Properties

Label 294.6.e.s.67.1
Level $294$
Weight $6$
Character 294.67
Analytic conductor $47.153$
Analytic rank $0$
Dimension $4$
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,6,Mod(67,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 294.e (of order \(3\), degree \(2\), not 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: \(47.1528430250\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{9601})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 2401x^{2} + 2400x + 5760000 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(24.7462 + 42.8616i\) of defining polynomial
Character \(\chi\) \(=\) 294.67
Dual form 294.6.e.s.79.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-37.7462 - 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(-37.7462 - 65.3783i) q^{5} +36.0000 q^{6} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(-150.985 + 261.513i) q^{10} +(74.7309 - 129.438i) q^{11} +(-72.0000 - 124.708i) q^{12} -349.416 q^{13} +679.431 q^{15} +(-128.000 - 221.703i) q^{16} +(-574.923 + 995.797i) q^{17} +(-162.000 + 280.592i) q^{18} +(-1397.60 - 2420.72i) q^{19} +1207.88 q^{20} -597.847 q^{22} +(-906.985 - 1570.94i) q^{23} +(-288.000 + 498.831i) q^{24} +(-1287.05 + 2229.23i) q^{25} +(698.832 + 1210.41i) q^{26} +729.000 q^{27} -759.033 q^{29} +(-1358.86 - 2353.62i) q^{30} +(4515.87 - 7821.72i) q^{31} +(-512.000 + 886.810i) q^{32} +(672.578 + 1164.94i) q^{33} +4599.39 q^{34} +1296.00 q^{36} +(-3897.45 - 6750.57i) q^{37} +(-5590.40 + 9682.86i) q^{38} +(1572.37 - 2723.43i) q^{39} +(-2415.76 - 4184.21i) q^{40} -7640.49 q^{41} +12188.8 q^{43} +(1195.69 + 2071.00i) q^{44} +(-3057.44 + 5295.64i) q^{45} +(-3627.94 + 6283.77i) q^{46} +(12299.4 + 21303.2i) q^{47} +2304.00 q^{48} +10296.4 q^{50} +(-5174.31 - 8962.17i) q^{51} +(2795.33 - 4841.65i) q^{52} +(-6798.11 + 11774.7i) q^{53} +(-1458.00 - 2525.33i) q^{54} -11283.2 q^{55} +25156.8 q^{57} +(1518.07 + 2629.37i) q^{58} +(-13179.4 + 22827.4i) q^{59} +(-5435.45 + 9414.47i) q^{60} +(17660.9 + 30589.5i) q^{61} -36127.0 q^{62} +4096.00 q^{64} +(13189.1 + 22844.2i) q^{65} +(2690.31 - 4659.76i) q^{66} +(-27186.0 + 47087.5i) q^{67} +(-9198.78 - 15932.7i) q^{68} +16325.7 q^{69} -70145.7 q^{71} +(-2592.00 - 4489.48i) q^{72} +(-22234.4 + 38511.1i) q^{73} +(-15589.8 + 27002.3i) q^{74} +(-11583.4 - 20063.1i) q^{75} +44723.2 q^{76} -12579.0 q^{78} +(-30806.2 - 53357.9i) q^{79} +(-9663.02 + 16736.8i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(15281.0 + 26467.5i) q^{82} +87142.0 q^{83} +86804.6 q^{85} +(-24377.7 - 42223.4i) q^{86} +(3415.65 - 5916.08i) q^{87} +(4782.78 - 8284.01i) q^{88} +(49284.7 + 85363.6i) q^{89} +24459.5 q^{90} +29023.5 q^{92} +(40642.9 + 70395.5i) q^{93} +(49197.6 - 85212.8i) q^{94} +(-105508. + 182745. i) q^{95} +(-4608.00 - 7981.29i) q^{96} -32342.3 q^{97} -12106.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 8 q^{2} - 18 q^{3} - 32 q^{4} - 53 q^{5} + 144 q^{6} + 256 q^{8} - 162 q^{9} - 212 q^{10} - 191 q^{11} - 288 q^{12} + 758 q^{13} + 954 q^{15} - 512 q^{16} - 340 q^{17} - 648 q^{18} - 1769 q^{19} + 1696 q^{20} + 1528 q^{22} - 3236 q^{23} - 1152 q^{24} + 45 q^{25} - 1516 q^{26} + 2916 q^{27} + 8918 q^{29} - 1908 q^{30} + 1994 q^{31} - 2048 q^{32} - 1719 q^{33} + 2720 q^{34} + 5184 q^{36} - 20587 q^{37} - 7076 q^{38} - 3411 q^{39} - 3392 q^{40} - 17628 q^{41} + 31706 q^{43} - 3056 q^{44} - 4293 q^{45} - 12944 q^{46} + 33912 q^{47} + 9216 q^{48} - 360 q^{50} - 3060 q^{51} - 6064 q^{52} - 49239 q^{53} - 5832 q^{54} - 37882 q^{55} + 31842 q^{57} - 17836 q^{58} - 56735 q^{59} - 7632 q^{60} + 67508 q^{61} - 15952 q^{62} + 16384 q^{64} + 42762 q^{65} - 6876 q^{66} - 75723 q^{67} - 5440 q^{68} + 58248 q^{69} - 17984 q^{71} - 10368 q^{72} - 3201 q^{73} - 82348 q^{74} + 405 q^{75} + 56608 q^{76} + 27288 q^{78} - 26612 q^{79} - 13568 q^{80} - 13122 q^{81} + 35256 q^{82} + 1898 q^{83} + 210040 q^{85} - 63412 q^{86} - 40131 q^{87} - 12224 q^{88} + 176562 q^{89} + 34344 q^{90} + 103552 q^{92} + 17946 q^{93} + 135648 q^{94} - 234098 q^{95} - 18432 q^{96} + 258846 q^{97} + 30942 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 3.46410i −0.353553 0.612372i
\(3\) −4.50000 + 7.79423i −0.288675 + 0.500000i
\(4\) −8.00000 + 13.8564i −0.250000 + 0.433013i
\(5\) −37.7462 65.3783i −0.675224 1.16952i −0.976403 0.215955i \(-0.930714\pi\)
0.301179 0.953568i \(-0.402620\pi\)
\(6\) 36.0000 0.408248
\(7\) 0 0
\(8\) 64.0000 0.353553
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) −150.985 + 261.513i −0.477456 + 0.826977i
\(11\) 74.7309 129.438i 0.186217 0.322537i −0.757769 0.652523i \(-0.773711\pi\)
0.943986 + 0.329986i \(0.107044\pi\)
\(12\) −72.0000 124.708i −0.144338 0.250000i
\(13\) −349.416 −0.573435 −0.286717 0.958015i \(-0.592564\pi\)
−0.286717 + 0.958015i \(0.592564\pi\)
\(14\) 0 0
\(15\) 679.431 0.779682
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) −574.923 + 995.797i −0.482489 + 0.835696i −0.999798 0.0201029i \(-0.993601\pi\)
0.517309 + 0.855799i \(0.326934\pi\)
\(18\) −162.000 + 280.592i −0.117851 + 0.204124i
\(19\) −1397.60 2420.72i −0.888176 1.53837i −0.842029 0.539432i \(-0.818639\pi\)
−0.0461468 0.998935i \(-0.514694\pi\)
\(20\) 1207.88 0.675224
\(21\) 0 0
\(22\) −597.847 −0.263350
\(23\) −906.985 1570.94i −0.357504 0.619214i 0.630040 0.776563i \(-0.283039\pi\)
−0.987543 + 0.157349i \(0.949705\pi\)
