Properties

Label 15.8.e.a.2.7
Level $15$
Weight $8$
Character 15.2
Analytic conductor $4.686$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,8,Mod(2,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.2");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 15.e (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.68577538226\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 2.7
Character \(\chi\) \(=\) 15.2
Dual form 15.8.e.a.8.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.72123 - 1.72123i) q^{2} +(36.7583 + 28.9107i) q^{3} +122.075i q^{4} +(-270.133 - 71.7849i) q^{5} +(113.031 - 13.5074i) q^{6} +(884.635 + 884.635i) q^{7} +(430.436 + 430.436i) q^{8} +(515.339 + 2125.42i) q^{9} +O(q^{10})\) \(q+(1.72123 - 1.72123i) q^{2} +(36.7583 + 28.9107i) q^{3} +122.075i q^{4} +(-270.133 - 71.7849i) q^{5} +(113.031 - 13.5074i) q^{6} +(884.635 + 884.635i) q^{7} +(430.436 + 430.436i) q^{8} +(515.339 + 2125.42i) q^{9} +(-588.519 + 341.403i) q^{10} -3163.77i q^{11} +(-3529.27 + 4487.25i) q^{12} +(4367.37 - 4367.37i) q^{13} +3045.32 q^{14} +(-7854.27 - 10448.4i) q^{15} -14143.8 q^{16} +(6264.66 - 6264.66i) q^{17} +(4545.34 + 2771.31i) q^{18} -17030.1i q^{19} +(8763.12 - 32976.4i) q^{20} +(6942.19 + 58093.1i) q^{21} +(-5445.58 - 5445.58i) q^{22} +(-43591.1 - 43591.1i) q^{23} +(3377.85 + 28266.3i) q^{24} +(67818.9 + 38782.9i) q^{25} -15034.5i q^{26} +(-42504.4 + 93025.4i) q^{27} +(-107992. + 107992. i) q^{28} +222298. q^{29} +(-31503.1 - 4465.15i) q^{30} +146894. q^{31} +(-79440.5 + 79440.5i) q^{32} +(91467.0 - 116295. i) q^{33} -21565.8i q^{34} +(-175466. - 302473. i) q^{35} +(-259460. + 62909.8i) q^{36} +(-234786. - 234786. i) q^{37} +(-29312.7 - 29312.7i) q^{38} +(286801. - 34273.0i) q^{39} +(-85376.2 - 147174. i) q^{40} +471176. i q^{41} +(111940. + 88042.3i) q^{42} +(297815. - 297815. i) q^{43} +386217. q^{44} +(13362.6 - 611139. i) q^{45} -150060. q^{46} +(-703959. + 703959. i) q^{47} +(-519902. - 408908. i) q^{48} +741614. i q^{49} +(183486. - 49977.4i) q^{50} +(411394. - 49162.1i) q^{51} +(533146. + 533146. i) q^{52} +(-8798.09 - 8798.09i) q^{53} +(86958.2 + 233278. i) q^{54} +(-227111. + 854640. i) q^{55} +761557. i q^{56} +(492352. - 625996. i) q^{57} +(382626. - 382626. i) q^{58} -37938.4 q^{59} +(1.27549e6 - 958808. i) q^{60} -250175. q^{61} +(252838. - 252838. i) q^{62} +(-1.42433e6 + 2.33610e6i) q^{63} -1.53694e6i q^{64} +(-1.49328e6 + 866261. i) q^{65} +(-42734.3 - 357605. i) q^{66} +(-1.78739e6 - 1.78739e6i) q^{67} +(764757. + 764757. i) q^{68} +(-342082. - 2.86258e6i) q^{69} +(-822641. - 218608. i) q^{70} -4.43696e6i q^{71} +(-693035. + 1.13668e6i) q^{72} +(560727. - 560727. i) q^{73} -808240. q^{74} +(1.37166e6 + 3.38629e6i) q^{75} +2.07894e6 q^{76} +(2.79878e6 - 2.79878e6i) q^{77} +(434658. - 552642. i) q^{78} +4.39243e6i q^{79} +(3.82071e6 + 1.01531e6i) q^{80} +(-4.25182e6 + 2.19062e6i) q^{81} +(811001. + 811001. i) q^{82} +(-263826. - 263826. i) q^{83} +(-7.09170e6 + 847466. i) q^{84} +(-2.14200e6 + 1.24259e6i) q^{85} -1.02522e6i q^{86} +(8.17130e6 + 6.42681e6i) q^{87} +(1.36180e6 - 1.36180e6i) q^{88} -9.13206e6 q^{89} +(-1.02891e6 - 1.07491e6i) q^{90} +7.72706e6 q^{91} +(5.32137e6 - 5.32137e6i) q^{92} +(5.39958e6 + 4.24682e6i) q^{93} +2.42335e6i q^{94} +(-1.22250e6 + 4.60039e6i) q^{95} +(-5.21678e6 + 623411. i) q^{96} +(-8.07294e6 - 8.07294e6i) q^{97} +(1.27649e6 + 1.27649e6i) q^{98} +(6.72434e6 - 1.63041e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 24 q^{3} + 924 q^{6} + 1344 q^{7} - 3180 q^{10} - 2028 q^{12} + 16848 q^{13} + 37560 q^{15} - 68868 q^{16} - 106560 q^{18} + 84144 q^{21} + 166020 q^{22} - 275760 q^{25} - 264168 q^{27} + 602028 q^{28} + 892380 q^{30} - 208992 q^{31} - 877800 q^{33} - 256212 q^{36} - 635616 q^{37} - 1574040 q^{40} + 1219380 q^{42} + 1397328 q^{43} + 570240 q^{45} + 2787168 q^{46} - 476796 q^{48} - 4028016 q^{51} - 6426336 q^{52} + 2324880 q^{55} + 8457264 q^{57} + 986340 q^{58} + 2037900 q^{60} + 12157968 q^{61} - 1973952 q^{63} - 25406040 q^{66} - 16720176 q^{67} - 13165860 q^{70} + 36245880 q^{72} + 4059528 q^{73} + 11226120 q^{75} + 37968816 q^{76} - 26156280 q^{78} - 31289976 q^{81} - 53633520 q^{82} - 34181760 q^{85} + 44480160 q^{87} + 74717340 q^{88} + 71623080 q^{90} + 67599648 q^{91} - 58742592 q^{93} - 103105308 q^{96} - 75148056 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

Coefficient data

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



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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.72123 1.72123i 0.152136 0.152136i −0.626935 0.779072i \(-0.715691\pi\)
0.779072 + 0.626935i \(0.215691\pi\)
\(3\) 36.7583 + 28.9107i 0.786014 + 0.618208i
\(4\) 122.075i 0.953709i
\(5\) −270.133 71.7849i −0.966458 0.256825i
\(6\) 113.031 13.5074i 0.213634 0.0255294i
\(7\) 884.635 + 884.635i 0.974812 + 0.974812i 0.999690 0.0248787i \(-0.00791994\pi\)
−0.0248787 + 0.999690i \(0.507920\pi\)
\(8\) 430.436 + 430.436i 0.297230 + 0.297230i
\(9\) 515.339 + 2125.42i 0.235637 + 0.971841i
\(10\) −588.519 + 341.403i −0.186106 + 0.107961i
\(11\) 3163.77i 0.716689i −0.933589 0.358345i \(-0.883341\pi\)
0.933589 0.358345i \(-0.116659\pi\)
\(12\) −3529.27 + 4487.25i −0.589591 + 0.749629i
\(13\) 4367.37 4367.37i 0.551339 0.551339i −0.375488 0.926827i \(-0.622525\pi\)
0.926827 + 0.375488i \(0.122525\pi\)
\(14\) 3045.32 0.296609
\(15\) −7854.27 10448.4i −0.600878 0.799341i
\(16\) −14143.8 −0.863270
\(17\) 6264.66 6264.66i 0.309262 0.309262i −0.535361 0.844623i \(-0.679825\pi\)
0.844623 + 0.535361i \(0.179825\pi\)
\(18\) 4545.34 + 2771.31i 0.183702 + 0.112003i
\(19\) 17030.1i 0.569612i −0.958585 0.284806i \(-0.908071\pi\)
0.958585 0.284806i \(-0.0919292\pi\)
\(20\) 8763.12 32976.4i 0.244937 0.921720i
\(21\) 6942.19 + 58093.1i 0.163579 + 1.36885i
\(22\) −5445.58 5445.58i −0.109035 0.109035i
\(23\) −43591.1 43591.1i −0.747051 0.747051i 0.226873 0.973924i \(-0.427150\pi\)
−0.973924 + 0.226873i \(0.927150\pi\)
\(24\) 3377.85 + 28266.3i 0.0498771 + 0.417378i
\(25\) 67818.9 + 38782.9i 0.868082 + 0.496422i
\(26\) 15034.5i 0.167757i
\(27\) −42504.4 + 93025.4i −0.415586 + 0.909554i
\(28\) −107992. + 107992.i −0.929687 + 0.929687i
\(29\) 222298. 1.69256 0.846278 0.532741i \(-0.178838\pi\)
0.846278 + 0.532741i \(0.178838\pi\)
\(30\) −31503.1 4465.15i −0.213024 0.0301934i
\(31\) 146894. 0.885603 0.442801 0.896620i \(-0.353985\pi\)
0.442801 + 0.896620i \(0.353985\pi\)
\(32\) −79440.5 + 79440.5i −0.428565 + 0.428565i
\(33\) 91467.0 116295.i 0.443063 0.563328i
\(34\) 21565.8i 0.0941001i
\(35\) −175466. 302473.i −0.691758 1.19247i
\(36\) −259460. + 62909.8i −0.926854 + 0.224729i
\(37\) −234786. 234786.i −0.762019 0.762019i 0.214668 0.976687i \(-0.431133\pi\)
−0.976687 + 0.214668i \(0.931133\pi\)
\(38\) −29312.7 29312.7i −0.0866588 0.0866588i
\(39\) 286801. 34273.0i 0.774202 0.0925181i
\(40\) −85376.2 147174.i −0.210924 0.363597i
\(41\) 471176.i 1.06768i 0.845587 + 0.533838i \(0.179251\pi\)
−0.845587 + 0.533838i \(0.820749\pi\)
\(42\) 111940. + 88042.3i 0.233139 + 0.183366i
\(43\) 297815. 297815.i 0.571225 0.571225i −0.361245 0.932471i \(-0.617648\pi\)
0.932471 + 0.361245i \(0.117648\pi\)
\(44\) 386217. 0.683513
\(45\) 13362.6 611139.i 0.0218599 0.999761i
\(46\) −150060. −0.227307
\(47\) −703959. + 703959.i −0.989019 + 0.989019i −0.999940 0.0109211i \(-0.996524\pi\)
0.0109211 + 0.999940i \(0.496524\pi\)
\(48\) −519902. 408908.i −0.678542 0.533680i
\(49\) 741614.i 0.900516i
\(50\) 183486. 49977.4i 0.207591 0.0565430i
\(51\) 411394. 49162.1i 0.434273 0.0518961i
\(52\) 533146. + 533146.i 0.525817 + 0.525817i
\(53\) −8798.09 8798.09i −0.00811751 0.00811751i 0.703036 0.711154i \(-0.251827\pi\)
−0.711154 + 0.703036i \(0.751827\pi\)
\(54\) 86958.2 + 233278.i 0.0751506 + 0.201602i
\(55\) −227111. + 854640.i −0.184064 + 0.692650i
\(56\) 761557.i 0.579487i
