Properties

Label 16.13.f.a.3.3
Level $16$
Weight $13$
Character 16.3
Analytic conductor $14.624$
Analytic rank $0$
Dimension $46$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [16,13,Mod(3,16)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(16, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 13, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("16.3");
 
S:= CuspForms(chi, 13);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 16 = 2^{4} \)
Weight: \( k \) \(=\) \( 13 \)
Character orbit: \([\chi]\) \(=\) 16.f (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.6239010764\)
Analytic rank: \(0\)
Dimension: \(46\)
Relative dimension: \(23\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 3.3
Character \(\chi\) \(=\) 16.3
Dual form 16.13.f.a.11.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-59.3506 - 23.9480i) q^{2} +(-234.930 + 234.930i) q^{3} +(2948.99 + 2842.66i) q^{4} +(-18167.9 + 18167.9i) q^{5} +(19569.4 - 8317.14i) q^{6} +112043. q^{7} +(-106948. - 239336. i) q^{8} +421057. i q^{9} +O(q^{10})\) \(q+(-59.3506 - 23.9480i) q^{2} +(-234.930 + 234.930i) q^{3} +(2948.99 + 2842.66i) q^{4} +(-18167.9 + 18167.9i) q^{5} +(19569.4 - 8317.14i) q^{6} +112043. q^{7} +(-106948. - 239336. i) q^{8} +421057. i q^{9} +(1.51336e6 - 643191. i) q^{10} +(1.85563e6 + 1.85563e6i) q^{11} +(-1.36063e6 + 24980.2i) q^{12} +(-4.76340e6 - 4.76340e6i) q^{13} +(-6.64979e6 - 2.68320e6i) q^{14} -8.53639e6i q^{15} +(615827. + 1.67659e7i) q^{16} -2.64070e7 q^{17} +(1.00835e7 - 2.49900e7i) q^{18} +(-1.10839e7 + 1.10839e7i) q^{19} +(-1.05222e8 + 1.93180e6i) q^{20} +(-2.63222e7 + 2.63222e7i) q^{21} +(-6.56940e7 - 1.54571e8i) q^{22} -1.47280e8 q^{23} +(8.13526e7 + 3.11018e7i) q^{24} -4.16006e8i q^{25} +(1.68637e8 + 3.96784e8i) q^{26} +(-2.23771e8 - 2.23771e8i) q^{27} +(3.30412e8 + 3.18499e8i) q^{28} +(6.85742e8 + 6.85742e8i) q^{29} +(-2.04429e8 + 5.06640e8i) q^{30} -1.41233e9i q^{31} +(3.64960e8 - 1.00981e9i) q^{32} -8.71886e8 q^{33} +(1.56727e9 + 6.32394e8i) q^{34} +(-2.03558e9 + 2.03558e9i) q^{35} +(-1.19692e9 + 1.24169e9i) q^{36} +(2.44312e8 - 2.44312e8i) q^{37} +(9.23277e8 - 3.92401e8i) q^{38} +2.23813e9 q^{39} +(6.29126e9 + 2.40521e9i) q^{40} -4.41701e9i q^{41} +(2.19260e9 - 9.31874e8i) q^{42} +(-1.55921e9 - 1.55921e9i) q^{43} +(1.97309e8 + 1.07471e10i) q^{44} +(-7.64972e9 - 7.64972e9i) q^{45} +(8.74116e9 + 3.52706e9i) q^{46} -4.61361e9i q^{47} +(-4.08350e9 - 3.79414e9i) q^{48} -1.28775e9 q^{49} +(-9.96251e9 + 2.46902e10i) q^{50} +(6.20380e9 - 6.20380e9i) q^{51} +(-5.06493e8 - 2.75879e10i) q^{52} +(-4.04467e8 + 4.04467e8i) q^{53} +(7.92206e9 + 1.86398e10i) q^{54} -6.74258e10 q^{55} +(-1.19827e10 - 2.68158e10i) q^{56} -5.20791e9i q^{57} +(-2.42770e10 - 5.71213e10i) q^{58} +(2.96444e9 + 2.96444e9i) q^{59} +(2.42660e10 - 2.51737e10i) q^{60} +(9.42146e9 + 9.42146e9i) q^{61} +(-3.38226e10 + 8.38229e10i) q^{62} +4.71763e10i q^{63} +(-4.58437e10 + 5.11930e10i) q^{64} +1.73082e11 q^{65} +(5.17470e10 + 2.08799e10i) q^{66} +(-3.68155e10 + 3.68155e10i) q^{67} +(-7.78738e10 - 7.50660e10i) q^{68} +(3.46006e10 - 3.46006e10i) q^{69} +(1.69561e11 - 7.20648e10i) q^{70} +5.60522e10 q^{71} +(1.00774e11 - 4.50312e10i) q^{72} +1.89998e10i q^{73} +(-2.03509e10 + 8.64929e9i) q^{74} +(9.77324e10 + 9.77324e10i) q^{75} +(-6.41943e10 + 1.17856e9i) q^{76} +(2.07909e11 + 2.07909e11i) q^{77} +(-1.32835e11 - 5.35988e10i) q^{78} +2.84842e10i q^{79} +(-3.15790e11 - 2.93413e11i) q^{80} -1.18626e11 q^{81} +(-1.05778e11 + 2.62152e11i) q^{82} +(-3.85877e11 + 3.85877e11i) q^{83} +(-1.52449e11 + 2.79885e9i) q^{84} +(4.79760e11 - 4.79760e11i) q^{85} +(5.51999e10 + 1.29880e11i) q^{86} -3.22203e11 q^{87} +(2.45662e11 - 6.42574e11i) q^{88} -2.19692e11i q^{89} +(2.70820e11 + 6.37211e11i) q^{90} +(-5.33703e11 - 5.33703e11i) q^{91} +(-4.34327e11 - 4.18667e11i) q^{92} +(3.31800e11 + 3.31800e11i) q^{93} +(-1.10487e11 + 2.73820e11i) q^{94} -4.02745e11i q^{95} +(1.51496e11 + 3.22976e11i) q^{96} +8.48143e10 q^{97} +(7.64287e10 + 3.08390e10i) q^{98} +(-7.81324e11 + 7.81324e11i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 46 q - 2 q^{2} - 2 q^{3} - 4232 q^{4} - 2 q^{5} + 72928 q^{6} - 4 q^{7} - 478172 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 46 q - 2 q^{2} - 2 q^{3} - 4232 q^{4} - 2 q^{5} + 72928 q^{6} - 4 q^{7} - 478172 q^{8} + 2806780 q^{10} + 2668318 q^{11} + 7885108 q^{12} - 2 q^{13} - 26829652 q^{14} + 49704280 q^{16} - 4 q^{17} + 15306190 q^{18} + 51868606 q^{19} - 72195860 q^{20} - 1062884 q^{21} + 47303908 q^{22} + 298270076 q^{23} - 131729232 q^{24} + 526315336 q^{26} + 970053760 q^{27} + 711713336 q^{28} + 704570398 q^{29} - 6112100060 q^{30} + 7182362248 q^{32} - 4 q^{33} - 6346386988 q^{34} - 3815032900 q^{35} - 11830365748 q^{36} + 364298398 q^{37} + 14395577488 q^{38} + 15553507196 q^{39} - 19774396184 q^{40} + 1899889176 q^{42} + 363863518 q^{43} - 12173301164 q^{44} + 489344130 q^{45} - 10837581892 q^{46} + 7988573928 q^{48} + 67229109258 q^{49} + 1530058950 q^{50} + 33806024892 q^{51} - 9789537692 q^{52} - 11168756642 q^{53} - 21820351456 q^{54} - 74491808260 q^{55} + 61228226264 q^{56} - 33805733192 q^{58} + 104334793054 q^{59} - 76265037280 q^{60} - 106371743810 q^{61} + 280885397040 q^{62} - 234402872384 q^{64} - 75186419620 q^{65} + 148565995972 q^{66} - 43778233922 q^{67} + 232865553776 q^{68} - 214340079908 q^{69} - 411016751104 q^{70} - 188251854340 q^{71} + 632336686420 q^{72} - 207892484228 q^{74} + 308961520610 q^{75} + 21519708868 q^{76} - 341607754084 q^{77} - 115706090484 q^{78} + 477844371304 q^{80} - 941431788274 q^{81} - 114119320560 q^{82} - 1025936323202 q^{83} - 718734617432 q^{84} + 436332718748 q^{85} + 2196044404900 q^{86} + 2368412421756 q^{87} - 2058716398472 q^{88} + 1566205087544 q^{90} - 2028231531652 q^{91} + 151792482776 q^{92} + 1534541270080 q^{93} - 1756088243280 q^{94} + 1830456305584 q^{96} - 4 q^{97} + 707523027114 q^{98} + 4950023059646 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −59.3506 23.9480i −0.927353 0.374188i
\(3\) −234.930 + 234.930i −0.322264 + 0.322264i −0.849635 0.527371i \(-0.823178\pi\)
0.527371 + 0.849635i \(0.323178\pi\)
\(4\) 2948.99 + 2842.66i 0.719967 + 0.694008i
\(5\) −18167.9 + 18167.9i −1.16275 + 1.16275i −0.178875 + 0.983872i \(0.557246\pi\)
−0.983872 + 0.178875i \(0.942754\pi\)
\(6\) 19569.4 8317.14i 0.419439 0.178265i
\(7\) 112043. 0.952346 0.476173 0.879352i \(-0.342024\pi\)
0.476173 + 0.879352i \(0.342024\pi\)
\(8\) −106948. 239336.i −0.407975 0.912993i
\(9\) 421057.i 0.792292i
\(10\) 1.51336e6 643191.i 1.51336 0.643191i
\(11\) 1.85563e6 + 1.85563e6i 1.04745 + 1.04745i 0.998817 + 0.0486367i \(0.0154877\pi\)
0.0486367 + 0.998817i \(0.484512\pi\)
\(12\) −1.36063e6 + 24980.2i −0.455673 + 0.00836582i
\(13\) −4.76340e6 4.76340e6i −0.986863 0.986863i 0.0130520 0.999915i \(-0.495845\pi\)
−0.999915 + 0.0130520i \(0.995845\pi\)
\(14\) −6.64979e6 2.68320e6i −0.883161 0.356356i
\(15\) 8.53639e6i 0.749422i
\(16\) 615827. + 1.67659e7i 0.0367061 + 0.999326i
\(17\) −2.64070e7 −1.09402 −0.547010 0.837126i \(-0.684234\pi\)
−0.547010 + 0.837126i \(0.684234\pi\)
\(18\) 1.00835e7 2.49900e7i 0.296466 0.734734i
\(19\) −1.10839e7 + 1.10839e7i −0.235599 + 0.235599i −0.815025 0.579426i \(-0.803277\pi\)
0.579426 + 0.815025i \(0.303277\pi\)
\(20\) −1.05222e8 + 1.93180e6i −1.64410 + 0.0301844i
\(21\) −2.63222e7 + 2.63222e7i −0.306907 + 0.306907i
\(22\) −6.56940e7 1.54571e8i −0.579415 1.36330i
\(23\) −1.47280e8 −0.994895 −0.497447 0.867494i \(-0.665729\pi\)
−0.497447 + 0.867494i \(0.665729\pi\)
\(24\) 8.13526e7 + 3.11018e7i 0.425700 + 0.162749i
\(25\) 4.16006e8i 1.70396i
\(26\) 1.68637e8 + 3.96784e8i 0.545899 + 1.28444i
\(27\) −2.23771e8 2.23771e8i −0.577591 0.577591i
\(28\) 3.30412e8 + 3.18499e8i 0.685658 + 0.660936i
\(29\) 6.85742e8 + 6.85742e8i 1.15285 + 1.15285i 0.985979 + 0.166871i \(0.0533663\pi\)
0.166871 + 0.985979i \(0.446634\pi\)
\(30\) −2.04429e8 + 5.06640e8i −0.280424 + 0.694979i
\(31\) 1.41233e9i 1.59136i −0.605719 0.795678i \(-0.707115\pi\)
0.605719 0.795678i \(-0.292885\pi\)
\(32\) 3.64960e8 1.00981e9i 0.339896 0.940463i
\(33\) −8.71886e8 −0.675113
\(34\) 1.56727e9 + 6.32394e8i 1.01454 + 0.409369i
\(35\) −2.03558e9 + 2.03558e9i −1.10734 + 1.10734i
\(36\) −1.19692e9 + 1.24169e9i −0.549857 + 0.570424i
