Properties

Label 16.14.e.a.5.3
Level $16$
Weight $14$
Character 16.5
Analytic conductor $17.157$
Analytic rank $0$
Dimension $50$
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] = [16,14,Mod(5,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1]))
 
N = Newforms(chi, 14, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.5");
 
S:= CuspForms(chi, 14);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 14 \)
Character orbit: \([\chi]\) \(=\) 16.e (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: \(17.1569486323\)
Analytic rank: \(0\)
Dimension: \(50\)
Relative dimension: \(25\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.3
Character \(\chi\) \(=\) 16.5
Dual form 16.14.e.a.13.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-85.7364 - 29.0046i) q^{2} +(-924.404 + 924.404i) q^{3} +(6509.46 + 4973.51i) q^{4} +(42023.8 + 42023.8i) q^{5} +(106067. - 52443.1i) q^{6} -291398. i q^{7} +(-413843. - 615215. i) q^{8} -114722. i q^{9} +O(q^{10})\) \(q+(-85.7364 - 29.0046i) q^{2} +(-924.404 + 924.404i) q^{3} +(6509.46 + 4973.51i) q^{4} +(42023.8 + 42023.8i) q^{5} +(106067. - 52443.1i) q^{6} -291398. i q^{7} +(-413843. - 615215. i) q^{8} -114722. i q^{9} +(-2.38408e6 - 4.82186e6i) q^{10} +(4.32527e6 + 4.32527e6i) q^{11} +(-1.06149e7 + 1.41984e6i) q^{12} +(1.83053e7 - 1.83053e7i) q^{13} +(-8.45191e6 + 2.49834e7i) q^{14} -7.76939e7 q^{15} +(1.76373e7 + 6.47497e7i) q^{16} +1.06181e8 q^{17} +(-3.32747e6 + 9.83584e6i) q^{18} +(5.47438e7 - 5.47438e7i) q^{19} +(6.45466e7 + 4.82558e8i) q^{20} +(2.69370e8 + 2.69370e8i) q^{21} +(-2.45380e8 - 4.96286e8i) q^{22} +1.00034e9i q^{23} +(9.51265e8 + 1.86149e8i) q^{24} +2.31130e9i q^{25} +(-2.10037e9 + 1.03849e9i) q^{26} +(-1.36775e9 - 1.36775e9i) q^{27} +(1.44927e9 - 1.89685e9i) q^{28} +(-1.19882e9 + 1.19882e9i) q^{29} +(6.66120e9 + 2.25348e9i) q^{30} -1.72398e9 q^{31} +(3.65883e8 - 6.06297e9i) q^{32} -7.99659e9 q^{33} +(-9.10358e9 - 3.07974e9i) q^{34} +(1.22457e10 - 1.22457e10i) q^{35} +(5.70570e8 - 7.46778e8i) q^{36} +(1.50899e10 + 1.50899e10i) q^{37} +(-6.28136e9 + 3.10571e9i) q^{38} +3.38429e10i q^{39} +(8.46243e9 - 4.32449e10i) q^{40} +1.44847e10i q^{41} +(-1.52818e10 - 3.09078e10i) q^{42} +(-3.22186e10 - 3.22186e10i) q^{43} +(6.64342e9 + 4.96669e10i) q^{44} +(4.82105e9 - 4.82105e9i) q^{45} +(2.90146e10 - 8.57658e10i) q^{46} -2.71199e10 q^{47} +(-7.61589e10 - 4.35509e10i) q^{48} +1.19760e10 q^{49} +(6.70384e10 - 1.98162e11i) q^{50} +(-9.81542e10 + 9.81542e10i) q^{51} +(2.10199e11 - 2.81160e10i) q^{52} +(-6.71571e9 - 6.71571e9i) q^{53} +(7.75948e10 + 1.56937e11i) q^{54} +3.63529e11i q^{55} +(-1.79273e11 + 1.20593e11i) q^{56} +1.01211e11i q^{57} +(1.37554e11 - 6.80111e10i) q^{58} +(1.48641e11 + 1.48641e11i) q^{59} +(-5.05746e11 - 3.86411e11i) q^{60} +(-5.33654e11 + 5.33654e11i) q^{61} +(1.47808e11 + 5.00033e10i) q^{62} -3.34298e10 q^{63} +(-2.07224e11 + 5.09205e11i) q^{64} +1.53851e12 q^{65} +(6.85599e11 + 2.31938e11i) q^{66} +(4.15581e11 - 4.15581e11i) q^{67} +(6.91181e11 + 5.28092e11i) q^{68} +(-9.24721e11 - 9.24721e11i) q^{69} +(-1.40508e12 + 6.94718e11i) q^{70} -1.42662e12i q^{71} +(-7.05786e10 + 4.74768e10i) q^{72} +9.89656e11i q^{73} +(-8.56079e11 - 1.73143e12i) q^{74} +(-2.13657e12 - 2.13657e12i) q^{75} +(6.28621e11 - 8.40839e10i) q^{76} +(1.26038e12 - 1.26038e12i) q^{77} +(9.81602e11 - 2.90157e12i) q^{78} -2.98138e12 q^{79} +(-1.97984e12 + 3.46222e12i) q^{80} +2.71161e12 q^{81} +(4.20123e11 - 1.24187e12i) q^{82} +(-2.36903e10 + 2.36903e10i) q^{83} +(4.13740e11 + 3.09316e12i) q^{84} +(4.46213e12 + 4.46213e12i) q^{85} +(1.82782e12 + 3.69680e12i) q^{86} -2.21639e12i q^{87} +(8.70990e11 - 4.45096e12i) q^{88} -3.85073e12i q^{89} +(-5.53172e11 + 2.73507e11i) q^{90} +(-5.33413e12 - 5.33413e12i) q^{91} +(-4.97522e12 + 6.51170e12i) q^{92} +(1.59365e12 - 1.59365e12i) q^{93} +(2.32517e12 + 7.86604e11i) q^{94} +4.60108e12 q^{95} +(5.26641e12 + 5.94286e12i) q^{96} -8.08912e12 q^{97} +(-1.02678e12 - 3.47360e11i) q^{98} +(4.96203e11 - 4.96203e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 50 q - 2 q^{2} - 2 q^{3} + 360 q^{4} - 2 q^{5} - 255056 q^{6} - 1076876 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 50 q - 2 q^{2} - 2 q^{3} + 360 q^{4} - 2 q^{5} - 255056 q^{6} - 1076876 q^{8} + 1809804 q^{10} - 4723998 q^{11} - 36466556 q^{12} - 2 q^{13} - 32192740 q^{14} + 91124996 q^{15} + 49054360 q^{16} - 4 q^{17} - 134185218 q^{18} + 422008902 q^{19} - 337515748 q^{20} + 3188644 q^{21} + 747130500 q^{22} + 4015997104 q^{24} - 7112421624 q^{26} - 2068699784 q^{27} + 10814980184 q^{28} - 3661663834 q^{29} - 7391197164 q^{30} - 10650044176 q^{31} + 161064008 q^{32} - 4 q^{33} + 21518457652 q^{34} + 7767977276 q^{35} - 45856853012 q^{36} + 21527986470 q^{37} + 42250712128 q^{38} + 62168140552 q^{40} - 221492896520 q^{42} - 18577860182 q^{43} + 260848874692 q^{44} + 2438217602 q^{45} - 86330105076 q^{46} + 215584306576 q^{47} - 204935679512 q^{48} - 525968913642 q^{49} + 726765984390 q^{50} - 551664571452 q^{51} - 560232726988 q^{52} + 223019793366 q^{53} + 183832923424 q^{54} + 377498473624 q^{56} + 770591295576 q^{58} + 1167423209882 q^{59} - 1652643345408 q^{60} + 81543039150 q^{61} + 1409787089968 q^{62} - 862914002556 q^{63} + 1414847226240 q^{64} - 27850095516 q^{65} - 4165850751116 q^{66} + 1390089097910 q^{67} + 1936048158032 q^{68} - 168685276844 q^{69} - 1514955295360 q^{70} - 931909002396 q^{72} + 2967549191692 q^{74} - 1675683188954 q^{75} - 6006275999532 q^{76} - 2147852144860 q^{77} + 33537158300 q^{78} + 8517123343488 q^{79} + 3800056341544 q^{80} - 9602604240358 q^{81} - 1354092283296 q^{82} + 2192965629438 q^{83} + 6692487540136 q^{84} + 2809965843748 q^{85} - 2175364294396 q^{86} - 2008707597832 q^{88} + 1744037438232 q^{90} + 3291182399236 q^{91} + 5983522987064 q^{92} + 3412032366928 q^{93} - 10384516980592 q^{94} + 7322122332660 q^{95} - 22107121515856 q^{96} - 4 q^{97} + 27036562854554 q^{98} + 19363874529854 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −85.7364 29.0046i −0.947262 0.320459i
\(3\) −924.404 + 924.404i −0.732105 + 0.732105i −0.971037 0.238931i \(-0.923203\pi\)
0.238931 + 0.971037i \(0.423203\pi\)
\(4\) 6509.46 + 4973.51i 0.794612 + 0.607118i
\(5\) 42023.8 + 42023.8i 1.20279 + 1.20279i 0.973314 + 0.229478i \(0.0737018\pi\)
0.229478 + 0.973314i \(0.426298\pi\)
\(6\) 106067. 52443.1i 0.928106 0.458886i
\(7\) 291398.i 0.936159i −0.883686 0.468080i \(-0.844946\pi\)
0.883686 0.468080i \(-0.155054\pi\)
\(8\) −413843. 615215.i −0.558150 0.829740i
\(9\) 114722.i 0.0719565i
\(10\) −2.38408e6 4.82186e6i −0.753914 1.52480i
\(11\) 4.32527e6 + 4.32527e6i 0.736141 + 0.736141i 0.971829 0.235688i \(-0.0757344\pi\)
−0.235688 + 0.971829i \(0.575734\pi\)
\(12\) −1.06149e7 + 1.41984e6i −1.02621 + 0.137266i
\(13\) 1.83053e7 1.83053e7i 1.05183 1.05183i 0.0532455 0.998581i \(-0.483043\pi\)
0.998581 0.0532455i \(-0.0169566\pi\)
\(14\) −8.45191e6 + 2.49834e7i −0.300001 + 0.886789i
\(15\) −7.76939e7 −1.76114
\(16\) 1.76373e7 + 6.47497e7i 0.262816 + 0.964846i
\(17\) 1.06181e8 1.06691 0.533457 0.845827i \(-0.320893\pi\)
0.533457 + 0.845827i \(0.320893\pi\)
\(18\) −3.32747e6 + 9.83584e6i −0.0230591 + 0.0681617i
\(19\) 5.47438e7 5.47438e7i 0.266954 0.266954i −0.560918 0.827872i \(-0.689552\pi\)
0.827872 + 0.560918i \(0.189552\pi\)
\(20\) 6.45466e7 + 4.82558e8i 0.225517 + 1.68599i
\(21\) 2.69370e8 + 2.69370e8i 0.685367 + 0.685367i
\(22\) −2.45380e8 4.96286e8i −0.461415 0.933221i
\(23\) 1.00034e9i 1.40902i 0.709692 + 0.704512i \(0.248834\pi\)
−0.709692 + 0.704512i \(0.751166\pi\)
\(24\) 9.51265e8 + 1.86149e8i 1.01608 + 0.198833i
\(25\) 2.31130e9i 1.89342i
\(26\) −2.10037e9 + 1.03849e9i −1.33342 + 0.659289i
\(27\) −1.36775e9 1.36775e9i −0.679426 0.679426i
\(28\) 1.44927e9 1.89685e9i 0.568359 0.743884i
\(29\) −1.19882e9 + 1.19882e9i −0.374254 + 0.374254i −0.869024 0.494770i \(-0.835252\pi\)
0.494770 + 0.869024i \(0.335252\pi\)
\(30\) 6.66120e9 + 2.25348e9i 1.66826 + 0.564373i
\(31\) −1.72398e9 −0.348883 −0.174442 0.984668i \(-0.555812\pi\)
−0.174442 + 0.984668i \(0.555812\pi\)
\(32\) 3.65883e8 6.06297e9i 0.0602375 0.998184i
\(33\) −7.99659e9 −1.07787
\(34\) −9.10358e9 3.07974e9i −1.01065 0.341902i
\(35\) 1.22457e10 1.22457e10i 1.12600 1.12600i
\(36\) 5.70570e8 7.46778e8i 0.0436860 0.0571775i
