Properties

Label 42.6.e.a.25.1
Level $42$
Weight $6$
Character 42.25
Analytic conductor $6.736$
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] = [42,6,Mod(25,42)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(42, 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("42.25");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 42 = 2 \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 42.e (of order \(3\), 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: \(6.73612043215\)
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 25.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 42.25
Dual form 42.6.e.a.37.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(3.00000 + 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 - 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +O(q^{10})\) \(q+(-2.00000 - 3.46410i) q^{2} +(-4.50000 + 7.79423i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(3.00000 + 5.19615i) q^{5} +36.0000 q^{6} +(59.5000 - 115.181i) q^{7} +64.0000 q^{8} +(-40.5000 - 70.1481i) q^{9} +(12.0000 - 20.7846i) q^{10} +(333.000 - 576.773i) q^{11} +(-72.0000 - 124.708i) q^{12} -559.000 q^{13} +(-518.000 + 24.2487i) q^{14} -54.0000 q^{15} +(-128.000 - 221.703i) q^{16} +(870.000 - 1506.88i) q^{17} +(-162.000 + 280.592i) q^{18} +(-578.500 - 1001.99i) q^{19} -96.0000 q^{20} +(630.000 + 982.073i) q^{21} -2664.00 q^{22} +(1734.00 + 3003.38i) q^{23} +(-288.000 + 498.831i) q^{24} +(1544.50 - 2675.15i) q^{25} +(1118.00 + 1936.43i) q^{26} +729.000 q^{27} +(1120.00 + 1745.91i) q^{28} +3372.00 q^{29} +(108.000 + 187.061i) q^{30} +(-3146.50 + 5449.90i) q^{31} +(-512.000 + 886.810i) q^{32} +(2997.00 + 5190.96i) q^{33} -6960.00 q^{34} +(777.000 - 36.3731i) q^{35} +1296.00 q^{36} +(-1565.50 - 2711.53i) q^{37} +(-2314.00 + 4007.97i) q^{38} +(2515.50 - 4356.97i) q^{39} +(192.000 + 332.554i) q^{40} -4866.00 q^{41} +(2142.00 - 4146.53i) q^{42} -11407.0 q^{43} +(5328.00 + 9228.37i) q^{44} +(243.000 - 420.888i) q^{45} +(6936.00 - 12013.5i) q^{46} +(-1155.00 - 2000.52i) q^{47} +2304.00 q^{48} +(-9726.50 - 13706.6i) q^{49} -12356.0 q^{50} +(7830.00 + 13562.0i) q^{51} +(4472.00 - 7745.73i) q^{52} +(14148.0 - 24505.1i) q^{53} +(-1458.00 - 2525.33i) q^{54} +3996.00 q^{55} +(3808.00 - 7371.61i) q^{56} +10413.0 q^{57} +(-6744.00 - 11681.0i) q^{58} +(-10272.0 + 17791.6i) q^{59} +(432.000 - 748.246i) q^{60} +(2315.00 + 4009.70i) q^{61} +25172.0 q^{62} +(-10489.5 + 491.036i) q^{63} +4096.00 q^{64} +(-1677.00 - 2904.65i) q^{65} +(11988.0 - 20763.8i) q^{66} +(9372.50 - 16233.6i) q^{67} +(13920.0 + 24110.1i) q^{68} -31212.0 q^{69} +(-1680.00 - 2618.86i) q^{70} -38226.0 q^{71} +(-2592.00 - 4489.48i) q^{72} +(-35294.5 + 61131.9i) q^{73} +(-6262.00 + 10846.1i) q^{74} +(13900.5 + 24076.4i) q^{75} +18512.0 q^{76} +(-46620.0 - 72673.4i) q^{77} -20124.0 q^{78} +(31146.5 + 53947.3i) q^{79} +(768.000 - 1330.22i) q^{80} +(-3280.50 + 5681.99i) q^{81} +(9732.00 + 16856.3i) q^{82} +79818.0 q^{83} +(-18648.0 + 872.954i) q^{84} +10440.0 q^{85} +(22814.0 + 39515.0i) q^{86} +(-15174.0 + 26282.1i) q^{87} +(21312.0 - 36913.5i) q^{88} +(9060.00 + 15692.4i) q^{89} -1944.00 q^{90} +(-33260.5 + 64386.4i) q^{91} -55488.0 q^{92} +(-28318.5 - 49049.1i) q^{93} +(-4620.00 + 8002.07i) q^{94} +(3471.00 - 6011.95i) q^{95} +(-4608.00 - 7981.29i) q^{96} +124754. q^{97} +(-28028.0 + 61106.8i) q^{98} -53946.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 9 q^{3} - 16 q^{4} + 6 q^{5} + 72 q^{6} + 119 q^{7} + 128 q^{8} - 81 q^{9} + 24 q^{10} + 666 q^{11} - 144 q^{12} - 1118 q^{13} - 1036 q^{14} - 108 q^{15} - 256 q^{16} + 1740 q^{17} - 324 q^{18} - 1157 q^{19} - 192 q^{20} + 1260 q^{21} - 5328 q^{22} + 3468 q^{23} - 576 q^{24} + 3089 q^{25} + 2236 q^{26} + 1458 q^{27} + 2240 q^{28} + 6744 q^{29} + 216 q^{30} - 6293 q^{31} - 1024 q^{32} + 5994 q^{33} - 13920 q^{34} + 1554 q^{35} + 2592 q^{36} - 3131 q^{37} - 4628 q^{38} + 5031 q^{39} + 384 q^{40} - 9732 q^{41} + 4284 q^{42} - 22814 q^{43} + 10656 q^{44} + 486 q^{45} + 13872 q^{46} - 2310 q^{47} + 4608 q^{48} - 19453 q^{49} - 24712 q^{50} + 15660 q^{51} + 8944 q^{52} + 28296 q^{53} - 2916 q^{54} + 7992 q^{55} + 7616 q^{56} + 20826 q^{57} - 13488 q^{58} - 20544 q^{59} + 864 q^{60} + 4630 q^{61} + 50344 q^{62} - 20979 q^{63} + 8192 q^{64} - 3354 q^{65} + 23976 q^{66} + 18745 q^{67} + 27840 q^{68} - 62424 q^{69} - 3360 q^{70} - 76452 q^{71} - 5184 q^{72} - 70589 q^{73} - 12524 q^{74} + 27801 q^{75} + 37024 q^{76} - 93240 q^{77} - 40248 q^{78} + 62293 q^{79} + 1536 q^{80} - 6561 q^{81} + 19464 q^{82} + 159636 q^{83} - 37296 q^{84} + 20880 q^{85} + 45628 q^{86} - 30348 q^{87} + 42624 q^{88} + 18120 q^{89} - 3888 q^{90} - 66521 q^{91} - 110976 q^{92} - 56637 q^{93} - 9240 q^{94} + 6942 q^{95} - 9216 q^{96} + 249508 q^{97} - 56056 q^{98} - 107892 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/42\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(31\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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
\(5\) 3.00000 + 5.19615i 0.0536656 + 0.0929516i 0.891610 0.452804i \(-0.149576\pi\)
−0.837945 + 0.545755i \(0.816243\pi\)
\(6\) 36.0000 0.408248
\(7\) 59.5000 115.181i 0.458957 0.888459i
\(8\) 64.0000 0.353553
\(9\) −40.5000 70.1481i −0.166667 0.288675i
\(10\) 12.0000 20.7846i 0.0379473 0.0657267i
\(11\) 333.000 576.773i 0.829779 1.43722i −0.0684322 0.997656i \(-0.521800\pi\)
0.898211 0.439564i \(-0.144867\pi\)
\(12\) −72.0000 124.708i −0.144338 0.250000i
\(13\) −559.000 −0.917389 −0.458694 0.888594i \(-0.651683\pi\)
−0.458694 + 0.888594i \(0.651683\pi\)
\(14\) −518.000 + 24.2487i −0.706333 + 0.0330650i
\(15\) −54.0000 −0.0619677
\(16\) −128.000 221.703i −0.125000 0.216506i
\(17\) 870.000 1506.88i 0.730125 1.26461i −0.226705 0.973963i \(-0.572795\pi\)
0.956830 0.290649i \(-0.0938713\pi\)
\(18\) −162.000 + 280.592i −0.117851 + 0.204124i
\(19\) −578.500 1001.99i −0.367637 0.636766i 0.621558 0.783368i \(-0.286500\pi\)
