Properties

Label 16.12.e.a.5.5
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 5.5
Character \(\chi\) = 16.5
Dual form 16.12.e.a.13.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-33.6365 - 30.2752i) q^{2} +(-4.32776 + 4.32776i) q^{3} +(214.830 + 2036.70i) q^{4} +(2233.99 + 2233.99i) q^{5} +(276.594 - 14.5472i) q^{6} -71414.8i q^{7} +(54435.3 - 75011.5i) q^{8} +177110. i q^{9} +O(q^{10})\) \(q+(-33.6365 - 30.2752i) q^{2} +(-4.32776 + 4.32776i) q^{3} +(214.830 + 2036.70i) q^{4} +(2233.99 + 2233.99i) q^{5} +(276.594 - 14.5472i) q^{6} -71414.8i q^{7} +(54435.3 - 75011.5i) q^{8} +177110. i q^{9} +(-7509.26 - 142778. i) q^{10} +(-236433. - 236433. i) q^{11} +(-9744.08 - 7884.62i) q^{12} +(-282.811 + 282.811i) q^{13} +(-2.16209e6 + 2.40215e6i) q^{14} -19336.4 q^{15} +(-4.10200e6 + 875089. i) q^{16} -8.99999e6 q^{17} +(5.36202e6 - 5.95735e6i) q^{18} +(-1.07066e7 + 1.07066e7i) q^{19} +(-4.07005e6 + 5.02991e6i) q^{20} +(309066. + 309066. i) q^{21} +(794737. + 1.51108e7i) q^{22} -3.55394e7i q^{23} +(89049.0 + 560215. i) q^{24} -3.88467e7i q^{25} +(18074.9 - 950.630i) q^{26} +(-1.53314e6 - 1.53314e6i) q^{27} +(1.45451e8 - 1.53421e7i) q^{28} +(-4.42357e7 + 4.42357e7i) q^{29} +(650408. + 585412. i) q^{30} -1.07402e8 q^{31} +(1.64470e8 + 9.47537e7i) q^{32} +2.04645e6 q^{33} +(3.02728e8 + 2.72476e8i) q^{34} +(1.59540e8 - 1.59540e8i) q^{35} +(-3.60719e8 + 3.80485e7i) q^{36} +(-4.45048e8 - 4.45048e8i) q^{37} +(6.84274e8 - 3.59886e7i) q^{38} -2447.88i q^{39} +(2.89183e8 - 4.59672e7i) q^{40} +1.29648e8i q^{41} +(-1.03888e6 - 1.97529e7i) q^{42} +(-5.58350e8 - 5.58350e8i) q^{43} +(4.30751e8 - 5.32337e8i) q^{44} +(-3.95662e8 + 3.95662e8i) q^{45} +(-1.07596e9 + 1.19542e9i) q^{46} +4.62220e8 q^{47} +(1.39653e7 - 2.15396e7i) q^{48} -3.12275e9 q^{49} +(-1.17609e9 + 1.30667e9i) q^{50} +(3.89498e7 - 3.89498e7i) q^{51} +(-636758. - 515245. i) q^{52} +(1.27823e9 + 1.27823e9i) q^{53} +(5.15342e6 + 9.79853e7i) q^{54} -1.05638e9i q^{55} +(-5.35694e9 - 3.88749e9i) q^{56} -9.26709e7i q^{57} +(2.82717e9 - 1.48692e8i) q^{58} +(5.52124e9 + 5.52124e9i) q^{59} +(-4.15403e6 - 3.93824e7i) q^{60} +(-1.52419e9 + 1.52419e9i) q^{61} +(3.61261e9 + 3.25160e9i) q^{62} +1.26482e10 q^{63} +(-2.66353e9 - 8.16655e9i) q^{64} -1.26360e6 q^{65} +(-6.88355e7 - 6.19567e7i) q^{66} +(1.43834e10 - 1.43834e10i) q^{67} +(-1.93347e9 - 1.83303e10i) q^{68} +(1.53806e8 + 1.53806e8i) q^{69} +(-1.01965e10 + 5.36272e8i) q^{70} +7.48815e9i q^{71} +(1.32853e10 + 9.64101e9i) q^{72} +1.59325e10i q^{73} +(1.49597e9 + 2.84438e10i) q^{74} +(1.68119e8 + 1.68119e8i) q^{75} +(-2.41062e10 - 1.95060e10i) q^{76} +(-1.68848e10 + 1.68848e10i) q^{77} +(-74109.8 + 82338.0i) q^{78} +6.06745e9 q^{79} +(-1.11188e10 - 7.20890e9i) q^{80} -3.13612e10 q^{81} +(3.92511e9 - 4.36090e9i) q^{82} +(8.65455e9 - 8.65455e9i) q^{83} +(-5.63079e8 + 6.95872e8i) q^{84} +(-2.01059e10 - 2.01059e10i) q^{85} +(1.87682e9 + 3.56851e10i) q^{86} -3.82883e8i q^{87} +(-3.06056e10 + 4.86491e9i) q^{88} -5.51864e10i q^{89} +(2.52874e10 - 1.32996e9i) q^{90} +(2.01969e7 + 2.01969e7i) q^{91} +(7.23832e10 - 7.63493e9i) q^{92} +(4.64808e8 - 4.64808e8i) q^{93} +(-1.55475e10 - 1.39938e10i) q^{94} -4.78368e10 q^{95} +(-1.12186e9 + 3.01717e8i) q^{96} -1.47835e11 q^{97} +(1.05038e11 + 9.45417e10i) q^{98} +(4.18746e10 - 4.18746e10i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −33.6365 30.2752i −0.743269 0.668993i
\(3\) −4.32776 + 4.32776i −0.0102824 + 0.0102824i −0.712229 0.701947i \(-0.752314\pi\)
0.701947 + 0.712229i \(0.252314\pi\)
\(4\) 214.830 + 2036.70i 0.104898 + 0.994483i
\(5\) 2233.99 + 2233.99i 0.319703 + 0.319703i 0.848653 0.528950i \(-0.177414\pi\)
−0.528950 + 0.848653i \(0.677414\pi\)
\(6\) 276.594 14.5472i 0.0145215 0.000763741i
\(7\) 71414.8i 1.60601i −0.595970 0.803007i \(-0.703232\pi\)
0.595970 0.803007i \(-0.296768\pi\)
\(8\) 54435.3 75011.5i 0.587335 0.809344i
\(9\) 177110.i 0.999789i
\(10\) −7509.26 142778.i −0.0237464 0.451505i
\(11\) −236433. 236433.i −0.442638 0.442638i 0.450259 0.892898i \(-0.351331\pi\)
−0.892898 + 0.450259i \(0.851331\pi\)
\(12\) −9744.08 7884.62i −0.0113043 0.00914711i
\(13\) −282.811 + 282.811i −0.000211256 + 0.000211256i −0.707212 0.707001i \(-0.750048\pi\)
0.707001 + 0.707212i \(0.250048\pi\)
\(14\) −2.16209e6 + 2.40215e6i −1.07441 + 1.19370i
\(15\) −19336.4 −0.00657466
\(16\) −4.10200e6 + 875089.i −0.977993 + 0.208638i
\(17\) −8.99999e6 −1.53735 −0.768675 0.639639i \(-0.779084\pi\)
−0.768675 + 0.639639i \(0.779084\pi\)
\(18\) 5.36202e6 5.95735e6i 0.668851 0.743112i
\(19\) −1.07066e7 + 1.07066e7i −0.991986 + 0.991986i −0.999968 0.00798250i \(-0.997459\pi\)
0.00798250 + 0.999968i \(0.497459\pi\)
\(20\) −4.07005e6 + 5.02991e6i −0.284403 + 0.351475i
\(21\) 309066. + 309066.i 0.0165137 + 0.0165137i
\(22\) 794737. + 1.51108e7i 0.0328775 + 0.625121i
\(23\) 3.55394e7i 1.15135i −0.817679 0.575675i \(-0.804740\pi\)
0.817679 0.575675i \(-0.195260\pi\)
\(24\) 89049.0 + 560215.i 0.00228280 + 0.0143613i
\(25\) 3.88467e7i 0.795580i
\(26\) 18074.9 950.630i 0.000298348 1.56913e-5i
\(27\) −1.53314e6 1.53314e6i −0.0205627 0.0205627i
\(28\) 1.45451e8 1.53421e7i 1.59715 0.168467i
\(29\) −4.42357e7 + 4.42357e7i −0.400482 + 0.400482i −0.878403 0.477921i \(-0.841391\pi\)
0.477921 + 0.878403i \(0.341391\pi\)
\(30\) 650408. + 585412.i 0.00488674 + 0.00439840i
\(31\) −1.07402e8 −0.673785 −0.336892 0.941543i \(-0.609376\pi\)
−0.336892 + 0.941543i \(0.609376\pi\)
\(32\) 1.64470e8 + 9.47537e7i 0.866489 + 0.499196i
\(33\) 2.04645e6 0.00910280
\(34\) 3.02728e8 + 2.72476e8i 1.14267 + 1.02848i
\(35\) 1.59540e8 1.59540e8i 0.513448 0.513448i
\(36\) −3.60719e8 + 3.80485e7i −0.994273 + 0.104875i
\(37\) −4.45048e8 4.45048e8i −1.05511 1.05511i −0.998390 0.0567195i \(-0.981936\pi\)
−0.0567195 0.998390i \(-0.518064\pi\)
\(38\) 6.84274e8 3.59886e7i 1.40094 0.0736810i
\(39\) 2447.88i 4.34444e-6i
\(40\) 2.89183e8 4.59672e7i 0.446523 0.0709770i
\(41\) 1.29648e8i 0.174765i 0.996175 + 0.0873824i \(0.0278502\pi\)
−0.996175 + 0.0873824i \(0.972150\pi\)
\(42\) −1.03888e6 1.97529e7i −0.00122658 0.0233217i
\(43\) −5.58350e8 5.58350e8i −0.579202 0.579202i 0.355481 0.934683i \(-0.384317\pi\)
−0.934683 + 0.355481i \(0.884317\pi\)
\(44\) 4.30751e8 5.32337e8i 0.393765 0.486628i
