Properties

Label 35.10.k.a.3.10
Level $35$
Weight $10$
Character 35.3
Analytic conductor $18.026$
Analytic rank $0$
Dimension $136$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [35,10,Mod(3,35)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(35, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 2]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("35.3");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 35 = 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 35.k (of order \(12\), degree \(4\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(18.0262542657\)
Analytic rank: \(0\)
Dimension: \(136\)
Relative dimension: \(34\) over \(\Q(\zeta_{12})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 3.10
Character \(\chi\) \(=\) 35.3
Dual form 35.10.k.a.12.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-22.3519 - 5.98917i) q^{2} +(-10.0261 - 37.4181i) q^{3} +(20.3322 + 11.7388i) q^{4} +(-924.440 + 1048.11i) q^{5} +896.413i q^{6} +(-6331.22 - 518.872i) q^{7} +(7993.56 + 7993.56i) q^{8} +(15746.4 - 9091.18i) q^{9} +(26940.3 - 17890.6i) q^{10} +(-30456.2 + 52751.6i) q^{11} +(235.390 - 878.486i) q^{12} +(-117199. + 117199. i) q^{13} +(138407. + 49516.6i) q^{14} +(48486.8 + 24082.3i) q^{15} +(-136807. - 236956. i) q^{16} +(315442. - 84522.3i) q^{17} +(-406410. + 108897. i) q^{18} +(-144650. - 250541. i) q^{19} +(-31099.4 + 10458.6i) q^{20} +(44062.6 + 242104. i) q^{21} +(996692. - 996692. i) q^{22} +(143682. - 536228. i) q^{23} +(218959. - 379248. i) q^{24} +(-243946. - 1.93783e6i) q^{25} +(3.32153e6 - 1.91769e6i) q^{26} +(-1.03721e6 - 1.03721e6i) q^{27} +(-122637. - 84870.7i) q^{28} -5.36320e6i q^{29} +(-939540. - 828680. i) q^{30} +(-885940. - 511497. i) q^{31} +(140685. + 525043. i) q^{32} +(2.27922e6 + 610716. i) q^{33} -7.55694e6 q^{34} +(6.39667e6 - 6.15616e6i) q^{35} +426878. q^{36} +(1.12669e7 + 3.01894e6i) q^{37} +(1.73267e6 + 6.46641e6i) q^{38} +(5.56039e6 + 3.21029e6i) q^{39} +(-1.57677e7 + 988567. i) q^{40} -2.35954e6i q^{41} +(465124. - 5.67539e6i) q^{42} +(-9.45901e6 - 9.45901e6i) q^{43} +(-1.23848e6 + 715037. i) q^{44} +(-5.02803e6 + 2.49082e7i) q^{45} +(-6.42312e6 + 1.11252e7i) q^{46} +(-1.13449e7 + 4.23397e7i) q^{47} +(-7.49480e6 + 7.49480e6i) q^{48} +(3.98152e7 + 6.57019e6i) q^{49} +(-6.15334e6 + 4.47752e7i) q^{50} +(-6.32533e6 - 1.09558e7i) q^{51} +(-3.75867e6 + 1.00713e6i) q^{52} +(5.23150e6 - 1.40178e6i) q^{53} +(1.69715e7 + 2.93955e7i) q^{54} +(-2.71346e7 - 8.06871e7i) q^{55} +(-4.64614e7 - 5.47566e7i) q^{56} +(-7.92449e6 + 7.92449e6i) q^{57} +(-3.21211e7 + 1.19878e8i) q^{58} +(4.55608e7 - 7.89137e7i) q^{59} +(703147. + 1.05882e6i) q^{60} +(1.10097e8 - 6.35646e7i) q^{61} +(1.67390e7 + 1.67390e7i) q^{62} +(-1.04411e8 + 4.93879e7i) q^{63} +1.27512e8i q^{64} +(-1.44940e7 - 2.31180e8i) q^{65} +(-4.72872e7 - 2.73013e7i) q^{66} +(5.87933e7 + 2.19419e8i) q^{67} +(7.40581e6 + 1.98438e6i) q^{68} -2.15052e7 q^{69} +(-1.79848e8 + 9.92910e7i) q^{70} -3.71610e7 q^{71} +(1.98541e8 + 5.31988e7i) q^{72} +(2.94824e7 + 1.10030e8i) q^{73} +(-2.33755e8 - 1.34958e8i) q^{74} +(-7.00640e7 + 2.85570e7i) q^{75} -6.79207e6i q^{76} +(2.20196e8 - 3.18179e8i) q^{77} +(-1.05058e8 - 1.05058e8i) q^{78} +(4.88106e8 - 2.81808e8i) q^{79} +(3.74826e8 + 7.56632e7i) q^{80} +(1.50531e8 - 2.60727e8i) q^{81} +(-1.41317e7 + 5.27402e7i) q^{82} +(-1.58033e8 + 1.58033e8i) q^{83} +(-1.94613e6 + 5.43975e6i) q^{84} +(-2.03018e8 + 4.08754e8i) q^{85} +(1.54775e8 + 2.68078e8i) q^{86} +(-2.00681e8 + 5.37722e7i) q^{87} +(-6.65126e8 + 1.78220e8i) q^{88} +(-2.79946e8 - 4.84880e8i) q^{89} +(2.61566e8 - 5.26632e8i) q^{90} +(8.02821e8 - 6.81199e8i) q^{91} +(9.21603e6 - 9.21603e6i) q^{92} +(-1.02567e7 + 3.82785e7i) q^{93} +(5.07159e8 - 8.78425e8i) q^{94} +(3.96316e8 + 8.00012e7i) q^{95} +(1.82356e7 - 1.05283e7i) q^{96} +(-9.93544e8 - 9.93544e8i) q^{97} +(-8.50594e8 - 3.85316e8i) q^{98} +1.10753e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 136 q - 2 q^{2} - 6 q^{3} - 1710 q^{5} + 5940 q^{7} - 3484 q^{8} + 153786 q^{10} - 87752 q^{11} + 3066 q^{12} - 318872 q^{15} + 3132804 q^{16} - 1578678 q^{17} - 239036 q^{18} - 5745396 q^{21} + 2132088 q^{22}+ \cdots + 5117393178 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/35\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −22.3519 5.98917i −0.987824 0.264687i −0.271488 0.962442i \(-0.587516\pi\)
−0.716336 + 0.697755i \(0.754182\pi\)
\(3\) −10.0261 37.4181i −0.0714641 0.266708i 0.920944 0.389695i \(-0.127419\pi\)
−0.992408 + 0.122987i \(0.960753\pi\)
\(4\) 20.3322 + 11.7388i 0.0397113 + 0.0229273i
\(5\) −924.440 + 1048.11i −0.661475 + 0.749967i
\(6\) 896.413i 0.282376i
\(7\) −6331.22 518.872i −0.996659 0.0816806i
\(8\) 7993.56 + 7993.56i 0.689978 + 0.689978i
\(9\) 15746.4 9091.18i 0.799999 0.461880i
\(10\) 26940.3 17890.6i 0.851927 0.565751i
\(11\) −30456.2 + 52751.6i −0.627203 + 1.08635i 0.360908 + 0.932602i \(0.382467\pi\)
−0.988110 + 0.153746i \(0.950866\pi\)
\(12\) 235.390 878.486i 0.00327696 0.0122298i
\(13\) −117199. + 117199.i −1.13809 + 1.13809i −0.149299 + 0.988792i \(0.547702\pi\)
−0.988792 + 0.149299i \(0.952298\pi\)
\(14\) 138407. + 49516.6i 0.962903 + 0.344488i
\(15\) 48486.8 + 24082.3i 0.247294 + 0.122825i
\(16\) −136807. 236956.i −0.521876 0.903916i
\(17\) 315442. 84522.3i 0.916007 0.245443i 0.230129 0.973160i \(-0.426085\pi\)
0.685878 + 0.727717i \(0.259418\pi\)
\(18\) −406410. + 108897.i −0.912512 + 0.244507i
\(19\) −144650. 250541.i −0.254641 0.441051i 0.710157 0.704043i \(-0.248624\pi\)
−0.964798 + 0.262993i \(0.915291\pi\)
\(20\) −31099.4 + 10458.6i −0.0434628 + 0.0146163i
\(21\) 44062.6 + 242104.i 0.0494405 + 0.271654i
\(22\) 996692. 996692.i 0.907107 0.907107i
\(23\) 143682. 536228.i 0.107060 0.399553i −0.891511 0.452999i \(-0.850354\pi\)
0.998571 + 0.0534467i \(0.0170207\pi\)
\(24\) 218959. 379248.i 0.134714 0.233331i
\(25\) −243946. 1.93783e6i −0.124901 0.992169i
\(26\) 3.32153e6 1.91769e6i 1.42547 0.822996i
\(27\) −1.03721e6 1.03721e6i −0.375602 0.375602i
\(28\) −122637. 84870.7i −0.0377059 0.0260944i
\(29\) 5.36320e6i 1.40810i −0.710151 0.704049i \(-0.751373\pi\)
0.710151 0.704049i \(-0.248627\pi\)
\(30\) −939540. 828680.i −0.211773 0.186785i
\(31\) −885940. 511497.i −0.172297 0.0994754i 0.411372 0.911468i \(-0.365050\pi\)
−0.583668 + 0.811992i \(0.698383\pi\)
\(32\) 140685. + 525043.i 0.0237177 + 0.0885156i
\(33\) 2.27922e6 + 610716.i 0.334560 + 0.0896450i
\(34\) −7.55694e6 −0.969819
\(35\) 6.39667e6 6.15616e6i 0.720523 0.693431i
\(36\) 426878. 0.0423587
\(37\) 1.12669e7 + 3.01894e6i 0.988314 + 0.264818i 0.716542 0.697544i \(-0.245724\pi\)
0.271772 + 0.962362i \(0.412390\pi\)
\(38\) 1.73267e6 + 6.46641e6i 0.134800 + 0.503080i
\(39\) 5.56039e6 + 3.21029e6i 0.384871 + 0.222205i
\(40\) −1.57677e7 + 988567.i −0.973864 + 0.0610571i
\(41\) 2.35954e6i 0.130407i −0.997872 0.0652034i \(-0.979230\pi\)
0.997872 0.0652034i \(-0.0207696\pi\)
\(42\) 465124. 5.67539e6i 0.0230646 0.281432i
\(43\) −9.45901e6 9.45901e6i −0.421927 0.421927i 0.463940 0.885867i \(-0.346435\pi\)
−0.885867 + 0.463940i \(0.846435\pi\)
\(44\) −1.23848e6 + 715037.i −0.0498141 + 0.0287602i
\(45\) −5.02803e6 + 2.49082e7i −0.182785 + 0.905495i
\(46\) −6.42312e6 + 1.11252e7i −0.211512 + 0.366350i
\(47\) −1.13449e7 + 4.23397e7i −0.339125 + 1.26563i 0.560203 + 0.828355i \(0.310723\pi\)
−0.899328 + 0.437275i \(0.855944\pi\)
\(48\) −7.49480e6 + 7.49480e6i −0.203786 + 0.203786i
\(49\) 3.98152e7 + 6.57019e6i 0.986657 + 0.162815i
\(50\) −6.15334e6 + 4.47752e7i −0.139234 + 1.01315i
\(51\) −6.32533e6 1.09558e7i −0.130923 0.226766i
\(52\) −3.75867e6 + 1.00713e6i −0.0712885 + 0.0191017i
\(53\) 5.23150e6 1.40178e6i 0.0910719 0.0244026i −0.212995 0.977053i \(-0.568322\pi\)
0.304067 + 0.952651i \(0.401655\pi\)
\(54\) 1.69715e7 + 2.93955e7i 0.271612 + 0.470445i
\(55\) −2.71346e7 8.06871e7i −0.399845 1.18897i
\(56\) −4.64614e7 5.47566e7i −0.631315 0.744030i
\(57\) −7.92449e6 + 7.92449e6i −0.0994340 + 0.0994340i
\(58\) −3.21211e7 + 1.19878e8i −0.372705 + 1.39095i
\(59\) 4.55608e7 7.89137e7i 0.489506 0.847849i −0.510421 0.859924i \(-0.670511\pi\)
0.999927 + 0.0120758i \(0.00384394\pi\)
\(60\) 703147. + 1.05882e6i 0.00700431 + 0.0105473i
\(61\) 1.10097e8 6.35646e7i 1.01810 0.587802i 0.104549 0.994520i \(-0.466660\pi\)
0.913554 + 0.406718i \(0.133327\pi\)
\(62\) 1.67390e7 + 1.67390e7i 0.143869 + 0.143869i
\(63\) −1.04411e8 + 4.93879e7i −0.835053 + 0.394992i
\(64\) 1.27512e8i 0.950036i