\(57\) 492352. 625996.i 0.352139 0.447723i
\(58\) 382626. 382626.i 0.257500 0.257500i
\(59\) −37938.4 −0.0240490 −0.0120245 0.999928i \(-0.503828\pi\)
−0.0120245 + 0.999928i \(0.503828\pi\)
\(60\) 1.27549e6 958808.i 0.762338 0.573063i
\(61\) −250175. −0.141120 −0.0705602 0.997508i \(-0.522479\pi\)
−0.0705602 + 0.997508i \(0.522479\pi\)
\(62\) 252838. 252838.i 0.134732 0.134732i
\(63\) −1.42433e6 + 2.33610e6i −0.717660 + 1.17706i
\(64\) 1.53694e6i 0.732869i
\(65\) −1.49328e6 + 866261.i −0.674443 + 0.391248i
\(66\) −42734.3 357605.i −0.0182967 0.153109i
\(67\) −1.78739e6 1.78739e6i −0.726034 0.726034i 0.243794 0.969827i \(-0.421608\pi\)
−0.969827 + 0.243794i \(0.921608\pi\)
\(68\) 764757. + 764757.i 0.294946 + 0.294946i
\(69\) −342082. 2.86258e6i −0.125360 1.04903i
\(70\) −822641. 218608.i −0.286660 0.0761767i
\(71\) 4.43696e6i 1.47123i −0.677399 0.735616i \(-0.736893\pi\)
0.677399 0.735616i \(-0.263107\pi\)
\(72\) −693035. + 1.13668e6i −0.218822 + 0.358899i
\(73\) 560727. 560727.i 0.168703 0.168703i −0.617706 0.786409i \(-0.711938\pi\)
0.786409 + 0.617706i \(0.211938\pi\)
\(74\) −808240. −0.231862
\(75\) 1.37166e6 + 3.38629e6i 0.375433 + 0.926850i
\(76\) 2.07894e6 0.543244
\(77\) 2.79878e6 2.79878e6i 0.698637 0.698637i
\(78\) 434658. 552642.i 0.103709 0.131860i
\(79\) 4.39243e6i 1.00233i 0.865352 + 0.501165i \(0.167095\pi\)
−0.865352 + 0.501165i \(0.832905\pi\)
\(80\) 3.82071e6 + 1.01531e6i 0.834314 + 0.221710i
\(81\) −4.25182e6 + 2.19062e6i −0.888950 + 0.458004i
\(82\) 811001. + 811001.i 0.162432 + 0.162432i
\(83\) −263826. 263826.i −0.0506459 0.0506459i 0.681330 0.731976i \(-0.261402\pi\)
−0.731976 + 0.681330i \(0.761402\pi\)
\(84\) −7.09170e6 + 847466.i −1.30549 + 0.156007i
\(85\) −2.14200e6 + 1.24259e6i −0.378315 + 0.219462i
\(86\) 1.02522e6i 0.173808i
\(87\) 8.17130e6 + 6.42681e6i 1.33037 + 1.04635i
\(88\) 1.36180e6 1.36180e6i 0.213022 0.213022i
\(89\) −9.13206e6 −1.37310 −0.686552 0.727080i \(-0.740877\pi\)
−0.686552 + 0.727080i \(0.740877\pi\)
\(90\) −1.02891e6 1.07491e6i −0.148774 0.155426i
\(91\) 7.72706e6 1.07490
\(92\) 5.32137e6 5.32137e6i 0.712469 0.712469i
\(93\) 5.39958e6 + 4.24682e6i 0.696096 + 0.547487i
\(94\) 2.42335e6i 0.300932i
\(95\) −1.22250e6 + 4.60039e6i −0.146291 + 0.550506i
\(96\) −5.21678e6 + 623411.i −0.601801 + 0.0719159i
\(97\) −8.07294e6 8.07294e6i −0.898112 0.898112i 0.0971567 0.995269i \(-0.469025\pi\)
−0.995269 + 0.0971567i \(0.969025\pi\)
\(98\) 1.27649e6 + 1.27649e6i 0.137001 + 0.137001i
\(99\) 6.72434e6 1.63041e6i 0.696508 0.168879i
\(100\) −4.73442e6 + 8.27897e6i −0.473442 + 0.827897i
\(101\) 8.21700e6i 0.793576i −0.917910 0.396788i \(-0.870125\pi\)
0.917910 0.396788i \(-0.129875\pi\)
\(102\) 623484. 792722.i 0.0581734 0.0739640i
\(103\) 1.57945e6 1.57945e6i 0.142421 0.142421i −0.632301 0.774723i \(-0.717889\pi\)
0.774723 + 0.632301i \(0.217889\pi\)
\(104\) 3.75975e6 0.327749
\(105\) 2.29489e6 1.61912e7i 0.193463 1.36495i
\(106\) −30287.0 −0.00246994
\(107\) −1.00980e7 + 1.00980e7i −0.796880 + 0.796880i −0.982602 0.185722i \(-0.940537\pi\)
0.185722 + 0.982602i \(0.440537\pi\)
\(108\) −1.13561e7 5.18871e6i −0.867450 0.396348i
\(109\) 1.32852e7i 0.982600i −0.870990 0.491300i \(-0.836522\pi\)
0.870990 0.491300i \(-0.163478\pi\)
\(110\) 1.08012e6 + 1.86194e6i 0.0773745 + 0.133380i
\(111\) −1.84249e6 1.54181e7i −0.127872 1.07004i
\(112\) −1.25121e7 1.25121e7i −0.841526 0.841526i
\(113\) 4.24721e6 + 4.24721e6i 0.276904 + 0.276904i 0.831872 0.554968i \(-0.187269\pi\)
−0.554968 + 0.831872i \(0.687269\pi\)
\(114\) −230032. 1.92493e6i −0.0145419 0.121688i
\(115\) 8.64622e6 + 1.49046e7i 0.530132 + 0.913855i
\(116\) 2.71370e7i 1.61421i
\(117\) 1.15332e7 + 7.03181e6i 0.665730 + 0.405898i
\(118\) −65300.7 + 65300.7i −0.00365873 + 0.00365873i
\(119\) 1.10839e7 0.602944
\(120\) 1.11662e6 7.87814e6i 0.0589890 0.416188i
\(121\) 9.47771e6 0.486356
\(122\) −430609. + 430609.i −0.0214696 + 0.0214696i
\(123\) −1.36220e7 + 1.73196e7i −0.660046 + 0.839208i
\(124\) 1.79321e7i 0.844607i
\(125\) −1.55361e7 1.53449e7i −0.711471 0.702716i
\(126\) 1.56937e6 + 6.47256e6i 0.0698921 + 0.288257i
\(127\) 4.70330e6 + 4.70330e6i 0.203746 + 0.203746i 0.801603 0.597857i \(-0.203981\pi\)
−0.597857 + 0.801603i \(0.703981\pi\)
\(128\) −1.28138e7 1.28138e7i −0.540061 0.540061i
\(129\) 1.95572e7 2.33711e6i 0.802128 0.0958552i
\(130\) −1.07925e6 + 4.06131e6i −0.0430844 + 0.162131i
\(131\) 1.91876e7i 0.745711i 0.927890 + 0.372855i \(0.121621\pi\)
−0.927890 + 0.372855i \(0.878379\pi\)
\(132\) 1.41967e7 + 1.11658e7i 0.537251 + 0.422553i
\(133\) 1.50654e7 1.50654e7i 0.555265 0.555265i
\(134\) −6.15300e6 −0.220912
\(135\) 1.81597e7 2.20781e7i 0.635243 0.772313i
\(136\) 5.39307e6 0.183844
\(137\) −2.16166e7 + 2.16166e7i −0.718232 + 0.718232i −0.968243 0.250011i \(-0.919566\pi\)
0.250011 + 0.968243i \(0.419566\pi\)
\(138\) −5.51596e6 4.33836e6i −0.178667 0.140523i
\(139\) 3.27651e7i 1.03481i 0.855742 + 0.517403i \(0.173101\pi\)
−0.855742 + 0.517403i \(0.826899\pi\)
\(140\) 3.69243e7 2.14199e7i 1.13727 0.659736i
\(141\) −4.62283e7 + 5.52433e6i −1.38880 + 0.165964i
\(142\) −7.63702e6 7.63702e6i −0.223828 0.223828i
\(143\) −1.38174e7 1.38174e7i −0.395139 0.395139i
\(144\) −7.28885e6 3.00615e7i −0.203419 0.838961i
\(145\) −6.00502e7 1.59577e7i −1.63578 0.434691i
\(146\) 1.93028e6i 0.0513316i
\(147\) −2.14406e7 + 2.72604e7i −0.556706 + 0.707819i
\(148\) 2.86614e7 2.86614e7i 0.726744 0.726744i
\(149\) 7.48929e7 1.85476 0.927382 0.374116i \(-0.122054\pi\)
0.927382 + 0.374116i \(0.122054\pi\)
\(150\) 8.18951e6 + 3.46763e6i 0.198125 + 0.0838907i
\(151\) 1.02410e7 0.242060 0.121030 0.992649i \(-0.461380\pi\)
0.121030 + 0.992649i \(0.461380\pi\)
\(152\) 7.33036e6 7.33036e6i 0.169306 0.169306i
\(153\) 1.65434e7 + 1.00866e7i 0.373427 + 0.227680i
\(154\) 9.63469e6i 0.212576i
\(155\) −3.96810e7 1.05448e7i −0.855898 0.227445i
\(156\) 4.18387e6 + 3.50112e7i 0.0882353 + 0.738364i
\(157\) −3.44091e7 3.44091e7i −0.709618 0.709618i 0.256837 0.966455i \(-0.417320\pi\)
−0.966455 + 0.256837i \(0.917320\pi\)
\(158\) 7.56038e6 + 7.56038e6i 0.152491 + 0.152491i
\(159\) −69043.2 577762.i −0.00136217 0.0113988i
\(160\) 2.71621e7 1.57569e7i 0.524257 0.304124i
\(161\) 7.71244e7i 1.45647i
\(162\) −3.54780e6 + 1.10889e7i −0.0655626 + 0.204921i
\(163\) −2.24266e7 + 2.24266e7i −0.405608 + 0.405608i −0.880204 0.474596i \(-0.842594\pi\)
0.474596 + 0.880204i \(0.342594\pi\)
\(164\) −5.75186e7 −1.01825
\(165\) −3.30565e7 + 2.48491e7i −0.572879 + 0.430643i
\(166\) −908209. −0.0154102
\(167\) 4.14619e7 4.14619e7i 0.688877 0.688877i −0.273107 0.961984i \(-0.588051\pi\)
0.961984 + 0.273107i \(0.0880512\pi\)
\(168\) −2.20172e7 + 2.79935e7i −0.358244 + 0.455486i
\(169\) 2.46006e7i 0.392051i
\(170\) −1.54810e6 + 5.82565e6i −0.0241673 + 0.0909437i
\(171\) 3.61960e7 8.77626e6i 0.553572 0.134222i
\(172\) 3.63557e7 + 3.63557e7i 0.544783 + 0.544783i
\(173\) 3.08157e7 + 3.08157e7i 0.452492 + 0.452492i 0.896181 0.443689i \(-0.146331\pi\)
−0.443689 + 0.896181i \(0.646331\pi\)
\(174\) 2.51267e7 3.00267e6i 0.361587 0.0432100i
\(175\) 2.56862e7 + 9.43037e7i 0.362298 + 1.33013i
\(176\) 4.47478e7i 0.618696i
\(177\) −1.39455e6 1.09683e6i −0.0189029 0.0148673i
\(178\) −1.57184e7 + 1.57184e7i −0.208899 + 0.208899i
\(179\) −4.69726e7 −0.612152 −0.306076 0.952007i \(-0.599016\pi\)
−0.306076 + 0.952007i \(0.599016\pi\)
\(180\) 7.46046e7 + 1.63124e6i 0.953481 + 0.0208480i
\(181\) 4.21050e7 0.527787 0.263894 0.964552i \(-0.414993\pi\)
0.263894 + 0.964552i \(0.414993\pi\)
\(182\) 1.33000e7 1.33000e7i 0.163532 0.163532i
\(183\) −9.19601e6 7.23275e6i −0.110923 0.0872418i
\(184\) 3.75263e7i 0.444093i
\(185\) 4.65694e7 + 8.02775e7i 0.540753 + 0.932165i
\(186\) 1.66036e7 1.98416e6i 0.189194 0.0226089i
\(187\) −1.98200e7 1.98200e7i −0.221645 0.221645i
\(188\) −8.59356e7 8.59356e7i −0.943237 0.943237i
\(189\) −1.19894e8 + 4.46926e7i −1.29176 + 0.481526i
