Properties

Label 16.12.e.a.5.11
Level 16
Weight 12
Character 16.5
Analytic conductor 12.293
Analytic rank 0
Dimension 42
CM no
Inner twists 2

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(12.2934908890\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(21\) over \(\Q(i)\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 5.11
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.11

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.51469 + 45.2295i) q^{2} +(442.035 - 442.035i) q^{3} +(-2043.41 - 137.018i) q^{4} +(2497.66 + 2497.66i) q^{5} +(19323.5 + 20662.6i) q^{6} -39392.3i q^{7} +(9292.38 - 92214.9i) q^{8} -213643. i q^{9} +O(q^{10})\) \(q+(-1.51469 + 45.2295i) q^{2} +(442.035 - 442.035i) q^{3} +(-2043.41 - 137.018i) q^{4} +(2497.66 + 2497.66i) q^{5} +(19323.5 + 20662.6i) q^{6} -39392.3i q^{7} +(9292.38 - 92214.9i) q^{8} -213643. i q^{9} +(-116751. + 109185. i) q^{10} +(-311395. - 311395. i) q^{11} +(-963826. + 842693. i) q^{12} +(1.47077e6 - 1.47077e6i) q^{13} +(1.78169e6 + 59667.2i) q^{14} +2.20811e6 q^{15} +(4.15676e6 + 559967. i) q^{16} +6.43972e6 q^{17} +(9.66297e6 + 323604. i) q^{18} +(-3.94625e6 + 3.94625e6i) q^{19} +(-4.76152e6 - 5.44597e6i) q^{20} +(-1.74128e7 - 1.74128e7i) q^{21} +(1.45559e7 - 1.36126e7i) q^{22} +2.40651e7i q^{23} +(-3.66547e7 - 4.48698e7i) q^{24} -3.63515e7i q^{25} +(6.42944e7 + 6.87499e7i) q^{26} +(-1.61326e7 - 1.61326e7i) q^{27} +(-5.39744e6 + 8.04947e7i) q^{28} +(1.10059e8 - 1.10059e8i) q^{29} +(-3.34461e6 + 9.98715e7i) q^{30} -2.26680e8 q^{31} +(-3.16232e7 + 1.87160e8i) q^{32} -2.75295e8 q^{33} +(-9.75420e6 + 2.91265e8i) q^{34} +(9.83886e7 - 9.83886e7i) q^{35} +(-2.92729e7 + 4.36561e8i) q^{36} +(-2.38575e8 - 2.38575e8i) q^{37} +(-1.72510e8 - 1.84464e8i) q^{38} -1.30026e9i q^{39} +(2.53531e8 - 2.07112e8i) q^{40} +1.45913e9i q^{41} +(8.13946e8 - 7.61196e8i) q^{42} +(1.31591e8 + 1.31591e8i) q^{43} +(5.93641e8 + 6.78974e8i) q^{44} +(5.33608e8 - 5.33608e8i) q^{45} +(-1.08845e9 - 3.64512e7i) q^{46} -2.03828e9 q^{47} +(2.08496e9 - 1.58991e9i) q^{48} +4.25574e8 q^{49} +(1.64416e9 + 5.50614e7i) q^{50} +(2.84658e9 - 2.84658e9i) q^{51} +(-3.20691e9 + 2.80387e9i) q^{52} +(1.22338e9 + 1.22338e9i) q^{53} +(7.54104e8 - 7.05233e8i) q^{54} -1.55552e9i q^{55} +(-3.63256e9 - 3.66048e8i) q^{56} +3.48877e9i q^{57} +(4.81119e9 + 5.14460e9i) q^{58} +(2.81701e9 + 2.81701e9i) q^{59} +(-4.51207e9 - 3.02549e8i) q^{60} +(-5.47457e8 + 5.47457e8i) q^{61} +(3.43350e8 - 1.02526e10i) q^{62} -8.41589e9 q^{63} +(-8.41724e9 - 1.71379e9i) q^{64} +7.34697e9 q^{65} +(4.16987e8 - 1.24514e10i) q^{66} +(-1.17485e10 + 1.17485e10i) q^{67} +(-1.31590e10 - 8.82355e8i) q^{68} +(1.06376e10 + 1.06376e10i) q^{69} +(4.30103e9 + 4.59909e9i) q^{70} -1.29025e9i q^{71} +(-1.97011e10 - 1.98525e9i) q^{72} +2.25767e10i q^{73} +(1.11520e10 - 1.04293e10i) q^{74} +(-1.60686e10 - 1.60686e10i) q^{75} +(8.60453e9 - 7.52311e9i) q^{76} +(-1.22666e10 + 1.22666e10i) q^{77} +(5.88103e10 + 1.96950e9i) q^{78} +3.10603e10 q^{79} +(8.98356e9 + 1.17808e10i) q^{80} +2.35839e10 q^{81} +(-6.59959e10 - 2.21014e9i) q^{82} +(3.09108e10 - 3.09108e10i) q^{83} +(3.31956e10 + 3.79673e10i) q^{84} +(1.60842e10 + 1.60842e10i) q^{85} +(-6.15113e9 + 5.75249e9i) q^{86} -9.72995e10i q^{87} +(-3.16088e10 + 2.58216e10i) q^{88} -7.63502e10i q^{89} +(2.33266e10 + 2.49431e10i) q^{90} +(-5.79370e10 - 5.79370e10i) q^{91} +(3.29734e9 - 4.91748e10i) q^{92} +(-1.00200e11 + 1.00200e11i) q^{93} +(3.08737e9 - 9.21903e10i) q^{94} -1.97128e10 q^{95} +(6.87526e10 + 9.67098e10i) q^{96} +5.73055e10 q^{97} +(-6.44614e8 + 1.92485e10i) q^{98} +(-6.65274e10 + 6.65274e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.51469 + 45.2295i −0.0334703 + 0.999440i
\(3\) 442.035 442.035i 1.05024 1.05024i 0.0515741 0.998669i \(-0.483576\pi\)
0.998669 0.0515741i \(-0.0164238\pi\)
\(4\) −2043.41 137.018i −0.997759 0.0669031i
\(5\) 2497.66 + 2497.66i 0.357436 + 0.357436i 0.862867 0.505431i \(-0.168666\pi\)
−0.505431 + 0.862867i \(0.668666\pi\)
\(6\) 19323.5 + 20662.6i 1.01450 + 1.08481i
\(7\) 39392.3i 0.885874i −0.896553 0.442937i \(-0.853936\pi\)
0.896553 0.442937i \(-0.146064\pi\)
\(8\) 9292.38 92214.9i 0.100261 0.994961i
\(9\) 213643.i 1.20602i
\(10\) −116751. + 109185.i −0.369199 + 0.345272i
\(11\) −311395. 311395.i −0.582977 0.582977i 0.352743 0.935720i \(-0.385249\pi\)
−0.935720 + 0.352743i \(0.885249\pi\)
\(12\) −963826. + 842693.i −1.11815 + 0.977626i
\(13\) 1.47077e6 1.47077e6i 1.09864 1.09864i 0.104072 0.994570i \(-0.466813\pi\)
0.994570 0.104072i \(-0.0331874\pi\)
\(14\) 1.78169e6 + 59667.2i 0.885378 + 0.0296505i
\(15\) 2.20811e6 0.750790
\(16\) 4.15676e6 + 559967.i 0.991048 + 0.133506i
\(17\) 6.43972e6 1.10001 0.550007 0.835160i \(-0.314625\pi\)
0.550007 + 0.835160i \(0.314625\pi\)
\(18\) 9.66297e6 + 323604.i 1.20535 + 0.0403659i
\(19\) −3.94625e6 + 3.94625e6i −0.365629 + 0.365629i −0.865880 0.500252i \(-0.833241\pi\)
0.500252 + 0.865880i \(0.333241\pi\)
\(20\) −4.76152e6 5.44597e6i −0.332722 0.380549i
\(21\) −1.74128e7 1.74128e7i −0.930383 0.930383i
\(22\) 1.45559e7 1.36126e7i 0.602163 0.563138i
\(23\) 2.40651e7i 0.779622i 0.920895 + 0.389811i \(0.127460\pi\)
−0.920895 + 0.389811i \(0.872540\pi\)
\(24\) −3.66547e7 4.48698e7i −0.939653 1.15025i
\(25\) 3.63515e7i 0.744479i
\(26\) 6.42944e7 + 6.87499e7i 1.06125 + 1.13480i
\(27\) −1.61326e7 1.61326e7i −0.216373 0.216373i
\(28\) −5.39744e6 + 8.04947e7i −0.0592677 + 0.883889i
\(29\) 1.10059e8 1.10059e8i 0.996403 0.996403i −0.00359065 0.999994i \(-0.501143\pi\)
0.999994 + 0.00359065i \(0.00114294\pi\)
\(30\) −3.34461e6 + 9.98715e7i −0.0251292 + 0.750369i
\(31\) −2.26680e8 −1.42208 −0.711039 0.703153i \(-0.751775\pi\)
−0.711039 + 0.703153i \(0.751775\pi\)
\(32\) −3.16232e7 + 1.87160e8i −0.166602 + 0.986024i
\(33\) −2.75295e8 −1.22454
\(34\) −9.75420e6 + 2.91265e8i −0.0368178 + 1.09940i
\(35\) 9.83886e7 9.83886e7i 0.316643 0.316643i
\(36\) −2.92729e7 + 4.36561e8i −0.0806866 + 1.20332i
\(37\) −2.38575e8 2.38575e8i −0.565608 0.565608i 0.365287 0.930895i \(-0.380971\pi\)
−0.930895 + 0.365287i \(0.880971\pi\)
\(38\) −1.72510e8 1.84464e8i −0.353186 0.377661i
\(39\) 1.30026e9i 2.30768i
\(40\) 2.53531e8 2.07112e8i 0.391472 0.319798i