\(65\) −1.44940e7 2.31180e8i −0.100711 1.60635i
\(66\) −4.72872e7 2.73013e7i −0.306758 0.177107i
\(67\) 5.87933e7 + 2.19419e8i 0.356444 + 1.33027i 0.878658 + 0.477452i \(0.158439\pi\)
−0.522214 + 0.852814i \(0.674894\pi\)
\(68\) 7.40581e6 + 1.98438e6i 0.0420032 + 0.0112547i
\(69\) −2.15052e7 −0.114215
\(70\) −1.79848e8 + 9.92910e7i −0.895291 + 0.494275i
\(71\) −3.71610e7 −0.173550 −0.0867750 0.996228i \(-0.527656\pi\)
−0.0867750 + 0.996228i \(0.527656\pi\)
\(72\) 1.98541e8 + 5.31988e7i 0.870669 + 0.233295i
\(73\) 2.94824e7 + 1.10030e8i 0.121510 + 0.453480i 0.999691 0.0248473i \(-0.00790996\pi\)
−0.878182 + 0.478327i \(0.841243\pi\)
\(74\) −2.33755e8 1.34958e8i −0.906186 0.523187i
\(75\) −7.00640e7 + 2.85570e7i −0.255693 + 0.104216i
\(76\) 6.79207e6i 0.0233529i
\(77\) 2.20196e8 3.18179e8i 0.713841 1.03149i
\(78\) −1.05058e8 1.05058e8i −0.321370 0.321370i
\(79\) 4.88106e8 2.81808e8i 1.40991 0.814014i 0.414534 0.910034i \(-0.363944\pi\)
0.995379 + 0.0960196i \(0.0306111\pi\)
\(80\) 3.74826e8 + 7.56632e7i 1.02311 + 0.206528i
\(81\) 1.50531e8 2.60727e8i 0.388546 0.672981i
\(82\) −1.41317e7 + 5.27402e7i −0.0345169 + 0.128819i
\(83\) −1.58033e8 + 1.58033e8i −0.365507 + 0.365507i −0.865836 0.500329i \(-0.833212\pi\)
0.500329 + 0.865836i \(0.333212\pi\)
\(84\) −1.94613e6 + 5.43975e6i −0.00426495 + 0.0119213i
\(85\) −2.03018e8 + 4.08754e8i −0.421842 + 0.849330i
\(86\) 1.54775e8 + 2.68078e8i 0.305111 + 0.528468i
\(87\) −2.00681e8 + 5.37722e7i −0.375551 + 0.100629i
\(88\) −6.65126e8 + 1.78220e8i −1.18231 + 0.316800i
\(89\) −2.79946e8 4.84880e8i −0.472954 0.819180i 0.526567 0.850134i \(-0.323479\pi\)
−0.999521 + 0.0309536i \(0.990146\pi\)
\(90\) 2.61566e8 5.26632e8i 0.420232 0.846089i
\(91\) 8.02821e8 6.81199e8i 1.22725 1.04133i
\(92\) 9.21603e6 9.21603e6i 0.0134122 0.0134122i
\(93\) −1.02567e7 + 3.82785e7i −0.0142179 + 0.0530618i
\(94\) 5.07159e8 8.78425e8i 0.669991 1.16046i
\(95\) 3.96316e8 + 8.00012e7i 0.499212 + 0.100772i
\(96\) 1.82356e7 1.05283e7i 0.0219128 0.0126514i
\(97\) −9.93544e8 9.93544e8i −1.13950 1.13950i −0.988540 0.150960i \(-0.951764\pi\)
−0.150960 0.988540i \(-0.548236\pi\)
\(98\) −8.50594e8 3.85316e8i −0.931548 0.421988i
\(99\) 1.10753e9i 1.15877i
\(100\) 1.77878e7 4.22640e7i 0.0177878 0.0422640i
\(101\) −9.77608e7 5.64422e7i −0.0934800 0.0539707i 0.452531 0.891749i \(-0.350521\pi\)
−0.546011 + 0.837778i \(0.683854\pi\)
\(102\) 7.57670e7 + 2.82766e8i 0.0693073 + 0.258658i
\(103\) 1.24533e9 + 3.33685e8i 1.09023 + 0.292126i 0.758779 0.651348i \(-0.225796\pi\)
0.331448 + 0.943473i \(0.392463\pi\)
\(104\) −1.87367e9 −1.57052
\(105\) −2.94485e8 1.77629e8i −0.236435 0.142614i
\(106\) −1.25329e8 −0.0964220
\(107\) 1.76606e9 + 4.73214e8i 1.30250 + 0.349004i 0.842396 0.538860i \(-0.181145\pi\)
0.460106 + 0.887864i \(0.347811\pi\)
\(108\) −8.91311e6 3.32642e7i −0.00630409 0.0235272i
\(109\) 9.71246e8 + 5.60749e8i 0.659038 + 0.380496i 0.791910 0.610638i \(-0.209087\pi\)
−0.132873 + 0.991133i \(0.542420\pi\)
\(110\) 1.23261e8 + 1.96602e9i 0.0802712 + 1.28033i
\(111\) 4.51852e8i 0.282516i
\(112\) 7.43204e8 + 1.57121e9i 0.446300 + 0.943523i
\(113\) −1.16486e9 1.16486e9i −0.672077 0.672077i 0.286117 0.958195i \(-0.407635\pi\)
−0.958195 + 0.286117i \(0.907635\pi\)
\(114\) 2.24589e8 1.29666e8i 0.124542 0.0719044i
\(115\) 4.29201e8 + 6.46305e8i 0.228834 + 0.344585i
\(116\) 6.29575e7 1.09046e8i 0.0322839 0.0559174i
\(117\) −7.79981e8 + 2.91093e9i −0.384811 + 1.43613i
\(118\) −1.49100e9 + 1.49100e9i −0.707959 + 0.707959i
\(119\) −2.04099e9 + 3.71456e8i −0.932994 + 0.169803i
\(120\) 1.95079e8 + 5.80085e8i 0.0858808 + 0.255374i
\(121\) −6.76182e8 1.17118e9i −0.286767 0.496695i
\(122\) −2.84158e9 + 7.61399e8i −1.16129 + 0.311167i
\(123\) −8.82895e7 + 2.36571e7i −0.0347805 + 0.00931941i
\(124\) −1.20087e7 2.07997e7i −0.00456141 0.00790060i
\(125\) 2.25657e9 + 1.53573e9i 0.826713 + 0.562624i
\(126\) 2.62958e9 4.78578e8i 0.929434 0.169155i
\(127\) −1.78977e9 + 1.78977e9i −0.610492 + 0.610492i −0.943074 0.332582i \(-0.892080\pi\)
0.332582 + 0.943074i \(0.392080\pi\)
\(128\) 8.35720e8 3.11895e9i 0.275180 1.02698i
\(129\) −2.59101e8 + 4.48775e8i −0.0823786 + 0.142684i
\(130\) −1.06061e9 + 5.25412e9i −0.325694 + 1.61345i
\(131\) 1.93710e9 1.11838e9i 0.574686 0.331795i −0.184333 0.982864i \(-0.559012\pi\)
0.759019 + 0.651069i \(0.225679\pi\)
\(132\) 3.91725e7 + 3.91725e7i 0.0112305 + 0.0112305i
\(133\) 7.85814e8 + 1.66129e9i 0.217765 + 0.460376i
\(134\) 5.25656e9i 1.40841i
\(135\) 2.04594e9 1.28272e8i 0.530140 0.0332375i
\(136\) 3.19714e9 + 1.84587e9i 0.801375 + 0.462674i
\(137\) −1.74290e9 6.50457e9i −0.422697 1.57753i −0.768902 0.639366i \(-0.779197\pi\)
0.346206 0.938159i \(-0.387470\pi\)
\(138\) 4.80682e8 + 1.28798e8i 0.112824 + 0.0302311i
\(139\) −6.73839e9 −1.53105 −0.765525 0.643406i \(-0.777521\pi\)
−0.765525 + 0.643406i \(0.777521\pi\)
\(140\) 2.02324e8 5.00789e7i 0.0445114 0.0110174i
\(141\) 1.69801e9 0.361789
\(142\) 8.30618e8 + 2.22563e8i 0.171437 + 0.0459363i
\(143\) −2.61299e9 9.75183e9i −0.522548 1.95018i
\(144\) −4.30842e9 2.48747e9i −0.835001 0.482088i
\(145\) 5.62123e9 + 4.95796e9i 1.05603 + 0.931422i
\(146\) 2.63595e9i 0.480120i
\(147\) −1.53349e8 1.55568e9i −0.0270864 0.274784i
\(148\) 1.93641e8 + 1.93641e8i 0.0331757 + 0.0331757i
\(149\) 4.23370e9 2.44433e9i 0.703691 0.406276i −0.105030 0.994469i \(-0.533494\pi\)
0.808721 + 0.588193i \(0.200160\pi\)
\(150\) 1.73710e9 2.18677e8i 0.280165 0.0352689i
\(151\) 4.36771e9 7.56509e9i 0.683687 1.18418i −0.290160 0.956978i \(-0.593709\pi\)
0.973847 0.227203i \(-0.0729580\pi\)
\(152\) 8.46448e8 3.15899e9i 0.128619 0.480012i
\(153\) 4.19866e9 4.19866e9i 0.619440 0.619440i
\(154\) −6.82743e9 + 5.79312e9i −0.978169 + 0.829983i
\(155\) 1.35510e9 4.55714e8i 0.188573 0.0634161i
\(156\) 7.53699e7 + 1.30545e8i 0.0101891 + 0.0176481i
\(157\) 8.20449e9 2.19839e9i 1.07771 0.288772i 0.324054 0.946038i \(-0.394954\pi\)
0.753658 + 0.657266i \(0.228287\pi\)
\(158\) −1.25979e10 + 3.37560e9i −1.60820 + 0.430917i
\(159\) −1.04903e8 1.81698e8i −0.0130168 0.0225457i
\(160\) −6.80357e8 3.37917e8i −0.0820724 0.0407634i
\(161\) −1.18791e9 + 3.32042e9i −0.139338 + 0.389473i
\(162\) −4.92618e9 + 4.92618e9i −0.561944 + 0.561944i
\(163\) −1.02258e9 + 3.81630e9i −0.113462 + 0.423447i −0.999167 0.0408016i \(-0.987009\pi\)
0.885705 + 0.464248i \(0.153676\pi\)
\(164\) 2.76982e7 4.79746e7i 0.00298988 0.00517862i
\(165\) −2.74710e9 + 1.82431e9i −0.288534 + 0.191611i
\(166\) 4.47881e9 2.58584e9i 0.457801 0.264312i
\(167\) 1.02529e10 + 1.02529e10i 1.02005 + 1.02005i 0.999795 + 0.0202573i \(0.00644854\pi\)
0.0202573 + 0.999795i \(0.493551\pi\)
\(168\) −1.58306e9 + 2.28749e9i −0.153322 + 0.221548i
\(169\) 1.68665e10i 1.59050i
\(170\) 6.98594e9 7.92051e9i 0.641512 0.727332i
\(171\) −4.55544e9 2.63008e9i −0.407425 0.235227i
\(172\) −8.12850e7 3.03360e8i −0.00708161 0.0264289i
\(173\) −3.96395e9 1.06214e9i −0.336450 0.0901515i 0.0866387 0.996240i \(-0.472387\pi\)
−0.423089 + 0.906088i \(0.639054\pi\)
\(174\) 4.80764e9 0.397613
\(175\) 5.38993e8 + 1.23954e10i 0.0434422 + 0.999056i
\(176\) 1.66664e10 1.30929
\(177\) −3.40960e9 9.13599e8i −0.261110 0.0699642i
\(178\) 3.35329e9 + 1.25146e10i 0.250369 + 0.934390i
\(179\) −5.18020e9 2.99079e9i −0.377145 0.217744i 0.299431 0.954118i \(-0.403203\pi\)
−0.676575 + 0.736374i \(0.736537\pi\)
\(180\) −3.94623e8 + 4.47415e8i −0.0280192 + 0.0317676i
\(181\) 1.10387e10i 0.764478i 0.924064 + 0.382239i \(0.124847\pi\)
−0.924064 + 0.382239i \(0.875153\pi\)
\(182\) −2.20244e10 + 1.04179e10i −1.48793 + 0.703813i
\(183\) −3.48232e9 3.48232e9i −0.229529 0.229529i
\(184\) 5.43489e9 3.13784e9i 0.349551 0.201814i
\(185\) −1.35797e10 + 9.01808e9i −0.852350 + 0.566032i
\(186\) 4.58513e8 7.94168e8i 0.0280895 0.0486524i
\(187\) −5.14845e9 + 1.92143e10i −0.307886 + 1.14904i
\(188\) −7.27682e8 + 7.27682e8i −0.0424846 + 0.0424846i
\(189\) 6.02860e9 + 7.10495e9i 0.343667 + 0.405026i
\(190\) −8.37926e9 4.16178e9i −0.466460 0.231680i
\(191\) −1.29060e10 2.23539e10i −0.701685 1.21535i −0.967874 0.251434i \(-0.919098\pi\)
0.266189 0.963921i \(-0.414235\pi\)
\(192\) 4.77124e9 1.27845e9i 0.253382 0.0678935i
\(193\) −2.26612e10 + 6.07206e9i −1.17564 + 0.315013i −0.793197 0.608965i \(-0.791585\pi\)
−0.382446 + 0.923978i \(0.624918\pi\)
\(194\) 1.62571e10 + 2.81581e10i 0.824015 + 1.42724i
\(195\) −8.50499e9 + 2.86018e9i −0.421229 + 0.141657i
\(196\) 7.32403e8 + 6.00968e8i 0.0354485 + 0.0290870i
