Properties

Label 54.9.f.a.5.3
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), 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: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(-71.9819 + 37.1430i) q^{3} +(-22.2270 + 126.055i) q^{4} +(242.781 + 667.036i) q^{5} +(845.386 + 353.737i) q^{6} +(702.244 + 3982.62i) q^{7} +(1254.14 - 724.077i) q^{8} +(3801.79 - 5347.25i) q^{9} +(4015.49 - 6955.03i) q^{10} +(-675.075 + 1854.75i) q^{11} +(-3082.14 - 9899.28i) q^{12} +(5274.86 + 4426.14i) q^{13} +(29409.7 - 35049.1i) q^{14} +(-42251.6 - 38996.9i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(85996.5 + 49650.1i) q^{17} +(-73991.4 + 5937.54i) q^{18} +(79817.2 + 138247. i) q^{19} +(-89479.7 + 15777.7i) q^{20} +(-198476. - 260593. i) q^{21} +(20984.1 - 7637.60i) q^{22} +(-383459. - 67614.1i) q^{23} +(-63380.9 + 98703.0i) q^{24} +(-86757.9 + 72798.6i) q^{25} -77904.4i q^{26} +(-75046.7 + 526116. i) q^{27} -517640. q^{28} +(584464. + 696538. i) q^{29} +(-30711.5 + 649784. i) q^{30} +(70920.0 - 402207. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-20298.0 - 158583. i) q^{33} +(-195086. - 1.10639e6i) q^{34} +(-2.48606e6 + 1.43533e6i) q^{35} +(589548. + 598089. i) q^{36} +(-1.78613e6 + 3.09367e6i) q^{37} +(617708. - 1.69714e6i) q^{38} +(-544095. - 122677. i) q^{39} +(787467. + 660763. i) q^{40} +(1.55285e6 - 1.85062e6i) q^{41} +(-815135. + 3.61526e6i) q^{42} +(-5.76395e6 - 2.09791e6i) q^{43} +(-218797. - 126322. i) q^{44} +(4.48981e6 + 1.23772e6i) q^{45} +(2.20263e6 + 3.81507e6i) q^{46} +(3.95927e6 - 698125. i) q^{47} +(1.31636e6 - 168489. i) q^{48} +(-9.95099e6 + 3.62187e6i) q^{49} +(1.26186e6 + 222500. i) q^{50} +(-8.03435e6 - 379737. i) q^{51} +(-675183. + 566545. i) q^{52} -9.23813e6i q^{53} +(5.10550e6 - 3.17566e6i) q^{54} -1.40108e6 q^{55} +(3.76444e6 + 4.48628e6i) q^{56} +(-1.08803e7 - 6.98666e6i) q^{57} +(1.78635e6 - 1.01309e7i) q^{58} +(2.34478e6 + 6.44224e6i) q^{59} +(5.85489e6 - 4.45926e6i) q^{60} +(-4.42096e6 - 2.50725e7i) q^{61} +(-4.00160e6 + 2.31033e6i) q^{62} +(2.39659e7 + 1.13860e7i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(-1.67175e6 + 4.59311e6i) q^{65} +(-1.22679e6 + 1.32918e6i) q^{66} +(-3.41561e6 - 2.86604e6i) q^{67} +(-8.17010e6 + 9.73675e6i) q^{68} +(3.01135e7 - 9.37583e6i) q^{69} +(3.05191e7 + 1.11080e7i) q^{70} +(1.78601e7 + 1.03116e7i) q^{71} +(896145. - 9.45899e6i) q^{72} +(-4.93456e6 - 8.54690e6i) q^{73} +(3.98015e7 - 7.01808e6i) q^{74} +(3.54104e6 - 8.46263e6i) q^{75} +(-1.92009e7 + 6.98857e6i) q^{76} +(-7.86085e6 - 1.38608e6i) q^{77} +(2.89361e6 + 5.60771e6i) q^{78} +(-2.85868e6 + 2.39872e6i) q^{79} -1.16301e7i q^{80} +(-1.41395e7 - 4.06583e7i) q^{81} -2.73318e7 q^{82} +(2.82890e6 + 3.37135e6i) q^{83} +(3.72607e7 - 1.92267e7i) q^{84} +(-1.22401e7 + 6.94168e7i) q^{85} +(2.37351e7 + 6.52116e7i) q^{86} +(-6.79424e7 - 2.84293e7i) q^{87} +(496347. + 2.81492e6i) q^{88} +(5.18273e7 - 2.99225e7i) q^{89} +(-2.19243e7 - 4.79134e7i) q^{90} +(-1.39234e7 + 2.41160e7i) q^{91} +(1.70463e7 - 4.68342e7i) q^{92} +(9.83425e6 + 3.15858e7i) q^{93} +(-3.48435e7 - 2.92372e7i) q^{94} +(-7.28379e7 + 8.68048e7i) q^{95} +(-1.10333e7 - 1.01834e7i) q^{96} +(-2.82465e7 - 1.02809e7i) q^{97} +(1.03757e8 + 5.99040e7i) q^{98} +(7.35134e6 + 1.06612e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) −71.9819 + 37.1430i −0.888665 + 0.458556i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 242.781 + 667.036i 0.388450 + 1.06726i 0.967699 + 0.252107i \(0.0811235\pi\)
−0.579249 + 0.815150i \(0.696654\pi\)
\(6\) 845.386 + 353.737i 0.652304 + 0.272945i
\(7\) 702.244 + 3982.62i 0.292480 + 1.65873i 0.677273 + 0.735732i \(0.263162\pi\)
−0.384793 + 0.923003i \(0.625727\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) 3801.79 5347.25i 0.579453 0.815006i
\(10\) 4015.49 6955.03i 0.401549 0.695503i
\(11\) −675.075 + 1854.75i −0.0461085 + 0.126682i −0.960610 0.277901i \(-0.910361\pi\)
0.914501 + 0.404583i \(0.132583\pi\)
\(12\) −3082.14 9899.28i −0.148637 0.477396i
\(13\) 5274.86 + 4426.14i 0.184688 + 0.154971i 0.730444 0.682973i \(-0.239313\pi\)
−0.545756 + 0.837944i \(0.683758\pi\)
\(14\) 29409.7 35049.1i 0.765558 0.912356i
\(15\) −42251.6 38996.9i −0.834599 0.770309i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) 85996.5 + 49650.1i 1.02964 + 0.594462i 0.916881 0.399160i \(-0.130698\pi\)
0.112758 + 0.993623i \(0.464032\pi\)
\(18\) −73991.4 + 5937.54i −0.704841 + 0.0565609i
\(19\) 79817.2 + 138247.i 0.612466 + 1.06082i 0.990823 + 0.135163i \(0.0431558\pi\)
−0.378357 + 0.925660i \(0.623511\pi\)
\(20\) −89479.7 + 15777.7i −0.559248 + 0.0986106i
\(21\) −198476. 260593.i −1.02054 1.33994i
\(22\) 20984.1 7637.60i 0.0895778 0.0326037i
\(23\) −383459. 67614.1i −1.37027 0.241616i −0.560401 0.828221i \(-0.689353\pi\)
−0.809873 + 0.586605i \(0.800464\pi\)
\(24\) −63380.9 + 98703.0i −0.191035 + 0.297499i
\(25\) −86757.9 + 72798.6i −0.222100 + 0.186364i
\(26\) 77904.4i 0.170478i
\(27\) −75046.7 + 526116.i −0.141214 + 0.989979i
\(28\) −517640. −0.842162
\(29\) 584464. + 696538.i 0.826354 + 0.984810i 1.00000 2.05117e-6i \(6.52909e-7\pi\)
−0.173646 + 0.984808i \(0.555555\pi\)
\(30\) −30711.5 + 649784.i −0.0379155 + 0.802202i
\(31\) 70920.0 402207.i 0.0767931 0.435515i −0.922035 0.387107i \(-0.873474\pi\)
0.998828 0.0484076i \(-0.0154146\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) −20298.0 158583.i −0.0171158 0.133721i
\(34\) −195086. 1.10639e6i −0.145985 0.827925i
\(35\) −2.48606e6 + 1.43533e6i −1.65668 + 0.956486i
\(36\) 589548. + 598089.i 0.351002 + 0.356087i
\(37\) −1.78613e6 + 3.09367e6i −0.953030 + 1.65070i −0.214216 + 0.976786i \(0.568720\pi\)
−0.738814 + 0.673910i \(0.764614\pi\)
\(38\) 617708. 1.69714e6i 0.296244 0.813923i
\(39\) −544095. 122677.i −0.235189 0.0530280i
\(40\) 787467. + 660763.i 0.307604 + 0.258111i
\(41\) 1.55285e6 1.85062e6i 0.549535 0.654910i −0.417762 0.908556i \(-0.637186\pi\)
0.967297 + 0.253646i \(0.0816300\pi\)
\(42\) −815135. + 3.61526e6i −0.261958 + 1.16183i
\(43\) −5.76395e6 2.09791e6i −1.68596 0.613638i −0.691849 0.722042i \(-0.743204\pi\)
−0.994107 + 0.108405i \(0.965426\pi\)
\(44\) −218797. 126322.i −0.0583755 0.0337031i
\(45\) 4.48981e6 + 1.23772e6i 1.09491 + 0.301836i
\(46\) 2.20263e6 + 3.81507e6i 0.491939 + 0.852063i
\(47\) 3.95927e6 698125.i 0.811378 0.143068i 0.247459 0.968898i \(-0.420404\pi\)
0.563918 + 0.825830i \(0.309293\pi\)
