Properties

Label 69.8.e.a.58.1
Level $69$
Weight $8$
Character 69.58
Analytic conductor $21.555$
Analytic rank $0$
Dimension $140$
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] = [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 58.1
Character \(\chi\) \(=\) 69.58
Dual form 69.8.e.a.25.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-18.1027 + 11.6339i) q^{2} +(-3.84250 + 26.7252i) q^{3} +(139.187 - 304.777i) q^{4} +(95.4011 - 28.0123i) q^{5} +(-241.358 - 528.501i) q^{6} +(921.010 + 1062.90i) q^{7} +(634.091 + 4410.20i) q^{8} +(-699.470 - 205.383i) q^{9} +O(q^{10})\) \(q+(-18.1027 + 11.6339i) q^{2} +(-3.84250 + 26.7252i) q^{3} +(139.187 - 304.777i) q^{4} +(95.4011 - 28.0123i) q^{5} +(-241.358 - 528.501i) q^{6} +(921.010 + 1062.90i) q^{7} +(634.091 + 4410.20i) q^{8} +(-699.470 - 205.383i) q^{9} +(-1401.12 + 1616.98i) q^{10} +(-3770.61 - 2423.23i) q^{11} +(7610.38 + 4890.90i) q^{12} +(8884.03 - 10252.7i) q^{13} +(-29038.4 - 8526.45i) q^{14} +(382.055 + 2657.25i) q^{15} +(-34701.5 - 40047.7i) q^{16} +(-9322.84 - 20414.2i) q^{17} +(15051.7 - 4419.58i) q^{18} +(-2289.60 + 5013.53i) q^{19} +(4741.08 - 32975.0i) q^{20} +(-31945.2 + 20529.9i) q^{21} +96449.8 q^{22} +(-54008.8 - 22088.0i) q^{23} -120300. q^{24} +(-57406.3 + 36892.8i) q^{25} +(-41545.8 + 288958. i) q^{26} +(8176.61 - 17904.3i) q^{27} +(452140. - 132760. i) q^{28} +(2363.88 + 5176.17i) q^{29} +(-37830.4 - 43658.6i) q^{30} +(-46769.5 - 325289. i) q^{31} +(546893. + 160582. i) q^{32} +(79249.8 - 91459.1i) q^{33} +(406265. + 261091. i) q^{34} +(117640. + 75602.4i) q^{35} +(-159953. + 184596. i) q^{36} +(132165. + 38807.3i) q^{37} +(-16878.9 - 117395. i) q^{38} +(239869. + 276823. i) q^{39} +(184033. + 402976. i) q^{40} +(-297558. + 87371.0i) q^{41} +(339451. - 743294. i) q^{42} +(92668.7 - 644525. i) q^{43} +(-1.26336e6 + 811914. i) q^{44} -72483.5 q^{45} +(1.23467e6 - 228481. i) q^{46} +166461. q^{47} +(1.20362e6 - 773521. i) q^{48} +(-164299. + 1.14272e6i) q^{49} +(610001. - 1.33572e6i) q^{50} +(581396. - 170713. i) q^{51} +(-1.88825e6 - 4.13469e6i) q^{52} +(438924. + 506545. i) q^{53} +(60277.8 + 419242. i) q^{54} +(-427601. - 125555. i) q^{55} +(-4.10361e6 + 4.73581e6i) q^{56} +(-125190. - 80454.6i) q^{57} +(-103012. - 66201.5i) q^{58} +(1.64060e6 - 1.89335e6i) q^{59} +(863044. + 253413. i) q^{60} +(31716.2 + 220591. i) q^{61} +(4.63103e6 + 5.34449e6i) q^{62} +(-425917. - 932628. i) q^{63} +(-5.26036e6 + 1.54458e6i) q^{64} +(560344. - 1.22698e6i) q^{65} +(-370608. + 2.57764e6i) q^{66} +(-1.58807e6 + 1.02059e6i) q^{67} -7.51938e6 q^{68} +(797833. - 1.35852e6i) q^{69} -3.00914e6 q^{70} +(2.42769e6 - 1.56018e6i) q^{71} +(462252. - 3.21504e6i) q^{72} +(1.55897e6 - 3.41366e6i) q^{73} +(-2.84403e6 + 835082. i) q^{74} +(-765382. - 1.67595e6i) q^{75} +(1.20932e6 + 1.39564e6i) q^{76} +(-897120. - 6.23961e6i) q^{77} +(-7.56281e6 - 2.22064e6i) q^{78} +(221061. - 255118. i) q^{79} +(-4.43239e6 - 2.84852e6i) q^{80} +(447077. + 287319. i) q^{81} +(4.37014e6 - 5.04341e6i) q^{82} +(255519. + 75027.1i) q^{83} +(1.81069e6 + 1.25937e7i) q^{84} +(-1.46126e6 - 1.68638e6i) q^{85} +(5.82078e6 + 1.27457e7i) q^{86} +(-147417. + 43285.6i) q^{87} +(8.29600e6 - 1.81657e7i) q^{88} +(-630358. + 4.38424e6i) q^{89} +(1.31215e6 - 843265. i) q^{90} +1.90799e7 q^{91} +(-1.42492e7 + 1.33863e7i) q^{92} +8.87311e6 q^{93} +(-3.01338e6 + 1.93658e6i) q^{94} +(-77990.2 + 542433. i) q^{95} +(-6.39302e6 + 1.39988e7i) q^{96} +(-4.78242e6 + 1.40425e6i) q^{97} +(-1.03201e7 - 2.25978e7i) q^{98} +(2.13974e6 + 2.46940e6i) 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 \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{10}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18.1027 + 11.6339i −1.60007 + 1.02830i −0.632875 + 0.774254i \(0.718125\pi\)
−0.967192 + 0.254046i \(0.918238\pi\)
\(3\) −3.84250 + 26.7252i −0.0821655 + 0.571474i
\(4\) 139.187 304.777i 1.08740 2.38107i
\(5\) 95.4011 28.0123i 0.341317 0.100220i −0.106582 0.994304i \(-0.533991\pi\)
0.447899 + 0.894084i \(0.352172\pi\)
\(6\) −241.358 528.501i −0.456176 0.998887i
\(7\) 921.010 + 1062.90i 1.01489 + 1.17125i 0.985150 + 0.171693i \(0.0549239\pi\)
0.0297443 + 0.999558i \(0.490531\pi\)
\(8\) 634.091 + 4410.20i 0.437861 + 3.04539i
\(9\) −699.470 205.383i −0.319831 0.0939109i
\(10\) −1401.12 + 1616.98i −0.443074 + 0.511335i
\(11\) −3770.61 2423.23i −0.854157 0.548933i 0.0387117 0.999250i \(-0.487675\pi\)
−0.892869 + 0.450317i \(0.851311\pi\)
\(12\) 7610.38 + 4890.90i 1.27137 + 0.817060i
\(13\) 8884.03 10252.7i 1.12152 1.29431i 0.170442 0.985368i \(-0.445481\pi\)
0.951082 0.308939i \(-0.0999740\pi\)
\(14\) −29038.4 8526.45i −2.82830 0.830463i
\(15\) 382.055 + 2657.25i 0.0292285 + 0.203288i
\(16\) −34701.5 40047.7i −2.11801 2.44432i
\(17\) −9322.84 20414.2i −0.460232 1.00777i −0.987435 0.158028i \(-0.949486\pi\)
0.527202 0.849740i \(-0.323241\pi\)
\(18\) 15051.7 4419.58i 0.608320 0.178619i
\(19\) −2289.60 + 5013.53i −0.0765813 + 0.167690i −0.944050 0.329802i \(-0.893018\pi\)
0.867469 + 0.497491i \(0.165745\pi\)
\(20\) 4741.08 32975.0i 0.132517 0.921678i
\(21\) −31945.2 + 20529.9i −0.752728 + 0.483749i
\(22\) 96449.8 1.93118
\(23\) −54008.8 22088.0i −0.925586 0.378537i
\(24\) −120300. −1.77634
\(25\) −57406.3 + 36892.8i −0.734800 + 0.472227i
\(26\) −41545.8 + 288958.i −0.463576 + 3.22424i
\(27\) 8176.61 17904.3i 0.0799467 0.175059i
\(28\) 452140. 132760.i 3.89242 1.14292i
\(29\) 2363.88 + 5176.17i 0.0179983 + 0.0394108i 0.918418 0.395612i \(-0.129468\pi\)
−0.900419 + 0.435023i \(0.856740\pi\)
\(30\) −37830.4 43658.6i −0.255809 0.295219i
\(31\) −46769.5 325289.i −0.281966 1.96111i −0.276089 0.961132i \(-0.589038\pi\)
−0.00587665 0.999983i \(-0.501871\pi\)
\(32\) 546893. + 160582.i 2.95037 + 0.866308i
\(33\) 79249.8 91459.1i 0.383883 0.443025i
\(34\) 406265. + 261091.i 1.77269 + 1.13924i
\(35\) 117640. + 75602.4i 0.463784 + 0.298056i
\(36\) −159953. + 184596.i −0.571391 + 0.659421i
\(37\) 132165. + 38807.3i 0.428955 + 0.125953i 0.489081 0.872238i \(-0.337332\pi\)
−0.0601263 + 0.998191i \(0.519150\pi\)
\(38\) −16878.9 117395.i −0.0499002 0.347063i
\(39\) 239869. + 276823.i 0.647512 + 0.747269i
\(40\) 184033. + 402976.i 0.454658 + 0.995563i
\(41\) −297558. + 87371.0i −0.674262 + 0.197981i −0.600900 0.799324i \(-0.705191\pi\)
−0.0733618 + 0.997305i \(0.523373\pi\)
\(42\) 339451. 743294.i 0.706976 1.54806i
\(43\) 92668.7 644525.i 0.177743 1.23623i −0.684225 0.729271i \(-0.739860\pi\)
0.861969 0.506961i \(-0.169231\pi\)
\(44\) −1.26336e6 + 811914.i −2.23585 + 1.43690i
\(45\) −72483.5 −0.118576
\(46\) 1.23467e6 228481.i 1.87025 0.346097i
\(47\) 166461. 0.233867 0.116934 0.993140i \(-0.462694\pi\)
0.116934 + 0.993140i \(0.462694\pi\)
\(48\) 1.20362e6 773521.i 1.57089 1.00955i
\(49\) −164299. + 1.14272e6i −0.199503 + 1.38757i
\(50\) 610001. 1.33572e6i 0.690138 1.51119i
\(51\) 581396. 170713.i 0.613728 0.180207i
\(52\) −1.88825e6 4.13469e6i −1.86229 4.07785i
\(53\) 438924. + 506545.i 0.404971 + 0.467361i 0.921200 0.389089i \(-0.127210\pi\)
−0.516229 + 0.856451i \(0.672665\pi\)
\(54\) 60277.8 + 419242.i 0.0520930 + 0.362315i
\(55\) −427601. 125555.i −0.346553 0.101757i
\(56\) −4.10361e6 + 4.73581e6i −3.12254 + 3.60360i
\(57\) −125190. 80454.6i −0.0895379 0.0575425i
\(58\) −103012. 66201.5i −0.0693247 0.0445523i
\(59\) 1.64060e6 1.89335e6i 1.03997 1.20019i 0.0605861 0.998163i \(-0.480703\pi\)
0.979381 0.202023i \(-0.0647515\pi\)
\(60\) 863044. + 253413.i 0.515826 + 0.151460i
\(61\) 31716.2 + 220591.i 0.0178907 + 0.124432i 0.996810 0.0798173i \(-0.0254337\pi\)
−0.978919 + 0.204250i \(0.934525\pi\)
\(62\) 4.63103e6 + 5.34449e6i 2.46778 + 2.84797i
\(63\) −425917. 932628.i −0.214602 0.469912i
\(64\) −5.26036e6 + 1.54458e6i −2.50834 + 0.736514i
\(65\) 560344. 1.22698e6i 0.253080 0.554168i
\(66\) −370608. + 2.57764e6i −0.158676 + 1.10362i
\(67\) −1.58807e6 + 1.02059e6i −0.645071 + 0.414562i −0.821862 0.569687i \(-0.807065\pi\)
0.176791 + 0.984248i \(0.443428\pi\)
\(68\) −7.51938e6 −2.90002
\(69\) 797833. 1.35852e6i 0.292375 0.497845i
\(70\) −3.00914e6 −1.04858
\(71\) 2.42769e6 1.56018e6i 0.804987 0.517333i −0.0722530 0.997386i \(-0.523019\pi\)
0.877240 + 0.480053i \(0.159383\pi\)