\(197\) 1.81492e10 1.81492e10i 0.858537 0.858537i −0.132628 0.991166i \(-0.542342\pi\)
0.991166 + 0.132628i \(0.0423417\pi\)
\(198\) 6.63319e9 2.47554e10i 0.306711 1.14466i
\(199\) −3.03084e9 + 5.24957e9i −0.137001 + 0.237293i −0.926360 0.376639i \(-0.877080\pi\)
0.789359 + 0.613932i \(0.210413\pi\)
\(200\) 1.35402e10 1.74402e10i 0.598396 0.770754i
\(201\) 7.62078e9 4.39986e9i 0.329319 0.190133i
\(202\) 1.84710e9 + 1.84710e9i 0.0780564 + 0.0780564i
\(203\) −2.78281e9 + 3.39556e10i −0.115014 + 1.40339i
\(204\) 2.97007e8i 0.0120069i
\(205\) 2.47306e9 + 2.18126e9i 0.0978008 + 0.0862609i
\(206\) −2.58370e10 1.49170e10i −0.999631 0.577137i
\(207\) −2.61247e9 9.74989e9i −0.0988975 0.369091i
\(208\) 4.38044e10 + 1.17374e10i 1.62268 + 0.434796i
\(209\) 1.76220e10 0.638845
\(210\) 5.51846e9 + 5.73406e9i 0.195808 + 0.203458i
\(211\) −8.88326e9 −0.308533 −0.154266 0.988029i \(-0.549301\pi\)
−0.154266 + 0.988029i \(0.549301\pi\)
\(212\) 1.22823e8 + 3.29103e7i 0.00417607 + 0.00111897i
\(213\) 3.72581e8 + 1.39049e9i 0.0124026 + 0.0462871i
\(214\) −3.66406e10 2.11545e10i −1.19427 0.689509i
\(215\) 1.86584e10 1.16980e9i 0.595526 0.0373369i
\(216\) 1.65819e10i 0.518314i
\(217\) 5.34368e9 + 3.69809e9i 0.163596 + 0.113216i
\(218\) −1.83508e10 1.83508e10i −0.550301 0.550301i
\(219\) 3.82151e9 2.20635e9i 0.112263 0.0648151i
\(220\) 3.95463e8 1.95907e9i 0.0113816 0.0563831i
\(221\) −2.70634e10 + 4.68752e10i −0.763163 + 1.32184i
\(222\) −2.70622e9 + 1.00998e10i −0.0747782 + 0.279076i
\(223\) −3.62273e10 + 3.62273e10i −0.980988 + 0.980988i −0.999823 0.0188344i \(-0.994004\pi\)
0.0188344 + 0.999823i \(0.494004\pi\)
\(224\) −6.18277e8 3.39716e9i −0.0164084 0.0901571i
\(225\) −2.14584e10 2.82961e10i −0.558183 0.736046i
\(226\) 1.90602e10 + 3.30133e10i 0.486004 + 0.841784i
\(227\) −1.45545e9 + 3.89988e8i −0.0363816 + 0.00974843i −0.276964 0.960880i \(-0.589328\pi\)
0.240582 + 0.970629i \(0.422662\pi\)
\(228\) −2.54146e8 + 6.80983e7i −0.00622841 + 0.00166890i
\(229\) 2.65942e10 + 4.60625e10i 0.639038 + 1.10685i 0.985644 + 0.168836i \(0.0540008\pi\)
−0.346606 + 0.938011i \(0.612666\pi\)
\(230\) −5.72262e9 1.70167e10i −0.134840 0.400959i
\(231\) −1.41134e10 5.04920e9i −0.326120 0.116673i
\(232\) 4.28710e10 4.28710e10i 0.971557 0.971557i
\(233\) 3.94319e9 1.47162e10i 0.0876488 0.327110i −0.908154 0.418637i \(-0.862508\pi\)
0.995803 + 0.0915269i \(0.0291747\pi\)
\(234\) 3.48681e10 6.03933e10i 0.760251 1.31679i
\(235\) −3.38890e10 5.10312e10i −0.724858 1.09152i
\(236\) 1.85270e9 1.06966e9i 0.0388778 0.0224461i
\(237\) −1.54385e10 1.54385e10i −0.317862 0.317862i
\(238\) 4.78447e10 + 3.92108e9i 0.966579 + 0.0792154i
\(239\) 7.73103e9i 0.153266i 0.997059 + 0.0766331i \(0.0244170\pi\)
−0.997059 + 0.0766331i \(0.975583\pi\)
\(240\) −9.26885e8 1.47839e10i −0.0180333 0.287632i
\(241\) 6.29437e10 + 3.63405e10i 1.20192 + 0.693928i 0.960982 0.276612i \(-0.0892118\pi\)
0.240938 + 0.970541i \(0.422545\pi\)
\(242\) 8.09954e9 + 3.02279e10i 0.151807 + 0.566551i
\(243\) −3.91530e10 1.04910e10i −0.720338 0.193014i
\(244\) 2.98469e9 0.0539069
\(245\) −4.36930e10 + 3.56569e10i −0.774755 + 0.632261i
\(246\) 2.11512e9 0.0368238
\(247\) 4.63159e10 + 1.24103e10i 0.791760 + 0.212151i
\(248\) −2.99313e9 1.11705e10i −0.0502449 0.187517i
\(249\) 7.49773e9 + 4.32882e9i 0.123604 + 0.0713629i
\(250\) −4.12410e10 4.78414e10i −0.667727 0.774593i
\(251\) 1.45028e9i 0.0230632i 0.999934 + 0.0115316i \(0.00367071\pi\)
−0.999934 + 0.0115316i \(0.996329\pi\)
\(252\) −2.70266e9 2.21495e8i −0.0422171 0.00345988i
\(253\) 2.39109e10 + 2.39109e10i 0.366905 + 0.366905i
\(254\) 5.07239e10 2.92855e10i 0.764647 0.441469i
\(255\) 1.73303e10 + 3.49833e9i 0.256669 + 0.0518119i
\(256\) −4.71687e9 + 8.16987e9i −0.0686396 + 0.118887i
\(257\) 1.59280e10 5.94443e10i 0.227753 0.849984i −0.753530 0.657413i \(-0.771651\pi\)
0.981283 0.192571i \(-0.0616827\pi\)
\(258\) 8.47918e9 8.47918e9i 0.119142 0.119142i
\(259\) −6.97665e10 2.49597e10i −0.963381 0.344659i
\(260\) 2.41908e9 4.87054e9i 0.0328299 0.0660993i
\(261\) −4.87578e10 8.44510e10i −0.650372 1.12648i
\(262\) −4.99960e10 + 1.33964e10i −0.655510 + 0.175643i
\(263\) 1.46476e11 3.92481e10i 1.88784 0.505846i 0.888991 0.457924i \(-0.151407\pi\)
0.998851 0.0479214i \(-0.0152597\pi\)
\(264\) 1.33373e10 + 2.31009e10i 0.168986 + 0.292692i
\(265\) −3.36699e9 + 6.77904e9i −0.0419407 + 0.0844427i
\(266\) −7.61468e9 4.18393e10i −0.0932576 0.512410i
\(267\) −1.53365e10 + 1.53365e10i −0.184682 + 0.184682i
\(268\) −1.38032e9 + 5.15144e9i −0.0163446 + 0.0609989i
\(269\) −2.63703e10 + 4.56746e10i −0.307064 + 0.531851i −0.977719 0.209919i \(-0.932680\pi\)
0.670655 + 0.741770i \(0.266013\pi\)
\(270\) −4.64989e10 9.38637e9i −0.532483 0.107488i
\(271\) −1.01529e11 + 5.86178e10i −1.14348 + 0.660188i −0.947290 0.320378i \(-0.896190\pi\)
−0.196189 + 0.980566i \(0.562857\pi\)
\(272\) −6.31826e10 6.31826e10i −0.699902 0.699902i
\(273\) −3.35383e10 2.32102e10i −0.365435 0.252899i
\(274\) 1.55828e11i 1.67020i
\(275\) 1.09653e11 + 4.61503e10i 1.15618 + 0.486606i
\(276\) −4.37247e8 2.52445e8i −0.00453561 0.00261864i
\(277\) −1.54616e10 5.77036e10i −0.157796 0.588903i −0.998850 0.0479513i \(-0.984731\pi\)
0.841054 0.540952i \(-0.181936\pi\)
\(278\) 1.50616e11 + 4.03574e10i 1.51241 + 0.405248i
\(279\) −1.86005e10 −0.183783
\(280\) 1.00342e11 + 1.92257e9i 0.975597 + 0.0186927i
\(281\) −1.49997e11 −1.43517 −0.717587 0.696469i \(-0.754753\pi\)
−0.717587 + 0.696469i \(0.754753\pi\)
\(282\) −3.79538e10 1.01697e10i −0.357384 0.0957606i
\(283\) −1.54516e10 5.76663e10i −0.143197 0.534420i −0.999829 0.0184916i \(-0.994114\pi\)
0.856632 0.515929i \(-0.172553\pi\)
\(284\) −7.55563e8 4.36225e8i −0.00689189 0.00397904i
\(285\) −9.80026e8 1.56315e10i −0.00879905 0.140345i
\(286\) 2.33622e11i 2.06474i
\(287\) −1.22430e9 + 1.49388e10i −0.0106517 + 0.129971i
\(288\) 6.98854e9 + 6.98854e9i 0.0598577 + 0.0598577i
\(289\) −1.03407e10 + 5.97020e9i −0.0871985 + 0.0503441i
\(290\) −9.59510e10 1.44486e11i −0.796634 1.19960i
\(291\) −2.72151e10 + 4.71379e10i −0.222480 + 0.385347i
\(292\) −6.92176e8 + 2.58324e9i −0.00557178 + 0.0207942i
\(293\) 1.48691e11 1.48691e11i 1.17864 1.17864i 0.198550 0.980091i \(-0.436377\pi\)
0.980091 0.198550i \(-0.0636232\pi\)
\(294\) −5.88960e9 + 3.56908e10i −0.0459751 + 0.278608i
\(295\) 4.05920e10 + 1.20704e11i 0.312062 + 0.927944i
\(296\) 6.59302e10 + 1.14194e11i 0.499196 + 0.864633i
\(297\) 8.63036e10 2.31250e10i 0.643613 0.172456i
\(298\) −1.09271e11 + 2.92790e10i −0.802659 + 0.215072i
\(299\) 4.60058e10 + 7.96844e10i 0.332883 + 0.576571i
\(300\) −1.75978e9 2.41842e8i −0.0125433 0.00172379i
\(301\) 5.49791e10 + 6.47951e10i 0.386054 + 0.454981i
\(302\) −1.42935e11 + 1.42935e11i −0.988799 + 0.988799i
\(303\) −1.13180e9 + 4.22392e9i −0.00771394 + 0.0287888i
\(304\) −3.95782e10 + 6.85515e10i −0.265782 + 0.460347i
\(305\) −3.51555e10 + 1.74156e11i −0.232618 + 1.15236i
\(306\) −1.18995e11 + 6.87015e10i −0.775855 + 0.447940i
\(307\) −1.20986e11 1.20986e11i −0.777346 0.777346i 0.202033 0.979379i \(-0.435245\pi\)
−0.979379 + 0.202033i \(0.935245\pi\)
\(308\) 8.21211e9 3.88445e9i 0.0519968 0.0245952i
\(309\) 4.99435e10i 0.311649i
\(310\) −3.30185e10 + 2.07012e9i −0.203062 + 0.0127312i
\(311\) 3.49223e10 + 2.01624e10i 0.211681 + 0.122214i 0.602092 0.798427i \(-0.294334\pi\)
−0.390412 + 0.920640i \(0.627667\pi\)
\(312\) 1.87856e10 + 7.01090e10i 0.112236 + 0.418869i
\(313\) 5.22373e10 + 1.39969e10i 0.307632 + 0.0824297i 0.409332 0.912385i \(-0.365762\pi\)
−0.101700 + 0.994815i \(0.532428\pi\)
\(314\) −1.96552e11 −1.14102
\(315\) 4.47577e10 1.55091e11i 0.256136 0.887540i
\(316\) 1.32324e10 0.0746527
\(317\) 7.75021e10 + 2.07666e10i 0.431069 + 0.115505i 0.467828 0.883820i \(-0.345037\pi\)
−0.0367590 + 0.999324i \(0.511703\pi\)
\(318\) 1.25657e9 + 4.68958e9i 0.00689072 + 0.0257165i
\(319\) 2.82917e11 + 1.63342e11i 1.52968 + 0.883163i
\(320\) −1.33646e11 1.17877e11i −0.712496 0.628426i
\(321\) 7.08270e10i 0.372329i
\(322\) 4.64387e10 6.71032e10i 0.240729 0.347850i
\(323\) −6.68050e10 6.68050e10i −0.341506 0.341506i
\(324\) 6.12123e9 3.53410e9i 0.0308593 0.0178166i
\(325\) 2.55701e11 + 1.98521e11i 1.27133 + 0.987031i
\(326\) 4.57130e10 7.91773e10i 0.224161 0.388259i
\(327\) 1.12443e10 4.19643e10i 0.0543836 0.202962i
\(328\) 1.88611e10 1.88611e10i 0.0899778 0.0899778i
\(329\) 9.37958e10 2.62175e11i 0.441369 1.23370i
\(330\) 7.23290e10 2.43238e10i 0.335737 0.112907i