\(48\) 1.31636e6 168489.i 0.247977 0.0317401i
\(49\) −9.95099e6 + 3.62187e6i −1.72616 + 0.628272i
\(50\) 1.26186e6 + 222500.i 0.201898 + 0.0356000i
\(51\) −8.03435e6 379737.i −1.18760 0.0561310i
\(52\) −675183. + 566545.i −0.0923438 + 0.0774857i
\(53\) 9.23813e6i 1.17079i −0.810747 0.585397i \(-0.800939\pi\)
0.810747 0.585397i \(-0.199061\pi\)
\(54\) 5.10550e6 3.17566e6i 0.600432 0.373473i
\(55\) −1.40108e6 −0.153113
\(56\) 3.76444e6 + 4.48628e6i 0.382779 + 0.456178i
\(57\) −1.08803e7 6.98666e6i −1.03072 0.661866i
\(58\) 1.78635e6 1.01309e7i 0.157853 0.895231i
\(59\) 2.34478e6 + 6.44224e6i 0.193506 + 0.531654i 0.998062 0.0622227i \(-0.0198189\pi\)
−0.804556 + 0.593877i \(0.797597\pi\)
\(60\) 5.85489e6 4.45926e6i 0.451766 0.344079i
\(61\) −4.42096e6 2.50725e7i −0.319299 1.81083i −0.547033 0.837111i \(-0.684243\pi\)
0.227734 0.973723i \(-0.426868\pi\)
\(62\) −4.00160e6 + 2.31033e6i −0.270812 + 0.156353i
\(63\) 2.39659e7 + 1.13860e7i 1.52136 + 0.722786i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) −1.67175e6 + 4.59311e6i −0.0936524 + 0.257308i
\(66\) −1.22679e6 + 1.32918e6i −0.0646541 + 0.0700502i
\(67\) −3.41561e6 2.86604e6i −0.169500 0.142227i 0.554092 0.832456i \(-0.313066\pi\)
−0.723592 + 0.690228i \(0.757510\pi\)
\(68\) −8.17010e6 + 9.73675e6i −0.382113 + 0.455385i
\(69\) 3.01135e7 9.37583e6i 1.32851 0.413631i
\(70\) 3.05191e7 + 1.11080e7i 1.27110 + 0.462642i
\(71\) 1.78601e7 + 1.03116e7i 0.702832 + 0.405780i 0.808401 0.588632i \(-0.200333\pi\)
−0.105569 + 0.994412i \(0.533666\pi\)
\(72\) 896145. 9.45899e6i 0.0333464 0.351977i
\(73\) −4.93456e6 8.54690e6i −0.173763 0.300966i 0.765970 0.642877i \(-0.222259\pi\)
−0.939732 + 0.341911i \(0.888926\pi\)
\(74\) 3.98015e7 7.01808e6i 1.32731 0.234041i
\(75\) 3.54104e6 8.46263e6i 0.111914 0.267461i
\(76\) −1.92009e7 + 6.98857e6i −0.575530 + 0.209476i
\(77\) −7.86085e6 1.38608e6i −0.223618 0.0394299i
\(78\) 2.89361e6 + 5.60771e6i 0.0781738 + 0.151498i
\(79\) −2.85868e6 + 2.39872e6i −0.0733934 + 0.0615844i −0.678746 0.734373i \(-0.737476\pi\)
0.605353 + 0.795957i \(0.293032\pi\)
\(80\) 1.16301e7i 0.283938i
\(81\) −1.41395e7 4.06583e7i −0.328469 0.944515i
\(82\) −2.73318e7 −0.604523
\(83\) 2.82890e6 + 3.37135e6i 0.0596080 + 0.0710381i 0.795025 0.606577i \(-0.207458\pi\)
−0.735417 + 0.677615i \(0.763013\pi\)
\(84\) 3.72607e7 1.92267e7i 0.748400 0.386178i
\(85\) −1.22401e7 + 6.94168e7i −0.234481 + 1.32981i
\(86\) 2.37351e7 + 6.52116e7i 0.433907 + 1.19215i
\(87\) −6.79424e7 2.84293e7i −1.18594 0.496237i
\(88\) 496347. + 2.81492e6i 0.00827666 + 0.0469392i
\(89\) 5.18273e7 2.99225e7i 0.826035 0.476911i −0.0264584 0.999650i \(-0.508423\pi\)
0.852493 + 0.522739i \(0.175090\pi\)
\(90\) −2.19243e7 4.79134e7i −0.334160 0.730276i
\(91\) −1.39234e7 + 2.41160e7i −0.203039 + 0.351674i
\(92\) 1.70463e7 4.68342e7i 0.237946 0.653750i
\(93\) 9.83425e6 + 3.15858e7i 0.131465 + 0.422241i
\(94\) −3.48435e7 2.92372e7i −0.446283 0.374476i
\(95\) −7.28379e7 + 8.68048e7i −0.894258 + 1.06574i
\(96\) −1.10333e7 1.01834e7i −0.129903 0.119896i
\(97\) −2.82465e7 1.02809e7i −0.319064 0.116130i 0.177523 0.984117i \(-0.443192\pi\)
−0.496587 + 0.867987i \(0.665414\pi\)
\(98\) 1.03757e8 + 5.99040e7i 1.12489 + 0.649458i
\(99\) 7.35134e6 + 1.06612e7i 0.0765290 + 0.110985i
\(100\) −7.24829e6 1.25544e7i −0.0724829 0.125544i
\(101\) −6.71968e7 + 1.18486e7i −0.645748 + 0.113863i −0.486925 0.873444i \(-0.661881\pi\)
−0.158824 + 0.987307i \(0.550770\pi\)
\(102\) 5.51372e7 + 7.23937e7i 0.509382 + 0.668806i
\(103\) −1.52788e8 + 5.56104e7i −1.35750 + 0.494091i −0.915282 0.402814i \(-0.868032\pi\)
−0.442222 + 0.896905i \(0.645810\pi\)
\(104\) 9.82028e6 + 1.73158e6i 0.0839441 + 0.0148016i
\(105\) 1.25639e8 1.95657e8i 1.03363 1.60968i
\(106\) −8.00651e7 + 6.71826e7i −0.634190 + 0.532149i
\(107\) 9.46785e7i 0.722297i 0.932508 + 0.361149i \(0.117615\pi\)
−0.932508 + 0.361149i \(0.882385\pi\)
\(108\) −6.46516e7 2.11540e7i −0.475209 0.155488i
\(109\) −1.08729e7 −0.0770264 −0.0385132 0.999258i \(-0.512262\pi\)
−0.0385132 + 0.999258i \(0.512262\pi\)
\(110\) 1.01891e7 + 1.21429e7i 0.0695930 + 0.0829377i
\(111\) 1.36608e7 2.89031e8i 0.0899880 1.90393i
\(112\) 1.15056e7 6.52513e7i 0.0731199 0.414684i
\(113\) −2.94142e7 8.08148e7i −0.180403 0.495652i 0.816223 0.577737i \(-0.196064\pi\)
−0.996625 + 0.0820853i \(0.973842\pi\)
\(114\) 1.85731e7 + 1.45107e8i 0.109968 + 0.859149i
\(115\) −4.79955e7 2.72196e8i −0.274416 1.55629i
\(116\) −1.00793e8 + 5.81930e7i −0.556672 + 0.321395i
\(117\) 4.37216e7 1.13788e7i 0.233320 0.0607230i
\(118\) 3.87817e7 6.71718e7i 0.200031 0.346465i
\(119\) −1.37347e8 + 3.77358e8i −0.684907 + 1.88177i
\(120\) −8.12261e7 1.83141e7i −0.391715 0.0883202i
\(121\) 1.61224e8 + 1.35283e8i 0.752122 + 0.631105i
\(122\) −1.85148e8 + 2.20651e8i −0.835757 + 0.996016i
\(123\) −4.30397e7 + 1.90889e8i −0.188040 + 0.833988i
\(124\) 4.91241e7 + 1.78797e7i 0.207782 + 0.0756264i
\(125\) 1.70512e8 + 9.84450e7i 0.698416 + 0.403231i
\(126\) −7.56070e7 2.90510e8i −0.299971 1.15260i
\(127\) −1.38425e6 2.39758e6i −0.00532106 0.00921635i 0.863353 0.504601i \(-0.168360\pi\)
−0.868674 + 0.495385i \(0.835027\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) 4.92822e8 6.30793e7i 1.77964 0.227787i
\(130\) 5.19651e7 1.89137e7i 0.181944 0.0662222i
\(131\) 1.11185e8 + 1.96049e7i 0.377538 + 0.0665702i 0.359197 0.933262i \(-0.383050\pi\)
0.0183409 + 0.999832i \(0.494162\pi\)
\(132\) 2.04414e7 + 966147.i 0.0673310 + 0.00318235i
\(133\) −4.94536e8 + 4.14965e8i −1.58049 + 1.32619i
\(134\) 5.04451e7i 0.156459i
\(135\) −3.69158e8 + 7.76721e7i −1.11142 + 0.233846i
\(136\) 1.43802e8 0.420348
\(137\) 2.70102e8 + 3.21895e8i 0.766736 + 0.913760i 0.998254 0.0590707i \(-0.0188137\pi\)
−0.231518 + 0.972831i \(0.574369\pi\)
\(138\) −3.00253e8 1.92804e8i −0.827888 0.531617i
\(139\) 1.30957e7 7.42693e7i 0.0350808 0.198953i −0.962230 0.272236i \(-0.912237\pi\)
0.997311 + 0.0732835i \(0.0233478\pi\)
\(140\) −1.25673e8 3.45284e8i −0.327138 0.898803i
\(141\) −2.59065e8 + 1.97312e8i −0.655439 + 0.499202i
\(142\) −4.05163e7 2.29779e8i −0.0996498 0.565142i
\(143\) −1.17703e7 + 6.79560e6i −0.0281478 + 0.0162511i
\(144\) −8.84962e7 + 6.10220e7i −0.205814 + 0.141918i
\(145\) −3.22719e8 + 5.58965e8i −0.730049 + 1.26448i
\(146\) −3.81887e7 + 1.04923e8i −0.0840472 + 0.230918i
\(147\) 5.81764e8 6.30319e8i 1.24588 1.34987i
\(148\) −3.50274e8 2.93914e8i −0.730063 0.612596i
