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Properties

Label 71.10.g.a.2.4
Level $71$
Weight $10$
Character 71.2
Analytic conductor $36.568$
Analytic rank $0$
Dimension $1272$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [71,10,Mod(2,71)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(71, base_ring=CyclotomicField(70))
 
chi = DirichletCharacter(H, H._module([6]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("71.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 71 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 71.g (of order \(35\), degree \(24\), 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: \(36.5675443676\)
Analytic rank: \(0\)
Dimension: \(1272\)
Relative dimension: \(53\) over \(\Q(\zeta_{35})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label 2.4
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.76410 + 39.2807i) q^{2} +(-78.6078 - 68.6776i) q^{3} +(-1029.92 - 92.6948i) q^{4} +(-479.392 - 1475.42i) q^{5} +(2836.38 - 2966.62i) q^{6} +(-2440.90 - 673.645i) q^{7} +(2755.62 - 20342.8i) q^{8} +(-1179.54 - 8707.68i) q^{9} +O(q^{10})\) \(q+(-1.76410 + 39.2807i) q^{2} +(-78.6078 - 68.6776i) q^{3} +(-1029.92 - 92.6948i) q^{4} +(-479.392 - 1475.42i) q^{5} +(2836.38 - 2966.62i) q^{6} +(-2440.90 - 673.645i) q^{7} +(2755.62 - 20342.8i) q^{8} +(-1179.54 - 8707.68i) q^{9} +(58801.2 - 16228.1i) q^{10} +(13008.3 - 24173.4i) q^{11} +(74594.0 + 78019.2i) q^{12} +(36922.4 + 68613.4i) q^{13} +(30767.3 - 94691.9i) q^{14} +(-63644.2 + 148903. i) q^{15} +(273276. + 49592.2i) q^{16} +(95950.0 + 69711.7i) q^{17} +(344125. - 30971.8i) q^{18} +(-391116. - 915062. i) q^{19} +(356974. + 1.56401e6i) q^{20} +(145609. + 220589. i) q^{21} +(926601. + 553619. i) q^{22} +(-46934.2 - 58853.6i) q^{23} +(-1.61371e6 + 1.40986e6i) q^{24} +(-366931. + 266591. i) q^{25} +(-2.76032e6 + 1.32930e6i) q^{26} +(-1.63716e6 + 2.48019e6i) q^{27} +(2.45150e6 + 920062. i) q^{28} +(-4.84606e6 + 2.89539e6i) q^{29} +(-5.73674e6 - 2.76267e6i) q^{30} +(-1.74467e6 + 316612. i) q^{31} +(-91263.8 + 399853. i) q^{32} +(-2.68272e6 + 1.00684e6i) q^{33} +(-2.90759e6 + 3.64601e6i) q^{34} +(176240. + 3.92429e6i) q^{35} +(407675. + 9.07758e6i) q^{36} +(-1.55617e6 + 1.95138e6i) q^{37} +(3.66343e7 - 1.37491e7i) q^{38} +(1.80981e6 - 7.92929e6i) q^{39} +(-3.13352e7 + 5.68650e6i) q^{40} +(6.02096e6 + 2.89954e6i) q^{41} +(-8.92175e6 + 5.33050e6i) q^{42} +(1.57181e7 + 5.89909e6i) q^{43} +(-1.56383e7 + 2.36910e7i) q^{44} +(-1.22820e7 + 5.91470e6i) q^{45} +(2.39461e6 - 1.73978e6i) q^{46} +(2.53260e7 - 2.21267e7i) q^{47} +(-1.80757e7 - 2.26662e7i) q^{48} +(-2.91373e7 - 1.74087e7i) q^{49} +(-9.82457e6 - 1.48836e7i) q^{50} +(-2.75478e6 - 1.20695e7i) q^{51} +(-3.16672e7 - 7.40891e7i) q^{52} +(2.50006e7 - 2.25010e6i) q^{53} +(-9.45354e7 - 6.86840e7i) q^{54} +(-4.19020e7 - 7.60409e6i) q^{55} +(-2.04300e7 + 4.77985e7i) q^{56} +(-3.20994e7 + 9.87919e7i) q^{57} +(-1.05184e8 - 1.95465e8i) q^{58} +(2.04729e7 + 2.14130e7i) q^{59} +(7.93512e7 - 1.47459e8i) q^{60} +(-1.57750e8 + 4.35363e7i) q^{61} +(-9.35896e6 - 6.90906e7i) q^{62} +(-2.98676e6 + 2.20491e7i) q^{63} +(1.21532e8 + 3.35408e7i) q^{64} +(8.35331e7 - 8.73688e7i) q^{65} +(-3.48169e7 - 1.07155e8i) q^{66} +(4.20175e7 + 3.78164e6i) q^{67} +(-9.23593e7 - 8.06919e7i) q^{68} +(-352529. + 7.84967e6i) q^{69} -1.54460e8 q^{70} +(-8.16885e7 + 1.97928e8i) q^{71} -1.80389e8 q^{72} +(-1.37964e7 + 3.07200e8i) q^{73} +(-7.39062e7 - 6.45699e7i) q^{74} +(4.71524e7 + 4.24379e6i) q^{75} +(3.17999e8 + 9.78699e8i) q^{76} +(-4.80362e7 + 5.02419e7i) q^{77} +(3.08276e8 + 8.50787e7i) q^{78} +(-4.22593e7 + 3.11971e8i) q^{79} +(-5.78370e7 - 4.26970e8i) q^{80} +(1.32301e8 - 3.65127e7i) q^{81} +(-1.24518e8 + 2.31393e8i) q^{82} +(-8.90904e7 - 9.31812e7i) q^{83} +(-1.29519e8 - 2.40687e8i) q^{84} +(5.68563e7 - 1.74986e8i) q^{85} +(-2.59449e8 + 6.07010e8i) q^{86} +(5.79787e8 + 1.05216e8i) q^{87} +(-4.55910e8 - 3.31238e8i) q^{88} +(4.84715e8 - 4.36251e7i) q^{89} +(-2.10667e8 - 4.92880e8i) q^{90} +(-4.39028e7 - 1.92351e8i) q^{91} +(4.28832e7 + 6.49653e7i) q^{92} +(1.58889e8 + 9.49318e7i) q^{93} +(8.24475e8 + 1.03386e9i) q^{94} +(-1.16260e9 + 1.01573e9i) q^{95} +(3.46350e7 - 2.51638e7i) q^{96} +(-1.12184e9 + 5.40250e8i) q^{97} +(7.35229e8 - 1.11382e9i) q^{98} +(-2.25838e8 - 8.47585e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 1272 q - 76 q^{2} - 395 q^{3} + 13542 q^{4} - 1610 q^{5} - 4334 q^{6} - 4827 q^{7} - 18627 q^{8} + 286810 q^{9} - 53448 q^{10} - 170685 q^{11} + 138323 q^{12} - 93291 q^{13} + 985964 q^{14} - 966194 q^{15} + 4755334 q^{16} + 2558412 q^{17} - 2619769 q^{18} - 172269 q^{19} + 738120 q^{20} + 1797929 q^{21} + 3015622 q^{22} + 6635088 q^{23} + 4803145 q^{24} - 115100016 q^{25} + 19254293 q^{26} - 17686931 q^{27} + 15761532 q^{28} - 10052927 q^{29} + 62637435 q^{30} - 23748991 q^{31} + 10388192 q^{32} - 15097203 q^{33} + 33217854 q^{34} - 24823174 q^{35} + 27856812 q^{36} - 27156308 q^{37} - 43400577 q^{38} + 251072838 q^{39} - 129856160 q^{40} + 62087988 q^{41} - 91873950 q^{42} - 167299067 q^{43} + 60914131 q^{44} - 31536191 q^{45} - 50201490 q^{46} - 23317743 q^{47} + 10641329 q^{48} + 338745866 q^{49} + 303770229 q^{50} + 448039613 q^{51} - 979580293 q^{52} + 12085215 q^{53} - 182583505 q^{54} - 243892552 q^{55} + 30440435 q^{56} + 714581966 q^{57} - 244549660 q^{58} - 859013315 q^{59} - 1894499000 q^{60} - 876373921 q^{61} + 186553636 q^{62} - 196611021 q^{63} + 5528242635 q^{64} + 867018244 q^{65} + 2727701199 q^{66} - 286780089 q^{67} - 1689988351 q^{68} - 3073308182 q^{69} - 41489396 q^{70} - 2538053548 q^{71} - 6821388000 q^{72} + 128479023 q^{73} + 3282772334 q^{74} + 3407782757 q^{75} + 7133788844 q^{76} + 1087098389 q^{77} + 2715049934 q^{78} + 144243625 q^{79} - 7443877603 q^{80} - 4083269278 q^{81} - 10375744380 q^{82} + 1543773955 q^{83} - 4117054288 q^{84} + 7843382686 q^{85} + 3545751759 q^{86} + 5261609811 q^{87} - 818728797 q^{88} - 1369081479 q^{89} + 10041256259 q^{90} - 7299574322 q^{91} + 602797624 q^{92} - 2146129677 q^{93} - 683447510 q^{94} - 7007204038 q^{95} + 6601829126 q^{96} - 10081488030 q^{97} - 5942379880 q^{98} - 4074592265 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Display 100 coefficients 10 coefficients

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/71\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{35}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.76410 + 39.2807i −0.0779629 + 1.73598i 0.455570 + 0.890200i \(0.349435\pi\)
−0.533533 + 0.845779i \(0.679136\pi\)
\(3\) −78.6078 − 68.6776i −0.560299 − 0.489519i 0.330568 − 0.943782i \(-0.392760\pi\)
−0.890867 + 0.454263i \(0.849902\pi\)
\(4\) −1029.92 − 92.6948i −2.01157 − 0.181045i
\(5\) −479.392 − 1475.42i −0.343025 − 1.05572i −0.962632 − 0.270811i \(-0.912708\pi\)
0.619607 − 0.784912i \(-0.287292\pi\)
\(6\) 2836.38 − 2966.62i 0.893477 − 0.934503i
\(7\) −2440.90 − 673.645i −0.384245 − 0.106045i 0.0685768 − 0.997646i \(-0.478154\pi\)
−0.452822 + 0.891601i \(0.649583\pi\)
\(8\) 2755.62 − 20342.8i 0.237856 − 1.75593i
\(9\) −1179.54 − 8707.68i −0.0599266 − 0.442396i
\(10\) 58801.2 − 16228.1i 1.85946 − 0.513177i
