Properties

Label 16.12.e.a.5.20
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 5.20
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.20

$q$-expansion

\(f(q)\) \(=\) \(q+(44.1073 - 10.1265i) q^{2} +(-179.701 + 179.701i) q^{3} +(1842.91 - 893.305i) q^{4} +(2961.29 + 2961.29i) q^{5} +(-6106.38 + 9745.87i) q^{6} -5179.04i q^{7} +(72239.7 - 58063.5i) q^{8} +112562. i q^{9} +O(q^{10})\) \(q+(44.1073 - 10.1265i) q^{2} +(-179.701 + 179.701i) q^{3} +(1842.91 - 893.305i) q^{4} +(2961.29 + 2961.29i) q^{5} +(-6106.38 + 9745.87i) q^{6} -5179.04i q^{7} +(72239.7 - 58063.5i) q^{8} +112562. i q^{9} +(160602. + 100627. i) q^{10} +(694803. + 694803. i) q^{11} +(-170645. + 491700. i) q^{12} +(524615. - 524615. i) q^{13} +(-52445.5 - 228434. i) q^{14} -1.06429e6 q^{15} +(2.59832e6 - 3.29256e6i) q^{16} +1.82572e6 q^{17} +(1.13986e6 + 4.96481e6i) q^{18} +(-601185. + 601185. i) q^{19} +(8.10272e6 + 2.81205e6i) q^{20} +(930679. + 930679. i) q^{21} +(3.76818e7 + 2.36100e7i) q^{22} +2.32829e7i q^{23} +(-2.54748e6 + 2.34156e7i) q^{24} -3.12896e7i q^{25} +(1.78268e7 - 2.84518e7i) q^{26} +(-5.20610e7 - 5.20610e7i) q^{27} +(-4.62646e6 - 9.54450e6i) q^{28} +(189495. - 189495. i) q^{29} +(-4.69431e7 + 1.07776e7i) q^{30} -2.48770e8 q^{31} +(8.12627e7 - 1.71538e8i) q^{32} -2.49713e8 q^{33} +(8.05277e7 - 1.84882e7i) q^{34} +(1.53366e7 - 1.53366e7i) q^{35} +(1.00552e8 + 2.07442e8i) q^{36} +(-4.30934e8 - 4.30934e8i) q^{37} +(-2.04288e7 + 3.26046e7i) q^{38} +1.88548e8i q^{39} +(3.85865e8 + 4.19799e7i) q^{40} -1.02672e8i q^{41} +(5.04742e7 + 3.16252e7i) q^{42} +(-6.91645e7 - 6.91645e7i) q^{43} +(1.90113e9 + 6.59787e8i) q^{44} +(-3.33329e8 + 3.33329e8i) q^{45} +(2.35774e8 + 1.02695e9i) q^{46} +2.50575e8 q^{47} +(1.24755e8 + 1.05860e9i) q^{48} +1.95050e9 q^{49} +(-3.16854e8 - 1.38010e9i) q^{50} +(-3.28084e8 + 3.28084e8i) q^{51} +(4.98176e8 - 1.43546e9i) q^{52} +(-1.76937e9 - 1.76937e9i) q^{53} +(-2.82347e9 - 1.76908e9i) q^{54} +4.11502e9i q^{55} +(-3.00713e8 - 3.74132e8i) q^{56} -2.16067e8i q^{57} +(6.43918e6 - 1.02770e7i) q^{58} +(3.82611e9 + 3.82611e9i) q^{59} +(-1.96140e9 + 9.50738e8i) q^{60} +(7.80093e9 - 7.80093e9i) q^{61} +(-1.09726e10 + 2.51917e9i) q^{62} +5.82964e8 q^{63} +(1.84721e9 - 8.38897e9i) q^{64} +3.10707e9 q^{65} +(-1.10142e10 + 2.52872e9i) q^{66} +(-6.53658e9 + 6.53658e9i) q^{67} +(3.36464e9 - 1.63093e9i) q^{68} +(-4.18397e9 - 4.18397e9i) q^{69} +(5.21152e8 - 8.31764e8i) q^{70} +1.53408e10i q^{71} +(6.53575e9 + 8.13145e9i) q^{72} -2.49847e10i q^{73} +(-2.33712e10 - 1.46435e10i) q^{74} +(5.62278e9 + 5.62278e9i) q^{75} +(-5.70888e8 + 1.64497e9i) q^{76} +(3.59841e9 - 3.59841e9i) q^{77} +(1.90933e9 + 8.31632e9i) q^{78} +2.46282e10 q^{79} +(1.74446e10 - 2.05584e9i) q^{80} -1.22922e9 q^{81} +(-1.03971e9 - 4.52858e9i) q^{82} +(-2.00793e10 + 2.00793e10i) q^{83} +(2.54653e9 + 8.83776e8i) q^{84} +(5.40649e9 + 5.40649e9i) q^{85} +(-3.75105e9 - 2.35027e9i) q^{86} +6.81047e7i q^{87} +(9.05349e10 + 9.84967e9i) q^{88} +3.72435e10i q^{89} +(-1.13268e10 + 1.80777e10i) q^{90} +(-2.71700e9 - 2.71700e9i) q^{91} +(2.07988e10 + 4.29083e10i) q^{92} +(4.47042e10 - 4.47042e10i) q^{93} +(1.10522e10 - 2.53744e9i) q^{94} -3.56057e9 q^{95} +(1.62225e10 + 4.54285e10i) q^{96} -1.06041e11 q^{97} +(8.60315e10 - 1.97518e10i) q^{98} +(-7.82084e10 + 7.82084e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 44.1073 10.1265i 0.974643 0.223766i
\(3\) −179.701 + 179.701i −0.426956 + 0.426956i −0.887590 0.460634i \(-0.847622\pi\)
0.460634 + 0.887590i \(0.347622\pi\)
\(4\) 1842.91 893.305i 0.899858 0.436184i
\(5\) 2961.29 + 2961.29i 0.423785 + 0.423785i 0.886505 0.462719i \(-0.153126\pi\)
−0.462719 + 0.886505i \(0.653126\pi\)
\(6\) −6106.38 + 9745.87i −0.320592 + 0.511668i
\(7\) 5179.04i 0.116469i −0.998303 0.0582345i \(-0.981453\pi\)
0.998303 0.0582345i \(-0.0185471\pi\)
\(8\) 72239.7 58063.5i 0.779437 0.626481i
\(9\) 112562.i 0.635416i
\(10\) 160602. + 100627.i 0.507868 + 0.318211i
\(11\) 694803. + 694803.i 1.30077 + 1.30077i 0.927870 + 0.372903i \(0.121638\pi\)
0.372903 + 0.927870i \(0.378362\pi\)
\(12\) −170645. + 491700.i −0.197968 + 0.570431i
\(13\) 524615. 524615.i 0.391879 0.391879i −0.483478 0.875357i \(-0.660627\pi\)
0.875357 + 0.483478i \(0.160627\pi\)
\(14\) −52445.5 228434.i −0.0260618 0.113516i
\(15\) −1.06429e6 −0.361876
\(16\) 2.59832e6 3.29256e6i 0.619487 0.785007i
\(17\) 1.82572e6 0.311864 0.155932 0.987768i \(-0.450162\pi\)
0.155932 + 0.987768i \(0.450162\pi\)
\(18\) 1.13986e6 + 4.96481e6i 0.142185 + 0.619304i
\(19\) −601185. + 601185.i −0.0557011 + 0.0557011i −0.734409 0.678708i \(-0.762540\pi\)
0.678708 + 0.734409i \(0.262540\pi\)
\(20\) 8.10272e6 + 2.81205e6i 0.566195 + 0.196498i
\(21\) 930679. + 930679.i 0.0497272 + 0.0497272i
\(22\) 3.76818e7 + 2.36100e7i 1.55886 + 0.976721i
\(23\) 2.32829e7i 0.754284i 0.926156 + 0.377142i \(0.123093\pi\)
−0.926156 + 0.377142i \(0.876907\pi\)
\(24\) −2.54748e6 + 2.34156e7i −0.0653054 + 0.600266i
\(25\) 3.12896e7i 0.640812i
\(26\) 1.78268e7 2.84518e7i 0.294253 0.469631i
\(27\) −5.20610e7 5.20610e7i −0.698252 0.698252i
\(28\) −4.62646e6 9.54450e6i −0.0508019 0.104805i
\(29\) 189495. 189495.i 0.00171557 0.00171557i −0.706248 0.707964i \(-0.749614\pi\)
0.707964 + 0.706248i \(0.249614\pi\)
\(30\) −4.69431e7 + 1.07776e7i −0.352700 + 0.0809755i
\(31\) −2.48770e8 −1.56066 −0.780330 0.625367i \(-0.784949\pi\)
−0.780330 + 0.625367i \(0.784949\pi\)
\(32\) 8.12627e7 1.71538e8i 0.428121 0.903721i
\(33\) −2.49713e8 −1.11075
\(34\) 8.05277e7 1.84882e7i 0.303956 0.0697846i
\(35\) 1.53366e7 1.53366e7i 0.0493578 0.0493578i
\(36\) 1.00552e8 + 2.07442e8i 0.277158 + 0.571784i
\(37\) −4.30934e8 4.30934e8i −1.02165 1.02165i −0.999760 0.0218884i \(-0.993032\pi\)
−0.0218884 0.999760i \(-0.506968\pi\)
\(38\) −2.04288e7 + 3.26046e7i −0.0418246 + 0.0667527i
\(39\) 1.88548e8i 0.334630i
\(40\) 3.85865e8 + 4.19799e7i 0.595807 + 0.0648204i
\(41\) 1.02672e8i 0.138401i −0.997603 0.0692007i \(-0.977955\pi\)
0.997603 0.0692007i \(-0.0220449\pi\)
\(42\) 5.04742e7 + 3.16252e7i 0.0595935 + 0.0373390i
\(43\) −6.91645e7 6.91645e7i −0.0717475 0.0717475i 0.670322 0.742070i \(-0.266156\pi\)
−0.742070 + 0.670322i \(0.766156\pi\)
