Properties

Label 54.9.f.a.5.6
Level $54$
Weight $9$
Character 54.5
Analytic conductor $21.998$
Analytic rank $0$
Dimension $144$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,9,Mod(5,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.5");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 54.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(21.9984449433\)
Analytic rank: \(0\)
Dimension: \(144\)
Relative dimension: \(24\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.6
Character \(\chi\) \(=\) 54.5
Dual form 54.9.f.a.11.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-7.27231 - 8.66680i) q^{2} +(-14.8240 - 79.6320i) q^{3} +(-22.2270 + 126.055i) q^{4} +(332.225 + 912.782i) q^{5} +(-582.350 + 707.585i) q^{6} +(238.226 + 1351.05i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6121.50 + 2360.92i) q^{9} +O(q^{10})\) \(q+(-7.27231 - 8.66680i) q^{2} +(-14.8240 - 79.6320i) q^{3} +(-22.2270 + 126.055i) q^{4} +(332.225 + 912.782i) q^{5} +(-582.350 + 707.585i) q^{6} +(238.226 + 1351.05i) q^{7} +(1254.14 - 724.077i) q^{8} +(-6121.50 + 2360.92i) q^{9} +(5494.85 - 9517.37i) q^{10} +(6463.89 - 17759.4i) q^{11} +(10367.5 - 98.6629i) q^{12} +(-20710.9 - 17378.5i) q^{13} +(9976.80 - 11889.9i) q^{14} +(67761.7 - 39986.8i) q^{15} +(-15395.9 - 5603.66i) q^{16} +(-76297.8 - 44050.6i) q^{17} +(64979.1 + 35884.5i) q^{18} +(8505.08 + 14731.2i) q^{19} +(-122445. + 21590.4i) q^{20} +(104055. - 38998.3i) q^{21} +(-200924. + 73130.5i) q^{22} +(46659.4 + 8227.30i) q^{23} +(-76251.0 - 89135.8i) q^{24} +(-423561. + 355410. i) q^{25} +305879. i q^{26} +(278750. + 452469. i) q^{27} -175602. q^{28} +(-484972. - 577967. i) q^{29} +(-839342. - 296481. i) q^{30} +(168597. - 956159. i) q^{31} +(63398.2 + 174185. i) q^{32} +(-1.51003e6 - 251468. i) q^{33} +(173084. + 981608. i) q^{34} +(-1.15407e6 + 666301. i) q^{35} +(-161545. - 824124. i) q^{36} +(1.55033e6 - 2.68525e6i) q^{37} +(65821.1 - 180842. i) q^{38} +(-1.07687e6 + 1.90687e6i) q^{39} +(1.07758e6 + 904198. i) q^{40} +(-2.28290e6 + 2.72065e6i) q^{41} +(-1.09471e6 - 618217. i) q^{42} +(-4.60117e6 - 1.67469e6i) q^{43} +(2.09499e6 + 1.20954e6i) q^{44} +(-4.18873e6 - 4.80324e6i) q^{45} +(-268017. - 464219. i) q^{46} +(-6.32013e6 + 1.11441e6i) q^{47} +(-218002. + 1.30908e6i) q^{48} +(3.64856e6 - 1.32797e6i) q^{49} +(6.16054e6 + 1.08627e6i) q^{50} +(-2.37680e6 + 6.72875e6i) q^{51} +(2.65099e6 - 2.22445e6i) q^{52} +4.04236e6i q^{53} +(1.89430e6 - 5.70636e6i) q^{54} +1.83579e7 q^{55} +(1.27703e6 + 1.52191e6i) q^{56} +(1.04700e6 - 895651. i) q^{57} +(-1.48226e6 + 8.40631e6i) q^{58} +(-2.68083e6 - 7.36551e6i) q^{59} +(3.53442e6 + 9.43052e6i) q^{60} +(-3.36027e6 - 1.90570e7i) q^{61} +(-9.51293e6 + 5.49229e6i) q^{62} +(-4.64802e6 - 7.70800e6i) q^{63} +(1.04858e6 - 1.81619e6i) q^{64} +(8.98209e6 - 2.46781e7i) q^{65} +(8.80202e6 + 1.49159e7i) q^{66} +(2.50926e7 + 2.10552e7i) q^{67} +(7.24868e6 - 8.63864e6i) q^{68} +(-36520.1 - 3.83754e6i) q^{69} +(1.41674e7 + 5.15652e6i) q^{70} +(-1.06532e7 - 6.15062e6i) q^{71} +(-5.96772e6 + 7.39336e6i) q^{72} +(-8.45017e6 - 1.46361e7i) q^{73} +(-3.45470e7 + 6.09158e6i) q^{74} +(3.45808e7 + 2.84604e7i) q^{75} +(-2.04599e6 + 744680. i) q^{76} +(2.55336e7 + 4.50227e6i) q^{77} +(2.43577e7 - 4.53433e6i) q^{78} +(-2.64361e7 + 2.21825e7i) q^{79} -1.59148e7i q^{80} +(3.18988e7 - 2.89048e7i) q^{81} +4.01813e7 q^{82} +(-7.33665e6 - 8.74347e6i) q^{83} +(2.60311e6 + 1.39835e7i) q^{84} +(1.48605e7 - 8.42780e7i) q^{85} +(1.89469e7 + 5.20563e7i) q^{86} +(-3.88354e7 + 4.71870e7i) q^{87} +(-4.75256e6 - 2.69531e7i) q^{88} +(-7.56650e7 + 4.36852e7i) q^{89} +(-1.11670e7 + 7.12335e7i) q^{90} +(1.85453e7 - 3.21214e7i) q^{91} +(-2.07419e6 + 5.69880e6i) q^{92} +(-7.86401e7 + 748381. i) q^{93} +(5.56203e7 + 4.66710e7i) q^{94} +(-1.06208e7 + 1.26574e7i) q^{95} +(1.29309e7 - 7.63063e6i) q^{96} +(-2.79578e7 - 1.01758e7i) q^{97} +(-3.80427e7 - 2.19640e7i) q^{98} +(2.35983e6 + 1.23975e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 144 q + 882 q^{5} + 768 q^{6} + 25908 q^{9} - 45756 q^{11} - 21504 q^{12} + 94464 q^{14} - 70002 q^{15} - 182784 q^{18} - 225792 q^{20} - 2071668 q^{21} + 185472 q^{22} + 552996 q^{23} - 1015182 q^{25} - 4137588 q^{27} - 2856132 q^{29} - 861696 q^{30} - 1841490 q^{31} + 10547334 q^{33} - 661248 q^{34} - 12450834 q^{35} - 5104128 q^{36} + 14063616 q^{38} + 4239102 q^{39} - 15673536 q^{41} - 11028480 q^{42} - 4412520 q^{43} - 12558942 q^{45} + 15173838 q^{47} + 3440640 q^{48} - 11347488 q^{49} - 27744768 q^{50} - 3281850 q^{51} + 16379136 q^{54} + 12091392 q^{56} - 13553658 q^{57} - 86547168 q^{59} - 26125056 q^{60} - 34059456 q^{61} + 108329070 q^{63} + 150994944 q^{64} + 22190346 q^{65} + 152091648 q^{66} + 167100948 q^{67} + 13411584 q^{68} - 40190130 q^{69} - 118080000 q^{70} - 251437608 q^{71} - 60948480 q^{72} + 15265278 q^{73} + 41902848 q^{74} + 138868662 q^{75} + 67995648 q^{76} + 564911586 q^{77} + 201203712 q^{78} + 137535768 q^{79} - 23838948 q^{81} - 482857578 q^{83} - 128300544 q^{84} - 343215000 q^{85} - 46237824 q^{86} + 34353810 q^{87} + 47480832 q^{88} + 375969762 q^{89} + 452712960 q^{90} - 155093598 q^{91} + 97042176 q^{92} + 285095622 q^{93} - 70995456 q^{94} - 966996432 q^{95} - 88080384 q^{96} - 484917300 q^{97} - 234233856 q^{98} + 26756370 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −7.27231 8.66680i −0.454519 0.541675i
\(3\) −14.8240 79.6320i −0.183012 0.983111i
\(4\) −22.2270 + 126.055i −0.0868241 + 0.492404i
\(5\) 332.225 + 912.782i 0.531561 + 1.46045i 0.857213 + 0.514962i \(0.172194\pi\)
−0.325653 + 0.945490i \(0.605584\pi\)
\(6\) −582.350 + 707.585i −0.449344 + 0.545976i
\(7\) 238.226 + 1351.05i 0.0992195 + 0.562702i 0.993372 + 0.114940i \(0.0366676\pi\)
−0.894153 + 0.447762i \(0.852221\pi\)
\(8\) 1254.14 724.077i 0.306186 0.176777i
\(9\) −6121.50 + 2360.92i −0.933013 + 0.359842i
\(10\) 5494.85 9517.37i 0.549485 0.951737i
\(11\) 6463.89 17759.4i 0.441492 1.21299i −0.497019 0.867740i \(-0.665572\pi\)
0.938511 0.345250i \(-0.112206\pi\)
\(12\) 10367.5 98.6629i 0.499977 0.00475805i
\(13\) −20710.9 17378.5i −0.725145 0.608469i 0.203658 0.979042i \(-0.434717\pi\)
−0.928803 + 0.370573i \(0.879161\pi\)
\(14\) 9976.80 11889.9i 0.259704 0.309504i
\(15\) 67761.7 39986.8i 1.33850 0.789863i
\(16\) −15395.9 5603.66i −0.234923 0.0855050i
\(17\) −76297.8 44050.6i −0.913517 0.527419i −0.0319559 0.999489i \(-0.510174\pi\)
−0.881561 + 0.472070i \(0.843507\pi\)
\(18\) 64979.1 + 35884.5i 0.618990 + 0.341835i
\(19\) 8505.08 + 14731.2i 0.0652625 + 0.113038i 0.896810 0.442415i \(-0.145878\pi\)
−0.831548 + 0.555453i \(0.812545\pi\)
\(20\) −122445. + 21590.4i −0.765284 + 0.134940i
