Properties

Label 1078.2.i.b.901.3
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 901.3
Root \(-1.40721 - 0.140577i\) of defining polynomial
Character \(\chi\) \(=\) 1078.901
Dual form 1078.2.i.b.1011.3

$q$-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} +(3.31297 + 0.155657i) 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} +(1.90397 - 0.983134i) 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} +(1.52168 + 2.94694i) 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} +(-2.14046 - 0.100567i) 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} +(0.155657 - 3.31297i) 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
\(11\) 3.31297 + 0.155657i 0.998898 + 0.0469323i
\(12\) 0.559525 + 0.323042i 0.161521 + 0.0932542i
\(13\) −0.646084 −0.179191 −0.0895957 0.995978i \(-0.528557\pi\)
−0.0895957 + 0.995978i \(0.528557\pi\)
\(14\) 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 0.544872 0.838519i \(-0.316578\pi\)
−0.998615 + 0.0526138i \(0.983245\pi\)
\(18\) 2.23658 1.29129i 0.527166 0.304359i
\(19\) −0.901703 + 1.56180i −0.206865 + 0.358300i −0.950725 0.310035i \(-0.899659\pi\)
0.743860 + 0.668335i \(0.232993\pi\)
\(20\) 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 \(-0.953058\pi\)
0.989146 0.146938i \(-0.0469419\pi\)
\(30\) 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
\(33\) 1.90397 0.983134i 0.331439 0.171142i
\(34\) 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 \(-0.217436\pi\)
0.775622 + 0.631198i \(0.217436\pi\)
\(42\) 0 0
\(43\) 7.16515i 1.09268i 0.837565 + 0.546338i \(0.183978\pi\)
−0.837565 + 0.546338i \(0.816022\pi\)
\(44\) 1.52168 + 2.94694i 0.229402 + 0.444269i
\(45\) 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 −0.797291 0.603596i \(-0.793734\pi\)
0.921374 + 0.388676i \(0.127067\pi\)
\(62\) 8.64064 1.09736
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.73205 + 1.00000i 0.214834 + 0.124035i
\(66\) −2.14046 0.100567i −0.263472 0.0123790i
\(67\) 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 \(0.225901\pi\)
0.185019 + 0.982735i \(0.440765\pi\)
\(74\) 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 0.292306 0.956325i \(-0.405577\pi\)
−0.682048 + 0.731307i \(0.738911\pi\)
\(80\) 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 \(-0.750233\pi\)
−0.707625 + 0.706589i \(0.750233\pi\)
\(84\) 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
\(88\) 0.155657 3.31297i 0.0165931 0.353164i
\(89\) −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 \(-0.968193\pi\)
0.411114 0.911584i \(-0.365140\pi\)
\(102\) 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 0.999506 0.0314237i \(-0.0100041\pi\)
0.472539 + 0.881310i \(0.343337\pi\)
\(108\) −3.12359 + 1.80341i −0.300568 + 0.173533i
\(109\) −14.8655 + 8.58258i −1.42385 + 0.822062i −0.996626 0.0820827i \(-0.973843\pi\)
−0.427227 + 0.904144i \(0.640509\pi\)
\(110\) 4.71048 + 9.12248i 0.449127 + 0.869795i
\(111\) 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
\(121\) 10.9515 + 1.03137i 0.995595 + 0.0937612i
\(122\) −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 \(0.0508112\pi\)
−0.987286 + 0.158951i \(0.949189\pi\)
\(128\) 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 \(0.428361\pi\)
−0.955767 + 0.294124i \(0.904972\pi\)
\(132\) 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 \(-0.272075\pi\)
0.656408 + 0.754406i \(0.272075\pi\)
\(140\) 0 0
\(141\) 6.41742 0.540445
\(142\) −1.73205 1.00000i −0.145350 0.0839181i