\(37\) 1.50899e10 + 1.50899e10i 0.966888 + 0.966888i 0.999469 0.0325811i \(-0.0103727\pi\)
−0.0325811 + 0.999469i \(0.510373\pi\)
\(38\) −6.28136e9 + 3.10571e9i −0.338423 + 0.167328i
\(39\) 3.38429e10i 1.54010i
\(40\) 8.46243e9 4.32449e10i 0.326667 1.66934i
\(41\) 1.44847e10i 0.476227i 0.971237 + 0.238114i \(0.0765290\pi\)
−0.971237 + 0.238114i \(0.923471\pi\)
\(42\) −1.52818e10 3.09078e10i −0.429591 0.868855i
\(43\) −3.22186e10 3.22186e10i −0.777252 0.777252i 0.202110 0.979363i \(-0.435220\pi\)
−0.979363 + 0.202110i \(0.935220\pi\)
\(44\) 6.64342e9 + 4.96669e10i 0.138022 + 1.03187i
\(45\) 4.82105e9 4.82105e9i 0.0865486 0.0865486i
\(46\) 2.90146e10 8.57658e10i 0.451534 1.33471i
\(47\) −2.71199e10 −0.366989 −0.183494 0.983021i \(-0.558741\pi\)
−0.183494 + 0.983021i \(0.558741\pi\)
\(48\) −7.61589e10 4.35509e10i −0.898778 0.513960i
\(49\) 1.19760e10 0.123605
\(50\) 6.70384e10 1.98162e11i 0.606762 1.79356i
\(51\) −9.81542e10 + 9.81542e10i −0.781093 + 0.781093i
\(52\) 2.10199e11 2.81160e10i 1.47438 0.197212i
\(53\) −6.71571e9 6.71571e9i −0.0416197 0.0416197i 0.685991 0.727610i \(-0.259369\pi\)
−0.727610 + 0.685991i \(0.759369\pi\)
\(54\) 7.75948e10 + 1.56937e11i 0.425866 + 0.861322i
\(55\) 3.63529e11i 1.77085i
\(56\) −1.79273e11 + 1.20593e11i −0.776769 + 0.522517i
\(57\) 1.01211e11i 0.390877i
\(58\) 1.37554e11 6.80111e10i 0.474450 0.234584i
\(59\) 1.48641e11 + 1.48641e11i 0.458776 + 0.458776i 0.898253 0.439478i \(-0.144837\pi\)
−0.439478 + 0.898253i \(0.644837\pi\)
\(60\) −5.05746e11 3.86411e11i −1.39942 1.06922i
\(61\) −5.33654e11 + 5.33654e11i −1.32622 + 1.32622i −0.417580 + 0.908640i \(0.637122\pi\)
−0.908640 + 0.417580i \(0.862878\pi\)
\(62\) 1.47808e11 + 5.00033e10i 0.330484 + 0.111803i
\(63\) −3.34298e10 −0.0673627
\(64\) −2.07224e11 + 5.09205e11i −0.376938 + 0.926239i
\(65\) 1.53851e12 2.53026
\(66\) 6.85599e11 + 2.31938e11i 1.02102 + 0.345412i
\(67\) 4.15581e11 4.15581e11i 0.561267 0.561267i −0.368400 0.929667i \(-0.620094\pi\)
0.929667 + 0.368400i \(0.120094\pi\)
\(68\) 6.91181e11 + 5.28092e11i 0.847782 + 0.647742i
\(69\) −9.24721e11 9.24721e11i −1.03155 1.03155i
\(70\) −1.40508e12 + 6.94718e11i −1.42746 + 0.705783i
\(71\) 1.42662e12i 1.32168i −0.750525 0.660842i \(-0.770199\pi\)
0.750525 0.660842i \(-0.229801\pi\)
\(72\) −7.05786e10 + 4.74768e10i −0.0597052 + 0.0401625i
\(73\) 9.89656e11i 0.765395i 0.923874 + 0.382698i \(0.125005\pi\)
−0.923874 + 0.382698i \(0.874995\pi\)
\(74\) −8.56079e11 1.73143e12i −0.606049 1.22574i
\(75\) −2.13657e12 2.13657e12i −1.38618 1.38618i
\(76\) 6.28621e11 8.40839e10i 0.374197 0.0500523i
\(77\) 1.26038e12 1.26038e12i 0.689145 0.689145i
\(78\) 9.81602e11 2.90157e12i 0.493538 1.45888i
\(79\) −2.98138e12 −1.37988 −0.689941 0.723866i \(-0.742363\pi\)
−0.689941 + 0.723866i \(0.742363\pi\)
\(80\) −1.97984e12 + 3.46222e12i −0.844395 + 1.47662i
\(81\) 2.71161e12 1.06678
\(82\) 4.20123e11 1.24187e12i 0.152611 0.451112i
\(83\) −2.36903e10 + 2.36903e10i −0.00795358 + 0.00795358i −0.711072 0.703119i \(-0.751790\pi\)
0.703119 + 0.711072i \(0.251790\pi\)
\(84\) 4.13740e11 + 3.09316e12i 0.128503 + 0.960700i
\(85\) 4.46213e12 + 4.46213e12i 1.28327 + 1.28327i
\(86\) 1.82782e12 + 3.69680e12i 0.487184 + 0.985339i
\(87\) 2.21639e12i 0.547987i
\(88\) 8.70990e11 4.45096e12i 0.199929 1.02168i
\(89\) 3.85073e12i 0.821312i −0.911790 0.410656i \(-0.865300\pi\)
0.911790 0.410656i \(-0.134700\pi\)
\(90\) −5.53172e11 + 2.73507e11i −0.109720 + 0.0542490i
\(91\) −5.33413e12 5.33413e12i −0.984678 0.984678i
\(92\) −4.97522e12 + 6.51170e12i −0.855443 + 1.11963i
\(93\) 1.59365e12 1.59365e12i 0.255419 0.255419i
\(94\) 2.32517e12 + 7.86604e11i 0.347635 + 0.117605i
\(95\) 4.60108e12 0.642180
\(96\) 5.26641e12 + 5.94286e12i 0.686676 + 0.774876i
\(97\) −8.08912e12 −0.986018 −0.493009 0.870024i \(-0.664103\pi\)
−0.493009 + 0.870024i \(0.664103\pi\)
\(98\) −1.02678e12 3.47360e11i −0.117087 0.0396105i
\(99\) 4.96203e11 4.96203e11i 0.0529701 0.0529701i
\(100\) −1.14953e13 + 1.50453e13i −1.14953 + 1.50453i
\(101\) 6.39323e12 + 6.39323e12i 0.599282 + 0.599282i 0.940122 0.340839i \(-0.110711\pi\)
−0.340839 + 0.940122i \(0.610711\pi\)
\(102\) 1.12623e13 5.56846e12i 0.990208 0.489591i
\(103\) 3.09837e11i 0.0255677i 0.999918 + 0.0127838i \(0.00406933\pi\)
−0.999918 + 0.0127838i \(0.995931\pi\)
\(104\) −1.88372e13 3.68617e12i −1.45982 0.285666i
\(105\) 2.26399e13i 1.64871i
\(106\) 3.80994e11 + 7.70567e11i 0.0260873 + 0.0527621i
\(107\) 9.90971e12 + 9.90971e12i 0.638361 + 0.638361i 0.950151 0.311790i \(-0.100929\pi\)
−0.311790 + 0.950151i \(0.600929\pi\)
\(108\) −2.10080e12 1.57058e13i −0.127388 0.952371i
\(109\) 1.52268e13 1.52268e13i 0.869634 0.869634i −0.122798 0.992432i \(-0.539187\pi\)
0.992432 + 0.122798i \(0.0391866\pi\)
\(110\) 1.05440e13 3.11676e13i 0.567484 1.67746i
\(111\) −2.78984e13 −1.41573
\(112\) 1.88680e13 5.13948e12i 0.903250 0.246038i
\(113\) 1.94386e13 0.878326 0.439163 0.898407i \(-0.355275\pi\)
0.439163 + 0.898407i \(0.355275\pi\)
\(114\) 2.93558e12 8.67744e12i 0.125260 0.370263i
\(115\) −4.20382e13 + 4.20382e13i −1.69476 + 1.69476i
\(116\) −1.37660e13 + 1.84133e12i −0.524603 + 0.0701705i
\(117\) −2.10001e12 2.10001e12i −0.0756858 0.0756858i
\(118\) −8.43266e12 1.70552e13i −0.287562 0.581600i
\(119\) 3.09410e13i 0.998801i
\(120\) 3.21531e13 + 4.77985e13i 0.982980 + 1.46129i
\(121\) 2.89322e12i 0.0838062i
\(122\) 6.12320e13 3.02751e13i 1.68128 0.831279i
\(123\) −1.33897e13 1.33897e13i −0.348648 0.348648i
\(124\) −1.12222e13 8.57421e12i −0.277227 0.211813i
\(125\) −4.58309e13 + 4.58309e13i −1.07459 + 1.07459i
\(126\) 2.86615e12 + 9.69618e11i 0.0638102 + 0.0215870i
\(127\) 3.12369e13 0.660609 0.330304 0.943874i \(-0.392849\pi\)
0.330304 + 0.943874i \(0.392849\pi\)
\(128\) 3.25359e13 3.76470e13i 0.653881 0.756598i
\(129\) 5.95660e13 1.13806
\(130\) −1.31907e14 4.46241e13i −2.39682 0.810844i
\(131\) −6.22998e12 + 6.22998e12i −0.107702 + 0.107702i −0.758904 0.651202i \(-0.774265\pi\)
0.651202 + 0.758904i \(0.274265\pi\)
\(132\) −5.20535e13 3.97711e13i −0.856484 0.654391i
\(133\) −1.59522e13 1.59522e13i −0.249911 0.249911i
\(134\) −4.76842e13 + 2.35767e13i −0.711531 + 0.351804i
\(135\) 1.14956e14i 1.63441i
\(136\) −4.39423e13 6.53242e13i −0.595497 0.885261i
\(137\) 7.41395e13i 0.958001i 0.877815 + 0.479001i \(0.159001\pi\)
−0.877815 + 0.479001i \(0.840999\pi\)
\(138\) 5.24611e13 + 1.06103e14i 0.646581 + 1.30772i
\(139\) 3.82711e13 + 3.82711e13i 0.450065 + 0.450065i 0.895376 0.445311i \(-0.146907\pi\)
−0.445311 + 0.895376i \(0.646907\pi\)
\(140\) 1.40617e14 1.88088e13i 1.57835 0.211120i
\(141\) 2.50698e13 2.50698e13i 0.268674 0.268674i
\(142\) −4.13785e13 + 1.22313e14i −0.423546 + 1.25198i
\(143\) 1.58350e14 1.54859
\(144\) 7.42821e12 2.02338e12i 0.0694269 0.0189113i
\(145\) −1.00758e14 −0.900299
\(146\) 2.87046e13 8.48496e13i 0.245278 0.725030i
\(147\) −1.10707e13 + 1.10707e13i −0.0904922 + 0.0904922i
\(148\) 2.31774e13 + 1.73277e14i 0.181286 + 1.35532i
\(149\) −1.55729e14 1.55729e14i −1.16589 1.16589i −0.983163 0.182732i \(-0.941506\pi\)
−0.182732 0.983163i \(-0.558494\pi\)
\(150\) 1.21212e14 + 2.45153e14i 0.868862 + 1.75729i
\(151\) 2.42011e14i 1.66144i 0.556688 + 0.830722i \(0.312072\pi\)
−0.556688 + 0.830722i \(0.687928\pi\)
\(152\) −5.63345e13 1.10239e13i −0.370503 0.0725021i
\(153\) 1.21813e13i 0.0767713i
\(154\) −1.44617e14 + 7.15034e13i −0.873644 + 0.431958i
\(155\) −7.24481e13 7.24481e13i −0.419634 0.419634i
\(156\) −1.68318e14 + 2.20299e14i −0.935020 + 1.22378i
\(157\) 2.23533e13 2.23533e13i 0.119122 0.119122i −0.645033 0.764155i \(-0.723156\pi\)
0.764155 + 0.645033i \(0.223156\pi\)
\(158\) 2.55613e14 + 8.64740e13i 1.30711 + 0.442195i
\(159\) 1.24160e13 0.0609400
\(160\) 2.70165e14 2.39413e14i 1.27306 1.12815i
\(161\) 2.91498e14 1.31907
\(162\) −2.32484e14 7.86492e13i −1.01052 0.341859i
\(163\) 6.71579e13 6.71579e13i 0.280464 0.280464i −0.552830 0.833294i \(-0.686452\pi\)
0.833294 + 0.552830i \(0.186452\pi\)
\(164\) −7.20397e13 + 9.42875e13i −0.289126 + 0.378416i
\(165\) −3.36047e14 3.36047e14i −1.29645 1.29645i
\(166\) 2.71825e12 1.34399e12i 0.0100829 0.00498533i
\(167\) 1.73881e14i 0.620291i 0.950689 + 0.310145i \(0.100378\pi\)
−0.950689 + 0.310145i \(0.899622\pi\)
\(168\) 5.42436e13 2.77197e14i 0.186139 0.951214i
\(169\) 3.67291e14i 1.21268i
