Properties

Label 10.9.c.b.3.2
Level $10$
Weight $9$
Character 10.3
Analytic conductor $4.074$
Analytic rank $0$
Dimension $4$
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] = [10,9,Mod(3,10)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(10, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("10.3");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\), 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: \(4.07378610061\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(i)\)
Coefficient field: \(\Q(i, \sqrt{601})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 301x^{2} + 22500 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.2
Root \(12.7577i\) of defining polynomial
Character \(\chi\) \(=\) 10.3
Dual form 10.9.c.b.7.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(8.00000 - 8.00000i) q^{2} +(82.7883 + 82.7883i) q^{3} -128.000i q^{4} +(-33.6352 + 624.094i) q^{5} +1324.61 q^{6} +(2718.55 - 2718.55i) q^{7} +(-1024.00 - 1024.00i) q^{8} +7146.79i q^{9} +O(q^{10})\) \(q+(8.00000 - 8.00000i) q^{2} +(82.7883 + 82.7883i) q^{3} -128.000i q^{4} +(-33.6352 + 624.094i) q^{5} +1324.61 q^{6} +(2718.55 - 2718.55i) q^{7} +(-1024.00 - 1024.00i) q^{8} +7146.79i q^{9} +(4723.67 + 5261.84i) q^{10} -20966.3 q^{11} +(10596.9 - 10596.9i) q^{12} +(-8095.66 - 8095.66i) q^{13} -43496.9i q^{14} +(-54452.3 + 48883.1i) q^{15} -16384.0 q^{16} +(-3141.02 + 3141.02i) q^{17} +(57174.3 + 57174.3i) q^{18} -69201.5i q^{19} +(79884.1 + 4305.31i) q^{20} +450129. q^{21} +(-167730. + 167730. i) q^{22} +(1084.70 + 1084.70i) q^{23} -169550. i q^{24} +(-388362. - 41983.1i) q^{25} -129531. q^{26} +(-48496.5 + 48496.5i) q^{27} +(-347975. - 347975. i) q^{28} -120633. i q^{29} +(-44553.6 + 826683. i) q^{30} +826466. q^{31} +(-131072. + 131072. i) q^{32} +(-1.73576e6 - 1.73576e6i) q^{33} +50256.4i q^{34} +(1.60519e6 + 1.78807e6i) q^{35} +914789. q^{36} +(-1.17029e6 + 1.17029e6i) q^{37} +(-553612. - 553612. i) q^{38} -1.34045e6i q^{39} +(673515. - 604630. i) q^{40} +1.74660e6 q^{41} +(3.60103e6 - 3.60103e6i) q^{42} +(3.03222e6 + 3.03222e6i) q^{43} +2.68368e6i q^{44} +(-4.46027e6 - 240384. i) q^{45} +17355.3 q^{46} +(-5.83610e6 + 5.83610e6i) q^{47} +(-1.35640e6 - 1.35640e6i) q^{48} -9.01626e6i q^{49} +(-3.44276e6 + 2.77103e6i) q^{50} -520080. q^{51} +(-1.03625e6 + 1.03625e6i) q^{52} +(1.97703e6 + 1.97703e6i) q^{53} +775944. i q^{54} +(705206. - 1.30849e7i) q^{55} -5.56760e6 q^{56} +(5.72907e6 - 5.72907e6i) q^{57} +(-965061. - 965061. i) q^{58} +1.58356e7i q^{59} +(6.25703e6 + 6.96989e6i) q^{60} -2.51723e6 q^{61} +(6.61173e6 - 6.61173e6i) q^{62} +(1.94289e7 + 1.94289e7i) q^{63} +2.09715e6i q^{64} +(5.32476e6 - 4.78016e6i) q^{65} -2.77722e7 q^{66} +(1.47668e7 - 1.47668e7i) q^{67} +(402051. + 402051. i) q^{68} +179602. i q^{69} +(2.71461e7 + 1.46303e6i) q^{70} -8.22222e6 q^{71} +(7.31831e6 - 7.31831e6i) q^{72} +(-3.03744e7 - 3.03744e7i) q^{73} +1.87246e7i q^{74} +(-2.86761e7 - 3.56275e7i) q^{75} -8.85779e6 q^{76} +(-5.69980e7 + 5.69980e7i) q^{77} +(-1.07236e7 - 1.07236e7i) q^{78} +4.69738e7i q^{79} +(551080. - 1.02252e7i) q^{80} +3.88602e7 q^{81} +(1.39728e7 - 1.39728e7i) q^{82} +(2.81305e7 + 2.81305e7i) q^{83} -5.76165e7i q^{84} +(-1.85465e6 - 2.06594e6i) q^{85} +4.85155e7 q^{86} +(9.98697e6 - 9.98697e6i) q^{87} +(2.14695e7 + 2.14695e7i) q^{88} -7.91918e7i q^{89} +(-3.76052e7 + 3.37591e7i) q^{90} -4.40170e7 q^{91} +(138842. - 138842. i) q^{92} +(6.84217e7 + 6.84217e7i) q^{93} +9.33776e7i q^{94} +(4.31883e7 + 2.32761e6i) q^{95} -2.17024e7 q^{96} +(1.47530e6 - 1.47530e6i) q^{97} +(-7.21301e7 - 7.21301e7i) q^{98} -1.49842e8i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 32 q^{2} + 86 q^{3} - 870 q^{5} + 1376 q^{6} + 5726 q^{7} - 4096 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 32 q^{2} + 86 q^{3} - 870 q^{5} + 1376 q^{6} + 5726 q^{7} - 4096 q^{8} - 4640 q^{10} - 14732 q^{11} + 11008 q^{12} + 45576 q^{13} - 115090 q^{15} - 65536 q^{16} + 3616 q^{17} + 60032 q^{18} + 37120 q^{20} + 877268 q^{21} - 117856 q^{22} - 456794 q^{23} - 913600 q^{25} + 729216 q^{26} - 889240 q^{27} - 732928 q^{28} + 421920 q^{30} + 4672348 q^{31} - 524288 q^{32} - 4553788 q^{33} + 2956030 q^{35} + 960512 q^{36} - 5554884 q^{37} - 3932480 q^{38} + 1187840 q^{40} + 10738708 q^{41} + 7018144 q^{42} + 4913286 q^{43} - 12173390 q^{45} - 7308704 q^{46} - 5448474 q^{47} - 1409024 q^{48} - 1827200 q^{50} - 1827812 q^{51} + 5833728 q^{52} + 20290316 q^{53} - 9506940 q^{55} - 11726848 q^{56} - 2593360 q^{57} - 4236800 q^{58} + 21482240 q^{60} - 43572012 q^{61} + 37378784 q^{62} + 37877126 q^{63} + 15450660 q^{65} - 72860608 q^{66} + 9518486 q^{67} - 462848 q^{68} + 52077760 q^{70} + 20406908 q^{71} + 7684096 q^{72} - 11608364 q^{73} - 21302450 q^{75} - 62919680 q^{76} - 110066908 q^{77} - 60769056 q^{78} + 14254080 q^{80} + 96218224 q^{81} + 85909664 q^{82} + 64264686 q^{83} - 12424120 q^{85} + 78612576 q^{86} + 8501600 q^{87} + 15085568 q^{88} - 79432480 q^{90} - 70189812 q^{91} - 58469632 q^{92} + 16706132 q^{93} - 82819000 q^{95} - 22544384 q^{96} + 34113396 q^{97} - 52691072 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/10\mathbb{Z}\right)^\times\).

\(n\) \(7\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\)

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 8.00000i 0.500000 0.500000i
\(3\) 82.7883 + 82.7883i 1.02208 + 1.02208i 0.999751 + 0.0223265i \(0.00710733\pi\)
0.0223265 + 0.999751i \(0.492893\pi\)
\(4\) 128.000i 0.500000i
\(5\) −33.6352 + 624.094i −0.0538164 + 0.998551i
\(6\) 1324.61 1.02208
\(7\) 2718.55 2718.55i 1.13226 1.13226i 0.142458 0.989801i \(-0.454499\pi\)
0.989801 0.142458i \(-0.0455006\pi\)
\(8\) −1024.00 1024.00i −0.250000 0.250000i
\(9\) 7146.79i 1.08928i
\(10\) 4723.67 + 5261.84i 0.472367 + 0.526184i
\(11\) −20966.3 −1.43203 −0.716013 0.698087i \(-0.754035\pi\)
−0.716013 + 0.698087i \(0.754035\pi\)
\(12\) 10596.9 10596.9i 0.511039 0.511039i
\(13\) −8095.66 8095.66i −0.283452 0.283452i 0.551032 0.834484i \(-0.314234\pi\)
−0.834484 + 0.551032i \(0.814234\pi\)
\(14\) 43496.9i 1.13226i
\(15\) −54452.3 + 48883.1i −1.07560 + 0.965592i
\(16\) −16384.0 −0.250000
\(17\) −3141.02 + 3141.02i −0.0376076 + 0.0376076i −0.725661 0.688053i \(-0.758466\pi\)
0.688053 + 0.725661i \(0.258466\pi\)
\(18\) 57174.3 + 57174.3i 0.544642 + 0.544642i
\(19\) 69201.5i 0.531008i −0.964110 0.265504i \(-0.914462\pi\)
0.964110 0.265504i \(-0.0855383\pi\)
\(20\) 79884.1 + 4305.31i 0.499275 + 0.0269082i
\(21\) 450129. 2.31451
\(22\) −167730. + 167730.i −0.716013 + 0.716013i
\(23\) 1084.70 + 1084.70i 0.00387615 + 0.00387615i 0.709042 0.705166i \(-0.249128\pi\)
−0.705166 + 0.709042i \(0.749128\pi\)
\(24\) 169550.i 0.511039i
\(25\) −388362. 41983.1i −0.994208 0.107477i
\(26\) −129531. −0.283452
\(27\) −48496.5 + 48496.5i −0.0912547 + 0.0912547i
\(28\) −347975. 347975.i −0.566129 0.566129i
\(29\) 120633.i 0.170558i −0.996357 0.0852792i \(-0.972822\pi\)
0.996357 0.0852792i \(-0.0271782\pi\)
\(30\) −44553.6 + 826683.i −0.0550045 + 1.02060i
\(31\) 826466. 0.894908 0.447454 0.894307i \(-0.352331\pi\)
0.447454 + 0.894307i \(0.352331\pi\)
\(32\) −131072. + 131072.i −0.125000 + 0.125000i
\(33\) −1.73576e6 1.73576e6i −1.46364 1.46364i
\(34\) 50256.4i 0.0376076i
\(35\) 1.60519e6 + 1.78807e6i 1.06968 + 1.19155i
\(36\) 914789. 0.544642
\(37\) −1.17029e6 + 1.17029e6i −0.624434 + 0.624434i −0.946662 0.322228i \(-0.895568\pi\)
0.322228 + 0.946662i \(0.395568\pi\)
\(38\) −553612. 553612.i −0.265504 0.265504i
\(39\) 1.34045e6i 0.579419i
\(40\) 673515. 604630.i 0.263092 0.236184i
\(41\) 1.74660e6 0.618099 0.309049 0.951046i \(-0.399989\pi\)
0.309049 + 0.951046i \(0.399989\pi\)
\(42\) 3.60103e6 3.60103e6i 1.15726 1.15726i