\(24\) −288.000 + 498.831i −0.102062 + 0.176777i
\(25\) −1287.05 + 2229.23i −0.411855 + 0.713354i
\(26\) 698.832 + 1210.41i 0.202740 + 0.351156i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −759.033 −0.167597 −0.0837984 0.996483i \(-0.526705\pi\)
−0.0837984 + 0.996483i \(0.526705\pi\)
\(30\) −1358.86 2353.62i −0.275659 0.477456i
\(31\) 4515.87 7821.72i 0.843990 1.46183i −0.0425050 0.999096i \(-0.513534\pi\)
0.886495 0.462738i \(-0.153133\pi\)
\(32\) −512.000 + 886.810i −0.0883883 + 0.153093i
\(33\) 672.578 + 1164.94i 0.107512 + 0.186217i
\(34\) 4599.39 0.682343
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) −3897.45 6750.57i −0.468032 0.810655i 0.531300 0.847183i \(-0.321704\pi\)
−0.999333 + 0.0365280i \(0.988370\pi\)
\(38\) −5590.40 + 9682.86i −0.628035 + 1.08779i
\(39\) 1572.37 2723.43i 0.165536 0.286717i
\(40\) −2415.76 4184.21i −0.238728 0.413489i
\(41\) −7640.49 −0.709842 −0.354921 0.934896i \(-0.615492\pi\)
−0.354921 + 0.934896i \(0.615492\pi\)
\(42\) 0 0
\(43\) 12188.8 1.00529 0.502645 0.864493i \(-0.332360\pi\)
0.502645 + 0.864493i \(0.332360\pi\)
\(44\) 1195.69 + 2071.00i 0.0931083 + 0.161268i
\(45\) −3057.44 + 5295.64i −0.225075 + 0.389841i
\(46\) −3627.94 + 6283.77i −0.252793 + 0.437851i
\(47\) 12299.4 + 21303.2i 0.812156 + 1.40670i 0.911352 + 0.411627i \(0.135039\pi\)
−0.0991964 + 0.995068i \(0.531627\pi\)
\(48\) 2304.00 0.144338
\(49\) 0 0
\(50\) 10296.4 0.582451
\(51\) −5174.31 8962.17i −0.278565 0.482489i
\(52\) 2795.33 4841.65i 0.143359 0.248305i
\(53\) −6798.11 + 11774.7i −0.332429 + 0.575783i −0.982988 0.183672i \(-0.941201\pi\)
0.650559 + 0.759456i \(0.274535\pi\)
\(54\) −1458.00 2525.33i −0.0680414 0.117851i
\(55\) −11283.2 −0.502952
\(56\) 0 0
\(57\) 25156.8 1.02558
\(58\) 1518.07 + 2629.37i 0.0592544 + 0.102632i
\(59\) −13179.4 + 22827.4i −0.492908 + 0.853742i −0.999967 0.00816991i \(-0.997399\pi\)
0.507059 + 0.861912i \(0.330733\pi\)
\(60\) −5435.45 + 9414.47i −0.194920 + 0.337612i
\(61\) 17660.9 + 30589.5i 0.607698 + 1.05256i 0.991619 + 0.129198i \(0.0412402\pi\)
−0.383921 + 0.923366i \(0.625427\pi\)
\(62\) −36127.0 −1.19358
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) 13189.1 + 22844.2i 0.387197 + 0.670645i
\(66\) 2690.31 4659.76i 0.0760226 0.131675i
\(67\) −27186.0 + 47087.5i −0.739874 + 1.28150i 0.212678 + 0.977122i \(0.431781\pi\)
−0.952552 + 0.304377i \(0.901552\pi\)
\(68\) −9198.78 15932.7i −0.241245 0.417848i
\(69\) 16325.7 0.412810
\(70\) 0 0
\(71\) −70145.7 −1.65141 −0.825706 0.564101i \(-0.809223\pi\)
−0.825706 + 0.564101i \(0.809223\pi\)
\(72\) −2592.00 4489.48i −0.0589256 0.102062i
\(73\) −22234.4 + 38511.1i −0.488335 + 0.845822i −0.999910 0.0134170i \(-0.995729\pi\)
0.511574 + 0.859239i \(0.329062\pi\)
\(74\) −15589.8 + 27002.3i −0.330949 + 0.573220i
\(75\) −11583.4 20063.1i −0.237785 0.411855i
\(76\) 44723.2 0.888176
\(77\) 0 0
\(78\) −12579.0 −0.234104
\(79\) −30806.2 53357.9i −0.555355 0.961903i −0.997876 0.0651450i \(-0.979249\pi\)
0.442521 0.896758i \(-0.354084\pi\)
\(80\) −9663.02 + 16736.8i −0.168806 + 0.292381i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 15281.0 + 26467.5i 0.250967 + 0.434688i
\(83\) 87142.0 1.38846 0.694228 0.719755i \(-0.255746\pi\)
0.694228 + 0.719755i \(0.255746\pi\)
\(84\) 0 0
\(85\) 86804.6 1.30315
\(86\) −24377.7 42223.4i −0.355423 0.615611i
\(87\) 3415.65 5916.08i 0.0483810 0.0837984i
\(88\) 4782.78 8284.01i 0.0658375 0.114034i
\(89\) 49284.7 + 85363.6i 0.659534 + 1.14235i 0.980736 + 0.195336i \(0.0625796\pi\)
−0.321203 + 0.947010i \(0.604087\pi\)
\(90\) 24459.5 0.318304
\(91\) 0 0
\(92\) 29023.5 0.357504
\(93\) 40642.9 + 70395.5i 0.487278 + 0.843990i
\(94\) 49197.6 85212.8i 0.574281 0.994684i
\(95\) −105508. + 182745.i −1.19944 + 2.07748i
\(96\) −4608.00 7981.29i −0.0510310 0.0883883i
\(97\) −32342.3 −0.349013 −0.174507 0.984656i \(-0.555833\pi\)
−0.174507 + 0.984656i \(0.555833\pi\)
\(98\) 0 0
\(99\) −12106.4 −0.124144
\(100\) −20592.8 35667.7i −0.205928 0.356677i
\(101\) 15673.2 27146.8i 0.152881 0.264798i −0.779404 0.626521i \(-0.784478\pi\)
0.932286 + 0.361723i \(0.117811\pi\)
\(102\) −20697.2 + 35848.7i −0.196975 + 0.341171i
\(103\) 49666.5 + 86024.8i 0.461286 + 0.798970i 0.999025 0.0441406i \(-0.0140549\pi\)
−0.537740 + 0.843111i \(0.680722\pi\)
\(104\) −22362.6 −0.202740
\(105\) 0 0
\(106\) 54384.9 0.470125
\(107\) 72634.0 + 125806.i 0.613310 + 1.06228i 0.990678 + 0.136221i \(0.0434959\pi\)
−0.377368 + 0.926063i \(0.623171\pi\)
\(108\) −5832.00 + 10101.3i −0.0481125 + 0.0833333i
\(109\) 90425.4 156621.i 0.728994 1.26265i −0.228315 0.973587i \(-0.573321\pi\)
0.957309 0.289067i \(-0.0933452\pi\)
\(110\) 22566.4 + 39086.2i 0.177820 + 0.307994i
\(111\) 70154.0 0.540437
\(112\) 0 0
\(113\) 197832. 1.45748 0.728738 0.684793i \(-0.240107\pi\)
0.728738 + 0.684793i \(0.240107\pi\)
\(114\) −50313.6 87145.8i −0.362596 0.628035i
\(115\) −68470.4 + 118594.i −0.482790 + 0.836217i
\(116\) 6072.27 10517.5i 0.0418992 0.0725715i
\(117\) 14151.3 + 24510.8i 0.0955725 + 0.165536i
\(118\) 105435. 0.697077
\(119\) 0 0
\(120\) 43483.6 0.275659
\(121\) 69356.1 + 120128.i 0.430647 + 0.745902i
\(122\) 70643.5 122358.i 0.429707 0.744275i
\(123\) 34382.2 59551.8i 0.204914 0.354921i
\(124\) 72254.0 + 125148.i 0.421995 + 0.730917i
\(125\) −41589.2 −0.238070
\(126\) 0 0
\(127\) −33517.2 −0.184399 −0.0921996 0.995741i \(-0.529390\pi\)
−0.0921996 + 0.995741i \(0.529390\pi\)
