Properties

Label 4.37.b.b.3.2
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 3.2
Root \(1.10776e7i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.37.b.b.3.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-227674. + 129939. i) q^{2} +1.77242e8i q^{3} +(3.49511e10 - 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 - 4.03533e13i) q^{6} +2.49971e15i q^{7} +(-2.69262e14 + 1.80124e16i) q^{8} +1.18680e17 q^{9} +O(q^{10})\) \(q+(-227674. + 129939. i) q^{2} +1.77242e8i q^{3} +(3.49511e10 - 5.91675e10i) q^{4} +5.55508e12 q^{5} +(-2.30307e13 - 4.03533e13i) q^{6} +2.49971e15i q^{7} +(-2.69262e14 + 1.80124e16i) q^{8} +1.18680e17 q^{9} +(-1.26475e18 + 7.21823e17i) q^{10} -5.40459e18i q^{11} +(1.04869e19 + 6.19479e18i) q^{12} +1.72435e20 q^{13} +(-3.24810e20 - 5.69117e20i) q^{14} +9.84593e20i q^{15} +(-2.27921e21 - 4.13593e21i) q^{16} +8.60485e21 q^{17} +(-2.70203e22 + 1.54212e22i) q^{18} -1.88804e23i q^{19} +(1.94156e23 - 3.28680e23i) q^{20} -4.43052e23 q^{21} +(7.02268e23 + 1.23048e24i) q^{22} -9.41760e23i q^{23} +(-3.19255e24 - 4.77245e22i) q^{24} +1.63070e25 q^{25} +(-3.92589e25 + 2.24060e25i) q^{26} +4.76381e25i q^{27} +(1.47901e26 + 8.73674e25i) q^{28} -4.55607e25 q^{29} +(-1.27937e26 - 2.24166e26i) q^{30} -5.01332e26i q^{31} +(1.05634e27 + 6.45484e26i) q^{32} +9.57919e26 q^{33} +(-1.95910e27 + 1.11811e27i) q^{34} +1.38861e28i q^{35} +(4.14799e27 - 7.02199e27i) q^{36} +1.31828e28 q^{37} +(2.45330e28 + 4.29857e28i) q^{38} +3.05627e28i q^{39} +(-1.49578e27 + 1.00060e29i) q^{40} +2.91126e27 q^{41} +(1.00871e29 - 5.75699e28i) q^{42} +6.20563e28i q^{43} +(-3.19776e29 - 1.88896e29i) q^{44} +6.59277e29 q^{45} +(1.22372e29 + 2.14414e29i) q^{46} -4.91358e29i q^{47} +(7.33060e29 - 4.03971e29i) q^{48} -3.59680e30 q^{49} +(-3.71268e30 + 2.11893e30i) q^{50} +1.52514e30i q^{51} +(6.02678e30 - 1.02025e31i) q^{52} +4.35112e29 q^{53} +(-6.19006e30 - 1.08459e31i) q^{54} -3.00230e31i q^{55} +(-4.50257e31 - 6.73077e29i) q^{56} +3.34639e31 q^{57} +(1.03730e31 - 5.92012e30i) q^{58} +5.43569e31i q^{59} +(5.82559e31 + 3.44126e31i) q^{60} -3.68830e31 q^{61} +(6.51427e31 + 1.14140e32i) q^{62} +2.96665e32i q^{63} +(-3.24374e32 - 9.70012e30i) q^{64} +9.57890e32 q^{65} +(-2.18093e32 + 1.24471e32i) q^{66} +9.33023e32i q^{67} +(3.00749e32 - 5.09127e32i) q^{68} +1.66919e32 q^{69} +(-1.80435e33 - 3.16149e33i) q^{70} -1.44228e33i q^{71} +(-3.19561e31 + 2.13771e33i) q^{72} +2.43678e33 q^{73} +(-3.00137e33 + 1.71296e33i) q^{74} +2.89029e33i q^{75} +(-1.11711e34 - 6.59890e33i) q^{76} +1.35099e34 q^{77} +(-3.97129e33 - 6.95831e33i) q^{78} +4.92391e33i q^{79} +(-1.26612e34 - 2.29755e34i) q^{80} +9.36977e33 q^{81} +(-6.62818e32 + 3.78287e32i) q^{82} +3.24535e34i q^{83} +(-1.54852e34 + 2.62143e34i) q^{84} +4.78007e34 q^{85} +(-8.06354e33 - 1.41286e34i) q^{86} -8.07526e33i q^{87} +(9.73496e34 + 1.45525e33i) q^{88} +9.08737e34 q^{89} +(-1.50100e35 + 8.56660e34i) q^{90} +4.31037e35i q^{91} +(-5.57215e34 - 3.29155e34i) q^{92} +8.88570e34 q^{93} +(6.38466e34 + 1.11869e35i) q^{94} -1.04882e36i q^{95} +(-1.14407e35 + 1.87227e35i) q^{96} -1.10168e36 q^{97} +(8.18897e35 - 4.67366e35i) q^{98} -6.41417e35i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −227674. + 129939.i −0.868506 + 0.495679i
\(3\) 1.77242e8i 0.457492i 0.973486 + 0.228746i \(0.0734625\pi\)
−0.973486 + 0.228746i \(0.926537\pi\)
\(4\) 3.49511e10 5.91675e10i 0.508605 0.861000i
\(5\) 5.55508e12 1.45623 0.728116 0.685454i \(-0.240396\pi\)
0.728116 + 0.685454i \(0.240396\pi\)
\(6\) −2.30307e13 4.03533e13i −0.226769 0.397334i
\(7\) 2.49971e15i 1.53506i 0.641015 + 0.767528i \(0.278514\pi\)
−0.641015 + 0.767528i \(0.721486\pi\)
\(8\) −2.69262e14 + 1.80124e16i −0.0149471 + 0.999888i
\(9\) 1.18680e17 0.790701
\(10\) −1.26475e18 + 7.21823e17i −1.26475 + 0.721823i
\(11\) 5.40459e18i 0.972063i −0.873941 0.486032i \(-0.838444\pi\)
0.873941 0.486032i \(-0.161556\pi\)
\(12\) 1.04869e19 + 6.19479e18i 0.393901 + 0.232683i
\(13\) 1.72435e20 1.53336 0.766681 0.642028i \(-0.221907\pi\)
0.766681 + 0.642028i \(0.221907\pi\)
\(14\) −3.24810e20 5.69117e20i −0.760895 1.33321i
\(15\) 9.84593e20i 0.666214i
\(16\) −2.27921e21 4.13593e21i −0.482642 0.875818i
\(17\) 8.60485e21 0.611875 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(18\) −2.70203e22 + 1.54212e22i −0.686729 + 0.391934i
\(19\) 1.88804e23i 1.81320i −0.421989 0.906601i \(-0.638668\pi\)
0.421989 0.906601i \(-0.361332\pi\)
\(20\) 1.94156e23 3.28680e23i 0.740647 1.25382i
\(21\) −4.43052e23 −0.702276
\(22\) 7.02268e23 + 1.23048e24i 0.481831 + 0.844243i
\(23\) 9.41760e23i 0.290295i −0.989410 0.145147i \(-0.953634\pi\)
0.989410 0.145147i \(-0.0463656\pi\)
\(24\) −3.19255e24 4.77245e22i −0.457441 0.00683816i
\(25\) 1.63070e25 1.12061
\(26\) −3.92589e25 + 2.24060e25i −1.33173 + 0.760055i
\(27\) 4.76381e25i 0.819231i
\(28\) 1.47901e26 + 8.73674e25i 1.32168 + 0.780738i
\(29\) −4.55607e25 −0.216484 −0.108242 0.994125i \(-0.534522\pi\)
−0.108242 + 0.994125i \(0.534522\pi\)
\(30\) −1.27937e26 2.24166e26i −0.330228 0.578611i
\(31\) 5.01332e26i 0.717158i −0.933499 0.358579i \(-0.883261\pi\)
0.933499 0.358579i \(-0.116739\pi\)
\(32\) 1.05634e27 + 6.45484e26i 0.853302 + 0.521418i
\(33\) 9.57919e26 0.444711
\(34\) −1.95910e27 + 1.11811e27i −0.531417 + 0.303293i
\(35\) 1.38861e28i 2.23540i
\(36\) 4.14799e27 7.02199e27i 0.402155 0.680794i
\(37\) 1.31828e28 0.780504 0.390252 0.920708i \(-0.372388\pi\)
0.390252 + 0.920708i \(0.372388\pi\)
\(38\) 2.45330e28 + 4.29857e28i 0.898766 + 1.57478i