\(43\) 3.03222e6 + 3.03222e6i 0.886925 + 0.886925i 0.994226 0.107302i \(-0.0342211\pi\)
−0.107302 + 0.994226i \(0.534221\pi\)
\(44\) 2.68368e6i 0.716013i
\(45\) −4.46027e6 240384.i −1.08771 0.0586213i
\(46\) 17355.3 0.00387615
\(47\) −5.83610e6 + 5.83610e6i −1.19600 + 1.19600i −0.220646 + 0.975354i \(0.570817\pi\)
−0.975354 + 0.220646i \(0.929183\pi\)
\(48\) −1.35640e6 1.35640e6i −0.255519 0.255519i
\(49\) 9.01626e6i 1.56402i
\(50\) −3.44276e6 + 2.77103e6i −0.550842 + 0.443365i
\(51\) −520080. −0.0768758
\(52\) −1.03625e6 + 1.03625e6i −0.141726 + 0.141726i
\(53\) 1.97703e6 + 1.97703e6i 0.250559 + 0.250559i 0.821200 0.570641i \(-0.193305\pi\)
−0.570641 + 0.821200i \(0.693305\pi\)
\(54\) 775944.i 0.0912547i
\(55\) 705206. 1.30849e7i 0.0770664 1.42995i
\(56\) −5.56760e6 −0.566129
\(57\) 5.72907e6 5.72907e6i 0.542731 0.542731i
\(58\) −965061. 965061.i −0.0852792 0.0852792i
\(59\) 1.58356e7i 1.30685i 0.756990 + 0.653427i \(0.226669\pi\)
−0.756990 + 0.653427i \(0.773331\pi\)
\(60\) 6.25703e6 + 6.96989e6i 0.482796 + 0.537800i
\(61\) −2.51723e6 −0.181804 −0.0909019 0.995860i \(-0.528975\pi\)
−0.0909019 + 0.995860i \(0.528975\pi\)
\(62\) 6.61173e6 6.61173e6i 0.447454 0.447454i
\(63\) 1.94289e7 + 1.94289e7i 1.23335 + 1.23335i
\(64\) 2.09715e6i 0.125000i
\(65\) 5.32476e6 4.78016e6i 0.298295 0.267787i
\(66\) −2.77722e7 −1.46364
\(67\) 1.47668e7 1.47668e7i 0.732802 0.732802i −0.238372 0.971174i \(-0.576614\pi\)
0.971174 + 0.238372i \(0.0766138\pi\)
\(68\) 402051. + 402051.i 0.0188038 + 0.0188038i
\(69\) 179602.i 0.00792344i
\(70\) 2.71461e7 + 1.46303e6i 1.13062 + 0.0609341i
\(71\) −8.22222e6 −0.323561 −0.161780 0.986827i \(-0.551724\pi\)
−0.161780 + 0.986827i \(0.551724\pi\)
\(72\) 7.31831e6 7.31831e6i 0.272321 0.272321i
\(73\) −3.03744e7 3.03744e7i −1.06959 1.06959i −0.997390 0.0721980i \(-0.976999\pi\)
−0.0721980 0.997390i \(-0.523001\pi\)
\(74\) 1.87246e7i 0.624434i
\(75\) −2.86761e7 3.56275e7i −0.906307 1.12601i
\(76\) −8.85779e6 −0.265504
\(77\) −5.69980e7 + 5.69980e7i −1.62142 + 1.62142i
\(78\) −1.07236e7 1.07236e7i −0.289710 0.289710i
\(79\) 4.69738e7i 1.20600i 0.797741 + 0.603000i \(0.206028\pi\)
−0.797741 + 0.603000i \(0.793972\pi\)
\(80\) 551080. 1.02252e7i 0.0134541 0.249638i
\(81\) 3.88602e7 0.902745
\(82\) 1.39728e7 1.39728e7i 0.309049 0.309049i
\(83\) 2.81305e7 + 2.81305e7i 0.592740 + 0.592740i 0.938371 0.345630i \(-0.112335\pi\)
−0.345630 + 0.938371i \(0.612335\pi\)
\(84\) 5.76165e7i 1.15726i
\(85\) −1.85465e6 2.06594e6i −0.0355292 0.0395770i
\(86\) 4.85155e7 0.886925
\(87\) 9.98697e6 9.98697e6i 0.174324 0.174324i
\(88\) 2.14695e7 + 2.14695e7i 0.358006 + 0.358006i
\(89\) 7.91918e7i 1.26218i −0.775711 0.631088i \(-0.782609\pi\)
0.775711 0.631088i \(-0.217391\pi\)
\(90\) −3.76052e7 + 3.37591e7i −0.573163 + 0.514542i
\(91\) −4.40170e7 −0.641881
\(92\) 138842. 138842.i 0.00193807 0.00193807i
\(93\) 6.84217e7 + 6.84217e7i 0.914665 + 0.914665i
\(94\) 9.33776e7i 1.19600i
\(95\) 4.31883e7 + 2.32761e6i 0.530238 + 0.0285769i
\(96\) −2.17024e7 −0.255519
\(97\) 1.47530e6 1.47530e6i 0.0166645 0.0166645i −0.698725 0.715390i \(-0.746249\pi\)
0.715390 + 0.698725i \(0.246249\pi\)
\(98\) −7.21301e7 7.21301e7i −0.782010 0.782010i
\(99\) 1.49842e8i 1.55988i
\(100\) −5.37384e6 + 4.97104e7i −0.0537384 + 0.497104i
\(101\) 1.61256e8 1.54964 0.774818 0.632185i \(-0.217842\pi\)
0.774818 + 0.632185i \(0.217842\pi\)
\(102\) −4.16064e6 + 4.16064e6i −0.0384379 + 0.0384379i
\(103\) −1.34152e8 1.34152e8i −1.19192 1.19192i −0.976526 0.215397i \(-0.930895\pi\)
−0.215397 0.976526i \(-0.569105\pi\)
\(104\) 1.65799e7i 0.141726i
\(105\) −1.51402e7 + 2.80923e8i −0.124559 + 2.31116i
\(106\) 3.16325e7 0.250559
\(107\) 2.02907e7 2.02907e7i 0.154796 0.154796i −0.625460 0.780256i \(-0.715089\pi\)
0.780256 + 0.625460i \(0.215089\pi\)
\(108\) 6.20755e6 + 6.20755e6i 0.0456274 + 0.0456274i
\(109\) 5.27998e7i 0.374047i 0.982355 + 0.187023i \(0.0598840\pi\)
−0.982355 + 0.187023i \(0.940116\pi\)
\(110\) −9.90379e7 1.10321e8i −0.676442 0.753508i
\(111\) −1.93772e8 −1.27644
\(112\) −4.45408e7 + 4.45408e7i −0.283065 + 0.283065i
\(113\) −1.25553e8 1.25553e8i −0.770041 0.770041i 0.208073 0.978113i \(-0.433281\pi\)
−0.978113 + 0.208073i \(0.933281\pi\)
\(114\) 9.16651e7i 0.542731i
\(115\) −713442. + 640474.i −0.00407913 + 0.00366193i
\(116\) −1.54410e7 −0.0852792
\(117\) 5.78580e7 5.78580e7i 0.308759 0.308759i
\(118\) 1.26685e8 + 1.26685e8i 0.653427 + 0.653427i
\(119\) 1.70781e7i 0.0851631i
\(120\) 1.05815e8 + 5.70287e6i 0.510298 + 0.0275022i
\(121\) 2.25226e8 1.05070
\(122\) −2.01378e7 + 2.01378e7i −0.0909019 + 0.0909019i
\(123\) 1.44598e8 + 1.44598e8i 0.631745 + 0.631745i
\(124\) 1.05788e8i 0.447454i
\(125\) 3.92641e7 2.40963e8i 0.160826 0.986983i
\(126\) 3.10863e8 1.23335
\(127\) −9.69572e7 + 9.69572e7i −0.372705 + 0.372705i −0.868462 0.495757i \(-0.834891\pi\)
0.495757 + 0.868462i \(0.334891\pi\)
\(128\) 1.67772e7 + 1.67772e7i 0.0625000 + 0.0625000i
\(129\) 5.02064e8i 1.81301i
\(130\) 4.35679e6 8.08393e7i 0.0152543 0.283041i
\(131\) 6.19413e7 0.210327 0.105164 0.994455i \(-0.466463\pi\)
0.105164 + 0.994455i \(0.466463\pi\)
\(132\) −2.22178e8 + 2.22178e8i −0.731820 + 0.731820i
\(133\) −1.88128e8 1.88128e8i −0.601238 0.601238i
\(134\) 2.36268e8i 0.732802i
\(135\) −2.86352e7 3.18976e7i −0.0862115 0.0960335i
\(136\) 6.43282e6 0.0188038
\(137\) 8.79898e6 8.79898e6i 0.0249776 0.0249776i −0.694508 0.719485i \(-0.744378\pi\)
0.719485 + 0.694508i \(0.244378\pi\)
\(138\) 1.43681e6 + 1.43681e6i 0.00396172 + 0.00396172i
\(139\) 2.71570e7i 0.0727482i −0.999338 0.0363741i \(-0.988419\pi\)
0.999338 0.0363741i \(-0.0115808\pi\)
\(140\) 2.28873e8 2.05465e8i 0.595776 0.534842i
\(141\) −9.66321e8 −2.44481
\(142\) −6.57777e7 + 6.57777e7i −0.161780 + 0.161780i
\(143\) 1.69736e8 + 1.69736e8i 0.405910 + 0.405910i
\(144\) 1.17093e8i 0.272321i
\(145\) 7.52862e7 + 4.05751e6i 0.170311 + 0.00917883i
\(146\) −4.85991e8 −1.06959
\(147\) 7.46441e8 7.46441e8i 1.59855 1.59855i
\(148\) 1.49797e8 + 1.49797e8i 0.312217 + 0.312217i
\(149\) 553367.i 0.00112271i −1.00000 0.000561355i \(-0.999821\pi\)
1.00000 0.000561355i \(-0.000178685\pi\)
\(150\) −5.14429e8 5.56113e7i −1.01616 0.109850i
\(151\) −1.27298e8 −0.244858 −0.122429 0.992477i \(-0.539068\pi\)
−0.122429 + 0.992477i \(0.539068\pi\)
\(152\) −7.08623e7 + 7.08623e7i −0.132752 + 0.132752i
\(153\) −2.24482e7 2.24482e7i −0.0409653 0.0409653i
\(154\) 9.11968e8i 1.62142i
\(155\) −2.77984e7 + 5.15793e8i −0.0481607 + 0.893611i
\(156\) −1.71578e8 −0.289710
\(157\) 5.28456e8 5.28456e8i 0.869782 0.869782i −0.122666 0.992448i \(-0.539144\pi\)
0.992448 + 0.122666i \(0.0391443\pi\)
\(158\) 3.75791e8 + 3.75791e8i 0.603000 + 0.603000i
\(159\) 3.27350e8i 0.512182i
\(160\) −7.73926e7 8.62099e7i −0.118092 0.131546i
\(161\) 5.89765e6 0.00877760
\(162\) 3.10882e8 3.10882e8i 0.451372 0.451372i
\(163\) 2.09644e8 + 2.09644e8i 0.296983 + 0.296983i 0.839831 0.542848i \(-0.182654\pi\)
−0.542848 + 0.839831i \(0.682654\pi\)
\(164\) 2.23565e8i 0.309049i
\(165\) 1.14166e9 1.02490e9i 1.54029 1.38275i
\(166\) 4.50087e8 0.592740
\(167\) −7.26269e8 + 7.26269e8i −0.933753 + 0.933753i −0.997938 0.0641853i \(-0.979555\pi\)
0.0641853 + 0.997938i \(0.479555\pi\)
\(168\) −4.60932e8 4.60932e8i −0.578628 0.578628i
\(169\) 6.84651e8i 0.839310i
\(170\) −3.13647e7 1.69039e6i −0.0375531 0.00202391i
\(171\) 4.94569e8 0.578418
\(172\) 3.88124e8 3.88124e8i 0.443462 0.443462i
\(173\) 6.00999e8 + 6.00999e8i 0.670949 + 0.670949i 0.957935 0.286986i \(-0.0926533\pi\)
−0.286986 + 0.957935i \(0.592653\pi\)
\(174\) 1.59791e8i 0.174324i
\(175\) −1.16992e9 + 9.41650e8i −1.24739 + 1.00401i
\(176\) 3.43512e8 0.358006