\(37\) 2.44312e8 2.44312e8i 0.0952215 0.0952215i −0.657891 0.753113i \(-0.728551\pi\)
0.753113 + 0.657891i \(0.228551\pi\)
\(38\) 9.23277e8 3.92401e8i 0.306641 0.130325i
\(39\) 2.23813e9 0.636060
\(40\) 6.29126e9 + 2.40521e9i 1.53595 + 0.587208i
\(41\) 4.41701e9i 0.929875i −0.885343 0.464938i \(-0.846077\pi\)
0.885343 0.464938i \(-0.153923\pi\)
\(42\) 2.19260e9 9.31874e8i 0.399452 0.169770i
\(43\) −1.55921e9 1.55921e9i −0.246657 0.246657i 0.572940 0.819597i \(-0.305803\pi\)
−0.819597 + 0.572940i \(0.805803\pi\)
\(44\) 1.97309e8 + 1.07471e10i 0.0271914 + 1.48107i
\(45\) −7.64972e9 7.64972e9i −0.921235 0.921235i
\(46\) 8.74116e9 + 3.52706e9i 0.922618 + 0.372277i
\(47\) 4.61361e9i 0.428010i −0.976833 0.214005i \(-0.931349\pi\)
0.976833 0.214005i \(-0.0686508\pi\)
\(48\) −4.08350e9 3.79414e9i −0.333876 0.310218i
\(49\) −1.28775e9 −0.0930368
\(50\) −9.96251e9 + 2.46902e10i −0.637601 + 1.58017i
\(51\) 6.20380e9 6.20380e9i 0.352563 0.352563i
\(52\) −5.06493e8 2.75879e10i −0.0256185 1.39540i
\(53\) −4.04467e8 + 4.04467e8i −0.0182485 + 0.0182485i −0.716172 0.697924i \(-0.754107\pi\)
0.697924 + 0.716172i \(0.254107\pi\)
\(54\) 7.92206e9 + 1.86398e10i 0.319503 + 0.751758i
\(55\) −6.74258e10 −2.43585
\(56\) −1.19827e10 2.68158e10i −0.388533 0.869486i
\(57\) 5.20791e9i 0.151850i
\(58\) −2.42770e10 5.71213e10i −0.637717 1.50048i
\(59\) 2.96444e9 + 2.96444e9i 0.0702799 + 0.0702799i 0.741373 0.671093i \(-0.234175\pi\)
−0.671093 + 0.741373i \(0.734175\pi\)
\(60\) 2.42660e10 2.51737e10i 0.520105 0.539560i
\(61\) 9.42146e9 + 9.42146e9i 0.182869 + 0.182869i 0.792605 0.609736i \(-0.208725\pi\)
−0.609736 + 0.792605i \(0.708725\pi\)
\(62\) −3.38226e10 + 8.38229e10i −0.595466 + 1.47575i
\(63\) 4.71763e10i 0.754536i
\(64\) −4.58437e10 + 5.11930e10i −0.667113 + 0.744957i
\(65\) 1.73082e11 2.29494
\(66\) 5.17470e10 + 2.08799e10i 0.626068 + 0.252619i
\(67\) −3.68155e10 + 3.68155e10i −0.406989 + 0.406989i −0.880687 0.473698i \(-0.842919\pi\)
0.473698 + 0.880687i \(0.342919\pi\)
\(68\) −7.78738e10 7.50660e10i −0.787659 0.759258i
\(69\) 3.46006e10 3.46006e10i 0.320618 0.320618i
\(70\) 1.69561e11 7.20648e10i 1.44124 0.612541i
\(71\) 5.60522e10 0.437565 0.218783 0.975774i \(-0.429791\pi\)
0.218783 + 0.975774i \(0.429791\pi\)
\(72\) 1.00774e11 4.50312e10i 0.723357 0.323235i
\(73\) 1.89998e10i 0.125549i 0.998028 + 0.0627743i \(0.0199948\pi\)
−0.998028 + 0.0627743i \(0.980005\pi\)
\(74\) −2.03509e10 + 8.64929e9i −0.123935 + 0.0526733i
\(75\) 9.77324e10 + 9.77324e10i 0.549125 + 0.549125i
\(76\) −6.41943e10 + 1.17856e9i −0.333131 + 0.00611603i
\(77\) 2.07909e11 + 2.07909e11i 0.997538 + 0.997538i
\(78\) −1.32835e11 5.35988e10i −0.589852 0.238006i
\(79\) 2.84842e10i 0.117177i 0.998282 + 0.0585883i \(0.0186599\pi\)
−0.998282 + 0.0585883i \(0.981340\pi\)
\(80\) −3.15790e11 2.93413e11i −1.20464 1.11928i
\(81\) −1.18626e11 −0.420019
\(82\) −1.05778e11 + 2.62152e11i −0.347948 + 0.862323i
\(83\) −3.85877e11 + 3.85877e11i −1.18027 + 1.18027i −0.200592 + 0.979675i \(0.564287\pi\)
−0.979675 + 0.200592i \(0.935713\pi\)
\(84\) −1.52449e11 + 2.79885e9i −0.433958 + 0.00796715i
\(85\) 4.79760e11 4.79760e11i 1.27207 1.27207i
\(86\) 5.51999e10 + 1.29880e11i 0.136442 + 0.321034i
\(87\) −3.22203e11 −0.743043
\(88\) 2.45662e11 6.42574e11i 0.528983 1.38365i
\(89\) 2.19692e11i 0.442054i −0.975268 0.221027i \(-0.929059\pi\)
0.975268 0.221027i \(-0.0709408\pi\)
\(90\) 2.70820e11 + 6.37211e11i 0.509595 + 1.19902i
\(91\) −5.33703e11 5.33703e11i −0.939835 0.939835i
\(92\) −4.34327e11 4.18667e11i −0.716292 0.690465i
\(93\) 3.31800e11 + 3.31800e11i 0.512837 + 0.512837i
\(94\) −1.10487e11 + 2.73820e11i −0.160156 + 0.396916i
\(95\) 4.02745e11i 0.547883i
\(96\) 1.51496e11 + 3.22976e11i 0.193541 + 0.412613i
\(97\) 8.48143e10 0.101821 0.0509107 0.998703i \(-0.483788\pi\)
0.0509107 + 0.998703i \(0.483788\pi\)
\(98\) 7.64287e10 + 3.08390e10i 0.0862779 + 0.0348132i
\(99\) −7.81324e11 + 7.81324e11i −0.829889 + 0.829889i
\(100\) 1.18256e12 1.22680e12i 1.18256 1.22680i
\(101\) 1.12035e10 1.12035e10i 0.0105542 0.0105542i −0.701810 0.712364i \(-0.747624\pi\)
0.712364 + 0.701810i \(0.247624\pi\)
\(102\) −5.16768e11 + 2.19631e11i −0.458875 + 0.195026i
\(103\) −1.55662e11 −0.130365 −0.0651823 0.997873i \(-0.520763\pi\)
−0.0651823 + 0.997873i \(0.520763\pi\)
\(104\) −6.30614e11 + 1.64949e12i −0.498384 + 1.30361i
\(105\) 9.56439e11i 0.713710i
\(106\) 3.36915e10 1.43192e10i 0.0237512 0.0100945i
\(107\) 4.90034e11 + 4.90034e11i 0.326530 + 0.326530i 0.851265 0.524735i \(-0.175836\pi\)
−0.524735 + 0.851265i \(0.675836\pi\)
\(108\) −2.37936e10 1.29600e12i −0.0149940 0.816699i
\(109\) −1.33356e12 1.33356e12i −0.795161 0.795161i 0.187167 0.982328i \(-0.440069\pi\)
−0.982328 + 0.187167i \(0.940069\pi\)
\(110\) 4.00176e12 + 1.61471e12i 2.25889 + 0.911463i
\(111\) 1.14793e11i 0.0613729i
\(112\) 6.89988e10 + 1.87850e12i 0.0349569 + 0.951704i
\(113\) −2.01643e12 −0.968530 −0.484265 0.874921i \(-0.660913\pi\)
−0.484265 + 0.874921i \(0.660913\pi\)
\(114\) −1.24719e11 + 3.09093e11i −0.0568203 + 0.140818i
\(115\) 2.67577e12 2.67577e12i 1.15681 1.15681i
\(116\) 7.29151e10 + 3.97157e12i 0.0299274 + 1.63010i
\(117\) 2.00566e12 2.00566e12i 0.781884 0.781884i
\(118\) −1.04949e11 2.46934e11i −0.0388764 0.0914721i
\(119\) −2.95871e12 −1.04189
\(120\) −2.04306e12 + 9.12951e11i −0.684217 + 0.305746i
\(121\) 3.74828e12i 1.19432i
\(122\) −3.33544e11 7.84794e11i −0.101157 0.238011i
\(123\) 1.03769e12 + 1.03769e12i 0.299665 + 0.299665i
\(124\) 4.01478e12 4.16496e12i 1.10441 1.14572i
\(125\) 3.12243e12 + 3.12243e12i 0.818527 + 0.818527i
\(126\) 1.12978e12 2.79994e12i 0.282338 0.699722i
\(127\) 3.42011e12i 0.815112i −0.913180 0.407556i \(-0.866381\pi\)
0.913180 0.407556i \(-0.133619\pi\)
\(128\) 3.94682e12 1.94047e12i 0.897403 0.441212i
\(129\) 7.32609e11 0.158977
\(130\) −1.02725e13 4.14497e12i −2.12822 0.858739i
\(131\) −6.43505e12 + 6.43505e12i −1.27328 + 1.27328i −0.328925 + 0.944356i \(0.606686\pi\)
−0.944356 + 0.328925i \(0.893314\pi\)
\(132\) −2.57118e12 2.47847e12i −0.486059 0.468533i
\(133\) −1.24187e12 + 1.24187e12i −0.224372 + 0.224372i
\(134\) 3.06668e12 1.30337e12i 0.529712 0.225132i
\(135\) 8.13089e12 1.34318
\(136\) 2.82418e12 + 6.32013e12i 0.446333 + 0.998833i
\(137\) 6.68889e11i 0.101165i −0.998720 0.0505825i \(-0.983892\pi\)
0.998720 0.0505825i \(-0.0161078\pi\)
\(138\) −2.88218e12 + 1.22495e12i −0.417298 + 0.177355i
\(139\) 3.86820e12 + 3.86820e12i 0.536315 + 0.536315i 0.922445 0.386129i \(-0.126188\pi\)
−0.386129 + 0.922445i \(0.626188\pi\)
\(140\) −1.17894e13 + 2.16444e11i −1.56575 + 0.0287460i
\(141\) 1.08388e12 + 1.08388e12i 0.137932 + 0.137932i
\(142\) −3.32673e12 1.34234e12i −0.405777 0.163731i
\(143\) 1.76782e13i 2.06739i
\(144\) −7.05940e12 + 2.59298e11i −0.791758 + 0.0290820i
\(145\) −2.49170e13 −2.68094
\(146\) 4.55007e11 1.12765e12i 0.0469787 0.116428i
\(147\) 3.02531e11 3.02531e11i 0.0299824 0.0299824i
\(148\) 1.41497e12 2.59778e10i 0.134641 0.00247191i
\(149\) −5.92466e12 + 5.92466e12i −0.541434 + 0.541434i −0.923949 0.382515i \(-0.875058\pi\)
0.382515 + 0.923949i \(0.375058\pi\)
\(150\) −3.45998e12 8.14097e12i −0.303757 0.714708i
\(151\) 1.85036e13 1.56097 0.780484 0.625176i \(-0.214973\pi\)
0.780484 + 0.625176i \(0.214973\pi\)
\(152\) 3.83819e12 + 1.46738e12i 0.311218 + 0.118982i
\(153\) 1.11188e13i 0.866783i
\(154\) −7.36053e12 1.73186e13i −0.551804 1.29834i
\(155\) 2.56592e13 + 2.56592e13i 1.85034 + 1.85034i
\(156\) 6.60022e12 + 6.36224e12i 0.457943 + 0.441431i
\(157\) 2.09910e13 + 2.09910e13i 1.40163 + 1.40163i 0.794921 + 0.606713i \(0.207512\pi\)
0.606713 + 0.794921i \(0.292488\pi\)
\(158\) 6.82139e11 1.69055e12i 0.0438460 0.108664i
\(159\) 1.90043e11i 0.0117617i
\(160\) 1.17157e13 + 2.49768e13i 0.698308 + 1.48873i
\(161\) −1.65016e13 −0.947484
\(162\) 7.04051e12 + 2.84085e12i 0.389506 + 0.157166i
\(163\) 2.00854e12 2.00854e12i 0.107092 0.107092i −0.651531 0.758622i \(-0.725873\pi\)
0.758622 + 0.651531i \(0.225873\pi\)
\(164\) 1.25560e13 1.30257e13i 0.645341 0.669480i
\(165\) 1.58404e13 1.58404e13i 0.784985 0.784985i
\(166\) 3.21430e13 1.36610e13i 1.53617 0.652883i
\(167\) −2.38823e13 −1.10098 −0.550488 0.834843i \(-0.685559\pi\)
−0.550488 + 0.834843i \(0.685559\pi\)
\(168\) 9.11495e12 + 3.48473e12i 0.405414 + 0.154993i
\(169\) 2.20818e13i 0.947796i
