Properties

Label 4.37.b.b.3.8
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 3.8
Root \(-8.47589e6i\) of defining polynomial
Character \(\chi\) \(=\) 4.3
Dual form 4.37.b.b.3.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +O(q^{10})\) \(q+(-39525.7 + 259147. i) q^{2} -1.35614e8i q^{3} +(-6.55949e10 - 2.04859e10i) q^{4} -1.24080e12 q^{5} +(3.51440e13 + 5.36025e12i) q^{6} +4.20496e14i q^{7} +(7.90156e15 - 1.61890e16i) q^{8} +1.31703e17 q^{9} +(4.90435e16 - 3.21549e17i) q^{10} -3.22138e18i q^{11} +(-2.77819e18 + 8.89561e18i) q^{12} -2.28918e19 q^{13} +(-1.08970e20 - 1.66204e19i) q^{14} +1.68270e20i q^{15} +(3.88302e21 + 2.68755e21i) q^{16} +6.53319e21 q^{17} +(-5.20567e21 + 3.41305e22i) q^{18} +1.34943e23i q^{19} +(8.13901e22 + 2.54189e22i) q^{20} +5.70253e22 q^{21} +(8.34811e23 + 1.27327e23i) q^{22} -4.96373e22i q^{23} +(-2.19546e24 - 1.07156e24i) q^{24} -1.30123e25 q^{25} +(9.04813e23 - 5.93233e24i) q^{26} -3.82158e25i q^{27} +(8.61427e24 - 2.75824e25i) q^{28} -1.19240e26 q^{29} +(-4.36067e25 - 6.65100e24i) q^{30} +7.37399e26i q^{31} +(-8.49949e26 + 9.00045e26i) q^{32} -4.36865e26 q^{33} +(-2.58229e26 + 1.69306e27i) q^{34} -5.21751e26i q^{35} +(-8.63907e27 - 2.69807e27i) q^{36} -2.48980e28 q^{37} +(-3.49701e28 - 5.33372e27i) q^{38} +3.10445e27i q^{39} +(-9.80425e27 + 2.00873e28i) q^{40} -1.04174e29 q^{41} +(-2.25397e27 + 1.47779e28i) q^{42} +2.34072e29i q^{43} +(-6.59930e28 + 2.11306e29i) q^{44} -1.63417e29 q^{45} +(1.28634e28 + 1.96195e27i) q^{46} -6.54567e29i q^{47} +(3.64470e29 - 5.26593e29i) q^{48} +2.47491e30 q^{49} +(5.14322e29 - 3.37211e30i) q^{50} -8.85993e29i q^{51} +(1.50158e30 + 4.68959e29i) q^{52} +8.42648e30 q^{53} +(9.90352e30 + 1.51051e30i) q^{54} +3.99708e30i q^{55} +(6.80742e30 + 3.32258e30i) q^{56} +1.83002e31 q^{57} +(4.71306e30 - 3.09007e31i) q^{58} +6.65287e31i q^{59} +(3.44717e30 - 1.10377e31i) q^{60} -1.74158e32 q^{61} +(-1.91095e32 - 2.91462e31i) q^{62} +5.53808e31i q^{63} +(-1.99649e32 - 2.55837e32i) q^{64} +2.84041e31 q^{65} +(1.72674e31 - 1.13212e32i) q^{66} +1.02480e33i q^{67} +(-4.28544e32 - 1.33839e32i) q^{68} -6.73153e30 q^{69} +(1.35210e32 + 2.06226e31i) q^{70} +3.10980e33i q^{71} +(1.04066e33 - 2.13215e33i) q^{72} +3.37473e33 q^{73} +(9.84112e32 - 6.45225e33i) q^{74} +1.76466e33i q^{75} +(2.76443e33 - 8.85157e33i) q^{76} +1.35458e33 q^{77} +(-8.04509e32 - 1.22706e32i) q^{78} +1.58850e34i q^{79} +(-4.81804e33 - 3.33471e33i) q^{80} +1.45854e34 q^{81} +(4.11757e33 - 2.69965e34i) q^{82} +6.39239e34i q^{83} +(-3.74057e33 - 1.16822e33i) q^{84} -8.10637e33 q^{85} +(-6.06590e34 - 9.25185e33i) q^{86} +1.61707e34i q^{87} +(-5.21509e34 - 2.54539e34i) q^{88} -1.63956e35 q^{89} +(6.45919e33 - 4.23491e34i) q^{90} -9.62590e33i q^{91} +(-1.01687e33 + 3.25596e33i) q^{92} +1.00002e35 q^{93} +(1.69629e35 + 2.58722e34i) q^{94} -1.67437e35i q^{95} +(1.22059e35 + 1.15265e35i) q^{96} +3.39752e35 q^{97} +(-9.78227e34 + 6.41367e35i) q^{98} -4.24267e35i 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −39525.7 + 259147.i −0.150779 + 0.988568i
\(3\) 1.35614e8i 0.350044i −0.984565 0.175022i \(-0.944000\pi\)
0.984565 0.175022i \(-0.0559997\pi\)
\(4\) −6.55949e10 2.04859e10i −0.954532 0.298110i
\(5\) −1.24080e12 −0.325268 −0.162634 0.986686i \(-0.551999\pi\)
−0.162634 + 0.986686i \(0.551999\pi\)
\(6\) 3.51440e13 + 5.36025e12i 0.346042 + 0.0527792i
\(7\) 4.20496e14i 0.258225i 0.991630 + 0.129112i \(0.0412128\pi\)
−0.991630 + 0.129112i \(0.958787\pi\)
\(8\) 7.90156e15 1.61890e16i 0.438625 0.898670i
\(9\) 1.31703e17 0.877469
\(10\) 4.90435e16 3.21549e17i 0.0490435 0.321549i
\(11\) 3.22138e18i 0.579394i −0.957118 0.289697i \(-0.906446\pi\)
0.957118 0.289697i \(-0.0935545\pi\)
\(12\) −2.77819e18 + 8.89561e18i −0.104352 + 0.334128i
\(13\) −2.28918e19 −0.203563 −0.101781 0.994807i \(-0.532454\pi\)
−0.101781 + 0.994807i \(0.532454\pi\)
\(14\) −1.08970e20 1.66204e19i −0.255272 0.0389348i
\(15\) 1.68270e20i 0.113858i
\(16\) 3.88302e21 + 2.68755e21i 0.822261 + 0.569110i
\(17\) 6.53319e21 0.464563 0.232281 0.972649i \(-0.425381\pi\)
0.232281 + 0.972649i \(0.425381\pi\)
\(18\) −5.20567e21 + 3.41305e22i −0.132304 + 0.867437i
\(19\) 1.34943e23i 1.29594i 0.761665 + 0.647971i \(0.224382\pi\)
−0.761665 + 0.647971i \(0.775618\pi\)
\(20\) 8.13901e22 + 2.54189e22i 0.310479 + 0.0969656i
\(21\) 5.70253e22 0.0903900
\(22\) 8.34811e23 + 1.27327e23i 0.572770 + 0.0873602i
\(23\) 4.96373e22i 0.0153006i −0.999971 0.00765028i \(-0.997565\pi\)
0.999971 0.00765028i \(-0.00243518\pi\)
\(24\) −2.19546e24 1.07156e24i −0.314574 0.153538i
\(25\) −1.30123e25 −0.894201
\(26\) 9.04813e23 5.93233e24i 0.0306930 0.201236i
\(27\) 3.82158e25i 0.657197i
\(28\) 8.61427e24 2.75824e25i 0.0769793 0.246484i
\(29\) −1.19240e26 −0.566577 −0.283288 0.959035i \(-0.591425\pi\)
−0.283288 + 0.959035i \(0.591425\pi\)
\(30\) −4.36067e25 6.65100e24i −0.112556 0.0171674i
\(31\) 7.37399e26i 1.05485i 0.849601 + 0.527427i \(0.176843\pi\)
−0.849601 + 0.527427i \(0.823157\pi\)
\(32\) −8.49949e26 + 9.00045e26i −0.686584 + 0.727051i
\(33\) −4.36865e26 −0.202813
\(34\) −2.58229e26 + 1.69306e27i −0.0700462 + 0.459252i
\(35\) 5.21751e26i 0.0839922i
\(36\) −8.63907e27 2.69807e27i −0.837572 0.261582i
\(37\) −2.48980e28 −1.47412 −0.737061 0.675826i \(-0.763787\pi\)
−0.737061 + 0.675826i \(0.763787\pi\)
\(38\) −3.49701e28 5.33372e27i −1.28113 0.195400i
\(39\) 3.10445e27i 0.0712560i
\(40\) −9.80425e27 + 2.00873e28i −0.142671 + 0.292309i