\(45\) −3.95662e8 + 3.95662e8i −0.319636 + 0.319636i
\(46\) −1.07596e9 + 1.19542e9i −0.770244 + 0.855762i
\(47\) 4.62220e8 0.293975 0.146988 0.989138i \(-0.453042\pi\)
0.146988 + 0.989138i \(0.453042\pi\)
\(48\) 1.39653e7 2.15396e7i 0.00791085 0.0122015i
\(49\) −3.12275e9 −1.57928
\(50\) −1.17609e9 + 1.30667e9i −0.532237 + 0.591330i
\(51\) 3.89498e7 3.89498e7i 0.0158077 0.0158077i
\(52\) −636758. 515245.i −0.000232250 0.000187930i
\(53\) 1.27823e9 + 1.27823e9i 0.419847 + 0.419847i 0.885151 0.465304i \(-0.154055\pi\)
−0.465304 + 0.885151i \(0.654055\pi\)
\(54\) 5.15342e6 + 9.79853e7i 0.00152732 + 0.0290399i
\(55\) 1.05638e9i 0.283026i
\(56\) −5.35694e9 3.88749e9i −1.29982 0.943267i
\(57\) 9.26709e7i 0.0204001i
\(58\) 2.82717e9 1.48692e8i 0.565586 0.0297463i
\(59\) 5.52124e9 + 5.52124e9i 1.00543 + 1.00543i 0.999985 + 0.00544223i \(0.00173232\pi\)
0.00544223 + 0.999985i \(0.498268\pi\)
\(60\) −4.15403e6 3.93824e7i −0.000689665 0.00653838i
\(61\) −1.52419e9 + 1.52419e9i −0.231060 + 0.231060i −0.813135 0.582075i \(-0.802241\pi\)
0.582075 + 0.813135i \(0.302241\pi\)
\(62\) 3.61261e9 + 3.25160e9i 0.500803 + 0.450757i
\(63\) 1.26482e10 1.60567
\(64\) −2.66353e9 8.16655e9i −0.310076 0.950712i
\(65\) −1.26360e6 −0.000135078
\(66\) −6.88355e7 6.19567e7i −0.00676583 0.00608971i
\(67\) 1.43834e10 1.43834e10i 1.30152 1.30152i 0.374150 0.927368i \(-0.377935\pi\)
0.927368 0.374150i \(-0.122065\pi\)
\(68\) −1.93347e9 1.83303e10i −0.161264 1.52887i
\(69\) 1.53806e8 + 1.53806e8i 0.0118387 + 0.0118387i
\(70\) −1.01965e10 + 5.36272e8i −0.725122 + 0.0381370i
\(71\) 7.48815e9i 0.492553i 0.969200 + 0.246277i \(0.0792072\pi\)
−0.969200 + 0.246277i \(0.920793\pi\)
\(72\) 1.32853e10 + 9.64101e9i 0.809173 + 0.587211i
\(73\) 1.59325e10i 0.899517i 0.893150 + 0.449759i \(0.148490\pi\)
−0.893150 + 0.449759i \(0.851510\pi\)
\(74\) 1.49597e9 + 2.84438e10i 0.0783696 + 1.49009i
\(75\) 1.68119e8 + 1.68119e8i 0.00818050 + 0.00818050i
\(76\) −2.41062e10 1.95060e10i −1.09057 0.882456i
\(77\) −1.68848e10 + 1.68848e10i −0.710883 + 0.710883i
\(78\) −74109.8 + 82338.0i −2.90640e−6 + 3.22909e-6i
\(79\) 6.06745e9 0.221849 0.110924 0.993829i \(-0.464619\pi\)
0.110924 + 0.993829i \(0.464619\pi\)
\(80\) −1.11188e10 7.20890e9i −0.379370 0.245965i
\(81\) −3.13612e10 −0.999366
\(82\) 3.92511e9 4.36090e9i 0.116916 0.129897i
\(83\) 8.65455e9 8.65455e9i 0.241165 0.241165i −0.576167 0.817332i \(-0.695452\pi\)
0.817332 + 0.576167i \(0.195452\pi\)
\(84\) −5.63079e8 + 6.95872e8i −0.0146904 + 0.0181549i
\(85\) −2.01059e10 2.01059e10i −0.491496 0.491496i
\(86\) 1.87682e9 + 3.56851e10i 0.0430210 + 0.817985i
\(87\) 3.82883e8i 0.00823587i
\(88\) −3.06056e10 + 4.86491e9i −0.618224 + 0.0982698i
\(89\) 5.51864e10i 1.04758i −0.851848 0.523790i \(-0.824518\pi\)
0.851848 0.523790i \(-0.175482\pi\)
\(90\) 2.52874e10 1.32996e9i 0.451409 0.0237413i
\(91\) 2.01969e7 + 2.01969e7i 0.000339279 + 0.000339279i
\(92\) 7.23832e10 7.63493e9i 1.14500 0.120774i
\(93\) 4.64808e8 4.64808e8i 0.00692815 0.00692815i
\(94\) −1.55475e10 1.39938e10i −0.218503 0.196667i
\(95\) −4.78368e10 −0.634282
\(96\) −1.12186e9 + 3.01717e8i −0.0140426 + 0.00377666i
\(97\) −1.47835e11 −1.74797 −0.873985 0.485953i \(-0.838473\pi\)
−0.873985 + 0.485953i \(0.838473\pi\)
\(98\) 1.05038e11 + 9.45417e10i 1.17383 + 1.05653i
\(99\) 4.18746e10 4.18746e10i 0.442545 0.442545i
\(100\) 7.91191e10 8.34543e9i 0.791191 0.0834543i
\(101\) 1.14815e11 + 1.14815e11i 1.08700 + 1.08700i 0.995836 + 0.0911655i \(0.0290592\pi\)
0.0911655 + 0.995836i \(0.470941\pi\)
\(102\) −2.48935e9 + 1.30924e8i −0.0223246 + 0.00117414i
\(103\) 6.84942e9i 0.0582169i −0.999576 0.0291084i \(-0.990733\pi\)
0.999576 0.0291084i \(-0.00926681\pi\)
\(104\) 5.81919e6 + 3.66090e7i 4.69007e−5 + 0.000295056i
\(105\) 1.38090e9i 0.0105590i
\(106\) −4.29659e9 8.16937e10i −0.0311847 0.592934i
\(107\) −1.10999e11 1.10999e11i −0.765080 0.765080i 0.212156 0.977236i \(-0.431952\pi\)
−0.977236 + 0.212156i \(0.931952\pi\)
\(108\) 2.79318e9 3.45191e9i 0.0182923 0.0226062i
\(109\) 1.01764e11 1.01764e11i 0.633501 0.633501i −0.315444 0.948944i \(-0.602153\pi\)
0.948944 + 0.315444i \(0.102153\pi\)
\(110\) −3.19821e10 + 3.55330e10i −0.189342 + 0.210364i
\(111\) 3.85212e9 0.0216982
\(112\) 6.24943e10 + 2.92944e11i 0.335075 + 1.57067i
\(113\) 9.78538e10 0.499627 0.249814 0.968294i \(-0.419631\pi\)
0.249814 + 0.968294i \(0.419631\pi\)
\(114\) −2.80562e9 + 3.11712e9i −0.0136475 + 0.0151627i
\(115\) 7.93948e10 7.93948e10i 0.368090 0.368090i
\(116\) −9.95980e10 8.05917e10i −0.440283 0.356263i
\(117\) −5.00885e7 5.00885e7i −0.000211211 0.000211211i
\(118\) −1.85589e10 3.52872e11i −0.0746794 1.41993i
\(119\) 6.42733e11i 2.46901i
\(120\) −1.05258e9 + 1.45045e9i −0.00386153 + 0.00532116i
\(121\) 1.73510e11i 0.608143i
\(122\) 9.74135e10 5.12335e9i 0.326317 0.0171623i
\(123\) −5.61084e8 5.61084e8i −0.00179701 0.00179701i
\(124\) −2.30731e10 2.18745e11i −0.0706783 0.670067i
\(125\) 1.95865e11 1.95865e11i 0.574053 0.574053i
\(126\) −4.25443e11 3.82928e11i −1.19345 1.07418i
\(127\) −6.75185e11 −1.81344 −0.906718 0.421738i \(-0.861420\pi\)
−0.906718 + 0.421738i \(0.861420\pi\)
\(128\) −1.57652e11 + 3.55333e11i −0.405550 + 0.914073i
\(129\) 4.83281e9 0.0119112
\(130\) 4.25030e7 + 3.82556e7i 0.000100399 + 9.03663e-5i
\(131\) 1.39014e11 1.39014e11i 0.314823 0.314823i −0.531952 0.846775i \(-0.678541\pi\)
0.846775 + 0.531952i \(0.178541\pi\)
\(132\) 4.39640e8 + 4.16801e9i 0.000954861 + 0.00905258i
\(133\) 7.64607e11 + 7.64607e11i 1.59314 + 1.59314i
\(134\) −9.19267e11 + 4.83478e10i −1.83808 + 0.0966719i
\(135\) 6.85004e9i 0.0131479i
\(136\) −4.89917e11 + 6.75103e11i −0.902940 + 1.24425i
\(137\) 7.40756e9i 0.0131133i 0.999979 + 0.00655665i \(0.00208706\pi\)
−0.999979 + 0.00655665i \(0.997913\pi\)
\(138\) −5.16997e8 9.83000e9i −0.000879333 0.0167193i
\(139\) −5.44962e10 5.44962e10i −0.0890810 0.0890810i 0.661162 0.750243i \(-0.270064\pi\)
−0.750243 + 0.661162i \(0.770064\pi\)
\(140\) 3.59210e11 + 2.90662e11i 0.564474 + 0.456755i
\(141\) −2.00038e9 + 2.00038e9i −0.00302278 + 0.00302278i
\(142\) 2.26705e11 2.51875e11i 0.329515 0.366100i
\(143\) 1.33732e8 0.000187020
\(144\) −1.54987e11 7.26503e11i −0.208593 0.977786i
\(145\) −1.97644e11 −0.256071