\(170\) −3.99633e13 + 1.69847e13i −1.65565 + 0.703664i
\(171\) −4.66697e12 4.66697e12i −0.186663 0.186663i
\(172\) −1.65791e11 9.03036e12i −0.00640309 0.348766i
\(173\) −1.38429e13 1.38429e13i −0.516356 0.516356i 0.400111 0.916467i \(-0.368972\pi\)
−0.916467 + 0.400111i \(0.868972\pi\)
\(174\) 1.91229e13 + 7.71612e12i 0.689064 + 0.278038i
\(175\) 4.66104e13i 1.62276i
\(176\) −2.99685e13 + 3.22540e13i −1.00830 + 1.08520i
\(177\) −1.39288e12 −0.0452973
\(178\) −5.26119e12 + 1.30389e13i −0.165411 + 0.409940i
\(179\) −1.16690e13 + 1.16690e13i −0.354745 + 0.354745i −0.861871 0.507127i \(-0.830708\pi\)
0.507127 + 0.861871i \(0.330708\pi\)
\(180\) −8.13397e11 4.43044e13i −0.0239148 1.30260i
\(181\) 9.10204e12 9.10204e12i 0.258861 0.258861i −0.565729 0.824591i \(-0.691405\pi\)
0.824591 + 0.565729i \(0.191405\pi\)
\(182\) 1.88945e13 + 4.44567e13i 0.519884 + 1.22323i
\(183\) −4.42677e12 −0.117864
\(184\) 1.57513e13 + 3.52494e13i 0.405892 + 0.908332i
\(185\) 8.87729e12i 0.221437i
\(186\) −1.17466e13 2.76385e13i −0.283684 0.667478i
\(187\) −4.90015e13 4.90015e13i −1.14593 1.14593i
\(188\) 1.31149e13 1.36055e13i 0.297042 0.308153i
\(189\) −2.50718e13 2.50718e13i −0.550066 0.550066i
\(190\) −9.64493e12 + 2.39031e13i −0.205011 + 0.508081i
\(191\) 1.26077e13i 0.259679i 0.991535 + 0.129840i \(0.0414462\pi\)
−0.991535 + 0.129840i \(0.958554\pi\)
\(192\) −1.25673e12 2.27969e13i −0.0250862 0.455059i
\(193\) −4.96508e13 −0.960688 −0.480344 0.877080i \(-0.659488\pi\)
−0.480344 + 0.877080i \(0.659488\pi\)
\(194\) −5.03378e12 2.03113e12i −0.0944243 0.0381003i
\(195\) −4.06622e13 + 4.06622e13i −0.739577 + 0.739577i
\(196\) −3.79755e12 3.66063e12i −0.0669834 0.0645683i
\(197\) 7.29222e13 7.29222e13i 1.24756 1.24756i 0.290770 0.956793i \(-0.406089\pi\)
0.956793 0.290770i \(-0.0939115\pi\)
\(198\) 6.50832e13 2.76609e13i 1.08013 0.459066i
\(199\) −3.98271e13 −0.641298 −0.320649 0.947198i \(-0.603901\pi\)
−0.320649 + 0.947198i \(0.603901\pi\)
\(200\) −9.95650e13 + 4.44911e13i −1.55570 + 0.695173i
\(201\) 1.72982e13i 0.262315i
\(202\) −9.33232e11 + 3.96631e11i −0.0137367 + 0.00583820i
\(203\) 7.68323e13 + 7.68323e13i 1.09791 + 1.09791i
\(204\) 3.59302e13 6.59651e11i 0.498515 0.00915237i
\(205\) 8.02478e13 + 8.02478e13i 1.08121 + 1.08121i
\(206\) 9.23864e12 + 3.72780e12i 0.120894 + 0.0487808i
\(207\) 6.20132e13i 0.788247i
\(208\) 7.69293e13 8.27961e13i 0.949974 1.02242i
\(209\) −4.11354e13 −0.493557
\(210\) −2.29048e13 + 5.67652e13i −0.267061 + 0.661861i
\(211\) −2.24775e13 + 2.24775e13i −0.254714 + 0.254714i −0.822900 0.568186i \(-0.807645\pi\)
0.568186 + 0.822900i \(0.307645\pi\)
\(212\) −2.34253e12 + 4.30071e10i −0.0258030 + 0.000473723i
\(213\) −1.31684e13 + 1.31684e13i −0.141011 + 0.141011i
\(214\) −1.73485e13 4.08191e13i −0.180625 0.424992i
\(215\) 5.66550e13 0.573598
\(216\) −2.96244e13 + 7.74881e13i −0.291694 + 0.762979i
\(217\) 1.58242e14i 1.51552i
\(218\) 4.72117e13 + 1.11084e14i 0.439856 + 1.03493i
\(219\) −4.46363e12 4.46363e12i −0.0404598 0.0404598i
\(220\) −1.98838e14 1.91668e14i −1.75373 1.69050i
\(221\) 1.25787e14 + 1.25787e14i 1.07965 + 1.07965i
\(222\) 2.74906e12 6.81302e12i 0.0229650 0.0569144i
\(223\) 1.19376e14i 0.970707i 0.874318 + 0.485353i \(0.161309\pi\)
−0.874318 + 0.485353i \(0.838691\pi\)
\(224\) 4.08911e13 1.13142e14i 0.323698 0.895646i
\(225\) 1.75162e14 1.35003
\(226\) 1.19676e14 + 4.82895e13i 0.898169 + 0.362412i
\(227\) −1.37896e14 + 1.37896e14i −1.00785 + 1.00785i −0.00788358 + 0.999969i \(0.502509\pi\)
−0.999969 + 0.00788358i \(0.997491\pi\)
\(228\) 1.48043e13 1.53581e13i 0.105385 0.109327i
\(229\) 2.76421e13 2.76421e13i 0.191672 0.191672i −0.604746 0.796418i \(-0.706726\pi\)
0.796418 + 0.604746i \(0.206726\pi\)
\(230\) −2.22888e14 + 9.47293e13i −1.50564 + 0.639908i
\(231\) −9.76884e13 −0.642941
\(232\) 9.07837e13 2.37461e14i 0.582210 1.52288i
\(233\) 2.59699e14i 1.62306i 0.584309 + 0.811531i \(0.301366\pi\)
−0.584309 + 0.811531i \(0.698634\pi\)
\(234\) −1.67069e14 + 7.10056e13i −1.01765 + 0.432511i
\(235\) 8.38196e13 + 8.38196e13i 0.497667 + 0.497667i
\(236\) 3.15210e11 + 1.71690e13i 0.00182443 + 0.0993740i
\(237\) −6.69179e12 6.69179e12i −0.0377618 0.0377618i
\(238\) 1.75601e14 + 7.08551e13i 0.966196 + 0.389861i
\(239\) 1.65145e14i 0.886090i −0.896499 0.443045i \(-0.853898\pi\)
0.896499 0.443045i \(-0.146102\pi\)
\(240\) 1.43120e14 5.25694e12i 0.748917 0.0275084i
\(241\) 1.22502e14 0.625229 0.312615 0.949880i \(-0.398795\pi\)
0.312615 + 0.949880i \(0.398795\pi\)
\(242\) 8.97637e13 2.22462e14i 0.446898 1.10755i
\(243\) 1.46790e14 1.46790e14i 0.712948 0.712948i
\(244\) 1.00179e12 + 5.45657e13i 0.00474718 + 0.258572i
\(245\) 2.33957e13 2.33957e13i 0.108178 0.108178i
\(246\) −3.67369e13 8.64380e13i −0.165764 0.390026i
\(247\) 1.05595e14 0.465007
\(248\) −3.38022e14 + 1.51047e14i −1.45290 + 0.649234i
\(249\) 1.81308e14i 0.760715i
\(250\) −1.10542e14 2.60094e14i −0.452781 1.06535i
\(251\) −2.15950e14 2.15950e14i −0.863596 0.863596i 0.128158 0.991754i \(-0.459094\pi\)
−0.991754 + 0.128158i \(0.959094\pi\)
\(252\) −1.34106e14 + 1.39122e14i −0.523654 + 0.543242i
\(253\) −2.73297e14 2.73297e14i −1.04211 1.04211i
\(254\) −8.19047e13 + 2.02985e14i −0.305005 + 0.755896i
\(255\) 2.25420e14i 0.819883i
\(256\) −2.80716e14 + 2.06498e13i −0.997305 + 0.0733628i
\(257\) −1.02035e14 −0.354120 −0.177060 0.984200i \(-0.556659\pi\)
−0.177060 + 0.984200i \(0.556659\pi\)
\(258\) −4.34808e13 1.75445e13i −0.147428 0.0594872i
\(259\) 2.73734e13 2.73734e13i 0.0906839 0.0906839i
\(260\) 5.10417e14 + 4.92013e14i 1.65228 + 1.59271i
\(261\) −2.88736e14 + 2.88736e14i −0.913394 + 0.913394i
\(262\) 5.36031e14 2.27818e14i 1.65723 0.704335i
\(263\) −3.99272e14 −1.20652 −0.603260 0.797544i \(-0.706132\pi\)
−0.603260 + 0.797544i \(0.706132\pi\)
\(264\) 9.32466e13 + 2.08673e14i 0.275429 + 0.616373i
\(265\) 1.46967e13i 0.0424368i
\(266\) 1.03446e14 4.39656e13i 0.292029 0.124115i
\(267\) 5.16124e13 + 5.16124e13i 0.142458 + 0.142458i
\(268\) −2.13222e14 + 3.91460e12i −0.575472 + 0.0105652i
\(269\) −4.28105e14 4.28105e14i −1.12989 1.12989i −0.990194 0.139698i \(-0.955387\pi\)
−0.139698 0.990194i \(-0.544613\pi\)
\(270\) −4.82573e14 1.94719e14i −1.24561 0.502603i
\(271\) 5.64942e14i 1.42622i 0.701050 + 0.713112i \(0.252715\pi\)
−0.701050 + 0.713112i \(0.747285\pi\)
\(272\) −1.62621e13 4.42737e14i −0.0401572 1.09328i
\(273\) 2.50766e14 0.605750
\(274\) −1.60185e13 + 3.96989e13i −0.0378547 + 0.0938157i
\(275\) 7.71952e14 7.71952e14i 1.78482 1.78482i
\(276\) 2.00394e14 3.67909e12i 0.453347 0.00832311i
\(277\) −3.75355e14 + 3.75355e14i −0.830929 + 0.830929i −0.987644 0.156715i \(-0.949910\pi\)
0.156715 + 0.987644i \(0.449910\pi\)
\(278\) −1.36944e14 3.22216e14i −0.296671 0.698036i
\(279\) 5.94673e14 1.26082
\(280\) 7.04889e14 + 2.69485e14i 1.46276 + 0.559226i
\(281\) 5.47262e14i 1.11162i 0.831309 + 0.555811i \(0.187592\pi\)
−0.831309 + 0.555811i \(0.812408\pi\)
\(282\) −3.83720e13 9.02854e13i −0.0762992 0.179524i
\(283\) −5.72598e14 5.72598e14i −1.11463 1.11463i −0.992516 0.122116i \(-0.961032\pi\)
−0.122116 0.992516i \(-0.538968\pi\)
\(284\) 1.65297e14 + 1.59337e14i 0.315033 + 0.303674i
\(285\) 9.46169e13 + 9.46169e13i 0.176563 + 0.176563i
\(286\) −4.23357e14 + 1.04921e15i −0.773590 + 1.91720i
\(287\) 4.94893e14i 0.885563i
\(288\) 4.25189e14 + 1.53669e14i 0.745121 + 0.269297i
\(289\) 1.14706e14 0.196879
\(290\) 1.47884e15 + 5.96712e14i 2.48618 + 1.00318i
\(291\) −1.99255e13 + 1.99255e13i −0.0328133 + 0.0328133i
\(292\) −5.40099e13 + 5.60302e13i −0.0871317 + 0.0903909i
\(293\) 1.64615e13 1.64615e13i 0.0260173 0.0260173i −0.693978 0.719996i \(-0.744144\pi\)
0.719996 + 0.693978i \(0.244144\pi\)
\(294\) −2.52004e13 + 1.07104e13i −0.0390233 + 0.0165852i
\(295\) −1.07716e14 −0.163435
\(296\) −8.46014e13 3.23439e13i −0.125785 0.0480886i
\(297\) 8.30469e14i 1.21000i
\(298\) 4.93516e14 2.09748e14i 0.704699 0.299503i
\(299\) 7.01554e14 + 7.01554e14i 0.981824 + 0.981824i
\(300\) 1.03919e13 + 5.66031e14i 0.0142550 + 0.776449i
\(301\) −1.74697e14 1.74697e14i −0.234902 0.234902i
\(302\) −1.09820e15 4.43123e14i −1.44757 0.584094i
\(303\) 5.26406e12i 0.00680245i
\(304\) −1.92658e14 1.79007e14i −0.244088 0.226792i
\(305\) −3.42336e14 −0.425260
\(306\) −2.66274e14 + 6.59909e14i −0.324339 + 0.803814i
\(307\) −1.63948e14 + 1.63948e14i −0.195829 + 0.195829i −0.798209 0.602380i \(-0.794219\pi\)
