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Properties

Label 74.8.f.b.9.4
Level $74$
Weight $8$
Character 74.9
Analytic conductor $23.116$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [74,8,Mod(7,74)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(74, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("74.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 74 = 2 \cdot 37 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 74.f (of order \(9\), degree \(6\), 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: \(23.1164918858\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.4
Character \(\chi\) \(=\) 74.9
Dual form 74.8.f.b.33.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.38919 - 7.87846i) q^{2} +(-6.48463 + 36.7762i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(381.143 + 319.817i) q^{5} +298.748 q^{6} +(975.665 + 818.680i) q^{7} +(256.000 + 443.405i) q^{8} +(744.672 + 271.038i) q^{9} +O(q^{10})\) \(q+(-1.38919 - 7.87846i) q^{2} +(-6.48463 + 36.7762i) q^{3} +(-60.1403 + 21.8893i) q^{4} +(381.143 + 319.817i) q^{5} +298.748 q^{6} +(975.665 + 818.680i) q^{7} +(256.000 + 443.405i) q^{8} +(744.672 + 271.038i) q^{9} +(1990.19 - 3447.11i) q^{10} +(-2028.02 - 3512.63i) q^{11} +(-415.016 - 2353.67i) q^{12} +(-13017.9 + 4738.13i) q^{13} +(5094.56 - 8824.04i) q^{14} +(-14233.2 + 11943.1i) q^{15} +(3137.72 - 2632.86i) q^{16} +(30986.2 + 11278.0i) q^{17} +(1100.88 - 6243.39i) q^{18} +(2200.99 - 12482.4i) q^{19} +(-29922.6 - 10890.9i) q^{20} +(-36434.7 + 30572.4i) q^{21} +(-24856.8 + 20857.4i) q^{22} +(12781.4 - 22138.0i) q^{23} +(-17966.8 + 6539.38i) q^{24} +(29420.8 + 166854. i) q^{25} +(55413.5 + 95979.0i) q^{26} +(-55631.8 + 96357.1i) q^{27} +(-76597.1 - 27879.1i) q^{28} +(-121149. - 209836. i) q^{29} +(113866. + 95544.6i) q^{30} +80737.7 q^{31} +(-25101.7 - 21062.9i) q^{32} +(142332. - 51804.6i) q^{33} +(45808.1 - 259791. i) q^{34} +(110040. + 624068. i) q^{35} -50717.7 q^{36} +(102099. + 290702. i) q^{37} -101400. q^{38} +(-89834.0 - 509474. i) q^{39} +(-44235.8 + 250874. i) q^{40} +(-48046.9 + 17487.6i) q^{41} +(291478. + 244579. i) q^{42} +187442. q^{43} +(198855. + 166859. i) q^{44} +(197144. + 341463. i) q^{45} +(-192169. - 69943.9i) q^{46} +(-146958. + 254538. i) q^{47} +(76479.5 + 132466. i) q^{48} +(138678. + 786483. i) q^{49} +(1.27368e6 - 463582. i) q^{50} +(-615697. + 1.06642e6i) q^{51} +(679187. - 569906. i) q^{52} +(-431939. + 362440. i) q^{53} +(836428. + 304435. i) q^{54} +(350434. - 1.98741e6i) q^{55} +(-113237. + 642197. i) q^{56} +(444783. + 161888. i) q^{57} +(-1.48489e6 + 1.24597e6i) q^{58} +(-372678. + 312714. i) q^{59} +(594564. - 1.02982e6i) q^{60} +(-1.80650e6 + 657514. i) q^{61} +(-112160. - 636089. i) q^{62} +(504657. + 874091. i) q^{63} +(-131072. + 227023. i) q^{64} +(-6.47702e6 - 2.35744e6i) q^{65} +(-605866. - 1.04939e6i) q^{66} +(1.54203e6 + 1.29392e6i) q^{67} -2.11039e6 q^{68} +(731268. + 613607. i) q^{69} +(4.76383e6 - 1.73389e6i) q^{70} +(926745. - 5.25583e6i) q^{71} +(70456.2 + 399577. i) q^{72} -3.69000e6 q^{73} +(2.14845e6 - 1.20822e6i) q^{74} -6.32703e6 q^{75} +(140863. + 798875. i) q^{76} +(897055. - 5.08745e6i) q^{77} +(-3.88907e6 + 1.41551e6i) q^{78} +(-2.29325e6 - 1.92427e6i) q^{79} +2.03795e6 q^{80} +(-1.85525e6 - 1.55674e6i) q^{81} +(204522. + 354242. i) q^{82} +(7.48542e6 + 2.72447e6i) q^{83} +(1.52199e6 - 2.63616e6i) q^{84} +(8.20326e6 + 1.42085e7i) q^{85} +(-260392. - 1.47676e6i) q^{86} +(8.50258e6 - 3.09469e6i) q^{87} +(1.03835e6 - 1.79847e6i) q^{88} +(5.72181e6 - 4.80117e6i) q^{89} +(2.41634e6 - 2.02755e6i) q^{90} +(-1.65801e7 - 6.03467e6i) q^{91} +(-284091. + 1.61116e6i) q^{92} +(-523554. + 2.96922e6i) q^{93} +(2.20952e6 + 804201. i) q^{94} +(4.83098e6 - 4.05368e6i) q^{95} +(937387. - 786561. i) q^{96} +(-2.72689e6 + 4.72311e6i) q^{97} +(6.00362e6 - 2.18514e6i) q^{98} +(-558151. - 3.16543e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 66 q - 39 q^{3} + 459 q^{5} - 918 q^{7} + 16896 q^{8} + 3237 q^{9} + 4704 q^{10} + 4539 q^{11} - 2496 q^{12} - 10542 q^{13} + 6744 q^{14} - 39894 q^{15} - 78822 q^{17} + 51792 q^{18} + 79461 q^{19} + 29376 q^{20} - 5835 q^{21} + 18168 q^{22} - 199479 q^{23} + 19968 q^{24} + 356301 q^{25} + 186744 q^{26} - 91689 q^{27} - 91584 q^{28} - 38526 q^{29} + 319152 q^{30} + 1917246 q^{31} - 902847 q^{33} - 205776 q^{34} - 1574793 q^{35} + 3079296 q^{36} - 396513 q^{37} - 692880 q^{38} + 2514306 q^{39} + 470016 q^{40} + 2989350 q^{41} + 46680 q^{42} + 6006348 q^{43} - 145344 q^{44} + 1083726 q^{45} - 588744 q^{46} - 894135 q^{47} + 7973742 q^{49} + 2012400 q^{50} - 524880 q^{51} - 2262720 q^{52} + 1457844 q^{53} + 1452312 q^{54} + 2415690 q^{55} - 1202688 q^{56} + 2734338 q^{57} - 3423360 q^{58} + 3099522 q^{59} - 3102912 q^{60} - 10968396 q^{61} - 3067320 q^{62} - 10727970 q^{63} - 8650752 q^{64} - 13497300 q^{65} - 4598712 q^{66} - 1978119 q^{67} + 5026176 q^{68} - 7251108 q^{69} + 435744 q^{70} - 19555002 q^{71} + 3314688 q^{72} - 31332840 q^{73} + 7607472 q^{74} + 44758074 q^{75} + 5085504 q^{76} + 1982007 q^{77} - 22512264 q^{78} + 10522902 q^{79} + 4816896 q^{80} - 7548876 q^{81} - 7150320 q^{82} + 19771926 q^{83} + 3556224 q^{84} - 6684072 q^{85} + 22982496 q^{86} - 67769667 q^{87} - 2323968 q^{88} - 42018963 q^{89} - 25158672 q^{90} + 4847565 q^{91} - 1096704 q^{92} - 14558475 q^{93} + 3175680 q^{94} + 4508415 q^{95} - 2555904 q^{96} - 39286662 q^{97} + 71630904 q^{98} + 66155463 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).

