Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [16,5,Mod(3,16)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("16.3");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 16 = 2^{4} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 16.f (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: | \(1.65391940934\) |
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: | \( x^{14} - 4 x^{13} + 15 x^{12} - 34 x^{11} + 62 x^{10} - 312 x^{9} + 1432 x^{8} - 4960 x^{7} + 11456 x^{6} - 19968 x^{5} + 31744 x^{4} - 139264 x^{3} + 491520 x^{2} + \cdots + 2097152 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{21} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 3.5 | ||
Root | \(1.03712 + 2.63142i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 16.3 |
Dual form | 16.5.f.a.11.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(15\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.59430 | + | 3.66854i | 0.398575 | + | 0.917136i | ||||
\(3\) | 11.5209 | − | 11.5209i | 1.28010 | − | 1.28010i | 0.339485 | − | 0.940612i | \(-0.389747\pi\) |
0.940612 | − | 0.339485i | \(-0.110253\pi\) | |||||||
\(4\) | −10.9164 | + | 11.6975i | −0.682276 | + | 0.731095i | ||||
\(5\) | −14.6016 | + | 14.6016i | −0.584063 | + | 0.584063i | −0.936017 | − | 0.351954i | \(-0.885517\pi\) |
0.351954 | + | 0.936017i | \(0.385517\pi\) | |||||||
\(6\) | 60.6325 | + | 23.8971i | 1.68424 | + | 0.663808i | ||||
\(7\) | −24.0210 | −0.490224 | −0.245112 | − | 0.969495i | \(-0.578825\pi\) | ||||
−0.245112 | + | 0.969495i | \(0.578825\pi\) | |||||||
\(8\) | −60.3169 | − | 21.3980i | −0.942451 | − | 0.334344i | ||||
\(9\) | − | 184.461i | − | 2.27729i | ||||||
\(10\) | −76.8459 | − | 30.2872i | −0.768459 | − | 0.302872i | ||||
\(11\) | 61.7287 | + | 61.7287i | 0.510154 | + | 0.510154i | 0.914574 | − | 0.404419i | \(-0.132526\pi\) |
−0.404419 | + | 0.914574i | \(0.632526\pi\) | |||||||
\(12\) | 8.99896 | + | 260.532i | 0.0624928 | + | 1.80925i | ||||
\(13\) | −37.5611 | − | 37.5611i | −0.222255 | − | 0.222255i | 0.587192 | − | 0.809447i | \(-0.300233\pi\) |
−0.809447 | + | 0.587192i | \(0.800233\pi\) | |||||||
\(14\) | −38.2966 | − | 88.1219i | −0.195391 | − | 0.449602i | ||||
\(15\) | 336.446i | 1.49531i | ||||||||
\(16\) | −17.6638 | − | 255.390i | −0.0689991 | − | 0.997617i | ||||
\(17\) | 96.8718 | 0.335197 | 0.167598 | − | 0.985855i | \(-0.446399\pi\) | ||||
0.167598 | + | 0.985855i | \(0.446399\pi\) | |||||||
\(18\) | 676.702 | − | 294.086i | 2.08859 | − | 0.907672i | ||||
\(19\) | −156.751 | + | 156.751i | −0.434214 | + | 0.434214i | −0.890059 | − | 0.455845i | \(-0.849337\pi\) |
0.455845 | + | 0.890059i | \(0.349337\pi\) | |||||||
\(20\) | −11.4053 | − | 330.199i | −0.0285133 | − | 0.825498i | ||||
\(21\) | −276.742 | + | 276.742i | −0.627534 | + | 0.627534i | ||||
\(22\) | −128.040 | + | 324.868i | −0.264546 | + | 0.671216i | ||||
\(23\) | 959.783 | 1.81433 | 0.907167 | − | 0.420770i | \(-0.138240\pi\) | ||||
0.907167 | + | 0.420770i | \(0.138240\pi\) | |||||||
\(24\) | −941.426 | + | 448.379i | −1.63442 | + | 0.778436i | ||||
\(25\) | 198.587i | 0.317740i | ||||||||
\(26\) | 77.9109 | − | 197.678i | 0.115253 | − | 0.292424i | ||||
\(27\) | −1191.96 | − | 1191.96i | −1.63506 | − | 1.63506i | ||||
\(28\) | 262.223 | − | 280.986i | 0.334468 | − | 0.358400i | ||||
\(29\) | −350.180 | − | 350.180i | −0.416385 | − | 0.416385i | 0.467571 | − | 0.883956i | \(-0.345129\pi\) |
−0.883956 | + | 0.467571i | \(0.845129\pi\) | |||||||
\(30\) | −1234.27 | + | 536.396i | −1.37141 | + | 0.595995i | ||||
\(31\) | 237.885i | 0.247539i | 0.992311 | + | 0.123769i | \(0.0394983\pi\) | ||||
−0.992311 | + | 0.123769i | \(0.960502\pi\) | |||||||
\(32\) | 908.747 | − | 471.968i | 0.887449 | − | 0.460907i | ||||
\(33\) | 1422.34 | 1.30609 | ||||||||
\(34\) | 154.443 | + | 355.378i | 0.133601 | + | 0.307421i | ||||
\(35\) | 350.744 | − | 350.744i | 0.286322 | − | 0.286322i | ||||
\(36\) | 2157.73 | + | 2013.65i | 1.66492 | + | 1.55374i | ||||
\(37\) | −560.815 | + | 560.815i | −0.409653 | + | 0.409653i | −0.881617 | − | 0.471965i | \(-0.843545\pi\) |
0.471965 | + | 0.881617i | \(0.343545\pi\) | |||||||
\(38\) | −824.957 | − | 325.140i | −0.571300 | − | 0.225166i | ||||
\(39\) | −865.473 | −0.569016 | ||||||||
\(40\) | 1193.17 | − | 568.278i | 0.745729 | − | 0.355173i | ||||
\(41\) | − | 1802.95i | − | 1.07255i | −0.844044 | − | 0.536274i | \(-0.819831\pi\) | ||
0.844044 | − | 0.536274i | \(-0.180169\pi\) | |||||||
\(42\) | −1456.45 | − | 574.031i | −0.825653 | − | 0.325414i | ||||
\(43\) | 206.090 | + | 206.090i | 0.111460 | + | 0.111460i | 0.760637 | − | 0.649177i | \(-0.224887\pi\) |
−0.649177 | + | 0.760637i | \(0.724887\pi\) | |||||||
\(44\) | −1395.93 | + | 48.2163i | −0.721037 | + | 0.0249051i | ||||
\(45\) | 2693.42 | + | 2693.42i | 1.33008 | + | 1.33008i | ||||
\(46\) | 1530.18 | + | 3521.01i | 0.723149 | + | 1.66399i | ||||
\(47\) | − | 1599.92i | − | 0.724274i | −0.932125 | − | 0.362137i | \(-0.882047\pi\) | ||
0.932125 | − | 0.362137i | \(-0.117953\pi\) | |||||||
\(48\) | −3145.81 | − | 2738.81i | −1.36537 | − | 1.18872i | ||||
\(49\) | −1823.99 | −0.759681 | ||||||||
\(50\) | −728.526 | + | 316.608i | −0.291410 | + | 0.126643i | ||||
\(51\) | 1116.05 | − | 1116.05i | 0.429084 | − | 0.429084i | ||||
\(52\) | 849.405 | − | 29.3390i | 0.314129 | − | 0.0108502i | ||||
\(53\) | −2234.17 | + | 2234.17i | −0.795360 | + | 0.795360i | −0.982360 | − | 0.187000i | \(-0.940124\pi\) |
0.187000 | + | 0.982360i | \(0.440124\pi\) | |||||||
\(54\) | 2472.41 | − | 6273.08i | 0.847877 | − | 2.15126i | ||||
\(55\) | −1802.67 | −0.595925 | ||||||||
\(56\) | 1448.87 | + | 514.000i | 0.462012 | + | 0.163903i | ||||
\(57\) | 3611.82i | 1.11167i | ||||||||
\(58\) | 726.358 | − | 1842.94i | 0.215921 | − | 0.547842i | ||||
\(59\) | 2353.11 | + | 2353.11i | 0.675988 | + | 0.675988i | 0.959090 | − | 0.283102i | \(-0.0913636\pi\) |
−0.283102 | + | 0.959090i | \(0.591364\pi\) | |||||||
\(60\) | −3935.58 | − | 3672.78i | −1.09322 | − | 1.02022i | ||||
\(61\) | −4443.45 | − | 4443.45i | −1.19415 | − | 1.19415i | −0.975890 | − | 0.218264i | \(-0.929961\pi\) |
−0.218264 | − | 0.975890i | \(-0.570039\pi\) | |||||||
\(62\) | −872.690 | + | 379.260i | −0.227027 | + | 0.0986627i | ||||
\(63\) | 4430.92i | 1.11638i | ||||||||
\(64\) | 3180.25 | + | 2581.32i | 0.776429 | + | 0.630205i | ||||
\(65\) | 1096.90 | 0.259622 | ||||||||
\(66\) | 2267.63 | + | 5217.90i | 0.520576 | + | 1.19786i | ||||
\(67\) | −3995.40 | + | 3995.40i | −0.890042 | + | 0.890042i | −0.994527 | − | 0.104485i | \(-0.966681\pi\) |
0.104485 | + | 0.994527i | \(0.466681\pi\) | |||||||
\(68\) | −1057.49 | + | 1133.16i | −0.228697 | + | 0.245060i | ||||
\(69\) | 11057.5 | − | 11057.5i | 2.32252 | − | 2.32252i | ||||
\(70\) | 1845.91 | + | 727.529i | 0.376717 | + | 0.148475i | ||||
\(71\) | 4929.25 | 0.977832 | 0.488916 | − | 0.872331i | \(-0.337392\pi\) | ||||
0.488916 | + | 0.872331i | \(0.337392\pi\) | |||||||
\(72\) | −3947.09 | + | 11126.1i | −0.761398 | + | 2.14624i | ||||
\(73\) | − | 2651.57i | − | 0.497574i | −0.968558 | − | 0.248787i | \(-0.919968\pi\) | ||
0.968558 | − | 0.248787i | \(-0.0800319\pi\) | |||||||
\(74\) | −2951.48 | − | 1163.27i | −0.538984 | − | 0.212430i | ||||
\(75\) | 2287.90 | + | 2287.90i | 0.406737 | + | 0.406737i | ||||
\(76\) | −122.438 | − | 3544.76i | −0.0211978 | − | 0.613705i | ||||
\(77\) | −1482.78 | − | 1482.78i | −0.250090 | − | 0.250090i | ||||
\(78\) | −1379.82 | − | 3175.03i | −0.226796 | − | 0.521865i | ||||
\(79\) | − | 8792.34i | − | 1.40880i | −0.709801 | − | 0.704402i | \(-0.751215\pi\) | ||
0.709801 | − | 0.704402i | \(-0.248785\pi\) | |||||||
\(80\) | 3987.02 | + | 3471.18i | 0.622971 | + | 0.542372i | ||||
\(81\) | −12523.4 | −1.90877 | ||||||||
\(82\) | 6614.21 | − | 2874.45i | 0.983672 | − | 0.427491i | ||||
\(83\) | −228.231 | + | 228.231i | −0.0331298 | + | 0.0331298i | −0.723478 | − | 0.690348i | \(-0.757458\pi\) |
0.690348 | + | 0.723478i | \(0.257458\pi\) | |||||||
\(84\) | −216.164 | − | 6258.23i | −0.0306354 | − | 0.886938i | ||||
\(85\) | −1414.48 | + | 1414.48i | −0.195776 | + | 0.195776i | ||||
\(86\) | −427.480 | + | 1084.62i | −0.0577988 | + | 0.146649i | ||||
\(87\) | −8068.75 | −1.06603 | ||||||||
\(88\) | −2402.41 | − | 5044.15i | −0.310229 | − | 0.651362i | ||||
\(89\) | 10596.7i | 1.33780i | 0.743353 | + | 0.668899i | \(0.233234\pi\) | ||||
−0.743353 | + | 0.668899i | \(0.766766\pi\) | |||||||
\(90\) | −5586.81 | + | 14175.0i | −0.689729 | + | 1.75001i | ||||
\(91\) | 902.254 | + | 902.254i | 0.108955 | + | 0.108955i | ||||
\(92\) | −10477.4 | + | 11227.1i | −1.23788 | + | 1.32645i | ||||
\(93\) | 2740.64 | + | 2740.64i | 0.316873 | + | 0.316873i | ||||
\(94\) | 5869.38 | − | 2550.75i | 0.664258 | − | 0.288677i | ||||
\(95\) | − | 4577.63i | − | 0.507217i | ||||||
\(96\) | 5032.07 | − | 15907.0i | 0.546015 | − | 1.72602i | ||||
\(97\) | 11048.3 | 1.17422 | 0.587111 | − | 0.809506i | \(-0.300265\pi\) | ||||
0.587111 | + | 0.809506i | \(0.300265\pi\) | |||||||
\(98\) | −2907.99 | − | 6691.40i | −0.302790 | − | 0.696730i | ||||
\(99\) | 11386.5 | − | 11386.5i | 1.16177 | − | 1.16177i | ||||
\(100\) | −2322.98 | − | 2167.86i | −0.232298 | − | 0.216786i | ||||
\(101\) | −7543.12 | + | 7543.12i | −0.739449 | + | 0.739449i | −0.972471 | − | 0.233022i | \(-0.925139\pi\) |
0.233022 | + | 0.972471i | \(0.425139\pi\) | |||||||
\(102\) | 5873.58 | + | 2314.95i | 0.564550 | + | 0.222506i | ||||
\(103\) | −6124.81 | −0.577322 | −0.288661 | − | 0.957431i | \(-0.593210\pi\) | ||||
−0.288661 | + | 0.957431i | \(0.593210\pi\) | |||||||
\(104\) | 1461.84 | + | 3069.30i | 0.135155 | + | 0.283774i | ||||
\(105\) | − | 8081.75i | − | 0.733039i | ||||||
\(106\) | −11758.1 | − | 4634.20i | −1.04646 | − | 0.412442i | ||||
\(107\) | 4636.79 | + | 4636.79i | 0.404995 | + | 0.404995i | 0.879989 | − | 0.474994i | \(-0.157550\pi\) |
−0.474994 | + | 0.879989i | \(0.657550\pi\) | |||||||
