Properties

Label 11.10.c.a.4.6
Level $11$
Weight $10$
Character 11.4
Analytic conductor $5.665$
Analytic rank $0$
Dimension $32$
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] = [11,10,Mod(3,11)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(11, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("11.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 11 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 11.c (of order \(5\), degree \(4\), 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: \(5.66539419780\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 4.6
Character \(\chi\) \(=\) 11.4
Dual form 11.10.c.a.3.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(12.1558 + 8.83167i) q^{2} +(13.4151 - 41.2873i) q^{3} +(-88.4528 - 272.230i) q^{4} +(1436.78 - 1043.88i) q^{5} +(527.706 - 383.401i) q^{6} +(741.893 + 2283.31i) q^{7} +(3706.29 - 11406.8i) q^{8} +(14399.2 + 10461.6i) q^{9} +O(q^{10})\) \(q+(12.1558 + 8.83167i) q^{2} +(13.4151 - 41.2873i) q^{3} +(-88.4528 - 272.230i) q^{4} +(1436.78 - 1043.88i) q^{5} +(527.706 - 383.401i) q^{6} +(741.893 + 2283.31i) q^{7} +(3706.29 - 11406.8i) q^{8} +(14399.2 + 10461.6i) q^{9} +26684.4 q^{10} +(-16035.3 - 45834.7i) q^{11} -12426.2 q^{12} +(16675.3 + 12115.3i) q^{13} +(-11147.2 + 34307.5i) q^{14} +(-23824.7 - 73324.8i) q^{15} +(27228.8 - 19782.9i) q^{16} +(-507763. + 368911. i) q^{17} +(82639.5 + 254338. i) q^{18} +(-87351.0 + 268839. i) q^{19} +(-411264. - 298801. i) q^{20} +104224. q^{21} +(209876. - 698773. i) q^{22} +1.63395e6 q^{23} +(-421236. - 306046. i) q^{24} +(371104. - 1.14214e6i) q^{25} +(95702.2 + 294541. i) q^{26} +(1.31639e6 - 956412. i) q^{27} +(555962. - 403930. i) q^{28} +(772434. + 2.37731e6i) q^{29} +(357974. - 1.10173e6i) q^{30} +(2.14690e6 + 1.55981e6i) q^{31} -5.63513e6 q^{32} +(-2.10751e6 + 47179.1i) q^{33} -9.43034e6 q^{34} +(3.44945e6 + 2.50617e6i) q^{35} +(1.57432e6 - 4.84525e6i) q^{36} +(4.75055e6 + 1.46207e7i) q^{37} +(-3.43611e6 + 2.49648e6i) q^{38} +(723908. - 525950. i) q^{39} +(-6.58224e6 - 2.02580e7i) q^{40} +(-314654. + 968404. i) q^{41} +(1.26693e6 + 920475. i) q^{42} -1.57589e7 q^{43} +(-1.10592e7 + 8.41948e6i) q^{44} +3.16093e7 q^{45} +(1.98619e7 + 1.44305e7i) q^{46} +(4.36297e6 - 1.34278e7i) q^{47} +(-451507. - 1.38959e6i) q^{48} +(2.79836e7 - 2.03313e7i) q^{49} +(1.45981e7 - 1.06061e7i) q^{50} +(8.41968e6 + 2.59131e7i) q^{51} +(1.82317e6 - 5.61114e6i) q^{52} +(-4.82226e7 - 3.50358e7i) q^{53} +2.44484e7 q^{54} +(-7.08854e7 - 4.91155e7i) q^{55} +2.87949e7 q^{56} +(9.92781e6 + 7.21298e6i) q^{57} +(-1.16061e7 + 3.57199e7i) q^{58} +(2.19532e7 + 6.75649e7i) q^{59} +(-1.78538e7 + 1.29716e7i) q^{60} +(-9.45200e7 + 6.86728e7i) q^{61} +(1.23214e7 + 3.79214e7i) q^{62} +(-1.32045e7 + 4.06393e7i) q^{63} +(-8.24404e7 - 5.98965e7i) q^{64} +3.66057e7 q^{65} +(-2.60350e7 - 1.80393e7i) q^{66} -2.19426e8 q^{67} +(1.45342e8 + 1.05597e8i) q^{68} +(2.19195e7 - 6.74614e7i) q^{69} +(1.97970e7 + 6.09289e7i) q^{70} +(3.30384e8 - 2.40038e8i) q^{71} +(1.72701e8 - 1.25475e8i) q^{72} +(-5.87823e7 - 1.80913e8i) q^{73} +(-7.13786e7 + 2.19681e8i) q^{74} +(-4.21776e7 - 3.06438e7i) q^{75} +8.09123e7 q^{76} +(9.27583e7 - 7.06180e7i) q^{77} +1.34447e7 q^{78} +(-1.95362e8 - 1.41939e8i) q^{79} +(1.84709e7 - 5.68475e7i) q^{80} +(8.64284e7 + 2.65999e8i) q^{81} +(-1.23775e7 + 8.99277e6i) q^{82} +(5.61623e8 - 4.08043e8i) q^{83} +(-9.21893e6 - 2.83730e7i) q^{84} +(-3.44444e8 + 1.06009e9i) q^{85} +(-1.91562e8 - 1.39178e8i) q^{86} +1.08515e8 q^{87} +(-5.82258e8 + 1.30346e7i) q^{88} -8.87682e8 q^{89} +(3.84235e8 + 2.79163e8i) q^{90} +(-1.52917e7 + 4.70631e7i) q^{91} +(-1.44527e8 - 4.44810e8i) q^{92} +(9.32013e7 - 6.77147e7i) q^{93} +(1.71625e8 - 1.24693e8i) q^{94} +(1.55132e8 + 4.77448e8i) q^{95} +(-7.55956e7 + 2.32659e8i) q^{96} +(-7.90895e8 - 5.74619e8i) q^{97} +5.19722e8 q^{98} +(2.48610e8 - 8.27738e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 21 q^{2} + 69 q^{3} - 1625 q^{4} + 225 q^{5} + 8173 q^{6} - 10675 q^{7} + 22863 q^{8} - 93587 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 21 q^{2} + 69 q^{3} - 1625 q^{4} + 225 q^{5} + 8173 q^{6} - 10675 q^{7} + 22863 q^{8} - 93587 q^{9} - 16272 q^{10} - 44637 q^{11} + 339622 q^{12} + 164099 q^{13} - 125832 q^{14} - 547009 q^{15} - 1428705 q^{16} + 1430145 q^{17} + 1483170 q^{18} + 2175116 q^{19} - 79194 q^{20} - 3427202 q^{21} - 4280751 q^{22} - 4045452 q^{23} + 15199185 q^{24} - 1591199 q^{25} - 11064048 q^{26} - 377496 q^{27} + 3790710 q^{28} + 2621889 q^{29} + 18259050 q^{30} + 3571591 q^{31} - 56548860 q^{32} + 10586762 q^{33} + 8515154 q^{34} + 3015333 q^{35} + 3379584 q^{36} + 20945529 q^{37} + 55333848 q^{38} + 16458893 q^{39} - 21310356 q^{40} - 53829591 q^{41} - 22644634 q^{42} - 4383434 q^{43} - 21997776 q^{44} - 165146020 q^{45} - 2025868 q^{46} + 78754497 q^{47} + 281712140 q^{48} + 227397397 q^{49} - 74287941 q^{50} - 117901326 q^{51} - 157487230 q^{52} - 30528081 q^{53} - 337412524 q^{54} - 248082383 q^{55} - 327187608 q^{56} + 326803764 q^{57} + 279888572 q^{58} + 254767908 q^{59} + 1309524756 q^{60} - 10620465 q^{61} + 686572332 q^{62} - 172608476 q^{63} - 1338445825 q^{64} - 869006394 q^{65} - 2484759594 q^{66} - 946203354 q^{67} + 2053775934 q^{68} + 1552022058 q^{69} - 10909448 q^{70} + 1396168719 q^{71} + 2446779799 q^{72} + 1566720997 q^{73} - 604530504 q^{74} - 2015724064 q^{75} - 4233309866 q^{76} - 3256040955 q^{77} - 4298015660 q^{78} + 2890358835 q^{79} + 5092570836 q^{80} + 1937450890 q^{81} + 4014664309 q^{82} - 480997020 q^{83} + 4617031020 q^{84} - 3775782881 q^{85} - 3721184697 q^{86} - 4032861402 q^{87} - 8695160705 q^{88} - 1559422158 q^{89} + 5473366174 q^{90} + 5038455823 q^{91} + 6839439726 q^{92} + 9679941995 q^{93} + 1219591670 q^{94} + 2592967899 q^{95} - 11940342116 q^{96} - 3010541778 q^{97} - 7371061380 q^{98} - 9888905941 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/11\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 12.1558 + 8.83167i 0.537214 + 0.390308i 0.823049 0.567970i \(-0.192271\pi\)
−0.285836 + 0.958279i \(0.592271\pi\)
\(3\) 13.4151 41.2873i 0.0956197 0.294287i −0.891795 0.452440i \(-0.850554\pi\)
0.987415 + 0.158153i \(0.0505538\pi\)
\(4\) −88.4528 272.230i −0.172759 0.531698i
\(5\) 1436.78 1043.88i 1.02808 0.746943i 0.0601557 0.998189i \(-0.480840\pi\)
0.967923 + 0.251246i \(0.0808403\pi\)
\(6\) 527.706 383.401i 0.166231 0.120774i
\(7\) 741.893 + 2283.31i 0.116788 + 0.359438i 0.992316 0.123731i \(-0.0394859\pi\)
−0.875527 + 0.483168i \(0.839486\pi\)
\(8\) 3706.29 11406.8i 0.319915 0.984597i
\(9\) 14399.2 + 10461.6i 0.731555 + 0.531506i
\(10\) 26684.4 0.843836
\(11\) −16035.3 45834.7i −0.330225 0.943902i
\(12\) −12426.2 −0.172991
\(13\) 16675.3 + 12115.3i 0.161930 + 0.117649i 0.665799 0.746131i \(-0.268091\pi\)
−0.503869 + 0.863780i \(0.668091\pi\)
\(14\) −11147.2 + 34307.5i −0.0775513 + 0.238678i
\(15\) −23824.7 73324.8i −0.121511 0.373973i
\(16\) 27228.8 19782.9i 0.103870 0.0754658i
\(17\) −507763. + 368911.i −1.47449 + 1.07128i −0.495203 + 0.868777i \(0.664906\pi\)
−0.979282 + 0.202499i \(0.935094\pi\)
\(18\) 82639.5 + 254338.i 0.185550 + 0.571064i
\(19\) −87351.0 + 268839.i −0.153772 + 0.473261i −0.998034 0.0626688i \(-0.980039\pi\)
0.844263 + 0.535930i \(0.180039\pi\)
\(20\) −411264. 298801.i −0.574759 0.417587i
\(21\) 104224. 0.116945
\(22\) 209876. 698773.i 0.191012 0.635967i
\(23\) 1.63395e6 1.21748 0.608742 0.793368i \(-0.291674\pi\)
0.608742 + 0.793368i \(0.291674\pi\)
\(24\) −421236. 306046.i −0.259164 0.188294i
\(25\) 371104. 1.14214e6i 0.190005 0.584777i
\(26\) 95702.2 + 294541.i 0.0410716 + 0.126405i
\(27\) 1.31639e6 956412.i 0.476702 0.346344i
\(28\) 555962. 403930.i 0.170936 0.124192i
\(29\) 772434. + 2.37731e6i 0.202801 + 0.624158i 0.999797 + 0.0201725i \(0.00642156\pi\)
−0.796995 + 0.603986i \(0.793578\pi\)
\(30\) 357974. 1.10173e6i 0.0806873 0.248330i
\(31\) 2.14690e6 + 1.55981e6i 0.417526 + 0.303351i 0.776642 0.629942i \(-0.216922\pi\)
−0.359115 + 0.933293i \(0.616922\pi\)
\(32\) −5.63513e6 −0.950012
\(33\) −2.10751e6 + 47179.1i −0.309354 + 0.00692527i
\(34\) −9.43034e6 −1.21024
\(35\) 3.44945e6 + 2.50617e6i 0.388547 + 0.282296i
\(36\) 1.57432e6 4.84525e6i 0.156218 0.480789i
\(37\) 4.75055e6 + 1.46207e7i 0.416712 + 1.28251i 0.910711 + 0.413045i \(0.135535\pi\)
−0.493999 + 0.869462i \(0.664465\pi\)
\(38\) −3.43611e6 + 2.49648e6i −0.267326 + 0.194224i
\(39\) 723908. 525950.i 0.0501063 0.0364044i
