Properties

Label 8.18.b.a.5.9
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 5.9
Root \(13.1473 + 179.780i\) of defining polynomial
Character \(\chi\) \(=\) 8.5
Dual form 8.18.b.a.5.10

$q$-expansion

\(f(q)\) \(=\) \(q+(42.2945 - 359.560i) q^{2} +16002.3i q^{3} +(-127494. - 30414.8i) q^{4} -1.27253e6i q^{5} +(5.75379e6 + 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 + 4.45555e7i) q^{8} -1.26934e8 q^{9} +O(q^{10})\) \(q+(42.2945 - 359.560i) q^{2} +16002.3i q^{3} +(-127494. - 30414.8i) q^{4} -1.27253e6i q^{5} +(5.75379e6 + 676810. i) q^{6} +5.50569e6 q^{7} +(-1.63282e7 + 4.45555e7i) q^{8} -1.26934e8 q^{9} +(-4.57551e8 - 5.38211e7i) q^{10} +1.09250e9i q^{11} +(4.86707e8 - 2.04020e9i) q^{12} +4.58081e9i q^{13} +(2.32860e8 - 1.97962e9i) q^{14} +2.03635e10 q^{15} +(1.53297e10 + 7.75543e9i) q^{16} -3.61463e10 q^{17} +(-5.36861e9 + 4.56403e10i) q^{18} +2.76727e10i q^{19} +(-3.87038e10 + 1.62241e11i) q^{20} +8.81037e10i q^{21} +(3.92817e11 + 4.62066e10i) q^{22} +2.20613e11 q^{23} +(-7.12990e11 - 2.61290e11i) q^{24} -8.56399e11 q^{25} +(1.64707e12 + 1.93743e11i) q^{26} +3.53044e10i q^{27} +(-7.01944e11 - 1.67454e11i) q^{28} +2.89192e11i q^{29} +(8.61263e11 - 7.32188e12i) q^{30} -6.06840e10 q^{31} +(3.43690e12 - 5.18395e12i) q^{32} -1.74825e13 q^{33} +(-1.52879e12 + 1.29967e13i) q^{34} -7.00616e12i q^{35} +(1.61834e13 + 3.86067e12i) q^{36} -1.88957e12i q^{37} +(9.94998e12 + 1.17040e12i) q^{38} -7.33035e13 q^{39} +(5.66983e13 + 2.07782e13i) q^{40} +6.37984e13 q^{41} +(3.16786e13 + 3.72630e12i) q^{42} +1.04353e14i q^{43} +(3.32280e13 - 1.39287e14i) q^{44} +1.61528e14i q^{45} +(9.33070e12 - 7.93234e13i) q^{46} -1.48111e14 q^{47} +(-1.24105e14 + 2.45311e14i) q^{48} -2.02318e14 q^{49} +(-3.62210e13 + 3.07927e14i) q^{50} -5.78424e14i q^{51} +(1.39324e14 - 5.84027e14i) q^{52} -4.05734e14i q^{53} +(1.26940e13 + 1.49318e12i) q^{54} +1.39024e15 q^{55} +(-8.98982e13 + 2.45308e14i) q^{56} -4.42827e14 q^{57} +(1.03982e14 + 1.22312e13i) q^{58} -7.77037e14i q^{59} +(-2.59623e15 - 6.19351e14i) q^{60} +2.64409e15i q^{61} +(-2.56660e12 + 2.18195e13i) q^{62} -6.98859e14 q^{63} +(-1.71858e15 - 1.45502e15i) q^{64} +5.82922e15 q^{65} +(-7.39412e14 + 6.28599e15i) q^{66} -1.78812e15i q^{67} +(4.60845e15 + 1.09938e15i) q^{68} +3.53031e15i q^{69} +(-2.51913e15 - 2.96322e14i) q^{70} -9.48422e14 q^{71} +(2.07261e15 - 5.65560e15i) q^{72} -6.41511e14 q^{73} +(-6.79414e14 - 7.99185e13i) q^{74} -1.37044e16i q^{75} +(8.41659e14 - 3.52811e15i) q^{76} +6.01494e15i q^{77} +(-3.10034e15 + 2.63570e16i) q^{78} -1.35339e16 q^{79} +(9.86904e15 - 1.95076e16i) q^{80} -1.69572e16 q^{81} +(2.69832e15 - 2.29393e16i) q^{82} -2.30035e16i q^{83} +(2.67966e15 - 1.12327e16i) q^{84} +4.59973e16i q^{85} +(3.75213e16 + 4.41358e15i) q^{86} -4.62775e15 q^{87} +(-4.86766e16 - 1.78385e16i) q^{88} -1.39186e16 q^{89} +(5.80788e16 + 6.83173e15i) q^{90} +2.52205e16i q^{91} +(-2.81269e16 - 6.70989e15i) q^{92} -9.71085e14i q^{93} +(-6.26427e15 + 5.32547e16i) q^{94} +3.52144e16 q^{95} +(8.29552e16 + 5.49984e16i) q^{96} -1.33747e15 q^{97} +(-8.55694e15 + 7.27454e16i) q^{98} -1.38675e17i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 42.2945 359.560i 0.116823 0.993153i
\(3\) 16002.3i 1.40816i 0.710120 + 0.704080i \(0.248640\pi\)
−0.710120 + 0.704080i \(0.751360\pi\)
\(4\) −127494. 30414.8i −0.972705 0.232046i
\(5\) 1.27253e6i 1.45688i −0.685110 0.728440i \(-0.740246\pi\)
0.685110 0.728440i \(-0.259754\pi\)
\(6\) 5.75379e6 + 676810.i 1.39852 + 0.164506i
\(7\) 5.50569e6 0.360976 0.180488 0.983577i \(-0.442232\pi\)
0.180488 + 0.983577i \(0.442232\pi\)
\(8\) −1.63282e7 + 4.45555e7i −0.344092 + 0.938936i
\(9\) −1.26934e8 −0.982916
\(10\) −4.57551e8 5.38211e7i −1.44690 0.170197i
\(11\) 1.09250e9i 1.53667i 0.640045 + 0.768337i \(0.278916\pi\)
−0.640045 + 0.768337i \(0.721084\pi\)
\(12\) 4.86707e8 2.04020e9i 0.326759 1.36972i
\(13\) 4.58081e9i 1.55748i 0.627345 + 0.778742i \(0.284142\pi\)
−0.627345 + 0.778742i \(0.715858\pi\)
\(14\) 2.32860e8 1.97962e9i 0.0421703 0.358504i
\(15\) 2.03635e10 2.05152
\(16\) 1.53297e10 + 7.75543e9i 0.892309 + 0.451425i
\(17\) −3.61463e10 −1.25675 −0.628373 0.777912i \(-0.716279\pi\)
−0.628373 + 0.777912i \(0.716279\pi\)
\(18\) −5.36861e9 + 4.56403e10i −0.114827 + 0.976186i
\(19\) 2.76727e10i 0.373806i 0.982378 + 0.186903i \(0.0598449\pi\)
−0.982378 + 0.186903i \(0.940155\pi\)
\(20\) −3.87038e10 + 1.62241e11i −0.338064 + 1.41711i
\(21\) 8.81037e10i 0.508312i
\(22\) 3.92817e11 + 4.62066e10i 1.52615 + 0.179519i
\(23\) 2.20613e11 0.587413 0.293707 0.955896i \(-0.405111\pi\)
0.293707 + 0.955896i \(0.405111\pi\)
\(24\) −7.12990e11 2.61290e11i −1.32217 0.484537i
\(25\) −8.56399e11 −1.12250
\(26\) 1.64707e12 + 1.93743e11i 1.54682 + 0.181950i
\(27\) 3.53044e10i 0.0240567i
\(28\) −7.01944e11 1.67454e11i −0.351123 0.0837632i
\(29\) 2.89192e11i 0.107350i 0.998558 + 0.0536752i \(0.0170936\pi\)
−0.998558 + 0.0536752i \(0.982906\pi\)
\(30\) 8.61263e11 7.32188e12i 0.239665 2.03747i
\(31\) −6.06840e10 −0.0127791 −0.00638954 0.999980i \(-0.502034\pi\)
−0.00638954 + 0.999980i \(0.502034\pi\)
\(32\) 3.43690e12 5.18395e12i 0.552577 0.833462i
\(33\) −1.74825e13 −2.16388
\(34\) −1.52879e12 + 1.29967e13i −0.146817 + 1.24814i
\(35\) 7.00616e12i 0.525899i
\(36\) 1.61834e13 + 3.86067e12i 0.956087 + 0.228082i
\(37\) 1.88957e12i 0.0884400i −0.999022 0.0442200i \(-0.985920\pi\)
0.999022 0.0442200i \(-0.0140803\pi\)
\(38\) 9.94998e12 + 1.17040e12i 0.371246 + 0.0436691i
\(39\) −7.33035e13 −2.19319
\(40\) 5.66983e13 + 2.07782e13i 1.36792 + 0.501301i
\(41\) 6.37984e13 1.24781 0.623903 0.781502i \(-0.285546\pi\)
0.623903 + 0.781502i \(0.285546\pi\)