\(39\) 3.05627e28i 0.701501i
\(40\) −1.49578e27 + 1.00060e29i −0.0217664 + 1.45607i
\(41\) 2.91126e27 0.0271626 0.0135813 0.999908i \(-0.495677\pi\)
0.0135813 + 0.999908i \(0.495677\pi\)
\(42\) 1.00871e29 5.75699e28i 0.609931 0.348103i
\(43\) 6.20563e28i 0.245671i 0.992427 + 0.122835i \(0.0391987\pi\)
−0.992427 + 0.122835i \(0.960801\pi\)
\(44\) −3.19776e29 1.88896e29i −0.836946 0.494396i
\(45\) 6.59277e29 1.15144
\(46\) 1.22372e29 + 2.14414e29i 0.143893 + 0.252123i
\(47\) 4.91358e29i 0.392316i −0.980572 0.196158i \(-0.937153\pi\)
0.980572 0.196158i \(-0.0628466\pi\)
\(48\) 7.33060e29 4.03971e29i 0.400680 0.220805i
\(49\) −3.59680e30 −1.35640
\(50\) −3.71268e30 + 2.11893e30i −0.973258 + 0.555464i
\(51\) 1.52514e30i 0.279928i
\(52\) 6.02678e30 1.02025e31i 0.779876 1.32022i
\(53\) 4.35112e29 0.0399609 0.0199805 0.999800i \(-0.493640\pi\)
0.0199805 + 0.999800i \(0.493640\pi\)
\(54\) −6.19006e30 1.08459e31i −0.406076 0.711507i
\(55\) 3.00230e31i 1.41555i
\(56\) −4.50257e31 6.73077e29i −1.53489 0.0229446i
\(57\) 3.34639e31 0.829525
\(58\) 1.03730e31 5.92012e30i 0.188018 0.107307i
\(59\) 5.43569e31i 0.724300i 0.932120 + 0.362150i \(0.117957\pi\)
−0.932120 + 0.362150i \(0.882043\pi\)
\(60\) 5.82559e31 + 3.44126e31i 0.573611 + 0.338840i
\(61\) −3.68830e31 −0.269705 −0.134853 0.990866i \(-0.543056\pi\)
−0.134853 + 0.990866i \(0.543056\pi\)
\(62\) 6.51427e31 + 1.14140e32i 0.355480 + 0.622856i
\(63\) 2.96665e32i 1.21377i
\(64\) −3.24374e32 9.70012e30i −0.999553 0.0298908i
\(65\) 9.57890e32 2.23293
\(66\) −2.18093e32 + 1.24471e32i −0.386234 + 0.220434i
\(67\) 9.33023e32i 1.26051i 0.776389 + 0.630254i \(0.217049\pi\)
−0.776389 + 0.630254i \(0.782951\pi\)
\(68\) 3.00749e32 5.09127e32i 0.311203 0.526824i
\(69\) 1.66919e32 0.132807
\(70\) −1.80435e33 3.16149e33i −1.10804 1.94146i
\(71\) 1.44228e33i 0.686118i −0.939314 0.343059i \(-0.888537\pi\)
0.939314 0.343059i \(-0.111463\pi\)
\(72\) −3.19561e31 + 2.13771e33i −0.0118187 + 0.790613i
\(73\) 2.43678e33 0.703079 0.351540 0.936173i \(-0.385658\pi\)
0.351540 + 0.936173i \(0.385658\pi\)
\(74\) −3.00137e33 + 1.71296e33i −0.677873 + 0.386879i
\(75\) 2.89029e33i 0.512671i
\(76\) −1.11711e34 6.59890e33i −1.56117 0.922204i
\(77\) 1.35099e34 1.49217
\(78\) −3.97129e33 6.95831e33i −0.347719 0.609258i
\(79\) 4.92391e33i 0.342786i 0.985203 + 0.171393i \(0.0548267\pi\)
−0.985203 + 0.171393i \(0.945173\pi\)
\(80\) −1.26612e34 2.29755e34i −0.702838 1.27539i
\(81\) 9.36977e33 0.415909
\(82\) −6.62818e32 + 3.78287e32i −0.0235909 + 0.0134639i
\(83\) 3.24535e34i 0.928659i 0.885663 + 0.464329i \(0.153705\pi\)
−0.885663 + 0.464329i \(0.846295\pi\)
\(84\) −1.54852e34 + 2.62143e34i −0.357181 + 0.604660i
\(85\) 4.78007e34 0.891032
\(86\) −8.06354e33 1.41286e34i −0.121774 0.213367i
\(87\) 8.07526e33i 0.0990398i
\(88\) 9.73496e34 + 1.45525e33i 0.971955 + 0.0145295i
\(89\) 9.08737e34 0.740317 0.370159 0.928969i \(-0.379303\pi\)
0.370159 + 0.928969i \(0.379303\pi\)
\(90\) −1.50100e35 + 8.56660e34i −1.00004 + 0.570747i
\(91\) 4.31037e35i 2.35380i
\(92\) −5.57215e34 3.29155e34i −0.249944 0.147645i
\(93\) 8.88570e34 0.328094
\(94\) 6.38466e34 + 1.11869e35i 0.194463 + 0.340729i
\(95\) 1.04882e36i 2.64044i
\(96\) −1.14407e35 + 1.87227e35i −0.238544 + 0.390379i
\(97\) −1.10168e36 −1.90618 −0.953089 0.302692i \(-0.902115\pi\)
−0.953089 + 0.302692i \(0.902115\pi\)
\(98\) 8.18897e35 4.67366e35i 1.17804 0.672338i
\(99\) 6.41417e35i 0.768612i
\(100\) 5.69949e35 9.64847e35i 0.569949 0.964847i
\(101\) −6.22174e35 −0.520148 −0.260074 0.965589i \(-0.583747\pi\)
−0.260074 + 0.965589i \(0.583747\pi\)
\(102\) −1.98175e35 3.47234e35i −0.138754 0.243119i
\(103\) 9.69079e35i 0.569232i 0.958642 + 0.284616i \(0.0918661\pi\)
−0.958642 + 0.284616i \(0.908134\pi\)
\(104\) −4.64302e34 + 3.10596e36i −0.0229193 + 1.53319i
\(105\) −2.46119e36 −1.02268
\(106\) −9.90636e34 + 5.65382e34i −0.0347063 + 0.0198078i
\(107\) 2.89529e36i 0.856612i −0.903634 0.428306i \(-0.859110\pi\)
0.903634 0.428306i \(-0.140890\pi\)
\(108\) 2.81862e36 + 1.66500e36i 0.705358 + 0.416665i
\(109\) 1.76879e36 0.374972 0.187486 0.982267i \(-0.439966\pi\)
0.187486 + 0.982267i \(0.439966\pi\)
\(110\) 3.90116e36 + 6.83544e36i 0.701658 + 1.22941i
\(111\) 2.33654e36i 0.357074i
\(112\) 1.03386e37 5.69736e36i 1.34443 0.740883i
\(113\) −9.72750e36 −1.07793 −0.538963 0.842329i \(-0.681184\pi\)
−0.538963 + 0.842329i \(0.681184\pi\)
\(114\) −7.61886e36 + 4.34828e36i −0.720448 + 0.411178i
\(115\) 5.23155e36i 0.422736i
\(116\) −1.59240e36 + 2.69571e36i −0.110105 + 0.186393i
\(117\) 2.04646e37 1.21243
\(118\) −7.06309e36 1.23756e37i −0.359020 0.629059i
\(119\) 2.15096e37i 0.939262i
\(120\) −1.77349e37 2.65114e35i −0.666140 0.00995795i
\(121\) 1.70307e36 0.0550930
\(122\) 8.39728e36 4.79255e36i 0.234240 0.133687i
\(123\) 5.15997e35i 0.0124267i
\(124\) −2.96625e37 1.75221e37i −0.617473 0.364750i
\(125\) 9.74991e36 0.175639
\(126\) −3.85484e37 6.75428e37i −0.601641 1.05417i
\(127\) 1.66370e37i 0.225220i −0.993639 0.112610i \(-0.964079\pi\)
0.993639 0.112610i \(-0.0359211\pi\)
\(128\) 7.51117e37 3.99404e37i 0.882934 0.469497i
\(129\) −1.09990e37 −0.112392
\(130\) −2.18086e38 + 1.24467e38i −1.93931 + 1.10682i
\(131\) 6.71691e37i 0.520339i −0.965563 0.260169i \(-0.916222\pi\)
0.965563 0.260169i \(-0.0837784\pi\)
\(132\) 3.34803e37 5.66777e37i 0.226182 0.382896i
\(133\) 4.71955e38 2.78337
\(134\) −1.21236e38 2.12425e38i −0.624807 1.09476i
\(135\) 2.64634e38i 1.19299i
\(136\) −2.31696e36 + 1.54994e38i −0.00914573 + 0.611806i