\(177\) −1.31100e9 + 1.31100e9i −1.33571 + 1.33571i
\(178\) −6.33534e8 6.33534e8i −0.631088 0.631088i
\(179\) 9.25251e8i 0.901255i −0.892712 0.450627i \(-0.851200\pi\)
0.892712 0.450627i \(-0.148800\pi\)
\(180\) −3.07692e7 + 5.70915e8i −0.0293107 + 0.543853i
\(181\) −8.31703e8 −0.774914 −0.387457 0.921888i \(-0.626647\pi\)
−0.387457 + 0.921888i \(0.626647\pi\)
\(182\) −3.52136e8 + 3.52136e8i −0.320941 + 0.320941i
\(183\) −2.08397e8 2.08397e8i −0.185818 0.185818i
\(184\) 2.22147e6i 0.00193807i
\(185\) −6.91008e8 7.69734e8i −0.589924 0.657134i
\(186\) 1.09475e9 0.914665
\(187\) 6.58556e7 6.58556e7i 0.0538551 0.0538551i
\(188\) 7.47021e8 + 7.47021e8i 0.598000 + 0.598000i
\(189\) 2.63681e8i 0.206648i
\(190\) 3.64127e8 3.26885e8i 0.279408 0.250831i
\(191\) 1.17089e9 0.879799 0.439900 0.898047i \(-0.355014\pi\)
0.439900 + 0.898047i \(0.355014\pi\)
\(192\) −1.73620e8 + 1.73620e8i −0.127760 + 0.127760i
\(193\) −1.41003e9 1.41003e9i −1.01624 1.01624i −0.999866 0.0163773i \(-0.994787\pi\)
−0.0163773 0.999866i \(-0.505213\pi\)
\(194\) 2.36047e7i 0.0166645i
\(195\) 8.36568e8 + 4.50864e7i 0.578579 + 0.0311822i
\(196\) −1.15408e9 −0.782010
\(197\) −7.98017e8 + 7.98017e8i −0.529843 + 0.529843i −0.920525 0.390683i \(-0.872239\pi\)
0.390683 + 0.920525i \(0.372239\pi\)
\(198\) −1.19873e9 1.19873e9i −0.779941 0.779941i
\(199\) 3.89588e8i 0.248424i 0.992256 + 0.124212i \(0.0396402\pi\)
−0.992256 + 0.124212i \(0.960360\pi\)
\(200\) 3.54692e8 + 4.40674e8i 0.221683 + 0.275421i
\(201\) 2.44503e9 1.49796
\(202\) 1.29005e9 1.29005e9i 0.774818 0.774818i
\(203\) −3.27946e8 3.27946e8i −0.193116 0.193116i
\(204\) 6.65702e7i 0.0384379i
\(205\) −5.87473e7 + 1.09004e9i −0.0332638 + 0.617203i
\(206\) −2.14643e9 −1.19192
\(207\) −7.75216e6 + 7.75216e6i −0.00422222 + 0.00422222i
\(208\) 1.32639e8 + 1.32639e8i 0.0708629 + 0.0708629i
\(209\) 1.45090e9i 0.760417i
\(210\) 2.12626e9 + 2.36850e9i 1.09330 + 1.21786i
\(211\) 3.73042e9 1.88204 0.941019 0.338354i \(-0.109870\pi\)
0.941019 + 0.338354i \(0.109870\pi\)
\(212\) 2.53060e8 2.53060e8i 0.125280 0.125280i
\(213\) −6.80703e8 6.80703e8i −0.330704 0.330704i
\(214\) 3.24651e8i 0.154796i
\(215\) −1.99438e9 + 1.79040e9i −0.933370 + 0.837908i
\(216\) 9.93209e7 0.0456274
\(217\) 2.24679e9 2.24679e9i 1.01327 1.01327i
\(218\) 4.22398e8 + 4.22398e8i 0.187023 + 0.187023i
\(219\) 5.02929e9i 2.18640i
\(220\) −1.67487e9 9.02664e7i −0.714975 0.0385332i
\(221\) 5.08574e7 0.0213199
\(222\) −1.55018e9 + 1.55018e9i −0.638220 + 0.638220i
\(223\) 2.58624e9 + 2.58624e9i 1.04580 + 1.04580i 0.998900 + 0.0469003i \(0.0149343\pi\)
0.0469003 + 0.998900i \(0.485066\pi\)
\(224\) 7.12652e8i 0.283065i
\(225\) 3.00045e8 2.77554e9i 0.117073 1.08297i
\(226\) −2.00885e9 −0.770041
\(227\) 2.28574e8 2.28574e8i 0.0860844 0.0860844i −0.662753 0.748838i \(-0.730612\pi\)
0.748838 + 0.662753i \(0.230612\pi\)
\(228\) −7.33321e8 7.33321e8i −0.271366 0.271366i
\(229\) 4.29778e9i 1.56280i 0.624033 + 0.781398i \(0.285493\pi\)
−0.624033 + 0.781398i \(0.714507\pi\)
\(230\) −583749. + 1.08313e7i −0.000208600 + 0.00387053i
\(231\) −9.43752e9 −3.31444
\(232\) −1.23528e8 + 1.23528e8i −0.0426396 + 0.0426396i
\(233\) 2.83013e8 + 2.83013e8i 0.0960247 + 0.0960247i 0.753487 0.657463i \(-0.228370\pi\)
−0.657463 + 0.753487i \(0.728370\pi\)
\(234\) 9.25728e8i 0.308759i
\(235\) −3.44598e9 3.83858e9i −1.12990 1.25863i
\(236\) 2.02696e9 0.653427
\(237\) −3.88888e9 + 3.88888e9i −1.23263 + 1.23263i
\(238\) 1.36625e8 + 1.36625e8i 0.0425815 + 0.0425815i
\(239\) 5.19198e9i 1.59126i −0.605782 0.795630i \(-0.707140\pi\)
0.605782 0.795630i \(-0.292860\pi\)
\(240\) 8.92146e8 8.00900e8i 0.268900 0.241398i
\(241\) 4.53061e9 1.34304 0.671519 0.740987i \(-0.265642\pi\)
0.671519 + 0.740987i \(0.265642\pi\)
\(242\) 1.80181e9 1.80181e9i 0.525349 0.525349i
\(243\) 3.53535e9 + 3.53535e9i 1.01393 + 1.01393i
\(244\) 3.22205e8i 0.0909019i
\(245\) 5.62700e9 + 3.03264e8i 1.56175 + 0.0841699i
\(246\) 2.31357e9 0.631745
\(247\) −5.60232e8 + 5.60232e8i −0.150515 + 0.150515i
\(248\) −8.46301e8 8.46301e8i −0.223727 0.223727i
\(249\) 4.65774e9i 1.21165i
\(250\) −1.61359e9 2.24181e9i −0.413079 0.573904i
\(251\) −3.40464e9 −0.857780 −0.428890 0.903357i \(-0.641095\pi\)
−0.428890 + 0.903357i \(0.641095\pi\)
\(252\) 2.48690e9 2.48690e9i 0.616675 0.616675i
\(253\) −2.27422e7 2.27422e7i −0.00555074 0.00555074i
\(254\) 1.55132e9i 0.372705i
\(255\) 1.74930e7 3.24579e8i 0.00413717 0.0767643i
\(256\) 2.68435e8 0.0625000
\(257\) 3.01159e7 3.01159e7i 0.00690341 0.00690341i −0.703647 0.710550i \(-0.748446\pi\)
0.710550 + 0.703647i \(0.248446\pi\)
\(258\) 4.01651e9 + 4.01651e9i 0.906505 + 0.906505i
\(259\) 6.36299e9i 1.41404i
\(260\) −6.11860e8 6.81569e8i −0.133893 0.149148i
\(261\) 8.62136e8 0.185786
\(262\) 4.95531e8 4.95531e8i 0.105164 0.105164i
\(263\) −2.01502e9 2.01502e9i −0.421169 0.421169i 0.464437 0.885606i \(-0.346257\pi\)
−0.885606 + 0.464437i \(0.846257\pi\)
\(264\) 3.55484e9i 0.731820i
\(265\) −1.30035e9 + 1.16736e9i −0.263680 + 0.236712i
\(266\) −3.01005e9 −0.601238
\(267\) 6.55615e9 6.55615e9i 1.29004 1.29004i
\(268\) −1.89015e9 1.89015e9i −0.366401 0.366401i
\(269\) 9.53840e9i 1.82166i −0.412785 0.910828i \(-0.635444\pi\)
0.412785 0.910828i \(-0.364556\pi\)
\(270\) −4.84262e8 2.60991e7i −0.0911225 0.00491100i
\(271\) −3.84233e9 −0.712390 −0.356195 0.934412i \(-0.615926\pi\)
−0.356195 + 0.934412i \(0.615926\pi\)
\(272\) 5.14625e7 5.14625e7i 0.00940190 0.00940190i
\(273\) −3.64409e9 3.64409e9i −0.656052 0.656052i
\(274\) 1.40784e8i 0.0249776i
\(275\) 8.14252e9 + 8.80230e8i 1.42373 + 0.153910i
\(276\) 2.29890e7 0.00396172
\(277\) −2.80174e9 + 2.80174e9i −0.475892 + 0.475892i −0.903815 0.427923i \(-0.859245\pi\)
0.427923 + 0.903815i \(0.359245\pi\)
\(278\) −2.17256e8 2.17256e8i −0.0363741 0.0363741i
\(279\) 5.90658e9i 0.974809i
\(280\) 1.87267e8 3.47471e9i 0.0304670 0.565309i
\(281\) −8.28718e9 −1.32917 −0.664586 0.747212i \(-0.731392\pi\)
−0.664586 + 0.747212i \(0.731392\pi\)
\(282\) −7.73057e9 + 7.73057e9i −1.22240 + 1.22240i
\(283\) −7.40766e7 7.40766e7i −0.0115488 0.0115488i 0.701309 0.712858i \(-0.252599\pi\)
−0.712858 + 0.701309i \(0.752599\pi\)
\(284\) 1.05244e9i 0.161780i
\(285\) 3.38278e9 + 3.76818e9i 0.512737 + 0.571152i
\(286\) 2.71578e9 0.405910
\(287\) 4.74822e9 4.74822e9i 0.699848 0.699848i
\(288\) −9.36744e8 9.36744e8i −0.136160 0.136160i
\(289\) 6.95603e9i 0.997171i
\(290\) 6.34749e8 5.69829e8i 0.0897450 0.0805662i
\(291\) 2.44274e8 0.0340648
\(292\) −3.88793e9 + 3.88793e9i −0.534794 + 0.534794i
\(293\) −6.33070e9 6.33070e9i −0.858977 0.858977i 0.132241 0.991218i \(-0.457783\pi\)
−0.991218 + 0.132241i \(0.957783\pi\)
\(294\) 1.19431e10i 1.59855i
\(295\) −9.88292e9 5.32635e8i −1.30496 0.0703302i
\(296\) 2.39675e9 0.312217
\(297\) 1.01679e9 1.01679e9i 0.130679 0.130679i
\(298\) −4.42693e6 4.42693e6i −0.000561355 0.000561355i
\(299\) 1.75628e7i 0.00219740i
\(300\) −4.56033e9 + 3.67054e9i −0.563003 + 0.453154i
\(301\) 1.64865e10 2.00846
\(302\) −1.01838e9 + 1.01838e9i −0.122429 + 0.122429i
\(303\) 1.33501e10 + 1.33501e10i 1.58385 + 1.58385i
\(304\) 1.13380e9i 0.132752i
\(305\) 8.46676e7 1.57099e9i 0.00978403 0.181540i
\(306\) −3.59172e8 −0.0409653
\(307\) 4.80692e9 4.80692e9i 0.541144 0.541144i −0.382720 0.923864i \(-0.625013\pi\)
0.923864 + 0.382720i \(0.125013\pi\)
\(308\) 7.29574e9 + 7.29574e9i 0.810712 + 0.810712i
\(309\) 2.22124e10i 2.43648i
\(310\) 3.90396e9 + 4.34873e9i 0.422725 + 0.470886i
\(311\) 1.06468e10 1.13809 0.569047 0.822305i \(-0.307312\pi\)
0.569047 + 0.822305i \(0.307312\pi\)
\(312\) −1.37262e9 + 1.37262e9i −0.144855 + 0.144855i
\(313\) −1.05889e10 1.05889e10i −1.10325 1.10325i −0.994016 0.109236i \(-0.965160\pi\)
−0.109236 0.994016i \(-0.534840\pi\)