\(170\) −2.53145e14 5.11990e14i −0.804360 1.62683i
\(171\) −6.28031e12 6.28031e12i −0.0192091 0.0192091i
\(172\) −4.94863e13 3.69965e14i −0.145730 1.08950i
\(173\) 1.11847e14 1.11847e14i 0.317194 0.317194i −0.530494 0.847688i \(-0.677994\pi\)
0.847688 + 0.530494i \(0.177994\pi\)
\(174\) −6.42855e13 + 1.90025e14i −0.175607 + 0.519087i
\(175\) 6.73508e14 1.77254
\(176\) −2.03774e14 + 3.56346e14i −0.516792 + 0.903732i
\(177\) −2.74808e14 −0.671744
\(178\) −1.11689e14 + 3.30148e14i −0.263197 + 0.777998i
\(179\) −1.09595e14 + 1.09595e14i −0.249027 + 0.249027i −0.820571 0.571544i \(-0.806345\pi\)
0.571544 + 0.820571i \(0.306345\pi\)
\(180\) 5.53600e13 7.40491e12i 0.121318 0.0162274i
\(181\) −5.44950e14 5.44950e14i −1.15198 1.15198i −0.986155 0.165828i \(-0.946970\pi\)
−0.165828 0.986155i \(-0.553030\pi\)
\(182\) 3.02614e14 + 6.12043e14i 0.617199 + 1.24830i
\(183\) 9.86623e14i 1.94187i
\(184\) 6.15427e14 4.13985e14i 1.16912 0.786446i
\(185\) 1.26827e15i 2.32593i
\(186\) −1.82857e14 + 9.04106e13i −0.323801 + 0.160098i
\(187\) 4.59262e14 + 4.59262e14i 0.785398 + 0.785398i
\(188\) −1.76536e14 1.34881e14i −0.291614 0.222805i
\(189\) −3.98560e14 + 3.98560e14i −0.636051 + 0.636051i
\(190\) −3.94480e14 1.33453e14i −0.608313 0.205792i
\(191\) 5.05178e14 0.752883 0.376441 0.926440i \(-0.377148\pi\)
0.376441 + 0.926440i \(0.377148\pi\)
\(192\) −2.79153e14 6.62270e14i −0.402146 0.954062i
\(193\) 7.87991e14 1.09749 0.548743 0.835991i \(-0.315107\pi\)
0.548743 + 0.835991i \(0.315107\pi\)
\(194\) 6.93532e14 + 2.34622e14i 0.934018 + 0.315978i
\(195\) −1.42221e15 + 1.42221e15i −1.85241 + 1.85241i
\(196\) 7.79574e13 + 5.95628e13i 0.0982184 + 0.0750430i
\(197\) −1.52484e14 1.52484e14i −0.185864 0.185864i 0.608041 0.793905i \(-0.291955\pi\)
−0.793905 + 0.608041i \(0.791955\pi\)
\(198\) −5.69349e13 + 2.81505e13i −0.0671513 + 0.0332018i
\(199\) 2.55993e14i 0.292202i −0.989270 0.146101i \(-0.953328\pi\)
0.989270 0.146101i \(-0.0466724\pi\)
\(200\) 1.42195e15 9.56514e14i 1.57104 1.05681i
\(201\) 7.68330e14i 0.821814i
\(202\) −3.62699e14 7.33566e14i −0.375632 0.759723i
\(203\) 3.49334e14 + 3.49334e14i 0.350362 + 0.350362i
\(204\) −1.12710e15 + 1.50760e14i −1.09488 + 0.146450i
\(205\) −6.08702e14 + 6.08702e14i −0.572802 + 0.572802i
\(206\) 8.98671e12 2.65643e13i 0.00819339 0.0242193i
\(207\) 1.14761e14 0.101388
\(208\) 1.50812e15 + 8.62405e14i 1.29129 + 0.738414i
\(209\) 4.73563e14 0.393031
\(210\) 6.56662e14 1.94106e15i 0.528343 1.56176i
\(211\) −1.72385e15 + 1.72385e15i −1.34482 + 1.34482i −0.453631 + 0.891190i \(0.649871\pi\)
−0.891190 + 0.453631i \(0.850129\pi\)
\(212\) −1.03150e13 7.71162e13i −0.00780345 0.0583395i
\(213\) 1.31877e15 + 1.31877e15i 0.967612 + 0.967612i
\(214\) −5.62195e14 1.13705e15i −0.400127 0.809264i
\(215\) 2.70790e15i 1.86975i
\(216\) −2.75427e14 + 1.40749e15i −0.184526 + 0.942968i
\(217\) 5.02364e14i 0.326611i
\(218\) −1.74714e15 + 8.63843e14i −1.10245 + 0.545089i
\(219\) −9.14842e14 9.14842e14i −0.560350 0.560350i
\(220\) −1.80801e15 + 2.36638e15i −1.07511 + 1.40714i
\(221\) 1.94367e15 1.94367e15i 1.12221 1.12221i
\(222\) 2.39191e15 + 8.09183e14i 1.34107 + 0.453683i
\(223\) −9.02602e14 −0.491490 −0.245745 0.969335i \(-0.579033\pi\)
−0.245745 + 0.969335i \(0.579033\pi\)
\(224\) −1.76674e15 1.06618e14i −0.934459 0.0563919i
\(225\) 2.65156e14 0.136243
\(226\) −1.66660e15 5.63810e14i −0.832005 0.281467i
\(227\) 1.45252e15 1.45252e15i 0.704617 0.704617i −0.260781 0.965398i \(-0.583980\pi\)
0.965398 + 0.260781i \(0.0839799\pi\)
\(228\) −5.03372e14 + 6.58827e14i −0.237308 + 0.310595i
\(229\) −2.34526e15 2.34526e15i −1.07463 1.07463i −0.996981 0.0776511i \(-0.975258\pi\)
−0.0776511 0.996981i \(-0.524742\pi\)
\(230\) 4.82351e15 2.38490e15i 2.14849 1.06228i
\(231\) 2.33019e15i 1.00905i
\(232\) 1.23365e15 + 2.41409e14i 0.519423 + 0.101644i
\(233\) 4.63366e14i 0.189719i 0.995491 + 0.0948594i \(0.0302402\pi\)
−0.995491 + 0.0948594i \(0.969760\pi\)
\(234\) 1.19138e14 + 2.40958e14i 0.0474401 + 0.0959485i
\(235\) −1.13968e15 1.13968e15i −0.441411 0.441411i
\(236\) 2.28306e14 + 1.70684e15i 0.0860178 + 0.643079i
\(237\) 2.75600e15 2.75600e15i 1.01022 1.01022i
\(238\) −8.97432e14 + 2.65277e15i −0.320075 + 0.946126i
\(239\) 3.53103e15 1.22550 0.612752 0.790275i \(-0.290062\pi\)
0.612752 + 0.790275i \(0.290062\pi\)
\(240\) −1.37031e15 5.03066e15i −0.462857 1.69923i
\(241\) 1.38870e15 0.456559 0.228279 0.973596i \(-0.426690\pi\)
0.228279 + 0.973596i \(0.426690\pi\)
\(242\) 8.39167e13 2.48054e14i 0.0268565 0.0793865i
\(243\) −3.25988e14 + 3.25988e14i −0.101569 + 0.101569i
\(244\) −6.12793e15 + 8.19668e14i −1.85900 + 0.248659i
\(245\) 5.03277e14 + 5.03277e14i 0.148672 + 0.148672i
\(246\) 7.59621e14 + 1.53635e15i 0.218534 + 0.441989i
\(247\) 2.00420e15i 0.561578i
\(248\) 7.13456e14 + 1.06062e15i 0.194729 + 0.289483i
\(249\) 4.37988e13i 0.0116457i
\(250\) 5.25869e15 2.60007e15i 1.36228 0.673558i
\(251\) −4.14200e15 4.14200e15i −1.04552 1.04552i −0.998914 0.0466021i \(-0.985161\pi\)
−0.0466021 0.998914i \(-0.514839\pi\)
\(252\) −2.17610e14 1.66263e14i −0.0535272 0.0408971i
\(253\) −4.32676e15 + 4.32676e15i −1.03724 + 1.03724i
\(254\) −2.67814e15 9.06016e14i −0.625770 0.211698i
\(255\) −8.24962e15 −1.87898
\(256\) −3.88145e15 + 2.28402e15i −0.861855 + 0.507155i
\(257\) 1.34905e15 0.292054 0.146027 0.989281i \(-0.453351\pi\)
0.146027 + 0.989281i \(0.453351\pi\)
\(258\) −5.10698e15 1.72769e15i −1.07804 0.364702i
\(259\) 4.39718e15 4.39718e15i 0.905161 0.905161i
\(260\) 1.00149e16 + 7.65181e15i 2.01057 + 1.53616i
\(261\) 1.37531e14 + 1.37531e14i 0.0269300 + 0.0269300i
\(262\) 7.14834e14 3.53438e14i 0.136536 0.0675079i
\(263\) 8.03771e14i 0.149768i −0.997192 0.0748842i \(-0.976141\pi\)
0.997192 0.0748842i \(-0.0238587\pi\)
\(264\) 3.30933e15 + 4.91963e15i 0.601610 + 0.894348i
\(265\) 5.64439e14i 0.100120i
\(266\) 9.04999e14 + 1.83038e15i 0.156645 + 0.316818i
\(267\) 3.55963e15 + 3.55963e15i 0.601287 + 0.601287i
\(268\) 4.77211e15 6.38314e14i 0.786745 0.105234i
\(269\) 1.50784e14 1.50784e14i 0.0242641 0.0242641i −0.694871 0.719135i \(-0.744538\pi\)
0.719135 + 0.694871i \(0.244538\pi\)
\(270\) −3.33426e15 + 9.85592e15i −0.523763 + 1.54822i
\(271\) 4.54743e15 0.697374 0.348687 0.937239i \(-0.386628\pi\)
0.348687 + 0.937239i \(0.386628\pi\)
\(272\) 1.87275e15 + 6.87519e15i 0.280402 + 1.02941i
\(273\) 9.86177e15 1.44178
\(274\) 2.15039e15 6.35646e15i 0.307000 0.907479i
\(275\) −9.99699e15 + 9.99699e15i −1.39382 + 1.39382i
\(276\) −1.42033e15 1.06185e16i −0.193410 1.44596i
\(277\) 6.40360e15 + 6.40360e15i 0.851738 + 0.851738i 0.990347 0.138610i \(-0.0442633\pi\)
−0.138610 + 0.990347i \(0.544263\pi\)
\(278\) −2.17119e15 4.39127e15i −0.282102 0.570557i
\(279\) 1.97778e14i 0.0251044i
\(280\) −1.26015e16 2.46594e15i −1.56277 0.305812i
\(281\) 6.28478e15i 0.761551i 0.924668 + 0.380776i \(0.124343\pi\)
−0.924668 + 0.380776i \(0.875657\pi\)
\(282\) −2.87653e15 + 1.42225e15i −0.340604 + 0.168406i
\(283\) −4.09687e15 4.09687e15i −0.474068 0.474068i 0.429160 0.903228i \(-0.358810\pi\)
−0.903228 + 0.429160i \(0.858810\pi\)
\(284\) 7.09528e15 9.28650e15i 0.802418 1.05023i
\(285\) −4.25326e15 + 4.25326e15i −0.470143 + 0.470143i
\(286\) −1.35764e16 4.59290e15i −1.46692 0.496258i
\(287\) 4.22082e15 0.445825
\(288\) −6.95555e14 4.19748e13i −0.0718258 0.00433448i
\(289\) 1.36984e15 0.138303
\(290\) 8.63862e15 + 2.92245e15i 0.852820 + 0.288509i
\(291\) 7.47761e15 7.47761e15i 0.721869 0.721869i
\(292\) −4.92206e15 + 6.44213e15i −0.464685 + 0.608192i
\(293\) −1.27827e16 1.27827e16i −1.18028 1.18028i −0.979672 0.200607i \(-0.935709\pi\)
−0.200607 0.979672i \(-0.564291\pi\)
\(294\) 1.27026e15 6.28058e14i 0.114719 0.0567208i
\(295\) 1.24929e16i 1.10362i
\(296\) 3.03869e15 1.55284e16i 0.262598 1.34193i
\(297\) 1.18318e16i 1.00031i
\(298\) 8.83479e15 + 1.78685e16i 0.730787 + 1.47803i
\(299\) 1.83116e16 + 1.83116e16i 1.48205 + 1.48205i
\(300\) −3.28168e15 2.45342e16i −0.259901 1.94305i
\(301\) −9.38845e15 + 9.38845e15i −0.727632 + 0.727632i
\(302\) 7.01945e15 2.07492e16i 0.532425 1.57382i
\(303\) −1.18199e16 −0.877475
\(304\) 4.51017e15 + 2.57911e15i 0.327729 + 0.187409i
\(305\) −4.48523e16 −3.19033
\(306\) −3.53314e14 + 1.04438e15i −0.0246021 + 0.0727226i
\(307\) 1.67312e16 1.67312e16i 1.14059 1.14059i 0.152243 0.988343i \(-0.451350\pi\)