0.602380 + 0.798209i \(0.294219\pi\)
\(308\) 2.21070e13 + 1.20414e15i 0.0258956 + 1.41049i
\(309\) 3.65698e13 3.65698e13i 0.0420118 0.0420118i
\(310\) −9.08402e14 2.13737e15i −1.02355 2.40830i
\(311\) 1.22600e15 1.35497 0.677485 0.735537i \(-0.263070\pi\)
0.677485 + 0.735537i \(0.263070\pi\)
\(312\) −2.39364e14 5.35665e14i −0.259497 0.580719i
\(313\) 7.00845e14i 0.745343i 0.927963 + 0.372671i \(0.121558\pi\)
−0.927963 + 0.372671i \(0.878442\pi\)
\(314\) −7.43135e14 1.74852e15i −0.775336 1.82428i
\(315\) −8.57094e14 8.57094e14i −0.877335 0.877335i
\(316\) −8.09707e13 + 8.39994e13i −0.0813215 + 0.0843633i
\(317\) 1.90237e13 + 1.90237e13i 0.0187473 + 0.0187473i 0.716418 0.697671i \(-0.245780\pi\)
−0.697671 + 0.716418i \(0.745780\pi\)
\(318\) −4.55115e12 + 1.12792e13i −0.00440108 + 0.0109072i
\(319\) 2.54496e15i 2.41511i
\(320\) −9.71869e13 1.76295e15i −0.0905124 1.64188i
\(321\) −2.30248e14 −0.210458
\(322\) 9.79382e14 + 3.95181e14i 0.878652 + 0.354537i
\(323\) 2.92694e14 2.92694e14i 0.257750 0.257750i
\(324\) −3.49826e14 3.37212e14i −0.302400 0.291496i
\(325\) −1.98160e15 + 1.98160e15i −1.68157 + 1.68157i
\(326\) −1.67309e14 + 7.11076e13i −0.139384 + 0.0592393i
\(327\) 6.26590e14 0.512503
\(328\) −1.05715e15 + 4.72391e14i −0.848970 + 0.379366i
\(329\) 5.16921e14i 0.407613i
\(330\) −1.31948e15 + 5.60790e14i −1.02169 + 0.434227i
\(331\) −6.98862e14 6.98862e14i −0.531402 0.531402i 0.389587 0.920989i \(-0.372618\pi\)
−0.920989 + 0.389587i \(0.872618\pi\)
\(332\) −2.23486e15 + 4.10304e13i −1.66887 + 0.0306392i
\(333\) 1.02869e14 + 1.02869e14i 0.0754433 + 0.0754433i
\(334\) 1.41743e15 + 5.71935e14i 1.02099 + 0.411972i
\(335\) 1.33772e15i 0.946449i
\(336\) −4.57525e14 4.25106e14i −0.317965 0.295435i
\(337\) 2.21494e15 1.51211 0.756055 0.654509i \(-0.227124\pi\)
0.756055 + 0.654509i \(0.227124\pi\)
\(338\) 5.28816e14 1.31057e15i 0.354654 0.878942i
\(339\) 4.73721e14 4.73721e14i 0.312122 0.312122i
\(340\) 2.77860e15 5.10130e13i 1.79867 0.0330223i
\(341\) 2.62077e15 2.62077e15i 1.66687 1.66687i
\(342\) 1.65223e14 + 3.88752e14i 0.103256 + 0.242949i
\(343\) −1.69510e15 −1.04095
\(344\) −2.06419e14 + 5.39928e14i −0.124566 + 0.325825i
\(345\) 1.25724e15i 0.745596i
\(346\) 4.90073e14 + 1.15309e15i 0.285630 + 0.672058i
\(347\) 1.37165e15 + 1.37165e15i 0.785720 + 0.785720i 0.980789 0.195070i \(-0.0624932\pi\)
−0.195070 + 0.980789i \(0.562493\pi\)
\(348\) −9.50173e14 9.15913e14i −0.534967 0.515678i
\(349\) −3.66453e14 3.66453e14i −0.202799 0.202799i 0.598399 0.801198i \(-0.295804\pi\)
−0.801198 + 0.598399i \(0.795804\pi\)
\(350\) −1.11623e15 + 2.76635e15i −0.607216 + 1.50487i
\(351\) 2.13182e15i 1.14001i
\(352\) 2.55107e15 1.19661e15i 1.34112 0.629066i
\(353\) 2.75673e15 1.42477 0.712386 0.701788i \(-0.247614\pi\)
0.712386 + 0.701788i \(0.247614\pi\)
\(354\) 8.26680e13 + 3.33566e13i 0.0420066 + 0.0169497i
\(355\) −1.01835e15 + 1.01835e15i −0.508778 + 0.508778i
\(356\) 6.24510e14 6.47870e14i 0.306789 0.318264i
\(357\) 6.95090e14 6.95090e14i 0.335762 0.335762i
\(358\) 9.72012e14 4.13113e14i 0.461714 0.196232i
\(359\) −3.94981e15 −1.84505 −0.922527 0.385932i \(-0.873880\pi\)
−0.922527 + 0.385932i \(0.873880\pi\)
\(360\) −1.01273e15 + 2.64897e15i −0.465241 + 1.21692i
\(361\) 1.96761e15i 0.888986i
\(362\) −7.58187e14 + 3.22236e14i −0.336919 + 0.143193i
\(363\) −8.80584e14 8.80584e14i −0.384885 0.384885i
\(364\) −5.67488e13 3.09102e15i −0.0243977 1.32890i
\(365\) −3.45187e14 3.45187e14i −0.145981 0.145981i
\(366\) 2.62732e14 + 1.06012e14i 0.109301 + 0.0441032i
\(367\) 2.22368e15i 0.910073i −0.890473 0.455036i \(-0.849626\pi\)
0.890473 0.455036i \(-0.150374\pi\)
\(368\) −9.06990e13 2.46928e15i −0.0365187 0.994224i
\(369\) 1.85981e15 0.736733
\(370\) 2.12593e14 5.26873e14i 0.0828590 0.205350i
\(371\) −4.53175e13 + 4.53175e13i −0.0173789 + 0.0173789i
\(372\) 3.52804e13 + 1.92167e15i 0.0133130 + 0.725138i
\(373\) −1.81548e15 + 1.81548e15i −0.674123 + 0.674123i −0.958664 0.284541i \(-0.908159\pi\)
0.284541 + 0.958664i \(0.408159\pi\)
\(374\) 1.73478e15 + 4.08176e15i 0.633891 + 1.49148i
\(375\) −1.46711e15 −0.527563
\(376\) −1.10420e15 + 4.93417e14i −0.390770 + 0.174617i
\(377\) 6.53292e15i 2.27541i
\(378\) 8.87608e14 + 2.08845e15i 0.304278 + 0.715934i
\(379\) 1.00772e15 + 1.00772e15i 0.340019 + 0.340019i 0.856374 0.516355i \(-0.172712\pi\)
−0.516355 + 0.856374i \(0.672712\pi\)
\(380\) 1.14486e15 1.18769e15i 0.380235 0.394458i
\(381\) 8.03487e14 + 8.03487e14i 0.262681 + 0.262681i
\(382\) 3.01930e14 7.48277e14i 0.0971686 0.240814i
\(383\) 5.95717e14i 0.188733i −0.995538 0.0943665i \(-0.969917\pi\)
0.995538 0.0943665i \(-0.0300825\pi\)
\(384\) −4.71352e14 + 1.38310e15i −0.147014 + 0.431387i
\(385\) −7.55456e15 −2.31977
\(386\) 2.94680e15 + 1.18904e15i 0.890897 + 0.359478i
\(387\) 6.56514e14 6.56514e14i 0.195424 0.195424i
\(388\) 2.50116e14 + 2.41098e14i 0.0733081 + 0.0706648i
\(389\) 1.53156e15 1.53156e15i 0.442013 0.442013i −0.450675 0.892688i \(-0.648817\pi\)
0.892688 + 0.450675i \(0.148817\pi\)
\(390\) 3.38711e15 1.43955e15i 0.962590 0.409109i
\(391\) 3.88922e15 1.08843
\(392\) 1.37722e14 + 3.08204e14i 0.0379567 + 0.0849419i
\(393\) 3.02358e15i 0.820665i
\(394\) −6.07432e15 + 2.58164e15i −1.62375 + 0.690109i
\(395\) −5.17498e14 5.17498e14i −0.136247 0.136247i
\(396\) −4.52515e15 + 8.30784e13i −1.17344 + 0.0215435i
\(397\) 1.95334e15 + 1.95334e15i 0.498925 + 0.498925i 0.911103 0.412179i \(-0.135232\pi\)
−0.412179 + 0.911103i \(0.635232\pi\)
\(398\) 2.36376e15 + 9.53779e14i 0.594710 + 0.239966i
\(399\) 5.83508e14i 0.144614i
\(400\) 6.97472e15 2.56188e14i 1.70281 0.0625458i
\(401\) −4.34637e15 −1.04535 −0.522674 0.852533i \(-0.675065\pi\)
−0.522674 + 0.852533i \(0.675065\pi\)
\(402\) −4.14257e14 + 1.02666e15i −0.0981551 + 0.243259i
\(403\) −6.72751e15 + 6.72751e15i −1.57045 + 1.57045i
\(404\) 6.48864e13 1.19127e12i 0.0149233 0.000273981i
\(405\) 2.15518e15 2.15518e15i 0.488376 0.488376i
\(406\) −2.72006e15 6.40002e15i −0.607327 1.42898i
\(407\) 9.06706e14 0.199480
\(408\) −2.14828e15 8.21305e14i −0.465724 0.178051i
\(409\) 1.48981e15i 0.318267i 0.987257 + 0.159134i \(0.0508701\pi\)
−0.987257 + 0.159134i \(0.949130\pi\)
\(410\) −2.84098e15 6.68453e15i −0.598088 1.40724i
\(411\) 1.57142e14 + 1.57142e14i 0.0326018 + 0.0326018i
\(412\) −4.59046e14 4.42494e14i −0.0938583 0.0904741i
\(413\) 3.32144e14 + 3.32144e14i 0.0669308 + 0.0669308i
\(414\) −1.48509e15 + 3.68052e15i −0.294952 + 0.730983i
\(415\) 1.40212e16i 2.74470i
\(416\) −6.54860e15 + 3.07170e15i −1.26354 + 0.592678i
\(417\) −1.81752e15 −0.345670
\(418\) 2.44141e15 + 9.85110e14i 0.457702 + 0.184683i
\(419\) −4.54133e15 + 4.54133e15i −0.839264 + 0.839264i −0.988762 0.149498i \(-0.952234\pi\)
0.149498 + 0.988762i \(0.452234\pi\)
\(420\) 2.71883e15 2.82053e15i 0.495320 0.513848i
\(421\) 3.03210e15 3.03210e15i 0.544567 0.544567i −0.380297 0.924864i \(-0.624178\pi\)
0.924864 + 0.380297i \(0.124178\pi\)
\(422\) 1.87234e15 7.95760e14i 0.331520 0.140899i
\(423\) 1.94259e15 0.339109
\(424\) 1.40060e14 + 5.35464e13i 0.0241057 + 0.00921584i
\(425\) 1.09855e16i 1.86417i
\(426\) 1.09691e15 4.66194e14i 0.183532 0.0780027i
\(427\) 1.05560e15 + 1.05560e15i 0.174154 + 0.174154i
\(428\) 5.21054e13 + 2.83810e15i 0.00847657 + 0.461706i
\(429\) 4.15314e15 + 4.15314e15i 0.666243 + 0.666243i
\(430\) −3.36251e15 1.35678e15i −0.531928 0.214633i
\(431\) 6.13060e15i 0.956399i 0.878251 + 0.478199i \(0.158710\pi\)
−0.878251 + 0.478199i \(0.841290\pi\)
\(432\) 3.61391e15 3.88952e15i 0.556000 0.598403i
\(433\) 2.82269e15 0.428287 0.214144 0.976802i \(-0.431304\pi\)
0.214144 + 0.976802i \(0.431304\pi\)
\(434\) −3.78957e15 + 9.39174e15i −0.567090 + 1.40542i
\(435\) 5.85376e15 5.85376e15i 0.863971 0.863971i
\(436\) −1.41798e14 7.72353e15i −0.0206420 1.12434i
\(437\) 1.63245e15 1.63245e15i 0.234396 0.234396i
\(438\) 1.58024e14 + 3.71814e14i 0.0223810 + 0.0526600i
\(439\) −3.59519e15 −0.502267 −0.251134 0.967952i \(-0.580803\pi\)
−0.251134 + 0.967952i \(0.580803\pi\)
\(440\) 7.21106e15 + 1.61374e16i 0.993764 + 2.22391i
\(441\) 5.42215e14i 0.0737123i
\(442\) −4.45318e15 1.04779e16i −0.597224 1.40520i
\(443\) 6.95131e15 + 6.95131e15i 0.919696 + 0.919696i 0.997007 0.0773112i \(-0.0246335\pi\)
−0.0773112 + 0.997007i \(0.524634\pi\)
