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Properties

Label 71.10.g.a.2.20
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 2.20
Character \(\chi\) \(=\) 71.2
Dual form 71.10.g.a.36.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.552600 + 12.3046i) q^{2} +(-87.2823 - 76.2563i) q^{3} +(358.841 + 32.2963i) q^{4} +(-62.7331 - 193.073i) q^{5} +(986.535 - 1031.83i) q^{6} +(-1072.51 - 295.994i) q^{7} +(-1442.20 + 10646.8i) q^{8} +(-838.927 - 6193.21i) q^{9} +O(q^{10})\) \(q+(-0.552600 + 12.3046i) q^{2} +(-87.2823 - 76.2563i) q^{3} +(358.841 + 32.2963i) q^{4} +(-62.7331 - 193.073i) q^{5} +(986.535 - 1031.83i) q^{6} +(-1072.51 - 295.994i) q^{7} +(-1442.20 + 10646.8i) q^{8} +(-838.927 - 6193.21i) q^{9} +(2410.35 - 665.213i) q^{10} +(-18173.2 + 33771.4i) q^{11} +(-28857.7 - 30182.8i) q^{12} +(-44429.7 - 82564.3i) q^{13} +(4234.75 - 13033.2i) q^{14} +(-9247.51 + 21635.6i) q^{15} +(51297.6 + 9309.14i) q^{16} +(97002.7 + 70476.6i) q^{17} +(76668.5 - 6900.29i) q^{18} +(64772.9 + 151544. i) q^{19} +(-16275.7 - 71308.5i) q^{20} +(71039.8 + 107621. i) q^{21} +(-405501. - 242276. i) q^{22} +(101038. + 126697. i) q^{23} +(937762. - 819298. i) q^{24} +(1.54677e6 - 1.12379e6i) q^{25} +(1.04047e6 - 501065. i) q^{26} +(-1.65581e6 + 2.50844e6i) q^{27} +(-375301. - 140853. i) q^{28} +(-3.83734e6 + 2.29270e6i) q^{29} +(-261107. - 125743. i) q^{30} +(4.55531e6 - 826667. i) q^{31} +(-1.36697e6 + 5.98907e6i) q^{32} +(4.16148e6 - 1.56183e6i) q^{33} +(-920790. + 1.15463e6i) q^{34} +(10133.5 + 225641. i) q^{35} +(-101024. - 2.24947e6i) q^{36} +(-1.36636e7 + 1.71337e7i) q^{37} +(-1.90048e6 + 713261. i) q^{38} +(-2.41811e6 + 1.05944e7i) q^{39} +(2.14607e6 - 389455. i) q^{40} +(6.63959e6 + 3.19746e6i) q^{41} +(-1.36349e6 + 814645. i) q^{42} +(1.53314e7 + 5.75396e6i) q^{43} +(-7.61198e6 + 1.15317e7i) q^{44} +(-1.14311e6 + 550493. i) q^{45} +(-1.61479e6 + 1.17322e6i) q^{46} +(-4.88726e7 + 4.26987e7i) q^{47} +(-3.76749e6 - 4.72429e6i) q^{48} +(-3.35788e7 - 2.00624e7i) q^{49} +(1.29731e7 + 1.96534e7i) q^{50} +(-3.09234e6 - 1.35484e7i) q^{51} +(-1.32767e7 - 3.10624e7i) q^{52} +(-7.82592e7 + 7.04346e6i) q^{53} +(-2.99503e7 - 2.17602e7i) q^{54} +(7.66040e6 + 1.39016e6i) q^{55} +(4.69816e6 - 1.09919e7i) q^{56} +(5.90263e6 - 1.81664e7i) q^{57} +(-2.60903e7 - 4.84839e7i) q^{58} +(6.88057e7 + 7.19651e7i) q^{59} +(-4.01714e6 + 7.46509e6i) q^{60} +(-5.46460e7 + 1.50813e7i) q^{61} +(7.65454e6 + 5.65080e7i) q^{62} +(-933395. + 6.89060e6i) q^{63} +(-4.72062e7 - 1.30281e7i) q^{64} +(-1.31537e7 + 1.37577e7i) q^{65} +(1.69181e7 + 5.20684e7i) q^{66} +(7.01807e7 + 6.31638e6i) q^{67} +(3.25325e7 + 2.84227e7i) q^{68} +(842657. - 1.87632e7i) q^{69} -2.78202e6 q^{70} +(-2.07498e8 + 5.28495e7i) q^{71} +6.71476e7 q^{72} +(-1.85506e7 + 4.13062e8i) q^{73} +(-2.03272e8 - 1.77594e8i) q^{74} +(-2.20702e8 - 1.98635e7i) q^{75} +(1.83489e7 + 5.64721e7i) q^{76} +(2.94871e7 - 3.08411e7i) q^{77} +(-1.29024e8 - 3.56084e7i) q^{78} +(-4.00903e7 + 2.95958e8i) q^{79} +(-1.42072e6 - 1.04881e7i) q^{80} +(2.17226e8 - 5.99505e7i) q^{81} +(-4.30125e7 + 7.99306e7i) q^{82} +(5.09406e8 + 5.32797e8i) q^{83} +(2.20163e7 + 4.09131e7i) q^{84} +(7.52182e6 - 2.31498e7i) q^{85} +(-7.92722e7 + 1.85467e8i) q^{86} +(5.09765e8 + 9.25088e7i) q^{87} +(-3.33347e8 - 2.42191e8i) q^{88} +(6.50394e8 - 5.85365e7i) q^{89} +(-6.14191e6 - 1.43697e7i) q^{90} +(2.32128e7 + 1.01702e8i) q^{91} +(3.21647e7 + 4.87274e7i) q^{92} +(-4.60637e8 - 2.75218e8i) q^{93} +(-4.98383e8 - 6.24953e8i) q^{94} +(2.51955e7 - 2.20127e7i) q^{95} +(5.76016e8 - 4.18500e8i) q^{96} +(8.77370e8 - 4.22519e8i) q^{97} +(2.65416e8 - 4.02087e8i) q^{98} +(2.24400e8 + 8.42186e7i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.552600 + 12.3046i −0.0244217 + 0.543791i 0.949070 + 0.315067i \(0.102027\pi\)
−0.973491 + 0.228724i \(0.926545\pi\)
\(3\) −87.2823 − 76.2563i −0.622129 − 0.543538i 0.288122 − 0.957594i \(-0.406969\pi\)
−0.910252 + 0.414056i \(0.864112\pi\)
\(4\) 358.841 + 32.2963i 0.700862 + 0.0630787i
\(5\) −62.7331 − 193.073i −0.0448881 − 0.138152i 0.926101 − 0.377277i \(-0.123139\pi\)
−0.970989 + 0.239125i \(0.923139\pi\)
\(6\) 986.535 − 1031.83i 0.310765 − 0.325034i
\(7\) −1072.51 − 295.994i −0.168834 − 0.0465953i 0.180598 − 0.983557i \(-0.442197\pi\)
−0.349432 + 0.936962i \(0.613625\pi\)
\(8\) −1442.20 + 10646.8i −0.124486 + 0.918995i
\(9\) −838.927 − 6193.21i −0.0426219 − 0.314648i
\(10\) 2410.35 − 665.213i 0.0762218 − 0.0210359i
\(11\) −18173.2 + 33771.4i −0.374252 + 0.695477i −0.996154 − 0.0876184i \(-0.972074\pi\)
0.621902 + 0.783095i \(0.286360\pi\)
\(12\) −28857.7 − 30182.8i −0.401741 − 0.420188i
\(13\) −44429.7 − 82564.3i −0.431448 − 0.801765i 0.568331 − 0.822800i \(-0.307589\pi\)
−0.999779 + 0.0210354i \(0.993304\pi\)
\(14\) 4234.75 − 13033.2i 0.0294613 − 0.0906726i
\(15\) −9247.51 + 21635.6i −0.0471644 + 0.110347i
\(16\) 51297.6 + 9309.14i 0.195685 + 0.0355115i
\(17\) 97002.7 + 70476.6i 0.281685 + 0.204656i 0.719652 − 0.694335i \(-0.244301\pi\)
−0.437967 + 0.898991i \(0.644301\pi\)
\(18\) 76668.5 − 6900.29i 0.172144 − 0.0154932i
\(19\) 64772.9 + 151544.i 0.114026 + 0.266776i 0.966814 − 0.255480i \(-0.0822334\pi\)
−0.852789 + 0.522256i \(0.825091\pi\)
\(20\) −16275.7 − 71308.5i −0.0227460 − 0.0996566i
\(21\) 71039.8 + 107621.i 0.0797104 + 0.120756i
\(22\) −405501. − 242276.i −0.369054 − 0.220500i
\(23\) 101038. + 126697.i 0.0752850 + 0.0944045i 0.818048 − 0.575150i \(-0.195056\pi\)
−0.742763 + 0.669555i \(0.766485\pi\)
\(24\) 937762. − 819298.i 0.576955 − 0.504071i
\(25\) 1.54677e6 − 1.12379e6i 0.791946 − 0.575383i
\(26\) 1.04047e6 − 501065.i 0.446529 − 0.215037i
\(27\) −1.65581e6 + 2.50844e6i −0.599615 + 0.908378i
\(28\) −375301. − 140853.i −0.115390 − 0.0433067i
\(29\) −3.83734e6 + 2.29270e6i −1.00749 + 0.601945i −0.919052 − 0.394137i \(-0.871044\pi\)
−0.0884350 + 0.996082i \(0.528187\pi\)
\(30\) −261107. − 125743.i −0.0588536 − 0.0283424i
\(31\) 4.55531e6 − 826667.i 0.885912 − 0.160769i 0.283516 − 0.958967i \(-0.408499\pi\)
0.602395 + 0.798198i \(0.294213\pi\)
\(32\) −1.36697e6 + 5.98907e6i −0.230453 + 1.00968i
\(33\) 4.16148e6 − 1.56183e6i 0.610851 − 0.229256i
\(34\) −920790. + 1.15463e6i −0.118169 + 0.148180i
\(35\) 10133.5 + 225641.i 0.00114145 + 0.0254163i
\(36\) −101024. − 2.24947e6i −0.0100245 − 0.223213i
\(37\) −1.36636e7 + 1.71337e7i −1.19856 + 1.50294i −0.383522 + 0.923532i \(0.625289\pi\)
−0.815035 + 0.579411i \(0.803283\pi\)
\(38\) −1.90048e6 + 713261.i −0.147855 + 0.0554910i
\(39\) −2.41811e6 + 1.05944e7i −0.167373 + 0.733310i
\(40\) 2.14607e6 − 389455.i 0.132549 − 0.0240540i
\(41\) 6.63959e6 + 3.19746e6i 0.366956 + 0.176717i 0.608270 − 0.793730i \(-0.291864\pi\)
−0.241314 + 0.970447i \(0.577578\pi\)
\(42\) −1.36349e6 + 814645.i −0.0676128 + 0.0403967i
\(43\) 1.53314e7 + 5.75396e6i 0.683869 + 0.256660i 0.669036 − 0.743230i \(-0.266707\pi\)
