Properties

Label 8.21.d.b.3.12
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 3.12
Root \(14907.4 - 4.14330e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.11

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(492.862 + 897.587i) q^{2}\) \(+53283.8 q^{3}\) \(+(-562749. + 884774. i) q^{4}\) \(+1.65732e7i q^{5}\) \(+(2.62616e7 + 4.78269e7i) q^{6}\) \(-1.30215e8i q^{7}\) \(+(-1.07152e9 - 6.90447e7i) q^{8}\) \(-6.47621e8 q^{9}\) \(+O(q^{10})\) \(q\)\(+(492.862 + 897.587i) q^{2}\) \(+53283.8 q^{3}\) \(+(-562749. + 884774. i) q^{4}\) \(+1.65732e7i q^{5}\) \(+(2.62616e7 + 4.78269e7i) q^{6}\) \(-1.30215e8i q^{7}\) \(+(-1.07152e9 - 6.90447e7i) q^{8}\) \(-6.47621e8 q^{9}\) \(+(-1.48759e10 + 8.16831e9i) q^{10}\) \(+2.41984e10 q^{11}\) \(+(-2.99854e10 + 4.71441e10i) q^{12}\) \(+6.71986e10i q^{13}\) \(+(1.16879e11 - 6.41782e10i) q^{14}\) \(+8.83083e11i q^{15}\) \(+(-4.66138e11 - 9.95812e11i) q^{16}\) \(-2.87376e12 q^{17}\) \(+(-3.19188e11 - 5.81296e11i) q^{18}\) \(+7.21183e12 q^{19}\) \(+(-1.46635e13 - 9.32656e12i) q^{20}\) \(-6.93836e12i q^{21}\) \(+(1.19265e13 + 2.17202e13i) q^{22}\) \(+2.96291e12i q^{23}\) \(+(-5.70946e13 - 3.67896e12i) q^{24}\) \(-1.79304e14 q^{25}\) \(+(-6.03166e13 + 3.31196e13i) q^{26}\) \(-2.20297e14 q^{27}\) \(+(1.15211e14 + 7.32785e13i) q^{28}\) \(+4.38340e14i q^{29}\) \(+(-7.92644e14 + 4.35239e14i) q^{30}\) \(-9.28550e14i q^{31}\) \(+(6.64086e14 - 9.09198e14i) q^{32}\) \(+1.28938e15 q^{33}\) \(+(-1.41637e15 - 2.57945e15i) q^{34}\) \(+2.15808e15 q^{35}\) \(+(3.64448e14 - 5.72998e14i) q^{36}\) \(+7.26660e15i q^{37}\) \(+(3.55444e15 + 6.47324e15i) q^{38}\) \(+3.58059e15i q^{39}\) \(+(1.14429e15 - 1.77585e16i) q^{40}\) \(-1.47814e15 q^{41}\) \(+(6.22778e15 - 3.41966e15i) q^{42}\) \(+3.77390e16 q^{43}\) \(+(-1.36177e16 + 2.14101e16i) q^{44}\) \(-1.07332e16i q^{45}\) \(+(-2.65947e15 + 1.46031e15i) q^{46}\) \(+5.25428e16i q^{47}\) \(+(-2.48376e16 - 5.30606e16i) q^{48}\) \(+6.28363e16 q^{49}\) \(+(-8.83720e16 - 1.60941e17i) q^{50}\) \(-1.53125e17 q^{51}\) \(+(-5.94555e16 - 3.78159e16i) q^{52}\) \(+2.49723e17i q^{53}\) \(+(-1.08576e17 - 1.97736e17i) q^{54}\) \(+4.01046e17i q^{55}\) \(+(-8.99066e15 + 1.39528e17i) q^{56}\) \(+3.84274e17 q^{57}\) \(+(-3.93448e17 + 2.16041e17i) q^{58}\) \(+2.43410e17 q^{59}\) \(+(-7.81329e17 - 4.96954e17i) q^{60}\) \(-5.14944e17i q^{61}\) \(+(8.33455e17 - 4.57647e17i) q^{62}\) \(+8.43301e16i q^{63}\) \(+(1.14339e18 + 1.47965e17i) q^{64}\) \(-1.11370e18 q^{65}\) \(+(6.35489e17 + 1.15734e18i) q^{66}\) \(+2.15425e18 q^{67}\) \(+(1.61721e18 - 2.54263e18i) q^{68}\) \(+1.57875e17i q^{69}\) \(+(1.06364e18 + 1.93707e18i) q^{70}\) \(-1.26970e18i q^{71}\) \(+(6.93939e17 + 4.47148e16i) q^{72}\) \(+3.77047e18 q^{73}\) \(+(-6.52240e18 + 3.58143e18i) q^{74}\) \(-9.55398e18 q^{75}\) \(+(-4.05845e18 + 6.38084e18i) q^{76}\) \(-3.15100e18i q^{77}\) \(+(-3.21390e18 + 1.76474e18i) q^{78}\) \(-2.34036e18i q^{79}\) \(+(1.65038e19 - 7.72540e18i) q^{80}\) \(-9.48014e18 q^{81}\) \(+(-7.28522e17 - 1.32676e18i) q^{82}\) \(-1.71472e19 q^{83}\) \(+(6.13888e18 + 3.90456e18i) q^{84}\) \(-4.76275e19i q^{85}\) \(+(1.86001e19 + 3.38740e19i) q^{86}\) \(+2.33564e19i q^{87}\) \(+(-2.59291e19 - 1.67077e18i) q^{88}\) \(+6.55204e18 q^{89}\) \(+(9.63394e18 - 5.28997e18i) q^{90}\) \(+8.75027e18 q^{91}\) \(+(-2.62150e18 - 1.66738e18i) q^{92}\) \(-4.94767e19i q^{93}\) \(+(-4.71617e19 + 2.58964e19i) q^{94}\) \(+1.19523e20i q^{95}\) \(+(3.53850e19 - 4.84455e19i) q^{96}\) \(+1.29767e20 q^{97}\) \(+(3.09696e19 + 5.64010e19i) q^{98}\) \(-1.56714e19 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 492.862 + 897.587i 0.481311 + 0.876550i
\(3\) 53283.8 0.902366 0.451183 0.892432i \(-0.351002\pi\)
0.451183 + 0.892432i \(0.351002\pi\)
\(4\) −562749. + 884774.i −0.536680 + 0.843786i
\(5\) 1.65732e7i 1.69710i 0.529118 + 0.848548i \(0.322523\pi\)
−0.529118 + 0.848548i \(0.677477\pi\)
\(6\) 2.62616e7 + 4.78269e7i 0.434319 + 0.790969i
\(7\) 1.30215e8i 0.460979i −0.973075 0.230490i \(-0.925967\pi\)
0.973075 0.230490i \(-0.0740327\pi\)
\(8\) −1.07152e9 6.90447e7i −0.997930 0.0643029i
\(9\) −6.47621e8 −0.185736
\(10\) −1.48759e10 + 8.16831e9i −1.48759 + 0.816831i
\(11\) 2.41984e10 0.932954 0.466477 0.884533i \(-0.345523\pi\)
0.466477 + 0.884533i \(0.345523\pi\)
\(12\) −2.99854e10 + 4.71441e10i −0.484281 + 0.761404i
\(13\) 6.71986e10i 0.487446i 0.969845 + 0.243723i \(0.0783688\pi\)
−0.969845 + 0.243723i \(0.921631\pi\)
\(14\) 1.16879e11 6.41782e10i 0.404071 0.221874i
\(15\) 8.83083e11i 1.53140i
\(16\) −4.66138e11 9.95812e11i −0.423950 0.905686i
\(17\) −2.87376e12 −1.42548 −0.712741 0.701427i \(-0.752547\pi\)
−0.712741 + 0.701427i \(0.752547\pi\)
\(18\) −3.19188e11 5.81296e11i −0.0893967 0.162807i
\(19\) 7.21183e12 1.17628 0.588138 0.808761i \(-0.299861\pi\)
0.588138 + 0.808761i \(0.299861\pi\)
\(20\) −1.46635e13 9.32656e12i −1.43199 0.910797i
\(21\) 6.93836e12i 0.415972i
\(22\) 1.19265e13 + 2.17202e13i 0.449041 + 0.817781i
\(23\) 2.96291e12i 0.0715221i 0.999360 + 0.0357610i \(0.0113855\pi\)
−0.999360 + 0.0357610i \(0.988614\pi\)
\(24\) −5.70946e13 3.67896e12i −0.900498 0.0580247i
\(25\) −1.79304e14 −1.88014
\(26\) −6.03166e13 + 3.31196e13i −0.427271 + 0.234613i
\(27\) −2.20297e14 −1.06997
\(28\) 1.15211e14 + 7.32785e13i 0.388968 + 0.247398i
\(29\) 4.38340e14i 1.04191i 0.853583 + 0.520956i \(0.174425\pi\)
−0.853583 + 0.520956i \(0.825575\pi\)
\(30\) −7.92644e14 + 4.35239e14i −1.34235 + 0.737080i
\(31\) 9.28550e14i 1.13289i −0.824099 0.566446i \(-0.808318\pi\)
0.824099 0.566446i \(-0.191682\pi\)
\(32\) 6.64086e14 9.09198e14i 0.589827 0.807530i
\(33\) 1.28938e15 0.841866
