Properties

Label 1078.2.i.b.901.7
Level $1078$
Weight $2$
Character 1078.901
Analytic conductor $8.608$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: 16.0.162447943996702457856.1
Defining polynomial: \(x^{16} - x^{12} - 15 x^{8} - 16 x^{4} + 256\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{6}\cdot 3^{4} \)
Twist minimal: no (minimal twist has level 154)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 901.7
Root \(0.140577 - 1.40721i\) of defining polynomial
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.b.1011.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.559525 - 0.323042i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 + 2.23658i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.559525 - 0.323042i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 + 2.23658i) q^{9} +(-1.54779 - 2.68085i) q^{10} +(-1.52168 + 2.94694i) q^{11} +(0.559525 + 0.323042i) q^{12} +0.646084 q^{13} -2.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.87083 + 3.24037i) q^{17} +(-2.23658 + 1.29129i) q^{18} +(0.901703 - 1.56180i) q^{19} -3.09557i q^{20} +(-2.79129 + 1.79129i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(0.323042 + 0.559525i) q^{24} +(2.29129 + 3.96863i) q^{25} +(0.559525 + 0.323042i) q^{26} +3.60681i q^{27} +1.58258i q^{29} +(-1.73205 - 1.00000i) q^{30} +(-7.48301 + 4.32032i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.100567 + 2.14046i) q^{33} +3.74166i q^{34} -2.58258 q^{36} +(-1.79129 + 3.10260i) q^{37} +(1.56180 - 0.901703i) q^{38} +(0.361500 - 0.208712i) q^{39} +(1.54779 - 2.68085i) q^{40} -9.93280 q^{41} -7.16515i q^{43} +(-3.31297 + 0.155657i) q^{44} +(6.92349 - 3.99728i) q^{45} +(-3.46410 + 2.00000i) q^{46} +(8.60206 + 4.96640i) q^{47} +0.646084i q^{48} +4.58258i q^{50} +(2.09355 + 1.20871i) q^{51} +(0.323042 + 0.559525i) q^{52} +(5.79129 + 10.0308i) q^{53} +(-1.80341 + 3.12359i) q^{54} +(8.64064 - 5.54506i) q^{55} -1.16515i q^{57} +(-0.791288 + 1.37055i) q^{58} +(-0.559525 + 0.323042i) q^{59} +(-1.00000 - 1.73205i) q^{60} +(-0.969126 + 1.67858i) q^{61} -8.64064 q^{62} -1.00000 q^{64} +(-1.73205 - 1.00000i) q^{65} +(-0.983134 + 1.90397i) q^{66} +(3.79129 + 6.56670i) q^{67} +(-1.87083 + 3.24037i) q^{68} +2.58434i q^{69} +2.00000 q^{71} +(-2.23658 - 1.29129i) q^{72} +(-8.06198 - 13.9638i) q^{73} +(-3.10260 + 1.79129i) q^{74} +(2.56407 + 1.48036i) q^{75} +1.80341 q^{76} +0.417424 q^{78} +(3.46410 + 2.00000i) q^{79} +(2.68085 - 1.54779i) q^{80} +(-2.70871 - 4.69163i) q^{81} +(-8.60206 - 4.96640i) q^{82} +12.8935 q^{83} -11.5826i q^{85} +(3.58258 - 6.20520i) q^{86} +(0.511238 + 0.885491i) q^{87} +(-2.94694 - 1.52168i) q^{88} +(-8.48528 - 4.89898i) q^{89} +7.99455 q^{90} -4.00000 q^{92} +(-2.79129 + 4.83465i) q^{93} +(4.96640 + 8.60206i) q^{94} +(-4.83465 + 2.79129i) q^{95} +(-0.323042 + 0.559525i) q^{96} -8.50579i q^{97} +(-4.62614 - 7.20871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 8 q^{4} + 16 q^{9} + O(q^{10}) \) \( 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.559525 0.323042i 0.323042 0.186508i −0.329706 0.944084i \(-0.606950\pi\)
0.652748 + 0.757575i \(0.273616\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.68085 1.54779i −1.19891 0.692191i −0.238598 0.971118i \(-0.576688\pi\)
−0.960312 + 0.278927i \(0.910021\pi\)
\(6\) 0.646084 0.263763
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) −1.29129 + 2.23658i −0.430429 + 0.745525i
\(10\) −1.54779 2.68085i −0.489453 0.847758i
\(11\) −1.52168 + 2.94694i −0.458804 + 0.888537i
\(12\) 0.559525 + 0.323042i 0.161521 + 0.0932542i
\(13\) 0.646084 0.179191 0.0895957 0.995978i \(-0.471443\pi\)
0.0895957 + 0.995978i \(0.471443\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.87083 + 3.24037i 0.453743 + 0.785905i 0.998615 0.0526138i \(-0.0167552\pi\)
−0.544872 + 0.838519i \(0.683422\pi\)
\(18\) −2.23658 + 1.29129i −0.527166 + 0.304359i
\(19\) 0.901703 1.56180i 0.206865 0.358300i −0.743860 0.668335i \(-0.767007\pi\)
0.950725 + 0.310035i \(0.100341\pi\)
\(20\) 3.09557i 0.692191i
\(21\) 0 0
\(22\) −2.79129 + 1.79129i −0.595105 + 0.381904i
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0.323042 + 0.559525i 0.0659407 + 0.114213i
\(25\) 2.29129 + 3.96863i 0.458258 + 0.793725i
\(26\) 0.559525 + 0.323042i 0.109732 + 0.0633537i
\(27\) 3.60681i 0.694131i
\(28\) 0 0
\(29\) 1.58258i 0.293877i 0.989146 + 0.146938i \(0.0469419\pi\)
−0.989146 + 0.146938i \(0.953058\pi\)
\(30\) −1.73205 1.00000i −0.316228 0.182574i
\(31\) −7.48301 + 4.32032i −1.34399 + 0.775952i −0.987390 0.158306i \(-0.949397\pi\)
−0.356598 + 0.934258i \(0.616064\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) 0.100567 + 2.14046i 0.0175065 + 0.372606i
\(34\) 3.74166i 0.641689i
\(35\) 0 0
\(36\) −2.58258 −0.430429
\(37\) −1.79129 + 3.10260i −0.294486 + 0.510065i −0.974865 0.222796i \(-0.928482\pi\)
0.680379 + 0.732860i \(0.261815\pi\)
\(38\) 1.56180 0.901703i 0.253357 0.146276i
\(39\) 0.361500 0.208712i 0.0578863 0.0334207i
\(40\) 1.54779 2.68085i 0.244727 0.423879i
\(41\) −9.93280 −1.55124 −0.775622 0.631198i \(-0.782564\pi\)
−0.775622 + 0.631198i \(0.782564\pi\)
\(42\) 0 0
\(43\) 7.16515i 1.09268i −0.837565 0.546338i \(-0.816022\pi\)
0.837565 0.546338i \(-0.183978\pi\)
\(44\) −3.31297 + 0.155657i −0.499449 + 0.0234662i