\(190\) 5.81412e6 + 1.00225e7i 0.0614959 + 0.106008i
\(191\) 2.73525e7i 0.284040i −0.989864 0.142020i \(-0.954640\pi\)
0.989864 0.142020i \(-0.0453598\pi\)
\(192\) 4.44340e7 5.64951e7i 0.453066 0.576046i
\(193\) 2.58245e7 2.58245e7i 0.258572 0.258572i −0.565901 0.824473i \(-0.691472\pi\)
0.824473 + 0.565901i \(0.191472\pi\)
\(194\) −2.77907e7 −0.273271
\(195\) −7.99347e7 1.13297e7i −0.771995 0.109420i
\(196\) −9.05323e7 −0.858830
\(197\) −1.96188e7 + 1.96188e7i −0.182827 + 0.182827i −0.792587 0.609759i \(-0.791266\pi\)
0.609759 + 0.792587i \(0.291266\pi\)
\(198\) 8.76780e6 1.43804e7i 0.0802717 0.131657i
\(199\) 1.42723e8i 1.28383i −0.766776 0.641915i \(-0.778140\pi\)
0.766776 0.641915i \(-0.221860\pi\)
\(200\) 1.24981e7 + 4.58852e7i 0.110469 + 0.405572i
\(201\) −1.40266e7 1.17376e8i −0.121833 1.01951i
\(202\) −1.41433e7 1.41433e7i −0.120732 0.120732i
\(203\) 1.96653e8 + 1.96653e8i 1.64992 + 1.64992i
\(204\) 6.00145e6 + 5.02208e7i 0.0494938 + 0.414170i
\(205\) 3.38233e7 1.27280e8i 0.274206 1.03186i
\(206\) 5.43718e6i 0.0433350i
\(207\) 7.01850e7 1.15113e8i 0.549982 0.902048i
\(208\) −6.17713e7 + 6.17713e7i −0.475954 + 0.475954i
\(209\) −5.38793e7 −0.408235
\(210\) −2.39187e7 3.18188e7i −0.178226 0.237092i
\(211\) 2.35457e6 0.0172553 0.00862765 0.999963i \(-0.497254\pi\)
0.00862765 + 0.999963i \(0.497254\pi\)
\(212\) 1.07402e6 1.07402e6i 0.00774174 0.00774174i
\(213\) 1.28276e8 1.63095e8i 0.909527 1.15641i
\(214\) 3.47620e7i 0.242469i
\(215\) −1.01828e8 + 5.90712e7i −0.698770 + 0.405360i
\(216\) −5.83369e7 + 2.17460e7i −0.393872 + 0.146822i
\(217\) 1.29948e8 + 1.29948e8i 0.863296 + 0.863296i
\(218\) −2.28669e7 2.28669e7i −0.149489 0.149489i
\(219\) 3.68224e7 4.40032e6i 0.236896 0.0283093i
\(220\) −1.04330e8 2.77245e7i −0.660587 0.175543i
\(221\) 5.47202e7i 0.341016i
\(222\) −2.97095e7 2.33668e7i −0.182247 0.143339i
\(223\) −7.49416e7 + 7.49416e7i −0.452539 + 0.452539i −0.896196 0.443658i \(-0.853681\pi\)
0.443658 + 0.896196i \(0.353681\pi\)
\(224\) −1.40552e8 −0.835541
\(225\) −4.74802e7 + 1.64130e8i −0.277891 + 0.960613i
\(226\) 1.46208e7 0.0842544
\(227\) −5.81623e7 + 5.81623e7i −0.330028 + 0.330028i −0.852597 0.522569i \(-0.824974\pi\)
0.522569 + 0.852597i \(0.324974\pi\)
\(228\) 7.64183e7 + 6.01038e7i 0.426998 + 0.335838i
\(229\) 1.72092e8i 0.946972i 0.880801 + 0.473486i \(0.157005\pi\)
−0.880801 + 0.473486i \(0.842995\pi\)
\(230\) 4.05363e7 + 1.07721e7i 0.219683 + 0.0583783i
\(231\) 1.83793e8 2.19635e7i 0.981042 0.117236i
\(232\) 9.56851e7 + 9.56851e7i 0.503079 + 0.503079i
\(233\) −9.91208e7 9.91208e7i −0.513356 0.513356i 0.402197 0.915553i \(-0.368247\pi\)
−0.915553 + 0.402197i \(0.868247\pi\)
\(234\) 3.19545e7 7.74785e6i 0.163034 0.0395299i
\(235\) 2.40696e8 1.39629e8i 1.20985 0.701840i
\(236\) 4.63132e6i 0.0229358i
\(237\) −1.26988e8 + 1.61458e8i −0.619648 + 0.787845i
\(238\) 1.90779e7 1.90779e7i 0.0917299 0.0917299i
\(239\) 3.53439e8 1.67464 0.837320 0.546713i \(-0.184121\pi\)
0.837320 + 0.546713i \(0.184121\pi\)
\(240\) 1.11089e8 + 1.47781e8i 0.518720 + 0.690047i
\(241\) −1.60031e8 −0.736453 −0.368227 0.929736i \(-0.620035\pi\)
−0.368227 + 0.929736i \(0.620035\pi\)
\(242\) 1.63133e7 1.63133e7i 0.0739925 0.0739925i
\(243\) −2.19622e8 4.23999e7i −0.981869 0.189559i
\(244\) 3.05401e7i 0.134588i
\(245\) 5.32366e7 2.00334e8i 0.231275 0.870311i
\(246\) 6.36434e6 + 5.32576e7i 0.0272572 + 0.228091i
\(247\) −7.43767e7 7.43767e7i −0.314049 0.314049i
\(248\) 6.32285e7 + 6.32285e7i 0.263228 + 0.263228i
\(249\) −2.07038e6 1.73252e7i −0.00849869 0.0711181i
\(250\) −5.31533e7 + 329046.i −0.215149 + 0.00133189i
\(251\) 2.02842e8i 0.809655i 0.914393 + 0.404828i \(0.132669\pi\)
−0.914393 + 0.404828i \(0.867331\pi\)
\(252\) −2.85179e8 1.73875e8i −1.12258 0.684439i
\(253\) −1.37912e8 + 1.37912e8i −0.535404 + 0.535404i
\(254\) 1.61909e7 0.0619944
\(255\) −1.14660e8 1.62516e7i −0.433034 0.0613768i
\(256\) 1.52617e8 0.568543
\(257\) 1.54186e8 1.54186e8i 0.566602 0.566602i −0.364573 0.931175i \(-0.618785\pi\)
0.931175 + 0.364573i \(0.118785\pi\)
\(258\) 2.96398e7 3.76852e7i 0.107450 0.136616i
\(259\) 4.15399e8i 1.48565i
\(260\) −1.05749e8 1.82292e8i −0.373137 0.643223i
\(261\) 1.14559e8 + 4.72477e8i 0.398829 + 1.64490i
\(262\) 3.30262e7 + 3.30262e7i 0.113450 + 0.113450i
\(263\) −3.22856e8 3.22856e8i −1.09437 1.09437i −0.995056 0.0993118i \(-0.968336\pi\)
−0.0993118 0.995056i \(-0.531664\pi\)
\(264\) 8.94281e7 1.06868e7i 0.299130 0.0357464i
\(265\) 1.74509e6 + 3.00823e6i 0.00576045 + 0.00993002i
\(266\) 5.18620e7i 0.168952i
\(267\) −3.35678e8 2.64014e8i −1.07928 0.848864i
\(268\) 2.18195e8 2.18195e8i 0.692425 0.692425i
\(269\) 6.12343e7 0.191806 0.0959030 0.995391i \(-0.469426\pi\)
0.0959030 + 0.995391i \(0.469426\pi\)
\(270\) −6.74448e6 6.92583e7i −0.0208533 0.214141i
\(271\) −6.33885e8 −1.93472 −0.967360 0.253407i \(-0.918449\pi\)
−0.967360 + 0.253407i \(0.918449\pi\)
\(272\) −8.86062e7 + 8.86062e7i −0.266977 + 0.266977i
\(273\) 2.84033e8 + 2.23395e8i 0.844889 + 0.664514i
\(274\) 7.44141e7i 0.218539i
\(275\) 1.22700e8 2.14564e8i 0.355780 0.622145i
\(276\) 3.49449e8 4.17596e7i 1.00047 0.119557i
\(277\) 3.46271e8 + 3.46271e8i 0.978897 + 0.978897i 0.999782 0.0208845i \(-0.00664823\pi\)
−0.0208845 + 0.999782i \(0.506648\pi\)
\(278\) 5.63961e7 + 5.63961e7i 0.157432 + 0.157432i
\(279\) 7.57003e7 + 3.12211e8i 0.208681 + 0.860665i
\(280\) 5.46682e7 2.05722e8i 0.148827 0.560050i
\(281\) 2.07883e7i 0.0558917i 0.999609 + 0.0279458i \(0.00889659\pi\)
−0.999609 + 0.0279458i \(0.991103\pi\)
\(282\) −7.00608e7 + 8.90780e7i −0.186039 + 0.236537i
\(283\) −4.09164e7 + 4.09164e7i −0.107311 + 0.107311i −0.758724 0.651413i \(-0.774177\pi\)
0.651413 + 0.758724i \(0.274177\pi\)
\(284\) 5.41640e8 1.40313
\(285\) −1.77938e8 + 1.33759e8i −0.455314 + 0.342268i
\(286\) −4.75657e7 −0.120230
\(287\) −4.16818e8 + 4.16818e8i −1.04078 + 1.04078i
\(288\) −2.09783e8 1.27905e8i −0.517483 0.315511i
\(289\) 3.31847e8i 0.808714i
\(290\) −1.30827e8 + 7.58932e7i −0.314995 + 0.182730i
\(291\) −6.33526e7 5.30142e8i −0.150709 1.26115i
\(292\) 6.84506e7 + 6.84506e7i 0.160893 + 0.160893i
\(293\) −309871. 309871.i −0.000719688 0.000719688i 0.706747 0.707467i \(-0.250162\pi\)
−0.707467 + 0.706747i \(0.750162\pi\)
\(294\) 1.00173e7 + 8.38256e7i 0.0229897 + 0.192380i
\(295\) 1.02484e7 + 2.72340e6i 0.0232423 + 0.00617639i
\(296\) 2.02120e8i 0.452991i
\(297\) 2.94311e8 + 1.34474e8i 0.651868 + 0.297846i
\(298\) 1.28908e8 1.28908e8i 0.282177 0.282177i
\(299\) −3.80757e8 −0.823756
\(300\) −4.13380e8 + 1.67445e8i −0.883945 + 0.358053i
\(301\) 5.26916e8 1.11367
\(302\) 1.76271e7 1.76271e7i 0.0368262 0.0368262i
\(303\) 2.37560e8 3.02043e8i 0.490595 0.623762i
\(304\) 2.40870e8i 0.491729i
\(305\) 6.75807e7 + 1.79588e7i 0.136387 + 0.0362433i
\(306\) 4.58364e7 1.11137e7i 0.0914503 0.0221735i
\(307\) −5.93484e7 5.93484e7i −0.117064 0.117064i 0.646148 0.763212i \(-0.276379\pi\)
−0.763212 + 0.646148i \(0.776379\pi\)
\(308\) 3.41661e8 + 3.41661e8i 0.666297 + 0.666297i
\(309\) 1.03721e8 1.23948e7i 0.199991 0.0238992i
\(310\) −8.64500e7 + 5.01501e7i −0.164816 + 0.0956105i
\(311\) 7.30350e8i 1.37680i 0.725333 + 0.688398i \(0.241686\pi\)
−0.725333 + 0.688398i \(0.758314\pi\)
\(312\) 1.38202e8 + 1.08697e8i 0.257616 + 0.202617i
\(313\) −5.06025e8 + 5.06025e8i −0.932753 + 0.932753i −0.997877 0.0651245i \(-0.979256\pi\)
0.0651245 + 0.997877i \(0.479256\pi\)
\(314\) −1.18452e8 −0.215918
\(315\) 5.52456e8 5.28814e8i 0.995888 0.953270i
\(316\) −5.36205e8 −0.955930
\(317\) 4.82296e8 4.82296e8i 0.850367 0.850367i −0.139811 0.990178i \(-0.544649\pi\)
0.990178 + 0.139811i \(0.0446495\pi\)
\(318\) −1.11330e6 875621.i −0.00194141 0.00152694i
\(319\) 7.03302e8i 1.21304i
\(320\) −1.10329e8 + 4.15178e8i −0.188219 + 0.708287i
\(321\) −6.63126e8 + 7.92444e7i −1.11900 + 0.133721i
\(322\) −1.32749e8 1.32749e8i −0.221582 0.221582i
