Properties

Label 43.10.e.a.4.4
Level $43$
Weight $10$
Character 43.4
Analytic conductor $22.147$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,10,Mod(4,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.4");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 43.e (of order \(7\), 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: \(22.1465409550\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(32\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 4.4
Character \(\chi\) \(=\) 43.4
Dual form 43.10.e.a.11.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-24.3918 + 30.5863i) q^{2} +(35.3753 + 44.3592i) q^{3} +(-226.634 - 992.949i) q^{4} +(417.253 + 200.939i) q^{5} -2219.65 q^{6} +5951.78 q^{7} +(17852.1 + 8597.14i) q^{8} +(3663.55 - 16051.1i) q^{9} +O(q^{10})\) \(q+(-24.3918 + 30.5863i) q^{2} +(35.3753 + 44.3592i) q^{3} +(-226.634 - 992.949i) q^{4} +(417.253 + 200.939i) q^{5} -2219.65 q^{6} +5951.78 q^{7} +(17852.1 + 8597.14i) q^{8} +(3663.55 - 16051.1i) q^{9} +(-16323.5 + 7861.00i) q^{10} +(-13517.2 + 59222.6i) q^{11} +(36029.2 - 45179.1i) q^{12} +(-68947.9 - 33203.5i) q^{13} +(-145175. + 182043. i) q^{14} +(5846.98 + 25617.3i) q^{15} +(-228578. + 110077. i) q^{16} +(-584668. + 281561. i) q^{17} +(401583. + 503569. i) q^{18} +(227433. + 996450. i) q^{19} +(104958. - 459851. i) q^{20} +(210546. + 264016. i) q^{21} +(-1.48170e6 - 1.85799e6i) q^{22} +(153977. - 674616. i) q^{23} +(250162. + 1.09603e6i) q^{24} +(-1.08403e6 - 1.35933e6i) q^{25} +(2.69734e6 - 1.29897e6i) q^{26} +(1.84778e6 - 889845. i) q^{27} +(-1.34888e6 - 5.90981e6i) q^{28} +(-2.24145e6 + 2.81068e6i) q^{29} +(-926157. - 446014. i) q^{30} +(1.14273e6 - 1.43294e6i) q^{31} +(-48901.9 + 214253. i) q^{32} +(-3.10524e6 + 1.49541e6i) q^{33} +(5.64917e6 - 2.47506e7i) q^{34} +(2.48340e6 + 1.19594e6i) q^{35} -1.67682e7 q^{36} -2.84738e6 q^{37} +(-3.60253e7 - 1.73488e7i) q^{38} +(-966167. - 4.23306e6i) q^{39} +(5.72137e6 + 7.17437e6i) q^{40} +(-7.02559e6 + 8.80981e6i) q^{41} -1.32109e7 q^{42} +(1.60160e7 - 1.56870e7i) q^{43} +6.18685e7 q^{44} +(4.75391e6 - 5.96122e6i) q^{45} +(1.68783e7 + 2.11647e7i) q^{46} +(1.38441e6 + 6.06549e6i) q^{47} +(-1.29690e7 - 6.24552e6i) q^{48} -4.92996e6 q^{49} +6.80184e7 q^{50} +(-3.31726e7 - 1.59751e7i) q^{51} +(-1.73435e7 + 7.59868e7i) q^{52} +(-9.12873e7 + 4.39617e7i) q^{53} +(-1.78536e7 + 7.82218e7i) q^{54} +(-1.75402e7 + 2.19947e7i) q^{55} +(1.06252e8 + 5.11683e7i) q^{56} +(-3.61562e7 + 4.53384e7i) q^{57} +(-3.12957e7 - 1.37115e8i) q^{58} +(-7.35555e7 + 3.54225e7i) q^{59} +(2.41115e7 - 1.16115e7i) q^{60} +(1.95237e7 + 2.44820e7i) q^{61} +(1.59551e7 + 6.99041e7i) q^{62} +(2.18046e7 - 9.55324e7i) q^{63} +(-8.63491e7 - 1.08278e8i) q^{64} +(-2.20969e7 - 2.77086e7i) q^{65} +(3.00034e7 - 1.31454e8i) q^{66} +(2.29434e7 + 1.00522e8i) q^{67} +(4.12082e8 + 5.16734e8i) q^{68} +(3.53724e7 - 1.70344e7i) q^{69} +(-9.71541e7 + 4.67869e7i) q^{70} +(-4.65381e7 - 2.03897e8i) q^{71} +(2.03396e8 - 2.55050e8i) q^{72} +(-8.89797e7 - 4.28504e7i) q^{73} +(6.94528e7 - 8.70910e7i) q^{74} +(2.19509e7 - 9.61733e7i) q^{75} +(9.37880e8 - 4.51659e8i) q^{76} +(-8.04512e7 + 3.52480e8i) q^{77} +(1.53040e8 + 7.37003e7i) q^{78} -5.16079e8 q^{79} -1.17494e8 q^{80} +(-1.87128e8 - 9.01159e7i) q^{81} +(-9.80932e7 - 4.29774e8i) q^{82} +(3.30495e8 + 4.14428e8i) q^{83} +(2.14438e8 - 2.68896e8i) q^{84} -3.00531e8 q^{85} +(8.91478e7 + 8.72504e8i) q^{86} -2.03971e8 q^{87} +(-7.50456e8 + 9.41042e8i) q^{88} +(-4.54950e8 - 5.70489e8i) q^{89} +(6.63754e7 + 2.90810e8i) q^{90} +(-4.10362e8 - 1.97620e8i) q^{91} -7.04755e8 q^{92} +1.03989e8 q^{93} +(-2.19289e8 - 1.05604e8i) q^{94} +(-1.05328e8 + 4.61472e8i) q^{95} +(-1.12340e7 + 5.41002e6i) q^{96} +(5.93075e7 - 2.59843e8i) q^{97} +(1.20251e8 - 1.50789e8i) q^{98} +(9.01065e8 + 4.33930e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q - 23 q^{2} + 141 q^{3} - 7771 q^{4} + 677 q^{5} - 6572 q^{6} - 23872 q^{7} + 40269 q^{8} - 322935 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 192 q - 23 q^{2} + 141 q^{3} - 7771 q^{4} + 677 q^{5} - 6572 q^{6} - 23872 q^{7} + 40269 q^{8} - 322935 q^{9} + 12467 q^{10} + 26107 q^{11} - 8535 q^{12} - 124789 q^{13} + 402537 q^{14} + 536701 q^{15} + 470873 q^{16} + 157321 q^{17} - 126108 q^{18} + 1524020 q^{19} - 3731811 q^{20} - 1204984 q^{21} + 5705415 q^{22} - 1812193 q^{23} + 1656287 q^{24} - 6908369 q^{25} + 11484147 q^{26} + 4196853 q^{27} + 13689789 q^{28} + 14198685 q^{29} - 43510444 q^{30} + 2623633 q^{31} + 68431179 q^{32} + 35109256 q^{33} - 31068733 q^{34} - 25357310 q^{35} + 251714416 q^{36} - 19142308 q^{37} + 119772015 q^{38} - 31427027 q^{39} - 33090881 q^{40} - 50107991 q^{41} - 162738222 q^{42} - 73848259 q^{43} - 321658712 q^{44} + 91481051 q^{45} + 137200254 q^{46} + 17832081 q^{47} + 196320169 q^{48} + 845134600 q^{49} - 440263230 q^{50} - 49676244 q^{51} - 317591839 q^{52} - 69882873 q^{53} - 60806391 q^{54} - 120195607 q^{55} - 926966829 q^{56} + 282620123 q^{57} + 1032073799 q^{58} - 5290157 q^{59} - 1271653181 q^{60} - 217057103 q^{61} - 185133921 q^{62} + 802790658 q^{63} - 1352549483 q^{64} + 503543227 q^{65} - 234740783 q^{66} - 688857817 q^{67} + 1407702672 q^{68} - 234230557 q^{69} - 207245722 q^{70} + 315865545 q^{71} + 2050452844 q^{72} - 1188540917 q^{73} - 580770182 q^{74} - 1096370858 q^{75} - 1030976936 q^{76} + 126981666 q^{77} + 712275668 q^{78} - 355387036 q^{79} + 1135667026 q^{80} + 816824016 q^{81} - 1149421181 q^{82} + 554073368 q^{83} - 5832481562 q^{84} - 6971027678 q^{85} + 3317069529 q^{86} - 3939884094 q^{87} + 5966424645 q^{88} + 172293025 q^{89} + 11626974152 q^{90} + 852733752 q^{91} + 7930102584 q^{92} + 1786213690 q^{93} + 3419396521 q^{94} - 439143565 q^{95} - 7908382084 q^{96} - 619685773 q^{97} - 4402632007 q^{98} - 5258298740 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{2}{7}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −24.3918 + 30.5863i −1.07798 + 1.35174i −0.145972 + 0.989289i \(0.546631\pi\)
−0.932003 + 0.362450i \(0.881940\pi\)
\(3\) 35.3753 + 44.3592i 0.252147 + 0.316183i 0.891755 0.452519i \(-0.149475\pi\)
−0.639608 + 0.768702i \(0.720903\pi\)
\(4\) −226.634 992.949i −0.442645 1.93935i
\(5\) 417.253 + 200.939i 0.298562 + 0.143780i 0.577168 0.816626i \(-0.304158\pi\)
−0.278605 + 0.960406i \(0.589872\pi\)
\(6\) −2219.65 −0.699205
\(7\) 5951.78 0.936926 0.468463 0.883483i \(-0.344808\pi\)
0.468463 + 0.883483i \(0.344808\pi\)
\(8\) 17852.1 + 8597.14i 1.54094 + 0.742077i
\(9\) 3663.55 16051.1i 0.186128 0.815479i
\(10\) −16323.5 + 7861.00i −0.516196 + 0.248587i
\(11\) −13517.2 + 59222.6i −0.278368 + 1.21961i 0.621489 + 0.783423i \(0.286528\pi\)
−0.899857 + 0.436186i \(0.856329\pi\)
\(12\) 36029.2 45179.1i 0.501578 0.628959i
\(13\) −68947.9 33203.5i −0.669539 0.322433i 0.0680511 0.997682i \(-0.478322\pi\)
−0.737590 + 0.675249i \(0.764036\pi\)
\(14\) −145175. + 182043.i −1.00998 + 1.26648i
\(15\) 5846.98 + 25617.3i 0.0298209 + 0.130654i
\(16\) −228578. + 110077.i −0.871956 + 0.419912i
\(17\) −584668. + 281561.i −1.69781 + 0.817622i −0.703548 + 0.710648i \(0.748402\pi\)
−0.994262 + 0.106974i \(0.965884\pi\)
\(18\) 401583. + 503569.i 0.901673 + 1.13066i
\(19\) 227433. + 996450.i 0.400371 + 1.75414i 0.625900 + 0.779903i \(0.284732\pi\)
−0.225529 + 0.974236i \(0.572411\pi\)
\(20\) 104958. 459851.i 0.146683 0.642661i
\(21\) 210546. + 264016.i 0.236243 + 0.296240i
\(22\) −1.48170e6 1.85799e6i −1.34852 1.69099i
\(23\) 153977. 674616.i 0.114731 0.502668i −0.884609 0.466333i \(-0.845575\pi\)
0.999340 0.0363345i \(-0.0115682\pi\)
\(24\) 250162. + 1.09603e6i 0.153912 + 0.674331i
\(25\) −1.08403e6 1.35933e6i −0.555023 0.695977i
\(26\) 2.69734e6 1.29897e6i 1.15759 0.557467i
\(27\) 1.84778e6 889845.i 0.669135 0.322238i
\(28\) −1.34888e6 5.90981e6i −0.414726 1.81703i
\(29\) −2.24145e6 + 2.81068e6i −0.588487 + 0.737940i −0.983534 0.180721i \(-0.942157\pi\)
0.395047 + 0.918661i \(0.370728\pi\)
\(30\) −926157. 446014.i −0.208756 0.100532i
\(31\) 1.14273e6 1.43294e6i 0.222237 0.278677i −0.658196 0.752847i \(-0.728680\pi\)
0.880434 + 0.474170i \(0.157252\pi\)
\(32\) −48901.9 + 214253.i −0.00824425 + 0.0361204i
\(33\) −3.10524e6 + 1.49541e6i −0.455809 + 0.219506i
\(34\) 5.64917e6 2.47506e7i 0.724986 3.17637i
\(35\) 2.48340e6 + 1.19594e6i 0.279731 + 0.134711i
\(36\) −1.67682e7 −1.66389
\(37\) −2.84738e6 −0.249769 −0.124884 0.992171i \(-0.539856\pi\)
−0.124884 + 0.992171i \(0.539856\pi\)
\(38\) −3.60253e7 1.73488e7i −2.80273 1.34972i
\(39\) −966167. 4.23306e6i −0.0668747 0.292997i