\(444\) −3.26316e14 + 3.38522e14i −0.0425933 + 0.0441865i
\(445\) 3.99135e15 + 3.99135e15i 0.513997 + 0.513997i
\(446\) 2.85882e15 7.08504e15i 0.363226 0.900188i
\(447\) 2.78376e15i 0.348969i
\(448\) −5.13644e15 + 5.73580e15i −0.635322 + 0.709457i
\(449\) −7.47373e15 −0.912136 −0.456068 0.889945i \(-0.650743\pi\)
−0.456068 + 0.889945i \(0.650743\pi\)
\(450\) −1.03960e16 4.19478e15i −1.25196 0.505166i
\(451\) 8.19632e15 8.19632e15i 0.974001 0.974001i
\(452\) −5.94643e15 5.73202e15i −0.697310 0.672167i
\(453\) −4.34705e15 + 4.34705e15i −0.503043 + 0.503043i
\(454\) 1.14866e16 4.88188e15i 1.31176 0.557509i
\(455\) 1.93926e16 2.18558
\(456\) −1.24644e15 + 5.56977e14i −0.138638 + 0.0619509i
\(457\) 3.00689e15i 0.330081i 0.986287 + 0.165040i \(0.0527754\pi\)
−0.986287 + 0.165040i \(0.947225\pi\)
\(458\) −2.30255e15 + 9.78602e14i −0.249469 + 0.106026i
\(459\) 5.90910e15 + 5.90910e15i 0.631896 + 0.631896i
\(460\) 1.54971e16 2.84516e14i 1.63570 0.0300303i
\(461\) −4.46299e15 4.46299e15i −0.464965 0.464965i 0.435314 0.900279i \(-0.356637\pi\)
−0.900279 + 0.435314i \(0.856637\pi\)
\(462\) 5.79786e15 + 2.33944e15i 0.596233 + 0.240580i
\(463\) 1.28293e16i 1.30232i 0.758942 + 0.651158i \(0.225717\pi\)
−0.758942 + 0.651158i \(0.774283\pi\)
\(464\) −1.10748e16 + 1.19194e16i −1.10976 + 1.19439i
\(465\) −1.20562e16 −1.19260
\(466\) 6.21928e15 1.54133e16i 0.607330 1.50515i
\(467\) 4.54721e13 4.54721e13i 0.00438373 0.00438373i −0.704912 0.709295i \(-0.749013\pi\)
0.709295 + 0.704912i \(0.249013\pi\)
\(468\) 1.16161e16 2.13262e14i 1.10556 0.0202973i
\(469\) −4.12491e15 + 4.12491e15i −0.387594 + 0.387594i
\(470\) −2.96743e15 6.98206e15i −0.275292 0.647734i
\(471\) −9.86283e15 −0.903392
\(472\) 3.92455e14 1.02654e15i 0.0354926 0.0928375i
\(473\) 5.78661e15i 0.516722i
\(474\) 2.36907e14 + 5.57417e14i 0.0208885 + 0.0491485i
\(475\) 4.61099e15 + 4.61099e15i 0.401451 + 0.401451i
\(476\) −8.72518e15 8.41058e15i −0.750124 0.723077i
\(477\) −1.70304e14 1.70304e14i −0.0144582 0.0144582i
\(478\) −3.95489e15 + 9.80145e15i −0.331564 + 0.821718i
\(479\) 1.06951e16i 0.885462i −0.896654 0.442731i \(-0.854010\pi\)
0.896654 0.442731i \(-0.145990\pi\)
\(480\) −8.62017e15 3.11544e15i −0.704804 0.254726i
\(481\) −2.32751e15 −0.187941
\(482\) −7.27054e15 2.93367e15i −0.579808 0.233953i
\(483\) 3.87674e15 3.87674e15i 0.305340 0.305340i
\(484\) −1.06551e16 + 1.10536e16i −0.828865 + 0.859869i
\(485\) −1.54090e15 + 1.54090e15i −0.118392 + 0.118392i
\(486\) −1.22274e16 + 5.19673e15i −0.927930 + 0.394378i
\(487\) −9.46324e15 −0.709359 −0.354680 0.934988i \(-0.615410\pi\)
−0.354680 + 0.934988i \(0.615410\pi\)
\(488\) 1.24728e15 3.26250e15i 0.0923520 0.241564i
\(489\) 9.43734e14i 0.0690235i
\(490\) −1.94883e15 + 8.28269e14i −0.140798 + 0.0598405i
\(491\) −1.57121e16 1.57121e16i −1.12136 1.12136i −0.991537 0.129821i \(-0.958560\pi\)
−0.129821 0.991537i \(-0.541440\pi\)
\(492\) 1.10338e14 + 6.00992e15i 0.00777917 + 0.423719i
\(493\) −1.81084e16 1.81084e16i −1.26124 1.26124i
\(494\) −6.26710e15 2.52878e15i −0.431226 0.174000i
\(495\) 2.83901e16i 1.92990i
\(496\) 2.36791e16 8.69754e14i 1.59028 0.0584126i
\(497\) 6.28024e15 0.416714
\(498\) −4.34197e15 + 1.07608e16i −0.284650 + 0.705451i
\(499\) −2.11332e16 + 2.11332e16i −1.36887 + 1.36887i −0.506813 + 0.862056i \(0.669177\pi\)
−0.862056 + 0.506813i \(0.830823\pi\)
\(500\) 3.32009e14 + 1.80840e16i 0.0212486 + 1.15738i
\(501\) 5.61069e15 5.61069e15i 0.354805 0.354805i
\(502\) 7.64518e15 + 1.79883e16i 0.477711 + 1.12401i
\(503\) 5.48523e15 0.338678 0.169339 0.985558i \(-0.445837\pi\)
0.169339 + 0.985558i \(0.445837\pi\)
\(504\) 1.12910e16 5.04541e15i 0.688886 0.307832i
\(505\) 4.07087e14i 0.0245436i
\(506\) 9.67542e15 + 2.27653e16i 0.576457 + 1.35634i
\(507\) −5.18769e15 5.18769e15i −0.305440 0.305440i
\(508\) 9.72219e15 1.00858e16i 0.565694 0.586854i
\(509\) 1.26265e16 + 1.26265e16i 0.726069 + 0.726069i 0.969834 0.243765i \(-0.0783826\pi\)
−0.243765 + 0.969834i \(0.578383\pi\)
\(510\) 5.39836e15 1.33788e16i 0.306790 0.760321i
\(511\) 2.12879e15i 0.119566i
\(512\) 1.71552e16 + 5.49702e15i 0.952306 + 0.305146i
\(513\) 4.96052e15 0.272159
\(514\) 6.05584e15 + 2.44354e15i 0.328395 + 0.132507i
\(515\) 2.82806e15 2.82806e15i 0.151581 0.151581i
\(516\) 2.16046e15 + 2.08256e15i 0.114458 + 0.110331i
\(517\) 8.56114e15 8.56114e15i 0.448320 0.448320i
\(518\) −2.28016e15 + 9.69089e14i −0.118029 + 0.0501632i
\(519\) 6.50422e15 0.332806
\(520\) −1.85108e16 4.14247e16i −0.936279 2.09527i
\(521\) 1.89229e16i 0.946155i −0.881021 0.473078i \(-0.843143\pi\)
0.881021 0.473078i \(-0.156857\pi\)
\(522\) 2.40513e16 1.02220e16i 1.18882 0.505258i
\(523\) 1.77132e15 + 1.77132e15i 0.0865539 + 0.0865539i 0.749058 0.662504i \(-0.230506\pi\)
−0.662504 + 0.749058i \(0.730506\pi\)
\(524\) −3.72695e16 + 6.84241e14i −1.80039 + 0.0330538i
\(525\) 1.09502e16 + 1.09502e16i 0.522957 + 0.522957i
\(526\) 2.36971e16 + 9.56177e15i 1.11887 + 0.451465i
\(527\) 3.72955e16i 1.74098i
\(528\) −5.36931e14 1.46180e16i −0.0247808 0.674658i
\(529\) −2.23199e14 −0.0101849
\(530\) −3.51955e14 + 8.72255e14i −0.0158793 + 0.0393539i
\(531\) −1.24820e15 + 1.24820e15i −0.0556822 + 0.0556822i
\(532\) −7.19249e15 + 1.32049e14i −0.317256 + 0.00582458i
\(533\) −2.10400e16 + 2.10400e16i −0.917659 + 0.917659i
\(534\) −1.82721e15 4.29924e15i −0.0788028 0.185415i
\(535\) −1.78058e16 −0.759344
\(536\) 1.27486e16 + 4.87392e15i 0.537619 + 0.205537i
\(537\) 5.48281e15i 0.228643i
\(538\) 1.51560e16 + 3.56606e16i 0.625017 + 1.47060i
\(539\) −2.38958e15 2.38958e15i −0.0974517 0.0974517i
\(540\) 2.39779e16 + 2.31133e16i 0.967049 + 0.932180i
\(541\) 1.07672e16 + 1.07672e16i 0.429455 + 0.429455i 0.888443 0.458988i \(-0.151788\pi\)
−0.458988 + 0.888443i \(0.651788\pi\)
\(542\) 1.35292e16 3.35296e16i 0.533675 1.32261i
\(543\) 4.27669e15i 0.166843i
\(544\) −9.63750e15 + 2.66661e16i −0.371853 + 1.02889i
\(545\) 4.84562e16 1.84914
\(546\) −1.48831e16 6.00535e15i −0.561744 0.226664i
\(547\) 2.39053e16 2.39053e16i 0.892422 0.892422i −0.102329 0.994751i \(-0.532629\pi\)
0.994751 + 0.102329i \(0.0326294\pi\)
\(548\) 1.90142e15 1.97254e15i 0.0702093 0.0728355i
\(549\) −3.96697e15 + 3.96697e15i −0.144885 + 0.144885i
\(550\) −6.43025e16 + 2.73291e16i −2.32301 + 0.987300i
\(551\) −1.52015e16 −0.543220
\(552\) −1.19816e16 4.58068e15i −0.423527 0.161918i
\(553\) 3.19144e15i 0.111593i
\(554\) 3.12666e16 1.32886e16i 1.08149 0.459641i
\(555\) −2.08555e15 2.08555e15i −0.0713611 0.0713611i
\(556\) 4.11307e14 + 2.24032e16i 0.0139225 + 0.758337i
\(557\) −3.88868e16 3.88868e16i −1.30218 1.30218i −0.926918 0.375263i \(-0.877552\pi\)
−0.375263 0.926918i \(-0.622448\pi\)
\(558\) −3.52942e16 1.42412e16i −1.16922 0.471783i
\(559\) 1.48542e16i 0.486832i
\(560\) −3.53819e16 3.28748e16i −1.14724 1.06595i
\(561\) 2.30239e16 0.738586
\(562\) 1.31058e16 3.24803e16i 0.415955 1.03087i
\(563\) −2.17968e16 + 2.17968e16i −0.684450 + 0.684450i −0.961000 0.276550i \(-0.910809\pi\)
0.276550 + 0.961000i \(0.410809\pi\)
\(564\) 1.15249e14 + 6.27742e15i 0.00358065 + 0.195032i
\(565\) 3.66344e16 3.66344e16i 1.12615 1.12615i
\(566\) 2.02715e16 + 4.76966e16i 0.616576 + 1.45074i
\(567\) −1.32911e16 −0.400003
\(568\) −5.99468e15 1.34153e16i −0.178516 0.399494i
\(569\) 1.54725e16i 0.455917i −0.973671 0.227959i \(-0.926795\pi\)
0.973671 0.227959i \(-0.0732051\pi\)
\(570\) −3.34968e15 7.88145e15i −0.0976685 0.229804i
\(571\) −1.82306e16 1.82306e16i −0.525997 0.525997i 0.393379 0.919376i \(-0.371306\pi\)
−0.919376 + 0.393379i \(0.871306\pi\)
\(572\) 5.02530e16 5.21327e16i 1.43478 1.48845i
\(573\) −2.96194e15 2.96194e15i −0.0836851 0.0836851i
\(574\) −1.18517e16 + 2.93722e16i −0.331367 + 0.821230i
\(575\) 6.12694e16i 1.69526i
\(576\) −2.15552e16 1.93028e16i −0.590223 0.528548i
\(577\) 3.70710e16 1.00457 0.502284 0.864703i \(-0.332493\pi\)
0.502284 + 0.864703i \(0.332493\pi\)
\(578\) −6.80788e15 2.74698e15i −0.182576 0.0736697i
\(579\) 1.16645e16 1.16645e16i 0.309595 0.309595i
\(580\) −7.34799e16 7.08305e16i −1.93019 1.86060i
\(581\) −4.32346e16 + 4.32346e16i −1.12402 + 1.12402i
\(582\) 1.65976e15 7.05413e14i 0.0427079 0.0181512i
\(583\) −1.50108e15 −0.0382290
\(584\) 4.54733e15 2.03199e15i 0.114625 0.0512207i
\(585\) 7.28773e16i 1.81827i
\(586\) −1.37122e15 + 5.82779e14i −0.0338626 + 0.0143919i
