Properties

Label 14.10.c.b.11.3
Level $14$
Weight $10$
Character 14.11
Analytic conductor $7.211$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [14,10,Mod(9,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.9");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 14.c (of order \(3\), degree \(2\), 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: \(7.21050170629\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{6} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{5} + 4038x^{4} - 137923x^{3} + 16368349x^{2} - 286546260x + 5038160400 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 2^{6}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.3
Root \(-35.2598 + 61.0717i\) of defining polynomial
Character \(\chi\) \(=\) 14.11
Dual form 14.10.c.b.9.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(8.00000 + 13.8564i) q^{2} +(86.7292 - 150.219i) q^{3} +(-128.000 + 221.703i) q^{4} +(-1172.77 - 2031.30i) q^{5} +2775.34 q^{6} +(-6347.68 + 246.066i) q^{7} -4096.00 q^{8} +(-5202.42 - 9010.85i) q^{9} +O(q^{10})\) \(q+(8.00000 + 13.8564i) q^{2} +(86.7292 - 150.219i) q^{3} +(-128.000 + 221.703i) q^{4} +(-1172.77 - 2031.30i) q^{5} +2775.34 q^{6} +(-6347.68 + 246.066i) q^{7} -4096.00 q^{8} +(-5202.42 - 9010.85i) q^{9} +(18764.4 - 32500.9i) q^{10} +(35554.8 - 61582.8i) q^{11} +(22202.7 + 38456.2i) q^{12} +89420.8 q^{13} +(-54191.0 - 85987.5i) q^{14} -406855. q^{15} +(-32768.0 - 56755.8i) q^{16} +(-16147.2 + 27967.9i) q^{17} +(83238.7 - 144174. i) q^{18} +(389534. + 674693. i) q^{19} +600460. q^{20} +(-513566. + 974886. i) q^{21} +1.13775e6 q^{22} +(-886420. - 1.53532e6i) q^{23} +(-355243. + 615299. i) q^{24} +(-1.77424e6 + 3.07307e6i) q^{25} +(715366. + 1.23905e6i) q^{26} +1.60938e6 q^{27} +(757950. - 1.43879e6i) q^{28} -212075. q^{29} +(-3.25484e6 - 5.63755e6i) q^{30} +(2.15631e6 - 3.73483e6i) q^{31} +(524288. - 908093. i) q^{32} +(-6.16728e6 - 1.06821e7i) q^{33} -516712. q^{34} +(7.94423e6 + 1.26055e7i) q^{35} +2.66364e6 q^{36} +(-3.10051e6 - 5.37024e6i) q^{37} +(-6.23254e6 + 1.07951e7i) q^{38} +(7.75540e6 - 1.34327e7i) q^{39} +(4.80368e6 + 8.32022e6i) q^{40} +6.40835e6 q^{41} +(-1.76169e7 + 682916. i) q^{42} -6.99951e6 q^{43} +(9.10203e6 + 1.57652e7i) q^{44} +(-1.22025e7 + 2.11354e7i) q^{45} +(1.41827e7 - 2.45652e7i) q^{46} +(1.75422e7 + 3.03840e7i) q^{47} -1.13678e7 q^{48} +(4.02325e7 - 3.12390e6i) q^{49} -5.67755e7 q^{50} +(2.80088e6 + 4.85126e6i) q^{51} +(-1.14459e7 + 1.98248e7i) q^{52} +(2.13451e7 - 3.69707e7i) q^{53} +(1.28750e7 + 2.23002e7i) q^{54} -1.66791e8 q^{55} +(2.60001e7 - 1.00789e6i) q^{56} +1.35136e8 q^{57} +(-1.69660e6 - 2.93860e6i) q^{58} +(1.45327e7 - 2.51714e7i) q^{59} +(5.20775e7 - 9.02008e7i) q^{60} +(-3.09391e7 - 5.35880e7i) q^{61} +6.90018e7 q^{62} +(3.52406e7 + 5.59179e7i) q^{63} +1.67772e7 q^{64} +(-1.04870e8 - 1.81641e8i) q^{65} +(9.86766e7 - 1.70913e8i) q^{66} +(-1.00325e8 + 1.73767e8i) q^{67} +(-4.13370e6 - 7.15977e6i) q^{68} -3.07514e8 q^{69} +(-1.11113e8 + 2.10922e8i) q^{70} +3.03014e7 q^{71} +(2.13091e7 + 3.69085e7i) q^{72} +(1.45923e8 - 2.52746e8i) q^{73} +(4.96082e7 - 8.59239e7i) q^{74} +(3.07756e8 + 5.33049e8i) q^{75} -1.99441e8 q^{76} +(-2.10537e8 + 3.99657e8i) q^{77} +2.48173e8 q^{78} +(5.44357e7 + 9.42854e7i) q^{79} +(-7.68589e7 + 1.33124e8i) q^{80} +(2.41979e8 - 4.19120e8i) q^{81} +(5.12668e7 + 8.87966e7i) q^{82} +2.16661e8 q^{83} +(-1.50398e8 - 2.38644e8i) q^{84} +7.57483e7 q^{85} +(-5.59961e7 - 9.69880e7i) q^{86} +(-1.83931e7 + 3.18578e7i) q^{87} +(-1.45633e8 + 2.52243e8i) q^{88} +(9.32523e7 + 1.61518e8i) q^{89} -3.90481e8 q^{90} +(-5.67615e8 + 2.20034e7i) q^{91} +4.53847e8 q^{92} +(-3.74030e8 - 6.47838e8i) q^{93} +(-2.80675e8 + 4.86144e8i) q^{94} +(9.13671e8 - 1.58252e9i) q^{95} +(-9.09422e7 - 1.57516e8i) q^{96} -9.53814e8 q^{97} +(3.65146e8 + 5.32487e8i) q^{98} -7.39884e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 48 q^{2} + 71 q^{3} - 768 q^{4} - 1085 q^{5} + 2272 q^{6} - 6796 q^{7} - 24576 q^{8} - 9106 q^{9} + 17360 q^{10} + 2555 q^{11} + 18176 q^{12} + 36140 q^{13} + 43504 q^{14} - 706146 q^{15} - 196608 q^{16} + 20759 q^{17} + 145696 q^{18} + 1220649 q^{19} + 555520 q^{20} + 1951577 q^{21} + 81760 q^{22} - 1960903 q^{23} - 290816 q^{24} - 863572 q^{25} + 289120 q^{26} + 5777318 q^{27} + 2435840 q^{28} - 5212292 q^{29} - 5649168 q^{30} - 9377989 q^{31} + 3145728 q^{32} - 10778103 q^{33} + 664288 q^{34} + 20361719 q^{35} + 4662272 q^{36} - 25814913 q^{37} - 19530384 q^{38} + 37990822 q^{39} + 4444160 q^{40} + 418500 q^{41} - 2053952 q^{42} + 5888616 q^{43} + 654080 q^{44} - 37350558 q^{45} + 31374448 q^{46} + 48391269 q^{47} - 9306112 q^{48} + 108466086 q^{49} - 27634304 q^{50} - 75441987 q^{51} - 4625920 q^{52} + 102186411 q^{53} + 46218544 q^{54} - 456557402 q^{55} + 27836416 q^{56} + 86169178 q^{57} - 41698336 q^{58} + 144220135 q^{59} + 90386688 q^{60} + 280936871 q^{61} - 300095648 q^{62} + 33751838 q^{63} + 100663296 q^{64} - 186819738 q^{65} + 172449648 q^{66} + 170710399 q^{67} + 5314304 q^{68} - 1807308342 q^{69} - 347247824 q^{70} + 939517376 q^{71} + 37298176 q^{72} + 613838539 q^{73} + 413038608 q^{74} + 902254676 q^{75} - 624972288 q^{76} - 729499715 q^{77} + 1215706304 q^{78} + 197445809 q^{79} - 71106560 q^{80} + 887872901 q^{81} + 3348000 q^{82} - 2148362872 q^{83} - 532466944 q^{84} + 822545038 q^{85} + 47108928 q^{86} + 753428670 q^{87} - 10465280 q^{88} + 805730427 q^{89} - 1195217856 q^{90} + 17178248 q^{91} + 1003982336 q^{92} - 1721516327 q^{93} - 774260304 q^{94} + 1799421743 q^{95} - 74448896 q^{96} - 4525836188 q^{97} - 597954960 q^{98} - 2607425268 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 8.00000 + 13.8564i 0.353553 + 0.612372i
\(3\) 86.7292 150.219i 0.618187 1.07073i −0.371629 0.928381i \(-0.621201\pi\)
0.989816 0.142350i \(-0.0454659\pi\)
\(4\) −128.000 + 221.703i −0.250000 + 0.433013i
\(5\) −1172.77 2031.30i −0.839169 1.45348i −0.890591 0.454806i \(-0.849709\pi\)
0.0514219 0.998677i \(-0.483625\pi\)
\(6\) 2775.34 0.874248
\(7\) −6347.68 + 246.066i −0.999249 + 0.0387356i
\(8\) −4096.00 −0.353553
\(9\) −5202.42 9010.85i −0.264310 0.457799i
\(10\) 18764.4 32500.9i 0.593382 1.02777i
\(11\) 35554.8 61582.8i 0.732203 1.26821i −0.223737 0.974650i \(-0.571826\pi\)
0.955940 0.293563i \(-0.0948410\pi\)
\(12\) 22202.7 + 38456.2i 0.309093 + 0.535366i
\(13\) 89420.8 0.868347 0.434174 0.900829i \(-0.357040\pi\)
0.434174 + 0.900829i \(0.357040\pi\)
\(14\) −54191.0 85987.5i −0.377009 0.598218i
\(15\) −406855. −2.07505
\(16\) −32768.0 56755.8i −0.125000 0.216506i
\(17\) −16147.2 + 27967.9i −0.0468898 + 0.0812155i −0.888518 0.458842i \(-0.848264\pi\)
0.841628 + 0.540058i \(0.181598\pi\)
\(18\) 83238.7 144174.i 0.186896 0.323713i
\(19\) 389534. + 674693.i 0.685732 + 1.18772i 0.973206 + 0.229934i \(0.0738510\pi\)
−0.287475 + 0.957788i \(0.592816\pi\)
\(20\) 600460. 0.839169
\(21\) −513566. + 974886.i −0.576248 + 1.09387i
\(22\) 1.13775e6 1.03549
\(23\) −886420. 1.53532e6i −0.660487 1.14400i −0.980488 0.196580i \(-0.937016\pi\)
0.320001 0.947417i \(-0.396317\pi\)
\(24\) −355243. + 615299.i −0.218562 + 0.378561i
\(25\) −1.77424e6 + 3.07307e6i −0.908408 + 1.57341i
\(26\) 715366. + 1.23905e6i 0.307007 + 0.531752i
\(27\) 1.60938e6 0.582801
\(28\) 757950. 1.43879e6i 0.233039 0.442372i
\(29\) −212075. −0.0556799 −0.0278399 0.999612i \(-0.508863\pi\)
−0.0278399 + 0.999612i \(0.508863\pi\)
\(30\) −3.25484e6 5.63755e6i −0.733642 1.27071i
\(31\) 2.15631e6 3.73483e6i 0.419356 0.726346i −0.576519 0.817084i \(-0.695589\pi\)
0.995875 + 0.0907380i \(0.0289226\pi\)
\(32\) 524288. 908093.i 0.0883883 0.153093i
\(33\) −6.16728e6 1.06821e7i −0.905277 1.56799i
\(34\) −516712. −0.0663122
\(35\) 7.94423e6 + 1.26055e7i 0.894840 + 1.41989i
\(36\) 2.66364e6 0.264310
\(37\) −3.10051e6 5.37024e6i −0.271973 0.471071i 0.697394 0.716688i \(-0.254343\pi\)
−0.969367 + 0.245617i \(0.921009\pi\)
\(38\) −6.23254e6 + 1.07951e7i −0.484886 + 0.839846i
\(39\) 7.75540e6 1.34327e7i 0.536801 0.929766i
\(40\) 4.80368e6 + 8.32022e6i 0.296691 + 0.513884i
\(41\) 6.40835e6 0.354176 0.177088 0.984195i \(-0.443332\pi\)