\(323\) −1.06688e8 1.06688e8i −0.176159 0.176159i
\(324\) −2.67419e8 5.19040e8i −0.436802 0.847800i
\(325\) 4.65570e8 1.26811e8i 0.752303 0.204910i
\(326\) 7.72026e7i 0.123416i
\(327\) 3.84086e8 4.88342e8i 0.607451 0.772338i
\(328\) −2.02811e8 + 2.02811e8i −0.317346 + 0.317346i
\(329\) −1.24549e9 −1.92822
\(330\) −1.41267e7 + 9.96688e7i −0.0216393 + 0.152672i
\(331\) 7.63573e8 1.15732 0.578659 0.815570i \(-0.303576\pi\)
0.578659 + 0.815570i \(0.303576\pi\)
\(332\) 3.22065e7 3.22065e7i 0.0483014 0.0483014i
\(333\) 3.78023e8 6.20012e8i 0.561001 0.920122i
\(334\) 1.42731e8i 0.209607i
\(335\) 3.54525e8 + 6.11140e8i 0.515217 + 0.888145i
\(336\) −9.81890e7 8.21657e8i −0.141213 1.18169i
\(337\) −6.74055e8 6.74055e8i −0.959380 0.959380i 0.0398266 0.999207i \(-0.487319\pi\)
−0.999207 + 0.0398266i \(0.987319\pi\)
\(338\) 4.23433e7 + 4.23433e7i 0.0596453 + 0.0596453i
\(339\) 3.33301e7 + 2.78910e8i 0.0464662 + 0.388835i
\(340\) −1.51688e8 2.61484e8i −0.209303 0.360802i
\(341\) 4.64740e8i 0.634702i
\(342\) 4.71957e7 7.74076e7i 0.0637985 0.104639i
\(343\) 7.24774e7 7.24774e7i 0.0969780 0.0969780i
\(344\) 2.56381e8 0.339571
\(345\) −1.13082e8 + 7.97835e8i −0.148261 + 1.04603i
\(346\) 1.06082e8 0.137681
\(347\) −1.10778e8 + 1.10778e8i −0.142331 + 0.142331i −0.774682 0.632351i \(-0.782090\pi\)
0.632351 + 0.774682i \(0.282090\pi\)
\(348\) −7.84551e8 + 9.97509e8i −0.997916 + 1.26879i
\(349\) 5.70244e8i 0.718078i −0.933323 0.359039i \(-0.883105\pi\)
0.933323 0.359039i \(-0.116895\pi\)
\(350\) 2.06530e8 + 1.18106e8i 0.257481 + 0.147243i
\(351\) 2.20644e8 + 5.91909e8i 0.272344 + 0.730601i
\(352\) 2.51332e8 + 2.51332e8i 0.307148 + 0.307148i
\(353\) −2.34804e7 2.34804e7i −0.0284116 0.0284116i 0.692758 0.721170i \(-0.256395\pi\)
−0.721170 + 0.692758i \(0.756395\pi\)
\(354\) −4.28823e6 + 512448.i −0.00513767 + 0.000613958i
\(355\) −3.18506e8 + 1.19857e9i −0.377850 + 1.42188i
\(356\) 1.11479e9i 1.30954i
\(357\) 4.07424e8 + 3.20443e8i 0.473923 + 0.372745i
\(358\) −8.08506e7 + 8.08506e7i −0.0931306 + 0.0931306i
\(359\) 5.24443e7 0.0598230 0.0299115 0.999553i \(-0.490477\pi\)
0.0299115 + 0.999553i \(0.490477\pi\)
\(360\) 2.68808e8 2.57304e8i 0.303657 0.290662i
\(361\) 6.03848e8 0.675542
\(362\) 7.24724e7 7.24724e7i 0.0802957 0.0802957i
\(363\) 3.48384e8 + 2.74008e8i 0.382283 + 0.300669i
\(364\) 9.43279e8i 1.02514i
\(365\) −1.91723e8 + 1.11219e8i −0.206371 + 0.119717i
\(366\) −2.82776e7 + 3.37921e6i −0.0301481 + 0.00360273i
\(367\) 3.20449e8 + 3.20449e8i 0.338398 + 0.338398i 0.855764 0.517366i \(-0.173088\pi\)
−0.517366 + 0.855764i \(0.673088\pi\)
\(368\) 6.16544e8 + 6.16544e8i 0.644907 + 0.644907i
\(369\) −1.00144e9 + 2.42815e8i −1.03761 + 0.251584i
\(370\) 2.18332e8 + 5.80194e7i 0.224085 + 0.0595480i
\(371\) 1.55662e7i 0.0158261i
\(372\) −5.18430e8 + 6.59152e8i −0.522143 + 0.663873i
\(373\) 8.34366e8 8.34366e8i 0.832484 0.832484i −0.155372 0.987856i \(-0.549658\pi\)
0.987856 + 0.155372i \(0.0496576\pi\)
\(374\) −6.82294e7 −0.0674405
\(375\) −1.27447e8 1.01321e9i −0.124801 0.992182i
\(376\) −6.06018e8 −0.587933
\(377\) 9.70860e8 9.70860e8i 0.933172 0.933172i
\(378\) −1.29439e8 + 2.83292e8i −0.123266 + 0.269782i
\(379\) 1.26366e9i 1.19232i 0.802867 + 0.596158i \(0.203307\pi\)
−0.802867 + 0.596158i \(0.796693\pi\)
\(380\) −5.61592e8 1.49237e8i −0.525023 0.139519i
\(381\) 3.69092e7 + 3.08861e8i 0.0341899 + 0.286105i
\(382\) −4.70799e7 4.70799e7i −0.0432129 0.0432129i
\(383\) −4.54621e8 4.54621e8i −0.413480 0.413480i 0.469469 0.882949i \(-0.344445\pi\)
−0.882949 + 0.469469i \(0.844445\pi\)
\(384\) −1.00557e8 8.41469e8i −0.0906257 0.758366i
\(385\) −9.56955e8 + 5.55134e8i −0.854631 + 0.495776i
\(386\) 8.88996e7i 0.0786763i
\(387\) 7.86457e8 + 4.79506e8i 0.689742 + 0.420538i
\(388\) 9.85502e8 9.85502e8i 0.856538 0.856538i
\(389\) 1.48893e8 0.128248 0.0641239 0.997942i \(-0.479575\pi\)
0.0641239 + 0.997942i \(0.479575\pi\)
\(390\) −1.57087e8 + 1.18085e8i −0.134095 + 0.100802i
\(391\) −5.46167e8 −0.462069
\(392\) −3.19217e8 + 3.19217e8i −0.267661 + 0.267661i
\(393\) −5.54727e8 + 7.05301e8i −0.461004 + 0.586139i
\(394\) 6.75369e7i 0.0556294i
\(395\) 3.15310e8 1.18654e9i 0.257424 0.968709i
\(396\) 1.99032e8 + 8.20872e8i 0.161061 + 0.664266i
\(397\) −1.39088e9 1.39088e9i −1.11563 1.11563i −0.992375 0.123259i \(-0.960665\pi\)
−0.123259 0.992375i \(-0.539335\pi\)
\(398\) −2.45658e8 2.45658e8i −0.195317 0.195317i
\(399\) 9.89330e8 1.18226e8i 0.779715 0.0931769i
\(400\) −9.59217e8 5.48539e8i −0.749389 0.428546i
\(401\) 5.11604e8i 0.396213i −0.980181 0.198106i \(-0.936521\pi\)
0.980181 0.198106i \(-0.0634792\pi\)
\(402\) −2.26174e8 1.77888e8i −0.173640 0.136570i
\(403\) 6.41542e8 6.41542e8i 0.488267 0.488267i
\(404\) 1.00309e9 0.756841
\(405\) 1.30581e9 2.86542e8i 0.976760 0.214337i
\(406\) 6.76969e8 0.502027
\(407\) −7.42809e8 + 7.42809e8i −0.546131 + 0.546131i
\(408\) 1.98240e8 + 1.55918e8i 0.144504 + 0.113654i
\(409\) 9.31820e8i 0.673442i −0.941604 0.336721i \(-0.890682\pi\)
0.941604 0.336721i \(-0.109318\pi\)
\(410\) −1.60861e8 2.77296e8i −0.115267 0.198701i
\(411\) −1.41954e9 + 1.69636e8i −1.00856 + 0.120524i
\(412\) 1.92811e8 + 1.92811e8i 0.135829 + 0.135829i
\(413\) −3.35616e7 3.35616e7i −0.0234433 0.0234433i
\(414\) −7.73319e7 3.18941e8i −0.0535621 0.220907i
\(415\) 5.23294e7 + 9.02068e7i 0.0359400 + 0.0619542i
\(416\) 6.93892e8i 0.472569i
\(417\) −9.47262e8 + 1.20439e9i −0.639726 + 0.813373i
\(418\) −9.27386e7 + 9.27386e7i −0.0621074 + 0.0621074i
\(419\) 1.87062e8 0.124233 0.0621165 0.998069i \(-0.480215\pi\)
0.0621165 + 0.998069i \(0.480215\pi\)
\(420\) 1.97654e9 + 2.80148e8i 1.30176 + 0.184508i
\(421\) 2.80609e8 0.183280 0.0916400 0.995792i \(-0.470789\pi\)
0.0916400 + 0.995792i \(0.470789\pi\)
\(422\) 4.05275e6 4.05275e6i 0.00262516 0.00262516i
\(423\) −1.85898e9 1.13343e9i −1.19422 0.728120i
\(424\) 7.57402e6i 0.00482554i
\(425\) 6.67824e8 1.81900e8i 0.421989 0.114940i
\(426\) −5.99316e7 5.01515e8i −0.0375597 0.314304i
\(427\) −2.21314e8 2.21314e8i −0.137566 0.137566i
\(428\) −1.23271e9 1.23271e9i −0.759991 0.759991i
\(429\) −1.08432e8 9.07373e8i −0.0663067 0.554863i
\(430\) −7.35950e7 + 2.76945e8i −0.0446384 + 0.167979i
\(431\) 2.93618e9i 1.76650i 0.468906 + 0.883248i \(0.344648\pi\)
−0.468906 + 0.883248i \(0.655352\pi\)
\(432\) 6.01174e8 1.31573e9i 0.358763 0.785190i
\(433\) −2.11328e9 + 2.11328e9i −1.25098 + 1.25098i −0.295695 + 0.955282i \(0.595551\pi\)
−0.955282 + 0.295695i \(0.904449\pi\)
\(434\) 4.47339e8 0.262678
\(435\) −1.74599e9 2.32267e9i −1.01702 1.35293i
\(436\) 1.62179e9 0.937114
\(437\) −7.42360e8 + 7.42360e8i −0.425529 + 0.425529i
\(438\) 5.58058e7 7.09537e7i 0.0317336 0.0403474i
\(439\) 2.53076e9i 1.42766i 0.700318 + 0.713831i \(0.253042\pi\)
−0.700318 + 0.713831i \(0.746958\pi\)
\(440\) −4.65624e8 + 2.70111e8i −0.260586 + 0.151167i
\(441\) −1.57624e9 + 3.82182e8i −0.875159 + 0.212195i
\(442\) −9.41860e7 9.41860e7i −0.0518810 0.0518810i
\(443\) 1.47424e9 + 1.47424e9i 0.805665 + 0.805665i 0.983974 0.178309i \(-0.0570628\pi\)
−0.178309 + 0.983974i \(0.557063\pi\)
\(444\) 1.88217e9 2.24921e8i 1.02051 0.121952i
\(445\) 2.46687e9 + 6.55543e8i 1.32705 + 0.352648i
\(446\) 2.57983e8i 0.137695i
\(447\) 2.75293e9 + 2.16521e9i 1.45787 + 1.14663i
\(448\) 1.35963e9 1.35963e9i 0.714409 0.714409i
\(449\) 2.67292e9 1.39355 0.696776 0.717289i \(-0.254617\pi\)
0.696776 + 0.717289i \(0.254617\pi\)
\(450\) 2.00780e8 + 3.64229e8i 0.103867 + 0.188422i
\(451\) 1.49069e9 0.765192
\(452\) −5.18477e8 + 5.18477e8i −0.264086 + 0.264086i
\(453\) 3.76442e8 + 2.96075e8i 0.190263 + 0.149644i
\(454\) 2.00221e8i 0.100419i
\(455\) −2.08733e9 5.54686e8i −1.03885 0.276062i
\(456\) 4.81377e8 5.75251e7i 0.237743 0.0284106i
\(457\) −1.29398e9 1.29398e9i −0.634193 0.634193i 0.314924 0.949117i \(-0.398021\pi\)
−0.949117 + 0.314924i \(0.898021\pi\)
\(458\) 2.96210e8 + 2.96210e8i 0.144069 + 0.144069i