\(108\) | 26954.8 | − | 931.038i | 2.31094 | − | 0.0798215i | ||||
\(109\) | 15235.6 | + | 15235.6i | 1.28235 | + | 1.28235i | 0.939327 | + | 0.343022i | \(0.111451\pi\) |
0.343022 | + | 0.939327i | \(0.388549\pi\) | |||||||
\(110\) | −2874.00 | − | 6613.18i | −0.237521 | − | 0.546544i | ||||
\(111\) | 12922.1i | 1.04879i | ||||||||
\(112\) | 424.301 | + | 6134.71i | 0.0338250 | + | 0.489055i | ||||
\(113\) | 2902.13 | 0.227279 | 0.113639 | − | 0.993522i | \(-0.463749\pi\) | ||||
0.113639 | + | 0.993522i | \(0.463749\pi\) | |||||||
\(114\) | −13250.1 | + | 5758.32i | −1.01955 | + | 0.443084i | ||||
\(115\) | −14014.4 | + | 14014.4i | −1.05969 | + | 1.05969i | ||||
\(116\) | 7918.94 | − | 273.526i | 0.588506 | − | 0.0203274i | ||||
\(117\) | −6928.55 | + | 6928.55i | −0.506140 | + | 0.506140i | ||||
\(118\) | −4880.93 | + | 12384.1i | −0.350541 | + | 0.889404i | ||||
\(119\) | −2326.95 | −0.164321 | ||||||||
\(120\) | 7199.26 | − | 20293.4i | 0.499949 | − | 1.40926i | ||||
\(121\) | − | 7020.14i | − | 0.479485i | ||||||
\(122\) | 9216.79 | − | 23385.2i | 0.619241 | − | 1.57116i | ||||
\(123\) | −20771.6 | − | 20771.6i | −1.37296 | − | 1.37296i | ||||
\(124\) | −2782.66 | − | 2596.85i | −0.180974 | − | 0.168890i | ||||
\(125\) | −12025.7 | − | 12025.7i | −0.769644 | − | 0.769644i | ||||
\(126\) | −16255.0 | + | 7064.22i | −1.02387 | + | 0.444962i | ||||
\(127\) | − | 3992.46i | − | 0.247533i | −0.992311 | − | 0.123766i | \(-0.960503\pi\) | ||
0.992311 | − | 0.123766i | \(-0.0394974\pi\) | |||||||
\(128\) | −4399.41 | + | 15782.3i | −0.268518 | + | 0.963275i | ||||
\(129\) | 4748.66 | 0.285359 | ||||||||
\(130\) | 1748.79 | + | 4024.04i | 0.103479 | + | 0.238109i | ||||
\(131\) | 16640.1 | − | 16640.1i | 0.969645 | − | 0.969645i | −0.0299081 | − | 0.999553i | \(-0.509521\pi\) |
0.999553 | + | 0.0299081i | \(0.00952147\pi\) | |||||||
\(132\) | −15526.8 | + | 16637.8i | −0.891116 | + | 0.954878i | ||||
\(133\) | 3765.31 | − | 3765.31i | 0.212862 | − | 0.212862i | ||||
\(134\) | −21027.2 | − | 8287.43i | −1.17104 | − | 0.461541i | ||||
\(135\) | 34808.9 | 1.90995 | ||||||||
\(136\) | −5843.01 | − | 2072.86i | −0.315906 | − | 0.112071i | ||||
\(137\) | 10746.6i | 0.572573i | 0.958144 | + | 0.286286i | \(0.0924209\pi\) | ||||
−0.958144 | + | 0.286286i | \(0.907579\pi\) | |||||||
\(138\) | 58194.1 | + | 22936.0i | 3.05577 | + | 1.20437i | ||||
\(139\) | −7583.76 | − | 7583.76i | −0.392514 | − | 0.392514i | 0.483069 | − | 0.875582i | \(-0.339522\pi\) |
−0.875582 | + | 0.483069i | \(0.839522\pi\) | |||||||
\(140\) | 273.967 | + | 7931.70i | 0.0139779 | + | 0.404679i | ||||
\(141\) | −18432.5 | − | 18432.5i | −0.927140 | − | 0.927140i | ||||
\(142\) | 7858.70 | + | 18083.2i | 0.389739 | + | 0.896805i | ||||
\(143\) | − | 4637.20i | − | 0.226769i | ||||||
\(144\) | −47109.4 | + | 3258.27i | −2.27187 | + | 0.157131i | ||||
\(145\) | 10226.4 | 0.486390 | ||||||||
\(146\) | 9727.41 | − | 4227.40i | 0.456343 | − | 0.198321i | ||||
\(147\) | −21014.0 | + | 21014.0i | −0.972464 | + | 0.972464i | ||||
\(148\) | −438.053 | − | 12682.2i | −0.0199988 | − | 0.578991i | ||||
\(149\) | 3385.37 | − | 3385.37i | 0.152487 | − | 0.152487i | −0.626741 | − | 0.779228i | \(-0.715611\pi\) |
0.779228 | + | 0.626741i | \(0.215611\pi\) | |||||||
\(150\) | −4745.66 | + | 12040.8i | −0.210918 | + | 0.535149i | ||||
\(151\) | 21697.8 | 0.951617 | 0.475809 | − | 0.879549i | \(-0.342155\pi\) | ||||
0.475809 | + | 0.879549i | \(0.342155\pi\) | |||||||
\(152\) | 12808.9 | − | 6100.58i | 0.554402 | − | 0.264049i | ||||
\(153\) | − | 17869.0i | − | 0.763341i | ||||||
\(154\) | 3075.65 | − | 7803.65i | 0.129687 | − | 0.329046i | ||||
\(155\) | −3473.49 | − | 3473.49i | −0.144578 | − | 0.144578i | ||||
\(156\) | 9447.87 | − | 10123.9i | 0.388226 | − | 0.416005i | ||||
\(157\) | 14212.7 | + | 14212.7i | 0.576603 | + | 0.576603i | 0.933966 | − | 0.357363i | \(-0.116324\pi\) |
−0.357363 | + | 0.933966i | \(0.616324\pi\) | |||||||
\(158\) | 32255.1 | − | 14017.6i | 1.29206 | − | 0.561514i | ||||
\(159\) | 51479.0i | 2.03627i | ||||||||
\(160\) | −6377.67 | + | 20160.6i | −0.249128 | + | 0.787525i | ||||
\(161\) | −23054.9 | −0.889430 | ||||||||
\(162\) | −19966.1 | − | 45942.8i | −0.760788 | − | 1.75060i | ||||
\(163\) | −7450.28 | + | 7450.28i | −0.280412 | + | 0.280412i | −0.833273 | − | 0.552861i | \(-0.813536\pi\) |
0.552861 | + | 0.833273i | \(0.313536\pi\) | |||||||
\(164\) | 21090.1 | + | 19681.8i | 0.784134 | + | 0.731773i | ||||
\(165\) | −20768.4 | + | 20768.4i | −0.762841 | + | 0.762841i | ||||
\(166\) | −1201.14 | − | 473.407i | −0.0435892 | − | 0.0171798i | ||||
\(167\) | −3997.25 | −0.143327 | −0.0716635 | − | 0.997429i | \(-0.522831\pi\) | ||||
−0.0716635 | + | 0.997429i | \(0.522831\pi\) | |||||||
\(168\) | 22614.0 | − | 10770.5i | 0.801232 | − | 0.381608i | ||||
\(169\) | − | 25739.3i | − | 0.901205i | ||||||
\(170\) | −7444.20 | − | 2933.98i | −0.257585 | − | 0.101522i | ||||
\(171\) | 28914.4 | + | 28914.4i | 0.988832 | + | 0.988832i | ||||
\(172\) | −4660.50 | + | 160.977i | −0.157534 | + | 0.00544134i | ||||
\(173\) | −16996.8 | − | 16996.8i | −0.567903 | − | 0.567903i | 0.363638 | − | 0.931540i | \(-0.381535\pi\) |
−0.931540 | + | 0.363638i | \(0.881535\pi\) | |||||||
\(174\) | −12864.0 | − | 29600.5i | −0.424891 | − | 0.977690i | ||||
\(175\) | − | 4770.26i | − | 0.155764i | ||||||
\(176\) | 14674.5 | − | 16855.2i | 0.473738 | − | 0.544139i | ||||
\(177\) | 54219.8 | 1.73066 | ||||||||
\(178\) | −38874.4 | + | 16894.3i | −1.22694 | + | 0.533213i | ||||
\(179\) | 24121.3 | − | 24121.3i | 0.752826 | − | 0.752826i | −0.222180 | − | 0.975006i | \(-0.571317\pi\) |
0.975006 | + | 0.222180i | \(0.0713173\pi\) | |||||||
\(180\) | −60908.8 | + | 2103.83i | −1.87990 | + | 0.0649331i | ||||
\(181\) | 13837.8 | − | 13837.8i | 0.422386 | − | 0.422386i | −0.463638 | − | 0.886025i | \(-0.653456\pi\) |
0.886025 | + | 0.463638i | \(0.153456\pi\) | |||||||
\(182\) | −1871.50 | + | 4748.42i | −0.0564997 | + | 0.143353i | ||||
\(183\) | −102385. | −3.05726 | ||||||||
\(184\) | −57891.1 | − | 20537.4i | −1.70992 | − | 0.606611i | ||||
\(185\) | − | 16377.6i | − | 0.478526i | ||||||
\(186\) | −5684.75 | + | 14423.5i | −0.164318 | + | 0.416914i | ||||
\(187\) | 5979.77 | + | 5979.77i | 0.171002 | + | 0.171002i | ||||
\(188\) | 18715.1 | + | 17465.4i | 0.529513 | + | 0.494155i | ||||
\(189\) | 28632.0 | + | 28632.0i | 0.801544 | + | 0.801544i | ||||
\(190\) | 16793.2 | − | 7298.12i | 0.465187 | − | 0.202164i | ||||
\(191\) | 11717.4i | 0.321193i | 0.987020 | + | 0.160596i | \(0.0513417\pi\) | ||||
−0.987020 | + | 0.160596i | \(0.948658\pi\) | |||||||
\(192\) | 66378.3 | − | 6900.22i | 1.80063 | − | 0.187180i | ||||
\(193\) | −68633.2 | −1.84255 | −0.921276 | − | 0.388910i | \(-0.872852\pi\) | ||||
−0.921276 | + | 0.388910i | \(0.872852\pi\) | |||||||
\(194\) | 17614.2 | + | 40531.0i | 0.468016 | + | 1.07692i | ||||
\(195\) | 12637.3 | − | 12637.3i | 0.332341 | − | 0.332341i | ||||
\(196\) | 19911.5 | − | 21336.2i | 0.518312 | − | 0.555399i | ||||
\(197\) | −22885.3 | + | 22885.3i | −0.589689 | + | 0.589689i | −0.937547 | − | 0.347858i | \(-0.886909\pi\) |
0.347858 | + | 0.937547i | \(0.386909\pi\) | |||||||
\(198\) | 59925.4 | + | 23618.4i | 1.52855 | + | 0.602449i | ||||
\(199\) | 59936.9 | 1.51352 | 0.756761 | − | 0.653692i | \(-0.226781\pi\) | ||||
0.756761 | + | 0.653692i | \(0.226781\pi\) | |||||||
\(200\) | 4249.37 | − | 11978.2i | 0.106234 | − | 0.299454i | ||||
\(201\) | 92060.9i | 2.27868i | ||||||||
\(202\) | −39698.3 | − | 15646.3i | −0.972901 | − | 0.383449i | ||||
\(203\) | 8411.65 | + | 8411.65i | 0.204122 | + | 0.204122i | ||||
\(204\) | 871.745 | + | 25238.2i | 0.0209474 | + | 0.606455i | ||||
\(205\) | 26326.0 | + | 26326.0i | 0.626436 | + | 0.626436i | ||||
\(206\) | −9764.78 | − | 22469.1i | −0.230106 | − | 0.529483i | ||||
\(207\) | − | 177042.i | − | 4.13177i | ||||||
\(208\) | −8929.26 | + | 10256.2i | −0.206390 | + | 0.237061i | ||||
\(209\) | −19352.1 | −0.443032 | ||||||||
\(210\) | 29648.3 | − | 12884.7i | 0.672296 | − | 0.292171i | ||||
\(211\) | −12558.8 | + | 12558.8i | −0.282086 | + | 0.282086i | −0.833941 | − | 0.551854i | \(-0.813920\pi\) |
0.551854 | + | 0.833941i | \(0.313920\pi\) | |||||||
\(212\) | −1745.11 | − | 50523.3i | −0.0388285 | − | 1.12414i | ||||
\(213\) | 56789.2 | − | 56789.2i | 1.25172 | − | 1.25172i | ||||
\(214\) | −9617.83 | + | 24402.7i | −0.210015 | + | 0.532856i | ||||
\(215\) | −6018.47 | −0.130199 | ||||||||
\(216\) | 46389.6 | + | 97400.6i | 0.994291 | + | 2.08763i | ||||
\(217\) | − | 5714.22i | − | 0.121349i | ||||||
\(218\) | −31602.3 | + | 80182.5i | −0.664976 | + | 1.68720i | ||||
\(219\) | −30548.4 | − | 30548.4i | −0.636943 | − | 0.636943i | ||||
\(220\) | 19678.7 | − | 21086.8i | 0.406585 | − | 0.435678i | ||||
\(221\) | −3638.61 | − | 3638.61i | −0.0744992 | − | 0.0744992i | ||||
\(222\) | −47405.4 | + | 20601.8i | −0.961883 | + | 0.418021i | ||||
\(223\) | 22761.5i | 0.457711i | 0.973460 | + | 0.228856i | \(0.0734983\pi\) | ||||
−0.973460 | + | 0.228856i | \(0.926502\pi\) | |||||||
\(224\) | −21829.0 | + | 11337.1i | −0.435048 | + | 0.225947i | ||||
\(225\) | 36631.6 | 0.723586 | ||||||||
\(226\) | 4626.86 | + | 10646.6i | 0.0905877 | + | 0.208446i | ||||
\(227\) | 6480.30 | − | 6480.30i | 0.125760 | − | 0.125760i | −0.641425 | − | 0.767186i | \(-0.721657\pi\) |
0.767186 | + | 0.641425i | \(0.221657\pi\) | |||||||
\(228\) | −42249.3 | − | 39428.1i | −0.812737 | − | 0.758466i | ||||
\(229\) | 36068.6 | − | 36068.6i | 0.687795 | − | 0.687795i | −0.273949 | − | 0.961744i | \(-0.588330\pi\) |
0.961744 | + | 0.273949i | \(0.0883301\pi\) | |||||||
\(230\) | −73755.4 | − | 29069.2i | −1.39424 | − | 0.549512i | ||||
\(231\) | −34165.9 | −0.640278 | ||||||||
\(232\) | 13628.6 | + | 28614.9i | 0.253207 | + | 0.531638i | ||||
\(233\) | 68226.4i | 1.25673i | 0.777920 | + | 0.628363i | \(0.216275\pi\) | ||||
−0.777920 | + | 0.628363i | \(0.783725\pi\) | |||||||