\(44\) 1.90113e9 + 6.59787e8i 1.73789 + 0.603134i
\(45\) −3.33329e8 + 3.33329e8i −0.269280 + 0.269280i
\(46\) 2.35774e8 + 1.02695e9i 0.168783 + 0.735157i
\(47\) 2.50575e8 0.159367 0.0796836 0.996820i \(-0.474609\pi\)
0.0796836 + 0.996820i \(0.474609\pi\)
\(48\) 1.24755e8 + 1.05860e9i 0.0706696 + 0.599658i
\(49\) 1.95050e9 0.986435
\(50\) −3.16854e8 1.38010e9i −0.143392 0.624563i
\(51\) −3.28084e8 + 3.28084e8i −0.133152 + 0.133152i
\(52\) 4.98176e8 1.43546e9i 0.181704 0.523567i
\(53\) −1.76937e9 1.76937e9i −0.581169 0.581169i 0.354056 0.935224i \(-0.384802\pi\)
−0.935224 + 0.354056i \(0.884802\pi\)
\(54\) −2.82347e9 1.76908e9i −0.836791 0.524301i
\(55\) 4.11502e9i 1.10250i
\(56\) −3.00713e8 3.74132e8i −0.0729656 0.0907802i
\(57\) 2.16067e8i 0.0475639i
\(58\) 6.43918e6 1.02770e7i 0.00128818 0.00205595i
\(59\) 3.82611e9 + 3.82611e9i 0.696742 + 0.696742i 0.963706 0.266964i \(-0.0860206\pi\)
−0.266964 + 0.963706i \(0.586021\pi\)
\(60\) −1.96140e9 + 9.50738e8i −0.325637 + 0.157844i
\(61\) 7.80093e9 7.80093e9i 1.18258 1.18258i 0.203512 0.979072i \(-0.434764\pi\)
0.979072 0.203512i \(-0.0652355\pi\)
\(62\) −1.09726e10 + 2.51917e9i −1.52109 + 0.349223i
\(63\) 5.82964e8 0.0740063
\(64\) 1.84721e9 8.38897e9i 0.215043 0.976605i
\(65\) 3.10707e9 0.332145
\(66\) −1.10142e10 + 2.52872e9i −1.08258 + 0.248547i
\(67\) −6.53658e9 + 6.53658e9i −0.591479 + 0.591479i −0.938031 0.346552i \(-0.887352\pi\)
0.346552 + 0.938031i \(0.387352\pi\)
\(68\) 3.36464e9 1.63093e9i 0.280633 0.136030i
\(69\) −4.18397e9 4.18397e9i −0.322046 0.322046i
\(70\) 5.21152e8 8.31764e8i 0.0370617 0.0591509i
\(71\) 1.53408e10i 1.00908i 0.863388 + 0.504541i \(0.168338\pi\)
−0.863388 + 0.504541i \(0.831662\pi\)
\(72\) 6.53575e9 + 8.13145e9i 0.398076 + 0.495267i
\(73\) 2.49847e10i 1.41058i −0.708917 0.705291i \(-0.750816\pi\)
0.708917 0.705291i \(-0.249184\pi\)
\(74\) −2.33712e10 1.46435e10i −1.22435 0.767133i
\(75\) 5.62278e9 + 5.62278e9i 0.273599 + 0.273599i
\(76\) −5.70888e8 + 1.64497e9i −0.0258271 + 0.0744189i
\(77\) 3.59841e9 3.59841e9i 0.151500 0.151500i
\(78\) 1.90933e9 + 8.31632e9i 0.0748789 + 0.326145i
\(79\) 2.46282e10 0.900499 0.450249 0.892903i \(-0.351335\pi\)
0.450249 + 0.892903i \(0.351335\pi\)
\(80\) 1.74446e10 2.05584e9i 0.595204 0.0701447i
\(81\) −1.22922e9 −0.0391706
\(82\) −1.03971e9 4.52858e9i −0.0309695 0.134892i
\(83\) −2.00793e10 + 2.00793e10i −0.559524 + 0.559524i −0.929172 0.369648i \(-0.879478\pi\)
0.369648 + 0.929172i \(0.379478\pi\)
\(84\) 2.54653e9 + 8.83776e8i 0.0664375 + 0.0230572i
\(85\) 5.40649e9 + 5.40649e9i 0.132163 + 0.132163i
\(86\) −3.75105e9 2.35027e9i −0.0859828 0.0538735i
\(87\) 6.81047e7i 0.00146495i
\(88\) 9.05349e10 + 9.84967e9i 1.82878 + 0.198961i
\(89\) 3.72435e10i 0.706978i 0.935439 + 0.353489i \(0.115005\pi\)
−0.935439 + 0.353489i \(0.884995\pi\)
\(90\) −1.13268e10 + 1.80777e10i −0.202196 + 0.322708i
\(91\) −2.71700e9 2.71700e9i −0.0456417 0.0456417i
\(92\) 2.07988e10 + 4.29083e10i 0.329006 + 0.678748i
\(93\) 4.47042e10 4.47042e10i 0.666334 0.666334i
\(94\) 1.10522e10 2.53744e9i 0.155326 0.0356609i
\(95\) −3.56057e9 −0.0472106
\(96\) 1.62225e10 + 4.54285e10i 0.203061 + 0.568639i
\(97\) −1.06041e11 −1.25381 −0.626904 0.779097i \(-0.715678\pi\)
−0.626904 + 0.779097i \(0.715678\pi\)
\(98\) 8.60315e10 1.97518e10i 0.961422 0.220731i
\(99\) −7.82084e10 + 7.82084e10i −0.826533 + 0.826533i
\(100\) −2.79512e10 5.76640e10i −0.279512 0.576640i
\(101\) −1.45309e11 1.45309e11i −1.37571 1.37571i −0.851735 0.523973i \(-0.824449\pi\)
−0.523973 0.851735i \(-0.675551\pi\)
\(102\) −1.11486e10 + 1.77932e10i −0.0999811 + 0.159571i
\(103\) 9.17356e10i 0.779710i −0.920876 0.389855i \(-0.872525\pi\)
0.920876 0.389855i \(-0.127475\pi\)
\(104\) 7.43705e9 6.83589e10i 0.0599401 0.550950i
\(105\) 5.51202e9i 0.0421473i
\(106\) −9.59599e10 6.01248e10i −0.696478 0.436386i
\(107\) −1.50629e11 1.50629e11i −1.03824 1.03824i −0.999239 0.0390029i \(-0.987582\pi\)
−0.0390029 0.999239i \(-0.512418\pi\)
\(108\) −1.42450e11 4.94373e10i −0.932893 0.323761i
\(109\) −7.29906e10 + 7.29906e10i −0.454382 + 0.454382i −0.896806 0.442424i \(-0.854119\pi\)
0.442424 + 0.896806i \(0.354119\pi\)
\(110\) 4.16708e10 + 1.81503e11i 0.246701 + 1.07454i
\(111\) 1.54879e11 0.872399
\(112\) −1.70523e10 1.34568e10i −0.0914289 0.0721510i
\(113\) 3.01998e11 1.54196 0.770979 0.636861i \(-0.219767\pi\)
0.770979 + 0.636861i \(0.219767\pi\)
\(114\) −2.18800e9 9.53014e9i −0.0106432 0.0463578i
\(115\) −6.89475e10 + 6.89475e10i −0.319654 + 0.319654i
\(116\) 1.79945e8 5.18498e8i 0.000795464 0.00229207i
\(117\) 5.90517e10 + 5.90517e10i 0.249006 + 0.249006i
\(118\) 2.07505e11 + 1.30014e11i 0.834982 + 0.523167i
\(119\) 9.45549e9i 0.0363225i
\(120\) −7.68842e10 + 6.17965e10i −0.282059 + 0.226708i
\(121\) 6.80189e11i 2.38402i
\(122\) 2.65082e11 4.23074e11i 0.887975 1.41722i
\(123\) 1.84502e10 + 1.84502e10i 0.0590913 + 0.0590913i
\(124\) −4.58460e11 + 2.22227e11i −1.40437 + 0.680735i
\(125\) 2.37252e11 2.37252e11i 0.695352 0.695352i
\(126\) 2.57130e10 5.90338e9i 0.0721297 0.0165601i
\(127\) 4.26018e11 1.14421 0.572107 0.820179i \(-0.306126\pi\)
0.572107 + 0.820179i \(0.306126\pi\)
\(128\) −3.47556e9 3.88721e11i −0.00894066 0.999960i
\(129\) 2.48578e10 0.0612661
\(130\) 1.37045e11 3.14637e10i 0.323723 0.0743228i
\(131\) 3.65762e11 3.65762e11i 0.828336 0.828336i −0.158951 0.987287i \(-0.550811\pi\)
0.987287 + 0.158951i \(0.0508111\pi\)
\(132\) −4.60199e11 + 2.23070e11i −0.999514 + 0.484490i
\(133\) 3.11356e9 + 3.11356e9i 0.00648744 + 0.00648744i
\(134\) −2.22118e11 + 3.54504e11i −0.444128 + 0.708834i
\(135\) 3.08335e11i 0.591817i
\(136\) 1.31890e11 1.06008e11i 0.243078 0.195377i
\(137\) 9.23893e11i 1.63553i 0.575552 + 0.817765i \(0.304787\pi\)
−0.575552 + 0.817765i \(0.695213\pi\)
\(138\) −2.26912e11 1.42175e11i −0.385943 0.241817i
\(139\) −4.31354e11 4.31354e11i −0.705103 0.705103i 0.260398 0.965501i \(-0.416146\pi\)
−0.965501 + 0.260398i \(0.916146\pi\)
\(140\) 1.45637e10 4.19643e10i 0.0228859 0.0659441i
\(141\) −4.50285e10 + 4.50285e10i −0.0680428 + 0.0680428i
\(142\) 1.55348e11 + 6.76641e11i 0.225798 + 0.983495i
\(143\) 7.29007e11 1.01949
\(144\) 3.70617e11 + 2.92472e11i 0.498806 + 0.393632i
