Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,5,Mod(31,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(4))
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("74.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.d (of order \(4\), 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: | \(7.64937726820\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 727 x^{12} + 198453 x^{10} + 24875201 x^{8} + 1392846203 x^{6} + 29089700589 x^{4} + 220261242916 x^{2} + 446074380544 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 43.1 | ||
Root | \(-14.0996i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.43 |
Dual form | 74.5.d.a.31.7 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.00000 | + | 2.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | − | 13.0996i | − | 1.45551i | −0.685838 | − | 0.727755i | \(-0.740564\pi\) | ||
0.685838 | − | 0.727755i | \(-0.259436\pi\) | |||||||
\(4\) | − | 8.00000i | − | 0.500000i | ||||||
\(5\) | −23.5442 | − | 23.5442i | −0.941766 | − | 0.941766i | 0.0566289 | − | 0.998395i | \(-0.481965\pi\) |
−0.998395 | + | 0.0566289i | \(0.981965\pi\) | |||||||
\(6\) | 26.1992 | + | 26.1992i | 0.727755 | + | 0.727755i | ||||
\(7\) | −19.7742 | −0.403555 | −0.201778 | − | 0.979431i | \(-0.564672\pi\) | ||||
−0.201778 | + | 0.979431i | \(0.564672\pi\) | |||||||
\(8\) | 16.0000 | + | 16.0000i | 0.250000 | + | 0.250000i | ||||
\(9\) | −90.5991 | −1.11851 | ||||||||
\(10\) | 94.1766 | 0.941766 | ||||||||
\(11\) | 152.071i | 1.25678i | 0.777897 | + | 0.628392i | \(0.216287\pi\) | ||||
−0.777897 | + | 0.628392i | \(0.783713\pi\) | |||||||
\(12\) | −104.797 | −0.727755 | ||||||||
\(13\) | 144.158 | + | 144.158i | 0.853004 | + | 0.853004i | 0.990502 | − | 0.137498i | \(-0.0439061\pi\) |
−0.137498 | + | 0.990502i | \(0.543906\pi\) | |||||||
\(14\) | 39.5484 | − | 39.5484i | 0.201778 | − | 0.201778i | ||||
\(15\) | −308.419 | + | 308.419i | −1.37075 | + | 1.37075i | ||||
\(16\) | −64.0000 | −0.250000 | ||||||||
\(17\) | −104.714 | − | 104.714i | −0.362333 | − | 0.362333i | 0.502338 | − | 0.864671i | \(-0.332473\pi\) |
−0.864671 | + | 0.502338i | \(0.832473\pi\) | |||||||
\(18\) | 181.198 | − | 181.198i | 0.559253 | − | 0.559253i | ||||
\(19\) | −227.423 | − | 227.423i | −0.629980 | − | 0.629980i | 0.318083 | − | 0.948063i | \(-0.396961\pi\) |
−0.948063 | + | 0.318083i | \(0.896961\pi\) | |||||||
\(20\) | −188.353 | + | 188.353i | −0.470883 | + | 0.470883i | ||||
\(21\) | 259.034i | 0.587378i | ||||||||
\(22\) | −304.142 | − | 304.142i | −0.628392 | − | 0.628392i | ||||
\(23\) | −346.188 | − | 346.188i | −0.654420 | − | 0.654420i | 0.299634 | − | 0.954054i | \(-0.403135\pi\) |
−0.954054 | + | 0.299634i | \(0.903135\pi\) | |||||||
\(24\) | 209.593 | − | 209.593i | 0.363877 | − | 0.363877i | ||||
\(25\) | 483.655i | 0.773848i | ||||||||
\(26\) | −576.631 | −0.853004 | ||||||||
\(27\) | 125.744i | 0.172488i | ||||||||
\(28\) | 158.194i | 0.201778i | ||||||||
\(29\) | −831.151 | + | 831.151i | −0.988289 | + | 0.988289i | −0.999932 | − | 0.0116431i | \(-0.996294\pi\) |
0.0116431 | + | 0.999932i | \(0.496294\pi\) | |||||||
\(30\) | − | 1233.67i | − | 1.37075i | ||||||
\(31\) | 237.857 | − | 237.857i | 0.247510 | − | 0.247510i | −0.572438 | − | 0.819948i | \(-0.694002\pi\) |
0.819948 | + | 0.572438i | \(0.194002\pi\) | |||||||
\(32\) | 128.000 | − | 128.000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 1992.07 | 1.82926 | ||||||||
\(34\) | 418.857 | 0.362333 | ||||||||
\(35\) | 465.567 | + | 465.567i | 0.380055 | + | 0.380055i | ||||
\(36\) | 724.792i | 0.559253i | ||||||||
\(37\) | −1250.02 | − | 558.226i | −0.913088 | − | 0.407762i | ||||
\(38\) | 909.692 | 0.629980 | ||||||||
\(39\) | 1888.41 | − | 1888.41i | 1.24156 | − | 1.24156i | ||||
\(40\) | − | 753.413i | − | 0.470883i | ||||||
\(41\) | − | 316.672i | − | 0.188383i | −0.995554 | − | 0.0941916i | \(-0.969973\pi\) | ||
0.995554 | − | 0.0941916i | \(-0.0300266\pi\) | |||||||
\(42\) | −518.068 | − | 518.068i | −0.293689 | − | 0.293689i | ||||
\(43\) | 2172.28 | + | 2172.28i | 1.17484 | + | 1.17484i | 0.981041 | + | 0.193801i | \(0.0620815\pi\) |
0.193801 | + | 0.981041i | \(0.437919\pi\) | |||||||
\(44\) | 1216.57 | 0.628392 | ||||||||
\(45\) | 2133.08 | + | 2133.08i | 1.05337 | + | 1.05337i | ||||
\(46\) | 1384.75 | 0.654420 | ||||||||
\(47\) | −613.021 | −0.277511 | −0.138755 | − | 0.990327i | \(-0.544310\pi\) | ||||
−0.138755 | + | 0.990327i | \(0.544310\pi\) | |||||||
\(48\) | 838.373i | 0.363877i | ||||||||
\(49\) | −2009.98 | −0.837143 | ||||||||
\(50\) | −967.310 | − | 967.310i | −0.386924 | − | 0.386924i | ||||
\(51\) | −1371.71 | + | 1371.71i | −0.527379 | + | 0.527379i | ||||
\(52\) | 1153.26 | − | 1153.26i | 0.426502 | − | 0.426502i | ||||
\(53\) | −2538.56 | −0.903723 | −0.451861 | − | 0.892088i | \(-0.649240\pi\) | ||||
−0.451861 | + | 0.892088i | \(0.649240\pi\) | |||||||
\(54\) | −251.487 | − | 251.487i | −0.0862439 | − | 0.0862439i | ||||
\(55\) | 3580.38 | − | 3580.38i | 1.18360 | − | 1.18360i | ||||
\(56\) | −316.387 | − | 316.387i | −0.100889 | − | 0.100889i | ||||
\(57\) | −2979.15 | + | 2979.15i | −0.916942 | + | 0.916942i | ||||
\(58\) | − | 3324.60i | − | 0.988289i | ||||||
\(59\) | −2732.58 | − | 2732.58i | −0.784998 | − | 0.784998i | 0.195672 | − | 0.980669i | \(-0.437311\pi\) |
−0.980669 | + | 0.195672i | \(0.937311\pi\) | |||||||
\(60\) | 2467.35 | + | 2467.35i | 0.685375 | + | 0.685375i | ||||
\(61\) | 1632.21 | − | 1632.21i | 0.438649 | − | 0.438649i | −0.452908 | − | 0.891557i | \(-0.649613\pi\) |
0.891557 | + | 0.452908i | \(0.149613\pi\) | |||||||
\(62\) | 951.430i | 0.247510i | ||||||||
\(63\) | 1791.52 | 0.451379 | ||||||||
\(64\) | 512.000i | 0.125000i | ||||||||
\(65\) | − | 6788.14i | − | 1.60666i | ||||||
\(66\) | −3984.13 | + | 3984.13i | −0.914631 | + | 0.914631i | ||||
\(67\) | − | 6634.72i | − | 1.47800i | −0.673708 | − | 0.738998i | \(-0.735299\pi\) | ||
0.673708 | − | 0.738998i | \(-0.264701\pi\) | |||||||
\(68\) | −837.714 | + | 837.714i | −0.181167 | + | 0.181167i | ||||
\(69\) | −4534.92 | + | 4534.92i | −0.952514 | + | 0.952514i | ||||
\(70\) | −1862.27 | −0.380055 | ||||||||
\(71\) | −9616.78 | −1.90771 | −0.953856 | − | 0.300265i | \(-0.902925\pi\) | ||||
−0.953856 | + | 0.300265i | \(0.902925\pi\) | |||||||
\(72\) | −1449.58 | − | 1449.58i | −0.279627 | − | 0.279627i | ||||
\(73\) | 5989.19i | 1.12389i | 0.827176 | + | 0.561943i | \(0.189946\pi\) | ||||
−0.827176 | + | 0.561943i | \(0.810054\pi\) | |||||||
\(74\) | 3616.49 | − | 1383.58i | 0.660425 | − | 0.252663i | ||||
\(75\) | 6335.68 | 1.12634 | ||||||||
\(76\) | −1819.38 | + | 1819.38i | −0.314990 | + | 0.314990i | ||||
\(77\) | − | 3007.08i | − | 0.507182i | ||||||
\(78\) | 7553.62i | 1.24156i | ||||||||
\(79\) | 7624.90 | + | 7624.90i | 1.22174 | + | 1.22174i | 0.967012 | + | 0.254732i | \(0.0819873\pi\) |
0.254732 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(80\) | 1506.83 | + | 1506.83i | 0.235442 | + | 0.235442i | ||||
\(81\) | −5691.33 | −0.867449 | ||||||||
\(82\) | 633.345 | + | 633.345i | 0.0941916 | + | 0.0941916i | ||||
\(83\) | −2358.53 | −0.342362 | −0.171181 | − | 0.985240i | \(-0.554758\pi\) | ||||
−0.171181 | + | 0.985240i | \(0.554758\pi\) | |||||||
\(84\) | 2072.27 | 0.293689 | ||||||||
\(85\) | 4930.82i | 0.682466i | ||||||||
\(86\) | −8689.13 | −1.17484 | ||||||||
\(87\) | 10887.7 | + | 10887.7i | 1.43846 | + | 1.43846i | ||||
\(88\) | −2433.13 | + | 2433.13i | −0.314196 | + | 0.314196i | ||||
\(89\) | 4769.82 | − | 4769.82i | 0.602174 | − | 0.602174i | −0.338715 | − | 0.940889i | \(-0.609992\pi\) |
0.940889 | + | 0.338715i | \(0.109992\pi\) | |||||||
\(90\) | −8532.31 | −1.05337 | ||||||||
\(91\) | −2850.60 | − | 2850.60i | −0.344234 | − | 0.344234i | ||||
\(92\) | −2769.51 | + | 2769.51i | −0.327210 | + | 0.327210i | ||||
\(93\) | −3115.83 | − | 3115.83i | −0.360254 | − | 0.360254i | ||||
\(94\) | 1226.04 | − | 1226.04i | 0.138755 | − | 0.138755i | ||||
\(95\) | 10709.0i | 1.18659i | ||||||||
\(96\) | −1676.75 | − | 1676.75i | −0.181939 | − | 0.181939i | ||||
\(97\) | 113.114 | + | 113.114i | 0.0120219 | + | 0.0120219i | 0.713092 | − | 0.701070i | \(-0.247294\pi\) |
−0.701070 | + | 0.713092i | \(0.747294\pi\) | |||||||
\(98\) | 4019.96 | − | 4019.96i | 0.418572 | − | 0.418572i | ||||
\(99\) | − | 13777.5i | − | 1.40572i | ||||||
\(100\) | 3869.24 | 0.386924 | ||||||||
\(101\) | − | 13533.1i | − | 1.32665i | −0.748333 | − | 0.663323i | \(-0.769146\pi\) | ||
0.748333 | − | 0.663323i | \(-0.230854\pi\) | |||||||
\(102\) | − | 5486.85i | − | 0.527379i | ||||||
\(103\) | 13459.1 | − | 13459.1i | 1.26865 | − | 1.26865i | 0.321870 | − | 0.946784i | \(-0.395689\pi\) |
0.946784 | − | 0.321870i | \(-0.104311\pi\) | |||||||
\(104\) | 4613.05i | 0.426502i | ||||||||
\(105\) | 6098.73 | − | 6098.73i | 0.553173 | − | 0.553173i | ||||
\(106\) | 5077.11 | − | 5077.11i | 0.451861 | − | 0.451861i | ||||
\(107\) | 6141.07 | 0.536385 | 0.268193 | − | 0.963365i | \(-0.413574\pi\) | ||||
0.268193 | + | 0.963365i | \(0.413574\pi\) | |||||||
\(108\) | 1005.95 | 0.0862439 | ||||||||
