Properties

Label 294.6.e.q.79.1
Level $294$
Weight $6$
Character 294.79
Analytic conductor $47.153$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 294.79
Dual form 294.6.e.q.67.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(13.0000 - 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(2.00000 - 3.46410i) q^{2} +(4.50000 + 7.79423i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(13.0000 - 22.5167i) q^{5} +36.0000 q^{6} -64.0000 q^{8} +(-40.5000 + 70.1481i) q^{9} +(-52.0000 - 90.0666i) q^{10} +(179.000 + 310.037i) q^{11} +(72.0000 - 124.708i) q^{12} -332.000 q^{13} +234.000 q^{15} +(-128.000 + 221.703i) q^{16} +(63.0000 + 109.119i) q^{17} +(162.000 + 280.592i) q^{18} +(-1100.00 + 1905.26i) q^{19} -416.000 q^{20} +1432.00 q^{22} +(1071.00 - 1855.03i) q^{23} +(-288.000 - 498.831i) q^{24} +(1224.50 + 2120.90i) q^{25} +(-664.000 + 1150.08i) q^{26} -729.000 q^{27} -3610.00 q^{29} +(468.000 - 810.600i) q^{30} +(2834.00 + 4908.63i) q^{31} +(512.000 + 886.810i) q^{32} +(-1611.00 + 2790.33i) q^{33} +504.000 q^{34} +1296.00 q^{36} +(1461.00 - 2530.53i) q^{37} +(4400.00 + 7621.02i) q^{38} +(-1494.00 - 2587.68i) q^{39} +(-832.000 + 1441.07i) q^{40} +2142.00 q^{41} +6388.00 q^{43} +(2864.00 - 4960.59i) q^{44} +(1053.00 + 1823.85i) q^{45} +(-4284.00 - 7420.11i) q^{46} +(-3260.00 + 5646.49i) q^{47} -2304.00 q^{48} +9796.00 q^{50} +(-567.000 + 982.073i) q^{51} +(2656.00 + 4600.33i) q^{52} +(5351.00 + 9268.20i) q^{53} +(-1458.00 + 2525.33i) q^{54} +9308.00 q^{55} -19800.0 q^{57} +(-7220.00 + 12505.4i) q^{58} +(21262.0 + 36826.9i) q^{59} +(-1872.00 - 3242.40i) q^{60} +(-22420.0 + 38832.6i) q^{61} +22672.0 q^{62} +4096.00 q^{64} +(-4316.00 + 7475.53i) q^{65} +(6444.00 + 11161.3i) q^{66} +(724.000 + 1254.00i) q^{67} +(1008.00 - 1745.91i) q^{68} +19278.0 q^{69} -4402.00 q^{71} +(2592.00 - 4489.48i) q^{72} +(10250.0 + 17753.5i) q^{73} +(-5844.00 - 10122.1i) q^{74} +(-11020.5 + 19088.1i) q^{75} +35200.0 q^{76} -11952.0 q^{78} +(-32618.0 + 56496.0i) q^{79} +(3328.00 + 5764.27i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(4284.00 - 7420.11i) q^{82} +102804. q^{83} +3276.00 q^{85} +(12776.0 - 22128.7i) q^{86} +(-16245.0 - 28137.2i) q^{87} +(-11456.0 - 19842.4i) q^{88} +(-64003.0 + 110856. i) q^{89} +8424.00 q^{90} -34272.0 q^{92} +(-25506.0 + 44177.7i) q^{93} +(13040.0 + 22585.9i) q^{94} +(28600.0 + 49536.7i) q^{95} +(-4608.00 + 7981.29i) q^{96} +113324. q^{97} -28998.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} + 9 q^{3} - 16 q^{4} + 26 q^{5} + 72 q^{6} - 128 q^{8} - 81 q^{9} - 104 q^{10} + 358 q^{11} + 144 q^{12} - 664 q^{13} + 468 q^{15} - 256 q^{16} + 126 q^{17} + 324 q^{18} - 2200 q^{19} - 832 q^{20} + 2864 q^{22} + 2142 q^{23} - 576 q^{24} + 2449 q^{25} - 1328 q^{26} - 1458 q^{27} - 7220 q^{29} + 936 q^{30} + 5668 q^{31} + 1024 q^{32} - 3222 q^{33} + 1008 q^{34} + 2592 q^{36} + 2922 q^{37} + 8800 q^{38} - 2988 q^{39} - 1664 q^{40} + 4284 q^{41} + 12776 q^{43} + 5728 q^{44} + 2106 q^{45} - 8568 q^{46} - 6520 q^{47} - 4608 q^{48} + 19592 q^{50} - 1134 q^{51} + 5312 q^{52} + 10702 q^{53} - 2916 q^{54} + 18616 q^{55} - 39600 q^{57} - 14440 q^{58} + 42524 q^{59} - 3744 q^{60} - 44840 q^{61} + 45344 q^{62} + 8192 q^{64} - 8632 q^{65} + 12888 q^{66} + 1448 q^{67} + 2016 q^{68} + 38556 q^{69} - 8804 q^{71} + 5184 q^{72} + 20500 q^{73} - 11688 q^{74} - 22041 q^{75} + 70400 q^{76} - 23904 q^{78} - 65236 q^{79} + 6656 q^{80} - 6561 q^{81} + 8568 q^{82} + 205608 q^{83} + 6552 q^{85} + 25552 q^{86} - 32490 q^{87} - 22912 q^{88} - 128006 q^{89} + 16848 q^{90} - 68544 q^{92} - 51012 q^{93} + 26080 q^{94} + 57200 q^{95} - 9216 q^{96} + 226648 q^{97} - 57996 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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
\(5\) 13.0000 22.5167i 0.232551 0.402790i −0.726007 0.687687i \(-0.758626\pi\)
0.958558 + 0.284897i \(0.0919594\pi\)
\(6\) 36.0000 0.408248
\(7\) 0 0
\(8\) −64.0000 −0.353553
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) −52.0000 90.0666i −0.164438 0.284816i
\(11\) 179.000 + 310.037i 0.446037 + 0.772560i 0.998124 0.0612274i \(-0.0195015\pi\)
−0.552086 + 0.833787i \(0.686168\pi\)
\(12\) 72.0000 124.708i 0.144338 0.250000i
\(13\) −332.000 −0.544853 −0.272427 0.962177i \(-0.587826\pi\)
−0.272427 + 0.962177i \(0.587826\pi\)
\(14\) 0 0
\(15\) 234.000 0.268527
\(16\) −128.000 + 221.703i −0.125000 + 0.216506i
\(17\) 63.0000 + 109.119i 0.0528711 + 0.0915754i 0.891250 0.453513i \(-0.149829\pi\)
−0.838379 + 0.545088i \(0.816496\pi\)
\(18\) 162.000 + 280.592i 0.117851 + 0.204124i
\(19\) −1100.00 + 1905.26i −0.699051 + 1.21079i 0.269745 + 0.962932i \(0.413061\pi\)
−0.968796 + 0.247860i \(0.920273\pi\)
\(20\) −416.000 −0.232551
\(21\) 0 0
\(22\) 1432.00 0.630792
\(23\) 1071.00 1855.03i 0.422153 0.731190i −0.573997 0.818858i \(-0.694608\pi\)
0.996150 + 0.0876671i \(0.0279412\pi\)
\(24\) −288.000 498.831i −0.102062 0.176777i
\(25\) 1224.50 + 2120.90i 0.391840 + 0.678687i
\(26\) −664.000 + 1150.08i −0.192635 + 0.333653i
\(27\) −729.000 −0.192450
\(28\) 0 0
\(29\) −3610.00 −0.797099 −0.398549 0.917147i \(-0.630486\pi\)
−0.398549 + 0.917147i \(0.630486\pi\)
\(30\) 468.000 810.600i 0.0949386 0.164438i
\(31\) 2834.00 + 4908.63i 0.529658 + 0.917395i 0.999402 + 0.0345917i \(0.0110131\pi\)
−0.469743 + 0.882803i \(0.655654\pi\)