\(459\) 3.16497e8 + 8.49049e8i 0.152766 + 0.409815i
\(460\) −1.81947e9 + 1.05548e9i −0.871552 + 0.505591i
\(461\) 2.19571e9i 1.04381i −0.853003 0.521906i \(-0.825221\pi\)
0.853003 0.521906i \(-0.174779\pi\)
\(462\) 2.78546e8 3.54154e8i 0.131417 0.167088i
\(463\) −8.89626e8 + 8.89626e8i −0.416557 + 0.416557i −0.884015 0.467458i \(-0.845170\pi\)
0.467458 + 0.884015i \(0.345170\pi\)
\(464\) −3.14415e9 −1.46113
\(465\) −1.15375e9 1.53482e9i −0.532139 0.707898i
\(466\) −3.41219e8 −0.156200
\(467\) −1.96829e9 + 1.96829e9i −0.894295 + 0.894295i −0.994924 0.100629i \(-0.967914\pi\)
0.100629 + 0.994924i \(0.467914\pi\)
\(468\) −8.58406e8 + 1.40791e9i −0.387108 + 0.634912i
\(469\) 3.16237e9i 1.41549i
\(470\) 1.73960e8 6.54626e8i 0.0772869 0.290838i
\(471\) −2.70026e8 2.25961e9i −0.119078 0.996462i
\(472\) −1.63300e7 1.63300e7i −0.00714810 0.00714810i
\(473\) −9.42220e8 9.42220e8i −0.409391 0.409391i
\(474\) 5.93302e7 + 4.96482e8i 0.0255889 + 0.214131i
\(475\) 6.60477e8 1.15496e9i 0.282768 0.494470i
\(476\) 1.35306e9i 0.575034i
\(477\) 1.41656e7 2.32336e7i 0.00597614 0.00980172i
\(478\) 6.08349e8 6.08349e8i 0.254774 0.254774i
\(479\) 2.28503e9 0.949988 0.474994 0.879989i \(-0.342450\pi\)
0.474994 + 0.879989i \(0.342450\pi\)
\(480\) 1.45398e9 + 2.06082e8i 0.600085 + 0.0850540i
\(481\) −2.05079e9 −0.840261
\(482\) −2.75450e8 + 2.75450e8i −0.112041 + 0.112041i
\(483\) 2.22972e9 2.83496e9i 0.900401 1.14481i
\(484\) 1.15699e9i 0.463842i
\(485\) 1.60125e9 + 2.76028e9i 0.637330 + 1.09865i
\(486\) −4.50999e8 + 3.05039e8i −0.178217 + 0.120539i
\(487\) −1.04806e8 1.04806e8i −0.0411182 0.0411182i 0.686249 0.727367i \(-0.259256\pi\)
−0.727367 + 0.686249i \(0.759256\pi\)
\(488\) −1.07684e8 1.07684e8i −0.0419453 0.0419453i
\(489\) −1.47273e9 + 1.75993e8i −0.569564 + 0.0680636i
\(490\) −2.53189e8 4.36454e8i −0.0972206 0.167591i
\(491\) 6.21274e8i 0.236864i 0.992962 + 0.118432i \(0.0377867\pi\)
−0.992962 + 0.118432i \(0.962213\pi\)
\(492\) −2.11428e9 1.66291e9i −0.800361 0.629492i
\(493\) 1.39262e9 1.39262e9i 0.523443 0.523443i
\(494\) −2.56039e8 −0.0955567
\(495\) −1.93351e9 4.22764e7i −0.716518 0.0156668i
\(496\) −2.07764e9 −0.764514
\(497\) 3.92509e9 3.92509e9i 1.43417 1.43417i
\(498\) −3.33842e7 2.62570e7i −0.0121126 0.00952669i
\(499\) 1.04126e9i 0.375151i −0.982250 0.187575i \(-0.939937\pi\)
0.982250 0.187575i \(-0.0600629\pi\)
\(500\) 1.87323e9 1.89657e9i 0.670187 0.678536i
\(501\) 2.72276e9 3.25373e8i 0.967337 0.115598i
\(502\) 3.49138e8 + 3.49138e8i 0.123178 + 0.123178i
\(503\) 8.74993e8 + 8.74993e8i 0.306561 + 0.306561i 0.843574 0.537013i \(-0.180447\pi\)
−0.537013 + 0.843574i \(0.680447\pi\)
\(504\) −1.61862e9 + 3.92460e8i −0.563170 + 0.136549i
\(505\) −5.89856e8 + 2.21968e9i −0.203810 + 0.766958i
\(506\) 4.74757e8i 0.162909i
\(507\) −7.11222e8 + 9.04276e8i −0.242369 + 0.308158i
\(508\) −5.74154e8 + 5.74154e8i −0.194315 + 0.194315i
\(509\) −5.23513e9 −1.75961 −0.879803 0.475339i \(-0.842325\pi\)
−0.879803 + 0.475339i \(0.842325\pi\)
\(510\) −2.25329e8 + 1.69384e8i −0.0752180 + 0.0565427i
\(511\) 9.92077e8 0.328906
\(512\) 1.90286e9 1.90286e9i 0.626557 0.626557i
\(513\) 1.58423e9 + 7.23854e8i 0.518093 + 0.236723i
\(514\) 5.30778e8i 0.172402i
\(515\) −5.40042e8 + 3.13281e8i −0.174222 + 0.101067i
\(516\) 2.85302e8 + 2.38744e9i 0.0914179 + 0.764996i
\(517\) 2.22717e9 + 2.22717e9i 0.708820 + 0.708820i
\(518\) −7.14997e8 7.14997e8i −0.226022 0.226022i
\(519\) 2.41827e8 + 2.02364e9i 0.0759309 + 0.635399i
\(520\) −1.01563e9 2.69893e8i −0.316756 0.0841743i
\(521\) 3.89754e9i 1.20742i −0.797203 0.603711i \(-0.793688\pi\)
0.797203 0.603711i \(-0.206312\pi\)
\(522\) 1.01042e9 + 6.16058e8i 0.310925 + 0.189572i
\(523\) −1.14045e9 + 1.14045e9i −0.348596 + 0.348596i −0.859586 0.510991i \(-0.829279\pi\)
0.510991 + 0.859586i \(0.329279\pi\)
\(524\) −2.34232e9 −0.711191
\(525\) −1.78221e9 + 4.20904e9i −0.537528 + 1.26948i
\(526\) −1.11142e9 −0.332987
\(527\) 9.20243e8 9.20243e8i 0.273883 0.273883i
\(528\) −1.29369e9 + 1.64485e9i −0.382483 + 0.486304i
\(529\) 3.95540e8i 0.116170i
\(530\) 8.18154e6 + 2.17415e6i 0.00238709 + 0.000634343i
\(531\) −1.95511e7 8.06349e7i −0.00566684 0.0233718i
\(532\) 1.83911e9 + 1.83911e9i 0.529561 + 0.529561i
\(533\) 2.05780e9 + 2.05780e9i 0.588651 + 0.588651i
\(534\) −1.03221e9 + 1.23350e8i −0.293341 + 0.0350546i
\(535\) 3.45269e9 2.00292e9i 0.974810 0.565492i
\(536\) 1.53871e9i 0.431599i
\(537\) −1.72663e9 1.35801e9i −0.481160 0.378437i
\(538\) 1.05398e8 1.05398e8i 0.0291807 0.0291807i
\(539\) 2.34630e9 0.645390
\(540\) 2.69518e9 + 2.21684e9i 0.736561 + 0.605837i
\(541\) 5.67463e9 1.54080 0.770402 0.637559i \(-0.220056\pi\)
0.770402 + 0.637559i \(0.220056\pi\)
\(542\) −1.09106e9 + 1.09106e9i −0.294341 + 0.294341i
\(543\) 1.54771e9 + 1.21729e9i 0.414848 + 0.326282i
\(544\) 9.95336e8i 0.265078i
\(545\) −9.53679e8 + 3.58878e9i −0.252357 + 0.949641i
\(546\) 8.73399e8 1.04372e8i 0.229635 0.0274417i
\(547\) −1.60556e9 1.60556e9i −0.419441 0.419441i 0.465570 0.885011i \(-0.345849\pi\)
−0.885011 + 0.465570i \(0.845849\pi\)
\(548\) −2.63884e9 2.63884e9i −0.684984 0.684984i
\(549\) −1.28925e8 5.31727e8i −0.0332532 0.137147i
\(550\) −1.58117e8 5.80508e8i −0.0405238 0.148778i
\(551\) 3.78576e9i 0.964101i
\(552\) 1.08491e9 1.37940e9i 0.274542 0.349063i
\(553\) −3.88570e9 + 3.88570e9i −0.977082 + 0.977082i
\(554\) 1.19202e9 0.297852
\(555\) −6.09073e8 + 4.29722e9i −0.151232 + 1.06699i
\(556\) −3.99979e9 −0.986904
\(557\) 8.47773e8 8.47773e8i 0.207867 0.207867i −0.595493 0.803360i \(-0.703043\pi\)
0.803360 + 0.595493i \(0.203043\pi\)
\(558\) 6.67685e8 + 4.07090e8i 0.162687 + 0.0991906i
\(559\) 2.60134e9i 0.629877i
\(560\) 2.48176e9 + 4.27811e9i 0.597174 + 1.02942i
\(561\) −1.55538e8 1.30156e9i −0.0371934 0.311239i
\(562\) 3.57814e7 + 3.57814e7i 0.00850316 + 0.00850316i
\(563\) 3.73177e8 + 3.73177e8i 0.0881323 + 0.0881323i 0.749799 0.661666i \(-0.230150\pi\)
−0.661666 + 0.749799i \(0.730150\pi\)
\(564\) −6.74381e8 5.64330e9i −0.158281 1.32451i
\(565\) −8.42427e8 1.45220e9i −0.196500 0.338732i
\(566\) 1.40853e8i 0.0326519i
\(567\) −5.69921e9 1.82341e9i −1.31303 0.420091i
\(568\) 1.90982e9 1.90982e9i 0.437295 0.437295i
\(569\) −4.11594e9 −0.936648 −0.468324 0.883557i \(-0.655142\pi\)
−0.468324 + 0.883557i \(0.655142\pi\)
\(570\) −7.60418e7 + 5.36501e8i −0.0171985 + 0.121341i
\(571\) −2.99821e9 −0.673962 −0.336981 0.941512i \(-0.609406\pi\)
−0.336981 + 0.941512i \(0.609406\pi\)
\(572\) 1.68675e9 1.68675e9i 0.376847 0.376847i
\(573\) 7.90781e8 1.00543e9i 0.175596 0.223260i
\(574\) 1.43488e9i 0.316682i
\(575\) −1.26571e9 4.64689e9i −0.277649 1.01935i
\(576\) 3.26663e9 7.92043e8i 0.712232 0.172691i
\(577\) 1.54684e9 + 1.54684e9i 0.335220 + 0.335220i 0.854565 0.519345i \(-0.173824\pi\)
−0.519345 + 0.854565i \(0.673824\pi\)
\(578\) 5.71184e8 + 5.71184e8i 0.123035 + 0.123035i
\(579\) 1.69587e9 2.02658e8i 0.363092 0.0433899i
\(580\) 1.94803e9 7.33061e9i 0.414569 1.56006i
\(581\) 4.66779e8i 0.0987404i
\(582\) −1.02154e9 8.03451e8i −0.214795 0.168939i
\(583\) −2.78352e7 + 2.78352e7i −0.00581773 + 0.00581773i
\(584\) 4.82714e8 0.100287
\(585\) −2.61071e9 2.72743e9i −0.539155 0.563259i
\(586\) −1.06672e6 −0.000218981
\(587\) −3.50513e9 + 3.50513e9i −0.715271 + 0.715271i −0.967633 0.252362i \(-0.918793\pi\)
0.252362 + 0.967633i \(0.418793\pi\)
\(588\) −3.32781e9 2.61736e9i −0.675053 0.530936i
\(589\) 2.50162e9i 0.504450i
\(590\) 2.23275e7 1.29523e7i 0.00447566 0.00259635i
\(591\) −1.28835e9 + 1.53959e8i −0.256730 + 0.0306795i
\(592\) 3.32077e9 + 3.32077e9i 0.657828 + 0.657828i
\(593\) 3.34493e9 + 3.34493e9i 0.658712 + 0.658712i 0.955075 0.296363i \(-0.0957739\pi\)
−0.296363 + 0.955075i \(0.595774\pi\)
\(594\) 7.38038e8 2.75116e8i 0.144486 0.0538596i
\(595\) −2.99412e9 7.95655e8i −0.582720 0.154851i
\(596\) 9.14253e9i 1.76890i
\(597\) 4.12622e9 5.24624e9i 0.793674 1.00911i