\(331\) −1.67191e11 2.89583e11i −0.765573 1.32601i −0.939943 0.341331i \(-0.889122\pi\)
0.174370 0.984680i \(-0.444211\pi\)
\(332\) −5.06826e9 + 1.35804e9i −0.0228948 + 0.00613465i
\(333\) 2.04858e11 5.48916e10i 0.912965 0.244628i
\(334\) −1.67765e11 2.90578e11i −0.737638 1.27763i
\(335\) −2.84327e11 1.41218e11i −1.23343 0.612617i
\(336\) 5.13401e10 4.35624e10i 0.219750 0.186460i
\(337\) 1.51131e11 1.51131e11i 0.638293 0.638293i −0.311841 0.950134i \(-0.600946\pi\)
0.950134 + 0.311841i \(0.100946\pi\)
\(338\) −1.01016e11 + 3.76998e11i −0.420985 + 1.57114i
\(339\) −3.19077e10 + 5.52657e10i −0.131219 + 0.227278i
\(340\) −8.92607e9 + 5.92766e9i −0.0362248 + 0.0240563i
\(341\) 5.39646e10 3.11565e10i 0.216130 0.124783i
\(342\) 8.60706e10 + 8.60706e10i 0.340202 + 0.340202i
\(343\) −2.48669e11 6.22563e10i −0.970061 0.242862i
\(344\) 1.51222e11i 0.582241i
\(345\) 1.98802e10 2.25398e10i 0.0755502 0.0856573i
\(346\) 8.22404e10 + 4.74815e10i 0.308491 + 0.178108i
\(347\) −7.07556e10 2.64064e11i −0.261986 0.977746i −0.964069 0.265651i \(-0.914413\pi\)
0.702083 0.712095i \(-0.252253\pi\)
\(348\) −4.71149e9 1.26244e9i −0.0172208 0.00461429i
\(349\) 2.89272e11 1.04374 0.521870 0.853025i \(-0.325235\pi\)
0.521870 + 0.853025i \(0.325235\pi\)
\(350\) 6.21908e10 2.80289e11i 0.221523 0.998390i
\(351\) 2.43118e11 0.854939
\(352\) −3.19816e10 8.56944e9i −0.111034 0.0297516i
\(353\) −4.92003e10 1.83618e11i −0.168648 0.629404i −0.997547 0.0700045i \(-0.977699\pi\)
0.828899 0.559399i \(-0.188968\pi\)
\(354\) 7.07393e10 + 4.08413e10i 0.239412 + 0.138225i
\(355\) 3.43531e10 3.89488e10i 0.114799 0.130157i
\(356\) 1.31449e10i 0.0433743i
\(357\) 3.43624e10 + 7.26456e10i 0.111964 + 0.236702i
\(358\) 9.78749e10 + 9.78749e10i 0.314918 + 0.314918i
\(359\) −3.11120e11 + 1.79625e11i −0.988561 + 0.570746i −0.904844 0.425744i \(-0.860013\pi\)
−0.0837171 + 0.996490i \(0.526679\pi\)
\(360\) −2.39297e11 + 1.58913e11i −0.750890 + 0.498654i
\(361\) 1.19497e11 2.06974e11i 0.370316 0.641407i
\(362\) 6.61128e10 2.46736e11i 0.202347 0.755169i
\(363\) −3.70438e10 + 3.70438e10i −0.111979 + 0.111979i
\(364\) 2.43196e10 4.42611e9i 0.0726105 0.0132150i
\(365\) −1.42578e11 7.08152e10i −0.420470 0.208838i
\(366\) 5.69802e10 + 9.86925e10i 0.165981 + 0.287488i
\(367\) −3.53593e11 + 9.47449e10i −1.01743 + 0.272621i −0.728732 0.684798i \(-0.759890\pi\)
−0.288702 + 0.957419i \(0.593224\pi\)
\(368\) −1.46719e11 + 3.93132e10i −0.417034 + 0.111744i
\(369\) −2.14510e10 3.71543e10i −0.0602323 0.104325i
\(370\) 3.57543e11 1.20240e11i 0.991793 0.333534i
\(371\) −3.38491e10 + 6.16047e9i −0.0927608 + 0.0168823i
\(372\) −6.57884e8 + 6.57884e8i −0.00178117 + 0.00178117i
\(373\) −1.55398e11 + 5.79951e11i −0.415675 + 1.55132i 0.367804 + 0.929904i \(0.380110\pi\)
−0.783479 + 0.621418i \(0.786557\pi\)
\(374\) 2.30155e11 3.98641e11i 0.608274 1.05356i
\(375\) 3.48391e10 9.98341e10i 0.0909760 0.260698i
\(376\) −4.29130e11 + 2.47759e11i −1.10725 + 0.639269i
\(377\) 6.28559e11 + 6.28559e11i 1.60254 + 1.60254i
\(378\) −9.21979e10 1.94916e11i −0.232278 0.491059i
\(379\) 2.29583e11i 0.571562i 0.958295 + 0.285781i \(0.0922530\pi\)
−0.958295 + 0.285781i \(0.907747\pi\)
\(380\) 7.11884e9 + 6.27886e9i 0.0175139 + 0.0154474i
\(381\) 8.49141e10 + 4.90252e10i 0.206451 + 0.119195i
\(382\) 1.54593e11 + 5.76948e11i 0.371453 + 1.38628i
\(383\) −4.54725e11 1.21843e11i −1.07983 0.289339i −0.325303 0.945610i \(-0.605466\pi\)
−0.754525 + 0.656271i \(0.772133\pi\)
\(384\) −1.25084e11 −0.293570
\(385\) 1.29929e11 + 5.24928e11i 0.301393 + 1.21766i
\(386\) 5.42888e11 1.24471
\(387\) −2.34939e11 6.29517e10i −0.532421 0.142662i
\(388\) −8.53791e9 3.18639e10i −0.0191253 0.0713767i
\(389\) −1.41271e10 8.15630e9i −0.0312810 0.0180601i 0.484278 0.874914i \(-0.339082\pi\)
−0.515559 + 0.856854i \(0.672416\pi\)
\(390\) 2.07233e11 1.29926e10i 0.453595 0.0284384i
\(391\) 1.81293e11i 0.392270i
\(392\) 2.65746e11 + 3.70784e11i 0.568432 + 0.793110i
\(393\) −6.12694e10 6.12694e10i −0.129562 0.129562i
\(394\) −5.14367e11 + 2.96970e11i −1.07533 + 0.620840i
\(395\) −1.55859e11 + 7.72104e11i −0.322140 + 1.59584i
\(396\) −1.30011e10 + 2.25185e10i −0.0265675 + 0.0460162i
\(397\) 1.63027e11 6.08423e11i 0.329383 1.22927i −0.580449 0.814297i \(-0.697123\pi\)
0.909832 0.414977i \(-0.136210\pi\)
\(398\) 9.91857e10 9.91857e10i 0.198141 0.198141i
\(399\) 5.42835e10 4.60599e10i 0.107224 0.0909799i
\(400\) −4.25807e11 + 3.22913e11i −0.831655 + 0.630689i
\(401\) −3.89262e11 6.74222e11i −0.751783 1.30213i −0.946958 0.321358i \(-0.895861\pi\)
0.195175 0.980768i \(-0.437473\pi\)
\(402\) −1.96690e11 + 5.27031e10i −0.375635 + 0.100651i
\(403\) 1.63778e11 4.38841e10i 0.309301 0.0828770i
\(404\) −1.32513e9 2.29519e9i −0.00247481 0.00428649i
\(405\) 1.34114e11 + 3.98799e11i 0.247700 + 0.736557i
\(406\) 2.65567e11 7.42306e11i 0.485073 1.35586i
\(407\) −5.02399e11 + 5.02399e11i −0.907558 + 0.907558i
\(408\) 3.70139e10 1.38138e11i 0.0661292 0.246798i
\(409\) 3.23504e11 5.60325e11i 0.571643 0.990114i −0.424755 0.905308i \(-0.639640\pi\)
0.996398 0.0848056i \(-0.0270269\pi\)
\(410\) −4.22137e10 6.35668e10i −0.0737778 0.111097i
\(411\) −2.25914e11 + 1.30432e11i −0.390531 + 0.225473i
\(412\) 2.14032e10 + 2.14032e10i 0.0365967 + 0.0365967i
\(413\) −3.29402e11 + 4.75980e11i −0.557123 + 0.805032i
\(414\) 2.33575e11i 0.390773i
\(415\) −1.95440e10 3.11727e11i −0.0323442 0.515892i
\(416\) −7.80223e10 4.50462e10i −0.127732 0.0737459i
\(417\) 6.75600e10 + 2.52137e11i 0.109415 + 0.408343i
\(418\) −3.93884e11 1.05541e11i −0.631067 0.169094i
\(419\) 4.97851e11 0.789107 0.394554 0.918873i \(-0.370899\pi\)
0.394554 + 0.918873i \(0.370899\pi\)
\(420\) −3.90239e9 7.06848e9i −0.00611939 0.0110842i
\(421\) 3.31117e11 0.513703 0.256851 0.966451i \(-0.417315\pi\)
0.256851 + 0.966451i \(0.417315\pi\)
\(422\) 1.98558e11 + 5.32034e10i 0.304776 + 0.0816645i
\(423\) 2.06277e11 + 7.69835e11i 0.313270 + 1.16914i
\(424\) 5.30234e10 + 3.06131e10i 0.0796749 + 0.0460003i
\(425\) −2.40741e11 5.90654e11i −0.357931 0.878178i
\(426\) 3.33116e10i 0.0490063i
\(427\) −7.30031e11 + 3.45315e11i −1.06271 + 0.502679i
\(428\) 3.03529e10 + 3.03529e10i 0.0437223 + 0.0437223i
\(429\) −3.38696e11 + 1.95546e11i −0.482784 + 0.278735i
\(430\) −4.24056e11 8.56010e10i −0.598157 0.120745i
\(431\) 3.23601e11 5.60493e11i 0.451713 0.782389i −0.546780 0.837276i \(-0.684147\pi\)
0.998493 + 0.0548873i \(0.0174799\pi\)
\(432\) −1.03876e11 + 3.87669e11i −0.143495 + 0.535530i
\(433\) −4.79907e8 + 4.79907e8i −0.000656087 + 0.000656087i −0.707435 0.706779i \(-0.750148\pi\)
0.706779 + 0.707435i \(0.250148\pi\)
\(434\) −9.72929e10 1.14664e11i −0.131637 0.155139i
\(435\) 1.29158e11 2.60045e11i 0.172950 0.348214i
\(436\) 1.31650e10 + 2.28025e10i 0.0174475 + 0.0302199i
\(437\) −1.55131e11 + 4.15672e10i −0.203485 + 0.0545235i
\(438\) −9.86323e10 + 2.64284e10i −0.128052 + 0.0343114i
\(439\) −1.35469e11 2.34639e11i −0.174080 0.301516i 0.765762 0.643124i \(-0.222362\pi\)
−0.939843 + 0.341608i \(0.889029\pi\)
\(440\) 4.28075e11 8.61880e11i 0.544481 1.09625i
\(441\) 6.86676e11 2.58510e11i 0.864526 0.325465i
\(442\) 8.85662e11 8.85662e11i 1.10374 1.10374i
\(443\) −1.70180e11 + 6.35120e11i −0.209938 + 0.783500i 0.777949 + 0.628327i \(0.216260\pi\)
−0.987887 + 0.155173i \(0.950407\pi\)
\(444\) 5.30420e9 9.18715e9i 0.00647734 0.0112191i
\(445\) 7.67001e11 + 1.54829e11i 0.927205 + 0.187168i
\(446\) 1.02672e12 5.92777e11i 1.22870 0.709389i
\(447\) −1.33910e11 1.33910e11i −0.158646 0.158646i
\(448\) 6.61623e10 8.07305e11i 0.0775996 0.946862i
\(449\) 1.05911e12i 1.22980i −0.788606 0.614898i \(-0.789197\pi\)
0.788606 0.614898i \(-0.210803\pi\)
\(450\) 3.10167e11 + 7.60989e11i 0.356565 + 0.874827i
\(451\) 1.24470e11 + 7.18626e10i 0.141667 + 0.0817916i
\(452\) −1.00101e10 3.73581e10i −0.0112801 0.0420980i
\(453\) −3.26862e11 8.75825e10i −0.364689 0.0977182i
\(454\) 3.48679e10 0.0385189
\(455\) −2.81881e10 + 1.47117e12i −0.0308329 + 1.60921i
\(456\) −1.26690e11 −0.137214
\(457\) −1.54783e11 4.14739e10i −0.165997 0.0444786i 0.174864 0.984593i \(-0.444052\pi\)
−0.340860 + 0.940114i \(0.610718\pi\)
\(458\) −3.18554e11 1.18886e12i −0.338290 1.26251i
\(459\) −4.14845e11 2.39511e11i −0.436243 0.251865i
\(460\) 1.13975e9 + 1.81791e10i 0.00118686 + 0.0189305i
\(461\) 1.81186e12i 1.86840i 0.356750 + 0.934200i \(0.383885\pi\)
−0.356750 + 0.934200i \(0.616115\pi\)
\(462\) 2.85220e11 + 1.97387e11i 0.291267 + 0.201571i
\(463\) −7.15780e11 7.15780e11i −0.723878 0.723878i 0.245515 0.969393i \(-0.421043\pi\)