\(32\) 512.000 + 886.810i 0.0883883 + 0.153093i
\(33\) −1611.00 + 2790.33i −0.257520 + 0.446037i
\(34\) 504.000 0.0747710
\(35\) 0 0
\(36\) 1296.00 0.166667
\(37\) 1461.00 2530.53i 0.175447 0.303883i −0.764869 0.644186i \(-0.777196\pi\)
0.940316 + 0.340303i \(0.110530\pi\)
\(38\) 4400.00 + 7621.02i 0.494303 + 0.856159i
\(39\) −1494.00 2587.68i −0.157286 0.272427i
\(40\) −832.000 + 1441.07i −0.0822192 + 0.142408i
\(41\) 2142.00 0.199003 0.0995015 0.995037i \(-0.468275\pi\)
0.0995015 + 0.995037i \(0.468275\pi\)
\(42\) 0 0
\(43\) 6388.00 0.526858 0.263429 0.964679i \(-0.415146\pi\)
0.263429 + 0.964679i \(0.415146\pi\)
\(44\) 2864.00 4960.59i 0.223019 0.386280i
\(45\) 1053.00 + 1823.85i 0.0775170 + 0.134263i
\(46\) −4284.00 7420.11i −0.298507 0.517030i
\(47\) −3260.00 + 5646.49i −0.215265 + 0.372850i −0.953354 0.301853i \(-0.902395\pi\)
0.738090 + 0.674703i \(0.235728\pi\)
\(48\) −2304.00 −0.144338
\(49\) 0 0
\(50\) 9796.00 0.554145
\(51\) −567.000 + 982.073i −0.0305251 + 0.0528711i
\(52\) 2656.00 + 4600.33i 0.136213 + 0.235928i
\(53\) 5351.00 + 9268.20i 0.261665 + 0.453217i 0.966684 0.255971i \(-0.0823952\pi\)
−0.705020 + 0.709188i \(0.749062\pi\)
\(54\) −1458.00 + 2525.33i −0.0680414 + 0.117851i
\(55\) 9308.00 0.414906
\(56\) 0 0
\(57\) −19800.0 −0.807194
\(58\) −7220.00 + 12505.4i −0.281817 + 0.488121i
\(59\) 21262.0 + 36826.9i 0.795196 + 1.37732i 0.922715 + 0.385483i \(0.125965\pi\)
−0.127519 + 0.991836i \(0.540701\pi\)
\(60\) −1872.00 3242.40i −0.0671317 0.116276i
\(61\) −22420.0 + 38832.6i −0.771456 + 1.33620i 0.165309 + 0.986242i \(0.447138\pi\)
−0.936765 + 0.349959i \(0.886196\pi\)
\(62\) 22672.0 0.749050
\(63\) 0 0
\(64\) 4096.00 0.125000
\(65\) −4316.00 + 7475.53i −0.126706 + 0.219462i
\(66\) 6444.00 + 11161.3i 0.182094 + 0.315396i
\(67\) 724.000 + 1254.00i 0.0197039 + 0.0341281i 0.875709 0.482839i \(-0.160394\pi\)
−0.856005 + 0.516967i \(0.827061\pi\)
\(68\) 1008.00 1745.91i 0.0264355 0.0457877i
\(69\) 19278.0 0.487460
\(70\) 0 0
\(71\) −4402.00 −0.103634 −0.0518172 0.998657i \(-0.516501\pi\)
−0.0518172 + 0.998657i \(0.516501\pi\)
\(72\) 2592.00 4489.48i 0.0589256 0.102062i
\(73\) 10250.0 + 17753.5i 0.225121 + 0.389922i 0.956356 0.292205i \(-0.0943888\pi\)
−0.731234 + 0.682126i \(0.761055\pi\)
\(74\) −5844.00 10122.1i −0.124060 0.214878i
\(75\) −11020.5 + 19088.1i −0.226229 + 0.391840i
\(76\) 35200.0 0.699051
\(77\) 0 0
\(78\) −11952.0 −0.222435
\(79\) −32618.0 + 56496.0i −0.588017 + 1.01847i 0.406475 + 0.913662i \(0.366758\pi\)
−0.994492 + 0.104813i \(0.966576\pi\)
\(80\) 3328.00 + 5764.27i 0.0581378 + 0.100698i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) 4284.00 7420.11i 0.0703582 0.121864i
\(83\) 102804. 1.63800 0.819002 0.573791i \(-0.194528\pi\)
0.819002 + 0.573791i \(0.194528\pi\)
\(84\) 0 0
\(85\) 3276.00 0.0491809
\(86\) 12776.0 22128.7i 0.186273 0.322633i
\(87\) −16245.0 28137.2i −0.230103 0.398549i
\(88\) −11456.0 19842.4i −0.157698 0.273141i
\(89\) −64003.0 + 110856.i −0.856496 + 1.48349i 0.0187543 + 0.999824i \(0.494030\pi\)
−0.875250 + 0.483670i \(0.839303\pi\)
\(90\) 8424.00 0.109626
\(91\) 0 0
\(92\) −34272.0 −0.422153
\(93\) −25506.0 + 44177.7i −0.305798 + 0.529658i
\(94\) 13040.0 + 22585.9i 0.152215 + 0.263644i
\(95\) 28600.0 + 49536.7i 0.325130 + 0.563142i
\(96\) −4608.00 + 7981.29i −0.0510310 + 0.0883883i
\(97\) 113324. 1.22290 0.611452 0.791281i \(-0.290586\pi\)
0.611452 + 0.791281i \(0.290586\pi\)
\(98\) 0 0
\(99\) −28998.0 −0.297358
\(100\) 19592.0 33934.3i 0.195920 0.339343i
\(101\) −69857.0 120996.i −0.681407 1.18023i −0.974552 0.224163i \(-0.928035\pi\)
0.293145 0.956068i \(-0.405298\pi\)
\(102\) 2268.00 + 3928.29i 0.0215845 + 0.0373855i
\(103\) −71090.0 + 123131.i −0.660261 + 1.14361i 0.320286 + 0.947321i \(0.396221\pi\)
−0.980547 + 0.196284i \(0.937112\pi\)
\(104\) 21248.0 0.192635
\(105\) 0 0
\(106\) 42808.0 0.370050
\(107\) 99259.0 171922.i 0.838128 1.45168i −0.0533296 0.998577i \(-0.516983\pi\)
0.891458 0.453104i \(-0.149683\pi\)
\(108\) 5832.00 + 10101.3i 0.0481125 + 0.0833333i
\(109\) −66269.0 114781.i −0.534250 0.925347i −0.999199 0.0400103i \(-0.987261\pi\)
0.464950 0.885337i \(-0.346072\pi\)
\(110\) 18616.0 32243.9i 0.146691 0.254077i
\(111\) 26298.0 0.202589
\(112\) 0 0
\(113\) 47026.0 0.346451 0.173226 0.984882i \(-0.444581\pi\)
0.173226 + 0.984882i \(0.444581\pi\)
\(114\) −39600.0 + 68589.2i −0.285386 + 0.494303i
\(115\) −27846.0 48230.7i −0.196344 0.340078i
\(116\) 28880.0 + 50021.6i 0.199275 + 0.345154i
\(117\) 13446.0 23289.2i 0.0908089 0.157286i
\(118\) 170096. 1.12458
\(119\) 0 0
\(120\) −14976.0 −0.0949386
\(121\) 16443.5 28481.0i 0.102101 0.176844i
\(122\) 89680.0 + 155330.i 0.545502 + 0.944836i
\(123\) 9639.00 + 16695.2i 0.0574472 + 0.0995015i
\(124\) 45344.0 78538.1i 0.264829 0.458697i
\(125\) 144924. 0.829593
\(126\) 0 0
\(127\) 165548. 0.910782 0.455391 0.890291i \(-0.349499\pi\)
0.455391 + 0.890291i \(0.349499\pi\)
\(128\) 8192.00 14189.0i 0.0441942 0.0765466i
\(129\) 28746.0 + 49789.5i 0.152091 + 0.263429i
\(130\) 17264.0 + 29902.1i 0.0895948 + 0.155183i
\(131\) −69654.0 + 120644.i −0.354624 + 0.614226i −0.987053 0.160391i \(-0.948724\pi\)
0.632430 + 0.774618i \(0.282058\pi\)
\(132\) 51552.0 0.257520
\(133\) 0 0
\(134\) 5792.00 0.0278655
\(135\) −9477.00 + 16414.6i −0.0447545 + 0.0775170i
