Properties

Label 147.6.e.l.79.2
Level $147$
Weight $6$
Character 147.79
Analytic conductor $23.576$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [147,6,Mod(67,147)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(147, 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("147.67");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 147 = 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 147.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: \(23.5764215125\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-83})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 20x^{2} - 21x + 441 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.2
Root \(-3.69493 + 2.71062i\) of defining polynomial
Character \(\chi\) \(=\) 147.79
Dual form 147.6.e.l.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.69493 - 8.13186i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(-35.8645 + 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +O(q^{10})\) \(q+(4.69493 - 8.13186i) q^{2} +(-4.50000 - 7.79423i) q^{3} +(-28.0848 - 48.6443i) q^{4} +(-35.8645 + 62.1192i) q^{5} -84.5088 q^{6} -226.949 q^{8} +(-40.5000 + 70.1481i) q^{9} +(336.763 + 583.291i) q^{10} +(280.305 + 485.503i) q^{11} +(-252.763 + 437.799i) q^{12} -533.509 q^{13} +645.562 q^{15} +(-166.798 + 288.903i) q^{16} +(502.850 + 870.962i) q^{17} +(380.290 + 658.681i) q^{18} +(684.263 - 1185.18i) q^{19} +4028.99 q^{20} +5264.05 q^{22} +(-1614.04 + 2795.60i) q^{23} +(1021.27 + 1768.90i) q^{24} +(-1010.03 - 1749.42i) q^{25} +(-2504.79 + 4338.42i) q^{26} +729.000 q^{27} -753.456 q^{29} +(3030.87 - 5249.62i) q^{30} +(4103.21 + 7106.97i) q^{31} +(-2064.97 - 3576.64i) q^{32} +(2522.75 - 4369.52i) q^{33} +9443.39 q^{34} +4549.74 q^{36} +(1404.33 - 2432.37i) q^{37} +(-6425.14 - 11128.7i) q^{38} +(2400.79 + 4158.29i) q^{39} +(8139.43 - 14097.9i) q^{40} -245.827 q^{41} -17504.5 q^{43} +(15744.6 - 27270.5i) q^{44} +(-2905.03 - 5031.65i) q^{45} +(15155.6 + 26250.3i) q^{46} +(-8172.74 + 14155.6i) q^{47} +3002.37 q^{48} -18968.1 q^{50} +(4525.65 - 7838.66i) q^{51} +(14983.5 + 25952.2i) q^{52} +(14820.8 + 25670.4i) q^{53} +(3422.61 - 5928.13i) q^{54} -40212.0 q^{55} -12316.7 q^{57} +(-3537.43 + 6127.00i) q^{58} +(-5178.05 - 8968.65i) q^{59} +(-18130.5 - 31402.9i) q^{60} +(477.089 - 826.343i) q^{61} +77057.2 q^{62} -49454.8 q^{64} +(19134.0 - 33141.1i) q^{65} +(-23688.2 - 41029.2i) q^{66} +(9907.60 + 17160.5i) q^{67} +(28244.9 - 48921.6i) q^{68} +29052.7 q^{69} +62125.4 q^{71} +(9191.45 - 15920.1i) q^{72} +(13554.8 + 23477.6i) q^{73} +(-13186.5 - 22839.7i) q^{74} +(-9090.27 + 15744.8i) q^{75} -76869.6 q^{76} +45086.2 q^{78} +(-22343.7 + 38700.4i) q^{79} +(-11964.3 - 20722.8i) q^{80} +(-3280.50 - 5681.99i) q^{81} +(-1154.14 + 1999.03i) q^{82} -15606.6 q^{83} -72137.9 q^{85} +(-82182.5 + 142344. i) q^{86} +(3390.55 + 5872.61i) q^{87} +(-63615.0 - 110184. i) q^{88} +(6817.66 - 11808.5i) q^{89} -54555.6 q^{90} +181320. q^{92} +(36928.9 - 63962.7i) q^{93} +(76740.9 + 132919. i) q^{94} +(49081.6 + 85011.8i) q^{95} +(-18584.8 + 32189.8i) q^{96} +12919.5 q^{97} -45409.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - 18 q^{3} - 65 q^{4} - 33 q^{5} - 54 q^{6} - 750 q^{8} - 162 q^{9} + 921 q^{10} + 1137 q^{11} - 585 q^{12} - 1850 q^{13} + 594 q^{15} + 895 q^{16} - 324 q^{17} + 243 q^{18} + 2311 q^{19} + 7374 q^{20} + 3162 q^{22} - 1596 q^{23} + 3375 q^{24} - 395 q^{25} - 2508 q^{26} + 2916 q^{27} - 4434 q^{29} + 8289 q^{30} + 4294 q^{31} - 1017 q^{32} + 10233 q^{33} + 35880 q^{34} + 10530 q^{36} + 19109 q^{37} - 6828 q^{38} + 8325 q^{39} + 10545 q^{40} + 25716 q^{41} - 5542 q^{43} + 36579 q^{44} - 2673 q^{45} + 40740 q^{46} - 23160 q^{47} - 16110 q^{48} - 58704 q^{50} - 2916 q^{51} + 33424 q^{52} + 31653 q^{53} + 2187 q^{54} - 35778 q^{55} - 41598 q^{57} + 2277 q^{58} + 41097 q^{59} - 33183 q^{60} + 42052 q^{61} + 204114 q^{62} - 60062 q^{64} + 23106 q^{65} - 14229 q^{66} - 30763 q^{67} + 44748 q^{68} + 28728 q^{69} + 204192 q^{71} + 30375 q^{72} - 28577 q^{73} + 77784 q^{74} - 3555 q^{75} - 170384 q^{76} + 45144 q^{78} + 18464 q^{79} - 71511 q^{80} - 13122 q^{81} - 86040 q^{82} - 122358 q^{83} - 247272 q^{85} - 258510 q^{86} + 19953 q^{87} - 212565 q^{88} + 29322 q^{89} - 149202 q^{90} + 333816 q^{92} + 38646 q^{93} + 109938 q^{94} + 61662 q^{95} - 9153 q^{96} + 19582 q^{97} - 184194 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).

