Properties

Label 17.10.d.a.15.5
Level $17$
Weight $10$
Character 17.15
Analytic conductor $8.756$
Analytic rank $0$
Dimension $52$
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] = [17,10,Mod(2,17)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(17, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([7]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("17.2");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 17 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 17.d (of order \(8\), 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: \(8.75560921479\)
Analytic rank: \(0\)
Dimension: \(52\)
Relative dimension: \(13\) over \(\Q(\zeta_{8})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 15.5
Character \(\chi\) \(=\) 17.15
Dual form 17.10.d.a.8.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-12.2939 - 12.2939i) q^{2} +(41.5316 + 100.266i) q^{3} -209.719i q^{4} +(-793.507 + 328.681i) q^{5} +(722.077 - 1743.25i) q^{6} +(7184.85 + 2976.06i) q^{7} +(-8872.76 + 8872.76i) q^{8} +(5589.57 - 5589.57i) q^{9} +O(q^{10})\) \(q+(-12.2939 - 12.2939i) q^{2} +(41.5316 + 100.266i) q^{3} -209.719i q^{4} +(-793.507 + 328.681i) q^{5} +(722.077 - 1743.25i) q^{6} +(7184.85 + 2976.06i) q^{7} +(-8872.76 + 8872.76i) q^{8} +(5589.57 - 5589.57i) q^{9} +(13796.1 + 5714.52i) q^{10} +(36020.0 - 86960.0i) q^{11} +(21027.7 - 8709.97i) q^{12} -69059.4i q^{13} +(-51742.5 - 124917. i) q^{14} +(-65911.1 - 65911.1i) q^{15} +110785. q^{16} +(268634. - 215462. i) q^{17} -137435. q^{18} +(567107. + 567107. i) q^{19} +(68930.8 + 166414. i) q^{20} +843997. i q^{21} +(-1.51191e6 + 626252. i) q^{22} +(636421. - 1.53646e6i) q^{23} +(-1.25814e6 - 521137. i) q^{24} +(-859447. + 859447. i) q^{25} +(-849010. + 849010. i) q^{26} +(2.76612e6 + 1.14577e6i) q^{27} +(624138. - 1.50680e6i) q^{28} +(-4.94229e6 + 2.04716e6i) q^{29} +1.62061e6i q^{30} +(-1.49259e6 - 3.60342e6i) q^{31} +(3.18086e6 + 3.18086e6i) q^{32} +1.02151e7 q^{33} +(-5.95143e6 - 653697. i) q^{34} -6.67940e6 q^{35} +(-1.17224e6 - 1.17224e6i) q^{36} +(4.00274e6 + 9.66348e6i) q^{37} -1.39439e7i q^{38} +(6.92431e6 - 2.86814e6i) q^{39} +(4.12428e6 - 9.95690e6i) q^{40} +(1.02441e7 + 4.24324e6i) q^{41} +(1.03760e7 - 1.03760e7i) q^{42} +(8.66131e6 - 8.66131e6i) q^{43} +(-1.82372e7 - 7.55409e6i) q^{44} +(-2.59817e6 + 6.27255e6i) q^{45} +(-2.67132e7 + 1.10650e7i) q^{46} -1.96866e7i q^{47} +(4.60109e6 + 1.11080e7i) q^{48} +(1.42308e7 + 1.42308e7i) q^{49} +2.11319e7 q^{50} +(3.27603e7 + 1.79864e7i) q^{51} -1.44831e7 q^{52} +(-5.00580e7 - 5.00580e7i) q^{53} +(-1.99205e7 - 4.80925e7i) q^{54} +8.08424e7i q^{55} +(-9.01553e7 + 3.73435e7i) q^{56} +(-3.33088e7 + 8.04145e7i) q^{57} +(8.59277e7 + 3.55924e7i) q^{58} +(-3.24953e7 + 3.24953e7i) q^{59} +(-1.38228e7 + 1.38228e7i) q^{60} +(5.98943e7 + 2.48090e7i) q^{61} +(-2.59504e7 + 6.26499e7i) q^{62} +(5.67951e7 - 2.35253e7i) q^{63} -1.34933e8i q^{64} +(2.26985e7 + 5.47991e7i) q^{65} +(-1.25584e8 - 1.25584e8i) q^{66} +5.04019e7 q^{67} +(-4.51865e7 - 5.63377e7i) q^{68} +1.80486e8 q^{69} +(8.21160e7 + 8.21160e7i) q^{70} +(-1.12991e8 - 2.72785e8i) q^{71} +9.91898e7i q^{72} +(-6.12788e7 + 2.53825e7i) q^{73} +(6.95926e7 - 1.68011e8i) q^{74} +(-1.21867e8 - 5.04792e7i) q^{75} +(1.18933e8 - 1.18933e8i) q^{76} +(5.17597e8 - 5.17597e8i) q^{77} +(-1.20388e8 - 4.98662e7i) q^{78} +(-1.82078e8 + 4.39575e8i) q^{79} +(-8.79090e7 + 3.64131e7i) q^{80} +1.69343e8i q^{81} +(-7.37739e7 - 1.78106e8i) q^{82} +(2.01989e8 + 2.01989e8i) q^{83} +1.77003e8 q^{84} +(-1.42345e8 + 2.59265e8i) q^{85} -2.12963e8 q^{86} +(-4.10522e8 - 4.10522e8i) q^{87} +(4.51978e8 + 1.09117e9i) q^{88} +7.06114e8i q^{89} +(1.09056e8 - 4.51724e7i) q^{90} +(2.05525e8 - 4.96181e8i) q^{91} +(-3.22225e8 - 1.33470e8i) q^{92} +(2.99312e8 - 2.99312e8i) q^{93} +(-2.42025e8 + 2.42025e8i) q^{94} +(-6.36401e8 - 2.63606e8i) q^{95} +(-1.86826e8 + 4.51039e8i) q^{96} +(-8.43523e8 + 3.49399e8i) q^{97} -3.49905e8i q^{98} +(-2.84733e8 - 6.87405e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 52 q - 4 q^{2} - 4 q^{3} - 1140 q^{5} + 12308 q^{6} - 4 q^{7} + 2044 q^{8} - 83224 q^{9} - 117636 q^{10} - 115768 q^{11} - 145528 q^{12} + 463660 q^{14} + 288244 q^{15} - 3407880 q^{16} - 271932 q^{17} + 2193336 q^{18} - 406700 q^{19} + 493564 q^{20} + 800964 q^{22} - 4172180 q^{23} + 15078440 q^{24} + 11946576 q^{25} - 14209012 q^{26} - 7973656 q^{27} + 13540804 q^{28} + 7833752 q^{29} + 5936252 q^{31} - 26730116 q^{32} - 1635208 q^{33} - 53493988 q^{34} + 46992776 q^{35} - 12761764 q^{36} + 74606796 q^{37} + 74096776 q^{39} - 69317672 q^{40} - 71362288 q^{41} - 308117664 q^{42} - 3765712 q^{43} + 163659820 q^{44} + 14167408 q^{45} + 72135428 q^{46} + 164621412 q^{48} - 284548508 q^{49} + 226223888 q^{50} - 406733132 q^{51} + 103553016 q^{52} - 244724728 q^{53} + 971226260 q^{54} + 470691652 q^{56} - 440646580 q^{57} - 308561768 q^{58} - 481734984 q^{59} + 379626176 q^{60} + 507966228 q^{61} + 358867236 q^{62} + 1070586456 q^{63} + 366263684 q^{65} - 2244715148 q^{66} - 311910088 q^{67} - 1839196668 q^{68} + 533688136 q^{69} + 34867672 q^{70} + 186006812 q^{71} + 487115192 q^{73} - 214149412 q^{74} + 533015920 q^{75} + 1104236912 q^{76} - 237869092 q^{77} - 2081523384 q^{78} - 136338052 q^{79} - 922534152 q^{80} + 1951892384 q^{82} + 1843663888 q^{83} - 2630025952 q^{84} - 395061976 q^{85} + 1538547296 q^{86} - 369395636 q^{87} - 3388839640 q^{88} + 874363684 q^{90} + 2087197720 q^{91} + 1061427500 q^{92} + 576415420 q^{93} + 6899365112 q^{94} + 5031766876 q^{95} + 490811364 q^{96} - 3419996368 q^{97} - 5630536112 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/17\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{3}{8}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −12.2939 12.2939i −0.543319 0.543319i 0.381181 0.924500i \(-0.375517\pi\)
−0.924500 + 0.381181i \(0.875517\pi\)
\(3\) 41.5316 + 100.266i 0.296028 + 0.714675i 0.999990 + 0.00443716i \(0.00141240\pi\)
−0.703962 + 0.710237i \(0.748588\pi\)
\(4\) 209.719i 0.409608i
\(5\) −793.507 + 328.681i −0.567787 + 0.235185i −0.648062 0.761588i \(-0.724420\pi\)
0.0802748 + 0.996773i \(0.474420\pi\)
\(6\) 722.077 1743.25i 0.227459 0.549134i
\(7\) 7184.85 + 2976.06i 1.13104 + 0.468491i 0.868133 0.496332i \(-0.165320\pi\)
0.262903 + 0.964822i \(0.415320\pi\)
\(8\) −8872.76 + 8872.76i −0.765867 + 0.765867i
\(9\) 5589.57 5589.57i 0.283980 0.283980i
\(10\) 13796.1 + 5714.52i 0.436270 + 0.180709i
\(11\) 36020.0 86960.0i 0.741783 1.79082i 0.143311 0.989678i \(-0.454225\pi\)
0.598472 0.801144i \(-0.295775\pi\)
\(12\) 21027.7 8709.97i 0.292736 0.121255i
\(13\) 69059.4i 0.670622i −0.942108 0.335311i \(-0.891159\pi\)
0.942108 0.335311i \(-0.108841\pi\)
\(14\) −51742.5 124917.i −0.359974 0.869054i
\(15\) −65911.1 65911.1i −0.336162 0.336162i
\(16\) 110785. 0.422613
\(17\) 268634. 215462.i 0.780083 0.625676i
\(18\) −137435. −0.308583
\(19\) 567107. + 567107.i 0.998330 + 0.998330i 0.999999 0.00166876i \(-0.000531184\pi\)
−0.00166876 + 0.999999i \(0.500531\pi\)
\(20\) 68930.8 + 166414.i 0.0963337 + 0.232570i
\(21\) 843997.i 0.947009i
\(22\) −1.51191e6 + 626252.i −1.37601 + 0.569963i
\(23\) 636421. 1.53646e6i 0.474209 1.14484i −0.488077 0.872800i \(-0.662302\pi\)
0.962286 0.272040i \(-0.0876984\pi\)
\(24\) −1.25814e6 521137.i −0.774064 0.320628i
\(25\) −859447. + 859447.i −0.440037 + 0.440037i
\(26\) −849010. + 849010.i −0.364362 + 0.364362i
\(27\) 2.76612e6 + 1.14577e6i 1.00169 + 0.414915i
\(28\) 624138. 1.50680e6i 0.191898 0.463282i
\(29\) −4.94229e6 + 2.04716e6i −1.29759 + 0.537479i −0.921238 0.388998i \(-0.872821\pi\)
−0.376351 + 0.926477i \(0.622821\pi\)
\(30\) 1.62061e6i 0.365286i
\(31\) −1.49259e6 3.60342e6i −0.290277 0.700789i 0.709717 0.704487i \(-0.248823\pi\)
−0.999993 + 0.00369775i \(0.998823\pi\)
\(32\) 3.18086e6 + 3.18086e6i 0.536254 + 0.536254i
\(33\) 1.02151e7 1.49944
\(34\) −5.95143e6 653697.i −0.763776 0.0838922i
\(35\) −6.67940e6 −0.752370
\(36\) −1.17224e6 1.17224e6i −0.116320 0.116320i
\(37\) 4.00274e6 + 9.66348e6i 0.351115 + 0.847668i 0.996483 + 0.0837955i \(0.0267042\pi\)
−0.645368 + 0.763872i \(0.723296\pi\)
\(38\) 1.39439e7i 1.08482i
\(39\) 6.92431e6 2.86814e6i 0.479276 0.198523i
\(40\) 4.12428e6 9.95690e6i 0.254729 0.614970i