0.0148325 + 0.999890i \(0.495279\pi\)
\(44\) −7.61198e6 + 1.15317e7i −0.306169 + 0.463826i
\(45\) −1.14311e6 + 550493.i −0.0415558 + 0.0200122i
\(46\) −1.61479e6 + 1.17322e6i −0.0531749 + 0.0386338i
\(47\) −4.88726e7 + 4.26987e7i −1.46092 + 1.27636i −0.570434 + 0.821343i \(0.693225\pi\)
−0.890481 + 0.455020i \(0.849632\pi\)
\(48\) −3.76749e6 − 4.72429e6i −0.102439 − 0.128455i
\(49\) −3.35788e7 − 2.00624e7i −0.832115 − 0.497166i
\(50\) 1.29731e7 + 1.96534e7i 0.293547 + 0.444705i
\(51\) −3.09234e6 − 1.35484e7i −0.0640061 − 0.280429i
\(52\) −1.32767e7 − 3.10624e7i −0.251811 − 0.589142i
\(53\) −7.82592e7 + 7.04346e6i −1.36237 + 0.122615i −0.746579 − 0.665297i \(-0.768305\pi\)
−0.615788 + 0.787912i \(0.711162\pi\)
\(54\) −2.99503e7 − 2.17602e7i −0.479324 − 0.348250i
\(55\) 7.66040e6 + 1.39016e6i 0.112881 + 0.0204848i
\(56\) 4.69816e6 − 1.09919e7i 0.0638383 − 0.149357i
\(57\) 5.90263e6 − 1.81664e7i 0.0740643 − 0.227946i
\(58\) −2.60903e7 − 4.84839e7i −0.302728 − 0.562563i
\(59\) 6.88057e7 + 7.19651e7i 0.739248 + 0.773193i 0.980341 − 0.197309i \(-0.0632203\pi\)
−0.241093 + 0.970502i \(0.577506\pi\)
\(60\) −4.01714e6 + 7.46509e6i −0.0400162 + 0.0743626i
\(61\) −5.46460e7 + 1.50813e7i −0.505329 + 0.139462i −0.509400 − 0.860530i \(-0.670133\pi\)
0.00407119 + 0.999992i \(0.498704\pi\)
\(62\) 7.65454e6 + 5.65080e7i 0.0657894 + 0.485677i
\(63\) −933395. + 6.89060e6i −0.00746505 + 0.0551092i
\(64\) −4.72062e7 − 1.30281e7i −0.351714 − 0.0970669i
\(65\) −1.31537e7 + 1.37577e7i −0.0913981 + 0.0955949i
\(66\) 1.69181e7 + 5.20684e7i 0.109750 + 0.337774i
\(67\) 7.01807e7 + 6.31638e6i 0.425482 + 0.0382941i 0.300312 − 0.953841i \(-0.402909\pi\)
0.125171 + 0.992135i \(0.460052\pi\)
\(68\) 3.25325e7 + 2.84227e7i 0.184513 + 0.161204i
\(69\) 842657. − 1.87632e7i 0.00447538 − 0.0996521i
\(70\) −2.78202e6 −0.0138490
\(71\) −2.07498e8 + 5.28495e7i −0.969062 + 0.246819i
\(72\) 6.71476e7 0.294465
\(73\) −1.85506e7 + 4.13062e8i −0.0764550 + 1.70240i 0.484691 + 0.874685i \(0.338932\pi\)
−0.561146 + 0.827717i \(0.689639\pi\)
\(74\) −2.03272e8 − 1.77594e8i −0.788017 − 0.688469i
\(75\) −2.20702e8 − 1.98635e7i −0.805435 − 0.0724905i
\(76\) 1.83489e7 + 5.64721e7i 0.0630883 + 0.194166i
\(77\) 2.94871e7 − 3.08411e7i 0.0955924 − 0.0999818i
\(78\) −1.29024e8 − 3.56084e7i −0.394680 − 0.108925i
\(79\) −4.00903e7 + 2.95958e8i −0.115802 + 0.854887i 0.836120 + 0.548547i \(0.184819\pi\)
−0.951922 + 0.306340i \(0.900895\pi\)
\(80\) −1.42072e6 − 1.04881e7i −0.00387795 − 0.0286282i
\(81\) 2.17226e8 − 5.99505e7i 0.560698 − 0.154743i
\(82\) −4.30125e7 + 7.99306e7i −0.105059 + 0.195232i
\(83\) 5.09406e8 + 5.32797e8i 1.17818 + 1.23228i 0.966983 + 0.254840i \(0.0820226\pi\)
0.211199 + 0.977443i \(0.432263\pi\)
\(84\) 2.20163e7 + 4.09131e7i 0.0482488 + 0.0896613i
\(85\) 7.52182e6 − 2.31498e7i 0.0156292 − 0.0481019i
\(86\) −7.92722e7 + 1.85467e8i −0.156271 + 0.365614i
\(87\) 5.09765e8 + 9.25088e7i 0.953968 + 0.173120i
\(88\) −3.33347e8 − 2.42191e8i −0.592550 − 0.430513i
\(89\) 6.50394e8 − 5.85365e7i 1.09881 − 0.0988944i 0.474636 − 0.880182i \(-0.342580\pi\)
0.624171 + 0.781288i \(0.285437\pi\)
\(90\) −6.14191e6 − 1.43697e7i −0.00986761 − 0.0230864i
\(91\) 2.32128e7 + 1.01702e8i 0.0354847 + 0.155469i
\(92\) 3.21647e7 + 4.87274e7i 0.0468095 + 0.0709134i
\(93\) −4.60637e8 − 2.75218e8i −0.638536 − 0.381507i
\(94\) −4.98383e8 − 6.24953e8i −0.658397 − 0.825604i
\(95\) 2.51955e7 − 2.20127e7i 0.0317371 − 0.0277279i
\(96\) 5.76016e8 − 4.18500e8i 0.692172 − 0.502892i
\(97\) 8.77370e8 − 4.22519e8i 1.00626 − 0.484589i 0.143201 − 0.989694i \(-0.454260\pi\)
0.863058 + 0.505105i \(0.168546\pi\)
\(98\) 2.65416e8 − 4.02087e8i 0.290676 − 0.440355i
\(99\) 2.24400e8 + 8.42186e7i 0.234781 + 0.0881149i
\(100\) 5.91339e8 − 3.53309e8i 0.591339 − 0.353309i
\(101\) −1.50136e9 − 7.23019e8i −1.43562 − 0.691358i −0.455587 − 0.890191i \(-0.650571\pi\)
−0.980033 + 0.198833i \(0.936285\pi\)
\(102\) 1.68417e8 − 3.05631e7i 0.154058 − 0.0279574i
\(103\) 2.03146e8 − 8.90041e8i 0.177845 − 0.779189i −0.804778 − 0.593576i \(-0.797716\pi\)
0.982623 − 0.185613i \(-0.0594271\pi\)
\(104\) 9.43120e8 − 3.53959e8i 0.790527 − 0.296690i
\(105\) 1.63221e7 − 2.04672e7i 0.0131046 − 0.0164326i
\(106\) −4.34208e7 − 9.66840e8i −0.0334058 − 0.743838i
\(107\) −5.34305e7 − 1.18972e9i −0.0394060 − 0.877443i −0.917205 − 0.398415i \(-0.869560\pi\)
0.877799 − 0.479029i \(-0.159011\pi\)
\(108\) −6.75185e8 + 8.46655e8i −0.477547 + 0.598825i
\(109\) −1.97895e9 + 7.42711e8i −1.34281 + 0.503965i −0.916291 − 0.400513i \(-0.868832\pi\)
−0.426519 + 0.904478i \(0.640260\pi\)
\(110\) −2.13385e7 + 9.34899e7i −0.0138962 + 0.0608832i
\(111\) 2.49914e9 − 4.53528e8i 1.56256 − 0.283564i
\(112\) −5.22617e7 − 2.51679e7i −0.0313836 − 0.0151135i
\(113\) 2.63620e9 − 1.57505e9i 1.52098 − 0.908746i 0.522562 − 0.852601i \(-0.324976\pi\)
0.998423 − 0.0561450i \(-0.0178809\pi\)
\(114\) 2.20269e8 + 8.26683e7i 0.122147 + 0.0458424i
\(115\) 1.81234e7 − 2.74558e7i 0.00966271 − 0.0146384i
\(116\) −1.45104e9 + 6.98785e8i −0.744079 + 0.358330i
\(117\) −4.74064e8 + 3.44428e8i −0.233884 + 0.169927i
\(118\) −9.23523e8 + 8.06858e8i −0.438509 + 0.383114i
\(119\) −8.31758e7 − 1.04299e8i −0.0380220 − 0.0476781i
\(120\) −2.17013e8 − 1.29659e8i −0.0955366 − 0.0570805i
\(121\) 4.88741e8 + 7.40411e8i 0.207274 + 0.314006i
\(122\) −1.55372e8 − 6.80731e8i −0.0634972 − 0.278199i
\(123\) −3.35693e8 − 7.85392e8i −0.132242 − 0.309395i
\(124\) 1.66133e9 − 1.49523e8i 0.631043 − 0.0567949i
\(125\) −6.34784e8 − 4.61197e8i −0.232558 − 0.168963i
\(126\) −8.42702e7 − 1.52928e7i −0.0297856 − 0.00540529i
\(127\) 1.52392e8 − 3.56539e8i 0.0519811 − 0.121616i −0.891524 − 0.452973i \(-0.850364\pi\)
0.943506 + 0.331357i \(0.107506\pi\)
\(128\) −7.85547e8 + 2.41767e9i −0.258659 + 0.796070i
\(129\) −8.99382e8 − 1.67133e9i −0.285950 − 0.531385i
\(130\) −1.62014e8 − 1.69453e8i −0.0497516 − 0.0520361i
\(131\) −4.92846e8 + 9.15861e8i −0.146214 + 0.271712i −0.943160 − 0.332339i \(-0.892162\pi\)
0.796945 + 0.604051i \(0.206448\pi\)
\(132\) 1.54375e9 − 4.26049e8i 0.442583 − 0.122145i
\(133\) −2.46136e7 − 1.81705e8i −0.00682091 − 0.0503540i
\(134\) −1.16502e8 + 8.60055e8i −0.0312150 + 0.230438i
\(135\) 5.88185e8 + 1.62329e8i 0.152409 + 0.0420623i
\(136\) −8.90246e8 + 9.31125e8i −0.223144 + 0.233390i
\(137\) 1.20028e9 + 3.69407e9i 0.291097 + 0.895906i 0.984504 + 0.175360i \(0.0561088\pi\)
−0.693407 + 0.720546i \(0.743891\pi\)
\(138\) 2.30408e8 + 2.07371e7i 0.0540806 + 0.00486735i
\(139\) −4.97533e9 − 4.34682e9i −1.13046 − 0.987654i −0.130468 − 0.991453i \(-0.541648\pi\)
−0.999993 + 0.00379870i \(0.998791\pi\)
\(140\) −3.65103e6 + 8.12965e7i −0.000803229 + 0.0178853i
\(141\) 7.52176e9 1.60263
\(142\) −5.35628e8 − 2.58238e9i −0.110552 − 0.532995i
\(143\) 3.59574e9 0.719079
\(144\) 1.46185e7 − 3.25506e8i 0.00283316 − 0.0630853i
\(145\) 6.83387e8 + 5.97057e8i 0.128384 + 0.112166i
