Properties

Label 8.18.b.a.5.6
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 5.6
Root \(-108.197 - 150.760i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +O(q^{10})\) \(q+(-200.394 + 301.520i) q^{2} -13481.8i q^{3} +(-50756.5 - 120846. i) q^{4} -1.59197e6i q^{5} +(4.06504e6 + 2.70168e6i) q^{6} -1.66055e7 q^{7} +(4.66086e7 + 8.91263e6i) q^{8} -5.26193e7 q^{9} +(4.80011e8 + 3.19021e8i) q^{10} +6.79322e8i q^{11} +(-1.62922e9 + 6.84290e8i) q^{12} -3.13276e9i q^{13} +(3.32765e9 - 5.00690e9i) q^{14} -2.14627e10 q^{15} +(-1.20274e10 + 1.22674e10i) q^{16} -1.26774e10 q^{17} +(1.05446e10 - 1.58658e10i) q^{18} +5.87947e9i q^{19} +(-1.92383e11 + 8.08028e10i) q^{20} +2.23873e11i q^{21} +(-2.04829e11 - 1.36132e11i) q^{22} +5.43400e11 q^{23} +(1.20158e11 - 6.28369e11i) q^{24} -1.77143e12 q^{25} +(9.44589e11 + 6.27786e11i) q^{26} -1.03164e12i q^{27} +(8.42839e11 + 2.00671e12i) q^{28} +2.82120e12i q^{29} +(4.30099e12 - 6.47142e12i) q^{30} +8.42117e11 q^{31} +(-1.28864e12 - 6.08482e12i) q^{32} +9.15850e12 q^{33} +(2.54047e12 - 3.82248e12i) q^{34} +2.64355e13i q^{35} +(2.67077e12 + 6.35881e12i) q^{36} +6.17985e12i q^{37} +(-1.77278e12 - 1.17821e12i) q^{38} -4.22353e13 q^{39} +(1.41886e13 - 7.41996e13i) q^{40} -6.38887e13 q^{41} +(-6.75021e13 - 4.48628e13i) q^{42} +5.41782e13i q^{43} +(8.20931e13 - 3.44800e13i) q^{44} +8.37684e13i q^{45} +(-1.08894e14 + 1.63846e14i) q^{46} -3.89159e13 q^{47} +(1.65387e14 + 1.62152e14i) q^{48} +4.31135e13 q^{49} +(3.54984e14 - 5.34121e14i) q^{50} +1.70914e14i q^{51} +(-3.78580e14 + 1.59008e14i) q^{52} -5.92171e14i q^{53} +(3.11060e14 + 2.06734e14i) q^{54} +1.08146e15 q^{55} +(-7.73962e14 - 1.47999e14i) q^{56} +7.92660e13 q^{57} +(-8.50647e14 - 5.65351e14i) q^{58} -7.11422e14i q^{59} +(1.08937e15 + 2.59367e15i) q^{60} -9.01392e14i q^{61} +(-1.68755e14 + 2.53915e14i) q^{62} +8.73773e14 q^{63} +(2.09293e15 + 8.30811e14i) q^{64} -4.98726e15 q^{65} +(-1.83531e15 + 2.76147e15i) q^{66} +8.96950e14i q^{67} +(6.43458e14 + 1.53200e15i) q^{68} -7.32602e15i q^{69} +(-7.97084e15 - 5.29752e15i) q^{70} +8.49830e13 q^{71} +(-2.45252e15 - 4.68977e14i) q^{72} +1.01538e16 q^{73} +(-1.86335e15 - 1.23840e15i) q^{74} +2.38821e16i q^{75} +(7.10508e14 - 2.98421e14i) q^{76} -1.12805e16i q^{77} +(8.46370e15 - 1.27348e16i) q^{78} +3.99449e15 q^{79} +(1.95293e16 + 1.91473e16i) q^{80} -2.07037e16 q^{81} +(1.28029e16 - 1.92637e16i) q^{82} -2.19564e15i q^{83} +(2.70540e16 - 1.13630e16i) q^{84} +2.01820e16i q^{85} +(-1.63358e16 - 1.08570e16i) q^{86} +3.80349e16 q^{87} +(-6.05455e15 + 3.16623e16i) q^{88} -6.74113e16 q^{89} +(-2.52578e16 - 1.67867e16i) q^{90} +5.20212e16i q^{91} +(-2.75811e16 - 6.56674e16i) q^{92} -1.13533e16i q^{93} +(7.79850e15 - 1.17339e16i) q^{94} +9.35994e15 q^{95} +(-8.20345e16 + 1.73732e16i) q^{96} -1.67025e15 q^{97} +(-8.63968e15 + 1.29996e16i) q^{98} -3.57455e16i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −200.394 + 301.520i −0.553515 + 0.832839i
\(3\) 13481.8i 1.18636i −0.805068 0.593182i \(-0.797871\pi\)
0.805068 0.593182i \(-0.202129\pi\)
\(4\) −50756.5 120846.i −0.387241 0.921978i
\(5\) 1.59197e6i 1.82259i −0.411750 0.911297i \(-0.635082\pi\)
0.411750 0.911297i \(-0.364918\pi\)
\(6\) 4.06504e6 + 2.70168e6i 0.988050 + 0.656671i
\(7\) −1.66055e7 −1.08873 −0.544364 0.838849i \(-0.683229\pi\)
−0.544364 + 0.838849i \(0.683229\pi\)
\(8\) 4.66086e7 + 8.91263e6i 0.982204 + 0.187820i
\(9\) −5.26193e7 −0.407459
\(10\) 4.80011e8 + 3.19021e8i 1.51793 + 1.00883i
\(11\) 6.79322e8i 0.955516i 0.878492 + 0.477758i \(0.158550\pi\)
−0.878492 + 0.477758i \(0.841450\pi\)
\(12\) −1.62922e9 + 6.84290e8i −1.09380 + 0.459409i
\(13\) 3.13276e9i 1.06514i −0.846385 0.532572i \(-0.821225\pi\)
0.846385 0.532572i \(-0.178775\pi\)
\(14\) 3.32765e9 5.00690e9i 0.602628 0.906736i
\(15\) −2.14627e10 −2.16226
\(16\) −1.20274e10 + 1.22674e10i −0.700088 + 0.714056i
\(17\) −1.26774e10 −0.440771 −0.220385 0.975413i \(-0.570732\pi\)
−0.220385 + 0.975413i \(0.570732\pi\)
\(18\) 1.05446e10 1.58658e10i 0.225535 0.339348i
\(19\) 5.87947e9i 0.0794205i 0.999211 + 0.0397103i \(0.0126435\pi\)
−0.999211 + 0.0397103i \(0.987357\pi\)
\(20\) −1.92383e11 + 8.08028e10i −1.68039 + 0.705784i
\(21\) 2.23873e11i 1.29163i
\(22\) −2.04829e11 1.36132e11i −0.795791 0.528893i
\(23\) 5.43400e11 1.44688 0.723441 0.690387i \(-0.242560\pi\)
0.723441 + 0.690387i \(0.242560\pi\)
\(24\) 1.20158e11 6.28369e11i 0.222822 1.16525i
\(25\) −1.77143e12 −2.32185
\(26\) 9.44589e11 + 6.27786e11i 0.887094 + 0.589574i
\(27\) 1.03164e12i 0.702969i
\(28\) 8.42839e11 + 2.00671e12i 0.421601 + 1.00378i
\(29\) 2.82120e12i 1.04725i 0.851949 + 0.523625i \(0.175421\pi\)
−0.851949 + 0.523625i \(0.824579\pi\)
\(30\) 4.30099e12 6.47142e12i 1.19684 1.80081i
\(31\) 8.42117e11 0.177336 0.0886682 0.996061i \(-0.471739\pi\)
0.0886682 + 0.996061i \(0.471739\pi\)
\(32\) −1.28864e12 6.08482e12i −0.207184 0.978302i
\(33\) 9.15850e12 1.13359
\(34\) 2.54047e12 3.82248e12i 0.243974 0.367091i
\(35\) 2.64355e13i 1.98431i
\(36\) 2.67077e12 + 6.35881e12i 0.157785 + 0.375669i
\(37\) 6.17985e12i 0.289243i 0.989487 + 0.144622i \(0.0461965\pi\)
−0.989487 + 0.144622i \(0.953804\pi\)
\(38\) −1.77278e12 1.17821e12i −0.0661445 0.0439605i
\(39\) −4.22353e13 −1.26365
\(40\) 1.41886e13 7.41996e13i 0.342319 1.79016i
\(41\) −6.38887e13 −1.24957 −0.624786 0.780796i \(-0.714814\pi\)
−0.624786 + 0.780796i \(0.714814\pi\)
\(42\) −6.75021e13 4.48628e13i −1.07572 0.714936i
\(43\) 5.41782e13i 0.706875i 0.935458 + 0.353438i \(0.114987\pi\)
−0.935458 + 0.353438i \(0.885013\pi\)
\(44\) 8.20931e13 3.44800e13i 0.880965 0.370015i