\(145\) 1.12230e9 0.00145406
\(146\) −2.53007e11 1.10201e12i −0.315640 1.37481i
\(147\) −3.50508e11 + 3.50508e11i −0.421165 + 0.421165i
\(148\) −1.17913e12 4.09217e11i −1.36497 0.473712i
\(149\) −6.92517e11 6.92517e11i −0.772513 0.772513i 0.206032 0.978545i \(-0.433945\pi\)
−0.978545 + 0.206032i \(0.933945\pi\)
\(150\) 3.04945e11 + 1.91067e11i 0.327883 + 0.205439i
\(151\) 1.06664e11i 0.110572i −0.998471 0.0552862i \(-0.982393\pi\)
0.998471 0.0552862i \(-0.0176071\pi\)
\(152\) −8.52254e9 + 7.83363e10i −0.00851979 + 0.0783111i
\(153\) 2.05507e11i 0.198164i
\(154\) 1.22277e11 1.95155e11i 0.113758 0.181559i
\(155\) −7.36680e11 7.36680e11i −0.661385 0.661385i
\(156\) 1.68430e11 + 3.47476e11i 0.145960 + 0.301120i
\(157\) −2.38255e11 + 2.38255e11i −0.199339 + 0.199339i −0.799717 0.600377i \(-0.795017\pi\)
0.600377 + 0.799717i \(0.295017\pi\)
\(158\) 1.08628e12 2.49397e11i 0.877665 0.201501i
\(159\) 6.35916e11 0.496267
\(160\) 7.48615e11 2.67330e11i 0.564415 0.201552i
\(161\) 1.20583e11 0.0878506
\(162\) −5.42174e10 + 1.24476e10i −0.0381774 + 0.00876505i
\(163\) −2.01643e12 + 2.01643e12i −1.37262 + 1.37262i −0.516082 + 0.856539i \(0.672610\pi\)
−0.856539 + 0.516082i \(0.827390\pi\)
\(164\) −9.17173e10 1.89215e11i −0.0603684 0.124541i
\(165\) −7.39474e11 7.39474e11i −0.470718 0.470718i
\(166\) −6.82310e11 + 1.08897e12i −0.420133 + 0.670538i
\(167\) 1.58210e12i 0.942525i −0.881993 0.471263i \(-0.843798\pi\)
0.881993 0.471263i \(-0.156202\pi\)
\(168\) 1.21270e11 + 1.31935e10i 0.0699123 + 0.00760605i
\(169\) 1.24172e12i 0.692862i
\(170\) 2.93215e11 + 1.83717e11i 0.158386 + 0.0992385i
\(171\) −6.76707e10 6.76707e10i −0.0353934 0.0353934i
\(172\) −1.89249e11 6.56788e10i −0.0958576 0.0332674i
\(173\) 2.50263e12 2.50263e12i 1.22784 1.22784i 0.263066 0.964778i \(-0.415266\pi\)
0.964778 0.263066i \(-0.0847337\pi\)
\(174\) 6.89662e8 + 3.00392e9i 0.000327805 + 0.00142780i
\(175\) −1.62050e11 −0.0746347
\(176\) 4.09299e12 4.82359e11i 1.82693 0.215303i
\(177\) −1.37511e12 −0.594957
\(178\) 3.77146e11 + 1.64271e12i 0.158198 + 0.689051i
\(179\) −1.34310e12 + 1.34310e12i −0.546283 + 0.546283i −0.925364 0.379081i \(-0.876240\pi\)
0.379081 + 0.925364i \(0.376240\pi\)
\(180\) −3.16531e11 + 9.12059e11i −0.124858 + 0.359769i
\(181\) −1.48029e12 1.48029e12i −0.566390 0.566390i 0.364725 0.931115i \(-0.381163\pi\)
−0.931115 + 0.364725i \(0.881163\pi\)
\(182\) −1.47353e11 9.23259e10i −0.0546975 0.0342713i
\(183\) 2.80367e12i 1.00982i
\(184\) 1.35189e12 + 1.68195e12i 0.472544 + 0.587916i
\(185\) 2.55224e12i 0.865920i
\(186\) 1.51908e12 2.42448e12i 0.500335 0.798541i
\(187\) 1.26852e12 + 1.26852e12i 0.405665 + 0.405665i
\(188\) 4.61786e11 2.23839e11i 0.143408 0.0695134i
\(189\) −2.69626e11 + 2.69626e11i −0.0813246 + 0.0813246i
\(190\) −1.57047e11 + 3.60561e10i −0.0460135 + 0.0105641i
\(191\) 3.79477e12 1.08020 0.540098 0.841602i \(-0.318387\pi\)
0.540098 + 0.841602i \(0.318387\pi\)
\(192\) 1.17556e12 + 1.83945e12i 0.325154 + 0.508782i
\(193\) 1.92445e12 0.517299 0.258650 0.965971i \(-0.416723\pi\)
0.258650 + 0.965971i \(0.416723\pi\)
\(194\) −4.67720e12 + 1.07383e12i −1.22201 + 0.280560i
\(195\) −5.58344e11 + 5.58344e11i −0.141811 + 0.141811i
\(196\) 3.59460e12 1.74239e12i 0.887651 0.430267i
\(197\) 1.87881e12 + 1.87881e12i 0.451147 + 0.451147i 0.895735 0.444588i \(-0.146650\pi\)
−0.444588 + 0.895735i \(0.646650\pi\)
\(198\) −2.65759e12 + 4.24154e12i −0.620624 + 0.990524i
\(199\) 3.42680e12i 0.778390i 0.921155 + 0.389195i \(0.127247\pi\)
−0.921155 + 0.389195i \(0.872753\pi\)
\(200\) −1.81678e12 2.26035e12i −0.401457 0.499472i
\(201\) 2.34926e12i 0.505071i
\(202\) −7.88068e12 4.93773e12i −1.64866 1.03299i
\(203\) −9.81400e8 9.81400e8i −0.000199810 0.000199810i
\(204\) −3.11550e11 + 8.97708e11i −0.0617393 + 0.177897i
\(205\) 3.04041e11 3.04041e11i 0.0586525 0.0586525i
\(206\) −9.28960e11 4.04621e12i −0.174473 0.759939i
\(207\) −2.62078e12 −0.479284
\(208\) −3.64208e11 3.09044e12i −0.0648636 0.550392i
\(209\) −8.35410e11 −0.144909
\(210\) 5.58174e10 + 2.43120e11i 0.00943113 + 0.0410785i
\(211\) 4.45545e12 4.45545e12i 0.733395 0.733395i −0.237896 0.971291i \(-0.576458\pi\)
0.971291 + 0.237896i \(0.0764578\pi\)
\(212\) −4.84138e12 1.68020e12i −0.776466 0.269473i
\(213\) −2.75675e12 2.75675e12i −0.430834 0.430834i
\(214\) −8.16920e12 5.11850e12i −1.24424 0.779592i
\(215\) 4.09632e11i 0.0608111i
\(216\) −6.78371e12 7.38028e11i −0.981684 0.106802i
\(217\) 1.28839e12i 0.181769i
\(218\) −2.48028e12 + 3.95856e12i −0.341185 + 0.544536i
\(219\) 4.48978e12 + 4.48978e12i 0.602257 + 0.602257i
\(220\) 3.67597e12 + 7.58361e12i 0.480891 + 0.992090i
\(221\) 9.57801e11 9.57801e11i 0.122213 0.122213i
\(222\) 6.83128e12 1.56838e12i 0.850277 0.195213i
\(223\) −5.95131e12 −0.722663 −0.361332 0.932437i \(-0.617678\pi\)
−0.361332 + 0.932437i \(0.617678\pi\)
\(224\) −8.88400e11 4.20863e11i −0.105255 0.0498628i
\(225\) 3.52203e12 0.407183
\(226\) 1.33203e13 3.05818e12i 1.50286 0.345038i
\(227\) 1.36916e12 1.36916e12i 0.150769 0.150769i −0.627692 0.778462i \(-0.716000\pi\)
0.778462 + 0.627692i \(0.216000\pi\)
\(228\) −1.93014e11 3.98192e11i −0.0207466 0.0428007i
\(229\) 5.82685e12 + 5.82685e12i 0.611419 + 0.611419i 0.943316 0.331897i \(-0.107689\pi\)
−0.331897 + 0.943316i \(0.607689\pi\)
\(230\) −2.34289e12 + 3.73929e12i −0.240021 + 0.383077i
\(231\) 1.29328e12i 0.129368i
\(232\) 2.68632e9 2.46917e10i 0.000262406 0.00241195i
\(233\) 2.78470e12i 0.265657i −0.991139 0.132828i \(-0.957594\pi\)
0.991139 0.132828i \(-0.0424059\pi\)
\(234\) 3.20260e12 + 2.00663e12i 0.298411 + 0.186973i
\(235\) 7.42024e11 + 7.42024e11i 0.0675375 + 0.0675375i
\(236\) 1.04691e13 + 3.63329e12i 0.930876 + 0.323061i
\(237\) −4.42571e12 + 4.42571e12i −0.384474 + 0.384474i
\(238\) −9.57509e10 4.17056e11i −0.00812774 0.0354015i
\(239\) −7.89713e12 −0.655059 −0.327530 0.944841i \(-0.606216\pi\)
−0.327530 + 0.944841i \(0.606216\pi\)
\(240\) −2.76537e12 + 3.50425e12i −0.224177 + 0.284075i
\(241\) 6.72861e12 0.533128 0.266564 0.963817i \(-0.414112\pi\)
0.266564 + 0.963817i \(0.414112\pi\)
\(242\) 6.88793e12 + 3.00013e13i 0.533463 + 2.32357i
\(243\) 9.44334e12 9.44334e12i 0.714976 0.714976i
\(244\) 7.40779e12 2.13450e13i 0.548333 1.57998i