\(234\) | −36463.9 | − | 14371.5i | −0.665934 | − | 0.262464i | ||||
\(235\) | 23361.4 | + | 23361.4i | 0.423022 | + | 0.423022i | ||||
\(236\) | −53213.1 | + | 1838.02i | −0.955421 | + | 0.0330009i | ||||
\(237\) | −101295. | − | 101295.i | −1.80340 | − | 1.80340i | ||||
\(238\) | −3709.86 | − | 8536.53i | −0.0654944 | − | 0.150705i | ||||
\(239\) | 100556.i | 1.76040i | 0.474599 | + | 0.880202i | \(0.342593\pi\) | ||||
−0.474599 | + | 0.880202i | \(0.657407\pi\) | |||||||
\(240\) | 85924.9 | − | 5942.90i | 1.49175 | − | 0.103175i | ||||
\(241\) | −35563.1 | −0.612302 | −0.306151 | − | 0.951983i | \(-0.599041\pi\) | ||||
−0.306151 | + | 0.951983i | \(0.599041\pi\) | |||||||
\(242\) | 25753.7 | − | 11192.2i | 0.439753 | − | 0.191111i | ||||
\(243\) | −47732.3 | + | 47732.3i | −0.808351 | + | 0.808351i | ||||
\(244\) | 100484. | − | 3470.78i | 1.68778 | − | 0.0582972i | ||||
\(245\) | 26633.2 | − | 26633.2i | 0.443702 | − | 0.443702i | ||||
\(246\) | 43085.3 | − | 109318.i | 0.711965 | − | 1.80642i | ||||
\(247\) | 11775.5 | 0.193013 | ||||||||
\(248\) | 5090.25 | − | 14348.5i | 0.0827630 | − | 0.233293i | ||||
\(249\) | 5258.84i | 0.0848186i | ||||||||
\(250\) | 24944.2 | − | 63289.3i | 0.399107 | − | 1.01263i | ||||
\(251\) | −29206.3 | − | 29206.3i | −0.463585 | − | 0.463585i | 0.436244 | − | 0.899829i | \(-0.356309\pi\) |
−0.899829 | + | 0.436244i | \(0.856309\pi\) | |||||||
\(252\) | −51830.8 | − | 48369.8i | −0.816182 | − | 0.761681i | ||||
\(253\) | 59246.1 | + | 59246.1i | 0.925591 | + | 0.925591i | ||||
\(254\) | 14646.5 | − | 6365.18i | 0.227021 | − | 0.0986604i | ||||
\(255\) | 32592.1i | 0.501224i | ||||||||
\(256\) | −64912.0 | + | 9022.29i | −0.990478 | + | 0.137669i | ||||
\(257\) | 2932.77 | 0.0444029 | 0.0222015 | − | 0.999754i | \(-0.492932\pi\) | ||||
0.0222015 | + | 0.999754i | \(0.492932\pi\) | |||||||
\(258\) | 7570.79 | + | 17420.7i | 0.113737 | + | 0.261713i | ||||
\(259\) | 13471.3 | − | 13471.3i | 0.200821 | − | 0.200821i | ||||
\(260\) | −11974.3 | + | 12831.1i | −0.177134 | + | 0.189808i | ||||
\(261\) | −64594.4 | + | 64594.4i | −0.948230 | + | 0.948230i | ||||
\(262\) | 87574.1 | + | 34515.5i | 1.27577 | + | 0.502820i | ||||
\(263\) | 23253.5 | 0.336184 | 0.168092 | − | 0.985771i | \(-0.446239\pi\) | ||||
0.168092 | + | 0.985771i | \(0.446239\pi\) | |||||||
\(264\) | −85790.8 | − | 30435.1i | −1.23093 | − | 0.436684i | ||||
\(265\) | − | 65244.7i | − | 0.929081i | ||||||
\(266\) | 19816.3 | + | 7810.18i | 0.280065 | + | 0.110382i | ||||
\(267\) | 122083. | + | 122083.i | 1.71251 | + | 1.71251i | ||||
\(268\) | −3120.81 | − | 90351.7i | −0.0434508 | − | 1.25796i | ||||
\(269\) | 56836.3 | + | 56836.3i | 0.785455 | + | 0.785455i | 0.980745 | − | 0.195290i | \(-0.0625649\pi\) |
−0.195290 | + | 0.980745i | \(0.562565\pi\) | |||||||
\(270\) | 55495.9 | + | 127698.i | 0.761260 | + | 1.75169i | ||||
\(271\) | − | 91679.6i | − | 1.24834i | −0.781287 | − | 0.624172i | \(-0.785436\pi\) | ||
0.781287 | − | 0.624172i | \(-0.214564\pi\) | |||||||
\(272\) | −1711.12 | − | 24740.1i | −0.0231283 | − | 0.334398i | ||||
\(273\) | 20789.5 | 0.278945 | ||||||||
\(274\) | −39424.4 | + | 17133.3i | −0.525127 | + | 0.228213i | ||||
\(275\) | −12258.5 | + | 12258.5i | −0.162096 | + | 0.162096i | ||||
\(276\) | 8637.05 | + | 250054.i | 0.113383 | + | 3.28259i | ||||
\(277\) | −75831.0 | + | 75831.0i | −0.988297 | + | 0.988297i | −0.999932 | − | 0.0116353i | \(-0.996296\pi\) |
0.0116353 | + | 0.999932i | \(0.496296\pi\) | |||||||
\(278\) | 15730.6 | − | 39912.1i | 0.203542 | − | 0.516435i | ||||
\(279\) | 43880.4 | 0.563718 | ||||||||
\(280\) | −28661.0 | + | 13650.6i | −0.365574 | + | 0.174114i | ||||
\(281\) | − | 77682.2i | − | 0.983805i | −0.870650 | − | 0.491903i | \(-0.836302\pi\) | ||
0.870650 | − | 0.491903i | \(-0.163698\pi\) | |||||||
\(282\) | 38233.4 | − | 97007.2i | 0.480779 | − | 1.21985i | ||||
\(283\) | −43834.7 | − | 43834.7i | −0.547325 | − | 0.547325i | 0.378341 | − | 0.925666i | \(-0.376495\pi\) |
−0.925666 | + | 0.378341i | \(0.876495\pi\) | |||||||
\(284\) | −53809.7 | + | 57660.0i | −0.667151 | + | 0.714888i | ||||
\(285\) | −52738.3 | − | 52738.3i | −0.649286 | − | 0.649286i | ||||
\(286\) | 17011.8 | − | 7393.08i | 0.207978 | − | 0.0903844i | ||||
\(287\) | 43308.7i | 0.525788i | ||||||||
\(288\) | −87059.6 | − | 167628.i | −1.04962 | − | 2.02098i | ||||
\(289\) | −74136.9 | −0.887643 | ||||||||
\(290\) | 16303.9 | + | 37515.8i | 0.193863 | + | 0.446086i | ||||
\(291\) | 127286. | − | 127286.i | 1.50312 | − | 1.50312i | ||||
\(292\) | 31016.8 | + | 28945.7i | 0.363774 | + | 0.339483i | ||||
\(293\) | 61916.9 | − | 61916.9i | 0.721231 | − | 0.721231i | −0.247625 | − | 0.968856i | \(-0.579650\pi\) |
0.968856 | + | 0.247625i | \(0.0796501\pi\) | |||||||
\(294\) | −110593. | − | 43588.1i | −1.27948 | − | 0.504282i | ||||
\(295\) | −68718.4 | −0.789639 | ||||||||
\(296\) | 45826.9 | − | 21826.3i | 0.523042 | − | 0.249113i | ||||
\(297\) | − | 147156.i | − | 1.66826i | ||||||
\(298\) | 17816.7 | + | 7022.09i | 0.200629 | + | 0.0790740i | ||||
\(299\) | −36050.5 | − | 36050.5i | −0.403245 | − | 0.403245i | ||||
\(300\) | −51738.4 | + | 1787.08i | −0.574871 | + | 0.0198564i | ||||
\(301\) | −4950.47 | − | 4950.47i | −0.0546404 | − | 0.0546404i | ||||
\(302\) | 34592.8 | + | 79599.4i | 0.379291 | + | 0.872762i | ||||
\(303\) | 173807.i | 1.89313i | ||||||||
\(304\) | 42801.5 | + | 37263.9i | 0.463139 | + | 0.403219i | ||||
\(305\) | 129763. | 1.39492 | ||||||||
\(306\) | 65553.4 | − | 28488.6i | 0.700087 | − | 0.304249i | ||||
\(307\) | −99698.5 | + | 99698.5i | −1.05782 | + | 1.05782i | −0.0595972 | + | 0.998223i | \(0.518982\pi\) |
−0.998223 | + | 0.0595972i | \(0.981018\pi\) | |||||||
\(308\) | 33531.5 | − | 1158.20i | 0.353470 | − | 0.0122091i | ||||
\(309\) | −70563.1 | + | 70563.1i | −0.739028 | + | 0.739028i | ||||
\(310\) | 7204.87 | − | 18280.5i | 0.0749726 | − | 0.190223i | ||||
\(311\) | −127678. | −1.32006 | −0.660031 | − | 0.751238i | \(-0.729457\pi\) | ||||
−0.660031 | + | 0.751238i | \(0.729457\pi\) | |||||||
\(312\) | 52202.7 | + | 18519.4i | 0.536270 | + | 0.190247i | ||||
\(313\) | − | 24132.5i | − | 0.246328i | −0.992386 | − | 0.123164i | \(-0.960696\pi\) | ||
0.992386 | − | 0.123164i | \(-0.0393042\pi\) | |||||||
\(314\) | −29480.6 | + | 74799.2i | −0.299004 | + | 0.758643i | ||||
\(315\) | −64698.5 | − | 64698.5i | −0.652039 | − | 0.652039i | ||||
\(316\) | 102849. | + | 95980.9i | 1.02997 | + | 0.961193i | ||||
\(317\) | −63739.0 | − | 63739.0i | −0.634289 | − | 0.634289i | 0.314852 | − | 0.949141i | \(-0.398045\pi\) |
−0.949141 | + | 0.314852i | \(0.898045\pi\) | |||||||
\(318\) | −188853. | + | 82073.0i | −1.86754 | + | 0.811608i | ||||
\(319\) | − | 43232.3i | − | 0.424841i | ||||||
\(320\) | −84128.1 | + | 8745.36i | −0.821563 | + | 0.0854039i | ||||
\(321\) | 106840. | 1.03687 | ||||||||
\(322\) | −36756.5 | − | 84578.0i | −0.354505 | − | 0.815728i | ||||
\(323\) | −15184.8 | + | 15184.8i | −0.145547 | + | 0.145547i | ||||
\(324\) | 136711. | − | 146493.i | 1.30231 | − | 1.39549i | ||||
\(325\) | 7459.16 | − | 7459.16i | 0.0706193 | − | 0.0706193i | ||||
\(326\) | −39209.6 | − | 15453.7i | −0.368942 | − | 0.145411i | ||||
\(327\) | 351055. | 3.28306 | ||||||||
\(328\) | −38579.6 | + | 108748.i | −0.358599 | + | 1.01082i | ||||
\(329\) | 38431.6i | 0.355056i | ||||||||
\(330\) | −109301. | − | 43078.6i | −1.00368 | − | 0.395580i | ||||
\(331\) | −111266. | − | 111266.i | −1.01556 | − | 1.01556i | −0.999877 | − | 0.0156868i | \(-0.995007\pi\) |
−0.0156868 | − | 0.999877i | \(-0.504993\pi\) | |||||||
\(332\) | −178.271 | − | 5161.20i | −0.00161736 | − | 0.0468247i | ||||
\(333\) | 103448. | + | 103448.i | 0.932899 | + | 0.932899i | ||||
\(334\) | −6372.81 | − | 14664.1i | −0.0571266 | − | 0.131450i | ||||
\(335\) | − | 116678.i | − | 1.03968i | ||||||
\(336\) | 75565.5 | + | 65788.9i | 0.669337 | + | 0.582739i | ||||
\(337\) | −89183.5 | −0.785280 | −0.392640 | − | 0.919692i | \(-0.628438\pi\) | ||||
−0.392640 | + | 0.919692i | \(0.628438\pi\) | |||||||
\(338\) | 94425.8 | − | 41036.2i | 0.826528 | − | 0.359198i | ||||
\(339\) | 33435.0 | − | 33435.0i | 0.290939 | − | 0.290939i | ||||
\(340\) | −1104.85 | − | 31987.0i | −0.00955755 | − | 0.276704i | ||||
\(341\) | −14684.3 | + | 14684.3i | −0.126283 | + | 0.126283i | ||||
\(342\) | −59975.6 | + | 152172.i | −0.512769 | + | 1.30102i | ||||
\(343\) | 101488. | 0.862637 | ||||||||
\(344\) | −8020.78 | − | 16840.6i | −0.0677797 | − | 0.142312i | ||||
\(345\) | 322915.i | 2.71300i | ||||||||
\(346\) | 35255.4 | − | 89451.3i | 0.294492 | − | 0.747196i | ||||
\(347\) | −17075.7 | − | 17075.7i | −0.141814 | − | 0.141814i | 0.632635 | − | 0.774450i | \(-0.281973\pi\) |
−0.774450 | + | 0.632635i | \(0.781973\pi\) | |||||||
\(348\) | 88081.8 | − | 94384.3i | 0.727323 | − | 0.779366i | ||||
\(349\) | −25961.7 | − | 25961.7i | −0.213149 | − | 0.213149i | 0.592455 | − | 0.805604i | \(-0.298159\pi\) |
−0.805604 | + | 0.592455i | \(0.798159\pi\) | |||||||
\(350\) | 17499.9 | − | 7605.22i | 0.142856 | − | 0.0620835i | ||||
\(351\) | 89542.5i | 0.726800i | ||||||||
\(352\) | 85229.8 | + | 26961.8i | 0.687869 | + | 0.217602i | ||||
\(353\) | 221897. | 1.78075 | 0.890374 | − | 0.455230i | \(-0.150443\pi\) | ||||
0.890374 | + | 0.455230i | \(0.150443\pi\) | |||||||
\(354\) | 86442.6 | + | 198908.i | 0.689797 | + | 1.58725i | ||||
\(355\) | −71974.9 | + | 71974.9i | −0.571116 | + | 0.571116i | ||||
\(356\) | −123955. | − | 115678.i | −0.978057 | − | 0.912747i | ||||
\(357\) | −26808.5 | + | 26808.5i | −0.210347 | + | 0.210347i | ||||
\(358\) | 126947. | + | 50033.4i | 0.990501 | + | 0.390386i | ||||
\(359\) | −106831. | −0.828908 | −0.414454 | − | 0.910070i | \(-0.636027\pi\) | ||||
−0.414454 | + | 0.910070i | \(0.636027\pi\) | |||||||
\(360\) | −104825. | − | 220092.i | −0.808834 | − | 1.69824i | ||||
\(361\) | 81179.1i | 0.622917i | ||||||||
\(362\) | 72826.1 | + | 28702.9i | 0.555738 | + | 0.219033i | ||||