\(136\) −4032.00 6983.63i −0.0186928 0.0323768i
\(137\) 166421. + 288250.i 0.757542 + 1.31210i 0.944101 + 0.329657i \(0.106933\pi\)
−0.186559 + 0.982444i \(0.559733\pi\)
\(138\) 38556.0 66781.0i 0.172343 0.298507i
\(139\) −8556.00 −0.0375607 −0.0187804 0.999824i \(-0.505978\pi\)
−0.0187804 + 0.999824i \(0.505978\pi\)
\(140\) 0 0
\(141\) −58680.0 −0.248566
\(142\) −8804.00 + 15249.0i −0.0366403 + 0.0634629i
\(143\) −59428.0 102932.i −0.243025 0.420932i
\(144\) −10368.0 17957.9i −0.0416667 0.0721688i
\(145\) −46930.0 + 81285.1i −0.185366 + 0.321064i
\(146\) 82000.0 0.318370
\(147\) 0 0
\(148\) −46752.0 −0.175447
\(149\) −34777.0 + 60235.5i −0.128329 + 0.222273i −0.923029 0.384729i \(-0.874295\pi\)
0.794700 + 0.607002i \(0.207628\pi\)
\(150\) 44082.0 + 76352.3i 0.159968 + 0.277073i
\(151\) −264620. 458335.i −0.944453 1.63584i −0.756843 0.653597i \(-0.773259\pi\)
−0.187610 0.982244i \(-0.560074\pi\)
\(152\) 70400.0 121936.i 0.247152 0.428079i
\(153\) −10206.0 −0.0352474
\(154\) 0 0
\(155\) 147368. 0.492690
\(156\) −23904.0 + 41402.9i −0.0786428 + 0.136213i
\(157\) 6520.00 + 11293.0i 0.0211105 + 0.0365645i 0.876388 0.481606i \(-0.159946\pi\)
−0.855277 + 0.518171i \(0.826613\pi\)
\(158\) 130472. + 225984.i 0.415791 + 0.720170i
\(159\) −48159.0 + 83413.8i −0.151072 + 0.261665i
\(160\) 26624.0 0.0822192
\(161\) 0 0
\(162\) −26244.0 −0.0785674
\(163\) 175620. 304183.i 0.517732 0.896738i −0.482056 0.876140i \(-0.660110\pi\)
0.999788 0.0205976i \(-0.00655687\pi\)
\(164\) −17136.0 29680.4i −0.0497508 0.0861709i
\(165\) 41886.0 + 72548.7i 0.119773 + 0.207453i
\(166\) 205608. 356124.i 0.579122 1.00307i
\(167\) −626128. −1.73729 −0.868644 0.495436i \(-0.835008\pi\)
−0.868644 + 0.495436i \(0.835008\pi\)
\(168\) 0 0
\(169\) −261069. −0.703135
\(170\) 6552.00 11348.4i 0.0173881 0.0301170i
\(171\) −89100.0 154326.i −0.233017 0.403597i
\(172\) −51104.0 88514.7i −0.131715 0.228136i
\(173\) −92413.0 + 160064.i −0.234757 + 0.406610i −0.959202 0.282722i \(-0.908763\pi\)
0.724445 + 0.689332i \(0.242096\pi\)
\(174\) −129960. −0.325414
\(175\) 0 0
\(176\) −91648.0 −0.223019
\(177\) −191358. + 331442.i −0.459107 + 0.795196i
\(178\) 256012. + 443426.i 0.605634 + 1.04899i
\(179\) 178761. + 309623.i 0.417004 + 0.722272i 0.995637 0.0933163i \(-0.0297468\pi\)
−0.578633 + 0.815588i \(0.696413\pi\)
\(180\) 16848.0 29181.6i 0.0387585 0.0671317i
\(181\) −696508. −1.58026 −0.790132 0.612937i \(-0.789988\pi\)
−0.790132 + 0.612937i \(0.789988\pi\)
\(182\) 0 0
\(183\) −403560. −0.890800
\(184\) −68544.0 + 118722.i −0.149254 + 0.258515i
\(185\) −37986.0 65793.7i −0.0816008 0.141337i
\(186\) 102024. + 176711.i 0.216232 + 0.374525i
\(187\) −22554.0 + 39064.7i −0.0471650 + 0.0816921i
\(188\) 104320. 0.215265
\(189\) 0 0
\(190\) 228800. 0.459803
\(191\) −34335.0 + 59470.0i −0.0681010 + 0.117954i −0.898065 0.439862i \(-0.855027\pi\)
0.829964 + 0.557816i \(0.188361\pi\)
\(192\) 18432.0 + 31925.2i 0.0360844 + 0.0625000i
\(193\) −413611. 716395.i −0.799280 1.38439i −0.920086 0.391717i \(-0.871881\pi\)
0.120806 0.992676i \(-0.461452\pi\)
\(194\) 226648. 392566.i 0.432362 0.748873i
\(195\) −77688.0 −0.146308
\(196\) 0 0
\(197\) −143382. −0.263226 −0.131613 0.991301i \(-0.542016\pi\)
−0.131613 + 0.991301i \(0.542016\pi\)
\(198\) −57996.0 + 100452.i −0.105132 + 0.182094i
\(199\) −271300. 469905.i −0.485643 0.841158i 0.514221 0.857658i \(-0.328081\pi\)
−0.999864 + 0.0164995i \(0.994748\pi\)
\(200\) −78368.0 135737.i −0.138536 0.239952i
\(201\) −6516.00 + 11286.0i −0.0113760 + 0.0197039i
\(202\) −558856. −0.963655
\(203\) 0 0
\(204\) 18144.0 0.0305251
\(205\) 27846.0 48230.7i 0.0462784 0.0801565i
\(206\) 284360. + 492526.i 0.466875 + 0.808651i
\(207\) 86751.0 + 150257.i 0.140718 + 0.243730i
\(208\) 42496.0 73605.2i 0.0681067 0.117964i
\(209\) −787600. −1.24721
\(210\) 0 0
\(211\) 1.12776e6 1.74385 0.871925 0.489640i \(-0.162872\pi\)
0.871925 + 0.489640i \(0.162872\pi\)
\(212\) 85616.0 148291.i 0.130832 0.226608i
\(213\) −19809.0 34310.2i −0.0299167 0.0518172i
\(214\) −397036. 687687.i −0.592646 1.02649i
\(215\) 83044.0 143836.i 0.122521 0.212213i
\(216\) 46656.0 0.0680414
\(217\) 0 0
\(218\) −530152. −0.755543
\(219\) −92250.0 + 159782.i −0.129974 + 0.225121i
\(220\) −74464.0 128975.i −0.103726 0.179660i
\(221\) −20916.0 36227.6i −0.0288070 0.0498952i
\(222\) 52596.0 91098.9i 0.0716259 0.124060i
\(223\) −897976. −1.20921 −0.604606 0.796525i \(-0.706669\pi\)
−0.604606 + 0.796525i \(0.706669\pi\)
\(224\) 0 0
\(225\) −198369. −0.261227
\(226\) 94052.0 162903.i 0.122489 0.212157i
\(227\) −233806. 404964.i −0.301156 0.521617i 0.675242 0.737596i \(-0.264039\pi\)
−0.976398 + 0.215979i \(0.930706\pi\)
\(228\) 158400. + 274357.i 0.201799 + 0.349525i
\(229\) −223070. + 386369.i −0.281095 + 0.486870i −0.971655 0.236405i \(-0.924031\pi\)
0.690560 + 0.723275i \(0.257364\pi\)
\(230\) −222768. −0.277673
\(231\) 0 0
\(232\) 231040. 0.281817
\(233\) −350743. + 607505.i −0.423252 + 0.733094i −0.996255 0.0864588i \(-0.972445\pi\)
0.573003 + 0.819553i \(0.305778\pi\)
\(234\) −53784.0 93156.6i −0.0642116 0.111218i
\(235\) 84760.0 + 146809.i 0.100120 + 0.173413i
\(236\) 340192. 589230.i 0.397598 0.688660i
\(237\) −587124. −0.678983
\(238\) 0 0
\(239\) −384198. −0.435071 −0.217536 0.976052i \(-0.569802\pi\)
−0.217536 + 0.976052i \(0.569802\pi\)
