Properties

Label 75.9.k.a.37.37
Level $75$
Weight $9$
Character 75.37
Analytic conductor $30.553$
Analytic rank $0$
Dimension $320$
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] = [75,9,Mod(13,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([0, 19]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.13");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.k (of order \(20\), degree \(8\), 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: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(320\)
Relative dimension: \(40\) over \(\Q(\zeta_{20})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label 37.37
Character \(\chi\) \(=\) 75.37
Dual form 75.9.k.a.73.37

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.47603 + 28.2605i) q^{2} +(41.6683 + 21.2310i) q^{3} +(-535.152 + 173.881i) q^{4} +(-597.986 + 181.764i) q^{5} +(-413.492 + 1272.60i) q^{6} +(1192.40 + 1192.40i) q^{7} +(-3983.91 - 7818.87i) q^{8} +(1285.49 + 1769.32i) q^{9} +O(q^{10})\) \(q+(4.47603 + 28.2605i) q^{2} +(41.6683 + 21.2310i) q^{3} +(-535.152 + 173.881i) q^{4} +(-597.986 + 181.764i) q^{5} +(-413.492 + 1272.60i) q^{6} +(1192.40 + 1192.40i) q^{7} +(-3983.91 - 7818.87i) q^{8} +(1285.49 + 1769.32i) q^{9} +(-7813.33 - 16085.8i) q^{10} +(-18162.1 - 13195.5i) q^{11} +(-25990.5 - 4116.50i) q^{12} +(84.9455 - 536.325i) q^{13} +(-28360.6 + 39035.0i) q^{14} +(-28776.1 - 5122.09i) q^{15} +(86595.0 - 62915.0i) q^{16} +(35193.1 - 17931.8i) q^{17} +(-44248.0 + 44248.0i) q^{18} +(-16555.1 - 5379.07i) q^{19} +(288408. - 201250. i) q^{20} +(24369.3 + 75001.0i) q^{21} +(291619. - 572334. i) q^{22} +(-212641. + 33679.0i) q^{23} -410381. i q^{24} +(324549. - 217384. i) q^{25} +15537.0 q^{26} +(15999.5 + 101017. i) q^{27} +(-845450. - 430779. i) q^{28} +(1.12940e6 - 366966. i) q^{29} +(15950.5 - 836153. i) q^{30} +(-322990. + 994060. i) q^{31} +(577109. + 577109. i) q^{32} +(-476628. - 935435. i) q^{33} +(664286. + 914312. i) q^{34} +(-929772. - 496303. i) q^{35} +(-995583. - 723333. i) q^{36} +(-1.74555e6 - 276467. i) q^{37} +(77914.4 - 491932. i) q^{38} +(14926.3 - 20544.2i) q^{39} +(3.80351e6 + 3.95144e6i) q^{40} +(945836. - 687190. i) q^{41} +(-2.01049e6 + 1.02440e6i) q^{42} +(-4.26743e6 + 4.26743e6i) q^{43} +(1.20139e7 + 3.90357e6i) q^{44} +(-1.09030e6 - 824374. i) q^{45} +(-1.90357e6 - 5.85860e6i) q^{46} +(3.11825e6 - 6.11991e6i) q^{47} +(4.94401e6 - 783055. i) q^{48} -2.92117e6i q^{49} +(7.59608e6 + 8.19891e6i) q^{50} +1.84714e6 q^{51} +(47798.2 + 301786. i) q^{52} +(-1.24164e6 - 632648. i) q^{53} +(-2.78317e6 + 904307. i) q^{54} +(1.32591e7 + 4.58954e6i) q^{55} +(4.57280e6 - 1.40736e7i) q^{56} +(-575618. - 575618. i) q^{57} +(1.54259e7 + 3.02750e7i) q^{58} +(5.90680e6 + 8.13001e6i) q^{59} +(1.62902e7 - 2.26253e6i) q^{60} +(223198. + 162163. i) q^{61} +(-2.95384e7 - 4.67842e6i) q^{62} +(-576923. + 3.64255e6i) q^{63} +(2.37999e6 - 3.27577e6i) q^{64} +(46688.1 + 336155. i) q^{65} +(2.43025e7 - 1.76568e7i) q^{66} +(-3.29770e7 + 1.68026e7i) q^{67} +(-1.57156e7 + 1.57156e7i) q^{68} +(-9.57542e6 - 3.11124e6i) q^{69} +(9.86409e6 - 2.84973e7i) q^{70} +(-1.04056e7 - 3.20253e7i) q^{71} +(8.71282e6 - 1.70999e7i) q^{72} +(-1.38082e7 + 2.18701e6i) q^{73} -5.05675e7i q^{74} +(1.81387e7 - 2.16750e6i) q^{75} +9.79481e6 q^{76} +(-5.92212e6 - 3.73908e7i) q^{77} +(647401. + 329868. i) q^{78} +(-4.11974e7 + 1.33858e7i) q^{79} +(-4.03469e7 + 5.33621e7i) q^{80} +(-1.47802e6 + 4.54887e6i) q^{81} +(2.36539e7 + 2.36539e7i) q^{82} +(-2.64595e7 - 5.19297e7i) q^{83} +(-2.60826e7 - 3.58996e7i) q^{84} +(-1.77856e7 + 1.71198e7i) q^{85} +(-1.39701e8 - 1.01499e8i) q^{86} +(5.48514e7 + 8.68760e6i) q^{87} +(-3.08180e7 + 1.94577e8i) q^{88} +(-7.22778e6 + 9.94819e6i) q^{89} +(1.84170e7 - 3.45024e7i) q^{90} +(740802. - 538224. i) q^{91} +(1.07939e8 - 5.49977e7i) q^{92} +(-3.45634e7 + 3.45634e7i) q^{93} +(1.86909e8 + 6.07305e7i) q^{94} +(1.08774e7 + 207498. i) q^{95} +(1.17945e7 + 3.62997e7i) q^{96} +(4.74457e7 - 9.31175e7i) q^{97} +(8.25539e7 - 1.30753e7i) q^{98} -4.90972e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 320 q + 444 q^{5} - 4540 q^{7} - 17460 q^{8} + 25496 q^{10} - 22680 q^{12} - 133420 q^{13} + 59616 q^{15} + 1310720 q^{16} + 168000 q^{17} - 718900 q^{19} - 641844 q^{20} + 2257100 q^{22} + 1089120 q^{23} - 1459756 q^{25} + 1827840 q^{26} + 3260740 q^{28} + 3913800 q^{29} + 3585384 q^{30} - 641460 q^{32} - 1458000 q^{33} - 4121600 q^{34} + 853140 q^{35} - 22394880 q^{36} - 14553460 q^{37} + 17491260 q^{38} + 3203652 q^{40} + 8749440 q^{41} + 9643860 q^{42} - 23946520 q^{43} + 4277700 q^{44} - 2204496 q^{45} + 26491200 q^{47} - 3661200 q^{48} - 47100924 q^{50} - 169691020 q^{52} - 97028940 q^{53} + 27431764 q^{55} - 4714200 q^{57} + 179119320 q^{58} + 95587200 q^{59} + 38705364 q^{60} + 36738240 q^{61} - 296094660 q^{62} - 9928980 q^{63} - 59695100 q^{64} + 24018972 q^{65} - 88558160 q^{67} + 197811840 q^{68} + 220501420 q^{70} + 38185020 q^{72} + 110964400 q^{73} + 51345576 q^{75} - 97175880 q^{77} - 131709240 q^{78} - 138506200 q^{79} - 339741204 q^{80} + 382637520 q^{81} + 217169400 q^{82} + 862340400 q^{83} + 743029200 q^{84} + 619431268 q^{85} - 335756340 q^{87} - 1380992420 q^{88} - 1141686000 q^{89} - 265834224 q^{90} - 407198400 q^{92} + 402028920 q^{93} + 290042200 q^{94} + 1436174256 q^{95} - 165325860 q^{96} + 1057772920 q^{97} + 1077594720 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(1\) \(e\left(\frac{9}{20}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.47603 + 28.2605i 0.279752 + 1.76628i 0.582131 + 0.813095i \(0.302219\pi\)
−0.302379 + 0.953188i \(0.597781\pi\)
\(3\) 41.6683 + 21.2310i 0.514423 + 0.262112i
\(4\) −535.152 + 173.881i −2.09044 + 0.679224i
\(5\) −597.986 + 181.764i −0.956777 + 0.290822i
\(6\) −413.492 + 1272.60i −0.319052 + 0.981942i
\(7\) 1192.40 + 1192.40i 0.496626 + 0.496626i 0.910386 0.413760i \(-0.135785\pi\)
−0.413760 + 0.910386i \(0.635785\pi\)
\(8\) −3983.91 7818.87i −0.972635 1.90890i
\(9\) 1285.49 + 1769.32i 0.195928 + 0.269672i
\(10\) −7813.33 16085.8i −0.781333 1.60858i
\(11\) −18162.1 13195.5i −1.24050 0.901273i −0.242864 0.970060i \(-0.578087\pi\)
−0.997631 + 0.0687876i \(0.978087\pi\)
\(12\) −25990.5 4116.50i −1.25340 0.198519i
\(13\) 84.9455 536.325i 0.00297418 0.0187782i −0.986157 0.165817i \(-0.946974\pi\)
0.989131 + 0.147038i \(0.0469741\pi\)
\(14\) −28360.6 + 39035.0i −0.738250 + 1.01611i
\(15\) −28776.1 5122.09i −0.568416 0.101177i
\(16\) 86595.0 62915.0i 1.32134 0.960006i
\(17\) 35193.1 17931.8i 0.421368 0.214698i −0.230432 0.973088i \(-0.574014\pi\)
0.651800 + 0.758391i \(0.274014\pi\)
\(18\) −44248.0 + 44248.0i −0.421506 + 0.421506i
\(19\) −16555.1 5379.07i −0.127033 0.0412756i 0.244811 0.969571i \(-0.421274\pi\)
−0.371844 + 0.928295i \(0.621274\pi\)
\(20\) 288408. 201250.i 1.80255 1.25781i
\(21\) 24369.3 + 75001.0i 0.125304 + 0.385647i
\(22\) 291619. 572334.i 1.24487 2.44320i
\(23\) −212641. + 33679.0i −0.759864 + 0.120351i −0.524329 0.851515i \(-0.675684\pi\)
−0.235534 + 0.971866i \(0.575684\pi\)
\(24\) 410381.i 1.23692i
\(25\) 324549. 217384.i 0.830845 0.556503i
\(26\) 15537.0 0.0339997
\(27\) 15999.5 + 101017.i 0.0301058 + 0.190081i
\(28\) −845450. 430779.i −1.37549 0.700845i
\(29\) 1.12940e6 366966.i 1.59683 0.518840i 0.630506 0.776185i \(-0.282847\pi\)
0.966320 + 0.257344i \(0.0828475\pi\)
\(30\) 15950.5 836153.i 0.0196920 1.03229i
\(31\) −322990. + 994060.i −0.349737 + 1.07638i 0.609261 + 0.792970i \(0.291466\pi\)
−0.958998 + 0.283411i \(0.908534\pi\)
\(32\) 577109. + 577109.i 0.550374 + 0.550374i
\(33\) −476628. 935435.i −0.401905 0.788783i
\(34\) 664286. + 914312.i 0.497095 + 0.684193i
\(35\) −929772. 496303.i −0.619590 0.330731i
\(36\) −995583. 723333.i −0.592744 0.430654i
\(37\) −1.74555e6 276467.i −0.931375 0.147515i −0.327732 0.944771i \(-0.606284\pi\)
−0.603642 + 0.797255i \(0.706284\pi\)
\(38\) 77914.4 491932.i 0.0373666 0.235923i
\(39\) 14926.3 20544.2i 0.00645198 0.00888038i
\(40\) 3.80351e6 + 3.95144e6i 1.48575 + 1.54353i
\(41\) 945836. 687190.i 0.334719 0.243188i −0.407711 0.913111i \(-0.633673\pi\)
0.742430 + 0.669923i \(0.233673\pi\)
\(42\) −2.01049e6 + 1.02440e6i −0.646108 + 0.329208i
\(43\) −4.26743e6 + 4.26743e6i −1.24822 + 1.24822i −0.291721 + 0.956503i \(0.594228\pi\)
−0.956503 + 0.291721i \(0.905772\pi\)
\(44\) 1.20139e7 + 3.90357e6i 3.20535 + 1.04148i
\(45\) −1.09030e6 824374.i −0.265886 0.201036i
\(46\) −1.90357e6 5.85860e6i −0.425146 1.30847i
\(47\) 3.11825e6 6.11991e6i 0.639027 1.25416i −0.313466 0.949599i \(-0.601490\pi\)
0.952493 0.304561i \(-0.0985099\pi\)
