Properties

Label 38.10.e.a.9.6
Level $38$
Weight $10$
Character 38.9
Analytic conductor $19.571$
Analytic rank $0$
Dimension $42$
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] = [38,10,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.5713617742\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.6
Character \(\chi\) \(=\) 38.9
Dual form 38.10.e.a.17.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.77837 - 15.7569i) q^{2} +(117.543 - 98.6302i) q^{3} +(-240.561 + 87.5572i) q^{4} +(-1860.80 - 677.275i) q^{5} +(-1880.69 - 1578.08i) q^{6} +(-1980.53 + 3430.38i) q^{7} +(2048.00 + 3547.24i) q^{8} +(670.500 - 3802.60i) q^{9} +O(q^{10})\) \(q+(-2.77837 - 15.7569i) q^{2} +(117.543 - 98.6302i) q^{3} +(-240.561 + 87.5572i) q^{4} +(-1860.80 - 677.275i) q^{5} +(-1880.69 - 1578.08i) q^{6} +(-1980.53 + 3430.38i) q^{7} +(2048.00 + 3547.24i) q^{8} +(670.500 - 3802.60i) q^{9} +(-5501.78 + 31202.1i) q^{10} +(21705.4 + 37594.9i) q^{11} +(-19640.5 + 34018.3i) q^{12} +(31908.2 + 26774.2i) q^{13} +(59554.9 + 21676.2i) q^{14} +(-285523. + 103922. i) q^{15} +(50203.5 - 42125.7i) q^{16} +(-21965.0 - 124570. i) q^{17} -61780.1 q^{18} +(-563277. - 73531.6i) q^{19} +506936. q^{20} +(105542. + 598557. i) q^{21} +(532074. - 446463. i) q^{22} +(717634. - 261198. i) q^{23} +(590593. + 214958. i) q^{24} +(1.50768e6 + 1.26510e6i) q^{25} +(333226. - 577164. i) q^{26} +(1.21386e6 + 2.10246e6i) q^{27} +(176085. - 998627. i) q^{28} +(-1.15548e6 + 6.55307e6i) q^{29} +(2.43078e6 + 4.21023e6i) q^{30} +(-174065. + 301490. i) q^{31} +(-803256. - 674012. i) q^{32} +(6.25931e6 + 2.27820e6i) q^{33} +(-1.90181e6 + 692201. i) q^{34} +(6.00868e6 - 5.04188e6i) q^{35} +(171648. + 973465. i) q^{36} +539830. q^{37} +(406361. + 9.07981e6i) q^{38} +6.39132e6 q^{39} +(-1.40846e6 - 7.98775e6i) q^{40} +(-5.62806e6 + 4.72250e6i) q^{41} +(9.13819e6 - 3.32603e6i) q^{42} +(-1.78211e7 - 6.48636e6i) q^{43} +(-8.51319e6 - 7.14341e6i) q^{44} +(-3.82307e6 + 6.62174e6i) q^{45} +(-6.10952e6 - 1.05820e7i) q^{46} +(-4.20680e6 + 2.38579e7i) q^{47} +(1.74619e6 - 9.90316e6i) q^{48} +(1.23318e7 + 2.13593e7i) q^{49} +(1.57451e7 - 2.72713e7i) q^{50} +(-1.48682e7 - 1.24759e7i) q^{51} +(-1.00201e7 - 3.64703e6i) q^{52} +(-9.56618e7 + 3.48181e7i) q^{53} +(2.97557e7 - 2.49680e7i) q^{54} +(-1.49273e7 - 8.46570e7i) q^{55} -1.62245e7 q^{56} +(-7.34616e7 + 4.69130e7i) q^{57} +1.06467e8 q^{58} +(6.13196e6 + 3.47761e7i) q^{59} +(5.95867e7 - 4.99992e7i) q^{60} +(-4.84419e7 + 1.76314e7i) q^{61} +(5.23417e6 + 1.90508e6i) q^{62} +(1.17164e7 + 9.83124e6i) q^{63} +(-8.38861e6 + 1.45295e7i) q^{64} +(-4.12412e7 - 7.14319e7i) q^{65} +(1.85068e7 - 1.04957e8i) q^{66} +(5.42040e7 - 3.07406e8i) q^{67} +(1.61909e7 + 2.80435e7i) q^{68} +(5.85909e7 - 1.01482e8i) q^{69} +(-9.61388e7 - 8.06701e7i) q^{70} +(1.56978e7 + 5.71354e6i) q^{71} +(1.48619e7 - 5.40929e6i) q^{72} +(-3.27339e8 + 2.74670e8i) q^{73} +(-1.49985e6 - 8.50606e6i) q^{74} +3.01994e8 q^{75} +(1.41941e8 - 3.16301e7i) q^{76} -1.71953e8 q^{77} +(-1.77575e7 - 1.00708e8i) q^{78} +(-3.41554e8 + 2.86598e8i) q^{79} +(-1.21949e8 + 4.43859e7i) q^{80} +(4.21464e8 + 1.53400e8i) q^{81} +(9.00490e7 + 7.55601e7i) q^{82} +(-8.31499e7 + 1.44020e8i) q^{83} +(-7.77973e7 - 1.34749e8i) q^{84} +(-4.34955e7 + 2.46675e8i) q^{85} +(-5.26914e7 + 2.98828e8i) q^{86} +(5.10512e8 + 8.84233e8i) q^{87} +(-8.89054e7 + 1.53989e8i) q^{88} +(1.21793e8 + 1.02196e8i) q^{89} +(1.14960e8 + 4.18421e7i) q^{90} +(-1.55041e8 + 5.64302e7i) q^{91} +(-1.49765e8 + 1.25668e8i) q^{92} +(9.27587e6 + 5.26061e7i) q^{93} +3.87616e8 q^{94} +(9.98342e8 + 5.18320e8i) q^{95} -1.60895e8 q^{96} +(-2.50398e8 - 1.42008e9i) q^{97} +(3.02294e8 - 2.53655e8i) q^{98} +(1.57512e8 - 5.73296e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{4}{9}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77837 15.7569i −0.122788 0.696364i
\(3\) 117.543 98.6302i 0.837820 0.703015i −0.119252 0.992864i \(-0.538050\pi\)
0.957072 + 0.289849i \(0.0936052\pi\)
\(4\) −240.561 + 87.5572i −0.469846 + 0.171010i
\(5\) −1860.80 677.275i −1.33148 0.484618i −0.424359 0.905494i \(-0.639501\pi\)
−0.907118 + 0.420876i \(0.861723\pi\)
\(6\) −1880.69 1578.08i −0.592428 0.497106i
\(7\) −1980.53 + 3430.38i −0.311775 + 0.540009i −0.978747 0.205073i \(-0.934257\pi\)
0.666972 + 0.745083i \(0.267590\pi\)
\(8\) 2048.00 + 3547.24i 0.176777 + 0.306186i
\(9\) 670.500 3802.60i 0.0340649 0.193192i
\(10\) −5501.78 + 31202.1i −0.173982 + 0.986699i
\(11\) 21705.4 + 37594.9i 0.446993 + 0.774215i 0.998189 0.0601610i \(-0.0191614\pi\)
−0.551195 + 0.834376i \(0.685828\pi\)
\(12\) −19640.5 + 34018.3i −0.273424 + 0.473585i
\(13\) 31908.2 + 26774.2i 0.309854 + 0.259998i 0.784432 0.620215i \(-0.212955\pi\)
−0.474578 + 0.880214i \(0.657399\pi\)
\(14\) 59554.9 + 21676.2i 0.414325 + 0.150802i
\(15\) −285523. + 103922.i −1.45623 + 0.530025i
\(16\) 50203.5 42125.7i 0.191511 0.160697i
\(17\) −21965.0 124570.i −0.0637839 0.361736i −0.999948 0.0101737i \(-0.996762\pi\)
0.936164 0.351563i \(-0.114350\pi\)
\(18\) −61780.1 −0.138715
\(19\) −563277. 73531.6i −0.991587 0.129444i
\(20\) 506936. 0.708464
\(21\) 105542. + 598557.i 0.118423 + 0.671613i
\(22\) 532074. 446463.i 0.484250 0.406334i
\(23\) 717634. 261198.i 0.534722 0.194623i −0.0605236 0.998167i \(-0.519277\pi\)
0.595245 + 0.803544i \(0.297055\pi\)
\(24\) 590593. + 214958.i 0.363360 + 0.132252i
\(25\) 1.50768e6 + 1.26510e6i 0.771933 + 0.647729i
\(26\) 333226. 577164.i 0.143007 0.247696i
\(27\) 1.21386e6 + 2.10246e6i 0.439572 + 0.761361i
\(28\) 176085. 998627.i 0.0541391 0.307038i
\(29\) −1.15548e6 + 6.55307e6i −0.303370 + 1.72050i 0.327709 + 0.944779i \(0.393723\pi\)
−0.631079 + 0.775718i \(0.717388\pi\)
\(30\) 2.43078e6 + 4.21023e6i 0.547898 + 0.948988i
\(31\) −174065. + 301490.i −0.0338520 + 0.0586334i −0.882455 0.470397i \(-0.844111\pi\)
0.848603 + 0.529030i \(0.177444\pi\)
\(32\) −803256. 674012.i −0.135419 0.113630i
\(33\) 6.25931e6 + 2.27820e6i 0.918785 + 0.334410i
\(34\) −1.90181e6 + 692201.i −0.244068 + 0.0888336i
\(35\) 6.00868e6 5.04188e6i 0.676819 0.567919i
\(36\) 171648. + 973465.i 0.0170325 + 0.0965959i
\(37\) 539830. 0.0473532 0.0236766 0.999720i \(-0.492463\pi\)
0.0236766 + 0.999720i \(0.492463\pi\)
\(38\) 406361. + 9.07981e6i 0.0316144 + 0.706400i
\(39\) 6.39132e6 0.442385
\(40\) −1.40846e6 7.98775e6i −0.0869908 0.493349i
\(41\) −5.62806e6 + 4.72250e6i −0.311051 + 0.261003i −0.784926 0.619589i \(-0.787299\pi\)
0.473875 + 0.880592i \(0.342855\pi\)
\(42\) 9.13819e6 3.32603e6i 0.453146 0.164932i
\(43\) −1.78211e7 6.48636e6i −0.794927 0.289330i −0.0875444 0.996161i \(-0.527902\pi\)
−0.707383 + 0.706831i \(0.750124\pi\)
\(44\) −8.51319e6 7.14341e6i −0.342417 0.287322i
\(45\) −3.82307e6 + 6.62174e6i −0.138981 + 0.240722i
\(46\) −6.10952e6 1.05820e7i −0.201186 0.348464i
\(47\) −4.20680e6 + 2.38579e7i −0.125751 + 0.713169i 0.855108 + 0.518450i \(0.173491\pi\)
−0.980859 + 0.194719i \(0.937620\pi\)
\(48\) 1.74619e6 9.90316e6i 0.0474796 0.269270i
\(49\) 1.23318e7 + 2.13593e7i 0.305593 + 0.529303i
\(50\) 1.57451e7 2.72713e7i 0.356271 0.617080i
\(51\) −1.48682e7 1.24759e7i −0.307745 0.258229i
\(52\) −1.00201e7 3.64703e6i −0.190046 0.0691711i
\(53\) −9.56618e7 + 3.48181e7i −1.66532 + 0.606126i −0.991185 0.132483i \(-0.957705\pi\)
−0.674133 + 0.738610i \(0.735483\pi\)
\(54\) 2.97557e7 2.49680e7i 0.476210 0.399588i
\(55\) −1.49273e7 8.46570e7i −0.219963 1.24747i
\(56\) −1.62245e7 −0.220458
\(57\) −7.34616e7 + 4.69130e7i −0.921773 + 0.588649i
\(58\) 1.06467e8 1.23534
\(59\) 6.13196e6 + 3.47761e7i 0.0658817 + 0.373634i 0.999867 + 0.0163218i \(0.00519564\pi\)
−0.933985 + 0.357312i \(0.883693\pi\)
\(60\) 5.95867e7 4.99992e7i 0.593566 0.498061i
\(61\) −4.84419e7 + 1.76314e7i −0.447958 + 0.163043i −0.556142 0.831088i \(-0.687719\pi\)
0.108184 + 0.994131i \(0.465497\pi\)
\(62\) 5.23417e6 + 1.90508e6i 0.0449868 + 0.0163739i
\(63\) 1.17164e7 + 9.83124e6i 0.0937049 + 0.0786277i
\(64\) −8.38861e6 + 1.45295e7i −0.0625000 + 0.108253i
\(65\) −4.12412e7 7.14319e7i −0.286564 0.496343i
\(66\) 1.85068e7 1.04957e8i 0.120056 0.680870i
\(67\) 5.42040e7 3.07406e8i 0.328620 1.86370i −0.154285 0.988026i \(-0.549307\pi\)
0.482905 0.875673i \(-0.339582\pi\)
\(68\) 1.61909e7 + 2.80435e7i 0.0918292 + 0.159053i
\(69\) 5.85909e7 1.01482e8i 0.311178 0.538976i
\(70\) −9.61388e7 8.06701e7i −0.478583 0.401579i
\(71\) 1.56978e7 + 5.71354e6i 0.0733122 + 0.0266835i 0.378416 0.925636i \(-0.376469\pi\)
