Properties

Label 12.16.b.a.11.15
Level 12
Weight 16
Character 12.11
Analytic conductor 17.123
Analytic rank 0
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 12 = 2^{2} \cdot 3 \)
Weight: \( k \) = \( 16 \)
Character orbit: \([\chi]\) = 12.b (of order \(2\) and degree \(1\))

Newform invariants

Self dual: No
Analytic conductor: \(17.123220612\)
Analytic rank: \(0\)
Dimension: \(28\)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 11.15
Character \(\chi\) = 12.11
Dual form 12.16.b.a.11.16

$q$-expansion

\(f(q)\) \(=\) \(q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. i) q^{6} -694274. i q^{7} +(-3.33920e6 + 4.90246e6i) q^{8} +(-3.84657e6 + 1.38237e7i) q^{9} +O(q^{10})\) \(q+(35.8416 - 177.436i) q^{2} +(2291.54 + 3016.25i) q^{3} +(-30198.8 - 12719.1i) q^{4} +33476.6i q^{5} +(617322. - 298494. i) q^{6} -694274. i q^{7} +(-3.33920e6 + 4.90246e6i) q^{8} +(-3.84657e6 + 1.38237e7i) q^{9} +(5.93994e6 + 1.19985e6i) q^{10} -5.49804e7 q^{11} +(-3.08377e7 - 1.20233e8i) q^{12} -2.93342e8 q^{13} +(-1.23189e8 - 2.48839e7i) q^{14} +(-1.00974e8 + 7.67131e7i) q^{15} +(7.50189e8 + 7.68204e8i) q^{16} +1.09024e9i q^{17} +(2.31495e9 + 1.17798e9i) q^{18} +5.34556e9i q^{19} +(4.25793e8 - 1.01095e9i) q^{20} +(2.09410e9 - 1.59096e9i) q^{21} +(-1.97058e9 + 9.75547e9i) q^{22} -1.46183e10 q^{23} +(-2.24389e10 + 1.16236e9i) q^{24} +2.93969e10 q^{25} +(-1.05138e10 + 5.20493e10i) q^{26} +(-5.05103e10 + 2.00755e10i) q^{27} +(-8.83057e9 + 2.09662e10i) q^{28} +7.94865e10i q^{29} +(9.99257e9 + 2.06658e10i) q^{30} -1.27900e11i q^{31} +(1.63195e11 - 1.05577e11i) q^{32} +(-1.25990e11 - 1.65834e11i) q^{33} +(1.93447e11 + 3.90759e10i) q^{34} +2.32419e10 q^{35} +(2.91987e11 - 3.68534e11i) q^{36} -4.22440e11 q^{37} +(9.48493e11 + 1.91593e11i) q^{38} +(-6.72206e11 - 8.84791e11i) q^{39} +(-1.64118e11 - 1.11785e11i) q^{40} +7.06327e11i q^{41} +(-2.07237e11 - 4.28591e11i) q^{42} -2.89245e12i q^{43} +(1.66034e12 + 6.99303e11i) q^{44} +(-4.62771e11 - 1.28770e11i) q^{45} +(-5.23941e11 + 2.59380e12i) q^{46} -6.40017e12 q^{47} +(-5.98002e11 + 4.02313e12i) q^{48} +4.26554e12 q^{49} +(1.05363e12 - 5.21606e12i) q^{50} +(-3.28843e12 + 2.49833e12i) q^{51} +(8.85857e12 + 3.73106e12i) q^{52} -7.99661e11i q^{53} +(1.75173e12 + 9.68186e12i) q^{54} -1.84055e12i q^{55} +(3.40365e12 + 2.31832e12i) q^{56} +(-1.61235e13 + 1.22496e13i) q^{57} +(1.41037e13 + 2.84892e12i) q^{58} -1.39217e13 q^{59} +(4.02500e12 - 1.03234e12i) q^{60} +9.62549e12 q^{61} +(-2.26940e13 - 4.58413e12i) q^{62} +(9.59745e12 + 2.67057e12i) q^{63} +(-1.28839e13 - 3.27406e13i) q^{64} -9.82009e12i q^{65} +(-3.39406e13 + 1.64113e13i) q^{66} -2.75795e13i q^{67} +(1.38669e13 - 3.29239e13i) q^{68} +(-3.34984e13 - 4.40923e13i) q^{69} +(8.33027e11 - 4.12395e12i) q^{70} +1.40051e14 q^{71} +(-5.49258e13 - 6.50178e13i) q^{72} +1.33684e14 q^{73} +(-1.51409e13 + 7.49559e13i) q^{74} +(6.73643e13 + 8.86683e13i) q^{75} +(6.79909e13 - 1.61429e14i) q^{76} +3.81714e13i q^{77} +(-1.81086e14 + 8.75609e13i) q^{78} +1.22264e14i q^{79} +(-2.57169e13 + 2.51138e13i) q^{80} +(-1.76299e14 - 1.06348e14i) q^{81} +(1.25327e14 + 2.53158e13i) q^{82} +8.03046e13 q^{83} +(-8.34749e13 + 2.14099e13i) q^{84} -3.64975e13 q^{85} +(-5.13224e14 - 1.03670e14i) q^{86} +(-2.39751e14 + 1.82147e14i) q^{87} +(1.83590e14 - 2.69539e14i) q^{88} +4.85416e14i q^{89} +(-3.94348e13 + 7.74967e13i) q^{90} +2.03660e14i q^{91} +(4.41454e14 + 1.85932e14i) q^{92} +(3.85777e14 - 2.93088e14i) q^{93} +(-2.29392e14 + 1.13562e15i) q^{94} -1.78951e14 q^{95} +(6.92413e14 + 2.50302e14i) q^{96} +1.97524e14 q^{97} +(1.52884e14 - 7.56859e14i) q^{98} +(2.11486e14 - 7.60033e14i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 26968q^{4} + 823656q^{6} - 3812052q^{9} + O(q^{10}) \) \( 28q + 26968q^{4} + 823656q^{6} - 3812052q^{9} - 43831600q^{10} - 226414248q^{12} + 124527272q^{13} - 1459325408q^{16} - 4234777584q^{18} - 7261350648q^{21} - 2533670160q^{22} - 18487781856q^{24} - 146804950740q^{25} + 5481093840q^{28} + 8237058960q^{30} + 204574669728q^{33} + 450165745472q^{34} + 232631927160q^{36} + 386069193224q^{37} + 1945471012160q^{40} + 1938106219632q^{42} - 5007113912640q^{45} + 2270790222432q^{46} + 5846474725152q^{48} - 18480860963084q^{49} - 6113229405424q^{52} + 1626598700568q^{54} + 8085872464056q^{57} - 19395437098192q^{58} - 10924219377600q^{60} - 16392792556696q^{61} + 21633892829056q^{64} + 4928819126448q^{66} + 137029869973056q^{69} + 91772543171040q^{70} + 66924493142592q^{72} + 158451626683736q^{73} - 205265768291280q^{76} + 58364283489648q^{78} + 116126816635836q^{81} - 750029796726880q^{82} - 92605433207856q^{84} - 30099357052160q^{85} - 619691835246912q^{88} - 471443548913520q^{90} - 777661615138584q^{93} + 1301107064491200q^{94} + 525428335287168q^{96} - 824166397720648q^{97} + O(q^{100}) \)

Character Values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/12\mathbb{Z}\right)^\times\).