\(40\) 5.72137e6 + 7.17437e6i 0.353370 + 0.443112i
\(41\) −7.02559e6 + 8.80981e6i −0.388289 + 0.486899i −0.937107 0.349043i \(-0.886507\pi\)
0.548817 + 0.835942i \(0.315078\pi\)
\(42\) −1.32109e7 −0.655103
\(43\) 1.60160e7 1.56870e7i 0.714407 0.699730i
\(44\) 6.18685e7 2.48847
\(45\) 4.75391e6 5.96122e6i 0.172820 0.216710i
\(46\) 1.68783e7 + 2.11647e7i 0.555799 + 0.696949i
\(47\) 1.38441e6 + 6.06549e6i 0.0413832 + 0.181312i 0.991395 0.130901i \(-0.0417870\pi\)
−0.950012 + 0.312213i \(0.898930\pi\)
\(48\) −1.29690e7 6.24552e6i −0.352630 0.169818i
\(49\) −4.92996e6 −0.122169
\(50\) 6.80184e7 1.53908
\(51\) −3.31726e7 1.59751e7i −0.686616 0.330657i
\(52\) −1.73435e7 + 7.59868e7i −0.328943 + 1.44120i
\(53\) −9.12873e7 + 4.39617e7i −1.58917 + 0.765302i −0.999115 0.0420643i \(-0.986607\pi\)
−0.590051 + 0.807366i \(0.700892\pi\)
\(54\) −1.78536e7 + 7.82218e7i −0.285729 + 1.25186i
\(55\) −1.75402e7 + 2.19947e7i −0.258465 + 0.324105i
\(56\) 1.06252e8 + 5.11683e7i 1.44375 + 0.695272i
\(57\) −3.61562e7 + 4.53384e7i −0.453676 + 0.568892i
\(58\) −3.12957e7 1.37115e8i −0.363127 1.59096i
\(59\) −7.35555e7 + 3.54225e7i −0.790280 + 0.380579i −0.785070 0.619408i \(-0.787373\pi\)
−0.00521045 + 0.999986i \(0.501659\pi\)
\(60\) 2.41115e7 1.16115e7i 0.240184 0.115667i
\(61\) 1.95237e7 + 2.44820e7i 0.180542 + 0.226393i 0.863865 0.503724i \(-0.168037\pi\)
−0.683323 + 0.730117i \(0.739466\pi\)
\(62\) 1.59551e7 + 6.99041e7i 0.137132 + 0.600814i
\(63\) 2.18046e7 9.55324e7i 0.174388 0.764044i
\(64\) −8.63491e7 1.08278e8i −0.643351 0.806736i
\(65\) −2.20969e7 2.77086e7i −0.153540 0.192533i
\(66\) 3.00034e7 1.31454e8i 0.194636 0.852756i
\(67\) 2.29434e7 + 1.00522e8i 0.139098 + 0.609428i 0.995634 + 0.0933412i \(0.0297547\pi\)
−0.856536 + 0.516087i \(0.827388\pi\)
\(68\) 4.12082e8 + 5.16734e8i 2.33718 + 2.93074i
\(69\) 3.53724e7 1.70344e7i 0.187864 0.0904705i
\(70\) −9.71541e7 + 4.67869e7i −0.483637 + 0.232908i
\(71\) −4.65381e7 2.03897e8i −0.217343 0.952243i −0.959432 0.281941i \(-0.909022\pi\)
0.742088 0.670302i \(-0.233835\pi\)
\(72\) 2.03396e8 2.55050e8i 0.891960 1.11848i
\(73\) −8.89797e7 4.28504e7i −0.366723 0.176604i 0.241442 0.970415i \(-0.422380\pi\)
−0.608165 + 0.793811i \(0.708094\pi\)
\(74\) 6.94528e7 8.70910e7i 0.269245 0.337622i
\(75\) 2.19509e7 9.61733e7i 0.0801083 0.350977i
\(76\) 9.37880e8 4.51659e8i 3.22467 1.55292i
\(77\) −8.04512e7 + 3.52480e8i −0.260810 + 1.14268i
\(78\) 1.53040e8 + 7.37003e7i 0.468145 + 0.225447i
\(79\) −5.16079e8 −1.49071 −0.745357 0.666665i \(-0.767721\pi\)
−0.745357 + 0.666665i \(0.767721\pi\)
\(80\) −1.17494e8 −0.320708
\(81\) −1.87128e8 9.01159e7i −0.483009 0.232605i
\(82\) −9.80932e7 4.29774e8i −0.239594 1.04973i
\(83\) 3.30495e8 + 4.14428e8i 0.764388 + 0.958512i 0.999911 0.0133566i \(-0.00425167\pi\)
−0.235523 + 0.971869i \(0.575680\pi\)
\(84\) 2.14438e8 2.68896e8i 0.469942 0.589288i
\(85\) −3.00531e8 −0.624460
\(86\) 8.91478e7 + 8.72504e8i 0.175739 + 1.71998i
\(87\) −2.03971e8 −0.381709
\(88\) −7.50456e8 + 9.41042e8i −1.33399 + 1.67277i
\(89\) −4.54950e8 5.70489e8i −0.768614 0.963812i 0.231345 0.972872i \(-0.425687\pi\)
−0.999959 + 0.00906028i \(0.997116\pi\)
\(90\) 6.63754e7 + 2.90810e8i 0.106639 + 0.467216i
\(91\) −4.10362e8 1.97620e8i −0.627309 0.302096i
\(92\) −7.04755e8 −1.02564
\(93\) 1.03989e8 0.144149
\(94\) −2.19289e8 1.05604e8i −0.289696 0.139510i
\(95\) −1.05328e8 + 4.61472e8i −0.132675 + 0.581285i
\(96\) −1.12340e7 + 5.41002e6i −0.0134994 + 0.00650097i
\(97\) 5.93075e7 2.59843e8i 0.0680200 0.298015i −0.929464 0.368914i \(-0.879730\pi\)
0.997483 + 0.0708990i \(0.0225868\pi\)
\(98\) 1.20251e8 1.50789e8i 0.131695 0.165140i
\(99\) 9.01065e8 + 4.33930e8i 0.942753 + 0.454006i
\(100\) −1.10407e9 + 1.38446e9i −1.10407 + 1.38446i
\(101\) 5.00262e7 + 2.19179e8i 0.0478356 + 0.209581i 0.993198 0.116441i \(-0.0371486\pi\)
−0.945362 + 0.326022i \(0.894291\pi\)
\(102\) 1.29776e9 6.24968e8i 1.18712 0.571685i
\(103\) −2.35836e8 + 1.13572e8i −0.206463 + 0.0994273i −0.534258 0.845322i \(-0.679409\pi\)
0.327795 + 0.944749i \(0.393695\pi\)
\(104\) −9.45412e8 1.18551e9i −0.792448 0.993699i
\(105\) 3.47999e7 + 1.52468e8i 0.0279400 + 0.122413i
\(106\) 8.82036e8 3.86445e9i 0.678594 2.97311i
\(107\) 1.50015e9 + 1.88113e9i 1.10639 + 1.38737i 0.913838 + 0.406079i \(0.133104\pi\)
0.192550 + 0.981287i \(0.438324\pi\)
\(108\) −1.30234e9 1.63308e9i −0.921123 1.15505i
\(109\) 1.29272e8 5.66378e8i 0.0877174 0.384315i −0.911945 0.410313i \(-0.865419\pi\)
0.999662 + 0.0259984i \(0.00827647\pi\)
\(110\) −2.44901e8 1.07298e9i −0.159486 0.698755i
\(111\) −1.00727e8 1.26308e8i −0.0629785 0.0789725i
\(112\) −1.36045e9 + 6.55156e8i −0.816959 + 0.393427i
\(113\) 1.01750e9 4.90003e8i 0.587059 0.282713i −0.116682 0.993169i \(-0.537226\pi\)
0.703741 + 0.710456i \(0.251511\pi\)
\(114\) −5.04822e8 2.21177e9i −0.279941 1.22650i
\(115\) 1.99804e8 2.50546e8i 0.106528 0.133582i
\(116\) 3.29885e9 + 1.58864e9i 1.69162 + 0.814640i
\(117\) −7.85546e8 + 9.85044e8i −0.387557 + 0.485981i
\(118\) 7.10707e8 3.11381e9i 0.337459 1.47851i
\(119\) −3.47981e9 + 1.67579e9i −1.59072 + 0.766052i
\(120\) −1.15854e8 + 5.07591e8i −0.0510031 + 0.223459i
\(121\) −1.20017e9 5.77970e8i −0.508988 0.245116i
\(122\) −1.22503e9 −0.500643
\(123\) −6.39328e8 −0.251855
\(124\) −1.68182e9 8.09922e8i −0.638825 0.307642i
\(125\) −3.80449e8 1.66685e9i −0.139380 0.610664i
\(126\) 2.39013e9 + 2.99713e9i 0.844801 + 1.05935i
\(127\) −6.30587e8 + 7.90730e8i −0.215094 + 0.269719i −0.877659 0.479285i \(-0.840896\pi\)
0.662566 + 0.749004i \(0.269468\pi\)
\(128\) 5.30553e9 1.74696
\(129\) 1.26243e9 + 1.55526e8i 0.401378 + 0.0494481i
\(130\) 1.38649e9 0.425766
\(131\) 3.39895e9 4.26215e9i 1.00838 1.26447i 0.0442535 0.999020i \(-0.485909\pi\)
0.964125 0.265447i \(-0.0855195\pi\)
\(132\) 2.18861e9 + 2.74444e9i 0.627461 + 0.786811i
\(133\) 1.35363e9 + 5.93065e9i 0.375118 + 1.64350i
\(134\) −3.63422e9 1.75015e9i −0.973732 0.468925i
\(135\) 9.49798e8 0.246110
\(136\) −1.28582e10 −3.22296
\(137\) 5.01103e9 + 2.41319e9i 1.21530 + 0.585259i 0.928000 0.372581i \(-0.121527\pi\)
0.287303 + 0.957840i \(0.407241\pi\)
\(138\) −3.41774e8 + 1.49741e9i −0.0802202 + 0.351468i
\(139\) −3.42856e9 + 1.65111e9i −0.779013 + 0.375153i −0.780749 0.624845i \(-0.785162\pi\)
0.00173508 + 0.999998i \(0.499448\pi\)
\(140\) 6.24687e8 2.73693e9i 0.137431 0.602126i
\(141\) −2.20086e8 + 2.75980e8i −0.0468929 + 0.0588019i
\(142\) 7.37161e9 + 3.54998e9i 1.52147 + 0.732703i
\(143\) 2.89838e9 3.63445e9i 0.579620 0.726820i
\(144\) 9.29453e8 + 4.07220e9i 0.180134 + 0.789219i
\(145\) −1.50003e9 + 7.22375e8i −0.281801 + 0.135708i
\(146\) 3.48101e9 1.67637e9i 0.634041 0.305338i
\(147\) −1.74399e8 2.18689e8i −0.0308045 0.0386277i
\(148\) 6.45314e8 + 2.82731e9i 0.110559 + 0.484390i
\(149\) −2.69816e8 + 1.18214e9i −0.0448465 + 0.196486i −0.992389 0.123146i \(-0.960702\pi\)
0.947542 + 0.319631i \(0.103559\pi\)
\(150\) 2.40617e9 + 3.01724e9i 0.388075 + 0.486630i
\(151\) 2.08224e9 + 2.61105e9i 0.325938 + 0.408713i 0.917620 0.397458i \(-0.130108\pi\)
−0.591683 + 0.806171i \(0.701536\pi\)
\(152\) −4.50645e9 + 1.97440e10i −0.684760 + 3.00013i
\(153\) 2.37740e9 + 1.04161e10i 0.350744 + 1.53671i
\(154\) −8.81872e9 1.10583e10i −1.26346 1.58433i
\(155\) 7.64743e8 3.68281e8i 0.106420 0.0512491i
\(156\) −3.98424e9 + 1.91871e9i −0.538623 + 0.259387i
\(157\) 1.27237e9 + 5.57463e9i 0.167135 + 0.732264i 0.987133 + 0.159899i \(0.0511169\pi\)
−0.819999 + 0.572365i \(0.806026\pi\)
\(158\) 1.25881e10 1.57850e10i 1.60695 2.01506i
\(159\) −5.17942e9 2.49428e9i −0.642679 0.309498i
\(160\) −6.34563e7 + 7.95717e7i −0.00765482 + 0.00959883i
\(161\) 9.16435e8 4.01516e9i 0.107494 0.470963i
\(162\) 7.32070e9 3.52546e9i 0.835093 0.402160i
\(163\) −2.52445e9 + 1.10604e10i −0.280107 + 1.22723i 0.617550 + 0.786532i \(0.288125\pi\)
−0.897657 + 0.440696i \(0.854732\pi\)
\(164\) 1.03399e10 + 4.97945e9i 1.11614 + 0.537507i
\(165\) −1.59616e9 −0.167648
\(166\) −2.07372e10 −2.11965
\(167\) −9.54370e9 4.59600e9i −0.949495 0.457253i −0.105986 0.994368i \(-0.533800\pi\)
−0.843509 + 0.537115i \(0.819514\pi\)
\(168\) 1.48891e9 + 6.52334e9i 0.144204 + 0.631798i
\(169\) −2.96046e9 3.71231e9i −0.279171 0.350069i
\(170\) 7.33050e9 9.19215e9i 0.673152 0.844106i
\(171\) 1.68273e10 1.50498
\(172\) −1.92061e10 1.23479e10i −1.67325 1.07576i
\(173\) −2.32833e10 −1.97623 −0.988113 0.153728i \(-0.950872\pi\)
−0.988113 + 0.153728i \(0.950872\pi\)
\(174\) 4.97523e9 6.23874e9i 0.411473 0.515971i