\(72\) 462252. 3.21504e6i 0.145954 1.01513i
\(73\) 1.55897e6 3.41366e6i 0.469036 1.02705i −0.516297 0.856409i \(-0.672690\pi\)
0.985334 0.170637i \(-0.0545826\pi\)
\(74\) −2.84403e6 + 835082.i −0.815874 + 0.239562i
\(75\) −765382. 1.67595e6i −0.209490 0.458720i
\(76\) 1.20932e6 + 1.39564e6i 0.316006 + 0.364690i
\(77\) −897120. 6.23961e6i −0.223941 1.55754i
\(78\) −7.56281e6 2.22064e6i −1.80448 0.529843i
\(79\) 221061. 255118.i 0.0504448 0.0582165i −0.729966 0.683483i \(-0.760464\pi\)
0.780411 + 0.625267i \(0.215010\pi\)
\(80\) −4.43239e6 2.84852e6i −0.967884 0.622021i
\(81\) 447077. + 287319.i 0.0934726 + 0.0600712i
\(82\) 4.37014e6 5.04341e6i 0.875280 1.01013i
\(83\) 255519. + 75027.1i 0.0490512 + 0.0144027i 0.306166 0.951978i \(-0.400954\pi\)
−0.257115 + 0.966381i \(0.582772\pi\)
\(84\) 1.81069e6 + 1.25937e7i 0.333325 + 2.31832i
\(85\) −1.46126e6 1.68638e6i −0.258084 0.297844i
\(86\) 5.82078e6 + 1.27457e7i 0.986817 + 2.16083i
\(87\) −147417. + 43285.6i −0.0240011 + 0.00704736i
\(88\) 8.29600e6 1.81657e7i 1.29772 2.84160i
\(89\) −630358. + 4.38424e6i −0.0947812 + 0.659218i 0.885939 + 0.463801i \(0.153515\pi\)
−0.980720 + 0.195416i \(0.937394\pi\)
\(90\) 1.31215e6 843265.i 0.189729 0.121931i
\(91\) 1.90799e7 2.65419
\(92\) −1.42492e7 + 1.33863e7i −1.90780 + 1.79226i
\(93\) 8.87311e6 1.14389
\(94\) −3.01338e6 + 1.93658e6i −0.374203 + 0.240486i
\(95\) −77990.2 + 542433.i −0.00933270 + 0.0649103i
\(96\) −6.39302e6 + 1.39988e7i −0.737491 + 1.61488i
\(97\) −4.78242e6 + 1.40425e6i −0.532043 + 0.156222i −0.536709 0.843767i \(-0.680333\pi\)
0.00466643 + 0.999989i \(0.498515\pi\)
\(98\) −1.03201e7 2.25978e7i −1.10762 2.42536i
\(99\) 2.13974e6 + 2.46940e6i 0.221635 + 0.255781i
\(100\) 3.25386e6 + 2.26311e7i 0.325386 + 2.26311i
\(101\) −8.22293e6 2.41447e6i −0.794149 0.233183i −0.140599 0.990067i \(-0.544903\pi\)
−0.653550 + 0.756884i \(0.726721\pi\)
\(102\) −8.53877e6 + 9.85426e6i −0.796699 + 0.919440i
\(103\) 1.36637e7 + 8.78114e6i 1.23208 + 0.791809i 0.984214 0.176985i \(-0.0566344\pi\)
0.247866 + 0.968794i \(0.420271\pi\)
\(104\) 5.08498e7 + 3.26792e7i 4.43275 + 2.84875i
\(105\) −2.47252e6 + 2.85344e6i −0.208438 + 0.240550i
\(106\) −1.38388e7 4.06344e6i −1.12857 0.331378i
\(107\) −2.78462e6 1.93675e7i −0.219747 1.52837i −0.738972 0.673737i \(-0.764688\pi\)
0.519224 0.854638i \(-0.326221\pi\)
\(108\) −4.31873e6 4.98408e6i −0.329893 0.380717i
\(109\) −4.54168e6 9.94489e6i −0.335911 0.735542i 0.664015 0.747719i \(-0.268851\pi\)
−0.999926 + 0.0121772i \(0.996124\pi\)
\(110\) 9.20142e6 2.70178e6i 0.659144 0.193542i
\(111\) −1.54498e6 + 3.38303e6i −0.107224 + 0.234787i
\(112\) 1.06063e7 7.37686e7i 0.713349 4.96145i
\(113\) 6.95225e6 4.46794e6i 0.453264 0.291295i −0.294021 0.955799i \(-0.594994\pi\)
0.747285 + 0.664504i \(0.231357\pi\)
\(114\) 3.20227e6 0.202438
\(115\) −5.77123e6 594306.i −0.353855 0.0364391i
\(116\) 1.90660e6 0.113411
\(117\) −8.31985e6 + 5.34684e6i −0.480247 + 0.308636i
\(118\) −7.67218e6 + 5.33612e7i −0.429865 + 2.98978i
\(119\) 1.31118e7 2.87109e7i 0.713262 1.56183i
\(120\) −1.14767e7 + 3.36988e6i −0.606295 + 0.178024i
\(121\) 250241. + 547952.i 0.0128413 + 0.0281186i
\(122\) −3.14048e6 3.62430e6i −0.156580 0.180703i
\(123\) −1.19164e6 8.28802e6i −0.0577399 0.401590i
\(124\) −1.05650e8 3.10217e7i −4.97615 1.46113i
\(125\) −9.53004e6 + 1.09982e7i −0.436425 + 0.503661i
\(126\) 1.85603e7 + 1.19280e7i 0.826588 + 0.531216i
\(127\) −6.12297e6 3.93499e6i −0.265246 0.170463i 0.401257 0.915965i \(-0.368573\pi\)
−0.666503 + 0.745502i \(0.732210\pi\)
\(128\) 2.94802e7 3.40220e7i 1.24250 1.43392i
\(129\) 1.68690e7 + 4.95317e6i 0.691870 + 0.203151i
\(130\) 4.13085e6 + 2.87307e7i 0.164906 + 1.14695i
\(131\) 6.78752e6 + 7.83321e6i 0.263792 + 0.304432i 0.872158 0.489225i \(-0.162720\pi\)
−0.608366 + 0.793657i \(0.708175\pi\)
\(132\) −1.68441e7 3.68834e7i −0.637438 1.39580i
\(133\) −7.43764e6 + 2.18389e6i −0.274129 + 0.0804914i
\(134\) 1.68749e7 3.69508e7i 0.605862 1.32665i
\(135\) 278518. 1.93713e6i 0.00974282 0.0677628i
\(136\) 8.41191e7 5.40601e7i 2.86753 1.84285i
\(137\) −2.53810e7 −0.843309 −0.421654 0.906757i \(-0.638550\pi\)
−0.421654 + 0.906757i \(0.638550\pi\)
\(138\) 1.36196e6 + 3.38748e7i 0.0441151 + 1.09724i
\(139\) 4.37674e6 0.138229 0.0691145 0.997609i \(-0.477983\pi\)
0.0691145 + 0.997609i \(0.477983\pi\)
\(140\) 3.94157e7 2.53309e7i 1.21401 0.780195i
\(141\) −639625. + 4.44869e6i −0.0192158 + 0.133649i
\(142\) −2.57967e7 + 5.64869e7i −0.756058 + 1.65554i
\(143\) −5.83429e7 + 1.71310e7i −1.66845 + 0.489900i
\(144\) 1.60476e7 + 3.51393e7i 0.447858 + 0.980673i
\(145\) 370513. + 427595.i 0.0100929 + 0.0116478i
\(146\) 1.14927e7 + 7.99333e7i 0.305623 + 2.12565i
\(147\) −2.99082e7 8.78184e6i −0.776568 0.228021i
\(148\) 3.02232e7 3.48794e7i 0.766346 0.884410i
\(149\) 4.79913e7 + 3.08421e7i 1.18853 + 0.763823i 0.976935 0.213535i \(-0.0684976\pi\)
0.211596 + 0.977357i \(0.432134\pi\)
\(150\) 3.33533e7 + 2.14349e7i 0.806900 + 0.518563i
\(151\) −1.03868e7 + 1.19870e7i −0.245506 + 0.283329i −0.865106 0.501589i \(-0.832749\pi\)
0.619601 + 0.784917i \(0.287295\pi\)
\(152\) −2.35625e7 6.91857e6i −0.544213 0.159795i
\(153\) 2.32833e6 + 1.61939e7i 0.0525562 + 0.365536i
\(154\) 8.88312e7 + 1.02517e8i 1.95994 + 2.26189i
\(155\) −1.35739e7 2.97228e7i −0.292782 0.641104i
\(156\) 1.17756e8 3.45762e7i 2.48340 0.729192i
\(157\) −3.22963e7 + 7.07191e7i −0.666046 + 1.45844i 0.210733 + 0.977544i \(0.432415\pi\)
−0.876779 + 0.480894i \(0.840312\pi\)
\(158\) −1.03378e6 + 7.19011e6i −0.0208511 + 0.145023i
\(159\) −1.52241e7 + 9.78393e6i −0.300359 + 0.193029i
\(160\) 5.66724e7 1.09384
\(161\) −2.62653e7 7.77492e7i −0.496011 1.46827i
\(162\) −1.14359e7 −0.211334
\(163\) 6.63214e7 4.26222e7i 1.19949 0.770867i 0.220624 0.975359i \(-0.429191\pi\)
0.978868 + 0.204492i \(0.0655544\pi\)
\(164\) −1.47875e7 + 1.02850e8i −0.261784 + 1.82075i
\(165\) 4.99853e6 1.09453e7i 0.0866261 0.189685i
\(166\) −5.49844e6 + 1.61449e6i −0.0932955 + 0.0273940i
\(167\) −3.59780e7 7.87809e7i −0.597764 1.30892i −0.930635 0.365948i \(-0.880745\pi\)
0.332871 0.942972i \(-0.391983\pi\)
\(168\) −1.10797e8 1.27867e8i −1.80280 2.08054i
\(169\) −1.72622e7 1.20061e8i −0.275101 1.91337i
\(170\) 4.60719e7 + 1.35279e7i 0.719225 + 0.211183i
\(171\) 2.63120e6 3.03657e6i 0.0402409 0.0464405i
\(172\) −1.83538e8 1.17953e8i −2.75027 1.76749i
\(173\) 7.73539e7 + 4.97124e7i 1.13585 + 0.729967i 0.966773 0.255636i \(-0.0822850\pi\)
0.169077 + 0.985603i \(0.445921\pi\)
\(174\) 2.16507e6 2.49862e6i 0.0311566 0.0359566i
\(175\) −9.20851e7 2.70386e7i −1.29884 0.381374i
\(176\) 3.38014e7 + 2.35094e8i 0.467348 + 3.25048i
\(177\) 4.42961e7 + 5.11204e7i 0.600425 + 0.692928i
\(178\) −3.95946e7 8.67000e7i −0.526218 1.15226i
\(179\) 6.74175e6 1.97956e6i 0.0878591 0.0257978i −0.237508 0.971386i \(-0.576330\pi\)
0.325367 + 0.945588i \(0.394512\pi\)
\(180\) −1.00887e7 + 2.20913e7i −0.128939 + 0.282336i
\(181\) −7.62985e6 + 5.30668e7i −0.0956403 + 0.665193i 0.884449 + 0.466636i \(0.154534\pi\)
−0.980089 + 0.198556i \(0.936375\pi\)
\(182\) −3.45398e8 + 2.21974e8i −4.24688 + 2.72930i
\(183\) −6.01720e6 −0.0725797
\(184\) 6.31658e7 2.52195e8i 0.747515 2.98452i
\(185\) 1.36958e7 0.159033
\(186\) −1.60627e8 + 1.03229e8i −1.83031 + 1.17627i
\(187\) −1.43153e7 + 9.95654e7i −0.160087 + 1.11343i
\(188\) 2.31691e7 5.07333e7i 0.254306 0.556853i
\(189\) 2.65612e7 7.79908e6i 0.286175 0.0840286i
\(190\) −4.89878e6 1.07268e7i −0.0518144 0.113458i
\(191\) −8.98060e7 1.03642e8i −0.932586 1.07626i −0.996927 0.0783334i \(-0.975040\pi\)
0.0643415 0.997928i \(-0.479505\pi\)
\(192\) −2.10663e7 1.46519e8i −0.214800 1.49396i
\(193\) 1.20952e8 + 3.55148e7i 1.21106 + 0.355598i 0.824070 0.566488i \(-0.191698\pi\)
0.386985 + 0.922086i \(0.373516\pi\)
\(194\) 7.02378e7 8.10588e7i 0.690661 0.797065i
\(195\) 3.06382e7 + 1.96900e7i 0.295898 + 0.190162i
\(196\) 3.25408e8 + 2.09127e8i 3.08696 + 1.98387i
\(197\) −4.90675e7 + 5.66269e7i −0.457258 + 0.527704i −0.936824 0.349802i \(-0.886249\pi\)
0.479565 + 0.877506i \(0.340794\pi\)
\(198\) −6.74638e7 1.98092e7i −0.617650 0.181358i
\(199\) 2.52606e7 + 1.75692e8i 0.227226 + 1.58039i 0.709714 + 0.704490i \(0.248824\pi\)
−0.482488 + 0.875903i \(0.660267\pi\)