\(41\) 1.02441e7 + 4.24324e6i 0.566169 + 0.234515i 0.647361 0.762184i \(-0.275873\pi\)
−0.0811920 + 0.996698i \(0.525873\pi\)
\(42\) 1.03760e7 1.03760e7i 0.514528 0.514528i
\(43\) 8.66131e6 8.66131e6i 0.386345 0.386345i −0.487037 0.873382i \(-0.661922\pi\)
0.873382 + 0.487037i \(0.161922\pi\)
\(44\) −1.82372e7 7.55409e6i −0.733535 0.303840i
\(45\) −2.59817e6 + 6.27255e6i −0.0944522 + 0.228028i
\(46\) −2.67132e7 + 1.10650e7i −0.879661 + 0.364367i
\(47\) 1.96866e7i 0.588478i −0.955732 0.294239i \(-0.904934\pi\)
0.955732 0.294239i \(-0.0950661\pi\)
\(48\) 4.60109e6 + 1.11080e7i 0.125105 + 0.302031i
\(49\) 1.42308e7 + 1.42308e7i 0.352653 + 0.352653i
\(50\) 2.11319e7 0.478161
\(51\) 3.27603e7 + 1.79864e7i 0.678081 + 0.372288i
\(52\) −1.44831e7 −0.274692
\(53\) −5.00580e7 5.00580e7i −0.871429 0.871429i 0.121200 0.992628i \(-0.461326\pi\)
−0.992628 + 0.121200i \(0.961326\pi\)
\(54\) −1.99205e7 4.80925e7i −0.318808 0.769671i
\(55\) 8.08424e7i 1.19126i
\(56\) −9.01553e7 + 3.73435e7i −1.22503 + 0.507422i
\(57\) −3.33088e7 + 8.04145e7i −0.417947 + 1.00901i
\(58\) 8.59277e7 + 3.55924e7i 0.997028 + 0.412983i
\(59\) −3.24953e7 + 3.24953e7i −0.349129 + 0.349129i −0.859785 0.510656i \(-0.829403\pi\)
0.510656 + 0.859785i \(0.329403\pi\)
\(60\) −1.38228e7 + 1.38228e7i −0.137695 + 0.137695i
\(61\) 5.98943e7 + 2.48090e7i 0.553862 + 0.229417i 0.642018 0.766690i \(-0.278097\pi\)
−0.0881561 + 0.996107i \(0.528097\pi\)
\(62\) −2.59504e7 + 6.26499e7i −0.223040 + 0.538465i
\(63\) 5.67951e7 2.35253e7i 0.454233 0.188149i
\(64\) 1.34933e8i 1.00533i
\(65\) 2.26985e7 + 5.47991e7i 0.157720 + 0.380770i
\(66\) −1.25584e8 1.25584e8i −0.814676 0.814676i
\(67\) 5.04019e7 0.305570 0.152785 0.988259i \(-0.451176\pi\)
0.152785 + 0.988259i \(0.451176\pi\)
\(68\) −4.51865e7 5.63377e7i −0.256282 0.319528i
\(69\) 1.80486e8 0.958567
\(70\) 8.21160e7 + 8.21160e7i 0.408777 + 0.408777i
\(71\) −1.12991e8 2.72785e8i −0.527693 1.27396i −0.933031 0.359797i \(-0.882846\pi\)
0.405337 0.914167i \(-0.367154\pi\)
\(72\) 9.91898e7i 0.434981i
\(73\) −6.12788e7 + 2.53825e7i −0.252556 + 0.104612i −0.505370 0.862903i \(-0.668644\pi\)
0.252814 + 0.967515i \(0.418644\pi\)
\(74\) 6.95926e7 1.68011e8i 0.269786 0.651322i
\(75\) −1.21867e8 5.04792e7i −0.444746 0.184220i
\(76\) 1.18933e8 1.18933e8i 0.408924 0.408924i
\(77\) 5.17597e8 5.17597e8i 1.67797 1.67797i
\(78\) −1.20388e8 4.98662e7i −0.368261 0.152539i
\(79\) −1.82078e8 + 4.39575e8i −0.525939 + 1.26973i 0.408223 + 0.912882i \(0.366148\pi\)
−0.934163 + 0.356848i \(0.883852\pi\)
\(80\) −8.79090e7 + 3.64131e7i −0.239954 + 0.0993923i
\(81\) 1.69343e8i 0.437103i
\(82\) −7.37739e7 1.78106e8i −0.180194 0.435027i
\(83\) 2.01989e8 + 2.01989e8i 0.467172 + 0.467172i 0.900997 0.433825i \(-0.142836\pi\)
−0.433825 + 0.900997i \(0.642836\pi\)
\(84\) 1.77003e8 0.387903
\(85\) −1.42345e8 + 2.59265e8i −0.295771 + 0.538715i
\(86\) −2.12963e8 −0.419818
\(87\) −4.10522e8 4.10522e8i −0.768245 0.768245i
\(88\) 4.51978e8 + 1.09117e9i 0.803425 + 1.93964i
\(89\) 7.06114e8i 1.19294i 0.802634 + 0.596471i \(0.203431\pi\)
−0.802634 + 0.596471i \(0.796569\pi\)
\(90\) 1.09056e8 4.51724e7i 0.175210 0.0725742i
\(91\) 2.05525e8 4.96181e8i 0.314180 0.758497i
\(92\) −3.22225e8 1.33470e8i −0.468936 0.194240i
\(93\) 2.99312e8 2.99312e8i 0.414906 0.414906i
\(94\) −2.42025e8 + 2.42025e8i −0.319731 + 0.319731i
\(95\) −6.36401e8 2.63606e8i −0.801631 0.332046i
\(96\) −1.86826e8 + 4.51039e8i −0.224501 + 0.541993i
\(97\) −8.43523e8 + 3.49399e8i −0.967440 + 0.400727i −0.809759 0.586763i \(-0.800402\pi\)
−0.157682 + 0.987490i \(0.550402\pi\)
\(98\) 3.49905e8i 0.383206i
\(99\) −2.84733e8 6.87405e8i −0.297906 0.719208i
\(100\) 1.80243e8 + 1.80243e8i 0.180243 + 0.180243i
\(101\) 1.09424e6 0.00104632 0.000523160 1.00000i \(-0.499833\pi\)
0.000523160 1.00000i \(0.499833\pi\)
\(102\) −1.81628e8 6.23875e8i −0.166143 0.570686i
\(103\) 1.13364e9 0.992451 0.496226 0.868194i \(-0.334719\pi\)
0.496226 + 0.868194i \(0.334719\pi\)
\(104\) 6.12747e8 + 6.12747e8i 0.513607 + 0.513607i
\(105\) −2.77406e8 6.69717e8i −0.222722 0.537700i
\(106\) 1.23082e9i 0.946928i
\(107\) −1.00058e9 + 4.14455e8i −0.737948 + 0.305668i −0.719813 0.694168i \(-0.755773\pi\)
−0.0181343 + 0.999836i \(0.505773\pi\)
\(108\) 2.40289e8 5.80110e8i 0.169953 0.410302i
\(109\) −152635. 63223.4i −0.000103570 4.29001e-5i 0.382632 0.923901i \(-0.375018\pi\)
−0.382735 + 0.923858i \(0.625018\pi\)
\(110\) 9.93870e8 9.93870e8i 0.647235 0.647235i
\(111\) −8.02679e8 + 8.02679e8i −0.501867 + 0.501867i
\(112\) 7.95977e8 + 3.29705e8i 0.477991 + 0.197990i
\(113\) 2.62058e8 6.32663e8i 0.151197 0.365023i −0.830074 0.557653i \(-0.811702\pi\)
0.981271 + 0.192631i \(0.0617019\pi\)
\(114\) 1.39810e9 5.79113e8i 0.775296 0.321138i
\(115\) 1.42837e9i 0.761553i
\(116\) 4.29330e8 + 1.03649e9i 0.220156 + 0.531503i
\(117\) −3.86012e8 3.86012e8i −0.190443 0.190443i
\(118\) 7.98988e8 0.379377
\(119\) 2.57132e9 7.48587e8i 1.17543 0.342201i
\(120\) 1.16963e9 0.514910
\(121\) −4.59728e9 4.59728e9i −1.94969 1.94969i
\(122\) −4.31336e8 1.04134e9i −0.176277 0.425571i
\(123\) 1.20336e9i 0.474049i
\(124\) −7.55707e8 + 3.13024e8i −0.287049 + 0.118900i
\(125\) 1.04145e9 2.51428e9i 0.381542 0.921124i
\(126\) −9.87453e8 4.09016e8i −0.349019 0.144568i
\(127\) −1.96126e8 + 1.96126e8i −0.0668989 + 0.0668989i −0.739765 0.672866i \(-0.765063\pi\)
0.672866 + 0.739765i \(0.265063\pi\)
\(128\) −3.02488e7 + 3.02488e7i −0.00996009 + 0.00996009i
\(129\) 1.22815e9 + 5.08718e8i 0.390480 + 0.161742i
\(130\) 3.94641e8 9.52749e8i 0.121187 0.292572i
\(131\) −2.22414e9 + 9.21267e8i −0.659843 + 0.273316i −0.687372 0.726305i \(-0.741236\pi\)
0.0275296 + 0.999621i \(0.491236\pi\)
\(132\) 2.14230e9i 0.614184i
\(133\) 2.38683e9 + 5.76233e9i 0.661439 + 1.59686i
\(134\) −6.19637e8 6.19637e8i −0.166022 0.166022i
\(135\) −2.57153e9 −0.666330
\(136\) −4.71786e8 + 4.29526e9i −0.118255 + 1.07663i
\(137\) 8.47234e8 0.205476 0.102738 0.994708i \(-0.467240\pi\)
0.102738 + 0.994708i \(0.467240\pi\)
\(138\) −2.21888e9 2.21888e9i −0.520808 0.520808i
\(139\) 2.25467e9 + 5.44325e9i 0.512290 + 1.23678i 0.942548 + 0.334072i \(0.108423\pi\)
−0.430257 + 0.902706i \(0.641577\pi\)
\(140\) 1.40080e9i 0.308177i
\(141\) 1.97390e9 8.17615e8i 0.420570 0.174206i
\(142\) −1.96449e9 + 4.74269e9i −0.405464 + 0.978876i
\(143\) −6.00540e9 2.48752e9i −1.20096 0.497455i
\(144\) 6.19243e8 6.19243e8i 0.120014 0.120014i
\(145\) 3.24888e9 3.24888e9i 0.610347 0.610347i
\(146\) 1.06541e9 + 4.41306e8i 0.194056 + 0.0803808i
\(147\) −8.35840e8 + 2.01790e9i −0.147637 + 0.356427i
\(148\) 2.02662e9 8.39453e8i 0.347212 0.143820i
\(149\) 2.49054e9i 0.413958i 0.978345 + 0.206979i \(0.0663632\pi\)
−0.978345 + 0.206979i \(0.933637\pi\)
\(150\) 8.77642e8 + 2.11881e9i 0.141549 + 0.341729i
\(151\) 4.40811e9 + 4.40811e9i 0.690011 + 0.690011i 0.962234 0.272223i \(-0.0877588\pi\)
−0.272223 + 0.962234i \(0.587759\pi\)
\(152\) −1.00636e10 −1.52918
\(153\) 2.97211e8 2.70589e9i 0.0438484 0.399207i
\(154\) −1.27266e10 −1.82334
\(155\) 2.36875e9 + 2.36875e9i 0.329631 + 0.329631i
\(156\) −6.01505e8 1.45216e9i −0.0813165 0.196315i
\(157\) 2.04937e9i 0.269198i −0.990900 0.134599i \(-0.957025\pi\)
0.990900 0.134599i \(-0.0429747\pi\)
\(158\) 7.64255e9 3.16565e9i 0.975622 0.404116i
\(159\) 2.94013e9 7.09810e9i 0.364821 0.880755i
\(160\) −3.56953e9 1.47855e9i −0.430597 0.178359i
\(161\) 9.14518e9 9.14518e9i 1.07269 1.07269i
\(162\) 2.08189e9 2.08189e9i 0.237487 0.237487i
\(163\) 1.41464e10 + 5.85965e9i 1.56965 + 0.650171i 0.986732 0.162359i \(-0.0519102\pi\)
0.582920 + 0.812530i \(0.301910\pi\)
\(164\) 8.89890e8 2.14838e9i 0.0960592 0.231907i
\(165\) −8.10575e9 + 3.35751e9i −0.851364 + 0.352647i
\(166\) 4.96648e9i 0.507647i
\(167\) 3.36501e8 + 8.12385e8i 0.0334782 + 0.0808236i 0.939734 0.341905i \(-0.111072\pi\)
−0.906256 + 0.422729i \(0.861072\pi\)
\(168\) −7.48858e9 7.48858e9i −0.725283 0.725283i
\(169\) 5.83530e9 0.550267
\(170\) 4.93736e9 1.43741e9i 0.453392 0.131996i
\(171\) 6.33977e9 0.567011
\(172\) −1.81644e9 1.81644e9i −0.158250 0.158250i
\(173\) −7.31181e8 1.76523e9i −0.0620608 0.149828i 0.889807 0.456337i \(-0.150839\pi\)
−0.951868 + 0.306509i \(0.900839\pi\)
\(174\) 1.00938e10i 0.834805i
\(175\) −8.73276e9 + 3.61723e9i −0.703850 + 0.291544i