\(48\) 4.94401e6 783055.i 0.931354 0.147512i
\(49\) 2.92117e6i 0.506726i
\(50\) 7.59608e6 + 8.19891e6i 1.21537 + 1.31183i
\(51\) 1.84714e6 0.273036
\(52\) 47798.2 + 301786.i 0.00653729 + 0.0412749i
\(53\) −1.24164e6 632648.i −0.157359 0.0801786i 0.373537 0.927615i \(-0.378145\pi\)
−0.530897 + 0.847437i \(0.678145\pi\)
\(54\) −2.78317e6 + 904307.i −0.327314 + 0.106351i
\(55\) 1.32591e7 + 4.58954e6i 1.44899 + 0.501554i
\(56\) 4.57280e6 1.40736e7i 0.464975 1.43105i
\(57\) −575618. 575618.i −0.0545299 0.0545299i
\(58\) 1.54259e7 + 3.02750e7i 1.36313 + 2.67530i
\(59\) 5.90680e6 + 8.13001e6i 0.487466 + 0.670939i 0.979918 0.199400i \(-0.0638994\pi\)
−0.492452 + 0.870339i \(0.663899\pi\)
\(60\) 1.62902e7 2.26253e6i 1.25696 0.174578i
\(61\) 223198. + 162163.i 0.0161202 + 0.0117120i 0.595816 0.803121i \(-0.296829\pi\)
−0.579696 + 0.814833i \(0.696829\pi\)
\(62\) −2.95384e7 4.67842e6i −1.99903 0.316616i
\(63\) −576923. + 3.64255e6i −0.0366231 + 0.231229i
\(64\) 2.37999e6 3.27577e6i 0.141858 0.195251i
\(65\) 46688.1 + 336155.i 0.00261549 + 0.0188315i
\(66\) 2.43025e7 1.76568e7i 1.28078 0.930542i
\(67\) −3.29770e7 + 1.68026e7i −1.63649 + 0.833831i −0.638553 + 0.769578i \(0.720466\pi\)
−0.997934 + 0.0642531i \(0.979534\pi\)
\(68\) −1.57156e7 + 1.57156e7i −0.735015 + 0.735015i
\(69\) −9.57542e6 3.11124e6i −0.422437 0.137258i
\(70\) 9.86409e6 2.84973e7i 0.410833 1.18689i
\(71\) −1.04056e7 3.20253e7i −0.409483 1.26026i −0.917094 0.398672i \(-0.869471\pi\)
0.507611 0.861586i \(-0.330529\pi\)
\(72\) 8.71282e6 1.70999e7i 0.324212 0.636301i
\(73\) −1.38082e7 + 2.18701e6i −0.486236 + 0.0770122i −0.394739 0.918793i \(-0.629165\pi\)
−0.0914966 + 0.995805i \(0.529165\pi\)
\(74\) 5.05675e7i 1.68634i
\(75\) 1.81387e7 2.16750e6i 0.573272 0.0685038i
\(76\) 9.79481e6 0.293590
\(77\) −5.92212e6 3.73908e7i −0.168467 1.06366i
\(78\) 647401. + 329868.i 0.0174902 + 0.00891171i
\(79\) −4.11974e7 + 1.33858e7i −1.05770 + 0.343667i −0.785685 0.618627i \(-0.787689\pi\)
−0.272013 + 0.962294i \(0.587689\pi\)
\(80\) −4.03469e7 + 5.33621e7i −0.985033 + 1.30278i
\(81\) −1.47802e6 + 4.54887e6i −0.0343352 + 0.105673i
\(82\) 2.36539e7 + 2.36539e7i 0.523176 + 0.523176i
\(83\) −2.64595e7 5.19297e7i −0.557531 1.09422i −0.982019 0.188783i \(-0.939546\pi\)
0.424488 0.905434i \(-0.360454\pi\)
\(84\) −2.60826e7 3.58996e7i −0.523882 0.721061i
\(85\) −1.77856e7 + 1.71198e7i −0.340716 + 0.327961i
\(86\) −1.39701e8 1.01499e8i −2.55391 1.85552i
\(87\) 5.48514e7 + 8.68760e6i 0.957438 + 0.151643i
\(88\) −3.08180e7 + 1.94577e8i −0.513894 + 3.24460i
\(89\) −7.22778e6 + 9.94819e6i −0.115198 + 0.158556i −0.862722 0.505678i \(-0.831242\pi\)
0.747524 + 0.664235i \(0.231242\pi\)
\(90\) 1.84170e7 3.45024e7i 0.280704 0.525871i
\(91\) 740802. 538224.i 0.0108028 0.00784870i
\(92\) 1.07939e8 5.49977e7i 1.50670 0.767703i
\(93\) −3.45634e7 + 3.45634e7i −0.462045 + 0.462045i
\(94\) 1.86909e8 + 6.07305e7i 2.39397 + 0.777849i
\(95\) 1.08774e7 + 207498.i 0.133546 + 0.00254753i
\(96\) 1.17945e7 + 3.62997e7i 0.138866 + 0.427384i
\(97\) 4.74457e7 9.31175e7i 0.535933 1.05183i −0.451275 0.892385i \(-0.649031\pi\)
0.987207 0.159442i \(-0.0509695\pi\)
\(98\) 8.25539e7 1.30753e7i 0.895021 0.141757i
\(99\) 4.90972e7i 0.511112i
\(100\) −1.35884e8 + 1.72767e8i −1.35884 + 1.72767i
\(101\) −4.63098e7 −0.445028 −0.222514 0.974930i \(-0.571426\pi\)
−0.222514 + 0.974930i \(0.571426\pi\)
\(102\) 8.26786e6 + 5.22012e7i 0.0763823 + 0.482259i
\(103\) −1.68810e8 8.60132e7i −1.49986 0.764216i −0.504775 0.863251i \(-0.668425\pi\)
−0.995084 + 0.0990344i \(0.968425\pi\)
\(104\) −4.53187e6 + 1.47249e6i −0.0387386 + 0.0125869i
\(105\) −2.82049e7 4.04201e7i −0.232043 0.332537i
\(106\) 1.23213e7 3.79212e7i 0.0975965 0.300371i
\(107\) 5.39839e7 + 5.39839e7i 0.411841 + 0.411841i 0.882379 0.470539i \(-0.155940\pi\)
−0.470539 + 0.882379i \(0.655940\pi\)
\(108\) −2.61271e7 5.12773e7i −0.192042 0.376903i
\(109\) −9.06978e7 1.24835e8i −0.642526 0.884361i 0.356221 0.934402i \(-0.384065\pi\)
−0.998747 + 0.0500406i \(0.984065\pi\)
\(110\) −7.03544e7 + 3.95253e8i −0.480530 + 2.69963i
\(111\) −6.68642e7 4.85797e7i −0.440455 0.320009i
\(112\) 1.78275e8 + 2.82361e7i 1.13297 + 0.179445i
\(113\) −3.35530e6 + 2.11846e7i −0.0205787 + 0.129929i −0.995839 0.0911313i \(-0.970952\pi\)
0.975260 + 0.221060i \(0.0709517\pi\)
\(114\) 1.36908e7 1.88437e7i 0.0810604 0.111570i
\(115\) 1.21035e8 5.87900e7i 0.692020 0.336134i
\(116\) −5.40595e8 + 3.92765e8i −2.98566 + 2.16921i
\(117\) 1.05813e6 539143.i 0.00564669 0.00287713i
\(118\) −2.03319e8 + 2.03319e8i −1.04870 + 1.04870i
\(119\) 6.33460e7 + 2.05823e7i 0.315887 + 0.102638i
\(120\) 7.45924e7 + 2.45402e8i 0.359724 + 1.18346i
\(121\) 8.94990e7 + 2.75450e8i 0.417520 + 1.28499i
\(122\) −3.58376e6 + 7.03353e6i −0.0161771 + 0.0317493i
\(123\) 5.40011e7 8.55293e6i 0.235929 0.0373675i
\(124\) 5.88135e8i 2.48766i
\(125\) −1.54563e8 + 1.88984e8i −0.633091 + 0.774077i
\(126\) −1.05523e8 −0.418662
\(127\) −1.90093e7 1.20020e8i −0.0730719 0.461358i −0.996909 0.0785710i \(-0.974964\pi\)
0.923837 0.382787i \(-0.125036\pi\)
\(128\) 2.89391e8 + 1.47452e8i 1.07807 + 0.549302i
\(129\) −2.68418e8 + 8.72144e7i −0.969289 + 0.314941i
\(130\) −9.29093e6 + 2.82407e6i −0.0325301 + 0.00988785i
\(131\) 8.88975e7 2.73599e8i 0.301859 0.929027i −0.678971 0.734165i \(-0.737574\pi\)
0.980831 0.194863i \(-0.0624261\pi\)
\(132\) 4.17723e8 + 4.17723e8i 1.37592 + 1.37592i
\(133\) −1.33263e7 2.61542e7i −0.0425894 0.0835864i
\(134\) −6.22457e8 8.56739e8i −1.93059 2.65723i
\(135\) −2.79286e7 5.74984e7i −0.0840842 0.173109i
\(136\) −2.80412e8 2.03731e8i −0.819674 0.595528i
\(137\) 1.32965e8 + 2.10596e7i 0.377446 + 0.0597815i 0.342275 0.939600i \(-0.388803\pi\)
0.0351706 + 0.999381i \(0.488803\pi\)
\(138\) 4.50655e7 2.84532e8i 0.124259 0.784541i
\(139\) 3.44440e8 4.74081e8i 0.922688 1.26997i −0.0399565 0.999201i \(-0.512722\pi\)
0.962644 0.270769i \(-0.0872781\pi\)
\(140\) 5.83867e8 + 1.03927e8i 1.51985 + 0.270531i
\(141\) 2.59864e8 1.88802e8i 0.657460 0.477673i
\(142\) 8.58475e8 4.37415e8i 2.11142 1.07582i
\(143\) −8.61988e6 + 8.61988e6i −0.0206138 + 0.0206138i
\(144\) 2.22633e8 + 7.23380e7i 0.517774 + 0.168235i
\(145\) −6.08667e8 + 4.24725e8i −1.37692 + 0.960806i
\(146\) −1.23612e8 3.80439e8i −0.272051 0.837286i
\(147\) 6.20195e7 1.21720e8i 0.132819 0.260671i
\(148\) 9.82205e8 1.55566e8i 2.04718 0.324241i
\(149\) 6.70538e8i 1.36044i 0.733009 + 0.680219i \(0.238115\pi\)
−0.733009 + 0.680219i \(0.761885\pi\)
\(150\) 1.42444e8 + 5.02907e8i 0.281371 + 0.993396i
\(151\) −5.52404e8 −1.06255 −0.531275 0.847200i \(-0.678287\pi\)
−0.531275 + 0.847200i \(0.678287\pi\)
\(152\) 2.38957e7 + 1.50872e8i 0.0447658 + 0.282640i
\(153\) 7.69672e7 + 3.92168e7i 0.140456 + 0.0715659i
\(154\) 1.03018e9 3.34724e8i 1.83159 0.595120i
\(155\) 1.24594e7 6.53142e8i 0.0215858 1.13157i
\(156\) −4.41556e6 + 1.35897e7i −0.00745568 + 0.0229462i
\(157\) −2.78240e8 2.78240e8i −0.457953 0.457953i 0.440030 0.897983i \(-0.354968\pi\)
−0.897983 + 0.440030i \(0.854968\pi\)
\(158\) −5.62692e8 1.10434e9i −0.902905 1.77205i
\(159\) −3.83052e7 5.27226e7i −0.0599335 0.0824914i
\(160\) −4.50000e8 2.40205e8i −0.686646 0.366524i
\(161\) −2.93712e8 2.13394e8i −0.437137 0.317599i
\(162\) −1.35169e8 2.14087e7i −0.196254 0.0310835i
\(163\) −2.02633e8 + 1.27938e9i −0.287052 + 1.81237i 0.249352 + 0.968413i \(0.419782\pi\)
−0.536404 + 0.843961i \(0.680218\pi\)
\(164\) −3.86676e8 + 5.32214e8i −0.534530 + 0.735718i
\(165\) 4.55045e8 + 4.72743e8i 0.613929 + 0.637807i
\(166\) 1.34913e9 9.80198e8i 1.77673 1.29087i
\(167\) 9.10900e7 4.64127e7i 0.117113 0.0596720i −0.394453 0.918916i \(-0.629066\pi\)
0.511565 + 0.859244i \(0.329066\pi\)
\(168\) 4.89338e8 4.89338e8i 0.614288 0.614288i
\(169\) 7.75526e8 + 2.51984e8i 0.950713 + 0.308905i
\(170\) −5.63422e8 4.26002e8i −0.674587 0.510054i
\(171\) −1.17640e7 3.62060e7i −0.0137585 0.0423444i
\(172\) 1.54170e9 3.02575e9i 1.76151 3.45716i
\(173\) −1.01921e9 + 1.61427e8i −1.13783 + 0.180215i −0.696793 0.717272i \(-0.745390\pi\)
−0.441040 + 0.897487i \(0.645390\pi\)
\(174\) 1.58901e9i 1.73353i
\(175\) 6.46200e8 + 1.27783e8i 0.688993 + 0.136245i
\(176\) −2.40294e9 −2.50434
\(177\) 7.35174e7 + 4.64171e8i 0.0749027 + 0.472917i
\(178\) −3.13493e8 1.59733e8i −0.312282 0.159116i
\(179\) −1.16389e9 + 3.78170e8i −1.13370 + 0.368362i −0.814982 0.579486i \(-0.803253\pi\)
−0.318721 + 0.947849i \(0.603253\pi\)
\(180\) 7.26820e8 + 2.51582e8i 0.692368 + 0.239657i
\(181\) −2.91283e8 + 8.96477e8i −0.271394 + 0.835266i 0.718757 + 0.695262i \(0.244712\pi\)
−0.990151 + 0.140004i \(0.955288\pi\)