\(146\) 4.82360e11 5.35915e11i 0.601771 0.668583i
\(147\) 1.35145e10 1.35145e10i 0.0162388 0.0162388i
\(148\) 8.10821e11 1.00204e12i 0.938610 1.15997i
\(149\) 6.09273e11 + 6.09273e11i 0.679653 + 0.679653i 0.959922 0.280268i \(-0.0904235\pi\)
−0.280268 + 0.959922i \(0.590423\pi\)
\(150\) −5.65108e8 1.07448e10i −0.000607617 0.0115530i
\(151\) 6.86276e11i 0.711419i 0.934597 + 0.355709i \(0.115761\pi\)
−0.934597 + 0.355709i \(0.884239\pi\)
\(152\) 2.20301e11 + 1.38593e12i 0.220230 + 1.38549i
\(153\) 1.59398e12i 1.53703i
\(154\) 1.07914e12 5.67560e10i 1.00395 0.0528017i
\(155\) −2.39934e11 2.39934e11i −0.215411 0.215411i
\(156\) 4.98559e6 525878.i 4.32048e−6 4.55721e-7i
\(157\) 1.50923e12 1.50923e12i 1.26272 1.26272i 0.312952 0.949769i \(-0.398682\pi\)
0.949769 0.312952i \(-0.101318\pi\)
\(158\) −2.04088e11 1.83693e11i −0.164893 0.148415i
\(159\) −1.10637e10 −0.00863411
\(160\) 1.55747e11 + 5.79105e11i 0.117425 + 0.436614i
\(161\) −2.53804e12 −1.84908
\(162\) 1.05488e12 + 9.49464e11i 0.742797 + 0.668568i
\(163\) 1.16350e12 1.16350e12i 0.792017 0.792017i −0.189805 0.981822i \(-0.560785\pi\)
0.981822 + 0.189805i \(0.0607854\pi\)
\(164\) −2.64054e11 + 2.78522e10i −0.173801 + 0.0183324i
\(165\) 4.57176e9 + 4.57176e9i 0.00291019 + 0.00291019i
\(166\) −5.53127e11 + 2.90910e10i −0.340589 + 0.0179129i
\(167\) 1.66142e12i 0.989777i 0.868956 + 0.494889i \(0.164791\pi\)
−0.868956 + 0.494889i \(0.835209\pi\)
\(168\) 4.00076e10 6.35942e9i 0.0230644 0.00366620i
\(169\) 1.79216e12i 1.00000i
\(170\) 6.75832e10 + 1.28500e12i 0.0365065 + 0.694121i
\(171\) −1.89623e12 1.89623e12i −0.991776 0.991776i
\(172\) 1.01724e12 1.25714e12i 0.515250 0.636764i
\(173\) −2.50410e12 + 2.50410e12i −1.22856 + 1.22856i −0.264058 + 0.964507i \(0.585061\pi\)
−0.964507 + 0.264058i \(0.914939\pi\)
\(174\) −1.15918e10 + 1.28788e10i −0.00550974 + 0.00612147i
\(175\) −2.77423e12 −1.27771
\(176\) 1.17675e12 + 7.62949e11i 0.525248 + 0.340546i
\(177\) −4.77892e10 −0.0206765
\(178\) −1.67078e12 + 1.85628e12i −0.700823 + 0.778633i
\(179\) 2.08597e12 2.08597e12i 0.848431 0.848431i −0.141506 0.989937i \(-0.545195\pi\)
0.989937 + 0.141506i \(0.0451946\pi\)
\(180\) −8.90845e11 7.20845e11i −0.351401 0.284343i
\(181\) −1.90878e12 1.90878e12i −0.730339 0.730339i 0.240348 0.970687i \(-0.422739\pi\)
−0.970687 + 0.240348i \(0.922739\pi\)
\(182\) −6.78891e7 1.29082e9i −2.52004e−5 0.000479151i
\(183\) 1.31927e10i 0.00475172i
\(184\) −2.66587e12 1.93460e12i −0.931838 0.676228i
\(185\) 1.98847e12i 0.674644i
\(186\) −2.97066e10 + 1.56239e9i −0.00978436 + 0.000514597i
\(187\) 2.12790e12 + 2.12790e12i 0.680490 + 0.680490i
\(188\) 9.92988e10 + 9.41405e11i 0.0308373 + 0.292353i
\(189\) −1.09489e11 + 1.09489e11i −0.0330240 + 0.0330240i
\(190\) 1.60906e12 + 1.44827e12i 0.471442 + 0.424330i
\(191\) 4.39175e12 1.25013 0.625064 0.780574i \(-0.285073\pi\)
0.625064 + 0.780574i \(0.285073\pi\)
\(192\) 4.68700e10 + 2.38158e10i 0.0129640 + 0.00658730i
\(193\) −5.30994e12 −1.42733 −0.713665 0.700487i \(-0.752966\pi\)
−0.713665 + 0.700487i \(0.752966\pi\)
\(194\) 4.97267e12 + 4.47574e12i 1.29921 + 1.16938i
\(195\) 5.46854e6 5.46854e6i 1.38893e−6 1.38893e-6i
\(196\) −6.70860e11 6.36011e12i −0.165662 1.57057i
\(197\) 3.61540e12 + 3.61540e12i 0.868146 + 0.868146i 0.992267 0.124121i \(-0.0396112\pi\)
−0.124121 + 0.992267i \(0.539611\pi\)
\(198\) −2.67628e12 + 1.40756e11i −0.624989 + 0.0328706i
\(199\) 2.20956e12i 0.501897i −0.968000 0.250948i \(-0.919258\pi\)
0.968000 0.250948i \(-0.0807424\pi\)
\(200\) −2.91395e12 2.11463e12i −0.643898 0.467272i
\(201\) 1.24496e11i 0.0267656i
\(202\) −3.85934e11 7.33800e12i −0.0807384 1.53513i
\(203\) 3.15908e12 + 3.15908e12i 0.643180 + 0.643180i
\(204\) 8.76967e10 + 7.09615e10i 0.0173787 + 0.0140623i
\(205\) −2.89632e11 + 2.89632e11i −0.0558729 + 0.0558729i
\(206\) −2.07367e11 + 2.30391e11i −0.0389467 + 0.0432708i
\(207\) 6.29437e12 1.15111
\(208\) 9.12606e8 1.40758e9i 0.000162531 0.000250682i
\(209\) 5.06278e12 0.878182
\(210\) 4.18071e10 4.64488e10i 0.00706388 0.00784817i
\(211\) −1.33456e11 + 1.33456e11i −0.0219676 + 0.0219676i −0.718005 0.696038i \(-0.754945\pi\)
0.696038 + 0.718005i \(0.254945\pi\)
\(212\) −2.32877e12 + 2.87797e12i −0.373490 + 0.461572i
\(213\) −3.24069e10 3.24069e10i −0.00506465 0.00506465i
\(214\) 3.73106e11 + 7.09411e12i 0.0568273 + 1.08049i
\(215\) 2.49470e12i 0.370346i
\(216\) −1.98460e11 + 3.15462e10i −0.0287195 + 0.00456511i
\(217\) 7.67006e12i 1.08211i
\(218\) −6.50389e12 + 3.42064e11i −0.894669 + 0.0470541i
\(219\) −6.89522e10 6.89522e10i −0.00924923 0.00924923i
\(220\) 2.15153e12 2.26942e11i 0.281464 0.0296887i
\(221\) 2.54530e9 2.54530e9i 0.000324774 0.000324774i
\(222\) −1.29572e11 1.16624e11i −0.0161276 0.0145159i
\(223\) 1.71920e12 0.208761 0.104380 0.994537i \(-0.466714\pi\)
0.104380 + 0.994537i \(0.466714\pi\)
\(224\) 6.76682e12 1.17456e13i 0.801716 1.39159i
\(225\) 6.88012e12 0.795412
\(226\) −3.29146e12 2.96254e12i −0.371358 0.334247i
\(227\) −4.83327e12 + 4.83327e12i −0.532230 + 0.532230i −0.921235 0.389006i \(-0.872819\pi\)
0.389006 + 0.921235i \(0.372819\pi\)
\(228\) 1.88743e11 1.99085e10i 0.0202875 0.00213992i
\(229\) −7.49588e12 7.49588e12i −0.786552 0.786552i 0.194375 0.980927i \(-0.437732\pi\)
−0.980927 + 0.194375i \(0.937732\pi\)
\(230\) −5.07426e12 + 2.66875e11i −0.519839 + 0.0273403i
\(231\) 1.46147e11i 0.0146192i
\(232\) 9.10203e11 + 5.72617e12i 0.0889108 + 0.559345i
\(233\) 3.54948e12i 0.338616i −0.985563 0.169308i \(-0.945847\pi\)
0.985563 0.169308i \(-0.0541532\pi\)
\(234\) 1.68366e8 + 3.20124e9i 1.56879e−5 + 0.000298285i
\(235\) 1.03260e12 + 1.03260e12i 0.0939848 + 0.0939848i
\(236\) −1.00590e13 + 1.24312e13i −0.894414 + 1.10535i
\(237\) −2.62585e10 + 2.62585e10i −0.00228115 + 0.00228115i
\(238\) 1.94588e13 2.16193e13i 1.65175 1.83514i
\(239\) −1.56707e13 −1.29987 −0.649936 0.759989i \(-0.725204\pi\)
−0.649936 + 0.759989i \(0.725204\pi\)
\(240\) 7.93178e10 1.69211e10i 0.00642997 0.00137172i
\(241\) 3.00251e12 0.237898 0.118949 0.992900i \(-0.462047\pi\)
0.118949 + 0.992900i \(0.462047\pi\)
\(242\) −5.25305e12 + 5.83628e12i −0.406843 + 0.452014i
\(243\) 4.07314e11 4.07314e11i 0.0308386 0.0308386i
\(244\) −3.43176e12 2.77688e12i −0.254023 0.205548i
