Properties

Label 4.37.b.b.3.6
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 3.6
Root \(3.83971e7i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.37.b.b.3.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +O(q^{10})\) \(q+(-167207. + 201894. i) q^{2} +6.14354e8i q^{3} +(-1.28029e10 - 6.75163e10i) q^{4} -3.33360e12 q^{5} +(-1.24034e14 - 1.02724e14i) q^{6} -2.74304e15i q^{7} +(1.57719e16 + 8.70438e15i) q^{8} -2.27336e17 q^{9} +(5.57402e17 - 6.73034e17i) q^{10} +5.16595e18i q^{11} +(4.14789e19 - 7.86554e18i) q^{12} +1.38994e20 q^{13} +(5.53804e20 + 4.58656e20i) q^{14} -2.04801e21i q^{15} +(-4.39454e21 + 1.72882e21i) q^{16} -2.51975e21 q^{17} +(3.80122e22 - 4.58978e22i) q^{18} -5.92452e22i q^{19} +(4.26799e22 + 2.25072e23i) q^{20} +1.68520e24 q^{21} +(-1.04297e24 - 8.63784e23i) q^{22} -3.10457e24i q^{23} +(-5.34757e24 + 9.68952e24i) q^{24} -3.43902e24 q^{25} +(-2.32408e25 + 2.80620e25i) q^{26} -4.74535e25i q^{27} +(-1.85200e26 + 3.51190e25i) q^{28} +3.37207e26 q^{29} +(4.13481e26 + 3.42442e26i) q^{30} +6.60623e26i q^{31} +(3.85761e26 - 1.17630e27i) q^{32} -3.17372e27 q^{33} +(4.21320e26 - 5.08722e26i) q^{34} +9.14420e27i q^{35} +(2.91057e27 + 1.53489e28i) q^{36} -1.26292e28 q^{37} +(1.19613e28 + 9.90623e27i) q^{38} +8.53913e28i q^{39} +(-5.25772e28 - 2.90169e28i) q^{40} +3.78073e28 q^{41} +(-2.81777e29 + 3.40231e29i) q^{42} -2.97798e29i q^{43} +(3.48786e29 - 6.61394e28i) q^{44} +7.57847e29 q^{45} +(6.26794e29 + 5.19106e29i) q^{46} +8.86953e29i q^{47} +(-1.06210e30 - 2.69980e30i) q^{48} -4.87254e30 q^{49} +(5.75029e29 - 6.94318e29i) q^{50} -1.54802e30i q^{51} +(-1.77953e30 - 9.38434e30i) q^{52} +8.62173e30 q^{53} +(9.58058e30 + 7.93457e30i) q^{54} -1.72212e31i q^{55} +(2.38765e31 - 4.32629e31i) q^{56} +3.63975e31 q^{57} +(-5.63834e31 + 6.80801e31i) q^{58} -1.68733e31i q^{59} +(-1.38274e32 + 2.62206e31i) q^{60} +7.55382e31 q^{61} +(-1.33376e32 - 1.10461e32i) q^{62} +6.23592e32i q^{63} +(1.72986e32 + 2.74569e32i) q^{64} -4.63350e32 q^{65} +(5.30669e32 - 6.40755e32i) q^{66} +5.97442e32i q^{67} +(3.22602e31 + 1.70124e32i) q^{68} +1.90730e33 q^{69} +(-1.84616e33 - 1.52898e33i) q^{70} +1.32742e33i q^{71} +(-3.58552e33 - 1.97882e33i) q^{72} +2.88532e33 q^{73} +(2.11170e33 - 2.54977e33i) q^{74} -2.11278e33i q^{75} +(-4.00002e33 + 7.58513e32i) q^{76} +1.41704e34 q^{77} +(-1.72400e34 - 1.42780e34i) q^{78} +1.29702e34i q^{79} +(1.46496e34 - 5.76318e33i) q^{80} -4.96866e33 q^{81} +(-6.32166e33 + 7.63308e33i) q^{82} +3.72688e34i q^{83} +(-2.15755e34 - 1.13778e35i) q^{84} +8.39984e33 q^{85} +(6.01236e34 + 4.97940e34i) q^{86} +2.07164e35i q^{87} +(-4.49664e34 + 8.14768e34i) q^{88} +1.48586e35 q^{89} +(-1.26718e35 + 1.53005e35i) q^{90} -3.81265e35i q^{91} +(-2.09609e35 + 3.97476e34i) q^{92} -4.05856e35 q^{93} +(-1.79071e35 - 1.48305e35i) q^{94} +1.97500e35i q^{95} +(7.22665e35 + 2.36993e35i) q^{96} +8.33681e35 q^{97} +(8.14724e35 - 9.83737e35i) q^{98} -1.17441e36i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −167207. + 201894.i −0.637845 + 0.770165i
\(3\) 6.14354e8i 1.58575i 0.609381 + 0.792877i \(0.291418\pi\)
−0.609381 + 0.792877i \(0.708582\pi\)
\(4\) −1.28029e10 6.75163e10i −0.186307 0.982491i
\(5\) −3.33360e12 −0.873883 −0.436942 0.899490i \(-0.643938\pi\)
−0.436942 + 0.899490i \(0.643938\pi\)
\(6\) −1.24034e14 1.02724e14i −1.22129 1.01147i
\(7\) 2.74304e15i 1.68449i −0.539098 0.842243i \(-0.681235\pi\)
0.539098 0.842243i \(-0.318765\pi\)
\(8\) 1.57719e16 + 8.70438e15i 0.875516 + 0.483190i
\(9\) −2.27336e17 −1.51462
\(10\) 5.57402e17 6.73034e17i 0.557402 0.673034i
\(11\) 5.16595e18i 0.929141i 0.885536 + 0.464571i \(0.153791\pi\)
−0.885536 + 0.464571i \(0.846209\pi\)
\(12\) 4.14789e19 7.86554e18i 1.55799 0.295438i
\(13\) 1.38994e20 1.23599 0.617995 0.786182i \(-0.287945\pi\)
0.617995 + 0.786182i \(0.287945\pi\)
\(14\) 5.53804e20 + 4.58656e20i 1.29733 + 1.07444i
\(15\) 2.04801e21i 1.38576i
\(16\) −4.39454e21 + 1.72882e21i −0.930579 + 0.366091i
\(17\) −2.51975e21 −0.179175 −0.0895873 0.995979i \(-0.528555\pi\)
−0.0895873 + 0.995979i \(0.528555\pi\)
\(18\) 3.80122e22 4.58978e22i 0.966091 1.16651i
\(19\) 5.92452e22i 0.568969i −0.958681 0.284484i \(-0.908178\pi\)
0.958681 0.284484i \(-0.0918224\pi\)
\(20\) 4.26799e22 + 2.25072e23i 0.162811 + 0.858583i
\(21\) 1.68520e24 2.67118
\(22\) −1.04297e24 8.63784e23i −0.715592 0.592648i
\(23\) 3.10457e24i 0.956974i −0.878095 0.478487i \(-0.841185\pi\)
0.878095 0.478487i \(-0.158815\pi\)
\(24\) −5.34757e24 + 9.68952e24i −0.766221 + 1.38835i
\(25\) −3.43902e24 −0.236328
\(26\) −2.32408e25 + 2.80620e25i −0.788370 + 0.951916i
\(27\) 4.74535e25i 0.816057i
\(28\) −1.85200e26 + 3.51190e25i −1.65499 + 0.313832i
\(29\) 3.37207e26 1.60226 0.801129 0.598492i \(-0.204233\pi\)
0.801129 + 0.598492i \(0.204233\pi\)
\(30\) 4.13481e26 + 3.42442e26i 1.06727 + 0.883903i
\(31\) 6.60623e26i 0.945025i 0.881324 + 0.472512i \(0.156653\pi\)
−0.881324 + 0.472512i \(0.843347\pi\)
\(32\) 3.85761e26 1.17630e27i 0.311615 0.950208i
\(33\) −3.17372e27 −1.47339
\(34\) 4.21320e26 5.08722e26i 0.114286 0.137994i
\(35\) 9.14420e27i 1.47204i
\(36\) 2.91057e27 + 1.53489e28i 0.282185 + 1.48810i
\(37\) −1.26292e28 −0.747732 −0.373866 0.927483i \(-0.621968\pi\)
−0.373866 + 0.927483i \(0.621968\pi\)
\(38\) 1.19613e28 + 9.90623e27i 0.438200 + 0.362914i
\(39\) 8.53913e28i 1.95998i
\(40\) −5.25772e28 2.90169e28i −0.765099 0.422252i
\(41\) 3.78073e28 0.352750 0.176375 0.984323i \(-0.443563\pi\)
