Properties

Label 8.21.d.b.3.4
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 3.4
Root \(-20011.7 + 4.20507e6i\)
Character \(\chi\) = 8.3
Dual form 8.21.d.b.3.3

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+(-980.704 + 294.612i) q^{2}\) \(-86392.9 q^{3}\) \(+(874983. - 577854. i) q^{4}\) \(-1.68203e7i q^{5}\) \(+(8.47258e7 - 2.54524e7i) q^{6}\) \(+3.64653e8i q^{7}\) \(+(-6.87856e8 + 8.24485e8i) q^{8}\) \(+3.97695e9 q^{9}\) \(+O(q^{10})\) \(q\)\(+(-980.704 + 294.612i) q^{2}\) \(-86392.9 q^{3}\) \(+(874983. - 577854. i) q^{4}\) \(-1.68203e7i q^{5}\) \(+(8.47258e7 - 2.54524e7i) q^{6}\) \(+3.64653e8i q^{7}\) \(+(-6.87856e8 + 8.24485e8i) q^{8}\) \(+3.97695e9 q^{9}\) \(+(4.95546e9 + 1.64957e10i) q^{10}\) \(+2.95556e10 q^{11}\) \(+(-7.55923e10 + 4.99225e10i) q^{12}\) \(-1.06510e11i q^{13}\) \(+(-1.07431e11 - 3.57616e11i) q^{14}\) \(+1.45315e12i q^{15}\) \(+(4.31680e11 - 1.01123e12i) q^{16}\) \(+2.31198e12 q^{17}\) \(+(-3.90021e12 + 1.17166e12i) q^{18}\) \(-8.42253e11 q^{19}\) \(+(-9.71968e12 - 1.47175e13i) q^{20}\) \(-3.15034e13i q^{21}\) \(+(-2.89852e13 + 8.70743e12i) q^{22}\) \(-2.92728e12i q^{23}\) \(+(5.94259e13 - 7.12296e13i) q^{24}\) \(-1.87555e14 q^{25}\) \(+(3.13790e13 + 1.04454e14i) q^{26}\) \(-4.23466e13 q^{27}\) \(+(2.10716e14 + 3.19065e14i) q^{28}\) \(-2.89106e14i q^{29}\) \(+(-4.28117e14 - 1.42511e15i) q^{30}\) \(-6.94432e14i q^{31}\) \(+(-1.25431e14 + 1.11889e15i) q^{32}\) \(-2.55339e15 q^{33}\) \(+(-2.26737e15 + 6.81138e14i) q^{34}\) \(+6.13357e15 q^{35}\) \(+(3.47976e15 - 2.29810e15i) q^{36}\) \(+2.39031e15i q^{37}\) \(+(8.26001e14 - 2.48138e14i) q^{38}\) \(+9.20166e15i q^{39}\) \(+(1.38681e16 + 1.15699e16i) q^{40}\) \(-8.44047e15 q^{41}\) \(+(9.28129e15 + 3.08955e16i) q^{42}\) \(-2.60268e16 q^{43}\) \(+(2.58606e16 - 1.70788e16i) q^{44}\) \(-6.68934e16i q^{45}\) \(+(8.62413e14 + 2.87080e15i) q^{46}\) \(-4.58565e16i q^{47}\) \(+(-3.72941e16 + 8.73627e16i) q^{48}\) \(-5.31795e16 q^{49}\) \(+(1.83935e17 - 5.52559e16i) q^{50}\) \(-1.99739e17 q^{51}\) \(+(-6.15470e16 - 9.31941e16i) q^{52}\) \(+2.23880e17i q^{53}\) \(+(4.15294e16 - 1.24758e16i) q^{54}\) \(-4.97133e17i q^{55}\) \(+(-3.00651e17 - 2.50829e17i) q^{56}\) \(+7.27647e16 q^{57}\) \(+(8.51741e16 + 2.83527e17i) q^{58}\) \(-3.72686e17 q^{59}\) \(+(8.39711e17 + 1.27148e18i) q^{60}\) \(-1.14075e18i q^{61}\) \(+(2.04588e17 + 6.81032e17i) q^{62}\) \(+1.45021e18i q^{63}\) \(+(-2.06628e17 - 1.13425e18i) q^{64}\) \(-1.79152e18 q^{65}\) \(+(2.50412e18 - 7.52260e17i) q^{66}\) \(+1.69388e18 q^{67}\) \(+(2.02295e18 - 1.33599e18i) q^{68}\) \(+2.52896e17i q^{69}\) \(+(-6.01521e18 + 1.80702e18i) q^{70}\) \(+1.43248e18i q^{71}\) \(+(-2.73557e18 + 3.27893e18i) q^{72}\) \(+6.55444e17 q^{73}\) \(+(-7.04214e17 - 2.34419e18i) q^{74}\) \(+1.62034e19 q^{75}\) \(+(-7.36958e17 + 4.86700e17i) q^{76}\) \(+1.07775e19i q^{77}\) \(+(-2.71092e18 - 9.02411e18i) q^{78}\) \(-3.74112e18i q^{79}\) \(+(-1.70091e19 - 7.26098e18i) q^{80}\) \(-1.02083e19 q^{81}\) \(+(8.27760e18 - 2.48666e18i) q^{82}\) \(-1.51998e19 q^{83}\) \(+(-1.82044e19 - 2.75650e19i) q^{84}\) \(-3.88882e19i q^{85}\) \(+(2.55246e19 - 7.66782e18i) q^{86}\) \(+2.49767e19i q^{87}\) \(+(-2.03300e19 + 2.43681e19i) q^{88}\) \(+2.12767e19 q^{89}\) \(+(1.97076e19 + 6.56026e19i) q^{90}\) \(+3.88390e19 q^{91}\) \(+(-1.69154e18 - 2.56132e18i) q^{92}\) \(+5.99940e19i q^{93}\) \(+(1.35099e19 + 4.49717e19i) q^{94}\) \(+1.41669e19i q^{95}\) \(+(1.08363e19 - 9.66643e19i) q^{96}\) \(-6.94557e19 q^{97}\) \(+(5.21533e19 - 1.56673e19i) q^{98}\) \(+1.17541e20 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut -\mathstrut 398q^{2} \) \(\mathstrut -\mathstrut 114228q^{3} \) \(\mathstrut +\mathstrut 724980q^{4} \) \(\mathstrut -\mathstrut 91643748q^{6} \) \(\mathstrut -\mathstrut 3105291368q^{8} \) \(\mathstrut +\mathstrut 10197650262q^{9} \) \(\mathstrut +\mathstrut 742754160q^{10} \) \(\mathstrut +\mathstrut 27862395020q^{11} \) \(\mathstrut -\mathstrut 212292734088q^{12} \) \(\mathstrut -\mathstrut 431248136928q^{14} \) \(\mathstrut -\mathstrut 958534870512q^{16} \) \(\mathstrut +\mathstrut 4343925139172q^{17} \) \(\mathstrut -\mathstrut 4517494524426q^{18} \) \(\mathstrut -\mathstrut 360681653556q^{19} \) \(\mathstrut -\mathstrut 32520172742880q^{20} \) \(\mathstrut -\mathstrut 66275482922148q^{22} \) \(\mathstrut +\mathstrut 22289322475152q^{24} \) \(\mathstrut -\mathstrut 395727477008910q^{25} \) \(\mathstrut +\mathstrut 154289718058128q^{26} \) \(\mathstrut -\mathstrut 1208398438889064q^{27} \) \(\mathstrut -\mathstrut 394619539621440q^{28} \) \(\mathstrut +\mathstrut 223250517248160q^{30} \) \(\mathstrut -\mathstrut 2833814588985248q^{32} \) \(\mathstrut +\mathstrut 4461969540487176q^{33} \) \(\mathstrut -\mathstrut 939462769526748q^{34} \) \(\mathstrut +\mathstrut 3615863153468160q^{35} \) \(\mathstrut +\mathstrut 1560521174396700q^{36} \) \(\mathstrut +\mathstrut 12905383833568412q^{38} \) \(\mathstrut +\mathstrut 11813880412973760q^{40} \) \(\mathstrut +\mathstrut 16990829756398820q^{41} \) \(\mathstrut +\mathstrut 38127588900300480q^{42} \) \(\mathstrut -\mathstrut 27498466356753396q^{43} \) \(\mathstrut +\mathstrut 33178844343953144q^{44} \) \(\mathstrut -\mathstrut 21739818881100192q^{46} \) \(\mathstrut +\mathstrut 28364131397385312q^{48} \) \(\mathstrut -\mathstrut 252965388018862638q^{49} \) \(\mathstrut +\mathstrut 41705619584456530q^{50} \) \(\mathstrut -\mathstrut 34182574557901800q^{51} \) \(\mathstrut -\mathstrut 44583718369992480q^{52} \) \(\mathstrut -\mathstrut 579400710808894920q^{54} \) \(\mathstrut -\mathstrut 505574909383001472q^{56} \) \(\mathstrut -\mathstrut 522453489061123704q^{57} \) \(\mathstrut -\mathstrut 677523738697093680q^{58} \) \(\mathstrut +\mathstrut 93112194700366220q^{59} \) \(\mathstrut +\mathstrut 1631640690429240000q^{60} \) \(\mathstrut +\mathstrut 1780090172849178240q^{62} \) \(\mathstrut +\mathstrut 175441813011570240q^{64} \) \(\mathstrut +\mathstrut 1575343920200472960q^{65} \) \(\mathstrut +\mathstrut 8001047667731567880q^{66} \) \(\mathstrut -\mathstrut 