Properties

Label 4.37.b.b.3.15
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 3.15
Root \(-1.85096e7i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.37.b.b.3.16

$q$-expansion

\(f(q)\) \(=\) \(q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +O(q^{10})\) \(q+(261200. - 22229.7i) q^{2} -2.96154e8i q^{3} +(6.77312e10 - 1.16128e10i) q^{4} +1.46296e12 q^{5} +(-6.58343e12 - 7.73554e13i) q^{6} +2.38729e15i q^{7} +(1.74332e16 - 4.53891e15i) q^{8} +6.23874e16 q^{9} +(3.82125e17 - 3.25212e16i) q^{10} +1.01014e19i q^{11} +(-3.43918e18 - 2.00589e19i) q^{12} -4.81295e19 q^{13} +(5.30689e19 + 6.23561e20i) q^{14} -4.33261e20i q^{15} +(4.45265e21 - 1.57310e21i) q^{16} +1.19657e22 q^{17} +(1.62956e22 - 1.38686e21i) q^{18} +1.66265e22i q^{19} +(9.90879e22 - 1.69891e22i) q^{20} +7.07007e23 q^{21} +(2.24553e23 + 2.63850e24i) q^{22} -2.63389e24i q^{23} +(-1.34422e24 - 5.16292e24i) q^{24} -1.24117e25 q^{25} +(-1.25714e25 + 1.06991e24i) q^{26} -6.29274e25i q^{27} +(2.77232e25 + 1.61694e26i) q^{28} +1.36780e26 q^{29} +(-9.63129e24 - 1.13168e26i) q^{30} +4.52800e26i q^{31} +(1.12806e27 - 5.09874e26i) q^{32} +2.99159e27 q^{33} +(3.12544e27 - 2.65994e26i) q^{34} +3.49251e27i q^{35} +(4.22557e27 - 7.24493e26i) q^{36} +5.31006e27 q^{37} +(3.69602e26 + 4.34283e27i) q^{38} +1.42538e28i q^{39} +(2.55041e28 - 6.64024e27i) q^{40} +1.73682e29 q^{41} +(1.84670e29 - 1.57166e28i) q^{42} -2.26096e29i q^{43} +(1.17306e29 + 6.84183e29i) q^{44} +9.12702e28 q^{45} +(-5.85506e28 - 6.87970e29i) q^{46} +1.08183e30i q^{47} +(-4.65879e29 - 1.31867e30i) q^{48} -3.04744e30 q^{49} +(-3.24192e30 + 2.75908e29i) q^{50} -3.54369e30i q^{51} +(-3.25987e30 + 5.58919e29i) q^{52} -1.23762e31 q^{53} +(-1.39886e30 - 1.64366e31i) q^{54} +1.47780e31i q^{55} +(1.08357e31 + 4.16182e31i) q^{56} +4.92399e30 q^{57} +(3.57270e31 - 3.04059e30i) q^{58} -9.54768e31i q^{59} +(-5.03138e30 - 2.93453e31i) q^{60} -5.38786e31 q^{61} +(1.00656e31 + 1.18271e32i) q^{62} +1.48937e32i q^{63} +(2.83315e32 - 1.58255e32i) q^{64} -7.04115e31 q^{65} +(7.81401e32 - 6.65022e31i) q^{66} +6.26685e32i q^{67} +(8.10450e32 - 1.38955e32i) q^{68} -7.80036e32 q^{69} +(7.76377e31 + 9.12244e32i) q^{70} -2.83770e33i q^{71} +(1.08761e33 - 2.83171e32i) q^{72} -6.34742e33 q^{73} +(1.38699e33 - 1.18041e32i) q^{74} +3.67577e33i q^{75} +(1.93080e32 + 1.12613e33i) q^{76} -2.41151e34 q^{77} +(3.16857e32 + 3.72308e33i) q^{78} -2.21307e34i q^{79} +(6.51405e33 - 2.30138e33i) q^{80} -9.27220e33 q^{81} +(4.53656e34 - 3.86089e33i) q^{82} +6.15416e34i q^{83} +(4.78864e34 - 8.21033e33i) q^{84} +1.75053e34 q^{85} +(-5.02606e33 - 5.90563e34i) q^{86} -4.05081e34i q^{87} +(4.58495e34 + 1.76101e35i) q^{88} -8.78919e34 q^{89} +(2.38398e34 - 2.02891e33i) q^{90} -1.14899e35i q^{91} +(-3.05868e34 - 1.78396e35i) q^{92} +1.34099e35 q^{93} +(2.40488e34 + 2.82573e35i) q^{94} +2.43238e34i q^{95} +(-1.51001e35 - 3.34080e35i) q^{96} +1.81673e35 q^{97} +(-7.95991e35 + 6.77438e34i) q^{98} +6.30203e35i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 261200. 22229.7i 0.996398 0.0847997i
\(3\) 2.96154e8i 0.764425i −0.924074 0.382213i \(-0.875162\pi\)
0.924074 0.382213i \(-0.124838\pi\)
\(4\) 6.77312e10 1.16128e10i 0.985618 0.168989i
\(5\) 1.46296e12 0.383506 0.191753 0.981443i \(-0.438583\pi\)
0.191753 + 0.981443i \(0.438583\pi\)
\(6\) −6.58343e12 7.73554e13i −0.0648231 0.761672i
\(7\) 2.38729e15i 1.46602i 0.680216 + 0.733012i \(0.261886\pi\)
−0.680216 + 0.733012i \(0.738114\pi\)
\(8\) 1.74332e16 4.53891e15i 0.967738 0.251960i
\(9\) 6.23874e16 0.415654
\(10\) 3.82125e17 3.25212e16i 0.382125 0.0325212i
\(11\) 1.01014e19i 1.81683i 0.418065 + 0.908417i \(0.362708\pi\)
−0.418065 + 0.908417i \(0.637292\pi\)
\(12\) −3.43918e18 2.00589e19i −0.129179 0.753432i
\(13\) −4.81295e19 −0.427988 −0.213994 0.976835i \(-0.568647\pi\)
−0.213994 + 0.976835i \(0.568647\pi\)
\(14\) 5.30689e19 + 6.23561e20i 0.124318 + 1.46074i
\(15\) 4.33261e20i 0.293162i
\(16\) 4.45265e21 1.57310e21i 0.942886 0.333116i
\(17\) 1.19657e22 0.850858 0.425429 0.904992i \(-0.360123\pi\)
0.425429 + 0.904992i \(0.360123\pi\)
\(18\) 1.62956e22 1.38686e21i 0.414156 0.0352473i
\(19\) 1.66265e22i 0.159674i 0.996808 + 0.0798371i \(0.0254400\pi\)
−0.996808 + 0.0798371i \(0.974560\pi\)
\(20\) 9.90879e22 1.69891e22i 0.377990 0.0648081i
\(21\) 7.07007e23 1.12067
\(22\) 2.24553e23 + 2.63850e24i 0.154067 + 1.81029i
\(23\) 2.63389e24i 0.811888i −0.913898 0.405944i \(-0.866943\pi\)
0.913898 0.405944i \(-0.133057\pi\)
\(24\) −1.34422e24 5.16292e24i −0.192605 0.739763i
\(25\) −1.24117e25 −0.852923
\(26\) −1.25714e25 + 1.06991e24i −0.426446 + 0.0362932i
\(27\) 6.29274e25i 1.08216i
\(28\) 2.77232e25 + 1.61694e26i 0.247741 + 1.44494i
\(29\) 1.36780e26 0.649920 0.324960 0.945728i \(-0.394649\pi\)
0.324960 + 0.945728i \(0.394649\pi\)
\(30\) −9.63129e24 1.13168e26i −0.0248600 0.292106i
\(31\) 4.52800e26i 0.647733i 0.946103 + 0.323866i \(0.104983\pi\)
−0.946103 + 0.323866i \(0.895017\pi\)
\(32\) 1.12806e27 5.09874e26i 0.911241 0.411873i
\(33\) 2.99159e27 1.38883
\(34\) 3.12544e27 2.65994e26i 0.847793 0.0721525i
\(35\) 3.49251e27i 0.562229i
\(36\) 4.22557e27 7.24493e26i 0.409676 0.0702407i
\(37\) 5.31006e27 0.314390 0.157195 0.987568i \(-0.449755\pi\)
0.157195 + 0.987568i \(0.449755\pi\)
\(38\) 3.69602e26 + 4.34283e27i 0.0135403 + 0.159099i
\(39\) 1.42538e28i 0.327165i
\(40\) 2.55041e28 6.64024e27i 0.371133 0.0966282i
\(41\) 1.73682e29 1.62048 0.810241 0.586097i \(-0.199336\pi\)
0.810241 + 0.586097i \(0.199336\pi\)