\(34\) −1.41637e15 2.57945e15i −0.686100 1.24951i
\(35\) 2.15808e15 0.782326
\(36\) 3.64448e14 5.72998e14i 0.0996807 0.156721i
\(37\) 7.26660e15i 1.51117i 0.655050 + 0.755586i \(0.272648\pi\)
−0.655050 + 0.755586i \(0.727352\pi\)
\(38\) 3.55444e15 + 6.47324e15i 0.566155 + 1.03106i
\(39\) 3.58059e15i 0.439855i
\(40\) 1.14429e15 1.77585e16i 0.109128 1.69358i
\(41\) −1.47814e15 −0.110123 −0.0550616 0.998483i \(-0.517536\pi\)
−0.0550616 + 0.998483i \(0.517536\pi\)
\(42\) 6.22778e15 3.41966e15i 0.364620 0.200212i
\(43\) 3.77390e16 1.74625 0.873124 0.487498i \(-0.162090\pi\)
0.873124 + 0.487498i \(0.162090\pi\)
\(44\) −1.36177e16 + 2.14101e16i −0.500698 + 0.787214i
\(45\) 1.07332e16i 0.315212i
\(46\) −2.65947e15 + 1.46031e15i −0.0626927 + 0.0344244i
\(47\) 5.25428e16i 0.998928i 0.866335 + 0.499464i \(0.166470\pi\)
−0.866335 + 0.499464i \(0.833530\pi\)
\(48\) −2.48376e16 5.30606e16i −0.382558 0.817260i
\(49\) 6.28363e16 0.787498
\(50\) −8.83720e16 1.60941e17i −0.904930 1.64803i
\(51\) −1.53125e17 −1.28631
\(52\) −5.94555e16 3.78159e16i −0.411300 0.261602i
\(53\) 2.49723e17i 1.42790i 0.700194 + 0.713952i \(0.253097\pi\)
−0.700194 + 0.713952i \(0.746903\pi\)
\(54\) −1.08576e17 1.97736e17i −0.514987 0.937880i
\(55\) 4.01046e17i 1.58331i
\(56\) −8.99066e15 + 1.39528e17i −0.0296423 + 0.460025i
\(57\) 3.84274e17 1.06143
\(58\) −3.93448e17 + 2.16041e17i −0.913288 + 0.501484i
\(59\) 2.43410e17 0.476232 0.238116 0.971237i \(-0.423470\pi\)
0.238116 + 0.971237i \(0.423470\pi\)
\(60\) −7.81329e17 4.96954e17i −1.29218 0.821872i
\(61\) 5.14944e17i 0.721874i −0.932590 0.360937i \(-0.882457\pi\)
0.932590 0.360937i \(-0.117543\pi\)
\(62\) 8.33455e17 4.57647e17i 0.993036 0.545273i
\(63\) 8.43301e16i 0.0856204i
\(64\) 1.14339e18 + 1.47965e17i 0.991730 + 0.128340i
\(65\) −1.11370e18 −0.827243
\(66\) 6.35489e17 + 1.15734e18i 0.405199 + 0.737938i
\(67\) 2.15425e18 1.18181 0.590906 0.806740i \(-0.298770\pi\)
0.590906 + 0.806740i \(0.298770\pi\)
\(68\) 1.61721e18 2.54263e18i 0.765027 1.20280i
\(69\) 1.57875e17i 0.0645391i
\(70\) 1.06364e18 + 1.93707e18i 0.376542 + 0.685748i
\(71\) 1.26970e18i 0.390048i −0.980799 0.195024i \(-0.937522\pi\)
0.980799 0.195024i \(-0.0624784\pi\)
\(72\) 6.93939e17 + 4.47148e16i 0.185352 + 0.0119434i
\(73\) 3.77047e18 0.877337 0.438668 0.898649i \(-0.355450\pi\)
0.438668 + 0.898649i \(0.355450\pi\)
\(74\) −6.52240e18 + 3.58143e18i −1.32462 + 0.727344i
\(75\) −9.55398e18 −1.69657
\(76\) −4.05845e18 + 6.38084e18i −0.631283 + 0.992526i
\(77\) 3.15100e18i 0.430072i
\(78\) −3.21390e18 + 1.76474e18i −0.385554 + 0.211707i
\(79\) 2.34036e18i 0.247179i −0.992333 0.123590i \(-0.960559\pi\)
0.992333 0.123590i \(-0.0394407\pi\)
\(80\) 1.65038e19 7.72540e18i 1.53704 0.719484i
\(81\) −9.48014e18 −0.779766
\(82\) −7.28522e17 1.32676e18i −0.0530035 0.0965284i
\(83\) −1.71472e19 −1.10513 −0.552563 0.833471i \(-0.686350\pi\)
−0.552563 + 0.833471i \(0.686350\pi\)
\(84\) 6.13888e18 + 3.90456e18i 0.350991 + 0.223244i
\(85\) 4.76275e19i 2.41918i
\(86\) 1.86001e19 + 3.38740e19i 0.840488 + 1.53067i
\(87\) 2.33564e19i 0.940186i
\(88\) −2.59291e19 1.67077e18i −0.931024 0.0599916i
\(89\) 6.55204e18 0.210124 0.105062 0.994466i \(-0.466496\pi\)
0.105062 + 0.994466i \(0.466496\pi\)
\(90\) 9.63394e18 5.28997e18i 0.276299 0.151715i
\(91\) 8.75027e18 0.224702
\(92\) −2.62150e18 1.66738e18i −0.0603493 0.0383844i
\(93\) 4.94767e19i 1.02228i
\(94\) −4.71617e19 + 2.58964e19i −0.875611 + 0.480795i
\(95\) 1.19523e20i 1.99625i
\(96\) 3.53850e19 4.84455e19i 0.532239 0.728687i
\(97\) 1.29767e20 1.75973 0.879866 0.475221i \(-0.157632\pi\)
0.879866 + 0.475221i \(0.157632\pi\)
\(98\) 3.09696e19 + 5.64010e19i 0.379032 + 0.690282i
\(99\) −1.56714e19 −0.173283
\(100\) 1.00903e20 1.58643e20i 1.00903 1.58643i
\(101\) 8.89506e19i 0.805258i 0.915363 + 0.402629i \(0.131904\pi\)
−0.915363 + 0.402629i \(0.868096\pi\)
\(102\) −7.54696e19 1.37443e20i −0.619113 1.12751i
\(103\) 2.01768e19i 0.150135i 0.997178 + 0.0750673i \(0.0239172\pi\)
−0.997178 + 0.0750673i \(0.976083\pi\)
\(104\) 4.63970e18 7.20046e19i 0.0313442 0.486437i
\(105\) 1.14991e20 0.705944
\(106\) −2.24148e20 + 1.23079e20i −1.25163 + 0.687266i
\(107\) −1.20079e20 −0.610423 −0.305211 0.952285i \(-0.598727\pi\)
−0.305211 + 0.952285i \(0.598727\pi\)
\(108\) 1.23972e20 1.94913e20i 0.574230 0.902824i
\(109\) 2.24102e20i 0.946633i −0.880893 0.473316i \(-0.843057\pi\)
0.880893 0.473316i \(-0.156943\pi\)
\(110\) −3.59973e20 + 1.97660e20i −1.38785 + 0.762066i
\(111\) 3.87192e20i 1.36363i
\(112\) −1.29670e20 + 6.06983e19i −0.417502 + 0.195432i
\(113\) −1.49362e20 −0.440003 −0.220001 0.975500i \(-0.570606\pi\)
−0.220001 + 0.975500i \(0.570606\pi\)
\(114\) 1.89394e20 + 3.44919e20i 0.510879 + 0.930398i
\(115\) −4.91049e19 −0.121380
\(116\) −3.87832e20 2.46676e20i −0.879151 0.559173i
\(117\) 4.35192e19i 0.0905362i
\(118\) 1.19968e20 + 2.18482e20i 0.229216 + 0.417441i
\(119\) 3.74208e20i 0.657118i
\(120\) 6.09722e19 9.46241e20i 0.0984735 1.52823i
\(121\) −8.71857e19 −0.129596
\(122\) 4.62207e20 2.53797e20i 0.632759 0.347446i
\(123\) −7.87612e19 −0.0993713
\(124\) 8.21557e20 + 5.22541e20i 0.955918 + 0.608000i
\(125\) 1.39109e21i 1.49367i
\(126\) −7.56936e19 + 4.15631e19i −0.0750505 + 0.0412100i
\(127\) 5.34974e20i 0.490112i 0.969509 + 0.245056i \(0.0788063\pi\)
−0.969509 + 0.245056i \(0.921194\pi\)
\(128\) 4.30721e20 + 1.09922e21i 0.364835 + 0.931072i
\(129\) 2.01088e21 1.57575
\(130\) −5.48899e20 9.99639e20i −0.398161 0.725119i
\(131\) −6.72549e20 −0.451868 −0.225934 0.974143i \(-0.572543\pi\)
−0.225934 + 0.974143i \(0.572543\pi\)
\(132\) −7.25600e20 + 1.14081e21i −0.451812 + 0.710355i