0.177088 + 0.984195i \(0.443332\pi\)
\(42\) −1.76169e7 + 682916.i −0.873592 + 0.0338645i
\(43\) −6.99951e6 −0.312219 −0.156110 0.987740i \(-0.549895\pi\)
−0.156110 + 0.987740i \(0.549895\pi\)
\(44\) 9.10203e6 + 1.57652e7i 0.366101 + 0.634106i
\(45\) −1.22025e7 + 2.11354e7i −0.443602 + 0.768341i
\(46\) 1.41827e7 2.45652e7i 0.467035 0.808928i
\(47\) 1.75422e7 + 3.03840e7i 0.524377 + 0.908248i 0.999597 + 0.0283808i \(0.00903509\pi\)
−0.475220 + 0.879867i \(0.657632\pi\)
\(48\) −1.13678e7 −0.309093
\(49\) 4.02325e7 3.12390e6i 0.996999 0.0774131i
\(50\) −5.67755e7 −1.28468
\(51\) 2.80088e6 + 4.85126e6i 0.0579733 + 0.100413i
\(52\) −1.14459e7 + 1.98248e7i −0.217087 + 0.376005i
\(53\) 2.13451e7 3.69707e7i 0.371583 0.643601i −0.618226 0.786000i \(-0.712148\pi\)
0.989809 + 0.142400i \(0.0454818\pi\)
\(54\) 1.28750e7 + 2.23002e7i 0.206051 + 0.356891i
\(55\) −1.66791e8 −2.45777
\(56\) 2.60001e7 1.00789e6i 0.353288 0.0136951i
\(57\) 1.35136e8 1.69564
\(58\) −1.69660e6 2.93860e6i −0.0196858 0.0340968i
\(59\) 1.45327e7 2.51714e7i 0.156139 0.270441i −0.777334 0.629088i \(-0.783428\pi\)
0.933473 + 0.358647i \(0.116762\pi\)
\(60\) 5.20775e7 9.02008e7i 0.518763 0.898524i
\(61\) −3.09391e7 5.35880e7i −0.286103 0.495546i 0.686773 0.726872i \(-0.259027\pi\)
−0.972876 + 0.231327i \(0.925693\pi\)
\(62\) 6.90018e7 0.593059
\(63\) 3.52406e7 + 5.59179e7i 0.281845 + 0.447217i
\(64\) 1.67772e7 0.125000
\(65\) −1.04870e8 1.81641e8i −0.728690 1.26213i
\(66\) 9.86766e7 1.70913e8i 0.640127 1.10873i
\(67\) −1.00325e8 + 1.73767e8i −0.608234 + 1.05349i 0.383297 + 0.923625i \(0.374789\pi\)
−0.991531 + 0.129867i \(0.958545\pi\)
\(68\) −4.13370e6 7.15977e6i −0.0234449 0.0406078i
\(69\) −3.07514e8 −1.63322
\(70\) −1.11113e8 + 2.10922e8i −0.553125 + 1.04998i
\(71\) 3.03014e7 0.141514 0.0707571 0.997494i \(-0.477458\pi\)
0.0707571 + 0.997494i \(0.477458\pi\)
\(72\) 2.13091e7 + 3.69085e7i 0.0934478 + 0.161856i
\(73\) 1.45923e8 2.52746e8i 0.601411 1.04167i −0.391197 0.920307i \(-0.627939\pi\)
0.992608 0.121367i \(-0.0387278\pi\)
\(74\) 4.96082e7 8.59239e7i 0.192314 0.333097i
\(75\) 3.07756e8 + 5.33049e8i 1.12313 + 1.94532i
\(76\) −1.99441e8 −0.685732
\(77\) −2.10537e8 + 3.99657e8i −0.682528 + 1.29562i
\(78\) 2.48173e8 0.759151
\(79\) 5.44357e7 + 9.42854e7i 0.157240 + 0.272347i 0.933872 0.357607i \(-0.116407\pi\)
−0.776633 + 0.629954i \(0.783074\pi\)
\(80\) −7.68589e7 + 1.33124e8i −0.209792 + 0.363371i
\(81\) 2.41979e8 4.19120e8i 0.624590 1.08182i
\(82\) 5.12668e7 + 8.87966e7i 0.125220 + 0.216887i
\(83\) 2.16661e8 0.501106 0.250553 0.968103i \(-0.419388\pi\)
0.250553 + 0.968103i \(0.419388\pi\)
\(84\) −1.50398e8 2.38644e8i −0.329599 0.522991i
\(85\) 7.57483e7 0.157394
\(86\) −5.59961e7 9.69880e7i −0.110386 0.191194i
\(87\) −1.83931e7 + 3.18578e7i −0.0344206 + 0.0596182i
\(88\) −1.45633e8 + 2.52243e8i −0.258873 + 0.448381i
\(89\) 9.32523e7 + 1.61518e8i 0.157545 + 0.272876i 0.933983 0.357318i \(-0.116309\pi\)
−0.776438 + 0.630194i \(0.782975\pi\)
\(90\) −3.90481e8 −0.627348
\(91\) −5.67615e8 + 2.20034e7i −0.867695 + 0.0336360i
\(92\) 4.53847e8 0.660487
\(93\) −3.74030e8 6.47838e8i −0.518481 0.898035i
\(94\) −2.80675e8 + 4.86144e8i −0.370791 + 0.642228i
\(95\) 9.13671e8 1.58252e9i 1.15089 1.99340i
\(96\) −9.09422e7 1.57516e8i −0.109281 0.189280i
\(97\) −9.53814e8 −1.09393 −0.546966 0.837155i \(-0.684217\pi\)
−0.546966 + 0.837155i \(0.684217\pi\)
\(98\) 3.65146e8 + 5.32487e8i 0.399898 + 0.583165i
\(99\) −7.39884e8 −0.774115
\(100\) −4.54204e8 7.86705e8i −0.454204 0.786705i
\(101\) 9.73745e8 1.68657e9i 0.931105 1.61272i 0.149670 0.988736i \(-0.452179\pi\)
0.781436 0.623986i \(-0.214488\pi\)
\(102\) −4.48140e7 + 7.76202e7i −0.0409933 + 0.0710025i
\(103\) 6.91594e8 + 1.19788e9i 0.605458 + 1.04868i 0.991979 + 0.126403i \(0.0403433\pi\)
−0.386521 + 0.922281i \(0.626323\pi\)
\(104\) −3.66268e8 −0.307007
\(105\) 2.58259e9 1.00113e8i 2.07350 0.0803784i
\(106\) 6.83042e8 0.525498
\(107\) 9.59157e8 + 1.66131e9i 0.707396 + 1.22525i 0.965820 + 0.259214i \(0.0834636\pi\)
−0.258424 + 0.966032i \(0.583203\pi\)
\(108\) −2.06000e8 + 3.56803e8i −0.145700 + 0.252360i
\(109\) −9.42525e8 + 1.63250e9i −0.639548 + 1.10773i 0.345983 + 0.938241i \(0.387545\pi\)
−0.985532 + 0.169490i \(0.945788\pi\)
\(110\) −1.33433e9 2.31113e9i −0.868952 1.50507i
\(111\) −1.07562e9 −0.672520
\(112\) 2.21967e8 + 3.52205e8i 0.133293 + 0.211502i
\(113\) −1.65917e9 −0.957277 −0.478639 0.878012i \(-0.658870\pi\)
−0.478639 + 0.878012i \(0.658870\pi\)
\(114\) 1.08109e9 + 1.87250e9i 0.599500 + 1.03836i
\(115\) −2.07914e9 + 3.60118e9i −1.10852 + 1.92001i
\(116\) 2.71456e7 4.70175e7i 0.0139200 0.0241101i
\(117\) −4.65204e8 8.05758e8i −0.229513 0.397528i
\(118\) 4.65046e8 0.220814
\(119\) 9.56157e7 1.81504e8i 0.0437087 0.0829709i
\(120\) 1.66648e9 0.733642
\(121\) −1.34932e9 2.33709e9i −0.572242 0.991152i
\(122\) 4.95025e8 8.57409e8i 0.202306 0.350404i
\(123\) 5.55791e8 9.62658e8i 0.218947 0.379227i
\(124\) 5.52014e8 + 9.56117e8i 0.209678 + 0.363173i
\(125\) 3.74196e9 1.37089
\(126\) −4.92897e8 + 9.35651e8i −0.174216 + 0.330709i
\(127\) −2.50752e9 −0.855319 −0.427659 0.903940i \(-0.640662\pi\)
−0.427659 + 0.903940i \(0.640662\pi\)
\(128\) 1.34218e8 + 2.32472e8i 0.0441942 + 0.0765466i
\(129\) −6.07062e8 + 1.05146e9i −0.193010 + 0.334303i
\(130\) 1.67793e9 2.90625e9i 0.515261 0.892459i
\(131\) 1.52573e9 + 2.64265e9i 0.452645 + 0.784004i 0.998549 0.0538433i \(-0.0171471\pi\)
−0.545904 + 0.837848i \(0.683814\pi\)
\(132\) 3.15765e9 0.905277
\(133\) −2.63866e9 4.18688e9i −0.731224 1.16027i
\(134\) −3.21039e9 −0.860173
\(135\) −1.88743e9 3.26913e9i −0.489069 0.847092i
\(136\) 6.61391e7 1.14556e8i 0.0165780 0.0287140i
\(137\) −3.65274e9 + 6.32673e9i −0.885882 + 1.53439i −0.0411834 + 0.999152i \(0.513113\pi\)
−0.844699 + 0.535242i \(0.820221\pi\)
\(138\) −2.46011e9 4.26104e9i −0.577430 1.00014i
\(139\) 2.79289e9 0.634581 0.317290 0.948328i \(-0.397227\pi\)
0.317290 + 0.948328i \(0.397227\pi\)
\(140\) −3.81153e9 + 1.47753e8i −0.838539 + 0.0325057i
\(141\) 6.08569e9 1.29665
\(142\) 2.42411e8 + 4.19868e8i 0.0500328 + 0.0866594i
\(143\) 3.17934e9 5.50678e9i 0.635806 1.10125i
\(144\) −3.40946e8 + 5.90535e8i −0.0660776 + 0.114450i
\(145\) 2.48716e8 + 4.30789e8i 0.0467248 + 0.0809298i
\(146\) 4.66954e9 0.850523
\(147\) 3.02006e9 6.31464e9i 0.533443 1.11537i
\(148\) 1.58746e9 0.271973
\(149\) 1.26713e9 + 2.19473e9i 0.210611 + 0.364789i 0.951906 0.306390i \(-0.0991212\pi\)
−0.741295 + 0.671180i \(0.765788\pi\)
\(150\) −4.92410e9 + 8.52879e9i −0.794175 + 1.37555i
\(151\) −1.55428e9 + 2.69210e9i −0.243295 + 0.421400i −0.961651 0.274276i \(-0.911562\pi\)
0.718356 + 0.695676i \(0.244895\pi\)
\(152\) −1.59553e9 2.76354e9i −0.242443 0.419923i
\(153\) 3.36019e8 0.0495738
\(154\) −7.22210e9 + 2.79963e8i −1.03471 + 0.0401104i
\(155\) −1.01154e10 −1.40764
\(156\) 1.98538e9 + 3.43878e9i 0.268400 + 0.464883i
\(157\) 5.81990e9 1.00804e10i 0.764481 1.32412i −0.176039 0.984383i \(-0.556329\pi\)
0.940520 0.339737i \(-0.110338\pi\)
\(158\) −8.70971e8 + 1.50857e9i −0.111185 + 0.192578i
\(159\) −3.70248e9 6.41288e9i −0.459415 0.795731i
\(160\) −2.45949e9 −0.296691
\(161\) 6.00450e9 + 9.52763e9i 0.704305 + 1.11755i
\(162\) 7.74333e9 0.883304
\(163\) 6.18632e9 + 1.07150e10i 0.686417 + 1.18891i 0.972989 + 0.230851i \(0.0741510\pi\)
−0.286572 + 0.958059i \(0.592516\pi\)
\(164\) −8.20268e8 + 1.42075e9i −0.0885439 + 0.153363i
\(165\) −1.44657e10 + 2.50553e10i −1.51936 + 2.63161i
\(166\) 1.73329e9 + 3.00215e9i 0.177168 + 0.306864i
\(167\) 6.26181e9 0.622982 0.311491 0.950249i \(-0.399172\pi\)
0.311491 + 0.950249i \(0.399172\pi\)
\(168\) 2.10356e9 3.99313e9i 0.203734 0.386743i
\(169\) −2.60842e9 −0.245973
\(170\) 6.05986e8 + 1.04960e9i 0.0556471 + 0.0963836i
\(171\) 4.05304e9 7.02007e9i 0.362492 0.627854i
\(172\) 8.95937e8 1.55181e9i 0.0780548 0.135195i
\(173\) 4.39565e8 + 7.61348e8i 0.0373091 + 0.0646213i 0.884077 0.467341i \(-0.154788\pi\)
−0.846768 + 0.531963i \(0.821455\pi\)
\(174\) −5.88579e8 −0.0486780
\(175\) 1.05061e10 1.99434e10i 0.846780 1.60742i
\(176\) −4.66024e9 −0.366101
\(177\) −2.52082e9 4.36619e9i −0.193047 0.334367i
