Properties

Label 16.12.e.a.5.12
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM No

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Newspace parameters

Level: \( N \) = \( 16 = 2^{4} \)
Weight: \( k \) = \( 12 \)
Character orbit: \([\chi]\) = 16.e (of order \(4\) and degree \(2\))

Newform invariants

Self dual: No
Analytic conductor: \(12.293490889\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.12
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.445844 + 45.2526i) q^{2} +(-296.568 + 296.568i) q^{3} +(-2047.60 - 40.3512i) q^{4} +(-2867.98 - 2867.98i) q^{5} +(-13288.2 - 13552.7i) q^{6} -8380.90i q^{7} +(2738.91 - 92641.4i) q^{8} +1242.24i q^{9} +O(q^{10})\) \(q+(-0.445844 + 45.2526i) q^{2} +(-296.568 + 296.568i) q^{3} +(-2047.60 - 40.3512i) q^{4} +(-2867.98 - 2867.98i) q^{5} +(-13288.2 - 13552.7i) q^{6} -8380.90i q^{7} +(2738.91 - 92641.4i) q^{8} +1242.24i q^{9} +(131062. - 128505. i) q^{10} +(84515.5 + 84515.5i) q^{11} +(619220. - 595286. i) q^{12} +(-385486. + 385486. i) q^{13} +(379258. + 3736.57i) q^{14} +1.70110e6 q^{15} +(4.19105e6 + 165246. i) q^{16} +1.56551e6 q^{17} +(-56214.7 - 553.845i) q^{18} +(9.59253e6 - 9.59253e6i) q^{19} +(5.75676e6 + 5.98822e6i) q^{20} +(2.48550e6 + 2.48550e6i) q^{21} +(-3.86223e6 + 3.78687e6i) q^{22} -3.88214e7i q^{23} +(2.66622e7 + 2.82867e7i) q^{24} -3.23775e7i q^{25} +(-1.72724e7 - 1.76161e7i) q^{26} +(-5.29045e7 - 5.29045e7i) q^{27} +(-338179. + 1.71608e7i) q^{28} +(-8.81048e7 + 8.81048e7i) q^{29} +(-758426. + 7.69794e7i) q^{30} -7.23333e7 q^{31} +(-9.34639e6 + 1.89582e8i) q^{32} -5.01291e7 q^{33} +(-697975. + 7.08437e7i) q^{34} +(-2.40363e7 + 2.40363e7i) q^{35} +(50125.9 - 2.54362e6i) q^{36} +(-9.98585e7 - 9.98585e7i) q^{37} +(4.29810e8 + 4.38364e8i) q^{38} -2.28645e8i q^{39} +(-2.73549e8 + 2.57839e8i) q^{40} -1.13304e9i q^{41} +(-1.13584e8 + 1.11367e8i) q^{42} +(-1.05585e9 - 1.05585e9i) q^{43} +(-1.69644e8 - 1.76465e8i) q^{44} +(3.56273e6 - 3.56273e6i) q^{45} +(1.75677e9 + 1.73083e7i) q^{46} +1.33450e9 q^{47} +(-1.29194e9 + 1.19392e9i) q^{48} +1.90709e9 q^{49} +(1.46517e9 + 1.44353e7i) q^{50} +(-4.64281e8 + 4.64281e8i) q^{51} +(8.04877e8 - 7.73767e8i) q^{52} +(2.50213e9 + 2.50213e9i) q^{53} +(2.41765e9 - 2.37048e9i) q^{54} -4.84778e8i q^{55} +(-7.76419e8 - 2.29545e7i) q^{56} +5.68967e9i q^{57} +(-3.94769e9 - 4.02626e9i) q^{58} +(-3.81835e9 - 3.81835e9i) q^{59} +(-3.48318e9 - 6.86415e7i) q^{60} +(-7.73084e9 + 7.73084e9i) q^{61} +(3.22493e7 - 3.27327e9i) q^{62} +1.04111e7 q^{63} +(-8.57493e9 - 5.07473e8i) q^{64} +2.21114e9 q^{65} +(2.23498e7 - 2.26848e9i) q^{66} +(2.91020e9 - 2.91020e9i) q^{67} +(-3.20555e9 - 6.31704e7i) q^{68} +(1.15132e10 + 1.15132e10i) q^{69} +(-1.07699e9 - 1.09842e9i) q^{70} -1.77198e10i q^{71} +(1.15083e8 + 3.40239e6i) q^{72} +2.04116e10i q^{73} +(4.56338e9 - 4.47434e9i) q^{74} +(9.60211e9 + 9.60211e9i) q^{75} +(-2.00287e10 + 1.92546e10i) q^{76} +(7.08316e8 - 7.08316e8i) q^{77} +(1.03468e10 + 1.01940e8i) q^{78} -3.60858e10 q^{79} +(-1.15459e10 - 1.24938e10i) q^{80} +3.11595e10 q^{81} +(5.12730e10 + 5.05158e8i) q^{82} +(5.73137e9 - 5.73137e9i) q^{83} +(-4.98903e9 - 5.18962e9i) q^{84} +(-4.48987e9 - 4.48987e9i) q^{85} +(4.82508e10 - 4.73094e10i) q^{86} -5.22581e10i q^{87} +(8.06112e9 - 7.59816e9i) q^{88} -1.07134e10i q^{89} +(1.59634e8 + 1.62811e8i) q^{90} +(3.23072e9 + 3.23072e9i) q^{91} +(-1.56649e9 + 7.94908e10i) q^{92} +(2.14517e10 - 2.14517e10i) q^{93} +(-5.94978e8 + 6.03896e10i) q^{94} -5.50224e10 q^{95} +(-5.34521e10 - 5.89958e10i) q^{96} -7.36209e9 q^{97} +(-8.50263e8 + 8.63007e10i) q^{98} +(-1.04989e8 + 1.04989e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} + O(q^{10}) \) \( 42q - 2q^{2} - 2q^{3} + 3080q^{4} - 2q^{5} + 30352q^{6} + 74836q^{8} - 988948q^{10} - 540846q^{11} + 2300260q^{12} - 2q^{13} - 1829956q^{14} - 6075004q^{15} - 3721448q^{16} - 4q^{17} - 32219106q^{18} - 11291290q^{19} + 68655164q^{20} + 354292q^{21} - 85011388q^{22} - 66180944q^{24} + 305685384q^{26} - 66463304q^{27} - 322075880q^{28} + 77673206q^{29} + 290643636q^{30} + 343549808q^{31} + 404698568q^{32} - 4q^{33} - 882461836q^{34} - 434731684q^{35} + 1854387628q^{36} - 522762058q^{37} - 1276252832q^{38} - 483241016q^{40} + 2372079160q^{42} + 3824193658q^{43} - 2657283740q^{44} + 97301954q^{45} - 1032658964q^{46} - 4586900144q^{47} - 1058870552q^{48} - 8474257474q^{49} + 6515930886q^{50} + 7074245796q^{51} - 13915491564q^{52} - 2100608058q^{53} + 4385621536q^{54} + 12910845976q^{56} - 21491153128q^{58} + 955824746q^{59} + 25615752768q^{60} + 2150827022q^{61} - 15814519760q^{62} + 27758037828q^{63} + 9674332160q^{64} - 1884965292q^{65} + 10932459412q^{66} - 3186519018q^{67} + 13817664656q^{68} - 16193060732q^{69} - 27206453120q^{70} - 20773133628q^{72} + 14141420908q^{74} + 28890034486q^{75} - 11786004940q^{76} - 22711870540q^{77} + 37031200508q^{78} + 48011833792q^{79} - 8952586328q^{80} - 90656394430q^{81} - 81555388352q^{82} + 55713221118q^{83} + 61178517160q^{84} - 84575506252q^{85} + 10047297860q^{86} - 162855622152q^{88} + 160133627736q^{90} - 147369662716q^{91} - 169766721928q^{92} - 69689773328q^{93} + 160320530128q^{94} + 375702304500q^{95} + 230764310192q^{96} - 4q^{97} - 108887063494q^{98} - 286271331106q^{99} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/16\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(15\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.445844 + 45.2526i −0.00985185 + 0.999951i
\(3\) −296.568 + 296.568i −0.704623 + 0.704623i −0.965399 0.260776i \(-0.916022\pi\)
0.260776 + 0.965399i \(0.416022\pi\)
\(4\) −2047.60 40.3512i −0.999806 0.0197027i
\(5\) −2867.98 2867.98i −0.410432 0.410432i 0.471457 0.881889i \(-0.343728\pi\)
−0.881889 + 0.471457i \(0.843728\pi\)
\(6\) −13288.2 13552.7i −0.697647 0.711531i
\(7\) 8380.90i 0.188474i −0.995550 0.0942370i \(-0.969959\pi\)
0.995550 0.0942370i \(-0.0300411\pi\)
\(8\) 2738.91 92641.4i 0.0295517 0.999563i
\(9\) 1242.24i 0.00701249i
\(10\) 131062. 128505.i 0.414456 0.406369i
\(11\) 84515.5 + 84515.5i 0.158226 + 0.158226i 0.781780 0.623554i \(-0.214312\pi\)
−0.623554 + 0.781780i \(0.714312\pi\)
\(12\) 619220. 595286.i 0.718369 0.690603i
\(13\) −385486. + 385486.i −0.287952 + 0.287952i −0.836270 0.548318i \(-0.815268\pi\)
0.548318 + 0.836270i \(0.315268\pi\)
\(14\) 379258. + 3736.57i 0.188465 + 0.00185682i
\(15\) 1.70110e6 0.578400
\(16\) 4.19105e6 + 165246.i 0.999224 + 0.0393978i
\(17\) 1.56551e6 0.267416 0.133708 0.991021i \(-0.457311\pi\)