−0.305104 + 0.952319i \(0.598691\pi\)
\(72\) 1.48619e7 5.40929e6i 0.0651746 0.0237216i
\(73\) −3.27339e8 + 2.74670e8i −1.34910 + 1.13203i −0.369914 + 0.929066i \(0.620613\pi\)
−0.979186 + 0.202964i \(0.934943\pi\)
\(74\) −1.49985e6 8.50606e6i −0.00581440 0.0329751i
\(75\) 3.01994e8 1.10210
\(76\) 1.41941e8 3.16301e7i 0.488030 0.108752i
\(77\) −1.71953e8 −0.557445
\(78\) −1.77575e7 1.00708e8i −0.0543194 0.308061i
\(79\) −3.41554e8 + 2.86598e8i −0.986592 + 0.827849i −0.985071 0.172150i \(-0.944929\pi\)
−0.00152126 + 0.999999i \(0.500484\pi\)
\(80\) −1.21949e8 + 4.43859e7i −0.332869 + 0.121155i
\(81\) 4.21464e8 + 1.53400e8i 1.08787 + 0.395953i
\(82\) 9.00490e7 + 7.55601e7i 0.219946 + 0.184557i
\(83\) −8.31499e7 + 1.44020e8i −0.192314 + 0.333097i −0.946017 0.324118i \(-0.894932\pi\)
0.753703 + 0.657215i \(0.228266\pi\)
\(84\) −7.77973e7 1.34749e8i −0.170493 0.295303i
\(85\) −4.34955e7 + 2.46675e8i −0.0903772 + 0.512555i
\(86\) −5.26914e7 + 2.98828e8i −0.103872 + 0.589085i
\(87\) 5.10512e8 + 8.84233e8i 0.955365 + 1.65474i
\(88\) −8.89054e7 + 1.53989e8i −0.158036 + 0.273726i
\(89\) 1.21793e8 + 1.02196e8i 0.205762 + 0.172655i 0.739845 0.672777i \(-0.234899\pi\)
−0.534083 + 0.845432i \(0.679343\pi\)
\(90\) 1.14960e8 + 4.18421e7i 0.184695 + 0.0672237i
\(91\) −1.55041e8 + 5.64302e7i −0.237006 + 0.0862632i
\(92\) −1.49765e8 + 1.25668e8i −0.217955 + 0.182886i
\(93\) 9.27587e6 + 5.26061e7i 0.0128582 + 0.0729227i
\(94\) 3.87616e8 0.512066
\(95\) 9.98342e8 + 5.18320e8i 1.25754 + 0.652893i
\(96\) −1.60895e8 −0.193340
\(97\) −2.50398e8 1.42008e9i −0.287182 1.62869i −0.697384 0.716697i \(-0.745653\pi\)
0.410202 0.911995i \(-0.365458\pi\)
\(98\) 3.02294e8 2.53655e8i 0.331065 0.277796i
\(99\) 1.57512e8 5.73296e7i 0.164799 0.0599819i
\(100\) −4.73458e8 1.72325e8i −0.473458 0.172325i
\(101\) −8.24088e7 6.91492e7i −0.0788002 0.0661212i 0.602537 0.798091i \(-0.294157\pi\)
−0.681337 + 0.731970i \(0.738601\pi\)
\(102\) −1.55272e8 + 2.68939e8i −0.142034 + 0.246010i
\(103\) −2.26422e8 3.92175e8i −0.198222 0.343330i 0.749730 0.661744i \(-0.230183\pi\)
−0.947952 + 0.318413i \(0.896850\pi\)
\(104\) −2.96264e7 + 1.68019e8i −0.0248330 + 0.140835i
\(105\) 2.08996e8 1.18527e9i 0.167798 0.951628i
\(106\) 8.14410e8 + 1.41060e9i 0.626566 + 1.08524i
\(107\) 7.74535e8 1.34153e9i 0.571234 0.989406i −0.425206 0.905097i \(-0.639798\pi\)
0.996440 0.0843094i \(-0.0268684\pi\)
\(108\) −4.76092e8 3.99488e8i −0.336732 0.282551i
\(109\) 5.50014e8 + 2.00189e8i 0.373211 + 0.135838i 0.521814 0.853059i \(-0.325255\pi\)
−0.148603 + 0.988897i \(0.547478\pi\)
\(110\) −1.29246e9 + 4.70417e8i −0.841686 + 0.306349i
\(111\) 6.34532e7 5.32436e7i 0.0396735 0.0332900i
\(112\) 4.50777e7 + 2.55648e8i 0.0270695 + 0.153519i
\(113\) 1.78304e8 0.102875 0.0514373 0.998676i \(-0.483620\pi\)
0.0514373 + 0.998676i \(0.483620\pi\)
\(114\) 9.43308e8 + 1.02719e9i 0.523097 + 0.569611i
\(115\) −1.51227e9 −0.806288
\(116\) −2.95804e8 1.67759e9i −0.151685 0.860249i
\(117\) 1.23206e8 1.03382e8i 0.0607847 0.0510045i
\(118\) 5.30927e8 1.93242e8i 0.252096 0.0917554i
\(119\) 4.70824e8 + 1.71366e8i 0.215227 + 0.0783363i
\(120\) −9.53388e8 7.99987e8i −0.419714 0.352182i
\(121\) 2.36723e8 4.10017e8i 0.100394 0.173887i
\(122\) 4.12407e8 + 7.14309e8i 0.168541 + 0.291922i
\(123\) −1.95757e8 + 1.11019e9i −0.0771160 + 0.437347i
\(124\) 1.54758e7 8.77674e7i 0.00587834 0.0333377i
\(125\) −1.48656e7 2.57480e7i −0.00544613 0.00943297i
\(126\) 1.22357e8 2.11929e8i 0.0432477 0.0749072i
\(127\) −3.81166e9 3.19836e9i −1.30016 1.09097i −0.990117 0.140244i \(-0.955211\pi\)
−0.310046 0.950722i \(-0.600344\pi\)
\(128\) 2.52247e8 + 9.18103e7i 0.0830579 + 0.0302306i
\(129\) −2.73450e9 + 9.95276e8i −0.869409 + 0.316439i
\(130\) −1.01096e9 + 8.48299e8i −0.310449 + 0.260498i
\(131\) 2.87436e8 + 1.63013e9i 0.0852747 + 0.483617i 0.997297 + 0.0734762i \(0.0234093\pi\)
−0.912022 + 0.410141i \(0.865480\pi\)
\(132\) −1.70522e9 −0.488875
\(133\) 1.36783e9 1.78662e9i 0.379053 0.495109i
\(134\) −4.99437e9 −1.33816
\(135\) −8.34795e8 4.73436e9i −0.216311 1.22676i
\(136\) 3.96894e8 3.33034e8i 0.0994832 0.0834763i
\(137\) −6.68194e8 + 2.43203e8i −0.162054 + 0.0589829i −0.421773 0.906701i \(-0.638592\pi\)
0.259719 + 0.965684i \(0.416370\pi\)
\(138\) −1.76184e9 6.41256e8i −0.413533 0.150514i
\(139\) −2.35255e8 1.97402e8i −0.0534529 0.0448523i 0.615670 0.788004i \(-0.288886\pi\)
−0.669123 + 0.743152i \(0.733330\pi\)
\(140\) −1.00400e9 + 1.73898e9i −0.220881 + 0.382577i
\(141\) 1.85863e9 + 3.21925e9i 0.396012 + 0.685912i
\(142\) 4.64134e7 2.63223e8i 0.00957957 0.0543284i
\(143\) −3.13991e8 + 1.78073e9i −0.0627920 + 0.356111i
\(144\) −1.26526e8 2.19149e8i −0.0245215 0.0424725i
\(145\) 6.58835e9 1.14114e10i 1.23771 2.14378i
\(146\) 5.23742e9 + 4.39471e9i 0.953958 + 0.800466i
\(147\) 3.55619e9 + 1.29435e9i 0.628140 + 0.228624i
\(148\) −1.29862e8 + 4.72660e7i −0.0222487 + 0.00809788i
\(149\) −1.38318e9 + 1.16063e9i −0.229901 + 0.192910i −0.750460 0.660916i \(-0.770168\pi\)
0.520559 + 0.853826i \(0.325724\pi\)
\(150\) −8.39051e8 4.75850e9i −0.135325 0.767466i
\(151\) 6.04760e9 0.946645 0.473322 0.880889i \(-0.343055\pi\)
0.473322 + 0.880889i \(0.343055\pi\)
\(152\) −8.92757e8 2.14867e9i −0.135655 0.326493i
\(153\) −4.88416e8 −0.0720573
\(154\) 4.77749e8 + 2.70945e9i 0.0684474 + 0.388185i
\(155\) 5.28091e8 4.43121e8i 0.0734880 0.0616637i
\(156\) −1.53751e9 + 5.59606e8i −0.207853 + 0.0756522i
\(157\) 1.39268e10 + 5.06893e9i 1.82937 + 0.665836i 0.993064 + 0.117573i \(0.0375115\pi\)
0.836306 + 0.548263i \(0.184711\pi\)
\(158\) 5.46487e9 + 4.58557e9i 0.697626 + 0.585378i
\(159\) −7.81026e9 + 1.35278e10i −0.969122 + 1.67857i
\(160\) 1.03820e9 + 1.79822e9i 0.125240 + 0.216922i
\(161\) −5.25290e8 + 2.97907e9i −0.0616145 + 0.349433i
\(162\) 1.24613e9 7.06717e9i 0.142150 0.806173i
\(163\) 6.87542e8 + 1.19086e9i 0.0762878 + 0.132134i 0.901646 0.432476i \(-0.142360\pi\)
−0.825358 + 0.564610i \(0.809027\pi\)
\(164\) 9.40405e8 1.62883e9i 0.101512 0.175824i
\(165\) −1.01043e10 8.47854e9i −1.06128 0.890520i
\(166\) 2.50033e9 + 9.10047e8i 0.255571 + 0.0930202i
\(167\) −1.46473e10 + 5.33118e9i −1.45725 + 0.530395i −0.944606 0.328207i \(-0.893556\pi\)
−0.512642 + 0.858602i \(0.671333\pi\)
\(168\) −1.90708e9 + 1.60023e9i −0.184704 + 0.154985i
\(169\) −1.54017e9 8.73476e9i −0.145238 0.823685i
\(170\) 4.00769e9 0.368022
\(171\) −6.57288e8 + 2.09261e9i −0.0587859 + 0.187157i
\(172\) 4.85500e9 0.422972
\(173\) 3.20179e9 + 1.81583e10i 0.271760 + 1.54123i 0.749068 + 0.662493i \(0.230502\pi\)
−0.477308 + 0.878736i \(0.658387\pi\)
\(174\) 1.25144e10 1.05008e10i 1.03500 0.868464i
\(175\) −7.32577e9 + 2.66636e9i −0.590449 + 0.214906i
\(176\) 2.67340e9 + 9.73038e8i 0.210018 + 0.0764404i
\(177\) 4.15074e9 + 3.48288e9i 0.317867 + 0.266722i
\(178\) 1.27191e9 2.20302e9i 0.0949658 0.164486i
\(179\) 1.02322e10 + 1.77226e10i 0.744953 + 1.29030i 0.950217 + 0.311590i \(0.100862\pi\)
−0.205263 + 0.978707i \(0.565805\pi\)
\(180\) 3.39901e8 1.92767e9i 0.0241338 0.136870i
\(181\) −2.15581e9 + 1.22262e10i −0.149299 + 0.846715i 0.814516 + 0.580141i \(0.197003\pi\)
−0.963815 + 0.266574i \(0.914108\pi\)
\(182\) 1.31993e9 + 2.28618e9i 0.0891721 + 0.154451i
\(183\) −3.95502e9 + 6.85029e9i −0.260686 + 0.451522i
\(184\) 2.39625e9 + 2.01069e9i 0.154117 + 0.129320i
\(185\) −1.00451e9 3.65613e8i −0.0630497 0.0229482i
\(186\) 8.03138e8 2.92318e8i 0.0492019 0.0179080i
\(187\) 4.20642e9 3.52961e9i 0.251551 0.211076i
\(188\) −1.07694e9 6.10763e9i −0.0628755 0.356585i
\(189\) −9.61631e9 −0.548189
\(190\) 5.39337e9 1.71709e10i 0.300240 0.955876i
\(191\) −2.05078e10 −1.11498 −0.557492 0.830182i \(-0.688236\pi\)
−0.557492 + 0.830182i \(0.688236\pi\)
\(192\) 4.47026e8 + 2.53521e9i 0.0237398 + 0.134635i
\(193\) 1.98029e10 1.66166e10i 1.02736 0.862055i 0.0368234 0.999322i \(-0.488276\pi\)
0.990534 + 0.137266i \(0.0438316\pi\)
\(194\) −2.16803e10 + 7.89100e9i −1.09890 + 0.399967i
\(195\) −1.18930e10 4.32868e9i −0.589025 0.214388i
\(196\) −4.83671e9 4.05848e9i −0.234098 0.196432i
\(197\) 2.06092e10 3.56962e10i 0.974906 1.68859i 0.294662 0.955601i \(-0.404793\pi\)
0.680244 0.732986i \(-0.261874\pi\)
\(198\) −1.34096e9 2.32262e9i −0.0620045 0.107395i
\(199\) −7.15570e9 + 4.05820e10i −0.323455 + 1.83440i 0.196865 + 0.980431i \(0.436924\pi\)
−0.520319 + 0.853972i \(0.674187\pi\)
\(200\) −1.39986e9 + 7.93903e9i −0.0618659 + 0.350859i