\(n\) \(5\) \(7\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 35.8416 177.436i 0.197998 0.980202i
\(3\) 2291.54 + 3016.25i 0.604949 + 0.796264i
\(4\) −30198.8 12719.1i −0.921593 0.388157i
\(5\) 33476.6i 0.191631i 0.995399 + 0.0958156i \(0.0305459\pi\)
−0.995399 + 0.0958156i \(0.969454\pi\)
\(6\) 617322. 298494.i 0.900279 0.435313i
\(7\) 694274.i 0.318637i −0.987227 0.159318i \(-0.949070\pi\)
0.987227 0.159318i \(-0.0509296\pi\)
\(8\) −3.33920e6 + 4.90246e6i −0.562947 + 0.826493i
\(9\) −3.84657e6 + 1.38237e7i −0.268074 + 0.963398i
\(10\) 5.93994e6 + 1.19985e6i 0.187837 + 0.0379427i
\(11\) −5.49804e7 −0.850673 −0.425336 0.905035i \(-0.639844\pi\)
−0.425336 + 0.905035i \(0.639844\pi\)
\(12\) −3.08377e7 1.20233e8i −0.248441 0.968647i
\(13\) −2.93342e8 −1.29658 −0.648290 0.761394i \(-0.724515\pi\)
−0.648290 + 0.761394i \(0.724515\pi\)
\(14\) −1.23189e8 2.48839e7i −0.312328 0.0630896i
\(15\) −1.00974e8 + 7.67131e7i −0.152589 + 0.115927i
\(16\) 7.50189e8 + 7.68204e8i 0.698668 + 0.715446i
\(17\) 1.09024e9i 0.644399i 0.946672 + 0.322199i \(0.104422\pi\)
−0.946672 + 0.322199i \(0.895578\pi\)
\(18\) 2.31495e9 + 1.17798e9i 0.891247 + 0.453518i
\(19\) 5.34556e9i 1.37196i 0.727620 + 0.685980i \(0.240626\pi\)
−0.727620 + 0.685980i \(0.759374\pi\)
\(20\) 4.25793e8 1.01095e9i 0.0743830 0.176606i
\(21\) 2.09410e9 1.59096e9i 0.253719 0.192759i
\(22\) −1.97058e9 + 9.75547e9i −0.168432 + 0.833831i
\(23\) −1.46183e10 −0.895235 −0.447618 0.894225i \(-0.647727\pi\)
−0.447618 + 0.894225i \(0.647727\pi\)
\(24\) −2.24389e10 + 1.16236e9i −0.998661 + 0.0517318i
\(25\) 2.93969e10 0.963277
\(26\) −1.05138e10 + 5.20493e10i −0.256721 + 1.27091i
\(27\) −5.05103e10 + 2.00755e10i −0.929291 + 0.369349i
\(28\) −8.83057e9 + 2.09662e10i −0.123681 + 0.293653i
\(29\) 7.94865e10i 0.855674i 0.903856 + 0.427837i \(0.140724\pi\)
−0.903856 + 0.427837i \(0.859276\pi\)
\(30\) 9.99257e9 + 2.06658e10i 0.0834196 + 0.172522i
\(31\) 1.27900e11i 0.834944i −0.908690 0.417472i \(-0.862916\pi\)
0.908690 0.417472i \(-0.137084\pi\)
\(32\) 1.63195e11 1.05577e11i 0.839617 0.543179i
\(33\) −1.25990e11 1.65834e11i −0.514613 0.677360i
\(34\) 1.93447e11 + 3.90759e10i 0.631641 + 0.127590i
\(35\) 2.32419e10 0.0610607
\(36\) 2.91987e11 3.68534e11i 0.621005 0.783807i
\(37\) −4.22440e11 −0.731564 −0.365782 0.930701i \(-0.619198\pi\)
−0.365782 + 0.930701i \(0.619198\pi\)
\(38\) 9.48493e11 + 1.91593e11i 1.34480 + 0.271646i
\(39\) −6.72206e11 8.84791e11i −0.784364 1.03242i
\(40\) −1.64118e11 1.11785e11i −0.158382 0.107878i
\(41\) 7.06327e11i 0.566405i 0.959060 + 0.283202i \(0.0913968\pi\)
−0.959060 + 0.283202i \(0.908603\pi\)
\(42\) −2.07237e11 4.28591e11i −0.138707 0.286862i
\(43\) 2.89245e12i 1.62275i −0.584523 0.811377i \(-0.698718\pi\)
0.584523 0.811377i \(-0.301282\pi\)
\(44\) 1.66034e12 + 6.99303e11i 0.783974 + 0.330195i
\(45\) −4.62771e11 1.28770e11i −0.184617 0.0513713i
\(46\) −5.23941e11 + 2.59380e12i −0.177255 + 0.877512i
\(47\) −6.40017e12 −1.84271 −0.921357 0.388718i \(-0.872918\pi\)
−0.921357 + 0.388718i \(0.872918\pi\)
\(48\) −5.98002e11 + 4.02313e12i −0.147026 + 0.989133i
\(49\) 4.26554e12 0.898471
\(50\) 1.05363e12 5.21606e12i 0.190727 0.944207i
\(51\) −3.28843e12 + 2.49833e12i −0.513112 + 0.389828i
\(52\) 8.85857e12 + 3.73106e12i 1.19492 + 0.503277i
\(53\) 7.99661e11i 0.0935055i −0.998906 0.0467527i \(-0.985113\pi\)
0.998906 0.0467527i \(-0.0148873\pi\)
\(54\) 1.75173e12 + 9.68186e12i 0.178039 + 0.984023i
\(55\) 1.84055e12i 0.163015i
\(56\) 3.40365e12 + 2.31832e12i 0.263351 + 0.179375i
\(57\) −1.61235e13 + 1.22496e13i −1.09244 + 0.829966i
\(58\) 1.41037e13 + 2.84892e12i 0.838733 + 0.169422i
\(59\) −1.39217e13 −0.728289 −0.364144 0.931343i \(-0.618639\pi\)
−0.364144 + 0.931343i \(0.618639\pi\)
\(60\) 4.02500e12 1.03234e12i 0.185623 0.0476090i
\(61\) 9.62549e12 0.392147 0.196074 0.980589i \(-0.437181\pi\)
0.196074 + 0.980589i \(0.437181\pi\)
\(62\) −2.26940e13 4.58413e12i −0.818414 0.165318i
\(63\) 9.59745e12 + 2.67057e12i 0.306974 + 0.0854181i
\(64\) −1.28839e13 3.27406e13i −0.366182 0.930543i
\(65\) 9.82009e12i 0.248465i
\(66\) −3.39406e13 + 1.64113e13i −0.765843 + 0.370309i
\(67\) 2.75795e13i 0.555937i −0.960590 0.277969i \(-0.910339\pi\)
0.960590 0.277969i \(-0.0896611\pi\)
\(68\) 1.38669e13 3.29239e13i 0.250128 0.593874i
\(69\) −3.34984e13 4.40923e13i −0.541572 0.712844i
\(70\) 8.33027e11 4.12395e12i 0.0120899 0.0598519i
\(71\) 1.40051e14 1.82746 0.913732 0.406318i \(-0.133187\pi\)
0.913732 + 0.406318i \(0.133187\pi\)
\(72\) −5.49258e13 6.50178e13i −0.645331 0.763903i
\(73\) 1.33684e14 1.41631 0.708153 0.706059i \(-0.249529\pi\)
0.708153 + 0.706059i \(0.249529\pi\)
\(74\) −1.51409e13 + 7.49559e13i −0.144849 + 0.717081i
\(75\) 6.73643e13 + 8.86683e13i 0.582734 + 0.767024i
\(76\) 6.79909e13 1.61429e14i 0.532536 1.26439i
\(77\) 3.81714e13i 0.271055i
\(78\) −1.81086e14 + 8.75609e13i −1.16728 + 0.564418i
\(79\) 1.22264e14i 0.716301i 0.933664 + 0.358150i \(0.116592\pi\)
−0.933664 + 0.358150i \(0.883408\pi\)
\(80\) −2.57169e13 + 2.51138e13i −0.137102 + 0.133887i
\(81\) −1.76299e14 1.06348e14i −0.856273 0.516524i
\(82\) 1.25327e14 + 2.53158e13i 0.555191 + 0.112147i
\(83\) 8.03046e13 0.324829 0.162414 0.986723i \(-0.448072\pi\)
0.162414 + 0.986723i \(0.448072\pi\)
\(84\) −8.34749e13 + 2.14099e13i −0.308646 + 0.0791624i
\(85\) −3.64975e13 −0.123487
\(86\) −5.13224e14 1.03670e14i −1.59063 0.321303i
\(87\) −2.39751e14 + 1.82147e14i −0.681342 + 0.517639i
\(88\) 1.83590e14 2.69539e14i 0.478883 0.703075i
\(89\) 4.85416e14i 1.16329i 0.813442 + 0.581646i \(0.197591\pi\)
−0.813442 + 0.581646i \(0.802409\pi\)
\(90\) −3.94348e13 + 7.74967e13i −0.0869082 + 0.170791i
\(91\) 2.03660e14i 0.413138i
\(92\) 4.41454e14 + 1.85932e14i 0.825043 + 0.347492i
\(93\) 3.85777e14 2.93088e14i 0.664836 0.505098i
\(94\) −2.29392e14 + 1.13562e15i −0.364854 + 1.80623i
\(95\) −1.78951e14 −0.262910
\(96\) 6.92413e14 + 2.50302e14i 0.940439 + 0.339962i
\(97\) 1.97524e14 0.248218 0.124109 0.992269i \(-0.460393\pi\)
0.124109 + 0.992269i \(0.460393\pi\)
\(98\) 1.52884e14 7.56859e14i 0.177896 0.880683i
\(99\) 2.11486e14 7.60033e14i 0.228043 0.819537i
\(100\) −8.87750e14 3.73903e14i −0.887750 0.373903i
\(101\) 7.20648e14i 0.668826i −0.942427 0.334413i \(-0.891462\pi\)
0.942427 0.334413i \(-0.108538\pi\)
\(102\) 3.25430e14 + 6.73028e14i 0.280515 + 0.580139i
\(103\) 1.54207e15i 1.23545i −0.786394 0.617725i \(-0.788055\pi\)