\(146\) −5.07231e9 − 4.56516e8i −0.923884 − 0.0831511i
\(147\) 1.40095e9 + 4.31169e9i 0.247455 + 0.761588i
\(148\) −5.45643e9 + 5.70698e9i −0.934827 + 0.977752i
\(149\) 5.84972e9 + 1.61442e9i 0.972293 + 0.268336i 0.715874 − 0.698230i \(-0.246029\pi\)
0.256419 + 0.966566i \(0.417457\pi\)
\(150\) 3.66373e8 − 2.70467e9i 0.0590898 − 0.436218i
\(151\) −7.98321e8 − 5.89344e9i −0.124963 − 0.922513i −0.939535 − 0.342452i \(-0.888743\pi\)
0.814573 − 0.580062i \(-0.196972\pi\)
\(152\) −1.70687e9 + 4.71066e8i −0.259361 + 0.0715790i
\(153\) 3.55098e8 − 6.59883e8i 0.0523886 − 0.0973544i
\(154\) 3.63192e8 + 3.79869e8i 0.0520347 + 0.0544240i
\(155\) −4.45375e8 − 8.27646e8i −0.0619774 − 0.115173i
\(156\) −1.20988e9 + 3.72363e9i −0.163562 + 0.503391i
\(157\) −3.02626e9 + 7.08028e9i −0.397518 + 0.930041i 0.594517 + 0.804083i \(0.297343\pi\)
−0.992036 + 0.125958i \(0.959800\pi\)
\(158\) −3.61949e9 − 6.56841e8i −0.462052 − 0.0838501i
\(159\) 7.36775e9 + 5.35299e9i 0.914214 + 0.664216i
\(160\) 1.24208e9 − 1.11789e8i 0.149834 − 0.0134853i
\(161\) −7.08624e7 − 1.65791e8i −0.00831188 − 0.0194466i
\(162\) 6.17627e8 + 2.70600e9i 0.0704546 + 0.308682i
\(163\) −6.81846e9 − 1.03295e10i −0.756558 − 1.14614i −0.984996 − 0.172578i \(-0.944790\pi\)
0.228438 − 0.973558i \(-0.426638\pi\)
\(164\) 2.27929e9 + 1.36181e9i 0.246038 + 0.147001i
\(165\) −5.62609e8 − 7.05490e8i −0.0590921 − 0.0740991i
\(166\) −6.83735e9 + 5.97361e9i −0.698878 + 0.610591i
\(167\) −2.96375e9 + 2.15329e9i −0.294861 + 0.214229i −0.725373 − 0.688356i \(-0.758333\pi\)
0.430513 + 0.902585i \(0.358333\pi\)
\(168\) −1.24827e9 + 6.01134e8i −0.120897 + 0.0582210i
\(169\) 9.99129e8 − 1.51362e9i 0.0942175 − 0.142733i
\(170\) 2.80692e8 + 1.05346e8i 0.0257757 + 0.00967377i
\(171\) 8.84203e8 − 5.28286e8i 0.0790805 − 0.0472484i
\(172\) 5.31569e9 + 2.55990e9i 0.463108 + 0.223021i
\(173\) −1.57560e10 + 2.85929e9i −1.33733 + 0.242689i −0.799653 − 0.600463i \(-0.794983\pi\)
−0.537675 + 0.843152i \(0.680697\pi\)
\(174\) −1.41998e9 + 6.22133e9i −0.117438 + 0.514531i
\(175\) −1.99156e9 + 7.47446e8i −0.160518 + 0.0602433i
\(176\) −1.24662e9 + 1.56322e9i −0.0979328 + 0.122804i
\(177\) −5.17730e8 − 1.15281e10i −0.0396482 − 0.882835i
\(178\) 3.60860e8 + 8.03517e9i 0.0269432 + 0.599936i
\(179\) −2.22359e9 + 2.78829e9i −0.161888 + 0.203002i −0.856159 − 0.516712i \(-0.827156\pi\)
0.694271 + 0.719714i \(0.255727\pi\)
\(180\) −4.27974e8 + 1.60621e8i −0.0303872 + 0.0114045i
\(181\) 2.14957e8 − 9.41788e8i 0.0148867 − 0.0652228i −0.966939 − 0.255008i \(-0.917922\pi\)
0.981826 + 0.189785i \(0.0607791\pi\)
\(182\) −1.26423e9 + 2.29424e8i −0.0854091 + 0.0154995i
\(183\) 5.91968e9 + 2.85077e9i 0.390183 + 0.187902i
\(184\) −1.49464e9 + 8.93003e8i −0.0961292 + 0.0574345i
\(185\) 4.16520e9 + 1.56323e9i 0.261435 + 0.0981181i
\(186\) 3.64099e9 − 5.51586e9i 0.223055 − 0.337913i
\(187\) −4.14295e9 + 1.99514e9i −0.247755 + 0.119312i
\(188\) −1.89165e10 + 1.37437e10i −1.10441 + 0.802402i
\(189\) 2.51835e9 − 2.20022e9i 0.143562 − 0.125426i
\(190\) 2.56934e8 + 3.22185e8i 0.0143031 + 0.0179355i
\(191\) −3.16531e9 − 1.89119e9i −0.172094 − 0.102822i 0.424269 − 0.905536i \(-0.360531\pi\)
−0.596363 + 0.802715i \(0.703388\pi\)
\(192\) 3.12680e9 + 4.73690e9i 0.166052 + 0.251558i
\(193\) 1.78956e9 + 7.84059e9i 0.0928408 + 0.406762i 0.999899 − 0.0142441i \(-0.00453418\pi\)
−0.907058 + 0.421006i \(0.861677\pi\)
\(194\) 4.71409e9 + 1.10292e10i 0.238941 + 0.559029i
\(195\) 2.19719e9 − 1.97751e8i 0.108821 − 0.00979406i
\(196\) −1.14015e10 − 8.28370e9i −0.551837 − 0.400933i
\(197\) −9.49022e9 − 1.72222e9i −0.448929 − 0.0814687i −0.0506163 − 0.998718i \(-0.516119\pi\)
−0.398313 + 0.917249i \(0.630404\pi\)
\(198\) −1.16028e9 + 2.71461e9i −0.0536499 + 0.125520i
\(199\) 2.88746e9 − 8.88670e9i 0.130520 − 0.401700i −0.864346 − 0.502897i \(-0.832267\pi\)
0.994866 + 0.101197i \(0.0322674\pi\)
\(200\) 9.73403e9 + 1.80888e10i 0.430187 + 0.799422i
\(201\) −5.64388e9 − 5.90303e9i −0.243891 − 0.255090i
\(202\) 9.72610e9 − 1.80741e10i 0.411015 − 0.763794i
\(203\) 4.79421e9 − 1.32312e9i 0.198146 − 0.0546848i
\(204\) −6.72095e8 − 4.96161e9i −0.0271703 − 0.200580i
\(205\) 2.00820e8 − 1.48251e9i 0.00794170 − 0.0586280i
\(206\) 1.08393e10 + 2.99147e9i 0.419373 + 0.115740i
\(207\) 6.99900e8 − 7.32038e8i 0.0264953 − 0.0277120i
\(208\) −1.51053e9 − 4.64895e9i −0.0559559 − 0.172215i
\(209\) −6.29498e9 − 5.66559e8i −0.228211 − 0.0205393i
\(210\) 2.42821e8 + 2.12146e8i 0.00861588 + 0.00752747i
\(211\) 9.76943e8 − 2.17533e10i 0.0339311 − 0.755535i −0.907847 − 0.419301i \(-0.862275\pi\)
0.941778 − 0.336234i \(-0.109153\pi\)
\(212\) −2.83101e10 −0.962565
\(213\) 2.21410e10 + 1.12102e10i 0.737037 + 0.373169i
\(214\) 1.46686e10 0.478108
\(215\) 1.49148e8 − 3.32103e9i 0.00476040 − 0.105998i
\(216\) −2.43188e10 − 2.12467e10i −0.760151 − 0.664124i
\(217\) −5.13031e9 − 4.61736e8i −0.157063 − 0.0141359i
\(218\) −8.04519e9 − 2.47605e10i −0.241258 − 0.742516i
\(219\) 3.31177e10 − 3.46384e10i 0.972885 − 1.01756i
\(220\) 2.70397e9 + 7.46248e8i 0.0778215 + 0.0214774i
\(221\) 1.50904e9 − 1.11402e10i 0.0425537 − 0.314144i
\(222\) 4.19945e9 + 3.10016e10i 0.116039 + 0.856634i
\(223\) 5.05729e9 − 1.39572e9i 0.136945 − 0.0377944i −0.196892 − 0.980425i \(-0.563085\pi\)
0.333837 + 0.942631i \(0.391656\pi\)
\(224\) 3.23881e9 − 6.01872e9i 0.0859547 − 0.159731i
\(225\) −8.25752e9 − 8.63669e9i −0.214797 − 0.224660i
\(226\) 1.79236e10 + 3.33077e10i 0.457023 + 0.849291i
\(227\) −5.05590e8 + 1.55605e9i −0.0126381 + 0.0388961i −0.957177 − 0.289504i \(-0.906510\pi\)
0.944539 + 0.328400i \(0.106510\pi\)
\(228\) 2.70482e9 − 6.32823e9i 0.0662874 − 0.155087i
\(229\) 5.70826e10 + 1.03590e10i 1.37165 + 0.248918i 0.813859 − 0.581062i \(-0.197363\pi\)
0.557793 + 0.829980i \(0.311648\pi\)
\(230\) 3.27817e8 + 2.38173e8i 0.00772424 + 0.00561199i
\(231\) −4.92552e9 + 4.43305e8i −0.113815 + 0.0102435i
\(232\) −1.88757e10 − 4.41619e10i −0.427766 − 1.00081i
\(233\) −8.72480e9 − 3.82259e10i −0.193934 − 0.849680i −0.974461 − 0.224558i \(-0.927906\pi\)
0.780527 − 0.625122i \(-0.214951\pi\)
\(234\) −3.97608e9 − 6.02350e9i −0.0866929 − 0.131334i
\(235\) 1.13099e10 + 6.75734e9i 0.241909 + 0.144534i
\(236\) 2.23661e10 + 2.80462e10i 0.469339 + 0.588532i
\(237\) 2.60679e10 − 2.27748e10i 0.536708 − 0.468908i
\(238\) 1.32932e9 − 9.65808e8i 0.0268555 − 0.0195117i
\(239\) 6.35884e9 − 3.06226e9i 0.126063 − 0.0607087i −0.369789 − 0.929116i \(-0.620570\pi\)
0.495852 + 0.868407i \(0.334856\pi\)
\(240\) −6.75784e8 + 1.02377e9i −0.0131479 + 0.0199182i
\(241\) 1.59238e10 + 5.97630e9i 0.304068 + 0.114118i 0.498745 − 0.866749i \(-0.333795\pi\)
−0.194677 + 0.980867i \(0.562366\pi\)
\(242\) −9.38053e9 + 5.60461e9i −0.175816 + 0.105045i
\(243\) 2.97700e10 + 1.43365e10i 0.547710 + 0.263763i
\(244\) −2.00963e10 + 3.64694e9i −0.362963 + 0.0658680i
