Properties

Label 8.18.b.a.5.13
Level 8
Weight 18
Character 8.5
Analytic conductor 14.658
Analytic rank 0
Dimension 16
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 18 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.6577669876\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 7 x^{15} + 4022 x^{14} - 1102776 x^{13} - 373411968 x^{12} + 2100004864 x^{11} - 3763915816960 x^{10} + 7317489121656832 x^{9} - 1108241988138827776 x^{8} + 163121042717484777472 x^{7} + 5699397839986467274752 x^{6} + 1127435088957285706235904 x^{5} - 217909345031306501735579648 x^{4} - 78950720850572326734309359616 x^{3} + 13720647095471028734661620662272 x^{2} - 5242030267748791654842336509165568 x + 1286374137827816254118965326485913600\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{120}\cdot 3^{14}\cdot 7 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 5.13
Root \(156.321 + 75.9390i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.14

$q$-expansion

\(f(q)\) \(=\) \(q+(328.641 - 151.878i) q^{2} +4248.51i q^{3} +(84938.1 - 99826.8i) q^{4} -663971. i q^{5} +(645256. + 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 - 4.57074e7i) q^{8} +1.11090e8 q^{9} +O(q^{10})\) \(q+(328.641 - 151.878i) q^{2} +4248.51i q^{3} +(84938.1 - 99826.8i) q^{4} -663971. i q^{5} +(645256. + 1.39624e6i) q^{6} -1.66742e7 q^{7} +(1.27527e7 - 4.57074e7i) q^{8} +1.11090e8 q^{9} +(-1.00843e8 - 2.18208e8i) q^{10} -1.05479e9i q^{11} +(4.24116e8 + 3.60861e8i) q^{12} +9.19407e7i q^{13} +(-5.47982e9 + 2.53244e9i) q^{14} +2.82089e9 q^{15} +(-2.75091e9 - 1.69582e10i) q^{16} -1.98326e10 q^{17} +(3.65088e10 - 1.68722e10i) q^{18} -8.44846e10i q^{19} +(-6.62821e10 - 5.63964e10i) q^{20} -7.08405e10i q^{21} +(-1.60199e11 - 3.46647e11i) q^{22} -2.72263e10 q^{23} +(1.94189e11 + 5.41799e10i) q^{24} +3.22082e11 q^{25} +(1.39638e10 + 3.02155e10i) q^{26} +1.02062e12i q^{27} +(-1.41627e12 + 1.66453e12i) q^{28} +3.75013e12i q^{29} +(9.27061e11 - 4.28431e11i) q^{30} +5.36921e12 q^{31} +(-3.47964e12 - 5.15536e12i) q^{32} +4.48129e12 q^{33} +(-6.51781e12 + 3.01214e12i) q^{34} +1.10712e13i q^{35} +(9.43580e12 - 1.10898e13i) q^{36} +1.92294e13i q^{37} +(-1.28314e13 - 2.77651e13i) q^{38} -3.90612e11 q^{39} +(-3.03484e13 - 8.46739e12i) q^{40} +5.42400e13 q^{41} +(-1.07591e13 - 2.32811e13i) q^{42} +3.96416e13i q^{43} +(-1.05296e14 - 8.95918e13i) q^{44} -7.37607e13i q^{45} +(-8.94769e12 + 4.13508e12i) q^{46} +4.48999e13 q^{47} +(7.20471e13 - 1.16873e13i) q^{48} +4.53979e13 q^{49} +(1.05850e14 - 4.89172e13i) q^{50} -8.42591e13i q^{51} +(9.17815e12 + 7.80927e12i) q^{52} +7.81803e14i q^{53} +(1.55010e14 + 3.35419e14i) q^{54} -7.00349e14 q^{55} +(-2.12640e14 + 7.62134e14i) q^{56} +3.58934e14 q^{57} +(5.69562e14 + 1.23245e15i) q^{58} -1.07092e15i q^{59} +(2.39601e14 - 2.81600e14i) q^{60} -1.92548e15i q^{61} +(1.76454e15 - 8.15466e14i) q^{62} -1.85234e15 q^{63} +(-1.92654e15 - 1.16578e15i) q^{64} +6.10460e13 q^{65} +(1.47274e15 - 6.80609e14i) q^{66} -3.68678e15i q^{67} +(-1.68454e15 + 1.97982e15i) q^{68} -1.15671e14i q^{69} +(1.68147e15 + 3.63844e15i) q^{70} -1.02421e16 q^{71} +(1.41670e15 - 5.07765e15i) q^{72} +1.25847e16 q^{73} +(2.92052e15 + 6.31956e15i) q^{74} +1.36837e15i q^{75} +(-8.43383e15 - 7.17596e15i) q^{76} +1.75877e16i q^{77} +(-1.28371e14 + 5.93253e13i) q^{78} +3.24102e15 q^{79} +(-1.12597e16 + 1.82652e15i) q^{80} +1.00101e16 q^{81} +(1.78255e16 - 8.23787e15i) q^{82} +4.28316e15i q^{83} +(-7.07178e15 - 6.01706e15i) q^{84} +1.31683e16i q^{85} +(6.02070e15 + 1.30279e16i) q^{86} -1.59325e16 q^{87} +(-4.82117e16 - 1.34514e16i) q^{88} +6.95255e16 q^{89} +(-1.12026e16 - 2.42408e16i) q^{90} -1.53304e15i q^{91} +(-2.31255e15 + 2.71792e15i) q^{92} +2.28112e16i q^{93} +(1.47560e16 - 6.81931e15i) q^{94} -5.60953e16 q^{95} +(2.19026e16 - 1.47833e16i) q^{96} -7.74223e16 q^{97} +(1.49196e16 - 6.89495e15i) q^{98} -1.17177e17i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + O(q^{10}) \) \( 16q + 270q^{2} - 27436q^{4} + 5839948q^{6} + 11529600q^{7} + 24334920q^{8} - 602654096q^{9} + 131002712q^{10} - 2795125400q^{12} + 16363788528q^{14} - 9993282176q^{15} + 26500434192q^{16} - 7489125600q^{17} - 113450563870q^{18} - 209445719856q^{20} + 223126527100q^{22} + 746845345920q^{23} - 1099415493232q^{24} - 1809682431664q^{25} + 2467726531080q^{26} + 3220542267040q^{28} - 1188624268048q^{30} - 318979758592q^{31} + 1455647316000q^{32} + 5633526177600q^{33} - 4461251980292q^{34} - 33088278002484q^{36} + 24076283913900q^{38} - 18457706051456q^{39} + 60626292962592q^{40} + 7482251536032q^{41} - 51630378688160q^{42} + 193654716236040q^{44} - 195097141003568q^{46} - 376698804821760q^{47} - 329350060416480q^{48} + 127691292101520q^{49} + 474997408872102q^{50} - 272251877663120q^{52} + 735354219382520q^{54} + 2209036687713152q^{55} - 162767516076480q^{56} - 190521298294720q^{57} - 623262610679960q^{58} - 1973616194963808q^{60} + 695695648144320q^{62} - 8131096607338880q^{63} + 1111931745501248q^{64} + 2385987975356160q^{65} + 3598826202828312q^{66} + 5981109959771880q^{68} - 10044559836180288q^{70} + 9025926285576576q^{71} - 19918679666289160q^{72} + 11332002046118560q^{73} + 11098735408189464q^{74} + 5959440926938280q^{76} + 4184252259031760q^{78} - 45299671392008448q^{79} + 1337342539452480q^{80} + 20101901999290832q^{81} + 15639739637081420q^{82} + 19796542864700224q^{84} - 14252032276026564q^{86} + 25965768920837760q^{87} - 66964872768837680q^{88} - 69879174608766048q^{89} + 136151511125051240q^{90} + 57336249810701280q^{92} - 192318922166254176q^{94} + 93790444358203776q^{95} - 342799224184788928q^{96} + 95593398602180640q^{97} + 339641261743253790q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 328.641 151.878i 0.907752 0.419508i
\(3\) 4248.51i 0.373858i 0.982373 + 0.186929i \(0.0598534\pi\)
−0.982373 + 0.186929i \(0.940147\pi\)
\(4\) 84938.1 99826.8i 0.648026 0.761618i
\(5\) 663971.i 0.760158i −0.924954 0.380079i \(-0.875897\pi\)