\(n\) \(39\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.38919 − 7.87846i −0.122788 − 0.696364i
\(3\) −6.48463 + 36.7762i −0.138663 + 0.786397i 0.833576 + 0.552406i \(0.186290\pi\)
−0.972239 + 0.233992i \(0.924821\pi\)
\(4\) −60.1403 + 21.8893i −0.469846 + 0.171010i
\(5\) 381.143 + 319.817i 1.36362 + 1.14421i 0.974846 + 0.222878i \(0.0715451\pi\)
0.388772 + 0.921334i \(0.372899\pi\)
\(6\) 298.748 0.564645
\(7\) 975.665 + 818.680i 1.07512 + 0.902134i 0.995507 − 0.0946919i \(-0.0301866\pi\)
0.0796146 + 0.996826i \(0.474631\pi\)
\(8\) 256.000 + 443.405i 0.176777 + 0.306186i
\(9\) 744.672 + 271.038i 0.340499 + 0.123932i
\(10\) 1990.19 − 3447.11i 0.629352 − 1.09007i
\(11\) −2028.02 − 3512.63i −0.459407 − 0.795716i 0.539523 − 0.841971i \(-0.318605\pi\)
−0.998930 + 0.0462548i \(0.985271\pi\)
\(12\) −415.016 − 2353.67i −0.0693315 − 0.393199i
\(13\) −13017.9 + 4738.13i −1.64339 + 0.598144i −0.987626 − 0.156826i \(-0.949874\pi\)
−0.655760 + 0.754970i \(0.727652\pi\)
\(14\) 5094.56 − 8824.04i 0.496202 − 0.859447i
\(15\) −14233.2 + 11943.1i −1.08889 + 0.913686i
\(16\) 3137.72 − 2632.86i 0.191511 − 0.160697i
\(17\) 30986.2 + 11278.0i 1.52967 + 0.556753i 0.963540 − 0.267565i \(-0.0862189\pi\)
0.566127 + 0.824318i \(0.308441\pi\)
\(18\) 1100.88 − 6243.39i 0.0444924 − 0.252329i
\(19\) 2200.99 − 12482.4i 0.0736173 − 0.417505i −0.925620 − 0.378454i \(-0.876456\pi\)
0.999237 − 0.0390502i \(-0.0124332\pi\)
\(20\) −29922.6 − 10890.9i −0.836363 − 0.304411i
\(21\) −36434.7 + 30572.4i −0.858515 + 0.720380i
\(22\) −24856.8 + 20857.4i −0.497699 + 0.417619i
\(23\) 12781.4 − 22138.0i 0.219044 − 0.379395i −0.735472 − 0.677555i \(-0.763040\pi\)
0.954516 + 0.298160i \(0.0963730\pi\)
\(24\) −17966.8 + 6539.38i −0.265296 + 0.0965600i
\(25\) 29420.8 + 166854.i 0.376587 + 2.13573i
\(26\) 55413.5 + 95979.0i 0.618314 + 1.07095i
\(27\) −55631.8 + 96357.1i −0.543939 + 0.942129i
\(28\) −76597.1 − 27879.1i −0.659416 − 0.240008i
\(29\) −121149. − 209836.i −0.922417 − 1.59767i −0.795664 − 0.605738i \(-0.792878\pi\)
−0.126753 − 0.991934i \(-0.540456\pi\)
\(30\) 113866. + 95544.6i 0.769960 + 0.646074i
\(31\) 80737.7 0.486755 0.243378 − 0.969932i \(-0.421745\pi\)
0.243378 + 0.969932i \(0.421745\pi\)
\(32\) −25101.7 − 21062.9i −0.135419 − 0.113630i
\(33\) 142332. − 51804.6i 0.689452 − 0.250940i
\(34\) 45808.1 − 259791.i 0.199879 − 1.13357i
\(35\) 110040. + 624068.i 0.433823 + 2.46033i
\(36\) −50717.7 −0.181176
\(37\) 102099. + 290702.i 0.331373 + 0.943500i
\(38\) −101400. −0.299775
\(39\) −89834.0 − 509474.i −0.242502 − 1.37529i
\(40\) −44235.8 + 250874.i −0.109286 + 0.619791i
\(41\) −48046.9 + 17487.6i −0.108873 + 0.0396266i −0.395882 − 0.918301i \(-0.629561\pi\)
0.287009 + 0.957928i \(0.407339\pi\)
\(42\) 291478. + 244579.i 0.607062 + 0.509385i
\(43\) 187442. 0.359524 0.179762 − 0.983710i \(-0.442467\pi\)
0.179762 + 0.983710i \(0.442467\pi\)
\(44\) 198855. + 166859.i 0.351926 + 0.295301i
\(45\) 197144. + 341463.i 0.322507 + 0.558599i
\(46\) −192169. − 69943.9i −0.291093 − 0.105949i
\(47\) −146958. + 254538.i −0.206467 + 0.357611i −0.950599 − 0.310421i \(-0.899530\pi\)
0.744132 + 0.668032i \(0.232863\pi\)
\(48\) 76479.5 + 132466.i 0.0998161 + 0.172887i
\(49\) 138678. + 786483.i 0.168392 + 0.954999i
\(50\) 1.27368e6 − 463582.i 1.44101 − 0.524483i
\(51\) −615697. + 1.06642e6i −0.649938 + 1.12572i
\(52\) 679187. − 569906.i 0.669850 − 0.562071i
\(53\) −431939. + 362440.i −0.398526 + 0.334403i −0.819924 − 0.572473i \(-0.805984\pi\)
0.421397 + 0.906876i \(0.361540\pi\)
\(54\) 836428. + 304435.i 0.722854 + 0.263097i
\(55\) 350434. − 1.98741e6i 0.284012 − 1.61071i
\(56\) −113237. + 642197.i −0.0861646 + 0.488664i
\(57\) 444783. + 161888.i 0.318117 + 0.115785i
\(58\) −1.48489e6 + 1.24597e6i −0.999301 + 0.838513i
\(59\) −372678. + 312714.i −0.236239 + 0.198228i −0.753220 − 0.657769i \(-0.771500\pi\)
0.516981 + 0.855997i \(0.327056\pi\)
\(60\) 594564. − 1.02982e6i 0.355361 − 0.615503i
\(61\) −1.80650e6 + 657514.i −1.01902 + 0.370895i −0.796892 − 0.604122i \(-0.793524\pi\)
−0.222132 + 0.975017i \(0.571302\pi\)
\(62\) −112160. − 636089.i −0.0597676 − 0.338959i
\(63\) 504657. + 874091.i 0.254275 + 0.440418i
\(64\) −131072. + 227023.i −0.0625000 + 0.108253i
\(65\) −6.47702e6 − 2.35744e6i −2.92535 − 1.06474i
\(66\) −605866. − 1.04939e6i −0.259402 − 0.449297i
\(67\) 1.54203e6 + 1.29392e6i 0.626372 + 0.525588i 0.899799 − 0.436304i \(-0.143713\pi\)
−0.273428 + 0.961893i \(0.588157\pi\)
\(68\) −2.11039e6 −0.813919
\(69\) 731268. + 613607.i 0.267982 + 0.224863i
\(70\) 4.76383e6 − 1.73389e6i 1.66002 − 0.604198i
\(71\) 926745. − 5.25583e6i 0.307295 − 1.74276i −0.305203 − 0.952287i \(-0.598724\pi\)
0.612498 − 0.790472i \(-0.290165\pi\)
\(72\) 70456.2 + 399577.i 0.0222462 + 0.126164i
\(73\) −3.69000e6 −1.11019 −0.555094 − 0.831788i \(-0.687318\pi\)
−0.555094 + 0.831788i \(0.687318\pi\)
\(74\) 2.14845e6 − 1.20822e6i 0.616331 − 0.346606i
\(75\) −6.32703e6 −1.73175
\(76\) 140863. + 798875.i 0.0368087 + 0.208752i
\(77\) 897055. − 5.08745e6i 0.223924 − 1.26994i
\(78\) −3.88907e6 + 1.41551e6i −0.927930 + 0.337739i
\(79\) −2.29325e6 − 1.92427e6i −0.523307 − 0.439107i 0.342476 − 0.939527i \(-0.388735\pi\)
−0.865783 + 0.500420i \(0.833179\pi\)
\(80\) 2.03795e6 0.445019
\(81\) −1.85525e6 − 1.55674e6i −0.387886 − 0.325475i
\(82\) 204522. + 354242.i 0.0409629 + 0.0709498i
\(83\) 7.48542e6 + 2.72447e6i 1.43695 + 0.523009i 0.938916 − 0.344146i \(-0.111832\pi\)
0.498039 + 0.867155i \(0.334054\pi\)
\(84\) 1.52199e6 − 2.63616e6i 0.280178 − 0.485283i
\(85\) 8.20326e6 + 1.42085e7i 1.44884 + 2.50946i
\(86\) −260392. − 1.47676e6i −0.0441452 − 0.250360i
\(87\) 8.50258e6 − 3.09469e6i 1.38431 − 0.503848i
\(88\) 1.03835e6 − 1.79847e6i 0.162425 − 0.281328i
\(89\) 5.72181e6 − 4.80117e6i 0.860337 − 0.721908i −0.101704 − 0.994815i \(-0.532429\pi\)
0.962041 + 0.272906i \(0.0879849\pi\)
\(90\) 2.41634e6 − 2.02755e6i 0.349388 − 0.293172i
\(91\) −1.65801e7 − 6.03467e6i −2.30644 − 0.839477i
\(92\) −284091. + 1.61116e6i −0.0380365 + 0.215716i
\(93\) −523554. + 2.96922e6i −0.0674950 + 0.382783i
\(94\) 2.20952e6 + 804201.i 0.274379 + 0.0998658i
\(95\) 4.83098e6 − 4.05368e6i 0.578100 − 0.485083i
\(96\) 937387. − 786561.i 0.108136 − 0.0907367i
\(97\) −2.72689e6 + 4.72311e6i −0.303365 + 0.525444i −0.976896 − 0.213715i \(-0.931444\pi\)
0.673531 + 0.739159i \(0.264777\pi\)
\(98\) 6.00362e6 − 2.18514e6i 0.644351 − 0.234524i
\(99\) −558151. − 3.16543e6i −0.0578134 − 0.327876i
\(100\) −5.42169e6 − 9.39064e6i −0.542169 − 0.939064i
\(101\) 5.34977e6 − 9.26607e6i 0.516666 − 0.894892i −0.483146 − 0.875540i \(-0.660506\pi\)
0.999813 − 0.0193528i \(-0.00616056\pi\)
\(102\) 9.25706e6 + 3.36929e6i 0.863719 + 0.314368i
\(103\) 6.58526e6 + 1.14060e7i 0.593804 + 1.02850i 0.993715 + 0.111944i \(0.0357077\pi\)
−0.399911 + 0.916554i \(0.630959\pi\)
\(104\) −5.43350e6 − 4.55925e6i −0.473656 − 0.397444i
\(105\) −2.36644e7 −1.99495