\(41\) −1.04174e29 −0.971968 −0.485984 0.873968i \(-0.661539\pi\)
−0.485984 + 0.873968i \(0.661539\pi\)
\(42\) −2.25397e27 + 1.47779e28i −0.0136289 + 0.0893566i
\(43\) 2.34072e29i 0.926651i 0.886188 + 0.463326i \(0.153344\pi\)
−0.886188 + 0.463326i \(0.846656\pi\)
\(44\) −6.59930e28 + 2.11306e29i −0.172723 + 0.553049i
\(45\) −1.63417e29 −0.285413
\(46\) 1.28634e28 + 1.96195e27i 0.0151256 + 0.00230700i
\(47\) 6.54567e29i 0.522628i −0.965254 0.261314i \(-0.915844\pi\)
0.965254 0.261314i \(-0.0841557\pi\)
\(48\) 3.64470e29 5.26593e29i 0.199214 0.287828i
\(49\) 2.47491e30 0.933320
\(50\) 5.14322e29 3.37211e30i 0.134826 0.883978i
\(51\) 8.85993e29i 0.162618i
\(52\) 1.50158e30 + 4.68959e29i 0.194307 + 0.0606841i
\(53\) 8.42648e30 0.773893 0.386946 0.922102i \(-0.373530\pi\)
0.386946 + 0.922102i \(0.373530\pi\)
\(54\) 9.90352e30 + 1.51051e30i 0.649684 + 0.0990913i
\(55\) 3.99708e30i 0.188458i
\(56\) 6.80742e30 + 3.32258e30i 0.232059 + 0.113264i
\(57\) 1.83002e31 0.453637
\(58\) 4.71306e30 3.09007e31i 0.0854277 0.560099i
\(59\) 6.65287e31i 0.886488i 0.896401 + 0.443244i \(0.146172\pi\)
−0.896401 + 0.443244i \(0.853828\pi\)
\(60\) 3.44717e30 1.10377e31i 0.0339422 0.108681i
\(61\) −1.74158e32 −1.27352 −0.636761 0.771062i \(-0.719726\pi\)
−0.636761 + 0.771062i \(0.719726\pi\)
\(62\) −1.91095e32 2.91462e31i −1.04279 0.159049i
\(63\) 5.53808e31i 0.226584i
\(64\) −1.99649e32 2.55837e32i −0.615217 0.788358i
\(65\) 2.84041e31 0.0662125
\(66\) 1.72674e31 1.13212e32i 0.0305799 0.200495i
\(67\) 1.02480e33i 1.38450i 0.721656 + 0.692252i \(0.243381\pi\)
−0.721656 + 0.692252i \(0.756619\pi\)
\(68\) −4.28544e32 1.33839e32i −0.443440 0.138491i
\(69\) −6.73153e30 −0.00535587
\(70\) 1.35210e32 + 2.06226e31i 0.0830319 + 0.0126642i
\(71\) 3.10980e33i 1.47939i 0.672942 + 0.739695i \(0.265030\pi\)
−0.672942 + 0.739695i \(0.734970\pi\)
\(72\) 1.04066e33 2.13215e33i 0.384880 0.788555i
\(73\) 3.37473e33 0.973704 0.486852 0.873484i \(-0.338145\pi\)
0.486852 + 0.873484i \(0.338145\pi\)
\(74\) 9.84112e32 6.45225e33i 0.222266 1.45727i
\(75\) 1.76466e33i 0.313010i
\(76\) 2.76443e33 8.85157e33i 0.386333 1.23702i
\(77\) 1.35458e33 0.149614
\(78\) −8.04509e32 1.22706e32i −0.0704414 0.0107439i
\(79\) 1.58850e34i 1.10586i 0.833228 + 0.552929i \(0.186490\pi\)
−0.833228 + 0.552929i \(0.813510\pi\)
\(80\) −4.81804e33 3.33471e33i −0.267455 0.185113i
\(81\) 1.45854e34 0.647421
\(82\) 4.11757e33 2.69965e34i 0.146552 0.960856i
\(83\) 6.39239e34i 1.82918i 0.404377 + 0.914592i \(0.367488\pi\)
−0.404377 + 0.914592i \(0.632512\pi\)
\(84\) −3.74057e33 1.16822e33i −0.0862801 0.0269461i
\(85\) −8.10637e33 −0.151107
\(86\) −6.06590e34 9.25185e33i −0.916058 0.139719i
\(87\) 1.61707e34i 0.198327i
\(88\) −5.21509e34 2.54539e34i −0.520684 0.254136i
\(89\) −1.63956e35 −1.33570 −0.667849 0.744296i \(-0.732785\pi\)
−0.667849 + 0.744296i \(0.732785\pi\)
\(90\) 6.45919e33 4.23491e34i 0.0430341 0.282150i
\(91\) 9.62590e33i 0.0525650i
\(92\) −1.01687e33 + 3.25596e33i −0.00456125 + 0.0146049i
\(93\) 1.00002e35 0.369245
\(94\) 1.69629e35 + 2.58722e34i 0.516653 + 0.0788011i
\(95\) 1.67437e35i 0.421528i
\(96\) 1.22059e35 + 1.15265e35i 0.254500 + 0.240335i
\(97\) 3.39752e35 0.587855 0.293928 0.955828i \(-0.405038\pi\)
0.293928 + 0.955828i \(0.405038\pi\)
\(98\) −9.78227e34 + 6.41367e35i −0.140725 + 0.922650i
\(99\) 4.24267e35i 0.508400i
\(100\) 8.53543e35 + 2.66570e35i 0.853543 + 0.266570i
\(101\) 5.85528e35 0.489512 0.244756 0.969585i \(-0.421292\pi\)
0.244756 + 0.969585i \(0.421292\pi\)
\(102\) 2.29603e35 + 3.50195e34i 0.160758 + 0.0245193i
\(103\) 2.61949e36i 1.53868i −0.638842 0.769338i \(-0.720586\pi\)
0.638842 0.769338i \(-0.279414\pi\)
\(104\) −1.80881e35 + 3.70595e35i −0.0892877 + 0.182936i
\(105\) −7.07570e34 −0.0294010
\(106\) −3.33063e35 + 2.18370e36i −0.116687 + 0.765045i
\(107\) 3.83523e36i 1.13471i −0.823474 0.567354i \(-0.807967\pi\)
0.823474 0.567354i \(-0.192033\pi\)
\(108\) −7.82888e35 + 2.50676e36i −0.195917 + 0.627315i
\(109\) −7.01177e36 −1.48645 −0.743226 0.669041i \(-0.766705\pi\)
−0.743226 + 0.669041i \(0.766705\pi\)
\(110\) −1.03583e36 1.57988e35i −0.186304 0.0284155i
\(111\) 3.37653e36i 0.516008i
\(112\) −1.13010e36 + 1.63280e36i −0.146958 + 0.212328i
\(113\) 1.16771e36 0.129396 0.0646981 0.997905i \(-0.479392\pi\)
0.0646981 + 0.997905i \(0.479392\pi\)
\(114\) −7.23328e35 + 4.74244e36i −0.0683987 + 0.448450i
\(115\) 6.15900e34i 0.00497678i
\(116\) 7.82155e36 + 2.44275e36i 0.540815 + 0.168902i
\(117\) −3.01492e36 −0.178620
\(118\) −1.72407e37 2.62959e36i −0.876353 0.133663i
\(119\) 2.74718e36i 0.119962i
\(120\) 2.72412e36 + 1.32960e36i 0.102321 + 0.0499410i
\(121\) 2.05354e37 0.664303
\(122\) 6.88372e36 4.51325e37i 0.192020 1.25896i
\(123\) 1.41275e37i 0.340232i
\(124\) 1.51063e37 4.83696e37i 0.314462 1.00689i
\(125\) 3.42017e37 0.616123
\(126\) −1.43518e37 2.18897e36i −0.223994 0.0341640i
\(127\) 5.02086e37i 0.679690i 0.940481 + 0.339845i \(0.110375\pi\)
−0.940481 + 0.339845i \(0.889625\pi\)
\(128\) 7.41906e37 4.16264e37i 0.872107 0.489316i
\(129\) 3.17434e37 0.324369
\(130\) −1.12269e36 + 7.36083e36i −0.00998343 + 0.0654555i
\(131\) 1.96393e38i 1.52140i 0.649106 + 0.760698i \(0.275143\pi\)
−0.649106 + 0.760698i \(0.724857\pi\)
\(132\) 2.86561e37 + 8.94960e36i 0.193592 + 0.0604606i
\(133\) −5.67430e37 −0.334644
\(134\) −2.65575e38 4.05061e37i −1.36867 0.208754i
\(135\) 4.74182e37i 0.213765i
\(136\) 5.16224e37 1.05766e38i 0.203769 0.417489i