0.176375 + 0.984323i \(0.443563\pi\)
\(42\) −2.81777e29 + 3.40231e29i −1.70380 + 2.05725i
\(43\) 2.97798e29i 1.17893i −0.807792 0.589467i \(-0.799338\pi\)
0.807792 0.589467i \(-0.200662\pi\)
\(44\) 3.48786e29 6.61394e28i 0.912874 0.173106i
\(45\) 7.57847e29 1.32360
\(46\) 6.26794e29 + 5.19106e29i 0.737028 + 0.610401i
\(47\) 8.86953e29i 0.708173i 0.935213 + 0.354086i \(0.115208\pi\)
−0.935213 + 0.354086i \(0.884792\pi\)
\(48\) −1.06210e30 2.69980e30i −0.580530 1.47567i
\(49\) −4.87254e30 −1.83749
\(50\) 5.75029e29 6.94318e29i 0.150741 0.182011i
\(51\) 1.54802e30i 0.284127i
\(52\) −1.77953e30 9.38434e30i −0.230274 1.21435i
\(53\) 8.62173e30 0.791824 0.395912 0.918288i \(-0.370428\pi\)
0.395912 + 0.918288i \(0.370428\pi\)
\(54\) 9.58058e30 + 7.93457e30i 0.628499 + 0.520518i
\(55\) 1.72212e31i 0.811961i
\(56\) 2.38765e31 4.32629e31i 0.813927 1.47479i
\(57\) 3.63975e31 0.902245
\(58\) −5.63834e31 + 6.80801e31i −1.02199 + 1.23400i
\(59\) 1.68733e31i 0.224835i −0.993661 0.112418i \(-0.964141\pi\)
0.993661 0.112418i \(-0.0358595\pi\)
\(60\) −1.38274e32 + 2.62206e31i −1.36150 + 0.258178i
\(61\) 7.55382e31 0.552369 0.276185 0.961105i \(-0.410930\pi\)
0.276185 + 0.961105i \(0.410930\pi\)
\(62\) −1.33376e32 1.10461e32i −0.727825 0.602779i
\(63\) 6.23592e32i 2.55135i
\(64\) 1.72986e32 + 2.74569e32i 0.533055 + 0.846081i
\(65\) −4.63350e32 −1.08011
\(66\) 5.30669e32 6.40755e32i 0.939795 1.13475i
\(67\) 5.97442e32i 0.807141i 0.914949 + 0.403571i \(0.132231\pi\)
−0.914949 + 0.403571i \(0.867769\pi\)
\(68\) 3.22602e31 + 1.70124e32i 0.0333816 + 0.176038i
\(69\) 1.90730e33 1.51753
\(70\) −1.84616e33 1.52898e33i −1.13372 0.938936i
\(71\) 1.32742e33i 0.631477i 0.948846 + 0.315739i \(0.102252\pi\)
−0.948846 + 0.315739i \(0.897748\pi\)
\(72\) −3.58552e33 1.97882e33i −1.32607 0.731848i
\(73\) 2.88532e33 0.832497 0.416249 0.909251i \(-0.363345\pi\)
0.416249 + 0.909251i \(0.363345\pi\)
\(74\) 2.11170e33 2.54977e33i 0.476937 0.575877i
\(75\) 2.11278e33i 0.374758i
\(76\) −4.00002e33 + 7.58513e32i −0.559007 + 0.106003i
\(77\) 1.41704e34 1.56513
\(78\) −1.72400e34 1.42780e34i −1.50950 1.25016i
\(79\) 1.29702e34i 0.902938i 0.892287 + 0.451469i \(0.149100\pi\)
−0.892287 + 0.451469i \(0.850900\pi\)
\(80\) 1.46496e34 5.76318e33i 0.813218 0.319921i
\(81\) −4.96866e33 −0.220551
\(82\) −6.32166e33 + 7.63308e33i −0.225000 + 0.271675i
\(83\) 3.72688e34i 1.06645i 0.845974 + 0.533224i \(0.179020\pi\)
−0.845974 + 0.533224i \(0.820980\pi\)
\(84\) −2.15755e34 1.13778e35i −0.497661 2.62441i
\(85\) 8.39984e33 0.156578
\(86\) 6.01236e34 + 4.97940e34i 0.907973 + 0.751977i
\(87\) 2.07164e35i 2.54079i
\(88\) −4.49664e34 + 8.14768e34i −0.448952 + 0.813478i
\(89\) 1.48586e35 1.21048 0.605238 0.796044i \(-0.293078\pi\)
0.605238 + 0.796044i \(0.293078\pi\)
\(90\) −1.26718e35 + 1.53005e35i −0.844251 + 1.01939i
\(91\) 3.81265e35i 2.08201i
\(92\) −2.09609e35 + 3.97476e34i −0.940219 + 0.178291i
\(93\) −4.05856e35 −1.49858
\(94\) −1.79071e35 1.48305e35i −0.545410 0.451704i
\(95\) 1.97500e35i 0.497212i
\(96\) 7.22665e35 + 2.36993e35i 1.50680 + 0.494145i
\(97\) 8.33681e35 1.44248 0.721238 0.692687i \(-0.243573\pi\)
0.721238 + 0.692687i \(0.243573\pi\)
\(98\) 8.14724e35 9.83737e35i 1.17204 1.41517i
\(99\) 1.17441e36i 1.40729i
\(100\) 4.40296e34 + 2.32190e35i 0.0440296 + 0.232190i
\(101\) −1.53819e36 −1.28595 −0.642976 0.765886i \(-0.722301\pi\)
−0.642976 + 0.765886i \(0.722301\pi\)
\(102\) 3.12535e35 + 2.58840e35i 0.218825 + 0.181229i
\(103\) 1.77261e36i 1.04122i −0.853794 0.520611i \(-0.825704\pi\)
0.853794 0.520611i \(-0.174296\pi\)
\(104\) 2.19219e36 + 1.20985e36i 1.08213 + 0.597218i
\(105\) −5.61778e36 −2.33430
\(106\) −1.44162e36 + 1.74068e36i −0.505061 + 0.609835i
\(107\) 1.57039e36i 0.464622i 0.972642 + 0.232311i \(0.0746287\pi\)
−0.972642 + 0.232311i \(0.925371\pi\)
\(108\) −3.20389e36 + 6.07545e35i −0.801769 + 0.152038i
\(109\) 5.61746e36 1.19087 0.595433 0.803405i \(-0.296980\pi\)
0.595433 + 0.803405i \(0.296980\pi\)
\(110\) 3.47686e36 + 2.87951e36i 0.625344 + 0.517905i
\(111\) 7.75882e36i 1.18572i
\(112\) 4.74221e36 + 1.20544e37i 0.616675 + 1.56755i
\(113\) 9.90271e36 1.09734 0.548671 0.836038i \(-0.315134\pi\)
0.548671 + 0.836038i \(0.315134\pi\)
\(114\) −6.08593e36 + 7.34844e36i −0.575492 + 0.694877i
\(115\) 1.03494e37i 0.836284i
\(116\) −4.31724e36 2.27670e37i −0.298513 1.57420i
\(117\) −3.15983e37 −1.87205
\(118\) 3.40662e36 + 2.82134e36i 0.173160 + 0.143410i
\(119\) 6.91177e36i 0.301817i
\(120\) 1.78267e37 3.23010e37i 0.669587 1.21326i
\(121\) 4.22565e36 0.136696
\(122\) −1.26305e37 + 1.52507e37i −0.352326 + 0.425415i
\(123\) 2.32271e37i 0.559374i
\(124\) 4.46028e37 8.45792e36i 0.928479 0.176065i
\(125\) 5.99746e37 1.08041
\(126\) −1.25900e38 1.04269e38i −1.96496 1.62737i
\(127\) 1.51207e37i 0.204694i −0.994749 0.102347i \(-0.967365\pi\)
0.994749 0.102347i \(-0.0326352\pi\)
\(128\) −8.43584e37 1.09850e37i −0.991628 0.129128i
\(129\) 1.82953e38 1.86950
\(130\) 7.74754e37 9.35475e37i 0.688943 0.831863i
\(131\) 1.98999e36i 0.0154158i −0.999970 0.00770791i \(-0.997546\pi\)
0.999970 0.00770791i \(-0.00245353\pi\)
\(132\) 4.06330e37 + 2.14278e38i 0.274504 + 1.44759i
\(133\) −1.62512e38 −0.958420
\(134\) −1.20620e38 9.98967e37i −0.621632 0.514831i
\(135\) 1.58191e38i 0.713139i
\(136\) −3.97412e37 2.19328e37i −0.156870 0.0865754i
\(137\) 2.35330e38 0.814154 0.407077 0.913394i \(-0.366548\pi\)
0.407077 + 0.913394i \(0.366548\pi\)
\(138\) −3.18915e38 + 3.85073e38i −0.967947 + 1.16875i
