225i | \(0.636675\pi\) | |||||||
\(224\) | −12996.5 | + | 7503.54i | −0.259019 | + | 0.149544i | ||||
\(225\) | 31031.1 | − | 53747.5i | 0.612961 | − | 1.06168i | ||||
\(226\) | −9297.45 | + | 16103.7i | −0.182032 | + | 0.315288i | ||||
\(227\) | 32899.8i | 0.638472i | 0.947675 | + | 0.319236i | \(0.103426\pi\) | ||||
−0.947675 | + | 0.319236i | \(0.896574\pi\) | |||||||
\(228\) | −13136.2 | − | 16617.1i | −0.252697 | − | 0.319659i | ||||
\(229\) | −34126.2 | −0.650753 | −0.325377 | − | 0.945584i | \(-0.605491\pi\) | ||||
−0.325377 | + | 0.945584i | \(0.605491\pi\) | |||||||
\(230\) | −100223. | − | 57863.6i | −1.89457 | − | 1.09383i | ||||
\(231\) | 15313.3 | + | 8841.13i | 0.286975 | + | 0.165685i | ||||
\(232\) | 7255.63 | + | 12567.1i | 0.134803 | + | 0.233485i | ||||
\(233\) | 45770.7 | − | 79277.2i | 0.843094 | − | 1.46028i | −0.0441722 | − | 0.999024i | \(-0.514065\pi\) |
0.887266 | − | 0.461258i | \(-0.152602\pi\) | |||||||
\(234\) | 37001.3 | + | 64088.2i | 0.675750 | + | 1.17043i | ||||
\(235\) | −35096.7 | −0.635522 | ||||||||
\(236\) | − | 26793.2i | − | 0.481062i | ||||||
\(237\) | 31251.9 | + | 54129.9i | 0.556391 | + | 0.963697i | ||||
\(238\) | 2353.22 | − | 1358.63i | 0.0415440 | − | 0.0239854i | ||||
\(239\) | −4322.59 | −0.0756742 | −0.0378371 | − | 0.999284i | \(-0.512047\pi\) | ||||
−0.0378371 | + | 0.999284i | \(0.512047\pi\) | |||||||
\(240\) | − | 151645.i | − | 2.63273i | ||||||
\(241\) | −38952.7 | + | 22489.4i | −0.670662 | + | 0.387207i | −0.796327 | − | 0.604866i | \(-0.793227\pi\) |
0.125665 | + | 0.992073i | \(0.459893\pi\) | |||||||
\(242\) | 42618.8 | + | 24606.0i | 0.727731 | + | 0.420156i | ||||
\(243\) | 60054.2 | − | 34672.3i | 1.01702 | − | 0.587179i | ||||
\(244\) | −7382.81 | + | 12787.4i | −0.124006 | + | 0.214784i | ||||
\(245\) | −37838.0 | + | 65537.4i | −0.630371 | + | 1.09183i | ||||
\(246\) | 44444.6i | 0.734427i | ||||||||
\(247\) | 38540.9 | − | 96982.5i | 0.631725 | − | 1.58964i | ||||
\(248\) | −21051.7 | −0.342282 | ||||||||
\(249\) | −7501.75 | − | 4331.14i | −0.120994 | − | 0.0698560i | ||||
\(250\) | 80473.8 | + | 46461.6i | 1.28758 | + | 0.743385i | ||||
\(251\) | 31250.4 | + | 54127.2i | 0.496030 | + | 0.859149i | 0.999990 | − | 0.00457824i | \(-0.00145730\pi\) |
−0.503960 | + | 0.863727i | \(0.668124\pi\) | |||||||
\(252\) | −3387.12 | + | 5866.67i | −0.0533371 | + | 0.0923826i | ||||
\(253\) | 18931.1 | + | 32789.7i | 0.295757 | + | 0.512267i | ||||
\(254\) | 51502.8 | 0.798296 | ||||||||
\(255\) | 11946.3i | 0.183719i | ||||||||
\(256\) | −28106.0 | − | 48681.0i | −0.428864 | − | 0.742813i | ||||
\(257\) | −64690.3 | + | 37349.0i | −0.979429 | + | 0.565474i | −0.902098 | − | 0.431532i | \(-0.857973\pi\) |
−0.0773313 | + | 0.997005i | \(0.524640\pi\) | |||||||
\(258\) | −67884.1 | −1.01983 | ||||||||
\(259\) | 48939.5i | 0.729559i | ||||||||
\(260\) | −52329.3 | + | 30212.3i | −0.774102 | + | 0.446928i | ||||
\(261\) | 13936.3 | + | 8046.11i | 0.204581 | + | 0.118115i | ||||
\(262\) | −23840.3 | + | 13764.2i | −0.347304 | + | 0.200516i | ||||
\(263\) | 12657.9 | − | 21924.1i | 0.182999 | − | 0.316964i | −0.759901 | − | 0.650038i | \(-0.774753\pi\) |
0.942900 | + | 0.333075i | \(0.108086\pi\) | |||||||
\(264\) | −18407.2 | + | 31882.1i | −0.264106 | + | 0.457446i | ||||
\(265\) | − | 151295.i | − | 2.15443i | ||||||
\(266\) | 39603.7 | − | 5796.68i | 0.559722 | − | 0.0819249i | ||||
\(267\) | 64692.4 | 0.907467 | ||||||||
\(268\) | 21042.1 | + | 12148.6i | 0.292967 | + | 0.169145i | ||||
\(269\) | −115616. | − | 66751.1i | −1.59777 | − | 0.922474i | −0.991916 | − | 0.126900i | \(-0.959497\pi\) |
−0.605856 | − | 0.795574i | \(-0.707169\pi\) | |||||||
\(270\) | 28111.9 | + | 48691.3i | 0.385623 | + | 0.667919i | ||||
\(271\) | 8684.87 | − | 15042.6i | 0.118256 | − | 0.204826i | −0.800820 | − | 0.598905i | \(-0.795603\pi\) |
0.919077 | + | 0.394079i | \(0.128936\pi\) | |||||||
\(272\) | 3812.10 | + | 6602.75i | 0.0515260 | + | 0.0892456i | ||||
\(273\) | −81788.0 | −1.09740 | ||||||||
\(274\) | − | 80530.5i | − | 1.07265i | ||||||
\(275\) | −34731.8 | − | 60157.2i | −0.459263 | − | 0.795467i | ||||
\(276\) | −30784.2 | + | 17773.3i | −0.404119 | + | 0.233318i | ||||
\(277\) | 151171. | 1.97020 | 0.985098 | − | 0.171996i | \(-0.0550217\pi\) | ||||
0.985098 | + | 0.171996i | \(0.0550217\pi\) | |||||||
\(278\) | − | 52241.9i | − | 0.675973i | ||||||
\(279\) | −20217.6 | + | 11672.6i | −0.259729 | + | 0.149955i | ||||
\(280\) | 43949.2 | + | 25374.1i | 0.560576 | + | 0.323649i | ||||
\(281\) | −71334.5 | + | 41185.0i | −0.903414 | + | 0.521586i | −0.878306 | − | 0.478098i | \(-0.841326\pi\) |
−0.0251079 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(282\) | −22583.4 | + | 39115.6i | −0.283982 | + | 0.491871i | ||||
\(283\) | 38305.5 | − | 66347.1i | 0.478287 | − | 0.828417i | −0.521403 | − | 0.853310i | \(-0.674591\pi\) |
0.999690 | + | 0.0248934i | \(0.00792465\pi\) | |||||||
\(284\) | − | 27732.2i | − | 0.343833i | ||||||
\(285\) | −64987.6 | + | 163532.i | −0.800094 | + | 2.01332i | ||||
\(286\) | 82827.9 | 1.01262 | ||||||||
\(287\) | −17359.0 | − | 10022.2i | −0.210746 | − | 0.121674i | ||||
\(288\) | −30006.6 | − | 17324.3i | −0.361769 | − | 0.208867i | ||||
\(289\) | 41460.2 | + | 71811.2i | 0.496404 | + | 0.859798i | ||||
\(290\) | −27526.1 | + | 47676.5i | −0.327301 | + | 0.566903i | ||||
\(291\) | 20056.2 | + | 34738.4i | 0.236844 | + | 0.410226i | ||||
\(292\) | 7952.56 | 0.0932699 | ||||||||
\(293\) | 97102.9i | 1.13109i | 0.824717 | + | 0.565545i | \(0.191334\pi\) | ||||
−0.824717 | + | 0.565545i | \(0.808666\pi\) | |||||||
\(294\) | 48694.7 | + | 84341.7i | 0.563361 | + | 0.975770i | ||||
\(295\) | −192764. | + | 111292.i | −2.21504 | + | 1.27885i | ||||
\(296\) | −101892. | −1.16294 | ||||||||
\(297\) | − | 18394.6i | − | 0.208535i | ||||||
\(298\) | 71173.8 | − | 41092.2i | 0.801470 | − | 0.462729i | ||||
\(299\) | −151666. | − | 87564.6i | −1.69647 | − | 0.979459i | ||||
\(300\) | 56477.8 | − | 32607.5i | 0.627532 | − | 0.362306i | ||||
\(301\) | 15307.8 | − | 26513.8i | 0.168958 | − | 0.292644i | ||||
\(302\) | −5846.96 | + | 10127.2i | −0.0641085 | + | 0.111039i | ||||
\(303\) | − | 16428.6i | − | 0.178943i | ||||||
\(304\) | 16264.5 | + | 111122.i | 0.175993 | + | 1.20241i | ||||
\(305\) | 122665. | 1.31863 | ||||||||
\(306\) | 5433.14 | + | 3136.83i | 0.0580241 | + | 0.0335002i | ||||
\(307\) | −32190.8 | − | 18585.4i | −0.341550 | − | 0.197194i | 0.319407 | − | 0.947618i | \(-0.396516\pi\) |
−0.660957 | + | 0.750423i | \(0.729850\pi\) | |||||||
\(308\) | 3791.05 | + | 6566.30i | 0.0399630 | + | 0.0692180i | ||||
\(309\) | 49274.5 | − | 85346.0i | 0.516066 | − | 0.893853i | ||||
\(310\) | −39932.5 | − | 69165.1i | −0.415531 | − | 0.719721i | ||||
\(311\) | 157167. | 1.62495 | 0.812476 | − | 0.582994i | \(-0.198119\pi\) | ||||
0.812476 | + | 0.582994i | \(0.198119\pi\) | |||||||
\(312\) | − | 170282.i | − | 1.74928i | ||||||
\(313\) | −6297.21 | − | 10907.1i | −0.0642776 | − | 0.111332i | 0.832096 | − | 0.554632i | \(-0.187141\pi\) |
−0.896373 | + | 0.443300i | \(0.853808\pi\) | |||||||
\(314\) | 159471. | − | 92070.8i | 1.61742 | − | 0.933819i | ||||
\(315\) | 56276.9 | 0.567165 | ||||||||
\(316\) | 26801.5i | 0.268401i | ||||||||
\(317\) | 11437.7 | − | 6603.57i | 0.113821 | − | 0.0657144i | −0.442009 | − | 0.897011i | \(-0.645734\pi\) |