\(200\) −1.99105e8 2.29780e8i −1.75986 2.03099i
\(201\) −2.11733e7 4.63630e7i −0.183909 0.402704i
\(202\) 1.76947e8 5.19563e7i 1.51047 0.443515i
\(203\) −3.32461e6 + 7.27987e6i −0.0278936 + 0.0610784i
\(204\) 2.88932e7 2.00957e8i 0.238282 1.65728i
\(205\) −2.59399e7 + 1.66706e7i −0.210296 + 0.135149i
\(206\) −3.49509e8 −2.78563
\(207\) 3.32410e7 + 2.65424e7i 0.260482 + 0.207990i
\(208\) −7.18887e8 −5.53910
\(209\) 2.07821e7 1.33559e7i 0.157463 0.101195i
\(210\) 1.15626e7 8.04199e7i 0.0861568 0.599233i
\(211\) 1.43292e7 3.13765e7i 0.105011 0.229941i −0.849832 0.527054i \(-0.823297\pi\)
0.954842 + 0.297113i \(0.0960238\pi\)
\(212\) 2.15476e8 6.32694e7i 1.55318 0.456056i
\(213\) 3.23677e7 + 7.08754e7i 0.229500 + 0.502536i
\(214\) 2.75728e8 + 3.18207e8i 1.92324 + 2.21954i
\(215\) −9.21392e6 6.40842e7i −0.0632280 0.439761i
\(216\) 8.41462e7 + 2.47076e7i 0.568128 + 0.166818i
\(217\) 3.02675e8 3.49305e8i 2.01079 2.32058i
\(218\) 1.97914e8 + 1.27192e8i 1.29384 + 0.831499i
\(219\) 8.52403e7 + 5.47806e7i 0.548391 + 0.352430i
\(220\) −9.77826e7 + 1.12847e8i −0.619130 + 0.714515i
\(221\) −2.92125e8 8.57757e7i −1.82052 0.534554i
\(222\) −1.13895e7 7.92160e7i −0.0698668 0.485934i
\(223\) −7.64336e7 8.82091e7i −0.461548 0.532655i 0.476493 0.879178i \(-0.341908\pi\)
−0.938042 + 0.346523i \(0.887362\pi\)
\(224\) 3.33010e8 + 7.29191e8i 1.97966 + 4.33484i
\(225\) 4.77311e7 1.40151e7i 0.279359 0.0820272i
\(226\) −7.38749e7 + 1.61763e8i −0.425713 + 0.932182i
\(227\) 2.40871e7 1.67530e8i 0.136677 0.950608i −0.799897 0.600137i \(-0.795113\pi\)
0.936574 0.350471i \(-0.113978\pi\)
\(228\) −4.19454e7 + 2.69567e7i −0.234376 + 0.150624i
\(229\) −2.02533e8 −1.11448 −0.557239 0.830352i \(-0.688139\pi\)
−0.557239 + 0.830352i \(0.688139\pi\)
\(230\) 1.11389e8 5.63833e7i 0.603663 0.305565i
\(231\) 1.70202e8 0.908494
\(232\) −2.13290e7 + 1.37073e7i −0.112141 + 0.0720685i
\(233\) −1.22587e7 + 8.52611e7i −0.0634890 + 0.441576i 0.933138 + 0.359517i \(0.117059\pi\)
−0.996627 + 0.0820587i \(0.973850\pi\)
\(234\) 8.84071e7 1.93585e8i 0.451057 0.987677i
\(235\) 1.58805e7 4.66294e6i 0.0798229 0.0234381i
\(236\) −3.48699e8 7.63544e8i −1.72687 3.78131i
\(237\) 5.96864e6 + 6.88818e6i 0.0291243 + 0.0336113i
\(238\) 9.66602e7 + 6.72287e8i 0.464760 + 3.23247i
\(239\) 1.47263e8 + 4.32405e7i 0.697754 + 0.204879i 0.611326 0.791379i \(-0.290636\pi\)
0.0864282 + 0.996258i \(0.472455\pi\)
\(240\) 9.31588e7 1.07511e8i 0.434995 0.502011i
\(241\) −2.30920e8 1.48404e8i −1.06268 0.682943i −0.112187 0.993687i \(-0.535785\pi\)
−0.950494 + 0.310744i \(0.899422\pi\)
\(242\) −1.09048e7 7.00812e6i −0.0494613 0.0317869i
\(243\) −9.39654e6 + 1.08442e7i −0.0420093 + 0.0484814i
\(244\) 7.16454e7 + 2.10370e7i 0.315736 + 0.0927084i
\(245\) 1.63360e7 + 1.13620e8i 0.0709684 + 0.493596i
\(246\) 1.17994e8 + 1.36172e8i 0.505343 + 0.583197i
\(247\) 3.10614e7 + 6.80150e7i 0.131154 + 0.287188i
\(248\) 1.40493e9 4.12525e8i 5.84890 1.71739i
\(249\) −2.98694e6 + 6.54050e6i −0.0122611 + 0.0268481i
\(250\) 4.45669e7 3.09969e8i 0.180394 1.25467i
\(251\) 4.16492e8 2.67663e8i 1.66245 1.06839i 0.747993 0.663707i \(-0.231018\pi\)
0.914456 0.404685i \(-0.132619\pi\)
\(252\) −3.43525e8 −1.35225
\(253\) 1.50122e8 + 2.14161e8i 0.582804 + 0.831415i
\(254\) 1.56621e8 0.599699
\(255\) 5.06837e7 3.25724e7i 0.191416 0.123015i
\(256\) −3.79932e7 + 2.64249e8i −0.141536 + 0.984404i
\(257\) 4.98953e7 1.09255e8i 0.183355 0.401492i −0.795527 0.605919i \(-0.792806\pi\)
0.978882 + 0.204426i \(0.0655329\pi\)
\(258\) −3.62998e8 + 1.06586e8i −1.31594 + 0.386394i
\(259\) 8.04773e7 + 1.76221e8i 0.287822 + 0.630242i
\(260\) −2.95963e8 3.41560e8i −1.04431 1.20520i
\(261\) −590365. 4.10608e6i −0.00205532 0.0142950i
\(262\) −2.14003e8 6.28370e7i −0.735132 0.215854i
\(263\) 2.13238e8 2.46090e8i 0.722802 0.834158i −0.268839 0.963185i \(-0.586640\pi\)
0.991641 + 0.129027i \(0.0411854\pi\)
\(264\) 4.53605e8 + 2.91514e8i 1.51727 + 0.975092i
\(265\) 5.60633e7 + 3.60297e7i 0.185062 + 0.118932i
\(266\) 1.09234e8 1.26063e8i 0.355855 0.410678i
\(267\) −1.14747e8 3.36929e7i −0.368938 0.108330i
\(268\) 9.00136e7 + 6.26058e8i 0.285651 + 1.98675i
\(269\) 7.00566e7 + 8.08496e7i 0.219440 + 0.253247i 0.854786 0.518980i \(-0.173688\pi\)
−0.635346 + 0.772227i \(0.719143\pi\)
\(270\) 1.74945e7 + 3.83076e7i 0.0540914 + 0.118444i
\(271\) −4.97599e8 + 1.46108e8i −1.51875 + 0.445946i −0.931587 0.363519i \(-0.881575\pi\)
−0.587167 + 0.809466i \(0.699757\pi\)
\(272\) −4.94024e8 + 1.08176e9i −1.48853 + 3.25942i
\(273\) −7.33146e7 + 5.09914e8i −0.218083 + 1.51680i
\(274\) 4.59464e8 2.95280e8i 1.34935 0.867175i
\(275\) 3.05856e8 0.886856
\(276\) −3.02998e8 4.32249e8i −0.867476 1.23752i
\(277\) −2.89620e8 −0.818747 −0.409373 0.912367i \(-0.634253\pi\)
−0.409373 + 0.912367i \(0.634253\pi\)
\(278\) −7.92308e7 + 5.09186e7i −0.221176 + 0.142141i
\(279\) −3.40949e7 + 2.37135e8i −0.0939886 + 0.653705i
\(280\) −2.58827e8 + 5.66753e8i −0.704624 + 1.54291i
\(281\) −2.31562e8 + 6.79927e7i −0.622579 + 0.182806i −0.577783 0.816190i \(-0.696082\pi\)
−0.0447962 + 0.998996i \(0.514264\pi\)
\(282\) −4.01766e7 8.79746e7i −0.106685 0.233607i
\(283\) 2.55531e8 + 2.94898e8i 0.670178 + 0.773427i 0.984404 0.175921i \(-0.0562904\pi\)
−0.314226 + 0.949348i \(0.601745\pi\)
\(284\) −1.37604e8 9.57059e8i −0.356466 2.47927i
\(285\) −1.41970e7 4.16860e6i −0.0363277 0.0106668i
\(286\) 8.56863e8 9.88873e8i 2.16586 2.49954i
\(287\) −3.66921e8 2.35806e8i −0.916190 0.588800i
\(288\) −3.49554e8 2.24645e8i −0.862265 0.554144i
\(289\) −6.11087e7 + 7.05232e7i −0.148923 + 0.171866i
\(290\) −1.16819e7 3.43011e6i −0.0281267 0.00825876i
\(291\) −1.91523e7 1.33207e8i −0.0455611 0.316885i
\(292\) −8.23416e8 9.50273e8i −1.93544 2.23361i
\(293\) −1.06229e7 2.32610e7i −0.0246722 0.0540247i 0.896895 0.442244i \(-0.145818\pi\)
−0.921567 + 0.388219i \(0.873090\pi\)
\(294\) 6.43586e8 1.88974e8i 1.47704 0.433697i
\(295\) 1.03478e8 2.26584e8i 0.234676 0.513869i
\(296\) −8.73429e7 + 6.07483e8i −0.195752 + 1.36149i
\(297\) −7.42170e7 + 4.76964e7i −0.164383 + 0.105642i
\(298\) −1.22759e9 −2.68717
\(299\) −7.06277e8 + 3.57507e8i −1.52801 + 0.773455i
\(300\) −6.17322e8 −1.32004
\(301\) 7.70415e8 4.95116e8i 1.62833 1.04646i
\(302\) 4.85734e7 3.37835e8i 0.101478 0.705798i
\(303\) 9.61238e7 2.10482e8i 0.198510 0.434675i
\(304\) 2.80233e8 8.22839e7i 0.572087 0.167980i
\(305\) 9.20501e6 + 2.01562e7i 0.0185770 + 0.0406779i
\(306\) −2.30547e8 2.66065e8i −0.459975 0.530839i
\(307\) −2.40530e7 1.67293e8i −0.0474445 0.329984i −0.999696 0.0246680i \(-0.992147\pi\)
0.952251 0.305316i \(-0.0987620\pi\)
\(308\) −2.02655e9 5.95050e8i −3.95212 1.16045i
\(309\) −2.87180e8 + 3.31424e8i −0.553733 + 0.639042i
\(310\) 5.91516e8 + 3.80144e8i 1.12772 + 0.724741i
\(311\) 1.20363e8 + 7.73528e7i 0.226899 + 0.145819i 0.649152 0.760659i \(-0.275124\pi\)
−0.422253 + 0.906478i \(0.638760\pi\)
\(312\) −1.06875e9 + 1.23340e9i −1.99221 + 2.29913i
\(313\) 1.11121e8 + 3.26281e7i 0.204829 + 0.0601432i 0.382538 0.923940i \(-0.375050\pi\)
−0.177709 + 0.984083i \(0.556868\pi\)
\(314\) −2.38088e8 1.65594e9i −0.433994 3.01849i
\(315\) −6.67580e7 7.70428e7i −0.120342 0.138882i
\(316\) −4.69852e7 1.02883e8i −0.0837637 0.183417i
\(317\) 7.04571e7 2.06881e7i 0.124227 0.0364764i −0.219028 0.975719i \(-0.570289\pi\)
0.343255 + 0.939242i \(0.388470\pi\)
\(318\) 1.61772e8 3.54231e8i 0.282103 0.617720i
\(319\) 3.62976e6 2.52456e7i 0.00626053 0.0435429i
\(320\) −4.58577e8 + 2.94710e8i −0.782326 + 0.502770i
\(321\) 5.28299e8 0.891481
\(322\) 1.38000e9 + 1.10190e9i 2.30347 + 1.83928i
\(323\) 1.23693e8 0.204238
\(324\) 1.49795e8 9.62675e7i 0.244675 0.157243i
\(325\) −1.31748e8 + 9.16327e8i −0.212888 + 1.48067i
\(326\) −7.04734e8 + 1.54315e9i −1.12658 + 2.46688i
\(327\) 2.83230e8 8.31640e7i 0.447943 0.131528i
\(328\) −5.74003e8 1.25689e9i −0.898164 1.96670i
\(329\) 1.53312e8 + 1.76931e8i 0.237350 + 0.273917i
\(330\) 3.68491e7 + 2.56291e8i 0.0564453 + 0.392586i
\(331\) −3.30786e8 9.71275e7i −0.501359 0.147212i 0.0212677 0.999774i \(-0.493230\pi\)
−0.522627 + 0.852561i \(0.675048\pi\)
\(332\) 5.84314e7 6.74334e7i 0.0876320 0.101133i
\(333\) −8.44754e7 5.42890e7i −0.125365 0.0805670i