\(133\) 9.39089e20i 0.542239i
\(134\) 1.06175e21 + 1.93363e21i 0.568819 + 1.03592i
\(135\) 3.65102e21i 1.81584i
\(136\) 3.07929e21 + 1.98418e20i 1.42253 + 0.0916626i
\(137\) −1.70376e21 −0.731479 −0.365739 0.930717i \(-0.619184\pi\)
−0.365739 + 0.930717i \(0.619184\pi\)
\(138\) −1.41707e20 + 7.78107e19i −0.0565717 + 0.0310634i
\(139\) −1.86111e21 −0.691231 −0.345615 0.938376i \(-0.612330\pi\)
−0.345615 + 0.938376i \(0.612330\pi\)
\(140\) −1.21446e21 + 1.90942e21i −0.419858 + 0.660116i
\(141\) 2.79968e21i 0.901399i
\(142\) 1.13967e21 6.25787e20i 0.341896 0.187734i
\(143\) 1.62610e21i 0.454765i
\(144\) 3.01881e20 + 6.44909e20i 0.0787428 + 0.168218i
\(145\) −7.26470e21 −1.76823
\(146\) 1.85832e21 + 3.38432e21i 0.422272 + 0.769030i
\(147\) 3.34816e21 0.710612
\(148\) −6.42930e21 4.08927e21i −1.27511 0.811015i
\(149\) 2.73667e21i 0.507412i 0.967281 + 0.253706i \(0.0816495\pi\)
−0.967281 + 0.253706i \(0.918350\pi\)
\(150\) −4.70880e21 8.57553e21i −0.816578 1.48713i
\(151\) 1.09639e22i 1.77909i −0.456852 0.889543i \(-0.651023\pi\)
0.456852 0.889543i \(-0.348977\pi\)
\(152\) −7.72761e21 4.97938e20i −1.17384 0.0756379i
\(153\) 1.86111e21 0.264763
\(154\) 2.82830e21 1.55301e21i 0.376980 0.206999i
\(155\) 1.53890e22 1.92263
\(156\) −3.16802e21 2.01498e21i −0.371143 0.236061i
\(157\) 1.41430e22i 1.55434i 0.629294 + 0.777168i \(0.283344\pi\)
−0.629294 + 0.777168i \(0.716656\pi\)
\(158\) 2.10068e21 1.15348e21i 0.216665 0.118970i
\(159\) 1.33062e22i 1.28849i
\(160\) 1.50683e22 + 1.10060e22i 1.37046 + 1.00099i
\(161\) 3.85816e20 0.0329702
\(162\) −4.67240e21 8.50925e21i −0.375310 0.683504i
\(163\) −7.62880e21 −0.576209 −0.288105 0.957599i \(-0.593025\pi\)
−0.288105 + 0.957599i \(0.593025\pi\)
\(164\) 8.31825e20 1.30782e21i 0.0591008 0.0929203i
\(165\) 2.13692e22i 1.42873i
\(166\) −8.45120e21 1.53911e22i −0.531909 0.968698i
\(167\) 2.74529e22i 1.62714i −0.581469 0.813568i \(-0.697522\pi\)
0.581469 0.813568i \(-0.302478\pi\)
\(168\) −4.79057e20 + 7.43459e21i −0.0267482 + 0.415111i
\(169\) 1.44893e22 0.762396
\(170\) 4.27498e22 2.34738e22i 2.12053 1.16438i
\(171\) −4.67053e21 −0.218477
\(172\) −2.12376e22 + 3.33905e22i −0.937175 + 1.47346i
\(173\) 2.01546e22i 0.839294i −0.907687 0.419647i \(-0.862154\pi\)
0.907687 0.419647i \(-0.137846\pi\)
\(174\) −2.09644e22 + 1.15115e22i −0.824120 + 0.452522i
\(175\) 2.33481e22i 0.866703i
\(176\) −1.12798e22 2.40971e22i −0.395526 0.844963i
\(177\) 1.29698e22 0.429736
\(178\) 3.22926e21 + 5.88103e21i 0.101135 + 0.184185i
\(179\) 4.76803e22 1.41192 0.705958 0.708254i \(-0.250517\pi\)
0.705958 + 0.708254i \(0.250517\pi\)
\(180\) 9.49642e21 + 6.04008e21i 0.265971 + 0.169168i
\(181\) 1.72375e22i 0.456761i −0.973572 0.228380i \(-0.926657\pi\)
0.973572 0.228380i \(-0.0733429\pi\)
\(182\) 4.31268e21 + 7.85413e21i 0.108152 + 0.196963i
\(183\) 2.74382e22i 0.651395i
\(184\) 2.04573e20 3.17482e21i 0.00459907 0.0713740i
\(185\) −1.20431e23 −2.56460
\(186\) 4.44096e22 2.43852e22i 0.896082 0.492036i
\(187\) −6.95406e22 −1.32991
\(188\) −4.64885e22 2.95684e22i −0.842882 0.536104i
\(189\) 2.86860e22i 0.493233i
\(190\) −1.07282e23 + 5.89084e22i −1.74982 + 0.960819i
\(191\) 4.60627e22i 0.712879i 0.934318 + 0.356440i \(0.116009\pi\)
−0.934318 + 0.356440i \(0.883991\pi\)
\(192\) 6.09240e22 + 7.88416e21i 0.894904 + 0.115809i
\(193\) 3.15850e22 0.440462 0.220231 0.975448i \(-0.429319\pi\)
0.220231 + 0.975448i \(0.429319\pi\)
\(194\) 6.39572e22 + 1.16477e23i 0.846979 + 1.54249i
\(195\) −5.93419e22 −0.746475
\(196\) −3.53611e22 + 5.55959e22i −0.422634 + 0.664480i
\(197\) 1.19350e23i 1.35569i −0.735205 0.677844i \(-0.762914\pi\)
0.735205 0.677844i \(-0.237086\pi\)
\(198\) −7.72385e21 1.40665e22i −0.0834031 0.151891i
\(199\) 1.35757e23i 1.39390i −0.717121 0.696949i \(-0.754540\pi\)
0.717121 0.696949i \(-0.245460\pi\)
\(200\) 1.92127e23 + 1.23800e22i 1.87624 + 0.120898i
\(201\) 1.14787e23 1.06643
\(202\) −7.98409e22 + 4.38404e22i −0.705849 + 0.387580i
\(203\) 5.70785e22 0.480300
\(204\) 8.61710e22 1.35481e23i 0.690334 1.08537i
\(205\) 2.44976e22i 0.186889i
\(206\) −1.81105e22 + 9.94441e21i −0.131601 + 0.0722615i
\(207\) 1.91884e21i 0.0132842i
\(208\) 6.69171e22 3.13238e22i 0.441473 0.206653i
\(209\) 1.74515e23 1.09741
\(210\) 5.66747e22 + 1.03214e23i 0.339779 + 0.618795i
\(211\) −1.62424e23 −0.928594 −0.464297 0.885680i \(-0.653693\pi\)
−0.464297 + 0.885680i \(0.653693\pi\)
\(212\) −2.20948e23 1.40531e23i −1.20485 0.766327i
\(213\) 6.76544e22i 0.351966i
\(214\) −5.91826e22 1.07782e23i −0.293803 0.535066i
\(215\) 6.25456e23i 2.96355i
\(216\) 2.36052e23 + 1.52103e22i 1.06775 + 0.0688020i
\(217\) −1.20911e23 −0.522239
\(218\) 2.01151e23 1.10452e23i 0.829771 0.455625i
\(219\) 2.00905e23 0.791679
\(220\) −3.54835e23 2.25688e23i −1.33598 0.849732i
\(221\) 1.93113e23i 0.694846i
\(222\) −3.47538e23 + 1.90832e23i −1.19529 + 0.656330i
\(223\) 4.02866e23i 1.32468i 0.749203 + 0.662341i \(0.230437\pi\)
−0.749203 + 0.662341i \(0.769563\pi\)
\(224\) −1.18391e23 8.64741e22i −0.372254 0.271898i
\(225\) 1.16121e23 0.349209
\(226\) −7.36149e22 1.34065e23i −0.211778 0.385684i
\(227\) 1.22521e23 0.337250 0.168625 0.985680i \(-0.446067\pi\)
0.168625 + 0.985680i \(0.446067\pi\)
\(228\) −2.16250e23 + 3.39995e23i −0.569649 + 0.895621i
\(229\) 1.04577e23i 0.263681i 0.991271 + 0.131841i \(0.0420887\pi\)
−0.991271 + 0.131841i \(0.957911\pi\)
\(230\) −2.42020e22 4.40759e22i −0.0584214 0.106395i
\(231\) 1.67897e23i 0.388083i
\(232\) 3.02650e22 4.69690e23i 0.0669979 1.03976i
\(233\) 1.59482e23 0.338185 0.169092 0.985600i \(-0.445916\pi\)
0.169092 + 0.985600i \(0.445916\pi\)