\(21\) 104055. 38998.3i 0.535040 0.200525i
\(22\) −200924. + 73130.5i −0.857713 + 0.312182i
\(23\) 46659.4 + 8227.30i 0.166735 + 0.0293999i 0.256392 0.966573i \(-0.417466\pi\)
−0.0896572 + 0.995973i \(0.528577\pi\)
\(24\) −76251.0 89135.8i −0.229827 0.268663i
\(25\) −423561. + 355410.i −1.08432 + 0.909849i
\(26\) 305879.i 0.669354i
\(27\) 278750. + 452469.i 0.524517 + 0.851400i
\(28\) −175602. −0.285691
\(29\) −484972. 577967.i −0.685685 0.817167i 0.305142 0.952307i \(-0.401296\pi\)
−0.990827 + 0.135140i \(0.956852\pi\)
\(30\) −839342. 296481.i −1.03622 0.366026i
\(31\) 168597. 956159.i 0.182559 1.03534i −0.746494 0.665393i \(-0.768264\pi\)
0.929052 0.369949i \(-0.120625\pi\)
\(32\) 63398.2 + 174185.i 0.0604612 + 0.166116i
\(33\) −1.51003e6 251468.i −1.27330 0.212044i
\(34\) 173084. + 981608.i 0.129521 + 0.734552i
\(35\) −1.15407e6 + 666301.i −0.769057 + 0.444015i
\(36\) −161545. 824124.i −0.0961795 0.490662i
\(37\) 1.55033e6 2.68525e6i 0.827214 1.43278i −0.0730022 0.997332i \(-0.523258\pi\)
0.900216 0.435444i \(-0.143409\pi\)
\(38\) 65821.1 180842.i 0.0315668 0.0867291i
\(39\) −1.07687e6 + 1.90687e6i −0.465482 + 0.824255i
\(40\) 1.07758e6 + 904198.i 0.420930 + 0.353202i
\(41\) −2.28290e6 + 2.72065e6i −0.807887 + 0.962803i −0.999827 0.0186042i \(-0.994078\pi\)
0.191940 + 0.981407i \(0.438522\pi\)
\(42\) −1.09471e6 618217.i −0.351805 0.198675i
\(43\) −4.60117e6 1.67469e6i −1.34584 0.489847i −0.434195 0.900819i \(-0.642967\pi\)
−0.911648 + 0.410972i \(0.865189\pi\)
\(44\) 2.09499e6 + 1.20954e6i 0.558949 + 0.322709i
\(45\) −4.18873e6 4.80324e6i −1.02148 1.17134i
\(46\) −268017. 464219.i −0.0598592 0.103679i
\(47\) −6.32013e6 + 1.11441e6i −1.29519 + 0.228377i −0.778419 0.627745i \(-0.783978\pi\)
−0.516774 + 0.856122i \(0.672867\pi\)
\(48\) −218002. + 1.30908e6i −0.0410672 + 0.246604i
\(49\) 3.64856e6 1.32797e6i 0.632904 0.230358i
\(50\) 6.16054e6 + 1.08627e6i 0.985686 + 0.173803i
\(51\) −2.37680e6 + 6.72875e6i −0.351327 + 0.994612i
\(52\) 2.65099e6 2.22445e6i 0.362573 0.304234i
\(53\) 4.04236e6i 0.512309i 0.966636 + 0.256154i \(0.0824555\pi\)
−0.966636 + 0.256154i \(0.917544\pi\)
\(54\) 1.89430e6 5.70636e6i 0.222779 0.671096i
\(55\) 1.83579e7 2.00619
\(56\) 1.27703e6 + 1.52191e6i 0.129852 + 0.154752i
\(57\) 1.04700e6 895651.i 0.0991851 0.0848476i
\(58\) −1.48226e6 + 8.40631e6i −0.130982 + 0.742837i
\(59\) −2.68083e6 7.36551e6i −0.221238 0.607847i 0.778567 0.627561i \(-0.215947\pi\)
−0.999806 + 0.0197137i \(0.993725\pi\)
\(60\) 3.53442e6 + 9.43052e6i 0.272717 + 0.727663i
\(61\) −3.36027e6 1.90570e7i −0.242692 1.37637i −0.825793 0.563974i \(-0.809272\pi\)
0.583101 0.812400i \(-0.301839\pi\)
\(62\) −9.51293e6 + 5.49229e6i −0.643795 + 0.371695i
\(63\) −4.64802e6 7.70800e6i −0.295057 0.489305i
\(64\) 1.04858e6 1.81619e6i 0.0625000 0.108253i
\(65\) 8.98209e6 2.46781e7i 0.503181 1.38248i
\(66\) 8.80202e6 + 1.49159e7i 0.463881 + 0.786094i
\(67\) 2.50926e7 + 2.10552e7i 1.24522 + 1.04486i 0.997098 + 0.0761342i \(0.0242577\pi\)
0.248122 + 0.968729i \(0.420187\pi\)
\(68\) 7.24868e6 8.63864e6i 0.339019 0.404027i
\(69\) −36520.1 3.83754e6i −0.00161115 0.169300i
\(70\) 1.41674e7 + 5.15652e6i 0.590064 + 0.214766i
\(71\) −1.06532e7 6.15062e6i −0.419224 0.242039i 0.275521 0.961295i \(-0.411150\pi\)
−0.694745 + 0.719256i \(0.744483\pi\)
\(72\) −5.96772e6 + 7.39336e6i −0.222064 + 0.275114i
\(73\) −8.45017e6 1.46361e7i −0.297560 0.515389i 0.678017 0.735046i \(-0.262839\pi\)
−0.975577 + 0.219657i \(0.929506\pi\)
\(74\) −3.45470e7 + 6.09158e6i −1.15208 + 0.203143i
\(75\) 3.45808e7 + 2.84604e7i 1.09293 + 0.899490i
\(76\) −2.04599e6 + 744680.i −0.0613267 + 0.0223211i
\(77\) 2.55336e7 + 4.50227e6i 0.726356 + 0.128076i
\(78\) 2.43577e7 4.53433e6i 0.658049 0.122500i
\(79\) −2.64361e7 + 2.21825e7i −0.678717 + 0.569512i −0.915631 0.402019i \(-0.868309\pi\)
0.236914 + 0.971531i \(0.423864\pi\)
\(80\) 1.59148e7i 0.388545i
\(81\) 3.18988e7 2.89048e7i 0.741028 0.671474i
\(82\) 4.01813e7 0.888727
\(83\) −7.33665e6 8.74347e6i −0.154591 0.184235i 0.683190 0.730241i \(-0.260592\pi\)
−0.837781 + 0.546006i \(0.816148\pi\)
\(84\) 2.60311e6 + 1.39835e7i 0.0522849 + 0.280866i
\(85\) 1.48605e7 8.42780e7i 0.284680 1.61450i
\(86\) 1.89469e7 + 5.20563e7i 0.346374 + 0.951655i
\(87\) −3.88354e7 + 4.71870e7i −0.677877 + 0.823655i
\(88\) −4.75256e6 2.69531e7i −0.0792495 0.449446i
\(89\) −7.56650e7 + 4.36852e7i −1.20597 + 0.696265i −0.961875 0.273488i \(-0.911823\pi\)
−0.244090 + 0.969753i \(0.578489\pi\)
\(90\) −1.11670e7 + 7.12335e7i −0.170203 + 1.08571i
\(91\) 1.85453e7 3.21214e7i 0.270438 0.468412i
\(92\) −2.07419e6 + 5.69880e6i −0.0289533 + 0.0795485i
\(93\) −7.86401e7 + 748381.i −1.05127 + 0.0100044i
\(94\) 5.56203e7 + 4.66710e7i 0.712397 + 0.597772i
\(95\) −1.06208e7 + 1.26574e7i −0.130396 + 0.155399i
\(96\) 1.29309e7 7.63063e6i 0.152245 0.0898412i
\(97\) −2.79578e7 1.01758e7i −0.315802 0.114943i 0.179256 0.983802i \(-0.442631\pi\)
−0.495058 + 0.868860i \(0.664853\pi\)
\(98\) −3.80427e7 2.19640e7i −0.412446 0.238126i
\(99\) 2.35983e6 + 1.23975e8i 0.0245664 + 1.29060i
\(100\) −3.53869e7 6.12918e7i −0.353869 0.612918i
\(101\) −6.75822e7 + 1.19166e7i −0.649452 + 0.114516i −0.488662 0.872473i \(-0.662515\pi\)
−0.160789 + 0.986989i \(0.551404\pi\)
\(102\) 7.56016e7 2.83343e7i 0.698442 0.261765i
\(103\) 8.95125e7 3.25799e7i 0.795307 0.289468i 0.0877665 0.996141i \(-0.472027\pi\)
0.707540 + 0.706673i \(0.249805\pi\)
\(104\) −3.85577e7 6.79876e6i −0.329593 0.0581161i
\(105\) 7.01667e7 + 8.20234e7i 0.577263 + 0.674808i
\(106\) 3.50344e7 2.93973e7i 0.277505 0.232854i
\(107\) 2.41895e8i 1.84540i −0.385516 0.922701i \(-0.625977\pi\)
0.385516 0.922701i \(-0.374023\pi\)
\(108\) −6.32319e7 + 2.50809e7i −0.464773 + 0.184352i
\(109\) −3.64851e6 −0.0258470 −0.0129235 0.999916i \(-0.504114\pi\)
−0.0129235 + 0.999916i \(0.504114\pi\)
\(110\) −1.33504e8 1.59104e8i −0.911853 1.08670i
\(111\) −2.36814e8 8.36499e7i −1.55997 0.551028i
\(112\) 3.90310e6 2.21356e7i 0.0248049 0.140675i
\(113\) −4.02792e7 1.10666e8i −0.247040 0.678736i −0.999791 0.0204315i \(-0.993496\pi\)
0.752751 0.658305i \(-0.228726\pi\)
\(114\) −1.53765e7 2.56067e6i −0.0910414 0.0151612i
\(115\) 7.99169e6 + 4.53231e7i 0.0456928 + 0.259137i
\(116\) 8.36353e7 4.82869e7i 0.461910 0.266684i
\(117\) 1.67811e8 + 5.74856e7i 0.895523 + 0.306772i
\(118\) −4.43396e7 + 7.67985e7i −0.228699 + 0.396118i
\(119\) 4.13383e7 1.13576e8i 0.206141 0.566368i
\(120\) 5.60291e7 9.92137e7i 0.270202 0.478461i
\(121\) −1.09405e8 9.18020e7i −0.510384 0.428263i
\(122\) −1.40727e8 + 1.67712e8i −0.635239 + 0.757048i
\(123\) 2.50492e8 + 1.41461e8i 1.09439 + 0.618038i
