Properties

Label 38.10.e.b.9.3
Level $38$
Weight $10$
Character 38.9
Analytic conductor $19.571$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

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

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(19.5713617742\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(8\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 9.3
Character \(\chi\) \(=\) 38.9
Dual form 38.10.e.b.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.77837 + 15.7569i) q^{2} +(-127.296 + 106.814i) q^{3} +(-240.561 + 87.5572i) q^{4} +(-1972.56 - 717.951i) q^{5} +(-2036.73 - 1709.02i) q^{6} +(-5187.34 + 8984.74i) q^{7} +(-2048.00 - 3547.24i) q^{8} +(1377.11 - 7809.96i) q^{9} +O(q^{10})\) \(q+(2.77837 + 15.7569i) q^{2} +(-127.296 + 106.814i) q^{3} +(-240.561 + 87.5572i) q^{4} +(-1972.56 - 717.951i) q^{5} +(-2036.73 - 1709.02i) q^{6} +(-5187.34 + 8984.74i) q^{7} +(-2048.00 - 3547.24i) q^{8} +(1377.11 - 7809.96i) q^{9} +(5832.22 - 33076.1i) q^{10} +(-6508.32 - 11272.7i) q^{11} +(21270.1 - 36841.0i) q^{12} +(-65661.1 - 55096.2i) q^{13} +(-155984. - 56773.6i) q^{14} +(327785. - 119304. i) q^{15} +(50203.5 - 42125.7i) q^{16} +(77342.4 + 438630. i) q^{17} +126887. q^{18} +(138403. + 550938. i) q^{19} +537382. q^{20} +(-299368. - 1.69780e6i) q^{21} +(159541. - 133871. i) q^{22} +(729729. - 265599. i) q^{23} +(639596. + 232794. i) q^{24} +(1.87934e6 + 1.57695e6i) q^{25} +(685716. - 1.18770e6i) q^{26} +(-976479. - 1.69131e6i) q^{27} +(461196. - 2.61557e6i) q^{28} +(-1.11687e6 + 6.33410e6i) q^{29} +(2.79057e6 + 4.83342e6i) q^{30} +(2.34412e6 - 4.06013e6i) q^{31} +(803256. + 674012. i) q^{32} +(2.03257e6 + 739794. i) q^{33} +(-6.69658e6 + 2.43736e6i) q^{34} +(1.66829e7 - 1.39986e7i) q^{35} +(352539. + 1.99935e6i) q^{36} -1.59448e7 q^{37} +(-8.29655e6 + 3.71151e6i) q^{38} +1.42434e7 q^{39} +(1.49305e6 + 8.46749e6i) q^{40} +(2.44557e7 - 2.05208e7i) q^{41} +(2.59204e7 - 9.43424e6i) q^{42} +(-8.63565e6 - 3.14312e6i) q^{43} +(2.55266e6 + 2.14193e6i) q^{44} +(-8.32359e6 + 1.44169e7i) q^{45} +(6.21249e6 + 1.07603e7i) q^{46} +(-2.53373e6 + 1.43695e7i) q^{47} +(-1.89108e6 + 1.07249e7i) q^{48} +(-3.36402e7 - 5.82666e7i) q^{49} +(-1.96264e7 + 3.39940e7i) q^{50} +(-5.66972e7 - 4.75746e7i) q^{51} +(2.06196e7 + 7.50492e6i) q^{52} +(-7.07629e7 + 2.57556e7i) q^{53} +(2.39368e7 - 2.00854e7i) q^{54} +(4.74474e6 + 2.69087e7i) q^{55} +4.24947e7 q^{56} +(-7.64659e7 - 5.53488e7i) q^{57} -1.02909e8 q^{58} +(4.80180e6 + 2.72323e7i) q^{59} +(-6.84065e7 + 5.73999e7i) q^{60} +(-8.30464e7 + 3.02264e7i) q^{61} +(7.04879e7 + 2.56555e7i) q^{62} +(6.30269e7 + 5.28859e7i) q^{63} +(-8.38861e6 + 1.45295e7i) q^{64} +(8.99638e7 + 1.55822e8i) q^{65} +(-6.00965e6 + 3.40824e7i) q^{66} +(2.88753e7 - 1.63760e8i) q^{67} +(-5.70108e7 - 9.87456e7i) q^{68} +(-6.45217e7 + 1.11755e8i) q^{69} +(2.66927e8 + 2.23978e8i) q^{70} +(-1.71185e8 - 6.23064e7i) q^{71} +(-3.05241e7 + 1.11099e7i) q^{72} +(1.26250e8 - 1.05937e8i) q^{73} +(-4.43004e7 - 2.51240e8i) q^{74} -4.07673e8 q^{75} +(-8.15329e7 - 1.20416e8i) q^{76} +1.35043e8 q^{77} +(3.95735e7 + 2.24433e8i) q^{78} +(2.65744e8 - 2.22986e8i) q^{79} +(-1.29273e8 + 4.70517e7i) q^{80} +(4.51638e8 + 1.64383e8i) q^{81} +(3.91291e8 + 3.28332e8i) q^{82} +(-6.06208e7 + 1.04998e8i) q^{83} +(2.20671e8 + 3.82213e8i) q^{84} +(1.62353e8 - 9.20751e8i) q^{85} +(2.55329e7 - 1.44804e8i) q^{86} +(-5.34397e8 - 9.25603e8i) q^{87} +(-2.66581e7 + 4.61731e7i) q^{88} +(-2.00737e8 - 1.68438e8i) q^{89} +(-2.50292e8 - 9.10987e7i) q^{90} +(8.35632e8 - 3.04145e8i) q^{91} +(-1.52289e8 + 1.27786e8i) q^{92} +(1.35282e8 + 7.67221e8i) q^{93} -2.33459e8 q^{94} +(1.22540e8 - 1.18612e9i) q^{95} -1.74245e8 q^{96} +(1.98124e8 + 1.12362e9i) q^{97} +(8.24638e8 - 6.91953e8i) q^{98} +(-9.70023e7 + 3.53059e7i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q + 33 q^{3} + 528 q^{6} - 25809 q^{7} - 98304 q^{8} + 7953 q^{9} - 55221 q^{11} - 62208 q^{12} + 21777 q^{13} + 28464 q^{14} - 280011 q^{15} + 1055055 q^{17} + 6083232 q^{18} + 2408220 q^{19} + 523776 q^{20} - 5105673 q^{21} - 2513280 q^{22} - 456708 q^{23} + 135168 q^{24} + 19417530 q^{25} - 1077120 q^{26} - 11729661 q^{27} - 30720 q^{28} + 4679889 q^{29} + 4879158 q^{31} - 12360834 q^{33} + 9206400 q^{34} - 47475759 q^{35} + 2035968 q^{36} + 119843604 q^{37} - 39471312 q^{38} + 16552668 q^{39} + 60082911 q^{41} + 59187024 q^{42} + 109939059 q^{43} - 40212480 q^{44} + 3067236 q^{45} - 4919424 q^{46} + 198627789 q^{47} - 4325376 q^{48} - 182954115 q^{49} - 229688016 q^{50} - 228228021 q^{51} - 49495296 q^{52} - 370799859 q^{53} + 111760416 q^{54} - 60369543 q^{55} + 211427328 q^{56} + 128158266 q^{57} + 166196064 q^{58} - 382689396 q^{59} - 36777216 q^{60} - 850085550 q^{61} + 42954480 q^{62} - 803298357 q^{63} - 402653184 q^{64} + 261122181 q^{65} + 516819888 q^{66} + 1146400764 q^{67} + 125611008 q^{68} - 178115667 q^{69} - 759612144 q^{70} + 363378456 q^{71} - 65150976 q^{72} + 1407478230 q^{73} - 12153360 q^{74} + 1715917770 q^{75} - 128288256 q^{76} - 193134048 q^{77} - 1199414208 q^{78} - 2098405449 q^{79} + 3082805319 q^{81} + 961326576 q^{82} + 358330707 q^{83} + 502249728 q^{84} - 1961566422 q^{85} - 588638592 q^{86} - 1222269090 q^{87} - 226185216 q^{88} - 368108670 q^{89} + 1740707616 q^{90} - 3296437032 q^{91} - 819648768 q^{92} + 6597152658 q^{93} + 2953278144 q^{94} - 881990403 q^{95} + 509607936 q^{96} - 3752161206 q^{97} - 458055696 q^{98} + 6061589742 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.77837 + 15.7569i 0.122788 + 0.696364i
\(3\) −127.296 + 106.814i −0.907337 + 0.761346i −0.971610 0.236586i \(-0.923971\pi\)
0.0642736 + 0.997932i \(0.479527\pi\)
\(4\) −240.561 + 87.5572i −0.469846 + 0.171010i
\(5\) −1972.56 717.951i −1.41145 0.513724i −0.479892 0.877328i \(-0.659324\pi\)
−0.931554 + 0.363603i \(0.881546\pi\)
\(6\) −2036.73 1709.02i −0.641584 0.538353i
\(7\) −5187.34 + 8984.74i −0.816589 + 1.41437i 0.0915915 + 0.995797i \(0.470805\pi\)
−0.908181 + 0.418578i \(0.862529\pi\)
\(8\) −2048.00 3547.24i −0.176777 0.306186i
\(9\) 1377.11 7809.96i 0.0699643 0.396787i
\(10\) 5832.22 33076.1i 0.184431 1.04596i
\(11\) −6508.32 11272.7i −0.134030 0.232147i 0.791197 0.611562i \(-0.209458\pi\)
−0.925226 + 0.379415i \(0.876125\pi\)
\(12\) 21270.1 36841.0i 0.296111 0.512879i
\(13\) −65661.1 55096.2i −0.637622 0.535029i 0.265665 0.964065i \(-0.414409\pi\)
−0.903287 + 0.429037i \(0.858853\pi\)
\(14\) −155984. 56773.6i −1.08519 0.394976i
\(15\) 327785. 119304.i 1.67178 0.608478i
\(16\) 50203.5 42125.7i 0.191511 0.160697i
\(17\) 77342.4 + 438630.i 0.224594 + 1.27373i 0.863461 + 0.504416i \(0.168292\pi\)
−0.638867 + 0.769317i \(0.720597\pi\)
\(18\) 126887. 0.284899
\(19\) 138403. + 550938.i 0.243642 + 0.969865i
\(20\) 537382. 0.751015
\(21\) −299368. 1.69780e6i −0.335907 1.90502i
\(22\) 159541. 133871.i 0.145201 0.121838i
\(23\) 729729. 265599.i 0.543733 0.197903i −0.0555266 0.998457i \(-0.517684\pi\)
0.599260 + 0.800554i \(0.295462\pi\)
\(24\) 639596. + 232794.i 0.393510 + 0.143226i
\(25\) 1.87934e6 + 1.57695e6i 0.962222 + 0.807400i
\(26\) 685716. 1.18770e6i 0.294283 0.509712i
\(27\) −976479. 1.69131e6i −0.353611 0.612472i
\(28\) 461196. 2.61557e6i 0.141799 0.804184i
\(29\) −1.11687e6 + 6.33410e6i −0.293233 + 1.66301i 0.381065 + 0.924548i \(0.375557\pi\)
−0.674298 + 0.738459i \(0.735554\pi\)
\(30\) 2.79057e6 + 4.83342e6i 0.628996 + 1.08945i
\(31\) 2.34412e6 4.06013e6i 0.455881 0.789609i −0.542857 0.839825i \(-0.682658\pi\)
0.998738 + 0.0502160i \(0.0159910\pi\)
\(32\) 803256. + 674012.i 0.135419 + 0.113630i
\(33\) 2.03257e6 + 739794.i 0.298354 + 0.108592i
\(34\) −6.69658e6 + 2.43736e6i −0.859405 + 0.312798i
\(35\) 1.66829e7 1.39986e7i 1.87917 1.57681i
\(36\) 352539. + 1.99935e6i 0.0349821 + 0.198394i
\(37\) −1.59448e7 −1.39865 −0.699327 0.714802i \(-0.746517\pi\)
−0.699327 + 0.714802i \(0.746517\pi\)
\(38\) −8.29655e6 + 3.71151e6i −0.645463 + 0.288752i
\(39\) 1.42434e7 0.985880
\(40\) 1.49305e6 + 8.46749e6i 0.0922154 + 0.522980i
\(41\) 2.44557e7 2.05208e7i 1.35161 1.13414i 0.373138 0.927776i \(-0.378282\pi\)
0.978476 0.206362i \(-0.0661626\pi\)
\(42\) 2.59204e7 9.43424e6i 1.28534 0.467827i
\(43\) −8.63565e6 3.14312e6i −0.385201 0.140202i 0.142159 0.989844i \(-0.454596\pi\)
−0.527359 + 0.849642i \(0.676818\pi\)
\(44\) 2.55266e6 + 2.14193e6i 0.102673 + 0.0861527i
\(45\) −8.32359e6 + 1.44169e7i −0.302590 + 0.524101i
\(46\) 6.21249e6 + 1.07603e7i 0.204576 + 0.354337i
\(47\) −2.53373e6 + 1.43695e7i −0.0757390 + 0.429537i 0.923234 + 0.384237i \(0.125536\pi\)