\(40\) −6.58224e6 2.02580e7i −0.406540 1.25120i
\(41\) −314654. + 968404.i −0.0173902 + 0.0535216i −0.959375 0.282134i \(-0.908958\pi\)
0.941985 + 0.335655i \(0.108958\pi\)
\(42\) 1.26693e6 + 920475.i 0.0628245 + 0.0456447i
\(43\) −1.57589e7 −0.702940 −0.351470 0.936199i \(-0.614318\pi\)
−0.351470 + 0.936199i \(0.614318\pi\)
\(44\) −1.10592e7 + 8.41948e6i −0.444822 + 0.338648i
\(45\) 3.16093e7 1.14910
\(46\) 1.98619e7 + 1.44305e7i 0.654049 + 0.475194i
\(47\) 4.36297e6 1.34278e7i 0.130419 0.401389i −0.864430 0.502753i \(-0.832321\pi\)
0.994849 + 0.101364i \(0.0323206\pi\)
\(48\) −451507. 1.38959e6i −0.0122766 0.0377835i
\(49\) 2.79836e7 2.03313e7i 0.693461 0.503829i
\(50\) 1.45981e7 1.06061e7i 0.330317 0.239989i
\(51\) 8.41968e6 + 2.59131e7i 0.174273 + 0.536357i
\(52\) 1.82317e6 5.61114e6i 0.0345789 0.106423i
\(53\) −4.82226e7 3.50358e7i −0.839478 0.609916i 0.0827471 0.996571i \(-0.473631\pi\)
−0.922225 + 0.386654i \(0.873631\pi\)
\(54\) 2.44484e7 0.391272
\(55\) −7.08854e7 4.91155e7i −1.04454 0.723747i
\(56\) 2.87949e7 0.391264
\(57\) 9.92781e6 + 7.21298e6i 0.124571 + 0.0905061i
\(58\) −1.16061e7 + 3.57199e7i −0.134667 + 0.414461i
\(59\) 2.19532e7 + 6.75649e7i 0.235865 + 0.725917i 0.997006 + 0.0773303i \(0.0246396\pi\)
−0.761141 + 0.648587i \(0.775360\pi\)
\(60\) −1.78538e7 + 1.29716e7i −0.177849 + 0.129215i
\(61\) −9.45200e7 + 6.86728e7i −0.874057 + 0.635039i −0.931672 0.363300i \(-0.881650\pi\)
0.0576158 + 0.998339i \(0.481650\pi\)
\(62\) 1.23214e7 + 3.79214e7i 0.105900 + 0.325928i
\(63\) −1.32045e7 + 4.06393e7i −0.105606 + 0.325022i
\(64\) −8.24404e7 5.98965e7i −0.614229 0.446263i
\(65\) 3.66057e7 0.254354
\(66\) −2.60350e7 1.80393e7i −0.168892 0.117023i
\(67\) −2.19426e8 −1.33030 −0.665152 0.746708i \(-0.731633\pi\)
−0.665152 + 0.746708i \(0.731633\pi\)
\(68\) 1.45342e8 + 1.05597e8i 0.824327 + 0.598909i
\(69\) 2.19195e7 6.74614e7i 0.116415 0.358290i
\(70\) 1.97970e7 + 6.09289e7i 0.0985503 + 0.303307i
\(71\) 3.30384e8 2.40038e8i 1.54296 1.12103i 0.594523 0.804079i \(-0.297341\pi\)
0.948442 0.316951i \(-0.102659\pi\)
\(72\) 1.72701e8 1.25475e8i 0.757355 0.550251i
\(73\) −5.87823e7 1.80913e8i −0.242267 0.745620i −0.996074 0.0885246i \(-0.971785\pi\)
0.753807 0.657096i \(-0.228215\pi\)
\(74\) −7.13786e7 + 2.19681e8i −0.276710 + 0.851626i
\(75\) −4.21776e7 3.06438e7i −0.153924 0.111832i
\(76\) 8.09123e7 0.278198
\(77\) 9.27583e7 7.06180e7i 0.300708 0.228932i
\(78\) 1.34447e7 0.0411268
\(79\) −1.95362e8 1.41939e8i −0.564310 0.409995i 0.268724 0.963217i \(-0.413398\pi\)
−0.833034 + 0.553222i \(0.813398\pi\)
\(80\) 1.84709e7 5.68475e7i 0.0504176 0.155170i
\(81\) 8.64284e7 + 2.65999e8i 0.223087 + 0.686590i
\(82\) −1.23775e7 + 8.99277e6i −0.0302322 + 0.0219650i
\(83\) 5.61623e8 4.08043e8i 1.29895 0.943745i 0.299009 0.954250i \(-0.403344\pi\)
0.999945 + 0.0105051i \(0.00334393\pi\)
\(84\) −9.21893e6 2.83730e7i −0.0202034 0.0621796i
\(85\) −3.44444e8 + 1.06009e9i −0.715705 + 2.20271i
\(86\) −1.91562e8 1.39178e8i −0.377629 0.274364i
\(87\) 1.08515e8 0.203073
\(88\) −5.82258e8 + 1.30346e7i −1.03501 + 0.0231699i
\(89\) −8.87682e8 −1.49969 −0.749846 0.661612i \(-0.769873\pi\)
−0.749846 + 0.661612i \(0.769873\pi\)
\(90\) 3.84235e8 + 2.79163e8i 0.617313 + 0.448504i
\(91\) −1.52917e7 + 4.70631e7i −0.0233760 + 0.0719439i
\(92\) −1.44527e8 4.44810e8i −0.210332 0.647335i
\(93\) 9.32013e7 6.77147e7i 0.129196 0.0938663i
\(94\) 1.71625e8 1.24693e8i 0.226729 0.164728i
\(95\) 1.55132e8 + 4.77448e8i 0.195409 + 0.601408i
\(96\) −7.55956e7 + 2.32659e8i −0.0908398 + 0.279576i
\(97\) −7.90895e8 5.74619e8i −0.907081 0.659033i 0.0331942 0.999449i \(-0.489432\pi\)
−0.940275 + 0.340416i \(0.889432\pi\)
\(98\) 5.19722e8 0.569185
\(99\) 2.48610e8 8.27738e8i 0.260112 0.866033i
\(100\) −3.43750e8 −0.343750
\(101\) 1.41664e9 + 1.02925e9i 1.35461 + 0.984183i 0.998767 + 0.0496379i \(0.0158067\pi\)
0.355845 + 0.934545i \(0.384193\pi\)
\(102\) −1.26509e8 + 3.89353e8i −0.115723 + 0.356158i
\(103\) −1.64606e8 5.06605e8i −0.144105 0.443508i 0.852790 0.522254i \(-0.174909\pi\)
−0.996895 + 0.0787454i \(0.974909\pi\)
\(104\) 2.00000e8 1.45309e8i 0.167641 0.121798i
\(105\) 1.49748e8 1.08798e8i 0.120229 0.0873514i
\(106\) −2.76758e8 8.51772e8i −0.212923 0.655310i
\(107\) −5.04386e8 + 1.55234e9i −0.371994 + 1.14488i 0.573490 + 0.819212i \(0.305589\pi\)
−0.945484 + 0.325668i \(0.894411\pi\)
\(108\) −3.76802e8 2.73762e8i −0.266505 0.193627i
\(109\) 1.37969e9 0.936187 0.468094 0.883679i \(-0.344941\pi\)
0.468094 + 0.883679i \(0.344941\pi\)
\(110\) −4.27893e8 1.22307e9i −0.278656 0.796499i
\(111\) 6.67378e8 0.417271
\(112\) 6.53714e7 + 4.74951e7i 0.0392560 + 0.0285212i
\(113\) −1.25434e8 + 3.86048e8i −0.0723709 + 0.222735i −0.980699 0.195524i \(-0.937359\pi\)
0.908328 + 0.418258i \(0.137359\pi\)
\(114\) 5.69774e7 + 1.75358e8i 0.0315959 + 0.0972422i
\(115\) 2.34763e9 1.70566e9i 1.25167 0.909392i
\(116\) 5.78850e8 4.20559e8i 0.296828 0.215658i
\(117\) 1.13365e8 + 3.48901e8i 0.0559297 + 0.172134i
\(118\) −3.29854e8 + 1.01519e9i −0.156622 + 0.482032i
\(119\) −1.21904e9 8.85687e8i −0.557260 0.404873i
\(120\) −9.24702e8 −0.407086
\(121\) −1.84369e9 + 1.46994e9i −0.781903 + 0.623400i
\(122\) −1.75546e9 −0.717416
\(123\) 3.57617e7 + 2.59824e7i 0.0140879 + 0.0102354i
\(124\) 2.34728e8 7.22419e8i 0.0891595 0.274405i
\(125\) 4.12813e8 + 1.27051e9i 0.151237 + 0.465459i
\(126\) −5.19423e8 + 3.77383e8i −0.183592 + 0.133387i
\(127\) 7.78177e7 5.65379e7i 0.0265437 0.0192851i −0.574434 0.818551i \(-0.694778\pi\)
0.600978 + 0.799266i \(0.294778\pi\)
\(128\) 4.18432e8 + 1.28780e9i 0.137778 + 0.424037i
\(129\) −2.11407e8 + 6.50644e8i −0.0672149 + 0.206866i
\(130\) 4.44970e8 + 3.23290e8i 0.136643 + 0.0992767i
\(131\) −2.64609e9 −0.785027 −0.392513 0.919746i \(-0.628394\pi\)
−0.392513 + 0.919746i \(0.628394\pi\)
\(132\) 1.99258e8 + 5.69552e8i 0.0571260 + 0.163287i
\(133\) −6.78648e8 −0.188067
\(134\) −2.66728e9 1.93790e9i −0.714657 0.519229i
\(135\) 8.92981e8 2.74831e9i 0.231388 0.712138i
\(136\) 2.32618e9 + 7.15924e9i 0.583066 + 1.79449i
\(137\) −1.05342e9 + 7.65354e8i −0.255481 + 0.185618i −0.708153 0.706059i \(-0.750471\pi\)
0.452671 + 0.891677i \(0.350471\pi\)
\(138\) 8.62246e8 6.26458e8i 0.202384 0.147040i
\(139\) −1.11551e9 3.43319e9i −0.253459 0.780066i −0.994129 0.108198i \(-0.965492\pi\)
0.740671 0.671868i \(-0.234508\pi\)
\(140\) 3.77141e8 1.16072e9i 0.0829713 0.255359i
\(141\) −4.95870e8 3.60271e8i −0.105653 0.0767614i
\(142\) 6.13600e9 1.26645
\(143\) 2.87908e8 9.58578e8i 0.0575760 0.191697i
\(144\) 5.99035e8 0.116097
\(145\) 3.59146e9 + 2.60935e9i 0.674706 + 0.490203i
\(146\) 8.83224e8 2.71828e9i 0.160873 0.495116i
\(147\) −4.64023e8 1.42812e9i −0.0819618 0.252252i
\(148\) 3.55998e9 2.58648e9i 0.609916 0.443130i
\(149\) −7.25264e8 + 5.26935e8i −0.120547 + 0.0875828i −0.646425 0.762977i \(-0.723737\pi\)
0.525878 + 0.850560i \(0.323737\pi\)
\(150\) −2.42064e8 7.44998e8i −0.0390409 0.120156i
\(151\) 3.65822e9 1.12588e10i 0.572630 1.76237i −0.0714828 0.997442i \(-0.522773\pi\)
0.644112 0.764931i \(-0.277227\pi\)
\(152\) 2.74284e9 + 1.99279e9i 0.416778 + 0.302807i
\(153\) −1.11708e10 −1.64806
\(154\) 1.75122e9 3.92032e7i 0.250899 0.00561667i
\(155\) 4.71290e9 0.655836
\(156\) −2.07211e8 1.50548e8i −0.0280125 0.0203523i
\(157\) −3.44228e9 + 1.05943e10i −0.452166 + 1.39163i 0.422263 + 0.906473i \(0.361236\pi\)
−0.874430 + 0.485152i \(0.838764\pi\)
\(158\) −1.12121e9 3.45074e9i −0.143130 0.440510i
\(159\) −2.09344e9 + 1.52097e9i −0.259761 + 0.188727i
\(160\) −8.09647e9 + 5.88243e9i −0.976687 + 0.709605i
\(161\) 1.21222e9 + 3.73082e9i 0.142188 + 0.437610i
\(162\) −1.29862e9 + 3.99673e9i −0.148137 + 0.455918i
\(163\) 6.35653e8 + 4.61829e8i 0.0705303 + 0.0512433i 0.622492 0.782626i \(-0.286120\pi\)
−0.551961 + 0.833870i \(0.686120\pi\)
\(164\) 2.91460e8 0.0314617
\(165\) −2.97878e9 + 2.26778e9i −0.312868 + 0.238190i
\(166\) 1.04307e10 1.06617
\(167\) −1.41244e9 1.02620e9i −0.140523 0.102096i 0.515303 0.857008i \(-0.327679\pi\)
−0.655826 + 0.754912i \(0.727679\pi\)
\(168\) 3.86286e8 1.18887e9i 0.0374125 0.115144i
\(169\) −3.14569e9 9.68143e9i −0.296637 0.912955i
\(170\) −1.35494e10 + 9.84419e9i −1.24422 + 0.903982i
\(171\) −4.07028e9 + 2.95723e9i −0.364034 + 0.264486i
\(172\) 1.39392e9 + 4.29005e9i 0.121440 + 0.373752i
\(173\) 1.14585e9 3.52656e9i 0.0972567 0.299325i −0.890579 0.454829i \(-0.849700\pi\)
0.987835 + 0.155504i \(0.0497002\pi\)
\(174\) 1.31908e9 + 9.58369e8i 0.109094 + 0.0792613i
\(175\) 2.88318e9 0.232381