\(106\) 3.45551e6 + 2.89952e6i 0.281801 + 0.236459i
\(107\) −1.25499e7 + 4.56779e6i −0.990368 + 0.360465i −0.785863 − 0.618401i \(-0.787781\pi\)
−0.204505 + 0.978865i \(0.565559\pi\)
\(108\) 1.23653e6 − 7.01269e6i 0.0944539 − 0.535675i
\(109\) −1.48168e6 − 8.40303e6i −0.109588 − 0.621503i −0.989288 − 0.145975i \(-0.953368\pi\)
0.879701 − 0.475528i \(-0.157743\pi\)
\(110\) −1.61445e7 −1.15652
\(111\) −1.13530e7 + 1.86973e6i −0.787915 + 0.129762i
\(112\) 5.21683e6 0.350868
\(113\) −401689. − 2.27809e6i −0.0261888 − 0.148524i 0.968909 − 0.247416i \(-0.0795814\pi\)
−0.995098 + 0.0988917i \(0.968470\pi\)
\(114\) 657541. − 3.72910e6i 0.0415677 − 0.235742i
\(115\) 1.19516e7 − 4.35004e6i 0.732800 − 0.266717i
\(116\) 1.18791e7 + 9.96776e6i 0.706612 + 0.592918i
\(117\) −1.09783e7 −0.633701
\(118\) 2.98142e6 + 2.50171e6i 0.167046 + 0.140168i
\(119\) 2.09990e7 + 3.63714e7i 1.14231 + 1.97854i
\(120\) −8.93932e6 − 3.25365e6i −0.472248 − 0.171884i
\(121\) 1.51786e6 − 2.62902e6i 0.0778904 − 0.134910i
\(122\) 7.68977e6 + 1.33191e7i 0.383401 + 0.664071i
\(123\) −331562. − 1.88038e6i −0.0160656 − 0.0911124i
\(124\) −4.85559e6 + 1.76729e6i −0.228700 + 0.0832400i
\(125\) −2.27137e7 + 3.93413e7i −1.04017 + 1.80162i
\(126\) 6.18543e6 − 5.19019e6i 0.275469 − 0.231146i
\(127\) 2.70072e7 − 2.26617e7i 1.16995 − 0.981702i 0.169954 − 0.985452i \(-0.445638\pi\)
0.999993 + 0.00374955i \(0.00119352\pi\)
\(128\) 1.97068e6 + 717268.i 0.0830579 + 0.0302306i
\(129\) −1.21550e6 + 6.89342e6i −0.0498528 + 0.282729i
\(130\) −9.57524e6 + 5.43039e7i −0.382250 + 2.16785i
\(131\) 2.05762e7 + 7.48911e6i 0.799678 + 0.291059i 0.709353 − 0.704853i \(-0.248987\pi\)
0.0903249 + 0.995912i \(0.471209\pi\)
\(132\) −7.42593e6 + 6.23110e6i −0.281023 + 0.235806i
\(133\) 1.23665e7 − 1.03768e7i 0.455793 − 0.382455i
\(134\) 8.05193e6 − 1.39463e7i 0.289090 − 0.500719i
\(135\) −5.20203e7 + 1.89338e7i −1.81972 + 0.662324i
\(136\) 2.93172e6 + 1.66266e7i 0.0999393 + 0.566784i
\(137\) −3.72528e6 − 6.45237e6i −0.123776 − 0.214386i 0.797478 − 0.603348i \(-0.206167\pi\)
−0.921254 + 0.388962i \(0.872834\pi\)
\(138\) 3.81841e6 − 6.61368e6i 0.123682 − 0.214223i
\(139\) 2.93807e7 + 1.06937e7i 0.927920 + 0.337735i 0.761385 − 0.648300i \(-0.224520\pi\)
0.166535 + 0.986036i \(0.446742\pi\)
\(140\) −2.02783e7 − 3.51230e7i −0.624572 − 1.08179i
\(141\) −8.40798e6 − 7.05513e6i −0.252595 − 0.211952i
\(142\) −4.26953e7 −1.25133
\(143\) 4.30439e7 + 3.61181e7i 1.23094 + 1.03288i
\(144\) 3.05018e6 − 1.11017e6i 0.0851248 − 0.0309829i
\(145\) 2.09341e7 − 1.18723e8i 0.570251 − 3.23406i
\(146\) 5.12609e6 + 2.90715e7i 0.136317 + 0.773095i
\(147\) −2.98231e7 −0.774358
\(148\) −1.25035e7 − 1.52480e7i −0.317042 − 0.386632i
\(149\) −1.30335e7 −0.322782 −0.161391 − 0.986891i \(-0.551598\pi\)
−0.161391 + 0.986891i \(0.551598\pi\)
\(150\) 8.78941e6 + 4.98472e7i 0.212638 + 1.20593i
\(151\) −387298. + 2.19647e6i −0.00915431 + 0.0519167i −0.989043 − 0.147630i \(-0.952836\pi\)
0.979888 + 0.199546i \(0.0639468\pi\)
\(152\) 6.09822e6 − 2.21957e6i 0.140848 − 0.0512645i
\(153\) 2.00178e7 + 1.67969e7i 0.451851 + 0.379148i
\(154\) −4.13274e7 −0.911835
\(155\) 3.07726e7 + 2.58213e7i 0.663748 + 0.556951i
\(156\) 1.65547e7 + 2.86735e7i 0.349128 + 0.604707i
\(157\) −1.23763e7 − 4.50461e6i −0.255236 − 0.0928984i 0.211233 − 0.977436i \(-0.432252\pi\)
−0.466469 + 0.884537i \(0.654474\pi\)
\(158\) −1.19745e7 + 2.07405e7i −0.241523 + 0.418330i
\(159\) −1.05282e7 − 1.82353e7i −0.207713 − 0.359769i
\(160\) −2.83109e6 − 1.60559e7i −0.0546430 − 0.309896i
\(161\) 3.05943e7 − 1.11354e7i 0.577763 − 0.210289i
\(162\) −9.68741e6 + 1.67791e7i −0.179021 + 0.310074i
\(163\) −3.89187e7 + 3.26567e7i −0.703885 + 0.590629i −0.922876 − 0.385097i \(-0.874168\pi\)
0.218991 + 0.975727i \(0.429723\pi\)
\(164\) 2.50676e6 − 2.10342e6i 0.0443772 − 0.0372369i
\(165\) 7.08169e7 + 2.57752e7i 1.22728 + 0.446693i
\(166\) 1.10660e7 − 6.27584e7i 0.187764 − 1.06486i
\(167\) 6.64783e6 − 3.77017e7i 0.110452 − 0.626403i −0.878450 − 0.477834i \(-0.841422\pi\)
0.988902 − 0.148569i \(-0.0474667\pi\)
\(168\) −2.28832e7 − 8.32881e6i −0.372336 − 0.135519i
\(169\) 9.89480e7 − 8.30272e7i 1.57690 − 1.32317i
\(170\) 1.00545e8 − 8.43672e7i 1.56960 − 1.31705i
\(171\) 5.02223e6 − 8.69876e6i 0.0768087 − 0.133037i
\(172\) −1.12729e7 + 4.10298e6i −0.168921 + 0.0614823i
\(173\) 1.22240e7 + 6.93258e7i 0.179495 + 1.01797i 0.932827 + 0.360326i \(0.117334\pi\)
−0.753332 + 0.657641i \(0.771554\pi\)
\(174\) −3.61930e7 − 6.26882e7i −0.520838 − 0.902118i
\(175\) −1.07895e8 + 1.86880e8i −1.52184 + 2.63590i
\(176\) −1.56116e7 − 5.68216e6i −0.215851 − 0.0785632i
\(177\) −9.08373e6 − 1.57335e7i −0.123128 − 0.213265i
\(178\) −4.57745e7 − 3.84094e7i −0.608350 − 0.510466i
\(179\) 1.32552e8 1.72743 0.863714 − 0.503983i \(-0.168132\pi\)
0.863714 + 0.503983i \(0.168132\pi\)
\(180\) −1.93307e7 − 1.62204e7i −0.247055 − 0.207304i
\(181\) 5.18477e6 − 1.88710e6i 0.0649912 − 0.0236549i −0.309320 − 0.950958i \(-0.600101\pi\)
0.374311 + 0.927303i \(0.377879\pi\)
\(182\) −2.45111e7 + 1.39009e8i −0.301379 + 1.70920i
\(183\) −1.24663e7 − 7.07000e7i −0.150369 − 0.852787i
\(184\) 1.30881e7 0.154887
\(185\) −5.40569e7 + 1.43452e8i −0.627698 + 1.66573i
\(186\) 2.41202e7 0.274844
\(187\) −2.32249e7 − 1.31715e8i −0.259722 − 1.47296i
\(188\) 3.26643e6 − 1.85248e7i 0.0358526 − 0.203330i
\(189\) −1.33164e8 + 4.84676e7i −1.43473 + 0.522198i
\(190\) −3.86479e7 − 3.24294e7i −0.408778 − 0.343006i
\(191\) −3.72119e7 −0.386425 −0.193213 − 0.981157i \(-0.561891\pi\)
−0.193213 + 0.981157i \(0.561891\pi\)
\(192\) −7.49909e6 − 6.29249e6i −0.0764636 − 0.0641605i
\(193\) −4.30425e7 − 7.45518e7i −0.430970 − 0.746462i 0.565987 − 0.824414i \(-0.308495\pi\)
−0.996957 + 0.0779521i \(0.975162\pi\)
\(194\) 4.09990e7 + 1.49224e7i 0.403150 + 0.146735i
\(195\) 1.28699e8 − 2.22913e8i 1.24295 − 2.15285i
\(196\) −2.55557e7 − 4.42638e7i −0.242433 − 0.419906i
\(197\) 1.80573e7 + 1.02408e8i 0.168275 + 0.954337i 0.945623 + 0.325266i \(0.105454\pi\)
−0.777347 + 0.629072i \(0.783435\pi\)
\(198\) −2.41633e7 + 8.79474e6i −0.221222 + 0.0805183i
\(199\) 8.35696e7 − 1.44747e8i 0.751731 − 1.30204i −0.195252 − 0.980753i \(-0.562552\pi\)
0.946983 − 0.321283i \(-0.104114\pi\)
\(200\) −6.64521e7 + 5.57599e7i −0.587359 + 0.492853i
\(201\) −5.75849e7 + 4.83195e7i −0.500176 + 0.419697i
\(202\) −8.04342e7 − 2.92757e7i −0.686611 − 0.249906i
\(203\) 5.35879e7 − 3.03912e8i 0.449605 − 2.54984i
\(204\) 1.36851e7 − 7.76120e7i 0.112860 − 0.640064i
\(205\) −2.39056e7 − 8.70091e6i −0.193803 − 0.0705385i
\(206\) 8.07137e7 − 6.77268e7i 0.643297 − 0.539791i
\(207\) 1.55182e7 − 1.30213e7i 0.121603 − 0.102037i
\(208\) −2.83717e7 + 4.91412e7i −0.218607 + 0.378638i
\(209\) −4.83098e7 + 1.75833e7i −0.366036 + 0.133226i
\(210\) 3.28742e7 + 1.86439e8i 0.244956 + 1.38921i
\(211\) −9.79913e7 − 1.69726e8i −0.718123 − 1.24383i −0.961743 − 0.273955i \(-0.911668\pi\)