\(137\) −3.97555e38 −1.37539 −0.687696 0.725998i \(-0.741378\pi\)
−0.687696 + 0.725998i \(0.741378\pi\)
\(138\) −3.80031e37 + 2.16893e37i −0.115344 + 0.0658298i
\(139\) 6.21549e38i 1.65657i 0.560310 + 0.828283i \(0.310682\pi\)
−0.560310 + 0.828283i \(0.689318\pi\)
\(140\) 8.21604e38 + 4.85334e38i 1.92468 + 1.13694i
\(141\) 8.70891e37 0.179482
\(142\) 1.87409e38 + 3.28369e38i 0.340094 + 0.595898i
\(143\) 9.31940e38i 1.49052i
\(144\) −2.70497e38 4.90852e38i −0.381625 0.692510i
\(145\) −2.53094e38 −0.315251
\(146\) −5.54790e38 + 3.16633e38i −0.610629 + 0.348502i
\(147\) 6.37504e38i 0.620542i
\(148\) 4.60752e38 7.79990e38i 0.396968 0.672014i
\(149\) −2.03376e39 −1.55220 −0.776099 0.630612i \(-0.782804\pi\)
−0.776099 + 0.630612i \(0.782804\pi\)
\(150\) −3.75562e38 6.58043e38i −0.254120 0.445258i
\(151\) 8.29777e38i 0.498169i −0.968482 0.249084i \(-0.919870\pi\)
0.968482 0.249084i \(-0.0801297\pi\)
\(152\) 3.40081e39 + 5.08378e37i 1.81300 + 0.0271021i
\(153\) 1.02122e39 0.483810
\(154\) −3.07585e39 + 1.75547e39i −1.29596 + 0.739638i
\(155\) 2.78494e39i 1.04435i
\(156\) 1.80831e39 + 1.06820e39i 0.603992 + 0.356787i
\(157\) −5.73764e39 −1.70820 −0.854102 0.520106i \(-0.825893\pi\)
−0.854102 + 0.520106i \(0.825893\pi\)
\(158\) −6.39809e38 1.12105e39i −0.169912 0.297711i
\(159\) 7.71201e37i 0.0182818i
\(160\) 5.86804e39 + 3.58572e39i 1.24261 + 0.759305i
\(161\) 2.35412e39 0.445619
\(162\) −2.13325e39 + 1.21750e39i −0.361220 + 0.206157i
\(163\) 1.05702e40i 1.60217i 0.598553 + 0.801083i \(0.295743\pi\)
−0.598553 + 0.801083i \(0.704257\pi\)
\(164\) 1.01752e38 1.72252e38i 0.0138151 0.0233870i
\(165\) 5.32132e39 0.647603
\(166\) −4.21699e39 7.38881e39i −0.460317 0.806546i
\(167\) 5.72510e39i 0.560902i 0.959868 + 0.280451i \(0.0904839\pi\)
−0.959868 + 0.280451i \(0.909516\pi\)
\(168\) 1.19297e38 7.98043e39i 0.0104970 0.702198i
\(169\) 1.70876e40 1.35120
\(170\) −1.08829e40 + 6.21118e39i −0.773866 + 0.441666i
\(171\) 2.24073e40i 1.43370i
\(172\) 3.67171e39 + 2.16893e39i 0.211523 + 0.124949i
\(173\) 3.94413e39 0.204701 0.102351 0.994748i \(-0.467364\pi\)
0.102351 + 0.994748i \(0.467364\pi\)
\(174\) 1.04929e39 + 1.83852e39i 0.0490919 + 0.0860167i
\(175\) 4.07628e40i 1.72020i
\(176\) −2.23530e40 + 1.23182e40i −0.851350 + 0.469158i
\(177\) −9.63431e39 −0.331361
\(178\) −2.06895e40 + 1.18081e40i −0.642970 + 0.366960i
\(179\) 1.65711e40i 0.465584i −0.972527 0.232792i \(-0.925214\pi\)
0.972527 0.232792i \(-0.0747861\pi\)
\(180\) 2.30425e40 3.90078e40i 0.585630 0.991394i
\(181\) 1.17619e40 0.270560 0.135280 0.990807i \(-0.456807\pi\)
0.135280 + 0.990807i \(0.456807\pi\)
\(182\) −5.60086e40 9.81357e40i −1.16673 2.04429i
\(183\) 6.53721e39i 0.123388i
\(184\) 1.69633e40 + 2.53581e38i 0.290262 + 0.00433905i
\(185\) 7.32313e40 1.13660
\(186\) −2.02304e40 + 1.15460e40i −0.284952 + 0.162629i
\(187\) 4.65057e40i 0.594781i
\(188\) −2.90724e40 1.71735e40i −0.337784 0.199534i
\(189\) −1.19081e41 −1.25757
\(190\) 1.36283e41 + 2.38789e41i 1.30881 + 2.29324i
\(191\) 3.43456e39i 0.0300103i 0.999887 + 0.0150052i \(0.00477647\pi\)
−0.999887 + 0.0150052i \(0.995224\pi\)
\(192\) 1.71927e39 5.74925e40i 0.0136748 0.457288i
\(193\) −1.70230e41 −1.23312 −0.616560 0.787308i \(-0.711474\pi\)
−0.616560 + 0.787308i \(0.711474\pi\)
\(194\) 2.50823e41 1.43151e41i 1.65553 0.944852i
\(195\) 1.69778e41i 1.02155i
\(196\) −1.25712e41 + 2.12814e41i −0.689871 + 1.16786i
\(197\) 2.06546e41 1.03425 0.517124 0.855911i \(-0.327003\pi\)
0.517124 + 0.855911i \(0.327003\pi\)
\(198\) 8.33452e40 + 1.46034e41i 0.380984 + 0.667544i
\(199\) 1.76694e41i 0.737677i −0.929493 0.368839i \(-0.879755\pi\)
0.929493 0.368839i \(-0.120245\pi\)
\(200\) −4.39088e39 + 2.93729e41i −0.0167499 + 1.12049i
\(201\) −1.65371e41 −0.576672
\(202\) 1.41653e41 8.08448e40i 0.451752 0.257826i
\(203\) 1.13888e41i 0.332316i
\(204\) 9.02386e40 + 5.33052e40i 0.241018 + 0.142373i
\(205\) 1.61723e40 0.0395551
\(206\) −1.25921e41 2.20634e41i −0.282156 0.494381i
\(207\) 1.11768e41i 0.229536i
\(208\) −3.93015e41 7.13179e41i −0.740065 1.34295i
\(209\) −1.02041e42 −1.76255
\(210\) 5.60349e41 3.19806e41i 0.888201 0.506919i
\(211\) 5.79120e41i 0.842721i −0.906893 0.421361i \(-0.861553\pi\)
0.906893 0.421361i \(-0.138447\pi\)
\(212\) 1.52076e40 2.57445e40i 0.0203243 0.0344064i
\(213\) 2.55632e41 0.313893
\(214\) 3.76212e41 + 6.59181e41i 0.424605 + 0.743973i
\(215\) 3.44728e41i 0.357754i
\(216\) −8.58076e41 1.28271e40i −0.819140 0.0122451i
\(217\) 1.25318e42 1.10088
\(218\) −4.02706e41 + 2.29835e41i −0.325665 + 0.185866i
\(219\) 4.31899e41i 0.321653i
\(220\) −1.77638e42 1.04933e42i −1.21879 0.719956i
\(221\) 1.48378e42 0.938226
\(222\) −3.03608e41 5.31967e41i −0.176994 0.310121i
\(223\) 3.33880e42i 1.79516i 0.440854 + 0.897579i \(0.354676\pi\)
−0.440854 + 0.897579i \(0.645324\pi\)
\(224\) −1.61352e42 + 2.64053e42i −0.800406 + 1.30987i
\(225\) 1.93532e42 0.886069
\(226\) 2.21470e42 1.26398e42i 0.936186 0.534306i
\(227\) 2.18249e42i 0.852094i −0.904701 0.426047i \(-0.859906\pi\)
0.904701 0.426047i \(-0.140094\pi\)
\(228\) 1.16960e42 1.97998e42i 0.421901 0.714221i
\(229\) −4.96346e41 −0.165480 −0.0827401 0.996571i \(-0.526367\pi\)
−0.0827401 + 0.996571i \(0.526367\pi\)
\(230\) 6.79784e41 + 1.19109e42i 0.209541 + 0.367149i
\(231\) 2.39452e42i 0.682657i
\(232\) 1.22678e40 8.20657e41i 0.00323581 0.216460i
\(233\) 9.17240e40 0.0223912 0.0111956 0.999937i \(-0.496436\pi\)
0.0111956 + 0.999937i \(0.496436\pi\)
\(234\) −4.65924e42 + 2.65915e42i −1.05300 + 0.600976i
\(235\) 2.72953e42i 0.571304i