\(109\) | −14823.0 | − | 14823.0i | −1.24762 | − | 1.24762i | −0.956768 | − | 0.290853i | \(-0.906061\pi\) |
−0.290853 | − | 0.956768i | \(-0.593939\pi\) | |||||||
\(110\) | 14321.5i | 1.18360i | ||||||||
\(111\) | −7312.53 | + | 16374.7i | −0.593501 | + | 1.32901i | ||||
\(112\) | 1265.55 | 0.100889 | ||||||||
\(113\) | −10121.6 | + | 10121.6i | −0.792673 | + | 0.792673i | −0.981928 | − | 0.189255i | \(-0.939393\pi\) |
0.189255 | + | 0.981928i | \(0.439393\pi\) | |||||||
\(114\) | − | 11916.6i | − | 0.916942i | ||||||
\(115\) | 16301.4i | 1.23262i | ||||||||
\(116\) | 6649.21 | + | 6649.21i | 0.494145 | + | 0.494145i | ||||
\(117\) | −13060.6 | − | 13060.6i | −0.954091 | − | 0.954091i | ||||
\(118\) | 10930.3 | 0.784998 | ||||||||
\(119\) | 2070.64 | + | 2070.64i | 0.146221 | + | 0.146221i | ||||
\(120\) | −9869.40 | −0.685375 | ||||||||
\(121\) | −8484.56 | −0.579507 | ||||||||
\(122\) | 6528.86i | 0.438649i | ||||||||
\(123\) | −4148.27 | −0.274194 | ||||||||
\(124\) | −1902.86 | − | 1902.86i | −0.123755 | − | 0.123755i | ||||
\(125\) | −3327.85 | + | 3327.85i | −0.212983 | + | 0.212983i | ||||
\(126\) | −3583.05 | + | 3583.05i | −0.225690 | + | 0.225690i | ||||
\(127\) | 12910.8 | 0.800472 | 0.400236 | − | 0.916412i | \(-0.368928\pi\) | ||||
0.400236 | + | 0.916412i | \(0.368928\pi\) | |||||||
\(128\) | −1024.00 | − | 1024.00i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | 28456.0 | − | 28456.0i | 1.70999 | − | 1.70999i | ||||
\(130\) | 13576.3 | + | 13576.3i | 0.803331 | + | 0.803331i | ||||
\(131\) | −3703.95 | + | 3703.95i | −0.215836 | + | 0.215836i | −0.806741 | − | 0.590905i | \(-0.798771\pi\) |
0.590905 | + | 0.806741i | \(0.298771\pi\) | |||||||
\(132\) | − | 15936.5i | − | 0.914631i | ||||||
\(133\) | 4497.11 | + | 4497.11i | 0.254232 | + | 0.254232i | ||||
\(134\) | 13269.4 | + | 13269.4i | 0.738998 | + | 0.738998i | ||||
\(135\) | 2960.53 | − | 2960.53i | 0.162443 | − | 0.162443i | ||||
\(136\) | − | 3350.86i | − | 0.181167i | ||||||
\(137\) | 10380.8 | 0.553083 | 0.276541 | − | 0.961002i | \(-0.410812\pi\) | ||||
0.276541 | + | 0.961002i | \(0.410812\pi\) | |||||||
\(138\) | − | 18139.7i | − | 0.952514i | ||||||
\(139\) | − | 28719.5i | − | 1.48644i | −0.669049 | − | 0.743219i | \(-0.733298\pi\) | ||
0.669049 | − | 0.743219i | \(-0.266702\pi\) | |||||||
\(140\) | 3724.54 | − | 3724.54i | 0.190027 | − | 0.190027i | ||||
\(141\) | 8030.32i | 0.403919i | ||||||||
\(142\) | 19233.6 | − | 19233.6i | 0.953856 | − | 0.953856i | ||||
\(143\) | −21922.2 | + | 21922.2i | −1.07204 | + | 1.07204i | ||||
\(144\) | 5798.34 | 0.279627 | ||||||||
\(145\) | 39137.5 | 1.86147 | ||||||||
\(146\) | −11978.4 | − | 11978.4i | −0.561943 | − | 0.561943i | ||||
\(147\) | 26329.9i | 1.21847i | ||||||||
\(148\) | −4465.81 | + | 10000.1i | −0.203881 | + | 0.456544i | ||||
\(149\) | −11007.7 | −0.495819 | −0.247909 | − | 0.968783i | \(-0.579744\pi\) | ||||
−0.247909 | + | 0.968783i | \(0.579744\pi\) | |||||||
\(150\) | −12671.4 | + | 12671.4i | −0.563171 | + | 0.563171i | ||||
\(151\) | 23264.9i | 1.02034i | 0.860072 | + | 0.510172i | \(0.170418\pi\) | ||||
−0.860072 | + | 0.510172i | \(0.829582\pi\) | |||||||
\(152\) | − | 7277.53i | − | 0.314990i | ||||||
\(153\) | 9487.01 | + | 9487.01i | 0.405272 | + | 0.405272i | ||||
\(154\) | 6014.16 | + | 6014.16i | 0.253591 | + | 0.253591i | ||||
\(155\) | −11200.3 | −0.466194 | ||||||||
\(156\) | −15107.2 | − | 15107.2i | −0.620778 | − | 0.620778i | ||||
\(157\) | −17848.9 | −0.724123 | −0.362062 | − | 0.932154i | \(-0.617927\pi\) | ||||
−0.362062 | + | 0.932154i | \(0.617927\pi\) | |||||||
\(158\) | −30499.6 | −1.22174 | ||||||||
\(159\) | 33254.0i | 1.31538i | ||||||||
\(160\) | −6027.30 | −0.235442 | ||||||||
\(161\) | 6845.59 | + | 6845.59i | 0.264095 | + | 0.264095i | ||||
\(162\) | 11382.7 | − | 11382.7i | 0.433725 | − | 0.433725i | ||||
\(163\) | 26691.5 | − | 26691.5i | 1.00461 | − | 1.00461i | 0.00462291 | − | 0.999989i | \(-0.498528\pi\) |
0.999989 | − | 0.00462291i | \(-0.00147152\pi\) | |||||||
\(164\) | −2533.38 | −0.0941916 | ||||||||
\(165\) | −46901.5 | − | 46901.5i | −1.72274 | − | 1.72274i | ||||
\(166\) | 4717.07 | − | 4717.07i | 0.171181 | − | 0.171181i | ||||
\(167\) | 12387.3 | + | 12387.3i | 0.444163 | + | 0.444163i | 0.893408 | − | 0.449246i | \(-0.148307\pi\) |
−0.449246 | + | 0.893408i | \(0.648307\pi\) | |||||||
\(168\) | −4144.54 | + | 4144.54i | −0.146845 | + | 0.146845i | ||||
\(169\) | 13001.9i | 0.455232i | ||||||||
\(170\) | −9861.64 | − | 9861.64i | −0.341233 | − | 0.341233i | ||||
\(171\) | 20604.3 | + | 20604.3i | 0.704637 | + | 0.704637i | ||||
\(172\) | 17378.3 | − | 17378.3i | 0.587421 | − | 0.587421i | ||||
\(173\) | 31584.6i | 1.05532i | 0.849457 | + | 0.527658i | \(0.176930\pi\) | ||||
−0.849457 | + | 0.527658i | \(0.823070\pi\) | |||||||
\(174\) | −43550.9 | −1.43846 | ||||||||
\(175\) | − | 9563.89i | − | 0.312290i | ||||||
\(176\) | − | 9732.54i | − | 0.314196i | ||||||
\(177\) | −35795.6 | + | 35795.6i | −1.14257 | + | 1.14257i | ||||
\(178\) | 19079.3i | 0.602174i | ||||||||
\(179\) | 33482.1 | − | 33482.1i | 1.04498 | − | 1.04498i | 0.0460373 | − | 0.998940i | \(-0.485341\pi\) |
0.998940 | − | 0.0460373i | \(-0.0146593\pi\) | |||||||
\(180\) | 17064.6 | − | 17064.6i | 0.526686 | − | 0.526686i | ||||
\(181\) | −47551.7 | −1.45147 | −0.725737 | − | 0.687972i | \(-0.758501\pi\) | ||||
−0.725737 | + | 0.687972i | \(0.758501\pi\) | |||||||
\(182\) | 11402.4 | 0.344234 | ||||||||
\(183\) | −21381.3 | − | 21381.3i | −0.638458 | − | 0.638458i | ||||
\(184\) | − | 11078.0i | − | 0.327210i | ||||||
\(185\) | 16287.7 | + | 42573.6i | 0.475899 | + | 1.24393i | ||||
\(186\) | 12463.3 | 0.360254 | ||||||||
\(187\) | 15924.0 | − | 15924.0i | 0.455375 | − | 0.455375i | ||||
\(188\) | 4904.17i | 0.138755i | ||||||||
\(189\) | − | 2486.48i | − | 0.0696084i | ||||||
\(190\) | −21417.9 | − | 21417.9i | −0.593294 | − | 0.593294i | ||||
\(191\) | 4475.00 | + | 4475.00i | 0.122666 | + | 0.122666i | 0.765775 | − | 0.643109i | \(-0.222356\pi\) |
−0.643109 | + | 0.765775i | \(0.722356\pi\) | |||||||
\(192\) | 6706.99 | 0.181939 | ||||||||
\(193\) | 12085.4 | + | 12085.4i | 0.324448 | + | 0.324448i | 0.850470 | − | 0.526023i | \(-0.176317\pi\) |
−0.526023 | + | 0.850470i | \(0.676317\pi\) | |||||||
\(194\) | −452.456 | −0.0120219 | ||||||||
\(195\) | −88921.8 | −2.33851 | ||||||||
\(196\) | 16079.8i | 0.418572i | ||||||||
\(197\) | −43196.6 | −1.11306 | −0.556528 | − | 0.830829i | \(-0.687867\pi\) | ||||
−0.556528 | + | 0.830829i | \(0.687867\pi\) | |||||||
\(198\) | 27555.0 | + | 27555.0i | 0.702861 | + | 0.702861i | ||||
\(199\) | 14458.4 | − | 14458.4i | 0.365101 | − | 0.365101i | −0.500586 | − | 0.865687i | \(-0.666882\pi\) |
0.865687 | + | 0.500586i | \(0.166882\pi\) | |||||||
\(200\) | −7738.48 | + | 7738.48i | −0.193462 | + | 0.193462i | ||||
\(201\) | −86912.1 | −2.15124 | ||||||||
\(202\) | 27066.2 | + | 27066.2i | 0.663323 | + | 0.663323i | ||||
\(203\) | 16435.3 | − | 16435.3i | 0.398829 | − | 0.398829i | ||||
\(204\) | 10973.7 | + | 10973.7i | 0.263690 | + | 0.263690i | ||||
\(205\) | −7455.78 | + | 7455.78i | −0.177413 | + | 0.177413i | ||||
\(206\) | 53836.6i | 1.26865i | ||||||||
\(207\) | 31364.3 | + | 31364.3i | 0.731973 | + | 0.731973i | ||||
\(208\) | −9226.09 | − | 9226.09i | −0.213251 | − | 0.213251i | ||||
\(209\) | 34584.4 | − | 34584.4i | 0.791749 | − | 0.791749i | ||||
\(210\) | 24394.9i | 0.553173i | ||||||||
\(211\) | 38389.4 | 0.862276 | 0.431138 | − | 0.902286i | \(-0.358112\pi\) | ||||
0.431138 | + | 0.902286i | \(0.358112\pi\) | |||||||
\(212\) | 20308.5i | 0.451861i | ||||||||
\(213\) | 125976.i | 2.77669i | ||||||||
\(214\) | −12282.1 | + | 12282.1i | −0.268193 | + | 0.268193i | ||||
\(215\) | − | 102289.i | − | 2.21285i | ||||||
\(216\) | −2011.90 | + | 2011.90i | −0.0431220 | + | 0.0431220i | ||||
\(217\) | −4703.44 | + | 4703.44i | −0.0998841 | + | 0.0998841i | ||||
\(218\) | 59291.9 | 1.24762 | ||||||||
\(219\) | 78455.9 | 1.63583 | ||||||||
\(220\) | −28643.1 | − | 28643.1i | −0.591799 | − | 0.591799i | ||||
\(221\) | − | 30190.7i | − | 0.618143i | ||||||
\(222\) | −18124.4 | − | 47374.5i | −0.367754 | − | 0.961255i | ||||
\(223\) | −6647.07 | −0.133666 | −0.0668329 | − | 0.997764i | \(-0.521289\pi\) | ||||
−0.0668329 | + | 0.997764i | \(0.521289\pi\) | |||||||
\(224\) | −2531.10 | + | 2531.10i | −0.0504444 | + | 0.0504444i | ||||
\(225\) | − | 43818.7i | − | 0.865554i | ||||||
\(226\) | − | 40486.5i | − | 0.792673i | ||||||
\(227\) | −17341.3 | − | 17341.3i | −0.336535 | − | 0.336535i | 0.518527 | − | 0.855061i | \(-0.326481\pi\) |
−0.855061 | + | 0.518527i | \(0.826481\pi\) | |||||||
\(228\) | 23833.2 | + | 23833.2i | 0.458471 | + | 0.458471i | ||||
\(229\) | −74769.8 | −1.42579 | −0.712895 | − | 0.701271i | \(-0.752616\pi\) | ||||
−0.712895 | + | 0.701271i | \(0.752616\pi\) | |||||||
\(230\) | −32602.8 | − | 32602.8i | −0.616311 | − | 0.616311i | ||||
\(231\) | −39391.5 | −0.738208 | ||||||||
\(232\) | −26596.8 | −0.494145 | ||||||||
\(233\) | − | 85523.8i | − | 1.57534i | −0.616096 | − | 0.787671i | \(-0.711287\pi\) | ||