0.243619 − 0.969871i \(-0.421665\pi\)
\(212\) 1.80434e7 − 3.12521e7i 0.130060 − 0.225270i
\(213\) 1.87280e8 + 6.81643e7i 1.32789 + 0.483313i
\(214\) 5.34213e7 + 9.25283e7i 0.372620 + 0.645396i
\(215\) 7.14424e7 + 5.99473e7i 0.490254 + 0.411372i
\(216\) −5.69670e7 −0.384623
\(217\) 7.87729e7 + 6.60983e7i 0.523321 + 0.439118i
\(218\) −6.41446e7 + 2.33467e7i −0.419336 + 0.152626i
\(219\) 2.39283e7 − 1.35704e8i 0.153942 − 0.873048i
\(220\) 2.24278e7 + 1.27194e8i 0.142006 + 0.805356i
\(221\) −4.56812e8 −2.84685
\(222\) 3.05020e7 + 8.68466e7i 0.187108 + 0.532743i
\(223\) 1.77763e8 1.07343 0.536716 − 0.843763i \(-0.319665\pi\)
0.536716 + 0.843763i \(0.319665\pi\)
\(224\) −7.24714e6 − 4.11006e7i −0.0430823 − 0.244332i
\(225\) −2.33149e7 + 1.32226e8i −0.136457 + 0.773885i
\(226\) −1.73899e7 + 6.32939e6i −0.100211 + 0.0364739i
\(227\) −1.90067e8 − 1.59485e8i −1.07849 − 0.904960i −0.0826951 − 0.996575i \(-0.526353\pi\)
−0.995795 + 0.0916146i \(0.970797\pi\)
\(228\) −3.02930e7 −0.169266
\(229\) 5.23607e7 + 4.39358e7i 0.288125 + 0.241766i 0.775381 − 0.631493i \(-0.217558\pi\)
−0.487256 + 0.873259i \(0.662002\pi\)
\(230\) −5.08747e7 − 8.81176e7i −0.275711 − 0.477546i
\(231\) 1.81280e8 + 6.59804e7i 0.967626 + 0.352187i
\(232\) 6.20283e7 − 1.07436e8i 0.326124 − 0.564863i
\(233\) 1.83931e7 + 3.18577e7i 0.0952595 + 0.164994i 0.909717 − 0.415229i \(-0.136299\pi\)
−0.814457 + 0.580223i \(0.802965\pi\)
\(234\) 1.52509e7 + 8.64921e7i 0.0778107 + 0.441287i
\(235\) −1.37418e8 + 5.00159e7i −0.690725 + 0.251403i
\(236\) 1.55679e7 − 2.69644e7i 0.0770970 − 0.133536i
\(237\) 8.56380e7 − 7.18588e7i 0.417876 − 0.350640i
\(238\) 2.57379e8 − 2.15967e8i 1.23752 − 1.03841i
\(239\) 1.79454e8 + 6.53160e7i 0.850279 + 0.309476i 0.730154 − 0.683283i \(-0.239448\pi\)
0.120125 + 0.992759i \(0.461671\pi\)
\(240\) −1.32154e7 + 7.49480e7i −0.0617077 + 0.349962i
\(241\) 6.19162e6 − 3.51144e7i 0.0284934 − 0.161594i −0.967241 − 0.253860i \(-0.918300\pi\)
0.995734 + 0.0922657i \(0.0294109\pi\)
\(242\) −2.28212e7 − 8.30624e6i −0.103511 − 0.0376748i
\(243\) −1.17123e8 + 9.82777e7i −0.523624 + 0.439373i
\(244\) 9.42512e7 − 7.90862e7i 0.415358 − 0.348527i
\(245\) −1.98674e8 + 3.44114e8i −0.863098 + 1.49493i
\(246\) −1.43539e7 + 5.22439e6i −0.0614748 + 0.0223750i
\(247\) 3.04911e7 + 1.72924e8i 0.128746 + 0.730155i
\(248\) 2.06689e7 + 3.57995e7i 0.0860470 + 0.149038i
\(249\) −1.48736e8 + 2.57618e8i −0.610545 + 1.05750i
\(250\) 3.41503e8 + 1.24297e8i 1.38230 + 0.503118i
\(251\) −3.60066e7 − 6.23652e7i −0.143722 − 0.248934i 0.785173 − 0.619276i \(-0.212574\pi\)
−0.928895 + 0.370342i \(0.879240\pi\)
\(252\) −4.94834e7 − 4.15215e7i −0.194786 − 0.163445i
\(253\) −1.03684e8 −0.402521
\(254\) −2.16057e8 − 1.81294e8i −0.827278 − 0.694168i
\(255\) −5.75728e8 + 2.09548e8i −2.17433 + 0.791393i
\(256\) 2.91333e6 − 1.65223e7i 0.0108530 − 0.0615505i
\(257\) 9.03795e7 + 5.12568e8i 0.332127 + 1.88358i 0.453941 + 0.891032i \(0.350018\pi\)
−0.121814 + 0.992553i \(0.538871\pi\)
\(258\) 5.59981e7 0.203004
\(259\) −1.38377e8 + 3.67214e8i −0.494897 + 1.31332i
\(260\) 4.41133e8 1.55655
\(261\) −3.33426e7 − 1.89095e8i −0.116080 − 0.658323i
\(262\) 3.04186e7 − 1.72512e8i 0.104492 − 0.592606i
\(263\) 8.79412e7 − 3.20080e7i 0.298090 − 0.108496i −0.188646 − 0.982045i \(-0.560410\pi\)
0.486736 + 0.873549i \(0.338188\pi\)
\(264\) 5.94074e7 + 4.98488e7i 0.198713 + 0.166740i
\(265\) −2.80545e8 −0.926066
\(266\) −9.89323e7 − 8.30141e7i −0.322294 − 0.270437i
\(267\) 1.39465e8 + 2.41560e8i 0.448410 + 0.776669i
\(268\) −1.21061e8 − 4.40627e7i −0.384179 − 0.139830i
\(269\) 1.07705e8 − 1.86550e8i 0.337367 − 0.584336i −0.646570 − 0.762855i \(-0.723797\pi\)
0.983937 + 0.178519i \(0.0571304\pi\)
\(270\) 2.21435e8 + 3.83537e8i 0.684658 + 1.18586i
\(271\) −6.41037e6 − 3.63550e7i −0.0195655 − 0.110961i 0.973461 − 0.228853i \(-0.0734975\pi\)
−0.993026 + 0.117892i \(0.962386\pi\)
\(272\) 1.26919e8 − 4.61949e7i 0.382417 − 0.139188i
\(273\) 3.29448e8 − 5.70621e8i 0.979981 − 1.69738i
\(274\) −4.56597e7 + 3.83130e7i −0.134093 + 0.112517i
\(275\) 5.26430e8 − 4.41727e8i 1.52643 − 1.28082i
\(276\) −5.74101e7 − 2.08956e7i −0.164364 − 0.0598236i
\(277\) 1.52576e7 − 8.65304e7i 0.0431329 − 0.244619i −0.955617 − 0.294613i \(-0.904809\pi\)
0.998749 + 0.0499944i \(0.0159204\pi\)
\(278\) 4.34347e7 − 2.46330e8i 0.121249 − 0.687640i
\(279\) 6.01231e7 + 2.18830e7i 0.165740 + 0.0603244i
\(280\) −2.48545e8 + 2.08554e8i −0.676630 + 0.567760i
\(281\) −1.84618e8 + 1.54913e8i −0.496365 + 0.416499i −0.856301 − 0.516478i \(-0.827243\pi\)
0.359936 + 0.932977i \(0.382799\pi\)
\(282\) −4.39034e7 + 7.60428e7i −0.116580 + 0.201923i
\(283\) 2.80440e8 − 1.02072e8i 0.735508 − 0.267703i 0.0530136 − 0.998594i \(-0.483117\pi\)
0.682495 + 0.730891i \(0.260895\pi\)
\(284\) 5.93117e7 + 3.36373e8i 0.153648 + 0.871380i
\(285\) 1.17751e8 + 2.03952e8i 0.301307 + 0.521879i
\(286\) 2.24759e8 − 3.89294e8i 0.568115 − 0.984004i
\(287\) −6.11944e7 − 2.22729e7i −0.152801 − 0.0556149i
\(288\) −1.29837e7 − 2.24885e7i −0.0320277 − 0.0554736i
\(289\) 5.18612e8 + 4.35167e8i 1.26386 + 1.06051i
\(290\) −9.64438e8 −2.32210
\(291\) −1.56015e8 − 1.30912e8i −0.371142 − 0.311426i
\(292\) 2.21918e8 − 8.07715e7i 0.521618 − 0.189853i
\(293\) −4.90121e7 + 2.77962e8i −0.113833 + 0.645577i 0.873489 + 0.486844i \(0.161852\pi\)
−0.987322 + 0.158733i \(0.949259\pi\)
\(294\) 4.14298e7 + 2.34960e8i 0.0950817 + 0.539235i
\(295\) −2.42055e8 −0.548954
\(296\) −1.02761e8 + 1.19691e8i −0.230308 + 0.268251i
\(297\) 4.51289e8 0.999557
\(298\) 1.81060e7 + 1.02684e8i 0.0396337 + 0.224774i
\(299\) −6.14941e7 + 3.48751e8i −0.133041 + 0.754511i
\(300\) 3.80509e8 − 1.38494e8i 0.813656 − 0.296147i
\(301\) 1.82881e8 + 1.53455e8i 0.386532 + 0.324339i
\(302\) 1.78429e7 0.0372769
\(303\) 3.06079e8 + 2.56831e8i 0.632098 + 0.530394i
\(304\) −2.59584e7 − 4.49612e7i −0.0529932 − 0.0917869i
\(305\) −8.98820e8 − 3.27144e8i −1.81394 − 0.660221i
\(306\) 1.04525e8 − 1.81043e8i 0.208543 − 0.361208i
\(307\) −1.77748e8 − 3.07868e8i −0.350606 − 0.607268i 0.635750 − 0.771895i \(-0.280691\pi\)
−0.986356 + 0.164628i \(0.947358\pi\)
\(308\) 5.74115e7 + 3.25597e8i 0.111962 + 0.634969i
\(309\) −4.62172e8 + 1.68217e8i −0.891147 + 0.324351i
\(310\) 1.60683e8 − 2.78311e8i 0.306341 − 0.530597i
\(311\) 7.05035e8 − 5.91595e8i 1.32908 − 1.11523i 0.344782 − 0.938683i \(-0.387953\pi\)
0.984293 − 0.176544i \(-0.0564917\pi\)
\(312\) 2.02906e8 − 1.70258e8i 0.378228 − 0.317371i
\(313\) −9.06587e8 − 3.29971e8i −1.67111 − 0.608234i −0.679059 − 0.734084i \(-0.737612\pi\)
−0.992049 + 0.125850i \(0.959834\pi\)
\(314\) −1.82964e7 + 1.03764e8i −0.0333512 + 0.189144i
\(315\) −8.72027e7 + 4.94551e8i −0.157197 + 0.891506i
\(316\) 1.80038e8 + 6.55284e7i 0.320966 + 0.116822i
\(317\) 2.62773e8 − 2.20493e8i 0.463312 − 0.388765i −0.381036 − 0.924560i \(-0.624433\pi\)
0.844348 + 0.535795i \(0.179988\pi\)
\(318\) −1.29041e8 + 1.08278e8i −0.225026 + 0.188819i
