Properties

Label 4.37.b.b.3.10
Level $4$
Weight $37$
Character 4.3
Analytic conductor $32.837$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 4 = 2^{2} \)
Weight: \( k \) \(=\) \( 37 \)
Character orbit: \([\chi]\) \(=\) 4.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(32.8365034637\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 6516989503065492 x^{14} + \)\(17\!\cdots\!98\)\( x^{12} + \)\(23\!\cdots\!44\)\( x^{10} + \)\(17\!\cdots\!45\)\( x^{8} + \)\(72\!\cdots\!20\)\( x^{6} + \)\(15\!\cdots\!00\)\( x^{4} + \)\(15\!\cdots\!00\)\( x^{2} + \)\(51\!\cdots\!00\)\(\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: multiple of \( 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 3.10
Root \(2.99676e7i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.37.b.b.3.9

$q$-expansion

\(f(q)\) \(=\) \(q+(98385.8 + 242981. i) q^{2} +4.79482e8i q^{3} +(-4.93600e10 + 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 + 4.71742e13i) q^{6} -2.27014e14i q^{7} +(-1.64737e16 - 7.28954e15i) q^{8} -7.98083e16 q^{9} +O(q^{10})\) \(q+(98385.8 + 242981. i) q^{2} +4.79482e8i q^{3} +(-4.93600e10 + 4.78117e10i) q^{4} +6.60636e12 q^{5} +(-1.16505e14 + 4.71742e13i) q^{6} -2.27014e14i q^{7} +(-1.64737e16 - 7.28954e15i) q^{8} -7.98083e16 q^{9} +(6.49972e17 + 1.60522e18i) q^{10} +8.91010e18i q^{11} +(-2.29249e19 - 2.36672e19i) q^{12} -1.69290e20 q^{13} +(5.51601e19 - 2.23350e19i) q^{14} +3.16763e21i q^{15} +(1.50445e20 - 4.71997e21i) q^{16} -1.04222e22 q^{17} +(-7.85200e21 - 1.93919e22i) q^{18} -7.97251e21i q^{19} +(-3.26090e23 + 3.15861e23i) q^{20} +1.08849e23 q^{21} +(-2.16498e24 + 8.76627e23i) q^{22} +1.29261e24i q^{23} +(3.49520e24 - 7.89882e24i) q^{24} +2.90921e25 q^{25} +(-1.66557e25 - 4.11341e25i) q^{26} +3.37010e25i q^{27} +(1.08539e25 + 1.12054e25i) q^{28} +6.13174e25 q^{29} +(-7.69674e26 + 3.11650e26i) q^{30} -7.63022e26i q^{31} +(1.16166e27 - 4.27823e26i) q^{32} -4.27223e27 q^{33} +(-1.02539e27 - 2.53239e27i) q^{34} -1.49974e27i q^{35} +(3.93934e27 - 3.81577e27i) q^{36} -1.94121e28 q^{37} +(1.93717e27 - 7.84381e26i) q^{38} -8.11713e28i q^{39} +(-1.08831e29 - 4.81573e28i) q^{40} +5.45164e28 q^{41} +(1.07092e28 + 2.64483e28i) q^{42} +1.65794e29i q^{43} +(-4.26007e29 - 4.39802e29i) q^{44} -5.27243e29 q^{45} +(-3.14080e29 + 1.27174e29i) q^{46} +5.00094e29i q^{47} +(2.26314e30 + 7.21357e28i) q^{48} +2.60020e30 q^{49} +(2.86225e30 + 7.06882e30i) q^{50} -4.99724e30i q^{51} +(8.35613e30 - 8.09403e30i) q^{52} -2.38312e30 q^{53} +(-8.18870e30 + 3.31570e30i) q^{54} +5.88633e31i q^{55} +(-1.65483e30 + 3.73975e30i) q^{56} +3.82267e30 q^{57} +(6.03276e30 + 1.48990e31i) q^{58} -7.57344e31i q^{59} +(-1.51450e32 - 1.56354e32i) q^{60} +1.15248e32 q^{61} +(1.85400e32 - 7.50705e31i) q^{62} +1.81176e31i q^{63} +(2.18244e32 + 2.40171e32i) q^{64} -1.11839e33 q^{65} +(-4.20327e32 - 1.03807e33i) q^{66} +9.05989e32i q^{67} +(5.14438e32 - 4.98302e32i) q^{68} -6.19784e32 q^{69} +(3.64408e32 - 1.47553e32i) q^{70} +7.34519e32i q^{71} +(1.31473e33 + 5.81766e32i) q^{72} +3.68724e33 q^{73} +(-1.90988e33 - 4.71677e33i) q^{74} +1.39491e34i q^{75} +(3.81179e32 + 3.93523e32i) q^{76} +2.02272e33 q^{77} +(1.97231e34 - 7.98610e33i) q^{78} +2.27270e34i q^{79} +(9.93894e32 - 3.11818e34i) q^{80} -2.81378e34 q^{81} +(5.36364e33 + 1.32465e34i) q^{82} -1.22370e34i q^{83} +(-5.37279e33 + 5.20427e33i) q^{84} -6.88526e34 q^{85} +(-4.02848e34 + 1.63118e34i) q^{86} +2.94006e34i q^{87} +(6.49505e34 - 1.46782e35i) q^{88} +8.48753e32 q^{89} +(-5.18732e34 - 1.28110e35i) q^{90} +3.84311e34i q^{91} +(-6.18019e34 - 6.38032e34i) q^{92} +3.65855e35 q^{93} +(-1.21513e35 + 4.92021e34i) q^{94} -5.26692e34i q^{95} +(2.05133e35 + 5.56997e35i) q^{96} -2.86871e35 q^{97} +(2.55822e35 + 6.31798e35i) q^{98} -7.11100e35i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 177228q^{2} - 5610707696q^{4} + 5816089539360q^{5} - 217628996575488q^{6} + 11897560228206528q^{8} - 935184460817545968q^{9} + O(q^{10}) \) \( 16q + 177228q^{2} - 5610707696q^{4} + 5816089539360q^{5} - 217628996575488q^{6} + 11897560228206528q^{8} - 935184460817545968q^{9} - 2378142919315561000q^{10} - 42882825786868930560q^{12} + \)\(19\!\cdots\!76\)\(q^{13} + \)\(36\!\cdots\!28\)\(q^{14} - \)\(22\!\cdots\!84\)\(q^{16} + \)\(41\!\cdots\!76\)\(q^{17} + \)\(13\!\cdots\!68\)\(q^{18} + \)\(10\!\cdots\!40\)\(q^{20} - \)\(17\!\cdots\!96\)\(q^{21} - \)\(43\!\cdots\!40\)\(q^{22} + \)\(51\!\cdots\!68\)\(q^{24} + \)\(61\!\cdots\!00\)\(q^{25} - \)\(70\!\cdots\!40\)\(q^{26} - \)\(30\!\cdots\!00\)\(q^{28} - \)\(95\!\cdots\!52\)\(q^{29} + \)\(36\!\cdots\!20\)\(q^{30} + \)\(46\!\cdots\!48\)\(q^{32} - \)\(87\!\cdots\!60\)\(q^{33} - \)\(90\!\cdots\!20\)\(q^{34} - \)\(92\!\cdots\!92\)\(q^{36} - \)\(30\!\cdots\!84\)\(q^{37} + \)\(78\!\cdots\!80\)\(q^{38} - \)\(13\!\cdots\!00\)\(q^{40} + \)\(99\!\cdots\!12\)\(q^{41} - \)\(19\!\cdots\!00\)\(q^{42} + \)\(30\!\cdots\!60\)\(q^{44} + \)\(15\!\cdots\!20\)\(q^{45} - \)\(91\!\cdots\!28\)\(q^{46} - \)\(15\!\cdots\!20\)\(q^{48} - \)\(11\!\cdots\!48\)\(q^{49} + \)\(11\!\cdots\!00\)\(q^{50} + \)\(16\!\cdots\!56\)\(q^{52} + \)\(20\!\cdots\!56\)\(q^{53} - \)\(42\!\cdots\!84\)\(q^{54} - \)\(18\!\cdots\!68\)\(q^{56} - \)\(17\!\cdots\!80\)\(q^{57} + \)\(33\!\cdots\!56\)\(q^{58} - \)\(69\!\cdots\!00\)\(q^{60} + \)\(21\!\cdots\!32\)\(q^{61} + \)\(40\!\cdots\!80\)\(q^{62} - \)\(26\!\cdots\!96\)\(q^{64} - \)\(20\!\cdots\!00\)\(q^{65} - \)\(81\!\cdots\!60\)\(q^{66} + \)\(35\!\cdots\!56\)\(q^{68} + \)\(39\!\cdots\!56\)\(q^{69} + \)\(31\!\cdots\!80\)\(q^{70} - \)\(18\!\cdots\!32\)\(q^{72} - \)\(13\!\cdots\!64\)\(q^{73} + \)\(76\!\cdots\!40\)\(q^{74} - \)\(15\!\cdots\!60\)\(q^{76} + \)\(22\!\cdots\!00\)\(q^{77} - \)\(18\!\cdots\!60\)\(q^{78} + \)\(67\!\cdots\!60\)\(q^{80} - \)\(40\!\cdots\!00\)\(q^{81} + \)\(43\!\cdots\!36\)\(q^{82} - \)\(37\!\cdots\!64\)\(q^{84} - \)\(20\!\cdots\!00\)\(q^{85} + \)\(10\!\cdots\!32\)\(q^{86} + \)\(39\!\cdots\!80\)\(q^{88} + \)\(46\!\cdots\!88\)\(q^{89} - \)\(36\!\cdots\!00\)\(q^{90} - \)\(17\!\cdots\!80\)\(q^{92} - \)\(23\!\cdots\!80\)\(q^{93} - \)\(69\!\cdots\!32\)\(q^{94} + \)\(10\!\cdots\!72\)\(q^{96} + \)\(45\!\cdots\!96\)\(q^{97} + \)\(10\!\cdots\!28\)\(q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 98385.8 + 242981.i 0.375312 + 0.926899i