−0.989196 + 0.146602i \(0.953166\pi\)
\(20\) −96.0000 −0.0536656
\(21\) 630.000 + 982.073i 0.311740 + 0.485954i
\(22\) −2664.00 −1.17348
\(23\) 1734.00 + 3003.38i 0.683486 + 1.18383i 0.973910 + 0.226934i \(0.0728702\pi\)
−0.290424 + 0.956898i \(0.593796\pi\)
\(24\) −288.000 + 498.831i −0.102062 + 0.176777i
\(25\) 1544.50 2675.15i 0.494240 0.856049i
\(26\) 1118.00 + 1936.43i 0.324346 + 0.561784i
\(27\) 729.000 0.192450
\(28\) 1120.00 + 1745.91i 0.269975 + 0.420849i
\(29\) 3372.00 0.744548 0.372274 0.928123i \(-0.378578\pi\)
0.372274 + 0.928123i \(0.378578\pi\)
\(30\) 108.000 + 187.061i 0.0219089 + 0.0379473i
\(31\) −3146.50 + 5449.90i −0.588063 + 1.01855i 0.406423 + 0.913685i \(0.366776\pi\)
−0.994486 + 0.104869i \(0.966558\pi\)
\(32\) −512.000 + 886.810i −0.0883883 + 0.153093i
\(33\) 2997.00 + 5190.96i 0.479073 + 0.829779i
\(34\) −6960.00 −1.03255
\(35\) 777.000 36.3731i 0.107214 0.00501891i
\(36\) 1296.00 0.166667
\(37\) −1565.50 2711.53i −0.187996 0.325619i 0.756586 0.653894i \(-0.226866\pi\)
−0.944582 + 0.328276i \(0.893533\pi\)
\(38\) −2314.00 + 4007.97i −0.259959 + 0.450262i
\(39\) 2515.50 4356.97i 0.264827 0.458694i
\(40\) 192.000 + 332.554i 0.0189737 + 0.0328634i
\(41\) −4866.00 −0.452077 −0.226039 0.974118i \(-0.572578\pi\)
−0.226039 + 0.974118i \(0.572578\pi\)
\(42\) 2142.00 4146.53i 0.187368 0.362712i
\(43\) −11407.0 −0.940806 −0.470403 0.882452i \(-0.655892\pi\)
−0.470403 + 0.882452i \(0.655892\pi\)
\(44\) 5328.00 + 9228.37i 0.414890 + 0.718610i
\(45\) 243.000 420.888i 0.0178885 0.0309839i
\(46\) 6936.00 12013.5i 0.483297 0.837096i
\(47\) −1155.00 2000.52i −0.0762671 0.132099i 0.825369 0.564593i \(-0.190967\pi\)
−0.901637 + 0.432494i \(0.857634\pi\)
\(48\) 2304.00 0.144338
\(49\) −9726.50 13706.6i −0.578717 0.815528i
\(50\) −12356.0 −0.698961
\(51\) 7830.00 + 13562.0i 0.421538 + 0.730125i
\(52\) 4472.00 7745.73i 0.229347 0.397241i
\(53\) 14148.0 24505.1i 0.691840 1.19830i −0.279395 0.960176i \(-0.590134\pi\)
0.971235 0.238125i \(-0.0765328\pi\)
\(54\) −1458.00 2525.33i −0.0680414 0.117851i
\(55\) 3996.00 0.178122
\(56\) 3808.00 7371.61i 0.162266 0.314118i
\(57\) 10413.0 0.424511
\(58\) −6744.00 11681.0i −0.263237 0.455941i
\(59\) −10272.0 + 17791.6i −0.384171 + 0.665404i −0.991654 0.128929i \(-0.958846\pi\)
0.607483 + 0.794333i \(0.292179\pi\)
\(60\) 432.000 748.246i 0.0154919 0.0268328i
\(61\) 2315.00 + 4009.70i 0.0796575 + 0.137971i 0.903102 0.429426i \(-0.141284\pi\)
−0.823445 + 0.567397i \(0.807951\pi\)
\(62\) 25172.0 0.831646
\(63\) −10489.5 + 491.036i −0.332969 + 0.0155870i
\(64\) 4096.00 0.125000
\(65\) −1677.00 2904.65i −0.0492322 0.0852728i
\(66\) 11988.0 20763.8i 0.338756 0.586742i
\(67\) 9372.50 16233.6i 0.255075 0.441803i −0.709841 0.704362i \(-0.751233\pi\)
0.964916 + 0.262559i \(0.0845664\pi\)
\(68\) 13920.0 + 24110.1i 0.365062 + 0.632306i
\(69\) −31212.0 −0.789221
\(70\) −1680.00 2618.86i −0.0409793 0.0638804i
\(71\) −38226.0 −0.899939 −0.449969 0.893044i \(-0.648565\pi\)
−0.449969 + 0.893044i \(0.648565\pi\)
\(72\) −2592.00 4489.48i −0.0589256 0.102062i
\(73\) −35294.5 + 61131.9i −0.775175 + 1.34264i 0.159521 + 0.987195i \(0.449005\pi\)
−0.934696 + 0.355448i \(0.884328\pi\)
\(74\) −6262.00 + 10846.1i −0.132933 + 0.230247i
\(75\) 13900.5 + 24076.4i 0.285350 + 0.494240i
\(76\) 18512.0 0.367637
\(77\) −46620.0 72673.4i −0.896077 1.39685i
\(78\) −20124.0 −0.374522
\(79\) 31146.5 + 53947.3i 0.561489 + 0.972528i 0.997367 + 0.0725221i \(0.0231048\pi\)
−0.435877 + 0.900006i \(0.643562\pi\)
\(80\) 768.000 1330.22i 0.0134164 0.0232379i
\(81\) −3280.50 + 5681.99i −0.0555556 + 0.0962250i
\(82\) 9732.00 + 16856.3i 0.159833 + 0.276840i
\(83\) 79818.0 1.27176 0.635881 0.771787i \(-0.280637\pi\)
0.635881 + 0.771787i \(0.280637\pi\)
\(84\) −18648.0 + 872.954i −0.288359 + 0.0134987i
\(85\) 10440.0 0.156730
\(86\) 22814.0 + 39515.0i 0.332625 + 0.576124i
\(87\) −15174.0 + 26282.1i −0.214932 + 0.372274i
\(88\) 21312.0 36913.5i 0.293371 0.508134i
\(89\) 9060.00 + 15692.4i 0.121242 + 0.209997i 0.920258 0.391313i \(-0.127979\pi\)
−0.799016 + 0.601310i \(0.794646\pi\)
\(90\) −1944.00 −0.0252982
\(91\) −33260.5 + 64386.4i −0.421042 + 0.815062i
\(92\) −55488.0 −0.683486
\(93\) −28318.5 49049.1i −0.339518 0.588063i
\(94\) −4620.00 + 8002.07i −0.0539290 + 0.0934078i
\(95\) 3471.00 6011.95i 0.0394590 0.0683449i
\(96\) −4608.00 7981.29i −0.0510310 0.0883883i
\(97\) 124754. 1.34625 0.673124 0.739530i \(-0.264952\pi\)
0.673124 + 0.739530i \(0.264952\pi\)
\(98\) −28028.0 + 61106.8i −0.294800 + 0.642723i
\(99\) −53946.0 −0.553186
\(100\) 24712.0 + 42802.4i 0.247120 + 0.428024i
\(101\) 46695.0 80878.1i 0.455478 0.788910i −0.543238 0.839579i \(-0.682802\pi\)
0.998716 + 0.0506685i \(0.0161352\pi\)
\(102\) 31320.0 54247.8i 0.298072 0.516276i
\(103\) 83865.5 + 145259.i 0.778915 + 1.34912i 0.932567 + 0.360996i \(0.117563\pi\)
−0.153652 + 0.988125i \(0.549103\pi\)
\(104\) −35776.0 −0.324346
\(105\) −3213.00 + 6219.79i −0.0284405 + 0.0550558i
\(106\) −113184. −0.978409
\(107\) −34590.0 59911.6i −0.292073 0.505885i 0.682227 0.731141i \(-0.261012\pi\)
−0.974300 + 0.225256i \(0.927678\pi\)
\(108\) −5832.00 + 10101.3i −0.0481125 + 0.0833333i
\(109\) 109779. 190144.i 0.885024 1.53291i 0.0393377 0.999226i \(-0.487475\pi\)
0.845686 0.533680i \(-0.179191\pi\)
\(110\) −7992.00 13842.6i −0.0629758 0.109077i
\(111\) 28179.0 0.217079
\(112\) −33152.0 + 1551.92i −0.249727 + 0.0116902i
\(113\) −39354.0 −0.289930 −0.144965 0.989437i \(-0.546307\pi\)
−0.144965 + 0.989437i \(0.546307\pi\)
\(114\) −20826.0 36071.7i −0.150087 0.259959i
\(115\) −10404.0 + 18020.3i −0.0733594 + 0.127062i
\(116\) −26976.0 + 46723.8i −0.186137 + 0.322399i
\(117\) 22639.5 + 39212.8i 0.152898 + 0.264827i
\(118\) 82176.0 0.543300
\(119\) −121800. 189867.i −0.788460 1.22909i
\(120\) −3456.00 −0.0219089
\(121\) −141252. 244657.i −0.877067 1.51912i
\(122\) 9260.00 16038.8i 0.0563263 0.0975601i