\(45\) 8.37684e13i 0.742633i
\(46\) −1.08894e14 + 1.63846e14i −0.800871 + 1.20502i
\(47\) −3.89159e13 −0.238394 −0.119197 0.992871i \(-0.538032\pi\)
−0.119197 + 0.992871i \(0.538032\pi\)
\(48\) 1.65387e14 + 1.62152e14i 0.847131 + 0.830559i
\(49\) 4.31135e13 0.185330
\(50\) 3.54984e14 5.34121e14i 1.28518 1.93373i
\(51\) 1.70914e14i 0.522915i
\(52\) −3.78580e14 + 1.59008e14i −0.982040 + 0.412468i
\(53\) 5.92171e14i 1.30648i −0.757152 0.653239i \(-0.773410\pi\)
0.757152 0.653239i \(-0.226590\pi\)
\(54\) 3.11060e14 + 2.06734e14i 0.585460 + 0.389104i
\(55\) 1.08146e15 1.74152
\(56\) −7.73962e14 1.47999e14i −1.06935 0.204485i
\(57\) 7.92660e13 0.0942216
\(58\) −8.50647e14 5.65351e14i −0.872191 0.579669i
\(59\) 7.11422e14i 0.630791i −0.948960 0.315395i \(-0.897863\pi\)
0.948960 0.315395i \(-0.102137\pi\)
\(60\) 1.08937e15 + 2.59367e15i 0.837316 + 1.99356i
\(61\) 9.01392e14i 0.602019i −0.953621 0.301009i \(-0.902676\pi\)
0.953621 0.301009i \(-0.0973236\pi\)
\(62\) −1.68755e14 + 2.53915e14i −0.0981585 + 0.147693i
\(63\) 8.73773e14 0.443612
\(64\) 2.09293e15 + 8.30811e14i 0.929448 + 0.368954i
\(65\) −4.98726e15 −1.94133
\(66\) −1.83531e15 + 2.76147e15i −0.627459 + 0.944097i
\(67\) 8.96950e14i 0.269856i 0.990855 + 0.134928i \(0.0430804\pi\)
−0.990855 + 0.134928i \(0.956920\pi\)
\(68\) 6.43458e14 + 1.53200e15i 0.170685 + 0.406381i
\(69\) 7.32602e15i 1.71653i
\(70\) −7.97084e15 5.29752e15i −1.65261 1.09835i
\(71\) 8.49830e13 0.0156184 0.00780919 0.999970i \(-0.497514\pi\)
0.00780919 + 0.999970i \(0.497514\pi\)
\(72\) −2.45252e15 4.68977e14i −0.400208 0.0765288i
\(73\) 1.01538e16 1.47361 0.736806 0.676104i \(-0.236333\pi\)
0.736806 + 0.676104i \(0.236333\pi\)
\(74\) −1.86335e15 1.23840e15i −0.240893 0.160101i
\(75\) 2.38821e16i 2.75456i
\(76\) 7.10508e14 2.98421e14i 0.0732240 0.0307549i
\(77\) 1.12805e16i 1.04030i
\(78\) 8.46370e15 1.27348e16i 0.699449 1.05242i
\(79\) 3.99449e15 0.296232 0.148116 0.988970i \(-0.452679\pi\)
0.148116 + 0.988970i \(0.452679\pi\)
\(80\) 1.95293e16 + 1.91473e16i 1.30143 + 1.27598i
\(81\) −2.07037e16 −1.24144
\(82\) 1.28029e16 1.92637e16i 0.691658 1.04069i
\(83\) 2.19564e15i 0.107003i −0.998568 0.0535016i \(-0.982962\pi\)
0.998568 0.0535016i \(-0.0170382\pi\)
\(84\) 2.70540e16 1.13630e16i 1.19085 0.500172i
\(85\) 2.01820e16i 0.803346i
\(86\) −1.63358e16 1.08570e16i −0.588713 0.391266i
\(87\) 3.80349e16 1.24242
\(88\) −6.05455e15 + 3.16623e16i −0.179465 + 0.938511i
\(89\) −6.74113e16 −1.81517 −0.907586 0.419866i \(-0.862077\pi\)
−0.907586 + 0.419866i \(0.862077\pi\)
\(90\) −2.52578e16 1.67867e16i −0.618493 0.411059i
\(91\) 5.20212e16i 1.15965i
\(92\) −2.75811e16 6.56674e16i −0.560292 1.33399i
\(93\) 1.13533e16i 0.210386i
\(94\) 7.79850e15 1.17339e16i 0.131955 0.198544i
\(95\) 9.35994e15 0.144751
\(96\) −8.20345e16 + 1.73732e16i −1.16062 + 0.245796i
\(97\) −1.67025e15 −0.0216383 −0.0108191 0.999941i \(-0.503444\pi\)
−0.0108191 + 0.999941i \(0.503444\pi\)
\(98\) −8.63968e15 + 1.29996e16i −0.102583 + 0.154350i
\(99\) 3.57455e16i 0.389334i
\(100\) 8.99116e16 + 2.14069e17i 0.899116 + 2.14069i
\(101\) 9.20491e16i 0.845840i −0.906167 0.422920i \(-0.861005\pi\)
0.906167 0.422920i \(-0.138995\pi\)
\(102\) −5.15339e16 3.42501e16i −0.435504 0.289441i
\(103\) −1.51701e17 −1.17998 −0.589988 0.807412i \(-0.700868\pi\)
−0.589988 + 0.807412i \(0.700868\pi\)
\(104\) 2.79211e16 1.46014e17i 0.200055 1.04619i
\(105\) 3.56399e17 2.35411
\(106\) 1.78551e17 + 1.18667e17i 1.08809 + 0.723156i
\(107\) 4.02158e15i 0.0226274i 0.999936 + 0.0113137i \(0.00360134\pi\)
−0.999936 + 0.0113137i \(0.996399\pi\)
\(108\) −1.24669e17 + 5.23624e16i −0.648122 + 0.272219i
\(109\) 6.68975e16i 0.321577i −0.986989 0.160788i \(-0.948596\pi\)
0.986989 0.160788i \(-0.0514037\pi\)
\(110\) −2.16718e17 + 3.26082e17i −0.963957 + 1.45040i
\(111\) 8.33156e16 0.343148
\(112\) 1.99722e17 2.03707e17i 0.762206 0.777414i
\(113\) −1.74001e17 −0.615721 −0.307860 0.951432i \(-0.599613\pi\)
−0.307860 + 0.951432i \(0.599613\pi\)
\(114\) −1.58844e16 + 2.39003e16i −0.0521531 + 0.0784714i
\(115\) 8.65076e17i 2.63708i
\(116\) 3.40929e17 1.43194e17i 0.965542 0.405539i
\(117\) 1.64844e17i 0.434003i
\(118\) 2.14508e17 + 1.42565e17i 0.525347 + 0.349153i
\(119\) 2.10514e17 0.479880
\(120\) −1.00035e18 1.91289e17i −2.12378 0.406115i
\(121\) 4.39685e16 0.0869893
\(122\) 2.71788e17 + 1.80634e17i 0.501385 + 0.333227i
\(123\) 8.61336e17i 1.48245i
\(124\) −4.27429e16 1.01766e17i −0.0686720 0.163500i
\(125\) 1.60549e18i 2.40919i
\(126\) −1.75099e17 + 2.63460e17i −0.245546 + 0.369458i
\(127\) −9.21764e17 −1.20861 −0.604307 0.796751i \(-0.706550\pi\)
−0.604307 + 0.796751i \(0.706550\pi\)
\(128\) −6.69917e17 + 4.64571e17i −0.821743 + 0.569858i
\(129\) 7.30421e17 0.838611
\(130\) 9.99417e17 1.50376e18i 1.07455 1.61681i
\(131\) 1.81435e18i 1.82774i −0.406003 0.913872i \(-0.633078\pi\)
0.406003 0.913872i \(-0.366922\pi\)
\(132\) −4.64853e17 1.10676e18i −0.438973 1.04515i
\(133\) 9.76318e16i 0.0864674i
\(134\) −2.70448e17 1.79743e17i −0.224747 0.149370i
\(135\) −1.64234e18 −1.28123
\(136\) −5.90874e17 1.12989e17i −0.432927 0.0827854i
\(137\) −2.37631e18 −1.63598 −0.817989 0.575234i \(-0.804911\pi\)
−0.817989 + 0.575234i \(0.804911\pi\)
\(138\) 2.20894e18 + 1.46809e18i 1.42959 + 0.950124i
\(139\) 2.37238e18i 1.44397i 0.691908 + 0.721986i \(0.256770\pi\)
−0.691908 + 0.721986i \(0.743230\pi\)
\(140\) 3.19462e18 1.34177e18i 1.82949 0.768407i
\(141\) 5.24657e17i 0.282822i
\(142\) −1.70301e16 + 2.56241e16i −0.00864501 + 0.0130076i
\(143\) 2.12815e18 1.01776
\(144\) 6.32875e17 6.45502e17i 0.285257 0.290949i