\(143\) −2.14046 0.100567i −0.178994 0.00840987i
\(144\) −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 −0.0870170 0.996207i \(-0.527733\pi\)
−0.906249 + 0.422744i \(0.861067\pi\)
\(150\) −1.48036 2.56407i −0.120871 0.209355i
\(151\) −4.83465 + 2.79129i −0.393438 + 0.227152i −0.683649 0.729811i \(-0.739608\pi\)
0.290210 + 0.956963i \(0.406275\pi\)
\(152\) 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
\(165\) −6.62594 0.311314i −0.515829 0.0242357i
\(166\) 11.1661 + 6.44677i 0.866660 + 0.500366i
\(167\) −1.29217 −0.0999909 −0.0499955 0.998749i \(-0.515921\pi\)
−0.0499955 + 0.998749i \(0.515921\pi\)
\(168\) 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 −0.587308 0.809363i \(-0.699812\pi\)
0.994583 + 0.103942i \(0.0331457\pi\)
\(174\) 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
\(187\) −5.69361 11.0265i −0.416358 0.806334i
\(188\) 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 −0.913523 0.406787i \(-0.866649\pi\)
−0.104473 + 0.994528i \(0.533316\pi\)
\(194\) −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 \(-0.899127\pi\)
0.950205 0.311625i \(-0.100873\pi\)
\(198\) 7.61071 3.92986i 0.540869 0.279283i
\(199\) −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 \(-0.804426\pi\)
0.817111 0.576481i \(-0.195574\pi\)
\(212\) −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
\(220\) 0.481847 10.2555i 0.0324861 0.691429i
\(221\) 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 0.857418 0.514621i \(-0.172067\pi\)
−0.874384 + 0.485235i \(0.838734\pi\)
\(228\) −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 \(-0.984160\pi\)
−0.542458 0.840083i \(-0.682506\pi\)
\(234\) −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 \(0.0877641\pi\)
−0.962230 + 0.272239i \(0.912236\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) −1.73598 3.00681i −0.111825 0.193686i 0.804681 0.593707i \(-0.202336\pi\)
−0.916506 + 0.400021i \(0.869003\pi\)
\(242\) −8.96863 6.36897i −0.576525 0.409413i
\(243\) −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 −0.260803 0.965392i \(-0.583987\pi\)
0.705653 + 0.708558i \(0.250654\pi\)
\(264\) −0.983134 1.90397i −0.0605077 0.117181i
\(265\) 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 −0.930783 0.365573i \(-0.880873\pi\)
0.781987 + 0.623295i \(0.214206\pi\)
\(272\) 3.74166 0.226871
\(273\) 0 0
\(274\) 3.16515i 0.191214i
\(275\) 6.97322 + 13.5046i 0.420501 + 0.814358i
\(276\) −2.23810 + 1.29217i −0.134718 + 0.0777794i
\(277\) −1.73205 + 1.00000i −0.104069 + 0.0600842i −0.551131 0.834419i \(-0.685804\pi\)
0.447062 + 0.894503i \(0.352470\pi\)
\(278\) −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 \(-0.891929\pi\)
0.942917 0.333029i \(-0.108071\pi\)
\(282\) −5.55765 3.20871i −0.330953 0.191076i
\(283\) −9.03110 15.6423i −0.536843 0.929840i −0.999072 0.0430789i \(-0.986283\pi\)
0.462228 0.886761i \(-0.347050\pi\)
\(284\) 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 \(-0.762525\pi\)
−0.734376 + 0.678743i \(0.762525\pi\)
\(294\) 0 0
\(295\) 2.00000 0.116445
\(296\) 3.10260 + 1.79129i 0.180335 + 0.104116i
\(297\) −0.561425 + 11.9493i −0.0325772 + 0.693366i
\(298\) 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 \(-0.402384\pi\)
0.301885 + 0.953344i \(0.402384\pi\)
\(308\) 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
\(319\) 0.246339 5.24303i 0.0137923 0.293553i
\(320\) 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 \(-0.904645\pi\)
0.955465 0.295106i \(-0.0953549\pi\)
\(338\) 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