\(178\) −1.49204e9 + 2.58428e9i −0.111401 + 0.192952i
\(179\) 8.36715e9 1.44923e10i 0.609170 1.05511i −0.382207 0.924077i \(-0.624836\pi\)
0.991377 0.131037i \(-0.0418308\pi\)
\(180\) −3.12385e9 5.41066e9i −0.221801 0.384170i
\(181\) −3.33844e9 −0.231201 −0.115601 0.993296i \(-0.536879\pi\)
−0.115601 + 0.993296i \(0.536879\pi\)
\(182\) −4.84580e9 7.68907e9i −0.327374 0.519461i
\(183\) −1.07333e10 −0.707462
\(184\) 3.63078e9 + 6.28869e9i 0.233517 + 0.404464i
\(185\) −7.27240e9 + 1.25962e10i −0.456462 + 0.790616i
\(186\) 5.98447e9 1.03654e10i 0.366621 0.635007i
\(187\) 1.14823e9 + 1.98878e9i 0.0686657 + 0.118932i
\(188\) −8.98161e9 −0.524377
\(189\) −1.02158e10 + 3.96013e8i −0.582364 + 0.0225752i
\(190\) 2.92375e10 1.62760
\(191\) 5.89031e9 + 1.02023e10i 0.320249 + 0.554688i 0.980539 0.196323i \(-0.0629000\pi\)
−0.660290 + 0.751011i \(0.729567\pi\)
\(192\) 1.45508e9 2.52026e9i 0.0772734 0.133841i
\(193\) 1.60936e10 2.78750e10i 0.834923 1.44613i −0.0591699 0.998248i \(-0.518845\pi\)
0.894093 0.447881i \(-0.147821\pi\)
\(194\) −7.63051e9 1.32164e10i −0.386764 0.669894i
\(195\) −3.63813e10 −1.80187
\(196\) −4.45719e9 + 9.31951e9i −0.215729 + 0.451067i
\(197\) −2.41075e10 −1.14039 −0.570195 0.821509i \(-0.693132\pi\)
−0.570195 + 0.821509i \(0.693132\pi\)
\(198\) −5.91908e9 1.02521e10i −0.273691 0.474047i
\(199\) −5.72788e9 + 9.92098e9i −0.258914 + 0.448452i −0.965951 0.258724i \(-0.916698\pi\)
0.707037 + 0.707176i \(0.250031\pi\)
\(200\) 7.26727e9 1.25873e10i 0.321171 0.556284i
\(201\) 1.74022e10 + 3.01414e10i 0.752005 + 1.30251i
\(202\) 3.11598e10 1.31678
\(203\) 1.34618e9 5.21844e7i 0.0556381 0.00215679i
\(204\) −1.43405e9 −0.0579733
\(205\) −7.51554e9 1.30173e10i −0.297213 0.514788i
\(206\) −1.10655e10 + 1.91660e10i −0.428123 + 0.741531i
\(207\) −9.22306e9 + 1.59748e10i −0.349147 + 0.604740i
\(208\) −2.93014e9 5.07515e9i −0.108543 0.188003i
\(209\) 5.53993e10 2.00838
\(210\) 2.20479e10 + 3.49845e10i 0.782313 + 1.24133i
\(211\) 2.03945e10 0.708339 0.354169 0.935181i \(-0.384764\pi\)
0.354169 + 0.935181i \(0.384764\pi\)
\(212\) 5.46433e9 + 9.46450e9i 0.185791 + 0.321800i
\(213\) 2.62802e9 4.55186e9i 0.0874822 0.151524i
\(214\) −1.53465e10 + 2.65809e10i −0.500205 + 0.866380i
\(215\) 8.20884e9 + 1.42181e10i 0.262005 + 0.453805i
\(216\) −6.59200e9 −0.206051
\(217\) −1.27685e10 + 2.42381e10i −0.390906 + 0.742045i
\(218\) −3.01608e10 −0.904458
\(219\) −2.53116e10 4.38410e10i −0.743568 1.28790i
\(220\) 2.13493e10 3.69780e10i 0.614442 1.06424i
\(221\) −1.44390e9 + 2.50091e9i −0.0407166 + 0.0705233i
\(222\) −8.60496e9 1.49042e10i −0.237772 0.411833i
\(223\) −5.72310e10 −1.54974 −0.774871 0.632119i \(-0.782185\pi\)
−0.774871 + 0.632119i \(0.782185\pi\)
\(224\) −3.10456e9 + 5.89330e9i −0.0823919 + 0.156402i
\(225\) 3.69213e10 0.960407
\(226\) −1.32734e10 2.29901e10i −0.338449 0.586210i
\(227\) −7.62484e9 + 1.32066e10i −0.190596 + 0.330122i −0.945448 0.325773i \(-0.894375\pi\)
0.754852 + 0.655895i \(0.227709\pi\)
\(228\) −1.72974e10 + 2.99600e10i −0.423910 + 0.734234i
\(229\) 1.74014e10 + 3.01402e10i 0.418144 + 0.724246i 0.995753 0.0920674i \(-0.0293475\pi\)
−0.577609 + 0.816313i \(0.696014\pi\)
\(230\) −6.65325e10 −1.56768
\(231\) 4.17764e10 + 6.62887e10i 0.965334 + 1.53174i
\(232\) 8.68659e8 0.0196858
\(233\) −3.71391e10 6.43268e10i −0.825524 1.42985i −0.901518 0.432741i \(-0.857546\pi\)
0.0759945 0.997108i \(-0.475787\pi\)
\(234\) 7.44327e9 1.28921e10i 0.162290 0.281095i
\(235\) 4.11461e10 7.12671e10i 0.880082 1.52435i
\(236\) 3.72037e9 + 6.44387e9i 0.0780697 + 0.135221i
\(237\) 1.88847e10 0.388814
\(238\) 3.27992e9 1.27145e8i 0.0662624 0.00256864i
\(239\) 6.12890e10 1.21504 0.607522 0.794303i \(-0.292164\pi\)
0.607522 + 0.794303i \(0.292164\pi\)
\(240\) 1.33318e10 + 2.30914e10i 0.259382 + 0.449262i
\(241\) 2.14369e10 3.71299e10i 0.409342 0.709001i −0.585474 0.810691i \(-0.699092\pi\)
0.994816 + 0.101690i \(0.0324251\pi\)
\(242\) 2.15891e10 3.73934e10i 0.404636 0.700851i
\(243\) −2.61347e10 4.52666e10i −0.480827 0.832816i
\(244\) 1.58408e10 0.286103
\(245\) −5.35292e10 7.80608e10i −0.949169 1.38416i
\(246\) 1.77853e10 0.309637
\(247\) 3.48324e10 + 6.03315e10i 0.595453 + 1.03136i
\(248\) −8.83223e9 + 1.52979e10i −0.148265 + 0.256802i
\(249\) 1.87909e10 3.25467e10i 0.309777 0.536550i
\(250\) 2.99357e10 + 5.18501e10i 0.484684 + 0.839498i
\(251\) −2.70921e10 −0.430835 −0.215417 0.976522i \(-0.569111\pi\)
−0.215417 + 0.976522i \(0.569111\pi\)
\(252\) −1.69079e10 + 6.55431e8i −0.264112 + 0.0102382i
\(253\) −1.26066e11 −1.93444
\(254\) −2.00602e10 3.47452e10i −0.302401 0.523774i
\(255\) 6.56959e9 1.13789e10i 0.0972988 0.168526i
\(256\) −2.14748e9 + 3.71955e9i −0.0312500 + 0.0541266i
\(257\) 4.17372e10 + 7.22909e10i 0.596793 + 1.03368i 0.993291 + 0.115641i \(0.0368921\pi\)
−0.396498 + 0.918036i \(0.629775\pi\)
\(258\) −1.94260e10 −0.272957
\(259\) 2.10025e10 + 3.33257e10i 0.290016 + 0.460182i
\(260\) 5.36936e10 0.728690
\(261\) 1.10330e9 + 1.91098e9i 0.0147168 + 0.0254902i
\(262\) −2.44117e10 + 4.22824e10i −0.320068 + 0.554375i
\(263\) −2.51663e10 + 4.35893e10i −0.324354 + 0.561797i −0.981381 0.192070i \(-0.938480\pi\)
0.657028 + 0.753866i \(0.271813\pi\)
\(264\) 2.52612e10 + 4.37537e10i 0.320064 + 0.554366i
\(265\) −1.00132e11 −1.24728
\(266\) 3.69059e10 7.00574e10i 0.451990 0.857998i
\(267\) 3.23508e10 0.389569
\(268\) −2.56831e10 4.44844e10i −0.304117 0.526746i
\(269\) −1.64843e10 + 2.85517e10i −0.191949 + 0.332466i −0.945896 0.324470i \(-0.894814\pi\)
0.753947 + 0.656935i \(0.228148\pi\)
\(270\) 3.01989e10 5.23061e10i 0.345824 0.598984i
\(271\) −1.18673e10 2.05547e10i −0.133656 0.231499i 0.791427 0.611263i \(-0.209338\pi\)
−0.925083 + 0.379764i \(0.876005\pi\)
\(272\) 2.11645e9 0.0234449
\(273\) −4.59234e10 + 8.71751e10i −0.500383 + 0.949862i
\(274\) −1.16888e11 −1.25283
\(275\) 1.26165e11 + 2.18525e11i 1.33028 + 2.30411i
\(276\) 3.93618e10 6.81767e10i 0.408305 0.707204i
\(277\) 4.15751e10 7.20101e10i 0.424301 0.734911i −0.572054 0.820216i \(-0.693853\pi\)
0.996355 + 0.0853053i \(0.0271866\pi\)
\(278\) 2.23431e10 + 3.86994e10i 0.224358 + 0.388600i
\(279\) −4.48720e10 −0.443360
\(280\) −3.25396e10 5.16321e10i −0.316374 0.502006i
\(281\) 1.48862e11 1.42431 0.712154 0.702023i \(-0.247720\pi\)
0.712154 + 0.702023i \(0.247720\pi\)
\(282\) 4.86855e10 + 8.43257e10i 0.458436 + 0.794034i
\(283\) −2.96776e10 + 5.14031e10i −0.275036 + 0.476377i −0.970144 0.242529i \(-0.922023\pi\)
0.695108 + 0.718905i \(0.255356\pi\)
\(284\) −3.87858e9 + 6.71789e9i −0.0353785 + 0.0612774i
\(285\) −1.58484e11 2.74502e11i −1.42293 2.46459i
\(286\) 1.01739e11 0.899166
\(287\) −4.06781e10 + 1.57688e9i −0.353910 + 0.0137192i
\(288\) −1.09103e10 −0.0934478
\(289\) 5.87725e10 + 1.01797e11i 0.495603 + 0.858409i
\(290\) −3.97946e9 + 6.89262e9i −0.0330394 + 0.0572260i
\(291\) −8.27235e10 + 1.43281e11i −0.676255 + 1.17131i
\(292\) 3.73563e10 + 6.47030e10i 0.300705 + 0.520837i
\(293\) 9.10565e10 0.721783 0.360892 0.932608i \(-0.382472\pi\)
0.360892 + 0.932608i \(0.382472\pi\)
\(294\) 1.11659e11 8.66986e9i 0.871625 0.0676783i
\(295\) −6.81743e10 −0.524109
\(296\) 1.26997e10 + 2.19965e10i 0.0961569 + 0.166549i
\(297\) 5.72211e10 9.91098e10i 0.426729 0.739116i
\(298\) −2.02740e10 + 3.51156e10i −0.148925 + 0.257945i
\(299\) −7.92644e10 1.37290e11i −0.573532 0.993387i
\(300\) −1.57571e11 −1.12313
\(301\) 4.44306e10 1.72234e9i 0.311985 0.0120940i
\(302\) −4.97370e10 −0.344071
\(303\) −1.68904e11 2.92551e11i −1.15119 1.99393i
\(304\) 2.55285e10 4.42167e10i 0.171433 0.296931i
\(305\) −7.25691e10 + 1.25693e11i −0.480178 + 0.831693i
\(306\) 2.68815e9 + 4.65602e9i 0.0175270 + 0.0303576i
\(307\) 6.61649e10 0.425114 0.212557 0.977149i \(-0.431821\pi\)
0.212557 + 0.977149i \(0.431821\pi\)
\(308\) −6.16561e10 9.78327e10i −0.390389 0.619449i
\(309\) 2.39926e11 1.49714
\(310\) −8.09235e10 1.40164e11i −0.497676 0.862001i
\(311\) −4.42158e9 + 7.65840e9i −0.0268013 + 0.0464212i −0.879115 0.476610i \(-0.841865\pi\)
0.852314 + 0.523031i \(0.175199\pi\)
\(312\) −3.17661e10 + 5.50205e10i −0.189788 + 0.328722i
\(313\) −7.90785e9 1.36968e10i −0.0465703 0.0806621i 0.841801 0.539789i \(-0.181496\pi\)