−0.998973 + 0.0453001i \(0.985576\pi\)
\(48\) −1.89108e6 + 1.07249e7i −0.0514191 + 0.291612i
\(49\) −3.36402e7 5.82666e7i −0.833637 1.44390i
\(50\) −1.96264e7 + 3.39940e7i −0.444095 + 0.769196i
\(51\) −5.66972e7 4.75746e7i −1.17353 0.984712i
\(52\) 2.06196e7 + 7.50492e6i 0.391080 + 0.142341i
\(53\) −7.07629e7 + 2.57556e7i −1.23187 + 0.448363i −0.874237 0.485500i \(-0.838638\pi\)
−0.357631 + 0.933863i \(0.616415\pi\)
\(54\) 2.39368e7 2.00854e7i 0.383085 0.321446i
\(55\) 4.74474e6 + 2.69087e7i 0.0699166 + 0.396517i
\(56\) 4.24947e7 0.577416
\(57\) −7.64659e7 5.53488e7i −0.959469 0.694498i
\(58\) −1.02909e8 −1.19406
\(59\) 4.80180e6 + 2.72323e7i 0.0515905 + 0.292584i 0.999677 0.0254295i \(-0.00809533\pi\)
−0.948086 + 0.318014i \(0.896984\pi\)
\(60\) −6.84065e7 + 5.73999e7i −0.681423 + 0.571782i
\(61\) −8.30464e7 + 3.02264e7i −0.767956 + 0.279513i −0.696141 0.717905i \(-0.745101\pi\)
−0.0718150 + 0.997418i \(0.522879\pi\)
\(62\) 7.04879e7 + 2.56555e7i 0.605832 + 0.220505i
\(63\) 6.30269e7 + 5.28859e7i 0.504073 + 0.422968i
\(64\) −8.38861e6 + 1.45295e7i −0.0625000 + 0.108253i
\(65\) 8.99638e7 + 1.55822e8i 0.625112 + 1.08273i
\(66\) −6.00965e6 + 3.40824e7i −0.0389854 + 0.221097i
\(67\) 2.88753e7 1.63760e8i 0.175061 0.992821i −0.763012 0.646384i \(-0.776280\pi\)
0.938073 0.346437i \(-0.112609\pi\)
\(68\) −5.70108e7 9.87456e7i −0.323346 0.560051i
\(69\) −6.45217e7 + 1.11755e8i −0.342677 + 0.593534i
\(70\) 2.66927e8 + 2.23978e8i 1.32877 + 1.11497i
\(71\) −1.71185e8 6.23064e7i −0.799474 0.290985i −0.0902052 0.995923i \(-0.528752\pi\)
−0.709268 + 0.704939i \(0.750975\pi\)
\(72\) −3.05241e7 + 1.11099e7i −0.133859 + 0.0487206i
\(73\) 1.26250e8 1.05937e8i 0.520331 0.436610i −0.344416 0.938817i \(-0.611923\pi\)
0.864747 + 0.502208i \(0.167479\pi\)
\(74\) −4.43004e7 2.51240e8i −0.171738 0.973972i
\(75\) −4.07673e8 −1.48777
\(76\) −8.15329e7 1.20416e8i −0.280331 0.414022i
\(77\) 1.35043e8 0.437790
\(78\) 3.95735e7 + 2.24433e8i 0.121054 + 0.686532i
\(79\) 2.65744e8 2.22986e8i 0.767611 0.644102i −0.172485 0.985012i \(-0.555180\pi\)
0.940096 + 0.340910i \(0.110735\pi\)
\(80\) −1.29273e8 + 4.70517e7i −0.352861 + 0.128431i
\(81\) 4.51638e8 + 1.64383e8i 1.16576 + 0.424301i
\(82\) 3.91291e8 + 3.28332e8i 0.955735 + 0.801957i
\(83\) −6.06208e7 + 1.04998e8i −0.140207 + 0.242846i −0.927575 0.373638i \(-0.878110\pi\)
0.787367 + 0.616484i \(0.211443\pi\)
\(84\) 2.20671e8 + 3.82213e8i 0.483602 + 0.837624i
\(85\) 1.62353e8 9.20751e8i 0.337346 1.91319i
\(86\) 2.55329e7 1.44804e8i 0.0503334 0.285455i
\(87\) −5.34397e8 9.25603e8i −1.00006 1.73216i
\(88\) −2.66581e7 + 4.61731e7i −0.0473867 + 0.0820762i
\(89\) −2.00737e8 1.68438e8i −0.339134 0.284568i 0.457275 0.889325i \(-0.348826\pi\)
−0.796410 + 0.604758i \(0.793270\pi\)
\(90\) −2.50292e8 9.10987e7i −0.402120 0.146360i
\(91\) 8.35632e8 3.04145e8i 1.27741 0.464938i
\(92\) −1.52289e8 + 1.27786e8i −0.221628 + 0.185968i
\(93\) 1.35282e8 + 7.67221e8i 0.187528 + 1.06352i
\(94\) −2.33459e8 −0.308414
\(95\) 1.22540e8 1.18612e9i 0.154355 1.49408i
\(96\) −1.74245e8 −0.209382
\(97\) 1.98124e8 + 1.12362e9i 0.227229 + 1.28868i 0.858377 + 0.513019i \(0.171473\pi\)
−0.631148 + 0.775662i \(0.717416\pi\)
\(98\) 8.24638e8 6.91953e8i 0.903121 0.757808i
\(99\) −9.70023e7 + 3.53059e7i −0.101490 + 0.0369394i
\(100\) −5.90170e8 2.14804e8i −0.590170 0.214804i
\(101\) 7.13689e8 + 5.98856e8i 0.682438 + 0.572633i 0.916717 0.399536i \(-0.130829\pi\)
−0.234280 + 0.972169i \(0.575273\pi\)
\(102\) 5.92103e8 1.02555e9i 0.541623 0.938118i
\(103\) 8.92740e8 + 1.54627e9i 0.781552 + 1.35369i 0.931038 + 0.364923i \(0.118905\pi\)
−0.149486 + 0.988764i \(0.547762\pi\)
\(104\) −6.09656e7 + 3.45753e8i −0.0511016 + 0.289812i
\(105\) −6.28418e8 + 3.56394e9i −0.504542 + 2.86140i
\(106\) −6.02434e8 1.04345e9i −0.463482 0.802775i
\(107\) −5.11484e8 + 8.85917e8i −0.377229 + 0.653380i −0.990658 0.136370i \(-0.956456\pi\)
0.613429 + 0.789750i \(0.289790\pi\)
\(108\) 3.82989e8 + 3.21366e8i 0.270882 + 0.227297i
\(109\) 5.15562e8 + 1.87649e8i 0.349834 + 0.127329i 0.510960 0.859605i \(-0.329290\pi\)
−0.161126 + 0.986934i \(0.551512\pi\)
\(110\) −4.10816e8 + 1.49525e8i −0.267535 + 0.0973748i
\(111\) 2.02970e9 1.70312e9i 1.26905 1.06486i
\(112\) 1.18066e8 + 6.69586e8i 0.0708996 + 0.402092i
\(113\) 7.99725e8 0.461411 0.230705 0.973024i \(-0.425897\pi\)
0.230705 + 0.973024i \(0.425897\pi\)
\(114\) 6.59676e8 1.35865e9i 0.365813 0.753416i
\(115\) −1.63012e9 −0.869118
\(116\) −2.85920e8 1.62153e9i −0.146617 0.831504i
\(117\) −5.20722e8 + 4.36938e8i −0.256903 + 0.215567i
\(118\) −4.15757e8 + 1.51323e8i −0.197410 + 0.0718515i
\(119\) −4.34218e9 1.58043e9i −1.98494 0.722458i
\(120\) −1.09450e9 9.18398e8i −0.481839 0.404311i
\(121\) 1.09426e9 1.89531e9i 0.464072 0.803796i
\(122\) −7.07009e8 1.22458e9i −0.288939 0.500457i
\(123\) −9.21205e8 + 5.22441e9i −0.362897 + 2.05809i
\(124\) −2.08410e8 + 1.18195e9i −0.0791629 + 0.448955i
\(125\) −5.24975e8 9.09283e8i −0.192328 0.333123i
\(126\) −6.58207e8 + 1.14005e9i −0.232646 + 0.402954i
\(127\) −2.75810e9 2.31432e9i −0.940790 0.789417i 0.0369322 0.999318i \(-0.488241\pi\)
−0.977723 + 0.209901i \(0.932686\pi\)
\(128\) −2.52247e8 9.18103e7i −0.0830579 0.0302306i
\(129\) 1.43501e9 5.22301e8i 0.456249 0.166061i
\(130\) −2.20532e9 + 1.85048e9i −0.677215 + 0.568251i
\(131\) −4.31264e8 2.44582e9i −0.127945 0.725610i −0.979515 0.201370i \(-0.935461\pi\)
0.851571 0.524240i \(-0.175651\pi\)
\(132\) −5.53731e8 −0.158751
\(133\) −5.66798e9 1.61439e9i −1.57071 0.447380i
\(134\) 2.66058e9 0.712861
\(135\) 7.11879e8 + 4.03727e9i 0.184461 + 1.04613i
\(136\) 1.39753e9 1.17267e9i 0.350297 0.293934i
\(137\) −2.77185e9 + 1.00887e9i −0.672245 + 0.244677i −0.655514 0.755183i \(-0.727548\pi\)
−0.0167310 + 0.999860i \(0.505326\pi\)
\(138\) −1.94018e9 7.06167e8i −0.455392 0.165749i
\(139\) 5.83291e9 + 4.89440e9i 1.32531 + 1.11207i 0.985148 + 0.171705i \(0.0549277\pi\)
0.340166 + 0.940365i \(0.389517\pi\)
\(140\) −2.78759e9 + 4.82824e9i −0.613271 + 1.06222i
\(141\) −1.21233e9 2.09981e9i −0.258306 0.447399i
\(142\) 5.06140e8 2.87047e9i 0.104466 0.592454i
\(143\) −1.93742e8 + 1.09876e9i −0.0387446 + 0.219732i
\(144\) −2.59865e8 4.50099e8i −0.0503635 0.0872322i
\(145\) 6.75067e9 1.16925e10i 1.26821 2.19660i
\(146\) 2.02001e9 + 1.69499e9i 0.367930 + 0.308730i
\(147\) 1.05059e10 + 3.82385e9i 1.85570 + 0.675419i
\(148\) 3.83569e9 1.39608e9i 0.657152 0.239184i
\(149\) −5.65674e9 + 4.74657e9i −0.940218 + 0.788936i −0.977623 0.210364i \(-0.932535\pi\)
0.0374056 + 0.999300i \(0.488091\pi\)
\(150\) −1.13267e9 6.42367e9i −0.182680 1.03603i
\(151\) 3.35960e9 0.525886 0.262943 0.964811i \(-0.415307\pi\)
0.262943 + 0.964811i \(0.415307\pi\)
\(152\) 1.67086e9 1.61927e9i 0.253889 0.246050i
\(153\) 3.53220e9 0.521115
\(154\) 3.75201e8 + 2.12787e9i 0.0537552 + 0.304861i
\(155\) −7.53887e9 + 6.32586e9i −1.04909 + 0.880293i
\(156\) −3.42642e9 + 1.24711e9i −0.463212 + 0.168595i
\(157\) 9.71382e9 + 3.53554e9i 1.27597 + 0.464416i 0.889098 0.457716i \(-0.151332\pi\)
0.386875 + 0.922132i \(0.373555\pi\)
\(158\) 4.25190e9 + 3.56777e9i 0.542783 + 0.455449i
\(159\) 6.25677e9 1.08370e10i 0.776360 1.34469i
\(160\) −1.10056e9 1.90622e9i −0.132762 0.229950i
\(161\) −1.39901e9 + 7.93418e9i −0.164098 + 0.930648i
\(162\) −1.33535e9 + 7.57315e9i −0.152327 + 0.863891i
\(163\) −5.17258e9 8.95918e9i −0.573936 0.994086i −0.996156 0.0875927i \(-0.972083\pi\)
0.422221 0.906493i \(-0.361251\pi\)
\(164\) −4.08635e9 + 7.07777e9i −0.441102 + 0.764010i
\(165\) −3.47821e9 2.91857e9i −0.365324 0.306543i
\(166\) −1.82288e9 6.63473e8i −0.186325 0.0678167i
\(167\) −4.95190e9 + 1.80234e9i −0.492660 + 0.179314i −0.576390 0.817175i \(-0.695539\pi\)
0.0837297 + 0.996489i \(0.473317\pi\)
\(168\) −5.40940e9 + 4.53903e9i −0.523911 + 0.439613i
\(169\) −5.65662e8 3.20803e9i −0.0533417 0.302516i
\(170\) 1.49593e10 1.37370
\(171\) 4.49340e9 3.22219e8i 0.401876 0.0288183i
\(172\) 2.35261e9 0.204961
\(173\) −1.58769e9 9.00422e9i −0.134759 0.764256i −0.975027 0.222085i \(-0.928714\pi\)
0.840268 0.542171i \(-0.182397\pi\)
\(174\) 1.30999e10 1.09921e10i 1.08342 0.909096i
\(175\) −2.39173e10 + 8.70518e9i −1.92771 + 0.701628i
\(176\) −8.01612e8 2.91763e8i −0.0629734 0.0229205i
\(177\) −3.52004e9 2.95366e9i −0.269568 0.226194i
\(178\) 2.09635e9 3.63098e9i 0.156521 0.271103i
\(179\) −5.42107e9 9.38958e9i −0.394681 0.683608i 0.598379 0.801213i \(-0.295812\pi\)
−0.993060 + 0.117605i \(0.962478\pi\)
\(180\) 7.40033e8 4.19693e9i 0.0525442 0.297993i
\(181\) 2.05678e9 1.16646e10i 0.142440 0.807820i −0.826946 0.562281i \(-0.809924\pi\)