\(234\) 3.90623e22 2.14490e22i 0.0793595 0.0435761i
\(235\) −8.70802e23 −1.69528
\(236\) −1.36979e23 + 2.15363e23i −0.255584 + 0.401838i
\(237\) 1.24703e23i 0.223046i
\(238\) −3.35884e23 + 1.84433e23i −0.575996 + 0.316278i
\(239\) 8.73131e23i 1.43582i −0.696136 0.717910i \(-0.745099\pi\)
0.696136 0.717910i \(-0.254901\pi\)
\(240\) 8.79385e23 4.11639e23i 1.38697 0.649238i
\(241\) 6.52500e22 0.0987211 0.0493605 0.998781i \(-0.484282\pi\)
0.0493605 + 0.998781i \(0.484282\pi\)
\(242\) −4.29705e22 7.82567e22i −0.0623759 0.113597i
\(243\) 2.62990e23 0.366333
\(244\) 4.55609e23 + 2.89784e23i 0.609108 + 0.387415i
\(245\) 1.04140e24i 1.33646i
\(246\) −3.88184e22 7.06950e22i −0.0478285 0.0871039i
\(247\) 4.84624e23i 0.573371i
\(248\) −6.41114e22 + 9.94960e23i −0.0728482 + 1.13055i
\(249\) −9.13667e23 −0.997228
\(250\) 1.24863e24 6.85617e23i 1.30928 0.718922i
\(251\) 1.14171e24 1.15032 0.575162 0.818040i \(-0.304939\pi\)
0.575162 + 0.818040i \(0.304939\pi\)
\(252\) −7.46131e22 4.74567e22i −0.0722453 0.0459507i
\(253\) 7.16978e22i 0.0667268i
\(254\) −4.80185e23 + 2.63668e23i −0.429607 + 0.235896i
\(255\) 2.53777e24i 2.18299i
\(256\) −7.74356e23 + 9.28372e23i −0.640532 + 0.767931i
\(257\) 1.02107e24 0.812318 0.406159 0.913802i \(-0.366868\pi\)
0.406159 + 0.913802i \(0.366868\pi\)
\(258\) 9.91086e23 + 1.80494e24i 0.758428 + 1.38123i
\(259\) 9.46221e23 0.696619
\(260\) 6.26731e23 9.85369e23i 0.443964 0.698016i
\(261\) 2.83878e23i 0.193521i
\(262\) −3.31474e23 6.03672e23i −0.217489 0.396085i
\(263\) 3.41230e23i 0.215521i 0.994177 + 0.107761i \(0.0343680\pi\)
−0.994177 + 0.107761i \(0.965632\pi\)
\(264\) −1.38160e24 8.90251e22i −0.840124 0.0541344i
\(265\) −4.13870e24 −2.42329
\(266\) 8.42915e23 4.62842e23i 0.475299 0.260985i
\(267\) 3.49118e23 0.189609
\(268\) −1.21230e24 + 1.90603e24i −0.634255 + 0.997197i
\(269\) 2.76279e23i 0.139259i 0.997573 + 0.0696297i \(0.0221818\pi\)
−0.997573 + 0.0696297i \(0.977818\pi\)
\(270\) 3.27711e24 1.79945e24i 1.59167 0.873983i
\(271\) 1.80384e24i 0.844318i −0.906522 0.422159i \(-0.861272\pi\)
0.906522 0.422159i \(-0.138728\pi\)
\(272\) 1.33957e24 + 2.86173e24i 0.604333 + 1.29104i
\(273\) 4.66248e23 0.202764
\(274\) −8.39717e23 1.52927e24i −0.352069 0.641178i
\(275\) −4.33887e24 −1.75408
\(276\) −1.39684e23 8.88441e22i −0.0544572 0.0346368i
\(277\) 1.40813e24i 0.529476i −0.964320 0.264738i \(-0.914715\pi\)
0.964320 0.264738i \(-0.0852854\pi\)
\(278\) −9.17269e23 1.67050e24i −0.332697 0.605898i
\(279\) 6.01349e23i 0.210419i
\(280\) −2.31243e24 1.49004e23i −0.780707 0.0503058i
\(281\) 1.85060e24 0.602906 0.301453 0.953481i \(-0.402528\pi\)
0.301453 + 0.953481i \(0.402528\pi\)
\(282\) −2.51296e24 + 1.37986e24i −0.790121 + 0.433853i
\(283\) 8.04995e22 0.0244303 0.0122152 0.999925i \(-0.496112\pi\)
0.0122152 + 0.999925i \(0.496112\pi\)
\(284\) 1.12340e24 + 7.14523e23i 0.329117 + 0.209331i
\(285\) 6.36864e24i 1.80135i
\(286\) −1.45957e24 + 8.01444e23i −0.398624 + 0.218883i
\(287\) 1.92477e23i 0.0507644i
\(288\) −4.30076e23 + 5.88816e23i −0.109552 + 0.149987i
\(289\) 4.19429e24 1.03200
\(290\) −3.58050e24 6.52070e24i −0.851066 1.54994i
\(291\) 6.91448e24 1.58792
\(292\) −2.12183e24 + 3.33601e24i −0.470849 + 0.740285i
\(293\) 2.22935e24i 0.478082i 0.971009 + 0.239041i \(0.0768331\pi\)
−0.971009 + 0.239041i \(0.923167\pi\)
\(294\) 1.65018e24 + 3.00526e24i 0.342025 + 0.622886i
\(295\) 4.03409e24i 0.808212i
\(296\) 5.01720e23 7.78630e24i 0.0971727 1.50804i
\(297\) −5.33084e24 −0.998231
\(298\) −2.45640e24 + 1.34880e24i −0.444772 + 0.244223i
\(299\) −1.99103e23 −0.0348631
\(300\) 5.37650e24 8.45311e24i 0.910514 1.43154i
\(301\) 4.91419e24i 0.804984i
\(302\) 9.84108e24 5.40371e24i 1.55946 0.856293i
\(303\) 4.73963e24i 0.726637i
\(304\) −3.36171e24 7.18162e24i −0.498683 1.06534i
\(305\) 8.53427e24 1.22509
\(306\) 9.17271e23 + 1.67051e24i 0.127433 + 0.232078i
\(307\) 4.70697e24 0.632933 0.316466 0.948604i \(-0.397504\pi\)
0.316466 + 0.948604i \(0.397504\pi\)
\(308\) 2.78793e24 + 1.77323e24i 0.362889 + 0.230811i
\(309\) 1.07510e24i 0.135476i
\(310\) 7.58468e24 + 1.38130e25i 0.925381 + 1.68528i
\(311\) 5.93399e24i 0.701040i −0.936555 0.350520i \(-0.886005\pi\)
0.936555 0.350520i \(-0.113995\pi\)
\(312\) 2.47221e23 3.83668e24i 0.0282839 0.438944i
\(313\) −3.32332e24 −0.368239 −0.184119 0.982904i \(-0.558943\pi\)
−0.184119 + 0.982904i \(0.558943\pi\)
\(314\) −1.26946e25 + 6.97055e24i −1.36245 + 0.748119i
\(315\) −1.39762e24 −0.145306
\(316\) 2.07069e24 + 1.31704e24i 0.208567 + 0.132656i
\(317\) 9.92638e24i 0.968720i −0.874869 0.484360i \(-0.839053\pi\)
0.874869 0.484360i \(-0.160947\pi\)
\(318\) −1.19434e25 + 6.55811e24i −1.12943 + 0.620165i
\(319\) 1.06071e25i 0.972057i
\(320\) −2.45226e24 + 1.89496e25i −0.217805 + 1.68306i
\(321\) −6.39828e24 −0.550824
\(322\) 1.90154e23 + 3.46303e23i 0.0158689 + 0.0289000i
\(323\) −2.07251e25 −1.67676
\(324\) 5.33494e24 8.38778e24i 0.418485 0.657956i
\(325\) 1.20489e25i 0.916464i
\(326\) −3.75995e24 6.84751e24i −0.277336 0.505076i
\(327\) 1.19410e25i 0.854209i
\(328\) 1.58386e24 + 1.02058e23i 0.109895 + 0.00708123i
\(329\) 6.84187e24 0.460485
\(330\) −1.91807e25 + 1.05321e25i −1.25235 + 0.687662i
\(331\) −2.33153e25 −1.47693 −0.738466 0.674290i \(-0.764450\pi\)
−0.738466 + 0.674290i \(0.764450\pi\)
\(332\) 9.64956e24 1.51714e25i 0.593099 0.932490i
\(333\) 4.70600e24i 0.280679i
\(334\) 2.46414e25 1.35305e25i 1.42627 0.783159i
\(335\) 3.57029e25i 2.00565i
\(336\) −6.90930e24 + 3.23423e24i −0.376740 + 0.176351i
\(337\) 1.72473e25 0.912899 0.456449 0.889749i \(-0.349121\pi\)
0.456449 + 0.889749i \(0.349121\pi\)