\(240\) −29952.0 + 51878.4i −0.0335659 + 0.0581378i
\(241\) −476890. 825998.i −0.528902 0.916086i −0.999432 0.0337017i \(-0.989270\pi\)
0.470529 0.882384i \(-0.344063\pi\)
\(242\) −65774.0 113924.i −0.0721964 0.125048i
\(243\) 29524.5 51137.9i 0.0320750 0.0555556i
\(244\) 717440. 0.771456
\(245\) 0 0
\(246\) 77112.0 0.0812427
\(247\) 365200. 632545.i 0.380880 0.659704i
\(248\) −181376. 314152.i −0.187262 0.324348i
\(249\) 462618. + 801278.i 0.472851 + 0.819002i
\(250\) 289848. 502031.i 0.293306 0.508020i
\(251\) −569540. −0.570611 −0.285305 0.958437i \(-0.592095\pi\)
−0.285305 + 0.958437i \(0.592095\pi\)
\(252\) 0 0
\(253\) 766836. 0.753184
\(254\) 331096. 573475.i 0.322010 0.557738i
\(255\) 14742.0 + 25533.9i 0.0141973 + 0.0245905i
\(256\) −32768.0 56755.8i −0.0312500 0.0541266i
\(257\) 533321. 923739.i 0.503681 0.872402i −0.496310 0.868146i \(-0.665312\pi\)
0.999991 0.00425609i \(-0.00135476\pi\)
\(258\) 229968. 0.215089
\(259\) 0 0
\(260\) 138112. 0.126706
\(261\) 146205. 253234.i 0.132850 0.230103i
\(262\) 278616. + 482577.i 0.250757 + 0.434324i
\(263\) 741215. + 1.28382e6i 0.660777 + 1.14450i 0.980412 + 0.196958i \(0.0631064\pi\)
−0.319635 + 0.947541i \(0.603560\pi\)
\(264\) 103104. 178581.i 0.0910470 0.157698i
\(265\) 278252. 0.243402
\(266\) 0 0
\(267\) −1.15205e6 −0.988996
\(268\) 11584.0 20064.1i 0.00985194 0.0170641i
\(269\) −107555. 186291.i −0.0906254 0.156968i 0.817149 0.576426i \(-0.195553\pi\)
−0.907774 + 0.419459i \(0.862220\pi\)
\(270\) 37908.0 + 65658.6i 0.0316462 + 0.0548128i
\(271\) 965518. 1.67233e6i 0.798614 1.38324i −0.121904 0.992542i \(-0.538900\pi\)
0.920519 0.390699i \(-0.127767\pi\)
\(272\) −32256.0 −0.0264355
\(273\) 0 0
\(274\) 1.33137e6 1.07133
\(275\) −438371. + 759281.i −0.349551 + 0.605439i
\(276\) −154224. 267124.i −0.121865 0.211077i
\(277\) −1.01878e6 1.76458e6i −0.797777 1.38179i −0.921061 0.389419i \(-0.872676\pi\)
0.123284 0.992371i \(-0.460657\pi\)
\(278\) −17112.0 + 29638.9i −0.0132797 + 0.0230011i
\(279\) −459108. −0.353105
\(280\) 0 0
\(281\) −639066. −0.482814 −0.241407 0.970424i \(-0.577609\pi\)
−0.241407 + 0.970424i \(0.577609\pi\)
\(282\) −117360. + 203273.i −0.0878815 + 0.152215i
\(283\) 18872.0 + 32687.3i 0.0140072 + 0.0242612i 0.872944 0.487820i \(-0.162208\pi\)
−0.858937 + 0.512082i \(0.828875\pi\)
\(284\) 35216.0 + 60995.9i 0.0259086 + 0.0448750i
\(285\) −257400. + 445830.i −0.187714 + 0.325130i
\(286\) −475424. −0.343689
\(287\) 0 0
\(288\) −82944.0 −0.0589256
\(289\) 701990. 1.21588e6i 0.494409 0.856342i
\(290\) 187720. + 325141.i 0.131074 + 0.227026i
\(291\) 509958. + 883273.i 0.353022 + 0.611452i
\(292\) 164000. 284056.i 0.112561 0.194961i
\(293\) 1.83921e6 1.25159 0.625795 0.779987i \(-0.284775\pi\)
0.625795 + 0.779987i \(0.284775\pi\)
\(294\) 0 0
\(295\) 1.10562e6 0.739695
\(296\) −93504.0 + 161954.i −0.0620299 + 0.107439i
\(297\) −130491. 226017.i −0.0858399 0.148679i
\(298\) 139108. + 240942.i 0.0907426 + 0.157171i
\(299\) −355572. + 615869.i −0.230012 + 0.398392i
\(300\) 352656. 0.226229
\(301\) 0 0
\(302\) −2.11696e6 −1.33566
\(303\) 628713. 1.08896e6i 0.393410 0.681407i
\(304\) −281600. 487746.i −0.174763 0.302698i
\(305\) 582920. + 1.00965e6i 0.358806 + 0.621470i
\(306\) −20412.0 + 35354.6i −0.0124618 + 0.0215845i
\(307\) 1.06472e6 0.644747 0.322374 0.946613i \(-0.395519\pi\)
0.322374 + 0.946613i \(0.395519\pi\)
\(308\) 0 0
\(309\) −1.27962e6 −0.762403
\(310\) 294736. 510498.i 0.174192 0.301710i
\(311\) −504760. 874270.i −0.295927 0.512560i 0.679273 0.733885i \(-0.262295\pi\)
−0.975200 + 0.221325i \(0.928962\pi\)
\(312\) 95616.0 + 165612.i 0.0556089 + 0.0963174i
\(313\) −724548. + 1.25495e6i −0.418029 + 0.724047i −0.995741 0.0921932i \(-0.970612\pi\)
0.577712 + 0.816241i \(0.303946\pi\)
\(314\) 52160.0 0.0298548
\(315\) 0 0
\(316\) 1.04378e6 0.588017
\(317\) −1.36155e6 + 2.35828e6i −0.761003 + 1.31810i 0.181331 + 0.983422i \(0.441959\pi\)
−0.942334 + 0.334674i \(0.891374\pi\)
\(318\) 192636. + 333655.i 0.106824 + 0.185025i
\(319\) −646190. 1.11923e6i −0.355536 0.615806i
\(320\) 53248.0 92228.2i 0.0290689 0.0503488i
\(321\) 1.78666e6 0.967787
\(322\) 0 0
\(323\) −277200. −0.147838
\(324\) −52488.0 + 90911.9i −0.0277778 + 0.0481125i
\(325\) −406534. 704138.i −0.213495 0.369785i
\(326\) −702480. 1.21673e6i −0.366092 0.634090i
\(327\) 596421. 1.03303e6i 0.308449 0.534250i
\(328\) −137088. −0.0703582
\(329\) 0 0
\(330\) 335088. 0.169385
\(331\) 550202. 952978.i 0.276027 0.478093i −0.694366 0.719622i \(-0.744315\pi\)
0.970394 + 0.241528i \(0.0776486\pi\)
\(332\) −822432. 1.42449e6i −0.409501 0.709276i
\(333\) 118341. + 204973.i 0.0584823 + 0.101294i
\(334\) −1.25226e6 + 2.16897e6i −0.614224 + 1.06387i
\(335\) 37648.0 0.0183286
\(336\) 0 0
\(337\) 1.73512e6 0.832251 0.416125 0.909307i \(-0.363388\pi\)
0.416125 + 0.909307i \(0.363388\pi\)
\(338\) −522138. + 904370.i −0.248596 + 0.430580i
\(339\) 211617. + 366531.i 0.100012 + 0.173226i
\(340\) −26208.0 45393.6i −0.0122952 0.0212960i
\(341\) −1.01457e6 + 1.75729e6i −0.472495 + 0.818385i
\(342\) −712800. −0.329536
\(343\) 0 0
\(344\) −408832. −0.186273
\(345\) 250614. 434076.i 0.113359 0.196344i
\(346\) 369652. + 640256.i 0.165998 + 0.287517i
\(347\) −795723. 1.37823e6i −0.354763 0.614467i 0.632314 0.774712i \(-0.282105\pi\)
−0.987077 + 0.160244i \(0.948772\pi\)