\(11\) 13008.3 − 24173.4i 0.267888 − 0.497818i −0.710741 − 0.703454i \(-0.751640\pi\)
0.978629 + 0.205635i \(0.0659260\pi\)
\(12\) 74594.0 + 78019.2i 1.03846 + 1.08614i
\(13\) 36922.4 + 68613.4i 0.358546 + 0.666291i 0.994419 − 0.105503i \(-0.0336453\pi\)
−0.635873 + 0.771794i \(0.719360\pi\)
\(14\) 30767.3 − 94691.9i 0.214049 − 0.658774i
\(15\) −63644.2 + 148903.i −0.324599 + 0.759438i
\(16\) 273276. + 49592.2i 1.04246 + 0.189179i
\(17\) 95950.0 + 69711.7i 0.278628 + 0.202435i 0.718319 − 0.695714i \(-0.244912\pi\)
−0.439691 + 0.898149i \(0.644912\pi\)
\(18\) 344125. − 30971.8i 0.772662 − 0.0695408i
\(19\) −391116. − 915062.i −0.688517 − 1.61087i −0.787890 − 0.615816i \(-0.788827\pi\)
0.0993732 − 0.995050i \(-0.468316\pi\)
\(20\) 356974. + 1.56401e6i 0.498886 + 2.18576i
\(21\) 145609. + 220589.i 0.163381 + 0.247512i
\(22\) 926601. + 553619.i 0.843317 + 0.503859i
\(23\) −46934.2 − 58853.6i −0.0349715 − 0.0438528i 0.764038 − 0.645171i \(-0.223214\pi\)
−0.799010 + 0.601318i \(0.794642\pi\)
\(24\) −1.61371e6 + 1.40986e6i −0.992830 + 0.867409i
\(25\) −366931. + 266591.i −0.187869 + 0.136494i
\(26\) −2.76032e6 + 1.32930e6i −1.18462 + 0.570483i
\(27\) −1.63716e6 + 2.48019e6i −0.592862 + 0.898147i
\(28\) 2.45150e6 + 920062.i 0.753737 + 0.282882i
\(29\) −4.84606e6 + 2.89539e6i −1.27233 + 0.760179i −0.980543 − 0.196306i \(-0.937105\pi\)
−0.291782 + 0.956485i \(0.594248\pi\)
\(30\) −5.73674e6 − 2.76267e6i −1.29306 − 0.622706i
\(31\) −1.74467e6 + 316612.i −0.339302 + 0.0615743i −0.345534 − 0.938406i \(-0.612302\pi\)
0.00623154 + 0.999981i \(0.498016\pi\)
\(32\) −91263.8 + 399853.i −0.0153859 + 0.0674101i
\(33\) −2.68272e6 + 1.00684e6i −0.393789 + 0.147791i
\(34\) −2.90759e6 + 3.64601e6i −0.373146 + 0.467910i
\(35\) 176240. + 3.92429e6i 0.0198517 + 0.442033i
\(36\) 407675. + 9.07758e6i 0.0404532 + 0.900760i
\(37\) −1.55617e6 + 1.95138e6i −0.136505 + 0.171172i −0.845386 − 0.534157i \(-0.820629\pi\)
0.708880 + 0.705329i \(0.249201\pi\)
\(38\) 3.66343e7 − 1.37491e7i 2.85011 − 1.06966i
\(39\) 1.80981e6 − 7.92929e6i 0.125269 − 0.548837i
\(40\) −3.13352e7 + 5.68650e6i −1.93536 + 0.351217i
\(41\) 6.02096e6 + 2.89954e6i 0.332766 + 0.160252i 0.592804 − 0.805347i \(-0.298021\pi\)
−0.260038 + 0.965598i \(0.583735\pi\)
\(42\) −8.92175e6 + 5.33050e6i −0.442414 + 0.264330i
\(43\) 1.57181e7 + 5.89909e6i 0.701118 + 0.263134i 0.676372 − 0.736560i \(-0.263551\pi\)
0.0247454 + 0.999694i \(0.492123\pi\)
\(44\) −1.56383e7 + 2.36910e7i −0.629002 + 0.952897i
\(45\) −1.22820e7 + 5.91470e6i −0.446491 + 0.215019i
\(46\) 2.39461e6 − 1.73978e6i 0.0788541 − 0.0572908i
\(47\) 2.53260e7 − 2.21267e7i 0.757054 − 0.661419i −0.190256 − 0.981734i \(-0.560932\pi\)
0.947311 + 0.320316i \(0.103789\pi\)
\(48\) −1.80757e7 − 2.26662e7i −0.491485 − 0.616303i
\(49\) −2.91373e7 − 1.74087e7i −0.722050 − 0.431405i
\(50\) −9.82457e6 − 1.48836e7i −0.222305 − 0.336777i
\(51\) −2.75478e6 − 1.20695e7i −0.0570193 − 0.249818i
\(52\) −3.16672e7 − 7.40891e7i −0.600613 − 1.40520i
\(53\) 2.50006e7 − 2.25010e6i 0.435221 − 0.0391706i 0.130137 − 0.991496i \(-0.458458\pi\)
0.305084 + 0.952325i \(0.401316\pi\)
\(54\) −9.45354e7 − 6.86840e7i −1.51294 − 1.09922i
\(55\) −4.19020e7 − 7.60409e6i −0.617451 − 0.112051i
\(56\) −2.04300e7 + 4.77985e7i −0.277602 + 0.649483i
\(57\) −3.20994e7 + 9.87919e7i −0.402773 + 1.23961i
\(58\) −1.05184e8 − 1.95465e8i −1.22046 − 2.26800i
\(59\) 2.04729e7 + 2.14130e7i 0.219961 + 0.230061i 0.823563 − 0.567225i \(-0.191983\pi\)
−0.603602 + 0.797285i \(0.706269\pi\)
\(60\) 7.93512e7 − 1.47459e8i 0.790447 − 1.46890i
\(61\) −1.57750e8 + 4.35363e7i −1.45877 + 0.402594i −0.903324 − 0.428959i \(-0.858880\pi\)
−0.555444 + 0.831554i \(0.687452\pi\)
\(62\) −9.35896e6 − 6.90906e7i −0.0804387 − 0.593822i
\(63\) −2.98676e6 + 2.20491e7i −0.0238873 + 0.176343i
\(64\) 1.21532e8 + 3.35408e7i 0.905486 + 0.249898i
\(65\) 8.35331e7 − 8.73688e7i 0.580428 − 0.607080i
\(66\) −3.48169e7 − 1.07155e8i −0.225862 − 0.695131i
\(67\) 4.20175e7 + 3.78164e6i 0.254738 + 0.0229268i 0.216272 − 0.976333i \(-0.430610\pi\)
0.0384655 + 0.999260i \(0.487753\pi\)
\(68\) −9.23593e7 − 8.06919e7i −0.523830 − 0.457656i
\(69\) −352529. + 7.84967e6i −0.00187230 + 0.0416899i
\(70\) −1.54460e8 −0.768907
\(71\) −8.16885e7 + 1.97928e8i −0.381503 + 0.924367i
\(72\) −1.80389e8 −0.791069
\(73\) −1.37964e7 + 3.07200e8i −0.0568606 + 1.26610i 0.744379 + 0.667757i \(0.232746\pi\)
−0.801240 + 0.598343i \(0.795826\pi\)
\(74\) −7.39062e7 − 6.45699e7i −0.286509 − 0.250315i
\(75\) 4.71524e7 + 4.24379e6i 0.172079 + 0.0154874i
\(76\) 3.17999e8 + 9.78699e8i 1.09336 + 3.36502i
\(77\) −4.80362e7 + 5.02419e7i −0.155726 + 0.162876i
\(78\) 3.08276e8 + 8.50787e7i 0.943004 + 0.260252i
\(79\) −4.22593e7 + 3.11971e8i −0.122068 + 0.901140i 0.821558 + 0.570125i \(0.193105\pi\)
−0.943626 + 0.331015i \(0.892609\pi\)
\(80\) −5.78370e7 − 4.26970e8i −0.157871 − 1.16545i
\(81\) 1.32301e8 − 3.65127e7i 0.341492 − 0.0942458i
\(82\) −1.24518e8 + 2.31393e8i −0.304137 + 0.565181i
\(83\) −8.90904e7 − 9.31812e7i −0.206053 − 0.215515i 0.611691 − 0.791097i \(-0.290490\pi\)
−0.817744 + 0.575582i \(0.804775\pi\)
\(84\) −1.29519e8 − 2.40687e8i −0.283842 − 0.527467i
\(85\) 5.68563e7 − 1.74986e8i 0.118139 − 0.363594i
\(86\) −2.59449e8 + 6.07010e8i −0.511456 + 1.19661i
\(87\) 5.79787e8 + 1.05216e8i 1.08500 + 0.196899i
\(88\) −4.55910e8 − 3.31238e8i −0.810414 − 0.588800i
\(89\) 4.84715e8 − 4.36251e7i 0.818901 − 0.0737024i 0.327736 − 0.944769i \(-0.393714\pi\)
0.491165 + 0.871067i \(0.336571\pi\)
\(90\) −2.10667e8 − 4.92880e8i −0.338459 − 0.791863i
\(91\) −4.39028e7 − 1.92351e8i −0.0671130 − 0.294041i
\(92\) 4.28832e7 + 6.49653e7i 0.0624082 + 0.0945444i
\(93\) 1.58889e8 + 9.49318e7i 0.220253 + 0.131595i
\(94\) 8.24475e8 + 1.03386e9i 1.08919 + 1.36580i
\(95\) −1.16260e9 + 1.01573e9i −1.46445 + 1.27945i
\(96\) 3.46350e7 − 2.51638e7i 0.0416192 − 0.0302381i
\(97\) −1.12184e9 + 5.40250e8i −1.28664 + 0.619615i −0.947089 − 0.320972i \(-0.895991\pi\)
−0.339554 + 0.940586i \(0.610276\pi\)
\(98\) 7.35229e8 − 1.11382e9i 0.805203 − 1.21983i
\(99\) −2.25838e8 − 8.47585e7i −0.236286 − 0.0886798i
\(100\) 4.02622e8 − 2.40556e8i 0.402622 − 0.240556i
\(101\) 4.25663e8 + 2.04988e8i 0.407024 + 0.196012i 0.626182 − 0.779677i \(-0.284617\pi\)
−0.219158 + 0.975689i \(0.570331\pi\)
\(102\) 4.78958e8 − 8.69181e7i 0.438124 − 0.0795078i
\(103\) −4.00019e7 + 1.75260e8i −0.0350197 + 0.153432i −0.989415 − 0.145115i \(-0.953645\pi\)
0.954395 + 0.298547i \(0.0965019\pi\)
\(104\) 1.49753e9 − 5.62034e8i 1.25524 − 0.471100i
\(105\) 2.55657e8 − 3.20583e8i 0.205260 − 0.257388i
\(106\) 4.42818e7 + 9.86012e8i 0.0340682 + 0.758588i
\(107\) 5.43886e7 + 1.21106e9i 0.0401126 + 0.893177i 0.913670 + 0.406456i \(0.133236\pi\)
−0.873558 + 0.486721i \(0.838193\pi\)
\(108\) 1.91605e9 − 2.40265e9i 1.35519 − 1.69935i
\(109\) 7.82853e8 − 2.93810e8i 0.531204 − 0.199364i −0.0713369 − 0.997452i \(-0.522727\pi\)
0.602541 + 0.798088i \(0.294155\pi\)
\(110\) 3.72613e8 − 1.63253e9i 0.242656 − 1.06315i
\(111\) 2.56343e8 − 4.65194e7i 0.160276 − 0.0290858i
\(112\) −6.33631e8 − 3.05140e8i −0.380500 − 0.183239i