\(363\) | −80878.1 | − | 80878.1i | −0.613787 | − | 0.613787i | ||||
\(364\) | −20403.5 | + | 704.752i | −0.153993 | + | 0.00531904i | ||||
\(365\) | 38717.2 | + | 38717.2i | 0.290615 | + | 0.290615i | ||||
\(366\) | −163232. | − | 375603.i | −1.21855 | − | 2.80393i | ||||
\(367\) | − | 79074.9i | − | 0.587093i | −0.955945 | − | 0.293546i | \(-0.905164\pi\) | ||
0.955945 | − | 0.293546i | \(-0.0948355\pi\) | |||||||
\(368\) | −16953.4 | − | 245119.i | −0.125187 | − | 1.81001i | ||||
\(369\) | −332574. | −2.44250 | ||||||||
\(370\) | 60081.8 | − | 26110.7i | 0.438874 | − | 0.190729i | ||||
\(371\) | 53666.8 | − | 53666.8i | 0.389904 | − | 0.389904i | ||||
\(372\) | −61976.6 | + | 2140.71i | −0.447859 | + | 0.0154694i | ||||
\(373\) | −86341.4 | + | 86341.4i | −0.620585 | + | 0.620585i | −0.945681 | − | 0.325096i | \(-0.894603\pi\) |
0.325096 | + | 0.945681i | \(0.394603\pi\) | |||||||
\(374\) | −12403.5 | + | 31470.6i | −0.0886749 | + | 0.224989i | ||||
\(375\) | −277093. | −1.97044 | ||||||||
\(376\) | −34235.1 | + | 96502.3i | −0.242156 | + | 0.682593i | ||||
\(377\) | 26306.3i | 0.185087i | ||||||||
\(378\) | −59389.6 | + | 150685.i | −0.415649 | + | 1.05460i | ||||
\(379\) | 168223. | + | 168223.i | 1.17114 | + | 1.17114i | 0.981939 | + | 0.189199i | \(0.0605890\pi\) |
0.189199 | + | 0.981939i | \(0.439411\pi\) | |||||||
\(380\) | 53546.9 | + | 49971.3i | 0.370824 | + | 0.346062i | ||||
\(381\) | −45996.6 | − | 45996.6i | −0.316866 | − | 0.316866i | ||||
\(382\) | −42985.9 | + | 18681.1i | −0.294577 | + | 0.128019i | ||||
\(383\) | − | 22177.8i | − | 0.151189i | −0.997139 | − | 0.0755946i | \(-0.975915\pi\) | ||
0.997139 | − | 0.0755946i | \(-0.0240855\pi\) | |||||||
\(384\) | 131141. | + | 232511.i | 0.889355 | + | 1.57681i | ||||
\(385\) | 43301.9 | 0.292137 | ||||||||
\(386\) | −109422. | − | 251784.i | −0.734395 | − | 1.68987i | ||||
\(387\) | 38015.4 | − | 38015.4i | 0.253827 | − | 0.253827i | ||||
\(388\) | −120607. | + | 129237.i | −0.801144 | + | 0.858468i | ||||
\(389\) | 163109. | − | 163109.i | 1.07790 | − | 1.07790i | 0.0812004 | − | 0.996698i | \(-0.474125\pi\) |
0.996698 | − | 0.0812004i | \(-0.0258754\pi\) | |||||||
\(390\) | 66508.0 | + | 26212.8i | 0.437265 | + | 0.172339i | ||||
\(391\) | 92975.9 | 0.608159 | ||||||||
\(392\) | 110018. | + | 39029.8i | 0.715962 | + | 0.253994i | ||||
\(393\) | − | 383416.i | − | 2.48248i | ||||||
\(394\) | −120442. | − | 47469.6i | −0.775861 | − | 0.305790i | ||||
\(395\) | 128382. | + | 128382.i | 0.822831 | + | 0.822831i | ||||
\(396\) | 8894.02 | + | 257494.i | 0.0567163 | + | 1.64201i | ||||
\(397\) | 110463. | + | 110463.i | 0.700868 | + | 0.700868i | 0.964597 | − | 0.263729i | \(-0.0849525\pi\) |
−0.263729 | + | 0.964597i | \(0.584953\pi\) | |||||||
\(398\) | 95557.5 | + | 219881.i | 0.603252 | + | 1.38810i | ||||
\(399\) | − | 86759.4i | − | 0.544968i | ||||||
\(400\) | 50717.2 | − | 3507.80i | 0.316982 | − | 0.0219237i | ||||
\(401\) | 43913.8 | 0.273094 | 0.136547 | − | 0.990634i | \(-0.456399\pi\) | ||||
0.136547 | + | 0.990634i | \(0.456399\pi\) | |||||||
\(402\) | −337729. | + | 146773.i | −2.08986 | + | 0.908224i | ||||
\(403\) | 8935.22 | − | 8935.22i | 0.0550168 | − | 0.0550168i | ||||
\(404\) | −5891.94 | − | 170580.i | −0.0360990 | − | 1.04512i | ||||
\(405\) | 182862. | − | 182862.i | 1.11484 | − | 1.11484i | ||||
\(406\) | −17447.8 | + | 44269.2i | −0.105850 | + | 0.268565i | ||||
\(407\) | −69236.7 | −0.417972 | ||||||||
\(408\) | −91197.7 | + | 43435.3i | −0.547852 | + | 0.260929i | ||||
\(409\) | − | 188666.i | − | 1.12784i | −0.825830 | − | 0.563919i | \(-0.809293\pi\) | ||
0.825830 | − | 0.563919i | \(-0.190707\pi\) | |||||||
\(410\) | −54606.5 | + | 138549.i | −0.324845 | + | 0.824208i | ||||
\(411\) | 123810. | + | 123810.i | 0.732948 | + | 0.732948i | ||||
\(412\) | 66861.0 | − | 71645.0i | 0.393893 | − | 0.422077i | ||||
\(413\) | −56524.0 | − | 56524.0i | −0.331385 | − | 0.331385i | ||||
\(414\) | 649487. | − | 282259.i | 3.78940 | − | 1.64682i | ||||
\(415\) | − | 6665.07i | − | 0.0386998i | ||||||
\(416\) | −51861.2 | − | 16405.9i | −0.299679 | − | 0.0948012i | ||||
\(417\) | −174743. | −1.00491 | ||||||||
\(418\) | −30853.0 | − | 70994.0i | −0.176582 | − | 0.406321i | ||||
\(419\) | −88556.3 | + | 88556.3i | −0.504419 | + | 0.504419i | −0.912808 | − | 0.408389i | \(-0.866091\pi\) |
0.408389 | + | 0.912808i | \(0.366091\pi\) | |||||||
\(420\) | 94536.4 | + | 88223.8i | 0.535921 | + | 0.500135i | ||||
\(421\) | −42983.4 | + | 42983.4i | −0.242514 | + | 0.242514i | −0.817889 | − | 0.575375i | \(-0.804856\pi\) |
0.575375 | + | 0.817889i | \(0.304856\pi\) | |||||||
\(422\) | −66094.8 | − | 26049.9i | −0.371144 | − | 0.146279i | ||||
\(423\) | −295123. | −1.64938 | ||||||||
\(424\) | 182565. | − | 86951.2i | 1.01551 | − | 0.483664i | ||||
\(425\) | 19237.5i | 0.106505i | ||||||||
\(426\) | 298873. | + | 117795.i | 1.64690 | + | 0.649092i | ||||
\(427\) | 106736. | + | 106736.i | 0.585403 | + | 0.585403i | ||||
\(428\) | −104856. | + | 3621.80i | −0.572408 | + | 0.0197714i | ||||
\(429\) | −53424.5 | − | 53424.5i | −0.290286 | − | 0.290286i | ||||
\(430\) | −9595.25 | − | 22079.0i | −0.0518942 | − | 0.119411i | ||||
\(431\) | 163696.i | 0.881219i | 0.897699 | + | 0.440609i | \(0.145238\pi\) | ||||
−0.897699 | + | 0.440609i | \(0.854762\pi\) | |||||||
\(432\) | −283359. | + | 325468.i | −1.51834 | + | 1.74398i | ||||
\(433\) | 49710.2 | 0.265137 | 0.132568 | − | 0.991174i | \(-0.457678\pi\) | ||||
0.132568 | + | 0.991174i | \(0.457678\pi\) | |||||||
\(434\) | 20962.9 | − | 9110.18i | 0.111294 | − | 0.0483668i | ||||
\(435\) | 117816. | − | 117816.i | 0.622626 | − | 0.622626i | ||||
\(436\) | −344537. | + | 11900.5i | −1.81244 | + | 0.0626028i | ||||
\(437\) | −150447. | + | 150447.i | −0.787809 | + | 0.787809i | ||||
\(438\) | 63364.8 | − | 160772.i | 0.330294 | − | 0.838032i | ||||
\(439\) | 182166. | 0.945233 | 0.472617 | − | 0.881268i | \(-0.343310\pi\) | ||||
0.472617 | + | 0.881268i | \(0.343310\pi\) | |||||||
\(440\) | 108732. | + | 38573.6i | 0.561630 | + | 0.199244i | ||||
\(441\) | 336455.i | 1.73002i | ||||||||
\(442\) | 7547.37 | − | 19149.5i | 0.0386324 | − | 0.0980194i | ||||
\(443\) | −3141.28 | − | 3141.28i | −0.0160066 | − | 0.0160066i | 0.699058 | − | 0.715065i | \(-0.253603\pi\) |
−0.715065 | + | 0.699058i | \(0.753603\pi\) | |||||||
\(444\) | −151157. | − | 141063.i | −0.766765 | − | 0.715564i | ||||
\(445\) | −154729. | − | 154729.i | −0.781359 | − | 0.781359i | ||||
\(446\) | −83501.6 | + | 36288.7i | −0.419783 | + | 0.182432i | ||||
\(447\) | − | 78004.9i | − | 0.390397i | ||||||
\(448\) | −76392.7 | − | 62005.8i | −0.380624 | − | 0.308941i | ||||
\(449\) | −108328. | −0.537341 | −0.268670 | − | 0.963232i | \(-0.586584\pi\) | ||||
−0.268670 | + | 0.963232i | \(0.586584\pi\) | |||||||
\(450\) | 58401.7 | + | 134384.i | 0.288403 | + | 0.663627i | ||||
\(451\) | 111294. | − | 111294.i | 0.547165 | − | 0.547165i | ||||
\(452\) | −31680.8 | + | 33947.7i | −0.155067 | + | 0.166162i | ||||
\(453\) | 249978. | − | 249978.i | 1.21816 | − | 1.21816i | ||||
\(454\) | 34104.8 | + | 13441.7i | 0.165464 | + | 0.0652143i | ||||
\(455\) | −26348.7 | −0.127273 | ||||||||
\(456\) | 77285.7 | − | 217854.i | 0.371680 | − | 1.04770i | ||||
\(457\) | 220908.i | 1.05774i | 0.848703 | + | 0.528870i | \(0.177384\pi\) | ||||
−0.848703 | + | 0.528870i | \(0.822616\pi\) | |||||||
\(458\) | 189824. | + | 74815.1i | 0.904939 | + | 0.356663i | ||||
\(459\) | −115467. | − | 115467.i | −0.548066 | − | 0.548066i | ||||
\(460\) | −10946.6 | − | 316920.i | −0.0517326 | − | 1.49773i | ||||
\(461\) | −137539. | − | 137539.i | −0.647176 | − | 0.647176i | 0.305133 | − | 0.952310i | \(-0.401299\pi\) |
−0.952310 | + | 0.305133i | \(0.901299\pi\) | |||||||
\(462\) | −54470.6 | − | 125339.i | −0.255199 | − | 0.587222i | ||||
\(463\) | − | 53332.6i | − | 0.248789i | −0.992233 | − | 0.124394i | \(-0.960301\pi\) | ||
0.992233 | − | 0.124394i | \(-0.0396988\pi\) | |||||||
\(464\) | −83246.8 | + | 95617.8i | −0.386662 | + | 0.444123i | ||||
\(465\) | −80035.3 | −0.370148 | ||||||||
\(466\) | −250291. | + | 108773.i | −1.15259 | + | 0.500899i | ||||
\(467\) | −207164. | + | 207164.i | −0.949908 | + | 0.949908i | −0.998804 | − | 0.0488961i | \(-0.984430\pi\) |
0.0488961 | + | 0.998804i | \(0.484430\pi\) | |||||||
\(468\) | −5411.90 | − | 156682.i | −0.0247092 | − | 0.715364i | ||||
\(469\) | 95973.3 | − | 95973.3i | 0.436320 | − | 0.436320i | ||||
\(470\) | −48457.2 | + | 122947.i | −0.219363 | + | 0.556575i | ||||
\(471\) | 327485. | 1.47622 | ||||||||
\(472\) | −91580.5 | − | 192284.i | −0.411073 | − | 0.863097i | ||||
\(473\) | 25443.3i | 0.113724i | ||||||||
\(474\) | 210111. | − | 533102.i | 0.935175 | − | 2.37276i | ||||
\(475\) | −31128.8 | − | 31128.8i | −0.137967 | − | 0.137967i | ||||
\(476\) | 25402.0 | − | 27219.6i | 0.112113 | − | 0.120134i | ||||
\(477\) | 412116. | + | 412116.i | 1.81127 | + | 1.81127i | ||||
\(478\) | −368894. | + | 160316.i | −1.61453 | + | 0.701653i | ||||
\(479\) | − | 269434.i | − | 1.17430i | −0.809477 | − | 0.587152i | \(-0.800249\pi\) | ||
0.809477 | − | 0.587152i | \(-0.199751\pi\) | |||||||
\(480\) | 158792. | + | 305744.i | 0.689200 | + | 1.32702i | ||||
\(481\) | 42129.6 | 0.182095 | ||||||||
\(482\) | −56698.2 | − | 130465.i | −0.244048 | − | 0.561564i | ||||
\(483\) | −265613. | + | 265613.i | −1.13856 | + | 1.13856i | ||||
\(484\) | 82118.2 | + | 76634.8i | 0.350549 | + | 0.327141i | ||||
\(485\) | −161322. | + | 161322.i | −0.685821 | + | 0.685821i | ||||
\(486\) | −251208. | − | 99008.4i | −1.06356 | − | 0.419179i | ||||
\(487\) | −114893. | −0.484436 | −0.242218 | − | 0.970222i | \(-0.577875\pi\) | ||||
−0.242218 | + | 0.970222i | \(0.577875\pi\) | |||||||
\(488\) | 172934. | + | 363096.i | 0.726174 | + | 1.52469i | ||||
\(489\) | 171667.i | 0.717910i | ||||||||
\(490\) | 140166. | + | 55243.7i | 0.583783 | + | 0.230086i | ||||