0.133708 + 0.991021i \(0.457311\pi\)
\(18\) −56214.7 553.845i −0.00701215 6.90860e-5i
\(19\) 9.59253e6 9.59253e6i 0.888768 0.888768i −0.105637 0.994405i \(-0.533688\pi\)
0.994405 + 0.105637i \(0.0336882\pi\)
\(20\) 5.75676e6 + 5.98822e6i 0.402266 + 0.418439i
\(21\) 2.48550e6 + 2.48550e6i 0.132803 + 0.132803i
\(22\) −3.86223e6 + 3.78687e6i −0.159777 + 0.156659i
\(23\) 3.88214e7i 1.25767i −0.777537 0.628837i \(-0.783531\pi\)
0.777537 0.628837i \(-0.216469\pi\)
\(24\) 2.66622e7 + 2.82867e7i 0.683493 + 0.725138i
\(25\) 3.23775e7i 0.663091i
\(26\) −1.72724e7 1.76161e7i −0.285101 0.290775i
\(27\) −5.29045e7 5.29045e7i −0.709564 0.709564i
\(28\) −338179. + 1.71608e7i −0.00371345 + 0.188437i
\(29\) −8.81048e7 + 8.81048e7i −0.797647 + 0.797647i −0.982724 0.185077i \(-0.940746\pi\)
0.185077 + 0.982724i \(0.440746\pi\)
\(30\) −758426. + 7.69794e7i −0.00569831 + 0.578372i
\(31\) −7.23333e7 −0.453784 −0.226892 0.973920i \(-0.572856\pi\)
−0.226892 + 0.973920i \(0.572856\pi\)
\(32\) −9.34639e6 + 1.89582e8i −0.0492401 + 0.998787i
\(33\) −5.01291e7 −0.222979
\(34\) −697975. + 7.08437e7i −0.00263455 + 0.267403i
\(35\) −2.40363e7 + 2.40363e7i −0.0773558 + 0.0773558i
\(36\) 50125.9 2.54362e6i 0.000138165 0.00701113i
\(37\) −9.98585e7 9.98585e7i −0.236742 0.236742i 0.578758 0.815500i \(-0.303538\pi\)
−0.815500 + 0.578758i \(0.803538\pi\)
\(38\) 4.29810e8 + 4.38364e8i 0.879968 + 0.897480i
\(39\) 2.28645e8i 0.405795i
\(40\) −2.73549e8 + 2.57839e8i −0.422382 + 0.398124i
\(41\) 1.13304e9i 1.52733i −0.645611 0.763667i \(-0.723397\pi\)
0.645611 0.763667i \(-0.276603\pi\)
\(42\) −1.13584e8 + 1.11367e8i −0.134105 + 0.131488i
\(43\) −1.05585e9 1.05585e9i −1.09528 1.09528i −0.994954 0.100329i \(-0.968010\pi\)
−0.100329 0.994954i \(-0.531990\pi\)
\(44\) −1.69644e8 1.76465e8i −0.155077 0.161312i
\(45\) 3.56273e6 3.56273e6i 0.00287815 0.00287815i
\(46\) 1.75677e9 + 1.73083e7i 1.25761 + 0.0123904i
\(47\) 1.33450e9 0.848750 0.424375 0.905486i \(-0.360494\pi\)
0.424375 + 0.905486i \(0.360494\pi\)
\(48\) −1.29194e9 + 1.19392e9i −0.731837 + 0.676315i
\(49\) 1.90709e9 0.964478
\(50\) 1.46517e9 + 1.44353e7i 0.663058 + 0.00653267i
\(51\) −4.64281e8 + 4.64281e8i −0.188428 + 0.188428i
\(52\) 8.04877e8 7.73767e8i 0.293570 0.282223i
\(53\) 2.50213e9 + 2.50213e9i 0.821850 + 0.821850i 0.986373 0.164523i \(-0.0526085\pi\)
−0.164523 + 0.986373i \(0.552608\pi\)
\(54\) 2.41765e9 2.37048e9i 0.716520 0.702539i
\(55\) 4.84778e8i 0.129882i
\(56\) −7.76419e8 2.29545e7i −0.188392 0.00556973i
\(57\) 5.68967e9i 1.25249i
\(58\) −3.94769e9 4.02626e9i −0.789750 0.805466i
\(59\) −3.81835e9 3.81835e9i −0.695329 0.695329i 0.268071 0.963399i \(-0.413614\pi\)
−0.963399 + 0.268071i \(0.913614\pi\)
\(60\) −3.48318e9 6.86415e7i −0.578288 0.0113961i
\(61\) −7.73084e9 + 7.73084e9i −1.17196 + 1.17196i −0.190218 + 0.981742i \(0.560919\pi\)
−0.981742 + 0.190218i \(0.939081\pi\)
\(62\) 3.22493e7 3.27327e9i 0.00447061 0.453762i
\(63\) 1.04111e7 0.00132167
\(64\) −8.57493e9 5.07473e8i −0.998253 0.0590776i
\(65\) 2.21114e9 0.236370
\(66\) 2.23498e7 2.26848e9i 0.00219675 0.222968i
\(67\) 2.91020e9 2.91020e9i 0.263337 0.263337i −0.563071 0.826408i \(-0.690380\pi\)
0.826408 + 0.563071i \(0.190380\pi\)
\(68\) −3.20555e9 6.31704e7i −0.267365 0.00526884i
\(69\) 1.15132e10 + 1.15132e10i 0.886186 + 0.886186i
\(70\) −1.07699e9 1.09842e9i −0.0765900 0.0781142i
\(71\) 1.77198e10i 1.16557i −0.812628 0.582783i \(-0.801964\pi\)
0.812628 0.582783i \(-0.198036\pi\)
\(72\) 1.15083e8 + 3.40239e6i 0.00700943 + 0.000207231i
\(73\) 2.04116e10i 1.15239i 0.817311 + 0.576197i \(0.195464\pi\)
−0.817311 + 0.576197i \(0.804536\pi\)
\(74\) 4.56338e9 4.47434e9i 0.239063 0.234398i
\(75\) 9.60211e9 + 9.60211e9i 0.467229 + 0.467229i
\(76\) −2.00287e10 + 1.92546e10i −0.906106 + 0.871084i
\(77\) 7.08316e8 7.08316e8i 0.0298214 0.0298214i
\(78\) 1.03468e10 + 1.01940e8i 0.405776 + 0.00399783i
\(79\) −3.60858e10 −1.31943 −0.659717 0.751514i \(-0.729324\pi\)
−0.659717 + 0.751514i \(0.729324\pi\)
\(80\) −1.15459e10 1.24938e10i −0.393944 0.426284i
\(81\) 3.11595e10 0.992938
\(82\) 5.12730e10 + 5.05158e8i 1.52726 + 0.0150471i
\(83\) 5.73137e9 5.73137e9i 0.159709 0.159709i −0.622729 0.782438i \(-0.713976\pi\)
0.782438 + 0.622729i \(0.213976\pi\)
\(84\) −4.98903e9 5.18962e9i −0.130161 0.135394i
\(85\) −4.48987e9 4.48987e9i −0.109756 0.109756i
\(86\) 4.82508e10 4.73094e10i 1.10602 1.08444i
\(87\) 5.22581e10i 1.12408i
\(88\) 8.06112e9 7.59816e9i 0.162832 0.153481i
\(89\) 1.07134e10i 0.203367i −0.994817 0.101684i \(-0.967577\pi\)
0.994817 0.101684i \(-0.0324230\pi\)
\(90\) 1.59634e8 + 1.62811e8i 0.00284966 + 0.00290637i
\(91\) 3.23072e9 + 3.23072e9i 0.0542715 + 0.0542715i
\(92\) −1.56649e9 + 7.94908e10i −0.0247796 + 1.25743i
\(93\) 2.14517e10 2.14517e10i 0.319746 0.319746i
\(94\) −5.94978e8 + 6.03896e10i −0.00836176 + 0.848709i
\(95\) −5.50224e10 −0.729558
\(96\) −5.34521e10 5.89958e10i −0.669073 0.738464i
\(97\) −7.36209e9 −0.0870475 −0.0435238 0.999052i \(-0.513858\pi\)
−0.0435238 + 0.999052i \(0.513858\pi\)
\(98\) −8.50263e8 + 8.63007e10i −0.00950188 + 0.964431i
\(99\) −1.04989e8 + 1.04989e8i −0.00110956 + 0.00110956i
\(100\) −1.30647e9 + 6.62962e10i −0.0130647 + 0.662962i
\(101\) −8.80812e10 8.80812e10i −0.833903 0.833903i 0.154145 0.988048i \(-0.450738\pi\)
−0.988048 + 0.154145i \(0.950738\pi\)
\(102\) −2.08029e10 2.12169e10i −0.186562 0.190275i
\(103\) 1.00874e11i 0.857383i −0.903451 0.428691i \(-0.858975\pi\)
0.903451 0.428691i \(-0.141025\pi\)
\(104\) 3.46562e10 + 3.67678e10i 0.279317 + 0.296336i
\(105\) 1.42568e10i 0.109013i
\(106\) −1.14344e11 + 1.12112e11i −0.829907 + 0.813714i
\(107\) 3.90961e10 + 3.90961e10i 0.269478 + 0.269478i 0.828890 0.559412i \(-0.188973\pi\)
−0.559412 + 0.828890i \(0.688973\pi\)
\(108\) 1.06193e11 + 1.10462e11i 0.695446 + 0.723407i
\(109\) −1.52858e11 + 1.52858e11i −0.951576 + 0.951576i −0.998881 0.0473045i \(-0.984937\pi\)
0.0473045 + 0.998881i \(0.484937\pi\)
\(110\) 2.19375e10 + 2.16135e8i 0.129876 + 0.00127958i
\(111\) 5.92296e10 0.333628
\(112\) 1.38491e9 3.51248e10i 0.00742547 0.188328i
\(113\) 8.86408e10 0.452587 0.226293 0.974059i \(-0.427339\pi\)
0.226293 + 0.974059i \(0.427339\pi\)
\(114\) −2.57472e11 2.53670e9i −1.25243 0.0123394i
\(115\) −1.11339e11 + 1.11339e11i −0.516190 + 0.516190i
\(116\) 1.83959e11 1.76848e11i 0.813208 0.781776i
\(117\) −4.78867e8 4.78867e8i −0.00201926 0.00201926i
\(118\) 1.74493e11 1.71088e11i 0.702145 0.688445i