\(176\) 3.99049e9 9.63390e9i 0.313487 0.756825i
\(177\) −4.60775e9 1.90859e9i −0.352866 0.146162i
\(178\) 8.68090e9 8.68090e9i 0.648149 0.648149i
\(179\) −1.45188e10 + 1.45188e10i −1.05704 + 1.05704i −0.0587698 + 0.998272i \(0.518718\pi\)
−0.998272 + 0.0587698i \(0.981282\pi\)
\(180\) 1.31547e9 + 5.44887e8i 0.0934020 + 0.0386884i
\(181\) 5.04127e9 1.21707e10i 0.349129 0.842872i −0.647594 0.761985i \(-0.724225\pi\)
0.996723 0.0808867i \(-0.0257752\pi\)
\(182\) −8.62672e9 + 3.57330e9i −0.582806 + 0.241406i
\(183\) 7.03573e9i 0.463745i
\(184\) 7.98579e9 + 1.92794e10i 0.513615 + 1.23998i
\(185\) −6.35241e9 6.35241e9i −0.398718 0.398718i
\(186\) −7.35942e9 −0.450853
\(187\) −9.06033e9 3.11213e10i −0.541822 1.86110i
\(188\) −4.12866e9 −0.241045
\(189\) 1.64643e10 + 1.64643e10i 0.938568 + 0.938568i
\(190\) 4.58311e9 + 1.10646e10i 0.255134 + 0.615949i
\(191\) 2.69258e10i 1.46392i 0.681345 + 0.731962i \(0.261395\pi\)
−0.681345 + 0.731962i \(0.738605\pi\)
\(192\) 1.35292e10 5.60397e9i 0.718482 0.297605i
\(193\) −6.07148e9 + 1.46578e10i −0.314983 + 0.760435i 0.684523 + 0.728991i \(0.260011\pi\)
−0.999506 + 0.0314438i \(0.989989\pi\)
\(194\) 1.46657e10 + 6.07472e9i 0.743352 + 0.307906i
\(195\) −4.55178e9 + 4.55178e9i −0.225437 + 0.225437i
\(196\) 2.98448e9 2.98448e9i 0.144450 0.144450i
\(197\) −5.41819e9 2.24429e9i −0.256304 0.106165i 0.250832 0.968031i \(-0.419296\pi\)
−0.507136 + 0.861866i \(0.669296\pi\)
\(198\) −4.95042e9 + 1.19514e10i −0.228902 + 0.552618i
\(199\) −2.98791e10 + 1.23763e10i −1.35060 + 0.559439i −0.936461 0.350773i \(-0.885919\pi\)
−0.414144 + 0.910212i \(0.635919\pi\)
\(200\) 1.52513e10i 0.674019i
\(201\) 2.09327e9 + 5.05360e9i 0.0904571 + 0.218383i
\(202\) −1.34524e7 1.34524e7i −0.000568486 0.000568486i
\(203\) −4.16021e10 −1.71942
\(204\) 3.77210e9 6.87046e9i 0.152492 0.277748i
\(205\) −9.52343e9 −0.376618
\(206\) −1.39369e10 1.39369e10i −0.539218 0.539218i
\(207\) −5.03081e9 1.21455e10i −0.190446 0.459777i
\(208\) 7.65078e9i 0.283413i
\(209\) 6.97428e10 2.88884e10i 2.52837 1.04729i
\(210\) −4.82304e9 + 1.16439e10i −0.171133 + 0.413152i
\(211\) 2.44637e10 + 1.01332e10i 0.849672 + 0.351946i 0.764660 0.644434i \(-0.222907\pi\)
0.0850120 + 0.996380i \(0.472907\pi\)
\(212\) −1.04981e10 + 1.04981e10i −0.356944 + 0.356944i
\(213\) 2.26583e10 2.26583e10i 0.754258 0.754258i
\(214\) 1.73963e10 + 7.20580e9i 0.567017 + 0.234866i
\(215\) −4.02600e9 + 9.71961e9i −0.128499 + 0.310224i
\(216\) −3.47093e10 + 1.43770e10i −1.08493 + 0.449394i
\(217\) 3.03321e10i 0.928610i
\(218\) 1.09922e6 + 2.65374e6i 3.29632e−5 + 7.95801e-5i
\(219\) −5.09001e9 5.09001e9i −0.149527 0.149527i
\(220\) 1.69542e10 0.487950
\(221\) −1.48796e10 1.85517e10i −0.419592 0.523140i
\(222\) 1.97361e10 0.545348
\(223\) −4.35511e10 4.35511e10i −1.17931 1.17931i −0.979921 0.199388i \(-0.936105\pi\)
−0.199388 0.979921i \(-0.563895\pi\)
\(224\) 1.33876e10 + 3.23205e10i 0.355292 + 0.857752i
\(225\) 9.60788e9i 0.249923i
\(226\) −1.09996e10 + 4.55619e9i −0.280472 + 0.116175i
\(227\) −1.47777e10 + 3.56766e10i −0.369395 + 0.891799i 0.624454 + 0.781061i \(0.285321\pi\)
−0.993850 + 0.110738i \(0.964679\pi\)
\(228\) 1.68645e10 + 6.98549e9i 0.413300 + 0.171195i
\(229\) 2.03005e10 2.03005e10i 0.487806 0.487806i −0.419807 0.907613i \(-0.637902\pi\)
0.907613 + 0.419807i \(0.137902\pi\)
\(230\) 1.75602e10 1.75602e10i 0.413766 0.413766i
\(231\) 7.33940e10 + 3.04008e10i 1.69592 + 0.702475i
\(232\) 2.56877e10 6.20157e10i 0.582144 1.40542i
\(233\) 8.07535e9 3.34492e9i 0.179498 0.0743505i −0.291124 0.956685i \(-0.594029\pi\)
0.470623 + 0.882335i \(0.344029\pi\)
\(234\) 9.49120e9i 0.206943i
\(235\) 6.47061e9 + 1.56214e10i 0.138401 + 0.334130i
\(236\) 6.81489e9 + 6.81489e9i 0.143006 + 0.143006i
\(237\) −5.16365e10 −1.06314
\(238\) −4.08147e10 2.24085e10i −0.824556 0.452707i
\(239\) −3.56000e10 −0.705765 −0.352882 0.935668i \(-0.614798\pi\)
−0.352882 + 0.935668i \(0.614798\pi\)
\(240\) −7.30200e9 7.30200e9i −0.142066 0.142066i
\(241\) −5.20146e9 1.25574e10i −0.0993227 0.239786i 0.866406 0.499341i \(-0.166424\pi\)
−0.965728 + 0.259554i \(0.916424\pi\)
\(242\) 1.13037e11i 2.11861i
\(243\) 3.74663e10 1.55190e10i 0.689307 0.285520i
\(244\) 5.20294e9 1.25610e10i 0.0939711 0.226866i
\(245\) −1.59697e10 6.61485e9i −0.283171 0.117293i
\(246\) 1.47940e10 1.47940e10i 0.257560 0.257560i
\(247\) 3.91641e10 3.91641e10i 0.669502 0.669502i
\(248\) 4.52156e10 + 1.87289e10i 0.759025 + 0.314399i
\(249\) −1.18637e10 + 2.86416e10i −0.195580 + 0.472172i
\(250\) −4.37138e10 + 1.81068e10i −0.707764 + 0.293165i
\(251\) 4.34080e10i 0.690300i −0.938548 0.345150i \(-0.887828\pi\)
0.938548 0.345150i \(-0.112172\pi\)
\(252\) −4.93371e9 1.19110e10i −0.0770676 0.186058i
\(253\) −1.10686e11 1.10686e11i −1.69845 1.69845i
\(254\) 4.82232e9 0.0726949
\(255\) −3.19073e10 3.50466e9i −0.472562 0.0519056i
\(256\) −6.83418e10 −0.994504
\(257\) 7.16173e10 + 7.16173e10i 1.02404 + 1.02404i 0.999704 + 0.0243402i \(0.00774850\pi\)
0.0243402 + 0.999704i \(0.492251\pi\)
\(258\) −8.84467e9 2.13529e10i −0.124278 0.300033i
\(259\) 8.13430e10i 1.12324i
\(260\) 1.14924e10 4.76032e9i 0.155967 0.0646035i
\(261\) −1.61825e10 + 3.90680e10i −0.215856 + 0.521122i
\(262\) 3.86693e10 + 1.60174e10i 0.507003 + 0.210008i
\(263\) −3.03609e10 + 3.03609e10i −0.391304 + 0.391304i −0.875152 0.483848i \(-0.839239\pi\)
0.483848 + 0.875152i \(0.339239\pi\)
\(264\) −9.06361e10 + 9.06361e10i −1.14837 + 1.14837i
\(265\) 5.61744e10 + 2.32682e10i 0.699733 + 0.289839i
\(266\) 4.14980e10 1.00185e11i 0.508230 1.22698i
\(267\) −7.07992e10 + 2.93260e10i −0.852566 + 0.353144i
\(268\) 1.05703e10i 0.125164i
\(269\) 3.62306e10 + 8.74684e10i 0.421881 + 1.01851i 0.981792 + 0.189959i \(0.0608354\pi\)
−0.559911 + 0.828553i \(0.689165\pi\)
\(270\) 3.16142e10 + 3.16142e10i 0.362030 + 0.362030i
\(271\) −5.24783e10 −0.591041 −0.295521 0.955336i \(-0.595493\pi\)
−0.295521 + 0.955336i \(0.595493\pi\)
\(272\) 2.97607e10 2.38700e10i 0.329673 0.264419i
\(273\) 5.82859e10 0.635085
\(274\) −1.04158e10 1.04158e10i −0.111639 0.111639i
\(275\) 4.37802e10 + 1.05695e11i 0.461616 + 1.11444i
\(276\) 3.78514e10i 0.392637i
\(277\) −1.85445e10 + 7.68138e9i −0.189259 + 0.0783936i −0.475300 0.879824i \(-0.657661\pi\)
0.286041 + 0.958217i \(0.407661\pi\)
\(278\) 3.92002e10 9.46376e10i 0.393628 0.950303i
\(279\) −2.84845e10 1.17987e10i −0.281443 0.116577i
\(280\) 5.92647e10 5.92647e10i 0.576216 0.576216i
\(281\) 1.19423e10 1.19423e10i 0.114264 0.114264i −0.647663 0.761927i \(-0.724254\pi\)
0.761927 + 0.647663i \(0.224254\pi\)
\(282\) −3.43186e10 1.42152e10i −0.323153 0.133854i
\(283\) −5.02585e9 + 1.21335e10i −0.0465769 + 0.112447i −0.945456 0.325751i \(-0.894383\pi\)
0.898879 + 0.438197i \(0.144383\pi\)
\(284\) −5.72082e10 + 2.36964e10i −0.521826 + 0.216147i
\(285\) 7.47574e10i 0.671200i
\(286\) 4.32485e10 + 1.04411e11i 0.382230 + 0.922784i
\(287\) 6.09741e10 + 6.09741e10i 0.530490 + 0.530490i
\(288\) 3.55593e10 0.304570
\(289\) 2.57405e10 1.15761e11i 0.217059 0.976159i
\(290\) −7.98828e10 −0.663227
\(291\) −7.00657e10 7.00657e10i −0.572779 0.572779i
\(292\) 5.32321e9 + 1.28514e10i 0.0428500 + 0.103449i
\(293\) 2.19107e10i 0.173681i −0.996222 0.0868403i \(-0.972323\pi\)
0.996222 0.0868403i \(-0.0276770\pi\)
\(294\) 3.50836e10 1.45321e10i 0.273868 0.113440i
\(295\) 1.51046e10 3.64658e10i 0.116121 0.280341i
\(296\) −1.21257e11 5.02263e10i −0.918109 0.380293i
\(297\) 1.99272e11 1.99272e11i 1.48608 1.48608i
\(298\) 3.06185e10 3.06185e10i 0.224911 0.224911i
\(299\) −1.06107e11 4.39508e10i −0.767755 0.318014i
\(300\) −1.05865e10 + 2.55580e10i −0.0754580 + 0.182172i
\(301\) 8.80068e10 3.64536e10i 0.617969 0.255971i
\(302\) 1.08386e11i 0.749793i
\(303\) 4.54453e7 + 1.09715e8i 0.000309740 + 0.000747779i
\(304\) 6.28273e10 + 6.28273e10i 0.421907 + 0.421907i
\(305\) −5.56808e10 −0.368431
\(306\) −3.69198e10 + 2.96120e10i −0.240721 + 0.193073i
\(307\) 1.46658e11 0.942289 0.471145 0.882056i \(-0.343841\pi\)
0.471145 + 0.882056i \(0.343841\pi\)
\(308\) −1.08550e11 1.08550e11i −0.687309 0.687309i
\(309\) 4.70820e10 + 1.13666e11i 0.293793 + 0.709280i
\(310\) 5.82425e10i 0.358189i
\(311\) 1.85506e11 7.68391e10i 1.12444 0.465758i 0.258552 0.965997i \(-0.416755\pi\)
0.865887 + 0.500239i \(0.166755\pi\)