\(491\) | 83485.8 | + | 83485.8i | 0.346298 | + | 0.346298i | 0.858728 | − | 0.512431i | \(-0.171255\pi\) |
−0.512431 | + | 0.858728i | \(0.671255\pi\) | |||||||
\(492\) | 469727. | − | 16224.7i | 1.94051 | − | 0.0670265i | ||||
\(493\) | −33922.5 | − | 33922.5i | −0.139571 | − | 0.139571i | ||||
\(494\) | 18773.7 | + | 43198.9i | 0.0769300 | + | 0.177019i | ||||
\(495\) | 332522.i | 1.35710i | ||||||||
\(496\) | 60753.3 | − | 4201.94i | 0.246949 | − | 0.0170799i | ||||
\(497\) | −118405. | −0.479356 | ||||||||
\(498\) | −19292.3 | + | 8384.17i | −0.0777902 | + | 0.0338066i | ||||
\(499\) | −8291.04 | + | 8291.04i | −0.0332972 | + | 0.0332972i | −0.723559 | − | 0.690262i | \(-0.757495\pi\) |
0.690262 | + | 0.723559i | \(0.257495\pi\) | |||||||
\(500\) | 271948. | − | 9393.27i | 1.08779 | − | 0.0375731i | ||||
\(501\) | −46051.8 | + | 46051.8i | −0.183472 | + | 0.183472i | ||||
\(502\) | 60581.0 | − | 153708.i | 0.240397 | − | 0.609944i | ||||
\(503\) | 302384. | 1.19515 | 0.597575 | − | 0.801813i | \(-0.296131\pi\) | ||||
0.597575 | + | 0.801813i | \(0.296131\pi\) | |||||||
\(504\) | 94812.9 | − | 267260.i | 0.373255 | − | 1.05214i | ||||
\(505\) | − | 220283.i | − | 0.863770i | ||||||
\(506\) | −122891. | + | 311803.i | −0.479975 | + | 1.21781i | ||||
\(507\) | −296539. | − | 296539.i | −1.15363 | − | 1.15363i | ||||
\(508\) | 46701.8 | + | 43583.3i | 0.180970 | + | 0.168886i | ||||
\(509\) | −41954.6 | − | 41954.6i | −0.161936 | − | 0.161936i | 0.621488 | − | 0.783424i | \(-0.286529\pi\) |
−0.783424 | + | 0.621488i | \(0.786529\pi\) | |||||||
\(510\) | −119566. | + | 51961.6i | −0.459691 | + | 0.199776i | ||||
\(511\) | 63693.3i | 0.243923i | ||||||||
\(512\) | −136588. | − | 223748.i | −0.521041 | − | 0.853532i | ||||
\(513\) | 373681. | 1.41993 | ||||||||
\(514\) | 4675.71 | + | 10759.0i | 0.0176979 | + | 0.0407235i | ||||
\(515\) | 89431.9 | − | 89431.9i | 0.337193 | − | 0.337193i | ||||
\(516\) | −51838.4 | + | 55547.5i | −0.194694 | + | 0.208625i | ||||
\(517\) | 98761.0 | − | 98761.0i | 0.369492 | − | 0.369492i | ||||
\(518\) | 70897.4 | + | 27942.8i | 0.264223 | + | 0.104138i | ||||
\(519\) | −391635. | −1.45394 | ||||||||
\(520\) | −66161.8 | − | 23471.5i | −0.244681 | − | 0.0868030i | ||||
\(521\) | 16852.7i | 0.0620860i | 0.999518 | + | 0.0310430i | \(0.00988289\pi\) | ||||
−0.999518 | + | 0.0310430i | \(0.990117\pi\) | |||||||
\(522\) | −339950. | − | 133984.i | −1.24760 | − | 0.491715i | ||||
\(523\) | −92911.9 | − | 92911.9i | −0.339678 | − | 0.339678i | 0.516568 | − | 0.856246i | \(-0.327209\pi\) |
−0.856246 | + | 0.516568i | \(0.827209\pi\) | |||||||
\(524\) | 12997.6 | + | 376297.i | 0.0473369 | + | 1.37047i | ||||
\(525\) | −54957.5 | − | 54957.5i | −0.199392 | − | 0.199392i | ||||
\(526\) | 37073.1 | + | 85306.6i | 0.133995 | + | 0.308327i | ||||
\(527\) | 23044.3i | 0.0829741i | ||||||||
\(528\) | −25123.8 | − | 363250.i | −0.0901192 | − | 1.30298i | ||||
\(529\) | 641343. | 2.29181 | ||||||||
\(530\) | 239353. | − | 104020.i | 0.852094 | − | 0.370309i | ||||
\(531\) | 434057. | − | 434057.i | 1.53942 | − | 1.53942i | ||||
\(532\) | 2941.09 | + | 85148.6i | 0.0103917 | + | 0.300853i | ||||
\(533\) | −67720.9 | + | 67720.9i | −0.238379 | + | 0.238379i | ||||
\(534\) | −253230. | + | 642504.i | −0.888041 | + | 2.25317i | ||||
\(535\) | −135409. | −0.473086 | ||||||||
\(536\) | 326483. | − | 155496.i | 1.13640 | − | 0.541241i | ||||
\(537\) | − | 555796.i | − | 1.92738i | ||||||
\(538\) | −117892. | + | 299121.i | −0.407306 | + | 1.03343i | ||||
\(539\) | −112593. | − | 112593.i | −0.387554 | − | 0.387554i | ||||
\(540\) | −379989. | + | 407178.i | −1.30312 | + | 1.39636i | ||||
\(541\) | −40690.8 | − | 40690.8i | −0.139028 | − | 0.139028i | 0.634168 | − | 0.773196i | \(-0.281343\pi\) |
−0.773196 | + | 0.634168i | \(0.781343\pi\) | |||||||
\(542\) | 336331. | − | 146165.i | 1.14490 | − | 0.497559i | ||||
\(543\) | − | 318847.i | − | 1.08139i | ||||||
\(544\) | 88032.0 | − | 45720.4i | 0.297470 | − | 0.154494i | ||||
\(545\) | −444928. | −1.49795 | ||||||||
\(546\) | 33144.7 | + | 76267.2i | 0.111181 | + | 0.255831i | ||||
\(547\) | 222264. | − | 222264.i | 0.742839 | − | 0.742839i | −0.230284 | − | 0.973123i | \(-0.573966\pi\) |
0.973123 | + | 0.230284i | \(0.0739656\pi\) | |||||||
\(548\) | −125709. | − | 117315.i | −0.418605 | − | 0.390653i | ||||
\(549\) | −819641. | + | 819641.i | −2.71944 | + | 2.71944i | ||||
\(550\) | −64514.7 | − | 25427.2i | −0.213272 | − | 0.0840568i | ||||
\(551\) | 109782. | 0.361600 | ||||||||
\(552\) | −903565. | + | 430347.i | −2.96539 | + | 1.41234i | ||||
\(553\) | 211201.i | 0.690629i | ||||||||
\(554\) | −399087. | − | 157292.i | −1.30031 | − | 0.512492i | ||||
\(555\) | −188684. | − | 188684.i | −0.612560 | − | 0.612560i | ||||
\(556\) | 171499. | − | 5923.68i | 0.554768 | − | 0.0191621i | ||||
\(557\) | 223795. | + | 223795.i | 0.721341 | + | 0.721341i | 0.968878 | − | 0.247537i | \(-0.0796213\pi\) |
−0.247537 | + | 0.968878i | \(0.579621\pi\) | |||||||
\(558\) | 69958.5 | + | 160977.i | 0.224684 | + | 0.517006i | ||||
\(559\) | − | 15481.9i | − | 0.0495451i | ||||||
\(560\) | −95772.0 | − | 83381.1i | −0.305395 | − | 0.265883i | ||||
\(561\) | 137784. | 0.437798 | ||||||||
\(562\) | 284981. | − | 123849.i | 0.902283 | − | 0.392120i | ||||
\(563\) | 201474. | − | 201474.i | 0.635626 | − | 0.635626i | −0.313847 | − | 0.949474i | \(-0.601618\pi\) |
0.949474 | + | 0.313847i | \(0.101618\pi\) | |||||||
\(564\) | 416831. | − | 14397.6i | 1.31039 | − | 0.0452619i | ||||
\(565\) | −42375.6 | + | 42375.6i | −0.132745 | + | 0.132745i | ||||
\(566\) | 90923.9 | − | 230695.i | 0.283821 | − | 0.720121i | ||||
\(567\) | 300825. | 0.935724 | ||||||||
\(568\) | −297317. | − | 105476.i | −0.921559 | − | 0.326932i | ||||
\(569\) | − | 473995.i | − | 1.46403i | −0.681289 | − | 0.732014i | \(-0.738580\pi\) | ||
0.681289 | − | 0.732014i | \(-0.261420\pi\) | |||||||
\(570\) | 109392. | − | 277553.i | 0.336694 | − | 0.854273i | ||||
\(571\) | 303262. | + | 303262.i | 0.930133 | + | 0.930133i | 0.997714 | − | 0.0675806i | \(-0.0215280\pi\) |
−0.0675806 | + | 0.997714i | \(0.521528\pi\) | |||||||
\(572\) | 54243.7 | + | 50621.6i | 0.165790 | + | 0.154719i | ||||
\(573\) | 134995. | + | 134995.i | 0.411158 | + | 0.411158i | ||||
\(574\) | −158880. | + | 69047.0i | −0.482219 | + | 0.209566i | ||||
\(575\) | 190601.i | 0.576486i | ||||||||
\(576\) | 476152. | − | 586632.i | 1.43516 | − | 1.76816i | ||||
\(577\) | −340809. | −1.02367 | −0.511834 | − | 0.859084i | \(-0.671034\pi\) | ||||
−0.511834 | + | 0.859084i | \(0.671034\pi\) | |||||||
\(578\) | −118196. | − | 271974.i | −0.353792 | − | 0.814089i | ||||
\(579\) | −790714. | + | 790714.i | −2.35864 | + | 2.35864i | ||||
\(580\) | −111635. | + | 119623.i | −0.331852 | + | 0.355597i | ||||
\(581\) | 5482.33 | − | 5482.33i | 0.0162410 | − | 0.0162410i | ||||
\(582\) | 669884. | + | 264021.i | 1.97767 | + | 0.779458i | ||||
\(583\) | −275824. | −0.811512 | ||||||||
\(584\) | −56738.3 | + | 159935.i | −0.166361 | + | 0.468939i | ||||
\(585\) | − | 202336.i | − | 0.591236i | ||||||
\(586\) | 325859. | + | 128431.i | 0.948931 | + | 0.374002i | ||||
\(587\) | −253433. | − | 253433.i | −0.735507 | − | 0.735507i | 0.236198 | − | 0.971705i | \(-0.424099\pi\) |
−0.971705 | + | 0.236198i | \(0.924099\pi\) | |||||||
\(588\) | −16414.0 | − | 475209.i | −0.0474745 | − | 1.37445i | ||||
\(589\) | −37288.7 | − | 37288.7i | −0.107485 | − | 0.107485i | ||||
\(590\) | −109558. | − | 252096.i | −0.314730 | − | 0.724206i | ||||
\(591\) | 527316.i | 1.50972i | ||||||||
\(592\) | 153132. | + | 133320.i | 0.436942 | + | 0.380411i | ||||
\(593\) | 117236. | 0.333390 | 0.166695 | − | 0.986009i | \(-0.446691\pi\) | ||||
0.166695 | + | 0.986009i | \(0.446691\pi\) | |||||||
\(594\) | 539848. | − | 234611.i | 1.53002 | − | 0.664928i | ||||
\(595\) | 33977.2 | − | 33977.2i | 0.0959741 | − | 0.0959741i | ||||
\(596\) | 2644.32 | + | 76556.6i | 0.00744425 | + | 0.215521i | ||||
\(597\) | 690526. | − | 690526.i | 1.93745 | − | 1.93745i | ||||
\(598\) | 74777.6 | − | 189728.i | 0.209107 | − | 0.530554i | ||||
\(599\) | 277087. | 0.772257 | 0.386129 | − | 0.922445i | \(-0.373812\pi\) | ||||
0.386129 | + | 0.922445i | \(0.373812\pi\) | |||||||
\(600\) | −89042.5 | − | 186955.i | −0.247340 | − | 0.519320i | ||||
\(601\) | 323876.i | 0.896665i | 0.893867 | + | 0.448333i | \(0.147982\pi\) | ||||
−0.893867 | + | 0.448333i | \(0.852018\pi\) | |||||||
\(602\) | 10268.5 | − | 26053.5i | 0.0283343 | − | 0.0718909i | ||||
\(603\) | 736994. | + | 736994.i | 2.02689 | + | 2.02689i | ||||
\(604\) | −236863. | + | 253811.i | −0.649266 | + | 0.695723i | ||||
\(605\) | 102505. | + | 102505.i | 0.280050 | + | 0.280050i | ||||
\(606\) | −637617. | + | 277100.i | −1.73626 | + | 0.754555i | ||||
\(607\) | 715467.i | 1.94184i | 0.239414 | + | 0.970918i | \(0.423045\pi\) | ||||
−0.239414 | + | 0.970918i | \(0.576955\pi\) | |||||||
\(608\) | −68465.6 | + | 216429.i | −0.185210 | + | 0.585475i | ||||
\(609\) | 193819. | 0.522591 | ||||||||
\(610\) | 206881. | + | 476040.i | 0.555982 | + | 1.27933i | ||||
\(611\) | −60094.8 | + | 60094.8i | −0.160974 | + | 0.160974i | ||||
\(612\) | 209023. | + | 195066.i | 0.558074 | + | 0.520809i | ||||
\(613\) | 137200. | − | 137200.i | 0.365117 | − | 0.365117i | −0.500576 | − | 0.865693i | \(-0.666878\pi\) |
0.865693 | + | 0.500576i | \(0.166878\pi\) | |||||||
\(614\) | −524697. | − | 206799.i | −1.39178 | − | 0.548544i | ||||
\(615\) | 606596. | 1.60380 | ||||||||
\(616\) | 57708.2 | + | 121165.i | 0.152082 | + | 0.319313i | ||||
\(617\) | 106650.i | 0.280149i | 0.990141 | + | 0.140074i | \(0.0447342\pi\) | ||||
−0.990141 | + | 0.140074i | \(0.955266\pi\) | |||||||
\(618\) | −371362. | − | 146365.i | −0.972347 | − | 0.383231i | ||||
\(619\) | −373667. | − | 373667.i | −0.975221 | − | 0.975221i | 0.0244790 | − | 0.999700i | \(-0.492207\pi\) |
−0.999700 | + | 0.0244790i | \(0.992207\pi\) | |||||||