1452645642074335668q^{67} \) \(\mathstrut +\mathstrut 1153770320813215592q^{68} \) \(\mathstrut -\mathstrut 6151558949299572480q^{70} \) \(\mathstrut -\mathstrut 5306529204268842936q^{72} \) \(\mathstrut +\mathstrut 9882821313863175972q^{73} \) \(\mathstrut -\mathstrut 5642095430673385488q^{74} \) \(\mathstrut +\mathstrut 13414715768769378060q^{75} \) \(\mathstrut -\mathstrut 8416781249057544840q^{76} \) \(\mathstrut -\mathstrut 14599907290310144160q^{78} \) \(\mathstrut -\mathstrut 22104885212702947200q^{80} \) \(\mathstrut -\mathstrut 32315102667184036518q^{81} \) \(\mathstrut +\mathstrut 10320950271478847652q^{82} \) \(\mathstrut -\mathstrut 46425529968268557748q^{83} \) \(\mathstrut +\mathstrut 17095266896298568320q^{84} \) \(\mathstrut +\mathstrut 33555485282446075868q^{86} \) \(\mathstrut +\mathstrut 32344350945394345872q^{88} \) \(\mathstrut -\mathstrut 28075170672250840156q^{89} \) \(\mathstrut -\mathstrut 33204348719592139440q^{90} \) \(\mathstrut +\mathstrut 161045136122144660736q^{91} \) \(\mathstrut -\mathstrut 932896292396925120q^{92} \) \(\mathstrut -\mathstrut 107259275077774974528q^{94} \) \(\mathstrut +\mathstrut 68580843917215697472q^{96} \) \(\mathstrut +\mathstrut 127276645173366650724q^{97} \) \(\mathstrut +\mathstrut 154837385163137764402q^{98} \) \(\mathstrut +\mathstrut 62802542261652714084q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −980.704 + 294.612i −0.957718 + 0.287707i
\(3\) −86392.9 −1.46307 −0.731536 0.681803i \(-0.761196\pi\)
−0.731536 + 0.681803i \(0.761196\pi\)
\(4\) 874983. 577854.i 0.834449 0.551085i
\(5\) 1.68203e7i 1.72240i −0.508269 0.861199i \(-0.669714\pi\)
0.508269 0.861199i \(-0.330286\pi\)
\(6\) 8.47258e7 2.54524e7i 1.40121 0.420936i
\(7\) 3.64653e8i 1.29092i 0.763794 + 0.645460i \(0.223334\pi\)
−0.763794 + 0.645460i \(0.776666\pi\)
\(8\) −6.87856e8 + 8.24485e8i −0.640616 + 0.767861i
\(9\) 3.97695e9 1.14058
\(10\) 4.95546e9 + 1.64957e10i 0.495546 + 1.64957i
\(11\) 2.95556e10 1.13949 0.569747 0.821820i \(-0.307041\pi\)
0.569747 + 0.821820i \(0.307041\pi\)
\(12\) −7.55923e10 + 4.99225e10i −1.22086 + 0.806276i
\(13\) 1.06510e11i 0.772600i −0.922373 0.386300i \(-0.873753\pi\)
0.922373 0.386300i \(-0.126247\pi\)
\(14\) −1.07431e11 3.57616e11i −0.371407 1.23634i
\(15\) 1.45315e12i 2.51999i
\(16\) 4.31680e11 1.01123e12i 0.392611 0.919705i
\(17\) 2.31198e12 1.14682 0.573410 0.819269i \(-0.305620\pi\)
0.573410 + 0.819269i \(0.305620\pi\)
\(18\) −3.90021e12 + 1.17166e12i −1.09235 + 0.328152i
\(19\) −8.42253e11 −0.137375 −0.0686873 0.997638i \(-0.521881\pi\)
−0.0686873 + 0.997638i \(0.521881\pi\)
\(20\) −9.71968e12 1.47175e13i −0.949187 1.43725i
\(21\) 3.15034e13i 1.88871i
\(22\) −2.89852e13 + 8.70743e12i −1.09132 + 0.327841i
\(23\) 2.92728e12i 0.0706621i −0.999376 0.0353310i \(-0.988751\pi\)
0.999376 0.0353310i \(-0.0112486\pi\)
\(24\) 5.94259e13 7.12296e13i 0.937267 1.12344i
\(25\) −1.87555e14 −1.96665
\(26\) 3.13790e13 + 1.04454e14i 0.222283 + 0.739934i
\(27\) −4.23466e13 −0.205675
\(28\) 2.10716e14 + 3.19065e14i 0.711407 + 1.07721i
\(29\) 2.89106e14i 0.687190i −0.939118 0.343595i \(-0.888355\pi\)
0.939118 0.343595i \(-0.111645\pi\)
\(30\) −4.28117e14 1.42511e15i −0.725019 2.41344i
\(31\) 6.94432e14i 0.847252i −0.905837 0.423626i \(-0.860757\pi\)
0.905837 0.423626i \(-0.139243\pi\)
\(32\) −1.25431e14 + 1.11889e15i −0.111405 + 0.993775i
\(33\) −2.55339e15 −1.66716
\(34\) −2.26737e15 + 6.81138e14i −1.09833 + 0.329948i
\(35\) 6.13357e15 2.22348
\(36\) 3.47976e15 2.29810e15i 0.951754 0.628555i
\(37\) 2.39031e15i 0.497092i 0.968620 + 0.248546i \(0.0799527\pi\)
−0.968620 + 0.248546i \(0.920047\pi\)
\(38\) 8.26001e14 2.48138e14i 0.131566 0.0395237i
\(39\) 9.20166e15i 1.13037i
\(40\) 1.38681e16 + 1.15699e16i 1.32256 + 1.10340i
\(41\) −8.44047e15 −0.628822 −0.314411 0.949287i \(-0.601807\pi\)
−0.314411 + 0.949287i \(0.601807\pi\)
\(42\) 9.28129e15 + 3.08955e16i 0.543395 + 1.80885i
\(43\) −2.60268e16 −1.20431 −0.602153 0.798381i \(-0.705690\pi\)
−0.602153 + 0.798381i \(0.705690\pi\)
\(44\) 2.58606e16 1.70788e16i 0.950850 0.627958i
\(45\) 6.68934e16i 1.96453i
\(46\) 8.62413e14 + 2.87080e15i 0.0203300 + 0.0676744i
\(47\) 4.58565e16i 0.871811i −0.899992 0.435906i \(-0.856428\pi\)
0.899992 0.435906i \(-0.143572\pi\)
\(48\) −3.72941e16 + 8.73627e16i −0.574418 + 1.34559i
\(49\) −5.31795e16 −0.666475
\(50\) 1.83935e17 5.52559e16i 1.88350 0.565820i
\(51\) −1.99739e17 −1.67788
\(52\) −6.15470e16 9.31941e16i −0.425768 0.644696i
\(53\) 2.23880e17i 1.28014i 0.768318 + 0.640068i \(0.221094\pi\)
−0.768318 + 0.640068i \(0.778906\pi\)
\(54\) 4.15294e16 1.24758e16i 0.196978 0.0591740i
\(55\) 4.97133e17i 1.96266i
\(56\) −3.00651e17 2.50829e17i −0.991247 0.826984i
\(57\) 7.27647e16 0.200989
\(58\) 8.51741e16 + 2.83527e17i 0.197710 + 0.658135i
\(59\) −3.72686e17 −0.729161 −0.364580 0.931172i \(-0.618788\pi\)
−0.364580 + 0.931172i \(0.618788\pi\)
\(60\) 8.39711e17 + 1.27148e18i 1.38873 + 2.10280i
\(61\) 1.14075e18i 1.59917i −0.600556 0.799583i \(-0.705054\pi\)
0.600556 0.799583i \(-0.294946\pi\)
\(62\) 2.04588e17 + 6.81032e17i 0.243761 + 0.811429i
\(63\) 1.45021e18i 1.47239i
\(64\) −2.06628e17 1.13425e18i −0.179222 0.983809i
\(65\) −1.79152e18 −1.33072
\(66\) 2.50412e18 7.52260e17i 1.59667 0.479654i
\(67\) 1.69388e18 0.929257 0.464628 0.885506i \(-0.346188\pi\)
0.464628 + 0.885506i \(0.346188\pi\)
\(68\) 2.02295e18 1.33599e18i 0.956963 0.631995i
\(69\) 2.52896e17i 0.103384i
\(70\) −6.01521e18 + 1.80702e18i −2.12947 + 0.639710i
\(71\) 1.43248e18i 0.440054i 0.975494 + 0.220027i \(0.0706146\pi\)
−0.975494 + 0.220027i \(0.929385\pi\)
\(72\) −2.73557e18 + 3.27893e18i −0.730672 + 0.875805i
\(73\) 6.55444e17 0.152513 0.0762565 0.997088i \(-0.475703\pi\)
0.0762565 + 0.997088i \(0.475703\pi\)
\(74\) −7.04214e17 2.34419e18i −0.143017 0.476074i
\(75\) 1.62034e19 2.87735
\(76\) −7.36958e17 + 4.86700e17i −0.114632 + 0.0757051i
\(77\) 1.07775e19i 1.47100i
\(78\) −2.71092e18 9.02411e18i −0.325215 1.08258i
\(79\) 3.74112e18i 0.395121i −0.980291 0.197561i \(-0.936698\pi\)
0.980291 0.197561i \(-0.0633019\pi\)