0.786394 0.617725i \(-0.211945\pi\)
\(104\) 9.79527e14 1.43810e15i 0.729905 1.07161i
\(105\) 5.32599e13 + 7.01034e13i 0.0369386 + 0.0486205i
\(106\) −1.41888e14 2.86611e13i −0.0916543 0.0185139i
\(107\) −1.67492e15 −1.00836 −0.504180 0.863599i \(-0.668205\pi\)
−0.504180 + 0.863599i \(0.668205\pi\)
\(108\) 1.78069e15 + 3.61933e13i 0.999794 + 0.0203212i
\(109\) −2.64556e15 −1.38618 −0.693089 0.720852i \(-0.743751\pi\)
−0.693089 + 0.720852i \(0.743751\pi\)
\(110\) −3.26580e14 6.59684e13i −0.159788 0.0322768i
\(111\) −9.68040e14 1.27418e15i −0.442559 0.582519i
\(112\) 5.33344e14 5.20837e14i 0.227967 0.222621i
\(113\) 4.64724e15i 1.85826i 0.369751 + 0.929131i \(0.379443\pi\)
−0.369751 + 0.929131i \(0.620557\pi\)
\(114\) 1.59562e15 + 3.29993e15i 0.597232 + 1.23515i
\(115\) 4.89370e14i 0.171555i
\(116\) 1.01100e15 2.40039e15i 0.332136 0.788583i
\(117\) 1.12836e15 4.05508e15i 0.347579 1.24912i
\(118\) −4.98977e14 + 2.47021e15i −0.144200 + 0.713870i
\(119\) 7.56925e14 0.205329
\(120\) −3.89120e13 7.51179e14i −0.00991343 0.191375i
\(121\) −1.15441e15 −0.276356
\(122\) 3.44992e14 1.70790e15i 0.0776445 0.384383i
\(123\) −2.13045e15 + 1.61858e15i −0.451008 + 0.342646i
\(124\) −1.62677e15 + 3.86242e15i −0.324089 + 0.769478i
\(125\) 2.00573e15i 0.376225i
\(126\) 8.17842e14 1.60721e15i 0.144507 0.283984i
\(127\) 9.47528e15i 1.57784i 0.614494 + 0.788922i \(0.289360\pi\)
−0.614494 + 0.788922i \(0.710640\pi\)
\(128\) −6.27112e15 + 1.11259e15i −0.984624 + 0.174687i
\(129\) 8.72434e15 6.62818e15i 1.29214 0.981683i
\(130\) −1.74243e15 3.51967e14i −0.243546 0.0491957i
\(131\) 6.95076e15 0.917270 0.458635 0.888625i \(-0.348339\pi\)
0.458635 + 0.888625i \(0.348339\pi\)
\(132\) 1.69547e15 + 6.61047e15i 0.211342 + 0.824001i
\(133\) 3.71129e15 0.437157
\(134\) −4.89359e15 9.88493e14i −0.544931 0.110075i
\(135\) −6.72058e14 1.69091e15i −0.0707788 0.178081i
\(136\) −5.34485e15 3.64052e15i −0.532591 0.362762i
\(137\) 1.81089e16i 1.70800i 0.520272 + 0.854001i \(0.325831\pi\)
−0.520272 + 0.854001i \(0.674169\pi\)
\(138\) −9.02417e15 + 4.36347e15i −0.805962 + 0.389708i
\(139\) 1.37379e15i 0.116228i −0.998310 0.0581140i \(-0.981491\pi\)
0.998310 0.0581140i \(-0.0185087\pi\)
\(140\) −7.01878e14 2.95617e14i −0.0562731 0.0237012i
\(141\) −1.46663e16 1.93045e16i −1.11475 1.46729i
\(142\) 5.01965e15 2.48500e16i 0.361835 1.79128i
\(143\) 1.61280e16 1.10296
\(144\) −1.35051e16 + 7.41545e15i −0.876554 + 0.481303i
\(145\) −2.66094e15 −0.163974
\(146\) 4.79143e15 2.37202e16i 0.280426 1.38827i
\(147\) 9.77468e15 + 1.28659e16i 0.543529 + 0.715420i
\(148\) 1.27572e16 + 5.37308e15i 0.674205 + 0.283962i
\(149\) 6.04298e14i 0.0303637i −0.999885 0.0151818i \(-0.995167\pi\)
0.999885 0.0151818i \(-0.00483271\pi\)
\(150\) 1.81473e16 8.77481e15i 0.867219 0.419327i
\(151\) 1.35196e16i 0.614664i −0.951602 0.307332i \(-0.900564\pi\)
0.951602 0.307332i \(-0.0994362\pi\)
\(152\) −2.62064e16 1.78499e16i −1.13392 0.772340i
\(153\) −1.50711e16 4.19368e15i −0.620813 0.172746i
\(154\) 6.77297e15 + 1.36812e15i 0.265689 + 0.0536686i
\(155\) 4.28165e15 0.160001
\(156\) 9.04601e15 + 3.52695e16i 0.322124 + 1.25593i
\(157\) 2.33116e16 0.791270 0.395635 0.918408i \(-0.370525\pi\)
0.395635 + 0.918408i \(0.370525\pi\)
\(158\) 2.16940e16 + 4.38213e15i 0.702120 + 0.141826i
\(159\) 2.41198e15 1.83246e15i 0.0744551 0.0565660i
\(160\) 3.53434e15 + 5.46320e15i 0.104090 + 0.160897i
\(161\) 1.01491e16i 0.285255i
\(162\) −2.51887e16 + 2.74700e16i −0.675838 + 0.737050i
\(163\) 1.11261e15i 0.0285060i −0.999898 0.0142530i \(-0.995463\pi\)
0.999898 0.0142530i \(-0.00453702\pi\)
\(164\) 8.98386e15 2.13302e16i 0.219854 0.521995i
\(165\) 5.55157e15 4.21771e15i 0.129803 0.0986160i
\(166\) 2.87824e15 1.42489e16i 0.0643156 0.318398i
\(167\) −7.24563e16 −1.54776 −0.773878 0.633334i \(-0.781686\pi\)
−0.773878 + 0.633334i \(0.781686\pi\)
\(168\) 8.06999e14 + 1.55788e16i 0.0164837 + 0.318210i
\(169\) 3.48636e16 0.681118
\(170\) −1.30813e15 + 6.47595e15i −0.0244502 + 0.121042i
\(171\) −7.38955e16 2.05621e16i −1.32174 0.367787i
\(172\) −3.67895e16 + 8.73485e16i −0.629884 + 1.49552i
\(173\) 6.62972e16i 1.08680i 0.839474 + 0.543400i \(0.182863\pi\)
−0.839474 + 0.543400i \(0.817137\pi\)
\(174\) 2.37263e16 + 4.90687e16i 0.372486 + 0.770345i
\(175\) 2.04095e16i 0.306935i
\(176\) −4.12457e16 4.22361e16i −0.594338 0.608610i
\(177\) −3.19023e16 4.19914e16i −0.440577 0.579910i
\(178\) 8.61301e16 + 1.73981e16i 1.14026 + 0.230330i
\(179\) −2.84284e16 −0.360874 −0.180437 0.983587i \(-0.557751\pi\)
−0.180437 + 0.983587i \(0.557751\pi\)
\(180\) 1.23373e16 + 9.77474e15i 0.150202 + 0.119004i
\(181\) −5.40077e16 −0.630764 −0.315382 0.948965i \(-0.602133\pi\)
−0.315382 + 0.948965i \(0.602133\pi\)
\(182\) 3.61365e16 + 7.29948e15i 0.404959 + 0.0818006i
\(183\) 2.20572e16 + 2.90328e16i 0.237229 + 0.312253i
\(184\) 4.88133e16 7.16655e16i 0.503970 0.739906i
\(185\) 1.41419e16i 0.140191i
\(186\) −3.81774e16 7.89553e16i −0.363462 0.751682i
\(187\) 5.99417e16i 0.548172i
\(188\) 1.93277e17 + 8.14047e16i 1.69823 + 0.715262i
\(189\) 1.39379e16 + 3.50680e16i 0.117688 + 0.296106i
\(190\) −6.41389e15 + 3.17523e16i −0.0520559 + 0.257705i
\(191\) 1.21047e17 0.944506 0.472253 0.881463i \(-0.343441\pi\)
0.472253 + 0.881463i \(0.343441\pi\)
\(192\) 6.92296e16 1.13887e17i 0.519437 0.854509i
\(193\) −5.51856e16 −0.398241 −0.199120 0.979975i \(-0.563808\pi\)
−0.199120 + 0.979975i \(0.563808\pi\)
\(194\) 7.07958e15 3.50479e16i 0.0491468 0.243304i
\(195\) 2.96198e16 2.25032e16i 0.197844 0.150309i
\(196\) −1.28814e17 5.42540e16i −0.828024 0.348748i
\(197\) 2.35075e16i 0.145449i −0.997352 0.0727244i \(-0.976831\pi\)
0.997352 0.0727244i \(-0.0231694\pi\)
\(198\) −1.27277e17 6.47658e16i −0.758160 0.385795i
\(199\) 3.43230e16i 0.196873i 0.995143 + 0.0984367i \(0.0313842\pi\)
−0.995143 + 0.0984367i \(0.968616\pi\)
\(200\) −9.81620e16 + 1.44117e17i −0.542274 + 0.796142i
\(201\) 8.31866e16 6.31997e16i 0.442673 0.336314i
\(202\) −1.27869e17 2.58292e16i −0.655585 0.132427i
\(203\) 5.51854e16 0.272649
\(204\) 1.31083e17 3.36205e16i 0.624195 0.160095i
\(205\) −2.36454e16 −0.108541
\(206\) −2.73618e17 5.52702e16i −1.21099 0.244617i
\(207\) 5.62301e16 2.02079e17i 0.239989 0.862468i
\(208\) −2.20062e17 2.25347e17i −0.905879 0.927633i
\(209\) 2.93901e17i 1.16709i
\(210\) 1.43477e16 6.93759e15i 0.0549717 0.0265805i