\(348\) −259920. + 450195.i −0.115051 + 0.199275i
\(349\) 2.33376e6 1.02563 0.512817 0.858498i \(-0.328602\pi\)
0.512817 + 0.858498i \(0.328602\pi\)
\(350\) 0 0
\(351\) 242028. 0.104857
\(352\) −183296. + 317478.i −0.0788490 + 0.136571i
\(353\) 1.40541e6 + 2.43424e6i 0.600296 + 1.03974i 0.992776 + 0.119982i \(0.0382838\pi\)
−0.392480 + 0.919760i \(0.628383\pi\)
\(354\) 765432. + 1.32577e6i 0.324637 + 0.562288i
\(355\) −57226.0 + 99118.3i −0.0241003 + 0.0417429i
\(356\) 2.04810e6 0.856496
\(357\) 0 0
\(358\) 1.43009e6 0.589733
\(359\) −469655. + 813466.i −0.192328 + 0.333122i −0.946021 0.324104i \(-0.894937\pi\)
0.753693 + 0.657226i \(0.228270\pi\)
\(360\) −67392.0 116726.i −0.0274064 0.0474693i
\(361\) −1.18195e6 2.04720e6i −0.477344 0.826784i
\(362\) −1.39302e6 + 2.41277e6i −0.558708 + 0.967710i
\(363\) 295983. 0.117896
\(364\) 0 0
\(365\) 533000. 0.209409
\(366\) −807120. + 1.39797e6i −0.314945 + 0.545502i
\(367\) 1.54926e6 + 2.68339e6i 0.600424 + 1.03996i 0.992757 + 0.120141i \(0.0383348\pi\)
−0.392333 + 0.919823i \(0.628332\pi\)
\(368\) 274176. + 474887.i 0.105538 + 0.182798i
\(369\) −86751.0 + 150257.i −0.0331672 + 0.0574472i
\(370\) −303888. −0.115401
\(371\) 0 0
\(372\) 816192. 0.305798
\(373\) 114133. 197684.i 0.0424756 0.0735698i −0.844006 0.536334i \(-0.819809\pi\)
0.886482 + 0.462764i \(0.153142\pi\)
\(374\) 90216.0 + 156259.i 0.0333507 + 0.0577651i
\(375\) 652158. + 1.12957e6i 0.239483 + 0.414797i
\(376\) 208640. 361375.i 0.0761076 0.131822i
\(377\) 1.19852e6 0.434302
\(378\) 0 0
\(379\) −1.03669e6 −0.370725 −0.185362 0.982670i \(-0.559346\pi\)
−0.185362 + 0.982670i \(0.559346\pi\)
\(380\) 457600. 792586.i 0.162565 0.281571i
\(381\) 744966. + 1.29032e6i 0.262920 + 0.455391i
\(382\) 137340. + 237880.i 0.0481547 + 0.0834064i
\(383\) −105888. + 183403.i −0.0368850 + 0.0638867i −0.883879 0.467716i \(-0.845077\pi\)
0.846994 + 0.531603i \(0.178410\pi\)
\(384\) 147456. 0.0510310
\(385\) 0 0
\(386\) −3.30889e6 −1.13035
\(387\) −258714. + 448106.i −0.0878097 + 0.152091i
\(388\) −906592. 1.57026e6i −0.305726 0.529533i
\(389\) −706623. 1.22391e6i −0.236763 0.410085i 0.723021 0.690826i \(-0.242753\pi\)
−0.959784 + 0.280741i \(0.909420\pi\)
\(390\) −155376. + 269119.i −0.0517276 + 0.0895948i
\(391\) 269892. 0.0892788
\(392\) 0 0
\(393\) −1.25377e6 −0.409484
\(394\) −286764. + 496690.i −0.0930645 + 0.161192i
\(395\) 848068. + 1.46890e6i 0.273488 + 0.473695i
\(396\) 231984. + 401808.i 0.0743396 + 0.128760i
\(397\) −545168. + 944259.i −0.173602 + 0.300687i −0.939676 0.342064i \(-0.888874\pi\)
0.766075 + 0.642751i \(0.222207\pi\)
\(398\) −2.17040e6 −0.686803
\(399\) 0 0
\(400\) −626944. −0.195920
\(401\) −1.32126e6 + 2.28849e6i −0.410325 + 0.710704i −0.994925 0.100617i \(-0.967918\pi\)
0.584600 + 0.811322i \(0.301252\pi\)
\(402\) 26064.0 + 45144.2i 0.00804407 + 0.0139327i
\(403\) −940888. 1.62967e6i −0.288586 0.499846i
\(404\) −1.11771e6 + 1.93593e6i −0.340703 + 0.590116i
\(405\) −170586. −0.0516780
\(406\) 0 0
\(407\) 1.04608e6 0.313024
\(408\) 36288.0 62852.7i 0.0107923 0.0186928i
\(409\) 3.12713e6 + 5.41635e6i 0.924354 + 1.60103i 0.792597 + 0.609746i \(0.208728\pi\)
0.131757 + 0.991282i \(0.457938\pi\)
\(410\) −111384. 192923.i −0.0327238 0.0566792i
\(411\) −1.49779e6 + 2.59425e6i −0.437367 + 0.757542i
\(412\) 2.27488e6 0.660261
\(413\) 0 0
\(414\) 694008. 0.199005
\(415\) 1.33645e6 2.31480e6i 0.380919 0.659772i
\(416\) −169984. 294421.i −0.0481587 0.0834133i
\(417\) −38502.0 66687.4i −0.0108428 0.0187804i
\(418\) −1.57520e6 + 2.72833e6i −0.440956 + 0.763758i
\(419\) 973924. 0.271013 0.135506 0.990776i \(-0.456734\pi\)
0.135506 + 0.990776i \(0.456734\pi\)
\(420\) 0 0
\(421\) 864618. 0.237749 0.118875 0.992909i \(-0.462071\pi\)
0.118875 + 0.992909i \(0.462071\pi\)
\(422\) 2.25551e6 3.90666e6i 0.616544 1.06789i
\(423\) −264060. 457365.i −0.0717549 0.124283i
\(424\) −342464. 593165.i −0.0925125 0.160236i
\(425\) −154287. + 267233.i −0.0414340 + 0.0717658i
\(426\) −158472. −0.0423086
\(427\) 0 0
\(428\) −3.17629e6 −0.838128
\(429\) 534852. 926391.i 0.140311 0.243025i
\(430\) −332176. 575346.i −0.0866357 0.150058i
\(431\) 1.83023e6 + 3.17005e6i 0.474583 + 0.822002i 0.999576 0.0291043i \(-0.00926551\pi\)
−0.524993 + 0.851106i \(0.675932\pi\)
\(432\) 93312.0 161621.i 0.0240563 0.0416667i
\(433\) 4.93667e6 1.26536 0.632681 0.774413i \(-0.281955\pi\)
0.632681 + 0.774413i \(0.281955\pi\)
\(434\) 0 0
\(435\) −844740. −0.214042
\(436\) −1.06030e6 + 1.83650e6i −0.267125 + 0.462674i
\(437\) 2.35620e6 + 4.08106e6i 0.590213 + 1.02228i
\(438\) 369000. + 639127.i 0.0919054 + 0.159185i
\(439\) 365652. 633328.i 0.0905538 0.156844i −0.817190 0.576368i \(-0.804470\pi\)
0.907744 + 0.419524i \(0.137803\pi\)
\(440\) −595712. −0.146691
\(441\) 0 0
\(442\) −167328. −0.0407392
\(443\) −2.43310e6 + 4.21425e6i −0.589048 + 1.02026i 0.405310 + 0.914179i \(0.367164\pi\)
−0.994357 + 0.106081i \(0.966170\pi\)
\(444\) −210384. 364396.i −0.0506472 0.0877235i
\(445\) 1.66408e6 + 2.88227e6i 0.398358 + 0.689976i
\(446\) −1.79595e6 + 3.11068e6i −0.427521 + 0.740488i
\(447\) −625986. −0.148182
\(448\) 0 0
\(449\) 5.71987e6 1.33897 0.669484 0.742827i \(-0.266515\pi\)
0.669484 + 0.742827i \(0.266515\pi\)
\(450\) −396738. + 687170.i −0.0923576 + 0.159968i
\(451\) 383418. + 664099.i 0.0887628 + 0.153742i