−0.888371 + 0.459126i \(0.848162\pi\)
\(314\) 1.86237e11 1.08114
\(315\) 7.22570e10 1.37163e11i 0.413507 0.784948i
\(316\) −2.78711e10 −0.157240
\(317\) −1.07701e11 1.86544e11i −0.599039 1.03757i −0.992963 0.118423i \(-0.962216\pi\)
0.393924 0.919143i \(-0.371117\pi\)
\(318\) 5.92397e10 1.02606e11i 0.324856 0.562667i
\(319\) −7.54029e9 + 1.30602e10i −0.0407690 + 0.0706139i
\(320\) −1.96759e10 3.40796e10i −0.104896 0.181685i
\(321\) 3.32748e11 1.74921
\(322\) −8.39827e10 + 1.59422e11i −0.435350 + 0.826412i
\(323\) −2.51596e10 −0.128615
\(324\) 6.19467e10 + 1.07295e11i 0.312295 + 0.540911i
\(325\) −1.58653e11 + 2.74796e11i −0.788814 + 1.36627i
\(326\) −9.89812e10 + 1.71440e11i −0.485370 + 0.840686i
\(327\) 1.63489e11 + 2.83171e11i 0.790721 + 1.36957i
\(328\) −2.62486e10 −0.125220
\(329\) −1.18829e11 1.88551e11i −0.559165 0.887254i
\(330\) −4.62901e11 −2.14870
\(331\) 2.01566e10 + 3.49123e10i 0.0922980 + 0.159865i 0.908478 0.417933i \(-0.137245\pi\)
−0.816180 + 0.577798i \(0.803912\pi\)
\(332\) −2.77326e10 + 4.80343e10i −0.125277 + 0.216985i
\(333\) −3.22603e10 + 5.58765e10i −0.143770 + 0.249018i
\(334\) 5.00945e10 + 8.67662e10i 0.220258 + 0.381497i
\(335\) 4.70632e11 2.04164
\(336\) 7.21590e10 2.79722e9i 0.308862 0.0119729i
\(337\) −1.47587e11 −0.623324 −0.311662 0.950193i \(-0.600886\pi\)
−0.311662 + 0.950193i \(0.600886\pi\)
\(338\) −2.08674e10 3.61434e10i −0.0869647 0.150627i
\(339\) −1.43898e11 + 2.49239e11i −0.591776 + 1.02499i
\(340\) −9.69578e9 + 1.67936e10i −0.0393485 + 0.0681535i
\(341\) −1.53334e11 2.65583e11i −0.614107 1.06367i
\(342\) 1.29697e11 0.512641
\(343\) −2.54614e11 + 2.97294e10i −0.993252 + 0.115974i
\(344\) 2.86700e10 0.110386
\(345\) 3.60645e11 + 6.24655e11i 1.37055 + 2.37385i
\(346\) −7.03303e9 + 1.21816e10i −0.0263816 + 0.0456942i
\(347\) 1.95063e11 3.37860e11i 0.722259 1.25099i −0.237833 0.971306i \(-0.576437\pi\)
0.960092 0.279683i \(-0.0902295\pi\)
\(348\) −4.70863e9 8.15559e9i −0.0172103 0.0298091i
\(349\) −2.60554e10 −0.0940119 −0.0470059 0.998895i \(-0.514968\pi\)
−0.0470059 + 0.998895i \(0.514968\pi\)
\(350\) 3.60393e11 1.39705e10i 1.28372 0.0497630i
\(351\) 1.43912e11 0.506074
\(352\) −3.72819e10 6.45742e10i −0.129436 0.224190i
\(353\) −3.75792e10 + 6.50892e10i −0.128814 + 0.223112i −0.923217 0.384279i \(-0.874450\pi\)
0.794404 + 0.607390i \(0.207784\pi\)
\(354\) 4.03331e10 6.98590e10i 0.136505 0.236433i
\(355\) −3.55367e10 6.15513e10i −0.118754 0.205688i
\(356\) −4.77452e10 −0.157545
\(357\) −1.89728e10 3.01051e10i −0.0618194 0.0980918i
\(358\) 2.67749e11 0.861497
\(359\) −1.43619e11 2.48755e11i −0.456338 0.790400i 0.542426 0.840103i \(-0.317506\pi\)
−0.998764 + 0.0497032i \(0.984172\pi\)
\(360\) 4.99815e10 8.65706e10i 0.156837 0.271650i
\(361\) −1.42130e11 + 2.46176e11i −0.440456 + 0.762892i
\(362\) −2.67075e10 4.62588e10i −0.0817420 0.141581i
\(363\) −4.68101e11 −1.41501
\(364\) 6.77765e10 1.28658e11i 0.202359 0.384132i
\(365\) −6.84539e11 −2.01874
\(366\) −8.58663e10 1.48725e11i −0.250125 0.433230i
\(367\) 2.54453e11 4.40726e11i 0.732168 1.26815i −0.223787 0.974638i \(-0.571842\pi\)
0.955955 0.293514i \(-0.0948247\pi\)
\(368\) −5.80924e10 + 1.00619e11i −0.165122 + 0.285999i
\(369\) −3.33389e10 5.77447e10i −0.0936122 0.162141i
\(370\) −2.32717e11 −0.645535
\(371\) −1.26394e11 + 2.39931e11i −0.346374 + 0.657511i
\(372\) 1.91503e11 0.518481
\(373\) −5.17260e10 8.95921e10i −0.138363 0.239651i 0.788514 0.615016i \(-0.210851\pi\)
−0.926877 + 0.375365i \(0.877517\pi\)
\(374\) −1.83716e10 + 3.18205e10i −0.0485540 + 0.0840980i
\(375\) 3.24537e11 5.62115e11i 0.847469 1.46786i
\(376\) −7.18528e10 1.24453e11i −0.185395 0.321114i
\(377\) −1.89639e10 −0.0483495
\(378\) −8.72137e10 1.38386e11i −0.219721 0.348642i
\(379\) 1.10894e11 0.276078 0.138039 0.990427i \(-0.455920\pi\)
0.138039 + 0.990427i \(0.455920\pi\)
\(380\) 2.33900e11 + 4.05126e11i 0.575445 + 0.996699i
\(381\) −2.17475e11 + 3.76679e11i −0.528747 + 0.915817i
\(382\) −9.42450e10 + 1.63237e11i −0.226450 + 0.392224i
\(383\) −1.29972e11 2.25118e11i −0.308642 0.534584i 0.669424 0.742881i \(-0.266541\pi\)
−0.978066 + 0.208297i \(0.933208\pi\)
\(384\) 4.65624e10 0.109281
\(385\) 1.05874e12 4.10416e10i 2.45592 0.0952031i
\(386\) 5.14997e11 1.18076
\(387\) 3.64144e10 + 6.30716e10i 0.0825227 + 0.142934i
\(388\) 1.22088e11 2.11463e11i 0.273483 0.473687i
\(389\) −2.91278e11 + 5.04508e11i −0.644963 + 1.11711i 0.339347 + 0.940661i \(0.389794\pi\)
−0.984310 + 0.176447i \(0.943540\pi\)
\(390\) −2.91050e11 5.04114e11i −0.637056 1.10341i
\(391\) 5.72530e10 0.123880
\(392\) −1.64792e11 + 1.27955e10i −0.352492 + 0.0273697i
\(393\) 5.29303e11 1.11928
\(394\) −1.92860e11 3.34043e11i −0.403189 0.698343i
\(395\) 1.27682e11 2.21151e11i 0.263901 0.457090i
\(396\) 9.47052e10 1.64034e11i 0.193529 0.335202i
\(397\) 9.35365e10 + 1.62010e11i 0.188983 + 0.327329i 0.944912 0.327326i \(-0.106147\pi\)
−0.755928 + 0.654655i \(0.772814\pi\)
\(398\) −1.83292e11 −0.366159
\(399\) −8.57800e11 + 3.32524e10i −1.69437 + 0.0656817i
\(400\) 2.32553e11 0.454204
\(401\) 4.41371e11 + 7.64477e11i 0.852420 + 1.47644i 0.879018 + 0.476789i \(0.158200\pi\)
−0.0265971 + 0.999646i \(0.508467\pi\)
\(402\) −2.78434e11 + 4.82263e11i −0.531748 + 0.921014i
\(403\) 1.92819e11 3.33972e11i 0.364147 0.630720i
\(404\) 2.49279e11 + 4.31763e11i 0.465553 + 0.806361i
\(405\) −1.13515e12 −2.09655
\(406\) 1.14926e10 + 1.82358e10i 0.0209918 + 0.0333087i
\(407\) −4.40953e11 −0.796557
\(408\) −1.14724e10 1.98708e10i −0.0204967 0.0355013i
\(409\) 1.97162e11 3.41495e11i 0.348393 0.603434i −0.637571 0.770391i \(-0.720061\pi\)
0.985964 + 0.166957i \(0.0533942\pi\)
\(410\) 1.20249e11 2.08277e11i 0.210161 0.364010i
\(411\) 6.33598e11 + 1.09742e12i 1.09528 + 1.89708i
\(412\) −3.54096e11 −0.605458
\(413\) −8.60551e10 + 1.63356e11i −0.145546 + 0.276286i
\(414\) −2.95138e11 −0.493769
\(415\) −2.54095e11 4.40105e11i −0.420513 0.728349i
\(416\) 4.68822e10 8.12024e10i 0.0767518 0.132938i
\(417\) 2.42225e11 4.19546e11i 0.392290 0.679465i
\(418\) 4.43194e11 + 7.67635e11i 0.710069 + 1.22988i
\(419\) −1.77960e11 −0.282072 −0.141036 0.990004i \(-0.545043\pi\)
−0.141036 + 0.990004i \(0.545043\pi\)
\(420\) −3.08376e11 + 5.85380e11i −0.483569 + 0.917944i
\(421\) 3.94445e11 0.611952 0.305976 0.952039i \(-0.401017\pi\)
0.305976 + 0.952039i \(0.401017\pi\)
\(422\) 1.63156e11 + 2.82594e11i 0.250436 + 0.433767i
\(423\) 1.82524e11 3.16140e11i 0.277196 0.480118i
\(424\) −8.74293e10 + 1.51432e11i −0.131374 + 0.227547i
\(425\) −5.72980e10 9.92431e10i −0.0851902 0.147554i
\(426\) 8.40965e10 0.123719
\(427\) 2.09578e11 + 3.32547e11i 0.305084 + 0.484091i
\(428\) −4.91088e11 −0.707396
\(429\) −5.51483e11 9.55197e11i −0.786094 1.36156i
\(430\) −1.31341e11 + 2.27490e11i −0.185265 + 0.320889i
\(431\) −4.03895e11 + 6.99567e11i −0.563795 + 0.976521i 0.433366 + 0.901218i \(0.357326\pi\)
−0.997161 + 0.0753033i \(0.976008\pi\)
\(432\) −5.27360e10 9.13415e10i −0.0728502 0.126180i
\(433\) 5.77686e11 0.789763 0.394881 0.918732i \(-0.370786\pi\)
0.394881 + 0.918732i \(0.370786\pi\)
\(434\) −4.38001e11 + 1.69790e10i −0.592614 + 0.0229725i
\(435\) 8.62838e10 0.115539
\(436\) −2.41286e11 4.17920e11i −0.319774 0.553865i
\(437\) 6.90582e11 1.19612e12i 0.905834 1.56895i
\(438\) 4.04985e11 7.01455e11i 0.525782 0.910682i
\(439\) 6.64142e11 + 1.15033e12i 0.853436 + 1.47819i 0.878089 + 0.478498i \(0.158819\pi\)
−0.0246530 + 0.999696i \(0.507848\pi\)
\(440\) 6.83176e11 0.868952
\(441\) −2.37455e11 3.46277e11i −0.298957 0.435964i
\(442\) −4.62048e10 −0.0575820
\(443\) −2.49733e11 4.32551e11i −0.308077 0.533606i 0.669864 0.742483i \(-0.266352\pi\)
−0.977942 + 0.208878i \(0.933019\pi\)
\(444\) 1.37679e11 2.38468e11i 0.168130 0.291210i
\(445\) 2.18728e11 3.78848e11i 0.264414 0.457978i
\(446\) −4.57848e11 7.93016e11i −0.547917 0.949020i
\(447\) 4.39588e11 0.520789
\(448\) −1.06496e11 + 4.12830e9i −0.124906 + 0.00484195i
\(449\) −4.51211e10 −0.0523927 −0.0261964 0.999657i \(-0.508340\pi\)
−0.0261964 + 0.999657i \(0.508340\pi\)
\(450\) 2.95370e11 + 5.11596e11i 0.339555 + 0.588127i
