Properties

Label 69.8.e.a.13.5
Level $69$
Weight $8$
Character 69.13
Analytic conductor $21.555$
Analytic rank $0$
Dimension $140$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [69,8,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(21.5545667584\)
Analytic rank: \(0\)
Dimension: \(140\)
Relative dimension: \(14\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 13.5
Character \(\chi\) \(=\) 69.13
Dual form 69.8.e.a.16.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.24555 - 7.20775i) q^{2} +(22.7138 + 14.5973i) q^{3} +(5.27156 - 36.6645i) q^{4} +(130.697 - 286.187i) q^{5} +(-36.6468 - 254.884i) q^{6} +(-922.772 - 270.950i) q^{7} +(-1324.16 + 850.988i) q^{8} +(302.838 + 663.122i) q^{9} +O(q^{10})\) \(q+(-6.24555 - 7.20775i) q^{2} +(22.7138 + 14.5973i) q^{3} +(5.27156 - 36.6645i) q^{4} +(130.697 - 286.187i) q^{5} +(-36.6468 - 254.884i) q^{6} +(-922.772 - 270.950i) q^{7} +(-1324.16 + 850.988i) q^{8} +(302.838 + 663.122i) q^{9} +(-2879.04 + 845.362i) q^{10} +(2219.74 - 2561.71i) q^{11} +(654.940 - 755.841i) q^{12} +(-4952.11 + 1454.07i) q^{13} +(3810.28 + 8343.34i) q^{14} +(7146.20 - 4592.58i) q^{15} +(9854.58 + 2893.57i) q^{16} +(-485.288 - 3375.25i) q^{17} +(2888.23 - 6324.33i) q^{18} +(2310.77 - 16071.8i) q^{19} +(-9803.93 - 6300.60i) q^{20} +(-17004.6 - 19624.3i) q^{21} -32327.7 q^{22} +(-57151.2 + 11771.5i) q^{23} -42499.0 q^{24} +(-13660.3 - 15764.8i) q^{25} +(41409.2 + 26612.1i) q^{26} +(-2801.18 + 19482.7i) q^{27} +(-14798.7 + 32404.6i) q^{28} +(12432.6 + 86470.7i) q^{29} +(-77734.1 - 22824.8i) q^{30} +(-28356.9 + 18223.9i) q^{31} +(43005.3 + 94168.4i) q^{32} +(87812.9 - 25784.2i) q^{33} +(-21297.1 + 24578.1i) q^{34} +(-198146. + 228673. i) q^{35} +(25909.4 - 7607.70i) q^{36} +(8757.78 + 19176.9i) q^{37} +(-130273. + 83721.5i) q^{38} +(-133707. - 39259.9i) q^{39} +(70477.3 + 490180. i) q^{40} +(-271007. + 593423. i) q^{41} +(-35244.3 + 245129. i) q^{42} +(-137608. - 88435.6i) q^{43} +(-82222.5 - 94889.8i) q^{44} +229357. q^{45} +(441787. + 338412. i) q^{46} -1.05199e6 q^{47} +(181597. + 209574. i) q^{48} +(85286.3 + 54810.2i) q^{49} +(-28312.8 + 196920. i) q^{50} +(38246.8 - 83748.9i) q^{51} +(27207.4 + 189232. i) q^{52} +(-1.86792e6 - 548472. i) q^{53} +(157921. - 101490. i) q^{54} +(-443016. - 970069. i) q^{55} +(1.45248e6 - 426486. i) q^{56} +(287091. - 331321. i) q^{57} +(545611. - 629668. i) q^{58} +(1.10239e6 - 323692. i) q^{59} +(-130713. - 286222. i) q^{60} +(924848. - 594364. i) q^{61} +(308458. + 90571.3i) q^{62} +(-99777.0 - 693964. i) q^{63} +(956271. - 2.09394e6i) q^{64} +(-231091. + 1.60727e6i) q^{65} +(-734286. - 471897. i) q^{66} +(-1.22069e6 - 1.40875e6i) q^{67} -126310. q^{68} +(-1.46996e6 - 566876. i) q^{69} +2.88575e6 q^{70} +(2.10523e6 + 2.42957e6i) q^{71} +(-965315. - 620371. i) q^{72} +(334388. - 2.32572e6i) q^{73} +(83524.8 - 182894. i) q^{74} +(-80153.9 - 557482. i) q^{75} +(-577082. - 169446. i) q^{76} +(-2.74241e6 + 1.76244e6i) q^{77} +(552098. + 1.20893e6i) q^{78} +(5.52840e6 - 1.62328e6i) q^{79} +(2.11607e6 - 2.44207e6i) q^{80} +(-348020. + 401636. i) q^{81} +(5.96983e6 - 1.75290e6i) q^{82} +(-285399. - 624937. i) q^{83} +(-809156. + 520013. i) q^{84} +(-1.02938e6 - 302253. i) q^{85} +(222019. + 1.54418e6i) q^{86} +(-979847. + 2.14557e6i) q^{87} +(-759308. + 5.28110e6i) q^{88} +(-5.59768e6 - 3.59741e6i) q^{89} +(-1.43246e6 - 1.65315e6i) q^{90} +4.96365e6 q^{91} +(130321. + 2.15747e6i) q^{92} -910114. q^{93} +(6.57025e6 + 7.58248e6i) q^{94} +(-4.29752e6 - 2.76185e6i) q^{95} +(-397790. + 2.76669e6i) q^{96} +(-1.75470e6 + 3.84225e6i) q^{97} +(-137602. - 957042. i) q^{98} +(2.37095e6 + 696173. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 140 q - 16 q^{2} - 378 q^{3} - 740 q^{4} - 6 q^{5} + 1647 q^{6} + 978 q^{7} - 824 q^{8} - 10206 q^{9} + 1322 q^{10} + 7892 q^{11} - 19980 q^{12} + 39810 q^{13} - 26296 q^{14} + 135 q^{15} - 142164 q^{16} - 97081 q^{17} - 11664 q^{18} + 120905 q^{19} + 124755 q^{20} + 26406 q^{21} - 837266 q^{22} - 224688 q^{23} - 60264 q^{24} - 180624 q^{25} + 385108 q^{26} - 275562 q^{27} + 1121760 q^{28} - 375654 q^{29} + 35694 q^{30} + 505029 q^{31} - 661528 q^{32} - 360423 q^{33} - 1872759 q^{34} - 964610 q^{35} - 1269189 q^{36} - 28802 q^{37} - 1459868 q^{38} + 1074870 q^{39} + 5371901 q^{40} - 1557480 q^{41} + 883116 q^{42} + 1160786 q^{43} - 4521825 q^{44} - 2009124 q^{45} - 4123580 q^{46} + 811422 q^{47} - 1563111 q^{48} - 10960262 q^{49} + 16636695 q^{50} + 4413852 q^{51} - 4843791 q^{52} + 4291672 q^{53} - 98415 q^{54} + 2093539 q^{55} - 12548382 q^{56} - 4007907 q^{57} - 7414367 q^{58} + 2955424 q^{59} + 7289973 q^{60} + 4919292 q^{61} + 16083211 q^{62} + 712962 q^{63} - 1673596 q^{64} - 13246221 q^{65} + 7219449 q^{66} + 148565 q^{67} - 23039568 q^{68} - 657018 q^{69} + 12781104 q^{70} - 7247645 q^{71} - 600696 q^{72} + 32596055 q^{73} + 32550658 q^{74} - 10061874 q^{75} + 12150569 q^{76} - 43349150 q^{77} - 17201700 q^{78} + 4815410 q^{79} + 36529590 q^{80} - 7440174 q^{81} + 20862470 q^{82} + 35160800 q^{83} - 5346540 q^{84} + 48578363 q^{85} + 76972708 q^{86} + 1505088 q^{87} - 35912212 q^{88} + 1401264 q^{89} + 963738 q^{90} - 91970208 q^{91} - 74293537 q^{92} + 555606 q^{93} - 32520253 q^{94} + 79436789 q^{95} + 41519736 q^{96} + 18296816 q^{97} - 38956823 q^{98} - 9731421 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{7}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.24555 7.20775i −0.552034 0.637081i 0.409322 0.912390i \(-0.365765\pi\)
−0.961356 + 0.275309i \(0.911220\pi\)
\(3\) 22.7138 + 14.5973i 0.485698 + 0.312139i
\(4\) 5.27156 36.6645i 0.0411840 0.286441i
\(5\) 130.697 286.187i 0.467597 1.02389i −0.518093 0.855324i \(-0.673358\pi\)
0.985690 0.168570i \(-0.0539148\pi\)
\(6\) −36.6468 254.884i −0.0692638 0.481740i
\(7\) −922.772 270.950i −1.01684 0.298570i −0.269489 0.963003i \(-0.586855\pi\)
−0.747348 + 0.664433i \(0.768673\pi\)
\(8\) −1324.16 + 850.988i −0.914380 + 0.587636i
\(9\) 302.838 + 663.122i 0.138472 + 0.303211i
\(10\) −2879.04 + 845.362i −0.910432 + 0.267327i
\(11\) 2219.74 2561.71i 0.502837 0.580305i −0.446413 0.894827i \(-0.647299\pi\)
0.949250 + 0.314522i \(0.101844\pi\)
\(12\) 654.940 755.841i 0.109413 0.126269i
\(13\) −4952.11 + 1454.07i −0.625157 + 0.183563i −0.578942 0.815369i \(-0.696534\pi\)
−0.0462149 + 0.998932i \(0.514716\pi\)
\(14\) 3810.28 + 8343.34i 0.371115 + 0.812628i
\(15\) 7146.20 4592.58i 0.546708 0.351348i
\(16\) 9854.58 + 2893.57i 0.601476 + 0.176609i
\(17\) −485.288 3375.25i −0.0239568 0.166623i 0.974331 0.225121i \(-0.0722779\pi\)
−0.998288 + 0.0584983i \(0.981369\pi\)
\(18\) 2888.23 6324.33i 0.116729 0.255600i
\(19\) 2310.77 16071.8i 0.0772893 0.537559i −0.913985 0.405747i \(-0.867011\pi\)
0.991275 0.131812i \(-0.0420795\pi\)
\(20\) −9803.93 6300.60i −0.274028 0.176107i
\(21\) −17004.6 19624.3i −0.400680 0.462410i
\(22\) −32327.7 −0.647284
\(23\) −57151.2 + 11771.5i −0.979440 + 0.201737i
\(24\) −42499.0 −0.627537
\(25\) −13660.3 15764.8i −0.174852 0.201789i
\(26\) 41409.2 + 26612.1i 0.462052 + 0.296943i
\(27\) −2801.18 + 19482.7i −0.0273885 + 0.190491i
\(28\) −14798.7 + 32404.6i −0.127400 + 0.278968i
\(29\) 12432.6 + 86470.7i 0.0946607 + 0.658379i 0.980808 + 0.194976i \(0.0624628\pi\)
−0.886147 + 0.463404i \(0.846628\pi\)
\(30\) −77734.1 22824.8i −0.525638 0.154341i
\(31\) −28356.9 + 18223.9i −0.170959 + 0.109869i −0.623322 0.781965i \(-0.714218\pi\)
0.452363 + 0.891834i \(0.350581\pi\)
\(32\) 43005.3 + 94168.4i 0.232005 + 0.508019i
\(33\) 87812.9 25784.2i 0.425363 0.124898i
\(34\) −21297.1 + 24578.1i −0.0929274 + 0.107244i
\(35\) −198146. + 228673.i −0.781174 + 0.901523i
\(36\) 25909.4 7607.70i 0.0925549 0.0271766i
\(37\) 8757.78 + 19176.9i 0.0284242 + 0.0622403i 0.923312 0.384052i \(-0.125472\pi\)
−0.894887 + 0.446292i \(0.852744\pi\)
\(38\) −130273. + 83721.5i −0.385135 + 0.247511i
\(39\) −133707. 39259.9i −0.360934 0.105980i
\(40\) 70477.3 + 490180.i 0.174116 + 1.21101i
\(41\) −271007. + 593423.i −0.614098 + 1.34469i 0.305638 + 0.952148i \(0.401130\pi\)
−0.919736 + 0.392539i \(0.871597\pi\)
\(42\) −35244.3 + 245129.i −0.0734033 + 0.510531i
\(43\) −137608. 88435.6i −0.263940 0.169624i 0.401977 0.915650i \(-0.368323\pi\)
−0.665917 + 0.746026i \(0.731960\pi\)
\(44\) −82222.5 94889.8i −0.145514 0.167933i
\(45\) 229357. 0.375204
\(46\) 441787. + 338412.i 0.669206 + 0.512617i
\(47\) −1.05199e6 −1.47798 −0.738991 0.673715i \(-0.764697\pi\)
−0.738991 + 0.673715i \(0.764697\pi\)