\(338\) 7.14124e24 + 1.30054e25i 0.366950 + 0.668279i
\(339\) −7.95857e24 −0.397043
\(340\) 4.21395e25 + 2.68023e25i 2.04127 + 1.29832i
\(341\) 2.24695e25i 1.05694i
\(342\) −2.30193e24 4.19221e24i −0.105155 0.191506i
\(343\) 1.85724e25i 0.823999i
\(344\) −4.04381e25 2.60568e24i −1.74263 0.112289i
\(345\) −2.61650e24 −0.109529
\(346\) 1.80905e25 9.93346e24i 0.735683 0.403961i
\(347\) 3.94050e25 1.55688 0.778442 0.627716i \(-0.216010\pi\)
0.778442 + 0.627716i \(0.216010\pi\)
\(348\) −2.06652e25 1.31438e25i −0.793316 0.504579i
\(349\) 1.08315e25i 0.404049i −0.979380 0.202025i \(-0.935248\pi\)
0.979380 0.202025i \(-0.0647521\pi\)
\(350\) −2.09569e25 + 1.15074e25i −0.759708 + 0.417154i
\(351\) 1.48036e25i 0.521551i
\(352\) 1.60698e25 2.20012e25i 0.550281 0.753389i
\(353\) −2.90728e25 −0.967697 −0.483849 0.875152i \(-0.660761\pi\)
−0.483849 + 0.875152i \(0.660761\pi\)
\(354\) 6.39234e24 + 1.16415e25i 0.206836 + 0.376685i
\(355\) 2.10430e25 0.661948
\(356\) −3.68716e24 + 5.79708e24i −0.112770 + 0.177300i
\(357\) 1.99392e25i 0.592960i
\(358\) 2.34998e25 + 4.27972e25i 0.679570 + 1.23761i
\(359\) 2.47565e25i 0.696218i 0.937454 + 0.348109i \(0.113176\pi\)
−0.937454 + 0.348109i \(0.886824\pi\)
\(360\) −7.41067e23 + 1.15008e25i −0.0202690 + 0.314559i
\(361\) 1.44205e25 0.383626
\(362\) 1.54722e25 8.49572e24i 0.400373 0.219844i
\(363\) −4.64558e24 −0.116943
\(364\) −4.92421e24 + 7.74201e24i −0.120593 + 0.189601i
\(365\) 6.24887e25i 1.48892i
\(366\) 2.46282e25 1.35232e25i 0.570980 0.313523i
\(367\) 9.71830e24i 0.219245i −0.993973 0.109623i \(-0.965036\pi\)
0.993973 0.109623i \(-0.0349642\pi\)
\(368\) 2.95050e24 1.38113e24i 0.0647765 0.0303218i
\(369\) 9.57278e23 0.0204538
\(370\) −5.93558e25 1.08097e26i −1.23437 2.24800i
\(371\) 3.25177e25 0.658234
\(372\) 4.37757e25 + 2.78430e25i 0.862588 + 0.548638i
\(373\) 6.08237e25i 1.16677i 0.812197 + 0.583384i \(0.198272\pi\)
−0.812197 + 0.583384i \(0.801728\pi\)
\(374\) −3.42739e25 6.24187e25i −0.640100 1.16573i
\(375\) 7.41227e25i 1.34784i
\(376\) 3.62780e24 5.63006e25i 0.0642340 0.996861i
\(377\) −2.94558e25 −0.507876
\(378\) −2.57482e25 + 1.41382e25i −0.432343 + 0.237398i
\(379\) −8.22232e24 −0.134463 −0.0672314 0.997737i \(-0.521417\pi\)
−0.0672314 + 0.997737i \(0.521417\pi\)
\(380\) −1.05751e26 6.72615e25i −1.68441 1.07135i
\(381\) 2.85054e25i 0.442260i
\(382\) −4.13453e25 + 2.27026e25i −0.624874 + 0.343117i
\(383\) 4.32837e24i 0.0637289i 0.999492 + 0.0318645i \(0.0101445\pi\)
−0.999492 + 0.0318645i \(0.989856\pi\)
\(384\) 2.29504e25 + 5.85704e25i 0.329214 + 0.840168i
\(385\) 5.22222e25 0.729874
\(386\) 1.55671e25 + 2.83503e25i 0.211999 + 0.386087i
\(387\) −2.44406e25 −0.324341
\(388\) −7.30262e25 + 1.14814e26i −0.944413 + 1.48484i
\(389\) 1.07897e26i 1.35993i 0.733247 + 0.679963i \(0.238004\pi\)
−0.733247 + 0.679963i \(0.761996\pi\)
\(390\) −2.92474e25 5.32646e25i −0.359287 0.654323i
\(391\) 8.51470e24i 0.101953i
\(392\) −6.73303e25 4.33851e24i −0.785869 0.0506384i
\(393\) −3.58360e25 −0.407750
\(394\) 1.07127e26 5.88231e25i 1.18833 0.652508i
\(395\) 3.87873e25 0.419487
\(396\) 8.81908e24 1.38657e25i 0.0929975 0.146214i
\(397\) 1.05083e26i 1.08051i −0.841502 0.540254i \(-0.818328\pi\)
0.841502 0.540254i \(-0.181672\pi\)
\(398\) 1.21854e26 6.69095e25i 1.22182 0.670898i
\(399\) 5.00383e25i 0.489298i
\(400\) 8.35803e25 + 1.78553e26i 0.797084 + 1.70281i
\(401\) −1.57729e26 −1.46713 −0.733563 0.679622i \(-0.762144\pi\)
−0.733563 + 0.679622i \(0.762144\pi\)
\(402\) 5.65741e25 + 1.03031e26i 0.513283 + 0.934777i
\(403\) 6.23972e25 0.552223
\(404\) −7.87012e25 5.00569e25i −0.679466 0.432166i
\(405\) 1.57116e26i 1.32334i
\(406\) 2.81319e25 + 5.12330e25i 0.231174 + 0.421007i
\(407\) 1.75840e26i 1.40985i
\(408\) 1.64076e26 + 1.05725e25i 1.28364 + 0.0827132i
\(409\) 6.00717e25 0.458603 0.229301 0.973355i \(-0.426356\pi\)
0.229301 + 0.973355i \(0.426356\pi\)
\(410\) 2.19887e25 1.20739e25i 0.163818 0.0899520i
\(411\) −9.07826e25 −0.660062
\(412\) −1.78519e25 1.13545e25i −0.126682 0.0805742i
\(413\) 3.16957e25i 0.219533i
\(414\) 1.72233e24 9.45726e23i 0.0116443 0.00639384i
\(415\) 2.84184e26i 1.87551i
\(416\) 6.10968e25 + 4.46256e25i 0.393627 + 0.287509i
\(417\) −9.91668e25 −0.623743
\(418\) 8.60119e25 + 1.56642e26i 0.528197 + 0.961937i
\(419\) 9.17104e25 0.549893 0.274947 0.961460i \(-0.411340\pi\)
0.274947 + 0.961460i \(0.411340\pi\)
\(420\) −6.47110e25 + 1.01741e26i −0.378866 + 0.595666i
\(421\) 2.84776e25i 0.162811i −0.996681 0.0814054i \(-0.974059\pi\)
0.996681 0.0814054i \(-0.0259408\pi\)
\(422\) −8.00527e25 1.45790e26i −0.446942 0.813959i
\(423\) 3.40278e25i 0.185537i
\(424\) 1.72420e25 2.67583e26i 0.0918183 1.42495i
\(425\) 5.15276e26 2.68010
\(426\) 6.07257e25 3.33443e25i 0.308515 0.169405i
\(427\) −6.70535e25 −0.332769
\(428\) 6.75746e25 1.06243e26i 0.327601 0.515066i
\(429\) 8.66448e25i 0.410364i
\(430\) −5.61401e26 + 3.08264e26i −2.59770 + 1.42639i
\(431\) 1.53210e25i 0.0692652i −0.999400 0.0346326i \(-0.988974\pi\)
0.999400 0.0346326i \(-0.0110261\pi\)
\(432\) 1.02689e26 + 2.19374e26i 0.453613 + 0.969054i
\(433\) −3.33355e26 −1.43889 −0.719447 0.694548i \(-0.755604\pi\)
−0.719447 + 0.694548i \(0.755604\pi\)
\(434\) −5.95926e25 1.08528e26i −0.251360 0.457769i
\(435\) −3.87091e26 −1.59559
\(436\) 1.98280e26 + 1.26113e26i 0.798756 + 0.508038i
\(437\) 2.13680e25i 0.0841297i
\(438\) 9.90184e25 + 1.80329e26i 0.381044 + 0.693946i
\(439\) 4.20421e26i 1.58139i 0.612210 + 0.790695i \(0.290281\pi\)
−0.612210 + 0.790695i \(0.709719\pi\)
\(440\) 2.76901e25 4.29728e26i 0.101812 1.58004i
\(441\) −4.06941e25 −0.146267
\(442\) 1.73336e26 9.51780e25i 0.609067 0.334437i