\(113\) −3.72231e8 + 2.22398e8i −0.214763 + 0.128315i −0.616252 − 0.787549i \(-0.711350\pi\)
0.401489 + 0.915864i \(0.368493\pi\)
\(114\) −3.82399e9 − 1.43517e9i −2.12053 − 0.795849i
\(115\) −6.43338e7 + 9.74615e7i −0.0343004 + 0.0519628i
\(116\) 5.25946e9 − 2.53282e9i 2.69700 − 1.29881i
\(117\) 5.53912e8 − 4.02441e8i 0.273278 − 0.198548i
\(118\) −8.77233e8 + 7.66415e8i −0.416530 + 0.363911i
\(119\) −1.87243e8 − 2.34796e8i −0.0855943 − 0.107332i
\(120\) 2.85373e9 + 1.70502e9i 1.25631 + 0.750610i
\(121\) 8.83847e8 + 1.33897e9i 0.374837 + 0.567854i
\(122\) −1.43185e9 − 6.27335e9i −0.585166 − 2.56378i
\(123\) −2.74161e8 − 6.41432e8i −0.108002 − 0.252684i
\(124\) 1.82623e9 − 1.64364e8i 0.693678 − 0.0624321i
\(125\) −1.88206e9 − 1.36740e9i −0.689508 − 0.500957i
\(126\) −8.60837e8 − 1.56219e8i −0.304266 − 0.0552162i
\(127\) 3.94110e8 − 9.22066e8i 0.134431 − 0.314518i −0.838765 − 0.544494i \(-0.816722\pi\)
0.973196 + 0.229976i \(0.0738647\pi\)
\(128\) −1.59679e9 + 4.91442e9i −0.525779 + 1.61818i
\(129\) −8.30427e8 − 1.54319e9i −0.264027 − 0.490644i
\(130\) 3.28455e9 + 3.43537e9i 1.00863 + 1.05494i
\(131\) −1.82817e9 + 3.39731e9i −0.542370 + 1.00789i 0.450956 + 0.892546i \(0.351083\pi\)
−0.993325 + 0.115346i \(0.963202\pi\)
\(132\) 2.85633e9 − 7.88297e8i 0.818890 − 0.225999i
\(133\) 3.38248e8 + 2.49705e9i 0.0937352 + 0.691981i
\(134\) −2.22668e8 + 1.64380e9i −0.0596605 + 0.440432i
\(135\) 4.44415e9 + 1.22651e9i 1.15156 + 0.317811i
\(136\) 1.68254e9 − 1.75979e9i 0.421735 − 0.441100i
\(137\) 5.51285e8 + 1.69668e9i 0.133701 + 0.411488i 0.995386 − 0.0959552i \(-0.0305905\pi\)
−0.861685 + 0.507444i \(0.830591\pi\)
\(138\) −3.07719e8 − 2.76952e7i −0.0722268 − 0.00650053i
\(139\) 6.21166e7 + 5.42696e7i 0.0141137 + 0.0123308i 0.664967 − 0.746873i \(-0.268446\pi\)
−0.650853 + 0.759204i \(0.725589\pi\)
\(140\) 1.82247e8 − 4.05805e9i 0.0400945 − 0.892774i
\(141\) −3.51043e9 −0.747954
\(142\) −7.63065e9 − 3.55795e9i −1.57494 − 0.734348i
\(143\) 2.13892e9 0.427742
\(144\) 1.09495e8 − 2.43809e9i 0.0212208 − 0.472519i
\(145\) 6.59507e9 + 5.76194e9i 1.23898 + 1.08246i
\(146\) −1.20427e10 − 1.08386e9i −2.19349 − 0.197418i
\(147\) 1.09483e9 + 3.36954e9i 0.193383 + 0.595173i
\(148\) 1.78362e9 − 1.86552e9i 0.305580 − 0.319611i
\(149\) −3.70927e9 − 1.02369e9i −0.616524 − 0.170150i −0.0561947 − 0.998420i \(-0.517897\pi\)
−0.560329 + 0.828270i \(0.689325\pi\)
\(150\) −2.49881e8 + 1.84469e9i −0.0403016 + 0.297518i
\(151\) 4.66864e8 + 3.44653e9i 0.0730793 + 0.539493i 0.990069 + 0.140582i \(0.0448974\pi\)
−0.916990 + 0.398911i \(0.869388\pi\)
\(152\) −1.96927e10 + 5.43485e9i −2.99233 + 0.825831i
\(153\) 4.93851e8 − 9.17729e8i 0.0728592 − 0.135395i
\(154\) −1.88880e9 − 1.97553e9i −0.270609 − 0.283035i
\(155\) 1.30352e9 + 2.42234e9i 0.181395 + 0.337088i
\(156\) −2.59897e9 + 7.99881e9i −0.351350 + 1.08135i
\(157\) 1.23852e9 − 2.89766e9i 0.162688 − 0.380627i −0.818274 − 0.574829i \(-0.805069\pi\)
0.980962 + 0.194202i \(0.0622116\pi\)
\(158\) −1.21799e10 − 2.21032e9i −1.55484 − 0.282162i
\(159\) −2.11978e9 − 1.54011e9i −0.263028 − 0.191101i
\(160\) 6.33701e8 − 5.70341e7i 0.0764442 − 0.00688010i
\(161\) 7.49151e7 + 1.75273e8i 0.00878725 + 0.0205588i
\(162\) 1.20085e9 + 5.26129e9i 0.136985 + 0.600170i
\(163\) 6.47039e9 + 9.80221e9i 0.717936 + 1.08763i 0.992040 + 0.125927i \(0.0401904\pi\)
−0.274103 + 0.961700i \(0.588381\pi\)
\(164\) −5.93236e9 − 3.54442e9i −0.640369 − 0.382603i
\(165\) 2.77159e9 + 3.47547e9i 0.291106 + 0.365036i
\(166\) 3.81739e9 − 3.33515e9i 0.390194 − 0.340902i
\(167\) 8.05698e9 − 5.85374e9i 0.801583 − 0.582384i −0.109795 − 0.993954i \(-0.535020\pi\)
0.911378 + 0.411570i \(0.135020\pi\)
\(168\) 4.88864e9 − 2.35425e9i 0.473474 − 0.228013i
\(169\) 2.49746e9 − 3.78348e9i 0.235509 − 0.356781i
\(170\) 6.77326e9 + 2.54205e9i 0.621982 + 0.233434i
\(171\) −7.50673e9 + 4.48506e9i −0.671380 + 0.401131i
\(172\) −1.56416e10 − 7.53259e9i −1.36271 − 0.656246i
\(173\) 1.94633e10 − 3.53207e9i 1.65200 − 0.299794i 0.728976 − 0.684539i \(-0.239996\pi\)
0.923023 + 0.384745i \(0.125711\pi\)
\(174\) −5.15575e9 + 2.25888e10i −0.426403 + 1.86819i
\(175\) 1.07523e9 − 4.03540e8i 0.0866621 − 0.0325248i
\(176\) 4.75366e9 − 5.96090e9i 0.373440 − 0.468279i
\(177\) −1.38739e8 − 3.08926e9i −0.0106247 − 0.236578i
\(178\) 8.58541e8 + 1.91169e10i 0.0641019 + 1.42734i
\(179\) −1.12370e8 + 1.40907e8i −0.00818110 + 0.0102588i −0.785905 − 0.618347i \(-0.787803\pi\)
0.777724 + 0.628606i \(0.216374\pi\)
\(180\) 1.31978e10 − 4.95322e9i 0.937077 − 0.351691i
\(181\) 2.53813e9 − 1.11203e10i 0.175776 − 0.770126i −0.807774 − 0.589492i \(-0.799328\pi\)
0.983550 − 0.180634i \(-0.0578149\pi\)
\(182\) 7.63313e9 − 1.38521e9i 0.515681 − 0.0935824i
\(183\) 1.53904e10 + 7.41162e9i 1.01442 + 0.488521i
\(184\) −1.32658e9 + 7.92595e8i −0.0853205 + 0.0509766i
\(185\) 3.62511e9 + 1.36053e9i 0.227535 + 0.0853954i
\(186\) −4.00929e9 + 6.07381e9i −0.245617 + 0.372094i
\(187\) 2.93331e9 − 1.41261e9i 0.175417 − 0.0844763i
\(188\) −2.81349e10 + 2.04412e10i −1.64261 + 1.19343i
\(189\) 5.66690e9 − 4.95102e9i 0.323048 − 0.282239i
\(190\) −3.78478e10 − 4.74597e10i −2.10693 − 2.64200i
\(191\) −2.29746e10 − 1.37267e10i −1.24910 − 0.746304i −0.272667 − 0.962109i \(-0.587906\pi\)
−0.976437 + 0.215804i \(0.930763\pi\)
\(192\) −7.24989e9 − 1.09831e10i −0.385013 − 0.583270i
\(193\) −6.34257e9 − 2.77886e10i −0.329046 − 1.44165i −0.820952 − 0.570998i \(-0.806557\pi\)
0.491905 − 0.870649i \(-0.336301\pi\)
\(194\) −1.92424e10 − 4.50197e10i −0.975327 − 2.28189i
\(195\) −1.25666e10 + 1.13102e9i −0.622391 + 0.0560162i
\(196\) 2.83955e10 + 2.06306e10i 1.37435 + 0.998524i
\(197\) −2.11706e10 − 3.84189e9i −1.00146 − 0.181739i −0.347026 − 0.937856i \(-0.612808\pi\)
−0.654436 + 0.756117i \(0.727094\pi\)
\(198\) 3.72777e9 − 8.72156e9i 0.172368 − 0.403275i
\(199\) 7.77776e9 − 2.39375e10i 0.351573 − 1.08203i −0.606397 − 0.795162i \(-0.707386\pi\)
0.957970 − 0.286868i \(-0.0926142\pi\)
\(200\) 4.41209e9 + 8.19903e9i 0.194989 + 0.362349i
\(201\) −3.04319e9 − 3.18292e9i −0.131506 − 0.137545i
\(202\) −8.80300e9 + 1.63587e10i −0.372006 + 0.691303i
\(203\) 1.37792e10 − 3.80282e9i 0.569498 − 0.157171i
\(204\) 1.71844e9 + 1.26860e10i 0.0694701 + 0.512849i
\(205\) 1.39163e9 − 1.02735e10i 0.0550342 − 0.406279i
\(206\) −6.81376e9 − 1.88048e9i −0.263624 − 0.0727555i
\(207\) −4.57118e8 + 4.78107e8i −0.0173046 + 0.0180992i
\(208\) 6.68731e9 + 2.05814e10i 0.247723 + 0.762414i
\(209\) −2.72079e10 − 2.44876e9i −0.986364 − 0.0887744i
\(210\) 1.21417e10 + 1.06079e10i 0.430818 + 0.376394i
\(211\) −1.01003e9 + 2.24902e10i −0.0350805 + 0.781127i 0.901942 + 0.431857i \(0.142142\pi\)
−0.937022 + 0.349269i \(0.886430\pi\)
\(212\) −2.59573e10 −0.882568
\(213\) 2.00146e10 − 9.94852e9i 0.666251 − 0.331169i
\(214\) −4.76671e10 −1.55366
\(215\) 1.16850e9 − 2.60187e10i 0.0372955 − 0.830448i
\(216\) 4.59426e10 + 4.01389e10i 1.43606 + 1.25465i
\(217\) 4.47186e9 + 4.02474e8i 0.136905 + 0.0123217i
\(218\) 1.01600e10 + 3.12693e10i 0.304678 + 0.937701i
\(219\) 2.21822e10 − 2.32008e10i 0.651639 − 0.681561i
\(220\) 4.24510e10 + 1.17157e10i 1.22176 + 0.337184i
\(221\) −1.24045e9 + 9.15738e9i −0.0349796 + 0.258230i