\(119\) 1.31204e10i 0.0504011i
\(120\) 4.65916e9 1.57593e11i 0.0170927 0.578148i
\(121\) 2.71026e11i 0.949929i
\(122\) −3.46394e11 3.53288e11i −1.16036 1.18345i
\(123\) 3.36023e11 + 3.36023e11i 1.07619 + 1.07619i
\(124\) 1.48110e11 + 2.91873e9i 0.453695 + 0.00894078i
\(125\) −2.32896e11 + 2.32896e11i −0.682586 + 0.682586i
\(126\) −4.64172e6 + 4.71130e8i −1.30209e−5 + 0.00132161i
\(127\) 1.85470e11 0.498142 0.249071 0.968485i \(-0.419875\pi\)
0.249071 + 0.968485i \(0.419875\pi\)
\(128\) 2.67876e10 3.87812e11i 0.0689094 0.997623i
\(129\) 6.26263e11 1.54352
\(130\) −9.85821e8 + 1.00060e11i −0.00232868 + 0.236358i
\(131\) −1.99872e11 + 1.99872e11i −0.452646 + 0.452646i −0.896232 0.443586i \(-0.853706\pi\)
0.443586 + 0.896232i \(0.353706\pi\)
\(132\) 1.02645e11 + 2.02277e9i 0.222936 + 0.00439329i
\(133\) −8.03940e10 8.03940e10i −0.167510 0.167510i
\(134\) 1.30397e11 + 1.32992e11i 0.260730 + 0.265918i
\(135\) 3.03458e11i 0.582456i
\(136\) 4.28780e9 1.45032e11i 0.00790262 0.267300i
\(137\) 1.03458e12i 1.83147i −0.401786 0.915734i \(-0.631610\pi\)
0.401786 0.915734i \(-0.368390\pi\)
\(138\) −5.26134e11 + 5.15868e11i −0.894874 + 0.877413i
\(139\) 7.75928e11 + 7.75928e11i 1.26835 + 1.26835i 0.946938 + 0.321415i \(0.104158\pi\)
0.321415 + 0.946938i \(0.395842\pi\)
\(140\) 5.01866e10 4.82469e10i 0.0788649 0.0758167i
\(141\) −3.95769e11 + 3.95769e11i −0.598049 + 0.598049i
\(142\) 8.01866e11 + 7.90024e9i 1.16551 + 0.0114830i
\(143\) −6.51591e10 −0.0911228
\(144\) −2.05276e8 + 5.20629e9i −0.000276277 + 0.00700704i
\(145\) 5.05366e11 0.654760
\(146\) −9.23678e11 9.10037e9i −1.15234 0.0113532i
\(147\) −5.65580e11 + 5.65580e11i −0.679593 + 0.679593i
\(148\) 2.00441e11 + 2.08500e11i 0.232032 + 0.241361i
\(149\) −8.48328e11 8.48328e11i −0.946323 0.946323i 0.0523077 0.998631i \(-0.483342\pi\)
−0.998631 + 0.0523077i \(0.983342\pi\)
\(150\) −4.38802e11 + 4.30240e11i −0.471809 + 0.462603i
\(151\) 8.18468e11i 0.848454i −0.905556 0.424227i \(-0.860546\pi\)
0.905556 0.424227i \(-0.139454\pi\)
\(152\) −8.62392e11 9.14938e11i −0.862115 0.914644i
\(153\) 1.94475e9i 0.00187526i
\(154\) 3.17374e10 + 3.23690e10i 0.0295262 + 0.0301138i
\(155\) 2.07451e11 + 2.07451e11i 0.186247 + 0.186247i
\(156\) −9.22612e9 + 4.68175e11i −0.00799528 + 0.405717i
\(157\) −5.92527e11 + 5.92527e11i −0.495747 + 0.495747i −0.910111 0.414364i \(-0.864004\pi\)
0.414364 + 0.910111i \(0.364004\pi\)
\(158\) 1.60886e10 1.63298e12i 0.0129989 1.31937i
\(159\) −1.48410e12 −1.15819
\(160\) 5.70524e11 5.16914e11i 0.430144 0.389725i
\(161\) −3.25358e11 −0.237039
\(162\) −1.38922e10 + 1.41005e12i −0.00978228 + 0.992890i
\(163\) 2.74040e11 2.74040e11i 0.186544 0.186544i −0.607656 0.794200i \(-0.707890\pi\)
0.794200 + 0.607656i \(0.207890\pi\)
\(164\) −4.57195e10 + 2.32001e12i −0.0300926 + 1.52704i
\(165\) 1.43770e11 + 1.43770e11i 0.0915177 + 0.0915177i
\(166\) 2.56804e11 + 2.61915e11i 0.158128 + 0.161275i
\(167\) 2.53745e12i 1.51167i −0.654762 0.755836i \(-0.727231\pi\)
0.654762 0.755836i \(-0.272769\pi\)
\(168\) 2.37068e11 2.23453e11i 0.136670 0.128821i
\(169\) 1.49496e12i 0.834167i
\(170\) 2.05180e11 2.01177e11i 0.110832 0.108670i
\(171\) 1.19162e10 + 1.19162e10i 0.00623247 + 0.00623247i
\(172\) 2.11936e12 + 2.20457e12i 1.07349 + 1.11665i
\(173\) 5.71348e11 5.71348e11i 0.280315 0.280315i −0.552919 0.833235i \(-0.686486\pi\)
0.833235 + 0.552919i \(0.186486\pi\)
\(174\) 2.36482e12 + 2.32989e10i 1.12403 + 0.0110743i
\(175\) −2.71352e11 −0.124975
\(176\) 3.40243e11 + 3.68174e11i 0.151869 + 0.164336i
\(177\) 2.26480e12 0.979889
\(178\) 4.84809e11 + 4.77649e9i 0.203358 + 0.00200354i
\(179\) 1.62660e12 1.62660e12i 0.661592 0.661592i −0.294163 0.955755i \(-0.595041\pi\)
0.955755 + 0.294163i \(0.0950410\pi\)
\(180\) −7.43881e9 + 7.15129e9i −0.00293430 + 0.00282089i
\(181\) −5.16199e11 5.16199e11i −0.197508 0.197508i 0.601423 0.798931i \(-0.294601\pi\)
−0.798931 + 0.601423i \(0.794601\pi\)
\(182\) −1.47639e11 + 1.44758e11i −0.0548035 + 0.0537342i
\(183\) 4.58543e12i 1.65158i
\(184\) −3.59647e12 1.06328e11i −1.25712 0.0371664i
\(185\) 5.72785e11i 0.194333i
\(186\) 9.61182e11 + 9.80310e11i 0.316581 + 0.322881i
\(187\) 1.32310e11 + 1.32310e11i 0.0423121 + 0.0423121i
\(188\) −2.73252e12 5.38486e10i −0.848586 0.0167227i
\(189\) −4.43387e11 + 4.43387e11i −0.133734 + 0.133734i
\(190\) 2.45314e10 2.48991e12i 0.00718749 0.729522i
\(191\) −2.22938e12 −0.634602 −0.317301 0.948325i \(-0.602776\pi\)
−0.317301 + 0.948325i \(0.602776\pi\)
\(192\) 2.69355e12 2.39255e12i 0.745020 0.661765i
\(193\) 1.44625e11 0.0388758 0.0194379 0.999811i \(-0.493812\pi\)
0.0194379 + 0.999811i \(0.493812\pi\)
\(194\) 3.28234e9 3.33154e11i 0.000857579 0.0870433i
\(195\) −6.55751e11 + 6.55751e11i −0.166552 + 0.166552i
\(196\) −3.90496e12 7.69533e10i −0.964290 0.0190028i
\(197\) 2.27490e12 + 2.27490e12i 0.546257 + 0.546257i 0.925356 0.379099i \(-0.123766\pi\)
−0.379099 + 0.925356i \(0.623766\pi\)
\(198\) −4.70421e9 4.79782e9i −0.00109857 0.00112043i
\(199\) 3.80350e12i 0.863956i 0.901884 + 0.431978i \(0.142184\pi\)
−0.901884 + 0.431978i \(0.857816\pi\)
\(200\) −2.99949e12 8.86789e10i −0.662801 0.0195955i
\(201\) 1.72614e12i 0.371106i
\(202\) 4.02518e12 3.94664e12i 0.842078 0.825647i
\(203\) 7.38398e11 + 7.38398e11i 0.150336 + 0.150336i
\(204\) 9.69397e11 9.31929e11i 0.192104 0.184679i
\(205\) −3.24954e12 + 3.24954e12i −0.626867 + 0.626867i
\(206\) 4.56482e12 + 4.49741e10i 0.857341 + 0.00844680i
\(207\) 4.82255e10 0.00881942
\(208\) −1.67929e12 + 1.55189e12i −0.299073 + 0.276384i
\(209\) 1.62143e12 0.281252
\(210\) 6.45156e11 + 6.35629e9i 0.109008 + 0.00107398i
\(211\) −4.90777e12 + 4.90777e12i −0.807849 + 0.807849i −0.984308 0.176459i \(-0.943536\pi\)
0.176459 + 0.984308i \(0.443536\pi\)
\(212\) −5.02240e12 5.22433e12i −0.805498 0.837883i
\(213\) 5.25511e12 + 5.25511e12i 0.821285 + 0.821285i
\(214\) −1.78663e12 + 1.75177e12i −0.272120 + 0.266810i
\(215\) 6.05633e12i 0.899080i
\(216\) −5.04605e12 + 4.75625e12i −0.730223 + 0.688286i
\(217\) 6.06218e11i 0.0855264i
\(218\) −6.84909e12 6.98540e12i −0.942155 0.960905i
\(219\) −6.05341e12 6.05341e12i −0.812003 0.812003i
\(220\) −1.95614e10 + 9.92633e11i −0.00255903 + 0.129857i
\(221\) −6.03484e11 + 6.03484e11i −0.0770031 + 0.0770031i
\(222\) −2.64071e10 + 2.68030e12i −0.00328685 + 0.333612i
\(223\) 4.65341e12 0.565060 0.282530 0.959259i \(-0.408826\pi\)
0.282530 + 0.959259i \(0.408826\pi\)
\(224\) 1.58887e12 + 7.83312e10i 0.188245 + 0.00928048i
\(225\) 4.02206e10 0.00464992