\(45\) 6.92349 3.99728i 1.03209 0.595879i
\(46\) −3.46410 + 2.00000i −0.510754 + 0.294884i
\(47\) 8.60206 + 4.96640i 1.25474 + 0.724424i 0.972047 0.234786i \(-0.0754390\pi\)
0.282693 + 0.959211i \(0.408772\pi\)
\(48\) 0.646084i 0.0932542i
\(49\) 0 0
\(50\) 4.58258i 0.648074i
\(51\) 2.09355 + 1.20871i 0.293156 + 0.169254i
\(52\) 0.323042 + 0.559525i 0.0447979 + 0.0775922i
\(53\) 5.79129 + 10.0308i 0.795495 + 1.37784i 0.922525 + 0.385938i \(0.126122\pi\)
−0.127030 + 0.991899i \(0.540544\pi\)
\(54\) −1.80341 + 3.12359i −0.245412 + 0.425067i
\(55\) 8.64064 5.54506i 1.16510 0.747696i
\(56\) 0 0
\(57\) 1.16515i 0.154328i
\(58\) −0.791288 + 1.37055i −0.103901 + 0.179962i
\(59\) −0.559525 + 0.323042i −0.0728440 + 0.0420565i −0.535980 0.844231i \(-0.680058\pi\)
0.463136 + 0.886287i \(0.346724\pi\)
\(60\) −1.00000 1.73205i −0.129099 0.223607i
\(61\) −0.969126 + 1.67858i −0.124084 + 0.214920i −0.921374 0.388676i \(-0.872933\pi\)
0.797291 + 0.603596i \(0.206266\pi\)
\(62\) −8.64064 −1.09736
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −1.73205 1.00000i −0.214834 0.124035i
\(66\) −0.983134 + 1.90397i −0.121015 + 0.234363i
\(67\) 3.79129 + 6.56670i 0.463180 + 0.802250i 0.999117 0.0420070i \(-0.0133752\pi\)
−0.535938 + 0.844257i \(0.680042\pi\)
\(68\) −1.87083 + 3.24037i −0.226871 + 0.392953i
\(69\) 2.58434i 0.311117i
\(70\) 0 0
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −2.23658 1.29129i −0.263583 0.152180i
\(73\) −8.06198 13.9638i −0.943583 1.63433i −0.758564 0.651599i \(-0.774099\pi\)
−0.185019 0.982735i \(-0.559235\pi\)
\(74\) −3.10260 + 1.79129i −0.360670 + 0.208233i
\(75\) 2.56407 + 1.48036i 0.296073 + 0.170938i
\(76\) 1.80341 0.206865
\(77\) 0 0
\(78\) 0.417424 0.0472640
\(79\) 3.46410 + 2.00000i 0.389742 + 0.225018i 0.682048 0.731307i \(-0.261089\pi\)
−0.292306 + 0.956325i \(0.594423\pi\)
\(80\) 2.68085 1.54779i 0.299728 0.173048i
\(81\) −2.70871 4.69163i −0.300968 0.521292i
\(82\) −8.60206 4.96640i −0.949939 0.548447i
\(83\) 12.8935 1.41525 0.707625 0.706589i \(-0.249767\pi\)
0.707625 + 0.706589i \(0.249767\pi\)
\(84\) 0 0
\(85\) 11.5826i 1.25631i
\(86\) 3.58258 6.20520i 0.386319 0.669124i
\(87\) 0.511238 + 0.885491i 0.0548105 + 0.0949346i
\(88\) −2.94694 1.52168i −0.314145 0.162212i
\(89\) −8.48528 4.89898i −0.899438 0.519291i −0.0224202 0.999749i \(-0.507137\pi\)
−0.877018 + 0.480458i \(0.840471\pi\)
\(90\) 7.99455 0.842700
\(91\) 0 0
\(92\) −4.00000 −0.417029
\(93\) −2.79129 + 4.83465i −0.289443 + 0.501330i
\(94\) 4.96640 + 8.60206i 0.512245 + 0.887235i
\(95\) −4.83465 + 2.79129i −0.496025 + 0.286380i
\(96\) −0.323042 + 0.559525i −0.0329703 + 0.0571063i
\(97\) 8.50579i 0.863632i −0.901962 0.431816i \(-0.857873\pi\)
0.901962 0.431816i \(-0.142127\pi\)
\(98\) 0 0
\(99\) −4.62614 7.20871i −0.464944 0.724503i
\(100\) −2.29129 + 3.96863i −0.229129 + 0.396863i
\(101\) 5.86811 + 10.1639i 0.583898 + 1.01134i 0.995012 + 0.0997573i \(0.0318067\pi\)
−0.411114 + 0.911584i \(0.634860\pi\)
\(102\) 1.20871 + 2.09355i 0.119680 + 0.207292i
\(103\) −5.24491 3.02815i −0.516796 0.298373i 0.218827 0.975764i \(-0.429777\pi\)
−0.735623 + 0.677391i \(0.763110\pi\)
\(104\) 0.646084i 0.0633537i
\(105\) 0 0
\(106\) 11.5826i 1.12500i
\(107\) −15.2270 8.79129i −1.47205 0.849886i −0.472539 0.881310i \(-0.656663\pi\)
−0.999506 + 0.0314237i \(0.989996\pi\)
\(108\) −3.12359 + 1.80341i −0.300568 + 0.173533i
\(109\) 14.8655 8.58258i 1.42385 0.822062i 0.427227 0.904144i \(-0.359491\pi\)
0.996626 + 0.0820827i \(0.0261572\pi\)
\(110\) 10.2555 0.481847i 0.977828 0.0459423i
\(111\) 2.31464i 0.219696i
\(112\) 0 0
\(113\) 10.7477 1.01106 0.505531 0.862809i \(-0.331297\pi\)
0.505531 + 0.862809i \(0.331297\pi\)
\(114\) 0.582576 1.00905i 0.0545632 0.0945063i
\(115\) 10.7234 6.19115i 0.999960 0.577327i
\(116\) −1.37055 + 0.791288i −0.127252 + 0.0734692i
\(117\) −0.834280 + 1.44502i −0.0771292 + 0.133592i
\(118\) −0.646084 −0.0594768
\(119\) 0 0
\(120\) 2.00000i 0.182574i
\(121\) −6.36897 8.96863i −0.578997 0.815330i
\(122\) −1.67858 + 0.969126i −0.151971 + 0.0877405i
\(123\) −5.55765 + 3.20871i −0.501117 + 0.289320i
\(124\) −7.48301 4.32032i −0.671994 0.387976i
\(125\) 1.29217i 0.115575i
\(126\) 0 0
\(127\) 3.58258i 0.317902i −0.987286 0.158951i \(-0.949189\pi\)
0.987286 0.158951i \(-0.0508112\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) −2.31464 4.00908i −0.203793 0.352980i
\(130\) −1.00000 1.73205i −0.0877058 0.151911i
\(131\) 8.38502 14.5233i 0.732602 1.26890i −0.223165 0.974781i \(-0.571639\pi\)
0.955767 0.294124i \(-0.0950278\pi\)
\(132\) −1.80341 + 1.15732i −0.156966 + 0.100732i
\(133\) 0 0
\(134\) 7.58258i 0.655035i
\(135\) 5.58258 9.66930i 0.480472 0.832201i
\(136\) −3.24037 + 1.87083i −0.277859 + 0.160422i
\(137\) 1.58258 + 2.74110i 0.135209 + 0.234188i 0.925677 0.378315i \(-0.123496\pi\)
−0.790469 + 0.612503i \(0.790163\pi\)
\(138\) −1.29217 + 2.23810i −0.109997 + 0.190520i
\(139\) −15.4779 −1.31282 −0.656408 0.754406i \(-0.727925\pi\)
−0.656408 + 0.754406i \(0.727925\pi\)
\(140\) 0 0
\(141\) 6.41742 0.540445
\(142\) 1.73205 + 1.00000i 0.145350 + 0.0839181i
\(143\) −0.983134 + 1.90397i −0.0822138 + 0.159218i
\(144\) −1.29129 2.23658i −0.107607 0.186381i
\(145\) 2.44949 4.24264i 0.203419 0.352332i