\(334\) 1.56783e9 + 1.00758e9i 2.30243 + 1.47968i
\(335\) −1.22914e8 + 1.41851e8i −0.178626 + 0.206146i
\(336\) 1.93073e9 + 5.66912e8i 2.77673 + 0.815320i
\(337\) −1.26864e8 8.82359e8i −0.180565 1.25586i −0.855431 0.517917i \(-0.826707\pi\)
0.674865 0.737941i \(-0.264202\pi\)
\(338\) 1.70927e9 + 1.97260e9i 2.40770 + 2.77863i
\(339\) 9.26925e7 + 2.02968e8i 0.129225 + 0.282963i
\(340\) −7.17357e8 + 2.10635e8i −0.989827 + 0.290639i
\(341\) −6.11899e8 + 1.33987e9i −0.835678 + 1.82988i
\(342\) −1.23047e7 + 8.55813e7i −0.0166334 + 0.115688i
\(343\) −3.91545e8 + 2.51631e8i −0.523905 + 0.336693i
\(344\) 2.90124e9 3.84264
\(345\) 3.80589e7 1.51954e8i 0.0498987 0.199225i
\(346\) −1.97866e9 −2.56806
\(347\) −8.25346e8 + 5.30418e8i −1.06043 + 0.681499i −0.949957 0.312380i \(-0.898874\pi\)
−0.110475 + 0.993879i \(0.535237\pi\)
\(348\) −7.32610e6 + 5.09541e7i −0.00931849 + 0.0648115i
\(349\) −4.01389e8 + 8.78920e8i −0.505448 + 1.10678i 0.469211 + 0.883086i \(0.344538\pi\)
−0.974660 + 0.223692i \(0.928189\pi\)
\(350\) 1.98155e9 5.81836e8i 2.47040 0.725375i
\(351\) −1.10926e8 2.42895e8i −0.136918 0.299808i
\(352\) −1.67299e9 1.93074e9i −2.04454 2.35952i
\(353\) −1.08877e8 7.57258e8i −0.131742 0.916288i −0.943282 0.331992i \(-0.892279\pi\)
0.811540 0.584297i \(-0.198630\pi\)
\(354\) −1.39661e9 4.10081e8i −1.67326 0.491313i
\(355\) 1.87900e8 2.16848e8i 0.222909 0.257250i
\(356\) 1.24847e9 + 8.02346e8i 1.46658 + 0.942512i
\(357\) 7.16922e8 + 4.60738e8i 0.833937 + 0.535939i
\(358\) −9.90138e7 + 1.14268e8i −0.114053 + 0.131624i
\(359\) −3.09308e8 9.08210e7i −0.352826 0.103599i 0.100517 0.994935i \(-0.467950\pi\)
−0.453343 + 0.891336i \(0.649769\pi\)
\(360\) −4.59611e7 3.19667e8i −0.0519197 0.361109i
\(361\) 5.65468e8 + 6.52585e8i 0.632606 + 0.730066i
\(362\) −4.79252e8 1.04942e9i −0.530987 1.16270i
\(363\) −1.56057e7 + 4.58223e6i −0.0171241 + 0.00502810i
\(364\) 2.65567e9 5.81511e9i 2.88615 6.31980i
\(365\) 5.31026e7 3.69337e8i 0.0571599 0.397556i
\(366\) 1.08927e8 7.00034e7i 0.116132 0.0746338i
\(367\) −9.56885e8 −1.01048 −0.505241 0.862978i \(-0.668596\pi\)
−0.505241 + 0.862978i \(0.668596\pi\)
\(368\) 9.89615e8 + 2.92941e9i 1.03514 + 3.06417i
\(369\) 2.26078e8 0.234242
\(370\) −2.47931e8 + 1.59335e8i −0.254463 + 0.163533i
\(371\) −1.34155e8 + 9.33067e8i −0.136395 + 0.948645i
\(372\) 1.23502e9 2.70432e9i 1.24387 2.72369i
\(373\) −1.57154e9 + 4.61447e8i −1.56800 + 0.460406i −0.946418 0.322945i \(-0.895327\pi\)
−0.621580 + 0.783351i \(0.713509\pi\)
\(374\) −8.99187e8 1.96894e9i −0.888790 1.94618i
\(375\) −2.57311e8 2.96953e8i −0.251970 0.290789i
\(376\) 1.05551e8 + 7.34125e8i 0.102401 + 0.712217i
\(377\) 7.40706e7 + 2.17491e7i 0.0711953 + 0.0209048i
\(378\) −3.90096e8 + 4.50195e8i −0.371493 + 0.428725i
\(379\) −8.54634e8 5.49240e8i −0.806385 0.518232i 0.0713083 0.997454i \(-0.477283\pi\)
−0.877694 + 0.479222i \(0.840919\pi\)
\(380\) 1.54466e8 + 9.92691e7i 0.144408 + 0.0928051i
\(381\) 1.28691e8 1.48517e8i 0.119209 0.137575i
\(382\) 2.83149e9 + 8.31400e8i 2.59892 + 0.763112i
\(383\) 1.96458e8 + 1.36640e9i 0.178679 + 1.24274i 0.859823 + 0.510592i \(0.170574\pi\)
−0.681144 + 0.732150i \(0.738517\pi\)
\(384\) 7.95965e8 + 9.18593e8i 0.717356 + 0.827873i
\(385\) −2.60372e8 5.70135e8i −0.232531 0.509173i
\(386\) −2.60274e9 + 7.64233e8i −2.30343 + 0.676348i
\(387\) −1.97193e8 + 4.31793e8i −0.172943 + 0.378693i
\(388\) −2.37669e8 + 1.65302e9i −0.206567 + 1.43670i
\(389\) 1.33754e9 8.59588e8i 1.15209 0.740401i 0.182032 0.983293i \(-0.441732\pi\)
0.970053 + 0.242892i \(0.0780961\pi\)
\(390\) −7.83705e8 −0.669001
\(391\) 5.26078e7 + 1.30847e9i 0.0445073 + 1.10699i
\(392\) −5.14383e9 −4.31306
\(393\) −2.35425e8 + 1.51299e8i −0.195650 + 0.125736i
\(394\) 2.29462e8 1.59594e9i 0.189005 1.31456i
\(395\) 1.39430e7 3.05309e7i 0.0113833 0.0249259i
\(396\) 1.05044e9 3.08436e8i 0.850036 0.249593i
\(397\) 3.62220e8 + 7.93151e8i 0.290540 + 0.636193i 0.997470 0.0710902i \(-0.0226478\pi\)
−0.706930 + 0.707283i \(0.749921\pi\)
\(398\) −2.50126e9 2.88661e9i −1.98870 2.29508i
\(399\) −2.97857e7 2.07164e8i −0.0234748 0.163271i
\(400\) 3.46956e9 + 1.01875e9i 2.71059 + 0.795901i
\(401\) −7.05759e8 + 8.14489e8i −0.546577 + 0.630783i −0.960082 0.279719i \(-0.909759\pi\)
0.413505 + 0.910502i \(0.364304\pi\)
\(402\) 9.22676e8 + 5.92968e8i 0.708366 + 0.455239i
\(403\) −3.75059e9 2.41036e9i −2.85452 1.83449i
\(404\) −1.88040e9 + 2.17009e9i −1.41878 + 1.63736i
\(405\) 5.07000e7 + 1.48869e7i 0.0379241 + 0.0111355i
\(406\) −2.45089e7 1.70463e8i −0.0181754 0.126412i
\(407\) −4.04306e8 4.66594e8i −0.297255 0.343051i
\(408\) 1.12154e9 + 2.45582e9i 0.817529 + 1.79014i
\(409\) 1.45449e9 4.27078e8i 1.05119 0.308657i 0.289891 0.957060i \(-0.406381\pi\)
0.761297 + 0.648403i \(0.224563\pi\)
\(410\) 2.75639e8 6.03564e8i 0.197513 0.432494i
\(411\) 9.75265e7 6.78311e8i 0.0692909 0.481929i
\(412\) 4.57810e9 2.94216e9i 3.22511 2.07265i
\(413\) 3.52345e9 2.46118
\(414\) −9.10543e8 9.37653e7i −0.630666 0.0649443i
\(415\) 2.64785e7 0.0181855
\(416\) 6.50502e9 4.18052e9i 4.43018 2.84711i
\(417\) −1.68176e7 + 1.16969e8i −0.0113577 + 0.0789943i
\(418\) −2.20832e8 + 4.83554e8i −0.147892 + 0.323838i
\(419\) 7.30551e8 2.14509e8i 0.485179 0.142461i −0.0299899 0.999550i \(-0.509548\pi\)
0.515169 + 0.857089i \(0.327729\pi\)
\(420\) 5.25519e8 + 1.15073e9i 0.346111 + 0.757878i
\(421\) −4.23955e8 4.89270e8i −0.276906 0.319566i 0.600213 0.799841i \(-0.295083\pi\)
−0.877118 + 0.480274i \(0.840537\pi\)
\(422\) 1.05634e8 + 7.34704e8i 0.0684246 + 0.475903i
\(423\) −1.16434e8 3.41882e7i −0.0747979 0.0219627i
\(424\) −1.95565e9 + 2.25694e9i −1.24598 + 1.43794i
\(425\) 1.28833e9 + 8.27956e8i 0.814075 + 0.523174i
\(426\) −1.41050e9 9.06473e8i −0.883973 0.568095i
\(427\) −2.05255e8 + 2.36877e8i −0.127584 + 0.147240i
\(428\) −6.29034e9 1.84701e9i −3.87811 1.13872i
\(429\) −2.33647e8 1.62505e9i −0.142876 0.993726i
\(430\) 9.12346e8 + 1.05290e9i 0.553375 + 0.638629i
\(431\) 1.27447e9 + 2.79071e9i 0.766762 + 1.67898i 0.733654 + 0.679523i \(0.237813\pi\)
0.0331084 + 0.999452i \(0.489459\pi\)
\(432\) −1.00077e9 + 2.93852e8i −0.597227 + 0.175362i
\(433\) 1.79781e8 3.93666e8i 0.106423 0.233034i −0.848927 0.528510i \(-0.822751\pi\)
0.955350 + 0.295476i \(0.0954781\pi\)
\(434\) −1.41545e9 + 9.84465e9i −0.831150 + 5.78078i
\(435\) −1.28512e7 + 8.25899e6i −0.00748570 + 0.00481077i
\(436\) −3.66311e9 −2.11664
\(437\) 2.34397e8 2.20202e8i 0.134359 0.126222i
\(438\) −2.18039e9 −1.23987
\(439\) −3.37836e8 + 2.17114e8i −0.190581 + 0.122479i −0.632452 0.774600i \(-0.717951\pi\)
0.441870 + 0.897079i \(0.354315\pi\)
\(440\) 2.82585e8 1.96542e9i 0.158148 1.09994i
\(441\) 3.49619e8 7.65558e8i 0.194115 0.425053i
\(442\) 6.28616e9 1.84578e9i 3.46264 1.01672i
\(443\) −4.35409e8 9.53413e8i −0.237949 0.521037i 0.752553 0.658532i \(-0.228822\pi\)
−0.990502 + 0.137495i \(0.956095\pi\)
\(444\) 8.16027e8 + 9.41745e8i 0.442450 + 0.510614i
\(445\) 6.26756e7 + 4.35919e8i 0.0337162 + 0.234501i
\(446\) 2.40987e9 + 7.07601e8i 1.28624 + 0.377674i
\(447\) −1.00867e9 + 1.16407e9i −0.534161 + 0.616454i
\(448\) −6.48659e9 4.16868e9i −3.40834 2.19041i
\(449\) 2.29162e8 + 1.47273e8i 0.119476 + 0.0767824i 0.599014 0.800739i \(-0.295559\pi\)
−0.479538 + 0.877521i \(0.659196\pi\)
\(450\) −7.01011e8 + 8.09010e8i −0.362645 + 0.418514i
\(451\) 1.33370e9 + 3.91609e8i 0.684604 + 0.201018i
\(452\) −3.94062e8 2.74076e9i −0.200715 1.39600i
\(453\) −2.80443e8 3.23648e8i −0.141743 0.163580i
\(454\) 1.51298e9 + 3.31297e9i 0.758819 + 1.66158i
\(455\) 1.82024e9 5.34472e8i 0.905920 0.266002i
\(456\) 2.75439e8 6.03127e8i 0.136034 0.297874i
\(457\) 1.46416e8 1.01835e9i 0.0717599 0.499101i −0.921967 0.387268i \(-0.873419\pi\)
0.993727 0.111833i \(-0.0356722\pi\)
\(458\) 3.66639e9 2.35624e9i 1.78324 1.14602i
\(459\) −4.41731e8 −0.213213
\(460\) −9.84409e8 + 1.67622e9i −0.471545 + 0.802930i
\(461\) 3.36161e9 1.59806 0.799032 0.601289i \(-0.205346\pi\)
0.799032 + 0.601289i \(0.205346\pi\)
\(462\) −3.08111e9 + 1.98011e9i −1.45365 + 0.934205i
\(463\) 4.80864e8 3.34449e9i 0.225159 1.56602i −0.492933 0.870067i \(-0.664075\pi\)
0.718092 0.695948i \(-0.245016\pi\)
\(464\) 1.25264e8 2.74289e8i 0.0582119 0.127466i
\(465\) 8.46504e8 2.48556e8i 0.390431 0.114641i