0.969387 0.245539i \(-0.0789650\pi\)
\(182\) 7.11409e9 + 1.23220e10i 0.480616 + 0.832451i
\(183\) 7.34286e9 1.27182e10i 0.483989 0.838293i
\(184\) −2.43663e9 2.04457e9i −0.156715 0.131499i
\(185\) 3.14519e10 + 1.14476e10i 1.97412 + 0.718522i
\(186\) −1.17132e10 + 4.26325e9i −0.717574 + 0.261176i
\(187\) 4.44120e9 3.72661e9i 0.265591 0.222857i
\(188\) −6.48634e8 3.67859e9i −0.0378695 0.214769i
\(189\) 2.02613e10 1.15502
\(190\) 1.90301e10 1.36464e9i 1.05937 0.0759671i
\(191\) 1.71879e10 0.934484 0.467242 0.884129i \(-0.345248\pi\)
0.467242 + 0.884129i \(0.345248\pi\)
\(192\) −4.84117e8 2.74556e9i −0.0257096 0.145806i
\(193\) 4.44688e9 3.73137e9i 0.230700 0.193580i −0.520109 0.854100i \(-0.674109\pi\)
0.750808 + 0.660520i \(0.229664\pi\)
\(194\) −1.71543e10 + 6.24365e9i −0.869491 + 0.316469i
\(195\) −2.80960e10 1.02261e10i −1.39152 0.506470i
\(196\) 1.31942e10 + 1.10713e10i 0.638603 + 0.535851i
\(197\) −1.90393e10 + 3.29770e10i −0.900643 + 1.55996i −0.0739812 + 0.997260i \(0.523570\pi\)
−0.826662 + 0.562699i \(0.809763\pi\)
\(198\) −8.25821e8 1.43036e9i −0.0381850 0.0661383i
\(199\) −1.14806e9 + 6.51098e9i −0.0518951 + 0.294311i −0.999699 0.0245429i \(-0.992187\pi\)
0.947804 + 0.318854i \(0.103298\pi\)
\(200\) 1.74494e9 9.89607e9i 0.0771164 0.437349i
\(201\) 1.38161e10 + 2.39302e10i 0.597041 + 1.03411i
\(202\) −7.45324e9 + 1.29094e10i −0.314966 + 0.545537i
\(203\) −5.11167e10 4.28920e10i −2.11266 1.77274i
\(204\) 1.78046e10 + 6.48036e9i 0.719776 + 0.261977i
\(205\) −6.29731e10 + 2.29203e10i −2.49036 + 0.906418i
\(206\) −2.18841e10 + 1.83630e10i −0.846694 + 0.710461i
\(207\) −1.06941e9 6.06491e9i −0.0404834 0.229593i
\(208\) −5.61739e9 −0.208089
\(209\) 5.30981e9 5.14585e9i 0.192495 0.186552i
\(210\) −5.79027e10 −2.05453
\(211\) −6.34359e9 3.59763e10i −0.220325 1.24953i −0.871423 0.490533i \(-0.836802\pi\)
0.651098 0.758994i \(-0.274309\pi\)
\(212\) 1.47677e10 1.23916e10i 0.502114 0.421324i
\(213\) 2.84464e10 1.03536e10i 0.946932 0.344655i
\(214\) −1.53804e10 5.59801e9i −0.501310 0.182462i
\(215\) 1.47777e10 + 1.24000e10i 0.471665 + 0.395774i
\(216\) −3.99966e9 + 6.92761e9i −0.125020 + 0.216542i
\(217\) 2.43195e10 + 4.21225e10i 0.744535 + 1.28957i
\(218\) −1.52435e9 + 8.64504e9i −0.0457121 + 0.259246i
\(219\) −4.75564e9 + 2.69706e10i −0.139705 + 0.792304i
\(220\) −3.49745e9 6.05777e9i −0.100658 0.174345i
\(221\) 1.90885e10 3.30623e10i 0.538278 0.932325i
\(222\) 3.24752e10 + 2.72499e10i 0.897354 + 0.752969i
\(223\) −3.88488e10 1.41398e10i −1.05198 0.382888i −0.242567 0.970135i \(-0.577990\pi\)
−0.809408 + 0.587247i \(0.800212\pi\)
\(224\) −1.02226e10 + 3.72072e9i −0.271297 + 0.0987439i
\(225\) 1.49040e10 1.25059e10i 0.387687 0.325308i
\(226\) 2.22193e9 + 1.26012e10i 0.0566556 + 0.321310i
\(227\) −9.51762e9 −0.237910 −0.118955 0.992900i \(-0.537954\pi\)
−0.118955 + 0.992900i \(0.537954\pi\)
\(228\) 2.32409e10 + 6.61964e9i 0.569569 + 0.162229i
\(229\) −5.30818e10 −1.27552 −0.637758 0.770237i \(-0.720138\pi\)
−0.637758 + 0.770237i \(0.720138\pi\)
\(230\) −4.52907e9 2.56856e10i −0.106717 0.605223i
\(231\) −1.71905e10 + 1.44245e10i −0.397223 + 0.333309i
\(232\) 2.47559e10 9.01042e9i 0.561027 0.204197i
\(233\) 6.43335e10 + 2.34155e10i 1.43000 + 0.520477i 0.936931 0.349514i \(-0.113653\pi\)
0.493067 + 0.869991i \(0.335876\pi\)
\(234\) −8.33155e9 6.99100e9i −0.181658 0.152429i
\(235\) 1.53145e10 2.65255e10i 0.327565 0.567360i
\(236\) −3.53951e9 6.13061e9i −0.0742744 0.128647i
\(237\) −1.00101e10 + 5.67703e10i −0.206097 + 1.16884i
\(238\) 1.28384e10 7.28105e10i 0.259368 1.47095i
\(239\) −1.03855e10 1.79883e10i −0.205892 0.356615i 0.744525 0.667595i \(-0.232676\pi\)
−0.950416 + 0.310980i \(0.899343\pi\)
\(240\) 1.14302e10 1.97977e10i 0.222384 0.385180i
\(241\) 4.21262e9 + 3.53481e9i 0.0804406 + 0.0674977i 0.682121 0.731239i \(-0.261058\pi\)
−0.601681 + 0.798737i \(0.705502\pi\)
\(242\) 3.29045e10 + 1.19763e10i 0.616717 + 0.224467i
\(243\) −3.89282e10 + 1.41687e10i −0.716203 + 0.260677i
\(244\) 1.73312e10 1.45426e10i 0.313022 0.262657i
\(245\) 2.45246e10 + 1.39086e11i 0.434866 + 2.46625i
\(246\) −8.48801e10 −1.47774
\(247\) 2.12669e10 4.38007e10i 0.363554 0.748763i
\(248\) −1.92030e10 −0.322356
\(249\) −3.49850e9 1.98410e10i −0.0576746 0.327089i
\(250\) 1.28689e10 1.07983e10i 0.208359 0.174834i
\(251\) 1.20134e10 4.37252e9i 0.191044 0.0695344i −0.244726 0.969592i \(-0.578698\pi\)
0.435771 + 0.900058i \(0.356476\pi\)
\(252\) −1.97924e10 7.20384e9i −0.309169 0.112528i
\(253\) −7.74334e9 6.49743e9i −0.118819 0.0997010i
\(254\) 2.88035e10 4.98892e10i 0.434204 0.752064i
\(255\) 7.76821e10 + 1.34549e11i 1.15051 + 1.99274i
\(256\) 7.45813e8 4.22972e9i 0.0108530 0.0615505i
\(257\) 1.02208e10 5.79648e10i 0.146145 0.828829i −0.820296 0.571939i \(-0.806191\pi\)
0.966441 0.256890i \(-0.0826977\pi\)
\(258\) 1.22169e10 + 2.11602e10i 0.171661 + 0.297325i
\(259\) 8.27109e10 1.43259e11i 1.14213 1.97822i
\(260\) −3.52851e10 2.96077e10i −0.478864 0.401814i
\(261\) 4.79310e10 + 1.74455e10i 0.639344 + 0.232702i
\(262\) 3.73404e10 1.35908e10i 0.489579 0.178192i
\(263\) −3.66173e10 + 3.07255e10i −0.471938 + 0.396003i −0.847501 0.530794i \(-0.821894\pi\)
0.375563 + 0.926797i \(0.377449\pi\)
\(264\) −1.53847e9 8.72510e9i −0.0194927 0.110548i
\(265\) 1.58075e11 1.96905
\(266\) 9.69011e9 9.37952e10i 0.118676 1.14872i
\(267\) 4.35445e10 0.524364
\(268\) 7.39208e9 + 4.19225e10i 0.0875306 + 0.496411i
\(269\) 8.56319e10 7.18537e10i 0.997127 0.836689i 0.0105430 0.999944i \(-0.496644\pi\)
0.986584 + 0.163256i \(0.0521995\pi\)
\(270\) −6.16371e10 + 2.24341e10i −0.705838 + 0.256904i
\(271\) −2.62055e10 9.53803e9i −0.295142 0.107423i 0.190205 0.981744i \(-0.439085\pi\)
−0.485347 + 0.874321i \(0.661307\pi\)
\(272\) 2.23605e10 + 1.87627e10i 0.247697 + 0.207843i
\(273\) −7.38856e10 + 1.27974e11i −0.805059 + 1.39440i
\(274\) −2.35980e10 4.08729e10i −0.252928 0.438084i
\(275\) 5.54524e9 3.14486e10i 0.0584687 0.331592i
\(276\) 5.73649e9 3.25332e10i 0.0595052 0.337471i
\(277\) −9.37534e10 1.62386e11i −0.956815 1.65725i −0.730159 0.683277i \(-0.760554\pi\)
−0.226655 0.973975i \(-0.572779\pi\)
\(278\) −6.09146e10 + 1.05507e11i −0.611674 + 1.05945i
\(279\) −2.84813e10 2.38987e10i −0.281411 0.236132i
\(280\) −8.38232e10 3.05091e10i −0.814991 0.296633i
\(281\) −1.54978e11 + 5.64075e10i −1.48283 + 0.539707i −0.951552 0.307489i \(-0.900511\pi\)
−0.531281 + 0.847196i \(0.678289\pi\)
\(282\) 2.97183e10 2.49366e10i 0.279836 0.234810i
\(283\) −2.51625e10 1.42704e11i −0.233193 1.32250i −0.846386 0.532570i \(-0.821226\pi\)
0.613193 0.789933i \(-0.289885\pi\)
\(284\) 4.66359e10 0.425391
\(285\) 1.11095e11 + 1.64077e11i 0.997458 + 1.47315i
\(286\) −1.78514e10 −0.157771
\(287\) 5.75137e10 + 3.26176e11i 0.500383 + 2.83781i
\(288\) 6.37017e9 5.34521e9i 0.0545613 0.0457824i
\(289\) −7.49787e10 + 2.72900e10i −0.632263 + 0.230125i
\(290\) 2.02994e11 + 7.38837e10i 1.68536 + 0.613420i
\(291\) −1.45238e11 1.21869e11i −1.18731 0.996268i
\(292\) −2.10954e10 + 3.65384e10i −0.169811 + 0.294121i
\(293\) 8.77003e9 + 1.51901e10i 0.0695179 + 0.120409i 0.898689 0.438586i \(-0.144521\pi\)
−0.829171 + 0.558995i \(0.811187\pi\)
\(294\) −3.10627e10 + 1.76166e11i −0.242480 + 1.37517i
\(295\) 1.00797e10 5.71647e10i 0.0774904 0.439470i
\(296\) 3.26549e10 + 5.65599e10i 0.247249 + 0.428248i
\(297\) −1.27105e10 + 2.20152e10i −0.0947889 + 0.164179i
\(298\) −9.05079e10 7.59452e10i −0.664834 0.557862i
\(299\) −6.25484e10 2.27657e10i −0.452580 0.164726i
\(300\) 9.80703e10 3.56947e10i 0.699023 0.254424i
\(301\) 7.30362e10 6.12846e10i 0.512848 0.430331i
\(302\) 9.33423e9 + 5.29370e10i 0.0645724 + 0.366208i
\(303\) −1.54816e11 −1.05517
\(304\) 3.01569e10 + 2.18287e10i 0.202515 + 0.146587i
\(305\) 1.85515e11 1.22752
\(306\) 9.81375e9 + 5.56565e10i 0.0639865 + 0.362886i
\(307\) 7.19938e10 6.04099e10i 0.462564 0.388138i −0.381509 0.924365i \(-0.624596\pi\)
0.844073 + 0.536227i \(0.180151\pi\)
\(308\) −3.24862e10 + 1.18240e10i −0.205694 + 0.0748664i
\(309\) −2.78805e11 1.01477e11i −1.73975 0.633219i
\(310\) −1.20622e11 1.01214e11i −0.741820 0.622461i
\(311\) 1.17611e11 2.03708e11i 0.712895 1.23477i −0.250870 0.968021i \(-0.580717\pi\)
0.963766 0.266750i \(-0.0859498\pi\)
\(312\) −2.91706e10 5.05249e10i −0.174281 0.301863i
\(313\) −3.68796e10 + 2.09155e11i −0.217188 + 1.23174i 0.659880 + 0.751371i \(0.270607\pi\)
−0.877068 + 0.480365i \(0.840504\pi\)
\(314\) −2.87207e10 + 1.62883e11i −0.166729 + 0.945567i
\(315\) −8.63546e10 1.49571e11i −0.494183 0.855951i
\(316\) −4.44037e10 + 7.69095e10i −0.250511 + 0.433898i