0.924954 0.380079i \(-0.124103\pi\)
\(6\) 645256. + 1.39624e6i 0.156836 + 0.339370i
\(7\) −1.66742e7 −1.09323 −0.546615 0.837384i \(-0.684084\pi\)
−0.546615 + 0.837384i \(0.684084\pi\)
\(8\) 1.27527e7 4.57074e7i 0.268742 0.963212i
\(9\) 1.11090e8 0.860230
\(10\) −1.00843e8 2.18208e8i −0.318892 0.690035i
\(11\) 1.05479e9i 1.48364i −0.670600 0.741819i \(-0.733963\pi\)
0.670600 0.741819i \(-0.266037\pi\)
\(12\) 4.24116e8 + 3.60861e8i 0.284737 + 0.242270i
\(13\) 9.19407e7i 0.0312600i 0.999878 + 0.0156300i \(0.00497539\pi\)
−0.999878 + 0.0156300i \(0.995025\pi\)
\(14\) −5.47982e9 + 2.53244e9i −0.992381 + 0.458618i
\(15\) 2.82089e9 0.284191
\(16\) −2.75091e9 1.69582e10i −0.160124 0.987097i
\(17\) −1.98326e10 −0.689547 −0.344773 0.938686i \(-0.612044\pi\)
−0.344773 + 0.938686i \(0.612044\pi\)
\(18\) 3.65088e10 1.68722e10i 0.780876 0.360873i
\(19\) 8.44846e10i 1.14123i −0.821219 0.570613i \(-0.806706\pi\)
0.821219 0.570613i \(-0.193294\pi\)
\(20\) −6.62821e10 5.63964e10i −0.578950 0.492602i
\(21\) 7.08405e10i 0.408712i
\(22\) −1.60199e11 3.46647e11i −0.622398 1.34677i
\(23\) −2.72263e10 −0.0724941 −0.0362470 0.999343i \(-0.511540\pi\)
−0.0362470 + 0.999343i \(0.511540\pi\)
\(24\) 1.94189e11 + 5.41799e10i 0.360104 + 0.100471i
\(25\) 3.22082e11 0.422160
\(26\) 1.39638e10 + 3.02155e10i 0.0131138 + 0.0283764i
\(27\) 1.02062e12i 0.695462i
\(28\) −1.41627e12 + 1.66453e12i −0.708441 + 0.832623i
\(29\) 3.75013e12i 1.39208i 0.718005 + 0.696038i \(0.245056\pi\)
−0.718005 + 0.696038i \(0.754944\pi\)
\(30\) 9.27061e11 4.28431e11i 0.257975 0.119220i
\(31\) 5.36921e12 1.13067 0.565336 0.824861i \(-0.308747\pi\)
0.565336 + 0.824861i \(0.308747\pi\)
\(32\) −3.47964e12 5.15536e12i −0.559448 0.828866i
\(33\) 4.48129e12 0.554669
\(34\) −6.51781e12 + 3.01214e12i −0.625937 + 0.289270i
\(35\) 1.10712e13i 0.831027i
\(36\) 9.43580e12 1.10898e13i 0.557452 0.655167i
\(37\) 1.92294e13i 0.900015i 0.893025 + 0.450008i \(0.148579\pi\)
−0.893025 + 0.450008i \(0.851421\pi\)
\(38\) −1.28314e13 2.77651e13i −0.478754 1.03595i
\(39\) −3.90612e11 −0.0116868
\(40\) −3.03484e13 8.46739e12i −0.732194 0.204287i
\(41\) 5.42400e13 1.06086 0.530429 0.847730i \(-0.322031\pi\)
0.530429 + 0.847730i \(0.322031\pi\)
\(42\) −1.07591e13 2.32811e13i −0.171458 0.371009i
\(43\) 3.96416e13i 0.517213i 0.965983 + 0.258607i \(0.0832634\pi\)
−0.965983 + 0.258607i \(0.916737\pi\)
\(44\) −1.05296e14 8.95918e13i −1.12996 0.961436i
\(45\) 7.37607e13i 0.653911i
\(46\) −8.94769e12 + 4.13508e12i −0.0658066 + 0.0304118i
\(47\) 4.48999e13 0.275051 0.137526 0.990498i \(-0.456085\pi\)
0.137526 + 0.990498i \(0.456085\pi\)
\(48\) 7.20471e13 1.16873e13i 0.369034 0.0598636i
\(49\) 4.53979e13 0.195150
\(50\) 1.05850e14 4.89172e13i 0.383216 0.177099i
\(51\) 8.42591e13i 0.257792i
\(52\) 9.17815e12 + 7.80927e12i 0.0238082 + 0.0202573i
\(53\) 7.81803e14i 1.72485i 0.506181 + 0.862427i \(0.331057\pi\)
−0.506181 + 0.862427i \(0.668943\pi\)
\(54\) 1.55010e14 + 3.35419e14i 0.291752 + 0.631306i
\(55\) −7.00349e14 −1.12780
\(56\) −2.12640e14 + 7.62134e14i −0.293797 + 1.05301i
\(57\) 3.58934e14 0.426656
\(58\) 5.69562e14 + 1.23245e15i 0.583987 + 1.26366i
\(59\) 1.07092e15i 0.949541i −0.880110 0.474770i \(-0.842531\pi\)
0.880110 0.474770i \(-0.157469\pi\)
\(60\) 2.39601e14 2.81600e14i 0.184163 0.216445i
\(61\) 1.92548e15i 1.28599i −0.765872 0.642993i \(-0.777692\pi\)
0.765872 0.642993i \(-0.222308\pi\)
\(62\) 1.76454e15 8.15466e14i 1.02637 0.474325i
\(63\) −1.85234e15 −0.940429
\(64\) −1.92654e15 1.16578e15i −0.855555 0.517711i
\(65\) 6.10460e13 0.0237626
\(66\) 1.47274e15 6.80609e14i 0.503502 0.232688i
\(67\) 3.68678e15i 1.10920i −0.832116 0.554602i \(-0.812871\pi\)
0.832116 0.554602i \(-0.187129\pi\)
\(68\) −1.68454e15 + 1.97982e15i −0.446845 + 0.525171i
\(69\) 1.15671e14i 0.0271025i
\(70\) 1.68147e15 + 3.63844e15i 0.348622 + 0.754366i
\(71\) −1.02421e16 −1.88232 −0.941162 0.337957i \(-0.890264\pi\)
−0.941162 + 0.337957i \(0.890264\pi\)
\(72\) 1.41670e15 5.07765e15i 0.231180 0.828584i
\(73\) 1.25847e16 1.82641 0.913204 0.407502i \(-0.133600\pi\)
0.913204 + 0.407502i \(0.133600\pi\)
\(74\) 2.92052e15 + 6.31956e15i 0.377564 + 0.816991i
\(75\) 1.36837e15i 0.157828i
\(76\) −8.43383e15 7.17596e15i −0.869179 0.739545i
\(77\) 1.75877e16i 1.62196i
\(78\) −1.28371e14 + 5.93253e13i −0.0106087 + 0.00490271i
\(79\) 3.24102e15 0.240354 0.120177 0.992752i \(-0.461654\pi\)
0.120177 + 0.992752i \(0.461654\pi\)
\(80\) −1.12597e16 + 1.82652e15i −0.750350 + 0.121720i
\(81\) 1.00101e16 0.600227
\(82\) 1.78255e16 8.23787e15i 0.962995 0.445038i
\(83\) 4.28316e15i 0.208737i 0.994539 + 0.104369i \(0.0332822\pi\)
−0.994539 + 0.104369i \(0.966718\pi\)
\(84\) −7.07178e15 6.01706e15i −0.311283 0.264856i
\(85\) 1.31683e16i 0.524165i
\(86\) 6.02070e15 + 1.30279e16i 0.216975 + 0.469501i
\(87\) −1.59325e16 −0.520439
\(88\) −4.82117e16 1.34514e16i −1.42906 0.398716i
\(89\) 6.95255e16 1.87210 0.936050 0.351868i \(-0.114453\pi\)
0.936050 + 0.351868i \(0.114453\pi\)
\(90\) −1.12026e16 2.42408e16i −0.274321 0.593589i
\(91\) 1.53304e15i 0.0341744i
\(92\) −2.31255e15 + 2.71792e15i −0.0469781 + 0.0552128i
\(93\) 2.28112e16i 0.422710i
\(94\) 1.47560e16 6.81931e15i 0.249678 0.115386i
\(95\) −5.60953e16 −0.867513
\(96\) 2.19026e16 1.47833e16i 0.309878 0.209154i
\(97\) −7.74223e16 −1.00301 −0.501507 0.865154i \(-0.667221\pi\)
−0.501507 + 0.865154i \(0.667221\pi\)
\(98\) 1.49196e16 6.89495e15i 0.177148 0.0818671i
\(99\) 1.17177e17i 1.27627i
\(100\) 2.73571e16 3.21524e16i 0.273571 0.321524i
\(101\) 8.38662e16i 0.770646i −0.922782 0.385323i \(-0.874090\pi\)
0.922782 0.385323i \(-0.125910\pi\)
\(102\) −1.27971e16 2.76910e16i −0.108146 0.234012i
\(103\) 8.10218e16 0.630210 0.315105 0.949057i \(-0.397960\pi\)
0.315105 + 0.949057i \(0.397960\pi\)
\(104\) 4.20238e15 + 1.17249e15i 0.0301101 + 0.00840089i
\(105\) −4.70360e16 −0.310686
\(106\) 1.18739e17 + 2.56933e17i 0.723590 + 1.56574i
\(107\) 1.60731e17i 0.904351i 0.891929 + 0.452175i \(0.149352\pi\)