\(182\) 1.85263e7 + 1.85263e7i 0.0168851 + 0.0168851i
\(183\) 5.85738e6 + 1.14958e7i 0.00522275 + 0.0102502i
\(184\) 1.11048e9 + 1.52844e9i 0.968808 + 1.33345i
\(185\) 1.09406e9 1.51953e8i 0.934019 0.129725i
\(186\) −1.13149e9 8.22072e8i −0.945360 0.686844i
\(187\) −8.75799e8 1.38713e8i −0.716206 0.113436i
\(188\) −6.04599e8 + 3.81729e9i −0.483989 + 3.05579i
\(189\) −1.01374e8 + 1.39530e8i −0.0794476 + 0.109350i
\(190\) 4.28236e7 + 3.08330e8i 0.0328601 + 0.236593i
\(191\) −1.43667e8 + 1.04380e8i −0.107950 + 0.0784306i −0.640451 0.767999i \(-0.721252\pi\)
0.532500 + 0.846430i \(0.321252\pi\)
\(192\) 1.68718e8 8.59662e7i 0.124153 0.0632590i
\(193\) −3.72770e8 + 3.72770e8i −0.268665 + 0.268665i −0.828562 0.559897i \(-0.810841\pi\)
0.559897 + 0.828562i \(0.310841\pi\)
\(194\) 2.84392e9 + 9.24045e8i 2.00775 + 0.652358i
\(195\) −5.19150e6 + 1.49982e7i −0.00359050 + 0.0103729i
\(196\) 5.07938e8 + 1.56327e9i 0.344181 + 1.05928i
\(197\) −1.14984e9 + 2.25669e9i −0.763437 + 1.49833i 0.100614 + 0.994926i \(0.467919\pi\)
−0.864051 + 0.503404i \(0.832081\pi\)
\(198\) 1.38751e9 2.19761e8i 0.902769 0.142985i
\(199\) 2.80251e9i 1.78704i 0.449019 + 0.893522i \(0.351774\pi\)
−0.449019 + 0.893522i \(0.648226\pi\)
\(200\) −2.99267e9 1.67157e9i −1.87042 1.04473i
\(201\) −1.73083e9 −1.06040
\(202\) −2.07284e8 1.30874e9i −0.124497 0.786045i
\(203\) 1.78427e9 + 9.09131e8i 1.05069 + 0.535355i
\(204\) −9.88503e8 + 3.21184e8i −0.570765 + 0.185453i
\(205\) −4.40690e8 + 5.82848e8i −0.249527 + 0.330020i
\(206\) 1.67518e9 5.15567e9i 0.930234 2.86297i
\(207\) −3.32936e8 3.32936e8i −0.181334 0.181334i
\(208\) −2.63870e7 5.17874e7i −0.0140973 0.0276676i
\(209\) 2.29695e8 + 3.16148e8i 0.120383 + 0.165694i
\(210\) 1.01605e9 9.78008e8i 0.522440 0.502881i
\(211\) 1.77056e9 + 1.28639e9i 0.893266 + 0.648996i 0.936727 0.350060i \(-0.113839\pi\)
−0.0434617 + 0.999055i \(0.513839\pi\)
\(212\) 7.74472e8 + 1.22664e8i 0.383409 + 0.0607260i
\(213\) 2.46345e8 1.55536e9i 0.119681 0.755636i
\(214\) −1.28398e9 + 1.76725e9i −0.612214 + 0.842641i
\(215\) 1.77620e9 3.32753e9i 0.831262 1.55728i
\(216\) 7.26096e8 5.27539e8i 0.333564 0.242348i
\(217\) −1.57045e9 + 8.00184e8i −0.708247 + 0.360870i
\(218\) 3.12193e9 3.12193e9i 1.38228 1.38228i
\(219\) −6.21798e8 2.02034e8i −0.270317 0.0878312i
\(220\) −7.89369e9 1.50580e8i −3.36969 0.0642803i
\(221\) −6.62776e6 2.03981e7i −0.00277842 0.00855109i
\(222\) 1.07360e9 2.10706e9i 0.442009 0.867491i
\(223\) −1.31385e9 + 2.08094e8i −0.531285 + 0.0841473i −0.416313 0.909221i \(-0.636678\pi\)
−0.114972 + 0.993369i \(0.536678\pi\)
\(224\) 1.37629e9i 0.546660i
\(225\) 8.01825e8 + 2.94787e8i 0.312860 + 0.115021i
\(226\) −6.13705e8 −0.235248
\(227\) 3.63537e8 + 2.29528e9i 0.136913 + 0.864436i 0.956553 + 0.291557i \(0.0941733\pi\)
−0.819640 + 0.572878i \(0.805827\pi\)
\(228\) 4.08132e8 + 2.07954e8i 0.151029 + 0.0769534i
\(229\) −5.95995e8 + 1.93651e8i −0.216721 + 0.0704169i −0.415365 0.909655i \(-0.636346\pi\)
0.198644 + 0.980072i \(0.436346\pi\)
\(230\) 2.20319e9 + 3.15736e9i 0.787301 + 1.12827i
\(231\) 5.47081e8 1.68374e9i 0.192134 0.591327i
\(232\) −7.36871e9 7.36871e9i −2.54354 2.54354i
\(233\) −6.00434e8 1.17842e9i −0.203724 0.399830i 0.766428 0.642331i \(-0.222032\pi\)
−0.970151 + 0.242500i \(0.922032\pi\)
\(234\) 1.99727e7 + 2.74900e7i 0.00666151 + 0.00916878i
\(235\) −7.52292e8 + 4.22640e9i −0.246669 + 1.38580i
\(236\) −4.57470e9 3.32371e9i −1.47474 1.07146i
\(237\) −2.00082e9 3.16899e8i −0.634183 0.100445i
\(238\) −2.98130e8 + 1.88232e9i −0.0929175 + 0.586658i
\(239\) −5.01953e8 + 6.90879e8i −0.153841 + 0.211744i −0.878980 0.476859i \(-0.841775\pi\)
0.725139 + 0.688602i \(0.241775\pi\)
\(240\) −2.81412e9 + 1.36690e9i −0.848198 + 0.411994i
\(241\) 3.75876e9 2.73090e9i 1.11423 0.809539i 0.130910 0.991394i \(-0.458210\pi\)
0.983325 + 0.181855i \(0.0582102\pi\)
\(242\) −7.38375e9 + 3.76221e9i −2.15286 + 1.09694i
\(243\) −1.58164e8 + 1.58164e8i −0.0453609 + 0.0453609i
\(244\) −1.47642e8 4.79717e7i −0.0416534 0.0135340i
\(245\) 5.30963e8 + 1.74682e9i 0.147367 + 0.484824i
\(246\) 4.83421e8 + 1.48782e9i 0.132003 + 0.406264i
\(247\) −4.29121e6 + 8.42197e6i −0.00115290 + 0.00226270i
\(248\) 9.05919e9 1.43484e9i 2.39487 0.379311i
\(249\) 2.72558e9i 0.709025i
\(250\) −6.03261e9 3.52214e9i −1.54435 0.901668i
\(251\) 3.32473e7 0.00837649 0.00418824 0.999991i \(-0.498667\pi\)
0.00418824 + 0.999991i \(0.498667\pi\)
\(252\) −3.24630e8 2.04963e9i −0.0804982 0.508246i
\(253\) 4.30642e9 + 2.19423e9i 1.05108 + 0.535550i
\(254\) 3.30674e9 1.07442e9i 0.794447 0.258131i
\(255\) −1.10457e9 + 3.35743e8i −0.261235 + 0.0794048i
\(256\) −2.55144e9 + 7.85251e9i −0.594052 + 1.82831i
\(257\) −3.82900e9 3.82900e9i −0.877714 0.877714i 0.115583 0.993298i \(-0.463126\pi\)
−0.993298 + 0.115583i \(0.963126\pi\)
\(258\) −3.66617e9 7.19527e9i −0.827436 1.62393i
\(259\) −1.75173e9 2.41105e9i −0.389285 0.535805i
\(260\) −8.34363e7 1.71776e8i −0.0182584 0.0375897i
\(261\) 2.10111e9 + 1.52655e9i 0.452780 + 0.328964i
\(262\) 8.12995e9 + 1.28766e9i 1.72537 + 0.273272i
\(263\) 1.31483e9 8.30153e9i 0.274820 1.73514i −0.334658 0.942340i \(-0.608621\pi\)
0.609478 0.792803i \(-0.291379\pi\)
\(264\) −5.41520e9 + 7.45338e9i −1.11480 + 1.53440i
\(265\) 8.57476e8 + 1.52629e8i 0.173876 + 0.0309495i
\(266\) 6.79484e8 4.93674e8i 0.135723 0.0986084i
\(267\) −5.12379e8 + 2.61070e8i −0.100820 + 0.0513703i
\(268\) 1.47261e10 1.47261e10i 2.85461 2.85461i
\(269\) 6.84036e8 + 2.22257e8i 0.130638 + 0.0424469i 0.373606 0.927587i \(-0.378121\pi\)
−0.242968 + 0.970034i \(0.578121\pi\)
\(270\) 1.49993e9 1.04664e9i 0.282238 0.196944i
\(271\) 2.43279e9 + 7.48737e9i 0.451053 + 1.38820i 0.875707 + 0.482844i \(0.160396\pi\)
−0.424653 + 0.905356i \(0.639604\pi\)
\(272\) 1.91937e9 3.76697e9i 0.350657 0.688203i
\(273\) 4.22950e7 6.69887e6i 0.00761444 0.00120601i
\(274\) 3.85192e9i 0.683400i
\(275\) −8.76299e9 3.34448e8i −1.53222 0.0584787i
\(276\) 5.66529e9 0.976306
\(277\) 1.68153e8 + 1.06168e9i 0.0285619 + 0.180333i 0.997845 0.0656150i \(-0.0209009\pi\)
−0.969283 + 0.245948i \(0.920901\pi\)
\(278\) 1.49395e10 + 7.61206e9i 2.50125 + 1.27445i
\(279\) −2.17401e9 + 7.06379e8i −0.358794 + 0.116579i
\(280\) −1.76396e8 + 9.24699e9i −0.0286983 + 1.50442i
\(281\) −2.06409e9 + 6.35261e9i −0.331057 + 1.01889i 0.637575 + 0.770388i \(0.279938\pi\)
−0.968632 + 0.248500i \(0.920062\pi\)
\(282\) 6.49881e9 + 6.49881e9i 1.02763 + 1.02763i
\(283\) 3.53496e9 + 6.93774e9i 0.551110 + 1.08161i 0.983665 + 0.180007i \(0.0576120\pi\)
−0.432555 + 0.901607i \(0.642388\pi\)
\(284\) 1.11372e10 + 1.53290e10i 1.71200 + 2.35636i
\(285\) 4.48838e8 + 2.39585e8i 0.0680315 + 0.0363145i
\(286\) −2.82185e8 2.05020e8i −0.0421765 0.0306430i
\(287\) 1.94722e9 + 3.08409e8i 0.287003 + 0.0454568i
\(288\) −2.79225e8 + 1.76296e9i −0.0405867 + 0.256254i
\(289\) −3.18324e9 + 4.38136e9i −0.456329 + 0.628084i
\(290\) −1.47274e10 1.53002e10i −2.08225 2.16324i
\(291\) 3.95396e9 2.87272e9i 0.551392 0.400610i
\(292\) 7.00923e9 3.57138e9i 0.964137 0.491253i
\(293\) 5.90513e9 5.90513e9i 0.801234 0.801234i −0.182055 0.983288i \(-0.558275\pi\)
0.983288 + 0.182055i \(0.0582748\pi\)
\(294\) 3.71748e9 + 1.20788e9i 0.497576 + 0.161672i
\(295\) −5.00992e9 3.78799e9i −0.661520 0.500174i
\(296\) 4.79244e9 + 1.47496e10i 0.624295 + 1.92138i
\(297\) 1.04239e9 2.04580e9i 0.133968 0.262928i
\(298\) −1.89498e10 + 3.00135e9i −2.40292 + 0.380585i
\(299\) 1.16906e8i 0.0146268i
\(300\) −9.33006e9 + 4.31392e9i −1.15186 + 0.532583i
\(301\) −1.01770e10 −1.23980
\(302\) −2.47258e9 1.56112e10i −0.297250 1.87676i
\(303\) −1.92965e9 9.83204e8i −0.228932 0.116647i
\(304\) −1.77201e9 + 5.75761e8i −0.207478 + 0.0674137i
\(305\) −1.62944e8 5.64017e7i −0.0188295 0.00651768i
\(306\) −7.63779e8 + 2.35067e9i −0.0871128 + 0.268106i
\(307\) 8.20857e9 + 8.20857e9i 0.924090 + 0.924090i 0.997315 0.0732255i \(-0.0233293\pi\)
−0.0732255 + 0.997315i \(0.523329\pi\)
\(308\) 9.67080e9 + 1.89800e10i 1.07463 + 2.10908i
\(309\) −5.20789e9 7.16804e9i −0.571252 0.786261i
\(310\) 1.85139e10 2.57137e9i 2.00471 0.278431i
\(311\) −1.29235e10 9.38950e9i −1.38146 1.00369i −0.996742 0.0806609i \(-0.974297\pi\)
−0.384723 0.923032i \(-0.625703\pi\)
\(312\) −2.20098e8 3.48601e7i −0.0232272 0.00367883i
\(313\) 1.40216e9 8.85290e9i 0.146090 0.922376i −0.800359 0.599522i \(-0.795358\pi\)
0.946449 0.322854i \(-0.104642\pi\)
\(314\) 6.61780e9 9.10862e9i 0.680761 0.936988i
\(315\) −3.17091e8 2.28305e9i −0.0322063 0.231886i
\(316\) 1.97193e10 1.43269e10i 1.97762 1.43683i
\(317\) −1.48596e9 + 7.57134e8i −0.147153 + 0.0749783i −0.526017 0.850474i \(-0.676315\pi\)