\(317\) 2.65800e11 + 2.23033e11i 1.47839 + 1.24051i 0.907885 + 0.419219i \(0.137696\pi\)
0.570502 + 0.821296i \(0.306748\pi\)
\(318\) 1.88142e11 + 6.84781e10i 1.03172 + 0.375517i
\(319\) 7.86716e10 2.86341e10i 0.425363 0.154820i
\(320\) 2.69785e10 2.26376e10i 0.143828 0.120686i
\(321\) −2.95184e10 1.67407e11i −0.155174 0.880038i
\(322\) −1.28905e11 −0.668219
\(323\) −2.30954e11 + 1.03318e11i −1.18063 + 0.528161i
\(324\) −1.23040e11 −0.620287
\(325\) −3.65154e10 2.07089e11i −0.181552 1.02963i
\(326\) 1.26798e11 1.06396e11i 0.621773 0.521730i
\(327\) −8.56725e10 + 3.11822e10i −0.414359 + 0.150814i
\(328\) −1.22877e11 4.47237e10i −0.586191 0.213356i
\(329\) −1.15963e11 9.73043e10i −0.545679 0.457879i
\(330\) 3.63239e10 6.29148e10i 0.168609 0.292039i
\(331\) −3.38799e10 5.86818e10i −0.155137 0.268706i 0.777972 0.628299i \(-0.216249\pi\)
−0.933109 + 0.359593i \(0.882915\pi\)
\(332\) 5.38966e9 3.05663e10i 0.0243467 0.138077i
\(333\) −2.19576e10 + 1.24528e11i −0.0978558 + 0.554968i
\(334\) −4.21576e10 7.30191e10i −0.185360 0.321053i
\(335\) −1.74530e11 + 3.02294e11i −0.757126 + 1.31138i
\(336\) −8.65504e10 7.26244e10i −0.370461 0.310854i
\(337\) −1.76983e11 6.44167e10i −0.747477 0.272059i −0.0599333 0.998202i \(-0.519089\pi\)
−0.687544 + 0.726143i \(0.741311\pi\)
\(338\) 4.89770e10 1.78262e10i 0.204111 0.0742905i
\(339\) −1.01802e11 + 8.54217e10i −0.418655 + 0.351293i
\(340\) 4.15624e10 + 2.35712e11i 0.168673 + 0.956593i
\(341\) −6.10250e10 −0.244407
\(342\) 1.75615e10 + 6.99069e10i 0.0694135 + 0.276314i
\(343\) 2.79358e11 1.08978
\(344\) 6.53641e9 + 3.70698e10i 0.0251667 + 0.142727i
\(345\) 2.07507e11 1.74119e11i 0.788583 0.661699i
\(346\) 1.37468e11 5.00341e10i 0.515654 0.187683i
\(347\) −4.84941e11 1.76504e11i −1.79558 0.653539i −0.998784 0.0492968i \(-0.984302\pi\)
−0.796800 0.604243i \(-0.793476\pi\)
\(348\) 2.09598e11 + 1.75874e11i 0.766093 + 0.642828i
\(349\) 9.33916e10 1.61759e11i 0.336972 0.583652i −0.646890 0.762584i \(-0.723931\pi\)
0.983862 + 0.178931i \(0.0572640\pi\)
\(350\) −2.03618e11 3.52677e11i −0.725287 1.25623i
\(351\) −2.90682e10 + 1.64854e11i −0.102220 + 0.579718i
\(352\) 2.37011e9 1.34416e10i 0.00822862 0.0466668i
\(353\) −4.21288e10 7.29692e10i −0.144408 0.250123i 0.784744 0.619821i \(-0.212795\pi\)
−0.929152 + 0.369698i \(0.879461\pi\)
\(354\) 3.67607e10 6.36714e10i 0.124414 0.215491i
\(355\) 2.92940e11 + 2.45806e11i 0.978928 + 0.821418i
\(356\) 6.30375e10 + 2.29438e10i 0.208005 + 0.0757076i
\(357\) 7.21553e11 2.62624e11i 2.35105 0.855711i
\(358\) 1.32889e11 1.11507e11i 0.427578 0.358781i
\(359\) 2.00300e10 + 1.13596e11i 0.0636436 + 0.360941i 0.999952 + 0.00976297i \(0.00310770\pi\)
−0.936309 + 0.351178i \(0.885781\pi\)
\(360\) 6.81869e10 0.213963
\(361\) −2.84377e11 + 1.52502e11i −0.881277 + 0.472601i
\(362\) 1.89512e11 0.580027
\(363\) 6.31510e10 + 3.58147e11i 0.190897 + 1.08263i
\(364\) −1.74391e11 + 1.46331e11i −0.520676 + 0.436899i
\(365\) −3.25093e11 + 1.18324e11i −0.958716 + 0.348944i
\(366\) 2.20801e11 + 8.03650e10i 0.643185 + 0.234100i
\(367\) 2.80677e10 + 2.35516e10i 0.0807625 + 0.0677678i 0.682275 0.731095i \(-0.260991\pi\)
−0.601513 + 0.798863i \(0.705435\pi\)
\(368\) 2.54463e10 4.40744e10i 0.0723286 0.125277i
\(369\) −1.26588e11 2.19257e11i −0.355447 0.615652i
\(370\) −9.29933e10 + 5.27391e11i −0.257955 + 1.46293i
\(371\) 1.35664e11 7.69389e11i 0.371777 2.10845i
\(372\) −9.97193e10 1.72719e11i −0.269983 0.467624i
\(373\) 5.75292e10 9.96434e10i 0.153886 0.266538i −0.778767 0.627313i \(-0.784155\pi\)
0.932653 + 0.360775i \(0.117488\pi\)
\(374\) 7.10591e10 + 5.96257e10i 0.187801 + 0.157584i
\(375\) 1.63951e11 + 5.96734e10i 0.428128 + 0.155826i
\(376\) 5.61611e10 2.04410e10i 0.144907 0.0527419i
\(377\) 4.22320e11 3.54369e11i 1.07673 0.903482i
\(378\) 5.62935e10 + 3.19256e11i 0.141822 + 0.804315i
\(379\) 6.42866e11 1.60046 0.800228 0.599696i \(-0.204712\pi\)
0.800228 + 0.599696i \(0.204712\pi\)
\(380\) 7.43751e10 + 2.96064e11i 0.182979 + 0.728383i
\(381\) 5.98296e11 1.45463
\(382\) 4.77543e10 + 2.70828e11i 0.114743 + 0.650741i
\(383\) −2.46356e11 + 2.06717e11i −0.585018 + 0.490888i −0.886591 0.462555i \(-0.846933\pi\)
0.301573 + 0.953443i \(0.402488\pi\)
\(384\) 4.19166e10 1.52564e10i 0.0983774 0.0358065i
\(385\) −2.66381e11 9.69547e10i −0.617916 0.224903i
\(386\) 7.11500e10 + 5.97020e10i 0.163129 + 0.136882i
\(387\) −3.64398e10 + 6.31157e10i −0.0825804 + 0.143034i
\(388\) −1.46042e11 2.52952e11i −0.327140 0.566624i
\(389\) −1.19795e9 + 6.79393e9i −0.00265257 + 0.0150435i −0.986105 0.166121i \(-0.946876\pi\)
0.983453 + 0.181165i \(0.0579868\pi\)
\(390\) 8.30708e10 4.71118e11i 0.181827 1.03119i
\(391\) 1.72939e11 + 2.99539e11i 0.374195 + 0.648124i
\(392\) −1.37790e11 + 2.38660e11i −0.294735 + 0.510496i
\(393\) 3.16145e11 + 2.65278e11i 0.668529 + 0.560963i
\(394\) −5.72514e11 2.08378e11i −1.19689 0.435631i
\(395\) −6.84287e11 + 2.49060e11i −1.41433 + 0.514775i
\(396\) 2.02437e10 1.69865e10i 0.0413677 0.0347116i
\(397\) 7.54531e10 + 4.27916e11i 0.152447 + 0.864571i 0.961083 + 0.276261i \(0.0890955\pi\)
−0.808635 + 0.588310i \(0.799793\pi\)
\(398\) −1.05783e11 −0.211320
\(399\) 8.93949e11 3.99913e11i 1.76577 0.789928i
\(400\) 1.60780e11 0.314023
\(401\) 3.04873e10 + 1.72902e11i 0.0588802 + 0.333926i 0.999991 0.00417136i \(-0.00132779\pi\)
−0.941111 + 0.338097i \(0.890217\pi\)
\(402\) −3.38681e11 + 2.84187e11i −0.646805 + 0.542734i
\(403\) −3.77615e11 + 1.37441e11i −0.713143 + 0.259563i
\(404\) −2.24120e11 8.15731e10i −0.418567 0.152346i
\(405\) −7.72863e11 6.48509e11i −1.42743 1.19776i
\(406\) 5.33825e11 9.24611e11i 0.975060 1.68885i
\(407\) 1.03774e11 + 1.79741e11i 0.187461 + 0.324693i
\(408\) −5.26427e10 + 2.98551e11i −0.0940518 + 0.533394i
\(409\) −2.44406e10 + 1.38610e11i −0.0431875 + 0.244928i −0.998757 0.0498362i \(-0.984130\pi\)
0.955570 + 0.294764i \(0.0952412\pi\)
\(410\) −5.36117e11 9.28581e11i −0.936983 1.62290i
\(411\) 2.45084e11 4.24498e11i 0.423669 0.733816i
\(412\) −3.50146e11 2.93807e11i −0.598703 0.502372i
\(413\) −2.69584e11 9.81206e10i −0.455952 0.165953i
\(414\) 9.25931e10 3.37011e10i 0.154909 0.0563823i
\(415\) 1.94961e11 1.63592e11i 0.322650 0.270736i
\(416\) −1.56072e10 8.85128e10i −0.0255508 0.144906i
\(417\) −1.26529e12 −2.04918
\(418\) 9.58354e10 + 6.93691e10i 0.153544 + 0.111141i
\(419\) 3.94519e11 0.625324 0.312662 0.949864i \(-0.398779\pi\)
0.312662 + 0.949864i \(0.398779\pi\)
\(420\) −1.60875e11 9.12368e11i −0.252271 1.43070i
\(421\) −4.55986e11 + 3.82618e11i −0.707428 + 0.593602i −0.923876 0.382692i \(-0.874997\pi\)
0.216448 + 0.976294i \(0.430553\pi\)
\(422\) 5.49251e11 1.99911e11i 0.843072 0.306853i
\(423\) 1.08736e11 + 3.95766e10i 0.165136 + 0.0601045i
\(424\) 2.36284e11 + 1.98266e11i 0.355048 + 0.297921i
\(425\) −5.46347e11 + 9.46301e11i −0.812304 + 1.40695i
\(426\) 2.42176e11 + 4.19461e11i 0.356277 + 0.617090i
\(427\) 1.59214e11 9.02945e11i 0.231769 1.31443i
\(428\) 4.54750e10 2.57901e11i 0.0655051 0.371498i
\(429\) −9.27008e10 1.60562e11i −0.132137 0.228869i
\(430\) −1.54327e11 + 2.67303e11i −0.217688 + 0.377047i
\(431\) −2.64747e11 2.22149e11i −0.369558 0.310096i 0.439028 0.898473i \(-0.355323\pi\)
−0.808587 + 0.588377i \(0.799767\pi\)
\(432\) −1.20270e11 4.37748e10i −0.166143 0.0604710i
\(433\) 1.18430e11 4.31050e10i 0.161907 0.0589295i −0.259795 0.965664i \(-0.583655\pi\)
0.421702 + 0.906734i \(0.361433\pi\)
\(434\) −5.96153e11 + 5.00232e11i −0.806592 + 0.676811i
\(435\) 3.89590e11 + 2.20947e12i 0.521682 + 2.95861i
\(436\) −1.40454e11 −0.186143
\(437\) 2.47325e11 + 3.65275e11i 0.324416 + 0.479131i
\(438\) −4.38186e11 −0.568886
\(439\) 8.18788e10 + 4.64357e11i 0.105216 + 0.596708i 0.991134 + 0.132867i \(0.0424182\pi\)
−0.885918 + 0.463842i \(0.846471\pi\)
\(440\) 8.57346e10 7.19398e10i 0.109048 0.0915024i
\(441\) −5.01386e11 + 1.82490e11i −0.631246 + 0.229755i
\(442\) 5.73994e11 + 2.08917e11i 0.715332 + 0.260359i
\(443\) 1.02682e12 + 8.61605e11i 1.26671 + 1.06290i 0.994933 + 0.100537i \(0.0320561\pi\)
0.271778 + 0.962360i \(0.412388\pi\)
\(444\) −3.39147e11 + 5.87420e11i −0.414157 + 0.717340i
\(445\) 2.75034e11 + 4.76373e11i 0.332481 + 0.575873i
\(446\) 1.14863e11 6.51423e11i 0.137460 0.779572i
\(447\) 2.13080e11 1.20844e12i 0.252441 1.43166i
\(448\) −8.70292e10 1.50739e11i −0.102074 0.176797i
\(449\) 1.14153e11 1.97719e11i 0.132550 0.229583i −0.792109 0.610380i \(-0.791017\pi\)
0.924659 + 0.380797i \(0.124350\pi\)
\(450\) 2.38464e11 + 2.00095e11i 0.274136 + 0.230028i
\(451\) −3.90490e11 1.42127e11i −0.444443 0.161764i
\(452\) −1.92383e11 + 7.00216e10i −0.216792 + 0.0789059i