\(123\) 21897.0 37926.7i 0.130503 0.226039i
\(124\) −50344.0 87198.4i −0.294031 0.509277i
\(125\) 37284.0 0.213426
\(126\) 22680.0 + 35354.6i 0.127267 + 0.198390i
\(127\) 317093. 1.74453 0.872263 0.489037i \(-0.162652\pi\)
0.872263 + 0.489037i \(0.162652\pi\)
\(128\) −8192.00 14189.0i −0.0441942 0.0765466i
\(129\) 51331.5 88908.8i 0.271587 0.470403i
\(130\) −6708.00 + 11618.6i −0.0348125 + 0.0602969i
\(131\) 77415.0 + 134087.i 0.394137 + 0.682665i 0.992991 0.118194i \(-0.0377103\pi\)
−0.598854 + 0.800858i \(0.704377\pi\)
\(132\) −95904.0 −0.479073
\(133\) −149832. + 7013.94i −0.734470 + 0.0343821i
\(134\) −74980.0 −0.360731
\(135\) 2187.00 + 3788.00i 0.0103280 + 0.0178885i
\(136\) 55680.0 96440.6i 0.258138 0.447108i
\(137\) −33666.0 + 58311.2i −0.153246 + 0.265430i −0.932419 0.361379i \(-0.882306\pi\)
0.779173 + 0.626809i \(0.215639\pi\)
\(138\) 62424.0 + 108122.i 0.279032 + 0.483297i
\(139\) −365215. −1.60329 −0.801644 0.597802i \(-0.796041\pi\)
−0.801644 + 0.597802i \(0.796041\pi\)
\(140\) −5712.00 + 11057.4i −0.0246302 + 0.0476797i
\(141\) 20790.0 0.0880657
\(142\) 76452.0 + 132419.i 0.318176 + 0.551098i
\(143\) −186147. + 322416.i −0.761230 + 1.31849i
\(144\) −10368.0 + 17957.9i −0.0416667 + 0.0721688i
\(145\) 10116.0 + 17521.4i 0.0399566 + 0.0692069i
\(146\) 282356. 1.09626
\(147\) 150602. 14130.9i 0.574825 0.0539359i
\(148\) 50096.0 0.187996
\(149\) 84030.0 + 145544.i 0.310076 + 0.537068i 0.978379 0.206822i \(-0.0663120\pi\)
−0.668302 + 0.743890i \(0.732979\pi\)
\(150\) 55602.0 96305.5i 0.201773 0.349480i
\(151\) −76768.0 + 132966.i −0.273992 + 0.474568i −0.969880 0.243582i \(-0.921678\pi\)
0.695888 + 0.718150i \(0.255011\pi\)
\(152\) −37024.0 64127.4i −0.129979 0.225131i
\(153\) −140940. −0.486750
\(154\) −158508. + 306843.i −0.538579 + 1.04259i
\(155\) −37758.0 −0.126235
\(156\) 40248.0 + 69711.6i 0.132414 + 0.229347i
\(157\) −101209. + 175299.i −0.327695 + 0.567585i −0.982054 0.188599i \(-0.939605\pi\)
0.654359 + 0.756184i \(0.272939\pi\)
\(158\) 124586. 215789.i 0.397033 0.687681i
\(159\) 127332. + 220545.i 0.399434 + 0.691840i
\(160\) −6144.00 −0.0189737
\(161\) 449106. 21023.6i 1.36548 0.0639209i
\(162\) 26244.0 0.0785674
\(163\) 89882.0 + 155680.i 0.264974 + 0.458949i 0.967557 0.252653i \(-0.0813032\pi\)
−0.702583 + 0.711602i \(0.747970\pi\)
\(164\) 38928.0 67425.3i 0.113019 0.195755i
\(165\) −17982.0 + 31145.7i −0.0514195 + 0.0890612i
\(166\) −159636. 276498.i −0.449636 0.778792i
\(167\) 217302. 0.602938 0.301469 0.953476i \(-0.402523\pi\)
0.301469 + 0.953476i \(0.402523\pi\)
\(168\) 40320.0 + 62852.7i 0.110217 + 0.171811i
\(169\) −58812.0 −0.158398
\(170\) −20880.0 36165.2i −0.0554126 0.0959774i
\(171\) −46858.5 + 81161.3i −0.122546 + 0.212255i
\(172\) 91256.0 158060.i 0.235202 0.407381i
\(173\) 36990.0 + 64068.6i 0.0939656 + 0.162753i 0.909176 0.416411i \(-0.136712\pi\)
−0.815211 + 0.579164i \(0.803379\pi\)
\(174\) 121392. 0.303960
\(175\) −216230. 337069.i −0.533729 0.832001i
\(176\) −170496. −0.414890
\(177\) −92448.0 160125.i −0.221801 0.384171i
\(178\) 36240.0 62769.5i 0.0857311 0.148491i
\(179\) −394683. + 683611.i −0.920695 + 1.59469i −0.122353 + 0.992487i \(0.539044\pi\)
−0.798342 + 0.602204i \(0.794289\pi\)
\(180\) 3888.00 + 6734.21i 0.00894427 + 0.0154919i
\(181\) −477739. −1.08391 −0.541956 0.840407i \(-0.682316\pi\)
−0.541956 + 0.840407i \(0.682316\pi\)
\(182\) 289562. 13555.0i 0.647982 0.0303335i
\(183\) −41670.0 −0.0919805
\(184\) 110976. + 192216.i 0.241649 + 0.418548i
\(185\) 9393.00 16269.2i 0.0201779 0.0349491i
\(186\) −113274. + 196196.i −0.240076 + 0.415823i
\(187\) −579420. 1.00358e6i −1.21168 2.09870i
\(188\) 36960.0 0.0762671
\(189\) 43375.5 83967.2i 0.0883263 0.170984i
\(190\) −27768.0 −0.0558034
\(191\) −179487. 310881.i −0.356000 0.616609i 0.631289 0.775548i \(-0.282526\pi\)
−0.987289 + 0.158938i \(0.949193\pi\)
\(192\) −18432.0 + 31925.2i −0.0360844 + 0.0625000i
\(193\) 90966.5 157559.i 0.175788 0.304473i −0.764646 0.644451i \(-0.777086\pi\)
0.940434 + 0.339978i \(0.110419\pi\)
\(194\) −249508. 432161.i −0.475971 0.824405i
\(195\) 30186.0 0.0568485
\(196\) 267736. 25121.7i 0.497813 0.0467098i
\(197\) 717924. 1.31799 0.658996 0.752146i \(-0.270981\pi\)
0.658996 + 0.752146i \(0.270981\pi\)
\(198\) 107892. + 186874.i 0.195581 + 0.338756i
\(199\) −101548. + 175886.i −0.181777 + 0.314847i −0.942486 0.334246i \(-0.891518\pi\)
0.760709 + 0.649093i \(0.224852\pi\)
\(200\) 98848.0 171210.i 0.174740 0.302659i
\(201\) 84352.5 + 146103.i 0.147268 + 0.255075i
\(202\) −373560. −0.644142
\(203\) 200634. 388392.i 0.341715 0.661500i
\(204\) −250560. −0.421538
\(205\) −14598.0 25284.5i −0.0242610 0.0420213i
\(206\) 335462. 581037.i 0.550776 0.953973i
\(207\) 140454. 243273.i 0.227829 0.394611i
\(208\) 71552.0 + 123932.i 0.114674 + 0.198620i
\(209\) −770562. −1.22023
\(210\) 27972.0 1309.43i 0.0437699 0.00204896i
\(211\) 1.17098e6 1.81069 0.905343 0.424680i \(-0.139613\pi\)
0.905343 + 0.424680i \(0.139613\pi\)
\(212\) 226368. + 392081.i 0.345920 + 0.599151i
\(213\) 172017. 297942.i 0.259790 0.449969i
\(214\) −138360. + 239647.i −0.206527 + 0.357715i
\(215\) −34221.0 59272.5i −0.0504890 0.0874495i
\(216\) 46656.0 0.0680414
\(217\) 440510. + 686687.i 0.635048 + 0.989942i
\(218\) −878236. −1.25161
\(219\) −317651. 550187.i −0.447548 0.775175i
\(220\) −31968.0 + 55370.2i −0.0445306 + 0.0771293i
\(221\) −486330. + 842348.i −0.669808 + 1.16014i
\(222\) −56358.0 97614.9i −0.0767491 0.132933i
\(223\) 1.24635e6 1.67833 0.839167 0.543873i \(-0.183043\pi\)
0.839167 + 0.543873i \(0.183043\pi\)
\(224\) 71680.0 + 111738.i 0.0954504 + 0.148793i
\(225\) −250209. −0.329493
\(226\) 78708.0 + 136326.i 0.102506 + 0.177545i
\(227\) 459471. 795827.i 0.591825 1.02507i −0.402161 0.915569i \(-0.631741\pi\)
0.993987 0.109503i \(-0.0349258\pi\)
\(228\) −83304.0 + 144287.i −0.106128 + 0.183819i
\(229\) −601874. 1.04248e6i −0.758433 1.31364i −0.943649 0.330947i \(-0.892632\pi\)