−0.969393 + 0.245515i \(0.921043\pi\)
\(464\) −1.27084e12 + 7.33721e11i −1.27280 + 0.734853i
\(465\) −3.06384e10 4.61363e10i −0.0303898 0.0457620i
\(466\) −1.76276e11 + 3.05318e11i −0.173163 + 0.299927i
\(467\) 3.67380e10 1.37108e11i 0.0357428 0.133394i −0.945749 0.324898i \(-0.894670\pi\)
0.981492 + 0.191504i \(0.0613366\pi\)
\(468\) −5.00295e10 + 5.00295e10i −0.0482080 + 0.0482080i
\(469\) −2.58383e11 1.41970e12i −0.246596 1.35494i
\(470\) 4.51849e11 + 1.34361e12i 0.427123 + 1.27009i
\(471\) −1.64519e11 2.84955e11i −0.154036 0.266798i
\(472\) 9.94994e11 2.66608e11i 0.922745 0.247249i
\(473\) 7.87063e11 2.10893e11i 0.722994 0.193726i
\(474\) 2.52617e11 + 4.37545e11i 0.229858 + 0.398126i
\(475\) −4.50220e11 + 3.41426e11i −0.405792 + 0.307734i
\(476\) −4.58582e10 1.64062e10i −0.0409436 0.0146480i
\(477\) 6.96334e10 6.96334e10i 0.0615864 0.0615864i
\(478\) 4.63025e10 1.72803e11i 0.0405675 0.151400i
\(479\) −4.29437e11 + 7.43807e11i −0.372726 + 0.645581i −0.989984 0.141180i \(-0.954910\pi\)
0.617258 + 0.786761i \(0.288244\pi\)
\(480\) −5.82285e9 + 2.88457e10i −0.00500669 + 0.0248025i
\(481\) −1.67427e12 + 9.66643e11i −1.42618 + 0.823405i
\(482\) −1.18926e12 1.18926e12i −1.00361 1.00361i
\(483\) 1.36154e11 + 1.11584e10i 0.113833 + 0.00932913i
\(484\) 3.17502e10i 0.0262992i
\(485\) 1.95982e12 1.22872e11i 1.60834 0.100836i
\(486\) 8.12311e11 + 4.68988e11i 0.660479 + 0.381328i
\(487\) −2.71878e11 1.01466e12i −0.219025 0.817412i −0.984711 0.174197i \(-0.944267\pi\)
0.765686 0.643215i \(-0.222400\pi\)
\(488\) 1.38818e12 + 3.71961e11i 1.10804 + 0.296898i
\(489\) 1.53051e11 0.121045
\(490\) 1.19018e12 5.35315e11i 0.932673 0.419495i
\(491\) 1.01910e12 0.791317 0.395658 0.918398i \(-0.370516\pi\)
0.395658 + 0.918398i \(0.370516\pi\)
\(492\) −2.07282e9 5.55412e8i −0.00159485 0.000427338i
\(493\) −4.53310e11 1.69178e12i −0.345608 1.28983i
\(494\) −9.60920e11 5.54788e11i −0.725966 0.419137i
\(495\) −1.16081e12 1.02385e12i −0.869039 0.766498i
\(496\) 2.79905e11i 0.207655i
\(497\) 2.35274e11 + 1.92818e10i 0.172970 + 0.0141757i
\(498\) −1.41663e11 1.41663e11i −0.103210 0.103210i
\(499\) 1.28296e12 7.40719e11i 0.926322 0.534812i 0.0406755 0.999172i \(-0.487049\pi\)
0.885646 + 0.464360i \(0.153716\pi\)
\(500\) 2.78535e10 + 5.77141e10i 0.0199304 + 0.0412969i
\(501\) 2.80847e11 4.86440e11i 0.199159 0.344953i
\(502\) 8.68598e9 3.24165e10i 0.00610453 0.0227824i
\(503\) −6.61569e11 + 6.61569e11i −0.460807 + 0.460807i −0.898920 0.438113i \(-0.855647\pi\)
0.438113 + 0.898920i \(0.355647\pi\)
\(504\) −1.22940e12 4.39830e11i −0.848704 0.303632i
\(505\) 1.49532e11 5.02867e10i 0.102311 0.0344066i
\(506\) −3.91247e11 6.77660e11i −0.265322 0.459552i
\(507\) −6.31112e11 + 1.69106e11i −0.424200 + 0.113664i
\(508\) −5.73996e10 + 1.53802e10i −0.0382404 + 0.0102465i
\(509\) 1.38306e12 + 2.39552e12i 0.913292 + 1.58187i 0.809383 + 0.587281i \(0.199802\pi\)
0.103909 + 0.994587i \(0.466865\pi\)
\(510\) −3.66412e11 1.81988e11i −0.239830 0.119118i
\(511\) −1.29568e11 7.11922e11i −0.0840630 0.461890i
\(512\) −1.01465e12 + 1.01465e12i −0.652533 + 0.652533i
\(513\) −1.09831e11 + 4.09895e11i −0.0700159 + 0.261303i
\(514\) −7.12044e11 + 1.23330e12i −0.449959 + 0.779352i
\(515\) −1.50097e12 + 9.96772e11i −0.940243 + 0.624401i
\(516\) −1.05362e10 + 6.08305e9i −0.00654272 + 0.00377744i
\(517\) −1.88796e12 1.88796e12i −1.16221 1.16221i
\(518\) 1.40993e12 + 9.75740e11i 0.860424 + 0.595457i
\(519\) 1.58972e11i 0.0961764i
\(520\) 1.73209e12 1.96381e12i 1.03886 1.17783i
\(521\) 1.27095e12 + 7.33781e11i 0.755714 + 0.436312i 0.827755 0.561090i \(-0.189618\pi\)
−0.0720408 + 0.997402i \(0.522951\pi\)
\(522\) 5.84038e11 + 2.17966e12i 0.344290 + 1.28491i
\(523\) 2.76686e12 + 7.41378e11i 1.61707 + 0.433294i 0.950140 0.311823i \(-0.100940\pi\)
0.666934 + 0.745117i \(0.267606\pi\)
\(524\) 5.25139e10 0.0304287
\(525\) 4.58408e11 1.44446e11i 0.263351 0.0829831i
\(526\) −3.50908e12 −1.99875
\(527\) −3.22695e11 8.64659e10i −0.182240 0.0488312i
\(528\) −1.67100e11 6.23625e11i −0.0935672 0.349198i
\(529\) 1.29295e12 + 7.46484e11i 0.717845 + 0.414448i
\(530\) 1.15859e11 1.31359e11i 0.0637808 0.0723133i
\(531\) 1.65681e12i 0.904371i
\(532\) −3.52422e9 + 4.30021e10i −0.00190748 + 0.0232749i
\(533\) 2.76535e11 + 2.76535e11i 0.148415 + 0.148415i
\(534\) 4.34653e11 2.50947e11i 0.231317 0.133551i
\(535\) −2.12860e12 + 1.41357e12i −1.12331 + 0.745975i
\(536\) −1.28397e12 + 2.22391e12i −0.671916 + 1.16379i
\(537\) −5.99722e10 + 2.23819e11i −0.0311218 + 0.116148i
\(538\) 8.62979e11 8.62979e11i 0.444099 0.444099i
\(539\) −1.55920e12 + 1.90021e12i −0.795708 + 0.969733i
\(540\) 4.31042e10 + 2.14088e10i 0.0218146 + 0.0108348i
\(541\) −4.81642e11 8.34228e11i −0.241733 0.418694i 0.719475 0.694519i \(-0.244383\pi\)
−0.961208 + 0.275824i \(0.911049\pi\)
\(542\) 2.62044e12 7.02144e11i 1.30430 0.349486i
\(543\) 4.13047e11 1.10676e11i 0.203892 0.0546328i
\(544\) 8.87557e10 + 1.53729e11i 0.0434511 + 0.0752596i
\(545\) −1.48559e12 + 4.99594e11i −0.721296 + 0.242568i
\(546\) 6.10636e11 + 7.19659e11i 0.294046 + 0.346545i
\(547\) −1.23049e12 + 1.23049e12i −0.587672 + 0.587672i −0.937000 0.349329i \(-0.886410\pi\)
0.349329 + 0.937000i \(0.386410\pi\)
\(548\) 4.09190e10 1.52712e11i 0.0193826 0.0723369i
\(549\) 1.15576e12 2.00183e12i 0.542988 0.940483i
\(550\) −2.17456e12 1.68828e12i −1.01330 0.786706i
\(551\) −1.34370e12 + 7.75788e11i −0.621043 + 0.358559i
\(552\) −1.71903e11 1.71903e11i −0.0788056 0.0788056i
\(553\) −3.23653e12 + 1.53093e12i −1.47169 + 0.696132i
\(554\) 1.38239e12i 0.623499i
\(555\) 4.73591e11 + 4.17710e11i 0.211878 + 0.186877i
\(556\) −1.37006e11 7.91005e10i −0.0608000 0.0351029i
\(557\) 1.92192e11 + 7.17270e11i 0.0846032 + 0.315743i 0.995239 0.0974671i \(-0.0310741\pi\)
−0.910636 + 0.413210i \(0.864407\pi\)
\(558\) 4.15756e11 + 1.11401e11i 0.181545 + 0.0486448i
\(559\) 2.21716e12 0.960384
\(560\) −2.33385e12 6.73527e11i −1.00283 0.289407i
\(561\) 7.70581e11 0.328462
\(562\) 3.35272e12 + 8.98358e11i 1.41770 + 0.379871i
\(563\) −8.84487e10 3.30095e11i −0.0371026 0.138469i 0.944890 0.327388i \(-0.106168\pi\)
−0.981993 + 0.188919i \(0.939502\pi\)
\(564\) 3.45243e10 + 1.99326e10i 0.0143671 + 0.00829485i
\(565\) 2.29774e12 1.44058e11i 0.948599 0.0594731i
\(566\) 1.38149e12i 0.565815i
\(567\) −1.08833e12 + 1.57261e12i −0.442217 + 0.638996i
\(568\) −2.97048e11 2.97048e11i −0.119746 0.119746i
\(569\) 3.14402e12 1.81520e12i 1.25742 0.725970i 0.284846 0.958573i \(-0.408058\pi\)
0.972572 + 0.232603i \(0.0747242\pi\)
\(570\) −7.17141e10 + 3.55262e11i −0.0284556 + 0.140965i
\(571\) −2.90001e11 + 5.02296e11i −0.114166 + 0.197741i −0.917446 0.397860i \(-0.869753\pi\)
0.803280 + 0.595601i \(0.203086\pi\)
\(572\) 6.13468e10 2.28949e11i 0.0239613 0.0894247i
\(573\) −7.07042e11 + 7.07042e11i −0.273999 + 0.273999i
\(574\) 1.16836e11 3.26578e11i 0.0449236 0.125569i
\(575\) −1.07417e12 1.47620e11i −0.409796 0.0563171i
\(576\) 1.15923e12 + 2.00785e12i 0.438803 + 0.760029i
\(577\) 9.68412e11 2.59485e11i 0.363722 0.0974589i −0.0723295 0.997381i \(-0.523043\pi\)
0.436051 + 0.899922i \(0.356377\pi\)
\(578\) 2.66890e11 7.15131e10i 0.0994621 0.0266508i
\(579\) 4.54409e11 + 7.87060e11i 0.168033 + 0.291041i
\(580\) 5.60914e10 + 1.66792e11i 0.0205812 + 0.0611999i
\(581\) 1.08254e12 9.18541e11i 0.394140 0.334431i
\(582\) 8.90626e11 8.90626e11i 0.321767 0.321767i
\(583\) −8.53854e10 + 3.18663e11i −0.0306108 + 0.114241i
\(584\) −6.43861e11 + 1.11520e12i −0.229052 + 0.396730i
\(585\) −2.32993e12 3.50848e12i −0.822510 1.23856i
\(586\) −4.21407e12 + 2.43300e12i −1.47626 + 0.852319i
\(587\) −2.84556e11 2.84556e11i −0.0989228 0.0989228i 0.655913 0.754836i \(-0.272284\pi\)
−0.754836 + 0.655913i \(0.772284\pi\)
\(588\) 1.51439e10 3.34305e10i 0.00522444 0.0115331i
\(589\) 2.95953e11i 0.101322i
\(590\) −1.84393e11 2.94107e12i −0.0626483 0.999244i
\(591\) −8.61074e11 4.97141e11i −0.290333 0.167624i
\(592\) −8.26024e11 3.08276e12i −0.276404 1.03155i
\(593\) 3.65323e12 + 9.78880e11i 1.21320 + 0.325075i 0.808015 0.589162i \(-0.200542\pi\)
0.405181 + 0.914237i \(0.367209\pi\)
\(594\) −2.06755e12 −0.681423
\(595\) 1.49744e12 2.48257e12i 0.489806 0.812036i
\(596\) 1.14774e11 0.0372593
\(597\) 2.26817e11 + 6.07753e10i 0.0730786 + 0.0195814i
\(598\) −5.51073e11 2.05663e12i −0.176220 0.657660i
\(599\) −2.48340e12 1.43379e12i −0.788180 0.455056i 0.0511416 0.998691i \(-0.483714\pi\)
−0.839321 + 0.543636i \(0.817047\pi\)