\(41\) 1.45913e9i 1.96691i 0.181160 + 0.983454i \(0.442015\pi\)
−0.181160 + 0.983454i \(0.557985\pi\)
\(42\) 8.13946e8 7.61196e8i 0.961002 0.898722i
\(43\) 1.31591e8 + 1.31591e8i 0.136506 + 0.136506i 0.772058 0.635552i \(-0.219227\pi\)
−0.635552 + 0.772058i \(0.719227\pi\)
\(44\) 5.93641e8 + 6.78974e8i 0.542668 + 0.620674i
\(45\) 5.33608e8 5.33608e8i 0.431076 0.431076i
\(46\) −1.08845e9 3.64512e7i −0.779185 0.0260942i
\(47\) −2.03828e9 −1.29636 −0.648180 0.761487i \(-0.724469\pi\)
−0.648180 + 0.761487i \(0.724469\pi\)
\(48\) 2.08496e9 1.58991e9i 1.18106 0.900627i
\(49\) 4.25574e8 0.215227
\(50\) 1.64416e9 + 5.50614e7i 0.744062 + 0.0249179i
\(51\) 2.84658e9 2.84658e9i 1.15528 1.15528i
\(52\) −3.20691e9 + 2.80387e9i −1.16968 + 1.02268i
\(53\) 1.22338e9 + 1.22338e9i 0.401832 + 0.401832i 0.878878 0.477047i \(-0.158293\pi\)
−0.477047 + 0.878878i \(0.658293\pi\)
\(54\) 7.54104e8 7.05233e8i 0.223494 0.209010i
\(55\) 1.55552e9i 0.416754i
\(56\) −3.63256e9 3.66048e8i −0.881410 0.0888186i
\(57\) 3.48877e9i 0.767998i
\(58\) 4.81119e9 + 5.14460e9i 0.962495 + 1.02919i
\(59\) 2.81701e9 + 2.81701e9i 0.512982 + 0.512982i 0.915439 0.402457i \(-0.131844\pi\)
−0.402457 + 0.915439i \(0.631844\pi\)
\(60\) −4.51207e9 3.02549e8i −0.749107 0.0502302i
\(61\) −5.47457e8 + 5.47457e8i −0.0829920 + 0.0829920i −0.747384 0.664392i \(-0.768690\pi\)
0.664392 + 0.747384i \(0.268690\pi\)
\(62\) 3.43350e8 1.02526e10i 0.0475974 1.42128i
\(63\) −8.41589e9 −1.06838
\(64\) −8.41724e9 1.71379e9i −0.979895 0.199511i
\(65\) 7.34697e9 0.785389
\(66\) 4.16987e8 1.24514e10i 0.0409856 1.22385i
\(67\) −1.17485e10 + 1.17485e10i −1.06309 + 1.06309i −0.0652213 + 0.997871i \(0.520775\pi\)
−0.997871 + 0.0652213i \(0.979225\pi\)
\(68\) −1.31590e10 8.82355e8i −1.09755 0.0735943i
\(69\) 1.06376e10 + 1.06376e10i 0.818792 + 0.818792i
\(70\) 4.30103e9 + 4.59909e9i 0.305868 + 0.327064i
\(71\) 1.29025e9i 0.0848696i −0.999099 0.0424348i \(-0.986489\pi\)
0.999099 0.0424348i \(-0.0135115\pi\)
\(72\) −1.97011e10 1.98525e9i −1.19994 0.120917i
\(73\) 2.25767e10i 1.27463i 0.770602 + 0.637317i \(0.219956\pi\)
−0.770602 + 0.637317i \(0.780044\pi\)
\(74\) 1.11520e10 1.04293e10i 0.584222 0.546360i
\(75\) −1.60686e10 1.60686e10i −0.781884 0.781884i
\(76\) 8.60453e9 7.52311e9i 0.389271 0.340348i
\(77\) −1.22666e10 + 1.22666e10i −0.516444 + 0.516444i
\(78\) 5.88103e10 + 1.96950e9i 2.30639 + 0.0772389i
\(79\) 3.10603e10 1.13568 0.567841 0.823138i \(-0.307779\pi\)
0.567841 + 0.823138i \(0.307779\pi\)
\(80\) 8.98356e9 + 1.17808e10i 0.306516 + 0.401956i
\(81\) 2.35839e10 0.751533
\(82\) −6.59959e10 2.21014e9i −1.96581 0.0658330i
\(83\) 3.09108e10 3.09108e10i 0.861352 0.861352i −0.130143 0.991495i \(-0.541544\pi\)
0.991495 + 0.130143i \(0.0415436\pi\)
\(84\) 3.31956e10 + 3.79673e10i 0.866053 + 0.990544i
\(85\) 1.60842e10 + 1.60842e10i 0.393184 + 0.393184i
\(86\) −6.15113e9 + 5.75249e9i −0.140998 + 0.131860i
\(87\) 9.72995e10i 2.09293i
\(88\) −3.16088e10 + 2.58216e10i −0.638489 + 0.521590i
\(89\) 7.63502e10i 1.44932i −0.689105 0.724661i \(-0.741996\pi\)
0.689105 0.724661i \(-0.258004\pi\)
\(90\) 2.33266e10 + 2.49431e10i 0.416406 + 0.445262i
\(91\) −5.79370e10 5.79370e10i −0.973259 0.973259i
\(92\) 3.29734e9 4.91748e10i 0.0521591 0.777875i
\(93\) −1.00200e11 + 1.00200e11i −1.49353 + 1.49353i
\(94\) 3.08737e9 9.21903e10i 0.0433895 1.29563i
\(95\) −1.97128e10 −0.261378
\(96\) 6.87526e10 + 9.67098e10i 0.860592 + 1.21054i
\(97\) 5.73055e10 0.677566 0.338783 0.940865i \(-0.389985\pi\)
0.338783 + 0.940865i \(0.389985\pi\)
\(98\) −6.44614e8 + 1.92485e10i −0.00720371 + 0.215106i
\(99\) −6.65274e10 + 6.65274e10i −0.703083 + 0.703083i
\(100\) −4.98080e9 + 7.42811e10i −0.0498080 + 0.742811i
\(101\) −2.12631e10 2.12631e10i −0.201307 0.201307i 0.599253 0.800560i \(-0.295464\pi\)
−0.800560 + 0.599253i \(0.795464\pi\)
\(102\) 1.24438e11 + 1.33061e11i 1.11597 + 1.19330i
\(103\) 7.20653e10i 0.612522i 0.951948 + 0.306261i \(0.0990780\pi\)
−0.951948 + 0.306261i \(0.900922\pi\)
\(104\) −1.21960e11 1.49294e11i −0.982955 1.20326i
\(105\) 8.69824e10i 0.665105i
\(106\) −5.71859e10 + 5.34798e10i −0.415056 + 0.388157i
\(107\) 1.42977e11 + 1.42977e11i 0.985500 + 0.985500i 0.999896 0.0143966i \(-0.00458275\pi\)
−0.0143966 + 0.999896i \(0.504583\pi\)
\(108\) 3.07551e10 + 3.51760e10i 0.201412 + 0.230364i
\(109\) 1.56363e10 1.56363e10i 0.0973394 0.0973394i −0.656760 0.754100i \(-0.728074\pi\)
0.754100 + 0.656760i \(0.228074\pi\)
\(110\) 7.03552e10 + 2.35613e9i 0.416521 + 0.0139489i
\(111\) −2.10917e11 −1.18805
\(112\) 2.20584e10 1.63744e11i 0.118270 0.877944i
\(113\) 8.94759e10 0.456851 0.228425 0.973561i \(-0.426642\pi\)
0.228425 + 0.973561i \(0.426642\pi\)
\(114\) −1.57795e11 5.28441e9i −0.767568 0.0257051i
\(115\) −6.01063e10 + 6.01063e10i −0.278665 + 0.278665i
\(116\) −2.39975e11 + 2.09815e11i −1.06083 + 0.927508i
\(117\) −3.14220e11 3.14220e11i −1.32499 1.32499i
\(118\) −1.31679e11 + 1.23145e11i −0.529865 + 0.495525i
\(119\) 2.53675e11i 0.974473i
\(120\) 2.05186e10 2.03620e11i 0.0752749 0.747006i
\(121\) 9.13783e10i 0.320275i
\(122\) −2.39320e10 2.55904e10i −0.0801677 0.0857233i
\(123\) 6.44988e11 + 6.44988e11i 2.06573 + 2.06573i
\(124\) 4.63200e11 + 3.10591e10i 1.41889 + 0.0951414i
\(125\) 2.12750e11 2.12750e11i 0.623540 0.623540i
\(126\) 1.27475e10 3.80647e11i 0.0357591 1.06779i
\(127\) 1.92066e11 0.515857 0.257929 0.966164i \(-0.416960\pi\)
0.257929 + 0.966164i \(0.416960\pi\)
\(128\) 9.02634e10 3.78111e11i 0.232197 0.972669i
\(129\) 1.16336e11 0.286729
\(130\) −1.11284e10 + 3.32299e11i −0.0262872 + 0.784949i
\(131\) −6.44827e10 + 6.44827e10i −0.146033 + 0.146033i −0.776343 0.630310i \(-0.782928\pi\)
0.630310 + 0.776343i \(0.282928\pi\)
\(132\) 5.62541e11 + 3.77202e10i 1.22179 + 0.0819252i
\(133\) 1.55452e11 + 1.55452e11i 0.323901 + 0.323901i
\(134\) −5.13583e11 5.49174e11i −1.02691 1.09808i
\(135\) 8.05874e10i 0.154679i
\(136\) 5.98403e10 5.93838e11i 0.110288 1.09447i
\(137\) 5.15465e11i 0.912507i 0.889850 + 0.456254i \(0.150809\pi\)
−0.889850 + 0.456254i \(0.849191\pi\)
\(138\) −4.97246e11 + 4.65021e11i −0.845739 + 0.790928i
\(139\) 7.00170e11 + 7.00170e11i 1.14452 + 1.14452i 0.987614 + 0.156903i \(0.0501510\pi\)