\(42\) 1.84670e29 1.57166e28i 1.11663 0.0950322i
\(43\) 2.26096e29i 0.895079i −0.894264 0.447539i \(-0.852300\pi\)
0.894264 0.447539i \(-0.147700\pi\)
\(44\) 1.17306e29 + 6.84183e29i 0.307024 + 1.79070i
\(45\) 9.12702e28 0.159406
\(46\) −5.85506e28 6.87970e29i −0.0688478 0.808963i
\(47\) 1.08183e30i 0.863768i 0.901929 + 0.431884i \(0.142151\pi\)
−0.901929 + 0.431884i \(0.857849\pi\)
\(48\) −4.65879e29 1.31867e30i −0.254643 0.720766i
\(49\) −3.04744e30 −1.14923
\(50\) −3.24192e30 + 2.75908e29i −0.849851 + 0.0723277i
\(51\) 3.54369e30i 0.650418i
\(52\) −3.25987e30 + 5.58919e29i −0.421832 + 0.0723250i
\(53\) −1.23762e31 −1.13664 −0.568319 0.822808i \(-0.692406\pi\)
−0.568319 + 0.822808i \(0.692406\pi\)
\(54\) −1.39886e30 1.64366e31i −0.0917670 1.07826i
\(55\) 1.47780e31i 0.696767i
\(56\) 1.08357e31 + 4.16182e31i 0.369379 + 1.41873i
\(57\) 4.92399e30 0.122059
\(58\) 3.57270e31 3.04059e30i 0.647579 0.0551131i
\(59\) 9.54768e31i 1.27222i −0.771599 0.636109i \(-0.780543\pi\)
0.771599 0.636109i \(-0.219457\pi\)
\(60\) −5.03138e30 2.93453e31i −0.0495410 0.288945i
\(61\) −5.38786e31 −0.393985 −0.196992 0.980405i \(-0.563117\pi\)
−0.196992 + 0.980405i \(0.563117\pi\)
\(62\) 1.00656e31 + 1.18271e32i 0.0549276 + 0.645400i
\(63\) 1.48937e32i 0.609358i
\(64\) 2.83315e32 1.58255e32i 0.873032 0.487662i
\(65\) −7.04115e31 −0.164136
\(66\) 7.81401e32 6.65022e31i 1.38383 0.117773i
\(67\) 6.26685e32i 0.846647i 0.905979 + 0.423324i \(0.139137\pi\)
−0.905979 + 0.423324i \(0.860863\pi\)
\(68\) 8.10450e32 1.38955e32i 0.838621 0.143785i
\(69\) −7.80036e32 −0.620628
\(70\) 7.76377e31 + 9.12244e32i 0.0476769 + 0.560204i
\(71\) 2.83770e33i 1.34994i −0.737843 0.674972i \(-0.764156\pi\)
0.737843 0.674972i \(-0.235844\pi\)
\(72\) 1.08761e33 2.83171e32i 0.402244 0.104728i
\(73\) −6.34742e33 −1.83141 −0.915705 0.401851i \(-0.868367\pi\)
−0.915705 + 0.401851i \(0.868367\pi\)
\(74\) 1.38699e33 1.18041e32i 0.313258 0.0266602i
\(75\) 3.67577e33i 0.651996i
\(76\) 1.93080e32 + 1.12613e33i 0.0269831 + 0.157378i
\(77\) −2.41151e34 −2.66352
\(78\) 3.16857e32 + 3.72308e33i 0.0277435 + 0.325986i
\(79\) 2.21307e34i 1.54066i −0.637645 0.770330i \(-0.720091\pi\)
0.637645 0.770330i \(-0.279909\pi\)
\(80\) 6.51405e33 2.30138e33i 0.361602 0.127752i
\(81\) −9.27220e33 −0.411578
\(82\) 4.53656e34 3.86089e33i 1.61464 0.137416i
\(83\) 6.15416e34i 1.76102i 0.474031 + 0.880508i \(0.342799\pi\)
−0.474031 + 0.880508i \(0.657201\pi\)
\(84\) 4.78864e34 8.21033e33i 1.10455 0.189380i
\(85\) 1.75053e34 0.326309
\(86\) −5.02606e33 5.90563e34i −0.0759024 0.891855i
\(87\) 4.05081e34i 0.496816i
\(88\) 4.58495e34 + 1.76101e35i 0.457770 + 1.75822i
\(89\) −8.78919e34 −0.716026 −0.358013 0.933717i \(-0.616546\pi\)
−0.358013 + 0.933717i \(0.616546\pi\)
\(90\) 2.38398e34 2.02891e33i 0.158831 0.0135176i
\(91\) 1.14899e35i 0.627440i
\(92\) −3.05868e34 1.78396e35i −0.137200 0.800211i
\(93\) 1.34099e35 0.495144
\(94\) 2.40488e34 + 2.82573e35i 0.0732473 + 0.860657i
\(95\) 2.43238e34i 0.0612360i
\(96\) −1.51001e35 3.34080e35i −0.314846 0.696576i
\(97\) 1.81673e35 0.314340 0.157170 0.987572i \(-0.449763\pi\)
0.157170 + 0.987572i \(0.449763\pi\)
\(98\) −7.95991e35 + 6.77438e34i −1.14509 + 0.0974541i
\(99\) 6.30203e35i 0.755174i
\(100\) −8.40656e35 + 1.44134e35i −0.840656 + 0.144134i
\(101\) 5.19200e35 0.434060 0.217030 0.976165i \(-0.430363\pi\)
0.217030 + 0.976165i \(0.430363\pi\)
\(102\) −7.87753e34 9.25611e35i −0.0551552 0.648075i
\(103\) 7.57511e35i 0.444958i −0.974937 0.222479i \(-0.928585\pi\)
0.974937 0.222479i \(-0.0714149\pi\)
\(104\) −8.39052e35 + 2.18455e35i −0.414180 + 0.107836i
\(105\) 1.03432e36 0.429782
\(106\) −3.23266e36 + 2.75120e35i −1.13254 + 0.0963866i
\(107\) 1.18309e36i 0.350034i 0.984565 + 0.175017i \(0.0559980\pi\)
−0.984565 + 0.175017i \(0.944002\pi\)
\(108\) −7.30764e35 4.26215e36i −0.182873 1.06660i
\(109\) 5.99820e36 1.27158 0.635791 0.771861i \(-0.280674\pi\)
0.635791 + 0.771861i \(0.280674\pi\)
\(110\) 3.28511e35 + 3.86001e36i 0.0590856 + 0.694257i
\(111\) 1.57260e36i 0.240328i
\(112\) 3.75545e36 + 1.06298e37i 0.488357 + 1.38229i
\(113\) 1.38128e37 1.53063 0.765314 0.643657i \(-0.222584\pi\)
0.765314 + 0.643657i \(0.222584\pi\)
\(114\) 1.28615e36 1.09459e35i 0.121619 0.0103506i
\(115\) 3.85327e36i 0.311364i
\(116\) 9.26430e36 1.58840e36i 0.640573 0.109829i
\(117\) −3.00268e36 −0.177895
\(118\) −2.12242e36 2.49385e37i −0.107884 1.26764i
\(119\) 2.85656e37i 1.24738i
\(120\) −1.96653e36 7.55314e36i −0.0738650 0.283704i
\(121\) −7.11266e37 −2.30089
\(122\) −1.40731e37 + 1.19771e36i −0.392566 + 0.0334098i
\(123\) 5.14365e37i 1.23874i
\(124\) 5.25828e36 + 3.06687e37i 0.109459 + 0.638417i
\(125\) −3.94466e37 −0.710607
\(126\) 3.31083e36 + 3.89023e37i 0.0516734 + 0.607163i
\(127\) 3.83191e37i 0.518739i 0.965778 + 0.259369i \(0.0835147\pi\)
−0.965778 + 0.259369i \(0.916485\pi\)
\(128\) 7.04839e37 4.76343e37i 0.828534 0.559939i
\(129\) −6.69594e37 −0.684221
\(130\) −1.83915e37 + 1.56523e36i −0.163545 + 0.0139187i
\(131\) 7.43704e37i 0.576125i −0.957612 0.288062i \(-0.906989\pi\)
0.957612 0.288062i \(-0.0930111\pi\)
\(132\) 2.02624e38 3.47407e37i 1.36886 0.234697i
\(133\) −3.96922e37 −0.234086
\(134\) 1.39310e37 + 1.63690e38i 0.0717955 + 0.843598i
\(135\) 9.20602e37i 0.415015i
\(136\) 2.08600e38 5.43112e37i 0.823408 0.214382i
\(137\) 6.29514e37 0.217788 0.108894 0.994053i \(-0.465269\pi\)
0.108894 + 0.994053i \(0.465269\pi\)
\(138\) −2.03745e38 + 1.73400e37i −0.618392 + 0.0526291i
