Properties

Label 8.21.d.b.3.18
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 3.18
Root \(-1372.90 + 1.21540e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.17

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(979.944 + 297.130i) q^{2}\) \(-11837.6 q^{3}\) \(+(872004. + 582341. i) q^{4}\) \(-4.86160e6i q^{5}\) \(+(-1.16002e7 - 3.51730e6i) q^{6}\) \(-3.96260e8i q^{7}\) \(+(6.81484e8 + 8.29760e8i) q^{8}\) \(-3.34666e9 q^{9}\) \(+O(q^{10})\) \(q\)\(+(979.944 + 297.130i) q^{2}\) \(-11837.6 q^{3}\) \(+(872004. + 582341. i) q^{4}\) \(-4.86160e6i q^{5}\) \(+(-1.16002e7 - 3.51730e6i) q^{6}\) \(-3.96260e8i q^{7}\) \(+(6.81484e8 + 8.29760e8i) q^{8}\) \(-3.34666e9 q^{9}\) \(+(1.44453e9 - 4.76409e9i) q^{10}\) \(+2.78400e10 q^{11}\) \(+(-1.03224e10 - 6.89351e9i) q^{12}\) \(-1.92255e11i q^{13}\) \(+(1.17741e11 - 3.88312e11i) q^{14}\) \(+5.75496e10i q^{15}\) \(+(4.21269e11 + 1.01561e12i) q^{16}\) \(+1.00761e12 q^{17}\) \(+(-3.27953e12 - 9.94391e11i) q^{18}\) \(+9.04652e11 q^{19}\) \(+(2.83111e12 - 4.23933e12i) q^{20}\) \(+4.69076e12i q^{21}\) \(+(2.72817e13 + 8.27211e12i) q^{22}\) \(-5.92847e13i q^{23}\) \(+(-8.06712e12 - 9.82235e12i) q^{24}\) \(+7.17323e13 q^{25}\) \(+(5.71247e13 - 1.88399e14i) q^{26}\) \(+8.08914e13 q^{27}\) \(+(2.30758e14 - 3.45540e14i) q^{28}\) \(-4.75437e14i q^{29}\) \(+(-1.70997e13 + 5.63953e13i) q^{30}\) \(+5.26254e14i q^{31}\) \(+(1.11053e14 + 1.12041e15i) q^{32}\) \(-3.29559e14 q^{33}\) \(+(9.87399e14 + 2.99390e14i) q^{34}\) \(-1.92645e15 q^{35}\) \(+(-2.91830e15 - 1.94890e15i) q^{36}\) \(+5.41855e15i q^{37}\) \(+(8.86508e14 + 2.68799e14i) q^{38}\) \(+2.27584e15i q^{39}\) \(+(4.03396e15 - 3.31310e15i) q^{40}\) \(-1.00310e16 q^{41}\) \(+(-1.39376e15 + 4.59668e15i) q^{42}\) \(-2.73018e16 q^{43}\) \(+(2.42766e16 + 1.62124e16i) q^{44}\) \(+1.62701e16i q^{45}\) \(+(1.76153e16 - 5.80957e16i) q^{46}\) \(+5.52785e16i q^{47}\) \(+(-4.98681e15 - 1.20223e16i) q^{48}\) \(-7.72294e16 q^{49}\) \(+(7.02936e16 + 2.13138e16i) q^{50}\) \(-1.19276e16 q^{51}\) \(+(1.11958e17 - 1.67647e17i) q^{52}\) \(+1.63835e16i q^{53}\) \(+(7.92691e16 + 2.40353e16i) q^{54}\) \(-1.35347e17i q^{55}\) \(+(3.28800e17 - 2.70044e17i) q^{56}\) \(-1.07089e16 q^{57}\) \(+(1.41266e17 - 4.65901e17i) q^{58}\) \(-5.08001e17 q^{59}\) \(+(-3.35135e16 + 5.01834e16i) q^{60}\) \(+2.76180e17i q^{61}\) \(+(-1.56366e17 + 5.15700e17i) q^{62}\) \(+1.32614e18i q^{63}\) \(+(-2.24081e17 + 1.13094e18i) q^{64}\) \(-9.34666e17 q^{65}\) \(+(-3.22949e17 - 9.79217e16i) q^{66}\) \(-7.08470e17 q^{67}\) \(+(8.78638e17 + 5.86772e17i) q^{68}\) \(+7.01788e17i q^{69}\) \(+(-1.88782e18 - 5.72407e17i) q^{70}\) \(-2.20639e18i q^{71}\) \(+(-2.28069e18 - 2.77692e18i) q^{72}\) \(+8.31823e18 q^{73}\) \(+(-1.61001e18 + 5.30988e18i) q^{74}\) \(-8.49137e17 q^{75}\) \(+(7.88860e17 + 5.26816e17i) q^{76}\) \(-1.10319e19i q^{77}\) \(+(-6.76218e17 + 2.23019e18i) q^{78}\) \(-2.46057e18i q^{79}\) \(+(4.93747e18 - 2.04804e18i) q^{80}\) \(+1.07115e19 q^{81}\) \(+(-9.82981e18 - 2.98051e18i) q^{82}\) \(+1.22709e19 q^{83}\) \(+(-2.73162e18 + 4.09036e18i) q^{84}\) \(-4.89858e18i q^{85}\) \(+(-2.67543e19 - 8.11219e18i) q^{86}\) \(+5.62802e18i q^{87}\) \(+(1.89725e19 + 2.31005e19i) q^{88}\) \(+3.83975e19 q^{89}\) \(+(-4.83433e18 + 1.59438e19i) q^{90}\) \(-7.61829e19 q^{91}\) \(+(3.45239e19 - 5.16965e19i) q^{92}\) \(-6.22958e18i q^{93}\) \(+(-1.64249e19 + 5.41699e19i) q^{94}\) \(-4.39805e18i q^{95}\) \(+(-1.31460e18 - 1.32629e19i) q^{96}\) \(+2.89133e19 q^{97}\) \(+(-7.56804e19 - 2.29471e19i) q^{98}\) \(-9.31710e19 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 979.944 + 297.130i 0.956976 + 0.290166i
\(3\) −11837.6 −0.200471 −0.100235 0.994964i \(-0.531960\pi\)
−0.100235 + 0.994964i \(0.531960\pi\)
\(4\) 872004. + 582341.i 0.831608 + 0.555364i
\(5\) 4.86160e6i 0.497827i −0.968526 0.248914i \(-0.919926\pi\)
0.968526 0.248914i \(-0.0800736\pi\)
\(6\) −1.16002e7 3.51730e6i −0.191846 0.0581697i
\(7\) 3.96260e8i 1.40281i −0.712762 0.701406i \(-0.752556\pi\)
0.712762 0.701406i \(-0.247444\pi\)
\(8\) 6.81484e8 + 8.29760e8i 0.634681 + 0.772774i
\(9\) −3.34666e9 −0.959812
\(10\) 1.44453e9 4.76409e9i 0.144453 0.476409i
\(11\) 2.78400e10 1.07335 0.536677 0.843788i \(-0.319679\pi\)
0.536677 + 0.843788i \(0.319679\pi\)
\(12\) −1.03224e10 6.89351e9i −0.166713 0.111334i
\(13\) 1.92255e11i 1.39458i −0.716788 0.697291i \(-0.754388\pi\)
0.716788 0.697291i \(-0.245612\pi\)
\(14\) 1.17741e11 3.88312e11i 0.407048 1.34246i
\(15\) 5.75496e10i 0.0997997i
\(16\) 4.21269e11 + 1.01561e12i 0.383142 + 0.923689i
\(17\) 1.00761e12 0.499807 0.249904 0.968271i \(-0.419601\pi\)
0.249904 + 0.968271i \(0.419601\pi\)
\(18\) −3.27953e12 9.94391e11i −0.918517 0.278505i
\(19\) 9.04652e11 0.147552 0.0737761 0.997275i \(-0.476495\pi\)
0.0737761 + 0.997275i \(0.476495\pi\)
\(20\) 2.83111e12 4.23933e12i 0.276475 0.413997i
\(21\) 4.69076e12i 0.281222i
\(22\) 2.72817e13 + 8.27211e12i 1.02717 + 0.311451i
\(23\) 5.92847e13i 1.43108i −0.698571 0.715541i \(-0.746180\pi\)
0.698571 0.715541i \(-0.253820\pi\)
\(24\) −8.06712e12 9.82235e12i −0.127235 0.154918i
\(25\) 7.17323e13 0.752168
\(26\) 5.71247e13 1.88399e14i 0.404660 1.33458i
\(27\) 8.08914e13 0.392884
\(28\) 2.30758e14 3.45540e14i 0.779071 1.16659i
\(29\) 4.75437e14i 1.13009i −0.825060 0.565045i \(-0.808859\pi\)
0.825060 0.565045i \(-0.191141\pi\)
\(30\) −1.70997e13 + 5.63953e13i −0.0289585 + 0.0955060i
\(31\) 5.26254e14i 0.642065i 0.947068 + 0.321032i \(0.104030\pi\)
−0.947068 + 0.321032i \(0.895970\pi\)
\(32\) 1.11053e14 + 1.12041e15i 0.0986351 + 0.995124i
\(33\) −3.29559e14 −0.215176
\(34\) 9.87399e14 + 2.99390e14i 0.478304 + 0.145027i