\(222\) 1.37510e9 + 1.01514e10i 0.0379967 + 0.280503i
\(223\) 4.48804e10 − 1.23862e10i 1.21530 − 0.335402i 0.401128 − 0.916022i \(-0.368618\pi\)
0.814175 + 0.580620i \(0.197190\pi\)
\(224\) 4.92124e8 − 9.14520e8i 0.0130605 − 0.0242704i
\(225\) 2.75419e9 + 2.88066e9i 0.0716429 + 0.0749326i
\(226\) −8.07928e9 − 1.50138e10i −0.206008 − 0.382828i
\(227\) −2.40544e10 + 7.40320e10i −0.601283 + 1.85056i −0.0807172 + 0.996737i \(0.525721\pi\)
−0.520566 + 0.853822i \(0.674279\pi\)
\(228\) 4.22175e10 − 9.87727e10i 1.03463 − 2.42064i
\(229\) 3.29635e10 + 5.98199e9i 0.792088 + 0.143743i 0.559498 − 0.828832i \(-0.310994\pi\)
0.232591 + 0.972575i \(0.425280\pi\)
\(230\) −3.71487e9 − 2.69901e9i −0.0875322 − 0.0635959i
\(231\) 7.22651e9 − 6.50398e8i 0.166984 − 0.0150288i
\(232\) 4.55465e10 + 1.06561e11i 1.03219 + 2.41492i
\(233\) −2.93939e8 − 1.28783e9i −0.00653364 − 0.0286258i 0.971556 − 0.236810i \(-0.0761018\pi\)
−0.978090 + 0.208184i \(0.933245\pi\)
\(234\) 1.48310e10 + 2.24680e10i 0.323370 + 0.489884i
\(235\) −4.47873e10 − 2.67591e10i −0.957964 − 0.572357i
\(236\) −1.91007e10 − 2.39515e10i −0.400815 − 0.502606i
\(237\) 2.47473e10 − 2.16211e10i 0.509519 − 0.445154i
\(238\) 9.55325e9 − 6.94084e9i 0.192999 − 0.140222i
\(239\) 9.95580e9 − 4.79446e9i 0.197372 − 0.0950493i −0.332587 − 0.943073i \(-0.607922\pi\)
0.529959 + 0.848023i \(0.322207\pi\)
\(240\) −2.47768e10 + 3.75353e10i −0.482053 + 0.730280i
\(241\) 7.95368e10 + 2.98506e10i 1.51877 + 0.570003i 0.964904 − 0.262605i \(-0.0845815\pi\)
0.553864 + 0.832607i \(0.313153\pi\)
\(242\) −5.41549e10 + 3.23561e10i −1.01501 + 0.606438i
\(243\) 3.97938e10 + 1.91637e10i 0.732128 + 0.352574i
\(244\) 1.66506e11 − 3.02165e10i 3.00730 − 0.545745i
\(245\) −1.17170e10 + 5.13353e10i −0.207763 + 0.910268i
\(246\) 2.56796e10 − 9.63770e9i 0.447074 − 0.167790i
\(247\) 4.83445e10 − 6.06221e10i 0.826440 − 1.03632i
\(248\) 1.63311e9 + 3.63641e10i 0.0274147 + 0.610436i
\(249\) 6.03738e8 + 1.34433e10i 0.00995295 + 0.221620i
\(250\) 5.70326e10 − 7.15166e10i 0.923406 − 1.15792i
\(251\) 8.76608e9 − 3.28997e9i 0.139404 − 0.0523190i −0.280698 − 0.959796i \(-0.590566\pi\)
0.420101 + 0.907477i \(0.361994\pi\)
\(252\) 5.11998e9 − 2.24321e10i 0.0799771 − 0.350403i
\(253\) −2.03322e9 + 3.68976e8i −0.0311992 + 0.00566181i
\(254\) 3.55242e10 + 1.71075e10i 0.535516 + 0.257891i
\(255\) −1.64869e10 + 9.85049e9i −0.244179 + 0.145890i
\(256\) −1.29790e11 − 4.87111e10i −1.88870 − 0.708840i
\(257\) −6.79091e10 + 1.02878e11i −0.971022 + 1.47103i −0.0911421 + 0.995838i \(0.529052\pi\)
−0.879879 + 0.475197i \(0.842377\pi\)
\(258\) 6.20827e10 − 2.98974e10i 0.872332 − 0.420093i
\(259\) 5.11299e9 − 3.71480e9i 0.0706035 − 0.0512964i
\(260\) −9.41314e10 + 8.22401e10i −1.27748 + 1.11610i
\(261\) 3.09282e10 + 3.87828e10i 0.412546 + 0.517316i
\(262\) −1.30224e11 − 7.78050e10i −1.70739 − 1.02012i
\(263\) −1.15781e9 − 1.75401e9i −0.0149223 − 0.0226064i 0.827036 − 0.562150i \(-0.190025\pi\)
−0.841958 + 0.539543i \(0.818597\pi\)
\(264\) 1.30895e10 + 5.73487e10i 0.165846 + 0.726617i
\(265\) −1.53049e10 − 3.58077e10i −0.190645 − 0.446036i
\(266\) −9.86825e10 + 8.88159e9i −1.20857 + 0.108774i
\(267\) −4.10984e10 − 2.98598e10i −0.494908 − 0.359572i
\(268\) −4.29242e10 − 7.78960e9i −0.508272 − 0.0922377i
\(269\) −3.04680e10 + 7.12835e10i −0.354780 + 0.830050i 0.643150 + 0.765740i \(0.277627\pi\)
−0.997930 + 0.0643092i \(0.979516\pi\)
\(270\) −5.60181e10 + 1.72406e11i −0.641492 + 1.97431i
\(271\) −3.43773e10 − 6.38837e10i −0.387177 − 0.719496i 0.610171 − 0.792269i \(-0.291101\pi\)
−0.997348 + 0.0727738i \(0.976815\pi\)
\(272\) 2.27636e10 + 2.38089e10i 0.252163 + 0.263742i
\(273\) −9.75909e9 + 1.81354e10i −0.106335 + 0.197604i
\(274\) −6.76194e10 + 1.86618e10i −0.724759 + 0.200021i
\(275\) 1.67128e9 + 1.23379e10i 0.0176218 + 0.130090i
\(276\) 1.09070e9 − 8.05189e9i 0.0113140 − 0.0835232i
\(277\) −1.11618e11 − 3.08046e10i −1.13914 − 0.314382i −0.354937 − 0.934890i \(-0.615498\pi\)
−0.784200 + 0.620509i \(0.786926\pi\)
\(278\) −2.24133e9 + 2.34425e9i −0.0225063 + 0.0235397i
\(279\) 4.81486e9 + 1.48186e10i 0.0475734 + 0.146416i
\(280\) 8.03167e10 + 7.22864e9i 0.780899 + 0.0702822i
\(281\) −8.21344e10 − 7.17587e10i −0.785863 − 0.686588i 0.168346 − 0.985728i \(-0.446157\pi\)
−0.954209 + 0.299140i \(0.903300\pi\)
\(282\) 6.19275e9 − 1.37892e11i 0.0583126 − 1.29843i
\(283\) 1.39783e11 1.29544 0.647718 − 0.761880i \(-0.275724\pi\)
0.647718 + 0.761880i \(0.275724\pi\)
\(284\) 1.02480e11 − 1.96279e11i 0.934773 − 1.79036i
\(285\) 1.61148e11 1.44685
\(286\) −3.77326e9 + 8.40182e10i −0.0333480 + 0.742551i
\(287\) −1.27433e10 − 1.11335e10i −0.110870 − 0.0968640i
\(288\) 3.58944e9 + 3.23055e8i 0.0307440 + 0.00276701i
\(289\) −3.22990e10 − 9.94061e10i −0.272363 − 0.838248i
\(290\) −2.37968e11 + 2.48895e11i −1.97573 + 2.06645i
\(291\) 1.25288e11 + 3.45774e10i 1.02422 + 0.282666i
\(292\) 4.26850e10 − 3.15114e11i 0.343600 − 2.53656i
\(293\) −2.59024e10 − 1.91220e11i −0.205322 − 1.51575i −0.741101 − 0.671393i \(-0.765696\pi\)
0.535779 − 0.844358i \(-0.320018\pi\)
\(294\) −1.34289e11 + 3.70615e10i −1.04828 + 0.289308i
\(295\) 2.17785e10 − 4.04713e10i 0.167429 − 0.311134i
\(296\) 3.54083e10 + 3.70342e10i 0.268097 + 0.280408i
\(297\) 3.86580e10 + 7.18387e10i 0.288294 + 0.535740i
\(298\) 4.67549e10 − 1.43897e11i 0.343442 − 1.05701i
\(299\) 2.30522e9 − 5.39333e9i 0.0166798 − 0.0390244i
\(300\) −4.81700e10 − 8.74157e9i −0.343345 − 0.0623080i
\(301\) −3.43923e10 − 2.49875e10i −0.241497 − 0.175458i
\(302\) −1.36206e11 + 1.22587e10i −0.942245 + 0.0848036i
\(303\) −1.93823e10 − 4.53472e10i −0.132103 − 0.309071i
\(304\) −6.15026e10 − 2.69461e11i −0.413012 − 1.80952i
\(305\) 1.39859e11 + 2.11877e11i 0.925423 + 1.40196i
\(306\) 3.51779e10 + 2.10178e10i 0.229363 + 0.137038i
\(307\) 1.46614e11 + 1.83849e11i 0.942006 + 1.18124i 0.983282 + 0.182090i \(0.0582864\pi\)
−0.0412758 + 0.999148i \(0.513142\pi\)
\(308\) 5.41308e10 − 4.72926e10i 0.342741 − 0.299444i
\(309\) 1.51809e10 − 1.10296e10i 0.0947291 − 0.0688248i
\(310\) −9.74509e10 + 4.69299e10i −0.599319 + 0.288617i
\(311\) 9.60731e9 − 1.45545e10i 0.0582345 − 0.0882215i −0.804289 − 0.594238i \(-0.797454\pi\)
0.862524 + 0.506016i \(0.168882\pi\)
\(312\) −1.56317e11 − 5.86668e10i −0.933922 − 0.350507i
\(313\) 9.38586e10 − 5.60779e10i 0.552745 − 0.330250i −0.209219 − 0.977869i \(-0.567092\pi\)
0.761964 + 0.647619i \(0.224235\pi\)
\(314\) 1.11637e11 + 5.37618e10i 0.648077 + 0.312097i
\(315\) 3.39635e10 − 6.16347e9i 0.194364 − 0.0352718i
\(316\) 7.24420e10 − 3.17389e11i 0.408694 − 1.79061i
\(317\) −8.60506e10 + 3.22953e10i −0.478616 + 0.179628i −0.579010 − 0.815320i \(-0.696561\pi\)
0.100395 + 0.994948i \(0.467989\pi\)
\(318\) 6.42360e10 − 8.05494e10i 0.352254 − 0.441713i
\(319\) 6.95252e9 + 1.54810e11i 0.0375910 + 0.837029i
\(320\) −8.77499e9 − 1.95390e11i −0.0467812 − 1.04166i
\(321\) 7.88970e10 − 9.89338e10i 0.414752 − 0.520082i
\(322\) −7.01699e9 + 2.63352e9i −0.0363747 + 0.0136517i
\(323\) 2.62630e10 − 1.15066e11i 0.134256 − 0.588212i
\(324\) −1.39644e11 + 2.53417e10i −0.703998 + 0.127757i
\(325\) −3.18397e10 − 1.53332e10i −0.158305 − 0.0762355i