\(175\) −6.45190e9 8.09043e9i −0.520016 0.652079i
\(176\) −3.42934e9 1.50249e10i −0.269404 1.18034i
\(177\) −4.17336e9 2.00978e9i −0.319599 0.153911i
\(178\) 2.85462e10 2.13137
\(179\) 9.15325e9 0.666403 0.333201 0.942856i \(-0.391871\pi\)
0.333201 + 0.942856i \(0.391871\pi\)
\(180\) −6.99658e9 3.36938e9i −0.496775 0.239234i
\(181\) 4.86774e8 2.13269e9i 0.0337111 0.147698i −0.955271 0.295731i \(-0.904437\pi\)
0.988982 + 0.148033i \(0.0472940\pi\)
\(182\) 1.60540e10 7.73118e9i 1.08458 0.522305i
\(183\) −3.95343e8 + 1.73211e9i −0.0260582 + 0.114168i
\(184\) 8.54858e9 1.07196e10i 0.549811 0.689442i
\(185\) −1.18808e9 5.72149e8i −0.0745715 0.0359118i
\(186\) −2.53647e9 + 3.18063e9i −0.155389 + 0.194852i
\(187\) −8.77173e9 3.84315e10i −0.524564 2.29826i
\(188\) 5.70897e9 2.74929e9i 0.333309 0.160513i
\(189\) 1.09976e10 5.29616e9i 0.626930 0.301914i
\(190\) −1.15456e10 1.44777e10i −0.642726 0.805953i
\(191\) 7.15110e9 + 3.13310e10i 0.388797 + 1.70343i 0.668809 + 0.743434i \(0.266804\pi\)
−0.280013 + 0.959996i \(0.590339\pi\)
\(192\) 1.74852e9 7.66075e9i 0.0928569 0.406833i
\(193\) 1.25448e10 + 1.57307e10i 0.650812 + 0.816092i 0.992308 0.123791i \(-0.0395051\pi\)
−0.341496 + 0.939883i \(0.610934\pi\)
\(194\) 6.50103e9 + 8.15204e9i 0.329514 + 0.413198i
\(195\) 4.47448e8 1.96040e9i 0.0221609 0.0970931i
\(196\) 1.11730e9 + 4.89520e9i 0.0540774 + 0.236929i
\(197\) −1.01286e10 1.27009e10i −0.479127 0.600807i 0.482252 0.876032i \(-0.339819\pi\)
−0.961380 + 0.275226i \(0.911247\pi\)
\(198\) −3.52509e10 + 1.69760e10i −1.62996 + 0.784948i
\(199\) −1.93958e10 + 9.34051e9i −0.876735 + 0.422213i −0.817431 0.576027i \(-0.804602\pi\)
−0.0593038 + 0.998240i \(0.518888\pi\)
\(200\) −7.66590e9 3.35865e10i −0.338788 1.48433i
\(201\) −3.64743e9 + 4.57373e9i −0.157617 + 0.197646i
\(202\) −7.92411e9 3.81605e9i −0.334865 0.161262i
\(203\) −1.33406e10 + 1.67286e10i −0.551369 + 0.691395i
\(204\) −8.34440e9 + 3.65592e10i −0.337333 + 1.47795i
\(205\) −4.70168e9 + 2.26421e9i −0.185935 + 0.0895416i
\(206\) 2.27869e9 9.98359e9i 0.0881622 0.386264i
\(207\) −1.02642e10 4.94298e9i −0.388560 0.187121i
\(208\) 1.94149e10 0.719202
\(209\) −6.20866e10 −2.25081
\(210\) −5.51228e9 2.65458e9i −0.195589 0.0941908i
\(211\) 2.41815e8 + 1.05946e9i 0.00839869 + 0.0367971i 0.978954 0.204083i \(-0.0654212\pi\)
−0.970555 + 0.240880i \(0.922564\pi\)
\(212\) 6.43405e10 + 8.06805e10i 2.18763 + 2.74320i
\(213\) 7.39840e9 9.27730e9i 0.246280 0.308826i
\(214\) −9.41281e10 −3.06802
\(215\) 9.83485e9 3.32720e9i 0.313902 0.106196i
\(216\) 4.06370e10 1.27022
\(217\) 6.80129e9 8.52855e9i 0.208220 0.261100i
\(218\) 1.41703e10 + 1.77689e10i 0.424936 + 0.532853i
\(219\) −1.24687e9 5.46291e9i −0.0366289 0.160482i
\(220\) 2.58148e10 + 1.24318e10i 0.742963 + 0.357792i
\(221\) 4.96604e10 1.40038
\(222\) 6.32020e9 0.174639
\(223\) 3.11366e10 + 1.49946e10i 0.843139 + 0.406034i 0.805026 0.593239i \(-0.202151\pi\)
0.0381126 + 0.999273i \(0.487865\pi\)
\(224\) −2.91053e8 + 1.27519e9i −0.00772425 + 0.0338422i
\(225\) −2.57901e10 + 1.24199e10i −0.670860 + 0.323069i
\(226\) −9.83129e9 + 4.30737e10i −0.250682 + 1.09831i
\(227\) 8.03255e9 1.00725e10i 0.200788 0.251780i −0.671236 0.741244i \(-0.734236\pi\)
0.872023 + 0.489464i \(0.162808\pi\)
\(228\) 5.32130e10 + 2.56260e10i 1.30410 + 0.628021i
\(229\) 2.75912e10 3.45983e10i 0.662997 0.831372i −0.330669 0.943747i \(-0.607274\pi\)
0.993666 + 0.112375i \(0.0358458\pi\)
\(230\) 2.78971e9 + 1.22225e10i 0.0657331 + 0.287996i
\(231\) −1.84817e10 + 8.90032e9i −0.427059 + 0.205661i
\(232\) −6.41785e10 + 3.09067e10i −1.45443 + 0.700417i
\(233\) −5.84774e8 7.33283e8i −0.0129983 0.0162993i 0.775290 0.631606i \(-0.217604\pi\)
−0.788288 + 0.615306i \(0.789032\pi\)
\(234\) −1.09680e10 4.80540e10i −0.239142 1.04775i
\(235\) −6.41142e8 + 2.80903e9i −0.0137135 + 0.0600829i
\(236\) 5.18429e10 + 6.50089e10i 1.08789 + 1.36417i
\(237\) −1.82564e10 2.28929e10i −0.375880 0.471338i
\(238\) 3.36226e10 1.47310e11i 0.679259 2.97603i
\(239\) 8.05450e9 + 3.52891e10i 0.159679 + 0.699600i 0.989853 + 0.142095i \(0.0453839\pi\)
−0.830174 + 0.557505i \(0.811759\pi\)
\(240\) −4.15638e9 5.21193e9i −0.0808657 0.101402i
\(241\) −2.32312e10 + 1.11876e10i −0.443603 + 0.213628i −0.642332 0.766426i \(-0.722033\pi\)
0.198729 + 0.980055i \(0.436319\pi\)
\(242\) 4.69522e10 2.26110e10i 0.880009 0.423790i
\(243\) −1.16048e10 5.08441e10i −0.213506 0.935433i
\(244\) 1.98846e10 2.49345e10i 0.359139 0.450346i
\(245\) −2.05704e9 9.90619e8i −0.0364750 0.0175654i
\(246\) 1.55944e10 1.95547e10i 0.271494 0.340442i
\(247\) 1.74046e10 7.62547e10i 0.297528 1.30356i
\(248\) 3.27194e10 1.57569e10i 0.549254 0.264507i
\(249\) −6.69233e9 + 2.93210e10i −0.110327 + 0.483372i
\(250\) 6.02628e10 + 2.90210e10i 0.975707 + 0.469876i
\(251\) 5.55485e10 0.883365 0.441683 0.897171i \(-0.354382\pi\)
0.441683 + 0.897171i \(0.354382\pi\)
\(252\) −9.98005e10 −1.55894
\(253\) 3.78712e10 + 1.82378e10i 0.581121 + 0.279853i
\(254\) −8.80442e9 3.85747e10i −0.132724 0.581501i
\(255\) −1.06314e10 1.33313e10i −0.157456 0.197443i
\(256\) −8.52007e10 + 1.06838e11i −1.23983 + 1.55470i
\(257\) −3.28443e10 −0.469635 −0.234818 0.972039i \(-0.575449\pi\)
−0.234818 + 0.972039i \(0.575449\pi\)
\(258\) −3.55499e10 + 3.48196e10i −0.499517 + 0.489255i
\(259\) −1.69470e10 −0.234015
\(260\) −2.25053e10 + 2.82208e10i −0.305425 + 0.382991i
\(261\) 3.69028e10 + 4.62747e10i 0.492241 + 0.617250i
\(262\) 4.74570e10 + 2.07923e11i 0.622221 + 2.72613i
\(263\) 1.25135e11 + 6.02617e10i 1.61279 + 0.776677i 0.999909 0.0135019i \(-0.00429793\pi\)
0.612877 + 0.790179i \(0.290012\pi\)
\(264\) −6.82914e10 −0.865264
\(265\) −4.69236e10 −0.584500
\(266\) −2.14414e11 1.03256e11i −2.62595 1.26459i
\(267\) 9.21245e9 4.03624e10i 0.110937 0.486045i
\(268\) 9.46130e10 4.55632e10i 1.12033 0.539520i
\(269\) 3.29901e10 1.44539e11i 0.384147 1.68306i −0.300178 0.953883i \(-0.597046\pi\)
0.684326 0.729176i \(-0.260097\pi\)
\(270\) −2.31673e10 + 2.90508e10i −0.265300 + 0.332676i
\(271\) −3.46820e10 1.67020e10i −0.390609 0.188107i 0.228262 0.973600i \(-0.426696\pi\)
−0.618872 + 0.785492i \(0.712410\pi\)
\(272\) 1.02649e11 1.28717e11i 1.13709 1.42586i
\(273\) −5.75041e9 2.51942e10i −0.0626566 0.274517i
\(274\) −1.96039e11 + 9.44072e10i −2.10118 + 1.01188i
\(275\) 9.51561e10 4.58248e10i 1.00332 0.483173i
\(276\) −2.49309e10 3.12624e10i −0.258611 0.324288i
\(277\) 2.96817e10 + 1.30044e11i 0.302921 + 1.32718i 0.865694 + 0.500573i \(0.166877\pi\)
−0.562773 + 0.826611i \(0.690265\pi\)
\(278\) 3.31274e10 1.45141e11i 0.332648 1.45743i
\(279\) −1.88138e10 2.35917e10i −0.185891 0.233099i
\(280\) 3.40523e10 + 4.27003e10i 0.331082 + 0.415164i
\(281\) 5.02061e8 2.19967e9i 0.00480373 0.0210465i −0.972469 0.233031i \(-0.925136\pi\)
0.977273 + 0.211985i \(0.0679927\pi\)
\(282\) −3.07291e9 1.34633e10i −0.0289353 0.126774i
\(283\) 4.55687e10 + 5.71414e10i 0.422307 + 0.529556i 0.946784 0.321868i \(-0.104311\pi\)
−0.524478 + 0.851424i \(0.675739\pi\)
\(284\) −1.91912e11 + 9.24200e10i −1.75053 + 0.843011i
\(285\) −2.41965e10 + 1.16524e10i −0.217246 + 0.104620i
\(286\) 4.04680e10 + 1.77302e11i 0.357655 + 1.56699i
\(287\) −4.18147e10 + 5.24340e10i −0.363799 + 0.456189i
\(288\) 3.25984e9 + 1.56986e9i 0.0279209 + 0.0134460i
\(289\) 1.88621e11 2.36524e11i 1.59056 1.99450i
\(290\) 1.44935e10 6.35003e10i 0.120333 0.527212i
\(291\) 1.36244e10 6.56118e9i 0.111378 0.0536369i
\(292\) −2.23824e10 + 9.80637e10i −0.180170 + 0.789378i
\(293\) 2.05152e11 + 9.87959e10i 1.62619 + 0.783132i 0.999994 + 0.00346591i \(0.00110324\pi\)
0.626196 + 0.779666i \(0.284611\pi\)
\(294\) 1.09428e10 0.0854211
\(295\) −3.78090e10 −0.290667
\(296\) −5.08319e10 2.44793e10i −0.384878 0.185348i
\(297\) 2.77221e10 + 1.21459e11i 0.206739 + 0.905784i
\(298\) −2.95760e10 3.70872e10i −0.217254 0.272427i
\(299\) −3.30160e10 + 4.14007e10i −0.238893 + 0.299563i
\(300\) −1.00470e11 −0.716128
\(301\) 9.53236e10 9.33653e10i 0.669347 0.655596i
\(302\) −1.30652e11 −0.903826
\(303\) −7.95291e9 + 9.97263e9i −0.0542044 + 0.0679701i
\(304\) −1.61673e11 2.02731e11i −1.08569 1.36141i
\(305\) 3.22697e9 + 1.41383e10i 0.0213523 + 0.0935506i
\(306\) −3.76578e11 1.81350e11i −2.45532 1.18242i
\(307\) −6.13136e10 −0.393944 −0.196972 0.980409i \(-0.563111\pi\)
−0.196972 + 0.980409i \(0.563111\pi\)
\(308\) 3.68227e11 2.33151
\(309\) −1.33807e10 6.44382e9i −0.0834962 0.0402097i
\(310\) −7.38909e9 + 3.23737e10i −0.0454426 + 0.199097i
\(311\) −1.55647e11 + 7.49554e10i −0.943447 + 0.454340i −0.841384 0.540438i \(-0.818259\pi\)