\(314\) 8.45530e9i 0.869782i
\(315\) −1.27790e10 + 1.14720e10i −1.29794 + 1.16519i
\(316\) 6.01265e9 0.603000
\(317\) −9.51101e9 + 9.51101e9i −0.941867 + 0.941867i −0.998401 0.0565338i \(-0.981995\pi\)
0.0565338 + 0.998401i \(0.481995\pi\)
\(318\) 2.61880e9 + 2.61880e9i 0.256091 + 0.256091i
\(319\) 2.52922e9i 0.244244i
\(320\) −1.30882e9 7.05382e7i −0.124819 0.00672705i
\(321\) 3.35966e9 0.316428
\(322\) 4.71812e7 4.71812e7i 0.00438880 0.00438880i
\(323\) 2.17364e8 + 2.17364e8i 0.0199699 + 0.0199699i
\(324\) 4.97411e9i 0.451372i
\(325\) 2.80417e9 + 3.48393e9i 0.251345 + 0.312274i
\(326\) 3.35430e9 0.296983
\(327\) −4.37120e9 + 4.37120e9i −0.382305 + 0.382305i
\(328\) −1.78852e9 1.78852e9i −0.154525 0.154525i
\(329\) 3.17315e10i 2.70836i
\(330\) 9.34125e8 1.73325e10i 0.0787679 1.46152i
\(331\) −1.31018e10 −1.09149 −0.545744 0.837952i \(-0.683753\pi\)
−0.545744 + 0.837952i \(0.683753\pi\)
\(332\) 3.60070e9 3.60070e9i 0.296370 0.296370i
\(333\) −8.36381e9 8.36381e9i −0.680186 0.680186i
\(334\) 1.16203e10i 0.933753i
\(335\) 8.71918e9 + 9.71254e9i 0.692303 + 0.771176i
\(336\) −7.37491e9 −0.578628
\(337\) 1.33341e10 1.33341e10i 1.03382 1.03382i 0.0344141 0.999408i \(-0.489043\pi\)
0.999408 0.0344141i \(-0.0109565\pi\)
\(338\) −5.47721e9 5.47721e9i −0.419655 0.419655i
\(339\) 2.07886e10i 1.57408i
\(340\) −2.64441e8 + 2.37395e8i −0.0197885 + 0.0177646i
\(341\) −1.73279e10 −1.28153
\(342\) 3.95655e9 3.95655e9i 0.289209 0.289209i
\(343\) −8.83927e9 8.83927e9i −0.638616 0.638616i
\(344\) 6.20998e9i 0.443462i
\(345\) −1.12088e8 6.04094e6i −0.00791196 0.000426411i
\(346\) 9.61599e9 0.670949
\(347\) −1.09024e10 + 1.09024e10i −0.751973 + 0.751973i −0.974847 0.222874i \(-0.928456\pi\)
0.222874 + 0.974847i \(0.428456\pi\)
\(348\) −1.27833e9 1.27833e9i −0.0871619 0.0871619i
\(349\) 9.67778e9i 0.652340i −0.945311 0.326170i \(-0.894242\pi\)
0.945311 0.326170i \(-0.105758\pi\)
\(350\) −1.82613e9 + 1.68925e10i −0.121692 + 1.12570i
\(351\) 7.85223e8 0.0517326
\(352\) 2.74809e9 2.74809e9i 0.179003 0.179003i
\(353\) 6.27335e9 + 6.27335e9i 0.404018 + 0.404018i 0.879646 0.475628i \(-0.157779\pi\)
−0.475628 + 0.879646i \(0.657779\pi\)
\(354\) 2.09761e10i 1.33571i
\(355\) 2.76556e8 5.13144e9i 0.0174129 0.323092i
\(356\) −1.01365e10 −0.631088
\(357\) −1.41386e9 + 1.41386e9i −0.0870432 + 0.0870432i
\(358\) −7.40201e9 7.40201e9i −0.450627 0.450627i
\(359\) 7.91205e9i 0.476334i −0.971224 0.238167i \(-0.923454\pi\)
0.971224 0.238167i \(-0.0765465\pi\)
\(360\) 4.32116e9 + 4.81347e9i 0.257271 + 0.286582i
\(361\) 1.21947e10 0.718031
\(362\) −6.65362e9 + 6.65362e9i −0.387457 + 0.387457i
\(363\) 1.86461e10 + 1.86461e10i 1.07389 + 1.07389i
\(364\) 5.63417e9i 0.320941i
\(365\) 1.99782e10 1.79349e10i 1.12560 1.01048i
\(366\) −3.33435e9 −0.185818
\(367\) 6.65934e9 6.65934e9i 0.367085 0.367085i −0.499328 0.866413i \(-0.666420\pi\)
0.866413 + 0.499328i \(0.166420\pi\)
\(368\) −1.77718e7 1.77718e7i −0.000969036 0.000969036i
\(369\) 1.24826e10i 0.673285i
\(370\) −1.16859e10 6.29808e8i −0.623529 0.0336048i
\(371\) 1.07493e10 0.567396
\(372\) 8.75798e9 8.75798e9i 0.457333 0.457333i
\(373\) 1.63417e10 + 1.63417e10i 0.844230 + 0.844230i 0.989406 0.145176i \(-0.0463748\pi\)
−0.145176 + 0.989406i \(0.546375\pi\)
\(374\) 1.05369e9i 0.0538551i
\(375\) 2.31995e10 1.66983e10i 1.17315 0.844396i
\(376\) 1.19523e10 0.598000
\(377\) −9.76602e8 + 9.76602e8i −0.0483450 + 0.0483450i
\(378\) 2.10945e9 + 2.10945e9i 0.103324 + 0.103324i
\(379\) 9.14573e9i 0.443263i 0.975130 + 0.221632i \(0.0711382\pi\)
−0.975130 + 0.221632i \(0.928862\pi\)
\(380\) 2.97934e8 5.52810e9i 0.0142885 0.265119i
\(381\) −1.60538e10 −0.761867
\(382\) 9.36714e9 9.36714e9i 0.439900 0.439900i
\(383\) −6.52966e9 6.52966e9i −0.303456 0.303456i 0.538909 0.842364i \(-0.318837\pi\)
−0.842364 + 0.538909i \(0.818837\pi\)
\(384\) 2.77791e9i 0.127760i
\(385\) −3.36550e10 3.74892e10i −1.53181 1.70633i
\(386\) −2.25604e10 −1.01624
\(387\) −2.16706e10 + 2.16706e10i −0.966112 + 0.966112i
\(388\) −1.88838e8 1.88838e8i −0.00833225 0.00833225i
\(389\) 2.04596e10i 0.893507i 0.894657 + 0.446754i \(0.147420\pi\)
−0.894657 + 0.446754i \(0.852580\pi\)
\(390\) 7.05324e9 6.33186e9i 0.304881 0.273699i
\(391\) −6.81417e6 −0.000291545
\(392\) −9.23265e9 + 9.23265e9i −0.391005 + 0.391005i
\(393\) 5.12801e9 + 5.12801e9i 0.214971 + 0.214971i
\(394\) 1.27683e10i 0.529843i
\(395\) −2.93161e10 1.57998e9i −1.20425 0.0649026i
\(396\) −1.91797e10 −0.779941
\(397\) −7.68996e9 + 7.68996e9i −0.309572 + 0.309572i −0.844744 0.535171i \(-0.820247\pi\)
0.535171 + 0.844744i \(0.320247\pi\)
\(398\) 3.11670e9 + 3.11670e9i 0.124212 + 0.124212i
\(399\) 3.11496e10i 1.22902i
\(400\) 6.36293e9 + 6.87851e8i 0.248552 + 0.0268692i
\(401\) −5.85624e9 −0.226486 −0.113243 0.993567i \(-0.536124\pi\)
−0.113243 + 0.993567i \(0.536124\pi\)
\(402\) 1.95602e10 1.95602e10i 0.748980 0.748980i
\(403\) −6.69079e9 6.69079e9i −0.253663 0.253663i
\(404\) 2.06407e10i 0.774818i
\(405\) −1.30707e9 + 2.42524e10i −0.0485825 + 0.901437i
\(406\) −5.24714e9 −0.193116
\(407\) 2.45366e10 2.45366e10i 0.894205 0.894205i
\(408\) 5.32562e8 + 5.32562e8i 0.0192189 + 0.0192189i
\(409\) 1.32972e10i 0.475191i −0.971364 0.237596i \(-0.923641\pi\)
0.971364 0.237596i \(-0.0763593\pi\)
\(410\) 8.25036e9 + 9.19032e9i 0.291970 + 0.325233i
\(411\) 1.45690e9 0.0510580
\(412\) −1.71715e10 + 1.71715e10i −0.595962 + 0.595962i
\(413\) 4.30500e10 + 4.30500e10i 1.47970 + 1.47970i
\(414\) 1.24034e8i 0.00422222i
\(415\) −1.85022e10 + 1.66099e10i −0.623780 + 0.559982i
\(416\) 2.12223e9 0.0708629
\(417\) 2.24828e9 2.24828e9i 0.0743542 0.0743542i
\(418\) 1.16072e10 + 1.16072e10i 0.380209 + 0.380209i
\(419\) 6.98994e9i 0.226786i 0.993550 + 0.113393i \(0.0361720\pi\)
−0.993550 + 0.113393i \(0.963828\pi\)
\(420\) 3.59581e10 + 1.93794e9i 1.15558 + 0.0622793i
\(421\) −2.54099e10 −0.808864 −0.404432 0.914568i \(-0.632531\pi\)
−0.404432 + 0.914568i \(0.632531\pi\)
\(422\) 2.98434e10 2.98434e10i 0.941019 0.941019i
\(423\) −4.17094e10 4.17094e10i −1.30278 1.30278i
\(424\) 4.04896e9i 0.125280i
\(425\) 1.35173e9 1.08799e9i 0.0414317 0.0333478i
\(426\) −1.08912e10 −0.330704
\(427\) −6.84322e9 + 6.84322e9i −0.205849 + 0.205849i
\(428\) −2.59720e9 2.59720e9i −0.0773982 0.0773982i
\(429\) 2.81043e10i 0.829743i
\(430\) −1.63183e9 + 3.02782e10i −0.0477311 + 0.885639i
\(431\) 3.72373e10 1.07912 0.539559 0.841948i \(-0.318591\pi\)
0.539559 + 0.841948i \(0.318591\pi\)
\(432\) 7.94567e8 7.94567e8i 0.0228137 0.0228137i
\(433\) 1.34378e10 + 1.34378e10i 0.382277 + 0.382277i 0.871922 0.489645i \(-0.162874\pi\)
−0.489645 + 0.871922i \(0.662874\pi\)
\(434\) 3.59487e10i 1.01327i
\(435\) 5.89689e9 + 6.56872e9i 0.164690 + 0.183453i
\(436\) 6.75837e9 0.187023
\(437\) 7.50632e7 7.50632e7i 0.00205826 0.00205826i
\(438\) −4.02343e10 4.02343e10i −1.09320 1.09320i
\(439\) 4.19540e10i 1.12957i 0.825237 + 0.564787i \(0.191042\pi\)
−0.825237 + 0.564787i \(0.808958\pi\)
\(440\) −1.41211e10 + 1.26768e10i −0.376754 + 0.338221i
\(441\) 6.44373e10 1.70366
\(442\) 4.06859e8 4.06859e8i 0.0106599 0.0106599i
\(443\) −3.76709e10 3.76709e10i −0.978119 0.978119i 0.0216469 0.999766i \(-0.493109\pi\)
−0.999766 + 0.0216469i \(0.993109\pi\)
\(444\) 2.48029e10i 0.638220i
\(445\) 4.94231e10 + 2.66363e9i 1.26035 + 0.0679258i
\(446\) 4.13798e10 1.04580
\(447\) 4.58122e7 4.58122e7i 0.00114750 0.00114750i
\(448\) 5.70122e9 + 5.70122e9i 0.141532 + 0.141532i
\(449\) 5.05667e10i 1.24417i −0.782950 0.622085i \(-0.786286\pi\)
0.782950 0.622085i \(-0.213714\pi\)
\(450\) −1.98040e10 2.46047e10i −0.482951 0.600023i
\(451\) −3.66197e10 −0.885133
\(452\) −1.60708e10 + 1.60708e10i −0.385020 + 0.385020i