\(48\) 181597. + 209574.i 0.237009 + 0.273523i
\(49\) 85286.3 + 54810.2i 0.103560 + 0.0665541i
\(50\) −28312.8 + 196920.i −0.0320322 + 0.222789i
\(51\) 38246.8 83748.9i 0.0403738 0.0884064i
\(52\) 27207.4 + 189232.i 0.0268334 + 0.186631i
\(53\) −1.86792e6 548472.i −1.72343 0.506045i −0.737808 0.675011i \(-0.764139\pi\)
−0.985622 + 0.168966i \(0.945957\pi\)
\(54\) 157921. 101490.i 0.136478 0.0877089i
\(55\) −443016. 970069.i −0.359046 0.786201i
\(56\) 1.45248e6 426486.i 1.10523 0.324524i
\(57\) 287091. 331321.i 0.205332 0.236966i
\(58\) 545611. 629668.i 0.367185 0.423754i
\(59\) 1.10239e6 323692.i 0.698804 0.205187i 0.0870132 0.996207i \(-0.472268\pi\)
0.611790 + 0.791020i \(0.290450\pi\)
\(60\) −130713. 286222.i −0.0781249 0.171070i
\(61\) 924848. 594364.i 0.521694 0.335272i −0.253148 0.967428i \(-0.581466\pi\)
0.774842 + 0.632155i \(0.217830\pi\)
\(62\) 308458. + 90571.3i 0.164371 + 0.0482636i
\(63\) −99777.0 693964.i −0.0502734 0.349659i
\(64\) 956271. 2.09394e6i 0.455986 0.998469i
\(65\) −231091. + 1.60727e6i −0.104373 + 0.725927i
\(66\) −734286. 471897.i −0.314385 0.202043i
\(67\) −1.22069e6 1.40875e6i −0.495840 0.572230i 0.451576 0.892232i \(-0.350862\pi\)
−0.947417 + 0.320002i \(0.896316\pi\)
\(68\) −126310. −0.0487144
\(69\) −1.46996e6 566876.i −0.538682 0.207738i
\(70\) 2.88575e6 1.00558
\(71\) 2.10523e6 + 2.42957e6i 0.698064 + 0.805609i 0.988490 0.151288i \(-0.0483422\pi\)
−0.290425 + 0.956898i \(0.593797\pi\)
\(72\) −965315. 620371.i −0.304793 0.195879i
\(73\) 334388. 2.32572e6i 0.100605 0.699725i −0.875625 0.482991i \(-0.839550\pi\)
0.976231 0.216734i \(-0.0695405\pi\)
\(74\) 83524.8 182894.i 0.0239610 0.0524672i
\(75\) −80153.9 557482.i −0.0219387 0.152587i
\(76\) −577082. 169446.i −0.150796 0.0442777i
\(77\) −2.74241e6 + 1.76244e6i −0.684565 + 0.439943i
\(78\) 552098. + 1.20893e6i 0.131730 + 0.288449i
\(79\) 5.52840e6 1.62328e6i 1.26155 0.370424i 0.418479 0.908227i \(-0.362563\pi\)
0.843071 + 0.537802i \(0.180745\pi\)
\(80\) 2.11607e6 2.44207e6i 0.462077 0.533266i
\(81\) −348020. + 401636.i −0.0727623 + 0.0839722i
\(82\) 5.96983e6 1.75290e6i 1.19568 0.351082i
\(83\) −285399. 624937.i −0.0547873 0.119967i 0.880258 0.474495i \(-0.157369\pi\)
−0.935046 + 0.354527i \(0.884642\pi\)
\(84\) −809156. + 520013.i −0.148955 + 0.0957275i
\(85\) −1.02938e6 302253.i −0.181807 0.0533832i
\(86\) 222019. + 1.54418e6i 0.0376396 + 0.261789i
\(87\) −979847. + 2.14557e6i −0.159529 + 0.349321i
\(88\) −759308. + 5.28110e6i −0.118776 + 0.826105i
\(89\) −5.59768e6 3.59741e6i −0.841673 0.540910i 0.0472943 0.998881i \(-0.484940\pi\)
−0.888967 + 0.457971i \(0.848576\pi\)
\(90\) −1.43246e6 1.65315e6i −0.207126 0.239036i
\(91\) 4.96365e6 0.690489
\(92\) 130321. + 2.15747e6i 0.0174485 + 0.288860i
\(93\) −910114. −0.117329
\(94\) 6.57025e6 + 7.58248e6i 0.815896 + 0.941594i
\(95\) −4.29752e6 2.76185e6i −0.514263 0.330497i
\(96\) −397790. + 2.76669e6i −0.0458885 + 0.319162i
\(97\) −1.75470e6 + 3.84225e6i −0.195209 + 0.427449i −0.981772 0.190061i \(-0.939131\pi\)
0.786563 + 0.617510i \(0.211859\pi\)
\(98\) −137602. 957042.i −0.0147684 0.102716i
\(99\) 2.37095e6 + 696173.i 0.245583 + 0.0721098i
\(100\) −650019. + 417742.i −0.0650019 + 0.0417742i
\(101\) −904659. 1.98093e6i −0.0873696 0.191313i 0.860904 0.508768i \(-0.169899\pi\)
−0.948273 + 0.317455i \(0.897172\pi\)
\(102\) −842513. + 247384.i −0.0786097 + 0.0230819i
\(103\) 1.15435e7 1.33220e7i 1.04090 1.20126i 0.0617563 0.998091i \(-0.480330\pi\)
0.979143 0.203171i \(-0.0651247\pi\)
\(104\) 5.32001e6 6.13962e6i 0.463763 0.535211i
\(105\) −7.83868e6 + 2.30164e6i −0.660815 + 0.194033i
\(106\) 7.71296e6 + 1.68890e7i 0.629000 + 1.37732i
\(107\) 1.14637e6 736730.i 0.0904656 0.0581387i −0.494626 0.869106i \(-0.664695\pi\)
0.585092 + 0.810967i \(0.301059\pi\)
\(108\) 699555. + 205408.i 0.0534366 + 0.0156904i
\(109\) −2.39304e6 1.66440e7i −0.176993 1.23102i −0.863672 0.504055i \(-0.831841\pi\)
0.686678 0.726962i \(-0.259068\pi\)
\(110\) −4.22514e6 + 9.25176e6i −0.302668 + 0.662750i
\(111\) −81007.6 + 563420.i −0.00562206 + 0.0391023i
\(112\) −8.30952e6 5.34020e6i −0.558873 0.359166i
\(113\) −1.61195e7 1.86029e7i −1.05094 1.21284i −0.976477 0.215621i \(-0.930822\pi\)
−0.0744590 0.997224i \(-0.523723\pi\)
\(114\) −4.18111e6 −0.264317
\(115\) −4.10064e6 + 1.78944e7i −0.251426 + 1.09717i
\(116\) 3.23594e6 0.192486
\(117\) −2.46391e6 2.84351e6i −0.142225 0.164136i
\(118\) −9.21815e6 5.92415e6i −0.516484 0.331924i
\(119\) −466716. + 3.24608e6i −0.0253886 + 0.176581i
\(120\) −5.55450e6 + 1.21627e7i −0.293434 + 0.642531i
\(121\) 1.13817e6 + 7.91615e6i 0.0584062 + 0.406224i
\(122\) −1.00602e7 2.95394e6i −0.501588 0.147280i
\(123\) −1.48180e7 + 9.52295e6i −0.717995 + 0.461428i
\(124\) 518684. + 1.13576e6i 0.0244302 + 0.0534947i
\(125\) 1.72869e7 5.07589e6i 0.791647 0.232449i
\(126\) −4.37876e6 + 5.05336e6i −0.195009 + 0.225052i
\(127\) −831019. + 959047.i −0.0359996 + 0.0415458i −0.773464 0.633840i \(-0.781478\pi\)
0.737464 + 0.675386i \(0.236023\pi\)
\(128\) −8.35077e6 + 2.45201e6i −0.351959 + 0.103344i
\(129\) −1.83470e6 4.01742e6i −0.0752489 0.164772i
\(130\) 1.30281e7 8.37266e6i 0.520092 0.334243i
\(131\) −6.66893e6 1.95818e6i −0.259183 0.0761030i 0.149559 0.988753i \(-0.452214\pi\)
−0.408743 + 0.912650i \(0.634033\pi\)
\(132\) −482454. 3.35554e6i −0.0182577 0.126985i
\(133\) −6.48697e6 + 1.42045e7i −0.239090 + 0.523533i
\(134\) −2.53003e6 + 1.75968e7i −0.0908364 + 0.631781i
\(135\) 5.20958e6 + 3.34799e6i 0.182236 + 0.117116i
\(136\) 3.51490e6 + 4.05641e6i 0.119819 + 0.138279i
\(137\) −1.52646e7 −0.507181 −0.253590 0.967312i \(-0.581612\pi\)
−0.253590 + 0.967312i \(0.581612\pi\)
\(138\) 5.09478e6 + 1.41355e7i 0.165024 + 0.457862i
\(139\) 3.87748e7 1.22461 0.612305 0.790621i \(-0.290242\pi\)
0.612305 + 0.790621i \(0.290242\pi\)
\(140\) 7.33964e6 + 8.47040e6i 0.226062 + 0.260889i
\(141\) −2.38947e7 1.53562e7i −0.717853 0.461336i
\(142\) 4.36337e6 3.03479e7i 0.127883 0.889447i
\(143\) −7.26748e6 + 1.59136e7i −0.207830 + 0.455083i
\(144\) 1.06555e6 + 7.41107e6i 0.0297376 + 0.206829i
\(145\) 2.63717e7 + 7.74344e6i 0.718374 + 0.210934i
\(146\) −1.88516e7 + 1.21152e7i −0.501319 + 0.322178i
\(147\) 1.13710e6 + 2.48990e6i 0.0295248 + 0.0646504i
\(148\) 749277. 220008.i 0.0189988 0.00557855i
\(149\) −7.81613e6 + 9.02029e6i −0.193571 + 0.223393i −0.844235 0.535973i \(-0.819945\pi\)
0.650665 + 0.759365i \(0.274490\pi\)
\(150\) −3.51759e6 + 4.05951e6i −0.0850992 + 0.0982097i
\(151\) −6.48544e7 + 1.90430e7i −1.53292 + 0.450107i −0.935944 0.352150i \(-0.885451\pi\)
−0.596979 + 0.802257i \(0.703633\pi\)
\(152\) 1.06170e7 + 2.32481e7i 0.245217 + 0.536951i
\(153\) 2.09124e6 1.34396e6i 0.0472046 0.0303365i
\(154\) 2.98311e7 + 8.75919e6i 0.658183 + 0.193260i
\(155\) 1.50927e6 + 1.04972e7i 0.0325541 + 0.226419i
\(156\) −2.14429e6 + 4.69534e6i −0.0452217 + 0.0990218i
\(157\) 1.02864e7 7.15432e7i 0.212135 1.47543i −0.553872 0.832602i \(-0.686850\pi\)
0.766007 0.642832i \(-0.222241\pi\)
\(158\) −4.62281e7 2.97090e7i −0.932408 0.599222i
\(159\) −3.44215e7 3.97245e7i −0.679110 0.783735i
\(160\) 3.25705e7 0.628643
\(161\) 5.59270e7 + 4.62270e6i 1.05616 + 0.0872981i
\(162\) 5.06847e6 0.0936643
\(163\) 2.78626e6 + 3.21551e6i 0.0503924 + 0.0581559i 0.780386 0.625298i \(-0.215023\pi\)
−0.729994 + 0.683454i \(0.760477\pi\)
\(164\) 2.03289e7 + 1.30646e7i 0.359883 + 0.231283i
\(165\) 4.09780e6 2.85008e7i 0.0710162 0.493928i
\(166\) −2.72192e6 + 5.96016e6i −0.0461845 + 0.101130i
\(167\) −705965. 4.91009e6i −0.0117294 0.0815797i 0.983116 0.182984i \(-0.0585756\pi\)
−0.994845 + 0.101404i \(0.967666\pi\)
\(168\) 3.92169e7 + 1.15151e7i 0.638103 + 0.187364i
\(169\) −3.03783e7 + 1.95230e7i −0.484128 + 0.311130i
\(170\) 4.25048e6 + 9.30725e6i 0.0663539 + 0.145295i
\(171\) 1.13573e7 3.33481e6i 0.173696 0.0510017i
\(172\) −3.96786e6 + 4.57915e6i −0.0594574 + 0.0686175i
\(173\) 6.14358e7 7.09007e7i 0.902112 1.04109i −0.0968395 0.995300i \(-0.530873\pi\)
0.998951 0.0457922i \(-0.0145812\pi\)
\(174\) 2.15844e7 6.33774e6i 0.310611 0.0912037i
\(175\) 8.33385e6 + 1.82486e7i 0.117547 + 0.257393i
\(176\) 2.92871e7 1.88217e7i 0.404932 0.260234i
\(177\) 2.97647e7 + 8.73969e6i 0.403454 + 0.118465i
\(178\) 9.03136e6 + 6.28145e7i 0.120028 + 0.834814i
\(179\) −9.63749e6 + 2.11032e7i −0.125597 + 0.275019i −0.961977 0.273132i \(-0.911941\pi\)
0.836380 + 0.548150i \(0.184668\pi\)
\(180\) 1.20907e6 8.40925e6i 0.0154524 0.107474i
\(181\) −8.78411e7 5.64521e7i −1.10109 0.707628i −0.141756 0.989902i \(-0.545275\pi\)