\(176\) −1.34336e9 9.30800e8i −0.105533 0.0731222i
\(177\) 3.08408e9 0.236181
\(178\) −1.07904e10 7.83972e9i −0.805655 0.585343i
\(179\) 3.96466e9 1.22020e10i 0.288647 0.888365i −0.696634 0.717426i \(-0.745320\pi\)
0.985282 0.170939i \(-0.0546800\pi\)
\(180\) −2.79593e9 8.60498e9i −0.198518 0.610975i
\(181\) −3.56523e9 + 2.59029e9i −0.246907 + 0.179389i −0.704355 0.709848i \(-0.748764\pi\)
0.457448 + 0.889236i \(0.348764\pi\)
\(182\) −6.01528e8 + 4.37036e8i −0.0406382 + 0.0295254i
\(183\) 1.56732e9 + 4.82373e9i 0.103307 + 0.317946i
\(184\) 6.05590e9 1.86381e10i 0.389492 1.19873i
\(185\) 2.20878e10 + 1.60477e10i 1.38637 + 1.00726i
\(186\) 1.73097e9 0.106043
\(187\) 2.50510e10 + 1.73575e10i 1.49809 + 1.03801i
\(188\) −4.04137e9 −0.235949
\(189\) 3.16040e9 + 2.29617e9i 0.180163 + 0.130896i
\(190\) −2.33091e9 + 7.17381e9i −0.129758 + 0.399355i
\(191\) −3.38498e9 1.04179e10i −0.184037 0.566408i 0.815893 0.578203i \(-0.196246\pi\)
−0.999930 + 0.0117944i \(0.996246\pi\)
\(192\) −3.57891e9 + 2.60023e9i −0.190062 + 0.138088i
\(193\) 7.65665e9 5.56288e9i 0.397220 0.288597i −0.371188 0.928558i \(-0.621049\pi\)
0.768408 + 0.639961i \(0.221049\pi\)
\(194\) −4.53908e9 1.39698e10i −0.230070 0.708083i
\(195\) 4.91069e8 1.51135e9i 0.0243213 0.0748532i
\(196\) −8.01002e9 5.81962e9i −0.387687 0.281671i
\(197\) −8.85354e9 −0.418812 −0.209406 0.977829i \(-0.567153\pi\)
−0.209406 + 0.977829i \(0.567153\pi\)
\(198\) 1.03324e10 7.86614e9i 0.477756 0.363721i
\(199\) −1.00560e10 −0.454555 −0.227278 0.973830i \(-0.572982\pi\)
−0.227278 + 0.973830i \(0.572982\pi\)
\(200\) −1.16528e10 8.46622e9i −0.514984 0.374158i
\(201\) −2.94361e9 + 9.05950e9i −0.127203 + 0.391491i
\(202\) 8.13037e9 + 2.50227e10i 0.343581 + 1.05743i
\(203\) −4.85507e9 + 3.52742e9i −0.200661 + 0.145789i
\(204\) 6.30958e9 4.58417e9i 0.255073 0.185321i
\(205\) 5.58813e8 + 1.71985e9i 0.0220991 + 0.0680140i
\(206\) 2.47326e9 7.61191e9i 0.0956901 0.294504i
\(207\) 2.35276e10 + 1.70938e10i 0.890657 + 0.647100i
\(208\) 6.93724e8 0.0256981
\(209\) 1.37228e10 3.07202e8i 0.497491 0.0111369i
\(210\) 2.78117e9 0.0986826
\(211\) −4.00772e10 2.91178e10i −1.39196 1.01132i −0.995647 0.0932007i \(-0.970290\pi\)
−0.396311 0.918116i \(-0.629710\pi\)
\(212\) −5.27235e9 + 1.62266e10i −0.179264 + 0.551718i
\(213\) −5.47840e9 1.68608e10i −0.182367 0.561267i
\(214\) −1.98410e10 + 1.44153e10i −0.646697 + 0.469853i
\(215\) −2.26422e10 + 1.64505e10i −0.722678 + 0.525057i
\(216\) −6.03067e9 1.85605e10i −0.188505 0.580160i
\(217\) −1.96877e9 + 6.05925e9i −0.0602735 + 0.185503i
\(218\) 1.67712e10 + 1.21850e10i 0.502933 + 0.365402i
\(219\) −8.25800e9 −0.242592
\(220\) −7.10070e9 + 2.36415e10i −0.204361 + 0.680414i
\(221\) −1.29365e10 −0.364799
\(222\) 8.11248e9 + 5.89406e9i 0.224164 + 0.162864i
\(223\) 3.79735e9 1.16870e10i 0.102827 0.316470i −0.886387 0.462945i \(-0.846793\pi\)
0.989214 + 0.146475i \(0.0467928\pi\)
\(224\) −4.18066e9 1.28668e10i −0.110950 0.341470i
\(225\) 1.72923e10 1.25636e10i 0.449812 0.326807i
\(226\) −4.93420e9 + 3.58490e9i −0.125814 + 0.0914091i
\(227\) 2.17812e10 + 6.70356e10i 0.544459 + 1.67567i 0.722273 + 0.691608i \(0.243098\pi\)
−0.177814 + 0.984064i \(0.556902\pi\)
\(228\) 1.08544e9 3.34065e9i 0.0266012 0.0818700i
\(229\) −5.29848e10 3.84957e10i −1.27318 0.925023i −0.273860 0.961770i \(-0.588301\pi\)
−0.999325 + 0.0367466i \(0.988301\pi\)
\(230\) 4.36010e10 1.02736
\(231\) −1.67127e9 4.77709e9i −0.0386182 0.110385i
\(232\) 2.99803e10 0.679424
\(233\) 2.14784e10 + 1.56050e10i 0.477420 + 0.346866i 0.800326 0.599565i \(-0.204660\pi\)
−0.322906 + 0.946431i \(0.604660\pi\)
\(234\) −1.70335e9 + 5.24236e9i −0.0371391 + 0.114302i
\(235\) −7.74847e9 2.38473e10i −0.165734 0.510076i
\(236\) 1.64513e10 1.19526e10i 0.345221 0.250818i
\(237\) −8.48106e9 + 6.16185e9i −0.174615 + 0.126866i
\(238\) −6.99630e9 2.15324e10i −0.141342 0.435007i
\(239\) 8.67117e9 2.66871e10i 0.171905 0.529068i −0.827574 0.561357i \(-0.810280\pi\)
0.999479 + 0.0322889i \(0.0102796\pi\)
\(240\) −2.09929e9 1.52523e9i −0.0408435 0.0296745i
\(241\) 9.62715e9 0.183832 0.0919160 0.995767i \(-0.470701\pi\)
0.0919160 + 0.995767i \(0.470701\pi\)
\(242\) −3.53935e10 + 1.58545e9i −0.663367 + 0.0297154i
\(243\) 4.41689e10 0.812622
\(244\) 2.70553e10 + 1.96569e10i 0.488651 + 0.355026i
\(245\) 1.89829e10 5.84234e10i 0.336601 1.03595i
\(246\) 2.05243e8 + 6.31672e8i 0.00357322 + 0.0109972i
\(247\) −4.71366e9 + 3.42468e9i −0.0805791 + 0.0585441i
\(248\) 2.57495e10 1.87081e10i 0.432251 0.314049i
\(249\) −9.31280e9 2.86619e10i −0.153526 0.472506i
\(250\) −6.20265e9 + 1.90898e10i −0.100426 + 0.309080i
\(251\) 5.02946e9 + 3.65412e9i 0.0799815 + 0.0581100i 0.627057 0.778973i \(-0.284259\pi\)
−0.547076 + 0.837083i \(0.684259\pi\)
\(252\) 1.22312e10 0.191058
\(253\) −2.62009e10 7.48915e10i −0.402044 1.14919i
\(254\) 1.44526e9 0.0217868
\(255\) 3.91476e10 + 2.84424e10i 0.579795 + 0.421245i
\(256\) −2.24097e10 + 6.89699e10i −0.326104 + 1.00364i
\(257\) 2.46833e10 + 7.59673e10i 0.352942 + 1.08624i 0.957193 + 0.289450i \(0.0934724\pi\)
−0.604251 + 0.796794i \(0.706528\pi\)
\(258\) −8.31609e9 + 6.04199e9i −0.116850 + 0.0848968i
\(259\) −2.98592e10 + 2.16939e10i −0.412315 + 0.299564i
\(260\) −3.23788e9 9.96517e9i −0.0439421 0.135240i
\(261\) −1.37481e10 + 4.23123e10i −0.183383 + 0.564396i
\(262\) −3.21653e10 2.33694e10i −0.421727 0.306403i
\(263\) −1.32225e11 −1.70417 −0.852086 0.523401i \(-0.824663\pi\)
−0.852086 + 0.523401i \(0.824663\pi\)
\(264\) −7.27287e9 + 2.42147e10i −0.0921485 + 0.306805i
\(265\) −1.05859e11 −1.31862
\(266\) −8.24947e9 5.99359e9i −0.101032 0.0734040i
\(267\) −1.19083e10 + 3.66500e10i −0.143400 + 0.441340i
\(268\) 1.94088e10 + 5.97342e10i 0.229822 + 0.707321i
\(269\) 6.80557e10 4.94454e10i 0.792464 0.575759i −0.116230 0.993222i \(-0.537081\pi\)
0.908694 + 0.417464i \(0.137081\pi\)
\(270\) 3.51271e10 2.55213e10i 0.402258 0.292258i
\(271\) −9.57344e9 2.94640e10i −0.107822 0.331841i 0.882561 0.470199i \(-0.155818\pi\)
−0.990382 + 0.138357i \(0.955818\pi\)
\(272\) −6.52765e9 + 2.00900e10i −0.0723097 + 0.222546i
\(273\) 1.73797e9 + 1.26271e9i 0.0189370 + 0.0137585i
\(274\) −1.95645e10 −0.209696
\(275\) −5.83005e10 + 1.30513e9i −0.614717 + 0.0137612i
\(276\) −2.03038e10 −0.210614
\(277\) 1.08418e11 + 7.87705e10i 1.10648 + 0.803905i 0.982106 0.188330i \(-0.0603076\pi\)
0.124374 + 0.992235i \(0.460308\pi\)
\(278\) 1.67609e10 5.15849e10i 0.168305 0.517989i
\(279\) 1.45954e10 + 4.49201e10i 0.144211 + 0.443836i
\(280\) 4.13721e10 3.00586e10i 0.402250 0.292252i
\(281\) 1.36956e11 9.95041e10i 1.31039 0.952056i 0.310394 0.950608i \(-0.399539\pi\)
0.999999 0.00144810i \(-0.000460944\pi\)
\(282\) −2.84588e9 8.75872e9i −0.0267976 0.0824745i
\(283\) −3.99277e10 + 1.22885e11i −0.370028 + 1.13883i 0.576744 + 0.816925i \(0.304323\pi\)
−0.946772 + 0.321905i \(0.895677\pi\)
\(284\) −9.45688e10 6.87082e10i −0.862611 0.626724i
\(285\) 2.17936e10 0.195672
\(286\) 1.19656e10 9.10953e9i 0.105752 0.0805098i
\(287\) −2.44461e9 −0.0212687
\(288\) −8.11414e10 5.89527e10i −0.694986 0.504937i
\(289\) 8.50817e10 2.61855e11i 0.717457 2.20811i
\(290\) 2.06120e10 + 6.34372e10i 0.171131 + 0.526687i
\(291\) −3.43344e10 + 2.49454e10i −0.280679 + 0.203926i
\(292\) −4.40505e10 + 3.20046e10i −0.354591 + 0.257626i
\(293\) 1.01468e10 + 3.12286e10i 0.0804311 + 0.247541i 0.983184 0.182618i \(-0.0584572\pi\)
−0.902753 + 0.430160i \(0.858457\pi\)
\(294\) 6.97210e9 2.14579e10i 0.0544253 0.167504i
\(295\) 1.02072e11 + 7.41596e10i 0.784706 + 0.570122i
\(296\) 1.84382e11 1.39607
\(297\) −6.49455e10 4.49999e10i −0.484334 0.335589i
\(298\) −1.34699e10 −0.0989440
\(299\) 2.72466e10 + 1.97958e10i 0.197148 + 0.143236i
\(300\) −4.61143e9 + 1.41925e10i −0.0328693 + 0.101161i
\(301\) −1.16914e10 3.59825e10i −0.0820953 0.252663i
\(302\) 1.43903e11 1.04552e11i 0.995493 0.723268i
\(303\) 6.14995e10 4.46820e10i 0.419160 0.304537i
\(304\) 2.93994e9 + 9.04822e9i 0.0197428 + 0.0607620i
\(305\) −6.41184e10 + 1.97336e11i −0.424261 + 1.30574i
\(306\) −1.35789e11 9.86567e10i −0.885359 0.643251i
\(307\) −2.42441e10 −0.155770 −0.0778849 0.996962i \(-0.524817\pi\)
−0.0778849 + 0.996962i \(0.524817\pi\)
\(308\) −2.74290e10 1.90052e10i −0.173673 0.120336i
\(309\) −2.31245e10 −0.144298
\(310\) 5.72888e10 + 4.16228e10i 0.352324 + 0.255978i
\(311\) −7.01181e10 + 2.15801e11i −0.425019 + 1.30807i 0.477957 + 0.878383i \(0.341378\pi\)
−0.902976 + 0.429691i \(0.858622\pi\)
\(312\) −3.31639e9 1.02068e10i −0.0198139 0.0609809i