\(453\) −4.27664e11 + 3.58852e11i −0.477156 + 0.400381i
\(454\) −2.64435e10 1.49968e11i −0.0292124 0.165672i
\(455\) −1.86669e12 −2.04184
\(456\) −3.97332e10 + 3.84597e11i −0.0430340 + 0.416547i
\(457\) −2.52427e11 −0.270715 −0.135358 0.990797i \(-0.543218\pi\)
−0.135358 + 0.990797i \(0.543218\pi\)
\(458\) −1.47481e11 8.36405e11i −0.156618 0.888223i
\(459\) 6.66337e11 5.59123e11i 0.700708 0.587964i
\(460\) 3.92143e11 1.42728e11i 0.408352 0.148628i
\(461\) −1.35625e12 4.93633e11i −1.39857 0.509038i −0.470816 0.882231i \(-0.656041\pi\)
−0.927754 + 0.373193i \(0.878263\pi\)
\(462\) −2.75048e11 2.30792e11i −0.280879 0.235685i
\(463\) 5.49683e11 9.52080e11i 0.555902 0.962850i −0.441931 0.897049i \(-0.645706\pi\)
0.997833 0.0658013i \(-0.0209603\pi\)
\(464\) 2.10758e11 + 3.65043e11i 0.211083 + 0.365606i
\(465\) 2.83977e11 1.61051e12i 0.281673 1.59744i
\(466\) −1.90214e11 + 1.07875e12i −0.186855 + 1.05971i
\(467\) 8.46089e11 + 1.46547e12i 0.823171 + 1.42577i 0.903309 + 0.428991i \(0.141131\pi\)
−0.0801373 + 0.996784i \(0.525536\pi\)
\(468\) 8.70085e10 1.50703e11i 0.0838408 0.145217i
\(469\) 1.32155e12 + 1.10892e12i 1.26127 + 1.05833i
\(470\) 4.60510e11 + 1.67612e11i 0.435310 + 0.158440i
\(471\) −1.61417e12 + 5.87511e11i −1.51132 + 0.550075i
\(472\) 8.67656e10 7.28049e10i 0.0804652 0.0675184i
\(473\) 2.07720e10 + 1.17804e11i 0.0190811 + 0.108214i
\(474\) −9.22337e11 −0.839241
\(475\) −6.08698e11 + 1.25365e12i −0.548631 + 1.12994i
\(476\) 1.18294e12 1.05616
\(477\) 1.03702e11 + 5.88124e11i 0.0917180 + 0.520159i
\(478\) 2.54585e11 2.13622e11i 0.223053 0.187163i
\(479\) 5.60841e11 2.04130e11i 0.486777 0.177172i −0.0869602 0.996212i \(-0.527715\pi\)
0.573737 + 0.819039i \(0.305493\pi\)
\(480\) 3.43708e11 + 1.25099e11i 0.295532 + 0.107565i
\(481\) 1.04695e12 + 8.78496e11i 0.891812 + 0.748319i
\(482\) −4.39935e10 + 7.61989e10i −0.0371258 + 0.0643039i
\(483\) −6.69392e11 1.15942e12i −0.559653 0.969347i
\(484\) −9.72881e10 + 5.51748e11i −0.0805853 + 0.457022i
\(485\) 4.15892e11 2.35864e12i 0.341305 1.93564i
\(486\) −3.31412e11 5.74023e11i −0.269467 0.466731i
\(487\) 1.04499e12 1.80997e12i 0.841841 1.45811i −0.0464948 0.998919i \(-0.514805\pi\)
0.888336 0.459194i \(-0.151862\pi\)
\(488\) 2.77299e11 + 2.32682e11i 0.221340 + 0.185726i
\(489\) 1.61541e12 + 5.87962e11i 1.27760 + 0.465007i
\(490\) −2.12343e12 + 7.72866e11i −1.66401 + 0.605650i
\(491\) 2.26259e11 1.89853e11i 0.175686 0.147418i −0.550704 0.834700i \(-0.685641\pi\)
0.726391 + 0.687282i \(0.241196\pi\)
\(492\) −2.35829e11 1.33745e12i −0.181449 1.02905i
\(493\) −2.86471e12 −2.18409
\(494\) 7.49251e11 + 2.13407e11i 0.566052 + 0.161227i
\(495\) 2.16690e11 0.162224
\(496\) −5.33530e10 3.02580e11i −0.0395814 0.224478i
\(497\) 1.44780e12 1.21485e12i 1.06440 0.893140i
\(498\) 3.02913e11 1.10251e11i 0.220691 0.0803251i
\(499\) −5.38991e11 1.96177e11i −0.389161 0.141643i 0.140027 0.990148i \(-0.455281\pi\)
−0.529188 + 0.848505i \(0.677503\pi\)
\(500\) 2.05903e11 + 1.72773e11i 0.147332 + 0.123626i
\(501\) 4.37840e11 7.58362e11i 0.310489 0.537783i
\(502\) 1.02275e11 + 1.77146e11i 0.0718792 + 0.124498i
\(503\) −2.76834e11 + 1.57000e12i −0.192825 + 1.09356i 0.722658 + 0.691206i \(0.242920\pi\)
−0.915483 + 0.402358i \(0.868191\pi\)
\(504\) 5.85198e10 3.31882e11i 0.0403985 0.229111i
\(505\) −9.77842e11 1.69367e12i −0.669048 1.15883i
\(506\) 8.08657e10 1.40063e11i 0.0548387 0.0949834i
\(507\) 4.14668e11 + 3.47948e11i 0.278718 + 0.233872i
\(508\) 8.66127e11 + 3.15244e11i 0.577025 + 0.210020i
\(509\) 2.05514e11 7.48011e10i 0.135710 0.0493944i −0.273272 0.961937i \(-0.588106\pi\)
0.408982 + 0.912542i \(0.365884\pi\)
\(510\) −1.90425e12 + 1.59786e12i −1.24640 + 1.04586i
\(511\) 2.96909e11 + 1.68386e12i 0.192633 + 1.09247i
\(512\) 6.87195e10 0.0441942
\(513\) 7.96660e11 7.72061e11i 0.507861 0.492179i
\(514\) 9.41743e11 0.595112
\(515\) −6.50832e11 3.69105e12i −0.407696 2.31216i
\(516\) −2.99477e11 + 2.51291e11i −0.185969 + 0.156046i
\(517\) 1.78474e11 6.49591e10i 0.109867 0.0399883i
\(518\) 2.48713e12 + 9.05242e11i 1.51780 + 0.552434i
\(519\) 1.16388e12 + 9.76613e11i 0.704135 + 0.590839i
\(520\) 3.68492e11 6.38247e11i 0.221010 0.382801i
\(521\) −7.11248e11 1.23192e12i −0.422913 0.732507i 0.573310 0.819339i \(-0.305659\pi\)
−0.996223 + 0.0868316i \(0.972326\pi\)
\(522\) −1.41717e11 + 8.03716e11i −0.0835418 + 0.473789i
\(523\) −2.61659e11 + 1.48394e12i −0.152925 + 0.867280i 0.807734 + 0.589548i \(0.200694\pi\)
−0.960658 + 0.277732i \(0.910417\pi\)
\(524\) 3.17894e11 + 5.50609e11i 0.184201 + 0.319045i
\(525\) 2.11474e12 3.66283e12i 1.21490 2.10426i
\(526\) −5.85876e11 4.91609e11i −0.333711 0.280016i
\(527\) 1.96220e12 + 7.14181e11i 1.10814 + 0.403330i
\(528\) 1.33206e11 4.84831e10i 0.0745885 0.0271480i
\(529\) −9.17802e11 + 7.70128e11i −0.509564 + 0.427575i
\(530\) 4.39191e11 + 2.49078e12i 0.241775 + 1.37118i
\(531\) 2.19296e11 0.119703
\(532\) 1.50485e12 1.07912e11i 0.814498 0.0584071i
\(533\) −2.73641e12 −1.46862
\(534\) 1.20983e11 + 6.86127e11i 0.0643855 + 0.365148i
\(535\) 1.64498e12 1.38030e12i 0.868095 0.728419i
\(536\) −6.40032e11 + 2.32953e11i −0.334935 + 0.121906i
\(537\) 1.69302e12 + 6.16208e11i 0.878572 + 0.319774i
\(538\) 1.37011e12 + 1.14966e12i 0.705075 + 0.591628i
\(539\) −4.37883e11 + 7.58435e11i −0.223464 + 0.387052i
\(540\) −5.24742e11 9.08880e11i −0.265567 0.459976i
\(541\) −1.75961e11 + 9.97924e11i −0.0883138 + 0.500852i 0.908278 + 0.418366i \(0.137397\pi\)
−0.996592 + 0.0824861i \(0.973714\pi\)
\(542\) 7.74814e10 4.39419e11i 0.0385656 0.218717i
\(543\) 9.84118e11 + 1.70454e12i 0.485789 + 0.841412i
\(544\) −2.33516e11 + 4.04462e11i −0.114320 + 0.198008i
\(545\) −8.82252e11 7.40297e11i −0.428360 0.359436i
\(546\) −2.22175e12 8.08652e11i −1.06986 0.389399i
\(547\) 2.37618e12 8.64860e11i 1.13485 0.413050i 0.294797 0.955560i \(-0.404748\pi\)
0.840050 + 0.542510i \(0.182526\pi\)
\(548\) 5.78467e11 4.85391e11i 0.274010 0.229921i
\(549\) 1.21703e11 + 6.90214e11i 0.0571777 + 0.324271i
\(550\) 5.10940e11 0.238088
\(551\) −3.64427e12 + 2.61329e11i −1.68434 + 0.120783i
\(552\) 5.28562e11 0.242309
\(553\) 6.24963e11 + 3.54434e12i 0.284179 + 1.61166i
\(554\) 2.29822e12 1.92843e12i 1.03657 0.869782i
\(555\) −5.22646e12 + 1.90227e12i −2.33824 + 0.851049i
\(556\) −1.83171e12 6.66689e11i −0.812869 0.295860i
\(557\) −3.10444e12 2.60493e12i −1.36658 1.14670i −0.973889 0.227024i \(-0.927100\pi\)
−0.392689 0.919671i \(-0.628455\pi\)
\(558\) 2.97438e11 5.15178e11i 0.129880 0.224959i
\(559\) 3.93853e11 + 6.82173e11i 0.170601 + 0.295489i
\(560\) 2.47838e11 1.40556e12i 0.106493 0.603954i
\(561\) −1.67293e11 + 9.48763e11i −0.0713089 + 0.404413i
\(562\) −1.31939e12 2.28526e12i −0.557906 0.966322i
\(563\) 1.93338e12 3.34871e12i 0.811016 1.40472i −0.101138 0.994872i \(-0.532248\pi\)
0.912154 0.409848i \(-0.134418\pi\)
\(564\) 4.75493e11 + 3.98986e11i 0.197874 + 0.166036i
\(565\) −1.57750e12 5.74164e11i −0.651256 0.237038i
\(566\) 2.17866e12 7.92968e11i 0.892311 0.324775i
\(567\) −3.81974e12 + 3.20514e12i −1.55207 + 1.30234i
\(568\) 1.29572e11 + 7.34839e11i 0.0522328 + 0.296227i
\(569\) −2.09633e12 −0.838408 −0.419204 0.907892i \(-0.637691\pi\)
−0.419204 + 0.907892i \(0.637691\pi\)
\(570\) −2.27669e12 + 2.20639e12i −0.903373 + 0.875479i
\(571\) −6.97411e11 −0.274553 −0.137277 0.990533i \(-0.543835\pi\)
−0.137277 + 0.990533i \(0.543835\pi\)
\(572\) −4.95979e10 2.81284e11i −0.0193723 0.109866i
\(573\) −2.18794e12 + 1.83590e12i −0.847892 + 0.711466i
\(574\) −4.97974e12 + 1.81248e12i −1.91471 + 0.696898i
\(575\) 1.79025e12 + 6.51596e11i 0.682979 + 0.248584i
\(576\) 1.01923e11 + 8.55234e10i 0.0385807 + 0.0323730i
\(577\) 4.51099e11 7.81327e11i 0.169426 0.293455i −0.768792 0.639499i \(-0.779142\pi\)
0.938218 + 0.346044i \(0.112475\pi\)
\(578\) −6.38325e11 1.10561e12i −0.237885 0.412029i
\(579\) −1.67506e11 + 9.49976e11i −0.0619410 + 0.351285i
\(580\) −6.00188e11 + 3.40383e12i −0.220222 + 1.24894i
\(581\) −6.28921e11 1.08932e12i −0.228983 0.396611i
\(582\) 1.51676e12 2.62711e12i 0.547979 0.949127i
\(583\) 7.50883e11 + 6.30066e11i 0.269193 + 0.225880i
\(584\) −6.34343e11 2.30882e11i −0.225666 0.0821358i
\(585\) 1.34085e12 4.88030e11i 0.473347 0.172284i
\(586\) −2.14983e11 + 1.80392e11i −0.0753123 + 0.0631945i
\(587\) 2.56518e11 + 1.45479e12i 0.0891758 + 0.505741i 0.996377 + 0.0850443i \(0.0271032\pi\)
−0.907201 + 0.420697i \(0.861786\pi\)
\(588\) −2.86213e12 −0.987396
\(589\) 2.56131e12 + 7.29530e11i 0.876886 + 0.249761i
\(590\) 9.28746e11 0.315546
\(591\) −1.09878e12 6.23150e12i −0.370482 2.10111i