\(443\) −1.38603e25 −0.0476141 −0.0238070 0.999717i \(-0.507579\pi\)
−0.0238070 + 0.999717i \(0.507579\pi\)
\(444\) −3.42577e26 2.17892e26i −1.15061 0.731832i
\(445\) 1.08588e26i 0.356601i
\(446\) −3.61607e26 + 1.98557e26i −1.16115 + 0.637584i
\(447\) 1.45820e26i 0.457871i
\(448\) 1.92673e25 1.48886e26i 0.0591619 0.457167i
\(449\) 8.14375e25 0.244546 0.122273 0.992496i \(-0.460982\pi\)
0.122273 + 0.992496i \(0.460982\pi\)
\(450\) 5.72316e25 + 1.04229e26i 0.168078 + 0.306099i
\(451\) −3.57688e25 −0.102740
\(452\) 8.40533e25 1.32151e26i 0.236140 0.371268i
\(453\) 5.84200e26i 1.60539i
\(454\) 6.03860e25 + 1.09973e26i 0.162322 + 0.295617i
\(455\) 1.45020e26i 0.381342i
\(456\) −4.11757e26 2.65320e25i −1.05923 0.0682531i
\(457\) −3.19651e26 −0.804478 −0.402239 0.915535i \(-0.631768\pi\)
−0.402239 + 0.915535i \(0.631768\pi\)
\(458\) −9.38665e25 + 5.15418e25i −0.231130 + 0.126913i
\(459\) 6.33081e26 1.52522
\(460\) 2.76337e25 4.34467e25i 0.0651421 0.102419i
\(461\) 1.06243e25i 0.0245071i −0.999925 0.0122535i \(-0.996099\pi\)
0.999925 0.0122535i \(-0.00390052\pi\)
\(462\) 1.50703e26 8.27503e25i 0.340174 0.186788i
\(463\) 1.83285e26i 0.404872i 0.979296 + 0.202436i \(0.0648858\pi\)
−0.979296 + 0.202436i \(0.935114\pi\)
\(464\) 4.36504e26 2.04327e26i 0.943645 0.441719i
\(465\) 8.19987e26 1.73491
\(466\) 7.86029e25 + 1.43149e26i 0.162772 + 0.296436i
\(467\) 5.41789e26 1.09815 0.549075 0.835773i \(-0.314980\pi\)
0.549075 + 0.835773i \(0.314980\pi\)
\(468\) 3.85047e25 + 2.44904e25i 0.0763932 + 0.0485889i
\(469\) 2.80516e26i 0.544791i
\(470\) −4.29186e26 7.81621e26i −0.815956 1.48600i
\(471\) 7.53592e26i 1.40258i
\(472\) −2.60819e26 1.68062e25i −0.475247 0.0306231i
\(473\) 9.13225e26 1.62917
\(474\) 1.11932e26 6.14617e25i 0.195511 0.107355i
\(475\) −1.29311e27 −2.21156
\(476\) −3.31089e26 2.10585e26i −0.554467 0.352662i
\(477\) 1.61726e26i 0.265213i
\(478\) 7.83711e26 4.30333e26i 1.25857 0.691076i
\(479\) 3.43182e26i 0.539721i 0.962899 + 0.269861i \(0.0869776\pi\)
−0.962899 + 0.269861i \(0.913022\pi\)
\(480\) 8.02897e26 + 5.86443e26i 1.23665 + 0.903261i
\(481\) −4.88305e26 −0.736615
\(482\) 3.21593e25 + 5.85675e25i 0.0475155 + 0.0865340i
\(483\) 2.05577e25 0.0297512
\(484\) 4.90637e25 7.71396e25i 0.0695515 0.109351i
\(485\) 2.15065e27i 2.98644i
\(486\) 1.29618e26 + 2.36056e26i 0.176320 + 0.321109i
\(487\) 1.33645e27i 1.78099i −0.454992 0.890496i \(-0.650358\pi\)
0.454992 0.890496i \(-0.349642\pi\)
\(488\) −3.55541e25 + 5.51773e26i −0.0464186 + 0.720380i
\(489\) −4.06491e26 −0.519951
\(490\) −9.34746e26 + 5.13266e26i −1.17147 + 0.643253i
\(491\) −3.05224e26 −0.374803 −0.187402 0.982283i \(-0.560007\pi\)
−0.187402 + 0.982283i \(0.560007\pi\)
\(492\) 4.43228e25 6.96858e25i 0.0533306 0.0838481i
\(493\) 1.25969e27i 1.48523i
\(494\) −4.34993e26 + 2.38853e26i −0.502588 + 0.275970i
\(495\) 2.59726e26i 0.294078i
\(496\) −9.24661e26 + 4.32833e26i −1.02604 + 0.480290i
\(497\) −1.65334e26 −0.179804
\(498\) −4.50312e26 8.20096e26i −0.479977 0.874120i
\(499\) 4.76885e26 0.498206 0.249103 0.968477i \(-0.419864\pi\)
0.249103 + 0.968477i \(0.419864\pi\)
\(500\) 1.23080e27 + 7.82836e26i 1.26034 + 0.801624i
\(501\) 1.46280e27i 1.46827i
\(502\) 5.62708e26 + 1.02479e27i 0.553663 + 1.00832i
\(503\) 1.99413e27i 1.92341i −0.274080 0.961707i \(-0.588373\pi\)
0.274080 0.961707i \(-0.411627\pi\)
\(504\) 5.82254e24 9.03614e25i 0.00550564 0.0854432i
\(505\) −1.47420e27 −1.36660
\(506\) −6.43550e25 + 3.53371e25i −0.0584894 + 0.0321164i
\(507\) 7.72046e26 0.687960
\(508\) −4.73331e26 3.01056e26i −0.413549 0.263033i
\(509\) 1.26697e27i 1.08539i 0.839929 + 0.542696i \(0.182597\pi\)
−0.839929 + 0.542696i \(0.817403\pi\)
\(510\) 2.27787e27 1.25077e27i 1.91350 1.05069i
\(511\) 4.90972e26i 0.404434i
\(512\) −1.21495e27 2.37493e26i −0.981425 0.191845i
\(513\) −1.58874e27 −1.25858
\(514\) 5.03249e26 + 9.16503e26i 0.390977 + 0.712037i
\(515\) −3.34395e26 −0.254793
\(516\) −1.13162e27 + 1.77917e27i −0.845675 + 1.32960i
\(517\) 1.27145e27i 0.931955i
\(518\) 4.66357e26 + 8.49316e26i 0.335290 + 0.610621i
\(519\) 1.07392e27i 0.757350i
\(520\) 1.19335e27 + 7.68947e25i 0.825531 + 0.0531941i
\(521\) −1.34331e27 −0.911592 −0.455796 0.890084i \(-0.650645\pi\)
−0.455796 + 0.890084i \(0.650645\pi\)
\(522\) 2.54806e26 1.39913e26i 0.169630 0.0931436i
\(523\) 8.25533e26 0.539160 0.269580 0.962978i \(-0.413115\pi\)
0.269580 + 0.962978i \(0.413115\pi\)
\(524\) 3.78477e26 5.95054e26i 0.242508 0.381280i
\(525\) 1.24407e27i 0.782083i
\(526\) −3.06284e26 + 1.68180e26i −0.188915 + 0.103733i
\(527\) 2.66843e27i 1.61492i
\(528\) −6.01031e26 1.28398e27i −0.356909 0.762466i
\(529\) 1.70738e27 0.994885
\(530\) −2.03981e27 3.71485e27i −1.16636 2.12414i
\(531\) −1.57638e26 −0.0884534
\(532\) 8.30882e26 + 5.28472e26i 0.457534 + 0.291008i
\(533\) 9.93292e25i 0.0536791i
\(534\) 1.72067e26 + 3.13364e26i 0.0912610 + 0.166202i
\(535\) 1.99010e27i 1.03595i
\(536\) −2.30832e27 1.48740e26i −1.17937 0.0759939i
\(537\) 2.54059e27 1.27406
\(538\) −2.47984e26 + 1.36167e26i −0.122068 + 0.0670271i
\(539\) 1.52054e27 0.734700
\(540\) 3.23033e27 + 2.05461e27i 1.53218 + 0.974523i
\(541\) 1.08634e27i 0.505816i 0.967490 + 0.252908i \(0.0813869\pi\)
−0.967490 + 0.252908i \(0.918613\pi\)
\(542\) 1.61911e27 8.89047e26i 0.740087 0.406380i
\(543\) 9.18480e26i 0.412165i
\(544\) −1.90843e27 + 2.61282e27i −0.840788 + 1.15112i
\(545\) 3.71409e27 1.60653
\(546\) 2.29796e26 + 4.18498e26i 0.0975924 + 0.177733i
\(547\) 1.79834e27 0.749890 0.374945 0.927047i \(-0.377662\pi\)
0.374945 + 0.927047i \(0.377662\pi\)
\(548\) 9.58788e26 1.50744e27i 0.392570 0.617212i
\(549\) 3.33489e26i 0.134078i