\(312\) −3.59894e10 + 8.68861e10i −0.215020 + 0.519104i
\(313\) −1.33244e11 5.51913e10i −0.784688 0.325028i −0.0458820 0.998947i \(-0.514610\pi\)
−0.738806 + 0.673919i \(0.764610\pi\)
\(314\) −2.51948e10 + 2.51948e10i −0.146261 + 0.146261i
\(315\) −3.73350e10 + 3.73350e10i −0.213658 + 0.213658i
\(316\) 9.21874e10 + 3.81853e10i 0.520092 + 0.215429i
\(317\) −1.03137e11 + 2.48994e11i −0.573650 + 1.38491i 0.324777 + 0.945791i \(0.394711\pi\)
−0.898427 + 0.439123i \(0.855289\pi\)
\(318\) −1.23409e11 + 5.11177e10i −0.676745 + 0.280317i
\(319\) 5.03520e11i 2.72244i
\(320\) 4.43498e10 + 1.07070e11i 0.236438 + 0.570812i
\(321\) −8.31114e10 8.31114e10i −0.436906 0.436906i
\(322\) −2.24860e11 −1.16563
\(323\) 2.74534e11 + 3.01545e10i 1.40341 + 0.154149i
\(324\) 3.55145e10 0.179041
\(325\) 5.93528e10 + 5.93528e10i 0.295098 + 0.295098i
\(326\) −1.01877e11 2.45953e11i −0.499572 1.20607i
\(327\) 1.79299e7i 8.67185e-5i
\(328\) −1.28543e11 + 5.32441e10i −0.613218 + 0.254003i
\(329\) 5.85885e10 1.41445e11i 0.275696 0.665590i
\(330\) 1.40928e11 + 5.83744e10i 0.654162 + 0.270963i
\(331\) −1.26092e11 + 1.26092e11i −0.577380 + 0.577380i −0.934181 0.356801i \(-0.883868\pi\)
0.356801 + 0.934181i \(0.383868\pi\)
\(332\) 4.23611e10 4.23611e10i 0.191357 0.191357i
\(333\) 7.63883e10 + 3.16411e10i 0.340430 + 0.141011i
\(334\) 5.85048e9 1.41243e10i 0.0257236 0.0621024i
\(335\) −3.99942e10 + 1.65662e10i −0.173499 + 0.0718654i
\(336\) 9.35026e10i 0.400218i
\(337\) −3.18965e10 7.70051e10i −0.134713 0.325226i 0.842100 0.539322i \(-0.181319\pi\)
−0.976813 + 0.214096i \(0.931319\pi\)
\(338\) −7.17387e10 7.17387e10i −0.298971 0.298971i
\(339\) 7.43183e10 0.305631
\(340\) 5.43729e10 + 2.98524e10i 0.220662 + 0.121150i
\(341\) −3.67116e11 −1.47031
\(342\) −7.79406e10 7.79406e10i −0.308068 0.308068i
\(343\) −6.02004e10 1.45337e11i −0.234842 0.566958i
\(344\) 1.53699e11i 0.591778i
\(345\) −1.43217e11 + 5.93224e10i −0.544262 + 0.225441i
\(346\) −1.27125e10 + 3.06906e10i −0.0476857 + 0.115123i
\(347\) −2.22564e11 9.21890e10i −0.824086 0.341347i −0.0695270 0.997580i \(-0.522149\pi\)
−0.754559 + 0.656233i \(0.772149\pi\)
\(348\) −8.60944e10 + 8.60944e10i −0.314679 + 0.314679i
\(349\) −7.37872e10 + 7.37872e10i −0.266236 + 0.266236i −0.827581 0.561346i \(-0.810284\pi\)
0.561346 + 0.827581i \(0.310284\pi\)
\(350\) 1.51830e11 + 6.28899e10i 0.540817 + 0.224014i
\(351\) 7.91259e10 1.91027e11i 0.278251 0.671757i
\(352\) 3.91183e11 1.62033e11i 1.35812 0.562551i
\(353\) 3.30958e11i 1.13445i −0.823562 0.567226i \(-0.808017\pi\)
0.823562 0.567226i \(-0.191983\pi\)
\(354\) 3.31832e10 + 8.01114e10i 0.112306 + 0.271131i
\(355\) 1.79318e11 + 1.79318e11i 0.599235 + 0.599235i
\(356\) 1.48086e11 0.488639
\(357\) 1.81849e11 + 2.26726e11i 0.592521 + 0.738746i
\(358\) 3.56986e11 1.14862
\(359\) −7.22092e10 7.22092e10i −0.229439 0.229439i 0.583019 0.812458i \(-0.301871\pi\)
−0.812458 + 0.583019i \(0.801871\pi\)
\(360\) −3.26018e10 7.87078e10i −0.102301 0.246977i
\(361\) 3.20534e11i 0.993325i
\(362\) −2.11602e11 + 8.76486e10i −0.647637 + 0.268260i
\(363\) 2.70019e11 6.51883e11i 0.816233 1.97056i
\(364\) −1.04059e11 4.31026e10i −0.310687 0.128691i
\(365\) 4.02824e10 4.02824e10i 0.118795 0.118795i
\(366\) 8.64966e10 8.64966e10i 0.251962 0.251962i
\(367\) −3.34308e11 1.38475e11i −0.961943 0.398450i −0.154236 0.988034i \(-0.549292\pi\)
−0.807707 + 0.589584i \(0.799292\pi\)
\(368\) 7.05062e10 1.70217e11i 0.200407 0.483825i
\(369\) 8.09780e10 3.35422e10i 0.227378 0.0941830i
\(370\) 1.56192e11i 0.433262i
\(371\) −2.10683e11 5.08635e11i −0.577361 1.39387i
\(372\) −6.27714e10 6.27714e10i −0.169949 0.169949i
\(373\) −6.15278e9 −0.0164582 −0.00822908 0.999966i \(-0.502619\pi\)
−0.00822908 + 0.999966i \(0.502619\pi\)
\(374\) −2.71216e11 + 4.93990e11i −0.716792 + 1.30556i
\(375\) 2.95350e11 0.771251
\(376\) 1.74674e11 + 1.74674e11i 0.450696 + 0.450696i
\(377\) 1.41376e11 + 3.41311e11i 0.360445 + 0.870191i
\(378\) 4.04822e11i 1.01988i
\(379\) −2.00552e11 + 8.30712e10i −0.499286 + 0.206811i −0.618091 0.786106i \(-0.712094\pi\)
0.118805 + 0.992918i \(0.462094\pi\)
\(380\) −5.52833e10 + 1.33466e11i −0.136009 + 0.328355i
\(381\) −2.78102e10 1.15194e10i −0.0676148 0.0280070i
\(382\) 3.31024e11 3.31024e11i 0.795379 0.795379i
\(383\) 2.08716e11 2.08716e11i 0.495633 0.495633i −0.414442 0.910076i \(-0.636023\pi\)
0.910076 + 0.414442i \(0.136023\pi\)
\(384\) −4.28921e9 1.77665e9i −0.0100667 0.00416976i
\(385\) −2.40592e11 + 5.80841e11i −0.558095 + 1.34736i
\(386\) 2.54844e11 1.05560e11i 0.584295 0.242023i
\(387\) 9.68260e10i 0.219428i
\(388\) 7.32757e10 + 1.76903e11i 0.164141 + 0.396271i
\(389\) 6.58559e10 + 6.58559e10i 0.145822 + 0.145822i 0.776249 0.630427i \(-0.217120\pi\)
−0.630427 + 0.776249i \(0.717120\pi\)
\(390\) 1.11918e11 0.244969
\(391\) −1.60083e11 5.49869e11i −0.346378 1.18977i
\(392\) −2.52533e11 −0.540171
\(393\) −1.84744e11 1.84744e11i −0.390664 0.390664i
\(394\) 3.90197e10 + 9.42018e10i 0.0815738 + 0.196936i
\(395\) 4.08651e11i 0.844629i
\(396\) −1.44162e11 + 5.97139e10i −0.294593 + 0.122025i
\(397\) −3.00906e11 + 7.26451e11i −0.607958 + 1.46774i 0.257260 + 0.966342i \(0.417180\pi\)
−0.865217 + 0.501397i \(0.832820\pi\)
\(398\) 5.19484e11 + 2.15177e11i 1.03776 + 0.429856i
\(399\) −4.78637e11 + 4.78637e11i −0.945427 + 0.945427i
\(400\) −9.52142e10 + 9.52142e10i −0.185965 + 0.185965i
\(401\) −4.46394e11 1.84902e11i −0.862121 0.357102i −0.0925843 0.995705i \(-0.529513\pi\)
−0.769537 + 0.638603i \(0.779513\pi\)
\(402\) 3.63940e10 8.78630e10i 0.0695045 0.167799i
\(403\) −2.48850e11 + 1.03077e11i −0.469965 + 0.194666i
\(404\) 2.29482e8i 0.000428581i
\(405\) −5.56598e10 1.34375e11i −0.102800 0.248182i
\(406\) 5.11453e11 + 5.11453e11i 0.934197 + 0.934197i
\(407\) 9.84514e11 1.77847
\(408\) −4.50263e11 + 1.31085e11i −0.804443 + 0.234197i
\(409\) 4.74605e11 0.838643 0.419321 0.907838i \(-0.362268\pi\)
0.419321 + 0.907838i \(0.362268\pi\)
\(410\) 1.17080e11 + 1.17080e11i 0.204624 + 0.204624i
\(411\) 3.51870e10 + 8.49488e10i 0.0608266 + 0.146848i
\(412\) 2.37747e11i 0.406516i
\(413\) −3.30182e11 + 1.36766e11i −0.558441 + 0.231314i
\(414\) −8.74668e10 + 2.11164e11i −0.146333 + 0.353279i
\(415\) −2.26670e11 9.38897e10i −0.375126 0.155382i
\(416\) 2.19668e11 2.19668e11i 0.359623 0.359623i
\(417\) −4.52134e11 + 4.52134e11i −0.732242 + 0.732242i
\(418\) −1.21256e12 5.02261e11i −1.94273 0.804703i
\(419\) 4.66723e10 1.12677e11i 0.0739768 0.178596i −0.882565 0.470190i \(-0.844186\pi\)
0.956542 + 0.291594i \(0.0941855\pi\)
\(420\) −1.40453e11 + 5.81774e10i −0.220246 + 0.0912289i
\(421\) 4.38690e11i 0.680594i −0.940318 0.340297i \(-0.889472\pi\)
0.940318 0.340297i \(-0.110528\pi\)
\(422\) −1.76178e11 4.25331e11i −0.270424 0.652862i
\(423\) −1.10040e11 1.10040e11i −0.167116 0.167116i
\(424\) 8.88304e11 1.33480
\(425\) −4.56989e10 + 4.16054e11i −0.0679446 + 0.618586i
\(426\) −5.57119e11 −0.819606
\(427\) 3.56499e11 + 3.56499e11i 0.518958 + 0.518958i
\(428\) 8.69191e10 + 2.09841e11i 0.125204 + 0.302269i
\(429\) 7.05448e11i 1.00556i
\(430\) 1.68987e11 6.99968e10i 0.238367 0.0987348i
\(431\) −1.68399e11 + 4.06551e11i −0.235067 + 0.567503i −0.996760 0.0804361i \(-0.974369\pi\)
0.761693 + 0.647939i \(0.224369\pi\)
\(432\) 3.06446e11 + 1.26934e11i 0.423329 + 0.175349i
\(433\) −8.27028e11 + 8.27028e11i −1.13064 + 1.13064i −0.140570 + 0.990071i \(0.544894\pi\)
−0.990071 + 0.140570i \(0.955106\pi\)
\(434\) −3.72900e11 + 3.72900e11i −0.504532 + 0.504532i
\(435\) 4.60683e11 + 1.90821e11i 0.616879 + 0.255520i
\(436\) −1.32592e7 + 3.20105e7i −1.75722e−5 + 4.24231e-5i
\(437\) 1.23225e12 5.10417e11i 1.61635 0.669512i
\(438\) 1.25152e11i 0.162482i
\(439\) −1.93458e11 4.67049e11i −0.248598 0.600168i 0.749488 0.662018i \(-0.230300\pi\)
−0.998085 + 0.0618505i \(0.980300\pi\)
\(440\) −7.17295e11 7.17295e11i −0.912348 0.912348i
\(441\) 1.59088e11 0.200293
\(442\) −4.51439e10 + 4.11002e11i −0.0562599 + 0.512205i
\(443\) 6.65355e11 0.820799 0.410399 0.911906i \(-0.365389\pi\)
0.410399 + 0.911906i \(0.365389\pi\)
\(444\) 1.68337e11 + 1.68337e11i 0.205569 + 0.205569i
\(445\) −2.32086e11 5.60306e11i −0.280562 0.677337i
\(446\) 1.07083e12i 1.28148i
\(447\) −2.49717e11 + 1.03436e11i −0.295845 + 0.122543i
\(448\) 4.01568e11 9.69471e11i 0.470986 1.13706i