\(139\) 3.85441e38i 1.02729i 0.858004 + 0.513643i \(0.171704\pi\)
−0.858004 + 0.513643i \(0.828296\pi\)
\(140\) 6.17383e38 1.17073e38i 1.44627 0.274253i
\(141\) −5.44903e38 −1.12299
\(142\) −2.67998e38 2.21954e38i −0.486341 0.402785i
\(143\) 7.18035e38i 1.14841i
\(144\) 9.99036e38 3.93022e38i 1.40947 0.554488i
\(145\) −1.12411e39 −1.40019
\(146\) −4.82447e38 + 5.82529e38i −0.531004 + 0.641160i
\(147\) 2.99346e39i 2.91382i
\(148\) 1.61691e38 + 8.52679e38i 0.139308 + 0.734640i
\(149\) 1.77368e39 1.35370 0.676850 0.736121i \(-0.263345\pi\)
0.676850 + 0.736121i \(0.263345\pi\)
\(150\) 4.26557e38 + 3.53272e38i 0.288625 + 0.239037i
\(151\) 2.04452e39i 1.22746i −0.789517 0.613729i \(-0.789669\pi\)
0.789517 0.613729i \(-0.210331\pi\)
\(152\) 5.15693e38 9.34409e38i 0.274920 0.498141i
\(153\) 5.72829e38 0.271381
\(154\) −2.36940e39 + 2.86092e39i −0.998308 + 1.20541i
\(155\) 2.20225e39i 0.825842i
\(156\) 5.76531e39 1.09326e39i 1.92566 0.365158i
\(157\) −3.45070e39 −1.02734 −0.513669 0.857988i \(-0.671714\pi\)
−0.513669 + 0.857988i \(0.671714\pi\)
\(158\) −2.61860e39 2.16871e39i −0.695411 0.575934i
\(159\) 5.29679e39i 1.25564i
\(160\) −1.28597e39 + 3.92132e39i −0.272315 + 0.830371i
\(161\) −8.51596e39 −1.61201
\(162\) 8.30796e38 1.00314e39i 0.140677 0.169861i
\(163\) 3.27030e39i 0.495691i 0.968800 + 0.247846i \(0.0797226\pi\)
−0.968800 + 0.247846i \(0.920277\pi\)
\(164\) −4.84045e38 2.55261e39i −0.0657199 0.346574i
\(165\) 1.05799e40 1.28757
\(166\) −7.52434e39 6.23161e39i −0.821340 0.680228i
\(167\) 2.45888e39i 0.240903i 0.992719 + 0.120451i \(0.0384342\pi\)
−0.992719 + 0.120451i \(0.961566\pi\)
\(168\) 2.65787e40 + 1.46686e40i 2.33866 + 1.29069i
\(169\) 6.67304e39 0.527671
\(170\) −1.40451e39 + 1.69588e39i −0.0998723 + 0.120591i
\(171\) 1.34686e40i 0.861770i
\(172\) −2.01062e40 + 3.81269e39i −1.15829 + 0.219644i
\(173\) 1.45782e40 0.756611 0.378305 0.925681i \(-0.376507\pi\)
0.378305 + 0.925681i \(0.376507\pi\)
\(174\) −4.18253e40 3.46394e40i −1.95683 1.62063i
\(175\) 9.43338e39i 0.398091i
\(176\) −8.93097e39 2.27019e40i −0.340150 0.864640i
\(177\) 1.03662e40 0.356534
\(178\) −2.48446e40 + 2.99985e40i −0.772096 + 0.932266i
\(179\) 4.38644e40i 1.23242i −0.787583 0.616209i \(-0.788668\pi\)
0.787583 0.616209i \(-0.211332\pi\)
\(180\) −9.70268e39 5.11671e40i −0.246596 1.30042i
\(181\) −6.61493e39 −0.152164 −0.0760818 0.997102i \(-0.524241\pi\)
−0.0760818 + 0.997102i \(0.524241\pi\)
\(182\) 7.69752e40 + 6.37504e40i 1.60349 + 1.32800i
\(183\) 4.64072e40i 0.875922i
\(184\) 2.70233e40 4.89649e40i 0.462400 0.837846i
\(185\) 4.21008e40 0.653430
\(186\) 6.78621e40 8.19400e40i 0.955860 1.15415i
\(187\) 1.30169e40i 0.166479i
\(188\) 5.98838e40 1.13556e40i 0.695774 0.131938i
\(189\) −1.30167e41 −1.37464
\(190\) −3.98741e40 3.30234e40i −0.382935 0.317144i
\(191\) 6.76496e40i 0.591105i 0.955326 + 0.295553i \(0.0955037\pi\)
−0.955326 + 0.295553i \(0.904496\pi\)
\(192\) −1.68682e41 + 1.06275e41i −1.34168 + 0.845295i
\(193\) −5.40480e40 −0.391515 −0.195757 0.980652i \(-0.562716\pi\)
−0.195757 + 0.980652i \(0.562716\pi\)
\(194\) −1.39398e41 + 1.68315e41i −0.920077 + 1.11094i
\(195\) 2.84661e41i 1.71279i
\(196\) 6.23829e40 + 3.28976e41i 0.342339 + 1.80532i
\(197\) 2.02102e41 1.01200 0.505998 0.862535i \(-0.331124\pi\)
0.505998 + 0.862535i \(0.331124\pi\)
\(198\) 2.37106e41 + 1.96369e41i 1.08385 + 0.897635i
\(199\) 3.80168e41i 1.58716i 0.608466 + 0.793580i \(0.291785\pi\)
−0.608466 + 0.793580i \(0.708215\pi\)
\(200\) −5.42399e40 2.99345e40i −0.206909 0.114191i
\(201\) −3.67041e41 −1.27993
\(202\) 2.57196e41 3.10551e41i 0.820238 0.990395i
\(203\) 9.24972e41i 2.69898i
\(204\) −1.04516e41 + 1.98192e40i −0.279152 + 0.0529350i
\(205\) −1.26035e41 −0.308262
\(206\) 3.57880e41 + 2.96393e41i 0.801913 + 0.664138i
\(207\) 7.05780e41i 1.44945i
\(208\) −6.10813e41 + 2.40295e41i −1.15019 + 0.452485i
\(209\) 3.06058e41 0.528652
\(210\) 9.39333e41 1.13420e42i 1.48892 1.79780i
\(211\) 1.04017e42i 1.51364i −0.653624 0.756819i \(-0.726752\pi\)
0.653624 0.756819i \(-0.273248\pi\)
\(212\) −1.10384e41 5.82107e41i −0.147523 0.777961i
\(213\) −8.15505e41 −1.00137
\(214\) −3.17053e41 2.62581e41i −0.357836 0.296357i
\(215\) 9.92739e41i 1.03025i
\(216\) 4.13053e41 7.48431e41i 0.394311 0.714471i
\(217\) 1.81212e42 1.59188
\(218\) −9.39280e41 + 1.13413e42i −0.759588 + 0.917164i
\(219\) 1.77261e42i 1.32014i
\(220\) −1.16271e42 + 2.20482e41i −0.797745 + 0.151274i
\(221\) −3.50229e41 −0.221458
\(222\) 1.56646e42 + 1.29733e42i 0.913199 + 0.756305i
\(223\) 2.32832e42i 1.25186i −0.779879 0.625930i \(-0.784719\pi\)
0.779879 0.625930i \(-0.215281\pi\)
\(224\) −3.22664e42 1.05816e42i −1.60061 0.524911i
\(225\) 7.81813e41 0.357946
\(226\) −1.65580e42 + 1.99930e42i −0.699934 + 0.845134i
\(227\) 1.68132e42i 0.656426i 0.944604 + 0.328213i \(0.106446\pi\)
−0.944604 + 0.328213i \(0.893554\pi\)
\(228\) −4.65996e41 2.45743e42i −0.168095 0.886448i
\(229\) 5.03000e42 1.67698 0.838492 0.544914i \(-0.183438\pi\)
0.838492 + 0.544914i \(0.183438\pi\)
\(230\) −2.08948e42 1.73049e42i −0.644076 0.533420i
\(231\) 8.70565e42i 2.48191i
\(232\) 5.31839e42 + 2.93518e42i 1.40280 + 0.774195i
\(233\) −3.15400e42 −0.769937 −0.384968 0.922930i \(-0.625788\pi\)
−0.384968 + 0.922930i \(0.625788\pi\)
\(234\) 5.28346e42 6.37950e42i 1.19408 1.44179i
\(235\) 2.95675e42i 0.618860i
\(236\) −1.13922e42 + 2.16028e41i −0.220899 + 0.0418885i
\(237\) −7.96827e42 −1.43184
