Properties

Label 8.21.d.b.3.1
Level 8
Weight 21
Character 8.3
Analytic conductor 20.281
Analytic rank 0
Dimension 18
CM No
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 8 = 2^{3} \)
Weight: \( k \) = \( 21 \)
Character orbit: \([\chi]\) = 8.d (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(20.2811012082\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.1
Root \(16622.8 - 2.05933e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.2

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-998.751 - 225.992i) q^{2}\) \(+60145.3 q^{3}\) \(+(946431. + 451420. i) q^{4}\) \(+8.23733e6i q^{5}\) \(+(-6.00701e7 - 1.35924e7i) q^{6}\) \(+5.26995e8i q^{7}\) \(+(-8.43231e8 - 6.64742e8i) q^{8}\) \(+1.30668e8 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-998.751 - 225.992i) q^{2}\) \(+60145.3 q^{3}\) \(+(946431. + 451420. i) q^{4}\) \(+8.23733e6i q^{5}\) \(+(-6.00701e7 - 1.35924e7i) q^{6}\) \(+5.26995e8i q^{7}\) \(+(-8.43231e8 - 6.64742e8i) q^{8}\) \(+1.30668e8 q^{9}\) \(+(1.86157e9 - 8.22704e9i) q^{10}\) \(+6.02652e9 q^{11}\) \(+(5.69233e10 + 2.71508e10i) q^{12}\) \(-1.38203e11i q^{13}\) \(+(1.19097e11 - 5.26337e11i) q^{14}\) \(+4.95436e11i q^{15}\) \(+(6.91951e11 + 8.54476e11i) q^{16}\) \(-1.98685e12 q^{17}\) \(+(-1.30505e11 - 2.95300e10i) q^{18}\) \(-8.88192e12 q^{19}\) \(+(-3.71850e12 + 7.79606e12i) q^{20}\) \(+3.16963e13i q^{21}\) \(+(-6.01899e12 - 1.36195e12i) q^{22}\) \(-2.01771e13i q^{23}\) \(+(-5.07164e13 - 3.99811e13i) q^{24}\) \(+2.75139e13 q^{25}\) \(+(-3.12327e13 + 1.38030e14i) q^{26}\) \(-2.01854e14 q^{27}\) \(+(-2.37896e14 + 4.98765e14i) q^{28}\) \(-2.99333e14i q^{29}\) \(+(1.11965e14 - 4.94817e14i) q^{30}\) \(+1.39233e15i q^{31}\) \(+(-4.97982e14 - 1.00978e15i) q^{32}\) \(+3.62466e14 q^{33}\) \(+(1.98437e15 + 4.49014e14i) q^{34}\) \(-4.34103e15 q^{35}\) \(+(1.23668e14 + 5.89862e13i) q^{36}\) \(+1.32225e15i q^{37}\) \(+(8.87083e15 + 2.00725e15i) q^{38}\) \(-8.31223e15i q^{39}\) \(+(5.47570e15 - 6.94597e15i) q^{40}\) \(+1.06415e16 q^{41}\) \(+(7.16311e15 - 3.16567e16i) q^{42}\) \(-1.54318e15 q^{43}\) \(+(5.70368e15 + 2.72049e15i) q^{44}\) \(+1.07636e15i q^{45}\) \(+(-4.55987e15 + 2.01519e16i) q^{46}\) \(+6.01114e16i q^{47}\) \(+(4.16176e16 + 5.13927e16i) q^{48}\) \(-1.97932e17 q^{49}\) \(+(-2.74795e16 - 6.21792e15i) q^{50}\) \(-1.19500e17 q^{51}\) \(+(6.23874e16 - 1.30799e17i) q^{52}\) \(+2.12573e17i q^{53}\) \(+(2.01602e17 + 4.56176e16i) q^{54}\) \(+4.96424e16i q^{55}\) \(+(3.50316e17 - 4.44379e17i) q^{56}\) \(-5.34206e17 q^{57}\) \(+(-6.76469e16 + 2.98959e17i) q^{58}\) \(+4.77160e15 q^{59}\) \(+(-2.23650e17 + 4.68896e17i) q^{60}\) \(-3.65093e16i q^{61}\) \(+(3.14655e17 - 1.39059e18i) q^{62}\) \(+6.88615e16i q^{63}\) \(+(2.69157e17 + 1.12106e18i) q^{64}\) \(+1.13842e18 q^{65}\) \(+(-3.62014e17 - 8.19146e16i) q^{66}\) \(+6.78003e17 q^{67}\) \(+(-1.88042e18 - 8.96906e17i) q^{68}\) \(-1.21356e18i q^{69}\) \(+(4.33561e18 + 9.81040e17i) q^{70}\) \(-2.60562e18i q^{71}\) \(+(-1.10183e17 - 8.68606e16i) q^{72}\) \(+2.08057e18 q^{73}\) \(+(2.98817e17 - 1.32059e18i) q^{74}\) \(+1.65483e18 q^{75}\) \(+(-8.40613e18 - 4.00948e18i) q^{76}\) \(+3.17595e18i q^{77}\) \(+(-1.87850e18 + 8.30185e18i) q^{78}\) \(+4.99331e18i q^{79}\) \(+(-7.03860e18 + 5.69983e18i) q^{80}\) \(-1.25962e19 q^{81}\) \(+(-1.06282e19 - 2.40489e18i) q^{82}\) \(+2.79468e19 q^{83}\) \(+(-1.43083e19 + 2.99983e19i) q^{84}\) \(-1.63664e19i q^{85}\) \(+(1.54125e18 + 3.48747e17i) q^{86}\) \(-1.80034e19i q^{87}\) \(+(-5.08175e18 - 4.00608e18i) q^{88}\) \(-2.07280e19 q^{89}\) \(+(2.43248e17 - 1.07501e18i) q^{90}\) \(+7.28321e19 q^{91}\) \(+(9.10834e18 - 1.90962e19i) q^{92}\) \(+8.37419e19i q^{93}\) \(+(1.35847e19 - 6.00363e19i) q^{94}\) \(-7.31633e19i q^{95}\) \(+(-2.99513e19 - 6.07337e19i) q^{96}\) \(-9.97818e19 q^{97}\) \(+(1.97685e20 + 4.47311e19i) q^{98}\) \(+7.87473e17 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −998.751 225.992i −0.975343 0.220696i
\(3\) 60145.3 1.01857 0.509283 0.860599i \(-0.329911\pi\)
0.509283 + 0.860599i \(0.329911\pi\)
\(4\) 946431. + 451420.i 0.902587 + 0.430508i
\(5\) 8.23733e6i 0.843502i 0.906712 + 0.421751i \(0.138584\pi\)
−0.906712 + 0.421751i \(0.861416\pi\)
\(6\) −6.00701e7 1.35924e7i −0.993450 0.224793i
\(7\) 5.26995e8i 1.86563i 0.360351 + 0.932817i \(0.382657\pi\)
−0.360351 + 0.932817i \(0.617343\pi\)
\(8\) −8.43231e8 6.64742e8i −0.785320 0.619090i
\(9\) 1.30668e8 0.0374752
\(10\) 1.86157e9 8.22704e9i 0.186157 0.822704i
\(11\) 6.02652e9 0.232348 0.116174 0.993229i \(-0.462937\pi\)
0.116174 + 0.993229i \(0.462937\pi\)
\(12\) 5.69233e10 + 2.71508e10i 0.919344 + 0.438500i
\(13\) 1.38203e11i 1.00250i −0.865304 0.501248i \(-0.832874\pi\)
0.865304 0.501248i \(-0.167126\pi\)
\(14\) 1.19097e11 5.26337e11i 0.411737 1.81963i
\(15\) 4.95436e11i 0.859162i
\(16\) 6.91951e11 + 8.54476e11i 0.629326 + 0.777141i
\(17\) −1.98685e12 −0.985546 −0.492773 0.870158i \(-0.664017\pi\)
−0.492773 + 0.870158i \(0.664017\pi\)
\(18\) −1.30505e11 2.95300e10i −0.0365512 0.00827062i
\(19\) −8.88192e12 −1.44867 −0.724337 0.689446i \(-0.757854\pi\)
−0.724337 + 0.689446i \(0.757854\pi\)
\(20\) −3.71850e12 + 7.79606e12i −0.363134 + 0.761334i
\(21\) 3.16963e13i 1.90027i
\(22\) −6.01899e12 1.36195e12i −0.226619 0.0512783i
\(23\) 2.01771e13i 0.487057i −0.969894 0.243529i \(-0.921695\pi\)
0.969894 0.243529i \(-0.0783050\pi\)
\(24\) −5.07164e13 3.99811e13i −0.799900 0.630583i
\(25\) 2.75139e13 0.288504
\(26\) −3.12327e13 + 1.38030e14i −0.221246 + 0.977777i
\(27\) −2.01854e14 −0.980394
\(28\) −2.37896e14 + 4.98765e14i −0.803170 + 1.68390i
\(29\) 2.99333e14i 0.711499i −0.934581 0.355749i \(-0.884226\pi\)
0.934581 0.355749i \(-0.115774\pi\)