\(236\) 3.21616e42 + 1.89983e42i 0.623622 + 0.368383i
\(237\) −8.72723e41 −0.156822
\(238\) −2.79494e42 4.89717e42i −0.465572 0.815755i
\(239\) 1.35213e42i 0.208861i 0.994532 + 0.104431i \(0.0333020\pi\)
−0.994532 + 0.104431i \(0.966698\pi\)
\(240\) 4.07221e42 2.24410e42i 0.583482 0.321543i
\(241\) 2.74106e42 0.364428 0.182214 0.983259i \(-0.441674\pi\)
0.182214 + 0.983259i \(0.441674\pi\)
\(242\) −3.87744e41 + 2.21296e41i −0.0478486 + 0.0273084i
\(243\) 8.81094e42i 1.00951i
\(244\) −1.28910e42 + 2.18227e42i −0.137173 + 0.232216i
\(245\) −1.99806e43 −1.97523
\(246\) −6.70483e40 1.17479e41i −0.00615965 0.0107927i
\(247\) 3.25564e43i 2.78030i
\(248\) 9.03019e42 + 1.34990e41i 0.717078 + 0.0107194i
\(249\) −5.75212e42 −0.424854
\(250\) −2.21980e42 + 1.26690e42i −0.152543 + 0.0870604i
\(251\) 1.24102e43i 0.793690i −0.917886 0.396845i \(-0.870105\pi\)
0.917886 0.396845i \(-0.129895\pi\)
\(252\) 1.75529e43 + 1.03688e43i 1.04506 + 0.617330i
\(253\) −5.08983e42 −0.282185
\(254\) 2.16179e42 + 3.78780e42i 0.111637 + 0.195605i
\(255\) 8.47227e42i 0.407640i
\(256\) −1.19111e43 + 1.88533e43i −0.534114 + 0.845413i
\(257\) 1.46390e43 0.611950 0.305975 0.952039i \(-0.401018\pi\)
0.305975 + 0.952039i \(0.401018\pi\)
\(258\) 2.50417e42 1.42920e42i 0.0976135 0.0557105i
\(259\) 3.29530e43i 1.19812i
\(260\) 3.34793e43 5.66759e43i 1.13568 1.92255i
\(261\) −5.40714e42 −0.171174
\(262\) 8.72790e42 + 1.52926e43i 0.257921 + 0.451917i
\(263\) 3.20359e43i 0.883961i 0.897025 + 0.441981i \(0.145724\pi\)
−0.897025 + 0.441981i \(0.854276\pi\)
\(264\) −2.57932e41 + 1.72544e43i −0.00664713 + 0.444661i
\(265\) 2.41709e42 0.0581924
\(266\) −1.07452e44 + 6.13254e43i −2.41737 + 1.37966i
\(267\) 1.61066e43i 0.338689i
\(268\) 5.52046e43 + 3.26101e43i 1.08530 + 0.641101i
\(269\) 8.67222e43 1.59437 0.797186 0.603734i \(-0.206321\pi\)
0.797186 + 0.603734i \(0.206321\pi\)
\(270\) −3.43863e43 6.02501e43i −0.591340 1.03612i
\(271\) 2.10087e43i 0.338028i −0.985614 0.169014i \(-0.945942\pi\)
0.985614 0.169014i \(-0.0540582\pi\)
\(272\) −1.96123e43 3.55891e43i −0.295316 0.535891i
\(273\) −7.63977e43 −1.07684
\(274\) 9.05127e43 5.16580e43i 1.19454 0.681753i
\(275\) 8.81329e43i 1.08931i
\(276\) 5.83400e42 9.87618e42i 0.0675465 0.114347i
\(277\) 6.95926e43 0.754965 0.377483 0.926017i \(-0.376790\pi\)
0.377483 + 0.926017i \(0.376790\pi\)
\(278\) −8.07636e43 1.41510e44i −0.821125 1.43874i
\(279\) 5.94981e43i 0.567058i
\(280\) −2.50122e44 3.73900e42i −2.23515 0.0334127i
\(281\) 1.66599e43 0.139623 0.0698116 0.997560i \(-0.477760\pi\)
0.0698116 + 0.997560i \(0.477760\pi\)
\(282\) −1.98279e43 + 1.13163e43i −0.155881 + 0.0889652i
\(283\) 2.44437e44i 1.80306i 0.432716 + 0.901530i \(0.357555\pi\)
−0.432716 + 0.901530i \(0.642445\pi\)
\(284\) −8.53360e43 5.04092e43i −0.590748 0.348963i
\(285\) 1.85895e44 1.20798
\(286\) 1.21096e44 + 2.12178e44i 0.738822 + 1.29453i
\(287\) 7.27731e42i 0.0416962i
\(288\) 1.25366e44 + 7.66060e43i 0.674707 + 0.412286i
\(289\) −1.23727e44 −0.625609
\(290\) 5.76227e43 3.28868e43i 0.273798 0.156263i
\(291\) 1.95263e44i 0.872061i
\(292\) 8.51680e43 1.44178e44i 0.357590 0.605351i
\(293\) −3.79928e44 −1.49998 −0.749989 0.661451i \(-0.769941\pi\)
−0.749989 + 0.661451i \(0.769941\pi\)
\(294\) 8.28368e43 + 1.45143e44i 0.307589 + 0.538944i
\(295\) 3.01957e44i 1.05475i
\(296\) −3.54962e42 + 2.37453e44i −0.0116663 + 0.780417i
\(297\) 2.57464e44 0.796345
\(298\) 4.63033e44 2.64265e44i 1.34809 0.769391i
\(299\) 1.62392e44i 0.445127i
\(300\) 1.71011e44 + 1.01019e44i 0.441410 + 0.260747i
\(301\) −1.55123e44 −0.377119
\(302\) 1.07821e44 + 1.88918e44i 0.246932 + 0.432663i
\(303\) 1.10275e44i 0.237964i
\(304\) −7.80880e44 + 4.30324e44i −1.58803 + 0.875127i
\(305\) −2.04888e44 −0.392753
\(306\) −2.32506e44 + 1.32697e44i −0.420192 + 0.239814i
\(307\) 2.56547e44i 0.437196i −0.975815 0.218598i \(-0.929852\pi\)
0.975815 0.218598i \(-0.0701483\pi\)
\(308\) 4.72185e44 7.99346e44i 0.758926 1.28476i
\(309\) −1.71761e44 −0.260419
\(310\) 3.61873e44 + 6.34058e44i 0.517662 + 0.907023i
\(311\) 1.36571e45i 1.84363i −0.387634 0.921813i \(-0.626708\pi\)
0.387634 0.921813i \(-0.373292\pi\)
\(312\) −5.50506e44 8.22937e42i −0.701422 0.0104854i
\(313\) 1.27288e43 0.0153105 0.00765526 0.999971i \(-0.497563\pi\)
0.00765526 + 0.999971i \(0.497563\pi\)
\(314\) 1.30631e45 7.45545e44i 1.48359 0.846720i
\(315\) 1.64800e45i 1.76753i
\(316\) 2.91335e44 + 1.72096e44i 0.295139 + 0.174343i
\(317\) −1.70217e45 −1.62906 −0.814530 0.580122i \(-0.803005\pi\)
−0.814530 + 0.580122i \(0.803005\pi\)
\(318\) −1.00209e43 1.75582e43i −0.00906191 0.0158779i
\(319\) 2.46237e44i 0.210436i
\(320\) −1.80192e45 5.38850e43i −1.45558 0.0435279i
\(321\) 5.13167e44 0.391893
\(322\) −5.35972e44 + 3.05893e44i −0.387023 + 0.220884i
\(323\) 1.62463e45i 1.10945i
\(324\) 3.27484e44 5.54386e44i 0.211534 0.358098i
\(325\) 2.81190e45 1.71830
\(326\) −1.37349e45 2.40656e45i −0.794160 1.39149i
\(327\) 3.13503e44i 0.171547i
\(328\) −7.83894e41 + 5.24388e43i −0.000406002 + 0.0271596i
\(329\) 1.22825e45 0.602228
\(330\) −1.21152e45 + 6.91448e44i −0.562447 + 0.321003i
\(331\) 2.28914e45i 1.00640i 0.864171 + 0.503198i \(0.167843\pi\)
−0.864171 + 0.503198i \(0.832157\pi\)
\(332\) 1.92019e45 + 1.13429e45i 0.799575 + 0.472321i
\(333\) 1.56453e45 0.617146
\(334\) −7.43915e44 1.30345e45i −0.278027 0.487146i
\(335\) 5.18302e45i 1.83559i
\(336\) 1.00981e45 + 1.83244e45i 0.338948 + 0.615066i
\(337\) 1.62264e45 0.516277 0.258139 0.966108i \(-0.416891\pi\)