\(149\) 4.67586e8 5.57248e8i 0.948674 1.13059i −0.0426432 0.999090i \(-0.513578\pi\)
0.991317 0.131495i \(-0.0419777\pi\)
\(150\) −9.90955e7 + 3.08534e7i −0.195744 + 0.0609450i
\(151\) −5.95781e6 2.16847e6i −0.0114599 0.00417105i 0.336284 0.941761i \(-0.390830\pi\)
−0.347744 + 0.937590i \(0.613052\pi\)
\(152\) 2.00204e8 + 1.15588e8i 0.375058 + 0.216540i
\(153\) 5.92432e8 2.71086e8i 1.08112 0.494699i
\(154\) 4.51537e7 + 7.82084e7i 0.0802805 + 0.139050i
\(155\) 2.85505e8 5.03422e7i 0.494637 0.0872178i
\(156\) 2.75577e7 6.58594e7i 0.0465312 0.111204i
\(157\) 2.34275e8 8.52691e7i 0.385591 0.140344i −0.141948 0.989874i \(-0.545337\pi\)
0.527540 + 0.849530i \(0.323115\pi\)
\(158\) 4.15784e7 + 7.33139e6i 0.0667174 + 0.0117641i
\(159\) 3.43132e8 + 6.64978e8i 0.536875 + 1.04044i
\(160\) −1.00796e8 + 8.45777e7i −0.153802 + 0.129055i
\(161\) 1.57465e9i 2.34359i
\(162\) −2.49550e8 + 4.18224e8i −0.362325 + 0.607224i
\(163\) 7.93998e8 1.12478 0.562392 0.826871i \(-0.309881\pi\)
0.562392 + 0.826871i \(0.309881\pi\)
\(164\) 1.98765e8 + 2.36879e8i 0.274767 + 0.327455i
\(165\) 1.00853e8 5.20405e7i 0.136067 0.0702110i
\(166\) 8.64619e6 4.90350e7i 0.0113866 0.0645764i
\(167\) 1.66507e8 + 4.57473e8i 0.214075 + 0.588166i 0.999527 0.0307566i \(-0.00979168\pi\)
−0.785452 + 0.618923i \(0.787569\pi\)
\(168\) −4.37606e8 1.83108e8i −0.549346 0.229864i
\(169\) −1.33417e8 7.56643e8i −0.163555 0.927565i
\(170\) 6.90636e8 3.98739e8i 0.826901 0.477411i
\(171\) 1.04269e9 + 9.87848e7i 1.21947 + 0.115533i
\(172\) 3.92567e8 6.79947e8i 0.448539 0.776893i
\(173\) 3.42628e8 9.41363e8i 0.382506 1.05093i −0.587791 0.809013i \(-0.700002\pi\)
0.970297 0.241915i \(-0.0777755\pi\)
\(174\) 2.47707e8 + 7.95590e8i 0.270235 + 0.867945i
\(175\) −3.50854e8 2.94402e8i −0.374089 0.313898i
\(176\) 2.07868e7 2.47728e7i 0.0216639 0.0258181i
\(177\) −4.08067e8 3.76633e8i −0.415755 0.383729i
\(178\) −6.36236e8 2.31571e8i −0.633780 0.230677i
\(179\) −1.59488e8 9.20804e7i −0.155352 0.0896923i 0.420309 0.907381i \(-0.361922\pi\)
−0.575661 + 0.817689i \(0.695255\pi\)
\(180\) −2.55816e8 + 5.38454e8i −0.243690 + 0.512931i
\(181\) 6.15746e8 + 1.06650e9i 0.573703 + 0.993683i 0.996181 + 0.0873096i \(0.0278269\pi\)
−0.422478 + 0.906373i \(0.638840\pi\)
\(182\) 3.10264e8 5.47079e7i 0.282778 0.0498614i
\(183\) 1.24950e9 + 1.64056e9i 1.11412 + 1.46281i
\(184\) −5.29869e8 + 1.92856e8i −0.462271 + 0.168253i
\(185\) −2.49723e9 4.40329e8i −2.13192 0.375915i
\(186\) 2.02231e8 3.14934e8i 0.168964 0.263128i
\(187\) −1.50143e8 + 1.25985e8i −0.122783 + 0.103027i
\(188\) 5.14604e8i 0.411947i
\(189\) −2.14802e9 + 7.05786e7i −1.68342 + 0.0553128i
\(190\) 1.28202e9 0.983740
\(191\) −1.29373e9 1.54181e9i −0.972097 1.15850i −0.987340 0.158617i \(-0.949297\pi\)
0.0152429 0.999884i \(-0.495148\pi\)
\(192\) −8.01979e6 + 1.69680e8i −0.00590144 + 0.124861i
\(193\) −1.28709e7 + 7.29942e7i −0.00927637 + 0.0526089i −0.989095 0.147282i \(-0.952948\pi\)
0.979818 + 0.199891i \(0.0640587\pi\)
\(194\) 1.16315e8 + 3.19573e8i 0.0821163 + 0.225613i
\(195\) −5.02659e7 3.92714e8i −0.0347644 0.271605i
\(196\) −2.35375e8 1.33488e9i −0.159491 0.904519i
\(197\) −8.60301e8 + 4.96695e8i −0.571196 + 0.329780i −0.757627 0.652688i \(-0.773641\pi\)
0.186431 + 0.982468i \(0.440308\pi\)
\(198\) 3.89371e7 1.41244e8i 0.0253339 0.0918987i
\(199\) −4.67190e8 + 8.09197e8i −0.297907 + 0.515991i −0.975657 0.219302i \(-0.929622\pi\)
0.677750 + 0.735293i \(0.262955\pi\)
\(200\) −5.60947e7 + 1.54119e8i −0.0350592 + 0.0963244i
\(201\) 3.52315e8 + 7.94366e7i 0.215848 + 0.0486672i
\(202\) 5.91366e8 + 4.96215e8i 0.355182 + 0.298033i
\(203\) −2.36361e9 + 2.81684e9i −1.39185 + 1.65874i
\(204\) 2.26447e8 1.00433e9i 0.130751 0.579905i
\(205\) 1.61143e9 + 5.86514e8i 0.912424 + 0.332095i
\(206\) 1.59309e9 + 9.19770e8i 0.884649 + 0.510752i
\(207\) −1.81938e9 + 1.79340e9i −0.990928 + 0.976776i
\(208\) −5.64088e7 9.77030e7i −0.0301366 0.0521981i
\(209\) −3.10298e8 + 5.47138e7i −0.162627 + 0.0286756i
\(210\) −2.60941e9 + 3.33994e8i −1.34173 + 0.171736i
\(211\) 2.78983e6 1.01542e6i 0.00140750 0.000512288i −0.341316 0.939949i \(-0.610873\pi\)
0.342724 + 0.939436i \(0.388651\pi\)
\(212\) 1.16452e9 + 2.05336e8i 0.576504 + 0.101653i
\(213\) −1.66861e9 7.88656e7i −0.810656 0.0383150i
\(214\) 8.20560e8 6.88531e8i 0.391251 0.328298i
\(215\) 4.35409e9i 2.03772i
\(216\) 2.86829e8 + 7.14161e8i 0.131768 + 0.328081i
\(217\) 1.65164e9 0.744864
\(218\) 7.90712e7 + 9.42334e7i 0.0350100 + 0.0417233i
\(219\) 6.72657e8 + 4.31938e8i 0.292427 + 0.187778i
\(220\) 3.11418e7 1.76614e8i 0.0132939 0.0753936i
\(221\) 2.33862e8 + 6.42530e8i 0.0980370 + 0.269354i
\(222\) −2.60432e9 + 1.98353e9i −1.07222 + 0.816631i
\(223\) 6.34114e8 + 3.59624e9i 0.256418 + 1.45422i 0.792407 + 0.609993i \(0.208828\pi\)
−0.535989 + 0.844225i \(0.680061\pi\)
\(224\) −6.49192e8 + 3.74811e8i −0.257858 + 0.148875i
\(225\) 5.94370e7 + 7.40682e8i 0.0231914 + 0.289002i
\(226\) −4.86497e8 + 8.42637e8i −0.186486 + 0.323003i
\(227\) 6.28627e8 1.72714e9i 0.236750 0.650464i −0.763241 0.646114i \(-0.776393\pi\)
0.999991 0.00435027i \(-0.00138474\pi\)
\(228\) 1.12254e9 1.21623e9i 0.415397 0.450067i
\(229\) −2.61461e9 2.19392e9i −0.950746 0.797771i 0.0286767 0.999589i \(-0.490871\pi\)
−0.979423 + 0.201818i \(0.935315\pi\)
\(230\) −2.01003e9 + 2.39546e9i −0.718277 + 0.856009i
\(231\) 6.17322e8 1.92203e8i 0.216802 0.0675014i
\(232\) 1.23735e9 + 4.50357e8i 0.427110 + 0.155455i
\(233\) 3.58659e9 + 2.07072e9i 1.21691 + 0.702583i 0.964256 0.264974i \(-0.0853633\pi\)
0.252654 + 0.967557i \(0.418697\pi\)
\(234\) −4.16575e8 2.96176e8i −0.138941 0.0987840i
\(235\) 1.42691e9 + 2.47148e9i 0.467870 + 0.810374i
\(236\) −8.64197e8 + 1.52381e8i −0.278590 + 0.0491228i
\(237\) 1.16677e8 2.78844e8i 0.0369823 0.0883829i
\(238\) 4.26932e9 1.55390e9i 1.33061 0.484302i
\(239\) −6.02082e9 1.06163e9i −1.84529 0.325374i −0.861927 0.507032i \(-0.830743\pi\)
−0.983362 + 0.181658i \(0.941854\pi\)
\(240\) 4.31977e8 + 8.37156e8i 0.130201 + 0.252326i
\(241\) 1.47882e9 1.24088e9i 0.438377 0.367842i −0.396725 0.917938i \(-0.629853\pi\)
0.835101 + 0.550096i \(0.185409\pi\)
\(242\) 2.38112e9i 0.694256i
\(243\) 2.52796e9 + 2.40147e9i 0.725012 + 0.688736i
\(244\) 3.25879e9 0.919385
\(245\) −4.83183e9 5.75835e9i −1.34106 1.59821i
\(246\) 1.96739e9 1.01519e9i 0.537218 0.277208i
\(247\) −1.90877e8 + 1.08252e9i −0.0512822 + 0.290836i
\(248\) −2.02286e8 5.55775e8i −0.0534759 0.146924i