\(80\) −1.70091e19 7.26098e18i −1.58410 0.676232i
\(81\) −1.02083e19 −0.839661
\(82\) 8.27760e18 2.48666e18i 0.602235 0.180917i
\(83\) −1.51998e19 −0.979621 −0.489811 0.871829i \(-0.662934\pi\)
−0.489811 + 0.871829i \(0.662934\pi\)
\(84\) −1.82044e19 2.75650e19i −1.04084 1.57603i
\(85\) 3.88882e19i 1.97528i
\(86\) 2.55246e19 7.66782e18i 1.15339 0.346488i
\(87\) 2.49767e19i 1.00541i
\(88\) −2.03300e19 + 2.43681e19i −0.729979 + 0.874974i
\(89\) 2.12767e19 0.682346 0.341173 0.940000i \(-0.389176\pi\)
0.341173 + 0.940000i \(0.389176\pi\)
\(90\) 1.97076e19 + 6.56026e19i 0.565209 + 1.88146i
\(91\) 3.88390e19 0.997365
\(92\) −1.69154e18 2.56132e18i −0.0389408 0.0589639i
\(93\) 5.99940e19i 1.23959i
\(94\) 1.35099e19 + 4.49717e19i 0.250826 + 0.834950i
\(95\) 1.41669e19i 0.236614i
\(96\) 1.08363e19 9.66643e19i 0.162993 1.45396i
\(97\) −6.94557e19 −0.941868 −0.470934 0.882168i \(-0.656083\pi\)
−0.470934 + 0.882168i \(0.656083\pi\)
\(98\) 5.21533e19 1.56673e19i 0.638295 0.191750i
\(99\) 1.17541e20 1.29968
\(100\) −1.64107e20 + 1.08379e20i −1.64107 + 1.08379i
\(101\) 6.91127e19i 0.625668i −0.949808 0.312834i \(-0.898722\pi\)
0.949808 0.312834i \(-0.101278\pi\)
\(102\) 1.95885e20 5.88455e19i 1.60694 0.482738i
\(103\) 7.42626e18i 0.0552584i −0.999618 0.0276292i \(-0.991204\pi\)
0.999618 0.0276292i \(-0.00879576\pi\)
\(104\) 8.78155e19 + 7.32633e19i 0.593250 + 0.494940i
\(105\) −5.29897e20 −3.25311
\(106\) −6.59577e19 2.19560e20i −0.368305 1.22601i
\(107\) 1.94444e20 0.988453 0.494227 0.869333i \(-0.335451\pi\)
0.494227 + 0.869333i \(0.335451\pi\)
\(108\) −3.70525e19 + 2.44701e19i −0.171625 + 0.113344i
\(109\) 3.23383e20i 1.36601i −0.730415 0.683003i \(-0.760673\pi\)
0.730415 0.683003i \(-0.239327\pi\)
\(110\) 1.46461e20 + 4.87540e20i 0.564672 + 1.87968i
\(111\) 2.06506e20i 0.727281i
\(112\) 3.68747e20 + 1.57413e20i 1.18727 + 0.506829i
\(113\) −4.42432e20 −1.30335 −0.651677 0.758496i \(-0.725934\pi\)
−0.651677 + 0.758496i \(0.725934\pi\)
\(114\) −7.13606e19 + 2.14374e19i −0.192491 + 0.0578260i
\(115\) −4.92377e19 −0.121708
\(116\) −1.67061e20 2.52963e20i −0.378700 0.573425i
\(117\) 4.23583e20i 0.881210i
\(118\) 3.65495e20 1.09798e20i 0.698331 0.209785i
\(119\) 8.43071e20i 1.48045i
\(120\) −1.19810e21 9.99561e20i −1.93500 1.61435i
\(121\) 2.00781e20 0.298448
\(122\) 3.36080e20 + 1.11874e21i 0.460091 + 1.53155i
\(123\) 7.29196e20 0.920012
\(124\) −4.01281e20 6.07616e20i −0.466908 0.706989i
\(125\) 1.55061e21i 1.66496i
\(126\) −4.27248e20 1.42222e21i −0.423618 1.41014i
\(127\) 4.00904e20i 0.367285i −0.982993 0.183643i \(-0.941211\pi\)
0.982993 0.183643i \(-0.0587889\pi\)
\(128\) 5.36806e20 + 1.05149e21i 0.454693 + 0.890648i
\(129\) 2.24853e21 1.76199
\(130\) 1.75695e21 5.27804e20i 1.27446 0.382859i
\(131\) 7.08938e20 0.476316 0.238158 0.971226i \(-0.423456\pi\)
0.238158 + 0.971226i \(0.423456\pi\)
\(132\) −2.23417e21 + 1.47549e21i −1.39116 + 0.918748i
\(133\) 3.07130e20i 0.177340i
\(134\) −1.66120e21 + 4.99039e20i −0.889966 + 0.267354i
\(135\) 7.12281e20i 0.354253i
\(136\) −1.59031e21 + 1.90619e21i −0.734671 + 0.880598i
\(137\) 8.38295e20 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(138\) −7.45063e19 2.48016e20i −0.0297442 0.0990124i
\(139\) −3.16274e21 −1.17467 −0.587335 0.809344i \(-0.699823\pi\)
−0.587335 + 0.809344i \(0.699823\pi\)
\(140\) 5.36677e21 3.54431e21i 1.85538 1.22532i
\(141\) 3.96168e21i 1.27552i
\(142\) −4.22027e20 1.40484e21i −0.126607 0.421448i
\(143\) 3.14795e21i 0.880374i
\(144\) 1.71677e21 4.02159e21i 0.447803 1.04899i
\(145\) −4.86284e21 −1.18361
\(146\) −6.42796e20 + 1.93102e20i −0.146064 + 0.0438791i
\(147\) 4.59433e21 0.975100
\(148\) 1.38125e21 + 2.09148e21i 0.273940 + 0.414798i
\(149\) 1.03338e22i 1.91602i −0.286740 0.958008i \(-0.592572\pi\)
0.286740 0.958008i \(-0.407428\pi\)
\(150\) −1.58907e22 + 4.77371e21i −2.75569 + 0.827835i
\(151\) 8.08356e21i 1.31170i 0.754893 + 0.655848i \(0.227689\pi\)
−0.754893 + 0.655848i \(0.772311\pi\)
\(152\) 5.79349e20 6.94425e20i 0.0880045 0.105485i
\(153\) 9.19463e21 1.30804
\(154\) −3.17519e21 1.05696e22i −0.423216 1.40880i
\(155\) −1.16805e22 −1.45931
\(156\) 5.31722e21 + 8.05130e21i 0.622929 + 0.943236i
\(157\) 3.88131e21i 0.426562i −0.976991 0.213281i \(-0.931585\pi\)
0.976991 0.213281i \(-0.0684149\pi\)
\(158\) 1.10218e21 + 3.66893e21i 0.113679 + 0.378415i
\(159\) 1.93416e22i 1.87293i
\(160\) 1.88201e22 + 2.10978e21i 1.71168 + 0.191884i
\(161\) 1.06744e21 0.0912191
\(162\) 1.00113e22 3.00749e21i 0.804159 0.241576i
\(163\) −2.16871e22 −1.63804 −0.819020 0.573765i \(-0.805482\pi\)
−0.819020 + 0.573765i \(0.805482\pi\)
\(164\) −7.38527e21 + 4.87736e21i −0.524720 + 0.346534i
\(165\) 4.29488e22i 2.87152i
\(166\) 1.49065e22 4.47806e21i 0.938201 0.281844i
\(167\) 1.36722e22i 0.810352i 0.914239 + 0.405176i \(0.132790\pi\)
−0.914239 + 0.405176i \(0.867210\pi\)
\(168\) 2.59741e22 + 2.16698e22i 1.45027 + 1.20994i
\(169\) 7.66069e21 0.403089
\(170\) 1.14569e22 + 3.81378e22i 0.568302 + 1.89176i
\(171\) −3.34960e21 −0.156686
\(172\) −2.27731e22 + 1.50397e22i −1.00493 + 0.663675i
\(173\) 3.92487e22i 1.63442i −0.576339 0.817211i \(-0.695519\pi\)
0.576339 0.817211i \(-0.304481\pi\)
\(174\) −7.35844e21 2.44947e22i −0.289263 0.962898i
\(175\) 6.83923e22i 2.53879i
\(176\) 1.27585e22 2.98873e22i 0.447378 1.04800i
\(177\) 3.21974e22 1.06681
\(178\) −2.08662e22 + 6.26838e21i −0.653496 + 0.196316i
\(179\) −4.77271e22 −1.41330 −0.706651 0.707562i \(-0.749795\pi\)
−0.706651 + 0.707562i \(0.749795\pi\)
\(180\) −3.86546e22 5.85306e22i −1.08262 1.63930i
\(181\) 1.43094e22i 0.379171i 0.981864 + 0.189585i \(0.0607144\pi\)
−0.981864 + 0.189585i \(0.939286\pi\)
\(182\) −3.80896e22 + 1.14424e22i −0.955195 + 0.286949i
\(183\) 9.85530e22i 2.33969i
\(184\) 2.41350e21 + 2.01355e21i 0.0542586 + 0.0452673i
\(185\) 4.02057e22 0.856190
\(186\) −1.76750e22 5.88363e22i −0.356639 1.18718i
\(187\) 6.83319e22 1.30680
\(188\) −2.64984e22 4.01237e22i −0.480442 0.727482i
\(189\) 1.54418e22i 0.265509i
\(190\) −4.17375e21 1.38936e22i −0.0680755 0.226609i
\(191\) 8.04614e22i 1.24524i 0.782524 + 0.622621i \(0.213932\pi\)