\(n\) \(50\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.69493 8.13186i 0.829955 1.43752i −0.0681181 0.997677i \(-0.521699\pi\)
0.898073 0.439847i \(-0.144967\pi\)
\(3\) −4.50000 7.79423i −0.288675 0.500000i
\(4\) −28.0848 48.6443i −0.877650 1.52013i
\(5\) −35.8645 + 62.1192i −0.641564 + 1.11122i 0.343519 + 0.939146i \(0.388381\pi\)
−0.985084 + 0.172076i \(0.944952\pi\)
\(6\) −84.5088 −0.958349
\(7\) 0 0
\(8\) −226.949 −1.25373
\(9\) −40.5000 + 70.1481i −0.166667 + 0.288675i
\(10\) 336.763 + 583.291i 1.06494 + 1.84453i
\(11\) 280.305 + 485.503i 0.698472 + 1.20979i 0.968996 + 0.247076i \(0.0794698\pi\)
−0.270524 + 0.962713i \(0.587197\pi\)
\(12\) −252.763 + 437.799i −0.506711 + 0.877650i
\(13\) −533.509 −0.875555 −0.437777 0.899083i \(-0.644234\pi\)
−0.437777 + 0.899083i \(0.644234\pi\)
\(14\) 0 0
\(15\) 645.562 0.740815
\(16\) −166.798 + 288.903i −0.162889 + 0.282132i
\(17\) 502.850 + 870.962i 0.422004 + 0.730932i 0.996135 0.0878311i \(-0.0279936\pi\)
−0.574132 + 0.818763i \(0.694660\pi\)
\(18\) 380.290 + 658.681i 0.276652 + 0.479175i
\(19\) 684.263 1185.18i 0.434850 0.753182i −0.562434 0.826842i \(-0.690135\pi\)
0.997283 + 0.0736606i \(0.0234682\pi\)
\(20\) 4028.99 2.25228
\(21\) 0 0
\(22\) 5264.05 2.31880
\(23\) −1614.04 + 2795.60i −0.636201 + 1.10193i 0.350058 + 0.936728i \(0.386162\pi\)
−0.986259 + 0.165205i \(0.947171\pi\)
\(24\) 1021.27 + 1768.90i 0.361921 + 0.626865i
\(25\) −1010.03 1749.42i −0.323209 0.559815i
\(26\) −2504.79 + 4338.42i −0.726671 + 1.25863i
\(27\) 729.000 0.192450
\(28\) 0 0
\(29\) −753.456 −0.166365 −0.0831827 0.996534i \(-0.526508\pi\)
−0.0831827 + 0.996534i \(0.526508\pi\)
\(30\) 3030.87 5249.62i 0.614843 1.06494i
\(31\) 4103.21 + 7106.97i 0.766866 + 1.32825i 0.939254 + 0.343222i \(0.111518\pi\)
−0.172389 + 0.985029i \(0.555148\pi\)
\(32\) −2064.97 3576.64i −0.356484 0.617448i
\(33\) 2522.75 4369.52i 0.403263 0.698472i
\(34\) 9443.39 1.40098
\(35\) 0 0
\(36\) 4549.74 0.585100
\(37\) 1404.33 2432.37i 0.168642 0.292096i −0.769301 0.638887i \(-0.779395\pi\)
0.937943 + 0.346791i \(0.112729\pi\)
\(38\) −6425.14 11128.7i −0.721811 1.25021i
\(39\) 2400.79 + 4158.29i 0.252751 + 0.437777i
\(40\) 8139.43 14097.9i 0.804348 1.39317i
\(41\) −245.827 −0.0228387 −0.0114193 0.999935i \(-0.503635\pi\)
−0.0114193 + 0.999935i \(0.503635\pi\)
\(42\) 0 0
\(43\) −17504.5 −1.44371 −0.721853 0.692047i \(-0.756709\pi\)
−0.721853 + 0.692047i \(0.756709\pi\)
\(44\) 15744.6 27270.5i 1.22603 2.12354i
\(45\) −2905.03 5031.65i −0.213855 0.370407i
\(46\) 15155.6 + 26250.3i 1.05604 + 1.82911i
\(47\) −8172.74 + 14155.6i −0.539663 + 0.934725i 0.459258 + 0.888303i \(0.348115\pi\)
−0.998922 + 0.0464219i \(0.985218\pi\)
\(48\) 3002.37 0.188088
\(49\) 0 0
\(50\) −18968.1 −1.07300
\(51\) 4525.65 7838.66i 0.243644 0.422004i
\(52\) 14983.5 + 25952.2i 0.768430 + 1.33096i
\(53\) 14820.8 + 25670.4i 0.724741 + 1.25529i 0.959081 + 0.283133i \(0.0913739\pi\)
−0.234340 + 0.972155i \(0.575293\pi\)
\(54\) 3422.61 5928.13i 0.159725 0.276652i
\(55\) −40212.0 −1.79246
\(56\) 0 0
\(57\) −12316.7 −0.502121
\(58\) −3537.43 + 6127.00i −0.138076 + 0.239154i
\(59\) −5178.05 8968.65i −0.193659 0.335426i 0.752801 0.658248i \(-0.228702\pi\)
−0.946460 + 0.322821i \(0.895369\pi\)
\(60\) −18130.5 31402.9i −0.650176 1.12614i
\(61\) 477.089 826.343i 0.0164163 0.0284339i −0.857701 0.514150i \(-0.828108\pi\)
0.874117 + 0.485716i \(0.161441\pi\)
\(62\) 77057.2 2.54586
\(63\) 0 0
\(64\) −49454.8 −1.50924
\(65\) 19134.0 33141.1i 0.561725 0.972935i
\(66\) −23688.2 41029.2i −0.669380 1.15940i
\(67\) 9907.60 + 17160.5i 0.269638 + 0.467027i 0.968768 0.247967i \(-0.0797626\pi\)
−0.699130 + 0.714994i \(0.746429\pi\)
\(68\) 28244.9 48921.6i 0.740743 1.28300i
\(69\) 29052.7 0.734622
\(70\) 0 0
\(71\) 62125.4 1.46259 0.731296 0.682060i \(-0.238916\pi\)
0.731296 + 0.682060i \(0.238916\pi\)
\(72\) 9191.45 15920.1i 0.208955 0.361921i
\(73\) 13554.8 + 23477.6i 0.297705 + 0.515641i 0.975611 0.219509i \(-0.0704454\pi\)
−0.677905 + 0.735149i \(0.737112\pi\)
\(74\) −13186.5 22839.7i −0.279930 0.484853i
\(75\) −9090.27 + 15744.8i −0.186605 + 0.323209i
\(76\) −76869.6 −1.52658
\(77\) 0 0
\(78\) 45086.2 0.839087
\(79\) −22343.7 + 38700.4i −0.402798 + 0.697666i −0.994062 0.108812i \(-0.965295\pi\)
0.591265 + 0.806477i \(0.298629\pi\)
\(80\) −11964.3 20722.8i −0.209008 0.362012i
\(81\) −3280.50 5681.99i −0.0555556 0.0962250i
\(82\) −1154.14 + 1999.03i −0.0189551 + 0.0328311i
\(83\) −15606.6 −0.248665 −0.124332 0.992241i \(-0.539679\pi\)
−0.124332 + 0.992241i \(0.539679\pi\)
\(84\) 0 0
\(85\) −72137.9 −1.08297
\(86\) −82182.5 + 142344.i −1.19821 + 2.07536i
\(87\) 3390.55 + 5872.61i 0.0480255 + 0.0831827i
\(88\) −63615.0 110184.i −0.875696 1.51675i
\(89\) 6817.66 11808.5i 0.0912347 0.158023i −0.816796 0.576926i \(-0.804252\pi\)
0.908031 + 0.418903i \(0.137585\pi\)
\(90\) −54555.6 −0.709959
\(91\) 0 0
\(92\) 181320. 2.23345
\(93\) 36928.9 63962.7i 0.442750 0.766866i
\(94\) 76740.9 + 132919.i 0.895793 + 1.55156i
\(95\) 49081.6 + 85011.8i 0.557968 + 0.966429i
\(96\) −18584.8 + 32189.8i −0.205816 + 0.356484i
\(97\) 12919.5 0.139417 0.0697086 0.997567i \(-0.477793\pi\)
0.0697086 + 0.997567i \(0.477793\pi\)
\(98\) 0 0
\(99\) −45409.4 −0.465648
\(100\) −56733.0 + 98264.4i −0.567330 + 0.982644i
\(101\) 12571.5 + 21774.4i 0.122626 + 0.212394i 0.920802 0.390029i \(-0.127535\pi\)
−0.798177 + 0.602424i \(0.794202\pi\)
\(102\) −42495.3 73604.0i −0.404427 0.700488i
\(103\) −80376.6 + 139216.i −0.746511 + 1.29300i 0.202974 + 0.979184i \(0.434939\pi\)