\(145\) 4.49126e18 1.90871
\(146\) −2.03476e18 + 3.06157e18i −0.815667 + 1.22728i
\(147\) 5.81248e17i 0.219869i
\(148\) 7.46807e17 3.13668e17i 0.266676 0.112007i
\(149\) 4.84759e17i 0.163472i −0.996654 0.0817359i \(-0.973954\pi\)
0.996654 0.0817359i \(-0.0260464\pi\)
\(150\) −7.20093e18 4.78583e18i −2.29410 1.52469i
\(151\) 3.48930e18 1.05059 0.525296 0.850920i \(-0.323955\pi\)
0.525296 + 0.850920i \(0.323955\pi\)
\(152\) −5.24015e16 + 2.74034e17i −0.0149167 + 0.0780071i
\(153\) 6.67074e17 0.179596
\(154\) 3.40130e18 + 2.26055e18i 0.866400 + 0.575821i
\(155\) 1.34063e18i 0.323212i
\(156\) 2.14372e18 + 5.10395e18i 0.489337 + 1.16506i
\(157\) 5.04719e18i 1.09120i −0.838047 0.545598i \(-0.816303\pi\)
0.838047 0.545598i \(-0.183697\pi\)
\(158\) −8.00472e17 + 1.20442e18i −0.163969 + 0.246713i
\(159\) −7.98354e18 −1.54996
\(160\) −9.68685e18 + 2.05148e18i −1.78305 + 0.377613i
\(161\) −9.02345e18 −1.57526
\(162\) 4.14889e18 6.24256e18i 0.687154 1.03392i
\(163\) 4.62747e18i 0.727359i 0.931524 + 0.363680i \(0.118480\pi\)
−0.931524 + 0.363680i \(0.881520\pi\)
\(164\) 3.24277e18 + 7.72067e18i 0.483886 + 1.15208i
\(165\) 1.45801e19i 2.06607i
\(166\) 6.62028e17 + 4.39993e17i 0.0891164 + 0.0592279i
\(167\) 6.00884e18 0.768600 0.384300 0.923208i \(-0.374443\pi\)
0.384300 + 0.923208i \(0.374443\pi\)
\(168\) −1.99530e18 + 1.04344e19i −0.242593 + 1.26864i
\(169\) −1.16377e18 −0.134533
\(170\) −6.08527e18 4.04435e18i −0.669058 0.444665i
\(171\) 3.09374e17i 0.0323606i
\(172\) 6.54720e18 2.74990e18i 0.651724 0.273731i
\(173\) 1.31182e19i 1.24304i 0.783400 + 0.621518i \(0.213484\pi\)
−0.783400 + 0.621518i \(0.786516\pi\)
\(174\) −7.62196e18 + 1.14683e19i −0.687699 + 1.03474i
\(175\) 2.94155e19 2.52786
\(176\) −8.33351e18 8.17050e18i −0.682292 0.668946i
\(177\) −9.59127e18 −0.748348
\(178\) 1.35088e19 2.03259e19i 1.00473 1.51175i
\(179\) 1.01351e19i 0.718749i 0.933193 + 0.359375i \(0.117010\pi\)
−0.933193 + 0.359375i \(0.882990\pi\)
\(180\) 1.01230e19 4.25179e18i 0.684691 0.287578i
\(181\) 5.37640e18i 0.346916i −0.984841 0.173458i \(-0.944506\pi\)
0.984841 0.173458i \(-0.0554940\pi\)
\(182\) −1.56854e19 1.04247e19i −0.965805 0.641886i
\(183\) −1.21524e19 −0.714213
\(184\) 2.53271e19 + 4.84312e18i 1.42113 + 0.271753i
\(185\) 9.83814e18 0.527173
\(186\) 3.42324e18 + 2.27513e18i 0.175217 + 0.116452i
\(187\) 8.61201e18i 0.421164i
\(188\) 1.97523e18 + 4.70281e18i 0.0923159 + 0.219794i
\(189\) 1.71309e19i 0.765343i
\(190\) −1.87568e18 + 2.82221e18i −0.0801221 + 0.120555i
\(191\) −3.15290e19 −1.28803 −0.644016 0.765012i \(-0.722733\pi\)
−0.644016 + 0.765012i \(0.722733\pi\)
\(192\) 1.12008e19 2.82165e19i 0.437714 1.10266i
\(193\) 5.88587e18 0.220077 0.110038 0.993927i \(-0.464903\pi\)
0.110038 + 0.993927i \(0.464903\pi\)
\(194\) 3.34709e17 5.03615e17i 0.0119771 0.0180212i
\(195\) 6.72373e19i 2.30312i
\(196\) −2.18829e18 5.21007e18i −0.0717675 0.170870i
\(197\) 4.95627e19i 1.55665i −0.627859 0.778327i \(-0.716069\pi\)
0.627859 0.778327i \(-0.283931\pi\)
\(198\) 1.07780e19 + 7.16318e18i 0.324252 + 0.215502i
\(199\) −2.52157e19 −0.726810 −0.363405 0.931631i \(-0.618386\pi\)
−0.363405 + 0.931631i \(0.618386\pi\)
\(200\) −8.25639e19 1.57881e19i −2.28053 0.436089i
\(201\) 1.20925e19 0.320148
\(202\) 2.77546e19 + 1.84461e19i 0.704448 + 0.468185i
\(203\) 4.68475e19i 1.14017i
\(204\) 2.06542e19 8.67499e18i 0.482116 0.202494i
\(205\) 1.01709e20i 2.27746i
\(206\) 3.04001e19 4.57410e19i 0.653135 0.982731i
\(207\) −2.85933e19 −0.589545
\(208\) 3.84308e19 + 3.76790e19i 0.760573 + 0.745695i
\(209\) −3.99405e18 −0.0758876
\(210\) −7.14202e19 + 1.07461e20i −1.30304 + 1.96060i
\(211\) 9.05451e19i 1.58659i −0.608839 0.793294i \(-0.708364\pi\)
0.608839 0.793294i \(-0.291636\pi\)
\(212\) −7.15612e19 + 3.00565e19i −1.20454 + 0.505922i
\(213\) 1.14573e18i 0.0185291i
\(214\) −1.21259e18 8.05901e17i −0.0188450 0.0125246i
\(215\) 8.62501e19 1.28835
\(216\) 9.19462e18 4.80833e19i 0.132031 0.690459i
\(217\) −1.39838e19 −0.193071
\(218\) 2.01709e19 + 1.34059e19i 0.267822 + 0.177998i
\(219\) 1.36891e20i 1.74824i
\(220\) −5.48912e19 1.30690e20i −0.674388 1.60564i
\(221\) 3.97151e19i 0.469485i
\(222\) −1.66959e19 + 2.51213e19i −0.189938 + 0.285787i
\(223\) 1.01974e20 1.11660 0.558302 0.829637i \(-0.311453\pi\)
0.558302 + 0.829637i \(0.311453\pi\)
\(224\) 2.13986e19 + 1.01042e20i 0.225567 + 1.06511i
\(225\) 9.32115e19 0.946058
\(226\) 3.48687e19 5.24646e19i 0.340811 0.512796i
\(227\) 4.34756e18i 0.0409285i 0.999791 + 0.0204643i \(0.00651443\pi\)
−0.999791 + 0.0204643i \(0.993486\pi\)
\(228\) −4.02326e18 9.57894e18i −0.0364865 0.0868703i
\(229\) 5.56510e19i 0.486263i −0.969993 0.243132i \(-0.921825\pi\)
0.969993 0.243132i \(-0.0781747\pi\)
\(230\) 2.60838e20 + 1.73356e20i 2.19626 + 1.45966i
\(231\) −1.52082e20 −1.23417
\(232\) −2.51443e19 + 1.31492e20i −0.196694 + 1.02861i
\(233\) 8.39273e19 0.632963 0.316481 0.948599i \(-0.397499\pi\)
0.316481 + 0.948599i \(0.397499\pi\)
\(234\) −4.97037e19 3.30337e19i −0.361455 0.240227i
\(235\) 6.19529e19i 0.434495i
\(236\) −8.59722e19 + 3.61093e19i −0.581576 + 0.244268i
\(237\) 5.38530e19i 0.351438i
\(238\) −4.21858e19 + 6.34743e19i −0.265621 + 0.399663i
\(239\) −2.51863e20 −1.53032 −0.765158 0.643842i \(-0.777339\pi\)
−0.765158 + 0.643842i \(0.777339\pi\)
\(240\) 2.58141e20 2.63291e20i 1.51377 1.54397i
\(241\) −5.48650e19 −0.310563 −0.155282 0.987870i \(-0.549629\pi\)
−0.155282 + 0.987870i \(0.549629\pi\)
\(242\) −8.81102e18 + 1.32574e19i −0.0481499 + 0.0724481i
\(243\) 1.45897e20i 0.769826i
\(244\) −1.08929e20 + 4.57515e19i −0.555048 + 0.233127i