0.616096 | − | 0.787671i | \(-0.288713\pi\) | |||||||
\(234\) | 52242.2 | 0.954091 | ||||||||
\(235\) | 14433.1 | + | 14433.1i | 0.261350 | + | 0.261350i | ||||
\(236\) | −21860.6 | + | 21860.6i | −0.392499 | + | 0.392499i | ||||
\(237\) | 99883.0 | − | 99883.0i | 1.77826 | − | 1.77826i | ||||
\(238\) | −8282.56 | −0.146221 | ||||||||
\(239\) | −14535.0 | − | 14535.0i | −0.254459 | − | 0.254459i | 0.568337 | − | 0.822796i | \(-0.307587\pi\) |
−0.822796 | + | 0.568337i | \(0.807587\pi\) | |||||||
\(240\) | 19738.8 | − | 19738.8i | 0.342687 | − | 0.342687i | ||||
\(241\) | 37780.9 | + | 37780.9i | 0.650486 | + | 0.650486i | 0.953110 | − | 0.302624i | \(-0.0978626\pi\) |
−0.302624 | + | 0.953110i | \(0.597863\pi\) | |||||||
\(242\) | 16969.1 | − | 16969.1i | 0.289753 | − | 0.289753i | ||||
\(243\) | 84739.3i | 1.43507i | ||||||||
\(244\) | −13057.7 | − | 13057.7i | −0.219325 | − | 0.219325i | ||||
\(245\) | 47323.3 | + | 47323.3i | 0.788393 | + | 0.788393i | ||||
\(246\) | 8296.55 | − | 8296.55i | 0.137097 | − | 0.137097i | ||||
\(247\) | − | 65569.5i | − | 1.07475i | ||||||
\(248\) | 7611.44 | 0.123755 | ||||||||
\(249\) | 30895.8i | 0.498312i | ||||||||
\(250\) | − | 13311.4i | − | 0.212983i | ||||||
\(251\) | 40564.8 | − | 40564.8i | 0.643876 | − | 0.643876i | −0.307630 | − | 0.951506i | \(-0.599536\pi\) |
0.951506 | + | 0.307630i | \(0.0995359\pi\) | |||||||
\(252\) | − | 14332.2i | − | 0.225690i | ||||||
\(253\) | 52645.1 | − | 52645.1i | 0.822465 | − | 0.822465i | ||||
\(254\) | −25821.6 | + | 25821.6i | −0.400236 | + | 0.400236i | ||||
\(255\) | 64591.7 | 0.993336 | ||||||||
\(256\) | 4096.00 | 0.0625000 | ||||||||
\(257\) | 15552.2 | + | 15552.2i | 0.235464 | + | 0.235464i | 0.814969 | − | 0.579505i | \(-0.196754\pi\) |
−0.579505 | + | 0.814969i | \(0.696754\pi\) | |||||||
\(258\) | 113824.i | 1.70999i | ||||||||
\(259\) | 24718.1 | + | 11038.5i | 0.368481 | + | 0.164554i | ||||
\(260\) | −54305.1 | −0.803331 | ||||||||
\(261\) | 75301.5 | − | 75301.5i | 1.10541 | − | 1.10541i | ||||
\(262\) | − | 14815.8i | − | 0.215836i | ||||||
\(263\) | 7873.27i | 0.113827i | 0.998379 | + | 0.0569133i | \(0.0181259\pi\) | ||||
−0.998379 | + | 0.0569133i | \(0.981874\pi\) | |||||||
\(264\) | 31873.0 | + | 31873.0i | 0.457315 | + | 0.457315i | ||||
\(265\) | 59768.2 | + | 59768.2i | 0.851096 | + | 0.851096i | ||||
\(266\) | −17988.4 | −0.254232 | ||||||||
\(267\) | −62482.7 | − | 62482.7i | −0.876470 | − | 0.876470i | ||||
\(268\) | −53077.8 | −0.738998 | ||||||||
\(269\) | 49063.4 | 0.678037 | 0.339018 | − | 0.940780i | \(-0.389905\pi\) | ||||
0.339018 | + | 0.940780i | \(0.389905\pi\) | |||||||
\(270\) | 11842.1i | 0.162443i | ||||||||
\(271\) | −21218.5 | −0.288919 | −0.144460 | − | 0.989511i | \(-0.546144\pi\) | ||||
−0.144460 | + | 0.989511i | \(0.546144\pi\) | |||||||
\(272\) | 6701.71 | + | 6701.71i | 0.0905833 | + | 0.0905833i | ||||
\(273\) | −37341.7 | + | 37341.7i | −0.501036 | + | 0.501036i | ||||
\(274\) | −20761.6 | + | 20761.6i | −0.276541 | + | 0.276541i | ||||
\(275\) | −73549.8 | −0.972560 | ||||||||
\(276\) | 36279.4 | + | 36279.4i | 0.476257 | + | 0.476257i | ||||
\(277\) | −48467.9 | + | 48467.9i | −0.631676 | + | 0.631676i | −0.948488 | − | 0.316812i | \(-0.897388\pi\) |
0.316812 | + | 0.948488i | \(0.397388\pi\) | |||||||
\(278\) | 57438.9 | + | 57438.9i | 0.743219 | + | 0.743219i | ||||
\(279\) | −21549.7 | + | 21549.7i | −0.276842 | + | 0.276842i | ||||
\(280\) | 14898.1i | 0.190027i | ||||||||
\(281\) | −4510.08 | − | 4510.08i | −0.0571178 | − | 0.0571178i | 0.677971 | − | 0.735089i | \(-0.262860\pi\) |
−0.735089 | + | 0.677971i | \(0.762860\pi\) | |||||||
\(282\) | −16060.6 | − | 16060.6i | −0.201960 | − | 0.201960i | ||||
\(283\) | −72880.9 | + | 72880.9i | −0.909999 | + | 0.909999i | −0.996272 | − | 0.0862730i | \(-0.972504\pi\) |
0.0862730 | + | 0.996272i | \(0.472504\pi\) | |||||||
\(284\) | 76934.2i | 0.953856i | ||||||||
\(285\) | 140283. | 1.72709 | ||||||||
\(286\) | − | 87688.8i | − | 1.07204i | ||||||
\(287\) | 6261.94i | 0.0760230i | ||||||||
\(288\) | −11596.7 | + | 11596.7i | −0.139813 | + | 0.139813i | ||||
\(289\) | − | 61590.8i | − | 0.737429i | ||||||
\(290\) | −78275.0 | + | 78275.0i | −0.930737 | + | 0.930737i | ||||
\(291\) | 1481.75 | − | 1481.75i | 0.0174980 | − | 0.0174980i | ||||
\(292\) | 47913.5 | 0.561943 | ||||||||
\(293\) | 23239.5 | 0.270702 | 0.135351 | − | 0.990798i | \(-0.456784\pi\) | ||||
0.135351 | + | 0.990798i | \(0.456784\pi\) | |||||||
\(294\) | −52659.8 | − | 52659.8i | −0.609235 | − | 0.609235i | ||||
\(295\) | 128672.i | 1.47857i | ||||||||
\(296\) | −11068.7 | − | 28931.9i | −0.126332 | − | 0.330213i | ||||
\(297\) | −19122.0 | −0.216780 | ||||||||
\(298\) | 22015.3 | − | 22015.3i | 0.247909 | − | 0.247909i | ||||
\(299\) | − | 99811.4i | − | 1.11645i | ||||||
\(300\) | − | 50685.4i | − | 0.563171i | ||||||
\(301\) | −42955.1 | − | 42955.1i | −0.474113 | − | 0.474113i | ||||
\(302\) | −46529.7 | − | 46529.7i | −0.510172 | − | 0.510172i | ||||
\(303\) | −177278. | −1.93094 | ||||||||
\(304\) | 14555.1 | + | 14555.1i | 0.157495 | + | 0.157495i | ||||
\(305\) | −76858.2 | −0.826211 | ||||||||
\(306\) | −37948.1 | −0.405272 | ||||||||
\(307\) | − | 8792.55i | − | 0.0932907i | −0.998912 | − | 0.0466453i | \(-0.985147\pi\) | ||
0.998912 | − | 0.0466453i | \(-0.0148531\pi\) | |||||||
\(308\) | −24056.6 | −0.253591 | ||||||||
\(309\) | −176309. | − | 176309.i | −1.84654 | − | 1.84654i | ||||
\(310\) | 22400.6 | − | 22400.6i | 0.233097 | − | 0.233097i | ||||
\(311\) | 87685.1 | − | 87685.1i | 0.906577 | − | 0.906577i | −0.0894171 | − | 0.995994i | \(-0.528500\pi\) |
0.995994 | + | 0.0894171i | \(0.0285004\pi\) | |||||||
\(312\) | 60429.0 | 0.620778 | ||||||||
\(313\) | 121488. | + | 121488.i | 1.24006 | + | 1.24006i | 0.959974 | + | 0.280091i | \(0.0903646\pi\) |
0.280091 | + | 0.959974i | \(0.409635\pi\) | |||||||
\(314\) | 35697.8 | − | 35697.8i | 0.362062 | − | 0.362062i | ||||
\(315\) | −42179.9 | − | 42179.9i | −0.425094 | − | 0.425094i | ||||
\(316\) | 60999.2 | − | 60999.2i | 0.610872 | − | 0.610872i | ||||
\(317\) | 164919.i | 1.64116i | 0.571532 | + | 0.820580i | \(0.306349\pi\) | ||||
−0.571532 | + | 0.820580i | \(0.693651\pi\) | |||||||
\(318\) | −66508.1 | − | 66508.1i | −0.657688 | − | 0.657688i | ||||
\(319\) | −126394. | − | 126394.i | −1.24207 | − | 1.24207i | ||||
\(320\) | 12054.6 | − | 12054.6i | 0.117721 | − | 0.117721i | ||||
\(321\) | − | 80445.5i | − | 0.780714i | ||||||
\(322\) | −27382.4 | −0.264095 | ||||||||
\(323\) | 47628.8i | 0.456525i | ||||||||
\(324\) | 45530.7i | 0.433725i | ||||||||
\(325\) | −69722.6 | + | 69722.6i | −0.660095 | + | 0.660095i | ||||
\(326\) | 106766.i | 1.00461i | ||||||||
\(327\) | −194175. | + | 194175.i | −1.81592 | + | 1.81592i | ||||
\(328\) | 5066.76 | − | 5066.76i | 0.0470958 | − | 0.0470958i | ||||
\(329\) | 12122.0 | 0.111991 | ||||||||
\(330\) | 187606. | 1.72274 | ||||||||
\(331\) | −125950. | − | 125950.i | −1.14958 | − | 1.14958i | −0.986634 | − | 0.162950i | \(-0.947899\pi\) |
−0.162950 | − | 0.986634i | \(-0.552101\pi\) | |||||||
\(332\) | 18868.3i | 0.171181i | ||||||||
\(333\) | 113250. | + | 50574.8i | 1.02130 | + | 0.456085i | ||||
\(334\) | −49549.0 | −0.444163 | ||||||||
\(335\) | −156209. | + | 156209.i | −1.39193 | + | 1.39193i | ||||
\(336\) | − | 16578.2i | − | 0.146845i | ||||||
\(337\) | − | 7186.65i | − | 0.0632800i | −0.999499 | − | 0.0316400i | \(-0.989927\pi\) | ||
0.999499 | − | 0.0316400i | \(-0.0100730\pi\) | |||||||
\(338\) | −26003.8 | − | 26003.8i | −0.227616 | − | 0.227616i | ||||
\(339\) | 132589. | + | 132589.i | 1.15374 | + | 1.15374i | ||||
\(340\) | 39446.5 | 0.341233 | ||||||||
\(341\) | 36171.2 | + | 36171.2i | 0.311067 | + | 0.311067i | ||||
\(342\) | −82417.2 | −0.704637 | ||||||||
\(343\) | 87223.6 | 0.741389 | ||||||||
\(344\) | 69513.0i | 0.587421i | ||||||||
\(345\) | 213542. | 1.79409 | ||||||||
\(346\) | −63169.2 | − | 63169.2i | −0.527658 | − | 0.527658i | ||||
\(347\) | −43965.3 | + | 43965.3i | −0.365133 | + | 0.365133i | −0.865699 | − | 0.500566i | \(-0.833125\pi\) |
0.500566 | + | 0.865699i | \(0.333125\pi\) | |||||||
\(348\) | 87101.9 | − | 87101.9i | 0.719232 | − | 0.719232i | ||||
\(349\) | −197535. | −1.62178 | −0.810891 | − | 0.585197i | \(-0.801017\pi\) | ||||
−0.810891 | + | 0.585197i | \(0.801017\pi\) | |||||||
\(350\) | 19127.8 | + | 19127.8i | 0.156145 | + | 0.156145i | ||||
\(351\) | −18126.9 | + | 18126.9i | −0.147133 | + | 0.147133i | ||||
\(352\) | 19465.1 | + | 19465.1i | 0.157098 | + | 0.157098i | ||||
\(353\) | 140884. | − | 140884.i | 1.13061 | − | 1.13061i | 0.140536 | − | 0.990076i | \(-0.455117\pi\) |
0.990076 | − | 0.140536i | \(-0.0448826\pi\) | |||||||
\(354\) | − | 143182.i | − | 1.14257i | ||||||
\(355\) | 226419. | + | 226419.i | 1.79662 | + | 1.79662i | ||||
\(356\) | −38158.6 | − | 38158.6i | −0.301087 | − | 0.301087i | ||||
\(357\) | 27124.5 | − | 27124.5i | 0.212827 | − | 0.212827i | ||||
\(358\) | 133928.i | 1.04498i | ||||||||