\(42\) 3.16786e13 + 3.72630e12i 0.504831 + 0.0593826i
\(43\) 1.04353e14i 1.36152i 0.732505 + 0.680761i \(0.238351\pi\)
−0.732505 + 0.680761i \(0.761649\pi\)
\(44\) 3.32280e13 1.39287e14i 0.356580 1.49473i
\(45\) 1.61528e14i 1.43199i
\(46\) 9.33070e12 7.93234e13i 0.0686235 0.583391i
\(47\) −1.48111e14 −0.907308 −0.453654 0.891178i \(-0.649880\pi\)
−0.453654 + 0.891178i \(0.649880\pi\)
\(48\) −1.24105e14 + 2.45311e14i −0.635679 + 1.25651i
\(49\) −2.02318e14 −0.869696
\(50\) −3.62210e13 + 3.07927e14i −0.131134 + 1.11481i
\(51\) 5.78424e14i 1.76970i
\(52\) 1.39324e14 5.84027e14i 0.361409 1.51497i
\(53\) 4.05734e14i 0.895151i −0.894246 0.447575i \(-0.852288\pi\)
0.894246 0.447575i \(-0.147712\pi\)
\(54\) 1.26940e13 + 1.49318e12i 0.0238920 + 0.00281038i
\(55\) 1.39024e15 2.23875
\(56\) −8.98982e13 + 2.45308e14i −0.124209 + 0.338933i
\(57\) −4.42827e14 −0.526378
\(58\) 1.03982e14 + 1.22312e13i 0.106615 + 0.0125410i
\(59\) 7.77037e14i 0.688969i −0.938792 0.344484i \(-0.888054\pi\)
0.938792 0.344484i \(-0.111946\pi\)
\(60\) −2.59623e15 6.19351e14i −1.99552 0.476048i
\(61\) 2.64409e15i 1.76592i 0.469445 + 0.882962i \(0.344454\pi\)
−0.469445 + 0.882962i \(0.655546\pi\)
\(62\) −2.56660e12 + 2.18195e13i −0.00149289 + 0.0126916i
\(63\) −6.98859e14 −0.354809
\(64\) −1.71858e15 1.45502e15i −0.763201 0.646161i
\(65\) 5.82922e15 2.26907
\(66\) −7.39412e14 + 6.28599e15i −0.252792 + 2.14907i
\(67\) 1.78812e15i 0.537973i −0.963144 0.268987i \(-0.913311\pi\)
0.963144 0.268987i \(-0.0866887\pi\)
\(68\) 4.60845e15 + 1.09938e15i 1.22244 + 0.291624i
\(69\) 3.53031e15i 0.827172i
\(70\) −2.51913e15 2.96322e14i −0.522298 0.0614371i
\(71\) −9.48422e14 −0.174303 −0.0871516 0.996195i \(-0.527776\pi\)
−0.0871516 + 0.996195i \(0.527776\pi\)
\(72\) 2.07261e15 5.65560e15i 0.338214 0.922895i
\(73\) −6.41511e14 −0.0931021 −0.0465511 0.998916i \(-0.514823\pi\)
−0.0465511 + 0.998916i \(0.514823\pi\)
\(74\) −6.79414e14 7.99185e13i −0.0878344 0.0103318i
\(75\) 1.37044e16i 1.58066i
\(76\) 8.41659e14 3.52811e15i 0.0867403 0.363602i
\(77\) 6.01494e15i 0.554702i
\(78\) −3.10034e15 + 2.63570e16i −0.256215 + 2.17817i
\(79\) −1.35339e16 −1.00367 −0.501836 0.864963i \(-0.667342\pi\)
−0.501836 + 0.864963i \(0.667342\pi\)
\(80\) 9.86904e15 1.95076e16i 0.657673 1.29999i
\(81\) −1.69572e16 −1.01679
\(82\) 2.69832e15 2.29393e16i 0.145773 1.23926i
\(83\) 2.30035e16i 1.12106i −0.828133 0.560532i \(-0.810597\pi\)
0.828133 0.560532i \(-0.189403\pi\)
\(84\) 2.67966e15 1.12327e16i 0.117952 0.494437i
\(85\) 4.59973e16i 1.83093i
\(86\) 3.75213e16 + 4.41358e15i 1.35220 + 0.159057i
\(87\) −4.62775e15 −0.151167
\(88\) −4.86766e16 1.78385e16i −1.44284 0.528757i
\(89\) −1.39186e16 −0.374785 −0.187392 0.982285i \(-0.560004\pi\)
−0.187392 + 0.982285i \(0.560004\pi\)
\(90\) 5.80788e16 + 6.83173e15i 1.42219 + 0.167290i
\(91\) 2.52205e16i 0.562214i
\(92\) −2.81269e16 6.70989e15i −0.571380 0.136307i
\(93\) 9.71085e14i 0.0179950i
\(94\) −6.26427e15 + 5.32547e16i −0.105995 + 0.901096i
\(95\) 3.52144e16 0.544590
\(96\) 8.29552e16 + 5.49984e16i 1.17365 + 0.778117i
\(97\) −1.33747e15 −0.0173270 −0.00866350 0.999962i \(-0.502758\pi\)
−0.00866350 + 0.999962i \(0.502758\pi\)
\(98\) −8.55694e15 + 7.27454e16i −0.101601 + 0.863741i
\(99\) 1.38675e17i 1.51042i
\(100\) 1.09186e17 + 2.60472e16i 1.09186 + 0.260472i
\(101\) 2.99972e16i 0.275645i 0.990457 + 0.137822i \(0.0440103\pi\)
−0.990457 + 0.137822i \(0.955990\pi\)
\(102\) −2.07978e17 2.44642e16i −1.75758 0.206742i
\(103\) 5.73300e15 0.0445929 0.0222965 0.999751i \(-0.492902\pi\)
0.0222965 + 0.999751i \(0.492902\pi\)
\(104\) −2.04100e17 7.47965e16i −1.46238 0.535918i
\(105\) 1.12115e17 0.740550
\(106\) −1.45885e17 1.71603e16i −0.889021 0.104574i
\(107\) 3.35465e17i 1.88749i 0.330670 + 0.943747i \(0.392725\pi\)
−0.330670 + 0.943747i \(0.607275\pi\)
\(108\) 1.07378e15 4.50111e15i 0.00558228 0.0234001i
\(109\) 2.00351e17i 0.963091i −0.876421 0.481545i \(-0.840076\pi\)
0.876421 0.481545i \(-0.159924\pi\)
\(110\) 5.87993e16 4.99873e17i 0.261538 2.22342i
\(111\) 3.02375e16 0.124538
\(112\) 8.44008e16 + 4.26990e16i 0.322102 + 0.162954i
\(113\) 4.77266e17 1.68886 0.844430 0.535665i \(-0.179939\pi\)
0.844430 + 0.535665i \(0.179939\pi\)
\(114\) −1.87292e16 + 1.59223e17i −0.0614932 + 0.522774i
\(115\) 2.80737e17i 0.855791i
\(116\) 8.79573e15 3.68704e16i 0.0249103 0.104420i
\(117\) 5.81460e17i 1.53088i
\(118\) −2.79391e17 3.28644e16i −0.684251 0.0804875i
\(119\) −1.99010e17 −0.453655
\(120\) −3.32500e17 + 9.07303e17i −0.705912 + 1.92625i
\(121\) −6.88100e17 −1.36137
\(122\) 9.50707e17 + 1.11830e17i 1.75383 + 0.206301i
\(123\) 1.02092e18i 1.75711i
\(124\) 7.73687e15 + 1.84569e15i 0.0124303 + 0.00296534i
\(125\) 1.18931e17i 0.178467i
\(126\) −2.95579e16 + 2.51281e17i −0.0414499 + 0.352380i
\(127\) 1.01392e18 1.32945 0.664723 0.747090i \(-0.268549\pi\)
0.664723 + 0.747090i \(0.268549\pi\)
\(128\) −5.95855e17 + 5.56391e17i −0.730896 + 0.682489i
\(129\) −1.66990e18 −1.91724
\(130\) 2.46544e17 2.09595e18i 0.265080 2.25353i
\(131\) 7.50169e17i 0.755706i 0.925866 + 0.377853i \(0.123338\pi\)
−0.925866 + 0.377853i \(0.876662\pi\)
\(132\) 2.22891e18 + 5.31725e17i 2.10482 + 0.502122i
\(133\) 1.52357e17i 0.134935i
\(134\) −6.42936e17 7.56276e16i −0.534290 0.0628477i
\(135\) 4.49260e16 0.0350478
\(136\) 5.90205e17 1.61051e18i 0.432437 1.18000i
\(137\) 1.03661e18 0.713659 0.356830 0.934170i \(-0.383858\pi\)
0.356830 + 0.934170i \(0.383858\pi\)
\(138\) 1.26936e18 + 1.49313e17i 0.821508 + 0.0966329i
\(139\) 8.10539e17i 0.493342i 0.969099 + 0.246671i \(0.0793367\pi\)
−0.969099 + 0.246671i \(0.920663\pi\)