−0.949485 + 0.313811i \(0.898394\pi\)
\(104\) 121079. 1.09771
\(105\) 0 0
\(106\) 278331. 2.40601
\(107\) 47187.8 81731.6i 0.398446 0.690129i −0.595088 0.803661i \(-0.702883\pi\)
0.993534 + 0.113531i \(0.0362162\pi\)
\(108\) −20473.8 35461.7i −0.168904 0.292550i
\(109\) 41696.7 + 72220.9i 0.336152 + 0.582233i 0.983705 0.179788i \(-0.0575410\pi\)
−0.647553 + 0.762020i \(0.724208\pi\)
\(110\) −188793. + 326999.i −1.48766 + 2.57670i
\(111\) −25278.0 −0.194731
\(112\) 0 0
\(113\) −179254. −1.32060 −0.660301 0.751001i \(-0.729571\pi\)
−0.660301 + 0.751001i \(0.729571\pi\)
\(114\) −57826.3 + 100158.i −0.416738 + 0.721811i
\(115\) −115774. 200526.i −0.816328 1.41392i
\(116\) 21160.7 + 36651.3i 0.146011 + 0.252898i
\(117\) 21607.1 37424.6i 0.145926 0.252751i
\(118\) −97242.5 −0.642911
\(119\) 0 0
\(120\) −146510. −0.928781
\(121\) −76616.4 + 132703.i −0.475727 + 0.823984i
\(122\) −4479.80 7759.25i −0.0272496 0.0471976i
\(123\) 1106.22 + 1916.04i 0.00659295 + 0.0114193i
\(124\) 230476. 399195.i 1.34608 2.33148i
\(125\) −79256.4 −0.453690
\(126\) 0 0
\(127\) −143674. −0.790440 −0.395220 0.918586i \(-0.629332\pi\)
−0.395220 + 0.918586i \(0.629332\pi\)
\(128\) −166108. + 287707.i −0.896117 + 1.55212i
\(129\) 78770.2 + 136434.i 0.416762 + 0.721853i
\(130\) −179666. 311191.i −0.932412 1.61498i
\(131\) 26144.9 45284.3i 0.133110 0.230553i −0.791764 0.610827i \(-0.790837\pi\)
0.924874 + 0.380274i \(0.124170\pi\)
\(132\) −283403. −1.41570
\(133\) 0 0
\(134\) 186062. 0.895150
\(135\) −26145.2 + 45284.9i −0.123469 + 0.213855i
\(136\) −114122. 197664.i −0.529079 0.916391i
\(137\) −4705.05 8149.39i −0.0214172 0.0370957i 0.855118 0.518433i \(-0.173484\pi\)
−0.876535 + 0.481337i \(0.840151\pi\)
\(138\) 136401. 236253.i 0.609703 1.05604i
\(139\) −183094. −0.803781 −0.401890 0.915688i \(-0.631647\pi\)
−0.401890 + 0.915688i \(0.631647\pi\)
\(140\) 0 0
\(141\) 147109. 0.623150
\(142\) 291674. 505195.i 1.21389 2.10251i
\(143\) −149545. 259020.i −0.611551 1.05924i
\(144\) −13510.7 23401.2i −0.0542964 0.0940441i
\(145\) 27022.3 46804.1i 0.106734 0.184869i
\(146\) 254556. 0.988328
\(147\) 0 0
\(148\) −157762. −0.592034
\(149\) 83500.8 144628.i 0.308123 0.533685i −0.669828 0.742516i \(-0.733632\pi\)
0.977952 + 0.208830i \(0.0669657\pi\)
\(150\) 85356.4 + 147842.i 0.309748 + 0.536499i
\(151\) −188132. 325855.i −0.671461 1.16300i −0.977490 0.210982i \(-0.932334\pi\)
0.306029 0.952022i \(-0.401000\pi\)
\(152\) −155293. + 268976.i −0.545184 + 0.944286i
\(153\) −81461.7 −0.281336
\(154\) 0 0
\(155\) −588639. −1.96797
\(156\) 134851. 233569.i 0.443654 0.768430i
\(157\) 19537.5 + 33840.0i 0.0632587 + 0.109567i 0.895920 0.444215i \(-0.146517\pi\)
−0.832662 + 0.553782i \(0.813184\pi\)
\(158\) 209804. + 363391.i 0.668608 + 1.15806i
\(159\) 133387. 231034.i 0.418429 0.724741i
\(160\) 296237. 0.914829
\(161\) 0 0
\(162\) −61606.9 −0.184434
\(163\) 238959. 413890.i 0.704458 1.22016i −0.262428 0.964951i \(-0.584523\pi\)
0.966887 0.255206i \(-0.0821433\pi\)
\(164\) 6904.01 + 11958.1i 0.0200444 + 0.0347178i
\(165\) 180954. + 313422.i 0.517439 + 0.896230i
\(166\) −73272.1 + 126911.i −0.206381 + 0.357462i
\(167\) −39793.4 −0.110413 −0.0552064 0.998475i \(-0.517582\pi\)
−0.0552064 + 0.998475i \(0.517582\pi\)
\(168\) 0 0
\(169\) −86661.4 −0.233404
\(170\) −338683. + 586616.i −0.898816 + 1.55680i
\(171\) 55425.3 + 95999.5i 0.144950 + 0.251061i
\(172\) 491610. + 851494.i 1.26707 + 2.19463i
\(173\) 24169.1 41862.1i 0.0613968 0.106342i −0.833693 0.552228i \(-0.813778\pi\)
0.895090 + 0.445886i \(0.147111\pi\)
\(174\) 63673.7 0.159436
\(175\) 0 0
\(176\) −187018. −0.455094
\(177\) −46602.5 + 80717.9i −0.111809 + 0.193659i
\(178\) −64016.9 110881.i −0.151441 0.262304i
\(179\) 71455.3 + 123764.i 0.166687 + 0.288711i 0.937253 0.348650i \(-0.113360\pi\)
−0.770566 + 0.637360i \(0.780026\pi\)
\(180\) −163174. + 282626.i −0.375379 + 0.650176i
\(181\) 77245.3 0.175257 0.0876285 0.996153i \(-0.472071\pi\)
0.0876285 + 0.996153i \(0.472071\pi\)
\(182\) 0 0
\(183\) −8587.61 −0.0189559
\(184\) 366305. 634459.i 0.797625 1.38153i
\(185\) 100731. + 174472.i 0.216389 + 0.374797i
\(186\) −346757. 600601.i −0.734925 1.27293i
\(187\) −281903. + 488270.i −0.589516 + 1.02107i
\(188\) 918119. 1.89454
\(189\) 0 0
\(190\) 921739. 1.85235
\(191\) −136027. + 235606.i −0.269800 + 0.467307i −0.968810 0.247805i \(-0.920291\pi\)
0.699010 + 0.715112i \(0.253624\pi\)
\(192\) 222546. + 385462.i 0.435680 + 0.754620i
\(193\) 8016.89 + 13885.7i 0.0154922 + 0.0268333i 0.873668 0.486523i \(-0.161735\pi\)
−0.858175 + 0.513357i \(0.828402\pi\)
\(194\) 60656.2 105060.i 0.115710 0.200415i
\(195\) −344413. −0.648624
\(196\) 0 0
\(197\) 1.03228e6 1.89510 0.947552 0.319603i \(-0.103549\pi\)
0.947552 + 0.319603i \(0.103549\pi\)
\(198\) −213194. + 369263.i −0.386467 + 0.669380i
\(199\) −440868. 763606.i −0.789180 1.36690i −0.926470 0.376369i \(-0.877173\pi\)
0.137290 0.990531i \(-0.456161\pi\)
\(200\) 229226. + 397030.i 0.405217 + 0.701857i
\(201\) 89168.4 154444.i 0.155676 0.269638i
\(202\) 236089. 0.407096
\(203\) 0 0
\(204\) −508408. −0.855337
\(205\) 8816.49 15270.6i 0.0146525 0.0253788i
\(206\) 754725. + 1.30722e6i 1.23914 + 2.14626i
\(207\) −130737. 226443.i −0.212067 0.367311i
\(208\) 88988.4 154132.i 0.142618 0.247022i
\(209\) 767210. 1.21492
\(210\) 0 0
\(211\) −372813. −0.576480 −0.288240 0.957558i \(-0.593070\pi\)
−0.288240 + 0.957558i \(0.593070\pi\)
\(212\) 832480. 1.44190e6i 1.27214 2.20341i
\(213\) −279564. 484219.i −0.422214 0.731296i
\(214\) −443087. 767449.i −0.661385 1.14555i