0.185216 0.982698i \(-0.440701\pi\)
\(230\) 83232.0 0.103746
\(231\) 776223. 36336.7i 0.957098 0.0448039i
\(232\) 215808. 0.263237
\(233\) 459531. + 795931.i 0.554530 + 0.960474i 0.997940 + 0.0641551i \(0.0204353\pi\)
−0.443410 + 0.896319i \(0.646231\pi\)
\(234\) 90558.0 156851.i 0.108115 0.187261i
\(235\) 6930.00 12003.1i 0.00818585 0.0141783i
\(236\) −164352. 284666.i −0.192086 0.332702i
\(237\) −560637. −0.648352
\(238\) −414120. + 801662.i −0.473897 + 0.917380i
\(239\) −625338. −0.708142 −0.354071 0.935219i \(-0.615203\pi\)
−0.354071 + 0.935219i \(0.615203\pi\)
\(240\) 6912.00 + 11971.9i 0.00774597 + 0.0134164i
\(241\) −626911. + 1.08584e6i −0.695286 + 1.20427i 0.274799 + 0.961502i \(0.411389\pi\)
−0.970084 + 0.242768i \(0.921945\pi\)
\(242\) −565010. + 978626.i −0.620180 + 1.07418i
\(243\) −29524.5 51137.9i −0.0320750 0.0555556i
\(244\) −74080.0 −0.0796575
\(245\) 42042.0 91660.1i 0.0447474 0.0975585i
\(246\) −175176. −0.184560
\(247\) 323382. + 560113.i 0.337266 + 0.584162i
\(248\) −201376. + 348793.i −0.207911 + 0.360113i
\(249\) −359181. + 622120.i −0.367126 + 0.635881i
\(250\) −74568.0 129156.i −0.0754575 0.130696i
\(251\) −1.51333e6 −1.51618 −0.758089 0.652152i \(-0.773867\pi\)
−0.758089 + 0.652152i \(0.773867\pi\)
\(252\) 77112.0 149275.i 0.0764928 0.148076i
\(253\) 2.30969e6 2.26857
\(254\) −634186. 1.09844e6i −0.616783 1.06830i
\(255\) −46980.0 + 81371.7i −0.0452442 + 0.0783652i
\(256\) −32768.0 + 56755.8i −0.0312500 + 0.0541266i
\(257\) 777465. + 1.34661e6i 0.734257 + 1.27177i 0.955049 + 0.296449i \(0.0958026\pi\)
−0.220792 + 0.975321i \(0.570864\pi\)
\(258\) −410652. −0.384083
\(259\) −405464. + 18980.7i −0.375581 + 0.0175818i
\(260\) 53664.0 0.0492322
\(261\) −136566. 236539.i −0.124091 0.214932i
\(262\) 309660. 536347.i 0.278697 0.482717i
\(263\) 557658. 965892.i 0.497140 0.861071i −0.502855 0.864371i \(-0.667717\pi\)
0.999995 + 0.00329949i \(0.00105026\pi\)
\(264\) 191808. + 332221.i 0.169378 + 0.293371i
\(265\) 169776. 0.148512
\(266\) 323960. + 505004.i 0.280729 + 0.437613i
\(267\) −163080. −0.139998
\(268\) 149960. + 259738.i 0.127538 + 0.220902i
\(269\) −17835.0 + 30891.1i −0.0150277 + 0.0260287i −0.873441 0.486929i \(-0.838117\pi\)
0.858414 + 0.512958i \(0.171450\pi\)
\(270\) 8748.00 15152.0i 0.00730297 0.0126491i
\(271\) 146384. + 253545.i 0.121079 + 0.209716i 0.920194 0.391464i \(-0.128031\pi\)
−0.799114 + 0.601179i \(0.794698\pi\)
\(272\) −445440. −0.365062
\(273\) −352170. 548979.i −0.285987 0.445809i
\(274\) 269328. 0.216723
\(275\) −1.02864e6 1.78165e6i −0.820220 1.42066i
\(276\) 249696. 432486.i 0.197305 0.341743i
\(277\) −431607. + 747564.i −0.337978 + 0.585395i −0.984052 0.177879i \(-0.943076\pi\)
0.646074 + 0.763275i \(0.276410\pi\)
\(278\) 730430. + 1.26514e6i 0.566848 + 0.981810i
\(279\) 509733. 0.392042
\(280\) 49728.0 2327.88i 0.0379058 0.00177445i
\(281\) 1.47110e6 1.11142 0.555709 0.831377i \(-0.312447\pi\)
0.555709 + 0.831377i \(0.312447\pi\)
\(282\) −41580.0 72018.7i −0.0311359 0.0539290i
\(283\) −344420. + 596554.i −0.255637 + 0.442775i −0.965068 0.261999i \(-0.915618\pi\)
0.709432 + 0.704774i \(0.248952\pi\)
\(284\) 305808. 529675.i 0.224985 0.389685i
\(285\) 31239.0 + 54107.5i 0.0227816 + 0.0394590i
\(286\) 1.48918e6 1.07654
\(287\) −289527. + 560473.i −0.207484 + 0.401652i
\(288\) 82944.0 0.0589256
\(289\) −803872. 1.39235e6i −0.566164 0.980624i
\(290\) 40464.0 70085.7i 0.0282536 0.0489367i
\(291\) −561393. + 972361.i −0.388628 + 0.673124i
\(292\) −564712. 978110.i −0.387588 0.671321i
\(293\) 722832. 0.491890 0.245945 0.969284i \(-0.420902\pi\)
0.245945 + 0.969284i \(0.420902\pi\)
\(294\) −350154. 493437.i −0.236260 0.332938i
\(295\) −123264. −0.0824672
\(296\) −100192. 173538.i −0.0664666 0.115124i
\(297\) 242757. 420467.i 0.159691 0.276593i
\(298\) 336120. 582177.i 0.219257 0.379764i
\(299\) −969306. 1.67889e6i −0.627022 1.08603i
\(300\) −444816. −0.285350
\(301\) −678716. + 1.31387e6i −0.431790 + 0.835868i
\(302\) 614144. 0.387483
\(303\) 420255. + 727903.i 0.262970 + 0.455478i
\(304\) −148096. + 256510.i −0.0919093 + 0.159192i
\(305\) −13890.0 + 24058.2i −0.00854973 + 0.0148086i
\(306\) 281880. + 488230.i 0.172092 + 0.298072i
\(307\) −20125.0 −0.0121868 −0.00609340 0.999981i \(-0.501940\pi\)
−0.00609340 + 0.999981i \(0.501940\pi\)
\(308\) 1.37995e6 64598.6i 0.828871 0.0388013i
\(309\) −1.50958e6 −0.899414
\(310\) 75516.0 + 130798.i 0.0446308 + 0.0773028i
\(311\) 871779. 1.50997e6i 0.511099 0.885250i −0.488818 0.872386i \(-0.662572\pi\)
0.999917 0.0128643i \(-0.00409496\pi\)
\(312\) 160992. 278846.i 0.0936306 0.162173i
\(313\) −904272. 1.56624e6i −0.521721 0.903647i −0.999681 0.0252651i \(-0.991957\pi\)
0.477960 0.878382i \(-0.341376\pi\)
\(314\) 809672. 0.463431
\(315\) −34020.0 53031.9i −0.0193178 0.0301135i
\(316\) −996688. −0.561489
\(317\) −511776. 886422.i −0.286043 0.495442i 0.686818 0.726829i \(-0.259007\pi\)
−0.972862 + 0.231388i \(0.925673\pi\)
\(318\) 509328. 882182.i 0.282442 0.489204i
\(319\) 1.12288e6 1.94488e6i 0.617810 1.07008i
\(320\) 12288.0 + 21283.4i 0.00670820 + 0.0116190i
\(321\) 622620. 0.337257
\(322\) −971040. 1.51370e6i −0.521912 0.813581i
\(323\) −2.01318e6 −1.07368
\(324\) −52488.0 90911.9i −0.0277778 0.0481125i
\(325\) −863376. + 1.49541e6i −0.453410 + 0.785330i
\(326\) 359528. 622721.i 0.187365 0.324526i
\(327\) 988016. + 1.71129e6i 0.510969 + 0.885024i
\(328\) −311424. −0.159833
\(329\) −299145. + 14003.6i −0.152367 + 0.00713265i
\(330\) 143856. 0.0727182
\(331\) 503766. + 872549.i 0.252731 + 0.437744i 0.964277 0.264896i \(-0.0853378\pi\)
−0.711545 + 0.702640i \(0.752004\pi\)
\(332\) −638544. + 1.10599e6i −0.317940 + 0.550689i
\(333\) −126806. + 219634.i −0.0626654 + 0.108540i
\(334\) −434604. 752756.i −0.213171 0.369223i
\(335\) 112470. 0.0547551
\(336\) 137088. 265378.i 0.0662447 0.128238i
\(337\) −1.56571e6 −0.750993 −0.375496 0.926824i \(-0.622528\pi\)
−0.375496 + 0.926824i \(0.622528\pi\)