\(139\) 5.21959e38i 1.39114i 0.718459 + 0.695569i \(0.244848\pi\)
−0.718459 + 0.695569i \(0.755152\pi\)
\(140\) 4.05579e37 + 2.36552e38i 0.0950103 + 0.554143i
\(141\) 3.20388e38 0.660286
\(142\) −6.30813e37 7.41206e38i −0.114475 1.34508i
\(143\) 4.86178e38i 0.777583i
\(144\) 2.77789e38 9.81414e37i 0.391914 0.138461i
\(145\) 2.00104e38 0.249248
\(146\) −1.65794e39 + 1.41101e38i −1.82481 + 0.155303i
\(147\) 9.02512e38i 0.878498i
\(148\) 3.59657e38 6.16648e37i 0.309868 0.0531283i
\(149\) 1.11386e39 0.850113 0.425056 0.905167i \(-0.360254\pi\)
0.425056 + 0.905167i \(0.360254\pi\)
\(150\) 8.17113e37 + 9.60109e38i 0.0552891 + 0.649648i
\(151\) 2.20582e39i 1.32430i −0.749372 0.662149i \(-0.769645\pi\)
0.749372 0.662149i \(-0.230355\pi\)
\(152\) 7.54660e37 + 2.89853e38i 0.0402315 + 0.154523i
\(153\) 7.46508e38 0.353662
\(154\) −6.29886e39 + 5.36073e38i −2.65393 + 0.225866i
\(155\) 6.62428e38i 0.248409i
\(156\) 1.65526e38 + 9.65423e38i 0.0552871 + 0.322459i
\(157\) −2.97211e39 −0.884853 −0.442427 0.896805i \(-0.645882\pi\)
−0.442427 + 0.896805i \(0.645882\pi\)
\(158\) −4.91959e38 5.78052e39i −0.130648 1.53511i
\(159\) 3.66527e39i 0.868875i
\(160\) 1.65031e39 7.45925e38i 0.349466 0.157956i
\(161\) 6.28786e39 1.19025
\(162\) −2.42190e39 + 2.06119e38i −0.410096 + 0.0349017i
\(163\) 5.14197e39i 0.779386i −0.920945 0.389693i \(-0.872581\pi\)
0.920945 0.389693i \(-0.127419\pi\)
\(164\) 1.17636e40 2.01693e39i 1.59718 0.273843i
\(165\) 4.37657e39 0.532626
\(166\) 1.36805e39 + 1.60747e40i 0.149334 + 1.75467i
\(167\) 8.78588e39i 0.860773i 0.902645 + 0.430387i \(0.141623\pi\)
−0.902645 + 0.430387i \(0.858377\pi\)
\(168\) 1.23254e40 3.20904e39i 1.08451 0.282363i
\(169\) −1.03298e40 −0.816827
\(170\) 4.57238e39 3.89139e38i 0.325134 0.0276709i
\(171\) 1.03728e39i 0.0663692i
\(172\) −2.62561e39 1.53138e40i −0.151258 0.882206i
\(173\) −1.25353e40 −0.650585 −0.325292 0.945613i \(-0.605463\pi\)
−0.325292 + 0.945613i \(0.605463\pi\)
\(174\) −9.00484e38 1.05807e40i −0.0421298 0.495026i
\(175\) 2.96303e40i 1.25041i
\(176\) 1.58906e40 + 4.49782e40i 0.605217 + 1.71307i
\(177\) −2.82758e40 −0.972516
\(178\) −2.29573e40 + 1.95381e39i −0.713447 + 0.0607188i
\(179\) 4.92645e39i 0.138414i −0.997602 0.0692070i \(-0.977953\pi\)
0.997602 0.0692070i \(-0.0220469\pi\)
\(180\) 6.18184e39 1.05990e39i 0.157113 0.0269377i
\(181\) −7.14294e40 −1.64310 −0.821548 0.570140i \(-0.806889\pi\)
−0.821548 + 0.570140i \(0.806889\pi\)
\(182\) −2.55418e39 3.00117e40i −0.0532068 0.625180i
\(183\) 1.59564e40i 0.301172i
\(184\) −1.19550e40 4.59171e40i −0.204563 0.785694i
\(185\) 7.76841e39 0.120570
\(186\) 3.50265e40 2.98098e39i 0.493360 0.0419880i
\(187\) 1.20871e41i 1.54587i
\(188\) 1.25631e40 + 7.32735e40i 0.145967 + 0.851345i
\(189\) 1.50226e41 1.58648
\(190\) 5.40712e38 + 6.35338e39i 0.00519280 + 0.0610155i
\(191\) 1.55729e41i 1.36072i −0.732876 0.680362i \(-0.761822\pi\)
0.732876 0.680362i \(-0.238178\pi\)
\(192\) −4.68680e40 8.39050e40i −0.372782 0.667368i
\(193\) 9.98102e40 0.723008 0.361504 0.932371i \(-0.382263\pi\)
0.361504 + 0.932371i \(0.382263\pi\)
\(194\) 4.74531e40 4.03855e39i 0.313208 0.0266560i
\(195\) 2.08527e40i 0.125470i
\(196\) −2.06407e41 + 3.53893e40i −1.13270 + 0.194206i
\(197\) 1.02224e41 0.511871 0.255935 0.966694i \(-0.417617\pi\)
0.255935 + 0.966694i \(0.417617\pi\)
\(198\) 1.40092e40 + 1.64609e41i 0.0640385 + 0.752454i
\(199\) 8.08444e40i 0.337516i −0.985657 0.168758i \(-0.946024\pi\)
0.985657 0.168758i \(-0.0539757\pi\)
\(200\) −2.16375e41 + 5.63354e40i −0.825406 + 0.214903i
\(201\) 1.85595e41 0.647199
\(202\) 1.35615e41 1.15417e40i 0.432497 0.0368082i
\(203\) 3.26535e41i 0.952799i
\(204\) −4.11522e40 2.40018e41i −0.109913 0.641063i
\(205\) 2.54089e41 0.621464
\(206\) −1.68393e40 1.97862e41i −0.0377323 0.443355i
\(207\) 1.64321e41i 0.337464i
\(208\) −2.14304e41 + 7.57124e40i −0.403543 + 0.142570i
\(209\) −1.67951e41 −0.290102
\(210\) 2.70165e41 2.29927e40i 0.428234 0.0364454i
\(211\) 5.10879e40i 0.0743420i −0.999309 0.0371710i \(-0.988165\pi\)
0.999309 0.0371710i \(-0.0118346\pi\)
\(212\) −8.38255e41 + 1.43723e41i −1.12029 + 0.192079i
\(213\) −8.40396e41 −1.03193
\(214\) 2.62998e40 + 3.09023e41i 0.0296828 + 0.348773i
\(215\) 3.30770e41i 0.343268i
\(216\) −2.85622e41 1.09703e42i −0.272661 1.04725i
\(217\) −1.08097e42 −0.949592
\(218\) 1.56673e42 1.33339e41i 1.26700 0.107830i
\(219\) 1.87981e42i 1.39998i
\(220\) 1.71614e41 + 1.00093e42i 0.117746 + 0.686746i
\(221\) −5.75903e41 −0.364157
\(222\) −3.49584e40 4.10762e41i −0.0203797 0.239462i
\(223\) 3.14384e42i 1.69033i −0.534503 0.845167i \(-0.679501\pi\)
0.534503 0.845167i \(-0.320499\pi\)
\(224\) 1.21722e42 + 2.69302e42i 0.603816 + 1.33590i
\(225\) −7.74331e41 −0.354521
\(226\) 3.60790e42 3.07055e41i 1.52512 0.129797i
\(227\) 2.54173e42i 0.992347i −0.868223 0.496174i \(-0.834738\pi\)
0.868223 0.496174i \(-0.165262\pi\)
\(228\) 3.33508e41 5.71814e40i 0.120304 0.0206266i
\(229\) 3.08692e42 1.02917 0.514585 0.857440i \(-0.327946\pi\)
0.514585 + 0.857440i \(0.327946\pi\)
\(230\) −8.56571e40 1.00647e42i −0.0264036 0.310242i
\(231\) 7.14179e42i 2.03606i
\(232\) 2.38452e42 6.20834e41i 0.628952 0.163754i
\(233\) 7.31206e41 0.178498 0.0892489 0.996009i \(-0.471553\pi\)
0.0892489 + 0.996009i \(0.471553\pi\)
\(234\) −7.84298e41 + 6.67487e40i −0.177254 + 0.0150854i
\(235\) 1.58267e42i 0.331260i
\(236\) −1.10875e42 6.46675e42i −0.214990 1.25392i
\(237\) −6.55409e42 −1.17772
\(238\) 6.35006e41 + 7.46133e42i 0.105777 + 1.24289i