\(215\) 627791. 1.08737e6i 0.926230 1.60428i
\(216\) −165446. −0.241280
\(217\) 0 0
\(218\) 783054. 1.11596
\(219\) 121993. 211299.i 0.171880 0.297705i
\(220\) 1.12935e6 + 1.95609e6i 1.57315 + 2.72478i
\(221\) −268275. 464666.i −0.369487 0.639971i
\(222\) −118678. + 205557.i −0.161618 + 0.279930i
\(223\) 1.08205e6 1.45708 0.728541 0.685002i \(-0.240199\pi\)
0.728541 + 0.685002i \(0.240199\pi\)
\(224\) 0 0
\(225\) 163625. 0.215473
\(226\) −841584. + 1.45767e6i −1.09604 + 1.89840i
\(227\) 276524. + 478954.i 0.356179 + 0.616921i 0.987319 0.158748i \(-0.0507459\pi\)
−0.631140 + 0.775669i \(0.717413\pi\)
\(228\) 345913. + 599139.i 0.440687 + 0.763292i
\(229\) 261512. 452952.i 0.329536 0.570773i −0.652884 0.757458i \(-0.726441\pi\)
0.982420 + 0.186685i \(0.0597743\pi\)
\(230\) −2.17420e6 −2.71006
\(231\) 0 0
\(232\) 170996. 0.208577
\(233\) 182090. 315390.i 0.219734 0.380590i −0.734993 0.678075i \(-0.762814\pi\)
0.954727 + 0.297485i \(0.0961477\pi\)
\(234\) −202888. 351412.i −0.242224 0.419544i
\(235\) −586223. 1.01537e6i −0.692458 1.19937i
\(236\) −290849. + 503766.i −0.339929 + 0.588774i
\(237\) 402186. 0.465111
\(238\) 0 0
\(239\) 371841. 0.421078 0.210539 0.977585i \(-0.432478\pi\)
0.210539 + 0.977585i \(0.432478\pi\)
\(240\) −107679. + 186505.i −0.120671 + 0.209008i
\(241\) −855737. 1.48218e6i −0.949069 1.64384i −0.747391 0.664384i \(-0.768694\pi\)
−0.201678 0.979452i \(-0.564640\pi\)
\(242\) 719417. + 1.24607e6i 0.789664 + 1.36774i
\(243\) −29524.5 + 51137.9i −0.0320750 + 0.0555556i
\(244\) −53595.8 −0.0576310
\(245\) 0 0
\(246\) 20774.6 0.0218874
\(247\) −365060. + 632303.i −0.380735 + 0.659452i
\(248\) −931221. 1.61292e6i −0.961443 1.66527i
\(249\) 70229.9 + 121642.i 0.0717833 + 0.124332i
\(250\) −372103. + 644502.i −0.376542 + 0.652190i
\(251\) −58134.1 −0.0582434 −0.0291217 0.999576i \(-0.509271\pi\)
−0.0291217 + 0.999576i \(0.509271\pi\)
\(252\) 0 0
\(253\) −1.80969e6 −1.77748
\(254\) −674540. + 1.16834e6i −0.656030 + 1.13628i
\(255\) 324621. + 562260.i 0.312627 + 0.541485i
\(256\) 768453. + 1.33100e6i 0.732853 + 1.26934i
\(257\) −155920. + 270061.i −0.147254 + 0.255052i −0.930212 0.367023i \(-0.880377\pi\)
0.782957 + 0.622075i \(0.213710\pi\)
\(258\) 1.47928e6 1.38357
\(259\) 0 0
\(260\) −2.14950e6 −1.97199
\(261\) 30515.0 52853.5i 0.0277276 0.0480255i
\(262\) −245497. 425214.i −0.220950 0.382696i
\(263\) −431983. 748216.i −0.385103 0.667018i 0.606681 0.794946i \(-0.292501\pi\)
−0.991783 + 0.127928i \(0.959167\pi\)
\(264\) −572535. + 991660.i −0.505583 + 0.875696i
\(265\) −2.12617e6 −1.85987
\(266\) 0 0
\(267\) −122718. −0.105349
\(268\) 556506. 963896.i 0.473296 0.819773i
\(269\) −560346. 970548.i −0.472145 0.817779i 0.527347 0.849650i \(-0.323187\pi\)
−0.999492 + 0.0318707i \(0.989854\pi\)
\(270\) 245500. + 425219.i 0.204948 + 0.354980i
\(271\) 570058. 987369.i 0.471515 0.816688i −0.527954 0.849273i \(-0.677041\pi\)
0.999469 + 0.0325848i \(0.0103739\pi\)
\(272\) −335498. −0.274959
\(273\) 0 0
\(274\) −88359.6 −0.0711013
\(275\) 566233. 980744.i 0.451506 0.782031i
\(276\) −815940. 1.41325e6i −0.644741 1.11672i
\(277\) 994005. + 1.72167e6i 0.778375 + 1.34819i 0.932878 + 0.360193i \(0.117289\pi\)
−0.154502 + 0.987992i \(0.549377\pi\)
\(278\) −859615. + 1.48890e6i −0.667102 + 1.15545i
\(279\) −664720. −0.511244
\(280\) 0 0
\(281\) 532321. 0.402168 0.201084 0.979574i \(-0.435554\pi\)
0.201084 + 0.979574i \(0.435554\pi\)
\(282\) 690668. 1.19627e6i 0.517186 0.895793i
\(283\) 1.31237e6 + 2.27308e6i 0.974067 + 1.68713i 0.682980 + 0.730437i \(0.260684\pi\)
0.291087 + 0.956697i \(0.405983\pi\)
\(284\) −1.74478e6 3.02205e6i −1.28364 2.22334i
\(285\) 441734. 765106.i 0.322143 0.557968i
\(286\) −2.80842e6 −2.03024
\(287\) 0 0
\(288\) 334526. 0.237656
\(289\) 204212. 353705.i 0.143826 0.249113i
\(290\) −253736. 439484.i −0.177169 0.306866i
\(291\) −58137.7 100697.i −0.0402463 0.0697086i
\(292\) 761369. 1.31873e6i 0.522562 0.905104i
\(293\) −609962. −0.415082 −0.207541 0.978226i \(-0.566546\pi\)
−0.207541 + 0.978226i \(0.566546\pi\)
\(294\) 0 0
\(295\) 742834. 0.496978
\(296\) −318712. + 552026.i −0.211431 + 0.366210i
\(297\) 204342. + 353931.i 0.134421 + 0.232824i
\(298\) −784061. 1.35803e6i −0.511457 0.885870i
\(299\) 861104. 1.49148e6i 0.557029 0.964802i
\(300\) 1.02119e6 0.655096
\(301\) 0 0
\(302\) −3.53307e6 −2.22913
\(303\) 113143. 195970.i 0.0707981 0.122626i
\(304\) 228268. + 395372.i 0.141665 + 0.245370i
\(305\) 34221.2 + 59272.8i 0.0210642 + 0.0364843i
\(306\) −382457. + 662436.i −0.233496 + 0.404427i
\(307\) 1.34843e6 0.816551 0.408275 0.912859i \(-0.366130\pi\)
0.408275 + 0.912859i \(0.366130\pi\)
\(308\) 0 0
\(309\) 1.44678e6 0.861997
\(310\) −2.76362e6 + 4.78673e6i −1.63333 + 2.82901i
\(311\) −1.66530e6 2.88439e6i −0.976320 1.69104i −0.675507 0.737353i \(-0.736075\pi\)
−0.300813 0.953683i \(-0.597258\pi\)
\(312\) −544858. 943721.i −0.316881 0.548854i
\(313\) −1.41835e6 + 2.45666e6i −0.818320 + 1.41737i 0.0885991 + 0.996067i \(0.471761\pi\)
−0.906919 + 0.421305i \(0.861572\pi\)
\(314\) 366909. 0.210007
\(315\) 0 0
\(316\) 2.51007e6 1.41406
\(317\) 544195. 942574.i 0.304163 0.526826i −0.672912 0.739723i \(-0.734957\pi\)
0.977075 + 0.212897i \(0.0682899\pi\)
\(318\) −1.25249e6 2.16938e6i −0.694555 1.20300i
\(319\) −211198. 365805.i −0.116202 0.201267i
\(320\) 1.77367e6 3.07209e6i 0.968274 1.67710i
\(321\) −849380. −0.460086
\(322\) 0 0
\(323\) 1.37633e6 0.734033
\(324\) −184264. + 319155.i −0.0975167 + 0.168904i
\(325\) 538860. + 933332.i 0.282988 + 0.490149i
\(326\) −2.24380e6 3.88637e6i −1.16934 2.02535i