\(128\) −8192.00 14189.0i −0.0441942 0.0765466i
\(129\) −54849.8 + 95002.6i −0.290202 + 0.502645i
\(130\) 52756.4 91376.8i 0.273790 0.474218i
\(131\) −5404.45 9360.79i −0.0275153 0.0476578i 0.851940 0.523640i \(-0.175426\pi\)
−0.879455 + 0.475982i \(0.842093\pi\)
\(132\) −21522.5 −0.107512
\(133\) 0 0
\(134\) 217488. 1.04634
\(135\) −27517.0 47660.8i −0.129947 0.225075i
\(136\) −36795.1 + 63731.0i −0.170586 + 0.295463i
\(137\) 9466.01 16395.6i 0.0430889 0.0746322i −0.843677 0.536852i \(-0.819613\pi\)
0.886766 + 0.462220i \(0.152947\pi\)
\(138\) −32651.4 56554.0i −0.145950 0.252793i
\(139\) 168897. 0.741457 0.370729 0.928741i \(-0.379108\pi\)
0.370729 + 0.928741i \(0.379108\pi\)
\(140\) 0 0
\(141\) −221389. −0.937797
\(142\) 140291. + 242992.i 0.583862 + 1.01128i
\(143\) −26112.1 + 45227.6i −0.106783 + 0.184954i
\(144\) −10368.0 + 17957.9i −0.0416667 + 0.0721688i
\(145\) 28650.6 + 49624.3i 0.113165 + 0.196008i
\(146\) 177875. 0.690611
\(147\) 0 0
\(148\) 124718. 0.468032
\(149\) −132001. 228633.i −0.487093 0.843670i 0.512797 0.858510i \(-0.328609\pi\)
−0.999890 + 0.0148402i \(0.995276\pi\)
\(150\) −46333.7 + 80252.3i −0.168139 + 0.291226i
\(151\) −139587. + 241772.i −0.498200 + 0.862908i −0.999998 0.00207707i \(-0.999339\pi\)
0.501798 + 0.864985i \(0.332672\pi\)
\(152\) −89446.4 154926.i −0.314018 0.543895i
\(153\) 93137.6 0.321660
\(154\) 0 0
\(155\) −681828. −2.27953
\(156\) 25157.9 + 43574.8i 0.0827682 + 0.143359i
\(157\) 94301.2 163334.i 0.305329 0.528845i −0.672006 0.740546i \(-0.734567\pi\)
0.977334 + 0.211701i \(0.0679003\pi\)
\(158\) −123225. + 213432.i −0.392695 + 0.680168i
\(159\) −61183.0 105972.i −0.191928 0.332429i
\(160\) 77304.2 0.238728
\(161\) 0 0
\(162\) 26244.0 0.0785674
\(163\) −44858.7 77697.5i −0.132244 0.229054i 0.792297 0.610136i \(-0.208885\pi\)
−0.924541 + 0.381081i \(0.875552\pi\)
\(164\) 61124.0 105870.i 0.177461 0.307371i
\(165\) 50774.5 87944.0i 0.145190 0.251476i
\(166\) −174284. 301869.i −0.490893 0.850252i
\(167\) −529411. −1.46893 −0.734467 0.678645i \(-0.762568\pi\)
−0.734467 + 0.678645i \(0.762568\pi\)
\(168\) 0 0
\(169\) −249202. −0.671172
\(170\) −173609. 300700.i −0.460734 0.798015i
\(171\) −113206. + 196078.i −0.296059 + 0.512789i
\(172\) −97510.7 + 168893.i −0.251322 + 0.435303i
\(173\) 16919.2 + 29304.8i 0.0429797 + 0.0744430i 0.886715 0.462316i \(-0.152982\pi\)
−0.843735 + 0.536759i \(0.819648\pi\)
\(174\) −27325.2 −0.0684211
\(175\) 0 0
\(176\) −38262.2 −0.0931083
\(177\) −118615. 205447.i −0.284581 0.492908i
\(178\) 197139. 341454.i 0.466361 0.807761i
\(179\) 123872. 214552.i 0.288962 0.500496i −0.684601 0.728918i \(-0.740023\pi\)
0.973562 + 0.228422i \(0.0733567\pi\)
\(180\) −48919.0 84730.3i −0.112537 0.194920i
\(181\) −369470. −0.838268 −0.419134 0.907924i \(-0.637666\pi\)
−0.419134 + 0.907924i \(0.637666\pi\)
\(182\) 0 0
\(183\) −317896. −0.701709
\(184\) −58047.0 100540.i −0.126397 0.218925i
\(185\) −294227. + 509617.i −0.632053 + 1.09475i
\(186\) 162571. 281582.i 0.344558 0.596791i
\(187\) 85929.1 + 148833.i 0.179695 + 0.311241i
\(188\) −393581. −0.812156
\(189\) 0 0
\(190\) 844065. 1.69626
\(191\) 242612. + 420217.i 0.481204 + 0.833470i 0.999767 0.0215693i \(-0.00686625\pi\)
−0.518563 + 0.855039i \(0.673533\pi\)
\(192\) −18432.0 + 31925.2i −0.0360844 + 0.0625000i
\(193\) 165409. 286496.i 0.319643 0.553637i −0.660771 0.750588i \(-0.729770\pi\)
0.980413 + 0.196950i \(0.0631038\pi\)
\(194\) 64684.7 + 112037.i 0.123395 + 0.213726i
\(195\) −237404. −0.447097
\(196\) 0 0
\(197\) −161963. −0.297337 −0.148669 0.988887i \(-0.547499\pi\)
−0.148669 + 0.988887i \(0.547499\pi\)
\(198\) 24212.8 + 41937.8i 0.0438917 + 0.0760226i
\(199\) 27698.1 47974.5i 0.0495813 0.0858773i −0.840170 0.542324i \(-0.817545\pi\)
0.889751 + 0.456446i \(0.150878\pi\)
\(200\) −82371.0 + 142671.i −0.145613 + 0.252209i
\(201\) −244674. 423787.i −0.427166 0.739874i
\(202\) −125386. −0.216207
\(203\) 0 0
\(204\) 165578. 0.278565
\(205\) 288399. + 499522.i 0.479303 + 0.830176i
\(206\) 198666. 344099.i 0.326178 0.564957i
\(207\) −73465.8 + 127246.i −0.119168 + 0.206405i
\(208\) 44725.2 + 77466.4i 0.0716794 + 0.124152i
\(209\) −417776. −0.661572
\(210\) 0 0
\(211\) 481748. 0.744926 0.372463 0.928047i \(-0.378513\pi\)
0.372463 + 0.928047i \(0.378513\pi\)
\(212\) −108770. 188395.i −0.166214 0.287892i
\(213\) 315656. 546732.i 0.476722 0.825706i
\(214\) 290536. 503223.i 0.433676 0.751149i
\(215\) −460082. 796885.i −0.678795 1.17571i
\(216\) 46656.0 0.0680414
\(217\) 0 0
\(218\) −723403. −1.03095
\(219\) −200110. 346600.i −0.281941 0.488335i
\(220\) 90265.7 156345.i 0.125738 0.217784i
\(221\) 200887. 347947.i 0.276676 0.479217i
\(222\) −140308. 243021.i −0.191073 0.330949i
\(223\) −638779. −0.860178 −0.430089 0.902787i \(-0.641518\pi\)
−0.430089 + 0.902787i \(0.641518\pi\)
\(224\) 0 0
\(225\) 208502. 0.274570
\(226\) −395665. 685312.i −0.515295 0.892518i
\(227\) −262841. + 455254.i −0.338554 + 0.586394i −0.984161 0.177277i \(-0.943271\pi\)
0.645607 + 0.763670i \(0.276605\pi\)
\(228\) −201255. + 348583.i −0.256394 + 0.444088i
\(229\) 466343. + 807730.i 0.587647 + 1.01784i 0.994540 + 0.104359i \(0.0332791\pi\)
−0.406892 + 0.913476i \(0.633388\pi\)
\(230\) 547763. 0.682768
\(231\) 0 0
\(232\) −48578.1 −0.0592544
\(233\) 353896. + 612967.i 0.427058 + 0.739685i 0.996610 0.0822696i \(-0.0262168\pi\)