−0.782524 + 0.622621i \(0.786068\pi\)
\(192\) 1.78512e22 + 9.79915e22i 0.262214 + 1.43938i
\(193\) −1.11689e23 −1.55753 −0.778766 0.627315i \(-0.784154\pi\)
−0.778766 + 0.627315i \(0.784154\pi\)
\(194\) 6.81154e22 2.04625e22i 0.902045 0.270982i
\(195\) 1.54775e23 1.94694
\(196\) −4.65312e22 + 3.07300e22i −0.556139 + 0.367284i
\(197\) 1.72505e22i 0.195948i −0.995189 0.0979738i \(-0.968764\pi\)
0.995189 0.0979738i \(-0.0312361\pi\)
\(198\) −1.15273e23 + 3.46290e22i −1.24473 + 0.373928i
\(199\) 1.69597e23i 1.74135i −0.491858 0.870676i \(-0.663682\pi\)
0.491858 0.870676i \(-0.336318\pi\)
\(200\) 1.29011e23 1.54636e23i 1.25987 1.51012i
\(201\) −1.46340e23 −1.35957
\(202\) 2.03614e22 + 6.77791e22i 0.180009 + 0.599214i
\(203\) 1.05423e23 0.887108
\(204\) −1.74768e23 + 1.15420e23i −1.40010 + 0.924654i
\(205\) 1.41971e23i 1.08308i
\(206\) 2.18787e21 + 7.28296e21i 0.0158982 + 0.0529219i
\(207\) 1.16416e22i 0.0805955i
\(208\) −1.07705e23 4.59780e22i −0.710564 0.303331i
\(209\) −2.48933e22 −0.156538
\(210\) 5.19672e23 1.56114e23i 3.11556 0.935942i
\(211\) −1.06851e22 −0.0610877 −0.0305439 0.999533i \(-0.509724\pi\)
−0.0305439 + 0.999533i \(0.509724\pi\)
\(212\) 1.29370e23 + 1.95891e23i 0.705464 + 1.06821i
\(213\) 1.23756e23i 0.643831i
\(214\) −1.90692e23 + 5.72855e22i −0.946660 + 0.284385i
\(215\) 4.37779e23i 2.07429i
\(216\) 2.91284e22 3.49141e22i 0.131758 0.157929i
\(217\) 2.53227e23 1.09374
\(218\) 9.52727e22 + 3.17143e23i 0.393010 + 1.30825i
\(219\) −5.66257e22 −0.223137
\(220\) −2.87270e23 4.34983e23i −1.08159 1.63774i
\(221\) 2.46248e23i 0.886033i
\(222\) 6.08391e22 + 2.02521e23i 0.209244 + 0.696531i
\(223\) 6.34169e22i 0.208524i −0.994550 0.104262i \(-0.966752\pi\)
0.994550 0.104262i \(-0.0332481\pi\)
\(224\) −4.08007e23 4.57387e22i −1.28288 0.143815i
\(225\) −7.45895e23 −2.24312
\(226\) 4.33895e23 1.30346e23i 1.24825 0.374984i
\(227\) −1.13881e23 −0.313468 −0.156734 0.987641i \(-0.550097\pi\)
−0.156734 + 0.987641i \(0.550097\pi\)
\(228\) 6.36679e22 4.20474e22i 0.167715 0.110762i
\(229\) 3.51437e23i 0.886121i −0.896492 0.443060i \(-0.853893\pi\)
0.896492 0.443060i \(-0.146107\pi\)
\(230\) 4.82876e22 1.45060e22i 0.116562 0.0350163i
\(231\) 9.31101e23i 2.15217i
\(232\) 2.38363e23 + 1.98863e23i 0.527667 + 0.440225i
\(233\) 4.48445e23 0.950933 0.475466 0.879734i \(-0.342279\pi\)
0.475466 + 0.879734i \(0.342279\pi\)
\(234\) 1.24793e23 + 4.15409e23i 0.253531 + 0.843951i
\(235\) −7.71320e23 −1.50161
\(236\) −3.26094e23 + 2.15358e23i −0.608448 + 0.401830i
\(237\) 3.23206e23i 0.578090i
\(238\) −2.48379e23 8.26803e23i −0.425937 1.41786i
\(239\) 6.35130e22i 0.104444i 0.998635 + 0.0522220i \(0.0166304\pi\)
−0.998635 + 0.0522220i \(0.983370\pi\)
\(240\) 1.46947e24 + 6.27297e23i 2.31765 + 0.989375i
\(241\) −1.20735e24 −1.82668 −0.913338 0.407202i \(-0.866504\pi\)
−0.913338 + 0.407202i \(0.866504\pi\)
\(242\) −1.96907e23 + 5.91525e22i −0.285829 + 0.0858657i
\(243\) 1.02958e24 1.43416
\(244\) −6.59189e23 9.98140e23i −0.881276 1.33442i
\(245\) 8.94495e23i 1.14793i
\(246\) −7.15126e23 + 2.14830e23i −0.881112 + 0.264694i
\(247\) 8.97080e22i 0.106136i
\(248\) 5.72549e23 + 4.77670e23i 0.650572 + 0.542764i
\(249\) 1.31316e24 1.43326
\(250\) −4.56830e23 1.52069e24i −0.479021 1.59456i
\(251\) 1.33605e24 1.34613 0.673065 0.739583i \(-0.264977\pi\)
0.673065 + 0.739583i \(0.264977\pi\)
\(252\) 8.38008e23 + 1.26891e24i 0.811414 + 1.22864i
\(253\) 8.65175e22i 0.0805190i
\(254\) 1.18111e23 + 3.93168e23i 0.105671 + 0.351756i
\(255\) 3.35966e24i 2.88997i
\(256\) −8.36230e23 8.73052e23i −0.691713 0.722172i
\(257\) 1.56338e24 1.24375 0.621875 0.783117i \(-0.286371\pi\)
0.621875 + 0.783117i \(0.286371\pi\)
\(258\) −2.20515e24 + 6.62445e23i −1.68749 + 0.506936i
\(259\) −8.71633e23 −0.641706
\(260\) −1.56755e24 + 1.03524e24i −1.11042 + 0.733342i
\(261\) 1.14976e24i 0.783794i
\(262\) −6.95258e23 + 2.08862e23i −0.456177 + 0.137040i
\(263\) 2.63570e24i 1.66471i −0.554244 0.832354i \(-0.686993\pi\)
0.554244 0.832354i \(-0.313007\pi\)
\(264\) 1.75637e24 2.10523e24i 1.06801 1.28015i
\(265\) 3.76572e24 2.20490
\(266\) 9.04843e22 + 3.01204e23i 0.0510219 + 0.169842i
\(267\) −1.83816e24 −0.998321
\(268\) 1.48212e24 9.78819e23i 0.775418 0.512099i
\(269\) 3.33951e24i 1.68329i 0.540027 + 0.841647i \(0.318414\pi\)
−0.540027 + 0.841647i \(0.681586\pi\)
\(270\) −2.09847e23 6.98537e23i −0.101921 0.339275i
\(271\) 8.24630e23i 0.385981i −0.981201 0.192991i \(-0.938181\pi\)
0.981201 0.192991i \(-0.0618187\pi\)
\(272\) 9.98037e23 2.33794e24i 0.450254 1.05474i
\(273\) −3.35541e24 −1.45922
\(274\) −8.22119e23 + 2.46972e23i −0.344690 + 0.103548i
\(275\) −5.54328e24 −2.24099
\(276\) 1.46137e23 + 2.21280e23i 0.0569732 + 0.0862684i
\(277\) 1.73553e24i 0.652580i −0.945270 0.326290i \(-0.894201\pi\)
0.945270 0.326290i \(-0.105799\pi\)
\(278\) 3.10171e24 9.31782e23i 1.12500 0.337961i
\(279\) 2.76172e24i 0.966357i
\(280\) −4.21901e24 + 5.05703e24i −1.42440 + 1.70732i
\(281\) 2.59074e24 0.844036 0.422018 0.906587i \(-0.361322\pi\)
0.422018 + 0.906587i \(0.361322\pi\)
\(282\) −1.16716e24 3.88523e24i −0.366977 1.22159i
\(283\) −1.50077e24 −0.455459 −0.227730 0.973724i \(-0.573130\pi\)
−0.227730 + 0.973724i \(0.573130\pi\)
\(284\) 8.27767e23 + 1.25340e24i 0.242507 + 0.367203i
\(285\) 1.22392e24i 0.346183i
\(286\) 9.27424e23 + 3.08720e24i 0.253290 + 0.843150i
\(287\) 3.07784e24i 0.811759i
\(288\) −4.98832e23 + 4.44977e24i −0.127066 + 1.13348i
\(289\) 1.28103e24 0.315196
\(290\) 4.76901e24 1.43265e24i 1.13357 0.340534i
\(291\) 6.00047e24 1.37802
\(292\) 5.73502e23 3.78751e23i 0.127264 0.0840476i
\(293\) 5.50029e24i 1.17953i 0.807574 + 0.589766i \(0.200780\pi\)
−0.807574 + 0.589766i \(0.799220\pi\)
\(294\) −4.50568e24 + 1.35355e24i −0.933871 + 0.280543i
\(295\) 6.26869e24i 1.25590i
\(296\) −1.97077e24 1.64419e24i −0.381698 0.318445i
\(297\) −1.25158e24 −0.234365
\(298\) 3.04448e24 + 1.01344e25i 0.551252 + 1.83500i
\(299\) −3.11783e23 −0.0545935
\(300\) 1.41777e25 9.36320e24i 2.40100 1.58567i
\(301\) 9.49076e24i 1.55466i
\(302\) −2.38151e24 7.92758e24i −0.377384 1.25624i