−0.959334 + 0.282274i \(0.908911\pi\)
\(182\) −3.10007e7 3.57768e7i −0.381173 0.439897i
\(183\) 2.96830e7 0.358037
\(184\) 6.56601e7 6.42224e7i 0.777032 0.760019i
\(185\) 6.63279e6 0.0770185
\(186\) 5.68416e6 + 6.55987e6i 0.0647696 + 0.0747481i
\(187\) −9.72365e6 6.24901e6i −0.108739 0.0698820i
\(188\) −5.54563e6 + 3.85707e7i −0.0608693 + 0.423355i
\(189\) 7.86369e6 1.72191e7i 0.0847247 0.185521i
\(190\) 6.93366e6 + 4.82247e7i 0.0733373 + 0.510072i
\(191\) −1.20113e7 3.52682e6i −0.124730 0.0366241i 0.218772 0.975776i \(-0.429795\pi\)
−0.343502 + 0.939152i \(0.611613\pi\)
\(192\) 5.22865e7 3.36025e7i 0.533133 0.342623i
\(193\) −5.91283e7 1.29473e8i −0.592031 1.29637i −0.934207 0.356731i \(-0.883891\pi\)
0.342176 0.939636i \(-0.388836\pi\)
\(194\) 3.86530e7 1.13495e7i 0.380082 0.111602i
\(195\) −2.87108e7 + 3.31341e7i −0.277284 + 0.320003i
\(196\) 2.45918e6 2.83804e6i 0.0233289 0.0269230i
\(197\) 5.66059e7 1.66210e7i 0.527509 0.154891i −0.00712460 0.999975i \(-0.502268\pi\)
0.534633 + 0.845084i \(0.320450\pi\)
\(198\) −9.79003e6 2.14372e7i −0.0896305 0.196263i
\(199\) 7.08912e7 4.55590e7i 0.637686 0.409816i −0.181462 0.983398i \(-0.558083\pi\)
0.819148 + 0.573582i \(0.194447\pi\)
\(200\) 3.15041e7 + 9.25044e6i 0.278460 + 0.0817631i
\(201\) −7.16257e6 4.98167e7i −0.0622132 0.432702i
\(202\) −8.62793e6 + 1.88925e7i −0.0736507 + 0.161273i
\(203\) 1.19568e7 8.31614e7i 0.100318 0.697728i
\(204\) −2.86899e6 1.84379e6i −0.0236605 0.0152057i
\(205\) 1.34410e8 + 1.55118e8i 1.08967 + 1.25754i
\(206\) −1.68117e8 −1.33991
\(207\) −2.51135e7 3.43333e7i −0.196793 0.269042i
\(208\) −5.30084e7 −0.408435
\(209\) −3.60420e7 4.15946e7i −0.273084 0.315156i
\(210\) 6.55465e7 + 4.21242e7i 0.488407 + 0.313880i
\(211\) 2.52085e7 1.75329e8i 0.184739 1.28489i −0.660634 0.750708i \(-0.729712\pi\)
0.845373 0.534177i \(-0.179378\pi\)
\(212\) −2.99563e7 + 6.55952e7i −0.215930 + 0.472820i
\(213\) 1.23528e7 + 8.59155e7i 0.0875863 + 0.609176i
\(214\) −1.24699e7 3.66149e6i −0.0869791 0.0255394i
\(215\) −4.32942e7 + 2.78235e7i −0.297095 + 0.190931i
\(216\) −1.28703e7 2.81820e7i −0.0868961 0.190276i
\(217\) 3.11047e7 9.13318e6i 0.206641 0.0606754i
\(218\) −1.05020e8 + 1.21199e8i −0.686551 + 0.792322i
\(219\) 4.15445e7 4.79449e7i 0.267275 0.308452i
\(220\) −3.79025e7 + 1.11292e7i −0.239987 + 0.0704666i
\(221\) 7.31106e6 + 1.60090e7i 0.0455625 + 0.0997680i
\(222\) 4.56693e6 2.93499e6i 0.0280149 0.0180041i
\(223\) −2.39762e8 7.04004e7i −1.44781 0.425117i −0.538996 0.842308i \(-0.681196\pi\)
−0.908818 + 0.417192i \(0.863014\pi\)
\(224\) −1.41691e7 9.85483e7i −0.0842315 0.585843i
\(225\) 6.31714e6 1.38326e7i 0.0369727 0.0809590i
\(226\) −3.34098e7 + 2.32370e8i −0.192528 + 1.33906i
\(227\) 1.07415e6 + 690315.i 0.00609501 + 0.00391703i 0.543685 0.839289i \(-0.317029\pi\)
−0.537590 + 0.843207i \(0.680665\pi\)
\(228\) −1.06343e7 1.22726e7i −0.0594205 0.0685749i
\(229\) −2.66249e8 −1.46509 −0.732543 0.680721i \(-0.761667\pi\)
−0.732543 + 0.680721i \(0.761667\pi\)
\(230\) 1.54589e8 8.22041e7i 0.837784 0.445499i
\(231\) −8.80176e7 −0.469816
\(232\) −9.00484e7 1.03921e8i −0.473443 0.546383i
\(233\) 2.89143e8 + 1.85821e8i 1.49750 + 0.962386i 0.995217 + 0.0976842i \(0.0311435\pi\)
0.502285 + 0.864702i \(0.332493\pi\)
\(234\) −5.10679e6 + 3.55185e7i −0.0260551 + 0.181217i
\(235\) −1.37492e8 + 3.01066e8i −0.691099 + 1.51330i
\(236\) −6.05668e6 4.21251e7i −0.0299946 0.208617i
\(237\) 1.49267e8 + 4.38287e7i 0.728356 + 0.213865i
\(238\) 2.63118e7 1.69096e7i 0.126512 0.0813043i
\(239\) 1.18160e8 + 2.58734e8i 0.559857 + 1.22592i 0.952024 + 0.306022i \(0.0989981\pi\)
−0.392167 + 0.919894i \(0.628275\pi\)
\(240\) 8.37117e7 2.45800e7i 0.390883 0.114774i
\(241\) −6.42887e7 + 7.41932e7i −0.295852 + 0.341432i −0.884142 0.467218i \(-0.845256\pi\)
0.588289 + 0.808650i \(0.299802\pi\)
\(242\) 4.99491e7 5.76444e7i 0.226555 0.261459i
\(243\) −1.37677e7 + 4.04255e6i −0.0615515 + 0.0180732i
\(244\) −1.69167e7 3.70423e7i −0.0745504 0.163243i
\(245\) 2.68327e7 1.72443e7i 0.116569 0.0749142i
\(246\) 1.61185e8 + 4.73283e7i 0.690324 + 0.202697i
\(247\) 1.19263e7 + 8.29492e7i 0.0503577 + 0.350246i
\(248\) 2.20409e7 4.82628e7i 0.0917589 0.200924i
\(249\) 2.63988e6 1.83608e7i 0.0108364 0.0753692i
\(250\) −1.44552e8 9.28978e7i −0.585104 0.376024i
\(251\) 9.75052e7 + 1.12527e8i 0.389197 + 0.449157i 0.916209 0.400700i \(-0.131233\pi\)
−0.527012 + 0.849858i \(0.676688\pi\)
\(252\) −2.59698e7 −0.102227
\(253\) −9.67053e7 + 1.72535e8i −0.375430 + 0.669814i
\(254\) 1.21027e7 0.0463410
\(255\) −1.89691e7 2.18915e7i −0.0716401 0.0826771i
\(256\) −1.78048e8 1.14425e8i −0.663281 0.426265i
\(257\) −2.95448e7 + 2.05488e8i −0.108571 + 0.755129i 0.860696 + 0.509119i \(0.170029\pi\)
−0.969267 + 0.246010i \(0.920880\pi\)
\(258\) −1.74979e7 + 3.83150e7i −0.0634332 + 0.138899i
\(259\) −2.88546e6 2.00688e7i −0.0103197 0.0717749i
\(260\) 5.77117e7 + 1.69457e7i 0.203637 + 0.0597932i
\(261\) −5.35756e7 + 3.44309e7i −0.186520 + 0.119869i
\(262\) 2.75371e7 + 6.02978e7i 0.0945940 + 0.207132i
\(263\) 1.76291e7 5.17637e6i 0.0597565 0.0175461i −0.251718 0.967801i \(-0.580995\pi\)
0.311474 + 0.950255i \(0.399177\pi\)
\(264\) −9.43366e7 + 1.08870e8i −0.315549 + 0.364163i
\(265\) −4.01098e8 + 4.62892e8i −1.32401 + 1.52798i
\(266\) 1.42897e8 4.19583e7i 0.465519 0.136689i
\(267\) −7.46324e7 1.63422e8i −0.239960 0.525438i
\(268\) −5.80859e7 + 3.73295e7i −0.184331 + 0.118462i
\(269\) −4.14890e8 1.21823e8i −1.29957 0.381588i −0.442491 0.896773i \(-0.645905\pi\)
−0.857079 + 0.515185i \(0.827723\pi\)
\(270\) −8.40519e6 5.84594e7i −0.0259881 0.180751i
\(271\) −8.21844e7 + 1.79959e8i −0.250840 + 0.549263i −0.992604 0.121398i \(-0.961262\pi\)
0.741764 + 0.670661i \(0.233990\pi\)
\(272\) 4.98421e6 3.46659e7i 0.0150178 0.104451i
\(273\) 1.12744e8 + 7.24560e7i 0.335369 + 0.215529i
\(274\) 9.53357e7 + 1.10023e8i 0.279981 + 0.323115i
\(275\) −7.07071e7 −0.205021
\(276\) −2.85332e7 + 5.09068e7i −0.0816899 + 0.145745i
\(277\) −2.32061e8 −0.656030 −0.328015 0.944673i \(-0.606380\pi\)
−0.328015 + 0.944673i \(0.606380\pi\)
\(278\) −2.42170e8 2.79479e8i −0.676026 0.780176i
\(279\) −2.06722e7 1.32852e7i −0.0569865 0.0366230i
\(280\) 6.77801e7 4.71421e8i 0.184522 1.28338i
\(281\) −1.58574e7 + 3.47229e7i −0.0426345 + 0.0933564i −0.929751 0.368189i \(-0.879978\pi\)
0.887116 + 0.461546i \(0.152705\pi\)
\(282\) 3.85520e7 + 2.68135e8i 0.102371 + 0.712003i
\(283\) 3.09506e8 + 9.08792e7i 0.811740 + 0.238348i 0.661156 0.750249i \(-0.270066\pi\)
0.150584 + 0.988597i \(0.451885\pi\)
\(284\) 1.00177e8 6.43796e7i 0.259509 0.166776i
\(285\) −5.72977e7 1.25464e8i −0.146616 0.321043i
\(286\) 1.60090e8 4.70067e7i 0.404654 0.118817i
\(287\) 4.10866e8 4.74165e8i 1.02592 1.18398i
\(288\) −4.94215e7 + 5.70355e7i −0.121911 + 0.140693i
\(289\) 3.82560e8 1.12330e8i 0.932304 0.273749i
\(290\) −1.08893e8 2.38443e8i −0.262185 0.574105i
\(291\) −9.59423e7 + 6.16584e7i −0.228236 + 0.146679i
\(292\) −8.35086e7 2.45203e7i −0.196287 0.0576350i
\(293\) −1.05289e8 7.32300e8i −0.244538 1.70080i −0.628795 0.777571i \(-0.716451\pi\)
0.384257 0.923226i \(-0.374458\pi\)
\(294\) 1.08448e7 2.37467e7i 0.0248888 0.0544989i
\(295\) 5.14434e7 3.57797e8i 0.116668 0.811446i
\(296\) −2.79160e7 1.79405e7i −0.0625652 0.0402082i
\(297\) 4.36911e7 + 5.04222e7i 0.0967710 + 0.111680i
\(298\) 1.13832e8 0.249177
\(299\) 2.65902e8 1.41396e8i 0.575272 0.305906i
\(300\) −2.08623e7 −0.0446107
\(301\) 1.03020e8 + 1.18891e8i 0.217739 + 0.251285i
\(302\) 5.42308e8 + 3.48520e8i 1.13298 + 0.728122i
\(303\) 8.36791e6 5.82001e7i 0.0172810 0.120192i
\(304\) 6.92764e7 1.51694e8i 0.141425 0.309679i
\(305\) −4.92241e7 3.42361e8i −0.0993410 0.690932i
\(306\) −2.27479e7 6.67937e6i −0.0453853 0.0133263i
\(307\) 6.65543e8 4.27718e8i 1.31278 0.843672i 0.318238 0.948011i \(-0.396909\pi\)
0.994542 + 0.104339i \(0.0332727\pi\)
\(308\) 5.01622e7 + 1.09840e8i 0.0978248 + 0.214206i
\(309\) 4.56663e8 1.34088e8i 0.880524 0.258545i
\(310\) 6.62349e7 7.64391e7i 0.126276 0.145730i
\(311\) −2.68534e8 + 3.09905e8i −0.506219 + 0.584208i −0.950127 0.311865i \(-0.899046\pi\)
0.443907 + 0.896073i \(0.353592\pi\)
\(312\) 2.10460e8 6.17966e7i 0.392309 0.115192i
\(313\) 4.24985e8 + 9.30587e8i 0.783372 + 1.71535i 0.694717 + 0.719283i \(0.255530\pi\)
0.0886555 + 0.996062i \(0.471743\pi\)
\(314\) −5.79909e8 + 3.72685e8i −1.05708 + 0.679342i
\(315\) −2.11644e8 6.21444e7i −0.381522 0.112025i
\(316\) −3.03736e7 2.11253e8i −0.0541492 0.376616i