\(35\) −1.92645e15 −0.698358
\(36\) −2.91830e15 1.94890e15i −0.798187 0.533044i
\(37\) 5.41855e15i 1.12685i 0.826167 + 0.563425i \(0.190517\pi\)
−0.826167 + 0.563425i \(0.809483\pi\)
\(38\) 8.86508e14 + 2.68799e14i 0.141204 + 0.0428146i
\(39\) 2.27584e15i 0.279573i
\(40\) 4.03396e15 3.31310e15i 0.384708 0.315962i
\(41\) −1.00310e16 −0.747318 −0.373659 0.927566i \(-0.621897\pi\)
−0.373659 + 0.927566i \(0.621897\pi\)
\(42\) −1.39376e15 + 4.59668e15i −0.0816011 + 0.269123i
\(43\) −2.73018e16 −1.26330 −0.631651 0.775253i \(-0.717622\pi\)
−0.631651 + 0.775253i \(0.717622\pi\)
\(44\) 2.42766e16 + 1.62124e16i 0.892609 + 0.596102i
\(45\) 1.62701e16i 0.477821i
\(46\) 1.76153e16 5.80957e16i 0.415251 1.36951i
\(47\) 5.52785e16i 1.05094i 0.850812 + 0.525470i \(0.176111\pi\)
−0.850812 + 0.525470i \(0.823889\pi\)
\(48\) −4.98681e15 1.20223e16i −0.0768087 0.185172i
\(49\) −7.72294e16 −0.967880
\(50\) 7.02936e16 + 2.13138e16i 0.719807 + 0.218253i
\(51\) −1.19276e16 −0.100197
\(52\) 1.11958e17 1.67647e17i 0.774500 1.15975i
\(53\) 1.63835e16i 0.0936804i 0.998902 + 0.0468402i \(0.0149152\pi\)
−0.998902 + 0.0468402i \(0.985085\pi\)
\(54\) 7.92691e16 + 2.40353e16i 0.375981 + 0.114002i
\(55\) 1.35347e17i 0.534345i
\(56\) 3.28800e17 2.70044e17i 1.08406 0.890338i
\(57\) −1.07089e16 −0.0295799
\(58\) 1.41266e17 4.65901e17i 0.327913 1.08147i
\(59\) −5.08001e17 −0.993904 −0.496952 0.867778i \(-0.665548\pi\)
−0.496952 + 0.867778i \(0.665548\pi\)
\(60\) −3.35135e16 + 5.01834e16i −0.0554251 + 0.0829942i
\(61\) 2.76180e17i 0.387164i 0.981084 + 0.193582i \(0.0620105\pi\)
−0.981084 + 0.193582i \(0.937990\pi\)
\(62\) −1.56366e17 + 5.15700e17i −0.186305 + 0.614441i
\(63\) 1.32614e18i 1.34643i
\(64\) −2.24081e17 + 1.13094e18i −0.194359 + 0.980930i
\(65\) −9.34666e17 −0.694261
\(66\) −3.22949e17 9.79217e16i −0.205918 0.0624367i
\(67\) −7.08470e17 −0.388663 −0.194332 0.980936i \(-0.562254\pi\)
−0.194332 + 0.980936i \(0.562254\pi\)
\(68\) 8.78638e17 + 5.86772e17i 0.415643 + 0.277575i
\(69\) 7.01788e17i 0.286890i
\(70\) −1.88782e18 5.72407e17i −0.668312 0.202640i
\(71\) 2.20639e18i 0.677795i −0.940823 0.338898i \(-0.889946\pi\)
0.940823 0.338898i \(-0.110054\pi\)
\(72\) −2.28069e18 2.77692e18i −0.609174 0.741717i
\(73\) 8.31823e18 1.93554 0.967770 0.251835i \(-0.0810342\pi\)
0.967770 + 0.251835i \(0.0810342\pi\)
\(74\) −1.61001e18 + 5.30988e18i −0.326973 + 1.07837i
\(75\) −8.49137e17 −0.150787
\(76\) 7.88860e17 + 5.26816e17i 0.122706 + 0.0819451i
\(77\) 1.10319e19i 1.50571i
\(78\) −6.76218e17 + 2.23019e18i −0.0811224 + 0.267544i
\(79\) 2.46057e18i 0.259875i −0.991522 0.129938i \(-0.958522\pi\)
0.991522 0.129938i \(-0.0414777\pi\)
\(80\) 4.93747e18 2.04804e18i 0.459838 0.190739i
\(81\) 1.07115e19 0.881050
\(82\) −9.82981e18 2.98051e18i −0.715166 0.216846i
\(83\) 1.22709e19 0.790851 0.395425 0.918498i \(-0.370597\pi\)
0.395425 + 0.918498i \(0.370597\pi\)
\(84\) −2.73162e18 + 4.09036e18i −0.156181 + 0.233867i
\(85\) 4.89858e18i 0.248818i
\(86\) −2.67543e19 8.11219e18i −1.20895 0.366567i
\(87\) 5.62802e18i 0.226550i
\(88\) 1.89725e19 + 2.31005e19i 0.681238 + 0.829460i
\(89\) 3.83975e19 1.23141 0.615706 0.787976i \(-0.288871\pi\)
0.615706 + 0.787976i \(0.288871\pi\)
\(90\) −4.83433e18 + 1.59438e19i −0.138647 + 0.457263i
\(91\) −7.61829e19 −1.95634
\(92\) 3.45239e19 5.16965e19i 0.794771 1.19010i
\(93\) 6.22958e18i 0.128715i
\(94\) −1.64249e19 + 5.41699e19i −0.304947 + 1.00572i
\(95\) 4.39805e18i 0.0734555i
\(96\) −1.31460e18 1.32629e19i −0.0197734 0.199493i
\(97\) 2.89133e19 0.392085 0.196043 0.980595i \(-0.437191\pi\)
0.196043 + 0.980595i \(0.437191\pi\)
\(98\) −7.56804e19 2.29471e19i −0.926239 0.280846i
\(99\) −9.31710e19 −1.03022
\(100\) 6.25508e19 + 4.17727e19i 0.625508 + 0.417727i
\(101\) 9.84179e19i 0.890964i 0.895291 + 0.445482i \(0.146968\pi\)
−0.895291 + 0.445482i \(0.853032\pi\)
\(102\) −1.16884e19 3.54406e18i −0.0958858 0.0290736i
\(103\) 2.53311e20i 1.88487i 0.334385 + 0.942436i \(0.391471\pi\)
−0.334385 + 0.942436i \(0.608529\pi\)
\(104\) 1.59525e20 1.31019e20i 1.07770 0.885115i
\(105\) 2.28046e19 0.140000
\(106\) −4.86803e18 + 1.60549e19i −0.0271828 + 0.0896499i
\(107\) −3.48945e20 −1.77386 −0.886931 0.461902i \(-0.847167\pi\)
−0.886931 + 0.461902i \(0.847167\pi\)
\(108\) 7.05376e19 + 4.71064e19i 0.326726 + 0.218194i
\(109\) 4.36494e20i 1.84380i −0.387429 0.921899i \(-0.626637\pi\)
0.387429 0.921899i \(-0.373363\pi\)
\(110\) 4.02156e19 1.32632e20i 0.155049 0.511356i
\(111\) 6.41426e19i 0.225900i
\(112\) 4.02444e20 1.66932e20i 1.29576 0.537477i
\(113\) 5.39787e20 1.59015 0.795075 0.606511i \(-0.207431\pi\)
0.795075 + 0.606511i \(0.207431\pi\)
\(114\) −1.04941e19 3.18193e18i −0.0283072 0.00858307i
\(115\) −2.88218e20 −0.712432
\(116\) 2.76866e20 4.14583e20i 0.627611 0.939791i
\(117\) 6.43411e20i 1.33854i
\(118\) −4.97813e20 1.50942e20i −0.951143 0.288397i
\(119\) 3.99274e20i 0.701135i
\(120\) −4.77523e19 + 3.92191e19i −0.0771226 + 0.0633410i
\(121\) 1.02318e20 0.152089
\(122\) −8.20614e19 + 2.70641e20i −0.112342 + 0.370506i
\(123\) 1.18743e20 0.149815
\(124\) −3.06459e20 + 4.58896e20i −0.356579 + 0.533946i
\(125\) 8.12371e20i 0.872277i
\(126\) −3.94037e20 + 1.29955e21i −0.390689 + 1.28851i
\(127\) 1.10768e21i 1.01479i 0.861713 + 0.507396i \(0.169392\pi\)
−0.861713 + 0.507396i \(0.830608\pi\)
\(128\) −5.55622e20 + 1.04167e21i −0.470630 + 0.882331i
\(129\) 3.23188e20 0.253255
\(130\) −9.15920e20 2.77717e20i −0.664392 0.201451i
\(131\) −2.07719e20 −0.139561 −0.0697804 0.997562i \(-0.522230\pi\)
−0.0697804 + 0.997562i \(0.522230\pi\)
\(132\) −2.87377e20 1.91916e20i −0.178942 0.119501i
\(133\) 3.58477e20i 0.206988i