\(239\) 3.35689e42i 0.518532i −0.965806 0.259266i \(-0.916519\pi\)
0.965806 0.259266i \(-0.0834806\pi\)
\(240\) −6.81562e41 1.92916e42i −0.0976570 0.276418i
\(241\) 2.11826e42 0.281626 0.140813 0.990036i \(-0.455028\pi\)
0.140813 + 0.990036i \(0.455028\pi\)
\(242\) −1.85782e43 + 1.58113e42i −2.29260 + 0.195115i
\(243\) 6.69907e42i 0.767541i
\(244\) −3.64926e42 + 6.25682e41i −0.388319 + 0.0665789i
\(245\) −4.45828e42 −0.440735
\(246\) −1.14342e42 1.34352e43i −0.105045 1.23428i
\(247\) 8.00224e41i 0.0683386i
\(248\) 2.05522e42 + 7.89376e42i 0.163203 + 0.626836i
\(249\) 1.82258e43 1.34617
\(250\) −1.03034e43 + 8.76888e41i −0.708047 + 0.0602593i
\(251\) 1.09661e43i 0.701336i 0.936500 + 0.350668i \(0.114045\pi\)
−0.936500 + 0.350668i \(0.885955\pi\)
\(252\) 1.72958e42 + 1.00877e43i 0.102975 + 0.600595i
\(253\) 2.66061e43 1.47507
\(254\) 8.51824e41 + 1.00089e43i 0.0439889 + 0.516870i
\(255\) 5.18427e42i 0.249439i
\(256\) 1.73515e43 1.40089e43i 0.778067 0.628181i
\(257\) −5.04919e42 −0.211070 −0.105535 0.994416i \(-0.533655\pi\)
−0.105535 + 0.994416i \(0.533655\pi\)
\(258\) −1.74898e43 + 1.48849e42i −0.681757 + 0.0580218i
\(259\) 1.26767e43i 0.460903i
\(260\) −4.76905e42 + 8.17675e41i −0.161775 + 0.0277371i
\(261\) 8.53337e42 0.270142
\(262\) −1.65323e42 1.94255e43i −0.0488552 0.574050i
\(263\) 2.22021e43i 0.612620i −0.951932 0.306310i \(-0.900906\pi\)
0.951932 0.306310i \(-0.0990943\pi\)
\(264\) 5.21529e43 1.35785e43i 1.34403 0.349931i
\(265\) −1.81059e43 −0.435907
\(266\) −1.03676e43 + 8.82348e41i −0.233243 + 0.0198505i
\(267\) 2.60296e43i 0.547349i
\(268\) 7.27757e42 + 4.24461e43i 0.143074 + 0.834471i
\(269\) −2.41057e43 −0.443178 −0.221589 0.975140i \(-0.571124\pi\)
−0.221589 + 0.975140i \(0.571124\pi\)
\(270\) −2.04648e42 2.40461e43i −0.0351932 0.413521i
\(271\) 4.83064e43i 0.777244i 0.921397 + 0.388622i \(0.127049\pi\)
−0.921397 + 0.388622i \(0.872951\pi\)
\(272\) 5.32791e43 1.88232e43i 0.802262 0.283435i
\(273\) −3.40279e43 −0.479631
\(274\) 1.64429e43 1.39939e42i 0.217004 0.0184684i
\(275\) 1.25376e44i 1.54962i
\(276\) −5.28327e43 + 9.05841e42i −0.611702 + 0.104879i
\(277\) −1.00881e44 −1.09439 −0.547196 0.837005i \(-0.684305\pi\)
−0.547196 + 0.837005i \(0.684305\pi\)
\(278\) 1.16030e43 + 1.36336e44i 0.117968 + 1.38613i
\(279\) 2.82490e43i 0.269233i
\(280\) 1.58522e43 + 6.08857e43i 0.141659 + 0.544090i
\(281\) −1.08851e44 −0.912261 −0.456130 0.889913i \(-0.650765\pi\)
−0.456130 + 0.889913i \(0.650765\pi\)
\(282\) 8.36853e43 7.12214e42i 0.657908 0.0559921i
\(283\) 2.09138e44i 1.54268i −0.636421 0.771342i \(-0.719586\pi\)
0.636421 0.771342i \(-0.280414\pi\)
\(284\) −3.29536e43 1.92201e44i −0.228125 1.33053i
\(285\) 7.20360e42 0.0468104
\(286\) −1.08076e43 1.26990e44i −0.0659388 0.774782i
\(287\) 4.14629e44i 2.37567i
\(288\) 7.03768e43 3.18097e43i 0.378761 0.171196i
\(289\) −5.45926e43 −0.276040
\(290\) 5.22672e43 4.44826e42i 0.248350 0.0211362i
\(291\) 5.38033e43i 0.240290i
\(292\) −4.29918e44 + 7.37113e43i −1.80507 + 0.309487i
\(293\) 1.29240e44 0.510246 0.255123 0.966909i \(-0.417884\pi\)
0.255123 + 0.966909i \(0.417884\pi\)
\(294\) 2.00626e43 + 2.35736e44i 0.0744964 + 0.875334i
\(295\) 1.39679e44i 0.487903i
\(296\) 9.25715e43 2.41019e43i 0.304247 0.0792137i
\(297\) 6.35658e44 1.96611
\(298\) 2.90939e44 2.47607e43i 0.847051 0.0720893i
\(299\) 1.26768e44i 0.347478i
\(300\) 4.26860e43 + 2.48964e44i 0.110180 + 0.642619i
\(301\) 5.39758e44 1.31221
\(302\) −4.90349e43 5.76160e44i −0.112300 1.31953i
\(303\) 1.53763e44i 0.331807i
\(304\) 2.61550e43 + 7.40318e43i 0.0531901 + 0.150555i
\(305\) −7.88222e43 −0.151096
\(306\) 1.94988e44 1.65947e43i 0.352388 0.0299905i
\(307\) 5.37830e44i 0.916546i 0.888812 + 0.458273i \(0.151532\pi\)
−0.888812 + 0.458273i \(0.848468\pi\)
\(308\) −1.63335e45 + 2.80044e44i −2.62522 + 0.450105i
\(309\) −2.24340e44 −0.340137
\(310\) 1.47256e43 + 1.73026e44i 0.0210651 + 0.247515i
\(311\) 1.27143e45i 1.71635i −0.513353 0.858177i \(-0.671597\pi\)
0.513353 0.858177i \(-0.328403\pi\)
\(312\) 6.46965e43 + 2.48489e44i 0.0824324 + 0.316610i
\(313\) −1.55517e44 −0.187059 −0.0935296 0.995616i \(-0.529815\pi\)
−0.0935296 + 0.995616i \(0.529815\pi\)
\(314\) −7.76315e44 + 6.60693e43i −0.881666 + 0.0750353i
\(315\) 2.17889e44i 0.233693i
\(316\) −2.56999e44 1.49894e45i −0.260354 1.51850i
\(317\) −1.28628e45 −1.23103 −0.615515 0.788125i \(-0.711052\pi\)
−0.615515 + 0.788125i \(0.711052\pi\)
\(318\) 8.14779e43 + 9.57367e44i 0.0736804 + 0.865745i
\(319\) 1.38168e45i 1.18080i
\(320\) 4.14479e44 2.31521e44i 0.334813 0.187021i
\(321\) 3.50377e44 0.267575
\(322\) 1.64239e45 1.39777e44i 1.18596 0.100933i
\(323\) 1.98947e44i 0.135860i
\(324\) −6.28017e44 + 1.07676e44i −0.405659 + 0.0695520i
\(325\) 5.97368e44 0.365041
\(326\) −1.14305e44 1.34308e45i −0.0660918 0.776579i
\(327\) 1.77639e45i 0.972030i
\(328\) 3.02783e45 7.88324e44i 1.56820 0.408297i
\(329\) −2.58264e45 −1.26630
\(330\) 1.14316e45 9.72899e43i 0.530708 0.0451666i
\(331\) 9.60496e44i 0.422271i 0.977457 + 0.211136i \(0.0677162\pi\)
−0.977457 + 0.211136i \(0.932284\pi\)
\(332\) 7.14671e44 + 4.16829e45i 0.297592 + 1.73569i
\(333\) 3.31281e44 0.130677
\(334\) 1.95308e44 + 2.29487e45i 0.0729933 + 0.857673i
\(335\) 9.16814e44i 0.324694i
\(336\) 3.14806e45 1.11219e45i 1.05666 0.373312i
\(337\) 2.40643e45 0.765658 0.382829 0.923819i \(-0.374950\pi\)
0.382829 + 0.923819i \(0.374950\pi\)
\(338\) −2.69813e45 + 2.29628e44i −0.813884 + 0.0692667i
\(339\) 4.09072e45i 1.17005i
\(340\) 1.18566e45 2.03286e44i 0.321616 0.0551425i