0.156903 + 0.987614i \(0.449849\pi\)
\(140\) −2.14529e11 + 1.87567e11i −0.337118 + 0.294749i
\(141\) −9.00991e11 + 9.00991e11i −1.36149 + 1.36149i
\(142\) 5.83572e10 + 1.95433e9i 0.0848221 + 0.00284061i
\(143\) −9.15980e11 −1.28097
\(144\) 1.19633e11 8.88063e11i 0.161012 1.19523i
\(145\) 5.49778e11 0.712301
\(146\) −1.02113e12 3.41968e10i −1.27392 0.0426624i
\(147\) 1.88119e11 1.88119e11i 0.226041 0.226041i
\(148\) 4.54818e11 + 5.20196e11i 0.526500 + 0.602182i
\(149\) −7.53741e11 7.53741e11i −0.840810 0.840810i 0.148154 0.988964i \(-0.452667\pi\)
−0.988964 + 0.148154i \(0.952667\pi\)
\(150\) 7.51116e11 7.02437e11i 0.807616 0.755276i
\(151\) 2.74710e11i 0.284775i −0.989811 0.142387i \(-0.954522\pi\)
0.989811 0.142387i \(-0.0454778\pi\)
\(152\) 3.27233e11 + 4.00573e11i 0.327128 + 0.400445i
\(153\) 1.37580e12i 1.32664i
\(154\) −5.36230e11 5.73390e11i −0.498870 0.533441i
\(155\) −5.66169e11 5.66169e11i −0.508302 0.508302i
\(156\) −1.78159e11 + 2.65697e12i −0.154391 + 2.30251i
\(157\) −4.05555e11 + 4.05555e11i −0.339314 + 0.339314i −0.856109 0.516795i \(-0.827125\pi\)
0.516795 + 0.856109i \(0.327125\pi\)
\(158\) −4.70469e10 + 1.40484e12i −0.0380117 + 1.13505i
\(159\) 1.08155e12 0.844042
\(160\) −5.46445e11 + 3.88477e11i −0.411990 + 0.292891i
\(161\) 9.47978e11 0.690647
\(162\) −3.57224e10 + 1.06669e12i −0.0251540 + 0.751112i
\(163\) −1.45795e12 + 1.45795e12i −0.992456 + 0.992456i −0.999972 0.00751598i \(-0.997608\pi\)
0.00751598 + 0.999972i \(0.497608\pi\)
\(164\) 1.99927e11 2.98161e12i 0.131592 1.96250i
\(165\) −6.87593e11 6.87593e11i −0.437693 0.437693i
\(166\) 1.35126e12 + 1.44490e12i 0.832040 + 0.889700i
\(167\) 2.75134e12i 1.63909i −0.573012 0.819547i \(-0.694225\pi\)
0.573012 0.819547i \(-0.305775\pi\)
\(168\) −1.76752e12 + 1.44391e12i −1.01898 + 0.832414i
\(169\) 2.53417e12i 1.41403i
\(170\) −7.51844e11 + 7.03119e11i −0.406124 + 0.379804i
\(171\) 8.43090e11 + 8.43090e11i 0.440956 + 0.440956i
\(172\) −2.50865e11 2.86926e11i −0.127067 0.145333i
\(173\) −1.33505e12 + 1.33505e12i −0.655005 + 0.655005i −0.954194 0.299189i \(-0.903284\pi\)
0.299189 + 0.954194i \(0.403284\pi\)
\(174\) 4.40081e12 + 1.47379e11i 2.09176 + 0.0700510i
\(175\) −1.43197e12 −0.659515
\(176\) −1.12002e12 1.46876e12i −0.499927 0.655589i
\(177\) 2.49044e12 1.07751
\(178\) 3.45328e12 + 1.15647e11i 1.44851 + 0.0485093i
\(179\) −1.92052e11 + 1.92052e11i −0.0781138 + 0.0781138i −0.745084 0.666970i \(-0.767591\pi\)
0.666970 + 0.745084i \(0.267591\pi\)
\(180\) −1.16349e12 + 1.01727e12i −0.458950 + 0.401270i
\(181\) 2.83749e12 + 2.83749e12i 1.08568 + 1.08568i 0.995968 + 0.0897141i \(0.0285953\pi\)
0.0897141 + 0.995968i \(0.471405\pi\)
\(182\) 2.70822e12 2.53270e12i 1.00529 0.940138i
\(183\) 4.83991e11i 0.174324i
\(184\) 2.21916e12 + 2.23622e11i 0.775693 + 0.0781656i
\(185\) 1.19176e12i 0.404337i
\(186\) −4.38024e12 4.68378e12i −1.44270 1.54268i
\(187\) −2.00529e12 2.00529e12i −0.641282 0.641282i
\(188\) 4.16504e12 + 2.79280e11i 1.29345 + 0.0867305i
\(189\) −6.35500e11 + 6.35500e11i −0.191679 + 0.191679i
\(190\) 2.98588e10 8.91600e11i 0.00874839 0.261231i
\(191\) −8.79909e11 −0.250469 −0.125235 0.992127i \(-0.539968\pi\)
−0.125235 + 0.992127i \(0.539968\pi\)
\(192\) −4.47827e12 + 2.96316e12i −1.23866 + 0.819593i
\(193\) −5.26060e11 −0.141407 −0.0707033 0.997497i \(-0.522524\pi\)
−0.0707033 + 0.997497i \(0.522524\pi\)
\(194\) −8.68002e10 + 2.59190e12i −0.0226783 + 0.677186i
\(195\) 3.24762e12 3.24762e12i 0.824849 0.824849i
\(196\) −8.69622e11 5.83111e10i −0.214745 0.0143993i
\(197\) 1.07233e12 + 1.07233e12i 0.257493 + 0.257493i 0.824034 0.566541i \(-0.191719\pi\)
−0.566541 + 0.824034i \(0.691719\pi\)
\(198\) −2.90823e12 3.10977e12i −0.679157 0.726222i
\(199\) 3.35856e12i 0.762889i −0.924392 0.381444i \(-0.875427\pi\)
0.924392 0.381444i \(-0.124573\pi\)
\(200\) −3.35215e12 3.37792e11i −0.740728 0.0746422i
\(201\) 1.03865e13i 2.23301i
\(202\) 9.93927e11 9.29513e11i 0.207932 0.194457i
\(203\) −4.33546e12 4.33546e12i −0.882688 0.882688i
\(204\) −6.20677e12 + 5.42671e12i −1.22998 + 1.07540i
\(205\) −3.64442e12 + 3.64442e12i −0.703044 + 0.703044i
\(206\) −3.25948e12 1.09157e11i −0.612178 0.0205013i
\(207\) 5.14134e12 0.940241
\(208\) 6.93721e12 5.29005e12i 1.23548 0.942131i
\(209\) 2.45769e12 0.426306
\(210\) 3.93417e12 + 1.31752e11i 0.664732 + 0.0222613i
\(211\) −1.61495e12 + 1.61495e12i −0.265831 + 0.265831i −0.827418 0.561587i \(-0.810191\pi\)
0.561587 + 0.827418i \(0.310191\pi\)
\(212\) −2.33224e12 2.66749e12i −0.374047 0.427815i
\(213\) −5.70335e11 5.70335e11i −0.0891338 0.0891338i
\(214\) −6.68336e12 + 6.25022e12i −1.01793 + 0.951963i
\(215\) 6.57341e11i 0.0975842i
\(216\) −1.63757e12 + 1.33775e12i −0.236977 + 0.193589i
\(217\) 8.92943e12i 1.25978i
\(218\) 6.83538e11 + 7.30906e11i 0.0940269 + 0.100543i
\(219\) 9.97971e12 + 9.97971e12i 1.33867 + 1.33867i
\(220\) −2.13133e11 + 3.17856e12i −0.0278821 + 0.415820i
\(221\) 9.47134e12 9.47134e12i 1.20852 1.20852i
\(222\) 3.19475e11 9.53967e12i 0.0397645 1.18739i
\(223\) −9.52794e12 −1.15697 −0.578485 0.815693i \(-0.696356\pi\)
−0.578485 + 0.815693i \(0.696356\pi\)
\(224\) 7.37265e12 + 1.24571e12i 0.873493 + 0.147589i
\(225\) −7.76625e12 −0.897858
\(226\) −1.35528e11 + 4.04695e12i −0.0152909 + 0.456595i
\(227\) −1.41637e12 + 1.41637e12i −0.155968 + 0.155968i −0.780777 0.624810i \(-0.785177\pi\)
0.624810 + 0.780777i \(0.285177\pi\)
\(228\) 4.78022e11 7.12898e12i 0.0513815 0.766277i
\(229\) 3.25593e11 + 3.25593e11i 0.0341649 + 0.0341649i 0.723983 0.689818i \(-0.242309\pi\)
−0.689818 + 0.723983i \(0.742309\pi\)
\(230\) −2.62754e12 2.80962e12i −0.269182 0.287836i
\(231\) 1.08445e13i 1.08478i
\(232\) −9.12634e12 1.11717e13i −0.891482 1.09128i
\(233\) 2.61304e12i 0.249280i −0.992202 0.124640i \(-0.960222\pi\)
0.992202 0.124640i \(-0.0397776\pi\)
\(234\) 1.46879e13 1.37361e13i 1.36859 1.27990i
\(235\) −5.09093e12 5.09093e12i −0.463365 0.463365i
\(236\) −5.37033e12 6.14229e12i −0.477513 0.546153i
\(237\) 1.37298e13 1.37298e13i 1.19274 1.19274i
\(238\) 1.14736e13 + 3.84240e11i 0.973927 + 0.0326159i
\(239\) −3.43720e12 −0.285113 −0.142556 0.989787i \(-0.545532\pi\)
−0.142556 + 0.989787i \(0.545532\pi\)