−0.569553 + 0.821955i \(0.692884\pi\)
\(234\) 56605.4 98043.4i 0.0675800 0.117052i
\(235\) 928511. 1.60823e6i 1.09677 1.89967i
\(236\) −210871. 365238.i −0.246454 0.426871i
\(237\) 554512. 0.641269
\(238\) 0 0
\(239\) −500614. −0.566902 −0.283451 0.958987i \(-0.591479\pi\)
−0.283451 + 0.958987i \(0.591479\pi\)
\(240\) −86967.2 150632.i −0.0974602 0.168806i
\(241\) 604109. 1.04635e6i 0.669997 1.16047i −0.307907 0.951416i \(-0.599629\pi\)
0.977904 0.209052i \(-0.0670379\pi\)
\(242\) 277424. 480513.i 0.304513 0.527432i
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) −565148. −0.607698
\(245\) 0 0
\(246\) −275058. −0.289792
\(247\) 488344. + 845836.i 0.509311 + 0.882153i
\(248\) 289016. 500590.i 0.298396 0.516836i
\(249\) −392139. + 679204.i −0.400813 + 0.694228i
\(250\) 83178.3 + 144069.i 0.0841705 + 0.145788i
\(251\) −97826.7 −0.0980106 −0.0490053 0.998799i \(-0.515605\pi\)
−0.0490053 + 0.998799i \(0.515605\pi\)
\(252\) 0 0
\(253\) −271119. −0.266292
\(254\) 67034.5 + 116107.i 0.0651949 + 0.112921i
\(255\) −390621. + 676575.i −0.376188 + 0.651577i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) −553956. 959481.i −0.523170 0.906157i −0.999636 0.0269643i \(-0.991416\pi\)
0.476466 0.879193i \(-0.341917\pi\)
\(258\) 438798. 0.410408
\(259\) 0 0
\(260\) −422052. −0.387197
\(261\) 30740.8 + 53244.7i 0.0279328 + 0.0483810i
\(262\) −21617.8 + 37443.2i −0.0194562 + 0.0336992i
\(263\) −753427. + 1.30497e6i −0.671663 + 1.16336i 0.305769 + 0.952106i \(0.401087\pi\)
−0.977432 + 0.211249i \(0.932247\pi\)
\(264\) 43045.0 + 74556.1i 0.0380113 + 0.0658375i
\(265\) 1.02641e6 0.897856
\(266\) 0 0
\(267\) −887125. −0.761564
\(268\) −434975. 753399.i −0.369937 0.640750i
\(269\) −1.06751e6 + 1.84898e6i −0.899481 + 1.55795i −0.0713221 + 0.997453i \(0.522722\pi\)
−0.828159 + 0.560493i \(0.810612\pi\)
\(270\) −110068. + 190643.i −0.0918864 + 0.159152i
\(271\) 614299. + 1.06400e6i 0.508108 + 0.880070i 0.999956 + 0.00938828i \(0.00298843\pi\)
−0.491847 + 0.870681i \(0.663678\pi\)
\(272\) 294361. 0.241245
\(273\) 0 0
\(274\) −75728.1 −0.0609369
\(275\) 192364. + 333185.i 0.153388 + 0.265677i
\(276\) −130606. + 226216.i −0.103202 + 0.178752i
\(277\) 923412. 1.59940e6i 0.723097 1.25244i −0.236656 0.971593i \(-0.576051\pi\)
0.959753 0.280847i \(-0.0906152\pi\)
\(278\) −337795. 585078.i −0.262145 0.454048i
\(279\) −731571. −0.562660
\(280\) 0 0
\(281\) −2.28326e6 −1.72500 −0.862500 0.506056i \(-0.831103\pi\)
−0.862500 + 0.506056i \(0.831103\pi\)
\(282\) 442779. + 766915.i 0.331561 + 0.574281i
\(283\) 668463. 1.15781e6i 0.496148 0.859354i −0.503842 0.863796i \(-0.668081\pi\)
0.999990 + 0.00444218i \(0.00141400\pi\)
\(284\) 561166. 971968.i 0.412853 0.715082i
\(285\) −949573. 1.64471e6i −0.692495 1.19944i
\(286\) 208897. 0.151014
\(287\) 0 0
\(288\) 82944.0 0.0589256
\(289\) 48854.5 + 84618.5i 0.0344081 + 0.0595965i
\(290\) 114602. 198497.i 0.0800200 0.138599i
\(291\) 145541. 252084.i 0.100751 0.174507i
\(292\) −355750. 616178.i −0.244168 0.422911i
\(293\) 2.23033e6 1.51775 0.758875 0.651236i \(-0.225749\pi\)
0.758875 + 0.651236i \(0.225749\pi\)
\(294\) 0 0
\(295\) 1.98989e6 1.33129
\(296\) −249436. 432037.i −0.165474 0.286610i
\(297\) 54478.8 94360.1i 0.0358374 0.0620722i
\(298\) −528004. + 914530.i −0.344427 + 0.596565i
\(299\) 316915. + 548913.i 0.205005 + 0.355079i
\(300\) 370670. 0.237785
\(301\) 0 0
\(302\) 1.11670e6 0.704561
\(303\) 141059. + 244321.i 0.0882661 + 0.152881i
\(304\) −357786. + 619703.i −0.222044 + 0.384592i
\(305\) 1.33326e6 2.30928e6i 0.820664 1.42143i
\(306\) −186275. 322638.i −0.113724 0.196975i
\(307\) −1.77782e6 −1.07657 −0.538284 0.842763i \(-0.680927\pi\)
−0.538284 + 0.842763i \(0.680927\pi\)
\(308\) 0 0
\(309\) −893996. −0.532647
\(310\) 1.36366e6 + 2.36192e6i 0.805936 + 1.39592i
\(311\) 701358. 1.21479e6i 0.411187 0.712196i −0.583833 0.811874i \(-0.698448\pi\)
0.995020 + 0.0996776i \(0.0317811\pi\)
\(312\) 100632. 174299.i 0.0585260 0.101370i
\(313\) 609472. + 1.05564e6i 0.351636 + 0.609051i 0.986536 0.163543i \(-0.0522922\pi\)
−0.634900 + 0.772594i \(0.718959\pi\)
\(314\) −754409. −0.431800
\(315\) 0 0
\(316\) 985799. 0.555355
\(317\) −1.34001e6 2.32096e6i −0.748961 1.29724i −0.948321 0.317312i \(-0.897220\pi\)
0.199361 0.979926i \(-0.436113\pi\)
\(318\) −244732. + 423888.i −0.135713 + 0.235063i
\(319\) −56723.2 + 98247.5i −0.0312093 + 0.0540561i
\(320\) −154608. 267789.i −0.0844030 0.146190i
\(321\) −1.30741e6 −0.708190
\(322\) 0 0
\(323\) 3.21405e6 1.71414
\(324\) −52488.0 90911.9i −0.0277778 0.0481125i
\(325\) 449715. 778929.i 0.236172 0.409062i
\(326\) −179435. + 310790.i −0.0935110 + 0.161966i
\(327\) 813828. + 1.40959e6i 0.420885 + 0.728994i
\(328\) −488992. −0.250967
\(329\) 0 0
\(330\) −406196. −0.205329
\(331\) −71280.1 123461.i −0.0357601 0.0619383i 0.847591 0.530649i \(-0.178052\pi\)
−0.883352 + 0.468711i \(0.844719\pi\)
\(332\) −697136. + 1.20747e6i −0.347114 + 0.601219i
\(333\) −315693. + 546796.i −0.156011 + 0.270218i
\(334\) 1.05882e6 + 1.83393e6i 0.519346 + 0.899534i
\(335\) 4.10466e6 1.99832
\(336\) 0 0
\(337\) −1.21206e6 −0.581367 −0.290683 0.956819i \(-0.593883\pi\)
−0.290683 + 0.956819i \(0.593883\pi\)
\(338\) 498403. + 863260.i 0.237295 + 0.411007i
\(339\) −890246. + 1.54195e6i −0.420737 + 0.728738i
\(340\) −694437. + 1.20280e6i −0.325788 + 0.564282i
\(341\) −674950. 1.16905e6i −0.314330 0.544435i