\(620\) | 78549.3 | − | 2713.15i | 0.204343 | − | 0.00705814i | ||||
\(621\) | −1.14402e6 | − | 1.14402e6i | −2.96654 | − | 2.96654i | ||||
\(622\) | −203557. | − | 468392.i | −0.526144 | − | 1.21068i | ||||
\(623\) | − | 254543.i | − | 0.655820i | ||||||
\(624\) | 15287.5 | + | 221033.i | 0.0392616 | + | 0.567660i | ||||
\(625\) | 227071. | 0.581302 | ||||||||
\(626\) | 88531.2 | − | 38474.5i | 0.225916 | − | 0.0981803i | ||||
\(627\) | −222953. | + | 222953.i | −0.567124 | + | 0.567124i | ||||
\(628\) | −321405. | + | 11101.5i | −0.814954 | + | 0.0281491i | ||||
\(629\) | −54327.1 | + | 54327.1i | −0.137314 | + | 0.137314i | ||||
\(630\) | 134200. | − | 340498.i | 0.338122 | − | 0.857894i | ||||
\(631\) | −445762. | −1.11955 | −0.559777 | − | 0.828644i | \(-0.689113\pi\) | ||||
−0.559777 | + | 0.828644i | \(0.689113\pi\) | |||||||
\(632\) | −188138. | + | 530327.i | −0.471024 | + | 1.32773i | ||||
\(633\) | 289376.i | 0.722195i | ||||||||
\(634\) | 132210. | − | 335449.i | 0.328917 | − | 0.834540i | ||||
\(635\) | 58296.2 | + | 58296.2i | 0.144575 | + | 0.144575i | ||||
\(636\) | −602177. | − | 561967.i | −1.48871 | − | 1.38930i | ||||
\(637\) | 68511.2 | + | 68511.2i | 0.168843 | + | 0.168843i | ||||
\(638\) | 158599. | − | 68925.2i | 0.389637 | − | 0.169331i | ||||
\(639\) | − | 909253.i | − | 2.22681i | ||||||
\(640\) | −166208. | − | 294685.i | −0.405782 | − | 0.719445i | ||||
\(641\) | −412550. | −1.00406 | −0.502031 | − | 0.864850i | \(-0.667414\pi\) | ||||
−0.502031 | + | 0.864850i | \(0.667414\pi\) | |||||||
\(642\) | 170334. | + | 391946.i | 0.413269 | + | 0.950946i | ||||
\(643\) | −71290.0 | + | 71290.0i | −0.172428 | + | 0.172428i | −0.788045 | − | 0.615617i | \(-0.788907\pi\) |
0.615617 | + | 0.788045i | \(0.288907\pi\) | |||||||
\(644\) | 251677. | − | 269685.i | 0.606837 | − | 0.650258i | ||||
\(645\) | −69338.0 | + | 69338.0i | −0.166668 | + | 0.166668i | ||||
\(646\) | −79915.1 | − | 31496.9i | −0.191498 | − | 0.0754750i | ||||
\(647\) | 138722. | 0.331388 | 0.165694 | − | 0.986177i | \(-0.447014\pi\) | ||||
0.165694 | + | 0.986177i | \(0.447014\pi\) | |||||||
\(648\) | 755375. | + | 267976.i | 1.79892 | + | 0.638185i | ||||
\(649\) | 290509.i | 0.689716i | ||||||||
\(650\) | 39256.4 | + | 15472.1i | 0.0929146 | + | 0.0366204i | ||||
\(651\) | −65832.7 | − | 65832.7i | −0.155339 | − | 0.155339i | ||||
\(652\) | −5819.42 | − | 168480.i | −0.0136894 | − | 0.396327i | ||||
\(653\) | 467444. | + | 467444.i | 1.09623 | + | 1.09623i | 0.994847 | + | 0.101387i | \(0.0323281\pi\) |
0.101387 | + | 0.994847i | \(0.467672\pi\) | |||||||
\(654\) | 559686. | + | 1.28786e6i | 1.30855 | + | 3.01101i | ||||
\(655\) | 485943.i | 1.13267i | ||||||||
\(656\) | −460456. | + | 31846.9i | −1.06999 | + | 0.0740048i | ||||
\(657\) | −489111. | −1.13312 | ||||||||
\(658\) | −140988. | + | 61271.6i | −0.325635 | + | 0.141517i | ||||
\(659\) | 180573. | − | 180573.i | 0.415797 | − | 0.415797i | −0.467955 | − | 0.883752i | \(-0.655009\pi\) |
0.883752 | + | 0.467955i | \(0.155009\pi\) | |||||||
\(660\) | −16222.2 | − | 469654.i | −0.0372410 | − | 1.07818i | ||||
\(661\) | 142726. | − | 142726.i | 0.326664 | − | 0.326664i | −0.524652 | − | 0.851317i | \(-0.675805\pi\) |
0.851317 | + | 0.524652i | \(0.175805\pi\) | |||||||
\(662\) | 230793. | − | 585576.i | 0.526631 | − | 1.33619i | ||||
\(663\) | −83840.0 | −0.190732 | ||||||||
\(664\) | 18649.9 | − | 8882.50i | 0.0422999 | − | 0.0201465i | ||||
\(665\) | 109959.i | 0.248650i | ||||||||
\(666\) | −214577. | + | 544432.i | −0.483765 | + | 1.22743i | ||||
\(667\) | −336097. | − | 336097.i | −0.755462 | − | 0.755462i | ||||
\(668\) | 43635.6 | − | 46757.9i | 0.0977886 | − | 0.104786i | ||||
\(669\) | 262232. | + | 262232.i | 0.585914 | + | 0.585914i | ||||
\(670\) | 428039. | − | 186020.i | 0.953529 | − | 0.414391i | ||||
\(671\) | − | 548576.i | − | 1.21841i | ||||||
\(672\) | −120875. | + | 382102.i | −0.267669 | + | 0.846138i | ||||
\(673\) | −272445. | −0.601517 | −0.300759 | − | 0.953700i | \(-0.597240\pi\) | ||||
−0.300759 | + | 0.953700i | \(0.597240\pi\) | |||||||
\(674\) | −142185. | − | 327173.i | −0.312993 | − | 0.720208i | ||||
\(675\) | 236708. | − | 236708.i | 0.519523 | − | 0.519523i | ||||
\(676\) | 301086. | + | 280981.i | 0.658866 | + | 0.614871i | ||||
\(677\) | 285404. | − | 285404.i | 0.622706 | − | 0.622706i | −0.323517 | − | 0.946222i | \(-0.604865\pi\) |
0.946222 | + | 0.323517i | \(0.104865\pi\) | |||||||
\(678\) | 175963. | + | 69352.3i | 0.382792 | + | 0.150870i | ||||
\(679\) | −265390. | −0.575632 | ||||||||
\(680\) | 115584. | − | 55050.1i | 0.249966 | − | 0.119053i | ||||
\(681\) | − | 149317.i | − | 0.321970i | ||||||
\(682\) | −77281.2 | − | 30458.8i | −0.166152 | − | 0.0654854i | ||||
\(683\) | 186551. | + | 186551.i | 0.399904 | + | 0.399904i | 0.878199 | − | 0.478295i | \(-0.158745\pi\) |
−0.478295 | + | 0.878199i | \(0.658745\pi\) | |||||||
\(684\) | −653869. | + | 22585.1i | −1.39759 | + | 0.0482736i | ||||
\(685\) | −156918. | − | 156918.i | −0.334419 | − | 0.334419i | ||||
\(686\) | 161803. | + | 372315.i | 0.343826 | + | 0.791155i | ||||
\(687\) | − | 831084.i | − | 1.76089i | ||||||
\(688\) | 48992.9 | − | 56273.5i | 0.103504 | − | 0.118885i | ||||
\(689\) | 167836. | 0.353546 | ||||||||
\(690\) | −1.18463e6 | + | 514823.i | −2.48819 | + | 1.08133i | ||||
\(691\) | 544261. | − | 544261.i | 1.13986 | − | 1.13986i | 0.151383 | − | 0.988475i | \(-0.451627\pi\) |
0.988475 | − | 0.151383i | \(-0.0483727\pi\) | |||||||
\(692\) | 384364. | − | 13276.2i | 0.802657 | − | 0.0277243i | ||||
\(693\) | −273515. | + | 273515.i | −0.569528 | + | 0.569528i | ||||
\(694\) | 35419.2 | − | 89866.9i | 0.0735394 | − | 0.186587i | ||||
\(695\) | 221470. | 0.458506 | ||||||||
\(696\) | 486682. | + | 172655.i | 1.00468 | + | 0.356419i | ||||
\(697\) | − | 174655.i | − | 0.359514i | ||||||
\(698\) | 53850.9 | − | 136632.i | 0.110531 | − | 0.280442i | ||||
\(699\) | 786027. | + | 786027.i | 1.60873 | + | 1.60873i | ||||
\(700\) | 55800.2 | + | 52074.1i | 0.113878 | + | 0.106274i | ||||
\(701\) | −69213.2 | − | 69213.2i | −0.140849 | − | 0.140849i | 0.633167 | − | 0.774015i | \(-0.281755\pi\) |
−0.774015 | + | 0.633167i | \(0.781755\pi\) | |||||||
\(702\) | −328490. | + | 142758.i | −0.666574 | + | 0.289684i | ||||
\(703\) | − | 175817.i | − | 0.355754i | ||||||
\(704\) | 36971.3 | + | 355654.i | 0.0745967 | + | 0.717600i | ||||
\(705\) | 538287. | 1.08302 | ||||||||
\(706\) | 353771. | + | 814040.i | 0.709762 | + | 1.63319i | ||||
\(707\) | 181193. | − | 181193.i | 0.362496 | − | 0.362496i | ||||
\(708\) | −591886. | + | 634237.i | −1.18079 | + | 1.26528i | ||||
\(709\) | 133745. | − | 133745.i | 0.266063 | − | 0.266063i | −0.561448 | − | 0.827512i | \(-0.689756\pi\) |
0.827512 | + | 0.561448i | \(0.189756\pi\) | |||||||
\(710\) | −378792. | − | 149293.i | −0.751423 | − | 0.296158i | ||||
\(711\) | −1.62184e6 | −3.20826 | ||||||||
\(712\) | 226748. | − | 639160.i | 0.447284 | − | 1.26081i | ||||
\(713\) | 228318.i | 0.449118i | ||||||||
\(714\) | −141089. | − | 55607.4i | −0.276756 | − | 0.109078i | ||||
\(715\) | 67710.4 | + | 67710.4i | 0.132447 | + | 0.132447i | ||||
\(716\) | 18841.2 | + | 545477.i | 0.0367520 | + | 1.06402i | ||||
\(717\) | 1.15849e6 | + | 1.15849e6i | 2.25349 | + | 2.25349i | ||||
\(718\) | −170320. | − | 391912.i | −0.330382 | − | 0.760221i | ||||
\(719\) | 762270.i | 1.47452i | 0.675609 | + | 0.737261i | \(0.263881\pi\) | ||||
−0.675609 | + | 0.737261i | \(0.736119\pi\) | |||||||
\(720\) | 640296. | − | 735448.i | 1.23514 | − | 1.41869i | ||||
\(721\) | 147124. | 0.283017 | ||||||||
\(722\) | −297809. | + | 129424.i | −0.571299 | + | 0.248279i | ||||
\(723\) | −409718. | + | 409718.i | −0.783805 | + | 0.783805i | ||||
\(724\) | 10808.7 | + | 312927.i | 0.0206204 | + | 0.596988i | ||||
\(725\) | 69541.2 | − | 69541.2i | 0.132302 | − | 0.132302i | ||||
\(726\) | 167761. | − | 425649.i | 0.318286 | − | 0.807566i | ||||
\(727\) | −664888. | −1.25800 | −0.628999 | − | 0.777406i | \(-0.716535\pi\) | ||||
−0.628999 | + | 0.777406i | \(0.716535\pi\) | |||||||
\(728\) | −35114.7 | − | 73727.6i | −0.0662562 | − | 0.139113i | ||||
\(729\) | 85436.8i | 0.160764i | ||||||||
\(730\) | −80308.8 | + | 203762.i | −0.150701 | + | 0.382365i | ||||
\(731\) | 19964.3 | + | 19964.3i | 0.0373610 | + | 0.0373610i | ||||
\(732\) | 1.11767e6 | − | 1.19765e6i | 2.08590 | − | 2.23515i | ||||
\(733\) | −616942. | − | 616942.i | −1.14825 | − | 1.14825i | −0.986897 | − | 0.161352i | \(-0.948414\pi\) |
−0.161352 | − | 0.986897i | \(-0.551586\pi\) | |||||||
\(734\) | 290090. | − | 126069.i | 0.538444 | − | 0.234001i | ||||
\(735\) | − | 613675.i | − | 1.13596i | ||||||
\(736\) | 872201. | − | 452987.i | 1.61013 | − | 0.836239i | ||||
\(737\) | −493261. | −0.908117 | ||||||||
\(738\) | −530223. | − | 1.22006e6i | −0.973521 | − | 2.24011i | ||||
\(739\) | −204895. | + | 204895.i | −0.375182 | + | 0.375182i | −0.869360 | − | 0.494179i | \(-0.835469\pi\) |
0.494179 | + | 0.869360i | \(0.335469\pi\) | |||||||
\(740\) | 191577. | + | 178784.i | 0.349848 | + | 0.326487i | ||||
\(741\) | 135664. | − | 135664.i | 0.247075 | − | 0.247075i | ||||
\(742\) | 282440. | + | 111318.i | 0.513001 | + | 0.202189i | ||||
\(743\) | 183598. | 0.332576 | 0.166288 | − | 0.986077i | \(-0.446822\pi\) | ||||
0.166288 | + | 0.986077i | \(0.446822\pi\) | |||||||
\(744\) | −106663. | − | 223951.i | −0.192693 | − | 0.404582i | ||||
\(745\) | 98863.7i | 0.178125i | ||||||||
\(746\) | −454401. | − | 179093.i | −0.816511 | − | 0.321811i | ||||
\(747\) | 42099.7 | + | 42099.7i | 0.0754462 | + | 0.0754462i | ||||
\(748\) | −135226. | + | 4670.80i | −0.241689 | + | 0.00834811i | ||||
\(749\) | −111380. | − | 111380.i | −0.198538 | − | 0.198538i | ||||
\(750\) | −441769. | − | 1.01653e6i | −0.785366 | − | 1.80716i | ||||
\(751\) | 167996.i | 0.297864i | 0.988847 | + | 0.148932i | \(0.0475836\pi\) | ||||
−0.988847 | + | 0.148932i | \(0.952416\pi\) | |||||||