\(3\) 4.79482e8i 1.23763i 0.785538 + 0.618813i \(0.212386\pi\)
−0.785538 + 0.618813i \(0.787614\pi\)
\(4\) −4.93600e10 + 4.78117e10i −0.718282 + 0.695752i
\(5\) 6.60636e12 1.73182 0.865909 0.500202i \(-0.166741\pi\)
0.865909 + 0.500202i \(0.166741\pi\)
\(6\) −1.16505e14 + 4.71742e13i −1.14715 + 0.464496i
\(7\) 2.27014e14i 0.139408i −0.997568 0.0697041i \(-0.977794\pi\)
0.997568 0.0697041i \(-0.0222055\pi\)
\(8\) −1.64737e16 7.28954e15i −0.914471 0.404650i
\(9\) −7.98083e16 −0.531720
\(10\) 6.49972e17 + 1.60522e18i 0.649972 + 1.60522i
\(11\) 8.91010e18i 1.60256i 0.598289 + 0.801280i \(0.295847\pi\)
−0.598289 + 0.801280i \(0.704153\pi\)
\(12\) −2.29249e19 2.36672e19i −0.861081 0.888965i
\(13\) −1.69290e20 −1.50539 −0.752696 0.658368i \(-0.771247\pi\)
−0.752696 + 0.658368i \(0.771247\pi\)
\(14\) 5.51601e19 2.23350e19i 0.129217 0.0523216i
\(15\) 3.16763e21i 2.14334i
\(16\) 1.50445e20 4.71997e21i 0.0318580 0.999492i
\(17\) −1.04222e22 −0.741101 −0.370551 0.928812i \(-0.620831\pi\)
−0.370551 + 0.928812i \(0.620831\pi\)
\(18\) −7.85200e21 1.93919e22i −0.199561 0.492851i
\(19\) 7.97251e21i 0.0765649i −0.999267 0.0382825i \(-0.987811\pi\)
0.999267 0.0382825i \(-0.0121887\pi\)
\(20\) −3.26090e23 + 3.15861e23i −1.24393 + 1.20492i
\(21\) 1.08849e23 0.172535
\(22\) −2.16498e24 + 8.76627e23i −1.48541 + 0.601460i
\(23\) 1.29261e24i 0.398443i 0.979954 + 0.199222i \(0.0638414\pi\)
−0.979954 + 0.199222i \(0.936159\pi\)
\(24\) 3.49520e24 7.89882e24i 0.500806 1.13177i
\(25\) 2.90921e25 1.99919
\(26\) −1.66557e25 4.11341e25i −0.564992 1.39535i
\(27\) 3.37010e25i 0.579556i
\(28\) 1.08539e25 + 1.12054e25i 0.0969936 + 0.100134i
\(29\) 6.13174e25 0.291353 0.145677 0.989332i \(-0.453464\pi\)
0.145677 + 0.989332i \(0.453464\pi\)
\(30\) −7.69674e26 + 3.11650e26i −1.98666 + 0.804423i
\(31\) 7.63022e26i 1.09151i −0.837946 0.545754i \(-0.816243\pi\)
0.837946 0.545754i \(-0.183757\pi\)
\(32\) 1.16166e27 4.27823e26i 0.938385 0.345592i
\(33\) −4.27223e27 −1.98337
\(34\) −1.02539e27 2.53239e27i −0.278144 0.686926i
\(35\) 1.49974e27i 0.241430i
\(36\) 3.93934e27 3.81577e27i 0.381925 0.369945i
\(37\) −1.94121e28 −1.14932 −0.574661 0.818392i \(-0.694866\pi\)
−0.574661 + 0.818392i \(0.694866\pi\)
\(38\) 1.93717e27 7.84381e26i 0.0709679 0.0287357i
\(39\) 8.11713e28i 1.86311i
\(40\) −1.08831e29 4.81573e28i −1.58370 0.700781i
\(41\) 5.45164e28 0.508649 0.254324 0.967119i \(-0.418147\pi\)
0.254324 + 0.967119i \(0.418147\pi\)
\(42\) 1.07092e28 + 2.64483e28i 0.0647546 + 0.159923i
\(43\) 1.65794e29i 0.656353i 0.944616 + 0.328176i \(0.106434\pi\)
−0.944616 + 0.328176i \(0.893566\pi\)
\(44\) −4.26007e29 4.39802e29i −1.11498 1.15109i
\(45\) −5.27243e29 −0.920842
\(46\) −3.14080e29 + 1.27174e29i −0.369317 + 0.149541i
\(47\) 5.00094e29i 0.399292i 0.979868 + 0.199646i \(0.0639791\pi\)
−0.979868 + 0.199646i \(0.936021\pi\)
\(48\) 2.26314e30 + 7.21357e28i 1.23700 + 0.0394283i
\(49\) 2.60020e30 0.980565
\(50\) 2.86225e30 + 7.06882e30i 0.750321 + 1.85305i
\(51\) 4.99724e30i 0.917207i
\(52\) 8.35613e30 8.09403e30i 1.08130 1.04738i
\(53\) −2.38312e30 −0.218867 −0.109433 0.993994i \(-0.534904\pi\)
−0.109433 + 0.993994i \(0.534904\pi\)
\(54\) −8.18870e30 + 3.31570e30i −0.537189 + 0.217514i
\(55\) 5.88633e31i 2.77534i
\(56\) −1.65483e30 + 3.73975e30i −0.0564116 + 0.127485i
\(57\) 3.82267e30 0.0947588
\(58\) 6.03276e30 + 1.48990e31i 0.109348 + 0.270055i
\(59\) 7.57344e31i 1.00915i −0.863367 0.504576i \(-0.831649\pi\)
0.863367 0.504576i \(-0.168351\pi\)
\(60\) −1.51450e32 1.56354e32i −1.49124 1.53953i
\(61\) 1.15248e32 0.842748 0.421374 0.906887i \(-0.361548\pi\)
0.421374 + 0.906887i \(0.361548\pi\)
\(62\) 1.85400e32 7.50705e31i 1.01172 0.409656i
\(63\) 1.81176e31i 0.0741261i
\(64\) 2.18244e32 + 2.40171e32i 0.672516 + 0.740083i
\(65\) −1.11839e33 −2.60707
\(66\) −4.20327e32 1.03807e33i −0.744383 1.83838i
\(67\) 9.05989e32i 1.22399i 0.790863 + 0.611993i \(0.209632\pi\)
−0.790863 + 0.611993i \(0.790368\pi\)
\(68\) 5.14438e32 4.98302e32i 0.532320 0.515623i
\(69\) −6.19784e32 −0.493124
\(70\) 3.64408e32 1.47553e32i 0.223781 0.0906114i
\(71\) 7.34519e32i 0.349424i 0.984620 + 0.174712i \(0.0558995\pi\)
−0.984620 + 0.174712i \(0.944101\pi\)
\(72\) 1.31473e33 + 5.81766e32i 0.486243 + 0.215161i
\(73\) 3.68724e33 1.06387 0.531937 0.846784i \(-0.321464\pi\)
0.531937 + 0.846784i \(0.321464\pi\)
\(74\) −1.90988e33 4.71677e33i −0.431354 1.06531i
\(75\) 1.39491e34i 2.47426i
\(76\) 3.81179e32 + 3.93523e32i 0.0532702 + 0.0549952i
\(77\) 2.02272e33 0.223410
\(78\) 1.97231e34 7.98610e33i 1.72692 0.699249i
\(79\) 2.27270e34i 1.58217i 0.611705 + 0.791086i \(0.290484\pi\)
−0.611705 + 0.791086i \(0.709516\pi\)
\(80\) 9.93894e32 3.11818e34i 0.0551722 1.73094i
\(81\) −2.81378e34 −1.24899
\(82\) 5.36364e33 + 1.32465e34i 0.190902 + 0.471466i
\(83\) 1.22370e34i 0.350163i −0.984554 0.175082i \(-0.943981\pi\)
0.984554 0.175082i \(-0.0560189\pi\)
\(84\) −5.37279e33 + 5.20427e33i −0.123929 + 0.120042i
\(85\) −6.88526e34 −1.28345
\(86\) −4.02848e34 + 1.63118e34i −0.608372 + 0.246337i
\(87\) 2.94006e34i 0.360586i
\(88\) 6.49505e34 1.46782e35i 0.648477 1.46550i
\(89\) 8.48753e32 0.00691451 0.00345725 0.999994i \(-0.498900\pi\)
0.00345725 + 0.999994i \(0.498900\pi\)
\(90\) −5.18732e34 1.28110e35i −0.345603 0.853527i
\(91\) 3.84311e34i 0.209864i
\(92\) −6.18019e34 6.38032e34i −0.277218 0.286195i
\(93\) 3.65855e35 1.35088
\(94\) −1.21513e35 + 4.92021e34i −0.370103 + 0.149859i
\(95\) 5.26692e34i 0.132597i
\(96\) 2.05133e35 + 5.56997e35i 0.427714 + 1.16137i