−0.102063 + 0.994778i \(0.532544\pi\)
\(312\) 1.91440e10 8.38754e10i 0.114377 0.501117i
\(313\) 1.56007e11 1.95626e11i 0.918744 1.15207i −0.0692541 0.997599i \(-0.522062\pi\)
0.987998 0.154469i \(-0.0493667\pi\)
\(314\) −2.01543e11 9.70581e10i −1.17000 0.563441i
\(315\) 2.82942e10 3.54798e10i 0.161920 0.203041i
\(316\) 1.16961e11 + 5.12440e11i 0.659857 + 2.89102i
\(317\) −6.73528e10 + 3.24354e10i −0.374618 + 0.180407i −0.611713 0.791080i \(-0.709519\pi\)
0.237095 + 0.971487i \(0.423805\pi\)
\(318\) 2.02626e11 9.75796e10i 1.11115 0.535103i
\(319\) −1.36158e11 1.70737e11i −0.736182 0.923143i
\(320\) −1.42722e10 6.25304e10i −0.0760877 0.333362i
\(321\) −3.03771e10 + 1.33091e11i −0.159689 + 0.699641i
\(322\) 1.00456e11 + 1.25967e11i 0.520742 + 0.652990i
\(323\) −4.13534e11 5.18556e11i −2.11398 2.65084i
\(324\) −4.70710e10 + 2.06232e11i −0.237302 + 1.03969i
\(325\) 2.96069e10 + 1.29717e11i 0.147204 + 0.644941i
\(326\) −2.76720e11 3.46996e11i −1.35694 1.70155i
\(327\) 2.96971e10 1.43014e10i 0.143631 0.0691692i
\(328\) −2.01161e11 + 9.68741e10i −0.959647 + 0.462142i
\(329\) 8.23969e9 + 3.61005e10i 0.0387730 + 0.169876i
\(330\) 3.89331e10 4.88206e10i 0.180720 0.226616i
\(331\) 2.72920e11 + 1.31431e11i 1.24971 + 0.601828i 0.937434 0.348163i \(-0.113195\pi\)
0.312275 + 0.949992i \(0.398909\pi\)
\(332\) 3.36604e11 4.22088e11i 1.52054 1.90670i
\(333\) −1.04315e10 + 4.57035e10i −0.0464889 + 0.203681i
\(334\) 3.73363e11 1.79802e11i 1.64162 0.790561i
\(335\) −1.06255e10 + 4.65532e10i −0.0460942 + 0.201952i
\(336\) −7.71883e10 3.71719e10i −0.330389 0.159107i
\(337\) 2.08891e11 0.882237 0.441118 0.897449i \(-0.354582\pi\)
0.441118 + 0.897449i \(0.354582\pi\)
\(338\) 1.85757e11 0.774141
\(339\) 5.77305e10 + 2.78015e10i 0.237414 + 0.114333i
\(340\) 6.81106e10 + 2.98412e11i 0.276414 + 1.21105i
\(341\) 6.94160e10 + 8.70450e10i 0.278013 + 0.348617i
\(342\) −4.10448e11 + 5.14686e11i −1.62234 + 2.03434i
\(343\) −2.69518e11 −1.05139
\(344\) 4.20783e11 1.42354e11i 1.62011 0.548096i
\(345\) 1.81821e10 0.0690969
\(346\) 5.67921e11 7.12151e11i 2.13032 2.67134i
\(347\) 2.16498e11 + 2.71480e11i 0.801625 + 1.00521i 0.999687 + 0.0250163i \(0.00796376\pi\)
−0.198062 + 0.980189i \(0.563465\pi\)
\(348\) 4.62269e10 + 2.02533e11i 0.168962 + 0.740269i
\(349\) 2.43159e11 + 1.17099e11i 0.877356 + 0.422512i 0.817658 0.575704i \(-0.195272\pi\)
0.0596978 + 0.998216i \(0.480986\pi\)
\(350\) 4.04830e11 1.44200
\(351\) −1.56947e11 −0.551912
\(352\) −1.20276e10 5.79220e9i −0.0417578 0.0201095i
\(353\) 6.21442e10 2.72272e11i 0.213017 0.933289i −0.749486 0.662020i \(-0.769699\pi\)
0.962503 0.271269i \(-0.0874434\pi\)
\(354\) 1.63268e11 7.86255e10i 0.552567 0.266102i
\(355\) 2.15526e10 9.44280e10i 0.0720230 0.315554i
\(356\) −4.63359e11 + 5.81034e11i −1.52895 + 1.91724i
\(357\) −1.97436e11 9.50801e10i −0.643308 0.309801i
\(358\) −2.23264e11 + 2.79965e11i −0.718366 + 0.900802i
\(359\) −6.04463e10 2.64833e11i −0.192064 0.841485i −0.975498 0.220010i \(-0.929391\pi\)
0.783434 0.621475i \(-0.213466\pi\)
\(360\) 1.36117e11 6.55504e10i 0.427121 0.205691i
\(361\) −6.50454e11 + 3.13242e11i −2.01574 + 0.970729i
\(362\) 5.33580e10 + 6.69089e10i 0.163309 + 0.204784i
\(363\) −1.68180e10 7.36843e10i −0.0508386 0.222738i
\(364\) −1.03225e11 + 4.52256e11i −0.308196 + 1.35029i
\(365\) −2.85168e10 3.57589e10i −0.0840974 0.105455i
\(366\) −4.33359e10 5.43415e10i −0.126236 0.158295i
\(367\) −1.92121e10 + 8.41738e10i −0.0552812 + 0.242203i −0.995018 0.0996961i \(-0.968213\pi\)
0.939737 + 0.341899i \(0.111070\pi\)
\(368\) 3.90643e10 + 1.71152e11i 0.111036 + 0.486481i
\(369\) 1.15668e11 + 1.45043e11i 0.324785 + 0.407267i
\(370\) 4.64794e10 2.23833e10i 0.128930 0.0620892i
\(371\) −5.43322e11 + 2.61650e11i −1.48893 + 0.717032i
\(372\) −2.35674e10 1.03255e11i −0.0638069 0.279556i
\(373\) −2.65168e11 + 3.32510e11i −0.709302 + 0.889437i −0.997680 0.0680798i \(-0.978313\pi\)
0.288378 + 0.957517i \(0.406884\pi\)
\(374\) 1.38944e12 + 6.69117e11i 3.67212 + 1.76840i
\(375\) 6.04818e10 7.58418e10i 0.157937 0.198047i
\(376\) −2.74312e10 + 1.20184e11i −0.0707782 + 0.310100i
\(377\) 2.47868e11 1.19367e11i 0.631951 0.304332i
\(378\) −1.06261e11 + 4.65559e11i −0.267707 + 1.17290i
\(379\) −4.30796e11 2.07460e11i −1.07249 0.516486i −0.187585 0.982248i \(-0.560066\pi\)
−0.884910 + 0.465762i \(0.845780\pi\)
\(380\) 4.82089e11 1.18605
\(381\) −5.73833e10 −0.139516
\(382\) −1.13273e12 5.45494e11i −2.72171 1.31070i
\(383\) 1.10196e11 + 4.82802e11i 0.261681 + 1.14650i 0.919427 + 0.393261i \(0.128653\pi\)
−0.657746 + 0.753240i \(0.728490\pi\)
\(384\) 1.87685e11 + 2.35349e11i 0.440492 + 0.552359i
\(385\) −1.04395e11 + 1.30908e11i −0.242163 + 0.303663i
\(386\) −7.87134e11 −1.80470
\(387\) −1.93117e11 3.14544e11i −0.437644 0.712823i
\(388\) −2.71452e11 −0.608065
\(389\) −3.21480e11 + 4.03124e11i −0.711838 + 0.892617i −0.997845 0.0656108i \(-0.979100\pi\)
0.286007 + 0.958227i \(0.407672\pi\)
\(390\) 4.90473e10 + 6.15034e10i 0.107356 + 0.134620i
\(391\) 9.99204e10 + 4.37780e11i 0.216202 + 0.947241i
\(392\) −8.80103e10 4.23835e10i −0.188255 0.0906588i
\(393\) 3.09304e11 0.654062
\(394\) 6.35527e11 1.32862
\(395\) −2.15336e11 1.03700e11i −0.445071 0.214335i
\(396\) 2.26658e11 9.93055e11i 0.463173 2.02929i
\(397\) 1.72244e11 8.29482e10i 0.348005 0.167591i −0.251713 0.967802i \(-0.580994\pi\)
0.599718 + 0.800212i \(0.295279\pi\)
\(398\) 1.87406e11 8.21078e11i 0.374377 1.64025i
\(399\) −2.15194e11 + 2.69844e11i −0.425061 + 0.533010i
\(400\) 3.97417e11 + 1.91386e11i 0.776205 + 0.373801i
\(401\) 4.38767e11 5.50196e11i 0.847391 1.06260i −0.149875 0.988705i \(-0.547887\pi\)
0.997266 0.0738901i \(-0.0235414\pi\)
\(402\) −5.09263e10 2.23123e11i −0.0972580 0.426115i
\(403\) −1.26368e11 + 6.08555e10i −0.238651 + 0.114928i
\(404\) 2.06296e11 9.93468e10i 0.385278 0.185540i
\(405\) −5.99719e10 7.52024e10i −0.110764 0.138894i
\(406\) −1.86265e11 8.16080e11i −0.340223 1.49061i
\(407\) 3.84886e10 1.68629e11i 0.0695276 0.304620i
\(408\) −4.54862e11 5.70379e11i −0.812660 1.01904i
\(409\) −4.38198e11 5.49483e11i −0.774311 0.970956i 0.225684 0.974201i \(-0.427538\pi\)
−0.999995 + 0.00324510i \(0.998967\pi\)
\(410\) 4.54286e10 1.99036e11i 0.0793966 0.347859i
\(411\) 7.02197e10 + 3.07652e11i 0.121387 + 0.531829i
\(412\) 1.66220e11 + 2.08433e11i 0.284214 + 0.356394i
\(413\) −4.37786e11 + 2.10827e11i −0.740434 + 0.356574i
\(414\) 4.01550e11 1.93376e11i 0.671797 0.323520i
\(415\) 5.46257e10 + 2.39331e11i 0.0904025 + 0.396079i
\(416\) 1.04857e10 1.31486e10i 0.0171663 0.0215258i
\(417\) −1.94528e11 9.36797e10i −0.315043 0.151717i
\(418\) 1.51440e12 1.89900e12i 2.42632 3.04251i
\(419\) −5.75547e10 + 2.52164e11i −0.0912258 + 0.399686i −0.999839 0.0179526i \(-0.994285\pi\)
0.908613 + 0.417639i \(0.137142\pi\)
\(420\) 1.43506e11 6.91091e10i 0.225035 0.108371i
\(421\) 2.72534e10 1.19405e11i 0.0422815 0.185247i −0.949377 0.314138i \(-0.898284\pi\)
0.991659 + 0.128891i \(0.0411416\pi\)
\(422\) −3.83033e10 1.84459e10i −0.0587936 0.0283135i
\(423\) 1.02429e11 0.155558
\(424\) −2.00762e12 −3.01672
\(425\) 1.01653e12 + 4.89536e11i 1.51137 + 0.727837i
\(426\) 1.03298e11 + 4.52580e11i 0.151967 + 0.665813i
\(427\) 1.16201e11 + 1.45711e11i 0.169155 + 0.212113i
\(428\) 1.52788e12 1.91590e12i 2.20086 2.75979i
\(429\) 2.63752e11 0.375957
\(430\) −1.38123e11 + 3.81968e11i −0.194830 + 0.538790i
\(431\) −8.02905e11 −1.12077 −0.560385 0.828232i \(-0.689347\pi\)
−0.560385 + 0.828232i \(0.689347\pi\)
\(432\) −3.24411e11 + 4.06798e11i −0.448145 + 0.561956i
\(433\) −2.90619e11 3.64424e11i −0.397308 0.498209i 0.542431 0.840100i \(-0.317504\pi\)
−0.939740 + 0.341891i \(0.888933\pi\)
\(434\) 9.49615e10 + 4.16053e11i 0.128482 + 0.562918i
\(435\) −8.51078e10 4.09857e10i −0.113964 0.0548822i
\(436\) −5.91682e11 −0.784150
\(437\) 7.07240e11 0.927684
\(438\) 1.97504e11 + 9.51129e10i 0.256414 + 0.123483i
\(439\) 2.12522e11 9.31120e11i 0.273095 1.19651i −0.633243 0.773953i \(-0.718277\pi\)
0.906338 0.422554i \(-0.138866\pi\)
\(440\) −5.02222e11 + 2.41857e11i −0.638791 + 0.307625i
\(441\) −1.80612e10 + 7.91311e10i −0.0227390 + 0.0996262i
\(442\) −1.21131e12 + 1.51893e12i −1.50957 + 1.89294i
\(443\) 5.71947e8 + 2.75435e8i 0.000705568 + 0.000339784i 0.434236 0.900799i \(-0.357018\pi\)
−0.433531 + 0.901139i \(0.642733\pi\)
\(444\) −1.02589e11 + 1.28642e11i −0.125279 + 0.157094i
\(445\) −7.51961e10 3.29455e11i −0.0909023 0.398269i
\(446\) −1.21811e12 + 5.86609e11i −1.45774 + 0.702008i
\(447\) −6.19836e10 + 2.98497e10i −0.0734332 + 0.0353636i