\(592\) −8.00482e11 + 6.71684e11i −0.267858 + 0.224759i
\(593\) −1.89235e12 + 6.88758e11i −0.628427 + 0.228729i −0.636546 0.771238i \(-0.719638\pi\)
0.00811967 + 0.999967i \(0.497415\pi\)
\(594\) −3.82206e11 1.39112e11i −0.125967 0.0458484i
\(595\) 7.43053e12 + 6.23495e12i 2.43049 + 2.03942i
\(596\) 9.45197e11 1.63713e12i 0.306842 0.531465i
\(597\) −5.49319e11 9.51449e11i −0.176987 0.306550i
\(598\) 1.84935e11 1.04882e12i 0.0591378 0.335387i
\(599\) −5.04576e11 + 2.86159e12i −0.160142 + 0.908211i 0.793791 + 0.608191i \(0.208105\pi\)
−0.953933 + 0.300020i \(0.903007\pi\)
\(600\) 8.34914e11 + 1.44611e12i 0.263003 + 0.455535i
\(601\) 7.17139e11 1.24212e12i 0.224217 0.388355i −0.731867 0.681447i \(-0.761351\pi\)
0.956084 + 0.293092i \(0.0946843\pi\)
\(602\) 1.16858e12 + 9.80554e11i 0.362638 + 0.304290i
\(603\) −1.23919e12 4.51030e11i −0.381691 0.138924i
\(604\) −8.08191e11 + 2.94157e11i −0.247086 + 0.0899319i
\(605\) −3.51922e12 + 2.95298e12i −1.06794 + 0.896110i
\(606\) −4.30136e11 2.43942e12i −0.129562 0.734785i
\(607\) −2.08747e12 −0.624125 −0.312062 0.950062i \(-0.601020\pi\)
−0.312062 + 0.950062i \(0.601020\pi\)
\(608\) −2.60166e11 + 5.35829e11i −0.0772119 + 0.159023i
\(609\) 1.10884e13 3.26656
\(610\) 5.15429e11 + 2.92314e12i 0.150725 + 0.854802i
\(611\) 9.58072e11 8.03918e11i 0.278108 0.233360i
\(612\) −8.49709e11 + 3.09269e11i −0.244844 + 0.0891158i
\(613\) −3.41904e12 1.24443e12i −0.977984 0.355957i −0.196928 0.980418i \(-0.563096\pi\)
−0.781056 + 0.624461i \(0.785319\pi\)
\(614\) 1.15190e12 + 9.66559e11i 0.327082 + 0.274455i
\(615\) 5.56800e12 9.64407e12i 1.56950 2.71845i
\(616\) −2.76569e11 4.79032e11i −0.0773910 0.134045i
\(617\) −6.68775e11 + 3.79281e12i −0.185779 + 1.05361i 0.739171 + 0.673517i \(0.235217\pi\)
−0.924950 + 0.380088i \(0.875894\pi\)
\(618\) 8.24339e11 4.67506e12i 0.227330 1.28925i
\(619\) −2.75491e12 4.77164e12i −0.754222 1.30635i −0.945760 0.324866i \(-0.894681\pi\)
0.191538 0.981485i \(-0.438652\pi\)
\(620\) 1.25969e12 2.18184e12i 0.342373 0.593008i
\(621\) −1.16178e12 9.74845e11i −0.313480 0.263041i
\(622\) 3.53658e12 + 1.28721e12i 0.947385 + 0.344820i
\(623\) 2.55466e12 9.29822e11i 0.679419 0.247288i
\(624\) 7.15070e11 6.00015e11i 0.188807 0.158428i
\(625\) −4.49333e11 2.54830e12i −0.117790 0.668020i
\(626\) −3.39810e12 −0.884405
\(627\) −1.26268e11 + 1.22221e12i −0.0326279 + 0.315821i
\(628\) −2.64633e12 −0.678931
\(629\) −1.23321e12 6.99386e12i −0.314129 1.78151i
\(630\) 2.11685e12 1.77625e12i 0.535374 0.449232i
\(631\) −5.71708e12 + 2.08085e12i −1.43563 + 0.522527i −0.938539 0.345172i \(-0.887821\pi\)
−0.497091 + 0.867699i \(0.665598\pi\)
\(632\) −1.33523e12 4.85983e11i −0.332911 0.121170i
\(633\) 4.65028e12 + 3.90205e12i 1.15123 + 0.965998i
\(634\) −2.77582e12 + 4.80786e12i −0.682322 + 1.18182i
\(635\) 3.77893e12 + 6.54530e12i 0.922332 + 1.59753i
\(636\) −5.56276e11 + 3.15480e12i −0.134813 + 0.764565i
\(637\) −1.00141e12 + 5.67930e12i −0.240983 + 1.36668i
\(638\) 6.69765e11 + 1.16007e12i 0.160040 + 0.277198i
\(639\) −7.22351e11 + 1.25115e12i −0.171393 + 0.296862i
\(640\) 4.31655e11 + 3.62202e11i 0.101701 + 0.0853377i
\(641\) −2.18484e12 7.95216e11i −0.511161 0.186047i 0.0735460 0.997292i \(-0.476568\pi\)
−0.584707 + 0.811244i \(0.698791\pi\)
\(642\) 2.55581e12 9.30238e11i 0.593773 0.216116i
\(643\) 5.67820e12 4.76457e12i 1.30997 1.09919i 0.321640 0.946862i \(-0.395766\pi\)
0.988329 0.152333i \(-0.0486786\pi\)
\(644\) −3.58146e11 2.03115e12i −0.0820492 0.465324i
\(645\) −3.20563e12 −0.729280
\(646\) −2.26966e12 3.35206e12i −0.512759 0.757296i
\(647\) −2.38608e12 −0.535323 −0.267662 0.963513i \(-0.586251\pi\)
−0.267662 + 0.963513i \(0.586251\pi\)
\(648\) −3.41850e11 1.93873e12i −0.0761636 0.431945i
\(649\) 2.75731e11 2.31366e11i 0.0610077 0.0511916i
\(650\) 3.16163e12 1.15074e12i 0.694707 0.252853i
\(651\) −7.59504e12 2.76437e12i −1.65736 0.603228i
\(652\) 2.02876e12 + 1.70233e12i 0.439660 + 0.368919i
\(653\) −1.88173e12 + 3.25925e12i −0.404994 + 0.701470i −0.994321 0.106425i \(-0.966060\pi\)
0.589327 + 0.807895i \(0.299393\pi\)
\(654\) −7.29366e11 1.26330e12i −0.155900 0.270027i
\(655\) −9.05287e11 + 5.13414e12i −0.192177 + 1.08989i
\(656\) 3.63309e11 2.06043e12i 0.0765965 0.434400i
\(657\) −6.53501e11 1.13190e12i −0.136836 0.237008i
\(658\) 1.21103e12 2.09756e12i 0.251848 0.436213i
\(659\) 4.14657e12 + 3.47939e12i 0.856455 + 0.718651i 0.961201 0.275848i \(-0.0889586\pi\)
−0.104746 + 0.994499i \(0.533403\pi\)
\(660\) 1.09227e12 + 3.97552e11i 0.224068 + 0.0815542i
\(661\) 3.93279e12 1.43142e12i 0.801299 0.291649i 0.0912743 0.995826i \(-0.470906\pi\)
0.710025 + 0.704177i \(0.248684\pi\)
\(662\) 8.30513e11 6.96883e11i 0.168068 0.141026i
\(663\) 1.10162e12 + 6.24761e12i 0.221422 + 1.25575i
\(664\) 4.96605e11 0.0991414
\(665\) 1.00213e13 + 7.25381e12i 1.98714 + 1.43836i
\(666\) −2.02318e12 −0.398475
\(667\) 8.67320e11 + 4.91882e12i 0.169673 + 0.962264i
\(668\) 1.03343e12 8.67148e11i 0.200810 0.168500i
\(669\) 6.45562e12 2.34965e12i 1.24601 0.453509i
\(670\) −5.24814e12 1.91017e12i −1.00616 0.366214i
\(671\) 8.81227e11 + 7.39437e11i 0.167817 + 0.140815i
\(672\) 9.03868e11 1.56555e12i 0.170979 0.296145i
\(673\) −1.38116e12 2.39223e12i −0.259522 0.449506i 0.706592 0.707622i \(-0.250232\pi\)
−0.966114 + 0.258115i \(0.916899\pi\)
\(674\) 5.23283e11 2.96769e12i 0.0976714 0.553922i
\(675\) 8.31983e11 4.71841e12i 0.154258 0.874840i
\(676\) 4.16962e11 + 7.22200e11i 0.0767956 + 0.133014i
\(677\) 9.51949e10 1.64882e11i 0.0174167 0.0301665i −0.857186 0.515007i \(-0.827789\pi\)
0.874602 + 0.484841i \(0.161122\pi\)
\(678\) −1.62883e12 1.36675e12i −0.296034 0.248402i
\(679\) −1.11231e13 4.04849e12i −2.00823 0.730936i
\(680\) −3.59862e12 + 1.30979e12i −0.645426 + 0.234916i
\(681\) 1.21155e12 1.01661e12i 0.215864 0.181132i
\(682\) −1.69550e11 9.61566e11i −0.0300102 0.170196i
\(683\) 3.57363e12 0.628371 0.314185 0.949362i \(-0.398269\pi\)
0.314185 + 0.949362i \(0.398269\pi\)
\(684\) −1.05272e12 + 4.70942e11i −0.183892 + 0.0822650i
\(685\) 6.19196e12 1.07453
\(686\) 7.76160e11 + 4.40182e12i 0.133811 + 0.758882i
\(687\) 6.75709e12 5.66987e12i 1.15732 0.971109i
\(688\) −5.65946e11 + 2.05987e11i −0.0963001 + 0.0350504i
\(689\) 6.06541e12 + 2.20763e12i 1.02535 + 0.373198i
\(690\) 3.32011e12 + 2.78591e12i 0.557612 + 0.467892i
\(691\) 4.19939e11 7.27355e11i 0.0700704 0.121366i −0.828862 0.559454i \(-0.811011\pi\)
0.898932 + 0.438088i \(0.144344\pi\)
\(692\) 1.17032e12 + 2.02705e12i 0.194011 + 0.336038i
\(693\) 1.85969e11 1.05468e12i 0.0306296 0.173709i
\(694\) 1.43381e12 8.13156e12i 0.234626 1.33063i
\(695\) −7.99181e12 1.38422e13i −1.29931 2.25047i
\(696\) −2.18889e12 + 3.79127e12i −0.353576 + 0.612411i
\(697\) 1.08925e13 + 9.13988e12i 1.74815 + 1.46688i
\(698\) 2.80830e12 + 1.02214e12i 0.447811 + 0.162990i
\(699\) −1.06905e13 + 3.89102e12i −1.69375 + 0.616476i
\(700\) 4.99137e12 4.18826e12i 0.785740 0.659314i
\(701\) 1.84948e12 + 1.04889e13i 0.289280 + 1.64059i 0.689582 + 0.724208i \(0.257794\pi\)
−0.400302 + 0.916383i \(0.631095\pi\)
\(702\) −2.67835e12 −0.416246
\(703\) −2.20680e12 8.78457e12i −0.340771 1.35651i
\(704\) 2.18383e11 0.0335075
\(705\) 8.83820e11 + 5.01239e12i 0.134745 + 0.764177i
\(706\) 1.03272e12 8.66556e11i 0.156445 0.131273i
\(707\) −9.08272e12 + 3.30584e12i −1.36719 + 0.497616i
\(708\) 1.10540e12 + 4.02333e11i 0.165337 + 0.0601777i
\(709\) −1.31775e11 1.10573e11i −0.0195851 0.0164339i 0.632943 0.774199i \(-0.281847\pi\)
−0.652528 + 0.757765i \(0.726291\pi\)
\(710\) −3.05924e12 + 5.29877e12i −0.451806 + 0.782550i
\(711\) −1.37555e12 2.38252e12i −0.201866 0.349642i
\(712\) −1.86382e11 + 1.05702e12i −0.0271796 + 0.154143i
\(713\) 6.32200e11 3.58539e12i 0.0916119 0.519557i
\(714\) 6.14289e12 + 1.06398e13i 0.884567 + 1.53211i
\(715\) 1.17103e12 2.02828e12i 0.167567 0.290235i
\(716\) 2.12623e12 + 1.78411e12i 0.302344 + 0.253696i
\(717\) 3.24344e12 + 1.18051e12i 0.458320 + 0.166815i
\(718\) −1.73427e12 + 6.31221e11i −0.243532 + 0.0886383i
\(719\) −1.93813e12 + 1.62628e12i −0.270459 + 0.226942i −0.767922 0.640543i \(-0.778709\pi\)
0.497463 + 0.867485i \(0.334265\pi\)
\(720\) 1.89448e11 + 1.07442e12i 0.0262721 + 0.148996i
\(721\) −1.85238e13 −2.55283
\(722\) −3.19307e12 4.05720e12i −0.437312 0.555660i
\(723\) −9.13815e11 −0.124376
\(724\) 5.26535e11 + 2.98613e12i 0.0712202 + 0.403910i
\(725\) −1.20876e13 + 1.01427e13i −1.62487 + 1.36343i
\(726\) −5.46784e12 + 1.99013e12i −0.730467 + 0.265868i
\(727\) 1.11229e13 + 4.04841e12i 1.47677 + 0.537502i 0.949931 0.312461i \(-0.101153\pi\)