0.258139 + 0.966108i \(0.416891\pi\)
\(338\) −3.89039e45 + 2.22034e45i −1.17352 + 0.669761i
\(339\) 1.72412e45i 0.493143i
\(340\) 1.67068e45 2.82824e45i 0.453183 0.767178i
\(341\) −2.70949e45 −0.697123
\(342\) 2.91158e45 + 5.10154e45i 0.710655 + 1.24518i
\(343\) 2.36241e45i 0.547092i
\(344\) −1.11778e45 1.67094e43i −0.245643 0.00367206i
\(345\) 9.27250e44 0.193398
\(346\) −8.97973e44 + 5.12497e44i −0.177784 + 0.101466i
\(347\) 4.94592e45i 0.929643i −0.885404 0.464821i \(-0.846119\pi\)
0.885404 0.464821i \(-0.153881\pi\)
\(348\) −4.77793e44 2.82239e44i −0.0852733 0.0503722i
\(349\) −1.07278e45 −0.181824 −0.0909120 0.995859i \(-0.528978\pi\)
−0.0909120 + 0.995859i \(0.528978\pi\)
\(350\) −5.29669e45 9.28062e45i −0.852668 1.49401i
\(351\) 8.21447e45i 1.25618i
\(352\) 3.48858e45 5.70907e45i 0.506851 0.829463i
\(353\) −2.96408e45 −0.409209 −0.204605 0.978845i \(-0.565591\pi\)
−0.204605 + 0.978845i \(0.565591\pi\)
\(354\) 2.19348e45 1.25188e45i 0.287789 0.164249i
\(355\) 8.01198e45i 0.999147i
\(356\) 3.17613e45 5.37677e45i 0.376529 0.637413i
\(357\) −3.81240e45 −0.429705
\(358\) 2.15324e45 + 3.77281e45i 0.230780 + 0.404362i
\(359\) 1.60495e46i 1.63592i −0.575277 0.817959i \(-0.695106\pi\)
0.575277 0.817959i \(-0.304894\pi\)
\(360\) −1.77519e44 + 1.18752e46i −0.0172107 + 1.15132i
\(361\) −2.48044e46 −2.28770
\(362\) −2.67788e45 + 1.52833e45i −0.234983 + 0.134111i
\(363\) 3.01855e44i 0.0252046i
\(364\) 2.55033e46 + 1.50652e46i 2.02662 + 1.19715i
\(365\) 1.35365e46 1.02385
\(366\) 8.49440e44 + 1.48835e45i 0.0611608 + 0.107163i
\(367\) 1.32063e46i 0.905296i 0.891689 + 0.452648i \(0.149521\pi\)
−0.891689 + 0.452648i \(0.850479\pi\)
\(368\) −3.89505e45 + 2.14647e45i −0.254245 + 0.140108i
\(369\) 3.45509e44 0.0214775
\(370\) −1.66728e46 + 9.51562e45i −0.987140 + 0.563386i
\(371\) 1.08765e45i 0.0613423i
\(372\) 3.10565e45 5.25744e45i 0.166870 0.282489i
\(373\) 1.36447e46 0.698561 0.349281 0.937018i \(-0.386426\pi\)
0.349281 + 0.937018i \(0.386426\pi\)
\(374\) 6.04291e45 + 1.05881e46i 0.294820 + 0.516571i
\(375\) 1.72809e45i 0.0803533i
\(376\) 8.85053e45 + 1.32304e44i 0.392272 + 0.00586398i
\(377\) −7.85625e45 −0.331949
\(378\) 2.71117e46 1.54733e46i 1.09220 0.623349i
\(379\) 4.54211e46i 1.74483i 0.488769 + 0.872413i \(0.337446\pi\)
−0.488769 + 0.872413i \(0.662554\pi\)
\(380\) −6.20561e46 3.66574e46i −2.27342 1.34294i
\(381\) 2.94876e45 0.103036
\(382\) −4.46284e44 7.81959e44i −0.0148755 0.0260642i
\(383\) 5.17389e46i 1.64528i −0.568564 0.822639i \(-0.692501\pi\)
0.568564 0.822639i \(-0.307499\pi\)
\(384\) 7.07910e45 + 1.33129e46i 0.214791 + 0.403935i
\(385\) 7.50486e46 2.17295
\(386\) 3.87569e46 2.21196e46i 1.07097 0.611231i
\(387\) 7.36484e45i 0.194252i
\(388\) −3.85048e46 + 6.51835e46i −0.969491 + 1.64122i
\(389\) −7.75327e46 −1.86377 −0.931884 0.362755i \(-0.881836\pi\)
−0.931884 + 0.362755i \(0.881836\pi\)
\(390\) −2.20608e46 3.86540e46i −0.506360 0.887220i
\(391\) 8.10370e45i 0.177624i
\(392\) 9.68484e44 6.47870e46i 0.0202742 1.35625i
\(393\) 1.19052e46 0.238051
\(394\) −4.70251e46 + 2.68384e46i −0.898250 + 0.512655i
\(395\) 2.73528e46i 0.499176i
\(396\) −3.79510e46 2.24182e46i −0.661774 0.390920i
\(397\) 1.56490e46 0.260770 0.130385 0.991463i \(-0.458379\pi\)
0.130385 + 0.991463i \(0.458379\pi\)
\(398\) 2.29595e46 + 4.02286e46i 0.365651 + 0.640677i
\(399\) 8.36500e46i 1.27337i
\(400\) −3.71672e46 6.74449e46i −0.540854 0.981452i
\(401\) 7.79235e46 1.08410 0.542051 0.840346i \(-0.317648\pi\)
0.542051 + 0.840346i \(0.317648\pi\)
\(402\) 3.76505e46 2.14881e46i 0.500843 0.285844i
\(403\) 8.64471e46i 1.09966i
\(404\) −2.17456e46 + 3.68124e46i −0.264550 + 0.447847i
\(405\) 5.20499e46 0.605661
\(406\) 1.47986e46 + 2.59294e46i 0.164722 + 0.288618i
\(407\) 7.12474e46i 0.758700i
\(408\) −2.74714e46 4.10662e44i −0.279897 0.00418410i
\(409\) −4.70283e46 −0.458501 −0.229250 0.973367i \(-0.573627\pi\)
−0.229250 + 0.973367i \(0.573627\pi\)
\(410\) −3.68201e45 + 2.10142e45i −0.0343539 + 0.0196066i
\(411\) 7.04633e46i 0.629231i
\(412\) 5.73380e46 + 3.38704e46i 0.490109 + 0.289514i
\(413\) −1.35876e47 −1.11184
\(414\) 1.45231e46 + 2.54466e46i 0.113776 + 0.199354i
\(415\) 1.80282e47i 1.35234i
\(416\) 1.82149e47 + 1.11304e47i 1.30842 + 0.799522i
\(417\) −1.10164e47 −0.757866
\(418\) 2.32320e47 1.32591e47i 1.53078 0.873657i
\(419\) 1.28693e47i 0.812271i 0.913813 + 0.406136i \(0.133124\pi\)
−0.913813 + 0.406136i \(0.866876\pi\)
\(420\) −8.60214e46 + 1.45623e47i −0.520139 + 0.880525i
\(421\) −9.75674e46 −0.565232 −0.282616 0.959233i \(-0.591202\pi\)
−0.282616 + 0.959233i \(0.591202\pi\)
\(422\) 7.52503e46 + 1.31850e47i 0.417719 + 0.731908i
\(423\) 5.83143e46i 0.310205i
\(424\) −1.17159e44 + 7.83741e45i −0.000597299 + 0.0399565i
\(425\) 1.40320e47 0.685674
\(426\) −5.82007e46 + 3.32166e46i −0.272618 + 0.155590i
\(427\) 9.21967e46i 0.414013i
\(428\) −1.71307e47 1.01194e47i −0.737543 0.435677i
\(429\) 1.65179e47 0.681903
\(430\) −4.47937e46 7.84854e46i −0.177331 0.310711i
\(431\) 3.43872e47i 1.30559i −0.757535 0.652794i \(-0.773597\pi\)
0.757535 0.652794i \(-0.226403\pi\)
\(432\) 1.97028e47 1.08577e47i 0.717497 0.395395i
\(433\) −3.22358e47 −1.12605 −0.563023 0.826441i \(-0.690362\pi\)
−0.563023 + 0.826441i \(0.690362\pi\)
\(434\) −2.85317e47 + 1.62838e47i −0.956119 + 0.545682i
\(435\) 4.48587e46i 0.144225i
\(436\) 6.18210e46 1.04655e47i 0.190713 0.322851i
\(437\) −1.77808e47 −0.526363
\(438\) −5.61206e46 9.83319e46i −0.159437 0.279358i
\(439\) 1.85153e47i 0.504857i −0.967616 0.252428i \(-0.918771\pi\)