0.378863 + 0.925453i \(0.376315\pi\)
\(318\) 1.31851e9 1.31851e9i 0.128937 0.128937i
\(319\) −2.53547e10 8.23823e9i −2.44847 0.795557i
\(320\) −8.27784e8 + 2.39146e9i −0.0789436 + 0.228068i
\(321\) 1.10328e9 + 3.39555e9i 0.103912 + 0.319809i
\(322\) 4.71596e9 9.25560e9i 0.438679 0.860956i
\(323\) −6.79080e8 + 1.07556e8i −0.0623894 + 0.00988151i
\(324\) 2.69134e9i 0.244224i
\(325\) −8.90195e7 1.92530e8i −0.00797906 0.0172569i
\(326\) −3.70628e10 −3.28147
\(327\) −1.12885e9 7.12725e9i −0.0987288 0.623349i
\(328\) −9.14117e9 4.65766e9i −0.789781 0.402413i
\(329\) 1.10156e10 3.57917e9i 0.940206 0.305491i
\(330\) −1.13232e10 + 1.49758e10i −0.954800 + 1.26280i
\(331\) 6.19578e9 1.90687e10i 0.516160 1.58858i −0.265002 0.964248i \(-0.585373\pi\)
0.781162 0.624329i \(-0.214627\pi\)
\(332\) 2.31895e10 + 2.31895e10i 1.90870 + 1.90870i
\(333\) −1.75472e9 3.44382e9i −0.142702 0.280068i
\(334\) 1.71937e9 + 2.36651e9i 0.138160 + 0.190161i
\(335\) 1.66657e10 1.60418e10i 1.32326 1.27372i
\(336\) 6.82895e9 + 4.96152e9i 0.535792 + 0.389276i
\(337\) −1.00293e10 1.58848e9i −0.777590 0.123158i −0.244991 0.969525i \(-0.578785\pi\)
−0.532600 + 0.846367i \(0.678785\pi\)
\(338\) −3.64991e9 + 2.30446e10i −0.279651 + 1.76564i
\(339\) −5.89580e8 + 8.11487e8i −0.0446420 + 0.0614445i
\(340\) 6.54120e9 1.22543e10i 0.489488 0.917005i
\(341\) 1.89833e10 1.37922e10i 1.40396 1.02004i
\(342\) 9.70543e8 4.94517e8i 0.0709432 0.0361473i
\(343\) 1.03571e10 1.03571e10i 0.748279 0.748279i
\(344\) 5.03676e10 + 1.63654e10i 3.59681 + 1.16867i
\(345\) 6.29148e9 + 1.20016e8i 0.444095 + 0.00847158i
\(346\) −9.12401e9 2.80808e10i −0.636621 1.95932i
\(347\) −4.53054e9 + 8.89168e9i −0.312487 + 0.613290i −0.992821 0.119613i \(-0.961835\pi\)
0.680334 + 0.732902i \(0.261835\pi\)
\(348\) −3.08644e10 + 4.88845e9i −2.10446 + 0.333314i
\(349\) 1.73335e10i 1.16838i 0.811615 + 0.584192i \(0.198589\pi\)
−0.811615 + 0.584192i \(0.801411\pi\)
\(350\) −7.18815e8 + 1.88339e10i −0.0479010 + 1.25507i
\(351\) 5.55369e7 0.00365892
\(352\) −2.86625e9 1.80968e10i −0.186699 1.17877i
\(353\) 8.69236e9 + 4.42898e9i 0.559807 + 0.285236i 0.710911 0.703282i \(-0.248283\pi\)
−0.151104 + 0.988518i \(0.548283\pi\)
\(354\) −1.27886e10 + 4.15528e9i −0.814351 + 0.264599i
\(355\) 1.20435e10 + 1.72593e10i 0.758294 + 1.08670i
\(356\) 2.13816e9 6.58057e9i 0.133119 0.409698i
\(357\) 2.20253e9 + 2.20253e9i 0.135597 + 0.135597i
\(358\) −1.58969e10 3.11994e10i −0.967787 1.89939i
\(359\) −1.40206e10 1.92978e10i −0.844092 1.16179i −0.985134 0.171790i \(-0.945045\pi\)
0.141041 0.990004i \(-0.454955\pi\)
\(360\) −2.10201e9 + 1.18092e10i −0.125148 + 0.703086i
\(361\) −1.34949e10 9.80459e9i −0.794583 0.577299i
\(362\) −2.66387e10 4.21916e9i −1.55124 0.245692i
\(363\) −2.11881e9 + 1.33777e10i −0.122030 + 0.770466i
\(364\) −3.02855e8 + 4.16843e8i −0.0172516 + 0.0237447i
\(365\) 7.85962e9 3.81764e9i 0.442823 0.215091i
\(366\) −2.98658e8 + 2.16988e8i −0.0166437 + 0.0120924i
\(367\) −1.17484e10 + 5.98612e9i −0.647613 + 0.329975i −0.746756 0.665098i \(-0.768390\pi\)
0.0991432 + 0.995073i \(0.468390\pi\)
\(368\) −1.62947e10 + 1.62947e10i −0.888497 + 0.888497i
\(369\) 2.43172e9 + 7.90113e8i 0.131162 + 0.0426171i
\(370\) 9.19133e9 + 3.02387e10i 0.490424 + 1.61345i
\(371\) −7.26163e8 2.23490e9i −0.0383299 0.117967i
\(372\) 1.24867e10 2.45066e10i 0.652044 1.27971i
\(373\) 1.92923e10 3.05561e9i 0.996666 0.157856i 0.363270 0.931684i \(-0.381660\pi\)
0.633396 + 0.773828i \(0.281660\pi\)
\(374\) 2.53714e10i 1.29676i
\(375\) −1.04527e10 + 4.59309e9i −0.528571 + 0.232263i
\(376\) −6.02736e10 −3.01561
\(377\) −1.00875e8 6.36900e8i −0.00499365 0.0315287i
\(378\) −4.39694e9 2.24035e9i −0.215369 0.109736i
\(379\) 6.78465e9 2.20447e9i 0.328829 0.106843i −0.139950 0.990159i \(-0.544694\pi\)
0.468779 + 0.883315i \(0.344694\pi\)
\(380\) −5.85716e9 + 1.78034e9i −0.280900 + 0.0853824i
\(381\) 1.75606e9 5.40460e9i 0.0833374 0.256486i
\(382\) −3.59291e9 3.59291e9i −0.168730 0.168730i
\(383\) 1.30369e10 + 2.55864e10i 0.605870 + 1.18909i 0.966569 + 0.256405i \(0.0825380\pi\)
−0.360699 + 0.932682i \(0.617462\pi\)
\(384\) 8.92786e9 + 1.22881e10i 0.410603 + 0.565147i
\(385\) 1.03376e10 + 2.12827e10i 0.470520 + 0.968689i
\(386\) −1.22032e10 8.86614e9i −0.549698 0.399379i
\(387\) −1.30362e10 2.06473e9i −0.581174 0.0920490i
\(388\) −9.19928e9 + 5.80820e10i −0.405907 + 2.56280i
\(389\) 4.47455e8 6.15869e8i 0.0195412 0.0268961i −0.799135 0.601152i \(-0.794709\pi\)
0.818676 + 0.574256i \(0.194709\pi\)
\(390\) −4.47095e8 7.95821e7i −0.0193260 0.00343999i
\(391\) −6.87956e9 + 4.99830e9i −0.294343 + 0.213853i
\(392\) −2.28403e10 + 1.16377e10i −0.967291 + 0.492859i
\(393\) 9.51298e9 9.51298e9i 0.398792 0.398792i
\(394\) −6.89220e10 2.23941e10i −2.86005 0.929286i
\(395\) 2.22024e10 1.54927e10i 0.912035 0.636414i
\(396\) 8.53710e9 + 2.62745e10i 0.347160 + 1.06845i
\(397\) −9.35422e9 + 1.83587e10i −0.376570 + 0.739060i −0.999050 0.0435753i \(-0.986125\pi\)
0.622480 + 0.782636i \(0.286125\pi\)
\(398\) −7.92005e10 + 1.25441e10i −3.15643 + 0.499929i
\(399\) 1.37273e9i 0.0541619i
\(400\) 1.44276e10 3.92434e10i 0.563579 1.53294i
\(401\) −2.76174e10 −1.06808 −0.534042 0.845458i \(-0.679328\pi\)
−0.534042 + 0.845458i \(0.679328\pi\)
\(402\) −7.74725e9 4.89142e10i −0.296649 1.87297i
\(403\) 5.05703e8 + 2.57668e8i 0.0191723 + 0.00976880i
\(404\) 2.47828e10 8.05241e9i 0.930303 0.302274i
\(405\) 5.70147e7 2.98881e9i 0.00211918 0.111091i
\(406\) −1.77061e10 + 5.44937e10i −0.651656 + 2.00559i
\(407\) 2.80546e10 + 2.80546e10i 1.02241 + 1.02241i
\(408\) −7.35886e9 1.44426e10i −0.265564 0.521199i
\(409\) 1.80073e10 + 2.47849e10i 0.643510 + 0.885715i 0.998797 0.0490423i \(-0.0156169\pi\)
−0.355287 + 0.934757i \(0.615617\pi\)
\(410\) −1.84441e10 9.84529e9i −0.652714 0.348412i
\(411\) 5.09329e9 + 3.70049e9i 0.178497 + 0.129686i
\(412\) 1.05295e11 + 1.66772e10i 3.65444 + 0.578806i
\(413\) −2.65096e9 + 1.67375e10i −0.0911176 + 0.575294i
\(414\) 7.91872e9 1.08992e10i 0.269559 0.371016i
\(415\) 2.52613e10 + 2.62438e10i 0.851655 + 0.884779i
\(416\) 3.58541e8 2.60495e8i 0.0119720 0.00869813i
\(417\) 2.44175e10 1.24413e10i 0.807526 0.411455i
\(418\) −7.90640e9 + 7.90640e9i −0.258984 + 0.258984i
\(419\) 2.44771e10 + 7.95311e9i 0.794154 + 0.258036i 0.677872 0.735180i \(-0.262902\pi\)
0.116282 + 0.993216i \(0.462902\pi\)
\(420\) 2.21222e10 + 1.67266e10i 0.710938 + 0.537539i
\(421\) 3.14949e9 + 9.69314e9i 0.100256 + 0.308558i 0.988588 0.150645i \(-0.0481351\pi\)
−0.888331 + 0.459203i \(0.848135\pi\)
\(422\) −2.84289e10 + 5.57948e10i −0.896417 + 1.75932i
\(423\) 1.48365e10 2.34988e9i 0.463416 0.0733979i
\(424\) 1.22286e10i 0.378368i
\(425\) 7.52380e9 1.34701e10i 0.230612 0.412873i
\(426\) 4.50579e10 1.36815
\(427\) 7.27781e7 + 4.59503e8i 0.00218922 + 0.0138222i
\(428\) −3.82764e10 1.95028e10i −1.14066 0.581195i
\(429\) −5.42184e8 + 1.76166e8i −0.0160073 + 0.00520109i
\(430\) 1.01988e11 + 3.53022e10i 2.98315 + 1.03259i
\(431\) 8.28659e9 2.55035e10i 0.240141 0.739079i −0.756256 0.654275i \(-0.772974\pi\)
0.996398 0.0848034i \(-0.0270262\pi\)
\(432\) 7.74094e9 + 7.74094e9i 0.222259 + 0.222259i
\(433\) −2.29318e10 4.50061e10i −0.652358 1.28032i −0.945925 0.324386i \(-0.894842\pi\)
0.293567 0.955938i \(-0.405158\pi\)
\(434\) −2.96430e10 4.08001e10i −0.835532 1.15001i
\(435\) −3.43794e10 + 4.77492e9i −0.960156 + 0.133355i
\(436\) 7.02436e10 + 5.10349e10i 1.94384 + 1.41228i
\(437\) 3.70145e9 + 5.86252e8i 0.101495 + 0.0160753i
\(438\) 2.92641e9 1.84766e10i 0.0795132 0.502027i
\(439\) 2.69901e10 3.71487e10i 0.726686 1.00020i −0.272589 0.962131i \(-0.587880\pi\)
0.999275 0.0380674i \(-0.0121202\pi\)
\(440\) −1.69383e10 1.21956e11i −0.451917 3.25381i
\(441\) 5.16849e9 3.75513e9i 0.136650 0.0992820i
\(442\) 5.46796e8 2.78607e8i 0.0143264 0.00729965i
\(443\) −3.22221e10 + 3.22221e10i −0.836640 + 0.836640i −0.988415 0.151775i \(-0.951501\pi\)
0.151775 + 0.988415i \(0.451501\pi\)
\(444\) 4.42296e10 + 1.43711e10i 1.13810 + 0.369792i
\(445\) 2.51389e9 7.26262e9i 0.0641072 0.185205i
\(446\) −1.17617e10 3.61988e10i −0.297256 0.914860i
\(447\) −1.42362e10 + 2.79402e10i −0.356586 + 0.699840i
\(448\) 6.74392e9 1.06813e9i 0.167417 0.0265163i
\(449\) 4.25193e10i 1.04617i −0.852281 0.523084i \(-0.824782\pi\)
0.852281 0.523084i \(-0.175218\pi\)
\(450\) −4.74184e9 + 2.39795e10i −0.115637 + 0.584776i
\(451\) −2.62462e10 −0.634396
\(452\) −1.88800e9 1.19204e10i −0.0452323 0.285586i
\(453\) −2.30177e10 1.17281e10i −0.546600 0.278506i
\(454\) −6.32387e10 + 2.05475e10i −1.48854 + 0.483655i
\(455\) −3.45160e8 + 4.56501e8i −0.00805331 + 0.0106511i