\(249\) −3.28851e8 1.37602e8i −0.0855465 0.0357955i
\(250\) −3.86811e8 2.19371e9i −0.0990236 0.561591i
\(251\) −5.97597e8 + 3.45023e8i −0.150561 + 0.0869267i −0.573388 0.819284i \(-0.694371\pi\)
0.422827 + 0.906211i \(0.361038\pi\)
\(252\) −1.96796e9 + 2.76795e9i −0.487993 + 0.686367i
\(253\) 3.84271e8 6.65577e8i 0.0937898 0.162449i
\(254\) −1.07127e7 + 2.94330e7i −0.00257374 + 0.00707130i
\(255\) −1.69729e9 5.45139e9i −0.401416 1.28928i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 3.98306e9 4.74683e9i 0.913029 1.08811i −0.0827723 0.996568i \(-0.526377\pi\)
0.995802 0.0915375i \(-0.0291781\pi\)
\(258\) −4.13065e9 3.81246e9i −0.932267 0.860452i
\(259\) −1.35752e10 4.94098e9i −3.01681 1.09803i
\(260\) −5.41828e8 3.12824e8i −0.118568 0.0684553i
\(261\) 5.94657e9 4.77191e8i 1.28146 0.102832i
\(262\) −6.38660e8 1.10619e9i −0.135539 0.234761i
\(263\) −6.66556e6 + 1.17532e6i −0.00139320 + 0.000245659i −0.174345 0.984685i \(-0.555781\pi\)
0.172952 + 0.984930i \(0.444670\pi\)
\(264\) −1.40283e8 1.84188e8i −0.0288795 0.0379180i
\(265\) 6.16217e9 2.24284e9i 1.24954 0.454795i
\(266\) 7.19285e9 + 1.26829e9i 1.43673 + 0.253334i
\(267\) −2.61921e9 + 4.07890e9i −0.515378 + 0.802598i
\(268\) 4.37198e8 3.66853e8i 0.0847499 0.0711136i
\(269\) 7.72710e9i 1.47573i 0.674948 + 0.737866i \(0.264166\pi\)
−0.674948 + 0.737866i \(0.735834\pi\)
\(270\) 3.35780e9 + 2.63456e9i 0.631829 + 0.495739i
\(271\) 2.76351e9 0.512370 0.256185 0.966628i \(-0.417534\pi\)
0.256185 + 0.966628i \(0.417534\pi\)
\(272\) −1.04577e9 1.24630e9i −0.191057 0.227692i
\(273\) 1.06490e8 2.25307e9i 0.0191716 0.405625i
\(274\) 8.25535e8 4.68184e9i 0.146465 0.830643i
\(275\) −7.64553e7 2.10059e8i −0.0133683 0.0367291i
\(276\) 5.12543e8 + 4.00436e9i 0.0883271 + 0.690077i
\(277\) 1.98050e9 + 1.12320e10i 0.336400 + 1.90782i 0.412949 + 0.910754i \(0.364499\pi\)
−0.0765485 + 0.997066i \(0.524390\pi\)
\(278\) −7.38914e8 + 4.26612e8i −0.123713 + 0.0714256i
\(279\) −1.88108e9 1.90833e9i −0.310449 0.314947i
\(280\) −2.07858e9 + 3.60020e9i −0.338169 + 0.585726i
\(281\) 5.48141e8 1.50601e9i 0.0879159 0.241547i −0.887941 0.459957i \(-0.847865\pi\)
0.975857 + 0.218410i \(0.0700871\pi\)
\(282\) 3.59406e9 + 8.10354e8i 0.568315 + 0.128138i
\(283\) 8.98926e9 + 7.54289e9i 1.40145 + 1.17596i 0.960450 + 0.278452i \(0.0898214\pi\)
0.441002 + 0.897506i \(0.354623\pi\)
\(284\) −1.69680e9 + 2.02217e9i −0.260831 + 0.310846i
\(285\) 2.01882e9 8.95380e9i 0.305997 1.35715i
\(286\) 1.44494e8 + 5.25913e7i 0.0215965 + 0.00786050i
\(287\) 8.46080e9 + 4.88484e9i 1.24705 + 0.719985i
\(288\) 1.17244e9 + 3.23209e8i 0.170420 + 0.0469800i
\(289\) 1.44238e9 + 2.49828e9i 0.206771 + 0.358138i
\(290\) 7.19135e9 1.26803e9i 1.01676 0.179282i
\(291\) 2.41510e9 3.09124e8i 0.336794 0.0431082i
\(292\) 1.18706e9 4.32056e8i 0.163284 0.0594304i
\(293\) −3.96303e9 6.98788e8i −0.537720 0.0948146i −0.101809 0.994804i \(-0.532463\pi\)
−0.435912 + 0.899989i \(0.643574\pi\)
\(294\) −9.69362e9 4.58162e8i −1.29747 0.0613238i
\(295\) −3.72794e9 + 3.12811e9i −0.492244 + 0.413042i
\(296\) 5.17319e9i 0.673894i
\(297\) −9.25152e8 4.94361e8i −0.118902 0.0635357i
\(298\) −8.22999e9 −1.04360
\(299\) −1.72342e9 2.05390e9i −0.215629 0.256977i
\(300\) 9.88054e8 + 6.34466e8i 0.121982 + 0.0783292i
\(301\) 4.30747e9 2.44289e10i 0.524754 2.97603i
\(302\) 2.45334e7 + 6.74050e7i 0.00294937 + 0.00810334i
\(303\) 4.39686e9 3.34878e9i 0.521642 0.397298i
\(304\) −4.54168e8 2.57572e9i −0.0531768 0.301581i
\(305\) 1.56509e10 9.03608e9i 1.80859 1.04419i
\(306\) −6.65780e9 3.16307e9i −0.759355 0.360764i
\(307\) −5.37386e9 + 9.30780e9i −0.604969 + 1.04784i 0.387088 + 0.922043i \(0.373481\pi\)
−0.992056 + 0.125793i \(0.959852\pi\)
\(308\) 3.49446e8 9.60094e8i 0.0388308 0.106687i
\(309\) 8.93245e9 9.67796e9i 0.979799 1.06157i
\(310\) −2.51259e9 2.10831e9i −0.272066 0.228290i
\(311\) −5.50012e9 + 6.55478e9i −0.587936 + 0.700675i −0.975208 0.221290i \(-0.928973\pi\)
0.387272 + 0.921966i \(0.373418\pi\)
\(312\) −7.71198e8 + 2.40113e8i −0.0813856 + 0.0253394i
\(313\) −1.01977e10 3.71165e9i −1.06249 0.386714i −0.249125 0.968471i \(-0.580143\pi\)
−0.813362 + 0.581758i \(0.802365\pi\)
\(314\) −2.44273e9 1.41031e9i −0.251280 0.145076i
\(315\) −1.77642e9 + 1.87504e10i −0.180427 + 1.90445i
\(316\) −2.38831e8 4.13668e8i −0.0239521 0.0414862i
\(317\) −8.13198e9 + 1.43389e9i −0.805303 + 0.141997i −0.561122 0.827733i \(-0.689630\pi\)
−0.244181 + 0.969730i \(0.578519\pi\)
\(318\) 3.26787e9 7.80979e9i 0.319563 0.763714i
\(319\) −1.68646e9 + 6.13822e8i −0.162860 + 0.0592761i
\(320\) 1.46604e9 + 2.58502e8i 0.139812 + 0.0246526i
\(321\) −3.51665e9 6.81514e9i −0.331214 0.641881i
\(322\) −1.36472e10 + 1.14514e10i −1.26946 + 1.06521i
\(323\) 1.58517e10i 1.45635i
\(324\) 5.43947e9 8.78653e8i 0.493602 0.0797329i
\(325\) −7.79853e8 −0.0699003
\(326\) −5.77420e9 6.88143e9i −0.511236 0.609268i
\(327\) 7.82653e8 4.03853e8i 0.0684507 0.0353209i
\(328\) 6.07503e8 3.44532e9i 0.0524871 0.297669i
\(329\) 5.56074e9 + 1.52780e10i 0.474623 + 1.30402i
\(330\) −1.18446e9 4.95615e8i −0.0998765 0.0417916i
\(331\) 1.65181e9 + 9.36789e9i 0.137610 + 0.780423i 0.973007 + 0.230776i \(0.0741265\pi\)
−0.835397 + 0.549647i \(0.814762\pi\)
\(332\) −4.87854e8 + 2.81663e8i −0.0401548 + 0.0231834i
\(333\) 9.75215e9 + 2.13124e10i 0.793091 + 1.73323i
\(334\) 2.75394e9 4.76997e9i 0.221294 0.383292i
\(335\) 1.08250e9 2.97415e9i 0.0859508 0.236148i
\(336\) 1.59544e9 + 5.12426e9i 0.125177 + 0.402045i
\(337\) −1.57499e10 1.32157e10i −1.22112 1.02464i −0.998766 0.0496732i \(-0.984182\pi\)
−0.222352 0.974966i \(-0.571374\pi\)
\(338\) −5.58743e9 + 6.65884e9i −0.428100 + 0.510190i
\(339\) 5.11899e9 + 4.72467e9i 0.387602 + 0.357744i
\(340\) −8.47831e9 3.08585e9i −0.634444 0.230919i
\(341\) 6.98119e8 + 4.03059e8i 0.0516312 + 0.0298093i
\(342\) −6.72664e9 9.75521e9i −0.491693 0.713070i
\(343\) −9.75595e9 1.68978e10i −0.704844 1.22083i
\(344\) −8.74784e9 + 1.54248e9i −0.624693 + 0.110150i
\(345\) 1.35650e10 + 1.78105e10i 0.957511 + 1.25719i
\(346\) −1.06503e10 + 3.87640e9i −0.743118 + 0.270473i
\(347\) 1.04431e8 + 1.84140e7i 0.00720297 + 0.00127008i 0.177249 0.984166i \(-0.443280\pi\)
−0.170046 + 0.985436i \(0.554391\pi\)
\(348\) 5.09382e9 7.93261e9i 0.347318 0.540877i
\(349\) −1.04354e10 + 8.75633e9i −0.703407 + 0.590229i −0.922741 0.385421i \(-0.874056\pi\)
0.219334 + 0.975650i \(0.429612\pi\)