\(97\) −2.86871e35 −0.496358 −0.248179 0.968714i \(-0.579832\pi\)
−0.248179 + 0.968714i \(0.579832\pi\)
\(98\) 2.55822e35 + 6.31798e35i 0.368018 + 0.908885i
\(99\) 7.11100e35i 0.852113i
\(100\) −1.43598e36 + 1.39094e36i −1.43598 + 1.39094i
\(101\) 5.18410e35 0.433400 0.216700 0.976238i \(-0.430471\pi\)
0.216700 + 0.976238i \(0.430471\pi\)
\(102\) 1.21423e36 4.91657e35i 0.850158 0.344239i
\(103\) 5.22189e35i 0.306731i −0.988170 0.153366i \(-0.950989\pi\)
0.988170 0.153366i \(-0.0490112\pi\)
\(104\) 2.78882e36 + 1.23404e36i 1.37664 + 0.609158i
\(105\) 7.19097e35 0.298800
\(106\) −2.34465e35 5.79052e35i −0.0821433 0.202867i
\(107\) 3.32310e36i 0.983184i −0.870826 0.491592i \(-0.836415\pi\)
0.870826 0.491592i \(-0.163585\pi\)
\(108\) −1.61130e36 1.66348e36i −0.403227 0.416285i
\(109\) 5.60436e36 1.18809 0.594044 0.804432i \(-0.297530\pi\)
0.594044 + 0.804432i \(0.297530\pi\)
\(110\) −1.43027e37 + 5.79132e36i −2.57246 + 1.04162i
\(111\) 9.30776e36i 1.42243i
\(112\) −1.07150e36 3.41532e34i −0.139337 0.00444126i
\(113\) −1.35908e37 −1.50603 −0.753016 0.658003i \(-0.771402\pi\)
−0.753016 + 0.658003i \(0.771402\pi\)
\(114\) 3.76097e35 + 9.28836e35i 0.0355641 + 0.0878318i
\(115\) 8.53945e36i 0.690032i
\(116\) −3.02662e36 + 2.93169e36i −0.209274 + 0.202710i
\(117\) 1.35107e37 0.800448
\(118\) 1.84020e37 7.45119e36i 0.935382 0.378747i
\(119\) 2.36598e36i 0.103316i
\(120\) 2.30906e37 5.21825e37i 0.867305 1.96003i
\(121\) −4.84772e37 −1.56820
\(122\) 1.13388e37 + 2.80031e37i 0.316293 + 0.781142i
\(123\) 2.61397e37i 0.629517i
\(124\) 3.64814e37 + 3.76627e37i 0.759418 + 0.784010i
\(125\) 9.60576e37 1.73042
\(126\) −4.40224e36 + 1.78252e36i −0.0687074 + 0.0278204i
\(127\) 1.31905e38i 1.78564i 0.450411 + 0.892822i \(0.351278\pi\)
−0.450411 + 0.892822i \(0.648722\pi\)
\(128\) −3.68848e37 + 7.66585e37i −0.433578 + 0.901116i
\(129\) −7.94953e37 −0.812320
\(130\) −1.10033e38 2.71747e38i −0.978463 2.41649i
\(131\) 2.23577e36i 0.0173198i −0.999963 0.00865992i \(-0.997243\pi\)
0.999963 0.00865992i \(-0.00275657\pi\)
\(132\) 2.10877e38 2.04263e38i 1.42462 1.37993i
\(133\) −1.80987e36 −0.0106738
\(134\) −2.20138e38 + 8.91365e37i −1.13451 + 0.459377i
\(135\) 2.22641e38i 1.00369i
\(136\) 1.71691e38 + 7.59728e37i 0.677716 + 0.299887i
\(137\) −2.11161e38 −0.730539 −0.365270 0.930902i \(-0.619023\pi\)
−0.365270 + 0.930902i \(0.619023\pi\)
\(138\) −6.09779e37 1.50596e38i −0.185075 0.457076i
\(139\) 3.04795e38i 0.812347i −0.913796 0.406173i \(-0.866863\pi\)
0.913796 0.406173i \(-0.133137\pi\)
\(140\) 7.17050e37 + 7.40270e37i 0.167975 + 0.173415i
\(141\) −2.39786e38 −0.494174
\(142\) −1.78474e38 + 7.22662e37i −0.323881 + 0.131143i
\(143\) 1.50839e39i 2.41248i
\(144\) −1.20068e37 + 3.76693e38i −0.0169395 + 0.531450i
\(145\) 4.05085e38 0.504570
\(146\) 3.62772e38 + 8.95930e38i 0.399285 + 0.986103i
\(147\) 1.24675e39i 1.21357i
\(148\) 9.58181e38 9.28127e38i 0.825537 0.799643i
\(149\) 1.09009e39 0.831976 0.415988 0.909370i \(-0.363436\pi\)
0.415988 + 0.909370i \(0.363436\pi\)
\(150\) −3.38937e39 + 1.37240e39i −2.29338 + 0.928617i
\(151\) 1.45223e39i 0.871869i 0.899978 + 0.435934i \(0.143582\pi\)
−0.899978 + 0.435934i \(0.856418\pi\)
\(152\) −5.81159e37 + 1.31336e38i −0.0309820 + 0.0700165i
\(153\) 8.31776e38 0.394058
\(154\) 1.99007e38 + 4.91482e38i 0.0838484 + 0.207078i
\(155\) 5.04080e39i 1.89029i
\(156\) 3.88094e39 + 4.00661e39i 1.29627 + 1.33824i
\(157\) 3.77925e39 1.12515 0.562576 0.826745i \(-0.309810\pi\)
0.562576 + 0.826745i \(0.309810\pi\)
\(158\) −5.52222e39 + 2.23601e39i −1.46651 + 0.593808i
\(159\) 1.14266e39i 0.270876i
\(160\) 7.67437e39 2.82635e39i 1.62511 0.598503i
\(161\) 2.93441e38 0.0555463
\(162\) −2.76836e39 6.83696e39i −0.468762 1.15769i
\(163\) 5.70992e39i 0.865472i −0.901521 0.432736i \(-0.857548\pi\)
0.901521 0.432736i \(-0.142452\pi\)
\(164\) −2.69093e39 + 2.60653e39i −0.365353 + 0.353894i
\(165\) −2.82239e40 −3.43484
\(166\) 2.97337e39 1.20395e39i 0.324566 0.131420i
\(167\) 2.00063e40i 1.96006i 0.198841 + 0.980032i \(0.436282\pi\)
−0.198841 + 0.980032i \(0.563718\pi\)
\(168\) −1.79314e39 7.93460e38i −0.157779 0.0698165i
\(169\) 1.60127e40 1.26621
\(170\) −6.77412e39 1.67299e40i −0.481695 1.18963i
\(171\) 6.36272e38i 0.0407111i
\(172\) −7.92691e39 8.18360e39i −0.456659 0.471446i
\(173\) −1.52851e39 −0.0793301 −0.0396651 0.999213i \(-0.512629\pi\)
−0.0396651 + 0.999213i \(0.512629\pi\)
\(174\) −7.14378e39 + 2.89260e39i −0.334227 + 0.135332i
\(175\) 6.60432e39i 0.278704i
\(176\) 4.20554e40 + 1.34048e39i 1.60175 + 0.0510543i
\(177\) 3.63133e40 1.24895
\(178\) 8.35052e37 + 2.06231e38i 0.00259510 + 0.00640905i
\(179\) 5.96587e40i 1.67617i 0.545536 + 0.838087i \(0.316326\pi\)
−0.545536 + 0.838087i \(0.683674\pi\)
\(180\) 2.60247e40 2.52084e40i 0.661424 0.640678i
\(181\) 2.49321e39 0.0573515 0.0286758 0.999589i \(-0.490871\pi\)
0.0286758 + 0.999589i \(0.490871\pi\)
\(182\) −9.33803e39 + 3.78108e39i −0.194523 + 0.0787645i
\(183\) 5.52595e40i 1.04301i
\(184\) 9.42253e39 2.12940e40i 0.161230 0.364365i
\(185\) −1.28243e41 −1.99042
\(186\) 3.59949e40 + 8.88958e40i 0.507001 + 1.25213i
\(187\) 9.28626e40i 1.18766i
\(188\) −2.39103e40 2.46846e40i −0.277808 0.286804i
\(189\) 7.65061e39 0.0807948
\(190\) 1.27976e40 5.18190e39i 0.122904 0.0497651i
\(191\) 2.34835e40i 0.205193i 0.994723 + 0.102596i \(0.0327150\pi\)
−0.994723 + 0.102596i \(0.967285\pi\)
\(192\) −1.15157e41 + 1.04644e41i −0.915946 + 0.832324i
\(193\) 1.49860e41 1.08556 0.542781 0.839874i \(-0.317371\pi\)
0.542781 + 0.839874i \(0.317371\pi\)
\(194\) −2.82240e40 6.97041e40i −0.186289 0.460073i
\(195\) 5.36247e41i 3.22658i
\(196\) −1.28346e41 + 1.24320e41i −0.704322 + 0.682230i
\(197\) 2.26156e41 1.13244 0.566222 0.824253i \(-0.308404\pi\)
0.566222 + 0.824253i \(0.308404\pi\)
\(198\) 1.72784e41 6.99621e40i 0.789823 0.319808i
\(199\) 2.93782e41i 1.22650i 0.789887 + 0.613252i \(0.210139\pi\)