\(30\) 1.11965e14 4.94817e14i 0.189613 0.837978i
\(31\) 1.39233e15i 1.69873i 0.527805 + 0.849366i \(0.323015\pi\)
−0.527805 + 0.849366i \(0.676985\pi\)
\(32\) −4.97982e14 1.00978e15i −0.442297 0.896869i
\(33\) 3.62466e14 0.236662
\(34\) 1.98437e15 + 4.49014e14i 0.961245 + 0.217506i
\(35\) −4.34103e15 −1.57367
\(36\) 1.23668e14 + 5.89862e13i 0.0338246 + 0.0161334i
\(37\) 1.32225e15i 0.274976i 0.990503 + 0.137488i \(0.0439029\pi\)
−0.990503 + 0.137488i \(0.956097\pi\)
\(38\) 8.87083e15 + 2.00725e15i 1.41295 + 0.319716i
\(39\) 8.31223e15i 1.02111i
\(40\) 5.47570e15 6.94597e15i 0.522204 0.662420i
\(41\) 1.06415e16 0.792798 0.396399 0.918078i \(-0.370260\pi\)
0.396399 + 0.918078i \(0.370260\pi\)
\(42\) 7.16311e15 3.16567e16i 0.419381 1.85341i
\(43\) −1.54318e15 −0.0714056 −0.0357028 0.999362i \(-0.511367\pi\)
−0.0357028 + 0.999362i \(0.511367\pi\)
\(44\) 5.70368e15 + 2.72049e15i 0.209715 + 0.100028i
\(45\) 1.07636e15i 0.0316104i
\(46\) −4.55987e15 + 2.01519e16i −0.107491 + 0.475048i
\(47\) 6.01114e16i 1.14282i 0.820664 + 0.571411i \(0.193604\pi\)
−0.820664 + 0.571411i \(0.806396\pi\)
\(48\) 4.16176e16 + 5.13927e16i 0.641010 + 0.791569i
\(49\) −1.97932e17 −2.48059
\(50\) −2.74795e16 6.21792e15i −0.281390 0.0636715i
\(51\) −1.19500e17 −1.00384
\(52\) 6.23874e16 1.30799e17i 0.431582 0.904840i
\(53\) 2.12573e17i 1.21549i 0.794134 + 0.607743i \(0.207925\pi\)
−0.794134 + 0.607743i \(0.792075\pi\)
\(54\) 2.01602e17 + 4.56176e16i 0.956220 + 0.216369i
\(55\) 4.96424e16i 0.195986i
\(56\) 3.50316e17 4.44379e17i 1.15499 1.46512i
\(57\) −5.34206e17 −1.47557
\(58\) −6.76469e16 + 2.98959e17i −0.157025 + 0.693955i
\(59\) 4.77160e15 0.00933563 0.00466782 0.999989i \(-0.498514\pi\)
0.00466782 + 0.999989i \(0.498514\pi\)
\(60\) −2.23650e17 + 4.68896e17i −0.369876 + 0.775469i
\(61\) 3.65093e16i 0.0511805i −0.999673 0.0255903i \(-0.991853\pi\)
0.999673 0.0255903i \(-0.00814652\pi\)
\(62\) 3.14655e17 1.39059e18i 0.374903 1.65685i
\(63\) 6.88615e16i 0.0699151i
\(64\) 2.69157e17 + 1.12106e18i 0.233456 + 0.972367i
\(65\) 1.13842e18 0.845608
\(66\) −3.62014e17 8.19146e16i −0.230826 0.0522303i
\(67\) 6.78003e17 0.371949 0.185975 0.982555i \(-0.440456\pi\)
0.185975 + 0.982555i \(0.440456\pi\)
\(68\) −1.88042e18 8.96906e17i −0.889541 0.424285i
\(69\) 1.21356e18i 0.496100i
\(70\) 4.33561e18 + 9.81040e17i 1.53486 + 0.347301i
\(71\) 2.60562e18i 0.800439i −0.916419 0.400220i \(-0.868934\pi\)
0.916419 0.400220i \(-0.131066\pi\)
\(72\) −1.10183e17 8.68606e16i −0.0294301 0.0232005i
\(73\) 2.08057e18 0.484121 0.242061 0.970261i \(-0.422177\pi\)
0.242061 + 0.970261i \(0.422177\pi\)
\(74\) 2.98817e17 1.32059e18i 0.0606860 0.268196i
\(75\) 1.65483e18 0.293860
\(76\) −8.40613e18 4.00948e18i −1.30756 0.623666i
\(77\) 3.17595e18i 0.433477i
\(78\) −1.87850e18 + 8.30185e18i −0.225354 + 0.995930i
\(79\) 4.99331e18i 0.527372i 0.964609 + 0.263686i \(0.0849383\pi\)
−0.964609 + 0.263686i \(0.915062\pi\)
\(80\) −7.03860e18 + 5.69983e18i −0.655520 + 0.530838i
\(81\) −1.25962e19 −1.03607
\(82\) −1.06282e19 2.40489e18i −0.773250 0.174967i
\(83\) 2.79468e19 1.80115 0.900577 0.434696i \(-0.143144\pi\)
0.900577 + 0.434696i \(0.143144\pi\)
\(84\) −1.43083e19 + 2.99983e19i −0.818081 + 1.71516i
\(85\) 1.63664e19i 0.831310i
\(86\) 1.54125e18 + 3.48747e17i 0.0696449 + 0.0157589i
\(87\) 1.80034e19i 0.724708i
\(88\) −5.08175e18 4.00608e18i −0.182468 0.143844i
\(89\) −2.07280e19 −0.664748 −0.332374 0.943148i \(-0.607850\pi\)
−0.332374 + 0.943148i \(0.607850\pi\)
\(90\) 2.43248e17 1.07501e18i 0.00697629 0.0308310i
\(91\) 7.28321e19 1.87029
\(92\) 9.10834e18 1.90962e19i 0.209682 0.439611i
\(93\) 8.37419e19i 1.73027i
\(94\) 1.35847e19 6.00363e19i 0.252216 1.11464i
\(95\) 7.31633e19i 1.22196i
\(96\) −2.99513e19 6.07337e19i −0.450508 0.913519i
\(97\) −9.97818e19 −1.35311 −0.676557 0.736391i \(-0.736529\pi\)
−0.676557 + 0.736391i \(0.736529\pi\)
\(98\) 1.97685e20 + 4.47311e19i 2.41942 + 0.547455i
\(99\) 7.87473e17 0.00870731
\(100\) 2.60400e19 + 1.24203e19i 0.260400 + 0.124203i
\(101\) 1.23930e20i 1.12192i −0.827843 0.560960i \(-0.810432\pi\)
0.827843 0.560960i \(-0.189568\pi\)
\(102\) 1.19351e20 + 2.70060e19i 0.979091 + 0.221544i
\(103\) 1.90114e20i 1.41463i 0.706901 + 0.707313i \(0.250093\pi\)
−0.706901 + 0.707313i \(0.749907\pi\)
\(104\) −9.18691e19 + 1.16537e20i −0.620635 + 0.787280i
\(105\) −2.61093e20 −1.60288
\(106\) 4.80399e19 2.12308e20i 0.268252 1.18551i
\(107\) −2.21231e18 −0.0112463 −0.00562314 0.999984i \(-0.501790\pi\)
−0.00562314 + 0.999984i \(0.501790\pi\)
\(108\) −1.91041e20 9.11212e19i −0.884891 0.422067i
\(109\) 2.92007e20i 1.23347i 0.787171 + 0.616734i \(0.211545\pi\)
−0.787171 + 0.616734i \(0.788455\pi\)
\(110\) 1.12188e19 4.95804e19i 0.0432533 0.191154i
\(111\) 7.95268e19i 0.280081i
\(112\) −4.50305e20 + 3.64655e20i −1.44986 + 1.17409i
\(113\) −1.48679e20 −0.437990 −0.218995 0.975726i \(-0.570278\pi\)
−0.218995 + 0.975726i \(0.570278\pi\)
\(114\) 5.33538e20 + 1.20726e20i 1.43919 + 0.325652i
\(115\) 1.66205e20 0.410834
\(116\) 1.35125e20 2.83298e20i 0.306306 0.642189i
\(117\) 1.80587e19i 0.0375688i
\(118\) −4.76564e18 1.07834e18i −0.00910544 0.00206033i
\(119\) 1.04706e21i 1.83867i
\(120\) 3.29337e20 4.17767e20i 0.531898 0.674718i
\(121\) −6.36431e20 −0.946014
\(122\) −8.25081e18 + 3.64637e19i −0.0112953 + 0.0499185i
\(123\) 6.40033e20 0.807516
\(124\) −6.28525e20 + 1.31774e21i −0.731317 + 1.53325i
\(125\) 1.01221e21i 1.08686i
\(126\) 1.55622e19 6.87754e19i 0.0154299 0.0681911i
\(127\) 1.29687e21i 1.18812i 0.804422 + 0.594058i \(0.202475\pi\)
−0.804422 + 0.594058i \(0.797525\pi\)
\(128\) −1.54688e19 1.18049e21i −0.0131026 0.999914i
\(129\) −9.28150e19 −0.0727313