\(245\) 6.86353e19i 0.337782i
\(246\) −2.59710e20 1.72607e20i −1.23464 0.820558i
\(247\) 1.84190e19 0.0845943
\(248\) 3.92499e19 + 7.50548e18i 0.174181 + 0.0333073i
\(249\) −2.96012e19 −0.126945
\(250\) −4.84086e20 3.21730e20i −2.00647 1.33353i
\(251\) 2.36559e20i 0.947792i 0.880581 + 0.473896i \(0.157153\pi\)
−0.880581 + 0.473896i \(0.842847\pi\)
\(252\) −4.43496e19 1.05592e20i −0.171785 0.409001i
\(253\) 3.69143e20i 1.38252i
\(254\) 1.84716e20 2.77930e20i 0.668987 1.00658i
\(255\) 2.72090e20 0.953061
\(256\) −5.83000e18 2.95090e20i −0.0197528 0.999805i
\(257\) −1.56566e20 −0.513177 −0.256588 0.966521i \(-0.582598\pi\)
−0.256588 + 0.966521i \(0.582598\pi\)
\(258\) −1.46372e20 + 2.20237e20i −0.464184 + 0.698428i
\(259\) 1.02620e20i 0.314907i
\(260\) 2.53136e20 + 6.02688e20i 0.751762 + 1.78986i
\(261\) 1.48450e20i 0.426712i
\(262\) 5.47063e20 + 3.63585e20i 1.52222 + 1.01168i
\(263\) 4.99732e20 1.34621 0.673106 0.739546i \(-0.264960\pi\)
0.673106 + 0.739546i \(0.264960\pi\)
\(264\) 4.26865e20 + 8.16263e19i 1.11342 + 0.212910i
\(265\) −9.42718e20 −2.38118
\(266\) 2.94379e19 + 1.95648e19i 0.0720134 + 0.0478610i
\(267\) 9.08827e20i 2.15345i
\(268\) 1.08392e20 4.55261e19i 0.248802 0.104500i
\(269\) 4.92718e20i 1.09573i −0.836566 0.547865i \(-0.815441\pi\)
0.836566 0.547865i \(-0.184559\pi\)
\(270\) 3.29115e20 4.95198e20i 0.709179 1.06706i
\(271\) −1.88474e20 −0.393561 −0.196780 0.980448i \(-0.563049\pi\)
−0.196780 + 0.980448i \(0.563049\pi\)
\(272\) 1.52476e20 1.55518e20i 0.308579 0.314735i
\(273\) 7.01340e20 1.37577
\(274\) 4.76197e20 7.16504e20i 0.905539 1.36251i
\(275\) 1.20337e21i 2.21856i
\(276\) −8.85317e20 + 3.71843e20i −1.58260 + 0.664710i
\(277\) 4.10225e20i 0.711122i −0.934653 0.355561i \(-0.884290\pi\)
0.934653 0.355561i \(-0.115710\pi\)
\(278\) −7.15320e20 4.75411e20i −1.20260 0.799260i
\(279\) −4.43116e19 −0.0722574
\(280\) −2.35610e20 + 1.23212e21i −0.372692 + 1.94900i
\(281\) 5.23813e20 0.803845 0.401922 0.915674i \(-0.368342\pi\)
0.401922 + 0.915674i \(0.368342\pi\)
\(282\) −1.58194e20 1.05138e20i −0.235545 0.156546i
\(283\) 8.12727e20i 1.17425i 0.809497 + 0.587124i \(0.199740\pi\)
−0.809497 + 0.587124i \(0.800260\pi\)
\(284\) −4.31344e18 1.02698e19i −0.00604808 0.0143998i
\(285\) 1.26189e20i 0.171728i
\(286\) −4.26469e20 + 6.41680e20i −0.563347 + 0.847632i
\(287\) 1.06091e21 1.36045
\(288\) 6.78074e19 + 3.20179e20i 0.0844191 + 0.398618i
\(289\) −6.66525e20 −0.805721
\(290\) −9.00022e20 + 1.35421e21i −1.05650 + 1.58965i
\(291\) 2.25181e19i 0.0256709i
\(292\) −5.15370e20 1.22704e21i −0.570644 1.35864i
\(293\) 1.33596e20i 0.143687i 0.997416 + 0.0718436i \(0.0228882\pi\)
−0.997416 + 0.0718436i \(0.977112\pi\)
\(294\) 1.75258e20 + 1.16479e20i 0.183115 + 0.121701i
\(295\) −1.13256e21 −1.14968
\(296\) −5.50787e19 + 2.88034e20i −0.0543255 + 0.284096i
\(297\) 7.00816e20 0.671698
\(298\) 1.46165e20 + 9.71428e19i 0.136146 + 0.0904841i
\(299\) 1.70234e21i 1.54114i
\(300\) 2.88605e21 1.21217e21i 2.53964 1.06668i
\(301\) 8.99659e20i 0.769596i
\(302\) −6.99234e20 + 1.05209e21i −0.581519 + 0.874974i
\(303\) −1.24099e21 −1.00347
\(304\) −7.21258e19 7.07149e19i −0.0567107 0.0556014i
\(305\) −1.43499e21 −1.09724
\(306\) −1.33678e20 + 2.01136e20i −0.0994092 + 0.149575i
\(307\) 1.20452e21i 0.871243i 0.900130 + 0.435622i \(0.143471\pi\)
−0.900130 + 0.435622i \(0.856529\pi\)
\(308\) −1.36320e21 + 5.72559e20i −0.959132 + 0.402846i
\(309\) 2.04521e21i 1.39988i
\(310\) 4.04225e20 + 2.68653e20i 0.269184 + 0.178903i
\(311\) 1.25790e21 0.815050 0.407525 0.913194i \(-0.366392\pi\)
0.407525 + 0.913194i \(0.366392\pi\)
\(312\) −1.96853e21 3.76428e20i −1.24116 0.237338i
\(313\) 2.89626e21 1.77709 0.888546 0.458787i \(-0.151716\pi\)
0.888546 + 0.458787i \(0.151716\pi\)
\(314\) 1.52183e21 + 1.01143e21i 0.908790 + 0.603993i
\(315\) 1.39102e21i 0.808525i
\(316\) −2.02746e20 4.82717e20i −0.114713 0.273119i
\(317\) 5.55170e20i 0.305789i −0.988242 0.152895i \(-0.951140\pi\)
0.988242 0.152895i \(-0.0488595\pi\)
\(318\) 1.59985e21 2.40720e21i 0.857926 1.29087i
\(319\) −1.91650e21 −1.00066
\(320\) 1.32263e21 3.33188e21i 0.672454 1.69401i
\(321\) 5.42182e19 0.0268443
\(322\) 1.80824e21 2.72075e21i 0.871931 1.31194i
\(323\) 7.45362e19i 0.0350063i
\(324\) 1.05085e21 + 2.50194e21i 0.480735 + 1.14458i
\(325\) 5.54946e21i 2.47310i
\(326\) −1.39527e21 9.27317e20i −0.605773 0.402605i
\(327\) −9.01900e20 −0.381507
\(328\) −2.97777e21 5.69416e20i −1.22733 0.234694i
\(329\) 6.46219e20 0.259546
\(330\) 4.39618e21 + 2.92176e21i 1.72071 + 1.14360i
\(331\) 8.74883e20i 0.333743i −0.985979 0.166871i \(-0.946634\pi\)
0.985979 0.166871i \(-0.0533665\pi\)
\(332\) −2.65333e20 + 1.11443e20i −0.0986547 + 0.0414361i
\(333\) 3.25180e20i 0.117855i
\(334\) −1.20414e21 + 1.81178e21i −0.425432 + 0.640120i
\(335\) 1.42792e21 0.491839
\(336\) −2.74634e21 2.69261e21i −0.922295 0.904254i
\(337\) 1.38557e21 0.453706 0.226853 0.973929i \(-0.427156\pi\)
0.226853 + 0.973929i \(0.427156\pi\)
\(338\) 2.33212e20 3.50899e20i 0.0744661 0.112044i
\(339\) 2.34584e21i 0.730469i
\(340\) 2.43890e21 1.02437e21i 0.740668 0.311089i
\(341\) 5.72069e20i 0.169448i
\(342\) 9.32824e19 + 6.19967e19i 0.0269512 + 0.0179121i
\(343\) 3.14703e21 0.886954
\(344\) −4.82870e20 + 2.52517e21i −0.132765 + 0.694296i
\(345\) −1.16628e22 −3.12853
\(346\) −3.95541e21 2.62882e21i −1.03525 0.688040i
\(347\) 3.85582e21i 0.984727i −0.870390 0.492364i \(-0.836133\pi\)
0.870390 0.492364i \(-0.163867\pi\)
\(348\) −1.93052e21 4.59635e21i −0.481116 1.14548i
\(349\) 1.47067e20i 0.0357684i 0.999840 + 0.0178842i \(0.00569302\pi\)