\(350\) 5.18177e9i 0.345307i
\(351\) −2.72452e9 + 2.44302e9i −0.179499 + 0.160953i
\(352\) −3.65869e8 −0.0238317
\(353\) −1.20150e10 1.43190e10i −0.773795 0.922174i 0.224840 0.974396i \(-0.427814\pi\)
−0.998635 + 0.0522222i \(0.983370\pi\)
\(354\) −2.96612e8 + 6.27562e9i −0.0188876 + 0.399617i
\(355\) −2.54207e9 + 1.44168e10i −0.160057 + 0.907728i
\(356\) 2.61993e9 + 7.19819e9i 0.163113 + 0.448150i
\(357\) −4.12972e9 3.22644e10i −0.254242 1.98633i
\(358\) 3.61803e8 + 2.05189e9i 0.0220262 + 0.124917i
\(359\) 1.74027e10 1.00474e10i 1.04770 0.604892i 0.125698 0.992069i \(-0.459883\pi\)
0.922006 + 0.387176i \(0.126550\pi\)
\(360\) 6.52705e9 1.69870e9i 0.388604 0.101136i
\(361\) −4.24980e9 + 7.36087e9i −0.250230 + 0.433411i
\(362\) 4.76528e9 1.30925e10i 0.277494 0.762409i
\(363\) −1.66300e10 3.74958e9i −0.957782 0.215951i
\(364\) −2.73048e9 2.29114e9i −0.155537 0.130511i
\(365\) 4.50307e9 5.36655e9i 0.253710 0.302360i
\(366\) 5.13166e9 2.27598e10i 0.285979 1.26837i
\(367\) −1.40639e8 5.11886e7i −0.00775252 0.00282169i 0.338141 0.941095i \(-0.390202\pi\)
−0.345893 + 0.938274i \(0.612424\pi\)
\(368\) 5.52482e9 + 3.18975e9i 0.301250 + 0.173927i
\(369\) −3.99211e9 1.53392e10i −0.215326 0.827363i
\(370\) 1.43444e10 + 2.48452e10i 0.765376 + 1.32567i
\(371\) 3.67920e10 6.48742e9i 1.94204 0.342434i
\(372\) −4.20015e9 + 5.37603e8i −0.219327 + 0.0280730i
\(373\) 1.13441e10 4.12890e9i 0.586048 0.213304i −0.0319421 0.999490i \(-0.510169\pi\)
0.617991 + 0.786186i \(0.287947\pi\)
\(374\) 2.18377e9 + 3.85058e8i 0.111614 + 0.0196806i
\(375\) −1.59303e10 7.52934e8i −0.805562 0.0380743i
\(376\) 4.45997e9 3.74236e9i 0.223142 0.187238i
\(377\) 6.26106e9i 0.309943i
\(378\) 1.62328e10 + 1.81032e10i 0.795107 + 0.886723i
\(379\) 8.29503e9 0.402033 0.201016 0.979588i \(-0.435576\pi\)
0.201016 + 0.979588i \(0.435576\pi\)
\(380\) −9.32325e9 1.11110e10i −0.447129 0.532868i
\(381\) 1.88694e8 + 1.21168e8i 0.00895486 + 0.00575025i
\(382\) −3.95413e9 + 2.24250e10i −0.185694 + 1.05312i
\(383\) 1.21645e10 + 3.34216e10i 0.565325 + 1.55322i 0.811720 + 0.584047i \(0.198532\pi\)
−0.246395 + 0.969169i \(0.579246\pi\)
\(384\) 1.52890e9 1.16446e9i 0.0703162 0.0535549i
\(385\) −9.83901e8 5.57998e9i −0.0447825 0.253974i
\(386\) 7.26228e8 4.19288e8i 0.0327132 0.0188870i
\(387\) −3.31313e10 + 2.28455e10i −1.47705 + 1.01849i
\(388\) 1.92380e9 3.33212e9i 0.0848853 0.147026i
\(389\) −1.18173e10 + 3.24677e10i −0.516082 + 1.41792i 0.358720 + 0.933445i \(0.383213\pi\)
−0.874803 + 0.484479i \(0.839009\pi\)
\(390\) −3.03803e9 + 3.29159e9i −0.131321 + 0.142281i
\(391\) −2.96191e10 2.48533e10i −1.26726 1.06335i
\(392\) −9.85742e9 + 1.17476e10i −0.417464 + 0.497514i
\(393\) −8.73150e9 + 2.71855e9i −0.366031 + 0.113964i
\(394\) 1.05611e10 + 3.84394e9i 0.438254 + 0.159511i
\(395\) −2.29406e9 1.32448e9i −0.0942360 0.0544072i
\(396\) −1.50730e9 + 6.89711e8i −0.0612940 + 0.0280470i
\(397\) 2.31647e10 + 4.01225e10i 0.932535 + 1.61520i 0.778971 + 0.627060i \(0.215742\pi\)
0.153564 + 0.988139i \(0.450925\pi\)
\(398\) 1.04107e10 1.83569e9i 0.414904 0.0731588i
\(399\) 2.01846e10 4.82386e10i 0.796395 1.90328i
\(400\) 1.74366e9 6.34639e8i 0.0681116 0.0247906i
\(401\) 1.22543e10 + 2.16077e9i 0.473927 + 0.0835661i 0.405510 0.914091i \(-0.367094\pi\)
0.0684171 + 0.997657i \(0.478205\pi\)
\(402\) −1.87369e9 3.63114e9i −0.0717451 0.139040i
\(403\) 2.15432e9 1.80769e9i 0.0816751 0.0685335i
\(404\) 8.73388e9i 0.327855i
\(405\) 2.36877e10 1.93026e10i 0.880446 0.717458i
\(406\) 4.16019e10 1.53112
\(407\) −4.53222e9 5.40129e9i −0.165171 0.196843i
\(408\) −1.03511e10 + 5.34124e9i −0.373549 + 0.192753i
\(409\) 9.14542e9 5.18662e10i 0.326821 1.85350i −0.169733 0.985490i \(-0.554291\pi\)
0.496554 0.868006i \(-0.334598\pi\)
\(410\) −6.63564e9 1.82313e10i −0.234827 0.645181i
\(411\) −3.13986e10 1.31382e10i −1.10038 0.460436i
\(412\) −3.61397e9 2.04958e10i −0.125428 0.711339i
\(413\) −2.40104e10 + 1.38624e10i −0.825276 + 0.476474i
\(414\) 2.87741e10 + 2.72606e9i 0.979491 + 0.0927971i
\(415\) −1.56201e9 + 2.70547e9i −0.0526612 + 0.0912118i
\(416\) −4.36550e8 + 1.19941e9i −0.0145767 + 0.0400493i
\(417\) 1.81594e9 + 5.83246e9i 0.0600560 + 0.192889i
\(418\) 2.73078e9 + 2.29139e9i 0.0894501 + 0.0750575i
\(419\) −3.58659e10 + 4.27433e10i −1.16366 + 1.38679i −0.256216 + 0.966620i \(0.582476\pi\)
−0.907443 + 0.420175i \(0.861969\pi\)
\(420\) 2.18711e10 + 2.01863e10i 0.702868 + 0.648724i
\(421\) 2.15748e10 + 7.85258e9i 0.686781 + 0.249968i 0.661756 0.749719i \(-0.269811\pi\)
0.0250247 + 0.999687i \(0.492034\pi\)
\(422\) −2.90889e7 1.67945e7i −0.000917229 0.000529562i
\(423\) 1.13192e10 2.38253e10i 0.353554 0.744179i
\(424\) −6.68912e9 1.15859e10i −0.206969 0.358481i
\(425\) −1.10753e10 + 1.95288e9i −0.339470 + 0.0598577i
\(426\) 1.14511e10 + 1.50351e10i 0.347705 + 0.456527i
\(427\) 9.67498e10 3.52141e10i 2.91031 1.05926i
\(428\) −1.19347e10 2.10441e9i −0.355662 0.0627128i
\(429\) 5.94841e8 9.26346e8i 0.0175619 0.0273492i
\(430\) −3.77361e10 + 3.16643e10i −1.10378 + 0.926182i
\(431\) 2.03309e10i 0.589181i −0.955624 0.294590i \(-0.904817\pi\)
0.955624 0.294590i \(-0.0951832\pi\)
\(432\) 4.10359e9 7.67950e9i 0.117823 0.220495i
\(433\) −4.65175e10 −1.32332 −0.661660 0.749804i \(-0.730148\pi\)
−0.661660 + 0.749804i \(0.730148\pi\)
\(434\) −1.20113e10 1.43145e10i −0.338555 0.403475i
\(435\) 2.46824e9 5.22221e10i 0.0689334 1.45847i
\(436\) 2.41672e8 1.37059e9i 0.00668775 0.0379281i
\(437\) −2.12591e10 5.84090e10i −0.582935 1.60160i
\(438\) −1.14825e9 8.97097e9i −0.0311989 0.243749i
\(439\) −9.64451e9 5.46967e10i −0.259670 1.47266i −0.783794 0.621020i \(-0.786718\pi\)
0.524124 0.851642i \(-0.324393\pi\)
\(440\) −1.75715e9 + 1.01449e9i −0.0468812 + 0.0270669i
\(441\) −1.84645e10 + 6.69801e10i −0.488185 + 1.77089i
\(442\) 3.86796e9 6.69951e9i 0.101343 0.175531i
\(443\) 1.68761e9 4.63668e9i 0.0438186 0.120390i −0.915853 0.401513i \(-0.868484\pi\)
0.959672 + 0.281122i \(0.0907067\pi\)
\(444\) 3.61302e10 + 8.14629e9i 0.929691 + 0.209618i
\(445\) 3.25421e10 + 2.73060e10i 0.829860 + 0.696335i
\(446\) 2.65564e10 3.16487e10i 0.671167 0.799865i
\(447\) −1.29599e10 + 5.74793e10i −0.324617 + 1.43973i
\(448\) 7.96954e9 + 2.90068e9i 0.197843 + 0.0720091i
\(449\) 2.41517e9 + 1.39440e9i 0.0594242 + 0.0343086i 0.529418 0.848361i \(-0.322410\pi\)
−0.469994 + 0.882670i \(0.655744\pi\)
\(450\) 5.98710e9 5.90160e9i 0.146005 0.143919i