\(448\) −5.13930e11 6.44448e11i −0.602772 0.755853i
\(449\) 2.92543e11 + 1.28171e12i 0.339688 + 1.48827i 0.799722 + 0.600371i \(0.204980\pi\)
−0.460033 + 0.887902i \(0.652163\pi\)
\(450\) 2.49189e11 1.09177e12i 0.286465 1.25509i
\(451\) −4.26774e11 5.35158e11i −0.485740 0.609098i
\(452\) −7.17148e11 8.99275e11i −0.808139 1.01337i
\(453\) −4.21641e10 + 1.84733e11i −0.0470436 + 0.206112i
\(454\) 1.12153e11 + 4.91373e11i 0.123896 + 0.542825i
\(455\) −1.31516e11 1.64915e11i −0.143855 0.180389i
\(456\) −1.03525e12 + 4.98548e11i −1.12125 + 0.539965i
\(457\) 6.10035e11 2.93778e11i 0.654233 0.315062i −0.0771597 0.997019i \(-0.524585\pi\)
0.731392 + 0.681957i \(0.238871\pi\)
\(458\) 3.85236e11 + 1.68783e12i 0.409103 + 1.79240i
\(459\) −8.29793e11 + 1.04053e12i −0.872595 + 1.09420i
\(460\) −2.94062e11 1.41613e11i −0.306216 0.147466i
\(461\) −7.02034e11 + 8.80322e11i −0.723942 + 0.907794i −0.998554 0.0537607i \(-0.982879\pi\)
0.274612 + 0.961555i \(0.411451\pi\)
\(462\) 1.78574e11 7.82382e11i 0.182360 0.798970i
\(463\) 1.32121e12 6.36263e11i 1.33616 0.643461i 0.376971 0.926225i \(-0.376966\pi\)
0.959189 + 0.282764i \(0.0912514\pi\)
\(464\) 2.02953e11 8.89193e11i 0.203266 0.890564i
\(465\) 4.33896e10 + 2.08953e10i 0.0430376 + 0.0207258i
\(466\) 3.66921e10 0.0360443
\(467\) −1.27587e12 −1.24131 −0.620654 0.784085i \(-0.713133\pi\)
−0.620654 + 0.784085i \(0.713133\pi\)
\(468\) 1.15613e12 + 5.56763e11i 1.11404 + 0.536493i
\(469\) 1.36554e11 + 5.98282e11i 0.130325 + 0.570989i
\(470\) −7.02793e10 8.81275e10i −0.0664335 0.0833050i
\(471\) −2.02276e11 + 2.53646e11i −0.189387 + 0.237483i
\(472\) −1.61765e12 −1.50019
\(473\) 7.12532e11 + 1.16055e12i 0.654529 + 1.06608i
\(474\) 1.14552e12 1.04231
\(475\) 1.10796e12 1.38934e12i 0.998626 1.25224i
\(476\) 2.45262e12 + 3.07549e12i 2.18977 + 2.74588i
\(477\) 3.71196e11 + 1.62632e12i 0.328300 + 1.43837i
\(478\) −1.27583e12 6.14406e11i −1.11781 0.538307i
\(479\) 1.64505e12 1.42781 0.713905 0.700243i \(-0.246925\pi\)
0.713905 + 0.700243i \(0.246925\pi\)
\(480\) −5.77452e9 −0.00496512
\(481\) 1.96321e11 + 9.45432e10i 0.167230 + 0.0805337i
\(482\) 2.24464e11 9.83442e11i 0.189424 0.829921i
\(483\) 2.10528e11 1.01385e11i 0.176015 0.0847642i
\(484\) −3.01896e11 + 1.32269e12i −0.250065 + 1.09561i
\(485\) 7.69588e10 9.65032e10i 0.0631568 0.0791961i
\(486\) 1.83820e12 + 8.85230e11i 1.49462 + 0.719769i
\(487\) 5.32470e11 6.67696e11i 0.428958 0.537896i −0.519638 0.854387i \(-0.673933\pi\)
0.948596 + 0.316490i \(0.102504\pi\)
\(488\) 1.38065e11 + 6.04904e11i 0.110204 + 0.482833i
\(489\) −5.79932e11 + 2.79280e11i −0.458656 + 0.220877i
\(490\) 8.04744e10 3.87544e10i 0.0630631 0.0303696i
\(491\) −4.56975e11 5.73029e11i −0.354835 0.444948i 0.572093 0.820189i \(-0.306132\pi\)
−0.926928 + 0.375240i \(0.877560\pi\)
\(492\) 1.44894e11 + 6.34820e11i 0.111482 + 0.488436i
\(493\) 5.19122e11 2.27442e12i 0.395784 1.73404i
\(494\) 1.90782e12 + 2.39233e12i 1.44134 + 1.80738i
\(495\) 2.88779e11 + 3.62118e11i 0.216194 + 0.271098i
\(496\) −1.03469e11 + 4.53328e11i −0.0767615 + 0.336314i
\(497\) −2.76985e11 1.21355e12i −0.203635 0.892182i
\(498\) −7.33584e11 9.19886e11i −0.534464 0.670196i
\(499\) −8.01752e10 + 3.86103e10i −0.0578879 + 0.0278773i −0.462604 0.886565i \(-0.653085\pi\)
0.404716 + 0.914442i \(0.367370\pi\)
\(500\) −1.56888e12 + 7.55532e11i −1.12260 + 0.540615i
\(501\) −1.33736e11 5.85935e11i −0.0948371 0.415509i
\(502\) −1.35493e12 + 1.69903e12i −0.952246 + 1.19408i
\(503\) −1.53520e12 7.39312e11i −1.06932 0.514958i −0.185434 0.982657i \(-0.559369\pi\)
−0.883888 + 0.467699i \(0.845083\pi\)
\(504\) 1.21056e12 1.51800e12i 0.835701 1.04794i
\(505\) −2.31679e10 + 1.01505e11i −0.0158517 + 0.0694509i
\(506\) −1.48157e12 + 7.13488e11i −1.00472 + 0.483849i
\(507\) 5.99476e10 2.62648e11i 0.0402936 0.176538i
\(508\) 9.28067e11 + 4.46934e11i 0.618291 + 0.297753i
\(509\) 2.28396e12 1.50820 0.754100 0.656759i \(-0.228073\pi\)
0.754100 + 0.656759i \(0.228073\pi\)
\(510\) 6.67075e11 0.436625
\(511\) −5.29587e11 2.55036e11i −0.343592 0.165465i
\(512\) −5.85132e11 2.56363e12i −0.376304 1.64870i
\(513\) 1.30693e12 + 1.63884e12i 0.833153 + 1.04474i
\(514\) 8.01131e11 1.00459e12i 0.506255 0.634824i
\(515\) −1.21224e11 −0.0759377
\(516\) −1.31680e11 1.28878e12i −0.0817706 0.800302i
\(517\) −3.77928e11 −0.232649
\(518\) 4.13368e11 5.18346e11i 0.252262 0.316327i
\(519\) −8.23652e11 1.03283e12i −0.498300 0.624848i
\(520\) −1.56262e11 6.84627e11i −0.0937212 0.410619i
\(521\) −5.50284e11 2.65003e11i −0.327203 0.157573i 0.263069 0.964777i \(-0.415265\pi\)
−0.590272 + 0.807204i \(0.700980\pi\)
\(522\) −2.31550e12 −1.36498
\(523\) 8.88766e11 0.519433 0.259717 0.965685i \(-0.416371\pi\)
0.259717 + 0.965685i \(0.416371\pi\)
\(524\) −5.00241e12 2.40903e12i −2.89860 1.39589i
\(525\) 1.30647e11 5.72402e11i 0.0750555 0.328840i
\(526\) −4.89544e12 + 2.35752e12i −2.78841 + 1.34283i
\(527\) −2.64658e11 + 1.15954e12i −0.149464 + 0.654847i
\(528\) 5.45180e11 6.83634e11i 0.305272 0.382799i
\(529\) 1.19138e12 + 5.73741e11i 0.661457 + 0.318541i
\(530\) 1.14455e12 1.43522e12i 0.630077 0.790091i
\(531\) 2.99094e11 + 1.31042e12i 0.163261 + 0.715293i
\(532\) 5.58205e12 2.68817e12i 3.02128 1.45497i
\(533\) 7.76916e11 3.74143e11i 0.416967 0.200801i
\(534\) 1.00983e12 + 1.26629e12i 0.537418 + 0.673901i
\(535\) 2.47951e11 + 1.08634e12i 0.130850 + 0.573292i
\(536\) −4.54609e11 + 1.99177e12i −0.237901 + 1.04231i
\(537\) 3.23799e11 + 4.06031e11i 0.168032 + 0.210705i
\(538\) 3.61623e12 + 4.53461e12i 1.86095 + 2.33356i
\(539\) 6.66391e10 2.91965e11i 0.0340079 0.148998i
\(540\) −2.15257e11 9.43101e11i −0.108939 0.477294i
\(541\) −7.16527e11 8.98497e11i −0.359621 0.450950i 0.568802 0.822474i \(-0.307407\pi\)
−0.928423 + 0.371524i \(0.878835\pi\)
\(542\) 1.35681e12 6.53405e11i 0.675339 0.325226i
\(543\) 1.11824e11 5.38518e10i 0.0551997 0.0265828i
\(544\) −3.17340e10 1.39036e11i −0.0155357 0.0680663i
\(545\) 1.67747e11 2.10348e11i 0.0814459 0.102130i
\(546\) 9.10861e11 + 4.38648e11i 0.438617 + 0.211227i
\(547\) 2.09917e11 2.63228e11i 0.100255 0.125716i −0.729173 0.684329i \(-0.760095\pi\)
0.829428 + 0.558614i \(0.188667\pi\)
\(548\) 1.26050e12 5.52261e12i 0.597077 2.61596i
\(549\) 4.64488e11 2.23686e11i 0.218222 0.105090i
\(550\) −9.19416e11 + 4.02823e12i −0.428430 + 1.87708i
\(551\) −3.31048e12 1.59425e12i −1.53006 0.736839i
\(552\) 7.77920e11 0.356623
\(553\) −3.07159e12 −1.39669
\(554\) −4.70156e12 2.26415e12i −2.12055 1.02120i
\(555\) −1.66486e10 7.29422e10i −0.00744833 0.0326333i
\(556\) 2.41649e12 + 3.03019e12i 1.07238 + 1.34472i
\(557\) 7.73061e11 9.69388e11i 0.340303 0.426726i −0.582003 0.813186i \(-0.697731\pi\)
0.922306 + 0.386460i \(0.126302\pi\)
\(558\) 1.18049e12 0.515475
\(559\) −1.62513e12 + 5.49794e11i −0.703939 + 0.238148i
\(560\) −6.99297e11 −0.300480
\(561\) 1.39449e12 1.74863e12i 0.594403 0.745358i
\(562\) 5.50338e10 + 6.90102e10i 0.0232711 + 0.0291810i
\(563\) −2.53874e11 1.11230e12i −0.106495 0.466587i −0.999851 0.0172372i \(-0.994513\pi\)
0.893356 0.449349i \(-0.148344\pi\)
\(564\) 3.23913e11 + 1.55988e11i 0.134794 + 0.0649136i
\(565\) 5.23016e11 0.215922
\(566\) −2.85925e12 −1.17106
\(567\) −1.11374e12 5.36350e11i −0.452544 0.217934i
\(568\) 9.22124e11 4.04009e12i 0.371725 1.62863i
\(569\) 1.07988e12 5.20045e11i 0.431889 0.207987i −0.205292 0.978701i \(-0.565815\pi\)
0.637181 + 0.770714i \(0.280100\pi\)
\(570\) 2.33792e11 1.02431e12i 0.0927667 0.406437i
\(571\) 6.50892e11 8.16193e11i 0.256240 0.321315i −0.637027 0.770842i \(-0.719836\pi\)
0.893267 + 0.449527i \(0.148407\pi\)
\(572\) −4.26570e12 2.05425e12i −1.66613 0.802365i
\(573\) −1.13685e12 + 1.42556e12i −0.440561 + 0.552446i
\(574\) −5.83829e11 2.55792e12i −0.224482 0.983521i
\(575\) −1.08394e12 + 5.21998e11i −0.413523 + 0.199142i
\(576\) −2.05433e12 + 9.89312e11i −0.777622 + 0.374483i
\(577\) 2.43369e12 + 3.05175e12i 0.914059 + 1.14619i 0.988838 + 0.148993i \(0.0476033\pi\)
−0.0747793 + 0.997200i \(0.523825\pi\)
\(578\) 2.63358e12 + 1.15385e13i 0.981458 + 4.30005i
\(579\) −2.54024e11 + 1.11295e12i −0.0939338 + 0.411551i
\(580\) 1.05724e12 + 1.32573e12i 0.387924 + 0.486442i
\(581\) 1.96703e12 + 2.46658e12i 0.716175 + 0.898055i
\(582\) −1.31642e11 + 5.76761e11i −0.0475599 + 0.208373i
\(583\) −1.36958e12 6.00051e12i −0.490996 2.15120i
\(584\) −1.22009e12 1.52994e12i −0.434044 0.544273i
\(585\) −5.25705e11 + 2.53166e11i −0.185584 + 0.0893727i
\(586\) −8.02583e12 + 3.86504e12i −2.81158 + 1.35399i