\(466\) −7.70003e8 1.68607e9i −0.352486 0.771837i
\(467\) −2.24105e9 2.58630e9i −1.01822 1.17509i −0.984451 0.175659i \(-0.943794\pi\)
−0.0337689 0.999430i \(-0.510751\pi\)
\(468\) 4.71579e8 + 3.27991e9i 0.212664 + 1.47911i
\(469\) −2.54741e9 7.47988e8i −1.14023 0.334803i
\(470\) −2.33232e8 + 2.69164e8i −0.103620 + 0.119584i
\(471\) −1.76588e9 1.13486e9i −0.778733 0.500461i
\(472\) 9.39033e9 + 6.03480e9i 4.11040 + 2.64159i
\(473\) −1.91125e9 + 2.20570e9i −0.830430 + 0.958367i
\(474\) −1.88185e8 5.52560e7i −0.0811634 0.0238317i
\(475\) −5.35255e7 3.72278e8i −0.0229157 0.159382i
\(476\) −6.92542e9 7.99236e9i −2.94321 3.39665i
\(477\) −2.02979e8 4.44461e8i −0.0856320 0.187508i
\(478\) −3.16892e9 + 9.30479e8i −1.32713 + 0.389681i
\(479\) 1.46801e9 3.21449e9i 0.610315 1.33640i −0.312043 0.950068i \(-0.601013\pi\)
0.922358 0.386336i \(-0.126259\pi\)
\(480\) −2.17764e8 + 1.51458e9i −0.0898755 + 0.625098i
\(481\) 1.57204e9 1.01029e9i 0.644104 0.413941i
\(482\) 5.90679e9 2.40263
\(483\) 2.17879e9 4.03193e8i 0.879832 0.162816i
\(484\) 2.01833e8 0.0809158
\(485\) −4.16912e8 + 2.67933e8i −0.165939 + 0.106642i
\(486\) 4.39425e7 3.05627e8i 0.0173643 0.120772i
\(487\) 4.89702e8 1.07230e9i 0.192124 0.420692i −0.788916 0.614502i \(-0.789357\pi\)
0.981039 + 0.193810i \(0.0620844\pi\)
\(488\) −9.52739e8 + 2.79749e8i −0.371111 + 0.108968i
\(489\) 8.84246e8 + 1.93623e9i 0.341973 + 0.748817i
\(490\) −1.61756e9 1.86677e9i −0.621120 0.716810i
\(491\) 7.00831e7 + 4.87438e8i 0.0267195 + 0.185838i 0.998810 0.0487674i \(-0.0155293\pi\)
−0.972091 + 0.234605i \(0.924620\pi\)
\(492\) −2.69185e9 7.90400e8i −1.01900 0.299205i
\(493\) 8.36292e7 9.65133e7i 0.0314336 0.0362763i
\(494\) −1.35358e9 8.69890e8i −0.505171 0.324653i
\(495\) 2.73307e8 + 1.75644e8i 0.101282 + 0.0650901i
\(496\) −1.14041e10 + 1.31610e10i −4.19638 + 4.84288i
\(497\) 3.89424e9 + 1.14345e9i 1.42290 + 0.417802i
\(498\) −2.20197e7 1.53150e8i −0.00798930 0.0555668i
\(499\) −1.90648e9 2.20019e9i −0.686878 0.792699i 0.300040 0.953927i \(-0.403000\pi\)
−0.986917 + 0.161228i \(0.948455\pi\)
\(500\) 2.02555e9 + 4.43534e9i 0.724684 + 1.58684i
\(501\) 2.24368e9 6.58804e8i 0.797129 0.234058i
\(502\) −4.42566e9 + 9.69084e9i −1.56140 + 3.41899i
\(503\) 2.29888e8 1.59890e9i 0.0805430 0.560189i −0.909093 0.416593i \(-0.863224\pi\)
0.989636 0.143596i \(-0.0458667\pi\)
\(504\) 3.84301e9 2.46975e9i 1.33710 0.859303i
\(505\) −8.52111e8 −0.294426
\(506\) −5.20914e9 2.13038e9i −1.78747 0.731021i
\(507\) 3.27499e9 1.11604
\(508\) −2.05153e9 + 1.31844e9i −0.694312 + 0.446207i
\(509\) 1.22578e8 8.52548e8i 0.0412002 0.286554i −0.958797 0.284093i \(-0.908308\pi\)
0.999997 0.00246099i \(-0.000783358\pi\)
\(510\) −5.38567e8 + 1.17930e9i −0.179781 + 0.393666i
\(511\) 5.06421e9 1.48699e9i 1.67895 0.492985i
\(512\) 7.25911e6 + 1.58952e7i 0.00239022 + 0.00523386i
\(513\) 7.10425e7 + 8.19874e7i 0.0232331 + 0.0268125i
\(514\) 3.67827e8 + 2.55829e9i 0.119474 + 0.830959i
\(515\) 1.54951e9 + 4.54978e8i 0.499885 + 0.146779i
\(516\) 3.85755e9 4.45185e9i 1.23605 1.42648i
\(517\) −6.27659e8 4.03372e8i −0.199759 0.128377i
\(518\) −3.50699e9 2.25380e9i −1.10861 0.712462i
\(519\) −1.62580e9 + 1.87628e9i −0.510484 + 0.589130i
\(520\) 5.76655e9 + 1.69321e9i 1.79847 + 0.528080i
\(521\) 1.77783e8 + 1.23650e9i 0.0550753 + 0.383057i 0.998652 + 0.0519035i \(0.0165288\pi\)
−0.943577 + 0.331154i \(0.892562\pi\)
\(522\) 5.84569e7 + 6.74628e7i 0.0179882 + 0.0207595i
\(523\) −7.57737e8 1.65921e9i −0.231613 0.507162i 0.757765 0.652528i \(-0.226291\pi\)
−0.989378 + 0.145366i \(0.953564\pi\)
\(524\) 3.33211e9 9.78397e8i 1.01172 0.297068i
\(525\) 1.07645e9 2.35709e9i 0.324665 0.710918i
\(526\) −9.97199e8 + 6.93567e9i −0.298766 + 2.07797i
\(527\) −6.20448e9 + 3.98738e9i −1.84658 + 1.18672i
\(528\) −6.41281e9 −1.89596
\(529\) 2.42907e9 + 2.38589e9i 0.713420 + 0.700737i
\(530\) −1.43406e9 −0.418411
\(531\) −1.53641e9 + 9.87391e8i −0.445324 + 0.286192i
\(532\) −3.69623e8 + 2.57079e9i −0.106431 + 0.740245i
\(533\) −1.74773e9 + 3.82699e9i −0.499952 + 1.09474i
\(534\) 2.46921e9 7.25027e8i 0.701721 0.206044i
\(535\) −8.08183e8 1.76967e9i −0.228177 0.499638i
\(536\) −5.50798e9 6.35655e9i −1.54496 1.78297i
\(537\) 2.69988e7 + 1.87781e8i 0.00752375 + 0.0523288i
\(538\) −2.20881e9 6.48564e8i −0.611533 0.179562i
\(539\) 3.38859e9 3.91064e9i 0.932091 1.07569i
\(540\) −5.51627e8 3.54509e8i −0.150753 0.0968834i
\(541\) −5.40279e9 3.47216e9i −1.46699 0.942778i −0.998231 0.0594525i \(-0.981065\pi\)
−0.468760 0.883326i \(-0.655299\pi\)
\(542\) 7.30808e9 8.43397e9i 1.97154 2.27528i
\(543\) −1.38890e9 4.07818e8i −0.372282 0.109312i
\(544\) −1.82044e9 1.26614e10i −0.484820 3.37200i
\(545\) −7.11860e8 8.21531e8i −0.188368 0.217388i
\(546\) −4.60509e9 1.00837e10i −1.21078 2.65123i
\(547\) 1.34742e9 3.95639e8i 0.352004 0.103358i −0.100950 0.994891i \(-0.532188\pi\)
0.452954 + 0.891534i \(0.350370\pi\)
\(548\) −3.53270e9 + 7.73553e9i −0.917011 + 2.00797i
\(549\) 2.31211e7 1.60811e8i 0.00596355 0.0414774i
\(550\) −5.53682e9 + 3.55830e9i −1.41903 + 0.911954i
\(551\) −3.13632e7 −0.00798712
\(552\) 6.49725e9 + 2.65718e9i 1.64416 + 0.672410i
\(553\) 4.74764e8 0.119382
\(554\) 5.24290e9 3.36941e9i 1.31005 0.841918i
\(555\) −5.26261e7 + 3.66023e8i −0.0130670 + 0.0908830i
\(556\) 6.09185e8 1.33393e9i 0.150310 0.329133i
\(557\) 1.81165e9 5.31949e8i 0.444203 0.130430i −0.0519791 0.998648i \(-0.516553\pi\)
0.496182 + 0.868218i \(0.334735\pi\)
\(558\) −2.14160e9 4.68945e9i −0.521817 1.14262i
\(559\) −5.78486e9 6.67608e9i −1.40072 1.61652i
\(560\) −1.05457e9 7.33472e9i −0.253757 1.76492i
\(561\) −2.60590e9 7.65160e8i −0.623142 0.182971i
\(562\) 3.40087e9 3.92481e9i 0.808189 0.932700i
\(563\) −3.76092e9 2.41699e9i −0.888207 0.570816i 0.0150638 0.999887i \(-0.495205\pi\)
−0.903271 + 0.429070i \(0.858841\pi\)
\(564\) 1.26683e9 + 8.14142e8i 0.297332 + 0.191083i
\(565\) 5.38095e8 6.20995e8i 0.125513 0.144850i
\(566\) −8.05660e9 2.36563e9i −1.86765 0.548390i
\(567\) 1.06370e8 + 7.39822e8i 0.0245064 + 0.170446i
\(568\) 8.42008e9 + 9.71729e9i 1.92796 + 2.22498i
\(569\) 1.97456e9 + 4.32368e9i 0.449342 + 0.983922i 0.989789 + 0.142543i \(0.0455280\pi\)
−0.540447 + 0.841378i \(0.681745\pi\)
\(570\) 3.05500e8 8.97029e7i 0.0690954 0.0202883i
\(571\) −2.45499e9 + 5.37568e9i −0.551853 + 1.20839i 0.404058 + 0.914734i \(0.367600\pi\)
−0.955911 + 0.293657i \(0.905128\pi\)
\(572\) −2.89943e9 + 2.01660e10i −0.647778 + 4.50540i
\(573\) 3.11492e9 2.00184e9i 0.691681 0.444517i
\(574\) 9.38559e9 2.07143
\(575\) 3.91533e9 7.24546e8i 0.858876 0.158938i
\(576\) 3.99670e9 0.871411
\(577\) 2.38300e9 1.53146e9i 0.516427 0.331887i −0.256330 0.966589i \(-0.582513\pi\)
0.772757 + 0.634702i \(0.218877\pi\)
\(578\) 2.85772e8 1.98759e9i 0.0615563 0.428134i
\(579\) −1.41390e9 + 3.09601e9i −0.302722 + 0.662868i
\(580\) 1.81891e8 5.34081e7i 0.0387092 0.0113660i
\(581\) 1.55589e8 + 3.40692e8i 0.0329126 + 0.0720685i
\(582\) 1.89642e9 + 2.18859e9i 0.398753 + 0.460186i
\(583\) −4.27539e8 2.97360e9i −0.0893585 0.621502i
\(584\) 1.60434e10 + 4.71078e9i 3.33313 + 0.978696i
\(585\) −6.43946e8 + 7.43153e8i −0.132985 + 0.153473i
\(586\) 4.62920e8 + 2.97501e8i 0.0950308 + 0.0610726i
\(587\) 6.53371e9 + 4.19896e9i 1.33329 + 0.856857i 0.996407 0.0846883i \(-0.0269894\pi\)
0.336887 + 0.941545i \(0.390626\pi\)
\(588\) −6.83933e9 + 7.89300e9i −1.38737 + 1.60111i
\(589\) 1.73793e9 + 5.10302e8i 0.350452 + 0.102902i
\(590\) 7.62835e8 + 5.30563e9i 0.152914 + 1.06354i
\(591\) −1.32482e9 1.52893e9i −0.263998 0.304670i
\(592\) −3.03220e9 6.63959e9i −0.600664 1.31527i
\(593\) −4.48972e9 + 1.31830e9i −0.884155 + 0.259611i −0.692125 0.721778i \(-0.743325\pi\)
−0.192030 + 0.981389i \(0.561507\pi\)
\(594\) 7.88633e8 1.72687e9i 0.154391 0.338069i
\(595\) 4.46625e8 3.10635e9i 0.0869228 0.604561i
\(596\) 1.60797e10 1.03338e10i 3.11112 1.99939i
\(597\) −4.79245e9 −0.921823
\(598\) 8.62632e9 1.46886e10i 1.64957 2.80883i
\(599\) −7.57566e9 −1.44021 −0.720106 0.693864i \(-0.755907\pi\)
−0.720106 + 0.693864i \(0.755907\pi\)
\(600\) 6.90597e9 4.43820e9i 1.30525 0.838836i
\(601\) −1.33185e9 + 9.26320e9i −0.250261 + 1.74061i 0.346376 + 0.938096i \(0.387412\pi\)
−0.596638 + 0.802511i \(0.703497\pi\)