\(134\) −6.94261e20 2.10508e20i −0.371942 0.112777i
\(135\) 3.93261e20i 0.195589i
\(136\) 6.86669e20 + 8.36073e20i 0.317218 + 0.386238i
\(137\) 7.35146e20 0.315622 0.157811 0.987469i \(-0.449556\pi\)
0.157811 + 0.987469i \(0.449556\pi\)
\(138\) −2.08522e20 + 6.87713e20i −0.0832456 + 0.274547i
\(139\) 3.82935e21 1.42225 0.711127 0.703064i \(-0.248185\pi\)
0.711127 + 0.703064i \(0.248185\pi\)
\(140\) −1.67988e21 1.12185e21i −0.580760 0.387843i
\(141\) 6.54364e20i 0.210683i
\(142\) 6.55584e20 2.16214e21i 0.196673 0.648634i
\(143\) 5.35239e21i 1.49688i
\(144\) −1.40984e21 3.39889e21i −0.367744 0.886568i
\(145\) −2.31138e21 −0.562590
\(146\) 8.15140e21 + 2.47159e21i 1.85227 + 0.561628i
\(147\) 9.14209e20 0.194031
\(148\) −3.15545e21 + 4.72500e21i −0.625811 + 0.937097i
\(149\) 3.97915e21i 0.737781i 0.929473 + 0.368891i \(0.120262\pi\)
−0.929473 + 0.368891i \(0.879738\pi\)
\(150\) −8.32107e20 2.52304e20i −0.144300 0.0437534i
\(151\) 3.56951e21i 0.579215i 0.957146 + 0.289607i \(0.0935247\pi\)
−0.957146 + 0.289607i \(0.906475\pi\)
\(152\) 6.16506e20 + 7.50644e20i 0.0936486 + 0.114024i
\(153\) −3.37212e21 −0.479721
\(154\) 3.27790e21 1.08106e22i 0.436907 1.44093i
\(155\) 2.55844e21 0.319637
\(156\) −1.32531e21 + 1.98454e21i −0.155265 + 0.232495i
\(157\) 8.79447e20i 0.0966525i 0.998832 + 0.0483263i \(0.0153887\pi\)
−0.998832 + 0.0483263i \(0.984611\pi\)
\(158\) 7.31109e20 2.41122e21i 0.0754069 0.248694i
\(159\) 1.93941e20i 0.0187802i
\(160\) 5.44698e21 5.39896e20i 0.495400 0.0491033i
\(161\) −2.34921e22 −2.00754
\(162\) 1.04967e22 + 3.18271e21i 0.843144 + 0.255651i
\(163\) 5.56367e21 0.420228 0.210114 0.977677i \(-0.432616\pi\)
0.210114 + 0.977677i \(0.432616\pi\)
\(164\) −8.74707e21 5.84146e21i −0.621475 0.415033i
\(165\) 1.60218e21i 0.107120i
\(166\) 1.20248e22 + 3.64604e21i 0.756826 + 0.229478i
\(167\) 1.51638e22i 0.898759i 0.893341 + 0.449379i \(0.148355\pi\)
−0.893341 + 0.449379i \(0.851645\pi\)
\(168\) −3.89220e21 + 3.19667e21i −0.217321 + 0.178487i
\(169\) −1.79570e22 −0.944860
\(170\) 1.45552e21 4.80034e21i 0.0721984 0.238113i
\(171\) −3.02756e21 −0.141622
\(172\) −2.38073e22 1.58990e22i −1.05057 0.701592i
\(173\) 4.65103e22i 1.93682i 0.249370 + 0.968408i \(0.419777\pi\)
−0.249370 + 0.968408i \(0.580223\pi\)
\(174\) −1.67225e21 + 5.51515e21i −0.0657370 + 0.216803i
\(175\) 2.84246e22i 1.05515i
\(176\) 1.17282e22 + 2.82745e22i 0.411247 + 0.991446i
\(177\) 6.01351e21 0.199249
\(178\) 3.76274e22 + 1.14091e22i 1.17843 + 0.357314i
\(179\) 2.15790e22 0.639001 0.319500 0.947586i \(-0.396485\pi\)
0.319500 + 0.947586i \(0.396485\pi\)
\(180\) −9.47474e21 + 1.41876e22i −0.265364 + 0.397359i
\(181\) 6.42549e22i 1.70263i −0.524654 0.851316i \(-0.675805\pi\)
0.524654 0.851316i \(-0.324195\pi\)
\(182\) −7.46550e22 2.26362e22i −1.87217 0.567662i
\(183\) 3.26931e21i 0.0776149i
\(184\) 4.91921e22 4.04016e22i 1.10590 0.908281i
\(185\) 2.63428e22 0.560977
\(186\) 1.85099e21 6.10464e21i 0.0373487 0.123177i
\(187\) 2.80519e22 0.536470
\(188\) −3.21910e22 + 4.82031e22i −0.583654 + 0.873970i
\(189\) 3.20540e22i 0.551143i
\(190\) 1.30679e21 4.30985e21i 0.0213143 0.0702952i
\(191\) 6.88101e21i 0.106492i −0.998581 0.0532462i \(-0.983043\pi\)
0.998581 0.0532462i \(-0.0169568\pi\)
\(192\) 2.65258e21 1.33875e22i 0.0389633 0.196648i
\(193\) 1.13196e23 1.57854 0.789272 0.614044i \(-0.210458\pi\)
0.789272 + 0.614044i \(0.210458\pi\)
\(194\) 2.83334e22 + 8.59101e21i 0.375216 + 0.113770i
\(195\) 1.10642e22 0.139179
\(196\) −6.73443e22 4.49738e22i −0.804897 0.537526i
\(197\) 1.59402e22i 0.181064i −0.995894 0.0905320i \(-0.971143\pi\)
0.995894 0.0905320i \(-0.0288567\pi\)
\(198\) −9.13024e22 2.76839e22i −0.985894 0.298934i
\(199\) 5.88531e22i 0.604280i −0.953264 0.302140i \(-0.902299\pi\)
0.953264 0.302140i \(-0.0977010\pi\)
\(200\) 4.88844e22 + 5.95206e22i 0.477387 + 0.581256i
\(201\) 8.38658e21 0.0779155
\(202\) −2.92429e22 + 9.64440e22i −0.258527 + 0.852632i
\(203\) −1.88396e23 −1.58530
\(204\) −1.04010e22 6.94596e21i −0.0833243 0.0556456i
\(205\) 4.87667e22i 0.372036i
\(206\) −7.52663e22 + 2.48231e23i −0.546926 + 1.80378i
\(207\) 1.98406e23i 1.37357i
\(208\) 1.95256e23 8.09912e22i 1.28816 0.534324i
\(209\) 2.51856e22 0.158376
\(210\) 2.23472e22 + 6.77591e21i 0.133977 + 0.0406233i
\(211\) −1.31609e23 −0.752424 −0.376212 0.926534i \(-0.622773\pi\)
−0.376212 + 0.926534i \(0.622773\pi\)
\(212\) −9.54080e21 + 1.42865e22i −0.0520267 + 0.0779053i
\(213\) 2.61183e22i 0.135878i
\(214\) −3.41947e23 1.03682e23i −1.69754 0.514714i
\(215\) 1.32730e23i 0.628906i
\(216\) 5.51262e22 + 6.71205e22i 0.249356 + 0.303611i
\(217\) 2.08533e23 0.900696
\(218\) 1.29695e23 4.27740e23i 0.535007 1.76447i
\(219\) −9.84677e22 −0.388019
\(220\) 7.88181e22 1.18023e23i 0.296756 0.444365i
\(221\) 1.93718e23i 0.697022i
\(222\) 1.90587e22 6.28561e22i 0.0655485 0.216181i
\(223\) 2.37547e23i 0.781090i −0.920584 0.390545i \(-0.872287\pi\)
0.920584 0.390545i \(-0.127713\pi\)
\(224\) 4.43973e23 4.40059e22i 1.39597 0.138366i
\(225\) −2.40063e23 −0.721939
\(226\) 5.28961e23 + 1.60387e23i 1.52174 + 0.461407i
\(227\) −3.05009e23 −0.839564 −0.419782 0.907625i \(-0.637893\pi\)
−0.419782 + 0.907625i \(0.637893\pi\)
\(228\) −9.33820e21 6.23623e21i −0.0245988 0.0164276i
\(229\) 2.03839e23i 0.513963i 0.966416 + 0.256981i \(0.0827279\pi\)
−0.966416 + 0.256981i \(0.917272\pi\)
\(230\) −2.82438e23 8.56383e22i −0.681781 0.206723i
\(231\) 1.30591e23i 0.301851i
\(232\) 3.94498e23 3.24003e23i 0.873304 0.717247i
\(233\) 1.55544e23 0.329834 0.164917 0.986307i \(-0.447264\pi\)
0.164917 + 0.986307i \(0.447264\pi\)
\(234\) −1.91177e23 + 6.30507e23i −0.388398 + 1.28095i