\(600\) −7.88333e11 3.31789e11i −0.248330 0.104516i
\(601\) 1.52213e12i 0.475901i 0.971277 + 0.237950i \(0.0764756\pi\)
−0.971277 + 0.237950i \(0.923524\pi\)
\(602\) −8.40818e11 1.77757e12i −0.260926 0.551624i
\(603\) 2.92056e12 + 2.92056e12i 0.899578 + 0.899578i
\(604\) 1.77610e11 1.02543e11i 0.0543002 0.0313502i
\(605\) 1.85262e12 + 3.73973e11i 0.562194 + 0.113486i
\(606\) 5.05956e10 8.76341e10i 0.0152400 0.0263965i
\(607\) 1.40560e12 5.24579e12i 0.420256 1.56842i −0.353813 0.935316i \(-0.615115\pi\)
0.774069 0.633101i \(-0.218218\pi\)
\(608\) 1.11195e11 1.11195e11i 0.0330004 0.0330004i
\(609\) 1.29845e12 2.36316e11i 0.382515 0.0696171i
\(610\) 1.82884e12 3.68216e12i 0.534800 1.07676i
\(611\) −3.63254e12 6.29175e12i −1.05445 1.82636i
\(612\) 1.34655e11 3.60807e10i 0.0388009 0.0103967i
\(613\) −1.03829e12 + 2.78209e11i −0.296993 + 0.0795791i −0.404239 0.914653i \(-0.632464\pi\)
0.107246 + 0.994233i \(0.465797\pi\)
\(614\) 1.97967e12 + 3.42889e12i 0.562127 + 0.973633i
\(615\) 5.68231e10 1.14407e11i 0.0160172 0.0322488i
\(616\) 4.30354e12 7.83235e11i 1.20424 0.219169i
\(617\) 2.24369e12 2.24369e12i 0.623275 0.623275i −0.323092 0.946367i \(-0.604722\pi\)
0.946367 + 0.323092i \(0.104722\pi\)
\(618\) −2.99120e11 + 1.11633e12i −0.0824892 + 0.307854i
\(619\) 1.53089e12 2.65157e12i 0.419117 0.725931i −0.576734 0.816932i \(-0.695673\pi\)
0.995851 + 0.0910006i \(0.0290065\pi\)
\(620\) 3.29018e10 + 6.64162e9i 0.00894245 + 0.00180514i
\(621\) −7.05206e11 + 4.07151e11i −0.190285 + 0.109861i
\(622\) −6.59823e11 6.59823e11i −0.176755 0.176755i
\(623\) 1.52081e12 + 3.21514e12i 0.404462 + 0.855074i
\(624\) 1.75676e12i 0.463854i
\(625\) −3.69568e12 + 9.45453e11i −0.968800 + 0.247845i
\(626\) −1.08377e12 6.25717e11i −0.282068 0.162852i
\(627\) −1.76680e11 6.59380e11i −0.0456545 0.170385i
\(628\) 1.92622e11 + 5.16128e10i 0.0494181 + 0.0132416i
\(629\) 3.80920e12 0.970301
\(630\) −1.92928e12 + 3.19851e12i −0.487937 + 0.808937i
\(631\) 1.59709e12 0.401048 0.200524 0.979689i \(-0.435735\pi\)
0.200524 + 0.979689i \(0.435735\pi\)
\(632\) 6.15436e12 + 1.64906e12i 1.53446 + 0.411158i
\(633\) 8.90648e10 + 3.32394e11i 0.0220490 + 0.0822881i
\(634\) −1.60794e12 9.28347e11i −0.395247 0.228196i
\(635\) −2.21341e11 3.53041e12i −0.0540233 0.861674i
\(636\) 4.92576e9i 0.00119376i
\(637\) −5.43629e12 + 3.89626e12i −1.30820 + 0.937607i
\(638\) −5.34546e12 5.34546e12i −1.27730 1.27730i
\(639\) −5.85151e11 + 3.37837e11i −0.138840 + 0.0801592i
\(640\) 2.49643e12 + 3.75921e12i 0.588180 + 0.885700i
\(641\) 2.46658e11 4.27224e11i 0.0577077 0.0999527i −0.835728 0.549143i \(-0.814954\pi\)
0.893436 + 0.449190i \(0.148288\pi\)
\(642\) −4.24195e11 + 1.58312e12i −0.0985504 + 0.367795i
\(643\) −9.60573e11 + 9.60573e11i −0.221606 + 0.221606i −0.809174 0.587569i \(-0.800085\pi\)
0.587569 + 0.809174i \(0.300085\pi\)
\(644\) −6.31307e10 + 5.35668e10i −0.0144629 + 0.0122718i
\(645\) −2.30843e11 6.86432e11i −0.0525168 0.156163i
\(646\) 1.09311e12 + 1.89333e12i 0.246955 + 0.427739i
\(647\) −2.37037e12 + 6.35139e11i −0.531798 + 0.142495i −0.514719 0.857359i \(-0.672104\pi\)
−0.0170798 + 0.999854i \(0.505437\pi\)
\(648\) 3.28741e12 8.80859e11i 0.732431 0.196254i
\(649\) 2.77522e12 + 4.80682e12i 0.614039 + 1.06355i
\(650\) −4.52643e12 5.96875e12i −0.994593 1.31152i
\(651\) 8.47990e10 2.37028e11i 0.0185045 0.0517231i
\(652\) −6.55900e10 + 6.55900e10i −0.0142142 + 0.0142142i
\(653\) 7.20578e11 2.68924e12i 0.155086 0.578788i −0.844012 0.536324i \(-0.819813\pi\)
0.999098 0.0424640i \(-0.0135208\pi\)
\(654\) −5.02663e11 + 8.70638e11i −0.107443 + 0.186096i
\(655\) −6.18541e11 + 3.06417e12i −0.131305 + 0.650470i
\(656\) −5.59108e11 + 3.22801e11i −0.117877 + 0.0680562i
\(657\) 1.46454e12 + 1.46454e12i 0.306661 + 0.306661i
\(658\) −3.66673e12 + 5.29836e12i −0.762539 + 1.10186i
\(659\) 8.40596e12i 1.73621i −0.496378 0.868106i \(-0.665337\pi\)
0.496378 0.868106i \(-0.334663\pi\)
\(660\) −7.72697e10 + 4.84448e9i −0.0158512 + 0.000993801i
\(661\) −2.66008e12 1.53580e12i −0.541985 0.312915i 0.203898 0.978992i \(-0.434639\pi\)
−0.745883 + 0.666077i \(0.767972\pi\)
\(662\) 2.00267e12 + 7.47407e12i 0.405274 + 1.51250i
\(663\) 2.02532e12 + 5.42683e11i 0.407083 + 0.109078i
\(664\) −2.52649e12 −0.504383
\(665\) −2.46765e12 7.12142e11i −0.489313 0.141211i
\(666\) −4.90772e12 −0.966598
\(667\) −2.87590e12 7.70594e11i −0.562609 0.150751i
\(668\) 8.81071e10 + 3.28820e11i 0.0171205 + 0.0638947i
\(669\) 1.71877e12 + 9.92335e11i 0.331743 + 0.191532i
\(670\) 5.50946e12 + 4.85938e12i 1.05626 + 0.931631i
\(671\) 7.74374e12i 1.47468i
\(672\) −1.20916e11 + 5.71951e10i −0.0228730 + 0.0108193i
\(673\) 1.91522e12 + 1.91522e12i 0.359874 + 0.359874i 0.863766 0.503893i \(-0.168099\pi\)
−0.503893 + 0.863766i \(0.668099\pi\)
\(674\) −4.28323e12 + 2.47292e12i −0.799469 + 0.461573i
\(675\) −1.75691e12 + 2.26295e12i −0.325748 + 0.419574i
\(676\) 1.97992e11 3.42933e11i 0.0364660 0.0631610i
\(677\) −2.27579e11 + 8.49337e11i −0.0416374 + 0.155393i −0.983615 0.180284i \(-0.942298\pi\)
0.941977 + 0.335677i \(0.108965\pi\)
\(678\) 1.04419e12 1.04419e12i 0.189778 0.189778i
\(679\) 5.77483e12 + 6.80587e12i 1.04262 + 1.22877i
\(680\) −4.89023e12 + 1.64456e12i −0.877080 + 0.294957i
\(681\) 2.91852e10 + 5.05502e10i 0.00519996 + 0.00900660i
\(682\) −1.39281e12 + 3.73203e11i −0.246526 + 0.0660565i
\(683\) −2.34263e12 + 6.27705e11i −0.411917 + 0.110373i −0.458826 0.888526i \(-0.651730\pi\)
0.0469085 + 0.998899i \(0.485063\pi\)
\(684\) −6.17480e10 1.06951e11i −0.0107862 0.0186823i
\(685\) 8.42871e12 + 4.18634e12i 1.46269 + 0.726486i
\(686\) 5.18537e12 + 2.88087e12i 0.893967 + 0.496667i
\(687\) 1.45693e12 1.45693e12i 0.249536 0.249536i
\(688\) −9.47314e11 + 3.53543e12i −0.161193 + 0.601581i
\(689\) −4.48838e11 + 7.77410e11i −0.0758757 + 0.131421i
\(690\) −5.79356e11 + 3.84741e11i −0.0973026 + 0.0646171i
\(691\) −1.15072e12 + 6.64371e11i −0.192008 + 0.110856i −0.592922 0.805260i \(-0.702026\pi\)
0.400914 + 0.916116i \(0.368693\pi\)
\(692\) −6.81275e10 6.81275e10i −0.0112939 0.0112939i
\(693\) 5.74666e11 7.01202e12i 0.0946490 1.15490i
\(694\) 6.32609e12i 1.03518i
\(695\) 6.22923e12 7.06257e12i 1.01275 1.14824i
\(696\) −2.03398e12 1.17432e12i −0.328553 0.189690i
\(697\) −1.99434e11 7.44298e11i −0.0320075 0.119454i
\(698\) −6.46578e12 1.73250e12i −1.03103 0.276264i
\(699\) −5.90186e11 −0.0935065
\(700\) −1.34548e11 + 2.58353e11i −0.0211805 + 0.0406698i
\(701\) 7.31544e12 1.14422 0.572109 0.820177i \(-0.306125\pi\)
0.572109 + 0.820177i \(0.306125\pi\)
\(702\) −5.43415e12 1.45608e12i −0.844529 0.226291i
\(703\) −8.73382e11 3.25951e12i −0.134867 0.503330i
\(704\) −6.72645e12 3.88352e12i −1.03207 0.595866i
\(705\) −1.56971e12 + 1.77971e12i −0.239314 + 0.271330i
\(706\) 4.39888e12i 0.666379i
\(707\) 5.89659e11 + 4.08074e11i 0.0887592 + 0.0614258i
\(708\) −5.86000e10 5.86000e10i −0.00876492 0.00876492i
\(709\) −7.01192e12 + 4.04833e12i −1.04215 + 0.601684i −0.920441 0.390883i \(-0.872170\pi\)
−0.121706 + 0.992566i \(0.538837\pi\)
\(710\) −1.00113e12 + 6.64833e11i −0.147852 + 0.0981861i
\(711\) 5.12394e12 8.87493e12i 0.751954 1.30242i
\(712\) 1.63816e12 6.11368e12i 0.238888 0.891544i
\(713\) −4.01572e11 + 4.01572e11i −0.0581917 + 0.0581917i
\(714\) −3.32978e11 1.82957e12i −0.0479483 0.263455i
\(715\) 1.26366e13 + 6.27627e12i 1.80822 + 0.898100i
\(716\) −7.02165e10 1.21619e11i −0.00998460 0.0172938i
\(717\) 2.89280e11 7.75124e10i 0.0408773 0.0109530i
\(718\) 8.02994e12 2.15162e12i 1.12759 0.302138i
\(719\) −3.08140e12 5.33714e12i −0.429999 0.744781i 0.566873 0.823805i \(-0.308153\pi\)
−0.996873 + 0.0790243i \(0.974820\pi\)
\(720\) 6.59002e12 2.21619e12i 0.913883 0.307334i
\(721\) −7.71133e12 2.75880e12i −1.06272 0.380200i
\(722\) −3.91058e12 + 3.91058e12i −0.535579 + 0.535579i
\(723\) 7.28711e11 2.71959e12i 0.0991820 0.370152i
\(724\) −1.29581e11 + 2.24441e11i −0.0175274 + 0.0303584i
\(725\) −1.03930e13 + 1.30833e12i −1.39707 + 0.175872i
\(726\) 1.04986e12 6.06138e11i 0.140255 0.0809761i
\(727\) −3.27755e12 3.27755e12i −0.435155 0.435155i 0.455223 0.890378i \(-0.349560\pi\)
−0.890378 + 0.455223i \(0.849560\pi\)
\(728\) 1.18626e13 + 9.72193e11i 1.56527 + 0.128281i
\(729\) 4.35558e12i 0.571179i
\(730\) 2.76277e12 + 2.43678e12i 0.360074 + 0.317588i
\(731\) −3.78326e12 2.18427e12i −0.490048 0.282929i
\(732\) −2.99249e10 1.11681e11i −0.00385241 0.0143774i
\(733\) −1.06542e13 2.85478e12i −1.36318 0.365262i −0.498194 0.867066i \(-0.666003\pi\)