\(326\) −3.96452e11 + 2.36869e11i −1.94407 + 1.16153i
\(327\) −8.17165e10 − 3.06687e10i −0.395225 − 0.148331i
\(328\) 7.55764e10 − 1.14493e11i 0.360540 − 0.546195i
\(329\) −7.67239e10 + 3.69483e10i −0.361035 + 0.173865i
\(330\) −1.41408e11 + 1.02739e11i −0.656390 + 0.476895i
\(331\) −2.20537e11 + 1.92678e11i −1.00985 + 0.882278i −0.993063 − 0.117581i \(-0.962486\pi\)
−0.0167848 + 0.999859i \(0.505343\pi\)
\(332\) 8.31189e10 + 1.04228e11i 0.375473 + 0.470828i
\(333\) 1.88275e10 + 1.12489e10i 0.0839062 + 0.0501316i
\(334\) 2.15726e11 + 3.26811e11i 0.948513 + 1.43694i
\(335\) −1.45634e10 − 6.38062e10i −0.0631771 − 0.276797i
\(336\) 2.88520e10 + 6.75026e10i 0.123495 + 0.288931i
\(337\) −2.30014e11 + 2.07016e10i −0.971447 + 0.0874318i −0.563980 − 0.825788i \(-0.690731\pi\)
−0.407467 + 0.913220i \(0.633588\pi\)
\(338\) 1.44212e11 + 1.04776e11i 0.601003 + 0.436654i
\(339\) 4.45340e10 + 8.08173e9i 0.183144 + 0.0332357i
\(340\) −7.47779e10 + 1.74952e11i −0.303472 + 0.710007i
\(341\) −1.50416e10 + 4.62933e10i −0.0602420 + 0.185406i
\(342\) −1.62934e11 − 3.02782e11i −0.644012 − 1.19677i
\(343\) 1.30008e11 + 1.35977e11i 0.507160 + 0.530448i
\(344\) 1.63317e11 − 3.03494e11i 0.628809 − 1.16852i
\(345\) 1.17506e10 − 3.24295e9i 0.0446552 − 0.0123241i
\(346\) 1.04407e11 + 7.70765e11i 0.391641 + 2.89121i
\(347\) 1.10828e10 − 8.18168e10i 0.0410363 − 0.302942i −0.958787 − 0.284127i \(-0.908296\pi\)
0.999823 − 0.0188154i \(-0.00598947\pi\)
\(348\) −5.87383e11 − 1.62107e11i −2.14692 − 0.592511i
\(349\) −1.61542e11 + 1.68960e11i −0.582869 + 0.609633i −0.946812 − 0.321788i \(-0.895716\pi\)
0.363943 + 0.931421i \(0.381430\pi\)
\(350\) 1.39545e10 + 4.29476e10i 0.0497060 + 0.152979i
\(351\) −2.30622e11 − 2.07564e10i −0.810996 − 0.0729909i
\(352\) 8.47862e9 + 7.40755e9i 0.0294363 + 0.0257177i
\(353\) −9.02318e9 + 2.00917e11i −0.0309295 + 0.688700i 0.922304 + 0.386465i \(0.126304\pi\)
−0.953234 + 0.302235i \(0.902267\pi\)
\(354\) 1.21593e11 0.411522
\(355\) 3.31187e11 + 2.56395e10i 1.10674 + 0.0856806i
\(356\) −5.03263e11 −1.66062
\(357\) −1.40641e9 + 3.13162e10i −0.00458253 + 0.102038i
\(358\) −5.33672e9 − 4.66255e9i −0.0171712 − 0.0150020i
\(359\) 3.94338e11 + 3.54911e10i 1.25298 + 0.112770i 0.696174 − 0.717873i \(-0.254884\pi\)
0.556805 + 0.830643i \(0.312027\pi\)
\(360\) 8.64772e10 + 2.66149e11i 0.271357 + 0.835150i
\(361\) −4.61369e11 + 4.82554e11i −1.42977 + 1.49542i
\(362\) 4.32335e11 + 1.19317e11i 1.32322 + 0.365185i
\(363\) 2.24800e10 − 1.65954e11i 0.0679542 − 0.501658i
\(364\) 2.73867e10 + 2.02176e11i 0.0817679 + 0.603635i
\(365\) 4.59862e11 − 1.26914e11i 1.35616 − 0.374275i
\(366\) −3.18284e11 + 5.91470e11i −0.927149 + 1.72293i
\(367\) 1.39252e11 + 1.45646e11i 0.400686 + 0.419085i 0.892098 − 0.451843i \(-0.149233\pi\)
−0.491412 + 0.870927i \(0.663519\pi\)
\(368\) −9.90729e9 − 1.84108e10i −0.0281604 − 0.0523309i
\(369\) 1.81464e10 − 5.58487e10i 0.0509531 − 0.156818i
\(370\) −5.98376e10 + 1.39997e11i −0.165984 + 0.388339i
\(371\) −6.25397e10 − 1.13493e10i −0.171385 − 0.0311018i
\(372\) −1.54844e11 − 1.12501e11i −0.419229 − 0.304588i
\(373\) −5.32514e11 + 4.79272e10i −1.42443 + 0.128201i −0.774876 − 0.632113i \(-0.782188\pi\)
−0.649555 + 0.760314i \(0.725045\pi\)
\(374\) 5.03137e10 + 1.17715e11i 0.132973 + 0.311106i
\(375\) 5.40352e10 + 2.36744e11i 0.141103 + 0.618213i
\(376\) −3.80331e11 − 5.76176e11i −0.981332 − 1.48665i
\(377\) −3.77591e11 − 2.25600e11i −0.962688 − 0.575179i
\(378\) 1.84483e11 + 2.31334e11i 0.464775 + 0.582809i
\(379\) 1.60760e11 − 1.40452e11i 0.400223 − 0.349664i −0.434173 − 0.900829i \(-0.642959\pi\)
0.834396 + 0.551165i \(0.185817\pi\)
\(380\) 1.29154e12 − 9.38362e11i 3.17748 − 2.30858i
\(381\) −9.43054e10 + 4.54151e10i −0.229284 + 0.110417i
\(382\) 5.79724e11 − 8.78245e11i 1.39295 − 2.11023i
\(383\) −6.15097e11 − 2.30850e11i −1.46066 − 0.548195i −0.510478 − 0.859891i \(-0.670531\pi\)
−0.950182 + 0.311696i \(0.899103\pi\)
\(384\) 4.63031e11 − 2.76648e11i 1.08672 − 0.649287i
\(385\) 9.71560e10 + 4.67879e10i 0.225370 + 0.108533i
\(386\) 1.10274e12 − 2.00119e11i 2.52832 − 0.458823i
\(387\) 3.28273e10 − 1.43826e11i 0.0743937 − 0.325940i
\(388\) 1.20549e12 − 4.52427e11i 2.70035 − 1.01346i
\(389\) −3.71423e11 + 4.65750e11i −0.822424 + 1.03129i 0.176472 + 0.984306i \(0.443531\pi\)
−0.998896 + 0.0469811i \(0.985040\pi\)
\(390\) −2.22584e10 − 4.95622e11i −0.0487195 − 1.08482i
\(391\) −4.00547e8 − 8.91886e9i −0.000866678 − 0.0192981i
\(392\) −4.34434e11 + 5.44763e11i −0.929259 + 1.16525i
\(393\) 3.77027e11 − 1.41501e11i 0.797271 − 0.299221i
\(394\) 1.88259e11 − 8.24818e11i 0.393571 − 1.72435i
\(395\) 4.80546e11 − 8.72063e10i 0.993227 − 0.180244i
\(396\) 2.24739e11 + 1.08229e11i 0.459252 + 0.221164i
\(397\) −2.28319e11 + 1.36414e11i −0.461301 + 0.275615i −0.724690 − 0.689075i \(-0.758017\pi\)
0.263389 + 0.964690i \(0.415160\pi\)
\(398\) 9.26560e11 + 3.47744e11i 1.85097 + 0.694681i
\(399\) 1.44902e11 − 2.19517e11i 0.286218 − 0.433602i
\(400\) −1.13494e11 + 5.46559e10i −0.221668 + 0.106750i
\(401\) −7.23466e11 + 5.25628e11i −1.39723 + 1.01515i −0.402203 + 0.915551i \(0.631755\pi\)
−0.995028 + 0.0995972i \(0.968245\pi\)
\(402\) 1.30396e11 − 1.13924e11i 0.249027 − 0.217569i
\(403\) −8.61414e10 − 1.08018e11i −0.162682 − 0.203997i
\(404\) −4.19399e11 − 2.50579e11i −0.783270 − 0.467982i
\(405\) −1.17296e11 − 1.77695e11i −0.216638 − 0.328192i
\(406\) 1.25070e11 + 5.47966e11i 0.228447 + 1.00089i
\(407\) 2.69283e10 + 6.30020e10i 0.0486446 + 0.113810i
\(408\) −2.53119e11 + 2.27811e10i −0.452224 + 0.0407009i
\(409\) 3.08408e11 + 2.24071e11i 0.544967 + 0.395942i 0.825926 − 0.563778i \(-0.190653\pi\)
−0.280959 + 0.959720i \(0.590653\pi\)
\(410\) 4.01094e11 + 7.27878e10i 0.701001 + 0.127213i
\(411\) 7.31886e10 − 1.71233e11i 0.126519 − 0.296006i
\(412\) 5.74446e10 − 1.76796e11i 0.0982226 − 0.302298i
\(413\) −3.55475e10 − 6.60583e10i −0.0601221 − 0.111726i
\(414\) −1.79740e10 − 1.87993e10i −0.0300707 − 0.0314515i
\(415\) −9.47720e10 + 1.76116e11i −0.156842 + 0.291462i
\(416\) −3.08049e10 + 8.50162e9i −0.0504313 + 0.0139182i
\(417\) −1.15574e9 − 8.53203e9i −0.00187175 − 0.0138178i
\(418\) 1.44186e11 − 1.06443e12i 0.231010 − 1.70539i
\(419\) −9.35253e11 − 2.58113e11i −1.48240 − 0.409117i −0.571109 − 0.820874i \(-0.693487\pi\)
−0.911294 + 0.411757i \(0.864915\pi\)
\(420\) −2.93023e11 + 3.06478e11i −0.459494 + 0.480594i
\(421\) 2.85621e11 + 8.79050e11i 0.443119 + 1.36378i 0.884533 + 0.466477i \(0.154477\pi\)
−0.441414 + 0.897303i \(0.645523\pi\)
\(422\) −8.81648e11 − 7.93498e10i −1.35328 − 0.121798i
\(423\) −2.22545e11 − 1.94432e11i −0.337977 − 0.295281i
\(424\) 2.31190e10 − 5.14784e11i 0.0347394 − 0.773532i
\(425\) −5.37915e10 −0.0799767
\(426\) 3.55477e11 + 8.03737e11i 0.522960 + 1.18242i
\(427\) 4.14381e11 0.603218
\(428\) 5.62425e10 − 1.25234e12i 0.0810155 − 1.80395i
\(429\) −1.68136e11 − 1.46896e11i −0.239664 − 0.209388i
\(430\) 1.01997e12 + 9.17991e10i 1.43873 + 0.129488i
\(431\) −3.09013e11 − 9.51044e11i −0.431349 − 1.32756i −0.896782 − 0.442473i \(-0.854101\pi\)
0.465433 − 0.885083i \(-0.345899\pi\)
\(432\) −5.70393e11 + 5.96585e11i −0.787948 + 0.824129i