\(140\) −2.13091e17 + 8.93246e17i −0.122033 + 0.511544i
\(141\) 2.37012e18i 1.27764i
\(142\) −4.01130e16 + 3.41014e17i −0.0203627 + 0.173110i
\(143\) −5.00451e18 −2.39335
\(144\) −1.94587e18 9.84427e17i −0.877065 0.443713i
\(145\) 3.68007e17 0.156397
\(146\) −2.71324e16 + 2.30661e17i −0.0108765 + 0.0924646i
\(147\) 3.23756e18i 1.22467i
\(148\) −5.74709e16 + 2.40910e17i −0.0205222 + 0.0860260i
\(149\) 2.43823e18i 0.822228i 0.911584 + 0.411114i \(0.134860\pi\)
−0.911584 + 0.411114i \(0.865140\pi\)
\(150\) −4.92754e18 5.79620e17i −1.56984 0.184658i
\(151\) 1.09271e18 0.329004 0.164502 0.986377i \(-0.447398\pi\)
0.164502 + 0.986377i \(0.447398\pi\)
\(152\) −1.23297e18 4.51846e17i −0.350979 0.128624i
\(153\) 4.58819e18 1.23528
\(154\) 2.16273e18 + 2.54399e17i 0.550904 + 0.0648021i
\(155\) 7.72224e16i 0.0186176i
\(156\) 9.34578e18 + 2.22951e18i 2.13332 + 0.508921i
\(157\) 3.20208e18i 0.692286i −0.938182 0.346143i \(-0.887491\pi\)
0.938182 0.346143i \(-0.112509\pi\)
\(158\) −5.72408e17 + 4.86623e18i −0.117252 + 0.996799i
\(159\) 6.49268e18 1.26052
\(160\) −6.59674e18 4.37357e18i −1.21425 0.805038i
\(161\) 1.21462e18 0.212042
\(162\) −7.17197e17 + 6.09713e18i −0.118785 + 1.00983i
\(163\) 5.19837e18i 0.817094i −0.912737 0.408547i \(-0.866036\pi\)
0.912737 0.408547i \(-0.133964\pi\)
\(164\) −8.13394e18 1.94042e18i −1.21375 0.289549i
\(165\) 2.22470e19i 3.15252i
\(166\) −8.27114e18 9.72922e17i −1.11339 0.130966i
\(167\) 1.13255e19 1.44866 0.724329 0.689455i \(-0.242150\pi\)
0.724329 + 0.689455i \(0.242150\pi\)
\(168\) −3.92550e18 1.43858e18i −0.477272 0.174906i
\(169\) −1.23334e19 −1.42576
\(170\) 1.65388e19 + 1.94543e18i 1.81839 + 0.213895i
\(171\) 3.51260e18i 0.367420i
\(172\) 3.17389e18 1.33045e19i 0.315937 1.32436i
\(173\) 6.41050e18i 0.607435i −0.952762 0.303717i \(-0.901772\pi\)
0.952762 0.303717i \(-0.0982279\pi\)
\(174\) −1.95728e17 + 1.66395e18i −0.0176598 + 0.150132i
\(175\) −4.71507e18 −0.405195
\(176\) −8.47277e18 + 1.67477e19i −0.693694 + 1.37119i
\(177\) 1.24344e19 0.970179
\(178\) −5.88682e17 + 5.00459e18i −0.0437836 + 0.372219i
\(179\) 7.04159e18i 0.499367i −0.968327 0.249684i \(-0.919673\pi\)
0.968327 0.249684i \(-0.0803266\pi\)
\(180\) 4.91283e18 2.05939e19i 0.332288 1.39290i
\(181\) 6.07746e18i 0.392152i −0.980589 0.196076i \(-0.937180\pi\)
0.980589 0.196076i \(-0.0628199\pi\)
\(182\) 9.06827e18 + 1.06669e18i 0.558364 + 0.0656796i
\(183\) −4.23115e19 −2.48670
\(184\) −3.60222e18 + 9.82949e18i −0.202124 + 0.551543i
\(185\) −2.40454e18 −0.128846
\(186\) −3.49163e17 4.10715e16i −0.0178718 0.00210223i
\(187\) 3.94896e19i 1.93121i
\(188\) 1.88833e19 + 4.50476e18i 0.882543 + 0.210538i
\(189\) 1.94375e17i 0.00868390i
\(190\) 1.48938e18 1.26617e19i 0.0636207 0.540861i
\(191\) 1.49750e19 0.611762 0.305881 0.952070i \(-0.401049\pi\)
0.305881 + 0.952070i \(0.401049\pi\)
\(192\) 2.32838e19 2.75012e19i 0.909898 1.07471i
\(193\) −2.19206e19 −0.819625 −0.409812 0.912170i \(-0.634406\pi\)
−0.409812 + 0.912170i \(0.634406\pi\)
\(194\) −5.65675e16 + 4.80899e17i −0.00202420 + 0.0172084i
\(195\) 9.32811e19i 3.19521i
\(196\) 2.57944e19 + 6.15346e18i 0.845958 + 0.201810i
\(197\) 4.49841e19i 1.41285i 0.707788 + 0.706425i \(0.249693\pi\)
−0.707788 + 0.706425i \(0.750307\pi\)
\(198\) −4.98619e19 5.86518e18i −1.50008 0.176452i
\(199\) 6.77221e17 0.0195200 0.00975999 0.999952i \(-0.496893\pi\)
0.00975999 + 0.999952i \(0.496893\pi\)
\(200\) 1.39835e19 3.81573e19i 0.386243 1.05396i
\(201\) 2.86141e19 0.757553
\(202\) 1.07858e19 + 1.26872e18i 0.273757 + 0.0322017i
\(203\) 1.59220e18i 0.0387509i
\(204\) −1.75927e19 + 7.37458e19i −0.410653 + 1.72140i
\(205\) 8.11855e19i 1.81790i
\(206\) 2.42475e17 2.06136e18i 0.00520948 0.0442876i
\(207\) −2.80032e19 −0.577378
\(208\) −3.55261e19 + 7.02226e19i −0.703088 + 1.38976i
\(209\) −3.02323e19 −0.574417
\(210\) 4.74184e18 4.03120e19i 0.0865133 0.735479i
\(211\) 1.50647e18i 0.0263974i 0.999913 + 0.0131987i \(0.00420139\pi\)
−0.999913 + 0.0131987i \(0.995799\pi\)
\(212\) −1.23403e19 + 5.17287e19i −0.207717 + 0.870717i
\(213\) 1.51769e19i 0.245447i
\(214\) 1.20620e20 + 1.41883e19i 1.87457 + 0.220503i
\(215\) 1.32793e20 1.98358
\(216\) −1.57300e18 5.76459e17i −0.0225877 0.00827773i
\(217\) −3.34107e17 −0.00461294
\(218\) −7.20383e19 8.47377e18i −0.956496 0.112511i
\(219\) 1.02657e19i 0.131103i
\(220\) −1.77247e20 4.22837e19i −2.17764 0.519494i
\(221\) 1.65579e20i 1.95736i
\(222\) 1.27888e18 1.08722e19i 0.0145489 0.123685i
\(223\) 4.18501e19 0.458252 0.229126 0.973397i \(-0.426413\pi\)
0.229126 + 0.973397i \(0.426413\pi\)
\(224\) 1.89225e19 2.85412e19i 0.199467 0.300860i
\(225\) 1.08706e20 1.10332
\(226\) 2.01857e19 1.71606e20i 0.197298 1.67730i
\(227\) 5.35510e19i 0.504137i 0.967709 + 0.252068i \(0.0811108\pi\)
−0.967709 + 0.252068i \(0.918889\pi\)
\(228\) 5.64580e19 + 1.34685e19i 0.512011 + 0.122144i
\(229\) 1.59891e20i 1.39708i 0.715571 + 0.698540i \(0.246166\pi\)
−0.715571 + 0.698540i \(0.753834\pi\)
\(230\) −1.00942e20 1.18736e19i −0.849931 0.0999762i
\(231\) −9.62529e19 −0.781110
\(232\) −1.28851e19 4.72200e18i −0.100795 0.0369384i
\(233\) −1.58383e20 −1.19449 −0.597246 0.802058i \(-0.703738\pi\)
−0.597246 + 0.802058i \(0.703738\pi\)
\(234\) −2.09070e20 2.45926e19i −1.52039 0.178842i
\(235\) 1.88476e20i 1.32184i
\(236\) −2.36334e19 + 9.90678e19i −0.159873 + 0.670163i
\(237\) 2.16573e20i 1.41333i
\(238\) −8.41703e18 + 7.15560e19i −0.0529974 + 0.450549i
\(239\) 8.94881e19 0.543730 0.271865 0.962335i \(-0.412360\pi\)
0.271865 + 0.962335i \(0.412360\pi\)
\(240\) 3.12167e20 + 1.57927e20i 1.83059 + 0.926109i
\(241\) 1.21178e19 0.0685926 0.0342963 0.999412i \(-0.489081\pi\)