\(453\) −1.05388e10 1.05388e10i −0.250264 0.250264i
\(454\) 3.65719e9i 0.0860844i
\(455\) 1.48052e9 2.74708e10i 0.0345437 0.640951i
\(456\) −1.17331e10 −0.271366
\(457\) 1.52066e10 1.52066e10i 0.348631 0.348631i −0.510968 0.859599i \(-0.670713\pi\)
0.859599 + 0.510968i \(0.170713\pi\)
\(458\) 3.43822e10 + 3.43822e10i 0.781398 + 0.781398i
\(459\) 3.04657e8i 0.00686374i
\(460\) 8.19806e7 + 9.13206e7i 0.00183096 + 0.00203956i
\(461\) −2.73791e10 −0.606199 −0.303100 0.952959i \(-0.598021\pi\)
−0.303100 + 0.952959i \(0.598021\pi\)
\(462\) −7.55002e10 + 7.55002e10i −1.65722 + 1.65722i
\(463\) 3.53408e10 + 3.53408e10i 0.769046 + 0.769046i 0.977939 0.208893i \(-0.0669859\pi\)
−0.208893 + 0.977939i \(0.566986\pi\)
\(464\) 1.97645e9i 0.0426396i
\(465\) −4.50030e10 + 4.04002e10i −0.962563 + 0.864116i
\(466\) 4.52821e9 0.0960247
\(467\) −4.85998e10 + 4.85998e10i −1.02180 + 1.02180i −0.0220454 + 0.999757i \(0.507018\pi\)
−0.999757 + 0.0220454i \(0.992982\pi\)
\(468\) −7.40583e9 7.40583e9i −0.154380 0.154380i
\(469\) 8.02885e10i 1.65944i
\(470\) −5.82764e10 3.14078e9i −1.19427 0.0643644i
\(471\) 8.75000e10 1.77797
\(472\) 1.62157e10 1.62157e10i 0.326713 0.326713i
\(473\) −6.35744e10 6.35744e10i −1.27010 1.27010i
\(474\) 6.22221e10i 1.23263i
\(475\) −2.90529e9 + 2.68753e10i −0.0570710 + 0.527932i
\(476\) 2.18600e9 0.0425815
\(477\) −1.41294e10 + 1.41294e10i −0.272930 + 0.272930i
\(478\) −4.15358e10 4.15358e10i −0.795630 0.795630i
\(479\) 5.06476e10i 0.962093i −0.876695 0.481047i \(-0.840257\pi\)
0.876695 0.481047i \(-0.159743\pi\)
\(480\) 7.29967e8 1.35444e10i 0.0137511 0.255149i
\(481\) 1.89485e10 0.353994
\(482\) 3.62449e10 3.62449e10i 0.671519 0.671519i
\(483\) 4.88257e8 + 4.88257e8i 0.00897139 + 0.00897139i
\(484\) 2.88290e10i 0.525349i
\(485\) 8.71102e8 + 9.70346e8i 0.0157435 + 0.0175372i
\(486\) 5.65657e10 1.01393
\(487\) 3.99713e9 3.99713e9i 0.0710612 0.0710612i −0.670683 0.741744i \(-0.733999\pi\)
0.741744 + 0.670683i \(0.233999\pi\)
\(488\) 2.57764e9 + 2.57764e9i 0.0454510 + 0.0454510i
\(489\) 3.47121e10i 0.607079i
\(490\) 4.74421e10 4.25899e10i 0.822962 0.738792i
\(491\) 4.99004e10 0.858575 0.429288 0.903168i \(-0.358765\pi\)
0.429288 + 0.903168i \(0.358765\pi\)
\(492\) 1.85085e10 1.85085e10i 0.315872 0.315872i
\(493\) 3.78910e8 + 3.78910e8i 0.00641429 + 0.00641429i
\(494\) 8.96371e9i 0.150515i
\(495\) 9.35153e10 + 5.03996e9i 1.55762 + 0.0839472i
\(496\) −1.35408e10 −0.223727
\(497\) −2.23525e10 + 2.23525e10i −0.366354 + 0.366354i
\(498\) 3.72619e10 + 3.72619e10i 0.605826 + 0.605826i
\(499\) 7.43519e10i 1.19920i 0.800302 + 0.599598i \(0.204673\pi\)
−0.800302 + 0.599598i \(0.795327\pi\)
\(500\) −3.08432e10 5.02580e9i −0.493491 0.0804128i
\(501\) −1.20253e11 −1.90873
\(502\) −2.72371e10 + 2.72371e10i −0.428890 + 0.428890i
\(503\) 5.52095e10 + 5.52095e10i 0.862465 + 0.862465i 0.991624 0.129158i \(-0.0412276\pi\)
−0.129158 + 0.991624i \(0.541228\pi\)
\(504\) 3.97904e10i 0.616675i
\(505\) −5.42387e9 + 1.00639e11i −0.0833958 + 1.54739i
\(506\) −3.63876e8 −0.00555074
\(507\) 5.66811e10 5.66811e10i 0.857840 0.857840i
\(508\) 1.24105e10 + 1.24105e10i 0.186352 + 0.186352i
\(509\) 1.27030e10i 0.189249i −0.995513 0.0946245i \(-0.969835\pi\)
0.995513 0.0946245i \(-0.0301650\pi\)
\(510\) −2.45669e9 2.73658e9i −0.0363136 0.0404508i
\(511\) −1.65149e11 −2.42210
\(512\) 2.14748e9 2.14748e9i 0.0312500 0.0312500i
\(513\) 3.35603e9 + 3.35603e9i 0.0484570 + 0.0484570i
\(514\) 4.81855e8i 0.00690341i
\(515\) 8.82358e10 7.92113e10i 1.25434 1.12605i
\(516\) 6.42642e10 0.906505
\(517\) 1.22361e11 1.22361e11i 1.71270 1.71270i
\(518\) 5.09039e10 + 5.09039e10i 0.707021 + 0.707021i
\(519\) 9.95114e10i 1.37152i
\(520\) −1.03474e10 5.57670e8i −0.141520 0.00762717i
\(521\) −3.13323e10 −0.425247 −0.212623 0.977134i \(-0.568201\pi\)
−0.212623 + 0.977134i \(0.568201\pi\)
\(522\) 6.89709e9 6.89709e9i 0.0928932 0.0928932i
\(523\) −1.15624e10 1.15624e10i −0.154539 0.154539i 0.625603 0.780142i \(-0.284853\pi\)
−0.780142 + 0.625603i \(0.784853\pi\)
\(524\) 7.92849e9i 0.105164i
\(525\) −1.74813e11 1.88978e10i −2.30111 0.248756i
\(526\) −3.22403e10 −0.421169
\(527\) −2.59595e9 + 2.59595e9i −0.0336553 + 0.0336553i
\(528\) 2.84387e10 + 2.84387e10i 0.365910 + 0.365910i
\(529\) 7.83086e10i 0.999970i
\(530\) −1.06397e9 + 1.97417e10i −0.0134842 + 0.250196i
\(531\) −1.13174e11 −1.42353
\(532\) −2.40804e10 + 2.40804e10i −0.300619 + 0.300619i
\(533\) −1.41399e10 1.41399e10i −0.175201 0.175201i
\(534\) 1.04898e11i 1.29004i
\(535\) 1.19808e10 + 1.33458e10i 0.146242 + 0.162903i
\(536\) −3.02424e10 −0.366401
\(537\) 7.65999e10 7.65999e10i 0.921152 0.921152i
\(538\) −7.63072e10 7.63072e10i −0.910828 0.910828i
\(539\) 1.89038e11i 2.23972i
\(540\) −4.08289e9 + 3.66531e9i −0.0480168 + 0.0431058i
\(541\) 1.21976e11 1.42392 0.711961 0.702219i \(-0.247807\pi\)
0.711961 + 0.702219i \(0.247807\pi\)
\(542\) −3.07387e10 + 3.07387e10i −0.356195 + 0.356195i
\(543\) −6.88552e10 6.88552e10i −0.792022 0.792022i
\(544\) 8.23401e8i 0.00940190i
\(545\) −3.29520e10 1.77593e9i −0.373505 0.0201298i
\(546\) −5.83054e10 −0.656052
\(547\) −1.11157e11 + 1.11157e11i −1.24161 + 1.24161i −0.282283 + 0.959331i \(0.591092\pi\)
−0.959331 + 0.282283i \(0.908908\pi\)
\(548\) −1.12627e9 1.12627e9i −0.0124888 0.0124888i
\(549\) 1.79901e10i 0.198036i
\(550\) 7.21820e10 5.80983e10i 0.788820 0.634911i
\(551\) −8.34796e9 −0.0905678
\(552\) 1.83912e8 1.83912e8i 0.00198086 0.00198086i
\(553\) 1.27701e11 + 1.27701e11i 1.36550 + 1.36550i
\(554\) 4.48278e10i 0.475892i
\(555\) 6.51758e9 1.20932e11i 0.0686933 1.27459i
\(556\) −3.47609e9 −0.0363741
\(557\) −2.14972e10 + 2.14972e10i −0.223337 + 0.223337i −0.809902 0.586565i \(-0.800480\pi\)
0.586565 + 0.809902i \(0.300480\pi\)
\(558\) 4.72526e10 + 4.72526e10i 0.487404 + 0.487404i
\(559\) 4.90957e10i 0.502801i
\(560\) −2.62995e10 2.92958e10i −0.267421 0.297888i
\(561\) 1.09041e10 0.110088
\(562\) −6.62974e10 + 6.62974e10i −0.664586 + 0.664586i
\(563\) −2.68020e10 2.68020e10i −0.266768 0.266768i 0.561029 0.827796i \(-0.310406\pi\)
−0.827796 + 0.561029i \(0.810406\pi\)
\(564\) 1.23689e11i 1.22240i
\(565\) 8.25800e10 7.41340e10i 0.810366 0.727484i
\(566\) −1.18523e9 −0.0115488
\(567\) 1.05644e11 1.05644e11i 1.02214 1.02214i
\(568\) 8.41955e9 + 8.41955e9i 0.0808901 + 0.0808901i
\(569\) 9.52278e10i 0.908479i 0.890880 + 0.454240i \(0.150089\pi\)
−0.890880 + 0.454240i \(0.849911\pi\)
\(570\) 5.72077e10 + 3.08318e9i 0.541945 + 0.0292078i
\(571\) 1.93929e11 1.82431 0.912154 0.409848i \(-0.134418\pi\)
0.912154 + 0.409848i \(0.134418\pi\)
\(572\) 2.17262e10 2.17262e10i 0.202955 0.202955i
\(573\) 9.69361e10 + 9.69361e10i 0.899223 + 0.899223i
\(574\) 7.59716e10i 0.699848i
\(575\) −3.75719e8 4.66798e8i −0.00343710 0.00427029i
\(576\) −1.49879e10 −0.136160
\(577\) −1.25849e11 + 1.25849e11i −1.13540 + 1.13540i −0.146131 + 0.989265i \(0.546682\pi\)
−0.989265 + 0.146131i \(0.953318\pi\)
\(578\) 5.56482e10 + 5.56482e10i 0.498586 + 0.498586i
\(579\) 2.33467e11i 2.07736i
\(580\) 5.19361e8 9.63663e9i 0.00458942 0.0851556i
\(581\) 1.52948e11 1.34227
\(582\) 1.95420e9 1.95420e9i 0.0170324 0.0170324i
\(583\) −4.14510e10 4.14510e10i −0.358807 0.358807i
\(584\) 6.22068e10i 0.534794i
\(585\) 3.41628e10 + 3.80549e10i 0.291696 + 0.324928i
\(586\) −1.01291e11 −0.858977
\(587\) 3.41535e10 3.41535e10i 0.287662 0.287662i −0.548493 0.836155i \(-0.684798\pi\)
0.836155 + 0.548493i \(0.184798\pi\)
\(588\) −9.55444e10 9.55444e10i −0.799275 0.799275i
\(589\) 5.71927e10i 0.475203i
\(590\) −8.33244e10 + 7.48023e10i −0.687645 + 0.617315i
\(591\) −1.32133e11 −1.08308
\(592\) 1.91740e10 1.91740e10i 0.156108 0.156108i
\(593\) −1.67663e11 1.67663e11i −1.35588 1.35588i −0.878937 0.476939i \(-0.841746\pi\)