\(124\) 1.16782e8 + 4.25050e7i 0.493956 + 0.179785i
\(125\) −1.36526e8 7.88235e7i −0.559211 0.322861i
\(126\) −3.30019e7 + 9.63384e7i −0.130935 + 0.382224i
\(127\) 4.21668e7 + 7.30351e7i 0.162090 + 0.280748i 0.935618 0.353014i \(-0.114843\pi\)
−0.773528 + 0.633762i \(0.781510\pi\)
\(128\) −2.33661e7 + 4.12008e6i −0.0870455 + 0.0153485i
\(129\) −6.51512e7 + 3.91226e8i −0.235268 + 1.41276i
\(130\) −2.79201e8 + 1.01621e8i −0.977559 + 0.355802i
\(131\) −4.06300e8 7.16416e7i −1.37963 0.243265i −0.565880 0.824487i \(-0.691464\pi\)
−0.813745 + 0.581222i \(0.802575\pi\)
\(132\) 6.52623e7 1.84759e8i 0.214965 0.608568i
\(133\) −1.78764e7 + 1.50001e7i −0.0571314 + 0.0479389i
\(134\) 3.70592e8i 1.14942i
\(135\) −3.20398e8 + 4.04759e8i −0.964616 + 1.21860i
\(136\) −1.27584e8 −0.372942
\(137\) 4.35416e8 + 5.18909e8i 1.23601 + 1.47302i 0.828664 + 0.559746i \(0.189101\pi\)
0.407346 + 0.913274i \(0.366454\pi\)
\(138\) −3.29936e7 + 2.82243e7i −0.0909732 + 0.0778228i
\(139\) 2.46669e7 1.39893e8i 0.0660777 0.374745i −0.933780 0.357849i \(-0.883510\pi\)
0.999857 0.0168966i \(-0.00537860\pi\)
\(140\) −5.83394e7 1.60286e8i −0.151862 0.417238i
\(141\) 1.82432e8 + 4.86764e8i 0.461556 + 1.23152i
\(142\) 2.41671e7 + 1.37058e8i 0.0594389 + 0.337095i
\(143\) −4.42504e8 + 2.55480e8i −1.05821 + 0.610959i
\(144\) 1.07476e8 2.04578e6i 0.249955 0.00475784i
\(145\) 3.66438e8 6.34689e8i 0.828950 1.43578i
\(146\) −6.53962e7 + 1.79674e8i −0.143927 + 0.395435i
\(147\) −1.59835e8 2.70857e8i −0.342296 0.580056i
\(148\) 3.04031e8 + 2.55113e8i 0.633682 + 0.531723i
\(149\) −3.79666e7 + 4.52468e7i −0.0770294 + 0.0918001i −0.803183 0.595733i \(-0.796862\pi\)
0.726153 + 0.687533i \(0.241306\pi\)
\(150\) −4.82182e6 5.06678e8i −0.00952459 1.00085i
\(151\) 3.92179e8 + 1.42741e8i 0.754355 + 0.274563i 0.690437 0.723392i \(-0.257418\pi\)
0.0639181 + 0.997955i \(0.479640\pi\)
\(152\) 2.13331e7 + 1.23167e7i 0.0399650 + 0.0230738i
\(153\) 5.71057e8 + 8.95224e7i 1.04211 + 0.163368i
\(154\) −1.46668e8 2.54037e8i −0.260767 0.451662i
\(155\) 9.28777e8 1.63768e8i 1.60911 0.283729i
\(156\) −2.16435e8 1.78129e8i −0.365451 0.300770i
\(157\) 6.33366e8 2.30527e8i 1.04245 0.379422i 0.236643 0.971597i \(-0.423953\pi\)
0.805810 + 0.592175i \(0.201730\pi\)
\(158\) 3.84503e8 + 6.77983e7i 0.616981 + 0.108790i
\(159\) 3.21901e8 5.99238e7i 0.503656 0.0937586i
\(160\) −1.37930e8 + 1.15737e8i −0.210465 + 0.176601i
\(161\) 6.49989e7i 0.0967393i
\(162\) −4.82490e8 6.62562e7i −0.700533 0.0961982i
\(163\) 5.98366e8 0.847650 0.423825 0.905744i \(-0.360687\pi\)
0.423825 + 0.905744i \(0.360687\pi\)
\(164\) −2.92211e8 3.48243e8i −0.403944 0.481401i
\(165\) −2.72137e8 1.46188e9i −0.367157 1.97231i
\(166\) −2.24236e7 + 1.27171e8i −0.0295306 + 0.167477i
\(167\) 4.36130e8 + 1.19826e9i 0.560725 + 1.54058i 0.818579 + 0.574394i \(0.194762\pi\)
−0.257854 + 0.966184i \(0.583015\pi\)
\(168\) 1.02262e8 1.24253e8i 0.128374 0.155981i
\(169\) −1.47217e7 8.34910e7i −0.0180473 0.102351i
\(170\) −8.38491e8 + 4.84103e8i −1.00393 + 0.579618i
\(171\) −8.68431e7 7.00974e7i −0.101567 0.0819818i
\(172\) 3.13374e8 5.42779e8i 0.358054 0.620168i
\(173\) 4.07499e7 1.11959e8i 0.0454927 0.124990i −0.914866 0.403758i \(-0.867704\pi\)
0.960359 + 0.278768i \(0.0899260\pi\)
\(174\) 6.91384e8 6.57958e6i 0.754262 0.00717796i
\(175\) −5.81079e8 4.87583e8i −0.619559 0.519872i
\(176\) −1.99035e8 + 2.37201e8i −0.207433 + 0.247210i
\(177\) −5.46789e8 + 3.22665e8i −0.557092 + 0.328745i
\(178\) 9.28870e8 + 3.38081e8i 0.925284 + 0.336776i
\(179\) 1.64197e9 + 9.47995e8i 1.59939 + 0.923408i 0.991605 + 0.129307i \(0.0412753\pi\)
0.607786 + 0.794101i \(0.292058\pi\)
\(180\) 6.98577e8 4.21250e8i 0.665463 0.401282i
\(181\) −6.87564e8 1.19090e9i −0.640618 1.10958i −0.985295 0.170861i \(-0.945345\pi\)
0.344677 0.938721i \(-0.387988\pi\)
\(182\) −4.13257e8 + 7.28683e7i −0.376647 + 0.0664130i
\(183\) −1.46774e9 + 5.50086e8i −1.30871 + 0.490485i
\(184\) 6.44745e7 2.34668e7i 0.0562493 0.0204731i
\(185\) 2.96611e9 + 5.23005e8i 2.53221 + 0.446498i
\(186\) 5.78382e8 + 6.76116e8i 0.483240 + 0.564897i
\(187\) −1.27549e9 + 1.07026e9i −1.04306 + 0.875235i
\(188\) 8.21456e8i 0.657587i
\(189\) −5.44901e8 + 4.84394e8i −0.427042 + 0.379622i
\(190\) 1.86937e8 0.143443
\(191\) −1.39014e9 1.65670e9i −1.04454 1.24483i −0.968837 0.247700i \(-0.920325\pi\)
−0.0756999 0.997131i \(-0.524119\pi\)
\(192\) −1.60171e8 5.65771e7i −0.117863 0.0416328i
\(193\) −4.03492e8 + 2.28832e9i −0.290808 + 1.64925i 0.392961 + 0.919555i \(0.371451\pi\)
−0.683769 + 0.729698i \(0.739660\pi\)
\(194\) 1.15126e8 + 3.16306e8i 0.0812767 + 0.223306i
\(195\) −2.09831e9 3.49434e8i −1.45122 0.241672i
\(196\) 8.63011e7 + 4.89438e8i 0.0584780 + 0.331645i
\(197\) −1.28035e9 + 7.39212e8i −0.850089 + 0.490799i −0.860681 0.509145i \(-0.829962\pi\)
0.0105916 + 0.999944i \(0.496629\pi\)
\(198\) 1.05730e9 9.22036e8i 0.687922 0.599911i
\(199\) −2.19821e8 + 3.80741e8i −0.140170 + 0.242782i −0.927561 0.373672i \(-0.878098\pi\)
0.787390 + 0.616455i \(0.211432\pi\)
\(200\) −2.73860e8 + 7.52424e8i −0.171163 + 0.470265i
\(201\) 1.30469e9 2.31029e9i 0.799326 1.41541i
\(202\) 5.94757e8 + 4.99061e8i 0.357219 + 0.299742i
\(203\) 6.65327e8 7.92906e8i 0.391788 0.466915i
\(204\) −7.95366e8 4.49168e8i −0.459247 0.259351i
\(205\) −3.24180e9 1.17992e9i −1.83557 0.668092i
\(206\) −9.33326e8 5.38856e8i −0.518280 0.299229i
\(207\) −3.05049e8 + 5.97957e7i −0.166146 + 0.0325678i
\(208\) 2.21480e8 + 3.83614e8i 0.118326 + 0.204947i
\(209\) 3.16593e8 5.58240e7i 0.165927 0.0292574i
\(210\) 2.00607e8 1.20462e9i 0.103150 0.619403i
\(211\) −2.21733e9 + 8.07041e8i −1.11866 + 0.407161i −0.834165 0.551516i \(-0.814050\pi\)
−0.284500 + 0.958676i \(0.591827\pi\)
\(212\) −5.09562e8 8.98495e7i −0.252263 0.0444807i
\(213\) −3.31863e8 + 9.39510e8i −0.161228 + 0.456439i
\(214\) −2.09645e9 + 1.75913e9i −0.999609 + 0.838771i
\(215\) 4.75624e9i 2.22592i
\(216\) 6.77213e8 + 3.65622e8i 0.311108 + 0.167965i
\(217\) 1.33198e9 0.600702
\(218\) 2.65331e7 + 3.16209e7i 0.0117480 + 0.0140007i
\(219\) −1.04024e9 + 8.89869e8i −0.452227 + 0.386856i
\(220\) −4.08041e8 + 2.31411e9i −0.174186 + 0.987857i
\(221\) 8.14662e8 + 2.23827e9i 0.341514 + 0.938302i
\(222\) 9.97208e8 + 2.66075e9i 0.410558 + 1.09545i
\(223\) 3.63437e8 + 2.06115e9i 0.146963 + 0.833471i 0.965770 + 0.259401i \(0.0835251\pi\)
−0.818806 + 0.574070i \(0.805364\pi\)
\(224\) −2.20229e8 + 1.27149e8i −0.0874747 + 0.0505035i
\(225\) 1.75373e9 3.17564e9i 0.684280 1.23908i
\(226\) −6.66199e8 + 1.15389e9i −0.255370 + 0.442314i
\(227\) −1.03079e9 + 2.83207e9i −0.388209 + 1.06660i 0.579598 + 0.814903i \(0.303210\pi\)
−0.967807 + 0.251693i \(0.919013\pi\)