0.526843 + 0.849963i \(0.323376\pi\)
\(728\) −2.79025e12 2.34130e12i −0.368173 0.308934i
\(729\) −1.28807e12 + 2.23100e12i −0.168914 + 0.292568i
\(730\) −2.76766e12 4.79372e12i −0.360711 0.624769i
\(731\) 7.10766e11 4.03096e12i 0.0920658 0.522131i
\(732\) −6.52838e11 + 3.70243e12i −0.0840438 + 0.476636i
\(733\) −5.04063e12 8.73063e12i −0.644936 1.11706i −0.984316 0.176413i \(-0.943551\pi\)
0.339380 0.940649i \(-0.389783\pi\)
\(734\) −2.93118e11 + 5.07696e11i −0.0372744 + 0.0645612i
\(735\) −1.79782e13 1.50855e13i −2.27224 1.90663i
\(736\) 7.65176e11 + 2.78501e11i 0.0961194 + 0.0349846i
\(737\) −2.03395e12 + 7.40298e11i −0.253943 + 0.0924279i
\(738\) 3.10311e12 2.60382e12i 0.385073 0.323115i
\(739\) −1.96327e12 1.11342e13i −0.242147 1.37328i −0.827026 0.562164i \(-0.809969\pi\)
0.584879 0.811121i \(-0.301142\pi\)
\(740\) −8.56843e12 −1.05041
\(741\) 1.97133e12 + 7.84725e12i 0.240202 + 0.956171i
\(742\) 1.25001e13 1.51390
\(743\) −2.15067e12 1.21971e13i −0.258895 1.46827i −0.785872 0.618389i \(-0.787786\pi\)
0.526977 0.849879i \(-0.323325\pi\)
\(744\) 2.44446e12 2.05115e12i 0.292486 0.245425i
\(745\) 1.45660e13 5.30161e12i 1.73236 0.630528i
\(746\) 1.72991e12 + 6.29636e11i 0.204503 + 0.0744329i
\(747\) 7.36551e11 + 6.18039e11i 0.0865486 + 0.0726229i
\(748\) −7.42089e11 + 1.28534e12i −0.0866760 + 0.150127i
\(749\) −5.30649e12 9.19111e12i −0.616083 1.06709i
\(750\) −4.84751e11 + 2.74916e12i −0.0559427 + 0.317267i
\(751\) 1.57996e12 8.96038e12i 0.181245 1.02789i −0.749441 0.662071i \(-0.769678\pi\)
0.930686 0.365819i \(-0.119211\pi\)
\(752\) 4.78123e11 + 8.28133e11i 0.0545204 + 0.0944322i
\(753\) −1.06221e12 + 1.83980e12i −0.120402 + 0.208542i
\(754\) 6.75713e12 + 5.66990e12i 0.761362 + 0.638858i
\(755\) −6.62700e12 2.41203e12i −0.742260 0.270161i
\(756\) −4.87409e12 + 1.77402e12i −0.542682 + 0.197520i
\(757\) −3.04737e12 + 2.55705e12i −0.337283 + 0.283014i −0.795660 0.605744i \(-0.792876\pi\)
0.458377 + 0.888758i \(0.348431\pi\)
\(758\) 1.78612e12 + 1.01296e13i 0.196516 + 1.11450i
\(759\) 1.67971e12 0.183716
\(760\) −4.45842e12 + 1.99450e12i −0.484752 + 0.216857i
\(761\) −5.57461e12 −0.602537 −0.301269 0.953539i \(-0.597410\pi\)
−0.301269 + 0.953539i \(0.597410\pi\)
\(762\) 1.66229e12 + 9.42730e12i 0.178611 + 1.01295i
\(763\) −4.36038e12 + 3.65879e12i −0.465762 + 0.390821i
\(764\) −4.13474e12 + 1.50492e12i −0.439064 + 0.159806i
\(765\) −6.96745e12 2.53594e12i −0.735525 0.267709i
\(766\) −3.94170e12 3.30748e12i −0.413670 0.347110i
\(767\) 1.18511e12 2.05267e12i 0.123646 0.214161i
\(768\) 3.56854e11 + 6.18089e11i 0.0370139 + 0.0641099i
\(769\) 1.37926e12 7.82219e12i 0.142226 0.806603i −0.827327 0.561721i \(-0.810140\pi\)
0.969553 0.244882i \(-0.0787493\pi\)
\(770\) 7.87603e11 4.46672e12i 0.0807419 0.457910i
\(771\) 4.89038e12 + 8.47039e12i 0.498423 + 0.863294i
\(772\) −7.43038e11 + 1.28698e12i −0.0752893 + 0.130405i
\(773\) 4.49891e12 + 3.77503e12i 0.453210 + 0.380288i 0.840626 0.541617i \(-0.182188\pi\)
−0.387415 + 0.921905i \(0.626632\pi\)
\(774\) −1.09575e12 3.98821e11i −0.109743 0.0399433i
\(775\) 1.08080e13 3.93380e12i 1.07619 0.391701i
\(776\) 3.57998e12 3.00396e12i 0.354408 0.297383i
\(777\) 4.77335e12 + 2.70710e13i 0.469817 + 2.66446i
\(778\) −1.10380e11 −0.0108014
\(779\) 1.46904e13 + 1.06334e13i 1.42927 + 1.03456i
\(780\) 7.65417e12 0.740410
\(781\) 4.11765e11 + 2.33524e12i 0.0396023 + 0.224596i
\(782\) −4.23933e12 + 3.55722e12i −0.405384 + 0.340157i
\(783\) 1.18035e13 4.29614e12i 1.12224 0.408461i
\(784\) −4.14338e12 1.50807e12i −0.391681 0.142560i
\(785\) −1.66227e13 1.39481e13i −1.56238 1.31100i
\(786\) −3.30159e12 + 5.71852e12i −0.308547 + 0.534419i
\(787\) 7.29916e12 + 1.26425e13i 0.678245 + 1.17475i 0.975509 + 0.219959i \(0.0705925\pi\)
−0.297264 + 0.954795i \(0.596074\pi\)
\(788\) 1.69274e12 9.60002e12i 0.156395 0.886960i
\(789\) 1.37931e12 7.82247e12i 0.126711 0.718617i
\(790\) −5.82563e12 1.00903e13i −0.532134 0.921682i
\(791\) −4.14845e12 + 7.18532e12i −0.376783 + 0.652607i
\(792\) 3.23899e11 + 2.71784e11i 0.0292514 + 0.0245448i
\(793\) 7.11828e12 + 2.59084e12i 0.639214 + 0.232655i
\(794\) −6.53300e12 + 2.37782e12i −0.583338 + 0.212318i
\(795\) −2.01223e13 + 1.68846e13i −1.78659 + 1.49913i
\(796\) −2.93904e11 1.66681e12i −0.0259475 0.147156i
\(797\) 1.99390e13 1.75041 0.875207 0.483749i \(-0.160725\pi\)
0.875207 + 0.483749i \(0.160725\pi\)
\(798\) 8.78512e12 + 1.29748e13i 0.766893 + 1.13263i
\(799\) −6.49886e12 −0.564127
\(800\) 4.46706e11 + 2.53339e12i 0.0385582 + 0.218674i
\(801\) −1.59193e12 + 1.33579e12i −0.136640 + 0.114655i
\(802\) −2.63970e12 + 9.60772e11i −0.225304 + 0.0820041i
\(803\) −2.01587e12 7.33718e11i −0.171097 0.0622743i
\(804\) −5.41889e12 4.54699e12i −0.457360 0.383771i
\(805\) 8.45598e12 1.46462e13i 0.709712 1.22926i
\(806\) −3.21480e12 5.56819e12i −0.268316 0.464736i
\(807\) −3.22561e12 + 1.82934e13i −0.267720 + 1.51832i
\(808\) 6.62652e11 3.75808e12i 0.0546933 0.310181i
\(809\) −3.88384e12 6.72702e12i −0.318782 0.552146i 0.661452 0.749987i \(-0.269940\pi\)
−0.980234 + 0.197841i \(0.936607\pi\)
\(810\) 8.07120e12 1.39797e13i 0.658803 1.14108i
\(811\) −7.71404e12 6.47285e12i −0.626164 0.525414i 0.273570 0.961852i \(-0.411795\pi\)
−0.899734 + 0.436438i \(0.856240\pi\)
\(812\) 1.60522e13 + 5.84252e12i 1.29578 + 0.471626i
\(813\) 4.35465e12 1.58496e12i 0.349579 0.127236i
\(814\) −2.54384e12 + 2.13454e12i −0.203086 + 0.170410i
\(815\) 3.77095e12 + 2.13861e13i 0.299393 + 1.69794i
\(816\) −4.85051e12 −0.382985
\(817\) 5.36467e11 5.19272e12i 0.0421254 0.407752i
\(818\) −2.25197e12 −0.175862
\(819\) −1.22461e12 6.94510e12i −0.0951085 0.539387i
\(820\) 1.31421e13 1.10275e13i 1.01508 0.851754i
\(821\) 7.72334e12 2.81107e12i 0.593282 0.215937i −0.0278903 0.999611i \(-0.508879\pi\)
0.621172 + 0.783674i \(0.286657\pi\)
\(822\) 7.36971e12 + 2.68236e12i 0.563025 + 0.204924i
\(823\) −9.29324e12 7.79795e12i −0.706102 0.592490i 0.217400 0.976083i \(-0.430242\pi\)
−0.923503 + 0.383592i \(0.874687\pi\)
\(824\) 3.65666e12 6.33353e12i 0.276320 0.478601i
\(825\) 2.65326e12 + 4.59559e12i 0.199406 + 0.345381i
\(826\) 7.97074e11 4.52043e12i 0.0595783 0.337886i
\(827\) 3.24594e12 1.84087e13i 0.241305 1.36851i −0.587615 0.809141i \(-0.699933\pi\)
0.828920 0.559367i \(-0.188956\pi\)
\(828\) 7.88284e11 + 1.36535e12i 0.0582836 + 0.100950i
\(829\) −7.70115e12 + 1.33388e13i −0.566318 + 0.980891i 0.430608 + 0.902539i \(0.358299\pi\)
−0.996926 + 0.0783521i \(0.975034\pi\)
\(830\) 3.11938e12 + 2.61747e12i 0.228148 + 0.191439i
\(831\) 2.92795e13 + 1.06568e13i 2.12990 + 0.775219i
\(832\) 1.35133e12 4.91843e11i 0.0977699 0.0355853i
\(833\) 2.29557e13 1.92621e13i 1.65192 1.38612i
\(834\) −3.51546e12 1.99372e13i −0.251614 1.42697i
\(835\) 1.10619e13 0.787481
\(836\) −8.26778e11 + 1.70280e12i −0.0585411 + 0.120569i
\(837\) −9.15591e12 −0.644818
\(838\) 1.09612e12 + 6.21641e12i 0.0767822 + 0.435453i
\(839\) −4.37765e11 + 3.67328e11i −0.0305008 + 0.0255932i −0.657911 0.753096i \(-0.728560\pi\)
0.627410 + 0.778689i \(0.284115\pi\)
\(840\) 1.39291e13 5.06979e12i 0.965312 0.351345i
\(841\) −2.52412e13 9.18704e12i −1.73991 0.633277i
\(842\) −7.29578e12 6.12188e12i −0.500227 0.419740i
\(843\) 1.37030e13 2.37343e13i 0.934525 1.61865i
\(844\) 4.67601e12 + 8.09908e12i 0.317201 + 0.549408i
\(845\) −1.18741e12 + 6.73413e12i −0.0801208 + 0.454387i
\(846\) −3.21497e11 + 1.82330e12i −0.0215780 + 0.122375i
\(847\) 1.13526e13 + 1.96632e13i 0.757913 + 1.31274i
\(848\) −2.46757e12 + 4.27396e12i −0.163866 + 0.283824i
\(849\) 1.84458e13 + 1.54779e13i 1.21847 + 1.02242i
\(850\) −1.64287e13 5.97957e12i −1.07949 0.392903i
\(851\) −1.16353e13 + 4.23492e12i −0.760495 + 0.276797i
\(852\) −5.93656e12 + 4.98137e12i −0.385973 + 0.323870i
\(853\) −3.04583e11 1.72738e12i −0.0196986 0.111716i 0.973373 0.229227i \(-0.0736197\pi\)
−0.993072 + 0.117510i \(0.962509\pi\)
\(854\) 1.46700e13 0.943777
\(855\) −9.09481e12 2.59045e12i −0.582031 0.165778i
\(856\) 4.19008e12 0.266741
\(857\) −3.72389e11 2.11193e12i −0.0235822 0.133741i 0.970744 0.240118i \(-0.0771861\pi\)
−0.994326 + 0.106377i \(0.966075\pi\)
\(858\) 2.27241e12 1.90678e12i 0.143151 0.120118i
\(859\) −8.48936e12 + 3.08987e12i −0.531993 + 0.193629i −0.594028 0.804445i \(-0.702463\pi\)
0.0620353 + 0.998074i \(0.480241\pi\)
\(860\) −4.64064e12 1.68906e12i −0.289291 0.105293i
\(861\) −4.21614e13 3.53776e13i −2.61457 2.19389i
\(862\) 2.76482e12 4.78881e12i 0.170563 0.295423i
\(863\) 5.50708e11 + 9.53855e11i 0.0337966 + 0.0585375i 0.882429 0.470446i \(-0.155907\pi\)
−0.848632 + 0.528983i \(0.822573\pi\)