\(313\) 6.33379e10 4.60177e10i 0.373004 0.271004i −0.385451 0.922728i \(-0.625954\pi\)
0.758456 + 0.651725i \(0.225954\pi\)
\(314\) −1.35409e11 + 9.83801e10i −0.786073 + 0.571116i
\(315\) 2.34507e10 + 7.21738e10i 0.134202 + 0.413031i
\(316\) −2.13596e10 + 6.57382e10i −0.120504 + 0.370873i
\(317\) −1.11252e11 8.08295e10i −0.618789 0.449576i 0.233710 0.972306i \(-0.424913\pi\)
−0.852498 + 0.522730i \(0.824913\pi\)
\(318\) −3.88801e10 −0.213209
\(319\) 9.65770e10 7.35251e10i 0.522174 0.397537i
\(320\) −1.80974e11 −0.964809
\(321\) 5.73256e10 + 4.16495e10i 0.301353 + 0.218946i
\(322\) −1.82139e10 + 5.60568e10i −0.0944175 + 0.290587i
\(323\) −5.48240e10 1.68731e11i −0.280259 0.862549i
\(324\) 6.47680e10 4.70567e10i 0.326519 0.237230i
\(325\) 2.00257e10 1.45495e10i 0.0995661 0.0723390i
\(326\) 3.64812e9 + 1.12278e10i 0.0178892 + 0.0550572i
\(327\) 1.85087e10 5.69638e10i 0.0895179 0.275508i
\(328\) 9.88019e9 + 7.17838e9i 0.0471339 + 0.0342448i
\(329\) 3.38968e10 0.159506
\(330\) −5.62376e10 + 1.25895e9i −0.261044 + 0.00584379i
\(331\) 1.67490e11 0.766943 0.383471 0.923553i \(-0.374728\pi\)
0.383471 + 0.923553i \(0.374728\pi\)
\(332\) −1.60759e11 1.16798e11i −0.726194 0.527611i
\(333\) −8.45521e10 + 2.60225e11i −0.376812 + 1.15971i
\(334\) −8.10625e9 2.49485e10i −0.0356419 0.109695i
\(335\) −3.15267e11 + 2.29055e11i −1.36766 + 0.993661i
\(336\) 2.83791e9 2.06186e9i 0.0121471 0.00882536i
\(337\) −2.77105e10 8.52840e10i −0.117033 0.360191i 0.875332 0.483522i \(-0.160643\pi\)
−0.992366 + 0.123330i \(0.960643\pi\)
\(338\) 4.72650e10 1.45467e11i 0.196977 0.606231i
\(339\) 1.42562e10 + 1.03577e10i 0.0586278 + 0.0425956i
\(340\) 3.19055e11 1.29482
\(341\) 3.70674e10 1.23414e11i 0.148456 0.494278i
\(342\) −7.55946e10 −0.298795
\(343\) 1.45562e11 + 1.05757e11i 0.567840 + 0.412560i
\(344\) −5.84072e10 + 1.79759e11i −0.224881 + 0.692113i
\(345\) −3.89283e10 1.19809e11i −0.147938 0.455306i
\(346\) 4.50740e10 3.27482e10i 0.169077 0.122841i
\(347\) 1.15697e11 8.40586e10i 0.428389 0.311243i −0.352615 0.935768i \(-0.614708\pi\)
0.781005 + 0.624525i \(0.214708\pi\)
\(348\) −9.59845e9 2.95410e10i −0.0350828 0.107974i
\(349\) −8.98715e10 + 2.76596e11i −0.324270 + 0.998002i 0.647498 + 0.762067i \(0.275815\pi\)
−0.971769 + 0.235935i \(0.924185\pi\)
\(350\) 3.50473e10 + 2.54633e10i 0.124838 + 0.0907004i
\(351\) 3.35383e10 0.117940
\(352\) 9.03609e10 + 2.58284e11i 0.313717 + 0.896718i
\(353\) 1.21750e10 0.0417331 0.0208666 0.999782i \(-0.493357\pi\)
0.0208666 + 0.999782i \(0.493357\pi\)
\(354\) 3.74893e10 + 2.72376e10i 0.126880 + 0.0921835i
\(355\) 2.24118e11 6.89765e11i 0.748945 2.30501i
\(356\) 7.85179e10 + 2.41653e11i 0.259086 + 0.797384i
\(357\) −5.29212e10 + 3.84495e10i −0.172434 + 0.125281i
\(358\) 1.55957e11 1.13310e11i 0.501802 0.364580i
\(359\) −7.22049e10 2.22224e11i −0.229425 0.706099i −0.997812 0.0661129i \(-0.978940\pi\)
0.768387 0.639986i \(-0.221060\pi\)
\(360\) 1.17153e11 3.60561e11i 0.367615 1.13140i
\(361\) 1.96416e11 + 1.42704e11i 0.608687 + 0.442237i
\(362\) −6.62146e10 −0.202659
\(363\) 3.59569e10 + 9.58403e10i 0.108693 + 0.289713i
\(364\) 1.41646e10 0.0422909
\(365\) −2.73310e11 1.98571e11i −0.806005 0.585597i
\(366\) −2.35496e10 + 7.24782e10i −0.0685991 + 0.211126i
\(367\) −1.31692e11 4.05306e11i −0.378933 1.16624i −0.940787 0.338999i \(-0.889912\pi\)
0.561854 0.827237i \(-0.310088\pi\)
\(368\) 4.44905e10 3.23243e10i 0.126460 0.0918784i
\(369\) −1.46619e10 + 1.06525e10i −0.0411690 + 0.0299110i
\(370\) 1.26766e11 + 3.90145e11i 0.351637 + 1.08223i
\(371\) 4.42216e10 1.36100e11i 0.121186 0.372971i
\(372\) −2.66779e10 1.93826e10i −0.0722284 0.0524770i
\(373\) −5.21244e11 −1.39428 −0.697142 0.716933i \(-0.745545\pi\)
−0.697142 + 0.716933i \(0.745545\pi\)
\(374\) 1.51218e11 + 4.32236e11i 0.399652 + 1.14235i
\(375\) 5.79937e10 0.151440
\(376\) −1.36998e11 9.95350e10i −0.353484 0.256821i
\(377\) −1.59212e10 + 4.90006e10i −0.0405920 + 0.124929i
\(378\) 1.81381e10 + 5.58233e10i 0.0456960 + 0.140638i
\(379\) −4.30844e11 + 3.13026e11i −1.07261 + 0.779300i −0.976380 0.216059i \(-0.930680\pi\)
−0.0962336 + 0.995359i \(0.530680\pi\)
\(380\) 1.16254e11 8.44631e10i 0.286009 0.207798i
\(381\) −1.29037e9 3.97134e9i −0.00313727 0.00965551i
\(382\) 5.08604e10 1.56532e11i 0.122207 0.376113i
\(383\) 5.18093e11 + 3.76417e11i 1.23031 + 0.893870i 0.996913 0.0785124i \(-0.0250170\pi\)
0.233393 + 0.972382i \(0.425017\pi\)
\(384\) 5.87832e10 0.137963
\(385\) 5.95567e10 1.98292e11i 0.138152 0.459972i
\(386\) 1.42202e11 0.326034
\(387\) −2.26916e11 1.64864e11i −0.514240 0.373617i
\(388\) −8.64714e10 + 2.66132e11i −0.193700 + 0.596147i
\(389\) 1.09525e11 + 3.37083e11i 0.242515 + 0.746386i 0.996035 + 0.0889604i \(0.0283545\pi\)
−0.753520 + 0.657425i \(0.771646\pi\)
\(390\) 1.93171e10 1.40347e10i 0.0422816 0.0307193i
\(391\) −8.29658e11 + 6.02782e11i −1.79516 + 1.30426i
\(392\) −1.28200e11 3.94558e11i −0.274220 0.843962i
\(393\) −3.54975e10 + 1.09250e11i −0.0750640 + 0.231023i
\(394\) −1.07621e11 7.81915e10i −0.224991 0.163466i
\(395\) −4.28861e11 −0.886399
\(396\) −2.47325e11 + 5.53667e9i −0.505405 + 0.0113141i
\(397\) 7.44742e10 0.150470 0.0752348 0.997166i \(-0.476029\pi\)
0.0752348 + 0.997166i \(0.476029\pi\)
\(398\) −1.22238e11 8.88113e10i −0.244193 0.177417i
\(399\) −9.10410e9 + 2.80195e10i −0.0179829 + 0.0553456i
\(400\) −1.24901e10 3.84407e10i −0.0243948 0.0750795i
\(401\) 1.00689e11 7.31550e10i 0.194461 0.141284i −0.486294 0.873795i \(-0.661652\pi\)
0.680755 + 0.732511i \(0.261652\pi\)
\(402\) −1.15792e11 + 8.41281e10i −0.221138 + 0.160666i
\(403\) 1.69025e10 + 5.20206e10i 0.0319212 + 0.0982433i
\(404\) 1.54887e11 4.76693e11i 0.289267 0.890272i
\(405\) 4.01851e11 + 2.91962e11i 0.742195 + 0.539236i
\(406\) −9.01701e10 −0.164701
\(407\) 5.93958e11 4.52187e11i 1.07295 0.816851i
\(408\) 3.26792e11 0.583848
\(409\) 2.96191e11 + 2.15196e11i 0.523381 + 0.380258i 0.817876 0.575395i \(-0.195152\pi\)
−0.294495 + 0.955653i \(0.595152\pi\)
\(410\) −8.39636e9 + 2.58413e10i −0.0146745 + 0.0451635i
\(411\) 1.74677e10 + 5.37602e10i 0.0301959 + 0.0929335i
\(412\) −1.23353e11 + 8.96212e10i −0.210917 + 0.153240i
\(413\) −1.37985e11 + 1.00252e11i −0.233376 + 0.169557i
\(414\) 1.35029e11 + 4.15576e11i 0.225904 + 0.695262i
\(415\) 3.80981e11 1.17254e12i 0.630503 1.94049i
\(416\) −9.39673e10 6.82713e10i −0.153836 0.111768i
\(417\) −1.56712e11 −0.253799
\(418\) 1.69525e11 + 1.17461e11i 0.271606 + 0.188192i
\(419\) 8.34488e11 1.32269 0.661343 0.750083i \(-0.269987\pi\)
0.661343 + 0.750083i \(0.269987\pi\)
\(420\) −4.28637e10 3.11423e10i −0.0672153 0.0488348i
\(421\) 2.48884e11 7.65986e11i 0.386125 1.18837i −0.549537 0.835470i \(-0.685196\pi\)
0.935661 0.352900i \(-0.114804\pi\)
\(422\) −2.30010e11 7.07897e11i −0.353053 1.08659i
\(423\) 2.03300e11 1.47706e11i 0.308750 0.224320i
\(424\) −5.78373e11 + 4.20212e11i −0.869084 + 0.631426i
\(425\) 2.32916e11 + 7.16841e11i 0.346297 + 1.06579i
\(426\) 8.23148e10 2.53339e11i 0.121097 0.372700i
\(427\) −2.26925e11 1.64871e11i −0.330337 0.240004i
\(428\) 4.67207e11 0.672996
\(429\) −3.57148e10 2.47463e10i −0.0509085 0.0352739i
\(430\) −4.20518e11 −0.593167
\(431\) −6.69709e10 4.86572e10i −0.0934842 0.0679203i 0.540061 0.841626i \(-0.318401\pi\)
−0.633545 + 0.773705i \(0.718401\pi\)
\(432\) 1.69231e10 5.20839e10i 0.0233778 0.0719494i
\(433\) 2.00157e11 + 6.16020e11i 0.273637 + 0.842169i 0.989577 + 0.144006i \(0.0459986\pi\)
−0.715940 + 0.698162i \(0.754001\pi\)
\(434\) −7.74452e10 + 5.62672e10i −0.104783 + 0.0761293i
\(435\) 1.55913e11 1.13277e11i 0.208776 0.151684i
\(436\) −1.22038e11 3.75593e11i −0.161735 0.497769i
\(437\) −1.42727e11 + 4.39269e11i −0.187215 + 0.576188i
\(438\) −1.00382e11 7.29319e10i −0.130324 0.0946856i
\(439\) 7.54541e9 0.00969600 0.00484800 0.999988i \(-0.498457\pi\)
0.00484800 + 0.999988i \(0.498457\pi\)
\(440\) −8.22973e11 + 6.26538e11i −1.04676 + 0.796912i
\(441\) 6.15641e11 0.775093
\(442\) −1.57253e11 1.14251e11i −0.195975 0.142384i
\(443\) −6.62622e9 + 2.03934e10i −0.00817427 + 0.0251578i −0.955060 0.296411i \(-0.904210\pi\)
0.946886 + 0.321569i \(0.104210\pi\)
\(444\) −5.90314e10 1.81680e11i −0.0720875 0.221862i
\(445\) −1.27541e12 + 9.26638e11i −1.54180 + 1.12019i
\(446\) 1.49376e11 1.08528e11i 0.178761 0.129877i
\(447\) 1.20263e10 + 3.70131e10i 0.0142478 + 0.0438502i
\(448\) 7.56003e10 2.32674e11i 0.0886692 0.272896i
\(449\) 7.57101e11 + 5.50066e11i 0.879114 + 0.638714i 0.933017 0.359833i \(-0.117166\pi\)