\(303\) 5.97084e24i 0.915397i
\(304\) −3.63584e23 + 8.51709e23i −0.0539348 + 0.126344i
\(305\) −1.91878e25 −2.75440
\(306\) −9.01721e24 + 2.70885e24i −1.25273 + 0.376331i
\(307\) −2.32060e24 −0.312044 −0.156022 0.987754i \(-0.549867\pi\)
−0.156022 + 0.987754i \(0.549867\pi\)
\(308\) 6.22784e24 + 9.43015e24i 0.810644 + 1.22747i
\(309\) 6.41576e23i 0.0808469i
\(310\) 1.14552e25 3.44123e24i 1.39760 0.419853i
\(311\) 3.94846e24i 0.466470i −0.972420 0.233235i \(-0.925069\pi\)
0.972420 0.233235i \(-0.0749312\pi\)
\(312\) −7.58663e24 6.32942e24i −0.867967 0.724133i
\(313\) 5.88598e24 0.652192 0.326096 0.945337i \(-0.394267\pi\)
0.326096 + 0.945337i \(0.394267\pi\)
\(314\) 1.14348e24 + 3.80642e24i 0.122725 + 0.408526i
\(315\) 2.43929e25 2.53605
\(316\) −2.16182e24 3.27341e24i −0.217745 0.329709i
\(317\) 1.40352e25i 1.36970i −0.728685 0.684849i \(-0.759868\pi\)
0.728685 0.684849i \(-0.240132\pi\)
\(318\) 5.69828e24 + 1.89684e25i 0.538856 + 1.79374i
\(319\) 8.54469e24i 0.783050i
\(320\) −1.90785e25 + 3.47555e24i −1.69451 + 0.308691i
\(321\) −1.67986e25 −1.44618
\(322\) −1.04684e24 + 3.14481e23i −0.0873622 + 0.0262444i
\(323\) −1.94727e24 −0.157544
\(324\) −8.93211e24 + 5.89892e24i −0.700654 + 0.462724i
\(325\) 1.99763e25i 1.51944i
\(326\) 2.12686e25 6.38927e24i 1.56878 0.471276i
\(327\) 2.79380e25i 1.99857i
\(328\) 5.80583e24 6.95904e24i 0.402834 0.482848i
\(329\) 1.67217e25 1.12544
\(330\) −1.26532e25 4.21200e25i −0.826155 2.75010i
\(331\) −1.16179e25 −0.735951 −0.367976 0.929835i \(-0.619949\pi\)
−0.367976 + 0.929835i \(0.619949\pi\)
\(332\) −1.32996e25 + 8.78329e24i −0.817444 + 0.539854i
\(333\) 9.50613e24i 0.566972i
\(334\) −4.02799e24 1.34084e25i −0.233144 0.776089i
\(335\) 2.84916e25i 1.60055i
\(336\) −3.18571e25 1.35994e25i −1.73705 0.741527i
\(337\) 7.90893e24 0.418619 0.209309 0.977849i \(-0.432878\pi\)
0.209309 + 0.977849i \(0.432878\pi\)
\(338\) −7.51286e24 + 2.25693e24i −0.386046 + 0.115972i
\(339\) 3.82230e25 1.90690
\(340\) −2.24717e25 3.40265e25i −1.08855 1.64827i
\(341\) 2.05243e25i 0.965440i
\(342\) 3.28496e24 9.86832e23i 0.150062 0.0450798i
\(343\) 9.70442e24i 0.430555i
\(344\) 1.79027e25 2.14587e25i 0.771498 0.924740i
\(345\) 4.25379e24 0.178068
\(346\) 1.15631e25 + 3.84913e25i 0.470235 + 1.56532i
\(347\) −3.29133e25 −1.30040 −0.650200 0.759763i \(-0.725315\pi\)
−0.650200 + 0.759763i \(0.725315\pi\)
\(348\) 1.44329e25 + 2.18542e25i 0.554065 + 0.838962i
\(349\) 4.94005e25i 1.84279i 0.388623 + 0.921397i \(0.372951\pi\)
−0.388623 + 0.921397i \(0.627049\pi\)
\(350\) 2.01492e25 + 6.70726e25i 0.730428 + 2.43145i
\(351\) 4.51031e24i 0.158904i
\(352\) −3.70718e24 + 3.30695e25i −0.126945 + 1.13240i
\(353\) 1.62932e25 0.542326 0.271163 0.962534i \(-0.412592\pi\)
0.271163 + 0.962534i \(0.412592\pi\)
\(354\) −3.15762e25 + 9.48576e24i −1.02171 + 0.306930i
\(355\) 2.40948e25 0.757948
\(356\) 1.86168e25 1.22949e25i 0.569383 0.376031i
\(357\) 7.28353e25i 2.16601i
\(358\) 4.68062e25 1.40610e25i 1.35355 0.406617i
\(359\) 5.41413e25i 1.52259i 0.648403 + 0.761297i \(0.275437\pi\)
−0.648403 + 0.761297i \(0.724563\pi\)
\(360\) 5.51526e25 + 4.60130e25i 1.50848 + 1.25851i
\(361\) −3.68806e25 −0.981128
\(362\) −4.21571e24 1.40333e25i −0.109090 0.363139i
\(363\) −1.73461e25 −0.436651
\(364\) 3.39835e25 2.24433e25i 0.832251 0.549633i
\(365\) 1.10247e25i 0.262688i
\(366\) −2.90349e25 9.66513e25i −0.673146 2.24077i
\(367\) 2.12308e25i 0.478968i −0.970900 0.239484i \(-0.923022\pi\)
0.970900 0.239484i \(-0.0769782\pi\)
\(368\) −2.96014e24 1.26365e24i −0.0649882 0.0277427i
\(369\) −3.35673e25 −0.717220
\(370\) −3.94299e25 + 1.18451e25i −0.819989 + 0.246332i
\(371\) −8.16385e25 −1.65255
\(372\) 3.46678e25 + 5.24937e25i 0.683120 + 1.03438i
\(373\) 4.08340e25i 0.783309i 0.920112 + 0.391655i \(0.128097\pi\)
−0.920112 + 0.391655i \(0.871903\pi\)
\(374\) −6.70134e25 + 2.01314e25i −1.25154 + 0.375974i
\(375\) 1.33962e26i 2.43595i
\(376\) 3.78080e25 + 3.15427e25i 0.669430 + 0.558496i
\(377\) −3.07925e25 −0.530923
\(378\) 4.54934e24 + 1.51438e25i 0.0763890 + 0.254283i
\(379\) 6.13221e25 1.00282 0.501412 0.865209i \(-0.332814\pi\)
0.501412 + 0.865209i \(0.332814\pi\)
\(380\) 8.18643e24 + 1.23958e25i 0.130394 + 0.197442i
\(381\) 3.46353e25i 0.537364i
\(382\) −2.37049e25 7.89087e25i −0.358265 1.19259i
\(383\) 5.66622e24i 0.0834268i 0.999130 + 0.0417134i \(0.0132816\pi\)
−0.999130 + 0.0417134i \(0.986718\pi\)
\(384\) −4.63763e25 9.08414e25i −0.665248 1.30308i
\(385\) 1.81281e26 2.53364
\(386\) 1.09534e26 3.29049e25i 1.49168 0.448113i
\(387\) −1.03507e26 −1.37360
\(388\) −6.07725e25 + 4.01353e25i −0.785941 + 0.519050i
\(389\) 2.56636e25i 0.323461i −0.986835 0.161730i \(-0.948292\pi\)
0.986835 0.161730i \(-0.0517075\pi\)
\(390\) −1.51788e26 + 4.55985e25i −1.86463 + 0.560150i
\(391\) 6.76782e24i 0.0810366i
\(392\) 3.65799e25 4.38457e25i 0.426954 0.511760i
\(393\) −6.12472e25 −0.696884
\(394\) 5.08221e24 + 1.69177e25i 0.0563755 + 0.187663i
\(395\) −6.29266e25 −0.680556
\(396\) 1.02846e26 6.79215e25i 1.08452 0.716235i
\(397\) 4.41470e25i 0.453938i −0.973902 0.226969i \(-0.927118\pi\)
0.973902 0.226969i \(-0.0728816\pi\)
\(398\) 4.99652e25 + 1.66324e26i 0.500999 + 1.66772i
\(399\) 2.65339e25i 0.259461i
\(400\) −8.09636e25 + 1.89660e26i −0.772129 + 1.80874i
\(401\) 8.39617e25 0.780976 0.390488 0.920608i \(-0.372306\pi\)
0.390488 + 0.920608i \(0.372306\pi\)
\(402\) 1.43516e26 4.31134e25i 1.30208 0.391158i
\(403\) −7.39636e25 −0.654587
\(404\) −3.99371e25 6.04724e25i −0.344796 0.522088i
\(405\) 1.71707e26i 1.44623i
\(406\) −1.03389e26 + 3.10590e25i −0.849599 + 0.255227i
\(407\) 7.06469e25i 0.566434i
\(408\) 1.37392e26 1.64682e26i 1.07488 1.28838i
\(409\) 1.78278e26 1.36102 0.680508 0.732740i \(-0.261759\pi\)
0.680508 + 0.732740i \(0.261759\pi\)
\(410\) −4.18264e25 1.39232e26i −0.311610 1.03729i
\(411\) −7.24227e25 −0.526571
\(412\) −4.29130e24 6.49786e24i −0.0304520 0.0461103i
\(413\) 1.35901e26i 0.941288i
\(414\) 3.42977e24 + 1.14170e25i 0.0231879 + 0.0771878i
\(415\) 2.55666e26i 1.68730i
\(416\) 1.19173e26 + 1.33596e25i 0.767791 + 0.0860715i