\(449\) 1.05800e12 + 4.38236e11i 1.22850 + 0.508862i 0.900103 0.435678i \(-0.143491\pi\)
0.328398 + 0.944539i \(0.393491\pi\)
\(450\) 1.18118e11 1.18118e11i 0.135788 0.135788i
\(451\) 7.37984e11 7.37984e11i 0.839948 0.839948i
\(452\) −1.32682e11 5.49586e10i −0.149516 0.0619316i
\(453\) −2.58908e11 + 6.25060e11i −0.288871 + 0.697396i
\(454\) 6.20281e11 2.56929e11i 0.685231 0.283832i
\(455\) 4.61275e11i 0.504555i
\(456\) −4.17957e11 1.00904e12i −0.452679 1.09286i
\(457\) −2.70834e11 2.70834e11i −0.290456 0.290456i 0.546805 0.837260i \(-0.315844\pi\)
−0.837260 + 0.546805i \(0.815844\pi\)
\(458\) −4.99146e11 −0.530069
\(459\) 9.89944e11 2.88202e11i 1.04101 0.303068i
\(460\) 2.99556e11 0.311938
\(461\) 6.95684e11 + 6.95684e11i 0.717395 + 0.717395i 0.968071 0.250676i \(-0.0806530\pi\)
−0.250676 + 0.968071i \(0.580653\pi\)
\(462\) −5.28555e11 1.27604e12i −0.539760 1.30310i
\(463\) 1.35928e12i 1.37466i −0.726347 0.687328i \(-0.758784\pi\)
0.726347 0.687328i \(-0.241216\pi\)
\(464\) −5.47534e11 + 2.26796e11i −0.548378 + 0.227146i
\(465\) −1.39128e11 + 3.35884e11i −0.137999 + 0.333158i
\(466\) −1.40400e11 5.81555e10i −0.137921 0.0571287i
\(467\) −1.17021e12 + 1.17021e12i −1.13851 + 1.13851i −0.149792 + 0.988717i \(0.547860\pi\)
−0.988717 + 0.149792i \(0.952140\pi\)
\(468\) −8.09542e10 + 8.09542e10i −0.0780069 + 0.0780069i
\(469\) 3.62130e11 + 1.49999e11i 0.345610 + 0.143157i
\(470\) 1.12499e11 2.71598e11i 0.106343 0.256735i
\(471\) 2.05483e11 8.51137e10i 0.192389 0.0796902i
\(472\) 5.76645e11i 0.534773i
\(473\) −4.41207e11 1.06517e12i −0.405291 0.978459i
\(474\) 6.34814e11 + 6.34814e11i 0.577623 + 0.577623i
\(475\) −9.74797e11 −0.878603
\(476\) −1.56993e11 5.39256e11i −0.140168 0.481464i
\(477\) −5.59605e11 −0.494936
\(478\) 4.37664e11 + 4.37664e11i 0.383456 + 0.383456i
\(479\) −3.05029e11 7.36406e11i −0.264748 0.639157i 0.734473 0.678638i \(-0.237430\pi\)
−0.999220 + 0.0394811i \(0.987430\pi\)
\(480\) 4.19309e11i 0.360536i
\(481\) 6.67354e11 2.76427e11i 0.568464 0.235466i
\(482\) −9.04337e10 + 2.18326e11i −0.0763165 + 0.184244i
\(483\) 1.29677e12 + 5.37138e11i 1.08417 + 0.449080i
\(484\) −9.64138e11 + 9.64138e11i −0.798610 + 0.798610i
\(485\) 5.54500e11 5.54500e11i 0.455055 0.455055i
\(486\) −6.51397e11 2.69818e11i −0.529642 0.219385i
\(487\) 4.23825e11 1.02321e12i 0.341434 0.824295i −0.656137 0.754642i \(-0.727811\pi\)
0.997571 0.0696530i \(-0.0221892\pi\)
\(488\) −7.51552e11 + 3.11303e11i −0.599888 + 0.248482i
\(489\) 1.66177e12i 1.31426i
\(490\) 1.15007e11 + 2.77652e11i 0.0901244 + 0.217580i
\(491\) 1.11740e12 + 1.11740e12i 0.867646 + 0.867646i 0.992211 0.124565i \(-0.0397536\pi\)
−0.124565 + 0.992211i \(0.539754\pi\)
\(492\) 2.52368e11 0.194174
\(493\) −8.86582e11 + 1.61481e12i −0.675939 + 1.23115i
\(494\) −9.62960e11 −0.727506
\(495\) 4.51874e11 + 4.51874e11i 0.338294 + 0.338294i
\(496\) −1.65357e11 3.99207e11i −0.122675 0.296163i
\(497\) 2.29619e12i 1.68812i
\(498\) 4.97969e11 2.06266e11i 0.362803 0.150278i
\(499\) −8.33811e11 + 2.01300e12i −0.602026 + 1.45342i 0.269467 + 0.963010i \(0.413153\pi\)
−0.871492 + 0.490409i \(0.836847\pi\)
\(500\) −5.27293e11 2.18412e11i −0.377300 0.156283i
\(501\) −6.74793e10 + 6.74793e10i −0.0478521 + 0.0478521i
\(502\) −5.33654e11 + 5.33654e11i −0.375053 + 0.375053i
\(503\) 3.08095e11 + 1.27617e11i 0.214600 + 0.0888901i 0.487394 0.873182i \(-0.337948\pi\)
−0.272794 + 0.962072i \(0.587948\pi\)
\(504\) −2.95195e11 + 7.12664e11i −0.203785 + 0.491980i
\(505\) −8.68283e8 + 3.59655e8i −0.000594087 + 0.000246079i
\(506\) 2.72154e12i 1.84560i
\(507\) 2.42349e11 + 5.85083e11i 0.162894 + 0.393262i
\(508\) 4.11314e10 + 4.11314e10i 0.0274023 + 0.0274023i
\(509\) −4.61088e11 −0.304477 −0.152238 0.988344i \(-0.548648\pi\)
−0.152238 + 0.988344i \(0.548648\pi\)
\(510\) 3.49179e11 + 4.35351e11i 0.228551 + 0.284954i
\(511\) −5.15819e11 −0.334660
\(512\) 8.55675e11 + 8.55675e11i 0.550293 + 0.550293i
\(513\) 9.18917e11 + 2.21846e12i 0.585798 + 1.41424i
\(514\) 1.76091e12i 1.11277i
\(515\) −8.99554e11 + 3.72607e11i −0.563501 + 0.233410i
\(516\) 1.06688e11 2.57567e11i 0.0662509 0.159944i
\(517\) −1.71195e12 7.09111e11i −1.05386 0.436523i
\(518\) 1.00002e12 1.00002e12i 0.610277 0.610277i
\(519\) 1.46625e11 1.46625e11i 0.0887066 0.0887066i
\(520\) −6.87617e11 2.84820e11i −0.412412 0.170827i
\(521\) −2.88167e11 + 6.95697e11i −0.171346 + 0.413667i −0.986103 0.166137i \(-0.946871\pi\)
0.814756 + 0.579803i \(0.196871\pi\)
\(522\) 6.79246e11 2.81353e11i 0.400414 0.165857i
\(523\) 3.35856e12i 1.96289i −0.191742 0.981445i \(-0.561414\pi\)
0.191742 0.981445i \(-0.438586\pi\)
\(524\) 1.93208e11 + 4.66444e11i 0.111952 + 0.270277i
\(525\) −7.25370e11 7.25370e11i −0.416719 0.416719i
\(526\) 7.46509e11 0.425206
\(527\) −1.17736e12 6.46407e11i −0.664907 0.365055i
\(528\) 1.13168e12 0.633684
\(529\) −6.82060e11 6.82060e11i −0.378680 0.378680i
\(530\) −4.04546e11 9.76661e11i −0.222703 0.537654i
\(531\) 3.63269e11i 0.198291i
\(532\) 1.20847e12 5.00565e11i 0.654085 0.270931i
\(533\) 2.93036e11 7.07450e11i 0.157271 0.379685i
\(534\) 1.23093e12 + 5.09868e11i 0.655086 + 0.271345i
\(535\) 6.57745e11 6.57745e11i 0.347109 0.347109i
\(536\) −4.47204e11 + 4.47204e11i −0.234026 + 0.234026i
\(537\) −2.05873e12 8.52754e11i −1.06835 0.442527i
\(538\) 6.29913e11 1.52075e12i 0.324161 0.782593i
\(539\) 1.75011e12 7.24918e11i 0.893130 0.369947i
\(540\) 5.39300e11i 0.272934i
\(541\) −2.65833e10 6.41777e10i −0.0133420 0.0322104i 0.917068 0.398730i \(-0.130549\pi\)
−0.930410 + 0.366520i \(0.880549\pi\)
\(542\) 6.45163e11 + 6.45163e11i 0.321124 + 0.321124i
\(543\) 1.42968e12 0.705731
\(544\) 1.53984e12 + 1.69134e11i 0.753843 + 0.0828012i
\(545\) 1.41897e8 6.88952e−5
\(546\) −7.16562e11 7.16562e11i −0.345054 0.345054i
\(547\) 3.36166e11 + 8.11577e11i 0.160550 + 0.387603i 0.983599 0.180368i \(-0.0577288\pi\)
−0.823049 + 0.567970i \(0.807729\pi\)
\(548\) 1.77681e11i 0.0841646i
\(549\) 4.73456e11 1.96112e11i 0.222435 0.0921357i
\(550\) 7.61172e11 1.83763e12i 0.354691 0.856301i
\(551\) −3.96377e12 1.64185e12i −1.83200 0.758841i
\(552\) −1.60141e12 + 1.60141e12i −0.734136 + 0.734136i
\(553\) −2.61641e12 + 2.61641e12i −1.18971 + 1.18971i
\(554\) 3.22419e11 + 1.33550e11i 0.145421 + 0.0602352i
\(555\) 3.73105e11 9.00756e11i 0.166922 0.402985i
\(556\) 1.14156e12 4.72848e11i 0.506594 0.209838i
\(557\) 8.34158e11i 0.367198i −0.983001 0.183599i \(-0.941225\pi\)
0.983001 0.183599i \(-0.0587748\pi\)
\(558\) 2.05134e11 + 4.95238e11i 0.0895745 + 0.216252i
\(559\) −5.98144e11 5.98144e11i −0.259091 0.259091i
\(560\) −7.39981e11 −0.317961
\(561\) 2.74412e12 2.20096e12i 1.16969 0.938166i
\(562\) −2.93635e11 −0.124164
\(563\) 1.89101e12 + 1.89101e12i 0.793241 + 0.793241i 0.982020 0.188779i \(-0.0604528\pi\)
−0.188779 + 0.982020i \(0.560453\pi\)
\(564\) −1.71470e11 4.13964e11i −0.0713561 0.172269i
\(565\) 5.88156e11i 0.242814i
\(566\) 2.10955e11 8.73806e10i 0.0864006 0.0357883i
\(567\) −5.03975e11 + 1.21670e12i −0.204779 + 0.494380i
\(568\) 3.42289e12 + 1.41781e12i 1.37983 + 0.571545i
\(569\) 2.71383e12 2.71383e12i 1.08537 1.08537i 0.0893699 0.995999i \(-0.471515\pi\)
0.995999 0.0893699i \(-0.0284853\pi\)
\(570\) −9.19061e11 + 9.19061e11i −0.364676 + 0.364676i
\(571\) 2.41681e12 + 1.00107e12i 0.951436 + 0.394098i 0.803770 0.594940i \(-0.202824\pi\)
0.147666 + 0.989037i \(0.452824\pi\)
\(572\) −5.21681e11 + 1.25945e12i −0.203762 + 0.491924i
\(573\) −2.69975e12 + 1.11827e12i −1.04623 + 0.433363i
\(574\) 1.49922e12i 0.576451i
\(575\) 7.73532e11 + 1.86747e12i 0.295103 + 0.712441i
\(576\) −7.54216e11 7.54216e11i −0.285492 0.285492i
\(577\) 2.98202e12 1.12000 0.560002 0.828492i \(-0.310800\pi\)
0.560002 + 0.828492i \(0.310800\pi\)
\(578\) −1.73960e12 + 1.10670e12i −0.648298 + 0.412434i
\(579\) −1.72184e12 −0.636707
\(580\) −6.81352e11 6.81352e11i −0.250003 0.250003i
\(581\) 8.50130e11 + 2.05240e12i 0.309523 + 0.747254i
\(582\) 1.72276e12i 0.622403i
\(583\) −6.15613e12 + 2.54995e12i −2.20698 + 0.914163i
\(584\) 3.18499e11 7.68925e11i 0.113305 0.273543i
\(585\) 4.33178e11 + 1.79428e11i 0.152920 + 0.0633417i
\(586\) −2.69368e11 + 2.69368e11i −0.0943640 + 0.0943640i
\(587\) 2.13771e11 2.13771e11i 0.0743151 0.0743151i −0.668972 0.743287i \(-0.733266\pi\)
0.743287 + 0.668972i \(0.233266\pi\)