\(245\) −1.76700e9 + 7.74173e9i −0.0313321 + 0.137275i
\(246\) 9.84944e9 − 3.69656e9i 0.171476 − 0.0643560i
\(247\) 9.63426e9 − 1.20810e10i 0.164696 − 0.206522i
\(248\) 2.23165e9 + 4.96916e10i 0.0374623 + 0.834162i
\(249\) −3.83304e9 − 8.53492e10i −0.0631896 − 1.40703i
\(250\) 6.02563e9 − 7.55590e9i 0.0975601 − 0.122336i
\(251\) 7.93974e10 − 2.97984e10i 1.26263 − 0.473872i 0.371841 − 0.928296i \(-0.378727\pi\)
0.890785 + 0.454425i \(0.150155\pi\)
\(252\) −5.57481e8 + 2.44249e9i −0.00870819 + 0.0381531i
\(253\) −6.11493e9 + 1.10970e9i −0.0938317 + 0.0170279i
\(254\) 4.30285e9 + 2.07214e9i 0.0648641 + 0.0312369i
\(255\) −2.42184e9 + 1.44698e9i −0.0358686 + 0.0214305i
\(256\) −5.27887e10 − 1.98119e10i −0.768176 − 0.288301i
\(257\) −5.15177e10 + 7.80459e10i −0.736643 + 1.11597i 0.252297 + 0.967650i \(0.418814\pi\)
−0.988940 + 0.148317i \(0.952615\pi\)
\(258\) 2.10621e10 − 1.01430e10i 0.295946 − 0.142520i
\(259\) 1.97259e10 − 1.43317e10i 0.272387 − 0.197901i
\(260\) −5.16441e9 + 4.51201e9i −0.0700875 + 0.0612336i
\(261\) 1.74184e10 + 2.18420e10i 0.232342 + 0.291347i
\(262\) −1.09969e10 − 6.57037e9i −0.144184 − 0.0861458i
\(263\) −4.26853e10 − 6.46655e10i −0.550146 − 0.833436i 0.448017 − 0.894025i \(-0.352130\pi\)
−0.998163 + 0.0605896i \(0.980702\pi\)
\(264\) 1.06268e10 + 4.65588e10i 0.134643 + 0.589908i
\(265\) 6.26934e9 + 1.46679e10i 0.0780936 + 0.182709i
\(266\) 2.24940e9 − 2.02450e8i 0.0275486 − 0.00247942i
\(267\) −6.12316e10 − 4.44874e10i −0.737353 − 0.535718i
\(268\) 2.49797e10 + 4.53316e9i 0.295789 + 0.0536777i
\(269\) 1.09692e9 − 2.56636e9i 0.0127729 − 0.0298836i −0.913020 − 0.407915i \(-0.866256\pi\)
0.925793 + 0.378031i \(0.123399\pi\)
\(270\) −2.32242e9 + 7.14767e9i −0.0265952 + 0.0818517i
\(271\) −1.37767e10 − 2.56013e10i −0.155161 − 0.288337i 0.791134 − 0.611643i \(-0.209491\pi\)
−0.946294 + 0.323306i \(0.895206\pi\)
\(272\) 4.31993e9 + 4.51829e9i 0.0478538 + 0.0500512i
\(273\) 5.72934e9 − 1.06469e10i 0.0624271 − 0.116009i
\(274\) −4.61173e10 + 1.27276e10i −0.494295 + 0.136417i
\(275\) 9.84241e9 + 7.26596e10i 0.103778 + 0.766118i
\(276\) 9.08362e8 − 6.70580e9i 0.00942255 − 0.0695600i
\(277\) 4.13313e9 + 1.14067e9i 0.0421813 + 0.0116413i 0.287064 − 0.957911i \(-0.407321\pi\)
−0.244883 + 0.969553i \(0.578749\pi\)
\(278\) 5.62352e10 − 5.88174e10i 0.564685 − 0.590615i
\(279\) −8.94130e9 − 2.75185e10i −0.0883449 − 0.271898i
\(280\) −2.41696e9 − 2.17531e8i −0.0234995 − 0.00211499i
\(281\) 1.18277e11 + 1.03336e11i 1.13168 + 0.988719i 0.999997 − 0.00257325i \(-0.000819092\pi\)
0.131683 + 0.991292i \(0.457962\pi\)
\(282\) −4.15652e9 + 9.25522e10i −0.0391390 + 0.871497i
\(283\) 9.37735e10 0.869043 0.434521 − 0.900662i \(-0.356918\pi\)
0.434521 + 0.900662i \(0.356918\pi\)
\(284\) −7.61657e10 + 1.22631e10i −0.694747 + 0.111859i
\(285\) −3.87773e9 −0.0348158
\(286\) −1.98701e9 + 4.42442e10i −0.0175611 + 0.391029i
\(287\) −6.17460e9 − 5.39459e9i −0.0537205 − 0.0469342i
\(288\) 3.82383e10 + 3.44151e9i 0.327516 + 0.0294770i
\(289\) −3.22031e10 − 9.91109e10i −0.271555 − 0.835759i
\(290\) −7.72418e9 + 8.07886e9i −0.0641300 + 0.0670748i
\(291\) −1.08799e11 − 3.00265e10i −0.889416 − 0.245463i
\(292\) −1.99971e10 + 1.47624e11i −0.160970 + 1.18833i
\(293\) 2.50000e10 + 1.84557e11i 0.198169 + 1.46294i 0.767614 + 0.640913i \(0.221444\pi\)
−0.569445 + 0.822030i \(0.692842\pi\)
\(294\) −5.38278e10 + 1.48555e10i −0.420188 + 0.115964i
\(295\) 9.57809e9 − 1.77991e10i 0.0736343 − 0.136835i
\(296\) −1.62713e11 − 1.70184e11i −1.23199 − 1.28856i
\(297\) −5.46223e10 − 1.01505e11i −0.407349 − 0.756980i
\(298\) −2.30974e10 + 7.10863e10i −0.169664 + 0.522171i
\(299\) 5.97160e9 − 1.39712e10i 0.0432086 − 0.101092i
\(300\) −7.85555e10 − 1.42557e10i −0.559926 − 0.101612i
\(301\) −1.47399e10 − 1.07092e10i −0.103501 − 0.0751980i
\(302\) 7.29575e10 − 6.56630e9i 0.504707 − 0.0454244i
\(303\) 7.59078e10 + 1.77595e11i 0.517362 + 1.21043i
\(304\) 1.91195e9 + 8.37681e9i 0.0128394 + 0.0562532i
\(305\) 6.33991e9 + 9.60455e9i 0.0419502 + 0.0635518i
\(306\) 7.92336e9 + 4.73399e9i 0.0516610 + 0.0308660i
\(307\) −1.35000e11 − 1.69285e11i −0.867385 − 1.08767i −0.995392 − 0.0958936i \(-0.969429\pi\)
0.128006 − 0.991773i \(-0.459142\pi\)
\(308\) 1.15772e10 − 1.01147e10i 0.0733038 − 0.0640436i
\(309\) −8.56023e10 + 6.21937e10i −0.534161 + 0.388091i
\(310\) 1.04300e10 − 5.02281e9i 0.0641439 − 0.0308901i
\(311\) 5.99334e10 − 9.07953e10i 0.363285 − 0.550353i −0.606260 − 0.795266i \(-0.707331\pi\)
0.969545 + 0.244913i \(0.0787595\pi\)
\(312\) −1.09309e11 − 4.10245e10i −0.653073 − 0.245102i
\(313\) −1.71677e11 + 1.02572e11i −1.01103 + 0.604061i −0.920054 − 0.391793i \(-0.871855\pi\)
−0.0909737 + 0.995853i \(0.528998\pi\)
\(314\) −8.54476e10 − 4.11494e10i −0.496040 − 0.238880i
\(315\) 1.38894e9 − 2.52055e8i 0.00794852 − 0.00144244i
\(316\) −2.39444e10 + 1.04907e11i −0.135087 + 0.591853i
\(317\) −1.24820e11 + 4.68458e10i −0.694253 + 0.260558i −0.673457 − 0.739226i \(-0.735191\pi\)
−0.0207959 + 0.999784i \(0.506620\pi\)
\(318\) −6.99377e10 + 8.76992e10i −0.383521 + 0.480921i
\(319\) −7.69122e9 − 1.71258e11i −0.0415850 − 0.925963i
\(320\) 4.46025e8 + 9.93152e9i 0.00237785 + 0.0529470i
\(321\) −8.60604e10 + 1.07916e11i −0.452408 + 0.567302i
\(322\) 2.07915e9 − 7.80317e8i 0.0107779 − 0.00404501i
\(323\) −4.39714e9 + 1.92651e10i −0.0224781 + 0.0984829i
\(324\) 7.98857e10 − 1.44971e10i 0.402733 − 0.0730852i
\(325\) −1.61508e11 − 7.77780e10i −0.803005 − 0.386707i
\(326\) 1.30869e11 − 7.81903e10i 0.641735 − 0.383419i
\(327\) 2.29363e11 + 8.60815e10i 1.10933 + 0.416337i
\(328\) −4.36183e10 + 6.60789e10i −0.208083 + 0.315232i
\(329\) 6.50549e10 − 3.13288e10i 0.306125 − 0.147422i
\(330\) 8.99166e9 − 6.53282e9i 0.0417376 − 0.0303241i
\(331\) 9.19893e10 − 8.03686e10i 0.421222 − 0.368011i −0.421073 − 0.907027i \(-0.638347\pi\)
0.842296 + 0.539016i \(0.181204\pi\)
\(332\) 1.65589e11 + 2.07641e11i 0.748012 + 0.937978i
\(333\) 1.17575e11 + 7.02479e10i 0.523982 + 0.313065i
\(334\) −2.48576e10 − 3.76576e10i −0.109295 − 0.165574i
\(335\) −3.18313e9 − 1.39462e10i −0.0138087 − 0.0604999i
\(336\) 2.64231e9 + 6.18200e9i 0.0113099 + 0.0264608i
\(337\) 3.64177e11 − 3.27765e10i 1.53808 − 0.138429i 0.712077 − 0.702101i \(-0.247755\pi\)
0.825999 + 0.563672i \(0.190612\pi\)
\(338\) 1.80723e10 + 1.31303e10i 0.0753162 + 0.0547204i
\(339\) −3.50201e11 − 6.35522e10i −1.44019 − 0.261356i
\(340\) 3.44679e9 − 8.06417e9i 0.0139881 − 0.0327269i
\(341\) −5.48668e10 + 1.68863e11i −0.219743 + 0.676299i
\(342\) 6.01174e9 + 1.11717e10i 0.0237620 + 0.0441572i
\(343\) 6.11024e10 + 6.39081e10i 0.238361 + 0.249306i
\(344\) −8.33720e10 + 1.54931e11i −0.321002 + 0.596521i
\(345\) −3.67553e9 + 1.01438e9i −0.0139680 + 0.00385492i
\(346\) −2.64756e10 − 1.95451e11i −0.0993125 − 0.733154i
\(347\) 1.13304e9 − 8.36443e9i 0.00419529 − 0.0309709i −0.988731 − 0.149702i \(-0.952168\pi\)