\(417\) 2.73238e26 1.71862
\(418\) 2.44129e25 7.33386e24i 0.149919 0.0450370i
\(419\) 2.19481e26 1.31600 0.658000 0.753018i \(-0.271403\pi\)
0.658000 + 0.753018i \(0.271403\pi\)
\(420\) −4.63651e26 + 3.06203e26i −2.71455 + 1.79274i
\(421\) 2.80463e25i 0.160345i 0.996781 + 0.0801723i \(0.0255471\pi\)
−0.996781 + 0.0801723i \(0.974453\pi\)
\(422\) 1.04789e25 3.14796e24i 0.0585048 0.0175754i
\(423\) 1.82369e26i 0.994368i
\(424\) −1.84586e26 1.53997e26i −0.982967 0.820076i
\(425\) −4.33623e26 −2.25540
\(426\) 3.64601e25 + 1.21368e26i 0.185235 + 0.616608i
\(427\) 4.15979e26 2.06439
\(428\) 1.70135e26 1.12360e26i 0.824814 0.544722i
\(429\) 2.71960e26i 1.28805i
\(430\) −1.28975e26 4.29331e26i −0.596789 1.98659i
\(431\) 2.93226e26i 1.32565i −0.748773 0.662826i \(-0.769357\pi\)
0.748773 0.662826i \(-0.230643\pi\)
\(432\) −1.82802e25 + 4.28219e25i −0.0807501 + 0.189160i
\(433\) −3.63565e26 −1.56929 −0.784646 0.619945i \(-0.787155\pi\)
−0.784646 + 0.619945i \(0.787155\pi\)
\(434\) −2.48340e26 + 7.46037e25i −1.04749 + 0.314675i
\(435\) 4.20115e26 1.73171
\(436\) −1.86869e26 2.82955e26i −0.752786 1.13986i
\(437\) 2.46551e24i 0.00970718i
\(438\) 5.55330e25 1.66826e25i 0.213703 0.0641982i
\(439\) 5.58045e24i 0.0209906i 0.999945 + 0.0104953i \(0.00334081\pi\)
−0.999945 + 0.0104953i \(0.996659\pi\)
\(440\) 4.09878e26 + 3.41956e26i 1.50705 + 1.25731i
\(441\) −2.11492e26 −0.760166
\(442\) 7.25477e25 + 2.41496e26i 0.254918 + 0.848570i
\(443\) −3.86486e26 −1.32769 −0.663845 0.747870i \(-0.731077\pi\)
−0.663845 + 0.747870i \(0.731077\pi\)
\(444\) −1.19330e26 1.80689e26i −0.400794 0.606879i
\(445\) 3.57881e26i 1.17527i
\(446\) 1.86834e25 + 6.21932e25i 0.0599939 + 0.199707i
\(447\) 8.92771e26i 2.80327i
\(448\) 4.13609e26 7.53477e25i 1.27002 0.231361i
\(449\) −2.54008e26 −0.762753 −0.381377 0.924420i \(-0.624550\pi\)
−0.381377 + 0.924420i \(0.624550\pi\)
\(450\) 7.31502e26 2.19750e26i 2.14828 0.645361i
\(451\) −2.49463e26 −0.716540
\(452\) −3.87121e26 + 2.55662e26i −1.08758 + 0.718259i
\(453\) 6.98362e26i 1.91910i
\(454\) 1.11684e26 3.35508e25i 0.300214 0.0901870i
\(455\) 6.53283e26i 1.71786i
\(456\) −5.00517e25 + 5.99934e25i −0.128757 + 0.154332i
\(457\) −4.82016e26 −1.21311 −0.606554 0.795042i \(-0.707449\pi\)
−0.606554 + 0.795042i \(0.707449\pi\)
\(458\) 1.03538e26 + 3.44656e26i 0.254943 + 0.848654i
\(459\) −9.79045e25 −0.235872
\(460\) −4.30822e25 + 2.84522e25i −0.101559 + 0.0670715i
\(461\) 4.12032e26i 0.950434i −0.879869 0.475217i \(-0.842370\pi\)
0.879869 0.475217i \(-0.157630\pi\)
\(462\) 2.74314e26 + 9.13134e26i 0.619196 + 2.06118i
\(463\) 2.63607e26i 0.582300i −0.956677 0.291150i \(-0.905962\pi\)
0.956677 0.291150i \(-0.0940378\pi\)
\(464\) −2.92351e26 1.24801e26i −0.632012 0.269798i
\(465\) 1.00912e27 2.13507
\(466\) −4.39792e26 + 1.32117e26i −0.910726 + 0.273590i
\(467\) 2.33101e26 0.472471 0.236236 0.971696i \(-0.424086\pi\)
0.236236 + 0.971696i \(0.424086\pi\)
\(468\) −2.44769e26 3.70628e26i −0.485622 0.735325i
\(469\) 6.17680e26i 1.19960i
\(470\) 7.56436e26 2.27240e26i 1.43812 0.432023i
\(471\) 3.35318e26i 0.624090i
\(472\) 2.56355e26 3.07274e26i 0.467112 0.559894i
\(473\) −7.69238e26 −1.37230
\(474\) −9.52204e25 3.16969e26i −0.166321 0.553648i
\(475\) 1.57968e26 0.270168
\(476\) 4.87172e26 + 7.37673e26i 0.815855 + 1.23536i
\(477\) 8.90358e26i 1.46009i
\(478\) −1.87117e25 6.22875e25i −0.0300493 0.100028i
\(479\) 3.33329e25i 0.0524226i 0.999656 + 0.0262113i \(0.00834427\pi\)
−0.999656 + 0.0262113i \(0.991656\pi\)
\(480\) −1.62592e27 1.82270e26i −2.50430 0.280739i
\(481\) 2.54591e26 0.384054
\(482\) 1.18405e27 3.55699e26i 1.74944 0.525548i
\(483\) −9.22194e25 −0.133460
\(484\) 1.75680e26 1.16022e26i 0.249040 0.164470i
\(485\) 1.16826e27i 1.62227i
\(486\) −1.00971e27 + 3.03327e26i −1.37352 + 0.412618i
\(487\) 5.35339e26i 0.713410i 0.934217 + 0.356705i \(0.116100\pi\)
−0.934217 + 0.356705i \(0.883900\pi\)
\(488\) 9.40534e26 + 7.84675e26i 1.22794 + 1.02445i
\(489\) 1.87361e27 2.39657
\(490\) −2.63529e26 8.77234e26i −0.330269 1.09940i
\(491\) −3.93131e26 −0.482750 −0.241375 0.970432i \(-0.577598\pi\)
−0.241375 + 0.970432i \(0.577598\pi\)
\(492\) 6.38035e26 4.21369e26i 0.767703 0.507005i
\(493\) 6.68408e26i 0.788083i
\(494\) −2.64291e25 8.79770e25i −0.0305360 0.101648i
\(495\) 1.97707e27i 2.23857i
\(496\) −7.02228e26 2.99773e26i −0.779222 0.332640i
\(497\) −5.22359e26 −0.568075
\(498\) −1.28782e27 + 3.86872e26i −1.37266 + 0.412358i
\(499\) 3.50826e26 0.366511 0.183255 0.983065i \(-0.441336\pi\)
0.183255 + 0.983065i \(0.441336\pi\)
\(500\) 8.96029e26 + 1.35676e27i 0.917534 + 1.38932i
\(501\) 1.18118e27i 1.18560i
\(502\) −1.31027e27 + 3.93618e26i −1.28921 + 0.387291i
\(503\) 7.83816e26i 0.756022i 0.925801 + 0.378011i \(0.123392\pi\)
−0.925801 + 0.378011i \(0.876608\pi\)
\(504\) −1.19567e27 9.97533e26i −1.13059 0.943240i
\(505\) −1.16250e27 −1.07765
\(506\) 2.54891e25 + 8.48480e25i 0.0231659 + 0.0771146i
\(507\) −6.61829e26 −0.589747
\(508\) −2.31664e26 3.50785e26i −0.202405 0.306481i
\(509\) 1.14995e27i 0.985148i −0.870271 0.492574i \(-0.836056\pi\)
0.870271 0.492574i \(-0.163944\pi\)
\(510\) −9.89798e26 3.29483e27i −0.831466 2.76778i
\(511\) 2.39009e26i 0.196882i
\(512\) 1.07731e27 + 6.09842e26i 0.870241 + 0.492627i
\(513\) 3.56665e25 0.0282545
\(514\) −1.53321e27 + 4.60590e26i −1.19116 + 0.357836i
\(515\) −1.24912e26 −0.0951768
\(516\) 1.96743e27 1.29933e27i 1.47029 0.971004i
\(517\) 1.35531e27i 0.993424i
\(518\) 8.54814e26 2.56794e26i 0.614574 0.184623i
\(519\) 3.39081e27i 2.39128i
\(520\) 1.23231e27 1.47708e27i 0.852484 1.02181i
\(521\) 1.79868e27 1.22061 0.610306 0.792166i \(-0.291047\pi\)
0.610306 + 0.792166i \(0.291047\pi\)
\(522\) 3.38733e26 + 1.12757e27i 0.225503 + 0.750654i
\(523\) 1.23394e27 0.805890 0.402945 0.915224i \(-0.367987\pi\)
0.402945 + 0.915224i \(0.367987\pi\)
\(524\) 6.20309e26 4.09663e26i 0.397461 0.262491i
\(525\) 5.90861e27i 3.71443i
\(526\) 7.76509e26 + 2.58484e27i 0.478949 + 1.59432i
\(527\) 1.60551e27i 0.971646i
\(528\) −1.10225e27 + 2.58205e27i −0.654546 + 1.53330i
\(529\) 1.70759e27 0.995007