\(598\) −6.55370e8 + 6.55370e8i −0.125323 + 0.125323i
\(599\) 4.84654e9 0.921378 0.460689 0.887562i \(-0.347602\pi\)
0.460689 + 0.887562i \(0.347602\pi\)
\(600\) −8.67167e8 + 2.04799e9i −0.163898 + 0.387078i
\(601\) −7.05160e9 −1.32503 −0.662517 0.749047i \(-0.730512\pi\)
−0.662517 + 0.749047i \(0.730512\pi\)
\(602\) 9.06942e8 9.06942e8i 0.169431 0.169431i
\(603\) 2.87783e9 4.72005e9i 0.534509 0.876670i
\(604\) 1.25017e9i 0.230855i
\(605\) −2.56024e9 6.80356e8i −0.470043 0.124909i
\(606\) −1.10990e8 9.28778e8i −0.0202596 0.169534i
\(607\) 2.33423e9 + 2.33423e9i 0.423627 + 0.423627i 0.886451 0.462823i \(-0.153164\pi\)
−0.462823 + 0.886451i \(0.653164\pi\)
\(608\) 1.35288e9 + 1.35288e9i 0.244116 + 0.244116i
\(609\) 1.54324e9 + 1.29140e10i 0.276868 + 2.31686i
\(610\) 1.47233e8 8.54105e7i 0.0262634 0.0152355i
\(611\) 6.14890e9i 1.09057i
\(612\) −1.23132e9 + 2.01954e9i −0.217140 + 0.356141i
\(613\) −3.01299e8 + 3.01299e8i −0.0528306 + 0.0528306i −0.733029 0.680198i \(-0.761894\pi\)
0.680198 + 0.733029i \(0.261894\pi\)
\(614\) −2.04304e8 −0.0356195
\(615\) 4.92305e9 3.70074e9i 0.853436 0.641543i
\(616\) 2.40939e9 0.415313
\(617\) −5.38935e9 + 5.38935e9i −0.923716 + 0.923716i −0.997290 0.0735741i \(-0.976559\pi\)
0.0735741 + 0.997290i \(0.476559\pi\)
\(618\) 1.57193e8 1.99861e8i 0.0267901 0.0340619i
\(619\) 1.22018e9i 0.206779i 0.994641 + 0.103390i \(0.0329689\pi\)
−0.994641 + 0.103390i \(0.967031\pi\)
\(620\) 1.28725e9 4.84405e9i 0.216917 0.816277i
\(621\) 5.90789e9 2.20227e9i 0.989947 0.369019i
\(622\) 1.25710e9 + 1.25710e9i 0.209461 + 0.209461i
\(623\) −8.07853e9 8.07853e9i −1.33852 1.33852i
\(624\) −4.05646e9 + 4.84751e8i −0.668345 + 0.0798680i
\(625\) 3.09528e9 + 5.26043e9i 0.507131 + 0.861869i
\(626\) 1.74197e9i 0.283811i
\(627\) −1.98051e9 1.55769e9i −0.320879 0.252374i
\(628\) 4.20048e9 4.20048e9i 0.676769 0.676769i
\(629\) −2.94171e9 −0.471327
\(630\) 4.06934e7 1.86111e9i 0.00648384 0.296538i
\(631\) −1.39179e9 −0.220532 −0.110266 0.993902i \(-0.535170\pi\)
−0.110266 + 0.993902i \(0.535170\pi\)
\(632\) −1.89066e9 + 1.89066e9i −0.297923 + 0.297923i
\(633\) 8.65498e7 + 6.80723e7i 0.0135629 + 0.0106674i
\(634\) 1.66028e9i 0.258744i
\(635\) −9.32891e8 1.60814e9i −0.144585 0.249239i
\(636\) 7.05301e7 8.42843e6i 0.0108711 0.00129911i
\(637\) 3.23890e9 + 3.23890e9i 0.496489 + 0.496489i
\(638\) −1.21054e9 1.21054e9i −0.184547 0.184547i
\(639\) 9.43038e9 2.28654e9i 1.42980 0.346677i
\(640\) 2.54160e9 + 4.38127e9i 0.383245 + 0.660648i
\(641\) 2.77059e9i 0.415498i −0.978182 0.207749i \(-0.933386\pi\)
0.978182 0.207749i \(-0.0666137\pi\)
\(642\) −1.00499e9 + 1.27779e9i −0.149896 + 0.190584i
\(643\) −5.82699e9 + 5.82699e9i −0.864383 + 0.864383i −0.991844 0.127461i \(-0.959317\pi\)
0.127461 + 0.991844i \(0.459317\pi\)
\(644\) 9.41494e9 1.38905
\(645\) −5.45083e9 7.72582e8i −0.799841 0.113367i
\(646\) −3.67268e8 −0.0536005
\(647\) −5.05616e9 + 5.05616e9i −0.733932 + 0.733932i −0.971396 0.237465i \(-0.923684\pi\)
0.237465 + 0.971396i \(0.423684\pi\)
\(648\) −2.77306e9 8.87215e8i −0.400356 0.128090i
\(649\) 1.20029e8i 0.0172357i
\(650\) 5.83082e8 1.01962e9i 0.0832785 0.145627i
\(651\) 1.01977e9 + 8.53354e9i 0.144866 + 1.21226i
\(652\) −2.73772e9 2.73772e9i −0.386832 0.386832i
\(653\) 4.26375e9 + 4.26375e9i 0.599232 + 0.599232i 0.940108 0.340876i \(-0.110724\pi\)
−0.340876 + 0.940108i \(0.610724\pi\)
\(654\) −1.79449e8 1.50165e9i −0.0250852 0.209916i
\(655\) 1.37738e9 5.18320e9i 0.191517 0.720698i
\(656\) 6.66422e9i 0.921692i
\(657\) 1.48074e9 + 9.02814e8i 0.203705 + 0.124199i
\(658\) −2.14378e9 + 2.14378e9i −0.293352 + 0.293352i
\(659\) 9.37824e9 1.27650 0.638252 0.769827i \(-0.279658\pi\)
0.638252 + 0.769827i \(0.279658\pi\)
\(660\) −3.03345e9 4.03536e9i −0.410708 0.546360i
\(661\) 7.09319e8 0.0955292 0.0477646 0.998859i \(-0.484790\pi\)
0.0477646 + 0.998859i \(0.484790\pi\)
\(662\) 1.31428e9 1.31428e9i 0.176070 0.176070i
\(663\) 1.58200e9 2.01142e9i 0.210819 0.268044i
\(664\) 2.27120e8i 0.0301070i
\(665\) −5.15113e9 + 2.98820e9i −0.679246 + 0.394034i
\(666\) −4.16517e8 1.71785e9i −0.0546353 0.225333i
\(667\) −9.69023e9 9.69023e9i −1.26443 1.26443i
\(668\) 5.06145e9 + 5.06145e9i 0.656988 + 0.656988i
\(669\) −4.92134e9 + 5.88106e8i −0.635465 + 0.0759388i
\(670\) 1.66213e9 + 4.41692e8i 0.213503 + 0.0567359i
\(671\) 7.91498e8i 0.101140i
\(672\) −5.16643e9 4.06345e9i −0.656747 0.516538i
\(673\) 3.47585e9 3.47585e9i 0.439550 0.439550i −0.452310 0.891861i \(-0.649400\pi\)
0.891861 + 0.452310i \(0.149400\pi\)
\(674\) −2.32040e9 −0.291913
\(675\) −6.49040e9 + 4.66043e9i −0.812285 + 0.583261i
\(676\) −3.00312e9 −0.373903
\(677\) 9.35828e9 9.35828e9i 1.15914 1.15914i 0.174478 0.984661i \(-0.444176\pi\)
0.984661 0.174478i \(-0.0558239\pi\)
\(678\) 5.37436e8 + 4.22699e8i 0.0662252 + 0.0520868i
\(679\) 1.42832e10i 1.75098i
\(680\) −1.45685e9 3.87141e8i −0.177678 0.0472158i
\(681\) −3.81946e9 + 4.56430e8i −0.463433 + 0.0553808i
\(682\) −7.99924e8 7.99924e8i −0.0965613 0.0965613i
\(683\) −6.79399e9 6.79399e9i −0.815930 0.815930i 0.169586 0.985515i \(-0.445757\pi\)
−0.985515 + 0.169586i \(0.945757\pi\)
\(684\) 1.07136e9 + 4.41862e9i 0.128009 + 0.527947i
\(685\) 7.39110e9 4.28761e9i 0.878601 0.509681i
\(686\) 2.49500e8i 0.0295078i
\(687\) −4.97531e9 + 6.32581e9i −0.585426 + 0.744334i
\(688\) −4.21224e9 + 4.21224e9i −0.493122 + 0.493122i
\(689\) −7.68491e7 −0.00895100
\(690\) 1.17861e9 + 1.56790e9i 0.136584 + 0.181696i
\(691\) 1.04165e10 1.20101 0.600506 0.799620i \(-0.294966\pi\)
0.600506 + 0.799620i \(0.294966\pi\)
\(692\) −3.76182e9 + 3.76182e9i −0.431545 + 0.431545i
\(693\) 7.39090e9 + 4.50626e9i 0.843589 + 0.514339i
\(694\) 3.81347e8i 0.0433075i
\(695\) 2.35204e9 8.85093e9i 0.265765 1.00010i
\(696\) 7.50891e8 + 6.28355e9i 0.0844198 + 0.706435i
\(697\) 2.95176e9 + 2.95176e9i 0.330191 + 0.330191i
\(698\) −9.81519e8 9.81519e8i −0.109246 0.109246i
\(699\) −7.77852e8 6.50916e9i −0.0861444 0.720867i
\(700\) −1.15121e10 + 3.13563e9i −1.26856 + 0.345527i
\(701\) 6.11757e8i 0.0670758i −0.999437 0.0335379i \(-0.989323\pi\)
0.999437 0.0335379i \(-0.0106774\pi\)
\(702\) 1.39859e9 + 6.39032e8i 0.152584 + 0.0697176i
\(703\) −3.99842e9 + 3.99842e9i −0.434055 + 0.434055i
\(704\) −4.86252e9 −0.525239
\(705\) 1.28844e10 + 1.82618e9i 1.38484 + 0.196283i
\(706\) −8.08304e7 −0.00864487
\(707\) 7.26904e9 7.26904e9i 0.773587 0.773587i
\(708\) 1.33895e8 1.70239e8i 0.0141791 0.0180278i
\(709\) 1.35614e10i 1.42904i 0.699616 + 0.714519i \(0.253354\pi\)
−0.699616 + 0.714519i \(0.746646\pi\)
\(710\) 1.51479e9 + 2.61123e9i 0.158836 + 0.273805i
\(711\) −9.33575e9 + 2.26359e9i −0.974105 + 0.236186i
\(712\) −3.93076e9 3.93076e9i −0.408128 0.408128i
\(713\) −6.40328e9 6.40328e9i −0.661590 0.661590i
\(714\) 1.25282e9 1.49714e8i 0.128809 0.0153928i
\(715\) 2.74065e9 + 4.72441e9i 0.280403 + 0.483366i
\(716\) 5.73417e9i 0.583815i
\(717\) 1.29918e10 + 1.02182e10i 1.31629 + 1.03528i
\(718\) 9.02686e7 9.02686e7i 0.00910126 0.00910126i
\(719\) −9.45342e9 −0.948501 −0.474250 0.880390i \(-0.657281\pi\)
−0.474250 + 0.880390i \(0.657281\pi\)
\(720\) −1.88999e8 + 8.64384e9i −0.0188710 + 0.863063i
\(721\) 2.79447e9 0.277668
\(722\) 1.03936e9 1.03936e9i 0.102775 0.102775i
\(723\) −5.88247e9 4.62662e9i −0.578863 0.455281i
\(724\) 5.13996e9i 0.503356i
\(725\) 1.50760e10 + 8.62138e9i 1.46928 + 0.840222i
\(726\) 1.07128e9 1.28019e8i 0.103902 0.0124164i
\(727\) 1.02901e10 + 1.02901e10i 0.993224 + 0.993224i 0.999977 0.00675331i \(-0.00214966\pi\)
−0.00675331 + 0.999977i \(0.502150\pi\)
\(728\) 3.32600e9 + 3.32600e9i 0.319494 + 0.319494i
\(729\) −6.84711e9 7.90798e9i −0.654577 0.755995i
\(730\) −1.38565e8 + 5.21432e8i −0.0131833 + 0.0496099i
\(731\) 3.73143e9i 0.353317i
\(732\) 8.82937e8 1.12260e9i 0.0832033 0.105788i
\(733\) 9.43421e9 9.43421e9i 0.884793 0.884793i −0.109224 0.994017i \(-0.534837\pi\)
0.994017 + 0.109224i \(0.0348366\pi\)