0.992926 + 0.118731i \(0.0378828\pi\)
\(348\) 1.79937e11 + 4.96595e10i 0.657679 + 0.181508i
\(349\) −1.98726e10 + 2.07851e10i −0.0717035 + 0.0749960i −0.757673 − 0.652634i \(-0.773664\pi\)
0.685970 + 0.727630i \(0.259378\pi\)
\(350\) −8.09648e9 − 2.49184e10i −0.0288397 − 0.0887593i
\(351\) 2.80674e11 + 2.52612e10i 0.987008 + 0.0888324i
\(352\) −1.77417e11 − 1.55005e11i −0.615962 − 0.538150i
\(353\) −1.57623e10 + 3.50976e11i −0.0540299 + 1.20307i 0.770571 + 0.637355i \(0.219971\pi\)
−0.824601 + 0.565715i \(0.808600\pi\)
\(354\) 1.42135e11 0.481046
\(355\) 2.32208e10 + 3.67468e10i 0.0775977 + 0.122798i
\(356\) 2.35279e11 0.776350
\(357\) −6.93687e8 + 1.54461e10i −0.00226025 + 0.0503284i
\(358\) −3.30800e10 − 2.89012e10i −0.106437 − 0.0929911i
\(359\) −2.90619e11 − 2.61562e10i −0.923420 − 0.0831093i −0.382285 − 0.924045i \(-0.624863\pi\)
−0.541136 + 0.840935i \(0.682005\pi\)
\(360\) −4.21238e9 − 1.29644e10i −0.0132180 − 0.0406808i
\(361\) 2.04227e11 − 2.13605e11i 0.632895 − 0.661956i
\(362\) 1.14695e10 + 3.16539e9i 0.0351040 + 0.00968810i
\(363\) 1.38025e10 − 1.01894e11i 0.0417233 − 0.308014i
\(364\) 5.04512e9 + 3.72445e10i 0.0150631 + 0.111200i
\(365\) 8.09147e10 − 2.23310e10i 0.238621 − 0.0658553i
\(366\) −3.83487e10 + 7.12639e10i −0.111708 + 0.207589i
\(367\) −9.05350e10 − 9.46922e10i −0.260507 − 0.272469i 0.579586 − 0.814911i \(-0.303214\pi\)
−0.840093 + 0.542442i \(0.817500\pi\)
\(368\) 4.00355e9 + 7.43984e9i 0.0113797 + 0.0211470i
\(369\) 1.42324e10 − 4.38028e10i 0.0399631 − 0.122994i
\(370\) −2.15366e10 + 5.03873e10i −0.0597405 + 0.139770i
\(371\) 8.60186e10 + 1.56101e10i 0.235727 + 0.0427782i
\(372\) −1.56407e11 − 1.13636e11i −0.423460 − 0.307662i
\(373\) −9.71657e10 + 8.74507e9i −0.259910 + 0.0233923i −0.218828 − 0.975763i \(-0.570223\pi\)
−0.0410821 + 0.999156i \(0.513081\pi\)
\(374\) −2.22600e10 − 5.20798e10i −0.0588305 − 0.137641i
\(375\) 2.02362e10 + 8.86606e10i 0.0528431 + 0.231521i
\(376\) −3.84119e11 − 5.81916e11i −0.991108 − 1.50146i
\(377\) 3.59787e11 + 2.14963e11i 0.917297 + 0.548059i
\(378\) 2.56811e10 + 3.22031e10i 0.0646995 + 0.0811307i
\(379\) −5.54388e11 + 4.84354e11i −1.38018 + 1.20583i −0.426699 + 0.904394i \(0.640323\pi\)
−0.953486 + 0.301437i \(0.902534\pi\)
\(380\) 9.75213e9 − 7.08534e9i 0.0239924 − 0.0174315i
\(381\) −4.04895e10 + 1.94987e10i −0.0984418 + 0.0474071i
\(382\) 2.50194e10 − 3.79028e10i 0.0601163 − 0.0910723i
\(383\) 5.44463e11 + 2.04340e11i 1.29293 + 0.485243i 0.900627 − 0.434594i \(-0.143108\pi\)
0.392300 + 0.919837i \(0.371679\pi\)
\(384\) 2.52927e11 − 1.51117e11i 0.593614 − 0.354668i
\(385\) −7.80438e9 − 3.75839e9i −0.0181036 − 0.00871824i
\(386\) −9.74641e10 + 1.76871e10i −0.223461 + 0.0405522i
\(387\) 2.27736e10 − 9.97775e10i 0.0516097 − 0.226117i
\(388\) 3.28482e11 − 1.23281e11i 0.735816 − 0.276156i
\(389\) 1.52715e11 − 1.91499e11i 0.338150 − 0.424026i −0.583462 − 0.812141i \(-0.698302\pi\)
0.921611 + 0.388115i \(0.126874\pi\)
\(390\) 1.21908e9 + 2.71448e10i 0.00266833 + 0.0594151i
\(391\) 8.71740e8 + 1.94108e10i 0.00188622 + 0.0419999i
\(392\) 2.62028e11 − 3.28572e11i 0.560480 − 0.702819i
\(393\) 1.12857e11 − 4.23559e10i 0.238650 − 0.0895668i
\(394\) 2.64355e10 − 1.15822e11i 0.0552656 − 0.242134i
\(395\) 5.96565e10 − 1.08261e10i 0.123302 − 0.0223760i
\(396\) 7.78039e10 + 3.74684e10i 0.158991 + 0.0765661i
\(397\) 3.49872e10 − 2.09039e10i 0.0706891 − 0.0422348i −0.477120 − 0.878838i \(-0.658319\pi\)
0.547809 + 0.836603i \(0.315462\pi\)
\(398\) 1.07752e11 + 4.04398e10i 0.215253 + 0.0807859i
\(399\) −1.17078e10 + 1.77365e10i −0.0231258 + 0.0350341i
\(400\) 8.98071e10 − 4.32488e10i 0.175404 − 0.0844703i
\(401\) −2.56529e11 + 1.86379e11i −0.495434 + 0.359954i −0.807270 − 0.590182i \(-0.799056\pi\)
0.311836 + 0.950136i \(0.399056\pi\)
\(402\) 7.57532e10 − 6.61836e10i 0.144672 − 0.126396i
\(403\) −2.70644e11 − 3.39377e11i −0.511124 − 0.640929i
\(404\) −5.15400e11 − 3.07937e11i −0.962562 − 0.575104i
\(405\) −2.52020e10 − 3.81795e10i −0.0465466 − 0.0705151i
\(406\) 1.36312e10 + 5.97220e10i 0.0248981 + 0.109086i
\(407\) −3.30317e11 − 7.72814e11i −0.596699 − 1.39605i
\(408\) 1.48707e11 − 1.33839e10i 0.265681 − 0.0239117i
\(409\) −6.42701e11 − 4.66950e11i −1.13568 − 0.825117i −0.149165 − 0.988812i \(-0.547658\pi\)
−0.986511 + 0.163696i \(0.947658\pi\)
\(410\) 1.81307e10 + 3.29024e9i 0.0316875 + 0.00575042i
\(411\) 1.76933e11 − 4.13955e11i 0.305859 − 0.715592i
\(412\) 1.01642e11 − 3.12823e11i 0.173795 − 0.534885i
\(413\) −5.24935e10 − 9.75493e10i −0.0887832 − 0.164987i
\(414\) 8.62067e9 + 9.01651e9i 0.0144225 + 0.0150847i
\(415\) 7.09119e10 − 1.31776e11i 0.117355 − 0.218083i
\(416\) 5.55217e11 − 1.53230e11i 0.908955 − 0.250856i
\(417\) 1.02787e11 + 7.58801e11i 0.166465 + 1.22890i
\(418\) 1.04499e10 − 7.71441e10i 0.0167424 − 0.123597i
\(419\) 3.44411e11 + 9.50513e10i 0.545901 + 0.150659i 0.528099 − 0.849183i \(-0.322905\pi\)
0.0178012 + 0.999842i \(0.494333\pi\)
\(420\) 6.51804e9 − 6.81734e9i 0.0102210 − 0.0106904i
\(421\) 9.24664e10 + 2.84582e11i 0.143455 + 0.441508i 0.996809 − 0.0798233i \(-0.0254356\pi\)
−0.853354 + 0.521331i \(0.825436\pi\)
\(422\) 2.67126e11 + 2.40418e10i 0.410025 + 0.0369029i
\(423\) 3.05443e11 + 2.66857e11i 0.463872 + 0.405272i
\(424\) 3.78756e10 − 8.43366e11i 0.0569133 − 1.26727i
\(425\) 2.29242e11 0.340835
\(426\) −1.50172e11 + 2.66241e11i −0.220926 + 0.391681i
\(427\) 6.30724e10 0.0918150
\(428\) 1.92506e10 − 4.28647e11i 0.0277298 − 0.617452i
\(429\) −3.13845e11 − 2.74198e11i −0.447360 − 0.390847i
\(430\) 4.07815e10 + 3.67040e9i 0.0575248 + 0.00517733i
\(431\) 4.81529e10 + 1.48199e11i 0.0672164 + 0.206871i 0.979023 − 0.203749i \(-0.0653125\pi\)
−0.911807 + 0.410619i \(0.865313\pi\)
\(432\) −1.08290e11 + 1.13263e11i −0.149593 + 0.156462i
\(433\) −1.06256e12 − 2.93249e11i −1.45265 − 0.400905i −0.551410 − 0.834234i \(-0.685910\pi\)
−0.901235 + 0.433330i \(0.857339\pi\)
\(434\) 8.51648e9 − 6.28712e10i 0.0115228 − 0.0850644i
\(435\) −1.41182e10 − 1.04225e11i −0.0189051 − 0.139563i
\(436\) −7.34114e11 + 2.02603e11i −0.972914 + 0.268507i
\(437\) −1.26557e10 + 2.35182e10i −0.0166004 + 0.0308488i
\(438\) 4.07911e11 + 4.26641e11i 0.529580 + 0.553897i
\(439\) 2.75664e11 + 5.12270e11i 0.354234 + 0.658277i 0.993889 − 0.110385i \(-0.0352084\pi\)
−0.639655 + 0.768662i \(0.720923\pi\)
\(440\) −2.58486e10 + 7.95537e10i −0.0328775 + 0.101187i
\(441\) −9.60806e10 + 2.24792e11i −0.120966 + 0.283013i
\(442\) 1.36242e11 + 2.47243e10i 0.169789 + 0.0308122i
\(443\) 6.03460e11 + 4.38439e11i 0.744443 + 0.540870i 0.894099 − 0.447868i \(-0.147817\pi\)
−0.149656 + 0.988738i \(0.547817\pi\)
\(444\) 9.11443e11 − 8.20314e10i 1.11303 − 0.100174i
\(445\) −5.21030e10 − 1.21901e11i −0.0629858 − 0.147363i
\(446\) 1.43791e10 + 6.29991e10i 0.0172078 + 0.0753924i
\(447\) −3.87468e11 − 5.86989e11i −0.459041 − 0.695418i