\(341\) −4.57394e45 −1.17682
\(342\) 2.30585e43 + 2.70938e44i 0.00562809 + 0.0661301i
\(343\) 9.44676e44i 0.218771i
\(344\) −1.02623e45 3.94159e45i −0.225524 0.866202i
\(345\) −1.14116e45 −0.238014
\(346\) −3.27421e45 + 2.78656e44i −0.648242 + 0.0551694i
\(347\) 5.95983e45i 1.12022i 0.828418 + 0.560110i \(0.189241\pi\)
−0.828418 + 0.560110i \(0.810759\pi\)
\(348\) −4.70413e44 2.74366e45i −0.0839562 0.489670i
\(349\) 3.96150e45 0.671432 0.335716 0.941963i \(-0.391022\pi\)
0.335716 + 0.941963i \(0.391022\pi\)
\(350\) −6.58674e44 7.73943e45i −0.106034 1.24590i
\(351\) 3.02867e45i 0.463152i
\(352\) 5.15047e45 + 1.13951e46i 0.748305 + 1.65557i
\(353\) −3.77639e45 −0.521353 −0.260677 0.965426i \(-0.583946\pi\)
−0.260677 + 0.965426i \(0.583946\pi\)
\(354\) −7.38564e45 + 6.28565e44i −0.969013 + 0.0824691i
\(355\) 4.15144e45i 0.517712i
\(356\) −5.95302e45 + 1.02067e45i −0.705728 + 0.121000i
\(357\) 8.45983e45 0.953528
\(358\) −1.09514e44 1.28679e45i −0.0117375 0.137915i
\(359\) 8.40831e45i 0.857054i −0.903529 0.428527i \(-0.859033\pi\)
0.903529 0.428527i \(-0.140967\pi\)
\(360\) 1.59113e45 4.14267e44i 0.154263 0.0401638i
\(361\) 1.05661e46 0.974504
\(362\) −1.86574e46 + 1.58786e45i −1.63718 + 0.139334i
\(363\) 2.10644e46i 1.75886i
\(364\) −1.33430e45 7.78226e45i −0.106030 0.618416i
\(365\) −9.28601e45 −0.702357
\(366\) 3.54706e44 + 4.16780e45i 0.0255393 + 0.300087i
\(367\) 8.59773e45i 0.589379i −0.955593 0.294689i \(-0.904784\pi\)
0.955593 0.294689i \(-0.0952162\pi\)
\(368\) −4.14336e45 1.17278e46i −0.270453 0.765517i
\(369\) 1.08355e46 0.673559
\(370\) 2.02911e45 1.72690e44i 0.120136 0.0102243i
\(371\) 2.95457e46i 1.66634i
\(372\) 9.08265e45 1.55726e45i 0.488022 0.0836736i
\(373\) 2.05825e46 1.05375 0.526876 0.849942i \(-0.323363\pi\)
0.526876 + 0.849942i \(0.323363\pi\)
\(374\) 2.68693e45 + 3.15714e46i 0.131089 + 1.54030i
\(375\) 1.16823e46i 0.543206i
\(376\) 4.91032e45 + 1.88597e46i 0.217635 + 0.835901i
\(377\) −6.58318e45 −0.278158
\(378\) 3.92391e46 3.33949e45i 1.58076 0.134533i
\(379\) 2.71367e46i 1.04244i 0.853422 + 0.521221i \(0.174523\pi\)
−0.853422 + 0.521221i \(0.825477\pi\)
\(380\) 2.82468e44 + 1.64748e45i 0.0103482 + 0.0603553i
\(381\) 1.13484e46 0.396537
\(382\) −3.46183e45 4.06765e46i −0.115389 1.35582i
\(383\) 2.21749e46i 0.705152i 0.935783 + 0.352576i \(0.114694\pi\)
−0.935783 + 0.352576i \(0.885306\pi\)
\(384\) −1.41071e46 2.08741e46i −0.428031 0.633353i
\(385\) −3.52794e46 −1.02148
\(386\) 2.60704e46 2.21875e45i 0.720404 0.0613109i
\(387\) 1.41056e46i 0.372043i
\(388\) 1.23050e46 2.10974e45i 0.309820 0.0531199i
\(389\) −6.09024e46 −1.46400 −0.732001 0.681303i \(-0.761414\pi\)
−0.732001 + 0.681303i \(0.761414\pi\)
\(390\) 4.63549e44 + 5.44671e45i 0.0106398 + 0.125018i
\(391\) 3.15163e46i 0.690801i
\(392\) −5.31267e46 + 1.38321e46i −1.11215 + 0.289559i
\(393\) −2.20251e46 −0.440405
\(394\) 2.67008e46 2.27241e45i 0.510027 0.0434065i
\(395\) 3.23763e46i 0.590852i
\(396\) 7.31842e45 + 4.26844e46i 0.127616 + 0.744313i
\(397\) −8.96756e46 −1.49433 −0.747163 0.664641i \(-0.768585\pi\)
−0.747163 + 0.664641i \(0.768585\pi\)
\(398\) −1.79715e45 2.11166e46i −0.0286213 0.336301i
\(399\) 1.17550e46i 0.178942i
\(400\) −5.52648e46 + 1.95248e46i −0.804209 + 0.284123i
\(401\) 3.36429e46 0.468052 0.234026 0.972230i \(-0.424810\pi\)
0.234026 + 0.972230i \(0.424810\pi\)
\(402\) 4.84774e46 4.12573e45i 0.644868 0.0548823i
\(403\) 2.17931e46i 0.277222i
\(404\) 3.51660e46 6.02937e45i 0.427817 0.0733512i
\(405\) −1.35649e46 −0.157843
\(406\) 7.25879e45 + 8.52909e46i 0.0807971 + 0.949367i
\(407\) 5.36393e46i 0.571195i
\(408\) −1.60845e46 6.17779e46i −0.163879 0.629434i
\(409\) 6.55074e46 0.638661 0.319331 0.947643i \(-0.396542\pi\)
0.319331 + 0.947643i \(0.396542\pi\)
\(410\) 6.63680e46 5.64833e45i 0.619226 0.0527000i
\(411\) 1.86433e46i 0.166483i
\(412\) −8.79683e45 5.13071e46i −0.0751928 0.438559i
\(413\) 2.27931e47 1.86510
\(414\) −3.65282e45 4.29207e46i −0.0286169 0.336249i
\(415\) 9.00329e46i 0.675360i
\(416\) −5.42931e46 + 2.45400e46i −0.390000 + 0.176277i
\(417\) 1.54580e47 1.06342
\(418\) −4.38688e46 + 3.73351e45i −0.289057 + 0.0246005i
\(419\) 3.50715e46i 0.221361i −0.993856 0.110681i \(-0.964697\pi\)
0.993856 0.110681i \(-0.0353031\pi\)
\(420\) 7.00558e46 1.20114e46i 0.423601 0.0726283i
\(421\) 4.57681e46 0.265146 0.132573 0.991173i \(-0.457676\pi\)
0.132573 + 0.991173i \(0.457676\pi\)
\(422\) −1.13567e45 1.33442e46i −0.00630418 0.0740742i
\(423\) 6.74925e46i 0.359028i
\(424\) −2.15757e47 + 5.61745e46i −1.09997 + 0.286387i
\(425\) −1.48514e47 −0.725717
\(426\) −2.19511e47 + 1.86818e46i −1.02822 + 0.0875076i
\(427\) 1.28624e47i 0.577591i
\(428\) 1.37390e46 + 8.01321e46i 0.0591517 + 0.345000i
\(429\) −1.43984e47 −0.594404
\(430\) −7.35292e45 8.63970e46i −0.0291090 0.342032i
\(431\) 1.74245e47i 0.661561i 0.943708 + 0.330780i \(0.107312\pi\)
−0.943708 + 0.330780i \(0.892688\pi\)
\(432\) −9.89910e46 2.80194e47i −0.360486 1.02035i
\(433\) 2.39178e47 0.835486 0.417743 0.908565i \(-0.362821\pi\)
0.417743 + 0.908565i \(0.362821\pi\)
\(434\) −2.82348e47 + 2.40296e46i −0.946172 + 0.0805252i
\(435\) 5.92617e46i 0.190532i
\(436\) 4.06265e47 6.96560e46i 1.25329 0.214883i
\(437\) 4.37922e46 0.129638
\(438\) 4.17878e46 + 4.91007e47i 0.118718 + 1.39493i
\(439\) 4.04214e47i 1.10217i −0.834448 0.551087i \(-0.814213\pi\)
0.834448 0.551087i \(-0.185787\pi\)
\(440\) 6.70760e46 + 2.57628e47i 0.175557 + 0.674287i
\(441\) −1.90122e47 −0.477680