\(146\) 16.1240i 1.33443i
\(147\) 0 0
\(148\) −3.58258 −0.294486
\(149\) 12.1244 + 7.00000i 0.993266 + 0.573462i 0.906249 0.422744i \(-0.138933\pi\)
0.0870170 + 0.996207i \(0.472267\pi\)
\(150\) 1.48036 + 2.56407i 0.120871 + 0.209355i
\(151\) 4.83465 2.79129i 0.393438 0.227152i −0.290210 0.956963i \(-0.593725\pi\)
0.683649 + 0.729811i \(0.260392\pi\)
\(152\) 1.56180 + 0.901703i 0.126678 + 0.0731378i
\(153\) −9.66311 −0.781216
\(154\) 0 0
\(155\) 26.7477 2.14843
\(156\) 0.361500 + 0.208712i 0.0289432 + 0.0167103i
\(157\) −11.3997 + 6.58161i −0.909794 + 0.525270i −0.880365 0.474297i \(-0.842702\pi\)
−0.0294291 + 0.999567i \(0.509369\pi\)
\(158\) 2.00000 + 3.46410i 0.159111 + 0.275589i
\(159\) 6.48074 + 3.74166i 0.513956 + 0.296733i
\(160\) 3.09557 0.244727
\(161\) 0 0
\(162\) 5.41742i 0.425633i
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) −4.96640 8.60206i −0.387811 0.671708i
\(165\) 3.04336 5.89389i 0.236926 0.458839i
\(166\) 11.1661 + 6.44677i 0.866660 + 0.500366i
\(167\) 1.29217 0.0999909 0.0499955 0.998749i \(-0.484079\pi\)
0.0499955 + 0.998749i \(0.484079\pi\)
\(168\) 0 0
\(169\) −12.5826 −0.967890
\(170\) 5.79129 10.0308i 0.444172 0.769328i
\(171\) 2.32872 + 4.03345i 0.178081 + 0.308446i
\(172\) 6.20520 3.58258i 0.473142 0.273169i
\(173\) −5.35687 + 9.27837i −0.407275 + 0.705421i −0.994583 0.103942i \(-0.966854\pi\)
0.587308 + 0.809363i \(0.300188\pi\)
\(174\) 1.02248i 0.0775137i
\(175\) 0 0
\(176\) −1.79129 2.79129i −0.135023 0.210401i
\(177\) −0.208712 + 0.361500i −0.0156878 + 0.0271720i
\(178\) −4.89898 8.48528i −0.367194 0.635999i
\(179\) −5.58258 9.66930i −0.417261 0.722718i 0.578402 0.815752i \(-0.303677\pi\)
−0.995663 + 0.0930344i \(0.970343\pi\)
\(180\) 6.92349 + 3.99728i 0.516046 + 0.297939i
\(181\) 5.41022i 0.402138i 0.979577 + 0.201069i \(0.0644416\pi\)
−0.979577 + 0.201069i \(0.935558\pi\)
\(182\) 0 0
\(183\) 1.25227i 0.0925707i
\(184\) −3.46410 2.00000i −0.255377 0.147442i
\(185\) 9.60433 5.54506i 0.706124 0.407681i
\(186\) −4.83465 + 2.79129i −0.354494 + 0.204667i
\(187\) −12.3960 + 0.582415i −0.906485 + 0.0425904i
\(188\) 9.93280i 0.724424i
\(189\) 0 0
\(190\) −5.58258 −0.405003
\(191\) 9.00000 15.5885i 0.651217 1.12794i −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) −0.559525 + 0.323042i −0.0403802 + 0.0233135i
\(193\) 14.1425 8.16515i 1.01800 0.587740i 0.104473 0.994528i \(-0.466684\pi\)
0.913523 + 0.406787i \(0.133351\pi\)
\(194\) 4.25290 7.36623i 0.305340 0.528865i
\(195\) −1.29217 −0.0925340
\(196\) 0 0
\(197\) 8.74773i 0.623250i 0.950205 + 0.311625i \(0.100873\pi\)
−0.950205 + 0.311625i \(0.899127\pi\)
\(198\) −0.401996 8.55600i −0.0285686 0.608048i
\(199\) −8.36850 + 4.83156i −0.593227 + 0.342500i −0.766373 0.642396i \(-0.777940\pi\)
0.173145 + 0.984896i \(0.444607\pi\)
\(200\) −3.96863 + 2.29129i −0.280624 + 0.162019i
\(201\) 4.24264 + 2.44949i 0.299253 + 0.172774i
\(202\) 11.7362i 0.825757i
\(203\) 0 0
\(204\) 2.41742i 0.169254i
\(205\) 26.6283 + 15.3739i 1.85980 + 1.07376i
\(206\) −3.02815 5.24491i −0.210981 0.365430i
\(207\) −5.16515 8.94630i −0.359003 0.621811i
\(208\) −0.323042 + 0.559525i −0.0223989 + 0.0387961i
\(209\) 3.23042 + 5.03383i 0.223453 + 0.348197i
\(210\) 0 0
\(211\) 16.7477i 1.15296i 0.817111 + 0.576481i \(0.195574\pi\)
−0.817111 + 0.576481i \(0.804426\pi\)
\(212\) −5.79129 + 10.0308i −0.397747 + 0.688919i
\(213\) 1.11905 0.646084i 0.0766760 0.0442689i
\(214\) −8.79129 15.2270i −0.600960 1.04089i
\(215\) −11.0901 + 19.2087i −0.756340 + 1.31002i
\(216\) −3.60681 −0.245412
\(217\) 0 0
\(218\) 17.1652 1.16257
\(219\) −9.02175 5.20871i −0.609634 0.351972i
\(220\) 9.12248 + 4.71048i 0.615038 + 0.317580i
\(221\) 1.20871 + 2.09355i 0.0813068 + 0.140827i
\(222\) −1.15732 + 2.00454i −0.0776744 + 0.134536i
\(223\) 16.1240i 1.07974i 0.841749 + 0.539870i \(0.181527\pi\)
−0.841749 + 0.539870i \(0.818473\pi\)
\(224\) 0 0
\(225\) −11.8348 −0.788990
\(226\) 9.30780 + 5.37386i 0.619146 + 0.357464i
\(227\) 0.255619 + 0.442745i 0.0169660 + 0.0293860i 0.874384 0.485235i \(-0.161266\pi\)
−0.857418 + 0.514621i \(0.827933\pi\)
\(228\) 1.00905 0.582576i 0.0668260 0.0385820i
\(229\) 4.91895 + 2.83995i 0.325053 + 0.187669i 0.653643 0.756803i \(-0.273240\pi\)
−0.328590 + 0.944473i \(0.606573\pi\)
\(230\) 12.3823 0.816464
\(231\) 0 0
\(232\) −1.58258 −0.103901
\(233\) 23.5257 + 13.5826i 1.54122 + 0.889824i 0.998762 + 0.0497415i \(0.0158397\pi\)
0.542458 + 0.840083i \(0.317494\pi\)
\(234\) −1.44502 + 0.834280i −0.0944636 + 0.0545386i
\(235\) −15.3739 26.6283i −1.00288 1.73704i
\(236\) −0.559525 0.323042i −0.0364220 0.0210282i
\(237\) 2.58434 0.167871
\(238\) 0 0
\(239\) 8.41742i 0.544478i −0.962230 0.272239i \(-0.912236\pi\)
0.962230 0.272239i \(-0.0877641\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) 1.73598 + 3.00681i 0.111825 + 0.193686i 0.916506 0.400021i \(-0.130997\pi\)
−0.804681 + 0.593707i \(0.797664\pi\)
\(242\) −1.03137 10.9515i −0.0662992 0.703992i
\(243\) −12.4020 7.16027i −0.795586 0.459332i
\(244\) −1.93825 −0.124084
\(245\) 0 0
\(246\) −6.41742 −0.409160
\(247\) 0.582576 1.00905i 0.0370684 0.0642044i
\(248\) −4.32032 7.48301i −0.274340 0.475172i
\(249\) 7.21425 4.16515i 0.457185 0.263956i
\(250\) −0.646084 + 1.11905i −0.0408619 + 0.0707749i