−0.891929 + 0.452175i \(0.850648\pi\)
\(108\) 1.01885e17 + 8.66897e16i 0.529676 + 0.450677i
\(109\) 1.05482e17i 0.507053i −0.967328 0.253526i \(-0.918410\pi\)
0.967328 0.253526i \(-0.0815905\pi\)
\(110\) −2.30164e17 + 1.06368e17i −1.02376 + 0.473121i
\(111\) −8.16962e16 −0.336478
\(112\) 4.58692e16 + 2.82764e17i 0.175052 + 1.07912i
\(113\) −1.30124e17 −0.460458 −0.230229 0.973136i \(-0.573948\pi\)
−0.230229 + 0.973136i \(0.573948\pi\)
\(114\) 1.17961e17 5.45142e16i 0.387298 0.178986i
\(115\) 1.80775e16i 0.0551069i
\(116\) 3.74363e17 + 3.18529e17i 1.06023 + 0.902102i
\(117\) 1.02137e16i 0.0268908i
\(118\) −1.62649e17 3.51947e17i −0.398340 0.861947i
\(119\) 3.30692e17 0.753833
\(120\) 3.59738e16 1.28936e17i 0.0763741 0.273736i
\(121\) −6.07133e17 −1.20118
\(122\) −2.92439e17 6.32794e17i −0.539481 1.16736i
\(123\) 2.30439e17i 0.396610i
\(124\) 4.56051e17 5.35991e17i 0.732705 0.861139i
\(125\) 7.20423e17i 1.08107i
\(126\) −6.08755e17 + 2.81330e17i −0.853676 + 0.394517i
\(127\) 1.12618e18 1.47664 0.738322 0.674448i \(-0.235619\pi\)
0.738322 + 0.674448i \(0.235619\pi\)
\(128\) −8.10197e17 9.05251e16i −0.993816 0.111041i
\(129\) −1.68418e17 −0.193364
\(130\) 2.00622e16 9.27154e15i 0.0215705 0.00996859i
\(131\) 3.73512e17i 0.376269i −0.982143 0.188134i \(-0.939756\pi\)
0.982143 0.188134i \(-0.0602440\pi\)
\(132\) 3.80632e17 4.47352e17i 0.359440 0.422446i
\(133\) 1.40871e18i 1.24762i
\(134\) −5.59941e17 1.21163e18i −0.465320 1.00688i
\(135\) 6.77664e17 0.528661
\(136\) −2.52918e17 + 9.06497e17i −0.185310 + 0.664180i
\(137\) −3.64355e17 −0.250842 −0.125421 0.992104i \(-0.540028\pi\)
−0.125421 + 0.992104i \(0.540028\pi\)
\(138\) −1.75680e16 3.80144e16i −0.0113697 0.0246023i
\(139\) 2.51151e18i 1.52866i 0.644828 + 0.764328i \(0.276929\pi\)
−0.644828 + 0.764328i \(0.723071\pi\)
\(140\) 1.10520e18 + 9.40364e17i 0.632925 + 0.538527i
\(141\) 1.90758e17i 0.102830i
\(142\) −3.36598e18 + 1.55555e18i −1.70868 + 0.789649i
\(143\) 9.69781e16 0.0463786
\(144\) −3.05599e17 1.88389e18i −0.137743 0.849131i
\(145\) 2.48998e18 1.05820
\(146\) 4.13585e18 1.91134e18i 1.65793 0.766193i
\(147\) 1.92874e17i 0.0729585i
\(148\) 1.91960e18 + 1.63330e18i 0.685468 + 0.583234i
\(149\) 2.83942e18i 0.957517i −0.877947 0.478758i \(-0.841087\pi\)
0.877947 0.478758i \(-0.158913\pi\)
\(150\) 2.07826e17 + 4.49703e17i 0.0662100 + 0.143268i
\(151\) −2.74195e18 −0.825574 −0.412787 0.910828i \(-0.635445\pi\)
−0.412787 + 0.910828i \(0.635445\pi\)
\(152\) −3.86157e18 1.07740e18i −1.09924 0.306696i
\(153\) −2.20321e18 −0.593169
\(154\) 2.67119e18 + 5.78006e18i 0.680423 + 1.47233i
\(155\) 3.56500e18i 0.859489i
\(156\) −3.31778e16 + 3.89935e16i −0.00757336 + 0.00890088i
\(157\) 3.26134e18i 0.705096i 0.935794 + 0.352548i \(0.114685\pi\)
−0.935794 + 0.352548i \(0.885315\pi\)
\(158\) 1.06513e18 4.92239e17i 0.218182 0.100830i
\(159\) −3.32150e18 −0.644850
\(160\) −3.42301e18 + 2.31038e18i −0.630069 + 0.425269i
\(161\) 4.53977e17 0.0792526
\(162\) 3.28973e18 1.52031e18i 0.544857 0.251800i
\(163\) 7.80461e18i 1.22675i −0.789791 0.613376i \(-0.789811\pi\)
0.789791 0.613376i \(-0.210189\pi\)
\(164\) 4.60704e18 5.41461e18i 0.687463 0.807968i
\(165\) 2.97544e18i 0.421636i
\(166\) 6.50518e17 + 1.40762e18i 0.0875670 + 0.189482i
\(167\) −8.54007e18 −1.09237 −0.546187 0.837663i \(-0.683921\pi\)
−0.546187 + 0.837663i \(0.683921\pi\)
\(168\) −3.23794e18 9.03405e17i −0.393677 0.109838i
\(169\) 8.64196e18 0.999023
\(170\) 1.99997e18 + 4.32764e18i 0.219891 + 0.475811i
\(171\) 9.38542e18i 0.981718i
\(172\) 3.95730e18 + 3.36709e18i 0.393919 + 0.335168i
\(173\) 2.07391e18i 0.196516i −0.995161 0.0982581i \(-0.968673\pi\)
0.995161 0.0982581i \(-0.0313271\pi\)
\(174\) −5.23607e18 + 2.41979e18i −0.472429 + 0.218328i
\(175\) −5.37046e18 −0.461517
\(176\) −1.78873e19 + 2.90163e18i −1.46449 + 0.237566i
\(177\) 4.54981e18 0.354993
\(178\) 2.28489e19 1.05594e19i 1.69940 0.785360i
\(179\) 1.67289e19i 1.18636i 0.805071 + 0.593179i \(0.202127\pi\)
−0.805071 + 0.593179i \(0.797873\pi\)
\(180\) −7.36329e18 6.26509e18i −0.498030 0.423752i
\(181\) 3.02297e19i 1.95059i 0.220907 + 0.975295i \(0.429098\pi\)
−0.220907 + 0.975295i \(0.570902\pi\)
\(182\) −2.32835e17 5.03819e17i −0.0143364 0.0310219i
\(183\) 8.18045e18 0.480776
\(184\) −3.47208e17 + 1.24445e18i −0.0194822 + 0.0698272i
\(185\) 1.27677e19 0.684154
\(186\) 3.46452e18 + 7.49669e18i 0.177330 + 0.383716i
\(187\) 2.09192e19i 1.02304i
\(188\) 3.81371e18 4.48221e18i 0.178240 0.209484i
\(189\) 1.70180e19i 0.760299i
\(190\) −1.84352e19 + 8.51965e18i −0.787486 + 0.363928i
\(191\) 1.22397e18 0.0500019 0.0250009 0.999687i \(-0.492041\pi\)
0.0250009 + 0.999687i \(0.492041\pi\)
\(192\) 4.95284e18 8.18493e18i 0.193550 0.319856i
\(193\) −6.70836e18 −0.250830 −0.125415 0.992104i \(-0.540026\pi\)
−0.125415 + 0.992104i \(0.540026\pi\)
\(194\) −2.54442e19 + 1.17588e19i −0.910487 + 0.420772i
\(195\) 2.59355e17i 0.00888382i
\(196\) 3.85601e18 4.53193e18i 0.126463 0.148630i
\(197\) 1.35900e19i 0.426832i 0.976961 + 0.213416i \(0.0684590\pi\)
−0.976961 + 0.213416i \(0.931541\pi\)
\(198\) −1.77966e19 3.85091e19i −0.535405 1.15854i
\(199\) 2.94272e19 0.848198 0.424099 0.905616i \(-0.360591\pi\)
0.424099 + 0.905616i \(0.360591\pi\)
\(200\) 4.10741e18 1.47216e19i 0.113452 0.406629i
\(201\) 1.56633e19 0.414685
\(202\) −1.27374e19 2.75619e19i −0.323292 0.699556i
\(203\) 6.25303e19i 1.52186i
\(204\) −8.41131e18 7.15681e18i −0.196339 0.167056i
\(205\) 3.60138e19i 0.806419i
\(206\) 2.66271e19 1.23054e19i 0.572074 0.264378i
\(207\) −3.02458e18 −0.0623616
\(208\) 1.55915e18 2.52921e17i 0.0308567 0.00500548i
\(209\) −8.91134e19 −1.69317
\(210\) −1.54580e19 + 7.14374e18i −0.282026 + 0.130335i
\(211\) 7.34029e19i 1.28621i 0.765777 + 0.643106i \(0.222355\pi\)
−0.765777 + 0.643106i \(0.777645\pi\)
\(212\) 7.80449e19 + 6.64049e19i 1.31368 + 1.11775i
\(213\) 4.35138e19i 0.703721i
\(214\) 2.44115e19 + 5.28228e19i 0.379382 + 0.820926i
\(215\) 2.63209e19 0.393164