\(201\) −2.39482e10 4.14796e10i −1.03488 1.79247i
\(202\) −8.60616e8 + 1.49063e9i −0.0363688 + 0.0629925i
\(203\) −2.01911e10 1.69423e10i −0.834501 0.700230i
\(204\) 4.66906e9 + 1.69940e9i 0.188753 + 0.0687004i
\(205\) 1.36711e10 4.97588e9i 0.540644 0.196778i
\(206\) −5.55038e9 + 4.65732e9i −0.214744 + 0.180191i
\(207\) −5.12055e8 2.90401e9i −0.0193843 0.109934i
\(208\) 2.72978e9 0.101121
\(209\) −9.46175e9 2.27724e10i −0.343015 0.825562i
\(210\) −1.92569e10 −0.683283
\(211\) −6.11408e9 3.46747e10i −0.212354 1.20432i −0.885440 0.464754i \(-0.846143\pi\)
0.673086 0.739564i \(-0.264968\pi\)
\(212\) 1.99640e10 1.67518e10i 0.678790 0.569573i
\(213\) 2.40869e9 8.76693e8i 0.0801813 0.0291836i
\(214\) −2.32904e10 8.47701e9i −0.759128 0.276300i
\(215\) 2.87685e10 + 2.41396e10i 0.918213 + 0.770472i
\(216\) −4.97195e9 + 8.61167e9i −0.155412 + 0.269182i
\(217\) −6.89483e8 1.19422e9i −0.0211084 0.0365608i
\(218\) 1.62622e9 9.22273e9i 0.0487668 0.276570i
\(219\) −1.13856e10 + 6.45709e10i −0.334470 + 1.89687i
\(220\) 1.10033e10 + 1.90582e10i 0.316679 + 0.548504i
\(221\) 2.63438e9 4.56289e9i 0.0742872 0.128669i
\(222\) −1.01525e9 8.51897e8i −0.0280534 0.0235396i
\(223\) 3.33060e10 + 1.21224e10i 0.901885 + 0.328259i 0.751008 0.660293i \(-0.229568\pi\)
0.150877 + 0.988553i \(0.451790\pi\)
\(224\) 3.90299e9 1.42057e9i 0.103581 0.0377005i
\(225\) 5.82155e9 4.88486e9i 0.151432 0.127066i
\(226\) −4.95395e8 2.80952e9i −0.0126317 0.0716382i
\(227\) 5.69288e10 1.42303 0.711517 0.702669i \(-0.248008\pi\)
0.711517 + 0.702669i \(0.248008\pi\)
\(228\) 1.35645e10 1.77175e10i 0.332427 0.434207i
\(229\) 1.31945e10 0.317054 0.158527 0.987355i \(-0.449326\pi\)
0.158527 + 0.987355i \(0.449326\pi\)
\(230\) 4.20166e9 + 2.38288e10i 0.0990023 + 0.561470i
\(231\) −2.02119e10 + 1.69598e10i −0.467038 + 0.391892i
\(232\) −2.56117e10 + 9.32191e9i −0.580421 + 0.211256i
\(233\) −4.35682e10 1.58575e10i −0.968429 0.352479i −0.191098 0.981571i \(-0.561205\pi\)
−0.777331 + 0.629092i \(0.783427\pi\)
\(234\) −1.97129e9 1.65411e9i −0.0429813 0.0360656i
\(235\) 2.39864e10 4.15456e10i 0.513049 0.888628i
\(236\) −4.52000e9 7.82888e9i −0.0948495 0.164284i
\(237\) −1.18801e10 + 6.73751e10i −0.244597 + 1.38718i
\(238\) 1.39208e9 7.89485e9i 0.0281233 0.159495i
\(239\) −2.49762e10 4.32601e10i −0.495150 0.857625i 0.504835 0.863216i \(-0.331554\pi\)
−0.999984 + 0.00559148i \(0.998220\pi\)
\(240\) −9.95647e9 + 1.72451e10i −0.193711 + 0.335518i
\(241\) −4.15968e10 3.49039e10i −0.794298 0.666495i 0.152507 0.988302i \(-0.451265\pi\)
−0.946805 + 0.321807i \(0.895710\pi\)
\(242\) −7.11831e9 2.59085e9i −0.133416 0.0485595i
\(243\) 1.97671e10 7.19464e9i 0.363676 0.132367i
\(244\) 1.01095e10 8.48288e9i 0.182589 0.153211i
\(245\) −8.48085e9 4.80973e10i −0.150381 0.852851i
\(246\) 1.80371e10 0.314021
\(247\) −1.60044e10 1.74275e10i −0.273592 0.297920i
\(248\) −1.42594e9 −0.0239370
\(249\) 4.43103e9 + 2.51296e10i 0.0730479 + 0.414275i
\(250\) −3.64407e8 + 3.05774e8i −0.00590007 + 0.00495074i
\(251\) −2.70961e10 + 9.86218e9i −0.430899 + 0.156834i −0.548359 0.836243i \(-0.684747\pi\)
0.117460 + 0.993078i \(0.462525\pi\)
\(252\) −3.67931e9 1.33916e9i −0.0574730 0.0209185i
\(253\) 2.53962e10 + 2.13100e10i 0.389697 + 0.326995i
\(254\) −3.98062e10 + 6.89463e10i −0.600066 + 1.03934i
\(255\) 1.92170e10 + 3.32849e10i 0.284614 + 0.492965i
\(256\) 7.45813e8 4.22972e9i 0.0108530 0.0615505i
\(257\) 6.87579e9 3.89945e10i 0.0983158 0.557577i −0.895365 0.445333i \(-0.853085\pi\)
0.993681 0.112243i \(-0.0358036\pi\)
\(258\) 2.32799e10 + 4.03221e10i 0.327110 + 0.566571i
\(259\) −1.06915e9 + 1.85182e9i −0.0147635 + 0.0255712i
\(260\) 1.61754e10 + 1.35728e10i 0.219521 + 0.184200i
\(261\) 2.41439e10 + 8.78767e9i 0.322052 + 0.117217i
\(262\) 2.48872e10 9.05821e9i 0.326303 0.118765i
\(263\) −2.02888e10 + 1.70243e10i −0.261490 + 0.219416i −0.764101 0.645096i \(-0.776817\pi\)
0.502611 + 0.864513i \(0.332373\pi\)
\(264\) 4.73774e9 + 2.68690e10i 0.0600279 + 0.340435i
\(265\) 2.01589e11 2.51107
\(266\) −3.19520e10 1.65889e10i −0.391319 0.203165i
\(267\) 2.43955e10 0.293771
\(268\) 1.38762e10 + 7.86960e10i 0.164310 + 0.931850i
\(269\) −7.39636e10 + 6.20628e10i −0.861256 + 0.722680i −0.962238 0.272208i \(-0.912246\pi\)
0.100982 + 0.994888i \(0.467802\pi\)
\(270\) −7.22796e10 + 2.63076e10i −0.827711 + 0.301262i
\(271\) 9.93545e10 + 3.61621e10i 1.11899 + 0.407278i 0.834283 0.551337i \(-0.185882\pi\)
0.284705 + 0.958615i \(0.408104\pi\)
\(272\) −6.35031e9 5.32854e9i −0.0703452 0.0590267i
\(273\) −1.26582e10 + 2.19247e10i −0.137924 + 0.238892i
\(274\) 5.68862e9 + 9.85298e9i 0.0609719 + 0.105606i
\(275\) −1.48363e10 + 8.41406e10i −0.156433 + 0.887173i
\(276\) −5.20919e9 + 2.95428e10i −0.0540355 + 0.306451i
\(277\) −3.86363e10 6.69200e10i −0.394308 0.682962i 0.598704 0.800970i \(-0.295682\pi\)
−0.993013 + 0.118008i \(0.962349\pi\)
\(278\) −2.45682e9 + 4.25535e9i −0.0246702 + 0.0427300i
\(279\) 1.02973e9 + 8.64048e8i 0.0101743 + 0.00853727i
\(280\) 3.01905e10 + 1.09885e10i 0.293535 + 0.106838i
\(281\) −7.99528e10 + 2.91005e10i −0.764989 + 0.278433i −0.694899 0.719107i \(-0.744551\pi\)
−0.0700904 + 0.997541i \(0.522329\pi\)
\(282\) 4.55615e10 3.82306e10i 0.429019 0.359990i
\(283\) 1.35502e10 + 7.68469e10i 0.125576 + 0.712176i 0.980964 + 0.194189i \(0.0622075\pi\)
−0.855388 + 0.517987i \(0.826681\pi\)
\(284\) −4.27655e9 −0.0390086
\(285\) 1.68470e11 3.75419e10i 1.51259 0.337065i
\(286\) 2.89312e10 0.255693
\(287\) −5.05344e9 2.86595e10i −0.0439661 0.249344i
\(288\) −3.10158e9 + 2.60253e9i −0.0265654 + 0.0222910i
\(289\) 9.64010e10 3.50871e10i 0.812908 0.295874i
\(290\) −1.98113e11 7.21071e10i −1.64483 0.598670i
\(291\) −1.69495e11 1.42223e11i −1.38560 1.16266i
\(292\) 5.46957e10 9.47357e10i 0.440281 0.762590i
\(293\) −3.93594e10 6.81724e10i −0.311992 0.540386i 0.666801 0.745236i \(-0.267663\pi\)
−0.978794 + 0.204849i \(0.934330\pi\)
\(294\) 1.05145e10 5.96307e10i 0.0820778 0.465486i
\(295\) 1.21426e10 6.88642e10i 0.0933497 0.529413i
\(296\) 1.10557e9 + 1.91491e9i 0.00837094 + 0.0144989i
\(297\) −5.26945e10 + 9.12695e10i −0.392971 + 0.680646i
\(298\) 2.21309e10 + 1.85700e10i 0.162564 + 0.136408i
\(299\) 2.98918e10 + 1.08797e10i 0.216287 + 0.0787222i
\(300\) −7.26481e10 + 2.64417e10i −0.517820 + 0.188471i
\(301\) 5.75460e10 4.82869e10i 0.404079 0.339062i
\(302\) −1.68025e10 9.52916e10i −0.116236 0.659210i
\(303\) −1.65068e10 −0.112505
\(304\) −3.13760e10 + 2.00369e10i −0.210701 + 0.134555i
\(305\) 1.02082e11 0.675460
\(306\) 1.35700e9 + 7.69593e9i 0.00884776 + 0.0501781i
\(307\) 2.86017e10 2.39997e10i 0.183768 0.154199i −0.546263 0.837614i \(-0.683950\pi\)
0.730031 + 0.683414i \(0.239506\pi\)
\(308\) 4.13653e10 1.50557e10i 0.261913 0.0953287i
\(309\) −6.52946e10 2.37653e10i −0.407440 0.148296i
\(310\) −8.44946e9 7.08994e9i −0.0519638 0.0436028i
\(311\) −1.28300e11 + 2.22222e11i −0.777687 + 1.34699i 0.155584 + 0.987823i \(0.450274\pi\)
−0.933272 + 0.359172i \(0.883059\pi\)
\(312\) 1.30894e10 + 2.26716e10i 0.0782033 + 0.135452i
\(313\) 2.80369e10 1.59005e11i 0.165113 0.936400i −0.783836 0.620968i \(-0.786740\pi\)
0.948948 0.315432i \(-0.102149\pi\)
\(314\) 4.11770e10 2.33526e11i 0.239040 1.35566i
\(315\) −1.51434e10 2.62292e10i −0.0866615 0.150102i
\(316\) 5.70710e10 9.88499e10i 0.321976 0.557679i
\(317\) −1.57245e11 1.31944e11i −0.874600 0.733877i 0.0904615 0.995900i \(-0.471166\pi\)
−0.965062 + 0.262023i \(0.915610\pi\)
\(318\) 2.34856e11 + 8.54805e10i 1.28789 + 0.468754i
\(319\) −2.71442e11 + 9.87969e10i −1.46764 + 0.534177i
\(320\) 2.54499e10 2.13550e10i 0.135679 0.113848i
\(321\) −4.12747e10 2.34080e11i −0.216976 1.23053i
\(322\) 4.84004e10 0.250898
\(323\) 3.21257e9 + 7.17823e10i 0.0164226 + 0.366949i
\(324\) −1.14819e11 −0.578844
\(325\) 1.42356e10 + 8.07338e10i 0.0707781 + 0.401403i
\(326\) 1.68540e10 1.41422e10i 0.0826464 0.0693486i
\(327\) 8.43949e10 3.07172e10i 0.408180 0.148565i
\(328\) −2.82781e10 1.02924e10i −0.134902 0.0491003i
\(329\) −7.35102e10 6.16824e10i −0.345912 0.290255i
\(330\) −1.05522e11 + 1.82770e11i −0.489814 + 0.848382i
\(331\) −5.54660e10 9.60698e10i −0.253981 0.439907i 0.710638 0.703558i \(-0.248407\pi\)
−0.964618 + 0.263651i \(0.915073\pi\)
\(332\) 7.39268e9 4.19260e10i 0.0333949 0.189392i
\(333\) 3.61956e8 2.05276e9i 0.00161308 0.00914826i
\(334\) 1.24699e11 + 2.15984e11i 0.548280 + 0.949649i
\(335\) −3.09061e11 + 5.35309e11i −1.34073 + 2.32222i