0.988343 0.152243i \(-0.0486496\pi\)
\(308\) 1.44729e16 1.93588e15i 0.965995 0.129211i
\(309\) −2.86414e14 2.86414e14i −0.0187182 0.0187182i
\(310\) 4.11011e15 + 8.31277e15i 0.263028 + 0.531979i
\(311\) 1.20045e16i 0.752320i 0.926555 + 0.376160i \(0.122756\pi\)
−0.926555 + 0.376160i \(0.877244\pi\)
\(312\) 2.08207e16 1.40057e16i 1.27788 0.859604i
\(313\) 1.97409e16i 1.18667i −0.804957 0.593333i \(-0.797812\pi\)
0.804957 0.593333i \(-0.202188\pi\)
\(314\) −2.56484e15 + 1.26814e15i −0.151014 + 0.0746664i
\(315\) −1.40485e15 1.40485e15i −0.0810233 0.0810233i
\(316\) −1.94072e16 1.48279e16i −1.09647 0.837750i
\(317\) 2.15261e16 2.15261e16i 1.19146 1.19146i 0.214804 0.976657i \(-0.431089\pi\)
0.976657 0.214804i \(-0.0689112\pi\)
\(318\) −1.06451e15 3.60123e14i −0.0577261 0.0195288i
\(319\) −1.03704e16 −0.551007
\(320\) −3.01071e16 + 1.26904e16i −1.56745 + 0.660694i
\(321\) −1.83211e16 −0.934695
\(322\) −2.49920e16 8.45481e15i −1.24951 0.422708i
\(323\) 5.81275e15 5.81275e15i 0.284817 0.284817i
\(324\) 1.76511e16 + 1.34862e16i 0.847675 + 0.647660i
\(325\) 4.23089e16 + 4.23089e16i 1.99155 + 1.99155i
\(326\) −7.70577e15 + 3.80999e15i −0.355551 + 0.175796i
\(327\) 2.81514e16i 1.27333i
\(328\) 8.91120e15 5.99439e15i 0.395145 0.265806i
\(329\) 7.90270e15i 0.343560i
\(330\) 1.90646e16 + 3.85584e16i 0.812617 + 1.64353i
\(331\) 1.99518e16 + 1.99518e16i 0.833874 + 0.833874i 0.988044 0.154170i \(-0.0492704\pi\)
−0.154170 + 0.988044i \(0.549270\pi\)
\(332\) −2.72035e14 + 3.63872e13i −0.0111488 + 0.00149125i
\(333\) 1.73115e15 1.73115e15i 0.0695738 0.0695738i
\(334\) 5.04336e15 1.49079e16i 0.198778 0.587578i
\(335\) 3.49286e16 1.35018
\(336\) −1.26907e16 + 2.21926e16i −0.481148 + 0.841400i
\(337\) −1.76153e16 −0.655081 −0.327541 0.944837i \(-0.606220\pi\)
−0.327541 + 0.944837i \(0.606220\pi\)
\(338\) −1.06531e16 + 3.14902e16i −0.388614 + 1.14873i
\(339\) −1.79691e16 + 1.79691e16i −0.643027 + 0.643027i
\(340\) 6.85363e15 + 5.12385e16i 0.240607 + 1.79880i
\(341\) −7.45666e15 7.45666e15i −0.256827 0.256827i
\(342\) 3.56293e14 + 7.20609e14i 0.0120403 + 0.0243517i
\(343\) 3.17231e16i 1.05187i
\(344\) −6.48794e15 + 3.31548e16i −0.211094 + 1.07874i
\(345\) 7.77206e16i 2.48149i
\(346\) −1.28335e16 + 6.34528e15i −0.402114 + 0.198818i
\(347\) −3.87727e16 3.87727e16i −1.19230 1.19230i −0.976421 0.215875i \(-0.930740\pi\)
−0.215875 0.976421i \(-0.569260\pi\)
\(348\) 1.10232e16 1.44275e16i 0.332692 0.435437i
\(349\) 1.63775e16 1.63775e16i 0.485156 0.485156i −0.421618 0.906774i \(-0.638538\pi\)
0.906774 + 0.421618i \(0.138538\pi\)
\(350\) −5.77442e16 1.95349e16i −1.67906 0.568026i
\(351\) −5.00740e16 −1.42928
\(352\) 2.78065e16 2.46414e16i 0.779147 0.690461i
\(353\) 7.04122e14 0.0193692 0.00968461 0.999953i \(-0.496917\pi\)
0.00968461 + 0.999953i \(0.496917\pi\)
\(354\) 2.35611e16 + 7.97072e15i 0.636318 + 0.215266i
\(355\) 5.99518e16 5.99518e16i 1.58971 1.58971i
\(356\) 1.91516e16 2.50662e16i 0.498633 0.652624i
\(357\) 2.86020e16 + 2.86020e16i 0.731227 + 0.731227i
\(358\) 1.25751e16 6.21754e15i 0.315697 0.156091i
\(359\) 4.92203e15i 0.121347i 0.998158 + 0.0606736i \(0.0193249\pi\)
−0.998158 + 0.0606736i \(0.980675\pi\)
\(360\) −4.96114e15 9.70826e14i −0.120120 0.0235058i
\(361\) 3.60592e16i 0.857471i
\(362\) 3.09160e16 + 6.25281e16i 0.722067 + 1.46039i
\(363\) −2.67450e15 2.67450e15i −0.0613550 0.0613550i
\(364\) −8.19297e15 6.12516e16i −0.184622 1.38025i
\(365\) −4.15891e16 + 4.15891e16i −0.920611 + 0.920611i
\(366\) −2.86167e16 + 8.45895e16i −0.622289 + 1.83946i
\(367\) −3.78453e14 −0.00808505 −0.00404253 0.999992i \(-0.501287\pi\)
−0.00404253 + 0.999992i \(0.501287\pi\)
\(368\) −6.47719e16 + 1.76434e16i −1.35949 + 0.370314i
\(369\) 1.66171e15 0.0342676
\(370\) 3.67858e16 1.08737e17i 0.745365 2.20327i
\(371\) −1.95695e15 + 1.95695e15i −0.0389626 + 0.0389626i
\(372\) 1.82998e16 2.44777e15i 0.358029 0.0478897i
\(373\) −1.10572e16 1.10572e16i −0.212587 0.212587i 0.592778 0.805366i \(-0.298031\pi\)
−0.805366 + 0.592778i \(0.798031\pi\)
\(374\) −2.60547e16 5.26962e16i −0.492290 0.995666i
\(375\) 8.47326e16i 1.57343i
\(376\) 1.12234e16 + 1.66846e16i 0.204835 + 0.304505i
\(377\) 4.38894e16i 0.787301i
\(378\) 4.57312e16 2.26110e16i 0.806335 0.398679i
\(379\) 7.09339e16 + 7.09339e16i 1.22942 + 1.22942i 0.964185 + 0.265232i \(0.0854486\pi\)
0.265232 + 0.964185i \(0.414551\pi\)
\(380\) 2.99506e16 + 2.28835e16i 0.510284 + 0.389879i
\(381\) −2.88755e16 + 2.88755e16i −0.483635 + 0.483635i
\(382\) −4.33121e16 1.46525e16i −0.713177 0.241268i
\(383\) −8.10892e16 −1.31272 −0.656358 0.754449i \(-0.727904\pi\)
−0.656358 + 0.754449i \(0.727904\pi\)
\(384\) 4.72465e15 + 6.48773e16i 0.0751998 + 1.03262i
\(385\) 1.05932e17 1.65780
\(386\) −6.75595e16 2.28554e16i −1.03961 0.351699i
\(387\) −3.69618e15 + 3.69618e15i −0.0559283 + 0.0559283i
\(388\) −5.26558e16 4.02313e16i −0.783502 0.598629i
\(389\) −7.58407e16 7.58407e16i −1.10976 1.10976i −0.993181 0.116580i \(-0.962807\pi\)
−0.116580 0.993181i \(-0.537193\pi\)
\(390\) 1.63186e17 8.06844e16i 2.34835 1.16110i
\(391\) 1.06218e17i 1.50331i
\(392\) −4.95619e15 7.36782e15i −0.0689903 0.102560i
\(393\) 1.15180e16i 0.157698i
\(394\) 8.65071e15 + 1.74962e16i 0.116500 + 0.235624i
\(395\) −1.25289e17 1.25289e17i −1.65971 1.65971i
\(396\) 5.69788e15 7.62145e14i 0.0742497 0.00993159i
\(397\) 3.94264e16 3.94264e16i 0.505415 0.505415i −0.407700 0.913116i \(-0.633669\pi\)
0.913116 + 0.407700i \(0.133669\pi\)
\(398\) −7.42498e15 + 2.19479e16i −0.0936387 + 0.276792i
\(399\) 2.94926e16 0.365923
\(400\) −1.49656e17 + 4.07651e16i −1.82685 + 0.497621i
\(401\) 1.15109e17 1.38251 0.691257 0.722609i \(-0.257057\pi\)
0.691257 + 0.722609i \(0.257057\pi\)
\(402\) 2.22851e16 6.58738e16i 0.263358 0.778473i
\(403\) −3.15579e16 + 3.15579e16i −0.366965 + 0.366965i
\(404\) 9.81971e15 + 7.34133e16i 0.112362 + 0.840032i
\(405\) 1.13952e17 + 1.13952e17i 1.28311 + 1.28311i
\(406\) −1.98183e16 4.00829e16i −0.219608 0.444161i
\(407\) 1.30536e17i 1.42353i
\(408\) 1.01006e17 + 1.97655e16i 1.08407 + 0.212137i
\(409\) 5.16299e16i 0.545381i −0.962102 0.272690i \(-0.912087\pi\)
0.962102 0.272690i \(-0.0879134\pi\)
\(410\) 6.98431e16 3.45327e16i 0.726153 0.359034i
\(411\) −6.85349e16 6.85349e16i −0.701358 0.701358i
\(412\) −1.54098e15 + 2.01687e15i −0.0155226 + 0.0203164i
\(413\) 4.33137e16 4.33137e16i 0.429487 0.429487i
\(414\) −9.83922e15 3.32861e15i −0.0960414 0.0324908i
\(415\) −1.99111e15 −0.0191330
\(416\) −1.04287e17 1.17682e17i −0.986557 1.11328i
\(417\) −7.07559e16 −0.658990
\(418\) −4.06016e16 1.37355e16i −0.372304 0.125950i
\(419\) −9.58800e16 + 9.58800e16i −0.865639 + 0.865639i −0.991986 0.126347i \(-0.959675\pi\)
0.126347 + 0.991986i \(0.459675\pi\)
\(420\) −1.12600e17 + 1.47373e17i −1.00096 + 1.31008i
\(421\) 1.87134e16 + 1.87134e16i 0.163802 + 0.163802i 0.784249 0.620447i \(-0.213049\pi\)
−0.620447 + 0.784249i \(0.713049\pi\)
\(422\) 1.97797e17 9.77972e16i 1.70486 0.842938i
\(423\) 3.11125e15i 0.0264072i
\(424\) −1.35236e15 + 6.91085e15i −0.0113035 + 0.0577635i
\(425\) 2.45416e17i 2.02011i
\(426\) −7.48161e16 1.51317e17i −0.606502 1.22666i
\(427\) 1.55506e17 + 1.55506e17i 1.24155 + 1.24155i
\(428\) 1.52209e16 + 1.13793e17i 0.119689 + 0.894810i
\(429\) −1.46380e17 + 1.46380e17i −1.13373 + 1.13373i
\(430\) −7.85416e16 + 2.32165e17i −0.599177 + 1.77114i
\(431\) −8.22316e16 −0.617926 −0.308963 0.951074i \(-0.599982\pi\)
−0.308963 + 0.951074i \(0.599982\pi\)
\(432\) 6.44379e16 1.12685e17i 0.476977 0.834105i
\(433\) −1.10188e17 −0.803458 −0.401729 0.915759i \(-0.631591\pi\)
−0.401729 + 0.915759i \(0.631591\pi\)
\(434\) 1.45709e16 4.30709e16i 0.104665 0.309386i
\(435\) 9.31409e16 9.31409e16i 0.659114 0.659114i
\(436\) 1.74849e17 2.33877e16i 1.21899 0.163051i
\(437\) 5.47626e16 + 5.47626e16i 0.376144 + 0.376144i
\(438\) 5.19006e16 + 1.04970e17i 0.351229 + 0.710368i
\(439\) 1.40740e17i 0.938422i −0.883086 0.469211i \(-0.844538\pi\)
0.883086 0.469211i \(-0.155462\pi\)
\(440\) 2.23648e17 1.50444e17i 1.46934 0.988398i
\(441\) 1.37391e15i 0.00889421i
\(442\) −2.23019e17 + 1.10268e17i −1.42265 + 0.703404i
\(443\) −5.15028e16 5.15028e16i −0.323747 0.323747i 0.526455 0.850203i \(-0.323521\pi\)
−0.850203 + 0.526455i \(0.823521\pi\)
\(444\) −1.81603e17 1.38753e17i −1.12495 0.859513i