−0.789887 + 0.613252i \(0.789861\pi\)
\(200\) −4.79253e41 2.12068e41i −1.82821 0.808975i
\(201\) −4.34406e41 −1.51484
\(202\) 5.10041e40 + 1.25964e41i 0.162660 + 0.401717i
\(203\) 1.39199e40i 0.0406170i
\(204\) 2.38927e41 + 2.46664e41i 0.638149 + 0.658813i
\(205\) 3.60155e41 0.880887
\(206\) 1.26882e41 5.13760e40i 0.284309 0.115120i
\(207\) 1.03161e41i 0.211860i
\(208\) −2.54688e40 + 7.99042e41i −0.0479588 + 1.50463i
\(209\) 7.10358e40 0.122700
\(210\) 7.07489e40 + 1.74727e41i 0.112143 + 0.276957i
\(211\) 6.82410e41i 0.993027i −0.868029 0.496513i \(-0.834613\pi\)
0.868029 0.496513i \(-0.165387\pi\)
\(212\) 1.17631e41 1.13941e41i 0.157208 0.152277i
\(213\) −3.52189e41 −0.432457
\(214\) 8.07449e41 3.26945e41i 0.911312 0.369001i
\(215\) 1.09530e42i 1.13668i
\(216\) 2.45665e41 5.55179e41i 0.234518 0.529987i
\(217\) −1.73217e41 −0.152165
\(218\) 5.51389e41 + 1.36175e42i 0.445904 + 1.10124i
\(219\) 1.76797e42i 1.31668i
\(220\) −2.81436e42 2.90549e42i −1.93095 1.99348i
\(221\) 1.76436e42 1.11565
\(222\) 2.26161e42 9.15751e41i 1.31845 0.533856i
\(223\) 2.30581e42i 1.23976i 0.784698 + 0.619878i \(0.212818\pi\)
−0.784698 + 0.619878i \(0.787182\pi\)
\(224\) −9.71218e40 2.63714e41i −0.0481784 0.130819i
\(225\) −2.32179e42 −1.06301
\(226\) −1.33714e42 3.30231e42i −0.565231 1.39594i
\(227\) 4.50702e42i 1.75964i −0.475304 0.879821i \(-0.657662\pi\)
0.475304 0.879821i \(-0.342338\pi\)
\(228\) −1.88687e41 + 1.82769e41i −0.0680636 + 0.0659287i
\(229\) −3.67329e42 −1.22466 −0.612331 0.790602i \(-0.709768\pi\)
−0.612331 + 0.790602i \(0.709768\pi\)
\(230\) −2.07492e42 + 8.40161e41i −0.639589 + 0.258977i
\(231\) 9.69858e41i 0.276498i
\(232\) −1.01012e42 4.46975e41i −0.266434 0.117896i
\(233\) 4.12814e42 1.00774 0.503869 0.863780i \(-0.331910\pi\)
0.503869 + 0.863780i \(0.331910\pi\)
\(234\) 1.32926e42 + 3.28285e42i 0.300417 + 0.741934i
\(235\) 3.30380e42i 0.691500i
\(236\) 3.62099e42 + 3.73825e42i 0.702120 + 0.724856i
\(237\) −1.08972e43 −1.95814
\(238\) −5.74888e41 + 2.32779e41i −0.0957631 + 0.0387756i
\(239\) 2.53834e41i 0.0392092i −0.999808 0.0196046i \(-0.993759\pi\)
0.999808 0.0196046i \(-0.00624074\pi\)
\(240\) 1.49511e43 + 4.76554e41i 2.14226 + 0.0682826i
\(241\) 1.11078e43 1.47680 0.738402 0.674360i \(-0.235581\pi\)
0.738402 + 0.674360i \(0.235581\pi\)
\(242\) −4.76947e42 1.17790e43i −0.588564 1.45356i
\(243\) 8.43324e42i 0.966232i
\(244\) −5.68865e42 + 5.51022e42i −0.605331 + 0.586344i
\(245\) 1.71778e43 1.69816
\(246\) −6.35144e42 + 2.57177e42i −0.583499 + 0.236265i
\(247\) 1.34966e42i 0.115260i
\(248\) −5.56208e42 + 1.25698e43i −0.441679 + 0.998152i
\(249\) 5.86744e42 0.433371
\(250\) 9.45070e42 + 2.33402e43i 0.649447 + 1.60392i
\(251\) 7.49923e41i 0.0479611i 0.999712 + 0.0239806i \(0.00763398\pi\)
−0.999712 + 0.0239806i \(0.992366\pi\)
\(252\) −8.66235e41 8.94285e41i −0.0515734 0.0532435i
\(253\) −1.15173e43 −0.638530
\(254\) −3.20504e43 + 1.29776e43i −1.65511 + 0.670173i
\(255\) 3.30136e43i 1.58844i
\(256\) −2.22555e43 1.42019e42i −0.997970 0.0636836i
\(257\) −1.46734e43 −0.613385 −0.306692 0.951809i \(-0.599222\pi\)
−0.306692 + 0.951809i \(0.599222\pi\)
\(258\) −7.82121e42 1.93158e43i −0.304873 0.752938i
\(259\) 4.40683e42i 0.160225i
\(260\) 5.52036e43 5.34721e43i 1.87261 1.81387i
\(261\) −4.89364e42 −0.154918
\(262\) 5.43249e41 2.19968e41i 0.0160537 0.00650034i
\(263\) 5.72464e42i 0.157959i 0.996876 + 0.0789796i \(0.0251662\pi\)
−0.996876 + 0.0789796i \(0.974834\pi\)
\(264\) 7.03793e43 + 3.11426e43i 1.81374 + 0.802572i
\(265\) −1.57437e43 −0.379038
\(266\) −1.78066e41 4.39764e41i −0.00400600 0.00989351i
\(267\) 4.06962e41i 0.00855758i
\(268\) −4.33169e43 4.47196e43i −0.851591 0.879167i
\(269\) −4.65647e42 −0.0856083 −0.0428041 0.999083i \(-0.513629\pi\)
−0.0428041 + 0.999083i \(0.513629\pi\)
\(270\) −5.40975e43 + 2.19047e43i −0.930314 + 0.376695i
\(271\) 5.26399e43i 0.846970i −0.905903 0.423485i \(-0.860807\pi\)
0.905903 0.423485i \(-0.139193\pi\)
\(272\) −1.56796e42 + 4.91923e43i −0.0236100 + 0.740725i
\(273\) −1.84270e43 −0.259733
\(274\) −2.07752e43 5.13081e43i −0.274180 0.677136i
\(275\) 2.59213e44i 3.20383i
\(276\) 3.05925e43 2.96329e43i 0.354202 0.343092i
\(277\) 1.07450e44 1.16565 0.582827 0.812597i \(-0.301947\pi\)
0.582827 + 0.812597i \(0.301947\pi\)
\(278\) 7.40594e43 2.99875e43i 0.752963 0.304883i
\(279\) 6.08955e43i 0.580376i
\(280\) −1.09324e43 + 2.47062e43i −0.0976946 + 0.220780i
\(281\) −4.65870e43 −0.390437 −0.195219 0.980760i \(-0.562542\pi\)
−0.195219 + 0.980760i \(0.562542\pi\)
\(282\) −2.35915e43 5.82634e43i −0.185469 0.458049i
\(283\) 2.53833e42i 0.0187237i −0.999956 0.00936186i \(-0.997020\pi\)
0.999956 0.00936186i \(-0.00298002\pi\)
\(284\) −3.51186e43 3.62558e43i −0.243113 0.250985i
\(285\) 2.52540e43 0.164105
\(286\) 3.66509e44 1.48404e44i 2.23613 0.905433i
\(287\) 1.23760e43i 0.0709098i
\(288\) −9.27105e43 + 3.41438e43i −0.498958 + 0.183758i
\(289\) −8.91487e43 −0.450769
\(290\) 3.98546e43 + 9.84278e43i 0.189371 + 0.467686i
\(291\) 1.37549e44i 0.614306i
\(292\) −1.82002e44 + 1.76293e44i −0.764162 + 0.740193i
\(293\) −1.58940e43 −0.0627504 −0.0313752 0.999508i \(-0.509989\pi\)
−0.0313752 + 0.999508i \(0.509989\pi\)
\(294\) −3.02936e44 + 1.22662e44i −1.12486 + 0.455469i
\(295\) 5.00329e44i 1.74767i
\(296\) 3.19788e44 + 1.41505e44i 1.05102 + 0.465074i
\(297\) −3.00280e44 −0.928773
\(298\) 1.07250e44 + 2.64872e44i 0.312251 + 0.771157i
\(299\) 2.18826e44i 0.599814i
\(300\) −6.66932e44 6.88529e44i −1.72147 1.77721i
\(301\) 3.76376e43 0.0915009
\(302\) −3.52865e44 + 1.42879e44i −0.808134 + 0.327223i
\(303\) 2.48568e44i 0.536387i
\(304\) −3.76300e43 1.19942e42i −0.0765261 0.00243920i
\(305\) 7.61372e44 1.45949
\(306\) 8.18349e43 + 2.02106e44i 0.147895 + 0.365252i
\(307\) 3.63013e44i 0.618630i 0.950960 + 0.309315i \(0.100100\pi\)
−0.950960 + 0.309315i \(0.899900\pi\)
\(308\) −9.98414e43 + 9.67097e43i −0.160471 + 0.155438i