\(216\) 4.66500e19 + 1.30157e19i 0.669877 + 0.186900i
\(217\) −8.95273e19 −1.23608
\(218\) −1.60204e19 3.46657e19i −0.212713 0.460278i
\(219\) 5.34662e19i 0.682817i
\(220\) −5.94863e19 + 6.99136e19i −0.730843 + 0.858952i
\(221\) 1.82342e18i 0.0215553i
\(222\) −2.68487e19 + 1.24079e19i −0.305438 + 0.141155i
\(223\) 7.73683e19 0.847172 0.423586 0.905856i \(-0.360771\pi\)
0.423586 + 0.905856i \(0.360771\pi\)
\(224\) 5.80202e19 + 8.59614e19i 0.611605 + 0.906140i
\(225\) 3.57802e19 0.363155
\(226\) −4.27641e19 + 1.97630e19i −0.417982 + 0.193166i
\(227\) 1.21923e20i 1.14780i −0.818924 0.573902i \(-0.805429\pi\)
0.818924 0.573902i \(-0.194571\pi\)
\(228\) 3.04872e19 3.58312e19i 0.276485 0.324949i
\(229\) 1.42038e19i 0.124109i −0.998073 0.0620543i \(-0.980235\pi\)
0.998073 0.0620543i \(-0.0197652\pi\)
\(230\) 2.74557e18 + 5.94101e18i 0.0231178 + 0.0500234i
\(231\) −7.47218e19 −0.606381
\(232\) 1.71409e20 + 4.78241e19i 1.34087 + 0.374110i
\(233\) −7.02873e19 −0.530092 −0.265046 0.964236i \(-0.585387\pi\)
−0.265046 + 0.964236i \(0.585387\pi\)
\(234\) 1.55124e18 + 3.35665e18i 0.0112809 + 0.0244102i
\(235\) 2.98122e19i 0.209082i
\(236\) −1.06906e20 9.09616e19i −0.723187 0.615327i
\(237\) 1.37695e19i 0.0898581i
\(238\) 1.08679e20 5.02249e19i 0.684293 0.316239i
\(239\) 4.12244e19 0.250480 0.125240 0.992126i \(-0.460030\pi\)
0.125240 + 0.992126i \(0.460030\pi\)
\(240\) −7.76001e18 4.78372e19i −0.0455058 0.280524i
\(241\) 9.34265e19 0.528841 0.264420 0.964408i \(-0.414819\pi\)
0.264420 + 0.964408i \(0.414819\pi\)
\(242\) −1.99529e20 + 9.22102e19i −1.09037 + 0.503904i
\(243\) 1.74331e20i 0.919861i
\(244\) −1.92215e20 1.63547e20i −0.979430 0.833353i
\(245\) 3.01429e19i 0.148345i
\(246\) 3.49987e19 + 7.57319e19i 0.166381 + 0.360023i
\(247\) 7.76758e18 0.0356748
\(248\) 6.84717e19 2.45413e20i 0.303859 1.08908i
\(249\) −1.81971e19 −0.0780381
\(250\) −1.09416e20 2.36761e20i −0.453516 0.981340i
\(251\) 8.23914e19i 0.330107i 0.986285 + 0.165054i \(0.0527797\pi\)
−0.986285 + 0.165054i \(0.947220\pi\)
\(252\) −1.57334e20 + 1.84913e20i −0.609423 + 0.716248i
\(253\) 2.87180e19i 0.107555i
\(254\) 3.70109e20 1.71042e20i 1.34043 0.619464i
\(255\) −5.59456e19 −0.195963
\(256\) −2.80013e20 + 9.33009e19i −0.948721 + 0.316116i
\(257\) 3.96731e20 1.30036 0.650182 0.759779i \(-0.274693\pi\)
0.650182 + 0.759779i \(0.274693\pi\)
\(258\) −5.53491e19 + 2.55790e19i −0.175527 + 0.0811178i
\(259\) 3.20634e20i 0.983923i
\(260\) 5.18513e18 6.09402e18i 0.0153988 0.0180980i
\(261\) 4.16603e20i 1.19751i
\(262\) −5.67282e19 1.22751e20i −0.157848 0.341559i
\(263\) −3.01079e20 −0.811066 −0.405533 0.914080i \(-0.632914\pi\)
−0.405533 + 0.914080i \(0.632914\pi\)
\(264\) 5.71483e19 2.04828e20i 0.149063 0.534264i
\(265\) 5.19094e20 1.31116
\(266\) 2.13952e20 + 4.62961e20i 0.523387 + 1.13253i
\(267\) 2.95380e20i 0.699899i
\(268\) −3.68039e20 3.13148e20i −0.844790 0.718793i
\(269\) 7.99834e19i 0.177871i 0.996037 + 0.0889356i \(0.0283465\pi\)
−0.996037 + 0.0889356i \(0.971653\pi\)
\(270\) 2.22708e20 1.02922e20i 0.479893 0.221777i
\(271\) −3.82151e20 −0.797986 −0.398993 0.916954i \(-0.630640\pi\)
−0.398993 + 0.916954i \(0.630640\pi\)
\(272\) 5.45577e19 + 3.36325e20i 0.110413 + 0.680650i
\(273\) 6.51313e18 0.0127764
\(274\) −1.19742e20 + 5.53375e19i −0.227702 + 0.105230i
\(275\) 3.39729e20i 0.626332i
\(276\) −1.15471e19 9.82491e18i −0.0206417 0.0175631i
\(277\) 3.87625e20i 0.671945i 0.941872 + 0.335972i \(0.109065\pi\)
−0.941872 + 0.335972i \(0.890935\pi\)
\(278\) 3.81444e20 + 8.25387e20i 0.641283 + 1.38764i
\(279\) 5.96467e20 0.972638
\(280\) 5.06035e20 + 1.41187e20i 0.800455 + 0.223332i
\(281\) −5.68349e20 −0.872190 −0.436095 0.899901i \(-0.643639\pi\)
−0.436095 + 0.899901i \(0.643639\pi\)
\(282\) 2.89719e19 + 6.26909e19i 0.0431380 + 0.0933441i
\(283\) 4.50897e20i 0.651467i −0.945462 0.325734i \(-0.894389\pi\)
0.945462 0.325734i \(-0.105611\pi\)
\(284\) −8.69947e20 + 1.02244e21i −1.21979 + 1.43361i
\(285\) 2.38322e20i 0.324326i
\(286\) 3.18710e19 1.47288e19i 0.0421002 0.0194562i
\(287\) −9.04408e20 −1.15976
\(288\) −3.86554e20 5.72710e20i −0.481254 0.713015i
\(289\) −4.33908e20 −0.524525
\(290\) 8.18309e20 3.78173e20i 0.960581 0.443923i
\(291\) 3.28930e20i 0.374984i
\(292\) 1.06892e21 1.25629e21i 1.18356 1.39103i
\(293\) 1.51002e21i 1.62408i −0.583602 0.812040i \(-0.698357\pi\)
0.583602 0.812040i \(-0.301643\pi\)
\(294\) 2.92933e19 + 6.33863e19i 0.0306067 + 0.0662282i
\(295\) −7.11057e20 −0.721801
\(296\) 8.78924e20 + 2.45225e20i 0.866906 + 0.241872i
\(297\) 1.07654e21 1.03181
\(298\) −4.31246e20 9.33150e20i −0.401686 0.869187i
\(299\) 2.50321e18i 0.00226617i
\(300\) 1.36600e20 + 1.16227e20i 0.120204 + 0.102276i
\(301\) 6.60992e20i 0.565433i
\(302\) −9.01119e20 + 4.16443e20i −0.749416 + 0.346335i
\(303\) 3.56307e20 0.288112
\(304\) −1.43271e21 + 2.32409e20i −1.12650 + 0.182738i
\(305\) −1.27847e21 −0.977553
\(306\) −7.24065e20 + 3.34619e20i −0.538450 + 0.248839i
\(307\) 7.15201e20i 0.517311i 0.965970 + 0.258655i \(0.0832794\pi\)
−0.965970 + 0.258655i \(0.916721\pi\)
\(308\) 1.75573e21 + 1.49387e21i 1.23531 + 1.05107i
\(309\) 3.44222e20i 0.235609i
\(310\) −5.41445e20 1.17161e21i −0.360562 0.780202i
\(311\) 1.55199e21 1.00560 0.502801 0.864402i \(-0.332303\pi\)
0.502801 + 0.864402i \(0.332303\pi\)
\(312\) −4.98134e18 + 1.78539e19i −0.00314074 + 0.0112569i
\(313\) −7.03438e20 −0.431617 −0.215809 0.976436i \(-0.569239\pi\)
−0.215809 + 0.976436i \(0.569239\pi\)
\(314\) 4.95325e20 + 1.07181e21i 0.295793 + 0.640052i
\(315\) 1.22990e21i 0.714875i
\(316\) 2.75286e20 3.23540e20i 0.155756 0.183058i
\(317\) 2.05646e21i 1.13270i 0.824163 + 0.566352i \(0.191646\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(318\) −1.09158e21 + 5.04463e20i −0.585364 + 0.270520i
\(319\) 3.95559e21 2.06534
\(320\) −7.74046e20 + 1.27917e21i −0.393543 + 0.650357i
\(321\) −6.82867e20 −0.338099
\(322\) 1.49195e20 6.89491e19i 0.0719417 0.0332471i
\(323\) 1.67555e21i 0.786929i