\(228\) 8.96301e7 + 1.51887e8i 0.0331676 + 0.0562059i
\(229\) −2.76704e9 2.32182e9i −1.00617 0.844280i −0.0183460 0.999832i \(-0.505840\pi\)
−0.987828 + 0.155552i \(0.950284\pi\)
\(230\) 3.34689e8 3.98866e8i 0.119600 0.142533i
\(231\) −1.99850e7 2.10003e9i −0.00701871 0.737528i
\(232\) −1.02671e9 3.73694e8i −0.354403 0.128992i
\(233\) 1.28628e9 + 7.42633e8i 0.436427 + 0.251971i 0.702081 0.712097i \(-0.252255\pi\)
−0.265654 + 0.964068i \(0.585588\pi\)
\(234\) −7.22156e8 1.87244e9i −0.240862 0.624516i
\(235\) −3.11692e9 5.39866e9i −1.02201 1.77017i
\(236\) 9.88049e8 1.74220e8i 0.318515 0.0561628i
\(237\) 2.15833e9 + 1.77633e9i 0.684106 + 0.563027i
\(238\) −1.28497e9 + 4.67689e8i −0.400483 + 0.145764i
\(239\) 3.01330e9 + 5.31327e8i 0.923531 + 0.162843i 0.615141 0.788417i \(-0.289099\pi\)
0.308389 + 0.951260i \(0.400210\pi\)
\(240\) −1.26733e9 + 2.35920e8i −0.381983 + 0.0711083i
\(241\) 3.70873e9 3.11200e9i 1.09940 0.922510i 0.102019 0.994782i \(-0.467470\pi\)
0.997385 + 0.0722728i \(0.0230252\pi\)
\(242\) 1.61581e9i 0.471116i
\(243\) −2.77461e9 2.11168e9i −0.795751 0.605625i
\(244\) 2.47693e9 0.698803
\(245\) 2.42429e9 + 2.88916e9i 0.672854 + 0.801876i
\(246\) −5.95646e8 3.19971e9i −0.162648 0.873717i
\(247\) 7.98588e7 4.52902e8i 0.0214553 0.121679i
\(248\) −4.80890e8 1.32123e9i −0.127127 0.349279i
\(249\) −5.87502e8 + 7.13845e8i −0.152831 + 0.185698i
\(250\) 3.09714e8 + 1.75647e9i 0.0792868 + 0.449658i
\(251\) 2.54004e9 1.46649e9i 0.639950 0.369475i −0.144645 0.989484i \(-0.546204\pi\)
0.784595 + 0.620008i \(0.212871\pi\)
\(252\) 1.07495e9 4.14582e8i 0.266554 0.102804i
\(253\) 4.47713e8 7.75461e8i 0.109274 0.189268i
\(254\) 3.26331e8 8.96586e8i 0.0784012 0.215406i
\(255\) −6.93152e9 + 6.59640e7i −1.63933 + 0.0156008i
\(256\) 2.05633e8 + 1.72547e8i 0.0478778 + 0.0401742i
\(257\) 3.06702e9 3.65513e9i 0.703046 0.837857i −0.289822 0.957081i \(-0.593596\pi\)
0.992867 + 0.119224i \(0.0380405\pi\)
\(258\) 3.86448e9 2.28046e9i 0.872191 0.514688i
\(259\) 3.99723e9 + 1.45487e9i 0.888301 + 0.323315i
\(260\) 2.91116e9 + 1.68076e9i 0.637049 + 0.367800i
\(261\) 4.33329e9 + 2.39304e9i 0.933804 + 0.515690i
\(262\) 2.33383e9 + 4.04232e9i 0.495296 + 0.857878i
\(263\) −6.49180e9 + 1.14468e9i −1.35688 + 0.239255i −0.804310 0.594210i \(-0.797465\pi\)
−0.552572 + 0.833465i \(0.686354\pi\)
\(264\) −2.07588e9 + 7.78007e8i −0.427352 + 0.160165i
\(265\) −3.68980e9 + 1.34298e9i −0.748202 + 0.272323i
\(266\) 2.60006e8 + 4.58461e7i 0.0519346 + 0.00915748i
\(267\) 4.60039e9 + 5.37776e9i 0.905211 + 1.05817i
\(268\) −3.21185e9 + 2.69506e9i −0.622610 + 0.522432i
\(269\) 8.30944e9i 1.58695i −0.608604 0.793474i \(-0.708270\pi\)
0.608604 0.793474i \(-0.291730\pi\)
\(270\) 5.83800e9 1.66713e8i 1.09852 0.0313700i
\(271\) −9.13449e8 −0.169359 −0.0846793 0.996408i \(-0.526987\pi\)
−0.0846793 + 0.996408i \(0.526987\pi\)
\(272\) 9.27831e8 + 1.10575e9i 0.169509 + 0.202013i
\(273\) −2.83280e9 1.00063e9i −0.509995 0.180145i
\(274\) 1.33080e9 7.54733e9i 0.236108 1.33903i
\(275\) 3.57401e9 + 9.81951e9i 0.624921 + 1.71696i
\(276\) 4.84554e8 + 8.06933e7i 0.0835037 + 0.0139060i
\(277\) 1.39547e9 + 7.91411e9i 0.237029 + 1.34426i 0.838298 + 0.545213i \(0.183551\pi\)
−0.601269 + 0.799047i \(0.705338\pi\)
\(278\) −1.39181e9 + 8.03562e8i −0.233024 + 0.134536i
\(279\) 1.22535e9 + 6.25117e9i 0.202229 + 1.03168i
\(280\) −9.64906e8 + 1.67127e9i −0.156983 + 0.271903i
\(281\) −1.26984e9 + 3.48884e9i −0.203668 + 0.559572i −0.998908 0.0467221i \(-0.985122\pi\)
0.795240 + 0.606294i \(0.207345\pi\)
\(282\) 2.89199e9 5.12100e9i 0.457299 0.809764i
\(283\) −3.72971e9 3.12960e9i −0.581473 0.487914i 0.303957 0.952686i \(-0.401692\pi\)
−0.885431 + 0.464772i \(0.846136\pi\)
\(284\) 1.01211e9 1.20618e9i 0.155580 0.185413i
\(285\) 1.16537e9 + 6.58122e8i 0.176639 + 0.0997533i
\(286\) 5.43222e9 + 1.97717e9i 0.811920 + 0.295515i
\(287\) −4.21957e9 2.43617e9i −0.621929 0.359071i
\(288\) −7.99329e8 9.16595e8i −0.116186 0.133232i
\(289\) 3.93029e8 + 6.80745e8i 0.0563421 + 0.0975873i
\(290\) −8.16557e9 + 1.43981e9i −1.15450 + 0.203570i
\(291\) −3.95874e8 + 2.37718e9i −0.0552058 + 0.331505i
\(292\) 2.03278e9 7.39873e8i 0.279615 0.101771i
\(293\) −3.77999e9 6.66514e8i −0.512885 0.0904355i −0.0887851 0.996051i \(-0.528298\pi\)
−0.424100 + 0.905615i \(0.639410\pi\)
\(294\) −1.18509e9 + 3.35501e9i −0.158622 + 0.449060i
\(295\) 5.83246e9 4.89402e9i 0.770130 0.646216i
\(296\) 4.49024e9i 0.584928i
\(297\) 9.83737e9 2.02572e9i 1.26431 0.260347i
\(298\) 6.68251e8 0.0847372
\(299\) −8.23378e8 9.81264e8i −0.103018 0.122772i
\(300\) −4.35622e9 + 3.72651e9i −0.537804 + 0.460063i
\(301\) 1.16646e9 6.61535e9i 0.142104 0.805911i
\(302\) −1.61493e9 4.43699e9i −0.194145 0.533410i
\(303\) 1.95077e9 + 5.20505e9i 0.231439 + 0.617525i
\(304\) −4.83948e7 2.74460e8i −0.00566636 0.0321355i
\(305\) 1.62786e10 9.39843e9i 1.88112 1.08607i
\(306\) −3.37703e9 5.60028e9i −0.385168 0.638739i
\(307\) 2.17697e9 3.77062e9i 0.245075 0.424482i −0.717078 0.696993i \(-0.754521\pi\)
0.962153 + 0.272511i \(0.0878542\pi\)
\(308\) −1.13507e9 + 3.11858e9i −0.126130 + 0.346540i
\(309\) −3.92133e9 6.64509e9i −0.430130 0.728898i
\(310\) −8.17371e9 6.85855e9i −0.885059 0.742653i
\(311\) −7.24374e9 + 8.63276e9i −0.774322 + 0.922801i −0.998662 0.0517099i \(-0.983533\pi\)
0.224340 + 0.974511i \(0.427977\pi\)
\(312\) 3.01789e7 + 3.17121e9i 0.00318482 + 0.334662i
\(313\) 1.28418e10 + 4.67402e9i 1.33797 + 0.486982i 0.909174 0.416417i \(-0.136714\pi\)
0.428799 + 0.903400i \(0.358937\pi\)
\(314\) −6.60397e9 3.81280e9i −0.679339 0.392216i
\(315\) 5.49153e9 6.80342e9i 0.557765 0.691011i
\(316\) −2.20863e9 3.82546e9i −0.221501 0.383650i
\(317\) 4.53231e8 7.99169e7i 0.0448831 0.00791410i −0.151162 0.988509i \(-0.548301\pi\)
0.196045 + 0.980595i \(0.437190\pi\)
\(318\) −2.86031e9 2.35407e9i −0.279708 0.230203i
\(319\) −1.33991e10 + 4.87689e9i −1.29394 + 0.470956i
\(320\) 2.00615e9 + 3.53738e8i 0.191321 + 0.0337351i
\(321\) −1.92625e10 + 3.58584e9i −1.81423 + 0.337730i
\(322\) 5.63333e8 4.72693e8i 0.0524013 0.0439699i
\(323\) 1.49861e9i 0.137683i
\(324\) 2.93459e9 + 4.66348e9i 0.266298 + 0.423185i
\(325\) 1.49488e10 1.33990
\(326\) −4.35151e9 5.18592e9i −0.385274 0.459151i
\(327\) 5.40854e7 + 2.90538e8i 0.00473030 + 0.0254104i
\(328\) −8.93108e8 + 5.06507e9i −0.0771629 + 0.437613i
\(329\) −3.01124e9 8.27331e9i −0.257017 0.706148i
\(330\) −1.06907e10 + 1.29898e10i −0.901471 + 1.09533i
\(331\) 2.01941e9 + 1.14527e10i 0.168234 + 0.954102i 0.945667 + 0.325136i \(0.105410\pi\)
−0.777433 + 0.628965i \(0.783479\pi\)
\(332\) 1.26523e9 7.30483e8i 0.104140 0.0601254i
\(333\) −3.15068e9 + 2.00980e10i −0.256229 + 1.63446i