−0.864981 + 0.501804i \(0.832670\pi\)
\(734\) 8.47092e12 1.07720
\(735\) 1.77229e12 + 1.27741e12i 0.223996 + 0.161449i
\(736\) 3.01756e11 0.0379058
\(737\) −1.33653e13 3.58123e12i −1.66869 0.447125i
\(738\) 2.56948e11 + 9.58942e11i 0.0318854 + 0.118998i
\(739\) 4.69583e11 + 2.71114e11i 0.0579178 + 0.0334389i 0.528679 0.848822i \(-0.322687\pi\)
−0.470761 + 0.882261i \(0.656021\pi\)
\(740\) −3.81967e11 + 2.39477e10i −0.0468255 + 0.00293576i
\(741\) 1.85748e12i 0.226330i
\(742\) 7.93488e11 + 6.50299e10i 0.0960999 + 0.00787581i
\(743\) −3.53551e12 3.53551e12i −0.425601 0.425601i 0.461526 0.887127i \(-0.347302\pi\)
−0.887127 + 0.461526i \(0.847302\pi\)
\(744\) −3.87969e11 + 2.23994e11i −0.0464214 + 0.0268014i
\(745\) −1.35188e12 + 6.69702e12i −0.160781 + 0.796487i
\(746\) 6.94686e12 1.20323e13i 0.821228 1.42241i
\(747\) −1.05174e12 + 3.92515e12i −0.123585 + 0.461225i
\(748\) −3.30232e11 + 3.30232e11i −0.0385711 + 0.0385711i
\(749\) −1.09358e13 3.91238e12i −1.26964 0.454227i
\(750\) −1.37664e12 + 2.02282e12i −0.158872 + 0.233444i
\(751\) 7.57235e12 + 1.31157e13i 0.868662 + 1.50457i 0.863364 + 0.504581i \(0.168353\pi\)
0.00529815 + 0.999986i \(0.498314\pi\)
\(752\) 1.15847e13 3.10411e12i 1.32100 0.353962i
\(753\) 5.42667e10 1.45407e10i 0.00615114 0.00164819i
\(754\) −1.02849e13 1.78140e13i −1.15886 2.00720i
\(755\) 3.89137e12 + 1.15713e13i 0.435854 + 1.29605i
\(756\) 3.91710e10 + 2.15228e11i 0.00436131 + 0.0239635i
\(757\) 8.94189e12 8.94189e12i 0.989687 0.989687i −0.0102606 0.999947i \(-0.503266\pi\)
0.999947 + 0.0102606i \(0.00326612\pi\)
\(758\) 1.37501e12 5.13162e12i 0.151285 0.564602i
\(759\) 6.54965e11 1.13443e12i 0.0716358 0.124077i
\(760\) 2.52848e12 + 3.80747e12i 0.274915 + 0.413976i
\(761\) 1.30630e13 7.54194e12i 1.41193 0.815178i 0.416359 0.909200i \(-0.363306\pi\)
0.995570 + 0.0940228i \(0.0299727\pi\)
\(762\) −1.60437e12 1.60437e12i −0.172388 0.172388i
\(763\) −5.85822e12 4.05418e12i −0.625756 0.433055i
\(764\) 6.06005e11i 0.0643511i
\(765\) 5.19250e11 + 8.28207e12i 0.0548151 + 0.874304i
\(766\) 9.43423e12 + 5.44686e12i 0.990095 + 0.571632i
\(767\) 3.90890e12 + 1.45882e13i 0.407827 + 1.52203i
\(768\) 3.52993e11 + 9.45841e10i 0.0366134 + 0.00981054i
\(769\) −1.03458e11 −0.0106683 −0.00533415 0.999986i \(-0.501698\pi\)
−0.00533415 + 0.999986i \(0.501698\pi\)
\(770\) 2.39720e11 1.25113e13i 0.0245751 1.28261i
\(771\) −2.38399e12 −0.242974
\(772\) −5.32031e11 1.42557e11i −0.0539087 0.0144448i
\(773\) −2.26660e12 8.45906e12i −0.228332 0.852147i −0.981042 0.193795i \(-0.937920\pi\)
0.752710 0.658352i \(-0.228746\pi\)
\(774\) 4.87430e12 + 2.81418e12i 0.488178 + 0.281850i
\(775\) −7.75074e11 + 1.84158e12i −0.0771766 + 0.183372i
\(776\) 1.58839e13i 1.57246i
\(777\) −2.34453e11 + 2.86078e12i −0.0230761 + 0.281572i
\(778\) 2.66919e11 + 2.66919e11i 0.0261199 + 0.0261199i
\(779\) −5.91163e11 + 3.41308e11i −0.0575160 + 0.0332069i
\(780\) −2.06500e11 4.16846e10i −0.0199754 0.00403227i
\(781\) 1.13178e12 1.96030e12i 0.108851 0.188535i
\(782\) −1.08579e12 + 4.05224e12i −0.103829 + 0.387494i
\(783\) −5.56274e12 + 5.56274e12i −0.528884 + 0.528884i
\(784\) −3.89013e12 1.03333e13i −0.367741 0.976824i
\(785\) −5.28041e12 + 1.06315e13i −0.496311 + 0.999265i
\(786\) 1.00253e12 + 1.73644e12i 0.0936909 + 0.162277i
\(787\) 1.25065e13 3.35110e12i 1.16211 0.311387i 0.374303 0.927306i \(-0.377882\pi\)
0.787809 + 0.615919i \(0.211215\pi\)
\(788\) 5.82062e11 1.55963e11i 0.0537776 0.0144097i
\(789\) −2.93718e12 5.08734e12i −0.269826 0.467352i
\(790\) 8.10801e12 1.63245e13i 0.740614 1.49114i
\(791\) 6.77055e12 + 7.97938e12i 0.614936 + 0.724727i
\(792\) −8.85311e12 + 8.85311e12i −0.799526 + 0.799526i
\(793\) −5.45354e12 + 2.03529e13i −0.489722 + 1.82767i
\(794\) −7.28791e12 + 1.26230e13i −0.650744 + 1.12712i
\(795\) 2.87417e11 + 5.80186e10i 0.0255188 + 0.00515128i
\(796\) −1.23247e11 + 7.11568e10i −0.0108810 + 0.00628214i
\(797\) −3.83196e12 3.83196e12i −0.336402 0.336402i 0.518609 0.855011i \(-0.326450\pi\)
−0.855011 + 0.518609i \(0.826450\pi\)
\(798\) −1.48920e12 + 7.04414e11i −0.129999 + 0.0614915i
\(799\) 1.43146e13i 1.24256i
\(800\) 9.83124e11 4.00705e11i 0.0848601 0.0345876i
\(801\) −8.81627e12 5.09007e12i −0.756726 0.436896i
\(802\) 4.66272e12 + 1.74015e13i 0.397974 + 1.48526i
\(803\) −6.70218e12 1.79584e12i −0.568848 0.152422i
\(804\) 2.06596e11 0.0174369
\(805\) −2.38202e12 4.31460e12i −0.199923 0.362125i
\(806\) −3.92357e12 −0.327472
\(807\) 1.97345e12 + 5.28784e11i 0.163793 + 0.0438882i
\(808\) −3.30282e11 1.23263e12i −0.0272605 0.101738i
\(809\) −4.10941e11 2.37257e11i −0.0337296 0.0194738i 0.483040 0.875598i \(-0.339532\pi\)
−0.516770 + 0.856124i \(0.672866\pi\)
\(810\) −6.09224e11 9.71715e12i −0.0497272 0.793152i
\(811\) 9.13605e12i 0.741591i 0.928714 + 0.370796i \(0.120915\pi\)
−0.928714 + 0.370796i \(0.879085\pi\)
\(812\) −4.55178e11 + 6.57725e11i −0.0367434 + 0.0530936i
\(813\) 3.21131e12 + 3.21131e12i 0.257795 + 0.257795i
\(814\) 1.42385e13 8.22062e12i 1.13673 0.656289i
\(815\) −3.05460e12 4.59972e12i −0.242519 0.365193i
\(816\) −1.73069e12 + 2.99765e12i −0.136652 + 0.236687i
\(817\) −1.00163e12 + 3.73812e12i −0.0786514 + 0.293531i
\(818\) −1.05868e13 + 1.05868e13i −0.826752 + 0.826752i
\(819\) 6.44863e12 1.80250e13i 0.500829 1.39990i
\(820\) 2.46774e10 + 7.33804e10i 0.00190606 + 0.00566784i
\(821\) −7.04092e12 1.21952e13i −0.540860 0.936798i −0.998855 0.0478426i \(-0.984765\pi\)
0.457995 0.888955i \(-0.348568\pi\)
\(822\) 5.83079e12 1.56235e12i 0.445455 0.119359i
\(823\) 5.24273e12 1.40478e12i 0.398344 0.106736i −0.0540852 0.998536i \(-0.517224\pi\)
0.452429 + 0.891800i \(0.350558\pi\)
\(824\) 7.28729e12 + 1.26220e13i 0.550673 + 0.953793i
\(825\) 6.27456e11 4.56573e12i 0.0471564 0.343137i
\(826\) 1.02135e13 8.66621e12i 0.763420 0.647767i
\(827\) 5.13734e12 5.13734e12i 0.381912 0.381912i −0.489878 0.871791i \(-0.662959\pi\)
0.871791 + 0.489878i \(0.162959\pi\)
\(828\) 6.13346e10 2.28904e11i 0.00453491 0.0169245i
\(829\) −8.10264e12 + 1.40342e13i −0.595842 + 1.03203i 0.397586 + 0.917565i \(0.369848\pi\)
−0.993427 + 0.114463i \(0.963485\pi\)
\(830\) −1.43014e12 + 7.08475e12i −0.104599 + 0.518171i
\(831\) −2.00414e12 + 1.15709e12i −0.145788 + 0.0841709i
\(832\) −1.49442e13 1.49442e13i −1.08123 1.08123i
\(833\) 1.31147e13 1.29276e12i 0.943747 0.0930283i
\(834\) 6.04038e12i 0.432332i
\(835\) −2.02244e13 + 1.26798e12i −1.43974 + 0.0902658i
\(836\) 3.58293e11 + 2.06860e11i 0.0253694 + 0.0146470i
\(837\) 3.88373e11 + 1.44943e12i 0.0273517 + 0.102078i
\(838\) −1.11279e13 2.98171e12i −0.779499 0.208866i
\(839\) 2.39905e12 0.167151 0.0835757 0.996501i \(-0.473366\pi\)
0.0835757 + 0.996501i \(0.473366\pi\)
\(840\) −9.34102e11 3.77387e12i −0.0647347 0.261535i
\(841\) −1.42568e13 −0.982741
\(842\) −7.40109e12 1.98312e12i −0.507448 0.135970i
\(843\) 1.50389e12 + 5.61260e12i 0.102563 + 0.382772i
\(844\) −1.80616e11 1.04279e11i −0.0122522 0.00707383i
\(845\) 1.76779e13 + 1.55921e13i 1.19282 + 1.05208i
\(846\) 1.84427e13i 1.23782i
\(847\) 3.67336e12 + 7.76586e12i 0.245238 + 0.518459i
\(848\) −1.04786e12 1.04786e12i −0.0695862 0.0695862i
\(849\) −2.00284e12 + 1.15634e12i −0.132301 + 0.0763838i
\(850\) 1.84349e12 + 1.46441e13i 0.121131 + 0.962225i
\(851\) 3.23768e12 5.60783e12i 0.211617 0.366532i
\(852\) −8.74730e9 + 3.26454e10i −0.000568717 + 0.00212248i
\(853\) −1.11316e13 + 1.11316e13i −0.719928 + 0.719928i −0.968590 0.248663i \(-0.920009\pi\)
0.248663 + 0.968590i \(0.420009\pi\)
\(854\) 1.83857e13 3.34617e12i 1.18283 0.215272i
\(855\) 6.96784e12 2.34325e12i 0.445914 0.149958i
\(856\) 1.03344e13 + 1.78998e13i 0.657892 + 1.13950i
\(857\) 1.51544e13 4.06061e12i 0.959677 0.257145i 0.255213 0.966885i \(-0.417854\pi\)
0.704463 + 0.709740i \(0.251188\pi\)
\(858\) 8.74167e12 2.34232e12i 0.550683 0.147555i
\(859\) −2.33636e12 4.04669e12i −0.146410 0.253589i 0.783488 0.621407i \(-0.213438\pi\)
−0.929898 + 0.367817i \(0.880105\pi\)
\(860\) 3.93098e11 + 1.95242e11i 0.0245051 + 0.0121711i
\(861\) 5.71256e11 1.03967e11i 0.0354255 0.00644738i
\(862\) −1.05900e13 + 1.05900e13i −0.653300 + 0.653300i
\(863\) 4.19071e12 1.56399e13i 0.257181 0.959813i −0.709683 0.704521i \(-0.751162\pi\)
0.966864 0.255292i \(-0.0821716\pi\)
\(864\) 3.98658e11 6.90496e11i 0.0243382 0.0421550i
\(865\) 4.77767e12 3.17277e12i 0.290164 0.192693i
\(866\) 1.36011e10 7.85259e9i 0.000821756 0.000474441i
\(867\) 3.27070e11 + 3.27070e11i 0.0196587 + 0.0196587i