\(245\) 5.77601e12 + 5.77601e12i 0.418037 + 0.418037i
\(246\) 1.00063e12 + 6.26954e11i 0.0708156 + 0.0443703i
\(247\) 6.30781e11i 0.0436562i
\(248\) −1.79711e13 + 1.44444e13i −1.21644 + 0.977724i
\(249\) 7.21653e12i 0.477784i
\(250\) 8.06201e12 1.28671e13i 0.522124 0.833316i
\(251\) −5.58474e12 5.58474e12i −0.353832 0.353832i 0.507701 0.861533i \(-0.330495\pi\)
−0.861533 + 0.507701i \(0.830495\pi\)
\(252\) 1.07435e12 5.20764e11i 0.0665951 0.0322803i
\(253\) −1.61770e13 + 1.61770e13i −0.981152 + 0.981152i
\(254\) 1.87905e13 4.31407e12i 1.11520 0.256036i
\(255\) −1.94310e12 −0.112856
\(256\) −4.08967e12 1.71102e13i −0.232471 0.972603i
\(257\) −2.56783e13 −1.42868 −0.714340 0.699799i \(-0.753273\pi\)
−0.714340 + 0.699799i \(0.753273\pi\)
\(258\) 1.09641e12 2.51723e11i 0.0597126 0.0137093i
\(259\) −2.23183e12 + 2.23183e12i −0.118990 + 0.118990i
\(260\) 5.72605e12 2.77556e12i 0.298883 0.144876i
\(261\) 2.13299e10 + 2.13299e10i 0.00109010 + 0.00109010i
\(262\) 1.24289e13 1.98367e13i 0.621978 0.992685i
\(263\) 2.11569e13i 1.03680i −0.855138 0.518401i \(-0.826527\pi\)
0.855138 0.518401i \(-0.173473\pi\)
\(264\) −1.80392e13 + 1.44992e13i −0.865757 + 0.695862i
\(265\) 1.04793e13i 0.492582i
\(266\) 1.68860e11 + 1.05801e11i 0.00777461 + 0.00487127i
\(267\) −6.69270e12 6.69270e12i −0.301849 0.301849i
\(268\) −6.20716e12 + 1.78855e13i −0.274253 + 0.790240i
\(269\) −1.13645e13 + 1.13645e13i −0.491940 + 0.491940i −0.908917 0.416977i \(-0.863089\pi\)
0.416977 + 0.908917i \(0.363089\pi\)
\(270\) −3.12236e12 1.35998e13i −0.132429 0.576811i
\(271\) −4.20682e13 −1.74833 −0.874163 0.485633i \(-0.838589\pi\)
−0.874163 + 0.485633i \(0.838589\pi\)
\(272\) 4.74381e12 6.01129e12i 0.193196 0.244816i
\(273\) 9.76495e11 0.0389741
\(274\) 9.35580e12 + 4.07504e13i 0.365976 + 1.59406i
\(275\) 2.17401e13 2.17401e13i 0.833551 0.833551i
\(276\) −1.14482e13 3.97311e12i −0.430267 0.149324i
\(277\) 2.99399e13 + 2.99399e13i 1.10309 + 1.10309i 0.994036 + 0.109056i \(0.0347829\pi\)
0.109056 + 0.994036i \(0.465217\pi\)
\(278\) −2.33940e13 1.46578e13i −0.845002 0.529446i
\(279\) 2.80021e13i 0.991670i
\(280\) 2.17416e11 1.99841e12i 0.00754956 0.0693930i
\(281\) 1.93200e13i 0.657844i 0.944357 + 0.328922i \(0.106685\pi\)
−0.944357 + 0.328922i \(0.893315\pi\)
\(282\) −1.53010e12 + 2.44207e12i −0.0510918 + 0.0815431i
\(283\) 2.01259e13 + 2.01259e13i 0.659068 + 0.659068i 0.955160 0.296092i \(-0.0956833\pi\)
−0.296092 + 0.955160i \(0.595683\pi\)
\(284\) 1.37040e13 + 2.82717e13i 0.440145 + 0.908030i
\(285\) 6.39837e11 6.39837e11i 0.0201569 0.0201569i
\(286\) 3.21545e13 7.38229e12i 0.993640 0.228128i
\(287\) −5.31742e11 −0.0161195
\(288\) 1.93086e13 + 9.14711e12i 0.574239 + 0.272035i
\(289\) −3.09386e13 −0.902741
\(290\) 4.95015e10 1.13649e10i 0.00141719 0.000325370i
\(291\) 1.90557e13 1.90557e13i 0.535321 0.535321i
\(292\) −2.23190e13 4.60445e13i −0.615273 1.26932i
\(293\) 1.16215e13 + 1.16215e13i 0.314406 + 0.314406i 0.846614 0.532207i \(-0.178637\pi\)
−0.532207 + 0.846614i \(0.678637\pi\)
\(294\) −1.19105e13 + 1.90094e13i −0.316243 + 0.504728i
\(295\) 2.26605e13i 0.590538i
\(296\) −5.61521e13 6.10902e12i −1.43635 0.156267i
\(297\) 7.23442e13i 1.81653i
\(298\) −3.75578e13 2.35323e13i −0.925787 0.580062i
\(299\) 1.22146e13 + 1.22146e13i 0.295588 + 0.295588i
\(300\) 1.53851e13 + 5.33941e12i 0.365539 + 0.126861i
\(301\) −3.58206e11 + 3.58206e11i −0.00835635 + 0.00835635i
\(302\) −1.08014e12 4.70468e12i −0.0247423 0.107769i
\(303\) 5.22245e13 1.17473
\(304\) 4.17366e11 + 3.54151e12i 0.00921961 + 0.0782318i
\(305\) 4.62016e13 1.00232
\(306\) 2.08107e12 + 9.06437e12i 0.0443423 + 0.193139i
\(307\) −2.57889e13 + 2.57889e13i −0.539723 + 0.539723i −0.923448 0.383724i \(-0.874641\pi\)
0.383724 + 0.923448i \(0.374641\pi\)
\(308\) 3.41706e12 9.84602e12i 0.0702464 0.202410i
\(309\) 1.64850e13 + 1.64850e13i 0.332902 + 0.332902i
\(310\) −3.99529e13 2.50330e13i −0.792610 0.496619i
\(311\) 8.96609e13i 1.74752i 0.486361 + 0.873758i \(0.338324\pi\)
−0.486361 + 0.873758i \(0.661676\pi\)
\(312\) 1.09477e13 + 1.36206e13i 0.209640 + 0.260823i
\(313\) 2.96628e13i 0.558108i 0.960275 + 0.279054i \(0.0900209\pi\)
−0.960275 + 0.279054i \(0.909979\pi\)
\(314\) −8.09609e12 + 1.29215e13i −0.149679 + 0.238890i
\(315\) 1.72633e12 + 1.72633e12i 0.0313628 + 0.0313628i
\(316\) 4.53875e13 2.20005e13i 0.810321 0.392783i
\(317\) 2.58883e13 2.58883e13i 0.454233 0.454233i −0.442524 0.896757i \(-0.645917\pi\)
0.896757 + 0.442524i \(0.145917\pi\)
\(318\) 2.80486e13 6.43960e12i 0.483684 0.111048i
\(319\) 2.63323e11 0.00446313
\(320\) 3.03123e13 1.93721e13i 0.505003 0.322739i
\(321\) 5.41365e13 0.886568
\(322\) 5.31860e12 1.22109e12i 0.0856230 0.0196580i
\(323\) −1.09760e12 + 1.09760e12i −0.0173712 + 0.0173712i
\(324\) −2.26533e12 + 1.09806e12i −0.0352480 + 0.0170856i
\(325\) −1.64150e13 1.64150e13i −0.251121 0.251121i
\(326\) −6.85198e13 + 1.09358e14i −1.03067 + 1.64496i
\(327\) 2.62330e13i 0.388003i
\(328\) −5.96148e12 7.41698e12i −0.0867058 0.107875i
\(329\) 1.29774e12i 0.0185613i
\(330\) −4.01045e13 2.51279e13i −0.564113 0.353451i
\(331\) 2.92511e13 + 2.92511e13i 0.404658 + 0.404658i 0.879871 0.475213i \(-0.157629\pi\)
−0.475213 + 0.879871i \(0.657629\pi\)
\(332\) −1.90673e13 + 5.49412e13i −0.259436 + 0.747547i
\(333\) 4.85069e13 4.85069e13i 0.649173 0.649173i
\(334\) −1.60211e13 6.97821e13i −0.210905 0.918625i
\(335\) −3.87134e13 −0.501320
\(336\) 5.48251e12 6.46113e11i 0.0698415 0.00823081i
\(337\) −1.74548e13 −0.218751 −0.109376 0.994000i \(-0.534885\pi\)
−0.109376 + 0.994000i \(0.534885\pi\)
\(338\) 1.25743e13 + 5.47689e13i 0.155039 + 0.675293i
\(339\) −5.42693e13 + 5.42693e13i −0.658349 + 0.658349i
\(340\) 1.47933e13 + 5.13403e12i 0.176576 + 0.0612807i
\(341\) −1.72846e14 1.72846e14i −2.03007 2.03007i
\(342\) −3.67004e12 2.29951e12i −0.0424157 0.0265761i
\(343\) 2.03424e13i 0.231358i
\(344\) −9.01235e12 9.80491e11i −0.100871 0.0109742i
\(345\) 2.47799e13i 0.272957i
\(346\) 8.50414e13 1.35727e14i 0.921960 1.47146i
\(347\) −1.65389e13 1.65389e13i −0.176480 0.176480i 0.613340 0.789819i \(-0.289826\pi\)
−0.789819 + 0.613340i \(0.789826\pi\)
\(348\) 6.08383e10 + 1.25511e11i 0.000638985 + 0.00131824i
