Properties

Label 8.18.b.a.5.2
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 5.2
Root \(-189.013 - 1.56793i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +O(q^{10})\) \(q+(-362.025 + 3.13586i) q^{2} -13867.2i q^{3} +(131052. - 2270.52i) q^{4} +665059. i q^{5} +(43485.7 + 5.02028e6i) q^{6} -7.57536e6 q^{7} +(-4.74371e7 + 1.23295e6i) q^{8} -6.31593e7 q^{9} +(-2.08553e6 - 2.40768e8i) q^{10} +1.97863e8i q^{11} +(-3.14858e7 - 1.81733e9i) q^{12} +4.74981e9i q^{13} +(2.74247e9 - 2.37553e7i) q^{14} +9.22251e9 q^{15} +(1.71696e10 - 5.95115e8i) q^{16} +3.37447e10 q^{17} +(2.28652e10 - 1.98059e8i) q^{18} -1.00829e11i q^{19} +(1.51003e9 + 8.71575e10i) q^{20} +1.05049e11i q^{21} +(-6.20471e8 - 7.16313e10i) q^{22} +3.16250e11 q^{23} +(1.70976e10 + 6.57820e11i) q^{24} +3.20636e11 q^{25} +(-1.48948e10 - 1.71955e12i) q^{26} -9.14971e11i q^{27} +(-9.92769e11 + 1.72000e10i) q^{28} +3.54291e12i q^{29} +(-3.33878e12 + 2.89205e10i) q^{30} +2.76965e11 q^{31} +(-6.21394e12 + 2.69288e11i) q^{32} +2.74380e12 q^{33} +(-1.22164e13 + 1.05819e11i) q^{34} -5.03806e12i q^{35} +(-8.27717e12 + 1.43405e11i) q^{36} -2.12889e13i q^{37} +(3.16187e11 + 3.65027e13i) q^{38} +6.58666e13 q^{39} +(-8.19983e11 - 3.15485e13i) q^{40} +8.47798e13 q^{41} +(-3.29420e11 - 3.80304e13i) q^{42} +1.38239e14i q^{43} +(4.49252e11 + 2.59304e13i) q^{44} -4.20047e13i q^{45} +(-1.14490e14 + 9.91717e11i) q^{46} +8.21469e13 q^{47} +(-8.25258e12 - 2.38094e14i) q^{48} -1.75244e14 q^{49} +(-1.16078e14 + 1.00547e12i) q^{50} -4.67945e14i q^{51} +(1.07846e13 + 6.22474e14i) q^{52} +3.16386e14i q^{53} +(2.86922e12 + 3.31242e14i) q^{54} -1.31590e14 q^{55} +(3.59353e14 - 9.34003e12i) q^{56} -1.39822e15 q^{57} +(-1.11101e13 - 1.28262e15i) q^{58} -3.29635e14i q^{59} +(1.20863e15 - 2.09399e13i) q^{60} +6.60732e14i q^{61} +(-1.00268e14 + 8.68526e11i) q^{62} +4.78454e14 q^{63} +(2.24876e15 - 1.16975e14i) q^{64} -3.15891e15 q^{65} +(-9.93326e14 + 8.60420e12i) q^{66} +3.64311e15i q^{67} +(4.42232e15 - 7.66181e13i) q^{68} -4.38551e15i q^{69} +(1.57987e13 + 1.82390e15i) q^{70} +9.19058e15 q^{71} +(2.99609e15 - 7.78722e13i) q^{72} -5.44264e15 q^{73} +(6.67591e13 + 7.70712e15i) q^{74} -4.44633e15i q^{75} +(-2.28935e14 - 1.32139e16i) q^{76} -1.49888e15i q^{77} +(-2.38454e16 + 2.06549e14i) q^{78} +1.06400e16 q^{79} +(3.95786e14 + 1.14188e16i) q^{80} -2.08445e16 q^{81} +(-3.06924e16 + 2.65858e14i) q^{82} +9.38898e15i q^{83} +(2.38516e14 + 1.37669e16i) q^{84} +2.24422e16i q^{85} +(-4.33498e14 - 5.00459e16i) q^{86} +4.91303e16 q^{87} +(-2.43955e14 - 9.38604e15i) q^{88} +2.24169e16 q^{89} +(1.31721e14 + 1.52067e16i) q^{90} -3.59815e16i q^{91} +(4.14453e16 - 7.18053e14i) q^{92} -3.84074e15i q^{93} +(-2.97392e16 + 2.57601e14i) q^{94} +6.70573e16 q^{95} +(3.73427e15 + 8.61701e16i) q^{96} -4.00962e16 q^{97} +(6.34429e16 - 5.49543e14i) q^{98} -1.24969e16i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −362.025 + 3.13586i −0.999962 + 0.00866168i
\(3\) 13867.2i 1.22028i −0.792295 0.610138i \(-0.791114\pi\)
0.792295 0.610138i \(-0.208886\pi\)
\(4\) 131052. 2270.52i 0.999850 0.0173227i
\(5\) 665059.i 0.761404i 0.924698 + 0.380702i \(0.124318\pi\)
−0.924698 + 0.380702i \(0.875682\pi\)
\(6\) 43485.7 + 5.02028e6i 0.0105697 + 1.22023i
\(7\) −7.57536e6 −0.496672 −0.248336 0.968674i \(-0.579884\pi\)
−0.248336 + 0.968674i \(0.579884\pi\)
\(8\) −4.74371e7 + 1.23295e6i −0.999662 + 0.0259824i
\(9\) −6.31593e7 −0.489075
\(10\) −2.08553e6 2.40768e8i −0.00659504 0.761375i
\(11\) 1.97863e8i 0.278308i 0.990271 + 0.139154i \(0.0444384\pi\)
−0.990271 + 0.139154i \(0.955562\pi\)
\(12\) −3.14858e7 1.81733e9i −0.0211385 1.22009i
\(13\) 4.74981e9i 1.61495i 0.589905 + 0.807473i \(0.299165\pi\)
−0.589905 + 0.807473i \(0.700835\pi\)
\(14\) 2.74247e9 2.37553e7i 0.496654 0.00430202i
\(15\) 9.22251e9 0.929124
\(16\) 1.71696e10 5.95115e8i 0.999400 0.0346402i
\(17\) 3.37447e10 1.17325 0.586624 0.809859i \(-0.300457\pi\)
0.586624 + 0.809859i \(0.300457\pi\)
\(18\) 2.28652e10 1.98059e8i 0.489057 0.00423622i
\(19\) 1.00829e11i 1.36201i −0.732278 0.681005i \(-0.761543\pi\)
0.732278 0.681005i \(-0.238457\pi\)
\(20\) 1.51003e9 + 8.71575e10i 0.0131896 + 0.761290i
\(21\) 1.05049e11i 0.606078i
\(22\) −6.20471e8 7.16313e10i −0.00241062 0.278298i
\(23\) 3.16250e11 0.842062 0.421031 0.907046i \(-0.361668\pi\)
0.421031 + 0.907046i \(0.361668\pi\)
\(24\) 1.70976e10 + 6.57820e11i 0.0317058 + 1.21986i
\(25\) 3.20636e11 0.420264
\(26\) −1.48948e10 1.71955e12i −0.0139881 1.61489i
\(27\) 9.14971e11i 0.623469i
\(28\) −9.92769e11 + 1.72000e10i −0.496598 + 0.00860371i
\(29\) 3.54291e12i 1.31516i 0.753386 + 0.657578i \(0.228419\pi\)
−0.753386 + 0.657578i \(0.771581\pi\)
\(30\) −3.33878e12 + 2.89205e10i −0.929089 + 0.00804777i
\(31\) 2.76965e11 0.0583245 0.0291623 0.999575i \(-0.490716\pi\)
0.0291623 + 0.999575i \(0.490716\pi\)
\(32\) −6.21394e12 + 2.69288e11i −0.999062 + 0.0432954i
\(33\) 2.74380e12 0.339613
\(34\) −1.22164e13 + 1.05819e11i −1.17320 + 0.0101623i
\(35\) 5.03806e12i 0.378168i
\(36\) −8.27717e12 + 1.43405e11i −0.489002 + 0.00847212i
\(37\) 2.12889e13i 0.996412i −0.867059 0.498206i \(-0.833992\pi\)
0.867059 0.498206i \(-0.166008\pi\)
\(38\) 3.16187e11 + 3.65027e13i 0.0117973 + 1.36196i
\(39\) 6.58666e13 1.97068
\(40\) −8.19983e11 3.15485e13i −0.0197831 0.761147i
\(41\) 8.47798e13 1.65817 0.829086 0.559121i \(-0.188861\pi\)
0.829086 + 0.559121i \(0.188861\pi\)
\(42\) −3.29420e11 3.80304e13i −0.00524965 0.606055i
\(43\) 1.38239e14i 1.80363i 0.432122 + 0.901815i \(0.357765\pi\)
−0.432122 + 0.901815i \(0.642235\pi\)
\(44\) 4.49252e11 + 2.59304e13i 0.00482106 + 0.278267i
\(45\) 4.20047e13i 0.372384i