\(359\) | −36497.2 | −0.283186 | −0.141593 | − | 0.989925i | \(-0.545222\pi\) | ||||
−0.141593 | + | 0.989925i | \(0.545222\pi\) | |||||||
\(360\) | 68258.5i | 0.526686i | ||||||||
\(361\) | − | 26878.6i | − | 0.206249i | ||||||
\(362\) | 95103.5 | − | 95103.5i | 0.725737 | − | 0.725737i | ||||
\(363\) | 111144.i | 0.843478i | ||||||||
\(364\) | −22804.8 | + | 22804.8i | −0.172117 | + | 0.172117i | ||||
\(365\) | 141011. | − | 141011.i | 1.05844 | − | 1.05844i | ||||
\(366\) | 85525.3 | 0.638458 | ||||||||
\(367\) | 91669.0 | 0.680598 | 0.340299 | − | 0.940317i | \(-0.389472\pi\) | ||||
0.340299 | + | 0.940317i | \(0.389472\pi\) | |||||||
\(368\) | 22156.0 | + | 22156.0i | 0.163605 | + | 0.163605i | ||||
\(369\) | 28690.2i | 0.210708i | ||||||||
\(370\) | −117722. | − | 52571.9i | −0.859916 | − | 0.384016i | ||||
\(371\) | 50197.9 | 0.364702 | ||||||||
\(372\) | −24926.7 | + | 24926.7i | −0.180127 | + | 0.180127i | ||||
\(373\) | 83737.2i | 0.601867i | 0.953645 | + | 0.300934i | \(0.0972983\pi\) | ||||
−0.953645 | + | 0.300934i | \(0.902702\pi\) | |||||||
\(374\) | 63696.0i | 0.455375i | ||||||||
\(375\) | 43593.5 | + | 43593.5i | 0.309998 | + | 0.309998i | ||||
\(376\) | −9808.34 | − | 9808.34i | −0.0693777 | − | 0.0693777i | ||||
\(377\) | −239634. | −1.68603 | ||||||||
\(378\) | 4972.96 | + | 4972.96i | 0.0348042 | + | 0.0348042i | ||||
\(379\) | −19315.2 | −0.134469 | −0.0672343 | − | 0.997737i | \(-0.521417\pi\) | ||||
−0.0672343 | + | 0.997737i | \(0.521417\pi\) | |||||||
\(380\) | 85671.7 | 0.593294 | ||||||||
\(381\) | − | 169126.i | − | 1.16509i | ||||||
\(382\) | −17900.0 | −0.122666 | ||||||||
\(383\) | 107304. | + | 107304.i | 0.731505 | + | 0.731505i | 0.970918 | − | 0.239413i | \(-0.0769549\pi\) |
−0.239413 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(384\) | −13414.0 | + | 13414.0i | −0.0909693 | + | 0.0909693i | ||||
\(385\) | −70799.2 | + | 70799.2i | −0.477647 | + | 0.477647i | ||||
\(386\) | −48341.4 | −0.324448 | ||||||||
\(387\) | −196807. | − | 196807.i | −1.31407 | − | 1.31407i | ||||
\(388\) | 904.912 | − | 904.912i | 0.00601094 | − | 0.00601094i | ||||
\(389\) | −45020.2 | − | 45020.2i | −0.297515 | − | 0.297515i | 0.542525 | − | 0.840040i | \(-0.317468\pi\) |
−0.840040 | + | 0.542525i | \(0.817468\pi\) | |||||||
\(390\) | 177844. | − | 177844.i | 1.16925 | − | 1.16925i | ||||
\(391\) | 72501.7i | 0.474236i | ||||||||
\(392\) | −32159.7 | − | 32159.7i | −0.209286 | − | 0.209286i | ||||
\(393\) | 48520.2 | + | 48520.2i | 0.314151 | + | 0.314151i | ||||
\(394\) | 86393.2 | − | 86393.2i | 0.556528 | − | 0.556528i | ||||
\(395\) | − | 359044.i | − | 2.30119i | ||||||
\(396\) | −110220. | −0.702861 | ||||||||
\(397\) | 259119.i | 1.64406i | 0.569441 | + | 0.822032i | \(0.307160\pi\) | ||||
−0.569441 | + | 0.822032i | \(0.692840\pi\) | |||||||
\(398\) | 57833.4i | 0.365101i | ||||||||
\(399\) | 58910.2 | − | 58910.2i | 0.370037 | − | 0.370037i | ||||
\(400\) | − | 30953.9i | − | 0.193462i | ||||||
\(401\) | 193875. | − | 193875.i | 1.20568 | − | 1.20568i | 0.233271 | − | 0.972412i | \(-0.425057\pi\) |
0.972412 | − | 0.233271i | \(-0.0749431\pi\) | |||||||
\(402\) | 173824. | − | 173824.i | 1.07562 | − | 1.07562i | ||||
\(403\) | 68578.0 | 0.422255 | ||||||||
\(404\) | −108265. | −0.663323 | ||||||||
\(405\) | 133998. | + | 133998.i | 0.816934 | + | 0.816934i | ||||
\(406\) | 65741.4i | 0.398829i | ||||||||
\(407\) | 84890.0 | − | 190091.i | 0.512469 | − | 1.14756i | ||||
\(408\) | −43894.8 | −0.263690 | ||||||||
\(409\) | 12139.7 | − | 12139.7i | 0.0725706 | − | 0.0725706i | −0.669890 | − | 0.742460i | \(-0.733659\pi\) |
0.742460 | + | 0.669890i | \(0.233659\pi\) | |||||||
\(410\) | − | 29823.1i | − | 0.177413i | ||||||
\(411\) | − | 135984.i | − | 0.805017i | ||||||
\(412\) | −107673. | − | 107673.i | −0.634327 | − | 0.634327i | ||||
\(413\) | 54034.5 | + | 54034.5i | 0.316790 | + | 0.316790i | ||||
\(414\) | −125457. | −0.731973 | ||||||||
\(415\) | 55529.7 | + | 55529.7i | 0.322425 | + | 0.322425i | ||||
\(416\) | 36904.4 | 0.213251 | ||||||||
\(417\) | −376213. | −2.16352 | ||||||||
\(418\) | 138338.i | 0.791749i | ||||||||
\(419\) | −87917.3 | −0.500779 | −0.250390 | − | 0.968145i | \(-0.580559\pi\) | ||||
−0.250390 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(420\) | −48789.9 | − | 48789.9i | −0.276586 | − | 0.276586i | ||||
\(421\) | 35067.3 | − | 35067.3i | 0.197851 | − | 0.197851i | −0.601227 | − | 0.799078i | \(-0.705321\pi\) |
0.799078 | + | 0.601227i | \(0.205321\pi\) | |||||||
\(422\) | −76778.8 | + | 76778.8i | −0.431138 | + | 0.431138i | ||||
\(423\) | 55539.1 | 0.310398 | ||||||||
\(424\) | −40616.9 | − | 40616.9i | −0.225931 | − | 0.225931i | ||||
\(425\) | 50645.6 | − | 50645.6i | 0.280391 | − | 0.280391i | ||||
\(426\) | −251951. | − | 251951.i | −1.38835 | − | 1.38835i | ||||
\(427\) | −32275.7 | + | 32275.7i | −0.177019 | + | 0.177019i | ||||
\(428\) | − | 49128.6i | − | 0.268193i | ||||||
\(429\) | 287172. | + | 287172.i | 1.56037 | + | 1.56037i | ||||
\(430\) | 204578. | + | 204578.i | 1.10643 | + | 1.10643i | ||||
\(431\) | −98575.3 | + | 98575.3i | −0.530656 | + | 0.530656i | −0.920768 | − | 0.390111i | \(-0.872437\pi\) |
0.390111 | + | 0.920768i | \(0.372437\pi\) | |||||||
\(432\) | − | 8047.59i | − | 0.0431220i | ||||||
\(433\) | −66346.3 | −0.353867 | −0.176934 | − | 0.984223i | \(-0.556618\pi\) | ||||
−0.176934 | + | 0.984223i | \(0.556618\pi\) | |||||||
\(434\) | − | 18813.8i | − | 0.0998841i | ||||||
\(435\) | − | 512685.i | − | 2.70939i | ||||||
\(436\) | −118584. | + | 118584.i | −0.623810 | + | 0.623810i | ||||
\(437\) | 157462.i | 0.824543i | ||||||||
\(438\) | −156912. | + | 156912.i | −0.817914 | + | 0.817914i | ||||
\(439\) | −194833. | + | 194833.i | −1.01096 | + | 1.01096i | −0.0110175 | + | 0.999939i | \(0.503507\pi\) |
−0.999939 | + | 0.0110175i | \(0.996493\pi\) | |||||||
\(440\) | 114572. | 0.591799 | ||||||||
\(441\) | 182102. | 0.936351 | ||||||||
\(442\) | 60381.5 | + | 60381.5i | 0.309072 | + | 0.309072i | ||||
\(443\) | − | 282981.i | − | 1.44195i | −0.692962 | − | 0.720974i | \(-0.743694\pi\) | ||
0.692962 | − | 0.720974i | \(-0.256306\pi\) | |||||||
\(444\) | 130998. | + | 58500.2i | 0.664504 | + | 0.296751i | ||||
\(445\) | −224603. | −1.13422 | ||||||||
\(446\) | 13294.1 | − | 13294.1i | 0.0668329 | − | 0.0668329i | ||||
\(447\) | 144196.i | 0.721669i | ||||||||
\(448\) | − | 10124.4i | − | 0.0504444i | ||||||
\(449\) | 175892. | + | 175892.i | 0.872475 | + | 0.872475i | 0.992742 | − | 0.120266i | \(-0.0383748\pi\) |
−0.120266 | + | 0.992742i | \(0.538375\pi\) | |||||||
\(450\) | 87637.3 | + | 87637.3i | 0.432777 | + | 0.432777i | ||||
\(451\) | 48156.6 | 0.236757 | ||||||||
\(452\) | 80973.1 | + | 80973.1i | 0.396336 | + | 0.396336i | ||||
\(453\) | 304760. | 1.48512 | ||||||||
\(454\) | 69365.2 | 0.336535 | ||||||||
\(455\) | 134230.i | 0.648376i | ||||||||
\(456\) | −95332.6 | −0.458471 | ||||||||
\(457\) | −116094. | − | 116094.i | −0.555873 | − | 0.555873i | 0.372257 | − | 0.928130i | \(-0.378584\pi\) |
−0.928130 | + | 0.372257i | \(0.878584\pi\) | |||||||
\(458\) | 149540. | − | 149540.i | 0.712895 | − | 0.712895i | ||||
\(459\) | 13167.2 | − | 13167.2i | 0.0624981 | − | 0.0624981i | ||||
\(460\) | 130411. | 0.616311 | ||||||||
\(461\) | −166216. | − | 166216.i | −0.782116 | − | 0.782116i | 0.198072 | − | 0.980188i | \(-0.436532\pi\) |
−0.980188 | + | 0.198072i | \(0.936532\pi\) | |||||||
\(462\) | 78783.0 | − | 78783.0i | 0.369104 | − | 0.369104i | ||||
\(463\) | −232696. | − | 232696.i | −1.08549 | − | 1.08549i | −0.995986 | − | 0.0895072i | \(-0.971471\pi\) |
−0.0895072 | − | 0.995986i | \(-0.528529\pi\) | |||||||
\(464\) | 53193.7 | − | 53193.7i | 0.247072 | − | 0.247072i | ||||
\(465\) | 146719.i | 0.678549i | ||||||||
\(466\) | 171048. | + | 171048.i | 0.787671 | + | 0.787671i | ||||
\(467\) | 13082.1 | + | 13082.1i | 0.0599851 | + | 0.0599851i | 0.736463 | − | 0.676478i | \(-0.236495\pi\) |
−0.676478 | + | 0.736463i | \(0.736495\pi\) | |||||||
\(468\) | −104484. | + | 104484.i | −0.477045 | + | 0.477045i | ||||
\(469\) | 131196.i | 0.596453i | ||||||||
\(470\) | −57732.3 | −0.261350 | ||||||||
\(471\) | 233813.i | 1.05397i | ||||||||
\(472\) | − | 87442.5i | − | 0.392499i | ||||||
\(473\) | −330341. | + | 330341.i | −1.47652 | + | 1.47652i | ||||
\(474\) | 399532.i | 1.77826i | ||||||||
\(475\) | 109994. | − | 109994.i | 0.487509 | − | 0.487509i | ||||
\(476\) | 16565.1 | − | 16565.1i | 0.0731107 | − | 0.0731107i | ||||
\(477\) | 229991. | 1.01082 | ||||||||
\(478\) | 58139.9 | 0.254459 | ||||||||
\(479\) | −25172.8 | − | 25172.8i | −0.109714 | − | 0.109714i | 0.650119 | − | 0.759832i | \(-0.274719\pi\) |
−0.759832 | + | 0.650119i | \(0.774719\pi\) | |||||||
\(480\) | 78955.2i | 0.342687i | ||||||||
\(481\) | −99727.1 | − | 260672.i | −0.431045 | − | 1.12669i | ||||
\(482\) | −151124. | −0.650486 | ||||||||
\(483\) | 89674.4 | − | 89674.4i | 0.384392 | − | 0.384392i | ||||
\(484\) | 67876.5i | 0.289753i | ||||||||
\(485\) | − | 5326.35i | − | 0.0226436i | ||||||
\(486\) | −169479. | − | 169479.i | −0.717534 | − | 0.717534i | ||||