\(550\) −2.13847e27 3.89451e27i −0.844258 1.53754i
\(551\) 3.16123e27i 1.22558i
\(552\) 1.09004e25 1.69166e26i 0.00415005 0.0644055i
\(553\) −3.04751e26 −0.113945
\(554\) 1.26392e27 6.94016e26i 0.464112 0.254842i
\(555\) −6.41701e27 −2.31421
\(556\) 1.04734e27 1.64666e27i 0.370969 0.583251i
\(557\) 2.52076e27i 0.876959i −0.898741 0.438479i \(-0.855517\pi\)
0.898741 0.438479i \(-0.144483\pi\)
\(558\) −5.39763e26 + 2.96382e26i −0.184442 + 0.101277i
\(559\) 2.53601e27i 0.851201i
\(560\) −1.00596e27 2.14904e27i −0.331667 0.708541i
\(561\) −3.70539e27 −1.20007
\(562\) 9.12092e26 + 1.66108e27i 0.290185 + 0.528477i
\(563\) 3.61466e27 1.12975 0.564876 0.825176i \(-0.308924\pi\)
0.564876 + 0.825176i \(0.308924\pi\)
\(564\) −2.47708e27 1.57552e27i −0.760588 0.483762i
\(565\) 2.47540e27i 0.746727i
\(566\) 3.96752e25 + 7.22553e25i 0.0117586 + 0.0214144i
\(567\) 1.23446e27i 0.359456i
\(568\) −8.76660e25 + 1.36051e27i −0.0250812 + 0.389240i
\(569\) −5.56745e27 −1.56507 −0.782535 0.622607i \(-0.786074\pi\)
−0.782535 + 0.622607i \(0.786074\pi\)
\(570\) −5.71641e27 + 3.13887e27i −1.57897 + 0.867010i
\(571\) −2.37197e27 −0.643795 −0.321897 0.946775i \(-0.604321\pi\)
−0.321897 + 0.946775i \(0.604321\pi\)
\(572\) −1.43873e27 9.15087e26i −0.383724 0.244063i
\(573\) 2.45440e27i 0.643278i
\(574\) −1.72765e26 + 9.48646e25i −0.0444976 + 0.0244335i
\(575\) 5.31261e26i 0.134471i
\(576\) −7.40482e26 9.58256e25i −0.184200 0.0238373i
\(577\) 6.44852e27 1.57653 0.788264 0.615337i \(-0.210980\pi\)
0.788264 + 0.615337i \(0.210980\pi\)
\(578\) 2.06721e27 + 3.76474e27i 0.496713 + 0.904599i
\(579\) 1.68297e27 0.397458
\(580\) 4.08820e27 6.42762e27i 0.948970 1.49200i
\(581\) 2.23282e27i 0.509440i
\(582\) 3.40789e27 + 6.20634e27i 0.764285 + 1.39189i
\(583\) 6.04290e27i 1.33217i
\(584\) −4.04013e27 2.60331e26i −0.875521 0.0564153i
\(585\) 7.21253e26 0.153649
\(586\) −2.00104e27 + 1.09876e27i −0.419063 + 0.230106i
\(587\) 1.54560e27 0.318211 0.159106 0.987262i \(-0.449139\pi\)
0.159106 + 0.987262i \(0.449139\pi\)
\(588\) −1.88417e27 + 2.96236e27i −0.381371 + 0.599604i
\(589\) 6.69654e27i 1.33259i
\(590\) −3.62094e27 + 1.98825e27i −0.708438 + 0.389001i
\(591\) 6.35942e27i 1.22333i
\(592\) 7.23616e27 3.38724e27i 1.36865 0.640662i
\(593\) 6.71123e26 0.124812 0.0624058 0.998051i \(-0.480123\pi\)
0.0624058 + 0.998051i \(0.480123\pi\)
\(594\) −2.62737e27 4.78489e27i −0.480460 0.874999i
\(595\) −6.20182e27 −1.11519
\(596\) −2.42134e27 1.54006e27i −0.428147 0.272317i
\(597\) 7.23364e27i 1.25781i
\(598\) −9.81305e25 1.78713e26i −0.0167800 0.0305593i
\(599\) 2.61339e26i 0.0439476i −0.999759 0.0219738i \(-0.993005\pi\)
0.999759 0.0219738i \(-0.00699504\pi\)
\(600\) 1.02373e28 + 6.59651e26i 1.69306 + 0.109094i
\(601\) −2.17843e26 −0.0354323 −0.0177161 0.999843i \(-0.505640\pi\)
−0.0177161 + 0.999843i \(0.505640\pi\)
\(602\) 4.41091e27 2.42202e27i 0.705608 0.387447i
\(603\) −1.39514e27 −0.219505
\(604\) 9.70060e27 + 6.16994e27i 1.50117 + 0.954799i
\(605\) 1.44495e27i 0.219937i
\(606\) −4.25423e27 + 2.33598e27i −0.636934 + 0.349739i
\(607\) 2.74208e27i 0.403824i −0.979404 0.201912i \(-0.935284\pi\)
0.979404 0.201912i \(-0.0647155\pi\)
\(608\) 4.78927e27 6.55698e27i 0.693799 0.949878i
\(609\) 3.04136e27 0.433406
\(610\) 4.20622e27 + 7.66025e27i 0.589649 + 1.07385i
\(611\) −3.53080e27 −0.486924
\(612\) −1.04734e27 + 1.64666e27i −0.142093 + 0.223404i
\(613\) 5.68816e27i 0.759218i 0.925147 + 0.379609i \(0.123942\pi\)
−0.925147 + 0.379609i \(0.876058\pi\)
\(614\) 2.31989e27 + 4.22491e27i 0.304637 + 0.554797i
\(615\) 1.30532e27i 0.168643i
\(616\) −2.17560e26 + 3.37636e27i −0.0276549 + 0.429182i
\(617\) 3.78592e26 0.0473500 0.0236750 0.999720i \(-0.492463\pi\)
0.0236750 + 0.999720i \(0.492463\pi\)
\(618\) −9.64995e26 + 5.29876e26i −0.118752 + 0.0652063i
\(619\) −3.37929e27 −0.409184 −0.204592 0.978847i \(-0.565587\pi\)
−0.204592 + 0.978847i \(0.565587\pi\)
\(620\) −8.66018e27 + 1.36158e28i −1.03183 + 1.62229i
\(621\) 6.52720e26i 0.0765263i
\(622\) 5.32627e27 2.92464e27i 0.614497 0.337418i
\(623\) 8.53175e26i 0.0968630i
\(624\) 3.56560e27 1.66905e27i 0.398370 0.186476i
\(625\) 5.95513e27 0.654773
\(626\) −1.63794e27 2.98297e27i −0.177237 0.322780i
\(627\) 9.29882e27 0.990267
\(628\) −1.25133e28 7.95896e27i −1.31153 0.834180i
\(629\) 2.08825e28i 2.15415i
\(630\) −6.88834e26 1.25449e27i −0.0699374 0.127368i
\(631\) 1.77177e28i 1.77058i 0.465043 + 0.885288i \(0.346039\pi\)
−0.465043 + 0.885288i \(0.653961\pi\)
\(632\) −1.61590e26 + 2.50775e27i −0.0158943 + 0.246668i
\(633\) −8.65457e27 −0.837931
\(634\) 8.90979e27 4.89234e27i 0.849131 0.466256i
\(635\) −8.86623e27 −0.831767
\(636\) −1.17730e28 7.48804e27i −1.08721 0.691507i
\(637\) 4.22251e27i 0.383863i
\(638\) −9.52084e27 + 5.22786e27i −0.852056 + 0.467862i
\(639\) 8.22284e26i 0.0724458i
\(640\) −1.82175e28 + 7.13842e27i −1.58012 + 0.619159i
\(641\) −1.53543e28 −1.31114 −0.655571 0.755134i \(-0.727572\pi\)
−0.655571 + 0.755134i \(0.727572\pi\)
\(642\) −3.15347e27 5.74302e27i −0.265118 0.482825i
\(643\) 2.16089e28 1.78864 0.894321 0.447425i \(-0.147659\pi\)
0.894321 + 0.447425i \(0.147659\pi\)
\(644\) −2.17118e26 + 3.41360e26i −0.0176944 + 0.0278198i
\(645\) 3.33267e28i 2.67421i
\(646\) −1.02146e28 1.86026e28i −0.807043 1.46976i
\(647\) 2.76915e27i 0.215429i −0.994182 0.107714i \(-0.965647\pi\)
0.994182 0.107714i \(-0.0343532\pi\)
\(648\) 1.01582e28 + 6.54553e26i 0.778152 + 0.0501412i
\(649\) 5.89015e27 0.444303
\(650\) 1.08150e28 5.93847e27i 0.803327 0.441104i
\(651\) −6.44261e27 −0.471251
\(652\) 4.29310e27 6.74976e27i 0.309240 0.486197i