\(587\) 7.70723e11 + 3.37676e12i 0.267933 + 1.17389i 0.912413 + 0.409271i \(0.134217\pi\)
−0.644480 + 0.764622i \(0.722926\pi\)
\(588\) −1.77622e11 + 2.22731e11i −0.0612773 + 0.0768392i
\(589\) 1.68775e12 + 8.12777e11i 0.577816 + 0.278261i
\(590\) 9.22230e11 1.15644e12i 0.313332 0.392906i
\(591\) 2.05098e11 8.98592e11i 0.0691540 0.302983i
\(592\) 6.50849e11 3.13433e11i 0.217787 0.104881i
\(593\) −1.52501e11 + 6.68150e11i −0.0506438 + 0.221885i −0.993917 0.110133i \(-0.964872\pi\)
0.943273 + 0.332018i \(0.107729\pi\)
\(594\) −4.39117e12 2.11468e12i −1.44724 0.696955i
\(595\) −1.78869e12 −0.585073
\(596\) 1.23495e12 0.400906
\(597\) −1.10047e12 5.29957e11i −0.354563 0.170748i
\(598\) −4.60978e11 2.01968e12i −0.147409 0.645842i
\(599\) −2.18473e12 2.73957e12i −0.693390 0.869484i 0.303120 0.952952i \(-0.401972\pi\)
−0.996510 + 0.0834683i \(0.973400\pi\)
\(600\) 1.21869e12 1.52818e12i 0.383894 0.481388i
\(601\) 3.27499e12 1.02394 0.511971 0.859003i \(-0.328916\pi\)
0.511971 + 0.859003i \(0.328916\pi\)
\(602\) 5.30588e11 + 5.19295e12i 0.164654 + 1.61150i
\(603\) 1.69753e12 0.522866
\(604\) 2.12073e12 2.65931e12i 0.648364 0.813023i
\(605\) −3.84637e11 4.82320e11i −0.116722 0.146365i
\(606\) −1.11041e11 4.86501e11i −0.0334469 0.146540i
\(607\) −8.79875e11 4.23726e11i −0.263070 0.126688i 0.297700 0.954660i \(-0.403781\pi\)
−0.560770 + 0.827972i \(0.689495\pi\)
\(608\) −2.24615e11 −0.0666610
\(609\) −1.21399e12 −0.357633
\(610\) −5.11149e11 2.46156e11i −0.149473 0.0719825i
\(611\) 1.05944e11 4.64170e11i 0.0307532 0.134738i
\(612\) 9.80381e12 4.72127e12i 2.82497 1.36043i
\(613\) −9.59839e11 + 4.20533e12i −0.274553 + 1.20289i 0.630021 + 0.776578i \(0.283046\pi\)
−0.904574 + 0.426317i \(0.859811\pi\)
\(614\) 1.49555e12 1.87536e12i 0.424662 0.532509i
\(615\) −2.66762e11 1.28466e11i −0.0751945 0.0362117i
\(616\) −4.46654e12 + 5.60087e12i −1.24985 + 1.56726i
\(617\) 3.65275e11 + 1.60037e12i 0.101470 + 0.444568i 0.999984 + 0.00562417i \(0.00179024\pi\)
−0.898514 + 0.438944i \(0.855353\pi\)
\(618\) 5.23473e11 2.52091e11i 0.144360 0.0695200i
\(619\) 1.26034e12 6.06947e11i 0.345048 0.166166i −0.253331 0.967380i \(-0.581526\pi\)
0.598379 + 0.801213i \(0.295812\pi\)
\(620\) −5.39001e11 6.75886e11i −0.146496 0.183701i
\(621\) −3.15788e11 1.38356e12i −0.0852086 0.373323i
\(622\) 1.50389e12 6.58896e12i 0.402864 1.76506i
\(623\) −2.70776e12 3.39542e12i −0.720135 0.903020i
\(624\) 6.86809e11 + 8.61231e11i 0.181345 + 0.227399i
\(625\) −5.79444e11 + 2.53871e12i −0.151898 + 0.665508i
\(626\) 2.17821e12 + 9.54336e12i 0.566912 + 2.48380i
\(627\) −2.19633e12 2.75411e12i −0.567536 0.711668i
\(628\) 5.24696e12 2.52680e12i 1.34614 0.648266i
\(629\) 1.66477e12 8.01712e11i 0.424060 0.204216i
\(630\) 3.95051e11 + 1.73083e12i 0.0999128 + 0.437747i
\(631\) 2.01256e12 2.52367e12i 0.505378 0.633724i −0.462055 0.886851i \(-0.652888\pi\)
0.967433 + 0.253127i \(0.0814591\pi\)
\(632\) −9.21312e12 4.43681e12i −2.29710 1.10623i
\(633\) −3.84425e10 + 4.82054e10i −0.00951688 + 0.0119338i
\(634\) 6.50775e11 2.85123e12i 0.159967 0.700859i
\(635\) −4.22003e11 + 2.03226e11i −0.102999 + 0.0496018i
\(636\) −1.30286e12 + 5.70819e12i −0.315747 + 1.38338i
\(637\) 3.39910e11 + 1.63692e11i 0.0817968 + 0.0393913i
\(638\) 8.54335e12 2.04143
\(639\) −3.44326e12 −0.816988
\(640\) 2.21375e12 + 1.06609e12i 0.521577 + 0.251178i
\(641\) −1.26603e12 5.54682e12i −0.296198 1.29773i −0.875739 0.482784i \(-0.839626\pi\)
0.579542 0.814943i \(-0.303232\pi\)
\(642\) −3.32981e12 4.17545e12i −0.773591 0.970053i
\(643\) 1.71682e12 2.15283e12i 0.396074 0.496660i −0.543308 0.839533i \(-0.682829\pi\)
0.939382 + 0.342873i \(0.111400\pi\)
\(644\) −4.19455e12 −0.960945
\(645\) 4.95502e11 + 3.18565e11i 0.112727 + 0.0724735i
\(646\) 2.59476e13 5.86206
\(647\) −2.01567e12 + 2.52756e12i −0.452219 + 0.567065i −0.954718 0.297513i \(-0.903843\pi\)
0.502498 + 0.864578i \(0.332414\pi\)
\(648\) −2.56589e12 3.21752e12i −0.571677 0.716860i
\(649\) −1.10355e12 4.83496e12i −0.244169 1.06977i
\(650\) −4.68972e12 2.25845e12i −1.03047 0.496250i
\(651\) 6.18917e11 0.135057
\(652\) 1.15545e13 2.50401
\(653\) 3.23703e11 + 1.55887e11i 0.0696686 + 0.0335506i 0.468394 0.883520i \(-0.344833\pi\)
−0.398725 + 0.917071i \(0.630547\pi\)
\(654\) −2.86939e11 + 1.25716e12i −0.0613324 + 0.268715i
\(655\) 2.27465e12 1.09542e12i 0.482869 0.232537i
\(656\) 6.36135e11 2.78709e12i 0.134116 0.587602i
\(657\) −1.01378e12 + 1.27123e12i −0.212274 + 0.266184i
\(658\) −1.30516e12 6.28533e11i −0.271424 0.130711i
\(659\) −5.36958e12 + 6.73324e12i −1.10906 + 1.39072i −0.197132 + 0.980377i \(0.563163\pi\)
−0.911931 + 0.410344i \(0.865409\pi\)
\(660\) 3.61744e11 + 1.58490e12i 0.0742084 + 0.325128i
\(661\) 1.49177e12 7.18401e11i 0.303946 0.146373i −0.275694 0.961246i \(-0.588908\pi\)
0.579640 + 0.814873i \(0.303193\pi\)
\(662\) −1.06770e13 + 5.14177e12i −2.16067 + 1.04052i
\(663\) 1.75675e12 + 2.20290e12i 0.353101 + 0.442775i
\(664\) 2.33715e12 + 1.02397e13i 0.466585 + 2.04424i
\(665\) −6.26889e11 + 2.74658e12i −0.124306 + 0.544622i
\(666\) −1.14346e12 1.43385e12i −0.225210 0.282404i
\(667\) 1.55100e12 + 1.94489e12i 0.303421 + 0.380478i
\(668\) −2.40067e12 + 1.05180e13i −0.466485 + 2.04381i
\(669\) 4.36317e11 + 1.91163e12i 0.0842141 + 0.368966i
\(670\) −1.16472e12 1.46051e12i −0.223298 0.280006i
\(671\) −1.71379e12 + 8.25319e11i −0.326367 + 0.157170i
\(672\) −6.68624e10 + 3.21992e10i −0.0126480 + 0.00609093i
\(673\) 5.03464e11 + 2.20582e12i 0.0946021 + 0.414479i 0.999948 0.0101961i \(-0.00324557\pi\)
−0.905346 + 0.424675i \(0.860388\pi\)
\(674\) −5.09523e12 + 6.38921e12i −0.951030 + 1.19255i
\(675\) −3.21264e12 1.54713e12i −0.595656 0.286853i
\(676\) −3.01519e12 + 3.78093e12i −0.555334 + 0.696367i
\(677\) 7.03720e11 3.08320e12i 0.128751 0.564095i −0.868863 0.495053i \(-0.835149\pi\)
0.997614 0.0690420i \(-0.0219942\pi\)
\(678\) −2.25850e12 + 1.08764e12i −0.410475 + 0.197674i
\(679\) 3.52985e11 1.54653e12i 0.0637297 0.279218i
\(680\) −5.36513e12 2.58371e12i −0.962254 0.463397i
\(681\) 7.30962e11 0.130237
\(682\) −4.35557e12 −0.770931
\(683\) 5.79878e12 + 2.79255e12i 1.01963 + 0.491029i 0.867556 0.497339i \(-0.165690\pi\)
0.152077 + 0.988369i \(0.451404\pi\)
\(684\) −3.81364e12 1.67086e13i −0.666173 2.91870i
\(685\) 1.60597e12 + 2.01382e12i 0.278695 + 0.349473i
\(686\) 6.57402e12 8.24356e12i 1.13337 1.42120i
\(687\) 2.51080e12 0.430038
\(688\) −1.93413e12 + 5.34869e12i −0.329107 + 0.910122i
\(689\) 7.75375e12 1.31077
\(690\) −4.43495e11 + 5.56125e11i −0.0744848 + 0.0934009i
\(691\) 6.48508e12 + 8.13203e12i 1.08209 + 1.35690i 0.929590 + 0.368596i \(0.120161\pi\)
0.152502 + 0.988303i \(0.451267\pi\)
\(692\) 5.27679e12 + 2.31191e13i 0.874766 + 3.83260i
\(693\) 5.36294e12 + 2.58266e12i 0.883290 + 0.425370i
\(694\) −1.35844e13 −2.22291
\(695\) −1.76235e12 −0.286524
\(696\) −3.64133e12 1.75357e12i −0.588191 0.283258i
\(697\) 1.62714e12 7.12895e12i 0.261142 1.14414i
\(698\) −9.51272e12 + 4.58108e12i −1.51689 + 0.730498i
\(699\) 1.18413e10 5.18802e10i 0.00187609 0.00821967i
\(700\) −6.57116e12 + 8.23998e12i −1.03443 + 1.29713i
\(701\) −1.34741e12 6.48878e11i −0.210750 0.101492i 0.325531 0.945531i \(-0.394457\pi\)
−0.536281 + 0.844039i \(0.680171\pi\)
\(702\) 3.82821e12 4.80042e12i 0.594948 0.746041i
\(703\) −6.47589e11 2.83727e12i −0.100000 0.438129i
\(704\) 7.57972e12 3.65020e12i 1.16299 0.560067i
\(705\) −1.47287e11 + 7.09296e10i −0.0224550 + 0.0108138i
\(706\) 6.81199e12 + 8.54196e12i 1.03194 + 1.29401i
\(707\) 2.97745e11 + 1.30450e12i 0.0448184 + 0.196362i
\(708\) −1.04979e12 + 4.59941e12i −0.157019 + 0.687944i
\(709\) −6.89484e12 8.64585e12i −1.02475 1.28499i −0.957862 0.287229i \(-0.907266\pi\)
−0.0668837 0.997761i \(-0.521306\pi\)
\(710\) 2.36250e12 + 2.96248e12i 0.348907 + 0.437515i
\(711\) −1.89068e12 + 8.28363e12i −0.277463 + 1.21565i
\(712\) −3.21725e12 1.40957e13i −0.469165 2.05555i
\(713\) −7.90731e11 9.91545e11i −0.114584 0.143684i
\(714\) 7.72397e12 3.71967e12i 1.11224 0.535627i
\(715\) 1.93966e12 9.34092e11i 0.277555 0.133663i
\(716\) −2.07444e12 9.08871e12i −0.294980 1.29239i
\(717\) −1.28046e12 + 1.60565e12i −0.180939 + 0.226890i
\(718\) 9.57466e12 + 4.61091e12i 1.34451 + 0.647481i
\(719\) 3.46438e12 4.34420e12i 0.483444 0.606219i −0.478962 0.877836i \(-0.658987\pi\)
0.962406 + 0.271616i \(0.0875582\pi\)
\(720\) −4.30445e11 + 1.88590e12i −0.0596927 + 0.261531i
\(721\) −1.40364e12 + 6.75958e11i −0.193441 + 0.0931561i
\(722\) 6.28481e12 2.75356e13i 0.860746 3.77118i
\(723\) −1.31808e12 6.34754e11i −0.179399 0.0863939i