\(433\) −7.57409e11 − 2.09031e11i −1.03546 − 0.285770i −0.293322 − 0.956014i \(-0.594761\pi\)
−0.742141 + 0.670244i \(0.766189\pi\)
\(434\) −2.36983e10 + 1.74948e11i −0.0320637 + 0.236703i
\(435\) −1.22708e11 − 9.05867e11i −0.164313 − 1.21301i
\(436\) −8.33514e11 + 2.30035e11i −1.10465 + 0.304863i
\(437\) −3.54980e10 + 6.59663e10i −0.0465626 + 0.0865278i
\(438\) 8.72213e11 + 9.12263e11i 1.13237 + 1.18437i
\(439\) 4.48593e11 + 8.33625e11i 0.576450 + 1.07122i 0.987202 + 0.159477i \(0.0509807\pi\)
−0.410751 + 0.911747i \(0.634734\pi\)
\(440\) −2.70155e11 + 8.31451e11i −0.343618 + 1.05755i
\(441\) −1.17221e11 + 2.74253e11i −0.147582 + 0.345285i
\(442\) −3.57520e11 − 6.48804e10i −0.445554 − 0.0808561i
\(443\) 2.73121e11 + 1.98434e11i 0.336928 + 0.244793i 0.743365 − 0.668886i \(-0.233229\pi\)
−0.406436 + 0.913679i \(0.633229\pi\)
\(444\) −2.68326e11 + 2.41498e10i −0.327672 + 0.0294910i
\(445\) −2.96734e11 − 6.94244e11i −0.358713 − 0.839251i
\(446\) 4.07365e11 + 1.78478e12i 0.487503 + 2.13589i
\(447\) 2.21273e11 + 3.35214e11i 0.262146 + 0.397135i
\(448\) −2.74053e11 − 1.63739e11i −0.321428 − 0.192045i
\(449\) −6.23035e11 − 7.81262e11i −0.723443 − 0.907169i 0.275084 − 0.961420i \(-0.411294\pi\)
−0.998527 + 0.0542514i \(0.982723\pi\)
\(450\) −1.18013e11 + 1.03105e11i −0.135667 + 0.118529i
\(451\) 1.48414e11 − 1.07829e11i 0.168920 − 0.122728i
\(452\) 4.03985e11 − 1.94549e11i 0.455241 − 0.219233i
\(453\) 2.00000e11 − 3.02987e11i 0.223146 − 0.338051i
\(454\) −2.86559e12 − 1.07548e12i −3.16565 − 1.18809i
\(455\) −2.62751e11 + 1.56987e11i −0.287405 + 0.171716i
\(456\) 1.92125e12 + 9.25227e11i 2.08086 + 1.00209i
\(457\) 6.58066e11 − 1.19421e11i 0.705743 − 0.128073i 0.186192 − 0.982513i \(-0.440385\pi\)
0.519550 + 0.854440i \(0.326099\pi\)
\(458\) −2.93128e11 + 1.28428e12i −0.311288 + 1.36384i
\(459\) −3.29983e11 + 1.23845e11i −0.347004 + 0.130233i
\(460\) 7.52931e10 − 9.44145e10i 0.0784052 − 0.0983170i
\(461\) −7.28412e10 − 1.62194e12i −0.0751144 − 1.67255i −0.584028 − 0.811734i \(-0.698524\pi\)
0.508913 − 0.860818i \(-0.330047\pi\)
\(462\) 1.27998e10 + 2.85010e11i 0.0130712 + 0.291052i
\(463\) 6.42653e11 − 8.05862e11i 0.649924 − 0.814979i −0.342281 − 0.939598i \(-0.611199\pi\)
0.992205 + 0.124619i \(0.0397709\pi\)
\(464\) −1.46790e12 + 5.50912e11i −1.47016 + 0.551762i
\(465\) 6.38939e10 − 2.79938e11i 0.0633755 − 0.277666i
\(466\) 5.11054e10 − 9.27427e9i 0.0502031 − 0.00911052i
\(467\) −2.96234e10 − 1.42659e10i −0.0288210 − 0.0138795i 0.419418 − 0.907793i \(-0.362234\pi\)
−0.448239 + 0.893914i \(0.647949\pi\)
\(468\) −6.07791e11 + 3.63138e11i −0.585664 + 0.349918i
\(469\) −1.00013e11 − 3.75355e10i −0.0954505 − 0.0358232i
\(470\) 1.13013e12 − 1.71207e12i 1.06828 − 1.61838i
\(471\) −2.96362e11 + 1.42720e11i −0.277478 + 0.133626i
\(472\) 4.92016e11 − 3.57470e11i 0.456289 − 0.331513i
\(473\) 3.47066e11 − 3.03222e11i 0.318814 − 0.278539i
\(474\) 8.05635e11 + 1.01023e12i 0.733054 + 0.919220i
\(475\) 3.87460e11 + 2.31496e11i 0.349225 + 0.208652i
\(476\) 1.71082e11 + 2.59178e11i 0.152747 + 0.231402i
\(477\) −4.90822e10 − 2.15043e11i −0.0434102 − 0.190192i
\(478\) 1.70767e11 + 3.99529e11i 0.149616 + 0.350044i
\(479\) 1.78203e11 − 1.60385e10i 0.154669 − 0.0139205i −0.0120340 − 0.999928i \(-0.503831\pi\)
0.166703 + 0.986007i \(0.446688\pi\)
\(480\) −5.37308e10 − 3.90377e10i −0.0461996 − 0.0335660i
\(481\) −1.91348e11 − 3.47246e10i −0.162994 − 0.0295790i
\(482\) −1.31287e12 + 3.07160e12i −1.10792 + 2.59211i
\(483\) 6.14838e9 − 1.89228e10i 0.00514042 − 0.0158206i
\(484\) −7.86180e11 − 1.46097e12i −0.651205 − 1.21014i
\(485\) 1.33490e12 + 1.39619e12i 1.09549 + 1.14580i
\(486\) −8.22963e11 + 1.52932e12i −0.669140 + 1.24347i
\(487\) −1.66276e12 + 4.58892e11i −1.33952 + 0.369684i −0.861094 − 0.508445i \(-0.830220\pi\)
−0.478424 + 0.878129i \(0.658792\pi\)
\(488\) 4.50952e11 + 3.32906e12i 0.359949 + 2.65725i
\(489\) 1.64570e11 − 1.21490e12i 0.130155 − 0.960840i
\(490\) −1.99582e12 − 5.50811e11i −1.56401 − 0.431639i
\(491\) −2.26391e11 + 2.36787e11i −0.175790 + 0.183861i −0.804820 − 0.593520i \(-0.797738\pi\)
0.629030 + 0.777381i \(0.283452\pi\)
\(492\) 2.22908e11 + 6.86039e11i 0.171507 + 0.527845i
\(493\) −6.66822e11 − 6.00151e10i −0.508392 − 0.0457561i
\(494\) 2.29600e12 + 2.00595e12i 1.73460 + 1.51548i
\(495\) −1.67891e10 + 3.73838e11i −0.0125691 + 0.279873i
\(496\) −4.92479e11 −0.365359
\(497\) 3.32727e11 − 4.28093e11i 0.244615 − 0.314727i
\(498\) −5.29127e11 −0.385503
\(499\) 4.78149e10 − 1.06468e12i 0.0345232 − 0.768719i −0.904831 − 0.425771i \(-0.860003\pi\)
0.939354 − 0.342948i \(-0.111426\pi\)
\(500\) 1.81163e12 + 1.58277e12i 1.29630 + 1.13254i
\(501\) −1.03536e12 − 9.31843e10i −0.734214 − 0.0660805i
\(502\) 1.13768e11 + 3.50142e11i 0.0799564 + 0.246081i
\(503\) −6.37300e11 + 6.66564e11i −0.443903 + 0.464286i −0.906453 − 0.422307i \(-0.861220\pi\)
0.462550 + 0.886593i \(0.346935\pi\)
\(504\) 4.40312e11 + 1.21518e11i 0.303964 + 0.0838888i
\(505\) 9.83841e10 − 7.26301e11i 0.0673153 − 0.496942i
\(506\) −1.09068e10 − 8.05174e10i −0.00739641 − 0.0546025i
\(507\) −4.56160e11 + 1.25892e11i −0.306606 + 0.0846180i
\(508\) −4.91374e11 + 9.13126e11i −0.327360 + 0.608336i
\(509\) −1.16783e12 − 1.22145e12i −0.771169 − 0.806579i 0.214240 − 0.976781i \(-0.431272\pi\)
−0.985409 + 0.170202i \(0.945558\pi\)
\(510\) −3.57850e11 − 6.64996e11i −0.234226 − 0.435264i
\(511\) 2.40619e11 − 7.40550e11i 0.156112 − 0.480463i
\(512\) 1.10256e12 − 2.57956e12i 0.709065 − 1.65894i
\(513\) 2.90984e12 + 5.28059e11i 1.85499 + 0.336631i
\(514\) −3.92132e12 − 2.84900e12i −2.47798 − 1.80036i
\(515\) 2.77758e11 − 2.49987e10i 0.173994 − 0.0156597i
\(516\) 7.12231e11 + 1.66635e12i 0.442280 + 1.03477i
\(517\) −2.05430e11 − 9.00047e11i −0.126461 − 0.554061i
\(518\) 1.36900e11 + 2.07395e11i 0.0835450 + 0.126565i
\(519\) −1.77254e12 − 1.05905e12i −1.07237 − 0.640710i
\(520\) −1.54714e12 − 1.94006e12i −0.927930 − 1.16359i
\(521\) 4.30620e11 − 3.76222e11i 0.256050 − 0.223704i −0.520336 − 0.853961i \(-0.674193\pi\)
0.776386 + 0.630257i \(0.217051\pi\)
\(522\) −1.57797e12 + 1.14647e12i −0.930214 + 0.675840i
\(523\) −2.52170e12 + 1.21439e12i −1.47379 + 0.709741i −0.986540 − 0.163521i \(-0.947715\pi\)
−0.487252 + 0.873261i \(0.662001\pi\)
\(524\) 2.19779e12 − 3.32951e12i 1.27349 − 1.92925i
\(525\) −1.12235e11 − 4.21227e10i −0.0644782 − 0.0241991i
\(526\) 7.09412e10 − 4.23854e10i 0.0404075 − 0.0241424i
\(527\) −1.89473e11 − 9.12454e10i −0.107004 − 0.0515304i
\(528\) −7.83055e11 + 1.42103e11i −0.438470 + 0.0795705i
\(529\) 3.99533e11 − 1.75047e12i 0.221821 − 0.971861i
\(530\) 1.43355e12 − 5.38021e11i 0.789172 − 0.296181i
\(531\) 1.62309e11 − 2.03529e11i 0.0885965 − 0.111097i
\(532\) −1.16906e11 − 2.60312e12i −0.0632755 − 1.40894i
\(533\) 2.33612e10 + 5.20177e11i 0.0125378 + 0.279176i
\(534\) 1.24541e12 − 1.56170e12i 0.662794 − 0.831117i
\(535\) 1.76074e12 − 6.60817e11i 0.929188 − 0.348730i
\(536\) 1.92713e11 − 8.44333e11i 0.100849 − 0.441847i
\(537\) 1.85103e10 − 3.35913e9i 0.00960572 − 0.00174318i
\(538\) −2.74632e12 − 1.32256e12i −1.41329 − 0.680604i
\(539\) −7.99855e11 + 4.77891e11i −0.408189 + 0.243882i