\(235\) 2.68742e23 0.523187
\(236\) −4.42979e23 2.95830e23i −0.826538 0.551978i
\(237\) 2.91272e22i 0.0520973i
\(238\) 1.18636e23 3.91266e23i 0.203446 0.670970i
\(239\) 1.59701e23i 0.262620i 0.991341 + 0.131310i \(0.0419184\pi\)
−0.991341 + 0.131310i \(0.958082\pi\)
\(240\) −5.84477e22 + 2.42439e22i −0.0921839 + 0.0382375i
\(241\) −3.71550e22 −0.0562143 −0.0281072 0.999605i \(-0.508948\pi\)
−0.0281072 + 0.999605i \(0.508948\pi\)
\(242\) 1.00266e23 + 3.04017e22i 0.145546 + 0.0441310i
\(243\) −4.08849e23 −0.569509
\(244\) −1.60831e23 + 2.40830e23i −0.215017 + 0.321968i
\(245\) 3.75458e23i 0.481837i
\(246\) 1.16361e23 + 3.52820e22i 0.143370 + 0.0434713i
\(247\) 1.73924e23i 0.205774i
\(248\) −4.36665e23 + 3.58634e23i −0.496171 + 0.407506i
\(249\) −1.45258e23 −0.158542
\(250\) 2.41380e23 7.96078e23i 0.253105 0.834749i
\(251\) 1.22841e24 1.23768 0.618838 0.785519i \(-0.287604\pi\)
0.618838 + 0.785519i \(0.287604\pi\)
\(252\) −7.72268e23 + 1.15640e24i −0.747761 + 1.11971i
\(253\) 1.65049e24i 1.53606i
\(254\) −3.29125e23 + 1.08546e24i −0.294458 + 0.971132i
\(255\) 5.79874e22i 0.0498806i
\(256\) −8.53990e23 + 8.55689e23i −0.706404 + 0.707809i
\(257\) −1.13022e24 −0.899150 −0.449575 0.893242i \(-0.648425\pi\)
−0.449575 + 0.893242i \(0.648425\pi\)
\(258\) 3.16706e23 + 9.60287e22i 0.242359 + 0.0734859i
\(259\) 2.14715e24 1.58076
\(260\) −8.15033e23 5.44295e23i −0.577353 0.385568i
\(261\) 1.59112e24i 1.08467i
\(262\) −2.03553e23 6.17196e22i −0.133556 0.0404958i
\(263\) 1.73822e24i 1.09786i −0.835868 0.548930i \(-0.815035\pi\)
0.835868 0.548930i \(-0.184965\pi\)
\(264\) −2.24589e23 2.73455e23i −0.136568 0.166282i
\(265\) 7.96501e22 0.0466367
\(266\) 1.06514e23 3.51287e23i 0.0600608 0.198083i
\(267\) −4.54534e23 −0.246862
\(268\) −6.17789e23 4.12571e23i −0.323215 0.215849i
\(269\) 1.91524e24i 0.965383i 0.875790 + 0.482691i \(0.160341\pi\)
−0.875790 + 0.482691i \(0.839659\pi\)
\(270\) 1.16850e23 3.85374e23i 0.0567531 0.187174i
\(271\) 2.24447e23i 0.105056i −0.998619 0.0525280i \(-0.983272\pi\)
0.998619 0.0525280i \(-0.0167279\pi\)
\(272\) 4.24475e23 + 1.02333e24i 0.191497 + 0.461667i
\(273\) 9.01821e23 0.392188
\(274\) 7.20402e23 + 2.18434e23i 0.302043 + 0.0915829i
\(275\) 1.99703e24 0.807342
\(276\) −4.08680e23 + 6.11962e23i −0.159328 + 0.238580i
\(277\) 3.22736e24i 1.21353i −0.794883 0.606763i \(-0.792468\pi\)
0.794883 0.606763i \(-0.207532\pi\)
\(278\) 3.75255e24 + 1.13781e24i 1.36106 + 0.412689i
\(279\) 1.76119e24i 0.616261i
\(280\) −1.31285e24 1.59849e24i −0.443235 0.539673i
\(281\) −4.13828e24 −1.34821 −0.674104 0.738636i \(-0.735470\pi\)
−0.674104 + 0.738636i \(0.735470\pi\)
\(282\) 1.94431e23 6.41240e23i 0.0611329 0.201618i
\(283\) 1.84766e24 0.560735 0.280368 0.959893i \(-0.409544\pi\)
0.280368 + 0.959893i \(0.409544\pi\)
\(284\) 1.28487e24 1.92398e24i 0.376423 0.563660i
\(285\) 5.20623e22i 0.0147257i
\(286\) 1.59035e24 5.24504e24i 0.434344 1.43248i
\(287\) 3.97488e24i 1.04835i
\(288\) −3.71657e23 3.74963e24i −0.0946711 0.955131i
\(289\) −3.04896e24 −0.750193
\(290\) −2.26502e24 6.86781e23i −0.538385 0.163244i
\(291\) −3.42264e23 −0.0786015
\(292\) 7.25353e24 + 4.84404e24i 1.60961 + 1.07493i
\(293\) 3.50629e22i 0.00751919i 0.999993 + 0.00375960i \(0.00119672\pi\)
−0.999993 + 0.00375960i \(0.998803\pi\)
\(294\) 8.95874e23 + 2.71639e23i 0.185684 + 0.0563013i
\(295\) 2.46970e24i 0.494793i
\(296\) −4.49610e24 + 3.69266e24i −0.870800 + 0.715190i
\(297\) 2.25202e24 0.421704
\(298\) −1.18232e24 + 3.89934e24i −0.214079 + 0.706039i
\(299\) −1.13978e25 −1.99576
\(300\) −7.40451e23 4.94487e23i −0.125396 0.0837419i
\(301\) 1.08186e25i 1.77217i
\(302\) −1.06061e24 + 3.49792e24i −0.168068 + 0.554295i
\(303\) 1.16503e24i 0.178612i
\(304\) 3.81102e23 + 9.18771e23i 0.0565335 + 0.136292i
\(305\) 1.34268e24 0.192741
\(306\) −3.30449e24 1.00196e24i −0.459081 0.139199i
\(307\) −8.38314e24 −1.12726 −0.563628 0.826028i \(-0.690595\pi\)
−0.563628 + 0.826028i \(0.690595\pi\)
\(308\) 6.42432e24 9.61984e24i 0.836219 1.25216i
\(309\) 2.99859e24i 0.377861i
\(310\) 2.50712e24 + 7.60188e23i 0.305885 + 0.0927478i
\(311\) 7.29114e24i 0.861374i 0.902501 + 0.430687i \(0.141729\pi\)
−0.902501 + 0.430687i \(0.858271\pi\)
\(312\) −1.88840e24 + 1.55094e24i −0.216046 + 0.177440i
\(313\) 7.51935e24 0.833177 0.416588 0.909095i \(-0.363226\pi\)
0.416588 + 0.909095i \(0.363226\pi\)
\(314\) −2.61310e23 + 8.61809e23i −0.0280453 + 0.0924942i
\(315\) 6.44718e24 0.670292
\(316\) 1.43289e24 2.14563e24i 0.144325 0.216114i
\(317\) 7.43530e24i 0.725615i −0.931864 0.362807i \(-0.881818\pi\)
0.931864 0.362807i \(-0.118182\pi\)
\(318\) 5.76257e22 1.90052e23i 0.00544936 0.0179722i
\(319\) 1.32362e25i 1.21299i
\(320\) 5.49815e24 + 1.08939e24i 0.488334 + 0.0967574i
\(321\) 4.13067e24 0.355607
\(322\) −2.30210e25 6.98022e24i −1.92117 0.582519i
\(323\) 9.11535e23 0.0737476
\(324\) 9.34048e24 + 6.23775e24i 0.732688 + 0.489303i
\(325\) 1.37909e25i 1.04896i
\(326\) 5.45209e24 + 1.65313e24i 0.402149 + 0.121936i
\(327\) 5.16704e24i 0.369627i
\(328\) −6.83596e24 8.32332e24i −0.474309 0.577508i
\(329\) 2.19046e25 1.47427
\(330\) −4.76056e23 + 1.57005e24i −0.0310827 + 0.102512i
\(331\) −7.67940e22 −0.00486460 −0.00243230 0.999997i \(-0.500774\pi\)
−0.00243230 + 0.999997i \(0.500774\pi\)
\(332\) 1.07002e25 + 7.14583e24i 0.657678 + 0.439210i
\(333\) 1.81340e25i 1.08156i
\(334\) −4.50562e24 + 1.48597e25i −0.260789 + 0.860091i
\(335\) 3.44430e24i 0.193487i
\(336\) −4.76396e24 + 1.97607e24i −0.259762 + 0.107748i
\(337\) 1.40411e25 0.743196 0.371598 0.928394i \(-0.378810\pi\)
0.371598 + 0.928394i \(0.378810\pi\)
\(338\) −1.75969e25 5.33557e24i −0.904209 0.274166i