\(327\) 375271. 649988.i 0.194078 0.336152i
\(328\) 55790.4 0.0286335
\(329\) 0 0
\(330\) 3.39827e6 1.71780
\(331\) −652773. + 1.13064e6i −0.327485 + 0.567221i −0.982012 0.188817i \(-0.939535\pi\)
0.654527 + 0.756039i \(0.272868\pi\)
\(332\) 438309. + 759174.i 0.218241 + 0.378004i
\(333\) 113751. + 197022.i 0.0562140 + 0.0973654i
\(334\) −186827. + 323594.i −0.0916376 + 0.158721i
\(335\) −1.42133e6 −0.691961
\(336\) 0 0
\(337\) −3.17016e6 −1.52057 −0.760285 0.649590i \(-0.774941\pi\)
−0.760285 + 0.649590i \(0.774941\pi\)
\(338\) −406869. + 704718.i −0.193715 + 0.335524i
\(339\) 806641. + 1.39714e6i 0.381225 + 0.660301i
\(340\) 2.02598e6 + 3.50910e6i 0.950469 + 1.64626i
\(341\) −2.30030e6 + 3.98424e6i −1.07127 + 1.85549i
\(342\) 1.04087e6 0.481207
\(343\) 0 0
\(344\) 3.97263e6 1.81002
\(345\) −1.04196e6 + 1.80473e6i −0.471307 + 0.816328i
\(346\) −226945. 393080.i −0.101913 0.176519i
\(347\) 857958. + 1.48603e6i 0.382510 + 0.662526i 0.991420 0.130713i \(-0.0417265\pi\)
−0.608911 + 0.793239i \(0.708393\pi\)
\(348\) 190446. 329862.i 0.0842992 0.146011i
\(349\) 2.95822e6 1.30007 0.650034 0.759905i \(-0.274755\pi\)
0.650034 + 0.759905i \(0.274755\pi\)
\(350\) 0 0
\(351\) −388928. −0.168501
\(352\) 1.15765e6 2.00510e6i 0.497988 0.862541i
\(353\) 1.88490e6 + 3.26474e6i 0.805103 + 1.39448i 0.916222 + 0.400672i \(0.131223\pi\)
−0.111119 + 0.993807i \(0.535443\pi\)
\(354\) 437591. + 757930.i 0.185592 + 0.321456i
\(355\) −2.22810e6 + 3.85918e6i −0.938347 + 1.62526i
\(356\) −765890. −0.320289
\(357\) 0 0
\(358\) 1.34191e6 0.553371
\(359\) −964935. + 1.67132e6i −0.395150 + 0.684420i −0.993120 0.117099i \(-0.962641\pi\)
0.597970 + 0.801518i \(0.295974\pi\)
\(360\) 659294. + 1.14193e6i 0.268116 + 0.464391i
\(361\) 301617. + 522416.i 0.121811 + 0.210984i
\(362\) 362662. 628148.i 0.145455 0.251936i
\(363\) 1.37909e6 0.549323
\(364\) 0 0
\(365\) −1.94455e6 −0.763988
\(366\) −40318.2 + 69833.2i −0.0157325 + 0.0272496i
\(367\) 1.18371e6 + 2.05025e6i 0.458754 + 0.794586i 0.998895 0.0469885i \(-0.0149624\pi\)
−0.540141 + 0.841575i \(0.681629\pi\)
\(368\) −538438. 932603.i −0.207260 0.358986i
\(369\) 9956.01 17244.3i 0.00380644 0.00659295i
\(370\) 1.89171e6 0.718373
\(371\) 0 0
\(372\) −4.14856e6 −1.55432
\(373\) −1.76914e6 + 3.06425e6i −0.658402 + 1.14039i 0.322627 + 0.946526i \(0.395434\pi\)
−0.981029 + 0.193860i \(0.937899\pi\)
\(374\) 2.64703e6 + 4.58479e6i 0.978543 + 1.69489i
\(375\) 356654. + 617742.i 0.130969 + 0.226845i
\(376\) 1.85480e6 3.21260e6i 0.676592 1.17189i
\(377\) 401975. 0.145662
\(378\) 0 0
\(379\) 1.79847e6 0.643139 0.321569 0.946886i \(-0.395790\pi\)
0.321569 + 0.946886i \(0.395790\pi\)
\(380\) 2.75689e6 4.77508e6i 0.979401 1.69637i
\(381\) 646533. + 1.11983e6i 0.228180 + 0.395220i
\(382\) 1.27728e6 + 2.21231e6i 0.447843 + 0.775687i
\(383\) 1.30407e6 2.25872e6i 0.454261 0.786802i −0.544385 0.838836i \(-0.683237\pi\)
0.998645 + 0.0520333i \(0.0165702\pi\)
\(384\) 2.98994e6 1.03475
\(385\) 0 0
\(386\) 150555. 0.0514313
\(387\) 708932. 1.22791e6i 0.240618 0.416762i
\(388\) −362841. 628460.i −0.122359 0.211933i
\(389\) 1.41498e6 + 2.45081e6i 0.474106 + 0.821175i 0.999560 0.0296466i \(-0.00943818\pi\)
−0.525455 + 0.850821i \(0.676105\pi\)
\(390\) −1.61700e6 + 2.80072e6i −0.538328 + 0.932412i
\(391\) −3.24648e6 −1.07392
\(392\) 0 0
\(393\) −470609. −0.153702
\(394\) 4.84650e6 8.39438e6i 1.57285 2.72426i
\(395\) −1.60269e6 2.77594e6i −0.516841 0.895195i
\(396\) 1.27531e6 + 2.20891e6i 0.408676 + 0.707848i
\(397\) −1.21531e6 + 2.10498e6i −0.387000 + 0.670303i −0.992044 0.125888i \(-0.959822\pi\)
0.605045 + 0.796191i \(0.293155\pi\)
\(398\) −8.27939e6 −2.61993
\(399\) 0 0
\(400\) 673885. 0.210589
\(401\) 1.21592e6 2.10604e6i 0.377611 0.654041i −0.613103 0.790003i \(-0.710079\pi\)
0.990714 + 0.135962i \(0.0434124\pi\)
\(402\) −837279. 1.45021e6i −0.258408 0.447575i
\(403\) −2.18910e6 3.79163e6i −0.671433 1.16296i
\(404\) 706134. 1.22306e6i 0.215245 0.372816i
\(405\) 470614. 0.142570
\(406\) 0 0
\(407\) 1.57457e6 0.471167
\(408\) −1.02709e6 + 1.77898e6i −0.305464 + 0.529079i
\(409\) −2.38733e6 4.13497e6i −0.705674 1.22226i −0.966448 0.256863i \(-0.917311\pi\)
0.260774 0.965400i \(-0.416022\pi\)
\(410\) −82785.6 143389.i −0.0243218 0.0421266i
\(411\) −42345.5 + 73344.5i −0.0123652 + 0.0214172i
\(412\) 9.02944e6 2.62070
\(413\) 0 0
\(414\) −2.45521e6 −0.704024
\(415\) 559725. 969472.i 0.159534 0.276322i
\(416\) 1.10168e6 + 1.90817e6i 0.312121 + 0.540609i
\(417\) 823924. + 1.42708e6i 0.232032 + 0.401890i
\(418\) 3.60200e6 6.23884e6i 1.00833 1.74648i
\(419\) 457181. 0.127219 0.0636097 0.997975i \(-0.479739\pi\)
0.0636097 + 0.997975i \(0.479739\pi\)
\(420\) 0 0
\(421\) −1.82396e6 −0.501545 −0.250773 0.968046i \(-0.580685\pi\)
−0.250773 + 0.968046i \(0.580685\pi\)
\(422\) −1.75033e6 + 3.03166e6i −0.478453 + 0.828704i
\(423\) −661992. 1.14660e6i −0.179888 0.311575i
\(424\) −3.36358e6 5.82589e6i −0.908629 1.57379i
\(425\) 1.01579e6 1.75939e6i 0.272791 0.472488i
\(426\) −5.25014e6 −1.40167
\(427\) 0 0
\(428\) −5.30104e6 −1.39879
\(429\) −1.34591e6 + 2.33118e6i −0.353079 + 0.611551i
\(430\) −5.89487e6 1.02102e7i −1.53746 2.66295i
\(431\) 1.69124e6 + 2.92932e6i 0.438544 + 0.759580i 0.997577 0.0695651i \(-0.0221612\pi\)
−0.559034 + 0.829145i \(0.688828\pi\)
\(432\) −121596. + 210611.i −0.0313480 + 0.0542964i
\(433\) 285266. 0.0731190 0.0365595 0.999331i \(-0.488360\pi\)
0.0365595 + 0.999331i \(0.488360\pi\)
\(434\) 0 0
\(435\) −486402. −0.123246
\(436\) 2.34209e6 4.05662e6i 0.590048 1.02199i