\(137\) −2.08851e38 −0.722547 −0.361273 0.932460i \(-0.617658\pi\)
−0.361273 + 0.932460i \(0.617658\pi\)
\(138\) 2.66069e35 1.74446e36i 0.000807551 0.00529464i
\(139\) 3.11254e38i 0.829563i −0.909921 0.414781i \(-0.863858\pi\)
0.909921 0.414781i \(-0.136142\pi\)
\(140\) −1.06886e37 + 3.42242e37i −0.0250389 + 0.0801732i
\(141\) −8.87686e37 −0.182943
\(142\) −8.05897e38 1.22917e38i −1.46248 0.223060i
\(143\) 7.37431e37i 0.117943i
\(144\) 5.11407e38 + 3.53959e38i 0.721509 + 0.499377i
\(145\) 1.47953e38 0.184289
\(146\) −1.33389e38 + 8.74550e38i −0.146814 + 0.962573i
\(147\) 3.35634e38i 0.326703i
\(148\) 1.63318e39 + 5.10059e38i 1.40710 + 0.439450i
\(149\) 4.95139e38 0.377897 0.188949 0.981987i \(-0.439492\pi\)
0.188949 + 0.981987i \(0.439492\pi\)
\(150\) −4.57306e38 6.97494e37i −0.309431 0.0471952i
\(151\) 2.72979e39i 1.63887i −0.573171 0.819436i \(-0.694287\pi\)
0.573171 0.819436i \(-0.305713\pi\)
\(152\) 2.18459e39 + 1.06626e39i 1.16462 + 0.568432i
\(153\) 8.60443e38 0.407640
\(154\) −5.35407e37 + 3.51035e38i −0.0225585 + 0.147903i
\(155\) 9.14964e38i 0.343110i
\(156\) 6.35976e37 2.03636e38i 0.0212421 0.0680161i
\(157\) −1.89635e39 −0.564579 −0.282290 0.959329i \(-0.591094\pi\)
−0.282290 + 0.959329i \(0.591094\pi\)
\(158\) −4.11655e39 6.27866e38i −1.09322 0.166740i
\(159\) 1.14275e39i 0.270897i
\(160\) 1.05462e39 1.11678e39i 0.223324 0.236486i
\(161\) 2.08723e37 0.00395098
\(162\) −5.76497e38 + 3.77975e39i −0.0976173 + 0.640019i
\(163\) 1.43646e38i 0.0217730i 0.999941 + 0.0108865i \(0.00346534\pi\)
−0.999941 + 0.0108865i \(0.996535\pi\)
\(164\) 6.83332e39 + 2.13411e39i 0.927774 + 0.289753i
\(165\) 5.42062e38 0.0659687
\(166\) −1.65657e40 2.52664e39i −1.80827 0.275802i
\(167\) 1.17608e40i 1.15223i 0.817368 + 0.576115i \(0.195432\pi\)
−0.817368 + 0.576115i \(0.804568\pi\)
\(168\) 4.50589e38 9.23183e38i 0.0396473 0.0812308i
\(169\) −1.21222e40 −0.958562
\(170\) 3.20410e38 2.10074e39i 0.0227838 0.149380i
\(171\) 1.77724e40i 1.13715i
\(172\) 4.79518e39 1.53539e40i 0.276244 0.884518i
\(173\) 1.17976e40 0.612297 0.306149 0.951984i \(-0.400960\pi\)
0.306149 + 0.951984i \(0.400960\pi\)
\(174\) −4.19058e39 6.39158e38i −0.196060 0.0299035i
\(175\) 5.47164e39i 0.230905i
\(176\) 8.65761e39 1.25087e40i 0.329739 0.476413i
\(177\) 9.02224e39 0.310310
\(178\) 6.48050e39 4.24888e40i 0.201395 1.32043i
\(179\) 1.15903e40i 0.325643i 0.986656 + 0.162821i \(0.0520595\pi\)
−0.986656 + 0.162821i \(0.947941\pi\)
\(180\) 1.07194e40 + 3.34776e39i 0.272435 + 0.0850843i
\(181\) 1.73830e40 0.399862 0.199931 0.979810i \(-0.435928\pi\)
0.199931 + 0.979810i \(0.435928\pi\)
\(182\) 2.49452e39 + 3.80471e38i 0.0519640 + 0.00792568i
\(183\) 2.36183e40i 0.445789i
\(184\) −8.03579e38 3.92212e38i −0.0137502 0.00671120i
\(185\) 3.08934e40 0.479485
\(186\) −3.95265e39 + 2.59152e40i −0.0556743 + 0.365024i
\(187\) 2.10459e40i 0.269165i
\(188\) −1.34094e40 + 4.29362e40i −0.155800 + 0.498865i
\(189\) 1.60696e40 0.169704
\(190\) 4.33908e40 + 6.61807e39i 0.416709 + 0.0635574i
\(191\) 4.26867e40i 0.372986i −0.982456 0.186493i \(-0.940288\pi\)
0.982456 0.186493i \(-0.0597121\pi\)
\(192\) −3.46951e40 + 2.70753e40i −0.275960 + 0.215353i
\(193\) −1.11984e41 −0.811197 −0.405599 0.914051i \(-0.632937\pi\)
−0.405599 + 0.914051i \(0.632937\pi\)
\(194\) −1.34289e40 + 8.80456e40i −0.0886360 + 0.581135i
\(195\) 3.85200e39i 0.0231773i
\(196\) −1.62342e41 5.07010e40i −0.890883 0.278232i
\(197\) −3.14173e41 −1.57317 −0.786586 0.617480i \(-0.788153\pi\)
−0.786586 + 0.617480i \(0.788153\pi\)
\(198\) 1.09947e41 + 1.67694e40i 0.502588 + 0.0766559i
\(199\) 4.13949e41i 1.72819i −0.503330 0.864094i \(-0.667892\pi\)
0.503330 0.864094i \(-0.332108\pi\)
\(200\) −1.02818e41 + 2.10657e41i −0.392219 + 0.803592i
\(201\) 1.38978e41 0.484637
\(202\) −2.31434e40 + 1.51738e41i −0.0738080 + 0.483916i
\(203\) 5.01401e40i 0.146304i
\(204\) −1.81504e40 + 5.81167e40i −0.0484779 + 0.155224i
\(205\) 1.29260e41 0.316150
\(206\) 6.78834e41 + 1.03537e41i 1.52108 + 0.231999i
\(207\) 6.53741e39i 0.0134258i
\(208\) −8.88891e40 6.15227e40i −0.167382 0.115850i
\(209\) 4.34702e41 0.750860
\(210\) 2.79672e39 1.83365e40i 0.00443304 0.0290649i
\(211\) 5.11268e41i 0.743985i 0.928236 + 0.371992i \(0.121325\pi\)
−0.928236 + 0.371992i \(0.878675\pi\)
\(212\) −5.52735e41 1.72625e41i −0.738705 0.230705i
\(213\) 4.21734e41 0.517852
\(214\) 9.93889e41 + 1.51590e41i 1.12173 + 0.171090i
\(215\) 2.90436e41i 0.301410i
\(216\) −6.18676e41 3.01965e41i −0.590604 0.288263i
\(217\) −3.10074e41 −0.272389
\(218\) 2.77145e41 1.81708e42i 0.224125 1.46946i
\(219\) 4.57661e41i 0.340840i
\(220\) 8.18841e40 2.62188e41i 0.0561812 0.179889i
\(221\) −1.49556e41 −0.0945678
\(222\) −8.75017e41 1.33460e41i −0.510109 0.0778030i
\(223\) 2.98870e42i 1.60692i 0.595356 + 0.803462i \(0.297011\pi\)
−0.595356 + 0.803462i \(0.702989\pi\)
\(224\) −3.78466e41 3.57401e41i −0.187742 0.177293i
\(225\) −1.71377e42 −0.784633
\(226\) −4.61544e40 + 3.02607e41i −0.0195102 + 0.127917i
\(227\) 3.18256e42i 1.24254i 0.783595 + 0.621272i \(0.213384\pi\)
−0.783595 + 0.621272i \(0.786616\pi\)
\(228\) −1.20040e42 3.74897e41i −0.433011 0.135234i
\(229\) −1.23648e41 −0.0412238 −0.0206119 0.999788i \(-0.506561\pi\)
−0.0206119 + 0.999788i \(0.506561\pi\)
\(230\) −1.59609e40 2.43439e39i −0.00491989 0.000750393i
\(231\) 1.83700e41i 0.0523714i
\(232\) −9.42184e41 + 1.93038e42i −0.248515 + 0.509166i
\(233\) 8.58420e41 0.209553 0.104776 0.994496i \(-0.466587\pi\)
0.104776 + 0.994496i \(0.466587\pi\)