−0.476939 0.878937i \(-0.658254\pi\)
\(594\) 1.62687e10i 0.130679i
\(595\) −1.06583e10 5.74426e8i −0.0850397 0.00458317i
\(596\) −7.08309e7 −0.000561355
\(597\) −3.22533e10 + 3.22533e10i −0.253908 + 0.253908i
\(598\) −1.40502e8 1.40502e8i −0.00109870 0.00109870i
\(599\) 2.21439e11i 1.72007i 0.510231 + 0.860037i \(0.329560\pi\)
−0.510231 + 0.860037i \(0.670440\pi\)
\(600\) −7.11825e9 + 6.58470e10i −0.0549248 + 0.508078i
\(601\) −2.25242e11 −1.72644 −0.863220 0.504828i \(-0.831556\pi\)
−0.863220 + 0.504828i \(0.831556\pi\)
\(602\) 1.31892e11 1.31892e11i 1.00423 1.00423i
\(603\) 1.05535e11 + 1.05535e11i 0.798229 + 0.798229i
\(604\) 1.62942e10i 0.122429i
\(605\) −7.57554e9 + 1.40562e11i −0.0565447 + 1.04917i
\(606\) 2.13601e11 1.58385
\(607\) −8.03075e10 + 8.03075e10i −0.591563 + 0.591563i −0.938054 0.346490i \(-0.887373\pi\)
0.346490 + 0.938054i \(0.387373\pi\)
\(608\) 9.07038e9 + 9.07038e9i 0.0663760 + 0.0663760i
\(609\) 5.43002e10i 0.394759i
\(610\) −1.18906e10 1.32452e10i −0.0858782 0.0956622i
\(611\) 9.44942e10 0.678017
\(612\) −2.87338e9 + 2.87338e9i −0.0204827 + 0.0204827i
\(613\) −5.38969e10 5.38969e10i −0.381700 0.381700i 0.490014 0.871714i \(-0.336992\pi\)
−0.871714 + 0.490014i \(0.836992\pi\)
\(614\) 7.69107e10i 0.541144i
\(615\) −9.51063e10 + 8.53791e10i −0.664827 + 0.596831i
\(616\) 1.16732e11 0.810712
\(617\) −1.37064e10 + 1.37064e10i −0.0945766 + 0.0945766i −0.752812 0.658235i \(-0.771303\pi\)
0.658235 + 0.752812i \(0.271303\pi\)
\(618\) −1.77699e11 1.77699e11i −1.21824 1.21824i
\(619\) 1.67460e11i 1.14064i −0.821423 0.570320i \(-0.806819\pi\)
0.821423 0.570320i \(-0.193181\pi\)
\(620\) 6.60215e10 + 3.55819e9i 0.446806 + 0.0240804i
\(621\) −1.05209e8 −0.000707433
\(622\) 8.51746e10 8.51746e10i 0.569047 0.569047i
\(623\) −2.15287e11 2.15287e11i −1.42911 1.42911i
\(624\) 2.19620e10i 0.144855i
\(625\) 1.49063e11 + 3.26093e10i 0.976897 + 0.213708i
\(626\) −1.69423e11 −1.10325
\(627\) −1.20117e11 + 1.20117e11i −0.777205 + 0.777205i
\(628\) −6.76424e10 6.76424e10i −0.434891 0.434891i
\(629\) 7.35182e9i 0.0469669i
\(630\) −1.04559e10 + 1.94008e11i −0.0663745 + 1.23156i
\(631\) 9.05920e10 0.571442 0.285721 0.958313i \(-0.407767\pi\)
0.285721 + 0.958313i \(0.407767\pi\)
\(632\) 4.81012e10 4.81012e10i 0.301500 0.301500i
\(633\) 3.08835e11 + 3.08835e11i 1.92359 + 1.92359i
\(634\) 1.52176e11i 0.941867i
\(635\) −5.72493e10 6.37716e10i −0.352107 0.392223i
\(636\) 4.19008e10 0.256091
\(637\) −7.29926e10 + 7.29926e10i −0.443324 + 0.443324i
\(638\) 2.02338e10 + 2.02338e10i 0.122122 + 0.122122i
\(639\) 5.87625e10i 0.352449i
\(640\) −1.10349e10 + 9.90626e9i −0.0657730 + 0.0590459i
\(641\) −2.71517e10 −0.160829 −0.0804147 0.996761i \(-0.525624\pi\)
−0.0804147 + 0.996761i \(0.525624\pi\)
\(642\) 2.68773e10 2.68773e10i 0.158214 0.158214i
\(643\) −2.63399e10 2.63399e10i −0.154089 0.154089i 0.625853 0.779941i \(-0.284751\pi\)
−0.779941 + 0.625853i \(0.784751\pi\)
\(644\) 7.54900e8i 0.00438880i
\(645\) −3.13335e11 1.68870e10i −1.81038 0.0975697i
\(646\) 3.47782e9 0.0199699
\(647\) −2.14034e9 + 2.14034e9i −0.0122142 + 0.0122142i −0.713188 0.700973i \(-0.752749\pi\)
0.700973 + 0.713188i \(0.252749\pi\)
\(648\) −3.97928e10 3.97928e10i −0.225686 0.225686i
\(649\) 3.32014e11i 1.87145i
\(650\) 5.03048e10 + 5.43810e9i 0.281810 + 0.0304645i
\(651\) 3.72016e11 2.07127
\(652\) 2.68344e10 2.68344e10i 0.148491 0.148491i
\(653\) 1.29525e11 + 1.29525e11i 0.712364 + 0.712364i 0.967029 0.254665i \(-0.0819653\pi\)
−0.254665 + 0.967029i \(0.581965\pi\)
\(654\) 6.99392e10i 0.382305i
\(655\) −2.08341e9 + 3.86572e10i −0.0113190 + 0.210022i
\(656\) −2.86163e10 −0.154525
\(657\) 2.17080e11 2.17080e11i 1.16509 1.16509i
\(658\) 2.53852e11 + 2.53852e11i 1.35418 + 1.35418i
\(659\) 1.29660e11i 0.687485i −0.939064 0.343742i \(-0.888305\pi\)
0.939064 0.343742i \(-0.111695\pi\)
\(660\) −1.31187e11 1.46133e11i −0.691376 0.770144i
\(661\) 4.35428e10 0.228092 0.114046 0.993475i \(-0.463619\pi\)
0.114046 + 0.993475i \(0.463619\pi\)
\(662\) −1.04814e11 + 1.04814e11i −0.545744 + 0.545744i
\(663\) 4.21039e9 + 4.21039e9i 0.0217906 + 0.0217906i
\(664\) 5.76112e10i 0.296370i
\(665\) 1.23737e11 1.11082e11i 0.632724 0.568011i
\(666\) −1.33821e11 −0.680186
\(667\) 1.30851e8 1.30851e8i 0.000661109 0.000661109i
\(668\) 9.29625e10 + 9.29625e10i 0.466876 + 0.466876i
\(669\) 4.28220e11i 2.13778i
\(670\) 1.47454e11 + 7.94694e9i 0.731740 + 0.0394367i
\(671\) 5.27769e10 0.260348
\(672\) −5.89993e10 + 5.89993e10i −0.289314 + 0.289314i
\(673\) 1.08117e11 + 1.08117e11i 0.527028 + 0.527028i 0.919685 0.392657i \(-0.128444\pi\)
−0.392657 + 0.919685i \(0.628444\pi\)
\(674\) 2.13346e11i 1.03382i
\(675\) 2.08703e10 1.67982e10i 0.100534 0.0809184i
\(676\) −8.76353e10 −0.419655
\(677\) −7.02840e10 + 7.02840e10i −0.334581 + 0.334581i −0.854323 0.519742i \(-0.826028\pi\)
0.519742 + 0.854323i \(0.326028\pi\)
\(678\) −1.66309e11 1.66309e11i −0.787041 0.787041i
\(679\) 8.02135e9i 0.0377371i
\(680\) −2.16369e8 + 4.01469e9i −0.00101195 + 0.0187766i
\(681\) 3.78466e10 0.175970
\(682\) −1.38623e11 + 1.38623e11i −0.640766 + 0.640766i
\(683\) −1.25091e11 1.25091e11i −0.574834 0.574834i 0.358642 0.933475i \(-0.383240\pi\)
−0.933475 + 0.358642i \(0.883240\pi\)
\(684\) 6.33048e10i 0.289209i
\(685\) 5.19544e9 + 5.78735e9i 0.0235972 + 0.0262856i
\(686\) −1.41428e11 −0.638616
\(687\) −3.55806e11 + 3.55806e11i −1.59730 + 1.59730i
\(688\) −4.96799e10 4.96799e10i −0.221731 0.221731i
\(689\) 3.20108e10i 0.142043i
\(690\) −9.45034e8 + 8.48379e8i −0.00416918 + 0.00374277i
\(691\) −1.67070e11 −0.732800 −0.366400 0.930457i \(-0.619410\pi\)
−0.366400 + 0.930457i \(0.619410\pi\)
\(692\) 7.69279e10 7.69279e10i 0.335475 0.335475i
\(693\) −4.07353e11 4.07353e11i −1.76619 1.76619i
\(694\) 1.74438e11i 0.751973i
\(695\) 1.69485e10 + 9.13431e8i 0.0726427 + 0.00391504i
\(696\) −2.04533e10 −0.0871619
\(697\) −5.48611e9 + 5.48611e9i −0.0232452 + 0.0232452i
\(698\) −7.74223e10 7.74223e10i −0.326170 0.326170i
\(699\) 4.68603e10i 0.196289i
\(700\) 1.20531e11 + 1.49749e11i 0.502004 + 0.623696i
\(701\) 1.66014e11 0.687498 0.343749 0.939062i \(-0.388303\pi\)
0.343749 + 0.939062i \(0.388303\pi\)
\(702\) 6.28178e9 6.28178e9i 0.0258663 0.0258663i
\(703\) 8.09858e10 + 8.09858e10i 0.331579 + 0.331579i
\(704\) 4.39695e10i 0.179003i
\(705\) 3.25024e10 6.03075e11i 0.131571 2.44127i
\(706\) 1.00374e11 0.404018
\(707\) 4.38382e11 4.38382e11i 1.75459 1.75459i
\(708\) 1.67808e11 + 1.67808e11i 0.667853 + 0.667853i
\(709\) 3.71810e11i 1.47142i 0.677297 + 0.735710i \(0.263151\pi\)
−0.677297 + 0.735710i \(0.736849\pi\)
\(710\) −3.88391e10 4.32640e10i −0.152839 0.170252i
\(711\) −3.35712e11 −1.31368
\(712\) −8.10924e10 + 8.10924e10i −0.315544 + 0.315544i
\(713\) 8.96472e8 + 8.96472e8i 0.00346879 + 0.00346879i
\(714\) 2.26218e10i 0.0870432i
\(715\) −1.11640e11 + 1.00222e11i −0.427167 + 0.383477i
\(716\) −1.18432e11 −0.450627
\(717\) 4.29835e11 4.29835e11i 1.62639 1.62639i
\(718\) −6.32964e10 6.32964e10i −0.238167 0.238167i
\(719\) 3.16803e11i 1.18543i 0.805414 + 0.592713i \(0.201943\pi\)
−0.805414 + 0.592713i \(0.798057\pi\)
\(720\) 7.30771e10 + 3.93845e9i 0.271926 + 0.0146553i
\(721\) −7.29399e11 −2.69913
\(722\) 9.75577e10 9.75577e10i 0.359015 0.359015i
\(723\) 3.75081e11 + 3.75081e11i 1.37269 + 1.37269i
\(724\) 1.06458e11i 0.387457i
\(725\) −5.06454e9 + 4.68492e10i −0.0183311 + 0.169570i
\(726\) 2.98338e11 1.07389
\(727\) 1.86694e11 1.86694e11i 0.668333 0.668333i −0.288997 0.957330i \(-0.593322\pi\)
0.957330 + 0.288997i \(0.0933218\pi\)
\(728\) 4.50734e10 + 4.50734e10i 0.160470 + 0.160470i
\(729\) 3.30410e11i 1.16988i
\(730\) 1.63464e10 3.03304e11i 0.0575614 1.06804i