\(46\) −1.14490e14 + 9.91717e11i −0.842030 + 0.00729367i
\(47\) 8.21469e13 0.503221 0.251611 0.967829i \(-0.419040\pi\)
0.251611 + 0.967829i \(0.419040\pi\)
\(48\) −8.25258e12 2.38094e14i −0.0422707 1.21954i
\(49\) −1.75244e14 −0.753317
\(50\) −1.16078e14 + 1.00547e12i −0.420248 + 0.00364019i
\(51\) 4.67945e14i 1.43169i
\(52\) 1.07846e13 + 6.22474e14i 0.0279752 + 1.61470i
\(53\) 3.16386e14i 0.698028i 0.937118 + 0.349014i \(0.113483\pi\)
−0.937118 + 0.349014i \(0.886517\pi\)
\(54\) 2.86922e12 + 3.31242e14i 0.00540029 + 0.623446i
\(55\) −1.31590e14 −0.211905
\(56\) 3.59353e14 9.34003e12i 0.496505 0.0129048i
\(57\) −1.39822e15 −1.66203
\(58\) −1.11101e13 1.28262e15i −0.0113915 1.31511i
\(59\) 3.29635e14i 0.292275i −0.989264 0.146138i \(-0.953316\pi\)
0.989264 0.146138i \(-0.0466842\pi\)
\(60\) 1.20863e15 2.09399e13i 0.928984 0.0160949i
\(61\) 6.60732e14i 0.441288i 0.975354 + 0.220644i \(0.0708159\pi\)
−0.975354 + 0.220644i \(0.929184\pi\)
\(62\) −1.00268e14 + 8.68526e11i −0.0583223 + 0.000505189i
\(63\) 4.78454e14 0.242910
\(64\) 2.24876e15 1.16975e14i 0.998650 0.0519474i
\(65\) −3.15891e15 −1.22963
\(66\) −9.93326e14 + 8.60420e12i −0.339600 + 0.00294162i
\(67\) 3.64311e15i 1.09607i 0.836457 + 0.548033i \(0.184623\pi\)
−0.836457 + 0.548033i \(0.815377\pi\)
\(68\) 4.42232e15 7.66181e13i 1.17307 0.0203238i
\(69\) 4.38551e15i 1.02755i
\(70\) 1.57987e13 + 1.82390e15i 0.00327557 + 0.378154i
\(71\) 9.19058e15 1.68907 0.844534 0.535502i \(-0.179878\pi\)
0.844534 + 0.535502i \(0.179878\pi\)
\(72\) 2.99609e15 7.78722e13i 0.488910 0.0127074i
\(73\) −5.44264e15 −0.789888 −0.394944 0.918705i \(-0.629236\pi\)
−0.394944 + 0.918705i \(0.629236\pi\)
\(74\) 6.67591e13 + 7.70712e15i 0.00863060 + 0.996374i
\(75\) 4.44633e15i 0.512838i
\(76\) −2.28935e14 1.32139e16i −0.0235937 1.36181i
\(77\) 1.49888e15i 0.138228i
\(78\) −2.38454e16 + 2.06549e14i −1.97061 + 0.0170694i
\(79\) 1.06400e16 0.789059 0.394529 0.918883i \(-0.370908\pi\)
0.394529 + 0.918883i \(0.370908\pi\)
\(80\) 3.95786e14 + 1.14188e16i 0.0263752 + 0.760947i
\(81\) −2.08445e16 −1.24988
\(82\) −3.06924e16 + 2.65858e14i −1.65811 + 0.0143626i
\(83\) 9.38898e15i 0.457567i 0.973477 + 0.228783i \(0.0734748\pi\)
−0.973477 + 0.228783i \(0.926525\pi\)
\(84\) 2.38516e14 + 1.37669e16i 0.0104989 + 0.605987i
\(85\) 2.24422e16i 0.893316i
\(86\) −4.33498e14 5.00459e16i −0.0156225 1.80356i
\(87\) 4.91303e16 1.60485
\(88\) −2.43955e14 9.38604e15i −0.00723113 0.278214i
\(89\) 2.24169e16 0.603616 0.301808 0.953369i \(-0.402410\pi\)
0.301808 + 0.953369i \(0.402410\pi\)
\(90\) 1.31721e14 + 1.52067e16i 0.00322547 + 0.372370i
\(91\) 3.59815e16i 0.802099i
\(92\) 4.14453e16 7.18053e14i 0.841936 0.0145868i
\(93\) 3.84074e15i 0.0711721i
\(94\) −2.97392e16 + 2.57601e14i −0.503203 + 0.00435874i
\(95\) 6.70573e16 1.03704
\(96\) 3.73427e15 + 8.61701e16i 0.0528324 + 1.21913i
\(97\) −4.00962e16 −0.519450 −0.259725 0.965683i \(-0.583632\pi\)
−0.259725 + 0.965683i \(0.583632\pi\)
\(98\) 6.34429e16 5.49543e14i 0.753288 0.00652499i
\(99\) 1.24969e16i 0.136114i
\(100\) 4.20201e16 7.28011e14i 0.420201 0.00728011i
\(101\) 3.80297e16i 0.349455i −0.984617 0.174728i \(-0.944096\pi\)
0.984617 0.174728i \(-0.0559045\pi\)
\(102\) 1.46741e15 + 1.69408e17i 0.0124008 + 1.43163i
\(103\) −2.07629e17 −1.61500 −0.807498 0.589870i \(-0.799179\pi\)
−0.807498 + 0.589870i \(0.799179\pi\)
\(104\) −5.85627e15 2.25317e17i −0.0419602 1.61440i
\(105\) −6.98638e16 −0.461470
\(106\) −9.92144e14 1.14540e17i −0.00604609 0.698001i
\(107\) 1.68191e17i 0.946325i 0.880975 + 0.473162i \(0.156888\pi\)
−0.880975 + 0.473162i \(0.843112\pi\)
\(108\) −2.07746e15 1.19909e17i −0.0108002 0.623376i
\(109\) 4.08973e15i 0.0196593i 0.999952 + 0.00982967i \(0.00312893\pi\)
−0.999952 + 0.00982967i \(0.996871\pi\)
\(110\) 4.76390e16 4.12650e14i 0.211897 0.00183545i
\(111\) −2.95218e17 −1.21590
\(112\) −1.30066e17 + 4.50821e15i −0.496374 + 0.0172048i
\(113\) 2.83148e16 0.100195 0.0500976 0.998744i \(-0.484047\pi\)
0.0500976 + 0.998744i \(0.484047\pi\)
\(114\) 5.06190e17 4.38462e15i 1.66197 0.0143960i
\(115\) 2.10325e17i 0.641149i
\(116\) 8.04426e15 + 4.64307e17i 0.0227821 + 1.31496i
\(117\) 2.99995e17i 0.789830i
\(118\) 1.03369e15 + 1.19336e17i 0.00253159 + 0.292264i
\(119\) −2.55628e17 −0.582720
\(120\) −4.37489e17 + 1.13709e16i −0.928810 + 0.0241409i
\(121\) 4.66297e17 0.922544
\(122\) −2.07197e15 2.39202e17i −0.00382229 0.441271i
\(123\) 1.17566e18i 2.02343i
\(124\) 3.62970e16 6.28856e14i 0.0583158 0.00101034i
\(125\) 7.20642e17i 1.08139i
\(126\) −1.73212e17 + 1.50037e15i −0.242901 + 0.00210401i
\(127\) −1.04849e17 −0.137478 −0.0687388 0.997635i \(-0.521898\pi\)
−0.0687388 + 0.997635i \(0.521898\pi\)
\(128\) −8.13741e17 + 4.93997e16i −0.998162 + 0.0605954i
\(129\) 1.91698e18 2.20093
\(130\) 1.14360e18 9.90590e15i 1.22958 0.0106506i
\(131\) 7.82237e17i 0.788011i 0.919108 + 0.394005i \(0.128911\pi\)
−0.919108 + 0.394005i \(0.871089\pi\)
\(132\) 3.59582e17 6.22987e15i 0.339562 0.00588302i
\(133\) 7.63817e17i 0.676473i
\(134\) −1.14243e16 1.31890e18i −0.00949377 1.09602i
\(135\) 6.08509e17 0.474712
\(136\) −1.60075e18 + 4.16055e16i −1.17285 + 0.0304839i
\(137\) 6.27442e17 0.431965 0.215983 0.976397i \(-0.430705\pi\)
0.215983 + 0.976397i \(0.430705\pi\)
\(138\) 1.37524e16 + 1.58766e18i 0.00890030 + 1.02751i
\(139\) 2.57262e17i 0.156585i −0.996930 0.0782924i \(-0.975053\pi\)
0.996930 0.0782924i \(-0.0249468\pi\)
\(140\) −1.14390e16 6.60250e17i −0.00655090 0.378112i
\(141\) 1.13915e18i 0.614069i
\(142\) −3.32722e18 + 2.88204e16i −1.68900 + 0.0146302i
\(143\) −9.39811e17 −0.449453
\(144\) −1.08442e18 + 3.75870e16i −0.488782 + 0.0169417i