\(442\) −1.50426e47 + 1.28022e46i −0.362845 + 0.0308804i
\(443\) 6.19474e46i 0.143468i −0.997424 0.0717341i \(-0.977147\pi\)
0.997424 0.0717341i \(-0.0228533\pi\)
\(444\) −1.82623e46 1.06514e47i −0.0406126 0.236871i
\(445\) −1.28582e47 −0.274600
\(446\) −6.98867e46 8.21169e47i −0.143340 1.68424i
\(447\) 3.29873e47i 0.649848i
\(448\) 3.77802e47 + 6.76357e47i 0.714925 + 1.27989i
\(449\) −5.94487e47 −1.08071 −0.540354 0.841438i \(-0.681710\pi\)
−0.540354 + 0.841438i \(0.681710\pi\)
\(450\) −2.02255e47 + 1.72132e46i −0.353244 + 0.0300633i
\(451\) 1.75443e48i 2.94415i
\(452\) 9.35557e47 1.60405e47i 1.50862 0.258659i
\(453\) −6.53263e47 −1.01233
\(454\) −5.65019e46 6.63899e47i −0.0841508 0.988773i
\(455\) 1.68093e47i 0.240627i
\(456\) 8.58410e46 2.23496e46i 0.118121 0.0307540i
\(457\) 2.64756e47 0.350231 0.175116 0.984548i \(-0.443970\pi\)
0.175116 + 0.984548i \(0.443970\pi\)
\(458\) 8.06303e47 6.86214e46i 1.02546 0.0872733i
\(459\) 7.52970e47i 0.920766i
\(460\) −4.47472e46 2.60986e47i −0.0526169 0.306886i
\(461\) 6.93782e47 0.784524 0.392262 0.919854i \(-0.371693\pi\)
0.392262 + 0.919854i \(0.371693\pi\)
\(462\) 1.58760e47 + 1.86543e48i 0.172658 + 2.02873i
\(463\) 1.29767e48i 1.35740i −0.734417 0.678698i \(-0.762544\pi\)
0.734417 0.678698i \(-0.237456\pi\)
\(464\) 6.09036e47 2.15169e47i 0.612800 0.216499i
\(465\) 1.96181e47 0.189891
\(466\) 1.90991e47 1.62545e46i 0.177855 0.0151366i
\(467\) 6.13925e47i 0.550062i 0.961435 + 0.275031i \(0.0886881\pi\)
−0.961435 + 0.275031i \(0.911312\pi\)
\(468\) −2.03375e47 + 3.48695e46i −0.175336 + 0.0300622i
\(469\) −1.49608e48 −1.24121
\(470\) 3.51824e46 + 4.13393e47i 0.0280908 + 0.330067i
\(471\) 8.80203e47i 0.676404i
\(472\) −4.33360e47 1.66447e48i −0.320548 1.23117i
\(473\) 2.28390e48 1.62621
\(474\) −1.71193e48 + 1.45696e47i −1.17348 + 0.0998703i
\(475\) 2.06362e47i 0.136190i
\(476\) 3.31727e47 + 1.93478e48i 0.210793 + 1.22944i
\(477\) −7.72120e47 −0.472448
\(478\) −7.46229e46 8.76820e47i −0.0439713 0.516664i
\(479\) 2.23667e47i 0.126929i 0.997984 + 0.0634646i \(0.0202150\pi\)
−0.997984 + 0.0634646i \(0.979785\pi\)
\(480\) −2.20909e47 4.88746e47i −0.120745 0.267141i
\(481\) −2.55571e47 −0.134555
\(482\) 5.53290e47 4.70884e46i 0.280612 0.0238818i
\(483\) 1.86218e48i 0.909855i
\(484\) −4.81748e48 + 8.25979e47i −2.26780 + 0.388824i
\(485\) 2.65781e47 0.120551
\(486\) −1.48919e47 1.74979e48i −0.0650872 0.764776i
\(487\) 2.09873e48i 0.883967i 0.897023 + 0.441984i \(0.145725\pi\)
−0.897023 + 0.441984i \(0.854275\pi\)
\(488\) −9.39278e47 + 2.44550e47i −0.381274 + 0.0992684i
\(489\) −1.52282e48 −0.595783
\(490\) −1.16450e48 + 9.91064e46i −0.439148 + 0.0373742i
\(491\) 9.13688e47i 0.332148i −0.986113 0.166074i \(-0.946891\pi\)
0.986113 0.166074i \(-0.0531090\pi\)
\(492\) −5.97322e47 3.48385e48i −0.209332 1.22092i
\(493\) 1.63667e48 0.552990
\(494\) −1.77888e46 2.09018e47i −0.00579510 0.0680925i
\(495\) 9.21961e47i 0.289614i
\(496\) 7.12299e47 + 2.01616e48i 0.215770 + 0.610738i
\(497\) 6.77442e48 1.97905
\(498\) 4.76058e48 4.05155e47i 1.34132 0.114155i
\(499\) 3.32131e47i 0.0902609i 0.998981 + 0.0451304i \(0.0143703\pi\)
−0.998981 + 0.0451304i \(0.985630\pi\)
\(500\) −2.67176e48 + 4.58086e47i −0.700387 + 0.120084i
\(501\) 2.60197e48 0.657997
\(502\) 2.43774e47 + 2.86435e48i 0.0594731 + 0.698810i
\(503\) 3.11350e48i 0.732868i 0.930444 + 0.366434i \(0.119421\pi\)
−0.930444 + 0.366434i \(0.880579\pi\)
\(504\) 6.76011e47 + 2.59645e48i 0.153534 + 0.589699i
\(505\) 7.59568e47 0.166465
\(506\) 6.94950e48 5.91446e47i 1.46975 0.125085i
\(507\) 3.05920e48i 0.624403i
\(508\) 4.44993e47 + 2.59540e48i 0.0876609 + 0.511278i
\(509\) −6.15463e48 −1.17026 −0.585129 0.810940i \(-0.698956\pi\)
−0.585129 + 0.810940i \(0.698956\pi\)
\(510\) −1.15245e47 1.35413e48i −0.0211524 0.248541i
\(511\) 1.51531e49i 2.68489i
\(512\) 4.22079e48 4.04484e48i 0.721995 0.691898i
\(513\) 1.04626e48 0.172793
\(514\) −1.31885e48 + 1.12242e47i −0.210309 + 0.0178986i
\(515\) 1.10821e48i 0.170644i
\(516\) −4.53523e48 + 7.77586e47i −0.674381 + 0.115626i
\(517\) −1.09280e49 −1.56932
\(518\) 2.81799e47 + 3.31115e48i 0.0390845 + 0.459243i
\(519\) 3.71237e48i 0.497324i
\(520\) −1.22750e48 + 3.19591e47i −0.158840 + 0.0413557i
\(521\) −5.37366e48 −0.671725 −0.335862 0.941911i \(-0.609028\pi\)
−0.335862 + 0.941911i \(0.609028\pi\)
\(522\) 2.22892e48 1.89695e47i 0.269169 0.0229079i
\(523\) 1.04564e49i 1.21998i 0.792411 + 0.609988i \(0.208826\pi\)
−0.792411 + 0.609988i \(0.791174\pi\)
\(524\) −8.63649e47 5.03719e48i −0.0973585 0.567839i
\(525\) −8.77513e48 −0.955842
\(526\) −4.93547e47 5.79919e48i −0.0519500 0.610413i
\(527\) 5.41807e48i 0.551129i
\(528\) 1.33205e49 4.70606e48i 1.30951 0.462643i
\(529\) 3.58716e48 0.340839
\(530\) −4.72925e48 + 4.02489e47i −0.434337 + 0.0369648i
\(531\) 5.95655e48i 0.528802i
\(532\) −2.68840e48 + 4.60938e47i −0.230720 + 0.0395579i
\(533\) −8.35921e48 −0.693546
\(534\) 5.78630e47 + 6.79891e48i 0.0464150 + 0.545377i
\(535\) 1.73081e48i 0.134240i
\(536\) 2.84446e48 + 1.09251e49i 0.213321 + 0.819332i
\(537\) −1.45899e48 −0.105807
\(538\) −6.29640e48 + 5.35863e47i −0.441582 + 0.0375814i
\(539\) 3.07836e49i 2.08796i
\(540\) −1.06908e48 6.23535e48i −0.0701329 0.409047i
\(541\) 1.77918e49 1.12894 0.564468 0.825455i \(-0.309081\pi\)
0.564468 + 0.825455i \(0.309081\pi\)
\(542\) 1.07384e48 + 1.26176e49i 0.0659100 + 0.774444i
\(543\) 2.11541e49i 1.25602i
\(544\) 1.34980e49 6.10099e48i 0.775337 0.350445i
\(545\) 8.77513e48 0.487659