\(734\) 1.10313e9 0.102965
\(735\) 7.74870e9 5.82484e9i 0.719819 0.541101i
\(736\) 6.92579e9 0.640320
\(737\) −5.65489e9 + 5.65489e9i −0.520341 + 0.520341i
\(738\) −1.30577e9 + 2.14165e9i −0.119583 + 0.196134i
\(739\) 1.21933e10i 1.11139i 0.831386 + 0.555695i \(0.187548\pi\)
−0.831386 + 0.555695i \(0.812452\pi\)
\(740\) −9.79986e9 + 5.68494e9i −0.889014 + 0.515721i
\(741\) −5.83673e8 4.88424e9i −0.0526994 0.440995i
\(742\) −2.67930e7 2.67930e7i −0.00240773 0.00240773i
\(743\) 1.24919e10 + 1.24919e10i 1.11729 + 1.11729i 0.992137 + 0.125154i \(0.0399425\pi\)
0.125154 + 0.992137i \(0.460057\pi\)
\(744\) 4.96187e8 + 4.15215e9i 0.0441713 + 0.369631i
\(745\) −2.02310e10 5.37617e9i −1.79255 0.476350i
\(746\) 2.87227e9i 0.253302i
\(747\) 4.24780e8 6.96699e8i 0.0372857 0.0611538i
\(748\) 2.41952e9 2.41952e9i 0.211385 0.211385i
\(749\) −1.78661e10 −1.55362
\(750\) −1.96334e9 1.52461e9i −0.169934 0.131960i
\(751\) −8.37358e9 −0.721392 −0.360696 0.932683i \(-0.617461\pi\)
−0.360696 + 0.932683i \(0.617461\pi\)
\(752\) 9.95666e9 9.95666e9i 0.853790 0.853790i
\(753\) −5.86432e9 + 7.45612e9i −0.500536 + 0.636401i
\(754\) 3.34214e9i 0.283939i
\(755\) −2.76644e9 7.35150e8i −0.233941 0.0621673i
\(756\) −5.45584e9 1.46361e10i −0.459236 1.23196i
\(757\) −7.21696e9 7.21696e9i −0.604670 0.604670i 0.336878 0.941548i \(-0.390629\pi\)
−0.941548 + 0.336878i \(0.890629\pi\)
\(758\) 2.17504e9 + 2.17504e9i 0.181395 + 0.181395i
\(759\) −9.05656e9 + 1.08227e9i −0.751826 + 0.0898440i
\(760\) −2.50638e9 + 1.45396e9i −0.207109 + 0.120145i
\(761\) 9.70805e9i 0.798520i 0.916838 + 0.399260i \(0.130733\pi\)
−0.916838 + 0.399260i \(0.869267\pi\)
\(762\) 5.95149e8 + 4.68091e8i 0.0487285 + 0.0383255i
\(763\) 1.17526e10 1.17526e10i 0.957850 0.957850i
\(764\) 3.33905e9 0.270892
\(765\) −3.74487e9 3.91229e9i −0.302428 0.315949i
\(766\) −1.56501e9 −0.125811
\(767\) −1.65691e8 + 1.65691e8i −0.0132591 + 0.0132591i
\(768\) 5.60994e9 + 4.41227e9i 0.446883 + 0.351478i
\(769\) 8.37544e9i 0.664149i −0.943253 0.332075i \(-0.892251\pi\)
0.943253 0.332075i \(-0.107749\pi\)
\(770\) −6.91625e8 + 2.60265e9i −0.0545950 + 0.205446i
\(771\) 1.01252e10 1.20998e9i 0.795636 0.0950794i
\(772\) 3.15252e9 + 3.15252e9i 0.246602 + 0.246602i
\(773\) −6.18804e8 6.18804e8i −0.0481864 0.0481864i 0.682603 0.730789i \(-0.260848\pi\)
−0.730789 + 0.682603i \(0.760848\pi\)
\(774\) 2.17901e9 5.28334e8i 0.168914 0.0409557i
\(775\) 9.96220e9 + 5.69699e9i 0.768775 + 0.439632i
\(776\) 6.94976e9i 0.533893i
\(777\) 1.20095e10 1.52694e10i 0.918441 1.16774i
\(778\) 2.56278e8 2.56278e8i 0.0195112 0.0195112i
\(779\) 8.02416e9 0.608161
\(780\) 1.38307e9 9.75801e9i 0.104355 0.736258i
\(781\) −1.40375e10 −1.05442
\(782\) −9.40078e8 + 9.40078e8i −0.0702975 + 0.0702975i
\(783\) −9.44866e9 + 2.06794e10i −0.703403 + 1.53947i
\(784\) 1.04892e10i 0.777388i
\(785\) 6.82499e9 + 1.17651e10i 0.503568 + 0.868064i
\(786\) 2.59174e8 + 2.16880e9i 0.0190376 + 0.159309i
\(787\) −1.30539e10 1.30539e10i −0.954616 0.954616i 0.0443978 0.999014i \(-0.485863\pi\)
−0.999014 + 0.0443978i \(0.985863\pi\)
\(788\) −2.39496e9 2.39496e9i −0.174364 0.174364i
\(789\) −2.53362e9 2.12016e10i −0.183642 1.53674i
\(790\) −1.49959e9 2.58503e9i −0.108212 0.186539i
\(791\) 7.51446e9i 0.539858i
\(792\) 3.59618e9 + 2.19261e9i 0.257219 + 0.156828i
\(793\) −1.09261e9 + 1.09261e9i −0.0778052 + 0.0778052i
\(794\) −4.78803e9 −0.339457
\(795\) −2.28237e7 + 1.61029e8i −0.00161102 + 0.0113663i
\(796\) 1.74228e10 1.22440
\(797\) −2.30188e9 + 2.30188e9i −0.161056 + 0.161056i −0.783035 0.621978i \(-0.786329\pi\)
0.621978 + 0.783035i \(0.286329\pi\)
\(798\) 1.49937e9 1.90636e9i 0.104448 0.132799i
\(799\) 8.82013e9i 0.611732i
\(800\) −8.46850e9 + 2.30663e9i −0.584779 + 0.159280i
\(801\) −4.70610e9 1.94094e10i −0.323555 1.33444i
\(802\) −8.80587e8 8.80587e8i −0.0602784 0.0602784i
\(803\) −1.77401e9 1.77401e9i −0.120907 0.120907i
\(804\) 1.43286e10 1.71229e9i 0.972318 0.116193i
\(805\) −5.53636e9 + 2.08339e10i −0.374058 + 1.40762i
\(806\) 2.20848e9i 0.148566i
\(807\) 2.25087e9 + 1.77033e9i 0.150762 + 0.118576i
\(808\) 3.53689e9 3.53689e9i 0.235875 0.235875i
\(809\) −1.09371e10 −0.726243 −0.363122 0.931742i \(-0.618289\pi\)
−0.363122 + 0.931742i \(0.618289\pi\)
\(810\) 1.75439e9 2.74080e9i 0.115992 0.181209i
\(811\) 8.81067e9 0.580011 0.290005 0.957025i \(-0.406343\pi\)
0.290005 + 0.957025i \(0.406343\pi\)
\(812\) −2.40063e10 + 2.40063e10i −1.57355 + 1.57355i
\(813\) −2.33005e10 1.83261e10i −1.52072 1.19606i
\(814\) 2.55709e9i 0.166173i
\(815\) 7.66806e9 4.44828e9i 0.496174 0.287833i
\(816\) −5.81868e9 + 6.95339e8i −0.374894 + 0.0448003i
\(817\) −5.07182e9 5.07182e9i −0.325377 0.325377i
\(818\) −1.60387e9 1.60387e9i −0.102455 0.102455i
\(819\) 3.98205e9 + 1.64232e10i 0.253287 + 1.04463i
\(820\) 1.55377e10 + 4.12897e9i 0.984097 + 0.261513i
\(821\) 6.77601e9i 0.427339i 0.976906 + 0.213670i \(0.0685416\pi\)
−0.976906 + 0.213670i \(0.931458\pi\)
\(822\) −2.15137e9 + 2.73533e9i −0.135102 + 0.171775i
\(823\) −1.05133e10 + 1.05133e10i −0.657416 + 0.657416i −0.954768 0.297352i \(-0.903897\pi\)
0.297352 + 0.954768i \(0.403897\pi\)
\(824\) 1.35970e9 0.0846640
\(825\) 1.07134e10 4.33962e9i 0.664263 0.269069i
\(826\) −1.15534e8 −0.00713315
\(827\) 1.82530e10 1.82530e10i 1.12218 1.12218i 0.130771 0.991413i \(-0.458255\pi\)
0.991413 0.130771i \(-0.0417453\pi\)
\(828\) 1.40524e10 + 8.56782e9i 0.860291 + 0.524523i
\(829\) 8.82320e9i 0.537880i 0.963157 + 0.268940i \(0.0866733\pi\)
−0.963157 + 0.268940i \(0.913327\pi\)
\(830\) 2.45337e8 + 6.51956e7i 0.0148933 + 0.00395772i
\(831\) 2.71737e9 + 2.27393e10i 0.164265 + 1.37459i
\(832\) −6.71238e9 6.71238e9i −0.404059 0.404059i
\(833\) 4.64596e9 + 4.64596e9i 0.278495 + 0.278495i
\(834\) 4.42570e8 + 3.70348e9i 0.0264180 + 0.221069i
\(835\) −1.41766e10 + 8.22390e9i −0.842692 + 0.488850i
\(836\) 6.57731e9i 0.389337i
\(837\) −6.24365e9 + 1.36649e10i −0.368044 + 0.805503i
\(838\) 3.21977e8 3.21977e8i 0.0189004 0.0189004i
\(839\) 1.27684e10 0.746399 0.373199 0.927751i \(-0.378261\pi\)
0.373199 + 0.927751i \(0.378261\pi\)
\(840\) 7.95707e9 5.98147e9i 0.463208 0.348201i
\(841\) 3.21667e10 1.86475
\(842\) 4.82993e8 4.82993e8i 0.0278836 0.0278836i
\(843\) −6.01005e8 + 7.64142e8i −0.0345527 + 0.0439317i
\(844\) 2.87433e8i 0.0164565i
\(845\) 1.76595e9 6.64545e9i 0.100689 0.378901i
\(846\) −5.15062e9 + 1.24884e9i −0.292458 + 0.0709108i
\(847\) 8.38431e9 + 8.38431e9i 0.474106 + 0.474106i
\(848\) 1.24439e8 + 1.24439e8i 0.00700760 + 0.00700760i
\(849\) −2.68694e9 + 3.21092e8i −0.150689 + 0.0180075i
\(850\) 8.36386e8 1.46257e9i 0.0467133 0.0816865i
\(851\) 2.04691e10i 1.13853i
\(852\) 1.99098e10 + 1.56592e10i 1.10288 + 0.867425i
\(853\) 1.08864e10 1.08864e10i 0.600570 0.600570i −0.339894 0.940464i \(-0.610391\pi\)
0.940464 + 0.339894i \(0.110391\pi\)
\(854\) −7.61863e8 −0.0418576
\(855\) −1.04078e10 2.27567e8i −0.569476 0.0124517i
\(856\) −8.69309e9 −0.473714
\(857\) 1.08166e10 1.08166e10i 0.587028 0.587028i −0.349797 0.936826i \(-0.613749\pi\)
0.936826 + 0.349797i \(0.113749\pi\)
\(858\) −1.74843e9 1.37516e9i −0.0945025 0.0743272i
\(859\) 2.68969e9i 0.144786i −0.997376 0.0723930i \(-0.976936\pi\)
0.997376 0.0723930i \(-0.0230636\pi\)
\(860\) −7.21110e9 1.24307e10i −0.386596 0.666424i
\(861\) −2.73720e10 + 3.27099e9i −1.46149 + 0.174650i
\(862\) 5.05384e9 + 5.05384e9i 0.268749 + 0.268749i
\(863\) −2.24927e10 2.24927e10i −1.19125 1.19125i −0.976716 0.214537i \(-0.931176\pi\)
−0.214537 0.976716i \(-0.568824\pi\)
\(864\) −4.01341e9 1.07666e10i −0.211698 0.567909i
\(865\) −6.11224e9 1.05364e10i −0.321103 0.553526i
\(866\) 7.27487e9i 0.380639i
\(867\) −9.59393e9 + 1.21981e10i −0.499954 + 0.635661i
\(868\) −1.58633e10 + 1.58633e10i −0.823333 + 0.823333i
\(869\) 1.38967e10 0.718359
\(870\) −7.00309e9 9.92595e8i −0.360556 0.0511040i
\(871\) −1.56124e10 −0.800581
\(872\) 5.71844e9 5.71844e9i 0.292059 0.292059i