\(238\) −1.39545e42 1.15570e42i −0.232449 0.192513i
\(239\) 4.63973e42i 0.716688i −0.933590 0.358344i \(-0.883341\pi\)
0.933590 0.358344i \(-0.116659\pi\)
\(240\) 3.54063e42 + 9.00005e42i 0.507316 + 1.28956i
\(241\) −4.00732e42 −0.532780 −0.266390 0.963865i \(-0.585831\pi\)
−0.266390 + 0.963865i \(0.585831\pi\)
\(242\) −7.06559e41 + 8.53133e41i −0.0871910 + 0.105279i
\(243\) 1.01750e43i 1.16580i
\(244\) −9.67112e41 5.10006e42i −0.102911 0.542698i
\(245\) 1.62431e43 1.60576
\(246\) −4.68941e42 3.88374e42i −0.430810 0.356794i
\(247\) 8.23471e42i 0.703240i
\(248\) −5.75031e42 + 1.04193e43i −0.456626 + 0.827384i
\(249\) −2.28962e43 −1.69112
\(250\) −1.00282e43 + 1.21085e43i −0.689132 + 0.832091i
\(251\) 1.88297e43i 1.20425i −0.798403 0.602124i \(-0.794321\pi\)
0.798403 0.602124i \(-0.205679\pi\)
\(252\) 4.21026e43 7.98382e42i 2.50668 0.475336i
\(253\) 1.60380e43 0.889165
\(254\) 3.05278e42 + 2.52829e42i 0.157648 + 0.130563i
\(255\) 5.16047e42i 0.248294i
\(256\) 1.63231e43 1.51947e43i 0.731955 0.681353i
\(257\) 2.39158e43 0.999744 0.499872 0.866099i \(-0.333380\pi\)
0.499872 + 0.866099i \(0.333380\pi\)
\(258\) −3.05911e43 + 3.69372e43i −1.19245 + 1.43982i
\(259\) 3.46425e43i 1.25954i
\(260\) 5.93224e42 + 3.12837e43i 0.201233 + 1.06120i
\(261\) −7.66593e43 −2.42681
\(262\) 4.01766e41 + 3.32740e41i 0.0118727 + 0.00983290i
\(263\) 9.96673e42i 0.275011i −0.990501 0.137505i \(-0.956092\pi\)
0.990501 0.137505i \(-0.0439084\pi\)
\(264\) −5.00556e43 2.76253e43i −1.28998 0.711927i
\(265\) −2.87414e43 −0.691962
\(266\) 2.71732e43 3.28102e43i 0.611324 0.738141i
\(267\) 9.12841e43i 1.91952i
\(268\) 4.03371e43 7.64902e42i 0.793009 0.150376i
\(269\) −7.17904e42 −0.131985 −0.0659926 0.997820i \(-0.521021\pi\)
−0.0659926 + 0.997820i \(0.521021\pi\)
\(270\) −3.19378e43 2.64507e43i −0.549234 0.454872i
\(271\) 2.81551e43i 0.453012i −0.974010 0.226506i \(-0.927270\pi\)
0.974010 0.226506i \(-0.0727303\pi\)
\(272\) 1.10731e43 4.35618e42i 0.166736 0.0655942i
\(273\) 2.34232e44 3.30155
\(274\) −3.93488e43 + 4.75117e43i −0.519304 + 0.627032i
\(275\) 1.77658e43i 0.219582i
\(276\) −2.44191e43 1.28774e44i −0.282726 1.49096i
\(277\) 1.33140e44 1.44436 0.722178 0.691708i \(-0.243141\pi\)
0.722178 + 0.691708i \(0.243141\pi\)
\(278\) −7.78183e43 6.44485e43i −0.791180 0.655249i
\(279\) 1.50183e44i 1.43135i
\(280\) −7.95946e43 + 1.44221e44i −0.711277 + 1.28880i
\(281\) −1.44307e44 −1.20941 −0.604705 0.796450i \(-0.706709\pi\)
−0.604705 + 0.796450i \(0.706709\pi\)
\(282\) 9.11117e43 1.10013e44i 0.716292 0.864886i
\(283\) 1.35543e44i 0.999815i 0.866079 + 0.499908i \(0.166633\pi\)
−0.866079 + 0.499908i \(0.833367\pi\)
\(284\) 8.96224e43 1.69949e43i 0.620421 0.117649i
\(285\) −1.21335e44 −0.788457
\(286\) −1.44967e44 1.20061e44i −0.884464 0.732507i
\(287\) 1.03707e44i 0.594202i
\(288\) −8.76973e43 + 2.67416e44i −0.471977 + 1.43920i
\(289\) −1.91421e44 −0.967896
\(290\) 1.87960e44 2.26952e44i 0.893102 1.07837i
\(291\) 5.12175e44i 2.28741i
\(292\) −3.69406e43 1.94806e44i −0.155100 0.817922i
\(293\) 1.90590e44 0.752458 0.376229 0.926527i \(-0.377221\pi\)
0.376229 + 0.926527i \(0.377221\pi\)
\(294\) 6.04363e44 + 5.00529e44i 2.24412 + 1.85856i
\(295\) 5.62489e43i 0.196480i
\(296\) −1.99187e44 1.09930e44i −0.654651 0.361296i
\(297\) 2.45142e44 0.758233
\(298\) −2.96572e44 + 3.58095e44i −0.863450 + 1.04257i
\(299\) 4.31516e44i 1.18281i
\(300\) −1.42647e44 + 2.70498e43i −0.368196 + 0.0698202i
\(301\) −8.16872e44 −1.98590
\(302\) 4.12777e44 + 3.41859e44i 0.945345 + 0.782928i
\(303\) 9.44992e44i 2.03920i
\(304\) 1.02424e44 + 2.60355e44i 0.208294 + 0.529470i
\(305\) −2.51814e44 −0.482706
\(306\) −9.57812e43 + 1.15651e44i −0.173099 + 0.209008i
\(307\) 2.25478e44i 0.384250i 0.981371 + 0.192125i \(0.0615378\pi\)
−0.981371 + 0.192125i \(0.938462\pi\)
\(308\) −1.81423e44 9.56734e44i −0.291595 1.53772i
\(309\) 1.08901e45 1.65112
\(310\) 4.44622e44 + 3.68233e44i 0.636034 + 0.526759i
\(311\) 4.40395e44i 0.594505i 0.954799 + 0.297253i \(0.0960704\pi\)
−0.954799 + 0.297253i \(0.903930\pi\)
\(312\) −7.43278e44 + 1.34678e45i −0.947041 + 1.71599i
\(313\) −3.57493e44 −0.430001 −0.215001 0.976614i \(-0.568975\pi\)
−0.215001 + 0.976614i \(0.568975\pi\)
\(314\) 5.76982e44 6.96676e44i 0.655282 0.791219i
\(315\) 2.07881e45i 2.22959i
\(316\) 8.75698e44 1.66056e44i 0.887129 0.168224i
\(317\) −1.47137e44 −0.140817 −0.0704084 0.997518i \(-0.522430\pi\)
−0.0704084 + 0.997518i \(0.522430\pi\)
\(318\) −1.06939e45 8.85662e44i −0.967049 0.800903i
\(319\) 1.74199e45i 1.48872i
\(320\) −5.76667e44 9.15303e44i −0.465828 0.739376i
\(321\) −9.64776e44 −0.736777
\(322\) 1.42393e45 1.71932e45i 1.02821 1.24151i
\(323\) 1.49283e44i 0.101945i
\(324\) 6.36135e43 + 3.35466e44i 0.0410903 + 0.216690i
\(325\) −4.78002e44 −0.292099
\(326\) −6.60255e44 5.46819e44i −0.381764 0.316174i
\(327\) 3.45111e45i 1.88842i
\(328\) 5.96293e44 + 3.29089e44i 0.308838 + 0.170445i
\(329\) 2.43295e45 1.19291
\(330\) −1.76904e45 + 2.13602e45i −0.821271 + 0.991642i
\(331\) 1.32037e45i 0.580486i −0.956953 0.290243i \(-0.906264\pi\)
0.956953 0.290243i \(-0.0937361\pi\)
\(332\) 2.51625e45 4.77150e44i 1.04778 0.198687i
\(333\) 2.87108e45 1.13253
\(334\) −4.96434e44 4.11143e44i −0.185535 0.153658i
\(335\) 1.99163e45i 0.705347i
\(336\) −7.40566e45 + 2.91340e45i −2.48575 + 0.977896i
\(337\) 3.36424e45 1.07041 0.535203 0.844724i \(-0.320235\pi\)
0.535203 + 0.844724i \(0.320235\pi\)
\(338\) −1.11578e45 + 1.34725e45i −0.336572 + 0.406393i