\(731\) −1.90485e10 −0.0667102
\(732\) −2.66748e10 + 2.66748e10i −0.0929088 + 0.0929088i
\(733\) 8.03537e10 + 8.03537e10i 0.278349 + 0.278349i 0.832450 0.554101i \(-0.186938\pi\)
−0.554101 + 0.832450i \(0.686938\pi\)
\(734\) 1.06549e11i 0.367085i
\(735\) 4.40743e11 + 4.90956e11i 1.51020 + 1.68226i
\(736\) −2.84349e8 −0.000969036
\(737\) −3.09604e11 + 3.09604e11i −1.04939 + 1.04939i
\(738\) 9.98606e10 + 9.98606e10i 0.336642 + 0.336642i
\(739\) 2.44359e11i 0.819315i −0.912239 0.409658i \(-0.865648\pi\)
0.912239 0.409658i \(-0.134352\pi\)
\(740\) −9.85260e10 + 8.84490e10i −0.328567 + 0.294962i
\(741\) −9.27613e10 −0.307676
\(742\) 8.59947e10 8.59947e10i 0.283698 0.283698i
\(743\) 1.76095e10 + 1.76095e10i 0.0577818 + 0.0577818i 0.735407 0.677625i \(-0.236991\pi\)
−0.677625 + 0.735407i \(0.736991\pi\)
\(744\) 1.40128e11i 0.457333i
\(745\) 3.45353e8 + 1.86126e7i 0.00112108 + 6.04202e-5i
\(746\) 2.61466e11 0.844230
\(747\) −2.01042e11 + 2.01042e11i −0.645662 + 0.645662i
\(748\) −8.42952e9 8.42952e9i −0.0269275 0.0269275i
\(749\) 1.10322e11i 0.350539i
\(750\) 5.20097e10 3.19182e11i 0.164376 1.00877i
\(751\) 9.35354e10 0.294047 0.147023 0.989133i \(-0.453031\pi\)
0.147023 + 0.989133i \(0.453031\pi\)
\(752\) 9.56187e10 9.56187e10i 0.299000 0.299000i
\(753\) −2.81864e11 2.81864e11i −0.876717 0.876717i
\(754\) 1.56256e10i 0.0483450i
\(755\) 4.28170e9 7.94460e10i 0.0131774 0.244503i
\(756\) 3.37511e10 0.103324
\(757\) 6.80194e10 6.80194e10i 0.207133 0.207133i −0.595915 0.803048i \(-0.703210\pi\)
0.803048 + 0.595915i \(0.203210\pi\)
\(758\) 7.31659e10 + 7.31659e10i 0.221632 + 0.221632i
\(759\) 3.76558e9i 0.0113466i
\(760\) −4.18413e10 4.66082e10i −0.125415 0.139704i
\(761\) 1.73217e11 0.516478 0.258239 0.966081i \(-0.416858\pi\)
0.258239 + 0.966081i \(0.416858\pi\)
\(762\) −1.28431e11 + 1.28431e11i −0.380933 + 0.380933i
\(763\) 1.43539e11 + 1.43539e11i 0.423518 + 0.423518i
\(764\) 1.49874e11i 0.439900i
\(765\) 1.47649e10 1.32548e10i 0.0431106 0.0387014i
\(766\) −1.04475e11 −0.303456
\(767\) 1.28200e11 1.28200e11i 0.370430 0.370430i
\(768\) 2.22233e10 + 2.22233e10i 0.0638798 + 0.0638798i
\(769\) 6.23925e11i 1.78413i −0.451905 0.892066i \(-0.649255\pi\)
0.451905 0.892066i \(-0.350745\pi\)
\(770\) −5.69154e11 3.06742e10i −1.61907 0.0872592i
\(771\) 4.98649e9 0.0141116
\(772\) −1.80483e11 + 1.80483e11i −0.508122 + 0.508122i
\(773\) −2.80444e11 2.80444e11i −0.785466 0.785466i 0.195281 0.980747i \(-0.437438\pi\)
−0.980747 + 0.195281i \(0.937438\pi\)
\(774\) 3.46730e11i 0.966112i
\(775\) −3.20968e11 3.46976e10i −0.889724 0.0961818i
\(776\) −3.02141e9 −0.00833225
\(777\) −5.26781e11 + 5.26781e11i −1.44526 + 1.44526i
\(778\) 1.63677e11 + 1.63677e11i 0.446754 + 0.446754i
\(779\) 1.20867e11i 0.328215i
\(780\) 5.77106e9 1.07081e11i 0.0155911 0.289290i
\(781\) 1.72389e11 0.463347
\(782\) −5.45133e7 + 5.45133e7i −0.000145773 + 0.000145773i
\(783\) 5.85026e9 + 5.85026e9i 0.0155643 + 0.0155643i
\(784\) 1.47722e11i 0.391005i
\(785\) 3.12032e11 + 3.47581e11i 0.821713 + 0.915330i
\(786\) 8.20482e10 0.214971
\(787\) −2.18147e10 + 2.18147e10i −0.0568656 + 0.0568656i −0.734968 0.678102i \(-0.762803\pi\)
0.678102 + 0.734968i \(0.262803\pi\)
\(788\) 1.02146e11 + 1.02146e11i 0.264921 + 0.264921i
\(789\) 3.33640e11i 0.860934i
\(790\) −2.47169e11 + 2.21889e11i −0.634578 + 0.569675i
\(791\) −6.82646e11 −1.74377
\(792\) −1.53438e11 + 1.53438e11i −0.389971 + 0.389971i
\(793\) 2.03786e10 + 2.03786e10i 0.0515326 + 0.0515326i
\(794\) 1.23039e11i 0.309572i
\(795\) −2.04297e11 1.10105e10i −0.511439 0.0275638i
\(796\) 4.98672e10 0.124212
\(797\) 1.10772e11 1.10772e11i 0.274534 0.274534i −0.556389 0.830922i \(-0.687813\pi\)
0.830922 + 0.556389i \(0.187813\pi\)
\(798\) −2.49197e11 2.49197e11i −0.614512 0.614512i
\(799\) 3.66627e10i 0.0899574i
\(800\) 5.64062e10 4.54006e10i 0.137711 0.110841i
\(801\) 5.65967e11 1.37487
\(802\) −4.68499e10 + 4.68499e10i −0.113243 + 0.113243i
\(803\) 6.36839e11 + 6.36839e11i 1.53168 + 1.53168i
\(804\) 3.12964e11i 0.748980i
\(805\) −1.98369e8 + 3.68069e9i −0.000472379 + 0.00876488i
\(806\) −1.07053e11 −0.253663
\(807\) 7.89668e11 7.89668e11i 1.86187 1.86187i
\(808\) −1.65126e11 1.65126e11i −0.387409 0.387409i
\(809\) 2.98150e11i 0.696051i 0.937485 + 0.348025i \(0.113148\pi\)
−0.937485 + 0.348025i \(0.886852\pi\)
\(810\) 1.83563e11 + 2.04476e11i 0.426427 + 0.475010i
\(811\) 6.76978e11 1.56492 0.782458 0.622704i \(-0.213966\pi\)
0.782458 + 0.622704i \(0.213966\pi\)
\(812\) −4.19771e10 + 4.19771e10i −0.0965581 + 0.0965581i
\(813\) −3.18100e11 3.18100e11i −0.728118 0.728118i
\(814\) 3.92586e11i 0.894205i
\(815\) −1.37889e11 + 1.23786e11i −0.312535 + 0.280570i
\(816\) 8.52099e9 0.0192189
\(817\) 2.09834e11 2.09834e11i 0.470964 0.470964i
\(818\) −1.06378e11 1.06378e11i −0.237596 0.237596i
\(819\) 3.14580e11i 0.699191i
\(820\) 1.39525e11 + 7.51965e9i 0.308601 + 0.0166319i
\(821\) −4.64293e10 −0.102193 −0.0510963 0.998694i \(-0.516272\pi\)
−0.0510963 + 0.998694i \(0.516272\pi\)
\(822\) 1.16552e10 1.16552e10i 0.0255290 0.0255290i
\(823\) −5.00668e11 5.00668e11i −1.09132 1.09132i −0.995388 0.0959282i \(-0.969418\pi\)
−0.0959282 0.995388i \(-0.530582\pi\)
\(824\) 2.74743e11i 0.595962i
\(825\) 6.01232e11 + 7.46977e11i 1.29786 + 1.61247i
\(826\) 6.88800e11 1.47970
\(827\) −6.00312e11 + 6.00312e11i −1.28338 + 1.28338i −0.344648 + 0.938732i \(0.612002\pi\)
−0.938732 + 0.344648i \(0.887998\pi\)
\(828\) 9.92276e8 + 9.92276e8i 0.00211111 + 0.00211111i
\(829\) 8.51434e11i 1.80274i 0.433051 + 0.901370i \(0.357437\pi\)
−0.433051 + 0.901370i \(0.642563\pi\)
\(830\) −1.51388e10 + 2.80897e11i −0.0318991 + 0.591881i
\(831\) −4.63902e11 −0.972797
\(832\) 1.69778e10 1.69778e10i 0.0354315 0.0354315i
\(833\) 2.83203e10 + 2.83203e10i 0.0588190 + 0.0588190i
\(834\) 3.59724e10i 0.0743542i
\(835\) −4.28832e11 4.77689e11i −0.882148 0.982651i
\(836\) 1.85715e11 0.380209
\(837\) −4.00807e10 + 4.00807e10i −0.0816646 + 0.0816646i
\(838\) 5.59195e10 + 5.59195e10i 0.113393 + 0.113393i
\(839\) 2.72456e11i 0.549856i 0.961465 + 0.274928i \(0.0886540\pi\)
−0.961465 + 0.274928i \(0.911346\pi\)
\(840\) 3.03168e11 2.72161e11i 0.608929 0.546650i
\(841\) 4.85694e11 0.970910
\(842\) −2.03280e11 + 2.03280e11i −0.404432 + 0.404432i
\(843\) −6.86081e11 6.86081e11i −1.35852 1.35852i
\(844\) 4.77494e11i 0.941019i
\(845\) 4.27287e11 + 2.30284e10i 0.838094 + 0.0451686i
\(846\) −6.67350e11 −1.30278
\(847\) 6.12290e11 6.12290e11i 1.18966 1.18966i
\(848\) −3.23917e10 3.23917e10i −0.0626398 0.0626398i
\(849\) 1.22653e10i 0.0236075i
\(850\) 2.10992e9 1.95177e10i 0.00404194 0.0373898i
\(851\) −2.53884e9 −0.00484079
\(852\) −8.71300e10 + 8.71300e10i −0.165352 + 0.165352i
\(853\) −1.59406e11 1.59406e11i −0.301099 0.301099i 0.540345 0.841444i \(-0.318294\pi\)
−0.841444 + 0.540345i \(0.818294\pi\)
\(854\) 1.09491e11i 0.205849i
\(855\) −1.66349e10 + 3.08657e11i −0.0311284 + 0.577580i
\(856\) −4.15553e10 −0.0773982
\(857\) −3.08378e11 + 3.08378e11i −0.571690 + 0.571690i −0.932601 0.360910i \(-0.882466\pi\)
0.360910 + 0.932601i \(0.382466\pi\)
\(858\) 2.24834e11 + 2.24834e11i 0.414871 + 0.414871i
\(859\) 7.24487e11i 1.33063i 0.746562 + 0.665316i \(0.231703\pi\)
−0.746562 + 0.665316i \(0.768297\pi\)
\(860\) 2.29171e11 + 2.55281e11i 0.418954 + 0.466685i
\(861\) 7.86194e11 1.43060
\(862\) 2.97898e11 2.97898e11i 0.539559 0.539559i
\(863\) −4.20245e10 4.20245e10i −0.0757634 0.0757634i 0.668210 0.743973i \(-0.267061\pi\)
−0.743973 + 0.668210i \(0.767061\pi\)
\(864\) 1.27131e10i 0.0228137i
\(865\) −3.95295e11 + 3.54865e11i −0.706085 + 0.633869i
\(866\) 2.15006e11 0.382277
\(867\) −5.75877e11 + 5.75877e11i −1.01919 + 1.01919i
\(868\) −2.87589e11 2.87589e11i −0.506634 0.506634i