\(342\) 905645. 0.418690
\(343\) 0 0
\(344\) 780085. 0.355423
\(345\) −616234. 1.06735e6i −0.278739 0.482790i
\(346\) 67676.6 117219.i 0.0303912 0.0526392i
\(347\) −1.73426e6 + 3.00383e6i −0.773199 + 1.33922i 0.162602 + 0.986692i \(0.448011\pi\)
−0.935801 + 0.352529i \(0.885322\pi\)
\(348\) 54650.4 + 94657.2i 0.0241905 + 0.0418992i
\(349\) −1.01692e6 −0.446911 −0.223456 0.974714i \(-0.571734\pi\)
−0.223456 + 0.974714i \(0.571734\pi\)
\(350\) 0 0
\(351\) −254724. −0.110358
\(352\) 76524.4 + 132544.i 0.0329187 + 0.0570169i
\(353\) 781927. 1.35434e6i 0.333987 0.578483i −0.649303 0.760530i \(-0.724939\pi\)
0.983290 + 0.182048i \(0.0582725\pi\)
\(354\) −474459. + 821786.i −0.201229 + 0.348539i
\(355\) 2.64773e6 + 4.58601e6i 1.11507 + 1.93136i
\(356\) −1.57711e6 −0.659534
\(357\) 0 0
\(358\) −990975. −0.408653
\(359\) −24776.6 42914.3i −0.0101462 0.0175738i 0.860908 0.508761i \(-0.169896\pi\)
−0.871054 + 0.491187i \(0.836563\pi\)
\(360\) −195676. + 338921.i −0.0795759 + 0.137830i
\(361\) −2.66853e6 + 4.62202e6i −1.07771 + 1.86666i
\(362\) 738940. + 1.27988e6i 0.296373 + 0.513332i
\(363\) −1.24841e6 −0.497268
\(364\) 0 0
\(365\) 3.35705e6 1.31894
\(366\) 635792. + 1.10122e6i 0.248092 + 0.429707i
\(367\) 1.77416e6 3.07293e6i 0.687585 1.19093i −0.285032 0.958518i \(-0.592004\pi\)
0.972617 0.232414i \(-0.0746626\pi\)
\(368\) −232188. + 402162.i −0.0893759 + 0.154804i
\(369\) 309440. + 535966.i 0.118307 + 0.204914i
\(370\) 2.35382e6 0.893858
\(371\) 0 0
\(372\) −1.30057e6 −0.487278
\(373\) 1.12787e6 + 1.95352e6i 0.419745 + 0.727020i 0.995914 0.0903112i \(-0.0287862\pi\)
−0.576169 + 0.817331i \(0.695453\pi\)
\(374\) 343716. 595334.i 0.127064 0.220081i
\(375\) 187151. 324155.i 0.0687250 0.119035i
\(376\) 787162. + 1.36340e6i 0.287140 + 0.497342i
\(377\) 265218. 0.0961059
\(378\) 0 0
\(379\) 4.39503e6 1.57168 0.785840 0.618430i \(-0.212231\pi\)
0.785840 + 0.618430i \(0.212231\pi\)
\(380\) −1.68813e6 2.92393e6i −0.599718 1.03874i
\(381\) 150828. 261241.i 0.0532315 0.0921996i
\(382\) 970449. 1.68087e6i 0.340263 0.589352i
\(383\) −613904. 1.06331e6i −0.213847 0.370394i 0.739068 0.673631i \(-0.235266\pi\)
−0.952915 + 0.303237i \(0.901933\pi\)
\(384\) 147456. 0.0510310
\(385\) 0 0
\(386\) −1.32327e6 −0.452043
\(387\) −493648. 855023.i −0.167548 0.290202i
\(388\) 258739. 448149.i 0.0872533 0.151127i
\(389\) −1.02712e6 + 1.77903e6i −0.344150 + 0.596086i −0.985199 0.171415i \(-0.945166\pi\)
0.641049 + 0.767500i \(0.278500\pi\)
\(390\) 474808. + 822391.i 0.158073 + 0.273790i
\(391\) 2.08579e6 0.689967
\(392\) 0 0
\(393\) 97280.2 0.0317719
\(394\) 323925. + 561055.i 0.105125 + 0.182081i
\(395\) −2.32563e6 + 4.02812e6i −0.749978 + 1.29900i
\(396\) 96851.2 167751.i 0.0310361 0.0537561i
\(397\) −1.90184e6 3.29408e6i −0.605615 1.04896i −0.991954 0.126599i \(-0.959594\pi\)
0.386339 0.922357i \(-0.373740\pi\)
\(398\) −221585. −0.0701185
\(399\) 0 0
\(400\) 658968. 0.205928
\(401\) −592622. 1.02645e6i −0.184042 0.318770i 0.759211 0.650844i \(-0.225585\pi\)
−0.943253 + 0.332074i \(0.892252\pi\)
\(402\) −978695. + 1.69515e6i −0.302052 + 0.523170i
\(403\) −1.57792e6 + 2.73303e6i −0.483974 + 0.838267i
\(404\) 250771. + 434349.i 0.0764406 + 0.132399i
\(405\) 495305. 0.150050
\(406\) 0 0
\(407\) −1.16504e6 −0.348621
\(408\) −331156. 573579.i −0.0984877 0.170586i
\(409\) −2.15197e6 + 3.72731e6i −0.636102 + 1.10176i 0.350178 + 0.936683i \(0.386121\pi\)
−0.986280 + 0.165079i \(0.947212\pi\)
\(410\) 1.15360e6 1.99809e6i 0.338918 0.587023i
\(411\) 85194.1 + 147560.i 0.0248774 + 0.0430889i
\(412\) −1.58933e6 −0.461286
\(413\) 0 0
\(414\) 587726. 0.168529
\(415\) −3.28928e6 5.69719e6i −0.937519 1.62383i
\(416\) 178901. 309865.i 0.0506850 0.0877889i
\(417\) −760038. + 1.31643e6i −0.214040 + 0.370729i
\(418\) 835551. + 1.44722e6i 0.233901 + 0.405129i
\(419\) 113725. 0.0316461 0.0158230 0.999875i \(-0.494963\pi\)
0.0158230 + 0.999875i \(0.494963\pi\)
\(420\) 0 0
\(421\) 443417. 0.121929 0.0609645 0.998140i \(-0.480582\pi\)
0.0609645 + 0.998140i \(0.480582\pi\)
\(422\) −963495. 1.66882e6i −0.263371 0.456172i
\(423\) 996252. 1.72556e6i 0.270719 0.468898i
\(424\) −435079. + 753579.i −0.117531 + 0.203570i
\(425\) −1.47991e6 2.56327e6i −0.397431 0.688371i
\(426\) −2.52525e6 −0.674186
\(427\) 0 0
\(428\) −2.32429e6 −0.613310
\(429\) −235009. 407048.i −0.0616512 0.106783i
\(430\) −1.84033e6 + 3.18754e6i −0.479981 + 0.831351i
\(431\) −2.31655e6 + 4.01239e6i −0.600688 + 1.04042i 0.392029 + 0.919953i \(0.371773\pi\)
−0.992717 + 0.120469i \(0.961560\pi\)
\(432\) −93312.0 161621.i −0.0240563 0.0416667i
\(433\) −6.57955e6 −1.68646 −0.843231 0.537552i \(-0.819349\pi\)
−0.843231 + 0.537552i \(0.819349\pi\)
\(434\) 0 0
\(435\) −515711. −0.130672
\(436\) 1.44681e6 + 2.50594e6i 0.364497 + 0.631327i
\(437\) −2.53520e6 + 4.39110e6i −0.635052 + 1.09994i
\(438\) −800438. + 1.38640e6i −0.199362 + 0.345305i
\(439\) −910348. 1.57677e6i −0.225448 0.390487i 0.731006 0.682371i \(-0.239051\pi\)
−0.956454 + 0.291884i \(0.905718\pi\)
\(440\) −722126. −0.177820
\(441\) 0 0
\(442\) −1.60710e6 −0.391279
\(443\) 1.03495e6 + 1.79259e6i 0.250559 + 0.433982i 0.963680 0.267060i \(-0.0860521\pi\)
−0.713121 + 0.701041i \(0.752719\pi\)
\(444\) −561232. + 972083.i −0.135109 + 0.234016i
\(445\) 3.72062e6 6.44430e6i 0.890666 1.54268i
\(446\) 1.27756e6 + 2.21279e6i 0.304119 + 0.526749i
\(447\) 2.37602e6 0.562447