\(451\) 2.27848e11 3.94644e11i 0.259328 0.449170i
\(452\) 2.12374e11 3.67842e11i 0.239319 0.414513i
\(453\) 2.69603e11 + 4.66967e11i 0.300804 + 0.521008i
\(454\) −2.43995e11 −0.269544
\(455\) 7.10379e11 + 1.12719e12i 0.777032 + 1.23295i
\(456\) −5.53517e11 −0.599500
\(457\) −3.17610e11 5.50117e11i −0.340621 0.589973i 0.643927 0.765087i \(-0.277304\pi\)
−0.984548 + 0.175114i \(0.943971\pi\)
\(458\) −2.78423e11 + 4.82243e11i −0.295672 + 0.512119i
\(459\) −2.59870e10 + 4.50108e10i −0.0273274 + 0.0473325i
\(460\) −5.32260e11 9.21901e11i −0.554260 0.960007i
\(461\) −1.21010e12 −1.24786 −0.623932 0.781479i \(-0.714466\pi\)
−0.623932 + 0.781479i \(0.714466\pi\)
\(462\) −5.84312e11 + 1.10918e12i −0.596699 + 1.13270i
\(463\) 9.73087e11 0.984095 0.492047 0.870568i \(-0.336249\pi\)
0.492047 + 0.870568i \(0.336249\pi\)
\(464\) 6.94927e9 + 1.20365e10i 0.00695999 + 0.0120550i
\(465\) −8.77304e11 + 1.51954e12i −0.870186 + 1.50721i
\(466\) 5.94225e11 1.02923e12i 0.583733 1.01106i
\(467\) −8.41530e11 1.45757e12i −0.818735 1.41809i −0.906614 0.421960i \(-0.861342\pi\)
0.0878789 0.996131i \(-0.471991\pi\)
\(468\) 2.38185e11 0.229513
\(469\) 5.94070e11 1.12771e12i 0.566970 1.07626i
\(470\) 1.31667e12 1.24462
\(471\) −1.00951e12 1.74852e12i −0.945185 1.63711i
\(472\) −5.95259e10 + 1.03102e11i −0.0552036 + 0.0956154i
\(473\) −2.48866e11 + 4.31049e11i −0.228608 + 0.395960i
\(474\) 1.51077e11 + 2.61674e11i 0.137466 + 0.238099i
\(475\) −2.76450e12 −2.49170
\(476\) 2.80012e10 + 4.44308e10i 0.0250003 + 0.0396691i
\(477\) −4.44184e11 −0.392853
\(478\) 4.90312e11 + 8.49245e11i 0.429583 + 0.744059i
\(479\) −5.82335e11 + 1.00863e12i −0.505432 + 0.875434i 0.494548 + 0.869150i \(0.335334\pi\)
−0.999980 + 0.00628383i \(0.998000\pi\)
\(480\) −2.13309e11 + 3.69462e11i −0.183410 + 0.317676i
\(481\) −2.77250e11 4.80211e11i −0.236167 0.409053i
\(482\) 6.85982e11 0.578897
\(483\) 1.95200e12 7.56688e10i 1.63199 0.0632637i
\(484\) 6.90850e11 0.572242
\(485\) 1.11861e12 + 1.93749e12i 0.917994 + 1.59001i
\(486\) 4.18155e11 7.24265e11i 0.339996 0.588890i
\(487\) −1.12077e12 + 1.94123e12i −0.902891 + 1.56385i −0.0791677 + 0.996861i \(0.525226\pi\)
−0.823723 + 0.566992i \(0.808107\pi\)
\(488\) 1.26726e11 + 2.19497e11i 0.101153 + 0.175202i
\(489\) 2.14614e12 1.69734
\(490\) 6.53409e11 1.36621e12i 0.512039 1.07062i
\(491\) 1.65508e11 0.128515 0.0642573 0.997933i \(-0.479532\pi\)
0.0642573 + 0.997933i \(0.479532\pi\)
\(492\) 1.42282e11 + 2.46440e11i 0.109473 + 0.189613i
\(493\) 3.42443e9 5.93128e9i 0.00261082 0.00452207i
\(494\) −5.57319e11 + 9.65305e11i −0.421049 + 0.729278i
\(495\) 8.67717e11 + 1.50293e12i 0.649613 + 1.12516i
\(496\) −2.82631e11 −0.209678
\(497\) −1.92344e11 + 7.45614e9i −0.141408 + 0.00548164i
\(498\) 6.01307e11 0.438091
\(499\) 6.06773e11 + 1.05096e12i 0.438100 + 0.758812i 0.997543 0.0700572i \(-0.0223182\pi\)
−0.559443 + 0.828869i \(0.688985\pi\)
\(500\) −4.78971e11 + 8.29602e11i −0.342724 + 0.593615i
\(501\) 5.43082e11 9.40646e11i 0.385120 0.667047i
\(502\) −2.16737e11 3.75399e11i −0.152323 0.263831i
\(503\) 8.95258e10 0.0623580 0.0311790 0.999514i \(-0.490074\pi\)
0.0311790 + 0.999514i \(0.490074\pi\)
\(504\) −1.44345e11 2.29040e11i −0.0996473 0.158115i
\(505\) −4.56793e12 −3.12542
\(506\) −1.00853e12 1.74682e12i −0.683929 1.18460i
\(507\) −2.26227e11 + 3.91836e11i −0.152058 + 0.263371i
\(508\) 3.20963e11 5.55924e11i 0.213830 0.370364i
\(509\) −6.66954e11 1.15520e12i −0.440419 0.762828i 0.557302 0.830310i \(-0.311837\pi\)
−0.997720 + 0.0674822i \(0.978503\pi\)
\(510\) 2.10227e11 0.137601
\(511\) −8.64081e11 + 1.64026e12i −0.560609 + 1.06419i
\(512\) −6.87195e10 −0.0441942
\(513\) 6.26907e11 + 1.08583e12i 0.399645 + 0.692206i
\(514\) −6.67795e11 + 1.15665e12i −0.421997 + 0.730919i
\(515\) 1.62217e12 2.80968e12i 1.01616 1.76005i
\(516\) −1.55408e11 2.69174e11i −0.0965049 0.167151i
\(517\) 2.49484e12 1.53580
\(518\) −2.93754e11 + 5.57624e11i −0.179267 + 0.340297i
\(519\) 1.52492e11 0.0922561
\(520\) 4.29549e11 + 7.44001e11i 0.257631 + 0.446230i
\(521\) 2.86045e11 4.95444e11i 0.170084 0.294595i −0.768365 0.640012i \(-0.778929\pi\)
0.938449 + 0.345417i \(0.112263\pi\)
\(522\) −1.76528e10 + 3.05756e10i −0.0104063 + 0.0180243i
\(523\) 1.25008e12 + 2.16521e12i 0.730602 + 1.26544i 0.956626 + 0.291318i \(0.0940938\pi\)
−0.226024 + 0.974122i \(0.572573\pi\)
\(524\) −7.81175e11 −0.452645
\(525\) −2.08470e12 3.30790e12i −1.19764 1.90036i
\(526\) −8.05322e11 −0.458705
\(527\) 6.96368e10 + 1.20615e11i 0.0393270 + 0.0681164i
\(528\) −4.04179e11 + 7.00059e11i −0.226319 + 0.391996i
\(529\) −6.70905e11 + 1.16204e12i −0.372486 + 0.645165i
\(530\) −8.01053e11 1.38747e12i −0.440981 0.763802i
\(531\) −3.02421e11 −0.165077
\(532\) 1.26599e12 4.90758e10i 0.685217 0.0265622i
\(533\) 5.73039e11 0.307547
\(534\) 2.58806e11 + 4.48266e11i 0.137733 + 0.238561i
\(535\) 2.24975e12 3.89668e12i 1.18725 2.05638i
\(536\) 4.10930e11 7.11751e11i 0.215043 0.372466i
\(537\) −1.45135e12 2.51382e12i −0.753162 1.30452i
\(538\) −5.27499e11 −0.271457
\(539\) 1.23808e12 2.58870e12i 0.631829 1.32109i
\(540\) 9.66366e11 0.489069
\(541\) −5.24154e11 9.07861e11i −0.263070 0.455650i 0.703986 0.710213i \(-0.251402\pi\)
−0.967056 + 0.254563i \(0.918068\pi\)
\(542\) 1.89876e11 3.28875e11i 0.0945091 0.163694i
\(543\) −2.89541e11 + 5.01499e11i −0.142926 + 0.247554i
\(544\) 1.69316e10 + 2.93264e10i 0.00828902 + 0.0143570i
\(545\) 4.42147e12 2.14676
\(546\) −1.57532e12 + 6.10668e10i −0.758581 + 0.0294062i
\(547\) −3.50622e12 −1.67454 −0.837272 0.546786i \(-0.815851\pi\)
−0.837272 + 0.546786i \(0.815851\pi\)
\(548\) −9.35101e11 1.61964e12i −0.442941 0.767197i
\(549\) −3.21916e11 + 5.57575e11i −0.151240 + 0.261956i
\(550\) −2.01864e12 + 3.49639e12i −0.940649 + 1.62925i
\(551\) −8.26104e10 1.43085e11i −0.0381815 0.0661322i
\(552\) 1.25958e12 0.577430
\(553\) −3.68741e11 5.85099e11i −0.167671 0.266052i
\(554\) 1.33040e12 0.600052
\(555\) 1.26146e12 + 2.18491e12i 0.564358 + 0.977497i
\(556\) −3.57490e11 + 6.19190e11i −0.158645 + 0.274782i
\(557\) −1.12138e12 + 1.94228e12i −0.493631 + 0.854994i −0.999973 0.00733847i \(-0.997664\pi\)
0.506342 + 0.862333i \(0.330997\pi\)
\(558\) −3.58976e11 6.21765e11i −0.156752 0.271502i
\(559\) −6.25901e11 −0.271115
\(560\) 4.55119e11 8.63938e11i 0.195559 0.371224i
\(561\) 3.98339e11 0.169793
\(562\) 1.19089e12 + 2.06269e12i 0.503569 + 0.872207i
\(563\) −1.01923e12 + 1.76536e12i −0.427547 + 0.740533i −0.996655 0.0817298i \(-0.973956\pi\)
0.569107 + 0.822263i \(0.307289\pi\)
\(564\) −7.78968e11 + 1.34921e12i −0.324163 + 0.561467i
\(565\) 1.94583e12 + 3.37028e12i 0.803317 + 1.39139i
\(566\) −9.49683e11 −0.388960
\(567\) −1.43288e12 + 2.71998e12i −0.582217 + 1.10520i
\(568\) −1.24114e11 −0.0500328
\(569\) −6.24361e11 1.08142e12i −0.249707 0.432505i 0.713738 0.700413i \(-0.247001\pi\)
−0.963444 + 0.267908i \(0.913668\pi\)
\(570\) 2.53574e12 4.39204e12i 1.00616 1.74273i
\(571\) −1.14336e12 + 1.98036e12i −0.450113 + 0.779619i −0.998393 0.0566765i \(-0.981950\pi\)
0.548280 + 0.836295i \(0.315283\pi\)
\(572\) 8.13911e11 + 1.40974e12i 0.317903 + 0.550624i
\(573\) 2.04345e12 0.791896
\(574\) −3.47275e11 5.51038e11i −0.133527 0.211874i
\(575\) 6.29087e12 2.39997
\(576\) −8.72821e10 1.51177e11i −0.0330388 0.0572249i
\(577\) 1.30799e12 2.26550e12i 0.491260 0.850888i −0.508689 0.860950i \(-0.669870\pi\)
0.999949 + 0.0100624i \(0.00320301\pi\)
\(578\) −9.40360e11 + 1.62875e12i −0.350444 + 0.606987i
\(579\) −2.79158e12 4.83516e12i −1.03228 1.78796i
\(580\) −1.27343e11 −0.0467248
\(581\) −1.37530e12 + 5.33129e10i −0.500730 + 0.0194107i
\(582\) −2.64715e12 −0.956369
\(583\) −1.51784e12 2.62897e12i −0.544148 0.942492i
\(584\) −5.97701e11 + 1.03525e12i −0.212631 + 0.368287i
\(585\) −1.09116e12 + 1.88994e12i −0.385200 + 0.667187i
\(586\) 7.28452e11 + 1.26172e12i 0.255189 + 0.442000i
\(587\) −3.09779e12 −1.07691 −0.538457 0.842653i \(-0.680993\pi\)
−0.538457 + 0.842653i \(0.680993\pi\)
\(588\) 1.01340e12 + 1.47783e12i 0.349610 + 0.509831i
\(589\) 3.35982e12 1.15026
\(590\) −5.45394e11 9.44651e11i −0.185301 0.320950i
\(591\) −2.09082e12 + 3.62141e12i −0.704974 + 1.22105i