\(245\) −6.97620e12 6.97620e12i −0.504900 0.504900i
\(246\) 1.88601e9 + 3.58598e10i 0.000133475 + 0.00253785i
\(247\) 6.05587e9i 0.000419125i
\(248\) −5.84643e12 + 8.05635e12i −0.395737 + 0.545324i
\(249\) 7.49096e10i 0.00495954i
\(250\) −1.25181e13 + 6.58372e11i −0.810712 + 0.0426385i
\(251\) −1.12730e13 1.12730e13i −0.714223 0.714223i 0.253193 0.967416i \(-0.418519\pi\)
−0.967416 + 0.253193i \(0.918519\pi\)
\(252\) 2.71722e12 + 2.57607e13i 0.168431 + 1.59682i
\(253\) −8.40270e12 + 8.40270e12i −0.509631 + 0.509631i
\(254\) 2.27109e13 + 2.04413e13i 1.34787 + 1.21317i
\(255\) 1.74027e11 0.0101076
\(256\) 1.60606e13 7.17923e12i 0.912941 0.408092i
\(257\) 2.38344e13 1.32609 0.663044 0.748580i \(-0.269264\pi\)
0.663044 + 0.748580i \(0.269264\pi\)
\(258\) −1.62559e11 1.46314e11i −0.00885324 0.00796852i
\(259\) −3.17830e13 + 3.17830e13i −1.69452 + 1.69452i
\(260\) −2.71459e8 2.57357e9i −1.41694e−5 0.000134333i
\(261\) −7.83456e12 7.83456e12i −0.400398 0.400398i
\(262\) −8.88462e12 + 4.67276e11i −0.444613 + 0.0233839i
\(263\) 3.02043e13i 1.48017i −0.672513 0.740085i \(-0.734785\pi\)
0.672513 0.740085i \(-0.265215\pi\)
\(264\) 1.11399e11 1.53508e11i 0.00534639 0.00736730i
\(265\) 5.71111e12i 0.268453i
\(266\) −2.57012e12 4.88673e13i −0.118333 2.24993i
\(267\) 2.38833e11 + 2.38833e11i 0.0107717 + 0.0107717i
\(268\) 3.23847e13 + 2.62047e13i 1.43086 + 1.15781i
\(269\) 2.50045e13 2.50045e13i 1.08238 1.08238i 0.0860954 0.996287i \(-0.472561\pi\)
0.996287 0.0860954i \(-0.0274390\pi\)
\(270\) −2.07386e11 + 2.30411e11i −0.00879587 + 0.00977244i
\(271\) 5.39216e12 0.224095 0.112047 0.993703i \(-0.464259\pi\)
0.112047 + 0.993703i \(0.464259\pi\)
\(272\) 3.69180e13 7.87580e12i 1.50352 0.320749i
\(273\) −1.74815e8 −6.97723e−6
\(274\) 2.24265e11 2.49164e11i 0.00877270 0.00974671i
\(275\) −9.18465e12 + 9.18465e12i −0.352154 + 0.352154i
\(276\) −2.80215e11 + 3.46299e11i −0.0105315 + 0.0130152i
\(277\) 9.61770e12 + 9.61770e12i 0.354350 + 0.354350i 0.861725 0.507375i \(-0.169384\pi\)
−0.507375 + 0.861725i \(0.669384\pi\)
\(278\) 1.83181e11 + 3.48294e12i 0.00661660 + 0.125806i
\(279\) 1.90218e13i 0.673642i
\(280\) −3.28274e12 2.06520e13i −0.113990 0.717121i
\(281\) 3.40138e12i 0.115817i −0.998322 0.0579083i \(-0.981557\pi\)
0.998322 0.0579083i \(-0.0184431\pi\)
\(282\) 1.27848e11 6.72399e9i 0.00426896 0.000224521i
\(283\) 1.89776e13 + 1.89776e13i 0.621465 + 0.621465i 0.945906 0.324441i \(-0.105176\pi\)
−0.324441 + 0.945906i \(0.605176\pi\)
\(284\) −1.52511e13 + 1.60868e12i −0.489836 + 0.0516676i
\(285\) 2.07026e11 2.07026e11i 0.00652197 0.00652197i
\(286\) −4.49828e9 4.04876e9i −0.000139006 0.000125115i
\(287\) 9.25877e12 0.280675
\(288\) −1.67818e13 + 2.91293e13i −0.499091 + 0.866306i
\(289\) 4.67279e13 1.36345
\(290\) 6.64807e12 + 5.98371e12i 0.190330 + 0.171310i
\(291\) 6.39796e11 6.39796e11i 0.0179734 0.0179734i
\(292\) −3.24498e13 + 3.42279e12i −0.894555 + 0.0943571i
\(293\) −2.15247e13 2.15247e13i −0.582325 0.582325i 0.353217 0.935542i \(-0.385088\pi\)
−0.935542 + 0.353217i \(0.885088\pi\)
\(294\) −8.63735e11 + 4.54271e10i −0.0229335 + 0.00120616i
\(295\) 2.46688e13i 0.642877i
\(296\) −5.76101e13 + 9.15742e12i −1.47365 + 0.234244i
\(297\) 7.24969e11i 0.0182037i
\(298\) −2.04798e12 3.89396e13i −0.0504821 0.959848i
\(299\) 1.00509e10 + 1.00509e10i 0.000243229 + 0.000243229i
\(300\) −3.06291e11 + 3.78525e11i −0.00727725 + 0.00899348i
\(301\) −3.98745e13 + 3.98745e13i −0.930207 + 0.930207i
\(302\) 2.07771e13 2.30839e13i 0.475934 0.528775i
\(303\) −9.93781e11 −0.0223540
\(304\) 3.45491e13 5.32875e13i 0.763190 1.17712i
\(305\) −6.81006e12 −0.147741
\(306\) −4.82581e13 + 5.36161e13i −1.02826 + 1.14242i
\(307\) −1.79843e13 + 1.79843e13i −0.376386 + 0.376386i −0.869796 0.493411i \(-0.835750\pi\)
0.493411 + 0.869796i \(0.335750\pi\)
\(308\) −3.80168e13 3.07620e13i −0.781531 0.632391i
\(309\) 2.96426e10 + 2.96426e10i 0.000598612 + 0.000598612i
\(310\) 8.06505e11 + 1.53346e13i 0.0159999 + 0.304217i
\(311\) 8.79750e12i 0.171466i −0.996318 0.0857328i \(-0.972677\pi\)
0.996318 0.0857328i \(-0.0273231\pi\)
\(312\) −1.83619e8 1.33251e8i −3.51615e−6 2.55164e-6i
\(313\) 5.86822e13i 1.10411i 0.833808 + 0.552055i \(0.186156\pi\)
−0.833808 + 0.552055i \(0.813844\pi\)
\(314\) −9.64574e13 + 5.07307e12i −1.78329 + 0.0937902i
\(315\) 2.82561e13 + 2.82561e13i 0.513339 + 0.513339i
\(316\) 1.30347e12 + 1.23576e13i 0.0232714 + 0.220625i
\(317\) −3.22343e13 + 3.22343e13i −0.565578 + 0.565578i −0.930887 0.365308i \(-0.880964\pi\)
0.365308 + 0.930887i \(0.380964\pi\)
\(318\) 3.72145e11 + 3.34956e11i 0.00641746 + 0.00577615i
\(319\) 2.09176e13 0.354538
\(320\) 1.22937e13 2.41943e13i 0.204813 0.403078i
\(321\) 9.60751e11 0.0157338
\(322\) 8.53708e13 + 7.68396e13i 1.37437 + 1.23702i
\(323\) 9.63590e13 9.63590e13i 1.52503 1.52503i
\(324\) −6.73732e12 6.38733e13i −0.104831 0.993852i
\(325\) 1.09863e10 + 1.09863e10i 0.000168071 + 0.000168071i
\(326\) −7.43612e13 + 3.91094e12i −1.11854 + 0.0588281i
\(327\) 8.80817e11i 0.0130279i
\(328\) 9.72508e12 + 7.05742e12i 0.141445 + 0.102645i
\(329\) 3.30094e13i 0.472128i
\(330\) −1.53673e10 2.92189e11i −0.000216158 0.00410996i
\(331\) −3.78052e13 3.78052e13i −0.522994 0.522994i 0.395480 0.918475i \(-0.370578\pi\)
−0.918475 + 0.395480i \(0.870578\pi\)
\(332\) 1.94860e13 + 1.57675e13i 0.265132 + 0.214537i
\(333\) 7.88223e13 7.88223e13i 1.05489 1.05489i
\(334\) 5.02996e13 5.58842e13i 0.662154 0.735671i
\(335\) 6.42649e13 0.832199
\(336\) −1.53825e12 9.97329e11i −0.0195957 0.0127049i
\(337\) −1.14761e14 −1.43823 −0.719115 0.694891i \(-0.755453\pi\)
−0.719115 + 0.694891i \(0.755453\pi\)
\(338\) 5.42579e13 6.02820e13i 0.668993 0.743269i
\(339\) −4.23488e11 + 4.23488e11i −0.00513739 + 0.00513739i
\(340\) 3.66304e13 4.52691e13i 0.437228 0.540341i
\(341\) 2.53933e13 + 2.53933e13i 0.298243 + 0.298243i
\(342\) 6.37393e12 + 1.21192e14i 0.0736654 + 1.40065i
\(343\) 8.18001e13i 0.930329i
\(344\) −7.22767e13 + 1.14887e13i −0.808960 + 0.128588i
\(345\) 6.87203e11i 0.00756973i
\(346\) 1.60041e14 8.41718e12i 1.73505 0.0912532i
\(347\) 1.50582e13 + 1.50582e13i 0.160679 + 0.160679i 0.782868 0.622188i \(-0.213756\pi\)
−0.622188 + 0.782868i \(0.713756\pi\)