\(211\) 3.73984e17i 1.38272i 0.722510 + 0.691360i \(0.242988\pi\)
−0.722510 + 0.691360i \(0.757012\pi\)
\(212\) −1.01710e16 + 2.41488e16i −0.0362948 + 0.0861740i
\(213\) 3.20933e17 + 4.22428e17i 1.10552 + 1.45514i
\(214\) −6.00317e16 + 2.97190e17i −0.199654 + 0.988396i
\(215\) 9.68294e16 0.310970
\(216\) 7.02447e16 3.14661e17i 0.217876 0.975976i
\(217\) −8.87975e16 −0.266044
\(218\) −9.48210e16 + 4.69417e17i −0.274461 + 1.35873i
\(219\) 3.06342e17 + 4.03223e17i 0.856792 + 1.12775i
\(220\) −2.34103e16 + 5.55825e16i −0.0632756 + 0.150234i
\(221\) 3.19813e17i 0.835514i
\(222\) −2.60782e17 + 1.26096e17i −0.658612 + 0.318460i
\(223\) 2.16121e17i 0.527728i 0.964560 + 0.263864i \(0.0849969\pi\)
−0.964560 + 0.263864i \(0.915003\pi\)
\(224\) −7.32991e16 1.13302e17i −0.173077 0.267533i
\(225\) −1.13077e17 + 4.06374e17i −0.258229 + 0.928020i
\(226\) 8.24586e17 + 1.66564e17i 1.82147 + 0.367933i
\(227\) −2.86031e17 −0.611250 −0.305625 0.952152i \(-0.598865\pi\)
−0.305625 + 0.952152i \(0.598865\pi\)
\(228\) 6.42715e17 1.64845e17i 1.32895 0.340851i
\(229\) −6.84429e16 −0.136950 −0.0684751 0.997653i \(-0.521813\pi\)
−0.0684751 + 0.997653i \(0.521813\pi\)
\(230\) −8.68316e16 1.75398e16i −0.168159 0.0339676i
\(231\) −1.15134e17 + 8.74715e16i −0.215832 + 0.163975i
\(232\) −3.89679e17 2.65421e17i −0.707209 0.481699i
\(233\) 4.77935e17i 0.839846i −0.907560 0.419923i \(-0.862057\pi\)
0.907560 0.419923i \(-0.137943\pi\)
\(234\) −6.79073e17 3.45551e17i −1.15557 0.588022i
\(235\) 2.14256e17i 0.353121i
\(236\) 4.20419e17 + 1.77073e17i 0.671186 + 0.282690i
\(237\) −3.68778e17 + 2.80173e17i −0.570365 + 0.433325i
\(238\) 2.71294e16 1.34305e17i 0.0406548 0.201264i
\(239\) −2.45440e17 −0.356419 −0.178210 0.983993i \(-0.557030\pi\)
−0.178210 + 0.983993i \(0.557030\pi\)
\(240\) −1.34681e17 2.00191e16i −0.189549 0.0281747i
\(241\) 2.59773e16 0.0354378 0.0177189 0.999843i \(-0.494360\pi\)
0.0177189 + 0.999843i \(0.494360\pi\)
\(242\) −4.13758e16 + 2.04833e17i −0.0547181 + 0.270885i
\(243\) −8.32261e16 7.75461e17i −0.106712 0.994290i
\(244\) −2.90678e17 1.22428e17i −0.361400 0.152215i
\(245\) 1.42796e17i 0.172175i
\(246\) 2.10835e17 + 4.36031e17i 0.246563 + 0.509922i
\(247\) 1.56808e18i 1.77886i
\(248\) 6.27024e17 + 4.27083e17i 0.690075 + 0.470029i
\(249\) 1.84021e17 + 2.42218e17i 0.196505 + 0.258650i
\(250\) 3.55888e17 + 7.18886e16i 0.368777 + 0.0744920i
\(251\) −7.40843e17 −0.745029 −0.372514 0.928026i \(-0.621504\pi\)
−0.372514 + 0.928026i \(0.621504\pi\)
\(252\) −2.55864e17 2.02719e17i −0.249750 0.197875i
\(253\) 8.03718e17 0.761552
\(254\) 1.68125e18 + 3.39609e17i 1.54661 + 0.312411i
\(255\) −8.36355e16 1.10085e17i −0.0747033 0.0983282i
\(256\) −2.73542e16 + 1.15260e18i −0.0237260 + 0.999718i
\(257\) 2.57141e17i 0.216607i −0.994118 0.108304i \(-0.965458\pi\)
0.994118 0.108304i \(-0.0345419\pi\)
\(258\) −8.63380e17 1.78557e18i −0.706406 1.46093i
\(259\) 2.93289e17i 0.233103i
\(260\) −1.24903e17 + 2.96555e17i −0.0964435 + 0.228984i
\(261\) −1.09880e18 3.05750e17i −0.824355 0.229384i
\(262\) 2.49126e17 1.23331e18i 0.181618 0.899110i
\(263\) 1.13536e18 0.804386 0.402193 0.915555i \(-0.368248\pi\)
0.402193 + 0.915555i \(0.368248\pi\)
\(264\) 1.23370e18 6.39072e16i 0.849534 0.0440068i
\(265\) 2.67699e16 0.0179186
\(266\) 1.33018e17 6.58514e17i 0.0865564 0.428502i
\(267\) −1.46413e18 + 1.11235e18i −0.926288 + 0.703733i
\(268\) −3.50788e17 + 8.32868e17i −0.215791 + 0.512348i
\(269\) 8.06335e17i 0.482362i −0.970480 0.241181i \(-0.922465\pi\)
0.970480 0.241181i \(-0.0775348\pi\)
\(270\) −3.24116e17 + 5.86420e16i −0.188570 + 0.0341178i
\(271\) 7.28020e17i 0.411977i −0.978554 0.205989i \(-0.933959\pi\)
0.978554 0.205989i \(-0.0660410\pi\)
\(272\) −8.37526e17 + 8.17885e17i −0.461033 + 0.450221i
\(273\) −6.14288e17 + 4.66695e17i −0.328967 + 0.249927i
\(274\) 3.21317e18 + 6.49052e17i 1.67419 + 0.338182i
\(275\) −1.61625e18 −0.819434
\(276\) 4.50794e17 + 1.75760e18i 0.222413 + 0.867167i
\(277\) 3.30992e17 0.158935 0.0794673 0.996837i \(-0.474678\pi\)
0.0794673 + 0.996837i \(0.474678\pi\)
\(278\) −2.43760e17 4.92389e16i −0.113927 0.0230130i
\(279\) 1.76805e18 + 4.91975e17i 0.804383 + 0.223826i
\(280\) −7.76094e16 + 1.13943e17i −0.0343739 + 0.0504663i
\(281\) 4.26270e18i 1.83818i 0.394053 + 0.919088i \(0.371073\pi\)
−0.394053 + 0.919088i \(0.628927\pi\)
\(282\) −3.95097e18 + 1.91042e18i −1.65896 + 0.802157i
\(283\) 3.24968e18i 1.32875i 0.747401 + 0.664373i \(0.231301\pi\)
−0.747401 + 0.664373i \(0.768699\pi\)
\(284\) −4.22937e18 1.78133e18i −1.68418 0.709343i
\(285\) −4.10075e17 5.39761e17i −0.159047 0.209346i
\(286\) 5.78054e17 2.86169e18i 0.218385 1.08113i
\(287\) 4.90384e17 0.180477
\(288\) 8.31721e17 + 2.66206e18i 0.298218 + 0.954498i
\(289\) 1.67380e18 0.584750
\(290\) −9.53721e16 + 4.72145e17i −0.0324666 + 0.160727i
\(291\) 4.52636e17 + 5.95782e17i 0.150159 + 0.197647i
\(292\) −4.03708e18 1.70034e18i −1.30526 0.549749i
\(293\) 4.82189e18i 1.51953i −0.650195 0.759767i \(-0.725313\pi\)
0.650195 0.759767i \(-0.274687\pi\)
\(294\) 2.63321e18 1.27324e18i 0.808874 0.391116i
\(295\) 4.66052e17i 0.139563i
\(296\) 1.41061e18 2.07100e18i 0.411832 0.604633i
\(297\) 2.77707e18 1.10376e18i 0.790522 0.314195i
\(298\) −1.07224e17 2.16590e16i −0.0297625 0.00601196i
\(299\) 4.28815e18 1.16074
\(300\) −9.06534e17 3.53449e18i −0.239318 0.933076i
\(301\) −2.00815e18 −0.517069
\(302\) −2.39886e18 4.84565e17i −0.602495 0.121703i
\(303\) 2.17365e18 1.65140e18i 0.532562 0.404605i
\(304\) −4.10649e18 + 4.01018e18i −0.981563 + 0.958545i
\(305\) 3.22228e17i 0.0751476i
\(306\) −1.28428e18 + 2.52385e18i −0.292246 + 0.574319i
\(307\) 2.84934e18i 0.632713i 0.948640 + 0.316357i \(0.102460\pi\)
−0.948640 + 0.316357i \(0.897540\pi\)
\(308\) 4.85508e17 1.15273e18i 0.105212 0.249803i
\(309\) 4.65126e18 3.53372e18i 0.983744 0.747384i
\(310\) 1.53461e17 7.59717e17i 0.0316800 0.156834i
\(311\) 4.50890e18 0.908589 0.454295 0.890851i \(-0.349891\pi\)
0.454295 + 0.890851i \(0.349891\pi\)
\(312\) 6.58228e18 3.40970e17i 1.29484 0.0670744i
\(313\) −3.78043e18 −0.726037 −0.363018 0.931782i \(-0.618254\pi\)
−0.363018 + 0.931782i \(0.618254\pi\)
\(314\) 8.35524e17 4.13631e18i 0.156670 0.775605i
\(315\) −8.94016e16 + 3.21290e17i −0.0163688 + 0.0588258i
\(316\) 1.55509e18 3.69222e18i 0.278037 0.660138i
\(317\) 1.09502e19i 1.91195i 0.293440 + 0.955977i \(0.405200\pi\)
−0.293440 + 0.955977i \(0.594800\pi\)