\(226\) −3.95199e10 + 4.01123e12i −0.00445882 + 0.452565i
\(227\) 7.96621e12 7.96621e12i 0.877222 0.877222i −0.116024 0.993246i \(-0.537015\pi\)
0.993246 + 0.116024i \(0.0370149\pi\)
\(228\) 2.29585e11 1.16502e13i 0.0246775 1.25225i
\(229\) −1.29670e12 1.29670e12i −0.136064 0.136064i 0.635794 0.771858i \(-0.280673\pi\)
−0.771858 + 0.635794i \(0.780673\pi\)
\(230\) −4.98875e12 5.08803e12i −0.511080 0.521250i
\(231\) 4.20127e11i 0.0420257i
\(232\) 7.92084e12 + 8.40347e12i 0.773727 + 0.820870i
\(233\) 4.73649e12i 0.451855i −0.974144 0.225928i \(-0.927459\pi\)
0.974144 0.225928i \(-0.0725413\pi\)
\(234\) 2.18835e10 2.14565e10i 0.00203906 0.00199927i
\(235\) −3.82732e12 3.82732e12i −0.348355 0.348355i
\(236\) 7.66440e12 + 7.97255e12i 0.681494 + 0.708894i
\(237\) 1.07019e13 1.07019e13i 0.929704 0.929704i
\(238\) 5.93734e11 + 5.84966e9i 0.0503986 + 0.000496543i
\(239\) 1.73692e13 1.44076 0.720381 0.693578i \(-0.243967\pi\)
0.720381 + 0.693578i \(0.243967\pi\)
\(240\) 7.12940e12 + 2.81101e11i 0.577951 + 0.0227877i
\(241\) −1.51130e13 −1.19745 −0.598725 0.800955i \(-0.704326\pi\)
−0.598725 + 0.800955i \(0.704326\pi\)
\(242\) 1.22646e13 + 1.20835e11i 0.949883 + 0.00935856i
\(243\) 1.30983e11 1.30983e11i 0.00991697 0.00991697i
\(244\) 1.61416e13 1.55177e13i 1.19482 1.14864i
\(245\) −5.46949e12 5.46949e12i −0.395853 0.395853i
\(246\) −1.53557e13 + 1.50561e13i −1.08674 + 1.06554i
\(247\) 7.39557e12i 0.511845i
\(248\) −1.98114e11 + 6.70106e12i −0.0134101 + 0.453585i
\(249\) 3.39948e12i 0.225069i
\(250\) −1.04353e13 1.06430e13i −0.675828 0.689278i
\(251\) −7.55409e12 7.55409e12i −0.478604 0.478604i 0.426081 0.904685i \(-0.359894\pi\)
−0.904685 + 0.426081i \(0.859894\pi\)
\(252\) −2.13178e10 4.20101e8i −0.00132142 2.60406e-5i
\(253\) 3.28101e12 3.28101e12i 0.198996 0.198996i
\(254\) −8.26906e10 + 8.39301e12i −0.00490762 + 0.498118i
\(255\) 2.66310e12 0.154674
\(256\) 1.75376e13 + 1.38511e12i 0.996896 + 0.0787345i
\(257\) −2.57756e13 −1.43409 −0.717045 0.697027i \(-0.754506\pi\)
−0.717045 + 0.697027i \(0.754506\pi\)
\(258\) −2.79216e11 + 2.83401e13i −0.0152066 + 1.54345i
\(259\) −8.36904e11 + 8.36904e11i −0.0446197 + 0.0446197i
\(260\) −4.52753e12 8.92220e10i −0.236324 0.00465713i
\(261\) −1.09447e11 1.09447e11i −0.00559349 0.00559349i
\(262\) −8.95560e12 9.13382e12i −0.448165 0.457084i
\(263\) 3.41102e13i 1.67158i 0.549047 + 0.835791i \(0.314991\pi\)
−0.549047 + 0.835791i \(0.685009\pi\)
\(264\) −1.37299e11 + 4.64404e12i −0.00658941 + 0.222881i
\(265\) 1.43521e13i 0.674628i
\(266\) 3.67388e12 3.60220e12i 0.169152 0.165851i
\(267\) 3.17724e12 + 3.17724e12i 0.143297 + 0.143297i
\(268\) −6.07637e12 + 5.84151e12i −0.268474 + 0.258097i
\(269\) 2.71092e13 2.71092e13i 1.17349 1.17349i 0.192117 0.981372i \(-0.438465\pi\)
0.981372 0.192117i \(-0.0615354\pi\)
\(270\) −1.37323e13 1.35295e11i −0.582428 0.00573827i
\(271\) −2.37221e13 −0.985876 −0.492938 0.870065i \(-0.664077\pi\)
−0.492938 + 0.870065i \(0.664077\pi\)
\(272\) 6.56115e12 + 2.58696e11i 0.267209 + 0.0105356i
\(273\) −1.91625e12 −0.0764819
\(274\) 4.68173e13 + 4.61259e11i 1.83138 + 0.0180433i
\(275\) 2.73640e12 2.73640e12i 0.104918 0.104918i
\(276\) −2.31098e13 2.40390e13i −0.868554 0.903474i
\(277\) −2.86303e13 2.86303e13i −1.05484 1.05484i −0.998406 0.0564356i \(-0.982026\pi\)
−0.0564356 0.998406i \(-0.517974\pi\)
\(278\) −3.54588e13 + 3.47669e13i −1.28079 + 1.25580i
\(279\) 8.98554e10i 0.00318215i
\(280\) 2.16092e12 + 2.29259e12i 0.0750360 + 0.0796080i
\(281\) 1.73419e13i 0.590488i 0.955422 + 0.295244i \(0.0954010\pi\)
−0.955422 + 0.295244i \(0.904599\pi\)
\(282\) −1.77332e13 1.80861e13i −0.592128 0.603912i
\(283\) 3.78495e12 + 3.78495e12i 0.123947 + 0.123947i 0.766359 0.642412i \(-0.222066\pi\)
−0.642412 + 0.766359i \(0.722066\pi\)
\(284\) −7.15014e11 + 3.62830e13i −0.0229648 + 1.16534i
\(285\) 1.63179e13 1.63179e13i 0.514063 0.514063i
\(286\) 2.90508e10 2.94862e12i 0.000897728 0.0911184i
\(287\) −9.49589e12 −0.287863
\(288\) −2.35507e11 1.16105e10i −0.00700398 0.000345296i
\(289\) −3.18211e13 −0.928488
\(290\) −2.25314e11 + 2.28692e13i −0.00645060 + 0.654728i
\(291\) 2.18336e12 2.18336e12i 0.0613357 0.0613357i
\(292\) 8.23632e11 4.17948e13i 0.0227053 1.15217i
\(293\) 3.44335e13 + 3.44335e13i 0.931556 + 0.931556i 0.997803 0.0662477i \(-0.0211027\pi\)
−0.0662477 + 0.997803i \(0.521103\pi\)
\(294\) −2.53418e13 2.58462e13i −0.672865 0.686255i
\(295\) 2.19020e13i 0.570771i
\(296\) −9.52454e12 + 8.97753e12i −0.243635 + 0.229643i
\(297\) 8.94250e12i 0.224542i
\(298\) 3.87673e13 3.80109e13i 0.955600 0.936954i
\(299\) 1.49651e13 + 1.49651e13i 0.362150 + 0.362150i
\(300\) −1.92738e13 2.00488e13i −0.457933 0.476344i
\(301\) −8.84899e12 + 8.84899e12i −0.206433 + 0.206433i
\(302\) 3.70378e13 + 3.64909e11i 0.848413 + 0.00835884i
\(303\) 5.22441e13 1.17518
\(304\) 4.17879e13 3.86176e13i 0.923093 0.853062i
\(305\) 4.43438e13 0.962020
\(306\) −8.80050e10 8.67053e8i −0.00187516 1.84747e-5i
\(307\) 1.03299e13 1.03299e13i 0.216190 0.216190i −0.590701 0.806891i \(-0.701149\pi\)
0.806891 + 0.590701i \(0.201149\pi\)
\(308\) −1.47893e12 + 1.42177e12i −0.0304032 + 0.0292281i
\(309\) 2.99160e13 + 2.99160e13i 0.604132 + 0.604132i
\(310\) −9.48018e12 + 9.29520e12i −0.188073 + 0.184404i
\(311\) 7.78955e12i 0.151820i 0.997115 + 0.0759102i \(0.0241862\pi\)
−0.997115 + 0.0759102i \(0.975814\pi\)
\(312\) −2.11820e13 6.26239e11i −0.405618 0.0119919i
\(313\) 9.37500e13i 1.76391i 0.471330 + 0.881957i \(0.343774\pi\)
−0.471330 + 0.881957i \(0.656226\pi\)
\(314\) −2.65492e13 2.70776e13i −0.490839 0.500607i
\(315\) −2.98589e10 2.98589e10i −0.000542457 0.000542457i
\(316\) 7.38895e13 + 1.45611e12i 1.31918 + 0.0259965i
\(317\) −2.94124e13 + 2.94124e13i −0.516065 + 0.516065i −0.916378 0.400313i \(-0.868901\pi\)
0.400313 + 0.916378i \(0.368901\pi\)
\(318\) 6.61678e11 6.71595e13i 0.0114103 1.15813i
\(319\) −1.48924e13 −0.252416
\(320\) 2.31373e13 + 2.60482e13i 0.385468 + 0.433963i
\(321\) −2.31893e13 −0.379761
\(322\) 1.45059e11 1.47233e13i 0.00233527 0.237027i
\(323\) 1.50172e13 1.50172e13i 0.237671 0.237671i
\(324\) −6.38022e13 1.25732e12i −0.992746 0.0195636i
\(325\) 1.24811e13 + 1.24811e13i 0.190938 + 0.190938i
\(326\) 1.22788e13 + 1.25232e13i 0.184697 + 0.188373i
\(327\) 9.06657e13i 1.34100i
\(328\) −1.04966e14 3.10329e12i −1.52667 0.0451353i
\(329\) 1.11843e13i 0.159967i
\(330\) −6.57005e12 + 6.44185e12i −0.0924149 + 0.0906117i