\(348\) 7.79817e11 8.22547e10i 0.00819044 0.000863922i
\(349\) −3.37156e13 + 3.37156e13i −0.348570 + 0.348570i −0.859577 0.511006i \(-0.829273\pi\)
0.511006 + 0.859577i \(0.329273\pi\)
\(350\) 9.33153e13 + 8.39902e13i 0.949683 + 0.854780i
\(351\) 8.67176e8 8.68797e−6
\(352\) −1.64834e13 6.12892e13i −0.162578 0.604505i
\(353\) −1.59363e14 −1.54748 −0.773741 0.633502i \(-0.781617\pi\)
−0.773741 + 0.633502i \(0.781617\pi\)
\(354\) 1.60746e12 + 1.44683e12i 0.0153682 + 0.0138324i
\(355\) −1.67285e13 + 1.67285e13i −0.157471 + 0.157471i
\(356\) 1.12398e14 1.18557e13i 1.04180 0.109888i
\(357\) −2.78159e12 2.78159e12i −0.0253874 0.0253874i
\(358\) −1.33318e14 + 7.01170e12i −1.19821 + 0.0630183i
\(359\) 9.53928e13i 0.844299i −0.906526 0.422150i \(-0.861276\pi\)
0.906526 0.422150i \(-0.138724\pi\)
\(360\) 8.14123e12 + 5.12172e13i 0.0709620 + 0.446428i
\(361\) 1.12771e14i 0.968071i
\(362\) 6.41611e12 + 1.21994e14i 0.0542468 + 1.03143i
\(363\) 7.50910e11 + 7.50910e11i 0.00625319 + 0.00625319i
\(364\) −3.67962e10 + 4.54740e10i −0.000301818 + 0.000372997i
\(365\) −3.55932e13 + 3.55932e13i −0.287579 + 0.287579i
\(366\) −3.99410e11 + 4.43755e11i −0.00317887 + 0.00353181i
\(367\) −4.96140e13 −0.388992 −0.194496 0.980903i \(-0.562307\pi\)
−0.194496 + 0.980903i \(0.562307\pi\)
\(368\) 3.11002e13 + 1.45783e14i 0.240215 + 1.12601i
\(369\) −2.29619e13 −0.174728
\(370\) −6.02012e13 + 6.68852e13i −0.451332 + 0.501442i
\(371\) 9.12845e13 9.12845e13i 0.674280 0.674280i
\(372\) 1.04653e12 + 8.46820e11i 0.00761667 + 0.00616318i
\(373\) 5.68027e13 + 5.68027e13i 0.407353 + 0.407353i 0.880814 0.473462i \(-0.156996\pi\)
−0.473462 + 0.880814i \(0.656996\pi\)
\(374\) −7.15263e12 1.35997e14i −0.0505443 0.961030i
\(375\) 1.69531e12i 0.0118053i
\(376\) 2.51611e13 3.46719e13i 0.172662 0.237927i
\(377\) 2.50207e10i 0.000169208i
\(378\) 6.99760e12 3.68031e11i 0.0466385 0.00245290i
\(379\) −1.11074e14 1.11074e14i −0.729621 0.729621i 0.240923 0.970544i \(-0.422550\pi\)
−0.970544 + 0.240923i \(0.922550\pi\)
\(380\) −1.02768e13 9.74293e13i −0.0665346 0.630783i
\(381\) 2.92204e12 2.92204e12i 0.0186465 0.0186465i
\(382\) −1.47723e14 1.32961e14i −0.929181 0.836326i
\(383\) −2.62650e14 −1.62849 −0.814244 0.580523i \(-0.802848\pi\)
−0.814244 + 0.580523i \(0.802848\pi\)
\(384\) −8.55517e11 2.22008e12i −0.00522886 0.0135689i
\(385\) −7.54413e13 −0.454543
\(386\) 1.78608e14 + 1.60759e14i 1.06089 + 0.954873i
\(387\) 9.88892e13 9.88892e13i 0.579080 0.579080i
\(388\) −3.17595e13 3.01097e14i −0.183358 1.73833i
\(389\) 8.87826e13 + 8.87826e13i 0.505365 + 0.505365i 0.913100 0.407735i \(-0.133681\pi\)
−0.407735 + 0.913100i \(0.633681\pi\)
\(390\) −3.49504e8 + 1.83817e7i −1.96154e−6 + 1.03165e-7i
\(391\) 3.19854e14i 1.77003i
\(392\) −1.69988e14 + 2.34242e14i −0.927565 + 1.27818i
\(393\) 1.20324e12i 0.00647430i
\(394\) −1.21527e13 2.31067e14i −0.0644826 1.22605i
\(395\) 1.35547e13 + 1.35547e13i 0.0709258 + 0.0709258i
\(396\) 9.42820e13 + 7.62901e13i 0.486525 + 0.393681i
\(397\) −2.85419e13 + 2.85419e13i −0.145256 + 0.145256i −0.775995 0.630739i \(-0.782752\pi\)
0.630739 + 0.775995i \(0.282752\pi\)
\(398\) −6.68948e13 + 7.43219e13i −0.335765 + 0.373044i
\(399\) −6.61807e12 −0.0327628
\(400\) 3.39943e13 + 1.59349e14i 0.165988 + 0.778071i
\(401\) 2.56296e14 1.23438 0.617189 0.786815i \(-0.288271\pi\)
0.617189 + 0.786815i \(0.288271\pi\)
\(402\) 3.76913e12 4.18760e12i 0.0179060 0.0198940i
\(403\) 3.03743e10 3.03743e10i 0.000142341 0.000142341i
\(404\) −2.09178e14 + 2.58509e14i −0.966981 + 1.19503i
\(405\) −7.00606e13 7.00606e13i −0.319500 0.319500i
\(406\) −1.06188e13 2.01902e14i −0.0477730 0.908339i
\(407\) 2.10448e14i 0.934064i
\(408\) −8.01440e11 5.04193e12i −0.00350946 0.0220783i
\(409\) 1.52405e14i 0.658447i −0.944252 0.329224i \(-0.893213\pi\)
0.944252 0.329224i \(-0.106787\pi\)
\(410\) 1.85109e13 9.73558e11i 0.0789071 0.00415003i
\(411\) −3.20581e10 3.20581e10i −0.000134837 0.000134837i
\(412\) 1.39502e13 1.47146e12i 0.0578957 0.00610681i
\(413\) 3.94298e14 3.94298e14i 1.61473 1.61473i
\(414\) −2.11721e14 1.90563e14i −0.855581 0.770081i
\(415\) 3.86684e13 0.154203
\(416\) −7.33115e10 + 1.97167e10i −0.000288509 + 7.75926e-5i
\(417\) 4.71693e11 0.00183194
\(418\) −1.70294e14 1.53276e14i −0.652725 0.587497i
\(419\) −1.00355e14 + 1.00355e14i −0.379631 + 0.379631i −0.870969 0.491338i \(-0.836508\pi\)
0.491338 + 0.870969i \(0.336508\pi\)
\(420\) −2.81249e12 + 2.96660e11i −0.0105007 + 0.00110761i
\(421\) 2.77863e14 + 2.77863e14i 1.02395 + 1.02395i 0.999706 + 0.0242456i \(0.00771836\pi\)
0.0242456 + 0.999706i \(0.492282\pi\)
\(422\) 8.52937e12 4.48592e11i 0.0310241 0.00163167i
\(423\) 8.18636e13i 0.293913i
\(424\) 1.65463e14 2.63011e13i 0.586392 0.0932099i
\(425\) 3.49620e14i 1.22309i
\(426\) 1.08931e11 + 2.07118e12i 0.000376183 + 0.00715261i
\(427\) 1.08850e14 + 1.08850e14i 0.371086 + 0.371086i
\(428\) 2.02225e14 2.49917e14i 0.680604 0.841114i
\(429\) −5.78760e8 + 5.78760e8i −1.92302e−6 + 1.92302e-6i
\(430\) −7.55275e13 + 8.39131e13i −0.247759 + 0.275266i
\(431\) 7.56776e13 0.245099 0.122550 0.992462i \(-0.460893\pi\)
0.122550 + 0.992462i \(0.460893\pi\)
\(432\) 7.63056e12 + 4.94730e12i 0.0244003 + 0.0158200i
\(433\) −2.91093e13 −0.0919070 −0.0459535 0.998944i \(-0.514633\pi\)
−0.0459535 + 0.998944i \(0.514633\pi\)
\(434\) 2.32212e14 2.57994e14i 0.723922 0.804297i
\(435\) 8.55357e11 8.55357e11i 0.00263303 0.00263303i
\(436\) 2.29124e14 + 1.85400e14i 0.696458 + 0.563553i
\(437\) 3.80505e14 + 3.80505e14i 1.14212 + 1.14212i
\(438\) 2.31773e11 + 4.40685e12i 0.000686998 + 0.0130623i
\(439\) 3.40756e14i 0.997445i −0.866762 0.498723i \(-0.833803\pi\)
0.866762 0.498723i \(-0.166197\pi\)
\(440\) −7.92408e13 5.75044e13i −0.229065 0.166231i
\(441\) 5.53069e14i 1.57894i
\(442\) −1.62674e11 + 8.55566e9i −0.000458666 + 2.41230e-5i
\(443\) −2.82666e14 2.82666e14i −0.787141 0.787141i 0.193884 0.981025i \(-0.437892\pi\)
−0.981025 + 0.193884i \(0.937892\pi\)
\(444\) 8.27552e11 + 7.84562e12i 0.00227609 + 0.0215785i
\(445\) 1.23286e14 1.23286e14i 0.334914 0.334914i
\(446\) −5.78278e13 5.20490e13i −0.155165 0.139660i
\(447\) −5.27357e12 −0.0139770
\(448\) −5.83213e14 + 1.90215e14i −1.52686 + 0.497985i
\(449\) −6.78315e13 −0.175419 −0.0877094 0.996146i \(-0.527955\pi\)