\(546\) −8.88808e48 + 7.56431e47i −0.477904 + 0.0406726i
\(547\) 3.11538e48i 0.162084i 0.996711 + 0.0810419i \(0.0258248\pi\)
−0.996711 + 0.0810419i \(0.974175\pi\)
\(548\) 4.26377e48 7.31042e47i 0.214656 0.0368038i
\(549\) −3.36135e48 −0.163761
\(550\) −2.78707e48 3.27481e49i −0.131407 1.54404i
\(551\) 2.27417e48i 0.103776i
\(552\) −1.35985e49 + 3.54051e48i −0.600605 + 0.156373i
\(553\) 5.28324e49 2.25865
\(554\) −2.63500e49 + 2.24255e48i −1.09045 + 0.0928041i
\(555\) 2.30065e48i 0.0921671i
\(556\) 6.06141e48 + 3.53529e49i 0.235086 + 1.37113i
\(557\) −2.68438e49 −1.00798 −0.503988 0.863711i \(-0.668134\pi\)
−0.503988 + 0.863711i \(0.668134\pi\)
\(558\) 6.27968e47 + 7.37864e48i 0.0228309 + 0.268263i
\(559\) 1.08819e49i 0.383083i
\(560\) 5.49406e48 + 1.55509e49i 0.187288 + 0.530118i
\(561\) 3.57964e49 1.18170
\(562\) −2.84319e49 + 2.41973e48i −0.908975 + 0.0773595i
\(563\) 5.69125e48i 0.176221i −0.996111 0.0881103i \(-0.971917\pi\)
0.996111 0.0881103i \(-0.0280828\pi\)
\(564\) 2.17002e49 3.72060e48i 0.650790 0.111581i
\(565\) 2.02076e49 0.587005
\(566\) −4.64908e48 5.46267e49i −0.130819 1.53713i
\(567\) 2.21355e49i 0.603384i
\(568\) −1.28801e49 4.94702e49i −0.340132 1.30639i
\(569\) −1.13238e49 −0.289714 −0.144857 0.989453i \(-0.546272\pi\)
−0.144857 + 0.989453i \(0.546272\pi\)
\(570\) 1.88158e48 1.60134e47i 0.0466418 0.00396951i
\(571\) 4.77390e49i 1.14663i 0.819335 + 0.573315i \(0.194343\pi\)
−0.819335 + 0.573315i \(0.805657\pi\)
\(572\) −5.64589e48 3.29294e49i −0.131403 0.766399i
\(573\) −4.61199e49 −1.04017
\(574\) 9.21709e48 + 1.08301e50i 0.201456 + 2.36711i
\(575\) 3.26909e49i 0.692478i
\(576\) 1.76753e49 9.87315e48i 0.362879 0.202699i
\(577\) 4.06405e49 0.808714 0.404357 0.914601i \(-0.367495\pi\)
0.404357 + 0.914601i \(0.367495\pi\)
\(578\) −1.42596e49 + 1.21358e48i −0.275046 + 0.0234081i
\(579\) 2.95592e49i 0.552686i
\(580\) 1.35533e49 2.32377e48i 0.245664 0.0421201i
\(581\) −1.46918e50 −2.58169
\(582\) −1.19603e48 1.40534e49i −0.0203765 0.239424i
\(583\) 1.25018e50i 2.06508i
\(584\) −1.10656e50 + 2.88103e49i −1.77232 + 0.461442i
\(585\) −4.39279e48 −0.0682236
\(586\) 3.37575e49 2.87297e48i 0.508409 0.0432688i
\(587\) 5.94523e49i 0.868326i 0.900834 + 0.434163i \(0.142956\pi\)
−0.900834 + 0.434163i \(0.857044\pi\)
\(588\) 1.04807e49 + 6.11282e49i 0.148456 + 0.865864i
\(589\) −7.52846e48 −0.103426
\(590\) −3.10502e48 3.64840e49i −0.0413741 0.486146i
\(591\) 3.02740e49i 0.391287i
\(592\) 2.36439e49 8.35325e48i 0.296434 0.104728i
\(593\) −1.47365e49 −0.179230 −0.0896148 0.995976i \(-0.528564\pi\)
−0.0896148 + 0.995976i \(0.528564\pi\)
\(594\) 1.66034e50 1.41305e49i 1.95903 0.166725i
\(595\) 4.17903e49i 0.478377i
\(596\) 7.54428e49 1.29350e49i 0.837886 0.143659i
\(597\) −2.39424e49 −0.258006
\(598\) 2.81801e48 + 3.31117e49i 0.0294660 + 0.346226i
\(599\) 2.00221e49i 0.203154i −0.994828 0.101577i \(-0.967611\pi\)
0.994828 0.101577i \(-0.0323889\pi\)
\(600\) 1.66840e49 + 6.40804e49i 0.164277 + 0.630961i
\(601\) 1.56279e50 1.49334 0.746670 0.665195i \(-0.231651\pi\)
0.746670 + 0.665195i \(0.231651\pi\)
\(602\) 1.40985e50 1.19987e49i 1.30748 0.111275i
\(603\) 3.90972e49i 0.351912i
\(604\) −2.56158e49 1.49403e50i −0.223791 1.30525i
\(605\) −1.04055e50 −0.882404
\(606\) −3.41812e48 4.01629e49i −0.0281371 0.330611i
\(607\) 1.63488e50i 1.30644i 0.757168 + 0.653220i \(0.226582\pi\)
−0.757168 + 0.653220i \(0.773418\pi\)
\(608\) 8.47740e48 + 1.87557e49i 0.0657655 + 0.145502i
\(609\) 9.67047e49 0.728344
\(610\) −2.05883e49 + 1.75220e48i −0.150551 + 0.0128129i
\(611\) 5.20679e49i 0.369682i
\(612\) 5.05619e49 8.66905e48i 0.348576 0.0597649i
\(613\) −9.89772e49 −0.662593 −0.331296 0.943527i \(-0.607486\pi\)
−0.331296 + 0.943527i \(0.607486\pi\)
\(614\) 1.19558e49 + 1.40481e50i 0.0777228 + 0.913244i
\(615\) 7.52495e49i 0.475063i
\(616\) −4.20404e50 + 1.09456e50i −2.57759 + 0.671101i
\(617\) 1.30487e50 0.777022 0.388511 0.921444i \(-0.372990\pi\)
0.388511 + 0.921444i \(0.372990\pi\)
\(618\) −5.85976e49 + 4.98702e48i −0.338912 + 0.0288436i
\(619\) 2.95569e49i 0.166046i −0.996548 0.0830228i \(-0.973543\pi\)
0.996548 0.0830228i \(-0.0264574\pi\)
\(620\) 7.69265e48 + 4.48670e49i 0.0419784 + 0.244837i
\(621\) −1.65744e50 −0.878594
\(622\) −2.82637e49 3.32098e50i −0.145546 1.71017i
\(623\) 2.09824e50i 1.04971i
\(624\) 2.24225e49 + 6.34670e49i 0.108984 + 0.308479i
\(625\) 1.22905e50 0.580401
\(626\) −4.06209e49 + 3.45710e48i −0.186385 + 0.0158626i
\(627\) 4.97395e49i 0.221761i
\(628\) −2.01304e50 + 3.45145e49i −0.872127 + 0.149530i
\(629\) 6.35386e49 0.267501
\(630\) 4.84361e48 + 5.69125e49i 0.0198171 + 0.232851i
\(631\) 1.95097e50i 0.775751i 0.921712 + 0.387876i \(0.126791\pi\)
−0.921712 + 0.387876i \(0.873209\pi\)
\(632\) −1.00449e50 3.85809e50i −0.388185 1.49095i
\(633\) −1.51299e49 −0.0568289
\(634\) −3.35976e50 + 2.85937e49i −1.22660 + 0.104391i
\(635\) 5.60593e49i 0.198939i
\(636\) 4.25640e49 + 2.48253e50i 0.146830 + 0.856379i
\(637\) 1.46672e50 0.491855
\(638\) 3.07144e49 + 3.60895e50i 0.100131 + 1.17654i
\(639\) 1.77037e50i 0.561109i
\(640\) 1.03115e50 6.96871e49i 0.317748 0.214740i
\(641\) 2.40479e50 0.720498 0.360249 0.932856i \(-0.382692\pi\)
0.360249 + 0.932856i \(0.382692\pi\)
\(642\) 9.15185e49 7.78880e48i 0.266611 0.0226903i
\(643\) 3.65575e50i 1.03557i −0.855511 0.517785i \(-0.826757\pi\)
0.855511 0.517785i \(-0.173243\pi\)
\(644\) 4.25884e50 7.30197e49i 1.17313 0.201138i
\(645\) −9.79588e49 −0.262403
\(646\) 4.42254e48 + 5.19649e49i 0.0115209 + 0.135371i