\(251\) 24.1185i 1.52235i 0.648549 + 0.761173i \(0.275376\pi\)
−0.648549 + 0.761173i \(0.724624\pi\)
\(252\) 0 0
\(253\) −7.16515 11.1652i −0.450469 0.701947i
\(254\) 1.79129 3.10260i 0.112395 0.194675i
\(255\) −3.74166 6.48074i −0.234312 0.405840i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 4.24264 + 2.44949i 0.264649 + 0.152795i 0.626453 0.779459i \(-0.284506\pi\)
−0.361805 + 0.932254i \(0.617839\pi\)
\(258\) 4.62929i 0.288207i
\(259\) 0 0
\(260\) 2.00000i 0.124035i
\(261\) −3.53955 2.04356i −0.219093 0.126493i
\(262\) 14.5233 8.38502i 0.897251 0.518028i
\(263\) −7.21425 + 4.16515i −0.444850 + 0.256834i −0.705653 0.708558i \(-0.749346\pi\)
0.260803 + 0.965392i \(0.416013\pi\)
\(264\) −2.14046 + 0.100567i −0.131736 + 0.00618949i
\(265\) 35.8547i 2.20254i
\(266\) 0 0
\(267\) −6.33030 −0.387408
\(268\) −3.79129 + 6.56670i −0.231590 + 0.401125i
\(269\) −14.2897 + 8.25017i −0.871259 + 0.503022i −0.867767 0.496972i \(-0.834445\pi\)
−0.00349288 + 0.999994i \(0.501112\pi\)
\(270\) 9.66930 5.58258i 0.588455 0.339745i
\(271\) 2.44949 4.24264i 0.148796 0.257722i −0.781987 0.623295i \(-0.785794\pi\)
0.930783 + 0.365573i \(0.119127\pi\)
\(272\) −3.74166 −0.226871
\(273\) 0 0
\(274\) 3.16515i 0.191214i
\(275\) −15.1819 + 0.713309i −0.915505 + 0.0430142i
\(276\) −2.23810 + 1.29217i −0.134718 + 0.0777794i
\(277\) 1.73205 1.00000i 0.104069 0.0600842i −0.447062 0.894503i \(-0.647530\pi\)
0.551131 + 0.834419i \(0.314196\pi\)
\(278\) −13.4042 7.73893i −0.803932 0.464150i
\(279\) 22.3151i 1.33597i
\(280\) 0 0
\(281\) 11.1652i 0.666057i 0.942917 + 0.333029i \(0.108071\pi\)
−0.942917 + 0.333029i \(0.891929\pi\)
\(282\) 5.55765 + 3.20871i 0.330953 + 0.191076i
\(283\) 9.03110 + 15.6423i 0.536843 + 0.929840i 0.999072 + 0.0430789i \(0.0137167\pi\)
−0.462228 + 0.886761i \(0.652950\pi\)
\(284\) 1.00000 + 1.73205i 0.0593391 + 0.102778i
\(285\) −1.80341 + 3.12359i −0.106825 + 0.185026i
\(286\) −1.80341 + 1.15732i −0.106638 + 0.0684339i
\(287\) 0 0
\(288\) 2.58258i 0.152180i
\(289\) 1.50000 2.59808i 0.0882353 0.152828i
\(290\) 4.24264 2.44949i 0.249136 0.143839i
\(291\) −2.74773 4.75920i −0.161075 0.278989i
\(292\) 8.06198 13.9638i 0.471791 0.817167i
\(293\) 25.1410 1.46875 0.734376 0.678743i \(-0.237475\pi\)
0.734376 + 0.678743i \(0.237475\pi\)
\(294\) 0 0
\(295\) 2.00000 0.116445
\(296\) −3.10260 1.79129i −0.180335 0.104116i
\(297\) −10.6291 5.48842i −0.616761 0.318471i
\(298\) 7.00000 + 12.1244i 0.405499 + 0.702345i
\(299\) −1.29217 + 2.23810i −0.0747280 + 0.129433i
\(300\) 2.96073i 0.170938i
\(301\) 0 0
\(302\) 5.58258 0.321241
\(303\) 6.56670 + 3.79129i 0.377247 + 0.217804i
\(304\) 0.901703 + 1.56180i 0.0517162 + 0.0895751i
\(305\) 5.19615 3.00000i 0.297531 0.171780i
\(306\) −8.36850 4.83156i −0.478395 0.276202i
\(307\) −10.5789 −0.603769 −0.301885 0.953344i \(-0.597616\pi\)
−0.301885 + 0.953344i \(0.597616\pi\)
\(308\) 0 0
\(309\) −3.91288 −0.222596
\(310\) 23.1642 + 13.3739i 1.31564 + 0.759584i
\(311\) 4.35942 2.51691i 0.247200 0.142721i −0.371281 0.928520i \(-0.621081\pi\)
0.618482 + 0.785799i \(0.287748\pi\)
\(312\) 0.208712 + 0.361500i 0.0118160 + 0.0204659i
\(313\) 20.3277 + 11.7362i 1.14899 + 0.663370i 0.948641 0.316355i \(-0.102459\pi\)
0.200349 + 0.979725i \(0.435792\pi\)
\(314\) −13.1632 −0.742844
\(315\) 0 0
\(316\) 4.00000i 0.225018i
\(317\) −4.58258 + 7.93725i −0.257383 + 0.445801i −0.965540 0.260254i \(-0.916194\pi\)
0.708157 + 0.706055i \(0.249527\pi\)
\(318\) 3.74166 + 6.48074i 0.209822 + 0.363422i
\(319\) −4.66376 2.40818i −0.261121 0.134832i
\(320\) 2.68085 + 1.54779i 0.149864 + 0.0865239i
\(321\) −11.3598 −0.634043
\(322\) 0 0
\(323\) 6.74773 0.375454
\(324\) 2.70871 4.69163i 0.150484 0.260646i
\(325\) 1.48036 + 2.56407i 0.0821158 + 0.142229i
\(326\) −3.46410 + 2.00000i −0.191859 + 0.110770i
\(327\) 5.54506 9.60433i 0.306643 0.531121i
\(328\) 9.93280i 0.548447i
\(329\) 0 0
\(330\) 5.58258 3.58258i 0.307311 0.197214i
\(331\) 11.7913 20.4231i 0.648108 1.12256i −0.335467 0.942052i \(-0.608894\pi\)
0.983574 0.180504i \(-0.0577727\pi\)
\(332\) 6.44677 + 11.1661i 0.353812 + 0.612821i
\(333\) −4.62614 8.01270i −0.253511 0.439093i
\(334\) 1.11905 + 0.646084i 0.0612317 + 0.0353521i
\(335\) 23.4724i 1.28244i
\(336\) 0 0
\(337\) 10.8348i 0.590212i 0.955465 + 0.295106i \(0.0953549\pi\)
−0.955465 + 0.295106i \(0.904645\pi\)
\(338\) −10.8968 6.29129i −0.592709 0.342201i
\(339\) 6.01362 3.47197i 0.326615 0.188571i
\(340\) 10.0308 5.79129i 0.543997 0.314077i
\(341\) −1.34497 28.6262i −0.0728344 1.55019i
\(342\) 4.65743i 0.251845i
\(343\) 0 0
\(344\) 7.16515 0.386319
\(345\) 4.00000 6.92820i 0.215353 0.373002i
\(346\) −9.27837 + 5.35687i −0.498808 + 0.287987i
\(347\) −16.5975 + 9.58258i −0.891001 + 0.514420i −0.874270 0.485440i \(-0.838659\pi\)
−0.0167312 + 0.999860i \(0.505326\pi\)
\(348\) −0.511238 + 0.885491i −0.0274052 + 0.0474673i
\(349\) 24.1185 1.29103 0.645517 0.763746i \(-0.276642\pi\)
0.645517 + 0.763746i \(0.276642\pi\)
\(350\) 0 0
\(351\) 2.33030i 0.124382i
\(352\) −0.155657 3.31297i −0.00829654 0.176582i
\(353\) 6.48074 3.74166i 0.344935 0.199148i −0.317517 0.948253i \(-0.602849\pi\)
0.662452 + 0.749104i \(0.269516\pi\)
\(354\) −0.361500 + 0.208712i −0.0192135 + 0.0110929i