\(456\) −2.20747e9 + 6.79389e9i −0.0510547 + 0.157130i
\(457\) −1.21288e10 1.21288e10i −0.278069 0.278069i 0.554269 0.832338i \(-0.312998\pi\)
−0.832338 + 0.554269i \(0.812998\pi\)
\(458\) −8.14036e9 1.59763e10i −0.185004 0.363091i
\(459\) 2.37448e9 + 3.26819e9i 0.0534955 + 0.0736303i
\(460\) −5.45495e10 + 5.25073e10i −1.21831 + 1.17270i
\(461\) 3.57442e10 + 2.59697e10i 0.791410 + 0.574993i 0.908382 0.418142i \(-0.137319\pi\)
−0.116971 + 0.993135i \(0.537319\pi\)
\(462\) 5.00322e10 + 7.92432e9i 1.09820 + 0.173938i
\(463\) −2.16474e9 + 1.36676e10i −0.0471065 + 0.297419i −0.999982 0.00594179i \(-0.998109\pi\)
0.952876 + 0.303361i \(0.0981087\pi\)
\(464\) 7.47132e10 1.02834e11i 1.61185 2.21852i
\(465\) 1.43860e10 2.69508e10i 0.307701 0.576447i
\(466\) 3.06151e10 2.22432e10i 0.649221 0.471687i
\(467\) −5.82047e10 + 2.96568e10i −1.22374 + 0.623529i −0.941888 0.335928i \(-0.890950\pi\)
−0.281857 + 0.959457i \(0.590950\pi\)
\(468\) −4.72512e8 + 4.72512e8i −0.00984984 + 0.00984984i
\(469\) −5.93572e10 1.92863e10i −1.22682 0.398619i
\(470\) −1.22808e11 2.34268e9i −2.51671 0.0480089i
\(471\) −5.68645e9 1.75011e10i −0.115547 0.355616i
\(472\) 4.00353e10 7.85738e10i 0.806632 1.58310i
\(473\) 1.33817e11 2.11945e10i 2.67341 0.423426i
\(474\) 5.79627e10i 1.14825i
\(475\) −6.54226e9 + 1.85304e9i −0.128515 + 0.0364007i
\(476\) −3.74786e10 −0.730055
\(477\) −4.76756e8 3.01012e9i −0.00920922 0.0581447i
\(478\) −2.17714e10 1.10931e10i −0.417036 0.212491i
\(479\) −5.41017e10 + 1.75787e10i −1.02771 + 0.333922i −0.773883 0.633329i \(-0.781688\pi\)
−0.253823 + 0.967251i \(0.581688\pi\)
\(480\) −1.36509e10 1.95629e10i −0.257156 0.368526i
\(481\) −2.96553e8 + 9.12695e8i −0.00554015 + 0.0170508i
\(482\) 9.40010e10 + 9.40010e10i 1.74158 + 1.74158i
\(483\) −7.70787e9 1.51276e10i −0.141627 0.277959i
\(484\) −9.57912e10 1.31845e11i −1.74560 2.40261i
\(485\) −1.14465e10 + 6.43068e10i −0.206874 + 1.16222i
\(486\) −5.17774e9 3.76185e9i −0.0928100 0.0674304i
\(487\) 4.94128e10 + 7.82622e9i 0.878463 + 0.139135i 0.579346 0.815082i \(-0.303308\pi\)
0.299117 + 0.954216i \(0.403308\pi\)
\(488\) 3.78728e8 2.39120e9i 0.00667803 0.0421634i
\(489\) −3.56059e10 + 4.90073e10i −0.622710 + 0.857087i
\(490\) −4.69895e10 + 2.28241e10i −0.815110 + 0.395922i
\(491\) 3.05914e10 2.22260e10i 0.526349 0.382415i −0.292642 0.956222i \(-0.594534\pi\)
0.818990 + 0.573808i \(0.194534\pi\)
\(492\) −2.74116e10 + 1.39669e10i −0.467815 + 0.238363i
\(493\) 3.31669e10 3.31669e10i 0.561457 0.561457i
\(494\) −2.57217e8 8.35749e7i −0.00431909 0.00140336i
\(495\) 8.92409e9 + 2.93595e10i 0.148643 + 0.489021i
\(496\) 3.45720e10 + 1.06402e11i 0.571212 + 1.75801i
\(497\) 2.57792e10 5.05946e10i 0.422517 0.829236i
\(498\) 7.70264e10 1.21998e10i 1.25234 0.198351i
\(499\) 8.30082e10i 1.33881i 0.742898 + 0.669405i \(0.233451\pi\)
−0.742898 + 0.669405i \(0.766549\pi\)
\(500\) 4.98541e10 1.28011e11i 0.797665 2.04817i
\(501\) 4.78095e9 0.0758863
\(502\) 1.48816e8 + 9.39587e8i 0.00234334 + 0.0147952i
\(503\) 3.15882e10 + 1.60950e10i 0.493461 + 0.251431i 0.682968 0.730449i \(-0.260689\pi\)
−0.189507 + 0.981879i \(0.560689\pi\)
\(504\) 3.07790e10 1.00007e10i 0.477015 0.154992i
\(505\) 2.76926e10 8.41743e9i 0.425792 0.129424i
\(506\) −4.27344e10 + 1.31523e11i −0.651893 + 2.00632i
\(507\) 2.69649e10 + 2.69649e10i 0.408101 + 0.408101i
\(508\) 3.10421e10 + 6.09235e10i 0.466118 + 0.914808i
\(509\) −1.94805e10 2.68126e10i −0.290221 0.399455i 0.638865 0.769319i \(-0.279404\pi\)
−0.929086 + 0.369864i \(0.879404\pi\)
\(510\) −1.44323e10 2.97128e10i −0.213332 0.439201i
\(511\) −1.90727e10 1.38571e10i −0.279724 0.203231i
\(512\) −1.51214e11 2.39499e10i −2.20045 0.348517i
\(513\) 2.78503e8 1.75840e9i 0.00402125 0.0253892i
\(514\) 9.10709e10 1.25348e11i 1.30475 1.79583i
\(515\) 1.16580e11 + 2.07511e10i 1.65728 + 0.294993i
\(516\) 1.28480e11 9.33460e10i 1.81232 1.31673i
\(517\) −1.37389e11 + 7.00034e10i −1.92305 + 0.979843i
\(518\) 6.02966e10 6.02966e10i 0.837479 0.837479i
\(519\) −4.58959e10 1.49125e10i −0.632564 0.205532i
\(520\) 2.44235e9 1.70426e9i 0.0334037 0.0233089i
\(521\) −3.81591e10 1.17442e11i −0.517902 1.59394i −0.777939 0.628339i \(-0.783735\pi\)
0.260037 0.965599i \(-0.416265\pi\)
\(522\) −3.37364e10 + 6.62115e10i −0.454378 + 0.891766i
\(523\) 7.43533e10 1.17764e10i 0.993787 0.157400i 0.361697 0.932296i \(-0.382197\pi\)
0.632090 + 0.774895i \(0.282197\pi\)
\(524\) 1.61874e11i 2.14710i
\(525\) 2.42131e10 + 1.90440e10i 0.318722 + 0.250681i
\(526\) 2.40491e11 3.14163
\(527\) 6.45825e9 + 4.07758e10i 0.0837284 + 0.528640i
\(528\) −1.00126e11 5.10170e10i −1.28829 0.656416i
\(529\) −3.03963e10 + 9.87634e9i −0.388148 + 0.126117i
\(530\) −4.75297e8 + 2.49159e10i −0.00602367 + 0.315772i
\(531\) −6.79149e9 + 2.09020e10i −0.0854253 + 0.262912i
\(532\) 1.16793e10 + 1.16793e10i 0.145804 + 0.145804i
\(533\) −2.88213e8 5.65649e8i −0.00357112 0.00700871i
\(534\) −9.67141e9 1.33116e10i −0.118939 0.163706i
\(535\) −4.20939e10 2.24693e10i −0.513812 0.274268i
\(536\) 2.62755e11 + 1.90903e11i 3.18341 + 2.31288i
\(537\) −5.65261e10 8.95286e9i −0.679754 0.107663i
\(538\) −3.21933e9 + 2.03260e10i −0.0384270 + 0.242618i
\(539\) −3.85464e10 + 5.30546e10i −0.456698 + 0.628591i
\(540\) 2.49440e10 + 2.59141e10i 0.293353 + 0.304763i
\(541\) 7.44451e10 5.40876e10i 0.869055 0.631405i −0.0612781 0.998121i \(-0.519518\pi\)
0.930333 + 0.366715i \(0.119518\pi\)
\(542\) −2.00708e11 + 1.02266e11i −2.32577 + 1.18504i
\(543\) −3.11704e10 + 3.11704e10i −0.358544 + 0.358544i
\(544\) 3.06588e10 + 9.96165e9i 0.350074 + 0.113746i
\(545\) 7.69264e10 + 5.81639e10i 0.871946 + 0.659276i
\(546\) 3.78627e8 + 1.16529e9i 0.00426031 + 0.0131119i
\(547\) 2.64457e10 5.19026e10i 0.295397 0.579749i −0.694837 0.719168i \(-0.744523\pi\)
0.990234 + 0.139419i \(0.0445234\pi\)
\(548\) −7.48182e10 + 1.18500e10i −0.829632 + 0.131401i
\(549\) 6.03366e8i 0.00664189i
\(550\) −2.97717e10 2.49144e11i −0.325352 2.72270i
\(551\) −2.06713e10 −0.224265
\(552\) 1.38212e10 + 8.72639e10i 0.148864 + 0.939893i
\(553\) −6.50850e10 3.31625e10i −0.695954 0.354606i
\(554\) −2.92510e10 + 9.50421e9i −0.310528 + 0.100897i
\(555\) 4.88138e10 + 1.68965e10i 0.514483 + 0.178084i
\(556\) −1.01894e11 + 3.13597e11i −1.06623 + 3.28151i
\(557\) 4.79795e9 + 4.79795e9i 0.0498466 + 0.0498466i 0.731591 0.681744i \(-0.238778\pi\)
−0.681744 + 0.731591i \(0.738778\pi\)
\(558\) −2.96936e10 5.82769e10i −0.306285 0.601118i
\(559\) 1.92623e9 + 2.65123e9i 0.0197270 + 0.0271519i
\(560\) −1.11738e11 + 1.55192e10i −1.13619 + 0.157804i
\(561\) −3.35480e10 2.43740e10i −0.338700 0.246080i
\(562\) −1.88767e11 2.98977e10i −1.89226 0.299704i
\(563\) 1.72192e10 1.08718e11i 0.171388 1.08210i −0.740618 0.671926i \(-0.765467\pi\)
0.912006 0.410176i \(-0.134533\pi\)
\(564\) −1.06237e11 + 1.46223e11i −1.04993 + 1.44511i
\(565\) −1.84416e9 1.32779e10i −0.0180969 0.130298i
\(566\) −1.80242e11 + 1.30953e11i −1.75626 + 1.27600i
\(567\) −7.18646e9 + 3.66168e9i −0.0695317 + 0.0354282i
\(568\) −2.08946e11 + 2.08946e11i −2.00743 + 2.00743i
\(569\) 1.07319e11 + 3.48701e10i 1.02383 + 0.332663i 0.772349 0.635199i \(-0.219082\pi\)
0.251483 + 0.967862i \(0.419082\pi\)
\(570\) −4.76179e9 + 1.37568e10i −0.0451098 + 0.130322i
\(571\) −5.88298e10 1.81059e11i −0.553417 1.70324i −0.700087 0.714058i \(-0.746855\pi\)
0.146669 0.989186i \(-0.453145\pi\)
\(572\) 3.11411e9 6.11179e9i 0.0290904 0.0570932i
\(573\) −8.20247e9 + 1.29914e9i −0.0760898 + 0.0120514i
\(574\) 5.64098e10i 0.519645i
\(575\) −6.16911e10 + 5.71553e10i −0.564354 + 0.522859i
\(576\) 8.85534e9 0.0804480
\(577\) −1.93795e10 1.22357e11i −0.174839 1.10389i −0.906495 0.422217i \(-0.861252\pi\)
0.731656 0.681674i \(-0.238748\pi\)
\(578\) −1.38068e11 7.03491e10i −1.23703 0.630299i
\(579\) −2.34469e10 + 7.61838e9i −0.208628 + 0.0677873i
\(580\) 2.51878e11 3.33128e11i 2.22576 2.94374i
\(581\) 3.03706e10 9.34711e10i 0.266532 0.820300i
\(582\) 9.88826e10 + 9.88826e10i 0.861843 + 0.861843i
\(583\) 1.42027e10 + 2.78743e10i 0.122941 + 0.241285i
\(584\) 7.21108e10 + 9.92520e10i 0.619939 + 0.853273i
\(585\) −5.34748e8 + 5.14728e8i −0.00456590 + 0.00439496i
\(586\) 1.93314e11 + 1.40451e11i 1.63935 + 1.19106i
\(587\) −6.50213e10 1.02984e10i −0.547650 0.0867393i −0.123523 0.992342i \(-0.539419\pi\)
−0.424128 + 0.905602i \(0.639419\pi\)
\(588\) −1.20250e10 + 7.59229e10i −0.100595 + 0.635131i
\(589\) 1.06942e10 1.47194e10i 0.0888564 0.122300i
\(590\) 8.46261e10 1.58538e11i 0.698387 1.30836i
\(591\) −9.58238e10 + 6.96201e10i −0.785459 + 0.570669i
\(592\) −1.68550e11 + 8.58803e10i −1.37227 + 0.699208i