\(452\) −376208. 651611.i −0.0866128 0.150018i
\(453\) 2.38158e6 4.12502e6i 0.545280 0.944453i
\(454\) −1.87045e6 −0.425898
\(455\) 0 0
\(456\) 1.26720e6 0.285386
\(457\) 3.41017e6 5.90659e6i 0.763811 1.32296i −0.177063 0.984200i \(-0.556660\pi\)
0.940873 0.338759i \(-0.110007\pi\)
\(458\) 892280. + 1.54547e6i 0.198764 + 0.344269i
\(459\) −45927.0 79547.9i −0.0101750 0.0176237i
\(460\) −445536. + 771691.i −0.0981721 + 0.170039i
\(461\) 7.45934e6 1.63474 0.817369 0.576115i \(-0.195432\pi\)
0.817369 + 0.576115i \(0.195432\pi\)
\(462\) 0 0
\(463\) −5.23848e6 −1.13567 −0.567836 0.823142i \(-0.692219\pi\)
−0.567836 + 0.823142i \(0.692219\pi\)
\(464\) 462080. 800346.i 0.0996374 0.172577i
\(465\) 663156. + 1.14862e6i 0.142227 + 0.246345i
\(466\) 1.40297e6 + 2.43002e6i 0.299284 + 0.518376i
\(467\) 4.47997e6 7.75954e6i 0.950568 1.64643i 0.206370 0.978474i \(-0.433835\pi\)
0.744199 0.667958i \(-0.232832\pi\)
\(468\) −430272. −0.0908089
\(469\) 0 0
\(470\) 678080. 0.141591
\(471\) −58680.0 + 101637.i −0.0121882 + 0.0211105i
\(472\) −1.36077e6 2.35692e6i −0.281144 0.486956i
\(473\) 1.14345e6 + 1.98052e6i 0.234998 + 0.407029i
\(474\) −1.17425e6 + 2.03386e6i −0.240057 + 0.415791i
\(475\) −5.38780e6 −1.09566
\(476\) 0 0
\(477\) −866862. −0.174443
\(478\) −768396. + 1.33090e6i −0.153821 + 0.266426i
\(479\) −876768. 1.51861e6i −0.174601 0.302417i 0.765422 0.643528i \(-0.222530\pi\)
−0.940023 + 0.341111i \(0.889197\pi\)
\(480\) 119808. + 207514.i 0.0237346 + 0.0411096i
\(481\) −485052. + 840135.i −0.0955929 + 0.165572i
\(482\) −3.81512e6 −0.747981
\(483\) 0 0
\(484\) −526192. −0.102101
\(485\) 1.47321e6 2.55168e6i 0.284388 0.492574i
\(486\) −118098. 204552.i −0.0226805 0.0392837i
\(487\) −463784. 803297.i −0.0886122 0.153481i 0.818313 0.574773i \(-0.194910\pi\)
−0.906925 + 0.421293i \(0.861577\pi\)
\(488\) 1.43488e6 2.48529e6i 0.272751 0.472418i
\(489\) 3.16116e6 0.597825
\(490\) 0 0
\(491\) 8.43733e6 1.57943 0.789716 0.613472i \(-0.210228\pi\)
0.789716 + 0.613472i \(0.210228\pi\)
\(492\) 154224. 267124.i 0.0287236 0.0497508i
\(493\) −227430. 393920.i −0.0421435 0.0729947i
\(494\) −1.46080e6 2.53018e6i −0.269323 0.466481i
\(495\) −376974. + 652938.i −0.0691510 + 0.119773i
\(496\) −1.45101e6 −0.264829
\(497\) 0 0
\(498\) 3.70094e6 0.668712
\(499\) −666390. + 1.15422e6i −0.119806 + 0.207509i −0.919691 0.392644i \(-0.871560\pi\)
0.799885 + 0.600153i \(0.204894\pi\)
\(500\) −1.15939e6 2.00813e6i −0.207398 0.359224i
\(501\) −2.81758e6 4.88018e6i −0.501512 0.868644i
\(502\) −1.13908e6 + 1.97294e6i −0.201741 + 0.349426i
\(503\) −3.64494e6 −0.642349 −0.321174 0.947020i \(-0.604078\pi\)
−0.321174 + 0.947020i \(0.604078\pi\)
\(504\) 0 0
\(505\) −3.63256e6 −0.633848
\(506\) 1.53367e6 2.65640e6i 0.266291 0.461229i
\(507\) −1.17481e6 2.03483e6i −0.202978 0.351567i
\(508\) −1.32438e6 2.29390e6i −0.227696 0.394380i
\(509\) −1.63083e6 + 2.82468e6i −0.279007 + 0.483254i −0.971138 0.238518i \(-0.923338\pi\)
0.692132 + 0.721771i \(0.256672\pi\)
\(510\) 117936. 0.0200780
\(511\) 0 0
\(512\) −262144. −0.0441942
\(513\) 801900. 1.38893e6i 0.134532 0.233017i
\(514\) −2.13328e6 3.69496e6i −0.356157 0.616881i
\(515\) 1.84834e6 + 3.20142e6i 0.307089 + 0.531893i
\(516\) 459936. 796633.i 0.0760454 0.131715i
\(517\) −2.33416e6 −0.384065
\(518\) 0 0
\(519\) −1.66343e6 −0.271074
\(520\) 276224. 478434.i 0.0447974 0.0775914i
\(521\) −1.09370e6 1.89435e6i −0.176525 0.305750i 0.764163 0.645023i \(-0.223152\pi\)
−0.940688 + 0.339273i \(0.889819\pi\)
\(522\) −584820. 1.01294e6i −0.0939390 0.162707i
\(523\) 5.19451e6 8.99716e6i 0.830406 1.43831i −0.0673110 0.997732i \(-0.521442\pi\)
0.897717 0.440573i \(-0.145225\pi\)
\(524\) 2.22893e6 0.354624
\(525\) 0 0
\(526\) 5.92972e6 0.934480
\(527\) −357084. + 618488.i −0.0560072 + 0.0970073i
\(528\) −412416. 714325.i −0.0643800 0.111509i
\(529\) 924090. + 1.60057e6i 0.143574 + 0.248677i
\(530\) 556504. 963893.i 0.0860555 0.149052i
\(531\) −3.44444e6 −0.530131
\(532\) 0 0
\(533\) −711144. −0.108428
\(534\) −2.30411e6 + 3.99083e6i −0.349663 + 0.605634i
\(535\) −2.58073e6 4.46996e6i −0.389815 0.675180i
\(536\) −46336.0 80256.3i −0.00696637 0.0120661i
\(537\) −1.60885e6 + 2.78661e6i −0.240757 + 0.417004i
\(538\) −860440. −0.128164
\(539\) 0 0
\(540\) 303264. 0.0447545
\(541\) −6.38620e6 + 1.10612e7i −0.938101 + 1.62484i −0.169091 + 0.985600i \(0.554083\pi\)
−0.769009 + 0.639238i \(0.779250\pi\)
\(542\) −3.86207e6 6.68930e6i −0.564706 0.978099i
\(543\) −3.13429e6 5.42874e6i −0.456183 0.790132i
\(544\) −64512.0 + 111738.i −0.00934638 + 0.0161884i
\(545\) −3.44599e6 −0.496961
\(546\) 0 0
\(547\) −5.22238e6 −0.746278 −0.373139 0.927776i \(-0.621719\pi\)
−0.373139 + 0.927776i \(0.621719\pi\)
\(548\) 2.66274e6 4.61199e6i 0.378771 0.656051i
\(549\) −1.81602e6 3.14544e6i −0.257152 0.445400i
\(550\) 1.75348e6 + 3.03712e6i 0.247170 + 0.428110i
\(551\) 3.97100e6 6.87797e6i 0.557213 0.965120i
\(552\) −1.23379e6 −0.172343
\(553\) 0 0
\(554\) −8.15025e6 −1.12823
\(555\) 341874. 592143.i 0.0471122 0.0816008i
\(556\) 68448.0 + 118555.i 0.00939018 + 0.0162643i
\(557\) 2.87024e6 + 4.97139e6i 0.391994 + 0.678954i 0.992712 0.120507i \(-0.0384520\pi\)
−0.600718 + 0.799461i \(0.705119\pi\)
\(558\) −918216. + 1.59040e6i −0.124842 + 0.216232i
\(559\) −2.12082e6 −0.287061
\(560\) 0 0
\(561\) −405972. −0.0544614