\(339\) −6.38978e24 −0.318778
\(340\) 2.85265e24 4.27158e24i 0.138184 0.206919i
\(341\) 1.46509e25i 0.689163i
\(342\) −2.96684e24 8.99578e23i −0.135529 0.0410940i
\(343\) 1.01557e24i 0.0450579i
\(344\) −1.86058e25 2.26540e25i −0.801794 0.976247i
\(345\) 3.41181e24 0.142822
\(346\) −1.38196e25 + 4.55775e25i −0.561998 + 1.85349i
\(347\) 4.44481e24 0.175614 0.0878068 0.996138i \(-0.472014\pi\)
0.0878068 + 0.996138i \(0.472014\pi\)
\(348\) −3.27743e24 + 4.90766e24i −0.125817 + 0.188400i
\(349\) 3.02572e25i 1.12869i 0.825539 + 0.564346i \(0.190871\pi\)
−0.825539 + 0.564346i \(0.809129\pi\)
\(350\) 8.44580e24 2.78545e25i 0.306168 1.00975i
\(351\) 1.55518e25i 0.547910i
\(352\) 3.09173e24 + 3.11922e25i 0.105870 + 1.06812i
\(353\) −3.47498e25 −1.15666 −0.578329 0.815804i \(-0.696295\pi\)
−0.578329 + 0.815804i \(0.696295\pi\)
\(354\) 5.89290e24 + 1.78679e24i 0.190676 + 0.0578151i
\(355\) −1.07266e25 −0.337425
\(356\) 3.34828e25 + 2.23605e25i 1.02405 + 0.683881i
\(357\) 4.72644e24i 0.140557i
\(358\) 2.11462e25 + 6.41177e24i 0.611509 + 0.185416i
\(359\) 1.38151e25i 0.388516i −0.980950 0.194258i \(-0.937770\pi\)
0.980950 0.194258i \(-0.0622300\pi\)
\(360\) −1.35003e25 + 1.10878e25i −0.369247 + 0.303264i
\(361\) −3.67716e25 −0.978228
\(362\) 1.90921e25 6.29662e25i 0.494045 1.62938i
\(363\) −1.21120e24 −0.0304894
\(364\) −6.64318e25 4.43644e25i −1.62690 1.08648i
\(365\) 4.04399e25i 0.963565i
\(366\) 9.71409e23 3.20374e24i 0.0225212 0.0742756i
\(367\) 8.35212e25i 1.88424i 0.335277 + 0.942120i \(0.391170\pi\)
−0.335277 + 0.942120i \(0.608830\pi\)
\(368\) 6.02100e25 2.49749e25i 1.32188 0.548308i
\(369\) 3.35703e25 0.717285
\(370\) 2.58145e25 + 7.82724e24i 0.536842 + 0.162776i
\(371\) 6.49213e24 0.131416
\(372\) 3.62774e24 5.43222e24i 0.0714836 0.107040i
\(373\) 5.09653e25i 0.977656i 0.872380 + 0.488828i \(0.162575\pi\)
−0.872380 + 0.488828i \(0.837425\pi\)
\(374\) 2.74892e25 + 8.33504e24i 0.513389 + 0.155665i
\(375\) 9.61652e24i 0.174866i
\(376\) −4.58679e25 + 3.76714e25i −0.812139 + 0.667012i
\(377\) −9.14051e25 −1.57600
\(378\) 9.52420e24 3.14111e25i 0.159923 0.527431i
\(379\) 2.21704e25 0.362562 0.181281 0.983431i \(-0.441976\pi\)
0.181281 + 0.983431i \(0.441976\pi\)
\(380\) 2.56117e24 3.83512e24i 0.0407945 0.0610862i
\(381\) 1.31123e25i 0.203436i
\(382\) 2.04455e24 6.74301e24i 0.0309005 0.101911i
\(383\) 1.03560e26i 1.52477i −0.647126 0.762383i \(-0.724029\pi\)
0.647126 0.762383i \(-0.275971\pi\)
\(384\) 6.57722e24 1.23309e25i 0.0943474 0.176881i
\(385\) −5.36326e25 −0.749586
\(386\) 1.10925e26 + 3.36338e25i 1.51063 + 0.458039i
\(387\) 9.13698e25 1.21253
\(388\) 2.52125e25 + 1.68374e25i 0.326061 + 0.217750i
\(389\) 7.82150e25i 0.985812i 0.870082 + 0.492906i \(0.164065\pi\)
−0.870082 + 0.492906i \(0.835935\pi\)
\(390\) 1.08423e25 + 3.28750e24i 0.133191 + 0.0403850i
\(391\) 5.97358e25i 0.715265i
\(392\) −5.26306e25 6.40818e25i −0.614295 0.747953i
\(393\) 2.45889e24 0.0279778
\(394\) 4.73631e24 1.56205e25i 0.0525386 0.173274i
\(395\) −1.19623e25 −0.129373
\(396\) −8.12455e25 5.42573e25i −0.856737 0.572145i
\(397\) 6.91197e25i 0.710718i −0.934730 0.355359i \(-0.884359\pi\)
0.934730 0.355359i \(-0.115641\pi\)
\(398\) 1.74870e25 5.76727e25i 0.175341 0.578282i
\(399\) 4.24350e24i 0.0414950i
\(400\) 3.02186e25 + 7.28518e25i 0.288187 + 0.694769i
\(401\) 9.67081e24 0.0899537 0.0449768 0.998988i \(-0.485679\pi\)
0.0449768 + 0.998988i \(0.485679\pi\)
\(402\) 8.21837e24 + 2.49190e24i 0.0745633 + 0.0226084i
\(403\) 1.01175e26 0.895412
\(404\) −5.73128e25 + 8.58208e25i −0.494809 + 0.740933i
\(405\) 5.20750e25i 0.438611i
\(406\) −1.84618e26 5.59782e25i −1.51710 0.460001i
\(407\) 1.50853e26i 1.20951i
\(408\) −8.12850e24 9.89708e24i −0.0635929 0.0774293i
\(409\) 3.70175e25 0.282601 0.141301 0.989967i \(-0.454872\pi\)
0.141301 + 0.989967i \(0.454872\pi\)
\(410\) −1.44900e25 + 4.77886e25i −0.107952 + 0.356029i
\(411\) −8.70235e24 −0.0632730
\(412\) −1.47513e26 + 2.20888e26i −1.04679 + 1.56747i
\(413\) 2.01300e26i 1.39426i
\(414\) −5.89522e25 + 1.94426e26i −0.398563 + 1.31447i
\(415\) 5.96560e25i 0.393707i
\(416\) 2.15404e26 2.13505e25i 1.38778 0.137555i
\(417\) −4.53302e25 −0.285120
\(418\) 2.46804e25 + 7.48338e24i 0.151562 + 0.0459552i
\(419\) −1.11094e26 −0.666118 −0.333059 0.942906i \(-0.608081\pi\)
−0.333059 + 0.942906i \(0.608081\pi\)
\(420\) 1.98857e25 + 1.32800e25i 0.116425 + 0.0777510i
\(421\) 2.76341e26i 1.57988i −0.613183 0.789941i \(-0.710111\pi\)
0.613183 0.789941i \(-0.289889\pi\)
\(422\) −1.28970e26 3.91051e25i −0.720052 0.218328i
\(423\) 1.84998e26i 1.00870i
\(424\) −1.35944e25 + 1.11651e25i −0.0723938 + 0.0594572i
\(425\) 7.22781e25 0.375939
\(426\) −7.76053e24 + 2.55945e25i −0.0394271 + 0.130032i
\(427\) 1.09439e26 0.543118
\(428\) −3.04282e26 2.03205e26i −1.47516 0.985138i
\(429\) 6.33593e25i 0.300080i
\(430\) −3.94382e25 + 1.30068e26i −0.182487 + 0.601849i
\(431\) 2.45142e26i 1.10827i 0.832427 + 0.554134i \(0.186950\pi\)
−0.832427 + 0.554134i \(0.813050\pi\)
\(432\) 3.40771e25 + 8.21539e25i 0.150531 + 0.362903i
\(433\) 3.48165e26 1.50282 0.751409 0.659837i \(-0.229375\pi\)
0.751409 + 0.659837i \(0.229375\pi\)
\(434\) 2.04351e26 + 6.19615e25i 0.861944 + 0.261351i
\(435\) 2.73612e25 0.112783
\(436\) 2.54189e26 3.80625e26i 1.02398 1.53332i
\(437\) 5.36321e25i 0.211159i
\(438\) −9.64928e25 2.92577e25i −0.371325 0.112590i
\(439\) 1.66012e26i 0.624445i −0.950009 0.312223i \(-0.898927\pi\)
0.950009 0.312223i \(-0.101073\pi\)
\(440\) 1.12306e26 9.22368e25i 0.412928 0.339139i
\(441\) 2.58460e26 0.928983
\(442\) 5.75593e25 1.89833e26i 0.202252 0.667034i