\(487\) | −264887. | − | 264887.i | −1.11687 | − | 1.11687i | −0.992198 | − | 0.124672i | \(-0.960212\pi\) |
−0.124672 | − | 0.992198i | \(-0.539788\pi\) | |||||||
\(488\) | 52230.9 | 0.219325 | ||||||||
\(489\) | −349648. | − | 349648.i | −1.46222 | − | 1.46222i | ||||
\(490\) | −189293. | −0.788393 | ||||||||
\(491\) | 130782. | 0.542483 | 0.271241 | − | 0.962511i | \(-0.412566\pi\) | ||||
0.271241 | + | 0.962511i | \(0.412566\pi\) | |||||||
\(492\) | 33186.2i | 0.137097i | ||||||||
\(493\) | 174067. | 0.716180 | ||||||||
\(494\) | 131139. | + | 131139.i | 0.537376 | + | 0.537376i | ||||
\(495\) | −324379. | + | 324379.i | −1.32386 | + | 1.32386i | ||||
\(496\) | −15222.9 | + | 15222.9i | −0.0618776 | + | 0.0618776i | ||||
\(497\) | 190164. | 0.769867 | ||||||||
\(498\) | −61791.6 | − | 61791.6i | −0.249156 | − | 0.249156i | ||||
\(499\) | −63580.0 | + | 63580.0i | −0.255340 | + | 0.255340i | −0.823156 | − | 0.567816i | \(-0.807789\pi\) |
0.567816 | + | 0.823156i | \(0.307789\pi\) | |||||||
\(500\) | 26622.8 | + | 26622.8i | 0.106491 | + | 0.106491i | ||||
\(501\) | 162268. | − | 162268.i | 0.646483 | − | 0.646483i | ||||
\(502\) | 162259.i | 0.643876i | ||||||||
\(503\) | 320918. | + | 320918.i | 1.26841 | + | 1.26841i | 0.946911 | + | 0.321497i | \(0.104186\pi\) |
0.321497 | + | 0.946911i | \(0.395814\pi\) | |||||||
\(504\) | 28664.4 | + | 28664.4i | 0.112845 | + | 0.112845i | ||||
\(505\) | −318626. | + | 318626.i | −1.24939 | + | 1.24939i | ||||
\(506\) | 210581.i | 0.822465i | ||||||||
\(507\) | 170319. | 0.662594 | ||||||||
\(508\) | − | 103287.i | − | 0.400236i | ||||||
\(509\) | − | 293144.i | − | 1.13148i | −0.824585 | − | 0.565738i | \(-0.808591\pi\) | ||
0.824585 | − | 0.565738i | \(-0.191409\pi\) | |||||||
\(510\) | −129183. | + | 129183.i | −0.496668 | + | 0.496668i | ||||
\(511\) | − | 118432.i | − | 0.453550i | ||||||
\(512\) | −8192.00 | + | 8192.00i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 28597.0 | − | 28597.0i | 0.108664 | − | 0.108664i | ||||
\(514\) | −62208.8 | −0.235464 | ||||||||
\(515\) | −633769. | −2.38955 | ||||||||
\(516\) | −227648. | − | 227648.i | −0.854996 | − | 0.854996i | ||||
\(517\) | − | 93222.7i | − | 0.348771i | ||||||
\(518\) | −71513.2 | + | 27359.3i | −0.266518 | + | 0.101964i | ||||
\(519\) | 413745. | 1.53602 | ||||||||
\(520\) | 108610. | − | 108610.i | 0.401665 | − | 0.401665i | ||||
\(521\) | − | 215318.i | − | 0.793242i | −0.917982 | − | 0.396621i | \(-0.870183\pi\) | ||
0.917982 | − | 0.396621i | \(-0.129817\pi\) | |||||||
\(522\) | 301206.i | 1.10541i | ||||||||
\(523\) | −308216. | − | 308216.i | −1.12681 | − | 1.12681i | −0.990692 | − | 0.136121i | \(-0.956536\pi\) |
−0.136121 | − | 0.990692i | \(-0.543464\pi\) | |||||||
\(524\) | 29631.6 | + | 29631.6i | 0.107918 | + | 0.107918i | ||||
\(525\) | −125283. | −0.454541 | ||||||||
\(526\) | −15746.5 | − | 15746.5i | −0.0569133 | − | 0.0569133i | ||||
\(527\) | −49814.1 | −0.179362 | ||||||||
\(528\) | −127492. | −0.457315 | ||||||||
\(529\) | − | 40148.5i | − | 0.143469i | ||||||
\(530\) | −239073. | −0.851096 | ||||||||
\(531\) | 247569. | + | 247569.i | 0.878025 | + | 0.878025i | ||||
\(532\) | 35976.8 | − | 35976.8i | 0.127116 | − | 0.127116i | ||||
\(533\) | 45650.7 | − | 45650.7i | 0.160692 | − | 0.160692i | ||||
\(534\) | 249931. | 0.876470 | ||||||||
\(535\) | −144586. | − | 144586.i | −0.505150 | − | 0.505150i | ||||
\(536\) | 106156. | − | 106156.i | 0.369499 | − | 0.369499i | ||||
\(537\) | −438602. | − | 438602.i | −1.52097 | − | 1.52097i | ||||
\(538\) | −98126.8 | + | 98126.8i | −0.339018 | + | 0.339018i | ||||
\(539\) | − | 305660.i | − | 1.05211i | ||||||
\(540\) | −23684.2 | − | 23684.2i | −0.0812216 | − | 0.0812216i | ||||
\(541\) | 161345. | + | 161345.i | 0.551265 | + | 0.551265i | 0.926806 | − | 0.375541i | \(-0.122543\pi\) |
−0.375541 | + | 0.926806i | \(0.622543\pi\) | |||||||
\(542\) | 42437.1 | − | 42437.1i | 0.144460 | − | 0.144460i | ||||
\(543\) | 622908.i | 2.11263i | ||||||||
\(544\) | −26806.9 | −0.0905833 | ||||||||
\(545\) | 697989.i | 2.34993i | ||||||||
\(546\) | − | 149367.i | − | 0.501036i | ||||||
\(547\) | 250164. | − | 250164.i | 0.836083 | − | 0.836083i | −0.152258 | − | 0.988341i | \(-0.548654\pi\) |
0.988341 | + | 0.152258i | \(0.0486544\pi\) | |||||||
\(548\) | − | 83046.5i | − | 0.276541i | ||||||
\(549\) | −147877. | + | 147877.i | −0.490632 | + | 0.490632i | ||||
\(550\) | 147100. | − | 147100.i | 0.486280 | − | 0.486280i | ||||
\(551\) | 378046. | 1.24521 | ||||||||
\(552\) | −145117. | −0.476257 | ||||||||
\(553\) | −150776. | − | 150776.i | −0.493041 | − | 0.493041i | ||||
\(554\) | − | 193872.i | − | 0.631676i | ||||||
\(555\) | 557696. | − | 213361.i | 1.81055 | − | 0.692676i | ||||
\(556\) | −229756. | −0.743219 | ||||||||
\(557\) | 191922. | − | 191922.i | 0.618606 | − | 0.618606i | −0.326567 | − | 0.945174i | \(-0.605892\pi\) |
0.945174 | + | 0.326567i | \(0.105892\pi\) | |||||||
\(558\) | − | 86198.6i | − | 0.276842i | ||||||
\(559\) | 626302.i | 2.00429i | ||||||||
\(560\) | −29796.3 | − | 29796.3i | −0.0950137 | − | 0.0950137i | ||||
\(561\) | −208598. | − | 208598.i | −0.662802 | − | 0.662802i | ||||
\(562\) | 18040.3 | 0.0571178 | ||||||||
\(563\) | −12868.7 | − | 12868.7i | −0.0405992 | − | 0.0405992i | 0.686516 | − | 0.727115i | \(-0.259139\pi\) |
−0.727115 | + | 0.686516i | \(0.759139\pi\) | |||||||
\(564\) | 64242.6 | 0.201960 | ||||||||
\(565\) | 476611. | 1.49302 | ||||||||
\(566\) | − | 291523.i | − | 0.909999i | ||||||
\(567\) | 112542. | 0.350064 | ||||||||
\(568\) | −153868. | − | 153868.i | −0.476928 | − | 0.476928i | ||||
\(569\) | −196332. | + | 196332.i | −0.606411 | + | 0.606411i | −0.942006 | − | 0.335595i | \(-0.891063\pi\) |
0.335595 | + | 0.942006i | \(0.391063\pi\) | |||||||
\(570\) | −280566. | + | 280566.i | −0.863545 | + | 0.863545i | ||||
\(571\) | 30220.9 | 0.0926906 | 0.0463453 | − | 0.998925i | \(-0.485243\pi\) | ||||
0.0463453 | + | 0.998925i | \(0.485243\pi\) | |||||||
\(572\) | 175378. | + | 175378.i | 0.536021 | + | 0.536021i | ||||
\(573\) | 58620.6 | − | 58620.6i | 0.178542 | − | 0.178542i | ||||
\(574\) | −12523.9 | − | 12523.9i | −0.0380115 | − | 0.0380115i | ||||
\(575\) | 167436. | − | 167436.i | 0.506421 | − | 0.506421i | ||||
\(576\) | − | 46386.7i | − | 0.139813i | ||||||
\(577\) | 96144.6 | + | 96144.6i | 0.288784 | + | 0.288784i | 0.836599 | − | 0.547815i | \(-0.184540\pi\) |
−0.547815 | + | 0.836599i | \(0.684540\pi\) | |||||||
\(578\) | 123182. | + | 123182.i | 0.368715 | + | 0.368715i | ||||
\(579\) | 158313. | − | 158313.i | 0.472237 | − | 0.472237i | ||||
\(580\) | − | 313100.i | − | 0.930737i | ||||||
\(581\) | 46638.1 | 0.138162 | ||||||||
\(582\) | 5926.98i | 0.0174980i | ||||||||
\(583\) | − | 386041.i | − | 1.13578i | ||||||
\(584\) | −95827.1 | + | 95827.1i | −0.280972 | + | 0.280972i | ||||
\(585\) | 614999.i | 1.79706i | ||||||||
\(586\) | −46479.1 | + | 46479.1i | −0.135351 | + | 0.135351i | ||||
\(587\) | 198548. | − | 198548.i | 0.576222 | − | 0.576222i | −0.357638 | − | 0.933860i | \(-0.616418\pi\) |
0.933860 | + | 0.357638i | \(0.116418\pi\) | |||||||
\(588\) | 210639. | 0.609235 | ||||||||
\(589\) | −108188. | −0.311853 | ||||||||
\(590\) | −257345. | − | 257345.i | −0.739284 | − | 0.739284i | ||||
\(591\) | 565858.i | 1.62006i | ||||||||
\(592\) | 80001.1 | + | 35726.5i | 0.228272 | + | 0.101940i | ||||
\(593\) | 118739. | 0.337664 | 0.168832 | − | 0.985645i | \(-0.446000\pi\) | ||||
0.168832 | + | 0.985645i | \(0.446000\pi\) | |||||||
\(594\) | 38243.9 | − | 38243.9i | 0.108390 | − | 0.108390i | ||||
\(595\) | − | 97503.0i | − | 0.275413i | ||||||
\(596\) | 88061.4i | 0.247909i | ||||||||
\(597\) | −189398. | − | 189398.i | −0.531407 | − | 0.531407i | ||||
\(598\) | 199623. | + | 199623.i | 0.558223 | + | 0.558223i | ||||
\(599\) | −134637. | −0.375240 | −0.187620 | − | 0.982242i | \(-0.560077\pi\) | ||||
−0.187620 | + | 0.982242i | \(0.560077\pi\) | |||||||
\(600\) | 101371. | + | 101371.i | 0.281586 | + | 0.281586i | ||||
\(601\) | 123225. | 0.341154 | 0.170577 | − | 0.985344i | \(-0.445437\pi\) | ||||
0.170577 | + | 0.985344i | \(0.445437\pi\) | |||||||
\(602\) | 171821. | 0.474113 | ||||||||
\(603\) | 601100.i | 1.65315i | ||||||||
\(604\) | 186119. | 0.510172 | ||||||||
\(605\) | 199762. | + | 199762.i | 0.545760 | + | 0.545760i | ||||
\(606\) | 354556. | − | 354556.i | 0.965472 | − | 0.965472i | ||||
\(607\) | 758.659 | − | 758.659i | 0.00205906 | − | 0.00205906i | −0.706077 | − | 0.708136i | \(-0.749537\pi\) |
0.708136 | + | 0.706077i | \(0.249537\pi\) | |||||||
\(608\) | −58220.3 | −0.157495 | ||||||||
\(609\) | −215296. | − | 215296.i | −0.580499 | − | 0.580499i | ||||
\(610\) | 153716. | − | 153716.i | 0.413105 | − | 0.413105i | ||||
\(611\) | −88371.7 | − | 88371.7i | −0.236718 | − | 0.236718i | ||||
\(612\) | 75896.1 | − | 75896.1i | 0.202636 | − | 0.202636i | ||||
\(613\) | − | 374042.i | − | 0.995404i | −0.867348 | − | 0.497702i | \(-0.834177\pi\) | ||
0.867348 | − | 0.497702i | \(-0.165823\pi\) | |||||||
\(614\) | 17585.1 | + | 17585.1i | 0.0466453 | + | 0.0466453i | ||||