\(602\) −8.18646e9 + 1.79259e10i −1.52936 + 3.34882i
\(603\) 1.32042e9 3.87710e8i 0.245245 0.0720106i
\(604\) 2.20765e9 + 4.83408e9i 0.407662 + 0.892656i
\(605\) 3.92226e7 + 4.52654e7i 0.00720101 + 0.00831040i
\(606\) 7.08623e8 + 4.92858e9i 0.129348 + 0.899637i
\(607\) −1.03671e8 3.04406e7i −0.0188147 0.00552450i 0.272312 0.962209i \(-0.412212\pi\)
−0.291126 + 0.956685i \(0.594030\pi\)
\(608\) −2.05725e9 + 2.37419e9i −0.371214 + 0.428404i
\(609\) −1.81781e8 1.16824e8i −0.0326128 0.0209590i
\(610\) −4.01130e8 2.57791e8i −0.0715535 0.0459846i
\(611\) 1.47884e9 1.70667e9i 0.262287 0.302696i
\(612\) 5.25958e9 + 1.54435e9i 0.927516 + 0.272343i
\(613\) 1.08138e9 + 7.52119e9i 0.189613 + 1.31879i 0.833011 + 0.553256i \(0.186615\pi\)
−0.643398 + 0.765532i \(0.722476\pi\)
\(614\) 2.38169e9 + 2.74861e9i 0.415237 + 0.479209i
\(615\) −3.45850e8 7.57306e8i −0.0599549 0.131283i
\(616\) 2.69491e10 7.91296e9i 4.64527 1.36398i
\(617\) 8.13413e8 1.78113e9i 0.139416 0.305279i −0.827026 0.562164i \(-0.809969\pi\)
0.966442 + 0.256885i \(0.0826963\pi\)
\(618\) 1.34299e9 9.34069e9i 0.228883 1.59191i
\(619\) 1.72754e9 1.11022e9i 0.292759 0.188145i −0.386014 0.922493i \(-0.626148\pi\)
0.678773 + 0.734348i \(0.262512\pi\)
\(620\) −1.09481e10 −1.84488
\(621\) −8.37078e8 + 7.86384e8i −0.140264 + 0.131769i
\(622\) −3.07881e9 −0.513000
\(623\) −5.24058e9 + 3.36792e9i −0.868302 + 0.558024i
\(624\) 2.76233e9 1.92124e10i 0.455123 3.16545i
\(625\) 1.61356e9 3.53320e9i 0.264365 0.578879i
\(626\) −2.39118e9 + 7.02114e8i −0.389585 + 0.114393i
\(627\) 2.77083e8 + 6.06726e8i 0.0448924 + 0.0983007i
\(628\) 1.70583e10 + 1.96863e10i 2.74838 + 3.17180i
\(629\) −4.39939e8 3.05984e9i −0.0704880 0.490255i
\(630\) 2.10481e9 + 6.18027e8i 0.335367 + 0.0984726i
\(631\) −2.87729e9 + 3.32057e9i −0.455911 + 0.526150i −0.936439 0.350830i \(-0.885900\pi\)
0.480528 + 0.876979i \(0.340445\pi\)
\(632\) 1.26529e9 + 8.13154e8i 0.199380 + 0.128134i
\(633\) 7.83484e8 + 5.03514e8i 0.122777 + 0.0789040i
\(634\) −1.03478e9 + 1.19420e9i −0.161263 + 0.186108i
\(635\) −6.94366e8 2.03884e8i −0.107617 0.0315992i
\(636\) 8.62920e8 + 6.00174e9i 0.133006 + 0.925075i
\(637\) 1.02564e10 + 1.18365e10i 1.57220 + 1.81441i
\(638\) 2.27996e8 + 4.99241e8i 0.0347579 + 0.0761093i
\(639\) −2.01853e9 + 5.92694e8i −0.306043 + 0.0898623i
\(640\) 1.85941e9 4.07154e9i 0.280379 0.613944i
\(641\) 9.79751e8 6.81432e9i 0.146931 1.02193i −0.774275 0.632849i \(-0.781885\pi\)
0.921206 0.389076i \(-0.127206\pi\)
\(642\) −9.56364e9 + 6.14618e9i −1.42643 + 0.916711i
\(643\) −7.20617e9 −1.06897 −0.534486 0.845178i \(-0.679495\pi\)
−0.534486 + 0.845178i \(0.679495\pi\)
\(644\) −2.73519e10 2.81663e9i −4.03541 0.415555i
\(645\) 1.74807e9 0.256507
\(646\) −2.23917e9 + 1.43903e9i −0.326794 + 0.210018i
\(647\) −2.09349e8 + 1.45606e9i −0.0303883 + 0.211355i −0.999358 0.0358238i \(-0.988594\pi\)
0.968970 + 0.247179i \(0.0795036\pi\)
\(648\) −9.83646e8 + 2.15388e9i −0.142012 + 0.310964i
\(649\) −1.07741e10 + 3.16355e9i −1.54712 + 0.454275i
\(650\) −8.27545e9 1.81207e10i −1.18194 2.58809i
\(651\) 8.17222e9 + 9.43124e9i 1.16093 + 1.33979i
\(652\) −3.75918e9 2.61457e10i −0.531161 3.69431i
\(653\) −1.62800e9 4.78024e8i −0.228801 0.0671821i 0.165322 0.986240i \(-0.447134\pi\)
−0.394124 + 0.919057i \(0.628952\pi\)
\(654\) −4.15971e9 + 4.80056e9i −0.581489 + 0.671074i
\(655\) 8.66963e8 + 5.57163e8i 0.120547 + 0.0774708i
\(656\) 1.38247e10 + 8.88462e9i 1.91202 + 1.22878i
\(657\) −1.79156e9 + 2.06757e9i −0.246463 + 0.284434i
\(658\) −4.83376e9 1.41932e9i −0.661445 0.194218i
\(659\) 1.64378e9 + 1.14327e10i 0.223740 + 1.55615i 0.723710 + 0.690104i \(0.242435\pi\)
−0.499970 + 0.866043i \(0.666656\pi\)
\(660\) −2.64013e9 3.04687e9i −0.357455 0.412525i
\(661\) −1.10108e9 2.41102e9i −0.148290 0.324710i 0.820881 0.571100i \(-0.193483\pi\)
−0.969171 + 0.246390i \(0.920756\pi\)
\(662\) 7.11809e9 2.09006e9i 0.953587 0.279998i
\(663\) 3.41486e9 7.47751e9i 0.455068 0.996459i
\(664\) −1.68862e8 + 1.17446e9i −0.0223844 + 0.155687i
\(665\) −6.48383e8 + 4.16691e8i −0.0854980 + 0.0549462i
\(666\) 2.16082e9 0.283439
\(667\) −1.33391e7 3.31772e8i −0.00174055 0.0432912i
\(668\) −2.90182e10 −3.76663
\(669\) 2.65110e9 1.70376e9i 0.342322 0.219997i
\(670\) 5.74804e8 3.99785e9i 0.0738343 0.513529i
\(671\) 4.14952e8 9.08618e8i 0.0530236 0.116105i
\(672\) −2.07673e10 + 6.09784e9i −2.63991 + 0.775147i
\(673\) 5.89891e8 + 1.29168e9i 0.0745966 + 0.163344i 0.943256 0.332065i \(-0.107745\pi\)
−0.868660 + 0.495409i \(0.835018\pi\)
\(674\) 1.25618e10 + 1.44971e10i 1.58032 + 1.82378i
\(675\) 1.91150e8 + 1.32948e9i 0.0239227 + 0.166386i
\(676\) −3.89945e10 1.14498e10i −4.85501 1.42556i
\(677\) −3.65748e8 + 4.22096e8i −0.0453025 + 0.0522819i −0.777949 0.628328i \(-0.783740\pi\)
0.732646 + 0.680610i \(0.238285\pi\)
\(678\) −4.03929e9 2.59590e9i −0.497739 0.319877i
\(679\) −5.89723e9 3.78992e9i −0.722943 0.464607i
\(680\) 6.51071e9 7.51376e9i 0.794048 0.916381i
\(681\) 4.38471e9 + 1.28747e9i 0.532017 + 0.156214i
\(682\) −4.51090e9 3.13740e10i −0.544526 3.78726i
\(683\) −8.26360e9 9.53670e9i −0.992422 1.14532i −0.989385 0.145321i \(-0.953578\pi\)
−0.00303788 0.999995i \(-0.500967\pi\)
\(684\) −5.59247e8 1.22458e9i −0.0668201 0.146316i
\(685\) −2.42137e9 + 7.10980e8i −0.287836 + 0.0845162i
\(686\) 4.16057e9 9.11039e9i 0.492061 1.07746i
\(687\) 7.78232e8 5.41273e9i 0.0915716 0.636894i
\(688\) −2.90275e10 + 1.86548e10i −3.39821 + 2.18389i
\(689\) 9.09289e9 1.05909
\(690\) 1.07884e9 + 3.19354e9i 0.125022 + 0.370084i
\(691\) 3.11398e9 0.359040 0.179520 0.983754i \(-0.442545\pi\)
0.179520 + 0.983754i \(0.442545\pi\)
\(692\) 2.59178e10 1.66564e10i 2.97322 1.91077i
\(693\) −6.54001e8 + 4.54867e9i −0.0746469 + 0.519181i
\(694\) 8.77016e9 1.92040e10i 0.995978 2.18089i
\(695\) 4.17546e8 1.22603e8i 0.0471800 0.0138533i
\(696\) −2.84374e8 6.22693e8i −0.0319711 0.0700070i
\(697\) 4.55770e9 + 5.25986e9i 0.509836 + 0.588382i
\(698\) −2.95903e9 2.05805e10i −0.329349 2.29067i
\(699\) −2.23152e9 6.55232e8i −0.247132 0.0725646i
\(700\) −2.10578e10 + 2.43020e10i −2.32043 + 2.67792i
\(701\) −3.60570e9 2.31725e9i −0.395346 0.254073i 0.327831 0.944736i \(-0.393682\pi\)
−0.723177 + 0.690663i \(0.757319\pi\)
\(702\) 4.83388e9 + 3.10654e9i 0.527370 + 0.338920i
\(703\) −4.97168e8 + 5.73762e8i −0.0539709 + 0.0622857i
\(704\) 2.35777e10 + 6.92303e9i 2.54681 + 0.747811i
\(705\) 6.35970e7 + 4.42327e8i 0.00683557 + 0.0475425i
\(706\) 1.07808e10 + 1.24417e10i 1.15302 + 1.33065i
\(707\) −5.00705e9 1.09639e10i −0.532861 1.16680i
\(708\) 2.17457e10 6.38512e9i 2.30281 0.676165i
\(709\) 6.99246e8 1.53114e9i 0.0736832 0.161344i −0.869206 0.494450i \(-0.835370\pi\)
0.942889 + 0.333106i \(0.108097\pi\)
\(710\) −8.78706e8 + 6.11154e9i −0.0921382 + 0.640835i
\(711\) −2.07022e8 + 1.33045e8i −0.0216010 + 0.0138821i
\(712\) −1.97351e10 −2.04908
\(713\) −4.65900e9 + 1.86015e10i −0.481371 + 1.92192i
\(714\) −1.83384e10 −1.88546
\(715\) −5.08610e9 + 3.26864e9i −0.520372 + 0.334423i
\(716\) 3.35040e8 2.33025e9i 0.0341115 0.237251i
\(717\) −1.72147e9 + 3.76949e9i −0.174414 + 0.381914i
\(718\) 6.65591e9 1.95435e9i 0.671076 0.197046i
\(719\) −1.89516e9 4.14982e9i −0.190149 0.416369i 0.790414 0.612573i \(-0.209866\pi\)
−0.980563 + 0.196205i \(0.937138\pi\)
\(720\) 2.51529e9 + 2.90280e9i 0.251145 + 0.289836i
\(721\) 3.25093e9 + 2.26107e10i 0.323023 + 2.24668i
\(722\) −1.78286e10 5.23495e9i −1.76294 0.517645i
\(723\) 4.85342e9 5.60115e9i 0.477600 0.551179i
\(724\) 1.51115e10 + 9.71159e9i 1.47987 + 0.951054i
\(725\) −3.26665e8 2.09935e8i −0.0318360 0.0204598i
\(726\) 2.29195e8 2.64505e8i 0.0222294 0.0256541i
\(727\) −2.23106e9 6.55097e8i −0.215348 0.0632317i 0.172279 0.985048i \(-0.444887\pi\)
−0.387627 + 0.921816i \(0.626705\pi\)
\(728\) 1.20984e10 + 8.41462e10i 1.16217 + 8.08304i
\(729\) −2.53706e8 2.92793e8i −0.0242541 0.0279907i
\(730\) 3.33553e9 + 7.30378e9i 0.317347 + 0.694893i
\(731\) −1.40214e10 + 4.11705e9i −1.32764 + 0.389830i
\(732\) −8.37514e8 + 1.83390e9i −0.0789230 + 0.172817i
\(733\) 1.05930e8 7.36761e8i 0.00993472 0.0690975i −0.984251 0.176777i \(-0.943433\pi\)
0.994186 + 0.107679i \(0.0343420\pi\)
\(734\) 1.73222e10 1.11323e10i 1.61684 1.03908i