\(341\) −25.4635 + 13.1483i −1.37892 + 0.712021i
\(342\) 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 0.0167312 0.999860i \(-0.494674\pi\)
0.874270 + 0.485440i \(0.161341\pi\)
\(348\) 0.511238 0.885491i 0.0274052 0.0474673i
\(349\) −24.1185 −1.29103 −0.645517 0.763746i \(-0.723358\pi\)
−0.645517 + 0.763746i \(0.723358\pi\)
\(350\) 0 0
\(351\) 2.33030i 0.124382i
\(352\) 2.94694 1.52168i 0.157073 0.0811059i
\(353\) 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 0.264754 0.964316i \(-0.414709\pi\)
−0.702745 + 0.711442i \(0.748043\pi\)
\(360\) −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 0.699216 0.714911i \(-0.253533\pi\)
−0.269523 + 0.962994i \(0.586866\pi\)
\(374\) −0.582415 + 12.3960i −0.0301159 + 0.640982i
\(375\) 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
\(396\) −8.55600 0.401996i −0.429955 0.0202010i
\(397\) 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 0.797066 0.603892i \(-0.206384\pi\)
−0.921519 + 0.388333i \(0.873051\pi\)
\(410\) 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
\(418\) 5.31454 2.74421i 0.259943 0.134224i
\(419\) 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
\(429\) −1.23013 + 0.635187i −0.0593911 + 0.0306671i
\(430\) −19.2087 + 11.0901i −0.926324 + 0.534813i
\(431\) 24.1733 13.9564i 1.16439 0.672258i 0.212034 0.977262i \(-0.431991\pi\)
0.952351 + 0.305004i \(0.0986579\pi\)
\(432\) −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 −0.582756 0.812647i \(-0.698026\pi\)
0.995151 + 0.0983579i \(0.0313590\pi\)
\(440\) −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
\(451\) 32.9071 + 1.54611i 1.54953 + 0.0728034i
\(452\) 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 0.987327 0.158700i \(-0.0507302\pi\)
0.356225 + 0.934400i \(0.384064\pi\)
\(458\) −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 \(-0.746616\pi\)
−0.699550 + 0.714583i \(0.746616\pi\)
\(462\) 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
\(473\) −1.11530 + 23.7379i −0.0512818 + 1.09147i
\(474\) 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 \(0.0833761\pi\)
−0.258689 + 0.965961i \(0.583291\pi\)
\(480\) −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 \(-0.727241\pi\)
0.654786 0.755814i \(-0.272759\pi\)
\(492\) 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
\(495\) 23.5595 12.1652i 1.05892 0.546784i
\(496\) 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 \(-0.376180\pi\)
0.379254 + 0.925292i \(0.376180\pi\)
\(504\) 0 0
\(505\) 36.3303i 1.61668i
\(506\) 11.7878 6.08673i 0.524031 0.270588i
\(507\) −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 −0.979659 0.200669i \(-0.935688\pi\)
0.663614 + 0.748075i \(0.269022\pi\)
\(524\) −16.7700 −0.732602
\(525\) 0 0
\(526\) −8.33030 −0.363218
\(527\) 27.9989 + 16.1652i 1.21965 + 0.704165i
\(528\) −0.100567 + 2.14046i −0.00437663 + 0.0931514i
\(529\) 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 −0.377537 0.925994i \(-0.623229\pi\)
−0.990703 + 0.136040i \(0.956562\pi\)
\(542\) 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 \(0.177458\pi\)
−0.848579 + 0.529068i \(0.822542\pi\)
\(548\) −1.58258 + 2.74110i −0.0676043 + 0.117094i
\(549\) 2.50284 + 4.33505i 0.106819 + 0.185015i
\(550\) 0.713309 15.1819i 0.0304156 0.647360i
\(551\) 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 0.334435 0.942419i \(-0.391454\pi\)
0.983376 + 0.181580i \(0.0581211\pi\)
\(558\) −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 1.00000 0.000332178i \(-0.000105736\pi\)