\(334\) 7.21338e9 1.24939e10i 0.579633 1.00395i
\(335\) −1.08824e10 + 2.98991e10i −0.864062 + 2.37399i
\(336\) −1.82056e9 + 1.73254e7i −0.142839 + 0.00135933i
\(337\) −4.81053e9 4.03651e9i −0.372970 0.312959i 0.436965 0.899478i \(-0.356053\pi\)
−0.809935 + 0.586520i \(0.800498\pi\)
\(338\) −6.16539e8 + 7.34763e8i −0.0472383 + 0.0562964i
\(339\) −8.21547e9 + 4.84802e9i −0.622062 + 0.367084i
\(340\) 1.02934e10 + 3.74649e9i 0.770270 + 0.280355i
\(341\) −1.58910e10 9.17468e9i −1.17526 0.678537i
\(342\) 2.40299e7 + 1.26242e9i 0.00175650 + 0.0922784i
\(343\) 6.61767e9 + 1.14621e10i 0.478111 + 0.828112i
\(344\) −6.98311e9 + 1.23131e9i −0.498672 + 0.0879294i
\(345\) 3.49070e9 1.30826e9i 0.246398 0.0923461i
\(346\) −1.26667e9 + 4.61032e8i −0.0883814 + 0.0321682i
\(347\) 1.23212e10 + 2.17257e9i 0.849839 + 0.149849i 0.581572 0.813495i \(-0.302438\pi\)
0.268267 + 0.963345i \(0.413549\pi\)
\(348\) −5.08498e9 5.94424e9i −0.346715 0.405303i
\(349\) 1.93829e10 1.62642e10i 1.30652 1.09630i 0.317543 0.948244i \(-0.397142\pi\)
0.988979 0.148058i \(-0.0473023\pi\)
\(350\) 8.58195e9i 0.571892i
\(351\) 2.09007e9 1.42153e10i 0.137700 0.936541i
\(352\) 3.50322e9 0.228190
\(353\) −1.10523e10 1.31716e10i −0.711791 0.848279i 0.282015 0.959410i \(-0.408997\pi\)
−0.993806 + 0.111131i \(0.964553\pi\)
\(354\) 6.77290e9 + 2.39239e9i 0.431282 + 0.152342i
\(355\) 2.07491e9 1.17674e10i 0.130643 0.740914i
\(356\) −3.82495e9 1.05090e10i −0.238137 0.654275i
\(357\) −9.65707e9 1.60820e9i −0.594529 0.0990074i
\(358\) −3.72487e9 2.11248e10i −0.226767 1.28606i
\(359\) −1.30954e10 + 7.56064e9i −0.788390 + 0.455177i −0.839395 0.543521i \(-0.817091\pi\)
0.0510054 + 0.998698i \(0.483757\pi\)
\(360\) −8.73116e9 2.99096e9i −0.519831 0.178074i
\(361\) 8.34711e9 1.44576e10i 0.491482 0.851271i
\(362\) −5.32108e9 + 1.46195e10i −0.309860 + 0.851333i
\(363\) −5.68855e9 + 1.00730e10i −0.327624 + 0.580141i
\(364\) 3.63687e9 + 3.05169e9i 0.207168 + 0.173834i
\(365\) 1.05522e10 1.25757e10i 0.594529 0.708532i
\(366\) 1.54413e10 + 8.72020e9i 0.860519 + 0.485962i
\(367\) −2.08186e10 7.57734e9i −1.14759 0.417689i −0.302941 0.953009i \(-0.597969\pi\)
−0.844649 + 0.535321i \(0.820191\pi\)
\(368\) −6.72261e8 3.88130e8i −0.0366561 0.0211634i
\(369\) 7.55151e9 2.20442e10i 0.407313 1.18902i
\(370\) −1.70377e10 2.95101e10i −0.909084 1.57458i
\(371\) −5.46142e9 + 9.62996e8i −0.288277 + 0.0508310i
\(372\) 1.65359e9 9.92965e9i 0.0863490 0.518516i
\(373\) −1.24122e10 + 4.51769e9i −0.641232 + 0.233389i −0.642113 0.766610i \(-0.721942\pi\)
0.000880763 1.00000i \(0.499720\pi\)
\(374\) 1.85515e10 + 3.27114e9i 0.948186 + 0.167191i
\(375\) −4.25301e9 + 1.20403e10i −0.215066 + 0.608854i
\(376\) −7.11940e9 + 5.97389e9i −0.356198 + 0.298886i
\(377\) 2.03983e10i 1.00978i
\(378\) 8.16084e9 + 1.19989e9i 0.399731 + 0.0587725i
\(379\) 5.23994e9 0.253962 0.126981 0.991905i \(-0.459471\pi\)
0.126981 + 0.991905i \(0.459471\pi\)
\(380\) −1.35946e9 1.62014e9i −0.0651978 0.0776997i
\(381\) 5.19085e9 4.44050e9i 0.246342 0.210733i
\(382\) −4.24879e9 + 2.40961e10i −0.199531 + 1.13160i
\(383\) 7.04274e7 + 1.93498e8i 0.00327300 + 0.00899251i 0.941318 0.337520i \(-0.109588\pi\)
−0.938045 + 0.346512i \(0.887366\pi\)
\(384\) 6.74468e8 + 1.79961e9i 0.0310196 + 0.0827664i
\(385\) 4.37333e9 + 2.48024e10i 0.199053 + 1.12889i
\(386\) 2.27667e10 1.31444e10i 1.02554 0.592094i
\(387\) 3.21199e10 6.11395e8i 1.43196 0.0272570i
\(388\) 1.90413e9 3.29805e9i 0.0840175 0.145523i
\(389\) 3.54413e8 9.73743e8i 0.0154779 0.0425252i −0.931713 0.363195i \(-0.881686\pi\)
0.947191 + 0.320670i \(0.103908\pi\)
\(390\) 1.22311e10 + 2.07269e10i 0.528698 + 0.895933i
\(391\) −3.19759e9 2.68310e9i −0.136809 0.114797i
\(392\) 3.61425e9 4.30730e9i 0.153064 0.182415i
\(393\) 3.18009e8 + 3.34164e10i 0.0133312 + 1.40084i
\(394\) 1.57177e10 + 5.72078e9i 0.652236 + 0.237394i
\(395\) −2.90305e10 1.67608e10i −1.19252 0.688504i
\(396\) −1.56801e10 2.45811e9i −0.637631 0.0999588i
\(397\) −2.72766e8 4.72444e8i −0.0109806 0.0190190i 0.860483 0.509479i \(-0.170162\pi\)
−0.871464 + 0.490460i \(0.836829\pi\)
\(398\) 4.89841e9 8.63722e8i 0.195219 0.0344225i
\(399\) 1.45949e9 + 1.20118e9i 0.0575850 + 0.0473931i
\(400\) 8.51271e9 3.09837e9i 0.332528 0.121030i
\(401\) −1.75900e10 3.10160e9i −0.680282 0.119952i −0.177179 0.984179i \(-0.556697\pi\)
−0.503103 + 0.864226i \(0.667808\pi\)
\(402\) −2.95110e10 + 5.49364e9i −1.13000 + 0.210357i
\(403\) −2.01084e10 + 1.68729e10i −0.762354 + 0.639691i
\(404\) 8.78397e9i 0.329735i
\(405\) 3.69814e10 + 1.95138e10i 1.37456 + 0.725305i
\(406\) −1.17104e10 −0.430992
\(407\) −3.76673e10 4.48901e10i −1.37273 1.63596i
\(408\) 1.89130e9 + 1.01598e10i 0.0682528 + 0.366643i
\(409\) −8.74260e9 + 4.95817e10i −0.312426 + 1.77186i 0.273877 + 0.961765i \(0.411694\pi\)
−0.586303 + 0.810092i \(0.699417\pi\)
\(410\) 1.33492e10 + 3.66767e10i 0.472412 + 1.29794i
\(411\) 3.48671e10 4.23653e10i 1.22194 1.48472i
\(412\) 2.11728e9 + 1.20077e10i 0.0734834 + 0.416745i
\(413\) 9.31250e9 5.37658e9i 0.320086 0.184802i
\(414\) 2.73665e9 + 2.20895e9i 0.0931576 + 0.0751942i
\(415\) 5.54347e9 9.60156e9i 0.186891 0.323705i
\(416\) 1.71404e9 4.70929e9i 0.0572331 0.157247i
\(417\) −1.15056e10 + 1.09493e8i −0.380509 + 0.00362113i
\(418\) −2.78618e9 2.33788e9i −0.0912650 0.0765804i
\(419\) 1.01251e10 1.20666e10i 0.328505 0.391497i −0.576360 0.817196i \(-0.695527\pi\)
0.904865 + 0.425699i \(0.139972\pi\)
\(420\) −1.18991e10 + 7.02176e9i −0.382399 + 0.225657i
\(421\) 1.65846e10 + 6.03631e9i 0.527931 + 0.192151i 0.592214 0.805780i \(-0.298254\pi\)
−0.0642831 + 0.997932i \(0.520476\pi\)
\(422\) 2.31196e10 + 1.33481e10i 0.729003 + 0.420890i
\(423\) 3.60576e10 2.17432e10i 1.12625 0.679144i
\(424\) 2.92698e9 + 5.06968e9i 0.0905642 + 0.156862i
\(425\) 4.79728e10 8.45890e9i 1.47041 0.259274i
\(426\) 1.05560e10 3.95622e9i 0.320523 0.120127i
\(427\) 2.49465e10 9.07977e9i 0.750408 0.273126i
\(428\) 3.04921e10 + 5.37658e9i 0.908683 + 0.160225i
\(429\) 2.69040e10 + 3.14502e10i 0.794306 + 0.928527i
\(430\) −4.12214e10 + 3.45889e10i −1.20573 + 1.01172i
\(431\) 1.96466e10i 0.569348i −0.958624 0.284674i \(-0.908115\pi\)
0.958624 0.284674i \(-0.0918853\pi\)
\(432\) −1.75613e9 8.52820e9i −0.0504222 0.244862i
\(433\) 7.85047e9 0.223329 0.111664 0.993746i \(-0.464382\pi\)
0.111664 + 0.993746i \(0.464382\pi\)
\(434\) −9.68658e9 1.15440e10i −0.273031 0.325385i
\(435\) −5.59736e10 1.97716e10i −1.56324 0.552184i
\(436\) 8.10954e7 4.59915e8i 0.00224414 0.0127272i
\(437\) 2.75643e8 + 7.57324e8i 0.00755826 + 0.0207661i
\(438\) 1.52773e10 + 2.54414e9i 0.415097 + 0.0691264i
\(439\) −2.49850e9 1.41697e10i −0.0672701 0.381508i −0.999792 0.0203943i \(-0.993508\pi\)