\(331\) −8.90138e13 8.90138e13i −1.23141 1.23141i −0.963422 0.267990i \(-0.913640\pi\)
−0.267990 0.963422i \(-0.586360\pi\)
\(332\) −1.19668e13 + 1.15043e13i −0.162825 + 0.156531i
\(333\) 1.24048e11 1.24048e11i 0.00166015 0.00166015i
\(334\) 1.14826e14 + 1.13131e12i 1.51160 + 0.0148928i
\(335\) −1.66928e13 −0.216164
\(336\) 1.00061e13 + 1.08276e13i 0.127468 + 0.137932i
\(337\) 4.94592e13 0.619844 0.309922 0.950762i \(-0.399697\pi\)
0.309922 + 0.950762i \(0.399697\pi\)
\(338\) −6.76509e13 6.66519e11i −0.834127 0.00821809i
\(339\) −2.62880e13 + 2.62880e13i −0.318903 + 0.318903i
\(340\) 9.01230e12 + 9.37464e12i 0.107573 + 0.111898i
\(341\) −6.11328e12 6.11328e12i −0.0718002 0.0718002i
\(342\) −5.44554e11 + 5.33928e11i −0.00629357 + 0.00617077i
\(343\) 3.25549e13i 0.370253i
\(344\) −1.00708e14 + 9.49238e13i −1.12717 + 1.06244i
\(345\) 6.60392e13i 0.727439i
\(346\) 2.56003e13 + 2.61097e13i 0.277540 + 0.283063i
\(347\) −4.93186e13 4.93186e13i −0.526258 0.526258i 0.393197 0.919454i \(-0.371369\pi\)
−0.919454 + 0.393197i \(0.871369\pi\)
\(348\) −2.10868e12 + 1.07004e14i −0.0221475 + 1.12386i
\(349\) −1.31044e14 + 1.31044e14i −1.35481 + 1.35481i −0.474610 + 0.880196i \(0.657411\pi\)
−0.880196 + 0.474610i \(0.842589\pi\)
\(350\) 1.20981e11 1.22794e13i 0.00123124 0.124969i
\(351\) 4.07879e13 0.408641
\(352\) −1.68126e13 + 1.52327e13i −0.165825 + 0.150243i
\(353\) 1.16944e14 1.13558 0.567791 0.823173i \(-0.307798\pi\)
0.567791 + 0.823173i \(0.307798\pi\)
\(354\) −1.00975e12 + 1.02488e14i −0.00965372 + 0.979842i
\(355\) −5.08200e13 + 5.08200e13i −0.478386 + 0.478386i
\(356\) −4.32298e11 + 2.19367e13i −0.00400689 + 0.203328i
\(357\) 3.89109e12 + 3.89109e12i 0.0355137 + 0.0355137i
\(358\) 7.28829e13 + 7.43333e13i 0.655042 + 0.668077i
\(359\) 4.01208e13i 0.355100i −0.984112 0.177550i \(-0.943183\pi\)
0.984112 0.177550i \(-0.0568171\pi\)
\(360\) −3.20298e11 3.39814e11i −0.00279184 0.00296195i
\(361\) 6.75428e13i 0.579815i
\(362\) 2.35895e13 2.31292e13i 0.199444 0.195553i
\(363\) 8.03775e13 + 8.03775e13i 0.669342 + 0.669342i
\(364\) −6.48487e12 6.74559e12i −0.0531916 0.0553302i
\(365\) 5.85401e13 5.85401e13i 0.472980 0.472980i
\(366\) 2.07503e14 + 2.04439e12i 1.65150 + 0.0162711i
\(367\) −1.48808e14 −1.16671 −0.583354 0.812218i \(-0.698260\pi\)
−0.583354 + 0.812218i \(0.698260\pi\)
\(368\) 6.41510e12 1.62702e14i 0.0495496 1.25670i
\(369\) 1.40751e12 0.0107104
\(370\) −2.59200e13 2.55373e11i −0.194324 0.00191454i
\(371\) 2.09701e13 2.09701e13i 0.154897 0.154897i
\(372\) −4.47902e13 + 4.30590e13i −0.325984 + 0.313384i
\(373\) −9.75473e13 9.75473e13i −0.699547 0.699547i 0.264766 0.964313i \(-0.414705\pi\)
−0.964313 + 0.264766i \(0.914705\pi\)
\(374\) −6.04638e12 + 5.92840e12i −0.0427269 + 0.0418932i
\(375\) 1.38139e14i 0.961932i
\(376\) 3.65507e12 1.23630e14i 0.0250820 0.848380i
\(377\) 6.79263e13i 0.459368i
\(378\) −1.98668e13 2.02621e13i −0.132410 0.135045i
\(379\) 1.24977e14 + 1.24977e14i 0.820944 + 0.820944i 0.986243 0.165299i \(-0.0528590\pi\)
−0.165299 + 0.986243i \(0.552859\pi\)
\(380\) 1.12664e14 + 2.22022e12i 0.729416 + 0.0143743i
\(381\) −5.50044e13 + 5.50044e13i −0.351002 + 0.351002i
\(382\) 9.93956e11 1.00885e14i 0.00625200 0.634571i
\(383\) −4.86299e13 −0.301516 −0.150758 0.988571i \(-0.548171\pi\)
−0.150758 + 0.988571i \(0.548171\pi\)
\(384\) 1.07068e14 + 1.22957e14i 0.654393 + 0.751503i
\(385\) −4.06288e12 −0.0244793
\(386\) −6.44803e10 + 6.54468e12i −0.000382998 + 0.0388739i
\(387\) 1.31162e12 1.31162e12i 0.00768067 0.00768067i
\(388\) 1.50746e13 + 2.97069e11i 0.0870306 + 0.00171507i
\(389\) 8.60395e12 + 8.60395e12i 0.0489751 + 0.0489751i 0.731170 0.682195i \(-0.238975\pi\)
−0.682195 + 0.731170i \(0.738975\pi\)
\(390\) −2.93821e13 2.99668e13i −0.164903 0.168184i
\(391\) 6.07755e13i 0.336323i
\(392\) 5.22334e12 1.76675e14i 0.0285020 0.964056i
\(393\) 1.18551e14i 0.637890i
\(394\) −1.03959e14 + 1.01931e14i −0.551612 + 0.540849i
\(395\) 1.03494e14 + 1.03494e14i 0.541539 + 0.541539i
\(396\) 2.19212e11 2.10739e11i 0.00113120 0.00108748i
\(397\) −4.00648e13 + 4.00648e13i −0.203899 + 0.203899i −0.801668 0.597769i \(-0.796054\pi\)
0.597769 + 0.801668i \(0.296054\pi\)
\(398\) −1.72118e14 1.69577e12i −0.863914 0.00851156i
\(399\) 4.76845e13 0.236062
\(400\) 5.35026e12 1.35696e14i 0.0261243 0.662576i
\(401\) 3.93054e14 1.89304 0.946518 0.322652i \(-0.104574\pi\)
0.946518 + 0.322652i \(0.104574\pi\)
\(402\) −7.81125e13 7.69590e11i −0.371088 0.00365608i
\(403\) 2.78835e13 2.78835e13i 0.130668 0.130668i
\(404\) 1.76801e14 + 1.83909e14i 0.817311 + 0.850172i
\(405\) −8.93648e13 8.93648e13i −0.407534 0.407534i
\(406\) −3.37437e13 + 3.30852e13i −0.151809 + 0.148847i
\(407\) 1.68792e13i 0.0749173i
\(408\) 4.17400e13 + 4.42833e13i 0.182777 + 0.193914i
\(409\) 3.20804e14i 1.38599i 0.720941 + 0.692997i \(0.243710\pi\)
−0.720941 + 0.692997i \(0.756290\pi\)
\(410\) −1.45601e14 1.48499e14i −0.620661 0.633012i
\(411\) 3.06822e14 + 3.06822e14i 1.29049 + 1.29049i
\(412\) −4.07039e12 + 2.06550e14i −0.0168928 + 0.857216i
\(413\) −3.20012e13 + 3.20012e13i −0.131051 + 0.131051i
\(414\) −2.15011e10 + 2.18233e12i −8.68876e−5 + 0.00881900i
\(415\) −3.28750e13 −0.131099
\(416\) −6.94784e13 7.66842e13i −0.273424 0.301782i
\(417\) −4.60231e14 −1.78742
\(418\) −7.22906e11 + 7.33742e13i −0.00277085 + 0.281238i
\(419\) −1.19903e14 + 1.19903e14i −0.453580 + 0.453580i −0.896541 0.442961i \(-0.853928\pi\)
0.442961 + 0.896541i \(0.353928\pi\)
\(420\) −5.75278e11 + 2.91922e13i −0.00214786 + 0.108992i
\(421\) 6.87949e13 + 6.87949e13i 0.253516 + 0.253516i 0.822410 0.568895i \(-0.192629\pi\)
−0.568895 + 0.822410i \(0.692629\pi\)
\(422\) −2.19901e14 2.24278e14i −0.799851 0.815769i
\(423\) 1.65777e12i 0.00595185i
\(424\) 2.38654e14 2.24948e14i 0.845778 0.797204i
\(425\) 5.06874e13i 0.177321i
\(426\) −2.40151e14 + 2.35465e14i −0.829336 + 0.813154i
\(427\) 6.47914e13 + 6.47914e13i 0.220884 + 0.220884i
\(428\) −7.84758e13 8.16309e13i −0.264116 0.274735i
\(429\) 1.93241e13 1.93241e13i 0.0642072 0.0642072i
\(430\) −2.74065e14 2.70018e12i −0.899036 0.00885760i
\(431\) −2.48651e14 −0.805314 −0.402657 0.915351i \(-0.631913\pi\)
−0.402657 + 0.915351i \(0.631913\pi\)
\(432\) −2.12983e14 2.30467e14i −0.681058 0.736969i
\(433\) 7.94573e13 0.250871 0.125435 0.992102i \(-0.459967\pi\)
0.125435 + 0.992102i \(0.459967\pi\)
\(434\) −2.74330e13 2.70278e11i −0.0855223 0.000842593i
\(435\) −1.49875e14 + 1.49875e14i −0.461359 + 0.461359i
\(436\) 3.19161e14 3.06825e14i 0.970140 0.932643i