\(130\) −1.13700e21 2.57274e20i −0.824757 0.186622i
\(131\) 2.73520e21 1.83770 0.918852 0.394603i \(-0.129118\pi\)
0.918852 + 0.394603i \(0.129118\pi\)
\(132\) 3.43049e20 + 1.63625e20i 0.213608 + 0.101885i
\(133\) 4.68073e21i 2.70270i
\(134\) −6.77156e20 1.53223e20i −0.362778 0.0820875i
\(135\) 1.66274e21i 0.826965i
\(136\) 1.67538e21 + 1.32075e21i 0.773969 + 0.610141i
\(137\) 3.47180e21 1.49056 0.745279 0.666753i \(-0.232316\pi\)
0.745279 + 0.666753i \(0.232316\pi\)
\(138\) −2.74254e20 + 1.21204e21i −0.109487 + 0.483867i
\(139\) −2.01290e19 −0.00747607 −0.00373804 0.999993i \(-0.501190\pi\)
−0.00373804 + 0.999993i \(0.501190\pi\)
\(140\) −4.10849e21 1.95963e21i −1.42037 0.677476i
\(141\) 3.61542e21i 1.16404i
\(142\) −5.88851e20 + 2.60237e21i −0.176653 + 0.780703i
\(143\) 8.32880e20i 0.232928i
\(144\) 9.04159e19 + 1.11653e20i 0.0235841 + 0.0291235i
\(145\) 2.46570e21 0.600151
\(146\) −2.07797e21 4.70193e20i −0.472184 0.106843i
\(147\) −1.19047e22 −2.52664
\(148\) −5.96888e20 + 1.25141e21i −0.118379 + 0.248190i
\(149\) 4.96578e21i 0.920714i 0.887734 + 0.460357i \(0.152279\pi\)
−0.887734 + 0.460357i \(0.847721\pi\)
\(150\) −1.65276e21 3.73979e20i −0.286614 0.0648536i
\(151\) 5.02251e21i 0.814988i 0.913208 + 0.407494i \(0.133597\pi\)
−0.913208 + 0.407494i \(0.866403\pi\)
\(152\) 7.48952e21 + 5.90419e21i 1.13767 + 0.896860i
\(153\) −2.59618e20 −0.0369335
\(154\) 7.17740e20 3.17198e21i 0.0956664 0.422789i
\(155\) −1.14691e22 −1.43288
\(156\) 3.75231e21 7.86695e21i 0.439595 0.921638i
\(157\) 1.25764e22i 1.38216i −0.722777 0.691081i \(-0.757135\pi\)
0.722777 0.691081i \(-0.242865\pi\)
\(158\) 1.12845e21 4.98707e21i 0.116389 0.514369i
\(159\) 1.27853e22i 1.23805i
\(160\) 8.31792e21 4.10204e21i 0.756511 0.373079i
\(161\) 1.06332e22 0.908670
\(162\) 1.25805e22 + 2.84664e21i 1.01052 + 0.228656i
\(163\) −5.79110e20 −0.0437406 −0.0218703 0.999761i \(-0.506962\pi\)
−0.0218703 + 0.999761i \(0.506962\pi\)
\(164\) 1.00714e22 + 4.80377e21i 0.715569 + 0.341306i
\(165\) 2.98575e21i 0.199625i
\(166\) −2.79119e22 6.31576e21i −1.75674 0.397507i
\(167\) 2.14950e22i 1.27401i −0.770861 0.637004i \(-0.780174\pi\)
0.770861 0.637004i \(-0.219826\pi\)
\(168\) 2.10699e22 2.67273e22i 1.17644 1.49232i
\(169\) −9.49847e19 −0.00499789
\(170\) −3.69867e21 + 1.63459e22i −0.183466 + 0.810812i
\(171\) −1.16058e21 −0.0542894
\(172\) −1.46051e21 6.96623e20i −0.0644498 0.0307407i
\(173\) 7.43145e21i 0.309466i −0.987956 0.154733i \(-0.950548\pi\)
0.987956 0.154733i \(-0.0494517\pi\)
\(174\) −4.06864e21 + 1.79810e22i −0.159940 + 0.706839i
\(175\) 1.44997e22i 0.538242i
\(176\) 4.17006e21 + 5.14951e21i 0.146223 + 0.180567i
\(177\) 2.86989e20 0.00950895
\(178\) 2.07021e22 + 4.68437e21i 0.648357 + 0.146707i
\(179\) −3.33062e21 −0.0986267 −0.0493134 0.998783i \(-0.515703\pi\)
−0.0493134 + 0.998783i \(0.515703\pi\)
\(180\) −4.85888e20 + 1.01870e21i −0.0136085 + 0.0285312i
\(181\) 5.92307e22i 1.56950i 0.619813 + 0.784750i \(0.287209\pi\)
−0.619813 + 0.784750i \(0.712791\pi\)
\(182\) −7.27411e22 1.64595e22i −1.82417 0.412765i
\(183\) 2.19586e21i 0.0521307i
\(184\) −1.34126e22 + 1.70139e22i −0.301532 + 0.382496i
\(185\) −1.08918e22 −0.231943
\(186\) 1.89250e22 8.36373e22i 0.381863 1.68760i
\(187\) −1.19738e22 −0.228990
\(188\) −2.71355e22 + 5.68913e22i −0.491994 + 1.03150i
\(189\) 1.06376e23i 1.82906i
\(190\) −1.65343e22 + 7.30719e22i −0.269681 + 1.19183i
\(191\) 1.05814e22i 0.163761i 0.996642 + 0.0818806i \(0.0260926\pi\)
−0.996642 + 0.0818806i \(0.973907\pi\)
\(192\) 1.61885e22 + 6.74266e22i 0.237790 + 0.990420i
\(193\) 4.43070e22 0.617873 0.308937 0.951083i \(-0.400027\pi\)
0.308937 + 0.951083i \(0.400027\pi\)
\(194\) 9.96572e22 + 2.25499e22i 1.31975 + 0.298626i
\(195\) 6.84706e22 0.861307
\(196\) −1.87329e23 8.93504e22i −2.23895 1.06791i
\(197\) 2.36624e22i 0.268779i 0.990929 + 0.134390i \(0.0429074\pi\)
−0.990929 + 0.134390i \(0.957093\pi\)
\(198\) −7.86490e20 1.77963e20i −0.00849261 0.00192166i
\(199\) 7.89983e22i 0.811123i −0.914068 0.405562i \(-0.867076\pi\)
0.914068 0.405562i \(-0.132924\pi\)
\(200\) −2.32006e22 1.82896e22i −0.226568 0.178610i
\(201\) 4.07787e22 0.378854
\(202\) −2.80072e22 + 1.23775e23i −0.247603 + 1.09426i
\(203\) 1.57747e23 1.32740
\(204\) −1.13098e23 5.39446e22i −0.906055 0.432162i
\(205\) 8.76572e22i 0.668727i
\(206\) 4.29643e22 1.89876e23i 0.312202 1.37974i
\(207\) 2.63650e21i 0.0182526i
\(208\) 1.18091e23 9.56295e22i 0.779081 0.630897i
\(209\) −5.35271e22 −0.336597
\(210\) 2.60766e23 + 5.90049e22i 1.56336 + 0.353749i
\(211\) 1.91400e22 0.109425 0.0547127 0.998502i \(-0.482576\pi\)
0.0547127 + 0.998502i \(0.482576\pi\)
\(212\) −9.59598e22 + 2.01186e23i −0.523276 + 1.09708i
\(213\) 1.56716e23i 0.815300i
\(214\) 2.20955e21 + 4.99966e20i 0.0109690 + 0.00248200i
\(215\) 1.27117e22i 0.0602308i
\(216\) 1.70210e23 + 1.34181e23i 0.769924 + 0.606952i
\(217\) −7.33751e23 −3.16921
\(218\) 6.59913e22 2.91642e23i 0.272221 1.20305i
\(219\) 1.25137e23 0.493109
\(220\) −2.24096e22 + 4.69831e22i −0.0843736 + 0.176895i
\(221\) 2.74588e23i 0.988005i
\(222\) 1.79725e22 7.94275e22i 0.0618127 0.273175i
\(223\) 5.23366e22i 0.172090i 0.996291 + 0.0860452i \(0.0274230\pi\)
−0.996291 + 0.0860452i \(0.972577\pi\)
\(224\) 5.32152e23 2.62434e23i 1.67323 0.825164i
\(225\) 3.59518e21 0.0108117
\(226\) 1.48493e23 + 3.36003e22i 0.427191 + 0.0966626i
\(227\) 8.58318e22 0.236260 0.118130 0.992998i \(-0.462310\pi\)
0.118130 + 0.992998i \(0.462310\pi\)
\(228\) −5.05589e23 2.41151e23i −1.33183 0.635244i
\(229\) 3.17833e23i 0.801391i 0.916211 + 0.400695i \(0.131231\pi\)
−0.916211 + 0.400695i \(0.868769\pi\)
\(230\) −1.65998e23 3.75611e22i −0.400704 0.0906692i
\(231\) 1.91018e23i 0.441525i