0.932522 0.361113i \(-0.117603\pi\)
\(440\) 2.30234e10 1.32925e10i 0.614268 0.354648i
\(441\) −1.91995e10 + 1.67431e10i −0.507615 + 0.442673i
\(442\) 1.34741e10 2.33379e10i 0.353030 0.611466i
\(443\) −3.80157e9 + 1.04447e10i −0.0987071 + 0.271196i −0.979211 0.202843i \(-0.934982\pi\)
0.880504 + 0.474038i \(0.157204\pi\)
\(444\) 1.58082e10 2.79924e10i 0.406771 0.720291i
\(445\) −6.50129e10 5.45523e10i −1.65790 1.39115i
\(446\) 1.52206e10 1.81392e10i 0.384673 0.458435i
\(447\) 4.16591e9 + 2.35262e9i 0.104347 + 0.0589280i
\(448\) 2.70355e9 + 9.84012e8i 0.0671155 + 0.0244280i
\(449\) −2.91247e10 1.68152e10i −0.716600 0.413729i 0.0969000 0.995294i \(-0.469107\pi\)
−0.813500 + 0.581565i \(0.802441\pi\)
\(450\) −4.02763e10 + 7.89495e9i −0.982199 + 0.192530i
\(451\) 3.35607e10 + 5.81288e10i 0.811194 + 1.40503i
\(452\) 1.48454e10 2.61764e9i 0.355661 0.0627127i
\(453\) 5.55313e9 3.33459e10i 0.131870 0.791863i
\(454\) 3.20412e10 1.16620e10i 0.754197 0.274505i
\(455\) 3.54810e10 + 6.25626e9i 0.827848 + 0.145972i
\(456\) 6.64560e8 1.88138e9i 0.0153700 0.0435128i
\(457\) 9.88638e7 8.29566e7i 0.00226659 0.00190189i −0.641654 0.766995i \(-0.721751\pi\)
0.643920 + 0.765093i \(0.277307\pi\)
\(458\) 4.08664e10i 0.928761i
\(459\) −1.33649e9 4.68015e10i −0.0301102 1.05441i
\(460\) −5.89086e9 −0.131567
\(461\) 4.87961e10 + 5.81529e10i 1.08039 + 1.28756i 0.955372 + 0.295407i \(0.0954552\pi\)
0.125021 + 0.992154i \(0.460100\pi\)
\(462\) −1.80552e10 + 1.54453e10i −0.396310 + 0.339023i
\(463\) 3.57441e9 2.02715e10i 0.0777821 0.441124i −0.920900 0.389799i \(-0.872544\pi\)
0.998682 0.0513252i \(-0.0163445\pi\)
\(464\) 4.22786e9 + 1.16159e10i 0.0912113 + 0.250601i
\(465\) −2.68094e10 7.15327e10i −0.573422 1.53000i
\(466\) −2.91796e9 1.65486e10i −0.0618780 0.350927i
\(467\) 1.96332e10 1.13352e10i 0.412784 0.238321i −0.279201 0.960233i \(-0.590070\pi\)
0.691985 + 0.721911i \(0.256736\pi\)
\(468\) −1.09763e10 + 1.98757e10i −0.228809 + 0.414324i
\(469\) −2.24688e10 + 3.89171e10i −0.464396 + 0.804358i
\(470\) −2.41219e10 + 6.62745e10i −0.494335 + 1.35817i
\(471\) −2.77463e10 4.70189e10i −0.563795 0.955408i
\(472\) −8.69532e9 7.29624e9i −0.175193 0.147005i
\(473\) −5.94829e10 + 7.08889e10i −1.18836 + 1.41623i
\(474\) −3.00949e8 3.16238e10i −0.00596182 0.626470i
\(475\) −8.83804e9 3.21678e9i −0.173613 0.0631899i
\(476\) 1.33980e10 + 7.73536e9i 0.260984 + 0.150679i
\(477\) −9.54370e9 2.47453e10i −0.184350 0.477991i
\(478\) −1.73088e10 2.99797e10i −0.331554 0.574269i
\(479\) 1.47001e10 2.59202e9i 0.279240 0.0492376i −0.0322739 0.999479i \(-0.510275\pi\)
0.311514 + 0.950241i \(0.399164\pi\)
\(480\) 1.12611e10 + 9.26799e9i 0.212136 + 0.174590i
\(481\) −7.87743e10 + 2.86715e10i −1.47165 + 0.535637i
\(482\) −5.39421e10 9.51145e9i −0.999401 0.176221i
\(483\) 5.17599e9 9.63542e8i 0.0951054 0.0177044i
\(484\) 1.40039e10 1.17507e10i 0.255192 0.214132i
\(485\) 2.89000e10i 0.522313i
\(486\) 1.87630e9 + 3.94038e10i 0.0336323 + 0.706306i
\(487\) −6.12226e9 −0.108842 −0.0544210 0.998518i \(-0.517331\pi\)
−0.0544210 + 0.998518i \(0.517331\pi\)
\(488\) −1.80130e10 2.14671e10i −0.317620 0.378524i
\(489\) −8.87016e9 4.76491e10i −0.155130 0.833334i
\(490\) 7.40956e9 4.20217e10i 0.128531 0.728936i
\(491\) 2.52725e10 + 6.94358e10i 0.434834 + 1.19470i 0.942812 + 0.333326i \(0.108171\pi\)
−0.507978 + 0.861370i \(0.669607\pi\)
\(492\) −2.33996e10 + 2.84317e10i −0.399344 + 0.485223i
\(493\) 1.15425e10 + 6.54609e10i 0.195395 + 1.10814i
\(494\) −4.50597e9 + 2.60152e9i −0.0756625 + 0.0436837i
\(495\) −1.12378e11 + 4.33416e10i −1.87180 + 0.721912i
\(496\) −7.95369e9 + 1.37762e10i −0.131414 + 0.227616i
\(497\) 5.77191e9 1.58582e10i 0.0946006 0.259913i
\(498\) 1.04592e10 9.95358e7i 0.170053 0.00161831i
\(499\) 3.82057e10 + 3.20584e10i 0.616206 + 0.517058i 0.896608 0.442825i \(-0.146024\pi\)
−0.280403 + 0.959882i \(0.590468\pi\)
\(500\) 1.29707e10 1.54579e10i 0.207531 0.247326i
\(501\) 8.89543e10 5.24928e10i 1.41194 0.833198i
\(502\) −3.11818e10 1.13493e10i −0.491006 0.178711i
\(503\) −2.01717e10 1.16461e10i −0.315115 0.181932i 0.334098 0.942538i \(-0.391568\pi\)
−0.649213 + 0.760606i \(0.724902\pi\)
\(504\) −1.14104e10 6.30138e9i −0.176840 0.0976593i
\(505\) −3.33297e10 5.77288e10i −0.512468 0.887620i
\(506\) −9.97667e9 + 1.75916e9i −0.152189 + 0.0268351i
\(507\) −6.43032e9 + 2.40999e9i −0.0973197 + 0.0364740i
\(508\) −1.01437e10 + 3.69201e9i −0.152315 + 0.0554380i
\(509\) −3.81836e10 6.73280e9i −0.568861 0.100306i −0.118182 0.992992i \(-0.537707\pi\)
−0.450678 + 0.892686i \(0.648818\pi\)
\(510\) 5.09798e10 + 5.95944e10i 0.753560 + 0.880896i
\(511\) 1.77610e10 1.49033e10i 0.260486 0.218574i
\(512\) 3.03700e9i 0.0441942i
\(513\) −4.29463e9 + 7.95461e9i −0.0620093 + 0.114855i
\(514\) −5.39826e10 −0.773394
\(515\) 5.94766e10 + 7.08815e10i 0.845508 + 1.00764i
\(516\) −4.78680e10 1.69084e10i −0.675222 0.238509i
\(517\) −2.10614e10 + 1.19445e11i −0.294798 + 1.67188i
\(518\) −1.64600e10 4.52235e10i −0.228618 0.628124i
\(519\) −9.51961e9 1.58531e9i −0.131205 0.0218497i
\(520\) −6.60406e9 3.74535e10i −0.0903228 0.512246i
\(521\) −4.49069e10 + 2.59270e10i −0.609484 + 0.351886i −0.772764 0.634694i \(-0.781126\pi\)
0.163279 + 0.986580i \(0.447793\pi\)
\(522\) −1.07730e10 5.49587e10i −0.145096 0.740210i
\(523\) −7.25562e10 + 1.25671e11i −0.969767 + 1.67969i −0.273547 + 0.961859i \(0.588197\pi\)
−0.696221 + 0.717828i \(0.745137\pi\)
\(524\) 1.80616e10 4.96239e10i 0.239569 0.658212i
\(525\) −3.02133e10 + 5.35004e10i −0.397705 + 0.704238i
\(526\) 5.71311e10 + 4.79387e10i 0.746328 + 0.626243i
\(527\) −5.49829e10 + 6.55261e10i −0.712829 + 0.849517i
\(528\) 2.18392e10 + 1.23333e10i 0.280997 + 0.158688i
\(529\) −7.14788e10 2.60162e10i −0.912756 0.332216i
\(530\) 3.84726e10 + 2.22122e10i 0.487583 + 0.281506i
\(531\) 3.38001e10 + 3.87587e10i 0.425147 + 0.487519i
\(532\) −1.49351e9 2.58683e9i −0.0186449 0.0322940i
\(533\) 9.45615e10 1.66737e10i 1.17167 0.206597i
\(534\) 1.31525e10 7.89795e10i 0.161750 0.971291i
\(535\) 2.20797e11 8.03635e10i 2.69512 0.980943i
\(536\) 4.67151e10 + 8.23714e9i 0.565976 + 0.0997969i
\(537\) 5.11501e10 1.44807e11i 0.615105 1.74137i
\(538\) −7.20163e10 + 6.04289e10i −0.859611 + 0.721299i
\(539\) 7.33801e10i 0.869407i
\(540\) −4.39006e10 4.93844e10i −0.516292 0.580785i
\(541\) −1.24636e11 −1.45497 −0.727485 0.686123i \(-0.759311\pi\)
−0.727485 + 0.686123i \(0.759311\pi\)
\(542\) 6.64289e9 + 7.91669e9i 0.0769768 + 0.0917374i
\(543\) −8.46410e10 + 7.24059e10i −0.973602 + 0.832865i
\(544\) 2.83581e9 1.60827e10i 0.0323803 0.183638i
\(545\) −1.21213e9 3.33030e9i −0.0137392 0.0377482i
\(546\) 1.19287e10 + 3.18282e10i 0.134222 + 0.358131i