\(752\) | −408604. | + | 28260.6i | −0.722548 | + | 0.0499742i | ||||
\(753\) | −672964. | −1.18687 | ||||||||
\(754\) | −96505.7 | + | 41940.1i | −0.169750 | + | 0.0737712i | ||||
\(755\) | −316823. | + | 316823.i | −0.555805 | + | 0.555805i | ||||
\(756\) | −647481. | + | 22364.4i | −1.13288 | + | 0.0391304i | ||||
\(757\) | −414105. | + | 414105.i | −0.722634 | + | 0.722634i | −0.969141 | − | 0.246507i | \(-0.920717\pi\) |
0.246507 | + | 0.969141i | \(0.420717\pi\) | |||||||
\(758\) | −348936. | + | 885333.i | −0.607306 | + | 1.54088i | ||||
\(759\) | 1.36513e6 | 2.36969 | ||||||||
\(760\) | −97952.1 | + | 276109.i | −0.169585 | + | 0.478027i | ||||
\(761\) | 315375.i | 0.544575i | 0.962216 | + | 0.272287i | \(0.0877801\pi\) | ||||
−0.962216 | + | 0.272287i | \(0.912220\pi\) | |||||||
\(762\) | 95408.1 | − | 242073.i | 0.164314 | − | 0.416904i | ||||
\(763\) | −365974. | − | 365974.i | −0.628638 | − | 0.628638i | ||||
\(764\) | −137065. | − | 127912.i | −0.234822 | − | 0.219142i | ||||
\(765\) | 260916. | + | 260916.i | 0.445839 | + | 0.445839i | ||||
\(766\) | 81360.2 | − | 35358.1i | 0.138661 | − | 0.0602603i | ||||
\(767\) | − | 176771.i | − | 0.300483i | ||||||
\(768\) | −643898. | + | 851787.i | −1.09168 | + | 1.44414i | ||||
\(769\) | 156016. | 0.263825 | 0.131913 | − | 0.991261i | \(-0.457888\pi\) | ||||
0.131913 | + | 0.991261i | \(0.457888\pi\) | |||||||
\(770\) | 69036.3 | + | 158855.i | 0.116438 | + | 0.267929i | ||||
\(771\) | 33788.0 | − | 33788.0i | 0.0568400 | − | 0.0568400i | ||||
\(772\) | 749229. | − | 802838.i | 1.25713 | − | 1.34708i | ||||
\(773\) | −151026. | + | 151026.i | −0.252751 | + | 0.252751i | −0.822098 | − | 0.569347i | \(-0.807196\pi\) |
0.569347 | + | 0.822098i | \(0.307196\pi\) | |||||||
\(774\) | 200069. | + | 78853.2i | 0.333963 | + | 0.131625i | ||||
\(775\) | −47240.9 | −0.0786529 | ||||||||
\(776\) | −666397. | − | 236411.i | −1.10665 | − | 0.392594i | ||||
\(777\) | − | 310402.i | − | 0.514142i | ||||||
\(778\) | 858415. | + | 338327.i | 1.41820 | + | 0.558956i | ||||
\(779\) | 282615. | + | 282615.i | 0.465715 | + | 0.465715i | ||||
\(780\) | 9870.99 | + | 285779.i | 0.0162245 | + | 0.469722i | ||||
\(781\) | 304276. | + | 304276.i | 0.498845 | + | 0.498845i | ||||
\(782\) | 148232. | + | 341086.i | 0.242397 | + | 0.557764i | ||||
\(783\) | 834798.i | 1.36163i | ||||||||
\(784\) | 32218.6 | + | 465829.i | 0.0524172 | + | 0.757870i | ||||
\(785\) | −415056. | −0.673546 | ||||||||
\(786\) | 1.40658e6 | − | 611280.i | 2.27677 | − | 0.989453i | ||||
\(787\) | 95574.5 | − | 95574.5i | 0.154310 | − | 0.154310i | −0.625730 | − | 0.780040i | \(-0.715199\pi\) |
0.780040 | + | 0.625730i | \(0.215199\pi\) | |||||||
\(788\) | −17875.7 | − | 517526.i | −0.0287879 | − | 0.833450i | ||||
\(789\) | 267901. | − | 267901.i | 0.430348 | − | 0.430348i | ||||
\(790\) | −266296. | + | 675655.i | −0.426688 | + | 1.08261i | ||||
\(791\) | −69711.8 | −0.111418 | ||||||||
\(792\) | −930448. | + | 443151.i | −1.48334 | + | 0.706482i | ||||
\(793\) | 333802.i | 0.530814i | ||||||||
\(794\) | −229127. | + | 581350.i | −0.363442 | + | 0.922139i | ||||
\(795\) | −751676. | − | 751676.i | −1.18931 | − | 1.18931i | ||||
\(796\) | −654297. | + | 701113.i | −1.03264 | + | 1.10653i | ||||
\(797\) | −497721. | − | 497721.i | −0.783555 | − | 0.783555i | 0.196874 | − | 0.980429i | \(-0.436921\pi\) |
−0.980429 | + | 0.196874i | \(0.936921\pi\) | |||||||
\(798\) | 318281. | − | 138320.i | 0.499809 | − | 0.217210i | ||||
\(799\) | − | 154987.i | − | 0.242774i | ||||||
\(800\) | 93726.9 | + | 180466.i | 0.146448 | + | 0.281978i | ||||
\(801\) | 1.95467e6 | 3.04656 | ||||||||
\(802\) | 70011.8 | + | 161100.i | 0.108849 | + | 0.250464i | ||||
\(803\) | 163678. | − | 163678.i | 0.253840 | − | 0.253840i | ||||
\(804\) | −1.07688e6 | − | 1.00497e6i | −1.66593 | − | 1.55469i | ||||
\(805\) | 336638. | − | 336638.i | 0.519484 | − | 0.519484i | ||||
\(806\) | 47024.6 | + | 18533.8i | 0.0723861 | + | 0.0285295i | ||||
\(807\) | 1.30961e6 | 2.01092 | ||||||||
\(808\) | 616385. | − | 293570.i | 0.944125 | − | 0.449665i | ||||
\(809\) | − | 363878.i | − | 0.555979i | −0.960584 | − | 0.277990i | \(-0.910332\pi\) | ||
0.960584 | − | 0.277990i | \(-0.0896681\pi\) | |||||||
\(810\) | 962374. | + | 379300.i | 1.46681 | + | 0.578114i | ||||
\(811\) | −53046.1 | − | 53046.1i | −0.0806513 | − | 0.0806513i | 0.665630 | − | 0.746282i | \(-0.268163\pi\) |
−0.746282 | + | 0.665630i | \(0.768163\pi\) | |||||||
\(812\) | −190221. | + | 6570.35i | −0.288500 | + | 0.00996498i | ||||
\(813\) | −1.05623e6 | − | 1.05623e6i | −1.59800 | − | 1.59800i | ||||
\(814\) | −110384. | − | 253998.i | −0.166593 | − | 0.383337i | ||||
\(815\) | − | 217572.i | − | 0.327557i | ||||||
\(816\) | −304741. | − | 265314.i | −0.457668 | − | 0.398455i | ||||
\(817\) | −64609.6 | −0.0967950 | ||||||||
\(818\) | 692129. | − | 300790.i | 1.03438 | − | 0.449528i | ||||
\(819\) | 166430. | − | 166430.i | 0.248122 | − | 0.248122i | ||||
\(820\) | −595334. | + | 20563.2i | −0.885386 | + | 0.0305818i | ||||
\(821\) | −540562. | + | 540562.i | −0.801972 | + | 0.801972i | −0.983404 | − | 0.181432i | \(-0.941927\pi\) |
0.181432 | + | 0.983404i | \(0.441927\pi\) | |||||||
\(822\) | −256813. | + | 651595.i | −0.380078 | + | 0.964348i | ||||
\(823\) | 956590. | 1.41230 | 0.706148 | − | 0.708064i | \(-0.250431\pi\) | ||||
0.706148 | + | 0.708064i | \(0.250431\pi\) | |||||||
\(824\) | 369429. | + | 131059.i | 0.544098 | + | 0.193024i | ||||
\(825\) | 282458.i | 0.414998i | ||||||||
\(826\) | 117245. | − | 297477.i | 0.171843 | − | 0.436007i | ||||
\(827\) | −83207.7 | − | 83207.7i | −0.121661 | − | 0.121661i | 0.643655 | − | 0.765316i | \(-0.277417\pi\) |
−0.765316 | + | 0.643655i | \(0.777417\pi\) | |||||||
\(828\) | 2.07095e6 | + | 1.93267e6i | 3.02072 | + | 2.81901i | ||||
\(829\) | −673529. | − | 673529.i | −0.980048 | − | 0.980048i | 0.0197565 | − | 0.999805i | \(-0.493711\pi\) |
−0.999805 | + | 0.0197565i | \(0.993711\pi\) | |||||||
\(830\) | 24451.1 | − | 10626.1i | 0.0354930 | − | 0.0154248i | ||||
\(831\) | 1.74728e6i | 2.53023i | ||||||||
\(832\) | −22496.6 | − | 216411.i | −0.0324990 | − | 0.312632i | ||||
\(833\) | −176694. | −0.254642 | ||||||||
\(834\) | −278593. | − | 641052.i | −0.400532 | − | 0.921640i | ||||
\(835\) | 58366.2 | − | 58366.2i | 0.0837121 | − | 0.0837121i | ||||
\(836\) | 211255. | − | 226371.i | 0.302270 | − | 0.323898i | ||||
\(837\) | 283548. | − | 283548.i | 0.404740 | − | 0.404740i | ||||
\(838\) | −466058. | − | 183687.i | −0.663670 | − | 0.261572i | ||||
\(839\) | −488503. | −0.693975 | −0.346987 | − | 0.937870i | \(-0.612795\pi\) | ||||
−0.346987 | + | 0.937870i | \(0.612795\pi\) | |||||||
\(840\) | −172933. | + | 487466.i | −0.245087 | + | 0.690853i | ||||
\(841\) | − | 462029.i | − | 0.653247i | ||||||
\(842\) | −226215. | − | 89158.1i | −0.319078 | − | 0.125758i | ||||
\(843\) | −894967. | − | 894967.i | −1.25937 | − | 1.25937i | ||||
\(844\) | −9809.66 | − | 284003.i | −0.0137711 | − | 0.398692i | ||||
\(845\) | 375835. | + | 375835.i | 0.526361 | + | 0.526361i | ||||
\(846\) | −470514. | − | 1.08267e6i | −0.657403 | − | 1.51271i | ||||
\(847\) | 168631.i | 0.235055i | ||||||||
\(848\) | 610047. | + | 531120.i | 0.848343 | + | 0.738585i | ||||
\(849\) | −1.01003e6 | −1.40126 | ||||||||
\(850\) | −70573.7 | + | 30670.4i | −0.0976798 | + | 0.0424503i | ||||
\(851\) | −538260. | + | 538260.i | −0.743247 | + | 0.743247i | ||||
\(852\) | 44358.1 | + | 1.28423e6i | 0.0611074 | + | 1.76914i | ||||
\(853\) | −462565. | + | 462565.i | −0.635733 | + | 0.635733i | −0.949500 | − | 0.313767i | \(-0.898409\pi\) |
0.313767 | + | 0.949500i | \(0.398409\pi\) | |||||||
\(854\) | −221396. | + | 561734.i | −0.303567 | + | 0.770221i | ||||
\(855\) | −844393. | −1.15508 | ||||||||
\(856\) | −180459. | − | 378895.i | −0.246281 | − | 0.517096i | ||||
\(857\) | − | 1.08100e6i | − | 1.47185i | −0.677064 | − | 0.735924i | \(-0.736748\pi\) | ||
0.677064 | − | 0.735924i | \(-0.263252\pi\) | |||||||
\(858\) | 110815. | − | 281165.i | 0.150531 | − | 0.381932i | ||||
\(859\) | 911196. | + | 911196.i | 1.23488 | + | 1.23488i | 0.962066 | + | 0.272816i | \(0.0879549\pi\) |
0.272816 | + | 0.962066i | \(0.412045\pi\) | |||||||
\(860\) | 65700.1 | − | 70401.1i | 0.0888320 | − | 0.0951881i | ||||
\(861\) | 498953. | + | 498953.i | 0.673060 | + | 0.673060i | ||||
\(862\) | −600526. | + | 260981.i | −0.808197 | + | 0.351232i | ||||
\(863\) | − | 35108.9i | − | 0.0471406i | −0.999722 | − | 0.0235703i | \(-0.992497\pi\) | ||
0.999722 | − | 0.0235703i | \(-0.00750335\pi\) | |||||||
\(864\) | −1.64575e6 | − | 520622.i | −2.20464 | − | 0.697421i | ||||
\(865\) | 496359. | 0.663382 | ||||||||
\(866\) | 79253.0 | + | 182364.i | 0.105677 | + | 0.243166i | ||||
\(867\) | −854121. | + | 854121.i | −1.13627 | + | 1.13627i | ||||
\(868\) | 66842.2 | + | 62378.8i | 0.0887179 | + | 0.0827937i | ||||
\(869\) | 542740. | − | 542740.i | 0.718707 | − | 0.718707i | ||||
\(870\) | 620050. | + | 244380.i | 0.819196 | + | 0.322870i | ||||
\(871\) | 300143. | 0.395633 | ||||||||
\(872\) | −592952. | − | 1.24497e6i | −0.779807 | − | 1.63730i | ||||
\(873\) | − | 2.03797e6i | − | 2.67405i | ||||||
\(874\) | −791780. | − | 312064.i | −1.03653 | − | 0.408527i | ||||
\(875\) | 288868. | + | 288868.i | 0.377298 | + | 0.377298i | ||||
\(876\) | 690820. | − | 23861.4i | 0.900236 | − | 0.0310948i | ||||
\(877\) | 134545. | + | 134545.i | 0.174931 | + | 0.174931i | 0.789142 | − | 0.614211i | \(-0.210526\pi\) |
−0.614211 | + | 0.789142i | \(0.710526\pi\) | |||||||
\(878\) | 290428. | + | 668285.i | 0.376746 | + | 0.866907i | ||||
\(879\) | − | 1.42667e6i | − | 1.84649i | ||||||
\(880\) | 31842.0 | + | 460384.i | 0.0411183 | + | 0.594505i | ||||
\(881\) | 1.27287e6 | 1.63995 | 0.819975 | − | 0.572399i | \(-0.193987\pi\) | ||||
0.819975 | + | 0.572399i | \(0.193987\pi\) | |||||||
\(882\) | −1.23430e6 | + | 536410.i | −1.58666 | + | 0.689541i | ||||