\(443\) −5.32389e26 −1.82891 −0.914454 0.404689i \(-0.867380\pi\)
−0.914454 + 0.404689i \(0.867380\pi\)
\(444\) 3.73528e25 5.59326e25i 0.125457 0.187860i
\(445\) 1.86673e26i 0.613031i
\(446\) 7.05823e25 2.32783e26i 0.226646 0.747485i
\(447\) 4.71035e25i 0.147903i
\(448\) 4.48144e26 + 8.87943e25i 1.37606 + 0.272650i
\(449\) −2.32273e26 −0.697487 −0.348743 0.937218i \(-0.613391\pi\)
−0.348743 + 0.937218i \(0.613391\pi\)
\(450\) −2.35249e26 7.13300e25i −0.690879 0.209482i
\(451\) −2.79263e26 −0.802137
\(452\) 4.70697e26 + 3.14340e26i 1.32238 + 0.883112i
\(453\) 4.22544e25i 0.116115i
\(454\) −2.98891e26 9.06272e25i −0.803442 0.243613i
\(455\) 3.70370e26i 0.973918i
\(456\) −7.29794e24 8.88581e24i −0.0187738 0.0228586i
\(457\) 5.64579e25 0.142090 0.0710449 0.997473i \(-0.477367\pi\)
0.0710449 + 0.997473i \(0.477367\pi\)
\(458\) −6.05665e25 + 1.99750e26i −0.149134 + 0.491850i
\(459\) 8.15069e25 0.196366
\(460\) −2.51328e26 1.67841e26i −0.592464 0.395659i
\(461\) 4.09880e26i 0.945469i 0.881205 + 0.472735i \(0.156733\pi\)
−0.881205 + 0.472735i \(0.843267\pi\)
\(462\) −3.88024e25 + 1.27972e26i −0.0875869 + 0.288864i
\(463\) 4.96909e26i 1.09766i 0.835935 + 0.548829i \(0.184926\pi\)
−0.835935 + 0.548829i \(0.815074\pi\)
\(464\) 4.82857e26 2.00287e26i 1.04385 0.432985i
\(465\) −3.02857e25 −0.0640779
\(466\) 1.52425e26 + 4.62169e25i 0.315643 + 0.0957064i
\(467\) −6.59837e26 −1.33742 −0.668710 0.743523i \(-0.733153\pi\)
−0.668710 + 0.743523i \(0.733153\pi\)
\(468\) −3.74685e26 + 5.61057e26i −0.743374 + 1.11314i
\(469\) 2.80738e26i 0.545221i
\(470\) 2.63352e26 + 7.98512e25i 0.500677 + 0.151811i
\(471\) 1.04105e25i 0.0193760i
\(472\) −3.46195e26 4.21519e26i −0.630812 0.768063i
\(473\) −7.60084e26 −1.35597
\(474\) −8.65456e24 + 2.85430e25i −0.0151169 + 0.0498559i
\(475\) 6.48928e25 0.110984
\(476\) 2.32514e26 3.48169e26i 0.389385 0.583069i
\(477\) 5.48300e25i 0.0899155i
\(478\) −4.74519e25 + 1.56498e26i −0.0762034 + 0.251321i
\(479\) 3.67403e26i 0.577813i −0.957357 0.288906i \(-0.906708\pi\)
0.957357 0.288906i \(-0.0932916\pi\)
\(480\) −6.44791e25 + 6.39107e24i −0.0993131 + 0.00984376i
\(481\) 1.04174e27 1.57148
\(482\) −3.64098e25 1.10399e25i −0.0537958 0.0163115i
\(483\) 2.78090e26 0.402452
\(484\) 8.92216e25 + 5.95839e25i 0.126478 + 0.0844647i
\(485\) 1.40565e26i 0.195191i
\(486\) −4.00649e26 1.21481e26i −0.545007 0.165252i
\(487\) 8.25813e26i 1.10051i −0.834998 0.550253i \(-0.814531\pi\)
0.834998 0.550253i \(-0.185469\pi\)
\(488\) −2.29163e26 + 1.88212e26i −0.299190 + 0.245725i
\(489\) −6.58604e25 −0.0842434
\(490\) −1.11560e26 + 3.67928e26i −0.139813 + 0.461107i
\(491\) 3.79623e26 0.466163 0.233082 0.972457i \(-0.425119\pi\)
0.233082 + 0.972457i \(0.425119\pi\)
\(492\) 1.03544e26 + 6.91488e25i 0.124588 + 0.0832020i
\(493\) 4.79054e26i 0.564827i
\(494\) 5.16780e25 1.70436e26i 0.0597085 0.196921i
\(495\) 4.52960e26i 0.512871i
\(496\) −5.34468e26 + 2.21695e26i −0.593068 + 0.246002i
\(497\) −8.74302e26 −0.950819
\(498\) −1.42344e26 4.31603e25i −0.151721 0.0460036i
\(499\) 1.58664e27 1.65757 0.828784 0.559568i \(-0.189033\pi\)
0.828784 + 0.559568i \(0.189033\pi\)
\(500\) 4.73077e26 7.08391e26i 0.484431 0.725392i
\(501\) 1.79503e26i 0.180175i
\(502\) 1.20378e27 + 3.64998e26i 1.18443 + 0.359131i
\(503\) 1.42295e27i 1.37249i 0.727372 + 0.686244i \(0.240742\pi\)
−0.727372 + 0.686244i \(0.759258\pi\)
\(504\) −1.10038e27 + 9.03746e26i −1.04049 + 0.854557i
\(505\) 4.78468e26 0.443547
\(506\) 4.90410e26 1.61739e27i 0.445712 1.46997i
\(507\) 2.12568e26 0.189417
\(508\) −6.45047e26 + 9.65901e26i −0.563579 + 0.843909i
\(509\) 9.54843e26i 0.818001i −0.912534 0.409001i \(-0.865877\pi\)
0.912534 0.409001i \(-0.134123\pi\)
\(510\) −1.72298e25 + 5.68244e25i −0.0144737 + 0.0477346i
\(511\) 3.29618e27i 2.71520i
\(512\) −1.09111e27 + 5.84781e26i −0.881394 + 0.472382i
\(513\) 7.31786e25 0.0579710
\(514\) −1.10755e27 3.35823e26i −0.860466 0.260903i
\(515\) 1.23150e27 0.938342
\(516\) 2.81821e26 + 1.88205e26i 0.210609 + 0.140649i
\(517\) 1.53896e27i 1.12803i
\(518\) 2.10409e27 + 6.37983e26i 1.51275 + 0.458682i
\(519\) 5.50570e26i 0.388275i
\(520\) −6.36960e26 7.75549e26i −0.440635 0.536507i
\(521\) −3.59622e26 −0.244044 −0.122022 0.992527i \(-0.538938\pi\)
−0.122022 + 0.992527i \(0.538938\pi\)
\(522\) −4.72770e26 + 1.55921e27i −0.314735 + 1.03801i
\(523\) −4.12832e26 −0.269623 −0.134811 0.990871i \(-0.543043\pi\)
−0.134811 + 0.990871i \(0.543043\pi\)
\(524\) −1.81132e26 1.20963e26i −0.116060 0.0775071i
\(525\) 3.36479e26i 0.211526i
\(526\) 5.16477e26 1.70336e27i 0.318562 1.05063i
\(527\) 5.30258e26i 0.320908i
\(528\) −1.38833e26 3.34702e26i −0.0824430 0.198756i
\(529\) −1.79852e27 −1.04800
\(530\) 7.80526e25 + 2.36664e25i 0.0446302 + 0.0135324i
\(531\) 1.70011e27 0.953961
\(532\) 2.08756e26 3.12593e26i 0.114954 0.172133i
\(533\) 1.92851e27i 1.04220i
\(534\) −4.45418e26 1.35056e26i −0.236241 0.0716309i
\(535\) 1.69643e27i 0.883077i
\(536\) −4.82811e26 5.87860e26i −0.246677 0.300349i
\(537\) −2.55443e26 −0.128101
\(538\) −5.69074e26 + 1.87682e27i −0.280121 + 0.923849i
\(539\) −2.15007e27 −1.03888
\(540\) 2.29012e26 3.42925e26i 0.108623 0.162653i
\(541\) 1.95235e27i 0.909045i −0.890735 0.454523i \(-0.849810\pi\)
0.890735 0.454523i \(-0.150190\pi\)
\(542\) 6.66899e25 2.19946e26i 0.0304837 0.100536i
\(543\) 7.60623e26i 0.341327i
\(544\) 1.11898e26 + 1.12893e27i 0.0492985 + 0.497370i
\(545\) −2.12206e27 −0.917894
\(546\) 8.83734e26 + 2.67958e26i 0.375314 + 0.113799i
\(547\) −8.12726e26 −0.338899 −0.169450 0.985539i \(-0.554199\pi\)
−0.169450 + 0.985539i \(0.554199\pi\)
\(548\) 6.41050e26 + 4.28106e26i 0.262474 + 0.175285i
\(549\) 9.24281e26i 0.371604i