\(339\) 6.08377e45i 1.74011i
\(340\) −1.07543e44 5.67126e44i −0.0291716 0.153836i
\(341\) −3.41275e45 −0.878062
\(342\) −2.71922e45 2.25204e45i −0.663705 0.549676i
\(343\) 6.09178e45i 1.41075i
\(344\) 2.59214e45 4.69683e45i 0.569649 1.03217i
\(345\) −6.35819e45 −1.32614
\(346\) −2.43757e45 + 2.94324e45i −0.482601 + 0.582715i
\(347\) 1.00518e46i 1.88935i −0.328011 0.944674i \(-0.606378\pi\)
0.328011 0.944674i \(-0.393622\pi\)
\(348\) 1.39870e46 2.65231e45i 2.49630 0.473368i
\(349\) 3.56047e45 0.603462 0.301731 0.953393i \(-0.402436\pi\)
0.301731 + 0.953393i \(0.402436\pi\)
\(350\) −1.90454e45 1.57733e45i −0.306596 0.253920i
\(351\) 6.59574e45i 1.00864i
\(352\) 6.07671e45 + 1.99282e45i 0.882878 + 0.289534i
\(353\) −2.76793e45 −0.382130 −0.191065 0.981577i \(-0.561194\pi\)
−0.191065 + 0.981577i \(0.561194\pi\)
\(354\) −1.73330e45 + 2.09287e45i −0.227413 + 0.274590i
\(355\) 4.42508e45i 0.551837i
\(356\) −1.90233e45 1.00319e46i −0.225521 1.18928i
\(357\) −4.24627e45 −0.478608
\(358\) 8.85597e45 + 7.33445e45i 0.949165 + 0.786092i
\(359\) 2.31432e45i 0.235897i −0.993020 0.117949i \(-0.962368\pi\)
0.993020 0.117949i \(-0.0376318\pi\)
\(360\) 1.19527e46 + 6.59659e45i 1.15883 + 0.639550i
\(361\) 7.33251e45 0.676275
\(362\) 1.10606e45 1.33551e45i 0.0970568 0.117191i
\(363\) 2.59604e45i 0.216767i
\(364\) −2.57416e46 + 4.88132e45i −2.04556 + 0.387894i
\(365\) −9.61851e45 −0.727506
\(366\) −9.36934e45 7.75962e45i −0.674605 0.558703i
\(367\) 3.24876e45i 0.222704i −0.993781 0.111352i \(-0.964482\pi\)
0.993781 0.111352i \(-0.0355181\pi\)
\(368\) 5.36723e45 + 1.36431e46i 0.350340 + 0.890540i
\(369\) −8.59497e45 −0.534281
\(370\) −7.03956e45 + 8.49990e45i −0.416787 + 0.503249i
\(371\) 2.36498e46i 1.33382i
\(372\) 5.19616e45 + 2.74019e46i 0.279196 + 1.47234i
\(373\) −1.44373e46 −0.739141 −0.369571 0.929203i \(-0.620495\pi\)
−0.369571 + 0.929203i \(0.620495\pi\)
\(374\) 2.62803e45 + 2.17652e45i 0.128216 + 0.106188i
\(375\) 3.68456e46i 1.71326i
\(376\) −7.72037e45 + 1.39889e46i −0.342182 + 0.620016i
\(377\) 4.68696e46 1.98037
\(378\) 2.17649e46 2.62799e46i 0.876806 1.05870i
\(379\) 1.15828e46i 0.444947i 0.974939 + 0.222473i \(0.0714130\pi\)
−0.974939 + 0.222473i \(0.928587\pi\)
\(380\) 1.33345e46 2.52858e45i 0.488507 0.0926344i
\(381\) 9.28947e45 0.324595
\(382\) −1.36581e46 1.13115e46i −0.455248 0.377033i
\(383\) 1.46515e46i 0.465913i −0.972487 0.232956i \(-0.925160\pi\)
0.972487 0.232956i \(-0.0748400\pi\)
\(384\) 6.74868e45 5.18259e46i 0.204765 1.57248i
\(385\) −4.72385e46 −1.36774
\(386\) 9.03722e45 1.09120e46i 0.249726 0.301531i
\(387\) 6.77002e46i 1.78563i
\(388\) −1.06736e46 5.62871e46i −0.268744 1.41722i
\(389\) 1.39471e46 0.335267 0.167633 0.985849i \(-0.446388\pi\)
0.167633 + 0.985849i \(0.446388\pi\)
\(390\) 5.74713e46 + 4.75973e46i 1.31913 + 1.09250i
\(391\) 7.82273e45i 0.171466i
\(392\) −7.68492e46 4.24124e46i −1.60876 0.887859i
\(393\) 1.22256e45 0.0244457
\(394\) −3.37929e46 + 4.08032e46i −0.645497 + 0.779404i
\(395\) 4.32374e46i 0.789062i
\(396\) −7.92916e46 + 1.50359e46i −1.38265 + 0.262189i
\(397\) 6.95252e46 1.15855 0.579273 0.815134i \(-0.303337\pi\)
0.579273 + 0.815134i \(0.303337\pi\)
\(398\) −7.67537e46 6.35669e46i −1.22237 1.01236i
\(399\) 9.98399e46i 1.51982i
\(400\) 1.51129e46 5.94543e45i 0.219922 0.0865175i
\(401\) 7.27154e46 1.01164 0.505822 0.862638i \(-0.331189\pi\)
0.505822 + 0.862638i \(0.331189\pi\)
\(402\) 6.13719e46 7.41034e46i 0.816396 0.985755i
\(403\) 9.18225e46i 1.16804i
\(404\) 1.96933e46 + 1.03853e47i 0.239582 + 1.26344i
\(405\) 1.65635e46 0.192736
\(406\) 1.86746e47 + 1.54662e47i 2.07866 + 1.72153i
\(407\) 6.52420e46i 0.694749i
\(408\) 1.34745e46 2.44151e46i 0.137287 0.248758i
\(409\) −9.48296e46 −0.924538 −0.462269 0.886740i \(-0.652964\pi\)
−0.462269 + 0.886740i \(0.652964\pi\)
\(410\) 2.10739e46 2.54456e46i 0.196623 0.237413i
\(411\) 1.44576e47i 1.29105i
\(412\) −1.19680e47 + 2.26947e46i −1.02299 + 0.193987i
\(413\) −4.62842e46 −0.378732
\(414\) −1.42493e47 1.18012e47i −1.11632 0.924525i
\(415\) 1.24239e47i 0.931951i
\(416\) 5.36183e46 1.63498e47i 0.385153 1.17445i
\(417\) −2.36797e47 −1.62902
\(418\) −5.11751e46 + 6.17912e46i −0.337198 + 0.407149i
\(419\) 2.48487e47i 1.56838i 0.620521 + 0.784190i \(0.286921\pi\)
−0.620521 + 0.784190i \(0.713079\pi\)
\(420\) 7.19241e46 + 3.79291e47i 0.434898 + 2.29343i
\(421\) 6.81753e46 0.394957 0.197478 0.980307i \(-0.436725\pi\)
0.197478 + 0.980307i \(0.436725\pi\)
\(422\) 2.10005e47 + 1.73925e47i 1.16575 + 0.965467i
\(423\) 2.01636e47i 1.07261i
\(424\) 1.35981e47 + 7.50468e46i 0.693255 + 0.382602i
\(425\) 8.66547e45 0.0423440
\(426\) 1.36358e47 1.64646e47i 0.638717 0.771218i
\(427\) 2.07204e47i 0.930459i
\(428\) 1.06027e47 2.01056e46i 0.456487 0.0865626i
\(429\) −4.41127e47 −1.82110
\(430\) −2.00428e47 1.65993e47i −0.793463 0.657140i
\(431\) 1.42738e47i 0.541937i 0.962588 + 0.270969i \(0.0873440\pi\)
−0.962588 + 0.270969i \(0.912656\pi\)
\(432\) 8.20384e46 + 2.08536e47i 0.298751 + 0.759406i
\(433\) 5.27128e47 1.84134 0.920670 0.390341i \(-0.127643\pi\)
0.920670 + 0.390341i \(0.127643\pi\)
\(434\) −3.02999e47 + 3.65855e47i −1.01537 + 1.22601i
\(435\) 6.90603e47i 2.22035i
\(436\) −7.19201e46 3.79270e47i −0.221867 1.17002i
\(437\) −1.83931e47 −0.544489
\(438\) −3.57879e47 2.96393e47i −1.01672 0.842042i
\(439\) 7.52444e46i 0.205169i −0.994724 0.102585i \(-0.967289\pi\)
0.994724 0.102585i \(-0.0327113\pi\)
\(440\) 1.49900e47 2.71611e47i 0.392331 0.710885i