−0.0539030 + 0.998546i \(0.517166\pi\)
\(450\) 3.21158e11 0.369201
\(451\) 4.94321e10 1.10660e9i 0.0562619 0.00125949i
\(452\) 1.16189e11 0.130930
\(453\) −4.15773e11 3.02076e11i −0.463889 0.337035i
\(454\) −3.27270e11 + 1.00723e12i −0.361538 + 1.11270i
\(455\) 2.71575e10 + 8.35823e10i 0.0297057 + 0.0914246i
\(456\) 1.19072e11 8.65111e10i 0.128964 0.0936980i
\(457\) 3.20996e11 2.33217e11i 0.344252 0.250114i −0.402202 0.915551i \(-0.631755\pi\)
0.746454 + 0.665437i \(0.231755\pi\)
\(458\) −3.04089e11 9.35888e11i −0.322928 0.993870i
\(459\) −3.15581e11 + 9.71260e11i −0.331860 + 1.02136i
\(460\) −6.71985e11 4.88225e11i −0.699760 0.508405i
\(461\) −1.52451e12 −1.57209 −0.786044 0.618171i \(-0.787874\pi\)
−0.786044 + 0.618171i \(0.787874\pi\)
\(462\) 2.18742e10 7.28292e10i 0.0223379 0.0743732i
\(463\) −7.74822e11 −0.783587 −0.391794 0.920053i \(-0.628145\pi\)
−0.391794 + 0.920053i \(0.628145\pi\)
\(464\) 6.80625e10 + 4.94503e10i 0.0681675 + 0.0495266i
\(465\) 6.32238e10 1.94583e11i 0.0627108 0.193004i
\(466\) 1.23268e11 + 3.79380e11i 0.121092 + 0.372682i
\(467\) 1.04790e12 7.61346e11i 1.01952 0.740723i 0.0533339 0.998577i \(-0.483015\pi\)
0.966184 + 0.257854i \(0.0830152\pi\)
\(468\) 8.49538e10 6.17226e10i 0.0818609 0.0594754i
\(469\) −1.62790e11 5.01017e11i −0.155364 0.478162i
\(470\) 1.16423e11 3.58314e11i 0.110053 0.338707i
\(471\) 3.91230e11 + 2.84245e11i 0.366301 + 0.266133i
\(472\) 8.52064e11 0.790193
\(473\) 2.52699e11 + 7.22305e11i 0.232128 + 0.663507i
\(474\) −1.57513e11 −0.143323
\(475\) 2.74636e11 + 1.99535e11i 0.247534 + 0.179844i
\(476\) −1.33283e11 + 4.10201e11i −0.118999 + 0.366240i
\(477\) −3.27836e11 1.00897e12i −0.289950 0.892375i
\(478\) 3.41097e11 2.47821e11i 0.298849 0.217127i
\(479\) 1.00989e12 7.33728e11i 0.876525 0.636833i −0.0558048 0.998442i \(-0.517772\pi\)
0.932330 + 0.361609i \(0.117772\pi\)
\(480\) 1.34255e11 + 4.13195e11i 0.115437 + 0.355279i
\(481\) −9.79172e10 + 3.01358e11i −0.0834077 + 0.256702i
\(482\) 1.17025e11 + 8.50239e10i 0.0987571 + 0.0717512i
\(483\) 1.70297e11 0.142379
\(484\) 5.63242e11 + 3.71886e11i 0.466542 + 0.308039i
\(485\) −1.73618e12 −1.42481
\(486\) 5.36907e11 + 3.90085e11i 0.436552 + 0.317173i
\(487\) 3.31303e10 1.01964e11i 0.0266897 0.0821426i −0.936824 0.349800i \(-0.886250\pi\)
0.963514 + 0.267657i \(0.0862495\pi\)
\(488\) 4.33018e11 + 1.33269e12i 0.345634 + 1.06375i
\(489\) 2.75950e10 2.00489e10i 0.0218243 0.0158563i
\(490\) 7.46728e11 5.42530e11i 0.585167 0.425149i
\(491\) −1.27254e11 3.91647e11i −0.0988108 0.304108i 0.889417 0.457096i \(-0.151110\pi\)
−0.988228 + 0.152988i \(0.951110\pi\)
\(492\) 3.90996e9 1.20336e10i 0.00300836 0.00925877i
\(493\) −1.26923e12 9.22149e11i −0.967673 0.703056i
\(494\) −8.75438e10 −0.0661384
\(495\) −5.06864e11 1.44880e12i −0.379462 1.08464i
\(496\) 8.93152e10 0.0662609
\(497\) 7.93190e11 + 5.76286e11i 0.583141 + 0.423677i
\(498\) 1.39928e11 4.30654e11i 0.101947 0.313759i
\(499\) −2.78482e11 8.57078e11i −0.201068 0.618825i −0.999852 0.0172065i \(-0.994523\pi\)
0.798783 0.601619i \(-0.205477\pi\)
\(500\) 3.09355e11 2.24760e11i 0.221357 0.160825i
\(501\) −6.13171e10 + 4.45495e10i −0.0434822 + 0.0315917i
\(502\) 2.88649e10 + 8.88371e10i 0.0202863 + 0.0624349i
\(503\) −6.24171e11 + 1.92100e12i −0.434758 + 1.33805i 0.458576 + 0.888655i \(0.348360\pi\)
−0.893334 + 0.449393i \(0.851640\pi\)
\(504\) 4.14624e11 + 3.01242e11i 0.286231 + 0.207959i
\(505\) 3.10983e12 2.12778
\(506\) 3.42926e11 1.14176e12i 0.232554 0.774279i
\(507\) −4.41920e11 −0.297035
\(508\) −2.22745e10 1.61834e10i −0.0148396 0.0107816i
\(509\) 1.21500e10 3.73939e10i 0.00802319 0.0246928i −0.946965 0.321337i \(-0.895868\pi\)
0.954988 + 0.296645i \(0.0958677\pi\)
\(510\) 2.24675e11 + 6.91477e11i 0.147058 + 0.452597i
\(511\) 3.69471e11 2.68437e11i 0.239710 0.174160i
\(512\) −3.20646e11 + 2.32963e11i −0.206210 + 0.149821i
\(513\) 1.42133e11 + 4.37440e11i 0.0906079 + 0.278862i
\(514\) −3.70874e11 + 1.14143e12i −0.234365 + 0.721301i
\(515\) −7.65340e11 5.56052e11i −0.479426 0.348324i
\(516\) 1.95824e11 0.121602
\(517\) −6.85422e11 + 1.53440e10i −0.421940 + 0.00944563i
\(518\) −5.54554e11 −0.338423
\(519\) −1.30230e11 9.46180e10i −0.0787879 0.0572428i
\(520\) 1.35672e11 4.17554e11i 0.0813718 0.250437i
\(521\) −5.72134e11 1.76085e12i −0.340195 1.04701i −0.964106 0.265517i \(-0.914457\pi\)
0.623911 0.781495i \(-0.285543\pi\)
\(522\) −5.40807e11 + 3.92919e11i −0.318805 + 0.231625i
\(523\) −4.36478e11 + 3.17120e11i −0.255097 + 0.185339i −0.707983 0.706230i \(-0.750395\pi\)
0.452886 + 0.891569i \(0.350395\pi\)
\(524\) 2.34054e11 + 7.20345e11i 0.135621 + 0.417397i
\(525\) 3.86781e10 1.19039e11i 0.0222202 0.0683868i
\(526\) −1.60730e12 1.16777e12i −0.915505 0.665153i
\(527\) −1.66555e12 −0.940609
\(528\) −5.64516e10 + 4.29772e10i −0.0316099 + 0.0240650i
\(529\) 8.68639e11 0.482268
\(530\) −1.28679e12 9.34910e11i −0.708382 0.514669i
\(531\) −3.90731e11 + 1.20255e12i −0.213281 + 0.656412i
\(532\) 6.00283e10 + 1.84748e11i 0.0324903 + 0.0999948i
\(533\) −1.69794e10 + 1.23363e10i −0.00911278 + 0.00662082i
\(534\) −4.68435e11 + 3.40338e11i −0.249295 + 0.181124i
\(535\) 8.95771e11 + 2.75690e12i 0.472721 + 1.45489i
\(536\) −8.13256e11 + 2.50294e12i −0.425584 + 1.30981i
\(537\) −4.50601e11 3.27381e11i −0.233834 0.169890i
\(538\) 1.26395e12 0.650446
\(539\) −1.38060e12 9.56603e11i −0.704563 0.488183i
\(540\) −8.27159e11 −0.418617
\(541\) 1.87360e12 + 1.36125e12i 0.940347 + 0.683202i 0.948504 0.316765i \(-0.102597\pi\)
−0.00815706 + 0.999967i \(0.502597\pi\)
\(542\) 1.43844e11 4.42707e11i 0.0715971 0.220353i
\(543\) 5.91184e10 + 1.81948e11i 0.0291825 + 0.0898146i
\(544\) 2.86131e12 2.07886e12i 1.40078 1.01773i
\(545\) 1.98232e12 1.44024e12i 0.962475 0.699279i
\(546\) 9.97450e9 + 3.06984e10i 0.00480313 + 0.0147825i
\(547\) −7.07088e11 + 2.17619e12i −0.337700 + 1.03933i 0.627677 + 0.778474i \(0.284006\pi\)
−0.965377 + 0.260859i \(0.915994\pi\)
\(548\) 3.01530e11 + 2.19074e11i 0.142830 + 0.103772i
\(549\) −2.07944e12 −0.976948
\(550\) −7.20213e11 4.99026e11i −0.335605 0.232536i
\(551\) −7.06586e11 −0.326575
\(552\) −6.88278e11 5.00063e11i −0.315528 0.229245i
\(553\) 1.79153e11 5.51375e11i 0.0814630 0.250717i
\(554\) 6.22231e11 + 1.91503e12i 0.280645 + 0.863737i
\(555\) 9.58878e11 6.96665e11i 0.428988 0.311678i
\(556\) −8.35946e11 + 6.07351e11i −0.370973 + 0.269527i
\(557\) −7.72790e11 2.37840e12i −0.340183 1.04698i −0.964112 0.265496i \(-0.914464\pi\)
0.623929 0.781481i \(-0.285536\pi\)
\(558\) −2.19301e11 + 6.74940e11i −0.0957607 + 0.294721i
\(559\) −2.62784e11 1.90924e11i −0.113827 0.0827004i
\(560\) 1.43504e11 0.0616620
\(561\) 1.05271e12 8.01438e11i 0.448719 0.341615i
\(562\) 2.54359e12 1.07556
\(563\) 2.77674e12 + 2.01742e12i 1.16479 + 0.846268i 0.990376 0.138405i \(-0.0441974\pi\)
0.174412 + 0.984673i \(0.444197\pi\)
\(564\) −5.42153e10 + 1.66857e11i −0.0225614 + 0.0694368i
\(565\) 2.22767e11 + 6.85606e11i 0.0919671 + 0.283046i
\(566\) −1.57063e12 + 1.14113e12i −0.643279 + 0.467370i
\(567\) −5.43238e11 + 3.94686e11i −0.220733 + 0.160372i
\(568\) −1.51356e12 4.65827e12i −0.610145 1.87783i
\(569\) 1.16745e12 3.59305e12i 0.466911 1.43700i −0.389652 0.920962i \(-0.627405\pi\)
0.856563 0.516042i \(-0.172595\pi\)
\(570\) 2.64918e11 + 1.92474e11i 0.105117 + 0.0763723i
\(571\) 2.35867e12 0.928550 0.464275 0.885691i \(-0.346315\pi\)
0.464275 + 0.885691i \(0.346315\pi\)
\(572\) −2.86420e11 + 6.41185e9i −0.111872 + 0.00250438i
\(573\) −4.75536e11 −0.184284
\(574\) −2.97160e10 2.15900e10i −0.0114258 0.00830135i
\(575\) 6.06366e11 1.86620e12i 0.231329 0.711956i
\(576\) −5.60461e11 1.72492e12i −0.212151 0.652933i
\(577\) 7.63828e11 5.54953e11i 0.286883 0.208432i −0.435031 0.900415i \(-0.643263\pi\)
0.721914 + 0.691983i \(0.243263\pi\)
\(578\) 3.34685e12 2.43163e12i 1.24727 0.906195i
\(579\) −1.26962e11 3.90749e11i −0.0469484 0.144492i
\(580\) 3.92667e11 1.20851e12i 0.144078 0.443427i
\(581\) 1.34835e12 + 9.79636e11i 0.490921 + 0.356675i
\(582\) −6.37670e11 −0.230379
\(583\) −8.32590e11 + 2.77208e12i −0.298485 + 0.993794i
\(584\) −2.28151e12 −0.811640
\(585\) 5.27094e11 + 3.82956e11i 0.186074 + 0.135191i
\(586\) −1.52459e11 + 4.69220e11i −0.0534089 + 0.164376i
\(587\) 1.45900e12 + 4.49035e12i 0.507207 + 1.56102i 0.797028 + 0.603942i \(0.206404\pi\)
−0.289822 + 0.957081i \(0.593596\pi\)
\(588\) −3.47731e11 + 2.52642e11i −0.119963 + 0.0871579i
\(589\) −6.06872e11 + 4.40918e11i −0.207768 + 0.150952i