\(437\) 2.20886e6 + 3.82585e6i 0.553304 + 0.958351i
\(438\) −1.14550e6 1.98407e6i −0.285306 0.494164i
\(439\) 2.17610e6 3.76911e6i 0.538911 0.933421i −0.460052 0.887892i \(-0.652169\pi\)
0.998963 0.0455294i \(-0.0144975\pi\)
\(440\) 9.12610e6 2.24726
\(441\) 0 0
\(442\) −5.03813e6 −1.22663
\(443\) 2.55280e6 4.42158e6i 0.618027 1.07045i −0.371819 0.928305i \(-0.621266\pi\)
0.989845 0.142148i \(-0.0454010\pi\)
\(444\) 709927. + 1.22963e6i 0.170906 + 0.296017i
\(445\) 489024. + 847015.i 0.117066 + 0.202764i
\(446\) 5.08014e6 8.79906e6i 1.20931 2.09459i
\(447\) −1.50301e6 −0.355790
\(448\) 0 0
\(449\) 3.04163e6 0.712016 0.356008 0.934483i \(-0.384138\pi\)
0.356008 + 0.934483i \(0.384138\pi\)
\(450\) 768208. 1.33057e6i 0.178833 0.309748i
\(451\) −68906.7 119350.i −0.0159522 0.0276300i
\(452\) 5.03430e6 + 8.71966e6i 1.15903 + 2.00749i
\(453\) −1.69319e6 + 2.93269e6i −0.387668 + 0.671461i
\(454\) 5.19305e6 1.18245
\(455\) 0 0
\(456\) 2.79528e6 0.629524
\(457\) 872162. 1.51063e6i 0.195347 0.338351i −0.751667 0.659542i \(-0.770750\pi\)
0.947014 + 0.321192i \(0.104083\pi\)
\(458\) −2.45556e6 4.25316e6i −0.547000 0.947432i
\(459\) 366578. + 634931.i 0.0812147 + 0.140668i
\(460\) −6.50295e6 + 1.12634e7i −1.43290 + 2.48186i
\(461\) 6.85701e6 1.50273 0.751367 0.659884i \(-0.229395\pi\)
0.751367 + 0.659884i \(0.229395\pi\)
\(462\) 0 0
\(463\) 5.13844e6 1.11398 0.556992 0.830518i \(-0.311955\pi\)
0.556992 + 0.830518i \(0.311955\pi\)
\(464\) 125675. 217676.i 0.0270991 0.0469370i
\(465\) 2.64887e6 + 4.58798e6i 0.568105 + 0.983987i
\(466\) −1.70980e6 2.96147e6i −0.364738 0.631746i
\(467\) −2.29085e6 + 3.96788e6i −0.486077 + 0.841910i −0.999872 0.0160029i \(-0.994906\pi\)
0.513795 + 0.857913i \(0.328239\pi\)
\(468\) −2.42733e6 −0.512287
\(469\) 0 0
\(470\) −1.10091e7 −2.29883
\(471\) 175838. 304560.i 0.0365224 0.0632587i
\(472\) 1.17516e6 + 2.03543e6i 0.242795 + 0.420534i
\(473\) −4.90660e6 8.49848e6i −1.00839 1.74658i
\(474\) 1.88824e6 3.27052e6i 0.386021 0.668608i
\(475\) −2.76450e6 −0.562190
\(476\) 0 0
\(477\) −2.40097e6 −0.483161
\(478\) 1.74577e6 3.02376e6i 0.349476 0.605310i
\(479\) −144261. 249868.i −0.0287284 0.0497590i 0.851304 0.524673i \(-0.175812\pi\)
−0.880032 + 0.474914i \(0.842479\pi\)
\(480\) −1.33307e6 2.30894e6i −0.264088 0.457414i
\(481\) −749223. + 1.29769e6i −0.147655 + 0.255746i
\(482\) −1.60705e7 −3.15074
\(483\) 0 0
\(484\) 8.60702e6 1.67009
\(485\) −463352. + 802549.i −0.0894451 + 0.154923i
\(486\) 277231. + 480178.i 0.0532416 + 0.0922172i
\(487\) 3.90842e6 + 6.76959e6i 0.746757 + 1.29342i 0.949369 + 0.314162i \(0.101723\pi\)
−0.202613 + 0.979259i \(0.564943\pi\)
\(488\) −108275. + 187538.i −0.0205816 + 0.0356484i
\(489\) −4.30127e6 −0.813438
\(490\) 0 0
\(491\) 3.14467e6 0.588669 0.294335 0.955702i \(-0.404902\pi\)
0.294335 + 0.955702i \(0.404902\pi\)
\(492\) 62136.1 107623.i 0.0115726 0.0200444i
\(493\) −378875. 656232.i −0.0702068 0.121602i
\(494\) 3.42787e6 + 5.93724e6i 0.631985 + 1.09463i
\(495\) 1.62859e6 2.82080e6i 0.298743 0.517439i
\(496\) −2.73763e6 −0.499656
\(497\) 0 0
\(498\) 1.31890e6 0.238308
\(499\) −3.36281e6 + 5.82456e6i −0.604577 + 1.04716i 0.387541 + 0.921852i \(0.373324\pi\)
−0.992118 + 0.125305i \(0.960009\pi\)
\(500\) 2.22590e6 + 3.85537e6i 0.398181 + 0.689670i
\(501\) 179070. + 310159.i 0.0318734 + 0.0552064i
\(502\) −272936. + 472738.i −0.0483394 + 0.0837262i
\(503\) 9.45056e6 1.66547 0.832737 0.553669i \(-0.186773\pi\)
0.832737 + 0.553669i \(0.186773\pi\)
\(504\) 0 0
\(505\) −1.80348e6 −0.314690
\(506\) −8.49639e6 + 1.47162e7i −1.47522 + 2.55516i
\(507\) 389976. + 675458.i 0.0673780 + 0.116702i
\(508\) 4.03506e6 + 6.98892e6i 0.693730 + 1.20158i
\(509\) −4.41851e6 + 7.65308e6i −0.755930 + 1.30931i 0.188981 + 0.981981i \(0.439481\pi\)
−0.944911 + 0.327328i \(0.893852\pi\)
\(510\) 6.09629e6 1.03786
\(511\) 0 0
\(512\) 3.80044e6 0.640707
\(513\) 498828. 863995.i 0.0836869 0.144950i
\(514\) 1.46406e6 + 2.53583e6i 0.244429 + 0.423363i
\(515\) −5.76534e6 9.98585e6i −0.957870 1.65908i
\(516\) 4.42449e6 7.66345e6i 0.731542 1.26707i
\(517\) −9.16344e6 −1.50776
\(518\) 0 0
\(519\) −435044. −0.0708949
\(520\) −4.34246e6 + 7.52136e6i −0.704251 + 1.21980i
\(521\) 347492. + 601874.i 0.0560855 + 0.0971430i 0.892705 0.450641i \(-0.148805\pi\)
−0.836619 + 0.547784i \(0.815471\pi\)
\(522\) −286531. 496287.i −0.0460252 0.0797181i
\(523\) 1.79105e6 3.10219e6i 0.286321 0.495923i −0.686607 0.727028i \(-0.740901\pi\)
0.972929 + 0.231105i \(0.0742342\pi\)
\(524\) −2.93710e6 −0.467294
\(525\) 0 0
\(526\) −8.11252e6 −1.27847
\(527\) −4.12660e6 + 7.14748e6i −0.647240 + 1.12105i
\(528\) 841580. + 1.45766e6i 0.131374 + 0.227547i
\(529\) −1.99208e6 3.45038e6i −0.309504 0.536077i
\(530\) −9.98222e6 + 1.72897e7i −1.54361 + 2.67361i
\(531\) 838845. 0.129106
\(532\) 0 0
\(533\) 131151. 0.0199965
\(534\) −576152. + 997925.i −0.0874347 + 0.151441i
\(535\) 3.38473e6 + 5.86253e6i 0.511258 + 0.885525i
\(536\) −2.24852e6 3.89456e6i −0.338053 0.585526i
\(537\) 643098. 1.11388e6i 0.0962368 0.166687i
\(538\) −1.05231e7 −1.56744
\(539\) 0 0
\(540\) 2.93714e6 0.433451
\(541\) 2.58423e6 4.47602e6i 0.379610 0.657504i −0.611395 0.791325i \(-0.709391\pi\)
0.991005 + 0.133821i \(0.0427248\pi\)
\(542\) −5.35277e6 9.27126e6i −0.782673 1.35563i
\(543\) −347604. 602068.i −0.0505924 0.0876285i
\(544\) 2.07675e6 3.59703e6i 0.300875 0.521131i
\(545\) −5.98174e6 −0.862653
\(546\) 0 0
\(547\) 8.47489e6 1.21106 0.605530 0.795822i \(-0.292961\pi\)
0.605530 + 0.795822i \(0.292961\pi\)
\(548\) −264281. + 457748.i −0.0375936 + 0.0651141i