0.555830 | + | 0.831296i | \(0.312401\pi\) | |||||||
\(318\) | −168619. | − | 97352.3i | −1.66745 | − | 0.962703i | ||||
\(319\) | 15598.2 | − | 9005.65i | 0.153283 | − | 0.0884981i | ||||
\(320\) | −44441.0 | + | 76974.1i | −0.433994 | + | 0.751700i | ||||
\(321\) | 48614.8 | − | 84203.3i | 0.471801 | − | 0.817183i | ||||
\(322\) | − | 67168.1i | − | 0.647816i | ||||||
\(323\) | −1281.29 | − | 8753.95i | −0.0122812 | − | 0.0839072i | ||||
\(324\) | 39957.2 | 0.380632 | ||||||||
\(325\) | 278253. | + | 160649.i | 2.63434 | + | 1.52094i | ||||
\(326\) | −33203.5 | − | 19170.1i | −0.312428 | − | 0.180380i | ||||
\(327\) | −54336.0 | − | 94112.7i | −0.508150 | − | 0.880142i | ||||
\(328\) | 20866.1 | − | 36141.2i | 0.193952 | − | 0.335935i | ||||
\(329\) | −10185.1 | − | 17641.0i | −0.0940961 | − | 0.162979i | ||||
\(330\) | −139664. | −1.28250 | ||||||||
\(331\) | 62057.0i | 0.566415i | 0.959059 | + | 0.283208i | \(0.0913985\pi\) | ||||
−0.959059 | + | 0.283208i | \(0.908601\pi\) | |||||||
\(332\) | −1857.18 | − | 3216.73i | −0.0168492 | − | 0.0291836i | ||||
\(333\) | −97854.3 | + | 56496.2i | −0.882453 | + | 0.509485i | ||||
\(334\) | −136890. | −1.22710 | ||||||||
\(335\) | − | 201849.i | − | 1.79861i | ||||||
\(336\) | 76223.3 | − | 44007.5i | 0.675164 | − | 0.389806i | ||||
\(337\) | 128238. | + | 74038.1i | 1.12916 | + | 0.651922i | 0.943724 | − | 0.330734i | \(-0.107296\pi\) |
0.185438 | + | 0.982656i | \(0.440630\pi\) | |||||||
\(338\) | −218396. | + | 126091.i | −1.91166 | + | 1.10370i | ||||
\(339\) | 23724.4 | − | 41091.9i | 0.206441 | − | 0.357566i | ||||
\(340\) | −2561.28 | + | 4436.27i | −0.0221564 | + | 0.0383760i | ||||
\(341\) | 26129.3i | 0.224708i | ||||||||
\(342\) | 57309.3 | + | 72495.6i | 0.489974 | + | 0.619811i | ||||
\(343\) | −101992. | −0.866917 | ||||||||
\(344\) | 55201.6 | + | 31870.7i | 0.466482 | + | 0.269323i | ||||
\(345\) | 255739. | + | 147651.i | 2.14862 | + | 1.24051i | ||||
\(346\) | −33735.5 | − | 58431.7i | −0.281796 | − | 0.488086i | ||||
\(347\) | −12650.7 | + | 21911.7i | −0.105064 | + | 0.181977i | −0.913765 | − | 0.406244i | \(-0.866838\pi\) |
0.808700 | + | 0.588221i | \(0.200172\pi\) | |||||||
\(348\) | 8454.84 | + | 14644.2i | 0.0698147 | + | 0.120923i | ||||
\(349\) | −155086. | −1.27327 | −0.636637 | − | 0.771164i | \(-0.719675\pi\) | ||||
−0.636637 | + | 0.771164i | \(0.719675\pi\) | |||||||
\(350\) | 123229.i | 1.00595i | ||||||||
\(351\) | 42541.5 | + | 73684.1i | 0.345302 | + | 0.598080i | ||||
\(352\) | −33585.0 | + | 19390.3i | −0.271057 | + | 0.156495i | ||||
\(353\) | −119944. | −0.962561 | −0.481280 | − | 0.876567i | \(-0.659828\pi\) | ||||
−0.481280 | + | 0.876567i | \(0.659828\pi\) | |||||||
\(354\) | 286449.i | 2.28582i | ||||||||
\(355\) | −199519. | + | 115192.i | −1.58317 | + | 0.914045i | ||||
\(356\) | 24023.5 | + | 13870.0i | 0.189555 | + | 0.109440i | ||||
\(357\) | −6004.73 | + | 3466.83i | −0.0471147 | + | 0.0272017i | ||||
\(358\) | 37908.6 | − | 65659.7i | 0.295782 | − | 0.512310i | ||||
\(359\) | 93344.7 | − | 161678.i | 0.724270 | − | 1.25447i | −0.235004 | − | 0.971995i | \(-0.575510\pi\) |
0.959274 | − | 0.282478i | \(-0.0911565\pi\) | |||||||
\(360\) | 117168.i | 0.904075i | ||||||||
\(361\) | 30081.7 | − | 126802.i | 0.230828 | − | 0.972995i | ||||
\(362\) | −54390.4 | −0.415055 | ||||||||
\(363\) | −108751. | − | 62787.4i | −0.825315 | − | 0.476496i | ||||
\(364\) | −30371.9 | − | 17535.2i | −0.229229 | − | 0.132345i | ||||
\(365\) | −33032.9 | − | 57214.7i | −0.247948 | − | 0.429459i | ||||
\(366\) | 78930.5 | − | 136712.i | 0.589227 | − | 1.02057i | ||||
\(367\) | 113839. | + | 197175.i | 0.845200 | + | 1.46393i | 0.885447 | + | 0.464740i | \(0.153852\pi\) |
−0.0402473 | + | 0.999190i | \(0.512815\pi\) | |||||||
\(368\) | 188463. | 1.39165 | ||||||||
\(369\) | − | 46278.9i | − | 0.339884i | ||||||
\(370\) | −193276. | − | 334764.i | −1.41180 | − | 2.44531i | ||||
\(371\) | 76046.9 | − | 43905.7i | 0.552502 | − | 0.318987i | ||||
\(372\) | −24531.2 | −0.177269 | ||||||||
\(373\) | 248937.i | 1.78925i | 0.446814 | + | 0.894627i | \(0.352558\pi\) | ||||
−0.446814 | + | 0.894627i | \(0.647442\pi\) | |||||||
\(374\) | 6081.08 | − | 3510.91i | 0.0434748 | − | 0.0251002i | ||||
\(375\) | −205346. | − | 118557.i | −1.46024 | − | 0.843069i | ||||
\(376\) | 36728.5 | − | 21205.2i | 0.259793 | − | 0.149992i | ||||
\(377\) | −41655.0 | + | 72148.5i | −0.293079 | + | 0.507627i | ||||
\(378\) | −16316.2 | + | 28260.4i | −0.114192 | + | 0.197786i | ||||
\(379\) | − | 236451.i | − | 1.64612i | −0.567952 | − | 0.823061i | \(-0.692264\pi\) | ||
0.567952 | − | 0.823061i | \(-0.307736\pi\) | |||||||
\(380\) | −59194.1 | + | 46794.1i | −0.409931 | + | 0.324059i | ||||
\(381\) | −131420. | −0.905342 | ||||||||
\(382\) | −200717. | − | 115884.i | −1.37549 | − | 0.794139i | ||||
\(383\) | 199085. | + | 114942.i | 1.35719 | + | 0.783576i | 0.989245 | − | 0.146270i | \(-0.0467267\pi\) |
0.367949 | + | 0.929846i | \(0.380060\pi\) | |||||||
\(384\) | 115260. | + | 199637.i | 0.781658 | + | 1.35387i | ||||
\(385\) | 31494.1 | − | 54549.4i | 0.212475 | − | 0.368018i | ||||
\(386\) | 110540. | + | 191461.i | 0.741898 | + | 1.28501i | ||||
\(387\) | 70685.7 | 0.471965 | ||||||||
\(388\) | 17200.1i | 0.114253i | ||||||||
\(389\) | −12134.5 | − | 21017.5i | −0.0801904 | − | 0.138894i | 0.823141 | − | 0.567837i | \(-0.192219\pi\) |
−0.903332 | + | 0.428943i | \(0.858886\pi\) | |||||||
\(390\) | 559458. | − | 323003.i | 3.67823 | − | 2.12363i | ||||
\(391\) | −14846.8 | −0.0971132 | ||||||||
\(392\) | − | 91446.1i | − | 0.595104i | ||||||
\(393\) | 60833.6 | − | 35122.3i | 0.393875 | − | 0.227404i | ||||
\(394\) | 155095. | + | 89544.2i | 0.999092 | + | 0.576826i | ||||
\(395\) | 192823. | − | 111326.i | 1.23585 | − | 0.713517i | ||||
\(396\) | −8752.85 | + | 15160.4i | −0.0558161 | + | 0.0966762i | ||||
\(397\) | −144488. | + | 250260.i | −0.916748 | + | 1.58785i | −0.112425 | + | 0.993660i | \(0.535862\pi\) |
−0.804322 | + | 0.594193i | \(0.797471\pi\) | |||||||
\(398\) | 118345.i | 0.747109i | ||||||||
\(399\) | −101057. | + | 14791.4i | −0.634777 | + | 0.0929105i | ||||
\(400\) | −345761. | −2.16101 | ||||||||
\(401\) | 8555.46 | + | 4939.50i | 0.0532052 | + | 0.0307181i | 0.526367 | − | 0.850258i | \(-0.323554\pi\) |
−0.473161 | + | 0.880976i | \(0.656887\pi\) | |||||||
\(402\) | −224963. | − | 129882.i | −1.39206 | − | 0.803708i | ||||
\(403\) | −60429.6 | − | 104667.i | −0.372083 | − | 0.644466i | ||||
\(404\) | 3522.27 | − | 6100.75i | 0.0215804 | − | 0.0373784i | ||||
\(405\) | −165972. | − | 287472.i | −1.01187 | − | 1.75261i | ||||
\(406\) | −31952.3 | −0.193843 | ||||||||
\(407\) | 126467.i | 0.763466i | ||||||||
\(408\) | −7217.91 | − | 12501.8i | −0.0433602 | − | 0.0751020i | ||||
\(409\) | 154121. | − | 88981.9i | 0.921331 | − | 0.531931i | 0.0372718 | − | 0.999305i | \(-0.488133\pi\) |
0.884060 | + | 0.467374i | \(0.154800\pi\) | |||||||
\(410\) | 158322. | 0.941832 | ||||||||
\(411\) | 205491.i | 1.21649i | ||||||||
\(412\) | 36596.2 | − | 21128.8i | 0.215596 | − | 0.124474i | ||||
\(413\) | −111880. | − | 64594.0i | −0.655923 | − | 0.378697i | ||||
\(414\) | 134302. | − | 77539.5i | 0.783579 | − | 0.452399i | ||||
\(415\) | −15428.5 | + | 26723.0i | −0.0895835 | + | 0.155163i | ||||
\(416\) | 89688.5 | − | 155345.i | 0.518263 | − | 0.897658i | ||||