\(590\) 5.85808e11 + 1.80293e12i 0.199031 + 0.612555i
\(591\) −1.18771e11 + 3.65539e11i −0.0400466 + 0.123251i
\(592\) 4.18591e11 + 3.04124e11i 0.140069 + 0.101766i
\(593\) −2.28230e12 −0.757925 −0.378962 0.925412i \(-0.623719\pi\)
−0.378962 + 0.925412i \(0.623719\pi\)
\(594\) −3.92037e11 1.12058e12i −0.129208 0.369322i
\(595\) −2.67606e12 −0.875325
\(596\) 2.07599e11 + 1.50830e11i 0.0673934 + 0.0489641i
\(597\) −1.34902e11 + 4.15186e11i −0.0434644 + 0.133770i
\(598\) 1.56373e11 + 4.81265e11i 0.0500041 + 0.153897i
\(599\) −5.84457e11 + 4.24633e11i −0.185495 + 0.134770i −0.676657 0.736298i \(-0.736572\pi\)
0.491162 + 0.871068i \(0.336572\pi\)
\(600\) −5.05870e11 + 3.67536e11i −0.159352 + 0.115776i
\(601\) 5.54294e11 + 1.70594e12i 0.173303 + 0.533371i 0.999552 0.0299341i \(-0.00952973\pi\)
−0.826249 + 0.563305i \(0.809530\pi\)
\(602\) 1.75668e11 5.40650e11i 0.0545140 0.167777i
\(603\) −3.15955e12 2.29555e12i −0.973191 0.707064i
\(604\) −3.38857e12 −1.03598
\(605\) −1.11453e12 + 4.03659e12i −0.338214 + 1.22494i
\(606\) 1.14219e12 0.344042
\(607\) 2.57519e11 + 1.87099e11i 0.0769946 + 0.0559399i 0.625617 0.780131i \(-0.284847\pi\)
−0.548622 + 0.836070i \(0.684847\pi\)
\(608\) 4.92234e11 1.51494e12i 0.146085 0.449604i
\(609\) 8.05065e10 + 2.47773e11i 0.0237166 + 0.0729923i
\(610\) −2.52221e12 + 1.83250e12i −0.737561 + 0.535869i
\(611\) 2.35436e11 1.71054e11i 0.0683419 0.0496533i
\(612\) 9.88087e11 + 3.04102e12i 0.284717 + 0.876270i
\(613\) 9.72591e11 2.99333e12i 0.278201 0.856213i −0.710154 0.704046i \(-0.751375\pi\)
0.988355 0.152167i \(-0.0486252\pi\)
\(614\) −2.94705e11 2.14116e11i −0.0836817 0.0607983i
\(615\) 7.85045e10 0.0221287
\(616\) −4.61735e11 1.31981e12i −0.129205 0.369315i
\(617\) 2.45770e12 0.682726 0.341363 0.939932i \(-0.389111\pi\)
0.341363 + 0.939932i \(0.389111\pi\)
\(618\) −2.81096e11 2.04228e11i −0.0775188 0.0563207i
\(619\) −5.62964e11 + 1.73263e12i −0.154125 + 0.474348i −0.998071 0.0620801i \(-0.980227\pi\)
0.843946 + 0.536428i \(0.180227\pi\)
\(620\) −4.16869e11 1.28299e12i −0.113302 0.348707i
\(621\) 2.15091e12 1.56273e12i 0.580377 0.421669i
\(622\) −2.75823e12 + 2.00397e12i −0.738879 + 0.536827i
\(623\) −6.58565e11 2.02685e12i −0.175147 0.539046i
\(624\) 9.30635e9 2.86420e10i 0.00245725 0.00756263i
\(625\) 3.81697e12 + 2.77319e12i 1.00060 + 0.726976i
\(626\) 1.17633e12 0.306158
\(627\) 1.71409e11 5.70700e11i 0.0442925 0.147470i
\(628\) 3.18855e12 0.818041
\(629\) −7.80588e12 5.67130e12i −1.98835 1.44462i
\(630\) −3.52355e11 + 1.08444e12i −0.0891143 + 0.274266i
\(631\) −8.34341e11 2.56784e12i −0.209513 0.644816i −0.999498 0.0316888i \(-0.989911\pi\)
0.789984 0.613127i \(-0.210089\pi\)
\(632\) −2.34313e12 + 1.70239e12i −0.584212 + 0.424455i
\(633\) −1.73983e12 + 1.26406e12i −0.430716 + 0.312934i
\(634\) −6.38496e11 1.96509e12i −0.156948 0.483037i
\(635\) 5.27882e10 1.62465e11i 0.0128841 0.0396533i
\(636\) 5.99225e11 + 4.35363e11i 0.145222 + 0.105510i
\(637\) 7.12955e11 0.171567
\(638\) 1.82332e12 4.08171e10i 0.435681 0.00975325i
\(639\) 7.26845e12 1.72460
\(640\) 1.94551e12 + 1.41350e12i 0.458379 + 0.333032i
\(641\) −1.52582e10 + 4.69600e10i −0.00356979 + 0.0109867i −0.952826 0.303518i \(-0.901839\pi\)
0.949256 + 0.314505i \(0.101839\pi\)
\(642\) 3.29001e11 + 1.01256e12i 0.0764346 + 0.235242i
\(643\) 6.56275e11 4.76812e11i 0.151404 0.110001i −0.509504 0.860468i \(-0.670171\pi\)
0.660908 + 0.750467i \(0.270171\pi\)
\(644\) 9.08415e11 6.60002e11i 0.208112 0.151202i
\(645\) 3.75451e11 + 1.15552e12i 0.0854151 + 0.262881i
\(646\) 8.23750e11 2.53524e12i 0.186101 0.572760i
\(647\) −7.81463e11 5.67766e11i −0.175323 0.127380i 0.496663 0.867944i \(-0.334559\pi\)
−0.671986 + 0.740564i \(0.734559\pi\)
\(648\) 3.35453e12 0.747384
\(649\) 2.74479e12 2.08964e12i 0.607306 0.462349i
\(650\) 3.71923e11 0.0817228
\(651\) 2.23759e11 + 1.62571e11i 0.0488277 + 0.0354754i
\(652\) 6.94983e10 2.13894e11i 0.0150612 0.0463536i
\(653\) 1.01261e11 + 3.11650e11i 0.0217938 + 0.0670745i 0.961362 0.275288i \(-0.0887731\pi\)
−0.939568 + 0.342362i \(0.888773\pi\)
\(654\) 7.28072e11 5.28975e11i 0.155623 0.113067i
\(655\) −3.80186e12 + 2.76222e12i −0.807069 + 0.586370i
\(656\) 1.05902e10 + 3.25933e10i 0.00223273 + 0.00687164i
\(657\) 1.04623e12 3.21997e12i 0.219070 0.674229i
\(658\) 4.12041e11 + 2.99365e11i 0.0856888 + 0.0622565i
\(659\) 2.05454e12 0.424355 0.212178 0.977231i \(-0.431944\pi\)
0.212178 + 0.977231i \(0.431944\pi\)
\(660\) 8.80838e11 + 6.10321e11i 0.180696 + 0.125202i
\(661\) −2.31093e12 −0.470848 −0.235424 0.971893i \(-0.575648\pi\)
−0.235424 + 0.971893i \(0.575648\pi\)
\(662\) 2.03597e12 + 1.47922e12i 0.412012 + 0.299344i
\(663\) −1.73545e11 + 5.34115e11i −0.0348819 + 0.107355i
\(664\) −2.57293e12 7.91865e12i −0.513654 1.58087i
\(665\) −9.75070e11 + 7.08430e11i −0.193347 + 0.140475i
\(666\) −3.32601e12 + 2.41649e12i −0.655073 + 0.475939i
\(667\) 1.26212e12 + 3.88440e12i 0.246907 + 0.759903i
\(668\) −1.54428e11 + 4.75279e11i −0.0300076 + 0.0923538i
\(669\) −4.31585e11 3.13565e11i −0.0833006 0.0605215i
\(670\) −5.85525e12 −1.12256
\(671\) 4.66325e12 + 3.23111e12i 0.888050 + 0.615318i
\(672\) −5.87318e11 −0.111099
\(673\) −5.50807e12 4.00185e12i −1.03498 0.751956i −0.0656798 0.997841i \(-0.520922\pi\)
−0.969299 + 0.245885i \(0.920922\pi\)
\(674\) 4.16359e11 1.28142e12i 0.0777138 0.239179i
\(675\) −6.03841e11 1.85843e12i −0.111958 0.344571i
\(676\) −2.35733e12 + 1.71270e12i −0.434170 + 0.315443i
\(677\) −6.90131e11 + 5.01410e11i −0.126265 + 0.0917368i −0.649125 0.760682i \(-0.724865\pi\)
0.522860 + 0.852418i \(0.324865\pi\)
\(678\) 8.18185e10 + 2.51811e11i 0.0148702 + 0.0457659i
\(679\) 7.25274e11 2.23216e12i 0.130945 0.403007i
\(680\) 1.08156e13 + 7.85802e12i 1.93982 + 1.40936i
\(681\) 3.05992e12 0.545190
\(682\) 1.54054e12 1.17283e12i 0.272673 0.207589i
\(683\) −7.87486e12 −1.38468 −0.692341 0.721571i \(-0.743420\pi\)
−0.692341 + 0.721571i \(0.743420\pi\)
\(684\) 1.16507e12 + 8.46475e11i 0.203517 + 0.147864i
\(685\) −7.14595e11 + 2.19930e12i −0.124009 + 0.381660i
\(686\) 8.35407e11 + 2.57112e12i 0.144026 + 0.443265i
\(687\) −2.30018e12 + 1.67118e12i −0.393964 + 0.286231i
\(688\) −4.29097e11 + 3.11757e11i −0.0730142 + 0.0530479i
\(689\) −3.79656e11 1.16846e12i −0.0641807 0.197528i
\(690\) 5.84911e11 1.80017e12i 0.0982356 0.302338i
\(691\) −1.86173e12 1.35263e12i −0.310646 0.225698i 0.421528 0.906816i \(-0.361494\pi\)
−0.732174 + 0.681118i \(0.761494\pi\)
\(692\) −1.06139e12 −0.175953
\(693\) 2.07443e12 4.64385e10i 0.341663 0.00764854i
\(694\) 2.14876e12 0.351617
\(695\) −5.18661e12 3.76829e12i −0.843241 0.612650i
\(696\) 4.02188e11 1.23781e12i 0.0649663 0.199946i
\(697\) −1.97486e11 6.07799e11i −0.0316948 0.0975466i
\(698\) −3.53526e12 + 2.56852e12i −0.563731 + 0.409575i
\(699\) 9.32421e11 6.77444e11i 0.147729 0.107331i
\(700\) −2.55026e11 7.84888e11i −0.0401460 0.123557i
\(701\) 1.43575e12 4.41880e12i 0.224569 0.691151i −0.773767 0.633471i \(-0.781630\pi\)
0.998335 0.0576800i \(-0.0183703\pi\)
\(702\) 4.07684e11 + 2.96200e11i 0.0633587 + 0.0460328i
\(703\) −4.34557e12 −0.671039
\(704\) −1.42338e12 + 4.73909e12i −0.218395 + 0.727139i
\(705\) −1.08854e12 −0.165956
\(706\) 1.47996e11 + 1.07525e11i 0.0224196 + 0.0162888i
\(707\) −1.29911e12 + 3.99824e12i −0.195550 + 0.601840i
\(708\) −2.72795e11 8.39577e11i −0.0408025 0.125577i
\(709\) −7.86860e12 + 5.71687e12i −1.16947 + 0.849670i −0.990945 0.134265i \(-0.957133\pi\)
−0.178525 + 0.983935i \(0.557133\pi\)
\(710\) 8.81611e12 6.40528e12i 1.30201 0.945965i
\(711\) −1.32814e12 4.08761e12i −0.194909 0.599869i
\(712\) −3.29001e12 + 1.01256e13i −0.479774 + 1.47659i
\(713\) 3.50792e12 + 2.54866e12i 0.508332 + 0.369325i
\(714\) −9.82871e11 −0.141532
\(715\) −5.86984e11 1.67781e12i −0.0839941 0.240086i
\(716\) −3.67242e12 −0.522209
\(717\) −9.85516e11 7.16019e11i −0.139260 0.101179i
\(718\) 1.08490e12 3.33899e12i 0.152346 0.468872i
\(719\) −2.64421e11 8.13804e11i −0.0368991 0.113564i 0.930910 0.365248i \(-0.119016\pi\)
−0.967810 + 0.251684i \(0.919016\pi\)
\(720\) 8.60684e11 6.25323e11i 0.119357 0.0867178i
\(721\) 1.03462e12 7.51693e11i 0.142584 0.103593i
\(722\) 1.12726e12 + 3.46936e12i 0.154386 + 0.475151i
\(723\) 1.29149e11 3.97479e11i 0.0175780 0.0540994i
\(724\) 1.02051e12 + 7.41442e11i 0.138036 + 0.100289i
\(725\) 3.00188e12 0.403526
\(726\) −4.09347e11 + 1.48257e12i −0.0546861 + 0.198062i
\(727\) 1.20392e13 1.59842 0.799210 0.601052i \(-0.205251\pi\)
0.799210 + 0.601052i \(0.205251\pi\)