0.0342963 + 0.999412i \(0.489081\pi\)
\(242\) −2.91028e19 + 2.47413e20i −0.159039 + 1.35205i
\(243\) 2.66796e20i 1.40775i
\(244\) 8.04193e19 3.37106e20i 0.409776 1.71772i
\(245\) 2.57456e20i 1.26704i
\(246\) 3.67082e20 + 4.31794e19i 1.74508 + 0.205271i
\(247\) −1.26763e20 −0.582196
\(248\) 9.90863e17 2.70380e18i 0.00439718 0.0119987i
\(249\) 3.68110e20 1.57864
\(250\) 4.27626e19 + 5.03011e18i 0.177245 + 0.0208491i
\(251\) 1.61721e19i 0.0647948i −0.999475 0.0323974i \(-0.989686\pi\)
0.999475 0.0323974i \(-0.0103142\pi\)
\(252\) 8.91005e19 + 2.12556e19i 0.345124 + 0.0823322i
\(253\) 2.41018e20i 0.902663i
\(254\) 4.28831e19 3.64564e20i 0.155310 1.32034i
\(255\) −7.36063e20 −2.57824
\(256\) 1.74855e20 + 2.37778e20i 0.592430 + 0.805622i
\(257\) −2.29544e20 −0.752376 −0.376188 0.926543i \(-0.622765\pi\)
−0.376188 + 0.926543i \(0.622765\pi\)
\(258\) −7.06274e19 + 6.00427e20i −0.223978 + 1.90411i
\(259\) 1.04034e19i 0.0319247i
\(260\) −7.43193e20 1.77295e20i −2.20713 0.526529i
\(261\) 3.67083e19i 0.105516i
\(262\) 2.69731e20 + 3.17280e19i 0.750532 + 0.0882840i
\(263\) 3.30068e20 0.889159 0.444579 0.895739i \(-0.353353\pi\)
0.444579 + 0.895739i \(0.353353\pi\)
\(264\) 2.85458e20 7.78939e20i 0.744575 2.03175i
\(265\) −5.16309e20 −1.30413
\(266\) 5.47815e19 + 6.44387e18i 0.134011 + 0.0157635i
\(267\) 2.22731e20i 0.527757i
\(268\) −5.43853e19 + 2.27975e20i −0.124835 + 0.523289i
\(269\) 3.65029e20i 0.811770i 0.913924 + 0.405885i \(0.133037\pi\)
−0.913924 + 0.405885i \(0.866963\pi\)
\(270\) 1.90012e18 1.61536e19i 0.00409439 0.0348078i
\(271\) 8.51437e20 1.77792 0.888962 0.457980i \(-0.151427\pi\)
0.888962 + 0.457980i \(0.151427\pi\)
\(272\) −5.54113e20 2.80330e20i −1.12141 0.567327i
\(273\) −4.03586e20 −0.791688
\(274\) 4.38429e19 3.72723e20i 0.0833719 0.708773i
\(275\) 9.35612e20i 1.72492i
\(276\) 1.07374e20 4.50095e20i 0.191942 0.804594i
\(277\) 1.55690e20i 0.269888i 0.990853 + 0.134944i \(0.0430854\pi\)
−0.990853 + 0.134944i \(0.956915\pi\)
\(278\) 2.91437e20 + 3.42814e19i 0.489964 + 0.0576338i
\(279\) 7.70286e18 0.0125608
\(280\) 3.12163e20 + 1.14398e20i 0.493785 + 0.180957i
\(281\) 9.25634e20 1.42048 0.710241 0.703959i \(-0.248586\pi\)
0.710241 + 0.703959i \(0.248586\pi\)
\(282\) −8.52198e20 1.00243e20i −1.26889 0.149257i
\(283\) 1.32593e20i 0.191574i 0.995402 + 0.0957869i \(0.0305367\pi\)
−0.995402 + 0.0957869i \(0.969463\pi\)
\(284\) 1.20918e20 + 2.88461e19i 0.169546 + 0.0404465i
\(285\) 5.63512e20i 0.766870i
\(286\) −2.11663e20 + 1.79942e21i −0.279598 + 2.37696i
\(287\) 3.51254e20 0.450428
\(288\) −4.36260e20 + 6.58019e20i −0.543137 + 0.819223i
\(289\) 4.79313e20 0.579412
\(290\) 1.55647e19 1.32320e20i 0.0182708 0.155326i
\(291\) 2.14026e19i 0.0243992i
\(292\) 8.17890e19 + 1.95114e19i 0.0905609 + 0.0216040i
\(293\) 1.61233e21i 1.73412i −0.498207 0.867058i \(-0.666008\pi\)
0.498207 0.867058i \(-0.333992\pi\)
\(294\) −1.16409e21 1.36931e20i −1.21629 0.143070i
\(295\) −9.88805e20 −1.00375
\(296\) 8.41907e19 + 3.08534e19i 0.0830395 + 0.0304315i
\(297\) −3.85699e19 −0.0369674
\(298\) 8.76691e20 + 1.03124e20i 0.816598 + 0.0960553i
\(299\) 1.01058e21i 0.914886i
\(300\) −4.16816e20 + 1.74723e21i −0.366787 + 1.53752i
\(301\) 5.74537e20i 0.491477i
\(302\) 4.62157e19 3.92895e20i 0.0384353 0.326751i
\(303\) −4.80025e20 −0.388152
\(304\) −2.14614e20 + 4.24215e20i −0.168745 + 0.333550i
\(305\) 3.36469e21 2.57274
\(306\) 1.94055e20 1.64973e21i 0.144309 1.22682i
\(307\) 1.25031e21i 0.904357i 0.891927 + 0.452178i \(0.149353\pi\)
−0.891927 + 0.452178i \(0.850647\pi\)
\(308\) 1.82943e20 7.66871e20i 0.128717 0.539562i
\(309\) 9.17413e19i 0.0627940i
\(310\) 2.77660e19 + 3.26608e18i 0.0184901 + 0.00217497i
\(311\) 2.50382e20 0.162234 0.0811168 0.996705i \(-0.474151\pi\)
0.0811168 + 0.996705i \(0.474151\pi\)
\(312\) 1.19692e21 3.26607e21i 0.754658 2.05926i
\(313\) −2.54935e21 −1.56423 −0.782117 0.623131i \(-0.785860\pi\)
−0.782117 + 0.623131i \(0.785860\pi\)
\(314\) −1.15134e21 1.35431e20i −0.687546 0.0808751i
\(315\) 8.89320e20i 0.516914i
\(316\) 1.72549e21 + 4.11630e20i 0.976276 + 0.232898i
\(317\) 1.11353e21i 0.613337i −0.951816 0.306668i \(-0.900786\pi\)
0.951816 0.306668i \(-0.0992143\pi\)
\(318\) 2.74605e20 2.33451e21i 0.147257 1.25188i
\(319\) −3.15941e20 −0.164963
\(320\) −1.85157e21 + 2.18694e21i −0.941379 + 1.11189i
\(321\) −5.36822e21 −2.65789
\(322\) 5.13719e19 4.36730e20i 0.0247714 0.210590i
\(323\) 1.00026e21i 0.469779i
\(324\) 2.16195e21 + 5.15751e20i 0.989038 + 0.235943i
\(325\) 3.92300e21i 1.74827i
\(326\) −1.86912e21 2.19862e20i −0.811499 0.0954555i
\(327\) 3.20609e21 1.35619
\(328\) −1.04172e21 + 2.84257e21i −0.429360 + 1.17161i
\(329\) −8.15452e20 −0.327516
\(330\) 7.99912e21 + 9.40926e20i 3.13093 + 0.368287i
\(331\) 1.36776e21i 0.521761i −0.965371 0.260880i \(-0.915987\pi\)
0.965371 0.260880i \(-0.0840128\pi\)
\(332\) −6.99647e20 + 2.93282e21i −0.260139 + 1.09046i
\(333\) 2.39851e20i 0.0869291i
\(334\) 4.79004e20 4.07218e21i 0.169237 1.43874i
\(335\) −2.27544e21 −0.783762
\(336\) −6.83282e20 + 1.35061e21i −0.229465 + 0.453571i
\(337\) −1.13951e21 −0.373133 −0.186567 0.982442i \(-0.559736\pi\)
−0.186567 + 0.982442i \(0.559736\pi\)
\(338\) −5.21634e20 + 4.43458e21i −0.166561 + 1.41599i
\(339\) 7.63736e21i 2.37819i
\(340\) 1.39900e21 5.86440e21i 0.424861 1.78095i
\(341\) 6.62970e19i 0.0196373i
\(342\) −1.26299e21 1.48564e20i −0.364904 0.0429231i
\(343\) −2.39469e21 −0.674915
\(344\) −4.64951e21 1.70391e21i −1.27838 0.468489i
\(345\) 4.49244e21 1.20509
\(346\) −2.30496e21 2.71129e20i −0.603276 0.0709625i
\(347\) 1.78923e21i 0.456946i −0.973550 0.228473i \(-0.926627\pi\)