\(355\) −5.36169 3.09557i −0.284569 0.164296i
\(356\) 9.79796i 0.519291i
\(357\) 0 0
\(358\) 11.1652i 0.590097i
\(359\) 8.29875 + 4.79129i 0.437991 + 0.252875i 0.702745 0.711442i \(-0.251957\pi\)
−0.264754 + 0.964316i \(0.585291\pi\)
\(360\) 3.99728 + 6.92349i 0.210675 + 0.364900i
\(361\) 7.87386 + 13.6379i 0.414414 + 0.717786i
\(362\) −2.70511 + 4.68539i −0.142177 + 0.246258i
\(363\) −6.46084 2.96073i −0.339106 0.155398i
\(364\) 0 0
\(365\) 49.9129i 2.61256i
\(366\) −0.626136 + 1.08450i −0.0327287 + 0.0566877i
\(367\) 18.2064 10.5115i 0.950366 0.548694i 0.0571714 0.998364i \(-0.481792\pi\)
0.893195 + 0.449670i \(0.148459\pi\)
\(368\) −2.00000 3.46410i −0.104257 0.180579i
\(369\) 12.8261 22.2155i 0.667701 1.15649i
\(370\) 11.0901 0.576548
\(371\) 0 0
\(372\) −5.58258 −0.289443
\(373\) −8.29875 4.79129i −0.429693 0.248083i 0.269523 0.962994i \(-0.413134\pi\)
−0.699216 + 0.714911i \(0.746467\pi\)
\(374\) −11.0265 5.69361i −0.570165 0.294410i
\(375\) 0.417424 + 0.723000i 0.0215557 + 0.0373356i
\(376\) −4.96640 + 8.60206i −0.256123 + 0.443617i
\(377\) 1.02248i 0.0526602i
\(378\) 0 0
\(379\) −22.3303 −1.14703 −0.573515 0.819195i \(-0.694421\pi\)
−0.573515 + 0.819195i \(0.694421\pi\)
\(380\) −4.83465 2.79129i −0.248012 0.143190i
\(381\) −1.15732 2.00454i −0.0592914 0.102696i
\(382\) 15.5885 9.00000i 0.797575 0.460480i
\(383\) −17.0873 9.86538i −0.873122 0.504097i −0.00473782 0.999989i \(-0.501508\pi\)
−0.868385 + 0.495891i \(0.834841\pi\)
\(384\) −0.646084 −0.0329703
\(385\) 0 0
\(386\) 16.3303 0.831191
\(387\) 16.0254 + 9.25227i 0.814617 + 0.470319i
\(388\) 7.36623 4.25290i 0.373964 0.215908i
\(389\) −5.00000 8.66025i −0.253510 0.439092i 0.710980 0.703213i \(-0.248252\pi\)
−0.964490 + 0.264120i \(0.914918\pi\)
\(390\) −1.11905 0.646084i −0.0566653 0.0327157i
\(391\) −14.9666 −0.756895
\(392\) 0 0
\(393\) 10.8348i 0.546546i
\(394\) −4.37386 + 7.57575i −0.220352 + 0.381661i
\(395\) −6.19115 10.7234i −0.311510 0.539552i
\(396\) 3.92986 7.61071i 0.197483 0.382452i
\(397\) 23.8940 + 13.7952i 1.19921 + 0.692363i 0.960379 0.278699i \(-0.0899030\pi\)
0.238829 + 0.971062i \(0.423236\pi\)
\(398\) −9.66311 −0.484368
\(399\) 0 0
\(400\) −4.58258 −0.229129
\(401\) −3.79129 + 6.56670i −0.189328 + 0.327926i −0.945026 0.326994i \(-0.893964\pi\)
0.755698 + 0.654920i \(0.227298\pi\)
\(402\) 2.44949 + 4.24264i 0.122169 + 0.211604i
\(403\) −4.83465 + 2.79129i −0.240831 + 0.139044i
\(404\) −5.86811 + 10.1639i −0.291949 + 0.505671i
\(405\) 16.7700i 0.833310i
\(406\) 0 0
\(407\) −6.41742 10.0000i −0.318100 0.495682i
\(408\) −1.20871 + 2.09355i −0.0598402 + 0.103646i
\(409\) 2.51691 + 4.35942i 0.124453 + 0.215559i 0.921519 0.388333i \(-0.126949\pi\)
−0.797066 + 0.603892i \(0.793616\pi\)
\(410\) 15.3739 + 26.6283i 0.759261 + 1.31508i
\(411\) 1.77098 + 1.02248i 0.0873561 + 0.0504350i
\(412\) 6.05630i 0.298373i
\(413\) 0 0
\(414\) 10.3303i 0.507707i
\(415\) −34.5656 19.9564i −1.69676 0.979623i
\(416\) −0.559525 + 0.323042i −0.0274330 + 0.0158384i
\(417\) −8.66025 + 5.00000i −0.424094 + 0.244851i
\(418\) 0.280712 + 5.97463i 0.0137301 + 0.292229i
\(419\) 13.0284i 0.636478i 0.948011 + 0.318239i \(0.103091\pi\)
−0.948011 + 0.318239i \(0.896909\pi\)
\(420\) 0 0
\(421\) 7.58258 0.369552 0.184776 0.982781i \(-0.440844\pi\)
0.184776 + 0.982781i \(0.440844\pi\)
\(422\) −8.37386 + 14.5040i −0.407633 + 0.706042i
\(423\) −22.2155 + 12.8261i −1.08015 + 0.623627i
\(424\) −10.0308 + 5.79129i −0.487139 + 0.281250i
\(425\) −8.57321 + 14.8492i −0.415862 + 0.720294i
\(426\) 1.29217 0.0626057
\(427\) 0 0
\(428\) 17.5826i 0.849886i
\(429\) 0.0649750 + 1.38291i 0.00313702 + 0.0667677i
\(430\) −19.2087 + 11.0901i −0.926324 + 0.534813i
\(431\) −24.1733 + 13.9564i −1.16439 + 0.672258i −0.952351 0.305004i \(-0.901342\pi\)
−0.212034 + 0.977262i \(0.568009\pi\)
\(432\) −3.12359 1.80341i −0.150284 0.0867664i
\(433\) 35.5850i 1.71011i 0.518540 + 0.855054i \(0.326476\pi\)
−0.518540 + 0.855054i \(0.673524\pi\)
\(434\) 0 0
\(435\) 3.16515i 0.151757i
\(436\) 14.8655 + 8.58258i 0.711926 + 0.411031i
\(437\) 3.60681 + 6.24718i 0.172537 + 0.298843i
\(438\) −5.20871 9.02175i −0.248882 0.431076i
\(439\) −8.64064 + 14.9660i −0.412395 + 0.714289i −0.995151 0.0983579i \(-0.968641\pi\)
0.582756 + 0.812647i \(0.301974\pi\)
\(440\) 5.54506 + 8.64064i 0.264351 + 0.411926i
\(441\) 0 0
\(442\) 2.41742i 0.114985i
\(443\) −7.58258 + 13.1334i −0.360259 + 0.623987i −0.988003 0.154433i \(-0.950645\pi\)
0.627744 + 0.778420i \(0.283978\pi\)
\(444\) −2.00454 + 1.15732i −0.0951313 + 0.0549241i
\(445\) 15.1652 + 26.2668i 0.718897 + 1.24517i
\(446\) −8.06198 + 13.9638i −0.381746 + 0.661203i
\(447\) 9.04517 0.427822
\(448\) 0 0
\(449\) 31.1652 1.47077 0.735387 0.677647i \(-0.237000\pi\)
0.735387 + 0.677647i \(0.237000\pi\)
\(450\) −10.2493 5.91742i −0.483156 0.278950i
\(451\) 15.1146 29.2714i 0.711717 1.37834i
\(452\) 5.37386 + 9.30780i 0.252765 + 0.437802i
\(453\) 1.80341 3.12359i 0.0847314 0.146759i
\(454\) 0.511238i 0.0239936i
\(455\) 0 0
\(456\) 1.16515 0.0545632
\(457\) −28.7219 16.5826i −1.34355 0.775700i −0.356225 0.934400i \(-0.615936\pi\)
−0.987327 + 0.158700i \(0.949270\pi\)
\(458\) 2.83995 + 4.91895i 0.132702 + 0.229847i
\(459\) −11.6874 + 6.74773i −0.545521 + 0.314957i