\(437\) −3.72395e14 3.72395e14i −1.11778 1.11778i
\(438\) 2.76632e14 2.71234e14i 0.819964 0.803964i
\(439\) 5.46704e14i 1.60029i 0.599809 + 0.800143i \(0.295243\pi\)
−0.599809 + 0.800143i \(0.704757\pi\)
\(440\) −4.49105e13 1.32776e12i −0.129825 0.00383823i
\(441\) 2.36906e12i 0.00676339i
\(442\) −2.70402e13 2.75783e13i −0.0762408 0.0777580i
\(443\) −7.74563e13 7.74563e13i −0.215693 0.215693i 0.590988 0.806681i \(-0.298738\pi\)
−0.806681 + 0.590988i \(0.798738\pi\)
\(444\) −1.21279e14 2.38999e12i −0.333563 0.00657338i
\(445\) −3.07258e13 + 3.07258e13i −0.0834686 + 0.0834686i
\(446\) −2.07469e12 + 2.10579e14i −0.00556688 + 0.565032i
\(447\) 5.03174e14 1.33360
\(448\) −4.25308e12 + 7.18656e13i −0.0111346 + 0.188145i
\(449\) 1.23108e14 0.318369 0.159184 0.987249i \(-0.449114\pi\)
0.159184 + 0.987249i \(0.449114\pi\)
\(450\) −1.79321e10 + 1.82009e12i −4.58103e−5 + 0.00464969i
\(451\) 9.57594e13 9.57594e13i 0.241663 0.241663i
\(452\) −1.81501e14 3.57676e12i −0.452499 0.00891720i
\(453\) 2.42731e14 + 2.42731e14i 0.597841 + 0.597841i
\(454\) 3.56940e14 + 3.64044e14i 0.868538 + 0.885822i
\(455\) 1.85313e13i 0.0445495i
\(456\) 5.27099e14 + 1.55835e13i 1.25195 + 0.0370133i
\(457\) 5.91954e14i 1.38915i −0.719421 0.694574i \(-0.755593\pi\)
0.719421 0.694574i \(-0.244407\pi\)
\(458\) 5.92571e13 5.81008e13i 0.137398 0.134717i
\(459\) −8.28228e13 8.28228e13i −0.189749 0.189749i
\(460\) 2.32471e14 2.23486e14i 0.526260 0.505919i
\(461\) 3.14114e14 3.14114e14i 0.702639 0.702639i −0.262337 0.964976i \(-0.584493\pi\)
0.964976 + 0.262337i \(0.0844932\pi\)
\(462\) −1.90119e13 1.87311e11i −0.0420237 0.000414031i
\(463\) 2.18707e14 0.477713 0.238857 0.971055i \(-0.423227\pi\)
0.238857 + 0.971055i \(0.423227\pi\)
\(464\) −3.83810e14 + 3.54692e14i −0.828453 + 0.765602i
\(465\) −1.23046e14 −0.262469
\(466\) 2.14339e14 + 2.11174e12i 0.451833 + 0.00445161i
\(467\) −1.13426e13 + 1.13426e13i −0.0236304 + 0.0236304i −0.718823 0.695193i \(-0.755319\pi\)
0.695193 + 0.718823i \(0.255319\pi\)
\(468\) 9.61206e11 + 9.99852e11i 0.00197908 + 0.00205865i
\(469\) −2.43901e13 2.43901e13i −0.0496322 0.0496322i
\(470\) 1.74903e14 1.71490e14i 0.351770 0.344906i
\(471\) 3.51449e14i 0.698629i
\(472\) −3.64196e14 + 3.43280e14i −0.715573 + 0.674477i
\(473\) 1.78472e14i 0.346604i
\(474\) 4.79518e14 + 4.89060e14i 0.920500 + 0.938818i
\(475\) −3.10582e14 3.10582e14i −0.589333 0.589333i
\(476\) −5.29425e11 + 2.68654e13i −0.000993039 + 0.0503913i
\(477\) −3.10825e12 + 3.10825e12i −0.00576322 + 0.00576322i
\(478\) −7.74397e12 + 7.86004e14i −0.0141942 + 1.44069i
\(479\) −2.93567e14 −0.531939 −0.265969 0.963981i \(-0.585692\pi\)
−0.265969 + 0.963981i \(0.585692\pi\)
\(480\) −1.58992e13 + 3.22499e14i −0.0284805 + 0.577699i
\(481\) 7.69881e13 0.136341
\(482\) 6.73804e12 6.83903e14i 0.0117971 1.19739i
\(483\) 9.64907e13 9.64907e13i 0.167023 0.167023i
\(484\) −1.09362e13 + 5.54953e14i −0.0187162 + 0.949745i
\(485\) 2.11143e13 + 2.11143e13i 0.0357271 + 0.0357271i
\(486\) 5.86891e12 + 5.98571e12i 0.00981879 + 0.0100142i
\(487\) 2.66029e13i 0.0440069i −0.999758 0.0220034i \(-0.992996\pi\)
0.999758 0.0220034i \(-0.00700448\pi\)
\(488\) 6.95022e14 + 7.37370e14i 1.13681 + 1.20608i
\(489\) 1.62543e14i 0.262887i
\(490\) 2.49948e14 2.45071e14i 0.399733 0.391934i
\(491\) −8.66005e14 8.66005e14i −1.36953 1.36953i −0.861104 0.508428i \(-0.830227\pi\)
−0.508428 0.861104i \(-0.669773\pi\)
\(492\) −6.74482e14 7.01600e14i −1.05478 1.09719i
\(493\) −1.37929e14 + 1.37929e14i −0.213304 + 0.213304i
\(494\) −3.34669e14 3.29727e12i −0.511820 0.00504262i
\(495\) 6.02212e11 0.000910795
\(496\) −3.03152e14 1.19528e13i −0.453431 0.0178781i
\(497\) −1.48508e14 −0.219679
\(498\) −1.53835e14 1.51564e12i −0.225058 0.00221735i
\(499\) 5.86185e14 5.86185e14i 0.848168 0.848168i −0.141736 0.989904i \(-0.545268\pi\)
0.989904 + 0.141736i \(0.0452684\pi\)
\(500\) 4.86277e14 4.67481e14i 0.695902 0.669005i
\(501\) 7.52526e14 + 7.52526e14i 1.06516 + 1.06516i
\(502\) 3.45210e14 3.38474e14i 0.483296 0.473866i
\(503\) 1.63209e14i 0.226006i 0.993595 + 0.113003i \(0.0360470\pi\)
−0.993595 + 0.113003i \(0.963953\pi\)
\(504\) 2.85151e10 9.64499e11i 3.90577e−5 0.00132109i
\(505\) 5.05231e14i 0.684522i
\(506\) 1.47012e14 + 1.49937e14i 0.197026 + 0.200947i
\(507\) −4.43357e14 4.43357e14i −0.587774 0.587774i
\(508\) −3.79769e14 7.48394e12i −0.498045 0.00981476i
\(509\) −2.22280e14 + 2.22280e14i −0.288372 + 0.288372i −0.836436 0.548065i \(-0.815365\pi\)
0.548065 + 0.836436i \(0.315365\pi\)
\(510\) −1.18733e12 + 1.20512e14i −0.00152382 + 0.154666i
\(511\) 1.71067e14 0.217196
\(512\) −7.04990e13 + 7.93004e14i −0.0885519 + 0.996072i
\(513\) −1.01498e15 −1.26128
\(514\) 1.14919e13 1.16641e15i 0.0141284 1.43402i
\(515\) −2.89305e14 + 2.89305e14i −0.351898 + 0.351898i
\(516\) −1.28234e15 2.52705e13i −1.54322 0.0304117i
\(517\) 1.12786e14 + 1.12786e14i 0.134294 + 0.134294i
\(518\) −3.74990e13 3.82453e13i −0.0441780 0.0450572i
\(519\) 3.38886e14i 0.395033i
\(520\) 6.05610e12 2.04843e14i 0.00698513 0.236266i
\(521\) 1.24751e15i 1.42375i 0.702304 + 0.711877i \(0.252155\pi\)
−0.702304 + 0.711877i \(0.747845\pi\)
\(522\) 5.00158e12 4.90399e12i 0.00564832 0.00553811i
\(523\) −4.96253e13 4.96253e13i −0.0554555 0.0554555i 0.678835 0.734291i \(-0.262485\pi\)
−0.734291 + 0.678835i \(0.762485\pi\)
\(524\) 4.17322e14 4.01192e14i 0.461477 0.443640i
\(525\) 8.04743e13 8.04743e13i 0.0880605 0.0880605i
\(526\) −1.54358e15 1.52078e13i −1.67150 0.0164682i
\(527\) −1.13239e14 −0.121349
\(528\) −2.10094e14 8.28366e12i −0.222806 0.00878488i
\(529\) −5.54291e14 −0.581744
\(530\) 6.49472e14 + 6.39881e12i 0.674595 + 0.00664633i
\(531\) 4.74332e12 4.74332e12i 0.00487598 0.00487598i
\(532\) 1.61371e14 + 1.67859e14i 0.164177 + 0.170777i
\(533\) 4.36771e14 + 4.36771e14i 0.439799 + 0.439799i
\(534\) −1.45195e14 + 1.42362e14i −0.144702 + 0.141879i
\(535\) 2.24254e14i 0.221205i
\(536\) −2.61634e14 2.77576e14i −0.255440 0.271004i
\(537\) 9.64796e14i 0.932346i
\(538\) 1.21468e15 + 1.23885e15i 1.16187 + 1.18499i
\(539\) 1.61178e14 + 1.61178e14i 0.152605 + 0.152605i
\(540\) 1.22449e13 6.21362e14i 0.0114760 0.582343i
\(541\) 9.45723e14 9.45723e14i 0.877363 0.877363i −0.115898 0.993261i \(-0.536975\pi\)
0.993261 + 0.115898i \(0.0369747\pi\)
\(542\) 1.05764e13 1.07349e15i 0.00971270 0.985828i
\(543\) 3.06176e14 0.278338
\(544\) −1.46319e13 + 2.96794e14i −0.0131676 + 0.267092i
\(545\) 8.76790e14 0.781115
\(546\) 8.54350e11 8.67156e13i 0.000753488 0.0764782i