\(735\) −3.09927e9 −0.287908
\(736\) −2.59901e10 2.07526e10i −2.40290 1.91867i
\(737\) 8.46111e9 0.778558
\(738\) −4.09261e9 + 2.63016e9i −0.374803 + 0.240872i
\(739\) −1.08578e8 + 7.55175e8i −0.00989659 + 0.0688323i −0.994171 0.107813i \(-0.965615\pi\)
0.984275 + 0.176645i \(0.0565244\pi\)
\(740\) 1.90627e9 4.17416e9i 0.172932 0.378667i
\(741\) −1.93707e9 + 5.68774e8i −0.174896 + 0.0513542i
\(742\) −8.42663e9 1.84518e10i −0.757252 1.65815i
\(743\) 4.52457e9 + 5.22163e9i 0.404684 + 0.467031i 0.921111 0.389301i \(-0.127283\pi\)
−0.516426 + 0.856332i \(0.672738\pi\)
\(744\) 5.62636e9 + 3.91322e10i 0.500867 + 3.48361i
\(745\) 5.44238e9 + 1.59803e9i 0.482216 + 0.141592i
\(746\) 2.30807e10 2.66366e10i 2.03547 2.34905i
\(747\) −1.63319e8 1.04958e8i −0.0143355 0.00921288i
\(748\) 2.83527e10 + 1.82212e10i 2.47707 + 1.59192i
\(749\) 1.80211e10 2.07974e10i 1.56709 1.80852i
\(750\) 8.11274e9 + 2.38211e9i 0.702187 + 0.206181i
\(751\) 1.07882e9 + 7.50338e9i 0.0929416 + 0.646423i 0.982035 + 0.188698i \(0.0604267\pi\)
−0.889094 + 0.457726i \(0.848664\pi\)
\(752\) −5.77644e9 6.66636e9i −0.495333 0.571645i
\(753\) 5.55297e9 + 1.21593e10i 0.473961 + 1.03783i
\(754\) −1.59390e9 + 4.68012e8i −0.135414 + 0.0397610i
\(755\) −6.55127e8 + 1.43453e9i −0.0554002 + 0.121309i
\(756\) 1.32000e9 9.18077e9i 0.111108 0.772775i
\(757\) 1.18331e10 7.60469e9i 0.991434 0.637156i 0.0589100 0.998263i \(-0.481238\pi\)
0.932524 + 0.361107i \(0.117601\pi\)
\(758\) 2.18610e10 1.82317
\(759\) −6.30033e9 + 3.18913e9i −0.523018 + 0.264744i
\(760\) −2.44169e9 −0.201764
\(761\) −6.26517e9 + 4.02638e9i −0.515331 + 0.331183i −0.772323 0.635230i \(-0.780905\pi\)
0.256992 + 0.966414i \(0.417269\pi\)
\(762\) −6.01818e8 + 4.18574e9i −0.0492745 + 0.342712i
\(763\) 6.38751e9 1.39867e10i 0.520590 1.13993i
\(764\) −4.40874e10 + 1.29452e10i −3.57674 + 1.05023i
\(765\) 6.75752e8 + 1.47969e9i 0.0545723 + 0.119497i
\(766\) −1.94529e10 2.24499e10i −1.56381 1.80473i
\(767\) −4.83686e9 3.36411e10i −0.387062 2.69207i
\(768\) −6.91611e9 2.03075e9i −0.550931 0.161768i
\(769\) 3.41063e9 3.93608e9i 0.270453 0.312120i −0.604234 0.796807i \(-0.706521\pi\)
0.874688 + 0.484687i \(0.161066\pi\)
\(770\) 1.13463e10 + 7.29184e9i 0.895648 + 0.575598i
\(771\) 2.72815e9 + 1.75327e9i 0.214377 + 0.137772i
\(772\) 2.76591e10 3.19203e10i 2.16360 2.49693i
\(773\) −1.88810e10 5.54395e9i −1.47027 0.431709i −0.554080 0.832463i \(-0.686930\pi\)
−0.916186 + 0.400754i \(0.868748\pi\)
\(774\) −1.45371e9 1.01107e10i −0.112689 0.783772i
\(775\) 1.46857e10 + 1.69482e10i 1.13328 + 1.30788i
\(776\) −9.22549e9 2.02010e10i −0.708718 1.55188i
\(777\) −5.01876e9 + 1.47364e9i −0.383816 + 0.112699i
\(778\) −1.42128e10 + 3.11217e10i −1.08206 + 2.36938i
\(779\) 2.43253e8 1.69186e9i 0.0184365 0.128228i
\(780\) 1.02655e10 6.59722e9i 0.774548 0.497771i
\(781\) −1.29345e10 −0.971567
\(782\) −1.61749e10 2.30747e10i −1.20953 1.72549i
\(783\) 1.12004e8 0.00833812
\(784\) 5.14649e10 3.30745e10i 3.81422 2.45125i
\(785\) −1.10010e9 + 7.65137e9i −0.0811687 + 0.564541i
\(786\) 2.50164e9 5.47782e9i 0.183758 0.402373i
\(787\) −5.55361e9 + 1.63069e9i −0.406128 + 0.119250i −0.478415 0.878134i \(-0.658789\pi\)
0.0722866 + 0.997384i \(0.476970\pi\)
\(788\) 1.04290e10 + 2.28363e10i 0.759278 + 1.66259i
\(789\) 5.75743e9 + 6.64442e9i 0.417310 + 0.481601i
\(790\) 1.02788e8 + 7.14903e8i 0.00741730 + 0.0515884i
\(791\) 1.11521e10 + 3.27454e9i 0.801194 + 0.235252i
\(792\) −9.53374e9 + 1.10025e10i −0.681907 + 0.786962i
\(793\) 2.54342e9 + 1.63456e9i 0.181118 + 0.116398i
\(794\) −1.57846e10 1.01441e10i −1.11908 0.719189i
\(795\) −1.17832e9 + 1.35986e9i −0.0831725 + 0.0959862i
\(796\) 5.70626e10 + 1.67551e10i 4.01011 + 1.17747i
\(797\) −2.57429e8 1.79046e9i −0.0180116 0.125274i 0.978832 0.204666i \(-0.0656110\pi\)
−0.996843 + 0.0793927i \(0.974702\pi\)
\(798\) 2.94932e9 + 3.40370e9i 0.205453 + 0.237105i
\(799\) −1.55189e9 3.39816e9i −0.107633 0.235684i
\(800\) −3.73194e10 + 1.09580e10i −2.57703 + 0.756684i
\(801\) 1.34136e9 2.93718e9i 0.0922217 0.201937i
\(802\) 3.30045e9 2.29552e10i 0.225925 1.57134i
\(803\) −1.41503e10 + 9.09386e9i −0.964411 + 0.619789i
\(804\) −1.70774e10 −1.15885
\(805\) −4.68367e9 6.68161e9i −0.316447 0.451435i
\(806\) 9.59377e10 6.45382
\(807\) −2.42991e9 + 1.56161e9i −0.162755 + 0.104596i
\(808\) 5.43421e9 3.77958e10i 0.362407 2.52060i
\(809\) −2.74965e8 + 6.02090e8i −0.0182582 + 0.0399799i −0.918541 0.395325i \(-0.870632\pi\)
0.900283 + 0.435305i \(0.143359\pi\)
\(810\) −1.09100e9 + 3.20346e8i −0.0721318 + 0.0211798i
\(811\) −6.60009e8 1.44522e9i −0.0434487 0.0951393i 0.886663 0.462416i \(-0.153017\pi\)
−0.930112 + 0.367277i \(0.880290\pi\)
\(812\) 1.75599e9 + 2.02652e9i 0.115100 + 0.132833i
\(813\) −1.99275e9 1.38599e10i −0.130057 0.904569i
\(814\) 1.27473e10 + 3.74295e9i 0.828388 + 0.243237i
\(815\) 5.13319e9 5.92402e9i 0.332151 0.383323i
\(816\) −2.70120e10 1.73596e10i −1.74037 1.11847i
\(817\) 3.01917e9 + 1.94030e9i 0.193691 + 0.124478i
\(818\) −2.13617e10 + 2.46527e10i −1.36458 + 1.57481i
\(819\) −1.33458e10 3.91869e9i −0.848891 0.249257i
\(820\) 1.47031e9 + 1.02262e10i 0.0931235 + 0.647688i
\(821\) 2.29041e9 + 2.64328e9i 0.144448 + 0.166702i 0.823363 0.567515i \(-0.192095\pi\)
−0.678915 + 0.734217i \(0.737549\pi\)
\(822\) 6.12591e9 + 1.34139e10i 0.384697 + 0.842370i
\(823\) 2.72958e10 8.01477e9i 1.70685 0.501177i 0.724669 0.689097i \(-0.241993\pi\)
0.982184 + 0.187920i \(0.0601745\pi\)
\(824\) −3.00626e10 + 6.58278e10i −1.87189 + 4.09887i
\(825\) −1.17525e9 + 8.17407e9i −0.0728690 + 0.506815i
\(826\) −6.37839e10 + 4.09914e10i −3.93805 + 2.53083i
\(827\) −1.11631e10 −0.686300 −0.343150 0.939281i \(-0.611494\pi\)
−0.343150 + 0.939281i \(0.611494\pi\)
\(828\) 1.27162e10 6.43675e9i 0.778487 0.394058i
\(829\) 1.14587e10 0.698545 0.349272 0.937021i \(-0.386429\pi\)
0.349272 + 0.937021i \(0.386429\pi\)
\(830\) −4.79331e8 + 3.08047e8i −0.0290980 + 0.0187001i
\(831\) 1.11287e9 7.74015e9i 0.0672728 0.467892i
\(832\) −3.08971e10 + 6.76552e10i −1.85988 + 4.07258i
\(833\) 2.48595e10 7.29942e9i 1.49017 0.437553i
\(834\) −1.05636e9 2.31311e9i −0.0630568 0.138075i
\(835\) −5.63918e9 6.50796e9i −0.335207 0.386849i
\(836\) −1.17796e9 8.19287e9i −0.0697280 0.484969i
\(837\) −6.20648e9 1.82239e9i −0.365853 0.107424i
\(838\) −1.07294e10 + 1.23823e10i −0.629825 + 0.726857i
\(839\) 7.27337e9 + 4.67431e9i 0.425176 + 0.273244i 0.735682 0.677327i \(-0.236862\pi\)
−0.310506 + 0.950572i \(0.600498\pi\)
\(840\) −1.41520e10 9.09496e9i −0.823837 0.529448i
\(841\) 1.12751e10 1.30121e10i 0.653631 0.754331i
\(842\) 1.33668e10 + 3.92486e9i 0.771678 + 0.226585i
\(843\) −9.27340e8 6.44979e9i −0.0533141 0.370808i
\(844\) −7.56840e9 8.73440e9i −0.433317 0.500074i
\(845\) −5.01002e9 1.09704e10i −0.285654 0.625496i
\(846\) 2.50551e9 7.35686e8i 0.142266 0.0417730i
\(847\) −3.51944e8 + 7.70650e8i −0.0199013 + 0.0435778i
\(848\) 5.05464e9 3.51558e10i 0.284646 1.97976i
\(849\) −8.86308e9 + 5.69596e9i −0.497059 + 0.319440i
\(850\) −3.29545e10 −1.84055
\(851\) −6.28092e9 5.01519e9i −0.349357 0.278955i
\(852\) 2.61063e10 1.44613
\(853\) −3.13328e9 + 2.01364e9i −0.172853 + 0.111086i −0.624207 0.781259i \(-0.714578\pi\)
0.451353 + 0.892345i \(0.350941\pi\)
\(854\) 9.59869e8 6.67604e9i 0.0527363 0.366789i
\(855\) 1.65958e8 3.63398e8i 0.00908067 0.0198839i
\(856\) 8.36488e10 2.45615e10i 4.55828 1.33843i
\(857\) −3.74081e9 8.19124e9i −0.203017 0.444546i 0.780549 0.625095i \(-0.214940\pi\)
−0.983566 + 0.180549i \(0.942213\pi\)
\(858\) 2.31353e10 + 2.66996e10i 1.25046 + 1.44311i
\(859\) 2.37518e9 + 1.65198e10i 0.127856 + 0.889258i 0.948265 + 0.317481i \(0.102837\pi\)
−0.820409 + 0.571777i \(0.806254\pi\)
\(860\) −2.08138e10 6.11149e9i −1.11585 0.327644i
\(861\) 7.71184e9 8.89994e9i 0.411763 0.475200i
\(862\) −5.55382e10 3.56923e10i −2.95336 1.89801i
\(863\) 1.74840e10 + 1.12363e10i 0.925982 + 0.595093i 0.914388 0.404840i \(-0.132673\pi\)
0.0115948 + 0.999933i \(0.496309\pi\)
\(864\) 7.34684e9 8.47870e9i 0.387527 0.447230i
\(865\) 8.77220e9 + 2.57575e9i 0.460842 + 0.135316i
\(866\) 1.32534e9 + 9.21797e9i 0.0693451 + 0.482306i
\(867\) −1.64993e9 1.90413e9i −0.0859805 0.0992267i
\(868\) −6.43317e10 1.40867e11i −3.33892 7.31122i