\(451\) 2.38415e9 + 4.12947e9i 0.0576272 + 0.0998132i
\(452\) 1.08409e10 1.91155e9i 0.259724 0.0457964i
\(453\) 5.09398e8 6.52009e7i 0.0120966 0.00154832i
\(454\) −1.95403e10 + 7.11210e9i −0.459948 + 0.167407i
\(455\) −1.94666e10 3.43248e9i −0.454197 0.0800872i
\(456\) −1.87043e10 8.84046e8i −0.432596 0.0204463i
\(457\) 1.24495e10 1.04464e10i 0.285422 0.239498i −0.488824 0.872383i \(-0.662574\pi\)
0.774246 + 0.632885i \(0.218129\pi\)
\(458\) 3.86151e10i 0.877598i
\(459\) −3.25754e10 + 4.15180e10i −0.733904 + 0.935375i
\(460\) 3.53786e10 0.790150
\(461\) 2.51076e10 + 2.99221e10i 0.555906 + 0.662503i 0.968675 0.248333i \(-0.0798826\pi\)
−0.412768 + 0.910836i \(0.635438\pi\)
\(462\) −6.15515e9 3.95245e9i −0.135105 0.0867558i
\(463\) −5.99186e9 + 3.39815e10i −0.130388 + 0.739468i 0.847573 + 0.530679i \(0.178063\pi\)
−0.977961 + 0.208788i \(0.933048\pi\)
\(464\) −5.09521e9 1.39990e10i −0.109923 0.302012i
\(465\) −1.86813e10 + 1.42282e10i −0.399572 + 0.304326i
\(466\) −8.13629e9 4.61432e10i −0.172537 0.978507i
\(467\) 6.86368e10 3.96275e10i 1.44308 0.833161i 0.445024 0.895519i \(-0.353195\pi\)
0.998054 + 0.0623571i \(0.0198618\pi\)
\(468\) 4.62561e8 + 5.76426e9i 0.00964240 + 0.120160i
\(469\) 9.01575e9 1.56157e10i 0.186342 0.322754i
\(470\) 1.10429e10 3.03401e10i 0.226304 0.621764i
\(471\) −1.36964e10 + 1.48395e10i −0.278306 + 0.301534i
\(472\) 7.60537e9 + 6.38166e9i 0.153233 + 0.128578i
\(473\) 7.78219e9 9.27446e9i 0.155474 0.185287i
\(474\) −3.26520e9 + 1.01662e9i −0.0646840 + 0.0201394i
\(475\) −1.69890e10 6.18349e9i −0.333729 0.121467i
\(476\) −4.45152e10 2.57009e10i −0.867123 0.500633i
\(477\) −4.93986e10 3.51214e10i −0.954205 0.678420i
\(478\) 3.45843e10 + 5.99018e10i 0.662473 + 1.14744i
\(479\) 1.87072e10 3.29859e9i 0.355359 0.0626594i 0.00688102 0.999976i \(-0.497810\pi\)
0.348478 + 0.937317i \(0.386699\pi\)
\(480\) 4.11400e9 9.83192e9i 0.0774995 0.185214i
\(481\) −2.31146e10 + 8.41303e9i −0.431823 + 0.157171i
\(482\) −2.15089e10 3.79260e9i −0.398501 0.0702665i
\(483\) 5.84874e10 + 1.13347e11i 1.07467 + 2.08267i
\(484\) −2.06367e10 + 1.73162e10i −0.376061 + 0.315553i
\(485\) 2.13375e10i 0.385634i
\(486\) 2.42898e9 3.93736e10i 0.0435391 0.705765i
\(487\) −3.15914e10 −0.561634 −0.280817 0.959761i \(-0.590605\pi\)
−0.280817 + 0.959761i \(0.590605\pi\)
\(488\) −2.36989e10 2.82433e10i −0.417878 0.498008i
\(489\) −5.71535e10 + 2.94915e10i −0.999557 + 0.515777i
\(490\) −1.47679e10 + 8.37530e10i −0.256174 + 1.45283i
\(491\) −2.70031e10 7.41904e10i −0.464609 1.27650i −0.921984 0.387229i \(-0.873432\pi\)
0.457375 0.889274i \(-0.348790\pi\)
\(492\) −2.31059e10 9.66827e9i −0.394333 0.165002i
\(493\) 1.56787e10 + 8.89185e10i 0.265414 + 1.50524i
\(494\) 1.07701e10 6.21812e9i 0.180847 0.104412i
\(495\) −5.32662e9 + 7.49194e9i −0.0887219 + 0.124788i
\(496\) −3.34571e9 + 5.79494e9i −0.0552792 + 0.0957464i
\(497\) −2.85249e10 + 7.83715e10i −0.467518 + 1.28449i
\(498\) 1.19894e9 + 3.85078e9i 0.0194930 + 0.0626082i
\(499\) −1.88053e10 1.57796e10i −0.303305 0.254503i 0.478414 0.878135i \(-0.341212\pi\)
−0.781718 + 0.623632i \(0.785656\pi\)
\(500\) −1.61995e10 + 1.93058e10i −0.259192 + 0.308893i
\(501\) −2.89774e10 2.67452e10i −0.459948 0.424517i
\(502\) 7.33616e9 + 2.67014e9i 0.115519 + 0.0420455i
\(503\) 2.60618e10 + 1.50468e10i 0.407129 + 0.235056i 0.689555 0.724233i \(-0.257806\pi\)
−0.282426 + 0.959289i \(0.591139\pi\)
\(504\) 3.83009e10 3.07351e9i 0.593590 0.0476334i
\(505\) −2.42176e10 4.19461e10i −0.372362 0.644950i
\(506\) −8.56297e9 + 1.50988e9i −0.130624 + 0.0230325i
\(507\) 3.77076e10 + 4.95091e10i 0.570686 + 0.749296i
\(508\) 3.32996e8 1.21201e8i 0.00500016 0.00181991i
\(509\) −6.41370e10 1.13091e10i −0.955515 0.168483i −0.325912 0.945400i \(-0.605671\pi\)
−0.629603 + 0.776917i \(0.716783\pi\)
\(510\) −3.49029e10 + 5.43543e10i −0.515918 + 0.803439i
\(511\) 3.05738e10 2.56545e10i 0.448401 0.376253i
\(512\) 3.03700e9i 0.0441942i
\(513\) −7.87242e10 + 3.16181e10i −1.13668 + 0.456526i
\(514\) −7.01059e10 −1.00439
\(515\) −7.41882e10 8.84141e10i −1.05464 1.25688i
\(516\) −3.00246e9 + 6.35250e10i −0.0423524 + 0.896078i
\(517\) −1.37795e9 + 7.81475e9i −0.0192873 + 0.109384i
\(518\) 5.59008e10 + 1.53586e11i 0.776424 + 2.13321i
\(519\) 1.03021e10 + 8.04874e10i 0.141989 + 1.10932i
\(520\) 1.22915e9 + 6.97087e9i 0.0168110 + 0.0953397i
\(521\) 2.91089e10 1.68060e10i 0.395071 0.228094i −0.289284 0.957243i \(-0.593417\pi\)
0.684355 + 0.729149i \(0.260084\pi\)
\(522\) −4.73811e10 4.80675e10i −0.638150 0.647395i
\(523\) 6.01584e10 1.04197e11i 0.804061 1.39268i −0.112861 0.993611i \(-0.536002\pi\)
0.916923 0.399064i \(-0.130665\pi\)
\(524\) −4.94261e9 + 1.35797e10i −0.0655588 + 0.180121i
\(525\) 3.61901e10 + 8.15980e9i 0.476380 + 0.107409i
\(526\) 5.86603e7 + 4.92219e7i 0.000766305 + 0.000643006i
\(527\) 2.60685e10 3.10672e10i 0.337966 0.402773i
\(528\) −5.76139e8 + 2.55528e9i −0.00741295 + 0.0328777i
\(529\) 6.88808e10 + 2.50706e10i 0.879580 + 0.320141i
\(530\) −6.42515e10 3.70956e10i −0.814291 0.470131i
\(531\) 4.33627e10 + 1.19539e10i 0.545429 + 0.150360i
\(532\) −4.13166e10 7.15624e10i −0.515796 0.893384i
\(533\) 1.63822e10 2.88862e9i 0.202985 0.0357916i
\(534\) 5.43988e10 6.96282e9i 0.668997 0.0856289i
\(535\) −6.31539e10 + 2.29861e10i −0.770877 + 0.280576i
\(536\) −6.35888e9 1.12124e9i −0.0770409 0.0135844i
\(537\) 1.49004e10 + 7.04256e8i 0.179185 + 0.00846902i
\(538\) 6.69692e10 5.61939e10i 0.799367 0.670749i
\(539\) 2.09017e10i 0.247643i
\(540\) −1.58573e9 4.82607e10i −0.0186489 0.567569i
\(541\) 1.37460e11 1.60468 0.802340 0.596868i \(-0.203588\pi\)
0.802340 + 0.596868i \(0.203588\pi\)
\(542\) −2.00971e10 2.39508e10i −0.232882 0.277538i
\(543\) −8.39357e10 5.38982e10i −0.965489 0.619977i
\(544\) −3.19628e9 + 1.81270e10i −0.0364964 + 0.206981i
\(545\) −2.63974e9 7.25262e9i −0.0299209 0.0822070i
\(546\) −2.03014e10 + 1.54621e10i −0.228431 + 0.173980i
\(547\) 2.71788e9 + 1.54139e10i 0.0303586 + 0.172172i 0.996217 0.0868974i \(-0.0276952\pi\)
−0.965859 + 0.259069i \(0.916584\pi\)
\(548\) −4.65802e10 + 2.68931e10i −0.516510 + 0.298207i
\(549\) −1.50877e11 7.16804e10i −1.66086 0.789062i
\(550\) −1.26453e9 + 2.19024e9i −0.0138191 + 0.0239354i
\(551\) −4.96442e10 + 1.36396e11i −0.538595 + 1.47978i
\(552\) 3.09777e10 3.35631e10i 0.333651 0.361498i
\(553\) −1.15607e10 9.70055e9i −0.123618 0.103728i
\(554\) 8.29426e10 9.88471e10i 0.880518 1.04936i