0.973550 0.228473i \(-0.0733732\pi\)
\(348\) 5.90012e20 + 1.40752e20i 0.147041 + 0.0350777i
\(349\) 7.51876e21i 1.82865i 0.404984 + 0.914324i \(0.367277\pi\)
−0.404984 + 0.914324i \(0.632723\pi\)
\(350\) −1.99421e20 + 1.69535e21i −0.0473362 + 0.402421i
\(351\) −1.61723e20 −0.0374680
\(352\) 5.66344e21 + 3.75480e21i 1.28076 + 0.849131i
\(353\) 6.92424e21 1.52858 0.764288 0.644875i \(-0.223091\pi\)
0.764288 + 0.644875i \(0.223091\pi\)
\(354\) 5.25906e20 4.47091e21i 0.113339 0.963536i
\(355\) 1.20690e21i 0.253939i
\(356\) 1.77455e21 + 4.23333e20i 0.364555 + 0.0869675i
\(357\) 3.18462e21i 0.638819i
\(358\) −2.53187e21 2.97821e20i −0.495948 0.0583377i
\(359\) 6.83078e21 1.30667 0.653337 0.757067i \(-0.273368\pi\)
0.653337 + 0.757067i \(0.273368\pi\)
\(360\) −7.19693e21 2.63746e21i −1.34455 0.492737i
\(361\) 4.71461e21 0.860269
\(362\) −2.18521e21 2.57043e20i −0.389467 0.0458124i
\(363\) 1.10112e22i 1.91703i
\(364\) 7.67076e20 3.21547e21i 0.130460 0.546868i
\(365\) 8.16343e20i 0.135639i
\(366\) −1.78954e21 + 1.52135e22i −0.290505 + 2.46968i
\(367\) −5.85117e21 −0.928071 −0.464036 0.885817i \(-0.653599\pi\)
−0.464036 + 0.885817i \(0.653599\pi\)
\(368\) 3.38194e21 + 1.71095e21i 0.524154 + 0.265173i
\(369\) −8.09818e21 −1.22649
\(370\) −1.01699e20 + 8.64576e20i −0.0150523 + 0.127964i
\(371\) 2.23384e21i 0.323128i
\(372\) −2.95353e19 + 1.23808e20i −0.00417568 + 0.0175038i
\(373\) 8.31710e21i 1.14933i −0.818387 0.574667i \(-0.805131\pi\)
0.818387 0.574667i \(-0.194869\pi\)
\(374\) −1.41989e22 1.67019e21i −1.91799 0.225610i
\(375\) −1.90316e21 −0.251310
\(376\) 2.41839e21 6.59914e21i 0.312198 0.851904i
\(377\) −1.32473e21 −0.167197
\(378\) 6.98894e19 + 8.22099e18i 0.00862444 + 0.00101448i
\(379\) 5.50827e21i 0.664633i −0.943168 0.332317i \(-0.892170\pi\)
0.943168 0.332317i \(-0.107830\pi\)
\(380\) −4.48964e21 1.07104e21i −0.529725 0.126370i
\(381\) 1.62250e22i 1.87207i
\(382\) 6.33360e20 5.38440e21i 0.0714680 0.607574i
\(383\) 1.37047e22 1.51244 0.756222 0.654315i \(-0.227043\pi\)
0.756222 + 0.654315i \(0.227043\pi\)
\(384\) −8.90355e21 9.53505e21i −0.961054 1.02922i
\(385\) 7.65420e21 0.808135
\(386\) −9.27120e20 + 7.88176e21i −0.0957512 + 0.814013i
\(387\) 1.32460e22i 1.33826i
\(388\) 1.70520e20 + 4.06788e19i 0.0168541 + 0.00402067i
\(389\) 1.27957e22i 1.23735i 0.785649 + 0.618673i \(0.212329\pi\)
−0.785649 + 0.618673i \(0.787671\pi\)
\(390\) 3.35401e22 + 3.94528e21i 3.17333 + 0.373275i
\(391\) −7.97432e21 −0.738230
\(392\) 3.30350e21 9.01437e21i 0.299256 0.816589i
\(393\) −1.20044e22 −1.06416
\(394\) 1.61745e22 + 1.90258e21i 1.40318 + 0.165054i
\(395\) 1.72223e22i 1.46223i
\(396\) −4.21777e21 + 1.76803e22i −0.350488 + 1.46919i
\(397\) 1.34055e22i 1.09035i −0.838324 0.545173i \(-0.816464\pi\)
0.838324 0.545173i \(-0.183536\pi\)
\(398\) 2.86427e19 2.43501e20i 0.00228039 0.0193863i
\(399\) −2.43807e21 −0.190010
\(400\) −1.31284e22 6.64174e21i −1.00162 0.506725i
\(401\) 3.18862e21 0.238164 0.119082 0.992884i \(-0.462005\pi\)
0.119082 + 0.992884i \(0.462005\pi\)
\(402\) 1.21022e21 1.02885e22i 0.0884997 0.752366i
\(403\) 2.77982e20i 0.0199032i
\(404\) 9.12360e20 3.82448e21i 0.0639624 0.268121i
\(405\) 2.15786e22i 1.48134i
\(406\) 5.72492e20 + 6.73414e19i 0.0384856 + 0.00452700i
\(407\) 2.06435e21 0.135903
\(408\) 2.57719e22 + 9.44465e21i 1.66164 + 0.608940i
\(409\) −1.47757e22 −0.933036 −0.466518 0.884512i \(-0.654492\pi\)
−0.466518 + 0.884512i \(0.654492\pi\)
\(410\) −2.91910e22 3.43370e21i −1.80546 0.212373i
\(411\) 1.65882e22i 1.00495i
\(412\) −7.30926e20 1.74368e20i −0.0433757 0.0103476i
\(413\) 4.27812e21i 0.248701i
\(414\) −1.18438e21 + 1.00688e22i −0.0674511 + 0.573425i
\(415\) −2.92727e22 −1.63326
\(416\) 2.37467e22 + 1.57438e22i 1.29810 + 0.860629i
\(417\) −1.29705e22 −0.694705
\(418\) −1.27866e21 + 1.08703e22i −0.0671053 + 0.570484i
\(419\) 2.32213e22i 1.19418i −0.802176 0.597088i \(-0.796324\pi\)
0.802176 0.597088i \(-0.203676\pi\)
\(420\) −1.42940e22 3.40995e21i −0.720336 0.171842i
\(421\) 9.61252e19i 0.00474722i −0.999997 0.00237361i \(-0.999244\pi\)
0.999997 0.00237361i \(-0.000755544\pi\)
\(422\) 5.41667e20 + 6.37156e19i 0.0262166 + 0.00308383i
\(423\) 1.88003e22 0.891808
\(424\) 1.80776e22 + 6.62492e21i 0.840489 + 0.308014i
\(425\) 3.09556e22 1.41070
\(426\) −5.45702e21 6.41901e20i −0.243766 0.0286739i
\(427\) 1.45575e22i 0.637456i
\(428\) 1.02031e22 4.27699e22i 0.437986 1.83597i
\(429\) 8.00838e22i 3.37021i
\(430\) 5.61642e21 4.77471e22i 0.231728 1.96999i
\(431\) −8.67397e21 −0.350882 −0.175441 0.984490i \(-0.556135\pi\)
−0.175441 + 0.984490i \(0.556135\pi\)
\(432\) −2.73801e20 + 5.41207e20i −0.0108598 + 0.0214660i
\(433\) −5.54728e21 −0.215741 −0.107871 0.994165i \(-0.534403\pi\)
−0.107871 + 0.994165i \(0.534403\pi\)
\(434\) −1.41309e19 + 1.20131e20i −0.000538898 + 0.00458136i
\(435\) 5.88896e21i 0.220232i
\(436\) −6.09365e21 + 2.55437e22i −0.223482 + 0.936803i
\(437\) 6.10494e21i 0.219578i
\(438\) −3.69112e21 4.34181e20i −0.130205 0.0153158i
\(439\) 2.90117e22 1.00375 0.501875 0.864940i \(-0.332644\pi\)
0.501875 + 0.864940i \(0.332644\pi\)
\(440\) −2.27001e22 + 6.19426e22i −0.770336 + 2.10204i
\(441\) 2.56810e22 0.854839
\(442\) −5.95356e22 7.00309e21i −1.94396 0.228665i
\(443\) 1.05398e22i 0.337600i 0.985650 + 0.168800i \(0.0539892\pi\)
−0.985650 + 0.168800i \(0.946011\pi\)
\(444\) −3.85511e21 9.19668e20i −0.121138 0.0288985i
\(445\) 1.77119e22i 0.546017i
\(446\) 1.77003e21 1.50476e22i 0.0535345 0.455115i
\(447\) −3.90174e22 −1.15783
\(448\) −9.46194e21 8.01091e21i −0.275497 0.233248i
\(449\) 2.19051e22 0.625824 0.312912 0.949782i \(-0.398696\pi\)
0.312912 + 0.949782i \(0.398696\pi\)