\(417\) | 133306.i | 0.766617i | ||||||||
\(418\) | 102342. | − | 14979.5i | 0.585736 | − | 0.0857325i | ||||
\(419\) | 28240.8 | 0.160860 | 0.0804301 | − | 0.996760i | \(-0.474371\pi\) | ||||
0.0804301 | + | 0.996760i | \(0.474371\pi\) | |||||||
\(420\) | 51213.1 | + | 29567.9i | 0.290324 | + | 0.167618i | ||||
\(421\) | −54520.9 | − | 31477.6i | −0.307609 | − | 0.177598i | 0.338247 | − | 0.941057i | \(-0.390166\pi\) |
−0.645856 | + | 0.763459i | \(0.723499\pi\) | |||||||
\(422\) | −15557.1 | − | 26945.6i | −0.0873580 | − | 0.151308i | ||||
\(423\) | 23515.4 | − | 40729.9i | 0.131423 | − | 0.227632i | ||||
\(424\) | 91411.3 | + | 158329.i | 0.508473 | + | 0.880701i | ||||
\(425\) | 27238.4 | 0.150801 | ||||||||
\(426\) | 296488.i | 1.63376i | ||||||||
\(427\) | 35597.5 | + | 61656.6i | 0.195238 | + | 0.338161i | ||||
\(428\) | 36106.2 | − | 20845.9i | 0.197103 | − | 0.113798i | ||||
\(429\) | −211353. | −1.14840 | ||||||||
\(430\) | 241819.i | 1.30783i | ||||||||
\(431\) | −144786. | + | 83592.1i | −0.779420 | + | 0.449998i | −0.836225 | − | 0.548387i | \(-0.815242\pi\) |
0.0568047 | + | 0.998385i | \(0.481909\pi\) | |||||||
\(432\) | −79294.2 | − | 45780.5i | −0.424887 | − | 0.245309i | ||||
\(433\) | 30557.5 | − | 17642.4i | 0.162983 | − | 0.0940982i | −0.416290 | − | 0.909232i | \(-0.636670\pi\) |
0.579273 | + | 0.815134i | \(0.303337\pi\) | |||||||
\(434\) | 23176.8 | − | 40143.5i | 0.123048 | − | 0.213125i | ||||
\(435\) | 70238.5 | − | 121657.i | 0.371190 | − | 0.642921i | ||||
\(436\) | − | 46598.3i | − | 0.245130i | ||||||
\(437\) | −203235. | − | 80765.7i | −1.06423 | − | 0.422926i | ||||
\(438\) | −85021.8 | −0.443182 | ||||||||
\(439\) | 163512. | + | 94403.8i | 0.848440 | + | 0.489847i | 0.860124 | − | 0.510085i | \(-0.170386\pi\) |
−0.0116842 | + | 0.999932i | \(0.503719\pi\) | |||||||
\(440\) | 113571. | + | 65570.5i | 0.586630 | + | 0.338691i | ||||
\(441\) | −50704.4 | − | 87822.6i | −0.260716 | − | 0.451574i | ||||
\(442\) | −16239.5 | + | 28127.6i | −0.0831241 | + | 0.143975i | ||||
\(443\) | −101510. | − | 175820.i | −0.517249 | − | 0.895901i | −0.999799 | − | 0.0200330i | \(-0.993623\pi\) |
0.482551 | − | 0.875868i | \(-0.339710\pi\) | |||||||
\(444\) | −118732. | −0.602287 | ||||||||
\(445\) | − | 230449.i | − | 1.16374i | ||||||
\(446\) | −21448.1 | − | 37149.3i | −0.107825 | − | 0.186759i | ||||
\(447\) | −181615. | + | 104855.i | −0.908942 | + | 0.524778i | ||||
\(448\) | −51587.1 | −0.257031 | ||||||||
\(449\) | 182146.i | 0.903497i | 0.892145 | + | 0.451748i | \(0.149199\pi\) | ||||
−0.892145 | + | 0.451748i | \(0.850801\pi\) | |||||||
\(450\) | −246396. | + | 142257.i | −1.21677 | + | 0.702503i | ||||
\(451\) | −44858.3 | − | 25898.9i | −0.220541 | − | 0.127329i | ||||
\(452\) | 17620.1 | − | 10173.0i | 0.0862445 | − | 0.0497933i | ||||
\(453\) | 14919.7 | − | 25841.7i | 0.0727051 | − | 0.125929i | ||||
\(454\) | 75411.8 | − | 130617.i | 0.365870 | − | 0.633706i | ||||
\(455\) | 291348.i | 1.40731i | ||||||||
\(456\) | −30795.7 | − | 210400.i | −0.148102 | − | 1.01185i | ||||
\(457\) | 66790.2 | 0.319801 | 0.159901 | − | 0.987133i | \(-0.448883\pi\) | ||||
0.159901 | + | 0.987133i | \(0.448883\pi\) | |||||||
\(458\) | 135486. | + | 78222.6i | 0.645895 | + | 0.372908i | ||||
\(459\) | 6246.65 | + | 3606.50i | 0.0296498 | + | 0.0171183i | ||||
\(460\) | 63312.5 | + | 109660.i | 0.299208 | + | 0.518244i | ||||
\(461\) | 34244.2 | − | 59312.7i | 0.161133 | − | 0.279091i | −0.774142 | − | 0.633012i | \(-0.781818\pi\) |
0.935275 | + | 0.353921i | \(0.115152\pi\) | |||||||
\(462\) | −40530.6 | − | 70201.0i | −0.189889 | − | 0.328897i | ||||
\(463\) | 390746. | 1.82277 | 0.911386 | − | 0.411552i | \(-0.135013\pi\) | ||||
0.911386 | + | 0.411552i | \(0.135013\pi\) | |||||||
\(464\) | − | 89652.9i | − | 0.416417i | ||||||
\(465\) | 101896. | + | 176489.i | 0.471251 | + | 0.816230i | ||||
\(466\) | −363432. | + | 209828.i | −1.67360 | + | 0.966254i | ||||
\(467\) | 72245.4 | 0.331266 | 0.165633 | − | 0.986187i | \(-0.447033\pi\) | ||||
0.165633 | + | 0.986187i | \(0.447033\pi\) | |||||||
\(468\) | − | 80971.3i | − | 0.369692i | ||||||
\(469\) | 101458. | − | 58576.7i | 0.461254 | − | 0.266305i | ||||
\(470\) | 139339. | + | 80447.3i | 0.630777 | + | 0.364180i | ||||
\(471\) | −406925. | + | 234938.i | −1.83431 | + | 1.05904i | ||||
\(472\) | 134484. | − | 232933.i | 0.603653 | − | 1.04556i | ||||
\(473\) | 39557.7 | − | 68515.9i | 0.176811 | − | 0.306245i | ||||
\(474\) | − | 286538.i | − | 1.27534i | ||||||
\(475\) | 372862. | + | 148176.i | 1.65258 | + | 0.656735i | ||||
\(476\) | −2973.14 | −0.0131220 | ||||||||
\(477\) | 175578. | + | 101370.i | 0.771675 | + | 0.445527i | ||||
\(478\) | 17161.3 | + | 9908.07i | 0.0751093 | + | 0.0433644i | ||||
\(479\) | −157819. | − | 273351.i | −0.687843 | − | 1.19138i | −0.972534 | − | 0.232760i | \(-0.925224\pi\) |
0.284691 | − | 0.958619i | \(-0.408109\pi\) | |||||||
\(480\) | −151233. | + | 261943.i | −0.656391 | + | 1.13690i | ||||
\(481\) | −292483. | − | 506595.i | −1.26418 | − | 2.18963i | ||||
\(482\) | 206197. | 0.887541 | ||||||||
\(483\) | 171394.i | 0.734684i | ||||||||
\(484\) | −26923.1 | − | 46632.1i | −0.114930 | − | 0.199065i | ||||
\(485\) | 123746. | − | 71444.8i | 0.526075 | − | 0.303730i | ||||
\(486\) | −317898. | −1.34591 | ||||||||
\(487\) | 15586.3i | 0.0657182i | 0.999460 | + | 0.0328591i | \(0.0104613\pi\) | ||||
−0.999460 | + | 0.0328591i | \(0.989539\pi\) | |||||||
\(488\) | −128369. | + | 74113.6i | −0.539038 | + | 0.311213i | ||||
\(489\) | 84725.8 | + | 48916.5i | 0.354322 | + | 0.204568i | ||||
\(490\) | 300445. | − | 173462.i | 1.25133 | − | 0.722456i | ||||
\(491\) | −72237.5 | + | 125119.i | −0.299640 | + | 0.518992i | −0.976054 | − | 0.217530i | \(-0.930200\pi\) |
0.676414 | + | 0.736522i | \(0.263533\pi\) | |||||||
\(492\) | 24314.9 | − | 42114.6i | 0.100448 | − | 0.173981i | ||||
\(493\) | 7062.69i | 0.0290587i | ||||||||
\(494\) | −375312. | + | 296692.i | −1.53794 | + | 1.21577i | ||||
\(495\) | 145428. | 0.593525 | ||||||||
\(496\) | 112636. | + | 65030.5i | 0.457841 | + | 0.264334i | ||||
\(497\) | −115801. | − | 66857.7i | −0.468813 | − | 0.270669i | ||||
\(498\) | 19855.3 | + | 34390.5i | 0.0800606 | + | 0.138669i | ||||
\(499\) | −127001. | + | 219972.i | −0.510042 | + | 0.883419i | 0.489890 | + | 0.871784i | \(0.337037\pi\) |
−0.999932 | + | 0.0116348i | \(0.996296\pi\) | |||||||
\(500\) | −50836.7 | − | 88051.8i | −0.203347 | − | 0.352207i | ||||
\(501\) | 349304. | 1.39164 | ||||||||
\(502\) | − | 286524.i | − | 1.13698i | ||||||
\(503\) | 166366. | + | 288154.i | 0.657548 | + | 1.13891i | 0.981248 | + | 0.192747i | \(0.0617398\pi\) |
−0.323700 | + | 0.946160i | \(0.604927\pi\) | |||||||
\(504\) | −58893.5 | + | 34002.2i | −0.231850 | + | 0.133858i | ||||
\(505\) | −58522.4 | −0.229477 | ||||||||
\(506\) | − | 173573.i | − | 0.677924i | ||||||
\(507\) | 557282. | − | 321747.i | 2.16800 | − | 1.25170i | ||||
\(508\) | −48802.9 | − | 28176.4i | −0.189112 | − | 0.109184i | ||||
\(509\) | 189141. | − | 109200.i | 0.730044 | − | 0.421491i | −0.0883942 | − | 0.996086i | \(-0.528174\pi\) |
0.818438 | + | 0.574594i | \(0.194840\pi\) | |||||||
\(510\) | 27382.9 | − | 47428.7i | 0.105279 | − | 0.182348i | ||||
\(511\) | 19172.3 | − | 33207.4i | 0.0734231 | − | 0.127173i | ||||
\(512\) | − | 57605.1i | − | 0.219746i | ||||||