\(309\) 2.50380e44 0.379619
\(310\) 1.22482e45 4.95943e44i 1.75211 0.709449i
\(311\) 9.78683e44i 1.32116i −0.750756 0.660580i \(-0.770311\pi\)
0.750756 0.660580i \(-0.229689\pi\)
\(312\) −5.91701e44 + 1.33719e45i −0.753910 + 1.70377i
\(313\) 2.69011e44 0.323573 0.161786 0.986826i \(-0.448274\pi\)
0.161786 + 0.986826i \(0.448274\pi\)
\(314\) 3.71824e44 + 9.18284e44i 0.422283 + 1.04290i
\(315\) 1.19692e44i 0.128373i
\(316\) −1.08661e45 1.12180e45i −1.10080 1.13645i
\(317\) −3.60812e44 −0.345314 −0.172657 0.984982i \(-0.555235\pi\)
−0.172657 + 0.984982i \(0.555235\pi\)
\(318\) 2.77645e44 1.12422e44i 0.251074 0.101663i
\(319\) 5.46344e44i 0.466911i
\(320\) 1.44180e45 + 1.58665e45i 1.16468 + 1.28169i
\(321\) 1.59336e45 1.21681
\(322\) 2.88704e43 + 7.13006e43i 0.0208472 + 0.0514858i
\(323\) 8.30908e43i 0.0567424i
\(324\) 1.38888e45 1.34532e45i 0.897130 0.868990i
\(325\) −4.92499e45 −3.00957
\(326\) 1.38740e45 5.61775e44i 0.802205 0.324822i
\(327\) 2.68719e45i 1.47041i
\(328\) −8.98085e44 3.97400e44i −0.465145 0.205825i
\(329\) 1.13528e44 0.0556645
\(330\) −2.77683e45 6.85787e45i −1.28914 3.18375i
\(331\) 1.74226e45i 0.765963i −0.923756 0.382982i \(-0.874897\pi\)
0.923756 0.382982i \(-0.125103\pi\)
\(332\) 5.85074e44 + 6.04020e44i 0.243627 + 0.251516i
\(333\) 1.54925e45 0.611118
\(334\) −4.86115e45 + 1.96833e45i −1.81678 + 0.735635i
\(335\) 5.98529e45i 2.11972i
\(336\) 1.63758e43 5.13765e44i 0.00549662 0.172448i
\(337\) −2.28010e45 −0.725464 −0.362732 0.931894i \(-0.618156\pi\)
−0.362732 + 0.931894i \(0.618156\pi\)
\(338\) 1.57543e45 + 3.89079e45i 0.475223 + 1.17365i
\(339\) 6.51656e45i 1.86390i
\(340\) 3.39856e45 3.29196e45i 0.921881 0.892965i
\(341\) 6.79860e45 1.74921
\(342\) −1.54602e44 + 6.26001e43i −0.0377351 + 0.0152794i
\(343\) 1.19226e45i 0.276107i
\(344\) 1.20856e45 2.73124e45i 0.265593 0.600216i
\(345\) −4.09451e45 −0.854001
\(346\) −1.50384e44 3.71399e44i −0.0297735 0.0735310i
\(347\) 6.07436e45i 1.14175i 0.821038 + 0.570873i \(0.193395\pi\)
−0.821038 + 0.570873i \(0.806605\pi\)
\(348\) −1.40569e45 1.45121e45i −0.250879 0.259003i
\(349\) 1.91350e44 0.0324317 0.0162159 0.999869i \(-0.494838\pi\)
0.0162159 + 0.999869i \(0.494838\pi\)
\(350\) 1.60472e45 6.49771e44i 0.258330 0.104601i
\(351\) 5.70523e45i 0.872459i
\(352\) 3.81194e45 + 1.03505e46i 0.553832 + 1.50382i
\(353\) −4.83055e45 −0.666887 −0.333443 0.942770i \(-0.608211\pi\)
−0.333443 + 0.942770i \(0.608211\pi\)
\(354\) 3.57271e45 + 8.82343e45i 0.468748 + 1.15765i
\(355\) 4.85250e45i 0.605139i
\(356\) −4.18944e43 + 4.05804e43i −0.00496657 + 0.00481078i
\(357\) −1.13445e45 −0.127866
\(358\) −1.44959e46 + 5.86957e45i −1.55364 + 0.629088i
\(359\) 4.78046e45i 0.487270i 0.969867 + 0.243635i \(0.0783400\pi\)
−0.969867 + 0.243635i \(0.921660\pi\)
\(360\) 8.68561e45 + 3.84335e45i 0.842084 + 0.372619i
\(361\) 1.07789e46 0.994138
\(362\) 2.45297e44 + 6.05803e44i 0.0215247 + 0.0531591i
\(363\) 2.32440e46i 1.94085i
\(364\) −1.83746e45 1.89696e45i −0.146013 0.150742i
\(365\) 2.43593e46 1.84244
\(366\) −1.34270e46 + 5.43675e45i −0.966762 + 0.391453i
\(367\) 2.65158e46i 1.81767i −0.417153 0.908836i \(-0.636972\pi\)
0.417153 0.908836i \(-0.363028\pi\)
\(368\) 6.10108e45 + 1.94467e44i 0.398241 + 0.0126936i
\(369\) −4.35087e45 −0.270459
\(370\) −1.26173e46 3.11607e46i −0.747027 1.84491i
\(371\) 5.41002e44i 0.0305118i
\(372\) −1.80586e46 + 1.74922e46i −0.970312 + 0.939876i
\(373\) −1.20802e46 −0.618466 −0.309233 0.950986i \(-0.600072\pi\)
−0.309233 + 0.950986i \(0.600072\pi\)
\(374\) 2.25638e46 9.13636e45i 1.10084 0.445743i
\(375\) 4.60579e46i 2.14161i
\(376\) 3.64545e45 8.23837e45i 0.161574 0.365141i
\(377\) −1.03804e46 −0.438601
\(378\) 7.52711e44 + 1.85895e45i 0.0303233 + 0.0748886i
\(379\) 1.04283e45i 0.0400596i 0.999799 + 0.0200298i \(0.00637611\pi\)
−0.999799 + 0.0200298i \(0.993624\pi\)
\(380\) 2.51821e45 + 2.59975e45i 0.0922543 + 0.0952417i
\(381\) −6.32461e46 −2.20996
\(382\) −5.70604e45 + 2.31044e45i −0.190193 + 0.0770113i
\(383\) 7.05484e45i 0.224341i −0.993689 0.112171i \(-0.964220\pi\)
0.993689 0.112171i \(-0.0357804\pi\)
\(384\) −3.67564e46 1.76856e46i −1.11525 0.536608i
\(385\) 1.33628e46 0.386905
\(386\) 1.47441e46 + 3.64132e46i 0.407424 + 1.00621i
\(387\) 1.32318e46i 0.348996i
\(388\) 1.41599e46 1.37158e46i 0.356525 0.345342i
\(389\) 4.05550e46 0.974881 0.487440 0.873156i \(-0.337931\pi\)
0.487440 + 0.873156i \(0.337931\pi\)
\(390\) 1.30298e47 5.27591e46i 2.99071 1.21097i
\(391\) 1.34718e46i 0.295287i
\(392\) −4.28347e46 1.89542e46i −0.896699 0.396786i
\(393\) 1.07201e45 0.0214355
\(394\) 2.22506e46 + 5.49517e46i 0.425020 + 1.04966i
\(395\) 1.50142e47i 2.74003i
\(396\) 3.39989e46 + 3.50999e46i 0.592860 + 0.612058i
\(397\) 5.04352e46 0.840436 0.420218 0.907423i \(-0.361954\pi\)
0.420218 + 0.907423i \(0.361954\pi\)
\(398\) −7.13833e46 + 2.89039e46i −1.13685 + 0.460322i
\(399\) 8.67801e44i 0.0132102i
\(400\) 4.37676e45 1.37314e47i 0.0636902 1.99818i
\(401\) 6.66873e46 0.927779 0.463889 0.885893i \(-0.346453\pi\)
0.463889 + 0.885893i \(0.346453\pi\)
\(402\) −4.27393e46 1.05552e47i −0.568537 1.40410i
\(403\) 1.29172e47i 1.64315i
\(404\) −2.55887e46 + 2.47861e46i −0.311303 + 0.301539i
\(405\) −1.85889e47 −2.16303
\(406\) 3.38227e45 1.36952e45i 0.0376478 0.0152440i
\(407\) 1.72964e47i 1.84186i
\(408\) −3.64276e46 + 8.23228e46i −0.371148 + 0.838759i
\(409\) 2.73256e46 0.266410 0.133205 0.991089i \(-0.457473\pi\)
0.133205 + 0.991089i \(0.457473\pi\)
\(410\) 3.54342e46 + 8.75109e46i 0.330607 + 0.816493i
\(411\) 1.01248e47i 0.904135i
\(412\) 2.49668e46 + 2.57752e46i 0.213409 + 0.220319i
\(413\) −1.71928e46 −0.140684
\(414\) 2.50662e46 1.01496e46i 0.196373 0.0795137i
\(415\) 8.08423e46i 0.606419i
\(416\) −1.96658e47 + 7.24259e46i −1.41264 + 0.520252i
\(417\) 1.46144e47 1.00538
\(418\) 6.98891e45 + 1.72604e46i 0.0460507 + 0.113730i
\(419\) 2.27184e47i 1.43392i −0.697113 0.716961i \(-0.745532\pi\)