\(540\) −4.46345e12 − 1.67516e12i −2.25891 − 0.847783i
\(541\) 6.70015e11 − 1.01503e12i 0.336277 − 0.509437i −0.626614 − 0.779330i \(-0.715560\pi\)
0.962890 + 0.269893i \(0.0869882\pi\)
\(542\) 2.57004e12 − 1.23767e12i 1.27921 − 0.616037i
\(543\) −9.63230e11 + 6.99827e11i −0.475478 + 0.345455i
\(544\) −3.66312e10 + 3.20037e10i −0.0179331 + 0.0156677i
\(545\) −8.08786e11 − 1.01419e12i −0.392690 − 0.492417i
\(546\) −6.95157e11 − 4.15337e11i −0.334746 − 0.200002i
\(547\) 1.39304e12 + 2.11037e12i 0.665307 + 1.00790i 0.997897 + 0.0648250i \(0.0206489\pi\)
−0.332590 + 0.943072i \(0.607923\pi\)
\(548\) −4.10508e11 − 1.79855e12i −0.194451 − 0.851944i
\(549\) 5.65173e11 + 1.32229e12i 0.265525 + 0.621227i
\(550\) −4.87588e11 + 4.38837e10i −0.227207 + 0.0204490i
\(551\) 4.54483e12 + 3.30202e12i 2.10056 + 1.52615i
\(552\) 1.58713e11 + 2.88022e10i 0.0727591 + 0.0132038i
\(553\) 3.13308e11 − 7.33022e11i 0.142465 − 0.333314i
\(554\) 1.40693e12 − 4.33010e12i 0.634570 − 1.95301i
\(555\) −1.91524e11 − 3.55912e11i −0.0856852 − 0.159230i
\(556\) −5.89448e10 − 6.16515e10i −0.0261583 − 0.0273594i
\(557\) −7.76652e11 + 1.44326e12i −0.341884 + 0.635326i −0.992245 − 0.124299i \(-0.960332\pi\)
0.650361 + 0.759625i \(0.274618\pi\)
\(558\) −5.90580e11 + 1.62990e11i −0.257884 + 0.0711715i
\(559\) 1.75593e11 + 1.29628e12i 0.0760595 + 0.561494i
\(560\) −1.46452e11 + 1.08115e12i −0.0629288 + 0.464559i
\(561\) −3.27596e11 − 9.04108e10i −0.139639 − 0.0385378i
\(562\) 2.96363e12 − 3.09971e12i 1.25317 − 1.31071i
\(563\) 9.92336e11 + 3.05410e12i 0.416266 + 1.28114i 0.911113 + 0.412156i \(0.135224\pi\)
−0.494847 + 0.868980i \(0.664776\pi\)
\(564\) 3.61548e12 + 3.25399e11i 1.50456 + 0.135413i
\(565\) 5.06574e11 + 4.42580e11i 0.209134 + 0.182715i
\(566\) −2.46591e11 + 5.49078e12i −0.100996 + 2.24885i
\(567\) −3.47530e11 −0.141211
\(568\) 3.80131e12 + 2.20719e12i 1.53238 + 0.889759i
\(569\) 1.64152e12 0.656509 0.328254 − 0.944589i \(-0.393540\pi\)
0.328254 + 0.944589i \(0.393540\pi\)
\(570\) −2.84280e11 + 6.33000e12i −0.112800 + 2.51169i
\(571\) 1.76037e12 + 1.53799e12i 0.693011 + 0.605466i 0.930660 − 0.365885i \(-0.119234\pi\)
−0.237649 + 0.971351i \(0.576377\pi\)
\(572\) −2.20292e12 − 1.98267e11i −0.860433 − 0.0774404i
\(573\) 8.63269e11 + 2.65687e12i 0.334542 + 1.02961i
\(574\) 4.59812e11 − 4.80925e11i 0.176798 − 0.184916i
\(575\) 3.29114e10 + 9.08297e9i 0.0125557 + 0.00346515i
\(576\) 1.48711e11 − 1.09783e12i 0.0562913 − 0.415559i
\(577\) −4.34955e11 − 3.21097e12i −0.163363 − 1.20599i −0.868051 − 0.496476i \(-0.834627\pi\)
0.704688 − 0.709517i \(-0.251087\pi\)
\(578\) 3.96172e12 − 1.09337e12i 1.47642 − 0.407465i
\(579\) −1.40988e12 + 2.61999e12i −0.521348 + 0.968828i
\(580\) −6.25832e12 − 6.54569e12i −2.29632 − 2.40176i
\(581\) 1.54689e11 + 2.87461e11i 0.0563207 + 0.104661i
\(582\) −1.57925e12 + 4.86042e12i −0.570554 + 1.75598i
\(583\) 2.70822e11 − 6.33620e11i 0.0970903 − 0.227154i
\(584\) 6.21130e12 + 1.12718e12i 2.20965 + 0.400993i
\(585\) −8.59310e11 − 6.24325e11i −0.303353 − 0.220399i
\(586\) 7.55694e12 − 6.80136e11i 2.64732 − 0.238263i
\(587\) −1.88924e12 − 4.42009e12i −0.656773 − 1.53660i −0.833608 − 0.552357i \(-0.813729\pi\)
0.176834 − 0.984241i \(-0.443414\pi\)
\(588\) −8.15253e11 − 3.57186e12i −0.281251 − 1.23224i
\(589\) 9.72090e11 + 1.47265e12i 0.332803 + 0.504176i
\(590\) 1.55132e12 + 9.26872e11i 0.527070 + 0.314909i
\(591\) 1.40032e12 + 1.75595e12i 0.472154 + 0.592062i
\(592\) −5.22037e11 + 4.56090e11i −0.174684 + 0.152617i
\(593\) −4.80087e11 + 3.48804e11i −0.159431 + 0.115834i −0.664641 − 0.747163i \(-0.731415\pi\)
0.505209 + 0.862997i \(0.331415\pi\)
\(594\) −2.89007e12 + 1.39178e12i −0.952510 + 0.458704i
\(595\) −2.56659e11 + 3.88821e11i −0.0839517 + 0.127181i
\(596\) 3.72537e12 + 1.39816e12i 1.20938 + 0.453886i
\(597\) −2.25536e12 + 1.34751e12i −0.726660 + 0.434159i
\(598\) 2.07787e11 + 1.00065e11i 0.0664452 + 0.0319983i
\(599\) −2.95233e12 + 5.35769e11i −0.937011 + 0.170042i −0.625521 − 0.780207i \(-0.715114\pi\)
−0.311490 + 0.950250i \(0.600828\pi\)
\(600\) 2.16265e11 − 9.47519e11i 0.0681249 − 0.298475i
\(601\) −9.16095e11 + 3.43816e11i −0.286421 + 0.107496i −0.490450 − 0.871469i \(-0.663168\pi\)
0.204029 + 0.978965i \(0.434596\pi\)
\(602\) 1.04220e12 − 1.30687e12i 0.323419 − 0.405555i
\(603\) −1.66318e10 − 3.70335e11i −0.00512284 − 0.114069i
\(604\) −1.61359e11 − 3.59294e12i −0.0493318 − 1.09846i
\(605\) 1.55183e12 − 1.94594e12i 0.470919 − 0.590513i
\(606\) 1.81546e12 − 6.81354e11i 0.546840 − 0.205233i
\(607\) 7.74746e11 − 3.39438e12i 0.231638 − 1.01487i −0.716643 − 0.697441i \(-0.754322\pi\)
0.948281 − 0.317433i \(-0.102821\pi\)
\(608\) 4.01585e11 − 7.28769e10i 0.119182 − 0.0216284i
\(609\) −1.34432e12 − 6.47391e11i −0.396028 − 0.190717i
\(610\) −8.56940e12 + 5.11998e12i −2.50591 + 1.49721i
\(611\) 2.45329e12 + 9.20734e11i 0.712136 + 0.267269i
\(612\) −5.93698e11 + 8.99414e11i −0.171074 + 0.259166i
\(613\) −1.91857e12 + 9.23935e11i −0.548790 + 0.264283i −0.687667 − 0.726027i \(-0.741365\pi\)
0.138877 + 0.990310i \(0.455651\pi\)
\(614\) −7.48034e12 + 5.43479e12i −2.12405 + 1.54321i
\(615\) −8.14950e11 + 7.12000e11i −0.229717 + 0.200698i
\(616\) 8.89693e11 + 1.11564e12i 0.248958 + 0.312184i
\(617\) −1.26081e12 − 7.53298e11i −0.350240 − 0.209259i 0.326994 − 0.945027i \(-0.393964\pi\)
−0.677234 + 0.735768i \(0.736822\pi\)
\(618\) 4.06468e11 + 6.15773e11i 0.112093 + 0.169814i
\(619\) 6.88947e11 + 3.01847e12i 0.188616 + 0.826379i 0.977347 + 0.211642i \(0.0678809\pi\)
−0.788732 + 0.614738i \(0.789262\pi\)
\(620\) −1.11799e12 − 2.61566e12i −0.303860 − 0.710916i
\(621\) 2.22807e11 − 2.00530e10i 0.0601195 − 0.00541086i
\(622\) 5.54761e11 + 4.03058e11i 0.148610 + 0.107972i
\(623\) −1.21253e12 − 2.20041e11i −0.322475 − 0.0585205i
\(624\) 8.87808e11 − 2.07713e12i 0.234417 − 0.548445i
\(625\) −1.38898e12 + 4.27484e12i −0.364113 + 1.12062i
\(626\) 2.03720e12 + 3.78576e12i 0.530213 + 0.985300i
\(627\) 1.97058e12 + 2.06107e12i 0.509202 + 0.532584i
\(628\) −1.54418e12 + 2.86957e12i −0.396168 + 0.736204i
\(629\) −2.85348e11 + 7.87512e10i −0.0726855 + 0.0200599i
\(630\) 1.82191e11 + 1.34499e12i 0.0460780 + 0.340161i
\(631\) 4.56108e11 − 3.36713e12i 0.114534 − 0.845527i −0.838976 − 0.544168i \(-0.816845\pi\)
0.953511 − 0.301359i \(-0.0974403\pi\)
\(632\) 6.22992e12 + 1.71935e12i 1.55330 + 0.428684i
\(633\) 1.62397e12 − 1.69854e12i 0.402032 − 0.420492i
\(634\) −1.11678e12 − 3.43710e12i −0.274515 − 0.844871i
\(635\) −1.54937e12 − 1.39445e11i −0.378157 − 0.0340348i
\(636\) 2.04045e12 + 1.78268e12i 0.494502 + 0.432034i
\(637\) 1.18652e11 − 2.64198e12i 0.0285526 − 0.635774i
\(638\) −6.09331e12 −1.45600
\(639\) 1.81985e12 + 4.77854e11i 0.431799 + 0.113381i
\(640\) 8.01631e12 1.88871
\(641\) −1.10209e11 + 2.45399e12i −0.0257842 + 0.574131i 0.943968 + 0.330038i \(0.107062\pi\)
−0.969752 + 0.244093i \(0.921510\pi\)
\(642\) 3.74701e12 + 3.27366e12i 0.870516 + 0.760547i
\(643\) −1.95629e12 − 1.76070e11i −0.451320 − 0.0406195i −0.138352 − 0.990383i \(-0.544180\pi\)
−0.312968 + 0.949764i \(0.601323\pi\)
\(644\) −6.09100e10 − 1.87462e11i −0.0139541 − 0.0429463i
\(645\) −1.87875e12 + 1.96502e12i −0.427416 + 0.447042i