−0.500288 + 0.865859i \(0.666772\pi\)
\(564\) 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 0.997416 0.0718399i \(-0.0228871\pi\)
0.436493 + 0.899708i \(0.356220\pi\)
\(570\) −3.12359 + 1.80341i −0.130833 + 0.0755364i
\(571\) 4.83465 2.79129i 0.202324 0.116812i −0.395415 0.918503i \(-0.629399\pi\)
0.597739 + 0.801691i \(0.296066\pi\)
\(572\) −0.983134 1.90397i −0.0411069 0.0796091i
\(573\) 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
\(583\) 17.6250 + 34.1332i 0.729953 + 1.41365i
\(584\) 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 −0.977158 0.212516i \(-0.931834\pi\)
0.672623 + 0.739985i \(0.265167\pi\)
\(594\) 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 \(-0.641053\pi\)
−0.428772 + 0.903413i \(0.641053\pi\)
\(602\) 0 0
\(603\) −19.5826 −0.797464
\(604\) −4.83465 2.79129i −0.196719 0.113576i
\(605\) −27.7630 19.7156i −1.12873 0.801553i
\(606\) 3.79129 + 6.56670i 0.154011 + 0.266754i
\(607\) 1.02248 1.77098i 0.0415010 0.0718819i −0.844529 0.535510i \(-0.820119\pi\)
0.886030 + 0.463628i \(0.153453\pi\)
\(608\) 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 −0.940444 0.339948i \(-0.889590\pi\)
−0.175818 + 0.984423i \(0.556257\pi\)
\(614\) −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
\(627\) −0.181364 + 3.86011i −0.00724297 + 0.154158i
\(628\) −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
\(649\) −1.90397 + 0.983134i −0.0747375 + 0.0385914i
\(650\) 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 \(0.0393467\pi\)
−0.992370 + 0.123297i \(0.960653\pi\)
\(660\) −3.04336 5.89389i −0.118463 0.229419i
\(661\) 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 \(0.114937\pi\)
−0.935514 + 0.353291i \(0.885063\pi\)
\(674\) −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 −0.810877 0.585217i \(-0.801009\pi\)
0.912251 + 0.409631i \(0.134343\pi\)
\(678\) −6.94393 −0.266680
\(679\) 0 0
\(680\) 11.5826 0.444172
\(681\) −0.286051 0.165151i −0.0109615 0.00632862i
\(682\) 28.6262 + 1.34497i 1.09615 + 0.0515017i
\(683\) 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 \(-0.925193\pi\)
0.972512 0.232855i \(-0.0748066\pi\)
\(702\) −1.16515 + 2.01810i −0.0439758 + 0.0761683i
\(703\) −3.23042 5.59525i −0.121838 0.211029i
\(704\) −3.31297 0.155657i −0.124862 0.00586654i
\(705\) −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
\(726\) −7.07561 0.666353i −0.262601 0.0247307i
\(727\) 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 −0.749974 0.661467i \(-0.769934\pi\)
0.947834 + 0.318763i \(0.103267\pi\)
\(734\) −21.0229 −0.775971
\(735\) 0 0
\(736\) 4.00000i 0.147442i
\(737\) 11.5383 + 22.3454i 0.425018 + 0.823105i
\(738\) 22.2155 12.8261i 0.817763 0.472136i
\(739\) −1.37055 + 0.791288i −0.0504165 + 0.0291080i −0.524996 0.851104i \(-0.675933\pi\)
0.474580 + 0.880212i \(0.342600\pi\)
\(740\) 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 \(-0.988829\pi\)
0.999384 0.0350884i \(-0.0111713\pi\)
\(744\) 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
\(759\) −0.402270 + 8.56183i −0.0146015 + 0.310775i
\(760\) −2.79129 4.83465i −0.101251 0.175371i
\(761\) 14.1183 24.4536i 0.511787 0.886441i −0.488119 0.872777i \(-0.662317\pi\)
0.999907 0.0136645i \(-0.00434969\pi\)
\(762\) 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 \(-0.412220\pi\)
0.272287 + 0.962216i \(0.412220\pi\)
\(770\) 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
\(781\) 6.62594 + 0.311314i 0.237095 + 0.0111397i
\(782\) −12.9615 7.48331i