\(441\) 1.10770e48 2.78310
\(442\) 5.85609e46 7.07092e46i 0.141256 0.170559i
\(443\) 1.06255e47i 0.246083i −0.992402 0.123041i \(-0.960735\pi\)
0.992402 0.123041i \(-0.0392648\pi\)
\(444\) −5.23847e47 + 9.93357e46i −1.16496 + 0.220908i
\(445\) −4.95325e47 −1.05782
\(446\) 4.70075e47 + 3.89313e47i 0.964139 + 0.798493i
\(447\) 1.08967e48i 2.14663i
\(448\) 7.53154e47 4.74508e47i 1.42521 0.897924i
\(449\) −8.30129e47 −1.50908 −0.754538 0.656256i \(-0.772139\pi\)
−0.754538 + 0.656256i \(0.772139\pi\)
\(450\) −1.30725e47 + 1.57843e47i −0.228314 + 0.275678i
\(451\) 1.95311e47i 0.327754i
\(452\) −1.26784e47 6.68594e47i −0.204443 1.07813i
\(453\) 1.25606e48 1.94645
\(454\) −3.39449e47 2.81129e47i −0.505556 0.418698i
\(455\) 1.27099e48i 1.81943i
\(456\) 5.74058e47 + 3.16818e47i 0.789929 + 0.435956i
\(457\) −1.27875e48 −1.69159 −0.845795 0.533508i \(-0.820873\pi\)
−0.845795 + 0.533508i \(0.820873\pi\)
\(458\) −8.41052e47 + 1.01553e48i −1.06966 + 1.29155i
\(459\) 1.19571e47i 0.146217i
\(460\) 6.98753e47 1.32503e47i 0.821642 0.155806i
\(461\) −4.72856e47 −0.534703 −0.267351 0.963599i \(-0.586148\pi\)
−0.267351 + 0.963599i \(0.586148\pi\)
\(462\) −1.75762e48 1.45565e48i −1.91148 1.58307i
\(463\) 2.03247e47i 0.212601i 0.994334 + 0.106301i \(0.0339006\pi\)
−0.994334 + 0.106301i \(0.966099\pi\)
\(464\) −1.48187e48 + 5.82969e47i −1.49103 + 0.586572i
\(465\) 1.35296e48 1.30958
\(466\) 5.27372e47 6.36774e47i 0.491100 0.592978i
\(467\) 3.67532e47i 0.329299i −0.986352 0.164650i \(-0.947351\pi\)
0.986352 0.164650i \(-0.0526494\pi\)
\(468\) 4.04551e47 + 2.13340e48i 0.348777 + 1.83928i
\(469\) 1.63881e48 1.35962
\(470\) 5.96950e47 + 4.94390e47i 0.476624 + 0.394737i
\(471\) 2.11995e48i 1.62911i
\(472\) 1.46872e47 2.66124e47i 0.108638 0.196847i
\(473\) 1.53841e48 1.09540
\(474\) 1.33235e48 1.60875e48i 0.913291 1.10275i
\(475\) 2.03746e47i 0.134463i
\(476\) 4.66657e47 8.84911e46i 0.296533 0.0562308i
\(477\) −1.96003e48 −1.19931
\(478\) 9.36733e47 + 7.75796e47i 0.551968 + 0.457136i
\(479\) 1.68095e48i 0.953925i 0.878924 + 0.476963i \(0.158262\pi\)
−0.878924 + 0.476963i \(0.841738\pi\)
\(480\) −2.40908e48 7.90042e47i −1.31677 0.431825i
\(481\) −1.75538e48 −0.924189
\(482\) 6.70054e47 8.09055e47i 0.339831 0.410328i
\(483\) 5.23181e48i 2.55625i
\(484\) −5.41008e46 2.85300e47i −0.0254675 0.134303i
\(485\) −2.77916e48 −1.26056
\(486\) 2.05428e48 + 1.70134e48i 0.897856 + 0.743598i
\(487\) 2.46020e48i 1.03621i −0.855316 0.518107i \(-0.826637\pi\)
0.855316 0.518107i \(-0.173363\pi\)
\(488\) 1.19138e48 + 6.57513e47i 0.483608 + 0.266899i
\(489\) −2.00912e48 −0.786045
\(490\) −2.71597e48 + 3.27939e48i −1.02422 + 1.23670i
\(491\) 3.35992e48i 1.22141i 0.791858 + 0.610706i \(0.209114\pi\)
−0.791858 + 0.610706i \(0.790886\pi\)
\(492\) 1.56821e48 2.97375e47i 0.549581 0.104216i
\(493\) −8.49677e47 −0.287084
\(494\) 1.66254e48 + 1.37690e48i 0.541610 + 0.448558i
\(495\) 3.91500e48i 1.22981i
\(496\) −1.14210e48 2.90313e48i −0.345965 0.879420i
\(497\) 3.64116e48 1.06371
\(498\) 3.82841e48 4.62261e48i 1.07867 1.30244i
\(499\) 1.40771e48i 0.382564i −0.981535 0.191282i \(-0.938735\pi\)
0.981535 0.191282i \(-0.0612645\pi\)
\(500\) −7.67852e47 4.04926e48i −0.201288 1.06149i
\(501\) −1.51062e48 −0.382012
\(502\) 3.80160e48 + 3.14846e48i 0.927469 + 0.768123i
\(503\) 2.31603e48i 0.545155i −0.962134 0.272578i \(-0.912124\pi\)
0.962134 0.272578i \(-0.0878761\pi\)
\(504\) −5.42798e48 + 9.83522e48i −1.23279 + 2.23375i
\(505\) 5.12771e48 1.12377
\(506\) −2.68168e48 + 3.23799e48i −0.567149 + 0.684803i
\(507\) 4.09961e48i 0.836756i
\(508\) −1.02089e48 + 1.93590e47i −0.201110 + 0.0381360i
\(509\) 3.39060e48 0.644698 0.322349 0.946621i \(-0.395528\pi\)
0.322349 + 0.946621i \(0.395528\pi\)
\(510\) −1.04187e48 8.62868e47i −0.191227 0.158373i
\(511\) 7.91456e48i 1.40233i
\(512\) 3.38369e47 + 5.83621e48i 0.0578804 + 0.998324i
\(513\) −2.81139e48 −0.464311
\(514\) −3.99890e48 + 4.82846e48i −0.637682 + 0.769968i
\(515\) 5.90918e48i 0.909907i
\(516\) −2.34234e48 1.23523e49i −0.348302 1.83677i
\(517\) −4.58195e48 −0.657993
\(518\) −6.99411e48 5.79248e48i −0.970057 0.803394i
\(519\) 8.95614e48i 1.19980i
\(520\) −7.30790e48 4.03317e48i −0.945654 0.521899i
\(521\) 8.79379e48 1.09925 0.549626 0.835411i \(-0.314770\pi\)
0.549626 + 0.835411i \(0.314770\pi\)
\(522\) 1.28180e49 1.54770e49i 1.54793 1.86904i
\(523\) 4.98961e48i 0.582152i 0.956700 + 0.291076i \(0.0940132\pi\)
−0.956700 + 0.291076i \(0.905987\pi\)
\(524\) −1.34356e47 + 2.54777e46i −0.0151459 + 0.00287208i
\(525\) −5.79543e48 −0.631275
\(526\) 2.01222e48 + 1.66651e48i 0.211803 + 0.175414i
\(527\) 1.66460e48i 0.169325i
\(528\) 1.39470e49 5.48678e48i 1.37111 0.539395i
\(529\) 8.86165e47 0.0842000
\(530\) 4.80577e48 5.80272e48i 0.441365 0.532925i
\(531\) 3.83591e48i 0.340540i
\(532\) 2.08063e48 + 1.09722e49i 0.178561 + 0.941640i
\(533\) 5.25498e48 0.435995
\(534\) −1.84297e49 1.52634e49i −1.47835 1.22436i
\(535\) 5.23506e48i 0.406026i
\(536\) −5.20036e48 + 9.42279e48i −0.390002 + 0.706665i
\(537\) 2.69483e49 1.95431
\(538\) 1.20039e48 1.44941e48i 0.0841862 0.101650i
\(539\) 2.51713e49i 1.70729i
\(540\) 1.06805e49 2.02531e48i 0.700653 0.132863i
\(541\) −2.06395e49 −1.30963 −0.654814 0.755790i \(-0.727253\pi\)
−0.654814 + 0.755790i \(0.727253\pi\)
\(542\) 5.68435e48 + 4.70774e48i 0.348894 + 0.288952i
\(543\) 4.06390e48i 0.241294i
\(544\) −9.72020e47 + 2.96398e48i −0.0558335 + 0.170253i