\(234\) 1.19167e41 7.81308e41i 0.0269321 0.176578i
\(235\) 8.12185e41i 0.169994i
\(236\) 1.36290e42 4.36394e42i 0.264271 0.846181i
\(237\) 2.15423e42 0.387099
\(238\) −7.11924e41 1.08584e41i −0.118590 0.0180876i
\(239\) 7.66299e42i 1.18368i −0.806054 0.591842i \(-0.798401\pi\)
0.806054 0.591842i \(-0.201599\pi\)
\(240\) −4.52234e41 + 6.53396e41i −0.0647979 + 0.0936211i
\(241\) 1.20673e42 0.160437 0.0802183 0.996777i \(-0.474438\pi\)
0.0802183 + 0.996777i \(0.474438\pi\)
\(242\) −8.11676e41 + 5.32169e42i −0.100163 + 0.656708i
\(243\) 7.71398e42i 0.883823i
\(244\) 1.14239e43 + 3.56779e42i 1.21562 + 0.379649i
\(245\) −3.07087e42 −0.303579
\(246\) −3.66111e42 5.58402e41i −0.336342 0.0512997i
\(247\) 3.08908e42i 0.263806i
\(248\) 1.19378e43 + 5.82660e42i 0.947966 + 0.462685i
\(249\) 8.66899e42 0.640296
\(250\) −1.35185e42 + 8.86327e42i −0.0928982 + 0.609079i
\(251\) 5.34548e42i 0.341869i −0.985282 0.170934i \(-0.945321\pi\)
0.985282 0.170934i \(-0.0546786\pi\)
\(252\) 1.13453e42 3.63270e42i 0.0675469 0.216282i
\(253\) −1.59901e41 −0.00886505
\(254\) −1.30114e43 1.98453e42i −0.671920 0.102483i
\(255\) 1.09934e42i 0.0528943i
\(256\) 7.85492e42 + 2.08716e43i 0.352227 + 0.935915i
\(257\) −2.19858e43 −0.919064 −0.459532 0.888161i \(-0.651983\pi\)
−0.459532 + 0.888161i \(0.651983\pi\)
\(258\) −1.25468e42 + 8.22622e42i −0.0489079 + 0.320661i
\(259\) 1.04695e43i 0.380655i
\(260\) −1.86316e42 5.81884e41i −0.0632019 0.0197386i
\(261\) −1.57043e43 −0.497154
\(262\) −5.08946e43 7.76257e42i −1.50400 0.229394i
\(263\) 2.34032e42i 0.0645762i −0.999479 0.0322881i \(-0.989721\pi\)
0.999479 0.0322881i \(-0.0102794\pi\)
\(264\) −3.45192e42 + 7.07241e42i −0.0889589 + 0.182262i
\(265\) −1.04556e43 −0.251723
\(266\) 2.24281e42 1.47048e43i 0.0504572 0.330818i
\(267\) 2.22348e43i 0.467554i
\(268\) 2.09941e43 6.72219e43i 0.412734 1.32155i
\(269\) 5.58028e43 1.02592 0.512961 0.858412i \(-0.328548\pi\)
0.512961 + 0.858412i \(0.328548\pi\)
\(270\) −1.22883e43 1.87424e42i −0.211321 0.0322312i
\(271\) 5.41976e43i 0.872033i 0.899939 + 0.436017i \(0.143611\pi\)
−0.899939 + 0.436017i \(0.856389\pi\)
\(272\) 2.53685e43 + 1.75583e43i 0.381992 + 0.264388i
\(273\) −1.30541e42 −0.0184001
\(274\) 8.25498e42 5.41231e43i 0.108945 0.714286i
\(275\) 4.19177e43i 0.518094i
\(276\) 4.41554e41 + 1.37902e41i 0.00511235 + 0.00159664i
\(277\) −2.91199e43 −0.315903 −0.157952 0.987447i \(-0.550489\pi\)
−0.157952 + 0.987447i \(0.550489\pi\)
\(278\) 8.06607e43 + 1.23026e43i 0.820079 + 0.125080i
\(279\) 9.71180e43i 0.925601i
\(280\) −8.44664e42 4.12265e42i −0.0754813 0.0368410i
\(281\) 1.85422e44 1.55399 0.776995 0.629507i \(-0.216743\pi\)
0.776995 + 0.629507i \(0.216743\pi\)
\(282\) 3.50864e42 2.30041e43i 0.0275839 0.180851i
\(283\) 5.61975e43i 0.414535i −0.978284 0.207268i \(-0.933543\pi\)
0.978284 0.207268i \(-0.0664571\pi\)
\(284\) 6.37073e43 2.03987e44i 0.441021 1.41212i
\(285\) −2.27069e43 −0.147553
\(286\) −1.91103e43 2.91475e42i −0.116595 0.0177833i
\(287\) 4.38050e43i 0.250986i
\(288\) −1.11941e44 + 1.18539e44i −0.602456 + 0.637965i
\(289\) −1.55088e44 −0.784181
\(290\) −5.84795e42 + 3.83416e43i −0.0277869 + 0.182182i
\(291\) 4.60752e43i 0.205775i
\(292\) −2.21365e44 6.91345e43i −0.929432 0.290271i
\(293\) −6.61412e43 −0.261129 −0.130564 0.991440i \(-0.541679\pi\)
−0.130564 + 0.991440i \(0.541679\pi\)
\(294\) 8.69785e43 + 1.32662e43i 0.322968 + 0.0492599i
\(295\) 8.25487e43i 0.288346i
\(296\) −1.96733e44 + 4.03074e44i −0.646586 + 1.32475i
\(297\) −1.23108e44 −0.380776
\(298\) −1.95707e43 + 1.28314e44i −0.0569789 + 0.373577i
\(299\) 1.13629e42i 0.00311463i
\(300\) 3.61507e43 1.15753e44i 0.0933113 0.298778i
\(301\) −9.84262e43 −0.239284
\(302\) 7.07418e44 + 1.07897e44i 1.62014 + 0.247107i
\(303\) 7.94060e43i 0.171351i
\(304\) −3.62666e44 + 5.23986e44i −0.737534 + 1.06560i
\(305\) 2.16095e44 0.414236
\(306\) −3.40096e43 + 2.22981e44i −0.0614633 + 0.402979i
\(307\) 6.49386e44i 1.10666i −0.832964 0.553328i \(-0.813358\pi\)
0.832964 0.553328i \(-0.186642\pi\)
\(308\) −8.88535e43 2.77498e43i −0.142811 0.0446013i
\(309\) −3.55241e44 −0.538604
\(310\) 2.37110e44 + 3.61646e43i 0.339187 + 0.0517337i
\(311\) 4.95093e44i 0.668344i −0.942512 0.334172i \(-0.891543\pi\)
0.942512 0.334172i \(-0.108457\pi\)
\(312\) 5.02580e43 + 2.45300e43i 0.0640357 + 0.0312547i
\(313\) −5.21360e43 −0.0627104 −0.0313552 0.999508i \(-0.509982\pi\)
−0.0313552 + 0.999508i \(0.509982\pi\)
\(314\) 7.49546e43 4.91434e44i 0.0851265 0.558125i
\(315\) 6.87164e43i 0.0737005i
\(316\) 3.25419e44 1.04197e45i 0.329667 1.05558i
\(317\) 1.74925e45 1.67411 0.837056 0.547117i \(-0.184275\pi\)
0.837056 + 0.547117i \(0.184275\pi\)
\(318\) 2.96141e44 + 4.51681e43i 0.267800 + 0.0408454i
\(319\) 3.84118e44i 0.328271i
\(320\) 2.47725e44 + 3.17442e44i 0.200110 + 0.256428i
\(321\) −5.20112e44 −0.397198
\(322\) −8.24994e41 + 5.40900e42i −0.000595724 + 0.00390581i
\(323\) 8.81607e44i 0.602046i
\(324\) −9.56725e44 2.98795e44i −0.617984 0.193003i
\(325\) 2.97875e44 0.182026
\(326\) −3.72255e43 5.67772e42i −0.0215240 0.00328290i
\(327\) 9.50897e44i 0.520324i
\(328\) −8.23141e44 + 1.68648e45i −0.426329 + 0.873479i
\(329\) 2.75243e44 0.134955
\(330\) −2.14254e43 + 1.40474e44i −0.00994667 + 0.0652145i
\(331\) 3.93879e45i 1.73164i 0.500352 + 0.865822i \(0.333204\pi\)
−0.500352 + 0.865822i \(0.666796\pi\)
\(332\) 1.30954e45 4.19308e45i 0.545298 1.74601i
\(333\) −3.27915e45 −1.29350
\(334\) −3.04777e45 4.64853e44i −1.13906 0.173732i