\(588\) 4.23192e11 + 1.75292e11i 0.145995 + 0.0604733i
\(589\) 1.19707e12 2.88998e12i 0.409827 0.989411i
\(590\) −6.34002e11 + 2.62612e11i −0.215406 + 0.0892239i
\(591\) 6.36469e11i 0.214602i
\(592\) 4.43446e11 + 1.07057e12i 0.148386 + 0.358235i
\(593\) −2.00252e12 2.00252e12i −0.665014 0.665014i 0.291544 0.956557i \(-0.405831\pi\)
−0.956557 + 0.291544i \(0.905831\pi\)
\(594\) −4.89966e12 −1.61483
\(595\) −1.79431e12 + 1.43915e12i −0.586911 + 0.470740i
\(596\) 5.22315e11 0.169561
\(597\) −2.48185e12 2.48185e12i −0.799633 0.799633i
\(598\) 7.64139e11 + 1.84480e12i 0.244353 + 0.589920i
\(599\) 1.12962e12i 0.358519i −0.983802 0.179260i \(-0.942630\pi\)
0.983802 0.179260i \(-0.0573702\pi\)
\(600\) 1.52919e12 6.33411e11i 0.481705 0.199529i
\(601\) −4.73282e11 + 1.14260e12i −0.147974 + 0.357241i −0.980435 0.196843i \(-0.936931\pi\)
0.832461 + 0.554083i \(0.186931\pi\)
\(602\) −1.53011e12 6.33790e11i −0.474829 0.196681i
\(603\) 2.81725e11 2.81725e11i 0.0867756 0.0867756i
\(604\) 9.24466e11 9.24466e11i 0.282634 0.282634i
\(605\) 5.15901e12 + 2.13693e12i 1.56555 + 0.648472i
\(606\) 7.90123e8 1.90752e9i 0.000237995 0.000574571i
\(607\) 4.60284e11 1.90656e11i 0.137619 0.0570035i −0.312811 0.949815i \(-0.601271\pi\)
0.450430 + 0.892812i \(0.351271\pi\)
\(608\) 3.60778e12i 1.07072i
\(609\) −1.72780e12 4.17128e12i −0.508998 1.22883i
\(610\) 6.84535e11 + 6.84535e11i 0.200176 + 0.200176i
\(611\) −1.35954e12 −0.394646
\(612\) −5.67477e11 6.23309e10i −0.163518 0.0179607i
\(613\) 3.80066e12 1.08714 0.543572 0.839363i \(-0.317072\pi\)
0.543572 + 0.839363i \(0.317072\pi\)
\(614\) −1.80301e12 1.80301e12i −0.511964 0.511964i
\(615\) −3.95523e11 9.54876e11i −0.111489 0.269159i
\(616\) 9.18502e12i 2.57020i
\(617\) 1.05312e12 4.36216e11i 0.292546 0.121177i −0.231584 0.972815i \(-0.574391\pi\)
0.524130 + 0.851638i \(0.324391\pi\)
\(618\) 8.18578e11 1.97622e12i 0.225742 0.544989i
\(619\) −4.75881e12 1.97116e12i −1.30284 0.539653i −0.380051 0.924965i \(-0.624094\pi\)
−0.922786 + 0.385312i \(0.874094\pi\)
\(620\) 4.96774e11 4.96774e11i 0.135019 0.135019i
\(621\) 3.52084e12 3.52084e12i 0.950023 0.950023i
\(622\) −3.22525e12 1.33594e12i −0.863985 0.357874i
\(623\) −2.10144e12 + 5.07332e12i −0.558882 + 1.34926i
\(624\) 7.67113e11 3.17749e11i 0.202548 0.0838983i
\(625\) 3.65078e10i 0.00957030i
\(626\) 9.59568e11 + 2.31660e12i 0.249742 + 0.602930i
\(627\) 5.79306e12 + 5.79306e12i 1.49694 + 1.49694i
\(628\) −4.29793e11 −0.110266
\(629\) 3.15738e12 + 1.73350e12i 0.804265 + 0.441567i
\(630\) 9.17986e11 0.232169
\(631\) −3.52887e12 3.52887e12i −0.886143 0.886143i 0.108007 0.994150i \(-0.465553\pi\)
−0.994150 + 0.108007i \(0.965553\pi\)
\(632\) −2.28471e12 5.51578e12i −0.569645 1.37524i
\(633\) 2.87373e12i 0.711424i
\(634\) 4.32907e12 1.79316e12i 1.06413 0.440775i
\(635\) 9.11644e10 2.20090e11i 0.0222507 0.0537179i
\(636\) −1.48861e12 6.16602e11i −0.360764 0.149434i
\(637\) 9.82771e11 9.82771e11i 0.236497 0.236497i
\(638\) 6.19023e12 6.19023e12i 1.47916 1.47916i
\(639\) −2.15632e12 8.93177e11i −0.511634 0.211926i
\(640\) 1.40604e10 3.39448e10i 0.00331274 0.00799767i
\(641\) −6.30908e12 + 2.61331e12i −1.47606 + 0.611406i −0.968233 0.250051i \(-0.919553\pi\)
−0.507831 + 0.861457i \(0.669553\pi\)
\(642\) 2.04353e12i 0.474759i
\(643\) 1.05335e12 + 2.54301e12i 0.243009 + 0.586676i 0.997579 0.0695438i \(-0.0221544\pi\)
−0.754570 + 0.656220i \(0.772154\pi\)
\(644\) −1.91792e12 1.91792e12i −0.439384 0.439384i
\(645\) −1.14175e12 −0.259749
\(646\) −3.00438e12 3.74582e12i −0.678748 0.846253i
\(647\) 1.87923e12 0.421610 0.210805 0.977528i \(-0.432391\pi\)
0.210805 + 0.977528i \(0.432391\pi\)
\(648\) −1.50254e12 1.50254e12i −0.334763 0.334763i
\(649\) 1.65531e12 + 3.99627e12i 0.366250 + 0.884206i
\(650\) 1.45936e12i 0.320665i
\(651\) 3.04128e12 1.25974e12i 0.663654 0.274895i
\(652\) 1.22888e12 2.96678e12i 0.266315 0.642942i
\(653\) 6.82513e12 + 2.82706e12i 1.46893 + 0.608451i 0.966615 0.256232i \(-0.0824812\pi\)
0.502316 + 0.864684i \(0.332481\pi\)
\(654\) −2.20428e8 + 2.20428e8i −4.71159e−5 + 4.71159e-5i
\(655\) 1.46206e12 1.46206e12i 0.310370 0.310370i
\(656\) 1.13490e12 + 4.70090e11i 0.239270 + 0.0991090i
\(657\) −2.00645e11 + 4.84400e11i −0.0420130 + 0.101428i
\(658\) −2.45920e12 + 1.01863e12i −0.511419 + 0.211837i
\(659\) 3.71726e12i 0.767784i −0.923378 0.383892i \(-0.874583\pi\)
0.923378 0.383892i \(-0.125417\pi\)
\(660\) 7.04135e11 + 1.69993e12i 0.144447 + 0.348726i
\(661\) −1.73041e12 1.73041e12i −0.352567 0.352567i 0.508497 0.861064i \(-0.330201\pi\)
−0.861064 + 0.508497i \(0.830201\pi\)
\(662\) 3.10033e12 0.627403
\(663\) 1.24213e12 2.26240e12i 0.249664 0.454736i
\(664\) −3.58440e12 −0.715584
\(665\) −3.78794e12 3.78794e12i −0.751113 0.751113i
\(666\) −5.50119e11 1.32810e12i −0.108348 0.261576i
\(667\) 8.89647e12i 1.74041i
\(668\) 1.70373e11 7.05708e10i 0.0331060 0.0137129i
\(669\) 2.55795e12 6.17544e12i 0.493713 1.19193i
\(670\) 6.95349e11 + 2.88023e11i 0.133311 + 0.0552192i
\(671\) 4.31479e12 4.31479e12i 0.821690 0.821690i
\(672\) −2.68464e12 + 2.68464e12i −0.507837 + 0.507837i
\(673\) 4.75457e12 + 1.96941e12i 0.893395 + 0.370056i 0.781677 0.623684i \(-0.214365\pi\)
0.111718 + 0.993740i \(0.464365\pi\)
\(674\) −5.54560e11 + 1.33883e12i −0.103509 + 0.249894i
\(675\) −3.36206e12 + 1.39261e12i −0.623360 + 0.258204i
\(676\) 1.22378e12i 0.225394i
\(677\) −1.02778e12 2.48127e12i −0.188040 0.453968i 0.801542 0.597938i \(-0.204013\pi\)
−0.989582 + 0.143970i \(0.954013\pi\)
\(678\) −9.13663e11 9.13663e11i −0.166055 0.166055i
\(679\) −7.10042e12 −1.28195
\(680\) −1.03741e12 3.56339e12i −0.186062 0.639106i
\(681\) −4.19089e12 −0.746697
\(682\) 4.51330e12 + 4.51330e12i 0.798848 + 0.798848i
\(683\) 1.35043e12 + 3.26023e12i 0.237454 + 0.573264i 0.997018 0.0771682i \(-0.0245879\pi\)
−0.759564 + 0.650432i \(0.774588\pi\)
\(684\) 1.32957e12i 0.232252i
\(685\) −6.72286e11 + 2.78470e11i −0.116667 + 0.0483249i
\(686\) −1.04666e12 + 2.52685e12i −0.180445 + 0.435634i
\(687\) 2.87856e12 + 1.19234e12i 0.493027 + 0.204218i
\(688\) 9.59547e11 9.59547e11i 0.163274 0.163274i
\(689\) −3.45697e12 + 3.45697e12i −0.584399 + 0.584399i
\(690\) 2.49000e12 + 1.03139e12i 0.418195 + 0.173222i
\(691\) −1.42627e12 + 3.44331e12i −0.237985 + 0.574546i −0.997074 0.0764403i \(-0.975645\pi\)
0.759089 + 0.650986i \(0.225645\pi\)
\(692\) −3.70202e11 + 1.53343e11i −0.0613708 + 0.0254206i
\(693\) 5.78629e12i 0.953016i
\(694\) 1.60282e12 + 3.86955e12i 0.262281 + 0.633202i
\(695\) −3.57819e12 3.57819e12i −0.581744 0.581744i
\(696\) 7.28492e12 1.17675
\(697\) 3.66617e12 1.06733e12i 0.588389 0.171297i
\(698\) 1.81427e12 0.289302
\(699\) 6.70764e11 + 6.70764e11i 0.106273 + 0.106273i
\(700\) 7.58603e11 + 1.83143e12i 0.119419 + 0.288303i
\(701\) 9.08459e12i 1.42094i 0.703730 + 0.710468i \(0.251517\pi\)
−0.703730 + 0.710468i \(0.748483\pi\)
\(702\) −3.32123e12 + 1.37570e12i −0.516158 + 0.213800i
\(703\) −3.21024e12 + 7.75021e12i −0.495723 + 1.19678i
\(704\) −1.17337e13 4.86028e12i −1.80036 0.745734i
\(705\) −1.29757e12 + 1.29757e12i −0.197824 + 0.197824i
\(706\) −4.06876e12 + 4.06876e12i −0.616370 + 0.616370i
\(707\) 7.86192e9 + 3.25651e9i 0.00118343 + 0.000490191i
\(708\) −4.00269e11 + 9.66335e11i −0.0598690 + 0.144537i
\(709\) 1.53978e12 6.37799e11i 0.228850 0.0947929i −0.265312 0.964163i \(-0.585475\pi\)
0.494162 + 0.869370i \(0.335475\pi\)
\(710\) 4.40905e12i 0.651152i
\(711\) 1.43930e12 + 3.47477e12i 0.211221 + 0.509933i
\(712\) −6.26517e12 6.26517e12i −0.913636 0.913636i
\(713\) −6.48642e12 −0.939944
\(714\) 5.51719e11 5.02299e12i 0.0794467 0.723303i
\(715\) 5.58293e12 0.798886
\(716\) 3.04487e12 + 3.04487e12i 0.432973 + 0.432973i
\(717\) −1.47852e12 3.56948e12i −0.208926 0.504392i
\(718\) 1.77547e12i 0.249317i
\(719\) −4.62379e12 + 1.91524e12i −0.645235 + 0.267265i −0.681211 0.732088i \(-0.738546\pi\)
0.0359755 + 0.999353i \(0.488546\pi\)
\(720\) −2.87840e11 + 6.94907e11i −0.0399167 + 0.0963675i
\(721\) 8.14506e12 + 3.37380e12i 1.12250 + 0.464954i
\(722\) 3.94061e12 3.94061e12i 0.539693 0.539693i
\(723\) 1.04306e12 1.04306e12i 0.141967 0.141967i
\(724\) −2.55243e12 1.05725e12i −0.345247 0.143006i
\(725\) 2.48821e12 6.00706e12i 0.334476 0.807497i
\(726\) −1.13338e13 + 4.69460e12i −1.51412 + 0.627168i