\(592\) −2.03195e11 + 3.51944e11i −0.0679932 + 0.117768i
\(593\) 1.31976e12 + 2.28590e12i 0.438278 + 0.759120i 0.997557 0.0698599i \(-0.0222552\pi\)
−0.559279 + 0.828980i \(0.688922\pi\)
\(594\) 1.83107e12 0.603486
\(595\) −4.80826e11 + 1.86391e10i −0.157276 + 0.00609675i
\(596\) −6.48769e11 −0.210611
\(597\) 9.93550e11 + 1.72088e12i 0.320114 + 0.554454i
\(598\) 1.26823e12 2.19664e12i 0.405548 0.702430i
\(599\) 1.89224e12 3.27745e12i 0.600558 1.04020i −0.392178 0.919889i \(-0.628278\pi\)
0.992737 0.120308i \(-0.0383882\pi\)
\(600\) −1.26057e12 2.18337e12i −0.397087 0.687775i
\(601\) −5.10190e11 −0.159513 −0.0797567 0.996814i \(-0.525414\pi\)
−0.0797567 + 0.996814i \(0.525414\pi\)
\(602\) 3.79311e11 + 6.01870e11i 0.117709 + 0.186775i
\(603\) 2.08772e12 0.643050
\(604\) −3.97896e11 6.89177e11i −0.121648 0.210700i
\(605\) −3.16489e12 + 5.48175e12i −0.960415 + 1.66349i
\(606\) 2.70247e12 4.68081e12i 0.814017 1.40992i
\(607\) −2.44927e12 4.24227e12i −0.732299 1.26838i −0.955898 0.293697i \(-0.905114\pi\)
0.223600 0.974681i \(-0.428219\pi\)
\(608\) 8.16912e11 0.242443
\(609\) 1.08914e11 2.06749e11i 0.0320854 0.0609067i
\(610\) −2.32221e12 −0.679074
\(611\) 1.56864e12 + 2.71696e12i 0.455341 + 0.788674i
\(612\) −4.30104e10 + 7.44963e10i −0.0123935 + 0.0214661i
\(613\) −2.18246e12 + 3.78013e12i −0.624272 + 1.08127i 0.364409 + 0.931239i \(0.381271\pi\)
−0.988681 + 0.150032i \(0.952062\pi\)
\(614\) 5.29319e11 + 9.16808e11i 0.150300 + 0.260328i
\(615\) −2.60727e12 −0.734933
\(616\) 8.62361e11 1.63699e12i 0.241310 0.458072i
\(617\) −3.81081e12 −1.05861 −0.529303 0.848433i \(-0.677547\pi\)
−0.529303 + 0.848433i \(0.677547\pi\)
\(618\) 1.91941e12 + 3.32451e12i 0.529321 + 0.916810i
\(619\) 7.62819e11 1.32124e12i 0.208840 0.361721i −0.742509 0.669836i \(-0.766365\pi\)
0.951349 + 0.308114i \(0.0996979\pi\)
\(620\) 1.29478e12 2.24262e12i 0.351910 0.609527i
\(621\) −1.42658e12 2.47091e12i −0.384933 0.666723i
\(622\) −1.41491e11 −0.0379028
\(623\) −6.31680e11 1.00232e12i −0.167997 0.266568i
\(624\) −1.01652e12 −0.268400
\(625\) −9.23168e11 1.59897e12i −0.242003 0.419162i
\(626\) 1.26526e11 2.19149e11i 0.0329302 0.0570367i
\(627\) 4.80473e12 8.32204e12i 1.24155 2.15043i
\(628\) 1.48989e12 + 2.58057e12i 0.382241 + 0.662060i
\(629\) 2.00259e11 0.0510110
\(630\) 2.47865e12 9.60840e10i 0.626877 0.0243007i
\(631\) −6.08153e12 −1.52715 −0.763573 0.645721i \(-0.776557\pi\)
−0.763573 + 0.645721i \(0.776557\pi\)
\(632\) −2.22969e11 3.86193e11i −0.0555926 0.0962892i
\(633\) 1.76880e12 3.06364e12i 0.437886 0.758441i
\(634\) 1.72322e12 2.98471e12i 0.423584 0.733670i
\(635\) 2.94076e12 + 5.09354e12i 0.717757 + 1.24319i
\(636\) 1.89567e12 0.459415
\(637\) 3.59762e12 2.79341e11i 0.865741 0.0672214i
\(638\) −2.41289e11 −0.0576560
\(639\) −1.57640e11 2.73041e11i −0.0374036 0.0647850i
\(640\) 3.14814e11 5.45274e11i 0.0741727 0.128471i
\(641\) 6.84081e11 1.18486e12i 0.160047 0.277209i −0.774839 0.632159i \(-0.782169\pi\)
0.934885 + 0.354950i \(0.115502\pi\)
\(642\) 2.66198e12 + 4.61069e12i 0.618440 + 1.07117i
\(643\) −2.94301e12 −0.678958 −0.339479 0.940614i \(-0.610251\pi\)
−0.339479 + 0.940614i \(0.610251\pi\)
\(644\) −2.88088e12 + 1.11676e11i −0.659991 + 0.0255844i
\(645\) 2.84779e12 0.647871
\(646\) −2.01277e11 3.48622e11i −0.0454724 0.0787605i
\(647\) 2.20167e12 3.81341e12i 0.493951 0.855547i −0.506025 0.862519i \(-0.668886\pi\)
0.999976 + 0.00697131i \(0.00221906\pi\)
\(648\) −9.91147e11 + 1.71672e12i −0.220826 + 0.382482i
\(649\) −1.03342e12 1.78993e12i −0.228651 0.396036i
\(650\) −5.07691e12 −1.11555
\(651\) 2.53363e12 + 4.02023e12i 0.552878 + 0.877277i
\(652\) −3.16740e12 −0.686417
\(653\) −3.43720e11 5.95340e11i −0.0739767 0.128131i 0.826664 0.562696i \(-0.190236\pi\)
−0.900641 + 0.434564i \(0.856902\pi\)
\(654\) −2.61582e12 + 4.53074e12i −0.559124 + 0.968432i
\(655\) 3.57868e12 6.19846e12i 0.759691 1.31582i
\(656\) −2.09989e11 3.63711e11i −0.0442719 0.0766813i
\(657\) −3.03661e12 −0.635836
\(658\) 1.66201e12 3.15495e12i 0.345635 0.656109i
\(659\) 7.48190e12 1.54535 0.772676 0.634800i \(-0.218918\pi\)
0.772676 + 0.634800i \(0.218918\pi\)
\(660\) −3.70321e12 6.41415e12i −0.759680 1.31580i
\(661\) −4.14386e12 + 7.17738e12i −0.844303 + 1.46238i 0.0419217 + 0.999121i \(0.486652\pi\)
−0.886225 + 0.463255i \(0.846681\pi\)
\(662\) −3.22506e11 + 5.58597e11i −0.0652645 + 0.113041i
\(663\) 2.50457e11 + 4.33804e11i 0.0503410 + 0.0871931i
\(664\) −8.87444e11 −0.177168
\(665\) −5.41029e12 + 1.02702e13i −1.07281 + 2.03648i
\(666\) −1.03233e12 −0.203322
\(667\) 1.87987e11 + 3.25604e11i 0.0367758 + 0.0636976i
\(668\) −8.01512e11 + 1.38826e12i −0.155746 + 0.269759i
\(669\) −4.96360e12 + 8.59721e12i −0.958031 + 1.65936i
\(670\) 3.76506e12 + 6.52127e12i 0.721830 + 1.25025i
\(671\) −4.40013e12 −0.837943
\(672\) 6.16032e11 + 9.77487e11i 0.116531 + 0.184905i
\(673\) −2.54077e11 −0.0477416 −0.0238708 0.999715i \(-0.507599\pi\)
−0.0238708 + 0.999715i \(0.507599\pi\)
\(674\) −1.18070e12 2.04503e12i −0.220378 0.381707i
\(675\) −2.85541e12 + 4.94572e12i −0.529422 + 0.916985i
\(676\) 3.33878e11 5.78294e11i 0.0614933 0.106510i
\(677\) −4.85902e12 8.41607e12i −0.888995 1.53979i −0.841065 0.540934i \(-0.818071\pi\)
−0.0479305 0.998851i \(-0.515263\pi\)
\(678\) −4.60475e12 −0.836898
\(679\) 6.05450e12 2.34701e11i 1.09311 0.0423742i
\(680\) −3.10265e11 −0.0556471
\(681\) 1.32259e12 + 2.29080e12i 0.235648 + 0.408155i
\(682\) 2.45335e12 4.24932e12i 0.434239 0.752125i
\(683\) 3.77058e12 6.53084e12i 0.663003 1.14835i −0.316820 0.948486i \(-0.602615\pi\)
0.979823 0.199869i \(-0.0640515\pi\)
\(684\) 1.03758e12 + 1.79714e12i 0.181246 + 0.313927i
\(685\) 1.71353e13 2.97362
\(686\) −2.44886e12 3.29021e12i −0.422187 0.567237i
\(687\) 6.03685e12 1.03396
\(688\) 2.29360e11 + 3.97263e11i 0.0390274 + 0.0675974i
\(689\) 1.90869e12 3.30595e12i 0.322663 0.558869i
\(690\) −5.77031e12 + 9.99448e12i −0.969122 + 1.67857i
\(691\) 5.14662e12 + 8.91420e12i 0.858758 + 1.48741i 0.873115 + 0.487515i \(0.162097\pi\)
−0.0143570 + 0.999897i \(0.504570\pi\)
\(692\) −2.25057e11 −0.0373091
\(693\) 4.69655e12 1.82060e11i 0.773534 0.0299858i
\(694\) 6.24203e12 1.02143
\(695\) −3.27543e12 5.67320e12i −0.532520 0.922352i
\(696\) 7.53381e10 1.30489e11i 0.0121695 0.0210782i
\(697\) −1.03477e11 + 1.79228e11i −0.0166072 + 0.0287646i
\(698\) −2.08443e11 3.61034e11i −0.0332382 0.0575703i
\(699\) −1.28842e13 −2.04131
\(700\) 3.07672e12 + 4.88199e12i 0.484337 + 0.768520i
\(701\) 9.10623e12 1.42432 0.712160 0.702017i \(-0.247717\pi\)
0.712160 + 0.702017i \(0.247717\pi\)
\(702\) 1.15129e12 + 1.99410e12i 0.178924 + 0.309906i
\(703\) 2.41551e12 4.18378e12i 0.373001 0.646056i
\(704\) 5.96511e11 1.03319e12i 0.0915254 0.158527i
\(705\) −7.13713e12 1.23619e13i −1.08811 1.88466i
\(706\) −1.20254e12 −0.182170
\(707\) −5.76601e12 + 1.09454e13i −0.867937 + 1.64758i
\(708\) 1.29066e12 0.193047
\(709\) −3.26486e12 5.65491e12i −0.485240 0.840461i 0.514616 0.857421i \(-0.327935\pi\)
−0.999856 + 0.0169599i \(0.994601\pi\)
\(710\) 5.68587e11 9.84821e11i 0.0839719 0.145444i
\(711\) 5.66395e11 9.81025e11i 0.0831201 0.143968i
\(712\) −3.81961e11 6.61577e11i −0.0557005 0.0964762i
\(713\) −7.64557e12 −1.10792
\(714\) 2.65366e11 5.03735e11i 0.0382122 0.0725372i
\(715\) −1.49146e13 −2.13419
\(716\) 2.14199e12 + 3.71004e12i 0.304585 + 0.527557i
\(717\) 5.31555e12 9.20680e12i 0.751124 1.30098i
\(718\) 2.29790e12 3.98008e12i 0.322680 0.558897i
\(719\) 5.24753e12 + 9.08899e12i 0.732276 + 1.26834i 0.955908 + 0.293666i \(0.0948754\pi\)
−0.223632 + 0.974674i \(0.571791\pi\)
\(720\) 1.59941e12 0.221801
\(721\) −4.68478e12 7.43356e12i −0.645625 1.02444i
\(722\) −4.54815e12 −0.622899
\(723\) −3.71842e12 6.44049e12i −0.506099 0.876590i
\(724\) 4.27321e11 7.40141e11i 0.0578003 0.100113i
\(725\) 3.76271e11 6.51720e11i 0.0505801 0.0876073i
\(726\) −3.74481e12 6.48620e12i −0.500282 0.866513i
\(727\) 3.77271e12 0.500898 0.250449 0.968130i \(-0.419422\pi\)
0.250449 + 0.968130i \(0.419422\pi\)
\(728\) 2.32495e12 9.01260e10i 0.306777 0.0118921i
\(729\) 4.59195e11 0.0602176
\(730\) −5.47631e12 9.48525e12i −0.713732 1.23622i