\(869\) 9.84867e11i 1.72702i
\(870\) 9.97249e10 + 5.37462e9i 0.174071 + 0.00938147i
\(871\) −2.39094e11 −0.415428
\(872\) 5.40670e10 5.40670e10i 0.0935117 0.0935117i
\(873\) 1.05436e10 + 1.05436e10i 0.0181524 + 0.0181524i
\(874\) 1.20101e9i 0.00205826i
\(875\) −5.48328e11 7.61811e11i −0.935424 1.29962i
\(876\) −6.43749e11 −1.09320
\(877\) −6.58815e11 + 6.58815e11i −1.11369 + 1.11369i −0.121045 + 0.992647i \(0.538624\pi\)
−0.992647 + 0.121045i \(0.961376\pi\)
\(878\) 3.35632e11 + 3.35632e11i 0.564787 + 0.564787i
\(879\) 1.04822e12i 1.75588i
\(880\) −1.15541e10 + 2.14384e11i −0.0192666 + 0.357488i
\(881\) −4.01192e11 −0.665961 −0.332981 0.942934i \(-0.608054\pi\)
−0.332981 + 0.942934i \(0.608054\pi\)
\(882\) 5.15499e11 5.15499e11i 0.851831 0.851831i
\(883\) 5.60683e11 + 5.60683e11i 0.922306 + 0.922306i 0.997192 0.0748864i \(-0.0238594\pi\)
−0.0748864 + 0.997192i \(0.523859\pi\)
\(884\) 6.50974e9i 0.0106599i
\(885\) −7.74094e11 8.62286e11i −1.26189 1.40565i
\(886\) −6.02735e11 −0.978119
\(887\) −2.69741e11 + 2.69741e11i −0.435765 + 0.435765i −0.890584 0.454819i \(-0.849704\pi\)
0.454819 + 0.890584i \(0.349704\pi\)
\(888\) 1.98423e11 + 1.98423e11i 0.319110 + 0.319110i
\(889\) 5.27167e11i 0.843997i
\(890\) 4.16694e11 3.74076e11i 0.664136 0.596211i
\(891\) −8.14754e11 −1.29275
\(892\) 3.31038e11 3.31038e11i 0.522900 0.522900i
\(893\) 4.03867e11 + 4.03867e11i 0.635086 + 0.635086i
\(894\) 7.32996e8i 0.00114750i
\(895\) 5.77444e11 + 3.11210e10i 0.899949 + 0.0485023i
\(896\) 9.12195e10 0.141532
\(897\) 1.45399e9 1.45399e9i 0.00224591 0.00224591i
\(898\) −4.04534e11 4.04534e11i −0.622085 0.622085i
\(899\) 9.96988e10i 0.152634i
\(900\) −3.55270e11 3.84057e10i −0.541487 0.0585364i
\(901\) −1.24198e10 −0.0188459
\(902\) −2.92958e11 + 2.92958e11i −0.442567 + 0.442567i
\(903\) 1.36489e12 + 1.36489e12i 2.05280 + 2.05280i
\(904\) 2.57133e11i 0.385020i
\(905\) 2.79745e10 5.19061e11i 0.0417031 0.773791i
\(906\) −1.68621e11 −0.250264
\(907\) 6.28908e11 6.28908e11i 0.929305 0.929305i −0.0683564 0.997661i \(-0.521775\pi\)
0.997661 + 0.0683564i \(0.0217755\pi\)
\(908\) −2.92575e10 2.92575e10i −0.0430422 0.0430422i
\(909\) 1.15246e12i 1.68799i
\(910\) −2.07922e11 2.31610e11i −0.303204 0.337747i
\(911\) 1.00441e12 1.45827 0.729134 0.684371i \(-0.239923\pi\)
0.729134 + 0.684371i \(0.239923\pi\)
\(912\) −9.38651e10 + 9.38651e10i −0.135683 + 0.135683i
\(913\) −5.89791e11 5.89791e11i −0.848819 0.848819i
\(914\) 2.43305e11i 0.348631i
\(915\) 1.37069e11 1.23050e11i 0.195548 0.175548i
\(916\) 5.50116e11 0.781398
\(917\) 1.68391e11 1.68391e11i 0.238145 0.238145i
\(918\) −2.43726e9 2.43726e9i −0.00343187 0.00343187i
\(919\) 1.58868e11i 0.222727i 0.993780 + 0.111364i \(0.0355218\pi\)
−0.993780 + 0.111364i \(0.964478\pi\)
\(920\) 1.38641e9 + 7.47198e7i 0.00193526 + 0.000104300i
\(921\) 7.95912e11 1.10618
\(922\) −2.19033e11 + 2.19033e11i −0.303100 + 0.303100i
\(923\) 6.65643e10 + 6.65643e10i 0.0917138 + 0.0917138i
\(924\) 1.20800e12i 1.65722i
\(925\) 5.03629e11 4.05364e11i 0.687929 0.553705i
\(926\) 5.65453e11 0.769046
\(927\) 9.58757e11 9.58757e11i 1.29834 1.29834i
\(928\) 1.58116e10 + 1.58116e10i 0.0213198 + 0.0213198i
\(929\) 5.94996e11i 0.798824i −0.916772 0.399412i \(-0.869214\pi\)
0.916772 0.399412i \(-0.130786\pi\)
\(930\) −3.68221e10 + 6.83225e11i −0.0492240 + 0.913340i
\(931\) −6.23939e11 −0.830507
\(932\) 3.62257e10 3.62257e10i 0.0480124 0.0480124i
\(933\) 8.81432e11 + 8.81432e11i 1.16322 + 1.16322i
\(934\) 7.77597e11i 1.02180i
\(935\) 3.88851e10 + 4.33152e10i 0.0508787 + 0.0566753i
\(936\) −1.18493e11 −0.154380
\(937\) −2.52202e11 + 2.52202e11i −0.327182 + 0.327182i −0.851514 0.524332i \(-0.824315\pi\)
0.524332 + 0.851514i \(0.324315\pi\)
\(938\) −6.42308e11 6.42308e11i −0.829721 0.829721i
\(939\) 1.75328e12i 2.25522i
\(940\) −4.91338e11 + 4.41085e11i −0.629316 + 0.564951i
\(941\) −9.55354e11 −1.21845 −0.609223 0.792999i \(-0.708518\pi\)
−0.609223 + 0.792999i \(0.708518\pi\)
\(942\) 7.00000e11 7.00000e11i 0.888985 0.888985i
\(943\) 1.89454e9 + 1.89454e9i 0.00239584 + 0.00239584i
\(944\) 2.59451e11i 0.326713i
\(945\) −1.64562e11 8.86896e9i −0.206349 0.0111210i
\(946\) −1.01719e12 −1.27010
\(947\) −5.84413e11 + 5.84413e11i −0.726641 + 0.726641i −0.969949 0.243308i \(-0.921767\pi\)
0.243308 + 0.969949i \(0.421767\pi\)
\(948\) 4.97777e11 + 4.97777e11i 0.616313 + 0.616313i
\(949\) 4.91802e11i 0.606353i
\(950\) 1.91760e11 + 2.38244e11i 0.235431 + 0.292502i
\(951\) −1.57480e12 −1.92532
\(952\) 1.74880e10 1.74880e10i 0.0212908 0.0212908i
\(953\) −4.48597e11 4.48597e11i −0.543857 0.543857i 0.380801 0.924657i \(-0.375648\pi\)
−0.924657 + 0.380801i \(0.875648\pi\)
\(954\) 2.26071e11i 0.272930i
\(955\) −3.93832e10 + 7.30747e11i −0.0473476 + 0.878524i
\(956\) −6.64573e11 −0.795630
\(957\) −2.09390e11 + 2.09390e11i −0.249636 + 0.249636i
\(958\) −4.05181e11 4.05181e11i −0.481047 0.481047i
\(959\) 4.78410e10i 0.0565621i
\(960\) −1.02515e11 1.14195e11i −0.120699 0.134450i
\(961\) −1.69845e11 −0.199140
\(962\) 1.51588e11 1.51588e11i 0.176997 0.176997i
\(963\) 1.45013e11 + 1.45013e11i 0.168617 + 0.168617i
\(964\) 5.79918e11i 0.671519i
\(965\) 9.27415e11 8.32562e11i 1.06946 0.960080i
\(966\) 7.81210e9 0.00897139
\(967\) 3.45450e11 3.45450e11i 0.395075 0.395075i −0.481417 0.876492i \(-0.659878\pi\)
0.876492 + 0.481417i \(0.159878\pi\)
\(968\) −2.30632e11 2.30632e11i −0.262674 0.262674i
\(969\) 3.59903e10i 0.0408216i
\(970\) 1.47316e10 + 7.93951e8i 0.0166404 + 0.000896823i
\(971\) −4.22522e10 −0.0475306 −0.0237653 0.999718i \(-0.507565\pi\)
−0.0237653 + 0.999718i \(0.507565\pi\)
\(972\) 4.52525e11 4.52525e11i 0.506965 0.506965i
\(973\) −7.38277e10 7.38277e10i −0.0823697 0.0823697i
\(974\) 6.39541e10i 0.0710612i
\(975\) −5.62764e10 + 5.20581e11i −0.0622741 + 0.576063i
\(976\) 4.12423e10 0.0454510
\(977\) 1.20249e12 1.20249e12i 1.31978 1.31978i 0.405840 0.913944i \(-0.366979\pi\)
0.913944 0.405840i \(-0.133021\pi\)
\(978\) 2.77697e11 + 2.77697e11i 0.303540 + 0.303540i
\(979\) 1.66036e12i 1.80747i
\(980\) 3.88178e10 7.20256e11i 0.0420849 0.780877i
\(981\) −3.77349e11 −0.407443
\(982\) 3.99204e11 3.99204e11i 0.429288 0.429288i
\(983\) −3.99506e11 3.99506e11i −0.427867 0.427867i 0.460034 0.887901i \(-0.347837\pi\)
−0.887901 + 0.460034i \(0.847837\pi\)
\(984\) 2.96136e11i 0.315872i
\(985\) −4.71196e11 5.24879e11i −0.500561 0.557589i
\(986\) 6.06256e9 0.00641429
\(987\) −2.62700e12 + 2.62700e12i −2.76816 + 2.76816i
\(988\) 7.17097e10 + 7.17097e10i 0.0752576 + 0.0752576i
\(989\) 6.57812e9i 0.00687570i
\(990\) 7.88442e11 7.07803e11i 0.820784 0.736837i
\(991\) 1.64837e12 1.70907 0.854533 0.519396i \(-0.173843\pi\)
0.854533 + 0.519396i \(0.173843\pi\)
\(992\) −1.08327e11 + 1.08327e11i −0.111863 + 0.111863i
\(993\) −1.08467e12 1.08467e12i −1.11558 1.11558i
\(994\) 3.57641e11i 0.366354i
\(995\) −2.43139e11 1.31039e10i −0.248064 0.0133693i
\(996\) 5.96191e11 0.605826
\(997\) −6.07220e11 + 6.07220e11i −0.614562 + 0.614562i −0.944131 0.329570i \(-0.893096\pi\)
0.329570 + 0.944131i \(0.393096\pi\)
\(998\) 5.94815e11 + 5.94815e11i 0.599598 + 0.599598i
\(999\) 1.13510e11i 0.113965i
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 10.9.c.b.3.2 4
3.2 odd 2 90.9.g.a.73.1 4
4.3 odd 2 80.9.p.a.33.1 4
5.2 odd 4 inner 10.9.c.b.7.2 yes 4
5.3 odd 4 50.9.c.b.7.1 4
5.4 even 2 50.9.c.b.43.1 4
15.2 even 4 90.9.g.a.37.1 4
20.7 even 4 80.9.p.a.17.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
10.9.c.b.3.2 4 1.1 even 1 trivial
10.9.c.b.7.2 yes 4 5.2 odd 4 inner
50.9.c.b.7.1 4 5.3 odd 4
50.9.c.b.43.1 4 5.4 even 2
80.9.p.a.17.1 4 20.7 even 4
80.9.p.a.33.1 4 4.3 odd 2
90.9.g.a.37.1 4 15.2 even 4
90.9.g.a.73.1 4 3.2 odd 2