−0.999840 + 0.0178842i \(0.994307\pi\)
\(350\) −5.89470e21 + 8.86937e21i −1.39921 + 2.10530i
\(351\) −3.23188e21 −0.748764
\(352\) 4.13355e21 8.75401e20i 0.934783 0.197968i
\(353\) 5.92536e21 1.30807 0.654033 0.756466i \(-0.273076\pi\)
0.654033 + 0.756466i \(0.273076\pi\)
\(354\) 1.92203e21 2.89196e21i 0.414222 0.623253i
\(355\) 1.35290e20i 0.0284660i
\(356\) 3.42156e21 + 8.14636e21i 0.702910 + 1.67355i
\(357\) 2.83812e21i 0.569312i
\(358\) −3.05593e21 2.03101e21i −0.598602 0.397839i
\(359\) −7.67655e21 −1.46846 −0.734232 0.678899i \(-0.762457\pi\)
−0.734232 + 0.678899i \(0.762457\pi\)
\(360\) −7.46597e20 + 3.90433e21i −0.139481 + 0.729416i
\(361\) 5.44582e21 0.993692
\(362\) 1.62109e21 + 1.07740e21i 0.288925 + 0.192023i
\(363\) 5.92775e20i 0.103201i
\(364\) 6.28653e21 2.64041e21i 1.06918 0.449066i
\(365\) 1.61645e22i 2.68580i
\(366\) 2.43527e21 3.66419e21i 0.395328 0.594825i
\(367\) 1.69701e21 0.269168 0.134584 0.990902i \(-0.457030\pi\)
0.134584 + 0.990902i \(0.457030\pi\)
\(368\) −6.53570e21 + 6.66610e21i −1.01294 + 1.03315i
\(369\) 3.36178e21 0.509150
\(370\) −1.97150e21 + 2.96639e21i −0.291798 + 0.439050i
\(371\) 9.83331e21i 1.42240i
\(372\) −1.37199e21 + 5.76252e20i −0.193971 + 0.0814700i
\(373\) 2.45745e21i 0.339594i −0.985479 0.169797i \(-0.945689\pi\)
0.985479 0.169797i \(-0.0543113\pi\)
\(374\) 2.59669e21 + 1.72580e21i 0.350762 + 0.233121i
\(375\) 2.16449e22 2.85818
\(376\) −1.81382e21 3.46843e20i −0.234151 0.0447750i
\(377\) 8.83814e21 1.11547
\(378\) −5.16532e21 3.43294e21i −0.637407 0.423629i
\(379\) 5.05987e21i 0.610529i 0.952268 + 0.305264i \(0.0987448\pi\)
−0.952268 + 0.305264i \(0.901255\pi\)
\(380\) −4.75078e20 1.13111e21i −0.0560537 0.133458i
\(381\) 1.24271e22i 1.43386i
\(382\) 6.31822e21 9.50662e21i 0.712945 1.07272i
\(383\) 2.16009e21 0.238387 0.119194 0.992871i \(-0.461969\pi\)
0.119194 + 0.992871i \(0.461969\pi\)
\(384\) 6.26326e21 + 9.03170e21i 0.676059 + 0.974886i
\(385\) −1.79582e22 −1.89604
\(386\) −1.17949e21 + 1.77471e21i −0.121816 + 0.183288i
\(387\) 2.85082e21i 0.288023i
\(388\) 8.47762e19 + 2.01843e20i 0.00837923 + 0.0199500i
\(389\) 1.57073e22i 1.51891i −0.650562 0.759453i \(-0.725467\pi\)
0.650562 0.759453i \(-0.274533\pi\)
\(390\) −2.02734e22 1.34740e22i −1.91813 1.27481i
\(391\) −6.88887e21 −0.637743
\(392\) 2.00946e21 + 3.84254e20i 0.182032 + 0.0348086i
\(393\) −2.44607e22 −2.16837
\(394\) 1.49441e22 + 9.93207e21i 1.29644 + 0.861632i
\(395\) 6.35911e21i 0.539910i
\(396\) −4.31968e21 + 1.81432e21i −0.358957 + 0.150766i
\(397\) 1.27818e21i 0.103961i 0.998648 + 0.0519807i \(0.0165534\pi\)
−0.998648 + 0.0519807i \(0.983447\pi\)
\(398\) 5.05308e21 7.60305e21i 0.402300 0.605315i
\(399\) −1.31625e21 −0.102582
\(400\) 2.13057e22 2.17308e22i 1.62550 1.65793i
\(401\) −1.13639e22 −0.848793 −0.424396 0.905477i \(-0.639514\pi\)
−0.424396 + 0.905477i \(0.639514\pi\)
\(402\) −2.42327e21 + 3.64614e21i −0.177207 + 0.266632i
\(403\) 2.63815e21i 0.188889i
\(404\) −1.11237e22 + 4.67209e21i −0.779846 + 0.327544i
\(405\) 3.29596e22i 2.26263i
\(406\) 1.41255e22 + 9.38796e21i 0.949579 + 0.631103i
\(407\) −4.19811e21 −0.276377
\(408\) −1.52329e21 + 7.96606e21i −0.0982136 + 0.513609i
\(409\) 1.19704e22 0.755891 0.377945 0.925828i \(-0.376631\pi\)
0.377945 + 0.925828i \(0.376631\pi\)
\(410\) −3.06673e22 2.03819e22i −1.89676 1.26061i
\(411\) 3.20369e22i 1.94087i
\(412\) 7.69984e21 + 1.83324e22i 0.456936 + 1.08791i
\(413\) 1.18136e22i 0.686760i
\(414\) 5.72993e21 8.62146e21i 0.326322 0.490996i
\(415\) −3.49539e21 −0.195023
\(416\) −1.90623e22 + 4.03700e21i −1.04203 + 0.220681i
\(417\) 3.19840e22 1.71308
\(418\) 8.00385e20 1.20429e21i 0.0420049 0.0632021i
\(419\) 4.18757e21i 0.215349i −0.994186 0.107674i \(-0.965660\pi\)
0.994186 0.107674i \(-0.0343404\pi\)
\(420\) −1.80896e22 4.30692e22i −0.911610 2.17044i
\(421\) 2.74877e22i 1.35750i −0.734368 0.678751i \(-0.762521\pi\)
0.734368 0.678751i \(-0.237479\pi\)
\(422\) 2.73011e22 + 1.81447e22i 1.32137 + 0.878201i
\(423\) 2.04773e21 0.0971357
\(424\) 5.27780e21 2.76003e22i 0.245382 1.28323i
\(425\) 2.24571e22 1.02340
\(426\) 3.45459e20 + 2.29596e20i 0.0154317 + 0.0102561i
\(427\) 1.49681e22i 0.655435i
\(428\) 4.85990e20 2.04121e20i 0.0208620 0.00876227i
\(429\) 2.86914e22i 1.20744i
\(430\) −1.72840e22 + 2.60061e22i −0.713120 + 1.07299i
\(431\) −4.37127e22 −1.76828 −0.884139 0.467224i \(-0.845254\pi\)
−0.884139 + 0.467224i \(0.845254\pi\)
\(432\) 1.26555e22 + 1.24080e22i 0.501959 + 0.492140i
\(433\) 6.06049e21 0.235701 0.117850 0.993031i \(-0.462400\pi\)
0.117850 + 0.993031i \(0.462400\pi\)
\(434\) 2.80227e21 4.21640e21i 0.106868 0.160797i
\(435\) 6.05504e22i 2.26443i
\(436\) −8.08426e21 + 3.39548e21i −0.296487 + 0.124528i
\(437\) 3.19490e21i 0.114912i
\(438\) 4.12755e22 + 2.74322e22i 1.45600 + 0.967678i
\(439\) 1.64448e22 0.568959 0.284480 0.958682i \(-0.408179\pi\)
0.284480 + 0.958682i \(0.408179\pi\)
\(440\) 5.04054e22 + 9.63866e21i 1.71052 + 0.327091i
\(441\) −2.26860e21 −0.0755145
\(442\) −1.19749e22 7.95867e21i −0.391005 0.259867i
\(443\) 3.31744e22i 1.06260i −0.847182 0.531302i \(-0.821703\pi\)
0.847182 0.531302i \(-0.178297\pi\)
\(444\) −4.22881e21 1.00683e22i −0.132881 0.316375i
\(445\) 1.07317e23i 3.30832i
\(446\) −2.04350e22 + 3.07473e22i −0.618058 + 0.929952i
\(447\) −6.53544e21 −0.193937
\(448\) −3.47542e22 1.37961e22i −1.01192 0.401691i
\(449\) −2.57130e22 −0.734615 −0.367307 0.930100i \(-0.619720\pi\)
−0.367307 + 0.930100i \(0.619720\pi\)
\(450\) −1.86790e22 + 2.81051e22i −0.523658 + 0.787914i
\(451\) 4.34010e22i 1.19399i
\(452\) 8.83166e21 + 2.10272e22i 0.238433 + 0.567681i