\(547\) 1.14467e15 1.14467e15i 0.999428 0.999428i −0.000571894 1.00000i \(-0.500182\pi\)
1.00000 0.000571894i \(0.000182040\pi\)
\(548\) −4.17464e13 + 2.11840e15i −0.0360849 + 1.83111i
\(549\) −9.60357e12 9.60357e12i −0.00821835 0.00821835i
\(550\) 1.22609e14 + 1.25049e14i 0.103879 + 0.105946i
\(551\) 1.69030e15i 1.41785i
\(552\) 1.09813e15 1.03506e15i 0.911987 0.859611i
\(553\) 3.02432e14i 0.248679i
\(554\) 1.30836e15 1.28283e15i 1.06518 1.04440i
\(555\) −1.69870e14 1.69870e14i −0.136932 0.136932i
\(556\) −1.55748e15 1.62010e15i −1.24312 1.29310i
\(557\) 1.26785e15 1.26785e15i 1.00199 1.00199i 0.00199459 0.999998i \(-0.499365\pi\)
0.999998 0.00199459i \(-0.000634897\pi\)
\(558\) 4.06619e12 + 4.00615e10i 0.00318200 + 3.13501e-5i
\(559\) 8.14033e14 0.630778
\(560\) −1.04709e14 + 9.67653e13i −0.0803434 + 0.0742481i
\(561\) −7.84779e13 −0.0596282
\(562\) −7.84765e14 7.73176e12i −0.590459 0.00581740i
\(563\) −9.53526e14 + 9.53526e14i −0.710455 + 0.710455i −0.966630 0.256175i \(-0.917538\pi\)
0.256175 + 0.966630i \(0.417538\pi\)
\(564\) 8.26348e14 7.94408e14i 0.609716 0.586150i
\(565\) −2.54220e14 2.54220e14i −0.185756 0.185756i
\(566\) −1.72967e14 + 1.69592e14i −0.125162 + 0.122720i
\(567\) 2.61144e14i 0.187143i
\(568\) −1.64158e15 4.85328e13i −1.16506 0.0344445i
\(569\) 5.93700e14i 0.417301i −0.977990 0.208650i \(-0.933093\pi\)
0.977990 0.208650i \(-0.0669071\pi\)
\(570\) 7.31151e14 + 7.45702e14i 0.508974 + 0.519103i
\(571\) 3.83062e14 + 3.83062e14i 0.264101 + 0.264101i 0.826718 0.562617i \(-0.190205\pi\)
−0.562617 + 0.826718i \(0.690205\pi\)
\(572\) 1.33420e14 + 2.62925e12i 0.0911051 + 0.00179537i
\(573\) 6.61163e14 6.61163e14i 0.447155 0.447155i
\(574\) 4.23368e12 4.29714e14i 0.00283598 0.287849i
\(575\) −1.25694e15 −0.833952
\(576\) 6.30404e11 1.06521e13i 0.000414281 0.00700024i
\(577\) −1.21498e15 −0.790867 −0.395434 0.918495i \(-0.629406\pi\)
−0.395434 + 0.918495i \(0.629406\pi\)
\(578\) 1.41872e13 1.43999e15i 0.00914733 0.928443i
\(579\) −4.28912e13 + 4.28912e13i −0.0273928 + 0.0273928i
\(580\) −1.03479e15 2.03921e13i −0.654633 0.0129006i
\(581\) −4.80341e13 4.80341e13i −0.0301010 0.0301010i
\(582\) 9.78292e13 + 9.97761e13i 0.0607284 + 0.0619370i
\(583\) 4.22938e14i 0.260076i
\(584\) 1.89096e15 + 5.59055e13i 1.15189 + 0.0340552i
\(585\) 2.74676e12i 0.00165754i
\(586\) −1.57356e15 + 1.54285e15i −0.940688 + 0.922333i
\(587\) 8.85634e14 + 8.85634e14i 0.524499 + 0.524499i 0.918927 0.394428i \(-0.129057\pi\)
−0.394428 + 0.918927i \(0.629057\pi\)
\(588\) 1.18091e15 1.13526e15i 0.692851 0.666071i
\(589\) −6.93859e14 + 6.93859e14i −0.403308 + 0.403308i
\(590\) −9.91121e14 9.76485e12i −0.570743 0.00562315i
\(591\) −1.34932e15 −0.769811
\(592\) −4.02011e14 4.35013e14i −0.227231 0.245885i
\(593\) −2.11099e14 −0.118218 −0.0591092 0.998252i \(-0.518826\pi\)
−0.0591092 + 0.998252i \(0.518826\pi\)
\(594\) 4.04672e14 + 3.98696e12i 0.224532 + 0.00221216i
\(595\) −3.76292e13 + 3.76292e13i −0.0206862 + 0.0206862i
\(596\) 1.70281e15 + 1.77127e15i 0.927494 + 0.964785i
\(597\) −1.12800e15 1.12800e15i −0.608763 0.608763i
\(598\) −6.83883e14 + 6.70538e14i −0.365700 + 0.358564i
\(599\) 1.04958e15i 0.556122i 0.960563 + 0.278061i \(0.0896917\pi\)
−0.960563 + 0.278061i \(0.910308\pi\)
\(600\) 9.15852e14 8.63254e14i 0.480832 0.453217i
\(601\) 1.43484e15i 0.746436i −0.927744 0.373218i \(-0.878254\pi\)
0.927744 0.373218i \(-0.121746\pi\)
\(602\) −3.96495e14 4.04386e14i −0.204389 0.208456i
\(603\) 3.61517e12 + 3.61517e12i 0.00184665 + 0.00184665i
\(604\) −3.30262e13 + 1.67590e15i −0.0167169 + 0.848290i
\(605\) −7.77298e14 + 7.77298e14i −0.389882 + 0.389882i
\(606\) −2.32927e13 + 2.36418e15i −0.0115776 + 1.17512i
\(607\) 2.30297e15 1.13436 0.567181 0.823593i \(-0.308034\pi\)
0.567181 + 0.823593i \(0.308034\pi\)
\(608\) 1.72892e15 + 1.90823e15i 0.843926 + 0.931452i
\(609\) −4.37970e14 −0.211860
\(610\) −1.97704e13 + 2.00668e15i −0.00947768 + 0.961974i
\(611\) −5.14431e14 + 5.14431e14i −0.244399 + 0.244399i
\(612\) 7.84729e10 3.98207e12i 3.69477e−5 0.00187489i
\(613\) −1.01165e15 1.01165e15i −0.472058 0.472058i 0.430522 0.902580i \(-0.358330\pi\)
−0.902580 + 0.430522i \(0.858330\pi\)
\(614\) 4.62850e14 + 4.72061e14i 0.214050 + 0.218309i
\(615\) 1.92742e15i 0.883410i
\(616\) −6.36794e13 6.75594e13i −0.0289271 0.0306897i
\(617\) 2.46635e15i 1.11042i −0.831711 0.555209i \(-0.812638\pi\)
0.831711 0.555209i \(-0.187362\pi\)
\(618\) −1.36712e15 + 1.34044e15i −0.610054 + 0.598151i
\(619\) 4.54673e14 + 4.54673e14i 0.201095 + 0.201095i 0.800469 0.599374i \(-0.204584\pi\)
−0.599374 + 0.800469i \(0.704584\pi\)
\(620\) −4.16405e14 4.33147e14i −0.182542 0.189881i
\(621\) −2.05383e15 + 2.05383e15i −0.892400 + 0.892400i
\(622\) −3.52498e14 3.47292e12i −0.151813 0.00149571i
\(623\) −8.97878e13 −0.0383295
\(624\) 3.77828e13 9.58264e14i 0.0159875 0.405480i
\(625\) −2.45046e14 −0.102780
\(626\) −4.24243e15 4.17978e13i −1.76383 0.0173778i
\(627\) −4.80865e14 + 4.80865e14i −0.198176 + 0.198176i
\(628\) 1.23717e15 1.18935e15i 0.505418 0.485883i
\(629\) −1.56330e14 1.56330e14i −0.0633088 0.0633088i
\(630\) 1.36450e12 1.33788e12i 0.000547775 0.000537086i
\(631\) 2.74681e15i 1.09312i −0.837420 0.546560i \(-0.815937\pi\)
0.837420 0.546560i \(-0.184063\pi\)
\(632\) −9.88359e13 + 3.34304e15i −0.0389916 + 1.31886i
\(633\) 2.91097e15i 1.13846i
\(634\) −1.31788e15 1.34410e15i −0.510956 0.521124i
\(635\) −5.31925e14 5.31925e14i −0.204454 0.204454i
\(636\) 3.03885e15 + 5.98853e13i 1.15796 + 0.0228195i
\(637\) −7.35156e14 + 7.35156e14i −0.277723 + 0.277723i
\(638\) 6.63970e12 6.73923e14i 0.00248677 0.252404i
\(639\) 2.20122e13 0.00817352
\(640\) −1.18906e15 + 1.03541e15i −0.437739 + 0.381174i
\(641\) 4.33345e15 1.58167 0.790833 0.612032i \(-0.209648\pi\)
0.790833 + 0.612032i \(0.209648\pi\)
\(642\) 1.03388e13 1.04938e15i 0.00374134 0.379742i
\(643\) 2.47930e15 2.47930e15i 0.889545 0.889545i −0.104934 0.994479i \(-0.533463\pi\)
0.994479 + 0.104934i \(0.0334632\pi\)
\(644\) 6.66204e14 + 1.31286e13i 0.236993 + 0.00467031i
\(645\) −1.79611e15 1.79611e15i −0.633512 0.633512i
\(646\) 6.72875e14 + 6.86265e14i 0.235318 + 0.240001i
\(647\) 1.92897e15i 0.668885i 0.942416 + 0.334443i \(0.108548\pi\)
−0.942416 + 0.334443i \(0.891452\pi\)
\(648\) 8.53429e13 2.88666e15i 0.0293430 0.992505i
\(649\) 6.45420e14i 0.220038i
\(650\) −5.70366e14 + 5.59236e14i −0.192810 + 0.189048i
\(651\) −1.79785e14 1.79785e14i −0.0602639 0.0602639i