\(545\) −1.87264e49 −1.04068
\(546\) −3.91653e49 + 4.72900e49i −2.10588 + 2.54274i
\(547\) 3.24152e49i 1.68646i 0.537551 + 0.843231i \(0.319350\pi\)
−0.537551 + 0.843231i \(0.680650\pi\)
\(548\) −3.01291e48 1.58886e49i −0.151683 0.799899i
\(549\) −1.71726e49 −0.836628
\(550\) 3.58681e48 + 2.97057e48i 0.169114 + 0.140059i
\(551\) 1.99779e49i 0.911635i
\(552\) 3.00818e49 + 1.66019e49i 1.32862 + 0.733253i
\(553\) 3.55777e49 1.52099
\(554\) −2.22620e49 + 2.68803e49i −0.921275 + 1.11239i
\(555\) 2.58648e49i 1.03618i
\(556\) 2.60236e49 4.93478e48i 1.00930 0.191391i
\(557\) −2.89906e49 −1.08859 −0.544295 0.838894i \(-0.683203\pi\)
−0.544295 + 0.838894i \(0.683203\pi\)
\(558\) 3.03211e49 + 2.51118e49i 1.10238 + 0.912980i
\(559\) 4.13920e49i 1.45715i
\(560\) −1.58086e49 4.01845e49i −0.538902 1.36985i
\(561\) 7.99698e48 0.263994
\(562\) 2.41292e49 2.91347e49i 0.771416 0.931445i
\(563\) 1.35622e49i 0.419932i 0.977709 + 0.209966i \(0.0673354\pi\)
−0.977709 + 0.209966i \(0.932665\pi\)
\(564\) 6.97637e48 + 3.67898e49i 0.209221 + 1.10333i
\(565\) −3.30117e49 −0.958949
\(566\) −2.73652e49 2.26637e49i −0.770022 0.637727i
\(567\) 1.36292e49i 0.371515i
\(568\) −1.15543e49 + 2.09359e49i −0.305123 + 0.552868i
\(569\) −2.26003e48 −0.0578220 −0.0289110 0.999582i \(-0.509204\pi\)
−0.0289110 + 0.999582i \(0.509204\pi\)
\(570\) 2.02881e49 2.44968e49i 0.502913 0.607242i
\(571\) 6.44223e49i 1.54734i −0.633588 0.773671i \(-0.718418\pi\)
0.633588 0.773671i \(-0.281582\pi\)
\(572\) 4.84790e49 9.19296e48i 1.12830 0.213957i
\(573\) −4.15608e49 −0.937348
\(574\) 2.09378e49 + 1.73406e49i 0.457634 + 0.379009i
\(575\) 1.06767e49i 0.226160i
\(576\) −3.93260e49 6.24194e49i −0.807375 1.28149i
\(577\) −1.18626e49 −0.236056 −0.118028 0.993010i \(-0.537657\pi\)
−0.118028 + 0.993010i \(0.537657\pi\)
\(578\) 3.20070e49 3.86468e49i 0.617368 0.745440i
\(579\) 3.32046e49i 0.620846i
\(580\) 1.43920e49 + 7.58960e49i 0.260865 + 1.37567i
\(581\) 1.02230e50 1.79642
\(582\) −1.03405e50 8.56394e49i −1.76169 1.45902i
\(583\) 4.45394e49i 0.735717i
\(584\) 4.55070e49 + 2.51149e49i 0.728864 + 0.402254i
\(585\) 1.05336e50 1.63596
\(586\) −3.18680e49 + 3.84789e49i −0.479952 + 0.579517i
\(587\) 1.66634e49i 0.243377i −0.992568 0.121688i \(-0.961169\pi\)
0.992568 0.121688i \(-0.0388308\pi\)
\(588\) −2.02108e50 + 3.83252e49i −2.86280 + 0.542866i
\(589\) 3.91387e49 0.537690
\(590\) −1.13563e49 9.40523e48i −0.151322 0.125324i
\(591\) 1.24162e50i 1.60478i
\(592\) 5.54996e49 2.18336e49i 0.695824 0.273738i
\(593\) 7.80412e49 0.949161 0.474580 0.880212i \(-0.342600\pi\)
0.474580 + 0.880212i \(0.342600\pi\)
\(594\) −4.09896e49 + 4.94928e49i −0.483635 + 0.583964i
\(595\) 2.30411e49i 0.263753i
\(596\) −2.27083e49 1.19752e50i −0.252204 1.33000i
\(597\) −2.33558e50 −2.51685
\(598\) 8.71205e49 + 7.21525e49i 0.910959 + 0.754450i
\(599\) 1.23378e50i 1.25185i 0.779882 + 0.625926i \(0.215279\pi\)
−0.779882 + 0.625926i \(0.784721\pi\)
\(600\) 1.83904e49 3.33225e49i 0.181079 0.328106i
\(601\) −1.56049e50 −1.49115 −0.745575 0.666421i \(-0.767825\pi\)
−0.745575 + 0.666421i \(0.767825\pi\)
\(602\) 1.36587e50 1.64922e50i 1.26670 1.52947i
\(603\) 1.35820e50i 1.22251i
\(604\) −1.38039e50 + 2.61759e49i −1.20597 + 0.228685i
\(605\) −1.40866e49 −0.119457
\(606\) 1.90788e50 + 1.58009e50i 1.57052 + 1.30070i
\(607\) 2.47790e50i 1.98010i 0.140701 + 0.990052i \(0.455064\pi\)
−0.140701 + 0.990052i \(0.544936\pi\)
\(608\) −6.96902e49 2.28545e49i −0.540639 0.177299i
\(609\) 5.68260e50 4.27992
\(610\) 4.21052e49 5.08398e49i 0.307892 0.371764i
\(611\) 1.23281e50i 0.875294i
\(612\) −7.33391e48 3.86753e49i −0.0505603 0.266630i
\(613\) −1.69578e50 −1.13522 −0.567610 0.823298i \(-0.692132\pi\)
−0.567610 + 0.823298i \(0.692132\pi\)
\(614\) −4.55227e49 3.77015e49i −0.295935 0.245092i
\(615\) 7.74298e49i 0.488828i
\(616\) 2.23494e50 + 1.23345e50i 1.37029 + 0.756253i
\(617\) −2.27776e50 −1.35636 −0.678180 0.734896i \(-0.737231\pi\)
−0.678180 + 0.734896i \(0.737231\pi\)
\(618\) −1.82090e50 + 2.19865e50i −1.05316 + 1.27164i
\(619\) 3.14061e50i 1.76434i −0.470932 0.882169i \(-0.656082\pi\)
0.470932 0.882169i \(-0.343918\pi\)
\(620\) −1.48688e50 + 2.81953e49i −0.811382 + 0.153860i
\(621\) −1.47323e50 −0.780946
\(622\) −8.89132e49 7.36373e49i −0.457867 0.379202i
\(623\) 4.07576e50i 2.03903i
\(624\) −1.47626e50 3.75255e50i −0.717530 1.82391i
\(625\) −1.49887e50 −0.707821
\(626\) 5.97755e49 7.21758e49i 0.274274 0.331172i
\(627\) 1.88028e50i 0.838313i
\(628\) 4.41791e49 + 2.32978e50i 0.191401 + 1.00935i
\(629\) 3.18225e49 0.133975
\(630\) 4.19699e50 + 3.47591e50i 1.71715 + 1.42213i
\(631\) 3.34685e50i 1.33079i −0.746493 0.665393i \(-0.768264\pi\)
0.746493 0.665393i \(-0.231736\pi\)
\(632\) −1.12897e50 + 2.04564e50i −0.436290 + 0.790536i
\(633\) 6.39035e50 2.40026
\(634\) 2.46023e49 2.97061e49i 0.0898193 0.108452i
\(635\) 5.04064e49i 0.178879i
\(636\) 3.57620e50 6.78146e49i 1.23365 0.233935i
\(637\) −6.77253e50 −2.27112
\(638\) −3.51698e50 2.91274e50i −1.14656 0.949575i
\(639\) 3.01770e50i 0.956446i
\(640\) 2.81217e50 + 3.66196e49i 0.866567 + 0.112843i
\(641\) 5.81399e50 1.74193 0.870963 0.491348i \(-0.163496\pi\)
0.870963 + 0.491348i \(0.163496\pi\)
\(642\) 1.61318e50 1.94783e50i 0.469949 0.567439i
\(643\) 4.72135e49i 0.133742i −0.997762 0.0668711i \(-0.978698\pi\)
0.997762 0.0668711i \(-0.0213016\pi\)
\(644\) 1.09029e50 + 5.74966e50i 0.300330 + 1.58379i
\(645\) −6.09893e50 −1.63372
\(646\) −3.01394e49 2.49612e49i −0.0785143 0.0650250i