\(550\) 1.95698e27 + 5.93377e26i 0.772608 + 0.234263i
\(551\) 4.30105e26i 0.166747i
\(552\) −5.82316e26 + 4.78257e26i −0.221701 + 0.182084i
\(553\) −9.75025e26 −0.364556
\(554\) 9.58944e26 3.16263e27i 0.352124 1.16132i
\(555\) −3.11835e26 −0.112459
\(556\) 3.33921e27 + 2.22999e27i 1.18276 + 0.789868i
\(557\) 4.65269e27i 1.61865i 0.587364 + 0.809323i \(0.300166\pi\)
−0.587364 + 0.809323i \(0.699834\pi\)
\(558\) 5.23303e26 1.72587e27i 0.178818 0.589747i
\(559\) 5.24891e27i 1.76178i
\(560\) −8.11556e26 1.95652e27i −0.267571 0.645066i
\(561\) −3.32066e26 −0.107546
\(562\) −4.05529e27 1.22961e27i −1.29020 0.391204i
\(563\) −1.62681e27 −0.508455 −0.254228 0.967144i \(-0.581821\pi\)
−0.254228 + 0.967144i \(0.581821\pi\)
\(564\) 3.81063e26 5.70608e26i 0.117005 0.175205i
\(565\) 2.62423e27i 0.791621i
\(566\) 1.81060e27 + 5.48995e26i 0.536610 + 0.162706i
\(567\) 4.24454e27i 1.23595i
\(568\) 1.83077e27 1.50362e27i 0.523782 0.430184i
\(569\) 3.69001e27 1.03730 0.518651 0.854986i \(-0.326435\pi\)
0.518651 + 0.854986i \(0.326435\pi\)
\(570\) −1.54693e25 + 5.10182e25i −0.00427289 + 0.0140921i
\(571\) 3.77393e26 0.102431 0.0512156 0.998688i \(-0.483690\pi\)
0.0512156 + 0.998688i \(0.483690\pi\)
\(572\) 3.11692e27 4.66730e27i 0.831313 1.24482i
\(573\) 8.14546e25i 0.0213486i
\(574\) −1.18105e27 + 3.89516e27i −0.304194 + 1.00324i
\(575\) 4.25263e27i 1.07641i
\(576\) 7.49922e26 3.78485e27i 0.186548 0.941508i
\(577\) 5.96875e27 1.45923 0.729617 0.683856i \(-0.239698\pi\)
0.729617 + 0.683856i \(0.239698\pi\)
\(578\) −2.98781e27 9.05936e26i −0.717917 0.217680i
\(579\) −1.33996e27 −0.316451
\(580\) −2.01553e27 1.34601e27i −0.467854 0.312442i
\(581\) 4.86245e27i 1.10941i
\(582\) −3.35399e26 1.01697e26i −0.0752198 0.0228075i
\(583\) 4.56118e26i 0.100552i
\(584\) 5.66874e27 + 6.90213e27i 1.22845 + 1.49574i
\(585\) 3.12801e27 0.666360
\(586\) −1.04182e25 + 3.43596e25i −0.00218181 + 0.00719569i
\(587\) −5.25622e27 −1.08216 −0.541081 0.840970i \(-0.681985\pi\)
−0.541081 + 0.840970i \(0.681985\pi\)
\(588\) 7.97194e26 + 5.32381e26i 0.161358 + 0.107758i
\(589\) 4.76077e26i 0.0947380i
\(590\) −7.33820e26 + 2.42016e27i −0.143572 + 0.473505i
\(591\) 1.88694e26i 0.0362980i
\(592\) −5.50312e27 + 2.28267e27i −1.04086 + 0.431744i
\(593\) 2.01007e27 0.373821 0.186911 0.982377i \(-0.440153\pi\)
0.186911 + 0.982377i \(0.440153\pi\)
\(594\) 2.20685e27 + 6.69142e26i 0.403561 + 0.122364i
\(595\) −1.94111e27 −0.349044
\(596\) −2.31722e27 + 3.46983e27i −0.409737 + 0.613545i
\(597\) 6.96678e26i 0.121140i
\(598\) −1.11692e28 3.38662e27i −1.90990 0.579102i
\(599\) 5.36055e27i 0.901448i 0.892663 + 0.450724i \(0.148834\pi\)
−0.892663 + 0.450724i \(0.851166\pi\)
\(600\) −5.78673e26 7.04580e26i −0.0957020 0.116525i
\(601\) 6.55184e25 0.0106566 0.00532830 0.999986i \(-0.498304\pi\)
0.00532830 + 0.999986i \(0.498304\pi\)
\(602\) −3.21453e27 + 1.06016e28i −0.514225 + 1.69593i
\(603\) 2.37101e27 0.373044
\(604\) −2.07867e27 + 3.11263e27i −0.321675 + 0.481679i
\(605\) 4.97428e26i 0.0757141i
\(606\) 3.46165e26 1.14166e27i 0.0518271 0.170928i
\(607\) 8.75457e27i 1.28928i 0.764485 + 0.644641i \(0.222993\pi\)
−0.764485 + 0.644641i \(0.777007\pi\)
\(608\) 1.00465e26 + 1.01358e27i 0.0145538 + 0.146833i
\(609\) 2.23016e27 0.317806
\(610\) 1.31575e27 + 3.98949e26i 0.184448 + 0.0559267i
\(611\) 1.06276e28 1.46562
\(612\) −2.94050e27 1.96372e27i −0.398939 0.266419i
\(613\) 3.98007e27i 0.531234i −0.964079 0.265617i \(-0.914424\pi\)
0.964079 0.265617i \(-0.0855756\pi\)
\(614\) −8.21500e27 2.49088e27i −1.07876 0.327091i
\(615\) 5.77279e26i 0.0745822i
\(616\) 9.15381e27 7.51805e27i 1.16358 0.955648i
\(617\) −1.86653e27 −0.233445 −0.116722 0.993165i \(-0.537239\pi\)
−0.116722 + 0.993165i \(0.537239\pi\)
\(618\) 8.90971e26 2.93845e27i 0.109642 0.361605i
\(619\) −1.35625e28 −1.64223 −0.821114 0.570764i \(-0.806647\pi\)
−0.821114 + 0.570764i \(0.806647\pi\)
\(620\) 2.23097e27 + 1.48988e27i 0.265813 + 0.177515i
\(621\) 4.79563e27i 0.562250i
\(622\) −2.16642e27 + 7.14491e27i −0.249941 + 0.824314i
\(623\) 1.52154e28i 1.72744i
\(624\) −2.31135e27 + 9.58740e26i −0.258238 + 0.107116i
\(625\) 2.89150e27 0.317924
\(626\) 7.36854e27 + 2.23422e27i 0.797330 + 0.241759i
\(627\) −2.98136e26 −0.0317497
\(628\) −5.12138e26 + 7.66881e26i −0.0536773 + 0.0803770i
\(629\) 5.45978e27i 0.563208i
\(630\) 6.31787e27 + 1.91565e27i 0.641454 + 0.194496i
\(631\) 1.05880e28i 1.05808i −0.848597 0.529040i \(-0.822552\pi\)
0.848597 0.529040i \(-0.177448\pi\)
\(632\) 2.04168e27 1.67684e27i 0.200825 0.164938i
\(633\) 1.55794e27 0.150839
\(634\) 2.20925e27 7.28618e27i 0.210549 0.694396i
\(635\) 5.38509e27 0.505191
\(636\) 1.12940e26 1.69118e26i 0.0104298 0.0156177i
\(637\) 1.48477e28i 1.34979i
\(638\) 3.93286e27 1.29707e28i 0.351967 1.16080i
\(639\) 7.38402e27i 0.650556i
\(640\) 5.06419e27 + 2.70121e27i 0.439248 + 0.234292i
\(641\) −4.49180e27 −0.383566 −0.191783 0.981437i \(-0.561427\pi\)
−0.191783 + 0.981437i \(0.561427\pi\)
\(642\) 4.04783e27 + 1.22735e27i 0.340308 + 0.103185i
\(643\) 9.22634e27 0.763694 0.381847 0.924225i \(-0.375288\pi\)
0.381847 + 0.924225i \(0.375288\pi\)
\(644\) −2.04852e28 1.36804e28i −1.66948 1.11491i
\(645\) 1.57121e27i 0.126077i
\(646\) 8.93253e26 + 2.70844e26i 0.0705748 + 0.0213990i
\(647\) 9.33398e27i 0.726146i 0.931761 + 0.363073i \(0.118272\pi\)
−0.931761 + 0.363073i \(0.881728\pi\)
\(648\) 7.29972e27 + 8.88798e27i 0.559186 + 0.680852i
\(649\) −1.41428e28 −1.06681
\(650\) 4.09769e27 1.35143e28i 0.304372 1.00383i
\(651\) −2.46853e27 −0.180563
\(652\) 4.85154e27 + 3.23995e27i 0.349465 + 0.233380i
\(653\) 1.60220e28i 1.13654i −0.822842 0.568270i \(-0.807613\pi\)