\(317\) 6.25131e7 1.36885e8i 0.110221 0.241350i −0.846481 0.532418i \(-0.821283\pi\)
0.956702 + 0.291068i \(0.0940107\pi\)
\(318\) −7.13432e7 + 4.96203e8i −0.124411 + 0.865296i
\(319\) 2.49110e8 + 1.60094e8i 0.429660 + 0.276125i
\(320\) −4.74277e8 5.47345e8i −0.809109 0.933762i
\(321\) 3.67929e7 0.0620863
\(322\) −3.15976e8 4.31979e8i −0.527422 0.721053i
\(323\) −5.53677e7 −0.0914213
\(324\) 1.28912e7 + 1.48772e7i 0.0210565 + 0.0243004i
\(325\) 9.05704e7 + 5.82061e7i 0.146351 + 0.0940538i
\(326\) 5.77490e6 4.01653e7i 0.00923172 0.0642080i
\(327\) 1.88602e8 4.12980e8i 0.298283 0.653149i
\(328\) −1.46138e8 1.01641e9i −0.228668 1.59042i
\(329\) 9.70747e8 + 2.85037e8i 1.50287 + 0.441282i
\(330\) −2.31020e8 + 1.48467e8i −0.353876 + 0.227422i
\(331\) −3.19680e7 7.00001e7i −0.0484526 0.106096i 0.883858 0.467756i \(-0.154937\pi\)
−0.932310 + 0.361660i \(0.882210\pi\)
\(332\) −2.44175e7 + 7.16963e6i −0.0366200 + 0.0107526i
\(333\) −1.00644e7 + 1.16149e7i −0.0149360 + 0.0172370i
\(334\) −3.09816e7 + 3.57546e7i −0.0454978 + 0.0525073i
\(335\) −5.62705e8 + 1.65225e8i −0.817756 + 0.240115i
\(336\) −1.10789e8 2.42593e8i −0.159334 0.348892i
\(337\) −4.09714e8 + 2.63307e8i −0.583145 + 0.374764i −0.798702 0.601727i \(-0.794480\pi\)
0.215557 + 0.976491i \(0.430843\pi\)
\(338\) 3.30446e8 + 9.70276e7i 0.465470 + 0.136674i
\(339\) −9.45836e7 6.57843e8i −0.131861 0.917115i
\(340\) −1.65084e7 + 3.61483e7i −0.0227787 + 0.0498784i
\(341\) −1.62605e7 + 1.13095e8i −0.0222072 + 0.154455i
\(342\) −9.49692e7 6.10330e7i −0.128378 0.0825037i
\(343\) 4.54817e8 + 5.24887e8i 0.608566 + 0.702322i
\(344\) 2.57474e8 0.341019
\(345\) −3.54352e8 + 3.46593e8i −0.464588 + 0.454415i
\(346\) −8.94735e8 −1.16126
\(347\) 3.09102e8 + 3.56723e8i 0.397145 + 0.458329i 0.918740 0.394864i \(-0.129208\pi\)
−0.521595 + 0.853193i \(0.674663\pi\)
\(348\) 7.35008e7 + 4.72361e7i 0.0934898 + 0.0600823i
\(349\) 7.28872e7 5.06941e8i 0.0917830 0.638365i −0.891055 0.453895i \(-0.850034\pi\)
0.982838 0.184470i \(-0.0590568\pi\)
\(350\) 7.94817e7 1.74041e8i 0.0990898 0.216976i
\(351\) −1.44574e7 1.00553e8i −0.0178449 0.124114i
\(352\) 3.36693e8 + 9.88620e7i 0.411467 + 0.120818i
\(353\) −9.15545e8 + 5.88385e8i −1.10782 + 0.711951i −0.960817 0.277185i \(-0.910599\pi\)
−0.147001 + 0.989136i \(0.546962\pi\)
\(354\) −1.22903e8 2.69120e8i −0.147249 0.322430i
\(355\) 9.70458e8 2.84952e8i 1.15127 0.338044i
\(356\) −1.61406e8 + 1.86272e8i −0.189603 + 0.218813i
\(357\) −5.79849e7 + 6.69182e7i −0.0674491 + 0.0778405i
\(358\) 2.12298e8 6.23362e7i 0.244543 0.0718042i
\(359\) 5.18512e8 + 1.13538e9i 0.591464 + 1.29513i 0.934553 + 0.355823i \(0.115800\pi\)
−0.343089 + 0.939303i \(0.611473\pi\)
\(360\) −3.03706e8 + 1.95180e8i −0.343080 + 0.220484i
\(361\) 6.04702e8 + 1.77556e8i 0.676497 + 0.198638i
\(362\) 1.41724e8 + 9.85711e8i 0.157023 + 1.09212i
\(363\) −8.97022e7 + 1.96420e8i −0.0984306 + 0.215533i
\(364\) 2.61662e7 1.81990e8i 0.0284371 0.197785i
\(365\) −6.21888e8 3.99663e8i −0.669402 0.430198i
\(366\) −1.85386e8 2.13947e8i −0.197649 0.228099i
\(367\) −6.23264e7 −0.0658174 −0.0329087 0.999458i \(-0.510477\pi\)
−0.0329087 + 0.999458i \(0.510477\pi\)
\(368\) −5.97262e8 4.93672e7i −0.624738 0.0516382i
\(369\) −4.75583e8 −0.492758
\(370\) −4.14254e7 4.78075e7i −0.0425168 0.0490670i
\(371\) 1.57506e9 + 1.01223e9i 1.60136 + 1.02913i
\(372\) −4.79772e6 + 3.33689e7i −0.00483208 + 0.0336079i
\(373\) −6.66578e8 + 1.45960e9i −0.665075 + 1.45631i 0.212642 + 0.977130i \(0.431793\pi\)
−0.877717 + 0.479180i \(0.840934\pi\)
\(374\) 1.56882e7 + 1.09114e8i 0.0155068 + 0.107853i
\(375\) 4.66746e8 + 1.37049e8i 0.457058 + 0.134204i
\(376\) 1.39301e9 8.95231e8i 1.35144 0.868516i
\(377\) −1.87302e8 4.10135e8i −0.180032 0.394214i
\(378\) −1.73224e8 + 5.08631e7i −0.164963 + 0.0484375i
\(379\) 8.26103e8 9.53373e8i 0.779465 0.899551i −0.217605 0.976037i \(-0.569825\pi\)
0.997071 + 0.0764860i \(0.0243701\pi\)
\(380\) −1.23916e8 + 1.43007e8i −0.115847 + 0.133695i
\(381\) −3.28751e7 + 9.65301e6i −0.0304530 + 0.00894181i
\(382\) 4.95964e7 + 1.08601e8i 0.0455228 + 0.0996810i
\(383\) −1.73117e9 + 1.11255e9i −1.57450 + 1.01187i −0.596668 + 0.802488i \(0.703509\pi\)
−0.977834 + 0.209383i \(0.932855\pi\)
\(384\) −2.25471e8 6.62042e7i −0.203203 0.0596659i
\(385\) 1.45962e8 + 1.01519e9i 0.130355 + 0.906638i
\(386\) −5.63919e8 + 1.23481e9i −0.499070 + 1.09281i
\(387\) 1.69705e7 1.18033e8i 0.0148836 0.103518i
\(388\) 1.31624e8 + 8.45896e7i 0.114400 + 0.0735201i
\(389\) −7.78722e8 8.98693e8i −0.670747 0.774083i 0.313746 0.949507i \(-0.398416\pi\)
−0.984493 + 0.175424i \(0.943870\pi\)
\(390\) 4.18137e8 0.356938
\(391\) 6.74667e7 + 1.87187e8i 0.0570783 + 0.158364i
\(392\) −1.59576e8 −0.133803
\(393\) −1.22893e8 1.41826e8i −0.102130 0.117864i
\(394\) −4.73335e8 3.04194e8i −0.389880 0.250561i
\(395\) 2.57984e8 1.79431e9i 0.210621 1.46490i
\(396\) 3.80234e7 8.32597e7i 0.0307693 0.0673754i
\(397\) −2.03136e8 1.41284e9i −0.162937 1.13325i −0.893061 0.449936i \(-0.851447\pi\)
0.730124 0.683315i \(-0.239462\pi\)
\(398\) −7.71132e8 2.26425e8i −0.613110 0.180025i
\(399\) −3.54691e8 + 2.27946e8i −0.279541 + 0.179650i
\(400\) −8.89998e7 1.94882e8i −0.0695311 0.152252i
\(401\) −1.76041e9 + 5.16904e8i −1.36336 + 0.400318i −0.879945 0.475075i \(-0.842421\pi\)
−0.483412 + 0.875393i \(0.660603\pi\)
\(402\) −3.14332e8 + 3.62759e8i −0.241323 + 0.278501i
\(403\) 1.13928e8 1.31480e8i 0.0867086 0.100067i
\(404\) −7.73987e7 + 2.27263e7i −0.0583981 + 0.0171472i
\(405\) 6.94579e7 + 1.52092e8i 0.0519552 + 0.113766i
\(406\) −6.74083e8 + 4.33207e8i −0.499888 + 0.321258i
\(407\) 6.85656e7 + 2.01327e7i 0.0504111 + 0.0148020i
\(408\) 2.06243e7 + 1.43445e8i 0.0150338 + 0.104562i
\(409\) 3.21947e8 7.04965e8i 0.232676 0.509490i −0.756894 0.653537i \(-0.773284\pi\)
0.989571 + 0.144047i \(0.0460116\pi\)
\(410\) 2.78583e8 1.93759e9i 0.199623 1.38841i
\(411\) −3.46717e8 2.22822e8i −0.246337 0.158311i
\(412\) −4.27590e8 4.93466e8i −0.301223 0.347629i
\(413\) −1.10496e9 −0.771832
\(414\) −9.06185e7 + 3.95442e8i −0.0627647 + 0.273893i
\(415\) −2.16150e8 −0.148452
\(416\) −3.49895e8 4.03800e8i −0.238293 0.275004i
\(417\) 8.80725e8 + 5.66008e8i 0.594791 + 0.382249i
\(418\) −7.47018e7 + 5.19563e8i −0.0500281 + 0.347953i
\(419\) 7.62570e8 1.66980e9i 0.506443 1.10896i −0.467878 0.883793i \(-0.654981\pi\)
0.974321 0.225163i \(-0.0722914\pi\)
\(420\) 4.30665e7 + 2.99534e8i 0.0283640 + 0.197276i
\(421\) 7.16238e8 + 2.10306e8i 0.467811 + 0.137362i 0.507138 0.861865i \(-0.330703\pi\)
−0.0393275 + 0.999226i \(0.512522\pi\)
\(422\) −1.42117e9 + 9.13327e8i −0.920558 + 0.591606i
\(423\) −3.18582e8 6.97597e8i −0.204659 0.448140i
\(424\) 2.94018e9 8.63315e8i 1.87324 0.550033i
\(425\) −4.65810e7 + 5.37574e7i −0.0294339 + 0.0339685i
\(426\) 5.42107e8 6.25625e8i 0.339744 0.392085i
\(427\) −1.01447e9 + 2.97874e8i −0.630580 + 0.185155i
\(428\) −2.09687e7 4.59150e7i −0.0129276 0.0283075i
\(429\) −3.97367e8 + 2.55372e8i −0.242992 + 0.156161i
\(430\) 4.70940e8 + 1.38281e8i 0.285645 + 0.0838729i
\(431\) 1.65613e8 + 1.15186e9i 0.0996375 + 0.692994i 0.977011 + 0.213187i \(0.0683843\pi\)
−0.877374 + 0.479807i \(0.840707\pi\)
\(432\) −8.39788e7 + 1.83888e8i −0.0501160 + 0.109739i
\(433\) −1.35585e8 + 9.43011e8i −0.0802606 + 0.558225i 0.909524 + 0.415652i \(0.136447\pi\)
−0.989784 + 0.142573i \(0.954462\pi\)
\(434\) −2.60096e8 1.67153e8i −0.152728 0.0981525i
\(435\) 4.85970e8 + 5.60839e8i 0.283072 + 0.326683i
\(436\) −6.22857e8 −0.359903
\(437\) 5.71259e7 + 9.45721e8i 0.0327452 + 0.542098i
\(438\) −6.05043e8 −0.344054
\(439\) 1.62607e9 + 1.87659e9i 0.917307 + 1.05863i 0.998083 + 0.0618965i \(0.0197149\pi\)
−0.0807755 + 0.996732i \(0.525740\pi\)
\(440\) 1.41214e9 + 9.07529e8i 0.790304 + 0.507898i
\(441\) −1.05179e7 + 7.31538e7i −0.00583976 + 0.0406164i
\(442\) 6.97272e7 1.52681e8i 0.0384082 0.0841023i
\(443\) −3.61786e8 2.51628e9i −0.197715 1.37514i −0.810894 0.585192i \(-0.801019\pi\)
0.613180 0.789943i \(-0.289890\pi\)
\(444\) 2.02305e7 + 5.94021e6i 0.0109690 + 0.00322078i
\(445\) −1.76114e9 + 1.13181e9i −0.947398 + 0.608856i
\(446\) 9.90015e8 + 2.16783e9i 0.528409 + 1.15705i
\(447\) −3.09206e8 + 9.07912e7i −0.163747 + 0.0480803i
\(448\) −1.44977e9 + 1.67313e9i −0.761776 + 0.879137i
\(449\) 2.32670e9 2.68516e9i 1.21305 1.39993i 0.321562 0.946888i \(-0.395792\pi\)
0.891487 0.453045i \(-0.149662\pi\)
\(450\) −1.39156e8 + 4.08598e7i −0.0719876 + 0.0211375i
\(451\) 9.18615e8 + 2.01149e9i 0.471537 + 1.03252i