\(448\) 0 0
\(449\) 5.72581e6 1.34036 0.670180 0.742199i \(-0.266217\pi\)
0.670180 + 0.742199i \(0.266217\pi\)
\(450\) −417003. 722271.i −0.0970752 0.168139i
\(451\) −570981. + 988968.i −0.132184 + 0.228950i
\(452\) −1.58266e6 + 2.74125e6i −0.364369 + 0.631105i
\(453\) −1.25629e6 2.17595e6i −0.287636 0.498200i
\(454\) 2.10273e6 0.478788
\(455\) 0 0
\(456\) 1.61004e6 0.362596
\(457\) −159338. 275982.i −0.0356886 0.0618144i 0.847629 0.530589i \(-0.178029\pi\)
−0.883318 + 0.468774i \(0.844696\pi\)
\(458\) 1.86537e6 3.23092e6i 0.415529 0.719718i
\(459\) −419119. + 725936.i −0.0928551 + 0.160830i
\(460\) −1.09553e6 1.89751e6i −0.241395 0.418108i
\(461\) 3.42470e6 0.750535 0.375267 0.926917i \(-0.377551\pi\)
0.375267 + 0.926917i \(0.377551\pi\)
\(462\) 0 0
\(463\) 3.82945e6 0.830201 0.415101 0.909775i \(-0.363746\pi\)
0.415101 + 0.909775i \(0.363746\pi\)
\(464\) 97156.2 + 168280.i 0.0209496 + 0.0362858i
\(465\) 3.06822e6 5.31432e6i 0.658044 1.13977i
\(466\) 1.41559e6 2.45187e6i 0.301975 0.523037i
\(467\) 1.42231e6 + 2.46351e6i 0.301788 + 0.522712i 0.976541 0.215332i \(-0.0690832\pi\)
−0.674753 + 0.738044i \(0.735750\pi\)
\(468\) −452843. −0.0955725
\(469\) 0 0
\(470\) −7.42809e6 −1.55107
\(471\) 848710. + 1.47001e6i 0.176282 + 0.305329i
\(472\) −843482. + 1.46095e6i −0.174269 + 0.301843i
\(473\) 910882. 1.57769e6i 0.187202 0.324243i
\(474\) −1.10902e6 1.92089e6i −0.226723 0.392695i
\(475\) 7.19511e6 1.46320
\(476\) 0 0
\(477\) 1.10129e6 0.221619
\(478\) 1.00123e6 + 1.73418e6i 0.200430 + 0.347155i
\(479\) 651827. 1.12900e6i 0.129806 0.224830i −0.793796 0.608185i \(-0.791898\pi\)
0.923601 + 0.383355i \(0.125231\pi\)
\(480\) −347869. + 602526.i −0.0689148 + 0.119364i
\(481\) 1.36183e6 + 2.35876e6i 0.268386 + 0.464858i
\(482\) −4.83287e6 −0.947519
\(483\) 0 0
\(484\) −2.21940e6 −0.430647
\(485\) 1.22080e6 + 2.11449e6i 0.235662 + 0.408179i
\(486\) −118098. + 204552.i −0.0226805 + 0.0392837i
\(487\) −3.11812e6 + 5.40074e6i −0.595759 + 1.03188i 0.397681 + 0.917524i \(0.369815\pi\)
−0.993439 + 0.114360i \(0.963518\pi\)
\(488\) 1.13030e6 + 1.95773e6i 0.214854 + 0.372137i
\(489\) 807456. 0.152703
\(490\) 0 0
\(491\) −3.93928e6 −0.737417 −0.368709 0.929545i \(-0.620200\pi\)
−0.368709 + 0.929545i \(0.620200\pi\)
\(492\) 550116. + 952828.i 0.102457 + 0.177461i
\(493\) 436386. 755843.i 0.0808637 0.140060i
\(494\) 1.95338e6 3.38335e6i 0.360137 0.623776i
\(495\) 456970. + 791496.i 0.0838253 + 0.145190i
\(496\) −2.31213e6 −0.421995
\(497\) 0 0
\(498\) 3.13711e6 0.566835
\(499\) −3.98785e6 6.90717e6i −0.716948 1.24179i −0.962203 0.272333i \(-0.912205\pi\)
0.245255 0.969459i \(-0.421128\pi\)
\(500\) 332713. 576276.i 0.0595176 0.103087i
\(501\) 2.38235e6 4.12635e6i 0.424045 0.734467i
\(502\) 195653. + 338882.i 0.0346520 + 0.0600190i
\(503\) 2.70777e6 0.477190 0.238595 0.971119i \(-0.423313\pi\)
0.238595 + 0.971119i \(0.423313\pi\)
\(504\) 0 0
\(505\) −2.36641e6 −0.412917
\(506\) 542238. + 939184.i 0.0941486 + 0.163070i
\(507\) 1.12141e6 1.94233e6i 0.193751 0.335586i
\(508\) 268138. 464428.i 0.0460998 0.0798472i
\(509\) 1.95025e6 + 3.37793e6i 0.333653 + 0.577904i 0.983225 0.182396i \(-0.0583852\pi\)
−0.649572 + 0.760300i \(0.725052\pi\)
\(510\) 3.12497e6 0.532010
\(511\) 0 0
\(512\) 262144. 0.0441942
\(513\) −1.01885e6 1.76470e6i −0.170930 0.296059i
\(514\) −2.21583e6 + 3.83792e6i −0.369937 + 0.640750i
\(515\) 3.74944e6 6.49422e6i 0.622943 1.07897i
\(516\) −877596. 1.52004e6i −0.145101 0.251322i
\(517\) 3.67658e6 0.604947
\(518\) 0 0
\(519\) −304545. −0.0496287
\(520\) 844103. + 1.46203e6i 0.136895 + 0.237109i
\(521\) 3.50032e6 6.06273e6i 0.564954 0.978529i −0.432100 0.901826i \(-0.642227\pi\)
0.997054 0.0767034i \(-0.0244394\pi\)
\(522\) 122963. 212979.i 0.0197515 0.0342106i
\(523\) −1.05604e6 1.82911e6i −0.168821 0.292406i 0.769185 0.639026i \(-0.220663\pi\)
−0.938005 + 0.346620i \(0.887329\pi\)
\(524\) 172943. 0.0275153
\(525\) 0 0
\(526\) 6.02741e6 0.949875
\(527\) 5.19256e6 + 8.99378e6i 0.814433 + 1.41064i
\(528\) 172180. 298224.i 0.0268780 0.0465541i
\(529\) 1.57293e6 2.72439e6i 0.244382 0.423283i
\(530\) −2.05282e6 3.55559e6i −0.317440 0.549822i
\(531\) 2.13506e6 0.328605
\(532\) 0 0
\(533\) 2.66971e6 0.407048
\(534\) 1.77425e6 + 3.07309e6i 0.269254 + 0.466361i
\(535\) 5.48331e6 9.49737e6i 0.828244 1.43456i
\(536\) −1.73990e6 + 3.01360e6i −0.261585 + 0.453078i
\(537\) 1.11485e6 + 1.93097e6i 0.166832 + 0.288962i
\(538\) 8.54009e6 1.27206
\(539\) 0 0
\(540\) 880543. 0.129947
\(541\) −2.85283e6 4.94125e6i −0.419067 0.725845i 0.576779 0.816900i \(-0.304309\pi\)
−0.995846 + 0.0910551i \(0.970976\pi\)
\(542\) 2.45720e6 4.25599e6i 0.359287 0.622303i
\(543\) 1.66262e6 2.87974e6i 0.241987 0.419134i
\(544\) −588722. 1.01970e6i −0.0852929 0.147732i
\(545\) −1.36528e7 −1.96894
\(546\) 0 0
\(547\) 2.28054e6 0.325888 0.162944 0.986635i \(-0.447901\pi\)
0.162944 + 0.986635i \(0.447901\pi\)
\(548\) 151456. + 262330.i 0.0215445 + 0.0373161i
\(549\) 1.43053e6 2.47775e6i 0.202566 0.350855i
\(550\) 769457. 1.33274e6i 0.108462 0.187862i
\(551\) 1.06083e6 + 1.83740e6i 0.148855 + 0.257825i
\(552\) 1.04485e6 0.145950
\(553\) 0 0
\(554\) −7.38730e6 −1.02261
\(555\) −2.64805e6 4.58655e6i −0.364916 0.632053i
\(556\) −1.35118e6 + 2.34031e6i −0.185364 + 0.321060i
\(557\) 3.36970e6 5.83650e6i 0.460208 0.797103i −0.538763 0.842457i \(-0.681108\pi\)