0.822842 0.568270i \(-0.192387\pi\)
\(654\) −1.53528e27 + 5.06341e27i −0.107253 + 0.353725i
\(655\) 1.00985e27i 0.0694772i
\(656\) −4.22575e27 1.01876e28i −0.286329 0.690290i
\(657\) −2.78382e28 −1.85775
\(658\) 2.14653e28 + 6.50852e27i 1.41084 + 0.427783i
\(659\) 2.39029e28 1.54738 0.773688 0.633566i \(-0.218410\pi\)
0.773688 + 0.633566i \(0.218410\pi\)
\(660\) −9.33016e26 + 1.39711e27i −0.0594908 + 0.0890822i
\(661\) 1.77129e28i 1.11243i 0.831037 + 0.556217i \(0.187748\pi\)
−0.831037 + 0.556217i \(0.812252\pi\)
\(662\) −7.52538e25 2.28178e25i −0.00465531 0.00141154i
\(663\) 2.29315e27i 0.139732i
\(664\) 8.36240e27 + 1.01819e28i 0.501938 + 0.611149i
\(665\) −1.74277e27 −0.103044
\(666\) 5.38816e27 1.77703e28i 0.313833 1.03503i
\(667\) −2.81862e28 −1.61725
\(668\) −8.83050e27 + 1.32229e28i −0.499138 + 0.747415i
\(669\) 2.81198e27i 0.156586i
\(670\) −1.02340e27 + 3.37522e27i −0.0561434 + 0.185163i
\(671\) 7.68887e27i 0.415564i
\(672\) −5.25557e27 + 5.20924e26i −0.279851 + 0.0277384i
\(673\) −2.07760e27 −0.108996 −0.0544981 0.998514i \(-0.517356\pi\)
−0.0544981 + 0.998514i \(0.517356\pi\)
\(674\) 1.37595e28 + 4.17204e27i 0.711221 + 0.215650i
\(675\) 5.80253e27 0.295515
\(676\) −1.56586e28 1.04571e28i −0.785753 0.524741i
\(677\) 6.05106e26i 0.0299188i 0.999888 + 0.0149594i \(0.00476191\pi\)
−0.999888 + 0.0149594i \(0.995238\pi\)
\(678\) −6.26162e27 1.89859e27i −0.305063 0.0924986i
\(679\) 1.14572e28i 0.550022i
\(680\) 4.06465e27 3.33831e27i 0.192280 0.157920i
\(681\) 3.61057e27 0.168308
\(682\) −4.35323e27 + 1.43571e28i −0.199971 + 0.659512i
\(683\) −2.09376e27 −0.0947809 −0.0473904 0.998876i \(-0.515090\pi\)
−0.0473904 + 0.998876i \(0.515090\pi\)
\(684\) −2.64004e27 1.76307e27i −0.117774 0.0786519i
\(685\) 3.57398e27i 0.157126i
\(686\) 3.01757e26 9.95206e26i 0.0130743 0.0431193i
\(687\) 2.41296e27i 0.103034i
\(688\) −1.15014e28 2.77279e28i −0.484025 1.16690i
\(689\) 3.14981e27 0.130645
\(690\) 3.34338e27 + 1.01375e27i 0.136677 + 0.0414420i
\(691\) 2.96337e28 1.19400 0.597002 0.802240i \(-0.296358\pi\)
0.597002 + 0.802240i \(0.296358\pi\)
\(692\) −2.70849e28 + 4.05572e28i −1.07564 + 1.61067i
\(693\) 3.69199e28i 1.44520i
\(694\) 4.35566e27 + 1.32069e27i 0.168058 + 0.0509571i
\(695\) 1.86168e28i 0.708037i
\(696\) −4.66991e27 + 3.83541e27i −0.175072 + 0.143787i
\(697\) −1.01073e28 −0.373515
\(698\) −8.99033e27 + 2.96504e28i −0.327508 + 1.08013i
\(699\) −1.84127e27 −0.0661219
\(700\) 1.65528e28 2.47864e28i 0.585992 0.877471i
\(701\) 2.48058e28i 0.865713i −0.901463 0.432856i \(-0.857506\pi\)
0.901463 0.432856i \(-0.142494\pi\)
\(702\) 4.62090e27 1.52399e28i 0.158985 0.524337i
\(703\) 4.90191e27i 0.166269i
\(704\) −6.23843e27 + 3.14853e28i −0.208616 + 1.05289i
\(705\) −3.18126e27 −0.104884
\(706\) −3.40528e28 1.03252e28i −1.10689 0.335622i
\(707\) 3.89990e28 1.24986
\(708\) 5.24380e27 + 3.50191e27i 0.165697 + 0.110655i
\(709\) 3.39191e28i 1.05677i −0.849003 0.528387i \(-0.822797\pi\)
0.849003 0.528387i \(-0.177203\pi\)
\(710\) −1.05114e28 3.18718e27i −0.322908 0.0979092i
\(711\) 8.23468e27i 0.249431i
\(712\) 2.61673e28 + 3.18607e28i 0.781554 + 0.951603i
\(713\) 3.11989e28 0.918847
\(714\) −1.40437e27 + 4.63165e27i −0.0407848 + 0.134510i
\(715\) −2.60211e28 −0.745188
\(716\) 1.88170e28 + 1.25663e28i 0.531398 + 0.354878i
\(717\) 1.89047e27i 0.0526476i
\(718\) 4.10488e27 1.35380e28i 0.112734 0.371801i
\(719\) 4.82927e28i 1.30795i −0.756515 0.653977i \(-0.773099\pi\)
0.756515 0.653977i \(-0.226901\pi\)
\(720\) −1.65240e28 + 6.85409e27i −0.441358 + 0.183073i
\(721\) 1.00377e29 2.64412
\(722\) −3.60341e28 1.09259e28i −0.936141 0.283848i
\(723\) 4.39826e26 0.0112693
\(724\) 3.74183e28 5.60305e28i 0.945580 1.41592i
\(725\) 3.41042e28i 0.850017i
\(726\) −1.18690e27 3.59882e26i −0.0291776 0.00884697i
\(727\) 3.90810e28i 0.947593i 0.880634 + 0.473797i \(0.157117\pi\)
−0.880634 + 0.473797i \(0.842883\pi\)
\(728\) −5.19174e28 6.32135e28i −1.24165 1.51181i
\(729\) −3.25089e28 −0.766880
\(730\) 1.20159e28 3.96288e28i 0.279594 0.922109i
\(731\) −2.75095e28 −0.631407
\(732\) 1.90385e27 2.85085e27i 0.0431045 0.0645451i
\(733\) 2.46670e28i 0.550905i −0.961315 0.275452i \(-0.911172\pi\)
0.961315 0.275452i \(-0.0888277\pi\)
\(734\) −2.48166e28 + 8.18461e28i −0.546742 + 1.80317i
\(735\) 4.44452e27i 0.0965942i
\(736\) 6.64232e28 6.58376e27i 1.42410 0.141155i
\(737\) −1.97238e28 −0.417173
\(738\) 3.28970e28 + 9.97474e27i 0.686424 + 0.208131i
\(739\) −3.59103e28 −0.739221 −0.369611 0.929187i \(-0.620509\pi\)
−0.369611 + 0.929187i \(0.620509\pi\)
\(740\) 2.29710e28 + 1.53405e28i 0.466513 + 0.311546i
\(741\) 2.05884e27i 0.0412516i
\(742\) 6.36192e27 + 1.92900e27i 0.125762 + 0.0381324i
\(743\) 4.29533e28i 0.837739i 0.908046 + 0.418869i \(0.137574\pi\)
−0.908046 + 0.418869i \(0.862426\pi\)
\(744\) 5.16905e27 4.24536e27i 0.0994676 0.0816930i
\(745\) 1.93450e28 0.367288
\(746\) −1.51433e28 + 4.99431e28i −0.283682 + 0.935594i
\(747\) −4.10664e28 −0.759068
\(748\) 2.44613e28 + 1.63357e28i 0.446133 + 0.297936i
\(749\) 1.38273e29i 2.48839i
\(750\) −2.85735e27 + 9.42364e27i −0.0507401 + 0.167343i
\(751\) 1.61560e28i 0.283096i −0.989931 0.141548i \(-0.954792\pi\)
0.989931 0.141548i \(-0.0452080\pi\)
\(752\) −5.61413e28 + 2.32872e28i −0.970742 + 0.402660i
\(753\) −1.45414e28 −0.248118
\(754\) −8.95719e28 2.71592e28i −1.50820 0.457302i
\(755\) 1.73535e28 0.288349
\(756\) 1.86664e28 2.79512e28i 0.306085 0.458335i
\(757\) 3.24624e28i 0.525317i −0.964889 0.262659i \(-0.915401\pi\)
0.964889 0.262659i \(-0.0845993\pi\)
\(758\) 2.17258e28 + 6.58750e27i 0.346963 + 0.105203i
\(759\) 1.95378e28i 0.307934i
\(760\) 3.64933e27