Properties

Label 570.2.k.b.77.1
Level $570$
Weight $2$
Character 570.77
Analytic conductor $4.551$
Analytic rank $0$
Dimension $36$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 570.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.55147291521\)
Analytic rank: \(0\)
Dimension: \(36\)
Relative dimension: \(18\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 77.1
Character \(\chi\) \(=\) 570.77
Dual form 570.2.k.b.533.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.69896 - 0.336929i) q^{3} -1.00000i q^{4} +(2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 + 0.804978i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77296 + 1.14486i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-1.69896 - 0.336929i) q^{3} -1.00000i q^{4} +(2.14526 - 0.630765i) q^{5} +(1.43959 - 0.963104i) q^{6} +(0.804978 + 0.804978i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.77296 + 1.14486i) q^{9} +(-1.07091 + 1.96295i) q^{10} -3.15590i q^{11} +(-0.336929 + 1.69896i) q^{12} +(-2.72994 + 2.72994i) q^{13} -1.13841 q^{14} +(-3.85724 + 0.348848i) q^{15} -1.00000 q^{16} +(2.04213 - 2.04213i) q^{17} +(-2.77032 + 1.15124i) q^{18} -1.00000i q^{19} +(-0.630765 - 2.14526i) q^{20} +(-1.09641 - 1.63885i) q^{21} +(2.23156 + 2.23156i) q^{22} +(-1.82163 - 1.82163i) q^{23} +(-0.963104 - 1.43959i) q^{24} +(4.20427 - 2.70631i) q^{25} -3.86071i q^{26} +(-4.32542 - 2.87936i) q^{27} +(0.804978 - 0.804978i) q^{28} +5.49359 q^{29} +(2.48081 - 2.97415i) q^{30} +5.07413 q^{31} +(0.707107 - 0.707107i) q^{32} +(-1.06331 + 5.36176i) q^{33} +2.88801i q^{34} +(2.23464 + 1.21913i) q^{35} +(1.14486 - 2.77296i) q^{36} +(7.25575 + 7.25575i) q^{37} +(0.707107 + 0.707107i) q^{38} +(5.55786 - 3.71827i) q^{39} +(1.96295 + 1.07091i) q^{40} -6.31900i q^{41} +(1.93412 + 0.383563i) q^{42} +(0.643335 - 0.643335i) q^{43} -3.15590 q^{44} +(6.67085 + 0.706935i) q^{45} +2.57617 q^{46} +(3.22573 - 3.22573i) q^{47} +(1.69896 + 0.336929i) q^{48} -5.70402i q^{49} +(-1.05922 + 4.88652i) q^{50} +(-4.15756 + 2.78145i) q^{51} +(2.72994 + 2.72994i) q^{52} +(3.16898 + 3.16898i) q^{53} +(5.09455 - 1.02252i) q^{54} +(-1.99063 - 6.77022i) q^{55} +1.13841i q^{56} +(-0.336929 + 1.69896i) q^{57} +(-3.88456 + 3.88456i) q^{58} +1.26612 q^{59} +(0.348848 + 3.85724i) q^{60} +2.70369 q^{61} +(-3.58795 + 3.58795i) q^{62} +(1.31058 + 3.15376i) q^{63} +1.00000i q^{64} +(-4.13447 + 7.57837i) q^{65} +(-3.03946 - 4.54321i) q^{66} +(3.86878 + 3.86878i) q^{67} +(-2.04213 - 2.04213i) q^{68} +(2.48112 + 3.70864i) q^{69} +(-2.44219 + 0.718070i) q^{70} +0.944610i q^{71} +(1.15124 + 2.77032i) q^{72} +(3.61892 - 3.61892i) q^{73} -10.2612 q^{74} +(-8.05474 + 3.18138i) q^{75} -1.00000 q^{76} +(2.54043 - 2.54043i) q^{77} +(-1.30079 + 6.55921i) q^{78} -15.0264i