\(240\) 9.17856e12 + 1.23647e12i 0.744068 + 0.100235i
\(241\) −2.16771e13 −1.71754 −0.858771 0.512359i \(-0.828772\pi\)
−0.858771 + 0.512359i \(0.828772\pi\)
\(242\) 4.13299e12 + 1.38410e11i 0.320096 + 0.0107197i
\(243\) 1.32828e13 1.32828e13i 1.00567 1.00567i
\(244\) 1.19369e12 1.04367e12i 0.0883585 0.0772536i
\(245\) 1.06294e12 + 1.06294e12i 0.0769298 + 0.0769298i
\(246\) −3.01495e13 + 2.81955e13i −2.13371 + 1.99543i
\(247\) 1.16081e13i 0.803390i
\(248\) −2.10639e12 + 2.09032e13i −0.142579 + 1.41491i
\(249\) 2.73273e13i 1.80926i
\(250\) 9.30031e12 + 9.94481e12i 0.602320 + 0.644060i
\(251\) 6.65993e12 + 6.65993e12i 0.421953 + 0.421953i 0.885876 0.463923i \(-0.153558\pi\)
−0.463923 + 0.885876i \(0.653558\pi\)
\(252\) 1.71971e13 + 1.15313e12i 1.06599 + 0.0714782i
\(253\) 7.49373e12 7.49373e12i 0.454502 0.454502i
\(254\) −2.90921e11 + 8.68703e12i −0.0172659 + 0.515568i
\(255\) 1.42196e13 0.825878
\(256\) 1.69651e13 + 4.65529e12i 0.964352 + 0.264623i
\(257\) 1.63980e13 0.912344 0.456172 0.889892i \(-0.349220\pi\)
0.456172 + 0.889892i \(0.349220\pi\)
\(258\) −1.76213e11 + 5.26182e12i −0.00959689 + 0.286568i
\(259\) −9.39802e12 + 9.39802e12i −0.501058 + 0.501058i
\(260\) −1.50129e13 1.00666e12i −0.783629 0.0525449i
\(261\) −2.35133e13 2.35133e13i −1.20168 1.20168i
\(262\) −2.81885e12 3.01419e12i −0.141063 0.150839i
\(263\) 2.65640e12i 0.130178i 0.997879 + 0.0650889i \(0.0207331\pi\)
−0.997879 + 0.0650889i \(0.979267\pi\)
\(264\) −2.55814e12 + 2.53863e13i −0.122773 + 1.21837i
\(265\) 6.11117e12i 0.287258i
\(266\) −7.26647e12 + 6.79555e12i −0.334561 + 0.312878i
\(267\) −3.37495e13 3.37495e13i −1.52214 1.52214i
\(268\) 2.56168e13 2.23973e13i 1.13183 0.989586i
\(269\) −1.05424e13 + 1.05424e13i −0.456355 + 0.456355i −0.897457 0.441102i \(-0.854588\pi\)
0.441102 + 0.897457i \(0.354588\pi\)
\(270\) 3.64493e12 + 1.22065e11i 0.154592 + 0.00517716i
\(271\) 2.11875e13 0.880537 0.440269 0.897866i \(-0.354883\pi\)
0.440269 + 0.897866i \(0.354883\pi\)
\(272\) 2.67683e13 + 3.60603e12i 1.09017 + 0.146859i
\(273\) −5.12204e13 −2.04432
\(274\) −2.33142e13 7.80772e11i −0.911996 0.0305419i
\(275\) −1.13197e13 + 1.13197e13i −0.434014 + 0.434014i
\(276\) −2.02795e13 2.31945e13i −0.762178 0.871738i
\(277\) 1.77991e13 + 1.77991e13i 0.655783 + 0.655783i 0.954379 0.298596i \(-0.0965184\pi\)
−0.298596 + 0.954379i \(0.596518\pi\)
\(278\) −3.27289e13 + 3.06078e13i −1.18218 + 1.10557i
\(279\) 4.84285e13i 1.71506i
\(280\) −8.15863e12 9.98715e12i −0.283301 0.346795i
\(281\) 3.07835e12i 0.104817i 0.998626 + 0.0524087i \(0.0166898\pi\)
−0.998626 + 0.0524087i \(0.983310\pi\)
\(282\) −3.93866e13 4.21161e13i −1.31516 1.40630i
\(283\) −2.82607e13 2.82607e13i −0.925459 0.925459i 0.0719491 0.997408i \(-0.477078\pi\)
−0.997408 + 0.0719491i \(0.977078\pi\)
\(284\) −1.76787e11 + 2.63651e12i −0.00567804 + 0.0846795i
\(285\) −8.71375e12 + 8.71375e12i −0.274510 + 0.274510i
\(286\) 1.38743e12 4.14293e13i 0.0428743 1.28025i
\(287\) 5.74786e13 1.74243
\(288\) 3.99854e13 + 6.75608e12i 1.18917 + 0.200926i
\(289\) 7.19809e12 0.210029
\(290\) −8.32745e11 + 2.48662e13i −0.0238409 + 0.711901i
\(291\) 2.53310e13 2.53310e13i 0.711609 0.711609i
\(292\) 3.09341e12 4.61335e13i 0.0852769 1.27178i
\(293\) 2.05827e13 + 2.05827e13i 0.556839 + 0.556839i 0.928406 0.371567i \(-0.121180\pi\)
−0.371567 + 0.928406i \(0.621180\pi\)
\(294\) 8.22356e12 + 8.79345e12i 0.218348 + 0.233480i
\(295\) 1.40719e13i 0.366717i
\(296\) −2.42171e13 + 1.97832e13i −0.619466 + 0.506050i
\(297\) 1.00472e13i 0.252281i
\(298\) 3.52330e13 3.29496e13i 0.868481 0.812197i
\(299\) 3.53942e13 + 3.53942e13i 0.856525 + 0.856525i
\(300\) 3.06332e13 + 3.50365e13i 0.727822 + 0.832443i
\(301\) 5.18369e12 5.18369e12i 0.120927 0.120927i
\(302\) 1.24250e13 + 4.16101e11i 0.284615 + 0.00953149i
\(303\) −1.87981e13 −0.422843
\(304\) −1.86134e13 + 1.41938e13i −0.411169 + 0.313542i
\(305\) −2.73472e12 −0.0593286
\(306\) 6.22268e13 + 2.08392e12i 1.32590 + 0.0444030i
\(307\) −7.38012e12 + 7.38012e12i −0.154455 + 0.154455i −0.780104 0.625649i \(-0.784834\pi\)
0.625649 + 0.780104i \(0.284834\pi\)
\(308\) 2.67463e13 2.33849e13i 0.549839 0.480736i
\(309\) 3.18554e13 + 3.18554e13i 0.643297 + 0.643297i
\(310\) 2.64651e13 2.47499e13i 0.525030 0.491004i
\(311\) 2.79295e13i 0.544354i −0.962247 0.272177i \(-0.912256\pi\)
0.962247 0.272177i \(-0.0877437\pi\)
\(312\) −1.19904e14 1.20825e13i −2.29606 0.231370i
\(313\) 1.75457e13i 0.330124i −0.986283 0.165062i \(-0.947218\pi\)
0.986283 0.165062i \(-0.0527825\pi\)
\(314\) −1.77287e13 1.89573e13i −0.327767 0.350481i
\(315\) −2.10200e13 2.10200e13i −0.381879 0.381879i
\(316\) −6.34690e13 4.25581e12i −1.13314 0.0759807i
\(317\) 7.03362e13 7.03362e13i 1.23411 1.23411i 0.271736 0.962372i \(-0.412402\pi\)
0.962372 0.271736i \(-0.0875976\pi\)
\(318\) −1.63822e12 + 4.89181e13i −0.0282503 + 0.843569i
\(319\) −6.85433e13 −1.16176
\(320\) −1.67429e13 2.53039e13i −0.278937 0.421563i
\(321\) 1.26402e14 2.07003
\(322\) −1.43590e12 + 4.28765e13i −0.0231162 + 0.690260i
\(323\) −2.54128e13 + 2.54128e13i −0.402196 + 0.402196i
\(324\) −4.81916e13 3.23141e12i −0.749849 0.0502799i
\(325\) −5.34647e13 5.34647e13i −0.817916 0.817916i
\(326\) −6.37340e13 6.81507e13i −0.958682 1.02512i
\(327\) 1.38236e13i 0.204460i
\(328\) 1.34554e14 + 1.35588e13i 1.95700 + 0.197204i
\(329\) 8.02925e13i 1.14841i
\(330\) 3.21410e13 3.00580e13i 0.452098 0.422798i
\(331\) 7.06915e13 + 7.06915e13i 0.977942 + 0.977942i 0.999762 0.0218198i \(-0.00694602\pi\)
−0.0218198 + 0.999762i \(0.506946\pi\)
\(332\) −6.73988e13 + 5.89282e13i −0.917050 + 0.801795i
\(333\) −5.09699e13 + 5.09699e13i −0.682136 + 0.682136i
\(334\) 1.24442e14 + 4.16744e12i 1.63818 + 0.0548610i
\(335\) −5.86875e13 −0.759975
\(336\) −6.26301e13 8.21313e13i −0.797842 1.04627i
\(337\) −1.52038e14 −1.90540 −0.952701 0.303908i \(-0.901708\pi\)
−0.952701 + 0.303908i \(0.901708\pi\)
\(338\) 1.14619e14 + 3.83849e12i 1.41324 + 0.0473280i
\(339\) 3.95515e13 3.95515e13i 0.479805 0.479805i
\(340\) −3.06629e13 3.50705e13i −0.365998 0.418609i
\(341\) 7.05868e13 + 7.05868e13i 0.829038 + 0.829038i
\(342\) −3.94095e13 + 3.68555e13i −0.455468 + 0.425950i
\(343\) 9.46558e13i 1.07654i