\(864\) 3.55601e11 2.01671e12i 0.0217096 0.123121i
\(865\) −3.33279e12 + 1.89012e13i −0.202412 + 1.14793i
\(866\) 1.00825e12 + 1.74633e12i 0.0609166 + 0.105511i
\(867\) 6.62952e12 1.14827e13i 0.398471 0.690171i
\(868\) −9.53845e12 8.00371e12i −0.570347 0.478578i
\(869\) −4.24320e12 1.54440e12i −0.252409 0.0918693i
\(870\) −3.37321e13 + 1.22775e13i −1.99621 + 0.726561i
\(871\) −1.09185e13 + 9.16175e12i −0.642811 + 0.539382i
\(872\) −3.90234e11 2.21313e12i −0.0228561 0.129623i
\(873\) 9.04824e12 0.527230
\(874\) −5.06846e12 + 4.91195e12i −0.293815 + 0.284743i
\(875\) 1.08929e13 0.628213
\(876\) −1.21744e12 6.90447e12i −0.0698523 0.396152i
\(877\) 1.86782e13 1.56729e13i 1.06620 0.894647i 0.0714957 0.997441i \(-0.477223\pi\)
0.994703 + 0.102794i \(0.0327783\pi\)
\(878\) −7.08936e12 + 2.58031e12i −0.402607 + 0.146537i
\(879\) −2.73891e12 9.96880e11i −0.154749 0.0563239i
\(880\) 1.37175e12 + 1.15104e12i 0.0771088 + 0.0647020i
\(881\) −8.34165e12 + 1.44482e13i −0.466509 + 0.808017i −0.999268 0.0382495i \(-0.987822\pi\)
0.532759 + 0.846267i \(0.321155\pi\)
\(882\) −4.26851e12 7.39328e12i −0.237502 0.411366i
\(883\) −2.47925e12 + 1.40605e13i −0.137245 + 0.778355i 0.836025 + 0.548691i \(0.184874\pi\)
−0.973270 + 0.229664i \(0.926237\pi\)
\(884\) −1.69712e12 + 9.62483e12i −0.0934710 + 0.530100i
\(885\) 4.82289e12 + 8.35348e12i 0.264279 + 0.457744i
\(886\) −1.07233e13 + 1.85734e13i −0.584627 + 1.01260i
\(887\) 4.14772e12 + 3.48035e12i 0.224985 + 0.188785i 0.748311 0.663348i \(-0.230865\pi\)
−0.523327 + 0.852132i \(0.675309\pi\)
\(888\) −1.01982e13 3.71184e12i −0.550384 0.200323i
\(889\) 3.51008e13 1.27756e13i 1.88477 0.686000i
\(890\) −6.74202e12 + 5.65723e12i −0.360193 + 0.302238i
\(891\) −1.08636e12 6.16106e12i −0.0577463 0.327496i
\(892\) 1.05836e13 0.559744
\(893\) −8.26737e12 + 5.92848e11i −0.435046 + 0.0311969i
\(894\) 1.96333e13 1.02795
\(895\) 3.95211e12 + 2.24135e13i 0.205885 + 1.16763i
\(896\) 2.13338e12 1.79012e12i 0.110582 0.0927890i
\(897\) 1.03938e13 3.78305e12i 0.536056 0.195108i
\(898\) 3.43260e12 + 1.24936e12i 0.176149 + 0.0641129i
\(899\) 2.30992e13 + 1.93825e13i 1.17945 + 0.989673i
\(900\) −2.49034e12 + 4.31340e12i −0.126522 + 0.219143i
\(901\) −1.67702e13 2.90468e13i −0.847765 1.46837i
\(902\) 1.15456e12 6.54781e12i 0.0580745 0.329357i
\(903\) −2.75115e12 + 1.56026e13i −0.137695 + 0.780910i
\(904\) −1.63784e12 2.83682e12i −0.0815666 0.141278i
\(905\) −1.24317e13 + 2.15323e13i −0.616044 + 1.06702i
\(906\) −6.84262e12 5.74164e12i −0.337400 0.283112i
\(907\) −2.06032e13 7.49895e12i −1.01089 0.367932i −0.217113 0.976147i \(-0.569664\pi\)
−0.793773 + 0.608214i \(0.791886\pi\)
\(908\) 2.28957e12 8.33336e11i 0.111781 0.0406849i
\(909\) 5.65987e12 4.74919e12i 0.274960 0.230719i
\(910\) −5.18636e12 2.94133e13i −0.250713 1.42186i
\(911\) −7.20024e12 −0.346349 −0.173175 0.984891i \(-0.555403\pi\)
−0.173175 + 0.984891i \(0.555403\pi\)
\(912\) −6.17046e12 + 4.42480e11i −0.295353 + 0.0211795i
\(913\) 1.57816e12 0.0751677
\(914\) −7.01335e11 3.97747e12i −0.0332405 0.188516i
\(915\) −2.36153e13 + 1.98156e13i −1.11378 + 0.934569i
\(916\) 1.27694e13 4.64769e12i 0.599296 0.218126i
\(917\) 2.42122e13 + 8.81251e12i 1.13076 + 0.411564i
\(918\) 1.06614e13 + 8.94597e12i 0.495475 + 0.415753i
\(919\) −6.59877e12 + 1.14294e13i −0.305171 + 0.528572i −0.977299 0.211863i \(-0.932047\pi\)
0.672128 + 0.740435i \(0.265380\pi\)
\(920\) 3.33848e12 + 5.78242e12i 0.153640 + 0.266112i
\(921\) −2.71189e12 + 1.53799e13i −0.124195 + 0.704343i
\(922\) 4.00999e12 2.27418e13i 0.182748 1.03642i
\(923\) 7.80738e12 + 1.35228e13i 0.354077 + 0.613279i
\(924\) 2.87239e12 4.97513e12i 0.129634 0.224533i
\(925\) −2.99656e13 2.51441e13i −1.34581 1.12927i
\(926\) 1.65291e13 + 6.01609e12i 0.738753 + 0.268884i
\(927\) 1.33057e13 4.84289e12i 0.591806 0.215400i
\(928\) −5.16639e12 + 4.33512e12i −0.228677 + 0.191882i
\(929\) 7.68767e12 + 4.35989e13i 0.338629 + 1.92046i 0.387958 + 0.921677i \(0.373180\pi\)
−0.0493296 + 0.998783i \(0.515708\pi\)
\(930\) 2.61657e13 1.14699
\(931\) 2.74454e13 2.65979e13i 1.19728 1.16031i
\(932\) −1.75263e13 −0.760886
\(933\) 6.78747e12 + 3.84937e13i 0.293252 + 1.66311i
\(934\) −2.07405e13 + 1.74034e13i −0.891783 + 0.748295i
\(935\) −1.14360e13 + 4.16237e12i −0.489354 + 0.178110i
\(936\) 2.61636e12 + 9.52277e11i 0.111418 + 0.0405529i
\(937\) 1.86687e12 + 1.56649e12i 0.0791198 + 0.0663894i 0.681490 0.731828i \(-0.261332\pi\)
−0.602370 + 0.798217i \(0.705777\pi\)
\(938\) −1.38013e13 + 2.39046e13i −0.582114 + 1.00825i
\(939\) −1.76460e13 3.05638e13i −0.740715 1.28296i
\(940\) −1.36158e12 + 7.72191e12i −0.0568811 + 0.322589i
\(941\) −9.77252e11 + 5.54227e12i −0.0406306 + 0.230427i −0.998360 0.0572420i \(-0.981769\pi\)
0.957730 + 0.287669i \(0.0928805\pi\)
\(942\) −1.37421e13 2.38021e13i −0.568624 0.984886i
\(943\) 1.23957e13 2.14700e13i 0.510468 0.884157i
\(944\) 1.38825e12 + 1.16488e12i 0.0568975 + 0.0477427i
\(945\) −3.99666e13 1.45466e13i −1.63025 0.593362i
\(946\) −1.79851e12 + 6.54605e11i −0.0730136 + 0.0265748i
\(947\) 5.82895e12 4.89107e12i 0.235513 0.197619i −0.517391 0.855749i \(-0.673097\pi\)
0.752904 + 0.658130i \(0.228652\pi\)
\(948\) −2.56259e12 1.45332e13i −0.103049 0.584418i
\(949\) −1.41265e13 −0.565373
\(950\) −2.14449e13 6.10809e12i −0.854217 0.243304i
\(951\) −5.76582e13 −2.28586
\(952\) 3.28664e12 + 1.86395e13i 0.129684 + 0.735474i
\(953\) 1.57849e11 1.32451e11i 0.00619904 0.00520161i −0.639683 0.768639i \(-0.720934\pi\)
0.645882 + 0.763437i \(0.276490\pi\)
\(954\) −8.97889e12 + 3.26805e12i −0.350958 + 0.127738i
\(955\) −3.39040e13 1.23401e13i −1.31897 0.480067i
\(956\) 4.07336e12 + 3.41796e12i 0.157722 + 0.132345i
\(957\) −6.95605e12 + 1.20482e13i −0.268077 + 0.464322i
\(958\) 4.77468e12 + 8.26999e12i 0.183147 + 0.317220i
\(959\) 5.31410e12 3.01378e13i 0.202883 1.15061i
\(960\) −1.01623e12 + 5.76335e12i −0.0386165 + 0.219005i
\(961\) 2.23006e12 + 3.86257e12i 0.0843452 + 0.146090i
\(962\) −1.09336e13 + 1.89375e13i −0.411599 + 0.712911i
\(963\) 6.21460e12 + 5.21467e12i 0.232860 + 0.195393i
\(964\) −1.32289e12 4.81493e11i −0.0493375 0.0179574i
\(965\) −1.14507e13 + 4.16770e12i −0.425067 + 0.154712i
\(966\) 1.64091e13 1.37689e13i 0.606300 0.508746i
\(967\) −4.09477e12 2.32226e13i −0.150595 0.854066i −0.962703 0.270559i \(-0.912791\pi\)
0.812108 0.583507i \(-0.198320\pi\)
\(968\) −8.96416e12 −0.328148
\(969\) 1.83636e13 3.78211e13i 0.669115 1.37809i
\(970\) 3.83204e13 1.38982
\(971\) −8.37382e12 4.74903e13i −0.302299 1.71443i −0.635952 0.771729i \(-0.719392\pi\)
0.333652 0.942696i \(-0.391719\pi\)
\(972\) 8.12405e12 6.81689e12i 0.291927 0.244956i
\(973\) −7.42322e13 + 2.70183e13i −2.65512 + 0.966385i
\(974\) 3.14229e13 + 1.14370e13i 1.11875 + 0.407190i
\(975\) 2.67683e13 + 2.24612e13i 0.948635 + 0.796000i
\(976\) −2.89591e12 + 5.01586e12i −0.102155 + 0.176938i
\(977\) 2.05632e13 + 3.56166e13i 0.722047 + 1.25062i 0.960178 + 0.279390i \(0.0901321\pi\)
−0.238130 + 0.971233i \(0.576535\pi\)
\(978\) −4.77626e12 + 2.70875e13i −0.166941 + 0.946770i
\(979\) −5.92300e11 + 3.35910e12i −0.0206072 + 0.116869i
\(980\) −1.80777e13 3.13114e13i −0.626073 1.08439i
\(981\) 2.17552e12 3.76811e12i 0.0749984 0.129901i
\(982\) 3.62014e12 + 3.03765e12i 0.124229 + 0.104241i
\(983\) 4.49497e13 + 1.63604e13i 1.53545 + 0.558858i 0.964949 0.262438i \(-0.0845264\pi\)
0.570502 + 0.821296i \(0.306749\pi\)
\(984\) 2.04189e13 7.43186e12i 0.694311 0.252708i
\(985\) 6.12319e13 5.13797e13i 2.07260 1.73912i
\(986\) −7.95923e12 4.51390e13i −0.268179 1.52092i
\(987\) 2.51550e13 0.843719
\(988\) −1.28094e12 + 1.23988e13i −0.0427683 + 0.413975i
\(989\) −7.13649e12 −0.237193
\(990\) 6.02046e11 + 3.41437e12i 0.0199192 + 0.112967i
\(991\) 1.99572e13 1.67461e13i 0.657308 0.551547i −0.251971 0.967735i \(-0.581079\pi\)
0.909279 + 0.416188i \(0.136634\pi\)
\(992\) 4.61950e12 1.68136e12i 0.151458 0.0551262i
\(993\) 1.05808e13 + 3.85110e12i 0.345340 + 0.125694i
\(994\) 2.31649e13 + 1.94376e13i 0.752646 + 0.631545i
\(995\) 6.93918e12 1.20190e13i 0.224442 0.388745i
\(996\) 2.57882e12 + 4.46665e12i 0.0830337 + 0.143819i
\(997\) −1.09135e11 + 6.18934e11i −0.00349812 + 0.0198388i −0.986507 0.163720i \(-0.947651\pi\)
0.983009 + 0.183559i \(0.0587618\pi\)
\(998\) 1.59362e12 9.03789e12i 0.0508509 0.288390i
\(999\) 1.55697e13 + 2.69675e13i 0.494579 + 0.856636i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 38.10.e.b.9.3 48
19.17 even 9 inner 38.10.e.b.17.3 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.10.e.b.9.3 48 1.1 even 1 trivial
38.10.e.b.17.3 yes 48 19.17 even 9 inner