\(453\) 4.70421e22i 1.24638i
\(454\) −1.31088e21 8.71226e20i −0.0340869 0.0226546i
\(455\) 8.28161e22 2.11358
\(456\) 3.69448e21 + 7.06468e20i 0.0925448 + 0.0176967i
\(457\) 2.71668e22 0.667960 0.333980 0.942580i \(-0.391608\pi\)
0.333980 + 0.942580i \(0.391608\pi\)
\(458\) 1.67799e22 + 1.11521e22i 0.404979 + 0.269154i
\(459\) 1.30785e22i 0.309848i
\(460\) −1.04541e23 + 4.39082e22i −2.43133 + 1.02119i
\(461\) 1.14852e22i 0.262230i −0.991367 0.131115i \(-0.958144\pi\)
0.991367 0.131115i \(-0.0418557\pi\)
\(462\) 3.04763e22 4.58557e22i 0.683133 1.02787i
\(463\) −4.81356e22 −1.05932 −0.529661 0.848209i \(-0.677681\pi\)
−0.529661 + 0.848209i \(0.677681\pi\)
\(464\) −3.46088e22 3.39318e22i −0.747796 0.733168i
\(465\) −1.80741e22 −0.383447
\(466\) −1.68185e22 + 2.53058e22i −0.350355 + 0.527156i
\(467\) 1.45571e22i 0.297770i 0.988855 + 0.148885i \(0.0475684\pi\)
−0.988855 + 0.148885i \(0.952432\pi\)
\(468\) 1.99206e22 8.36689e21i 0.400141 0.168064i
\(469\) 1.48943e22i 0.293800i
\(470\) −1.86800e22 1.24150e22i −0.361864 0.240500i
\(471\) −6.80453e22 −1.29455
\(472\) 6.34064e21 3.31584e22i 0.118475 0.619565i
\(473\) −3.68045e22 −0.675431
\(474\) 1.62378e22 + 1.07918e22i 0.292692 + 0.194527i
\(475\) 1.04151e22i 0.184402i
\(476\) −1.06850e22 2.54397e22i −0.185829 0.442439i
\(477\) 3.11596e22i 0.532336i
\(478\) 5.04717e22 7.59416e22i 0.847054 1.27451i
\(479\) 4.36285e22 0.719314 0.359657 0.933085i \(-0.382894\pi\)
0.359657 + 0.933085i \(0.382894\pi\)
\(480\) 2.76576e22 + 1.30596e23i 0.447986 + 2.11534i
\(481\) 1.93600e22 0.308086
\(482\) 1.09946e22 1.65429e22i 0.171902 0.258649i
\(483\) 1.21652e23i 1.86883i
\(484\) −2.23169e21 5.31340e21i −0.0336859 0.0802022i
\(485\) 2.65899e21i 0.0394378i
\(486\) −4.39908e22 2.92368e22i −0.641141 0.426111i
\(487\) 1.77302e22 0.253932 0.126966 0.991907i \(-0.459476\pi\)
0.126966 + 0.991907i \(0.459476\pi\)
\(488\) 8.03377e21 4.20127e22i 0.113071 0.591305i
\(489\) 6.23867e22 0.862913
\(490\) 2.06949e22 + 1.37541e22i 0.281318 + 0.186967i
\(491\) 3.92177e20i 0.00523949i 0.999997 + 0.00261975i \(0.000833892\pi\)
−0.999997 + 0.00261975i \(0.999166\pi\)
\(492\) 1.04089e23 4.37184e22i 1.36678 0.574065i
\(493\) 3.57653e22i 0.461598i
\(494\) −3.69105e21 + 5.55369e21i −0.0468243 + 0.0704534i
\(495\) −5.69057e22 −0.709597
\(496\) −1.01285e22 + 1.03306e22i −0.124151 + 0.126628i
\(497\) −1.41119e21 −0.0170042
\(498\) 5.93190e21 8.92535e21i 0.0702659 0.105725i
\(499\) 3.85769e22i 0.449234i 0.974447 + 0.224617i \(0.0721130\pi\)
−0.974447 + 0.224617i \(0.927887\pi\)
\(500\) 1.94016e23 8.14889e22i 2.22122 0.932939i
\(501\) 8.10101e22i 0.911840i
\(502\) −7.13273e22 4.74050e22i −0.789358 0.524618i
\(503\) 1.70508e23 1.85531 0.927656 0.373435i \(-0.121820\pi\)
0.927656 + 0.373435i \(0.121820\pi\)
\(504\) 4.07253e22 + 7.78761e21i 0.435718 + 0.0833191i
\(505\) −1.46539e23 −1.54162
\(506\) −1.11304e23 7.39741e22i −1.15141 0.765245i
\(507\) 1.56897e22i 0.159605i
\(508\) 4.67855e22 + 1.11391e23i 0.468026 + 1.11432i
\(509\) 1.15058e23i 1.13192i 0.824434 + 0.565959i \(0.191494\pi\)
−0.824434 + 0.565959i \(0.808506\pi\)
\(510\) −5.45252e22 + 8.20405e22i −0.527534 + 0.793746i
\(511\) −1.68609e23 −1.60436
\(512\) 9.01439e22 + 5.73765e22i 0.843610 + 0.536957i
\(513\) 6.06550e21 0.0558302
\(514\) 3.13750e22 4.72079e22i 0.284051 0.427394i
\(515\) 2.41504e23i 2.15062i
\(516\) −3.70736e22 8.82681e22i −0.324745 0.773182i
\(517\) 2.64364e22i 0.227789i
\(518\) 3.09419e22 + 2.05644e22i 0.262267 + 0.174306i
\(519\) 1.76858e23 1.47469
\(520\) −2.32449e23 4.44496e22i −1.90678 0.364619i
\(521\) −1.62883e23 −1.31448 −0.657241 0.753680i \(-0.728277\pi\)
−0.657241 + 0.753680i \(0.728277\pi\)
\(522\) 4.47605e22 + 2.97484e22i 0.355382 + 0.236192i
\(523\) 2.36470e23i 1.84719i −0.383366 0.923596i \(-0.625235\pi\)
0.383366 0.923596i \(-0.374765\pi\)
\(524\) −2.19256e23 + 9.20901e22i −1.68514 + 0.707778i
\(525\) 3.96575e23i 2.99897i
\(526\) −1.00143e23 + 1.50679e23i −0.745149 + 1.12118i
\(527\) −1.06758e22 −0.0781648
\(528\) −1.10153e23 + 1.12351e23i −0.793613 + 0.809447i
\(529\) 1.54233e23 1.09346
\(530\) 1.88915e23 2.84248e23i 1.31802 1.98314i
\(531\) 3.74346e22i 0.257022i
\(532\) −1.17984e22 + 4.95545e21i −0.0797211 + 0.0334837i
\(533\) 2.00148e23i 1.33098i
\(534\) −2.74030e23 1.82124e23i −1.79348 1.19197i
\(535\) 6.40224e21 0.0412406
\(536\) −7.99419e21 + 4.18056e22i −0.0506843 + 0.265054i
\(537\) 1.36640e23 0.852698
\(538\) 1.48564e23 + 9.87377e22i 0.912567 + 0.606504i
\(539\) 2.92879e22i 0.177086i
\(540\) 8.33594e22 + 1.98470e23i 0.496144 + 1.18126i
\(541\) 1.05868e23i 0.620281i 0.950691 + 0.310141i \(0.100376\pi\)
−0.950691 + 0.310141i \(0.899624\pi\)
\(542\) 3.77690e22 5.68286e22i 0.217842 0.327773i
\(543\) −7.24837e22 −0.411568
\(544\) 1.63365e22 + 7.71395e22i 0.0913208 + 0.431207i
\(545\) −1.06499e23 −0.586104
\(546\) −1.40544e23 + 2.11468e23i −0.761510 + 1.14580i
\(547\) 2.89118e23i 1.54235i −0.636625 0.771174i \(-0.719670\pi\)
0.636625 0.771174i \(-0.280330\pi\)
\(548\) 1.20613e23 + 2.87166e23i 0.633518 + 1.50834i
\(549\) 4.74307e22i 0.245298i
\(550\) 3.62840e23 + 2.41148e23i 1.84771 + 1.22801i
\(551\) −1.65872e22 −0.0831732
\(552\) 6.52941e22 3.41456e23i 0.322397 1.68598i
\(553\) −6.63307e22 −0.322516
\(554\) 1.23691e23 + 8.22066e22i 0.592250 + 0.393617i
\(555\) 1.32636e23i 0.625419i
\(556\) 2.86692e23 1.20414e23i 1.33131 0.559165i
\(557\) 3.41183e23i 1.56034i −0.625570 0.780168i \(-0.715134\pi\)
0.625570 0.780168i \(-0.284866\pi\)
\(558\) 8.87979e21 1.33608e22i 0.0399956 0.0601787i
\(559\) 1.69727e23 0.752925
\(560\) −3.24295e23 3.17951e23i −1.41691 1.38919i