\(450\) 4.59767e21 3.90863e22i 0.128894 1.09577i
\(451\) 6.96995e22i 1.91747i
\(452\) −6.08487e22 1.45160e22i −1.64276 0.391894i
\(453\) 1.74859e22i 0.463291i
\(454\) 1.92548e22 + 2.26491e21i 0.500685 + 0.0588948i
\(455\) 3.20939e22 0.819078
\(456\) 7.23059e21 1.97304e22i 0.181123 0.494235i
\(457\) −1.81055e22 −0.445168 −0.222584 0.974914i \(-0.571449\pi\)
−0.222584 + 0.974914i \(0.571449\pi\)
\(458\) 5.74902e22 + 6.76249e21i 1.38751 + 0.163211i
\(459\) 1.27612e21i 0.0302332i
\(460\) −8.53855e21 + 3.57923e22i −0.198583 + 0.832432i
\(461\) 5.23537e22i 1.19534i −0.801744 0.597668i \(-0.796094\pi\)
0.801744 0.597668i \(-0.203906\pi\)
\(462\) −4.07097e21 + 3.46087e22i −0.0912517 + 0.775761i
\(463\) 8.11473e22 1.78581 0.892906 0.450244i \(-0.148663\pi\)
0.892906 + 0.450244i \(0.148663\pi\)
\(464\) −2.24281e21 + 4.43325e21i −0.0484607 + 0.0957897i
\(465\) −1.23574e21 −0.0262166
\(466\) −6.69873e21 + 5.69481e22i −0.139544 + 1.18631i
\(467\) 6.19948e22i 1.26812i −0.773282 0.634062i \(-0.781386\pi\)
0.773282 0.634062i \(-0.218614\pi\)
\(468\) −1.76850e22 + 7.41329e22i −0.355234 + 1.48909i
\(469\) 9.84482e21i 0.194195i
\(470\) 6.77683e22 + 7.97149e21i 1.31279 + 0.154421i
\(471\) 5.12408e22 0.974850
\(472\) 3.46212e22 + 1.26877e22i 0.646898 + 0.237069i
\(473\) −1.14006e23 −2.09222
\(474\) −7.78710e22 9.15985e21i −1.40365 0.165110i
\(475\) 2.36989e22i 0.419597i
\(476\) 2.53727e22 + 6.05285e21i 0.441273 + 0.105269i
\(477\) 5.15014e22i 0.879858i
\(478\) 3.78485e21 3.21763e22i 0.0635202 0.540007i
\(479\) −9.58348e22 −1.58005 −0.790026 0.613073i \(-0.789933\pi\)
−0.790026 + 0.613073i \(0.789933\pi\)
\(480\) 6.99873e22 1.05563e23i 1.13362 1.70986i
\(481\) 8.65576e21 0.137744
\(482\) 5.12514e20 4.35705e21i 0.00801320 0.0681229i
\(483\) 1.94368e22i 0.298589i
\(484\) 8.77288e22 + 2.09284e22i 1.32421 + 0.315901i
\(485\) 1.70197e21i 0.0252434i
\(486\) −9.59290e22 1.12840e22i −1.39811 0.164458i
\(487\) −1.77480e22 −0.254187 −0.127094 0.991891i \(-0.540565\pi\)
−0.127094 + 0.991891i \(0.540565\pi\)
\(488\) −1.17808e23 4.31733e22i −1.65809 0.607640i
\(489\) 8.31859e22 1.15060
\(490\) 9.25708e22 + 1.08890e22i 1.25837 + 0.148020i
\(491\) 2.79794e22i 0.373805i 0.982378 + 0.186903i \(0.0598449\pi\)
−0.982378 + 0.186903i \(0.940155\pi\)
\(492\) 3.10511e22 1.30162e23i 0.407731 1.70915i
\(493\) 1.04532e22i 0.134912i
\(494\) −5.36139e21 + 4.55790e22i −0.0680140 + 0.578210i
\(495\) −1.76468e23 −2.20050
\(496\) −9.30271e20 4.70631e20i −0.0114029 0.00576880i
\(497\) −5.22171e21 −0.0629193
\(498\) 1.55690e22 1.32357e23i 0.184422 1.56783i
\(499\) 2.93207e22i 0.341444i −0.985319 0.170722i \(-0.945390\pi\)
0.985319 0.170722i \(-0.0546100\pi\)
\(500\) 3.61725e21 1.51630e22i 0.0414127 0.173596i
\(501\) 1.81233e23i 2.03994i
\(502\) −5.81484e21 6.83992e20i −0.0643511 0.00756953i
\(503\) −5.05003e22 −0.549498 −0.274749 0.961516i \(-0.588595\pi\)
−0.274749 + 0.961516i \(0.588595\pi\)
\(504\) 1.14111e22 3.11380e22i 0.122087 0.333143i
\(505\) 3.81725e22 0.401581
\(506\) 8.66605e22 + 1.01937e22i 0.896482 + 0.105452i
\(507\) 1.97363e23i 2.00769i
\(508\) −1.29269e23 3.08381e22i −1.29316 0.308493i
\(509\) 6.53584e22i 0.642984i 0.946912 + 0.321492i \(0.104184\pi\)
−0.946912 + 0.321492i \(0.895816\pi\)
\(510\) −3.11314e22 + 2.64659e23i −0.301198 + 2.56059i
\(511\) −3.53196e21 −0.0336076
\(512\) 9.28906e22 5.28140e22i 0.869315 0.494258i
\(513\) −9.76967e20 −0.00899254
\(514\) −9.70846e21 + 8.25349e22i −0.0878949 + 0.747224i
\(515\) 7.29543e21i 0.0649665i
\(516\) 2.12902e23 + 5.07896e22i 1.86491 + 0.444889i
\(517\) 1.61810e23i 1.39424i
\(518\) −3.74064e21 4.40006e20i −0.0317061 0.00372954i
\(519\) 1.02583e23 0.855366
\(520\) −9.51810e22 + 2.59724e23i −0.780768 + 2.13051i
\(521\) 2.48515e22 0.200555 0.100277 0.994960i \(-0.468027\pi\)
0.100277 + 0.994960i \(0.468027\pi\)
\(522\) −1.31988e22 1.55256e21i −0.104794 0.0123268i
\(523\) 4.03025e22i 0.314824i 0.987533 + 0.157412i \(0.0503151\pi\)
−0.987533 + 0.157412i \(0.949685\pi\)
\(524\) 2.28162e22 9.56423e22i 0.175359 0.735079i
\(525\) 7.54520e22i 0.570580i
\(526\) 1.39601e22 1.18679e23i 0.103874 0.883070i
\(527\) 2.19350e21 0.0160601
\(528\) −2.68002e23 1.35584e23i −1.93085 0.976832i
\(529\) −9.23801e22 −0.654946
\(530\) −2.18370e22 + 1.85644e23i −0.152352 + 1.29520i
\(531\) 9.86324e22i 0.677199i
\(532\) 4.63391e21 1.94247e22i 0.0313111 0.131252i
\(533\) 2.92248e23i 1.94344i
\(534\) −8.00850e22 9.42028e21i −0.524144 0.0616543i
\(535\) 4.26890e23 2.74985
\(536\) 7.96705e22 + 2.91969e22i 0.505122 + 0.185112i
\(537\) 1.12682e23 0.703189
\(538\) 1.31250e23 + 1.54387e22i 0.806211 + 0.0948335i
\(539\) 2.21031e23i 1.33644i
\(540\) −5.72781e21 1.36641e21i −0.0340911 0.00813271i
\(541\) 2.15571e23i 1.26303i 0.775365 + 0.631514i \(0.217566\pi\)
−0.775365 + 0.631514i \(0.782434\pi\)
\(542\) 3.60111e22 3.06142e23i 0.207703 1.76575i
\(543\) 9.72535e22 0.552213
\(544\) −1.24231e23 + 1.87380e23i −0.694449 + 1.04745i
\(545\) −2.54954e23 −1.40311
\(546\) −1.70695e22 + 1.45113e23i −0.0924874 + 0.786267i
\(547\) 1.65986e23i 0.885483i 0.896649 + 0.442742i \(0.145994\pi\)
−0.896649 + 0.442742i \(0.854006\pi\)
\(548\) −1.32162e23 3.15283e22i −0.694180 0.165602i
\(549\) 3.35624e23i 1.73576i
\(550\) −3.36408e23 3.95713e22i −1.71311 0.201510i
\(551\) −8.00273e21 −0.0401282
\(552\) −1.57295e23 5.76438e22i −0.776662 0.284623i
\(553\) −7.45132e22 −0.362301
\(554\) 5.59799e22 + 6.58483e21i 0.268040 + 0.0315291i
\(555\) 3.84782e22i 0.181437i
\(556\) 2.46524e22 1.03339e23i 0.114478 0.479876i
\(557\) 1.22488e23i 0.560177i −0.959974 0.280089i \(-0.909636\pi\)
0.959974 0.280089i \(-0.0903639\pi\)