\(647\) 7.82816e50i 1.98327i 0.129059 + 0.991637i \(0.458804\pi\)
−0.129059 + 0.991637i \(0.541196\pi\)
\(648\) −1.61644e50 + 4.20857e49i −0.398300 + 0.103701i
\(649\) 9.64454e50 2.31141
\(650\) 1.56032e50 1.32793e49i 0.363726 0.0309553i
\(651\) 3.20133e50i 0.725893i
\(652\) −5.97127e49 3.48272e50i −0.131707 0.768177i
\(653\) −7.97111e50 −1.71034 −0.855169 0.518350i \(-0.826547\pi\)
−0.855169 + 0.518350i \(0.826547\pi\)
\(654\) −3.94888e49 4.63993e50i −0.0824278 0.968528i
\(655\) 1.08801e50i 0.220947i
\(656\) 7.73343e50 2.73218e50i 1.52793 0.539809i
\(657\) −3.95999e50 −0.761232
\(658\) −6.74586e50 + 5.74115e49i −1.26174 + 0.107382i
\(659\) 7.45713e50i 1.35717i −0.734522 0.678585i \(-0.762593\pi\)
0.734522 0.678585i \(-0.237407\pi\)
\(660\) 2.96430e50 5.08242e49i 0.524966 0.0900077i
\(661\) −3.41956e50 −0.589310 −0.294655 0.955604i \(-0.595205\pi\)
−0.294655 + 0.955604i \(0.595205\pi\)
\(662\) 2.13516e49 + 2.50881e50i 0.0358085 + 0.420750i
\(663\) 1.70556e50i 0.278371i
\(664\) 2.79332e50 + 1.07287e51i 0.443706 + 1.70420i
\(665\) −5.80681e49 −0.0897735
\(666\) 8.65305e49 7.36429e48i 0.130207 0.0110814i
\(667\) 3.60264e50i 0.527662i
\(668\) 1.02029e50 + 5.95078e50i 0.145461 + 0.848394i
\(669\) −9.31060e50 −1.29213
\(670\) 2.03805e49 + 2.39472e50i 0.0275340 + 0.323525i
\(671\) 5.44252e50i 0.715805i
\(672\) 7.97548e50 3.60484e50i 1.02120 0.461572i
\(673\) 8.55644e50 1.06665 0.533325 0.845911i \(-0.320942\pi\)
0.533325 + 0.845911i \(0.320942\pi\)
\(674\) 6.28559e50 5.34943e49i 0.762900 0.0649276i
\(675\) 7.81034e50i 0.923001i
\(676\) −6.99647e50 + 1.19958e50i −0.805079 + 0.138034i
\(677\) −8.83947e50 −0.990444 −0.495222 0.868766i \(-0.664913\pi\)
−0.495222 + 0.868766i \(0.664913\pi\)
\(678\) −9.09356e49 1.06849e51i −0.0992201 1.16584i
\(679\) 4.33708e50i 0.460831i
\(680\) 3.05174e50 7.94550e49i 0.315782 0.0822169i
\(681\) −7.52743e50 −0.758575
\(682\) −1.19471e51 + 1.01677e50i −1.17258 + 0.0997943i
\(683\) 1.05574e50i 0.100922i −0.998726 0.0504608i \(-0.983931\pi\)
0.998726 0.0504608i \(-0.0160690\pi\)
\(684\) 1.20457e49 + 7.02563e49i 0.0112156 + 0.0654147i
\(685\) 9.20953e49 0.0835232
\(686\) −2.09999e49 2.46749e50i −0.0185517 0.217983i
\(687\) 9.14204e50i 0.786723i
\(688\) −3.55672e50 1.00673e51i −0.298165 0.843957i
\(689\) 5.95661e50 0.486467
\(690\) −2.98071e50 + 2.53677e49i −0.237157 + 0.0201836i
\(691\) 4.73080e50i 0.366716i 0.983046 + 0.183358i \(0.0586967\pi\)
−0.983046 + 0.183358i \(0.941303\pi\)
\(692\) −8.49029e50 + 1.45570e50i −0.641228 + 0.109941i
\(693\) −1.50448e51 −1.10710
\(694\) 1.32485e50 + 1.55671e51i 0.0949943 + 1.11618i
\(695\) 7.63605e50i 0.533510i
\(696\) −1.83862e50 7.06186e50i −0.125178 0.480787i
\(697\) 2.07822e51 1.37880
\(698\) 1.03474e51 8.80631e49i 0.669013 0.0569372i
\(699\) 2.16550e50i 0.136448i
\(700\) −3.44091e50 2.00689e51i −0.211304 1.23242i
\(701\) 1.72691e51 1.03358 0.516791 0.856112i \(-0.327127\pi\)
0.516791 + 0.856112i \(0.327127\pi\)
\(702\) 6.73265e49 + 7.91087e50i 0.0392752 + 0.461484i
\(703\) 8.82876e49i 0.0502000i
\(704\) 1.59861e51 + 2.86189e51i 0.886002 + 1.58615i
\(705\) 4.68714e50 0.253224
\(706\) −9.86392e50 + 8.39482e49i −0.519475 + 0.0442106i
\(707\) 1.23948e51i 0.636343i
\(708\) −1.91516e51 + 3.28362e50i −0.958529 + 0.164344i
\(709\) 3.74194e51 1.82585 0.912924 0.408130i \(-0.133819\pi\)
0.912924 + 0.408130i \(0.133819\pi\)
\(710\) −9.22854e49 1.08435e51i −0.0439018 0.515847i
\(711\) 1.38067e51i 0.640381i
\(712\) −1.53224e51 + 3.98933e50i −0.692925 + 0.180410i
\(713\) 1.19262e51 0.525886
\(714\) 2.20970e51 1.88060e50i 0.950094 0.0808589i
\(715\) 7.11258e50i 0.298208i
\(716\) −5.72099e49 3.33674e50i −0.0233904 0.136423i
\(717\) −9.94158e50 −0.396379
\(718\) −1.86914e50 2.19625e51i −0.0726780 0.853967i
\(719\) 3.21231e50i 0.121814i −0.998143 0.0609070i \(-0.980601\pi\)
0.998143 0.0609070i \(-0.0193993\pi\)
\(720\) 4.06394e50 1.43577e50i 0.150301 0.0531006i
\(721\) 1.80840e51 0.652319
\(722\) 2.75985e51 2.34881e50i 0.970994 0.0826377i
\(723\) 6.27332e50i 0.215282i
\(724\) −4.83800e51 + 8.29496e50i −1.61946 + 0.277664i
\(725\) −1.69767e51 −0.554332
\(726\) 4.68257e50 + 5.50202e51i 0.149151 + 1.75252i
\(727\) 2.83677e51i 0.881464i 0.897639 + 0.440732i \(0.145281\pi\)
−0.897639 + 0.440732i \(0.854719\pi\)
\(728\) −5.21517e50 2.00306e51i −0.158090 0.607198i
\(729\) −3.37566e51 −0.998306
\(730\) −2.42550e51 + 2.06426e50i −0.699827 + 0.0595596i
\(731\) 2.70540e51i 0.761585i
\(732\) 1.85298e50 + 1.08074e51i 0.0508946 + 0.296841i
\(733\) −4.57843e51 −1.22700 −0.613500 0.789695i \(-0.710239\pi\)
−0.613500 + 0.789695i \(0.710239\pi\)
\(734\) −1.91125e50 2.24572e51i −0.0499792 0.587256i
\(735\) 1.32034e51i 0.336909i
\(736\) −1.34295e51 2.97119e51i −0.334395 0.739825i
\(737\) −6.33042e51 −1.53822
\(738\) 2.83024e51 2.40871e50i 0.671133 0.0571176i
\(739\) 1.18843e51i 0.275026i 0.990500 + 0.137513i \(0.0439108\pi\)
−0.990500 + 0.137513i \(0.956089\pi\)
\(740\) 5.26163e50 9.02130e49i 0.118836 0.0203750i
\(741\) −2.36990e50 −0.0522398
\(742\) −6.56792e50 7.71732e51i −0.141305 1.66034i
\(743\) 1.36253e51i 0.286119i 0.989714 + 0.143059i \(0.0456940\pi\)
−0.989714 + 0.143059i \(0.954306\pi\)
\(744\) 2.33777e51 6.08661e50i 0.479169 0.124756i
\(745\) 1.62953e51 0.326023
\(746\) 5.37613e51 4.57543e50i 1.04996 0.0893578i
\(747\) 3.83942e51i 0.731973i
\(748\) 1.40365e51 + 8.18672e51i 0.261234 + 1.52364i
\(749\) −2.82439e51 −0.513158
\(750\) 2.59694e50 + 3.05141e51i 0.0460637 + 0.541250i
\(751\) 9.12443e51i 1.58011i