\(232\) −1.98979e23 + 2.52407e23i −0.440481 + 0.558754i
\(233\) −3.29360e23 −0.698411 −0.349206 0.937046i \(-0.613549\pi\)
−0.349206 + 0.937046i \(0.613549\pi\)
\(234\) −4.08112e21 + 1.80361e22i −0.00829126 + 0.0366424i
\(235\) −4.95158e23 −0.963973
\(236\) 4.51599e21 + 2.15400e21i 0.00842622 + 0.00401906i
\(237\) 3.00324e23i 0.537163i
\(238\) −2.36628e23 + 1.04576e24i −0.405786 + 1.79333i
\(239\) 5.66048e23i 0.930839i −0.885090 0.465419i \(-0.845904\pi\)
0.885090 0.465419i \(-0.154096\pi\)
\(240\) −4.23338e23 + 3.42818e23i −0.667690 + 0.540693i
\(241\) 3.83872e23 0.580786 0.290393 0.956907i \(-0.406214\pi\)
0.290393 + 0.956907i \(0.406214\pi\)
\(242\) 6.35636e23 + 1.43829e23i 0.922688 + 0.208781i
\(243\) −5.37788e22 −0.0749115
\(244\) 1.64810e22 3.45535e22i 0.0220336 0.0461949i
\(245\) 1.63043e24i 2.09238i
\(246\) −6.39234e23 1.44643e23i −0.787605 0.178215i
\(247\) 1.22750e24i 1.45229i
\(248\) 9.25540e23 1.17405e24i 1.05167 1.33405i
\(249\) 1.68087e24 1.83459
\(250\) 2.28752e23 1.01095e24i 0.239864 1.06006i
\(251\) 1.74402e23 0.175717 0.0878586 0.996133i \(-0.471998\pi\)
0.0878586 + 0.996133i \(0.471998\pi\)
\(252\) −3.10854e22 + 6.51726e22i −0.0300990 + 0.0631044i
\(253\) 1.21598e23i 0.113167i
\(254\) 2.93082e23 1.29525e24i 0.262212 1.15882i
\(255\) 9.84359e23i 0.846744i
\(256\) −2.51332e23 + 1.18251e24i −0.207897 + 0.978151i
\(257\) 2.21521e24 1.76231 0.881157 0.472824i \(-0.156765\pi\)
0.881157 + 0.472824i \(0.156765\pi\)
\(258\) 9.26991e22 + 2.09755e22i 0.0709379 + 0.0160515i
\(259\) −6.96818e23 −0.513005
\(260\) 1.07744e24 + 5.13906e23i 0.763234 + 0.364041i
\(261\) 3.91132e22i 0.0266636i
\(262\) −2.73178e24 6.18133e23i −1.79239 0.405573i
\(263\) 5.35900e23i 0.338475i −0.985575 0.169237i \(-0.945870\pi\)
0.985575 0.169237i \(-0.0541305\pi\)
\(264\) −3.05643e23 2.40947e23i −0.185855 0.146515i
\(265\) −1.75103e24 −1.02526
\(266\) −1.05781e24 + 4.67489e24i −0.596473 + 2.63606i
\(267\) −1.24669e24 −0.677089
\(268\) 6.41683e23 + 3.06064e23i 0.335716 + 0.160127i
\(269\) 1.60976e24i 0.811408i 0.914004 + 0.405704i \(0.132974\pi\)
−0.914004 + 0.405704i \(0.867026\pi\)
\(270\) −3.75767e23 + 1.66066e24i −0.182508 + 0.806574i
\(271\) 2.62551e22i 0.0122891i 0.999981 + 0.00614457i \(0.00195589\pi\)
−0.999981 + 0.00614457i \(0.998044\pi\)
\(272\) −1.37481e24 1.69772e24i −0.620230 0.765908i
\(273\) 4.38051e24 1.90501
\(274\) −3.46746e24 7.84600e23i −1.45380 0.328960i
\(275\) 1.65813e23 0.0670334
\(276\) 5.47823e23 1.14855e24i 0.213575 0.447773i
\(277\) 5.84599e22i 0.0219817i −0.999940 0.0109908i \(-0.996501\pi\)
0.999940 0.0109908i \(-0.00349856\pi\)
\(278\) 2.01038e22 + 4.54899e21i 0.00729173 + 0.00164994i
\(279\) 1.81933e23i 0.0636603i
\(280\) 3.66050e24 + 2.88567e24i 1.23583 + 0.974241i
\(281\) −5.61456e24 −1.82916 −0.914581 0.404402i \(-0.867480\pi\)
−0.914581 + 0.404402i \(0.867480\pi\)
\(282\) 8.17057e23 3.61090e24i 0.256898 1.13534i
\(283\) 1.26250e24 0.383149 0.191574 0.981478i \(-0.438641\pi\)
0.191574 + 0.981478i \(0.438641\pi\)
\(284\) 1.17623e24 2.46604e24i 0.344595 0.722466i
\(285\) 4.40043e24i 1.24465i
\(286\) −1.88225e23 + 8.31840e23i −0.0514062 + 0.227185i
\(287\) 5.60800e24i 1.47907i
\(288\) −6.50704e22 1.31947e23i −0.0165752 0.0336104i
\(289\) −1.16643e23 −0.0286998
\(290\) −2.46262e24 5.57230e23i −0.585353 0.132451i
\(291\) −6.00141e24 −1.37823
\(292\) 1.96912e24 + 9.39212e23i 0.436962 + 0.208418i
\(293\) 4.18336e24i 0.897117i 0.893753 + 0.448559i \(0.148062\pi\)
−0.893753 + 0.448559i \(0.851938\pi\)
\(294\) 1.18898e25 + 2.69036e24i 2.46434 + 0.557619i
\(295\) 3.93052e22i 0.00787463i
\(296\) 8.78953e23 1.11496e24i 0.170235 0.215944i
\(297\) −1.21648e24 −0.227793
\(298\) 1.12223e24 4.95958e24i 0.203198 0.898012i
\(299\) −2.78852e24 −0.488273
\(300\) 1.56618e24 + 7.47023e23i 0.265234 + 0.126509i
\(301\) 8.13249e23i 0.133217i
\(302\) 1.13505e24 5.01624e24i 0.179864 0.794893i
\(303\) 7.45378e24i 1.14275i
\(304\) −6.14586e24 7.58939e24i −0.911689 1.12583i
\(305\) 3.00739e23 0.0431709
\(306\) 2.59294e23 + 5.86717e22i 0.0360229 + 0.00815107i
\(307\) 7.79220e24 1.04780 0.523898 0.851781i \(-0.324477\pi\)
0.523898 + 0.851781i \(0.324477\pi\)
\(308\) −1.43369e24 + 3.00581e24i −0.186615 + 0.391251i
\(309\) 1.14344e25i 1.44089i
\(310\) 1.14547e25 + 2.59192e24i 1.39755 + 0.316231i
\(311\) 3.44553e24i 0.407054i −0.979069 0.203527i \(-0.934760\pi\)
0.979069 0.203527i \(-0.0652404\pi\)
\(312\) −5.52549e24 + 7.00913e24i −0.632157 + 0.801896i
\(313\) 1.01897e24 0.112906 0.0564531 0.998405i \(-0.482021\pi\)
0.0564531 + 0.998405i \(0.482021\pi\)
\(314\) −2.84217e24 + 1.25607e25i −0.305037 + 1.34808i
\(315\) −5.67234e23 −0.0589735
\(316\) −2.25408e24 + 4.72582e24i −0.227038 + 0.475999i
\(317\) 1.18213e25i 1.15365i −0.816868 0.576825i \(-0.804292\pi\)
0.816868 0.576825i \(-0.195708\pi\)
\(318\) 2.88937e24 1.27693e25i 0.273232 1.20752i
\(319\) 1.80393e24i 0.165316i
\(320\) −9.23456e24 + 2.21713e24i −0.820194 + 0.196921i
\(321\) −1.33060e23 −0.0114551
\(322\) −1.06199e25 2.40303e24i −0.886265 0.200540i
\(323\) 1.76471e25 1.42774
\(324\) −1.19214e25 5.68618e24i −0.935144 0.446037i
\(325\) 3.80249e24i 0.289224i
\(326\) 5.78387e23 + 1.30874e23i 0.0426621 + 0.00965336i
\(327\) 1.75628e25i 1.25637i
\(328\) −8.97321e24 7.07383e24i −0.622600 0.490813i
\(329\) −3.16784e25 −2.13209
\(330\) 6.74758e23 2.98203e24i 0.0440563 0.194703i
\(331\) 2.48437e25 1.57375 0.786877 0.617110i \(-0.211697\pi\)
0.786877 + 0.617110i \(0.211697\pi\)
\(332\) 2.64497e25 + 1.26157e25i 1.62570 + 0.775411i
\(333\) 1.72775e23i 0.0103048i
\(334\) −4.85770e24 + 2.14681e25i −0.281168 + 1.24259i
\(335\) 5.58493e24i 0.313740i
\(336\) −2.70837e25 + 2.19323e25i −1.47678 + 1.19589i