\(587\) −9.10567e15 9.10567e15i −0.222579 0.222579i 0.587005 0.809583i \(-0.300307\pi\)
−0.809583 + 0.587005i \(0.800307\pi\)
\(588\) 1.75215e15 3.21682e13i 0.0423944 0.000778329i
\(589\) 1.56542e16 + 1.56542e16i 0.374922 + 0.374922i
\(590\) 6.39298e15 + 2.57957e15i 0.151562 + 0.0611555i
\(591\) 3.42633e16i 0.804089i
\(592\) 4.24657e15 + 3.94567e15i 0.0986526 + 0.0916621i
\(593\) 3.86395e16 0.888594 0.444297 0.895880i \(-0.353453\pi\)
0.444297 + 0.895880i \(0.353453\pi\)
\(594\) −1.98881e16 + 4.92889e16i −0.452766 + 1.12210i
\(595\) 5.37535e16 5.37535e16i 1.21145 1.21145i
\(596\) −3.43135e16 + 6.29971e14i −0.765575 + 0.0140554i
\(597\) 9.35659e15 9.35659e15i 0.206667 0.206667i
\(598\) −2.48368e16 5.84384e16i −0.543111 1.27788i
\(599\) 4.02516e16 0.871409 0.435704 0.900090i \(-0.356499\pi\)
0.435704 + 0.900090i \(0.356499\pi\)
\(600\) 1.29385e16 3.38431e16i 0.277318 0.725376i
\(601\) 4.66828e16i 0.990627i 0.868714 + 0.495314i \(0.164947\pi\)
−0.868714 + 0.495314i \(0.835053\pi\)
\(602\) 6.18474e15 + 1.45521e16i 0.129940 + 0.305735i
\(603\) −1.55014e16 1.55014e16i −0.322454 0.322454i
\(604\) 5.45668e16 + 5.25993e16i 1.12385 + 1.08332i
\(605\) −6.80984e16 6.80984e16i −1.38869 1.38869i
\(606\) 1.26064e14 3.12425e14i 0.00254539 0.00630827i
\(607\) 2.60801e15i 0.0521407i 0.999660 + 0.0260704i \(0.00829940\pi\)
−0.999660 + 0.0260704i \(0.991701\pi\)
\(608\) 7.14753e15 + 1.52379e16i 0.141493 + 0.301651i
\(609\) −3.61005e16 −0.707635
\(610\) 2.03179e16 + 8.19827e15i 0.394366 + 0.159127i
\(611\) −2.19765e16 + 2.19765e16i −0.422387 + 0.422387i
\(612\) 3.16070e16 3.27893e16i 0.601554 0.624056i
\(613\) −4.55348e15 + 4.55348e15i −0.0858185 + 0.0858185i −0.748713 0.662894i \(-0.769328\pi\)
0.662894 + 0.748713i \(0.269328\pi\)
\(614\) 1.36567e16 5.80419e15i 0.254879 0.108326i
\(615\) −3.77053e16 −0.696869
\(616\) 2.75246e16 7.19956e16i 0.503775 1.31772i
\(617\) 9.59914e16i 1.73989i −0.493150 0.869945i \(-0.664154\pi\)
0.493150 0.869945i \(-0.335846\pi\)
\(618\) −3.04621e15 + 1.29466e15i −0.0546801 + 0.0232395i
\(619\) −3.14861e16 3.14861e16i −0.559726 0.559726i 0.369503 0.929229i \(-0.379528\pi\)
−0.929229 + 0.369503i \(0.879528\pi\)
\(620\) 2.72835e15 + 1.48609e17i 0.0480341 + 2.61634i
\(621\) 3.29569e16 + 3.29569e16i 0.574642 + 0.574642i
\(622\) −7.27641e16 2.93603e16i −1.25654 0.507013i
\(623\) 2.46149e16i 0.420988i
\(624\) 1.37830e15 + 3.75243e16i 0.0233473 + 0.635632i
\(625\) −1.18923e16 −0.199519
\(626\) 1.67838e16 4.15956e16i 0.278898 0.691196i
\(627\) 9.66394e15 9.66394e15i 0.159056 0.159056i
\(628\) 2.23198e15 + 1.21572e17i 0.0363858 + 1.98188i
\(629\) −6.45155e15 + 6.45155e15i −0.104174 + 0.104174i
\(630\) 3.03434e16 + 7.13948e16i 0.485311 + 1.14189i
\(631\) 8.02183e16 1.27086 0.635429 0.772159i \(-0.280823\pi\)
0.635429 + 0.772159i \(0.280823\pi\)
\(632\) 6.81727e15 3.04633e15i 0.106981 0.0478051i
\(633\) 1.05613e16i 0.164170i
\(634\) −6.73487e14 1.58464e15i −0.0103704 0.0244004i
\(635\) 6.21362e16 + 6.21362e16i 0.947769 + 0.947769i
\(636\) 5.40227e14 5.60435e14i 0.00816270 0.00846803i
\(637\) 6.13406e15 + 6.13406e15i 0.0918145 + 0.0918145i
\(638\) 6.09468e16 1.51045e17i 0.903705 2.23966i
\(639\) 2.36012e16i 0.346679i
\(640\) −3.64511e16 + 1.06960e17i −0.530434 + 1.55647i
\(641\) −1.17631e17 −1.69579 −0.847897 0.530160i \(-0.822132\pi\)
−0.847897 + 0.530160i \(0.822132\pi\)
\(642\) 1.36653e16 + 5.51397e15i 0.195169 + 0.0787507i
\(643\) −2.37318e16 + 2.37318e16i −0.335788 + 0.335788i −0.854780 0.518991i \(-0.826308\pi\)
0.518991 + 0.854780i \(0.326308\pi\)
\(644\) −4.86631e16 4.69085e16i −0.682158 0.657561i
\(645\) −1.33100e16 + 1.33100e16i −0.184850 + 0.184850i
\(646\) −2.43810e16 + 1.03621e16i −0.335472 + 0.142578i
\(647\) 6.31664e16 0.861114 0.430557 0.902563i \(-0.358317\pi\)
0.430557 + 0.902563i \(0.358317\pi\)
\(648\) 1.26868e16 + 2.83914e16i 0.171357 + 0.383474i
\(649\) 1.10018e16i 0.147230i
\(650\) 1.65065e17 7.01538e16i 2.18864 0.930189i
\(651\) 3.71758e16 + 3.71758e16i 0.488398 + 0.488398i
\(652\) 1.16328e16 2.13569e14i 0.151425 0.00278005i
\(653\) 2.13290e16 + 2.13290e16i 0.275101 + 0.275101i 0.831150 0.556049i \(-0.187683\pi\)
−0.556049 + 0.831150i \(0.687683\pi\)
\(654\) −3.71885e16 1.50056e16i −0.475271 0.191772i
\(655\) 2.33823e17i 2.96101i
\(656\) 7.40551e16 2.72011e15i 0.929249 0.0341321i
\(657\) −7.99999e15 −0.0994712
\(658\) −1.23792e16 + 3.06795e16i −0.152524 + 0.378001i
\(659\) 5.76492e16 5.76492e16i 0.703851 0.703851i −0.261384 0.965235i \(-0.584179\pi\)
0.965235 + 0.261384i \(0.0841789\pi\)
\(660\) 9.17417e16 1.68431e15i 1.10995 0.0203778i
\(661\) −9.71109e16 + 9.71109e16i −1.16428 + 1.16428i −0.180757 + 0.983528i \(0.557855\pi\)
−0.983528 + 0.180757i \(0.942145\pi\)
\(662\) 2.47415e16 + 5.82142e16i 0.293953 + 0.691641i
\(663\) −5.91023e16 −0.695863
\(664\) 1.33623e17 + 5.10853e16i 1.55909 + 0.596056i
\(665\) 4.51245e16i 0.521775i
\(666\) −3.64184e15 8.56887e15i −0.0417326 0.0981925i
\(667\) −1.00996e17 1.00996e17i −1.14696 1.14696i
\(668\) −7.04287e16 6.78893e16i −0.792668 0.764087i
\(669\) −2.80451e16 2.80451e16i −0.312824 0.312824i
\(670\) −3.20358e16 + 7.93947e16i −0.354150 + 0.877693i
\(671\) 3.49654e16i 0.383093i
\(672\) 1.69740e16 + 3.61871e16i 0.184318 + 0.392951i
\(673\) −3.50984e15 −0.0377744 −0.0188872 0.999822i \(-0.506012\pi\)
−0.0188872 + 0.999822i \(0.506012\pi\)
\(674\) −1.31458e17 5.30435e16i −1.40226 0.565812i
\(675\) −9.30898e16 + 9.30898e16i −0.984192 + 0.984192i
\(676\) −6.27711e16 + 6.51191e16i −0.657778 + 0.682383i
\(677\) 8.20967e16 8.20967e16i 0.852695 0.852695i −0.137769 0.990464i \(-0.543993\pi\)
0.990464 + 0.137769i \(0.0439932\pi\)
\(678\) −3.94603e16 + 1.67710e16i −0.406240 + 0.172655i
\(679\) 9.50282e15 0.0969692
\(680\) −1.66133e17 6.35142e16i −1.68036 0.642417i
\(681\) 6.47920e16i 0.649589i
\(682\) −2.18306e17 + 9.27820e16i −2.16950 + 0.922056i
\(683\) 7.71474e16 + 7.71474e16i 0.759971 + 0.759971i 0.976317 0.216346i \(-0.0694139\pi\)
−0.216346 + 0.976317i \(0.569414\pi\)
\(684\) −4.96240e14 2.70294e16i −0.00484568 0.263937i
\(685\) 1.21523e16 + 1.21523e16i 0.117629 + 0.117629i
\(686\) 1.00605e17 + 4.05942e16i 0.965328 + 0.389510i
\(687\) 1.29879e16i 0.123538i
\(688\) 2.51813e16 2.71017e16i 0.237437 0.255544i
\(689\) 3.85328e15 0.0360176
\(690\) 3.01084e16 7.46180e16i 0.278993 0.691431i
\(691\) 8.81364e16 8.81364e16i 0.809631 0.809631i −0.174947 0.984578i \(-0.555975\pi\)
0.984578 + 0.174947i \(0.0559753\pi\)
\(692\) −1.47192e15 8.01729e16i −0.0134044 0.730115i
\(693\) −8.75415e16 + 8.75415e16i −0.790342 + 0.790342i
\(694\) −4.85601e16 1.14257e17i −0.434633 1.02265i
\(695\) −1.40554e17 −1.24720
\(696\) 3.44590e16 + 7.71147e16i 0.303143 + 0.678394i
\(697\) 1.16640e17i 1.01730i
\(698\) 1.29734e16 + 3.05250e16i 0.112181 + 0.263951i
\(699\) −6.10112e16 6.10112e16i −0.523054 0.523054i
\(700\) 1.32497e17 1.37453e17i 1.12621 1.16833i
\(701\) −1.77056e16 1.77056e16i −0.149212 0.149212i 0.628554 0.777766i \(-0.283647\pi\)
−0.777766 + 0.628554i \(0.783647\pi\)
\(702\) 5.10527e16 1.26525e17i 0.426576 1.05719i
\(703\) 5.41589e15i 0.0448681i
\(704\) −1.80064e17 + 9.92644e15i −1.47908 + 0.0815375i
\(705\) −3.93836e16 −0.320760
\(706\) −1.63613e17 6.60181e16i −1.32127 0.533132i
\(707\) 1.25526e15 1.25526e15i 0.0100512 0.0100512i
\(708\) −4.10757e15 3.95946e15i −0.0326126 0.0314367i
\(709\) 5.33550e16 5.33550e16i 0.420047 0.420047i −0.465173 0.885220i \(-0.654008\pi\)
0.885220 + 0.465173i \(0.154008\pi\)
\(710\) 8.48273e16 3.60523e16i 0.662195 0.281438i
\(711\) −1.19934e16 −0.0928381
\(712\) −5.25802e16 + 2.34957e16i −0.403592 + 0.180347i
\(713\) 2.08009e17i 1.58323i
\(714\) −5.79000e16 + 2.46080e16i −0.437008 + 0.185732i
\(715\) 3.21176e17 + 3.21176e17i 2.40385 + 2.40385i
\(716\) −6.75827e16 + 1.24077e15i −0.501600 + 0.00920900i
\(717\) 3.87975e16 + 3.87975e16i 0.285555 + 0.285555i
\(718\) 2.34423e17 + 9.45900e16i 1.71102 + 0.690396i
\(719\) 3.77094e16i 0.272946i 0.990644 + 0.136473i \(0.0435767\pi\)
−0.990644 + 0.136473i \(0.956423\pi\)
\(720\) 1.23544e17 1.32965e17i 0.886799 0.954429i
\(721\) −1.74408e16 −0.124152
\(722\) 4.71203e16 1.16779e17i 0.332648 0.824404i
\(723\) −2.87793e16 + 2.87793e16i −0.201489 + 0.201489i
\(724\) 5.27158e16 9.67822e14i 0.366024 0.00671992i
\(725\) 2.85273e17 2.85273e17i 1.96441 1.96441i
\(726\) 3.11750e16 + 7.33514e16i 0.212905 + 0.500943i