\(335\) 1.27157e45i 0.450335i
\(336\) 2.21430e44 + 1.53258e44i 0.0743242 + 0.0514419i
\(337\) −1.37207e45 −0.436553 −0.218277 0.975887i \(-0.570044\pi\)
−0.218277 + 0.975887i \(0.570044\pi\)
\(338\) 4.79138e44 3.14143e45i 0.144531 0.947603i
\(339\) 1.58358e44i 0.0452944i
\(340\) 5.31737e44 + 1.66067e44i 0.144237 + 0.0450466i
\(341\) 2.37544e45 0.611175
\(342\) −4.60568e45 7.02469e44i −1.12415 0.171458i
\(343\) 2.15574e45i 0.499231i
\(344\) 3.78939e45 + 1.84953e45i 0.832754 + 0.406452i
\(345\) 8.35248e42 0.00174209
\(346\) −4.66307e44 + 3.05730e45i −0.0923214 + 0.605297i
\(347\) 3.78358e45i 0.711169i −0.934644 0.355585i \(-0.884282\pi\)
0.934644 0.355585i \(-0.115718\pi\)
\(348\) 3.31272e44 1.06071e45i 0.0591232 0.189309i
\(349\) −1.87966e45 −0.318581 −0.159291 0.987232i \(-0.550921\pi\)
−0.159291 + 0.987232i \(0.550921\pi\)
\(350\) 1.41796e45 + 2.16271e44i 0.228265 + 0.0348155i
\(351\) 8.74828e44i 0.133781i
\(352\) 2.89939e45 + 2.73801e45i 0.421249 + 0.397802i
\(353\) 1.31475e46 1.81509 0.907545 0.419954i \(-0.137954\pi\)
0.907545 + 0.419954i \(0.137954\pi\)
\(354\) −3.56611e44 + 2.33809e45i −0.0467881 + 0.306762i
\(355\) 3.85864e45i 0.481198i
\(356\) 1.07547e46 + 3.35880e45i 1.27497 + 0.398185i
\(357\) 3.72557e44 0.0419918
\(358\) −3.00360e45 4.58117e44i −0.321920 0.0491000i
\(359\) 1.37878e46i 1.40539i −0.711493 0.702693i \(-0.751981\pi\)
0.711493 0.702693i \(-0.248019\pi\)
\(360\) −1.29125e45 + 2.64557e45i −0.125189 + 0.256492i
\(361\) −7.36708e45 −0.679463
\(362\) −6.87076e44 + 4.50475e45i −0.0602907 + 0.395291i
\(363\) 2.78489e45i 0.232535i
\(364\) −1.97196e44 + 6.31410e44i −0.0156701 + 0.0501749i
\(365\) −4.18736e45 −0.316715
\(366\) −6.12061e45 9.33531e44i −0.440692 0.0672154i
\(367\) 2.09789e45i 0.143811i −0.997411 0.0719057i \(-0.977092\pi\)
0.997411 0.0719057i \(-0.0229081\pi\)
\(368\) 1.33403e44 1.92743e44i 0.00870771 0.0125811i
\(369\) −1.37201e46 −0.852872
\(370\) −1.22108e45 + 8.00594e45i −0.0722961 + 0.474003i
\(371\) 3.54331e45i 0.199838i
\(372\) −6.55961e45 2.04863e45i −0.352456 0.110076i
\(373\) −5.35973e45 −0.274400 −0.137200 0.990543i \(-0.543810\pi\)
−0.137200 + 0.990543i \(0.543810\pi\)
\(374\) 5.45398e45 + 8.31854e44i 0.266088 + 0.0405843i
\(375\) 4.63824e45i 0.215670i
\(376\) −1.05968e46 5.17210e45i −0.469670 0.229237i
\(377\) 2.72962e45 0.115334
\(378\) −6.35164e44 + 4.16440e45i −0.0255878 + 0.167764i
\(379\) 3.69366e45i 0.141890i 0.997480 + 0.0709449i \(0.0226014\pi\)
−0.997480 + 0.0709449i \(0.977399\pi\)
\(380\) −3.43011e45 + 1.09830e46i −0.125662 + 0.402362i
\(381\) 6.80900e45 0.237922
\(382\) 1.10621e46 + 1.68722e45i 0.368722 + 0.0562383i
\(383\) 4.03454e46i 1.28297i 0.767136 + 0.641485i \(0.221681\pi\)
−0.767136 + 0.641485i \(0.778319\pi\)
\(384\) −5.64513e45 1.00613e46i −0.171282 0.305276i
\(385\) −1.68076e45 −0.0486645
\(386\) 4.42627e45 2.90205e46i 0.122311 0.801923i
\(387\) 3.08280e46i 0.813108i
\(388\) −2.22860e46 6.96013e45i −0.561126 0.175245i
\(389\) 4.29638e46 1.03278 0.516392 0.856352i \(-0.327275\pi\)
0.516392 + 0.856352i \(0.327275\pi\)
\(390\) 9.98234e44 + 1.52253e44i 0.0229123 + 0.00349464i
\(391\) 3.24290e44i 0.00710807i
\(392\) 1.95557e46 4.00664e46i 0.409377 0.838747i
\(393\) 2.66337e46 0.532556
\(394\) 1.24179e46 8.14169e46i 0.237201 1.55519i
\(395\) 1.97101e46i 0.359700i
\(396\) −8.69151e45 + 2.78297e46i −0.151559 + 0.485284i
\(397\) −4.06613e46 −0.677567 −0.338784 0.940864i \(-0.610015\pi\)
−0.338784 + 0.940864i \(0.610015\pi\)
\(398\) 1.07274e47 + 1.63616e46i 1.70843 + 0.260574i
\(399\) 7.69516e45i 0.117140i
\(400\) −5.05271e46 3.49713e46i −0.735267 0.508899i
\(401\) 3.03189e46 0.421808 0.210904 0.977507i \(-0.432359\pi\)
0.210904 + 0.977507i \(0.432359\pi\)
\(402\) −5.49320e45 + 3.60157e46i −0.0730730 + 0.479097i
\(403\) 1.68804e46i 0.214729i
\(404\) −3.84077e46 1.19951e46i −0.467255 0.145928i
\(405\) −1.80975e46 −0.210585
\(406\) 1.29937e46 + 1.98182e45i 0.144631 + 0.0220595i
\(407\) 8.02060e46i 0.854097i
\(408\) −1.43434e46 7.00073e45i −0.146140 0.0713281i
\(409\) −2.61966e46 −0.255403 −0.127701 0.991813i \(-0.540760\pi\)
−0.127701 + 0.991813i \(0.540760\pi\)
\(410\) −5.10908e45 + 3.34972e46i −0.0476687 + 0.312536i
\(411\) 2.83232e46i 0.252923i
\(412\) −5.36628e46 + 1.71825e47i −0.458694 + 1.46871i
\(413\) −2.79751e46 −0.228913
\(414\) 1.69415e45 + 2.58396e44i 0.0132723 + 0.00202432i
\(415\) 7.93167e46i 0.594975i
\(416\) 1.94568e46 2.06036e46i 0.139763 0.148001i
\(417\) −4.22106e46 −0.290384
\(418\) −1.71819e46 + 1.12652e47i −0.113214 + 0.742276i
\(419\) 2.06412e47i 1.30281i −0.758730 0.651406i \(-0.774180\pi\)
0.758730 0.651406i \(-0.225820\pi\)
\(420\) 4.64130e45 + 1.44952e45i 0.0280642 + 0.00876472i
\(421\) −3.68409e46 −0.213429 −0.106714 0.994290i \(-0.534033\pi\)
−0.106714 + 0.994290i \(0.534033\pi\)
\(422\) −1.32493e47 2.02082e46i −0.735479 0.112177i
\(423\) 8.62086e46i 0.458590i
\(424\) 6.65824e46 1.36416e47i 0.339448 0.695474i
\(425\) −8.50120e46 −0.415412
\(426\) −1.66693e46 + 1.09291e47i −0.0780810 + 0.511932i
\(427\) 7.32328e46i 0.328855i
\(428\) −7.85684e46 + 2.51572e47i −0.338267 + 1.08311i
\(429\) 1.00006e46 0.0412853
\(430\) 7.52656e46 + 1.14797e46i 0.297964 + 0.0454462i
\(431\) 1.33320e47i 0.506181i −0.967443 0.253091i \(-0.918553\pi\)
0.967443 0.253091i \(-0.0814470\pi\)
\(432\) 1.02707e47 1.48393e47i 0.374018 0.540388i
\(433\) 2.32639e47 0.812646 0.406323 0.913730i \(-0.366811\pi\)
0.406323 + 0.913730i \(0.366811\pi\)