\(338\) 117624. + 203731.i 0.0560021 + 0.0969985i
\(339\) 177093. 306734.i 0.0836955 0.144965i
\(340\) −83520.0 + 144661.i −0.0391826 + 0.0678662i
\(341\) 2.09557e6 + 3.62963e6i 0.975924 + 1.69035i
\(342\) 374868. 0.173306
\(343\) −2.15747e6 + 304770.i −0.990169 + 0.139874i
\(344\) −730048. −0.332625
\(345\) −93636.0 162182.i −0.0423541 0.0733594i
\(346\) 147960. 256274.i 0.0664437 0.115084i
\(347\) −378642. + 655827.i −0.168813 + 0.292392i −0.938003 0.346628i \(-0.887327\pi\)
0.769190 + 0.639020i \(0.220660\pi\)
\(348\) −242784. 420514.i −0.107466 0.186137i
\(349\) −455638. −0.200243 −0.100121 0.994975i \(-0.531923\pi\)
−0.100121 + 0.994975i \(0.531923\pi\)
\(350\) −735182. + 1.42318e6i −0.320793 + 0.620998i
\(351\) −407511. −0.176552
\(352\) 340992. + 590615.i 0.146686 + 0.254067i
\(353\) 1.81569e6 3.14487e6i 0.775543 1.34328i −0.158946 0.987287i \(-0.550810\pi\)
0.934489 0.355992i \(-0.115857\pi\)
\(354\) −369792. + 640499.i −0.156837 + 0.271650i
\(355\) −114678. 198628.i −0.0482958 0.0836508i
\(356\) −289920. −0.121242
\(357\) 2.02797e6 94933.7i 0.842153 0.0394230i
\(358\) 3.15746e6 1.30206
\(359\) 2.01242e6 + 3.48561e6i 0.824104 + 1.42739i 0.902602 + 0.430476i \(0.141654\pi\)
−0.0784980 + 0.996914i \(0.525012\pi\)
\(360\) 15552.0 26936.9i 0.00632456 0.0109545i
\(361\) 568725. 985061.i 0.229686 0.397828i
\(362\) 955478. + 1.65494e6i 0.383221 + 0.663758i
\(363\) 2.54254e6 1.01275
\(364\) −626080. 975962.i −0.247672 0.386082i
\(365\) −423534. −0.166401
\(366\) 83340.0 + 144349.i 0.0325200 + 0.0563263i
\(367\) −1.28894e6 + 2.23251e6i −0.499536 + 0.865222i −1.00000 0.000535822i \(-0.999829\pi\)
0.500464 + 0.865757i \(0.333163\pi\)
\(368\) 443904. 768864.i 0.170871 0.295958i
\(369\) 197073. + 341340.i 0.0753462 + 0.130503i
\(370\) −75144.0 −0.0285358
\(371\) −1.98072e6 3.08764e6i −0.747116 1.16464i
\(372\) 906192. 0.339518
\(373\) 1.26566e6 + 2.19220e6i 0.471028 + 0.815844i 0.999451 0.0331372i \(-0.0105498\pi\)
−0.528423 + 0.848981i \(0.677216\pi\)
\(374\) −2.31768e6 + 4.01434e6i −0.856790 + 1.48400i
\(375\) −167778. + 290600.i −0.0616108 + 0.106713i
\(376\) −73920.0 128033.i −0.0269645 0.0467039i
\(377\) −1.88495e6 −0.683040
\(378\) −377622. + 17677.3i −0.135934 + 0.00636336i
\(379\) −3.06677e6 −1.09669 −0.548344 0.836253i \(-0.684742\pi\)
−0.548344 + 0.836253i \(0.684742\pi\)
\(380\) 55536.0 + 96191.2i 0.0197295 + 0.0341725i
\(381\) −1.42692e6 + 2.47150e6i −0.503601 + 0.872263i
\(382\) −717948. + 1.24352e6i −0.251730 + 0.436009i
\(383\) 1.96260e6 + 3.39932e6i 0.683652 + 1.18412i 0.973859 + 0.227155i \(0.0729425\pi\)
−0.290207 + 0.956964i \(0.593724\pi\)
\(384\) 147456. 0.0510310
\(385\) 237762. 460265.i 0.0817505 0.158254i
\(386\) −727732. −0.248601
\(387\) 461984. + 800179.i 0.156801 + 0.271587i
\(388\) −998032. + 1.72864e6i −0.336562 + 0.582943i
\(389\) 2.01334e6 3.48722e6i 0.674597 1.16844i −0.301990 0.953311i \(-0.597651\pi\)
0.976587 0.215125i \(-0.0690158\pi\)
\(390\) −60372.0 104567.i −0.0200990 0.0348125i
\(391\) 6.03432e6 1.99612
\(392\) −622496. 877221.i −0.204607 0.288333i
\(393\) −1.39347e6 −0.455110
\(394\) −1.43585e6 2.48696e6i −0.465981 0.807102i
\(395\) −186879. + 323684.i −0.0602654 + 0.104383i
\(396\) 431568. 747498.i 0.138297 0.239537i
\(397\) −2.28720e6 3.96155e6i −0.728329 1.26150i −0.957589 0.288138i \(-0.906964\pi\)
0.229260 0.973365i \(-0.426370\pi\)
\(398\) 812384. 0.257071
\(399\) 619574. 1.19938e6i 0.194832 0.377160i
\(400\) −790784. −0.247120
\(401\) 1.13472e6 + 1.96539e6i 0.352393 + 0.610363i 0.986668 0.162744i \(-0.0520346\pi\)
−0.634275 + 0.773108i \(0.718701\pi\)
\(402\) 337410. 584411.i 0.104134 0.180365i
\(403\) 1.75889e6 3.04649e6i 0.539482 0.934410i
\(404\) 747120. + 1.29405e6i 0.227739 + 0.394455i
\(405\) −39366.0 −0.0119257
\(406\) −1.74670e6 + 81766.7i −0.525899 + 0.0246185i
\(407\) −2.08525e6 −0.623981
\(408\) 501120. + 867965.i 0.149036 + 0.258138i
\(409\) 2.02298e6 3.50391e6i 0.597976 1.03572i −0.395144 0.918619i \(-0.629305\pi\)
0.993120 0.117105i \(-0.0373615\pi\)
\(410\) −58392.0 + 101138.i −0.0171551 + 0.0297135i
\(411\) −302994. 524801.i −0.0884768 0.153246i
\(412\) −2.68370e6 −0.778915
\(413\) 1.43808e6 + 2.24174e6i 0.414866 + 0.646712i
\(414\) −1.12363e6 −0.322198
\(415\) 239454. + 414746.i 0.0682499 + 0.118212i
\(416\) 286208. 495727.i 0.0810865 0.140446i
\(417\) 1.64347e6 2.84657e6i 0.462829 0.801644i
\(418\) 1.54112e6 + 2.66931e6i 0.431417 + 0.747236i
\(419\) −3.91281e6 −1.08881 −0.544407 0.838821i \(-0.683245\pi\)
−0.544407 + 0.838821i \(0.683245\pi\)
\(420\) −60480.0 94279.0i −0.0167297 0.0260790i
\(421\) −2.78086e6 −0.764671 −0.382335 0.924024i \(-0.624880\pi\)
−0.382335 + 0.924024i \(0.624880\pi\)
\(422\) −2.34196e6 4.05639e6i −0.640174 1.10881i
\(423\) −93555.0 + 162042.i −0.0254224 + 0.0440328i
\(424\) 905472. 1.56832e6i 0.244602 0.423663i
\(425\) −2.68743e6 4.65477e6i −0.721714 1.25004i
\(426\) −1.37614e6 −0.367398
\(427\) 599585. 28067.9i 0.159141 0.00744972i
\(428\) 1.10688e6 0.292073
\(429\) −1.67532e6 2.90174e6i −0.439496 0.761230i
\(430\) −136884. + 237090.i −0.0357011 + 0.0618361i
\(431\) 2.19104e6 3.79498e6i 0.568141 0.984049i −0.428609 0.903490i \(-0.640996\pi\)
0.996750 0.0805589i \(-0.0256705\pi\)
\(432\) −93312.0 161621.i −0.0240563 0.0416667i
\(433\) 1.24946e6 0.320261 0.160130 0.987096i \(-0.448809\pi\)
0.160130 + 0.987096i \(0.448809\pi\)
\(434\) 1.49773e6 2.89935e6i 0.381690 0.738883i
\(435\) −182088. −0.0461379
\(436\) 1.75647e6 + 3.04230e6i 0.442512 + 0.766453i
\(437\) 2.00624e6 3.47491e6i 0.502550 0.870441i
\(438\) −1.27060e6 + 2.20075e6i −0.316464 + 0.548132i
\(439\) 3.37210e6 + 5.84066e6i 0.835102 + 1.44644i 0.893947 + 0.448172i \(0.147925\pi\)
−0.0588449 + 0.998267i \(0.518742\pi\)
\(440\) 255744. 0.0629758
\(441\) −567567. + 1.23741e6i −0.138970 + 0.302983i
\(442\) 3.89064e6 0.947252
\(443\) −239448. 414736.i −0.0579698 0.100407i 0.835584 0.549362i \(-0.185129\pi\)