\(337\) −2.67940e24 −0.141821 −0.0709103 0.997483i \(-0.522590\pi\)
−0.0709103 + 0.997483i \(0.522590\pi\)
\(338\) 9.48661e22 + 2.14658e22i 0.00487466 + 0.00110301i
\(339\) −8.94233e24 −0.446122
\(340\) 7.38811e24 1.54896e25i 0.357885 0.750330i
\(341\) 8.39089e24i 0.394697i
\(342\) 1.15913e24 + 2.62283e23i 0.0529508 + 0.0119814i
\(343\) 6.22590e25i 2.76224i
\(344\) 1.30126e24 + 1.02582e24i 0.0560763 + 0.0442065i
\(345\) 9.99646e24 0.418461
\(346\) −1.67945e24 + 7.42216e24i −0.0682977 + 0.301835i
\(347\) 9.41337e24 0.371921 0.185960 0.982557i \(-0.440460\pi\)
0.185960 + 0.982557i \(0.440460\pi\)
\(348\) 8.12712e24 1.70390e25i 0.311992 0.654112i
\(349\) 3.63487e25i 1.35592i 0.735098 + 0.677960i \(0.237136\pi\)
−0.735098 + 0.677960i \(0.762864\pi\)
\(350\) 3.27682e24 1.44816e25i 0.118788 0.524971i
\(351\) 2.78968e25i 0.982841i
\(352\) −3.00110e24 6.08548e24i −0.102767 0.208386i
\(353\) 1.59639e25 0.531364 0.265682 0.964061i \(-0.414403\pi\)
0.265682 + 0.964061i \(0.414403\pi\)
\(354\) −2.86631e23 6.48573e22i −0.00927449 0.00209858i
\(355\) 2.14634e25 0.675172
\(356\) −1.96176e25 9.35703e24i −0.599993 0.286179i
\(357\) 6.29759e25i 1.87280i
\(358\) 3.32646e24 + 7.52694e23i 0.0961949 + 0.0217665i
\(359\) 3.25820e24i 0.0916292i −0.998950 0.0458146i \(-0.985412\pi\)
0.998950 0.0458146i \(-0.0145883\pi\)
\(360\) 7.15499e23 9.07617e23i 0.0195697 0.0248243i
\(361\) 4.12986e25 1.09866
\(362\) 1.33857e25 5.91567e25i 0.346382 1.53080i
\(363\) −3.82783e25 −0.963577
\(364\) 6.89306e25 + 3.28779e25i 1.68810 + 0.805174i
\(365\) 1.71384e25i 0.408358i
\(366\) −4.96247e23 + 2.19312e24i −0.0115050 + 0.0508453i
\(367\) 2.00995e25i 0.453445i 0.973959 + 0.226722i \(0.0728010\pi\)
−0.973959 + 0.226722i \(0.927199\pi\)
\(368\) 1.72408e25 1.39616e25i 0.378512 0.306518i
\(369\) 1.39050e24 0.0297103
\(370\) 1.08782e25 + 2.46146e24i 0.226224 + 0.0511888i
\(371\) −1.12025e26 −2.26765
\(372\) −3.78028e25 + 7.92560e25i −0.744894 + 1.56172i
\(373\) 5.49354e25i 1.05381i −0.849923 0.526907i \(-0.823352\pi\)
0.849923 0.526907i \(-0.176648\pi\)
\(374\) 1.19589e25 + 2.70599e24i 0.223344 + 0.0505371i
\(375\) 6.08798e25i 1.10703i
\(376\) 3.99586e25 5.06878e25i 0.707509 0.897481i
\(377\) −4.13685e25 −0.713275
\(378\) −2.40402e25 + 1.06244e26i −0.403665 + 1.78396i
\(379\) −8.50762e25 −1.39129 −0.695643 0.718388i \(-0.744880\pi\)
−0.695643 + 0.718388i \(0.744880\pi\)
\(380\) 3.30274e25 6.92440e25i 0.526064 1.10293i
\(381\) 7.80005e25i 1.21017i
\(382\) 2.39132e24 1.05682e25i 0.0361414 0.159723i
\(383\) 4.26912e25i 0.628565i 0.949330 + 0.314282i \(0.101764\pi\)
−0.949330 + 0.314282i \(0.898236\pi\)
\(384\) −9.30377e23 7.10009e25i −0.0133459 1.01848i
\(385\) −2.61613e25 −0.365639
\(386\) −4.42517e25 1.00130e25i −0.602638 0.136362i
\(387\) −2.01644e23 −0.00267594
\(388\) −9.44366e25 4.50435e25i −1.22130 0.582526i
\(389\) 1.17009e26i 1.47477i 0.675472 + 0.737386i \(0.263940\pi\)
−0.675472 + 0.737386i \(0.736060\pi\)
\(390\) −6.83850e25 1.54738e25i −0.840069 0.190087i
\(391\) 4.00889e25i 0.480017i
\(392\) 1.66902e26 + 1.31574e26i 1.94806 + 1.53571i
\(393\) 1.64509e26 1.87182
\(394\) 5.34751e24 2.36328e25i 0.0593184 0.262152i
\(395\) −4.11315e25 −0.444840
\(396\) 7.45289e23 + 3.55481e23i 0.00785910 + 0.00374856i
\(397\) 1.54508e26i 1.58872i −0.607450 0.794358i \(-0.707807\pi\)
0.607450 0.794358i \(-0.292193\pi\)
\(398\) −1.78530e25 + 7.88996e25i −0.179011 + 0.791123i
\(399\) 2.81524e26i 2.75287i
\(400\) 1.90383e25 + 2.35099e25i 0.181563 + 0.224208i
\(401\) −6.14125e25 −0.571232 −0.285616 0.958344i \(-0.592198\pi\)
−0.285616 + 0.958344i \(0.592198\pi\)
\(402\) −4.07277e25 9.21566e24i −0.369513 0.0836115i
\(403\) 1.92423e26 1.70297
\(404\) 5.59443e25 1.17291e26i 0.482995 1.01263i
\(405\) 1.03759e26i 0.873928i
\(406\) −1.57550e26 3.56496e25i −1.29467 0.292951i
\(407\) 7.96854e24i 0.0638903i
\(408\) 1.00766e26 + 7.94366e25i 0.788338 + 0.621468i
\(409\) 1.42600e26 1.08865 0.544323 0.838876i \(-0.316787\pi\)
0.544323 + 0.838876i \(0.316787\pi\)
\(410\) 1.98098e25 8.75477e25i 0.147585 0.652238i
\(411\) 2.08812e26 1.51823
\(412\) −8.58212e25 + 1.79930e26i −0.609007 + 1.27682i
\(413\) 2.51461e24i 0.0174169i
\(414\) −5.95829e23 + 2.63321e24i −0.00402826 + 0.0178025i
\(415\) 2.30207e26i 1.51928i
\(416\) −1.39555e26 + 6.88224e25i −0.899107 + 0.443401i
\(417\) −1.21066e24 −0.00761487
\(418\) 5.34602e25 + 1.20967e25i 0.328298 + 0.0742855i
\(419\) −1.80660e26 −1.08323 −0.541616 0.840626i \(-0.682187\pi\)
−0.541616 + 0.840626i \(0.682187\pi\)
\(420\) −2.47106e26 1.17862e26i −1.44674 0.690053i
\(421\) 8.46001e25i 0.483671i 0.970317 + 0.241835i \(0.0777494\pi\)
−0.970317 + 0.241835i \(0.922251\pi\)
\(422\) −1.91161e25 4.32550e24i −0.106727 0.0241497i
\(423\) 7.85464e24i 0.0428275i
\(424\) 1.41306e26 1.79248e26i 0.752494 0.954546i
\(425\) −5.46660e25 −0.284334
\(426\) −3.54166e25 + 1.56520e26i −0.179933 + 0.795197i
\(427\) 1.92402e25 0.0954841
\(428\) −2.09380e24 9.98682e23i −0.0101507 0.00484161i
\(429\) 5.00938e25i 0.237253i
\(430\) −2.87274e24 + 1.26958e25i −0.0132927 + 0.0587457i
\(431\) 2.88333e26i 1.30353i −0.758420 0.651766i \(-0.774028\pi\)
0.758420 0.651766i \(-0.225972\pi\)
\(432\) −1.39674e26 1.72480e26i −0.616988 0.761905i
\(433\) −9.66878e25 −0.417343 −0.208671 0.977986i \(-0.566914\pi\)
−0.208671 + 0.977986i \(0.566914\pi\)
\(434\) 7.32834e26 + 1.65822e26i 3.09107 + 0.699431i
\(435\) 1.48300e26 0.611293
\(436\) −1.31818e26 + 2.76364e26i −0.531018 + 1.11331i
\(437\) 1.79211e26i 0.705588i
\(438\) −1.24980e26 2.82799e25i −0.480951 0.108827i
\(439\) 6.67083e25i 0.250920i −0.992099 0.125460i \(-0.959959\pi\)
0.992099 0.125460i \(-0.0400406\pi\)