\(324\) 8.50238e20 9.99275e20i 0.388963 0.457143i
\(325\) 2.96125e19i 0.0131967i
\(326\) −1.18535e21 2.56492e21i −0.514632 1.11359i
\(327\) 4.48142e20 0.189566
\(328\) 6.91704e20 2.47917e21i 0.285097 1.02183i
\(329\) −7.48669e20 −0.300694
\(330\) −4.51905e20 9.77853e20i −0.176880 0.382741i
\(331\) 7.03264e20i 0.268275i 0.990963 + 0.134138i \(0.0428264\pi\)
−0.990963 + 0.134138i \(0.957174\pi\)
\(332\) 4.27574e20 + 3.63803e20i 0.158978 + 0.135267i
\(333\) 2.13619e21i 0.774221i
\(334\) −2.80662e21 + 1.29705e21i −0.991605 + 0.458260i
\(335\) −2.44791e21 −0.843170
\(336\) −1.20133e21 + 1.94876e20i −0.403439 + 0.0654446i
\(337\) 8.84366e20 0.289586 0.144793 0.989462i \(-0.453748\pi\)
0.144793 + 0.989462i \(0.453748\pi\)
\(338\) 2.84011e21 1.31252e21i 0.906865 0.419098i
\(339\) 5.52833e20i 0.172146i
\(340\) 1.31455e21 + 1.11849e21i 0.399213 + 0.339672i
\(341\) 5.66339e21i 1.67751i
\(342\) −1.42544e21 3.08444e21i −0.411838 0.891156i
\(343\) 3.12195e21 0.879885
\(344\) 1.81192e21 + 5.05536e20i 0.498186 + 0.138997i
\(345\) −7.68024e19 −0.0206022
\(346\) −3.14982e20 6.81573e20i −0.0824401 0.178388i
\(347\) 5.48605e21i 1.40107i −0.713620 0.700533i \(-0.752945\pi\)
0.713620 0.700533i \(-0.247055\pi\)
\(348\) −1.35327e21 + 1.59049e21i −0.337258 + 0.396375i
\(349\) 2.09596e19i 0.00509762i 0.999997 + 0.00254881i \(0.000811312\pi\)
−0.999997 + 0.00254881i \(0.999189\pi\)
\(350\) −1.76495e21 + 8.15655e20i −0.418943 + 0.193610i
\(351\) −9.38368e19 −0.0217402
\(352\) −5.43782e21 + 3.67029e21i −1.22974 + 0.830018i
\(353\) −8.34131e20 −0.184141 −0.0920703 0.995753i \(-0.529348\pi\)
−0.0920703 + 0.995753i \(0.529348\pi\)
\(354\) 1.49525e21 6.91016e20i 0.322246 0.148922i
\(355\) 6.80047e21i 1.43086i
\(356\) 5.90536e21 6.94051e21i 1.21317 1.42582i
\(357\) 1.40495e21i 0.281826i
\(358\) 2.54075e21 + 5.49780e21i 0.497687 + 1.07692i
\(359\) −7.98650e21 −1.52775 −0.763877 0.645361i \(-0.776707\pi\)
−0.763877 + 0.645361i \(0.776707\pi\)
\(360\) −3.37141e21 9.40645e20i −0.629855 0.175733i
\(361\) −1.65726e21 −0.302398
\(362\) 4.59123e21 + 9.93473e21i 0.818288 + 1.77065i
\(363\) 2.57941e21i 0.449071i
\(364\) −1.53038e20 1.30213e20i −0.0260278 0.0221459i
\(365\) 8.35586e21i 1.38836i
\(366\) 2.68843e21 1.24243e21i 0.436425 0.201689i
\(367\) −4.95976e21 −0.786682 −0.393341 0.919393i \(-0.628681\pi\)
−0.393341 + 0.919393i \(0.628681\pi\)
\(368\) 7.48971e19 + 4.61709e20i 0.0116080 + 0.0715587i
\(369\) 6.02554e21 0.912581
\(370\) 4.19600e21 1.93914e21i 0.621042 0.287008i
\(371\) 1.30359e22i 1.88566i
\(372\) 2.27717e21 + 1.93754e21i 0.321944 + 0.273927i
\(373\) 1.32602e22i 1.83243i 0.400692 + 0.916213i \(0.368770\pi\)
−0.400692 + 0.916213i \(0.631230\pi\)
\(374\) 3.17717e21 + 6.87491e21i 0.429172 + 0.928664i
\(375\) 3.06073e21 0.404165
\(376\) 5.72593e20 2.05226e21i 0.0739178 0.264933i
\(377\) −3.44790e20 −0.0435164
\(378\) −2.58467e21 5.59283e21i −0.318951 0.690163i
\(379\) 4.66066e21i 0.562360i 0.959655 + 0.281180i \(0.0907258\pi\)
−0.959655 + 0.281180i \(0.909274\pi\)
\(380\) −4.76463e21 + 5.59981e21i −0.562171 + 0.660713i
\(381\) 4.78459e21i 0.552055i
\(382\) 4.02246e20 1.85894e20i 0.0453893 0.0209762i
\(383\) −9.41823e21 −1.03939 −0.519696 0.854351i \(-0.673955\pi\)
−0.519696 + 0.854351i \(0.673955\pi\)
\(384\) 3.84597e20 3.44213e21i 0.0415136 0.371546i
\(385\) 1.16778e22 1.23294
\(386\) −2.20464e21 + 1.01885e21i −0.227691 + 0.105225i
\(387\) 4.40380e21i 0.444923i
\(388\) −6.57611e21 + 7.72882e21i −0.649979 + 0.763913i
\(389\) 2.84056e21i 0.274683i −0.990524 0.137342i \(-0.956144\pi\)
0.990524 0.137342i \(-0.0438558\pi\)
\(390\) 3.93903e19 + 8.52346e19i 0.00372683 + 0.00806431i
\(391\) 5.39969e20 0.0499881
\(392\) 5.78944e20 2.07502e21i 0.0524451 0.187971i
\(393\) 1.58687e21 0.140671
\(394\) 2.06403e21 + 4.46624e21i 0.179059 + 0.387458i
\(395\) 2.15194e21i 0.182707i
\(396\) −1.16974e22 9.95278e21i −0.972030 0.827056i
\(397\) 6.92645e20i 0.0563367i 0.999603 + 0.0281683i \(0.00896745\pi\)
−0.999603 + 0.0281683i \(0.991033\pi\)
\(398\) 9.67098e21 4.46934e21i 0.769953 0.355826i
\(399\) −5.98493e21 −0.466433
\(400\) −8.86019e20 5.46193e21i −0.0675979 0.416713i
\(401\) −4.47868e21 −0.334521 −0.167260 0.985913i \(-0.553492\pi\)
−0.167260 + 0.985913i \(0.553492\pi\)
\(402\) 5.14762e21 2.37892e21i 0.376431 0.173963i
\(403\) 4.93650e20i 0.0353448i
\(404\) −8.37209e21 7.12343e21i −0.586938 0.499399i
\(405\) 6.64641e21i 0.456267i
\(406\) −9.49699e21 2.05500e22i −0.638432 1.38147i
\(407\) 2.02829e22 1.33530
\(408\) −3.85127e21 1.07453e21i −0.248309 0.0692797i
\(409\) 1.38245e22 0.872972 0.436486 0.899711i \(-0.356223\pi\)
0.436486 + 0.899711i \(0.356223\pi\)
\(410\) −5.46970e21 1.18356e22i −0.338299 0.732028i
\(411\) 1.54797e21i 0.0937791i
\(412\) 6.88184e21 8.08815e21i 0.408393 0.479979i
\(413\) 1.78567e22i 1.03807i
\(414\) −9.94002e20 + 4.59367e20i −0.0566088 + 0.0261612i
\(415\) 2.84389e21 0.158673
\(416\) 4.73988e20 3.19921e20i 0.0259104 0.0174884i
\(417\) −1.06702e22 −0.571500
\(418\) −2.92863e22 + 1.35344e22i −1.53697 + 0.710297i
\(419\) 4.06502e21i 0.209047i −0.994522 0.104523i \(-0.966668\pi\)
0.994522 0.104523i \(-0.0333317\pi\)
\(420\) −3.99515e21 + 4.69546e21i −0.201333 + 0.236624i
\(421\) 8.16114e21i 0.403045i −0.979484 0.201522i \(-0.935411\pi\)
0.979484 0.201522i \(-0.0645888\pi\)
\(422\) 1.11483e22 + 2.41232e22i 0.539576 + 1.16756i
\(423\) 4.98794e21 0.236607
\(424\) 3.57342e22 + 9.97007e21i 1.66140 + 0.463541i
\(425\) −6.38773e21 −0.291099
\(426\) −6.60880e21 1.43004e22i −0.295217 0.638804i
\(427\) 3.21059e22i 1.40588i
\(428\) 1.60452e22 + 1.36522e22i 0.688770 + 0.586043i
\(429\) 4.12013e20i 0.0173390i
\(430\) 8.65013e21 3.99757e21i 0.356895 0.164935i
\(431\) −9.79174e21 −0.396098 −0.198049 0.980192i \(-0.563461\pi\)
−0.198049 + 0.980192i \(0.563461\pi\)
\(432\) 1.73079e22 2.80764e21i 0.686488 0.111360i
\(433\) −2.60425e22 −1.01283 −0.506414 0.862290i \(-0.669029\pi\)
−0.506414 + 0.862290i \(0.669029\pi\)