\(615\) | 97667.6 | + | 97667.6i | 0.258226 | + | 0.258226i | ||||
\(616\) | 48113.3 | − | 48113.3i | 0.126795 | − | 0.126795i | ||||
\(617\) | 300323.i | 0.788894i | 0.918919 | + | 0.394447i | \(0.129064\pi\) | ||||
−0.918919 | + | 0.394447i | \(0.870936\pi\) | |||||||
\(618\) | 705237. | 1.84654 | ||||||||
\(619\) | 62524.1i | 0.163180i | 0.996666 | + | 0.0815898i | \(0.0259997\pi\) | ||||
−0.996666 | + | 0.0815898i | \(0.974000\pi\) | |||||||
\(620\) | 89602.5i | 0.233097i | ||||||||
\(621\) | 43531.0 | − | 43531.0i | 0.112880 | − | 0.112880i | ||||
\(622\) | 350740.i | 0.906577i | ||||||||
\(623\) | −94319.4 | + | 94319.4i | −0.243011 | + | 0.243011i | ||||
\(624\) | −120858. | + | 120858.i | −0.310389 | + | 0.310389i | ||||
\(625\) | 458987. | 1.17501 | ||||||||
\(626\) | −485951. | −1.24006 | ||||||||
\(627\) | −453041. | − | 453041.i | −1.15240 | − | 1.15240i | ||||
\(628\) | 142791.i | 0.362062i | ||||||||
\(629\) | 72440.5 | + | 189349.i | 0.183096 | + | 0.478588i | ||||
\(630\) | 168720. | 0.425094 | ||||||||
\(631\) | 155309. | − | 155309.i | 0.390065 | − | 0.390065i | −0.484645 | − | 0.874711i | \(-0.661051\pi\) |
0.874711 | + | 0.484645i | \(0.161051\pi\) | |||||||
\(632\) | 243997.i | 0.610872i | ||||||||
\(633\) | − | 502885.i | − | 1.25505i | ||||||
\(634\) | −329837. | − | 329837.i | −0.820580 | − | 0.820580i | ||||
\(635\) | −303974. | − | 303974.i | −0.753858 | − | 0.753858i | ||||
\(636\) | 266032. | 0.657688 | ||||||||
\(637\) | −289754. | − | 289754.i | −0.714087 | − | 0.714087i | ||||
\(638\) | 505576. | 1.24207 | ||||||||
\(639\) | 871271. | 2.13379 | ||||||||
\(640\) | 48218.4i | 0.117721i | ||||||||
\(641\) | −602346. | −1.46599 | −0.732993 | − | 0.680236i | \(-0.761877\pi\) | ||||
−0.732993 | + | 0.680236i | \(0.761877\pi\) | |||||||
\(642\) | 160891. | + | 160891.i | 0.390357 | + | 0.390357i | ||||
\(643\) | −203681. | + | 203681.i | −0.492640 | + | 0.492640i | −0.909137 | − | 0.416497i | \(-0.863258\pi\) |
0.416497 | + | 0.909137i | \(0.363258\pi\) | |||||||
\(644\) | 54764.7 | − | 54764.7i | 0.132047 | − | 0.132047i | ||||
\(645\) | −1.33994e6 | −3.22083 | ||||||||
\(646\) | −95257.7 | − | 95257.7i | −0.228263 | − | 0.228263i | ||||
\(647\) | 108538. | − | 108538.i | 0.259282 | − | 0.259282i | −0.565480 | − | 0.824762i | \(-0.691309\pi\) |
0.824762 | + | 0.565480i | \(0.191309\pi\) | |||||||
\(648\) | −91061.3 | − | 91061.3i | −0.216862 | − | 0.216862i | ||||
\(649\) | 415545. | − | 415545.i | 0.986573 | − | 0.986573i | ||||
\(650\) | − | 278890.i | − | 0.660095i | ||||||
\(651\) | 61613.1 | + | 61613.1i | 0.145382 | + | 0.145382i | ||||
\(652\) | −213532. | − | 213532.i | −0.502306 | − | 0.502306i | ||||
\(653\) | −329684. | + | 329684.i | −0.773165 | + | 0.773165i | −0.978658 | − | 0.205494i | \(-0.934120\pi\) |
0.205494 | + | 0.978658i | \(0.434120\pi\) | |||||||
\(654\) | − | 776700.i | − | 1.81592i | ||||||
\(655\) | 174413. | 0.406533 | ||||||||
\(656\) | 20267.0i | 0.0470958i | ||||||||
\(657\) | − | 542615.i | − | 1.25708i | ||||||
\(658\) | −24244.0 | + | 24244.0i | −0.0559954 | + | 0.0559954i | ||||
\(659\) | 685736.i | 1.57901i | 0.613741 | + | 0.789507i | \(0.289664\pi\) | ||||
−0.613741 | + | 0.789507i | \(0.710336\pi\) | |||||||
\(660\) | −375212. | + | 375212.i | −0.861368 | + | 0.861368i | ||||
\(661\) | −487186. | + | 487186.i | −1.11504 | + | 1.11504i | −0.122585 | + | 0.992458i | \(0.539118\pi\) |
−0.992458 | + | 0.122585i | \(0.960882\pi\) | |||||||
\(662\) | 503798. | 1.14958 | ||||||||
\(663\) | −395486. | −0.899713 | ||||||||
\(664\) | −37736.6 | − | 37736.6i | −0.0855906 | − | 0.0855906i | ||||
\(665\) | − | 211761.i | − | 0.478854i | ||||||
\(666\) | −327650. | + | 125351.i | −0.738690 | + | 0.282605i | ||||
\(667\) | 575469. | 1.29351 | ||||||||
\(668\) | 99098.0 | − | 99098.0i | 0.222081 | − | 0.222081i | ||||
\(669\) | 87073.8i | 0.194552i | ||||||||
\(670\) | − | 624836.i | − | 1.39193i | ||||||
\(671\) | 248212. | + | 248212.i | 0.551288 | + | 0.551288i | ||||
\(672\) | 33156.3 | + | 33156.3i | 0.0734223 | + | 0.0734223i | ||||
\(673\) | 644106. | 1.42209 | 0.711045 | − | 0.703146i | \(-0.248222\pi\) | ||||
0.711045 | + | 0.703146i | \(0.248222\pi\) | |||||||
\(674\) | 14373.3 | + | 14373.3i | 0.0316400 | + | 0.0316400i | ||||
\(675\) | −60816.5 | −0.133479 | ||||||||
\(676\) | 104015. | 0.227616 | ||||||||
\(677\) | − | 380512.i | − | 0.830215i | −0.909772 | − | 0.415107i | \(-0.863744\pi\) | ||
0.909772 | − | 0.415107i | \(-0.136256\pi\) | |||||||
\(678\) | −530357. | −1.15374 | ||||||||
\(679\) | −2236.74 | − | 2236.74i | −0.00485149 | − | 0.00485149i | ||||
\(680\) | −78893.1 | + | 78893.1i | −0.170617 | + | 0.170617i | ||||
\(681\) | −227164. | + | 227164.i | −0.489829 | + | 0.489829i | ||||
\(682\) | −144685. | −0.311067 | ||||||||
\(683\) | 290940. | + | 290940.i | 0.623680 | + | 0.623680i | 0.946470 | − | 0.322791i | \(-0.104621\pi\) |
−0.322791 | + | 0.946470i | \(0.604621\pi\) | |||||||
\(684\) | 164834. | − | 164834.i | 0.352319 | − | 0.352319i | ||||
\(685\) | −244407. | − | 244407.i | −0.520875 | − | 0.520875i | ||||
\(686\) | −174447. | + | 174447.i | −0.370694 | + | 0.370694i | ||||
\(687\) | 979453.i | 2.07525i | ||||||||
\(688\) | −139026. | − | 139026.i | −0.293710 | − | 0.293710i | ||||
\(689\) | −365952. | − | 365952.i | −0.770879 | − | 0.770879i | ||||
\(690\) | −427084. | + | 427084.i | −0.897046 | + | 0.897046i | ||||
\(691\) | 676751.i | 1.41734i | 0.705542 | + | 0.708668i | \(0.250704\pi\) | ||||
−0.705542 | + | 0.708668i | \(0.749296\pi\) | |||||||
\(692\) | 252677. | 0.527658 | ||||||||
\(693\) | 272439.i | 0.567286i | ||||||||
\(694\) | − | 175861.i | − | 0.365133i | ||||||
\(695\) | −676175. | + | 676175.i | −1.39988 | + | 1.39988i | ||||
\(696\) | 348407.i | 0.719232i | ||||||||
\(697\) | −33160.1 | + | 33160.1i | −0.0682575 | + | 0.0682575i | ||||
\(698\) | 395069. | − | 395069.i | 0.810891 | − | 0.810891i | ||||
\(699\) | −1.12033e6 | −2.29293 | ||||||||
\(700\) | −76511.1 | −0.156145 | ||||||||
\(701\) | 358626. | + | 358626.i | 0.729802 | + | 0.729802i | 0.970580 | − | 0.240778i | \(-0.0774026\pi\) |
−0.240778 | + | 0.970580i | \(0.577403\pi\) | |||||||
\(702\) | − | 72507.7i | − | 0.147133i | ||||||
\(703\) | 157329. | + | 411236.i | 0.318346 | + | 0.832110i | ||||
\(704\) | −77860.3 | −0.157098 | ||||||||
\(705\) | 189067. | − | 189067.i | 0.380398 | − | 0.380398i | ||||
\(706\) | 563538.i | 1.13061i | ||||||||
\(707\) | 267606.i | 0.535375i | ||||||||
\(708\) | 286365. | + | 286365.i | 0.571286 | + | 0.571286i | ||||
\(709\) | 395349. | + | 395349.i | 0.786481 | + | 0.786481i | 0.980916 | − | 0.194434i | \(-0.0622871\pi\) |
−0.194434 | + | 0.980916i | \(0.562287\pi\) | |||||||
\(710\) | −905676. | −1.79662 | ||||||||
\(711\) | −690809. | − | 690809.i | −1.36653 | − | 1.36653i | ||||
\(712\) | 152634. | 0.301087 | ||||||||
\(713\) | −164687. | −0.323951 | ||||||||
\(714\) | 108498.i | 0.212827i | ||||||||
\(715\) | 1.03228e6 | 2.01923 | ||||||||
\(716\) | −267857. | − | 267857.i | −0.522489 | − | 0.522489i | ||||
\(717\) | −190402. | + | 190402.i | −0.370368 | + | 0.370368i | ||||
\(718\) | 72994.5 | − | 72994.5i | 0.141593 | − | 0.141593i | ||||
\(719\) | −623995. | −1.20705 | −0.603523 | − | 0.797346i | \(-0.706237\pi\) | ||||
−0.603523 | + | 0.797346i | \(0.706237\pi\) | |||||||
\(720\) | −136517. | − | 136517.i | −0.263343 | − | 0.263343i | ||||
\(721\) | −266144. | + | 266144.i | −0.511972 | + | 0.511972i | ||||
\(722\) | 53757.3 | + | 53757.3i | 0.103125 | + | 0.103125i | ||||
\(723\) | 494914. | − | 494914.i | 0.946788 | − | 0.946788i | ||||
\(724\) | 380414.i | 0.725737i | ||||||||
\(725\) | −401990. | − | 401990.i | −0.764785 | − | 0.764785i | ||||
\(726\) | −222288. | − | 222288.i | −0.421739 | − | 0.421739i | ||||
\(727\) | −13044.1 | + | 13044.1i | −0.0246800 | + | 0.0246800i | −0.719339 | − | 0.694659i | \(-0.755555\pi\) |
0.694659 | + | 0.719339i | \(0.255555\pi\) | |||||||
\(728\) | − | 91219.3i | − | 0.172117i | ||||||
\(729\) | 649052. | 1.22131 | ||||||||
\(730\) | 564042.i | 1.05844i | ||||||||
\(731\) | − | 454938.i | − | 0.851368i | ||||||
\(732\) | −171051. | + | 171051.i | −0.319229 | + | 0.319229i | ||||
\(733\) | − | 324175.i | − | 0.603354i | −0.953410 | − | 0.301677i | \(-0.902454\pi\) | ||
0.953410 | − | 0.301677i | \(-0.0975464\pi\) | |||||||
\(734\) | −183338. | + | 183338.i | −0.340299 | + | 0.340299i | ||||
\(735\) | 619916. | − | 619916.i | 1.14751 | − | 1.14751i | ||||
\(736\) | −88624.2 | −0.163605 | ||||||||
\(737\) | 1.00895e6 | 1.85752 | ||||||||
\(738\) | −57380.4 | − | 57380.4i | −0.105354 | − | 0.105354i | ||||
\(739\) | 412435.i | 0.755207i | 0.925967 | + | 0.377604i | \(0.123252\pi\) | ||||
−0.925967 | + | 0.377604i | \(0.876748\pi\) | |||||||
\(740\) | 340589. | − | 130301.i | 0.621966 | − | 0.237950i | ||||
\(741\) | −858933. | −1.56431 | ||||||||
\(742\) | −100396. | + | 100396.i | −0.182351 | + | 0.182351i | ||||
\(743\) | 65043.9i | 0.117823i | 0.998263 | + | 0.0589114i | \(0.0187629\pi\) | ||||