\(434\) 1.22559e46 8.03547e46i 0.0410705 0.269275i
\(435\) 2.00646e46i 0.0645094i
\(436\) 4.59937e47 + 1.43643e47i 1.41887 + 0.443126i
\(437\) 6.69821e45 0.0198286
\(438\) 1.18602e47 + 1.80894e46i 0.336943 + 0.0513913i
\(439\) 1.54201e47i 0.420462i 0.977652 + 0.210231i \(0.0674216\pi\)
−0.977652 + 0.210231i \(0.932578\pi\)
\(440\) 6.47088e46 + 3.15832e46i 0.169362 + 0.0826624i
\(441\) 3.25955e47 0.818959
\(442\) 5.91131e45 3.87570e46i 0.0142588 0.0934867i
\(443\) 5.24128e47i 1.21386i 0.794754 + 0.606932i \(0.207600\pi\)
−0.794754 + 0.606932i \(0.792400\pi\)
\(444\) 6.91713e46 2.21483e47i 0.153827 0.492546i
\(445\) 2.03437e47 0.434460
\(446\) −7.74514e47 1.18131e47i −1.58855 0.242290i
\(447\) 6.71479e46i 0.132281i
\(448\) 1.07578e47 8.39518e46i 0.203573 0.158864i
\(449\) −6.42975e47 −1.16885 −0.584427 0.811447i \(-0.698681\pi\)
−0.584427 + 0.811447i \(0.698681\pi\)
\(450\) 6.77379e46 4.44118e47i 0.118306 0.775663i
\(451\) 3.35586e47i 0.563152i
\(452\) −7.65955e46 2.39215e46i −0.123513 0.0385742i
\(453\) −3.70199e47 −0.573678
\(454\) −8.24752e47 1.25793e47i −1.22834 0.187349i
\(455\) 1.19438e46i 0.0170977i
\(456\) 1.44600e47 2.96262e47i 0.198976 0.407670i
\(457\) 9.18113e47 1.21452 0.607260 0.794503i \(-0.292269\pi\)
0.607260 + 0.794503i \(0.292269\pi\)
\(458\) 4.88727e45 3.20430e46i 0.00621567 0.0407525i
\(459\) 2.49671e47i 0.305309i
\(460\) 1.26173e45 4.03999e45i 0.00148363 0.00475050i
\(461\) −9.35047e47 −1.05735 −0.528673 0.848826i \(-0.677310\pi\)
−0.528673 + 0.848826i \(0.677310\pi\)
\(462\) 4.76054e46 + 7.26089e45i 0.0517727 + 0.00789649i
\(463\) 1.13538e48i 1.18764i 0.804599 + 0.593818i \(0.202380\pi\)
−0.804599 + 0.593818i \(0.797620\pi\)
\(464\) −4.63012e47 3.20464e47i −0.465874 0.322445i
\(465\) −1.24082e47 −0.120104
\(466\) −3.39297e46 + 2.22457e47i −0.0315961 + 0.207157i
\(467\) 1.04572e48i 0.936940i 0.883479 + 0.468470i \(0.155195\pi\)
−0.883479 + 0.468470i \(0.844805\pi\)
\(468\) 1.97764e47 + 6.17635e46i 0.170499 + 0.0532484i
\(469\) −4.30926e47 −0.357513
\(470\) −2.10475e47 3.21022e46i −0.168051 0.0256315i
\(471\) 2.57172e47i 0.197628i
\(472\) 1.07703e48 + 5.25680e47i 0.796660 + 0.388835i
\(473\) 7.54033e47 0.536896
\(474\) −8.51476e46 + 5.58263e47i −0.0583663 + 0.382674i
\(475\) 1.75592e48i 1.15883i
\(476\) 5.62786e46 1.80201e47i 0.0357617 0.114507i
\(477\) 1.10980e48 0.679067
\(478\) 1.98584e48 + 3.02885e47i 1.17015 + 0.178474i
\(479\) 2.65599e48i 1.50726i −0.657300 0.753629i \(-0.728302\pi\)
0.657300 0.753629i \(-0.271698\pi\)
\(480\) −1.51451e47 1.43021e47i −0.0827807 0.0781731i
\(481\) 5.69959e47 0.300077
\(482\) −4.76969e46 + 3.12721e47i −0.0241904 + 0.158602i
\(483\) 2.83059e45i 0.00138302i
\(484\) −1.34702e48 4.20687e47i −0.634098 0.198035i
\(485\) −4.21563e47 −0.191210
\(486\) 1.99905e48 + 3.04900e47i 0.873719 + 0.133262i
\(487\) 3.04604e48i 1.28296i −0.767139 0.641481i \(-0.778320\pi\)
0.767139 0.641481i \(-0.221680\pi\)
\(488\) −1.37612e48 + 2.81944e48i −0.558598 + 1.14448i
\(489\) 1.94805e46 0.00762150
\(490\) 1.21378e47 7.95807e47i 0.0457733 0.300108i
\(491\) 1.05583e48i 0.383821i 0.981412 + 0.191911i \(0.0614683\pi\)
−0.981412 + 0.191911i \(0.938532\pi\)
\(492\) 2.89416e47 9.26695e47i 0.101426 0.324762i
\(493\) −7.79019e47 −0.263211
\(494\) 8.00526e47 + 1.22098e47i 0.260790 + 0.0397763i
\(495\) 5.26430e47i 0.165366i
\(496\) −1.98180e48 + 2.86333e48i −0.600328 + 0.867365i
\(497\) −1.30766e48 −0.382015
\(498\) −3.42648e47 + 2.24654e48i −0.0965429 + 0.632975i
\(499\) 4.01580e48i 1.09135i −0.837998 0.545673i \(-0.816274\pi\)
0.837998 0.545673i \(-0.183726\pi\)
\(500\) −2.24346e48 7.00654e47i −0.588109 0.183672i
\(501\) 1.59493e48 0.403332
\(502\) 1.38527e48 + 2.11284e47i 0.337961 + 0.0515465i
\(503\) 5.68934e48i 1.33918i 0.742732 + 0.669589i \(0.233530\pi\)
−0.742732 + 0.669589i \(0.766470\pi\)
\(504\) 8.96560e47 + 4.37595e47i 0.203624 + 0.0993854i
\(505\) −7.26523e47 −0.159223
\(506\) 6.32019e45 4.14378e46i 0.00133666 0.00876370i
\(507\) 1.64394e48i 0.335539i
\(508\) 1.02857e48 3.29343e48i 0.202622 0.648786i
\(509\) −9.32459e48 −1.77300 −0.886501 0.462726i \(-0.846871\pi\)
−0.886501 + 0.462726i \(0.846871\pi\)
\(510\) −2.84891e47 4.34522e46i −0.0522896 0.00797533i
\(511\) 1.41906e48i 0.251434i
\(512\) −5.71928e48 + 1.21061e48i −0.978323 + 0.207084i
\(513\) 5.15696e48 0.851689
\(514\) 8.69004e47 5.69755e48i 0.138575 0.908556i
\(515\) 3.25026e48i 0.500482i
\(516\) −2.08221e48 6.50295e47i −0.309620 0.0966976i
\(517\) −2.10861e48 −0.302807
\(518\) 2.71315e48 + 4.13815e47i 0.376303 + 0.0573946i
\(519\) 1.59992e48i 0.214331i
\(520\) 2.24436e47 4.59834e47i 0.0290424 0.0595032i
\(521\) 1.06132e49 1.32669 0.663344 0.748314i \(-0.269137\pi\)
0.663344 + 0.748314i \(0.269137\pi\)
\(522\) 6.20725e47 4.06973e48i 0.0749602 0.491470i
\(523\) 3.03586e47i 0.0354202i 0.999843 + 0.0177101i \(0.00563759\pi\)
−0.999843 + 0.0177101i \(0.994362\pi\)
\(524\) 4.02329e48 1.28824e49i 0.453543 1.45222i
\(525\) −7.42033e47 −0.0808268
\(526\) 6.06488e47 + 9.25030e46i 0.0638379 + 0.00973672i
\(527\) 4.81757e48i 0.490046i
\(528\) −1.69636e48 1.17410e48i −0.166766 0.115423i
\(529\) 1.05221e49 0.999766
\(530\) 4.13264e47 2.70953e48i 0.0379544 0.248845i
\(531\) 8.76205e48i 0.777866i
\(532\) 3.72205e48 + 1.16243e48i 0.319428 + 0.0997606i
\(533\) 2.38474e48 0.197857
\(534\) −5.76209e48 8.78848e47i −0.462208 0.0704971i
\(535\) 4.75875e48i 0.369084i
\(536\) 1.65905e49 + 8.09754e48i 1.24421 + 0.607277i