\(349\) −4.01630e13 + 4.01630e13i −0.415228 + 0.415228i −0.883555 0.468327i \(-0.844857\pi\)
0.468327 + 0.883555i \(0.344857\pi\)
\(350\) −7.14760e12 + 1.64100e12i −0.0727422 + 0.0167007i
\(351\) −5.46239e13 −0.547260
\(352\) 1.75646e14 6.27232e13i 1.73243 0.618648i
\(353\) −6.14061e13 −0.596281 −0.298140 0.954522i \(-0.596366\pi\)
−0.298140 + 0.954522i \(0.596366\pi\)
\(354\) −6.06525e13 + 1.39251e13i −0.579870 + 0.133131i
\(355\) −4.54285e13 + 4.54285e13i −0.427634 + 0.427634i
\(356\) 3.32698e13 + 6.86364e13i 0.308372 + 0.636179i
\(357\) 1.69916e12 + 1.69916e12i 0.0155081 + 0.0155081i
\(358\) −4.56397e13 + 7.28415e13i −0.410191 + 0.654670i
\(359\) 2.12990e13i 0.188512i 0.995548 + 0.0942560i \(0.0300472\pi\)
−0.995548 + 0.0942560i \(0.969953\pi\)
\(360\) −4.72535e12 + 4.34338e13i −0.0411879 + 0.378586i
\(361\) 1.15767e14i 0.993795i
\(362\) −8.02819e13 5.03016e13i −0.678767 0.425289i
\(363\) −1.22231e14 1.22231e14i −1.01787 1.01787i
\(364\) −7.43429e12 2.58007e12i −0.0609792 0.0211629i
\(365\) 7.39870e13 7.39870e13i 0.597784 0.597784i
\(366\) 2.83913e13 + 1.23662e14i 0.225964 + 0.984218i
\(367\) 1.60814e14 1.26084 0.630420 0.776254i \(-0.282883\pi\)
0.630420 + 0.776254i \(0.282883\pi\)
\(368\) 7.66604e13 + 6.04965e13i 0.592118 + 0.467269i
\(369\) 1.15570e13 0.0879425
\(370\) −2.58453e13 1.12573e14i −0.193763 0.843962i
\(371\) −9.16366e12 + 9.16366e12i −0.0676881 + 0.0676881i
\(372\) 4.24513e13 1.22320e14i 0.308962 0.890250i
\(373\) −5.26476e13 5.26476e13i −0.377555 0.377555i 0.492665 0.870219i \(-0.336023\pi\)
−0.870219 + 0.492665i \(0.836023\pi\)
\(374\) 6.87964e13 + 4.31052e13i 0.486152 + 0.304604i
\(375\) 8.52688e13i 0.593770i
\(376\) 1.81014e13 1.45492e13i 0.124217 0.0998405i
\(377\) 1.98823e11i 0.00134459i
\(378\) −9.16211e12 + 1.46228e13i −0.0610648 + 0.0974601i
\(379\) −1.01266e13 1.01266e13i −0.0665196 0.0665196i 0.673064 0.739584i \(-0.264978\pi\)
−0.739584 + 0.673064i \(0.764978\pi\)
\(380\) −6.56180e12 + 3.18067e12i −0.0424828 + 0.0205925i
\(381\) −7.65558e13 + 7.65558e13i −0.488529 + 0.488529i
\(382\) 1.67377e14 3.84277e13i 1.05280 0.241711i
\(383\) 2.19772e14 1.36263 0.681315 0.731990i \(-0.261408\pi\)
0.681315 + 0.731990i \(0.261408\pi\)
\(384\) 7.04780e13 + 6.92289e13i 0.430757 + 0.423122i
\(385\) 2.13119e13 0.128407
\(386\) 8.48824e13 1.94879e13i 0.504182 0.115754i
\(387\) 7.78530e12 7.78530e12i 0.0455895 0.0455895i
\(388\) −1.95425e14 + 9.47273e13i −1.12825 + 0.546891i
\(389\) 1.11456e14 + 1.11456e14i 0.634428 + 0.634428i 0.949175 0.314748i \(-0.101920\pi\)
−0.314748 + 0.949175i \(0.601920\pi\)
\(390\) −1.89730e13 + 3.02811e13i −0.106483 + 0.169948i
\(391\) 4.25082e13i 0.235234i
\(392\) 1.40904e14 1.13253e14i 0.768864 0.617983i
\(393\) 1.31456e14i 0.707327i
\(394\) 1.01895e14 + 6.38434e13i 0.540659 + 0.338756i
\(395\) 7.29312e13 + 7.29312e13i 0.381618 + 0.381618i
\(396\) −7.42670e13 + 2.13995e14i −0.383242 + 1.10428i
\(397\) 1.72989e14 1.72989e14i 0.880379 0.880379i −0.113194 0.993573i \(-0.536108\pi\)
0.993573 + 0.113194i \(0.0361081\pi\)
\(398\) 3.47015e13 + 1.51147e14i 0.174177 + 0.758653i
\(399\) −1.11902e12 −0.00553971
\(400\) −1.03023e14 8.13005e13i −0.503042 0.396975i
\(401\) −6.99669e13 −0.336976 −0.168488 0.985704i \(-0.553888\pi\)
−0.168488 + 0.985704i \(0.553888\pi\)
\(402\) −2.37898e13 1.03620e14i −0.113018 0.492264i
\(403\) −1.30508e14 + 1.30508e14i −0.611590 + 0.611590i
\(404\) −3.97598e14 1.37986e14i −1.83800 0.637880i
\(405\) −3.64006e12 3.64006e12i −0.0165999 0.0165999i
\(406\) −5.32251e10 3.33488e10i −0.000239455 0.000150033i
\(407\) 5.98829e14i 2.65787i
\(408\) −4.65099e12 + 4.27504e13i −0.0203664 + 0.187201i
\(409\) 3.35300e14i 1.44862i 0.689472 + 0.724312i \(0.257843\pi\)
−0.689472 + 0.724312i \(0.742157\pi\)
\(410\) 1.03316e13 1.64893e13i 0.0440408 0.0702896i
\(411\) −1.66025e14 1.66025e14i −0.698300 0.698300i
\(412\) −8.19478e13 1.69060e14i −0.340097 0.701628i
\(413\) 1.98156e13 1.98156e13i 0.0811488 0.0811488i
\(414\) −1.15595e14 + 2.65393e13i −0.467131 + 0.107248i
\(415\) −1.18921e14 −0.474236
\(416\) −4.73595e13 1.32623e14i −0.186378 0.521921i
\(417\) 1.55030e14 0.602097
\(418\) −3.68477e13 + 8.45977e12i −0.141234 + 0.0324257i
\(419\) 2.19319e13 2.19319e13i 0.0829657 0.0829657i −0.664406 0.747372i \(-0.731315\pi\)
0.747372 + 0.664406i \(0.231315\pi\)
\(420\) 4.92391e12 + 1.01581e13i 0.0183840 + 0.0379265i
\(421\) 2.94928e13 + 2.94928e13i 0.108684 + 0.108684i 0.759357 0.650674i \(-0.225513\pi\)
−0.650674 + 0.759357i \(0.725513\pi\)
\(422\) 1.51400e14 2.41636e14i 0.550689 0.878907i
\(423\) 2.82052e13i 0.101265i
\(424\) −2.30555e14 2.50830e13i −0.817076 0.0888931i
\(425\) 5.71262e13i 0.199846i
\(426\) −1.49509e14 9.36767e13i −0.516316 0.323503i
\(427\) −4.04013e13 4.04013e13i −0.137734 0.137734i
\(428\) −4.12154e14 1.43038e14i −1.38713 0.481406i
\(429\) −1.31003e14 + 1.31003e14i −0.435278 + 0.435278i
\(430\) −4.14814e12 1.80678e13i −0.0136074 0.0592691i
\(431\) 4.93229e14 1.59744 0.798718 0.601705i \(-0.205512\pi\)
0.798718 + 0.601705i \(0.205512\pi\)
\(432\) −3.06685e14 + 3.61428e13i −0.980690 + 0.115574i
\(433\) 2.29557e14 0.724781 0.362391 0.932026i \(-0.381961\pi\)
0.362391 + 0.932026i \(0.381961\pi\)
\(434\) 1.30469e13 + 5.68274e13i 0.0406736 + 0.177159i
\(435\) −2.01678e11 + 2.01678e11i −0.000620822 + 0.000620822i
\(436\) −6.93122e13 + 1.99718e14i −0.210685 + 0.607073i
\(437\) −1.39974e13 1.39974e13i −0.0420144 0.0420144i
\(438\) 2.43498e14 + 1.52566e14i 0.721751 + 0.452221i
\(439\) 1.66738e14i 0.488067i 0.969767 + 0.244033i \(0.0784707\pi\)
−0.969767 + 0.244033i \(0.921529\pi\)
\(440\) 2.38932e14 + 2.97268e14i 0.690694 + 0.859327i
\(441\) 2.19553e14i 0.626797i
\(442\) 3.25468e13 5.19452e13i 0.0917670 0.146461i
\(443\) 4.92405e13 + 4.92405e13i 0.137120 + 0.137120i 0.772335 0.635215i \(-0.219089\pi\)
−0.635215 + 0.772335i \(0.719089\pi\)
\(444\) 2.85427e14 1.38354e14i 0.785035 0.380526i
\(445\) −1.10289e14 + 1.10289e14i −0.299607 + 0.299607i
\(446\) −2.62496e14 + 6.02659e13i −0.704339 + 0.161707i
\(447\) 2.48892e14 0.659659
\(448\) −4.34468e13 9.56676e12i −0.113744 0.0250458i
\(449\) −4.21793e14 −1.09080 −0.545399 0.838177i \(-0.683622\pi\)