\(873\) 1.29981e10 2.13187e10i 0.661194 1.08445i
\(874\) 2.55554e9i 0.129477i
\(875\) −1.69115e8 2.73184e10i −0.00853404 1.37857i
\(876\) 5.37168e8 + 4.49508e9i 0.0269989 + 0.225930i
\(877\) −2.81331e10 2.81331e10i −1.40838 1.40838i −0.768361 0.640017i \(-0.778927\pi\)
−0.640017 0.768361i \(-0.721073\pi\)
\(878\) 4.35602e9 + 4.35602e9i 0.217200 + 0.217200i
\(879\) −2.43172e6 2.03489e7i −0.000120768 0.00101060i
\(880\) 3.21222e9 1.20879e10i 0.158897 0.597944i
\(881\) 2.23778e9i 0.110256i 0.998479 + 0.0551280i \(0.0175567\pi\)
−0.998479 + 0.0551280i \(0.982443\pi\)
\(882\) −2.05524e9 + 3.37089e9i −0.100861 + 0.165426i
\(883\) 7.10936e9 7.10936e9i 0.347510 0.347510i −0.511671 0.859181i \(-0.670973\pi\)
0.859181 + 0.511671i \(0.170973\pi\)
\(884\) 6.67996e9 0.325230
\(885\) 2.97979e8 + 3.96397e8i 0.0144505 + 0.0192233i
\(886\) 5.07500e9 0.245142
\(887\) −2.88502e10 + 2.88502e10i −1.38809 + 1.38809i −0.558747 + 0.829338i \(0.688718\pi\)
−0.829338 + 0.558747i \(0.811282\pi\)
\(888\) 5.84345e9 7.42959e9i 0.280042 0.356057i
\(889\) 8.32140e9i 0.397228i
\(890\) 5.37439e9 3.11771e9i 0.255543 0.148242i
\(891\) 6.93062e9 + 1.34518e10i 0.328247 + 0.637101i
\(892\) −9.14847e9 9.14847e9i −0.431590 0.431590i
\(893\) 1.19885e10 + 1.19885e10i 0.563357 + 0.563357i
\(894\) 8.46524e9 1.01161e9i 0.396240 0.0473511i
\(895\) 1.26889e10 + 3.37192e9i 0.591619 + 0.157216i
\(896\) 2.26711e10i 1.05292i
\(897\) −1.39960e10 1.10080e10i −0.647484 0.509253i
\(898\) 4.60070e9 4.60070e9i 0.212010 0.212010i
\(899\) 3.26543e10 1.49893
\(900\) −2.00361e10 5.79614e9i −0.916145 0.265027i
\(901\) −1.10234e8 −0.00502088
\(902\) 2.56582e9 2.56582e9i 0.116414 0.116414i
\(903\) 1.93685e10 + 1.52335e10i 0.875364 + 0.688483i
\(904\) 3.65630e9i 0.164609i
\(905\) −1.13740e10 3.02250e9i −0.510084 0.135549i
\(906\) 1.15756e9 1.38329e8i 0.0517122 0.00617967i
\(907\) 2.32931e10 + 2.32931e10i 1.03658 + 1.03658i 0.999305 + 0.0372739i \(0.0118674\pi\)
0.0372739 + 0.999305i \(0.488133\pi\)
\(908\) −7.10015e9 7.10015e9i −0.314751 0.314751i
\(909\) 1.74645e10 4.23454e9i 0.771230 0.186996i
\(910\) −4.54752e9 + 2.63804e9i −0.200046 + 0.116048i
\(911\) 3.14386e10i 1.37768i −0.724913 0.688840i \(-0.758120\pi\)
0.724913 0.688840i \(-0.241880\pi\)
\(912\) −6.96374e9 + 8.85397e9i −0.303991 + 0.386506i
\(913\) −8.34685e8 + 8.34685e8i −0.0362974 + 0.0362974i
\(914\) −4.45448e9 −0.192968
\(915\) 1.96495e9 + 2.61394e9i 0.0847962 + 0.112803i
\(916\) −2.10081e10 −0.903136
\(917\) −1.69740e10 + 1.69740e10i −0.726927 + 0.726927i
\(918\) 2.00617e9 + 9.16643e8i 0.0855891 + 0.0391067i
\(919\) 2.30372e10i 0.979095i −0.871977 0.489548i \(-0.837162\pi\)
0.871977 0.489548i \(-0.162838\pi\)
\(920\) −2.69382e9 + 1.01371e10i −0.114054 + 0.429197i
\(921\) −4.65738e8 3.89735e9i −0.0196441 0.164385i
\(922\) −3.77932e9 3.77932e9i −0.158802 0.158802i
\(923\) −1.93778e10 1.93778e10i −0.811147 0.811147i
\(924\) 2.68119e9 + 2.24365e10i 0.111809 + 0.935629i
\(925\) −6.81722e9 2.50286e10i −0.283212 1.03978i
\(926\) 3.06250e9i 0.126747i
\(927\) 4.17094e9 + 2.54304e9i 0.171971 + 0.104851i
\(928\) −1.76595e10 + 1.76595e10i −0.725371 + 0.725371i
\(929\) 7.81807e9 0.319923 0.159961 0.987123i \(-0.448863\pi\)
0.159961 + 0.987123i \(0.448863\pi\)
\(930\) −4.62763e9 6.55905e8i −0.188655 0.0267393i
\(931\) 1.26297e10 0.512945
\(932\) 1.21001e10 1.21001e10i 0.489593 0.489593i
\(933\) −2.11150e10 + 2.68464e10i −0.851147 + 1.08218i
\(934\) 6.77576e9i 0.272110i
\(935\) 3.93126e9 + 6.77681e9i 0.157286 + 0.271134i
\(936\) 1.93754e9 + 7.99102e9i 0.0772300 + 0.318520i
\(937\) 2.14206e10 + 2.14206e10i 0.850634 + 0.850634i 0.990211 0.139577i \(-0.0445743\pi\)
−0.139577 + 0.990211i \(0.544574\pi\)
\(938\) −5.44316e9 5.44316e9i −0.215348 0.215348i
\(939\) −3.32301e10 + 3.97104e9i −1.30979 + 0.156522i
\(940\) 1.70452e10 + 2.93829e10i 0.669351 + 1.15385i
\(941\) 1.29439e10i 0.506409i 0.967413 + 0.253204i \(0.0814845\pi\)
−0.967413 + 0.253204i \(0.918515\pi\)
\(942\) −4.35408e9 3.42453e9i −0.169714 0.133482i
\(943\) 2.05391e10 2.05391e10i 0.797608 0.797608i
\(944\) 5.36594e8 0.0207608
\(945\) 3.55957e10 3.46637e9i 1.37210 0.133617i
\(946\) −3.24355e9 −0.124567
\(947\) 1.02474e10 1.02474e10i 0.392094 0.392094i −0.483339 0.875433i \(-0.660576\pi\)
0.875433 + 0.483339i \(0.160576\pi\)
\(948\) −1.97100e10 1.55021e10i −0.751375 0.590964i
\(949\) 4.89781e9i 0.186025i
\(950\) −8.51120e8 3.12478e9i −0.0322076 0.118246i
\(951\) 3.16719e10 3.78483e9i 1.19410 0.142697i
\(952\) 4.77090e9 + 4.77090e9i 0.179213 + 0.179213i
\(953\) 3.48353e10 + 3.48353e10i 1.30375 + 1.30375i 0.925844 + 0.377906i \(0.123356\pi\)
0.377906 + 0.925844i \(0.376644\pi\)
\(954\) −1.56081e7 6.43726e7i −0.000582010 0.00240039i
\(955\) −1.96349e9 + 7.38882e9i −0.0729488 + 0.274513i
\(956\) 4.31459e10i 1.59712i
\(957\) 2.03330e10 2.58521e10i 0.749910 0.953465i
\(958\) 3.93306e9 3.93306e9i 0.144528 0.144528i
\(959\) −3.82455e10 −1.40028
\(960\) −1.60586e10 + 1.20715e10i −0.585812 + 0.440365i
\(961\) −5.93469e9 −0.215708
\(962\) −3.52988e9 + 3.52988e9i −0.127834 + 0.127834i
\(963\) −2.66664e10 1.62586e10i −0.962215 0.586666i
\(964\) 1.95358e10i 0.702362i
\(965\) −8.82985e9 + 5.12224e9i −0.316306 + 0.183491i
\(966\) −1.04175e9 8.71747e9i −0.0371828 0.311150i
\(967\) 5.74773e9 + 5.74773e9i 0.204411 + 0.204411i 0.801887 0.597476i \(-0.203830\pi\)
−0.597476 + 0.801887i \(0.703830\pi\)
\(968\) 4.07954e9 + 4.07954e9i 0.144560 + 0.144560i
\(969\) −8.37234e8 7.00608e9i −0.0295606 0.247367i
\(970\) 7.50720e9 + 1.99495e9i 0.264105 + 0.0701830i
\(971\) 1.77158e9i 0.0621003i −0.999518 0.0310501i \(-0.990115\pi\)
0.999518 0.0310501i \(-0.00988516\pi\)
\(972\) 5.17596e9 2.68103e10i 0.180784 0.936418i
\(973\) −2.89851e10 + 2.89851e10i −1.00874 + 1.00874i
\(974\) −3.60789e8 −0.0125111
\(975\) 2.07797e10 + 8.79863e9i 0.717999 + 0.304018i
\(976\) 3.53843e9 0.121825
\(977\) 1.53673e10 1.53673e10i 0.527190 0.527190i −0.392543 0.919734i \(-0.628405\pi\)
0.919734 + 0.392543i \(0.128405\pi\)
\(978\) −2.23198e9 + 2.83783e9i −0.0762966 + 0.0970065i
\(979\) 2.88918e10i 0.984089i
\(980\) 2.44558e10 + 6.49885e9i 0.830023 + 0.220569i
\(981\) 2.82367e10 6.84640e9i 0.954931 0.231537i
\(982\) 1.06935e9 + 1.06935e9i 0.0360356 + 0.0360356i
\(983\) 9.18416e9 + 9.18416e9i 0.308391 + 0.308391i 0.844285 0.535894i \(-0.180025\pi\)
−0.535894 + 0.844285i \(0.680025\pi\)
\(984\) −1.33184e10 + 1.59156e9i −0.445624 + 0.0532526i
\(985\) 6.70802e9 3.89136e9i 0.223649 0.129740i
\(986\) 4.79405e9i 0.159270i
\(987\) −4.57821e10 3.60081e10i −1.51561 1.19204i
\(988\) 9.07952e9 9.07952e9i 0.299512 0.299512i
\(989\) −2.59642e10 −0.853469
\(990\) −3.40077e9 + 3.25524e9i −0.111392 + 0.106625i
\(991\) −4.39131e10 −1.43330 −0.716648 0.697435i \(-0.754325\pi\)
−0.716648 + 0.697435i \(0.754325\pi\)
\(992\) −1.16694e10 + 1.16694e10i −0.379539 + 0.379539i
\(993\) 2.80676e10 + 2.20755e10i 0.909668 + 0.715463i
\(994\) 1.35119e10i 0.436380i
\(995\) −1.02453e10 + 3.85541e10i −0.329720 + 1.24077i
\(996\) 2.11497e9 2.52741e8i 0.0678259 0.00810528i
\(997\) 1.72444e10 + 1.72444e10i 0.551082 + 0.551082i 0.926753 0.375671i \(-0.122588\pi\)
−0.375671 + 0.926753i \(0.622588\pi\)
\(998\) −1.79224e9 1.79224e9i −0.0570741 0.0570741i
\(999\) 3.18205e10 1.18616e10i 1.00978 0.376413i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 15.8.e.a.2.7 yes 24
3.2 odd 2 inner 15.8.e.a.2.6 24
5.2 odd 4 75.8.e.d.68.7 24
5.3 odd 4 inner 15.8.e.a.8.6 yes 24
5.4 even 2 75.8.e.d.32.6 24
15.2 even 4 75.8.e.d.68.6 24
15.8 even 4 inner 15.8.e.a.8.7 yes 24
15.14 odd 2 75.8.e.d.32.7 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.8.e.a.2.6 24 3.2 odd 2 inner
15.8.e.a.2.7 yes 24 1.1 even 1 trivial
15.8.e.a.8.6 yes 24 5.3 odd 4 inner
15.8.e.a.8.7 yes 24 15.8 even 4 inner
75.8.e.d.32.6 24 5.4 even 2
75.8.e.d.32.7 24 15.14 odd 2
75.8.e.d.68.6 24 15.2 even 4
75.8.e.d.68.7 24 5.2 odd 4