\(537\) 1.57182e48 0.113989
\(538\) −2.20564e48 + 1.44611e49i −0.154687 + 1.01419i
\(539\) 7.97264e48i 0.540760i
\(540\) 9.71406e47 3.11039e48i 0.0637255 0.204046i
\(541\) −2.03164e49 −1.28913 −0.644564 0.764550i \(-0.722961\pi\)
−0.644564 + 0.764550i \(0.722961\pi\)
\(542\) −1.40452e49 2.14220e48i −0.862064 0.131484i
\(543\) 2.35738e48i 0.139969i
\(544\) −5.55288e48 + 5.88016e48i −0.318961 + 0.337761i
\(545\) 8.70020e48 0.483495
\(546\) 5.15973e46 3.38293e47i 0.00277434 0.0181897i
\(547\) 1.38426e49i 0.720187i −0.932916 0.360093i \(-0.882745\pi\)
0.932916 0.360093i \(-0.117255\pi\)
\(548\) 1.36996e49 + 4.27851e48i 0.689694 + 0.215398i
\(549\) −2.29372e49 −1.11748
\(550\) −1.08628e49 1.65683e48i −0.512171 0.0781175i
\(551\) 1.60906e49i 0.734250i
\(552\) −5.31896e46 + 1.08977e47i −0.00234922 + 0.00481316i
\(553\) −6.67958e48 −0.285560
\(554\) 1.15098e48 7.54633e48i 0.0476315 0.312292i
\(555\) 4.18959e48i 0.167841i
\(556\) −6.37634e48 + 2.04167e49i −0.247301 + 0.791844i
\(557\) −6.90930e48 −0.259442 −0.129721 0.991551i \(-0.541408\pi\)
−0.129721 + 0.991551i \(0.541408\pi\)
\(558\) −2.51678e49 3.83866e48i −0.915019 0.139561i
\(559\) 5.35831e48i 0.188632i
\(560\) 1.40223e48 2.02597e48i 0.0478008 0.0690635i
\(561\) −2.85412e48 −0.0942196
\(562\) −7.32895e48 + 4.80517e49i −0.234309 + 1.53622i
\(563\) 1.68532e49i 0.521834i −0.965361 0.260917i \(-0.915975\pi\)
0.965361 0.260917i \(-0.0840249\pi\)
\(564\) 5.82277e48 + 1.81851e48i 0.174625 + 0.0545370i
\(565\) −1.44889e48 −0.0420884
\(566\) 1.45634e49 + 2.22125e48i 0.409796 + 0.0625030i
\(567\) 6.13309e48i 0.167180i
\(568\) 5.03446e49 + 2.45723e49i 1.32948 + 0.648897i
\(569\) 6.09249e49 1.55874 0.779370 0.626564i \(-0.215539\pi\)
0.779370 + 0.626564i \(0.215539\pi\)
\(570\) 8.97505e47 5.88441e48i 0.0222479 0.145867i
\(571\) 1.00419e48i 0.0241194i −0.999927 0.0120597i \(-0.996161\pi\)
0.999927 0.0120597i \(-0.00383882\pi\)
\(572\) 1.51070e48 4.83717e48i 0.0351600 0.112580i
\(573\) −5.78893e48 −0.130561
\(574\) 1.13519e49 + 1.73142e48i 0.248117 + 0.0378433i
\(575\) 6.45898e47i 0.0136818i
\(576\) −2.62945e49 3.36946e49i −0.539834 0.691760i
\(577\) 4.23848e49 0.843423 0.421711 0.906730i \(-0.361430\pi\)
0.421711 + 0.906730i \(0.361430\pi\)
\(578\) 6.12996e48 4.01906e49i 0.118238 0.775216i
\(579\) 1.51867e49i 0.283955i
\(580\) −9.70497e48 3.03096e48i −0.175910 0.0549384i
\(581\) −2.68798e49 −0.472341
\(582\) 1.19402e49 + 1.82115e48i 0.203423 + 0.0310265i
\(583\) 2.71449e49i 0.448388i
\(584\) 2.66656e49 5.46335e49i 0.427091 0.875039i
\(585\) 3.74091e48 0.0580994
\(586\) 2.61428e48 1.71403e49i 0.0393727 0.258144i
\(587\) 6.40630e49i 0.935667i 0.883817 + 0.467833i \(0.154965\pi\)
−0.883817 + 0.467833i \(0.845035\pi\)
\(588\) −6.87577e48 + 2.20159e49i −0.0973934 + 0.311849i
\(589\) −9.95068e49 −1.36703
\(590\) 2.13923e49 + 3.26280e48i 0.285050 + 0.0434764i
\(591\) 4.26063e49i 0.550680i
\(592\) −9.66794e49 6.69146e49i −1.21211 0.838938i
\(593\) 8.41910e49 1.02396 0.511978 0.858999i \(-0.328913\pi\)
0.511978 + 0.858999i \(0.328913\pi\)
\(594\) 4.86592e48 3.19030e49i 0.0574129 0.376423i
\(595\) 3.40870e48i 0.0390196i
\(596\) −3.24786e49 1.01434e49i −0.360715 0.112655i
\(597\) −5.61373e49 −0.604942
\(598\) −2.94465e47 4.49125e46i −0.00307902 0.000469620i
\(599\) 1.23174e50i 1.24978i 0.780711 + 0.624892i \(0.214857\pi\)
−0.780711 + 0.624892i \(0.785143\pi\)
\(600\) 2.85681e49 + 1.39436e49i 0.281293 + 0.137294i
\(601\) 6.16907e49 0.589494 0.294747 0.955575i \(-0.404765\pi\)
0.294747 + 0.955575i \(0.404765\pi\)
\(602\) 3.89037e48 2.55069e49i 0.0360790 0.236549i
\(603\) 1.34970e50i 1.21486i
\(604\) −5.59224e49 + 1.79061e50i −0.488564 + 1.56435i
\(605\) −2.54803e49 −0.216077
\(606\) 2.05778e49 + 3.13858e48i 0.169392 + 0.0258360i
\(607\) 1.56513e50i 1.25071i −0.780342 0.625353i \(-0.784955\pi\)
0.780342 0.625353i \(-0.215045\pi\)
\(608\) −1.21455e50 1.14695e50i −0.942215 0.889772i
\(609\) −6.79971e48 −0.0512129
\(610\) −8.54131e48 + 5.60004e49i −0.0624579 + 0.409500i
\(611\) 1.49842e49i 0.106388i
\(612\) −5.64407e49 1.76270e49i −0.389105 0.121521i
\(613\) −2.39697e50 −1.60462 −0.802312 0.596905i \(-0.796397\pi\)
−0.802312 + 0.596905i \(0.796397\pi\)
\(614\) 1.68287e50 + 2.56675e49i 1.09400 + 0.166860i
\(615\) 1.75294e49i 0.110666i
\(616\) 1.07033e49 2.19293e49i 0.0656242 0.134453i
\(617\) 2.72430e50 1.62227 0.811134 0.584861i \(-0.198851\pi\)
0.811134 + 0.584861i \(0.198851\pi\)
\(618\) 1.40411e49 9.20596e49i 0.0812101 0.532447i
\(619\) 2.09904e50i 1.17920i −0.807695 0.589601i \(-0.799285\pi\)
0.807695 0.589601i \(-0.200715\pi\)
\(620\) −1.87439e49 + 6.00170e49i −0.102284 + 0.327509i
\(621\) −1.89693e48 −0.0100555
\(622\) 1.28302e50 + 1.95689e49i 0.660703 + 0.100772i
\(623\) 6.89431e49i 0.344910i
\(624\) −8.34336e48 + 1.20546e49i −0.0405526 + 0.0585911i
\(625\) 1.46917e50 0.693796
\(626\) 2.06071e48 1.35109e49i 0.00945538 0.0619934i
\(627\) 5.89519e49i 0.262834i
\(628\) 1.24391e50 + 3.88485e49i 0.538909 + 0.168307i
\(629\) −1.62663e50 −0.684823
\(630\) 1.78077e49 + 2.71607e48i 0.0728580 + 0.0111125i
\(631\) 3.26117e50i 1.29672i −0.761336 0.648358i \(-0.775456\pi\)
0.761336 0.648358i \(-0.224544\pi\)
\(632\) 2.57162e50 + 1.25516e50i 0.993802 + 0.485057i
\(633\) 6.93352e49 0.260428
\(634\) −6.91403e49 + 4.53312e50i −0.252420 + 1.65497i
\(635\) 6.22987e49i 0.221081i
\(636\) −2.34104e49 + 7.49587e49i −0.0807569 + 0.258579i
\(637\) −5.66551e49 −0.189989
\(638\) −9.95431e49 1.51825e49i −0.324518 0.0494963i