\(434\) −2.94223e22 + 1.35972e22i −1.12206 + 0.518546i
\(435\) 1.05787e22i 0.395616i
\(436\) −1.05299e22 8.95944e21i −0.386181 0.328584i
\(437\) 2.30020e21i 0.0827321i
\(438\) 8.12034e21 + 1.75712e22i 0.286447 + 0.619828i
\(439\) 2.68066e22 0.927455 0.463727 0.885978i \(-0.346512\pi\)
0.463727 + 0.885978i \(0.346512\pi\)
\(440\) −8.93131e21 + 3.20112e22i −0.303087 + 1.08631i
\(441\) 5.04327e21 0.167874
\(442\) −2.76938e20 5.99252e20i −0.00904260 0.0195668i
\(443\) 6.73832e21i 0.215834i 0.994160 + 0.107917i \(0.0344181\pi\)
−0.994160 + 0.107917i \(0.965582\pi\)
\(444\) −6.93912e21 + 8.15547e21i −0.218046 + 0.256268i
\(445\) 4.61629e22i 1.42309i
\(446\) 2.54264e22 1.17506e22i 0.769022 0.355396i
\(447\) 1.20633e22 0.357975
\(448\) 3.21235e22 + 1.94385e22i 0.935318 + 0.565977i
\(449\) −3.12876e22 −0.893878 −0.446939 0.894564i \(-0.647486\pi\)
−0.446939 + 0.894564i \(0.647486\pi\)
\(450\) 1.17589e22 5.43423e21i 0.329654 0.152346i
\(451\) 5.72118e22i 1.57393i
\(452\) −1.10525e22 + 1.29899e22i −0.298389 + 0.350693i
\(453\) 1.16492e22i 0.308647i
\(454\) −1.85175e22 4.00691e22i −0.481512 1.04192i
\(455\) −1.01789e21 −0.0259779
\(456\) 4.57736e21 1.64060e22i 0.114661 0.410961i
\(457\) −5.48338e22 −1.34822 −0.674110 0.738631i \(-0.735473\pi\)
−0.674110 + 0.738631i \(0.735473\pi\)
\(458\) −2.15724e21 4.66794e21i −0.0520645 0.112660i
\(459\) 2.02416e22i 0.479553i
\(460\) 1.80462e21 + 1.53547e21i 0.0419704 + 0.0357107i
\(461\) 6.78571e22i 1.54931i −0.632386 0.774653i \(-0.717924\pi\)
0.632386 0.774653i \(-0.282076\pi\)
\(462\) −2.45567e22 + 1.13486e22i −0.550443 + 0.254382i
\(463\) −1.64300e21 −0.0361576 −0.0180788 0.999837i \(-0.505755\pi\)
−0.0180788 + 0.999837i \(0.505755\pi\)
\(464\) 6.35954e22 1.03163e22i 1.37411 0.222905i
\(465\) 1.51460e22 0.321327
\(466\) −2.30993e22 + 1.06751e22i −0.481192 + 0.222378i
\(467\) 4.77673e22i 0.977096i 0.872537 + 0.488548i \(0.162473\pi\)
−0.872537 + 0.488548i \(0.837527\pi\)
\(468\) 1.01960e21 + 8.67534e20i 0.0204805 + 0.0174260i
\(469\) 6.14740e22i 1.21261i
\(470\) −4.52782e21 9.79752e21i −0.0877117 0.189795i
\(471\) −1.38558e22 −0.263606
\(472\) −4.89489e22 1.36570e22i −0.914609 0.255182i
\(473\) 4.18136e22 0.767357
\(474\) 2.09129e21 + 4.52523e21i 0.0376962 + 0.0815689i
\(475\) 2.72110e22i 0.481780i
\(476\) 2.80884e22 3.30120e22i 0.488504 0.574133i
\(477\) 8.68507e22i 1.48377i
\(478\) 1.35480e22 6.26109e21i 0.227373 0.105078i
\(479\) −5.48658e22 −0.904585 −0.452293 0.891870i \(-0.649394\pi\)
−0.452293 + 0.891870i \(0.649394\pi\)
\(480\) −9.81568e21 1.45427e22i −0.158990 0.235556i
\(481\) −1.76796e21 −0.0281345
\(482\) 3.07038e22 1.41894e22i 0.480056 0.221853i
\(483\) 1.92873e21i 0.0296292i
\(484\) −5.15687e22 + 6.06081e22i −0.778396 + 0.914840i
\(485\) 5.14062e22i 0.762448i
\(486\) 2.64771e22 + 5.72925e22i 0.385889 + 0.835005i
\(487\) 1.26074e23 1.80564 0.902818 0.430022i \(-0.141494\pi\)
0.902818 + 0.430022i \(0.141494\pi\)
\(488\) −8.80089e22 2.45550e22i −1.23868 0.345599i
\(489\) 3.31580e22 0.458630
\(490\) −4.57805e21 9.90620e21i −0.0622320 0.134661i
\(491\) 1.93871e22i 0.259013i 0.991579 + 0.129506i \(0.0413393\pi\)
−0.991579 + 0.129506i \(0.958661\pi\)
\(492\) 2.30040e22 + 1.95731e22i 0.302065 + 0.257013i
\(493\) 7.43748e22i 0.959902i
\(494\) 2.55275e21 1.17972e21i 0.0323839 0.0149659i
\(495\) −7.78020e22 −0.970167
\(496\) −1.47702e22 9.10522e22i −0.181048 1.11608i
\(497\) 1.70779e23 2.05781
\(498\) −5.98030e21 + 2.76373e21i −0.0708392 + 0.0327376i
\(499\) 8.94608e22i 1.04178i 0.853622 + 0.520892i \(0.174401\pi\)
−0.853622 + 0.520892i \(0.825599\pi\)
\(500\) −7.19175e22 6.11913e22i −0.823359 0.700559i
\(501\) 3.62826e22i 0.408393i
\(502\) 1.25134e22 + 2.70772e22i 0.138483 + 0.299655i
\(503\) 3.84163e22 0.418011 0.209005 0.977914i \(-0.432977\pi\)
0.209005 + 0.977914i \(0.432977\pi\)
\(504\) −2.36223e22 + 8.46657e22i −0.252733 + 0.905833i
\(505\) −5.56847e22 −0.585813
\(506\) 4.36164e21 + 9.43793e21i 0.0451201 + 0.0976331i
\(507\) 3.67155e22i 0.373492i
\(508\) 9.56555e22 1.12423e23i 0.956904 1.12464i
\(509\) 1.79276e23i 1.76369i 0.471541 + 0.881844i \(0.343698\pi\)
−0.471541 + 0.881844i \(0.656302\pi\)
\(510\) −1.83860e22 + 8.49691e21i −0.177886 + 0.0822080i
\(511\) −2.09839e23 −1.99668
\(512\) −7.78534e22 + 7.31903e22i −0.728590 + 0.684950i
\(513\) 8.62269e22 0.793679
\(514\) 1.30382e23 6.02547e22i 1.18041 0.545513i
\(515\) 5.37961e22i 0.479059i
\(516\) −1.43051e22 + 1.68126e22i −0.125305 + 0.147270i
\(517\) 4.73599e22i 0.408076i
\(518\) −4.86972e22 1.05373e23i −0.412764 0.893158i
\(519\) 8.81104e21 0.0734691
\(520\) 7.78498e20 2.79025e21i 0.00638601 0.0228884i
\(521\) 6.78107e22 0.547240 0.273620 0.961838i \(-0.411779\pi\)
0.273620 + 0.961838i \(0.411779\pi\)
\(522\) 6.32728e22 + 1.36913e23i 0.502363 + 1.08704i
\(523\) 2.09501e23i 1.63652i −0.574845 0.818262i \(-0.694938\pi\)
0.574845 0.818262i \(-0.305062\pi\)
\(524\) −3.72865e22 3.17254e22i −0.286573 0.243832i
\(525\) 2.28165e22i 0.172542i
\(526\) −9.89468e22 + 4.57272e22i −0.736246 + 0.340248i
\(527\) −1.06485e23 −0.779651
\(528\) −1.23276e22 7.59945e22i −0.0888158 0.547512i
\(529\) −1.40309e23 −0.994745
\(530\) 1.70596e23 7.88390e22i 1.19021 0.550043i
\(531\) 1.18968e23i 0.816824i
\(532\) 1.40627e23 + 1.19653e23i 0.950212 + 0.808492i
\(533\) 4.98687e21i 0.0331624i
\(534\) 4.48617e22 + 9.70740e22i 0.293613 + 0.635334i
\(535\) 1.06721e23 0.687450
\(536\) −1.68513e23 4.70162e22i −1.06840 0.298090i
\(537\) −7.10728e22 −0.443529
\(538\) 1.21477e22 + 2.62858e22i 0.0746184 + 0.161463i
\(539\) 4.78852e22i 0.289532i
\(540\) 5.75595e22 6.76490e22i 0.342586 0.402638i
\(541\) 1.24185e23i 0.727600i −0.931477 0.363800i \(-0.881479\pi\)
0.931477 0.363800i \(-0.118521\pi\)
\(542\) −1.25590e23 + 5.80403e22i −0.724374 + 0.334762i
\(543\) −1.28431e23 −0.729243
\(544\) 6.90103e22 + 1.02244e23i 0.385765 + 0.571542i
\(545\) −7.00370e22 −0.385440
\(546\) 2.14048e21 9.89202e20i 0.0115978 0.00535979i