q^{79} +(-2.14526 + 0.630765i) q^{80} +(6.37859 + 6.34930i) q^{81} +(4.46821 + 4.46821i) q^{82} +(-5.54904 - 5.54904i) q^{83} +(-1.63885 + 1.09641i) q^{84} +(3.09279 - 5.66900i) q^{85} +0.909814i q^{86} +(-9.33342 - 1.85095i) q^{87} +(2.23156 - 2.23156i) q^{88} -3.27340 q^{89} +(-5.21688 + 4.21712i) q^{90} -4.39508 q^{91} +(-1.82163 + 1.82163i) q^{92} +(-8.62077 - 1.70962i) q^{93} +4.56187i q^{94} +(-0.630765 - 2.14526i) q^{95} +(-1.43959 + 0.963104i) q^{96} +(2.89748 + 2.89748i) q^{97} +(4.03335 + 4.03335i) q^{98} +(3.61306 - 8.75117i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} + 20q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} + 16q^{21} - 4q^{22} + 16q^{25} - 44q^{27} + 20q^{28} + 32q^{30} - 24q^{31} - 4q^{33} + 4q^{36} - 8q^{40} + 12q^{42} - 8q^{43} + 28q^{45} - 16q^{46} - 4q^{48} + 40q^{51} - 8q^{52} - 36q^{55} - 4q^{57} + 44q^{58} + 16q^{60} - 120q^{61} - 12q^{63} + 80q^{67} - 36q^{70} + 44q^{73} + 4q^{75} - 36q^{76} - 64q^{78} + 36q^{81} + 8q^{82} - 24q^{85} - 28q^{87} - 4q^{88} + 44q^{90} - 72q^{93} - 4q^{96} + 92q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −1.69896 0.336929i −0.980897 0.194526i
\(4\) 1.00000i 0.500000i
\(5\) 2.14526 0.630765i 0.959389 0.282087i
\(6\) 1.43959 0.963104i 0.587712 0.393186i
\(7\) 0.804978 + 0.804978i 0.304253 + 0.304253i 0.842675 0.538422i \(-0.180979\pi\)
−0.538422 + 0.842675i \(0.680979\pi\)
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 2.77296 + 1.14486i 0.924319 + 0.381620i
\(10\) −1.07091 + 1.96295i −0.338651 + 0.620738i
\(11\) 3.15590i 0.951539i −0.879570 0.475769i \(-0.842170\pi\)
0.879570 0.475769i \(-0.157830\pi\)
\(12\) −0.336929 + 1.69896i −0.0972629 + 0.490449i
\(13\) −2.72994 + 2.72994i −0.757148 + 0.757148i −0.975802 0.218654i \(-0.929833\pi\)
0.218654 + 0.975802i \(0.429833\pi\)
\(14\) −1.13841 −0.304253
\(15\) −3.85724 + 0.348848i −0.995935 + 0.0900721i
\(16\) −1.00000 −0.250000
\(17\) 2.04213 2.04213i 0.495289 0.495289i −0.414679 0.909968i \(-0.636106\pi\)
0.909968 + 0.414679i \(0.136106\pi\)
\(18\) −2.77032 + 1.15124i −0.652970 + 0.271350i
\(19\) 1.00000i 0.229416i
\(20\) −0.630765 2.14526i −0.141043 0.479694i
\(21\) −1.09641 1.63885i −0.239256 0.357626i
\(22\) 2.23156 + 2.23156i 0.475769 + 0.475769i
\(23\) −1.82163 1.82163i −0.379835 0.379835i 0.491207 0.871043i \(-0.336556\pi\)
−0.871043 + 0.491207i \(0.836556\pi\)
\(24\) −0.963104 1.43959i −0.196593 0.293856i
\(25\) 4.20427 2.70631i 0.840854 0.541262i
\(26\) 3.86071i 0.757148i
\(27\) −4.32542 2.87936i −0.832428 0.554134i
\(28\) 0.804978 0.804978i 0.152127 0.152127i
\(29\) 5.49359 1.02013 0.510067 0.860134i \(-0.329620\pi\)
0.510067 + 0.860134i \(0.329620\pi\)
\(30\) 2.48081 2.97415i 0.452932 0.543004i
\(31\) 5.07413 0.911341 0.455671 0.890148i \(-0.349400\pi\)