0.998971 + 0.0453541i \(0.0144416\pi\)
\(558\) 1.46314e6 + 2.53424e6i 0.198930 + 0.344558i
\(559\) −4.25897e6 −0.576468
\(560\) 0 0
\(561\) −1.54672e6 −0.207494
\(562\) 4.56652e6 + 7.90944e6i 0.609880 + 1.05634i
\(563\) −4.83410e6 + 8.37291e6i −0.642754 + 1.11328i 0.342061 + 0.939678i \(0.388875\pi\)
−0.984815 + 0.173605i \(0.944458\pi\)
\(564\) 1.77111e6 3.06766e6i 0.234449 0.406078i
\(565\) −7.46742e6 1.29339e7i −0.984123 1.70455i
\(566\) −5.34770e6 −0.701659
\(567\) 0 0
\(568\) −4.48933e6 −0.583862
\(569\) 6.97934e6 + 1.20886e7i 0.903719 + 1.56529i 0.822627 + 0.568581i \(0.192507\pi\)
0.0810922 + 0.996707i \(0.474159\pi\)
\(570\) −3.79829e6 + 6.57884e6i −0.489668 + 0.848129i
\(571\) 1.17920e6 2.04244e6i 0.151355 0.262155i −0.780371 0.625317i \(-0.784970\pi\)
0.931726 + 0.363162i \(0.118303\pi\)
\(572\) −417794. 723641.i −0.0533915 0.0924769i
\(573\) −4.36702e6 −0.555647
\(574\) 0 0
\(575\) 4.66933e6 0.588959
\(576\) −165888. 287326.i −0.0208333 0.0360844i
\(577\) 2.50549e6 4.33963e6i 0.313295 0.542642i −0.665779 0.746149i \(-0.731901\pi\)
0.979074 + 0.203507i \(0.0652339\pi\)
\(578\) 195418. 338474.i 0.0243302 0.0421411i
\(579\) 1.48868e6 + 2.57846e6i 0.184546 + 0.319643i
\(580\) −916819. −0.113165
\(581\) 0 0
\(582\) −1.16432e6 −0.142484
\(583\) 1.01606e6 + 1.75986e6i 0.123807 + 0.214441i
\(584\) −1.42300e6 + 2.46471e6i −0.172653 + 0.299043i
\(585\) 1.06832e6 1.85038e6i 0.129066 0.223548i
\(586\) −4.46066e6 7.72609e6i −0.536606 0.929428i
\(587\) −3.95106e6 −0.473280 −0.236640 0.971597i \(-0.576046\pi\)
−0.236640 + 0.971597i \(0.576046\pi\)
\(588\) 0 0
\(589\) −2.52455e7 −2.99845
\(590\) −3.97978e6 6.89318e6i −0.470683 0.815247i
\(591\) 728832. 1.26237e6i 0.0858339 0.148669i
\(592\) −997746. + 1.72815e6i −0.117008 + 0.202664i
\(593\) −1.26840e6 2.19694e6i −0.148122 0.256555i 0.782411 0.622762i \(-0.213990\pi\)
−0.930533 + 0.366207i \(0.880656\pi\)
\(594\) −435830. −0.0506817
\(595\) 0 0
\(596\) 4.22403e6 0.487093
\(597\) 249283. + 431771.i 0.0286258 + 0.0495813i
\(598\) 1.26766e6 2.19565e6i 0.144960 0.251079i
\(599\) −3.58857e6 + 6.21558e6i −0.408652 + 0.707807i −0.994739 0.102442i \(-0.967335\pi\)
0.586087 + 0.810248i \(0.300668\pi\)
\(600\) −741339. 1.28404e6i −0.0840696 0.145613i
\(601\) −1.12527e7 −1.27078 −0.635392 0.772190i \(-0.719162\pi\)
−0.635392 + 0.772190i \(0.719162\pi\)
\(602\) 0 0
\(603\) 4.40413e6 0.493249
\(604\) −2.23340e6 3.86836e6i −0.249100 0.431454i
\(605\) 5.23585e6 9.06877e6i 0.581566 1.00730i
\(606\) 564235. 977284.i 0.0624135 0.108103i
\(607\) −7.01851e6 1.21564e7i −0.773167 1.33916i −0.935819 0.352481i \(-0.885338\pi\)
0.162652 0.986684i \(-0.447995\pi\)
\(608\) 2.86229e6 0.314018
\(609\) 0 0
\(610\) −1.06661e7 −1.16059
\(611\) −4.29761e6 7.44367e6i −0.465719 0.806648i
\(612\) −745101. + 1.29055e6i −0.0804149 + 0.139283i
\(613\) 3.81436e6 6.60667e6i 0.409988 0.710119i −0.584900 0.811105i \(-0.698866\pi\)
0.994888 + 0.100986i \(0.0321997\pi\)
\(614\) 3.55564e6 + 6.15855e6i 0.380624 + 0.659261i
\(615\) −5.19119e6 −0.553451
\(616\) 0 0
\(617\) −4.41080e6 −0.466450 −0.233225 0.972423i \(-0.574928\pi\)
−0.233225 + 0.972423i \(0.574928\pi\)
\(618\) 1.78799e6 + 3.09689e6i 0.188319 + 0.326178i
\(619\) −4.52178e6 + 7.83195e6i −0.474332 + 0.821567i −0.999568 0.0293895i \(-0.990644\pi\)
0.525236 + 0.850957i \(0.323977\pi\)
\(620\) 5.45462e6 9.44768e6i 0.569883 0.987065i
\(621\) −661192. 1.14522e6i −0.0688016 0.119168i
\(622\) −5.61087e6 −0.581506
\(623\) 0 0
\(624\) −805054. −0.0827682
\(625\) 5.59185e6 + 9.68538e6i 0.572606 + 0.991782i
\(626\) 2.43789e6 4.22255e6i 0.248644 0.430664i
\(627\) 1.87999e6 3.25624e6i 0.190980 0.330786i
\(628\) 1.50882e6 + 2.61335e6i 0.152664 + 0.264423i
\(629\) 8.96293e6 0.903282
\(630\) 0 0
\(631\) −7.33039e6 −0.732916 −0.366458 0.930435i \(-0.619430\pi\)
−0.366458 + 0.930435i \(0.619430\pi\)
\(632\) −1.97160e6 3.41491e6i −0.196348 0.340084i
\(633\) −2.16786e6 + 3.75485e6i −0.215042 + 0.372463i
\(634\) −5.36003e6 + 9.28384e6i −0.529595 + 0.917286i
\(635\) 1.26515e6 + 2.19130e6i 0.124511 + 0.215659i
\(636\) 1.95786e6 0.191928
\(637\) 0 0
\(638\) 453786. 0.0441366
\(639\) 2.84090e6 + 4.92059e6i 0.275235 + 0.476722i
\(640\) −618433. + 1.07116e6i −0.0596819 + 0.103372i
\(641\) −1.84412e6 + 3.19411e6i −0.177273 + 0.307047i −0.940946 0.338558i \(-0.890061\pi\)
0.763672 + 0.645604i \(0.223394\pi\)
\(642\) 2.61482e6 + 4.52901e6i 0.250383 + 0.433676i
\(643\) 1.17584e7 1.12155 0.560776 0.827968i \(-0.310503\pi\)
0.560776 + 0.827968i \(0.310503\pi\)
\(644\) 0 0
\(645\) 8.28147e6 0.783806
\(646\) −6.42811e6 1.11338e7i −0.606041 1.04969i
\(647\) −4.97025e6 + 8.60873e6i −0.466786 + 0.808497i −0.999280 0.0379368i \(-0.987921\pi\)
0.532494 + 0.846434i \(0.321255\pi\)
\(648\) −209952. + 363648.i −0.0196419 + 0.0340207i
\(649\) 1.96982e6 + 3.41182e6i 0.183575 + 0.317962i
\(650\) −3.59772e6 −0.333998
\(651\) 0 0
\(652\) 1.43548e6 0.132244
\(653\) 513100. + 888714.i 0.0470889 + 0.0815604i 0.888609 0.458665i \(-0.151672\pi\)
−0.841520 + 0.540226i \(0.818339\pi\)
\(654\) 3.25531e6 5.63837e6i 0.297611 0.515477i
\(655\) −407995. + 706668.i −0.0371579 + 0.0643594i
\(656\) 977983. + 1.69392e6i 0.0887303 + 0.153685i
\(657\) 3.60197e6 0.325557
\(658\) 0 0
\(659\) 1.00207e7 0.898846 0.449423 0.893319i \(-0.351630\pi\)
0.449423 + 0.893319i \(0.351630\pi\)
\(660\) 812392. + 1.40710e6i 0.0725948 + 0.125738i