\(319\) −4.91385e8 + 8.51104e8i −0.847529 + 1.46796i
\(320\) −1.22563e8 + 4.46093e7i −0.209091 + 0.0761028i
\(321\) −8.66043e7 − 4.91157e8i −0.146141 − 0.828806i
\(322\) −1.30231e8 − 2.25567e8i −0.217380 − 0.376513i
\(323\) 2.08978e8 − 3.61960e8i 0.345057 − 0.597656i
\(324\) 1.45651e8 + 5.30126e7i 0.237906 + 0.0865908i
\(325\) −1.17357e9 − 2.03269e9i −1.89635 − 3.28457i
\(326\) 3.11349e8 + 2.61253e8i 0.497722 + 0.417638i
\(327\) 3.18639e8 0.503944
\(328\) −2.00541e7 − 1.68274e7i −0.0313794 − 0.0263304i
\(329\) −3.51767e8 + 1.28033e8i −0.544590 + 0.198214i
\(330\) 1.04691e8 − 5.93735e8i 0.160366 − 0.909481i
\(331\) −9.34899e7 − 5.30208e8i −0.141699 − 0.803615i −0.969959 − 0.243270i \(-0.921780\pi\)
0.828259 − 0.560345i \(-0.189331\pi\)
\(332\) −5.09813e8 −0.764588
\(333\) −2.76088e6 + 2.44150e8i −0.00409725 + 0.362329i
\(334\) −3.06267e8 −0.449766
\(335\) 1.73918e8 + 9.86337e8i 0.252748 + 1.43340i
\(336\) −3.38292e7 + 1.91855e8i −0.0486524 + 0.275921i
\(337\) −8.60675e8 + 3.13260e8i −1.22500 + 0.445862i −0.871881 − 0.489718i \(-0.837100\pi\)
−0.353115 + 0.935580i \(0.614878\pi\)
\(338\) −7.91584e8 − 6.64218e8i −1.11503 − 0.935625i
\(339\) 8.63843e7 0.120430
\(340\) −8.04360e8 − 6.74938e8i −1.10987 − 0.931296i
\(341\) −1.63738e8 − 2.83602e8i −0.223619 − 0.387319i
\(342\) −7.55097e7 − 2.74833e7i −0.102073 − 0.0371516i
\(343\) 1.58744e7 − 2.74953e7i 0.0212407 − 0.0367899i
\(344\) 4.79853e7 + 8.31129e7i 0.0635555 + 0.110081i
\(345\) 8.24759e7 + 4.67744e8i 0.108133 + 0.613255i
\(346\) 5.29199e8 − 1.92613e8i 0.686836 − 0.249988i
\(347\) −3.91239e8 + 6.77645e8i −0.502677 + 0.870661i 0.497319 + 0.867568i \(0.334318\pi\)
−0.999995 + 0.00309346i \(0.999015\pi\)
\(348\) −4.43608e8 + 3.72231e8i −0.564250 + 0.473462i
\(349\) 7.19110e8 − 6.03405e8i 0.905538 − 0.759836i −0.0657271 − 0.997838i \(-0.520937\pi\)
0.971265 + 0.238001i \(0.0764922\pi\)
\(350\) 1.62221e9 + 5.90436e8i 2.02241 + 0.736097i
\(351\) 2.67657e8 − 1.51796e9i 0.330372 − 1.87364i
\(352\) −2.30793e7 + 1.30889e8i −0.0282048 + 0.159957i
\(353\) 1.19513e9 + 4.34990e8i 1.44611 + 0.526342i 0.941502 − 0.337006i \(-0.109414\pi\)
0.504609 + 0.863348i \(0.331636\pi\)
\(354\) −1.11337e8 + 9.34226e7i −0.133391 + 0.111928i
\(355\) 2.03413e9 − 1.70684e9i 2.41312 − 2.02485i
\(356\) −2.39017e8 + 4.13990e8i −0.280773 + 0.486312i
\(357\) −1.47377e9 + 5.36408e8i −1.71432 + 0.623960i
\(358\) −1.84139e8 − 1.04430e9i −0.212107 − 1.20292i
\(359\) 6.91288e8 + 1.19735e9i 0.788548 + 1.36581i 0.926856 + 0.375416i \(0.122500\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(360\) −1.00938e8 + 1.74829e8i −0.114024 + 0.197495i
\(361\) 6.88998e8 + 2.50775e8i 0.770802 + 0.280549i
\(362\) −2.20701e7 − 3.82265e7i −0.0244525 − 0.0423530i
\(363\) 8.68424e7 + 7.28694e7i 0.0952925 + 0.0799599i
\(364\) 1.12923e9 1.22723
\(365\) −1.40642e9 − 1.18012e9i −1.51387 − 1.27029i
\(366\) −5.39689e8 + 1.96431e8i −0.575387 + 0.209424i
\(367\) 1.81444e8 − 1.02902e9i 0.191607 − 1.08666i −0.725561 − 0.688157i \(-0.758420\pi\)
0.917168 − 0.398500i \(-0.130469\pi\)
\(368\) −1.81819e7 − 1.03114e8i −0.0190183 − 0.107858i
\(369\) −4.05190e7 −0.0419823
\(370\) 1.20528e9 + 2.26604e8i 1.23703 + 0.232574i
\(371\) −7.18150e8 −0.730140
\(372\) −3.35075e7 − 1.90030e8i −0.0337475 − 0.191391i
\(373\) −1.45831e8 + 8.27051e8i −0.145502 + 0.825185i 0.821460 + 0.570266i \(0.193160\pi\)
−0.966962 + 0.254919i \(0.917951\pi\)
\(374\) −1.00545e9 + 3.65954e8i −0.993824 + 0.361722i
\(375\) −1.29953e9 − 1.09044e9i −1.27256 − 1.06780i
\(376\) −1.50485e8 −0.145994
\(377\) 2.57134e9 + 2.15761e9i 2.47152 + 2.07386i
\(378\) 5.66839e8 + 9.81794e8i 0.539807 + 0.934973i
\(379\) 1.96795e8 + 7.16274e7i 0.185685 + 0.0675837i 0.433189 − 0.901303i \(-0.357388\pi\)
−0.247504 + 0.968887i \(0.579610\pi\)
\(380\) −2.01805e8 + 3.49536e8i −0.188664 + 0.326775i
\(381\) 6.58279e8 + 1.14017e9i 0.609780 + 1.05617i
\(382\) 5.16943e7 + 2.93173e8i 0.0474483 + 0.269093i
\(383\) 1.85008e9 − 6.73373e8i 1.68265 − 0.612435i 0.688983 − 0.724778i \(-0.258058\pi\)
0.993670 + 0.112343i \(0.0358354\pi\)
\(384\) −3.91575e7 + 6.78228e7i −0.0352903 + 0.0611246i
\(385\) 1.96896e9 − 1.65215e9i 1.75843 − 1.47549i
\(386\) −5.27560e8 + 4.42675e8i −0.466892 + 0.391769i
\(387\) 1.39583e8 + 5.08041e7i 0.122418 + 0.0445565i
\(388\) 6.06104e7 − 3.43739e8i 0.0526789 − 0.298757i
\(389\) 1.84277e6 − 1.04509e7i 0.00158726 − 0.00900179i −0.984004 − 0.178147i \(-0.942990\pi\)
0.985591 + 0.169145i \(0.0541008\pi\)
\(390\) −1.93500e9 − 7.04281e8i −1.65179 − 0.601201i
\(391\) 6.45720e8 − 5.41823e8i 0.546293 − 0.458394i
\(392\) −3.13229e8 + 2.62830e8i −0.262640 + 0.220381i
\(393\) −4.08850e8 + 7.08149e8i −0.339774 + 0.588505i
\(394\) 7.81732e8 − 2.84527e8i 0.643904 − 0.234362i
\(395\) −2.58644e8 − 1.46684e9i −0.211160 − 1.19755i
\(396\) 1.02856e8 + 1.78152e8i 0.0832335 + 0.144165i
\(397\) 2.68602e7 − 4.65233e7i 0.0215448 − 0.0373167i −0.855052 − 0.518542i \(-0.826475\pi\)
0.876597 + 0.481226i \(0.159808\pi\)
\(398\) −1.25648e9 − 4.57320e8i −0.998995 − 0.363604i
\(399\) 3.01425e8 + 5.22083e8i 0.237560 + 0.411467i
\(400\) 5.31617e8 + 4.46079e8i 0.415326 + 0.348500i
\(401\) −1.37036e9 −1.06128 −0.530638 − 0.847599i \(-0.678047\pi\)
−0.530638 + 0.847599i \(0.678047\pi\)
\(402\) 4.60679e8 + 3.86556e8i 0.353678 + 0.296771i
\(403\) −1.05104e9 + 3.82546e8i −0.799927 + 0.291149i
\(404\) −1.18909e8 + 6.74367e8i −0.0897182 + 0.508817i
\(405\) −2.09243e8 − 1.18668e9i −0.156516 − 0.887648i
\(406\) −2.46881e9 −1.83082
\(407\) 8.14069e8 − 9.48186e8i 0.598523 − 0.697129i
\(408\) −6.30474e8 −0.459575
\(409\) −4.03587e8 − 2.28886e9i −0.291679 − 1.65420i −0.680401 − 0.732840i \(-0.738194\pi\)
0.388722 − 0.921355i \(-0.372917\pi\)
\(410\) −3.53405e7 + 2.00426e8i −0.0253239 + 0.143619i
\(411\) 2.61451e8 − 9.51602e7i 0.185756 − 0.0676097i
\(412\) −6.45709e8 − 5.41814e8i −0.454880 − 0.381690i
\(413\) −6.19621e8 −0.432814
\(414\) −1.24146e8 − 1.04170e8i −0.0859864 − 0.0721512i
\(415\) 1.98168e9 + 3.43238e9i 1.36103 + 2.35737i
\(416\) 4.26571e8 + 1.55259e8i 0.290512 + 0.105738i
\(417\) −5.83796e8 + 1.01116e9i −0.394262 + 0.682882i
\(418\) 2.05641e8 + 3.56180e8i 0.137719 + 0.238536i
\(419\) −3.58847e7 − 2.03512e8i −0.0238320 − 0.135158i 0.970570 − 0.240818i \(-0.0774156\pi\)
−0.994402 + 0.105660i \(0.966305\pi\)
\(420\) 1.42318e9 − 5.17997e8i 0.937322 − 0.341157i
\(421\) −1.34097e9 + 2.32263e9i −0.875854 + 1.51702i −0.0200035 + 0.999800i \(0.506368\pi\)
−0.855850 + 0.517224i \(0.826966\pi\)
\(422\) −1.20105e9 + 1.00780e9i −0.777979 + 0.652802i
\(423\) −1.78425e8 + 1.49716e8i −0.114621 + 0.0961786i
\(424\) −2.71284e8 − 9.87393e7i −0.172840 − 0.0629085i
\(425\) −9.70146e8 + 5.50197e9i −0.613022 + 3.47662i
\(426\) 2.76863e8 − 1.57017e9i 0.173513 − 0.984040i
\(427\) −2.30084e9 − 8.37436e8i −1.43017 − 0.520540i
\(428\) 6.54769e8 − 5.49416e8i 0.403678 − 0.338726i
\(429\) −1.60741e9 + 1.34878e9i −0.982937 + 0.824782i