\(513\) | 65890.2 | + | 83350.4i | 0.250372 | + | 0.316718i | ||||
\(514\) | 342439. | 1.29616 | ||||||||
\(515\) | −304022. | − | 175527.i | −1.14628 | − | 0.661805i | ||||
\(516\) | 64325.3 | + | 37138.2i | 0.241592 | + | 0.139483i | ||||
\(517\) | −26319.8 | − | 45587.2i | −0.0984694 | − | 0.170554i | ||||
\(518\) | 112177. | − | 194297.i | 0.418067 | − | 0.724113i | ||||
\(519\) | 86083.3 | + | 149101.i | 0.319584 | + | 0.553535i | ||||
\(520\) | −606583. | −2.24328 | ||||||||
\(521\) | − | 199162.i | − | 0.733722i | −0.930276 | − | 0.366861i | \(-0.880432\pi\) | ||
0.930276 | − | 0.366861i | \(-0.119568\pi\) | |||||||
\(522\) | −36886.0 | − | 63888.3i | −0.135369 | − | 0.234466i | ||||
\(523\) | −317690. | + | 183419.i | −1.16145 | + | 0.670564i | −0.951651 | − | 0.307181i | \(-0.900614\pi\) |
−0.209799 | + | 0.977744i | \(0.567281\pi\) | |||||||
\(524\) | 30120.7 | 0.109699 | ||||||||
\(525\) | − | 314445.i | − | 1.14084i | ||||||
\(526\) | −100507. | + | 58027.8i | −0.363266 | + | 0.209732i | ||||
\(527\) | −8873.26 | − | 5122.98i | −0.0319493 | − | 0.0184460i | ||||
\(528\) | 196973. | − | 113722.i | 0.706543 | − | 0.407923i | ||||
\(529\) | −43578.5 | + | 75480.1i | −0.155726 | + | 0.269725i | ||||
\(530\) | −346791. | + | 600660.i | −1.23457 | + | 2.13834i | ||||
\(531\) | − | 298271.i | − | 1.05785i | ||||||
\(532\) | −40698.8 | − | 16173.7i | −0.143800 | − | 0.0571462i | ||||
\(533\) | 239587. | 0.843353 | ||||||||
\(534\) | −256838. | − | 148285.i | −0.900693 | − | 0.520015i | ||||
\(535\) | −299952. | − | 173177.i | −1.04796 | − | 0.605039i | ||||
\(536\) | 121956. | + | 211234.i | 0.424497 | + | 0.735250i | ||||
\(537\) | −96731.9 | + | 167545.i | −0.335445 | + | 0.581007i | ||||
\(538\) | 306009. | + | 530023.i | 1.05723 | + | 1.83118i | ||||
\(539\) | −113502. | −0.390685 | ||||||||
\(540\) | − | 61518.3i | − | 0.210968i | ||||||
\(541\) | 20782.0 | + | 35995.5i | 0.0710058 | + | 0.122986i | 0.899342 | − | 0.437245i | \(-0.144046\pi\) |
−0.828337 | + | 0.560231i | \(0.810712\pi\) | |||||||
\(542\) | −68960.3 | + | 39814.2i | −0.234747 | + | 0.135531i | ||||
\(543\) | 138789. | 0.470711 | ||||||||
\(544\) | − | 15206.9i | − | 0.0513857i | ||||||
\(545\) | −335251. | + | 193557.i | −1.12870 | + | 0.651653i | ||||
\(546\) | 324710. | + | 187471.i | 1.08921 | + | 0.628853i | ||||
\(547\) | −58247.7 | + | 33629.4i | −0.194672 | + | 0.112394i | −0.594168 | − | 0.804341i | \(-0.702519\pi\) |
0.399496 | + | 0.916735i | \(0.369185\pi\) | |||||||
\(548\) | −44056.9 | + | 76308.8i | −0.146708 | + | 0.254105i | ||||
\(549\) | −82188.0 | + | 142354.i | −0.272687 | + | 0.472307i | ||||
\(550\) | 318443.i | 1.05271i | ||||||||
\(551\) | −38420.7 | + | 96680.0i | −0.126550 | + | 0.318444i | ||||
\(552\) | −356840. | −1.17110 | ||||||||
\(553\) | 111915. | + | 64613.9i | 0.365962 | + | 0.211288i | ||||
\(554\) | −600170. | − | 346509.i | −1.95549 | − | 1.12900i | ||||
\(555\) | 493184. | + | 854220.i | 1.60112 | + | 2.77322i | ||||
\(556\) | −28580.7 | + | 49503.2i | −0.0924535 | + | 0.160134i | ||||
\(557\) | 140576. | + | 243485.i | 0.453107 | + | 0.784805i | 0.998577 | − | 0.0533254i | \(-0.0169821\pi\) |
−0.545470 | + | 0.838131i | \(0.683649\pi\) | |||||||
\(558\) | 107022. | 0.343720 | ||||||||
\(559\) | 365942.i | 1.17109i | ||||||||
\(560\) | −156765. | − | 271525.i | −0.499888 | − | 0.865832i | ||||
\(561\) | −15517.1 | + | 8958.83i | −0.0493045 | + | 0.0284659i | ||||
\(562\) | 377611. | 1.19556 | ||||||||
\(563\) | − | 559461.i | − | 1.76503i | −0.470282 | − | 0.882516i | \(-0.655848\pi\) | ||
0.470282 | − | 0.882516i | \(-0.344152\pi\) | |||||||
\(564\) | 42799.0 | − | 24710.0i | 0.134547 | − | 0.0776810i | ||||
\(565\) | −146379. | − | 84511.8i | −0.458544 | − | 0.264741i | ||||
\(566\) | −304156. | + | 175605.i | −0.949433 | + | 0.548155i | ||||
\(567\) | 96330.3 | − | 166849.i | 0.299638 | − | 0.518988i | ||||
\(568\) | 139197. | − | 241097.i | 0.431454 | − | 0.747299i | ||||
\(569\) | 95700.7i | 0.295590i | 0.989018 | + | 0.147795i | \(0.0472177\pi\) | ||||
−0.989018 | + | 0.147795i | \(0.952782\pi\) | |||||||
\(570\) | 632851. | − | 500281.i | 1.94783 | − | 1.53980i | ||||
\(571\) | −562671. | −1.72577 | −0.862883 | − | 0.505403i | \(-0.831344\pi\) | ||||
−0.862883 | + | 0.505403i | \(0.831344\pi\) | |||||||
\(572\) | −78485.8 | − | 45313.8i | −0.239883 | − | 0.138496i | ||||
\(573\) | 512172. | + | 295702.i | 1.55993 | + | 0.900628i | ||||
\(574\) | 45945.0 | + | 79579.1i | 0.139449 | + | 0.241532i | ||||
\(575\) | 336654. | − | 583102.i | 1.01824 | − | 1.76364i | ||||
\(576\) | −59552.6 | − | 103148.i | −0.179496 | − | 0.310897i | ||||
\(577\) | −384557. | −1.15507 | −0.577536 | − | 0.816365i | \(-0.695986\pi\) | ||||
−0.577536 | + | 0.816365i | \(0.695986\pi\) | |||||||
\(578\) | − | 380134.i | − | 1.13784i | ||||||
\(579\) | −282066. | − | 488552.i | −0.841382 | − | 1.45732i | ||||
\(580\) | 52166.1 | − | 30118.1i | 0.155072 | − | 0.0895306i | ||||
\(581\) | −17909.4 | −0.0530554 | ||||||||
\(582\) | − | 183888.i | − | 0.542885i | ||||||
\(583\) | 196517. | − | 113459.i | 0.578180 | − | 0.333812i | ||||
\(584\) | 69137.6 | + | 39916.6i | 0.202716 | + | 0.117038i | ||||
\(585\) | −582548. | + | 336334.i | −1.70224 | + | 0.982787i | ||||
\(586\) | 222576. | − | 385512.i | 0.648160 | − | 1.12265i | ||||
\(587\) | −176824. | + | 306269.i | −0.513176 | + | 0.888846i | 0.486708 | + | 0.873565i | \(0.338198\pi\) |
−0.999883 | + | 0.0152813i | \(0.995136\pi\) | |||||||
\(588\) | − | 106560.i | − | 0.308206i | ||||||
\(589\) | −93595.9 | − | 118398.i | −0.269790 | − | 0.341282i | ||||
\(590\) | 1.02040e6 | 2.93134 | ||||||||
\(591\) | −395758. | − | 228491.i | −1.13306 | − | 0.654175i | ||||
\(592\) | 545166. | + | 314752.i | 1.55555 | + | 0.898100i | ||||
\(593\) | −316633. | − | 548424.i | −0.900423 | − | 1.55958i | −0.826946 | − | 0.562282i | \(-0.809924\pi\) |
−0.0734773 | − | 0.997297i | \(-0.523410\pi\) | |||||||
\(594\) | −42163.5 | + | 73029.3i | −0.119499 | + | 0.206978i | ||||
\(595\) | 12349.6 | + | 21390.2i | 0.0348835 | + | 0.0604201i | ||||
\(596\) | −89923.4 | −0.253151 | ||||||||
\(597\) | − | 301982.i | − | 0.847292i | ||||||
\(598\) | 401424. | + | 695287.i | 1.12254 | + | 1.94429i | ||||
\(599\) | 126946. | − | 73292.3i | 0.353806 | − | 0.204270i | −0.312554 | − | 0.949900i | \(-0.601185\pi\) |
0.666360 | + | 0.745630i | \(0.267851\pi\) | |||||||
\(600\) | 654672. | 1.81853 | ||||||||
\(601\) | − | 565825.i | − | 1.56651i | −0.621701 | − | 0.783255i | \(-0.713558\pi\) | ||
0.621701 | − | 0.783255i | \(-0.286442\pi\) | |||||||
\(602\) | −121548. | + | 70175.8i | −0.335394 | + | 0.193640i | ||||
\(603\) | 234248. | + | 135243.i | 0.644229 | + | 0.371946i | ||||
\(604\) | 11080.9 | − | 6397.55i | 0.0303739 | − | 0.0175364i | ||||
\(605\) | −223663. | + | 387396.i | −0.611060 | + | 1.05839i | ||||
\(606\) | −37657.0 | + | 65223.8i | −0.102542 | + | 0.177607i | ||||
\(607\) | 360850.i | 0.979376i | 0.871898 | + | 0.489688i | \(0.162889\pi\) | ||||
−0.871898 | + | 0.489688i | \(0.837111\pi\) | |||||||
\(608\) | 82724.7 | − | 208164.i | 0.223784 | − | 0.563118i | ||||
\(609\) | 81532.9 | 0.219836 | ||||||||
\(610\) | −486998. | − | 281169.i | −1.30878 | − | 0.755626i | ||||
\(611\) | 210860. | + | 121740.i | 0.564823 | + | 0.326101i | ||||
\(612\) | −3432.21 | − | 5944.77i | −0.00916371 | − | 0.0158720i | ||||