\(460\) 10.7234 + 6.19115i 0.499980 + 0.288664i
\(461\) 30.0400 1.39910 0.699550 0.714583i \(-0.253384\pi\)
0.699550 + 0.714583i \(0.253384\pi\)
\(462\) 0 0
\(463\) 5.16515 0.240045 0.120022 0.992771i \(-0.461703\pi\)
0.120022 + 0.992771i \(0.461703\pi\)
\(464\) −1.37055 0.791288i −0.0636262 0.0367346i
\(465\) 14.9660 8.64064i 0.694033 0.400700i
\(466\) 13.5826 + 23.5257i 0.629201 + 1.08981i
\(467\) 10.1639 + 5.86811i 0.470327 + 0.271544i 0.716377 0.697714i \(-0.245799\pi\)
−0.246049 + 0.969257i \(0.579133\pi\)
\(468\) −1.66856 −0.0771292
\(469\) 0 0
\(470\) 30.7477i 1.41829i
\(471\) −4.25227 + 7.36515i −0.195934 + 0.339368i
\(472\) −0.323042 0.559525i −0.0148692 0.0257542i
\(473\) 21.1153 + 10.9031i 0.970883 + 0.501324i
\(474\) 2.23810 + 1.29217i 0.102799 + 0.0593512i
\(475\) 8.26424 0.379190
\(476\) 0 0
\(477\) −29.9129 −1.36962
\(478\) 4.20871 7.28970i 0.192502 0.333423i
\(479\) −15.4779 26.8085i −0.707202 1.22491i −0.965891 0.258949i \(-0.916624\pi\)
0.258689 0.965961i \(-0.416709\pi\)
\(480\) 1.73205 1.00000i 0.0790569 0.0456435i
\(481\) −1.15732 + 2.00454i −0.0527693 + 0.0913992i
\(482\) 3.47197i 0.158144i
\(483\) 0 0
\(484\) 4.58258 10.0000i 0.208299 0.454545i
\(485\) −13.1652 + 22.8027i −0.597799 + 1.03542i
\(486\) −7.16027 12.4020i −0.324797 0.562564i
\(487\) −10.7477 18.6156i −0.487026 0.843554i 0.512863 0.858471i \(-0.328585\pi\)
−0.999889 + 0.0149168i \(0.995252\pi\)
\(488\) −1.67858 0.969126i −0.0759855 0.0438703i
\(489\) 2.58434i 0.116868i
\(490\) 0 0
\(491\) 33.4955i 1.51163i 0.654786 + 0.755814i \(0.272759\pi\)
−0.654786 + 0.755814i \(0.727241\pi\)
\(492\) −5.55765 3.20871i −0.250558 0.144660i
\(493\) −5.12813 + 2.96073i −0.230959 + 0.133344i
\(494\) 1.00905 0.582576i 0.0453993 0.0262113i
\(495\) 1.24441 + 26.4857i 0.0559319 + 1.19044i
\(496\) 8.64064i 0.387976i
\(497\) 0 0
\(498\) 8.33030 0.373290
\(499\) 8.95644 15.5130i 0.400945 0.694458i −0.592895 0.805280i \(-0.702015\pi\)
0.993840 + 0.110822i \(0.0353484\pi\)
\(500\) −1.11905 + 0.646084i −0.0500454 + 0.0288937i
\(501\) 0.723000 0.417424i 0.0323013 0.0186491i
\(502\) −12.0593 + 20.8872i −0.538231 + 0.932243i
\(503\) −17.0116 −0.758509 −0.379254 0.925292i \(-0.623820\pi\)
−0.379254 + 0.925292i \(0.623820\pi\)
\(504\) 0 0
\(505\) 36.3303i 1.61668i
\(506\) −0.622627 13.2519i −0.0276792 0.589118i
\(507\) −7.04027 + 4.06470i −0.312669 + 0.180520i
\(508\) 3.10260 1.79129i 0.137656 0.0794755i
\(509\) −0.676305 0.390465i −0.0299767 0.0173070i 0.484937 0.874549i \(-0.338843\pi\)
−0.514913 + 0.857242i \(0.672176\pi\)
\(510\) 7.48331i 0.331367i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 5.63310 + 3.25227i 0.248708 + 0.143591i
\(514\) 2.44949 + 4.24264i 0.108042 + 0.187135i
\(515\) 9.37386 + 16.2360i 0.413062 + 0.715444i
\(516\) 2.31464 4.00908i 0.101897 0.176490i
\(517\) −27.7253 + 17.7925i −1.21936 + 0.782514i
\(518\) 0 0
\(519\) 6.92197i 0.303841i
\(520\) 1.00000 1.73205i 0.0438529 0.0759555i
\(521\) −24.3368 + 14.0509i −1.06621 + 0.615579i −0.927145 0.374703i \(-0.877745\pi\)
−0.139070 + 0.990283i \(0.544411\pi\)
\(522\) −2.04356 3.53955i −0.0894442 0.154922i
\(523\) 7.22770 12.5187i 0.316045 0.547406i −0.663614 0.748075i \(-0.730978\pi\)
0.979659 + 0.200669i \(0.0643116\pi\)
\(524\) 16.7700 0.732602
\(525\) 0 0
\(526\) −8.33030 −0.363218
\(527\) −27.9989 16.1652i −1.21965 0.704165i
\(528\) −1.90397 0.983134i −0.0828598 0.0427854i
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 17.9274 31.0511i 0.778715 1.34877i
\(531\) 1.66856i 0.0724094i
\(532\) 0 0
\(533\) −6.41742 −0.277970
\(534\) −5.48220 3.16515i −0.237238 0.136969i
\(535\) 27.2141 + 47.1362i 1.17657 + 2.03787i
\(536\) −6.56670 + 3.79129i −0.283638 + 0.163759i
\(537\) −6.24718 3.60681i −0.269586 0.155645i
\(538\) −16.5003 −0.711380
\(539\) 0 0
\(540\) 11.1652 0.480472
\(541\) 31.8245 + 18.3739i 1.36824 + 0.789954i 0.990703 0.136040i \(-0.0434377\pi\)
0.377537 + 0.925994i \(0.376771\pi\)
\(542\) 4.24264 2.44949i 0.182237 0.105215i
\(543\) 1.74773 + 3.02715i 0.0750021 + 0.129908i
\(544\) −3.24037 1.87083i −0.138930 0.0802111i
\(545\) −53.1360 −2.27610
\(546\) 0 0
\(547\) 24.7477i 1.05814i −0.848579 0.529068i \(-0.822542\pi\)
0.848579 0.529068i \(-0.177458\pi\)
\(548\) −1.58258 + 2.74110i −0.0676043 + 0.117094i
\(549\) −2.50284 4.33505i −0.106819 0.185015i
\(550\) −13.5046 6.97322i −0.575838 0.297339i
\(551\) 2.47166 + 1.42701i 0.105296 + 0.0607928i
\(552\) −2.58434 −0.109997
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 3.58258 6.20520i 0.152072 0.263396i
\(556\) −7.73893 13.4042i −0.328204 0.568466i
\(557\) −31.1015 + 17.9564i −1.31781 + 0.760839i −0.983376 0.181580i \(-0.941879\pi\)
−0.334435 + 0.942419i \(0.608546\pi\)
\(558\) 11.1575 19.3254i 0.472337 0.818111i
\(559\) 4.62929i 0.195798i
\(560\) 0 0
\(561\) −6.74773 + 4.33030i −0.284889 + 0.182826i
\(562\) −5.58258 + 9.66930i −0.235487 + 0.407875i
\(563\) −11.8570 20.5369i −0.499712 0.865527i 0.500288 0.865859i \(-0.333228\pi\)
−1.00000 0.000332178i \(0.999894\pi\)
\(564\) 3.20871 + 5.55765i 0.135111 + 0.234019i
\(565\) −28.8130 16.6352i −1.21217 0.699848i
\(566\) 18.0622i 0.759211i
\(567\) 0 0
\(568\) 2.00000i 0.0839181i
\(569\) −34.2041 19.7477i −1.43391 0.827868i −0.436493 0.899708i \(-0.643780\pi\)