\(558\) 3.25789e20 2.76964e21i 0.00146739 0.0124748i
\(559\) −4.78023e23 −2.12055
\(560\) 5.43358e22 1.07403e23i 0.237404 0.469264i
\(561\) 6.31926e23 2.71945
\(562\) 3.91492e22 3.32821e23i 0.165945 1.41075i
\(563\) 1.24421e23i 0.519484i 0.965678 + 0.259742i \(0.0836376\pi\)
−0.965678 + 0.259742i \(0.916362\pi\)
\(564\) −7.20866e22 + 3.02176e23i −0.296471 + 1.24276i
\(565\) 6.07337e23i 2.46047i
\(566\) 4.76751e22 + 5.60796e21i 0.190262 + 0.0223803i
\(567\) −9.33612e22 −0.367037
\(568\) 1.54861e22 4.22574e22i 0.0599764 0.163660i
\(569\) −4.42193e22 −0.168716 −0.0843582 0.996435i \(-0.526884\pi\)
−0.0843582 + 0.996435i \(0.526884\pi\)
\(570\) 2.02616e23 + 2.38335e22i 0.761619 + 0.0895882i
\(571\) 3.40211e23i 1.25992i 0.776629 + 0.629958i \(0.216928\pi\)
−0.776629 + 0.629958i \(0.783072\pi\)
\(572\) 6.38047e23 + 1.52211e23i 2.32802 + 0.555367i
\(573\) 2.39634e23i 0.861460i
\(574\) 1.48561e22 1.26297e23i 0.0526204 0.447344i
\(575\) −1.88932e23 −0.659371
\(576\) 2.18146e23 + 1.84692e23i 0.750163 + 0.635122i
\(577\) 2.03213e23 0.688584 0.344292 0.938863i \(-0.388119\pi\)
0.344292 + 0.938863i \(0.388119\pi\)
\(578\) 2.02723e22 1.72342e23i 0.0676887 0.575445i
\(579\) 3.50780e23i 1.15416i
\(580\) −4.69188e22 1.11928e22i −0.152128 0.0362913i
\(581\) 1.26650e23i 0.404677i
\(582\) −7.69551e21 9.05212e20i −0.0242321 0.00285039i
\(583\) 4.43262e23 1.37555
\(584\) 1.04747e22 2.85828e22i 0.0320357 0.0874169i
\(585\) −7.39927e23 −2.23030
\(586\) −5.79728e23 6.81925e22i −1.72224 0.202585i
\(587\) 5.86095e23i 1.71611i 0.513561 + 0.858053i \(0.328326\pi\)
−0.513561 + 0.858053i \(0.671674\pi\)
\(588\) −9.84696e22 + 4.12770e23i −0.284181 + 1.19124i
\(589\) 1.67929e21i 0.00477689i
\(590\) −4.18210e22 + 3.55534e23i −0.117261 + 0.996872i
\(591\) −7.19850e23 −1.98952
\(592\) 1.46544e22 2.89667e22i 0.0399241 0.0789158i
\(593\) −6.25760e23 −1.68052 −0.840259 0.542185i \(-0.817597\pi\)
−0.840259 + 0.542185i \(0.817597\pi\)
\(594\) −1.63129e21 + 1.38682e22i −0.00431864 + 0.0367142i
\(595\) 2.53247e23i 0.660921i
\(596\) 7.41584e22 3.10861e23i 0.190795 0.799785i
\(597\) 1.08371e22i 0.0274873i
\(598\) 3.63365e23 + 4.27421e22i 0.908622 + 0.106880i
\(599\) 5.45652e23 1.34520 0.672601 0.740005i \(-0.265177\pi\)
0.672601 + 0.740005i \(0.265177\pi\)
\(600\) 6.10604e23 + 2.23768e23i 1.48414 + 0.543892i
\(601\) 5.66889e23 1.35852 0.679259 0.733899i \(-0.262301\pi\)
0.679259 + 0.733899i \(0.262301\pi\)
\(602\) 2.06580e23 + 2.42998e22i 0.488111 + 0.0574159i
\(603\) 2.26973e23i 0.528783i
\(604\) −1.39314e23 3.32346e22i −0.320024 0.0763442i
\(605\) 8.75629e23i 1.98335i
\(606\) −2.03024e22 + 1.72598e23i −0.0453451 + 0.385494i
\(607\) −4.77180e23 −1.05094 −0.525470 0.850812i \(-0.676111\pi\)
−0.525470 + 0.850812i \(0.676111\pi\)
\(608\) 1.43454e23 + 9.51084e22i 0.311553 + 0.206556i
\(609\) −2.54789e22 −0.0545675
\(610\) 1.42308e23 1.20981e24i 0.300556 2.55512i
\(611\) 6.78467e23i 1.41312i
\(612\) −5.84968e23 1.39549e23i −1.20156 0.286642i
\(613\) 7.99469e23i 1.61952i −0.586758 0.809762i \(-0.699596\pi\)
0.586758 0.809762i \(-0.300404\pi\)
\(614\) 4.49559e23 + 5.28810e22i 0.898165 + 0.105650i
\(615\) 1.29916e24 2.55990
\(616\) −2.67998e23 9.82134e22i −0.520830 0.190869i
\(617\) 1.83317e23 0.351381 0.175691 0.984445i \(-0.443784\pi\)
0.175691 + 0.984445i \(0.443784\pi\)
\(618\) 3.29865e22 + 3.88015e21i 0.0623640 + 0.00733579i
\(619\) 5.31085e23i 0.990361i 0.868790 + 0.495181i \(0.164898\pi\)
−0.868790 + 0.495181i \(0.835102\pi\)
\(620\) 2.34870e21 9.84541e21i 0.00432015 0.0181094i
\(621\) 7.78859e21i 0.0141312i
\(622\) 1.05898e22 9.00275e22i 0.0189526 0.161123i
\(623\) −7.66317e22 −0.135288
\(624\) −1.12372e24 5.68500e23i −1.95700 0.990060i
\(625\) −5.02038e23 −0.862494
\(626\) −1.07823e23 + 9.16642e23i −0.182739 + 1.55352i
\(627\) 4.83787e23i 0.808872i
\(628\) −9.73907e22 + 4.08248e23i −0.160643 + 0.673390i
\(629\) 6.83010e22i 0.111147i
\(630\) 3.19764e23 + 3.76134e22i 0.513375 + 0.0603875i
\(631\) −5.48119e23 −0.868211 −0.434105 0.900862i \(-0.642935\pi\)
−0.434105 + 0.900862i \(0.642935\pi\)
\(632\) 2.20984e23 6.03007e23i 0.345355 0.942383i
\(633\) −2.41071e22 −0.0371717
\(634\) −4.00381e23 4.70963e22i −0.609137 0.0716520i
\(635\) 1.29024e24i 1.93684i
\(636\) −8.27780e23 1.97473e23i −1.22611 0.292498i
\(637\) 9.26779e23i 1.35454i
\(638\) −1.33626e22 + 1.13600e23i −0.0192715 + 0.163833i
\(639\) 1.20387e23 0.171326
\(640\) 7.08026e23 + 7.58244e23i 0.994305 + 1.06483i
\(641\) 9.52772e23 1.32037 0.660185 0.751103i \(-0.270478\pi\)
0.660185 + 0.751103i \(0.270478\pi\)
\(642\) −2.27046e23 + 1.93020e24i −0.310504 + 2.63969i
\(643\) 1.01291e24i 1.36703i −0.729935 0.683517i \(-0.760449\pi\)
0.729935 0.683517i \(-0.239551\pi\)
\(644\) −1.54858e23 3.69425e22i −0.206254 0.0492036i
\(645\) 2.12500e24i 2.79319i
\(646\) −3.59655e23 4.23057e22i −0.466562 0.0548811i
\(647\) −1.18216e24 −1.51352 −0.756762 0.653690i \(-0.773220\pi\)
−0.756762 + 0.653690i \(0.773220\pi\)
\(648\) 2.76882e23 7.55537e23i 0.349870 0.954702i
\(649\) 8.48910e23 1.05872
\(650\) −1.41055e24 1.65921e23i −1.73630 0.204239i
\(651\) 5.34649e21i 0.00649576i
\(652\) −1.58107e23 + 6.62762e23i −0.189604 + 0.794792i
\(653\) 1.00840e23i 0.119363i 0.998217 + 0.0596815i \(0.0190085\pi\)
−0.998217 + 0.0596815i \(0.980992\pi\)
\(654\) 1.35600e23 1.15278e24i 0.158434 1.34690i
\(655\) 9.54614e23 1.10097
\(656\) 9.78013e23 + 4.94784e23i 1.11343 + 0.563291i
\(657\) 8.14295e22 0.0915116
\(658\) −3.44891e22 + 2.93204e23i −0.0382615 + 0.325274i
\(659\) 1.65436e24i 1.81177i 0.423523 + 0.905885i \(0.360793\pi\)
−0.423523 + 0.905885i \(0.639207\pi\)
\(660\) 6.76638e23 2.83637e24i 0.731531 3.06647i