\(727\) 5.68648e12i 0.754986i 0.926013 + 0.377493i \(0.123214\pi\)
−0.926013 + 0.377493i \(0.876786\pi\)
\(728\) 2.57892e12 + 6.22607e12i 0.340288 + 0.821529i
\(729\) 5.46898e12 + 5.46898e12i 0.717187 + 0.717187i
\(730\) −9.90457e11 −0.129087
\(731\) 4.60543e11 4.19290e12i 0.0596543 0.543108i
\(732\) 1.47553e12 0.189954
\(733\) −1.71112e12 1.71112e12i −0.218934 0.218934i 0.589115 0.808049i \(-0.299476\pi\)
−0.808049 + 0.589115i \(0.799476\pi\)
\(734\) 2.40756e12 + 5.81235e12i 0.306157 + 0.739128i
\(735\) 1.87594e12i 0.237097i
\(736\) 6.91163e12 2.86289e12i 0.868221 0.359629i
\(737\) 1.81548e12 4.38295e12i 0.226666 0.547221i
\(738\) −1.40790e12 5.83172e11i −0.174710 0.0723674i
\(739\) 8.31115e12 8.31115e12i 1.02509 1.02509i 0.0254111 0.999677i \(-0.491911\pi\)
0.999677 0.0254111i \(-0.00808948\pi\)
\(740\) −1.33222e12 + 1.33222e12i −0.163318 + 0.163318i
\(741\) 5.55337e12 + 2.30028e12i 0.676667 + 0.280285i
\(742\) −3.66299e12 + 8.84323e12i −0.443627 + 1.07101i
\(743\) −4.90537e12 + 2.03187e12i −0.590503 + 0.244594i −0.657867 0.753134i \(-0.728541\pi\)
0.0673642 + 0.997728i \(0.478541\pi\)
\(744\) 5.31144e12i 0.635527i
\(745\) −8.18595e11 1.97626e12i −0.0973567 0.235040i
\(746\) 7.56417e10 + 7.56417e10i 0.00894204 + 0.00894204i
\(747\) 2.25807e12 0.265335
\(748\) −6.52674e12 + 1.90013e12i −0.762324 + 0.221935i
\(749\) −8.42247e12 −0.977848
\(750\) −3.63100e12 3.63100e12i −0.419036 0.419036i
\(751\) 1.26079e12 + 3.04383e12i 0.144632 + 0.349173i 0.979550 0.201202i \(-0.0644848\pi\)
−0.834918 + 0.550375i \(0.814485\pi\)
\(752\) 2.18099e12i 0.248698i
\(753\) 4.35235e12 1.80280e12i 0.493340 0.204348i
\(754\) 2.45799e12 5.93412e12i 0.276955 0.668629i
\(755\) −4.94673e12 2.04900e12i −0.554060 0.229499i
\(756\) 3.45289e12 3.45289e12i 0.384445 0.384445i
\(757\) 7.80215e12 7.80215e12i 0.863540 0.863540i −0.128207 0.991747i \(-0.540922\pi\)
0.991747 + 0.128207i \(0.0409222\pi\)
\(758\) 3.48683e12 + 1.44429e12i 0.383636 + 0.158907i
\(759\) 6.50111e12 1.56951e13i 0.711049 1.71662i
\(760\) 7.98554e12 3.30772e12i 0.868247 0.359640i
\(761\) 1.53034e13i 1.65409i −0.562138 0.827043i \(-0.690021\pi\)
0.562138 0.827043i \(-0.309979\pi\)
\(762\) 2.00278e11 + 4.83515e11i 0.0215197 + 0.0519532i
\(763\) −9.08501e8 9.08501e8i −9.70432e−5 9.70432e-5i
\(764\) 5.64686e12 0.599635
\(765\) 6.53535e11 + 2.24483e12i 0.0689910 + 0.236977i
\(766\) −5.13186e12 −0.538574
\(767\) 2.24410e12 + 2.24410e12i 0.234134 + 0.234134i
\(768\) −2.83834e12 6.85236e12i −0.294401 0.710747i
\(769\) 1.87850e13i 1.93706i −0.248902 0.968529i \(-0.580070\pi\)
0.248902 0.968529i \(-0.419930\pi\)
\(770\) 1.00986e13 4.18299e12i 1.03527 0.428823i
\(771\) −4.20640e12 + 1.01552e13i −0.428713 + 1.03500i
\(772\) 3.07403e12 + 1.27331e12i 0.311480 + 0.129019i
\(773\) −1.04712e13 + 1.04712e13i −1.05485 + 1.05485i −0.0564419 + 0.998406i \(0.517976\pi\)
−0.998406 + 0.0564419i \(0.982024\pi\)
\(774\) −1.19037e12 + 1.19037e12i −0.119220 + 0.119220i
\(775\) 4.37975e12 + 1.81415e12i 0.436105 + 0.180641i
\(776\) 4.38425e12 1.05845e13i 0.434027 1.04783i
\(777\) −8.15595e12 + 3.37830e12i −0.802749 + 0.332510i
\(778\) 1.61925e12i 0.158455i
\(779\) 3.40313e12 + 8.21587e12i 0.331100 + 0.799347i
\(780\) 9.54597e11 + 9.54597e11i 0.0923409 + 0.0923409i
\(781\) −2.77913e13 −2.67288
\(782\) −4.79199e12 + 8.72809e12i −0.458232 + 0.834620i
\(783\) −1.60166e13 −1.52279
\(784\) 1.57657e12 + 1.57657e12i 0.149036 + 0.149036i
\(785\) 6.73590e11 + 1.62619e12i 0.0633115 + 0.152847i
\(786\) 4.54245e12i 0.424510i
\(787\) 1.03561e13 4.28966e12i 0.962303 0.398599i 0.154462 0.987999i \(-0.450636\pi\)
0.807842 + 0.589400i \(0.200636\pi\)
\(788\) −4.70670e11 + 1.13630e12i −0.0434859 + 0.104984i
\(789\) −4.30510e12 1.78323e12i −0.395491 0.163818i
\(790\) −5.02393e12 + 5.02393e12i −0.458903 + 0.458903i
\(791\) 3.76569e12 3.76569e12i 0.342019 0.342019i
\(792\) 8.62554e12 + 3.57282e12i 0.778974 + 0.322662i
\(793\) 1.71330e12 4.13627e12i 0.153852 0.371432i
\(794\) 1.26302e13 5.23161e12i 1.12777 0.467136i
\(795\) 6.59876e12i 0.585882i
\(796\) 2.59555e12 + 6.26622e12i 0.229151 + 0.553218i
\(797\) 1.08530e13 + 1.08530e13i 0.952770 + 0.952770i 0.998934 0.0461637i \(-0.0146996\pi\)
−0.0461637 + 0.998934i \(0.514700\pi\)
\(798\) 1.17686e13 1.02734
\(799\) −4.24170e12 5.28849e12i −0.368197 0.459061i
\(800\) −5.46756e12 −0.471942
\(801\) 3.94687e12 + 3.94687e12i 0.338771 + 0.338771i
\(802\) 3.21475e12 + 7.76110e12i 0.274386 + 0.662428i
\(803\) 6.24308e12i 0.529882i
\(804\) 1.05984e12 4.38999e11i 0.0894514 0.0370520i
\(805\) −4.25091e12 + 1.02626e13i −0.356780 + 0.861344i
\(806\) 4.32656e12 + 1.79212e12i 0.361107 + 0.149575i
\(807\) −7.26540e12 + 7.26540e12i −0.603016 + 0.603016i
\(808\) −9.70889e9 + 9.70889e9i −0.000801343 + 0.000801343i
\(809\) −7.13497e12 2.95540e12i −0.585631 0.242576i 0.0701387 0.997537i \(-0.477656\pi\)
−0.655770 + 0.754961i \(0.727656\pi\)
\(810\) −9.67713e11 + 2.33627e12i −0.0789885 + 0.190695i
\(811\) 7.96125e12 3.29766e12i 0.646230 0.267677i −0.0354009 0.999373i \(-0.511271\pi\)
0.681631 + 0.731696i \(0.261271\pi\)
\(812\) 8.72477e12i 0.704290i
\(813\) −2.17950e12 5.26179e12i −0.174965 0.422402i
\(814\) −1.21035e13 1.21035e13i −0.966279 0.966279i
\(815\) −1.31513e13 −1.04414
\(816\) 3.62936e12 + 1.99263e12i 0.286566 + 0.157334i
\(817\) 9.82378e12 0.771400
\(818\) −5.83475e12 5.83475e12i −0.455651 0.455651i
\(819\) −1.62464e12 3.92224e12i −0.126177 0.304618i
\(820\) 1.99725e12i 0.154266i
\(821\) −9.14275e12 + 3.78705e12i −0.702316 + 0.290909i −0.705121 0.709087i \(-0.749107\pi\)
0.00280460 + 0.999996i \(0.499107\pi\)
\(822\) 6.11768e11 1.47694e12i 0.0467373 0.112834i
\(823\) −1.45100e11 6.01024e10i −0.0110247 0.00456660i 0.377164 0.926146i \(-0.376899\pi\)
−0.388189 + 0.921580i \(0.626899\pi\)
\(824\) −1.00585e13 + 1.00585e13i −0.760086 + 0.760086i
\(825\) −8.77933e12 + 8.77933e12i −0.659810 + 0.659810i
\(826\) 5.74061e12 + 2.37784e12i 0.429089 + 0.177735i
\(827\) 7.05592e11 1.70345e12i 0.0524540 0.126635i −0.895480 0.445101i \(-0.853168\pi\)
0.947934 + 0.318466i \(0.103168\pi\)
\(828\) −2.54714e12 + 1.05506e12i −0.188328 + 0.0780082i
\(829\) 1.86280e13i 1.36984i 0.728618 + 0.684920i \(0.240163\pi\)
−0.728618 + 0.684920i \(0.759837\pi\)
\(830\) 1.63239e12 + 3.94093e12i 0.119391 + 0.288236i
\(831\) −1.54036e12 1.54036e12i −0.112052 0.112052i
\(832\) −9.31837e12 −0.674194
\(833\) 6.88908e12 + 7.56687e11i 0.495745 + 0.0544520i
\(834\) 1.11170e13 0.795682
\(835\) −5.34032e11 5.34032e11i −0.0380170 0.0380170i
\(836\) −6.05846e12 1.46264e13i −0.428977 1.03564i
\(837\) 1.16777e13i 0.822416i
\(838\) −1.95902e12 + 8.11454e11i −0.137228 + 0.0568416i
\(839\) −9.13112e11 + 2.20445e12i −0.0636203 + 0.153593i −0.952492 0.304563i \(-0.901490\pi\)
0.888872 + 0.458155i \(0.151490\pi\)
\(840\) 8.40359e12 + 3.48088e12i 0.582382 + 0.241231i
\(841\) 9.97725e12 9.97725e12i 0.687747 0.687747i
\(842\) −5.39321e12 + 5.39321e12i −0.369780 + 0.369780i
\(843\) 1.69339e12 + 7.01425e11i 0.115487 + 0.0478362i
\(844\) 2.12513e12 5.13051e12i 0.144160 0.348032i
\(845\) −4.63035e12 + 1.91795e12i −0.312434 + 0.129415i
\(846\) 2.70563e12i 0.181594i
\(847\) −1.93490e13 4.67125e13i −1.29176 3.11859i
\(848\) −5.54570e12 5.54570e12i −0.368277 0.368277i
\(849\) −1.42531e12 −0.0941508
\(850\) 5.67675e12 4.55312e12i 0.373005 0.299174i
\(851\) 1.73949e13 1.13695
\(852\) −4.75189e12 4.75189e12i −0.308950 0.308950i
\(853\) 3.85584e12 + 9.30881e12i 0.249372 + 0.602038i 0.998151 0.0607821i \(-0.0193595\pi\)
−0.748779 + 0.662820i \(0.769359\pi\)
\(854\) 8.76553e12i 0.563920i
\(855\) −5.03065e12 + 2.08376e12i −0.321941 + 0.133352i
\(856\) 5.20056e12 1.25553e13i 0.331069 0.799271i
\(857\) 1.08408e13 + 4.49040e12i 0.686511 + 0.284362i 0.698546 0.715565i \(-0.253831\pi\)
−0.0120347 + 0.999928i \(0.503831\pi\)
\(858\) −8.67272e12 + 8.67272e12i −0.546340 + 0.546340i
\(859\) −1.61833e13 + 1.61833e13i −1.01414 + 1.01414i −0.0142442 + 0.999899i \(0.504534\pi\)
−0.999899 + 0.0142442i \(0.995466\pi\)
\(860\) 2.03839e12 + 8.44329e11i 0.127070 + 0.0526343i
\(861\) −3.58128e12 + 8.64598e12i −0.222088 + 0.536167i
\(862\) 7.06839e12 2.92782e12i 0.436052 0.180619i
\(863\) 2.58136e13i 1.58417i −0.610413 0.792083i \(-0.708997\pi\)
0.610413 0.792083i \(-0.291003\pi\)