\(647\) 4.55310e50i 1.15353i 0.816909 + 0.576767i \(0.195686\pi\)
−0.816909 + 0.576767i \(0.804314\pi\)
\(648\) −7.83652e49 4.32491e49i −0.193096 0.106568i
\(649\) 8.71668e49 0.208904
\(650\) 7.99255e49 9.65059e49i 0.186314 0.224964i
\(651\) 1.11328e51i 2.52433i
\(652\) 2.20799e50 4.18695e49i 0.487012 0.0923510i
\(653\) −3.29954e50 −0.707972 −0.353986 0.935251i \(-0.615174\pi\)
−0.353986 + 0.935251i \(0.615174\pi\)
\(654\) −6.96759e50 5.77051e50i −1.45440 1.20452i
\(655\) 6.63382e48i 0.0134716i
\(656\) −1.66146e50 + 6.53619e49i −0.328261 + 0.129138i
\(657\) −6.55938e50 −1.26092
\(658\) −4.06807e50 + 4.91198e50i −0.760890 + 0.918735i
\(659\) 4.14820e50i 0.754957i 0.926018 + 0.377479i \(0.123209\pi\)
−0.926018 + 0.377479i \(0.876791\pi\)
\(660\) −1.35454e50 7.14317e50i −0.239884 1.26503i
\(661\) 7.07141e50 1.21865 0.609326 0.792920i \(-0.291440\pi\)
0.609326 + 0.792920i \(0.291440\pi\)
\(662\) 2.66575e50 + 2.20775e50i 0.447070 + 0.370260i
\(663\) 2.15165e50i 0.351178i
\(664\) −3.24401e50 + 5.87799e50i −0.515297 + 0.933691i
\(665\) 5.41750e50 0.837548
\(666\) −4.80065e50 + 5.79654e50i −0.722377 + 0.872233i
\(667\) 1.04688e51i 1.53332i
\(668\) 1.66015e50 3.14810e49i 0.236685 0.0448819i
\(669\) 1.43041e51 1.98514
\(670\) 4.02099e50 + 3.33016e50i 0.543234 + 0.449902i
\(671\) 3.90227e50i 0.513229i
\(672\) 6.50083e50 1.98230e51i 0.832380 2.53818i
\(673\) 9.28631e50 1.15764 0.578818 0.815457i \(-0.303514\pi\)
0.578818 + 0.815457i \(0.303514\pi\)
\(674\) −5.62525e50 + 6.79220e50i −0.682753 + 0.824389i
\(675\) 1.63194e50i 0.192857i
\(676\) −8.54346e49 4.50539e50i −0.0983090 0.518432i
\(677\) −3.08900e50 −0.346117 −0.173058 0.984912i \(-0.555365\pi\)
−0.173058 + 0.984912i \(0.555365\pi\)
\(678\) −1.22828e51 1.01725e51i −1.34018 1.10992i
\(679\) 2.28682e51i 2.42983i
\(680\) 1.32481e50 + 7.31153e49i 0.137086 + 0.0756568i
\(681\) −1.03293e51 −1.04093
\(682\) 5.70636e50 6.89013e50i 0.560067 0.676252i
\(683\) 1.95997e51i 1.87360i 0.349864 + 0.936801i \(0.386228\pi\)
−0.349864 + 0.936801i \(0.613772\pi\)
\(684\) 9.09348e50 1.72437e50i 0.846682 0.160554i
\(685\) −7.84495e50 −0.711475
\(686\) −1.22989e51 1.01859e51i −1.08651 0.899839i
\(687\) 3.09020e51i 2.65929i
\(688\) 5.14838e50 + 1.30868e51i 0.431597 + 1.09709i
\(689\) 1.19837e51 0.978687
\(690\) 1.06314e51 1.28368e51i 0.845873 1.02135i
\(691\) 2.05067e51i 1.58961i −0.606866 0.794804i \(-0.707574\pi\)
0.606866 0.794804i \(-0.292426\pi\)
\(692\) −1.86643e50 9.84263e50i −0.140962 0.743364i
\(693\) −3.22144e51 −2.37057
\(694\) 2.02939e51 + 1.68073e51i 1.45511 + 1.20511i
\(695\) 1.28491e51i 0.897728i
\(696\) −1.80324e51 + 3.26737e51i −1.22768 + 2.22450i
\(697\) −9.52650e49 −0.0632038
\(698\) −5.95337e50 + 7.18838e50i −0.384915 + 0.464765i
\(699\) 1.93767e51i 1.22093i
\(700\) 6.36907e50 1.20775e50i 0.391121 0.0741673i
\(701\) 7.95968e48 0.00476400 0.00238200 0.999997i \(-0.499242\pi\)
0.00238200 + 0.999997i \(0.499242\pi\)
\(702\) 1.33164e51 + 1.10286e51i 0.776818 + 0.643355i
\(703\) 7.48221e50i 0.425436i
\(704\) −1.41841e51 + 8.93638e50i −0.786128 + 0.495284i
\(705\) 1.81649e51 0.981361
\(706\) 4.62819e50 5.58829e50i 0.243740 0.294303i
\(707\) 4.21931e51i 2.16617i
\(708\) −1.32718e50 6.99887e50i −0.0664249 0.350291i
\(709\) −2.55500e51 −1.24669 −0.623346 0.781946i \(-0.714227\pi\)
−0.623346 + 0.781946i \(0.714227\pi\)
\(710\) 8.93398e50 + 7.39906e50i 0.425006 + 0.351987i
\(711\) 2.94859e51i 1.36761i
\(712\) 2.34347e51 + 1.29334e51i 1.05979 + 0.584890i
\(713\) 2.05095e51 0.904365
\(714\) 7.10008e50 8.57298e50i 0.305278 0.368607i
\(715\) 2.39364e51i 1.00358i
\(716\) −2.96156e51 + 5.61594e50i −1.21084 + 0.229609i
\(717\) 2.85043e51 1.13649
\(718\) 4.67247e50 + 3.86971e50i 0.181680 + 0.150466i
\(719\) 4.33731e50i 0.164475i −0.996613 0.0822375i \(-0.973793\pi\)
0.996613 0.0822375i \(-0.0262066\pi\)
\(720\) −3.33039e51 + 1.31018e51i −1.23171 + 0.484558i
\(721\) −4.86234e51 −1.75392
\(722\) −1.22605e51 + 1.48039e51i −0.431358 + 0.520843i
\(723\) 2.46191e51i 0.844858i
\(724\) 8.46906e49 + 4.46615e50i 0.0283492 + 0.149499i
\(725\) −1.15966e51 −0.378658
\(726\) −5.24126e50 4.34077e50i −0.166946 0.138264i
\(727\) 5.09920e50i 0.158447i −0.996857 0.0792233i \(-0.974756\pi\)
0.996857 0.0792233i \(-0.0252440\pi\)
\(728\) 3.31868e51 6.01328e51i 1.00601 1.82283i
\(729\) 5.50530e51 1.62812
\(730\) 1.60828e51 1.94192e51i 0.464036 0.560299i
\(731\) 7.50376e50i 0.211235i
\(732\) 3.13324e51 5.94149e50i 0.860586 0.163191i
\(733\) −3.32731e51 −0.891705 −0.445853 0.895106i \(-0.647099\pi\)
−0.445853 + 0.895106i \(0.647099\pi\)
\(734\) 6.55905e50 + 5.43216e50i 0.171519 + 0.142051i
\(735\) 9.97902e51i 2.54634i
\(736\) −3.65191e51 1.19762e51i −0.909325 0.298207i
\(737\) −3.08636e51 −0.749948
\(738\) 1.43714e51 1.73527e51i 0.340788 0.411484i
\(739\) 3.62282e50i 0.0838391i 0.999121 + 0.0419195i \(0.0133473\pi\)
−0.999121 + 0.0419195i \(0.986653\pi\)
\(740\) −5.39015e50 2.84249e51i −0.121739 0.641990i
\(741\) 5.05903e51 1.11517
\(742\) 4.77475e51 + 3.95441e51i 1.02726 + 0.850769i
\(743\) 3.12893e51i 0.657048i −0.944496 0.328524i \(-0.893449\pi\)
0.944496 0.328524i \(-0.106551\pi\)
\(744\) −6.40112e51 3.53273e51i −1.31203 0.724097i
\(745\) −5.91274e51 −1.18298
\(746\) 2.41402e51 2.91481e51i 0.471458 0.569261i
\(747\) 8.47253e51i 1.61526i
\(748\) −8.78852e50 + 1.66655e50i −0.163564 + 0.0310162i
\(749\) 4.30765e51 0.782650
\(750\) −7.43891e51 6.16086e51i −1.31949 1.09279i
\(751\) 7.90348e51i