−0.893554 + 0.448956i \(0.851796\pi\)
\(444\) −225432. + 390460.i −0.0542698 + 0.0939980i
\(445\) −54360.0 + 94154.3i −0.0130131 + 0.0225393i
\(446\) −2.49270e6 4.31749e6i −0.593381 1.02777i
\(447\) −1.51254e6 −0.358045
\(448\) 243712. 471783.i 0.0573696 0.111057i
\(449\) 724506. 0.169600 0.0848001 0.996398i \(-0.472975\pi\)
0.0848001 + 0.996398i \(0.472975\pi\)
\(450\) 500418. + 866749.i 0.116493 + 0.201773i
\(451\) −1.62038e6 + 2.80658e6i −0.375124 + 0.649734i
\(452\) 314832. 545305.i 0.0724824 0.125543i
\(453\) −690912. 1.19669e6i −0.158189 0.273992i
\(454\) −3.67577e6 −0.836967
\(455\) −434343. + 20332.5i −0.0983568 + 0.00460430i
\(456\) 666432. 0.150087
\(457\) 1.16978e6 + 2.02612e6i 0.262008 + 0.453811i 0.966775 0.255627i \(-0.0822820\pi\)
−0.704768 + 0.709438i \(0.748949\pi\)
\(458\) −2.40750e6 + 4.16991e6i −0.536293 + 0.928887i
\(459\) 634230. 1.09852e6i 0.140513 0.243375i
\(460\) −166464. 288324.i −0.0366797 0.0635311i
\(461\) 2.98247e6 0.653617 0.326809 0.945091i \(-0.394027\pi\)
0.326809 + 0.945091i \(0.394027\pi\)
\(462\) −1.67832e6 2.61624e6i −0.365822 0.570260i
\(463\) 4.28423e6 0.928795 0.464398 0.885627i \(-0.346271\pi\)
0.464398 + 0.885627i \(0.346271\pi\)
\(464\) −431616. 747581.i −0.0930685 0.161199i
\(465\) 169911. 294294.i 0.0364409 0.0631175i
\(466\) 1.83812e6 3.18372e6i 0.392112 0.679158i
\(467\) 2.87018e6 + 4.97129e6i 0.608998 + 1.05482i 0.991406 + 0.130822i \(0.0417618\pi\)
−0.382407 + 0.923994i \(0.624905\pi\)
\(468\) −724464. −0.152898
\(469\) −1.31215e6 2.04544e6i −0.275455 0.429393i
\(470\) −55440.0 −0.0115765
\(471\) −910881. 1.57769e6i −0.189195 0.327695i
\(472\) −657408. + 1.13866e6i −0.135825 + 0.235256i
\(473\) −3.79853e6 + 6.57925e6i −0.780662 + 1.35215i
\(474\) 1.12127e6 + 1.94210e6i 0.229227 + 0.397033i
\(475\) −3.57397e6 −0.726804
\(476\) 3.60528e6 168771.i 0.729326 0.0341413i
\(477\) −2.29198e6 −0.461226
\(478\) 1.25068e6 + 2.16623e6i 0.250366 + 0.433646i
\(479\) −1.32526e6 + 2.29541e6i −0.263913 + 0.457111i −0.967278 0.253718i \(-0.918347\pi\)
0.703365 + 0.710829i \(0.251680\pi\)
\(480\) 27648.0 47887.7i 0.00547723 0.00948683i
\(481\) 875114. + 1.51574e6i 0.172465 + 0.298719i
\(482\) 5.01529e6 0.983282
\(483\) −1.85711e6 + 3.59504e6i −0.362219 + 0.701191i
\(484\) 4.52008e6 0.877067
\(485\) 374262. + 648241.i 0.0722473 + 0.125136i
\(486\) −118098. + 204552.i −0.0226805 + 0.0392837i
\(487\) −1.40277e6 + 2.42967e6i −0.268018 + 0.464221i −0.968350 0.249597i \(-0.919702\pi\)
0.700332 + 0.713817i \(0.253035\pi\)
\(488\) 148160. + 256621.i 0.0281632 + 0.0487800i
\(489\) −1.61788e6 −0.305966
\(490\) −401604. + 37682.5i −0.0755628 + 0.00709005i
\(491\) −4.68450e6 −0.876919 −0.438460 0.898751i \(-0.644476\pi\)
−0.438460 + 0.898751i \(0.644476\pi\)
\(492\) 350352. + 606827.i 0.0652517 + 0.113019i
\(493\) 2.93364e6 5.08121e6i 0.543613 0.941565i
\(494\) 1.29353e6 2.24045e6i 0.238483 0.413065i
\(495\) −161838. 280312.i −0.0296871 0.0514195i
\(496\) 1.61101e6 0.294031
\(497\) −2.27445e6 + 4.40292e6i −0.413033 + 0.799558i
\(498\) 2.87345e6 0.519194
\(499\) −737876. 1.27804e6i −0.132658 0.229770i 0.792043 0.610466i \(-0.209018\pi\)
−0.924700 + 0.380696i \(0.875684\pi\)
\(500\) −298272. + 516622.i −0.0533565 + 0.0924162i
\(501\) −977859. + 1.69370e6i −0.174053 + 0.301469i
\(502\) 3.02666e6 + 5.24234e6i 0.536050 + 0.928465i
\(503\) 63606.0 0.0112093 0.00560465 0.999984i \(-0.498216\pi\)
0.00560465 + 0.999984i \(0.498216\pi\)
\(504\) −671328. + 31426.3i −0.117722 + 0.00551083i
\(505\) 560340. 0.0977740
\(506\) −4.61938e6 8.00099e6i −0.802060 1.38921i
\(507\) 264654. 458394.i 0.0457255 0.0791989i
\(508\) −2.53674e6 + 4.39377e6i −0.436131 + 0.755402i
\(509\) −3.10578e6 5.37937e6i −0.531345 0.920317i −0.999331 0.0365806i \(-0.988353\pi\)
0.467986 0.883736i \(-0.344980\pi\)
\(510\) 375840. 0.0639849
\(511\) 4.94123e6 + 7.70262e6i 0.837111 + 1.30493i
\(512\) 262144. 0.0441942
\(513\) −421726. 730452.i −0.0707518 0.122546i
\(514\) 3.10986e6 5.38644e6i 0.519198 0.899277i
\(515\) −503193. + 871556.i −0.0836020 + 0.144803i
\(516\) 821304. + 1.42254e6i 0.135794 + 0.235202i
\(517\) −1.53846e6 −0.253139
\(518\) 876680. + 1.36661e6i 0.143554 + 0.223779i
\(519\) −665820. −0.108502
\(520\) −107328. 185898.i −0.0174062 0.0301485i
\(521\) −706026. + 1.22287e6i −0.113953 + 0.197373i −0.917361 0.398057i \(-0.869685\pi\)
0.803408 + 0.595429i \(0.203018\pi\)
\(522\) −546264. + 946157.i −0.0877458 + 0.151980i
\(523\) −2.61467e6 4.52875e6i −0.417987 0.723976i 0.577749 0.816214i \(-0.303931\pi\)
−0.995737 + 0.0922386i \(0.970598\pi\)
\(524\) −2.47728e6 −0.394137
\(525\) 3.60023e6 168535.i 0.570075 0.0266865i
\(526\) −4.46126e6 −0.703062
\(527\) 5.47491e6 + 9.48282e6i 0.858718 + 1.48734i
\(528\) 767232. 1.32888e6i 0.119768 0.207445i
\(529\) −2.79534e6 + 4.84167e6i −0.434306 + 0.752240i
\(530\) −339552. 588121.i −0.0525069 0.0909447i
\(531\) 1.66406e6 0.256114
\(532\) 1.10146e6 2.13224e6i 0.168730 0.326630i
\(533\) 2.72009e6 0.414730
\(534\) 326160. + 564926.i 0.0494968 + 0.0857311i
\(535\) 207540. 359470.i 0.0313485 0.0542973i
\(536\) 599840. 1.03895e6i 0.0901827 0.156201i
\(537\) −3.55215e6 6.15250e6i −0.531564 0.920695i
\(538\) 142680. 0.0212524
\(539\) −1.11445e7 + 1.04569e6i −1.65230 + 0.155035i
\(540\) −69984.0 −0.0103280
\(541\) −2.20686e6 3.82240e6i −0.324177 0.561491i 0.657169 0.753744i \(-0.271754\pi\)
−0.981345 + 0.192253i \(0.938421\pi\)
\(542\) 585536. 1.01418e6i 0.0856161 0.148291i
\(543\) 2.14983e6 3.72361e6i 0.312899 0.541956i
\(544\) 890880. + 1.54305e6i 0.129069 + 0.223554i
\(545\) 1.31735e6 0.189981
\(546\) −1.19738e6 + 2.31791e6i −0.171890 + 0.332748i
\(547\) −1.19038e7 −1.70105 −0.850523 0.525938i \(-0.823714\pi\)
−0.850523 + 0.525938i \(0.823714\pi\)
\(548\) −538656. 932980.i −0.0766232 0.132715i
\(549\) 187515. 324786.i 0.0265525 0.0459903i
\(550\) −4.11455e6 + 7.12661e6i −0.579983 + 1.00456i
\(551\) −1.95070e6 3.37871e6i −0.273723 0.474103i
\(552\) −1.99757e6 −0.279032