\(547\) −1.48206e10 8.40517e10i −0.165545 0.938852i −0.948501 0.316775i \(-0.897400\pi\)
0.782956 0.622077i \(-0.213711\pi\)
\(548\) −7.50892e10 + 4.33528e10i −0.832636 + 0.480723i
\(549\) 6.55621e10 + 1.08724e11i 0.721711 + 1.19684i
\(550\) 5.91125e10 1.02386e11i 0.645994 1.11889i
\(551\) 4.38944e9 1.20599e10i 0.0476214 0.130839i
\(552\) −2.82448e9 4.78636e9i −0.0304216 0.0515524i
\(553\) −3.62674e10 3.04320e10i −0.387807 0.325409i
\(554\) 5.84417e10 6.96482e10i 0.620418 0.739385i
\(555\) −2.32156e9 2.43950e11i −0.0244685 2.57116i
\(556\) 1.70860e10 + 6.21879e9i 0.178789 + 0.0650739i
\(557\) 5.89985e10 + 3.40628e10i 0.612943 + 0.353883i 0.774116 0.633043i \(-0.218195\pi\)
−0.161173 + 0.986926i \(0.551528\pi\)
\(558\) 4.52665e10 5.60804e10i 0.466918 0.578461i
\(559\) 6.61907e10 + 1.14646e11i 0.677875 + 1.17411i
\(560\) 2.15016e10 3.79132e9i 0.218635 0.0385512i
\(561\) 1.04135e11 + 8.57044e10i 1.05135 + 0.865270i
\(562\) 3.94718e10 1.43665e10i 0.395677 0.144015i
\(563\) 6.11949e10 + 1.07903e10i 0.609090 + 0.107399i 0.469681 0.882836i \(-0.344369\pi\)
0.139408 + 0.990235i \(0.455480\pi\)
\(564\) −6.54142e10 + 1.21772e10i −0.646481 + 0.120346i
\(565\) 8.76323e10 7.35322e10i 0.859945 0.721579i
\(566\) 5.50841e10i 0.536736i
\(567\) 4.66508e10 + 3.62109e10i 0.451364 + 0.350354i
\(568\) −1.78141e10 −0.171147
\(569\) −1.29634e11 1.54491e11i −1.23671 1.47386i −0.827548 0.561394i \(-0.810265\pi\)
−0.409163 0.912461i \(-0.634179\pi\)
\(570\) −2.77114e9 1.48861e10i −0.0262518 0.141021i
\(571\) −2.41217e9 + 1.36801e10i −0.0226915 + 0.128690i −0.994049 0.108932i \(-0.965257\pi\)
0.971358 + 0.237622i \(0.0763679\pi\)
\(572\) −2.23691e10 6.14585e10i −0.208960 0.574114i
\(573\) −1.11319e11 + 1.35258e11i −1.03264 + 1.25471i
\(574\) 9.57222e9 + 5.42868e10i 0.0881790 + 0.500088i
\(575\) −2.26872e10 + 1.30984e10i −0.207543 + 0.119825i
\(576\) −2.13098e9 + 1.35934e10i −0.0193593 + 0.123492i
\(577\) 9.58908e10 1.66088e11i 0.865115 1.49842i −0.00181803 0.999998i \(-0.500579\pi\)
0.866933 0.498425i \(-0.166088\pi\)
\(578\) 3.04166e9 8.35689e9i 0.0272521 0.0748744i
\(579\) 1.88205e11 1.79106e9i 1.67462 0.0159366i
\(580\) 7.18611e10 + 6.02987e10i 0.635012 + 0.532839i
\(581\) 1.00651e10 1.19951e10i 0.0883308 0.105269i
\(582\) 2.34814e10 1.38566e10i 0.204660 0.120772i
\(583\) 7.17899e10 + 2.61294e10i 0.621425 + 0.226180i
\(584\) −2.11954e10 1.22372e10i −0.182217 0.105203i
\(585\) 3.27918e9 + 1.72273e11i 0.0279989 + 1.47094i
\(586\) 2.17127e10 + 3.76075e10i 0.184130 + 0.318922i
\(587\) 1.22292e11 2.15633e10i 1.03002 0.181620i 0.366997 0.930222i \(-0.380386\pi\)
0.663019 + 0.748602i \(0.269275\pi\)
\(588\) 3.76956e10 1.41277e10i 0.315342 0.118185i
\(589\) 1.55193e10 5.64857e9i 0.128947 0.0469329i
\(590\) −8.48310e10 1.49580e10i −0.700078 0.123443i
\(591\) 7.78448e10 + 9.09989e10i 0.638087 + 0.745910i
\(592\) −3.89160e10 + 3.26544e10i −0.316841 + 0.265861i
\(593\) 9.56319e10i 0.773364i 0.922213 + 0.386682i \(0.126379\pi\)
−0.922213 + 0.386682i \(0.873621\pi\)
\(594\) −8.90969e10 7.05270e10i −0.715677 0.566512i
\(595\) 1.17404e11 0.936729
\(596\) −4.85973e9 5.79160e9i −0.0385147 0.0459001i
\(597\) 3.35778e10 + 1.18607e10i 0.264335 + 0.0933710i
\(598\) −2.51656e9 + 1.42721e10i −0.0196790 + 0.111605i
\(599\) 2.23794e10 + 6.14868e10i 0.173836 + 0.477612i 0.995760 0.0919857i \(-0.0293214\pi\)
−0.821924 + 0.569597i \(0.807099\pi\)
\(600\) 6.39767e10 + 1.06541e10i 0.493647 + 0.0822076i
\(601\) −1.54093e10 8.73906e10i −0.118110 0.669833i −0.985163 0.171619i \(-0.945100\pi\)
0.867054 0.498215i \(-0.166011\pi\)
\(602\) −6.58168e10 + 3.79994e10i −0.501131 + 0.289328i
\(603\) −2.03314e11 6.96476e10i −1.53779 0.526789i
\(604\) −2.67103e10 + 4.62635e10i −0.200692 + 0.347609i
\(605\) 4.74480e10 1.30362e11i 0.354157 0.973039i
\(606\) 3.09245e10 5.47597e10i 0.229304 0.406042i
\(607\) 2.92355e10 + 2.45315e10i 0.215355 + 0.180705i 0.744084 0.668087i \(-0.232886\pi\)
−0.528728 + 0.848791i \(0.677331\pi\)
\(608\) −2.02675e9 + 2.41539e9i −0.0148315 + 0.0176755i
\(609\) −7.30035e10 4.12273e10i −0.530731 0.299720i
\(610\) −1.99837e11 7.27348e10i −1.44330 0.525318i
\(611\) 1.50262e11 + 8.67539e10i 1.07816 + 0.622478i
\(612\) −2.39777e10 + 6.99950e10i −0.170923 + 0.498955i
\(613\) 1.28645e10 + 2.22820e10i 0.0911070 + 0.157802i 0.907977 0.419020i \(-0.137626\pi\)
−0.816870 + 0.576822i \(0.804293\pi\)
\(614\) −4.85108e10 + 8.55376e9i −0.341323 + 0.0601844i
\(615\) −4.59029e10 + 2.75642e11i −0.320878 + 1.92683i
\(616\) 3.52827e10 1.28419e10i 0.245041 0.0891877i
\(617\) −1.90741e11 3.36328e10i −1.31615 0.232072i −0.528885 0.848693i \(-0.677390\pi\)
−0.787260 + 0.616621i \(0.788501\pi\)
\(618\) −2.90746e10 + 8.23106e10i −0.199324 + 0.564289i
\(619\) 8.92504e10 7.48900e10i 0.607922 0.510107i −0.286059 0.958212i \(-0.592345\pi\)
0.893981 + 0.448105i \(0.147901\pi\)
\(620\) 1.20717e11i 0.816965i
\(621\) 9.28369e9 + 2.34053e10i 0.0624244 + 0.157379i
\(622\) 1.27497e11 0.851803
\(623\) −7.70461e10 9.18200e10i −0.511445 0.609516i
\(624\) 2.72648e10 2.33236e10i 0.179830 0.153835i
\(625\) −1.09141e10 + 6.18971e10i −0.0715269 + 0.405649i
\(626\) −5.28805e10 1.45288e11i −0.344349 0.946090i
\(627\) −9.13854e9 2.43834e10i −0.0591298 0.157770i
\(628\) 1.49813e10 + 8.49632e10i 0.0963188 + 0.546251i
\(629\) −2.36574e11 + 1.36586e11i −1.51135 + 0.872577i
\(630\) −9.89001e10 + 1.88254e9i −0.627819 + 0.0119504i
\(631\) 4.03214e10 6.98387e10i 0.254342 0.440533i −0.710375 0.703824i \(-0.751475\pi\)
0.964717 + 0.263291i \(0.0848078\pi\)
\(632\) −1.70927e10 + 4.69617e10i −0.107138 + 0.294358i
\(633\) 9.71358e10 + 1.64607e11i 0.605013 + 1.02526i
\(634\) −3.98866e9 3.34689e9i −0.0246871 0.0207149i
\(635\) −5.26562e10 + 6.27532e10i −0.323858 + 0.385959i
\(636\) 3.98831e8 + 4.19093e10i 0.00243759 + 0.256143i
\(637\) −9.86430e10 3.59031e10i −0.599113 0.218059i
\(638\) 1.39710e11 + 8.06614e10i 0.843226 + 0.486837i
\(639\) 7.97346e10 + 1.24997e10i 0.478237 + 0.0749713i
\(640\) −1.15235e10 1.99594e10i −0.0686857 0.118967i
\(641\) 2.36416e11 4.16865e10i 1.40037 0.246924i 0.578077 0.815982i \(-0.303803\pi\)
0.822297 + 0.569058i \(0.192692\pi\)
\(642\) 1.71161e11 + 1.40867e11i 1.00755 + 0.829221i
\(643\) −1.05213e11 + 3.82942e10i −0.615494 + 0.224021i −0.630905 0.775860i \(-0.717316\pi\)
0.0154116 + 0.999881i \(0.495094\pi\)
\(644\) −8.19347e9 1.44473e9i −0.0476348 0.00839930i
\(645\) −3.78749e11 + 7.05063e10i −2.18833 + 0.407370i
\(646\) −1.29882e10 + 1.08984e10i −0.0745794 + 0.0625795i
\(647\) 3.23031e11i 1.84343i −0.387864 0.921716i \(-0.626787\pi\)
0.387864 0.921716i \(-0.373213\pi\)
\(648\) 1.90762e10 5.93478e10i 0.108191 0.336593i