\(145\) −2.35625e18 −1.00137
\(146\) 1.97037e18 1.70674e16i 0.789859 0.00684176i
\(147\) 2.43015e18i 0.919255i
\(148\) −4.83370e16 2.78996e18i −0.0172606 0.996262i
\(149\) 5.12586e18i 1.72855i −0.503016 0.864277i \(-0.667776\pi\)
0.503016 0.864277i \(-0.332224\pi\)
\(150\) 1.39431e16 + 1.60968e18i 0.00444204 + 0.512819i
\(151\) −1.51399e18 −0.455848 −0.227924 0.973679i \(-0.573194\pi\)
−0.227924 + 0.973679i \(0.573194\pi\)
\(152\) 1.24317e17 + 4.78304e18i 0.0353884 + 1.36155i
\(153\) −2.13129e18 −0.573807
\(154\) 4.70029e15 + 5.42633e17i 0.00119729 + 0.138223i
\(155\) 1.84198e17i 0.0444085i
\(156\) 8.63198e18 1.49552e17i 1.97039 0.0341375i
\(157\) 6.31795e18i 1.36593i 0.730450 + 0.682966i \(0.239310\pi\)
−0.730450 + 0.682966i \(0.760690\pi\)
\(158\) −3.85193e18 + 3.33654e16i −0.789029 + 0.00683458i
\(159\) 4.38739e18 0.851787
\(160\) −1.79092e17 4.13264e18i −0.0329653 0.760690i
\(161\) −2.39571e18 −0.418229
\(162\) 7.54623e18 6.53655e16i 1.24983 0.0108261i
\(163\) 7.62696e18i 1.19883i −0.800439 0.599414i \(-0.795400\pi\)
0.800439 0.599414i \(-0.204600\pi\)
\(164\) 1.11106e19 1.92494e17i 1.65792 0.0287240i
\(165\) 1.82479e18i 0.258583i
\(166\) −2.94426e16 3.39905e18i −0.00396330 0.457550i
\(167\) 7.60518e18 0.972791 0.486396 0.873739i \(-0.338311\pi\)
0.486396 + 0.873739i \(0.338311\pi\)
\(168\) −1.29520e17 4.98323e18i −0.0157474 0.605873i
\(169\) −1.39103e19 −1.60805
\(170\) −7.03757e16 8.12465e18i −0.00773762 0.893282i
\(171\) 6.36830e18i 0.666126i
\(172\) 3.13874e17 + 1.81165e19i 0.0312438 + 1.80336i
\(173\) 9.85927e18i 0.934228i 0.884197 + 0.467114i \(0.154706\pi\)
−0.884197 + 0.467114i \(0.845294\pi\)
\(174\) −1.77864e19 + 1.54066e17i −1.60479 + 0.0139007i
\(175\) −2.42893e18 −0.208734
\(176\) 1.17751e17 + 3.39722e18i 0.00964067 + 0.278141i
\(177\) −4.57112e18 −0.356657
\(178\) −8.11549e18 + 7.02964e16i −0.603593 + 0.00522833i
\(179\) 1.05371e19i 0.747257i −0.927578 0.373628i \(-0.878114\pi\)
0.927578 0.373628i \(-0.121886\pi\)
\(180\) −9.53725e16 5.50481e18i −0.00645070 0.372328i
\(181\) 2.64819e19i 1.70876i −0.519649 0.854380i \(-0.673937\pi\)
0.519649 0.854380i \(-0.326063\pi\)
\(182\) 1.12833e17 + 1.30262e19i 0.00694753 + 0.802069i
\(183\) 9.16251e18 0.538493
\(184\) −1.50020e19 + 3.89920e17i −0.841778 + 0.0218788i
\(185\) 1.41584e19 0.758672
\(186\) 1.20440e16 + 1.39044e18i 0.000616470 + 0.0711694i
\(187\) 6.67682e18i 0.326525i
\(188\) 1.07655e19 1.86516e17i 0.503146 0.00871716i
\(189\) 6.93123e18i 0.309660i
\(190\) −2.42764e19 + 2.10283e17i −1.03700 + 0.00898251i
\(191\) 2.32908e19 0.951484 0.475742 0.879585i \(-0.342180\pi\)
0.475742 + 0.879585i \(0.342180\pi\)
\(192\) −1.62212e18 3.11840e19i −0.0633901 1.21863i
\(193\) −2.61228e17 −0.00976748 −0.00488374 0.999988i \(-0.501555\pi\)
−0.00488374 + 0.999988i \(0.501555\pi\)
\(194\) 1.45158e19 1.25736e17i 0.519431 0.00449931i
\(195\) 4.38052e19i 1.50048i
\(196\) −2.29662e19 + 3.97896e17i −0.753204 + 0.0130495i
\(197\) 6.46253e18i 0.202974i −0.994837 0.101487i \(-0.967640\pi\)
0.994837 0.101487i \(-0.0323600\pi\)
\(198\) 3.91885e16 + 4.52418e18i 0.00117897 + 0.136109i
\(199\) −1.82250e19 −0.525311 −0.262655 0.964890i \(-0.584598\pi\)
−0.262655 + 0.964890i \(0.584598\pi\)
\(200\) −1.52100e19 + 3.95328e17i −0.420122 + 0.0109195i
\(201\) 5.05198e19 1.33750
\(202\) 1.19256e17 + 1.37677e19i 0.00302687 + 0.349442i
\(203\) 2.68388e19i 0.653202i
\(204\) −1.06248e18 6.13253e19i −0.0248007 1.43147i
\(205\) 5.63836e19i 1.26254i
\(206\) 7.51669e19 6.51096e17i 1.61494 0.0139886i
\(207\) −1.99741e19 −0.411832
\(208\) 2.82668e18 + 8.15522e19i 0.0559421 + 1.61398i
\(209\) 1.99503e19 0.379059
\(210\) 2.52925e19 2.19084e17i 0.461453 0.00399711i
\(211\) 7.73859e19i 1.35600i −0.735060 0.678002i \(-0.762846\pi\)
0.735060 0.678002i \(-0.237154\pi\)
\(212\) 7.18362e17 + 4.14631e19i 0.0120917 + 0.697923i
\(213\) 1.27448e20i 2.06113i
\(214\) −5.27424e17 6.08893e19i −0.00819677 0.946289i
\(215\) −9.19369e19 −1.37329
\(216\) 1.12811e18 + 4.34036e19i 0.0161993 + 0.623259i
\(217\) −2.09811e18 −0.0289682
\(218\) −1.28248e16 1.48058e18i −0.000170283 0.0196586i
\(219\) 7.54743e19i 0.963882i
\(220\) −1.72452e19 + 2.98779e17i −0.211873 + 0.00367077i
\(221\) 1.60281e20i 1.89473i
\(222\) 1.06876e20 9.25763e17i 1.21585 0.0105317i
\(223\) −1.34556e20 −1.47337 −0.736685 0.676236i \(-0.763610\pi\)
−0.736685 + 0.676236i \(0.763610\pi\)
\(224\) 4.70729e19 2.03995e18i 0.496207 0.0215036i
\(225\) −2.02511e19 −0.205541
\(226\) −1.02507e19 + 8.87915e16i −0.100192 + 0.000867860i
\(227\) 7.95558e19i 0.748949i −0.927237 0.374474i \(-0.877823\pi\)
0.927237 0.374474i \(-0.122177\pi\)
\(228\) −1.83240e20 + 3.17469e18i −1.66178 + 0.0287909i
\(229\) 3.46397e19i 0.302673i 0.988482 + 0.151336i \(0.0483576\pi\)
−0.988482 + 0.151336i \(0.951642\pi\)
\(230\) −6.59550e17 7.61429e19i −0.00555343 0.641125i
\(231\) −2.07853e19 −0.168676
\(232\) −4.36823e18 1.68066e20i −0.0341710 1.31471i
\(233\) −1.21528e20 −0.916538 −0.458269 0.888814i \(-0.651530\pi\)
−0.458269 + 0.888814i \(0.651530\pi\)
\(234\) 9.40743e17 + 1.08606e20i 0.00684126 + 0.789801i
\(235\) 5.46325e19i 0.383155i
\(236\) −7.48445e17 4.31995e19i −0.00506300 0.292231i
\(237\) 1.47546e20i 0.962870i
\(238\) 9.25438e19 8.01616e17i 0.582698 0.00504733i
\(239\) −2.25849e19 −0.137226 −0.0686129 0.997643i \(-0.521857\pi\)
−0.0686129 + 0.997643i \(0.521857\pi\)
\(240\) 1.58346e20 5.48845e18i 0.928566 0.0321851i
\(241\) 2.85622e20 1.61677 0.808383 0.588657i \(-0.200343\pi\)
0.808383 + 0.588657i \(0.200343\pi\)
\(242\) −1.68811e20 + 1.46225e18i −0.922510 + 0.00799079i
\(243\) 1.70895e20i 0.901731i
\(244\) 1.50021e18 + 8.65905e19i 0.00764430 + 0.441222i