\(336\) 3.05132e10 + 2.56036e10i 0.130606 + 0.109591i
\(337\) −1.58508e11 5.76921e10i −0.669447 0.243659i −0.0151372 0.999885i \(-0.504819\pi\)
−0.654310 + 0.756227i \(0.727041\pi\)
\(338\) −1.33354e11 + 4.85368e10i −0.555751 + 0.202277i
\(339\) 2.09584e10 1.75862e10i 0.0861904 0.0723223i
\(340\) −1.11348e10 6.31488e10i −0.0451886 0.256277i
\(341\) −1.51126e10 −0.0605265
\(342\) 3.47993e10 + 4.54279e9i 0.137548 + 0.0179558i
\(343\) −2.57537e11 −1.00465
\(344\) −1.34890e10 7.64999e10i −0.0519358 0.294542i
\(345\) −1.77757e11 + 1.49156e11i −0.675524 + 0.566832i
\(346\) 2.77223e11 1.00901e11i 1.03989 0.378488i
\(347\) 2.67386e11 + 9.73207e10i 0.990049 + 0.360348i 0.785739 0.618558i \(-0.212283\pi\)
0.204310 + 0.978906i \(0.434505\pi\)
\(348\) −2.00230e11 1.68013e11i −0.731852 0.614097i
\(349\) 1.36180e11 2.35871e11i 0.491359 0.851059i −0.508591 0.861008i \(-0.669834\pi\)
0.999951 + 0.00994880i \(0.00316685\pi\)
\(350\) 6.23674e10 + 1.08024e11i 0.222153 + 0.384780i
\(351\) −1.75596e10 + 9.95856e10i −0.0617495 + 0.350199i
\(352\) 7.90439e9 4.48280e10i 0.0274427 0.155635i
\(353\) 1.95805e11 + 3.39144e11i 0.671178 + 1.16251i 0.977570 + 0.210609i \(0.0675448\pi\)
−0.306392 + 0.951905i \(0.599122\pi\)
\(354\) 4.33472e10 7.50796e10i 0.146706 0.254102i
\(355\) −2.53408e10 2.12635e10i −0.0846823 0.0710569i
\(356\) −3.82466e10 1.39206e10i −0.126202 0.0459339i
\(357\) 7.22439e10 2.62946e10i 0.235393 0.0856761i
\(358\) 2.50825e11 2.10468e11i 0.807045 0.677192i
\(359\) 8.56405e10 + 4.85691e11i 0.272116 + 1.54325i 0.747976 + 0.663726i \(0.231026\pi\)
−0.475860 + 0.879521i \(0.657863\pi\)
\(360\) −3.13186e10 −0.0982744
\(361\) 3.11874e11 + 8.28373e10i 0.966488 + 0.256710i
\(362\) 1.98637e11 0.607954
\(363\) −1.26149e10 7.15427e10i −0.0381333 0.216265i
\(364\) 3.23559e10 2.71499e10i 0.0966046 0.0810609i
\(365\) 7.95137e11 2.89406e11i 2.34490 0.853473i
\(366\) 1.18928e11 + 4.32863e10i 0.346433 + 0.126091i
\(367\) −2.65507e11 2.22787e11i −0.763974 0.641050i 0.175184 0.984536i \(-0.443948\pi\)
−0.939158 + 0.343485i \(0.888392\pi\)
\(368\) 2.50246e10 4.33439e10i 0.0711299 0.123201i
\(369\) 1.41842e10 + 2.45677e10i 0.0398277 + 0.0689836i
\(370\) −2.97003e9 + 1.68439e10i −0.00823859 + 0.0467233i
\(371\) 7.00221e10 3.97115e11i 0.191890 1.08826i
\(372\) −6.83745e9 1.18428e10i −0.0185119 0.0320636i
\(373\) −2.15865e11 + 3.73890e11i −0.577422 + 1.00012i 0.418352 + 0.908285i \(0.362608\pi\)
−0.995774 + 0.0918390i \(0.970725\pi\)
\(374\) −6.73028e10 5.64737e10i −0.177873 0.149253i
\(375\) −4.28688e9 1.56030e9i −0.0111944 0.00407443i
\(376\) −9.32454e10 + 3.39385e10i −0.240592 + 0.0875685i
\(377\) −2.12322e11 + 1.78160e11i −0.541327 + 0.454227i
\(378\) 2.67177e10 + 1.51524e11i 0.0673110 + 0.381739i
\(379\) 5.74229e11 1.42958 0.714790 0.699339i \(-0.246522\pi\)
0.714790 + 0.699339i \(0.246522\pi\)
\(380\) −2.85545e11 3.72758e10i −0.702504 0.0917066i
\(381\) −7.63489e11 −1.85627
\(382\) 5.69782e10 + 3.23140e11i 0.136906 + 0.776435i
\(383\) 2.59236e11 2.17525e11i 0.615603 0.516552i −0.280815 0.959762i \(-0.590605\pi\)
0.896418 + 0.443210i \(0.146160\pi\)
\(384\) 3.87051e10 1.40875e10i 0.0908401 0.0330631i
\(385\) 3.19970e11 + 1.16459e11i 0.742225 + 0.270148i
\(386\) −3.16847e11 2.65866e11i −0.726452 0.609565i
\(387\) −3.66141e10 + 6.34175e10i −0.0829753 + 0.143717i
\(388\) 1.84574e11 + 3.19691e11i 0.413454 + 0.716124i
\(389\) 7.82837e8 4.43969e9i 0.00173340 0.00983058i −0.983929 0.178561i \(-0.942856\pi\)
0.985662 + 0.168731i \(0.0539668\pi\)
\(390\) −3.51637e10 + 1.99423e11i −0.0769668 + 0.436500i
\(391\) −4.83001e10 8.36583e10i −0.104509 0.181015i
\(392\) −5.05110e10 + 8.74876e10i −0.108044 + 0.187137i
\(393\) 1.94566e11 + 1.63260e11i 0.411435 + 0.345235i
\(394\) −6.19722e11 2.25560e11i −1.29558 0.471552i
\(395\) 8.29668e11 3.01975e11i 1.71482 0.624142i
\(396\) −3.28716e10 + 2.75825e10i −0.0671727 + 0.0563645i
\(397\) 5.78600e10 + 3.28140e11i 0.116902 + 0.662983i 0.985791 + 0.167976i \(0.0537232\pi\)
−0.868889 + 0.495006i \(0.835166\pi\)
\(398\) 6.59329e11 1.31713
\(399\) −1.54364e10 3.44914e11i −0.0304907 0.681292i
\(400\) 1.28984e11 0.251922
\(401\) 1.00513e11 + 5.70040e11i 0.194122 + 1.10092i 0.913664 + 0.406471i \(0.133241\pi\)
−0.719542 + 0.694449i \(0.755648\pi\)
\(402\) −5.87053e11 + 4.92596e11i −1.12114 + 0.940749i
\(403\) −1.36262e10 + 4.95954e9i −0.0257338 + 0.00936632i
\(404\) 2.58789e10 + 9.41914e9i 0.0483314 + 0.0175912i
\(405\) −6.80364e11 5.70893e11i −1.25659 1.05440i
\(406\) −2.10861e11 + 3.65221e11i −0.385148 + 0.667097i
\(407\) 1.17172e10 + 2.02949e10i 0.0211666 + 0.0366616i
\(408\) 1.38049e10 7.82915e10i 0.0246640 0.139876i
\(409\) −2.03932e10 + 1.15655e11i −0.0360354 + 0.204367i −0.997510 0.0705273i \(-0.977532\pi\)
0.961474 + 0.274894i \(0.0886429\pi\)
\(410\) −1.16388e11 2.01590e11i −0.203414 0.352323i
\(411\) −5.45544e10 + 9.44909e10i −0.0943064 + 0.163344i
\(412\) 8.88061e10 + 7.45172e10i 0.151847 + 0.127415i
\(413\) −1.31440e11 4.78401e10i −0.222306 0.0809128i
\(414\) −4.43355e10 + 1.61368e10i −0.0741738 + 0.0269970i
\(415\) 2.52266e11 2.11676e11i 0.417487 0.350313i
\(416\) −7.58435e9 4.30130e10i −0.0124165 0.0704173i
\(417\) −4.71223e10 −0.0763158
\(418\) −3.32534e11 + 2.12358e11i −0.532774 + 0.340232i
\(419\) −6.35388e10 −0.100711 −0.0503554 0.998731i \(-0.516035\pi\)
−0.0503554 + 0.998731i \(0.516035\pi\)
\(420\) 5.35029e10 + 3.03430e11i 0.0838988 + 0.475814i
\(421\) −2.38154e11 + 1.99835e11i −0.369478 + 0.310029i −0.808555 0.588420i \(-0.799750\pi\)
0.439077 + 0.898449i \(0.355306\pi\)
\(422\) −5.29379e11 + 1.92678e11i −0.812570 + 0.295751i
\(423\) 8.79015e10 + 3.19935e10i 0.133495 + 0.0485881i
\(424\) −3.19423e11 2.68028e11i −0.479977 0.402749i
\(425\) 1.24476e11 2.15599e11i 0.185070 0.320551i
\(426\) −2.05062e10 3.55178e10i −0.0301677 0.0522520i
\(427\) 3.54583e10 2.01094e11i 0.0516170 0.292734i
\(428\) −6.88622e10 + 3.90537e11i −0.0991937 + 0.562556i
\(429\) 1.38726e11 + 2.40281e11i 0.197743 + 0.342501i
\(430\) 3.00436e11 5.20371e11i 0.423784 0.734015i
\(431\) −6.22105e11 5.22008e11i −0.868393 0.728668i 0.0953662 0.995442i \(-0.469598\pi\)
−0.963759 + 0.266774i \(0.914042\pi\)
\(432\) 1.49507e11 + 5.44162e10i 0.206531 + 0.0751712i
\(433\) 2.95903e10 1.07700e10i 0.0404533 0.0147238i −0.321714 0.946837i \(-0.604259\pi\)
0.362168 + 0.932113i \(0.382037\pi\)
\(434\) −1.69016e10 + 1.41821e10i −0.0228678 + 0.0191883i
\(435\) −3.51091e11 1.99113e12i −0.470130 2.66624i
\(436\) −1.49840e11 −0.198581
\(437\) −4.23433e11 + 9.43578e10i −0.555416 + 0.123769i
\(438\) 1.04907e12 1.36198
\(439\) −1.59023e11 9.01865e11i −0.204348 1.15891i −0.898463 0.439050i \(-0.855315\pi\)
0.694115 0.719864i \(-0.255796\pi\)
\(440\) 2.69727e11 2.26328e11i 0.343074 0.287873i
\(441\) 8.94892e10 3.25714e10i 0.112667 0.0410075i
\(442\) −7.92164e10 2.88324e10i −0.0987222 0.0359319i
\(443\) 1.68458e11 + 1.41353e11i 0.207815 + 0.174377i 0.740754 0.671776i \(-0.234468\pi\)
−0.532940 + 0.846153i \(0.678913\pi\)
\(444\) −1.06025e10 + 1.83641e10i −0.0129475 + 0.0224257i
\(445\) −1.57416e11 2.72653e11i −0.190296 0.329603i
\(446\) 9.84753e10 5.58481e11i 0.117848 0.668347i
\(447\) −4.81102e10 + 2.72847e11i −0.0569972 + 0.323247i
\(448\) −3.32278e10 5.75523e10i −0.0389718 0.0675012i
\(449\) −6.64556e11 + 1.15104e12i −0.771655 + 1.33655i 0.165001 + 0.986293i \(0.447237\pi\)
−0.936656 + 0.350252i \(0.886096\pi\)
\(450\) −9.31448e10 7.81577e10i −0.107078 0.0898495i
\(451\) −2.99701e11 1.09082e11i −0.341110 0.124154i
\(452\) −4.28930e10 + 1.56118e10i −0.0483352 + 0.0175926i
\(453\) 7.10853e11 5.96477e11i 0.793118 0.665505i
\(454\) −1.58169e11 8.97022e11i −0.174731 0.990950i
\(455\) 3.26718e11 0.357373
\(456\) −3.16861e11 1.64508e11i −0.343184 0.178175i
\(457\) −1.40230e12 −1.50390 −0.751950 0.659221i \(-0.770886\pi\)
−0.751950 + 0.659221i \(0.770886\pi\)
\(458\) −3.66592e10 2.07905e11i −0.0389303 0.220785i
\(459\) 2.35240e11 1.97390e11i 0.247374 0.207572i
\(460\) 3.63795e11 1.32410e11i 0.378831 0.137883i
\(461\) −4.51797e11 1.64441e11i −0.465896 0.169572i 0.0983961 0.995147i \(-0.468629\pi\)
−0.564293 + 0.825575i \(0.690851\pi\)
\(462\) 3.23390e11 + 2.71356e11i 0.330246 + 0.277109i
\(463\) 2.45909e11 4.25926e11i 0.248691 0.430745i −0.714472 0.699664i \(-0.753333\pi\)
0.963163 + 0.268919i \(0.0866664\pi\)
\(464\) 2.18044e11 + 3.77663e11i 0.218380 + 0.378245i
\(465\) 1.83682e10 1.04171e11i 0.0182192 0.103326i