\(547\) 1.22112e23i 0.651429i 0.945468 + 0.325714i \(0.105605\pi\)
−0.945468 + 0.325714i \(0.894395\pi\)
\(548\) −3.09476e22 + 3.63724e22i −0.162552 + 0.191046i
\(549\) 2.13903e23i 1.10624i
\(550\) −5.15974e22 1.11649e23i −0.262751 0.568554i
\(551\) 3.16828e23 1.58867
\(552\) −5.28704e21 1.47512e21i −0.0261054 0.00728358i
\(553\) −5.40413e22 −0.262762
\(554\) 5.88717e22 + 1.27389e23i 0.281886 + 0.609959i
\(555\) 5.42439e22i 0.255776i
\(556\) 2.50716e23 + 2.13323e23i 1.16425 + 0.990609i
\(557\) 2.07273e23i 0.947924i 0.880545 + 0.473962i \(0.157177\pi\)
−0.880545 + 0.473962i \(0.842823\pi\)
\(558\) 1.96024e23 9.05903e22i 0.882913 0.408029i
\(559\) −3.64468e21 −0.0161681
\(560\) 1.87747e23 3.04558e22i 0.820304 0.133067i
\(561\) −8.88756e22 −0.382471
\(562\) −1.86783e23 + 8.63197e22i −0.791732 + 0.365891i
\(563\) 1.43541e23i 0.599314i 0.954047 + 0.299657i \(0.0968722\pi\)
−0.954047 + 0.299657i \(0.903128\pi\)
\(564\) 1.90427e22 + 1.62026e22i 0.0783172 + 0.0666365i
\(565\) 8.63985e22i 0.350021i
\(566\) −6.84813e22 1.48183e23i −0.273296 0.591370i
\(567\) −1.66910e23 −0.656185
\(568\) −1.30614e23 + 4.68141e23i −0.505860 + 1.81308i
\(569\) 1.29010e23 0.492231 0.246116 0.969240i \(-0.420846\pi\)
0.246116 + 0.969240i \(0.420846\pi\)
\(570\) −3.61958e22 7.83223e22i −0.136057 0.294408i
\(571\) 2.64243e23i 0.978579i 0.872121 + 0.489290i \(0.162744\pi\)
−0.872121 + 0.489290i \(0.837256\pi\)
\(572\) 8.23713e21 9.68101e21i 0.0300545 0.0353228i
\(573\) 5.20005e21i 0.0186936i
\(574\) −2.97226e23 + 1.37360e23i −1.05277 + 0.486529i
\(575\) −8.76912e21 −0.0306041
\(576\) −2.14020e23 1.29507e23i −0.735975 0.445351i
\(577\) −9.70397e22 −0.328818 −0.164409 0.986392i \(-0.552572\pi\)
−0.164409 + 0.986392i \(0.552572\pi\)
\(578\) −1.42600e23 + 6.59011e22i −0.476138 + 0.220042i
\(579\) 2.85005e22i 0.0937746i
\(580\) 2.11494e23 2.48566e23i 0.685740 0.805943i
\(581\) 7.14182e22i 0.228198i
\(582\) −4.99573e22 1.08100e23i −0.157309 0.340393i
\(583\) 8.24637e23 2.55906
\(584\) 1.60488e23 5.75214e23i 0.490833 1.75922i
\(585\) 6.78161e21 0.0204413
\(586\) −2.29339e23 4.96254e23i −0.681314 1.47426i
\(587\) 3.02349e23i 0.885288i 0.896697 + 0.442644i \(0.145959\pi\)
−0.896697 + 0.442644i \(0.854041\pi\)
\(588\) 1.92540e22 + 1.63823e22i 0.0555665 + 0.0472790i
\(589\) 4.53616e23i 1.29035i
\(590\) −2.33683e23 + 1.07994e23i −0.655216 + 0.302801i
\(591\) −5.77374e22 −0.159574
\(592\) 3.26095e23 5.28982e22i 0.888402 0.144114i
\(593\) −3.18008e23 −0.854030 −0.427015 0.904245i \(-0.640435\pi\)
−0.427015 + 0.904245i \(0.640435\pi\)
\(594\) 3.53796e23 1.63503e23i 0.936630 0.432854i
\(595\) 2.19570e23i 0.573032i
\(596\) −2.83450e23 2.41175e23i −0.729262 0.620496i
\(597\) 1.25022e23i 0.317105i
\(598\) −3.80183e20 8.22657e20i −0.000950675 0.00205712i
\(599\) 3.24737e23 0.800578 0.400289 0.916389i \(-0.368910\pi\)
0.400289 + 0.916389i \(0.368910\pi\)
\(600\) 6.25447e22 + 1.74504e22i 0.152022 + 0.0424150i
\(601\) −3.78448e23 −0.906929 −0.453464 0.891274i \(-0.649812\pi\)
−0.453464 + 0.891274i \(0.649812\pi\)
\(602\) −1.00390e23 2.17229e23i −0.237204 0.513273i
\(603\) 4.09565e23i 0.954171i
\(604\) −2.32896e23 + 2.73721e23i −0.534994 + 0.628772i
\(605\) 4.03118e23i 0.913087i
\(606\) 1.17097e23 5.41152e22i 0.261534 0.120865i
\(607\) −2.72859e23 −0.600945 −0.300472 0.953791i \(-0.597144\pi\)
−0.300472 + 0.953791i \(0.597144\pi\)
\(608\) −4.35548e23 + 2.93976e23i −0.945924 + 0.638457i
\(609\) 2.65661e23 0.568959
\(610\) −4.20156e23 + 1.94171e23i −0.887375 + 0.410091i
\(611\) 4.12813e21i 0.00859811i
\(612\) −1.87136e23 + 2.19939e23i −0.384389 + 0.451768i
\(613\) 2.23929e23i 0.453625i 0.973938 + 0.226813i \(0.0728305\pi\)
−0.973938 + 0.226813i \(0.927169\pi\)
\(614\) 1.08623e23 + 2.35044e23i 0.217016 + 0.469590i
\(615\) 1.53005e23 0.301486
\(616\) 8.03891e23 + 2.24291e23i 1.56229 + 0.435888i
\(617\) 9.37688e23 1.79736 0.898679 0.438608i \(-0.144528\pi\)
0.898679 + 0.438608i \(0.144528\pi\)
\(618\) 5.22798e22 + 1.13126e23i 0.0988398 + 0.213874i
\(619\) 8.46873e23i 1.57924i 0.613597 + 0.789619i \(0.289722\pi\)
−0.613597 + 0.789619i \(0.710278\pi\)
\(620\) −3.55883e23 3.02804e23i −0.654602 0.556971i
\(621\) 2.77878e22i 0.0504168i
\(622\) 5.10048e23 2.35714e23i 0.912837 0.421858i
\(623\) −1.15928e24 −2.04663
\(624\) 1.07454e21 + 6.62407e21i 0.00187134 + 0.0115360i
\(625\) −2.32610e23 −0.399622
\(626\) −2.31179e23 + 1.06837e23i −0.391801 + 0.181067i
\(627\) 3.78600e23i 0.633003i
\(628\) 3.25569e23 + 2.77012e23i 0.537014 + 0.456921i
\(629\) 3.81368e23i 0.620603i
\(630\) 1.86795e23 + 4.04196e23i 0.299896 + 0.648929i
\(631\) 5.75474e23 0.911541 0.455771 0.890097i \(-0.349364\pi\)
0.455771 + 0.890097i \(0.349364\pi\)
\(632\) 4.13316e22 1.48139e23i 0.0645932 0.231512i
\(633\) −3.11853e23 −0.480860
\(634\) 3.12331e23 + 6.75837e23i 0.475178 + 1.02821i
\(635\) 7.47750e23i 1.12248i
\(636\) −2.82122e23 + 3.31575e23i −0.417880 + 0.491130i
\(637\) 4.17392e21i 0.00610041i
\(638\) 1.29997e24 6.00768e23i 1.87481 0.866425i
\(639\) −1.13780e24 −1.61923
\(640\) −6.01060e22 + 5.37947e23i −0.0844089 + 0.755457i
\(641\) 4.70111e23 0.651489 0.325745 0.945458i \(-0.394385\pi\)
0.325745 + 0.945458i \(0.394385\pi\)
\(642\) −2.24418e23 + 1.03713e23i −0.306910 + 0.141835i
\(643\) 1.44971e23i 0.195653i 0.995203 + 0.0978266i \(0.0311891\pi\)
−0.995203 + 0.0978266i \(0.968811\pi\)
\(644\) 3.85599e22 4.53190e22i 0.0513578 0.0603602i
\(645\) 1.11825e23i 0.146987i
\(646\) 2.54479e23 + 5.50655e23i 0.330123 + 0.714336i
\(647\) 1.43169e23 0.183300 0.0916502 0.995791i \(-0.470786\pi\)
0.0916502 + 0.995791i \(0.470786\pi\)
\(648\) 1.27655e23 4.57535e23i 0.161306 0.578146i
\(649\) −1.12959e24 −1.40877
\(650\) 4.49749e21 + 9.73188e21i 0.00553613 + 0.0119794i
\(651\) 3.80358e23i 0.462119i
\(652\) −7.79109e23 6.62909e23i −0.934316 0.794967i
\(653\) 3.23785e23i 0.383260i 0.981467 + 0.191630i \(0.0613774\pi\)
−0.981467 + 0.191630i \(0.938623\pi\)
\(654\) 1.47278e23 6.80629e22i 0.172079 0.0795243i
\(655\) −2.48001e23 −0.286024