\(245\) 1.16548e20i 0.573578i
\(246\) 3.68671e18 + 4.25618e20i 0.0175263 + 2.02335i
\(247\) 4.78920e20 2.19957
\(248\) −1.31384e19 + 3.41484e17i −0.0583048 + 0.00151541i
\(249\) 1.30199e20 0.558358
\(250\) −2.25983e18 2.60890e20i −0.00936670 1.08135i
\(251\) 1.47186e20i 0.589713i −0.955541 0.294857i \(-0.904728\pi\)
0.955541 0.294857i \(-0.0952719\pi\)
\(252\) 6.27026e19 1.08634e18i 0.242874 0.00420787i
\(253\) 6.25741e19i 0.234353i
\(254\) 3.79579e19 3.28792e17i 0.137472 0.00119079i
\(255\) 3.11211e20 1.09009
\(256\) 2.94440e20 2.04357e19i 0.997600 0.0692389i
\(257\) −3.49632e20 −1.14599 −0.572993 0.819560i \(-0.694218\pi\)
−0.572993 + 0.819560i \(0.694218\pi\)
\(258\) −6.93996e20 + 6.01140e18i −2.20085 + 0.0190637i
\(259\) 1.61271e20i 0.494890i
\(260\) −4.13982e20 + 7.17237e18i −1.22944 + 0.0213005i
\(261\) 2.23768e20i 0.643211i
\(262\) −2.45299e18 2.83189e20i −0.00682550 0.787981i
\(263\) −2.56287e20 −0.690402 −0.345201 0.938529i \(-0.612189\pi\)
−0.345201 + 0.938529i \(0.612189\pi\)
\(264\) −1.30158e20 + 3.38297e18i −0.339499 + 0.00882398i
\(265\) −2.10415e20 −0.531481
\(266\) −2.39523e18 2.76521e20i −0.00585939 0.676448i
\(267\) 3.10860e20i 0.736579i
\(268\) 8.27177e18 + 4.77438e20i 0.0189868 + 1.09590i
\(269\) 6.85596e20i 1.52466i 0.647187 + 0.762331i \(0.275945\pi\)
−0.647187 + 0.762331i \(0.724055\pi\)
\(270\) −2.20296e20 + 1.90820e18i −0.474694 + 0.00411180i
\(271\) 5.06814e20 1.05830 0.529151 0.848528i \(-0.322511\pi\)
0.529151 + 0.848528i \(0.322511\pi\)
\(272\) 5.79382e20 2.00820e19i 1.17254 0.0406416i
\(273\) −4.98964e20 −0.978783
\(274\) −2.27150e20 + 1.96757e18i −0.431949 + 0.00374154i
\(275\) 6.34419e19i 0.116963i
\(276\) −9.95739e18 5.74731e20i −0.0177999 1.02739i
\(277\) 5.87639e20i 1.01867i 0.860569 + 0.509334i \(0.170108\pi\)
−0.860569 + 0.509334i \(0.829892\pi\)
\(278\) 8.06738e17 + 9.31352e19i 0.00135629 + 0.156579i
\(279\) −1.74929e19 −0.0285251
\(280\) 6.21167e18 + 2.38991e20i 0.00982574 + 0.378041i
\(281\) −5.24336e20 −0.804647 −0.402324 0.915498i \(-0.631797\pi\)
−0.402324 + 0.915498i \(0.631797\pi\)
\(282\) 3.57221e18 + 4.12400e20i 0.00531887 + 0.614046i
\(283\) 7.51546e20i 1.08585i −0.839780 0.542927i \(-0.817316\pi\)
0.839780 0.542927i \(-0.182684\pi\)
\(284\) 1.20445e21 2.08674e19i 1.68881 0.0292592i
\(285\) 9.29898e20i 1.26548i
\(286\) 3.40235e20 2.94712e18i 0.449436 0.00389302i
\(287\) −6.42237e20 −0.823568
\(288\) 3.92468e20 1.70080e19i 0.488617 0.0211747i
\(289\) 3.11465e20 0.376511
\(290\) 8.53020e20 7.38887e18i 1.00133 0.00867351i
\(291\) 5.56023e20i 0.633873i
\(292\) −7.13271e20 + 1.23576e19i −0.789770 + 0.0136830i
\(293\) 7.51033e20i 0.807764i −0.914811 0.403882i \(-0.867661\pi\)
0.914811 0.403882i \(-0.132339\pi\)
\(294\) −7.62062e18 8.79776e20i −0.00796229 0.919220i
\(295\) 2.19227e20 0.222539
\(296\) 2.62481e19 + 1.00988e21i 0.0258892 + 0.996075i
\(297\) 1.81039e20 0.173517
\(298\) 1.60740e19 + 1.85569e21i 0.0149722 + 1.72849i
\(299\) 1.50213e21i 1.35988i
\(300\) −1.00955e19 5.82701e20i −0.00888375 0.512762i
\(301\) 1.04721e21i 0.895813i
\(302\) 5.48104e20 4.74768e18i 0.455831 0.00394841i
\(303\) −5.27366e20 −0.426432
\(304\) −6.00049e19 1.73119e21i −0.0471804 1.36119i
\(305\) −4.39426e20 −0.335998
\(306\) 7.71581e20 6.68344e18i 0.573785 0.00497013i
\(307\) 5.89249e19i 0.0426209i −0.999773 0.0213105i \(-0.993216\pi\)
0.999773 0.0213105i \(-0.00678384\pi\)
\(308\) −3.40325e18 1.96432e20i −0.00239449 0.138207i
\(309\) 2.87923e21i 1.97074i
\(310\) −5.77621e17 6.66844e19i −0.000384653 0.0444069i
\(311\) −9.05717e20 −0.586853 −0.293427 0.955982i \(-0.594796\pi\)
−0.293427 + 0.955982i \(0.594796\pi\)
\(312\) −3.12452e21 + 8.12102e19i −1.97002 + 0.0512031i
\(313\) 2.51738e21 1.54462 0.772311 0.635245i \(-0.219101\pi\)
0.772311 + 0.635245i \(0.219101\pi\)
\(314\) −1.98122e19 2.28726e21i −0.0118313 1.36588i
\(315\) 3.18200e20i 0.184953i
\(316\) 1.39439e21 2.41583e19i 0.788940 0.0136686i
\(317\) 1.88675e21i 1.03923i −0.854401 0.519614i \(-0.826076\pi\)
0.854401 0.519614i \(-0.173924\pi\)
\(318\) −1.58835e21 + 1.37583e19i −0.851755 + 0.00737791i
\(319\) −7.01010e20 −0.366019
\(320\) 7.77953e19 + 1.49556e21i 0.0395529 + 0.760376i
\(321\) 2.33234e21 1.15478
\(322\) 8.67307e20 7.51262e18i 0.418213 0.00362257i
\(323\) 3.40245e21i 1.59798i
\(324\) −2.73172e21 + 4.73279e19i −1.24969 + 0.0216513i
\(325\) 1.52296e21i 0.678704i
\(326\) 2.39171e19 + 2.76115e21i 0.0103839 + 1.19878i
\(327\) 5.67131e19 0.0239898
\(328\) −4.02171e21 + 1.04529e20i −1.65761 + 0.0430834i
\(329\) −6.22292e20 −0.249936
\(330\) −5.72230e18 6.60620e20i −0.00223976 0.258573i
\(331\) 1.03084e21i 0.393236i −0.980480 0.196618i \(-0.937004\pi\)
0.980480 0.196618i \(-0.0629959\pi\)
\(332\) 2.13179e19 + 1.23045e21i 0.00792630 + 0.457498i
\(333\) 1.34459e21i 0.487321i
\(334\) −2.75327e21 + 2.38488e19i −0.972755 + 0.00842601i
\(335\) −2.42288e21 −0.834549
\(336\) 6.25163e19 + 1.80365e21i 0.0209947 + 0.605714i
\(337\) 2.14822e21 0.703435 0.351717 0.936106i \(-0.385598\pi\)
0.351717 + 0.936106i \(0.385598\pi\)
\(338\) 5.03588e21 4.36208e19i 1.60799 0.0139284i
\(339\) 3.92648e20i 0.122266i
\(340\) 5.09556e19 + 2.94110e21i 0.0154747 + 0.893181i
\(341\) 5.48012e19i 0.0162322i
\(342\) −1.99701e19 2.30548e21i −0.00576977 0.666101i
\(343\) 3.08980e21 0.870824
\(344\) −1.70441e20 6.55764e21i −0.0468627 1.80302i
\(345\) 2.91662e21 0.782380
\(346\) −3.09173e19 3.56930e21i −0.00809199 0.934193i
\(347\) 4.67482e21i 1.19389i 0.802282 + 0.596945i \(0.203619\pi\)
−0.802282 + 0.596945i \(0.796381\pi\)
\(348\) 6.43864e21 1.11551e20i 1.60461 0.0278004i
\(349\) 4.72313e21i 1.14872i −0.818603 0.574360i \(-0.805251\pi\)