\(344\) 1.33575e13 1.09119e13i 0.149504 0.122132i
\(345\) 5.31382e13i 0.585332i
\(346\) −5.83615e13 6.24059e13i −0.632715 0.676561i
\(347\) −3.15383e13 3.15383e13i −0.336532 0.336532i 0.518528 0.855060i \(-0.326480\pi\)
−0.855060 + 0.518528i \(0.826480\pi\)
\(348\) −1.33317e13 + 1.98823e14i −0.140024 + 2.08824i
\(349\) −6.13903e13 + 6.13903e13i −0.634688 + 0.634688i −0.949240 0.314552i \(-0.898146\pi\)
0.314552 + 0.949240i \(0.398146\pi\)
\(350\) 2.16899e12 6.47672e13i 0.0220742 0.659145i
\(351\) −4.74546e13 −0.475433
\(352\) 6.81279e13 4.84333e13i 0.671955 0.477704i
\(353\) 2.62960e13 0.255346 0.127673 0.991816i \(-0.459249\pi\)
0.127673 + 0.991816i \(0.459249\pi\)
\(354\) −3.77225e12 + 1.12641e14i −0.0360647 + 1.07691i
\(355\) 3.22260e12 3.22260e12i 0.0303355 0.0303355i
\(356\) −1.04613e13 + 1.56015e14i −0.0969642 + 1.44608i
\(357\) −1.12133e14 1.12133e14i −1.02343 1.02343i
\(358\) −8.39552e12 8.97733e12i −0.0754556 0.0806845i
\(359\) 1.59995e14i 1.41607i −0.706175 0.708037i \(-0.749581\pi\)
0.706175 0.708037i \(-0.250419\pi\)
\(360\) −4.42481e13 5.41651e13i −0.385683 0.472124i
\(361\) 8.53444e13i 0.732631i
\(362\) −1.32636e14 + 1.24040e14i −1.12141 + 1.04874i
\(363\) −4.03924e13 4.03924e13i −0.336367 0.336367i
\(364\) 1.10451e14 + 1.26328e14i 0.905964 + 1.03619i
\(365\) −5.63890e13 + 5.63890e13i −0.455600 + 0.455600i
\(366\) −2.18906e13 7.33098e11i −0.174226 0.00583466i
\(367\) −1.11883e14 −0.877205 −0.438603 0.898681i \(-0.644526\pi\)
−0.438603 + 0.898681i \(0.644526\pi\)
\(368\) −1.34756e13 + 1.00033e14i −0.104084 + 0.772642i
\(369\) 3.11734e14 2.37213
\(370\) 5.39026e13 + 1.80515e12i 0.404111 + 0.0135333i
\(371\) 4.81917e13 4.81917e13i 0.355972 0.355972i
\(372\) 2.18480e14 1.91021e14i 1.59010 1.39026i
\(373\) 3.32001e13 + 3.32001e13i 0.238090 + 0.238090i 0.816059 0.577969i \(-0.196154\pi\)
−0.577969 + 0.816059i \(0.696154\pi\)
\(374\) 9.37358e13 8.76610e13i 0.662387 0.619459i
\(375\) 1.88086e14i 1.30974i
\(376\) −1.89405e13 + 1.87960e14i −0.129974 + 1.28983i
\(377\) 3.23742e14i 2.18938i
\(378\) −2.77807e13 2.97059e13i −0.185156 0.197988i
\(379\) 8.37605e13 + 8.37605e13i 0.550204 + 0.550204i 0.926500 0.376296i \(-0.122802\pi\)
−0.376296 + 0.926500i \(0.622802\pi\)
\(380\) 4.02814e13 + 2.70100e12i 0.260792 + 0.0174870i
\(381\) 8.48998e13 8.48998e13i 0.541775 0.541775i
\(382\) 1.33279e12 3.97978e13i 0.00838328 0.250329i
\(383\) 1.08618e14 0.673454 0.336727 0.941602i \(-0.390680\pi\)
0.336727 + 0.941602i \(0.390680\pi\)
\(384\) −1.27239e14 2.07038e14i −0.777675 1.26540i
\(385\) −6.12754e13 −0.369192
\(386\) 7.96819e11 2.37934e13i 0.00473293 0.141327i
\(387\) 2.81136e13 2.81136e13i 0.164629 0.164629i
\(388\) −1.17099e14 7.85186e12i −0.676048 0.0453313i
\(389\) −5.41093e13 5.41093e13i −0.307999 0.307999i 0.536134 0.844133i \(-0.319884\pi\)
−0.844133 + 0.536134i \(0.819884\pi\)
\(390\) 1.41969e14 + 1.51807e14i 0.796779 + 0.851995i
\(391\) 1.54972e14i 0.857594i
\(392\) 3.95459e12 3.92442e13i 0.0215788 0.214142i
\(393\) 5.70072e13i 0.306740i
\(394\) −5.01254e13 + 4.68769e13i −0.265967 + 0.248731i
\(395\) 7.75781e13 + 7.75781e13i 0.405934 + 0.405934i
\(396\) 1.45058e14 1.26827e14i 0.748546 0.654469i
\(397\) −2.53330e14 + 2.53330e14i −1.28926 + 1.28926i −0.354019 + 0.935238i \(0.615185\pi\)
−0.935238 + 0.354019i \(0.884815\pi\)
\(398\) 1.51906e14 + 5.08719e12i 0.762461 + 0.0255341i
\(399\) 1.37430e14 0.680350
\(400\) 2.03556e13 1.51104e14i 0.0993927 0.737814i
\(401\) −2.18349e14 −1.05162 −0.525809 0.850603i \(-0.676237\pi\)
−0.525809 + 0.850603i \(0.676237\pi\)
\(402\) −4.69776e14 1.57324e13i −2.23176 0.0747396i
\(403\) −3.33394e14 + 3.33394e14i −1.56235 + 1.56235i
\(404\) 4.05359e13 + 4.63627e13i 0.187388 + 0.214324i
\(405\) 5.89046e13 + 5.89046e13i 0.268625 + 0.268625i
\(406\) 2.02658e14 1.89524e14i 0.911737 0.852649i
\(407\) 1.48582e14i 0.659473i
\(408\) −2.36046e14 2.88949e14i −1.03363 1.26529i
\(409\) 2.85062e14i 1.23157i −0.787912 0.615787i \(-0.788838\pi\)
0.787912 0.615787i \(-0.211162\pi\)
\(410\) −1.59315e14 1.70355e14i −0.679119 0.726181i
\(411\) 2.27854e14 + 2.27854e14i 0.958355 + 0.958355i
\(412\) 9.87421e12 1.47259e14i 0.0409796 0.611149i
\(413\) 1.10969e14 1.10969e14i 0.454438 0.454438i
\(414\) −7.78755e12 + 2.32540e14i −0.0314701 + 0.939714i
\(415\) 1.54409e14 0.615757
\(416\) 2.28758e14 + 3.21779e14i 0.900251 + 1.26632i
\(417\) 6.19000e14 2.40404
\(418\) −3.72264e12 + 1.11160e14i −0.0142686 + 0.426067i
\(419\) −2.90019e14 + 2.90019e14i −1.09711 + 1.09711i −0.102359 + 0.994747i \(0.532639\pi\)
−0.994747 + 0.102359i \(0.967361\pi\)
\(420\) −1.19181e13 + 1.77741e14i −0.0444976 + 0.663615i
\(421\) −1.26128e14 1.26128e14i −0.464792 0.464792i 0.435431 0.900222i \(-0.356596\pi\)
−0.900222 + 0.435431i \(0.856596\pi\)
\(422\) −7.05972e13 7.54895e13i −0.256785 0.274580i
\(423\) 4.35464e14i 1.56344i
\(424\) 1.24182e14 1.01446e14i 0.440095 0.359519i
\(425\) 2.34094e14i 0.818937i
\(426\) 2.66598e13 2.49321e13i 0.0920672 0.0861005i
\(427\) 2.15656e13 + 2.15656e13i 0.0735205 + 0.0735205i
\(428\) −2.72571e14 3.11752e14i −0.917359 1.04922i
\(429\) −4.04895e14 + 4.04895e14i −1.34533 + 1.34533i
\(430\) −2.97312e13 9.95670e11i −0.0975295 0.00326617i
\(431\) 1.50794e14 0.488382 0.244191 0.969727i \(-0.421478\pi\)
0.244191 + 0.969727i \(0.421478\pi\)
\(432\) −5.80255e13 7.60929e13i −0.185549 0.243323i
\(433\) −1.75867e14 −0.555266 −0.277633 0.960687i \(-0.589550\pi\)
−0.277633 + 0.960687i \(0.589550\pi\)
\(434\) −4.03873e14 1.35253e13i −1.25908 0.0421653i
\(435\) 2.43021e14 2.43021e14i 0.748089 0.748089i
\(436\) −3.40939e13 + 2.98090e13i −0.103634 + 0.0906090i
\(437\) −9.49668e13 9.49668e13i −0.285052 0.285052i
\(438\) −4.66493e14 + 4.36261e14i −1.38273 + 1.29312i
\(439\) 3.08609e14i 0.903345i −0.892184 0.451673i \(-0.850827\pi\)
0.892184 0.451673i \(-0.149173\pi\)
\(440\) −1.43442e14 1.44544e13i −0.414654 0.0417842i
\(441\) 9.09209e13i 0.259568i
\(442\) 4.14038e14 + 4.42730e14i 1.16739 + 1.24829i
\(443\) −3.80486e13 3.80486e13i −0.105954 0.105954i 0.652142 0.758097i \(-0.273870\pi\)
−0.758097 + 0.652142i \(0.773870\pi\)
\(444\) 4.30990e14 + 2.88994e13i 1.18539 + 0.0794844i
\(445\) 1.90697e14 1.90697e14i 0.518040 0.518040i