−0.998263 | + | 0.0589114i | \(0.981237\pi\) | |||||||
\(744\) | − | 99706.7i | − | 0.180127i | ||||||
\(745\) | 259166. | + | 259166.i | 0.466945 | + | 0.466945i | ||||
\(746\) | −167474. | − | 167474.i | −0.300934 | − | 0.300934i | ||||
\(747\) | 213681. | 0.382935 | ||||||||
\(748\) | −127392. | − | 127392.i | −0.227687 | − | 0.227687i | ||||
\(749\) | −121435. | −0.216461 | ||||||||
\(750\) | −174374. | −0.309998 | ||||||||
\(751\) | 53025.2i | 0.0940161i | 0.998895 | + | 0.0470081i | \(0.0149687\pi\) | ||||
−0.998895 | + | 0.0470081i | \(0.985031\pi\) | |||||||
\(752\) | 39233.4 | 0.0693777 | ||||||||
\(753\) | −531382. | − | 531382.i | −0.937167 | − | 0.937167i | ||||
\(754\) | 479267. | − | 479267.i | 0.843015 | − | 0.843015i | ||||
\(755\) | 547752. | − | 547752.i | 0.960925 | − | 0.960925i | ||||
\(756\) | −19891.8 | −0.0348042 | ||||||||
\(757\) | 139987. | + | 139987.i | 0.244285 | + | 0.244285i | 0.818620 | − | 0.574335i | \(-0.194739\pi\) |
−0.574335 | + | 0.818620i | \(0.694739\pi\) | |||||||
\(758\) | 38630.4 | − | 38630.4i | 0.0672343 | − | 0.0672343i | ||||
\(759\) | −689629. | − | 689629.i | −1.19710 | − | 1.19710i | ||||
\(760\) | −171343. | + | 171343.i | −0.296647 | + | 0.296647i | ||||
\(761\) | 996640.i | 1.72095i | 0.509490 | + | 0.860477i | \(0.329834\pi\) | ||||
−0.509490 | + | 0.860477i | \(0.670166\pi\) | |||||||
\(762\) | 338253. | + | 338253.i | 0.582547 | + | 0.582547i | ||||
\(763\) | 293113. | + | 293113.i | 0.503484 | + | 0.503484i | ||||
\(764\) | 35800.0 | − | 35800.0i | 0.0613332 | − | 0.0613332i | ||||
\(765\) | − | 446728.i | − | 0.763343i | ||||||
\(766\) | −429215. | −0.731505 | ||||||||
\(767\) | − | 787844.i | − | 1.33921i | ||||||
\(768\) | − | 53655.9i | − | 0.0909693i | ||||||
\(769\) | −401157. | + | 401157.i | −0.678362 | + | 0.678362i | −0.959630 | − | 0.281267i | \(-0.909245\pi\) |
0.281267 | + | 0.959630i | \(0.409245\pi\) | |||||||
\(770\) | − | 283197.i | − | 0.477647i | ||||||
\(771\) | 203727. | − | 203727.i | 0.342721 | − | 0.342721i | ||||
\(772\) | 96682.8 | − | 96682.8i | 0.162224 | − | 0.162224i | ||||
\(773\) | 176385. | 0.295191 | 0.147595 | − | 0.989048i | \(-0.452847\pi\) | ||||
0.147595 | + | 0.989048i | \(0.452847\pi\) | |||||||
\(774\) | 787227. | 1.31407 | ||||||||
\(775\) | 115041. | + | 115041.i | 0.191535 | + | 0.191535i | ||||
\(776\) | 3619.65i | 0.00601094i | ||||||||
\(777\) | 144599. | − | 323797.i | 0.239510 | − | 0.536328i | ||||
\(778\) | 180081. | 0.297515 | ||||||||
\(779\) | −72018.5 | + | 72018.5i | −0.118678 | + | 0.118678i | ||||
\(780\) | 711375.i | 1.16925i | ||||||||
\(781\) | − | 1.46243e6i | − | 2.39758i | ||||||
\(782\) | −145003. | − | 145003.i | −0.237118 | − | 0.237118i | ||||
\(783\) | −104512. | − | 104512.i | −0.170468 | − | 0.170468i | ||||
\(784\) | 128639. | 0.209286 | ||||||||
\(785\) | 420238. | + | 420238.i | 0.681955 | + | 0.681955i | ||||
\(786\) | −194081. | −0.314151 | ||||||||
\(787\) | 99310.4 | 0.160341 | 0.0801706 | − | 0.996781i | \(-0.474453\pi\) | ||||
0.0801706 | + | 0.996781i | \(0.474453\pi\) | |||||||
\(788\) | 345573.i | 0.556528i | ||||||||
\(789\) | 103137. | 0.165676 | ||||||||
\(790\) | 718088. | + | 718088.i | 1.15060 | + | 1.15060i | ||||
\(791\) | 200147. | − | 200147.i | 0.319887 | − | 0.319887i | ||||
\(792\) | 220440. | − | 220440.i | 0.351430 | − | 0.351430i | ||||
\(793\) | 470593. | 0.748340 | ||||||||
\(794\) | −518239. | − | 518239.i | −0.822032 | − | 0.822032i | ||||
\(795\) | 782938. | − | 782938.i | 1.23878 | − | 1.23878i | ||||
\(796\) | −115667. | − | 115667.i | −0.182550 | − | 0.182550i | ||||
\(797\) | −333443. | + | 333443.i | −0.524934 | + | 0.524934i | −0.919057 | − | 0.394123i | \(-0.871048\pi\) |
0.394123 | + | 0.919057i | \(0.371048\pi\) | |||||||
\(798\) | 235641.i | 0.370037i | ||||||||
\(799\) | 64192.1 | + | 64192.1i | 0.100551 | + | 0.100551i | ||||
\(800\) | 61907.8 | + | 61907.8i | 0.0967310 | + | 0.0967310i | ||||
\(801\) | −432141. | + | 432141.i | −0.673536 | + | 0.673536i | ||||
\(802\) | 775500.i | 1.20568i | ||||||||
\(803\) | −910782. | −1.41248 | ||||||||
\(804\) | 695297.i | 1.07562i | ||||||||
\(805\) | − | 322347.i | − | 0.497431i | ||||||
\(806\) | −137156. | + | 137156.i | −0.211127 | + | 0.211127i | ||||
\(807\) | − | 642710.i | − | 0.986889i | ||||||
\(808\) | 216530. | − | 216530.i | 0.331661 | − | 0.331661i | ||||
\(809\) | 332499. | − | 332499.i | 0.508035 | − | 0.508035i | −0.405888 | − | 0.913923i | \(-0.633038\pi\) |
0.913923 | + | 0.405888i | \(0.133038\pi\) | |||||||
\(810\) | −535991. | −0.816934 | ||||||||
\(811\) | 5920.83 | 0.00900204 | 0.00450102 | − | 0.999990i | \(-0.498567\pi\) | ||||
0.00450102 | + | 0.999990i | \(0.498567\pi\) | |||||||
\(812\) | −131483. | − | 131483.i | −0.199415 | − | 0.199415i | ||||
\(813\) | 277954.i | 0.420525i | ||||||||
\(814\) | 210403. | + | 549963.i | 0.317543 | + | 0.830012i | ||||
\(815\) | −1.25686e6 | −1.89222 | ||||||||
\(816\) | 87789.6 | − | 87789.6i | 0.131845 | − | 0.131845i | ||||
\(817\) | − | 988053.i | − | 1.48025i | ||||||
\(818\) | 48558.7i | 0.0725706i | ||||||||
\(819\) | 258262. | + | 258262.i | 0.385028 | + | 0.385028i | ||||
\(820\) | 59646.3 | + | 59646.3i | 0.0887065 | + | 0.0887065i | ||||
\(821\) | −119154. | −0.176776 | −0.0883878 | − | 0.996086i | \(-0.528171\pi\) | ||||
−0.0883878 | + | 0.996086i | \(0.528171\pi\) | |||||||
\(822\) | 271968. | + | 271968.i | 0.402508 | + | 0.402508i | ||||
\(823\) | 648844. | 0.957945 | 0.478972 | − | 0.877830i | \(-0.341009\pi\) | ||||
0.478972 | + | 0.877830i | \(0.341009\pi\) | |||||||
\(824\) | 430693. | 0.634327 | ||||||||
\(825\) | 963472.i | 1.41557i | ||||||||
\(826\) | −216138. | −0.316790 | ||||||||
\(827\) | 516877. | + | 516877.i | 0.755747 | + | 0.755747i | 0.975545 | − | 0.219799i | \(-0.0705400\pi\) |
−0.219799 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(828\) | 250915. | − | 250915.i | 0.365987 | − | 0.365987i | ||||
\(829\) | 74845.0 | − | 74845.0i | 0.108906 | − | 0.108906i | −0.650554 | − | 0.759460i | \(-0.725463\pi\) |
0.759460 | + | 0.650554i | \(0.225463\pi\) | |||||||
\(830\) | −222119. | −0.322425 | ||||||||
\(831\) | 634909. | + | 634909.i | 0.919410 | + | 0.919410i | ||||
\(832\) | −73808.7 | + | 73808.7i | −0.106626 | + | 0.106626i | ||||
\(833\) | 210474. | + | 210474.i | 0.303325 | + | 0.303325i | ||||
\(834\) | 752426. | − | 752426.i | 1.08176 | − | 1.08176i | ||||
\(835\) | − | 583295.i | − | 0.836595i | ||||||
\(836\) | −276675. | − | 276675.i | −0.395875 | − | 0.395875i | ||||
\(837\) | 29909.1 | + | 29909.1i | 0.0426925 | + | 0.0426925i | ||||
\(838\) | 175835. | − | 175835.i | 0.250390 | − | 0.250390i | ||||
\(839\) | 877210.i | 1.24618i | 0.782152 | + | 0.623088i | \(0.214122\pi\) | ||||
−0.782152 | + | 0.623088i | \(0.785878\pi\) | |||||||
\(840\) | 195159. | 0.276586 | ||||||||
\(841\) | − | 674343.i | − | 0.953431i | ||||||
\(842\) | 140269.i | 0.197851i | ||||||||
\(843\) | −59080.1 | + | 59080.1i | −0.0831354 | + | 0.0831354i | ||||
\(844\) | − | 307115.i | − | 0.431138i | ||||||
\(845\) | 306118. | − | 306118.i | 0.428722 | − | 0.428722i | ||||
\(846\) | −111078. | + | 111078.i | −0.155199 | + | 0.155199i | ||||
\(847\) | 167775. | 0.233863 | ||||||||
\(848\) | 162468. | 0.225931 | ||||||||
\(849\) | 954709. | + | 954709.i | 1.32451 | + | 1.32451i | ||||
\(850\) | 202582.i | 0.280391i | ||||||||
\(851\) | 239490. | + | 625993.i | 0.330696 | + | 0.864391i | ||||
\(852\) | 1.00781e6 | 1.38835 | ||||||||
\(853\) | 459593. | − | 459593.i | 0.631648 | − | 0.631648i | −0.316833 | − | 0.948481i | \(-0.602619\pi\) |
0.948481 | + | 0.316833i | \(0.102619\pi\) | |||||||
\(854\) | − | 129103.i | − | 0.177019i | ||||||
\(855\) | − | 970222.i | − | 1.32721i | ||||||
\(856\) | 98257.2 | + | 98257.2i | 0.134096 | + | 0.134096i | ||||
\(857\) | −44773.2 | − | 44773.2i | −0.0609616 | − | 0.0609616i | 0.675969 | − | 0.736930i | \(-0.263725\pi\) |
−0.736930 | + | 0.675969i | \(0.763725\pi\) | |||||||
\(858\) | −1.14869e6 | −1.56037 | ||||||||
\(859\) | −884239. | − | 884239.i | −1.19835 | − | 1.19835i | −0.974661 | − | 0.223687i | \(-0.928191\pi\) |
−0.223687 | − | 0.974661i | \(-0.571809\pi\) | |||||||
\(860\) | −818313. | −1.10643 | ||||||||
\(861\) | 82028.8 | 0.110652 | ||||||||
\(862\) | − | 394301.i | − | 0.530656i | ||||||
\(863\) | −861576. | −1.15684 | −0.578419 | − | 0.815740i | \(-0.696330\pi\) | ||||
−0.578419 | + | 0.815740i | \(0.696330\pi\) | |||||||
\(864\) | 16095.2 | + | 16095.2i | 0.0215610 | + | 0.0215610i | ||||
\(865\) | 743632. | − | 743632.i | 0.993862 | − | 0.993862i | ||||
\(866\) | 132693. | − | 132693.i | 0.176934 | − | 0.176934i | ||||
\(867\) | −806814. | −1.07334 | ||||||||
\(868\) | 37627.5 | + | 37627.5i | 0.0499420 | + | 0.0499420i | ||||
\(869\) | −1.15953e6 | + | 1.15953e6i | −1.53547 | + | 1.53547i | ||||
\(870\) | 1.02537e6 | + | 1.02537e6i | 1.35470 | + | 1.35470i | ||||
\(871\) | 956446. | − | 956446.i | 1.26074 | − | 1.26074i | ||||
\(872\) | − | 474335.i | − | 0.623810i | ||||||
\(873\) | −10248.0 | − | 10248.0i | −0.0134466 | − | 0.0134466i | ||||