\(553\) 8.06694e6 377631.i 1.12175 0.0525116i
\(554\) 3.45285e6 0.477973
\(555\) 84537.0 + 146422.i 0.0116497 + 0.0201779i
\(556\) 2.92172e6 5.06057e6i 0.400822 0.694244i
\(557\) −6.45665e6 + 1.11832e7i −0.881798 + 1.52732i −0.0324587 + 0.999473i \(0.510334\pi\)
−0.849340 + 0.527847i \(0.823000\pi\)
\(558\) −1.01947e6 1.76577e6i −0.138608 0.240076i
\(559\) 6.37651e6 0.863085
\(560\) −107520. 167607.i −0.0144884 0.0225851i
\(561\) 1.04296e7 1.39913
\(562\) −2.94221e6 5.09605e6i −0.392946 0.680602i
\(563\) 5.68492e6 9.84657e6i 0.755881 1.30922i −0.189055 0.981967i \(-0.560542\pi\)
0.944935 0.327257i \(-0.106124\pi\)
\(564\) −166320. + 288075.i −0.0220164 + 0.0381336i
\(565\) −118062. 204489.i −0.0155593 0.0269494i
\(566\) 2.75536e6 0.361525
\(567\) 459270. + 715931.i 0.0599944 + 0.0935220i
\(568\) −2.44646e6 −0.318176
\(569\) 2.84898e6 + 4.93457e6i 0.368900 + 0.638953i 0.989394 0.145258i \(-0.0464013\pi\)
−0.620494 + 0.784211i \(0.713068\pi\)
\(570\) 124956. 216430.i 0.0161091 0.0279017i
\(571\) 3.52110e6 6.09873e6i 0.451948 0.782797i −0.546559 0.837421i \(-0.684063\pi\)
0.998507 + 0.0546236i \(0.0173959\pi\)
\(572\) −2.97835e6 5.15866e6i −0.380615 0.659245i
\(573\) 3.23077e6 0.411073
\(574\) 2.52059e6 117994.i 0.319317 0.0149479i
\(575\) 1.07127e7 1.35122
\(576\) −165888. 287326.i −0.0208333 0.0360844i
\(577\) 1.29098e6 2.23605e6i 0.161429 0.279603i −0.773952 0.633244i \(-0.781723\pi\)
0.935381 + 0.353641i \(0.115056\pi\)
\(578\) −3.21549e6 + 5.56939e6i −0.400338 + 0.693406i
\(579\) 818698. + 1.41803e6i 0.101491 + 0.175788i
\(580\) −323712. −0.0399566
\(581\) 4.74917e6 9.19355e6i 0.583684 1.12991i
\(582\) 4.49114e6 0.549604
\(583\) −9.42257e6 1.63204e7i −1.14815 1.98865i
\(584\) −2.25885e6 + 3.91244e6i −0.274066 + 0.474696i
\(585\) −135837. + 235277.i −0.0164107 + 0.0284243i
\(586\) −1.44566e6 2.50396e6i −0.173910 0.301220i
\(587\) 4.69459e6 0.562345 0.281172 0.959657i \(-0.409277\pi\)
0.281172 + 0.959657i \(0.409277\pi\)
\(588\) −1.00901e6 + 2.19984e6i −0.120351 + 0.262391i
\(589\) 7.28100e6 0.864774
\(590\) 246528. + 426999.i 0.0291566 + 0.0505006i
\(591\) −3.23066e6 + 5.59566e6i −0.380472 + 0.658996i
\(592\) −400768. + 694151.i −0.0469990 + 0.0814047i
\(593\) −6.71175e6 1.16251e7i −0.783789 1.35756i −0.929720 0.368268i \(-0.879951\pi\)
0.145931 0.989295i \(-0.453382\pi\)
\(594\) −1.94206e6 −0.225837
\(595\) 621180. 1.20249e6i 0.0719325 0.139248i
\(596\) −2.68896e6 −0.310076
\(597\) −913932. 1.58298e6i −0.104949 0.181777i
\(598\) −3.87722e6 + 6.71555e6i −0.443372 + 0.767942i
\(599\) −2.52301e6 + 4.36997e6i −0.287310 + 0.497636i −0.973167 0.230101i \(-0.926094\pi\)
0.685856 + 0.727737i \(0.259428\pi\)
\(600\) 889632. + 1.54089e6i 0.100886 + 0.174740i
\(601\) −1.06391e7 −1.20148 −0.600742 0.799443i \(-0.705128\pi\)
−0.600742 + 0.799443i \(0.705128\pi\)
\(602\) 5.90883e6 276605.i 0.664523 0.0311078i
\(603\) −1.51834e6 −0.170050
\(604\) −1.22829e6 2.12746e6i −0.136996 0.237284i
\(605\) 847515. 1.46794e6i 0.0941367 0.163050i
\(606\) 1.68102e6 2.91161e6i 0.185948 0.322071i
\(607\) −708041. 1.22636e6i −0.0779986 0.135098i 0.824388 0.566026i \(-0.191520\pi\)
−0.902386 + 0.430928i \(0.858186\pi\)
\(608\) 1.18477e6 0.129979
\(609\) 2.12436e6 + 3.31155e6i 0.232105 + 0.361816i
\(610\) 111120. 0.0120912
\(611\) 645645. + 1.11829e6i 0.0699666 + 0.121186i
\(612\) 1.12752e6 1.95292e6i 0.121687 0.210769i
\(613\) −4.73152e6 + 8.19523e6i −0.508568 + 0.880866i 0.491383 + 0.870944i \(0.336492\pi\)
−0.999951 + 0.00992215i \(0.996842\pi\)
\(614\) 40250.0 + 69715.0i 0.00430869 + 0.00746286i
\(615\) 262764. 0.0280142
\(616\) −2.98368e6 4.65110e6i −0.316811 0.493860i
\(617\) 1.29388e7 1.36830 0.684148 0.729343i \(-0.260174\pi\)
0.684148 + 0.729343i \(0.260174\pi\)
\(618\) 3.01916e6 + 5.22934e6i 0.317991 + 0.550776i
\(619\) 1.90188e6 3.29415e6i 0.199506 0.345555i −0.748862 0.662726i \(-0.769400\pi\)
0.948368 + 0.317171i \(0.102733\pi\)
\(620\) 302064. 523190.i 0.0315587 0.0546614i
\(621\) 1.26409e6 + 2.18946e6i 0.131537 + 0.227829i
\(622\) −6.97423e6 −0.722804
\(623\) 2.34654e6 109847.i 0.242219 0.0113388i
\(624\) −1.28794e6 −0.132414
\(625\) −4.71471e6 8.16612e6i −0.482786 0.836210i
\(626\) −3.61709e6 + 6.26498e6i −0.368912 + 0.638975i
\(627\) 3.46753e6 6.00594e6i 0.352250 0.610115i
\(628\) −1.61934e6 2.80479e6i −0.163848 0.283792i
\(629\) −5.44794e6 −0.549042
\(630\) −115668. + 223913.i −0.0116108 + 0.0224764i
\(631\) −9.17498e6 −0.917343 −0.458671 0.888606i \(-0.651674\pi\)
−0.458671 + 0.888606i \(0.651674\pi\)
\(632\) 1.99338e6 + 3.45263e6i 0.198516 + 0.343841i
\(633\) −5.26941e6 + 9.12689e6i −0.522700 + 0.905343i
\(634\) −2.04710e6 + 3.54569e6i −0.202263 + 0.350330i
\(635\) 951279. + 1.64766e6i 0.0936211 + 0.162156i
\(636\) −4.07462e6 −0.399434
\(637\) 5.43711e6 + 7.66198e6i 0.530909 + 0.748157i
\(638\) −8.98301e6 −0.873716
\(639\) 1.54815e6 + 2.68148e6i 0.149990 + 0.259790i
\(640\) 49152.0 85133.8i 0.00474342 0.00821584i
\(641\) −5.12269e6 + 8.87275e6i −0.492439 + 0.852930i −0.999962 0.00870851i \(-0.997228\pi\)
0.507523 + 0.861638i \(0.330561\pi\)
\(642\) −1.24524e6 2.15682e6i −0.119238 0.206527i
\(643\) −5.72346e6 −0.545922 −0.272961 0.962025i \(-0.588003\pi\)
−0.272961 + 0.962025i \(0.588003\pi\)
\(644\) −3.30154e6 + 6.39118e6i −0.313691 + 0.607249i
\(645\) 615978. 0.0582996
\(646\) 4.02636e6 + 6.97386e6i 0.379604 + 0.657494i
\(647\) 4.99397e6 8.64981e6i 0.469013 0.812355i −0.530359 0.847773i \(-0.677943\pi\)
0.999373 + 0.0354179i \(0.0112762\pi\)
\(648\) −209952. + 363648.i −0.0196419 + 0.0340207i
\(649\) 6.84115e6 + 1.18492e7i 0.637555 + 1.10428i
\(650\) 6.90700e6 0.641219
\(651\) −7.33449e6 + 343344.i −0.678293 + 0.0317524i
\(652\) −2.87622e6 −0.264974
\(653\) 599439. + 1.03826e6i 0.0550126 + 0.0952846i 0.892220 0.451601i \(-0.149147\pi\)
−0.837208 + 0.546885i \(0.815813\pi\)
\(654\) 3.95206e6 6.84517e6i 0.361309 0.625806i
\(655\) −464490. + 804520.i −0.0423032 + 0.0732713i