−0.997416 + 0.0718399i \(0.977113\pi\)
\(570\) −3.12359 + 1.80341i −0.130833 + 0.0755364i
\(571\) −4.83465 + 2.79129i −0.202324 + 0.116812i −0.597739 0.801691i \(-0.703934\pi\)
0.395415 + 0.918503i \(0.370601\pi\)
\(572\) −2.14046 + 0.100567i −0.0894970 + 0.00420493i
\(573\) 11.6295i 0.485830i
\(574\) 0 0
\(575\) −18.3303 −0.764426
\(576\) 1.29129 2.23658i 0.0538037 0.0931907i
\(577\) 25.6894 14.8318i 1.06946 0.617455i 0.141429 0.989948i \(-0.454830\pi\)
0.928035 + 0.372493i \(0.121497\pi\)
\(578\) 2.59808 1.50000i 0.108066 0.0623918i
\(579\) 5.27537 9.13721i 0.219237 0.379730i
\(580\) 4.89898 0.203419
\(581\) 0 0
\(582\) 5.49545i 0.227794i
\(583\) −38.3727 + 1.80291i −1.58924 + 0.0746688i
\(584\) 13.9638 8.06198i 0.577824 0.333607i
\(585\) 4.47315 2.58258i 0.184942 0.106776i
\(586\) 21.7727 + 12.5705i 0.899423 + 0.519282i
\(587\) 39.0851i 1.61322i −0.591087 0.806608i \(-0.701301\pi\)
0.591087 0.806608i \(-0.298699\pi\)
\(588\) 0 0
\(589\) 15.5826i 0.642069i
\(590\) 1.73205 + 1.00000i 0.0713074 + 0.0411693i
\(591\) 2.82588 + 4.89457i 0.116241 + 0.201336i
\(592\) −1.79129 3.10260i −0.0736215 0.127516i
\(593\) 7.41589 12.8447i 0.304534 0.527469i −0.672623 0.739985i \(-0.734833\pi\)
0.977158 + 0.212516i \(0.0681659\pi\)
\(594\) −6.46084 10.0677i −0.265091 0.413081i
\(595\) 0 0
\(596\) 14.0000i 0.573462i
\(597\) −3.12159 + 5.40675i −0.127758 + 0.221284i
\(598\) −2.23810 + 1.29217i −0.0915227 + 0.0528407i
\(599\) 10.5826 + 18.3296i 0.432392 + 0.748925i 0.997079 0.0763801i \(-0.0243362\pi\)
−0.564686 + 0.825306i \(0.691003\pi\)
\(600\) −1.48036 + 2.56407i −0.0604356 + 0.104678i
\(601\) 21.0229 0.857543 0.428772 0.903413i \(-0.358947\pi\)
0.428772 + 0.903413i \(0.358947\pi\)
\(602\) 0 0
\(603\) −19.5826 −0.797464
\(604\) 4.83465 + 2.79129i 0.196719 + 0.113576i
\(605\) 3.19269 + 33.9013i 0.129801 + 1.37828i
\(606\) 3.79129 + 6.56670i 0.154011 + 0.266754i
\(607\) −1.02248 + 1.77098i −0.0415010 + 0.0718819i −0.886030 0.463628i \(-0.846547\pi\)
0.844529 + 0.535510i \(0.179881\pi\)
\(608\) 1.80341i 0.0731378i
\(609\) 0 0
\(610\) 6.00000 0.242933
\(611\) 5.55765 + 3.20871i 0.224839 + 0.129811i
\(612\) −4.83156 8.36850i −0.195304 0.338277i
\(613\) 27.6374 15.9564i 1.11626 0.644475i 0.175818 0.984423i \(-0.443743\pi\)
0.940444 + 0.339948i \(0.110410\pi\)
\(614\) −9.16159 5.28944i −0.369732 0.213465i
\(615\) 19.8656 0.801059
\(616\) 0 0
\(617\) −19.9129 −0.801662 −0.400831 0.916152i \(-0.631279\pi\)
−0.400831 + 0.916152i \(0.631279\pi\)
\(618\) −3.38865 1.95644i −0.136312 0.0786995i
\(619\) −15.5255 + 8.96368i −0.624024 + 0.360281i −0.778434 0.627726i \(-0.783986\pi\)
0.154410 + 0.988007i \(0.450652\pi\)
\(620\) 13.3739 + 23.1642i 0.537107 + 0.930297i
\(621\) −12.4944 7.21362i −0.501382 0.289473i
\(622\) 5.03383 0.201838
\(623\) 0 0
\(624\) 0.417424i 0.0167103i
\(625\) 13.4564 23.3072i 0.538258 0.932289i
\(626\) 11.7362 + 20.3277i 0.469073 + 0.812459i
\(627\) 3.43364 + 1.77299i 0.137126 + 0.0708064i
\(628\) −11.3997 6.58161i −0.454897 0.262635i
\(629\) −13.4048 −0.534483
\(630\) 0 0
\(631\) 13.1652 0.524096 0.262048 0.965055i \(-0.415602\pi\)
0.262048 + 0.965055i \(0.415602\pi\)
\(632\) −2.00000 + 3.46410i −0.0795557 + 0.137795i
\(633\) 5.41022 + 9.37077i 0.215037 + 0.372455i
\(634\) −7.93725 + 4.58258i −0.315229 + 0.181997i
\(635\) −5.54506 + 9.60433i −0.220049 + 0.381136i
\(636\) 7.48331i 0.296733i
\(637\) 0 0
\(638\) −2.83485 4.41742i −0.112233 0.174888i
\(639\) −2.58258 + 4.47315i −0.102165 + 0.176955i
\(640\) 1.54779 + 2.68085i 0.0611816 + 0.105970i
\(641\) 7.95644 + 13.7810i 0.314260 + 0.544315i 0.979280 0.202511i \(-0.0649101\pi\)
−0.665020 + 0.746826i \(0.731577\pi\)
\(642\) −9.83789 5.67991i −0.388271 0.224168i
\(643\) 9.42157i 0.371550i −0.982592 0.185775i \(-0.940520\pi\)
0.982592 0.185775i \(-0.0594796\pi\)
\(644\) 0 0
\(645\) 14.3303i 0.564255i
\(646\) 5.84370 + 3.37386i 0.229917 + 0.132743i
\(647\) −26.0397 + 15.0341i −1.02373 + 0.591050i −0.915182 0.403042i \(-0.867953\pi\)
−0.108546 + 0.994091i \(0.534620\pi\)
\(648\) 4.69163 2.70871i 0.184305 0.106408i
\(649\) −0.100567 2.14046i −0.00394761 0.0840203i
\(650\) 2.96073i 0.116129i
\(651\) 0 0
\(652\) −4.00000 −0.156652
\(653\) 3.00000 5.19615i 0.117399 0.203341i −0.801337 0.598213i \(-0.795878\pi\)
0.918736 + 0.394872i \(0.129211\pi\)
\(654\) 9.60433 5.54506i 0.375559 0.216829i
\(655\) −44.9579 + 25.9564i −1.75665 + 1.01420i
\(656\) 4.96640 8.60206i 0.193905 0.335854i
\(657\) 41.6413 1.62458
\(658\) 0 0
\(659\) 6.33030i 0.246594i −0.992370 0.123297i \(-0.960653\pi\)
0.992370 0.123297i \(-0.0393467\pi\)
\(660\) 6.62594 0.311314i 0.257914 0.0121179i
\(661\) 7.15705 4.13212i 0.278377 0.160721i −0.354312 0.935127i \(-0.615285\pi\)
0.632688 + 0.774407i \(0.281951\pi\)
\(662\) 20.4231 11.7913i 0.793767 0.458281i
\(663\) 1.35261 + 0.780929i 0.0525310 + 0.0303288i
\(664\) 12.8935i 0.500366i
\(665\) 0 0
\(666\) 9.25227i 0.358518i
\(667\) −5.48220 3.16515i −0.212272 0.122555i
\(668\) 0.646084 + 1.11905i 0.0249977 + 0.0432973i
\(669\) 5.20871 + 9.02175i 0.201380 + 0.348801i
\(670\) 11.7362 20.3277i 0.453409 0.785328i
\(671\) −3.47197 5.41022i −0.134034 0.208859i
\(672\) 0 0
\(673\) 18.3303i 0.706581i −0.935514 0.353291i \(-0.885063\pi\)
0.935514 0.353291i \(-0.114937\pi\)