\(561\) −1.16106e23 −0.499653
\(562\) −1.04969e23 + 1.57940e23i −0.444941 + 0.669473i
\(563\) 1.44889e23i 0.604941i −0.953159 0.302471i \(-0.902189\pi\)
0.953159 0.302471i \(-0.0978114\pi\)
\(564\) 6.34024e22 2.66297e22i 0.260756 0.109520i
\(565\) 2.77004e23i 1.12221i
\(566\) −2.45053e23 1.62866e23i −0.977960 0.649965i
\(567\) 3.43795e23 1.35159
\(568\) 3.96094e21 + 7.57422e20i 0.0153404 + 0.00293344i
\(569\) 4.55076e23 1.73632 0.868160 0.496285i \(-0.165303\pi\)
0.868160 + 0.496285i \(0.165303\pi\)
\(570\) 3.80485e22 + 2.52875e22i 0.143022 + 0.0950540i
\(571\) 2.17154e23i 0.804193i 0.915597 + 0.402097i \(0.131718\pi\)
−0.915597 + 0.402097i \(0.868282\pi\)
\(572\) −1.08018e23 2.57178e23i −0.394120 0.938355i
\(573\) 4.25068e23i 1.52807i
\(574\) −2.12599e23 + 3.19884e23i −0.753027 + 1.13303i
\(575\) −9.62594e23 −3.35944
\(576\) −1.10129e23 4.37167e22i −0.378712 0.150334i
\(577\) 2.28537e23 0.774394 0.387197 0.921997i \(-0.373443\pi\)
0.387197 + 0.921997i \(0.373443\pi\)
\(578\) 1.33568e23 2.00970e23i 0.445979 0.671036i
\(579\) 7.93523e22i 0.261091i
\(580\) −2.27961e23 5.42749e23i −0.739132 1.75979i
\(581\) 3.64597e22i 0.116497i
\(582\) −6.78964e21 4.51248e21i −0.0213797 0.0142092i
\(583\) 4.02275e23 1.24836
\(584\) 4.73254e23 + 9.04968e22i 1.44739 + 0.276773i
\(585\) 2.62426e23 0.791011
\(586\) −4.02818e22 2.67718e22i −0.119668 0.0795331i
\(587\) 5.49823e23i 1.60990i 0.593342 + 0.804951i \(0.297808\pi\)
−0.593342 + 0.804951i \(0.702192\pi\)
\(588\) −7.02412e22 + 2.95021e22i −0.202714 + 0.0851424i
\(589\) 4.95120e21i 0.0140842i
\(590\) 2.26959e23 3.41490e23i 0.636363 0.957495i
\(591\) −6.68196e23 −1.84676
\(592\) −7.58106e22 7.43277e22i −0.206536 0.202496i
\(593\) −4.92814e23 −1.32348 −0.661741 0.749732i \(-0.730182\pi\)
−0.661741 + 0.749732i \(0.730182\pi\)
\(594\) −1.40439e23 + 2.11310e23i −0.371795 + 0.559416i
\(595\) 3.35133e23i 0.874626i
\(596\) −5.85810e22 + 2.46047e22i −0.150717 + 0.0633030i
\(597\) 3.39954e23i 0.862261i
\(598\) 5.13290e23 + 3.41139e23i 1.28352 + 0.853043i
\(599\) −4.19943e23 −1.03529 −0.517646 0.855595i \(-0.673191\pi\)
−0.517646 + 0.855595i \(0.673191\pi\)
\(600\) −2.12852e23 + 1.11311e24i −0.517360 + 2.70554i
\(601\) 2.16713e23 0.519341 0.259671 0.965697i \(-0.416386\pi\)
0.259671 + 0.965697i \(0.416386\pi\)
\(602\) 2.71265e23 + 1.80286e23i 0.640949 + 0.425983i
\(603\) 4.71969e22i 0.109955i
\(604\) −1.77105e23 4.21666e23i −0.406833 0.968623i
\(605\) 6.99965e22i 0.158546i
\(606\) 2.48687e23 3.74183e23i 0.555438 0.835732i
\(607\) −4.33551e23 −0.954852 −0.477426 0.878672i \(-0.658430\pi\)
−0.477426 + 0.878672i \(0.658430\pi\)
\(608\) 3.57755e22 7.57652e21i 0.0776972 0.0164547i
\(609\) −6.31590e23 −1.35266
\(610\) 2.87563e23 4.32678e23i 0.607337 0.913821i
\(611\) 1.21914e23i 0.253924i
\(612\) −3.38584e22 8.06130e22i −0.0695471 0.165584i
\(613\) 2.71131e23i 0.549244i 0.961552 + 0.274622i \(0.0885528\pi\)
−0.961552 + 0.274622i \(0.911447\pi\)
\(614\) −3.63188e23 2.41380e23i −0.725605 0.482247i
\(615\) 1.37122e24 2.70190
\(616\) 1.00539e23 5.25769e23i 0.195388 1.02178i
\(617\) −5.91051e23 −1.13292 −0.566462 0.824088i \(-0.691688\pi\)
−0.566462 + 0.824088i \(0.691688\pi\)
\(618\) −6.16672e23 4.09848e23i −1.16588 0.774856i
\(619\) 9.44262e23i 1.76085i −0.474187 0.880424i \(-0.657258\pi\)
0.474187 0.880424i \(-0.342742\pi\)
\(620\) −1.62009e23 + 6.80454e22i −0.297995 + 0.125161i
\(621\) 5.60593e23i 1.01711i
\(622\) −2.52077e23 + 3.79283e23i −0.451143 + 0.678806i
\(623\) 1.11940e24 1.97623
\(624\) 5.07982e23 5.18117e23i 0.884666 0.902317i
\(625\) 1.20439e24 2.06913
\(626\) −5.80392e23 + 8.73279e23i −0.983648 + 1.48003i
\(627\) 5.38471e22i 0.0900303i
\(628\) −6.09930e23 + 2.56178e23i −1.00606 + 0.422556i
\(629\) 7.83442e22i 0.127490i
\(630\) 4.19420e23 + 2.78752e23i 0.673371 + 0.447531i
\(631\) 3.35285e23 0.531086 0.265543 0.964099i \(-0.414449\pi\)
0.265543 + 0.964099i \(0.414449\pi\)
\(632\) 1.86178e23 + 3.56014e22i 0.290960 + 0.0556381i
\(633\) −1.22071e24 −1.88227
\(634\) 1.67395e23 + 1.11253e23i 0.254673 + 0.169259i
\(635\) 1.46742e24i 2.20281i
\(636\) 4.05216e23 + 9.64775e23i 0.600208 + 1.42903i
\(637\) 1.35064e23i 0.197403i
\(638\) 3.84056e23 5.77864e23i 0.553883 0.833392i
\(639\) −4.47175e21 −0.00636385
\(640\) 7.39582e23 + 1.06649e24i 1.03862 + 1.49770i
\(641\) 1.02554e24 1.42122 0.710609 0.703587i \(-0.248419\pi\)
0.710609 + 0.703587i \(0.248419\pi\)
\(642\) −1.08650e22 + 1.63479e22i −0.0148588 + 0.0223570i
\(643\) 1.00641e24i 1.35826i −0.734017 0.679131i \(-0.762357\pi\)
0.734017 0.679131i \(-0.237643\pi\)
\(644\) 4.57999e23 + 1.09044e24i 0.610006 + 1.45236i
\(645\) 1.16281e24i 1.52845i
\(646\) 2.24741e22 + 1.49366e22i 0.0291546 + 0.0193765i
\(647\) 3.80957e23 0.487742 0.243871 0.969808i \(-0.421583\pi\)
0.243871 + 0.969808i \(0.421583\pi\)
\(648\) −9.64969e23 1.84524e23i −1.21934 0.233166i
\(649\) 4.83285e23 0.602731
\(650\) −1.67327e24 1.11208e24i −2.05970 1.36890i
\(651\) 1.88527e23i 0.229053i
\(652\) 5.59209e23 2.34874e23i 0.670610 0.281664i
\(653\) 4.03993e23i 0.478202i −0.970995 0.239101i \(-0.923147\pi\)
0.970995 0.239101i \(-0.0768527\pi\)
\(654\) 1.80735e23 2.71941e23i 0.211170 0.317734i
\(655\) −2.88839e24 −3.33123
\(656\) 7.68417e23 7.83748e23i 0.874811 0.892265i
\(657\) −5.34285e23 −0.600437
\(658\) −1.29498e23 + 1.94848e23i −0.143663 + 0.216160i
\(659\) 3.09111e23i 0.338523i 0.985571 + 0.169262i \(0.0541383\pi\)
−0.985571 + 0.169262i \(0.945862\pi\)
\(660\) −1.76194e24 + 7.40033e23i −1.90487 + 0.800069i
\(661\) 4.95209e23i 0.528537i −0.964449 0.264269i \(-0.914869\pi\)