\(445\) 1.61822e17 1.61822e17i 0.987867 0.987867i
\(446\) 7.73858e16 + 2.61796e16i 0.465570 + 0.157502i
\(447\) 2.87913e17 1.70712
\(448\) 1.48382e17 + 6.03847e16i 0.867107 + 0.352874i
\(449\) −9.91483e16 −0.571063 −0.285532 0.958369i \(-0.592170\pi\)
−0.285532 + 0.958369i \(0.592170\pi\)
\(450\) −2.27336e16 7.69077e15i −0.129058 0.0436605i
\(451\) −6.26502e16 + 6.26502e16i −0.350570 + 0.350570i
\(452\) 1.26535e17 + 9.66781e16i 0.697928 + 0.533247i
\(453\) −2.23716e17 2.23716e17i −1.21635 1.21635i
\(454\) −1.66663e17 + 8.24039e16i −0.893259 + 0.441657i
\(455\) 4.48320e17i 2.36872i
\(456\) 6.22663e16 4.18853e16i 0.324326 0.218168i
\(457\) 1.89700e16i 0.0974119i 0.998813 + 0.0487059i \(0.0155097\pi\)
−0.998813 + 0.0487059i \(0.984490\pi\)
\(458\) 1.33051e17 + 2.69097e17i 0.673583 + 1.36233i
\(459\) −1.45229e17 1.45229e17i −0.724888 0.724888i
\(460\) −4.82724e17 + 6.45688e16i −2.37560 + 0.317758i
\(461\) 8.20877e16 8.20877e16i 0.398311 0.398311i −0.479326 0.877637i \(-0.659119\pi\)
0.877637 + 0.479326i \(0.159119\pi\)
\(462\) 6.75864e16 1.99782e17i 0.323360 0.955838i
\(463\) 9.75992e16 0.460437 0.230218 0.973139i \(-0.426056\pi\)
0.230218 + 0.973139i \(0.426056\pi\)
\(464\) −9.87671e16 5.64792e16i −0.459458 0.262737i
\(465\) 1.33943e17 0.614433
\(466\) 1.34398e16 3.97273e16i 0.0607971 0.179714i
\(467\) −1.00759e17 + 1.00759e17i −0.449495 + 0.449495i −0.895186 0.445692i \(-0.852958\pi\)
0.445692 + 0.895186i \(0.352958\pi\)
\(468\) −3.22553e15 2.41144e16i −0.0141907 0.106091i
\(469\) −1.21100e17 1.21100e17i −0.525436 0.525436i
\(470\) 6.46562e16 + 1.30768e17i 0.276678 + 0.559586i
\(471\) 4.13269e16i 0.174420i
\(472\) 2.99322e16 1.52960e17i 0.124599 0.636730i
\(473\) 2.78709e17i 1.14433i
\(474\) −3.16227e17 + 1.56353e17i −1.28068 + 0.633208i
\(475\) 1.26529e17 + 1.26529e17i 0.505454 + 0.505454i
\(476\) 1.53885e17 2.01409e17i 0.606390 0.793659i
\(477\) −7.70438e14 + 7.70438e14i −0.00299480 + 0.00299480i
\(478\) −3.02738e17 1.02416e17i −1.16087 0.392724i
\(479\) 2.22931e17 0.843314 0.421657 0.906756i \(-0.361449\pi\)
0.421657 + 0.906756i \(0.361449\pi\)
\(480\) −2.84269e16 + 4.71056e17i −0.106087 + 1.75794i
\(481\) 5.52451e17 2.03400
\(482\) −1.19062e17 4.02786e16i −0.432481 0.146308i
\(483\) −2.69462e17 + 2.69462e17i −0.965699 + 0.965699i
\(484\) −1.43894e16 + 1.88333e16i −0.0508802 + 0.0665934i
\(485\) −3.39936e17 3.39936e17i −1.18597 1.18597i
\(486\) 3.74042e16 1.84938e16i 0.128761 0.0636637i
\(487\) 4.12184e17i 1.40008i −0.714103 0.700040i \(-0.753165\pi\)
0.714103 0.700040i \(-0.246835\pi\)
\(488\) 5.49161e17 + 1.07463e17i 1.84065 + 0.360189i
\(489\) 1.24162e17i 0.410659i
\(490\) −2.85518e16 5.77466e16i −0.0931878 0.188474i
\(491\) 3.83217e17 + 3.83217e17i 1.23428 + 1.23428i 0.962302 + 0.271982i \(0.0876791\pi\)
0.271982 + 0.962302i \(0.412321\pi\)
\(492\) −2.05660e16 1.53754e17i −0.0653696 0.488711i
\(493\) −1.27292e17 + 1.27292e17i −0.399297 + 0.399297i
\(494\) −5.81311e16 + 1.71833e17i −0.179963 + 0.531962i
\(495\) 4.17047e16 0.127424
\(496\) −3.04063e16 1.11627e17i −0.0916923 0.336619i
\(497\) −4.15713e17 −1.23731
\(498\) −1.27037e15 + 3.75515e15i −0.00373198 + 0.0110316i
\(499\) −7.30964e16 + 7.30964e16i −0.211954 + 0.211954i −0.805097 0.593143i \(-0.797887\pi\)
0.593143 + 0.805097i \(0.297887\pi\)
\(500\) −5.26275e17 + 7.03942e16i −1.50629 + 0.201480i
\(501\) −1.60736e17 1.60736e17i −0.454118 0.454118i
\(502\) 2.34983e17 + 4.75257e17i 0.655333 + 1.32542i
\(503\) 3.90765e17i 1.07578i 0.843015 + 0.537890i \(0.180779\pi\)
−0.843015 + 0.537890i \(0.819221\pi\)
\(504\) 1.38347e16 + 2.05665e16i 0.0375985 + 0.0558936i
\(505\) 5.37336e17i 1.44162i
\(506\) 4.96456e17 2.45464e17i 1.31493 0.650145i
\(507\) 3.39525e17 + 3.39525e17i 0.887810 + 0.887810i
\(508\) 2.03336e17 + 1.55357e17i 0.524928 + 0.401067i
\(509\) 1.15663e17 1.15663e17i 0.294801 0.294801i −0.544173 0.838973i \(-0.683156\pi\)
0.838973 + 0.544173i \(0.183156\pi\)
\(510\) 7.07293e17 + 2.39277e17i 1.77989 + 0.602137i
\(511\) 2.88384e17 0.716532
\(512\) 3.99029e17 8.32437e16i 0.978925 0.204219i
\(513\) −1.49751e17 −0.362751
\(514\) −1.15663e17 3.91288e16i −0.276652 0.0935915i
\(515\) −1.30205e16 + 1.30205e16i −0.0307526 + 0.0307526i
\(516\) 3.87743e17 + 2.96252e17i 0.904317 + 0.690937i
\(517\) −1.17301e17 1.17301e17i −0.270155 0.270155i
\(518\) −5.04537e17 + 2.49460e17i −1.14749 + 0.567358i
\(519\) 2.06784e17i 0.464439i
\(520\) −6.36703e17 9.46517e17i −1.41226 2.09946i
\(521\) 3.03961e17i 0.665844i −0.942954 0.332922i \(-0.891965\pi\)
0.942954 0.332922i \(-0.108035\pi\)
\(522\) −7.80236e15 1.57804e16i −0.0168798 0.0341397i
\(523\) −4.73096e17 4.73096e17i −1.01085 1.01085i −0.999940 0.0109141i \(-0.996526\pi\)
−0.0109141 0.999940i \(-0.503474\pi\)
\(524\) −7.15387e16 + 9.56896e15i −0.150969 + 0.0201935i
\(525\) −6.22594e17 + 6.22594e17i −1.29768 + 1.29768i
\(526\) −2.33131e16 + 6.89125e16i −0.0479946 + 0.141870i
\(527\) −1.83054e17 −0.372228
\(528\) −1.41038e17 5.17777e17i −0.283281 1.03997i
\(529\) −4.96651e17 −0.985347
\(530\) −1.63714e16 + 4.83930e16i −0.0320842 + 0.0948395i
\(531\) 1.70524e16 1.70524e16i 0.0330119 0.0330119i
\(532\) −2.45019e16 1.83179e17i −0.0468570 0.350308i
\(533\) 2.65146e17 + 2.65146e17i 0.500909 + 0.500909i
\(534\) −2.01944e17 4.08436e17i −0.376888 0.762264i
\(535\) 8.32888e17i 1.53563i
\(536\) −4.27657e17 8.36865e16i −0.778977 0.152435i
\(537\) 2.02621e17i 0.364629i
\(538\) −1.73011e16 + 8.55423e15i −0.0307602 + 0.0152088i
\(539\) 5.17995e16 + 5.17995e16i 0.0909910 + 0.0909910i
\(540\) 5.71735e17 7.48302e17i 0.992282 1.29873i
\(541\) 3.15544e17 3.15544e17i 0.541100 0.541100i −0.382751 0.923851i \(-0.625023\pi\)
0.923851 + 0.382751i \(0.125023\pi\)
\(542\) −3.89880e17 1.31897e17i −0.660596 0.223480i
\(543\) 1.00751e18 1.68675
\(544\) 3.88498e16 6.43773e17i 0.0642682 1.06498i
\(545\) 1.27978e18 2.09198
\(546\) −8.45513e17 2.86037e17i −1.36574 0.462030i
\(547\) 3.54032e17 3.54032e17i 0.565099 0.565099i −0.365652 0.930751i \(-0.619154\pi\)
0.930751 + 0.365652i \(0.119154\pi\)
\(548\) −3.68733e17 + 4.82608e17i −0.581619 + 0.761239i
\(549\) 6.12218e16 + 6.12218e16i 0.0954301 + 0.0954301i
\(550\) 1.14706e18 5.67147e17i 1.76698 0.873651i
\(551\) 1.31256e17i 0.199817i
\(552\) −1.86213e17 + 9.51592e17i −0.280160 + 1.43168i
\(553\) 8.68770e17i 1.29179i
\(554\) −3.63288e17 7.34756e17i −0.533872 1.07977i
\(555\) −1.17240e18 1.17240e18i −1.70283 1.70283i
\(556\) 5.87827e16 + 4.39466e17i 0.0843846 + 0.630869i
\(557\) 4.85314e17 4.85314e17i 0.688596 0.688596i −0.273326 0.961921i \(-0.588124\pi\)
0.961921 + 0.273326i \(0.0881238\pi\)
\(558\) 5.73647e15 1.69568e16i 0.00804494 0.0237805i
\(559\) −1.17954e18 −1.63507
\(560\) 1.00888e18 + 5.76923e17i 1.38235 + 0.790489i
\(561\) −8.49087e17 −1.14999
\(562\) 1.82288e17 5.38834e17i 0.244046 0.721389i
\(563\) 5.46499e17 5.46499e17i 0.723244 0.723244i −0.246020 0.969265i \(-0.579123\pi\)
0.969265 + 0.246020i \(0.0791230\pi\)
\(564\) 2.87875e17 3.85060e16i 0.376609 0.0503749i
\(565\) 8.16885e17 + 8.16885e17i 1.05644 + 1.05644i
\(566\) 2.32423e17 + 4.70080e17i 0.297148 + 0.600986i
\(567\) 7.90158e17i 0.998675i
\(568\) −8.77675e17 + 5.90395e17i −1.09665 + 0.737697i
\(569\) 4.11487e17i 0.508307i −0.967164 0.254153i \(-0.918203\pi\)
0.967164 0.254153i \(-0.0817968\pi\)
\(570\) 4.88023e17 2.41295e17i 0.596011 0.294687i
\(571\) −8.46975e16 8.46975e16i −0.102267 0.102267i 0.654122 0.756389i \(-0.273038\pi\)
−0.756389 + 0.654122i \(0.773038\pi\)
\(572\) 1.03078e18 + 7.87557e17i 1.23052 + 0.940173i
\(573\) −4.66988e17 + 4.66988e17i −0.551189 + 0.551189i
\(574\) −3.61877e17 1.22423e17i −0.422313 0.142869i
\(575\) −2.31209e18 −2.66787
\(576\) 5.84169e16 + 2.37731e16i 0.0666489 + 0.0271231i
\(577\) 9.65171e17 1.08883 0.544417 0.838815i \(-0.316751\pi\)
0.544417 + 0.838815i \(0.316751\pi\)
\(578\) −1.17445e17 3.97316e16i −0.131010 0.0443206i
\(579\) −7.28422e17 + 7.28422e17i −0.803475 + 0.803475i
\(580\) −6.55879e17 5.01120e17i −0.715389 0.546588i
\(581\) 6.90331e15 + 6.90331e15i 0.00744582 + 0.00744582i
\(582\) −8.57989e17 + 4.24218e17i −0.915129 + 0.452470i
\(583\) 5.80945e16i 0.0612759i
\(584\) 6.08852e17 4.09562e17i 0.635079 0.427205i
\(585\) 1.76501e17i 0.182068i
\(586\) 7.25187e17 + 1.46671e18i 0.739802 + 1.49626i