\(656\) −1.49209e23 9.19813e23i −0.169869 1.04717i
\(657\) 1.39804e24 1.57113
\(658\) −2.46043e23 + 1.13706e23i −0.272955 + 0.126143i
\(659\) 8.58094e23i 0.939742i −0.882735 0.469871i \(-0.844300\pi\)
0.882735 0.469871i \(-0.155700\pi\)
\(660\) −2.97029e23 2.52728e23i −0.321126 0.273231i
\(661\) 7.30451e23i 0.779612i −0.920897 0.389806i \(-0.872542\pi\)
0.920897 0.389806i \(-0.127458\pi\)
\(662\) 1.06810e23 + 2.31121e23i 0.112543 + 0.243527i
\(663\) 7.74684e21 0.00805860
\(664\) 1.95772e23 + 5.46216e22i 0.201058 + 0.0560965i
\(665\) 9.35343e23 0.948390
\(666\) 3.24441e23 + 7.02041e23i 0.324792 + 0.702800i
\(667\) 1.02102e23i 0.100917i
\(668\) −7.25378e23 + 8.52528e23i −0.707887 + 0.831972i
\(669\) 3.28700e23i 0.316722i
\(670\) −8.04485e23 + 3.71784e23i −0.765389 + 0.353717i
\(671\) −2.03098e24 −1.90794
\(672\) −3.65208e23 + 2.46499e23i −0.338768 + 0.228653i
\(673\) −1.25481e23 −0.114934 −0.0574671 0.998347i \(-0.518302\pi\)
−0.0574671 + 0.998347i \(0.518302\pi\)
\(674\) 2.90639e23 1.34316e23i 0.262872 0.121484i
\(675\) 3.28724e23i 0.293596i
\(676\) 7.34032e23 8.62699e23i 0.647393 0.760874i
\(677\) 3.68442e22i 0.0320897i 0.999871 + 0.0160448i \(0.00510745\pi\)
−0.999871 + 0.0160448i \(0.994893\pi\)
\(678\) −8.39633e22 1.81684e23i −0.0722166 0.156266i
\(679\) 1.29095e24 1.09652
\(680\) 6.01888e23 + 1.67930e23i 0.504882 + 0.140865i
\(681\) 5.17993e23 0.429115
\(682\) −8.60144e23 1.86122e24i −0.703727 1.52276i
\(683\) 3.46565e23i 0.280033i 0.990149 + 0.140016i \(0.0447155\pi\)
−0.990149 + 0.140016i \(0.955285\pi\)
\(684\) −9.36916e23 7.97180e23i −0.747694 0.636179i
\(685\) 2.41921e23i 0.190679i
\(686\) 1.02600e24 4.74156e23i 0.798717 0.369119i
\(687\) 6.03449e22 0.0463990
\(688\) 6.72251e23 1.09051e23i 0.510540 0.0828183i
\(689\) −7.18795e22 −0.0539190
\(690\) −2.52404e22 + 1.16646e22i −0.0187016 + 0.00864277i
\(691\) 1.64173e24i 1.20154i 0.799421 + 0.600771i \(0.205140\pi\)
−0.799421 + 0.600771i \(0.794860\pi\)
\(692\) −2.07032e23 1.76154e23i −0.149670 0.127348i
\(693\) 1.95383e24i 1.39526i
\(694\) −8.33210e23 1.80294e24i −0.587759 1.27182i
\(695\) 1.66757e24 1.16202
\(696\) −2.03181e23 + 7.28233e23i −0.139864 + 0.501293i
\(697\) −1.07572e24 −0.731511
\(698\) 3.18331e21 + 6.88820e21i 0.00213849 + 0.00462737i
\(699\) 2.98617e23i 0.198179i
\(700\) −4.56157e23 + 5.36116e23i −0.299075 + 0.351500i
\(701\) 1.08179e24i 0.700709i −0.936617 0.350355i \(-0.886061\pi\)
0.936617 0.350355i \(-0.113939\pi\)
\(702\) −3.08386e22 + 1.42518e22i −0.0197347 + 0.00912017i
\(703\) 1.62458e24 1.02712
\(704\) −1.22965e24 + 2.03209e24i −0.768096 + 1.26933i
\(705\) 1.26658e23 0.0781670
\(706\) −2.74130e23 + 1.26686e23i −0.167154 + 0.0772484i
\(707\) 1.39840e24i 0.842493i
\(708\) 3.86452e23 4.54192e23i 0.230045 0.270369i
\(709\) 1.54173e23i 0.0906808i 0.998972 + 0.0453404i \(0.0144372\pi\)
−0.998972 + 0.0453404i \(0.985563\pi\)
\(710\) 1.03284e24 + 2.23492e24i 0.600258 + 1.29887i
\(711\) 3.60045e23 0.206760
\(712\) 8.86635e23 3.17783e24i 0.503112 1.80323i
\(713\) −1.46184e23 −0.0819669
\(714\) 2.13381e23 + 4.61725e23i 0.118228 + 0.255828i
\(715\) 6.43906e22i 0.0352550i
\(716\) 1.66999e24 + 1.42092e24i 0.903552 + 0.768791i
\(717\) 1.75143e23i 0.0936438i
\(718\) −2.62469e24 + 1.21297e24i −1.38682 + 0.640905i
\(719\) −1.87407e24 −0.978565 −0.489283 0.872125i \(-0.662741\pi\)
−0.489283 + 0.872125i \(0.662741\pi\)
\(720\) −1.25085e24 + 2.02909e23i −0.645474 + 0.104707i
\(721\) −1.35097e24 −0.688964
\(722\) −5.44644e23 + 2.51701e23i −0.274502 + 0.126858i
\(723\) 3.96924e23i 0.197711i
\(724\) 3.01773e24 + 2.56765e24i 1.48560 + 1.26403i
\(725\) 1.20785e24i 0.587679i
\(726\) −3.91756e23 8.47701e23i −0.188389 0.407645i
\(727\) 3.49121e24 1.65933 0.829667 0.558259i \(-0.188531\pi\)
0.829667 + 0.558259i \(0.188531\pi\)
\(728\) −7.00712e22 1.95503e22i −0.0329172 0.00918410i
\(729\) 5.52055e23 0.256329
\(730\) −1.26907e24 2.74608e24i −0.582428 1.26029i
\(731\) 7.86197e23i 0.356643i
\(732\) 6.94832e23 8.16628e23i 0.311556 0.366168i
\(733\) 4.17586e24i 1.85081i −0.378979 0.925405i \(-0.623725\pi\)
0.378979 0.925405i \(-0.376275\pi\)
\(734\) −1.62998e24 + 7.53279e23i −0.714112 + 0.330019i
\(735\) 1.28063e23 0.0554600
\(736\) 9.47378e22 + 1.40361e23i 0.0405566 + 0.0600878i
\(737\) −3.88877e24 −1.64566
\(738\) 1.98024e24 9.15147e23i 0.828397 0.382835i
\(739\) 3.77789e24i 1.56233i −0.624327 0.781163i \(-0.714627\pi\)
0.624327 0.781163i \(-0.285373\pi\)
\(740\) 1.08447e24 1.27456e24i 0.443350 0.521064i
\(741\) 3.30007e22i 0.0133373i
\(742\) −1.97987e24 4.28414e24i −0.791050 1.71171i
\(743\) −2.48774e24 −0.982651 −0.491326 0.870976i \(-0.663487\pi\)
−0.491326 + 0.870976i \(0.663487\pi\)
\(744\) 1.04264e24 + 2.90903e23i 0.407160 + 0.113600i
\(745\) −1.88529e24 −0.727864
\(746\) 2.01394e24 + 4.35786e24i 0.768717 + 1.66339i
\(747\) 4.75817e23i 0.179562i
\(748\) 2.08830e24 + 1.77684e24i 0.779164 + 0.662955i
\(749\) 2.68005e24i 0.988663i
\(750\) 1.00588e24 4.64857e23i 0.366881 0.169550i
\(751\) 1.46920e22 0.00529836 0.00264918 0.999996i \(-0.499157\pi\)
0.00264918 + 0.999996i \(0.499157\pi\)
\(752\) −1.23515e23 7.61421e23i −0.0440423 0.271502i
\(753\) −3.50041e23 −0.123413
\(754\) −1.13312e23 + 5.23660e22i −0.0395021 + 0.0182555i
\(755\) 1.82058e24i 0.627567i
\(756\) −1.69886e24 1.44548e24i −0.579057 0.492694i
\(757\) 4.58159e24i 1.54419i −0.635506 0.772096i \(-0.719208\pi\)
0.635506 0.772096i \(-0.280792\pi\)
\(758\) 7.07853e23 + 1.53169e24i 0.235914 + 0.510483i
\(759\) −1.22009e23 −0.0402102
\(760\) −7.15364e23 + 2.56397e24i −0.233137 + 0.835599i
\(761\) 2.36360e24 0.761736 0.380868 0.924629i \(-0.375625\pi\)
0.380868 + 0.924629i \(0.375625\pi\)
\(762\) 7.26674e23 + 1.57241e24i 0.231591 + 0.501129i
\(763\) 1.75883e24i 0.554325i
\(764\) 1.03962e23 1.22185e23i 0.0324025 0.0380823i
\(765\) 1.46287e24i 0.450902i
\(766\) −3.09522e24 + 1.43042e24i −0.943510 + 0.436033i
\(767\) 9.84609e22 0.0296827
\(768\) −3.96390e23 1.18964e24i −0.118182 0.354687i