\(430\) 3.73046e8 − 6.46134e8i 0.226268 − 0.391907i
\(431\) −8.01973e8 + 2.91894e8i −0.482491 + 0.175612i −0.571802 − 0.820391i \(-0.693756\pi\)
0.0893114 + 0.996004i \(0.471533\pi\)
\(432\) 7.91377e7 + 4.48812e8i 0.0472270 + 0.267837i
\(433\) −1.57816e8 − 2.73345e8i −0.0934208 − 0.161810i 0.815528 − 0.578718i \(-0.196447\pi\)
−0.908948 + 0.416909i \(0.863114\pi\)
\(434\) 4.11323e8 − 7.12433e8i 0.241529 − 0.418340i
\(435\) 4.23043e9 + 1.53975e9i 2.46418 + 0.896888i
\(436\) 2.73045e8 + 4.72928e8i 0.157773 + 0.273270i
\(437\) −2.48204e8 − 2.08268e8i −0.142274 − 0.119382i
\(438\) −1.10238e9 −0.626862
\(439\) 8.60993e8 + 7.22459e8i 0.485706 + 0.407556i 0.852485 − 0.522752i \(-0.175095\pi\)
−0.366778 + 0.930308i \(0.619539\pi\)
\(440\) 9.70938e8 − 3.53393e8i 0.543385 − 0.197776i
\(441\) −1.09897e8 + 6.23259e8i −0.0610172 + 0.346046i
\(442\) 6.34597e8 + 3.59898e9i 0.349559 + 1.98245i
\(443\) 9.85818e8 0.538746 0.269373 − 0.963036i \(-0.413184\pi\)
0.269373 + 0.963036i \(0.413184\pi\)
\(444\) 6.41845e8 − 3.60955e8i 0.348008 − 0.195710i
\(445\) 3.71632e9 1.99919
\(446\) −2.46946e8 − 1.40050e9i −0.131804 − 0.747499i
\(447\) 8.45175e7 − 4.79323e8i 0.0447580 − 0.253835i
\(448\) −3.13742e8 + 1.14193e8i −0.164854 + 0.0600019i
\(449\) 5.81499e8 + 4.87936e8i 0.303171 + 0.254390i 0.781662 − 0.623702i \(-0.214372\pi\)
−0.478492 + 0.878092i \(0.658816\pi\)
\(450\) 1.07412e9 0.555661
\(451\) 1.58868e8 + 1.33306e8i 0.0815487 + 0.0684275i
\(452\) 7.40236e7 + 1.28213e8i 0.0377038 + 0.0653050i
\(453\) −7.82664e7 − 2.84866e7i −0.0395578 − 0.0143978i
\(454\) −9.92459e8 + 1.71899e9i −0.497757 + 0.862140i
\(455\) −4.38941e9 − 7.60268e9i −2.18457 − 3.78379i
\(456\) 4.20826e7 + 2.38662e8i 0.0207838 + 0.117871i
\(457\) 6.59387e8 − 2.39997e8i 0.323172 − 0.117625i −0.175340 − 0.984508i \(-0.556102\pi\)
0.498512 + 0.866883i \(0.333880\pi\)
\(458\) 2.73408e8 − 4.73557e8i 0.132979 − 0.230326i
\(459\) −2.81054e9 + 2.35832e9i −1.35658 + 1.13830i
\(460\) −6.23557e8 + 5.23226e8i −0.298692 + 0.250632i
\(461\) 8.41979e8 + 3.06455e8i 0.400266 + 0.145685i 0.534306 − 0.845291i \(-0.320573\pi\)
−0.134040 + 0.990976i \(0.542795\pi\)
\(462\) 2.67993e8 − 1.51986e9i 0.126438 − 0.717064i
\(463\) −9.99537e7 + 5.66866e8i −0.0468021 + 0.265428i −0.999225 − 0.0393502i \(-0.987471\pi\)
0.952423 + 0.304778i \(0.0985823\pi\)
\(464\) −9.32601e8 − 3.39439e8i −0.433394 − 0.157743i
\(465\) −1.14916e9 + 9.64257e8i −0.530022 + 0.444741i
\(466\) 2.25438e8 − 1.89165e8i 0.103199 − 0.0865946i
\(467\) 3.81198e8 − 6.60254e8i 0.173197 − 0.299987i −0.766339 − 0.642437i \(-0.777923\pi\)
0.939536 + 0.342450i \(0.111257\pi\)
\(468\) 6.60238e8 − 2.40307e8i 0.297742 − 0.108369i
\(469\) 4.45202e8 + 2.52486e9i 0.199275 + 1.13014i
\(470\) 5.84947e8 + 1.01316e9i 0.259881 + 0.450127i
\(471\) 2.45918e8 − 4.25942e8i 0.108447 − 0.187835i
\(472\) −2.34064e8 − 8.51925e7i −0.102456 − 0.0372910i
\(473\) −3.80137e8 − 6.58416e8i −0.165168 − 0.286079i
\(474\) −6.85104e8 − 5.74871e8i −0.295483 − 0.247940i
\(475\) 2.14750e9 0.919400
\(476\) −2.05903e9 − 1.72773e9i −0.875061 − 0.734264i
\(477\) −4.19888e8 + 1.52827e8i −0.177141 + 0.0644741i
\(478\) 2.65295e8 − 1.50456e9i 0.111104 − 0.630103i
\(479\) −2.21595e8 − 1.25673e9i −0.0921269 − 0.522478i −0.995590 − 0.0938117i \(-0.970095\pi\)
0.903463 − 0.428666i \(-0.141016\pi\)
\(480\) 6.08834e8 0.251278
\(481\) −2.70650e9 − 3.30057e9i −1.10892 − 1.35233i
\(482\) −2.85249e8 −0.116027
\(483\) 2.11125e8 + 1.19735e9i 0.0852560 + 0.483511i
\(484\) −3.37375e7 + 1.91335e8i −0.0135255 + 0.0767071i
\(485\) −2.54986e9 + 9.28075e8i −1.01489 + 0.369391i
\(486\) 9.36983e8 + 7.86222e8i 0.370258 + 0.310683i
\(487\) −5.89215e8 −0.231165 −0.115583 − 0.993298i \(-0.536874\pi\)
−0.115583 + 0.993298i \(0.536874\pi\)
\(488\) −7.54010e8 − 6.32689e8i −0.293703 − 0.246446i
\(489\) −9.48613e8 − 1.64305e9i −0.366867 − 0.635432i
\(490\) 2.98708e9 + 1.08721e9i 1.14699 + 0.417472i
\(491\) −1.65450e9 + 2.86568e9i −0.630786 + 1.09255i 0.356606 + 0.934255i \(0.383934\pi\)
−0.987391 + 0.158298i \(0.949399\pi\)
\(492\) 6.11004e7 + 1.05829e8i 0.0231295 + 0.0400615i
\(493\) −1.38740e9 − 7.86836e9i −0.521481 − 2.95747i
\(494\) 1.32001e9 − 4.80446e8i 0.492645 − 0.179308i
\(495\) 7.99623e8 − 1.38499e9i 0.296324 − 0.513248i
\(496\) 2.53332e8 − 2.12571e8i 0.0932190 − 0.0782200i
\(497\) 5.20704e9 − 4.36922e9i 1.90258 − 1.59646i
\(498\) 2.23626e9 + 8.13930e8i 0.811369 + 0.295314i
\(499\) −1.80381e8 + 1.02299e9i −0.0649888 + 0.368570i 0.934917 + 0.354866i \(0.115473\pi\)
−0.999906 + 0.0137041i \(0.995638\pi\)
\(500\) 5.04857e8 − 2.86319e9i 0.180623 − 1.02436i
\(501\) 1.34342e9 + 4.88963e8i 0.477286 + 0.173718i
\(502\) −4.41322e8 + 3.70313e8i −0.155701 + 0.130649i
\(503\) −6.05571e8 + 5.08135e8i −0.212167 + 0.178029i −0.742678 − 0.669649i \(-0.766445\pi\)
0.530511 + 0.847678i \(0.322000\pi\)
\(504\) −2.58384e8 + 4.47534e8i −0.0898999 + 0.155711i
\(505\) 5.00247e9 − 1.82075e9i 1.72848 − 0.629116i
\(506\) 1.44036e8 + 8.16867e8i 0.0494246 + 0.280301i
\(507\) 2.41178e9 + 4.17733e9i 0.821883 + 1.42354i
\(508\) −1.12817e9 + 1.95405e9i −0.381814 + 0.661322i
\(509\) 9.35187e8 + 3.40380e8i 0.314330 + 0.114407i 0.494368 − 0.869253i \(-0.335400\pi\)
−0.180037 + 0.983660i \(0.557622\pi\)
\(510\) 2.45071e9 + 4.24475e9i 0.818080 + 1.41696i
\(511\) −3.60020e9 − 3.02093e9i −1.19359 − 1.00154i
\(512\) −1.34218e8 −0.0441942
\(513\) 1.08033e9 + 9.06500e8i 0.353300 + 0.296454i
\(514\) 3.91269e9 − 1.42410e9i 1.27088 − 0.462562i
\(515\) −1.13791e9 + 6.45340e9i −0.367098 + 2.08192i
\(516\) −7.77917e7 − 4.41179e8i −0.0249264 − 0.141365i
\(517\) 1.19213e9 0.379409
\(518\) 3.08532e9 + 5.80070e8i 0.975316 + 0.183369i
\(519\) −2.62881e9 −0.825416
\(520\) −6.12815e8 − 3.47545e9i −0.191125 − 1.08392i
\(521\) −5.24672e8 + 2.97556e9i −0.162538 + 0.921801i 0.789028 + 0.614357i \(0.210585\pi\)
−0.951566 + 0.307444i \(0.900526\pi\)
\(522\) −1.44346e9 + 5.25377e8i −0.444180 + 0.161668i
\(523\) 5.99919e8 + 5.03392e8i 0.183374 + 0.153869i 0.729854 − 0.683603i \(-0.239588\pi\)
−0.546480 + 0.837472i \(0.684033\pi\)
\(524\) −1.40139e9 −0.425500
\(525\) −6.17306e9 − 5.17981e9i −1.86184 − 1.56227i
\(526\) −3.74340e8 − 6.48376e8i −0.112154 − 0.194257i
\(527\) 2.50175e9 + 9.10564e8i 0.744573 + 0.271003i
\(528\) 3.10204e8 − 5.37288e8i 0.0917124 − 0.158851i
\(529\) 1.37569e9 + 2.38276e9i 0.404040 + 0.699818i
\(530\) 3.89729e8 + 2.21026e9i 0.113710 + 0.644879i
\(531\) −3.62280e8 + 1.31859e8i −0.105006 + 0.0382190i
\(532\) −5.16588e8 + 8.94756e8i −0.148749 + 0.257640i
\(533\) 5.42611e8 − 4.55305e8i 0.155218 − 0.130244i
\(534\) 1.70938e9 − 1.43434e9i 0.485785 − 0.407622i
\(535\) −6.24416e9 − 2.27269e9i −1.76293 − 0.641655i
\(536\) −1.78970e8 + 1.01499e9i −0.0502000 + 0.284698i
\(537\) −8.59549e8 + 4.87474e9i −0.239530 + 1.35844i
\(538\) −1.61935e9 − 5.89396e8i −0.448335 − 0.163181i
\(539\) 2.48138e9 − 2.08213e9i 0.682548 − 0.572725i