\(593\) −2.34786e10 + 2.34786e10i −0.189869 + 0.189869i −0.795639 0.605771i \(-0.792865\pi\)
0.605771 + 0.795639i \(0.292865\pi\)
\(594\) 6.24810e10 + 2.03013e10i 0.501883 + 0.163072i
\(595\) −4.16211e10 7.93966e8i −0.332082 0.00633482i
\(596\) −1.16594e11 3.58840e11i −0.924042 2.84391i
\(597\) −5.95003e10 + 1.16776e11i −0.468405 + 0.919297i
\(598\) −3.30381e9 + 5.23273e8i −0.0258351 + 0.00409188i
\(599\) 8.17773e10i 0.635222i 0.948221 + 0.317611i \(0.102881\pi\)
−0.948221 + 0.317611i \(0.897119\pi\)
\(600\) −8.92103e10 1.33189e11i −0.688351 1.02769i
\(601\) 6.32173e10 0.484549 0.242275 0.970208i \(-0.422107\pi\)
0.242275 + 0.970208i \(0.422107\pi\)
\(602\) −4.55523e10 2.87606e11i −0.346836 2.18984i
\(603\) −7.21208e10 3.67474e10i −0.545495 0.277944i
\(604\) 2.95620e11 9.60528e10i 2.22119 0.721709i
\(605\) −1.03586e11 1.48447e11i −0.773177 1.10803i
\(606\) 1.91487e10 5.89337e10i 0.141987 0.436992i
\(607\) −2.21158e10 2.21158e10i −0.162910 0.162910i 0.620945 0.783855i \(-0.286749\pi\)
−0.783855 + 0.620945i \(0.786749\pi\)
\(608\) −6.44977e9 1.26584e10i −0.0471987 0.0926327i
\(609\) 5.50456e10 + 7.57638e10i 0.400178 + 0.550798i
\(610\) 8.64600e8 4.85735e9i 0.00624447 0.0350816i
\(611\) −3.01738e9 2.19225e9i −0.0216503 0.0157299i
\(612\) −4.80082e10 7.60376e9i −0.342224 0.0542029i
\(613\) −3.35050e9 + 2.11542e10i −0.0237284 + 0.149815i −0.996708 0.0810764i \(-0.974164\pi\)
0.972980 + 0.230891i \(0.0741642\pi\)
\(614\) −1.95237e11 + 2.68720e11i −1.37369 + 1.89072i
\(615\) −3.07373e10 + 1.49300e10i −0.214865 + 0.104366i
\(616\) −2.68760e11 + 1.95266e11i −1.86656 + 1.35614i
\(617\) −1.23068e11 + 6.27063e10i −0.849190 + 0.432684i −0.823723 0.566992i \(-0.808107\pi\)
−0.0254664 + 0.999676i \(0.508107\pi\)
\(618\) 1.79262e11 1.79262e11i 1.22895 1.22895i
\(619\) −8.03479e10 2.61066e10i −0.547283 0.177823i 0.0223084 0.999751i \(-0.492898\pi\)
−0.569591 + 0.821928i \(0.692898\pi\)
\(620\) 1.06902e11 + 3.51697e11i 0.723465 + 2.38013i
\(621\) −6.80429e9 2.09414e10i −0.0457526 0.140812i
\(622\) 2.07506e11 4.07254e11i 1.38634 2.72084i
\(623\) −2.04806e10 + 3.24381e9i −0.135954 + 0.0215329i
\(624\) 2.71811e9i 0.0179279i
\(625\) 5.80762e10 1.41104e11i 0.380608 0.924736i
\(626\) 2.56464e11 1.67005
\(627\) 2.85884e9 + 1.80500e10i 0.0184978 + 0.116790i
\(628\) 1.97281e11 + 1.00520e11i 1.26837 + 0.646269i
\(629\) −6.63887e10 + 2.15710e10i −0.424123 + 0.137806i
\(630\) 6.31010e10 1.91802e10i 0.400566 0.121756i
\(631\) 1.70632e10 5.25152e10i 0.107632 0.331259i −0.882707 0.469924i \(-0.844281\pi\)
0.990339 + 0.138665i \(0.0442813\pi\)
\(632\) 2.68789e11 + 2.68789e11i 1.68478 + 1.68478i
\(633\) 4.64648e10 + 9.11923e10i 0.289407 + 0.567993i
\(634\) −2.80482e10 3.86050e10i −0.173599 0.238939i
\(635\) 3.31825e10 + 6.83150e10i 0.204087 + 0.420166i
\(636\) 2.96666e10 + 2.15541e10i 0.181317 + 0.131735i
\(637\) −1.56670e9 2.48141e8i −0.00951541 0.00150709i
\(638\) 1.19329e11 7.53411e11i 0.720214 4.54725i
\(639\) 4.32867e10 5.95790e10i 0.259627 0.357347i
\(640\) −1.99853e11 3.55735e10i −1.19122 0.212035i
\(641\) 8.60807e10 6.25413e10i 0.509887 0.370454i −0.302894 0.953024i \(-0.597953\pi\)
0.812781 + 0.582570i \(0.197953\pi\)
\(642\) −9.10217e10 + 4.63779e10i −0.535803 + 0.273005i
\(643\) −2.01543e11 + 2.01543e11i −1.17902 + 1.17902i −0.199031 + 0.979993i \(0.563779\pi\)
−0.979993 + 0.199031i \(0.936221\pi\)
\(644\) 1.94286e11 + 6.31272e10i 1.12953 + 0.367006i
\(645\) 1.44658e11 1.00942e11i 0.835802 0.583219i
\(646\) −6.07916e9 1.87097e10i −0.0349071 0.107433i
\(647\) −1.14125e11 + 2.23982e11i −0.651272 + 1.27819i 0.295208 + 0.955433i \(0.404611\pi\)
−0.946480 + 0.322761i \(0.895389\pi\)
\(648\) 4.14554e10 6.56588e9i 0.235115 0.0372386i
\(649\) 2.25601e11i 1.27164i
\(650\) 5.04253e9 3.37751e9i 0.0282485 0.0189209i
\(651\) −8.24266e10 −0.458927
\(652\) −1.14020e11 7.19895e11i −0.630945 3.98363i
\(653\) 8.44608e10 + 4.30349e10i 0.464518 + 0.236684i 0.670554 0.741861i \(-0.266056\pi\)
−0.206036 + 0.978544i \(0.566056\pi\)
\(654\) 1.96367e11 6.38036e10i 1.07339 0.348766i
\(655\) −3.42923e9 + 1.79766e11i −0.0186308 + 0.976660i
\(656\) 3.86701e10 1.19014e11i 0.208814 0.642664i
\(657\) −2.16198e10 2.16198e10i −0.116035 0.116035i
\(658\) 1.50455e11 + 2.95285e11i 0.802608 + 1.57521i
\(659\) −1.81157e11 2.49342e11i −0.960538 1.32207i −0.946684 0.322163i \(-0.895590\pi\)
−0.0138540 0.999904i \(-0.504410\pi\)
\(660\) −3.25719e11 1.73866e11i −1.71660 0.916301i
\(661\) −1.85926e11 1.35083e11i −0.973944 0.707611i −0.0175966 0.999845i \(-0.505601\pi\)
−0.956347 + 0.292234i \(0.905601\pi\)
\(662\) 5.66623e11 + 8.97443e10i 2.95027 + 0.467277i
\(663\) 1.56907e8 9.90669e8i 0.000812058 0.00512713i
\(664\) −3.00619e11 + 4.13767e11i −1.54648 + 2.12855i
\(665\) 1.27228e10 + 1.32176e10i 0.0650573 + 0.0675877i
\(666\) 8.94701e10 6.50039e10i 0.454759 0.330402i
\(667\) −2.27799e11 + 1.16069e11i −1.15093 + 0.586427i
\(668\) −4.06767e10 + 4.06767e10i −0.204287 + 0.204287i
\(669\) −5.91641e10 1.92236e10i −0.295361 0.0959687i
\(670\) 5.27945e11 + 3.99178e11i 2.61993 + 1.98092i
\(671\) −1.91392e9 5.89043e9i −0.00944132 0.0290574i
\(672\) −2.92200e10 + 5.73475e10i −0.143286 + 0.281214i
\(673\) 7.75690e10 1.22857e10i 0.378118 0.0598881i 0.0355173 0.999369i \(-0.488692\pi\)
0.342601 + 0.939481i \(0.388692\pi\)
\(674\) 2.90543e11i 1.40790i
\(675\) 2.71520e10 + 2.93068e10i 0.130794 + 0.141174i
\(676\) −4.58839e11 −2.19722
\(677\) 3.37815e10 + 2.13288e11i 0.160814 + 1.01534i 0.927637 + 0.373483i \(0.121836\pi\)
−0.766823 + 0.641859i \(0.778164\pi\)
\(678\) −2.55720e10 1.30296e10i −0.121017 0.0616612i
\(679\) 1.67607e11 5.44589e10i 0.788522 0.256206i
\(680\) 2.04713e11 + 7.08598e10i 0.957438 + 0.331409i
\(681\) −3.35833e10 + 1.03359e11i −0.156147 + 0.480572i
\(682\) 4.74745e11 + 4.74745e11i 2.19443 + 2.19443i
\(683\) 1.23808e11 + 2.42987e11i 0.568940 + 1.11661i 0.978869 + 0.204490i \(0.0655535\pi\)
−0.409929 + 0.912117i \(0.634447\pi\)
\(684\) 1.25911e10 + 1.73301e10i 0.0575227 + 0.0791731i
\(685\) −8.33389e10 + 1.15748e10i −0.378517 + 0.0525718i
\(686\) 3.39057e11 + 2.46339e11i 1.53100 + 1.11234i
\(687\) −2.89455e10 4.58451e9i −0.129943 0.0205810i
\(688\) −1.01053e11 + 6.38024e11i −0.451020 + 2.84763i
\(689\) −4.44777e8 + 6.12182e8i −0.00197363 + 0.00271646i
\(690\) 2.47691e10 + 1.78338e11i 0.109273 + 0.786768i
\(691\) −2.04202e11 + 1.48362e11i −0.895671 + 0.650743i −0.937350 0.348388i \(-0.886729\pi\)
0.0416793 + 0.999131i \(0.486729\pi\)
\(692\) 5.17362e11 2.63609e11i 2.25616 1.14957i
\(693\) 5.85435e10 5.85435e10i 0.253832 0.253832i
\(694\) −2.71562e11 8.82359e10i −1.17066 0.380371i
\(695\) −1.19800e11 + 3.46101e11i −0.513472 + 1.48342i
\(696\) −1.50596e11 4.63486e11i −0.641765 1.97515i
\(697\) 2.09643e10 4.11448e10i 0.0888280 0.174335i
\(698\) −4.89855e11 + 7.75855e10i −2.06370 + 0.326858i
\(699\) 6.18504e10i 0.259080i
\(700\) −3.68035e11 + 4.39787e10i −1.53284 + 0.183168i
\(701\) 2.92361e11 1.21073 0.605365 0.795948i \(-0.293027\pi\)
0.605365 + 0.795948i \(0.293027\pi\)
\(702\) 2.48584e8 + 1.56950e9i 0.00102359 + 0.00646269i
\(703\) 2.74105e10 + 1.39664e10i 0.112227 + 0.0571823i
\(704\) −8.64512e10 + 2.80897e10i −0.351950 + 0.114355i
\(705\) −1.21078e11 + 1.60135e11i −0.490125 + 0.648230i
\(706\) −8.62580e10 + 2.65475e11i −0.347201 + 1.06857i
\(707\) −5.52197e10 5.52197e10i −0.221012 0.221012i
\(708\) −1.20054e11 2.35619e11i −0.477796 0.937728i
\(709\) 1.14553e9 + 1.57668e9i 0.00453336 + 0.00623963i 0.811278 0.584661i \(-0.198772\pi\)
−0.806744 + 0.590901i \(0.798772\pi\)
\(710\) −4.33850e11 + 4.17608e11i −1.70729 + 1.64337i
\(711\) −7.66426e10 5.56841e10i −0.299910 0.217898i
\(712\) 1.06578e11 + 1.68804e10i 0.414715 + 0.0656843i
\(713\) 3.52019e10 2.22256e11i 0.136210 0.859994i
\(714\) −5.23861e10 + 7.21033e10i −0.201569 + 0.277436i
\(715\) 3.58779e9 6.72135e9i 0.0137278 0.0257177i
\(716\) 5.57100e11 4.04757e11i 2.11973 1.54008i
\(717\) −3.55836e10 + 1.81307e10i −0.134640 + 0.0686023i
\(718\) 4.82608e11 4.82608e11i 1.81592 1.81592i
\(719\) 2.58911e11 + 8.41252e10i 0.968801 + 0.314783i 0.750332 0.661061i \(-0.229894\pi\)
0.218469 + 0.975844i \(0.429894\pi\)
\(720\) −1.46280e11 2.79045e9i −0.544321 0.0103835i
\(721\) −9.87273e10 3.03851e11i −0.365339 1.12440i
\(722\) 2.16679e11 4.25257e11i 0.797387 1.56496i
\(723\) 2.14601e11 3.39895e10i 0.785377 0.124392i
\(724\) 5.30400e11i 1.93041i
\(725\) 2.86775e11 3.64613e11i 1.03798 1.31971i
\(726\) −3.87544e11 −1.39500
\(727\) 4.99607e10 + 3.15439e11i 0.178851 + 1.12922i 0.899823 + 0.436255i \(0.143695\pi\)
−0.720972 + 0.692964i \(0.756305\pi\)
\(728\) −7.15959e9 3.64800e9i −0.0254896 0.0129876i