−0.545399 + 0.838177i \(0.683622\pi\)
\(450\) 1.55347e14 3.56658e13i 0.396858 0.0911136i
\(451\) 7.13367e13 7.13367e13i 0.180029 0.180029i
\(452\) 5.56554e14 2.69776e14i 1.38754 0.672577i
\(453\) 1.91677e13 + 1.91677e13i 0.0472096 + 0.0472096i
\(454\) 4.65253e13 7.42549e13i 0.113209 0.180683i
\(455\) 1.60917e13i 0.0386846i
\(456\) −1.25456e13 1.56086e13i −0.0297979 0.0370730i
\(457\) 6.74966e13i 0.158396i −0.996859 0.0791978i \(-0.974764\pi\)
0.996859 0.0791978i \(-0.0252359\pi\)
\(458\) 3.16012e14 + 1.98001e14i 0.732730 + 0.459100i
\(459\) −9.50489e13 9.50489e13i −0.217760 0.217760i
\(460\) −6.54728e13 + 1.88655e14i −0.148215 + 0.427071i
\(461\) −1.27861e14 + 1.27861e14i −0.286011 + 0.286011i −0.835501 0.549489i \(-0.814822\pi\)
0.549489 + 0.835501i \(0.314822\pi\)
\(462\) 1.30963e13 + 5.70429e13i 0.0289480 + 0.126087i
\(463\) −7.04481e14 −1.53877 −0.769385 0.638785i \(-0.779437\pi\)
−0.769385 + 0.638785i \(0.779437\pi\)
\(464\) −1.31554e11 1.11629e12i −0.000283960 0.00240950i
\(465\) 2.64764e14 0.564765
\(466\) −2.81992e13 1.22826e14i −0.0594450 0.258920i
\(467\) 3.44528e14 3.44528e14i 0.717764 0.717764i −0.250383 0.968147i \(-0.580557\pi\)
0.968147 + 0.250383i \(0.0805566\pi\)
\(468\) 1.61578e14 + 5.60758e13i 0.332683 + 0.115458i
\(469\) 3.38532e13 + 3.38532e13i 0.0688889 + 0.0688889i
\(470\) 4.02428e13 + 2.52146e13i 0.0809375 + 0.0507123i
\(471\) 8.56292e13i 0.170219i
\(472\) 4.98555e14 + 5.42399e13i 0.979562 + 0.106571i
\(473\) 9.61113e13i 0.186654i
\(474\) −1.50389e14 + 2.40023e14i −0.288692 + 0.460757i
\(475\) 1.88109e13 + 1.88109e13i 0.0356939 + 0.0356939i
\(476\) −8.44663e12 1.74256e13i −0.0158433 0.0326851i
\(477\) 1.99164e14 1.99164e14i 0.369284 0.369284i
\(478\) −3.48321e14 + 7.99702e13i −0.638449 + 0.146580i
\(479\) −6.93135e14 −1.25595 −0.627975 0.778234i \(-0.716116\pi\)
−0.627975 + 0.778234i \(0.716116\pi\)
\(480\) −8.64874e13 + 1.82566e14i −0.154927 + 0.327035i
\(481\) −4.52149e14 −0.800726
\(482\) 2.96781e14 6.81372e13i 0.519610 0.119296i
\(483\) −2.16689e13 + 2.16689e13i −0.0375084 + 0.0375084i
\(484\) 6.07616e14 + 1.25353e15i 1.03987 + 2.14528i
\(485\) −3.14019e14 3.14019e14i −0.531345 0.531345i
\(486\) 3.20892e14 5.12148e14i 0.536859 0.856833i
\(487\) 2.22683e14i 0.368365i 0.982892 + 0.184182i \(0.0589637\pi\)
−0.982892 + 0.184182i \(0.941036\pi\)
\(488\) 1.10588e14 1.01649e15i 0.180883 1.66262i
\(489\) 7.24708e14i 1.17210i
\(490\) 3.13255e14 + 1.96273e14i 0.500979 + 0.313894i
\(491\) 5.87841e14 + 5.87841e14i 0.929634 + 0.929634i 0.997682 0.0680481i \(-0.0216771\pi\)
−0.0680481 + 0.997682i \(0.521677\pi\)
\(492\) 5.04838e13 + 1.75204e13i 0.0789485 + 0.0273991i
\(493\) 3.45964e11 3.45964e11i 0.000535024 0.000535024i
\(494\) 6.38760e12 + 2.78221e13i 0.00976876 + 0.0425492i
\(495\) −4.63196e14 −0.700545
\(496\) −6.46383e14 + 8.19089e14i −0.966810 + 1.22513i
\(497\) 7.94506e13 0.117527
\(498\) −7.30781e13 3.18302e14i −0.106912 0.465669i
\(499\) −9.60683e13 + 9.60683e13i −0.139004 + 0.139004i −0.773185 0.634181i \(-0.781337\pi\)
0.634181 + 0.773185i \(0.281337\pi\)
\(500\) 2.25295e14 6.49172e14i 0.322416 0.929019i
\(501\) 2.84305e14 + 2.84305e14i 0.402417 + 0.402417i
\(502\) −3.02881e14 1.89774e14i −0.424035 0.265684i
\(503\) 9.12018e14i 1.26293i 0.775404 + 0.631466i \(0.217546\pi\)
−0.775404 + 0.631466i \(0.782454\pi\)
\(504\) 4.21131e13 3.38489e13i 0.0576832 0.0463635i
\(505\) 8.60607e14i 1.16601i
\(506\) −5.49709e14 + 8.77342e14i −0.736724 + 1.17582i
\(507\) −2.23138e14 2.23138e14i −0.295822 0.295822i
\(508\) 7.85112e14 3.80564e14i 1.02963 0.499088i
\(509\) −4.32018e14 + 4.32018e14i −0.560472 + 0.560472i −0.929441 0.368970i \(-0.879711\pi\)
0.368970 + 0.929441i \(0.379711\pi\)
\(510\) −8.57051e13 + 1.96768e13i −0.109994 + 0.0252534i
\(511\) −1.29397e14 −0.164289
\(512\) −3.53651e14 7.13272e14i −0.444212 0.895922i
\(513\) 6.25966e13 0.0777867
\(514\) −1.13260e15 + 2.60032e14i −1.39245 + 0.319690i
\(515\) 2.71656e14 2.71656e14i 0.330430 0.330430i
\(516\) 4.58107e13 2.22056e13i 0.0551307 0.0267233i
\(517\) 1.74100e14 + 1.74100e14i 0.207301 + 0.207301i
\(518\) −7.58393e13 + 1.21040e14i −0.0893471 + 0.142599i
\(519\) 8.99450e14i 1.04847i
\(520\) 2.24454e14 1.80407e14i 0.258886 0.208083i
\(521\) 1.04084e15i 1.18789i −0.804504 0.593947i \(-0.797569\pi\)
0.804504 0.593947i \(-0.202431\pi\)
\(522\) 1.15680e12 + 7.24808e11i 0.00130639 + 0.000818531i
\(523\) −2.46703e12 2.46703e12i −0.00275686 0.00275686i 0.705727 0.708484i \(-0.250621\pi\)
−0.708484 + 0.705727i \(0.750621\pi\)
\(524\) 3.47329e14 1.00080e15i 0.384078 1.10669i
\(525\) 2.91206e13 2.91206e13i 0.0318658 0.0318658i
\(526\) −2.14245e14 9.33175e14i −0.232001 1.01051i
\(527\) −4.54185e14 −0.486714
\(528\) −6.48835e14 + 8.22195e14i −0.688094 + 0.871944i
\(529\) 4.10715e14 0.431056
\(530\) −1.06118e14 4.62212e14i −0.110223 0.480091i
\(531\) −4.30676e14 + 4.30676e14i −0.442721 + 0.442721i
\(532\) 8.51937e12 + 2.95665e12i 0.00866749 + 0.00300806i
\(533\) −5.38632e13 5.38632e13i −0.0542366 0.0542366i
\(534\) −3.62970e14 2.27423e14i −0.361738 0.226651i
\(535\) 8.92114e14i 0.879983i
\(536\) −9.26640e13 + 8.51737e14i −0.0904701 + 0.831571i
\(537\) 4.82714e14i 0.466478i
\(538\) −3.86174e14 + 6.16339e14i −0.369386 + 0.589545i
\(539\) 1.35522e15 + 1.35522e15i 1.28313 + 1.28313i
\(540\) −2.75437e14 5.68234e14i −0.258141 0.532551i
\(541\) 1.03487e15 1.03487e15i 0.960065 0.960065i −0.0391680 0.999233i \(-0.512471\pi\)
0.999233 + 0.0391680i \(0.0124708\pi\)
\(542\) −1.85551e15 + 4.26003e14i −1.70399 + 0.391216i
\(543\) 5.32020e14 0.483648
\(544\) 1.48363e14 3.13180e14i 0.133516 0.281838i
\(545\) −4.32293e14 −0.385121
\(546\) 4.30706e13 9.88847e12i 0.0379858 0.00872107i
\(547\) 5.79056e14 5.79056e14i 0.505580 0.505580i −0.407586 0.913167i \(-0.633629\pi\)
0.913167 + 0.407586i \(0.133629\pi\)
\(548\) 8.25318e14 + 1.70265e15i 0.713392 + 1.47174i
\(549\) 8.78089e14 + 8.78089e14i 0.751434 + 0.751434i
\(550\) 7.38747e14 1.17905e15i 0.625894 0.998935i
\(551\) 2.27843e11i 0.000191118i
\(552\) −5.45184e14 5.93128e13i −0.452770 0.0492588i
\(553\) 1.27550e14i 0.104880i
\(554\) 1.62375e15 + 1.01738e15i 1.32196 + 0.828286i
\(555\) 4.58641e14 + 4.58641e14i 0.369710 + 0.369710i