\(661\) 1.31413e6 2.27614e6i 0.116986 0.202626i −0.801586 0.597880i \(-0.796010\pi\)
0.918572 + 0.395254i \(0.129343\pi\)
\(662\) −285120. + 493843.i −0.0252862 + 0.0437970i
\(663\) 1.80799e6 + 3.13152e6i 0.159739 + 0.276676i
\(664\) 5.57709e6 0.490893
\(665\) 0 0
\(666\) 2.52554e6 0.220632
\(667\) 688431. + 1.19240e6i 0.0599165 + 0.103778i
\(668\) 4.23529e6 7.33574e6i 0.367233 0.636067i
\(669\) 2.87450e6 4.97879e6i 0.248312 0.430089i
\(670\) −8.20933e6 1.42190e7i −0.706514 1.22372i
\(671\) 5.27925e6 0.452654
\(672\) 0 0
\(673\) −1.50220e7 −1.27847 −0.639233 0.769013i \(-0.720748\pi\)
−0.639233 + 0.769013i \(0.720748\pi\)
\(674\) 2.42412e6 + 4.19871e6i 0.205544 + 0.356013i
\(675\) −938257. + 1.62511e6i −0.0792616 + 0.137285i
\(676\) 1.99361e6 3.45304e6i 0.167793 0.290626i
\(677\) −3.01655e6 5.22482e6i −0.252953 0.438127i 0.711385 0.702803i \(-0.248068\pi\)
−0.964337 + 0.264676i \(0.914735\pi\)
\(678\) 7.12197e6 0.595012
\(679\) 0 0
\(680\) 5.55550e6 0.460734
\(681\) −2.36557e6 4.09729e6i −0.195465 0.338554i
\(682\) −2.69980e6 + 4.67619e6i −0.222265 + 0.384974i
\(683\) −5.53601e6 + 9.58865e6i −0.454093 + 0.786513i −0.998636 0.0522205i \(-0.983370\pi\)
0.544542 + 0.838734i \(0.316703\pi\)
\(684\) −1.81129e6 3.13725e6i −0.148029 0.256394i
\(685\) −1.42922e6 −0.116379
\(686\) 0 0
\(687\) −8.39417e6 −0.678557
\(688\) −1.56017e6 2.70230e6i −0.125661 0.217652i
\(689\) 2.37537e6 4.11426e6i 0.190626 0.330174i
\(690\) −2.46493e6 + 4.26939e6i −0.197098 + 0.341384i
\(691\) −5.27739e6 9.14071e6i −0.420460 0.728257i 0.575525 0.817784i \(-0.304798\pi\)
−0.995984 + 0.0895269i \(0.971464\pi\)
\(692\) −541413. −0.0429797
\(693\) 0 0
\(694\) 1.38741e7 1.09347
\(695\) −6.37523e6 1.10422e7i −0.500650 0.867151i
\(696\) 218602. 378629.i 0.0171053 0.0296272i
\(697\) 4.39270e6 7.60838e6i 0.342491 0.593212i
\(698\) 2.03383e6 + 3.52270e6i 0.158007 + 0.273676i
\(699\) −6.37014e6 −0.493124
\(700\) 0 0
\(701\) −7.20675e6 −0.553917 −0.276958 0.960882i \(-0.589326\pi\)
−0.276958 + 0.960882i \(0.589326\pi\)
\(702\) 509448. + 882390.i 0.0390173 + 0.0675800i
\(703\) −1.08941e7 + 1.88692e7i −0.831390 + 1.44001i
\(704\) 306098. 530177.i 0.0232771 0.0403171i
\(705\) 8.35660e6 + 1.44741e7i 0.633223 + 1.09677i
\(706\) −6.25542e6 −0.472329
\(707\) 0 0
\(708\) 3.79567e6 0.284581
\(709\) −1.34687e6 2.33284e6i −0.100626 0.174289i 0.811317 0.584607i \(-0.198751\pi\)
−0.911943 + 0.410318i \(0.865418\pi\)
\(710\) 1.05909e7 1.83440e7i 0.788476 1.36568i
\(711\) −2.49530e6 + 4.32199e6i −0.185118 + 0.320634i
\(712\) 3.15422e6 + 5.46327e6i 0.233180 + 0.403880i
\(713\) −1.63833e7 −1.20692
\(714\) 0 0
\(715\) 3.94253e6 0.288410
\(716\) 1.98195e6 + 3.43284e6i 0.144481 + 0.250248i
\(717\) 2.25276e6 3.90190e6i 0.163651 0.283451i
\(718\) −99106.3 + 171657.i −0.00717447 + 0.0124266i
\(719\) 3.46275e6 + 5.99766e6i 0.249804 + 0.432673i 0.963471 0.267812i \(-0.0863005\pi\)
−0.713667 + 0.700485i \(0.752967\pi\)
\(720\) 1.56541e6 0.112537
\(721\) 0 0
\(722\) 2.13482e7 1.52412
\(723\) 5.43698e6 + 9.41713e6i 0.386823 + 0.669997i
\(724\) 2.95576e6 5.11953e6i 0.209567 0.362981i
\(725\) 976911. 1.69206e6i 0.0690256 0.119556i
\(726\) 2.49682e6 + 4.32462e6i 0.175811 + 0.304513i
\(727\) −4.11366e6 −0.288664 −0.144332 0.989529i \(-0.546103\pi\)
−0.144332 + 0.989529i \(0.546103\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −6.71411e6 1.16292e7i −0.466317 0.807685i
\(731\) −7.00765e6 + 1.21376e7i −0.485041 + 0.840116i
\(732\) 2.54317e6 4.40489e6i 0.175427 0.303849i
\(733\) 3.96019e6 + 6.85925e6i 0.272243 + 0.471538i 0.969436 0.245345i \(-0.0789013\pi\)
−0.697193 + 0.716883i \(0.745568\pi\)
\(734\) −1.41932e7 −0.972392
\(735\) 0 0
\(736\) 1.85750e6 0.126397
\(737\) 4.06326e6 + 7.03777e6i 0.275554 + 0.477273i
\(738\) 1.23776e6 2.14386e6i 0.0836557 0.144896i
\(739\) −8.02050e6 + 1.38919e7i −0.540245 + 0.935731i 0.458645 + 0.888620i \(0.348335\pi\)
−0.998890 + 0.0471115i \(0.984998\pi\)
\(740\) −4.70764e6 8.15387e6i −0.316027 0.547374i
\(741\) −8.79019e6 −0.588102
\(742\) 0 0
\(743\) 1.53453e7 1.01977 0.509887 0.860241i \(-0.329687\pi\)
0.509887 + 0.860241i \(0.329687\pi\)
\(744\) 2.60114e6 + 4.50531e6i 0.172279 + 0.298396i
\(745\) −9.96507e6 + 1.72600e7i −0.657794 + 1.13933i
\(746\) 4.51147e6 7.81409e6i 0.296805 0.514081i
\(747\) −3.52925e6 6.11284e6i −0.231409 0.400813i
\(748\) −2.74973e6 −0.179695
\(749\) 0 0
\(750\) −1.49721e6 −0.0971918
\(751\) −1.12488e7 1.94835e7i −0.727790 1.26057i −0.957815 0.287385i \(-0.907214\pi\)
0.230025 0.973185i \(-0.426119\pi\)
\(752\) 3.14865e6 5.45362e6i 0.203039 0.351674i
\(753\) 440220. 762483.i 0.0282932 0.0490053i
\(754\) −530436. 918743.i −0.0339786 0.0588526i
\(755\) 2.10756e7 1.34559
\(756\) 0 0
\(757\) 2.30349e7 1.46099 0.730494 0.682919i \(-0.239290\pi\)
0.730494 + 0.682919i \(0.239290\pi\)
\(758\) −8.79006e6 1.52248e7i −0.555673 0.962453i
\(759\) 1.22004e6 2.11316e6i 0.0768720 0.133146i
\(760\) −6.75252e6 + 1.16957e7i −0.424065 + 0.734501i
\(761\) 2.70368e6 + 4.68290e6i 0.169236 + 0.293126i 0.938152 0.346225i \(-0.112537\pi\)
−0.768915 + 0.639351i \(0.779203\pi\)
\(762\) −1.20662e6 −0.0752806
\(763\) 0 0
\(764\) −7.76359e6 −0.481204
\(765\) −3.51559e6 6.08918e6i −0.217192 0.376188i
\(766\) −2.45562e6 + 4.25325e6i −0.151213 + 0.261908i
\(767\) 4.60509e6 7.97626e6i 0.282651 0.489565i
\(768\) −294912. 510803.i −0.0180422 0.0312500i
\(769\) 7.93100e6