\(729\) −9.94839e9 + 3.23243e9i −0.0352243 + 0.0114451i
\(730\) 1.43068e11 + 2.05029e11i 0.503793 + 0.721978i
\(731\) −7.36614e10 + 2.26707e11i −0.257971 + 0.793953i
\(732\) −5.13349e9 5.13349e9i −0.0178800 0.0178800i
\(733\) 8.86164e10 + 1.73919e11i 0.306971 + 0.602465i 0.992027 0.126025i \(-0.0402221\pi\)
−0.685056 + 0.728491i \(0.740222\pi\)
\(734\) −2.21757e11 3.05223e11i −0.764001 1.05156i
\(735\) −1.49625e10 + 8.40598e10i −0.0512690 + 0.288031i
\(736\) −1.42153e11 1.03281e11i −0.484447 0.351971i
\(737\) 8.20652e11 + 1.29978e11i 2.78156 + 0.440556i
\(738\) −1.14446e10 + 7.22582e10i −0.0385811 + 0.243591i
\(739\) −3.31602e10 + 4.56411e10i −0.111183 + 0.153031i −0.860982 0.508635i \(-0.830150\pi\)
0.749799 + 0.661666i \(0.230150\pi\)
\(740\) −5.59069e11 + 2.71555e11i −1.86440 + 0.905590i
\(741\) −3.57614e8 + 2.59822e8i −0.00118616 + 0.000861794i
\(742\) 5.99091e10 3.05252e10i 0.197641 0.100703i
\(743\) −1.77081e11 + 1.77081e11i −0.581053 + 0.581053i −0.935193 0.354140i \(-0.884774\pi\)
0.354140 + 0.935193i \(0.384774\pi\)
\(744\) 4.07944e11 + 1.32549e11i 1.33140 + 0.432598i
\(745\) −1.21879e11 4.00972e11i −0.395645 1.30164i
\(746\) 1.72706e11 + 5.31535e11i 0.557638 + 1.71623i
\(747\) 5.78669e10 1.13570e11i 0.185844 0.364739i
\(748\) 4.92805e11 7.80527e10i 1.57423 0.249334i
\(749\) 1.28741e11i 0.409061i
\(750\) −1.76590e11 2.74840e11i −0.558110 0.868630i
\(751\) −2.87996e11 −0.905370 −0.452685 0.891670i \(-0.649534\pi\)
−0.452685 + 0.891670i \(0.649534\pi\)
\(752\) −1.15009e11 7.26138e11i −0.359634 2.27064i
\(753\) 1.38536e9 + 7.05875e8i 0.00430906 + 0.00219557i
\(754\) 1.75476e10 5.70156e9i 0.0542916 0.0176404i
\(755\) 3.30330e11 1.00407e11i 1.01662 0.309012i
\(756\) 2.99891e10 9.22968e10i 0.0918070 0.282553i
\(757\) 2.74645e11 + 2.74645e11i 0.836351 + 0.836351i 0.988377 0.152026i \(-0.0485797\pi\)
−0.152026 + 0.988377i \(0.548580\pi\)
\(758\) 9.26677e10 + 1.81871e11i 0.280706 + 0.550916i
\(759\) 1.32855e11 + 1.82859e11i 0.400324 + 0.550998i
\(760\) −4.17123e10 8.58758e10i −0.125029 0.257405i
\(761\) −8.06138e10 5.85693e10i −0.240365 0.174635i 0.461081 0.887358i \(-0.347462\pi\)
−0.701446 + 0.712723i \(0.747462\pi\)
\(762\) 1.60597e11 + 2.54361e10i 0.476341 + 0.0754450i
\(763\) 4.07049e10 2.57001e11i 0.120102 0.758291i
\(764\) 5.87341e10 8.08405e10i 0.172392 0.237277i
\(765\) −5.31535e10 9.46123e9i −0.155198 0.0276250i
\(766\) −6.64731e11 + 4.82955e11i −1.93077 + 1.40279i
\(767\) 4.86209e9 2.47736e9i 0.0140489 0.00715825i
\(768\) −2.73031e11 + 2.73031e11i −0.784814 + 0.784814i
\(769\) 5.09607e11 + 1.65581e11i 1.45724 + 0.473485i 0.927225 0.374506i \(-0.122188\pi\)
0.530011 + 0.847991i \(0.322188\pi\)
\(770\) −5.55190e11 + 3.87409e11i −1.57935 + 1.10206i
\(771\) −7.82542e10 2.40842e11i −0.221457 0.681575i
\(772\) 1.34671e11 2.64306e11i 0.379144 0.744112i
\(773\) −5.69565e11 + 9.02103e10i −1.59524 + 0.252661i −0.889882 0.456191i \(-0.849213\pi\)
−0.705357 + 0.708852i \(0.749213\pi\)
\(774\) 3.77651e11i 1.05227i
\(775\) 1.11267e11 + 3.92834e11i 0.308432 + 1.08894i
\(776\) −9.17093e11 −2.52910
\(777\) −2.18024e10 1.37655e11i −0.0598164 0.377666i
\(778\) 1.94076e10 + 9.88866e9i 0.0529728 + 0.0269910i
\(779\) −1.93548e10 + 6.28876e9i −0.0525581 + 0.0170772i
\(780\) 1.70331e8 8.92903e9i 0.000460166 0.0241227i
\(781\) −2.33602e11 + 7.18954e11i −0.627875 + 1.93240i
\(782\) −1.72048e11 1.72048e11i −0.460068 0.460068i
\(783\) 5.51395e10 + 1.08217e11i 0.146695 + 0.287906i
\(784\) −1.83786e11 2.52959e11i −0.486460 0.669555i
\(785\) 2.16957e11 + 1.15810e11i 0.571342 + 0.304976i
\(786\) 3.11422e11 + 2.26262e11i 0.815943 + 0.592817i
\(787\) −4.87178e11 7.71614e10i −1.26996 0.201141i −0.515156 0.857096i \(-0.672266\pi\)
−0.754800 + 0.655955i \(0.772266\pi\)
\(788\) 2.22943e11 1.40761e12i 0.578216 3.65071i
\(789\) 2.31037e11 3.17995e11i 0.596174 0.820564i
\(790\) 5.37211e11 + 5.58106e11i 1.37923 + 1.43287i
\(791\) −2.92613e10 + 2.12596e10i −0.0747459 + 0.0543061i
\(792\) −3.83885e11 + 1.95599e11i −0.975664 + 0.497126i
\(793\) 1.05932e8 1.05932e8i 0.000267875 0.000267875i
\(794\) −5.60696e11 1.82181e11i −1.41074 0.458376i
\(795\) 3.24890e10 + 2.45649e10i 0.0813333 + 0.0614959i
\(796\) −4.87305e11 1.49977e12i −1.21380 3.73571i
\(797\) 2.10538e11 4.13203e11i 0.521791 1.02407i −0.468291 0.883575i \(-0.655130\pi\)
0.990081 0.140497i \(-0.0448701\pi\)
\(798\) 3.87941e10 6.14439e9i 0.0956653 0.0151519i
\(799\) 2.71294e11i 0.665661i
\(800\) 3.12754e11 + 6.18458e10i 0.763560 + 0.150991i
\(801\) −2.68927e10 −0.0653289
\(802\) −1.23616e11 7.80482e11i −0.298798 1.88654i
\(803\) 2.79645e11 + 1.42486e11i 0.672582 + 0.342698i
\(804\) 9.26259e11 3.00960e11i 2.21671 0.720251i
\(805\) 2.14423e11 + 7.42205e10i 0.510607 + 0.176742i
\(806\) −5.01831e9 + 1.54448e10i −0.0118910 + 0.0365966i
\(807\) 2.37838e10 + 2.37838e10i 0.0560774 + 0.0560774i
\(808\) 1.84494e11 + 3.62090e11i 0.432850 + 0.849515i
\(809\) −1.70014e11 2.34004e11i −0.396908 0.546297i 0.563057 0.826418i \(-0.309625\pi\)
−0.959965 + 0.280121i \(0.909625\pi\)
\(810\) 8.47206e10 1.17667e10i 0.196811 0.0273348i
\(811\) 1.71726e11 + 1.24766e11i 0.396965 + 0.288412i 0.768304 0.640085i \(-0.221101\pi\)
−0.371339 + 0.928498i \(0.621101\pi\)
\(812\) −1.11294e12 1.76272e11i −2.56004 0.405470i
\(813\) −5.75943e10 + 3.63636e11i −0.131831 + 0.832348i
\(814\) −6.67266e11 + 9.18412e11i −1.51985 + 2.09190i
\(815\) −1.11372e11 8.01880e11i −0.252433 1.81752i
\(816\) 1.59953e11 1.16213e11i 0.360772 0.262116i
\(817\) 9.36025e10 4.76928e10i 0.210087 0.107045i
\(818\) −6.19833e11 + 6.19833e11i −1.38440 + 1.38440i
\(819\) 1.90458e9 + 6.18836e8i 0.00423315 + 0.00137543i
\(820\) 1.34490e11 3.88540e11i 0.297464 0.859371i
\(821\) −1.40441e11 4.32232e11i −0.309115 0.951358i −0.978109 0.208091i \(-0.933275\pi\)
0.668994 0.743267i \(-0.266725\pi\)
\(822\) −8.17802e10 + 1.60503e11i −0.179127 + 0.351556i
\(823\) −2.48182e11 + 3.93081e10i −0.540967 + 0.0856807i −0.420938 0.907090i \(-0.638299\pi\)
−0.120029 + 0.992770i \(0.538299\pi\)
\(824\) 1.66258e12i 3.60639i
\(825\) −3.58038e11 1.99983e11i −0.772882 0.431696i
\(826\) −4.84876e11 −1.04162
\(827\) −9.88725e10 6.24256e11i −0.211375 1.33457i −0.833877 0.551950i \(-0.813884\pi\)
0.622502 0.782618i \(-0.286116\pi\)
\(828\) 2.36063e11 + 1.20280e11i 0.502234 + 0.255901i
\(829\) −7.67106e10 + 2.49248e10i −0.162419 + 0.0527732i −0.389098 0.921196i \(-0.627213\pi\)
0.226679 + 0.973970i \(0.427213\pi\)
\(830\) −6.28594e11 + 8.31366e11i −1.32452 + 1.75178i
\(831\) −1.55339e10 + 4.78084e10i −0.0325744 + 0.100254i
\(832\) −1.55471e9 1.55471e9i −0.00324456 0.00324456i
\(833\) −5.23818e10 1.02805e11i −0.108793 0.213518i
\(834\) 4.60891e11 + 6.34363e11i 0.952652 + 1.31121i
\(835\) −4.60344e10 + 4.43109e10i −0.0946970 + 0.0911518i
\(836\) −1.77894e11 1.29248e11i −0.364197 0.264605i
\(837\) −1.05584e11 1.67229e10i −0.215128 0.0340730i
\(838\) −1.15199e11 + 7.27335e11i −0.233599 + 1.47489i
\(839\) 8.96070e10 1.23333e11i 0.180840 0.248905i −0.708967 0.705241i \(-0.750839\pi\)
0.889807 + 0.456337i \(0.150839\pi\)
\(840\) −2.03673e11 + 3.81561e11i −0.409088 + 0.766385i
\(841\) 7.36183e11 5.34868e11i 1.47164 1.06921i
\(842\) −2.59836e11 + 1.32393e11i −0.516953 + 0.263401i
\(843\) −2.20879e11 + 2.20879e11i −0.437366 + 0.437366i
\(844\) −1.17120e12 3.80545e11i −2.30813 0.749957i
\(845\) −5.09555e11 9.72029e9i −0.999457 0.0190657i
\(846\) 1.32817e11 + 4.08770e11i 0.259283 + 0.797991i
\(847\) −2.21727e11 + 4.35164e11i −0.430810 + 0.845512i
\(848\) −1.47323e11 + 2.33337e10i −0.284896 + 0.0451231i
\(849\) 3.64134e11i 0.700859i
\(850\) 4.14350e11 + 1.52334e11i 0.793765 + 0.291823i
\(851\) 3.80486e11 0.725471
\(852\) 1.38616e11 + 8.75189e11i 0.263061 + 1.66090i
\(853\) 1.39343e11 + 7.09986e10i 0.263201 + 0.134108i 0.580612 0.814181i \(-0.302813\pi\)
−0.317411 + 0.948288i \(0.602813\pi\)
\(854\) −1.26600e10 + 4.11350e9i −0.0238015 + 0.00773356i
\(855\) 1.36156e10 + 1.95124e10i 0.0254785 + 0.0365128i
\(856\) 2.07026e11 6.37161e11i 0.385594 1.18674i
\(857\) −7.65246e10 7.65246e10i −0.141866 0.141866i 0.632607 0.774473i \(-0.281985\pi\)
−0.774473 + 0.632607i \(0.781985\pi\)
\(858\) −7.40539e9 1.45339e10i −0.0136647 0.0268184i
\(859\) 3.83019e11 + 5.27180e11i 0.703473 + 0.968247i 0.999913 + 0.0131956i \(0.00420040\pi\)
−0.296440 + 0.955051i \(0.595800\pi\)
\(860\) −3.71942e11 + 2.08958e12i −0.679957 + 3.82002i
\(861\) 7.45893e10 + 5.41923e10i 0.135726 + 0.0986109i
\(862\) 7.57833e11 + 1.20029e11i 1.37260 + 0.217399i
\(863\) −9.35150e10 + 5.90430e11i −0.168592 + 1.06445i 0.747728 + 0.664005i \(0.231145\pi\)