\(731\) 1.13023e11 1.95761e11i 0.0146399 0.0253570i
\(732\) 1.37386e12 2.37960e12i 0.176865 0.306340i
\(733\) 6.93047e12 + 1.20039e13i 0.886737 + 1.53587i 0.843710 + 0.536799i \(0.180367\pi\)
0.0430263 + 0.999074i \(0.486300\pi\)
\(734\) 8.14250e12 1.03544
\(735\) −1.63688e13 + 1.27097e12i −2.06883 + 0.160636i
\(736\) −1.85896e12 −0.233517
\(737\) 7.13405e12 + 1.23565e13i 0.890702 + 1.54274i
\(738\) 5.33422e11 9.23915e11i 0.0661939 0.114651i
\(739\) 7.34297e11 1.27184e12i 0.0905673 0.156867i −0.817183 0.576379i \(-0.804465\pi\)
0.907750 + 0.419512i \(0.137799\pi\)
\(740\) −1.86173e12 3.22462e12i −0.228231 0.395308i
\(741\) 1.20840e13 1.47241
\(742\) −4.33573e12 + 1.68073e11i −0.525103 + 0.0203555i
\(743\) −4.86883e12 −0.586104 −0.293052 0.956096i \(-0.594671\pi\)
−0.293052 + 0.956096i \(0.594671\pi\)
\(744\) 1.53203e12 + 2.65355e12i 0.183311 + 0.317503i
\(745\) 2.97211e12 5.14784e12i 0.353477 0.612240i
\(746\) 8.27616e11 1.43347e12i 0.0978372 0.169459i
\(747\) −1.12716e12 1.95230e12i −0.132447 0.229406i
\(748\) −5.87891e11 −0.0686657
\(749\) −6.49721e12 1.03094e13i −0.754326 1.19693i
\(750\) 1.03852e13 1.19850
\(751\) 5.71359e12 + 9.89624e12i 0.655435 + 1.13525i 0.981785 + 0.189998i \(0.0608481\pi\)
−0.326349 + 0.945249i \(0.605819\pi\)
\(752\) 1.14965e12 1.99124e12i 0.131094 0.227062i
\(753\) −2.34968e12 + 4.06976e12i −0.266336 + 0.461308i
\(754\) −1.51711e11 2.62772e11i −0.0170941 0.0296079i
\(755\) 7.29129e12 0.816663
\(756\) 1.21983e12 2.31556e12i 0.135816 0.257815i
\(757\) 4.87971e12 0.540085 0.270043 0.962848i \(-0.412962\pi\)
0.270043 + 0.962848i \(0.412962\pi\)
\(758\) 8.87152e11 + 1.53659e12i 0.0976083 + 0.169063i
\(759\) −1.09336e13 + 1.89376e13i −1.19585 + 2.07127i
\(760\) −3.74240e12 + 6.48202e12i −0.406901 + 0.704773i
\(761\) −5.62833e12 9.74856e12i −0.608343 1.05368i −0.991514 0.130004i \(-0.958501\pi\)
0.383170 0.923678i \(-0.374832\pi\)
\(762\) −6.95922e12 −0.747761
\(763\) 5.58114e12 1.05945e13i 0.596160 1.13167i
\(764\) −3.01584e12 −0.320249
\(765\) −3.94074e11 6.82557e11i −0.0416008 0.0720547i
\(766\) 2.07955e12 3.60189e12i 0.218243 0.378008i
\(767\) 1.29953e12 2.25084e12i 0.135583 0.234837i
\(768\) 3.72499e11 + 6.45188e11i 0.0386367 + 0.0669207i
\(769\) −1.61412e13 −1.66444 −0.832220 0.554446i \(-0.812930\pi\)
−0.832220 + 0.554446i \(0.812930\pi\)
\(770\) 9.03858e12 + 1.43420e13i 0.926599 + 1.47028i
\(771\) 1.44793e13 1.47572
\(772\) 4.11997e12 + 7.13600e12i 0.417462 + 0.723065i
\(773\) −7.01910e12 + 1.21574e13i −0.707089 + 1.22471i 0.258844 + 0.965919i \(0.416658\pi\)
−0.965932 + 0.258794i \(0.916675\pi\)
\(774\) −5.82630e11 + 1.00914e12i −0.0583524 + 0.101069i
\(775\) 7.65159e12 + 1.32529e13i 0.761893 + 1.31964i
\(776\) 3.90682e12 0.386764
\(777\) 6.82769e12 2.64673e11i 0.672016 0.0260505i
\(778\) −9.32090e12 −0.912115
\(779\) 2.49627e12 + 4.32366e12i 0.242869 + 0.420662i
\(780\) 4.65681e12 8.06583e12i 0.450467 0.780231i
\(781\) 1.07736e12 1.86604e12i 0.103617 0.179470i
\(782\) 4.58024e11 + 7.93321e11i 0.0437983 + 0.0758610i
\(783\) −3.41308e11 −0.0324503
\(784\) −1.49564e12 2.18107e12i −0.141385 0.206180i
\(785\) −2.73017e13 −2.56612
\(786\) 4.23442e12 + 7.33423e12i 0.395724 + 0.685414i
\(787\) −6.72141e11 + 1.16418e12i −0.0624560 + 0.108177i −0.895563 0.444935i \(-0.853227\pi\)
0.833107 + 0.553112i \(0.186560\pi\)
\(788\) 3.08575e12 5.34468e12i 0.285097 0.493803i
\(789\) 4.36531e12 + 7.56094e12i 0.401022 + 0.694591i
\(790\) 4.08581e12 0.373213
\(791\) 1.05319e13 4.08265e11i 0.956559 0.0370807i
\(792\) 3.03057e12 0.273691
\(793\) −2.76660e12 4.79188e12i −0.248437 0.430306i
\(794\) −1.49658e12 + 2.59216e12i −0.133631 + 0.231456i
\(795\) −8.68434e12 + 1.50417e13i −0.771054 + 1.33551i
\(796\) −1.46634e12 2.53977e12i −0.129457 0.224226i
\(797\) −9.34992e12 −0.820815 −0.410408 0.911902i \(-0.634614\pi\)
−0.410408 + 0.911902i \(0.634614\pi\)
\(798\) −7.32316e12 1.16200e13i −0.639272 1.01436i
\(799\) −1.13303e12 −0.0983517
\(800\) 1.86042e12 + 3.22234e12i 0.160585 + 0.278142i
\(801\) 9.70275e11 1.68057e12i 0.0832815 0.144248i
\(802\) −7.06193e12 + 1.22316e13i −0.602752 + 1.04400i
\(803\) −1.03765e13 1.79727e13i −0.880709 1.52543i
\(804\) −8.90990e12 −0.752005
\(805\) 1.23116e13 2.33707e13i 1.03332 1.96151i
\(806\) 6.17019e12 0.514981
\(807\) 2.85935e12 + 4.95253e12i 0.237321 + 0.411052i
\(808\) −3.98846e12 + 6.90821e12i −0.329195 + 0.570183i
\(809\) 2.73458e12 4.73643e12i 0.224451 0.388761i −0.731703 0.681623i \(-0.761274\pi\)
0.956155 + 0.292862i \(0.0946077\pi\)
\(810\) −9.08118e12 1.57291e13i −0.741241 1.28387i
\(811\) 6.82318e12 0.553851 0.276925 0.960891i \(-0.410685\pi\)
0.276925 + 0.960891i \(0.410685\pi\)
\(812\) −1.60742e11 + 3.05132e11i −0.0129756 + 0.0246312i
\(813\) −4.11695e12 −0.330498
\(814\) −3.52762e12 6.11002e12i −0.281626 0.487790i
\(815\) 1.45103e13 2.51326e13i 1.15204 1.99539i
\(816\) 1.83558e11 3.17932e11i 0.0144933 0.0251032i
\(817\) −2.72655e12 4.72252e12i −0.214099 0.370830i
\(818\) 6.30919e12 0.492702
\(819\) 3.15124e12 + 5.00022e12i 0.244739 + 0.388340i
\(820\) 3.84796e12 0.297213
\(821\) −1.13840e12 1.97176e12i −0.0874479 0.151464i 0.818984 0.573817i \(-0.194538\pi\)
−0.906432 + 0.422352i \(0.861204\pi\)
\(822\) −1.01376e13 + 1.75588e13i −0.774481 + 1.34144i
\(823\) −1.08962e13 + 1.88728e13i −0.827897 + 1.43396i 0.0717871 + 0.997420i \(0.477130\pi\)
−0.899685 + 0.436541i \(0.856204\pi\)
\(824\) −2.83277e12 4.90650e12i −0.214062 0.370766i
\(825\) 4.37689e13 3.28944
\(826\) −2.95197e12 + 1.14432e11i −0.220649 + 0.00855338i
\(827\) 1.32468e13 0.984772 0.492386 0.870377i \(-0.336125\pi\)
0.492386 + 0.870377i \(0.336125\pi\)
\(828\) −2.36110e12 4.08955e12i −0.174574 0.302370i
\(829\) −3.21919e12 + 5.57580e12i −0.236729 + 0.410026i −0.959774 0.280775i \(-0.909409\pi\)
0.723045 + 0.690801i \(0.242742\pi\)
\(830\) 4.06551e12 7.04168e12i 0.297347 0.515021i
\(831\) −7.21155e12 1.24908e13i −0.524595 0.908624i
\(832\) 1.50023e12 0.108543
\(833\) −5.62276e11 + 1.17566e12i −0.0404619 + 0.0846017i
\(834\) 7.75120e12 0.554781
\(835\) −7.34369e12 1.27196e13i −0.522787 0.905494i
\(836\) −7.09110e12 + 1.22822e13i −0.502095 + 0.869654i
\(837\) 3.47031e12 6.01075e12i 0.244401 0.423315i
\(838\) −1.42368e12 2.46589e12i −0.0997274 0.172733i
\(839\) 2.25634e12 0.157208 0.0786041 0.996906i \(-0.474954\pi\)
0.0786041 + 0.996906i \(0.474954\pi\)
\(840\) −1.05783e13 + 4.10064e11i −0.733091 + 0.0284181i
\(841\) −1.44622e13 −0.996900
\(842\) 3.15556e12 + 5.46559e12i 0.216358 + 0.374742i
\(843\) 1.29106e13 2.23619e13i 0.880489 1.52505i
\(844\) −2.61049e12 + 4.52150e12i −0.177085 + 0.306720i
\(845\) 3.05909e12 + 5.29850e12i 0.206413 + 0.357518i
\(846\) 5.84076e12 0.392015
\(847\) 9.14011e12 + 1.45031e13i 0.610206 + 0.968242i
\(848\) −2.79774e12 −0.185791
\(849\) 5.14783e12 + 8.91630e12i 0.340047 + 0.588980i
\(850\) 9.16768e11 1.58789e12i 0.0602385 0.104336i
\(851\) −5.49671e12 + 9.52058e12i −0.359269 + 0.622272i
\(852\) 6.72772e11 + 1.16528e12i 0.0437411 + 0.0757618i
\(853\) −2.07580e13 −1.34250 −0.671252 0.741229i \(-0.734243\pi\)
−0.671252 + 0.741229i \(0.734243\pi\)
\(854\) −2.93128e12 + 5.56437e12i −0.188581 + 0.357977i
\(855\) −1.90132e13 −1.21677
\(856\) −3.92871e12 6.80472e12i −0.250102 0.433190i
\(857\) −1.58626e12 + 2.74749e12i −0.100453 + 0.173989i −0.911871 0.410476i \(-0.865362\pi\)
0.811419 + 0.584466i \(0.198696\pi\)
\(858\) 8.82373e12 1.52832e13i 0.555853 0.962765i
\(859\) 1.46559e11 + 2.53848e11i 0.00918426 + 0.0159076i 0.870581 0.492025i \(-0.163743\pi\)
−0.861397 + 0.507933i \(0.830410\pi\)
\(860\) −4.20293e12 −0.262005
\(861\) −3.29111e12 + 6.24741e12i −0.204093 + 0.387423i
\(862\) −1.29247e13 −0.797326
\(863\) −6.09714e12 1.05606e13i −0.374178 0.648095i 0.616026 0.787726i \(-0.288742\pi\)
−0.990204 + 0.139631i \(0.955408\pi\)
\(864\) 8.43776e11 1.46146e12i 0.0515128 0.0892229i
\(865\) 1.03102e12 1.78578e12i 0.0626173 0.108456i
\(866\) 4.62149e12 + 8.00466e12i 0.279223 + 0.483629i
\(867\) 2.03892e13 1.22550
\(868\) −3.73928e12 5.93329e12i −0.223588 0.354778i
\(869\) 7.74181e12 0.460525
\(870\) 6.90270e11 + 1.19558e12i 0.0408491 + 0.0707527i