\(653\) 1.65324e28i 1.17275i 0.810041 + 0.586374i \(0.199445\pi\)
−0.810041 + 0.586374i \(0.800555\pi\)
\(654\) 1.07181e28 5.88528e27i 0.748757 0.411140i
\(655\) 1.11463e28i 0.766863i
\(656\) 6.89020e26 + 1.47195e27i 0.0466867 + 0.0997369i
\(657\) −2.44183e27 −0.162953
\(658\) 3.37210e27 + 6.14117e27i 0.221637 + 0.403638i
\(659\) 2.52135e27 0.163222 0.0816112 0.996664i \(-0.473993\pi\)
0.0816112 + 0.996664i \(0.473993\pi\)
\(660\) −1.89069e28 1.20255e28i −1.20554 0.766769i
\(661\) 1.53460e28i 0.963783i −0.876231 0.481892i \(-0.839950\pi\)
0.876231 0.481892i \(-0.160050\pi\)
\(662\) −1.14912e28 2.09275e28i −0.710864 1.29461i
\(663\) 1.02898e28i 0.627005i
\(664\) 1.83735e28 + 1.18392e27i 1.10284 + 0.0710628i
\(665\) 1.55637e28 0.920231
\(666\) 4.22405e27 2.31941e27i 0.246029 0.135094i
\(667\) −1.29876e27 −0.0745197
\(668\) 2.42896e28 + 1.54491e28i 1.37296 + 0.873251i
\(669\) 2.14662e28i 1.19535i
\(670\) −3.20464e28 + 1.75966e28i −1.75805 + 0.965341i
\(671\) 1.24608e28i 0.673476i
\(672\) −6.30834e27 4.60767e27i −0.335910 0.245351i
\(673\) −5.30782e27 −0.278462 −0.139231 0.990260i \(-0.544463\pi\)
−0.139231 + 0.990260i \(0.544463\pi\)
\(674\) 8.50056e27 + 1.54810e28i 0.439388 + 0.800201i
\(675\) 3.95000e28 2.01168
\(676\) −8.15385e27 + 1.28198e28i −0.409163 + 0.643300i
\(677\) 3.58407e28i 1.77211i 0.463581 + 0.886054i \(0.346564\pi\)
−0.463581 + 0.886054i \(0.653436\pi\)
\(678\) −3.92248e27 7.14351e27i −0.191101 0.348028i
\(679\) 1.68976e28i 0.811200i
\(680\) −3.28842e27 + 5.10338e28i −0.155560 + 2.41417i
\(681\) 6.52839e27 0.304323
\(682\) 2.01683e28 1.10744e28i 0.926457 0.508715i
\(683\) −2.36613e28 −1.07111 −0.535553 0.844502i \(-0.679897\pi\)
−0.535553 + 0.844502i \(0.679897\pi\)
\(684\) 2.62834e27 4.13237e27i 0.117252 0.184348i
\(685\) 2.82367e28i 1.24139i
\(686\) 1.66703e28 9.15364e27i 0.722277 0.396600i
\(687\) 5.57223e27i 0.237937i
\(688\) −1.75916e28 3.75809e28i −0.740322 1.58155i
\(689\) −1.67810e28 −0.696026
\(690\) −1.28957e27 2.34853e27i −0.0527175 0.0960076i
\(691\) −7.90476e27 −0.318499 −0.159250 0.987238i \(-0.550907\pi\)
−0.159250 + 0.987238i \(0.550907\pi\)
\(692\) 1.78323e28 + 1.13420e28i 0.708184 + 0.450432i
\(693\) 2.04066e27i 0.0798799i
\(694\) 1.94212e28 + 3.53694e28i 0.749345 + 1.36469i
\(695\) 3.08445e28i 1.17309i
\(696\) 1.61264e27 2.50269e28i 0.0604567 0.938240i
\(697\) 4.24784e27 0.156979
\(698\) 9.72221e27 5.33844e27i 0.354169 0.194473i
\(699\) 8.49783e27 0.305166
\(700\) −2.06578e28 1.31391e28i −0.731312 0.465142i
\(701\) 2.73811e28i 0.955586i −0.878472 0.477793i \(-0.841437\pi\)
0.878472 0.477793i \(-0.158563\pi\)
\(702\) 1.32875e28 7.29615e27i 0.457166 0.251028i
\(703\) 5.24054e28i 1.77756i
\(704\) 2.76682e28 + 3.58053e27i 0.925239 + 0.119735i
\(705\) −4.63996e28 −1.52976
\(706\) −1.43289e28 2.60953e28i −0.465763 0.848235i
\(707\) 1.15827e28 0.371207
\(708\) −7.29876e27 + 1.14754e28i −0.230630 + 0.362605i
\(709\) 1.71589e27i 0.0534597i −0.999643 0.0267299i \(-0.991491\pi\)
0.999643 0.0267299i \(-0.00850939\pi\)
\(710\) 1.03713e28 + 1.88879e28i 0.318603 + 0.580231i
\(711\) 1.51567e27i 0.0459101i
\(712\) −7.02064e27 4.52384e26i −0.209690 0.0135116i
\(713\) 2.75121e27 0.0810267
\(714\) −1.78972e28 + 9.82728e27i −0.519759 + 0.285398i
\(715\) −2.69497e28 −0.771780
\(716\) −2.68321e28 + 4.21863e28i −0.757746 + 1.19135i
\(717\) 4.65237e28i 1.29564i
\(718\) −2.22211e28 + 1.22016e28i −0.610270 + 0.335097i
\(719\) 1.73205e28i 0.469106i −0.972103 0.234553i \(-0.924637\pi\)
0.972103 0.234553i \(-0.0753626\pi\)
\(720\) −1.06882e28 + 5.00313e27i −0.285483 + 0.133634i
\(721\) 2.62733e27 0.0692089
\(722\) 7.10731e27 + 1.29436e28i 0.184643 + 0.336267i
\(723\) 3.47677e27 0.0890825
\(724\) 1.52513e28 + 9.70039e27i 0.385408 + 0.245134i
\(725\) 7.85960e28i 1.95894i
\(726\) −2.28963e27 4.16982e27i −0.0562859 0.102506i
\(727\) 2.91046e28i 0.705697i 0.935680 + 0.352848i \(0.114787\pi\)
−0.935680 + 0.352848i \(0.885213\pi\)
\(728\) −9.37609e27 6.04160e26i −0.224237 0.0144490i
\(729\) 4.70683e28 1.11033
\(730\) −5.60890e28 + 3.07983e28i −1.30512 + 0.716636i
\(731\) −1.08453e29 −2.48925
\(732\) 2.42766e28 + 1.54408e28i 0.549638 + 0.349590i
\(733\) 6.11377e28i 1.36543i 0.730685 + 0.682714i \(0.239201\pi\)
−0.730685 + 0.682714i \(0.760799\pi\)
\(734\) 8.72302e27 4.78979e27i 0.192179 0.105525i
\(735\) 5.54897e28i 1.20598i
\(736\) 2.69387e27 + 1.96763e27i 0.0577562 + 0.0421856i
\(737\) 5.21295e28 1.10258
\(738\) 4.71806e26 + 8.59240e26i 0.00984465 + 0.0179288i
\(739\) −3.00879e28 −0.619367 −0.309683 0.950840i \(-0.600223\pi\)
−0.309683 + 0.950840i \(0.600223\pi\)
\(740\) 6.77723e28 1.06554e29i 1.37637 2.16398i
\(741\) 2.58226e28i 0.517390i
\(742\) 1.60267e28 + 2.91874e28i 0.316815 + 0.576975i
\(743\) 8.91348e28i 1.73844i −0.494428 0.869218i \(-0.664623\pi\)
0.494428 0.869218i \(-0.335377\pi\)
\(744\) −3.41610e27 + 5.30152e28i −0.0657357 + 1.02017i
\(745\) −4.53555e28 −0.861126
\(746\) −5.45946e28 + 2.99777e28i −1.02273 + 0.561578i
\(747\) 1.11049e28 0.205262
\(748\) 3.91339e28 6.15277e28i 0.713736 1.12216i
\(749\) 1.56362e28i 0.281392i
\(750\) 6.65316e28 3.65323e28i 1.18145 0.648730i
\(751\) 8.75074e28i 1.53336i 0.642026 + 0.766682i \(0.278094\pi\)
−0.642026 + 0.766682i \(0.721906\pi\)
\(752\) 5.23227e28 2.44922e28i 0.904715 0.423496i
\(753\) 6.08348e28 1.03801
\(754\) −1.45177e28 2.64392e28i −0.244446 0.445179i
\(755\) 1.81707e29 3.01928
\(756\) −2.53806e28 1.61430e28i −0.416183 0.264708i
\(757\) 6.81060e28i 1.10211i −0.834468 0.551057i \(-0.814225\pi\)
0.834468 0.551057i \(-0.185775\pi\)
\(758\) −4.05247e27 7.38024e27i −0.0647184 0.117863i
\(759\) 3.82033e27i 0.0602120i
\(760\) 8.25243e27