\(555\) 1.96110e11 6.10589e10i 2.06694 0.643543i
\(556\) 9.07097e9 + 3.30156e9i 0.0949193 + 0.0345478i
\(557\) 8.78769e10 + 5.07358e10i 0.912965 + 0.527101i 0.881384 0.472401i \(-0.156612\pi\)
0.0315811 + 0.999501i \(0.489946\pi\)
\(558\) −2.85935e9 + 3.01810e10i −0.0294938 + 0.311312i
\(559\) −2.11184e10 3.65782e10i −0.216279 0.374606i
\(560\) 4.63183e10 8.16716e9i 0.470978 0.0830461i
\(561\) 6.12810e9 1.46454e10i 0.0618692 0.147859i
\(562\) −1.70385e10 + 6.20151e9i −0.170799 + 0.0621659i
\(563\) 3.88073e9 + 6.84278e8i 0.0386260 + 0.00681081i 0.192928 0.981213i \(-0.438202\pi\)
−0.154302 + 0.988024i \(0.549313\pi\)
\(564\) −1.91140e10 3.70422e10i −0.188901 0.366083i
\(565\) 4.67651e10 3.92406e10i 0.458911 0.385072i
\(566\) 1.32762e11i 1.29363i
\(567\) 1.51997e11 8.48644e10i 1.47063 0.821095i
\(568\) 2.98655e10 0.286930
\(569\) 6.55995e10 + 7.81784e10i 0.625823 + 0.745826i 0.982060 0.188569i \(-0.0603850\pi\)
−0.356237 + 0.934396i \(0.615941\pi\)
\(570\) −9.22823e10 + 4.76181e10i −0.874216 + 0.451100i
\(571\) −1.88156e10 + 1.06708e11i −0.177000 + 1.00382i 0.758811 + 0.651311i \(0.225781\pi\)
−0.935810 + 0.352504i \(0.885330\pi\)
\(572\) −5.95003e8 1.63476e9i −0.00555821 0.0152711i
\(573\) 1.50392e11 + 6.29291e10i 1.39511 + 0.583758i
\(574\) −1.91936e10 1.08852e11i −0.176811 1.00274i
\(575\) 3.81903e10 2.20492e10i 0.349367 0.201707i
\(576\) −5.72515e9 1.25118e10i −0.0520112 0.113665i
\(577\) −1.53465e10 + 2.65809e10i −0.138454 + 0.239810i −0.926912 0.375279i \(-0.877547\pi\)
0.788457 + 0.615089i \(0.210880\pi\)
\(578\) 1.11627e10 3.06691e10i 0.100013 0.274783i
\(579\) −1.78476e9 5.73233e9i −0.0158805 0.0510055i
\(580\) −6.32875e10 5.31045e10i −0.559250 0.469266i
\(581\) −1.14402e10 + 1.36339e10i −0.100399 + 0.119651i
\(582\) −2.02425e10 1.86832e10i −0.176430 0.162839i
\(583\) 1.71345e10 + 6.23643e9i 0.148319 + 0.0539836i
\(584\) −1.23772e10 7.14600e9i −0.106408 0.0614344i
\(585\) 1.82048e10 + 2.64013e10i 0.155440 + 0.225425i
\(586\) 2.27641e10 + 3.94286e10i 0.193046 + 0.334365i
\(587\) 1.44651e11 2.55058e10i 1.21834 0.214826i 0.472729 0.881208i \(-0.343269\pi\)
0.745611 + 0.666381i \(0.232158\pi\)
\(588\) 6.65243e10 + 8.73446e10i 0.556507 + 0.730679i
\(589\) 6.12648e10 2.22986e10i 0.509038 0.185275i
\(590\) 5.42214e10 + 9.56070e9i 0.447469 + 0.0789009i
\(591\) 4.34773e10 6.77072e10i 0.356380 0.554990i
\(592\) 4.48350e10 3.76210e10i 0.365032 0.306298i
\(593\) 6.91940e10i 0.559563i −0.960064 0.279782i \(-0.909738\pi\)
0.960064 0.279782i \(-0.0902621\pi\)
\(594\) 2.44347e9 + 1.16133e10i 0.0196273 + 0.0932842i
\(595\) −2.85057e11 −2.27438
\(596\) 5.98511e10 + 7.13277e10i 0.474337 + 0.565293i
\(597\) 3.57320e9 7.56004e10i 0.0281293 0.595151i
\(598\) −5.26744e9 + 2.98732e10i −0.0411903 + 0.233602i
\(599\) −7.20305e10 1.97902e11i −0.559511 1.53724i −0.820350 0.571862i \(-0.806221\pi\)
0.260838 0.965382i \(-0.416001\pi\)
\(600\) −1.68664e9 1.31773e10i −0.0130142 0.101677i
\(601\) 2.08879e10 + 1.18461e11i 0.160102 + 0.907982i 0.953972 + 0.299895i \(0.0969517\pi\)
−0.793870 + 0.608087i \(0.791937\pi\)
\(602\) −2.43045e11 + 1.40322e11i −1.85055 + 1.06842i
\(603\) −2.83108e10 + 7.36806e9i −0.214133 + 0.0557294i
\(604\) 4.05771e8 7.02816e8i 0.00304883 0.00528073i
\(605\) −5.10965e10 + 1.40386e11i −0.381390 + 1.04786i
\(606\) −6.09986e10 1.37534e10i −0.452303 0.101981i
\(607\) −9.53115e10 7.99759e10i −0.702087 0.589121i 0.220280 0.975437i \(-0.429303\pi\)
−0.922366 + 0.386316i \(0.873747\pi\)
\(608\) −1.90204e10 + 2.26676e10i −0.139189 + 0.165879i
\(609\) 6.55111e10 2.90553e11i 0.476262 2.11230i
\(610\) −1.92132e11 6.99305e10i −1.38765 0.505065i
\(611\) 2.39746e10 + 1.38417e10i 0.172023 + 0.0993174i
\(612\) 2.10039e10 + 8.07047e10i 0.149725 + 0.575298i
\(613\) 5.49077e10 + 9.51030e10i 0.388859 + 0.673523i 0.992296 0.123887i \(-0.0395361\pi\)
−0.603438 + 0.797410i \(0.706203\pi\)
\(614\) 1.19749e11 2.11150e10i 0.842557 0.148566i
\(615\) −1.37779e11 + 1.76352e10i −0.963124 + 0.123276i
\(616\) −1.08622e10 + 3.95353e9i −0.0754390 + 0.0274576i
\(617\) 1.09270e11 + 1.92672e10i 0.753979 + 0.132947i 0.537411 0.843321i \(-0.319403\pi\)
0.216568 + 0.976268i \(0.430514\pi\)
\(618\) −1.48837e11 7.03465e9i −1.02037 0.0482268i
\(619\) 8.50284e10 7.13473e10i 0.579164 0.485976i −0.305509 0.952189i \(-0.598827\pi\)
0.884672 + 0.466213i \(0.154382\pi\)
\(620\) 3.71084e10i 0.251134i
\(621\) 6.43502e10 1.96669e11i 0.432697 1.32242i
\(622\) 9.68076e10 0.646767
\(623\) 1.55565e11 + 1.85396e11i 1.03267 + 1.23069i
\(624\) 7.68940e9 + 4.93765e9i 0.0507171 + 0.0325673i
\(625\) −3.19515e10 + 1.81206e11i −0.209397 + 1.18755i
\(626\) 4.19925e10 + 1.15373e11i 0.273448 + 0.751292i
\(627\) 2.03036e10 1.54638e10i 0.131372 0.100057i
\(628\) 5.54141e9 + 3.14269e10i 0.0356272 + 0.202052i
\(629\) −3.07202e11 + 1.77363e11i −1.96255 + 1.13308i
\(630\) 1.75425e11 1.20963e11i 1.11360 0.767874i
\(631\) −7.66099e10 + 1.32692e11i −0.483245 + 0.837006i −0.999815 0.0192397i \(-0.993875\pi\)
0.516569 + 0.856245i \(0.327209\pi\)
\(632\) −1.84832e9 + 5.07823e9i −0.0115854 + 0.0318305i
\(633\) −1.63102e8 + 1.76714e8i −0.00101588 + 0.00110067i
\(634\) 7.15655e10 + 6.00506e10i 0.442942 + 0.371673i
\(635\) 1.26321e9 1.50543e9i 0.00776925 0.00925903i
\(636\) −9.14509e10 + 2.84732e10i −0.558933 + 0.174024i
\(637\) −6.85210e10 2.49396e10i −0.416165 0.151472i
\(638\) 1.75844e10 + 1.01523e10i 0.106131 + 0.0612750i
\(639\) 1.23039e11 5.63004e10i 0.737971 0.337682i
\(640\) −8.42109e9 1.45858e10i −0.0501936 0.0869379i
\(641\) −1.24077e11 + 2.18781e10i −0.734950 + 0.129592i −0.528581 0.848883i \(-0.677276\pi\)
−0.206369 + 0.978474i \(0.566165\pi\)
\(642\) −3.34913e10 + 8.00399e10i −0.197148 + 0.471158i
\(643\) 3.23763e10 1.17840e10i 0.189402 0.0689366i −0.245578 0.969377i \(-0.578978\pi\)
0.434980 + 0.900440i \(0.356756\pi\)
\(644\) 1.98494e11 + 3.49998e10i 1.15399 + 0.203480i
\(645\) 1.61724e11 + 3.13416e11i 0.934407 + 1.81085i
\(646\) 1.37384e11 1.15279e11i 0.788870 0.661941i
\(647\) 8.19366e10i 0.467585i −0.972286 0.233793i \(-0.924886\pi\)
0.972286 0.233793i \(-0.0751137\pi\)
\(648\) −4.71726e10 4.07530e10i −0.267541 0.231132i
\(649\) −1.35317e10 −0.0762734
\(650\) 5.67133e9 + 6.75883e9i 0.0317711 + 0.0378633i
\(651\) −1.18888e11 + 6.13470e10i −0.661935 + 0.341562i
\(652\) −1.76482e10 + 1.00088e11i −0.0976584 + 0.553848i
\(653\) 2.54459e10 + 6.99121e10i 0.139948 + 0.384503i 0.989790 0.142534i \(-0.0455251\pi\)