\(556\) −1.18028e15 4.09616e14i −0.942047 0.326938i
\(557\) −7.19074e14 + 7.19074e14i −0.568290 + 0.568290i −0.931649 0.363359i \(-0.881630\pi\)
0.363359 + 0.931649i \(0.381630\pi\)
\(558\) −2.83563e14 1.23510e15i −0.221902 0.966524i
\(559\) −7.25694e13 −0.0562327
\(560\) −1.06473e13 9.03462e13i −0.00816968 0.0693228i
\(561\) −4.55907e14 −0.346402
\(562\) 1.95644e14 + 8.52154e14i 0.147203 + 0.641163i
\(563\) 5.57706e14 5.57706e14i 0.415536 0.415536i −0.468126 0.883662i \(-0.655071\pi\)
0.883662 + 0.468126i \(0.155071\pi\)
\(564\) −4.27592e13 + 1.23208e14i −0.0315497 + 0.0909080i
\(565\) 8.94303e14 + 8.94303e14i 0.653459 + 0.653459i
\(566\) 1.09150e15 + 6.83895e14i 0.789833 + 0.494879i
\(567\) 6.36616e12i 0.00456216i
\(568\) 8.90739e14 + 1.10821e15i 0.632171 + 0.786516i
\(569\) 1.80466e15i 1.26846i 0.773143 + 0.634231i \(0.218683\pi\)
−0.773143 + 0.634231i \(0.781317\pi\)
\(570\) 2.17422e13 3.47008e13i 0.0151353 0.0241562i
\(571\) 1.82563e14 + 1.82563e14i 0.125868 + 0.125868i 0.767235 0.641367i \(-0.221632\pi\)
−0.641367 + 0.767235i \(0.721632\pi\)
\(572\) 1.34349e15 6.51225e14i 0.917397 0.444686i
\(573\) −6.81924e14 + 6.81924e14i −0.461196 + 0.461196i
\(574\) −2.34537e13 + 5.38468e12i −0.0157107 + 0.00360699i
\(575\) 7.28515e14 0.483354
\(576\) 9.44280e14 + 2.07925e14i 0.620551 + 0.136642i
\(577\) 2.15369e15 1.40190 0.700950 0.713211i \(-0.252760\pi\)
0.700950 + 0.713211i \(0.252760\pi\)
\(578\) −1.36462e15 + 3.13300e14i −0.879850 + 0.202003i
\(579\) −3.45826e14 + 3.45826e14i −0.220864 + 0.220864i
\(580\) 2.06829e12 1.00255e12i 0.00130845 0.000634240i
\(581\) 1.03991e14 + 1.03991e14i 0.0651671 + 0.0651671i
\(582\) 6.47530e14 1.03347e15i 0.401960 0.641534i
\(583\) 2.45873e15i 1.51194i
\(584\) −1.45070e15 1.80489e15i −0.883703 1.09946i
\(585\) 3.49739e14i 0.211051i
\(586\) 6.30280e14 + 3.94909e14i 0.376787 + 0.236081i
\(587\) −1.54304e15 1.54304e15i −0.913833 0.913833i 0.0827383 0.996571i \(-0.473633\pi\)
−0.996571 + 0.0827383i \(0.973633\pi\)
\(588\) −3.32843e14 + 9.59063e14i −0.195283 + 0.562694i
\(589\) 1.49557e14 1.49557e14i 0.0869305 0.0869305i
\(590\) 2.29471e14 + 9.99492e14i 0.132142 + 0.575564i
\(591\) −6.75247e14 −0.385240
\(592\) −2.53858e15 + 2.99171e14i −1.43490 + 0.169103i
\(593\) −2.91327e15 −1.63147 −0.815737 0.578424i \(-0.803668\pi\)
−0.815737 + 0.578424i \(0.803668\pi\)
\(594\) −7.32593e14 3.19091e15i −0.406478 1.77047i
\(595\) 2.80004e13 2.80004e13i 0.0153929 0.0153929i
\(596\) −1.89487e15 6.57617e14i −1.03211 0.358194i
\(597\) −6.15800e14 6.15800e14i −0.332339 0.332339i
\(598\) 6.62443e14 + 4.15061e14i 0.354235 + 0.221950i
\(599\) 1.31209e15i 0.695210i 0.937641 + 0.347605i \(0.113005\pi\)
−0.937641 + 0.347605i \(0.886995\pi\)
\(600\) 7.32666e14 + 7.97098e13i 0.384657 + 0.0418485i
\(601\) 2.98203e15i 1.55132i −0.631148 0.775662i \(-0.717416\pi\)
0.631148 0.775662i \(-0.282584\pi\)
\(602\) −1.21721e13 + 1.94269e13i −0.00627459 + 0.0100143i
\(603\) −7.35772e14 7.35772e14i −0.375836 0.375836i
\(604\) −9.52839e13 1.96573e14i −0.0482299 0.0994994i
\(605\) −2.01424e15 + 2.01424e15i −1.01031 + 1.01031i
\(606\) 2.30348e15 5.28851e14i 1.14495 0.262866i
\(607\) −8.61957e14 −0.424569 −0.212284 0.977208i \(-0.568090\pi\)
−0.212284 + 0.977208i \(0.568090\pi\)
\(608\) 5.42719e13 + 1.51980e14i 0.0264914 + 0.0741851i
\(609\) 3.52717e11 0.000170621
\(610\) 2.03783e15 4.67860e14i 0.976908 0.224286i
\(611\) 1.31455e14 1.31455e14i 0.0624526 0.0624526i
\(612\) 1.83580e14 + 3.78731e14i 0.0864358 + 0.178319i
\(613\) −8.86904e14 8.86904e14i −0.413851 0.413851i 0.469227 0.883078i \(-0.344533\pi\)
−0.883078 + 0.469227i \(0.844533\pi\)
\(614\) −8.76326e14 + 1.39863e15i −0.405266 + 0.646809i
\(615\) 1.09273e14i 0.0500841i
\(616\) 5.10119e13 4.68884e14i 0.0231727 0.212996i
\(617\) 3.31474e15i 1.49239i 0.665730 + 0.746193i \(0.268120\pi\)
−0.665730 + 0.746193i \(0.731880\pi\)
\(618\) 8.94043e14 + 5.60173e14i 0.398953 + 0.249969i
\(619\) −2.60524e15 2.60524e15i −1.15226 1.15226i −0.986099 0.166156i \(-0.946864\pi\)
−0.166156 0.986099i \(-0.553136\pi\)
\(620\) −2.01571e15 6.99554e14i −0.883638 0.306667i
\(621\) 1.21213e15 1.21213e15i 0.526680 0.526680i
\(622\) 9.07951e14 + 3.95470e15i 0.391035 + 1.70320i
\(623\) 1.92886e14 0.0823409
\(624\) 6.20803e14 + 4.89906e14i 0.262687 + 0.207299i
\(625\) −1.22671e14 −0.0514520
\(626\) 3.00380e14 + 1.30835e15i 0.124886 + 0.543956i
\(627\) 1.50124e14 1.50124e14i 0.0618698 0.0618698i
\(628\) −2.26248e14 + 6.51915e14i −0.0924285 + 0.266326i
\(629\) −7.86766e14 7.86766e14i −0.318616 0.318616i
\(630\) 9.36252e13 + 5.86619e13i 0.0375854 + 0.0235496i
\(631\) 2.45185e15i 0.975737i −0.872917 0.487868i \(-0.837775\pi\)
0.872917 0.487868i \(-0.162225\pi\)
\(632\) 1.77913e15 1.43000e15i 0.701882 0.564146i
\(633\) 1.60130e15i 0.626255i
\(634\) 8.79707e14 1.40402e15i 0.341073 0.544357i
\(635\) 1.26156e15 + 1.26156e15i 0.484901 + 0.484901i
\(636\) 1.17194e15 5.68067e14i 0.446570 0.216464i
\(637\) 1.02326e15 1.02326e15i 0.386563 0.386563i
\(638\) 1.16145e13 2.66654e12i 0.00434996 0.000998697i
\(639\) −1.72679e15 −0.641188
\(640\) 1.14082e15 1.16141e15i 0.419979 0.427557i
\(641\) −5.41404e14 −0.197607 −0.0988035 0.995107i \(-0.531502\pi\)
−0.0988035 + 0.995107i \(0.531502\pi\)
\(642\) 2.38781e15 5.48212e14i 0.864087 0.198384i
\(643\) 6.59814e14 6.59814e14i 0.236734 0.236734i −0.578762 0.815496i \(-0.696464\pi\)
0.815496 + 0.578762i \(0.196464\pi\)
\(644\) 2.22224e14 1.07718e14i 0.0790530 0.0383190i
\(645\) 7.36113e13 + 7.36113e13i 0.0259637 + 0.0259637i
\(646\) −3.72972e13 + 5.95269e13i −0.0130436 + 0.0208178i
\(647\) 1.35482e15i 0.469795i 0.972020 + 0.234898i \(0.0754755\pi\)
−0.972020 + 0.234898i \(0.924524\pi\)
\(648\) −8.87981e13 + 7.13725e13i −0.0305310 + 0.0245397i
\(649\) 5.31679e15i 1.81261i
\(650\) −8.90248e14 5.57795e14i −0.300945 0.188561i
\(651\) −2.31525e14 2.31525e14i −0.0776072 0.0776072i
\(652\) −1.91481e15 + 5.51737e15i −0.636448 + 1.83388i
\(653\) 9.93736e14 9.93736e14i 0.327528 0.327528i −0.524118 0.851646i \(-0.675605\pi\)
0.851646 + 0.524118i \(0.175605\pi\)
\(654\) −2.65648e14 1.15707e15i −0.0868218 0.378164i
\(655\) 2.16625e15 0.702073
\(656\) −3.38053e14 2.66774e14i −0.108646 0.0857379i