\(649\) −1.48135e11 −0.834988
\(650\) −1.08712e11 1.29558e11i −0.609011 0.725792i
\(651\) −1.97452e10 1.06068e11i −0.109936 0.590556i
\(652\) −1.32999e10 + 7.54273e10i −0.0735965 + 0.417386i
\(653\) −6.63656e10 1.82338e11i −0.364998 1.00282i −0.977237 0.212151i \(-0.931953\pi\)
0.612239 0.790673i \(-0.290269\pi\)
\(654\) 2.12471e9 2.58163e9i 0.0116142 0.0141118i
\(655\) −6.95899e10 3.94664e11i −0.378078 2.14419i
\(656\) 5.03929e10 2.90943e10i 0.272116 0.157106i
\(657\) 8.62825e10 + 6.96449e10i 0.463086 + 0.373790i
\(658\) −4.98045e10 + 8.62639e10i −0.265684 + 0.460178i
\(659\) −3.10653e10 + 8.53512e10i −0.164715 + 0.452551i −0.994400 0.105681i \(-0.966298\pi\)
0.829685 + 0.558232i \(0.188520\pi\)
\(660\) 1.90326e11 1.81125e9i 1.00305 0.00954556i
\(661\) −1.58113e11 1.32673e11i −0.828251 0.694985i 0.126638 0.991949i \(-0.459581\pi\)
−0.954889 + 0.296964i \(0.904026\pi\)
\(662\) 8.45722e10 1.00789e11i 0.440348 0.524786i
\(663\) 1.66161e11 9.80531e10i 0.859954 0.507467i
\(664\) −1.55321e10 5.65323e9i −0.0799022 0.0290820i
\(665\) −1.96309e10 1.13339e10i −0.100381 0.0579551i
\(666\) 1.97098e11 1.18852e11i 1.00181 0.604103i
\(667\) −1.78734e10 3.09576e10i −0.0903032 0.156410i
\(668\) −1.60740e11 + 2.83429e10i −0.807271 + 0.142344i
\(669\) 1.58746e11 5.94956e10i 0.792498 0.297016i
\(670\) 3.38270e11 1.23120e11i 1.67866 0.610984i
\(671\) −3.60162e11 6.35062e10i −1.77667 0.313275i
\(672\) 1.33898e10 + 1.56524e10i 0.0656595 + 0.0767546i
\(673\) 5.46214e10 4.58328e10i 0.266258 0.223417i −0.499878 0.866096i \(-0.666622\pi\)
0.766135 + 0.642679i \(0.222177\pi\)
\(674\) 7.10467e10i 0.344274i
\(675\) −2.78879e11 9.25778e10i −1.34339 0.445956i
\(676\) 1.08517e10 0.0519651
\(677\) −1.17688e10 1.40256e10i −0.0560247 0.0667676i 0.737304 0.675561i \(-0.236098\pi\)
−0.793329 + 0.608793i \(0.791654\pi\)
\(678\) 1.01762e11 + 3.59455e10i 0.481580 + 0.170108i
\(679\) 7.08771e9 4.01964e10i 0.0333447 0.189107i
\(680\) −4.23867e10 1.16456e11i −0.198241 0.544663i
\(681\) 2.40803e11 + 4.01012e10i 1.11963 + 0.186453i
\(682\) 3.60492e10 + 2.04445e11i 0.166632 + 0.945017i
\(683\) −2.24895e11 + 1.29843e11i −1.03347 + 0.596674i −0.917976 0.396635i \(-0.870178\pi\)
−0.115492 + 0.993308i \(0.536845\pi\)
\(684\) 1.07664e10 9.38899e9i 0.0491866 0.0428938i
\(685\) −3.28994e11 + 5.69834e11i −1.49426 + 2.58813i
\(686\) 5.12143e10 1.40710e11i 0.231257 0.635374i
\(687\) −1.43873e11 + 2.54763e11i −0.645879 + 1.14369i
\(688\) 6.14549e10 + 5.15668e10i 0.274285 + 0.230153i
\(689\) 7.02501e10 8.37208e10i 0.311724 0.371498i
\(690\) −3.67239e10 2.07391e10i −0.162014 0.0914944i
\(691\) 1.19951e11 + 4.36587e10i 0.526130 + 0.191495i 0.591409 0.806372i \(-0.298572\pi\)
−0.0652798 + 0.997867i \(0.520794\pi\)
\(692\) 1.32073e10 + 7.62525e9i 0.0575958 + 0.0332529i
\(693\) −1.66934e11 + 3.27223e10i −0.723787 + 0.141877i
\(694\) −7.07747e10 1.22585e11i −0.305098 0.528446i
\(695\) 1.35887e11 2.39605e10i 0.582422 0.102697i
\(696\) −1.45380e10 + 8.72989e10i −0.0619537 + 0.372025i
\(697\) 2.94026e11 1.07017e11i 1.24582 0.453441i
\(698\) −2.81917e11 4.97095e10i −1.18768 0.209420i
\(699\) 4.00696e10 1.13438e11i 0.167844 0.475169i
\(700\) 7.43781e10 6.24106e10i 0.309780 0.259936i
\(701\) 1.79046e11i 0.741470i 0.928739 + 0.370735i \(0.120894\pi\)
−0.928739 + 0.370735i \(0.879106\pi\)
\(702\) −1.38401e11 + 8.52636e10i −0.569888 + 0.351087i
\(703\) 5.27428e10 0.215944
\(704\) −2.54765e10 3.03617e10i −0.103717 0.123605i
\(705\) −3.83701e11 + 3.28236e11i −1.55323 + 1.32871i
\(706\) −3.37799e10 + 1.91576e11i −0.135969 + 0.771119i
\(707\) −3.21997e10 8.84679e10i −0.128877 0.354085i
\(708\) −2.85202e10 7.60976e10i −0.113506 0.302857i
\(709\) −5.03568e10 2.85587e11i −0.199284 1.13020i −0.906184 0.422883i \(-0.861018\pi\)
0.706900 0.707313i \(-0.250093\pi\)
\(710\) −1.17075e11 + 6.75935e10i −0.460715 + 0.265994i
\(711\) 1.09457e11 1.98204e11i 0.428318 0.775593i
\(712\) −6.32629e10 + 1.09575e11i −0.246167 + 0.426373i
\(713\) 1.57332e10 4.32267e10i 0.0608779 0.167261i
\(714\) 5.62913e10 + 9.53913e10i 0.216595 + 0.367042i
\(715\) −3.80208e11 3.19033e11i −1.45478 1.22071i
\(716\) −1.55996e11 + 1.85909e11i −0.593555 + 0.707372i
\(717\) −2.35850e9 2.47832e11i −0.00892399 0.937735i
\(718\) 1.60760e11 + 5.85120e10i 0.604897 + 0.220164i
\(719\) 1.09735e11 + 6.33556e10i 0.410610 + 0.237066i 0.691052 0.722805i \(-0.257148\pi\)
−0.280442 + 0.959871i \(0.590481\pi\)
\(720\) 3.75736e10 + 9.74225e10i 0.139815 + 0.362518i
\(721\) 6.53411e10 + 1.13174e11i 0.241794 + 0.418800i
\(722\) −1.86004e11 + 3.27975e10i −0.684500 + 0.120696i
\(723\) −3.02792e11 2.49202e11i −1.10813 0.912006i
\(724\) 1.65401e11 6.02012e10i 0.601984 0.219104i
\(725\) 4.10830e11 + 7.24405e10i 1.48700 + 0.262198i
\(726\) 1.28670e11 2.39527e10i 0.463160 0.0862199i
\(727\) 2.74808e11 2.30591e11i 0.983766 0.825478i −0.000886983 1.00000i \(-0.500282\pi\)
0.984653 + 0.174522i \(0.0558379\pi\)
\(728\) 5.37129e10i 0.191229i
\(729\) −1.27027e11 + 2.52251e11i −0.449764 + 0.893147i
\(730\) −1.85730e11 −0.654019
\(731\) 2.77288e11 + 3.30459e11i 0.971096 + 1.15731i
\(732\) −3.67179e10 1.97243e11i −0.127889 0.687001i
\(733\) −1.76662e10 + 1.00190e11i −0.0611966 + 0.347063i 0.938800 + 0.344463i \(0.111939\pi\)
−0.999997 + 0.00260052i \(0.999172\pi\)
\(734\) 8.57279e10 + 2.35535e11i 0.295350 + 0.811469i
\(735\) 1.94132e11 2.35880e11i 0.665192 0.808242i
\(736\) 1.52504e9 + 8.64896e9i 0.00519722 + 0.0294749i
\(737\) 5.36122e11 3.09530e11i 1.81716 1.04914i
\(738\) −2.45970e11 + 9.48649e10i −0.829194 + 0.319801i
\(739\) −7.45975e10 + 1.29207e11i −0.250119 + 0.433219i −0.963558 0.267498i \(-0.913803\pi\)
0.713440 + 0.700717i \(0.247136\pi\)
\(740\) −1.31855e11 + 3.62269e11i −0.439714 + 1.20810i
\(741\) −3.72493e10 + 3.54484e8i −0.123551 + 0.00117577i
\(742\) 4.80633e10 + 4.03299e10i 0.158561 + 0.133049i
\(743\) −2.63575e11 + 3.14116e11i −0.864865 + 1.03071i 0.134344 + 0.990935i \(0.457107\pi\)
−0.999209 + 0.0397713i \(0.987337\pi\)
\(744\) −9.80837e10 + 5.78801e10i −0.320114 + 0.188902i
\(745\) −5.39140e10 1.96231e10i −0.175015 0.0637004i
\(746\) 1.29420e11 + 7.47205e10i 0.417874 + 0.241259i
\(747\) 6.55539e10 + 3.62019e10i 0.210531 + 0.116265i
\(748\) −1.06562e11 1.84571e11i −0.340406 0.589601i
\(749\) 3.26811e11 5.76256e10i 1.03841 0.183100i
\(750\) 1.35280e11 5.07010e10i 0.427553 0.160240i
\(751\) 5.83956e11 2.12543e11i 1.83578 0.668169i 0.844640 0.535334i \(-0.179814\pi\)
0.991138 0.132835i \(-0.0424080\pi\)
\(752\) 1.03549e11 + 1.82585e10i 0.323798 + 0.0570944i
\(753\) −1.54433e11 1.80529e11i −0.480354 0.561524i
\(754\) 1.76788e11 1.48343e11i 0.546974 0.458966i
\(755\) 4.05396e11i 1.24765i