\(727\) 1.64276e17 1.11267 0.556337 0.830957i \(-0.312206\pi\)
0.556337 + 0.830957i \(0.312206\pi\)
\(728\) −7.06557e16 + 1.84813e17i −0.474634 + 1.24149i
\(729\) 5.92808e15i 0.0394956i
\(730\) 1.22205e16 + 2.87536e16i 0.0807518 + 0.190001i
\(731\) 4.11739e16 + 4.11739e16i 0.269847 + 0.269847i
\(732\) −1.30545e16 1.25838e16i −0.0848581 0.0817984i
\(733\) 5.69705e16 + 5.69705e16i 0.367304 + 0.367304i 0.866493 0.499189i \(-0.166369\pi\)
−0.499189 + 0.866493i \(0.666369\pi\)
\(734\) −5.32527e16 + 1.31977e17i −0.340538 + 0.843959i
\(735\) 1.09927e16i 0.0697238i
\(736\) −5.37514e16 + 1.48726e17i −0.338160 + 0.935662i
\(737\) −1.36632e17 −0.852603
\(738\) −1.10381e17 4.45387e16i −0.683212 0.275676i
\(739\) −3.03904e16 + 3.03904e16i −0.186582 + 0.186582i −0.794217 0.607635i \(-0.792118\pi\)
0.607635 + 0.794217i \(0.292118\pi\)
\(740\) −2.52351e16 + 2.61790e16i −0.153679 + 0.159427i
\(741\) −2.48074e16 + 2.48074e16i −0.149855 + 0.149855i
\(742\) 3.77489e15 1.60436e15i 0.0226194 0.00961342i
\(743\) 1.16869e17 0.694650 0.347325 0.937745i \(-0.387090\pi\)
0.347325 + 0.937745i \(0.387090\pi\)
\(744\) 4.39262e16 1.14897e17i 0.258992 0.677441i
\(745\) 2.15278e17i 1.25910i
\(746\) 1.51227e17 6.42728e16i 0.877398 0.372901i
\(747\) −1.62476e17 1.62476e17i −0.935116 0.935116i
\(748\) −5.21034e15 2.83799e17i −0.0297479 1.62032i
\(749\) 5.49047e16 + 5.49047e16i 0.310970 + 0.310970i
\(750\) 8.70738e16 + 3.51343e16i 0.489237 + 0.197408i
\(751\) 1.63669e17i 0.912277i −0.889909 0.456139i \(-0.849232\pi\)
0.889909 0.456139i \(-0.150768\pi\)
\(752\) 7.73513e16 2.84118e15i 0.427721 0.0157106i
\(753\) 1.01466e17 0.556611
\(754\) −1.56450e17 + 3.87733e17i −0.851430 + 2.11011i
\(755\) −3.36171e17 + 3.36171e17i −1.81501 + 1.81501i
\(756\) −2.66589e15 1.45207e17i −0.0142795 0.777780i
\(757\) −2.69853e15 + 2.69853e15i −0.0143401 + 0.0143401i −0.714240 0.699900i \(-0.753228\pi\)
0.699900 + 0.714240i \(0.253228\pi\)
\(758\) −3.56758e16 8.39414e16i −0.188087 0.442549i
\(759\) 1.28411e17 0.671666
\(760\) −9.63911e16 + 4.30728e16i −0.500214 + 0.223523i
\(761\) 3.52484e16i 0.181481i −0.995875 0.0907406i \(-0.971077\pi\)
0.995875 0.0907406i \(-0.0289234\pi\)
\(762\) −2.84455e16 6.69293e16i −0.145306 0.341890i
\(763\) −1.49416e17 1.49416e17i −0.757269 0.757269i
\(764\) −3.58395e16 + 3.71800e16i −0.180219 + 0.186960i
\(765\) 2.02006e17 + 2.02006e17i 1.00785 + 1.00785i
\(766\) −1.42662e16 + 3.53562e16i −0.0706215 + 0.175022i
\(767\) 2.82416e16i 0.138713i
\(768\) 6.10975e16 7.08001e16i 0.297753 0.345038i
\(769\) 3.56080e17 1.72182 0.860912 0.508753i \(-0.169893\pi\)
0.860912 + 0.508753i \(0.169893\pi\)
\(770\) 4.48367e17 + 1.80917e17i 2.15124 + 0.868028i
\(771\) 2.39711e16 2.39711e16i 0.114120 0.114120i
\(772\) −1.46420e17 1.41140e17i −0.691664 0.666725i
\(773\) 1.00963e16 1.00963e16i 0.0473243 0.0473243i −0.683049 0.730373i \(-0.739346\pi\)
0.730373 + 0.683049i \(0.239346\pi\)
\(774\) −5.46867e16 + 2.32423e16i −0.254352 + 0.108102i
\(775\) −5.87540e17 −2.71161
\(776\) −9.07074e15 2.02991e16i −0.0415406 0.0929622i
\(777\) 1.28617e16i 0.0584483i
\(778\) −1.27576e17 + 5.42211e16i −0.575298 + 0.244507i
\(779\) 4.89579e16 + 4.89579e16i 0.219077 + 0.219077i
\(780\) −2.35501e17 + 4.32362e15i −1.04574 + 0.0191991i
\(781\) 1.04012e17 + 1.04012e17i 0.458329 + 0.458329i
\(782\) −2.30828e17 9.31391e16i −1.00936 0.407278i
\(783\) 3.06898e17i 1.33175i
\(784\) −7.93030e14 2.15903e16i −0.00341502 0.0929741i
\(785\) −7.62724e17 −3.25949
\(786\) −7.24086e16 + 1.79451e17i −0.307082 + 0.761046i
\(787\) −1.91634e17 + 1.91634e17i −0.806536 + 0.806536i −0.984108 0.177572i \(-0.943176\pi\)
0.177572 + 0.984108i \(0.443176\pi\)
\(788\) 4.22339e17 7.75384e15i 1.76402 0.0323862i
\(789\) 9.38012e16 9.38012e16i 0.388818 0.388818i
\(790\) 1.83208e16 + 4.31068e16i 0.0753670 + 0.177331i
\(791\) −2.25926e17 −0.922376
\(792\) 2.70560e17 + 1.03438e17i 1.09626 + 0.419109i
\(793\) 8.97563e16i 0.360932i
\(794\) −6.91533e16 1.62711e17i −0.275988 0.649371i
\(795\) 3.45269e15 + 3.45269e15i 0.0136759 + 0.0136759i
\(796\) −1.17450e17 1.13215e17i −0.461714 0.445066i
\(797\) 3.74988e16 + 3.74988e16i 0.146308 + 0.146308i 0.776466 0.630159i \(-0.217010\pi\)
−0.630159 + 0.776466i \(0.717010\pi\)
\(798\) −1.39738e16 + 3.46315e16i −0.0541126 + 0.134108i
\(799\) 1.21831e17i 0.468251i
\(800\) −4.20089e17 1.51826e17i −1.60251 0.579169i
\(801\) 9.25029e16 0.350236
\(802\) 2.57960e17 + 1.04087e17i 0.969406 + 0.391156i
\(803\) −3.52566e16 + 3.52566e16i −0.131506 + 0.131506i
\(804\) 4.91727e16 5.10121e16i 0.182049 0.188859i
\(805\) 2.99800e17 2.99800e17i 1.10168 1.10168i
\(806\) 5.60392e17 2.38171e17i 2.04401 0.868719i
\(807\) 2.01150e17 0.728247
\(808\) −3.87958e15 1.48320e15i −0.0139417 0.00533004i
\(809\) 5.29536e17i 1.88888i −0.328682 0.944441i \(-0.606604\pi\)
0.328682 0.944441i \(-0.393396\pi\)
\(810\) −1.79524e17 + 7.62991e16i −0.635641 + 0.270153i
\(811\) −2.07628e17 2.07628e17i −0.729726 0.729726i 0.240839 0.970565i \(-0.422577\pi\)
−0.970565 + 0.240839i \(0.922577\pi\)
\(812\) 8.16960e15 + 4.44985e17i 0.0285013 + 1.55242i
\(813\) −1.32722e17 1.32722e17i −0.459621 0.459621i
\(814\) −5.38135e16 2.17138e16i −0.184989 0.0746430i
\(815\) 7.29820e16i 0.249041i
\(816\) 1.07833e17 + 1.00192e17i 0.365267 + 0.339384i
\(817\) 3.45643e16 0.116224
\(818\) 3.56781e16 8.84214e16i 0.119092 0.295146i
\(819\) 2.24719e17 2.24719e17i 0.744624 0.744624i
\(820\) 8.53277e15 + 4.64767e17i 0.0280677 + 1.52880i
\(821\) −1.15543e17 + 1.15543e17i −0.377297 + 0.377297i −0.870126 0.492829i \(-0.835963\pi\)
0.492829 + 0.870126i \(0.335963\pi\)
\(822\) −5.56324e15 1.30897e16i −0.0180342 0.0424326i
\(823\) −3.12933e16 −0.100705 −0.0503527 0.998732i \(-0.516035\pi\)
−0.0503527 + 0.998732i \(0.516035\pi\)
\(824\) 1.66478e16 + 3.72555e16i 0.0531855 + 0.119022i
\(825\) 3.62710e17i 1.15036i
\(826\) −1.17588e16 2.76671e16i −0.0370238 0.0871131i
\(827\) 3.66759e17 + 3.66759e17i 1.14643 + 1.14643i 0.987250 + 0.159180i \(0.0508849\pi\)
0.159180 + 0.987250i \(0.449115\pi\)
\(828\) 1.76282e17 1.82876e17i 0.547050 0.567512i
\(829\) −3.80727e17 3.80727e17i −1.17297 1.17297i −0.981498 0.191472i \(-0.938674\pi\)
−0.191472 0.981498i \(-0.561326\pi\)
\(830\) −3.35779e17 + 8.32164e17i −1.02703 + 2.54531i
\(831\) 1.76365e17i 0.535557i
\(832\) 4.62224e17 2.54812e16i 1.39352 0.0768210i
\(833\) 3.40056e16 0.101784
\(834\) 1.07871e17 + 4.35259e16i 0.320558 + 0.129345i
\(835\) 4.33893e17 4.33893e17i 1.28016 1.28016i
\(836\) −1.21308e17 1.16934e17i −0.355345 0.342533i
\(837\) −3.16039e17 + 3.16039e17i −0.919153 + 0.919153i
\(838\) 3.78286e17 1.60775e17i 1.09234 0.464252i
\(839\) 3.71726e17 1.06574 0.532869 0.846198i \(-0.321114\pi\)
0.532869 + 0.846198i \(0.321114\pi\)
\(840\) −2.28910e17 + 1.02289e17i −0.651612 + 0.291176i
\(841\) 5.86669e17i 1.65812i
\(842\) −2.52570e17 + 1.07344e17i −0.708776 + 0.301236i
\(843\) −1.28568e17 1.28568e17i −0.358236 0.358236i
\(844\) −1.30181e17 + 2.39003e15i −0.360159 + 0.00661225i
\(845\) −4.01181e17 4.01181e17i −1.10205 1.10205i
\(846\) −1.15294e17 4.65211e16i −0.314473 0.126890i
\(847\) 4.19967e17i 1.13740i
\(848\) −7.03034e15 6.53218e15i −0.0189061 0.0175664i
\(849\) 2.69041e17 0.718411
\(850\) 2.63080e17 6.51993e17i 0.697548 1.72874i
\(851\) −3.59824e16 + 3.59824e16i −0.0947354 + 0.0947354i
\(852\) −7.62665e16 + 1.40020e15i −0.199387 + 0.00366059i
\(853\) −4.11974e17 + 4.11974e17i −1.06949 + 1.06949i −0.0720901 + 0.997398i \(0.522967\pi\)
−0.997398 + 0.0720901i \(0.977033\pi\)
\(854\) −3.73711e16 8.79303e16i −0.0963361 0.226669i
\(855\) 1.69578e17 0.434084
\(856\) 6.48744e16 1.69691e17i 0.164904 0.431336i
\(857\) 1.54273e16i 0.0389407i 0.999810 + 0.0194703i \(0.00619800\pi\)
−0.999810 + 0.0194703i \(0.993802\pi\)
\(858\) −1.47032e17 3.45951e17i −0.368543 0.867143i
\(859\) −1.51797e17 1.51797e17i −0.377837 0.377837i 0.492484 0.870321i \(-0.336089\pi\)
−0.870321 + 0.492484i \(0.836089\pi\)
\(860\) 1.67075e17 + 1.61051e17i 0.412972 + 0.398082i
\(861\) 1.16265e17 + 1.16265e17i 0.285385 + 0.285385i
\(862\) 1.46816e17 3.63855e17i 0.357873 0.886919i
\(863\) 5.49707e17i 1.33066i 0.746550 + 0.665330i \(0.231709\pi\)
−0.746550 + 0.665330i \(0.768291\pi\)
\(864\) −3.07634e17 + 1.44299e17i −0.739524 + 0.346882i
\(865\) 5.02992e17 1.20078
\(866\) −1.67528e17 6.75977e16i −0.397173 0.160260i