0.818603 0.574360i \(-0.194749\pi\)
\(350\) 8.79335e20 7.61680e18i 0.208726 0.00180798i
\(351\) 4.34594e21 1.00687
\(352\) −5.32820e19 1.22951e21i −0.0120495 0.278047i
\(353\) −4.29922e21 −0.949084 −0.474542 0.880233i \(-0.657386\pi\)
−0.474542 + 0.880233i \(0.657386\pi\)
\(354\) 1.65486e21 1.43344e19i 0.356643 0.00308925i
\(355\) 6.11228e21i 1.28606i
\(356\) 2.93779e21 5.08981e19i 0.603525 0.0104563i
\(357\) 3.54485e21i 0.711079i
\(358\) 3.30429e19 + 3.81469e21i 0.00647250 + 0.747229i
\(359\) −5.26993e21 −1.00810 −0.504048 0.863675i \(-0.668157\pi\)
−0.504048 + 0.863675i \(0.668157\pi\)
\(360\) 5.17896e19 + 1.99258e21i 0.00967545 + 0.372258i
\(361\) −4.68613e21 −0.855073
\(362\) 8.30436e19 + 9.58710e21i 0.0148007 + 1.70870i
\(363\) 6.46624e21i 1.12576i
\(364\) −8.16969e19 4.71546e21i −0.0138945 0.801979i
\(365\) 3.61968e21i 0.601424i
\(366\) −3.31706e21 + 2.87324e19i −0.538473 + 0.00466426i
\(367\) −7.39416e21 −1.17281 −0.586405 0.810018i \(-0.699457\pi\)
−0.586405 + 0.810018i \(0.699457\pi\)
\(368\) 5.42987e21 1.88205e20i 0.841557 0.0291692i
\(369\) −5.35463e21 −0.810971
\(370\) −5.12569e21 + 4.43988e19i −0.758643 + 0.00657137i
\(371\) 2.39674e21i 0.346691i
\(372\) −8.72048e18 5.03338e20i −0.00123289 0.0711614i
\(373\) 3.45714e21i 0.477740i −0.971052 0.238870i \(-0.923223\pi\)
0.971052 0.238870i \(-0.0767769\pi\)
\(374\) −2.09376e19 2.41718e21i −0.00282825 0.326512i
\(375\) 9.99329e21 1.31960
\(376\) −3.89681e21 + 1.01283e20i −0.503052 + 0.0130749i
\(377\) −1.68282e22 −2.12391
\(378\) −2.17354e19 2.50928e21i −0.00268218 0.309648i
\(379\) 3.17249e21i 0.382795i 0.981513 + 0.191398i \(0.0613020\pi\)
−0.981513 + 0.191398i \(0.938698\pi\)
\(380\) 8.78802e21 1.52255e20i 1.03688 0.0179644i
\(381\) 1.45396e21i 0.167761i
\(382\) −8.43187e21 + 7.30369e19i −0.951448 + 0.00824145i
\(383\) 3.27971e21 0.361947 0.180974 0.983488i \(-0.442075\pi\)
0.180974 + 0.983488i \(0.442075\pi\)
\(384\) 6.85036e20 + 1.12843e22i 0.0739432 + 1.21803i
\(385\) 9.96845e20 0.105247
\(386\) 9.45711e19 8.19175e17i 0.00976711 8.46028e-5i
\(387\) 8.73105e21i 0.882112i
\(388\) −5.25471e21 + 9.10394e19i −0.519372 + 0.00899829i
\(389\) 1.09936e22i 1.06308i 0.847032 + 0.531542i \(0.178387\pi\)
−0.847032 + 0.531542i \(0.821613\pi\)
\(390\) −1.37367e20 1.58586e22i −0.0129967 1.50043i
\(391\) 1.06718e22 0.987947
\(392\) 8.31309e21 2.16067e20i 0.753062 0.0195730i
\(393\) 1.08474e22 0.961591
\(394\) 2.02656e19 + 2.33960e21i 0.00175809 + 0.202966i
\(395\) 7.07620e21i 0.600792i
\(396\) −2.83744e19 1.63774e21i −0.00235786 0.136093i
\(397\) 9.01100e21i 0.732915i 0.930435 + 0.366458i \(0.119430\pi\)
−0.930435 + 0.366458i \(0.880570\pi\)
\(398\) 6.59791e21 5.71511e19i 0.525291 0.00455008i
\(399\) 1.05920e22 0.825484
\(400\) 5.50518e21 1.90815e20i 0.420012 0.0145580i
\(401\) 1.05004e22 0.784296 0.392148 0.919902i \(-0.371732\pi\)
0.392148 + 0.919902i \(0.371732\pi\)
\(402\) −1.82894e22 + 1.58423e20i −1.33745 + 0.0115850i
\(403\) 1.31553e21i 0.0941910i
\(404\) −8.63473e19 4.98388e21i −0.00605351 0.349403i
\(405\) 1.38628e22i 0.951664i
\(406\) 8.41629e19 + 9.71633e21i 0.00565783 + 0.653177i
\(407\) 4.21228e21 0.277310
\(408\) 5.76952e20 + 2.21979e22i 0.0371987 + 1.43120i
\(409\) 5.86541e21 0.370382 0.185191 0.982703i \(-0.440710\pi\)
0.185191 + 0.982703i \(0.440710\pi\)
\(410\) −1.76811e20 2.04123e22i −0.0109357 1.26249i
\(411\) 8.70087e21i 0.527117i
\(412\) −2.72103e22 + 4.71426e20i −1.61475 + 0.0279761i
\(413\) 2.49711e21i 0.145165i
\(414\) 7.23114e21 6.26362e19i 0.411816 0.00356716i
\(415\) −6.24423e21 −0.348393
\(416\) −1.27907e21 2.95151e22i −0.0699198 1.61343i
\(417\) −3.56750e21 −0.191077
\(418\) −7.22252e21 + 6.25615e19i −0.379045 + 0.00328329i
\(419\) 5.02281e21i 0.258302i 0.991625 + 0.129151i \(0.0412252\pi\)
−0.991625 + 0.129151i \(0.958775\pi\)
\(420\) −9.15582e21 + 1.58627e20i −0.461401 + 0.00799391i
\(421\) 1.55885e22i 0.769848i −0.922948 0.384924i \(-0.874228\pi\)
0.922948 0.384924i \(-0.125772\pi\)
\(422\) 2.42672e20 + 2.80156e22i 0.0117453 + 1.35595i
\(423\) −5.18834e21 −0.246113
\(424\) −3.90088e20 1.50084e22i −0.0181365 0.697792i
\(425\) 1.08198e22 0.493074
\(426\) 3.99659e20 + 4.61393e22i 0.0178529 + 2.06105i
\(427\) 5.00528e21i 0.219175i
\(428\) 3.81881e20 + 2.20418e22i 0.0163929 + 0.946183i
\(429\) 1.30326e22i 0.548457i
\(430\) 3.32834e22 2.88301e20i 1.37324 0.0118950i
\(431\) −2.78561e22 −1.12684 −0.563421 0.826170i \(-0.690515\pi\)
−0.563421 + 0.826170i \(0.690515\pi\)
\(432\) −5.44512e20 1.57096e22i −0.0215971 0.623095i
\(433\) −1.24470e21 −0.0484079 −0.0242040 0.999707i \(-0.507705\pi\)
−0.0242040 + 0.999707i \(0.507705\pi\)
\(434\) 7.59570e20 6.57940e18i 0.0289671 0.000250913i
\(435\) 3.26745e22i 1.22194i
\(436\) 9.28581e18 + 5.35968e20i 0.000340553 + 0.0196564i
\(437\) 3.18872e22i 1.14690i
\(438\) −2.36677e20 2.73236e22i −0.00834884 0.963846i
\(439\) −2.09614e22 −0.725224 −0.362612 0.931940i \(-0.618115\pi\)
−0.362612 + 0.931940i \(0.618115\pi\)
\(440\) 6.24227e21 1.62244e20i 0.211834 0.00550581i
\(441\) 1.10683e22 0.368429
\(442\) −5.02619e20 5.80257e22i −0.0164116 1.89466i
\(443\) 1.11978e22i 0.358674i −0.983788 0.179337i \(-0.942605\pi\)
0.983788 0.179337i \(-0.0573952\pi\)
\(444\) −3.86890e22 + 6.70299e20i −1.21572 + 0.0210627i
\(445\) 1.49086e22i 0.459596i
\(446\) 4.87127e22 4.21950e20i 1.47332 0.0127619i
\(447\) −7.10813e22 −2.10931
\(448\) −1.70352e22 + 8.86128e20i −0.496002 + 0.0258008i
\(449\) −1.44200e22 −0.411975 −0.205987 0.978555i \(-0.566041\pi\)
−0.205987 + 0.978555i \(0.566041\pi\)
\(450\) 7.33142e21 6.35048e19i 0.205533 0.00178033i
\(451\) 1.67748e22i 0.461483i