\(452\) −7.67039e8 + 4.92946e8i −0.390691 + 0.251082i
\(453\) −1.75107e9 5.14160e8i −0.885033 0.259869i
\(454\) −1.73305e6 1.20536e7i −0.000869190 0.00604535i
\(455\) 6.48736e8 1.42053e9i 0.322870 0.706987i
\(456\) −9.82054e7 + 6.83034e8i −0.0485019 + 0.337338i
\(457\) −1.08748e9 6.98882e8i −0.532985 0.342529i 0.246304 0.969193i \(-0.420784\pi\)
−0.779290 + 0.626664i \(0.784420\pi\)
\(458\) 1.66287e9 + 1.91905e9i 0.808777 + 0.933378i
\(459\) 6.71183e7 0.0323964
\(460\) 6.34474e8 + 2.44680e8i 0.303921 + 0.117205i
\(461\) −1.95267e9 −0.928273 −0.464137 0.885764i \(-0.653635\pi\)
−0.464137 + 0.885764i \(0.653635\pi\)
\(462\) 5.49718e8 + 6.34408e8i 0.259354 + 0.299310i
\(463\) −1.45714e9 9.36446e8i −0.682287 0.438479i 0.153049 0.988219i \(-0.451091\pi\)
−0.835336 + 0.549739i \(0.814727\pi\)
\(464\) −1.27691e8 + 8.88107e8i −0.0593398 + 0.412717i
\(465\) −1.18949e8 + 2.60463e8i −0.0548627 + 0.120132i
\(466\) −4.66507e8 3.24463e9i −0.213554 1.48530i
\(467\) 3.86910e9 + 1.13607e9i 1.75793 + 0.516174i 0.991943 0.126684i \(-0.0404335\pi\)
0.765985 + 0.642858i \(0.222252\pi\)
\(468\) −1.17244e8 + 7.53484e7i −0.0528727 + 0.0339792i
\(469\) 7.44714e8 + 1.63070e9i 0.333338 + 0.729908i
\(470\) 3.02872e9 8.89313e8i 1.34560 0.395105i
\(471\) 1.27798e9 1.47487e9i 0.563574 0.650399i
\(472\) −1.18429e9 + 1.36675e9i −0.518397 + 0.598262i
\(473\) −5.32001e8 + 1.56210e8i −0.231153 + 0.0678725i
\(474\) −6.16347e8 1.34961e9i −0.265828 0.582082i
\(475\) −2.84934e8 + 1.83116e8i −0.121988 + 0.0783968i
\(476\) 1.16556e8 + 3.42238e7i 0.0495346 + 0.0145447i
\(477\) −2.01974e8 1.40476e9i −0.0852081 0.592635i
\(478\) 1.12692e9 2.46760e9i 0.471948 1.03342i
\(479\) 4.27126e8 2.97073e9i 0.177575 1.23506i −0.684777 0.728752i \(-0.740101\pi\)
0.862352 0.506309i \(-0.168990\pi\)
\(480\) 7.39800e8 + 4.75441e8i 0.305330 + 0.196224i
\(481\) −7.12540e7 8.22315e7i −0.0291945 0.0336923i
\(482\) 9.36284e8 0.380840
\(483\) 1.20284e9 + 9.21383e8i 0.485727 + 0.372070i
\(484\) 2.96242e8 0.118765
\(485\) 8.70268e8 + 1.00434e9i 0.346383 + 0.399747i
\(486\) 1.15124e8 + 7.39859e7i 0.0454926 + 0.0292363i
\(487\) 2.37503e8 1.65187e9i 0.0931788 0.648072i −0.888690 0.458509i \(-0.848384\pi\)
0.981868 0.189563i \(-0.0607073\pi\)
\(488\) −7.18854e8 + 1.57407e9i −0.280008 + 0.613133i
\(489\) 1.63488e7 + 1.13709e8i 0.00632274 + 0.0439756i
\(490\) −2.91877e8 8.57029e7i −0.112076 0.0329086i
\(491\) 1.10637e9 7.11022e8i 0.421809 0.271080i −0.312470 0.949927i \(-0.601157\pi\)
0.734280 + 0.678847i \(0.237520\pi\)
\(492\) 2.71040e8 + 5.93495e8i 0.102602 + 0.224667i
\(493\) 2.85827e8 8.39265e7i 0.107433 0.0315453i
\(494\) 5.23391e8 6.04025e8i 0.195336 0.225429i
\(495\) 5.09112e8 5.87547e8i 0.188667 0.217733i
\(496\) −3.32177e8 + 9.75361e7i −0.122232 + 0.0358905i
\(497\) −1.28436e9 2.81235e9i −0.469287 1.02759i
\(498\) −1.48827e8 + 9.56456e7i −0.0539983 + 0.0347026i
\(499\) −2.81754e9 8.27305e8i −1.01512 0.298067i −0.268475 0.963287i \(-0.586520\pi\)
−0.746648 + 0.665220i \(0.768338\pi\)
\(500\) −9.49760e7 6.60573e8i −0.0339796 0.236334i
\(501\) 5.56389e7 1.21832e8i 0.0197673 0.0432843i
\(502\) 2.02093e8 1.40558e9i 0.0712997 0.495900i
\(503\) −1.52964e9 9.83039e8i −0.535921 0.344416i 0.244521 0.969644i \(-0.421369\pi\)
−0.780442 + 0.625228i \(0.785006\pi\)
\(504\) 7.22677e8 + 8.34013e8i 0.251442 + 0.290179i
\(505\) −6.85152e8 −0.236738
\(506\) 1.84756e9 3.80546e8i 0.633976 0.130581i
\(507\) −9.74991e8 −0.332256
\(508\) 3.07822e7 + 3.55246e7i 0.0104178 + 0.0120228i
\(509\) −1.31358e9 8.44187e8i −0.441514 0.283744i 0.300937 0.953644i \(-0.402701\pi\)
−0.742451 + 0.669900i \(0.766337\pi\)
\(510\) −3.93160e7 + 2.73449e8i −0.0131242 + 0.0912810i
\(511\) −9.38719e8 + 2.05551e9i −0.311216 + 0.681469i
\(512\) 4.45807e8 + 3.10066e9i 0.146792 + 1.02096i
\(513\) 3.06648e8 + 9.00399e7i 0.100283 + 0.0294459i
\(514\) 1.66563e9 1.07044e9i 0.541013 0.347688i
\(515\) −2.30386e9 5.04476e9i −0.743244 1.62748i
\(516\) −1.56968e8 + 4.60901e7i −0.0502966 + 0.0147684i
\(517\) −2.33514e9 + 2.69490e9i −0.743184 + 0.857680i
\(518\) −1.26630e8 + 1.46138e8i −0.0400296 + 0.0461966i
\(519\) 2.43040e9 7.13631e8i 0.763119 0.224072i
\(520\) −1.06177e9 2.32495e9i −0.331145 0.725107i
\(521\) −1.16414e9 + 7.48148e8i −0.360640 + 0.231769i −0.708395 0.705816i \(-0.750580\pi\)
0.347755 + 0.937585i \(0.386944\pi\)
\(522\) 5.82778e8 + 1.71119e8i 0.179331 + 0.0526565i
\(523\) −1.92619e8 1.33970e9i −0.0588768 0.409497i −0.997852 0.0655116i \(-0.979132\pi\)
0.938975 0.343985i \(-0.111777\pi\)
\(524\) −1.06951e8 + 2.34190e8i −0.0324733 + 0.0711065i
\(525\) −7.70863e7 + 5.36147e8i −0.0232498 + 0.161706i
\(526\) −1.47413e8 9.47369e7i −0.0441659 0.0283837i
\(527\) 7.52715e7 + 8.68679e7i 0.0224023 + 0.0258537i
\(528\) 9.39967e8 0.277904
\(529\) 3.12769e9 1.34551e9i 0.918604 0.395178i
\(530\) 5.84148e9 1.70435
\(531\) 5.48494e8 + 6.32996e8i 0.158979 + 0.183472i
\(532\) 4.86603e8 + 3.12721e8i 0.140115 + 0.0900464i
\(533\) 4.79179e8 3.33276e9i 0.137073 0.953365i
\(534\) −7.11785e8 + 1.55859e9i −0.202281 + 0.442933i
\(535\) −6.10147e7 4.24366e8i −0.0172265 0.119813i
\(536\) 2.81521e9 + 8.26621e8i 0.789650 + 0.231862i
\(537\) −5.26954e8 + 3.38653e8i −0.146846 + 0.0943723i
\(538\) 1.71315e9 + 3.75127e9i 0.474304 + 1.03858i
\(539\) 3.29721e8 9.68149e7i 0.0906956 0.0266306i
\(540\) 1.50215e8 1.73357e8i 0.0410521 0.0473766i
\(541\) −1.66803e9 + 1.92501e9i −0.452913 + 0.522689i −0.935580 0.353114i \(-0.885123\pi\)
0.482667 + 0.875804i \(0.339668\pi\)
\(542\) 1.81038e9 5.31577e8i 0.488397 0.143406i
\(543\) −1.17116e9 2.56449e9i −0.313919 0.687387i
\(544\) 2.96972e8 1.90853e8i 0.0790897 0.0508279i
\(545\) −5.07605e9 1.49046e9i −1.34319 0.394397i
\(546\) −1.81902e8 1.26515e9i −0.0478259 0.332636i
\(547\) 1.90175e9 4.16424e9i 0.496818 1.08788i −0.480673 0.876900i \(-0.659608\pi\)
0.977491 0.210979i \(-0.0676651\pi\)
\(548\) −8.04681e7 + 5.59668e8i −0.0208878 + 0.145278i
\(549\) 6.74214e8 + 4.33291e8i 0.173898 + 0.111757i
\(550\) 4.41605e8 + 5.09639e8i 0.113179 + 0.130615i
\(551\) 1.41847e9 0.361234
\(552\) 2.42887e9 5.00278e8i 0.614635 0.126597i
\(553\) −5.54128e9 −1.39339
\(554\) 1.44935e9 + 1.67264e9i 0.362151 + 0.417944i
\(555\) 1.50656e8 + 9.68208e7i 0.0374077 + 0.0240405i
\(556\) 2.04404e8 1.42166e9i 0.0504344 0.350779i
\(557\) −1.14998e9 + 2.51811e9i −0.281967 + 0.617422i −0.996628 0.0820489i \(-0.973854\pi\)
0.714661 + 0.699471i \(0.246581\pi\)
\(558\) 3.33527e7 + 2.31973e8i 0.00812665 + 0.0565221i
\(559\) 8.10044e8 + 2.37850e8i 0.196140 + 0.0575920i
\(560\) −2.61433e9 + 1.68013e9i −0.629075 + 0.404282i
\(561\) −1.29643e8 2.83878e8i −0.0310012 0.0678831i
\(562\) 3.49312e8 1.02567e8i 0.0830113 0.0243743i
\(563\) −2.72214e9 + 3.14152e9i −0.642881 + 0.741925i −0.979882 0.199580i \(-0.936042\pi\)
0.337000 + 0.941505i \(0.390588\pi\)
\(564\) −6.88990e8 + 7.95137e8i −0.161710 + 0.186623i
\(565\) −7.43067e9 + 2.18184e9i −1.73324 + 0.508925i
\(566\) −1.27800e9 2.79843e9i −0.296261 0.648720i
\(567\) 4.29967e8 2.76323e8i 0.0990590 0.0636614i
\(568\) −4.85520e9 1.42562e9i −1.11170 0.326425i
\(569\) 4.50460e8 + 3.13302e9i 0.102509 + 0.712968i 0.974654 + 0.223719i \(0.0718198\pi\)
−0.872144 + 0.489249i \(0.837271\pi\)
\(570\) −5.46460e8 + 1.19658e9i −0.123594 + 0.270633i
\(571\) −2.76487e7 + 1.92301e8i −0.00621510 + 0.0432270i −0.992693 0.120667i \(-0.961497\pi\)
0.986478 + 0.163894i \(0.0524056\pi\)
\(572\) 5.45151e8 + 3.50348e8i 0.121795 + 0.0782732i
\(573\) −2.21340e8 2.55440e8i −0.0491494 0.0567214i
\(574\) −5.98375e9 −1.32063
\(575\) 9.66277e8 + 7.40175e8i 0.211965 + 0.162367i
\(576\) 1.67813e9 0.365888
\(577\) 5.74385e9 + 6.62875e9i 1.24477 + 1.43654i 0.857433 + 0.514595i \(0.172058\pi\)
0.387332 + 0.921940i \(0.373397\pi\)
\(578\) −3.19894e9 2.05584e9i −0.689063 0.442834i
\(579\) 5.46924e8 3.80394e9i 0.117099 0.814439i
\(580\) 4.22929e8 9.26086e8i 0.0900056 0.197085i
\(581\) 9.40316e7 + 6.54004e8i 0.0198910 + 0.138345i
\(582\) 1.04363e9 + 3.06438e8i 0.219440 + 0.0644335i
\(583\) −5.55133e9 + 3.56762e9i −1.16026 + 0.745657i
\(584\) 1.53638e9 + 3.36420e9i 0.319192 + 0.698934i
\(585\) −1.13580e9 + 3.33501e8i −0.234562 + 0.0688735i
\(586\) −4.62065e9 + 5.33251e9i −0.948552 + 1.09469i
\(587\) 1.15732e9 1.33562e9i 0.236167 0.272552i −0.625278 0.780402i \(-0.715014\pi\)
0.861445 + 0.507851i \(0.169560\pi\)
\(588\) 9.72852e7 2.85655e7i 0.0197345 0.00579457i
\(589\) 2.27364e8 + 4.97857e8i 0.0458477 + 0.100392i
\(590\) −2.90020e9 + 1.86385e9i −0.581361 + 0.373618i