0.967616 0.252428i \(-0.0812292\pi\)
\(440\) 5.40785e47 + 8.08406e45i 1.41539 + 0.0211583i
\(441\) −4.26869e47 −1.07251
\(442\) −3.37817e47 + 1.92801e47i −0.814854 + 0.465058i
\(443\) 3.20119e47i 0.741386i 0.928756 + 0.370693i \(0.120880\pi\)
−0.928756 + 0.370693i \(0.879120\pi\)
\(444\) 1.38247e47 + 8.16644e46i 0.307441 + 0.181610i
\(445\) 5.04811e47 1.07807
\(446\) −4.33841e47 7.60156e47i −0.889822 1.55911i
\(447\) 3.60467e47i 0.710118i
\(448\) 2.42475e46 8.10839e47i 0.0458841 1.53437i
\(449\) 1.01672e48 1.84827 0.924136 0.382065i \(-0.124787\pi\)
0.924136 + 0.382065i \(0.124787\pi\)
\(450\) −4.40621e47 + 2.51474e47i −0.769556 + 0.439206i
\(451\) 1.57342e46i 0.0264038i
\(452\) −3.39987e47 + 5.75552e47i −0.548239 + 0.928095i
\(453\) 1.47071e47 0.227908
\(454\) 2.83591e47 + 4.96896e47i 0.422365 + 0.740048i
\(455\) 2.39444e48i 3.42768i
\(456\) −9.01058e45 + 6.02765e47i −0.0123990 + 0.829433i
\(457\) −1.12133e47 −0.148335 −0.0741675 0.997246i \(-0.523630\pi\)
−0.0741675 + 0.997246i \(0.523630\pi\)
\(458\) 1.13005e47 6.44948e46i 0.143720 0.0820250i
\(459\) 4.09918e47i 0.501267i
\(460\) −3.09538e47 1.82848e47i −0.363976 0.215006i
\(461\) 1.02919e48 1.16380 0.581900 0.813260i \(-0.302309\pi\)
0.581900 + 0.813260i \(0.302309\pi\)
\(462\) −3.11142e47 5.45168e47i −0.338378 0.592891i
\(463\) 1.07221e48i 1.12156i −0.827966 0.560778i \(-0.810502\pi\)
0.827966 0.560778i \(-0.189498\pi\)
\(464\) 1.03842e47 + 1.88436e47i 0.104484 + 0.189601i
\(465\) 4.93608e47 0.477781
\(466\) −2.08831e46 + 1.19185e46i −0.0194469 + 0.0110988i
\(467\) 2.64750e47i 0.237210i 0.992942 + 0.118605i \(0.0378422\pi\)
−0.992942 + 0.118605i \(0.962158\pi\)
\(468\) 7.15259e47 1.21084e48i 0.616649 1.04390i
\(469\) −2.33228e48 −1.93495
\(470\) 3.54673e47 + 6.21443e47i 0.283183 + 0.496181i
\(471\) 1.01695e48i 0.781489i
\(472\) −9.79098e47 1.46363e46i −0.724219 0.0108262i
\(473\) 3.35389e47 0.238808
\(474\) 1.98696e47 1.13401e47i 0.136201 0.0777332i
\(475\) 3.07883e48i 2.03190i
\(476\) 1.27267e48 + 7.51783e47i 0.808705 + 0.477714i
\(477\) 5.16391e46 0.0315972
\(478\) −1.75695e47 3.07845e47i −0.103528 0.181397i
\(479\) 1.15049e48i 0.652897i 0.945215 + 0.326449i \(0.105852\pi\)
−0.945215 + 0.326449i \(0.894148\pi\)
\(480\) −6.35539e47 + 1.04006e48i −0.347376 + 0.568482i
\(481\) 2.27317e48 1.19680
\(482\) −6.24067e47 + 3.56171e47i −0.316508 + 0.180639i
\(483\) 4.17249e47i 0.203867i
\(484\) 5.95242e46 1.00766e47i 0.0280206 0.0474351i
\(485\) −6.11991e48 −2.77584
\(486\) −1.14489e48 2.00602e48i −0.500391 0.876762i
\(487\) 2.97014e48i 1.25099i 0.780226 + 0.625497i \(0.215104\pi\)
−0.780226 + 0.625497i \(0.784896\pi\)
\(488\) 9.93121e45 6.64351e47i 0.00403130 0.269675i
\(489\) −1.87349e48 −0.732978
\(490\) 4.54904e48 2.59626e48i 1.71550 0.979080i
\(491\) 3.36774e48i 1.22425i −0.790759 0.612127i \(-0.790314\pi\)
0.790759 0.612127i \(-0.209686\pi\)
\(492\) 3.05303e46 + 1.80347e46i 0.0106994 + 0.00632028i
\(493\) −3.92043e47 −0.132461
\(494\) 4.23035e48 + 7.41223e48i 1.37813 + 2.41470i
\(495\) 3.56313e48i 1.11928i
\(496\) −2.07348e48 + 1.14264e48i −0.628100 + 0.346131i
\(497\) 3.60527e48 1.05323
\(498\) 1.30961e48 7.47426e47i 0.368988 0.210591i
\(499\) 4.09580e48i 1.11309i 0.830818 + 0.556544i \(0.187873\pi\)
−0.830818 + 0.556544i \(0.812127\pi\)
\(500\) 3.40770e47 5.76877e47i 0.0893308 0.151225i
\(501\) −1.01473e48 −0.256608
\(502\) 1.61257e48 + 2.82547e48i 0.393415 + 0.689325i
\(503\) 4.07583e48i 0.959383i −0.877437 0.479692i \(-0.840749\pi\)
0.877437 0.479692i \(-0.159251\pi\)
\(504\) −5.34365e48 7.98808e46i −1.21364 0.0181423i
\(505\) −3.45623e48 −0.757456
\(506\) 1.15882e48 6.61368e47i 0.245079 0.139873i
\(507\) 3.02863e48i 0.618163i
\(508\) −9.84367e47 5.81480e47i −0.193914 0.114548i
\(509\) 8.39304e48 1.59588 0.797938 0.602740i \(-0.205924\pi\)
0.797938 + 0.602740i \(0.205924\pi\)
\(510\) −1.10088e48 1.92891e48i −0.202058 0.354038i
\(511\) 6.09123e48i 1.07927i
\(512\) 2.62064e47 5.84013e48i 0.0448278 0.998995i
\(513\) 8.99426e48 1.48543
\(514\) −3.33292e48 + 1.90218e48i −0.531483 + 0.303331i
\(515\) 5.38332e48i 0.828934i
\(516\) −3.84426e47 + 6.50781e47i −0.0571633 + 0.0967699i
\(517\) −2.65559e48 −0.381356
\(518\) −4.28189e48 7.50254e48i −0.593882 1.04057i
\(519\) 6.99064e47i 0.0936493i
\(520\) −2.57924e47 + 1.72539e49i −0.0333758 + 2.23268i
\(521\) −2.34160e48 −0.292708 −0.146354 0.989232i \(-0.546754\pi\)
−0.146354 + 0.989232i \(0.546754\pi\)
\(522\) 1.23106e48 7.02600e47i 0.148666 0.0848475i
\(523\) 8.19584e48i 0.956232i −0.878297 0.478116i \(-0.841320\pi\)
0.878297 0.478116i \(-0.158680\pi\)
\(524\) −3.97423e48 2.34763e48i −0.448012 0.264647i
\(525\) −7.22488e48 −0.786979
\(526\) −4.16272e48 7.29372e48i −0.438161 0.767725i
\(527\) 4.31389e48i 0.438811i
\(528\) −2.18330e48 3.96189e48i −0.214636 0.389486i
\(529\) 9.63760e48 0.915729
\(530\) −5.50307e47 + 3.14074e47i −0.0505405 + 0.0288447i
\(531\) 6.45108e48i 0.572705i
\(532\) 1.64953e49 2.79244e49i 1.41564 2.39648i
\(533\) 5.02003e47 0.0416502
\(534\) −2.09288e48 3.66705e48i −0.167881 0.294154i
\(535\) 1.60836e49i 1.24743i
\(536\) −1.68060e49 2.51228e47i −1.26037 0.0188409i
\(537\) 2.93710e48 0.213001
\(538\) −1.97444e49 + 1.12686e49i −1.38472 + 0.790296i
\(539\) 1.94393e49i 1.31851i
\(540\) 1.56577e49 + 9.24923e48i 1.02717 + 0.606761i
\(541\) −8.30545e48 −0.527002 −0.263501 0.964659i \(-0.584877\pi\)
−0.263501 + 0.964659i \(0.584877\pi\)
\(542\) 2.72986e48 + 4.78313e48i 0.167553 + 0.293579i
\(543\) 2.08470e48i 0.123779i