\(318\) −2.38694e17 4.93648e17i −0.0407042 0.0841810i
\(319\) 4.37019e18i 0.727898i
\(320\) 1.09604e18 4.31309e17i 0.178321 0.0701719i
\(321\) −3.83815e18 5.05197e18i −0.610006 0.802921i
\(322\) 1.80081e18 + 3.63759e17i 0.279607 + 0.0564800i
\(323\) −5.82794e18 −0.884090
\(324\) 3.97136e18 + 5.45394e18i 0.588643 + 0.808393i
\(325\) −8.62334e18 −1.24897
\(326\) −1.97417e17 3.98777e16i −0.0279416 0.00564414i
\(327\) −6.06242e18 7.97966e18i −0.838567 1.10376i
\(328\) −3.46274e18 2.35856e18i −0.468130 0.318856i
\(329\) 4.44348e18i 0.587156i
\(330\) −5.49395e17 1.13621e18i −0.0709627 0.146759i
\(331\) 3.37469e18i 0.426112i 0.977040 + 0.213056i \(0.0683417\pi\)
−0.977040 + 0.213056i \(0.931658\pi\)
\(332\) −2.42510e18 1.02140e18i −0.299360 0.126085i
\(333\) 1.62494e18 5.83969e18i 0.196113 0.704788i
\(334\) −2.59695e18 + 1.28563e19i −0.306454 + 1.51711i
\(335\) 9.23268e17 0.106535
\(336\) 2.79315e18 + 4.15177e17i 0.315174 + 0.0468478i
\(337\) 8.45680e18 0.933215 0.466608 0.884464i \(-0.345476\pi\)
0.466608 + 0.884464i \(0.345476\pi\)
\(338\) 1.24957e18 6.18605e18i 0.134860 0.667633i
\(339\) −1.40172e19 + 1.06494e19i −1.47967 + 1.12415i
\(340\) 1.10218e18 + 4.64216e17i 0.113805 + 0.0479323i
\(341\) 7.03198e18i 0.710264i
\(342\) −6.29697e18 + 1.23747e19i −0.622209 + 1.22276i
\(343\) 6.25757e18i 0.604922i
\(344\) 1.41801e19 + 9.65847e18i 1.34120 + 0.913524i
\(345\) 1.47606e18 1.12141e18i 0.136603 0.103782i
\(346\) 1.17635e19 + 2.37620e18i 1.06528 + 0.215185i
\(347\) −1.70796e19 −1.51359 −0.756793 0.653654i \(-0.773235\pi\)
−0.756793 + 0.653654i \(0.773235\pi\)
\(348\) 9.55692e18 2.45118e18i 0.828846 0.212584i
\(349\) 1.14186e19 0.969222 0.484611 0.874730i \(-0.338961\pi\)
0.484611 + 0.874730i \(0.338961\pi\)
\(350\) −3.62137e18 7.31508e17i −0.300859 0.0607728i
\(351\) 1.48168e19 5.88897e18i 1.20490 0.478890i
\(352\) −8.97250e18 + 5.80464e18i −0.714239 + 0.462067i
\(353\) 4.25349e18i 0.331463i −0.986171 0.165731i \(-0.947002\pi\)
0.986171 0.165731i \(-0.0529985\pi\)
\(354\) −8.59419e18 + 4.15556e18i −0.655663 + 0.317034i
\(355\) 4.68843e18i 0.350199i
\(356\) 6.17407e18 1.46590e19i 0.451540 1.07208i
\(357\) 1.73453e18 + 2.28307e18i 0.124214 + 0.163496i
\(358\) −1.01892e18 + 5.04421e18i −0.0714524 + 0.353729i
\(359\) 8.34588e18 0.573144 0.286572 0.958059i \(-0.407484\pi\)
0.286572 + 0.958059i \(0.407484\pi\)
\(360\) 2.17657e18 1.83873e18i 0.146388 0.123666i
\(361\) −1.33939e19 −0.882275
\(362\) −1.93572e18 + 9.58290e18i −0.124890 + 0.618276i
\(363\) −2.64538e18 3.48198e18i −0.167181 0.220053i
\(364\) 2.59038e18 6.15027e18i 0.160362 0.380745i
\(365\) 4.47527e18i 0.271408i
\(366\) 5.94202e18 2.87315e18i 0.353042 0.170707i
\(367\) 2.22875e19i 1.29737i −0.761055 0.648687i \(-0.775318\pi\)
0.761055 0.648687i \(-0.224682\pi\)
\(368\) −1.09665e19 1.12298e19i −0.625472 0.640492i
\(369\) −9.76406e18 2.71693e18i −0.545673 0.151838i
\(370\) −2.50927e18 5.06866e17i −0.137415 0.0277575i
\(371\) −5.55184e17 −0.0297943
\(372\) −1.53778e19 + 3.94414e18i −0.808766 + 0.207434i
\(373\) 6.53051e18 0.336613 0.168306 0.985735i \(-0.446170\pi\)
0.168306 + 0.985735i \(0.446170\pi\)
\(374\) −1.06358e19 2.14840e18i −0.537320 0.108537i
\(375\) −6.04978e18 + 4.59622e18i −0.299575 + 0.227597i
\(376\) 2.13714e19 3.13766e19i 1.03735 1.52299i
\(377\) 2.33167e19i 1.10945i
\(378\) 6.72186e18 1.21618e18i 0.313546 0.0567297i
\(379\) 2.46209e19i 1.12592i 0.826482 + 0.562962i \(0.190338\pi\)
−0.826482 + 0.562962i \(0.809662\pi\)
\(380\) 5.40411e18 + 2.27610e18i 0.242296 + 0.102051i
\(381\) −2.85798e19 + 2.17130e19i −1.25638 + 0.954515i
\(382\) 4.33852e18 2.14781e19i 0.187011 0.925807i
\(383\) 2.66962e19 1.12839 0.564195 0.825642i \(-0.309187\pi\)
0.564195 + 0.825642i \(0.309187\pi\)
\(384\) −1.77264e19 1.63657e19i −0.734744 0.678345i
\(385\) −1.27785e18 −0.0519427
\(386\) −1.97794e18 + 9.79188e18i −0.0788511 + 0.390356i
\(387\) 3.99844e19 + 1.11260e19i 1.56336 + 0.435018i
\(388\) −5.96500e18 2.51234e18i −0.228756 0.0963475i
\(389\) 1.39097e19i 0.523232i −0.965172 0.261616i \(-0.915745\pi\)
0.965172 0.261616i \(-0.0842555\pi\)
\(390\) −2.93124e18 6.06215e18i −0.108160 0.223688i
\(391\) 1.59374e19i 0.576889i
\(392\) −1.42435e19 + 2.09117e19i −0.505791 + 0.742580i
\(393\) 1.59280e19 + 2.09652e19i 0.554902 + 0.730390i
\(394\) −4.17107e18 8.42546e17i −0.142569 0.0287986i
\(395\) −4.09298e18 −0.137266
\(396\) −1.60536e19 + 2.02621e19i −0.528272 + 0.666763i
\(397\) 3.59590e19 1.16113 0.580563 0.814216i \(-0.302833\pi\)
0.580563 + 0.814216i \(0.302833\pi\)
\(398\) 6.09012e18 + 1.23019e18i 0.192976 + 0.0389806i
\(399\) 8.50457e18 + 1.11942e19i 0.264457 + 0.348092i
\(400\) 2.20532e19 + 2.25828e19i 0.673011 + 0.689173i
\(401\) 3.03739e19i 0.909742i −0.890557 0.454871i \(-0.849685\pi\)
0.890557 0.454871i \(-0.150315\pi\)
\(402\) −8.23233e18 1.70254e19i −0.242007 0.500499i
\(403\) 3.75184e19i 1.08257i
\(404\) −9.16602e18 + 2.17627e19i −0.259610 + 0.616385i
\(405\) 3.56016e18 5.90189e18i 0.0989820 0.164089i
\(406\) 1.97793e18 9.79185e18i 0.0539841 0.267251i
\(407\) 2.32259e19 0.622322
\(408\) −1.26725e18 2.44638e19i −0.0333359 0.643536i
\(409\) 3.50607e19 0.905515 0.452758 0.891634i \(-0.350440\pi\)
0.452758 + 0.891634i \(0.350440\pi\)
\(410\) −8.47488e17 + 4.19554e18i −0.0214909 + 0.106392i
\(411\) −5.46209e19 + 4.14974e19i −1.36002 + 1.03325i
\(412\) −1.96138e19 + 4.65686e19i −0.479549 + 1.13858i
\(413\) 9.66551e18i 0.232059i
\(414\) −3.38406e19 1.72200e19i −0.797876 0.406005i
\(415\) 2.68832e18i 0.0622474i
\(416\) −4.78719e19 + 3.09700e19i −1.08863 + 0.704274i
\(417\) 4.14370e18 3.14811e18i 0.0925482 0.0703119i
\(418\) −5.21485e19 1.05339e19i −1.14398 0.231082i
\(419\) −6.29350e19 −1.35609 −0.678043 0.735022i \(-0.737172\pi\)
−0.678043 + 0.735022i \(0.737172\pi\)
\(420\) −7.16729e17 2.79445e18i −0.0151700 0.0591463i
\(421\) −6.75888e19 −1.40527 −0.702634 0.711551i \(-0.747993\pi\)
−0.702634 + 0.711551i \(0.747993\pi\)
\(422\) 6.63580e19 + 1.34042e19i 1.35535 + 0.273777i
\(423\) 2.46187e19 8.84742e19i 0.493983 1.77527i
\(424\) 3.92031e18 + 2.67023e18i 0.0772817 + 0.0526386i
\(425\) 3.20496e19i 0.620735i
\(426\) 8.64566e19 4.18045e19i 1.64523 0.795519i
\(427\) 6.68273e18i 0.124952i
\(428\) 5.05805e19 + 2.13035e19i 0.929297 + 0.391402i
\(429\) 3.69581e19 + 4.86462e19i 0.667237 + 0.878251i
\(430\) 3.47052e18 1.71810e19i 0.0615716 0.304814i
\(431\) −3.94732e18 −0.0688213 −0.0344106 0.999408i \(-0.510955\pi\)