\(587\) 9.68056e17 + 9.68056e17i 0.976682 + 0.976682i 0.999734 0.0230527i \(-0.00733857\pi\)
−0.0230527 + 0.999734i \(0.507339\pi\)
\(588\) −1.27124e17 + 1.70040e16i −0.126846 + 0.0169668i
\(589\) −9.43769e16 + 9.43769e16i −0.0931358 + 0.0931358i
\(590\) 3.62352e17 1.07110e18i 0.353666 1.04542i
\(591\) 2.81914e17 0.272144
\(592\) −7.10923e17 + 1.24321e18i −0.678784 + 1.18701i
\(593\) 4.67898e17 0.441871 0.220935 0.975288i \(-0.429089\pi\)
0.220935 + 0.975288i \(0.429089\pi\)
\(594\) −3.43176e17 + 1.01441e18i −0.320557 + 0.947552i
\(595\) 1.30026e18 1.30026e18i 1.20135 1.20135i
\(596\) −2.39193e17 1.78823e18i −0.218599 1.63427i
\(597\) 2.36641e17 + 2.36641e17i 0.213923 + 0.213923i
\(598\) −1.03885e18 2.10109e18i −0.928953 1.87882i
\(599\) 3.00408e17i 0.265728i 0.991134 + 0.132864i \(0.0424173\pi\)
−0.991134 + 0.132864i \(0.957583\pi\)
\(600\) −4.30246e17 + 2.19866e18i −0.376473 + 1.92386i
\(601\) 2.18547e17i 0.189173i −0.995517 0.0945867i \(-0.969847\pi\)
0.995517 0.0945867i \(-0.0301530\pi\)
\(602\) 1.07724e18 5.32624e17i 0.922435 0.456082i
\(603\) −4.76763e16 4.76763e16i −0.0403868 0.0403868i
\(604\) −1.20365e18 + 1.57536e18i −1.00869 + 1.32020i
\(605\) −1.21584e17 + 1.21584e17i −0.100801 + 0.100801i
\(606\) 1.01339e18 + 3.42831e17i 0.831199 + 0.281195i
\(607\) 1.30131e18 1.05598 0.527989 0.849251i \(-0.322946\pi\)
0.527989 + 0.849251i \(0.322946\pi\)
\(608\) −3.11880e17 3.51940e17i −0.250388 0.282550i
\(609\) −6.45851e17 −0.513003
\(610\) 3.84548e18 + 1.30093e18i 3.02208 + 1.02237i
\(611\) −4.96438e17 + 4.96438e17i −0.386009 + 0.386009i
\(612\) 6.05837e16 7.92936e16i 0.0466092 0.0610034i
\(613\) −4.42238e17 4.42238e17i −0.336638 0.336638i 0.518463 0.855100i \(-0.326505\pi\)
−0.855100 + 0.518463i \(0.826505\pi\)
\(614\) −1.91976e18 + 9.49191e17i −1.44595 + 0.714923i
\(615\) 1.12537e18i 0.838703i
\(616\) −1.29700e18 2.53805e17i −0.956458 0.187165i
\(617\) 6.56472e17i 0.479030i −0.970893 0.239515i \(-0.923012\pi\)
0.970893 0.239515i \(-0.0769884\pi\)
\(618\) 1.62488e16 + 3.28635e16i 0.0117326 + 0.0237295i
\(619\) −4.68829e17 4.68829e17i −0.334985 0.334985i 0.519491 0.854476i \(-0.326122\pi\)
−0.854476 + 0.519491i \(0.826122\pi\)
\(620\) −1.11277e17 8.31919e17i −0.0786790 0.588213i
\(621\) 1.36822e18 1.36822e18i 0.957327 0.957327i
\(622\) 3.48187e17 1.02923e18i 0.241088 0.712645i
\(623\) −1.12210e18 −0.768879
\(624\) −2.19132e18 + 5.96898e17i −1.48596 + 0.404763i
\(625\) −1.03057e18 −0.691606
\(626\) −5.72577e17 + 1.69251e18i −0.380278 + 1.12408i
\(627\) −4.37764e17 + 4.37764e17i −0.287740 + 0.287740i
\(628\) 2.56682e17 3.43336e16i 0.166977 0.0223348i
\(629\) 1.60227e18 + 1.60227e18i 1.03159 + 1.03159i
\(630\) 7.96994e16 + 1.61193e17i 0.0507857 + 0.102715i
\(631\) 1.44870e18i 0.913668i −0.889552 0.456834i \(-0.848983\pi\)
0.889552 0.456834i \(-0.151017\pi\)
\(632\) 1.23382e18 + 1.83419e18i 0.770180 + 1.14494i
\(633\) 3.18707e18i 1.96910i
\(634\) −2.46993e18 + 1.22121e18i −1.51044 + 0.746812i
\(635\) 1.31270e18 + 1.31270e18i 0.794575 + 0.794575i
\(636\) 8.08218e16 + 6.17513e16i 0.0484236 + 0.0369977i
\(637\) 2.19224e17 2.19224e17i 0.130012 0.130012i
\(638\) 8.89123e17 + 3.00791e17i 0.521948 + 0.176575i
\(639\) −1.63664e17 −0.0951037
\(640\) 2.94935e18 2.14785e17i 1.69651 0.123547i
\(641\) −2.08753e18 −1.18865 −0.594326 0.804224i \(-0.702581\pi\)
−0.594326 + 0.804224i \(0.702581\pi\)
\(642\) 1.57079e18 + 5.31398e17i 0.885402 + 0.299532i
\(643\) −3.18091e17 + 3.18091e17i −0.177493 + 0.177493i −0.790262 0.612769i \(-0.790055\pi\)
0.612769 + 0.790262i \(0.290055\pi\)
\(644\) 1.89750e18 + 1.44977e18i 1.04815 + 0.800831i
\(645\) 2.50319e18 + 2.50319e18i 1.36885 + 1.36885i
\(646\) −6.66961e17 + 3.29767e17i −0.361068 + 0.178524i
\(647\) 1.16503e18i 0.624392i 0.950018 + 0.312196i \(0.101065\pi\)
−0.950018 + 0.312196i \(0.898935\pi\)
\(648\) −1.12218e18 1.66822e18i −0.595422 0.885149i
\(649\) 1.28582e18i 0.675447i
\(650\) −2.40026e18 4.85457e18i −1.24831 2.52472i
\(651\) −4.64387e17 4.64387e17i −0.239113 0.239113i
\(652\) 7.71172e17 1.03151e17i 0.393135 0.0525855i
\(653\) −8.37881e17 + 8.37881e17i −0.422909 + 0.422909i −0.886204 0.463295i \(-0.846667\pi\)
0.463295 + 0.886204i \(0.346667\pi\)
\(654\) 8.16522e17 2.41360e18i 0.408049 1.20618i
\(655\) −5.23615e17 −0.259086
\(656\) −9.37880e17 + 2.55471e17i −0.459486 + 0.125160i
\(657\) 1.13535e17 0.0550751
\(658\) 2.29215e17 6.77549e17i 0.110097 0.325441i
\(659\) 2.06602e18 2.06602e18i 0.982605 0.982605i −0.0172460 0.999851i \(-0.505490\pi\)
0.999851 + 0.0172460i \(0.00548985\pi\)
\(660\) −5.16153e17 3.85882e18i −0.243077 1.81727i
\(661\) −1.98935e17 1.98935e17i −0.0927686 0.0927686i 0.659200 0.751968i \(-0.270895\pi\)
−0.751968 + 0.659200i \(0.770895\pi\)
\(662\) −1.13190e18 2.28929e18i −0.522675 1.05712i
\(663\) 3.59348e18i 1.64315i
\(664\) 2.43787e16 + 4.77057e15i 0.0110387 + 0.00216012i
\(665\) 1.34075e18i 0.601183i
\(666\) −1.98633e17 + 9.82109e16i −0.0882003 + 0.0436091i
\(667\) −1.19923e18 1.19923e18i −0.527333 0.527333i
\(668\) −8.64799e17 + 1.13187e18i −0.376589 + 0.492890i
\(669\) 8.34368e17 8.34368e17i 0.359822 0.359822i
\(670\) −2.99465e18 1.01309e18i −1.27897 0.432676i
\(671\) −4.61639e18 −1.95257
\(672\) 1.73174e18 1.53462e18i 0.725408 0.642838i
\(673\) −3.16557e18 −1.31327 −0.656636 0.754208i \(-0.728021\pi\)
−0.656636 + 0.754208i \(0.728021\pi\)
\(674\) 1.51027e18 + 5.10925e17i 0.620534 + 0.209927i
\(675\) 3.16128e18 3.16128e18i 1.28643 1.28643i
\(676\) 1.82672e18 2.39086e18i 0.736239 0.963610i
\(677\) −6.90800e17 6.90800e17i −0.275756 0.275756i 0.555656 0.831412i \(-0.312467\pi\)
−0.831412 + 0.555656i \(0.812467\pi\)
\(678\) 2.06180e18 1.01942e18i 0.815179 0.403051i
\(679\) 2.35716e18i 0.923070i
\(680\) 8.98550e17 4.59179e18i 0.348525 1.78104i
\(681\) 2.68543e18i 1.03171i
\(682\) 4.23030e17 + 8.55585e17i 0.160980 + 0.325585i
\(683\) 6.22816e17 + 6.22816e17i 0.234760 + 0.234760i 0.814676 0.579916i \(-0.196915\pi\)
−0.579916 + 0.814676i \(0.696915\pi\)
\(684\) −9.64626e15 7.21165e16i −0.00360159 0.0269259i
\(685\) −3.11563e18 + 3.11563e18i −1.15228 + 1.15228i
\(686\) −9.20117e17 + 2.71982e18i −0.337083 + 0.996401i
\(687\) 4.33593e18 1.57349
\(688\) 1.51790e18 2.65440e18i 0.545654 0.954203i
\(689\) −2.45866e17 −0.0875534
\(690\) −2.25426e18 + 6.66349e18i −0.795215 + 2.35062i
\(691\) −2.43218e18 + 2.43218e18i −0.849939 + 0.849939i −0.990125 0.140186i \(-0.955230\pi\)
0.140186 + 0.990125i \(0.455230\pi\)
\(692\) 1.28434e18 1.71792e17i 0.444620 0.0594721i
\(693\) −1.44593e17 1.44593e17i −0.0495884 0.0495884i
\(694\) 2.19964e18 + 4.44882e18i 0.747335 + 1.51150i
\(695\) 3.21660e18i 1.08267i
\(696\) −1.36355e18 + 9.17236e17i −0.454687 + 0.305859i
\(697\) 1.53800e18i 0.508093i
\(698\) −1.87917e18 + 9.29122e17i −0.615042 + 0.304097i
\(699\) −4.28337e17 4.28337e17i −0.138894 0.138894i
\(700\) 4.38418e18 + 3.34970e18i 1.40848 + 1.07614i
\(701\) 1.94584e18 1.94584e18i 0.619355 0.619355i −0.326011 0.945366i \(-0.605705\pi\)
0.945366 + 0.326011i \(0.105705\pi\)
\(702\) 4.29317e18 + 1.45238e18i 1.35390 + 0.458025i
\(703\) 1.65216e18 0.516229
\(704\) −3.09875e18 + 1.30615e18i −0.959321 + 0.404363i
\(705\) 2.10705e18 0.646318
\(706\) −6.03689e16 2.04228e16i −0.0183477 0.00620704i
\(707\) 1.86298e18 1.86298e18i 0.561024 0.561024i
\(708\) −1.78885e18 1.36676e18i −0.533776 0.407828i
\(709\) −3.88390e18 3.88390e18i −1.14833 1.14833i −0.986881 0.161451i \(-0.948383\pi\)
−0.161451 0.986881i \(-0.551617\pi\)
\(710\) −6.87893e18 + 3.40117e18i −2.01531 + 0.996436i
\(711\) 3.42030e17i 0.0992914i
\(712\) −2.36903e18 + 1.59360e18i −0.681475 + 0.458415i
\(713\) 1.72457e18i 0.491585i
\(714\) −1.62264e18 3.28182e18i −0.458336 0.926993i
\(715\) 6.65449e18 + 6.65449e18i 1.86263 + 1.86263i
\(716\) −1.25848e18 + 1.68333e17i −0.349069 + 0.0466913i
\(717\) −3.26410e18 + 3.26410e18i −0.897199 + 0.897199i
\(718\) 1.42762e17 4.21997e17i 0.0388868 0.114948i
\(719\) 5.31503e18 1.43472 0.717362 0.696701i \(-0.245349\pi\)
0.717362 + 0.696701i \(0.245349\pi\)
\(720\) 3.97192e17 + 2.27131e17i 0.106252 + 0.0607597i
\(721\) 9.02859e16 0.0239354
\(722\) 1.04589e18 3.09159e18i 0.274784 0.812250i
\(723\) −1.28372e18 + 1.28372e18i −0.334249 + 0.334249i
\(724\) −8.37018e17 6.25764e18i −0.215990 1.61477i
\(725\) −2.77083e18 2.77083e18i −0.708618 0.708618i
\(726\) 1.51729e17 + 3.06875e17i 0.0384575 + 0.0777810i