\(591\) 1.52836e9 + 4.48767e8i 0.304557 + 0.0894261i
\(592\) 3.08147e7 + 2.14321e8i 0.00610425 + 0.0424560i
\(593\) −3.80358e9 + 8.32868e9i −0.749034 + 1.64016i 0.0190603 + 0.999818i \(0.493933\pi\)
−0.768094 + 0.640337i \(0.778795\pi\)
\(594\) 9.05557e7 6.29829e8i 0.0177281 0.123302i
\(595\) 8.67988e8 + 5.57822e8i 0.168929 + 0.108564i
\(596\) 2.89521e8 + 3.34125e8i 0.0560168 + 0.0646469i
\(597\) 2.27525e9 0.437642
\(598\) −2.67985e9 1.03346e9i −0.512456 0.197624i
\(599\) −9.17711e8 −0.174467 −0.0872333 0.996188i \(-0.527803\pi\)
−0.0872333 + 0.996188i \(0.527803\pi\)
\(600\) 5.80548e8 + 6.69988e8i 0.109726 + 0.126630i
\(601\) 1.24055e9 + 7.97253e8i 0.233106 + 0.149808i 0.651980 0.758236i \(-0.273939\pi\)
−0.418874 + 0.908044i \(0.637575\pi\)
\(602\) 2.13522e8 1.48508e9i 0.0398892 0.277435i
\(603\) 5.64501e8 1.23608e9i 0.104846 0.229582i
\(604\) 3.56317e8 + 2.47824e9i 0.0657972 + 0.457630i
\(605\) 2.41426e9 + 7.08890e8i 0.443241 + 0.130147i
\(606\) −4.71754e8 + 3.03178e8i −0.0861115 + 0.0553405i
\(607\) 9.89595e8 + 2.16691e9i 0.179596 + 0.393261i 0.977924 0.208963i \(-0.0670088\pi\)
−0.798327 + 0.602224i \(0.794282\pi\)
\(608\) 1.61283e9 4.73569e8i 0.291022 0.0854517i
\(609\) 1.48552e9 1.71438e9i 0.266512 0.307572i
\(610\) −2.16022e9 + 2.49303e9i −0.385340 + 0.444706i
\(611\) 5.20957e9 1.52967e9i 0.923970 0.271302i
\(612\) −3.82515e7 8.37590e7i −0.00674556 0.0147707i
\(613\) 2.56594e9 1.64903e9i 0.449920 0.289146i −0.295992 0.955190i \(-0.595650\pi\)
0.745912 + 0.666044i \(0.232014\pi\)
\(614\) −7.23957e9 2.12573e9i −1.26219 0.370611i
\(615\) 7.88673e8 + 5.48534e9i 0.136721 + 0.950913i
\(616\) 2.13158e9 4.66752e9i 0.367426 0.804551i
\(617\) −6.91131e8 + 4.80692e9i −0.118457 + 0.823890i 0.840798 + 0.541349i \(0.182086\pi\)
−0.959255 + 0.282541i \(0.908823\pi\)
\(618\) −3.81858e9 2.45406e9i −0.650793 0.418239i
\(619\) 5.42551e8 + 6.26137e8i 0.0919439 + 0.106109i 0.799857 0.600191i \(-0.204909\pi\)
−0.707913 + 0.706300i \(0.750363\pi\)
\(620\) 3.92830e8 0.0661964
\(621\) −6.92497e7 1.14643e9i −0.0116037 0.192100i
\(622\) 3.91086e9 0.651638
\(623\) 4.19067e9 + 4.83629e9i 0.694345 + 0.801316i
\(624\) −1.20403e9 7.73780e8i −0.198376 0.127489i
\(625\) 1.03862e9 7.22377e9i 0.170168 1.18354i
\(626\) 4.05317e9 8.87521e9i 0.660366 1.44600i
\(627\) −2.11482e8 1.47089e9i −0.0342639 0.238311i
\(628\) −2.56887e9 7.54288e8i −0.413889 0.121529i
\(629\) 6.04767e7 3.88660e7i 0.00968972 0.00622720i
\(630\) 8.73913e8 + 1.91360e9i 0.139244 + 0.304902i
\(631\) 1.08683e10 3.19123e9i 1.72211 0.505656i 0.736750 0.676165i \(-0.236359\pi\)
0.985356 + 0.170509i \(0.0545411\pi\)
\(632\) −5.93911e9 + 6.85410e9i −0.935861 + 1.08004i
\(633\) 3.13191e9 3.61441e9i 0.490790 0.566402i
\(634\) −1.37706e9 + 4.04341e8i −0.214605 + 0.0630137i
\(635\) 1.65855e8 + 3.63172e8i 0.0257052 + 0.0562865i
\(636\) −1.63794e9 + 1.05264e9i −0.252462 + 0.162248i
\(637\) −5.02045e8 1.47414e8i −0.0769582 0.0225970i
\(638\) −4.01917e8 2.79540e9i −0.0612723 0.426158i
\(639\) −9.73555e8 + 2.13179e9i −0.147607 + 0.323215i
\(640\) −3.89690e8 + 2.71035e9i −0.0587610 + 0.408692i
\(641\) 2.16746e8 + 1.39294e8i 0.0325048 + 0.0208896i 0.556792 0.830652i \(-0.312032\pi\)
−0.524287 + 0.851541i \(0.675668\pi\)
\(642\) −2.29792e8 2.65194e8i −0.0342737 0.0395540i
\(643\) 2.64662e9 0.392603 0.196301 0.980544i \(-0.437107\pi\)
0.196301 + 0.980544i \(0.437107\pi\)
\(644\) 4.64311e8 2.02617e9i 0.0685029 0.298934i
\(645\) −1.38952e9 −0.203895
\(646\) 3.45801e8 + 3.99076e8i 0.0504676 + 0.0582428i
\(647\) −1.01046e10 6.49384e9i −1.46674 0.942619i −0.998249 0.0591536i \(-0.981160\pi\)
−0.468496 0.883466i \(-0.655204\pi\)
\(648\) 1.19047e8 8.27993e8i 0.0171873 0.119540i
\(649\) 1.61782e9 3.54253e9i 0.232313 0.508695i
\(650\) −1.46127e8 1.01634e9i −0.0208706 0.145158i
\(651\) 8.39828e8 + 2.46596e8i 0.119305 + 0.0350310i
\(652\) 1.32583e8 8.52060e7i 0.0187336 0.0120394i
\(653\) 3.26797e9 + 7.15586e9i 0.459285 + 1.00569i 0.987650 + 0.156677i \(0.0500780\pi\)
−0.528365 + 0.849017i \(0.677195\pi\)
\(654\) −4.15458e9 + 1.21989e9i −0.580771 + 0.170530i
\(655\) −1.43202e9 + 1.65263e9i −0.199115 + 0.229791i
\(656\) −4.38777e9 + 5.06376e9i −0.606849 + 0.700341i
\(657\) 1.64350e9 4.82575e8i 0.226095 0.0663875i
\(658\) −4.00837e9 8.77711e9i −0.548501 1.20105i
\(659\) −3.31936e9 + 2.13322e9i −0.451810 + 0.290360i −0.746688 0.665174i \(-0.768357\pi\)
0.294878 + 0.955535i \(0.404721\pi\)
\(660\) −1.02337e9 3.00488e8i −0.138557 0.0406839i
\(661\) 1.49388e8 + 1.03902e9i 0.0201193 + 0.139932i 0.997405 0.0719926i \(-0.0229358\pi\)
−0.977286 + 0.211925i \(0.932027\pi\)
\(662\) −3.04885e8 + 6.67606e8i −0.0408445 + 0.0894370i
\(663\) −6.76258e7 + 4.70348e8i −0.00901187 + 0.0626789i
\(664\) 9.09730e8 + 5.84648e8i 0.120594 + 0.0775008i
\(665\) 3.21731e9 + 3.71297e9i 0.424245 + 0.489605i
\(666\) 1.46575e8 0.0192265
\(667\) −1.72843e9 4.79555e9i −0.225534 0.625746i
\(668\) −1.83748e8 −0.0238509
\(669\) −4.41825e9 5.09894e9i −0.570505 0.658398i
\(670\) 4.70530e9 + 3.02391e9i 0.604402 + 0.388425i
\(671\) 5.30330e8 3.68853e9i 0.0677669 0.471329i
\(672\) 1.11670e9 2.44524e9i 0.141953 0.310835i
\(673\) −1.25569e9 8.73350e9i −0.158792 1.10442i −0.900863 0.434102i \(-0.857066\pi\)
0.742071 0.670321i \(-0.233844\pi\)
\(674\) 4.45674e9 + 1.30862e9i 0.560671 + 0.164628i
\(675\) 3.45405e8 2.21978e8i 0.0432280 0.0277810i
\(676\) 5.55658e8 + 1.21672e9i 0.0691822 + 0.151488i
\(677\) 1.76102e9 5.17083e8i 0.218125 0.0640471i −0.170844 0.985298i \(-0.554650\pi\)
0.388969 + 0.921251i \(0.372831\pi\)
\(678\) −4.15084e9 + 4.79033e9i −0.511484 + 0.590284i
\(679\) 2.66024e9 3.07008e9i 0.326120 0.376362i
\(680\) 1.62028e9 4.75758e8i 0.197610 0.0580236i
\(681\) 1.43214e7 + 3.13594e7i 0.00173768 + 0.00380498i
\(682\) 9.16713e8 5.89135e8i 0.110659 0.0711164i
\(683\) 5.98085e9 + 1.75614e9i 0.718275 + 0.210905i 0.620390 0.784293i \(-0.286974\pi\)
0.0978846 + 0.995198i \(0.468792\pi\)
\(684\) −6.23984e7 4.33990e8i −0.00745550 0.0518541i
\(685\) −1.99504e9 + 4.36853e9i −0.237156 + 0.519300i
\(686\) 9.42670e8 6.55642e9i 0.111487 0.775411i
\(687\) −6.04753e9 3.88651e9i −0.711589 0.457311i
\(688\) −1.10018e9 1.26967e9i −0.128796 0.148639i
\(689\) 1.00477e10 1.17030
\(690\) 4.71128e9 + 3.89415e8i 0.545967 + 0.0451274i
\(691\) 1.38113e10 1.59243 0.796217 0.605011i \(-0.206831\pi\)
0.796217 + 0.605011i \(0.206831\pi\)
\(692\) −2.27568e9 2.62627e9i −0.261059 0.301278i
\(693\) −1.99922e9 1.28482e9i −0.228188 0.146648i
\(694\) 6.40656e8 4.45586e9i 0.0727556 0.506026i
\(695\) 5.06776e9 1.10969e10i 0.572624 1.25387i
\(696\) −5.28374e8 3.67492e9i −0.0594031 0.413157i
\(697\) 2.13447e9 + 6.26737e8i 0.238768 + 0.0701085i
\(698\) −4.10913e9 + 2.64077e9i −0.457357 + 0.293926i
\(699\) 3.85507e9 + 8.44143e9i 0.426935 + 0.934858i
\(700\) 7.13007e8 2.09358e8i 0.0785689 0.0230699i
\(701\) 7.17728e9 8.28302e9i 0.786949 0.908188i −0.210641 0.977563i \(-0.567555\pi\)
0.997591 + 0.0693754i \(0.0221006\pi\)
\(702\) −6.34469e8 + 7.32216e8i −0.0692198 + 0.0798840i
\(703\) 3.28443e8 9.64396e7i 0.0356547 0.0104692i
\(704\) −3.24141e9 7.09769e9i −0.350130 0.766678i
\(705\) −7.51773e9 + 4.83135e9i −0.808025 + 0.519286i
\(706\) 9.95901e9 + 2.92423e9i 1.06512 + 0.312748i
\(707\) 2.98061e8 + 2.07306e9i 0.0317203 + 0.220620i
\(708\) 4.77343e8 1.04523e9i 0.0505491 0.110687i
\(709\) 7.02649e8 4.88703e9i 0.0740417 0.514971i −0.918724 0.394901i \(-0.870779\pi\)
0.992765 0.120070i \(-0.0383120\pi\)
\(710\) −8.11491e9 5.21513e9i −0.850902 0.546841i
\(711\) 2.75064e9 + 3.17441e9i 0.287006 + 0.331222i
\(712\) 1.04736e10 1.08747
\(713\) 1.40611e9 1.37532e9i 0.145280 0.142099i
\(714\) 8.44477e8 0.0868249
\(715\) 3.60441e9 + 4.15972e9i 0.368777 + 0.425591i
\(716\) 7.22932e8 + 4.64600e8i 0.0736041 + 0.0473025i
\(717\) −1.09295e9 + 7.60166e9i −0.110735 + 0.770178i
\(718\) 4.94516e9 1.08284e10i 0.498592 1.09176i
\(719\) −1.73794e9 1.20877e10i −0.174375 1.21281i −0.869506 0.493922i \(-0.835563\pi\)
0.695131 0.718883i \(-0.255346\pi\)
\(720\) 2.26022e9 + 6.63659e8i 0.225676 + 0.0662646i
\(721\) −1.42617e10 + 9.16541e9i −1.41709 + 0.910706i
\(722\) −2.49691e9 5.46747e9i −0.246901 0.540638i
\(723\) −2.54326e9 + 7.46770e8i −0.250269 + 0.0734857i
\(724\) −2.53285e9 + 2.92306e9i −0.248041 + 0.286255i
\(725\) 1.19336e9 1.37721e9i 0.116302 0.134220i
\(726\) 1.97599e9 5.80203e8i 0.191649 0.0562732i
\(727\) 6.96651e9 + 1.52545e10i 0.672427 + 1.47241i 0.870473 + 0.492216i \(0.163813\pi\)