\(440\) 3.29994e25 4.18600e25i 0.121333 0.153912i
\(441\) −2.58634e25 −0.0929607
\(442\) 6.20548e25 2.74245e26i 0.218048 0.963644i
\(443\) −2.09664e26 −0.720257 −0.360129 0.932903i \(-0.617267\pi\)
−0.360129 + 0.932903i \(0.617267\pi\)
\(444\) −3.59000e25 + 7.52667e25i −0.120577 + 0.252798i
\(445\) 1.70743e26i 0.560717i
\(446\) 1.18277e25 5.22712e25i 0.0379796 0.167847i
\(447\) 2.98668e26i 0.937808i
\(448\) −5.90795e26 + 1.41844e26i −1.81408 + 0.435544i
\(449\) −5.39396e26 −1.61974 −0.809868 0.586613i \(-0.800461\pi\)
−0.809868 + 0.586613i \(0.800461\pi\)
\(450\) −3.59069e24 8.12484e23i −0.0105452 0.00238610i
\(451\) 6.41309e25 0.184205
\(452\) −1.40714e26 6.71166e25i −0.395324 0.188558i
\(453\) 3.02080e26i 0.830118i
\(454\) −8.57246e25 1.93973e25i −0.230434 0.0521415i
\(455\) 5.99942e26i 1.57759i
\(456\) 4.50459e26 + 3.55109e26i 1.15880 + 0.913510i
\(457\) 1.14132e25 0.0287240 0.0143620 0.999897i \(-0.495428\pi\)
0.0143620 + 0.999897i \(0.495428\pi\)
\(458\) 7.18278e25 3.17436e26i 0.176863 0.781631i
\(459\) 4.01055e26 0.966223
\(460\) 1.57302e26 + 7.50284e25i 0.370813 + 0.176867i
\(461\) 4.34604e25i 0.100250i −0.998743 0.0501250i \(-0.984038\pi\)
0.998743 0.0501250i \(-0.0159620\pi\)
\(462\) 4.31686e25 1.90780e26i 0.0974425 0.430638i
\(463\) 7.99415e26i 1.76588i −0.469482 0.882942i \(-0.655559\pi\)
0.469482 0.882942i \(-0.344441\pi\)
\(464\) 2.55773e26 2.07124e26i 0.552935 0.447765i
\(465\) −6.89810e26 −1.45949
\(466\) 3.28948e26 + 7.44328e25i 0.681191 + 0.154136i
\(467\) 2.20079e26 0.446077 0.223039 0.974810i \(-0.428402\pi\)
0.223039 + 0.974810i \(0.428402\pi\)
\(468\) 8.15204e24 1.70913e25i 0.0161736 0.0339091i
\(469\) 3.57304e26i 0.693921i
\(470\) 4.94539e26 + 1.11902e26i 0.940204 + 0.212745i
\(471\) 7.56410e26i 1.40782i
\(472\) −4.02356e24 3.17188e24i −0.00733146 0.00577959i
\(473\) −9.30001e24 −0.0165910
\(474\) 6.78709e25 2.99949e26i 0.118550 0.523918i
\(475\) −2.44376e26 −0.417948
\(476\) 4.72665e26 9.90973e26i 0.791560 1.65956i
\(477\) 2.77765e25i 0.0455506i
\(478\) −1.27923e26 + 5.65341e26i −0.205432 + 0.907887i
\(479\) 1.06198e27i 1.67017i 0.550122 + 0.835084i \(0.314581\pi\)
−0.550122 + 0.835084i \(0.685419\pi\)
\(480\) 5.00284e26 2.46718e26i 0.770556 0.380005i
\(481\) 1.82738e26 0.275662
\(482\) −3.83393e26 8.67522e25i −0.566466 0.128177i
\(483\) 6.39538e26 0.925540
\(484\) −6.02338e26 2.87298e26i −0.853860 0.407266i
\(485\) 8.21936e26i 1.14135i
\(486\) 5.37116e25 + 1.21536e25i 0.0730644 + 0.0165326i
\(487\) 2.80248e26i 0.373468i −0.982411 0.186734i \(-0.940210\pi\)
0.982411 0.186734i \(-0.0597902\pi\)
\(488\) −2.42693e25 + 3.07858e25i −0.0316853 + 0.0401931i
\(489\) −3.48307e25 −0.0445527
\(490\) −3.68465e26 + 1.62839e27i −0.461780 + 2.04079i
\(491\) −5.74718e26 −0.705732 −0.352866 0.935674i \(-0.614793\pi\)
−0.352866 + 0.935674i \(0.614793\pi\)
\(492\) 6.05747e26 + 2.88924e26i 0.728854 + 0.347642i
\(493\) 5.94730e26i 0.701215i
\(494\) 2.77407e26 1.22597e27i 0.320514 1.41648i
\(495\) 6.48667e24i 0.00734463i
\(496\) −1.18971e27 + 9.63424e26i −1.32015 + 1.06906i
\(497\) 1.37315e27 1.49333
\(498\) −1.67877e27 3.79863e26i −1.78936 0.404887i
\(499\) −5.06644e26 −0.529295 −0.264648 0.964345i \(-0.585256\pi\)
−0.264648 + 0.964345i \(0.585256\pi\)
\(500\) −4.56934e26 + 9.57990e26i −0.467900 + 0.980982i
\(501\) 1.29282e27i 1.29766i
\(502\) −1.74184e26 3.94135e25i −0.171385 0.0387800i
\(503\) 2.15458e26i 0.207818i 0.994587 + 0.103909i \(0.0331351\pi\)
−0.994587 + 0.103909i \(0.966865\pi\)
\(504\) 4.57751e25 5.80661e25i 0.0432837 0.0549057i
\(505\) 1.02085e27 0.946342
\(506\) −2.74801e25 + 1.21446e26i −0.0249754 + 0.110377i
\(507\) −5.71288e24 −0.00509068
\(508\) −5.85432e26 + 1.22740e27i −0.511493 + 1.07238i
\(509\) 2.11869e26i 0.181506i 0.995873 + 0.0907528i \(0.0289273\pi\)
−0.995873 + 0.0907528i \(0.971073\pi\)
\(510\) −2.22458e26 + 9.83130e26i −0.186873 + 0.825865i
\(511\) 1.09645e27i 0.903193i
\(512\) 5.18257e26 1.12424e27i 0.418645 0.908150i
\(513\) 1.79286e27 1.42027
\(514\) −2.21244e27 5.00620e26i −1.71886 0.388935i
\(515\) −1.56603e27 −1.19324
\(516\) −8.78430e25 4.18986e25i −0.0656463 0.0313114i
\(517\) 3.62263e26i 0.265533i
\(518\) 6.95947e26 + 1.57475e26i 0.500356 + 0.113218i
\(519\) 4.46966e26i 0.315211i
\(520\) −9.59951e26 7.56756e26i −0.664073 0.523507i
\(521\) −4.14659e26 −0.281393 −0.140697 0.990053i \(-0.544934\pi\)
−0.140697 + 0.990053i \(0.544934\pi\)
\(522\) −8.83929e24 + 3.90644e25i −0.00588453 + 0.0260061i
\(523\) −8.08616e26 −0.528111 −0.264056 0.964507i \(-0.585060\pi\)
−0.264056 + 0.964507i \(0.585060\pi\)
\(524\) 2.58867e27 + 1.23472e27i 1.65869 + 0.791145i
\(525\) 8.72087e26i 0.548235i
\(526\) −1.21109e26 + 5.35231e26i −0.0746999 + 0.330129i
\(527\) 2.76635e27i 1.67418i
\(528\) 2.50809e26 + 3.09719e26i 0.148938 + 0.183920i
\(529\) 1.30904e27 0.762775
\(530\) 1.74885e27 + 3.95720e26i 0.999985 + 0.226271i
\(531\) 6.23495e23 0.000349855
\(532\) 2.11298e27 4.42999e27i 1.16353 2.43942i
\(533\) 1.47068e27i 0.794777i
\(534\) 1.24513e27 + 2.81742e26i 0.660394 + 0.149431i
\(535\) 1.82235e25i 0.00948626i
\(536\) −5.71713e26 4.50697e26i −0.292099 0.230270i
\(537\) −2.00321e26 −0.100458
\(538\) 3.63794e26 1.60775e27i 0.179074 0.791401i
\(539\) −1.19284e27 −0.576361
\(540\) 7.50595e26 1.57367e27i 0.356015 0.746408i
\(541\) 3.78702e26i 0.176330i −0.996106 0.0881648i \(-0.971900\pi\)
0.996106 0.0881648i \(-0.0281002\pi\)
\(542\) 5.93346e24 2.62223e25i 0.00271216 0.0119861i
\(543\) 3.56245e27i 1.59864i
\(544\) 9.89418e26 + 2.00629e27i 0.435904 + 0.883905i
\(545\) −2.40536e27 −1.04043
\(546\) −4.37503e27 9.89961e26i −1.85804 0.420428i
\(547\) 3.78029e27 1.57635 0.788173 0.615453i \(-0.211027\pi\)
0.788173 + 0.615453i \(0.211027\pi\)