\(728\) 4.80163e11 + 3.48859e11i 0.0633575 + 0.0460319i
\(729\) −1.10864e12 + 3.41204e12i −0.145384 + 0.447446i
\(730\) −1.56857e12 4.82757e12i −0.204433 0.629181i
\(731\) 8.00179e12 5.81364e12i 1.03648 0.753044i
\(732\) 1.17453e12 8.53344e11i 0.151204 0.109856i
\(733\) 1.98651e12 + 6.11384e12i 0.254169 + 0.782250i 0.993992 + 0.109450i \(0.0349089\pi\)
−0.739824 + 0.672801i \(0.765091\pi\)
\(734\) 1.97872e12 6.08987e12i 0.251624 0.774418i
\(735\) −2.15749e12 1.56751e12i −0.272681 0.198115i
\(736\) −9.20752e12 −1.15662
\(737\) 3.51855e12 + 1.00573e13i 0.439299 + 1.25568i
\(738\) −2.72305e11 −0.0337911
\(739\) 1.28772e12 + 9.35582e11i 0.158826 + 0.115394i 0.664360 0.747413i \(-0.268704\pi\)
−0.505534 + 0.862807i \(0.668704\pi\)
\(740\) 2.41494e12 7.43242e12i 0.296049 0.911145i
\(741\) 7.81617e10 + 2.40557e11i 0.00952383 + 0.0293113i
\(742\) 1.73954e12 1.26385e12i 0.210676 0.153065i
\(743\) 6.67205e12 4.84753e12i 0.803174 0.583540i −0.108670 0.994078i \(-0.534659\pi\)
0.911843 + 0.410538i \(0.134659\pi\)
\(744\) −4.26977e11 1.31410e12i −0.0510888 0.157235i
\(745\) −4.91988e11 + 1.51418e12i −0.0585129 + 0.180084i
\(746\) −6.33611e12 4.60345e12i −0.749028 0.544201i
\(747\) 1.23557e13 1.45186
\(748\) 2.50940e12 8.35496e12i 0.293098 0.975859i
\(749\) −3.91868e12 −0.454958
\(750\) 7.04958e11 + 5.12182e11i 0.0813556 + 0.0591083i
\(751\) −2.27007e12 + 6.98655e12i −0.260411 + 0.801462i 0.732304 + 0.680977i \(0.238445\pi\)
−0.992715 + 0.120485i \(0.961555\pi\)
\(752\) −1.46843e11 4.51936e11i −0.0167445 0.0515344i
\(753\) 2.18339e11 1.58633e11i 0.0247488 0.0179811i
\(754\) −6.26292e11 + 4.55028e11i −0.0705676 + 0.0512704i
\(755\) −6.49687e12 1.99953e13i −0.727684 2.23958i
\(756\) 3.45538e11 1.06346e12i 0.0384723 0.118406i
\(757\) −1.49278e12 1.08456e12i −0.165220 0.120039i 0.502103 0.864808i \(-0.332560\pi\)
−0.667323 + 0.744768i \(0.732560\pi\)
\(758\) −8.00178e12 −0.880390
\(759\) −3.44356e12 + 7.70882e10i −0.376634 + 0.00843140i
\(760\) 6.02111e12 0.654660
\(761\) 7.79929e12 + 5.66651e12i 0.842993 + 0.612470i 0.923205 0.384308i \(-0.125560\pi\)
−0.0802121 + 0.996778i \(0.525560\pi\)
\(762\) 1.93882e10 5.96708e10i 0.00208325 0.00641157i
\(763\) 1.02358e12 + 3.15027e12i 0.109336 + 0.336501i
\(764\) −2.53665e12 + 1.84298e12i −0.269364 + 0.195705i
\(765\) −1.60500e13 + 1.16610e13i −1.69433 + 1.23101i
\(766\) 2.97342e12 + 9.15126e12i 0.312052 + 0.960398i
\(767\) −4.52494e11 + 1.39263e12i −0.0472099 + 0.145297i
\(768\) 2.54696e12 + 1.85047e12i 0.264178 + 0.191936i
\(769\) 1.36679e13 1.40940 0.704700 0.709506i \(-0.251082\pi\)
0.704700 + 0.709506i \(0.251082\pi\)
\(770\) 2.47520e12 1.88440e12i 0.253748 0.193181i
\(771\) 3.46761e12 0.353416
\(772\) −2.19163e12 1.59232e12i −0.222070 0.161343i
\(773\) 6.34400e11 1.95248e12i 0.0639081 0.196689i −0.914004 0.405705i \(-0.867026\pi\)
0.977912 + 0.209016i \(0.0670261\pi\)
\(774\) −1.30231e12 4.00810e12i −0.130431 0.401424i
\(775\) 2.57825e12 1.87321e12i 0.256725 0.186521i
\(776\) −9.48584e12 + 6.89187e12i −0.939071 + 0.682275i
\(777\) 4.95123e11 + 1.52383e12i 0.0487324 + 0.149983i
\(778\) −1.64565e12 + 5.06478e12i −0.161038 + 0.495624i
\(779\) −2.32859e11 1.69182e11i −0.0226556 0.0164602i
\(780\) −4.54872e11 −0.0440011
\(781\) −1.62999e13 1.12940e13i −1.56767 1.08622i
\(782\) −1.54087e13 −1.47345
\(783\) 3.29051e12 + 2.39069e12i 0.312849 + 0.227298i
\(784\) 3.59750e11 1.10720e12i 0.0340078 0.104665i
\(785\) 6.11337e12 + 1.88150e13i 0.574602 + 1.76844i
\(786\) −1.39636e12 + 1.01452e12i −0.130496 + 0.0948106i
\(787\) 3.13616e12 2.27855e12i 0.291415 0.211725i −0.432466 0.901650i \(-0.642357\pi\)
0.723881 + 0.689925i \(0.242357\pi\)
\(788\) 7.83120e11 + 2.41019e12i 0.0723536 + 0.222681i
\(789\) −1.77381e12 + 5.45923e12i −0.162952 + 0.501516i
\(790\) −5.21312e12 3.78756e12i −0.476185 0.345969i
\(791\) −9.74525e11 −0.0885114
\(792\) −8.52042e12 5.90368e12i −0.769480 0.533163i
\(793\) −2.40814e12 −0.216248
\(794\) 9.05290e11 + 6.57732e11i 0.0808343 + 0.0587295i
\(795\) −1.42010e12 + 4.37063e12i −0.126086 + 0.388053i
\(796\) 8.89481e11 + 2.73754e12i 0.0785286 + 0.241686i
\(797\) 2.33556e12 1.69688e12i 0.205035 0.148967i −0.480529 0.876979i \(-0.659555\pi\)
0.685565 + 0.728012i \(0.259555\pi\)
\(798\) −3.58127e11 + 2.60194e11i −0.0312625 + 0.0227135i
\(799\) 2.73833e12 + 8.42770e12i 0.237697 + 0.731558i
\(800\) −2.09122e12 + 6.43612e12i −0.180507 + 0.555545i
\(801\) −1.27819e13 9.28660e12i −1.09711 0.797096i
\(802\) 1.87003e12 0.159612
\(803\) −7.34951e12 + 5.59526e12i −0.623790 + 0.474898i
\(804\) 2.72663e12 0.230131
\(805\) 5.63623e12 + 4.09496e12i 0.473050 + 0.343691i
\(806\) −2.53966e11 + 7.81628e11i −0.0211967 + 0.0652367i
\(807\) −1.12850e12 3.47315e12i −0.0936632 0.288266i
\(808\) 1.69910e13 1.23447e13i 1.40238 1.01889i
\(809\) 1.18071e13 8.57836e12i 0.969114 0.704103i 0.0138646 0.999904i \(-0.495587\pi\)
0.955250 + 0.295801i \(0.0955866\pi\)
\(810\) 2.30629e12 + 7.09804e12i 0.188249 + 0.579370i
\(811\) 5.58533e12 1.71899e13i 0.453372 1.39534i −0.419663 0.907680i \(-0.637852\pi\)
0.873035 0.487657i \(-0.162148\pi\)
\(812\) 1.38971e12 + 1.00968e12i 0.112182 + 0.0815049i
\(813\) −1.34492e12 −0.107966
\(814\) 1.12136e13 2.51029e11i 0.895229 0.0200408i
\(815\) 1.39539e12 0.110787
\(816\) 7.41895e11 + 5.39018e11i 0.0585783 + 0.0425596i
\(817\) 1.37656e12 4.23661e12i 0.108092 0.332674i
\(818\) 1.69989e12 + 5.23173e12i 0.132749 + 0.408560i
\(819\) −7.12545e11 + 5.17695e11i −0.0553395 + 0.0402065i
\(820\) 4.18766e11 3.04251e11i 0.0323451 0.0235001i
\(821\) −3.13780e12 9.65716e12i −0.241036 0.741831i −0.996263 0.0863686i \(-0.972474\pi\)
0.755228 0.655462i \(-0.227526\pi\)
\(822\) −2.62459e11 + 8.07765e11i −0.0200511 + 0.0617109i
\(823\) −6.25532e8 4.54475e8i −4.75281e−5 3.45312e-5i 0.587761 0.809034i \(-0.300009\pi\)
−0.587809 + 0.809000i \(0.700009\pi\)
\(824\) −6.38881e12 −0.482778
\(825\) −7.28219e11 + 2.42458e12i −0.0547293 + 0.182219i
\(826\) −2.56270e12 −0.191552
\(827\) −1.05270e13 7.64830e12i −0.782580 0.568578i 0.123172 0.992385i \(-0.460693\pi\)
−0.905752 + 0.423807i \(0.860693\pi\)
\(828\) 2.57235e12 7.91689e12i 0.190193 0.585354i
\(829\) 2.55032e12 + 7.84907e12i 0.187542 + 0.577195i 0.999983 0.00584846i \(-0.00186163\pi\)
−0.812441 + 0.583044i \(0.801862\pi\)
\(830\) 1.49866e13 1.08884e13i 1.09610 0.796366i
\(831\) 4.70666e12 3.41959e12i 0.342380 0.248754i
\(832\) −6.49053e11 1.99758e12i −0.0469597 0.144527i
\(833\) −6.70860e12 + 2.06470e13i −0.482758 + 1.48578i
\(834\) −1.90495e12 1.38403e12i −0.136344 0.0990599i
\(835\) −3.10061e12 −0.220728
\(836\) −1.29745e12 3.70859e12i −0.0918678 0.262591i
\(837\) 4.31797e12 0.304099
\(838\) 1.01438e13 + 7.36992e12i 0.710565 + 0.516256i
\(839\) 5.35676e12 1.64864e13i 0.373228 1.14868i −0.571439 0.820644i \(-0.693615\pi\)
0.944667 0.328032i \(-0.106385\pi\)
\(840\) −6.86029e11 2.11138e12i −0.0475429 0.146322i
\(841\) 6.68159e12 4.85446e12i 0.460572 0.334625i
\(842\) 9.79031e12 7.11308e12i 0.671262 0.487700i
\(843\) −2.27099e12 6.98939e12i −0.154878 0.476667i
\(844\) −4.38179e12 + 1.34857e13i −0.297242 + 0.914817i
\(845\) −1.46260e13 1.06264e13i −0.986891 0.717019i
\(846\) 3.77576e12 0.253418
\(847\) −4.72416e12 3.11917e12i −0.315391 0.208240i
\(848\) −2.00615e12 −0.133224
\(849\) 4.53795e12 + 3.29701e12i 0.299761 + 0.217789i
\(850\) −3.49964e12 + 1.07708e13i −0.229953 + 0.707721i
\(851\) 7.76215e12 + 2.38895e13i 0.507340 + 1.56143i
\(852\) −4.10543e12 + 2.98277e12i −0.266919 + 0.193928i
\(853\) 1.29388e13 9.40057e12i 0.836802 0.607972i −0.0846736 0.996409i \(-0.526985\pi\)
0.921475 + 0.388437i \(0.126985\pi\)
\(854\) −1.30236e12 4.00826e12i −0.0837859 0.257867i
\(855\) −2.76110e12 + 8.49780e12i −0.176699 + 0.543825i
\(856\) 1.58378e13 + 1.15069e13i 1.00824 + 0.732529i
\(857\) −4.63914e12 −0.293781 −0.146891 0.989153i \(-0.546927\pi\)
−0.146891 + 0.989153i \(0.546927\pi\)
\(858\) −2.15589e11 6.16232e11i −0.0135811 0.0388196i
\(859\) −7.49881e12 −0.469919 −0.234960 0.972005i \(-0.575496\pi\)
−0.234960 + 0.972005i \(0.575496\pi\)
\(860\) 6.48108e12 + 4.70878e12i 0.404021 + 0.293539i
\(861\) −3.27946e10 + 1.00931e11i −0.00203370 + 0.00625910i
\(862\) −3.84357e11 1.18293e12i −0.0237111 0.0729754i
\(863\) −1.67219e13 + 1.21491e13i −1.02621 + 0.745585i −0.967547 0.252693i \(-0.918684\pi\)
−0.0586630 + 0.998278i \(0.518684\pi\)
\(864\) −7.41802e12 + 5.38950e12i −0.452872 + 0.329031i
\(865\) −2.03498e12 6.26303e12i −0.123591 0.380375i
\(866\) −3.00743e12 + 9.25591e12i −0.181704 + 0.559227i