\(869\) −1.45174e9 + 4.26270e8i −0.0750448 + 0.0220351i
\(870\) 1.36558e8 2.99020e8i 0.00703071 0.0153951i
\(871\) −3.64463e9 + 2.53490e10i −0.186892 + 1.29986i
\(872\) 4.09791e10 2.63357e10i 2.09293 1.34505i
\(873\) 3.63357e9 0.184835
\(874\) −1.68142e9 + 6.71320e9i −0.0851893 + 0.340126i
\(875\) −2.04673e10 −1.03284
\(876\) 2.85602e10 1.83545e10i 1.43548 0.922526i
\(877\) −2.18788e9 + 1.52171e10i −0.109528 + 0.761785i 0.858837 + 0.512249i \(0.171187\pi\)
−0.968365 + 0.249537i \(0.919722\pi\)
\(878\) 3.58986e9 7.86071e9i 0.178998 0.391950i
\(879\) 6.62473e8 1.94520e8i 0.0329009 0.00966057i
\(880\) 9.81022e9 + 2.14814e10i 0.485276 + 1.06261i
\(881\) −1.94956e9 2.24991e9i −0.0960553 0.110854i 0.705687 0.708524i \(-0.250639\pi\)
−0.801742 + 0.597670i \(0.796093\pi\)
\(882\) 2.57738e9 + 1.79261e10i 0.126485 + 0.879722i
\(883\) 2.80017e10 + 8.22205e9i 1.36875 + 0.401900i 0.881837 0.471553i \(-0.156307\pi\)
0.486908 + 0.873453i \(0.338125\pi\)
\(884\) −6.68024e10 + 7.70941e10i −3.25244 + 3.75352i
\(885\) 5.65789e9 + 3.63611e9i 0.274381 + 0.176334i
\(886\) 1.89740e10 + 1.21938e10i 0.916517 + 0.589010i
\(887\) −1.54831e10 + 1.78684e10i −0.744946 + 0.859714i −0.994068 0.108758i \(-0.965313\pi\)
0.249122 + 0.968472i \(0.419858\pi\)
\(888\) −1.58995e10 4.66851e9i −0.761969 0.223734i
\(889\) −1.45680e9 1.01323e10i −0.0695415 0.483672i
\(890\) −6.20603e9 7.16214e9i −0.295086 0.340547i
\(891\) −9.89515e8 2.16674e9i −0.0468652 0.102620i
\(892\) −3.75226e10 + 1.10176e10i −1.77017 + 0.519770i
\(893\) −3.81129e8 + 8.34556e8i −0.0179098 + 0.0392171i
\(894\) 4.71700e9 3.28074e10i 0.220793 1.53565i
\(895\) 5.87718e8 3.77703e8i 0.0274024 0.0176104i
\(896\) 6.33136e10 2.94048
\(897\) −6.84056e9 2.02491e10i −0.316459 0.936769i
\(898\) −5.86181e9 −0.270125
\(899\) 1.57319e9 1.01103e9i 0.0722143 0.0464093i
\(900\) 2.37206e9 1.64980e10i 0.108462 0.754369i
\(901\) 6.24869e9 1.36827e10i 0.284611 0.623212i
\(902\) −2.86994e10 + 8.42692e9i −1.30212 + 0.382336i
\(903\) 1.02717e10 + 2.24920e10i 0.464234 + 1.01653i
\(904\) 2.41129e10 + 2.78277e10i 1.08557 + 1.25282i
\(905\) 7.58625e8 + 5.27635e9i 0.0340218 + 0.236627i
\(906\) 8.84206e9 + 2.59626e9i 0.395007 + 0.115985i
\(907\) −3.43363e8 + 3.96262e8i −0.0152802 + 0.0176342i −0.763338 0.645999i \(-0.776441\pi\)
0.748058 + 0.663633i \(0.230986\pi\)
\(908\) −4.77065e10 3.06591e10i −2.11484 1.35912i
\(909\) 5.25581e9 + 3.37770e9i 0.232095 + 0.149158i
\(910\) −2.67333e10 + 3.08519e10i −1.17600 + 1.35718i
\(911\) −4.00234e10 1.17519e10i −1.75388 0.514986i −0.762613 0.646855i \(-0.776084\pi\)
−0.991267 + 0.131870i \(0.957902\pi\)
\(912\) 1.12226e9 + 7.80546e9i 0.0489903 + 0.340735i
\(913\) −7.81655e8 9.02078e8i −0.0339913 0.0392280i
\(914\) 9.19681e9 + 2.01382e10i 0.398405 + 0.872386i
\(915\) −5.74047e8 + 1.68555e8i −0.0247727 + 0.00727393i
\(916\) −2.81899e10 + 6.17273e10i −1.21188 + 2.65364i
\(917\) −2.07457e9 + 1.44289e10i −0.0888454 + 0.617933i
\(918\) 7.99651e9 5.13905e9i 0.341155 0.219247i
\(919\) 2.35320e10 1.00012 0.500062 0.865990i \(-0.333311\pi\)
0.500062 + 0.865990i \(0.333311\pi\)
\(920\) −1.03848e9 2.58291e10i −0.0439683 1.09358i
\(921\) 4.56335e9 0.192475
\(922\) −6.08542e10 + 3.91086e10i −2.55701 + 1.64329i
\(923\) 5.57157e9 3.87511e10i 0.233223 1.62210i
\(924\) 2.36898e10 5.18735e10i 0.987894 2.16319i
\(925\) −9.01883e9 + 2.64817e9i −0.374674 + 0.110014i
\(926\) 3.02044e10 + 6.61385e10i 1.25006 + 2.73726i
\(927\) −7.75387e9 8.94845e9i −0.319698 0.368951i
\(928\) 4.61587e8 + 3.21041e9i 0.0189599 + 0.131869i
\(929\) 8.43291e9 + 2.47612e9i 0.345082 + 0.101325i 0.449681 0.893189i \(-0.351538\pi\)
−0.104599 + 0.994514i \(0.533356\pi\)
\(930\) −1.24323e10 + 1.43477e10i −0.506830 + 0.584913i
\(931\) −5.35291e9 3.44011e9i −0.217403 0.139717i
\(932\) 2.42793e10 + 1.56034e10i 0.982384 + 0.631340i
\(933\) −2.52976e9 + 2.91950e9i −0.101975 + 0.117686i
\(934\) 7.06577e10 + 2.07470e10i 2.83756 + 0.833184i
\(935\) 1.42335e9 + 9.89965e9i 0.0569472 + 0.396077i
\(936\) −2.88562e10 3.33018e10i −1.15020 1.32740i
\(937\) −2.98407e9 6.53420e9i −0.118501 0.259480i 0.841082 0.540908i \(-0.181919\pi\)
−0.959582 + 0.281428i \(0.909192\pi\)
\(938\) 5.48170e10 1.60957e10i 2.16873 0.636797i
\(939\) −1.29897e9 + 2.84436e9i −0.0512001 + 0.112113i
\(940\) 7.89203e8 5.48903e9i 0.0309914 0.215550i
\(941\) −4.16285e9 + 2.67530e9i −0.162865 + 0.104667i −0.619534 0.784970i \(-0.712679\pi\)
0.456670 + 0.889636i \(0.349042\pi\)
\(942\) 4.51701e10 1.76065
\(943\) 1.80006e10 + 1.85365e9i 0.699030 + 0.0719843i
\(944\) −1.32755e11 −5.13630
\(945\) 2.31550e9 1.48808e9i 0.0892552 0.0573608i
\(946\) 8.93788e9 6.21643e10i 0.343254 2.38738i
\(947\) 7.73389e9 1.69348e10i 0.295919 0.647972i −0.702019 0.712158i \(-0.747718\pi\)
0.997938 + 0.0641860i \(0.0204451\pi\)
\(948\) 2.93011e9 8.60358e8i 0.111700 0.0327982i
\(949\) −2.11494e10 4.63107e10i −0.803278 1.75893i
\(950\) 5.30000e9 + 6.11652e9i 0.200559 + 0.231458i
\(951\) 2.82161e8 + 1.96247e9i 0.0106381 + 0.0739898i
\(952\) 1.34935e11 + 3.96205e10i 5.06869 + 1.48830i
\(953\) 2.59979e9 3.00032e9i 0.0973002 0.112290i −0.705011 0.709196i \(-0.749058\pi\)
0.802311 + 0.596906i \(0.203603\pi\)
\(954\) 8.84527e9 + 5.68451e9i 0.329831 + 0.211970i
\(955\) −1.14708e10 7.37186e9i −0.426170 0.273883i
\(956\) 3.36758e10 3.88640e10i 1.24657 1.43861i
\(957\) 6.60745e8 + 1.94012e8i 0.0243692 + 0.00715545i
\(958\) 1.08221e10 + 7.52695e10i 0.397680 + 2.76592i
\(959\) −2.33761e10 2.69775e10i −0.855870 0.987726i
\(960\) −6.11409e9 1.33880e10i −0.223040 0.488389i
\(961\) −7.72272e10 + 2.26759e10i −2.80697 + 0.824202i
\(962\) −1.67046e10 + 3.65779e10i −0.604954 + 1.32467i
\(963\) −2.02999e9 + 1.41189e10i −0.0732490 + 0.509458i
\(964\) −7.73710e10 + 4.97233e10i −2.78169 + 1.78768i
\(965\) 1.25338e10 0.448992
\(966\) −3.47512e10 + 3.26466e10i −1.24037 + 1.16525i
\(967\) 4.23219e10 1.50513 0.752563 0.658521i \(-0.228818\pi\)
0.752563 + 0.658521i \(0.228818\pi\)
\(968\) −2.25790e9 + 1.45106e9i −0.0800094 + 0.0514189i
\(969\) −4.75290e8 + 3.30571e9i −0.0167813 + 0.116716i
\(970\) 4.43012e9 9.70062e9i 0.155853 0.341270i
\(971\) 3.22905e10 9.48135e9i 1.13190 0.332355i 0.338445 0.940986i \(-0.390099\pi\)
0.793454 + 0.608631i \(0.208281\pi\)
\(972\) 1.99718e9 + 4.37321e9i 0.0697565 + 0.152746i
\(973\) 4.03102e9 + 4.65205e9i 0.140288 + 0.161901i
\(974\) 3.61008e9 + 2.51086e10i 0.125187 + 0.870696i
\(975\) −2.39828e10 7.04197e9i −0.828672 0.243320i
\(976\) 7.73355e9 8.92500e9i 0.266259 0.307280i
\(977\) 2.70657e10 + 1.73940e10i 0.928512 + 0.596719i 0.915116 0.403192i \(-0.132099\pi\)
0.0133967 + 0.999910i \(0.495736\pi\)
\(978\) −3.85331e10 2.47637e10i −1.31719 0.846506i
\(979\) 1.30008e10 1.50038e10i 0.442825 0.511047i
\(980\) 3.69023e10 + 1.08355e10i 1.25246 + 0.367754i
\(981\) 1.13426e9 + 7.88894e9i 0.0383593 + 0.266795i
\(982\) −6.93950e9 8.00861e9i −0.233850 0.269878i
\(983\) 2.35469e10 + 5.15605e10i 0.790671 + 1.73133i 0.674719 + 0.738074i \(0.264265\pi\)
0.115952 + 0.993255i \(0.463008\pi\)
\(984\) 3.57962e10 1.05107e10i 1.19772 0.351682i
\(985\) −3.09484e9 + 6.77676e9i −0.103184 + 0.225941i
\(986\) −3.91089e8 + 2.72008e9i −0.0129929 + 0.0903676i
\(987\) −5.31762e9 + 3.41743e9i −0.176038 + 0.113133i
\(988\) 2.50527e10 0.826429
\(989\) −1.92412e10 + 3.27631e10i −0.632476 + 1.07696i
\(990\) −6.99102e9 −0.228990
\(991\) 3.17761e10 2.04213e10i 1.03715 0.666538i 0.0928726 0.995678i \(-0.470395\pi\)
0.944281 + 0.329140i \(0.106759\pi\)
\(992\) 2.66577e10 1.85408e11i 0.867025 6.03029i
\(993\) 3.86680e9 8.46710e9i 0.125322 0.274418i
\(994\) −8.37991e10 + 2.46056e10i −2.70637 + 0.794661i
\(995\) 7.33141e9 + 1.60536e10i 0.235943 + 0.516643i
\(996\) 1.57765e9 + 1.82070e9i 0.0505944 + 0.0583890i
\(997\) 3.65385e9 + 2.54131e10i 0.116766 + 0.812127i 0.961079 + 0.276275i \(0.0891002\pi\)
−0.844312 + 0.535851i \(0.819991\pi\)
\(998\) 6.01091e10 + 1.76496e10i 1.91418 + 0.562055i
\(999\) 1.77548e9 2.04901e9i 0.0563426 0.0650228i
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.58.1 yes 140
23.2 even 11 inner 69.8.e.a.25.1 140
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.8.e.a.25.1 140 23.2 even 11 inner
69.8.e.a.58.1 yes 140 1.1 even 1 trivial