\(646\) 4.47353e12 + 1.23462e12i 1.01066 + 0.278924i
\(647\) 4.15405e11 − 3.06665e12i 0.0931972 − 0.688009i −0.882725 − 0.469890i \(-0.844294\pi\)
0.975922 − 0.218119i \(-0.0699922\pi\)
\(648\) −3.78201e11 − 2.79199e12i −0.0842626 − 0.622052i
\(649\) 7.83942e11 − 2.16354e11i 0.173453 − 0.0478701i
\(650\) 6.58467e11 − 1.22364e12i 0.144685 − 0.268870i
\(651\) −3.23882e11 − 3.38754e11i −0.0706760 − 0.0739213i
\(652\) −5.75539e12 − 1.06953e13i −1.24727 − 2.31782i
\(653\) −2.50143e12 + 7.69861e12i −0.538368 + 1.65693i 0.197889 + 0.980224i \(0.436591\pi\)
−0.736257 + 0.676702i \(0.763409\pi\)
\(654\) 1.34885e12 − 3.15578e12i 0.288312 − 0.674539i
\(655\) 5.88886e12 + 1.06867e12i 1.25010 + 0.226860i
\(656\) 1.50159e12 + 1.09097e12i 0.316580 + 0.230009i
\(657\) 2.69127e12 − 2.42219e11i 0.563525 − 0.0507182i
\(658\) −1.31601e12 − 3.07895e12i −0.273679 − 0.640304i
\(659\) 3.97975e11 + 1.74364e12i 0.0821999 + 0.360141i 0.999254 − 0.0386218i \(-0.0122968\pi\)
−0.917054 + 0.398763i \(0.869440\pi\)
\(660\) −2.53237e12 − 3.83638e12i −0.519493 − 0.786998i
\(661\) 2.84497e12 + 1.69979e12i 0.579658 + 0.346329i 0.772612 − 0.634878i \(-0.218950\pi\)
−0.192954 + 0.981208i \(0.561807\pi\)
\(662\) −7.17947e12 − 9.00277e12i −1.45288 − 1.82186i
\(663\) 7.26416e11 − 6.34650e11i 0.146007 − 0.127563i
\(664\) −2.14107e12 + 1.55558e12i −0.427439 + 0.310553i
\(665\) 3.52204e12 − 1.69612e12i 0.698387 − 0.336326i
\(666\) −4.75079e11 + 7.19714e11i −0.0935690 + 0.141751i
\(667\) 3.97850e11 + 1.49316e11i 0.0778311 + 0.0292105i
\(668\) −8.84069e12 + 5.28207e12i −1.71788 + 1.02638i
\(669\) −4.37860e12 − 2.10862e12i −0.845119 − 0.406988i
\(670\) 2.53204e12 − 4.59498e11i 0.485439 − 0.0880942i
\(671\) −9.99638e11 + 4.37970e12i −0.190367 + 0.834052i
\(672\) −1.01492e11 + 3.80905e10i −0.0191986 + 0.00720535i
\(673\) 2.13129e11 − 2.67256e11i 0.0400475 − 0.0502180i −0.761404 − 0.648277i \(-0.775490\pi\)
0.801452 + 0.598059i \(0.204061\pi\)
\(674\) −4.07407e11 − 9.07162e12i −0.0760430 − 1.69323i
\(675\) −6.04717e10 − 1.34651e12i −0.0112121 − 0.249656i
\(676\) −2.92290e12 + 3.66520e12i −0.538336 + 0.675052i
\(677\) −8.31011e12 + 3.11884e12i −1.52040 + 0.570616i −0.965294 − 0.261164i \(-0.915894\pi\)
−0.555106 + 0.831780i \(0.687322\pi\)
\(678\) −3.96018e11 + 1.73507e12i −0.0719750 + 0.315343i
\(679\) 3.10223e12 − 5.62972e11i 0.560094 − 0.101642i
\(680\) −3.40303e12 − 1.63881e12i −0.610345 − 0.293927i
\(681\) 6.97520e12 − 4.16749e12i 1.24278 − 0.742527i
\(682\) −1.79190e12 − 6.72511e11i −0.317164 − 0.119034i
\(683\) 4.09238e12 − 6.19969e12i 0.719586 − 1.09013i −0.272203 − 0.962240i \(-0.587752\pi\)
0.991789 − 0.127886i \(-0.0408191\pi\)
\(684\) 8.14710e12 − 3.92344e12i 1.42315 − 0.685353i
\(685\) 2.23903e12 − 1.62675e12i 0.388555 − 0.282302i
\(686\) −5.57063e12 + 4.86692e12i −0.960387 + 0.839065i
\(687\) −2.18036e12 − 2.73408e12i −0.373442 − 0.468281i
\(688\) 4.00282e12 + 2.39157e12i 0.681110 + 0.406945i
\(689\) 1.07747e12 + 1.63230e12i 0.182146 + 0.275939i
\(690\) 1.06656e11 + 4.67291e11i 0.0179129 + 0.0784814i
\(691\) 4.20611e12 + 9.84068e12i 0.701825 + 1.64200i 0.765024 + 0.644001i \(0.222727\pi\)
−0.0631991 + 0.998001i \(0.520130\pi\)
\(692\) −2.03732e13 + 1.83362e12i −3.37739 + 0.303970i
\(693\) 4.94151e11 + 3.59022e11i 0.0813879 + 0.0591318i
\(694\) 3.19427e12 + 5.79675e11i 0.522702 + 0.0948565i
\(695\) 5.02922e10 − 1.17664e11i 0.00817652 − 0.0191299i
\(696\) 3.73806e12 − 1.15046e13i 0.603816 − 1.85835i
\(697\) 3.75579e11 + 6.97943e11i 0.0602773 + 0.112014i
\(698\) −6.35188e12 − 6.64354e12i −1.01287 − 1.05938i
\(699\) −6.53392e10 + 1.21421e11i −0.0103520 + 0.0192373i
\(700\) −1.14481e12 + 3.15947e11i −0.180215 + 0.0497363i
\(701\) −7.57747e11 − 5.59392e12i −0.118520 − 0.874953i −0.948415 − 0.317033i \(-0.897314\pi\)
0.829894 − 0.557921i \(-0.188401\pi\)
\(702\) 1.22216e12 − 9.02238e12i 0.189938 − 1.40218i
\(703\) 2.39427e12 + 6.60778e11i 0.369722 + 0.102037i
\(704\) 2.39172e12 − 2.50154e12i 0.366973 − 0.383823i
\(705\) 1.68288e12 + 5.17936e12i 0.256567 + 0.789632i
\(706\) −7.87624e12 − 7.08874e11i −1.19316 − 0.107386i
\(707\) −9.00910e11 − 7.87102e11i −0.135611 − 0.118480i
\(708\) −1.43468e11 + 3.19456e12i −0.0214588 + 0.477816i
\(709\) 1.67341e12 0.248711 0.124356 − 0.992238i \(-0.460314\pi\)
0.124356 + 0.992238i \(0.460314\pi\)
\(710\) −1.59139e12 + 1.29640e13i −0.235025 + 1.91460i
\(711\) 2.76639e12 0.405976
\(712\) 4.48233e11 − 9.98069e12i 0.0653648 − 1.45546i
\(713\) 1.00519e11 + 8.78204e10i 0.0145661 + 0.0127260i
\(714\) −1.22764e12 − 1.10490e11i −0.176778 − 0.0159103i
\(715\) −1.02538e12 − 3.15580e12i −0.146726 − 0.451577i
\(716\) 1.28794e11 − 1.34708e11i 0.0183141 − 0.0191551i
\(717\) −1.11188e12 − 3.06858e11i −0.157116 − 0.0433612i
\(718\) −2.08977e12 + 1.54273e13i −0.293452 + 2.16635i
\(719\) 1.31923e12 + 9.73895e12i 0.184094 + 1.35904i 0.813320 + 0.581817i \(0.197658\pi\)
−0.629226 + 0.777223i \(0.716628\pi\)
\(720\) −3.64970e12 + 1.00725e12i −0.506128 + 0.139683i
\(721\) 2.15703e11 − 4.00844e11i 0.0297268 − 0.0552417i
\(722\) −1.81412e13 − 1.89742e13i −2.48455 − 2.59864i
\(723\) −4.20214e12 − 7.80888e12i −0.571937 − 1.06284i
\(724\) −3.64487e12 + 1.12178e13i −0.493013 + 1.51734i
\(725\) 1.00629e12 − 2.35432e12i 0.135270 − 0.316479i
\(726\) 6.47914e12 + 1.17579e12i 0.865570 + 0.157078i
\(727\) 1.07881e13 + 7.83802e12i 1.43232 + 1.04064i 0.989579 + 0.143993i \(0.0459944\pi\)
0.442743 + 0.896649i \(0.354006\pi\)
\(728\) −4.03394e12 + 3.63061e11i −0.532278 + 0.0479059i
\(729\) −2.87372e12 − 6.72340e12i −0.376851 − 0.881688i
\(730\) 4.17403e12 + 1.82876e13i 0.544004 + 2.38344i
\(731\) 1.09691e12 + 1.66175e12i 0.142083 + 0.215247i
\(732\) −1.51639e13 − 9.06001e12i −1.95214 − 1.16635i
\(733\) −7.64863e12 − 9.59107e12i −0.978623 − 1.22715i −0.973856 − 0.227166i \(-0.927054\pi\)
−0.00476714 − 0.999989i \(-0.501517\pi\)
\(734\) −5.96674e12 + 5.21298e12i −0.758761 + 0.662909i
\(735\) 4.44663e12 − 3.23067e12i 0.562002 − 0.408319i
\(736\) 2.78162e10 − 1.33956e10i 0.00349419 − 0.00168271i
\(737\) 6.37990e11 − 9.66513e11i 0.0796544 − 0.120671i
\(738\) 2.16177e12 + 8.11325e11i 0.268260 + 0.100679i
\(739\) 6.94771e12 − 4.15106e12i 0.856923 − 0.511987i −0.0159854 − 0.999872i \(-0.505089\pi\)
0.872908 + 0.487885i \(0.162231\pi\)
\(740\) −3.60748e12 − 1.73727e12i −0.442243 − 0.212973i
\(741\) −7.96364e12 + 1.44519e12i −0.970353 + 0.176093i
\(742\) 5.56135e11 − 2.43658e12i 0.0673538 − 0.295096i
\(743\) −7.74523e12 + 2.90683e12i −0.932362 + 0.349921i −0.770899 − 0.636957i \(-0.780193\pi\)
−0.161463 + 0.986879i \(0.551621\pi\)
\(744\) 2.36902e12 − 2.97066e12i 0.283459 − 0.355447i
\(745\) 2.67820e11 + 5.96347e12i 0.0318522 + 0.709244i
\(746\) −9.43205e11 − 2.10021e13i −0.111502 − 2.48278i
\(747\) −7.06307e11 + 8.85681e11i −0.0829948 + 0.104072i
\(748\) −3.15203e12 + 1.18298e12i −0.368157 + 0.138172i
\(749\) 6.83065e11 − 2.99270e12i 0.0793038 − 0.347453i
\(750\) −9.39479e12 + 1.70490e12i −1.08420 + 0.196754i
\(751\) 1.55278e11 + 7.47777e10i 0.0178127 + 0.00857813i 0.442769 − 0.896636i \(-0.353996\pi\)
−0.424956 + 0.905214i \(0.639711\pi\)
\(752\) 8.01831e12 − 4.79071e12i 0.914329 −