\(549\) 38644.2 + 66933.8i 0.00547210 + 0.00947795i
\(550\) −5.31685e6 9.20906e6i −0.749459 1.29810i
\(551\) −515562. + 892980.i −0.0723439 + 0.125303i
\(552\) −6.59349e6 −0.921018
\(553\) 0 0
\(554\) 1.86671e7 2.58407
\(555\) 906583. 1.57025e6i 0.124932 0.216389i
\(556\) 5.14217e6 + 8.90649e6i 0.705438 + 1.22186i
\(557\) 5.21063e6 + 9.02508e6i 0.711627 + 1.23257i 0.964246 + 0.265009i \(0.0853748\pi\)
−0.252619 + 0.967566i \(0.581292\pi\)
\(558\) −3.12082e6 + 5.40541e6i −0.424309 + 0.734925i
\(559\) 9.33880e6 1.26404
\(560\) 0 0
\(561\) 5.07425e6 0.680714
\(562\) 2.49921e6 4.32876e6i 0.333781 0.578126i
\(563\) −3.62039e6 6.27069e6i −0.481375 0.833767i 0.518396 0.855141i \(-0.326529\pi\)
−0.999772 + 0.0213739i \(0.993196\pi\)
\(564\) −4.13154e6 7.15603e6i −0.546907 0.947271i
\(565\) 6.42885e6 1.11351e7i 0.847251 1.46748i
\(566\) 2.46459e7 3.23373
\(567\) 0 0
\(568\) −1.40993e7 −1.83369
\(569\) −458268. + 793743.i −0.0593388 + 0.102778i −0.894169 0.447730i \(-0.852233\pi\)
0.834830 + 0.550508i \(0.185566\pi\)
\(570\) −4.14782e6 7.18424e6i −0.534728 0.926177i
\(571\) −5.03538e6 8.72154e6i −0.646312 1.11944i −0.983997 0.178186i \(-0.942977\pi\)
0.337685 0.941259i \(-0.390356\pi\)
\(572\) −8.39990e6 + 1.45490e7i −1.07345 + 1.85928i
\(573\) 2.44849e6 0.311538
\(574\) 0 0
\(575\) 6.52091e6 0.822505
\(576\) 2.00292e6 3.46916e6i 0.251540 0.435680i
\(577\) 5.84987e6 + 1.01323e7i 0.731488 + 1.26697i 0.956247 + 0.292560i \(0.0945070\pi\)
−0.224760 + 0.974414i \(0.572160\pi\)
\(578\) −1.91752e6 3.32125e6i −0.238738 0.413506i
\(579\) 72152.0 124971.i 0.00894442 0.0154922i
\(580\) −3.03567e6 −0.374701
\(581\) 0 0
\(582\) −1.09181e6 −0.133610
\(583\) −8.30871e6 + 1.43911e7i −1.01242 + 1.75357i
\(584\) −3.07626e6 5.32823e6i −0.373242 0.646474i
\(585\) 1.54986e6 + 2.68443e6i 0.187242 + 0.324312i
\(586\) −2.86373e6 + 4.96013e6i −0.344499 + 0.596690i
\(587\) 6.92367e6 0.829357 0.414678 0.909968i \(-0.363894\pi\)
0.414678 + 0.909968i \(0.363894\pi\)
\(588\) 0 0
\(589\) 1.12307e7 1.33389
\(590\) 3.48756e6 6.04062e6i 0.412469 0.714417i
\(591\) −4.64527e6 8.04584e6i −0.547069 0.947552i
\(592\) 468481. + 811432.i 0.0549398 + 0.0951586i
\(593\) 7.88850e6 1.36633e7i 0.921208 1.59558i 0.123660 0.992325i \(-0.460537\pi\)
0.797548 0.603255i \(-0.206130\pi\)
\(594\) 3.83750e6 0.446254
\(595\) 0 0
\(596\) −9.38041e6 −1.08170
\(597\) −3.96781e6 + 6.87245e6i −0.455633 + 0.789180i
\(598\) −8.08565e6 1.40048e7i −0.924618 1.60148i
\(599\) −7.13541e6 1.23589e7i −0.812553 1.40738i −0.911072 0.412248i \(-0.864744\pi\)
0.0985183 0.995135i \(-0.468590\pi\)
\(600\) 2.06303e6 3.57327e6i 0.233952 0.405217i
\(601\) −7.63222e6 −0.861916 −0.430958 0.902372i \(-0.641824\pi\)
−0.430958 + 0.902372i \(0.641824\pi\)
\(602\) 0 0
\(603\) −1.60503e6 −0.179759
\(604\) −1.05673e7 + 1.83031e7i −1.17862 + 2.04142i
\(605\) −5.49562e6 9.51869e6i −0.610419 1.05728i
\(606\) −1.06240e6 1.84013e6i −0.117518 0.203548i
\(607\) −1.78017e6 + 3.08335e6i −0.196106 + 0.339665i −0.947262 0.320459i \(-0.896163\pi\)
0.751157 + 0.660124i \(0.229496\pi\)
\(608\) −5.65194e6 −0.620067
\(609\) 0 0
\(610\) 642664. 0.0699294
\(611\) 4.36023e6 7.55214e6i 0.472505 0.818402i
\(612\) 2.28784e6 + 3.96265e6i 0.246914 + 0.427668i
\(613\) 6.86420e6 + 1.18891e7i 0.737800 + 1.27791i 0.953484 + 0.301445i \(0.0974688\pi\)
−0.215683 + 0.976463i \(0.569198\pi\)
\(614\) 6.33080e6 1.09653e7i 0.677700 1.17381i
\(615\) −158697. −0.0169192
\(616\) 0 0
\(617\) −6.51173e6 −0.688626 −0.344313 0.938855i \(-0.611888\pi\)
−0.344313 + 0.938855i \(0.611888\pi\)
\(618\) 6.79253e6 1.17650e7i 0.715419 1.23914i
\(619\) 4.42555e6 + 7.66527e6i 0.464238 + 0.804083i 0.999167 0.0408136i \(-0.0129950\pi\)
−0.534929 + 0.844897i \(0.679662\pi\)
\(620\) 1.65318e7 + 2.86339e7i 1.72719 + 2.99159i
\(621\) −1.17663e6 + 2.03799e6i −0.122437 + 0.212067i
\(622\) −3.12739e7 −3.24121
\(623\) 0 0
\(624\) −1.60179e6 −0.164681
\(625\) 5.99884e6 1.03903e7i 0.614281 1.06397i
\(626\) 1.33181e7 + 2.30677e7i 1.35834 + 2.35271i
\(627\) −3.45244e6 5.97981e6i −0.350718 0.607461i
\(628\) 1.09741e6 1.90078e6i 0.111038 0.192323i
\(629\) 2.82467e6 0.284670
\(630\) 0 0
\(631\) −6.89663e6 −0.689546 −0.344773 0.938686i \(-0.612044\pi\)
−0.344773 + 0.938686i \(0.612044\pi\)
\(632\) 5.07088e6 8.78303e6i 0.504999 0.874685i
\(633\) 1.67766e6 + 2.90579e6i 0.166416 + 0.288240i
\(634\) −5.10992e6 8.85064e6i −0.504883 0.874483i
\(635\) 5.15280e6 8.92492e6i 0.507118 0.878355i
\(636\) −1.49846e7 −1.46894
\(637\) 0 0
\(638\) −3.96623e6 −0.385768
\(639\) −2.51608e6 + 4.35797e6i −0.243765 + 0.422214i
\(640\) −1.19147e7 2.06369e7i −1.14983 1.99157i
\(641\) 8.33473e6 + 1.44362e7i 0.801210 + 1.38774i 0.918820 + 0.394677i \(0.129144\pi\)
−0.117610 + 0.993060i \(0.537523\pi\)
\(642\) −3.98778e6 + 6.90704e6i −0.381851 + 0.661385i
\(643\) 1.28697e7 1.22756 0.613779 0.789478i \(-0.289649\pi\)
0.613779 + 0.789478i \(0.289649\pi\)
\(644\) 0 0
\(645\) −1.13002e7 −1.06952
\(646\) 6.46177e6 1.11921e7i 0.609214 1.05519i
\(647\) −5.73656e6 9.93601e6i −0.538754 0.933150i −0.998971 0.0453435i \(-0.985562\pi\)
0.460217 0.887806i \(-0.347772\pi\)
\(648\) 744507. + 1.28952e6i 0.0696517 + 0.120640i
\(649\) 2.90287e6 5.02792e6i 0.270530 0.468572i
\(650\) 1.01196e7 0.939467
\(651\) 0 0
\(652\) −2.68445e7 −2.47307
\(653\) 6.59005e6 1.14143e7i 0.604791 1.04753i −0.387293 0.921957i \(-0.626590\pi\)
0.992084 0.125573i \(-0.0400768\pi\)
\(654\) −3.52374e6 6.10330e6i −0.322151 0.557982i
\(655\) 1.87535e6 + 3.24820e6i 0.170797 + 0.295829i
\(656\) 41003.6 71020.4i 0.00372017 0.00644352i