\(466\) −1.28817e11 + 7.30559e11i −0.126543 + 0.717659i
\(467\) 8.88321e11 + 1.53862e12i 0.864259 + 1.49694i 0.867781 + 0.496947i \(0.165546\pi\)
−0.00352188 + 0.999994i \(0.501121\pi\)
\(468\) −2.05867e10 + 3.56572e10i −0.0198372 + 0.0343591i
\(469\) 9.47168e11 + 7.94768e11i 0.903960 + 0.758512i
\(470\) −7.21274e11 2.62522e11i −0.681805 0.248157i
\(471\) 2.13694e12 7.77783e11i 2.00078 0.728223i
\(472\) −1.10801e11 + 9.29729e10i −0.102755 + 0.0862219i
\(473\) −1.42961e11 8.10773e11i −0.131324 0.744773i
\(474\) 1.09463e12 0.996014
\(475\) −7.56218e11 8.23461e11i −0.681594 0.742202i
\(476\) −1.28266e11 −0.114520
\(477\) 6.82577e10 + 3.87109e11i 0.0603697 + 0.342374i
\(478\) −6.12253e11 + 5.13742e11i −0.536421 + 0.450110i
\(479\) 6.80952e11 2.47846e11i 0.591026 0.215116i −0.0291545 0.999575i \(-0.509281\pi\)
0.620181 + 0.784459i \(0.287059\pi\)
\(480\) 2.99393e11 + 1.08970e11i 0.257428 + 0.0936961i
\(481\) 1.72250e10 + 1.44535e10i 0.0146726 + 0.0123118i
\(482\) −4.34406e11 + 7.52414e11i −0.366593 + 0.634958i
\(483\) 2.32082e11 + 4.01978e11i 0.194035 + 0.336078i
\(484\) −2.10466e10 + 1.19361e11i −0.0174332 + 0.0988686i
\(485\) −4.95842e11 + 2.81206e12i −0.406917 + 2.30774i
\(486\) −1.68286e11 2.91480e11i −0.136831 0.236998i
\(487\) −9.31386e11 + 1.61321e12i −0.750325 + 1.29960i 0.197340 + 0.980335i \(0.436770\pi\)
−0.947665 + 0.319266i \(0.896564\pi\)
\(488\) −1.61752e11 1.35726e11i −0.129110 0.108336i
\(489\) 1.98270e11 + 7.21645e10i 0.156808 + 0.0570734i
\(490\) −7.34302e11 + 2.67264e11i −0.575430 + 0.209439i
\(491\) 6.83165e11 5.73244e11i 0.530468 0.445115i −0.337795 0.941220i \(-0.609681\pi\)
0.868263 + 0.496104i \(0.165237\pi\)
\(492\) −5.01138e10 2.84210e11i −0.0385580 0.218673i
\(493\) 8.41694e11 0.641716
\(494\) −2.30138e11 + 3.00600e11i −0.173867 + 0.227100i
\(495\) −3.31925e11 −0.248494
\(496\) 3.96179e9 + 2.24685e10i 0.00293917 + 0.0166689i
\(497\) −5.06896e10 + 4.25336e10i −0.0372662 + 0.0312701i
\(498\) 3.83654e11 1.39639e11i 0.279517 0.101736i
\(499\) 1.17072e11 + 4.26106e10i 0.0845277 + 0.0307656i 0.383938 0.923359i \(-0.374568\pi\)
−0.299410 + 0.954124i \(0.596790\pi\)
\(500\) 5.83052e9 + 4.89238e9i 0.00417198 + 0.00350070i
\(501\) −1.19587e12 + 2.07131e12i −0.848036 + 1.46884i
\(502\) 2.30681e11 + 3.99551e11i 0.162123 + 0.280805i
\(503\) −6.35847e9 + 3.60607e10i −0.00442891 + 0.0251176i −0.986942 0.161075i \(-0.948504\pi\)
0.982513 + 0.186193i \(0.0596149\pi\)
\(504\) −1.08785e10 + 6.16953e10i −0.00750989 + 0.0425907i
\(505\) 1.06513e11 + 1.84486e11i 0.0728772 + 0.126227i
\(506\) 2.65220e11 4.59374e11i 0.179857 0.311522i
\(507\) −1.04255e12 8.74802e11i −0.700746 0.587995i
\(508\) 1.19698e12 + 4.35664e11i 0.797443 + 0.290245i
\(509\) 1.58263e12 5.76030e11i 1.04508 0.380378i 0.238276 0.971198i \(-0.423418\pi\)
0.806804 + 0.590820i \(0.201196\pi\)
\(510\) 4.71075e11 3.95279e11i 0.308336 0.258725i
\(511\) −2.93917e11 1.66689e12i −0.190691 1.08146i
\(512\) −6.87195e10 −0.0441942
\(513\) −5.29139e11 1.27352e12i −0.337320 0.811855i
\(514\) −6.33537e11 −0.400348
\(515\) 1.55716e11 + 8.83107e11i 0.0975438 + 0.553198i
\(516\) 5.70671e11 4.78850e11i 0.354374 0.297355i
\(517\) −9.88247e11 + 3.59693e11i −0.608356 + 0.221424i
\(518\) 3.21495e10 + 1.17015e10i 0.0196196 + 0.00714096i
\(519\) 2.16730e12 + 1.81858e12i 1.31119 + 1.10022i
\(520\) 1.68924e11 2.92585e11i 0.101316 0.175484i
\(521\) −1.16401e12 2.01612e12i −0.692127 1.19880i −0.971140 0.238512i \(-0.923340\pi\)
0.279012 0.960287i \(-0.409993\pi\)
\(522\) 7.13859e10 4.04850e11i 0.0420819 0.238658i
\(523\) −4.20848e11 + 2.38675e12i −0.245962 + 1.39492i 0.572286 + 0.820054i \(0.306057\pi\)
−0.818248 + 0.574865i \(0.805055\pi\)
\(524\) −2.11876e11 3.66979e11i −0.122769 0.212643i
\(525\) −5.98109e11 + 1.03595e12i −0.343608 + 0.595147i
\(526\) 3.24620e11 + 2.72389e11i 0.184901 + 0.155151i
\(527\) 4.13798e10 + 1.50610e10i 0.0233690 + 0.00850563i
\(528\) 4.10210e11 1.49304e11i 0.229696 0.0836026i
\(529\) −9.32988e11 + 7.82870e11i −0.517995 + 0.434649i
\(530\) −5.60088e11 3.17642e12i −0.308329 1.74862i
\(531\) 1.36351e11 0.0744273
\(532\) −1.72615e11 + 5.49556e11i −0.0934279 + 0.297447i
\(533\) −3.06022e11 −0.164241
\(534\) −6.77797e10 3.84398e11i −0.0360715 0.204572i
\(535\) −2.34984e12 + 1.97175e12i −1.24007 + 1.04054i
\(536\) 1.20145e12 4.37293e11i 0.628731 0.228840i
\(537\) 2.95071e12 + 1.07397e12i 1.53123 + 0.557324i
\(538\) 1.18342e12 + 9.93005e11i 0.609000 + 0.511012i
\(539\) −5.35333e11 + 9.27225e11i −0.273196 + 0.473190i
\(540\) 6.15347e11 + 1.06581e12i 0.311421 + 0.539397i
\(541\) 2.90876e11 1.64964e12i 0.145989 0.827945i −0.820579 0.571534i \(-0.806349\pi\)
0.966568 0.256412i \(-0.0825403\pi\)
\(542\) 2.93759e11 1.66599e12i 0.146216 0.829232i
\(543\) 9.52471e11 + 1.64973e12i 0.470167 + 0.814354i
\(544\) −6.63179e10 + 1.14866e11i −0.0324665 + 0.0562337i
\(545\) −8.87881e11 7.45021e11i −0.431093 0.361730i
\(546\) 3.80635e11 + 1.38540e11i 0.183291 + 0.0667125i
\(547\) −2.81293e12 + 1.02382e12i −1.34343 + 0.488970i −0.910892 0.412644i \(-0.864605\pi\)
−0.432541 + 0.901614i \(0.642383\pi\)
\(548\) 1.39448e11 1.17010e11i 0.0660539 0.0554258i
\(549\) 3.45649e10 + 1.96027e11i 0.0162390 + 0.0920959i
\(550\) 1.36702e12 0.637004
\(551\) 1.13271e12 3.60623e12i 0.523526 1.66675i
\(552\) 4.79976e11 0.220036
\(553\) −3.06682e11 1.73928e12i −0.139452 0.790871i
\(554\) −9.47107e11 + 7.94717e11i −0.427174 + 0.358442i
\(555\) −1.54134e11 + 5.61002e10i −0.0689573 + 0.0250984i
\(556\) 7.38771e10 + 2.68891e10i 0.0327849 + 0.0119327i
\(557\) 1.26552e12 + 1.06190e12i 0.557084 + 0.467449i 0.877331 0.479885i \(-0.159322\pi\)
−0.320247 + 0.947334i \(0.603766\pi\)
\(558\) 1.07538e10 1.86261e10i 0.00469577 0.00813331i
\(559\) −3.94973e11 6.84114e11i −0.171086 0.296330i
\(560\) 8.92637e10 5.06240e11i 0.0383556 0.217525i
\(561\) 1.46309e11 8.29761e11i 0.0623647 0.353688i
\(562\) 6.80672e11 + 1.17896e12i 0.287822 + 0.498523i
\(563\) 1.80915e12 3.13353e12i 0.758903 1.31446i −0.184508 0.982831i \(-0.559069\pi\)
0.943411 0.331627i \(-0.107597\pi\)
\(564\) −7.28984e11 6.11690e11i −0.303363 0.254551i
\(565\) −3.31787e11 1.20761e11i −0.136975 0.0498549i
\(566\) 1.17322e12 4.27018e11i 0.480515 0.174893i
\(567\) −1.36094e12 + 1.14197e12i −0.552989 + 0.464013i
\(568\) 1.18818e10 + 6.73852e10i 0.00478978 + 0.0271642i
\(569\) 2.58483e12 1.03378 0.516888 0.856053i \(-0.327090\pi\)
0.516888 + 0.856053i \(0.327090\pi\)
\(570\) −1.05962e12 2.55027e12i −0.420448 1.01193i
\(571\) −3.57888e12 −1.40892 −0.704458 0.709746i \(-0.748810\pi\)
−0.704458 + 0.709746i \(0.748810\pi\)
\(572\) −8.03816e10 4.55867e11i −0.0313960 0.178056i
\(573\) −2.41054e12 + 2.02269e12i −0.934156 + 0.783850i
\(574\) −4.37545e11 + 1.59253e11i −0.168236 + 0.0612329i
\(575\) 1.41240e12 + 5.14073e11i 0.538832 + 0.196119i
\(576\) 4.96252e10 + 4.16405e10i 0.0187846 + 0.0157621i
\(577\) −5.74912e11 + 9.95777e11i −0.215929 + 0.374000i −0.953559 0.301205i \(-0.902611\pi\)
0.737631 + 0.675204i \(0.235945\pi\)
\(578\) −8.20703e11 1.42150e12i −0.305851 0.529750i
\(579\) 6.88792e11 3.90634e12i 0.254703 1.44449i
\(580\) −5.85756e11 + 3.32199e12i −0.214927 + 1.21891i
\(581\) −3.29362e11 5.70472e11i −0.119917 0.207703i
\(582\) −1.77008e12 + 3.06587e12i −0.639498 + 1.10764i
\(583\) −3.38536e12 2.84066e12i −1.21366 1.01838i
\(584\) −1.64471e12 5.98625e11i −0.585101 0.212959i
\(585\) −2.99279e11 + 1.08929e11i −0.105651 + 0.0384539i
\(586\) −9.64833e11 + 8.09591e11i −0.337997 + 0.283613i
\(587\) 6.61721e9 + 3.75280e10i 0.00230040 + 0.0130462i 0.985936 0.167121i \(-0.0534471\pi\)
−0.983636 + 0.180167i \(0.942336\pi\)
\(588\) −9.68810e11 −0.334226
\(589\) 1.20216e11 1.57023e11i 0.0411569 0.0537581i
\(590\) −1.11882e12 −0.380126
\(591\) −1.09826e12 6.22852e12i −0.370305 2.10011i
\(592\) 2.71014e10 2.27407e10i 0.00906867 0.00760951i
\(593\) 3.76087e12 1.36884e12i 1.24894 0.454577i 0.368898 0.929470i \(-0.379735\pi\)
0.880044 + 0.474893i \(0.157513\pi\)
\(594\) 1.58453e12 + 5.76722e11i 0.522230 + 0.190076i
\(595\) −7.60046e11 6.37754e11i −0.248607 0.208606i
\(596\) 2.31118e11 4.00309e11i 0.0750285 0.129953i
\(597\) 3.16151e12 + 5.47590e12i 1.01861 + 1.76429i
\(598\) 8.83804e10 5.01230e11i 0.0282618 0.160281i
\(599\) −5.54134e11 + 3.14265e12i −0.175871 + 0.997414i 0.761263 + 0.648444i \(0.224580\pi\)
−0.937134 + 0.348970i \(0.886531\pi\)
\(600\) 6.18484e11 + 1.07125e12i 0.194826 + 0.337449i