\(548\) 3.28582e27 + 1.56724e27i 1.34536 + 0.641697i
\(549\) 4.77059e24i 0.00191800i
\(550\) −1.65606e26 3.74724e25i −0.0653805 0.0147940i
\(551\) 2.65865e27i 1.03073i
\(552\) −8.06702e26 + 1.02331e27i −0.307130 + 0.389597i
\(553\) −2.63145e27 −0.983884
\(554\) −1.32115e25 + 5.83869e25i −0.00485126 + 0.0214397i
\(555\) −6.55089e26 −0.236249
\(556\) −1.90507e25 9.08662e24i −0.00674781 0.00321851i
\(557\) 1.66373e27i 0.578803i 0.957208 + 0.289401i \(0.0934563\pi\)
−0.957208 + 0.289401i \(0.906544\pi\)
\(558\) 4.11154e25 1.81706e26i 0.0140496 0.0620907i
\(559\) 2.13272e26i 0.0715838i
\(560\) −3.00378e27 3.70931e27i −0.990350 1.22296i
\(561\) −7.20168e26 −0.233241
\(562\) 5.60754e27 + 1.26885e27i 1.78406 + 0.403688i
\(563\) −1.91718e27 −0.599211 −0.299606 0.954063i \(-0.596855\pi\)
−0.299606 + 0.954063i \(0.596855\pi\)
\(564\) −1.63207e27 + 3.42174e27i −0.501128 + 1.05065i
\(565\) 1.22472e27i 0.369446i
\(566\) −1.26092e27 2.85316e26i −0.373701 0.0845593i
\(567\) 6.63814e27i 1.93293i
\(568\) −1.73207e27 + 2.19714e27i −0.495544 + 0.628601i
\(569\) −4.08427e27 −1.14813 −0.574066 0.818809i \(-0.694635\pi\)
−0.574066 + 0.818809i \(0.694635\pi\)
\(570\) −9.94462e26 + 4.39493e27i −0.274688 + 1.21396i
\(571\) −5.81506e26 −0.157831 −0.0789157 0.996881i \(-0.525146\pi\)
−0.0789157 + 0.996881i \(0.525146\pi\)
\(572\) 3.75979e26 7.88264e26i 0.100277 0.210238i
\(573\) 6.36423e26i 0.166801i
\(574\) 1.26736e27 5.60099e27i 0.326424 1.44260i
\(575\) 5.55150e26i 0.140518i
\(576\) 3.51702e25 + 1.46487e26i 0.00874883 + 0.0364397i
\(577\) 2.69062e27 0.657801 0.328901 0.944365i \(-0.393322\pi\)
0.328901 + 0.944365i \(0.393322\pi\)
\(578\) 1.16497e26 + 2.63603e25i 0.0279921 + 0.00633392i
\(579\) 2.66486e27 0.629344
\(580\) 2.33362e27 + 1.11307e27i 0.541688 + 0.258370i
\(581\) 1.47278e28i 3.36030i
\(582\) 5.99391e27 + 1.35627e27i 1.34425 + 0.304170i
\(583\) 1.28108e27i 0.282416i
\(584\) −1.75440e27 1.38304e27i −0.380190 0.299715i
\(585\) 1.48755e26 0.0316893
\(586\) 9.45408e26 4.17814e27i 0.197990 0.874997i
\(587\) −8.87574e26 −0.182736 −0.0913678 0.995817i \(-0.529124\pi\)
−0.0913678 + 0.995817i \(0.529124\pi\)
\(588\) −1.12669e28 5.37400e27i −2.28051 1.08774i
\(589\) 1.23666e28i 2.46091i
\(590\) 8.88268e24 3.92561e25i 0.00173790 0.00768046i
\(591\) 1.42318e27i 0.273769i
\(592\) −1.12983e27 + 9.14930e26i −0.213695 + 0.173050i
\(593\) 2.28118e27 0.424241 0.212120 0.977244i \(-0.431963\pi\)
0.212120 + 0.977244i \(0.431963\pi\)
\(594\) 1.21496e27 + 2.74915e26i 0.222176 + 0.0502729i
\(595\) 8.62500e27 1.55092
\(596\) −2.24165e27 + 4.69977e27i −0.396375 + 0.831025i
\(597\) 4.75137e27i 0.826182i
\(598\) 2.78504e27 + 6.30185e26i 0.476233 + 0.107760i
\(599\) 4.01414e27i 0.675032i 0.941320 + 0.337516i \(0.109587\pi\)
−0.941320 + 0.337516i \(0.890413\pi\)
\(600\) −1.39540e27 1.10003e27i −0.230774 0.181926i
\(601\) −9.03918e27 −1.47023 −0.735114 0.677944i \(-0.762871\pi\)
−0.735114 + 0.677944i \(0.762871\pi\)
\(602\) −1.83788e26 + 8.12234e26i −0.0294003 + 0.129932i
\(603\) 8.85933e25 0.0139389
\(604\) −2.26726e27 + 4.75346e27i −0.350859 + 0.735597i
\(605\) 5.24249e27i 0.797965i
\(606\) −1.68450e27 + 7.44447e27i −0.252199 + 1.11457i
\(607\) 9.64789e27i 1.42084i −0.703777 0.710421i \(-0.748505\pi\)
0.703777 0.710421i \(-0.251495\pi\)
\(608\) 4.42304e27 + 8.96883e27i 0.640745 + 1.29927i
\(609\) 9.48773e27 1.35204
\(610\) −3.00363e26 6.79646e25i −0.0421064 0.00952763i
\(611\) 8.30755e27 1.14567
\(612\) −2.45711e26 1.17197e26i −0.0333357 0.0159002i
\(613\) 3.72539e26i 0.0497241i 0.999691 + 0.0248620i \(0.00791465\pi\)
−0.999691 + 0.0248620i \(0.992085\pi\)
\(614\) −7.78247e27 1.76098e27i −1.02196 0.231244i
\(615\) 5.27216e27i 0.681142i
\(616\) 2.11119e27 2.67806e27i 0.268361 0.340418i
\(617\) 4.15904e27 0.520165 0.260083 0.965586i \(-0.416250\pi\)
0.260083 + 0.965586i \(0.416250\pi\)
\(618\) 2.58410e27 1.14202e28i 0.317998 1.40536i
\(619\) 1.08544e28 1.31431 0.657154 0.753756i \(-0.271760\pi\)
0.657154 + 0.753756i \(0.271760\pi\)
\(620\) −1.08547e28 5.17737e27i −1.29330 0.616868i
\(621\) 4.07283e27i 0.477508i
\(622\) −7.78662e26 + 3.44122e27i −0.0898349 + 0.397017i
\(623\) 1.09236e28i 1.24018i
\(624\) 7.10260e27 5.75166e27i 0.793545 0.642610i
\(625\) −5.71401e27 −0.628262
\(626\) −1.01770e27 2.30279e26i −0.110122 0.0249179i
\(627\) −3.21940e27 −0.342846
\(628\) 5.67723e27 1.19027e28i 0.595032 1.24752i
\(629\) 2.62711e27i 0.271002i
\(630\) 5.66526e26 + 1.28191e26i 0.0575194 + 0.0130152i
\(631\) 3.07267e27i 0.307060i 0.988144 + 0.153530i \(0.0490641\pi\)
−0.988144 + 0.153530i \(0.950936\pi\)
\(632\) 3.31926e27 4.21051e27i 0.326491 0.414156i
\(633\) 1.15118e27 0.111457
\(634\) −2.67153e27 + 1.18066e28i −0.254605 + 1.12520i
\(635\) −1.06827e28 −1.00218
\(636\) −5.77153e27 + 1.21004e28i −0.532991 + 1.11745i
\(637\) 2.73547e28i 2.48678i
\(638\) −4.07675e26 + 1.80168e27i −0.0364844 + 0.161239i
\(639\) 3.40472e26i 0.0299966i
\(640\) 9.72409e27 1.27422e26i 0.843430 0.0110521i
\(641\) −1.90529e28 −1.62697 −0.813485 0.581586i \(-0.802433\pi\)
−0.813485 + 0.581586i \(0.802433\pi\)
\(642\) 1.32894e26 + 3.00706e25i 0.0111726 + 0.00252808i
\(643\) −1.05796e28 −0.875711 −0.437856 0.899045i \(-0.644262\pi\)
−0.437856 + 0.899045i \(0.644262\pi\)
\(644\) 1.00636e28 + 4.80005e27i 0.820154 + 0.391190i
\(645\) 7.64548e26i 0.0613490i
\(646\) −1.76250e28 3.98810e27i −1.39253 0.315095i
\(647\) 3.30511e27i 0.257124i 0.991701 + 0.128562i \(0.0410361\pi\)
−0.991701 + 0.128562i \(0.958964\pi\)
\(648\) 1.06215e28 + 8.37323e27i 0.813648 + 0.641421i
\(649\) 2.87561e25 0.00216912
\(650\) −8.59333e26 + 3.79774e27i −0.0638304 + 0.282092i
\(651\) −4.41316e28 −3.22805