\(613\) | 19524.2 | − | 33816.9i | 0.0519580 | − | 0.0899938i | −0.838877 | − | 0.544322i | \(-0.816787\pi\) |
0.890835 | + | 0.454328i | \(0.150120\pi\) | |||||||
\(614\) | 85201.3 | + | 147573.i | 0.226001 | + | 0.391444i | ||||
\(615\) | −403992. | −1.06813 | ||||||||
\(616\) | 76114.3i | 0.200588i | ||||||||
\(617\) | 169457. | + | 293507.i | 0.445131 | + | 0.770990i | 0.998061 | − | 0.0622378i | \(-0.0198237\pi\) |
−0.552930 | + | 0.833228i | \(0.686490\pi\) | |||||||
\(618\) | −391254. | + | 225890.i | −1.02443 | + | 0.591454i | ||||
\(619\) | 308686. | 0.805631 | 0.402815 | − | 0.915281i | \(-0.368032\pi\) | ||||
0.402815 | + | 0.915281i | \(0.368032\pi\) | |||||||
\(620\) | 87385.7i | 0.227330i | ||||||||
\(621\) | 154411. | − | 89149.4i | 0.400402 | − | 0.231172i | ||||
\(622\) | −623975. | − | 360252.i | −1.61282 | − | 0.931163i | ||||
\(623\) | 115833. | − | 66876.4i | 0.298440 | − | 0.172305i | ||||
\(624\) | −526014. | + | 911083.i | −1.35092 | + | 2.33985i | ||||
\(625\) | −75003.9 | + | 129911.i | −0.192010 | + | 0.332571i | ||||
\(626\) | 57736.9i | 0.147335i | ||||||||
\(627\) | −261147. | + | 38223.4i | −0.664279 | + | 0.0972286i | ||||
\(628\) | −201482. | −0.510877 | ||||||||
\(629\) | −42947.1 | − | 24795.5i | −0.108551 | − | 0.0626718i | ||||
\(630\) | −223427. | − | 128996.i | −0.562931 | − | 0.325008i | ||||
\(631\) | 132924. | + | 230231.i | 0.333845 | + | 0.578237i | 0.983262 | − | 0.182195i | \(-0.0583204\pi\) |
−0.649417 | + | 0.760432i | \(0.724987\pi\) | |||||||
\(632\) | −134526. | + | 233005.i | −0.336799 | + | 0.583353i | ||||
\(633\) | 39697.1 | + | 68757.4i | 0.0990721 | + | 0.171598i | ||||
\(634\) | −60545.8 | −0.150628 | ||||||||
\(635\) | 468150.i | 1.16101i | ||||||||
\(636\) | 106520. | + | 184498.i | 0.263339 | + | 0.456117i | ||||
\(637\) | 454660. | − | 262498.i | 1.12049 | − | 0.646916i | ||||
\(638\) | −82569.6 | −0.202852 | ||||||||
\(639\) | − | 308725.i | − | 0.756083i | ||||||
\(640\) | 711151. | − | 410583.i | 1.73621 | − | 1.00240i | ||||
\(641\) | 474195. | + | 273776.i | 1.15409 | + | 0.666316i | 0.949881 | − | 0.312611i | \(-0.101204\pi\) |
0.204211 | + | 0.978927i | \(0.434537\pi\) | |||||||
\(642\) | −386015. | + | 222866.i | −0.936557 | + | 0.540722i | ||||
\(643\) | 123976. | − | 214732.i | 0.299857 | − | 0.519368i | −0.676246 | − | 0.736676i | \(-0.736394\pi\) |
0.976103 | + | 0.217308i | \(0.0697276\pi\) | |||||||
\(644\) | −36746.6 | + | 63646.9i | −0.0886023 | + | 0.153464i | ||||
\(645\) | − | 617051.i | − | 1.48321i | ||||||
\(646\) | −14978.6 | + | 37691.3i | −0.0358926 | + | 0.0903184i | ||||
\(647\) | −140129. | −0.334749 | −0.167375 | − | 0.985893i | \(-0.553529\pi\) | ||||
−0.167375 | + | 0.985893i | \(0.553529\pi\) | |||||||
\(648\) | 347378. | + | 200559.i | 0.827280 | + | 0.477630i | ||||
\(649\) | −289116. | − | 166921.i | −0.686408 | − | 0.396298i | ||||
\(650\) | −736468. | − | 1.27560e6i | −1.74312 | − | 3.01917i | ||||
\(651\) | −59140.6 | + | 102434.i | −0.139548 | + | 0.241704i | ||||
\(652\) | 20975.3 | + | 36330.2i | 0.0493415 | + | 0.0854620i | ||||
\(653\) | −457094. | −1.07196 | −0.535980 | − | 0.844231i | \(-0.680058\pi\) | ||||
−0.535980 | + | 0.844231i | \(0.680058\pi\) | |||||||
\(654\) | 498187.i | 1.16476i | ||||||||
\(655\) | −125114. | − | 216703.i | −0.291623 | − | 0.505106i | ||||
\(656\) | −223286. | + | 128914.i | −0.518865 | + | 0.299567i | ||||
\(657\) | 88530.7 | 0.205099 | ||||||||
\(658\) | 93383.2i | 0.215684i | ||||||||
\(659\) | 357061. | − | 206149.i | 0.822188 | − | 0.474691i | −0.0289821 | − | 0.999580i | \(-0.509227\pi\) |
0.851171 | + | 0.524889i | \(0.175893\pi\) | |||||||
\(660\) | 132343. | + | 76408.0i | 0.303817 | + | 0.175409i | ||||
\(661\) | 26307.5 | − | 15188.7i | 0.0602111 | − | 0.0347629i | −0.469592 | − | 0.882883i | \(-0.655599\pi\) |
0.529803 | + | 0.848121i | \(0.322266\pi\) | |||||||
\(662\) | 142245. | − | 246375.i | 0.324579 | − | 0.562187i | ||||
\(663\) | 41438.4 | − | 71773.4i | 0.0942705 | − | 0.163281i | ||||
\(664\) | − | 37287.3i | − | 0.0845716i | ||||||
\(665\) | 52690.5 | + | 359989.i | 0.119149 | + | 0.814040i | ||||
\(666\) | 517994. | 1.16782 | ||||||||
\(667\) | 151193. | + | 87291.5i | 0.339845 | + | 0.196210i | ||||
\(668\) | 129714. | + | 74890.4i | 0.290693 | + | 0.167831i | ||||
\(669\) | 54729.5 | + | 94794.2i | 0.122284 | + | 0.211802i | ||||
\(670\) | −462671. | + | 801370.i | −1.03068 | + | 1.78519i | ||||
\(671\) | 91989.4 | + | 159330.i | 0.204312 | + | 0.353878i | ||||
\(672\) | −175551. | −0.388745 | ||||||||
\(673\) | − | 517440.i | − | 1.14243i | −0.820801 | − | 0.571215i | \(-0.806472\pi\) | ||
0.820801 | − | 0.571215i | \(-0.193528\pi\) | |||||||
\(674\) | −339415. | − | 587883.i | −0.747155 | − | 1.29411i | ||||
\(675\) | −283289. | + | 163557.i | −0.621759 | + | 0.358972i | ||||
\(676\) | 275929. | 0.603815 | ||||||||
\(677\) | 391079.i | 0.853272i | 0.904423 | + | 0.426636i | \(0.140301\pi\) | ||||
−0.904423 | + | 0.426636i | \(0.859699\pi\) | |||||||
\(678\) | −188378. | + | 108760.i | −0.409800 | + | 0.236598i | ||||
\(679\) | 71822.2 | + | 41466.6i | 0.155783 | + | 0.0899412i | ||||
\(680\) | −44534.2 | + | 25711.9i | −0.0963111 | + | 0.0556052i | ||||
\(681\) | −192429. | + | 333297.i | −0.414931 | + | 0.718682i | ||||
\(682\) | 59892.6 | − | 103737.i | 0.128767 | − | 0.223031i | ||||
\(683\) | 416919.i | 0.893739i | 0.894599 | + | 0.446869i | \(0.147461\pi\) | ||||
−0.894599 | + | 0.446869i | \(0.852539\pi\) | |||||||
\(684\) | −14643.7 | − | 100048.i | −0.0312997 | − | 0.213844i | ||||
\(685\) | 732005. | 1.56003 | ||||||||
\(686\) | 404922. | + | 233782.i | 0.860446 | + | 0.496778i | ||||
\(687\) | −345720. | − | 199602.i | −0.732506 | − | 0.422912i | ||||
\(688\) | −196902. | − | 341044.i | −0.415981 | − | 0.720500i | ||||
\(689\) | −524797. | + | 908975.i | −1.10548 | + | 1.91476i | ||||
\(690\) | −676881. | − | 1.17239e6i | −1.42172 | − | 2.46249i | ||||
\(691\) | −430225. | −0.901031 | −0.450516 | − | 0.892769i | \(-0.648760\pi\) | ||||
−0.450516 | + | 0.892769i | \(0.648760\pi\) | |||||||
\(692\) | 73824.6i | 0.154166i | ||||||||
\(693\) | 42203.3 | + | 73098.3i | 0.0878780 | + | 0.152209i | ||||
\(694\) | 100450. | − | 57994.9i | 0.208560 | − | 0.120412i | ||||
\(695\) | 474868. | 0.983112 | ||||||||
\(696\) | 169751.i | 0.350424i | ||||||||
\(697\) | 17590.1 | − | 10155.6i | 0.0362078 | − | 0.0209046i | ||||
\(698\) | 615713. | + | 355482.i | 1.26377 | + | 0.729637i | ||||
\(699\) | 927374. | − | 535420.i | 1.89802 | − | 1.09582i | ||||
\(700\) | 67416.6 | − | 116769.i | 0.137585 | − | 0.238304i | ||||
\(701\) | 432212. | − | 748612.i | 0.879550 | − | 1.52342i | 0.0277137 | − | 0.999616i | \(-0.491177\pi\) |
0.851836 | − | 0.523809i | \(-0.175489\pi\) | |||||||
\(702\) | − | 390048.i | − | 0.791488i | ||||||
\(703\) | −453010. | − | 573053.i | −0.916636 | − | 1.15954i | ||||
\(704\) | −133309. | −0.268977 | ||||||||
\(705\) | −355552. | − | 205278.i | −0.715361 | − | 0.413014i | ||||
\(706\) | 476193. | + | 274930.i | 0.955375 | + | 0.551586i | ||||
\(707\) | −16983.2 | − | 29415.8i | −0.0339767 | − | 0.0588493i | ||||
\(708\) | 156712. | − | 271433.i | 0.312633 | − | 0.541496i | ||||
\(709\) | 162798. | + | 281974.i | 0.323859 | + | 0.560941i | 0.981281 | − | 0.192582i | \(-0.0616863\pi\) |