−0.0344106 + 0.999408i \(0.510955\pi\)
\(432\) −5.33143e19 2.37418e19i −0.913515 0.406805i
\(433\) −7.21093e19 −1.21432 −0.607159 0.794581i \(-0.707691\pi\)
−0.607159 + 0.794581i \(0.707691\pi\)
\(434\) −3.18264e18 + 1.57558e19i −0.0526762 + 0.260777i
\(435\) −6.09765e18 8.02604e18i −0.0991957 0.130566i
\(436\) 7.98927e19 + 3.36492e19i 1.27749 + 0.538055i
\(437\) 7.81429e19i 1.22823i
\(438\) 8.25258e19 3.99038e19i 1.27507 0.616536i
\(439\) 2.88017e19i 0.437455i −0.975786 0.218728i \(-0.929809\pi\)
0.975786 0.218728i \(-0.0701906\pi\)
\(440\) 9.02325e18 + 6.14598e18i 0.134731 + 0.0917690i
\(441\) −1.64077e19 + 5.89657e19i −0.240856 + 0.865585i
\(442\) −5.67462e19 1.14626e19i −0.818973 0.165431i
\(443\) −1.56016e19 −0.221381 −0.110691 0.993855i \(-0.535306\pi\)
−0.110691 + 0.993855i \(0.535306\pi\)
\(444\) 1.30271e19 + 5.07914e19i 0.181751 + 0.708628i
\(445\) −1.62501e19 −0.222923
\(446\) 3.83475e19 + 7.74610e18i 0.517280 + 0.104489i
\(447\) 1.82271e18 1.38478e18i 0.0241775 0.0183685i
\(448\) −2.27309e19 + 8.94495e18i −0.296505 + 0.116679i
\(449\) 3.01854e19i 0.387213i −0.981079 0.193606i \(-0.937982\pi\)
0.981079 0.193606i \(-0.0620184\pi\)
\(450\) 6.80524e19 + 3.46290e19i 0.858518 + 0.436864i
\(451\) 3.88341e19i 0.481825i
\(452\) 5.91089e19 1.40341e20i 0.721298 1.71256i
\(453\) 4.07785e19 3.09808e19i 0.489435 0.371840i
\(454\) −1.02518e19 + 5.07521e19i −0.121027 + 0.599149i
\(455\) −6.81783e18 −0.0791701
\(456\) −6.21349e18 1.19949e20i −0.0709740 1.37012i
\(457\) 2.51719e19 0.282843 0.141421 0.989949i \(-0.454833\pi\)
0.141421 + 0.989949i \(0.454833\pi\)
\(458\) −2.45310e18 + 1.21442e19i −0.0271159 + 0.134239i
\(459\) −2.18870e19 5.50683e19i −0.238008 0.598834i
\(460\) −6.22436e18 + 1.47784e19i −0.0665903 + 0.158104i
\(461\) 6.57492e19i 0.692044i −0.938226 0.346022i \(-0.887532\pi\)
0.938226 0.346022i \(-0.112468\pi\)
\(462\) 1.13940e19 + 2.35641e19i 0.117994 + 0.244026i
\(463\) 1.03671e20i 1.05633i −0.849143 0.528163i \(-0.822881\pi\)
0.849143 0.528163i \(-0.177119\pi\)
\(464\) −6.10618e19 + 5.96299e19i −0.612188 + 0.597832i
\(465\) 9.81158e18 + 1.29145e19i 0.0967925 + 0.127403i
\(466\) −8.48027e19 1.71299e19i −0.823219 0.166288i
\(467\) −2.32853e19 −0.222436 −0.111218 0.993796i \(-0.535475\pi\)
−0.111218 + 0.993796i \(0.535475\pi\)
\(468\) −8.56521e19 + 1.08107e20i −0.805182 + 1.01627i
\(469\) −1.91478e19 −0.177142
\(470\) −3.80166e19 7.67927e18i −0.346130 0.0699175i
\(471\) 5.34195e19 + 7.03135e19i 0.478678 + 0.630060i
\(472\) 4.64875e19 6.82508e19i 0.409988 0.601926i
\(473\) 1.59028e20i 1.38043i
\(474\) 3.64951e19 + 7.54762e19i 0.311815 + 0.644870i
\(475\) 1.57143e20i 1.32158i
\(476\) −2.28582e19 9.62743e18i −0.189230 0.0796999i
\(477\) 1.10543e19 + 3.07595e18i 0.0900830 + 0.0250664i
\(478\) −8.79695e18 + 4.35498e19i −0.0705704 + 0.349363i
\(479\) −1.24139e20 −0.980377 −0.490188 0.871617i \(-0.663072\pi\)
−0.490188 + 0.871617i \(0.663072\pi\)
\(480\) −8.37926e18 + 2.31796e19i −0.0651473 + 0.180217i
\(481\) 1.23920e20 0.948531
\(482\) 9.31069e17 4.60931e18i 0.00701663 0.0347362i
\(483\) −3.06121e19 + 2.32571e19i −0.227138 + 0.172565i
\(484\) 3.48617e19 + 1.46831e19i 0.254688 + 0.107270i
\(485\) 6.61245e18i 0.0475663i
\(486\) −1.40577e20 1.30265e19i −0.995734 0.0922687i
\(487\) 1.13270e20i 0.790040i 0.918673 + 0.395020i \(0.129262\pi\)
−0.918673 + 0.395020i \(0.870738\pi\)
\(488\) −3.21414e19 + 4.71886e19i −0.220758 + 0.324107i
\(489\) 3.35591e18 2.54959e18i 0.0226983 0.0172447i
\(490\) 2.53371e19 + 5.11803e18i 0.168766 + 0.0340904i
\(491\) 2.07059e20 1.35826 0.679130 0.734018i \(-0.262357\pi\)
0.679130 + 0.734018i \(0.262357\pi\)
\(492\) 8.49240e19 2.17815e19i 0.548646 0.140718i
\(493\) −8.66592e19 −0.551395
\(494\) −2.78233e20 5.62024e19i −1.74364 0.352211i
\(495\) 2.54433e19 + 7.07982e18i 0.157049 + 0.0437002i
\(496\) 9.82532e19 9.59490e19i 0.597357 0.583348i
\(497\) 9.72338e19i 0.582297i
\(498\) 4.95738e19 2.39705e19i 0.292437 0.141402i
\(499\) 1.45331e20i 0.844509i 0.906477 + 0.422255i \(0.138761\pi\)
−0.906477 + 0.422255i \(0.861239\pi\)
\(500\) 2.55112e19 6.05706e19i 0.146034 0.346727i
\(501\) −1.66037e20 2.18546e20i −0.936314 1.23242i
\(502\) −2.65530e19 + 1.31452e20i −0.147515 + 0.730279i
\(503\) 2.35769e20 1.29041 0.645203 0.764011i \(-0.276773\pi\)
0.645203 + 0.764011i \(0.276773\pi\)
\(504\) −4.51401e19 + 3.81336e19i −0.243407 + 0.205626i
\(505\) 2.41248e19 0.128168
\(506\) 2.88065e19 1.42608e20i 0.150786 0.746475i
\(507\) 7.98915e19 + 1.05157e20i 0.412042 + 0.542350i
\(508\) 1.20517e20 2.86142e20i 0.612451 1.45413i
\(509\) 3.29459e20i 1.64975i 0.565314 + 0.824876i \(0.308755\pi\)
−0.565314 + 0.824876i \(0.691245\pi\)
\(510\) −2.25307e19 + 1.08943e19i −0.111173 + 0.0537555i
\(511\) 9.28131e19i 0.451287i
\(512\) 2.03531e20 + 4.61645e19i 0.975229 + 0.221199i
\(513\) −1.07315e20 2.70006e20i −0.506732 1.27495i
\(514\) −4.56260e19 9.21634e18i −0.212319 0.0428879i
\(515\) 5.16232e19 0.236751
\(516\) −3.47769e20 + 8.91967e19i −1.57188 + 0.403159i
\(517\) 3.51884e20 1.56755
\(518\) 5.20400e19 + 1.05119e19i 0.228488 + 0.0461541i
\(519\) −1.99969e20 + 1.51923e20i −0.865380 + 0.657458i
\(520\) 4.81426e19 + 3.27912e19i 0.205355 + 0.139873i
\(521\) 3.04901e20i 1.28197i 0.767555 + 0.640983i \(0.221473\pi\)
−0.767555 + 0.640983i \(0.778527\pi\)
\(522\) −9.36335e19 + 1.84007e20i −0.388063 + 0.762617i
\(523\) 3.94730e20i 1.61264i −0.591479 0.806320i \(-0.701456\pi\)
0.591479 0.806320i \(-0.298544\pi\)
\(524\) −2.09904e20 8.84076e19i −0.845350 0.356045i
\(525\) 6.15601e19 4.67693e19i 0.244402 0.185680i
\(526\) 4.06930e19 2.01453e20i 0.159267 0.788461i
\(527\) 1.39441e20 0.538037
\(528\) 3.28784e19 2.21193e20i 0.125071 0.841428i
\(529\) −5.29415e19 −0.198554
\(530\) 9.59476e17 4.74994e18i 0.00354785 0.0175638i
\(531\) 5.35509e19 1.92450e20i 0.195235 0.701632i
\(532\) −1.12076e20 4.72044e19i −0.402881 0.169686i
\(533\) 2.07195e20i 0.734388i
\(534\) 1.44894e20 + 2.99658e20i 0.506397 + 1.04729i
\(535\) 5.60706e19i 0.193233i
\(536\) 1.35208e20 + 9.20935e19i 0.459478 + 0.312963i
\(537\) −6.51450e19 8.57471e19i −0.218310 0.287351i
\(538\) −1.43072e20 2.89003e19i −0.472813 0.0955070i
\(539\) −2.34521e20 −0.764304
\(540\) −1.21163e18 + 5.96114e19i −0.00389418 + 0.191592i
\(541\) −1.95036e20 −0.618209 −0.309104 0.951028i \(-0.600029\pi\)
−0.309104 + 0.951028i \(0.600029\pi\)
\(542\) −1.29177e20 2.60934e19i −0.403821 0.0815709i