\(544\) 9.08961e48 + 5.55429e48i 0.522114 + 0.319042i
\(545\) 9.82576e48 0.546046
\(546\) 1.73937e49 9.92705e48i 0.935245 0.533768i
\(547\) 1.87034e49i 0.973080i −0.873658 0.486540i \(-0.838259\pi\)
0.873658 0.486540i \(-0.161741\pi\)
\(548\) −1.38950e49 + 2.35223e49i −0.699532 + 1.18421i
\(549\) −4.37727e48 −0.213256
\(550\) 1.14519e49 + 2.00655e49i 0.539946 + 0.946068i
\(551\) 8.60204e48i 0.392530i
\(552\) −4.49451e46 + 3.00661e48i −0.00198508 + 0.132793i
\(553\) −1.23083e49 −0.526196
\(554\) −1.58444e49 + 9.04280e48i −0.655692 + 0.374220i
\(555\) 1.29797e49i 0.519983i
\(556\) 3.67755e49 + 2.17238e49i 1.42630 + 0.842538i
\(557\) −2.22627e49 −0.835957 −0.417979 0.908457i \(-0.637261\pi\)
−0.417979 + 0.908457i \(0.637261\pi\)
\(558\) 7.73113e48 + 1.35461e49i 0.281079 + 0.492493i
\(559\) 1.07007e49i 0.376702i
\(560\) 5.74319e49 3.16493e49i 1.95780 1.07890i
\(561\) 8.24275e48 0.272108
\(562\) −3.79301e48 + 2.16477e48i −0.121264 + 0.0692082i
\(563\) 5.58851e49i 1.73039i −0.501433 0.865197i \(-0.667194\pi\)
0.501433 0.865197i \(-0.332806\pi\)
\(564\) 3.04386e48 5.15284e48i 0.0912852 0.154534i
\(565\) −5.40371e49 −1.56971
\(566\) −3.17619e49 5.56518e49i −0.893739 1.56597i
\(567\) 2.34217e49i 0.638444i
\(568\) 2.59789e49 + 3.88351e47i 0.686041 + 0.0102555i
\(569\) 2.83847e49 0.726213 0.363106 0.931748i \(-0.381716\pi\)
0.363106 + 0.931748i \(0.381716\pi\)
\(570\) −4.23234e49 + 2.41551e49i −1.04914 + 0.598771i
\(571\) 1.22959e49i 0.295333i −0.989037 0.147666i \(-0.952824\pi\)
0.989037 0.147666i \(-0.0471762\pi\)
\(572\) −5.51405e49 3.25723e49i −1.28334 0.758088i
\(573\) −6.08748e47 −0.0137295
\(574\) −9.45608e47 1.65685e48i −0.0206679 0.0362134i
\(575\) 1.53573e49i 0.325308i
\(576\) −3.84967e49 1.15121e48i −0.790348 0.0236347i
\(577\) 5.25738e49 1.04618 0.523088 0.852279i \(-0.324780\pi\)
0.523088 + 0.852279i \(0.324780\pi\)
\(578\) 2.81694e49 1.60770e49i 0.543345 0.310101i
\(579\) 3.01719e49i 0.564142i
\(580\) −8.84589e48 + 1.49749e49i −0.160338 + 0.271431i
\(581\) −8.11243e49 −1.42554
\(582\) 2.53724e49 + 4.44563e49i 0.432262 + 0.757390i
\(583\) 2.35160e48i 0.0388446i
\(584\) −6.56133e47 + 4.38922e49i −0.0105090 + 0.703001i
\(585\) 1.13682e50 1.76558
\(586\) 8.64997e49 4.93676e49i 1.30274 0.743507i
\(587\) 5.78785e49i 0.845340i 0.906284 + 0.422670i \(0.138907\pi\)
−0.906284 + 0.422670i \(0.861093\pi\)
\(588\) −3.77195e49 2.22814e49i −0.534286 0.315611i
\(589\) −9.46535e49 −1.30035
\(590\) −3.92361e49 6.87477e49i −0.522817 0.916056i
\(591\) 3.66086e49i 0.473160i
\(592\) −3.00463e49 5.45230e49i −0.376704 0.683580i
\(593\) 1.05326e50 1.28100 0.640502 0.767956i \(-0.278726\pi\)
0.640502 + 0.767956i \(0.278726\pi\)
\(594\) −5.86178e49 + 3.34547e49i −0.691630 + 0.394731i
\(595\) 1.19488e50i 1.36778i
\(596\) −7.10821e49 + 1.20332e50i −0.789455 + 1.33644i
\(597\) 3.13176e49 0.337481
\(598\) 2.11011e49 + 3.69724e49i 0.220640 + 0.386595i
\(599\) 1.30983e50i 1.32902i −0.747278 0.664511i \(-0.768640\pi\)
0.747278 0.664511i \(-0.231360\pi\)
\(600\) −5.20610e49 7.78246e47i −0.512614 0.00766293i
\(601\) 1.73160e50 1.65466 0.827329 0.561718i \(-0.189859\pi\)
0.827329 + 0.561718i \(0.189859\pi\)
\(602\) 3.53173e49 2.01565e49i 0.327530 0.186930i
\(603\) 1.10731e50i 0.996685i
\(604\) −4.90958e49 2.90016e49i −0.428923 0.253371i
\(605\) 9.46071e48 0.0802282
\(606\) 1.43291e49 + 2.51067e49i 0.117953 + 0.206673i
\(607\) 9.98769e49i 0.798121i 0.916925 + 0.399060i \(0.130664\pi\)
−0.916925 + 0.399060i \(0.869336\pi\)
\(608\) 1.21870e50 1.99440e50i 0.945436 1.54721i
\(609\) 2.01858e49 0.152032
\(610\) 4.66476e49 2.66230e49i 0.341108 0.194679i
\(611\) 8.47272e49i 0.601563i
\(612\) 3.56928e49 6.04232e49i 0.246068 0.416560i
\(613\) −2.26002e50 −1.51294 −0.756472 0.654026i \(-0.773079\pi\)
−0.756472 + 0.654026i \(0.773079\pi\)
\(614\) 3.33355e49 + 5.84089e49i 0.216709 + 0.379707i
\(615\) 2.86641e48i 0.0180961i
\(616\) −3.63771e48 + 2.43345e50i −0.0223036 + 1.49201i
\(617\) −1.84910e50 −1.10110 −0.550552 0.834801i \(-0.685583\pi\)
−0.550552 + 0.834801i \(0.685583\pi\)
\(618\) 3.91055e49 2.23185e49i 0.226175 0.129084i
\(619\) 2.69650e50i 1.51485i −0.652924 0.757424i \(-0.726458\pi\)
0.652924 0.757424i \(-0.273542\pi\)
\(620\) −1.64778e50 9.73367e49i −0.899184 0.531161i
\(621\) 4.48636e49 0.237818
\(622\) 1.77460e50 + 3.10937e50i 0.913847 + 1.60120i
\(623\) 2.27158e50i 1.13643i
\(624\) 1.26405e50 6.96587e49i 0.614387 0.338574i
\(625\) −1.83137e50 −0.864841
\(626\) −2.89801e48 + 1.65397e48i −0.0132973 + 0.00758910i
\(627\) 1.80859e50i 0.806351i
\(628\) −2.00537e50 + 3.39482e50i −0.868801 + 1.47076i
\(629\) 1.13436e50 0.477571
\(630\) −2.14140e50 3.75206e50i −0.876128 1.53511i
\(631\) 3.25280e50i 1.29339i −0.762749 0.646694i \(-0.776151\pi\)
0.762749 0.646694i \(-0.223849\pi\)
\(632\) −8.86914e49 1.32583e48i −0.342747 0.00512364i
\(633\) 1.02644e50 0.385538
\(634\) 3.87540e50 2.21179e50i 1.41485 0.807490i
\(635\) 9.24197e49i 0.327973i
\(636\) 4.56300e48 + 2.69543e48i 0.0157406 + 0.00929822i
\(637\) −6.20214e50 −2.07985
\(638\) −3.19958e49 5.60617e49i −0.104309 0.182765i
\(639\) 1.71170e50i 0.542514i
\(640\) 4.17252e50 2.21872e50i 1.28576 0.683697i
\(641\) 2.58731e50 0.775183 0.387591 0.921831i \(-0.373307\pi\)
0.387591 + 0.921831i \(0.373307\pi\)
\(642\) −1.16834e50 + 6.66805e49i −0.340362 + 0.194253i
\(643\) 1.55303e50i 0.439928i 0.975508 + 0.219964i \(0.0705940\pi\)
−0.975508 + 0.219964i \(0.929406\pi\)
\(644\) 8.22791e49 1.39288e50i 0.226644 0.383678i
\(645\) −6.11002e49 −0.163669
\(646\) 2.11103e50 + 3.69885e50i 0.549932 + 0.963566i