\(652\) −5.48087e26 2.61422e26i −0.0394797 0.0188307i
\(653\) 1.75915e28i 1.24787i −0.781475 0.623937i \(-0.785532\pi\)
0.781475 0.623937i \(-0.214468\pi\)
\(654\) 3.96906e27 1.75409e28i 0.277275 1.22539i
\(655\) 2.25307e28i 1.55011i
\(656\) 7.36337e27 + 9.09287e27i 0.498928 + 0.616116i
\(657\) 2.71864e26 0.0181426
\(658\) 3.16389e28 + 7.15909e27i 2.07952 + 0.470542i
\(659\) 1.99713e28 1.29287 0.646433 0.762971i \(-0.276260\pi\)
0.646433 + 0.762971i \(0.276260\pi\)
\(660\) −1.34783e27 + 2.82581e27i −0.0859401 + 0.180179i
\(661\) 9.97708e27i 0.626598i −0.949655 0.313299i \(-0.898566\pi\)
0.949655 0.313299i \(-0.101434\pi\)
\(662\) −2.48127e28 5.61449e27i −1.53495 0.347320i
\(663\) 1.65152e28i 1.00635i
\(664\) −2.35656e28 1.85774e28i −1.41448 1.11508i
\(665\) 3.85567e28 2.27973
\(666\) 3.90459e25 1.72560e26i 0.00227422 0.0100507i
\(667\) −6.03966e27 −0.346541
\(668\) 9.70326e27 2.03435e28i 0.548470 1.14990i
\(669\) 3.14780e27i 0.175285i
\(670\) 1.26215e27 5.57796e27i 0.0692410 0.306004i
\(671\) 2.20024e26i 0.0118917i
\(672\) 3.20064e28 1.57842e28i 1.70429 0.840484i
\(673\) 1.56242e28 0.819683 0.409841 0.912157i \(-0.365584\pi\)
0.409841 + 0.912157i \(0.365584\pi\)
\(674\) 2.67606e27 + 6.05525e26i 0.138324 + 0.0312992i
\(675\) −5.55380e27 −0.282847
\(676\) −8.98965e25 4.28780e25i −0.00451103 0.00215163i
\(677\) 2.96609e28i 1.46655i −0.679932 0.733275i \(-0.737991\pi\)
0.679932 0.733275i \(-0.262009\pi\)
\(678\) 8.93116e27 + 2.02090e27i 0.435122 + 0.0984571i
\(679\) 5.25846e28i 2.52441i
\(680\) −1.08794e28 + 1.38006e28i −0.514655 + 0.652845i
\(681\) 5.16238e27 0.240646
\(682\) 1.89628e27 8.38041e27i 0.0871080 0.384965i
\(683\) −8.85063e27 −0.400652 −0.200326 0.979729i \(-0.564200\pi\)
−0.200326 + 0.979729i \(0.564200\pi\)
\(684\) −1.09841e27 5.23911e26i −0.0490009 0.0233720i
\(685\) 2.85983e28i 1.25729i
\(686\) −1.40701e28 + 6.21813e28i −0.609614 + 2.69413i
\(687\) 1.91162e28i 0.816269i
\(688\) −1.06781e27 1.31861e27i −0.0449374 0.0554923i
\(689\) 2.93782e28 1.21852
\(690\) −9.98397e27 2.25912e27i −0.408143 0.0923525i
\(691\) 2.99742e27 0.120772 0.0603862 0.998175i \(-0.480767\pi\)
0.0603862 + 0.998175i \(0.480767\pi\)
\(692\) 3.35470e27 7.03335e27i 0.133227 0.279320i
\(693\) 4.14995e26i 0.0162446i
\(694\) −9.40161e27 2.12735e27i −0.362750 0.0820813i
\(695\) 1.65809e26i 0.00630609i
\(696\) −1.19677e28 + 1.51811e28i −0.448659 + 0.569128i
\(697\) −2.11430e28 −0.781339
\(698\) 8.21452e27 3.63033e28i 0.299246 1.32249i
\(699\) −1.98094e28 −0.711378
\(700\) −6.54545e27 + 1.37229e28i −0.231718 + 0.485811i
\(701\) 3.99234e26i 0.0139331i 0.999976 + 0.00696655i \(0.00221754\pi\)
−0.999976 + 0.00696655i \(0.997782\pi\)
\(702\) 6.30446e27 2.78620e28i 0.216909 0.958607i
\(703\) 1.17441e28i 0.398351i
\(704\) 1.62208e27 + 6.75611e27i 0.0542432 + 0.225928i
\(705\) −2.97814e28 −0.981869
\(706\) −1.59440e28 3.60772e27i −0.518262 0.117270i
\(707\) 6.53104e28 2.09309
\(708\) 2.71615e26 + 1.29553e26i 0.00858265 + 0.00409368i
\(709\) 2.52620e28i 0.787055i 0.919313 + 0.393528i \(0.128745\pi\)
−0.919313 + 0.393528i \(0.871255\pi\)
\(710\) −2.14366e28 4.85056e27i −0.658524 0.149008i
\(711\) 6.52466e26i 0.0197634i
\(712\) 1.74785e28 + 1.37788e28i 0.522040 + 0.411539i
\(713\) 2.80931e28 0.827379
\(714\) −1.42321e28 + 6.28972e28i −0.413319 + 1.82662i
\(715\) 6.86071e27 0.196476
\(716\) −3.15220e27 1.50351e27i −0.0890192 0.0424596i
\(717\) 3.40451e28i 0.948120i
\(718\) −7.36329e26 + 3.25413e27i −0.0202222 + 0.0893699i
\(719\) 2.54621e28i 0.689612i 0.938674 + 0.344806i \(0.112055\pi\)
−0.938674 + 0.344806i \(0.887945\pi\)
\(720\) −9.19720e26 + 7.44786e26i −0.0245658 + 0.0198933i
\(721\) −1.00189e29 −2.63917
\(722\) −4.12470e28 9.33316e27i −1.07157 0.242469i
\(723\) 2.30881e28 0.591569
\(724\) −2.67379e28 + 5.60578e28i −0.675682 + 1.41661i
\(725\) 8.23580e27i 0.205270i
\(726\) 3.82305e28 + 8.65060e27i 0.939818 + 0.212657i
\(727\) 4.09725e28i 0.993455i 0.867907 + 0.496728i \(0.165465\pi\)
−0.867907 + 0.496728i \(0.834535\pi\)
\(728\) −6.14143e28 4.84146e28i −1.46878 1.15788i
\(729\) 4.06857e28 0.959769
\(730\) 3.87314e27 1.71170e28i 0.0901227 0.398289i
\(731\) 3.06608e27 0.0703735
\(732\) 9.91255e26 2.07823e27i 0.0224427 0.0470525i
\(733\) 1.43241e28i 0.319911i −0.987124 0.159955i \(-0.948865\pi\)
0.987124 0.159955i \(-0.0511350\pi\)
\(734\) 4.54233e27 2.00744e28i 0.100073 0.442264i
\(735\) 9.80626e28i 2.13123i
\(736\) −2.03745e28 + 1.00478e28i −0.436826 + 0.215424i
\(737\) 4.08600e27 0.0864217
\(738\) −1.38876e27 3.14242e26i −0.0289777 0.00655693i
\(739\) 7.87579e28 1.62125 0.810624 0.585567i \(-0.199128\pi\)
0.810624 + 0.585567i \(0.199128\pi\)
\(740\) −1.03083e28 4.91677e27i −0.209349 0.0998533i
\(741\) 7.38286e28i 1.47925i
\(742\) 1.11885e29 + 2.53168e28i 2.21174 + 0.500461i
\(743\) 5.32560e28i 1.03868i −0.854569 0.519338i \(-0.826178\pi\)
0.854569 0.519338i \(-0.173822\pi\)
\(744\) 5.56668e28 7.06138e28i 1.07119 1.35882i
\(745\) −4.09048e28 −0.776625
\(746\) −1.24150e28 + 5.48668e28i −0.232572 + 1.02783i
\(747\) 3.65175e27 0.0674987
\(748\) −1.13324e28 5.40522e27i −0.206683 0.0985819i
\(749\) 1.16588e27i 0.0209814i
\(750\) 1.37584e28 6.08038e28i 0.244318 1.07974i
\(751\) 9.40055e28i 1.64723i 0.567151 + 0.823614i \(0.308046\pi\)
−0.567151 + 0.823614i \(0.691954\pi\)
\(752\) −5.13638e28 + 4.15942e28i −0.888134 + 0.719208i
\(753\) 1.04895e28 0.178979
\(754\) 4.13169e28 + 9.34897e27i 0.695687 + 0.157417i
\(755\) −4.13720e28 −0.687444
\(756\) 4.80204e28 1.00678e29i 0.787423 1.65088i
\(757\) 5.34938e28i 0.865654i −0.901477 0.432827i \(-0.857516\pi\)
0.901477 0.432827i \(-0.142484\pi\)
\(758\) 8.49700e28 + 1.92266e28i 1.35698 + 0.307051i
\(759\) 7.31352e27i 0.115268i
\(760\)