\(883\) | 484264. | − | 484264.i | 0.621098 | − | 0.621098i | −0.324714 | − | 0.945812i | \(-0.605268\pi\) |
0.945812 | + | 0.324714i | \(0.105268\pi\) | |||||||
\(884\) | 82283.4 | − | 2842.12i | 0.105295 | − | 0.00363696i | ||||
\(885\) | −791695. | + | 791695.i | −1.01081 | + | 1.01081i | ||||
\(886\) | 6515.77 | − | 16532.1i | 0.00830039 | − | 0.0210600i | ||||
\(887\) | −66348.3 | −0.0843301 | −0.0421650 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421650 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(888\) | 276508. | − | 779423.i | 0.350656 | − | 0.988433i | ||||
\(889\) | 95902.7i | 0.121347i | ||||||||
\(890\) | 320945. | − | 814312.i | 0.405182 | − | 1.02804i | ||||
\(891\) | −773055. | − | 773055.i | −0.973767 | − | 0.973767i | ||||
\(892\) | −266253. | − | 248474.i | −0.334630 | − | 0.312285i | ||||
\(893\) | 250790. | + | 250790.i | 0.314490 | + | 0.314490i | ||||
\(894\) | 286164. | − | 124363.i | 0.358047 | − | 0.155603i | ||||
\(895\) | 704418.i | 0.879396i | ||||||||
\(896\) | 105678. | − | 379106.i | 0.131634 | − | 0.472220i | ||||
\(897\) | −830667. | −1.03239 | ||||||||
\(898\) | −172708. | − | 397407.i | −0.214171 | − | 0.492814i | ||||
\(899\) | 83302.4 | − | 83302.4i | 0.103071 | − | 0.103071i | ||||
\(900\) | −399885. | + | 428498.i | −0.493686 | + | 0.529010i | ||||
\(901\) | −216428. | + | 216428.i | −0.266602 | + | 0.266602i | ||||
\(902\) | 585722. | + | 230851.i | 0.719911 | + | 0.283738i | ||||
\(903\) | −114067. | −0.139890 | ||||||||
\(904\) | −175047. | − | 62099.6i | −0.214199 | − | 0.0759893i | ||||
\(905\) | 404107.i | 0.493401i | ||||||||
\(906\) | 1.31559e6 | + | 518515.i | 1.60275 | + | 0.631691i | ||||
\(907\) | 846133. | + | 846133.i | 1.02855 | + | 1.02855i | 0.999580 | + | 0.0289661i | \(0.00922147\pi\) |
0.0289661 | + | 0.999580i | \(0.490779\pi\) | |||||||
\(908\) | 5061.77 | + | 146545.i | 0.00613946 | + | 0.177746i | ||||
\(909\) | 1.39141e6 | + | 1.39141e6i | 1.68394 | + | 1.68394i | ||||
\(910\) | −42007.7 | − | 96661.3i | −0.0507278 | − | 0.116727i | ||||
\(911\) | 133938.i | 0.161386i | 0.996739 | + | 0.0806932i | \(0.0257134\pi\) | ||||
−0.996739 | + | 0.0806932i | \(0.974287\pi\) | |||||||
\(912\) | 922422. | − | 63798.3i | 1.10902 | − | 0.0767043i | ||||
\(913\) | −28176.8 | −0.0338026 | ||||||||
\(914\) | −810410. | + | 352194.i | −0.970091 | + | 0.421589i | ||||
\(915\) | 1.49498e6 | − | 1.49498e6i | 1.78564 | − | 1.78564i | ||||
\(916\) | 28173.2 | + | 815654.i | 0.0335773 | + | 0.972109i | ||||
\(917\) | −399711. | + | 399711.i | −0.475343 | + | 0.475343i | ||||
\(918\) | 239507. | − | 607685.i | 0.284205 | − | 0.721096i | ||||
\(919\) | −469228. | −0.555589 | −0.277794 | − | 0.960641i | \(-0.589603\pi\) | ||||
−0.277794 | + | 0.960641i | \(0.589603\pi\) | |||||||
\(920\) | 1.14518e6 | − | 545423.i | 1.35300 | − | 0.644404i | ||||
\(921\) | 2.29723e6i | 2.70822i | ||||||||
\(922\) | 285288. | − | 723844.i | 0.335600 | − | 0.851497i | ||||
\(923\) | −185148. | − | 185148.i | −0.217328 | − | 0.217328i | ||||
\(924\) | 372969. | − | 399656.i | 0.436846 | − | 0.468104i | ||||
\(925\) | −111371. | − | 111371.i | −0.130163 | − | 0.130163i | ||||
\(926\) | 195653. | − | 85028.1i | 0.228173 | − | 0.0991609i | ||||
\(927\) | 1.12979e6i | 1.31473i | ||||||||
\(928\) | −483499. | − | 152951.i | −0.561435 | − | 0.177606i | ||||
\(929\) | 728330. | 0.843911 | 0.421955 | − | 0.906617i | \(-0.361344\pi\) | ||||
0.421955 | + | 0.906617i | \(0.361344\pi\) | |||||||
\(930\) | −127600. | − | 293613.i | −0.147532 | − | 0.339476i | ||||
\(931\) | 285913. | − | 285913.i | 0.329864 | − | 0.329864i | ||||
\(932\) | −798079. | − | 744787.i | −0.918785 | − | 0.857434i | ||||
\(933\) | −1.47096e6 | + | 1.47096e6i | −1.68981 | + | 1.68981i | ||||
\(934\) | −1.09027e6 | − | 429709.i | −1.24980 | − | 0.492585i | ||||
\(935\) | −174628. | −0.199752 | ||||||||
\(936\) | 566166. | − | 269652.i | 0.646237 | − | 0.307788i | ||||
\(937\) | 572084.i | 0.651599i | 0.945439 | + | 0.325800i | \(0.105634\pi\) | ||||
−0.945439 | + | 0.325800i | \(0.894366\pi\) | |||||||
\(938\) | 505092. | + | 199072.i | 0.574070 | + | 0.226258i | ||||
\(939\) | −278028. | − | 278028.i | −0.315324 | − | 0.315324i | ||||
\(940\) | −528293. | + | 18247.6i | −0.597887 | + | 0.0206514i | ||||
\(941\) | −270062. | − | 270062.i | −0.304989 | − | 0.304989i | 0.537973 | − | 0.842962i | \(-0.319190\pi\) |
−0.842962 | + | 0.537973i | \(0.819190\pi\) | |||||||
\(942\) | 522109. | + | 1.20139e6i | 0.588382 | + | 1.35389i | ||||
\(943\) | − | 1.73044e6i | − | 1.94596i | ||||||
\(944\) | 559396. | − | 642526.i | 0.627734 | − | 0.721019i | ||||
\(945\) | −836144. | −0.936305 | ||||||||
\(946\) | −93339.7 | + | 40564.2i | −0.104300 | + | 0.0453274i | ||||
\(947\) | −803359. | + | 803359.i | −0.895797 | + | 0.895797i | −0.995061 | − | 0.0992642i | \(-0.968351\pi\) |
0.0992642 | + | 0.995061i | \(0.468351\pi\) | |||||||
\(948\) | 2.29069e6 | − | 79121.9i | 2.54888 | − | 0.0880400i | ||||
\(949\) | −99596.1 | + | 99596.1i | −0.110588 | + | 0.110588i | ||||
\(950\) | 64568.7 | − | 163826.i | 0.0715443 | − | 0.181525i | ||||
\(951\) | −1.46866e6 | −1.62390 | ||||||||
\(952\) | 140355. | + | 49792.1i | 0.154865 | + | 0.0549398i | ||||
\(953\) | 188445.i | 0.207491i | 0.994604 | + | 0.103746i | \(0.0330827\pi\) | ||||
−0.994604 | + | 0.103746i | \(0.966917\pi\) | |||||||
\(954\) | −854828. | + | 2.16890e6i | −0.939252 | + | 2.38310i | ||||
\(955\) | −171093. | − | 171093.i | −0.187597 | − | 0.187597i | ||||
\(956\) | −1.17626e6 | − | 1.09771e6i | −1.28702 | − | 1.20108i | ||||
\(957\) | −498073. | − | 498073.i | −0.543837 | − | 0.543837i | ||||
\(958\) | 988429. | − | 429558.i | 1.07700 | − | 0.468048i | ||||
\(959\) | − | 258144.i | − | 0.280689i | ||||||
\(960\) | −868474. | + | 1.06998e6i | −0.942355 | + | 1.16101i | ||||
\(961\) | 866932. | 0.938725 | ||||||||
\(962\) | 67167.3 | + | 154554.i | 0.0725785 | + | 0.167006i | ||||
\(963\) | 855306. | − | 855306.i | 0.922293 | − | 0.922293i | ||||
\(964\) | 388221. | − | 416000.i | 0.417759 | − | 0.447650i | ||||
\(965\) | 1.00215e6 | − | 1.00215e6i | 1.07617 | − | 1.07617i | ||||
\(966\) | −1.39788e6 | − | 550945.i | −1.49801 | − | 0.590411i | ||||
\(967\) | 1.17554e6 | 1.25715 | 0.628573 | − | 0.777751i | \(-0.283639\pi\) | ||||
0.628573 | + | 0.777751i | \(0.283639\pi\) | |||||||
\(968\) | −150217. | + | 423433.i | −0.160313 | + | 0.451891i | ||||
\(969\) | 349883.i | 0.372628i | ||||||||
\(970\) | −849013. | − | 334621.i | −0.902341 | − | 0.355640i | ||||
\(971\) | −784226. | − | 784226.i | −0.831769 | − | 0.831769i | 0.155989 | − | 0.987759i | \(-0.450143\pi\) |
−0.987759 | + | 0.155989i | \(0.950143\pi\) | |||||||
\(972\) | −37283.7 | − | 1.07942e6i | −0.0394627 | − | 1.14250i | ||||
\(973\) | 182169. | + | 182169.i | 0.192420 | + | 0.192420i | ||||
\(974\) | −183174. | − | 421491.i | −0.193084 | − | 0.444293i | ||||
\(975\) | − | 171872.i | − | 0.180799i | ||||||
\(976\) | −1.05632e6 | + | 1.21330e6i | −1.10891 | + | 1.27370i | ||||
\(977\) | 710097. | 0.743924 | 0.371962 | − | 0.928248i | \(-0.378685\pi\) | ||||
0.371962 | + | 0.928248i | \(0.378685\pi\) | |||||||
\(978\) | −629769. | + | 273689.i | −0.658421 | + | 0.286141i | ||||
\(979\) | −654120. | + | 654120.i | −0.682483 | + | 0.682483i | ||||
\(980\) | 20803.2 | + | 602281.i | 0.0216610 | + | 0.627115i | ||||
\(981\) | 2.81037e6 | − | 2.81037e6i | 2.92029 | − | 2.92029i | ||||
\(982\) | −173170. | + | 439373.i | −0.179576 | + | 0.455628i | ||||
\(983\) | 471799. | 0.488259 | 0.244129 | − | 0.969743i | \(-0.421498\pi\) | ||||
0.244129 | + | 0.969743i | \(0.421498\pi\) | |||||||
\(984\) | 808407. | + | 1.69735e6i | 0.834910 | + | 1.75299i | ||||
\(985\) | − | 668322.i | − | 0.688832i | ||||||
\(986\) | 70363.6 | − | 178529.i | 0.0723759 | − | 0.183635i | ||||
\(987\) | 442766. | + | 442766.i | 0.454506 | + | 0.454506i | ||||
\(988\) | −128546. | + | 137744.i | −0.131688 | + | 0.141110i | ||||
\(989\) | 197801. | + | 197801.i | 0.202226 | + | 0.202226i | ||||
\(990\) | −1.21987e6 | + | 530140.i | −1.24464 | + | 0.540904i | ||||
\(991\) | − | 1.06681e6i | − | 1.08627i | −0.839644 | − | 0.543137i | \(-0.817237\pi\) | ||
0.839644 | − | 0.543137i | \(-0.182763\pi\) | |||||||
\(992\) | 112274. | + | 216177.i | 0.114092 | + | 0.219678i | ||||
\(993\) | −2.56377e6 | −2.60004 | ||||||||
\(994\) | −188774. | − | 434375.i | −0.191059 | − | 0.439635i | ||||
\(995\) | −875175. | + | 875175.i | −0.883992 | + | 0.883992i | ||||
\(996\) | −61515.4 | − | 57407.7i | −0.0620105 | − | 0.0578697i | ||||
\(997\) | −303115. | + | 303115.i | −0.304942 | + | 0.304942i | −0.842944 | − | 0.538002i | \(-0.819179\pi\) |
0.538002 | + | 0.842944i | \(0.319179\pi\) | |||||||
\(998\) | −43634.4 | − | 17197.6i | −0.0438095 | − | 0.0172666i | ||||
\(999\) | 1.33693e6 | 1.33961 |
(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 | 16.5.f.a.3.5 | ✓ | 14 | |
3.2 | odd | 2 | 144.5.m.a.19.3 | 14 | |||
4.3 | odd | 2 | 64.5.f.a.47.1 | 14 | |||
8.3 | odd | 2 | 128.5.f.a.95.7 | 14 | |||
8.5 | even | 2 | 128.5.f.b.95.1 | 14 | |||
12.11 | even | 2 | 576.5.m.a.559.6 | 14 | |||
16.3 | odd | 4 | 128.5.f.b.31.1 | 14 | |||
16.5 | even | 4 | 64.5.f.a.15.1 | 14 | |||
16.11 | odd | 4 | inner | 16.5.f.a.11.5 | yes | 14 | |
16.13 | even | 4 | 128.5.f.a.31.7 | 14 | |||
48.5 | odd | 4 | 576.5.m.a.271.6 | 14 | |||
48.11 | even | 4 | 144.5.m.a.91.3 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.5.f.a.3.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
16.5.f.a.11.5 | yes | 14 | 16.11 | odd | 4 | inner | |
64.5.f.a.15.1 | 14 | 16.5 | even | 4 | |||
64.5.f.a.47.1 | 14 | 4.3 | odd | 2 | |||
128.5.f.a.31.7 | 14 | 16.13 | even | 4 | |||
128.5.f.a.95.7 | 14 | 8.3 | odd | 2 | |||
128.5.f.b.31.1 | 14 | 16.3 | odd | 4 | |||
128.5.f.b.95.1 | 14 | 8.5 | even | 2 | |||
144.5.m.a.19.3 | 14 | 3.2 | odd | 2 | |||
144.5.m.a.91.3 | 14 | 48.11 | even | 4 | |||
576.5.m.a.271.6 | 14 | 48.5 | odd | 4 | |||
576.5.m.a.559.6 | 14 | 12.11 | even | 2 |