\(601\) 1.32168e12 2.28922e12i 0.413229 0.715734i −0.582011 0.813181i \(-0.697734\pi\)
0.995241 + 0.0974463i \(0.0310674\pi\)
\(602\) −9.20736e11 7.72590e11i −0.285727 0.239753i
\(603\) −1.13260e12 4.12232e11i −0.348857 0.126974i
\(604\) −1.45482e12 + 5.29511e11i −0.444778 + 0.161886i
\(605\) −7.18188e11 + 6.02631e11i −0.217941 + 0.182874i
\(606\) 4.58619e10 + 2.60096e11i 0.0138142 + 0.0783442i
\(607\) 4.50126e12 1.34581 0.672907 0.739727i \(-0.265045\pi\)
0.672907 + 0.739727i \(0.265045\pi\)
\(608\) 4.02894e11 + 4.38720e11i 0.119571 + 0.130203i
\(609\) −4.04434e12 −1.19143
\(610\) −2.83621e11 1.60850e12i −0.0829382 0.470366i
\(611\) −7.73008e11 + 6.48630e11i −0.224387 + 0.188283i
\(612\) 1.17494e11 4.27643e10i 0.0338559 0.0123225i
\(613\) 2.37694e11 + 8.65136e10i 0.0679902 + 0.0247464i 0.375791 0.926704i \(-0.377371\pi\)
−0.307801 + 0.951451i \(0.599593\pi\)
\(614\) −4.57627e11 3.83994e11i −0.129943 0.109035i
\(615\) 1.11617e12 1.93326e12i 0.314624 0.544945i
\(616\) −3.52160e11 6.09959e11i −0.0985432 0.170682i
\(617\) 8.50397e11 4.82284e12i 0.236232 1.33974i −0.603772 0.797157i \(-0.706336\pi\)
0.840004 0.542580i \(-0.182553\pi\)
\(618\) −1.93055e11 + 1.09487e12i −0.0532395 + 0.301936i
\(619\) 2.90881e12 + 5.03820e12i 0.796356 + 1.37933i 0.921975 + 0.387250i \(0.126575\pi\)
−0.125619 + 0.992079i \(0.540092\pi\)
\(620\) −8.82399e10 + 1.52836e11i −0.0239829 + 0.0415397i
\(621\) 1.42026e12 + 1.19174e12i 0.383227 + 0.321566i
\(622\) 3.85800e12 + 1.40420e12i 1.03349 + 0.376159i
\(623\) −5.91786e11 + 2.15393e11i −0.157387 + 0.0572841i
\(624\) 3.20867e11 2.69239e11i 0.0847216 0.0710898i
\(625\) −6.57284e11 3.72764e12i −0.172303 0.977179i
\(626\) −2.58333e12 −0.672350
\(627\) −3.35820e12 1.74352e12i −0.867767 0.450528i
\(628\) −3.79406e12 −0.973388
\(629\) −1.18574e10 6.72465e10i −0.00302037 0.0171294i
\(630\) −3.71217e11 + 3.11488e11i −0.0938848 + 0.0787787i
\(631\) 3.25565e12 1.18496e12i 0.817533 0.297558i 0.100801 0.994907i \(-0.467859\pi\)
0.716732 + 0.697349i \(0.245637\pi\)
\(632\) −1.71613e12 6.24622e11i −0.427882 0.155736i
\(633\) −4.13864e12 3.47273e12i −1.02457 0.859714i
\(634\) −1.64215e12 + 2.84428e12i −0.403655 + 0.699151i
\(635\) 4.92656e12 + 8.53305e12i 1.20244 + 2.08268i
\(636\) 6.94393e11 3.93810e12i 0.168286 0.954399i
\(637\) −1.78392e11 + 1.01171e12i −0.0429286 + 0.243460i
\(638\) 2.31090e12 + 4.00260e12i 0.552190 + 0.956421i
\(639\) 3.22517e10 5.58615e10i 0.00765241 0.0132544i
\(640\) −4.07199e11 3.41681e11i −0.0959394 0.0805027i
\(641\) 3.37258e12 + 1.22752e12i 0.789043 + 0.287188i 0.704938 0.709269i \(-0.250975\pi\)
0.0841049 + 0.996457i \(0.473197\pi\)
\(642\) −3.57371e12 + 1.30072e12i −0.830255 + 0.302188i
\(643\) −3.80664e12 + 3.19415e12i −0.878198 + 0.736896i −0.965808 0.259259i \(-0.916522\pi\)
0.0876096 + 0.996155i \(0.472077\pi\)
\(644\) −1.34474e11 7.62642e11i −0.0308073 0.174717i
\(645\) 5.76242e12 1.31095
\(646\) 1.12214e12 2.50058e11i 0.253514 0.0564930i
\(647\) 2.96000e12 0.664083 0.332042 0.943265i \(-0.392263\pi\)
0.332042 + 0.943265i \(0.392263\pi\)
\(648\) 3.19010e11 + 1.80920e12i 0.0710750 + 0.403086i
\(649\) −1.17431e12 + 9.85359e11i −0.259824 + 0.218019i
\(650\) 1.23257e12 4.48617e11i 0.270832 0.0985747i
\(651\) −1.98830e11 7.23682e10i −0.0433878 0.0157919i
\(652\) −2.69664e11 2.26275e11i −0.0584399 0.0490369i
\(653\) −1.62227e12 + 2.80985e12i −0.349151 + 0.604748i −0.986099 0.166159i \(-0.946863\pi\)
0.636948 + 0.770907i \(0.280197\pi\)
\(654\) −7.18489e11 1.24446e12i −0.153575 0.266000i
\(655\) 5.69186e11 3.22801e12i 0.120828 0.685251i
\(656\) −8.36094e10 + 4.74172e11i −0.0176274 + 0.0999698i
\(657\) 8.24977e11 + 1.42890e12i 0.172742 + 0.299198i
\(658\) −7.67686e11 + 1.32967e12i −0.159649 + 0.276521i
\(659\) 1.04271e12 + 8.74934e11i 0.215366 + 0.180714i 0.744088 0.668081i \(-0.232884\pi\)
−0.528722 + 0.848795i \(0.677329\pi\)
\(660\) 3.17307e12 + 1.15490e12i 0.650926 + 0.236918i
\(661\) 1.95956e11 7.13223e10i 0.0399257 0.0145318i −0.321980 0.946746i \(-0.604348\pi\)
0.361906 + 0.932215i \(0.382126\pi\)
\(662\) −1.35966e12 + 1.14089e12i −0.275150 + 0.230878i
\(663\) −1.40385e11 7.96165e11i −0.0282170 0.160027i
\(664\) −6.81164e11 −0.135986
\(665\) −3.75529e12 + 2.39815e12i −0.744639 + 0.475530i
\(666\) −3.33508e10 −0.00656859
\(667\) 8.82432e11 + 5.00452e12i 0.172629 + 0.979030i
\(668\) 3.05679e12 2.56495e12i 0.593980 0.498408i
\(669\) 5.11052e12 1.86008e12i 0.986388 0.359016i
\(670\) 9.29351e12 + 3.38256e12i 1.78174 + 0.648499i
\(671\) −1.71430e12 1.43847e12i −0.326465 0.273937i
\(672\) 3.18658e11 5.51931e11i 0.0602785 0.104405i
\(673\) −2.72281e12 4.71605e12i −0.511623 0.886156i −0.999909 0.0134730i \(-0.995711\pi\)
0.488287 0.872683i \(-0.337622\pi\)
\(674\) −4.68657e11 + 2.65789e12i −0.0874753 + 0.496097i
\(675\) −8.29703e11 + 4.70548e12i −0.153835 + 0.872443i
\(676\) 1.13530e12 + 1.96639e12i 0.209098 + 0.362168i
\(677\) −2.07982e12 + 3.60236e12i −0.380520 + 0.659080i −0.991137 0.132846i \(-0.957588\pi\)
0.610617 + 0.791926i \(0.290922\pi\)
\(678\) −3.35334e11 2.81379e11i −0.0609458 0.0511396i
\(679\) 5.36733e12 + 1.95355e12i 0.969045 + 0.352704i
\(680\) −9.64095e11 + 3.50902e11i −0.172914 + 0.0629355i
\(681\) 6.69157e12 5.61490e12i 1.19225 1.00041i
\(682\) 4.19885e10 + 2.38129e11i 0.00743191 + 0.0421485i
\(683\) 4.13847e12 0.727690 0.363845 0.931460i \(-0.381464\pi\)
0.363845 + 0.931460i \(0.381464\pi\)
\(684\) −2.51050e10 5.60952e11i −0.00438539 0.0979880i
\(685\) 1.40809e12 0.244356
\(686\) 7.15534e11 + 4.05799e12i 0.123359 + 0.699605i
\(687\) 1.55092e12 1.30138e12i 0.265634 0.222893i
\(688\) −1.16793e12 + 4.25090e11i −0.198732 + 0.0723324i
\(689\) −3.98462e12 1.45028e12i −0.673598 0.245169i
\(690\) 2.84411e12 + 2.38649e12i 0.477668 + 0.400811i
\(691\) 8.16394e11 1.41404e12i 0.136222 0.235944i −0.789841 0.613311i \(-0.789837\pi\)
0.926064 + 0.377367i \(0.123170\pi\)
\(692\) −2.36012e12 4.08784e12i −0.391251 0.677667i
\(693\) −1.15295e11 + 6.53868e11i −0.0189893 + 0.107694i
\(694\) 7.90576e11 4.48358e12i 0.129368 0.733681i
\(695\) 3.04066e11 + 5.26657e11i 0.0494351 + 0.0856242i
\(696\) −2.09106e12 + 3.62182e12i −0.337773 + 0.585039i
\(697\) 7.11901e11 + 5.97356e11i 0.114254 + 0.0958707i
\(698\) −4.09496e12 1.49044e12i −0.652980 0.237665i
\(699\) −6.68516e12 + 2.43320e12i −1.05917 + 0.385505i
\(700\) 1.52884e12 1.28285e12i 0.240669 0.201945i
\(701\) −1.23622e12 7.01094e12i −0.193359 1.09659i −0.914736 0.404051i \(-0.867602\pi\)
0.721378 0.692542i \(-0.243509\pi\)
\(702\) 1.61795e12 0.251448
\(703\) −3.04074e11 3.96946e10i −0.0469548 0.00612960i
\(704\) −7.28313e11 −0.111748
\(705\) −1.27823e12 7.24917e12i −0.194875 1.10519i
\(706\) 4.79985e12 4.02756e12i 0.727121 0.610127i
\(707\) 4.00421e11 1.45741e11i 0.0602740 0.0219379i
\(708\) −1.30346e12 4.74420e11i −0.194961 0.0709600i
\(709\) −7.15596e12 6.00456e12i −1.06355 0.892428i −0.0691013 0.997610i \(-0.522013\pi\)
−0.994453 + 0.105182i \(0.966458\pi\)
\(710\) −2.64640e11 + 4.58371e11i −0.0390835 + 0.0676946i
\(711\) 8.60804e11 + 1.49096e12i 0.126326 + 0.218802i
\(712\) −1.13083e11 + 6.41325e11i −0.0164906 + 0.0935230i
\(713\) −4.61668e10 + 2.61825e11i −0.00669001 + 0.0379409i
\(714\) −6.15043e11 1.06529e12i −0.0885652 0.153399i
\(715\) 1.79032e12 3.10092e12i 0.256184 0.443724i
\(716\) −4.01321e12 3.36748e12i −0.570667 0.478847i
\(717\) −7.20254e12 2.62151e12i −1.01777 0.370438i
\(718\) 7.41506e12 2.69886e12i 1.04125 0.378984i
\(719\) −9.79947e12 + 8.22273e12i −1.36748 + 1.14746i −0.393894 + 0.919156i \(0.628872\pi\)
−0.973591 + 0.228300i \(0.926683\pi\)
\(720\) 8.70146e10 + 4.93484e11i 0.0120669 + 0.0684348i
\(721\) 1.79375e12 0.247202
\(722\) 4.38759e11 5.14433e12i 0.0600909 0.704549i
\(723\) −8.33199e12 −1.13403
\(724\) −5.51886e11 3.12990e12i −0.0746493 0.423357i
\(725\) −1.00324e13 + 8.41815e12i −1.34860 + 1.13161i
\(726\) −1.09224e12 + 3.97544e11i −0.145917 + 0.0531093i
\(727\) 3.79837e12 + 1.38249e12i 0.504304 + 0.183552i 0.581629 0.813454i \(-0.302416\pi\)
−0.0773250 + 0.997006i \(0.524638\pi\)
\(728\) −5.17695e11 4.34398e11i −0.0683098 0.0573187i
\(729\) −2.80016e12 + 4.85002e12i −0.367205 + 0.636018i
\(730\) −6.76934e12 1.17248e13i −0.882253 1.52811i
\(731\) −4.16563e11 + 2.36245e12i −0.0539576 + 0.306009i
\(732\) 3.51632e11 1.99420e12i 0.0452677 0.256726i
\(733\) −9.89437e11 1.71376e12i −0.126596 0.219271i 0.795760 0.605613i \(-0.207072\pi\)
−0.922356 + 0.386342i \(0.873739\pi\)