\(452\) 3.71072e21 6.42895e19i 0.100180 0.00173565i
\(453\) 2.09949e22i 0.556261i
\(454\) 2.49476e20 + 2.88012e22i 0.00648716 + 0.748921i
\(455\) 2.39298e22 0.610721
\(456\) 6.63275e22 1.72393e21i 1.66147 0.0431836i
\(457\) 2.99851e22 0.737254 0.368627 0.929577i \(-0.379828\pi\)
0.368627 + 0.929577i \(0.379828\pi\)
\(458\) −1.08626e20 1.25405e22i −0.00262165 0.302661i
\(459\) 3.08754e22i 0.731484i
\(460\) 4.77548e20 + 2.75636e22i 0.0111064 + 0.641053i
\(461\) 4.32706e22i 0.987950i 0.869476 + 0.493975i \(0.164456\pi\)
−0.869476 + 0.493975i \(0.835544\pi\)
\(462\) 7.52480e21 6.51799e19i 0.168670 0.00146102i
\(463\) −1.79925e22 −0.395962 −0.197981 0.980206i \(-0.563438\pi\)
−0.197981 + 0.980206i \(0.563438\pi\)
\(464\) 2.10844e21 + 6.08302e22i 0.0455573 + 1.31437i
\(465\) 2.55432e21 0.0541907
\(466\) 4.39961e22 3.81095e20i 0.916504 0.00793876i
\(467\) 5.53566e22i 1.13234i −0.824289 0.566169i \(-0.808425\pi\)
0.824289 0.566169i \(-0.191575\pi\)
\(468\) −6.81145e20 3.93150e22i −0.0136820 0.789712i
\(469\) 2.75979e22i 0.544386i
\(470\) −1.71320e20 1.97783e22i −0.00331877 0.383140i
\(471\) 8.76123e22 1.66682
\(472\) 4.06424e20 + 1.56370e22i 0.00759402 + 0.292176i
\(473\) −2.73523e22 −0.501965
\(474\) 4.62686e20 + 5.34155e22i 0.00834008 + 0.962834i
\(475\) 3.23295e22i 0.572404i
\(476\) −3.35007e22 + 5.80410e20i −0.582632 + 0.0100943i
\(477\) 1.99827e22i 0.341388i
\(478\) 8.17630e21 7.08232e19i 0.137221 0.00118861i
\(479\) −1.18108e22 −0.194727 −0.0973637 0.995249i \(-0.531041\pi\)
−0.0973637 + 0.995249i \(0.531041\pi\)
\(480\) −5.73082e22 + 2.48351e21i −0.928252 + 0.0402268i
\(481\) 1.01118e23 1.60915
\(482\) −1.03402e23 + 8.95672e20i −1.61670 + 0.0140039i
\(483\) 3.32218e22i 0.510355i
\(484\) 6.11094e22 1.05874e21i 0.922406 0.0159810i
\(485\) 2.66664e22i 0.395511i
\(486\) −5.35905e20 6.18684e22i −0.00781051 0.901697i
\(487\) 2.16692e22 0.310347 0.155173 0.987887i \(-0.450406\pi\)
0.155173 + 0.987887i \(0.450406\pi\)
\(488\) −8.14649e20 3.13432e22i −0.0114657 0.441139i
\(489\) −1.05765e23 −1.46290
\(490\) 3.65478e20 + 4.21933e22i 0.00496815 + 0.573557i
\(491\) 1.30265e23i 1.74034i 0.492749 + 0.870172i \(0.335992\pi\)
−0.492749 + 0.870172i \(0.664008\pi\)
\(492\) −2.66936e21 1.54073e23i −0.0350513 2.02312i
\(493\) 1.19555e23i 1.54300i
\(494\) −1.73381e23 + 1.50183e21i −2.19949 + 0.0190520i
\(495\) 8.31116e21 0.103638
\(496\) 4.75537e21 1.64826e20i 0.0582895 0.00202038i
\(497\) −6.96220e22 −0.838913
\(498\) −4.71353e22 + 4.08286e20i −0.558337 + 0.00483632i
\(499\) 5.17276e22i 0.602376i −0.953565 0.301188i \(-0.902617\pi\)
0.953565 0.301188i \(-0.0973832\pi\)
\(500\) 1.63623e21 + 9.44418e22i 0.0187327 + 1.08123i
\(501\) 1.05463e23i 1.18707i
\(502\) 4.61556e20 + 5.32852e22i 0.00510791 + 0.589691i
\(503\) 1.07219e23 1.16665 0.583327 0.812237i \(-0.301751\pi\)
0.583327 + 0.812237i \(0.301751\pi\)
\(504\) −2.26965e22 + 5.89910e20i −0.242828 + 0.00631140i
\(505\) 2.52920e22 0.266076
\(506\) −1.96224e20 2.26534e22i −0.00202989 0.234344i
\(507\) 1.92897e23i 1.96227i
\(508\) −1.37407e22 + 2.38062e20i −0.137457 + 0.00238148i
\(509\) 1.48328e23i 1.45922i −0.683861 0.729612i \(-0.739701\pi\)
0.683861 0.729612i \(-0.260299\pi\)
\(510\) −1.12666e23 + 9.75915e20i −1.09005 + 0.00944203i
\(511\) 4.12300e22 0.392316
\(512\) −1.06530e23 + 8.32156e21i −0.996963 + 0.0778772i
\(513\) −9.22557e22 −0.849172
\(514\) 1.26576e23 1.09640e21i 1.14594 0.00992617i
\(515\) 1.38086e23i 1.22966i
\(516\) 2.51225e23 4.35256e21i 2.20060 0.0381261i
\(517\) 1.62538e22i 0.140051i
\(518\) −5.05725e20 5.83842e22i −0.00428658 0.494872i
\(519\) 1.36721e23 1.14002
\(520\) 1.49849e23 3.89477e21i 1.22921 0.0319487i
\(521\) 7.01242e22 0.565910 0.282955 0.959133i \(-0.408685\pi\)
0.282955 + 0.959133i \(0.408685\pi\)
\(522\) 7.01705e20 + 8.10096e22i 0.00557129 + 0.643187i
\(523\) 2.14598e23i 1.67634i −0.545410 0.838169i \(-0.683626\pi\)
0.545410 0.838169i \(-0.316374\pi\)
\(524\) 1.77609e21 + 1.02514e23i 0.0136505 + 0.787893i
\(525\) 3.36825e22i 0.254713i
\(526\) 9.27822e22 8.03680e20i 0.690376 0.00598005i
\(527\) 9.34612e21 0.0684291
\(528\) 4.71099e22 1.63288e21i 0.339409 0.0117643i
\(529\) −4.10359e22 −0.290932
\(530\) 7.61757e22 6.59834e20i 0.531461 0.00460352i
\(531\) 2.08195e22i 0.142945i
\(532\) 1.73426e21 + 1.00100e23i 0.0117183 + 0.676371i
\(533\) 4.02688e23i 2.67786i
\(534\) 9.74815e20 + 1.12539e23i 0.00638001 + 0.736551i
\(535\) −1.11857e23 −0.720536
\(536\) −4.49177e21 1.72819e23i −0.0284785 1.09570i
\(537\) −1.46120e23 −0.911860
\(538\) −2.14993e21 2.48203e23i −0.0132061 1.52460i
\(539\) 3.46743e22i 0.209654i
\(540\) 7.97466e22 1.38163e21i 0.474641 0.00822330i
\(541\) 1.34761e23i 0.789565i −0.918775 0.394783i \(-0.870820\pi\)
0.918775 0.394783i \(-0.129180\pi\)
\(542\) −1.83479e23 + 1.58930e21i −1.05826 + 0.00916667i
\(543\) −3.67230e23 −2.08516
\(544\) −2.09688e23 + 9.08704e21i −1.17215 + 0.0507963i
\(545\) −2.71991e21 −0.0149687
\(546\) 1.80637e23 1.56468e21i 0.978746 0.00847791i
\(547\) 2.17960e23i 1.16274i 0.813638 + 0.581372i \(0.197484\pi\)
−0.813638 + 0.581372i \(0.802516\pi\)
\(548\) 8.22277e22 1.42462e21i 0.431900 0.00748281i
\(549\) 4.17314e22i 0.215823i
\(550\) −1.98945e20 2.29676e22i −0.00101310 0.116959i
\(551\) 3.57229e23 1.79126
\(552\) 5.40710e21 + 2.08036e23i 0.0266982 + 1.02720i
\(553\) −8.06015e22 −0.391904
\(554\) −1.84276e21 2.12740e23i −0.00882337 1.01863i
\(555\) 1.96337e23i 0.925790i
\(556\) −5.84119e20 3.37148e22i −0.00271247 0.156561i
\(557\) 7.39588e22i 0.338237i −0.985596 0.169118i \(-0.945908\pi\)
0.985596 0.169118i \(-0.0540920\pi\)
\(558\) 6.33288e21 5.48555e19i 0.0285240 0.000247075i
\(559\) −6.56608e23 −2.91277