\(540\) 2.71407e9 − 2.27737e9i 0.741725 − 0.622381i
\(541\) 1.38686e9 − 2.40212e9i 0.376567 − 0.652234i −0.613993 − 0.789312i \(-0.710438\pi\)
0.990560 + 0.137078i \(0.0437710\pi\)
\(542\) −2.77516e8 + 1.01008e8i −0.0748671 + 0.0272494i
\(543\) 3.57791e7 + 2.02913e8i 0.00959024 + 0.0543889i
\(544\) −5.40259e8 − 9.35757e8i −0.143882 − 0.249211i
\(545\) 2.12270e9 − 3.67662e9i 0.561695 − 0.972885i
\(546\) −4.95328e9 − 1.80285e9i −1.30232 − 0.474007i
\(547\) −3.43246e9 − 5.94520e9i −0.896706 − 1.55314i −0.831679 − 0.555257i \(-0.812620\pi\)
−0.0650273 − 0.997883i \(-0.520713\pi\)
\(548\) 3.65277e8 + 3.06504e8i 0.0948180 + 0.0795617i
\(549\) −1.52346e9 −0.392943
\(550\) −4.21144e9 − 3.53382e9i −1.07935 − 0.905680i
\(551\) −2.88591e9 + 1.05039e9i −0.734942 + 0.267497i
\(552\) −8.48717e7 + 4.81332e8i −0.0214771 + 0.121803i
\(553\) −6.62086e8 − 3.75488e9i −0.166486 − 0.944187i
\(554\) −7.02922e8 −0.175640
\(555\) −4.92508e9 − 2.91824e9i −1.22289 − 0.724596i
\(556\) −2.00104e9 −0.493736
\(557\) −4.29176e8 − 2.43398e9i −0.105231 − 0.596793i −0.991128 − 0.132911i \(-0.957567\pi\)
0.885897 − 0.463882i \(-0.153544\pi\)
\(558\) 8.88824e7 − 5.04077e8i 0.0216569 − 0.122822i
\(559\) −2.44011e9 + 8.88127e8i −0.590837 + 0.215047i
\(560\) 1.98836e9 + 1.66843e9i 0.478450 + 0.401467i
\(561\) 4.99458e9 1.19434
\(562\) 1.47694e9 + 1.23930e9i 0.350983 + 0.294510i
\(563\) −6.84876e7 − 1.18624e8i −0.0161746 − 0.0280152i 0.857825 − 0.513942i \(-0.171815\pi\)
−0.873999 + 0.485927i \(0.838482\pi\)
\(564\) 6.60090e8 + 2.40253e8i 0.154927 + 0.0563888i
\(565\) 5.75472e8 − 9.96746e8i 0.134231 − 0.232496i
\(566\) −1.19375e9 − 2.06764e9i −0.276730 − 0.479311i
\(567\) −5.35630e8 − 3.03771e9i −0.123402 − 0.699850i
\(568\) 2.56771e9 − 9.34570e8i 0.587932 − 0.213990i
\(569\) −1.47496e9 + 2.55470e9i −0.335649 + 0.581362i −0.983609 − 0.180313i \(-0.942289\pi\)
0.647960 + 0.761674i \(0.275622\pi\)
\(570\) 1.44325e9 − 1.21103e9i 0.326421 − 0.273900i
\(571\) −5.81297e9 + 4.87766e9i −1.30669 + 1.09644i −0.317739 + 0.948178i \(0.602923\pi\)
−0.988948 + 0.148262i \(0.952632\pi\)
\(572\) −3.37927e9 − 1.22995e9i −0.754983 − 0.274791i
\(573\) 2.41306e8 − 1.36851e9i 0.0535829 − 0.303884i
\(574\) −9.04661e7 + 5.13059e8i −0.0199662 + 0.113234i
\(575\) 4.06985e9 + 1.48130e9i 0.892773 + 0.324943i
\(576\) −1.59138e8 + 1.33532e8i −0.0346972 + 0.0291144i
\(577\) −2.59867e9 + 2.18054e9i −0.563165 + 0.472551i −0.879370 − 0.476140i \(-0.842036\pi\)
0.316205 + 0.948691i \(0.397591\pi\)
\(578\) 2.70800e9 − 4.69039e9i 0.583312 − 1.01033i
\(579\) 3.02084e9 − 1.09950e9i 0.646775 − 0.235407i
\(580\) 1.33978e9 + 7.59828e9i 0.285126 + 1.61703i
\(581\) 5.07279e9 + 8.78634e9i 1.07308 + 1.85862i
\(582\) −8.14652e8 + 1.41102e9i −0.171294 + 0.296690i
\(583\) 2.14910e9 + 7.82208e8i 0.449176 + 0.163487i
\(584\) −9.44640e8 − 1.63616e9i −0.196255 − 0.339924i
\(585\) −4.18430e9 − 3.51104e9i −0.864126 − 0.725088i
\(586\) 2.25800e9 0.463534
\(587\) 3.39020e8 + 2.84472e8i 0.0691819 + 0.0580505i 0.676723 − 0.736238i \(-0.263400\pi\)
−0.607541 + 0.794288i \(0.707844\pi\)
\(588\) 1.79357e9 − 6.52806e8i 0.363829 − 0.132423i
\(589\) 1.77703e8 − 1.00780e9i 0.0358336 − 0.203223i
\(590\) 3.36259e8 + 1.90702e9i 0.0674049 + 0.382272i
\(591\) −3.88327e9 −0.773822
\(592\) 1.08574e9 + 6.43328e8i 0.215079 + 0.127440i
\(593\) −8.96389e9 −1.76525 −0.882623 − 0.470082i \(-0.844224\pi\)
−0.882623 + 0.470082i \(0.844224\pi\)
\(594\) −6.26924e8 − 3.55547e9i −0.122733 − 0.696056i
\(595\) −3.62855e9 + 2.05785e10i −0.706194 + 4.00502i
\(596\) 7.83840e8 − 2.85294e8i 0.151658 − 0.0551990i
\(597\) 4.78131e9 + 4.01200e9i 0.919681 + 0.771704i
\(598\) 2.83304e9 0.541750
\(599\) 1.78313e9 + 1.49623e9i 0.338992 + 0.284448i 0.796352 − 0.604833i \(-0.206760\pi\)
−0.457360 + 0.889282i \(0.651205\pi\)
\(600\) −1.61972e9 − 2.80544e9i −0.306133 − 0.530238i
\(601\) 1.32348e9 + 4.81709e8i 0.248690 + 0.0905157i 0.463358 − 0.886171i \(-0.346645\pi\)
−0.214668 + 0.976687i \(0.568867\pi\)
\(602\) 9.54937e8 − 1.65400e9i 0.178397 − 0.308992i
\(603\) 7.97607e8 + 1.38150e9i 0.148142 + 0.256590i
\(604\) −2.47871e7 − 1.40574e8i −0.00457715 − 0.0259583i
\(605\) 1.41933e9 − 5.16593e8i 0.260579 − 0.0948429i
\(606\) 1.59823e9 − 2.76822e9i 0.291733 − 0.505297i
\(607\) 3.86678e9 − 3.24462e9i 0.701761 − 0.588848i −0.220513 − 0.975384i \(-0.570773\pi\)
0.922274 + 0.386536i \(0.126329\pi\)
\(608\) −3.18164e8 + 2.66972e8i −0.0574102 + 0.0481729i
\(609\) 1.08292e10 + 3.94152e9i 1.94284 + 0.707136i
\(610\) −1.32876e9 + 7.53579e9i −0.237024 + 1.34423i
\(611\) 7.07047e8 − 4.00986e9i 0.125402 − 0.711190i
\(612\) −1.57155e9 − 5.71996e8i −0.277139 − 0.100870i
\(613\) −5.43829e8 + 4.56327e8i −0.0953566 + 0.0800137i −0.689220 − 0.724552i \(-0.742047\pi\)
0.593863 + 0.804566i \(0.297602\pi\)
\(614\) −2.17860e9 + 1.82806e9i −0.379829 + 0.318715i
\(615\) 4.75005e8 − 8.22732e8i 0.0823446 − 0.142625i
\(616\) 2.48545e9 − 9.04628e8i 0.428422 − 0.155933i
\(617\) −5.11226e8 − 2.89931e9i −0.0876224 − 0.496931i −0.996760 − 0.0804350i \(-0.974369\pi\)
0.909137 − 0.416496i \(-0.136742\pi\)
\(618\) 1.96733e9 + 3.40752e9i 0.335288 + 0.580736i
\(619\) −1.38650e9 + 2.40149e9i −0.234964 + 0.406970i −0.959262 − 0.282517i \(-0.908831\pi\)
0.724298 + 0.689487i \(0.242164\pi\)
\(620\) −2.41588e9 − 8.79310e8i −0.407104 − 0.148174i
\(621\) 1.42210e9 + 2.46315e9i 0.238292 + 0.412735i
\(622\) −5.64028e9 − 4.73276e9i −0.939798 − 0.788584i
\(623\) 9.51319e9 1.57622
\(624\) −1.62325e9 − 1.36207e9i −0.267447 − 0.224415i
\(625\) −8.80090e9 + 3.20327e9i −1.44194 + 0.524823i
\(626\) −1.34024e9 + 7.60090e9i −0.218360 + 1.23838i
\(627\) −3.33376e8 − 1.89067e9i −0.0540130 − 0.306323i
\(628\) 8.42918e8 0.135808
\(629\) −1.14881e8 + 1.01592e10i −0.0184066 + 1.62773i
\(630\) 4.01744e9 0.640115
\(631\) −4.55278e8 − 2.58201e9i −0.0721396 − 0.409124i −0.999398 − 0.0347012i \(-0.988952\pi\)
0.927258 − 0.374423i \(-0.122159\pi\)
\(632\) 2.66157e8 − 1.50945e9i 0.0419400 − 0.237853i
\(633\) 6.87730e9 − 2.50313e9i 1.07772 − 0.392257i
\(634\) −2.10218e9 − 1.76394e9i −0.327611 − 0.274898i
\(635\) 1.75412e10 2.71864
\(636\) 1.03233e9 + 8.66225e8i 0.159117 + 0.133515i
\(637\) −5.53176e9 − 9.58129e9i −0.847960 − 1.46871i
\(638\) 7.38802e9 + 2.68902e9i 1.12630 + 0.409941i
\(639\) 2.11465e9 − 3.66269e9i 0.320617 − 0.555325i
\(640\) 5.21716e8 + 9.03638e8i 0.0786691 + 0.136259i
\(641\) −1.72469e9 − 9.78118e9i −0.258647 − 1.46686i −0.786535 − 0.617545i \(-0.788127\pi\)
0.527889 − 0.849314i \(-0.322984\pi\)
\(642\) −3.74925e9 + 1.36462e9i −0.559207 + 0.203535i
\(643\) −3.91531e9 + 6.78151e9i −0.580801 + 1.00598i 0.414584 + 0.910011i \(0.363927\pi\)
−0.995385 + 0.0959655i \(0.969406\pi\)
\(644\) −1.59620e9 + 1.33937e9i −0.235498 + 0.197607i
\(645\) −2.66791e9 + 2.23864e9i −0.391482 + 0.328492i
\(646\) −3.14200e9 − 1.14359e9i −0.458555 − 0.166901i
\(647\) 5.60016e8 − 3.17601e9i 0.0812897 − 0.461017i −0.916806 − 0.399333i \(-0.869242\pi\)