\(656\) 622848. + 1.07880e6i 0.0565096 + 0.0978776i
\(657\) 5.71771e6 0.516783
\(658\) 646800. + 1.00826e6i 0.0582378 + 0.0907838i
\(659\) 1.18065e7 1.05903 0.529516 0.848300i \(-0.322374\pi\)
0.529516 + 0.848300i \(0.322374\pi\)
\(660\) −287712. 498332.i −0.0257098 0.0445306i
\(661\) −2.36020e6 + 4.08798e6i −0.210109 + 0.363919i −0.951748 0.306879i \(-0.900715\pi\)
0.741640 + 0.670799i \(0.234049\pi\)
\(662\) 2.01507e6 3.49020e6i 0.178708 0.309532i
\(663\) −4.37697e6 7.58113e6i −0.386714 0.669808i
\(664\) 5.10835e6 0.449636
\(665\) −485940. 757505.i −0.0426117 0.0664250i
\(666\) 1.01444e6 0.0886222
\(667\) 5.84705e6 + 1.01274e7i 0.508888 + 0.881420i
\(668\) −1.73842e6 + 3.01102e6i −0.150734 + 0.261080i
\(669\) −5.60858e6 + 9.71435e6i −0.484493 + 0.839167i
\(670\) −224940. 389608.i −0.0193589 0.0335305i
\(671\) 3.08358e6 0.264392
\(672\) −1.19347e6 + 55869.0i −0.101950 + 0.00477252i
\(673\) −8.70826e6 −0.741129 −0.370564 0.928807i \(-0.620836\pi\)
−0.370564 + 0.928807i \(0.620836\pi\)
\(674\) 3.13141e6 + 5.42377e6i 0.265516 + 0.459887i
\(675\) 1.12594e6 1.95019e6i 0.0951165 0.164747i
\(676\) 470496. 814923.i 0.0395995 0.0685883i
\(677\) −2.55553e6 4.42630e6i −0.214293 0.371167i 0.738760 0.673968i \(-0.235412\pi\)
−0.953054 + 0.302801i \(0.902078\pi\)
\(678\) −1.41674e6 −0.118363
\(679\) 7.42286e6 1.43693e7i 0.617870 1.19609i
\(680\) 668160. 0.0554126
\(681\) 4.13524e6 + 7.16244e6i 0.341690 + 0.591825i
\(682\) 8.38228e6 1.45185e7i 0.690083 1.19526i
\(683\) 8.85989e6 1.53458e7i 0.726736 1.25874i −0.231520 0.972830i \(-0.574370\pi\)
0.958256 0.285913i \(-0.0922968\pi\)
\(684\) −749736. 1.29858e6i −0.0612729 0.106128i
\(685\) −403992. −0.0328962
\(686\) 5.37069e6 + 6.86416e6i 0.435733 + 0.556899i
\(687\) 1.08337e7 0.875763
\(688\) 1.46010e6 + 2.52896e6i 0.117601 + 0.203691i
\(689\) −7.90873e6 + 1.36983e7i −0.634686 + 1.09931i
\(690\) −374544. + 648729.i −0.0299488 + 0.0518729i
\(691\) 1.12997e7 + 1.95716e7i 0.900265 + 1.55931i 0.827149 + 0.561982i \(0.189961\pi\)
0.0731160 + 0.997323i \(0.476706\pi\)
\(692\) −1.18368e6 −0.0939656
\(693\) −3.20979e6 + 6.21357e6i −0.253889 + 0.491483i
\(694\) 3.02914e6 0.238737
\(695\) −1.09564e6 1.89771e6i −0.0860415 0.149028i
\(696\) −971136. + 1.68206e6i −0.0759901 + 0.131619i
\(697\) −4.23342e6 + 7.33250e6i −0.330073 + 0.571702i
\(698\) 911276. + 1.57838e6i 0.0707964 + 0.122623i
\(699\) −8.27156e6 −0.640316
\(700\) 6.40041e6 299617.i 0.493699 0.0231111i
\(701\) −818148. −0.0628835 −0.0314418 0.999506i \(-0.510010\pi\)
−0.0314418 + 0.999506i \(0.510010\pi\)
\(702\) 815022. + 1.41166e6i 0.0624204 + 0.108115i
\(703\) −1.81128e6 + 3.13724e6i −0.138229 + 0.239419i
\(704\) 1.36397e6 2.36246e6i 0.103722 0.179652i
\(705\) 62370.0 + 108028.i 0.00472610 + 0.00818585i
\(706\) −1.45255e7 −1.09678
\(707\) −6.53730e6 1.01906e7i −0.491869 0.766749i
\(708\) 2.95834e6 0.221801
\(709\) 2.54591e6 + 4.40965e6i 0.190208 + 0.329449i 0.945319 0.326147i \(-0.105751\pi\)
−0.755111 + 0.655597i \(0.772417\pi\)
\(710\) −458712. + 794512.i −0.0341503 + 0.0591500i
\(711\) 2.52287e6 4.36973e6i 0.187163 0.324176i
\(712\) 579840. + 1.00431e6i 0.0428655 + 0.0742453i
\(713\) −2.18241e7 −1.60773
\(714\) −4.38480e6 6.83523e6i −0.321888 0.501773i
\(715\) −2.23376e6 −0.163408
\(716\) −6.31493e6 1.09378e7i −0.460348 0.797345i
\(717\) 2.81402e6 4.87403e6i 0.204423 0.354071i
\(718\) 8.04967e6 1.39424e7i 0.582730 1.00932i
\(719\) 240429. + 416435.i 0.0173446 + 0.0300418i 0.874567 0.484904i \(-0.161145\pi\)
−0.857223 + 0.514946i \(0.827812\pi\)
\(720\) −124416. −0.00894427
\(721\) 2.17212e7 1.01682e6i 1.55613 0.0728457i
\(722\) −4.54980e6 −0.324825
\(723\) −5.64220e6 9.77258e6i −0.401423 0.695286i
\(724\) 3.82191e6 6.61975e6i 0.270978 0.469348i
\(725\) 5.20805e6 9.02061e6i 0.367985 0.637369i
\(726\) −5.08509e6 8.80763e6i −0.358061 0.620180i
\(727\) −1.40783e7 −0.987905 −0.493952 0.869489i \(-0.664448\pi\)
−0.493952 + 0.869489i \(0.664448\pi\)
\(728\) −2.12867e6 + 4.12073e6i −0.148861 + 0.288168i
\(729\) 531441. 0.0370370
\(730\) 847068. + 1.46716e6i 0.0588317 + 0.101899i
\(731\) −9.92409e6 + 1.71890e7i −0.686906 + 1.18976i
\(732\) 333360. 577396.i 0.0229951 0.0398287i
\(733\) −1.01966e6 1.76610e6i −0.0700964 0.121411i 0.828847 0.559475i \(-0.188997\pi\)
−0.898943 + 0.438065i \(0.855664\pi\)
\(734\) 1.03115e7 0.706450
\(735\) 525231. + 740156.i 0.0358618 + 0.0505364i
\(736\) −3.55123e6 −0.241649
\(737\) −6.24209e6 1.08116e7i −0.423312 0.733199i
\(738\) 788292. 1.36536e6i 0.0532778 0.0922798i
\(739\) 8.24785e6 1.42857e7i 0.555558 0.962255i −0.442302 0.896866i \(-0.645838\pi\)
0.997860 0.0653888i \(-0.0208288\pi\)
\(740\) 150288. + 260306.i 0.0100889 + 0.0174745i
\(741\) −5.82087e6 −0.389441
\(742\) −6.73445e6 + 1.30367e7i −0.449047 + 0.869276i
\(743\) −2.38121e7 −1.58243 −0.791217 0.611536i \(-0.790552\pi\)
−0.791217 + 0.611536i \(0.790552\pi\)
\(744\) −1.81238e6 3.13914e6i −0.120038 0.207911i
\(745\) −504180. + 873265.i −0.0332809 + 0.0576442i
\(746\) 5.06266e6 8.76878e6i 0.333067 0.576889i
\(747\) −3.23263e6 5.59908e6i −0.211960 0.367126i
\(748\) 1.85414e7 1.21168
\(749\) −8.95881e6 + 419381.i −0.583507 + 0.0273152i
\(750\) 1.34222e6 0.0871308
\(751\) −962480. 1.66707e6i −0.0622719 0.107858i 0.833209 0.552959i \(-0.186501\pi\)
−0.895481 + 0.445101i \(0.853168\pi\)
\(752\) −295680. + 512133.i −0.0190668 + 0.0330246i
\(753\) 6.80999e6 1.17953e7i 0.437683 0.758089i
\(754\) 3.76990e6 + 6.52965e6i 0.241491 + 0.418275i
\(755\) −921216. −0.0588158
\(756\) 816480. + 1.27277e6i 0.0519566 + 0.0809924i
\(757\) 8.98092e6 0.569615 0.284807 0.958585i \(-0.408070\pi\)
0.284807 + 0.958585i \(0.408070\pi\)
\(758\) 6.13354e6 + 1.06236e7i 0.387738 + 0.671581i
\(759\) −1.03936e7 + 1.80022e7i −0.654879 + 1.13428i
\(760\) 222144. 384765.i 0.0139508 0.0241636i
\(761\) −7.29955e6 1.26432e7i −0.456914 0.791398i 0.541882 0.840454i \(-0.317712\pi\)
−0.998796 + 0.0490566i \(0.984379\pi\)
\(762\)