0.697113 0.716961i \(-0.254468\pi\)
\(420\) −3.54946e46 + 3.43813e46i −0.214622 + 0.207891i
\(421\) −1.97959e47 −1.14683 −0.573414 0.819266i \(-0.694381\pi\)
−0.573414 + 0.819266i \(0.694381\pi\)
\(422\) 1.65813e47 6.71394e46i 0.920435 0.372695i
\(423\) 3.99117e46i 0.212311i
\(424\) 3.92587e46 + 1.73718e46i 0.200148 + 0.0885646i
\(425\) −3.03203e47 −1.48160
\(426\) −3.46504e46 8.55752e46i −0.162306 0.400844i
\(427\) 2.61630e46i 0.117486i
\(428\) 1.58883e47 + 1.64028e47i 0.684052 + 0.706203i
\(429\) 7.23245e47 2.98575
\(430\) −2.66136e47 + 1.07762e47i −1.05359 + 0.426611i
\(431\) 3.25686e47i 1.23654i 0.785965 + 0.618270i \(0.212166\pi\)
−0.785965 + 0.618270i \(0.787834\pi\)
\(432\) 1.59068e47 + 5.07015e45i 0.579262 + 0.0184635i
\(433\) 1.63248e47 0.570251 0.285126 0.958490i \(-0.407965\pi\)
0.285126 + 0.958490i \(0.407965\pi\)
\(434\) −1.70421e46 4.20884e46i −0.0571093 0.141042i
\(435\) 1.94231e47i 0.624470i
\(436\) −2.76631e47 + 2.67954e47i −0.853382 + 0.826615i
\(437\) 1.03053e46 0.0305068
\(438\) −4.29582e47 + 1.73943e47i −1.22043 + 0.494165i
\(439\) 2.84803e47i 0.776574i −0.921539 0.388287i \(-0.873067\pi\)
0.921539 0.388287i \(-0.126933\pi\)
\(440\) 4.29086e47 9.69694e47i 1.12304 2.53797i
\(441\) −2.07517e47 −0.521386
\(442\) 1.73588e47 + 4.28707e47i 0.418716 + 1.03409i
\(443\) 1.55992e47i 0.361272i −0.983550 0.180636i \(-0.942184\pi\)
0.983550 0.180636i \(-0.0578157\pi\)
\(444\) 4.45020e47 + 4.59431e47i 0.989660 + 1.02171i
\(445\) 5.60717e45 0.0119747
\(446\) −5.60268e47 + 2.26859e47i −1.14913 + 0.465295i
\(447\) 5.22680e47i 1.02968i
\(448\) 5.45221e46 4.95445e46i 0.103174 0.0937542i
\(449\) −6.78002e46 −0.123253 −0.0616264 0.998099i \(-0.519629\pi\)
−0.0616264 + 0.998099i \(0.519629\pi\)
\(450\) −2.28431e47 5.64151e47i −0.398961 0.985303i
\(451\) 4.85747e47i 0.815140i
\(452\) 6.70843e47 6.49801e47i 1.08176 1.04782i
\(453\) −6.96319e47 −1.07905
\(454\) 1.09512e48 4.43427e47i 1.63101 0.660415i
\(455\) 2.53890e47i 0.363446i
\(456\) −6.29734e46 2.78655e46i −0.0866542 0.0383442i
\(457\) −1.03943e48 −1.37500 −0.687498 0.726186i \(-0.741291\pi\)
−0.687498 + 0.726186i \(0.741291\pi\)
\(458\) −3.61399e47 8.92538e47i −0.459630 1.13514i
\(459\) 3.51238e47i 0.429510i
\(460\) −4.08286e47 4.21507e47i −0.480091 0.495637i
\(461\) −5.48232e47 −0.619937 −0.309968 0.950747i \(-0.600318\pi\)
−0.309968 + 0.950747i \(0.600318\pi\)
\(462\) −2.35657e47 + 9.54202e46i −0.256286 + 0.103773i
\(463\) 6.58825e46i 0.0689148i 0.999406 + 0.0344574i \(0.0109703\pi\)
−0.999406 + 0.0344574i \(0.989030\pi\)
\(464\) 9.22489e45 2.89416e47i 0.00928192 0.291205i
\(465\) 2.41697e48 2.33948
\(466\) 4.06150e47 + 1.00306e48i 0.378216 + 0.934070i
\(467\) 1.28722e48i 1.15332i −0.816984 0.576660i \(-0.804356\pi\)
0.816984 0.576660i \(-0.195644\pi\)
\(468\) −6.66888e47 + 6.45971e47i −0.574947 + 0.556913i
\(469\) 2.05672e47 0.170634
\(470\) −8.02760e47 + 3.25047e47i −0.640951 + 0.259528i
\(471\) 1.81208e48i 1.39252i
\(472\) −5.52069e47 + 1.24762e48i −0.408354 + 0.922842i
\(473\) −1.47724e48 −1.05184
\(474\) −1.07213e48 2.64780e48i −0.734912 1.81500i
\(475\) 2.31937e47i 0.153068i
\(476\) −1.13122e47 1.16785e47i −0.0718820 0.0742097i
\(477\) 1.90193e47 0.116376
\(478\) 6.16769e46 2.49737e46i 0.0363430 0.0147157i
\(479\) 1.18212e47i 0.0670847i 0.999437 + 0.0335423i \(0.0106789\pi\)
−0.999437 + 0.0335423i \(0.989321\pi\)
\(480\) 1.35518e48 + 3.67972e48i 0.740723 + 2.01128i
\(481\) 3.28627e48 1.73018
\(482\) 1.09285e48 + 2.69899e48i 0.554262 + 1.36885i
\(483\) 1.40700e47i 0.0687456i
\(484\) 2.39283e48 2.31778e48i 1.12641 1.09108i
\(485\) −1.89517e48 −0.859601
\(486\) 2.04912e48 8.29711e47i 0.895599 0.362639i
\(487\) 6.47797e47i 0.272846i −0.990651 0.136423i \(-0.956439\pi\)
0.990651 0.136423i \(-0.0435606\pi\)
\(488\) −1.89856e48 8.40107e47i −0.770669 0.341018i
\(489\) 2.73780e48 1.07113
\(490\) 1.69005e48 + 4.17388e48i 0.637340 + 1.57402i
\(491\) 4.44317e48i 1.61520i −0.589731 0.807600i \(-0.700766\pi\)
0.589731 0.807600i \(-0.299234\pi\)
\(492\) −1.24978e48 1.29025e48i −0.437988 0.452171i
\(493\) −6.39060e47 −0.215922
\(494\) −3.27942e47 + 1.32788e47i −0.106835 + 0.0432586i
\(495\) 4.69779e48i 1.47571i
\(496\) −3.60144e48 1.14793e47i −1.09095 0.0347732i
\(497\) 1.66746e47 0.0487126
\(498\) 5.77272e47 + 1.42568e48i 0.162649 + 0.401691i
\(499\) 9.00710e47i 0.244779i 0.992482 + 0.122390i \(0.0390558\pi\)
−0.992482 + 0.122390i \(0.960944\pi\)
\(500\) −4.74140e48 + 4.59268e48i −1.24293 + 1.20394i
\(501\) −9.59266e48 −2.42583
\(502\) −1.82217e47 + 7.37817e46i −0.0444551 + 0.0180004i
\(503\) 2.54884e48i 0.599954i 0.953946 + 0.299977i \(0.0969791\pi\)
−0.953946 + 0.299977i \(0.903021\pi\)
\(504\) 1.32069e47 2.98463e47i 0.0299952 0.0677862i
\(505\) 3.42480e48 0.750569
\(506\) −1.13314e48 2.79848e48i −0.239648 0.591852i
\(507\) 7.67782e48i 1.56709i
\(508\) −6.30661e48 6.51083e48i −1.24236 1.28260i
\(509\) 6.81591e48 1.29600 0.647998 0.761642i \(-0.275606\pi\)
0.647998 + 0.761642i \(0.275606\pi\)
\(510\) 8.02167e48 3.24807e48i 1.47232 0.596159i
\(511\) 8.37057e47i 0.148313i
\(512\) −1.84454e48 5.54738e48i −0.315522 0.948918i
\(513\) 2.68682e47 0.0443737
\(514\) −1.44365e48 3.56534e48i −0.230211 0.568546i
\(515\) 3.44977e48i 0.531203i
\(516\) 3.92389e48 3.80081e48i 0.583474 0.565173i
\(517\) −4.45589e48 −0.639889
\(518\) −1.07077e48 + 4.33569e47i −0.148512 + 0.0601343i
\(519\) 7.32893e47i 0.0981811i
\(520\) 1.84239e49 + 8.15253e48i 2.38409 + 1.05495i
\(521\) −5.58419e48 −0.698041 −0.349020 0.937115i \(-0.613486\pi\)
−0.349020 + 0.937115i \(0.613486\pi\)
\(522\) −4.81464e47 1.18906e48i −0.0581427 0.143594i
\(523\) 1.22870e49i 1.43356i 0.697298 + 0.716781i \(0.254385\pi\)
−0.697298 + 0.716781i \(0.745615\pi\)
\(524\) 1.06896e47 + 1.10357e47i 0.0120503 + 0.0124405i
\(525\) 3.16665e48 0.344931
\(526\) −1.39098e48 + 5.63223e47i −0.146412 + 0.0592839i
\(527\) 7.95234e48i 0.808917i