\(871\) −8.97110e12 + 1.55384e13i −0.528158 + 0.914797i
\(872\) 3.86058e12 6.68672e12i 0.226115 0.391642i
\(873\) 4.96214e12 + 8.59468e12i 0.289138 + 0.500801i
\(874\) 2.20986e13 1.28104
\(875\) −2.37528e13 + 9.20769e11i −1.36987 + 0.0531024i
\(876\) 1.29595e13 0.743568
\(877\) 9.23674e12 + 1.59985e13i 0.527255 + 0.913233i 0.999495 + 0.0317628i \(0.0101121\pi\)
−0.472240 + 0.881470i \(0.656555\pi\)
\(878\) −1.06263e13 + 1.84053e13i −0.603470 + 1.04524i
\(879\) 7.89726e12 1.36785e13i 0.446197 0.772836i
\(880\) 5.46541e12 + 9.46637e12i 0.307221 + 0.532122i
\(881\) 2.16016e13 1.20808 0.604039 0.796955i \(-0.293557\pi\)
0.604039 + 0.796955i \(0.293557\pi\)
\(882\) 2.89852e12 6.06050e12i 0.161275 0.337209i
\(883\) −1.00085e13 −0.554043 −0.277022 0.960864i \(-0.589347\pi\)
−0.277022 + 0.960864i \(0.589347\pi\)
\(884\) −3.69638e11 6.40232e11i −0.0203583 0.0352616i
\(885\) −5.91270e12 + 1.02411e13i −0.323997 + 0.561180i
\(886\) 3.99573e12 6.92081e12i 0.217844 0.377316i
\(887\) 7.52738e12 + 1.30378e13i 0.408307 + 0.707209i 0.994700 0.102818i \(-0.0327858\pi\)
−0.586393 + 0.810027i \(0.699452\pi\)
\(888\) 4.40574e12 0.237772
\(889\) 1.59170e13 6.17016e11i 0.854677 0.0331313i
\(890\) 6.99929e12 0.373937
\(891\) −1.72071e13 2.98035e13i −0.914654 1.58423i
\(892\) 7.32557e12 1.26883e13i 0.387436 0.671058i
\(893\) −1.36666e13 + 2.36712e13i −0.719164 + 1.24563i
\(894\) 3.51670e12 + 6.09110e12i 0.184127 + 0.318917i
\(895\) −3.92511e13 −2.04479
\(896\) −9.09175e11 1.44263e12i −0.0471261 0.0747772i
\(897\) −2.74982e13 −1.41820
\(898\) −3.60969e11 6.25216e11i −0.0185236 0.0320839i
\(899\) −4.57298e11 + 7.92064e11i −0.0233497 + 0.0404429i
\(900\) −4.72592e12 + 8.18554e12i −0.240102 + 0.415868i
\(901\) 6.89328e11 + 1.19395e12i 0.0348469 + 0.0603566i
\(902\) 7.29112e12 0.366746
\(903\) 3.59471e12 6.82372e12i 0.179916 0.341528i
\(904\) 6.79596e12 0.338449
\(905\) 3.91524e12 + 6.78139e12i 0.194017 + 0.336047i
\(906\) −4.31366e12 + 7.47147e12i −0.212701 + 0.368408i
\(907\) −1.14679e13 + 1.98630e13i −0.562668 + 0.974569i 0.434595 + 0.900626i \(0.356892\pi\)
−0.997262 + 0.0739431i \(0.976442\pi\)
\(908\) −1.95196e12 3.38089e12i −0.0952981 0.165061i
\(909\) −2.02633e13 −0.984403
\(910\) −9.93581e12 + 1.88608e13i −0.480305 + 0.911748i
\(911\) 4.04241e13 1.94450 0.972248 0.233952i \(-0.0751657\pi\)
0.972248 + 0.233952i \(0.0751657\pi\)
\(912\) −4.42813e12 7.66975e12i −0.211955 0.367117i
\(913\) 7.70335e12 1.33426e13i 0.366911 0.635509i
\(914\) 5.08176e12 8.80187e12i 0.240856 0.417174i
\(915\) 1.25877e13 + 2.18026e13i 0.593680 + 1.02828i
\(916\) −8.90954e12 −0.418144
\(917\) −1.03351e13 1.63993e13i −0.482674 0.765882i
\(918\) −8.31584e11 −0.0386468
\(919\) −2.09498e12 3.62862e12i −0.0968859 0.167811i 0.813508 0.581553i \(-0.197555\pi\)
−0.910394 + 0.413742i \(0.864222\pi\)
\(920\) 8.51616e12 1.47504e13i 0.391921 0.678827i
\(921\) 5.73843e12 9.93925e12i 0.262800 0.455182i
\(922\) −9.68080e12 1.67676e13i −0.441186 0.764157i
\(923\) 2.70957e12 0.122883
\(924\) −2.00438e13 + 7.76990e11i −0.904597 + 0.0350664i
\(925\) 2.20041e13 0.988250
\(926\) 7.78469e12 + 1.34835e13i 0.347930 + 0.602633i
\(927\) 7.19593e12 1.24637e13i 0.320057 0.554356i
\(928\) −1.11188e11 + 1.92584e11i −0.00492145 + 0.00852421i
\(929\) −2.41805e12 4.18818e12i −0.106511 0.184482i 0.807844 0.589397i \(-0.200635\pi\)
−0.914355 + 0.404915i \(0.867301\pi\)
\(930\) −2.80737e13 −1.23063
\(931\) 1.77796e13 + 2.59277e13i 0.775619 + 1.13107i
\(932\) 1.90152e13 0.825524
\(933\) 7.66961e11 + 1.32841e12i 0.0331364 + 0.0573940i
\(934\) 1.34645e13 2.33212e13i 0.578933 1.00274i
\(935\) 2.69322e12 4.66479e12i 0.115244 0.199609i
\(936\) 1.90548e12 + 3.30038e12i 0.0811451 + 0.140547i
\(937\) −1.70190e12 −0.0721282 −0.0360641 0.999349i \(-0.511482\pi\)
−0.0360641 + 0.999349i \(0.511482\pi\)
\(938\) 2.03785e13 7.89967e11i 0.859528 0.0333193i
\(939\) −2.74337e12 −0.115157
\(940\) 1.05334e13 + 1.82444e13i 0.440041 + 0.762173i
\(941\) −1.41493e12 + 2.45074e12i −0.0588278 + 0.101893i −0.893939 0.448188i \(-0.852070\pi\)
0.835112 + 0.550080i \(0.185403\pi\)
\(942\) 1.61522e13 2.79764e13i 0.668347 1.15761i
\(943\) −5.68049e12 9.83889e12i −0.233928 0.405176i
\(944\) −1.90483e12 −0.0780697
\(945\) 1.27853e13 + 2.02870e13i 0.521514 + 0.827512i
\(946\) −7.96372e12 −0.323300
\(947\) −1.85318e13 3.20981e13i −0.748761 1.29689i −0.948417 0.317026i \(-0.897316\pi\)
0.199656 0.979866i \(-0.436018\pi\)
\(948\) −2.41724e12 + 4.18678e12i −0.0972035 + 0.168361i
\(949\) 1.30486e13 2.26008e13i 0.522233 0.904534i
\(950\) −2.21160e13 3.83060e13i −0.880948 1.52585i
\(951\) −3.73635e13 −1.48127
\(952\) −3.91642e11 + 7.43442e11i −0.0154534 + 0.0293346i
\(953\) −1.53995e12 −0.0604768 −0.0302384 0.999543i \(-0.509627\pi\)
−0.0302384 + 0.999543i \(0.509627\pi\)
\(954\) −3.55347e12 6.15479e12i −0.138894 0.240572i
\(955\) 1.38160e13 2.39300e13i 0.537486 0.930953i
\(956\) −7.84499e12 + 1.35879e13i −0.303761 + 0.526129i
\(957\) 1.30793e12 + 2.26540e12i 0.0504057 + 0.0873052i
\(958\) −1.86347e13 −0.714789
\(959\) 2.16296e13 4.10589e13i 0.825782 1.56756i
\(960\) −6.82590e12 −0.259382
\(961\) 3.92050e12 + 6.79050e12i 0.148281 + 0.256830i
\(962\) 4.43600e12 7.68338e12i 0.166995 0.289244i
\(963\) 9.97987e12 1.72856e13i 0.373944 0.647690i
\(964\) 5.48786e12 + 9.50524e12i 0.204671 + 0.354500i
\(965\) −7.54968e13 −2.80257
\(966\) 1.66645e13 + 2.64424e13i 0.615737 + 0.977020i
\(967\) −1.09919e13 −0.404254 −0.202127 0.979359i \(-0.564785\pi\)
−0.202127 + 0.979359i \(0.564785\pi\)
\(968\) 5.52680e12 + 9.57270e12i 0.202318 + 0.350425i
\(969\) −2.18207e12 + 3.77946e12i −0.0795083 + 0.137712i
\(970\) −1.78977e13 + 3.09998e13i −0.649120 + 1.12431i
\(971\) 6.62794e11 + 1.14799e12i 0.0239272 + 0.0414432i 0.877741 0.479135i \(-0.159050\pi\)
−0.853814 + 0.520578i \(0.825716\pi\)
\(972\) 1.33809e13 0.480827
\(973\) −1.77284e13 + 6.87235e11i −0.634104 + 0.0245809i
\(974\) −3.58646e13 −1.27688
\(975\) 2.75198e13 + 4.76657e13i 0.975269 + 1.68922i
\(976\) −2.02762e12 + 3.51195e12i −0.0715258 + 0.123886i
\(977\) 1.36658e12 2.36699e12i 0.0479856 0.0831135i −0.841035 0.540981i \(-0.818053\pi\)
0.889021 + 0.457867i \(0.151387\pi\)
\(978\) 1.71691e13 + 2.97378e13i 0.600099 + 1.03940i
\(979\) 1.32623e13 0.461419
\(980\) 2.41580e13 1.87578e12i 0.836650 0.0649626i
\(981\) 1.96136e13 0.676157
\(982\) 1.32407e12 + 2.29335e12i 0.0454368 + 0.0786988i
\(983\) −3.24327e11 + 5.61751e11i −0.0110788 + 0.0191890i −0.871512 0.490375i \(-0.836860\pi\)
0.860433 + 0.509564i \(0.170193\pi\)
\(984\) −2.27652e12 + 3.94305e12i −0.0774094 + 0.134077i
\(985\) 2.82726e13 + 4.89696e13i 0.956980 + 1.65754i
\(986\) 1.09582e11 0.00369226
\(987\) −3.86300e13 + 1.49748e12i −1.29568 + 0.0502266i
\(988\) −1.78342e13 −0.595453
\(989\) 6.20451e12 + 1.07465e13i 0.206217 + 0.357178i
\(990\) −1.38835e13 + 2.40469e13i −0.459346 + 0.795610i
\(991\) 1.97923e13 3.42812e13i 0.651874 1.12908i −0.330793 0.943703i \(-0.607316\pi\)
0.982668 0.185376i \(-0.0593504\pi\)
\(992\) −2.26105e12 3.91626e12i −0.0741324 0.128401i
\(993\) 6.99268e12 0.228230
\(994\) −1.64206e12 2.60554e12i −0.0533521 0.0846563i
\(995\) 2.68700e13 0.869090
\(996\) 4.81046e12 + 8.33196e12i 0.154889 + 0.268275i
\(997\) −1.05624e13 + 1.82947e13i −0.338560 + 0.586404i −0.984162 0.177270i \(-0.943273\pi\)
0.645602 + 0.763674i \(0.276607\pi\)
\(998\) −9.70836e12 + 1.68154e13i −0.309784 + 0.536561i
\(999\) −4.98989e12 8.64274e12i −0.158506 0.274541i
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 14.10.c.b.11.3 yes 6
3.2 odd 2 126.10.g.e.109.3 6
4.3 odd 2 112.10.i.a.81.1 6
7.2 even 3 inner 14.10.c.b.9.3 6
7.3 odd 6 98.10.a.h.1.3 3
7.4 even 3 98.10.a.g.1.1 3
7.5 odd 6 98.10.c.l.79.1 6
7.6 odd 2 98.10.c.l.67.1 6
21.2 odd 6 126.10.g.e.37.3 6
28.23 odd 6 112.10.i.a.65.1 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.10.c.b.9.3 6 7.2 even 3 inner
14.10.c.b.11.3 yes 6 1.1 even 1 trivial
98.10.a.g.1.1 3 7.4 even 3
98.10.a.h.1.3 3 7.3 odd 6
98.10.c.l.67.1 6 7.6 odd 2
98.10.c.l.79.1 6 7.5 odd 6
112.10.i.a.65.1 6 28.23 odd 6
112.10.i.a.81.1 6 4.3 odd 2
126.10.g.e.37.3 6 21.2 odd 6
126.10.g.e.109.3 6 3.2 odd 2