\(560\) −2.99822e21 8.65013e22i −0.0130998 0.377941i
\(561\) 9.25888e22 0.398450
\(562\) 1.89823e23 1.64424e21i 0.804617 0.00696960i
\(563\) 6.46778e21i 0.0270044i −0.999909 0.0135022i \(-0.995702\pi\)
0.999909 0.0135022i \(-0.00429801\pi\)
\(564\) −2.58646e21 1.49288e23i −0.0106374 0.613977i
\(565\) 1.88310e22i 0.0762891i
\(566\) 2.35675e21 + 2.72079e23i 0.00940532 + 1.08581i
\(567\) 1.57904e23 0.620781
\(568\) −4.35975e23 + 1.13315e22i −1.68850 + 0.0438861i
\(569\) 3.40211e23 1.29806 0.649029 0.760764i \(-0.275176\pi\)
0.649029 + 0.760764i \(0.275176\pi\)
\(570\) 2.91603e21 + 3.36646e23i 0.0109612 + 1.26543i
\(571\) 4.01054e23i 1.48524i 0.669715 + 0.742619i \(0.266416\pi\)
−0.669715 + 0.742619i \(0.733584\pi\)
\(572\) −1.23164e23 + 2.13386e21i −0.449385 + 0.00778575i
\(573\) 3.22979e23i 1.16107i
\(574\) 2.32506e23 2.01397e21i 0.823537 0.00713348i
\(575\) 1.01401e23 0.353888
\(576\) −1.42030e23 + 7.38806e21i −0.488415 + 0.0254062i
\(577\) 1.92304e23 0.651619 0.325810 0.945435i \(-0.394363\pi\)
0.325810 + 0.945435i \(0.394363\pi\)
\(578\) −1.12758e23 + 9.76711e20i −0.376496 + 0.00326121i
\(579\) 3.62250e21i 0.0119190i
\(580\) −3.08791e23 + 5.34991e21i −1.00122 + 0.0173464i
\(581\) 7.11249e22i 0.227261i
\(582\) −1.74361e21 2.01294e23i −0.00549041 0.633849i
\(583\) −6.26010e22 −0.194267
\(584\) 2.58183e23 6.71050e21i 0.789622 0.0205232i
\(585\) 1.99514e23 0.601380
\(586\) 2.35514e21 + 2.71893e23i 0.00699659 + 0.807733i
\(587\) 1.13316e23i 0.331793i −0.986143 0.165896i \(-0.946948\pi\)
0.986143 0.165896i \(-0.0530517\pi\)
\(588\) 5.51771e21 + 3.18477e23i 0.0159240 + 0.919117i
\(589\) 2.79262e22i 0.0794386i
\(590\) −7.93657e22 + 6.87466e20i −0.222531 + 0.00192757i
\(591\) −8.96173e22 −0.247684
\(592\) −1.26693e22 3.65521e23i −0.0345159 0.995814i
\(593\) 4.06278e23 1.09108 0.545542 0.838084i \(-0.316324\pi\)
0.545542 + 0.838084i \(0.316324\pi\)
\(594\) −6.55405e22 + 5.67712e20i −0.173510 + 0.00150295i
\(595\) 1.70008e23i 0.443685i
\(596\) −1.16384e22 6.71755e23i −0.0299433 1.72830i
\(597\) 2.52730e23i 0.641025i
\(598\) −4.71047e21 5.43808e23i −0.0117789 1.35983i
\(599\) 5.15444e23 1.27073 0.635365 0.772212i \(-0.280850\pi\)
0.635365 + 0.772212i \(0.280850\pi\)
\(600\) 5.48209e21 + 2.10921e23i 0.0133248 + 0.512665i
\(601\) 3.97639e23 0.952918 0.476459 0.879197i \(-0.341920\pi\)
0.476459 + 0.879197i \(0.341920\pi\)
\(602\) 3.28390e21 + 3.79115e23i 0.00775925 + 0.895780i
\(603\) 2.30096e23i 0.536059i
\(604\) −1.98413e23 + 3.43756e21i −0.455780 + 0.00789653i
\(605\) 3.10115e23i 0.702429i
\(606\) 1.90920e23 1.65375e21i 0.426416 0.00369362i
\(607\) −6.76629e23 −1.49021 −0.745104 0.666948i \(-0.767600\pi\)
−0.745104 + 0.666948i \(0.767600\pi\)
\(608\) 2.71521e22 + 6.26547e23i 0.0589688 + 1.36073i
\(609\) −3.72180e23 −0.797087
\(610\) 1.59083e23 1.37798e21i 0.335986 0.00291031i
\(611\) 3.90182e23i 0.812675i
\(612\) −2.79311e23 + 4.83915e21i −0.573721 + 0.00993989i
\(613\) 6.69956e23i 1.35716i 0.734525 + 0.678582i \(0.237405\pi\)
−0.734525 + 0.678582i \(0.762595\pi\)
\(614\) 1.84781e20 + 2.13323e22i 0.000369169 + 0.0426193i
\(615\) 7.81882e23 1.54065
\(616\) 1.84804e21 + 7.11026e22i 0.00359150 + 0.138181i
\(617\) −2.38236e23 −0.456649 −0.228325 0.973585i \(-0.573325\pi\)
−0.228325 + 0.973585i \(0.573325\pi\)
\(618\) −9.02889e21 1.04236e24i −0.0170699 1.97067i
\(619\) 1.75944e23i 0.328099i −0.986452 0.164049i \(-0.947544\pi\)
0.986452 0.164049i \(-0.0524556\pi\)
\(620\) 4.18227e20 + 2.41396e22i 0.000769276 + 0.0444019i
\(621\) 2.89360e23i 0.525000i
\(622\) 3.27892e23 2.84021e21i 0.586831 0.00508314i
\(623\) −1.69816e23 −0.299799
\(624\) 1.13090e24 3.91982e22i 1.96950 0.0682648i
\(625\) −2.34643e23 −0.403114
\(626\) −9.11355e23 + 7.89416e21i −1.54456 + 0.0133790i
\(627\) 2.76655e23i 0.462557i
\(628\) 1.43451e22 + 8.27982e23i 0.0236617 + 1.36573i
\(629\) 7.18388e23i 1.16904i
\(630\) −9.97833e20 1.15197e23i −0.00160200 0.184946i
\(631\) −5.34532e23 −0.846689 −0.423344 0.905969i \(-0.639144\pi\)
−0.423344 + 0.905969i \(0.639144\pi\)
\(632\) −5.04729e23 + 1.31185e22i −0.788792 + 0.0205017i
\(633\) −1.07313e24 −1.65470
\(634\) 5.91659e21 + 6.83051e23i 0.00900146 + 1.03919i
\(635\) 6.97306e22i 0.104676i
\(636\) 5.74978e23 9.96168e21i 0.851659 0.0147553i
\(637\) 8.32378e23i 1.21657i
\(638\) 2.53783e23 2.19827e21i 0.366005 0.00317034i
\(639\) −5.80471e23 −0.826082
\(640\) −3.28537e22 5.41185e23i −0.0461376 0.760005i
\(641\) −1.21663e24 −1.68603 −0.843017 0.537887i \(-0.819223\pi\)
−0.843017 + 0.537887i \(0.819223\pi\)
\(642\) −8.44365e23 + 7.31389e21i −1.15474 + 0.0100023i
\(643\) 2.18465e23i 0.294842i −0.989074 0.147421i \(-0.952903\pi\)
0.989074 0.147421i \(-0.0470972\pi\)
\(644\) −3.13963e23 + 5.43951e21i −0.418166 + 0.00724486i
\(645\) 1.27491e24i 1.67580i
\(646\) 1.06696e22 + 1.23177e24i 0.0138412 + 1.59792i
\(647\) 1.14703e24 1.46855 0.734275 0.678852i \(-0.237522\pi\)
0.734275 + 0.678852i \(0.237522\pi\)
\(648\) 9.88802e23 2.57002e22i 1.24946 0.0324750i
\(649\) 6.52226e22 0.0813426
\(650\) −4.77580e21 5.51350e23i −0.00587872 0.678678i
\(651\) 2.90950e22i 0.0353492i
\(652\) −1.73172e22 9.99531e23i −0.0207670 1.19865i
\(653\) 1.50867e23i 0.178580i 0.996006 + 0.0892898i \(0.0284597\pi\)
−0.996006 + 0.0892898i \(0.971540\pi\)
\(654\) −2.05316e22 + 1.77844e20i −0.0239889 + 0.000207792i
\(655\) −5.20234e23 −0.599995
\(656\) 1.45563e24 5.04537e22i 1.65718 0.0574395i
\(657\) 3.43754e23 0.386315
\(658\) 2.25285e23 1.95142e21i 0.249927 0.00216487i
\(659\) 1.33218e24i 1.45894i 0.684013 + 0.729470i \(0.260233\pi\)
−0.684013 + 0.729470i \(0.739767\pi\)
\(660\) 4.14323e21 + 2.39143e23i 0.00447936 + 0.258544i