−0.916321 + 0.400446i \(0.868855\pi\)
\(864\) −4.90642e10 + 6.75310e10i −0.0880460 + 0.121185i
\(865\) 5.80130e11 2.81786e11i 1.03624 0.503332i
\(866\) 1.16925e12 8.49512e11i 2.07892 1.51042i
\(867\) −2.25661e11 + 1.14980e11i −0.399374 + 0.203491i
\(868\) 7.01292e11 7.01292e11i 1.23543 1.23543i
\(869\) 9.24865e11 + 3.00507e11i 1.62181 + 0.526957i
\(870\) −2.88825e11 9.50208e11i −0.504148 1.65860i
\(871\) 6.21042e9 + 1.91137e10i 0.0107907 + 0.0332103i
\(872\) −6.14735e11 + 1.20648e12i −1.06322 + 2.08668i
\(873\) 2.25745e11 3.57546e10i 0.388653 0.0615566i
\(874\) 1.07229e11i 0.183767i
\(875\) −4.09645e11 + 4.10430e10i −0.698836 + 0.0700176i
\(876\) 3.67886e11 0.624737
\(877\) −6.65918e10 4.20444e11i −0.112570 0.710739i −0.977828 0.209411i \(-0.932845\pi\)
0.865258 0.501327i \(-0.167155\pi\)
\(878\) 1.17065e12 + 5.96477e11i 1.96992 + 1.00373i
\(879\) 3.71429e11 1.20684e11i 0.622185 0.202160i
\(880\) 1.43693e12 4.36768e11i 2.39609 0.728316i
\(881\) 1.81341e10 5.58111e10i 0.0301018 0.0926439i −0.934877 0.354972i \(-0.884490\pi\)
0.964979 + 0.262328i \(0.0844903\pi\)
\(882\) 1.29256e11 + 1.29256e11i 0.213588 + 0.213588i
\(883\) −3.08088e11 6.04657e11i −0.506795 0.994641i −0.992698 0.120628i \(-0.961509\pi\)
0.485903 0.874013i \(-0.338491\pi\)
\(884\) 7.09372e9 + 9.76366e9i 0.0116162 + 0.0159884i
\(885\) −1.28332e11 2.64205e11i −0.209200 0.430693i
\(886\) −1.05484e12 7.66386e11i −1.71179 1.24369i
\(887\) −3.58655e11 5.68053e10i −0.579405 0.0917687i −0.140148 0.990131i \(-0.544758\pi\)
−0.439256 + 0.898362i \(0.644758\pi\)
\(888\) −1.13457e11 + 7.16339e11i −0.182465 + 1.15204i
\(889\) 1.20445e11 1.65778e11i 0.192833 0.265412i
\(890\) 2.16498e11 + 3.85362e10i 0.345059 + 0.0614199i
\(891\) 8.68687e10 6.31138e10i 0.137833 0.100141i
\(892\) 6.66928e11 3.39817e11i 1.05346 0.536767i
\(893\) −8.45422e10 + 8.45422e10i −0.132944 + 0.132944i
\(894\) −8.53325e11 2.77262e11i −1.33587 0.434051i
\(895\) 6.27251e11 4.37693e11i 0.977573 0.682146i
\(896\) 1.69248e11 + 5.20891e11i 0.262598 + 0.808193i
\(897\) −2.48203e9 + 4.87125e9i −0.00383386 + 0.00752438i
\(898\) 1.20162e12 1.90318e11i 1.84783 0.292667i
\(899\) 1.24122e12i 1.90025i
\(900\) −4.80356e11 1.83333e10i −0.732139 0.0279428i
\(901\) −5.50416e10 −0.0835203
\(902\) −1.17479e11 7.41731e11i −0.177473 1.12052i
\(903\) −4.24056e11 2.16067e11i −0.637782 0.324966i
\(904\) 1.79007e11 5.81628e10i 0.268037 0.0870906i
\(905\) 1.12363e10 5.89025e11i 0.0167505 0.878091i
\(906\) 2.28415e11 7.02988e11i 0.339009 1.04336i
\(907\) −2.81032e10 2.81032e10i −0.0415266 0.0415266i 0.686039 0.727565i \(-0.259348\pi\)
−0.727565 + 0.686039i \(0.759348\pi\)
\(908\) −5.93655e11 1.16511e12i −0.873354 1.71405i
\(909\) −5.95306e10 8.19368e10i −0.0871936 0.120012i
\(910\) −1.44459e10 7.71108e9i −0.0210659 0.0112447i
\(911\) −1.62174e11 1.17826e11i −0.235455 0.171068i 0.463801 0.885939i \(-0.346485\pi\)
−0.699256 + 0.714872i \(0.746485\pi\)
\(912\) −8.60606e10 1.36307e10i −0.124401 0.0197032i
\(913\) −2.04680e11 + 1.29230e12i −0.294573 + 1.85986i
\(914\) 2.88477e11 3.97055e11i 0.413358 0.568939i
\(915\) −5.59214e9 5.80964e9i −0.00797799 0.00828829i
\(916\) 2.85276e11 2.07265e11i 0.405213 0.294404i
\(917\) 4.32240e11 2.20237e11i 0.611290 0.311468i
\(918\) −8.17325e10 + 8.17325e10i −0.115086 + 0.115086i
\(919\) 1.95723e11 + 6.35943e10i 0.274398 + 0.0891572i 0.442983 0.896530i \(-0.353920\pi\)
−0.168586 + 0.985687i \(0.553920\pi\)
\(920\) −9.41863e11 7.12140e11i −1.31473 0.994064i
\(921\) 1.67760e11 + 5.16313e11i 0.233158 + 0.717588i
\(922\) −5.73925e11 + 1.12639e12i −0.794202 + 1.55871i
\(923\) −1.80599e10 + 2.86040e9i −0.0248833 + 0.00394113i
\(924\) 9.96185e11i 1.36663i
\(925\) −6.26615e11 + 2.89727e11i −0.855921 + 0.395751i
\(926\) −3.95943e11 −0.538504
\(927\) −6.48186e10 4.09249e11i −0.0877770 0.554202i
\(928\) 8.63568e11 + 4.40010e11i 1.16441 + 0.593295i
\(929\) −2.26571e11 + 7.36174e10i −0.304188 + 0.0988365i −0.457134 0.889398i \(-0.651124\pi\)
0.152946 + 0.988235i \(0.451124\pi\)
\(930\) 8.26035e11 + 2.85925e11i 1.10425 + 0.382226i
\(931\) −1.57132e10 + 4.83603e10i −0.0209154 + 0.0643709i
\(932\) 5.26228e11 + 5.26228e11i 0.697446 + 0.697446i
\(933\) −3.39152e11 6.65624e11i −0.447578 0.878420i
\(934\) −1.09864e12 1.51215e12i −1.44367 1.98705i
\(935\) 5.48928e11 7.62400e10i 0.718239 0.0997554i
\(936\) −8.43097e9 6.12546e9i −0.0109843 0.00798059i
\(937\) −9.79973e11 1.55213e11i −1.27132 0.201358i −0.515931 0.856630i \(-0.672554\pi\)
−0.755392 + 0.655273i \(0.772554\pi\)
\(938\) 2.79357e11 1.76379e12i 0.360868 2.27843i
\(939\) 2.46382e11 3.39115e11i 0.316917 0.436199i
\(940\) −3.32302e11 2.39258e12i −0.425620 3.06446i
\(941\) −3.80413e11 + 2.76386e11i −0.485173 + 0.352499i −0.803325 0.595541i \(-0.796938\pi\)
0.318152 + 0.948040i \(0.396938\pi\)
\(942\) 4.69137e11 2.39037e11i 0.595794 0.303572i
\(943\) −1.77980e11 + 1.77980e11i −0.225073 + 0.225073i
\(944\) 1.02300e12 + 3.32393e11i 1.28821 + 0.418565i
\(945\) 3.52590e10 1.01863e11i 0.0442123 0.127729i
\(946\) 1.19793e12 + 3.68686e12i 1.49578 + 4.60354i
\(947\) 3.50835e11 6.88552e11i 0.436217 0.856124i −0.563336 0.826228i \(-0.690482\pi\)
0.999553 0.0298961i \(-0.00951763\pi\)
\(948\) 1.12585e12 1.78316e11i 1.39394 0.220779i
\(949\) 7.59148e9i 0.00935970i
\(950\) −8.16512e10 1.76593e11i −0.100246 0.216810i
\(951\) −7.79920e10 −0.0953516
\(952\) −9.14341e10 5.77292e11i −0.111317 0.702826i
\(953\) −7.43679e11 3.78923e11i −0.901600 0.459388i −0.0592033 0.998246i \(-0.518856\pi\)
−0.842397 + 0.538858i \(0.818856\pi\)
\(954\) 8.29336e10 2.69468e10i 0.100124 0.0325322i
\(955\) 6.69385e10 8.85315e10i 0.0804752 0.106435i
\(956\) 1.48490e11 4.57006e11i 0.177773 0.547129i
\(957\) −8.81578e11 8.81578e11i −1.05103 1.05103i
\(958\) −7.38944e11 1.45026e12i −0.877303 1.72180i
\(959\) 1.33436e11 + 1.83658e11i 0.157760 + 0.217138i
\(960\) −8.52655e10 + 8.20734e10i −0.100390 + 0.0966312i
\(961\) −1.93830e11 1.40826e11i −0.227263 0.165116i
\(962\) −2.71206e10 4.29549e9i −0.0316665 0.00501547i
\(963\) −2.61192e10 + 1.64910e11i −0.0303708 + 0.191753i
\(964\) −1.53666e12 + 2.11503e12i −1.77938 + 2.44911i
\(965\) 1.55155e11 2.90667e11i 0.178919 0.335186i
\(966\) 3.93012e11 2.85540e11i 0.451333 0.327913i
\(967\) 2.93990e11 1.49795e11i 0.336222 0.171314i −0.277726 0.960660i \(-0.589581\pi\)
0.613948 + 0.789347i \(0.289581\pi\)
\(968\) 1.79715e12 1.79715e12i 2.04683 2.04683i
\(969\) −3.05796e10 9.93592e9i −0.0346846 0.0112697i
\(970\) −1.86858e12 3.56451e10i −2.11069 0.0402637i
\(971\) 1.68430e11 + 5.18375e11i 0.189471 + 0.583132i 0.999997 0.00257122i \(-0.000818447\pi\)
−0.810526 + 0.585703i \(0.800818\pi\)
\(972\) 5.71399e10 1.12143e11i 0.0640139 0.125634i
\(973\) 9.76004e11 1.54584e11i 1.08893 0.172470i
\(974\) 1.43146e12i 1.59054i
\(975\) 3.78314e8 9.91235e9i 0.000418634 0.0109688i
\(976\) 2.95303e10 0.0325438
\(977\) 1.02294e11 + 6.45859e11i 0.112272 + 0.708859i 0.978041 + 0.208414i \(0.0668301\pi\)
−0.865769 + 0.500445i \(0.833170\pi\)
\(978\) −1.54434e12 7.86882e11i −1.68806 0.860111i
\(979\) 2.62543e11 8.53055e10i 0.285805 0.0928637i
\(980\) −5.87885e11 8.42490e11i −0.637365 0.913399i
\(981\) 1.04282e11 3.20947e11i 0.112599 0.346543i
\(982\) 7.65045e11 + 7.65045e11i 0.822699 + 0.822699i
\(983\) 4.20591e10 + 8.25457e10i 0.0450450 + 0.0884057i 0.912432 0.409229i \(-0.134202\pi\)
−0.867387 + 0.497634i \(0.834202\pi\)
\(984\) −2.82010e11 3.88153e11i −0.300804 0.414021i
\(985\) 2.77405e11 1.55847e12i 0.294692 1.65559i
\(986\) 1.08577e12 + 7.88857e11i 1.14876 + 0.834624i
\(987\) 5.34989e11 + 8.47339e10i 0.563736 + 0.0892870i
\(988\) 8.32025e8 5.25320e9i 0.000873190 0.00551310i
\(989\) 7.63708e11 1.05115e12i 0.798256 1.09871i
\(990\) −7.89769e11 + 3.83613e11i −0.822166 + 0.399349i
\(991\) −6.88325e10 + 5.00097e10i −0.0713672 + 0.0518513i −0.622897 0.782304i \(-0.714044\pi\)
0.551530 + 0.834155i \(0.314044\pi\)
\(992\) −7.60081e11 + 3.87281e11i −0.784898 + 0.399926i
\(993\) 6.63015e11 6.63015e11i 0.681909 0.681909i
\(994\) 1.54522e12 + 5.02072e11i 1.58287 + 0.514304i
\(995\) −5.09395e11 1.67586e12i −0.519711 1.70980i
\(996\) 4.73928e11 + 1.45860e12i 0.481587 + 1.48217i
\(997\) 4.07798e10 8.00350e10i 0.0412729 0.0810026i −0.869449 0.494023i \(-0.835526\pi\)
0.910722 + 0.413020i \(0.135526\pi\)
\(998\) −2.34586e12 + 3.71547e11i −2.36472 + 0.374535i
\(999\) 1.80753e11i 0.181477i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 75.9.k.a.37.37 320
25.23 odd 20 inner 75.9.k.a.73.37 yes 320
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
75.9.k.a.37.37 320 1.1 even 1 trivial
75.9.k.a.73.37 yes 320 25.23 odd 20 inner