−0.657422 | + | 0.753523i | \(0.728353\pi\) | |||||||
\(710\) | 1.05616e6 | 2.09514 | ||||||||
\(711\) | 298363.i | 0.590210i | ||||||||
\(712\) | 139236. | + | 241164.i | 0.274658 | + | 0.475721i | ||||
\(713\) | −219339. | + | 126635.i | −0.431456 | + | 0.249101i | ||||
\(714\) | 31786.1 | 0.0623507 | ||||||||
\(715\) | 752888.i | 1.47271i | ||||||||
\(716\) | −71842.7 | + | 41478.4i | −0.140138 | + | 0.0809088i | ||||
\(717\) | −43790.6 | − | 25282.5i | −0.0851810 | − | 0.0491793i | ||||
\(718\) | −741183. | + | 427922.i | −1.43773 | + | 0.830072i | ||||
\(719\) | 263310. | − | 456066.i | 0.509341 | − | 0.882205i | −0.490600 | − | 0.871385i | \(-0.663222\pi\) |
0.999941 | − | 0.0108204i | \(-0.00344430\pi\) | |||||||
\(720\) | 361942. | − | 626901.i | 0.698190 | − | 1.20930i | ||||
\(721\) | − | 203752.i | − | 0.391951i | ||||||
\(722\) | −410079. | + | 434468.i | −0.786670 | + | 0.833457i | ||||
\(723\) | −526155. | −1.00655 | ||||||||
\(724\) | 51539.1 | + | 29756.1i | 0.0983240 | + | 0.0567674i | ||||
\(725\) | −277385. | − | 160148.i | −0.527724 | − | 0.304682i | ||||
\(726\) | 287838. | + | 498549.i | 0.546103 | + | 0.945877i | ||||
\(727\) | 345843. | − | 599018.i | 0.654351 | − | 1.13337i | −0.327706 | − | 0.944780i | \(-0.606275\pi\) |
0.982056 | − | 0.188589i | \(-0.0603913\pi\) | |||||||
\(728\) | −176030. | − | 304894.i | −0.332143 | − | 0.575289i | ||||
\(729\) | 165944. | 0.312253 | ||||||||
\(730\) | 302867.i | 0.568338i | ||||||||
\(731\) | 15511.6 | + | 26866.8i | 0.0290283 | + | 0.0502784i | ||||
\(732\) | −149585. | + | 86363.1i | −0.279169 | + | 0.161178i | ||||
\(733\) | −248355. | −0.462238 | −0.231119 | − | 0.972926i | \(-0.574239\pi\) | ||||
−0.231119 | + | 0.972926i | \(0.574239\pi\) | |||||||
\(734\) | − | 1.04375e6i | − | 1.93733i | ||||||
\(735\) | −766648. | + | 442624.i | −1.41913 | + | 0.819333i | ||||
\(736\) | −325539. | − | 187950.i | −0.600962 | − | 0.346966i | ||||
\(737\) | 262183. | − | 151371.i | 0.482691 | − | 0.278682i | ||||
\(738\) | −106079. | + | 183734.i | −0.194767 | + | 0.337346i | ||||
\(739\) | −363794. | + | 630109.i | −0.666141 | + | 1.15379i | 0.312833 | + | 0.949808i | \(0.398722\pi\) |
−0.978975 | + | 0.203982i | \(0.934612\pi\) | |||||||
\(740\) | 422952.i | 0.772374i | ||||||||
\(741\) | 957688. | − | 757072.i | 1.74417 | − | 1.37880i | ||||
\(742\) | −402556. | −0.731170 | ||||||||
\(743\) | −602317. | − | 347748.i | −1.09106 | − | 0.629922i | −0.157199 | − | 0.987567i | \(-0.550247\pi\) |
−0.933858 | + | 0.357645i | \(0.883580\pi\) | |||||||
\(744\) | −213268. | − | 123130.i | −0.385282 | − | 0.222443i | ||||
\(745\) | 373519. | + | 646954.i | 0.672977 | + | 1.16563i | ||||
\(746\) | 570604. | − | 988315.i | 1.02531 | − | 1.77590i | ||||
\(747\) | −20674.8 | − | 35809.8i | −0.0370510 | − | 0.0641742i | ||||
\(748\) | −7683.05 | −0.0137319 | ||||||||
\(749\) | − | 201024.i | − | 0.358331i | ||||||
\(750\) | 543501. | + | 941372.i | 0.966225 | + | 1.67355i | ||||
\(751\) | 631954. | − | 364859.i | 1.12048 | − | 0.646912i | 0.178960 | − | 0.983856i | \(-0.442727\pi\) |
0.941524 | + | 0.336945i | \(0.109393\pi\) | |||||||
\(752\) | −262018. | −0.463336 | ||||||||
\(753\) | 731125.i | 1.28944i | ||||||||
\(754\) | 330752. | − | 190960.i | 0.581782 | − | 0.335892i | ||||
\(755\) | −92054.3 | − | 53147.5i | −0.161492 | − | 0.0932372i | ||||
\(756\) | 30921.6 | − | 17852.6i | 0.0541027 | − | 0.0312362i | ||||
\(757\) | −141571. | + | 245208.i | −0.247049 | + | 0.427901i | −0.962706 | − | 0.270551i | \(-0.912794\pi\) |
0.715657 | + | 0.698452i | \(0.246128\pi\) | |||||||
\(758\) | −541983. | + | 938743.i | −0.943295 | + | 1.63383i | ||||
\(759\) | 442908.i | 0.768829i | ||||||||
\(760\) | −749494. | + | 109701.i | −1.29760 | + | 0.189926i | ||||
\(761\) | −319277. | −0.551313 | −0.275657 | − | 0.961256i | \(-0.588895\pi\) | ||||
−0.275657 | + | 0.961256i | \(0.588895\pi\) | |||||||
\(762\) | 521757. | + | 301237.i | 0.898584 | + | 0.518798i | ||||
\(763\) | −194580. | − | 112341.i | −0.334233 | − | 0.192969i | ||||
\(764\) | 126796. | + | 219618.i | 0.217230 | + | 0.376254i | ||||
\(765\) | −28513.1 | + | 49386.1i | −0.0487216 | + | 0.0843882i | ||||
\(766\) | −526931. | − | 912672.i | −0.898042 | − | 1.55545i | ||||
\(767\) | 1.54416e6 | 2.62483 | ||||||||
\(768\) | − | 657560.i | − | 1.11484i | ||||||
\(769\) | 219721. | + | 380569.i | 0.371552 | + | 0.643547i | 0.989805 | − | 0.142432i | \(-0.0454924\pi\) |
−0.618252 | + | 0.785980i | \(0.712159\pi\) | |||||||
\(770\) | −250072. | + | 144379.i | −0.421778 | + | 0.243514i | ||||
\(771\) | −873806. | −1.46996 | ||||||||
\(772\) | − | 241898.i | − | 0.405880i | ||||||
\(773\) | −785095. | + | 453275.i | −1.31390 | + | 0.758583i | −0.982740 | − | 0.184991i | \(-0.940774\pi\) |
−0.331163 | + | 0.943573i | \(0.607441\pi\) | |||||||
\(774\) | −280632. | − | 162023.i | −0.468442 | − | 0.270455i | ||||
\(775\) | 402407. | − | 232330.i | 0.669980 | − | 0.386813i | ||||
\(776\) | −86333.1 | + | 149533.i | −0.143369 | + | 0.248322i | ||||
\(777\) | −286244. | + | 495789.i | −0.474127 | + | 0.821212i | ||||
\(778\) | 111257.i | 0.183809i | ||||||||
\(779\) | 296034. | − | 43329.6i | 0.487828 | − | 0.0714019i | ||||
\(780\) | −706839. | −1.16180 | ||||||||
\(781\) | −299248. | − | 172771.i | −0.490602 | − | 0.283249i | ||||
\(782\) | 58943.7 | + | 34031.2i | 0.0963882 | + | 0.0556498i | ||||
\(783\) | −42408.9 | − | 73454.3i | −0.0691725 | − | 0.119810i | ||||
\(784\) | −282484. | + | 489277.i | −0.459581 | + | 0.796017i | ||||
\(785\) | 836904. | + | 1.44956e6i | 1.35811 | + | 2.35232i | ||||
\(786\) | −322024. | −0.521246 | ||||||||
\(787\) | − | 461769.i | − | 0.745548i | −0.927922 | − | 0.372774i | \(-0.878407\pi\) | ||
0.927922 | − | 0.372774i | \(-0.121593\pi\) | |||||||
\(788\) | −97976.3 | − | 169700.i | −0.157786 | − | 0.273293i | ||||
\(789\) | 256465. | − | 148070.i | 0.411978 | − | 0.237855i | ||||
\(790\) | −1.02071e6 | −1.63550 | ||||||||
\(791\) | − | 98101.3i | − | 0.156791i | ||||||
\(792\) | −152190. | + | 87867.0i | −0.242625 | + | 0.140080i | ||||
\(793\) | −736971. | − | 425490.i | −1.17194 | − | 0.676617i | ||||
\(794\) | 1.14727e6 | − | 662378.i | 1.81981 | − | 1.05067i | ||||
\(795\) | 884911. | − | 1.53271e6i | 1.40012 | − | 2.42508i | ||||
\(796\) | 64744.7 | − | 112141.i | 0.102183 | − | 0.176986i | ||||
\(797\) | 936748.i | 1.47471i | 0.675506 | + | 0.737354i | \(0.263925\pi\) | ||||
−0.675506 | + | 0.737354i | \(0.736075\pi\) | |||||||
\(798\) | 435115. | + | 172915.i | 0.683280 | + | 0.271536i | ||||
\(799\) | 20641.3 | 0.0323328 | ||||||||
\(800\) | 597245. | + | 344820.i | 0.933196 | + | 0.538781i | ||||
\(801\) | 267438. | + | 154405.i | 0.416829 | + | 0.240656i | ||||
\(802\) | −22644.2 | − | 39221.0i | −0.0352054 | − | 0.0609775i | ||||
\(803\) | 49544.2 | − | 85813.2i | 0.0768355 | − | 0.133083i | ||||
\(804\) | 142113. | + | 246147.i | 0.219848 | + | 0.380788i | ||||
\(805\) | 610544. | 0.942160 | ||||||||
\(806\) | 554057.i | 0.852873i | ||||||||
\(807\) | −780846. | − | 1.35246e6i | −1.19900 | − | 2.07672i | ||||
\(808\) | 61243.4 | − | 35358.9i | 0.0938073 | − | 0.0541597i | ||||
\(809\) | −55778.3 | −0.0852252 | −0.0426126 | − | 0.999092i | \(-0.513568\pi\) | ||||
−0.0426126 | + | 0.999092i | \(0.513568\pi\) | |||||||
\(810\) | 1.52174e6i | 2.31937i | ||||||||