−0.0877094 + 0.996146i \(0.527955\pi\)
\(450\) −2.31423e14 2.08297e14i −0.591205 0.532125i
\(451\) 3.06531e13 3.06531e13i 0.0773576 0.0773576i
\(452\) 2.10219e13 + 1.99299e14i 0.0524097 + 0.496871i
\(453\) −2.97004e12 2.97004e12i −0.00731512 0.00731512i
\(454\) 3.08903e14 1.62464e13i 0.751648 0.0395320i
\(455\) 9.02395e10i 0.000216937i
\(456\) −6.95138e12 5.04457e12i −0.0165107 0.0119817i
\(457\) 1.33927e14i 0.314289i 0.987576 + 0.157144i \(0.0502288\pi\)
−0.987576 + 0.157144i \(0.949771\pi\)
\(458\) 2.51963e13 + 4.79074e14i 0.0584221 + 1.11082i
\(459\) 1.37982e13 + 1.37982e13i 0.0316121 + 0.0316121i
\(460\) 1.78760e14 + 1.44647e14i 0.404671 + 0.327448i
\(461\) −4.21772e14 + 4.21772e14i −0.943457 + 0.943457i −0.998485 0.0550276i \(-0.982475\pi\)
0.0550276 + 0.998485i \(0.482475\pi\)
\(462\) −4.42462e12 + 4.91588e12i −0.00978015 + 0.0108660i
\(463\) −5.89482e14 −1.28758 −0.643792 0.765201i \(-0.722640\pi\)
−0.643792 + 0.765201i \(0.722640\pi\)
\(464\) 1.42745e14 2.20165e14i 0.308113 0.475225i
\(465\) 2.07676e12 0.00442990
\(466\) −1.07461e14 + 1.19392e14i −0.226532 + 0.251683i
\(467\) −3.66542e14 + 3.66542e14i −0.763627 + 0.763627i −0.976976 0.213349i \(-0.931563\pi\)
0.213349 + 0.976976i \(0.431563\pi\)
\(468\) 9.12549e10 1.12776e11i 0.000187890 0.000232201i
\(469\) −1.02719e15 1.02719e15i −2.09026 2.09026i
\(470\) −3.47093e12 6.59950e13i −0.00698084 0.132731i
\(471\) 1.30632e13i 0.0259677i
\(472\) 7.14707e14 1.13606e14i 1.40426 0.223214i
\(473\) 2.64025e14i 0.512754i
\(474\) 1.67822e12 8.82641e10i 0.00322158 0.000169435i
\(475\) 4.15914e14 + 4.15914e14i 0.789204 + 0.789204i
\(476\) −1.30905e15 + 1.38078e14i −2.45538 + 0.258993i
\(477\) −2.26386e14 + 2.26386e14i −0.419758 + 0.419758i
\(478\) 5.27109e14 + 4.74434e14i 0.966155 + 0.869605i
\(479\) 3.11241e14 0.563964 0.281982 0.959420i \(-0.409008\pi\)
0.281982 + 0.959420i \(0.409008\pi\)
\(480\) −3.18026e12 1.83219e12i −0.00569687 0.00328204i
\(481\) 2.51729e11 0.000445795
\(482\) −1.00994e14 9.09015e13i −0.176822 0.159152i
\(483\) 1.09840e13 1.09840e13i 0.0190131 0.0190131i
\(484\) 3.53388e14 3.72752e13i 0.604788 0.0637927i
\(485\) −3.30263e14 3.30263e14i −0.558832 0.558832i
\(486\) −2.60321e13 + 1.36913e12i −0.0435522 + 0.00229058i
\(487\) 1.03101e13i 0.0170551i 0.999964 + 0.00852757i \(0.00271444\pi\)
−0.999964 + 0.00852757i \(0.997286\pi\)
\(488\) 3.13621e13 + 1.97302e14i 0.0512975 + 0.322717i
\(489\) 1.00707e13i 0.0162877i
\(490\) 2.34495e13 + 4.45861e14i 0.0375021 + 0.713051i
\(491\) −4.62895e14 4.62895e14i −0.732039 0.732039i 0.238984 0.971023i \(-0.423186\pi\)
−0.971023 + 0.238984i \(0.923186\pi\)
\(492\) 1.02222e12 1.26330e12i 0.00159859 0.00197560i
\(493\) 3.98121e14 3.98121e14i 0.615682 0.615682i
\(494\) −1.83342e11 + 2.03698e11i −0.000280391 + 0.000311523i
\(495\) 1.87095e14 0.282966
\(496\) 4.40561e14 9.39859e13i 0.658957 0.140577i
\(497\) 5.34765e14 0.791047
\(498\) 2.26790e12 2.51970e12i 0.00331789 0.00368627i
\(499\) 3.82763e14 3.82763e14i 0.553831 0.553831i −0.373713 0.927544i \(-0.621916\pi\)
0.927544 + 0.373713i \(0.121916\pi\)
\(500\) 4.40996e14 + 3.56841e14i 0.631102 + 0.510669i
\(501\) −7.19020e12 7.19020e12i −0.0101773 0.0101773i
\(502\) 3.78926e13 + 7.20476e14i 0.0530498 + 1.00867i
\(503\) 1.37272e15i 1.90090i −0.310877 0.950450i \(-0.600623\pi\)
0.310877 0.950450i \(-0.399377\pi\)
\(504\) 6.88511e14 9.48764e14i 0.943068 1.29954i
\(505\) 5.12991e14i 0.695036i
\(506\) 5.37031e14 2.82445e13i 0.719733 0.0378535i
\(507\) −7.75604e12 7.75604e12i −0.0102824 0.0102824i
\(508\) −1.45050e14 1.37515e15i −0.190225 1.80343i
\(509\) −1.01553e15 + 1.01553e15i −1.31748 + 1.31748i −0.401716 + 0.915764i \(0.631586\pi\)
−0.915764 + 0.401716i \(0.868414\pi\)
\(510\) −5.85367e12 5.26870e12i −0.00751263 0.00676188i
\(511\) 1.13782e15 1.44464
\(512\) −7.57576e14 2.44753e14i −0.951571 0.307428i
\(513\) 3.28293e13 0.0407958
\(514\) −8.01707e14 7.21591e14i −0.985640 0.887144i
\(515\) 1.53016e13 1.53016e13i 0.0186121 0.0186121i
\(516\) 1.03823e12 + 9.84299e12i 0.00124946 + 0.0118455i
\(517\) −1.09284e14 1.09284e14i −0.130125 0.130125i
\(518\) 2.03131e15 1.06834e14i 2.39311 0.125863i
\(519\) 2.16743e13i 0.0252653i
\(520\) −6.87843e10 + 9.47843e10i −7.93361e−5 + 0.000109325i
\(521\) 1.84458e14i 0.210518i 0.994445 + 0.105259i \(0.0335672\pi\)
−0.994445 + 0.105259i \(0.966433\pi\)
\(522\) 2.63348e13 + 5.00720e14i 0.0297400 + 0.565466i
\(523\) 1.02732e15 + 1.02732e15i 1.14801 + 1.14801i 0.986944 + 0.161066i \(0.0514931\pi\)
0.161066 + 0.986944i \(0.448507\pi\)
\(524\) 3.12994e14 + 2.53266e14i 0.346110 + 0.280062i
\(525\) 1.20062e13 1.20062e13i 0.0131380 0.0131380i
\(526\) −9.14439e14 + 1.01597e15i −0.990223 + 1.10016i
\(527\) 9.66613e14 1.03584
\(528\) −8.39455e12 + 1.79083e12i −0.00890248 + 0.00189919i
\(529\) −3.10240e14 −0.325605
\(530\) 1.72905e14 1.92102e14i 0.179593 0.199533i
\(531\) −9.77865e14 + 9.77865e14i −1.00521 + 1.00521i
\(532\) −1.39302e15 + 1.72154e15i −1.41724 + 1.75147i
\(533\) −3.66658e10 3.66658e10i −3.69200e−5 3.69200e-5i
\(534\) −8.02805e11 1.52642e13i −0.000800079 0.0152124i
\(535\) 4.95941e14i 0.489197i
\(536\) −2.95956e14 1.86189e15i −0.288949 1.81780i
\(537\) 1.80552e13i 0.0174479i
\(538\) −1.59808e15 + 8.40491e13i −1.52861 + 0.0803953i
\(539\) 7.38322e14 + 7.38322e14i 0.699049 + 0.699049i
\(540\) 1.39515e13 1.47159e12i 0.0130754 0.00137918i
\(541\) 3.99095e14 3.99095e14i 0.370247 0.370247i −0.497320 0.867567i \(-0.665683\pi\)
0.867567 + 0.497320i \(0.165683\pi\)
\(542\) −1.81373e14 1.63248e14i −0.166563 0.149918i
\(543\) 1.65215e13 0.0150193
\(544\) −1.48023e15 8.52783e14i −1.33210 0.767440i
\(545\) 4.54679e14 0.405064
\(546\) 5.88016e9 + 5.29254e9i 5.18596e−6 + 4.66772e-6i
\(547\) −5.81181e14 + 5.81181e14i −0.507436 + 0.507436i −0.913739 0.406303i \(-0.866818\pi\)
0.406303 + 0.913739i \(0.366818\pi\)
\(548\) −1.50870e13 + 1.59137e12i −0.0130410 + 0.00137555i
\(549\) −2.69949e14 2.69949e14i −0.231011 0.231011i
\(550\) 5.87006e14 3.08729e13i 0.497334 0.0261567i
\(551\) 9.47224e14i 0.794546i
\(552\) 1.99097e13 3.16475e12i 0.0165348 0.00262830i
\(553\) 4.33306e14i 0.356292i
\(554\) −3.23286e13 6.14683e14i −0.0263198 0.500435i
\(555\) 8.60562e12 + 8.60562e12i 0.00693698 + 0.00693698i