\(446\) 1.44319e13 4.30944e14i 0.0387242 1.15632i
\(447\) −6.66360e14 −1.76611
\(448\) −6.75102e13 + 3.31574e14i −0.176742 + 0.868064i
\(449\) 5.30636e13 0.137228 0.0686139 0.997643i \(-0.478142\pi\)
0.0686139 + 0.997643i \(0.478142\pi\)
\(450\) 1.17635e13 3.51264e14i 0.0300516 0.897355i
\(451\) 4.54367e14 4.54367e14i 1.14666 1.14666i
\(452\) −1.82836e14 1.22598e13i −0.455827 0.0305647i
\(453\) −1.21431e14 1.21431e14i −0.299083 0.299083i
\(454\) −6.19163e13 6.62070e13i −0.150660 0.161101i
\(455\) 2.89414e14i 0.695755i
\(456\) 3.21716e14 + 3.24189e13i 0.764128 + 0.0770002i
\(457\) 5.16434e14i 1.21192i 0.795493 + 0.605962i \(0.207212\pi\)
−0.795493 + 0.605962i \(0.792788\pi\)
\(458\) −1.52196e13 + 1.42332e13i −0.0352892 + 0.0330022i
\(459\) −1.03889e14 1.03889e14i −0.238013 0.238013i
\(460\) 1.31058e14 1.14586e14i 0.296684 0.259397i
\(461\) 1.82198e14 1.82198e14i 0.407557 0.407557i −0.473329 0.880886i \(-0.656948\pi\)
0.880886 + 0.473329i \(0.156948\pi\)
\(462\) −4.90491e14 1.64261e13i −1.08418 0.0363081i
\(463\) 6.22341e14 1.35936 0.679678 0.733511i \(-0.262120\pi\)
0.679678 + 0.733511i \(0.262120\pi\)
\(464\) 5.19116e14 3.95858e14i 1.12051 0.854457i
\(465\) −5.00533e14 −1.06768
\(466\) 1.18186e14 + 3.95795e12i 0.249141 + 0.00834349i
\(467\) −1.19775e14 + 1.19775e14i −0.249530 + 0.249530i −0.820778 0.571248i \(-0.806460\pi\)
0.571248 + 0.820778i \(0.306460\pi\)
\(468\) 5.99027e14 + 6.85134e14i 1.23337 + 1.41066i
\(469\) 4.62800e14 + 4.62800e14i 0.941766 + 0.941766i
\(470\) 2.37971e14 2.22549e14i 0.478615 0.447597i
\(471\) 3.58539e14i 0.712724i
\(472\) 2.85947e14 2.33594e14i 0.561830 0.458966i
\(473\) 8.19538e13i 0.159159i
\(474\) 6.00193e14 + 6.41786e14i 1.15215 + 1.23200i
\(475\) 1.43452e14 + 1.43452e14i 0.272203 + 0.272203i
\(476\) −3.47580e13 + 5.18363e14i −0.0651953 + 0.972290i
\(477\) 2.61367e14 2.61367e14i 0.484618 0.484618i
\(478\) 5.20630e12 1.55463e14i 0.00954281 0.284953i
\(479\) −6.82971e14 −1.23753 −0.618767 0.785575i \(-0.712367\pi\)
−0.618767 + 0.785575i \(0.712367\pi\)
\(480\) −6.98274e13 + 4.13269e14i −0.125083 + 0.740297i
\(481\) −7.01778e14 −1.24280
\(482\) 3.28342e13 9.80444e14i 0.0574867 1.71658i
\(483\) 4.19040e14 4.19040e14i 0.725347 0.725347i
\(484\) −1.25204e13 + 1.86723e14i −0.0214274 + 0.319558i
\(485\) 1.43130e14 + 1.43130e14i 0.242186 + 0.242186i
\(486\) 5.80653e14 + 6.20891e14i 0.971442 + 1.03876i
\(487\) 1.00427e15i 1.66127i −0.556819 0.830634i \(-0.687978\pi\)
0.556819 0.830634i \(-0.312022\pi\)
\(488\) 4.53965e13 + 5.55709e13i 0.0742529 + 0.0908947i
\(489\) 1.28893e15i 2.08464i
\(490\) −4.96862e13 + 4.64661e13i −0.0794616 + 0.0743119i
\(491\) −1.60361e14 1.60361e14i −0.253600 0.253600i 0.568845 0.822445i \(-0.307391\pi\)
−0.822445 + 0.568845i \(0.807391\pi\)
\(492\) −1.22960e15 1.40635e15i −1.92290 2.19931i
\(493\) 7.08746e14 7.08746e14i 1.09606 1.09606i
\(494\) −5.25027e14 1.75827e13i −0.802940 0.0268897i
\(495\) −3.32325e14 −0.502614
\(496\) −9.42252e14 1.26933e14i −1.40935 0.189856i
\(497\) −5.08258e13 −0.0751838
\(498\) 1.23600e15 + 4.13925e13i 1.80825 + 0.0605565i
\(499\) −4.37270e14 + 4.37270e14i −0.632699 + 0.632699i −0.948744 0.316045i \(-0.897645\pi\)
0.316045 + 0.948744i \(0.397645\pi\)
\(500\) −4.63886e14 + 4.05585e14i −0.663859 + 0.580426i
\(501\) −1.21619e15 1.21619e15i −1.72145 1.72145i
\(502\) −3.11313e14 + 2.91138e14i −0.435840 + 0.407594i
\(503\) 4.46036e14i 0.617655i 0.951118 + 0.308828i \(0.0999366\pi\)
−0.951118 + 0.308828i \(0.900063\pi\)
\(504\) −7.82036e13 + 7.76071e14i −0.107117 + 1.06300i
\(505\) 1.06216e14i 0.143909i
\(506\) 3.27587e14 + 3.50288e14i 0.439035 + 0.469459i
\(507\) −1.12019e15 1.12019e15i −1.48507 1.48507i
\(508\) −3.92469e14 2.63164e13i −0.514701 0.0345124i
\(509\) 7.31318e14 7.31318e14i 0.948765 0.948765i −0.0499851 0.998750i \(-0.515917\pi\)
0.998750 + 0.0499851i \(0.0159174\pi\)
\(510\) −2.15383e13 + 6.43145e14i −0.0276424 + 0.825416i
\(511\) 8.89349e14 1.12916
\(512\) −2.36253e14 + 7.60270e14i −0.296751 + 0.954955i
\(513\) 1.27327e14 0.158224
\(514\) −2.48379e13 + 7.41673e14i −0.0305364 + 0.911833i
\(515\) −1.79995e14 + 1.79995e14i −0.218937 + 0.218937i
\(516\) −2.37722e14 1.59401e13i −0.286086 0.0191830i
\(517\) 6.34709e14 + 6.34709e14i 0.755748 + 0.755748i
\(518\) −4.10832e14 4.39303e14i −0.484006 0.517547i
\(519\) 1.18028e15i 1.37583i
\(520\) 6.82708e13 6.77500e14i 0.0787438 0.781431i
\(521\) 1.07962e14i 0.123215i 0.998100 + 0.0616074i \(0.0196227\pi\)
−0.998100 + 0.0616074i \(0.980377\pi\)
\(522\) 1.09911e15 1.02788e15i 1.24123 1.16079i
\(523\) −2.56475e14 2.56475e14i −0.286606 0.286606i 0.549130 0.835737i \(-0.314959\pi\)
−0.835737 + 0.549130i \(0.814959\pi\)
\(524\) 1.40600e14 1.22929e14i 0.155476 0.135936i
\(525\) −6.32981e14 + 6.32981e14i −0.692651 + 0.692651i
\(526\) −1.20148e14 4.02363e12i −0.130105 0.00435709i
\(527\) −1.45975e15 −1.56430
\(528\) −1.14433e15 1.54156e14i −1.21357 0.163483i
\(529\) 3.73683e14 0.392190
\(530\) −2.76405e14 9.25655e12i −0.287097 0.00961462i
\(531\) 6.01835e14 6.01835e14i 0.618668 0.618668i
\(532\) −2.96353e14 3.38952e14i −0.301505 0.344845i
\(533\) 2.14605e15 + 2.14605e15i 2.16093 + 2.16093i
\(534\) 1.57759e15 1.47535e15i 1.57223 1.47034i
\(535\) 7.14218e14i 0.704506i
\(536\) 9.74215e14 + 1.19256e15i 0.951149 + 1.16432i
\(537\) 1.69788e14i 0.164077i
\(538\) −4.60859e14 4.92796e14i −0.440825 0.471373i
\(539\) −1.32521e14 1.32521e14i −0.125472 0.125472i
\(540\) −1.10419e13 + 1.64673e14i −0.0103485 + 0.154333i
\(541\) −1.27658e15 + 1.27658e15i −1.18430 + 1.18430i −0.205682 + 0.978619i \(0.565941\pi\)
−0.978619 + 0.205682i \(0.934059\pi\)
\(542\) −3.20925e13 + 9.58298e14i −0.0294719 + 0.880044i
\(543\) 2.50854e15 2.28046
\(544\) −2.03645e14 + 1.20526e15i −0.183265 + 1.08464i
\(545\) 7.81084e13 0.0695852
\(546\) 7.75832e13 2.31667e15i 0.0684239 2.04317i
\(547\) 4.87504e14 4.87504e14i 0.425646 0.425646i −0.461496 0.887142i \(-0.652687\pi\)
0.887142 + 0.461496i \(0.152687\pi\)
\(548\) 7.06278e13 1.05331e15i 0.0610496 0.910463i
\(549\) 1.16961e14 + 1.16961e14i 0.100090 + 0.100090i
\(550\) −4.94837e14 5.29129e14i −0.419244 0.448298i
\(551\) 8.68638e14i 0.728627i
\(552\) 1.07979e15 8.82097e14i 0.896759 0.732574i