\(528\) −6.42736e47 + 2.01648e49i −0.0631862 + 1.98236i
\(529\) 8.85367e48 0.841243
\(530\) −1.54896e48 3.82543e48i −0.142257 0.351329i
\(531\) 6.04424e48i 0.536587i
\(532\) 8.93352e46 8.65331e46i 0.00766679 0.00742631i
\(533\) −9.22907e48 −0.765716
\(534\) −9.88840e46 + 4.00393e46i −0.00793201 + 0.00321176i
\(535\) 2.19536e49i 1.70270i
\(536\) 6.60424e48 1.49250e49i 0.495287 1.11930i
\(537\) −2.86053e49 −2.07448
\(538\) −4.58130e47 1.13143e48i −0.0321298 0.0793502i
\(539\) 2.31680e49i 1.57141i
\(540\) −1.06449e49 1.09896e49i −0.698316 0.720929i
\(541\) 2.08018e49 1.31993 0.659964 0.751297i \(-0.270572\pi\)
0.659964 + 0.751297i \(0.270572\pi\)
\(542\) 1.27905e49 5.17902e48i 0.785055 0.317878i
\(543\) 1.19545e48i 0.0709798i
\(544\) −1.21071e49 + 4.45884e48i −0.695438 + 0.256119i
\(545\) 3.70244e49 2.05755
\(546\) −1.81296e48 4.47742e48i −0.0974811 0.240747i
\(547\) 2.21627e49i 1.15305i −0.817078 0.576527i \(-0.804407\pi\)
0.817078 0.576527i \(-0.195593\pi\)
\(548\) 1.04229e49 1.00960e49i 0.524733 0.508274i
\(549\) −9.19778e48 −0.448106
\(550\) −6.29839e49 + 2.55029e49i −2.96962 + 1.20243i
\(551\) 4.88853e47i 0.0223074i
\(552\) 1.02101e49 + 4.51793e48i 0.450948 + 0.199543i
\(553\) 5.15934e48 0.220568
\(554\) 1.05715e49 + 2.61082e49i 0.437484 + 1.08044i
\(555\) 6.14904e49i 2.46339i
\(556\) 1.45728e49 + 1.50447e49i 0.565192 + 0.583494i
\(557\) −3.43445e49 −1.28962 −0.644812 0.764341i \(-0.723065\pi\)
−0.644812 + 0.764341i \(0.723065\pi\)
\(558\) −1.47964e49 + 5.99125e48i −0.537950 + 0.217822i
\(559\) 2.80672e49i 0.988069i
\(560\) −7.07872e48 2.25628e47i −0.241307 0.00769146i
\(561\) 4.45259e49 1.46988
\(562\) −4.58350e48 1.13198e49i −0.146536 0.361896i
\(563\) 3.38206e49i 1.04720i 0.851964 + 0.523601i \(0.175412\pi\)
−0.851964 + 0.523601i \(0.824588\pi\)
\(564\) 1.18358e49 1.14646e49i 0.354956 0.343823i
\(565\) −8.97859e49 −2.60817
\(566\) 6.16766e47 2.49735e47i 0.0173550 0.00702724i
\(567\) 6.38769e48i 0.174120i
\(568\) 5.35431e48 1.21002e49i 0.141395 0.319538i
\(569\) 6.96348e49 1.78158 0.890791 0.454414i \(-0.150151\pi\)
0.890791 + 0.454414i \(0.150151\pi\)
\(570\) 2.48463e48 + 6.13623e48i 0.0615906 + 0.152109i
\(571\) 1.13276e48i 0.0272076i −0.999907 0.0136038i \(-0.995670\pi\)
0.999907 0.0136038i \(-0.00433035\pi\)
\(572\) 7.21186e49 + 7.44539e49i 1.67849 + 1.73284i
\(573\) −1.12599e49 −0.253952
\(574\) 3.00713e48 1.21762e48i 0.0657262 0.0266133i
\(575\) 3.76047e49i 0.796565i
\(576\) −1.74177e49 1.91676e49i −0.357590 0.393517i
\(577\) 3.94515e48 0.0785052 0.0392526 0.999229i \(-0.487502\pi\)
0.0392526 + 0.999229i \(0.487502\pi\)
\(578\) −8.77097e48 2.16614e49i −0.169179 0.417817i
\(579\) 7.18553e49i 1.34352i
\(580\) −1.99950e49 + 1.93678e49i −0.362424 + 0.351056i
\(581\) −2.77798e48 −0.0488156
\(582\) 3.34219e49 1.35329e49i 0.569399 0.230556i
\(583\) 2.12338e49i 0.350747i
\(584\) −6.07424e49 2.68783e49i −0.972882 0.430497i
\(585\) 8.92567e49 1.38623
\(586\) −1.56374e48 3.86194e48i −0.0235510 0.0581633i
\(587\) 7.75747e49i 1.13301i −0.824058 0.566506i \(-0.808295\pi\)
0.824058 0.566506i \(-0.191705\pi\)
\(588\) −5.96091e49 6.15394e49i −0.844347 0.871688i
\(589\) −6.08320e48 −0.0835712
\(590\) 1.21570e50 4.92252e49i 1.61991 0.655921i
\(591\) 1.08438e50i 1.40154i
\(592\) −2.92046e48 + 9.16246e49i −0.0366151 + 1.14874i
\(593\) 3.70508e49 0.450623 0.225311 0.974287i \(-0.427660\pi\)
0.225311 + 0.974287i \(0.427660\pi\)
\(594\) −2.95432e49 7.29622e49i −0.348580 0.860878i
\(595\) 1.56305e49i 0.178924i
\(596\) −5.38070e49 + 5.21192e49i −0.597593 + 0.578849i
\(597\) −1.40863e50 −1.51796
\(598\) 5.31704e49 2.15293e49i 0.555967 0.225117i
\(599\) 1.01866e50i 1.03359i 0.856109 + 0.516795i \(0.172875\pi\)
−0.856109 + 0.516795i \(0.827125\pi\)
\(600\) 1.01683e50 2.29793e50i 1.00121 2.26264i
\(601\) −6.84375e49 −0.653963 −0.326982 0.945031i \(-0.606032\pi\)
−0.326982 + 0.945031i \(0.606032\pi\)
\(602\) 3.70301e48 + 9.14523e48i 0.0343414 + 0.0848121i
\(603\) 7.23055e49i 0.650818i
\(604\) −6.94337e49 7.16821e49i −0.606605 0.626248i
\(605\) −3.20258e50 −2.71584
\(606\) −6.03973e49 + 2.44556e49i −0.497176 + 0.201312i
\(607\) 4.26011e49i 0.340428i −0.985407 0.170214i \(-0.945554\pi\)
0.985407 0.170214i \(-0.0544458\pi\)
\(608\) −3.41082e48 9.26137e48i −0.0264603 0.0718474i
\(609\) 6.67435e48 0.0502687
\(610\) 7.49082e49 + 1.84999e50i 0.547762 + 1.35280i
\(611\) 8.46607e49i 0.601091i
\(612\) −4.10564e49 + 3.97686e49i −0.283045 + 0.274167i
\(613\) 2.84023e50 1.90137 0.950683 0.310165i \(-0.100384\pi\)
0.950683 + 0.310165i \(0.100384\pi\)
\(614\) −8.82051e49 + 3.57153e49i −0.573407 + 0.232179i
\(615\) 1.72688e50i 1.09021i
\(616\) −3.33216e49 1.47447e49i −0.204302 0.0904030i
\(617\) 1.94103e50 1.15584 0.577921 0.816093i \(-0.303864\pi\)
0.577921 + 0.816093i \(0.303864\pi\)
\(618\) 2.46339e49 + 6.08376e49i 0.142475 + 0.351868i
\(619\) 2.91886e50i 1.63976i −0.572533 0.819882i \(-0.694039\pi\)
0.572533 0.819882i \(-0.305961\pi\)
\(620\) 2.41009e50 + 2.48814e50i 1.31517 + 1.35776i
\(621\) −4.35623e49 −0.230920
\(622\) 2.37801e50 9.62885e49i 1.22458 0.495847i
\(623\) 1.92679e47i 0.000963939i
\(624\) −3.83126e50 1.22118e49i −1.86217 0.0593550i
\(625\) 2.11246e50 0.997580
\(626\) 2.64668e49 + 6.53645e49i 0.121441 + 0.299919i
\(627\) 3.40604e49i 0.151857i
\(628\) −1.86543e50 + 1.80692e50i −0.808177 + 0.782827i
\(629\) 2.02316e50 0.851764
\(630\) −2.90828e49 + 1.17759e49i −0.118989 + 0.0481799i
\(631\) 4.24994e50i 1.68988i −0.534864 0.844938i \(-0.679637\pi\)
0.534864 0.844938i \(-0.320363\pi\)
\(632\) 1.65669e50 3.74396e50i 0.640226 1.44685i
\(633\) 3.27203e50 1.22900
\(634\) −3.54988e49 8.76704e49i −0.129600 0.320071i
\(635\) 8.71413e50i 3.09241i
\(636\) 5.46327e49 + 5.64018e49i 0.188462 + 0.194565i
\(637\) −4.40186e50 −1.47614
\(638\) −1.32751e50 + 5.37525e49i −0.432779 + 0.175237i
\(639\) 5.86208e49i 0.185796i
\(640\) −2.43674e50 + 5.06433e50i −0.750879 + 1.56057i