\(867\) −9.66990e12 7.02559e12i −0.581214 0.422277i
\(868\) 1.82365e12 0.109044
\(869\) −3.37303e12 + 1.12304e13i −0.200646 + 0.668044i
\(870\) 2.89566e12 0.171361
\(871\) −3.65898e12 2.65841e12i −0.215416 0.156509i
\(872\) 5.11354e12 1.57379e13i 0.299500 0.921768i
\(873\) −5.37680e12 1.65481e13i −0.313300 0.964238i
\(874\) −5.61444e12 + 4.07913e12i −0.325465 + 0.236464i
\(875\) −2.59470e12 + 1.88516e12i −0.149641 + 0.108721i
\(876\) 7.30443e11 + 2.24807e12i 0.0419100 + 0.128986i
\(877\) 2.48589e12 7.65078e12i 0.141900 0.436725i −0.854699 0.519124i \(-0.826258\pi\)
0.996599 + 0.0823994i \(0.0262583\pi\)
\(878\) 9.17202e10 + 6.66386e10i 0.00520882 + 0.00378443i
\(879\) 1.42546e12 0.0805390
\(880\) −2.90177e12 + 6.49597e10i −0.163114 + 0.00365150i
\(881\) −2.72603e13 −1.52454 −0.762271 0.647258i \(-0.775916\pi\)
−0.762271 + 0.647258i \(0.775916\pi\)
\(882\) 7.48358e12 + 5.43714e12i 0.416390 + 0.302525i
\(883\) −7.56868e12 + 2.32940e13i −0.418983 + 1.28950i 0.489656 + 0.871916i \(0.337123\pi\)
−0.908639 + 0.417583i \(0.862877\pi\)
\(884\) 1.14427e12 + 3.52171e12i 0.0630224 + 0.193963i
\(885\) 4.43115e12 3.21942e12i 0.242813 0.176414i
\(886\) −2.60655e11 + 1.89377e11i −0.0142106 + 0.0103246i
\(887\) −3.10971e12 9.57070e12i −0.168680 0.519143i 0.830609 0.556857i \(-0.187993\pi\)
−0.999289 + 0.0377132i \(0.987993\pi\)
\(888\) 2.47350e12 7.61264e12i 0.133491 0.410844i
\(889\) 1.86826e11 + 1.35737e11i 0.0100318 + 0.00728854i
\(890\) −2.36873e13 −1.26550
\(891\) 1.08061e13 8.22679e12i 0.574405 0.437301i
\(892\) −3.51744e12 −0.186031
\(893\) 3.22881e12 + 2.34587e12i 0.169907 + 0.123445i
\(894\) −1.80699e11 + 5.56134e11i −0.00946099 + 0.0291179i
\(895\) −7.04109e12 2.16702e13i −0.366806 1.12891i
\(896\) −2.63002e12 + 1.91082e12i −0.136324 + 0.0990454i
\(897\) 1.18283e12 8.59376e11i 0.0610037 0.0443218i
\(898\) 4.34513e12 + 1.33729e13i 0.222977 + 0.686251i
\(899\) −2.04982e12 + 6.30870e12i −0.104664 + 0.322122i
\(900\) −4.94973e12 3.59619e12i −0.251472 0.182705i
\(901\) 3.74107e13 1.89119
\(902\) 6.10657e11 + 4.23116e11i 0.0307162 + 0.0212829i
\(903\) −1.64246e12 −0.0822055
\(904\) 3.93867e12 + 2.86161e12i 0.196151 + 0.142512i
\(905\) −2.41850e12 + 7.44337e12i −0.119847 + 0.368851i
\(906\) −2.38619e12 7.34393e12i −0.117660 0.362119i
\(907\) 1.83727e13 1.33485e13i 0.901445 0.654938i −0.0373918 0.999301i \(-0.511905\pi\)
0.938837 + 0.344363i \(0.111905\pi\)
\(908\) 1.63225e13 1.18590e13i 0.796892 0.578976i
\(909\) 9.63089e12 + 2.96408e13i 0.467874 + 1.43997i
\(910\) −4.08051e11 + 1.25585e12i −0.0197255 + 0.0607089i
\(911\) 3.12747e13 + 2.27224e13i 1.50439 + 1.09300i 0.968592 + 0.248655i \(0.0799885\pi\)
0.535796 + 0.844347i \(0.320012\pi\)
\(912\) 4.13016e11 0.0197693
\(913\) −2.77083e13 1.91987e13i −1.31975 0.914437i
\(914\) 5.96165e12 0.282559
\(915\) 7.28733e12 + 5.29455e12i 0.343695 + 0.249709i
\(916\) −5.79302e12 + 1.78291e13i −0.271879 + 0.836757i
\(917\) −1.96312e12 6.04185e12i −0.0916820 0.282168i
\(918\) −1.24140e13 + 9.01929e12i −0.576925 + 0.419160i
\(919\) −3.21513e13 + 2.33593e13i −1.48689 + 1.08029i −0.511636 + 0.859202i \(0.670960\pi\)
−0.975254 + 0.221087i \(0.929040\pi\)
\(920\) −1.07550e13 3.31006e13i −0.494956 1.52332i
\(921\) −3.25236e11 + 1.00097e12i −0.0148947 + 0.0458411i
\(922\) −1.85316e13 1.34640e13i −0.844547 0.613599i
\(923\) 8.41737e12 0.381741
\(924\) −1.15264e12 + 8.77515e11i −0.0520198 + 0.0396032i
\(925\) 1.84618e13 0.829158
\(926\) −9.41854e12 6.84297e12i −0.420954 0.305841i
\(927\) 2.92972e12 9.01675e12i 0.130307 0.401043i
\(928\) −4.35277e12 1.33964e13i −0.192664 0.592958i
\(929\) −7.68923e12 + 5.58656e12i −0.338698 + 0.246078i −0.744112 0.668055i \(-0.767127\pi\)
0.405414 + 0.914133i \(0.367127\pi\)
\(930\) 2.48703e12 1.80693e12i 0.109020 0.0792078i
\(931\) 3.02144e12 + 9.29905e12i 0.131808 + 0.405663i
\(932\) 2.34831e12 7.22736e12i 0.101949 0.313767i
\(933\) 7.96922e12 + 5.78998e12i 0.344309 + 0.250155i
\(934\) 1.94620e13 0.836809
\(935\) 5.41122e13 1.21137e12i 2.31549 0.0518350i
\(936\) 4.40001e12 0.187375
\(937\) −3.37357e13 2.45104e13i −1.42975 1.03878i −0.990062 0.140629i \(-0.955088\pi\)
−0.439692 0.898149i \(-0.644912\pi\)
\(938\) 2.44598e12 7.52795e12i 0.103167 0.317515i
\(939\) −1.05026e12 3.23238e12i −0.0440863 0.135684i
\(940\) −5.80658e12 + 4.21873e12i −0.242574 + 0.176241i
\(941\) 2.47139e13 1.79557e13i 1.02752 0.746534i 0.0597061 0.998216i \(-0.480984\pi\)
0.967810 + 0.251682i \(0.0809837\pi\)
\(942\) 2.24534e12 + 6.91044e12i 0.0929079 + 0.285941i
\(943\) −5.14128e11 + 1.58232e12i −0.0211723 + 0.0651618i
\(944\) 1.93439e12 + 1.40542e12i 0.0792811 + 0.0576011i
\(945\) 6.93775e12 0.282993
\(946\) −3.30742e12 + 1.10119e13i −0.134270 + 0.447047i
\(947\) 2.15949e13 0.872521 0.436261 0.899820i \(-0.356303\pi\)
0.436261 + 0.899820i \(0.356303\pi\)
\(948\) 2.42761e12 + 1.76376e12i 0.0976207 + 0.0709256i
\(949\) 1.21161e12 3.72894e12i 0.0484913 0.149241i
\(950\) 1.57618e12 + 4.85099e12i 0.0627841 + 0.193230i
\(951\) −4.82969e12 + 3.50898e12i −0.191473 + 0.139113i
\(952\) −1.46210e13 + 1.06228e13i −0.576913 + 0.419152i
\(953\) 5.21586e12 + 1.60528e13i 0.204837 + 0.630423i 0.999720 + 0.0236604i \(0.00753205\pi\)
−0.794883 + 0.606762i \(0.792468\pi\)
\(954\) 4.92584e12 1.51602e13i 0.192536 0.592566i
\(955\) −1.57386e13 1.14347e13i −0.612279 0.444847i
\(956\) −8.03202e12 −0.311003
\(957\) −1.74007e12 4.97375e12i −0.0670599 0.191681i
\(958\) 1.87560e13 0.719442
\(959\) −2.52907e12 1.83747e12i −0.0965554 0.0701516i
\(960\) −2.42778e12 + 7.47194e12i −0.0922547 + 0.283931i
\(961\) −5.99414e12 1.84481e13i −0.226710 0.697743i
\(962\) −3.85175e12 + 2.79846e12i −0.145001 + 0.105349i
\(963\) −2.35028e13 + 1.70758e13i −0.880645 + 0.639826i
\(964\) −8.51548e11 2.62080e12i −0.0317587 0.0977432i
\(965\) 5.19395e12 1.59853e13i 0.192808 0.593402i
\(966\) 2.07009e12 + 1.50401e12i 0.0764879 + 0.0555717i
\(967\) −3.91786e13 −1.44089 −0.720443 0.693514i \(-0.756062\pi\)
−0.720443 + 0.693514i \(0.756062\pi\)
\(968\) 9.93411e12 + 2.64786e13i 0.363655 + 0.969295i
\(969\) −7.70192e12 −0.280635
\(970\) −2.11046e13 1.53334e13i −0.765427 0.556116i
\(971\) −3.45396e12 + 1.06302e13i −0.124690 + 0.383755i −0.993844 0.110785i \(-0.964664\pi\)
0.869155 + 0.494540i \(0.164664\pi\)
\(972\) −3.90686e12 1.20241e13i −0.140388 0.432070i
\(973\) 7.01145e12 5.09412e12i 0.250784 0.182205i
\(974\) 1.30324e12 9.46859e11i 0.0463990 0.0337109i
\(975\) −3.32064e11 1.02199e12i −0.0117680 0.0362181i
\(976\) −1.21512e12 + 3.73976e12i −0.0428643 + 0.131923i
\(977\) 6.16699e12 + 4.48058e12i 0.216545 + 0.157329i 0.690770 0.723075i \(-0.257272\pi\)
−0.474225 + 0.880404i \(0.657272\pi\)
\(978\) 5.12504e11 0.0179132
\(979\) 1.42342e13 + 4.06866e13i 0.495236 + 1.41556i
\(980\) −1.75837e13 −0.608965
\(981\) 1.98665e13 + 1.44338e13i 0.684873 + 0.497589i
\(982\) 1.91203e12 5.88463e12i 0.0656135 0.201938i
\(983\) 1.27534e13 + 3.92509e13i 0.435647 + 1.34079i 0.892422 + 0.451202i \(0.149005\pi\)
−0.456774 + 0.889583i \(0.650995\pi\)
\(984\) 4.28919e11 3.11628e11i 0.0145847 0.0105964i
\(985\) −1.27206e13 + 9.24207e12i −0.430571 + 0.312828i
\(986\) −7.28432e12 2.24188e13i −0.245439 0.755382i
\(987\) 4.54728e11 1.39951e12i 0.0152519 0.0469405i
\(988\) 1.34924e12 + 9.80277e11i 0.0450486 + 0.0327297i
\(989\) −2.57493e13 −0.855819
\(990\) 6.63402e12 2.20877e13i 0.219492 0.730790i
\(991\) −3.11534e13 −1.02606 −0.513032 0.858370i \(-0.671478\pi\)
−0.513032 + 0.858370i \(0.671478\pi\)
\(992\) −1.20981e13 8.78975e12i −0.396655 0.288187i
\(993\) 2.24689e12 6.91522e12i 0.0733348 0.225701i
\(994\) 4.55225e12 + 1.40104e13i 0.147907 + 0.455210i
\(995\) −1.44483e13 + 1.04973e13i −0.467319 + 0.339527i
\(996\) −6.97886e12 + 5.07044e12i −0.224708 + 0.163260i
\(997\) 3.50052e12 + 1.07735e13i 0.112203 + 0.345325i 0.991353 0.131219i \(-0.0418891\pi\)
−0.879150 + 0.476544i \(0.841889\pi\)
\(998\) 4.18428e12 1.28779e13i 0.133516 0.410920i
\(999\) 2.02369e13 + 1.47030e13i 0.642836 + 0.467048i
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 11.10.c.a.4.6 yes 32
3.2 odd 2 99.10.f.a.37.3 32
11.3 even 5 inner 11.10.c.a.3.6 32
11.5 even 5 121.10.a.h.1.6 16
11.6 odd 10 121.10.a.i.1.11 16
33.14 odd 10 99.10.f.a.91.3 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
11.10.c.a.3.6 32 11.3 even 5 inner
11.10.c.a.4.6 yes 32 1.1 even 1 trivial
99.10.f.a.37.3 32 3.2 odd 2
99.10.f.a.91.3 32 33.14 odd 10
121.10.a.h.1.6 16 11.5 even 5
121.10.a.i.1.11 16 11.6 odd 10