\(674\) −5.41742 + 9.38325i −0.208671 + 0.361429i
\(675\) −14.3141 + 8.26424i −0.550950 + 0.318091i
\(676\) −6.29129 10.8968i −0.241973 0.419109i
\(677\) −2.63769 + 4.56861i −0.101375 + 0.175586i −0.912251 0.409631i \(-0.865657\pi\)
0.810877 + 0.585217i \(0.198991\pi\)
\(678\) 6.94393 0.266680
\(679\) 0 0
\(680\) 11.5826 0.444172
\(681\) 0.286051 + 0.165151i 0.0109615 + 0.00632862i
\(682\) 13.1483 25.4635i 0.503475 0.975047i
\(683\) 4.74773 + 8.22330i 0.181667 + 0.314656i 0.942448 0.334352i \(-0.108517\pi\)
−0.760782 + 0.649008i \(0.775184\pi\)
\(684\) −2.32872 + 4.03345i −0.0890407 + 0.154223i
\(685\) 9.79796i 0.374361i
\(686\) 0 0
\(687\) 3.66970 0.140008
\(688\) 6.20520 + 3.58258i 0.236571 + 0.136584i
\(689\) 3.74166 + 6.48074i 0.142546 + 0.246897i
\(690\) 6.92820 4.00000i 0.263752 0.152277i
\(691\) 3.44956 + 1.99160i 0.131227 + 0.0757641i 0.564177 0.825654i \(-0.309194\pi\)
−0.432949 + 0.901418i \(0.642527\pi\)
\(692\) −10.7137 −0.407275
\(693\) 0 0
\(694\) −19.1652 −0.727499
\(695\) 41.4938 + 23.9564i 1.57395 + 0.908720i
\(696\) −0.885491 + 0.511238i −0.0335644 + 0.0193784i
\(697\) −18.5826 32.1860i −0.703865 1.21913i
\(698\) 20.8872 + 12.0593i 0.790594 + 0.456449i
\(699\) 17.5510 0.663838
\(700\) 0 0
\(701\) 12.3303i 0.465709i 0.972512 + 0.232855i \(0.0748066\pi\)
−0.972512 + 0.232855i \(0.925193\pi\)
\(702\) −1.16515 + 2.01810i −0.0439758 + 0.0761683i
\(703\) 3.23042 + 5.59525i 0.121838 + 0.211029i
\(704\) 1.52168 2.94694i 0.0573506 0.111067i
\(705\) −17.2041 9.93280i −0.647945 0.374091i
\(706\) 7.48331 0.281638
\(707\) 0 0
\(708\) −0.417424 −0.0156878
\(709\) −26.1652 + 45.3194i −0.982653 + 1.70200i −0.330718 + 0.943730i \(0.607291\pi\)
−0.651935 + 0.758275i \(0.726042\pi\)
\(710\) −3.09557 5.36169i −0.116175 0.201221i
\(711\) −8.94630 + 5.16515i −0.335513 + 0.193708i
\(712\) 4.89898 8.48528i 0.183597 0.317999i
\(713\) 34.5625i 1.29438i
\(714\) 0 0
\(715\) 5.58258 3.58258i 0.208776 0.133981i
\(716\) 5.58258 9.66930i 0.208631 0.361359i
\(717\) −2.71918 4.70976i −0.101550 0.175889i
\(718\) 4.79129 + 8.29875i 0.178809 + 0.309707i
\(719\) 20.2109 + 11.6688i 0.753741 + 0.435172i 0.827044 0.562137i \(-0.190021\pi\)
−0.0733033 + 0.997310i \(0.523354\pi\)
\(720\) 7.99455i 0.297939i
\(721\) 0 0
\(722\) 15.7477i 0.586070i
\(723\) 1.94265 + 1.12159i 0.0722480 + 0.0417124i
\(724\) −4.68539 + 2.70511i −0.174131 + 0.100535i
\(725\) −6.28065 + 3.62614i −0.233258 + 0.134671i
\(726\) −4.11489 5.79448i −0.152718 0.215054i
\(727\) 37.5514i 1.39271i 0.717700 + 0.696353i \(0.245195\pi\)
−0.717700 + 0.696353i \(0.754805\pi\)
\(728\) 0 0
\(729\) 7.00000 0.259259
\(730\) −24.9564 + 43.2258i −0.923679 + 1.59986i
\(731\) 23.2177 13.4048i 0.858739 0.495793i
\(732\) −1.08450 + 0.626136i −0.0400843 + 0.0231427i
\(733\) −5.35687 + 9.27837i −0.197860 + 0.342704i −0.947834 0.318763i \(-0.896733\pi\)
0.749974 + 0.661467i \(0.230066\pi\)
\(734\) 21.0229 0.775971
\(735\) 0 0
\(736\) 4.00000i 0.147442i
\(737\) −25.1208 + 1.18028i −0.925338 + 0.0434762i
\(738\) 22.2155 12.8261i 0.817763 0.472136i
\(739\) 1.37055 0.791288i 0.0504165 0.0291080i −0.474580 0.880212i \(-0.657400\pi\)
0.524996 + 0.851104i \(0.324067\pi\)
\(740\) 9.60433 + 5.54506i 0.353062 + 0.203841i
\(741\) 0.752785i 0.0276543i
\(742\) 0 0
\(743\) 1.91288i 0.0701767i 0.999384 + 0.0350884i \(0.0111713\pi\)
−0.999384 + 0.0350884i \(0.988829\pi\)
\(744\) −4.83465 2.79129i −0.177247 0.102334i
\(745\) −21.6690 37.5318i −0.793891 1.37506i
\(746\) −4.79129 8.29875i −0.175422 0.303839i
\(747\) −16.6493 + 28.8374i −0.609165 + 1.05510i
\(748\) −6.70239 10.4440i −0.245063 0.381872i
\(749\) 0 0
\(750\) 0.834849i 0.0304844i
\(751\) 20.7477 35.9361i 0.757095 1.31133i −0.187231 0.982316i \(-0.559951\pi\)
0.944326 0.329012i \(-0.106716\pi\)
\(752\) −8.60206 + 4.96640i −0.313685 + 0.181106i
\(753\) 7.79129 + 13.4949i 0.283930 + 0.491782i
\(754\) −0.511238 + 0.885491i −0.0186182 + 0.0322477i
\(755\) −17.2813 −0.628930
\(756\) 0 0
\(757\) −30.8348 −1.12071 −0.560356 0.828252i \(-0.689336\pi\)
−0.560356 + 0.828252i \(0.689336\pi\)
\(758\) −19.3386 11.1652i −0.702410 0.405537i
\(759\) −7.61589 3.93254i −0.276439 0.142742i
\(760\) −2.79129 4.83465i −0.101251 0.175371i
\(761\) −14.1183 + 24.4536i −0.511787 + 0.886441i 0.488119 + 0.872777i \(0.337683\pi\)
−0.999907 + 0.0136645i \(0.995650\pi\)
\(762\) 2.31464i 0.0838507i
\(763\) 0 0
\(764\) 18.0000 0.651217
\(765\) 25.9053 + 14.9564i 0.936609 + 0.540751i
\(766\) −9.86538 17.0873i −0.356451 0.617391i
\(767\) −0.361500 + 0.208712i −0.0130530 + 0.00753616i
\(768\) −0.559525 0.323042i −0.0201901 0.0116568i
\(769\) −15.1015 −0.544573 −0.272287 0.962216i \(-0.587780\pi\)
−0.272287 + 0.962216i \(0.587780\pi\)
\(770\) 0 0
\(771\) 3.16515 0.113990
\(772\) 14.1425 + 8.16515i 0.508998 + 0.293870i
\(773\) 8.69447 5.01975i 0.312718 0.180548i −0.335424 0.942067i \(-0.608880\pi\)
0.648142 + 0.761519i \(0.275546\pi\)
\(774\) 9.25227 + 16.0254i 0.332566 + 0.576021i
\(775\) −34.2915 19.7982i −1.23179 0.711172i
\(776\) 8.50579 0.305340
\(777\) 0 0
\(778\) 10.0000i 0.358517i
\(779\) −8.95644 + 15.5130i −0.320898 + 0.555811i
\(780\) −0.646084 1.11905i −0.0231335 0.0400684i
\(781\) −3.04336 + 5.89389i −0.108900 + 0.210900i
\(782\) −12.9615 7.48331i −0.463502