\(734\) −2.77276e12 + 4.80256e12i −0.352598 + 0.610717i
\(735\) −5.74071e12 4.81703e12i −0.725559 0.608816i
\(736\) −7.52494e11 2.73885e11i −0.0945264 0.0344048i
\(737\) 1.27334e13 4.63458e12i 1.58980 0.578638i
\(738\) 3.47702e11 2.91757e11i 0.0431473 0.0362049i
\(739\) 5.24971e11 + 2.97726e12i 0.0647494 + 0.367212i 0.999915 + 0.0130024i \(0.00413892\pi\)
−0.935166 + 0.354210i \(0.884750\pi\)
\(740\) 2.73659e11 0.0335481
\(741\) −3.60008e12 4.69964e11i −0.438663 0.0572641i
\(742\) −6.45186e12 −0.781389
\(743\) 1.77877e12 + 1.00879e13i 0.214126 + 1.21437i 0.882416 + 0.470470i \(0.155916\pi\)
−0.668289 + 0.743901i \(0.732973\pi\)
\(744\) −1.67609e11 + 1.40641e11i −0.0200549 + 0.0168280i
\(745\) 3.35988e12 1.22290e12i 0.399595 0.145441i
\(746\) 6.49111e12 + 2.36257e12i 0.767351 + 0.279293i
\(747\) 4.91898e11 + 4.12751e11i 0.0578005 + 0.0485004i
\(748\) −7.02860e11 + 1.21739e12i −0.0820941 + 0.142191i
\(749\) 3.06798e12 + 5.31390e12i 0.356192 + 0.616943i
\(750\) −1.26749e10 + 7.18831e10i −0.00146275 + 0.00829567i
\(751\) −3.41559e11 + 1.93708e12i −0.0391819 + 0.222212i −0.998111 0.0614337i \(-0.980433\pi\)
0.958929 + 0.283645i \(0.0915438\pi\)
\(752\) 7.93837e11 + 1.37497e12i 0.0905214 + 0.156788i
\(753\) −2.21225e12 + 3.83173e12i −0.250759 + 0.434327i
\(754\) 3.39716e12 + 2.85055e12i 0.382776 + 0.321187i
\(755\) −1.12534e13 4.09589e12i −1.26044 0.458761i
\(756\) 2.31331e12 8.41977e11i 0.257565 0.0937459i
\(757\) 8.06629e12 6.76842e12i 0.892776 0.749128i −0.0759889 0.997109i \(-0.524211\pi\)
0.968765 + 0.247981i \(0.0797669\pi\)
\(758\) −1.59542e12 9.04808e12i −0.175535 0.995509i
\(759\) 5.08696e12 0.556378
\(760\) 2.05999e11 + 4.60288e12i 0.0223977 + 0.500459i
\(761\) 1.20684e13 1.30442 0.652211 0.758038i \(-0.273842\pi\)
0.652211 + 0.758038i \(0.273842\pi\)
\(762\) 2.12126e12 + 1.20302e13i 0.227927 + 1.29264i
\(763\) −1.77604e12 + 1.49028e12i −0.189711 + 0.159187i
\(764\) 4.93338e12 1.79560e12i 0.523871 0.190673i
\(765\) 9.08842e11 + 3.30791e11i 0.0959427 + 0.0349203i
\(766\) −4.14777e12 3.48040e12i −0.435297 0.365258i
\(767\) −7.35440e11 + 1.27382e12i −0.0767305 + 0.132901i
\(768\) −3.29513e11 5.70733e11i −0.0341780 0.0591981i
\(769\) 5.85257e11 3.31916e12i 0.0603501 0.342263i −0.939650 0.342138i \(-0.888849\pi\)
1.00000 0.000125025i \(-3.97965e-5\pi\)
\(770\) 9.46048e11 5.36531e12i 0.0969851 0.550030i
\(771\) −3.03784e12 5.26169e12i −0.309614 0.536266i
\(772\) −3.30891e12 + 5.73121e12i −0.335280 + 0.580722i
\(773\) 6.55769e12 + 5.50256e12i 0.660607 + 0.554315i 0.910269 0.414018i \(-0.135875\pi\)
−0.249662 + 0.968333i \(0.580319\pi\)
\(774\) 1.10099e12 + 4.00728e11i 0.110268 + 0.0401343i
\(775\) −6.43848e11 + 2.34342e11i −0.0641100 + 0.0233341i
\(776\) 4.52454e12 3.79654e12i 0.447916 0.375846i
\(777\) 5.69747e10 + 3.23119e11i 0.00560773 + 0.0318030i
\(778\) −7.21308e10 −0.00705850
\(779\) 3.51741e12 2.24624e12i 0.342219 0.218543i
\(780\) 3.23999e12 0.313414
\(781\) 1.25928e11 + 7.14172e11i 0.0121113 + 0.0686868i
\(782\) −1.18400e12 + 9.93495e11i −0.113220 + 0.0950026i
\(783\) −1.51802e13 + 5.52512e12i −1.44327 + 0.525308i
\(784\) 1.51887e12 + 5.52825e11i 0.143582 + 0.0522595i
\(785\) −2.24818e13 1.88645e13i −2.11309 1.77309i
\(786\) 2.03190e12 3.51936e12i 0.189890 0.328899i
\(787\) 2.32966e12 + 4.03508e12i 0.216474 + 0.374944i 0.953728 0.300672i \(-0.0972110\pi\)
−0.737254 + 0.675616i \(0.763878\pi\)
\(788\) −1.83232e12 + 1.03916e13i −0.169291 + 0.960095i
\(789\) −7.05691e11 + 4.00217e12i −0.0648288 + 0.367663i
\(790\) −7.06332e12 1.22340e13i −0.645189 1.11750i
\(791\) −3.53137e11 + 6.11651e11i −0.0320737 + 0.0555532i
\(792\) 5.25946e11 + 4.41321e11i 0.0474982 + 0.0398558i
\(793\) −2.01776e12 7.34405e11i −0.181193 0.0659487i
\(794\) 5.00972e12 1.82339e12i 0.447323 0.162812i
\(795\) 2.36953e13 1.98827e13i 2.10383 1.76532i
\(796\) −1.83186e12 1.03890e13i −0.161727 0.917201i
\(797\) −5.53353e12 −0.485780 −0.242890 0.970054i \(-0.578095\pi\)
−0.242890 + 0.970054i \(0.578095\pi\)
\(798\) −5.39190e12 + 1.20153e12i −0.470683 + 0.104887i
\(799\) 3.06438e12 0.266000
\(800\) −3.58365e11 2.03239e12i −0.0309329 0.175429i
\(801\) 4.70273e11 3.94606e11i 0.0403649 0.0338701i
\(802\) 8.70281e12 3.16756e12i 0.742805 0.270359i
\(803\) −1.74312e13 6.34444e12i −1.47947 0.538484i
\(804\) 9.39285e12 + 7.88154e12i 0.792766 + 0.665210i
\(805\) 2.99511e12 5.18768e12i 0.251380 0.435403i
\(806\) 1.16006e11 + 2.00928e11i 0.00968216 + 0.0167700i
\(807\) −2.57263e12 + 1.45901e13i −0.213523 + 1.21095i
\(808\) 7.65156e10 4.33941e11i 0.00631537 0.0358162i
\(809\) 2.48005e12 + 4.29558e12i 0.203560 + 0.352576i 0.949673 0.313243i \(-0.101415\pi\)
−0.746113 + 0.665819i \(0.768082\pi\)
\(810\) −7.10522e12 + 1.23066e13i −0.579956 + 1.00451i
\(811\) −4.28403e11 3.59473e11i −0.0347743 0.0291791i 0.625235 0.780437i \(-0.285003\pi\)
−0.660009 + 0.751258i \(0.729448\pi\)
\(812\) 6.34061e12 + 2.30779e12i 0.511834 + 0.186292i
\(813\) 1.52451e13 5.54876e12i 1.22383 0.445439i
\(814\) 2.87230e11 2.41014e11i 0.0229308 0.0192412i
\(815\) −4.72838e11 2.68160e12i −0.0375408 0.212904i
\(816\) −1.27199e12 −0.100433
\(817\) 9.56128e12 + 4.96403e12i 0.750787 + 0.389794i
\(818\) 1.87903e12 0.146739
\(819\) 1.10626e11 + 6.27394e11i 0.00859175 + 0.0487262i
\(820\) −2.85307e12 + 2.39401e12i −0.220369 + 0.184911i
\(821\) 1.62920e13 5.92979e12i 1.25150 0.455507i 0.370589 0.928797i \(-0.379156\pi\)
0.880907 + 0.473290i \(0.156934\pi\)
\(822\) 1.64046e12 + 5.97078e11i 0.125326 + 0.0456150i
\(823\) 9.64643e12 + 8.09432e12i 0.732938 + 0.615008i 0.930931 0.365195i \(-0.118998\pi\)
−0.197993 + 0.980204i \(0.563442\pi\)
\(824\) 9.27425e11 1.60635e12i 0.0700820 0.121386i
\(825\) 6.55491e12 + 1.13534e13i 0.492633 + 0.853266i
\(826\) −3.88625e11 + 2.20400e12i −0.0290483 + 0.164741i
\(827\) −2.55473e12 + 1.44886e13i −0.189920 + 1.07709i 0.729550 + 0.683928i \(0.239730\pi\)
−0.919470 + 0.393161i \(0.871381\pi\)
\(828\) 3.77447e11 + 6.53758e11i 0.0279074 + 0.0483371i
\(829\) −8.59729e12 + 1.48909e13i −0.632217 + 1.09503i 0.354881 + 0.934912i \(0.384521\pi\)
−0.987098 + 0.160120i \(0.948812\pi\)
\(830\) −4.03626e12 3.38682e12i −0.295208 0.247709i
\(831\) −1.11417e13 4.05526e12i −0.810492 0.294995i
\(832\) −6.56680e11 + 2.39012e11i −0.0475115 + 0.0172928i
\(833\) 2.38985e12 2.00532e12i 0.171976 0.144305i
\(834\) 1.30923e11 + 7.42503e11i 0.00937065 + 0.0531436i
\(835\) 3.08663e13 2.19733
\(836\) 4.27001e12 + 4.64971e12i 0.302344 + 0.329228i
\(837\) −8.45159e11 −0.0595215
\(838\) 1.76534e11 + 1.00118e12i 0.0123661 + 0.0701314i
\(839\) −6.65693e12 + 5.58583e12i −0.463815 + 0.389187i −0.844532 0.535504i \(-0.820122\pi\)
0.380717 + 0.924691i \(0.375677\pi\)
\(840\) 4.63248e12 1.68608e12i 0.321038 0.116848i
\(841\) −2.79753e13 1.01822e13i −1.92838 0.701874i
\(842\) 3.81047e12 + 3.19736e12i 0.261260 + 0.219224i
\(843\) −6.52771e12 + 1.13063e13i −0.445181 + 0.771076i
\(844\) 4.50683e12 + 7.80605e12i 0.305724 + 0.529530i
\(845\) −3.04988e12 + 1.72967e13i −0.205792 + 1.16710i
\(846\) 2.59897e11 1.47395e12i 0.0174435 0.0989271i
\(847\) 9.37677e11 + 1.62410e12i 0.0626005 + 0.108427i
\(848\) −3.33582e12 + 5.77781e12i −0.221524 + 0.383691i
\(849\) 9.17216e12 + 7.69635e12i 0.605880 + 0.508394i
\(850\) −3.74302e12 1.36235e12i −0.245945 0.0895165i
\(851\) 3.87401e11 1.41002e11i 0.0253208 0.00921602i
\(852\) −5.02678e11 + 4.21797e11i −0.0326822 + 0.0274236i
\(853\) 4.46744e12 + 2.53361e13i 0.288927 + 1.63859i 0.690910 + 0.722941i \(0.257210\pi\)
−0.401983 + 0.915647i \(0.631679\pi\)
\(854\) −3.26714e12 −0.210188
\(855\) 2.64035e12 3.44876e12i 0.168972 0.220707i
\(856\) 6.34499e12 0.403923
\(857\) 4.62802e12 + 2.62468e13i 0.293077 + 1.66212i 0.674916 + 0.737894i \(0.264180\pi\)
−0.381839 + 0.924229i \(0.624709\pi\)
\(858\) 3.40066e12 2.85349e12i 0.214225 0.179756i
\(859\) −2.16864e13 + 7.89322e12i −1.35900 + 0.494635i −0.915744 0.401761i \(-0.868398\pi\)
−0.443254 + 0.896396i \(0.646176\pi\)
\(860\) −9.03417e12 3.28817e12i −0.563178 0.204980i
\(861\) −3.42069e12 2.87030e12i −0.212129 0.177997i
\(862\) −6.49681e12 + 1.12528e13i −0.400790 + 0.694189i
\(863\) −2.78876e12 4.83027e12i −0.171144 0.296431i 0.767676 0.640838i \(-0.221413\pi\)
−0.938820 + 0.344408i \(0.888080\pi\)
\(864\) 4.42045e11 2.50696e12i 0.0269870 0.153051i
\(865\) 6.34025e12 3.59574e13i 0.385065 2.18381i
\(866\) −2.51915e11 4.36329e11i −0.0152203 0.0263623i