\(811\) | −562443. | + | 324727.i | −0.855140 | + | 0.493715i | −0.862382 | − | 0.506259i | \(-0.831028\pi\) |
0.00724190 | + | 0.999974i | \(0.497695\pi\) | |||||||
\(812\) | 30277.2 | + | 17480.6i | 0.0459202 | + | 0.0265120i | ||||
\(813\) | 175967. | − | 101594.i | 0.266225 | − | 0.153705i | ||||
\(814\) | 289884. | − | 502093.i | 0.437497 | − | 0.757767i | ||||
\(815\) | 174252. | − | 301813.i | 0.262339 | − | 0.454384i | ||||
\(816\) | 89186.8i | 0.133943i | ||||||||
\(817\) | 66181.1 | + | 452158.i | 0.0991493 | + | 0.677402i | ||||
\(818\) | −815844. | −1.21927 | ||||||||
\(819\) | −338111. | − | 195208.i | −0.504071 | − | 0.291025i | ||||
\(820\) | −150022. | − | 86615.3i | −0.223114 | − | 0.128815i | ||||
\(821\) | 160712. | + | 278361.i | 0.238431 | + | 0.412974i | 0.960264 | − | 0.279093i | \(-0.0900337\pi\) |
−0.721834 | + | 0.692067i | \(0.756700\pi\) | |||||||
\(822\) | 471017. | − | 815826.i | 0.697097 | − | 1.20741i | ||||
\(823\) | −239960. | − | 415622.i | −0.354273 | − | 0.613619i | 0.632720 | − | 0.774381i | \(-0.281938\pi\) |
−0.986993 | + | 0.160761i | \(0.948605\pi\) | |||||||
\(824\) | 424210. | 0.624779 | ||||||||
\(825\) | − | 812575.i | − | 1.19387i | ||||||
\(826\) | 296120. | + | 512894.i | 0.434017 | + | 0.751740i | ||||
\(827\) | 650685. | − | 375673.i | 0.951393 | − | 0.549287i | 0.0578795 | − | 0.998324i | \(-0.481566\pi\) |
0.893513 | + | 0.449037i | \(0.148233\pi\) | |||||||
\(828\) | −169682. | −0.247500 | ||||||||
\(829\) | 96570.8i | 0.140520i | 0.997529 | + | 0.0702598i | \(0.0223828\pi\) | ||||
−0.997529 | + | 0.0702598i | \(0.977617\pi\) | |||||||
\(830\) | 122507. | − | 70729.3i | 0.177830 | − | 0.102670i | ||||
\(831\) | 1.53146e6 | + | 884190.i | 2.21771 | + | 1.28039i | ||||
\(832\) | 534001. | − | 308306.i | 0.771429 | − | 0.445385i | ||||
\(833\) | 22253.6 | − | 38544.3i | 0.0320708 | − | 0.0555482i | ||||
\(834\) | 305559. | − | 529244.i | 0.439302 | − | 0.760894i | ||||
\(835\) | − | 1.24430e6i | − | 1.78465i | ||||||
\(836\) | −105172. | − | 41795.5i | −0.150483 | − | 0.0598021i | ||||
\(837\) | 123047. | 0.175638 | ||||||||
\(838\) | −112120. | − | 64732.5i | −0.159659 | − | 0.0921794i | ||||
\(839\) | −1.05400e6 | − | 608525.i | −1.49732 | − | 0.864479i | −0.497326 | − | 0.867563i | \(-0.665685\pi\) |
−0.999995 | + | 0.00308436i | \(0.999018\pi\) | |||||||
\(840\) | 296822. | + | 514111.i | 0.420666 | + | 0.728616i | ||||
\(841\) | −312115. | + | 540600.i | −0.441289 | + | 0.764335i | ||||
\(842\) | 144304. | + | 249941.i | 0.203542 | + | 0.352544i | ||||
\(843\) | −963553. | −1.35588 | ||||||||
\(844\) | 34044.0i | 0.0477921i | ||||||||
\(845\) | −1.14614e6 | − | 1.98517e6i | −1.60518 | − | 2.78025i | ||||
\(846\) | −186719. | + | 107802.i | −0.260884 | + | 0.150622i | ||||
\(847\) | −259628. | −0.361897 | ||||||||
\(848\) | − | 1.12951e6i | − | 1.57071i | ||||||
\(849\) | 776119. | − | 448093.i | 1.07675 | − | 0.621659i | ||||
\(850\) | −108140. | − | 62434.8i | −0.149675 | − | 0.0864150i | ||||
\(851\) | −1.06161e6 | + | 612923.i | −1.46591 | + | 0.846343i | ||||
\(852\) | 162204. | − | 280945.i | 0.223451 | − | 0.387028i | ||||
\(853\) | −119586. | + | 207129.i | −0.164355 | + | 0.284671i | −0.936426 | − | 0.350865i | \(-0.885888\pi\) |
0.772071 | + | 0.635536i | \(0.219221\pi\) | |||||||
\(854\) | − | 326381.i | − | 0.447516i | ||||||
\(855\) | −658969. | + | 520929.i | −0.901432 | + | 0.712600i | ||||
\(856\) | 418531. | 0.571189 | ||||||||
\(857\) | 1.00185e6 | + | 578418.i | 1.36408 | + | 0.787553i | 0.990164 | − | 0.139908i | \(-0.0446808\pi\) |
0.373918 | + | 0.927462i | \(0.378014\pi\) | |||||||
\(858\) | 839101. | + | 484455.i | 1.13983 | + | 0.658080i | ||||
\(859\) | 475365. | + | 823357.i | 0.644230 | + | 1.11584i | 0.984479 | + | 0.175504i | \(0.0561555\pi\) |
−0.340249 | + | 0.940336i | \(0.610511\pi\) | |||||||
\(860\) | 132295. | − | 229142.i | 0.178874 | − | 0.309818i | ||||
\(861\) | −117238. | − | 203063.i | −0.158148 | − | 0.273920i | ||||
\(862\) | 766427. | 1.03147 | ||||||||
\(863\) | 38746.3i | 0.0520246i | 0.999662 | + | 0.0260123i | \(0.00828090\pi\) | ||||
−0.999662 | + | 0.0260123i | \(0.991719\pi\) | |||||||
\(864\) | 91311.8 | + | 158157.i | 0.122320 | + | 0.211865i | ||||
\(865\) | 531131. | − | 306649.i | 0.709855 | − | 0.409835i | ||||
\(866\) | −161757. | −0.215688 | ||||||||
\(867\) | 969991.i | 1.29042i | ||||||||
\(868\) | −43923.7 | + | 25359.3i | −0.0582987 | + | 0.0336588i | ||||
\(869\) | 289205. | + | 166972.i | 0.382971 | + | 0.221108i | ||||
\(870\) | −557714. | + | 321996.i | −0.736839 | + | 0.425414i | ||||
\(871\) | −700157. | + | 1.21271e6i | −0.922910 | + | 1.59853i | ||||
\(872\) | 233892. | − | 405114.i | 0.307598 | − | 0.532775i | ||||
\(873\) | 191478.i | 0.251240i | ||||||||
\(874\) | 621743. | + | 786499.i | 0.813932 | + | 1.02962i | ||||
\(875\) | −490236. | −0.640308 | ||||||||
\(876\) | 80564.6 | + | 46514.0i | 0.104987 | + | 0.0606144i | ||||
\(877\) | 315242. | + | 182005.i | 0.409869 | + | 0.236638i | 0.690733 | − | 0.723110i | \(-0.257288\pi\) |
−0.280865 | + | 0.959747i | \(0.590621\pi\) | |||||||
\(878\) | −432778. | − | 749593.i | −0.561404 | − | 0.972381i | ||||
\(879\) | −567949. | + | 983716.i | −0.735074 | + | 1.27319i | ||||
\(880\) | −405105. | − | 701663.i | −0.523121 | − | 0.906073i | ||||
\(881\) | −243497. | −0.313720 | −0.156860 | − | 0.987621i | \(-0.550137\pi\) | ||||
−0.156860 | + | 0.987621i | \(0.550137\pi\) | |||||||
\(882\) | 464891.i | 0.597604i | ||||||||
\(883\) | 714345. | + | 1.23728e6i | 0.916193 | + | 1.58689i | 0.805146 | + | 0.593077i | \(0.202087\pi\) |
0.111047 | + | 0.993815i | \(0.464580\pi\) | |||||||
\(884\) | 30776.3 | − | 17768.7i | 0.0393832 | − | 0.0227379i | ||||
\(885\) | −2.60376e6 | −3.32441 | ||||||||
\(886\) | 930705.i | 1.18562i | ||||||||
\(887\) | −963132. | + | 556064.i | −1.22416 | + | 0.706769i | −0.965802 | − | 0.259280i | \(-0.916515\pi\) |
−0.258358 | + | 0.966049i | \(0.583182\pi\) | |||||||
\(888\) | −1.03223e6 | − | 595958.i | −1.30903 | − | 0.755770i | ||||
\(889\) | −235311. | + | 135857.i | −0.297741 | + | 0.171901i | ||||
\(890\) | −528227. | + | 914916.i | −0.666869 | + | 1.15505i | ||||
\(891\) | 248933. | − | 431164.i | 0.313564 | − | 0.543109i | ||||
\(892\) | 46935.7i | 0.0589894i | ||||||||
\(893\) | 282556. | + | 112288.i | 0.354324 | + | 0.140809i | ||||
\(894\) | 961382. | 1.20288 | ||||||||
\(895\) | 596832. | + | 344581.i | 0.745086 | + | 0.430175i | ||||
\(896\) | 412752. | + | 238303.i | 0.514131 | + | 0.296833i | ||||
\(897\) | −1.02432e6 | − | 1.77417e6i | −1.27306 | − | 2.20501i | ||||
\(898\) | 417508. | − | 723144.i | 0.517740 | − | 0.896752i | ||||
\(899\) | 60241.1 | + | 104341.i | 0.0745373 | + | 0.129102i | ||||
\(900\) | 311305. | 0.384328 | ||||||||
\(901\) | 88980.4i | 0.109609i | ||||||||
\(902\) | 118729. | + | 205645.i | 0.145930 | + | 0.252758i | ||||
\(903\) | 310155. | − | 179068.i | 0.380368 | − | 0.219606i | ||||
\(904\) | 204246. | 0.249929 | ||||||||
\(905\) | − | 494397.i | − | 0.603641i | ||||||
\(906\) | −118467. | + | 68396.9i | −0.144325 | + | 0.0833259i | ||||
\(907\) | −1.07643e6 | − | 621477.i | −1.30849 | − | 0.755458i | −0.326647 | − | 0.945146i | \(-0.605919\pi\) |
−0.981844 | + | 0.189688i | \(0.939252\pi\) | |||||||
\(908\) | −142917. | + | 82513.1i | −0.173345 | + | 0.100081i | ||||
\(909\) | 39211.1 | − | 67915.6i | 0.0474549 | − | 0.0821944i | ||||