0.455671 + 0.890148i \(0.349400\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) −1.06331 + 5.36176i −0.185099 + 0.933362i
\(34\) 2.88801i 0.495289i
\(35\) 2.23464 + 1.21913i 0.377723 + 0.206071i
\(36\) 1.14486 2.77296i 0.190810 0.462160i
\(37\) 7.25575 + 7.25575i 1.19284 + 1.19284i 0.976267 + 0.216570i \(0.0694871\pi\)
0.216570 + 0.976267i \(0.430513\pi\)
\(38\) 0.707107 + 0.707107i 0.114708 + 0.114708i
\(39\) 5.55786 3.71827i 0.889970 0.595400i
\(40\) 1.96295 + 1.07091i 0.310369 + 0.169326i
\(41\) 6.31900i 0.986862i −0.869785 0.493431i \(-0.835743\pi\)
0.869785 0.493431i \(-0.164257\pi\)
\(42\) 1.93412 + 0.383563i 0.298441 + 0.0591851i
\(43\) 0.643335 0.643335i 0.0981077 0.0981077i −0.656349 0.754457i \(-0.727900\pi\)
0.754457 + 0.656349i \(0.227900\pi\)
\(44\) −3.15590 −0.475769
\(45\) 6.67085 + 0.706935i 0.994432 + 0.105384i
\(46\) 2.57617 0.379835
\(47\) 3.22573 3.22573i 0.470521 0.470521i −0.431562 0.902083i \(-0.642037\pi\)
0.902083 + 0.431562i \(0.142037\pi\)
\(48\) 1.69896 + 0.336929i 0.245224 + 0.0486315i
\(49\) 5.70402i 0.814860i
\(50\) −1.05922 + 4.88652i −0.149796 + 0.691058i
\(51\) −4.15756 + 2.78145i −0.582174 + 0.389481i
\(52\) 2.72994 + 2.72994i 0.378574 + 0.378574i
\(53\) 3.16898 + 3.16898i 0.435292 + 0.435292i 0.890424 0.455132i \(-0.150408\pi\)
−0.455132 + 0.890424i \(0.650408\pi\)
\(54\) 5.09455 1.02252i 0.693281 0.139147i
\(55\) −1.99063 6.77022i −0.268416 0.912896i
\(56\) 1.13841i 0.152127i
\(57\) −0.336929 + 1.69896i −0.0446273 + 0.225033i
\(58\) −3.88456 + 3.88456i −0.510067 + 0.510067i
\(59\) 1.26612 0.164834 0.0824171 0.996598i \(-0.473736\pi\)
0.0824171 + 0.996598i \(0.473736\pi\)
\(60\) 0.348848 + 3.85724i 0.0450360 + 0.497968i
\(61\) 2.70369 0.346172 0.173086 0.984907i \(-0.444626\pi\)
0.173086 + 0.984907i \(0.444626\pi\)
\(62\) −3.58795 + 3.58795i −0.455671 + 0.455671i
\(63\) 1.31058 + 3.15376i 0.165118 + 0.397336i
\(64\) 1.00000i 0.125000i
\(65\) −4.13447 + 7.57837i −0.512818 + 0.939981i
\(66\) −3.03946 4.54321i −0.374131 0.559230i
\(67\) 3.86878 + 3.86878i 0.472647 + 0.472647i 0.902770 0.430123i \(-0.141530\pi\)
−0.430123 + 0.902770i \(0.641530\pi\)
\(68\) −2.04213 2.04213i −0.247645 0.247645i
\(69\) 2.48112 + 3.70864i 0.298692 + 0.446467i
\(70\) −2.44219 + 0.718070i −0.291897 + 0.0858257i
\(71\) 0.944610i 0.112105i 0.998428 + 0.0560523i \(0.0178514\pi\)
−0.998428 + 0.0560523i \(0.982149\pi\)
\(72\) 1.15124 + 2.77032i 0.135675 + 0.326485i
\(73\) 3.61892 3.61892i 0.423563 0.423563i −0.462866 0.886428i \(-0.653179\pi\)
0.886428 + 0.462866i \(0.153179\pi\)
\(74\) −10.2612 −1.19284
\(75\) −8.05474 + 3.18138i −0.930081 + 0.367354i
\(76\) −1.00000 −0.114708
\(77\) 2.54043 2.54043i 0.289509 0.289509i
\(78\) −1.30079 + 6.55921i −0.147285 + 0.742685i