\(553\) 1.22354e15i 1.00607i
\(554\) −8.32006e14 + 7.78085e14i −0.677365 + 0.633466i
\(555\) −5.26799e14 5.26799e14i −0.424653 0.424653i
\(556\) −1.33480e15 1.52667e15i −1.06538 1.21852i
\(557\) 6.58261e14 6.58261e14i 0.520229 0.520229i −0.397412 0.917640i \(-0.630091\pi\)
0.917640 + 0.397412i \(0.130091\pi\)
\(558\) −2.19040e15 7.33544e13i −1.71410 0.0574035i
\(559\) 3.87081e14 0.299942
\(560\) 4.64072e14 3.53883e14i 0.356083 0.271535i
\(561\) −1.77282e15 −1.34701
\(562\) −1.39232e14 4.66275e12i −0.104759 0.00350827i
\(563\) −4.20852e14 + 4.20852e14i −0.313569 + 0.313569i −0.846291 0.532721i \(-0.821169\pi\)
0.532721 + 0.846291i \(0.321169\pi\)
\(564\) 1.96455e15 1.71764e15i 1.44953 1.26735i
\(565\) 2.23480e14 + 2.23480e14i 0.163295 + 0.163295i
\(566\) 1.32102e15 1.23541e15i 0.955916 0.893965i
\(567\) 9.29024e14i 0.665764i
\(568\) −1.18980e14 1.19895e13i −0.0844420 0.00850911i
\(569\) 1.88191e15i 1.32276i 0.750051 + 0.661380i \(0.230029\pi\)
−0.750051 + 0.661380i \(0.769971\pi\)
\(570\) −3.80920e14 4.07317e14i −0.265168 0.283544i
\(571\) −2.64020e13 2.64020e13i −0.0182028 0.0182028i 0.697947 0.716150i \(-0.254097\pi\)
−0.716150 + 0.697947i \(0.754097\pi\)
\(572\) 1.87172e15 + 1.25505e14i 1.27810 + 0.0857006i
\(573\) −3.88951e14 + 3.88951e14i −0.263053 + 0.263053i
\(574\) −8.70625e13 + 2.59973e15i −0.0583198 + 1.74146i
\(575\) 8.74801e14 0.580412
\(576\) −3.66140e14 + 1.79829e15i −0.240615 + 1.18178i
\(577\) 6.93306e14 0.451292 0.225646 0.974209i \(-0.427551\pi\)
0.225646 + 0.974209i \(0.427551\pi\)
\(578\) −1.09029e13 + 3.25566e14i −0.00702973 + 0.209911i
\(579\) −2.32537e14 + 2.32537e14i −0.148511 + 0.148511i
\(580\) −1.12342e15 7.53292e13i −0.710705 0.0476551i
\(581\) −1.21765e15 1.21765e15i −0.763050 0.763050i
\(582\) 1.10734e15 + 1.18408e15i 0.687392 + 0.735028i
\(583\) 7.61908e14i 0.468517i
\(584\) 2.08191e15 + 2.09791e14i 1.26821 + 0.127796i
\(585\) 1.56963e15i 0.947196i
\(586\) −9.62119e14 + 8.99766e14i −0.575164 + 0.537889i
\(587\) −7.68642e14 7.68642e14i −0.455213 0.455213i 0.441867 0.897080i \(-0.354316\pi\)
−0.897080 + 0.441867i \(0.854316\pi\)
\(588\) −4.10179e14 + 3.58628e14i −0.240657 + 0.210411i
\(589\) 8.94535e14 8.94535e14i 0.519952 0.519952i
\(590\) −6.36463e14 2.13146e13i −0.366511 0.0122741i
\(591\) 9.48019e14 0.540861
\(592\) −8.58104e14 1.12529e15i −0.485032 0.636057i
\(593\) 1.98651e15 1.11247 0.556236 0.831024i \(-0.312245\pi\)
0.556236 + 0.831024i \(0.312245\pi\)
\(594\) −4.54430e14 1.52184e13i −0.252140 0.00844393i
\(595\) 6.33595e14 6.33595e14i 0.348312 0.348312i
\(596\) 1.43693e15 + 1.64348e15i 0.782673 + 0.895179i
\(597\) −1.48460e15 1.48460e15i −0.801219 0.801219i
\(598\) −1.65447e15 + 1.54725e15i −0.884713 + 0.827377i
\(599\) 7.63858e13i 0.0404730i −0.999795 0.0202365i \(-0.993558\pi\)
0.999795 0.0202365i \(-0.00644192\pi\)
\(600\) −1.63108e15 + 1.33245e15i −0.856337 + 0.699552i
\(601\) 8.65598e14i 0.450305i −0.974324 0.225152i \(-0.927712\pi\)
0.974324 0.225152i \(-0.0722880\pi\)
\(602\) 2.26604e14 + 2.42307e14i 0.116812 + 0.124907i
\(603\) 2.50999e15 + 2.50999e15i 1.28211 + 1.28211i
\(604\) −3.76401e13 + 5.61345e14i −0.0190523 + 0.284137i
\(605\) 2.28232e14 2.28232e14i 0.114478 0.114478i
\(606\) 2.84733e13 8.50228e14i 0.0141527 0.422606i
\(607\) −2.33784e15 −1.15154 −0.575768 0.817613i \(-0.695297\pi\)
−0.575768 + 0.817613i \(0.695297\pi\)
\(608\) −6.13787e14 8.63373e14i −0.299604 0.421433i
\(609\) −3.83285e15 −1.85407
\(610\) 4.14227e12 1.23690e14i 0.00198575 0.0592954i
\(611\) −2.99784e15 + 2.99784e15i −1.42423 + 1.42423i
\(612\) −1.88509e14 + 2.81133e15i −0.0887563 + 1.32367i
\(613\) −6.47053e14 6.47053e14i −0.301931 0.301931i 0.539838 0.841769i \(-0.318485\pi\)
−0.841769 + 0.539838i \(0.818485\pi\)
\(614\) −3.22620e14 3.44978e14i −0.149199 0.159538i
\(615\) 3.22192e15i 1.47673i
\(616\) 1.01717e15 + 1.24514e15i 0.462063 + 0.565621i
\(617\) 2.16481e15i 0.974655i −0.873219 0.487328i \(-0.837972\pi\)
0.873219 0.487328i \(-0.162028\pi\)
\(618\) −1.48905e15 + 1.39255e15i −0.664468 + 0.621405i
\(619\) 2.47175e14 + 2.47175e14i 0.109321 + 0.109321i 0.759652 0.650330i \(-0.225369\pi\)
−0.650330 + 0.759652i \(0.725369\pi\)
\(620\) 1.07934e15 + 1.23449e15i 0.473156 + 0.541170i
\(621\) 3.88232e14 3.88232e14i 0.168689 0.168689i
\(622\) 1.26324e15 + 4.23047e13i 0.544049 + 0.0182197i
\(623\) −3.00761e15 −1.28392
\(624\) 7.28104e14 5.40488e15i 0.308091 2.28702i
\(625\) −7.12223e14 −0.298728
\(626\) 7.93584e14 + 2.65764e13i 0.329939 + 0.0110494i
\(627\) 1.08638e15 1.08638e15i 0.447725 0.447725i
\(628\) 8.84283e14 7.73147e14i 0.361255 0.315852i
\(629\) −1.53636e15 1.53636e15i −0.622176 0.622176i
\(630\) 9.82565e14 9.18887e14i 0.394446 0.368883i
\(631\) 8.14979e14i 0.324329i −0.986764 0.162164i \(-0.948153\pi\)
0.986764 0.162164i \(-0.0518474\pi\)
\(632\) 2.88624e14 2.86423e15i 0.113865 1.12996i
\(633\) 1.42773e15i 0.558375i
\(634\) 3.07473e15 + 3.28781e15i 1.19211 + 1.27472i
\(635\) 4.79715e14 + 4.79715e14i 0.184386 + 0.184386i
\(636\) −2.21006e15 1.48192e14i −0.842151 0.0564690i
\(637\) 6.25921e14 6.25921e14i 0.236457 0.236457i
\(638\) 1.03822e14 3.10018e15i 0.0388845 1.16111i
\(639\) −2.75653e14 −0.102355
\(640\) 1.16984e15 7.18947e14i 0.430662 0.264671i
\(641\) 1.93350e15 0.705707 0.352853 0.935679i \(-0.385211\pi\)
0.352853 + 0.935679i \(0.385211\pi\)
\(642\) −1.91460e14 + 5.71710e15i −0.0692845 + 2.06887i
\(643\) 2.71298e15 2.71298e15i 0.973389 0.973389i −0.0262664 0.999655i \(-0.508362\pi\)
0.999655 + 0.0262664i \(0.00836180\pi\)
\(644\) −1.93711e15 1.29890e14i −0.689099 0.0462064i
\(645\) 2.90568e14 + 2.90568e14i 0.102487 + 0.102487i
\(646\) −1.11091e15 1.18790e15i −0.388509 0.415433i
\(647\) 2.80893e14i 0.0974017i −0.998813 0.0487009i \(-0.984492\pi\)
0.998813 0.0487009i \(-0.0155081\pi\)
\(648\) 2.19150e14 2.17479e15i 0.0753494 0.747746i
\(649\) 1.75441e15i 0.598114i
\(650\) 2.49916e15 2.33720e15i 0.844834 0.790082i
\(651\) 3.94712e15 + 3.94712e15i 1.32308 + 1.32308i
\(652\) 3.17896e15 2.77943e15i 1.05663 0.923834i
\(653\) 6.82058e14 6.82058e14i 0.224801 0.224801i −0.585715 0.810517i \(-0.699186\pi\)
0.810517 + 0.585715i \(0.199186\pi\)
\(654\) 6.25234e14 + 2.09385e13i 0.204345 + 0.00684334i