\(727\) 4.82122e18i 1.21111i −0.795803 0.605555i \(-0.792951\pi\)
0.795803 0.605555i \(-0.207049\pi\)
\(728\) −1.07414e18 + 5.48913e18i −0.267429 + 1.36662i
\(729\) 3.72049e18i 0.918061i
\(730\) 4.77198e18 2.35942e18i 1.16708 0.577042i
\(731\) −3.42101e18 3.42101e18i −0.829261 0.829261i
\(732\) 4.90698e18 6.42239e18i 1.17894 1.54303i
\(733\) −1.17471e18 + 1.17471e18i −0.279741 + 0.279741i −0.833006 0.553265i \(-0.813382\pi\)
0.553265 + 0.833006i \(0.313382\pi\)
\(734\) 3.24472e16 + 1.09769e16i 0.00765867 + 0.00259093i
\(735\) −9.30463e17 −0.217686
\(736\) 6.06505e18 + 3.66008e17i 1.40646 + 0.0848761i
\(737\) 3.59500e18 0.826343
\(738\) −1.42469e17 4.81973e16i −0.0324604 0.0109814i
\(739\) 1.29761e18 1.29761e18i 0.293060 0.293060i −0.545228 0.838288i \(-0.683557\pi\)
0.838288 + 0.545228i \(0.183557\pi\)
\(740\) −6.30777e18 + 8.25577e18i −1.41211 + 1.84821i
\(741\) 1.85269e18 + 1.85269e18i 0.411135 + 0.411135i
\(742\) 2.24542e17 1.11021e17i 0.0493938 0.0244219i
\(743\) 7.02991e17i 0.153293i 0.997058 + 0.0766465i \(0.0244213\pi\)
−0.997058 + 0.0766465i \(0.975579\pi\)
\(744\) −1.63996e18 3.20917e17i −0.354494 0.0693695i
\(745\) 1.30887e19i 2.80466i
\(746\) 6.27294e17 + 1.26871e18i 0.133250 + 0.269501i
\(747\) 2.71779e15 + 2.71779e15i 0.000572312 + 0.000572312i
\(748\) 7.05405e17 + 5.27369e18i 0.147258 + 1.10092i
\(749\) 2.88767e18 2.88767e18i 0.597608 0.597608i
\(750\) −2.45764e18 + 7.26467e18i −0.504220 + 1.49045i
\(751\) −5.01063e18 −1.01914 −0.509569 0.860430i \(-0.670195\pi\)
−0.509569 + 0.860430i \(0.670195\pi\)
\(752\) −4.78323e17 1.75601e18i −0.0964506 0.354087i
\(753\) 7.65775e18 1.53086
\(754\) 1.27300e18 3.76292e18i 0.252298 0.745781i
\(755\) −1.01702e19 + 1.01702e19i −1.99837 + 1.99837i
\(756\) −4.57665e18 + 6.12169e17i −0.891571 + 0.119256i
\(757\) −6.00737e18 6.00737e18i −1.16028 1.16028i −0.984415 0.175861i \(-0.943729\pi\)
−0.175861 0.984415i \(-0.556271\pi\)
\(758\) −4.02421e18 8.13903e18i −0.770603 1.55856i
\(759\) 7.99934e18i 1.51874i
\(760\) −1.90413e18 2.83066e18i −0.358432 0.532842i
\(761\) 8.73410e17i 0.163011i −0.996673 0.0815057i \(-0.974027\pi\)
0.996673 0.0815057i \(-0.0259729\pi\)
\(762\) 3.31321e18 1.63816e18i 0.613115 0.303144i
\(763\) −4.43707e18 4.43707e18i −0.814116 0.814116i
\(764\) 3.28843e18 + 2.51250e18i 0.598249 + 0.457088i
\(765\) 5.11904e17 5.11904e17i 0.0923399 0.0923399i
\(766\) 6.95229e18 + 2.35196e18i 1.24349 + 0.420672i
\(767\) 5.44182e18 0.965105
\(768\) 1.47667e18 5.69939e18i 0.259678 1.00226i
\(769\) −4.24909e18 −0.740926 −0.370463 0.928847i \(-0.620801\pi\)
−0.370463 + 0.928847i \(0.620801\pi\)
\(770\) −9.08220e18 3.07251e18i −1.57037 0.531256i
\(771\) −1.24707e18 + 1.24707e18i −0.213815 + 0.213815i
\(772\) 5.12940e18 + 3.91908e18i 0.872075 + 0.666303i
\(773\) −2.03402e18 2.03402e18i −0.342917 0.342917i 0.514546 0.857463i \(-0.327960\pi\)
−0.857463 + 0.514546i \(0.827960\pi\)
\(774\) 4.24104e17 2.09691e17i 0.0709015 0.0350561i
\(775\) 3.98462e18i 0.660581i
\(776\) 3.34762e18 + 4.97655e18i 0.550346 + 0.818139i
\(777\) 8.12954e18i 1.32535i
\(778\) 4.30257e18 + 8.70204e18i 0.695602 + 1.40687i
\(779\) 7.92946e17 + 7.92946e17i 0.127131 + 0.127131i
\(780\) −1.63312e19 + 2.18445e18i −2.59658 + 0.347317i
\(781\) 6.17050e18 6.17050e18i 0.972945 0.972945i
\(782\) 3.08080e18 9.10671e18i 0.481748 1.42402i
\(783\) 3.27937e18 0.508556
\(784\) 2.11225e17 + 7.75443e17i 0.0324855 + 0.119260i
\(785\) 1.87874e18 0.286559
\(786\) −3.34077e17 + 9.87515e17i −0.0505358 + 0.149382i
\(787\) 7.35756e18 7.35756e18i 1.10382 1.10382i 0.109874 0.993946i \(-0.464955\pi\)
0.993946 0.109874i \(-0.0350447\pi\)
\(788\) −2.34209e17 1.75097e18i −0.0348484 0.260531i
\(789\) 7.43009e17 + 7.43009e17i 0.109646 + 0.109646i
\(790\) 7.10787e18 + 1.43758e19i 1.04031 + 2.10405i
\(791\) 5.66438e18i 0.822253i
\(792\) −5.10622e17 9.99215e16i −0.0735167 0.0143862i
\(793\) 1.95374e19i 2.78991i
\(794\) −4.52382e18 + 2.23673e18i −0.640726 + 0.316796i
\(795\) 5.21770e17 + 5.21770e17i 0.0732981 + 0.0732981i
\(796\) 1.27318e18 1.66638e18i 0.177401 0.232187i
\(797\) 2.53938e18 2.53938e18i 0.350952 0.350952i −0.509512 0.860464i \(-0.670174\pi\)
0.860464 + 0.509512i \(0.170174\pi\)
\(798\) −2.52859e18 8.55423e17i −0.346625 0.117263i
\(799\) −2.87962e18 −0.391545
\(800\) 1.40133e19 + 8.45664e17i 1.88998 + 0.114055i
\(801\) −4.41763e17 −0.0590987
\(802\) −9.86900e18 3.33869e18i −1.30960 0.443039i
\(803\) −4.28053e18 + 4.28053e18i −0.563439 + 0.563439i
\(804\) −3.82129e18 + 5.00141e18i −0.498938 + 0.653023i
\(805\) 1.22499e19 + 1.22499e19i 1.58657 + 1.58657i
\(806\) 3.62098e18 1.79033e18i 0.465209 0.230015i
\(807\) 2.78770e17i 0.0355278i
\(808\) 1.28742e18 6.57901e18i 0.162759 0.831738i
\(809\) 1.01192e19i 1.26906i 0.772899 + 0.634529i \(0.218806\pi\)
−0.772899 + 0.634529i \(0.781194\pi\)
\(810\) −6.46470e18 1.30750e19i −0.804259 1.62663i
\(811\) −2.77927e18 2.77927e18i −0.343001 0.343001i 0.514494 0.857494i \(-0.327980\pi\)
−0.857494 + 0.514494i \(0.827980\pi\)
\(812\) 5.36561e17 + 4.01139e18i 0.0656908 + 0.491112i
\(813\) −4.20366e18 + 4.20366e18i −0.510551 + 0.510551i
\(814\) 3.78615e18 1.11917e19i 0.456183 1.34846i
\(815\) 5.64446e18 0.674680
\(816\) −8.08663e18 4.62428e18i −0.958918 0.548350i
\(817\) −3.52754e18 −0.414981
\(818\) −1.49751e18 + 4.42656e18i −0.174772 + 0.516619i
\(819\) −6.11941e17 + 6.11941e17i −0.0708539 + 0.0708539i
\(820\) −6.98970e18 + 9.34938e17i −0.802914 + 0.107397i
\(821\) 9.20688e17 + 9.20688e17i 0.104926 + 0.104926i 0.757621 0.652695i \(-0.226362\pi\)
−0.652695 + 0.757621i \(0.726362\pi\)
\(822\) 3.88810e18 + 7.86376e18i 0.439613 + 0.889126i
\(823\) 1.09451e18i 0.122779i −0.998114 0.0613893i \(-0.980447\pi\)
0.998114 0.0613893i \(-0.0195531\pi\)
\(824\) 1.90616e17 1.28224e17i 0.0212145 0.0142706i
\(825\) 1.84825e19i 2.04085i
\(826\) −4.96986e18 + 2.45726e18i −0.544470 + 0.269204i
\(827\) −8.80074e17 8.80074e17i −0.0956606 0.0956606i 0.657657 0.753318i \(-0.271548\pi\)
−0.753318 + 0.657657i \(0.771548\pi\)
\(828\) 7.47034e17 + 5.70766e17i 0.0805644 + 0.0615547i
\(829\) −1.00955e19 + 1.00955e19i −1.08025 + 1.08025i −0.0837653 + 0.996486i \(0.526695\pi\)
−0.996486 + 0.0837653i \(0.973305\pi\)
\(830\) 1.70711e17 + 5.77515e16i 0.0181240 + 0.00613135i
\(831\) −1.18390e19 −1.24712
\(832\) 5.52785e18 + 1.31144e19i 0.577769 + 1.37072i
\(833\) 1.27163e18 0.131876
\(834\) 6.06636e18 + 2.05225e18i 0.624236 + 0.211179i
\(835\) −7.30715e18 + 7.30715e18i −0.746080 + 0.746080i
\(836\) 3.08264e18 + 2.35527e18i 0.312307 + 0.238616i
\(837\) 2.35797e18 + 2.35797e18i 0.237040 + 0.237040i
\(838\) 1.10014e19 5.43944e18i 1.09739 0.542585i
\(839\) 9.58634e18i 0.948856i 0.880294 + 0.474428i \(0.157345\pi\)
−0.880294 + 0.474428i \(0.842655\pi\)
\(840\) 1.39284e19 9.36936e18i 1.36800 0.920226i
\(841\) 7.38630e18i 0.719868i
\(842\) −1.06164e18 2.14720e18i −0.102672 0.207655i
\(843\) −5.80968e18 5.80968e18i −0.557536 0.557536i
\(844\) −1.97950e19 + 2.64776e18i −1.88507 + 0.252146i
\(845\) 1.54349e19 1.54349e19i 1.45860 1.45860i
\(846\) 9.02407e16 2.66747e17i 0.00846243 0.0250146i
\(847\) 8.43079e17 0.0784560
\(848\) 3.16393e17 5.53287e17i 0.0292182 0.0510949i
\(849\) 7.57433e18 0.694136
\(850\) 7.11820e18 2.10411e19i 0.647362 1.91357i
\(851\) −1.50951e19 + 1.50951e19i −1.36237 + 1.36237i
\(852\) 2.02557e18 + 1.51434e19i 0.181422 + 1.35633i
\(853\) −1.71955e18 1.71955e18i −0.152843 0.152843i 0.626543 0.779387i \(-0.284469\pi\)
−0.779387 + 0.626543i \(0.784469\pi\)
\(854\) −8.82212e18 1.78429e19i −0.778210 1.57394i
\(855\) 5.27845e17i 0.0462090i
\(856\) 1.99554e18 1.01977e19i 0.173373 0.885975i
\(857\) 1.06162e19i 0.915364i 0.889116 + 0.457682i \(0.151320\pi\)
−0.889116 + 0.457682i \(0.848680\pi\)
\(858\) 1.67958e19 8.30438e18i 1.43725 0.710624i
\(859\) −6.12496e17 6.12496e17i −0.0520173 0.0520173i 0.680620 0.732637i \(-0.261711\pi\)
−0.732637 + 0.680620i \(0.761711\pi\)
\(860\) 1.34678e19 1.76270e19i 1.13516 1.48572i
\(861\) −3.90174e18 + 3.90174e18i −0.326391 + 0.326391i
\(862\) 7.05024e18 + 2.38510e18i 0.585338 + 0.198020i
\(863\) −4.01180e18 −0.330574 −0.165287 0.986245i \(-0.552855\pi\)
−0.165287 + 0.986245i \(0.552855\pi\)
\(864\) −8.79306e18 + 7.79219e18i −0.719119 + 0.637265i
\(865\) 9.40048e18 0.763037
\(866\) 9.44713e18 + 3.19597e18i 0.761086 + 0.257475i