−0.198047 + 0.980193i \(0.563460\pi\)
\(728\) −6.57269e9 + 4.22401e9i −0.631369 + 0.405756i
\(729\) −3.71727e8 1.09149e8i −0.0355368 0.0104345i
\(730\) 1.00336e9 + 6.97852e9i 0.0954612 + 0.663947i
\(731\) −2.31713e8 + 5.07380e8i −0.0219401 + 0.0480422i
\(732\) 1.56475e8 1.08831e9i 0.0147454 0.102557i
\(733\) −1.07572e10 6.91321e9i −1.00887 0.648360i −0.0717676 0.997421i \(-0.522864\pi\)
−0.937100 + 0.349062i \(0.886500\pi\)
\(734\) 3.89263e8 + 4.49233e8i 0.0363334 + 0.0419310i
\(735\) 8.61193e8 0.0800009
\(736\) −3.56631e9 4.87560e9i −0.329721 0.450771i
\(737\) −6.31841e9 −0.581395
\(738\) 2.97028e9 + 3.42788e9i 0.272019 + 0.313927i
\(739\) 1.55173e9 + 9.97234e8i 0.141436 + 0.0908954i 0.609445 0.792828i \(-0.291392\pi\)
−0.468009 + 0.883724i \(0.655029\pi\)
\(740\) 3.49651e7 2.43188e8i 0.00317193 0.0220613i
\(741\) −9.39943e8 + 2.05819e9i −0.0848668 + 0.185832i
\(742\) −2.54122e9 1.76746e10i −0.228364 1.58831i
\(743\) 1.26499e9 + 3.71434e8i 0.113143 + 0.0332217i 0.337814 0.941213i \(-0.390313\pi\)
−0.224671 + 0.974435i \(0.572131\pi\)
\(744\) 1.20514e9 7.74496e8i 0.107283 0.0689468i
\(745\) 1.55995e9 + 3.41580e9i 0.138217 + 0.302654i
\(746\) 1.46836e10 4.31149e9i 1.29493 0.380226i
\(747\) 3.27980e8 3.78509e8i 0.0287889 0.0332242i
\(748\) −2.80376e8 + 3.23571e8i −0.0244954 + 0.0282692i
\(749\) −1.25746e9 + 3.69224e8i −0.109347 + 0.0321073i
\(750\) −1.92727e9 4.22013e9i −0.166812 0.365268i
\(751\) 3.47614e9 2.23398e9i 0.299473 0.192460i −0.382271 0.924050i \(-0.624858\pi\)
0.681744 + 0.731591i \(0.261222\pi\)
\(752\) −1.03669e10 3.04400e9i −0.888970 0.261025i
\(753\) 5.72127e8 + 3.97923e9i 0.0488326 + 0.339638i
\(754\) −1.78634e9 + 3.91155e9i −0.151763 + 0.332314i
\(755\) −3.02644e9 + 2.10494e10i −0.255928 + 1.78002i
\(756\) −5.89875e8 3.79089e8i −0.0496516 0.0319092i
\(757\) 2.51277e7 + 2.89989e7i 0.00210531 + 0.00242966i 0.756801 0.653645i \(-0.226761\pi\)
−0.754696 + 0.656075i \(0.772216\pi\)
\(758\) −1.20311e10 −1.00338
\(759\) −4.71509e9 + 2.50729e9i −0.391421 + 0.208141i
\(760\) 8.04092e9 0.664444
\(761\) 5.66188e9 + 6.53416e9i 0.465709 + 0.537457i 0.939213 0.343335i \(-0.111557\pi\)
−0.473504 + 0.880792i \(0.657011\pi\)
\(762\) 2.74900e8 + 1.76667e8i 0.0225077 + 0.0144648i
\(763\) −2.30146e9 + 1.60070e10i −0.187572 + 1.30459i
\(764\) −1.92627e8 + 4.21795e8i −0.0156276 + 0.0342196i
\(765\) −1.11304e8 7.74138e8i −0.00898869 0.0625177i
\(766\) 1.88311e10 + 5.52931e9i 1.51382 + 0.444498i
\(767\) −4.98851e9 + 3.20592e9i −0.399197 + 0.256548i
\(768\) −2.37387e9 5.19804e9i −0.189100 0.414072i
\(769\) −7.21966e9 + 2.11988e9i −0.572499 + 0.168101i −0.555152 0.831749i \(-0.687340\pi\)
−0.0173466 + 0.999850i \(0.505522\pi\)
\(770\) 6.40561e9 7.39247e9i 0.505642 0.583542i
\(771\) −3.67065e9 + 4.23616e9i −0.288438 + 0.332875i
\(772\) −5.05875e9 + 1.48538e9i −0.395715 + 0.116193i
\(773\) −4.17706e8 9.14649e8i −0.0325269 0.0712240i 0.892671 0.450709i \(-0.148829\pi\)
−0.925198 + 0.379485i \(0.876101\pi\)
\(774\) −9.56740e8 + 6.14860e8i −0.0741653 + 0.0476631i
\(775\) 6.74659e8 + 1.98098e8i 0.0520629 + 0.0152870i
\(776\) −9.46204e8 6.58099e9i −0.0726890 0.505563i
\(777\) 2.27411e8 4.97960e8i 0.0173915 0.0380821i
\(778\) −1.61401e9 + 1.12257e10i −0.122879 + 0.854640i
\(779\) 8.91112e9 + 5.72683e9i 0.675385 + 0.434043i
\(780\) 1.06349e9 + 1.22734e9i 0.0802423 + 0.0926046i
\(781\) 1.08969e10 0.818512
\(782\) 9.27831e8 1.65537e9i 0.0693818 0.123786i
\(783\) −1.71951e9 −0.128008
\(784\) 6.81864e8 + 7.86913e8i 0.0505349 + 0.0583204i
\(785\) −1.91303e10 1.22943e10i −1.41149 0.907112i
\(786\) −2.54712e8 + 1.77156e9i −0.0187099 + 0.130130i
\(787\) 8.63401e9 1.89058e10i 0.631395 1.38256i −0.275540 0.961290i \(-0.588857\pi\)
0.906935 0.421272i \(-0.138416\pi\)
\(788\) −3.10999e8 2.16304e9i −0.0226421 0.157479i
\(789\) 4.75986e8 + 1.39762e8i 0.0345004 + 0.0101302i
\(790\) −1.45442e10 + 9.34700e9i −1.04953 + 0.674493i
\(791\) 9.83415e9 + 2.15338e10i 0.706511 + 1.54704i
\(792\) −3.73196e9 + 1.09580e9i −0.266931 + 0.0783780i
\(793\) −3.71570e9 + 4.28815e9i −0.264597 + 0.305361i
\(794\) −8.91469e9 + 1.02881e10i −0.632026 + 0.729396i
\(795\) −1.58674e10 + 4.65910e9i −1.12001 + 0.328865i
\(796\) −1.29669e9 2.83936e9i −0.0911257 0.199537i
\(797\) −7.43528e9 + 4.77836e9i −0.520227 + 0.334330i −0.774262 0.632865i \(-0.781879\pi\)
0.254035 + 0.967195i \(0.418242\pi\)
\(798\) 3.85822e9 + 1.13287e9i 0.268767 + 0.0789172i
\(799\) 5.10518e8 + 3.55073e9i 0.0354077 + 0.246266i
\(800\) 8.97082e8 1.96434e9i 0.0619466 0.135644i
\(801\) 6.90334e8 4.80138e9i 0.0474619 0.330105i
\(802\) 1.47205e10 + 9.46027e9i 1.00765 + 0.647580i
\(803\) −5.21558e9 6.01910e9i −0.355466 0.410229i
\(804\) −1.86426e9 −0.126506
\(805\) 8.63246e9 1.54014e10i 0.583243 1.04058i
\(806\) −1.65921e9 −0.111617
\(807\) −7.64546e9 8.82333e9i −0.512090 0.590983i
\(808\) 2.88366e9 + 1.85322e9i 0.192311 + 0.123591i
\(809\) −3.31643e9 + 2.30663e10i −0.220217 + 1.53164i 0.516999 + 0.855986i \(0.327049\pi\)
−0.737216 + 0.675657i \(0.763860\pi\)
\(810\) 6.62435e8 1.45053e9i 0.0437971 0.0959023i
\(811\) −3.13152e9 2.17802e10i −0.206149 1.43380i −0.785571 0.618772i \(-0.787631\pi\)
0.579421 0.815028i \(-0.303279\pi\)
\(812\) −2.98604e9 8.76781e8i −0.195726 0.0574705i
\(813\) −4.49364e9 + 2.88789e9i −0.293279 + 0.188479i
\(814\) −2.83119e8 6.19943e8i −0.0183985 0.0402871i
\(815\) 1.28439e9 3.77132e8i 0.0831088 0.0244029i
\(816\) 6.19240e8 7.14640e8i 0.0398973 0.0460439i
\(817\) −1.73930e9 + 2.00726e9i −0.111583 + 0.128773i
\(818\) −7.09194e9 + 2.08238e9i −0.453032 + 0.133022i
\(819\) 1.50318e9 + 3.29151e9i 0.0956131 + 0.209364i
\(820\) 6.39586e9 4.11037e9i 0.405089 0.260335i
\(821\) −4.99655e9 1.46712e9i −0.315115 0.0925260i 0.120351 0.992731i \(-0.461598\pi\)
−0.435466 + 0.900205i \(0.643416\pi\)
\(822\) 5.59397e8 + 3.89069e9i 0.0351293 + 0.244329i
\(823\) −1.42689e9 + 3.12444e9i −0.0892256 + 0.195377i −0.948984 0.315324i \(-0.897887\pi\)
0.859758 + 0.510701i \(0.170614\pi\)
\(824\) −3.94871e9 + 2.74639e10i −0.245872 + 1.71008i
\(825\) −1.60603e9 1.03213e9i −0.0995784 0.0639952i
\(826\) 6.90111e9 + 7.96430e9i 0.426077 + 0.491720i
\(827\) 2.32411e10 1.42885 0.714427 0.699710i \(-0.246687\pi\)
0.714427 + 0.699710i \(0.246687\pi\)
\(828\) −1.39120e9 + 7.39783e8i −0.0851694 + 0.0452895i
\(829\) −3.18335e10 −1.94063 −0.970316 0.241839i \(-0.922249\pi\)
−0.970316 + 0.241839i \(0.922249\pi\)
\(830\) 1.34997e9 + 1.55795e9i 0.0819506 + 0.0945761i
\(831\) −5.27101e9 3.38747e9i −0.318632 0.204773i
\(832\) −1.69082e9 + 1.17599e10i −0.101781 + 0.707901i
\(833\) 1.43610e8 3.14462e8i 0.00860849 0.0188500i
\(834\) −1.42097e9 9.88307e9i −0.0848212 0.589944i
\(835\) −1.49747e9 4.39698e8i −0.0890136 0.0261367i
\(836\) −1.71504e9 + 1.10219e9i −0.101520 + 0.0652432i
\(837\) −2.75617e8 6.03516e8i −0.0162467 0.0355754i
\(838\) −1.67981e10 + 4.93238e9i −0.986068 + 0.289536i
\(839\) 1.63629e10 1.88838e10i 0.956516 1.10388i −0.0379978 0.999278i \(-0.512098\pi\)
0.994514 0.104601i \(-0.0333566\pi\)
\(840\) 8.42102e9 9.71837e9i 0.490216 0.565739i
\(841\) 9.22852e9 2.70974e9i 0.534990 0.157087i
\(842\) −2.95746e9 6.47594e9i −0.170737 0.373861i
\(843\) −8.67044e8 + 5.57216e8i −0.0498477 + 0.0320351i
\(844\) −6.29545e9 1.84851e9i −0.360436 0.105834i
\(845\) 1.61686e9 + 1.12455e10i 0.0921877 + 0.641179i
\(846\) −3.03839e9 + 6.65314e9i −0.172523 + 0.377772i
\(847\) 1.09461e9 7.61319e9i 0.0618968 0.430502i
\(848\) −1.68206e10 1.08099e10i −0.947229 0.608747i
\(849\) 5.70348e9 + 6.58217e9i 0.319863 + 0.369141i
\(850\) 6.78394e8 0.0378892
\(851\) −7.26258e8 9.92888e8i −0.0403959 0.0552264i
\(852\) 3.21517e9 0.178100
\(853\) 5.14795e9 + 5.94105e9i 0.283996 + 0.327749i 0.879767 0.475405i \(-0.157699\pi\)
−0.595770 + 0.803155i \(0.703153\pi\)
\(854\) 8.48291e9 + 5.45163e9i 0.466060 + 0.299519i
\(855\) 5.29991e8 3.68617e9i 0.0289993 0.201694i
\(856\) −8.91039e8 + 1.95110e9i −0.0485555 + 0.106322i
\(857\) −2.22103e9 1.54476e10i −0.120537 0.838357i −0.956949 0.290255i \(-0.906260\pi\)
0.836412 0.548101i \(-0.184649\pi\)
\(858\) 4.32244e9 + 1.26918e9i 0.233627 + 0.0685991i
\(859\) −2.42174e10 + 1.55636e10i −1.30362 + 0.837788i −0.993602 0.112942i \(-0.963973\pi\)
−0.310022 + 0.950729i \(0.600336\pi\)
\(860\) 7.91905e8 + 1.73403e9i 0.0424550 + 0.0929635i
\(861\) 1.62539e10 4.77257e9i 0.867853 0.254825i
\(862\) 7.26798e9 8.38770e9i 0.386490 0.446033i
\(863\) −1.54160e10 + 1.77911e10i −0.816460 + 0.942246i −0.999162 0.0409228i \(-0.986970\pi\)