0.998096 − 0.0616841i \(-0.0196471\pi\)
\(648\) 2.15322e8 − 1.22115e9i 0.0310868 − 0.176302i
\(649\) 1.85425e9 + 6.74890e8i 0.266263 + 0.0969118i
\(650\) −1.43841e10 + 1.20697e10i −2.05441 + 1.72386i
\(651\) −2.94166e9 + 2.46834e9i −0.417887 + 0.350649i
\(652\) 1.62575e9 − 2.81588e9i 0.229714 − 0.397876i
\(653\) 3.39140e9 − 1.23437e9i 0.476631 − 0.173480i −0.0925226 − 0.995711i \(-0.529493\pi\)
0.569154 + 0.822231i \(0.307271\pi\)
\(654\) −4.42649e8 − 2.51039e9i −0.0618782 − 0.350929i
\(655\) 5.44732e9 + 9.43503e9i 0.757422 + 1.31189i
\(656\) −1.04715e8 + 1.81372e8i −0.0144826 + 0.0250845i
\(657\) −2.74784e9 − 1.00013e9i −0.378018 − 0.137587i
\(658\) 1.49737e9 + 2.59352e9i 0.204898 + 0.354895i
\(659\) −1.10940e10 − 9.30896e9i −1.51004 − 1.26707i −0.863678 − 0.504044i \(-0.831845\pi\)
−0.646362 − 0.763031i \(-0.723710\pi\)
\(660\) −4.82315e9 −0.653021
\(661\) 8.11493e9 + 6.80923e9i 1.09290 + 0.917050i 0.996927 − 0.0783343i \(-0.0249602\pi\)
0.0959704 + 0.995384i \(0.469405\pi\)
\(662\) −4.04735e9 + 1.47311e9i −0.542210 + 0.197348i
\(663\) 2.96226e9 − 1.67998e10i 0.394753 − 2.23876i
\(664\) 7.08224e8 + 4.01654e9i 0.0938820 + 0.532432i
\(665\) 8.03208e9 1.05914
\(666\) 1.92737e9 − 3.17419e8i 0.252816 − 0.0416364i
\(667\) −6.19381e9 −0.808198
\(668\) 4.25461e8 + 2.41291e9i 0.0552258 + 0.313201i
\(669\) −1.15273e9 + 6.53744e9i −0.148845 + 0.844143i
\(670\) 7.52921e9 − 2.74041e9i 0.967137 − 0.352009i
\(671\) 5.97323e9 + 5.01213e9i 0.763274 + 0.640463i
\(672\) 1.55852e9 0.198116
\(673\) −2.45280e8 − 2.05814e8i −0.0310176 − 0.0260269i 0.627147 − 0.778901i \(-0.284223\pi\)
−0.658165 + 0.752874i \(0.728667\pi\)
\(674\) 3.66365e9 + 6.34562e9i 0.460897 + 0.798297i
\(675\) −1.77143e10 − 6.44747e9i −2.21697 − 0.806912i
\(676\) −4.13336e9 + 7.15918e9i −0.514623 + 0.891354i
\(677\) 4.82426e8 + 8.35587e8i 0.0597545 + 0.103498i 0.894355 − 0.447358i \(-0.147635\pi\)
−0.834601 + 0.550855i \(0.814302\pi\)
\(678\) −1.20004e8 − 6.80576e8i −0.0147874 − 0.0838634i
\(679\) −6.52724e9 + 2.37572e9i −0.800176 + 0.291240i
\(680\) −4.20007e9 + 7.27473e9i −0.512242 + 0.887229i
\(681\) 7.09776e9 − 5.95573e9i 0.861205 − 0.722637i
\(682\) −2.00688e9 + 1.68398e9i −0.242257 + 0.203278i
\(683\) −4.37637e9 − 1.59287e9i −0.525583 − 0.191296i 0.0655822 − 0.997847i \(-0.479110\pi\)
−0.591165 + 0.806551i \(0.701332\pi\)
\(684\) −1.11629e8 + 6.33079e8i −0.0133377 + 0.0756418i
\(685\) 6.43714e8 − 3.65068e9i 0.0765202 − 0.433967i
\(686\) −2.38673e8 − 8.68699e7i −0.0282273 − 0.0102739i
\(687\) −1.95533e9 + 1.64072e9i −0.230076 + 0.193057i
\(688\) 5.88142e8 − 4.93509e8i 0.0688529 − 0.0577745i
\(689\) 3.90566e9 − 6.76479e9i 0.454911 − 0.787929i
\(690\) 3.57053e9 − 1.29957e9i 0.413772 − 0.150601i
\(691\) −1.33523e9 − 7.57245e9i −0.153951 − 0.873098i −0.959739 − 0.280894i \(-0.909369\pi\)
0.805788 − 0.592204i \(-0.201742\pi\)
\(692\) −2.25265e9 − 3.90170e9i −0.258418 − 0.447592i
\(693\) 2.04691e9 − 3.54535e9i 0.233632 − 0.404662i
\(694\) 5.88231e9 + 2.14098e9i 0.668020 + 0.243139i
\(695\) 7.77822e9 + 1.34723e10i 0.878888 + 1.52228i
\(696\) 3.54886e9 + 2.97785e9i 0.398985 + 0.334788i
\(697\) −1.68602e9 −0.188602
\(698\) −5.75288e9 − 4.82724e9i −0.640312 − 0.537285i
\(699\) −1.29088e9 + 4.69841e8i −0.142960 + 0.0520332i
\(700\) 2.39818e9 − 1.36007e10i 0.264264 − 1.49872i
\(701\) 2.55412e8 + 1.44851e9i 0.0280045 + 0.158822i 0.995603 − 0.0936720i \(-0.0298605\pi\)
−0.967599 + 0.252493i \(0.918749\pi\)
\(702\) −1.23310e10 −1.34530
\(703\) 3.85338e9 − 6.34616e8i 0.418310 − 0.0688918i
\(704\) 1.06327e9 0.114852
\(705\) −9.48291e8 − 5.37803e9i −0.101925 − 0.578044i
\(706\) 1.76680e9 − 1.00200e10i 0.188961 − 1.07165i
\(707\) 1.28055e10 − 4.66083e9i 1.36279 − 0.496016i
\(708\) 8.90694e8 + 7.47381e8i 0.0943218 + 0.0791454i
\(709\) 2.08909e8 0.0220139 0.0110069 − 0.999939i \(-0.496496\pi\)
0.0110069 + 0.999939i \(0.496496\pi\)
\(710\) −1.62730e10 − 1.36547e10i −1.70633 − 1.43178i
\(711\) −1.18617e9 − 2.05451e9i −0.123767 − 0.214370i
\(712\) 3.59365e9 + 1.30798e9i 0.373126 + 0.135807i
\(713\) 1.03194e9 − 1.78737e9i 0.106621 − 0.184672i
\(714\) 6.27341e9 + 1.08659e10i 0.645001 + 1.11717i
\(715\) 4.85469e9 + 2.75323e10i 0.496696 + 2.81690i
\(716\) −7.97171e9 + 2.90146e9i −0.811626 + 0.295408i
\(717\) −3.56577e9 + 6.17609e9i −0.361273 + 0.625744i
\(718\) 8.47291e9 − 7.10962e9i 0.854274 − 0.716821i
\(719\) −1.28375e10 + 1.07719e10i −1.28804 + 1.08079i −0.295953 + 0.955203i \(0.595637\pi\)
−0.992083 + 0.125587i \(0.959919\pi\)
\(720\) 1.51761e9 + 5.52363e8i 0.151529 + 0.0551520i
\(721\) −2.91286e9 + 1.65197e10i −0.289432 + 1.64145i
\(722\) 1.01857e9 − 5.77662e9i 0.100719 − 0.571207i
\(723\) 1.25122e9 + 4.55408e8i 0.123126 + 0.0448143i
\(724\) −2.70506e8 + 2.26982e8i −0.0264907 + 0.0222283i
\(725\) 3.14477e10 − 2.63878e10i 3.06483 − 2.57169i
\(726\) 4.53459e8 − 7.85414e8i 0.0439804 − 0.0761764i
\(727\) −8.00882e9 + 2.91497e9i −0.773033 + 0.281361i −0.698265 − 0.715840i \(-0.746044\pi\)
−0.0747689 + 0.997201i \(0.523822\pi\)
\(728\) −1.56871e9 − 8.89659e9i −0.150689 − 0.854602i
\(729\) −5.50308e9 − 9.53161e9i −0.526089 − 0.911213i
\(730\) −7.34379e9 + 1.27198e10i −0.698699 + 1.21018i
\(731\) 5.80813e9 + 2.11399e9i 0.549953 + 0.200166i
\(732\) 2.29730e9 + 3.97904e9i 0.216486 + 0.374964i
\(733\) −6.37892e9 − 5.35255e9i −0.598251 − 0.501992i 0.292632 − 0.956225i \(-0.405469\pi\)
−0.890883 + 0.454233i \(0.849913\pi\)
\(734\) −8.35915e9 −0.780236
\(735\) −1.13669e10 − 9.53793e9i −1.05593 − 0.886030i
\(736\) −7.87125e8 + 2.86490e8i −0.0727732 + 0.0264873i
\(737\) 1.41779e9 − 8.04069e9i 0.130460 − 0.739873i
\(738\) 5.62884e7 + 3.19227e8i 0.00515491 + 0.0292350i
\(739\) −1.79038e9 −0.163188 −0.0815941 − 0.996666i \(-0.526001\pi\)
−0.0815941 + 0.996666i \(0.526001\pi\)
\(740\) 1.10938e8 − 9.81052e9i 0.0100640 − 0.889982i
\(741\) −6.55719e9 −0.592044
\(742\) 9.97643e8 + 5.65792e9i 0.0896523 + 0.508444i
\(743\) 1.77960e9 − 1.00926e10i 0.159170 − 0.902700i −0.795703 − 0.605687i \(-0.792898\pi\)
0.954873 − 0.297013i \(-0.0959905\pi\)
\(744\) −1.45060e9 + 5.27975e8i −0.129134 + 0.0470011i
\(745\) −4.96763e9 − 4.16834e9i −0.440152 − 0.369331i
\(746\) 6.71848e9 0.592495
\(747\) 4.83575e9 + 4.05768e9i 0.424465 + 0.356168i
\(748\) 4.27991e9 + 7.41302e9i 0.373920 + 0.647648i
\(749\) −1.59840e10 − 5.81771e9i −1.38995 − 0.505902i
\(750\) −6.78567e9 + 1.17531e10i −0.587325 + 1.01728i
\(751\) −5.94822e8 − 1.03026e9i −0.0512445 − 0.0887580i 0.839265 − 0.543722i \(-0.182985\pi\)
−0.890510 + 0.454964i \(0.849652\pi\)
\(752\) 2.09051e8 + 1.18559e9i 0.0179263 + 0.101665i
\(753\) 2.52704e9 − 9.19768e8i 0.215690 − 0.0785047i
\(754\) 1.34266e10 − 2.32555e10i 1.14069 − 1.97573i
\(755\) −8.50085e8 + 7.13306e8i −0.0718866 + 0.0603201i
\(756\) 6.94758e9 − 5.82971e9i 0.584800 − 0.490705i
\(757\) 9.48092e9 + 3.45077e9i 0.794356 + 0.289122i 0.707145 − 0.707068i \(-0.249983\pi\)
0.0872102 + 0.996190i \(0.472205\pi\)