\(724\) −2.22798e12 −0.301361
\(725\) 6.25044e12 0.840213
\(726\) 2.66395e12 + 1.28289e12i 0.355887 + 0.171386i
\(727\) −1.82883e12 8.01264e12i −0.242812 1.06383i −0.938445 0.345430i \(-0.887733\pi\)
0.695633 0.718397i \(-0.255124\pi\)
\(728\) −5.62688e12 7.05588e12i −0.742466 0.931023i
\(729\) −7.03996e11 + 8.82783e11i −0.0923201 + 0.115766i
\(730\) 1.78931e12 0.233202
\(731\) −4.94720e12 + 1.36811e13i −0.640813 + 1.77212i
\(732\) 1.80950e12 0.232948
\(733\) −2.91543e12 + 3.65584e12i −0.373023 + 0.467756i −0.932542 0.361062i \(-0.882414\pi\)
0.559519 + 0.828817i \(0.310986\pi\)
\(734\) −2.10595e12 2.64078e12i −0.267803 0.335815i
\(735\) −2.88253e10 1.26292e11i −0.00364319 0.0159618i
\(736\) 1.37009e11 + 6.59800e10i 0.0172107 + 0.00828824i
\(737\) −6.26328e12 −0.781984
\(738\) −7.25771e12 −0.900629
\(739\) −9.75550e12 4.69800e12i −1.20323 0.579446i −0.278637 0.960396i \(-0.589883\pi\)
−0.924596 + 0.380950i \(0.875597\pi\)
\(740\) −2.98856e11 + 1.30937e12i −0.0366369 + 0.160517i
\(741\) 3.99829e12 1.92547e12i 0.487183 0.234615i
\(742\) 5.24968e12 2.30003e13i 0.635792 2.78559i
\(743\) 1.78202e12 2.23458e12i 0.214517 0.268996i −0.662917 0.748693i \(-0.730682\pi\)
0.877434 + 0.479697i \(0.159253\pi\)
\(744\) 1.85642e12 + 8.94005e11i 0.222125 + 0.106970i
\(745\) −3.50119e11 + 4.39035e11i −0.0416402 + 0.0522151i
\(746\) −3.70235e12 1.62210e13i −0.437676 1.91758i
\(747\) 7.86280e12 3.78652e12i 0.923920 0.444937i
\(748\) −3.61725e13 + 1.74198e13i −4.22495 + 2.03463i
\(749\) 8.92855e12 + 1.11961e13i 1.03660 + 1.29986i
\(750\) 8.44464e11 + 3.69984e12i 0.0974553 + 0.426979i
\(751\) −1.50275e12 + 6.58398e12i −0.172388 + 0.755281i 0.812623 + 0.582790i \(0.198039\pi\)
−0.985011 + 0.172491i \(0.944818\pi\)
\(752\) −9.84119e11 1.23405e12i −0.112219 0.140719i
\(753\) 1.96504e12 + 2.46409e12i 0.222738 + 0.279305i
\(754\) −2.39494e12 + 1.04929e13i −0.269851 + 1.18229i
\(755\) 3.44162e11 + 1.50787e12i 0.0385479 + 0.168890i
\(756\) −7.75124e12 9.71975e12i −0.863025 1.08220i
\(757\) 1.97449e12 9.50867e11i 0.218537 0.105242i −0.321413 0.946939i \(-0.604158\pi\)
0.539949 + 0.841697i \(0.318443\pi\)
\(758\) 1.68533e13 8.11614e12i 1.85428 0.892973i
\(759\) 5.30689e11 + 2.32510e12i 0.0580433 + 0.254304i
\(760\) −5.84767e12 + 7.33275e12i −0.635802 + 0.797270i
\(761\) −6.66709e12 3.21070e12i −0.720619 0.347032i 0.0373681 0.999302i \(-0.488103\pi\)
−0.757987 + 0.652270i \(0.773817\pi\)
\(762\) 1.39968e12 1.75515e12i 0.150395 0.188589i
\(763\) 7.69399e11 3.37096e12i 0.0821847 0.360075i
\(764\) 2.94894e13 1.42014e13i 3.13145 1.50803i
\(765\) −1.10101e12 + 4.82385e12i −0.116229 + 0.509234i
\(766\) −1.74550e13 8.40590e12i −1.83186 0.882175i
\(767\) 6.24764e12 0.651834
\(768\) −7.75325e12 −0.804190
\(769\) 1.13974e13 + 5.48872e12i 1.17527 + 0.565981i 0.916530 0.399965i \(-0.130978\pi\)
0.258742 + 0.965946i \(0.416692\pi\)
\(770\) −1.45760e12 6.38615e12i −0.149427 0.654682i
\(771\) −1.16188e12 1.45695e12i −0.118417 0.148490i
\(772\) 1.27767e13 1.60214e13i 1.29461 1.62339i
\(773\) −1.83389e13 −1.84742 −0.923711 0.383089i \(-0.874860\pi\)
−0.923711 + 0.383089i \(0.874860\pi\)
\(774\) 1.43312e13 + 1.76555e12i 1.43532 + 0.176825i
\(775\) −3.18660e12 −0.317300
\(776\) 3.29267e12 4.12888e12i 0.325965 0.408747i
\(777\) −5.99504e11 7.51755e11i −0.0590062 0.0739914i
\(778\) −4.48859e12 1.96658e13i −0.439240 1.92444i
\(779\) −1.03764e13 4.99700e12i −1.00955 0.486173i
\(780\) −2.04798e12 −0.198107
\(781\) 1.27044e13 1.22187
\(782\) −1.58273e13 7.62204e12i −1.51348 0.728854i
\(783\) −1.64063e12 + 7.18807e12i −0.155985 + 0.683415i
\(784\) 1.12688e12 5.42677e11i 0.106526 0.0513002i
\(785\) −5.89257e11 + 2.58170e12i −0.0553849 + 0.242657i
\(786\) −7.54448e12 + 9.46048e12i −0.705063 + 0.884121i
\(787\) −1.62423e13 7.82190e12i −1.50925 0.726819i −0.517585 0.855632i \(-0.673169\pi\)
−0.991669 + 0.128813i \(0.958883\pi\)
\(788\) −1.03158e13 + 1.29356e13i −0.953093 + 1.19514i
\(789\) 1.75351e12 + 7.68264e12i 0.161088 + 0.705771i
\(790\) 8.42424e12 4.05690e12i 0.769501 0.370572i
\(791\) 6.05594e12 2.91639e12i 0.550031 0.264881i
\(792\) 1.23554e13 + 1.54932e13i 1.11582 + 1.39919i
\(793\) −5.33231e11 2.33624e12i −0.0478835 0.209791i
\(794\) −1.66425e12 + 7.29156e12i −0.148603 + 0.651071i
\(795\) −1.65993e12 2.08149e12i −0.147380 0.184809i
\(796\) 1.36704e13 + 1.71421e13i 1.20690 + 1.51341i
\(797\) −4.95644e12 + 2.17156e13i −0.435118 + 1.90638i −0.0128260 + 0.999918i \(0.504083\pi\)
−0.422292 + 0.906460i \(0.638774\pi\)
\(798\) −3.00459e12 1.31640e13i −0.262284 1.14914i
\(799\) −2.51723e12 3.15650e12i −0.218505 0.273997i
\(800\) 3.44252e11 1.65783e11i 0.0297147 0.0143099i
\(801\) −1.08237e13 + 5.21241e12i −0.929028 + 0.447396i
\(802\) 6.12618e12 + 2.68405e13i 0.522884 + 2.29090i
\(803\) 3.74046e12 4.69039e12i 0.317472 0.398097i
\(804\) 5.36811e12 + 2.58514e12i 0.453074 + 0.218189i
\(805\) 1.18919e12 1.49119e12i 0.0998088 0.125156i
\(806\) 1.22099e12 5.34950e12i 0.101907 0.446484i
\(807\) 7.57866e12 3.64969e12i 0.629016 0.302918i
\(808\) −9.91238e11 + 4.34290e12i −0.0818138 + 0.358450i
\(809\) −9.20728e12 4.43399e12i −0.755723 0.363937i 0.0160197 0.999872i \(-0.494901\pi\)
−0.771743 + 0.635934i \(0.780615\pi\)
\(810\) 3.76299e12 0.307150
\(811\) −1.47158e12 −0.119451 −0.0597256 0.998215i \(-0.519023\pi\)
−0.0597256 + 0.998215i \(0.519023\pi\)
\(812\) 1.96340e13 + 9.45526e12i 1.58492 + 0.763258i
\(813\) −4.85999e11 2.12930e12i −0.0390147 0.170935i
\(814\) 4.21895e12 + 5.29040e12i 0.336818 + 0.422356i
\(815\) −3.27579e12 + 4.10771e12i −0.260080 + 0.326130i
\(816\) 9.34103e12 0.737546
\(817\) 1.92738e13 + 1.23914e13i 1.51345 + 0.973018i
\(818\) 2.74951e13 2.14717
\(819\) −4.67540e12 + 5.86276e12i −0.363112 + 0.455328i
\(820\) 3.31381e12 + 4.15538e12i 0.255956 + 0.320959i
\(821\) −2.66071e12 1.16573e13i −0.204387 0.895477i −0.968227 0.250072i \(-0.919546\pi\)
0.763841 0.645405i \(-0.223311\pi\)
\(822\) −1.11227e13 5.35643e12i −0.849745 0.409216i
\(823\) −8.16197e12 −0.620149 −0.310074 0.950712i \(-0.600354\pi\)
−0.310074 + 0.950712i \(0.600354\pi\)
\(824\) −5.18657e12 −0.391929
\(825\) 5.39892e12 + 2.59998e12i 0.405755 + 0.195401i
\(826\) 4.22997e12 1.85327e13i 0.316175 1.38525i
\(827\) −5.52016e12 + 2.65837e12i −0.410371 + 0.197624i −0.627668 0.778481i \(-0.715990\pi\)
0.217297 + 0.976106i \(0.430276\pi\)
\(828\) −2.58191e12 + 1.13121e13i −0.190899 + 0.836384i
\(829\) 7.59288e12 9.52117e12i 0.558356 0.700156i −0.419897 0.907572i \(-0.637934\pi\)
0.978253 + 0.207416i \(0.0665052\pi\)
\(830\) −8.65267e12 4.16691e12i −0.632847 0.304763i
\(831\) −4.71865e12 + 5.91700e12i −0.343252 + 0.430424i
\(832\) 2.35836e12 + 1.03327e13i 0.170630 + 0.747579i
\(833\) 2.88239e12 1.38808e12i 0.207420 0.0998880i
\(834\) 7.61021e12 3.66488e12i 0.544690 0.262309i
\(835\) −3.05863e12 3.83540e12i −0.217740 0.273037i
\(836\) 1.40709e13 + 6.16488e13i 0.996311 + 4.36512i
\(837\) 8.36425e11 3.66462e12i 0.0589064 0.258086i
\(838\) −6.30890e12 7.91111e12i −0.441932 0.554166i
\(839\) 4.40694e12 + 5.52613e12i 0.307049 + 0.385028i 0.911284 0.411779i \(-0.135092\pi\)
−0.604234 + 0.796807i \(0.706521\pi\)
\(840\) −6.89539e11 + 3.02107e12i −0.0477861 + 0.209365i
\(841\) 3.52278e11 + 1.54343e12i 0.0242831 + 0.106391i
\(842\) 2.98740e12 + 3.74608e12i 0.204828 + 0.256846i
\(843\) 1.15336e11 5.55430e10i 0.00786578 0.00378796i
\(844\) 9.97185e11 4.80219e11i 0.0676449 0.0325761i
\(845\) −4.89318e11 2.14384e12i −0.0330169 0.144657i
\(846\) −2.49844e12 + 3.13294e12i −0.167688 + 0.210274i
\(847\) −7.14312e12 3.43995e12i −0.476884 0.229655i
\(848\) 1.60271e13 2.00974e13i 1.06432 1.33462i
\(849\) −9.22739e11 + 4.04278e12i −0.0609529 + 0.267052i
\(850\) −3.97681e13 + 1.91513e13i −2.61306 + 1.25839i
\(851\) −4.38430e11 + 1.92089e12i −0.0286561 + 0.125551i
\(852\) −1.08886e13 5.24368e12i −0.707937 0.340924i
\(853\) −2.84033e13 −1.83695 −0.918477 0.395475i \(-0.870580\pi\)
−0.918477 + 0.395475i \(0.870580\pi\)
\(854\) −7.29112e12 −0.469066
\(855\) 7.02125e12 + 3.38125e12i 0.449331 + 0.216387i
\(856\) 1.06086e13 + 4.64791e13i 0.675343 + 2.95887i
\(857\) −8.40125e12 1.05348e13i −0.532023 0.667135i 0.441091 0.897463i \(-0.354592\pi\)
−0.973113 + 0.230327i \(0.926020\pi\)
\(858\) −6.43340e12 + 8.06722e12i −0.405273 + 0.508196i
\(859\) −1.00828e13 −0.631844 −0.315922 0.948785i \(-0.602314\pi\)
−0.315922 + 0.948785i \(0.602314\pi\)
\(860\) −5.53266e12 9.01144e12i −0.344898 0.561761i
\(861\) −3.80514e12 −0.235970
\(862\) 1.95843e13 2.45579e13i 1.20816 1.51499i