\(661\) 6.63378e22i 0.0708025i 0.999373 + 0.0354012i \(0.0112709\pi\)
−0.999373 + 0.0354012i \(0.988729\pi\)
\(662\) −4.91791e23 5.78486e22i −0.518188 0.0609537i
\(663\) 2.64965e24 2.75628
\(664\) 1.02493e24 + 3.75607e23i 1.05261 + 0.385749i
\(665\) 1.93879e23 0.196584
\(666\) 8.62407e22 + 1.01444e22i 0.0863339 + 0.0101553i
\(667\) 6.37995e22i 0.0630591i
\(668\) −1.44393e24 3.44461e23i −1.40912 0.336156i
\(669\) 6.69698e23i 0.645293i
\(670\) −9.62386e22 + 8.18156e23i −0.0915616 + 0.778396i
\(671\) −2.88865e24 −2.71365
\(672\) 4.56725e23 + 3.02804e23i 0.423659 + 0.280881i
\(673\) −7.36498e23 −0.674595 −0.337298 0.941398i \(-0.609513\pi\)
−0.337298 + 0.941398i \(0.609513\pi\)
\(674\) −4.81950e22 + 4.09722e23i −0.0435906 + 0.370578i
\(675\) 3.02346e22i 0.0270037i
\(676\) 1.57244e24 + 3.75117e23i 1.38684 + 0.330841i
\(677\) 1.40187e24i 1.22097i 0.792029 + 0.610483i \(0.209025\pi\)
−0.792029 + 0.610483i \(0.790975\pi\)
\(678\) 2.74609e24 + 3.23019e23i 2.36190 + 0.277827i
\(679\) −7.36368e21 −0.00625463
\(680\) −2.04943e24 7.51055e23i −1.71913 0.630008i
\(681\) −8.56941e23 −0.709905
\(682\) −2.38377e22 2.80400e21i −0.0195028 0.00229409i
\(683\) 1.74717e24i 1.41175i −0.708334 0.705877i \(-0.750553\pi\)
0.708334 0.705877i \(-0.249447\pi\)
\(684\) −1.06835e23 + 4.47837e23i −0.0852584 + 0.357391i
\(685\) 1.31912e24i 1.03972i
\(686\) −1.01282e23 + 8.61034e23i −0.0788457 + 0.670294i
\(687\) −2.55862e24 −1.96731
\(688\) −8.09306e23 + 1.59971e24i −0.614626 + 1.21490i
\(689\) 1.85859e24 1.39418
\(690\) 1.90005e23 1.61530e24i 0.140783 1.19684i
\(691\) 1.43755e24i 1.05211i 0.850451 + 0.526053i \(0.176329\pi\)
−0.850451 + 0.526053i \(0.823671\pi\)
\(692\) −1.94974e23 + 8.17302e23i −0.140953 + 0.590855i
\(693\) 7.63500e23i 0.545226i
\(694\) −6.43334e23 7.56744e22i −0.453817 0.0533818i
\(695\) 1.03144e24 0.718740
\(696\) 7.55630e22 2.06191e23i 0.0520152 0.141936i
\(697\) −2.30607e24 −1.56818
\(698\) 2.70344e24 + 3.18002e23i 1.81613 + 0.213628i
\(699\) 2.53449e24i 1.68204i
\(700\) 6.01144e23 + 1.43408e23i 0.394135 + 0.0940241i
\(701\) 2.46688e24i 1.59788i −0.601411 0.798940i \(-0.705395\pi\)
0.601411 0.798940i \(-0.294605\pi\)
\(702\) −6.83997e21 + 5.81489e22i −0.00437713 + 0.0372114i
\(703\) 5.22895e22 0.0330594
\(704\) 1.58961e24 1.87754e24i 0.992939 1.17279i
\(705\) −3.01605e24 −1.86136
\(706\) 2.92857e23 2.48968e24i 0.178573 1.51811i
\(707\) 1.65155e23i 0.0995011i
\(708\) −1.58531e24 3.78190e23i −0.943698 0.225127i
\(709\) 4.96755e23i 0.292179i 0.989271 + 0.146090i \(0.0466688\pi\)
−0.989271 + 0.146090i \(0.953331\pi\)
\(710\) 4.33952e23 + 5.10451e22i 0.252200 + 0.0296660i
\(711\) 1.71791e24 0.986525
\(712\) 2.27267e23 6.20152e23i 0.128960 0.351899i
\(713\) −1.33877e22 −0.00750660
\(714\) −1.14506e24 1.34692e23i −0.634445 0.0746289i
\(715\) 6.36840e24i 3.48682i
\(716\) −2.14169e23 + 8.97763e23i −0.115876 + 0.485737i
\(717\) 1.43202e24i 0.765659i
\(718\) 2.88904e23 2.45607e24i 0.152650 1.29773i
\(719\) 2.19102e24 1.14407 0.572033 0.820231i \(-0.306155\pi\)
0.572033 + 0.820231i \(0.306155\pi\)
\(720\) −1.25272e24 + 2.47618e24i −0.646437 + 1.27778i
\(721\) 3.15641e22 0.0160970
\(722\) 1.99402e23 1.69518e24i 0.100499 0.854379i
\(723\) 1.93912e23i 0.0965894i
\(724\) −1.84845e23 + 7.74842e23i −0.0909975 + 0.381448i
\(725\) 2.47664e23i 0.120501i
\(726\) −3.95918e24 4.65713e23i −1.90390 0.223953i
\(727\) 5.04345e23 0.239710 0.119855 0.992791i \(-0.461757\pi\)
0.119855 + 0.992791i \(0.461757\pi\)
\(728\) −1.12371e24 4.11806e23i −0.527883 0.193453i
\(729\) 2.07949e24 0.965546
\(730\) 2.93524e23 + 3.45268e22i 0.134710 + 0.0158457i
\(731\) 3.77199e24i 1.71109i
\(732\) 5.39448e24 + 1.28690e24i 2.41883 + 0.577031i
\(733\) 3.20975e24i 1.42261i −0.702882 0.711307i \(-0.748104\pi\)
0.702882 0.711307i \(-0.251896\pi\)
\(734\) −2.47472e23 + 2.10385e24i −0.108420 + 0.921716i
\(735\) −4.11989e24 −1.78420
\(736\) 7.58224e23 1.14364e24i 0.324591 0.489587i
\(737\) 1.95351e24 0.826690
\(738\) −3.42509e23 + 2.91178e24i −0.143282 + 1.21809i
\(739\) 3.55163e24i 1.46876i 0.678741 + 0.734378i \(0.262526\pi\)
−0.678741 + 0.734378i \(0.737474\pi\)
\(740\) 3.06565e23 + 7.31336e22i 0.125330 + 0.0298984i
\(741\) 2.02851e24i 0.819825i
\(742\) −8.03200e23 9.44792e22i −0.320915 0.0377488i
\(743\) 4.55330e24 1.79854 0.899272 0.437389i \(-0.144097\pi\)
0.899272 + 0.437389i \(0.144097\pi\)
\(744\) 4.32671e22 + 1.58561e22i 0.0168962 + 0.00619194i
\(745\) 3.10273e24 1.19789
\(746\) −2.99049e24 3.51767e23i −1.14147 0.134269i
\(747\) 2.91993e24i 1.10191i
\(748\) −1.20107e24 + 5.03471e24i −0.448131 + 1.87850i
\(749\) 1.84697e24i 0.681339i
\(750\) −8.04934e22 + 6.84301e23i −0.0293589 + 0.249590i
\(751\) −2.50774e24 −0.904362 −0.452181 0.891926i \(-0.649354\pi\)
−0.452181 + 0.891926i \(0.649354\pi\)
\(752\) −2.27050e24 1.14866e24i −0.809599 0.409582i
\(753\) 2.58791e23 0.0912415
\(754\) −5.60290e22 + 4.76321e23i −0.0195324 + 0.166052i
\(755\) 1.39051e24i 0.479319i
\(756\) 5.91187e21 2.47817e22i 0.00201507 0.00844687i
\(757\) 1.69510e24i 0.571323i 0.958331 + 0.285661i \(0.0922133\pi\)
−0.958331 + 0.285661i \(0.907787\pi\)
\(758\) −1.98055e24 2.32970e23i −0.660083 0.0776446i
\(759\) −3.85685e24 −1.27109
\(760\) −5.74989e23 + 1.56899e24i −0.187389 + 0.511335i
\(761\) 1.92045e23 0.0618919 0.0309459 0.999521i \(-0.490148\pi\)
0.0309459 + 0.999521i \(0.490148\pi\)
\(762\) 5.83386e24 + 6.86229e23i 1.85926 + 0.218702i
\(763\) 1.10307e24i 0.347653i
\(764\) −1.90923e24 4.55461e23i −0.595064 0.141957i
\(765\) 5.83862e24i 1.79965i
\(766\) 5.79633e23 4.92765e24i 0.176689 1.50209i
\(767\) 3.55946e24 1.07306
\(768\) −3.80499e24 + 2.79808e24i −1.13