\(652\) −5.72182e14 + 5.50067e14i −0.190183 + 0.182833i
\(653\) 6.57083e14 6.57083e14i 0.216570 0.216570i −0.590481 0.807051i \(-0.701062\pi\)
0.807051 + 0.590481i \(0.201062\pi\)
\(654\) 4.10286e15 + 4.04227e13i 1.34094 + 0.0132114i
\(655\) 1.14646e15 0.371561
\(656\) 1.87231e14 4.74862e15i 0.0601736 1.52615i
\(657\) −2.53561e13 −0.00808115
\(658\) 5.06119e14 + 4.98645e12i 0.159960 + 0.00157597i
\(659\) −3.43636e15 + 3.43636e15i −1.07703 + 1.07703i −0.0802587 + 0.996774i \(0.525575\pi\)
−0.996774 + 0.0802587i \(0.974425\pi\)
\(660\) −2.88582e14 3.00184e14i −0.0896968 0.0933031i
\(661\) 2.46547e15 + 2.46547e15i 0.759963 + 0.759963i 0.976315 0.216353i \(-0.0694161\pi\)
−0.216353 + 0.976315i \(0.569416\pi\)
\(662\) 4.06780e15 3.98842e15i 1.24348 1.21922i
\(663\) 3.57948e14i 0.108516i
\(664\) −5.15265e14 5.46660e14i −0.154919 0.164359i
\(665\) 4.61137e14i 0.137503i
\(666\) 5.55821e12 + 5.66882e12i 0.00164372 + 0.00167643i
\(667\) 3.42035e15 + 3.42035e15i 1.00318 + 1.00318i
\(668\) −1.02389e14 + 5.19569e15i −0.0297841 + 1.51138i
\(669\) −1.38005e15 + 1.38005e15i −0.398154 + 0.398154i
\(670\) 7.44239e12 7.55394e14i 0.00212961 0.216153i
\(671\) −1.30675e15 −0.370868
\(672\) −4.94438e14 + 4.47977e14i −0.139181 + 0.126103i
\(673\) 5.59870e15 1.56316 0.781581 0.623803i \(-0.214413\pi\)
0.781581 + 0.623803i \(0.214413\pi\)
\(674\) −2.20510e13 + 2.23816e15i −0.00610661 + 0.619814i
\(675\) −1.71291e15 + 1.71291e15i −0.470505 + 0.470505i
\(676\) 6.03235e13 3.06109e15i 0.0164354 0.834005i
\(677\) 9.69257e14 + 9.69257e14i 0.261940 + 0.261940i 0.825842 0.563902i \(-0.190700\pi\)
−0.563902 + 0.825842i \(0.690700\pi\)
\(678\) −1.17788e15 1.20132e15i −0.315746 0.322030i
\(679\) 6.17009e13i 0.0164062i
\(680\) −4.28245e14 + 4.03651e14i −0.112952 + 0.106465i
\(681\) 4.72504e15i 1.23622i
\(682\) 2.79368e14 2.73917e14i 0.0725041 0.0710893i
\(683\) 6.09310e14 + 6.09310e14i 0.156864 + 0.156864i 0.781176 0.624311i \(-0.214620\pi\)
−0.624311 + 0.781176i \(0.714620\pi\)
\(684\) −2.39189e13 2.48805e13i −0.00610847 0.00635406i
\(685\) −2.96715e15 + 2.96715e15i −0.751693 + 0.751693i
\(686\) 1.47319e15 + 1.45144e13i 0.370235 + 0.00364768i
\(687\) 7.69116e14 0.191748
\(688\) −4.25065e15 4.59960e15i −1.05128 1.13759i
\(689\) −1.92907e15 −0.473307
\(690\) 2.98845e15 + 2.94431e13i 0.727404 + 0.00716662i
\(691\) −2.63310e14 + 2.63310e14i −0.0635826 + 0.0635826i −0.738183 0.674600i \(-0.764316\pi\)
0.674600 + 0.738183i \(0.264316\pi\)
\(692\) −1.19295e15 + 1.14684e15i −0.285784 + 0.274738i
\(693\) 8.79900e11 + 8.79900e11i 0.000209122 + 0.000209122i
\(694\) 2.25378e15 2.20981e15i 0.531417 0.521047i
\(695\) 4.45070e15i 1.04115i
\(696\) −4.84126e15 1.43130e14i −1.12359 0.0332185i
\(697\) 1.77379e15i 0.408434i
\(698\) −5.87166e15 5.98851e15i −1.34139 1.36809i
\(699\) 1.40469e15 + 1.40469e15i 0.318388 + 0.318388i
\(700\) 5.55622e14 + 1.09494e13i 0.124951 + 0.00246236i
\(701\) 3.81857e15 3.81857e15i 0.852024 0.852024i −0.138358 0.990382i \(-0.544182\pi\)
0.990382 + 0.138358i \(0.0441824\pi\)
\(702\) −1.81850e13 + 1.84576e15i −0.00402587 + 0.408621i
\(703\) −1.91579e15 −0.420817
\(704\) −6.81826e14 7.67604e14i −0.148602 0.167297i
\(705\) 2.27012e15 0.490918
\(706\) −5.21389e13 + 5.29204e15i −0.0111876 + 1.13553i
\(707\) −7.38200e14 + 7.38200e14i −0.157169 + 0.157169i
\(708\) −4.63741e15 9.13874e13i −0.979699 0.0193065i
\(709\) −2.06573e15 2.06573e15i −0.433031 0.433031i 0.456627 0.889658i \(-0.349057\pi\)
−0.889658 + 0.456627i \(0.849057\pi\)
\(710\) −2.27708e15 2.32240e15i −0.473650 0.483076i
\(711\) 4.48273e13i 0.00925252i
\(712\) −9.92503e14 2.93430e13i −0.203279 0.00600986i
\(713\) 2.80808e15i 0.570712i
\(714\) −1.77817e14 + 1.74347e14i −0.0358619 + 0.0351621i
\(715\) 1.86875e14 + 1.86875e14i 0.0373997 + 0.0373997i
\(716\) −3.39627e15 + 3.26500e15i −0.674498 + 0.648428i
\(717\) −5.15116e15 + 5.15116e15i −1.01519 + 1.01519i
\(718\) 1.81557e15 + 1.78876e13i 0.355083 + 0.00349839i
\(719\) −9.28686e15 −1.80244 −0.901218 0.433366i \(-0.857326\pi\)
−0.901218 + 0.433366i \(0.857326\pi\)
\(720\) 1.55203e13 1.43428e13i 0.00298931 0.00276253i
\(721\) −8.45416e14 −0.161594
\(722\) 3.05649e15 + 3.01135e13i 0.579787 + 0.00571225i
\(723\) 4.48203e15 4.48203e15i 0.843751 0.843751i
\(724\) 1.03614e15 + 1.07780e15i 0.193578 + 0.201361i
\(725\) 2.85261e15 + 2.85261e15i 0.528912 + 0.528912i
\(726\) −3.67313e15 + 3.60146e15i −0.675904 + 0.662715i
\(727\) 7.23879e15i 1.32198i −0.750393 0.660992i \(-0.770136\pi\)
0.750393 0.660992i \(-0.229864\pi\)
\(728\) 3.08147e14 2.90450e14i 0.0558516 0.0526440i
\(729\) 5.59749e15i 1.00691i
\(730\) 2.62299e15 + 2.67519e15i 0.468297 + 0.477616i
\(731\) −1.65295e15 1.65295e15i −0.292897 0.292897i
\(732\) −1.85028e14 + 9.38915e15i −0.0325406 + 1.65126i
\(733\) 1.06411e15 1.06411e15i 0.185743 0.185743i −0.608110 0.793853i \(-0.708072\pi\)
0.793853 + 0.608110i \(0.208072\pi\)
\(734\) 6.63450e13 6.73394e15i 0.0114942 1.16665i
\(735\) 3.24415e15 0.557854
\(736\) 7.35985e15 + 3.62840e14i 1.25615 + 0.0619280i
\(737\) 4.91914e14 0.0833333
\(738\) −6.27529e11 + 6.36935e13i −0.000105517 + 0.0107099i
\(739\) 2.11437e15 2.11437e15i 0.352887 0.352887i −0.508295 0.861183i \(-0.669724\pi\)
0.861183 + 0.508295i \(0.169724\pi\)
\(740\) 2.31126e13 1.17284e15i 0.00382890 0.194296i
\(741\) −2.19329e15 2.19329e15i −0.360658 0.360658i
\(742\) 9.39603e14 + 9.58302e14i 0.153364 + 0.156416i
\(743\) 5.36629e15i 0.869432i −0.900568 0.434716i \(-0.856849\pi\)
0.900568 0.434716i \(-0.143151\pi\)
\(744\) −1.92856e15 2.04607e15i −0.310158 0.329056i
\(745\) 4.86598e15i 0.776803i
\(746\) 4.45776e15 4.37078e15i 0.706404 0.692621i
\(747\) 7.11975e12 + 7.11975e12i 0.00111996 + 0.00111996i
\(748\) −2.65580e14 2.76258e14i −0.0414703 0.0431376i
\(749\) 3.27661e14 3.27661e14i 0.0507896 0.0507896i
\(750\) 6.25115e15 + 6.15884e13i 0.961885 + 0.00947681i
\(751\) −6.27521e15 −0.958536 −0.479268 0.877669i \(-0.659098\pi\)
−0.479268 + 0.877669i \(0.659098\pi\)
\(752\) 5.59295e15 + 2.20521e14i 0.848092 + 0.0334389i
\(753\) 4.48060e15 0.674471
\(754\) 3.07385e15 + 3.02845e13i 0.459346 + 0.00452562i
\(755\) −2.34735e15 + 2.34735e15i −0.348233 + 0.348233i
\(756\) 9.25772e14 8.89989e14i 0.136343 0.131074i
\(757\) 5.57647e15 + 5.57647e15i 0.815327 + 0.815327i 0.985427 0.170100i \(-0.0544091\pi\)
−0.170100 + 0.985427i \(0.554409\pi\)
\(758\) −5.71125e15 + 5.59981e15i −0.828992 + 0.812816i
\(759\) 1.94608e15i 0.280435i
\(760\) −1.50701e14 + 5.09735e15i −0.0215597 + 0.729239i
\(761\)