\(543\) −1.23761e20 1.62901e20i −0.381580 0.502255i
\(544\) 1.15104e20 + 1.77921e20i 0.350024 + 0.541048i
\(545\) 8.85643e19i 0.265635i
\(546\) 6.07913e19 + 1.25724e20i 0.179844 + 0.371939i
\(547\) 1.38572e20i 0.404363i −0.979348 0.202182i \(-0.935197\pi\)
0.979348 0.202182i \(-0.0648031\pi\)
\(548\) 2.30330e20 5.46867e20i 0.662973 1.57408i
\(549\) −3.70251e19 + 1.33060e20i −0.105124 + 0.377794i
\(550\) −5.79290e19 + 2.86781e20i −0.162247 + 0.803211i
\(551\) −4.24900e20 −1.17395
\(552\) 3.28019e20 1.69917e19i 0.894037 0.0463121i
\(553\) 8.48847e19 0.228240
\(554\) 1.18633e19 5.87297e19i 0.0314688 0.155788i
\(555\) 4.26553e19 3.24067e19i 0.111629 0.0848081i
\(556\) −1.74735e19 + 4.14869e19i −0.0451147 + 0.107115i
\(557\) 4.79131e20i 1.22051i 0.792206 + 0.610253i \(0.208932\pi\)
−0.792206 + 0.610253i \(0.791068\pi\)
\(558\) 1.50664e20 2.96082e20i 0.378662 0.744141i
\(559\) 8.48478e20i 2.10403i
\(560\) 1.74358e19 + 1.78546e19i 0.0426612 + 0.0436856i
\(561\) 1.80799e20 1.37359e20i 0.436490 0.331616i
\(562\) 7.56354e20 + 1.52782e20i 1.80178 + 0.363956i
\(563\) −1.00595e20 −0.236463 −0.118232 0.992986i \(-0.537723\pi\)
−0.118232 + 0.992986i \(0.537723\pi\)
\(564\) 1.97367e20 + 7.69514e20i 0.457806 + 1.78494i
\(565\) −1.55574e20 −0.356101
\(566\) 5.76608e20 + 1.16473e20i 1.30244 + 0.263090i
\(567\) −7.38344e19 + 1.22400e20i −0.164583 + 0.272840i
\(568\) −4.67658e20 + 6.86595e20i −1.02876 + 1.51039i
\(569\) 9.92056e19i 0.215375i −0.994185 0.107687i \(-0.965655\pi\)
0.994185 0.107687i \(-0.0343445\pi\)
\(570\) −1.10470e20 + 5.34159e19i −0.236693 + 0.114448i
\(571\) 6.09538e20i 1.28893i −0.764633 0.644466i \(-0.777080\pi\)
0.764633 0.644466i \(-0.222920\pi\)
\(572\) −4.87047e20 2.05135e20i −1.01648 0.428124i
\(573\) 2.77385e20 + 3.65108e20i 0.571378 + 0.752076i
\(574\) 1.75761e19 8.70116e19i 0.0357342 0.176904i
\(575\) −4.29732e20 −0.862360
\(576\) 5.02155e20 5.21644e19i 0.994648 0.103325i
\(577\) −8.52542e20 −1.66685 −0.833426 0.552630i \(-0.813624\pi\)
−0.833426 + 0.552630i \(0.813624\pi\)
\(578\) 5.99917e19 2.96992e20i 0.115780 0.573174i
\(579\) −1.26460e20 1.66453e20i −0.240915 0.317105i
\(580\) 8.03570e19 + 3.38448e19i 0.151117 + 0.0636476i
\(581\) 5.57534e19i 0.103502i
\(582\) 1.21936e20 5.89599e19i 0.223465 0.108052i
\(583\) 4.39657e19i 0.0795426i
\(584\) −4.46396e20 + 6.55379e20i −0.797304 + 1.17057i
\(585\) 1.35750e20 + 3.77736e19i 0.239371 + 0.0666070i
\(586\) −8.55576e20 1.72824e20i −1.48945 0.300866i
\(587\) 2.43095e20 0.417822 0.208911 0.977935i \(-0.433008\pi\)
0.208911 + 0.977935i \(0.433008\pi\)
\(588\) −1.31540e20 5.12861e20i −0.223217 0.870301i
\(589\) 6.83696e20 1.14551
\(590\) −8.26943e19 1.67040e19i −0.136800 0.0276332i
\(591\) 7.09045e19 5.38685e19i 0.115816 0.0879891i
\(592\) −3.16910e20 3.24521e20i −0.511121 0.523395i
\(593\) 6.80668e20i 1.08399i −0.840382 0.541995i \(-0.817669\pi\)
0.840382 0.541995i \(-0.182331\pi\)
\(594\) −9.63109e19 5.32312e20i −0.151453 0.837082i
\(595\) 2.53393e19i 0.0393474i
\(596\) −7.68615e18 + 1.82491e19i −0.0117859 + 0.0279830i
\(597\) −1.03527e20 + 7.86526e19i −0.156763 + 0.119098i
\(598\) 1.53694e20 7.60871e20i 0.229825 1.13776i
\(599\) −3.33728e19 −0.0492824 −0.0246412 0.999696i \(-0.507844\pi\)
−0.0246412 + 0.999696i \(0.507844\pi\)
\(600\) −6.59635e20 + 3.41699e19i −0.961988 + 0.0498321i
\(601\) 4.44009e20 0.639489 0.319744 0.947504i \(-0.396403\pi\)
0.319744 + 0.947504i \(0.396403\pi\)
\(602\) −7.19754e19 + 3.56318e20i −0.102379 + 0.506832i
\(603\) 3.81251e20 + 1.06086e20i 0.535589 + 0.149032i
\(604\) −1.71958e20 + 4.08276e20i −0.238586 + 0.566470i
\(605\) 3.86456e19i 0.0529585i
\(606\) −2.15109e20 4.44872e20i −0.291149 0.602130i
\(607\) 5.34672e19i 0.0714780i −0.999361 0.0357390i \(-0.988621\pi\)
0.999361 0.0357390i \(-0.0113785\pi\)
\(608\) 5.64366e20 + 8.72368e20i 0.745220 + 1.15192i
\(609\) 1.26460e20 + 1.66453e20i 0.164939 + 0.217101i
\(610\) 5.71748e19 + 1.15492e19i 0.0736598 + 0.0148791i
\(611\) 1.87744e21 2.38922
\(612\) 4.01790e20 + 3.18336e20i 0.505084 + 0.400175i
\(613\) −1.20047e21 −1.49072 −0.745361 0.666661i \(-0.767723\pi\)
−0.745361 + 0.666661i \(0.767723\pi\)
\(614\) 5.05575e20 + 1.02125e20i 0.620187 + 0.125276i
\(615\) −5.41845e19 7.13204e19i −0.0656616 0.0864271i
\(616\) −1.87134e20 1.27462e20i −0.224026 0.152590i
\(617\) 3.16260e20i 0.374030i −0.982357 0.187015i \(-0.940119\pi\)
0.982357 0.187015i \(-0.0598812\pi\)
\(618\) −4.60299e20 9.51953e20i −0.537807 1.11225i
\(619\) 5.05346e20i 0.583322i 0.956522 + 0.291661i \(0.0942080\pi\)
−0.956522 + 0.291661i \(0.905792\pi\)
\(620\) −1.29300e20 5.44589e19i −0.147456 0.0621056i
\(621\) 7.38373e20 2.93468e20i 0.831934 0.330654i
\(622\) 1.61606e20 8.00039e20i 0.179899 0.890601i
\(623\) 3.37012e20 0.370668
\(624\) 1.75419e20 1.18015e21i 0.190631 1.28249i
\(625\) 8.29977e20 0.891181
\(626\) −1.35496e20 + 6.70783e20i −0.143754 + 0.711663i
\(627\) 8.86478e20 6.73487e20i 0.929311 0.706029i
\(628\) −7.03982e20 2.96503e20i −0.729229 0.307137i
\(629\) 4.60561e20i 0.471419i
\(630\) 5.38039e19 + 2.73786e19i 0.0544202 + 0.0276921i
\(631\) 1.43095e21i 1.43022i 0.699010 + 0.715112i \(0.253624\pi\)
−0.699010 + 0.715112i \(0.746376\pi\)
\(632\) −5.99394e20 4.08264e20i −0.592018 0.403239i
\(633\) −1.12803e21 + 8.57000e20i −1.10101 + 0.836475i
\(634\) 1.94296e21 + 3.92472e20i 1.87410 + 0.378564i
\(635\) −3.17200e20 −0.302364
\(636\) −9.61460e19 + 2.46598e19i −0.0905738 + 0.0232306i
\(637\) −1.25126e21 −1.16494
\(638\) −7.75428e20 1.56635e20i −0.713487 0.144123i
\(639\) −5.38716e20 + 1.93603e21i −0.489895 + 1.76058i
\(640\) −3.72456e19 2.09936e20i −0.0334754 0.188685i
\(641\) 2.62366e20i 0.233062i 0.993187 + 0.116531i \(0.0371775\pi\)
−0.993187 + 0.116531i \(0.962823\pi\)
\(642\) −1.03396e21 + 4.99954e20i −0.907805 + 0.438952i
\(643\) 1.31607e21i 1.14208i −0.820923 0.571039i \(-0.806540\pi\)
0.820923 0.571039i \(-0.193460\pi\)
\(644\) 1.29088e20 3.06490e20i 0.110724 0.262889i
\(645\) 2.21889e20 + 2.92061e20i 0.188121 + 0.247615i
\(646\) −2.08882e20 + 1.03408e21i −0.175048 + 0.866587i
\(647\) −1.95960e21 −1.62325 −0.811625 0.584179i \(-0.801417\pi\)
−0.811625 + 0.584179i \(0.801417\pi\)
\(648\) 1.11006e21 5.09183e20i 0.908939 0.416928i
\(649\) 7.65422e20 0.619535
\(650\) −3.09074e20 + 1.53009e21i −0.247293 + 1.22424i
\(651\) −2.03483e20 2.67835e20i −0.160943 0.211841i
\(652\) −1.41514e19 + 3.35995e19i −0.0110648 + 0.0262709i