\(530\) −3.69306e27 + 1.10943e27i −2.11168 + 0.634367i
\(531\) −1.48215e27 −0.831664
\(532\) −1.77477e26 2.68734e26i −0.0977293 0.147981i
\(533\) 8.98990e26i 0.485828i
\(534\) 1.80269e27 5.41544e26i 0.956111 0.287224i
\(535\) 3.27060e27i 1.70251i
\(536\) −1.16515e27 + 1.39658e27i −0.595297 + 0.713540i
\(537\) 4.12328e27 2.06776
\(538\) −9.83861e26 3.27507e27i −0.484296 1.61212i
\(539\) −1.57175e27 −0.759444
\(540\) 4.11595e26 + 6.23234e26i 0.195224 + 0.295606i
\(541\) 3.90282e26i 0.181721i −0.995864 0.0908607i \(-0.971038\pi\)
0.995864 0.0908607i \(-0.0289618\pi\)
\(542\) 2.42946e26 + 8.08718e26i 0.111050 + 0.369662i
\(543\) 1.23623e27i 0.554754i
\(544\) −2.89994e26 + 2.58686e27i −0.127761 + 1.13968i
\(545\) −5.43940e27 −2.35281
\(546\) 3.29067e27 9.88546e26i 1.39752 0.419827i
\(547\) −5.54597e26 −0.231262 −0.115631 0.993292i \(-0.536889\pi\)
−0.115631 + 0.993292i \(0.536889\pi\)
\(548\) 7.33494e26 4.84412e26i 0.300325 0.198340i
\(549\) 4.53672e27i 1.82397i
\(550\) 5.43632e27 1.63312e27i 2.14624 0.644749i
\(551\) 2.43500e26i 0.0944026i
\(552\) −2.08509e26 1.73956e26i −0.0793843 0.0662292i
\(553\) 1.36421e27 0.510070
\(554\) 5.11308e26 + 1.70204e27i 0.187752 + 0.624988i
\(555\) −3.47349e27 −1.25267
\(556\) −2.76735e27 + 1.82760e27i −0.980202 + 0.647343i
\(557\) 2.54412e27i 0.885087i −0.896747 0.442543i \(-0.854076\pi\)
0.896747 0.442543i \(-0.145924\pi\)
\(558\) 8.13636e26 + 2.70843e27i 0.278028 + 0.925498i
\(559\) 2.77211e27i 0.930447i
\(560\) 2.64774e27 6.20242e27i 0.872961 2.04494i
\(561\) −5.90339e27 −1.91193
\(562\) −2.54075e27 + 7.63264e26i −0.808349 + 0.242835i
\(563\) −1.04936e27 −0.327976 −0.163988 0.986462i \(-0.552436\pi\)
−0.163988 + 0.986462i \(0.552436\pi\)
\(564\) 2.28927e27 + 3.46640e27i 0.702921 + 1.06436i
\(565\) 7.44184e27i 2.24489i
\(566\) 1.47181e27 4.42145e26i 0.436202 0.131039i
\(567\) 3.72249e27i 1.08393i
\(568\) −1.18106e27 9.85343e26i −0.337900 0.281906i
\(569\) 1.91505e27 0.538340 0.269170 0.963093i \(-0.413251\pi\)
0.269170 + 0.963093i \(0.413251\pi\)
\(570\) 3.60583e26 + 1.20031e27i 0.0995993 + 0.331546i
\(571\) 9.26020e26 0.251339 0.125669 0.992072i \(-0.459892\pi\)
0.125669 + 0.992072i \(0.459892\pi\)
\(572\) −1.81906e27 2.75440e27i −0.485161 0.734627i
\(573\) 6.95129e27i 1.82188i
\(574\) 9.06769e26 + 3.01845e27i 0.233549 + 0.777437i
\(575\) 5.49025e26i 0.138968i
\(576\) −8.21750e26 4.51087e27i −0.204416 1.12211i
\(577\) −8.98956e26 −0.219776 −0.109888 0.993944i \(-0.535049\pi\)
−0.109888 + 0.993944i \(0.535049\pi\)
\(578\) −1.25631e27 + 3.77406e26i −0.301869 + 0.0906840i
\(579\) 9.64912e27 2.27878
\(580\) −4.25491e27 + 2.81002e27i −0.987666 + 0.652272i
\(581\) 5.54267e27i 1.26461i
\(582\) −5.88469e27 + 1.76781e27i −1.31976 + 0.396466i
\(583\) 6.61689e27i 1.45871i
\(584\) −4.50851e26 + 5.40403e26i −0.0977023 + 0.117109i
\(585\) −7.12478e27 −1.51779
\(586\) −1.62045e27 5.39416e27i −0.339360 1.12966i
\(587\) 8.28104e26 0.170492 0.0852460 0.996360i \(-0.472832\pi\)
0.0852460 + 0.996360i \(0.472832\pi\)
\(588\) 4.01996e27 2.65486e27i 0.813671 0.537363i
\(589\) 5.84888e26i 0.116391i
\(590\) −1.84683e27 6.14773e27i −0.361333 1.20280i
\(591\) 1.49032e27i 0.286685i
\(592\) 2.41714e27 + 1.03185e27i 0.457178 + 0.195164i
\(593\) 2.16861e27 0.403306 0.201653 0.979457i \(-0.435369\pi\)
0.201653 + 0.979457i \(0.435369\pi\)
\(594\) 1.22743e27 3.68730e26i 0.224456 0.0674285i
\(595\) 1.41807e28 2.54993
\(596\) −5.97146e27 9.04194e27i −1.05589 1.59882i
\(597\) 1.46519e28i 2.54772i
\(598\) 3.05767e26 9.18552e25i 0.0522852 0.0157069i
\(599\) 6.16313e26i 0.103641i −0.998656 0.0518207i \(-0.983498\pi\)
0.998656 0.0518207i \(-0.0165024\pi\)
\(600\) −1.11456e28 + 1.33594e28i −1.84328 + 2.20941i
\(601\) −8.17765e26 −0.133010 −0.0665049 0.997786i \(-0.521185\pi\)
−0.0665049 + 0.997786i \(0.521185\pi\)
\(602\) 2.79609e27 + 9.30763e27i 0.447288 + 1.48893i
\(603\) 6.73649e27 1.05989
\(604\) 4.67112e27 + 7.07298e27i 0.722856 + 1.09454i
\(605\) 3.37719e27i 0.514046i
\(606\) −1.75908e27 5.85563e27i −0.263366 0.876692i
\(607\) 7.48374e27i 1.10213i 0.834463 + 0.551064i \(0.185778\pi\)
−0.834463 + 0.551064i \(0.814222\pi\)
\(608\) 1.05645e26 9.42390e26i 0.0153042 0.136520i
\(609\) −9.10783e27 −1.29790
\(610\) 1.88175e28 5.65296e27i 2.63794 0.792460i
\(611\) −4.88416e27 −0.673562
\(612\) 8.04515e27 5.31316e27i 1.09149 0.720839i
\(613\) 2.92871e27i 0.390906i −0.980713 0.195453i \(-0.937382\pi\)
0.980713 0.195453i \(-0.0626177\pi\)
\(614\) 2.27582e27 6.83676e26i 0.298850 0.0897773i
\(615\) 1.22653e28i 1.58463i
\(616\) −8.88590e27 7.41339e27i −1.12952 0.942344i
\(617\) 1.27218e28 1.59109 0.795547 0.605891i \(-0.207183\pi\)
0.795547 + 0.605891i \(0.207183\pi\)
\(618\) −1.89016e26 6.29196e26i −0.0232602 0.0774286i
\(619\) −1.60929e28 −1.94863 −0.974314 0.225195i \(-0.927698\pi\)
−0.974314 + 0.225195i \(0.927698\pi\)
\(620\) −1.02203e28 + 6.74965e27i −1.21772 + 0.804201i
\(621\) 1.23960e26i 0.0145334i
\(622\) 1.16326e27 + 3.87227e27i 0.134207 + 0.446747i
\(623\) 7.75862e27i 0.880854i
\(624\) 9.30496e27 + 3.97218e27i 1.03961 + 0.443795i
\(625\) 8.19518e27 0.901069
\(626\) −5.77240e27 + 1.73408e27i −0.624616 + 0.187640i
\(627\) 2.15060e27 0.229026
\(628\) −2.24283e27 3.39608e27i −0.235072 0.355944i
\(629\) 5.52635e27i 0.570075i
\(630\) −2.39222e28 + 7.18644e27i −2.42882 + 0.729639i
\(631\) 9.82154e27i 0.981490i −0.871303 0.490745i \(-0.836725\pi\)
0.871303 0.490745i \(-0.163275\pi\)
\(632\) 3.08449e27 + 2.57335e27i 0.303398 + 0.253121i
\(633\) 9.23116e26 0.0893757
\(634\) 4.13493e27 + 1.37643e28i 0.394072 + 1.31178i
\(635\) −6.74332e27 −0.632611
\(636\) −1.11766e28 1.69236e28i −1.03214 1.56287i
\(637\) 5.66412e27i 0.514918i
\(638\) 2.51737e27 + 8.37981e27i 0.225289 + 0.749941i
\(639\) 5.69691e27i 0.501916i
\(640\) 1.76864e28 9.02924e27i 1.53405 0.783161i
\(641\) 7.29542e27 0.622974 0.311487 0.950250i \(-0.399173\pi\)
0.311487 + 0.950250i \(0.399173\pi\)
\(642\) 1.64744e28 4.94906e27i 1.38503 0.416076i
\(643\) −3.08089e26 −0.0255016 −0.0127508 0.999919i \(-0.504059\pi\)
−0.0127508 + 0.999919i \(0.504059\pi\)