\(874\) | −314924. | − | 314924.i | −0.412272 | − | 0.412272i | ||||
\(875\) | 65805.6 | − | 65805.6i | 0.0859502 | − | 0.0859502i | ||||
\(876\) | − | 627647.i | − | 0.817914i | ||||||
\(877\) | −681977. | −0.886687 | −0.443343 | − | 0.896352i | \(-0.646208\pi\) | ||||
−0.443343 | + | 0.896352i | \(0.646208\pi\) | |||||||
\(878\) | − | 779330.i | − | 1.01096i | ||||||
\(879\) | − | 304428.i | − | 0.394010i | ||||||
\(880\) | −229144. | + | 229144.i | −0.295899 | + | 0.295899i | ||||
\(881\) | 961721.i | 1.23907i | 0.784968 | + | 0.619537i | \(0.212680\pi\) | ||||
−0.784968 | + | 0.619537i | \(0.787320\pi\) | |||||||
\(882\) | −364205. | + | 364205.i | −0.468175 | + | 0.468175i | ||||
\(883\) | −415913. | + | 415913.i | −0.533434 | + | 0.533434i | −0.921593 | − | 0.388158i | \(-0.873111\pi\) |
0.388158 | + | 0.921593i | \(0.373111\pi\) | |||||||
\(884\) | −241526. | −0.309072 | ||||||||
\(885\) | 1.68556e6 | 2.15207 | ||||||||
\(886\) | 565962. | + | 565962.i | 0.720974 | + | 0.720974i | ||||
\(887\) | − | 886720.i | − | 1.12704i | −0.826102 | − | 0.563520i | \(-0.809447\pi\) | ||
0.826102 | − | 0.563520i | \(-0.190553\pi\) | |||||||
\(888\) | −378996. | + | 144995.i | −0.480627 | + | 0.183877i | ||||
\(889\) | −255301. | −0.323035 | ||||||||
\(890\) | 449206. | − | 449206.i | 0.567108 | − | 0.567108i | ||||
\(891\) | − | 865486.i | − | 1.09020i | ||||||
\(892\) | 53176.5i | 0.0668329i | ||||||||
\(893\) | 139415. | + | 139415.i | 0.174826 | + | 0.174826i | ||||
\(894\) | −288392. | − | 288392.i | −0.360834 | − | 0.360834i | ||||
\(895\) | −1.57662e6 | −1.96825 | ||||||||
\(896\) | 20248.8 | + | 20248.8i | 0.0252222 | + | 0.0252222i | ||||
\(897\) | −1.30749e6 | −1.62500 | ||||||||
\(898\) | −703568. | −0.872475 | ||||||||
\(899\) | 395391.i | 0.489224i | ||||||||
\(900\) | −350549. | −0.432777 | ||||||||
\(901\) | 265823. | + | 265823.i | 0.327449 | + | 0.327449i | ||||
\(902\) | −96313.3 | + | 96313.3i | −0.118379 | + | 0.118379i | ||||
\(903\) | −562694. | + | 562694.i | −0.690076 | + | 0.690076i | ||||
\(904\) | −323892. | −0.396336 | ||||||||
\(905\) | 1.11957e6 | + | 1.11957e6i | 1.36695 | + | 1.36695i | ||||
\(906\) | −609520. | + | 609520.i | −0.742560 | + | 0.742560i | ||||
\(907\) | 64166.1 | + | 64166.1i | 0.0779994 | + | 0.0779994i | 0.745030 | − | 0.667031i | \(-0.232435\pi\) |
−0.667031 | + | 0.745030i | \(0.732435\pi\) | |||||||
\(908\) | −138730. | + | 138730.i | −0.168267 | + | 0.168267i | ||||
\(909\) | 1.22609e6i | 1.48386i | ||||||||
\(910\) | −268460. | − | 268460.i | −0.324188 | − | 0.324188i | ||||
\(911\) | 938674. | + | 938674.i | 1.13104 | + | 1.13104i | 0.990005 | + | 0.141035i | \(0.0450431\pi\) |
0.141035 | + | 0.990005i | \(0.454957\pi\) | |||||||
\(912\) | 190665. | − | 190665.i | 0.229236 | − | 0.229236i | ||||
\(913\) | − | 358665.i | − | 0.430276i | ||||||
\(914\) | 464374. | 0.555873 | ||||||||
\(915\) | 1.00681e6i | 1.20256i | ||||||||
\(916\) | 598158.i | 0.712895i | ||||||||
\(917\) | 73242.7 | − | 73242.7i | 0.0871015 | − | 0.0871015i | ||||
\(918\) | 52668.6i | 0.0624981i | ||||||||
\(919\) | 426749. | − | 426749.i | 0.505291 | − | 0.505291i | −0.407786 | − | 0.913077i | \(-0.633699\pi\) |
0.913077 | + | 0.407786i | \(0.133699\pi\) | |||||||
\(920\) | −260823. | + | 260823.i | −0.308155 | + | 0.308155i | ||||
\(921\) | −115179. | −0.135785 | ||||||||
\(922\) | 664864. | 0.782116 | ||||||||
\(923\) | −1.38633e6 | − | 1.38633e6i | −1.62729 | − | 1.62729i | ||||
\(924\) | 315132.i | 0.369104i | ||||||||
\(925\) | 269989. | − | 604577.i | 0.315546 | − | 0.706591i | ||||
\(926\) | 930785. | 1.08549 | ||||||||
\(927\) | −1.21939e6 | + | 1.21939e6i | −1.41900 | + | 1.41900i | ||||
\(928\) | 212775.i | 0.247072i | ||||||||
\(929\) | − | 1.61843e6i | − | 1.87526i | −0.347630 | − | 0.937632i | \(-0.613014\pi\) | ||
0.347630 | − | 0.937632i | \(-0.386986\pi\) | |||||||
\(930\) | −293439. | − | 293439.i | −0.339275 | − | 0.339275i | ||||
\(931\) | 457116. | + | 457116.i | 0.527384 | + | 0.527384i | ||||
\(932\) | −684190. | −0.787671 | ||||||||
\(933\) | −1.14864e6 | − | 1.14864e6i | −1.31953 | − | 1.31953i | ||||
\(934\) | −52328.3 | −0.0599851 | ||||||||
\(935\) | −749834. | −0.857713 | ||||||||
\(936\) | − | 417938.i | − | 0.477045i | ||||||
\(937\) | −1.16817e6 | −1.33053 | −0.665266 | − | 0.746607i | \(-0.731682\pi\) | ||||
−0.665266 | + | 0.746607i | \(0.731682\pi\) | |||||||
\(938\) | −262393. | − | 262393.i | −0.298226 | − | 0.298226i | ||||
\(939\) | 1.59144e6 | − | 1.59144e6i | 1.80492 | − | 1.80492i | ||||
\(940\) | 115465. | − | 115465.i | 0.130675 | − | 0.130675i | ||||
\(941\) | 938243. | 1.05959 | 0.529793 | − | 0.848127i | \(-0.322270\pi\) | ||||
0.529793 | + | 0.848127i | \(0.322270\pi\) | |||||||
\(942\) | −467627. | − | 467627.i | −0.526984 | − | 0.526984i | ||||
\(943\) | −109628. | + | 109628.i | −0.123282 | + | 0.123282i | ||||
\(944\) | 174885. | + | 174885.i | 0.196249 | + | 0.196249i | ||||
\(945\) | −58542.1 | + | 58542.1i | −0.0655548 | + | 0.0655548i | ||||
\(946\) | − | 1.32136e6i | − | 1.47652i | ||||||
\(947\) | 100085. | + | 100085.i | 0.111602 | + | 0.111602i | 0.760702 | − | 0.649101i | \(-0.224855\pi\) |
−0.649101 | + | 0.760702i | \(0.724855\pi\) | |||||||
\(948\) | −799064. | − | 799064.i | −0.889130 | − | 0.889130i | ||||
\(949\) | −863388. | + | 863388.i | −0.958680 | + | 0.958680i | ||||
\(950\) | 439977.i | 0.487509i | ||||||||
\(951\) | 2.16036e6 | 2.38872 | ||||||||
\(952\) | 66260.5i | 0.0731107i | ||||||||
\(953\) | 484459.i | 0.533423i | 0.963776 | + | 0.266711i | \(0.0859370\pi\) | ||||
−0.963776 | + | 0.266711i | \(0.914063\pi\) | |||||||
\(954\) | −459982. | + | 459982.i | −0.505410 | + | 0.505410i | ||||
\(955\) | − | 210720.i | − | 0.231046i | ||||||
\(956\) | −116280. | + | 116280.i | −0.127230 | + | 0.127230i | ||||
\(957\) | −1.65571e6 | + | 1.65571e6i | −1.80784 | + | 1.80784i | ||||
\(958\) | 100691. | 0.109714 | ||||||||
\(959\) | −205272. | −0.223199 | ||||||||
\(960\) | −157910. | − | 157910.i | −0.171344 | − | 0.171344i | ||||
\(961\) | 810369.i | 0.877477i | ||||||||
\(962\) | 720799. | + | 321890.i | 0.778868 | + | 0.347823i | ||||
\(963\) | −556376. | −0.599951 | ||||||||
\(964\) | 302247. | − | 302247.i | 0.325243 | − | 0.325243i | ||||
\(965\) | − | 569079.i | − | 0.611108i | ||||||
\(966\) | 358698.i | 0.384392i | ||||||||
\(967\) | −581569. | − | 581569.i | −0.621940 | − | 0.621940i | 0.324087 | − | 0.946027i | \(-0.394943\pi\) |
−0.946027 | + | 0.324087i | \(0.894943\pi\) | |||||||
\(968\) | −135753. | − | 135753.i | −0.144877 | − | 0.144877i | ||||
\(969\) | 623918. | 0.664477 | ||||||||
\(970\) | 10652.7 | + | 10652.7i | 0.0113218 | + | 0.0113218i | ||||
\(971\) | −376664. | −0.399499 | −0.199750 | − | 0.979847i | \(-0.564013\pi\) | ||||
−0.199750 | + | 0.979847i | \(0.564013\pi\) | |||||||
\(972\) | 677915. | 0.717534 | ||||||||
\(973\) | 567904.i | 0.599859i | ||||||||
\(974\) | 1.05955e6 | 1.11687 | ||||||||
\(975\) | 913336. | + | 913336.i | 0.960775 | + | 0.960775i | ||||
\(976\) | −104462. | + | 104462.i | −0.109662 | + | 0.109662i | ||||
\(977\) | 597853. | − | 597853.i | 0.626333 | − | 0.626333i | −0.320811 | − | 0.947143i | \(-0.603955\pi\) |
0.947143 | + | 0.320811i | \(0.103955\pi\) | |||||||
\(978\) | 1.39859e6 | 1.46222 | ||||||||
\(979\) | 725351. | + | 725351.i | 0.756803 | + | 0.756803i | ||||
\(980\) | 378587. | − | 378587.i | 0.394197 | − | 0.394197i | ||||
\(981\) | 1.34295e6 | + | 1.34295e6i | 1.39547 | + | 1.39547i | ||||
\(982\) | −261564. | + | 261564.i | −0.271241 | + | 0.271241i | ||||
\(983\) | 187343.i | 0.193878i | 0.995290 | + | 0.0969392i | \(0.0309052\pi\) | ||||
−0.995290 | + | 0.0969392i | \(0.969095\pi\) | |||||||
\(984\) | −66372.4 | − | 66372.4i | −0.0685484 | − | 0.0685484i | ||||
\(985\) | 1.01703e6 | + | 1.01703e6i | 1.04824 | + | 1.04824i | ||||
\(986\) | −348134. | + | 348134.i | −0.358090 | + | 0.358090i | ||||
\(987\) | − | 158793.i | − | 0.163004i | ||||||
\(988\) | −524556. | −0.537376 | ||||||||
\(989\) | − | 1.50404e6i | − | 1.53768i | ||||||
\(990\) | − | 1.29752e6i | − | 1.32386i | ||||||
\(991\) | −74918.1 | + | 74918.1i | −0.0762850 | + | 0.0762850i | −0.744220 | − | 0.667935i | \(-0.767178\pi\) |
0.667935 | + | 0.744220i | \(0.267178\pi\) | |||||||
\(992\) | − | 60891.5i | − | 0.0618776i | ||||||
\(993\) | −1.64989e6 | + | 1.64989e6i | −1.67323 | + | 1.67323i | ||||
\(994\) | −380328. | + | 380328.i | −0.384933 | + | 0.384933i | ||||
\(995\) | −680819. | −0.687679 | ||||||||
\(996\) | 247167. | 0.249156 | ||||||||
\(997\) | −838142. | − | 838142.i | −0.843194 | − | 0.843194i | 0.146079 | − | 0.989273i | \(-0.453335\pi\) |
−0.989273 | + | 0.146079i | \(0.953335\pi\) | |||||||
\(998\) | − | 254320.i | − | 0.255340i | ||||||
\(999\) | 70193.4 | − | 157182.i | 0.0703340 | − | 0.157497i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 74.5.d.a.43.1 | yes | 14 | |
37.31 | odd | 4 | inner | 74.5.d.a.31.7 | ✓ | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.5.d.a.31.7 | ✓ | 14 | 37.31 | odd | 4 | inner | |
74.5.d.a.43.1 | yes | 14 | 1.1 | even | 1 | trivial |