\(448\) 4.67729e10 + 2.79455e10i 0.0548585 + 0.0327764i
\(449\) −4.94359e10 − 6.19907e10i −0.0574029 − 0.0719810i 0.752301 − 0.658819i \(-0.228944\pi\)
−0.809704 + 0.586838i \(0.800372\pi\)
\(450\) 1.10834e11 − 9.68328e10i 0.127414 − 0.111318i
\(451\) −2.28645e11 + 1.66121e11i −0.260236 + 0.189073i
\(452\) 9.96845e11 − 4.80055e11i 1.12332 − 0.540964i
\(453\) −3.79733e11 + 5.75270e11i −0.423678 + 0.641845i
\(454\) −1.88671e10 − 7.08095e9i −0.0208427 − 0.00782240i
\(455\) 1.81796e10 − 1.08618e10i 0.0198854 − 0.0118810i
\(456\) 1.84901e11 + 8.90437e10i 0.200262 + 0.0964409i
\(457\) −1.74117e12 + 3.15976e11i −1.86732 + 0.338868i −0.990003 − 0.141049i \(-0.954952\pi\)
−0.877314 + 0.479917i \(0.840667\pi\)
\(458\) −1.59007e11 + 6.96654e11i −0.168858 + 0.739814i
\(459\) −3.37404e11 + 1.26630e11i −0.354808 + 0.133162i
\(460\) 7.39014e9 − 9.26694e9i 0.00769560 − 0.00964997i
\(461\) 3.25485e10 + 7.24749e11i 0.0335643 + 0.747366i 0.943253 + 0.332075i \(0.107749\pi\)
−0.909689 + 0.415291i \(0.863680\pi\)
\(462\) −2.73285e9 − 6.08515e10i −0.00279078 − 0.0621416i
\(463\) −9.60966e11 + 1.20501e12i −0.971837 + 1.21865i 0.00396564 + 0.999992i \(0.498738\pi\)
−0.975803 + 0.218653i \(0.929834\pi\)
\(464\) −2.18189e11 + 8.18878e10i −0.218526 + 0.0820141i
\(465\) −2.42398e10 + 1.06202e11i −0.0240431 + 0.105340i
\(466\) 4.75175e11 − 8.62315e10i 0.466785 − 0.0847090i
\(467\) 5.83735e11 + 2.81112e11i 0.567924 + 0.273498i 0.695732 − 0.718301i \(-0.255080\pi\)
−0.127808 + 0.991799i \(0.540794\pi\)
\(468\) −1.81238e11 + 1.08284e11i −0.174639 + 0.104342i
\(469\) −7.33999e10 − 2.75475e10i −0.0700516 − 0.0262908i
\(470\) −8.93961e10 + 1.35429e11i −0.0845042 + 0.128018i
\(471\) 8.04055e11 − 3.87212e11i 0.752820 − 0.362539i
\(472\) −8.65428e11 + 6.28770e11i −0.802587 + 0.583113i
\(473\) −4.72939e11 + 4.13194e11i −0.434440 + 0.379559i
\(474\) 2.65830e11 + 3.33340e11i 0.241881 + 0.303309i
\(475\) 2.70493e11 + 1.61612e11i 0.243800 + 0.145664i
\(476\) −2.64784e10 − 4.01131e10i −0.0236407 − 0.0358142i
\(477\) 1.09275e11 + 4.78767e11i 0.0966473 + 0.423439i
\(478\) 3.41659e10 + 7.99352e10i 0.0299342 + 0.0700346i
\(479\) −1.11816e12 + 1.00637e11i −0.970501 + 0.0873467i −0.563531 − 0.826095i \(-0.690557\pi\)
−0.406970 + 0.913442i \(0.633415\pi\)
\(480\) −1.16936e11 − 8.49591e10i −0.100546 − 0.0730507i
\(481\) 2.02170e12 + 3.66885e11i 1.72212 + 0.312519i
\(482\) −8.23355e10 + 1.92633e11i −0.0694825 + 0.162562i
\(483\) −6.45756e9 + 1.98743e10i −0.00539891 + 0.0166161i
\(484\) 1.51468e11 + 2.81474e11i 0.125463 + 0.233150i
\(485\) −1.36617e11 − 1.42890e11i −0.112116 − 0.117264i
\(486\) −1.92856e11 + 3.58386e11i −0.156808 + 0.291399i
\(487\) −1.74233e12 + 4.80851e11i −1.40362 + 0.387374i −0.884185 − 0.467137i \(-0.845286\pi\)
−0.519434 + 0.854511i \(0.673857\pi\)
\(488\) −8.17570e10 − 6.03554e11i −0.0652583 − 0.481756i
\(489\) −1.92560e11 + 1.42154e12i −0.152292 + 1.12426i
\(490\) −9.42824e10 − 2.60203e10i −0.0738836 − 0.0203906i
\(491\) −1.53966e10 + 1.61035e10i −0.0119552 + 0.0125042i −0.728745 − 0.684785i \(-0.759896\pi\)
0.716790 + 0.697289i \(0.245611\pi\)
\(492\) −9.50952e10 − 2.92673e11i −0.0731670 − 0.225185i
\(493\) −5.33815e11 − 4.80442e10i −0.406986 − 0.0366294i
\(494\) 1.43328e11 + 1.25222e11i 0.108283 + 0.0946036i
\(495\) 2.18302e9 − 4.86087e10i 0.00163431 − 0.0363907i
\(496\) 2.41372e11 0.179068
\(497\) 2.38187e11 + 4.73659e9i 0.175111 + 0.00348227i
\(498\) 1.05230e12 0.766672
\(499\) 6.53764e10 − 1.45572e12i 0.0472029 − 1.05105i −0.825992 − 0.563683i \(-0.809384\pi\)
0.873194 − 0.487372i \(-0.162044\pi\)
\(500\) −2.12892e11 − 1.85998e11i −0.152333 − 0.133089i
\(501\) 4.22884e11 + 3.80603e10i 0.299883 + 0.0269900i
\(502\) 3.22782e11 + 9.93420e11i 0.226852 + 0.698178i
\(503\) 2.58366e10 − 2.70230e10i 0.0179962 − 0.0188225i −0.713736 − 0.700415i \(-0.752998\pi\)
0.731732 + 0.681593i \(0.238712\pi\)
\(504\) −7.20165e10 − 1.98753e10i −0.0497158 − 0.0137207i
\(505\) −4.54099e10 + 3.35229e11i −0.0310699 + 0.229367i
\(506\) −1.02753e10 − 7.58550e10i −0.00696811 − 0.0514407i
\(507\) −2.02629e11 + 5.59221e10i −0.136197 + 0.0375879i
\(508\) 6.61994e10 − 1.23019e11i 0.0441029 − 0.0819570i
\(509\) −1.16665e12 − 1.22022e12i −0.770389 − 0.805764i 0.214904 − 0.976635i \(-0.431056\pi\)
−0.985293 + 0.170871i \(0.945342\pi\)
\(510\) −1.64662e10 − 3.05993e10i −0.0107777 − 0.0200284i
\(511\) 1.42160e11 − 4.37522e11i 0.0922321 − 0.283861i
\(512\) −2.38592e11 + 5.58214e11i −0.153441 + 0.358993i
\(513\) −4.87390e11 − 8.84482e10i −0.310705 − 0.0563846i
\(514\) −9.31855e11 − 6.77032e11i −0.588863 − 0.427834i
\(515\) −1.84587e11 + 1.66131e10i −0.115629 + 0.0104068i
\(516\) −2.68758e11 − 6.28789e11i −0.166893 − 0.390465i
\(517\) −5.53826e11 − 2.42647e12i −0.340930 − 1.49371i
\(518\) 1.65445e11 + 2.50638e11i 0.100965 + 0.152955i
\(519\) 1.59326e12 + 9.51927e11i 0.963902 + 0.575905i
\(520\) −1.27505e11 − 1.59886e11i −0.0764735 − 0.0958947i
\(521\) 2.99370e11 − 2.61551e11i 0.178007 − 0.155520i −0.564324 − 0.825554i \(-0.690863\pi\)
0.742331 + 0.670033i \(0.233720\pi\)
\(522\) −2.78383e11 + 2.02257e11i −0.164106 + 0.119230i
\(523\) −2.52306e12 + 1.21504e12i −1.47458 + 0.710122i −0.986665 − 0.162766i \(-0.947958\pi\)
−0.487920 + 0.872889i \(0.662244\pi\)
\(524\) −2.06432e11 + 3.12731e11i −0.119615 + 0.181209i
\(525\) 2.30826e11 + 8.66303e10i 0.132607 + 0.0497683i
\(526\) 8.19271e11 − 4.89492e11i 0.466650 − 0.278811i
\(527\) 5.00138e11 + 2.40854e11i 0.282451 + 0.136021i
\(528\) 2.28013e11 − 4.13783e10i 0.127675 − 0.0231697i
\(529\) 3.94951e11 − 1.73039e12i 0.219277 − 0.960713i
\(530\) −1.83946e11 + 6.90362e10i −0.101263 + 0.0380045i
\(531\) 3.87972e11 − 4.86501e11i 0.211775 − 0.265558i
\(532\) −2.96398e9 − 6.59980e10i −0.00160425 − 0.0357214i
\(533\) −3.09994e10 − 6.90255e11i −0.0166372 − 0.370457i
\(534\) 5.81236e11 − 7.28847e11i 0.309326 − 0.387883i
\(535\) −2.26351e11 + 8.49510e10i −0.119451 + 0.0448308i
\(536\) −1.68464e11 + 7.38089e11i −0.0881588 + 0.386249i
\(537\) 4.06705e11 − 7.38060e10i 0.211055 − 0.0383008i
\(538\) 3.09719e10 + 1.49153e10i 0.0159385 + 0.00767557i
\(539\) 1.28777e12 − 7.69408e11i 0.657188 − 0.392651i
\(540\) 2.05822e11 + 7.72464e10i 0.104165 + 0.0390937i
\(541\) −9.62965e11 + 1.45883e12i −0.483306 + 0.732178i −0.991647 − 0.128978i \(-0.958830\pi\)
0.508341 + 0.861156i \(0.330259\pi\)
\(542\) 3.22627e11 − 1.55369e11i 0.160584 − 0.0773334i
\(543\) −9.05792e10 + 6.58096e10i −0.0447125 + 0.0324855i
\(544\) −5.54688e11 + 4.84617e11i −0.271553 + 0.237248i
\(545\) 2.67543e11 + 3.35488e11i 0.129900 + 0.162889i
\(546\) 1.27840e11 + 7.63807e10i 0.0615601 + 0.0367804i
\(547\) −5.87324e11 − 8.89758e11i −0.280501 − 0.424941i 0.666824 − 0.745216i \(-0.267653\pi\)
−0.947325 + 0.320274i \(0.896225\pi\)
\(548\) 3.11404e11 + 1.36435e12i 0.147506 + 0.646268i
\(549\) 1.39246e11 + 3.25782e11i 0.0654195 + 0.153056i