\(868\) 6.52375e10 + 1.37919e11i 0.00390084 + 0.00824678i
\(869\) 3.43312e13i 2.04221i
\(870\) −4.44438e12 + 5.03894e12i −0.263011 + 0.298197i
\(871\) −3.26061e13 1.88252e13i −1.91963 1.10830i
\(872\) 3.28133e12 + 1.22461e13i 0.192188 + 0.717255i
\(873\) −2.46772e13 6.61224e12i −1.43791 0.385287i
\(874\) 3.71642e12 0.215439
\(875\) −1.34900e13 1.08939e13i −0.777995 0.628271i
\(876\) 1.03600e11 0.00594415
\(877\) 8.36958e10 + 2.24262e10i 0.00477755 + 0.00128014i 0.261207 0.965283i \(-0.415879\pi\)
−0.256429 + 0.966563i \(0.582546\pi\)
\(878\) 1.62269e12 + 6.05598e12i 0.0921534 + 0.343921i
\(879\) −7.05454e12 4.07294e12i −0.398583 0.230122i
\(880\) −1.54071e13 + 1.74683e13i −0.866062 + 0.981923i
\(881\) 2.39476e13i 1.33928i 0.742687 + 0.669639i \(0.233551\pi\)
−0.742687 + 0.669639i \(0.766449\pi\)
\(882\) −1.68968e13 + 1.66557e12i −0.940145 + 0.0926733i
\(883\) 1.42084e13 + 1.42084e13i 0.786545 + 0.786545i 0.980926 0.194381i \(-0.0622699\pi\)
−0.194381 + 0.980926i \(0.562270\pi\)
\(884\) −1.10052e12 + 6.35383e11i −0.0606124 + 0.0349946i
\(885\) 4.10952e12 2.72907e12i 0.225189 0.149544i
\(886\) 7.60769e12 1.31769e13i 0.414764 0.718392i
\(887\) 5.31167e12 1.98234e13i 0.288121 1.07528i −0.658408 0.752661i \(-0.728770\pi\)
0.946529 0.322620i \(-0.104564\pi\)
\(888\) 3.61191e12 3.61191e12i 0.194930 0.194930i
\(889\) 1.22601e13 1.04028e13i 0.658317 0.558586i
\(890\) −1.62166e13 8.05441e12i −0.866374 0.430308i
\(891\) 9.16917e12 + 1.58815e13i 0.487394 + 0.844192i
\(892\) −1.16184e12 + 3.11315e11i −0.0614477 + 0.0164649i
\(893\) 1.22489e13 3.28208e12i 0.644562 0.172710i
\(894\) 2.19113e12 + 3.79515e12i 0.114723 + 0.198705i
\(895\) 7.92346e12 2.66462e12i 0.412773 0.138813i
\(896\) −6.90947e12 + 1.93131e13i −0.358145 + 1.00108i
\(897\) 2.52038e12 2.52038e12i 0.129987 0.129987i
\(898\) −6.34320e12 + 2.36732e13i −0.325511 + 1.21482i
\(899\) −2.74326e12 + 4.75147e12i −0.140071 + 0.242610i
\(900\) −1.04135e11 8.27217e11i −0.00529062 0.0420270i
\(901\) 1.53175e12 8.84357e11i 0.0774331 0.0447060i
\(902\) −2.35174e12 2.35174e12i −0.118293 0.118293i
\(903\) 1.87328e12 2.70686e12i 0.0937579 0.135478i
\(904\) 1.86227e13i 0.927437i
\(905\) −1.15698e13 1.02046e13i −0.573333 0.505683i
\(906\) 6.78145e12 + 3.91527e12i 0.334384 + 0.193057i
\(907\) 6.84027e12 + 2.55282e13i 0.335614 + 1.25253i 0.903202 + 0.429217i \(0.141210\pi\)
−0.567587 + 0.823313i \(0.692123\pi\)
\(908\) −3.41705e10 9.15597e9i −0.00166827 0.000447011i
\(909\) −2.05251e12 −0.0997119
\(910\) 9.44117e12 3.27147e13i 0.456393 1.58145i
\(911\) 2.21543e13 1.06568 0.532839 0.846217i \(-0.321125\pi\)
0.532839 + 0.846217i \(0.321125\pi\)
\(912\) 2.96188e12 + 7.93634e11i 0.141772 + 0.0379877i
\(913\) −3.52341e12 1.31495e13i −0.167820 0.626314i
\(914\) 3.21129e12 + 1.85404e12i 0.152202 + 0.0878741i
\(915\) 6.86904e12 4.30660e11i 0.323967 0.0203114i
\(916\) 1.24873e12i 0.0586057i
\(917\) −1.28445e13 + 6.07563e12i −0.599867 + 0.283746i
\(918\) 7.83810e12 + 7.83810e12i 0.364266 + 0.364266i
\(919\) 2.59112e13 1.49598e13i 1.19830 0.691842i 0.238128 0.971234i \(-0.423466\pi\)
0.960177 + 0.279392i \(0.0901330\pi\)
\(920\) −1.73543e12 + 8.59711e12i −0.0798661 + 0.395647i
\(921\) −3.31405e12 + 5.74011e12i −0.151772 + 0.262877i
\(922\) 1.08515e13 4.04985e13i 0.494540 1.84565i
\(923\) 4.35521e12 4.35521e12i 0.197516 0.197516i
\(924\) −2.27684e11 2.68335e11i −0.0102756 0.0121103i
\(925\) 3.10170e12 2.25697e13i 0.139303 1.01365i
\(926\) 1.17121e13 + 2.02860e13i 0.523463 + 0.906664i
\(927\) 2.26431e13 6.06719e12i 1.00711 0.269854i
\(928\) 2.81591e12 7.54520e11i 0.124639 0.0333968i
\(929\) −2.69415e12 4.66641e12i −0.118673 0.205547i 0.800569 0.599240i \(-0.204531\pi\)
−0.919242 + 0.393693i \(0.871197\pi\)
\(930\) 4.08508e11 + 1.21473e12i 0.0179072 + 0.0532485i
\(931\) −4.11316e12 1.09257e13i −0.179433 0.476625i
\(932\) 2.52924e11 2.52924e11i 0.0109804 0.0109804i
\(933\) 4.04302e11 1.50888e12i 0.0174678 0.0651908i
\(934\) −1.64233e12 + 2.84459e12i −0.0706153 + 0.122309i
\(935\) −1.53793e13 2.31586e13i −0.658087 0.990969i
\(936\) −2.95035e13 + 1.70338e13i −1.25641 + 0.725390i
\(937\) 4.64335e12 + 4.64335e12i 0.196790 + 0.196790i 0.798622 0.601832i \(-0.205562\pi\)
−0.601832 + 0.798622i \(0.705562\pi\)
\(938\) −2.72748e12 + 3.32805e13i −0.115040 + 1.40371i
\(939\) 2.09495e12i 0.0879386i
\(940\) −8.99929e10 1.43539e12i −0.00375952 0.0599646i
\(941\) −2.44520e13 1.41174e13i −1.01663 0.586949i −0.103501 0.994629i \(-0.533005\pi\)
−0.913125 + 0.407680i \(0.866338\pi\)
\(942\) 1.97066e12 + 7.35461e12i 0.0815423 + 0.304320i
\(943\) −1.26525e12 3.39023e11i −0.0521044 0.0139613i
\(944\) −2.49321e13 −1.02184
\(945\) −1.30199e13 2.49464e11i −0.531084 0.0101757i
\(946\) −1.88554e13 −0.765467
\(947\) −7.27166e12 1.94844e12i −0.293805 0.0787247i 0.108906 0.994052i \(-0.465265\pi\)
−0.402711 + 0.915327i \(0.631932\pi\)
\(948\) −1.32669e11 4.95129e11i −0.00533499 0.0199105i
\(949\) −1.63506e13 9.44005e12i −0.654390 0.377813i
\(950\) 1.21081e13 4.93508e12i 0.482304 0.196579i
\(951\) 3.10819e12i 0.123224i
\(952\) −1.92840e13 1.33455e13i −0.760906 0.526585i
\(953\) −2.08350e13 2.08350e13i −0.818231 0.818231i 0.167621 0.985852i \(-0.446392\pi\)
−0.985852 + 0.167621i \(0.946392\pi\)
\(954\) −1.97348e12 + 1.13939e12i −0.0771376 + 0.0445354i
\(955\) 3.53602e13 + 7.13789e12i 1.37562 + 0.277687i
\(956\) −9.07529e10 + 1.57189e11i −0.00351399 + 0.00608640i
\(957\) 3.27539e12 1.22239e13i 0.126229 0.471093i
\(958\) 1.40535e13 1.40535e13i 0.539064 0.539064i
\(959\) 7.65962e12 + 4.20862e13i 0.292431 + 1.60678i
\(960\) −3.07077e12 + 6.18264e12i −0.116688 + 0.234938i
\(961\) −1.26966e13 2.19911e13i −0.480209 0.831747i
\(962\) 4.32126e13 1.15788e13i 1.62676 0.435888i
\(963\) 3.21111e13 8.60415e12i 1.20320 0.322396i
\(964\) 8.53188e11 + 1.47776e12i 0.0318198 + 0.0551136i
\(965\) 1.45848e13 2.93647e13i 0.541410 1.09007i
\(966\) −2.97647e12 1.06486e12i −0.109978 0.0393456i
\(967\) 2.26860e13 2.26860e13i 0.834330 0.834330i −0.153775 0.988106i \(-0.549143\pi\)
0.988106 + 0.153775i \(0.0491432\pi\)
\(968\) 3.95681e12 1.47670e13i 0.144846 0.540572i
\(969\) −1.82992e12 + 3.16951e12i −0.0666768 + 0.115488i
\(970\) −4.45415e13 8.99125e12i −1.61544 0.326097i
\(971\) 1.92722e13 1.11268e13i 0.695735 0.401683i −0.110022 0.993929i \(-0.535092\pi\)
0.805757 + 0.592247i \(0.201759\pi\)
\(972\) −6.72914e11 6.72914e11i −0.0241803 0.0241803i
\(973\) 4.26622e13 + 3.49636e12i 1.52593 + 0.125057i
\(974\) 2.43079e13i 0.865432i
\(975\) 4.86457e12 1.15582e13i 0.172395 0.409610i
\(976\) −3.01240e13 1.73921e13i −1.06265 0.613520i
\(977\) −7.25525e12 2.70769e13i −0.254757 0.950767i −0.968225 0.250079i \(-0.919543\pi\)
0.713468 0.700688i \(-0.247123\pi\)
\(978\) −3.42099e12 9.16651e11i −0.119571 0.0320390i
\(979\) 3.41043e13 1.18655
\(980\) −1.30694e12 + 2.12080e11i −0.0452626 + 0.00734485i
\(981\) 2.03915e13 0.702973
\(982\) −2.27788e13 6.10357e12i −0.781681 0.209451i
\(983\) −2.28867e12 8.54142e12i −0.0781793 0.291769i 0.915756 0.401735i \(-0.131593\pi\)
−0.993935 + 0.109966i \(0.964926\pi\)
\(984\) −8.94852e11 5.16643e11i −0.0304280 0.0175676i
\(985\) 2.24452e12 + 3.58002e13i 0.0759732 + 1.21178i
\(986\) 4.05294e13i 1.36560i
\(987\) −1.07505e13 8.81051e11i −0.360580 0.0295511i
\(988\) 7.96021e11 + 7.96021e11i 0.0265778 + 0.0265778i
\(989\) −6.43127e12 + 3.71310e12i −0.213754 + 0.123411i
\(990\) 1.98144e13 + 2.98372e13i 0.655576 + 0.987187i
\(991\) −3.83070e12 + 6.63496e12i −0.126167 + 0.218528i −0.922189 0.386741i \(-0.873601\pi\)
0.796021 + 0.605268i \(0.206934\pi\)
\(992\) 1.43920e11 5.37116e11i 0.00471865 0.0176103i
\(993\) −9.15936e12 + 9.15936e12i −0.298947 + 0.298947i
\(994\) −5.14335e12 1.84008e12i −0.167112 0.0597859i
\(995\) −2.70030e12 8.02957e12i −0.0873390 0.259710i
\(996\) 1.01630e11 + 1.76029e11i 0.00327232 + 0.00566782i
\(997\) −4.40756e13 + 1.18100e13i −1.41277 + 0.378550i −0.882912 0.469539i \(-0.844420\pi\)
−0.529855 + 0.848088i \(0.677754\pi\)
\(998\) −3.31130e13 + 8.87259e12i −1.05660 + 0.283115i
\(999\) −8.55478e12 1.48173e13i −0.271747 0.470679i
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 35.10.k.a.3.10 136
5.2 odd 4 inner 35.10.k.a.17.25 yes 136
7.5 odd 6 inner 35.10.k.a.33.25 yes 136
35.12 even 12 inner 35.10.k.a.12.10 yes 136
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.k.a.3.10 136 1.1 even 1 trivial
35.10.k.a.12.10 yes 136 35.12 even 12 inner
35.10.k.a.17.25 yes 136 5.2 odd 4 inner
35.10.k.a.33.25 yes 136 7.5 odd 6 inner