0.182702 + 0.983168i \(0.441516\pi\)
\(864\) −1.95512e9 + 5.74074e8i −0.103128 + 0.0302810i
\(865\) −1.22614e10 2.68487e10i −0.644144 1.41048i
\(866\) 7.64379e9 4.91236e9i 0.399941 0.257026i
\(867\) 1.03291e10 + 3.03291e9i 0.538266 + 0.158049i
\(868\) −1.70893e8 1.18859e9i −0.00886961 0.0616895i
\(869\) 8.11320e9 1.77654e10i 0.419395 0.918347i
\(870\) 1.00724e9 7.00550e9i 0.0518579 0.360680i
\(871\) 8.09339e9 + 5.20130e9i 0.415018 + 0.266716i
\(872\) 1.73326e10 + 2.00029e10i 0.885230 + 1.02161i
\(873\) −3.07927e9 −0.156638
\(874\) 6.45974e9 6.31830e9i 0.327284 0.320118i
\(875\) −1.73272e10 −0.874379
\(876\) −1.53887e9 1.77595e9i −0.0773460 0.0892620i
\(877\) −1.54064e10 9.90108e9i −0.771262 0.495660i 0.0948612 0.995491i \(-0.469759\pi\)
−0.866123 + 0.499830i \(0.833396\pi\)
\(878\) 3.37026e9 2.34407e10i 0.168048 1.16880i
\(879\) 8.29809e9 1.81703e10i 0.412114 0.902404i
\(880\) −1.55878e9 1.08415e10i −0.0771071 0.536291i
\(881\) 1.31054e10 + 3.84811e9i 0.645708 + 0.189597i 0.588158 0.808746i \(-0.299853\pi\)
0.0575494 + 0.998343i \(0.481671\pi\)
\(882\) 5.92964e8 3.81075e8i 0.0290997 0.0187012i
\(883\) −1.36017e10 2.97835e10i −0.664858 1.45584i −0.877925 0.478799i \(-0.841072\pi\)
0.213066 0.977038i \(-0.431655\pi\)
\(884\) 6.25502e8 1.83664e8i 0.0304541 0.00894214i
\(885\) 6.39135e9 7.37601e9i 0.309950 0.357701i
\(886\) −1.58771e10 + 1.83232e10i −0.766927 + 0.885081i
\(887\) −9.51165e9 + 2.79287e9i −0.457639 + 0.134375i −0.502423 0.864622i \(-0.667558\pi\)
0.0447843 + 0.998997i \(0.485740\pi\)
\(888\) −3.72197e8 8.14997e8i −0.0178372 0.0390581i
\(889\) 1.02670e9 6.59817e8i 0.0490101 0.0314969i
\(890\) 1.91571e10 + 5.62502e9i 0.910886 + 0.267460i
\(891\) 2.56365e8 + 1.78305e9i 0.0121419 + 0.0844486i
\(892\) −3.84511e9 + 8.41962e9i −0.181398 + 0.397206i
\(893\) −2.43091e9 + 1.69073e10i −0.114232 + 0.794502i
\(894\) 2.58556e9 + 1.66164e9i 0.121025 + 0.0777778i
\(895\) 4.77986e9 + 5.51625e9i 0.222861 + 0.257196i
\(896\) 8.37023e9 0.388740
\(897\) 8.10366e9 + 6.69815e8i 0.374893 + 0.0309871i
\(898\) −3.38855e10 −1.56152
\(899\) −1.92838e9 2.22547e9i −0.0885186 0.102156i
\(900\) −4.73864e8 3.04534e8i −0.0216673 0.0139247i
\(901\) −9.44750e8 + 6.57088e9i −0.0430309 + 0.299286i
\(902\) 8.76103e9 1.91840e10i 0.397496 0.870394i
\(903\) 6.04484e8 + 4.20428e9i 0.0273198 + 0.190013i
\(904\) 3.71756e10 + 1.09158e10i 1.67367 + 0.491433i
\(905\) −2.76365e10 + 1.77609e10i −1.23940 + 0.796515i
\(906\) 7.23045e9 + 1.58325e10i 0.323011 + 0.707294i
\(907\) 3.73432e10 1.09650e10i 1.66183 0.487957i 0.690031 0.723779i \(-0.257597\pi\)
0.971796 + 0.235823i \(0.0757785\pi\)
\(908\) 3.09725e7 3.57442e7i 0.00137302 0.00158455i
\(909\) 1.03963e9 1.19980e9i 0.0459098 0.0529828i
\(910\) −1.42906e10 + 4.19609e9i −0.628643 + 0.184586i
\(911\) −1.58683e10 3.47467e10i −0.695369 1.52265i −0.845498 0.533979i \(-0.820696\pi\)
0.150129 0.988666i \(-0.452031\pi\)
\(912\) 3.78786e9 2.43431e9i 0.165353 0.106266i
\(913\) −2.23442e9 6.56086e8i −0.0971667 0.0285307i
\(914\) 1.75455e9 + 1.22032e10i 0.0760073 + 0.528642i
\(915\) 3.87948e9 8.49488e9i 0.167417 0.366592i
\(916\) −1.40354e9 + 9.76187e9i −0.0603382 + 0.419661i
\(917\) 5.62334e9 + 3.61390e9i 0.240825 + 0.154769i
\(918\) −4.19191e8 4.83772e8i −0.0178839 0.0206391i
\(919\) 3.24679e10 1.37991 0.689953 0.723854i \(-0.257631\pi\)
0.689953 + 0.723854i \(0.257631\pi\)
\(920\) −9.79803e9 2.71848e10i −0.414841 1.15098i
\(921\) 2.13606e10 0.900957
\(922\) 1.21955e10 + 1.40744e10i 0.512438 + 0.591385i
\(923\) −1.39581e10 8.97033e9i −0.584279 0.375493i
\(924\) −4.63990e8 + 3.22712e9i −0.0193489 + 0.134575i
\(925\) 1.82686e8 4.00026e8i 0.00758942 0.0166185i
\(926\) 2.35096e9 + 1.63513e10i 0.0972987 + 0.676727i
\(927\) 1.23299e10 + 3.62038e9i 0.508371 + 0.149271i
\(928\) −7.60815e9 + 4.88946e9i −0.312508 + 0.200837i
\(929\) 8.57080e9 + 1.87674e10i 0.350725 + 0.767980i 0.999973 + 0.00740285i \(0.00235642\pi\)
−0.649248 + 0.760577i \(0.724916\pi\)
\(930\) 2.62025e9 7.69376e8i 0.106820 0.0313652i
\(931\) 1.07797e9 1.24405e9i 0.0437808 0.0505258i
\(932\) 8.33727e9 9.62173e9i 0.337340 0.389312i
\(933\) −1.06232e10 + 3.11926e9i −0.428224 + 0.125738i
\(934\) −1.59762e10 3.49829e10i −0.641591 1.40489i
\(935\) −3.05924e9 + 1.96605e9i −0.122398 + 0.0786602i
\(936\) 5.68241e9 + 1.66851e9i 0.226500 + 0.0665063i
\(937\) 3.81885e9 + 2.65607e10i 0.151650 + 1.05475i 0.913454 + 0.406943i \(0.133405\pi\)
−0.761803 + 0.647809i \(0.775686\pi\)
\(938\) 7.10250e9 1.55523e10i 0.280997 0.615297i
\(939\) −3.93102e9 + 2.73408e10i −0.154944 + 1.07766i
\(940\) 1.03136e10 + 6.62817e9i 0.405008 + 0.260283i
\(941\) 1.92484e10 + 2.22138e10i 0.753061 + 0.869079i 0.994861 0.101247i \(-0.0322832\pi\)
−0.241800 + 0.970326i \(0.577738\pi\)
\(942\) −1.86122e10 −0.725469
\(943\) 8.50289e9 3.71050e10i 0.330199 1.44093i
\(944\) 1.18003e10 0.456551
\(945\) −3.90011e9 4.50097e9i −0.150337 0.173498i
\(946\) 4.44856e9 + 2.85891e9i 0.170844 + 0.109795i
\(947\) −2.09281e9 + 1.45558e10i −0.0800764 + 0.556944i 0.909804 + 0.415038i \(0.136232\pi\)
−0.989880 + 0.141905i \(0.954677\pi\)
\(948\) 2.39382e9 5.24174e9i 0.0912563 0.199824i
\(949\) 1.72584e9 + 1.20035e10i 0.0655493 + 0.455905i
\(950\) 3.09942e9 + 9.10072e8i 0.117286 + 0.0344384i
\(951\) 3.41806e9 2.19665e9i 0.128869 0.0828189i
\(952\) −2.14437e9 4.69551e9i −0.0805508 0.176382i
\(953\) 4.79206e10 1.40708e10i 1.79348 0.526614i 0.796527 0.604603i \(-0.206668\pi\)
0.996954 + 0.0779890i \(0.0248499\pi\)
\(954\) −8.86371e9 + 1.02293e10i −0.330519 + 0.381439i
\(955\) −2.57917e9 + 2.97652e9i −0.0958227 + 0.110585i
\(956\) 1.01092e10 2.96834e9i 0.374210 0.109878i
\(957\) 3.32132e9 + 7.27268e9i 0.122495 + 0.268227i
\(958\) −2.40799e10 + 1.54752e10i −0.884861 + 0.568666i
\(959\) 1.40857e10 + 4.13594e9i 0.515720 + 0.151429i
\(960\) −2.78290e9 1.93555e10i −0.101519 0.706081i
\(961\) −1.09571e10 + 2.39928e10i −0.398259 + 0.872066i
\(962\) −1.47684e8 + 1.02716e9i −0.00534835 + 0.0371986i
\(963\) 8.35707e8 + 5.37076e8i 0.0301552 + 0.0193796i
\(964\) 2.38135e9 + 2.74823e9i 0.0856158 + 0.0988059i
\(965\) −4.47814e10 −1.60417
\(966\) −8.71294e8 1.44243e10i −0.0310989 0.514843i
\(967\) 2.62900e10 0.934970 0.467485 0.884001i \(-0.345160\pi\)
0.467485 + 0.884001i \(0.345160\pi\)
\(968\) −8.24368e9 9.51371e9i −0.292117 0.337121i
\(969\) −1.25761e9 8.08219e8i −0.0444031 0.0285362i
\(970\) 1.80375e9 1.25453e10i 0.0634563 0.441348i
\(971\) 2.60067e9 5.69468e9i 0.0911629 0.199619i −0.858558 0.512716i \(-0.828639\pi\)
0.949721 + 0.313097i \(0.101367\pi\)
\(972\) 7.56411e7 + 5.26095e8i 0.00264196 + 0.0183752i
\(973\) −3.57803e10 1.05061e10i −1.24523 0.365632i
\(974\) −1.33896e10 + 8.60495e9i −0.464312 + 0.298395i
\(975\) 1.20755e9 + 2.64417e9i 0.0417243 + 0.0913635i
\(976\) 1.08338e10 3.18110e9i 0.372999 0.109522i
\(977\) 6.11361e9 7.05548e9i 0.209733 0.242045i −0.641130 0.767432i \(-0.721534\pi\)
0.850863 + 0.525387i \(0.176080\pi\)
\(978\) 7.17475e8 8.28010e8i 0.0245257 0.0283041i
\(979\) −2.16409e10 + 6.35435e9i −0.737117 + 0.216437i
\(980\) −4.90804e8 1.07471e9i −0.0166578 0.0364754i
\(981\) 1.03123e10 6.62729e9i 0.348749 0.224127i
\(982\) −1.20348e10 3.53373e9i −0.405553 0.119081i
\(983\) −3.26025e9 2.26755e10i −0.109475 0.761413i −0.968416 0.249339i \(-0.919787\pi\)
0.858942 0.512074i \(-0.171122\pi\)
\(984\) 1.15175e10 2.52199e10i 0.385369 0.843840i
\(985\) 2.64152e9 1.83722e10i 0.0880699 0.612540i
\(986\) −2.39007e9 1.53600e9i −0.0794038 0.0510297i
\(987\) 1.78886e10 + 2.06446e10i 0.592198 + 0.683433i
\(988\) 3.10416e9 0.102399
\(989\) 8.90550e9 + 3.43433e9i 0.292733 + 0.112890i
\(990\) −7.41457e9 −0.242864
\(991\) −2.93785e10 3.39046e10i −0.958897 1.10663i −0.994232 0.107251i \(-0.965795\pi\)
0.0353350 0.999376i \(-0.488750\pi\)
\(992\) −2.93561e9 1.88660e9i −0.0954789 0.0613606i
\(993\) 2.95697e8 2.05662e9i 0.00958351 0.0666547i
\(994\) −1.22492e10 + 2.68220e10i −0.395599 + 0.866241i
\(995\) −3.77311e9 2.62426e10i −0.121428 0.844551i
\(996\) −6.59273e8 1.93580e8i −0.0211426 0.00620801i
\(997\) 1.77117e10 1.13826e10i 0.566013 0.363754i −0.226124 0.974099i \(-0.572605\pi\)
0.792136 + 0.610344i \(0.208969\pi\)
\(998\) 1.16341e10 + 2.54751e10i 0.370489 + 0.811258i
\(999\) −3.98148e8 + 1.16907e8i −0.0126347 + 0.00370989i
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 69.8.e.a.13.5 140
23.16 even 11 inner 69.8.e.a.16.5 yes 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.e.a.13.5 140 1.1 even 1 trivial
69.8.e.a.16.5 yes 140 23.16 even 11 inner