\(556\) 9.92851e13 1.22700e14i 0.0792452 0.0979339i
\(557\) −5.50142e14 + 5.50142e14i −0.434781 + 0.434781i −0.890251 0.455470i \(-0.849471\pi\)
0.455470 + 0.890251i \(0.349471\pi\)
\(558\) −5.75889e14 + 6.39828e14i −0.450662 + 0.500697i
\(559\) 3.15815e11 0.000244719
\(560\) −5.14822e14 + 7.94046e14i −0.395024 + 0.609273i
\(561\) −1.84181e13 −0.0139942
\(562\) −1.02977e14 + 1.14411e14i −0.0774804 + 0.0860829i
\(563\) 1.01942e15 1.01942e15i 0.759549 0.759549i −0.216691 0.976240i \(-0.569526\pi\)
0.976240 + 0.216691i \(0.0695264\pi\)
\(564\) −4.50391e12 3.64443e12i −0.00332319 0.00268902i
\(565\) 2.18605e14 + 2.18605e14i 0.159732 + 0.159732i
\(566\) −6.37906e13 1.21289e15i −0.0461601 0.877671i
\(567\) 2.23965e15i 1.60499i
\(568\) 5.61697e14 + 4.07620e14i 0.398645 + 0.289294i
\(569\) 1.97572e15i 1.38870i 0.719639 + 0.694349i \(0.244307\pi\)
−0.719639 + 0.694349i \(0.755693\pi\)
\(570\) −1.32314e13 + 6.95889e11i −0.00921072 + 0.000484427i
\(571\) −1.21475e15 1.21475e15i −0.837506 0.837506i 0.151024 0.988530i \(-0.451743\pi\)
−0.988530 + 0.151024i \(0.951743\pi\)
\(572\) 2.87296e10 + 2.72372e11i 1.96179e−5 + 0.000185988i
\(573\) −1.90064e13 + 1.90064e13i −0.0128544 + 0.0128544i
\(574\) −3.11433e14 2.80311e14i −0.208617 0.187769i
\(575\) −1.38059e15 −0.915990
\(576\) 1.44637e15 4.71736e14i 0.950511 0.310010i
\(577\) 2.06710e15 1.34553 0.672767 0.739855i \(-0.265106\pi\)
0.672767 + 0.739855i \(0.265106\pi\)
\(578\) −1.57176e15 1.41470e15i −1.01341 0.912137i
\(579\) 2.29801e13 2.29801e13i 0.0146764 0.0146764i
\(580\) −4.24600e13 4.02543e14i −0.0268612 0.254658i
\(581\) −6.18063e14 6.18063e14i −0.387315 0.387315i
\(582\) −4.08904e13 + 2.15058e12i −0.0253831 + 0.00133500i
\(583\) 6.04432e14i 0.371681i
\(584\) 1.19513e15 + 8.67293e14i 0.728019 + 0.528318i
\(585\) 2.23795e11i 0.000135050i
\(586\) 7.23523e13 + 1.37568e15i 0.0432529 + 0.822395i
\(587\) −1.55286e15 1.55286e15i −0.919649 0.919649i 0.0773550 0.997004i \(-0.475353\pi\)
−0.997004 + 0.0773550i \(0.975353\pi\)
\(588\) 3.04283e13 + 2.46217e13i 0.0178527 + 0.0144458i
\(589\) 1.14990e15 1.14990e15i 0.668385 0.668385i
\(590\) 7.46853e14 8.29774e14i 0.430080 0.477830i
\(591\) −3.12932e13 −0.0178533
\(592\) 2.21504e15 + 1.43613e15i 1.25203 + 0.811754i
\(593\) 7.38350e13 0.0413487 0.0206743 0.999786i \(-0.493419\pi\)
0.0206743 + 0.999786i \(0.493419\pi\)
\(594\) 2.19486e13 2.43854e13i 0.0121781 0.0135302i
\(595\) −1.43586e15 + 1.43586e15i −0.789349 + 0.789349i
\(596\) −1.11002e15 + 1.37180e15i −0.604610 + 0.747197i
\(597\) 9.56245e12 + 9.56245e12i 0.00516072 + 0.00516072i
\(598\) −3.37848e10 6.42372e11i −1.80661e−5 0.000343503i
\(599\) 7.76586e12i 0.00411474i −0.999998 0.00205737i \(-0.999345\pi\)
0.999998 0.00205737i \(-0.000654881\pi\)
\(600\) 2.17625e13 3.45926e12i 0.0114255 0.00181615i
\(601\) 2.17882e15i 1.13348i −0.823898 0.566738i \(-0.808205\pi\)
0.823898 0.566738i \(-0.191795\pi\)
\(602\) 2.54844e15 1.34032e14i 1.31370 0.0690923i
\(603\) 2.54744e15 + 2.54744e15i 1.30124 + 1.30124i
\(604\) −1.39774e15 + 1.47433e14i −0.707494 + 0.0746261i
\(605\) 3.87621e14 3.87621e14i 0.194425 0.194425i
\(606\) 3.34273e13 + 3.00869e13i 0.0166151 + 0.0149547i
\(607\) 2.72034e14 0.133994 0.0669971 0.997753i \(-0.478658\pi\)
0.0669971 + 0.997753i \(0.478658\pi\)
\(608\) −2.77540e15 + 7.46427e14i −1.35474 + 0.364349i
\(609\) −2.73435e13 −0.0132269
\(610\) 2.29067e14 + 2.06176e14i 0.109812 + 0.0988379i
\(611\) −1.30721e11 + 1.30721e11i −6.21039e−5 + 6.21039e-5i
\(612\) 3.24647e15 3.42436e14i 1.52855 0.161230i
\(613\) −8.56076e14 8.56076e14i −0.399466 0.399466i 0.478579 0.878045i \(-0.341152\pi\)
−0.878045 + 0.478579i \(0.841152\pi\)
\(614\) 1.14941e15 6.04518e13i 0.531555 0.0279565i
\(615\) 2.50692e12i 0.00114902i
\(616\) 3.47426e14 + 2.18569e15i 0.157823 + 0.992875i
\(617\) 1.51170e15i 0.680607i −0.940316 0.340304i \(-0.889470\pi\)
0.940316 0.340304i \(-0.110530\pi\)
\(618\) −9.96395e10 1.89451e12i −4.44626e−5 0.000845396i
\(619\) −1.60958e15 1.60958e15i −0.711892 0.711892i 0.255038 0.966931i \(-0.417912\pi\)
−0.966931 + 0.255038i \(0.917912\pi\)
\(620\) 4.37129e14 5.40220e14i 0.191627 0.236819i
\(621\) −5.44868e13 + 5.44868e13i −0.0236749 + 0.0236749i
\(622\) −2.66346e14 + 2.95917e14i −0.114709 + 0.127445i
\(623\) −3.94113e15 −1.68243
\(624\) 2.14211e9 + 1.00412e10i 9.06414e−7 + 4.24884e-6i
\(625\) −1.02169e15 −0.428527
\(626\) 1.77661e15 1.97386e15i 0.738641 0.820651i
\(627\) −2.19105e13 + 2.19105e13i −0.00902985 + 0.00902985i
\(628\) 3.39808e15 + 2.74962e15i 1.38821 + 1.12330i
\(629\) 4.00543e15 + 4.00543e15i 1.62207 + 1.62207i
\(630\) −9.49789e13 1.80589e15i −0.0381289 0.724969i
\(631\) 7.27946e14i 0.289693i 0.989454 + 0.144846i \(0.0462688\pi\)
−0.989454 + 0.144846i \(0.953731\pi\)
\(632\) 3.30284e14 4.55129e14i 0.130300 0.179552i
\(633\) 1.15513e12i 0.000451762i
\(634\) 2.06015e15 1.08351e14i 0.798744 0.0420090i
\(635\) −1.50836e15 1.50836e15i −0.579761 0.579761i
\(636\) −2.37682e12 2.25335e13i −0.000905696 0.00858647i
\(637\) 8.83148e11 8.83148e11i 0.000333631 0.000333631i
\(638\) −7.03594e14 6.33283e14i −0.263517 0.237183i
\(639\) −1.32622e15 −0.492449
\(640\) −1.14601e15 + 4.41619e14i −0.421888 + 0.162576i
\(641\) −1.21415e15 −0.443153 −0.221576 0.975143i \(-0.571120\pi\)
−0.221576 + 0.975143i \(0.571120\pi\)
\(642\) −3.23163e13 2.90869e13i −0.0116944 0.0105258i
\(643\) 2.15423e15 2.15423e15i 0.772916 0.772916i −0.205699 0.978615i \(-0.565947\pi\)
0.978615 + 0.205699i \(0.0659469\pi\)
\(644\) −5.45247e14 5.16923e15i −0.193964 1.83888i
\(645\) 1.07965e13 + 1.07965e13i 0.00380806 + 0.00380806i
\(646\) −6.15846e15 + 3.23897e14i −2.15374 + 0.113274i
\(647\) 3.90532e14i 0.135420i −0.997705 0.0677101i \(-0.978431\pi\)
0.997705 0.0677101i \(-0.0215693\pi\)
\(648\) −1.70715e15 + 2.35245e15i −0.586962 + 0.808831i
\(649\) 2.61081e15i 0.890081i
\(650\) −3.69288e10 7.02151e11i −1.24837e−5 0.000237360i
\(651\) −3.31942e13 3.31942e13i −0.0111267 0.0111267i
\(652\) 2.61966e15 + 2.11975e15i 0.870728 + 0.704567i
\(653\) 1.73093e15 1.73093e15i 0.570501 0.570501i −0.361767 0.932268i \(-0.617826\pi\)
0.932268 + 0.361767i \(0.117826\pi\)
\(654\) 2.66669e13 2.96276e13i 0.00871555 0.00968321i
\(655\) 6.21113e14 0.201300