\(655\) −3.22112e14 −0.104395
\(656\) −8.17066e14 + 6.06526e15i −0.262595 + 1.94930i
\(657\) 4.82336e15 1.53724
\(658\) −3.63159e15 1.21618e14i −1.14777 0.0384377i
\(659\) −2.80302e15 + 2.80302e15i −0.878530 + 0.878530i −0.993383 0.114853i \(-0.963360\pi\)
0.114853 + 0.993383i \(0.463360\pi\)
\(660\) 1.31082e15 + 1.49925e15i 0.407429 + 0.465995i
\(661\) −2.60423e15 2.60423e15i −0.802734 0.802734i 0.180788 0.983522i \(-0.442135\pi\)
−0.983522 + 0.180788i \(0.942135\pi\)
\(662\) −3.30441e15 + 3.09026e15i −1.01013 + 0.944662i
\(663\) 8.37333e15i 2.53848i
\(664\) −2.56320e15 3.13767e15i −0.770652 0.943372i
\(665\) 7.76532e14i 0.231548i
\(666\) −2.22814e15 2.38255e15i −0.658922 0.704585i
\(667\) 2.64857e15 + 2.64857e15i 0.776817 + 0.776817i
\(668\) −3.76982e14 + 5.62212e15i −0.109660 + 1.63542i
\(669\) −4.21168e15 + 4.21168e15i −1.21510 + 1.21510i
\(670\) 8.88936e13 2.65441e15i 0.0254366 0.759549i
\(671\) 3.40951e14 0.0967649
\(672\) 3.80962e15 2.70832e15i 1.07238 0.762377i
\(673\) 1.02827e15 0.287095 0.143547 0.989643i \(-0.454149\pi\)
0.143547 + 0.989643i \(0.454149\pi\)
\(674\) 2.30290e14 6.87658e15i 0.0637744 1.90433i
\(675\) −5.86444e14 + 5.86444e14i −0.161085 + 0.161085i
\(676\) −3.47225e14 + 5.17835e15i −0.0946030 + 1.41086i
\(677\) 2.74024e15 + 2.74024e15i 0.740543 + 0.740543i 0.972683 0.232139i \(-0.0745725\pi\)
−0.232139 + 0.972683i \(0.574572\pi\)
\(678\) 1.72898e15 + 1.84880e15i 0.463476 + 0.495595i
\(679\) 2.25739e15i 0.600238i
\(680\) 1.63267e15 1.33374e15i 0.430624 0.351782i
\(681\) 1.25217e15i 0.327608i
\(682\) −3.29952e15 + 3.08569e15i −0.856322 + 0.800826i
\(683\) −1.61771e15 1.61771e15i −0.416473 0.416473i 0.467513 0.883986i \(-0.345150\pi\)
−0.883986 + 0.467513i \(0.845150\pi\)
\(684\) −1.60726e15 1.83830e15i −0.410467 0.469469i
\(685\) −1.28746e15 + 1.28746e15i −0.326163 + 0.326163i
\(686\) 4.28123e15 + 1.43374e14i 1.07593 + 0.0360321i
\(687\) 2.87847e14 0.0717629
\(688\) 4.73307e14 + 6.20680e14i 0.117059 + 0.153508i
\(689\) 3.59862e15 0.882938
\(690\) −2.40341e15 8.04881e13i −0.585004 0.0195912i
\(691\) 4.09473e15 4.09473e15i 0.988771 0.988771i −0.0111668 0.999938i \(-0.503555\pi\)
0.999938 + 0.0111668i \(0.00355456\pi\)
\(692\) 2.91099e15 2.54513e15i 0.697359 0.609715i
\(693\) 2.62067e15 + 2.62067e15i 0.622843 + 0.622843i
\(694\) 1.47423e15 1.37869e15i 0.347607 0.325080i
\(695\) 3.49757e15i 0.818183i
\(696\) −8.97247e15 9.04144e14i −2.08239 0.209839i
\(697\) 9.39641e15i 2.16362i
\(698\) −2.68367e15 2.86964e15i −0.613089 0.655575i
\(699\) −1.15505e15 1.15505e15i −0.261805 0.261805i
\(700\) 2.92610e15 + 1.96205e14i 0.658037 + 0.0441236i
\(701\) −4.14977e15 + 4.14977e15i −0.925924 + 0.925924i −0.997439 0.0715154i \(-0.977217\pi\)
0.0715154 + 0.997439i \(0.477217\pi\)
\(702\) 7.18792e13 2.14635e15i 0.0159129 0.475167i
\(703\) 1.88296e15 0.413605
\(704\) 2.08742e15 + 3.15475e15i 0.454946 + 0.687567i
\(705\) −4.50074e15 −0.973293
\(706\) −3.98304e13 + 1.18936e15i −0.00854651 + 0.255203i
\(707\) −8.37603e14 + 8.37603e14i −0.178333 + 0.178333i
\(708\) −5.08899e15 3.41234e14i −1.07510 0.0720890i
\(709\) 4.80553e15 + 4.80553e15i 1.00737 + 1.00737i 0.999973 + 0.00739243i \(0.00235310\pi\)
0.00739243 + 0.999973i \(0.497647\pi\)
\(710\) 1.40875e14 + 1.50638e14i 0.0293031 + 0.0313338i
\(711\) 6.63583e15i 1.36966i
\(712\) −7.04062e15 7.09474e14i −1.44202 0.145310i
\(713\) 5.45506e15i 1.10868i
\(714\) 5.24158e15 4.90189e15i 1.05712 0.988606i
\(715\) −2.28781e15 2.28781e15i −0.457864 0.457864i
\(716\) 4.18756e14 3.66127e14i 0.0831649 0.0727127i
\(717\) −1.51936e15 + 1.51936e15i −0.299438 + 0.299438i
\(718\) 7.23648e15 + 2.42343e14i 1.41528 + 0.0473965i
\(719\) −6.77646e15 −1.31521 −0.657603 0.753365i \(-0.728430\pi\)
−0.657603 + 0.753365i \(0.728430\pi\)
\(720\) 2.51688e15 1.91928e15i 0.484768 0.369665i
\(721\) 2.83882e15 0.542617
\(722\) −3.86008e15 1.29271e14i −0.732221 0.0245214i
\(723\) −9.58204e15 + 9.58204e15i −1.80384 + 1.80384i
\(724\) −5.40938e15 6.18695e15i −1.01061 1.15588i
\(725\) −4.00080e15 4.00080e15i −0.741801 0.741801i
\(726\) 1.88811e15 1.76575e15i 0.347437 0.324920i
\(727\) 7.26392e15i 1.32658i 0.748365 + 0.663288i \(0.230839\pi\)
−0.748365 + 0.663288i \(0.769161\pi\)
\(728\) −5.88103e15 + 4.80428e15i −1.06593 + 0.870775i
\(729\) 7.56507e15i 1.36085i
\(730\) −2.46503e15 2.63586e15i −0.440095 0.470594i
\(731\) 8.47412e14 + 8.47412e14i 0.150158 + 0.150158i
\(732\) 6.63152e13 9.88992e14i 0.0116628 0.173933i
\(733\) −3.96841e15 + 3.96841e15i −0.692700 + 0.692700i −0.962825 0.270125i \(-0.912935\pi\)
0.270125 + 0.962825i \(0.412935\pi\)
\(734\) 1.69469e14 5.06041e15i 0.0293603 0.876714i
\(735\) 9.39712e14 0.161590
\(736\) −4.50401e15 7.61014e14i −0.768726 0.129887i
\(737\) 7.31684e15 1.23952
\(738\) −4.72181e14 + 1.40996e16i −0.0793960 + 2.37080i
\(739\) 3.06139e15 3.06139e15i 0.510945 0.510945i −0.403871 0.914816i \(-0.632335\pi\)
0.914816 + 0.403871i \(0.132335\pi\)
\(740\) −1.63292e14 + 2.43525e15i −0.0270514 + 0.403431i
\(741\) 5.13117e15 + 5.13117e15i 0.843755 + 0.843755i
\(742\) 2.10669e15 + 2.25268e15i 0.343858 + 0.367687i
\(743\) 1.78850e15i 0.289769i −0.989449 0.144884i \(-0.953719\pi\)
0.989449 0.144884i \(-0.0462810\pi\)
\(744\) 8.30887e15 + 1.01711e16i 1.33626 + 1.63574i
\(745\) 3.76518e15i 0.601071i
\(746\) −1.55191e15 + 1.45134e15i −0.245926 + 0.229988i
\(747\) −6.60388e15 6.60388e15i −1.03881 1.03881i
\(748\) 3.82288e15 + 4.37240e15i 0.596942 + 0.682749i
\(749\) 5.63221e15 5.63221e15i 0.873029 0.873029i
\(750\) 8.50702e15 + 2.84892e14i 1.30900 + 0.0438373i
\(751\) 6.56576e15 1.00292 0.501459 0.865182i \(-0.332797\pi\)
0.501459 + 0.865182i \(0.332797\pi\)
\(752\) −8.47263e15 1.14137e15i −1.28475 0.173072i
\(753\) 5.88785e15 0.886307
\(754\) 1.46427e16 + 4.90369e14i 2.18815 + 0.0732792i
\(755\) 6.86132e14 6.86132e14i 0.101789 0.101789i
\(756\) 1.38566e15 1.21151e15i 0.204074 0.178426i
\(757\) −5.29530e15 5.29530e15i −0.774218 0.774218i 0.204623 0.978841i \(-0.434403\pi\)
−0.978841 + 0.204623i \(0.934403\pi\)
\(758\) −3.91532e15 + 3.66157e15i −0.568311 + 0.531480i
\(759\) 6.62499e15i 0.954674i
\(760\) −1.83179e14 + 1.81781e15i −0.0262060 + 0.260061i
\(761\)