\(867\) −2.69480e16 + 2.69480e16i −0.0634470 + 0.0634470i
\(868\) 4.49827e17 4.66652e17i 1.05178 1.09113i
\(869\) −5.28560e16 + 5.28560e16i −0.122737 + 0.122737i
\(870\) −4.87610e17 + 2.07238e17i −1.12449 + 0.477919i
\(871\) 3.50734e17 0.803284
\(872\) −1.76547e17 + 4.61792e17i −0.401571 + 1.05038i
\(873\) 3.57116e16i 0.0806723i
\(874\) −1.35980e17 + 5.77928e16i −0.305076 + 0.129660i
\(875\) 3.49845e17 + 3.49845e17i 0.779521 + 0.779521i
\(876\) −4.74619e14 2.58517e16i −0.00105032 0.0572091i
\(877\) 2.89920e17 + 2.89920e17i 0.637207 + 0.637207i 0.949866 0.312659i \(-0.101220\pi\)
−0.312659 + 0.949866i \(0.601220\pi\)
\(878\) 2.13377e17 + 8.60976e16i 0.465779 + 0.187942i
\(879\) 7.73459e15i 0.0167689i
\(880\) −4.15226e16 1.13045e18i −0.0894105 2.43420i
\(881\) 6.85444e17 1.46594 0.732970 0.680261i \(-0.238133\pi\)
0.732970 + 0.680261i \(0.238133\pi\)
\(882\) −1.29850e16 + 3.21808e16i −0.0275822 + 0.0683573i
\(883\) −6.52321e16 + 6.52321e16i −0.137625 + 0.137625i −0.772563 0.634938i \(-0.781026\pi\)
0.634938 + 0.772563i \(0.281026\pi\)
\(884\) 1.33750e16 + 7.28513e17i 0.0280271 + 1.52659i
\(885\) 2.53056e16 2.53056e16i 0.0526693 0.0526693i
\(886\) −2.46094e17 5.79034e17i −0.508744 1.19702i
\(887\) −6.77810e17 −1.39177 −0.695883 0.718155i \(-0.744987\pi\)
−0.695883 + 0.718155i \(0.744987\pi\)
\(888\) 2.74740e16 1.22769e16i 0.0560330 0.0250386i
\(889\) 3.83197e17i 0.776269i
\(890\) −1.41304e17 3.32474e17i −0.284325 0.668987i
\(891\) −2.20125e17 2.20125e17i −0.439950 0.439950i
\(892\) −3.39345e17 + 3.52038e17i −0.673678 + 0.698877i
\(893\) 5.11370e16 + 5.11370e16i 0.100839 + 0.100839i
\(894\) −6.66656e16 + 1.65218e17i −0.130580 + 0.323618i
\(895\) 4.24003e17i 0.824956i
\(896\) 4.42212e17 2.17416e17i 0.854638 0.420187i
\(897\) −3.29632e17 −0.632813
\(898\) 4.43571e17 + 1.78981e17i 0.845872 + 0.341310i
\(899\) 9.68497e17 9.68497e17i 1.83460 1.83460i
\(900\) 5.16550e17 + 4.97925e17i 0.971980 + 0.936934i
\(901\) 1.06808e16 1.06808e16i 0.0199643 0.0199643i
\(902\) −6.82742e17 + 2.90171e17i −1.26770 + 0.538784i
\(903\) 8.20834e16 0.151401
\(904\) 2.15654e17 + 4.82604e17i 0.395136 + 0.884261i
\(905\) 3.30730e17i 0.601981i
\(906\) 3.62103e17 1.53897e17i 0.654731 0.278266i
\(907\) 1.14829e17 + 1.14829e17i 0.206257 + 0.206257i 0.802674 0.596418i \(-0.203410\pi\)
−0.596418 + 0.802674i \(0.703410\pi\)
\(908\) −7.98645e17 + 1.46625e16i −1.42508 + 0.0261634i
\(909\) 4.71729e15 + 4.71729e15i 0.00836198 + 0.00836198i
\(910\) −1.15096e18 4.64413e17i −2.02680 0.817817i
\(911\) 4.69446e17i 0.821251i 0.911804 + 0.410625i \(0.134690\pi\)
−0.911804 + 0.410625i \(0.865310\pi\)
\(912\) 8.73154e16 3.20717e15i 0.151748 0.00557382i
\(913\) −1.43209e18 −2.47255
\(914\) 7.20090e16 1.78461e17i 0.123512 0.306101i
\(915\) 8.04252e16 8.04252e16i 0.137046 0.137046i
\(916\) 1.60093e17 2.93919e15i 0.271019 0.00497571i
\(917\) −7.21000e17 + 7.21000e17i −1.21260 + 1.21260i
\(918\) −2.09198e17 4.92220e17i −0.349543 0.822438i
\(919\) −4.70950e17 −0.781776 −0.390888 0.920438i \(-0.627832\pi\)
−0.390888 + 0.920438i \(0.627832\pi\)
\(920\) −9.26577e17 3.54239e17i −1.52811 0.584210i
\(921\) 7.70328e16i 0.126217i
\(922\) 1.58001e17 + 3.71761e17i 0.257203 + 0.605171i
\(923\) −2.66999e17 2.66999e17i −0.431817 0.431817i
\(924\) −2.88082e17 2.77694e17i −0.462896 0.446206i
\(925\) −1.01635e17 1.01635e17i −0.162254 0.162254i
\(926\) 3.07236e17 7.61426e17i 0.487311 1.20771i
\(927\) 6.55426e16i 0.103287i
\(928\) 9.42741e17 4.42204e17i 1.47606 0.692364i
\(929\) 7.78802e17 1.21153 0.605763 0.795645i \(-0.292868\pi\)
0.605763 + 0.795645i \(0.292868\pi\)
\(930\) 7.15545e17 + 2.88723e17i 1.10596 + 0.446255i
\(931\) 1.42733e16 1.42733e16i 0.0219193 0.0219193i
\(932\) −7.38236e17 + 7.65850e17i −1.12642 + 1.16855i
\(933\) −2.88025e17 + 2.88025e17i −0.436658 + 0.436658i
\(934\) −3.78776e15 + 1.60983e15i −0.00570560 + 0.00242493i
\(935\) 1.78051e18 2.66486
\(936\) −6.94528e17 2.65524e17i −1.03284 0.394865i
\(937\) 2.66635e16i 0.0393985i −0.999806 0.0196992i \(-0.993729\pi\)
0.999806 0.0196992i \(-0.00627087\pi\)
\(938\) 3.43599e17 1.46032e17i 0.504469 0.214404i
\(939\) −1.64650e17 1.64650e17i −0.240197 0.240197i
\(940\) 8.91256e15 + 4.85453e17i 0.0129192 + 0.703689i
\(941\) −4.96768e17 4.96768e17i −0.715511 0.715511i 0.252172 0.967682i \(-0.418855\pi\)
−0.967682 + 0.252172i \(0.918855\pi\)
\(942\) 5.85365e17 + 2.36195e17i 0.837763 + 0.338038i
\(943\) 6.50537e17i 0.925128i
\(944\) −4.78760e16 + 5.15272e16i −0.0676528 + 0.0728122i
\(945\) 9.11006e17 1.27918
\(946\) −1.38578e17 + 3.43439e17i −0.193351 + 0.479184i
\(947\) −9.61826e17 + 9.61826e17i −1.33351 + 1.33351i −0.431305 + 0.902206i \(0.641947\pi\)
−0.902206 + 0.431305i \(0.858053\pi\)
\(948\) −7.11540e14 3.87565e16i −0.000980278 0.0533942i
\(949\) 9.05036e16 9.05036e16i 0.123899 0.123899i
\(950\) −1.63241e17 3.84089e17i −0.222069 0.522504i
\(951\) −8.93847e15 −0.0120831
\(952\) 3.16428e17 + 7.08124e17i 0.425063 + 0.951234i
\(953\) 1.09045e18i 1.45563i −0.685776 0.727813i \(-0.740537\pi\)
0.685776 0.727813i \(-0.259463\pi\)
\(954\) 6.02919e15 + 1.41860e16i 0.00799776 + 0.0188179i
\(955\) −2.29056e17 2.29056e17i −0.301941 0.301941i
\(956\) 4.69450e17 4.87010e17i 0.614953 0.637956i
\(957\) −5.97889e17 5.97889e17i −0.778303 0.778303i
\(958\) −2.56125e17 + 6.34758e17i −0.331329 + 0.821136i
\(959\) 7.49440e16i 0.0963441i
\(960\) 4.37004e17 + 3.91339e17i 0.558287 + 0.499949i
\(961\) −1.20703e18 −1.53242
\(962\) 1.38139e17 + 5.57393e16i 0.174288 + 0.0703252i
\(963\) −2.06332e17 + 2.06332e17i −0.258707 + 0.258707i
\(964\) 3.61255e17 + 3.48230e17i 0.450145 + 0.433914i
\(965\) 9.02052e17 9.02052e17i 1.11704 1.11704i
\(966\) −3.22927e17 + 1.37246e17i −0.397412 + 0.168903i
\(967\) 1.03468e17 0.126545 0.0632727 0.997996i \(-0.479846\pi\)
0.0632727 + 0.997996i \(0.479846\pi\)
\(968\) 8.97096e17 4.00871e17i 1.09040 0.487251i
\(969\) 1.37525e17i 0.166127i
\(970\) 1.28355e17 5.45519e16i 0.154093 0.0654906i
\(971\) −7.06931e17 7.06931e17i −0.843455 0.843455i 0.145852 0.989306i \(-0.453408\pi\)
−0.989306 + 0.145852i \(0.953408\pi\)
\(972\) 8.50153e17 1.56082e16i 1.00809 0.0185078i
\(973\) 4.33403e17 + 4.33403e17i 0.510758 + 0.510758i
\(974\) 5.61649e17 + 2.26626e17i 0.657826 + 0.265433i
\(975\) 9.31076e17i 1.08382i
\(976\) −1.52157e17 + 1.63761e17i −0.176033 + 0.189458i
\(977\) 1.36952e18 1.57471 0.787357 0.616498i \(-0.211449\pi\)
0.787357 + 0.616498i \(0.211449\pi\)
\(978\) 2.26006e16 5.60112e16i 0.0258277 0.0640091i
\(979\) 4.07667e17 4.07667e17i 0.463031 0.463031i
\(980\) 1.35500e17 2.48767e15i 0.152961 0.00280826i
\(981\) 5.61506e17 5.61506e17i 0.630000 0.630000i
\(982\) 5.56248e17 + 1.30879e18i 0.620297 + 1.45949i
\(983\) −1.33679e18 −1.48164 −0.740818 0.671705i \(-0.765562\pi\)
−0.740818 + 0.671705i \(0.765562\pi\)
\(984\) 1.37377e17 3.59335e17i 0.151336 0.395848i
\(985\) 2.64969e18i 2.90120i
\(986\) 6.41083e17 + 1.50840e18i 0.697675 + 1.64156i
\(987\) 1.21440e17 + 1.21440e17i 0.131359 + 0.131359i
\(988\) 3.11397e17 + 3.00169e17i 0.334790 + 0.322719i
\(989\) 2.29640e17 + 2.29640e17i 0.245397 + 0.245397i
\(990\) −6.79885e17 + 1.68497e18i −0.722145 + 1.78970i
\(991\) 1.50296e18i 1.58674i 0.608741 + 0.793369i \(0.291675\pi\)
−0.608741 + 0.793369i \(0.708325\pi\)
\(992\) −1.42620e18 5.15446e17i −1.49661 0.540895i
\(993\) 3.28368e17 0.342503
\(994\) −3.72736e17 1.50399e17i −0.386441 0.155929i
\(995\) 7.23575e17 7.23575e17i 0.745668 0.745668i
\(996\) 5.15397e17 5.34676e17i 0.527942 0.547690i
\(997\) −4.41546e17 + 4.41546e17i −0.449578 + 0.449578i −0.895214 0.445636i \(-0.852977\pi\)
0.445636 + 0.895214i \(0.352977\pi\)
\(998\) 1.76037e18 7.48170e17i 1.78164 0.757211i
\(999\) −1.09340e17 −0.109998
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 16.13.f.a.3.3 46
4.3 odd 2 64.13.f.a.47.14 46
8.3 odd 2 128.13.f.a.95.10 46
8.5 even 2 128.13.f.b.95.14 46
16.3 odd 4 128.13.f.b.31.14 46
16.5 even 4 64.13.f.a.15.14 46
16.11 odd 4 inner 16.13.f.a.11.3 yes 46
16.13 even 4 128.13.f.a.31.10 46
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
16.13.f.a.3.3 46 1.1 even 1 trivial
16.13.f.a.11.3 yes 46 16.11 odd 4 inner
64.13.f.a.15.14 46 16.5 even 4
64.13.f.a.47.14 46 4.3 odd 2
128.13.f.a.31.10 46 16.13 even 4
128.13.f.a.95.10 46 8.3 odd 2
128.13.f.b.31.14 46 16.3 odd 4
128.13.f.b.95.14 46 8.5 even 2