\(641\) −4.30618e50 −1.29017 −0.645085 0.764111i \(-0.723178\pi\)
−0.645085 + 0.764111i \(0.723178\pi\)
\(642\) 1.56764e50 + 3.87157e50i 0.456685 + 1.12786i
\(643\) 4.66172e50i 1.32053i −0.751032 0.660266i \(-0.770444\pi\)
0.751032 0.660266i \(-0.229556\pi\)
\(644\) −1.44842e49 + 1.40299e49i −0.0398979 + 0.0386464i
\(645\) −5.25175e50 −1.40679
\(646\) −2.01895e49 + 8.17495e48i −0.0525944 + 0.0212961i
\(647\) 7.15036e50i 1.81155i −0.423758 0.905776i \(-0.639289\pi\)
0.423758 0.905776i \(-0.360711\pi\)
\(648\) 4.63533e50 + 2.05112e50i 1.14217 + 0.505406i
\(649\) 6.74801e50 1.61723
\(650\) −4.84549e50 1.19668e51i −1.12953 2.78957i
\(651\) 8.30543e49i 0.188324i
\(652\) 2.73001e50 + 2.81841e50i 0.602154 + 0.621653i
\(653\) −9.56236e49 −0.205177 −0.102588 0.994724i \(-0.532712\pi\)
−0.102588 + 0.994724i \(0.532712\pi\)
\(654\) −6.52935e50 + 2.64381e50i −1.36292 + 0.551862i
\(655\) 1.47703e49i 0.0299948i
\(656\) 8.20173e48 2.57316e50i 0.0162045 0.508391i
\(657\) −2.94273e50 −0.565683
\(658\) 1.11696e49 + 2.75852e49i 0.0208916 + 0.0515954i
\(659\) 4.92362e50i 0.896080i 0.894014 + 0.448040i \(0.147878\pi\)
−0.894014 + 0.448040i \(0.852122\pi\)
\(660\) 1.39313e51 1.34943e51i 2.46718 2.38980i
\(661\) 3.31963e50 0.572088 0.286044 0.958216i \(-0.407660\pi\)
0.286044 + 0.958216i \(0.407660\pi\)
\(662\) 4.23335e50 1.71413e50i 0.709970 0.287475i
\(663\) 8.45981e50i 1.38076i
\(664\) −8.92023e49 + 2.01589e50i −0.141694 + 0.320214i
\(665\) −1.19567e49 −0.0184850
\(666\) 1.52424e50 + 3.76438e50i 0.229360 + 0.566444i
\(667\) 7.92595e49i 0.116088i
\(668\) −9.56535e50 9.87510e50i −1.36372 1.40788i
\(669\) −1.10559e51 −1.53436
\(670\) −1.45431e51 + 5.88868e50i −1.96477 + 0.795557i
\(671\) 1.02687e51i 1.35055i
\(672\) 1.26446e50 4.65681e49i 0.161905 0.0596269i
\(673\) 1.51276e51 1.88582 0.942908 0.333054i \(-0.108079\pi\)
0.942908 + 0.333054i \(0.108079\pi\)
\(674\) −2.24329e50 5.54021e50i −0.272275 0.672431i
\(675\) 9.80433e50i 1.15864i
\(676\) −7.90388e50 + 7.65597e50i −0.909494 + 0.880967i
\(677\) −1.31869e51 −1.47757 −0.738785 0.673942i \(-0.764600\pi\)
−0.738785 + 0.673942i \(0.764600\pi\)
\(678\) 1.58340e51 6.41137e50i 1.72765 0.699546i
\(679\) 6.51237e49i 0.0691964i
\(680\) 1.13425e51 + 5.01904e50i 1.17368 + 0.519350i
\(681\) 2.16104e51 2.17778
\(682\) 6.68886e50 + 1.65193e51i 0.656498 + 1.62134i
\(683\) 7.41047e50i 0.708391i −0.935171 0.354196i \(-0.884755\pi\)
0.935171 0.354196i \(-0.115245\pi\)
\(684\) −3.04213e49 3.14064e49i −0.0283248 0.0292421i
\(685\) −1.39501e51 −1.26516
\(686\) 2.89697e50 1.17302e50i 0.255923 0.103626i
\(687\) 1.76127e51i 1.51567i
\(688\) 7.82544e50 + 2.49429e49i 0.656019 + 0.0209101i
\(689\) 4.03437e50 0.329481
\(690\) −4.02842e50 9.94889e50i −0.320517 0.791573i
\(691\) 3.66751e50i 0.284293i 0.989846 + 0.142147i \(0.0454004\pi\)
−0.989846 + 0.142147i \(0.954600\pi\)
\(692\) 7.54472e49 7.30807e49i 0.0569814 0.0551941i
\(693\) −1.61430e50 −0.118792
\(694\) −1.47595e51 + 5.97630e50i −1.05828 + 0.428511i
\(695\) 2.01359e51i 1.40684i
\(696\) 2.14317e50 4.84335e50i 0.145911 0.329746i
\(697\) −5.68180e50 −0.376960
\(698\) 1.88261e49 + 4.64943e49i 0.0121720 + 0.0300609i
\(699\) 1.97937e51i 1.24720i
\(700\) 3.15764e50 + 3.25989e50i 0.193909 + 0.200188i
\(701\) 1.61915e49 0.00969085 0.00484542 0.999988i \(-0.498458\pi\)
0.00484542 + 0.999988i \(0.498458\pi\)
\(702\) 1.38626e51 5.61314e50i 0.808681 0.327444i
\(703\) 1.54763e50i 0.0879978i
\(704\) −2.13994e51 + 1.94458e51i −1.18603 + 1.07775i
\(705\) −1.58411e51 −0.855819
\(706\) −4.75258e50 1.17373e51i −0.250291 0.618136i
\(707\) 1.17686e50i 0.0604194i
\(708\) −1.79242e51 + 1.73620e51i −0.897102 + 0.868963i
\(709\) 2.41201e51 1.17692 0.588460 0.808527i \(-0.299735\pi\)
0.588460 + 0.808527i \(0.299735\pi\)
\(710\) −1.17906e51 + 4.77417e50i −0.560903 + 0.227116i
\(711\) 1.81380e51i 0.841272i
\(712\) −1.39821e49 6.18702e48i −0.00632312 0.00279796i
\(713\) 9.86290e50 0.434904
\(714\) −1.11613e50 2.75648e50i −0.0479897 0.118519i
\(715\) 9.96495e51i 4.17798i
\(716\) −2.85239e51 2.94475e51i −1.16620 1.20397i
\(717\) 1.21709e50 0.0485264
\(718\) −1.16156e51 + 4.70330e50i −0.451650 + 0.182878i
\(719\) 3.96171e51i 1.50232i 0.660120 + 0.751160i \(0.270505\pi\)
−0.660120 + 0.751160i \(0.729495\pi\)
\(720\) −7.93210e49 + 2.48857e51i −0.0293362 + 0.920375i
\(721\) −1.18544e50 −0.0427608
\(722\) 1.06049e51 + 2.61908e51i 0.373112 + 0.921465i
\(723\) 5.32601e51i 1.82773i
\(724\) −1.23065e50 + 1.19205e50i −0.0411946 + 0.0399025i
\(725\) 1.78385e51 0.582471
\(726\) 5.64784e51 2.28687e51i 1.79897 0.728422i
\(727\) 1.85957e51i 0.577821i 0.957356 + 0.288910i \(0.0932929\pi\)
−0.957356 + 0.288910i \(0.906707\pi\)
\(728\) 2.80145e50 6.33101e50i 0.0849216 0.191915i
\(729\) −1.79751e50 −0.0531588
\(730\) 2.39660e51 + 5.91883e51i 0.691488 + 1.70775i
\(731\) 1.72794e51i 0.486424i
\(732\) −2.64205e51 2.72761e51i −0.725675 0.749173i
\(733\) 5.64939e50 0.151401 0.0757007 0.997131i \(-0.475881\pi\)
0.0757007 + 0.997131i \(0.475881\pi\)
\(734\) 6.44283e51 2.60878e51i 1.68480 0.682194i
\(735\) 8.23646e51i 2.10169i
\(736\) 5.53008e50 + 1.50158e51i 0.137699 + 0.373893i
\(737\) −8.07246e51 −1.96151
\(738\) −4.28063e50 1.05718e51i −0.101506 0.250688i
\(739\) 3.16982e51i 0.733558i −0.930308 0.366779i \(-0.880461\pi\)
0.930308 0.366779i \(-0.119539\pi\)
\(740\) 6.33009e51 6.13154e51i 1.42968 1.38484i
\(741\) −6.47139e50 −0.142649
\(742\) −1.31453e50 + 5.32269e49i −0.0282814 + 0.0114515i
\(743\) 3.80186e50i 0.0798358i 0.999203 + 0.0399179i \(0.0127096\pi\)
−0.999203 + 0.0399179i \(0.987290\pi\)
\(744\) −6.02697e51 2.66691e51i −1.23534 0.546634i
\(745\) 7.20155e51 1.44083
\(746\) −1.18852e51 2.93526e51i −0.232118 0.573255i
\(747\) 9.76617e50i 0.186189i
\(748\) 4.43992e51 + 4.58369e51i 0.826316 + 0.853074i
\(749\) −7.54390e50 −0.137064
\(750\) −1.11912e52 + 4.53144e51i −1.98506 + 0.803774i
\(751\) 2.08756e51i