\(657\) 2.81233e15 0.896308
\(658\) −1.31415e13 5.72396e13i −0.00415339 0.0180907i
\(659\) −1.25994e15 + 1.25994e15i −0.394894 + 0.394894i −0.876428 0.481534i \(-0.840080\pi\)
0.481534 + 0.876428i \(0.340080\pi\)
\(660\) −2.02336e15 7.02207e14i −0.628899 0.218260i
\(661\) −7.61831e14 7.61831e14i −0.234828 0.234828i 0.579876 0.814705i \(-0.303101\pi\)
−0.814705 + 0.579876i \(0.803101\pi\)
\(662\) 1.58640e15 + 9.93975e14i 0.484945 + 0.303848i
\(663\) 3.44235e14i 0.104359i
\(664\) −2.84648e14 + 2.61639e15i −0.0855823 + 0.786644i
\(665\) 1.84403e13i 0.00549857i
\(666\) 1.64830e15 2.63071e15i 0.487449 0.777974i
\(667\) 4.41199e12 + 4.41199e12i 0.00129402 + 0.00129402i
\(668\) −1.41330e15 2.91566e15i −0.411114 0.848138i
\(669\) 1.06946e15 1.06946e15i 0.308546 0.308546i
\(670\) −1.70755e15 + 3.92031e14i −0.488608 + 0.112178i
\(671\) 1.08402e16 3.07655
\(672\) 2.35276e14 8.40169e13i 0.0662287 0.0236503i
\(673\) 4.75717e15 1.32821 0.664103 0.747641i \(-0.268814\pi\)
0.664103 + 0.747641i \(0.268814\pi\)
\(674\) −7.69884e14 + 1.76756e14i −0.213204 + 0.0489491i
\(675\) −1.62897e15 + 1.62897e15i −0.447448 + 0.447448i
\(676\) 1.10923e15 + 2.28837e15i 0.302215 + 0.623477i
\(677\) −1.85656e15 1.85656e15i −0.501733 0.501733i 0.410243 0.911976i \(-0.365444\pi\)
−0.911976 + 0.410243i \(0.865444\pi\)
\(678\) −1.84411e15 + 2.94323e15i −0.494339 + 0.788971i
\(679\) 5.49193e14i 0.146030i
\(680\) 7.04483e14 + 7.66436e13i 0.185811 + 0.0202152i
\(681\) 4.92080e14i 0.128744i
\(682\) −9.37409e15 5.87345e15i −2.43285 1.52433i
\(683\) −4.05012e14 4.05012e14i −0.104269 0.104269i 0.653048 0.757317i \(-0.273490\pi\)
−0.757317 + 0.653048i \(0.773490\pi\)
\(684\) −1.85161e14 6.42603e13i −0.0472870 0.0164110i
\(685\) −2.73592e15 + 2.73592e15i −0.693114 + 0.693114i
\(686\) −2.05997e14 8.97248e14i −0.0517700 0.225491i
\(687\) −2.09418e15 −0.522098
\(688\) −4.07439e14 + 4.80167e13i −0.100769 + 0.0118756i
\(689\) −1.85648e15 −0.455496
\(690\) −2.50933e14 1.09297e15i −0.0610785 0.266036i
\(691\) −2.79390e15 + 2.79390e15i −0.674656 + 0.674656i −0.958786 0.284130i \(-0.908295\pi\)
0.284130 + 0.958786i \(0.408295\pi\)
\(692\) 2.37651e15 6.84773e15i 0.569319 1.64045i
\(693\) 4.05045e14 + 4.05045e14i 0.0962654 + 0.0962654i
\(694\) −8.96968e14 5.62006e14i −0.211495 0.132515i
\(695\) 2.55473e15i 0.597625i
\(696\) 3.95440e12 + 4.91986e12i 0.000917760 + 0.00114183i
\(697\) 1.87450e14i 0.0431624i
\(698\) −1.36477e15 + 2.17819e15i −0.311785 + 0.497613i
\(699\) 5.00413e14 + 5.00413e14i 0.113424 + 0.113424i
\(700\) −2.98644e14 + 1.44760e14i −0.0671606 + 0.0325544i
\(701\) 3.76553e15 3.76553e15i 0.840189 0.840189i −0.148694 0.988883i \(-0.547507\pi\)
0.988883 + 0.148694i \(0.0475069\pi\)
\(702\) −2.40931e15 + 5.53149e14i −0.533383 + 0.122458i
\(703\) 5.18143e14 0.113814
\(704\) 7.11212e15 4.54523e15i 1.55006 0.990619i
\(705\) −2.66685e14 −0.0576711
\(706\) −2.70846e15 + 6.21828e14i −0.581161 + 0.133427i
\(707\) −7.52564e14 + 7.52564e14i −0.160227 + 0.160227i
\(708\) −2.53421e15 + 1.22839e15i −0.535376 + 0.259511i
\(709\) −3.41294e15 3.41294e15i −0.715442 0.715442i 0.252226 0.967668i \(-0.418837\pi\)
−0.967668 + 0.252226i \(0.918837\pi\)
\(710\) −1.54370e15 + 2.46376e15i −0.321101 + 0.512481i
\(711\) 2.77220e15i 0.572192i
\(712\) 2.16249e15 + 2.69046e15i 0.442908 + 0.551044i
\(713\) 5.79209e15i 1.17718i
\(714\) 9.21519e13 + 5.77389e13i 0.0185851 + 0.0116447i
\(715\) 2.15880e15 + 2.15880e15i 0.432046 + 0.432046i
\(716\) −1.27542e15 + 3.67501e15i −0.253297 + 0.729856i
\(717\) 1.41912e15 1.41912e15i 0.279682 0.279682i
\(718\) 2.15684e14 + 9.39440e14i 0.0421826 + 0.183732i
\(719\) 4.05222e15 0.786474 0.393237 0.919437i \(-0.371355\pi\)
0.393237 + 0.919437i \(0.371355\pi\)
\(720\) 2.31410e14 + 1.96360e15i 0.0445711 + 0.378202i
\(721\) −4.75102e14 −0.0908120
\(722\) 1.17232e15 + 5.10619e15i 0.222377 + 0.968595i
\(723\) −1.20914e15 + 1.20914e15i −0.227623 + 0.227623i
\(724\) −4.05040e15 1.40569e15i −0.756720 0.262620i
\(725\) −5.92922e12 5.92922e12i −0.00109936 0.00109936i
\(726\) −6.62903e15 4.15350e15i −1.21983 0.764298i
\(727\) 3.88621e15i 0.709720i 0.934920 + 0.354860i \(0.115471\pi\)
−0.934920 + 0.354860i \(0.884529\pi\)
\(728\) −3.54034e14 3.85168e13i −0.0641685 0.00698116i
\(729\) 3.17620e15i 0.571356i
\(730\) 2.51414e15 4.01259e15i 0.448862 0.716390i
\(731\) −1.26275e14 1.26275e14i −0.0223755 0.0223755i
\(732\) 2.50453e15 + 5.16690e15i 0.440469 + 0.908698i
\(733\) 5.83093e15 5.83093e15i 1.01781 1.01781i 0.0179691 0.999839i \(-0.494280\pi\)
0.999839 0.0179691i \(-0.00572005\pi\)
\(734\) 7.09307e15 1.62848e15i 1.22887 0.282133i
\(735\) −2.07591e15 −0.356967
\(736\) 3.99390e15 + 1.89204e15i 0.681662 + 0.322925i
\(737\) −9.08327e15 −1.53876
\(738\) 5.09747e14 1.17032e14i 0.0857125 0.0196785i
\(739\) −3.69206e15 + 3.69206e15i −0.616203 + 0.616203i −0.944555 0.328352i \(-0.893507\pi\)
0.328352 + 0.944555i \(0.393507\pi\)
\(740\) −2.27993e15 4.70355e15i −0.377700 0.779204i
\(741\) −1.13352e14 1.13352e14i −0.0186393 0.0186393i
\(742\) −3.11389e14 + 4.96980e14i −0.0508254 + 0.0811180i
\(743\) 1.42369e15i 0.230663i 0.993327 + 0.115331i \(0.0367930\pi\)
−0.993327 + 0.115331i \(0.963207\pi\)
\(744\) 6.33737e14 5.82510e15i 0.101920 0.936811i
\(745\) 4.10149e15i 0.654759i
\(746\) −2.85528e15 1.78901e15i −0.452465 0.283497i
\(747\) −2.26017e15 2.26017e15i −0.355531 0.355531i
\(748\) 3.47093e15 + 1.20459e15i 0.541985 + 0.188096i
\(749\) −7.80115e14 + 7.80115e14i −0.120923 + 0.120923i
\(750\) 8.63474e14 + 3.76098e15i 0.132866 + 0.578714i
\(751\) −1.14591e16 −1.75037 −0.875185 0.483788i \(-0.839261\pi\)
−0.875185 + 0.483788i \(0.839261\pi\)
\(752\) 6.51072e14 8.25031e14i 0.0987259 0.125104i
\(753\) 2.00716e15 0.302142
\(754\) −2.01338e12 8.76956e12i −0.000300874 0.00131050i
\(755\) 3.15865e14 3.15865e14i 0.0468590 0.0468590i
\(756\) −2.56038e14 + 7.37754e14i −0.0377081 + 0.108653i
\(757\) 5.28545e15 + 5.28545e15i 0.772778 + 0.772778i 0.978591 0.205813i \(-0.0659839\pi\)
−0.205813 + 0.978591i \(0.565984\pi\)
\(758\) −5.49206e14 3.44111e14i −0.0797176 0.0499480i
\(759\) 5.81406e15i 0.837818i
\(760\) −2.57214e14 + 2.06739e14i −0.0367977 + 0.0295765i
\(761\) 1.00264e15i 0.142407i