\(647\) 6.88086e50i 1.74327i 0.490152 + 0.871637i \(0.336941\pi\)
−0.490152 + 0.871637i \(0.663059\pi\)
\(648\) −2.52293e48 + 1.68772e50i −0.00621663 + 0.415863i
\(649\) 2.93777e50 0.704066
\(650\) −6.40196e50 + 3.65377e50i −1.49236 + 0.851727i
\(651\) 2.22116e50i 0.503643i
\(652\) 6.25414e50 + 3.69441e50i 1.37947 + 0.814870i
\(653\) −1.99284e50 −0.427596 −0.213798 0.976878i \(-0.568584\pi\)
−0.213798 + 0.976878i \(0.568584\pi\)
\(654\) −4.07363e49 7.13763e49i −0.0850320 0.148989i
\(655\) 3.73130e50i 0.757734i
\(656\) −6.63539e48 1.20408e49i −0.0131098 0.0237895i
\(657\) 2.89197e50 0.555926
\(658\) −2.79640e50 + 1.59598e50i −0.523038 + 0.298512i
\(659\) 3.60744e50i 0.656541i 0.944584 + 0.328270i \(0.106466\pi\)
−0.944584 + 0.328270i \(0.893534\pi\)
\(660\) 1.85986e50 3.14849e50i 0.329374 0.557586i
\(661\) −4.59971e50 −0.792691 −0.396346 0.918101i \(-0.629722\pi\)
−0.396346 + 0.918101i \(0.629722\pi\)
\(662\) −2.97449e50 5.21177e50i −0.498849 0.874060i
\(663\) 2.62987e50i 0.429231i
\(664\) −5.84565e50 8.73852e48i −0.928555 0.0138807i
\(665\) 2.62175e51 4.05323
\(666\) −3.56202e50 + 2.03294e50i −0.535995 + 0.305906i
\(667\) 4.29072e49i 0.0628442i
\(668\) 3.38740e50 + 2.00098e50i 0.482936 + 0.285277i
\(669\) −5.91774e50 −0.821270
\(670\) −6.73478e50 1.18004e51i −0.909864 1.59422i
\(671\) 1.99338e50i 0.262170i
\(672\) −4.68012e50 2.85983e50i −0.599253 0.366179i
\(673\) −8.21833e50 −1.02450 −0.512251 0.858836i \(-0.671188\pi\)
−0.512251 + 0.858836i \(0.671188\pi\)
\(674\) −3.69432e50 + 2.10844e50i −0.448390 + 0.255908i
\(675\) 7.76837e50i 0.918040i
\(676\) 5.97228e50 1.01103e51i 0.687227 1.16338i
\(677\) 3.47381e50 0.389234 0.194617 0.980879i \(-0.437654\pi\)
0.194617 + 0.980879i \(0.437654\pi\)
\(678\) 2.24031e50 + 3.92536e50i 0.244440 + 0.428297i
\(679\) 2.75387e51i 2.92609i
\(680\) −1.28709e49 + 8.61004e50i −0.0133183 + 0.890932i
\(681\) 3.86829e50 0.389826
\(682\) 6.16880e50 3.52070e50i 0.605456 0.345549i
\(683\) 8.87361e50i 0.848257i −0.905602 0.424129i \(-0.860580\pi\)
0.905602 0.424129i \(-0.139420\pi\)
\(684\) −1.32578e51 7.83157e50i −1.23442 0.729188i
\(685\) −2.20845e51 −2.00289
\(686\) 3.06969e50 + 5.37858e50i 0.271182 + 0.475153i
\(687\) 8.79732e49i 0.0757058i
\(688\) 2.56661e50 1.41439e50i 0.215163 0.118571i
\(689\) 7.50285e49 0.0612746
\(690\) −2.11110e50 + 1.20486e50i −0.167968 + 0.0958635i
\(691\) 1.71672e51i 1.33074i 0.746512 + 0.665372i \(0.231727\pi\)
−0.746512 + 0.665372i \(0.768273\pi\)
\(692\) 1.37851e50 2.33364e50i 0.104112 0.176248i
\(693\) 1.60335e51 1.17986
\(694\) 6.42668e50 + 1.12605e51i 0.460804 + 0.807400i
\(695\) 3.45276e51i 2.41234i
\(696\) 1.45455e50 + 2.17436e48i 0.0990288 + 0.00148035i
\(697\) 2.50510e49 0.0166201
\(698\) 2.44243e50 1.39396e50i 0.157915 0.0901263i
\(699\) 1.62573e49i 0.0102438i
\(700\) 2.41183e51 + 1.42471e51i 1.48109 + 0.874904i
\(701\) −2.04153e51 −1.22189 −0.610944 0.791674i \(-0.709210\pi\)
−0.610944 + 0.791674i \(0.709210\pi\)
\(702\) −1.06738e51 1.87022e51i −0.622661 1.09100i
\(703\) 2.48896e51i 1.41521i
\(704\) −5.24252e49 + 1.75311e51i −0.0290557 + 0.971629i
\(705\) 4.83787e50 0.261367
\(706\) 6.74843e50 3.85151e50i 0.355401 0.202836i
\(707\) 1.55525e51i 0.798457i
\(708\) −3.36730e50 + 5.70038e50i −0.168532 + 0.285302i
\(709\) −1.72817e50 −0.0843245 −0.0421622 0.999111i \(-0.513425\pi\)
−0.0421622 + 0.999111i \(0.513425\pi\)
\(710\) 1.04107e51 + 1.82412e51i 0.495256 + 0.867765i
\(711\) 5.84370e50i 0.271041i
\(712\) −2.44689e49 + 1.63685e51i −0.0110656 + 0.740235i
\(713\) −4.72134e50 −0.208187
\(714\) 8.67983e50 4.95380e50i 0.373201 0.212996i
\(715\) 5.17700e51i 2.17055i
\(716\) −9.80472e50 5.79179e50i −0.400867 0.236798i
\(717\) −2.39655e50 −0.0955523
\(718\) 2.08546e51 + 3.65405e51i 0.810889 + 1.42080i
\(719\) 3.23849e51i 1.22807i 0.789279 + 0.614034i \(0.210454\pi\)
−0.789279 + 0.614034i \(0.789546\pi\)
\(720\) −1.50263e51 2.72673e51i −0.555735 1.00846i
\(721\) −2.42241e51 −0.873803
\(722\) 5.64731e51 3.22307e51i 1.98688 1.13397i
\(723\) 4.85830e50i 0.166723i
\(724\) 4.11091e50 6.95922e50i 0.137608 0.232952i
\(725\) −7.42960e50 −0.242595
\(726\) −3.92229e49 6.87245e49i −0.0124934 0.0218903i
\(727\) 2.42075e51i 0.752196i 0.926580 + 0.376098i \(0.122734\pi\)
−0.926580 + 0.376098i \(0.877266\pi\)
\(728\) −7.76400e51 1.16062e50i −2.35353 0.0351824i
\(729\) −1.55313e50 −0.0459317
\(730\) −3.08190e51 + 1.75892e51i −0.889217 + 0.507499i
\(731\) 5.33985e50i 0.150320i
\(732\) −3.86790e50 2.28482e50i −0.106237 0.0627557i
\(733\) 2.02046e51 0.541475 0.270738 0.962653i \(-0.412732\pi\)
0.270738 + 0.962653i \(0.412732\pi\)
\(734\) −1.71601e51 3.00672e51i −0.448736 0.786255i
\(735\) 3.54139e51i 0.903652i
\(736\) 6.07891e50 9.94815e50i 0.151365 0.247709i
\(737\) 5.04261e51 1.22529
\(738\) −7.86632e49 + 4.48951e49i −0.0186534 + 0.0106460i
\(739\) 2.96849e51i 0.686966i 0.939159 + 0.343483i \(0.111607\pi\)
−0.939159 + 0.343483i \(0.888393\pi\)
\(740\) 2.55951e51 4.33291e51i 0.578078 0.978608i
\(741\) 5.77035e51 1.27196
\(742\) −1.41329e50 2.47630e50i −0.0304061 0.0532762i
\(743\) 3.73279e51i 0.783854i −0.919996 0.391927i \(-0.871809\pi\)
0.919996 0.391927i \(-0.128191\pi\)
\(744\) −2.39258e49 + 1.60053e51i −0.00490404 + 0.328057i
\(745\) −1.12977e52 −2.26036
\(746\) −3.10653e51 + 1.77298e51i −0.606704 + 0.346262i
\(747\) 3.85158e51i 0.734292i
\(748\) −2.75162e51 1.62542e51i −0.512106 0.302509i
\(749\) 7.23738e51 1.31495
\(750\) −2.24547e50 3.93441e50i −0.0398294 0.0697873i
\(751\) 4.60658e51i