\(864\) 5.15414e12 + 1.24432e13i 0.314662 + 0.759661i
\(865\) 1.16039e12 + 1.16039e12i 0.0704747 + 0.0704747i
\(866\) 2.03348e13 1.22860
\(867\) 1.26759e13 2.22682e12i 0.761891 0.133844i
\(868\) −6.36123e12 −0.380366
\(869\) 3.16670e13 + 3.16670e13i 1.88373 + 1.88373i
\(870\) −3.31766e12 8.00953e12i −0.196334 0.473991i
\(871\) 3.48072e12i 0.204922i
\(872\) 1.91526e9 7.93326e8i 0.000112177 4.64651e-5i
\(873\) −2.76194e12 + 6.66792e12i −0.160935 + 0.388532i
\(874\) −2.14243e13 8.87422e12i −1.24195 0.514433i
\(875\) 1.49653e13 1.49653e13i 0.863076 0.863076i
\(876\) −1.06747e12 + 1.06747e12i −0.0612476 + 0.0612476i
\(877\) −2.66165e13 1.10249e13i −1.51933 0.629329i −0.541876 0.840458i \(-0.682286\pi\)
−0.977458 + 0.211130i \(0.932286\pi\)
\(878\) −3.36351e12 + 8.12022e12i −0.191015 + 0.461150i
\(879\) 2.19690e12 9.09984e11i 0.124125 0.0514143i
\(880\) 8.95616e12i 0.503443i
\(881\) 5.94633e12 + 1.43557e13i 0.332551 + 0.802848i 0.998388 + 0.0567514i \(0.0180743\pi\)
−0.665838 + 0.746096i \(0.731926\pi\)
\(882\) −1.95582e12 1.95582e12i −0.108823 0.108823i
\(883\) 3.44887e13 1.90921 0.954604 0.297876i \(-0.0962783\pi\)
0.954604 + 0.297876i \(0.0962783\pi\)
\(884\) −3.89065e12 + 3.12055e12i −0.214283 + 0.171868i
\(885\) 4.28360e12 0.234728
\(886\) −8.17982e12 8.17982e12i −0.445956 0.445956i
\(887\) 7.78029e10 + 1.87833e11i 0.00422026 + 0.0101886i 0.925976 0.377583i \(-0.123245\pi\)
−0.921755 + 0.387772i \(0.873245\pi\)
\(888\) 1.42439e13i 0.768726i
\(889\) −1.99282e12 + 8.25453e11i −0.107007 + 0.0443236i
\(890\) −4.03510e12 + 9.74160e12i −0.215576 + 0.520445i
\(891\) 1.47260e13 + 6.09973e12i 0.782774 + 0.324236i
\(892\) −9.13351e12 + 9.13351e12i −0.483054 + 0.483054i
\(893\) 1.11644e13 1.11644e13i 0.587495 0.587495i
\(894\) 4.34164e12 + 1.79836e12i 0.227318 + 0.0941584i
\(895\) 6.74871e12 1.62928e13i 0.351574 0.848775i
\(896\) −3.07355e11 + 1.27311e11i −0.0159314 + 0.00659901i
\(897\) 1.24643e13i 0.642836i
\(898\) −7.61927e12 1.83945e13i −0.390994 0.943942i
\(899\) 1.47536e13 + 1.47536e13i 0.753319 + 0.753319i
\(900\) 2.01496e12 0.102370
\(901\) −2.42328e13 2.66170e12i −1.22502 0.134554i
\(902\) −1.81454e13 −0.912721
\(903\) 7.31012e12 + 7.31012e12i 0.365872 + 0.365872i
\(904\) 3.28829e12 + 7.93864e12i 0.163762 + 0.395356i
\(905\) 1.13145e13i 0.560682i
\(906\) 1.08674e13 4.50143e12i 0.535858 0.221960i
\(907\) −4.18412e12 + 1.01014e13i −0.205292 + 0.495618i −0.992671 0.120851i \(-0.961438\pi\)
0.787379 + 0.616469i \(0.211438\pi\)
\(908\) 7.48207e12 + 3.09918e12i 0.365288 + 0.151307i
\(909\) 6.11631e9 6.11631e9i 0.000297134 0.000297134i
\(910\) 5.67088e12 5.67088e12i 0.274135 0.274135i
\(911\) −3.70616e13 1.53514e13i −1.78275 0.738441i −0.991990 0.126319i \(-0.959684\pi\)
−0.790764 0.612122i \(-0.790316\pi\)
\(912\) −3.69013e12 + 8.90876e12i −0.176630 + 0.426423i
\(913\) 2.48406e13 1.02893e13i 1.18316 0.490082i
\(914\) 6.65921e12i 0.315620i
\(915\) −2.31251e12 5.58290e12i −0.109066 0.263308i
\(916\) −4.25741e12 4.25741e12i −0.199809 0.199809i
\(917\) −1.87218e13 −0.874352
\(918\) −1.57134e13 8.62715e12i −0.730261 0.400936i
\(919\) 2.20829e13 1.02126 0.510631 0.859800i \(-0.329412\pi\)
0.510631 + 0.859800i \(0.329412\pi\)
\(920\) −1.26736e13 1.26736e13i −0.583248 0.583248i
\(921\) 6.09095e12 + 1.47049e13i 0.278944 + 0.673430i
\(922\) 1.71054e13i 0.779549i
\(923\) −1.88383e13 + 7.80309e12i −0.854348 + 0.353883i
\(924\) 6.37563e12 1.53921e13i 0.287739 0.694664i
\(925\) −1.17454e13 4.86510e12i −0.527509 0.218501i
\(926\) −1.67109e13 + 1.67109e13i −0.746877 + 0.746877i
\(927\) 6.33658e12 6.33658e12i 0.281836 0.281836i
\(928\) −2.22325e13 9.20900e12i −0.984062 0.407612i
\(929\) −1.60938e13 + 3.88539e13i −0.708906 + 1.71145i −0.00618976 + 0.999981i \(0.501970\pi\)
−0.702716 + 0.711470i \(0.748030\pi\)
\(930\) 5.83975e12 2.41890e12i 0.255989 0.106034i
\(931\) 1.61408e13i 0.704128i
\(932\) −7.01494e11 1.69356e12i −0.0304546 0.0735239i
\(933\) 1.54087e13 + 1.54087e13i 0.665731 + 0.665731i
\(934\) 2.87729e13 1.23715
\(935\) 1.74184e13 + 2.17170e13i 0.745344 + 0.929283i
\(936\) 6.84998e12 0.291708
\(937\) 1.35606e13 + 1.35606e13i 0.574712 + 0.574712i 0.933442 0.358729i \(-0.116790\pi\)
−0.358729 + 0.933442i \(0.616790\pi\)
\(938\) −2.60792e12 6.29607e12i −0.109997 0.265557i
\(939\) 1.56520e13i 0.657014i
\(940\) 3.27612e12 1.35701e12i 0.136862 0.0566903i
\(941\) 1.49205e13 3.60212e13i 0.620339 1.49763i −0.230968 0.972961i \(-0.574189\pi\)
0.851307 0.524668i \(-0.175811\pi\)
\(942\) −3.57256e12 1.47980e12i −0.147826 0.0612316i
\(943\) 1.30391e13 1.30391e13i 0.536964 0.536964i
\(944\) −3.60000e12 + 3.60000e12i −0.147547 + 0.147547i
\(945\) −1.84761e13 7.65303e12i −0.753644 0.312170i
\(946\) −7.67092e12 + 1.85192e13i −0.311413 + 0.751818i
\(947\) −5.49297e12 + 2.27526e12i −0.221939 + 0.0919299i −0.490882 0.871226i \(-0.663325\pi\)
0.268944 + 0.963156i \(0.413325\pi\)
\(948\) 1.08292e13i 0.435469i
\(949\) 1.75290e12 + 4.23188e12i 0.0701551 + 0.169369i
\(950\) 1.19841e13 + 1.19841e13i 0.477362 + 0.477362i
\(951\) −2.92491e13 −1.15958
\(952\) −1.61727e13 + 2.94567e13i −0.638140 + 1.16230i
\(953\) −1.15782e13 −0.454697 −0.227349 0.973813i \(-0.573006\pi\)
−0.227349 + 0.973813i \(0.573006\pi\)
\(954\) 6.87974e12 + 6.87974e12i 0.268908 + 0.268908i
\(955\) −8.85001e12 2.13658e13i −0.344293 0.831198i
\(956\) 7.46602e12i 0.289087i
\(957\) −5.04860e13 + 2.09120e13i −1.94566 + 0.805919i
\(958\) −5.30331e12 + 1.28033e13i −0.203424 + 0.491109i
\(959\) 6.08725e12 + 2.52142e12i 0.232401 + 0.0962635i
\(960\) −8.89357e12 + 8.89357e12i −0.337952 + 0.337952i
\(961\) 7.93880e12 7.93880e12i 0.300261 0.300261i
\(962\) −1.16028e13 4.80602e12i −0.436791 0.180925i
\(963\) −3.27620e12 + 7.90945e12i −0.122759 + 0.296366i
\(964\) −2.63354e12 + 1.09085e12i −0.0982183 + 0.0406834i
\(965\) 1.36267e13i 0.505844i
\(966\) −9.33879e12 2.25458e13i −0.345059 0.833047i
\(967\) 1.09351e13 + 1.09351e13i 0.402163 + 0.402163i 0.878995 0.476832i \(-0.158215\pi\)
−0.476832 + 0.878995i \(0.658215\pi\)
\(968\) 8.15810e13 2.98641
\(969\) 8.37836e12 + 2.87788e13i 0.305283 + 1.04861i
\(970\) −1.36340e13 −0.494481
\(971\) −6.70216e12 6.70216e12i −0.241952 0.241952i 0.575705 0.817657i \(-0.304727\pi\)
−0.817657 + 0.575705i \(0.804727\pi\)
\(972\) −3.25464e12 7.85741e12i −0.116951 0.282346i
\(973\) 4.58190e13i 1.63884i
\(974\) −1.77897e13 + 7.36872e12i −0.633363 + 0.262348i
\(975\) −3.48606e12 + 8.41609e12i −0.123542 + 0.298256i
\(976\) 6.63542e12 + 2.74848e12i 0.234069 + 0.0969547i
\(977\) 1.31478e13 1.31478e13i 0.461666 0.461666i −0.437535 0.899201i \(-0.644149\pi\)
0.899201 + 0.437535i \(0.144149\pi\)
\(978\) 2.04296e13 2.04296e13i 0.714062 0.714062i
\(979\) 6.14036e13 + 2.54342e13i 2.13635 + 0.884904i
\(980\) −1.38726e12 + 3.34914e12i −0.0480442 + 0.115989i
\(981\) −1.20655e9 + 4.99771e8i −4.15946e−5 + 1.72290e-5i
\(982\) 2.74745e13i 0.942818i
\(983\) −1.99520e13 4.81684e13i −0.681546 1.64540i −0.761154 0.648572i \(-0.775367\pi\)
0.0796075 0.996826i \(-0.474633\pi\)
\(984\) −1.06771e13 1.06771e13i −0.363059 0.363059i
\(985\) 5.03702e12 0.170495
\(986\) 3.07519e13 8.95279e12i 1.03616 0.301656i
\(987\) 1.66154e13 0.557294
\(988\) −8.21346e12 8.21346e12i −0.274233 0.274233i
\(989\) −7.79548e12 1.88200e13i −0.259095 0.625512i
\(990\) 1.11106e13i 0.367603i
\(991\) −4.26360e13 + 1.76604e13i −1.40425 + 0.581660i −0.950851 0.309648i \(-0.899789\pi\)
−0.453399 + 0.891307i \(0.649789\pi\)
\(992\) 6.71428e12 1.62097e13i 0.220139 0.531463i
\(993\) −1.78795e13 7.40595e12i −0.583559 0.241718i
\(994\) −2.82291e13 + 2.82291e13i −0.917188 + 0.917188i
\(995\) 1.96414e13 1.96414e13i 0.635284 0.635284i
\(996\) 6.00670e12 + 2.48806e12i 0.193405 + 0.0801112i
\(997\) 1.94223e13 4.68896e13i 0.622548 1.50296i −0.226153 0.974092i \(-0.572615\pi\)
0.848701 0.528872i \(-0.177385\pi\)
\(998\) 3.49984e13 1.44968e13i 1.11676 0.462578i
\(999\) 3.13166e13i 0.994786i
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 17.10.d.a.15.5 yes 52
17.5 odd 16 289.10.a.i.1.33 52
17.8 even 8 inner 17.10.d.a.8.5 52
17.12 odd 16 289.10.a.i.1.34 52
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
17.10.d.a.8.5 52 17.8 even 8 inner
17.10.d.a.15.5 yes 52 1.1 even 1 trivial
289.10.a.i.1.33 52 17.5 odd 16
289.10.a.i.1.34 52 17.12 odd 16