\(910\) | 667816. | − | 1.15669e6i | 0.806443 | − | 1.39680i | ||||
\(911\) | − | 298558.i | − | 0.359743i | −0.983690 | − | 0.179871i | \(-0.942432\pi\) | ||
0.983690 | − | 0.179871i | \(-0.0575682\pi\) | |||||||
\(912\) | −485172. | + | 1.22086e6i | −0.583319 | + | 1.46784i | ||||
\(913\) | −46280.8 | −0.0555212 | ||||||||
\(914\) | −265166. | − | 153094.i | −0.317414 | − | 0.183259i | ||||
\(915\) | 1.24268e6 | + | 717461.i | 1.48428 | + | 0.856951i | ||||
\(916\) | −85588.6 | − | 148244.i | −0.102006 | − | 0.176679i | ||||
\(917\) | 72616.0 | − | 125775.i | 0.0863562 | − | 0.149573i | ||||
\(918\) | −16533.4 | − | 28636.6i | −0.0196190 | − | 0.0339811i | ||||
\(919\) | −1.19613e6 | −1.41628 | −0.708138 | − | 0.706074i | \(-0.750464\pi\) | ||||
−0.708138 | + | 0.706074i | \(0.750464\pi\) | |||||||
\(920\) | 1.27115e6i | 1.50183i | ||||||||
\(921\) | −217409. | − | 376564.i | −0.256306 | − | 0.443935i | ||||
\(922\) | −271908. | + | 156986.i | −0.319861 | + | 0.184672i | ||||
\(923\) | 1.59828e6 | 1.87607 | ||||||||
\(924\) | 88694.5i | 0.103885i | ||||||||
\(925\) | 1.94767e6 | − | 1.12449e6i | 2.27632 | − | 1.31423i | ||||
\(926\) | −1.55132e6 | − | 895653.i | −1.80917 | − | 1.04452i | ||||
\(927\) | 407401. | − | 235213.i | 0.474092 | − | 0.273717i | ||||
\(928\) | −89408.8 | + | 154861.i | −0.103821 | + | 0.179823i | ||||
\(929\) | 234694. | − | 406501.i | 0.271938 | − | 0.471010i | −0.697420 | − | 0.716662i | \(-0.745669\pi\) |
0.969358 | + | 0.245652i | \(0.0790022\pi\) | |||||||
\(930\) | − | 934250.i | − | 1.08018i | ||||||
\(931\) | 514305. | − | 406569.i | 0.593364 | − | 0.469067i | ||||
\(932\) | 459173. | 0.528622 | ||||||||
\(933\) | 1.59220e6 | + | 919259.i | 1.82909 | + | 1.05603i | ||||
\(934\) | −286824. | − | 165598.i | −0.328793 | − | 0.189829i | ||||
\(935\) | 31913.4 | + | 55275.7i | 0.0365048 | + | 0.0632282i | ||||
\(936\) | 406422. | − | 703944.i | 0.463901 | − | 0.803501i | ||||
\(937\) | −48982.6 | − | 84840.4i | −0.0557908 | − | 0.0966326i | 0.836781 | − | 0.547538i | \(-0.184435\pi\) |
−0.892572 | + | 0.450905i | \(0.851101\pi\) | |||||||
\(938\) | −537069. | −0.610414 | ||||||||
\(939\) | − | 147328.i | − | 0.167091i | ||||||
\(940\) | −88022.7 | − | 152460.i | −0.0996183 | − | 0.172544i | ||||
\(941\) | −253995. | + | 146644.i | −0.286844 | + | 0.165609i | −0.636518 | − | 0.771262i | \(-0.719626\pi\) |
0.349674 | + | 0.936872i | \(0.386292\pi\) | |||||||
\(942\) | 2.15406e6 | 2.42749 | ||||||||
\(943\) | − | 502075.i | − | 0.564606i | ||||||
\(944\) | −1.43910e6 | + | 830864.i | −1.61490 | + | 0.932365i | ||||
\(945\) | −256881. | − | 148310.i | −0.287653 | − | 0.166076i | ||||
\(946\) | −314099. | + | 181345.i | −0.350982 | + | 0.202639i | ||||
\(947\) | 273771. | − | 474186.i | 0.305273 | − | 0.528748i | −0.672049 | − | 0.740506i | \(-0.734586\pi\) |
0.977322 | + | 0.211759i | \(0.0679190\pi\) | |||||||
\(948\) | −156760. | + | 271516.i | −0.174429 | + | 0.302120i | ||||
\(949\) | 458326.i | 0.508912i | ||||||||
\(950\) | −1.14067e6 | − | 1.44294e6i | −1.26390 | − | 1.59883i | ||||
\(951\) | 154495. | 0.170826 | ||||||||
\(952\) | −25847.7 | − | 14923.2i | −0.0285199 | − | 0.0164660i | ||||
\(953\) | −978151. | − | 564736.i | −1.07701 | − | 0.621812i | −0.146922 | − | 0.989148i | \(-0.546937\pi\) |
−0.930088 | + | 0.367336i | \(0.880270\pi\) | |||||||
\(954\) | −464714. | − | 804908.i | −0.510609 | − | 0.884401i | ||||
\(955\) | 1.05336e6 | − | 1.82447e6i | 1.15497 | − | 2.00046i | ||||
\(956\) | −10841.1 | − | 18777.3i | −0.0118620 | − | 0.0205455i | ||||
\(957\) | 210694. | 0.230053 | ||||||||
\(958\) | 1.44699e6i | 1.57665i | ||||||||
\(959\) | 212428. | + | 367936.i | 0.230980 | + | 0.400069i | ||||
\(960\) | −900432. | + | 519865.i | −0.977031 | + | 0.564089i | ||||
\(961\) | 748735. | 0.810740 | ||||||||
\(962\) | 2.68167e6i | 2.89771i | ||||||||
\(963\) | 401947. | − | 232064.i | 0.433427 | − | 0.250239i | ||||
\(964\) | −195387. | − | 112807.i | −0.210253 | − | 0.121390i | ||||
\(965\) | −1.74034e6 | + | 1.00478e6i | −1.86887 | + | 1.07899i | ||||
\(966\) | 392862. | − | 680457.i | 0.421003 | − | 0.729199i | ||||
\(967\) | −551522. | + | 955264.i | −0.589807 | + | 1.02158i | 0.404451 | + | 0.914560i | \(0.367463\pi\) |
−0.994257 | + | 0.107015i | \(0.965871\pi\) | |||||||
\(968\) | − | 540544.i | − | 0.576873i | ||||||
\(969\) | 38221.0 | − | 96177.4i | 0.0407056 | − | 0.102430i | ||||
\(970\) | −655052. | −0.696198 | ||||||||
\(971\) | 156634. | + | 90432.6i | 0.166130 | + | 0.0959150i | 0.580760 | − | 0.814075i | \(-0.302756\pi\) |
−0.414630 | + | 0.909990i | \(0.636089\pi\) | |||||||
\(972\) | 301233. | + | 173917.i | 0.318838 | + | 0.184081i | ||||
\(973\) | 137807. | + | 238688.i | 0.145561 | + | 0.252119i | ||||
\(974\) | 35726.4 | − | 61879.9i | 0.0376592 | − | 0.0652276i | ||||
\(975\) | 1.87925e6 | + | 3.25496e6i | 1.97686 | + | 3.42402i | ||||
\(976\) | 915772. | 0.961363 | ||||||||
\(977\) | − | 962182.i | − | 1.00802i | −0.863698 | − | 0.504009i | \(-0.831858\pi\) | ||
0.863698 | − | 0.504009i | \(-0.168142\pi\) | |||||||
\(978\) | −224249. | − | 388411.i | −0.234451 | − | 0.406082i | ||||
\(979\) | 299331. | − | 172819.i | 0.312311 | − | 0.180313i | ||||
\(980\) | −379592. | −0.395244 | ||||||||
\(981\) | − | 518748.i | − | 0.539037i | ||||||
\(982\) | 573586. | − | 331160.i | 0.594806 | − | 0.343411i | ||||
\(983\) | 286561. | + | 165446.i | 0.296558 | + | 0.171218i | 0.640896 | − | 0.767628i | \(-0.278563\pi\) |
−0.344338 | + | 0.938846i | \(0.611896\pi\) | |||||||
\(984\) | 422775. | − | 244089.i | 0.436636 | − | 0.252092i | ||||
\(985\) | −813937. | + | 1.40978e6i | −0.838915 | + | 1.45304i | ||||
\(986\) | 16188.8 | − | 28039.9i | 0.0166518 | − | 0.0288418i | ||||
\(987\) | − | 238287.i | − | 0.244605i | ||||||
\(988\) | 517952. | − | 75811.2i | 0.530611 | − | 0.0776639i | ||||
\(989\) | 766863. | 0.784017 | ||||||||
\(990\) | −577371. | − | 333345.i | −0.589094 | − | 0.340114i | ||||
\(991\) | 1.08063e6 | + | 623905.i | 1.10035 | + | 0.635288i | 0.936313 | − | 0.351166i | \(-0.114215\pi\) |
0.164038 | + | 0.986454i | \(0.447548\pi\) | |||||||
\(992\) | −129707. | − | 224659.i | −0.131807 | − | 0.228297i | ||||
\(993\) | −362967. | + | 628678.i | −0.368103 | + | 0.637572i | ||||
\(994\) | 306497. | + | 530869.i | 0.310209 | + | 0.537297i | ||||
\(995\) | −1.07573e6 | −1.08657 | ||||||||
\(996\) | − | 43450.1i | − | 0.0437998i | ||||||
\(997\) | −932962. | − | 1.61594e6i | −0.938585 | − | 1.62568i | −0.768114 | − | 0.640313i | \(-0.778804\pi\) |
−0.170471 | − | 0.985363i | \(-0.554529\pi\) | |||||||
\(998\) | 1.00842e6 | − | 582214.i | 1.01247 | − | 0.584549i | ||||
\(999\) | 595553. | 0.596746 |
(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 | 19.5.d.a.8.2 | ✓ | 10 | |
3.2 | odd | 2 | 171.5.p.a.46.4 | 10 | |||
4.3 | odd | 2 | 304.5.r.a.65.1 | 10 | |||
19.12 | odd | 6 | inner | 19.5.d.a.12.2 | yes | 10 | |
57.50 | even | 6 | 171.5.p.a.145.4 | 10 | |||
76.31 | even | 6 | 304.5.r.a.145.1 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
19.5.d.a.8.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
19.5.d.a.12.2 | yes | 10 | 19.12 | odd | 6 | inner | |
171.5.p.a.46.4 | 10 | 3.2 | odd | 2 | |||
171.5.p.a.145.4 | 10 | 57.50 | even | 6 | |||
304.5.r.a.65.1 | 10 | 4.3 | odd | 2 | |||
304.5.r.a.145.1 | 10 | 76.31 | even | 6 |