\(656\) −1.13453e14 5.31815e14i −0.0364625 0.170919i
\(657\) −2.82181e15 −0.899327
\(658\) −9.99364e14 + 1.11032e15i −0.315850 + 0.350918i
\(659\) −1.30838e15 + 1.30838e15i −0.410074 + 0.410074i −0.881764 0.471690i \(-0.843644\pi\)
0.471690 + 0.881764i \(0.343644\pi\)
\(660\) −8.32916e12 + 1.02935e13i −0.00258887 + 0.00319941i
\(661\) 5.59792e14 + 5.59792e14i 0.172551 + 0.172551i 0.788099 0.615548i \(-0.211065\pi\)
−0.615548 + 0.788099i \(0.711065\pi\)
\(662\) 1.27077e14 + 2.41619e15i 0.0388461 + 0.738605i
\(663\) 2.20309e10i 6.67893e-6i
\(664\) −1.78078e14 1.12030e15i −0.0535409 0.336831i
\(665\) 3.41626e15i 1.01867i
\(666\) −5.03766e15 + 2.64950e14i −1.48978 + 0.0783530i
\(667\) 1.57211e15 + 1.57211e15i 0.461095 + 0.461095i
\(668\) −3.38381e15 + 3.56922e14i −0.984317 + 0.103825i
\(669\) −7.44027e12 + 7.44027e12i −0.00214657 + 0.00214657i
\(670\) −2.16165e15 1.94563e15i −0.618548 0.556735i
\(671\) 7.20739e14 0.204552
\(672\) 2.15471e13 + 8.01174e13i 0.00606537 + 0.0225526i
\(673\) −1.85001e15 −0.516525 −0.258262 0.966075i \(-0.583150\pi\)
−0.258262 + 0.966075i \(0.583150\pi\)
\(674\) 3.86015e15 + 3.47440e15i 1.06899 + 0.962166i
\(675\) −5.95573e13 + 5.95573e13i −0.0163593 + 0.0163593i
\(676\) −3.65010e15 + 3.85010e14i −0.994483 + 0.104897i
\(677\) 2.70150e15 + 2.70150e15i 0.730073 + 0.730073i 0.970634 0.240561i \(-0.0773313\pi\)
−0.240561 + 0.970634i \(0.577331\pi\)
\(678\) 2.70658e13 1.42349e12i 0.00725534 0.000381586i
\(679\) 1.05576e16i 2.80726i
\(680\) −2.60265e15 + 4.13704e14i −0.686462 + 0.109117i
\(681\) 4.18345e13i 0.0109452i
\(682\) −8.53560e13 1.62293e15i −0.0221524 0.421197i
\(683\) −1.32278e15 1.32278e15i −0.340545 0.340545i 0.516027 0.856572i \(-0.327410\pi\)
−0.856572 + 0.516027i \(0.827410\pi\)
\(684\) 3.45470e15 4.26943e15i 0.882269 1.09034i
\(685\) −1.65484e13 + 1.65484e13i −0.00419236 + 0.00419236i
\(686\) 2.47651e15 2.75147e15i 0.622383 0.691484i
\(687\) 6.48807e13 0.0161753
\(688\) 2.77896e15 + 1.80175e15i 0.687299 + 0.445612i
\(689\) −7.22995e11 −0.000177390
\(690\) 2.08052e13 2.31151e13i 0.00506409 0.00562634i
\(691\) 5.16356e15 5.16356e15i 1.24687 1.24687i 0.289772 0.957096i \(-0.406421\pi\)
0.957096 0.289772i \(-0.0935794\pi\)
\(692\) −5.63806e15 4.56215e15i −1.35066 1.09291i
\(693\) −2.99047e15 2.99047e15i −0.710733 0.710733i
\(694\) −5.06159e13 9.62392e14i −0.0119347 0.226921i
\(695\) 2.43488e14i 0.0569590i
\(696\) −2.87206e13 2.08423e13i −0.00666565 0.00483722i
\(697\) 1.16683e15i 0.268675i
\(698\) 2.15482e15 1.13330e14i 0.492273 0.0258905i
\(699\) 1.53613e13 + 1.53613e13i 0.00348180 + 0.00348180i
\(700\) −5.95988e14 5.65027e15i −0.134029 1.27066i
\(701\) −1.42137e15 + 1.42137e15i −0.317146 + 0.317146i −0.847670 0.530524i \(-0.821995\pi\)
0.530524 + 0.847670i \(0.321995\pi\)
\(702\) −2.91688e10 2.62539e10i −6.45750e−6 5.81219e-6i
\(703\) 9.52988e15 2.09331
\(704\) −1.30110e15 + 2.56059e15i −0.283570 + 0.558073i
\(705\) −8.93767e12 −0.00193279
\(706\) 5.36040e15 + 4.82473e15i 1.15020 + 1.03525i
\(707\) 8.19947e15 8.19947e15i 1.74574 1.74574i
\(708\) −1.02666e13 9.73323e13i −0.00216891 0.0205624i
\(709\) 3.04676e15 + 3.04676e15i 0.638682 + 0.638682i 0.950230 0.311549i \(-0.100848\pi\)
−0.311549 + 0.950230i \(0.600848\pi\)
\(710\) 1.06914e15 5.62304e13i 0.222390 0.0116963i
\(711\) 1.07460e15i 0.221802i
\(712\) −4.13962e15 3.00409e15i −0.847852 0.615280i
\(713\) 3.81699e15i 0.775761i
\(714\) 9.34993e12 + 1.77776e14i 0.00188568 + 0.0358537i
\(715\) 2.98756e11 + 2.98756e11i 5.97907e−5 + 5.97907e-5i
\(716\) 4.69663e15 + 3.80037e15i 0.932748 + 0.754752i
\(717\) 6.78192e13 6.78192e13i 0.0133659 0.0133659i
\(718\) −2.88803e15 + 3.20868e15i −0.564830 + 0.627541i
\(719\) −6.32346e15 −1.22729 −0.613643 0.789583i \(-0.710297\pi\)
−0.613643 + 0.789583i \(0.710297\pi\)
\(720\) 1.27676e15 1.96924e15i 0.245913 0.379289i
\(721\) −4.89150e14 −0.0934971
\(722\) −3.41415e15 + 3.79322e15i −0.647632 + 0.719537i
\(723\) −1.29942e13 + 1.29942e13i −0.00244617 + 0.00244617i
\(724\) 3.47756e15 4.29769e15i 0.649699 0.802921i
\(725\) 1.71841e15 + 1.71841e15i 0.318616 + 0.318616i
\(726\) −2.52408e12 4.79919e13i −0.000464464 0.00883114i
\(727\) 5.66978e15i 1.03544i −0.855549 0.517722i \(-0.826780\pi\)
0.855549 0.517722i \(-0.173220\pi\)
\(728\) 2.61443e12 4.15576e11i 0.000473864 7.53231e-5i
\(729\) 5.55201e15i 0.998731i
\(730\) 2.27482e15 1.19642e14i 0.406136 0.0213603i
\(731\) 5.02515e15 + 5.02515e15i 0.890437 + 0.890437i
\(732\) 2.68695e13 2.83418e12i 0.00472551 0.000498444i
\(733\) 3.73094e14 3.73094e14i 0.0651248 0.0651248i −0.673794 0.738919i \(-0.735337\pi\)
0.738919 + 0.673794i \(0.235337\pi\)
\(734\) 1.66884e15 + 1.50207e15i 0.289126 + 0.260233i
\(735\) 6.03826e13 0.0103832
\(736\) 3.36749e15 5.84518e15i 0.574749 0.997631i
\(737\) −6.80143e15 −1.15220
\(738\) 7.72357e14 + 6.95174e14i 0.129870 + 0.116892i
\(739\) −6.78605e15 + 6.78605e15i −1.13259 + 1.13259i −0.142845 + 0.989745i \(0.545625\pi\)
−0.989745 + 0.142845i \(0.954375\pi\)
\(740\) 4.04992e15 4.27183e14i 0.670922 0.0707684i
\(741\) 2.62084e10 + 2.62084e10i 4.30963e−6 + 4.30963e-6i
\(742\) −5.83414e15 + 3.06840e14i −0.952260 + 0.0500830i
\(743\) 5.57329e15i 0.902970i −0.892279 0.451485i \(-0.850894\pi\)
0.892279 0.451485i \(-0.149106\pi\)
\(744\) −9.56400e12 6.01679e13i −0.00153811 0.00967640i
\(745\) 2.72222e15i 0.434575i
\(746\) −1.90934e14 3.63036e15i −0.0302566 0.575289i
\(747\) 1.53280e15 + 1.53280e15i 0.241114 + 0.241114i
\(748\) −3.87676e15 + 4.79103e15i −0.605354 + 0.748118i
\(749\) −7.92695e15 + 7.92695e15i −1.22873 + 1.22873i
\(750\) 5.13258e13 5.70244e13i 0.00789767 0.00877453i
\(751\) 2.77591e14 0.0424020 0.0212010 0.999775i \(-0.493251\pi\)
0.0212010 + 0.999775i \(0.493251\pi\)
\(752\) −1.89603e15 + 4.04484e14i −0.287506 + 0.0613343i
\(753\) 9.75736e13 0.0146879
\(754\) −7.57505e11 + 8.41608e11i −0.000113199 + 0.000125767i
\(755\) −1.53314e15 + 1.53314e15i −0.227443 + 0.227443i
\(756\) −2.46517e14 1.99474e14i −0.0363059 0.0293776i
\(757\) −9.24724e15 9.24724e15i −1.35203 1.35203i −0.883393 0.468632i \(-0.844747\pi\)
−0.468632 0.883393i \(-0.655253\pi\)
\(758\) 3.73360e14 + 7.09893e15i 0.0541935 + 1.03042i
\(759\) 7.27297e13i 0.0104805i
\(760\) −2.60401e15 + 3.58831e15i −0.372536 + 0.513352i