\(550\) −8.99485e11 + 8.09551e10i −0.419143 + 0.0377235i
\(551\) −5.96001e11 − 4.33020e11i −0.275464 − 0.200136i
\(552\) 1.98552e11 + 3.60320e10i 0.0910226 + 0.0165182i
\(553\) 1.30599e11 − 3.05552e11i 0.0593851 − 0.138938i
\(554\) −1.63194e10 + 5.02261e10i −0.00736057 + 0.0226535i
\(555\) −2.44343e11 − 4.54065e11i −0.109315 − 0.203142i
\(556\) −1.64497e12 − 1.72050e12i −0.729997 − 0.763517i
\(557\) 1.26525e12 − 2.35124e12i 0.556967 − 1.03502i −0.434000 − 0.900913i \(-0.642898\pi\)
0.990967 − 0.134105i \(-0.0428160\pi\)
\(558\) 3.43545e11 − 9.48123e10i 0.150013 − 0.0414010i
\(559\) −2.06097e11 − 1.52147e12i −0.0892727 − 0.659038i
\(560\) −1.58070e9 + 1.16692e10i −0.000679207 + 0.00501411i
\(561\) 5.13748e11 + 1.41785e11i 0.218986 + 0.0604364i
\(562\) −1.33687e12 + 1.39825e12i −0.565294 + 0.591251i
\(563\) 4.84623e11 + 1.49152e12i 0.203290 + 0.625662i 0.999779 + 0.0210096i \(0.00668804\pi\)
−0.796489 + 0.604653i \(0.793312\pi\)
\(564\) 2.69912e12 + 2.42925e11i 1.12322 + 0.101092i
\(565\) −4.69477e11 − 4.10169e11i −0.193819 − 0.169334i
\(566\) −5.18192e10 + 1.15384e12i −0.0212235 + 0.472578i
\(567\) −2.50722e11 −0.101875
\(568\) −2.63422e11 − 2.28540e12i −0.106190 − 0.921288i
\(569\) −2.28899e12 −0.915460 −0.457730 − 0.889091i \(-0.651337\pi\)
−0.457730 + 0.889091i \(0.651337\pi\)
\(570\) 2.14283e9 − 4.77139e10i 0.000850260 − 0.0189325i
\(571\) 1.89473e12 + 1.65538e12i 0.745909 + 0.651681i 0.944541 − 0.328393i \(-0.106507\pi\)
−0.198632 + 0.980074i \(0.563650\pi\)
\(572\) 1.29030e12 + 1.16129e11i 0.503975 + 0.0453586i
\(573\) 1.32061e11 + 4.06442e11i 0.0511775 + 0.157508i
\(574\) 6.97903e10 − 7.29949e10i 0.0268344 − 0.0280665i
\(575\) 2.98664e11 + 8.24260e10i 0.113940 + 0.0314455i
\(576\) −4.10831e10 + 3.03288e11i −0.0155511 + 0.114803i
\(577\) 2.88816e11 + 2.13213e12i 0.108475 + 0.800796i 0.960694 + 0.277610i \(0.0895423\pi\)
−0.852219 + 0.523186i \(0.824743\pi\)
\(578\) 1.23731e12 − 3.41477e11i 0.461110 − 0.127258i
\(579\) 4.41697e11 − 8.20810e11i 0.163332 − 0.303521i
\(580\) 2.25945e11 + 2.36320e11i 0.0829041 + 0.0867109i
\(581\) −3.88638e11 − 7.22211e11i −0.141499 − 0.262949i
\(582\) 4.29586e11 − 1.32213e12i 0.155202 − 0.477662i
\(583\) 1.18435e12 − 2.77093e12i 0.424592 − 0.993383i
\(584\) −4.37102e12 − 7.93224e11i −1.55498 − 0.282188i
\(585\) 9.62391e10 + 6.99218e10i 0.0339743 + 0.0246838i
\(586\) −2.28472e12 + 2.05628e11i −0.800375 + 0.0720350i
\(587\) 2.09526e12 + 4.90212e12i 0.728396 + 1.70417i 0.709864 + 0.704339i \(0.248756\pi\)
0.0185317 + 0.999828i \(0.494101\pi\)
\(588\) 3.63468e11 + 1.59246e12i 0.125392 + 0.549377i
\(589\) 4.20337e11 + 6.36783e11i 0.143906 + 0.218008i
\(590\) 2.13718e11 + 1.27690e11i 0.0726116 + 0.0433834i
\(591\) 6.96998e11 + 8.74008e11i 0.235011 + 0.294694i
\(592\) −8.60411e11 + 7.51719e11i −0.287911 + 0.251540i
\(593\) 4.15823e12 − 3.02113e12i 1.38090 − 1.00328i 0.384105 − 0.923289i \(-0.374510\pi\)
0.996795 − 0.0799935i \(-0.0254899\pi\)
\(594\) 1.27917e12 − 6.16014e11i 0.421588 − 0.203026i
\(595\) −1.49194e10 + 2.26020e10i −0.00488007 + 0.00739299i
\(596\) 2.04698e12 + 7.68245e11i 0.664517 + 0.249397i
\(597\) −9.29691e11 + 5.55465e11i −0.299540 + 0.178967i
\(598\) 1.68611e11 + 8.11986e10i 0.0539175 + 0.0259653i
\(599\) 3.47834e12 − 6.31226e11i 1.10395 − 0.200338i 0.404164 − 0.914686i \(-0.367562\pi\)
0.699791 + 0.714348i \(0.253277\pi\)
\(600\) 5.29780e11 − 2.32112e12i 0.166884 − 0.731167i
\(601\) −3.35996e11 + 1.26101e11i −0.105051 + 0.0394262i −0.403347 − 0.915047i \(-0.632153\pi\)
0.298296 + 0.954473i \(0.403582\pi\)
\(602\) 1.39917e11 − 1.75451e11i 0.0434197 − 0.0544466i
\(603\) −1.97579e10 − 4.39943e11i −0.00608572 − 0.135509i
\(604\) −9.61341e10 − 2.14059e12i −0.0293908 − 0.654437i
\(605\) 1.12293e11 − 1.40811e11i 0.0340763 − 0.0427304i
\(606\) −2.22718e12 + 8.35876e11i −0.670856 + 0.251776i
\(607\) −3.68008e11 + 1.61235e12i −0.110029 + 0.482069i 0.889648 + 0.456648i \(0.150950\pi\)
−0.999677 + 0.0254216i \(0.991907\pi\)
\(608\) −9.96148e11 + 1.80774e11i −0.295636 + 0.0536501i
\(609\) −5.19346e11 − 2.50104e11i −0.152996 − 0.0736789i
\(610\) −1.21683e11 + 7.27025e10i −0.0355834 + 0.0212601i
\(611\) 5.69678e12 + 2.13804e12i 1.65365 + 0.620626i
\(612\) 1.48736e11 − 2.25325e11i 0.0428582 − 0.0649274i
\(613\) 4.54849e12 − 2.19044e12i 1.30105 − 0.626554i 0.350339 − 0.936623i \(-0.386066\pi\)
0.950714 + 0.310069i \(0.100352\pi\)
\(614\) 2.15758e12 − 1.56758e12i 0.612647 − 0.445114i
\(615\) −1.30579e11 + 1.14083e11i −0.0368073 + 0.0321576i
\(616\) 2.85831e11 + 3.58421e11i 0.0799828 + 0.100295i
\(617\) −3.42843e12 − 2.04839e12i −0.952385 − 0.569023i −0.0494387 − 0.998777i \(-0.515743\pi\)
−0.902946 + 0.429754i \(0.858600\pi\)
\(618\) −7.17965e11 − 1.08767e12i −0.197995 − 0.299950i
\(619\) −1.09399e12 − 4.79308e12i −0.299506 − 1.31222i −0.870865 − 0.491521i \(-0.836441\pi\)
0.571359 − 0.820700i \(-0.306416\pi\)
\(620\) −1.33089e11 − 3.11378e11i −0.0361726 − 0.0846301i
\(621\) −4.85112e11 + 4.36609e10i −0.130897 + 0.0117809i
\(622\) 1.08408e12 + 7.87630e11i 0.290405 + 0.210992i
\(623\) −7.14880e11 − 1.29732e11i −0.190124 − 0.0345024i
\(624\) −2.22669e11 + 5.20959e11i −0.0587933 + 0.137554i
\(625\) 1.10471e12 − 3.39995e12i 0.289593 − 0.891276i
\(626\) −1.16724e12 − 2.16910e12i −0.303792 − 0.564540i
\(627\) 5.06237e11 + 5.29482e11i 0.130813 + 0.136819i
\(628\) −1.31461e12 + 2.44296e12i −0.337271 + 0.626755i
\(629\) −2.53293e12 + 6.99045e11i −0.645202 + 0.178065i
\(630\) 2.33391e9 + 1.72296e10i 0.000590272 + 0.00435756i
\(631\) 9.10522e11 − 6.72174e12i 0.228643 − 1.68791i −0.405024 − 0.914306i \(-0.632737\pi\)
0.633667 − 0.773606i \(-0.281549\pi\)
\(632\) −3.09319e12 − 8.53665e11i −0.771221 − 0.212844i
\(633\) −1.74410e12 + 1.82418e12i −0.431772 + 0.451598i
\(634\) −5.07442e11 − 1.56175e12i −0.124734 − 0.383892i
\(635\) −7.83979e10 − 7.05594e9i −0.0191347 − 0.00172216i
\(636\) 2.47097e12 + 2.15882e12i 0.598840 + 0.523191i
\(637\) −1.64541e11 + 3.66378e12i −0.0395955 + 0.881662i
\(638\) 2.11151e12 0.504546
\(639\) 5.01383e11 + 1.24074e12i 0.118964 + 0.294393i
\(640\) 5.16065e11 0.121589
\(641\) 9.46733e10 − 2.10806e12i 0.0221496 − 0.493200i −0.957004 − 0.290076i \(-0.906319\pi\)
0.979153 − 0.203123i \(-0.0651093\pi\)
\(642\) −1.28031e12 − 1.11857e12i −0.297445 − 0.259870i
\(643\) 2.59975e12 + 2.33981e11i 0.599766 + 0.0539799i 0.385362 − 0.922765i \(-0.374076\pi\)
0.214403 + 0.976745i \(0.431219\pi\)
\(644\) −2.00739e10 − 6.17812e10i −0.00459881 − 0.0141537i
\(645\) −2.66267e11 + 2.78494e11i −0.0605758 + 0.0633573i
\(646\) −2.34620e11 − 6.47509e10i −0.0530052 − 0.0146285i
\(647\) −6.33313e11 + 4.67531e12i −0.142085 + 1.04892i 0.769746 + 0.638351i \(0.220383\pi\)
−0.911831 + 0.410566i \(0.865331\pi\)
\(648\) 3.24996e11 + 2.39921e12i 0.0724086 + 0.534542i
\(649\) −3.68078e12 + 1.01583e12i −0.814402 + 0.224761i
\(650\) 1.04628e12 − 1.94431e12i 0.229899 − 0.427223i