\(639\) 4.09572e50i 1.29812i
\(640\) −9.20556e49 + 5.16500e49i −0.283668 + 0.159159i
\(641\) 4.77352e49 0.143019 0.0715095 0.997440i \(-0.477218\pi\)
0.0715095 + 0.997440i \(0.477218\pi\)
\(642\) 2.05578e49 1.34786e50i 0.0598889 0.392657i
\(643\) 3.60916e50i 1.02237i −0.859470 0.511186i \(-0.829206\pi\)
0.859470 0.511186i \(-0.170794\pi\)
\(644\) −1.36912e48 4.27589e47i −0.00377134 0.00117783i
\(645\) −3.93872e49 −0.105507
\(646\) −2.28466e50 3.48462e49i −0.595163 0.0907757i
\(647\) 2.90885e50i 0.736962i 0.929635 + 0.368481i \(0.120122\pi\)
−0.929635 + 0.368481i \(0.879878\pi\)
\(648\) 1.15247e50 2.36122e50i 0.283975 0.581818i
\(649\) 2.14314e50 0.513625
\(650\) −1.17737e49 + 7.71935e49i −0.0274457 + 0.179945i
\(651\) 4.20504e49i 0.0953482i
\(652\) 2.94273e48 9.42246e48i 0.00649073 0.0207830i
\(653\) −7.81253e50 −1.67631 −0.838155 0.545432i \(-0.816365\pi\)
−0.838155 + 0.545432i \(0.816365\pi\)
\(654\) −2.46422e50 3.75849e49i −0.514375 0.0784537i
\(655\) 2.43684e50i 0.494861i
\(656\) −4.04511e50 2.79974e50i −0.799211 0.553157i
\(657\) 4.44463e50 0.854395
\(658\) −1.08792e49 + 7.13284e49i −0.0203484 + 0.133412i
\(659\) 7.80856e50i 1.42113i 0.703632 + 0.710565i \(0.251561\pi\)
−0.703632 + 0.710565i \(0.748439\pi\)
\(660\) −3.55565e49 1.11047e49i −0.0629692 0.0196659i
\(661\) −7.08006e50 −1.22014 −0.610072 0.792346i \(-0.708859\pi\)
−0.610072 + 0.792346i \(0.708859\pi\)
\(662\) −1.02073e51 1.55683e50i −1.71185 0.261095i
\(663\) 2.02819e49i 0.0331029i
\(664\) 1.03486e51 + 5.05099e50i 1.64383 + 0.802326i
\(665\) 7.04067e49 0.108849
\(666\) 1.29611e50 8.49783e50i 0.195032 1.27871i
\(667\) 5.91877e48i 0.00866894i
\(668\) 2.40931e50 7.71447e50i 0.343491 1.09984i
\(669\) 4.05311e50 0.562494
\(670\) 3.29525e50 + 5.02599e49i 0.445186 + 0.0679008i
\(671\) 5.61029e50i 0.737870i
\(672\) −4.84686e49 + 5.13254e49i −0.0620603 + 0.0657181i
\(673\) 1.17951e51 1.47038 0.735190 0.677861i \(-0.237093\pi\)
0.735190 + 0.677861i \(0.237093\pi\)
\(674\) 5.42320e49 3.55567e50i 0.0658229 0.431562i
\(675\) 4.97277e50i 0.587666i
\(676\) 7.95154e50 + 2.48334e50i 0.914978 + 0.285757i
\(677\) −3.48039e50 −0.389971 −0.194986 0.980806i \(-0.562466\pi\)
−0.194986 + 0.980806i \(0.562466\pi\)
\(678\) 4.10379e49 + 6.25919e48i 0.0447765 + 0.00682942i
\(679\) 1.42864e50i 0.151799i
\(680\) −6.40530e49 + 1.31234e50i −0.0662794 + 0.135796i
\(681\) 4.31601e50 0.434945
\(682\) −9.38911e49 + 6.15589e50i −0.0921522 + 0.604188i
\(683\) 1.02243e49i 0.00977376i 0.999988 + 0.00488688i \(0.00155555\pi\)
−0.999988 + 0.00488688i \(0.998444\pi\)
\(684\) 3.64085e50 1.16578e51i 0.338995 1.08544i
\(685\) 2.59142e50 0.235021
\(686\) −5.58653e50 8.52070e49i −0.493523 0.0752733i
\(687\) 1.67684e49i 0.0144301i
\(688\) −6.29079e50 + 9.08904e50i −0.527367 + 0.761949i
\(689\) −1.92897e50 −0.157536
\(690\) −3.30138e47 + 2.16452e48i −0.000262671 + 0.00172218i
\(691\) 1.93134e51i 1.49711i −0.663072 0.748556i \(-0.730748\pi\)
0.663072 0.748556i \(-0.269252\pi\)
\(692\) −7.73860e50 2.41684e50i −0.584457 0.182532i
\(693\) 1.78403e50 0.131281
\(694\) 9.80505e50 + 1.49549e50i 0.703039 + 0.107229i
\(695\) 3.86204e50i 0.269830i
\(696\) 2.61787e50 + 1.27774e50i 0.178231 + 0.0869911i
\(697\) −6.80591e50 −0.451540
\(698\) 7.42947e49 4.87107e50i 0.0480353 0.314939i
\(699\) 1.16414e50i 0.0733527i
\(700\) −1.12092e50 + 3.58912e50i −0.0688349 + 0.220406i
\(701\) −1.77887e51 −1.06468 −0.532342 0.846530i \(-0.678688\pi\)
−0.532342 + 0.846530i \(0.678688\pi\)
\(702\) −2.26709e50 3.45782e49i −0.132252 0.0201713i
\(703\) 3.35981e51i 1.91038i
\(704\) −8.24148e50 + 6.43146e50i −0.456770 + 0.356453i
\(705\) 1.10144e50 0.0595054
\(706\) −5.19664e50 + 3.40713e51i −0.273677 + 1.79434i
\(707\) 2.46213e50i 0.126404i
\(708\) −5.91813e50 1.84829e50i −0.296201 0.0925064i
\(709\) −8.79132e50 −0.428965 −0.214483 0.976728i \(-0.568807\pi\)
−0.214483 + 0.976728i \(0.568807\pi\)
\(710\) 9.99955e50 + 1.52516e50i 0.475697 + 0.0725544i
\(711\) 2.09211e51i 0.970356i
\(712\) −1.29551e51 + 2.65429e51i −0.585870 + 1.20035i
\(713\) 3.66025e49 0.0161399
\(714\) −1.47256e49 + 9.65471e49i −0.00633147 + 0.0415118i
\(715\) 9.15003e49i 0.0383631i
\(716\) 2.37439e50 7.60267e50i 0.0970773 0.310836i
\(717\) −1.03921e51 −0.414342
\(718\) 3.57307e51 + 5.44974e50i 1.38932 + 0.211902i
\(719\) 4.94759e50i 0.187618i 0.995590 + 0.0938088i \(0.0299042\pi\)
−0.995590 + 0.0938088i \(0.970096\pi\)
\(720\) −6.34553e50 4.39192e50i −0.234684 0.162431i
\(721\) 1.10149e51 0.397324
\(722\) 2.91189e50 1.90916e51i 0.102449 0.671695i
\(723\) 1.63650e50i 0.0561599i
\(724\) −1.14024e51 3.56107e50i −0.381681 0.119203i
\(725\) 1.55159e51 0.506633
\(726\) 7.21697e50 + 1.10075e50i 0.229877 + 0.0350614i
\(727\) 4.79107e51i 1.48872i −0.667779 0.744359i \(-0.732755\pi\)
0.667779 0.744359i \(-0.267245\pi\)
\(728\) −1.55834e50 7.60596e49i −0.0472386 0.0230563i
\(729\) 1.14306e51 0.338044
\(730\) 1.65508e50 1.08514e51i 0.0477538 0.313094i
\(731\) 1.52923e51i 0.430488i
\(732\) 4.83843e50 1.54924e51i 0.132894 0.425519i
\(733\) 1.73318e50 0.0464486 0.0232243 0.999730i \(-0.492607\pi\)
0.0232243 + 0.999730i \(0.492607\pi\)
\(734\) 5.43661e50 + 8.29205e49i 0.142167 + 0.0216837i
\(735\) 4.16454e50i 0.106266i
\(736\) 4.46759e49 + 4.21892e49i 0.0111243 + 0.0105051i
\(737\) 3.30128e51 0.802172
\(738\) 5.42298e50 3.55553e51i 0.128595 0.843121i
\(739\) 2.48623e51i 0.575363i −0.957726 0.287682i \(-0.907115\pi\)
0.957726 0.287682i \(-0.0928845\pi\)