\(653\) 1.59848e21i 1.23555i −0.786356 0.617773i \(-0.788035\pi\)
0.786356 0.617773i \(-0.211965\pi\)
\(654\) −1.63316e21 + 7.89685e20i −1.24795 + 0.603421i
\(655\) 2.32688e20i 0.175778i
\(656\) −5.42603e20 + 5.29879e20i −0.405232 + 0.395729i
\(657\) −5.14223e20 + 1.84800e21i −0.379674 + 1.36447i
\(658\) 7.88431e20 + 1.59261e20i 0.575532 + 0.116256i
\(659\) −4.07387e20 −0.294013 −0.147006 0.989136i \(-0.546964\pi\)
−0.147006 + 0.989136i \(0.546964\pi\)
\(660\) −2.21296e20 + 5.67586e19i −0.157904 + 0.0404997i
\(661\) 2.34291e21 1.65289 0.826445 0.563017i \(-0.190359\pi\)
0.826445 + 0.563017i \(0.190359\pi\)
\(662\) 5.98790e20 + 1.20954e20i 0.417676 + 0.0843696i
\(663\) 9.64634e20 7.32865e20i 0.665290 0.505443i
\(664\) −2.68153e20 + 3.93690e20i −0.182861 + 0.268469i
\(665\) 1.24241e20i 0.0837729i
\(666\) −9.77929e20 4.97627e20i −0.652005 0.331778i
\(667\) 1.16195e21i 0.766029i
\(668\) 2.18809e21 + 9.21582e20i 1.42640 + 0.600773i
\(669\) −6.51873e20 + 4.95250e20i −0.420211 + 0.319248i
\(670\) 3.30914e19 1.63821e20i 0.0210938 0.104426i
\(671\) −5.29213e20 −0.333589
\(672\) 1.73778e20 4.80724e20i 0.108324 0.299658i
\(673\) 1.04917e21 0.646746 0.323373 0.946272i \(-0.395183\pi\)
0.323373 + 0.946272i \(0.395183\pi\)
\(674\) 3.03105e20 1.50054e21i 0.184775 0.914740i
\(675\) −1.48485e21 + 5.90156e20i −0.895165 + 0.355786i
\(676\) −1.05284e21 4.43435e20i −0.627714 0.264381i
\(677\) 8.49037e20i 0.500624i −0.968165 0.250312i \(-0.919467\pi\)
0.968165 0.250312i \(-0.0805332\pi\)
\(678\) 1.38718e21 + 2.86884e21i 0.808926 + 1.67295i
\(679\) 1.37136e20i 0.0790913i
\(680\) 1.21872e20 1.78927e20i 0.0695165 0.102061i
\(681\) −6.55452e20 8.62739e20i −0.369775 0.486717i
\(682\) 1.24772e21 + 2.52037e20i 0.696202 + 0.140631i
\(683\) −2.85892e20 −0.157778 −0.0788889 0.996883i \(-0.525137\pi\)
−0.0788889 + 0.996883i \(0.525137\pi\)
\(684\) 1.97002e21 + 1.56084e21i 1.07535 + 0.851994i
\(685\) −6.06225e20 −0.327306
\(686\) −1.11031e21 2.24281e20i −0.592946 0.119774i
\(687\) −1.56840e20 2.06441e20i −0.0828478 0.109049i
\(688\) 2.22199e21 2.16989e21i 1.16099 1.13377i
\(689\) 2.34574e20i 0.121237i
\(690\) −1.46074e20 3.02099e20i −0.0746801 0.154447i
\(691\) 1.38315e21i 0.699496i −0.936844 0.349748i \(-0.886267\pi\)
0.936844 0.349748i \(-0.113733\pi\)
\(692\) 8.43243e20 2.00209e21i 0.421849 1.00159i
\(693\) −5.27671e20 1.46829e20i −0.261134 0.0726629i
\(694\) −6.12160e20 + 3.03053e21i −0.299688 + 1.48362i
\(695\) 4.59899e19 0.0222729
\(696\) −9.23922e19 1.78359e21i −0.0442656 0.854528i
\(697\) −7.70065e20 −0.364990
\(698\) 4.09261e20 2.02607e21i 0.191904 0.950033i
\(699\) 1.44157e21 1.09521e21i 0.668740 0.508064i
\(700\) −2.59591e20 + 6.16342e20i −0.119139 + 0.282870i
\(701\) 5.12041e20i 0.232498i 0.993220 + 0.116249i \(0.0370871\pi\)
−0.993220 + 0.116249i \(0.962913\pi\)
\(702\) −5.13857e20 2.84010e21i −0.230841 1.27586i
\(703\) 2.25818e21i 1.00368i
\(704\) 7.08361e20 + 1.80009e21i 0.311501 + 0.791588i
\(705\) 6.46249e20 4.90977e20i 0.281178 0.213620i
\(706\) −7.54720e20 1.52452e20i −0.324901 0.0656292i
\(707\) −5.00328e20 −0.213112
\(708\) 4.29315e20 + 1.67386e21i 0.180937 + 0.705455i
\(709\) −3.47919e21 −1.45088 −0.725440 0.688285i \(-0.758364\pi\)
−0.725440 + 0.688285i \(0.758364\pi\)
\(710\) 8.31895e20 + 1.68041e20i 0.343266 + 0.0693389i
\(711\) −1.69014e21 4.70296e20i −0.690083 0.192021i
\(712\) −2.37973e21 1.62090e21i −0.961454 0.654872i
\(713\) 1.86967e21i 0.747471i
\(714\) 4.67266e20 2.25938e20i 0.184853 0.0893824i
\(715\) 5.39912e20i 0.211362i
\(716\) 8.58503e20 + 3.61585e20i 0.332579 + 0.140076i
\(717\) −5.62436e20 7.40307e20i −0.215615 0.283804i
\(718\) 2.99129e20 1.48086e21i 0.113482 0.561797i
\(719\) 8.54186e20 0.320690 0.160345 0.987061i \(-0.448739\pi\)
0.160345 + 0.987061i \(0.448739\pi\)
\(720\) −2.48244e20 4.52104e20i −0.0922327 0.167975i
\(721\) −1.07062e21 −0.393659
\(722\) −4.80059e20 + 2.37656e21i −0.174689 + 0.864808i
\(723\) 5.95282e19 + 7.83541e19i 0.0214381 + 0.0282179i
\(724\) 1.63097e21 + 6.86932e20i 0.581308 + 0.244835i
\(725\) 2.33666e21i 0.824251i
\(726\) −7.12641e20 + 3.44584e20i −0.248798 + 0.120301i
\(727\) 3.69552e21i 1.27693i 0.769651 + 0.638465i \(0.220430\pi\)
−0.769651 + 0.638465i \(0.779570\pi\)
\(728\) −9.98434e20 6.80060e20i −0.341456 0.232574i
\(729\) 2.14827e21 2.02803e21i 0.727162 0.686465i
\(730\) 7.94073e20 + 1.60401e20i 0.266035 + 0.0537384i
\(731\) 3.15346e21 1.04570
\(732\) −2.96828e20 1.15730e21i −0.0974254 0.379852i
\(733\) 3.61825e21 1.17549 0.587745 0.809046i \(-0.300016\pi\)
0.587745 + 0.809046i \(0.300016\pi\)
\(734\) −3.95459e21 7.98817e20i −1.27169 0.256878i
\(735\) −4.30707e20 + 3.27223e20i −0.137097 + 0.104157i
\(736\) −2.38562e21 + 1.54335e21i −0.751655 + 0.486273i
\(737\) 1.51633e21i 0.472921i
\(738\) −8.32039e20 + 1.63511e21i −0.256875 + 0.504806i
\(739\) 3.74316e21i 1.14395i 0.820273 + 0.571973i \(0.193822\pi\)
−0.820273 + 0.571973i \(0.806178\pi\)
\(740\) −1.79872e20 + 4.27067e20i −0.0544160 + 0.129199i
\(741\) 4.72971e21 3.59332e21i 1.41644 1.07612i
\(742\) −1.98987e19 + 9.85094e19i −0.00589922 + 0.0292044i
\(743\) 6.23817e20 0.183080 0.0915401 0.995801i \(-0.470821\pi\)
0.0915401 + 0.995801i \(0.470821\pi\)
\(744\) 1.48666e20 + 2.86994e21i 0.0431931 + 0.833826i
\(745\) 2.02298e19 0.00581863
\(746\) 2.34063e20 1.15874e21i 0.0666488 0.329949i
\(747\) −3.08897e20 + 1.11011e21i −0.0870781 + 0.312940i
\(748\) −7.62407e20 + 1.81017e21i −0.212777 + 0.505192i
\(749\) 1.16285e21i 0.321300i
\(750\) 5.98700e20 + 1.23818e21i 0.163776 + 0.338708i
\(751\) 1.37628e21i 0.372741i 0.982479 + 0.186371i \(0.0596725\pi\)
−0.982479 + 0.186371i \(0.940327\pi\)
\(752\) −4.80134e21 4.91664e21i −1.28745 1.31836i
\(753\) −1.69767e21 2.23456e21i −0.450704 0.593240i
\(754\) −4.13722e21 8.35707e20i −1.08748 0.219669i
\(755\) 4.52591e20 0.117789
\(756\) 2.51280e19 1.23629e21i 0.00647508 0.318571i
\(757\) −5.99725e20 −0.153015 −0.0765073 0.997069i \(-0.524377\pi\)
−0.0765073 + 0.997069i \(0.524377\pi\)
\(758\) 4.36862e21 + 8.82451e20i 1.10363 + 0.222931i
\(759\) 1.84175e21 + 2.42421e21i 0.460700 + 0.606397i
\(760\) 5.97554e20 8.77302e20i 0.148004 0.217294i
\(761\) 2.91406e21i 0.714684i −0.933974 0.357342i \(-0.883683\pi\)
0.933974 0.357342i \(-0.116317\pi\)
\(762\) 2.82832e21 + 5.84929e21i 0.686856 + 1.42050i
\(763\) 1.83674e21i 0.441687i
\(764\) −3.65548e21 1.53962e21i −0.870450