\(661\) 1.50165e24i 1.60272i −0.598183 0.801359i \(-0.704111\pi\)
0.598183 0.801359i \(-0.295889\pi\)
\(662\) 3.23257e21 + 3.73190e23i 0.00340609 + 0.393221i
\(663\) 2.22265e24 2.31210
\(664\) −1.15761e22 4.45386e23i −0.0118887 0.457413i
\(665\) −5.07983e23 −0.515069
\(666\) −4.21646e21 4.86776e23i −0.00422102 0.487302i
\(667\) 1.12045e24i 1.10744i
\(668\) 9.96677e23 1.72677e22i 0.972645 0.0168514i
\(669\) 1.86592e24i 1.79792i
\(670\) 8.77145e23 7.59783e21i 0.834517 0.00722860i
\(671\) −1.30734e23 −0.122814
\(672\) −2.82884e22 6.52769e23i −0.0262404 0.605509i
\(673\) 1.95354e24 1.78935 0.894673 0.446722i \(-0.147409\pi\)
0.894673 + 0.446722i \(0.147409\pi\)
\(674\) −7.77708e23 + 6.73651e21i −0.703408 + 0.00609293i
\(675\) 2.93373e23i 0.262022i
\(676\) −1.82298e24 + 3.15837e22i −1.60781 + 0.0278558i
\(677\) 1.79219e24i 1.56092i −0.625208 0.780458i \(-0.714986\pi\)
0.625208 0.780458i \(-0.285014\pi\)
\(678\) 1.23129e21 + 1.42148e23i 0.00105903 + 0.122261i
\(679\) 3.03743e23 0.257997
\(680\) −2.76701e22 1.06459e24i −0.0232105 0.893014i
\(681\) −1.10322e24 −0.913925
\(682\) −1.71849e20 1.98394e22i −0.000140598 0.0162316i
\(683\) 2.23745e24i 1.80791i −0.427628 0.903955i \(-0.640651\pi\)
0.427628 0.903955i \(-0.359349\pi\)
\(684\) 1.44594e22 + 8.34580e23i 0.0115391 + 0.666026i
\(685\) 4.17286e23i 0.328900i
\(686\) −1.11858e24 + 9.68919e21i −0.870791 + 0.00754280i
\(687\) 4.80356e23 0.369344
\(688\) 8.22678e22 + 2.37350e24i 0.0624782 + 1.80255i
\(689\) −1.50278e24 −1.12728
\(690\) −1.05589e24 + 9.14612e21i −0.782350 + 0.00677672i
\(691\) 1.07548e24i 0.787114i −0.919300 0.393557i \(-0.871244\pi\)
0.919300 0.393557i \(-0.128756\pi\)
\(692\) 2.23857e22 + 1.29208e24i 0.0161834 + 0.934088i
\(693\) 9.46683e22i 0.0676040i
\(694\) −1.46596e22 1.69240e24i −0.0103411 1.19384i
\(695\) 1.71094e23 0.119224
\(696\) −2.33060e24 + 6.05751e22i −1.60431 + 0.0416981i
\(697\) 2.86087e24 1.94545
\(698\) 1.48111e22 + 1.70989e24i 0.00994985 + 1.14868i
\(699\) 1.68525e24i 1.11843i
\(700\) −3.18317e23 + 5.51495e21i −0.208702 + 0.00361583i
\(701\) 4.83049e23i 0.312887i 0.987687 + 0.156444i \(0.0500030\pi\)
−0.987687 + 0.156444i \(0.949997\pi\)
\(702\) −1.57334e24 + 1.36283e22i −1.00683 + 0.00872118i
\(703\) −2.14654e24 −1.35712
\(704\) 2.31450e22 + 4.44946e23i 0.0144574 + 0.277933i
\(705\) 7.57600e23 0.467555
\(706\) 1.55642e24 1.34818e22i 0.949048 0.00822066i
\(707\) 2.88089e23i 0.173565i
\(708\) −5.99056e23 + 1.03788e22i −0.356603 + 0.00617826i
\(709\) 6.46817e23i 0.380442i 0.981741 + 0.190221i \(0.0609204\pi\)
−0.981741 + 0.190221i \(0.939080\pi\)
\(710\) −1.91673e22 2.21280e24i −0.0111395 1.28601i
\(711\) −6.72012e23 −0.385909
\(712\) −1.06339e24 + 2.76389e22i −0.603412 + 0.0156834i
\(713\) 8.75904e22 0.0491129
\(714\) −1.11162e22 1.28332e24i −0.00615914 0.711053i
\(715\) 6.25030e23i 0.342215i
\(716\) −2.39247e22 1.38091e24i −0.0129445 0.747145i
\(717\) 3.13189e23i 0.167454i
\(718\) 1.90785e24 1.65258e22i 1.00806 0.00873181i
\(719\) −2.08660e24 −1.08954 −0.544770 0.838586i \(-0.683383\pi\)
−0.544770 + 0.838586i \(0.683383\pi\)
\(720\) −2.49976e22 7.21201e23i −0.0128995 0.372161i
\(721\) 1.57286e24 0.802124
\(722\) 1.69650e24 1.46951e22i 0.855041 0.00740637i
\(723\) 3.96078e24i 1.97290i
\(724\) −6.01277e22 3.47051e24i −0.0296003 1.70850i
\(725\) 1.13599e24i 0.552713i
\(726\) 2.02773e22 + 2.34094e24i 0.00975097 + 1.12572i
\(727\) 2.50710e24 1.19160 0.595799 0.803134i \(-0.296836\pi\)
0.595799 + 0.803134i \(0.296836\pi\)
\(728\) 4.43634e22 + 1.70686e24i 0.0208405 + 0.801828i
\(729\) −3.22019e23 −0.149519
\(730\) 1.13508e22 + 1.31041e24i 0.00520934 + 0.601401i
\(731\) 4.66482e24i 2.11611i
\(732\) 1.20077e24 2.08037e22i 0.538412 0.00932816i
\(733\) 2.50202e24i 1.10894i 0.832205 + 0.554469i \(0.187079\pi\)
−0.832205 + 0.554469i \(0.812921\pi\)
\(734\) 2.67687e24 2.31871e22i 1.17277 0.0101585i
\(735\) −1.61619e24 −0.699924
\(736\) −1.96516e24 + 8.51623e22i −0.841272 + 0.0364574i
\(737\) −7.20836e23 −0.305044
\(738\) 1.93851e24 1.67914e22i 0.810941 0.00702437i
\(739\) 1.98150e24i 0.819440i 0.912211 + 0.409720i \(0.134374\pi\)
−0.912211 + 0.409720i \(0.865626\pi\)
\(740\) 1.85549e24 3.21469e22i 0.758558 0.0131423i
\(741\) 6.64128e24i 2.68409i
\(742\) 7.51585e21 + 8.67680e23i 0.00300293 + 0.346678i
\(743\) −1.48113e24 −0.585043 −0.292521 0.956259i \(-0.594494\pi\)
−0.292521 + 0.956259i \(0.594494\pi\)
\(744\) 4.73543e21 + 1.82194e23i 0.00184922 + 0.0711480i
\(745\) 3.40900e24 1.31613
\(746\) 1.08411e22 + 1.25157e24i 0.00413803 + 0.477722i
\(747\) 5.93001e23i 0.223785i
\(748\) 1.51599e22 + 8.75013e23i 0.00565629 + 0.326476i
\(749\) 1.27411e24i 0.470013i
\(750\) −3.61782e24 + 3.13376e22i −1.31955 + 0.0114300i
\(751\) −5.06055e24 −1.82498 −0.912490 0.409100i \(-0.865843\pi\)
−0.912490 + 0.409100i \(0.865843\pi\)
\(752\) 1.41043e24 4.88868e22i 0.502919 0.0174317i
\(753\) −2.04106e24 −0.719614
\(754\) 6.09222e24 5.27709e22i 2.12383 0.0183966i
\(755\) 1.00690e24i 0.347085i
\(756\) 1.57375e22 + 9.08354e23i 0.00536415 + 0.309613i
\(757\) 1.15475e23i 0.0389200i −0.999811 0.0194600i \(-0.993805\pi\)
0.999811 0.0194600i \(-0.00619470\pi\)
\(758\) −9.94849e21 1.14852e24i −0.00331565 0.382781i
\(759\) 8.67728e23 0.285975
\(760\) −3.18101e24 + 8.26782e22i −1.03669 + 0.0269448i
\(761\) −3.07347e24 −0.990510 −0.495255 0.868748i \(-0.664925\pi\)
−0.495255 + 0.868748i \(0.664925\pi\)
\(762\) −4.55942e21 5.26370e23i −0.00145309 0.167754i
\(763\) 3.09811e22i 0.00976425i
\(764\) 3.05232e24 5.28824e22i 0.951341 0.0164823i
\(765\) 1.41743e24i 0.436899i
\(766\) −1.18734e24 + 1.02847e22i −0.361934 + 0.00313507i
\(767\) 1.56571e24 0.472008
\(768\) −2.8338