\(867\) −1.26628e18 + 1.26628e18i −0.101253 + 0.101253i
\(868\) −2.49851e18 + 3.27012e18i −0.198291 + 0.259529i
\(869\) −1.28953e19 1.28953e19i −1.01579 1.01579i
\(870\) −1.06871e19 + 5.28405e18i −0.835573 + 0.413135i
\(871\) 1.52147e19i 1.18071i
\(872\) −1.56693e19 3.06626e18i −1.20696 0.236184i
\(873\) 9.27999e17i 0.0709504i
\(874\) −3.10678e18 6.28351e18i −0.235768 0.476846i
\(875\) 1.33551e19 + 1.33551e19i 1.00599 + 1.00599i
\(876\) −1.40515e18 1.05051e19i −0.105062 0.785459i
\(877\) −3.06738e18 + 3.06738e18i −0.227651 + 0.227651i −0.811711 0.584060i \(-0.801463\pi\)
0.584060 + 0.811711i \(0.301463\pi\)
\(878\) −4.08211e18 + 1.20665e19i −0.300726 + 0.888932i
\(879\) 2.36328e19 1.72818
\(880\) −2.35384e19 + 6.41167e18i −1.70859 + 0.465408i
\(881\) 1.87018e19 1.34754 0.673769 0.738942i \(-0.264674\pi\)
0.673769 + 0.738942i \(0.264674\pi\)
\(882\) −3.98498e16 + 1.17794e17i −0.00285023 + 0.00842515i
\(883\) 7.65845e18 7.65845e18i 0.543746 0.543746i −0.380879 0.924625i \(-0.624378\pi\)
0.924625 + 0.380879i \(0.124378\pi\)
\(884\) 2.23191e19 2.98539e18i 1.57303 0.210408i
\(885\) −1.15485e19 1.15485e19i −0.807968 0.807968i
\(886\) 2.92184e18 + 5.90948e18i 0.202926 + 0.410422i
\(887\) 1.31407e19i 0.905971i 0.891518 + 0.452986i \(0.149641\pi\)
−0.891518 + 0.452986i \(0.850359\pi\)
\(888\) 1.15456e19 + 1.71635e19i 0.790188 + 1.17469i
\(889\) 9.10239e18i 0.618435i
\(890\) −1.85677e19 + 9.18046e18i −1.25234 + 0.619198i
\(891\) 1.17284e19 + 1.17284e19i 0.785299 + 0.785299i
\(892\) −5.87545e18 4.48910e18i −0.390544 0.298392i
\(893\) −1.48465e18 + 1.48465e18i −0.0979690 + 0.0979690i
\(894\) −2.46847e19 8.35082e18i −1.61709 0.547061i
\(895\) −9.21122e18 −0.599056
\(896\) −1.09703e19 9.48092e18i −0.708296 0.612137i
\(897\) −3.38545e19 −2.17003
\(898\) 8.50062e18 + 2.87576e18i 0.540947 + 0.183002i
\(899\) 2.06674e18 2.06674e18i 0.130571 0.130571i
\(900\) 1.72603e18 + 1.31876e18i 0.108261 + 0.0827158i
\(901\) −7.13081e17 7.13081e17i −0.0444046 0.0444046i
\(902\) 7.18855e18 3.55426e18i 0.444425 0.219739i
\(903\) 1.73574e19i 1.06541i
\(904\) −8.04454e18 1.19589e19i −0.490237 0.728782i
\(905\) 4.58018e19i 2.77119i
\(906\) 1.26918e19 + 2.56694e19i 0.762413 + 1.54200i
\(907\) −8.39003e18 8.39003e18i −0.500399 0.500399i 0.411163 0.911562i \(-0.365123\pi\)
−0.911562 + 0.411163i \(0.865123\pi\)
\(908\) 1.66792e19 2.23100e18i 0.987683 0.132112i
\(909\) 7.33443e17 7.33443e17i 0.0431222 0.0431222i
\(910\) −1.30034e19 + 3.84374e19i −0.759079 + 2.24380i
\(911\) 5.76256e18 0.334000 0.167000 0.985957i \(-0.446592\pi\)
0.167000 + 0.985957i \(0.446592\pi\)
\(912\) −6.55336e18 + 1.78508e18i −0.377136 + 0.102729i
\(913\) −2.04934e17 −0.0117099
\(914\) 5.50218e17 1.62642e18i 0.0312165 0.0922746i
\(915\) 4.14617e19 4.14617e19i 2.33566 2.33566i
\(916\) −3.60221e18 2.69305e19i −0.201487 1.50634i
\(917\) 1.81541e18 + 1.81541e18i 0.100826 + 0.100826i
\(918\) 8.23910e18 + 1.66637e19i 0.454362 + 0.918956i
\(919\) 3.59447e18i 0.196827i 0.995146 + 0.0984133i \(0.0313767\pi\)
−0.995146 + 0.0984133i \(0.968623\pi\)
\(920\) 4.32598e19 + 8.46534e18i 2.35214 + 0.460281i
\(921\) 3.09328e19i 1.67006i
\(922\) −9.41883e18 + 4.65698e18i −0.504947 + 0.249663i
\(923\) −2.61146e19 2.61146e19i −1.39018 1.39018i
\(924\) −1.15892e19 + 1.51683e19i −0.612614 + 0.801806i
\(925\) −3.48773e19 + 3.48773e19i −1.83072 + 1.83072i
\(926\) −8.36781e18 2.83083e18i −0.436154 0.147551i
\(927\) 3.55451e16 0.00183976
\(928\) 6.82978e18 + 7.70703e18i 0.351030 + 0.396119i
\(929\) 3.06946e19 1.56661 0.783303 0.621641i \(-0.213534\pi\)
0.783303 + 0.621641i \(0.213534\pi\)
\(930\) −1.14837e19 3.88496e18i −0.582029 0.196901i
\(931\) 6.55612e17 6.55612e17i 0.0329969 0.0329969i
\(932\) −2.30455e18 + 3.01626e18i −0.115182 + 0.150753i
\(933\) −1.10970e19 1.10970e19i −0.550778 0.550778i
\(934\) 1.15612e19 5.71624e18i 0.569834 0.281745i
\(935\) 3.85999e19i 1.88934i
\(936\) −4.22885e17 + 2.16104e18i −0.0205555 + 0.105044i
\(937\) 1.67374e19i 0.807944i −0.914771 0.403972i \(-0.867629\pi\)
0.914771 0.403972i \(-0.132371\pi\)
\(938\) 6.87020e18 + 1.38951e19i 0.329345 + 0.666106i
\(939\) 1.82485e19 + 1.82485e19i 0.868764 + 0.868764i
\(940\) −1.75050e18 1.30869e19i −0.0827620 0.618739i
\(941\) 2.27298e19 2.27298e19i 1.06724 1.06724i 0.0696717 0.997570i \(-0.477805\pi\)
0.997570 0.0696717i \(-0.0221952\pi\)
\(942\) 1.19867e18 3.54322e18i 0.0558946 0.165222i
\(943\) −1.44897e19 −0.671015
\(944\) −7.00283e18 + 1.22461e19i −0.322074 + 0.563221i
\(945\) −3.34980e19 −1.53007
\(946\) −8.08384e18 + 2.38955e19i −0.366712 + 1.08398i
\(947\) −4.36791e18 + 4.36791e18i −0.196788 + 0.196788i −0.798622 0.601834i \(-0.794437\pi\)
0.601834 + 0.798622i \(0.294437\pi\)
\(948\) 3.16471e19 4.23309e18i 1.41605 0.189410i
\(949\) 1.81159e19 + 1.81159e19i 0.805063 + 0.805063i
\(950\) −7.17822e18 1.45181e19i −0.316820 0.640775i
\(951\) 3.97976e19i 1.74455i
\(952\) −1.90354e19 + 1.28047e19i −0.828745 + 0.557480i
\(953\) 5.42952e18i 0.234778i −0.993086 0.117389i \(-0.962548\pi\)
0.993086 0.117389i \(-0.0374525\pi\)
\(954\) 8.84009e16 4.37083e16i 0.00379658 0.00187715i
\(955\) 2.12295e19 + 2.12295e19i 0.905561 + 0.905561i
\(956\) 2.29851e19 + 1.75616e19i 0.973801 + 0.744026i
\(957\) 9.58647e18 9.58647e18i 0.403395 0.403395i
\(958\) −1.91133e19 6.46603e18i −0.798839 0.270247i
\(959\) 2.16041e19 0.896842
\(960\) 1.61000e19 3.95621e19i 0.663840 1.63124i
\(961\) −2.14455e19 −0.878280
\(962\) −4.73651e19 1.60236e19i −1.92673 0.651813i
\(963\) 1.13686e18 1.13686e18i 0.0459342 0.0459342i
\(964\) 9.03967e18 + 6.90669e18i 0.362787 + 0.277185i
\(965\) 3.31144e19 + 3.31144e19i 1.32005 + 1.32005i
\(966\) 3.09184e19 1.52871e19i 1.22424 0.605303i
\(967\) 1.55747e19i 0.612558i −0.951942 0.306279i \(-0.900916\pi\)
0.951942 0.306279i \(-0.0990841\pi\)
\(968\) 1.77995e18 1.19734e18i 0.0695374 0.0467764i
\(969\) 1.07467e19i 0.417031i
\(970\) 1.92851e19 + 3.90046e19i 0.743373 + 1.50348i
\(971\) −2.07562e19 2.07562e19i −0.794738 0.794738i 0.187523 0.982260i \(-0.439954\pi\)
−0.982260 + 0.187523i \(0.939954\pi\)
\(972\) −3.74331e18 + 5.00702e17i −0.142372 + 0.0190436i
\(973\) 1.11521e19 1.11521e19i 0.421332 0.421332i
\(974\) −1.19553e19 + 3.53392e19i −0.448668 + 1.32624i
\(975\) −7.82211e19 −2.91604
\(976\) −4.39661e19 2.51417e19i −1.62815 0.931046i
\(977\) −4.01694e19 −1.47768 −0.738841 0.673880i \(-0.764626\pi\)
−0.738841 + 0.673880i \(0.764626\pi\)
\(978\) 3.60128e18 1.06452e19i 0.131599 0.389002i
\(979\) 1.66554e19 1.66554e19i 0.604601 0.604601i
\(980\) 7.73011e17 + 5.77912e18i 0.0278751 + 0.208397i
\(981\) −1.74685e18 1.74685e18i −0.0625758 0.0625758i
\(982\) −2.17406e19 4.39707e19i −0.773653 1.56473i
\(983\) 1.08830e19i 0.384725i 0.981324 + 0.192362i \(0.0616149\pi\)
−0.981324 + 0.192362i \(0.938385\pi\)
\(984\) −2.69631e18 + 1.37788e19i −0.0946896 + 0.483886i
\(985\) 1.28160e19i 0.447111i
\(986\) 1.46056e19 7.22149e18i 0.506197 0.250280i
\(987\) −7.30529e18 7.30529e18i −0.251522 0.251522i
\(988\) 9.96789e18 1.30463e19i 0.340944 0.446237i
\(989\) 3.22297e19 3.22297e19i 1.09517 1.09517i
\(990\) −3.57561e18 1.20963e18i −0.120704 0.0408342i
\(991\) 4.18369e19 1.40307 0.701537 0.712633i \(-0.252498\pi\)
0.701537 + 0.712633i \(0.252498\pi\)
\(992\) −6.30773e17 + 1.04524e19i −0.0210159 + 0.348250i
\(993\) −3.68871e19 −1.22097
\(994\) 3.56418e19 + 1.20576e19i 1.17205 + 0.396506i
\(995\) 1.07578e19 1.07578e19i 0.351458 0.351458i
\(996\) 2.17834e17 2.85107e17i 0.00707032 0.00925383i
\(997\) 1.70833e19 + 1.70833e19i 0.550874 + 0.550874i 0.926693 0.375819i \(-0.122638\pi\)
−0.375819 + 0.926693i \(0.622638\pi\)
\(998\) 8.38716e18 4.14689e18i 0.268699 0.132854i
\(999\) 4.12785e19i 1.31386i
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 16.14.e.a.5.3 50
4.3 odd 2 64.14.e.a.49.19 50
8.3 odd 2 128.14.e.a.97.7 50
8.5 even 2 128.14.e.b.97.19 50
16.3 odd 4 64.14.e.a.17.19 50
16.5 even 4 128.14.e.b.33.19 50
16.11 odd 4 128.14.e.a.33.7 50
16.13 even 4 inner 16.14.e.a.13.3 yes 50
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.14.e.a.5.3 50 1.1 even 1 trivial
16.14.e.a.13.3 yes 50 16.13 even 4 inner
64.14.e.a.17.19 50 16.3 odd 4
64.14.e.a.49.19 50 4.3 odd 2
128.14.e.a.33.7 50 16.11 odd 4
128.14.e.a.97.7 50 8.3 odd 2
128.14.e.b.33.19 50 16.5 even 4
128.14.e.b.97.19 50 8.5 even 2