\(562\) −1.27813e6 + 2.21379e6i −0.170701 + 0.295662i
\(563\) −1.15224e6 1.99573e6i −0.153204 0.265358i 0.779199 0.626776i \(-0.215626\pi\)
−0.932404 + 0.361418i \(0.882293\pi\)
\(564\) 469440. + 813094.i 0.0621416 + 0.107632i
\(565\) 611338. 1.05887e6i 0.0805676 0.139547i
\(566\) 150976. 0.0198092
\(567\) 0 0
\(568\) 281728. 0.0366403
\(569\) 2.56075e6 4.43535e6i 0.331578 0.574311i −0.651243 0.758869i \(-0.725752\pi\)
0.982822 + 0.184558i \(0.0590855\pi\)
\(570\) 1.02960e6 + 1.78332e6i 0.132734 + 0.229902i
\(571\) 1.19318e6 + 2.06666e6i 0.153150 + 0.265264i 0.932384 0.361470i \(-0.117725\pi\)
−0.779234 + 0.626733i \(0.784392\pi\)
\(572\) −950848. + 1.64692e6i −0.121513 + 0.210466i
\(573\) −618030. −0.0786363
\(574\) 0 0
\(575\) 5.24576e6 0.661666
\(576\) −165888. + 287326.i −0.0208333 + 0.0360844i
\(577\) −2.62076e6 4.53928e6i −0.327708 0.567607i 0.654349 0.756193i \(-0.272943\pi\)
−0.982057 + 0.188586i \(0.939610\pi\)
\(578\) −2.80796e6 4.86353e6i −0.349600 0.605525i
\(579\) 3.72250e6 6.44756e6i 0.461464 0.799280i
\(580\) 1.50176e6 0.185366
\(581\) 0 0
\(582\) 4.07966e6 0.499249
\(583\) −1.91566e6 + 3.31802e6i −0.233425 + 0.404303i
\(584\) −656000. 1.13623e6i −0.0795924 0.137858i
\(585\) −349596. 605518.i −0.0422354 0.0731539i
\(586\) 3.67842e6 6.37121e6i 0.442504 0.766440i
\(587\) −9.11548e6 −1.09190 −0.545952 0.837816i \(-0.683832\pi\)
−0.545952 + 0.837816i \(0.683832\pi\)
\(588\) 0 0
\(589\) −1.24696e7 −1.48103
\(590\) 2.21125e6 3.82999e6i 0.261522 0.452969i
\(591\) −645219. 1.11755e6i −0.0759869 0.131613i
\(592\) 374016. + 647815.i 0.0438617 + 0.0759708i
\(593\) 1.52522e6 2.64175e6i 0.178112 0.308500i −0.763122 0.646255i \(-0.776334\pi\)
0.941234 + 0.337755i \(0.109668\pi\)
\(594\) −1.04393e6 −0.121396
\(595\) 0 0
\(596\) 1.11286e6 0.128329
\(597\) 2.44170e6 4.22915e6i 0.280386 0.485643i
\(598\) 1.42229e6 + 2.46348e6i 0.162643 + 0.281705i
\(599\) −7.17041e6 1.24195e7i −0.816539 1.41429i −0.908217 0.418499i \(-0.862556\pi\)
0.0916783 0.995789i \(-0.470777\pi\)
\(600\) 705312. 1.22164e6i 0.0799840 0.138536i
\(601\) 3.12662e6 0.353092 0.176546 0.984292i \(-0.443508\pi\)
0.176546 + 0.984292i \(0.443508\pi\)
\(602\) 0 0
\(603\) −117288. −0.0131359
\(604\) −4.23392e6 + 7.33336e6i −0.472226 + 0.817920i
\(605\) −427531. 740505.i −0.0474875 0.0822507i
\(606\) −2.51485e6 4.35585e6i −0.278183 0.481827i
\(607\) 5.75492e6 9.96782e6i 0.633969 1.09807i −0.352764 0.935712i \(-0.614758\pi\)
0.986733 0.162354i \(-0.0519086\pi\)
\(608\) −2.25280e6 −0.247152
\(609\) 0 0
\(610\) 4.66336e6 0.507428
\(611\) 1.08232e6 1.87463e6i 0.117288 0.203148i
\(612\) 81648.0 + 141418.i 0.00881185 + 0.0152626i
\(613\) 6.08910e6 + 1.05466e7i 0.654488 + 1.13361i 0.982022 + 0.188767i \(0.0604492\pi\)
−0.327534 + 0.944840i \(0.606217\pi\)
\(614\) 2.12944e6 3.68830e6i 0.227953 0.394825i
\(615\) 501228. 0.0534377
\(616\) 0 0
\(617\) 1.77629e6 0.187845 0.0939226 0.995580i \(-0.470059\pi\)
0.0939226 + 0.995580i \(0.470059\pi\)
\(618\) −2.55924e6 + 4.43273e6i −0.269550 + 0.466875i
\(619\) −2.97758e6 5.15732e6i −0.312347 0.541001i 0.666523 0.745484i \(-0.267782\pi\)
−0.978870 + 0.204484i \(0.934448\pi\)
\(620\) −1.17894e6 2.04199e6i −0.123173 0.213341i
\(621\) −780759. + 1.35231e6i −0.0812434 + 0.140718i
\(622\) −4.03808e6 −0.418503
\(623\) 0 0
\(624\) 764928. 0.0786428
\(625\) −1.94255e6 + 3.36460e6i −0.198917 + 0.344535i
\(626\) 2.89819e6 + 5.01982e6i 0.295591 + 0.511979i
\(627\) −3.54420e6 6.13873e6i −0.360039 0.623606i
\(628\) 104320. 180688.i 0.0105552 0.0182822i
\(629\) 368172. 0.0371043
\(630\) 0 0
\(631\) −1.45351e7 −1.45327 −0.726633 0.687026i \(-0.758916\pi\)
−0.726633 + 0.687026i \(0.758916\pi\)
\(632\) 2.08755e6 3.61575e6i 0.207895 0.360085i
\(633\) 5.07490e6 + 8.78999e6i 0.503406 + 0.871925i
\(634\) 5.44621e6 + 9.43312e6i 0.538110 + 0.932035i
\(635\) 2.15212e6 3.72759e6i 0.211803 0.366854i
\(636\) 1.54109e6 0.151072
\(637\) 0 0
\(638\) −5.16952e6 −0.502804
\(639\) 178281. 308792.i 0.0172724 0.0299167i
\(640\) −212992. 368913.i −0.0205548 0.0356020i
\(641\) 5.36747e6 + 9.29673e6i 0.515970 + 0.893686i 0.999828 + 0.0185398i \(0.00590175\pi\)
−0.483858 + 0.875146i \(0.660765\pi\)
\(642\) 3.57332e6 6.18918e6i 0.342164 0.592646i
\(643\) −1.62815e7 −1.55298 −0.776492 0.630127i \(-0.783003\pi\)
−0.776492 + 0.630127i \(0.783003\pi\)
\(644\) 0 0
\(645\) 1.49479e6 0.141476
\(646\) −554400. + 960249.i −0.0522687 + 0.0905321i
\(647\) −3.95974e6 6.85846e6i −0.371882 0.644119i 0.617973 0.786199i \(-0.287954\pi\)
−0.989855 + 0.142080i \(0.954621\pi\)
\(648\) 209952. + 363648.i 0.0196419 + 0.0340207i
\(649\) −7.61180e6 + 1.31840e7i −0.709374 + 1.22867i
\(650\) −3.25227e6 −0.301928
\(651\) 0 0
\(652\) −5.61984e6 −0.517732
\(653\) −672391. + 1.16462e6i −0.0617076 + 0.106881i −0.895229 0.445607i \(-0.852988\pi\)
0.833521 + 0.552488i \(0.186321\pi\)
\(654\) −2.38568e6 4.13213e6i −0.218106 0.377771i
\(655\) 1.81100e6 + 3.13675e6i 0.164936 + 0.285678i
\(656\) −274176. + 474887.i −0.0248754 + 0.0430854i
\(657\) −1.66050e6 −0.150081
\(658\) 0 0
\(659\) 2.02235e7 1.81402 0.907010 0.421109i \(-0.138359\pi\)
0.907010 + 0.421109i \(0.138359\pi\)
\(660\) 670176. 1.16078e6i 0.0598865 0.103726i
\(661\) 3.58901e6 + 6.21635e6i 0.319500 + 0.553391i 0.980384 0.197098i \(-0.0631516\pi\)
−0.660884 + 0.750488i \(0.729818\pi\)
\(662\) −2.20081e6 3.81191e6i −0.195181 0.338063i