\(657\) −2.19588e6 −0.198470
\(658\) 0 0
\(659\) −1.13068e7 −1.01421 −0.507104 0.861885i \(-0.669284\pi\)
−0.507104 + 0.861885i \(0.669284\pi\)
\(660\) 1.01641e7 1.76048e7i 0.908260 1.57315i
\(661\) 1.10160e6 + 1.90802e6i 0.0980661 + 0.169856i 0.910884 0.412662i \(-0.135401\pi\)
−0.812818 + 0.582518i \(0.802068\pi\)
\(662\) 6.12945e6 + 1.06165e7i 0.543596 + 0.941536i
\(663\) −2.41447e6 + 4.18199e6i −0.213324 + 0.369487i
\(664\) 3.54192e6 0.311758
\(665\) 0 0
\(666\) 2.13621e6 0.186620
\(667\) 1.21611e6 2.10636e6i 0.105842 0.183323i
\(668\) 1.11759e6 + 1.93572e6i 0.0969038 + 0.167842i
\(669\) −4.86921e6 8.43372e6i −0.420623 0.728541i
\(670\) −6.67303e6 + 1.15580e7i −0.574296 + 0.994710i
\(671\) 534922. 0.0458653
\(672\) 0 0
\(673\) −1.89787e7 −1.61521 −0.807606 0.589723i \(-0.799237\pi\)
−0.807606 + 0.589723i \(0.799237\pi\)
\(674\) −1.48837e7 + 2.57793e7i −1.26200 + 2.18586i
\(675\) −736312. 1.27533e6i −0.0622017 0.107736i
\(676\) 2.43387e6 + 4.21558e6i 0.204847 + 0.354806i
\(677\) −9.82377e6 + 1.70153e7i −0.823771 + 1.42681i 0.0790842 + 0.996868i \(0.474800\pi\)
−0.902855 + 0.429945i \(0.858533\pi\)
\(678\) 1.51485e7 1.26560
\(679\) 0 0
\(680\) 1.63717e7 1.35775
\(681\) 2.48872e6 4.31059e6i 0.205640 0.356179i
\(682\) 2.15995e7 + 3.74115e7i 1.77821 + 3.07995i
\(683\) −8.13523e6 1.40906e7i −0.667295 1.15579i −0.978658 0.205498i \(-0.934119\pi\)
0.311363 0.950291i \(-0.399215\pi\)
\(684\) 3.11322e6 5.39225e6i 0.254431 0.440687i
\(685\) 674978. 0.0549621
\(686\) 0 0
\(687\) −4.70722e6 −0.380515
\(688\) 2.91972e6 5.05711e6i 0.235164 0.407316i
\(689\) −7.90704e6 1.36954e7i −0.634550 1.09907i
\(690\) 9.78388e6 + 1.69462e7i 0.782327 + 1.35503i
\(691\) 9.72335e6 1.68413e7i 0.774677 1.34178i −0.160299 0.987069i \(-0.551246\pi\)
0.934976 0.354712i \(-0.115421\pi\)
\(692\) −2.71514e6 −0.215539
\(693\) 0 0
\(694\) 1.61122e7 1.26986
\(695\) 6.56659e6 1.13737e7i 0.515677 0.893179i
\(696\) −769484. 1.33278e6i −0.0602111 0.104289i
\(697\) −123614. 214106.i −0.00963800 0.0166935i
\(698\) 1.38886e7 2.40558e7i 1.07900 1.86888i
\(699\) −3.27763e6 −0.253727
\(700\) 0 0
\(701\) 1.49625e7 1.15003 0.575014 0.818144i \(-0.304997\pi\)
0.575014 + 0.818144i \(0.304997\pi\)
\(702\) −1.82599e6 + 3.16271e6i −0.139848 + 0.242224i
\(703\) −1.92187e6 3.32877e6i −0.146668 0.254036i
\(704\) −1.38624e7 2.40104e7i −1.05416 1.82586i
\(705\) −5.27601e6 + 9.13831e6i −0.399791 + 0.692458i
\(706\) 3.53979e7 2.67280
\(707\) 0 0
\(708\) 5.23529e6 0.392516
\(709\) −793193. + 1.37385e6i −0.0592603 + 0.102642i −0.894134 0.447800i \(-0.852208\pi\)
0.834873 + 0.550442i \(0.185541\pi\)
\(710\) 2.09215e7 + 3.62372e7i 1.55757 + 2.69779i
\(711\) −1.80984e6 3.13473e6i −0.134266 0.232555i
\(712\) −1.54726e6 + 2.67994e6i −0.114384 + 0.198118i
\(713\) −2.64910e7 −1.95152
\(714\) 0 0
\(715\) 2.14535e7 1.56940
\(716\) 4.01362e6 6.95179e6i 0.292586 0.506774i
\(717\) −1.67329e6 2.89822e6i −0.121555 0.210539i
\(718\) 9.06061e6 + 1.56934e7i 0.655913 + 1.13607i
\(719\) −9.08376e6 + 1.57335e7i −0.655305 + 1.13502i 0.326512 + 0.945193i \(0.394127\pi\)
−0.981817 + 0.189829i \(0.939207\pi\)
\(720\) 1.93822e6 0.139338
\(721\) 0 0
\(722\) 5.66429e6 0.404392
\(723\) −7.70164e6 + 1.33396e7i −0.547945 + 0.949069i
\(724\) −2.16942e6 3.75754e6i −0.153814 0.266414i
\(725\) 761013. + 1.31811e6i 0.0537709 + 0.0931339i
\(726\) 6.47476e6 1.12146e7i 0.455913 0.789664i
\(727\) −1.26903e7 −0.890506 −0.445253 0.895405i \(-0.646886\pi\)
−0.445253 + 0.895405i \(0.646886\pi\)
\(728\) 0 0
\(729\) 531441. 0.0370370
\(730\) −9.12953e6 + 1.58128e7i −0.634076 + 1.09825i
\(731\) −8.80214e6 1.52458e7i −0.609249 1.05525i
\(732\) 241181. + 417738.i 0.0166366 + 0.0288155i
\(733\) −1.55701e6 + 2.69681e6i −0.107036 + 0.185392i −0.914568 0.404432i \(-0.867469\pi\)
0.807532 + 0.589824i \(0.200803\pi\)
\(734\) 2.22298e7 1.52298
\(735\) 0 0
\(736\) 1.33318e7 0.907182
\(737\) −5.55430e6 + 9.62033e6i −0.376670 + 0.652411i
\(738\) −93485.6 161922.i −0.00631835 0.0109437i
\(739\) −4.54950e6 7.87996e6i −0.306445 0.530778i 0.671137 0.741333i \(-0.265806\pi\)
−0.977582 + 0.210555i \(0.932473\pi\)
\(740\) 5.65804e6 9.80002e6i 0.379828 0.657881i
\(741\) 6.57109e6 0.439634
\(742\) 0 0
\(743\) −8.79218e6 −0.584285 −0.292142 0.956375i \(-0.594368\pi\)
−0.292142 + 0.956375i \(0.594368\pi\)
\(744\) −8.38098e6 + 1.45163e7i −0.555089 + 0.961443i
\(745\) 5.98943e6 + 1.03740e7i 0.395362 + 0.684787i
\(746\) 1.66120e7 + 2.87729e7i 1.09289 + 1.89294i
\(747\) 632069. 1.09478e6i 0.0414441 0.0717833i
\(748\) 3.16687e7 2.06955
\(749\) 0 0
\(750\) 6.69786e6 0.434793
\(751\) 1.40459e7 2.43282e7i 0.908759 1.57402i 0.0929698 0.995669i \(-0.470364\pi\)
0.815790 0.578349i \(-0.196303\pi\)
\(752\) −2.72640e6 4.72226e6i −0.175811 0.304513i
\(753\) 261603. + 453110.i 0.0168134 + 0.0291217i
\(754\) 1.88725e6 3.26881e6i 0.120893 0.209393i
\(755\) 2.69891e7 1.72314
\(756\) 0 0
\(757\) −4.18815e6 −0.265634 −0.132817 0.991141i \(-0.542402\pi\)
−0.132817 + 0.991141i \(0.542402\pi\)
\(758\) 8.44369e6 1.46249e7i 0.533776 0.924527i
\(759\) 8.14362e6 + 1.41052e7i 0.513113 + 0.888738i
\(760\) −1.11390e7 1.92934e7i −0.699541 1.21164i
\(761\) −196591. + 340506.i −0.0123056 + 0.0213139i −0.872113 0.489305i \(-0.837250\pi\)
0.859807 + 0.510619i \(0.170584\pi\)
\(762\) 1.21417e7 0.757518
\(763\) 0 0
\(764\) 1.52812e7 0.947159
\(765\) 2.92159e6 5.06034e6i 0.180495 0.312627i
\(766\) −1.22451e7 2.12091e7i −0.754031 1.30602i
\(767\) 2.76254e6 + 4.78486e6i 0.169559 + 0.293684i
\(768\) 6.91607e6 1.19790e7i 0.423113 0.732853i