\(644\) 9.33994e26 6.16826e26i 0.0761177 0.0502694i
\(645\) 3.78210e28i 3.03484i
\(646\) 1.90970e27 5.73691e26i 0.150883 0.0453265i
\(647\) 4.11006e27i 0.319746i −0.987138 0.159873i \(-0.948891\pi\)
0.987138 0.159873i \(-0.0511085\pi\)
\(648\) 7.02186e27 8.41660e27i 0.537900 0.644743i
\(649\) −1.10150e28 −0.830875
\(650\) −5.88527e27 1.95909e28i −0.437153 1.45519i
\(651\) −2.18770e28 −1.60021
\(652\) −1.89758e28 + 1.25320e28i −1.36686 + 0.902699i
\(653\) 2.18243e28i 1.54813i 0.633105 + 0.774066i \(0.281780\pi\)
−0.633105 + 0.774066i \(0.718220\pi\)
\(654\) −8.23088e27 2.73989e28i −0.575001 1.91406i
\(655\) 1.19245e28i 0.820405i
\(656\) −3.64358e27 + 8.53522e27i −0.246882 + 0.578331i
\(657\) 2.60666e27 0.173953
\(658\) −1.63990e28 + 4.92642e27i −1.07785 + 0.323797i
\(659\) −1.03384e28 −0.669265 −0.334632 0.942349i \(-0.608612\pi\)
−0.334632 + 0.942349i \(0.608612\pi\)
\(660\) 2.48181e28 + 3.75794e28i 1.58245 + 2.39613i
\(661\) 3.34206e27i 0.209894i −0.994478 0.104947i \(-0.966533\pi\)
0.994478 0.104947i \(-0.0334672\pi\)
\(662\) 1.13938e28 3.42279e27i 0.704834 0.211739i
\(663\) 2.12741e28i 1.29633i
\(664\) 1.04553e28 1.25320e28i 0.627561 0.752213i
\(665\) −5.16602e27 −0.305450
\(666\) −2.80062e27 9.32270e27i −0.163122 0.543000i
\(667\) −8.46295e26 −0.0485583
\(668\) 7.90054e27 + 1.19629e28i 0.446573 + 0.676197i
\(669\) 5.47877e27i 0.305086i
\(670\) 8.39398e27 + 2.79418e28i 0.460490 + 1.53288i
\(671\) 3.37156e28i 1.82224i
\(672\) 3.52489e28 + 3.95150e27i 1.87695 + 0.210412i
\(673\) −7.36345e27 −0.386306 −0.193153 0.981169i \(-0.561871\pi\)
−0.193153 + 0.981169i \(0.561871\pi\)
\(674\) −7.75632e27 + 2.33007e27i −0.400919 + 0.120440i
\(675\) 7.94229e27 0.404490
\(676\) 6.70297e27 4.42676e27i 0.336357 0.222136i
\(677\) 1.68918e28i 0.835199i 0.908631 + 0.417600i \(0.137129\pi\)
−0.908631 + 0.417600i \(0.862871\pi\)
\(678\) −3.74855e28 + 1.12610e28i −1.82627 + 0.548629i
\(679\) 2.53272e28i 1.21588i
\(680\) 3.20627e28 + 2.67495e28i 1.51674 + 1.26540i
\(681\) 9.83853e27 0.458626
\(682\) 6.04672e27 + 2.01283e28i 0.277764 + 0.924619i
\(683\) 2.83245e28 1.28220 0.641100 0.767457i \(-0.278478\pi\)
0.641100 + 0.767457i \(0.278478\pi\)
\(684\) −2.93084e27 + 1.93558e27i −0.130747 + 0.0863475i
\(685\) 1.41004e28i 0.619904i
\(686\) −2.85904e27 9.51716e27i −0.123874 0.412350i
\(687\) 3.03617e28i 1.29646i
\(688\) −1.12353e28 + 2.63190e28i −0.472824 + 1.10761i
\(689\) 2.38453e28 0.989034
\(690\) −4.17171e27 + 1.25322e27i −0.170539 + 0.0512313i
\(691\) 9.01687e26 0.0363308 0.0181654 0.999835i \(-0.494217\pi\)
0.0181654 + 0.999835i \(0.494217\pi\)
\(692\) −2.26800e28 3.43420e28i −0.900705 1.36384i
\(693\) 4.28616e28i 1.67779i
\(694\) 3.22782e28 9.69666e27i 1.24542 0.374134i
\(695\) 5.31982e28i 2.02325i
\(696\) −2.05929e28 1.71804e28i −0.772014 0.644081i
\(697\) −1.95142e28 −0.721146
\(698\) −1.45540e28 4.84472e28i −0.530185 1.76488i
\(699\) −3.87425e28 −1.39128
\(700\) −3.95208e28 5.98422e28i −1.39909 2.11849i
\(701\) 1.13211e28i 0.395100i −0.980293 0.197550i \(-0.936702\pi\)
0.980293 0.197550i \(-0.0632985\pi\)
\(702\) −1.32879e27 4.42328e27i −0.0457179 0.152186i
\(703\) 2.01325e27i 0.0682879i
\(704\) −6.10702e27 3.35235e28i −0.204222 1.12104i
\(705\) 6.66365e28 2.19696
\(706\) −1.59788e28 + 4.80018e27i −0.519395 + 0.156031i
\(707\) 2.52021e28 0.807687
\(708\) 2.81722e28 1.86054e28i 0.890202 0.587905i
\(709\) 5.95923e28i 1.85664i −0.371783 0.928320i \(-0.621253\pi\)
0.371783 0.928320i \(-0.378747\pi\)
\(710\) −2.36298e28 + 7.09861e27i −0.725901 + 0.218067i
\(711\) 1.48782e28i 0.450666i
\(712\) −1.46353e28 + 1.75423e28i −0.437122 + 0.523947i
\(713\) −2.03280e27 −0.0598686
\(714\) 2.14582e28 + 7.14299e28i 0.623176 + 2.07443i
\(715\) −5.29494e28 −1.51635
\(716\) −4.17604e28 + 2.75793e28i −1.17933 + 0.778849i
\(717\) 5.48707e27i 0.152809i
\(718\) −1.59507e28 5.30966e28i −0.438061 1.45822i
\(719\) 2.54256e28i 0.688623i −0.938855 0.344312i \(-0.888112\pi\)
0.938855 0.344312i \(-0.111888\pi\)
\(720\) −6.76443e28 2.88765e28i −1.80678 0.771295i
\(721\) 2.70801e27 0.0713341
\(722\) 3.61689e28 1.08655e28i 0.939645 0.282278i
\(723\) 1.04306e29 2.67256
\(724\) 8.26873e27 + 1.25205e28i 0.208955 + 0.316399i
\(725\) 5.42231e28i 1.35146i
\(726\) 1.70113e28 5.11036e27i 0.418189 0.125628i
\(727\) 4.74565e28i 1.15067i 0.817917 + 0.575337i \(0.195129\pi\)
−0.817917 + 0.575337i \(0.804871\pi\)
\(728\) −2.67157e28 + 3.20222e28i −0.638928 + 0.765838i
\(729\) −5.33541e28 −1.25861
\(730\) 3.24802e27 + 1.08120e28i 0.0755772 + 0.251581i
\(731\) −6.01736e28 −1.38112
\(732\) 5.69493e28 + 8.62322e28i 1.28937 + 1.95236i
\(733\) 3.45216e27i 0.0770995i −0.999257 0.0385498i \(-0.987726\pi\)
0.999257 0.0385498i \(-0.0122738\pi\)
\(734\) 6.25486e27 + 2.08211e28i 0.137802 + 0.458716i
\(735\) 7.72780e28i 1.67951i
\(736\) 3.27531e27 + 3.67172e26i 0.0702222 + 0.00787211i
\(737\) 5.00637e28 1.05888
\(738\) 3.29196e28 9.88933e27i 0.686895 0.206349i
\(739\) 6.30447e28 1.29779 0.648895 0.760878i \(-0.275232\pi\)
0.648895 + 0.760878i \(0.275232\pi\)
\(740\) 3.51793e28 2.32330e28i 0.714447 0.471833i
\(741\) 7.75013e27i 0.155284i
\(742\) 8.00631e28 2.40517e28i 1.58268 0.475452i
\(743\) 1.06032e28i 0.206799i 0.994640 + 0.103400i \(0.0329721\pi\)
−0.994640 + 0.103400i \(0.967028\pi\)
\(744\) −4.94641e28 4.12673e28i −0.951833 0.794102i
\(745\) −1.73818e29 −3.30014
\(746\) −1.20302e28 4.00460e28i −0.225364 0.750190i
\(747\) −6.04490e28 −1.11733
\(748\) 5.97893e28 3.94859e28i 1.09045 0.720155i
\(749\) 7.09045e28i 1.27601i
\(750\) 3.94668e28 + 1.31377e29i 0.700841 + 2.33296i
\(751\) 1.67963e28i 0.294316i 0.989113 + 0.147158i \(0.0470126\pi\)
−0.989113 + 0.147158i \(0.952987\pi\)
\(752\) −4.63713e28 1.97953e28i −0.801809 0.342283i
\(753\) −1.15426e29 −1.96948
\(754\) 3.01983e28 9.07185e27i 0.508475 0.152750i
\(755\) 1.35968e29 2.25926
\(756\) −8.92311e27 1.35113e28i −0.146318 0.221554i
\(757\) 3.68923e28i 0.597003i −0.954409 0.298502i \(-0.903513\pi\)
0.954409 0.298502i \(-0.0964868\pi\)
\(758\) −6.01388e28 + 1.80662e28i −0.960423 + 0.288520i
\(759\) 7.47449e27i 0.117805i
\(760\) &