0.964449 0.264269i \(-0.0851306\pi\)
\(662\) 2.63794e23 + 1.75321e23i 0.277954 + 0.184732i
\(663\) 5.35432e23 0.556980
\(664\) 1.95689e22 1.02336e23i 0.0200973 0.105099i
\(665\) −1.55427e23 −0.157595
\(666\) 9.80481e22 + 6.51640e22i 0.0981541 + 0.0652345i
\(667\) 1.53304e24i 1.51525i
\(668\) −3.04988e23 7.26142e23i −0.297634 0.708633i
\(669\) 1.37480e24i 1.32470i
\(670\) −2.86146e23 + 4.30546e23i −0.272240 + 0.409622i
\(671\) 6.12336e23 0.575239
\(672\) 1.36223e24 2.88492e23i 1.26360 0.267605i
\(673\) −7.41478e23 −0.679157 −0.339579 0.940578i \(-0.610284\pi\)
−0.339579 + 0.940578i \(0.610284\pi\)
\(674\) −2.77660e23 + 4.17777e23i −0.251133 + 0.377864i
\(675\) 1.82748e24i 1.63219i
\(676\) 5.90687e22 + 1.40636e23i 0.0520968 + 0.124037i
\(677\) 1.13904e22i 0.00992051i −0.999988 0.00496025i \(-0.998421\pi\)
0.999988 0.00496025i \(-0.00157890\pi\)
\(678\) −7.07319e23 4.70093e23i −0.608363 0.404326i
\(679\) 2.77355e22 0.0235582
\(680\) −1.79874e23 + 9.40655e23i −0.150884 + 0.789050i
\(681\) 5.86131e22 0.0485561
\(682\) −1.72490e23 1.14639e23i −0.141123 0.0937920i
\(683\) 2.41181e24i 1.94880i −0.224828 0.974398i \(-0.572182\pi\)
0.224828 0.974398i \(-0.427818\pi\)
\(684\) −3.73865e22 + 1.57027e22i −0.0298358 + 0.0125314i
\(685\) 3.78301e24i 2.98172i
\(686\) −6.30647e23 + 9.48893e23i −0.490943 + 0.738690i
\(687\) −7.50277e23 −0.576885
\(688\) −6.64626e23 6.51625e23i −0.504749 0.494875i
\(689\) −1.85513e24 −1.39159
\(690\) 2.33716e24 3.51657e24i 1.73169 2.60556i
\(691\) 3.17702e23i 0.232518i 0.993219 + 0.116259i \(0.0370902\pi\)
−0.993219 + 0.116259i \(0.962910\pi\)
\(692\) 1.58528e24 6.65836e23i 1.14605 0.481355i
\(693\) 5.93573e23i 0.423879i
\(694\) 1.16261e24 + 7.72683e23i 0.820119 + 0.545062i
\(695\) 3.77676e24 2.63177
\(696\) 1.77275e24 + 3.38991e23i 1.22031 + 0.233351i
\(697\) 8.09940e23 0.550775
\(698\) −4.43437e22 2.94714e22i −0.0297893 0.0197984i
\(699\) 1.13149e24i 0.750924i
\(700\) −1.49303e24 3.55474e24i −0.978893 2.33063i
\(701\) 3.50256e23i 0.226873i 0.993545 + 0.113436i \(0.0361858\pi\)
−0.993545 + 0.113436i \(0.963814\pi\)
\(702\) 6.47649e23 9.74476e23i 0.414452 0.623600i
\(703\) −3.63342e22 −0.0229718
\(704\) −5.64388e23 + 1.42177e24i −0.352542 + 0.888102i
\(705\) 8.35238e23 0.515469
\(706\) −1.18741e24 + 1.78661e24i −0.724035 + 1.08941i
\(707\) 1.52853e24i 0.920890i
\(708\) 4.86819e23 + 1.15906e24i 0.289791 + 0.689960i
\(709\) 3.69006e23i 0.217041i 0.994094 + 0.108520i \(0.0346112\pi\)
−0.994094 + 0.108520i \(0.965389\pi\)
\(710\) 4.07927e22 + 2.71114e22i 0.0237076 + 0.0157563i
\(711\) −2.10188e23 −0.120702
\(712\) −3.14195e24 6.00812e23i −1.78287 0.340925i
\(713\) 4.57606e23 0.256585
\(714\) 8.55749e23 + 5.68742e23i 0.474145 + 0.315123i
\(715\) 3.38796e24i 1.85497i
\(716\) 1.22478e24 5.14422e23i 0.662671 0.278329i
\(717\) 3.39557e24i 1.81551i
\(718\) 1.53833e24 2.31463e24i 0.812817 1.22299i
\(719\) −3.63965e24 −1.90048 −0.950242 0.311512i \(-0.899165\pi\)
−0.950242 + 0.311512i \(0.899165\pi\)
\(720\) −1.02762e24 1.00752e24i −0.530281 0.519908i
\(721\) 2.51909e24 1.28467
\(722\) −1.09131e24 + 1.64202e24i −0.550024 + 0.827586i
\(723\) 7.39680e23i 0.368441i
\(724\) −6.49714e23 + 2.72887e23i −0.319849 + 0.134340i
\(725\) 4.99755e24i 2.43156i
\(726\) 1.78734e23 + 1.18789e23i 0.0859498 + 0.0571233i
\(727\) −2.92373e24 −1.38962 −0.694808 0.719196i \(-0.744510\pi\)
−0.694808 + 0.719196i \(0.744510\pi\)
\(728\) −4.63645e23 + 2.42464e24i −0.217806 + 1.13902i
\(729\) −7.06719e23 −0.328143
\(730\) 4.87392e24 + 3.23927e24i 2.23684 + 1.48663i
\(731\) 6.86837e23i 0.311570i
\(732\) 6.16814e23 + 1.46856e24i 0.276573 + 0.658489i
\(733\) 8.20457e22i 0.0363640i −0.999835 0.0181820i \(-0.994212\pi\)
0.999835 0.0181820i \(-0.00578783\pi\)
\(734\) −3.40071e23 + 5.11684e23i −0.148989 + 0.224174i
\(735\) −9.25329e23 −0.400732
\(736\) −7.00246e23 3.30649e24i −0.299771 1.41549i
\(737\) −6.09318e23 −0.257852
\(738\) −6.73681e23 + 1.01364e24i −0.281822 + 0.424040i
\(739\) 3.42591e22i 0.0141677i 0.999975 + 0.00708383i \(0.00225487\pi\)
−0.999975 + 0.00708383i \(0.997745\pi\)
\(740\) −4.99349e23 1.18889e24i −0.204143 0.486042i
\(741\) 2.48321e23i 0.100360i
\(742\) −2.96494e24 1.97054e24i −1.18463 0.787320i
\(743\) 1.12234e24 0.443324 0.221662 0.975124i \(-0.428852\pi\)
0.221662 + 0.975124i \(0.428852\pi\)
\(744\) 1.01187e23 5.29160e23i 0.0395145 0.206641i
\(745\) −7.71722e23 −0.297943
\(746\) 7.40971e23 + 4.92459e23i 0.282827 + 0.187971i
\(747\) 1.15533e23i 0.0435994i
\(748\) −1.04072e24 + 4.37116e23i −0.388304 + 0.163092i
\(749\) 6.67805e22i 0.0246351i
\(750\) −4.33750e24 + 6.52636e24i −1.58205 + 2.38040i
\(751\) 5.53313e22 0.0199540 0.00997702 0.999950i \(-0.496824\pi\)
0.00997702 + 0.999950i \(0.496824\pi\)
\(752\) 4.68058e23 4.77396e23i 0.166897 0.170227i
\(753\) 3.18925e24 1.12443
\(754\) −1.77111e24 + 2.66487e24i −0.617432 + 0.929010i
\(755\) 5.55486e24i 1.91480i
\(756\) 2.07020e24 8.69507e23i 0.705629 0.296372i
\(757\) 4.11071e24i 1.38548i 0.721185 + 0.692742i \(0.243598\pi\)
−0.721185 + 0.692742i \(0.756402\pi\)
\(758\) −1.52565e24 1.01397e24i −0.508472 0.337937i
\(759\) 4.97673e24 1.64017
\(760\) 4.36254e23 + 8.34217e22i 0.142175 + 0.0271871i
\(761\) 5.58495e24 1.79991 0.899954 0.435986i \(-0.143600\pi\)
0.899954 + 0.435986i \(0.143600\pi\)
\(762\) −3.74700e24 2.49031e24i −1.19417 0.793662i
\(763\) 1.11087e24i 0.350110i
\(764\) 1.60030e24 + 3.81014e24i 0.498779 + 1.18754i
\(765\) 1.06196e24i 0.327331i
\(766\) −4.32870e23 + 6.51311e23i −0.131951 + 0.198538i
\(767\) −2.22872e24 −0.671884
\(768\) −3.97835e24 + 7.85990e22i −1.18613 + 0.0234340i