\(863\) −2.35457e12 2.95254e12i −0.144498 0.181195i 0.704315 0.709887i \(-0.251254\pi\)
−0.848814 + 0.528692i \(0.822683\pi\)
\(864\) 1.00292e11 + 4.39409e11i 0.00612287 + 0.0268260i
\(865\) −9.71503e12 4.67851e12i −0.590027 0.284142i
\(866\) 1.82351e13 1.10174
\(867\) 1.71645e13 1.03168
\(868\) −1.00098e13 4.82048e12i −0.598532 0.288238i
\(869\) 6.97594e12 3.05636e13i 0.414967 1.81809i
\(870\) 3.32954e12 1.60342e12i 0.197037 0.0948879i
\(871\) 1.75577e12 7.69255e12i 0.103368 0.452886i
\(872\) 7.17702e12 8.99970e12i 0.420359 0.527113i
\(873\) −3.95348e12 1.90390e12i −0.230365 0.110938i
\(874\) −1.72509e13 + 2.16319e13i −1.00002 + 1.25399i
\(875\) −2.26435e12 9.92075e12i −0.130589 0.572148i
\(876\) −5.14181e12 + 2.47616e12i −0.295017 + 0.142073i
\(877\) −1.14012e13 + 5.49051e12i −0.650805 + 0.313411i −0.729999 0.683448i \(-0.760480\pi\)
0.0791944 + 0.996859i \(0.474765\pi\)
\(878\) 2.32958e13 + 2.92120e13i 1.32297 + 1.65896i
\(879\) 2.87480e12 + 1.25953e13i 0.162427 + 0.711637i
\(880\) 1.58818e12 6.95829e12i 0.0892748 0.391139i
\(881\) 6.25976e12 + 7.84949e12i 0.350079 + 0.438985i 0.925428 0.378923i \(-0.123705\pi\)
−0.575349 + 0.817908i \(0.695134\pi\)
\(882\) −1.97979e12 2.48257e12i −0.110156 0.138132i
\(883\) 2.74881e12 1.20433e13i 0.152168 0.666690i −0.840085 0.542455i \(-0.817495\pi\)
0.992253 0.124235i \(-0.0396478\pi\)
\(884\) −1.12547e13 4.93103e13i −0.619870 2.71583i
\(885\) −1.33750e12 1.67718e12i −0.0732910 0.0919040i
\(886\) −2.23754e10 + 1.07754e10i −0.00121988 + 0.000587465i
\(887\) 2.04285e12 9.83786e11i 0.110810 0.0533635i −0.377657 0.925945i \(-0.623270\pi\)
0.488468 + 0.872582i \(0.337556\pi\)
\(888\) −7.12308e11 3.12082e12i −0.0384423 0.168427i
\(889\) −3.75311e12 + 4.70625e12i −0.201527 + 0.252707i
\(890\) 1.19110e13 + 5.73604e12i 0.636346 + 0.306448i
\(891\) 7.86634e12 9.86407e12i 0.418141 0.524332i
\(892\) 7.83225e12 3.43153e13i 0.414233 1.81487i
\(893\) −5.72910e12 + 2.75899e12i −0.301477 + 0.145184i
\(894\) 5.98897e11 2.62394e12i 0.0313569 0.137384i
\(895\) 3.81923e12 + 1.83924e12i 0.198963 + 0.0958154i
\(896\) 3.15773e13 1.63678
\(897\) −3.00445e12 −0.154953
\(898\) −4.63386e13 2.23155e13i −2.37793 1.14515i
\(899\) 1.46617e12 + 6.42372e12i 0.0748629 + 0.327996i
\(900\) 1.81772e13 + 2.27935e13i 0.923497 + 1.15803i
\(901\) 4.09949e13 5.14059e13i 2.07237 2.59867i
\(902\) 2.67783e13 1.34696
\(903\) 7.51371e12 + 9.25657e11i 0.376062 + 0.0463292i
\(904\) 2.23772e13 1.11442
\(905\) 6.31649e11 7.92063e11i 0.0313009 0.0392501i
\(906\) −4.62185e12 5.79561e12i −0.227897 0.285774i
\(907\) 8.37412e12 + 3.66894e13i 0.410872 + 1.80015i 0.580071 + 0.814566i \(0.303025\pi\)
−0.169199 + 0.985582i \(0.554118\pi\)
\(908\) −1.18219e13 5.69314e12i −0.577168 0.277949i
\(909\) 3.70133e12 0.179813
\(910\) 8.25206e12 0.398911
\(911\) 8.78077e11 + 4.22860e11i 0.0422377 + 0.0203406i 0.454883 0.890551i \(-0.349681\pi\)
−0.412646 + 0.910892i \(0.635395\pi\)
\(912\) 3.27378e12 1.43434e13i 0.156701 0.686553i
\(913\) −2.90109e13 + 1.39709e13i −1.38179 + 0.665435i
\(914\) −5.89428e12 + 2.58245e13i −0.279365 + 1.22398i
\(915\) −5.13007e11 + 6.43290e11i −0.0241951 + 0.0303398i
\(916\) −4.06075e13 1.95555e13i −1.90580 0.917783i
\(917\) 2.02298e13 2.53673e13i 0.944777 1.18471i
\(918\) −1.15858e13 5.07607e13i −0.538435 2.35904i
\(919\) −1.09154e13 + 5.25657e12i −0.504800 + 0.243099i −0.668910 0.743343i \(-0.733239\pi\)
0.164110 + 0.986442i \(0.447525\pi\)
\(920\) 5.72090e12 2.75504e12i 0.263281 0.126789i
\(921\) −2.16899e12 2.71982e12i −0.0993318 0.124558i
\(922\) −9.80198e12 4.29453e13i −0.446709 1.95716i
\(923\) −3.56139e12 + 1.56035e13i −0.161515 + 0.707642i
\(924\) 1.30261e13 + 1.63343e13i 0.587885 + 0.737184i
\(925\) 3.08665e12 + 3.87053e12i 0.138627 + 0.173833i
\(926\) −1.27658e13 + 5.59307e13i −0.570557 + 2.49977i
\(927\) 9.58964e11 + 4.20149e12i 0.0426524 + 0.186872i
\(928\) −4.92587e11 6.17685e11i −0.0218031 0.0273402i
\(929\) 2.88715e12 1.39038e12i 0.127174 0.0612438i −0.369215 0.929344i \(-0.620373\pi\)
0.496389 + 0.868100i \(0.334659\pi\)
\(930\) −1.69746e12 + 8.17455e11i −0.0744093 + 0.0358336i
\(931\) −1.12124e12 4.91245e12i −0.0489129 0.214301i
\(932\) −5.95583e11 + 7.46838e11i −0.0258566 + 0.0324231i
\(933\) −8.83100e12 4.25278e12i −0.381542 0.183741i
\(934\) 3.11207e13 3.90241e13i 1.33810 1.67792i
\(935\) 4.06233e12 1.77982e13i 0.173829 0.761596i
\(936\) −2.24922e13 + 1.08317e13i −0.957837 + 0.461270i
\(937\) −8.36873e12 + 3.66658e13i −0.354676 + 1.55394i 0.411564 + 0.911381i \(0.364983\pi\)
−0.766239 + 0.642555i \(0.777874\pi\)
\(938\) −2.16301e13 1.04165e13i −0.912315 0.439348i
\(939\) 1.41966e13 0.595922
\(940\) 2.93453e12 0.122592
\(941\) −3.37638e13 1.62598e13i −1.40378 0.676024i −0.429854 0.902898i \(-0.641435\pi\)
−0.973924 + 0.226874i \(0.927149\pi\)
\(942\) −2.82423e12 1.23737e13i −0.116861 0.512003i
\(943\) 4.86146e12 + 6.09608e12i 0.200200 + 0.251043i
\(944\) 1.29140e13 1.61936e13i 0.529280 0.663696i
\(945\) 5.65298e12 0.230587
\(946\) −5.28770e13 6.51422e12i −2.14663 0.264455i
\(947\) 2.24310e13 0.906305 0.453152 0.891433i \(-0.350299\pi\)
0.453152 + 0.891433i \(0.350299\pi\)
\(948\) −1.85939e13 + 2.33160e13i −0.747710 + 0.937599i
\(949\) 4.71218e12 + 5.90888e12i 0.188592 + 0.236487i
\(950\) 1.54696e13 + 6.77769e13i 0.616203 + 2.69976i
\(951\) −3.82143e12 1.84030e12i −0.151500 0.0729587i
\(952\) −7.65291e13 −3.01968
\(953\) −1.60601e12 −0.0630710 −0.0315355 0.999503i \(-0.510040\pi\)
−0.0315355 + 0.999503i \(0.510040\pi\)
\(954\) −5.87972e13 2.83152e13i −2.29821 1.10676i
\(955\) −3.31179e12 + 1.45099e13i −0.128839 + 0.564481i
\(956\) 3.32148e13 1.59954e13i 1.28609 0.619348i
\(957\) 2.75712e12 1.20797e13i 0.106256 0.465536i
\(958\) −4.01258e13 + 5.03162e13i −1.53914 + 1.93003i
\(959\) 2.98245e13 + 1.43627e13i 1.13865 + 0.548345i
\(960\) 2.26892e12 2.84513e12i 0.0862180 0.108114i
\(961\) 5.13589e12 + 2.25018e13i 0.194250 + 0.851063i
\(962\) −7.68035e12 + 3.69866e12i −0.289130 + 0.139238i
\(963\) 3.56900e13 1.71874e13i 1.33730 0.644009i
\(964\) 1.63736e13 + 2.05319e13i 0.610659 + 0.765742i
\(965\) 2.07346e12 + 9.08441e12i 0.0769701 + 0.337228i
\(966\) −2.03417e12 + 8.91226e12i −0.0751604 + 0.329299i
\(967\) 2.93014e13 + 3.67428e13i 1.07763 + 1.35130i 0.932203 + 0.361935i \(0.117884\pi\)
0.145426 + 0.989369i \(0.453545\pi\)
\(968\) −1.64567e13 2.06360e13i −0.602425 0.755416i
\(969\) 8.37382e12 3.66881e13i 0.305117 1.33681i
\(970\) 1.07452e12 + 4.70777e12i 0.0389710 + 0.170743i
\(971\) −2.00631e13 2.51583e13i −0.724288 0.908228i 0.274284 0.961649i \(-0.411559\pi\)
−0.998572 + 0.0534203i \(0.982988\pi\)
\(972\) −4.78556e13 + 2.30460e13i −1.71963 + 0.828129i
\(973\) −2.04060e13 + 9.82702e12i −0.729878 + 0.351491i
\(974\) 7.43449e12 + 3.25726e13i 0.264689 + 1.15968i
\(975\) −4.70676e12 + 5.90210e12i −0.166802 + 0.209163i
\(976\) −7.15761e12 3.44692e12i −0.252490 0.121593i
\(977\) −2.01507e13 + 2.52682e13i −0.707562 + 0.887255i −0.997563 0.0697713i \(-0.977773\pi\)
0.290001 + 0.957026i \(0.406344\pi\)
\(978\) 5.60341e12 2.45501e13i 0.195852 0.858083i
\(979\) 3.99355e13 1.92319e13i 1.38943 0.669114i
\(980\) −5.17438e11 + 2.26705e12i −0.0179201 + 0.0785132i
\(981\) −8.61738e12 4.14991e12i −0.297074 0.143063i
\(982\) 2.86733e13 0.983957
\(983\) 3.26218e12 0.111434 0.0557170 0.998447i \(-0.482256\pi\)
0.0557170 + 0.998447i \(0.482256\pi\)
\(984\) −1.14134e13 5.49639e12i −0.388093 0.186896i
\(985\) −1.67410e12 7.33470e12i −0.0566654 0.248267i
\(986\) 5.69039e13 + 7.13552e13i 1.91733 + 2.40425i
\(987\) −1.30991e12 + 1.64257e12i −0.0439352 + 0.0550930i
\(988\) −7.96615e13 −2.65976
\(989\) −8.11658e12 1.32201e13i −0.269768 0.439390i
\(990\) −1.81197e13 −0.599505
\(991\) 4.12923e12 5.17789e12i 0.136000 0.170538i −0.709168 0.705040i \(-0.750929\pi\)
0.845167 + 0.534502i \(0.179501\pi\)
\(992\) 2.51131e11 + 3.14908e11i 0.00823374 + 0.0103248i
\(993\) 3.82443e12 + 1.67559e13i 0.124823 + 0.546886i
\(994\) 4.38742e13 + 2.11287e13i 1.42551 + 0.686489i
\(995\) −9.96982e12 −0.322466
\(996\) 3.06310e13 0.986265
\(997\) 4.52843e13 + 2.18078e13i 1.45151 + 0.699010i 0.982856 0.184373i \(-0.0590254\pi\)
0.468652 + 0.883383i \(0.344740\pi\)
\(998\) 7.74668e11 3.39404e12i 0.0247188 0.108300i
\(999\) −5.26134e12 + 2.53373e12i −0.167129 + 0.0804851i
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 43.10.e.a.4.4 192
43.11 even 7 inner 43.10.e.a.11.4 yes 192
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.10.e.a.4.4 192 1.1 even 1 trivial
43.10.e.a.11.4 yes 192 43.11 even 7 inner