\(651\) 4.12575e11 + 4.31519e11i 0.0900302 + 0.0941642i
\(652\) −2.11314e12 − 3.92687e12i −0.457946 − 0.851006i
\(653\) 1.51703e12 − 4.66893e12i 0.326501 − 1.00487i −0.644258 − 0.764809i \(-0.722834\pi\)
0.970759 − 0.240058i \(-0.0771664\pi\)
\(654\) −1.18594e12 + 2.77465e12i −0.253492 + 0.593074i
\(655\) 2.07745e11 + 3.77002e10i 0.0441007 + 0.00800309i
\(656\) 3.10829e11 + 2.25831e11i 0.0655322 + 0.0476119i
\(657\) 2.57374e12 − 2.31641e11i 0.538915 − 0.0485033i
\(658\) 3.49539e11 + 8.17786e11i 0.0726907 + 0.170068i
\(659\) −5.25316e11 − 2.30156e12i −0.108502 − 0.475377i −0.999761 − 0.0218821i \(-0.993034\pi\)
0.891259 − 0.453495i \(-0.149823\pi\)
\(660\) −1.79103e11 − 2.71329e11i −0.0367413 − 0.0556607i
\(661\) 6.52231e12 + 3.89690e12i 1.32891 + 0.793985i 0.989204 − 0.146547i \(-0.0468160\pi\)
0.339704 + 0.940532i \(0.389673\pi\)
\(662\) 9.38070e11 + 1.17630e12i 0.189834 + 0.238044i
\(663\) −9.81225e11 + 8.57270e11i −0.197223 + 0.172309i
\(664\) −6.40724e12 + 4.65513e12i −1.27913 + 0.929342i
\(665\) −3.35381e10 + 1.61511e10i −0.00665030 + 0.00320261i
\(666\) −9.29344e11 + 1.40790e12i −0.183038 + 0.277291i
\(667\) −6.78196e11 − 2.54531e11i −0.132675 − 0.0497938i
\(668\) −1.13306e12 + 6.76970e11i −0.220170 + 0.131545i
\(669\) −5.47844e11 − 2.63828e11i −0.105740 − 0.0509217i
\(670\) 1.73362e11 − 3.14605e10i 0.0332366 − 0.00603155i
\(671\) 4.83773e11 − 2.11955e12i 0.0921278 − 0.403638i
\(672\) −7.41656e11 + 2.78348e11i −0.140295 + 0.0526534i
\(673\) −4.82710e12 + 6.05299e12i −0.907024 + 1.13737i 0.0830111 + 0.996549i \(0.473546\pi\)
−0.990035 + 0.140823i \(0.955025\pi\)
\(674\) 2.02058e11 + 4.49916e12i 0.0377142 + 0.839773i
\(675\) 2.57818e11 + 5.74076e12i 0.0478020 + 1.06439i
\(676\) 4.07413e11 − 5.10880e11i 0.0750369 − 0.0940933i
\(677\) −1.87373e12 + 7.03222e11i −0.342813 + 0.128660i −0.516842 − 0.856081i \(-0.672893\pi\)
0.174029 + 0.984740i \(0.444321\pi\)
\(678\) 9.75505e11 − 4.27396e12i 0.177295 − 0.776779i
\(679\) −1.06605e12 + 1.93460e11i −0.192470 + 0.0349282i
\(680\) 2.35623e11 + 1.13470e11i 0.0422597 + 0.0203512i
\(681\) 1.62787e11 − 9.72609e10i 0.0290041 − 0.0173291i
\(682\) −2.04747e12 − 7.68427e11i −0.362399 − 0.136011i
\(683\) −6.10785e11 + 9.25300e11i −0.107398 + 0.162701i −0.884298 − 0.466923i \(-0.845362\pi\)
0.776900 + 0.629624i \(0.216791\pi\)
\(684\) 3.34350e11 − 1.61014e11i 0.0584048 − 0.0281263i
\(685\) 6.37926e11 − 4.63481e11i 0.110704 − 0.0804311i
\(686\) −8.20128e11 + 7.16524e11i −0.141391 + 0.123530i
\(687\) −4.19237e12 − 5.25706e12i −0.718049 − 0.900405i
\(688\) 7.32897e11 + 4.37886e11i 0.124708 + 0.0745097i
\(689\) 4.05857e12 + 6.14847e12i 0.686099 + 1.03940i
\(690\) −1.04504e10 − 4.57864e10i −0.00175515 − 0.00768981i
\(691\) −3.47191e12 − 8.12294e12i −0.579319 − 1.35538i −0.911162 − 0.412049i \(-0.864813\pi\)
0.331843 − 0.943335i \(-0.392330\pi\)
\(692\) −5.74624e12 + 5.17171e11i −0.952590 + 0.0857347i
\(693\) −2.15743e11 − 1.56746e11i −0.0355334 − 0.0258165i
\(694\) 1.02295e11 + 1.85638e10i 0.0167392 + 0.00303772i
\(695\) −5.27133e11 + 1.23329e12i −0.0857016 + 0.200509i
\(696\) −1.72011e12 + 5.29394e12i −0.277852 + 0.855140i
\(697\) 4.18713e11 + 7.78098e11i 0.0671999 + 0.124878i
\(698\) −2.44771e11 − 2.56010e11i −0.0390311 − 0.0408233i
\(699\) −2.15344e12 + 4.00176e12i −0.341182 + 0.634022i
\(700\) −7.38794e11 + 2.03894e11i −0.116301 + 0.0320970i
\(701\) 1.35575e12 + 1.00086e13i 0.212055 + 1.56546i 0.713743 + 0.700407i \(0.246998\pi\)
−0.501688 + 0.865049i \(0.667287\pi\)
\(702\) −4.65929e11 + 3.43963e12i −0.0724107 + 0.534557i
\(703\) −3.48153e12 − 9.60842e11i −0.537615 − 0.148372i
\(704\) 1.29787e12 − 1.35746e12i 0.199137 − 0.208281i
\(705\) −4.71863e11 − 1.45225e12i −0.0719391 − 0.221406i
\(706\) −4.30990e12 − 3.87898e11i −0.652899 − 0.0587620i
\(707\) 1.39622e12 + 1.21984e12i 0.210168 + 0.183618i
\(708\) 1.86534e11 − 4.15349e12i 0.0279002 − 0.621247i
\(709\) −8.85581e12 −1.31620 −0.658098 − 0.752933i \(-0.728639\pi\)
−0.658098 + 0.752933i \(0.728639\pi\)
\(710\) −4.64986e11 + 2.65416e11i −0.0686716 + 0.0391980i
\(711\) 1.86657e12 0.273924
\(712\) −3.14775e11 + 7.00902e12i −0.0459029 + 1.02211i
\(713\) 5.64995e11 + 4.93621e11i 0.0818732 + 0.0715305i
\(714\) −1.89675e11 − 1.70711e10i −0.0273130 − 0.00245821i
\(715\) −2.25572e11 − 6.94240e11i −0.0322781 − 0.0993418i
\(716\) −8.87967e11 + 9.28740e11i −0.126266 + 0.132064i
\(717\) −7.88531e11 − 2.17621e11i −0.111425 − 0.0307513i
\(718\) 4.82438e11 − 3.56150e12i 0.0677456 − 0.500118i
\(719\) −5.54915e11 − 4.09655e12i −0.0774366 − 0.571660i −0.987551 − 0.157302i \(-0.949720\pi\)
0.910114 − 0.414358i \(-0.135994\pi\)
\(720\) −6.37634e10 + 1.75976e10i −0.00884250 + 0.00244038i
\(721\) −4.81323e11 + 8.94448e11i −0.0663328 + 0.123267i
\(722\) 2.51547e12 + 2.63097e12i 0.344510 + 0.360329i
\(723\) −9.34136e11 − 1.73592e12i −0.127142 − 0.236269i
\(724\) 1.07552e11 − 3.31010e11i 0.0145477 − 0.0447731i
\(725\) −3.35896e12 + 7.85867e12i −0.451526 + 1.05640i
\(726\) 1.24614e12 + 2.26141e11i 0.166476 + 0.0302110i
\(727\) 6.29210e12 + 4.57148e12i 0.835393 + 0.606949i 0.921080 − 0.389373i \(-0.127308\pi\)
−0.0856867 + 0.996322i \(0.527308\pi\)
\(728\) −1.11628e12 + 1.00467e11i −0.147292 + 0.0132565i
\(729\) −3.24841e12 − 7.60004e12i −0.425988 − 0.996648i
\(730\) 2.30061e11 + 1.00796e12i 0.0299840 + 0.131369i
\(731\) 1.08167e12 + 1.63865e12i 0.140109 + 0.212255i
\(732\) 2.03216e12 + 1.21416e12i 0.261612 + 0.156306i
\(733\) −4.43116e12 − 5.55650e12i −0.566956 − 0.710940i 0.412871 − 0.910790i \(-0.364526\pi\)
−0.979827 + 0.199849i \(0.935955\pi\)
\(734\) 1.21518e12 − 1.06167e12i 0.154528 − 0.135007i
\(735\) 7.44584e11 − 5.40972e11i 0.0941067 − 0.0683725i
\(736\) −8.96914e11 + 4.31931e11i −0.112668 + 0.0542581i
\(737\) −1.48872e12 + 2.25532e12i −0.185870 + 0.281581i
\(738\) 5.31111e11 + 1.99329e11i 0.0659070 + 0.0247353i
\(739\) 1.20139e13 − 7.17800e12i 1.48179 − 0.885326i 0.481828 − 0.876266i \(-0.339973\pi\)
0.999959 − 0.00906037i \(-0.00288404\pi\)
\(740\) 1.44416e12 + 6.95471e11i 0.177041 + 0.0852582i
\(741\) −1.76215e12 + 3.19783e11i −0.214714 + 0.0389649i
\(742\) −2.39609e11 + 1.04980e12i −0.0290193 + 0.127142i
\(743\) 1.28147e13 − 4.80945e12i 1.54262 − 0.578957i 0.572147 − 0.820151i \(-0.306111\pi\)
0.970477 + 0.241194i \(0.0775391\pi\)
\(744\) 3.59451e12 − 4.50738e12i 0.430092 − 0.539319i
\(745\) −5.52708e10 − 1.23070e12i −0.00657343 − 0.146369i
\(746\) −5.39108e10 − 1.20042e12i −0.00637310 − 0.141908i
\(747\) 2.87237e12 − 3.60184e12i 0.337518 − 0.423235i
\(748\) −1.55110e12 + 5.82136e11i −0.181168 + 0.0679935i
\(749\) −2.94846e11 + 1.29181e12i −0.0342316 + 0.149979i
\(750\) −1.10212e12 + 2.00004e11i −0.127190 + 0.0230815i
\(751\) 6.65568e12 + 3.20521e12i 0.763507 + 0.367685i 0.774763 − 0.632251i \(-0.217869\pi\)
−0.0112569 + 0.999937i \(0.503583\pi\)
\(752\) −2.90453e12 + 1.73538e12i