\(867\) 7.87061e12 1.36323e13i 0.473067 0.819375i
\(868\) 2.70425e11 + 2.26914e11i 0.0161700 + 0.0135682i
\(869\) −1.81882e13 6.61996e12i −1.08193 0.393792i
\(870\) −3.03987e13 + 1.10642e13i −1.79895 + 0.654763i
\(871\) 9.96009e12 8.35751e12i 0.586383 0.492034i
\(872\) 4.16311e11 + 2.36102e12i 0.0243834 + 0.138285i
\(873\) −5.56787e12 −0.324433
\(874\) 2.66324e12 + 6.40984e12i 0.154386 + 0.371574i
\(875\) 1.17767e11 0.00679186
\(876\) −2.91471e12 1.65302e13i −0.167235 0.948437i
\(877\) 6.58551e12 5.52590e12i 0.375917 0.315431i −0.435180 0.900343i \(-0.643315\pi\)
0.811097 + 0.584912i \(0.198871\pi\)
\(878\) −1.37688e13 + 5.01143e12i −0.781935 + 0.284601i
\(879\) −1.13503e13 4.13116e12i −0.641293 0.233412i
\(880\) −4.31564e12 3.62125e12i −0.242590 0.203557i
\(881\) 1.45262e13 2.51601e13i 0.812382 1.40709i −0.0988101 0.995106i \(-0.531504\pi\)
0.911192 0.411981i \(-0.135163\pi\)
\(882\) −7.61859e11 1.31958e12i −0.0423903 0.0734221i
\(883\) 3.60736e12 2.04583e13i 0.199695 1.13252i −0.705878 0.708333i \(-0.749447\pi\)
0.905573 0.424191i \(-0.139441\pi\)
\(884\) −2.34217e11 + 1.32831e12i −0.0128998 + 0.0731586i
\(885\) −5.36481e12 9.29213e12i −0.293975 0.509179i
\(886\) 1.75926e12 3.04712e12i 0.0959129 0.166126i
\(887\) 9.07411e12 + 7.61408e12i 0.492207 + 0.413010i 0.854816 0.518931i \(-0.173670\pi\)
−0.362610 + 0.931941i \(0.618114\pi\)
\(888\) 3.18820e11 + 1.16041e11i 0.0172063 + 0.00626258i
\(889\) 1.85207e13 6.74099e12i 0.994490 0.361965i
\(890\) −3.85882e12 + 3.23793e12i −0.206157 + 0.172987i
\(891\) 3.38098e12 + 1.91745e13i 0.179719 + 1.01923i
\(892\) −9.07355e12 −0.479883
\(893\) 4.12390e12 1.31293e13i 0.217009 0.690891i
\(894\) 4.43289e12 0.232096
\(895\) −7.03689e12 3.99082e13i −0.366587 2.07902i
\(896\) −8.14527e11 + 6.83470e11i −0.0422201 + 0.0354269i
\(897\) 4.58663e12 1.66940e12i 0.236553 0.0860982i
\(898\) 1.99833e13 + 7.27333e12i 1.02547 + 0.373241i
\(899\) −1.77455e12 1.48903e12i −0.0906089 0.0760299i
\(900\) −9.72735e11 + 1.68483e12i −0.0494201 + 0.0855980i
\(901\) 6.43849e12 + 1.11518e13i 0.325478 + 0.563745i
\(902\) −8.86121e11 + 5.02544e12i −0.0445722 + 0.252781i
\(903\) 2.00159e12 1.13516e13i 0.100180 0.568147i
\(904\) 3.65167e11 + 6.32487e11i 0.0181858 + 0.0314988i
\(905\) 1.22920e13 2.12904e13i 0.609121 1.05503i
\(906\) −1.13736e13 9.54362e12i −0.560819 0.470583i
\(907\) 2.39019e13 + 8.69958e12i 1.17273 + 0.426840i 0.853630 0.520879i \(-0.174396\pi\)
0.319104 + 0.947720i \(0.396618\pi\)
\(908\) −1.36949e13 + 4.98452e12i −0.668607 + 0.243353i
\(909\) −3.18202e11 + 2.67003e11i −0.0154584 + 0.0129711i
\(910\) −9.07744e11 5.14807e12i −0.0438811 0.248862i
\(911\) −1.28164e12 −0.0616499 −0.0308250 0.999525i \(-0.509813\pi\)
−0.0308250 + 0.999525i \(0.509813\pi\)
\(912\) −1.71179e12 + 5.44982e12i −0.0819356 + 0.260859i
\(913\) −7.21922e12 −0.343852
\(914\) 3.89612e12 + 2.20960e13i 0.184660 + 1.04726i
\(915\) 1.19990e13 1.00684e13i 0.565914 0.474858i
\(916\) −3.17408e12 + 1.15527e12i −0.148967 + 0.0542194i
\(917\) −6.16125e12 2.24251e12i −0.287744 0.104730i
\(918\) −3.76384e12 3.15824e12i −0.174920 0.146775i
\(919\) −6.12416e12 + 1.06073e13i −0.283222 + 0.490554i −0.972176 0.234250i \(-0.924737\pi\)
0.688955 + 0.724804i \(0.258070\pi\)
\(920\) −3.09714e12 5.36440e12i −0.142533 0.246874i
\(921\) 9.94833e11 5.64198e12i 0.0455598 0.258383i
\(922\) −1.33582e12 + 7.57581e12i −0.0608778 + 0.345255i
\(923\) 3.47914e11 + 6.02604e11i 0.0157784 + 0.0273290i
\(924\) 3.37724e12 5.84956e12i 0.152419 0.263997i
\(925\) 8.13892e11 + 6.82937e11i 0.0365535 + 0.0306720i
\(926\) −7.39451e12 2.69138e12i −0.330491 0.120289i
\(927\) −1.64310e12 + 5.98039e11i −0.0730810 + 0.0265993i
\(928\) 5.34500e12 4.48498e12i 0.236582 0.198516i
\(929\) −9.90372e11 5.61668e12i −0.0436242 0.247405i 0.955196 0.295975i \(-0.0956447\pi\)
−0.998820 + 0.0485702i \(0.984534\pi\)
\(930\) −1.69246e12 −0.0741898
\(931\) −5.37563e12 1.29380e13i −0.234507 0.564407i
\(932\) 1.18693e13 0.515290
\(933\) 6.83706e12 + 3.87749e13i 0.295394 + 1.67526i
\(934\) 2.17758e13 1.82721e13i 0.936295 0.785645i
\(935\) −1.02178e13 + 3.71898e12i −0.437226 + 0.159137i
\(936\) 6.19046e11 + 2.25314e11i 0.0263622 + 0.00959505i
\(937\) −2.02927e13 1.70276e13i −0.860028 0.721649i 0.101946 0.994790i \(-0.467493\pi\)
−0.961974 + 0.273141i \(0.911937\pi\)
\(938\) 9.89152e12 1.71326e13i 0.417206 0.722621i
\(939\) −1.23872e13 2.14552e13i −0.519968 0.900612i
\(940\) −2.13258e12 + 1.20944e13i −0.0890901 + 0.505255i
\(941\) 6.86220e12 3.89175e13i 0.285305 1.61805i −0.418887 0.908038i \(-0.637580\pi\)
0.704192 0.710009i \(-0.251309\pi\)
\(942\) −1.81927e13 3.15106e13i −0.752779 1.30385i
\(943\) −2.80538e12 + 4.85907e12i −0.115529 + 0.200101i
\(944\) 1.77281e12 + 1.48757e12i 0.0726589 + 0.0609681i
\(945\) 1.78940e13 + 6.51288e12i 0.729902 + 0.265663i
\(946\) −1.23781e13 + 4.50525e12i −0.502508 + 0.182898i
\(947\) −2.65511e13 + 2.22790e13i −1.07277 + 0.900164i −0.995301 0.0968305i \(-0.969130\pi\)
−0.0774727 + 0.996994i \(0.524685\pi\)
\(948\) −3.04129e12 1.72480e13i −0.122298 0.693589i
\(949\) −1.77988e13 −0.712350
\(950\) −1.08742e13 + 1.42035e13i −0.433151 + 0.565771i
\(951\) −3.14967e13 −1.24868
\(952\) 3.56371e11 + 2.02108e12i 0.0140617 + 0.0797476i
\(953\) −1.17630e13 + 9.87030e12i −0.461954 + 0.387626i −0.843849 0.536580i \(-0.819716\pi\)
0.381895 + 0.924206i \(0.375272\pi\)
\(954\) 5.91000e12 2.15106e12i 0.231004 0.0840786i
\(955\) 3.81608e13 + 1.38894e13i 1.48458 + 0.540341i
\(956\) 9.79605e12 + 8.21986e12i 0.379307 + 0.318276i
\(957\) −2.21618e13 + 3.83853e13i −0.854084 + 1.47932i
\(958\) −5.79723e12 1.00411e13i −0.222370 0.385156i
\(959\) 4.89102e11 2.77383e12i 0.0186731 0.105900i
\(960\) 8.85209e11 5.02027e12i 0.0336376 0.190768i
\(961\) 1.31592e13 + 2.27924e13i 0.497708 + 0.862056i
\(962\) 1.79885e11 3.11570e11i 0.00677185 0.0117292i
\(963\) −4.58198e12 3.84474e12i −0.171686 0.144062i
\(964\) 1.30627e13 + 4.75442e12i 0.487175 + 0.177317i
\(965\) −4.81032e13 + 1.75082e13i −1.78567 + 0.649931i
\(966\) 5.68913e12 4.77375e12i 0.210208 0.176385i
\(967\) 4.51335e12 + 2.55965e13i 0.165989 + 0.941371i 0.948039 + 0.318155i \(0.103063\pi\)
−0.782050 + 0.623216i \(0.785826\pi\)
\(968\) 1.93924e12 0.0709892
\(969\) 7.45752e12 + 8.12065e12i 0.271730 + 0.295892i
\(970\) 4.56871e13 1.65699
\(971\) −7.19118e11 4.07832e12i −0.0259605 0.147229i 0.969072 0.246777i \(-0.0793715\pi\)
−0.995033 + 0.0995476i \(0.968260\pi\)
\(972\) −4.12526e12 + 3.46151e12i −0.148236 + 0.124385i
\(973\) 1.14309e12 4.16052e11i 0.0408860 0.0148813i
\(974\) 2.80069e13 + 1.01937e13i 0.997127 + 0.362924i
\(975\) 9.63608e12 + 8.08563e12i 0.341491 + 0.286545i
\(976\) −1.68922e12 + 2.92581e12i −0.0595884 + 0.103210i
\(977\) −1.77735e13 3.07846e13i −0.624091 1.08096i −0.988716 0.149803i \(-0.952136\pi\)
0.364625 0.931154i \(-0.381197\pi\)
\(978\) 5.86222e11 3.32463e12i 0.0204898 0.116203i
\(979\) −1.19849e12 + 6.79699e12i −0.0416978 + 0.236480i
\(980\) 6.25143e12 + 1.08278e13i 0.216502 + 0.374992i
\(981\) 1.13002e12 1.95725e12i 0.0389562 0.0674740i
\(982\) −1.09306e13 9.17190e12i −0.375098 0.314744i
\(983\) 1.43001e13 + 5.20482e12i 0.488483 + 0.177793i 0.574507 0.818500i \(-0.305194\pi\)
−0.0860240 + 0.996293i \(0.527416\pi\)
\(984\) −4.33903e12 + 1.57928e12i −0.147542 + 0.0537008i
\(985\) −6.25256e13 + 5.24652e13i −2.11639 + 1.77586i
\(986\) −2.33854e12 1.32625e13i −0.0787950 0.446868i
\(987\) −1.47243e13 −0.493866
\(988\) 5.37594e12 + 2.79109e12i 0.179493 + 0.0931895i
\(989\) −1.44833e13 −0.481375
\(990\) 9.22211e11 + 5.23012e12i 0.0305121 + 0.173043i
\(991\) 3.65132e13 3.06382e13i 1.20259 1.00910i 0.203041 0.979170i \(-0.434918\pi\)
0.999552 0.0299249i \(-0.00952683\pi\)
\(992\) 3.43026e11 1.24851e11i 0.0112467 0.00409346i
\(993\) −1.59950e13 5.82171e12i −0.522051 0.190011i
\(994\) 8.11034e11 + 6.80538e11i 0.0263512 + 0.0221113i
\(995\) 4.08005e13 7.06685e13i 1.31966 2.28571i
\(996\) −3.26621e12 5.65725e12i −0.105166 0.182154i
\(997\) −8.37456e12 + 4.74945e13i −0.268432 + 1.52235i 0.490651 + 0.871356i \(0.336759\pi\)
−0.759082 + 0.650995i \(0.774352\pi\)
\(998\) 3.46143e11 1.96308e12i 0.0110451 0.0626397i
\(999\) 6.55276e11 + 1.13497e12i 0.0208151 + 0.0360529i
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 38.10.e.a.9.6 42
19.17 even 9 inner 38.10.e.a.17.6 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.10.e.a.9.6 42 1.1 even 1 trivial
38.10.e.a.17.6 yes 42 19.17 even 9 inner