−0.849842 + 0.527037i \(0.823303\pi\)
\(654\) −9.19181e9 3.84615e9i −0.0502447 0.0210240i
\(655\) 1.39164e10 + 7.89241e10i 0.0756072 + 0.428790i
\(656\) −3.42779e10 + 1.97903e10i −0.185097 + 0.106866i
\(657\) −6.44626e10 6.10719e9i −0.345976 0.0327778i
\(658\) 9.19720e10 1.59300e11i 0.490628 0.849792i
\(659\) 2.56927e8 7.05901e8i 0.00136229 0.00374285i −0.939010 0.343891i \(-0.888255\pi\)
0.940372 + 0.340148i \(0.110477\pi\)
\(660\) 4.31833e9 + 1.38697e10i 0.0227583 + 0.0730957i
\(661\) −1.83035e11 1.53585e11i −0.958802 0.804530i 0.0219558 0.999759i \(-0.493011\pi\)
−0.980758 + 0.195229i \(0.937455\pi\)
\(662\) 6.91772e10 8.24422e10i 0.360189 0.429257i
\(663\) −4.06993e10 3.75642e10i −0.210636 0.194410i
\(664\) 5.98894e9 + 2.17980e9i 0.0308090 + 0.0112136i
\(665\) −3.96861e11 2.29128e11i −2.02933 1.17163i
\(666\) 1.13790e11 2.39510e11i 0.578370 1.21738i
\(667\) −1.77022e11 3.06612e11i −0.894385 1.54912i
\(668\) −6.13679e10 + 1.08208e10i −0.308202 + 0.0543443i
\(669\) −1.79220e11 2.35311e11i −0.894710 1.17473i
\(670\) −3.36487e10 + 1.22471e10i −0.166982 + 0.0607764i
\(671\) 4.94878e10 + 8.72604e9i 0.244123 + 0.0430454i
\(672\) 3.28085e10 5.10926e10i 0.160882 0.250542i
\(673\) −2.08496e11 + 1.74949e11i −1.01634 + 0.852808i −0.989163 0.146822i \(-0.953095\pi\)
−0.0271745 + 0.999631i \(0.508651\pi\)
\(674\) 2.32610e11i 1.12717i
\(675\) −3.17896e10 5.11080e10i −0.153133 0.246192i
\(676\) 9.83444e10 0.470937
\(677\) 1.33683e11 + 1.59318e11i 0.636389 + 0.758419i 0.983795 0.179296i \(-0.0573819\pi\)
−0.347406 + 0.937715i \(0.612937\pi\)
\(678\) 3.72086e9 7.87246e10i 0.0176086 0.372556i
\(679\) 2.11090e10 1.19715e11i 0.0993089 0.563209i
\(680\) 3.49124e10 + 9.59211e10i 0.163284 + 0.448620i
\(681\) 1.89014e10 + 1.47672e11i 0.0878831 + 0.686608i
\(682\) −1.58370e9 8.98163e9i −0.00732043 0.0415162i
\(683\) −1.05924e11 + 6.11550e10i −0.486754 + 0.281028i −0.723227 0.690610i \(-0.757342\pi\)
0.236473 + 0.971638i \(0.424009\pi\)
\(684\) −3.56283e10 + 1.29241e11i −0.162768 + 0.590442i
\(685\) −1.49140e11 + 2.58318e11i −0.677379 + 1.17325i
\(686\) −7.55016e10 + 2.07439e11i −0.340926 + 0.936685i
\(687\) 2.69693e11 + 6.08078e10i 1.21072 + 0.272981i
\(688\) 7.69854e10 + 6.45984e10i 0.343601 + 0.288315i
\(689\) 4.08892e10 4.87299e10i 0.181440 0.216231i
\(690\) 5.57112e10 2.47089e11i 0.245780 1.09008i
\(691\) 3.16234e11 + 1.15100e11i 1.38706 + 0.504849i 0.924312 0.381639i \(-0.124640\pi\)
0.462751 + 0.886488i \(0.346862\pi\)
\(692\) 1.11048e11 + 6.41138e10i 0.484270 + 0.279593i
\(693\) −3.72970e10 + 3.67644e10i −0.161712 + 0.159402i
\(694\) −5.99864e8 1.03900e9i −0.00258592 0.00447895i
\(695\) 5.27197e10 9.29590e9i 0.225961 0.0398430i
\(696\) −1.05794e11 + 1.35412e10i −0.450843 + 0.0577061i
\(697\) 2.25423e11 8.20474e10i 0.955142 0.347643i
\(698\) 1.51779e11 + 2.67627e10i 0.639424 + 0.112748i
\(699\) −3.35083e11 1.58374e10i −1.40360 0.0663400i
\(700\) 4.49094e10 3.76834e10i 0.187044 0.156949i
\(701\) 1.43165e11i 0.592877i −0.955052 0.296438i \(-0.904201\pi\)
0.955052 0.296438i \(-0.0957990\pi\)
\(702\) 4.09867e10 + 5.84647e9i 0.168770 + 0.0240739i
\(703\) −5.70256e11 −2.33479
\(704\) 2.66071e9 + 3.17091e9i 0.0108320 + 0.0129090i
\(705\) −1.94510e11 1.24902e11i −0.787382 0.505607i
\(706\) −3.67225e10 + 2.08264e11i −0.147813 + 0.838292i
\(707\) −9.43771e10 2.59299e11i −0.377737 1.03782i
\(708\) 5.65466e10 4.30676e10i 0.225047 0.171403i
\(709\) 6.31309e10 + 3.58033e11i 0.249837 + 1.41690i 0.808985 + 0.587829i \(0.200017\pi\)
−0.559148 + 0.829068i \(0.688872\pi\)
\(710\) 1.43434e11 8.28119e10i 0.564443 0.325881i
\(711\) 1.95845e9 + 2.44055e10i 0.00766363 + 0.0955013i
\(712\) 4.33324e10 7.50539e10i 0.168614 0.292047i
\(713\) −5.43898e10 + 1.49435e11i −0.210455 + 0.578221i
\(714\) −2.49597e11 + 2.70428e11i −0.960387 + 1.04054i
\(715\) −7.39052e9 6.20138e9i −0.0282781 0.0237282i
\(716\) 1.51522e10 1.80577e10i 0.0576531 0.0687083i
\(717\) 4.72823e11 1.47213e11i 1.78905 0.557020i
\(718\) −2.13637e11 7.77575e10i −0.803857 0.292580i
\(719\) 4.30933e11 + 2.48799e11i 1.61248 + 0.930966i 0.988793 + 0.149291i \(0.0476991\pi\)
0.623686 + 0.781675i \(0.285634\pi\)
\(720\) −6.21891e10 4.42152e10i −0.231411 0.164529i
\(721\) −3.28770e11 5.69446e11i −1.21661 2.10723i
\(722\) 9.47010e10 1.66983e10i 0.348503 0.0614504i
\(723\) −6.03583e10 + 1.44249e11i −0.220894 + 0.527908i
\(724\) −1.48125e11 + 5.39129e10i −0.539104 + 0.196218i
\(725\) −1.01414e11 1.78820e10i −0.367067 0.0647238i
\(726\) 8.84419e10 + 1.71397e11i 0.318355 + 0.616961i
\(727\) 3.80302e10 3.19111e10i 0.136142 0.114236i −0.572174 0.820132i \(-0.693900\pi\)
0.708316 + 0.705896i \(0.249455\pi\)
\(728\) 4.03264e10i 0.143570i
\(729\) −2.71166e11 7.89665e10i −0.960117 0.279597i
\(730\) −7.92586e10 −0.279097
\(731\) −3.91518e11 4.66593e11i −1.37114 1.63406i
\(732\) −2.34574e11 + 1.21041e11i −0.817025 + 0.421589i
\(733\) −9.00309e10 + 5.10591e11i −0.311872 + 1.76871i 0.277379 + 0.960761i \(0.410534\pi\)
−0.589250 + 0.807951i \(0.700577\pi\)
\(734\) 5.79133e8 + 1.59115e9i 0.00199523 + 0.00548186i
\(735\) 5.61687e11 + 2.35028e11i 1.92462 + 0.805324i
\(736\) −1.25332e10 7.10794e10i −0.0427121 0.242233i
\(737\) 7.62158e9 4.40032e9i 0.0258330 0.0149147i
\(738\) −1.03910e11 + 1.46150e11i −0.350292 + 0.492690i
\(739\) 3.44230e10 5.96224e10i 0.115417 0.199909i −0.802529 0.596613i \(-0.796513\pi\)
0.917946 + 0.396704i \(0.129846\pi\)
\(740\) 1.11012e11 3.05002e11i 0.370204 1.01713i
\(741\) −2.64683e10 8.50115e10i −0.0877917 0.281971i
\(742\) −3.23788e11 2.71690e11i −1.06818 0.896311i
\(743\) 3.59436e11 4.28359e11i 1.17941 1.40557i 0.284886 0.958561i \(-0.408044\pi\)
0.894529 0.447011i \(-0.147511\pi\)
\(744\) 3.52041e10 + 3.24923e10i 0.114895 + 0.106045i
\(745\) 4.85225e11 + 1.76608e11i 1.57514 + 0.573303i
\(746\) −1.18282e11 6.82901e10i −0.381912 0.220497i
\(747\) 2.87823e10 2.30968e9i 0.0924365 0.00741769i
\(748\) −1.25438e10 2.17266e10i −0.0400704 0.0694040i
\(749\) −3.77069e11 + 6.64874e10i −1.19810 + 0.211257i
\(750\) 1.09325e11 + 1.43540e11i 0.345520 + 0.453659i
\(751\) 1.86899e11 6.80257e10i 0.587553 0.213852i −0.0310996 0.999516i \(-0.509901\pi\)
0.618653 + 0.785664i \(0.287679\pi\)
\(752\) −6.48686e10 1.14381e10i −0.202844 0.0357670i
\(753\) 3.02010e10 4.70320e10i 0.0939380 0.146290i
\(754\) 5.42634e10 4.55324e10i 0.167889 0.140875i
\(755\) 4.50054e9i 0.0138509i