\(663\) 188244. 326048.i 0.0166317 0.0288070i
\(664\) −6.57946e6 −0.579122
\(665\) 0 0
\(666\) 946728. 0.0827065
\(667\) −3.86631e6 + 6.69665e6i −0.336498 + 0.582831i
\(668\) 5.00902e6 + 8.67588e6i 0.434322 + 0.752268i
\(669\) −4.04089e6 6.99903e6i −0.349070 0.604606i
\(670\) 75296.0 130416.i 0.00648015 0.0112239i
\(671\) −1.60527e7 −1.37639
\(672\) 0 0
\(673\) 9.61217e6 0.818057 0.409029 0.912522i \(-0.365868\pi\)
0.409029 + 0.912522i \(0.365868\pi\)
\(674\) 3.47024e6 6.01063e6i 0.294245 0.509647i
\(675\) −892660. 1.54613e6i −0.0754096 0.130613i
\(676\) 2.08855e6 + 3.61748e6i 0.175784 + 0.304466i
\(677\) −4.83408e6 + 8.37287e6i −0.405361 + 0.702106i −0.994363 0.106025i \(-0.966187\pi\)
0.589002 + 0.808131i \(0.299521\pi\)
\(678\) 1.69294e6 0.141438
\(679\) 0 0
\(680\) −209664. −0.0173881
\(681\) 2.10425e6 3.64467e6i 0.173872 0.301156i
\(682\) 4.05829e6 + 7.02916e6i 0.334104 + 0.578685i
\(683\) −194927. 337623.i −0.0159890 0.0276937i 0.857920 0.513783i \(-0.171756\pi\)
−0.873909 + 0.486089i \(0.838423\pi\)
\(684\) −1.42560e6 + 2.46921e6i −0.116508 + 0.201799i
\(685\) 8.65389e6 0.704669
\(686\) 0 0
\(687\) −4.01526e6 −0.324580
\(688\) −817664. + 1.41624e6i −0.0658573 + 0.114068i
\(689\) −1.77653e6 3.07704e6i −0.142569 0.246937i
\(690\) −1.00246e6 1.73630e6i −0.0801572 0.138836i
\(691\) 1.86993e6 3.23881e6i 0.148980 0.258042i −0.781870 0.623441i \(-0.785734\pi\)
0.930851 + 0.365399i \(0.119068\pi\)
\(692\) 2.95722e6 0.234757
\(693\) 0 0
\(694\) −6.36578e6 −0.501711
\(695\) −111228. + 192653.i −0.00873478 + 0.0151291i
\(696\) 1.03968e6 + 1.80078e6i 0.0813536 + 0.140909i
\(697\) 134946. + 233733.i 0.0105215 + 0.0182238i
\(698\) 4.66752e6 8.08438e6i 0.362617 0.628070i
\(699\) −6.31337e6 −0.488730
\(700\) 0 0
\(701\) 2.49886e7 1.92064 0.960322 0.278893i \(-0.0899674\pi\)
0.960322 + 0.278893i \(0.0899674\pi\)
\(702\) 484056. 838410.i 0.0370726 0.0642116i
\(703\) 3.21420e6 + 5.56716e6i 0.245293 + 0.424859i
\(704\) 733184. + 1.26991e6i 0.0557547 + 0.0965699i
\(705\) −762840. + 1.32128e6i −0.0578044 + 0.100120i
\(706\) 1.12433e7 0.848947
\(707\) 0 0
\(708\) 6.12346e6 0.459107
\(709\) 4.91792e6 8.51809e6i 0.367423 0.636394i −0.621739 0.783224i \(-0.713574\pi\)
0.989162 + 0.146830i \(0.0469070\pi\)
\(710\) 228904. + 396473.i 0.0170415 + 0.0295167i
\(711\) −2.64206e6 4.57618e6i −0.196006 0.339492i
\(712\) 4.09619e6 7.09481e6i 0.302817 0.524495i
\(713\) 1.21409e7 0.894387
\(714\) 0 0
\(715\) −3.09026e6 −0.226063
\(716\) 2.86018e6 4.95397e6i 0.208502 0.361136i
\(717\) −1.72889e6 2.99453e6i −0.125594 0.217536i
\(718\) 1.87862e6 + 3.25387e6i 0.135997 + 0.235553i
\(719\) −1.06812e7 + 1.85004e7i −0.770546 + 1.33463i 0.166717 + 0.986005i \(0.446683\pi\)
−0.937264 + 0.348621i \(0.886650\pi\)
\(720\) −539136. −0.0387585
\(721\) 0 0
\(722\) −9.45560e6 −0.675066
\(723\) 4.29201e6 7.43398e6i 0.305362 0.528902i
\(724\) 5.57206e6 + 9.65110e6i 0.395066 + 0.684274i
\(725\) −4.42044e6 7.65644e6i −0.312335 0.540980i
\(726\) 591966. 1.02532e6i 0.0416826 0.0721964i
\(727\) −6.53025e6 −0.458241 −0.229120 0.973398i \(-0.573585\pi\)
−0.229120 + 0.973398i \(0.573585\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) 1.06600e6 1.84637e6i 0.0740372 0.128236i
\(731\) 402444. + 697053.i 0.0278556 + 0.0482473i
\(732\) 3.22848e6 + 5.59189e6i 0.222700 + 0.385728i
\(733\) −8.32855e6 + 1.44255e7i −0.572545 + 0.991677i 0.423759 + 0.905775i \(0.360710\pi\)
−0.996304 + 0.0859016i \(0.972623\pi\)
\(734\) 1.23940e7 0.849128
\(735\) 0 0
\(736\) 2.19341e6 0.149254
\(737\) −259192. + 448934.i −0.0175773 + 0.0304448i
\(738\) 347004. + 601029.i 0.0234527 + 0.0406213i
\(739\) 1.19768e7 + 2.07444e7i 0.806733 + 1.39730i 0.915115 + 0.403192i \(0.132099\pi\)
−0.108383 + 0.994109i \(0.534567\pi\)
\(740\) −607776. + 1.05270e6i −0.0408004 + 0.0706683i
\(741\) 6.57360e6 0.439803
\(742\) 0 0
\(743\) −7.48982e6 −0.497736 −0.248868 0.968537i \(-0.580059\pi\)
−0.248868 + 0.968537i \(0.580059\pi\)
\(744\) 1.63238e6 2.82737e6i 0.108116 0.187262i
\(745\) 904202. + 1.56612e6i 0.0596863 + 0.103380i
\(746\) −456532. 790737.i −0.0300348 0.0520217i
\(747\) −4.16356e6 + 7.21150e6i −0.273001 + 0.472851i
\(748\) 721728. 0.0471650
\(749\) 0 0
\(750\) 5.21726e6 0.338680
\(751\) 2.35922e6 4.08630e6i 0.152640 0.264381i −0.779557 0.626331i \(-0.784556\pi\)
0.932197 + 0.361950i \(0.117889\pi\)
\(752\) −834560. 1.44550e6i −0.0538162 0.0932124i
\(753\) −2.56293e6 4.43912e6i −0.164721 0.285305i
\(754\) 2.39704e6 4.15180e6i 0.153549 0.265955i
\(755\) −1.37602e7 −0.878534
\(756\) 0 0
\(757\) −2.67397e7 −1.69597 −0.847983 0.530024i \(-0.822183\pi\)
−0.847983 + 0.530024i \(0.822183\pi\)
\(758\) −2.07338e6 + 3.59121e6i −0.131071 + 0.227022i
\(759\) 3.45076e6 + 5.97690e6i 0.217426 + 0.376592i
\(760\) −1.83040e6 3.17035e6i −0.114951 0.199101i
\(761\) −7.21654e6 + 1.24994e7i −0.451718 + 0.782398i −0.998493 0.0548815i \(-0.982522\pi\)
0.546775 + 0.837279i \(0.315855\pi\)
\(762\) 5.95973e6 0.371825
\(763\) 0 0
\(764\) 1.09872e6 0.0681010
\(765\) −132678. + 229805.i −0.00819682 + 0.0141973i
\(766\) 423552. + 733614.i 0.0260816 + 0.0451747i
\(767\) −7.05898e6 1.22265e7i −0.433265 0.750437i
\(768\) 294912. 510803.i 0.0180422 0.0312500i
\(769\) 8.55510e6 0.521686 0.260843 0.965381i \(-0.415999\pi\)
0.260843 + 0.965381i \(0.415999\pi\)
\(770\)