\(79\) 15.0264i 1.69060i −0.534292 0.845300i \(-0.679422\pi\)
0.534292 0.845300i \(-0.320578\pi\)
\(80\) −2.14526 + 0.630765i −0.239847 + 0.0705217i
\(81\) 6.37859 + 6.34930i 0.708733 + 0.705477i
\(82\) 4.46821 + 4.46821i 0.493431 + 0.493431i
\(83\) −5.54904 5.54904i −0.609086 0.609086i 0.333621 0.942707i \(-0.391729\pi\)
−0.942707 + 0.333621i \(0.891729\pi\)
\(84\) −1.63885 + 1.09641i −0.178813 + 0.119628i
\(85\) 3.09279 5.66900i 0.335460 0.614889i
\(86\) 0.909814i 0.0981077i
\(87\) −9.33342 1.85095i −1.00065 0.198443i
\(88\) 2.23156 2.23156i 0.237885 0.237885i
\(89\) −3.27340 −0.346979 −0.173490 0.984836i \(-0.555504\pi\)
−0.173490 + 0.984836i \(0.555504\pi\)
\(90\) −5.21688 + 4.21712i −0.549908 + 0.444524i
\(91\) −4.39508 −0.460729
\(92\) −1.82163 + 1.82163i −0.189918 + 0.189918i
\(93\) −8.62077 1.70962i −0.893932 0.177279i
\(94\) 4.56187i 0.470521i
\(95\) −0.630765 2.14526i −0.0647151 0.220099i
\(96\) −1.43959 + 0.963104i −0.146928 + 0.0982964i
\(97\) 2.89748 + 2.89748i 0.294195 + 0.294195i 0.838735 0.544540i \(-0.183296\pi\)
−0.544540 + 0.838735i \(0.683296\pi\)
\(98\) 4.03335 + 4.03335i 0.407430 + 0.407430i
\(99\) 3.61306 8.75117i 0.363126 0.879526i
\(100\) −2.70631 4.20427i −0.270631 0.420427i
\(101\) 16.8808i 1.67971i 0.542813 + 0.839853i \(0.317359\pi\)
−0.542813 + 0.839853i \(0.682641\pi\)
\(102\) 0.973053 4.90662i 0.0963466 0.485828i
\(103\) 1.47281 1.47281i 0.145121 0.145121i −0.630814 0.775934i \(-0.717279\pi\)
0.775934 + 0.630814i \(0.217279\pi\)
\(104\) −3.86071 −0.378574
\(105\) −3.38581 2.82418i −0.330421 0.275612i
\(106\) −4.48161 −0.435292
\(107\) −8.84697 + 8.84697i −0.855269 + 0.855269i −0.990776 0.135507i \(-0.956734\pi\)
0.135507 + 0.990776i \(0.456734\pi\)
\(108\) −2.87936 + 4.32542i −0.277067 + 0.416214i
\(109\) 6.83921i 0.655077i 0.944838 + 0.327539i \(0.106219\pi\)
−0.944838 + 0.327539i \(0.893781\pi\)
\(110\) 6.19485 + 3.37968i 0.590656 + 0.322240i
\(111\) −9.88258 14.7719i −0.938013 1.40209i
\(112\) −0.804978 0.804978i −0.0760633 0.0760633i
\(113\) −14.3560 14.3560i −1.35050 1.35050i −0.885101 0.465400i \(-0.845911\pi\)
−0.465400 0.885101i \(-0.654089\pi\)
\(114\) −0.963104 1.43959i −0.0902030 0.134830i
\(115\) −5.05688 2.75884i −0.471556 0.257263i
\(116\) 5.49359i 0.510067i
\(117\) −10.6954 + 4.44461i −0.988790 + 0.410904i
\(118\) −0.895279 + 0.895279i −0.0824171 + 0.0824171i
\(119\) 3.28774 0.301386
\(120\) −2.97415 2.48081i −0.271502 0.226466i
\(121\) 1.04032 0.0945742
\(122\) −1.91180 + 1.91180i −0.173086 + 0.173086i
\(123\) −2.12905 + 10.7357i −0.191970 + 0.968010i
\(124\) 5.07413i 0.455671i
\(125\) 7.31221 8.45764i 0.654024 0.756474i
\(126\) −3.15677 1.30332i −0.281227 0.116109i
\(127\) −1.57598 1.57598i −0.139845 0.139845i 0.633718 0.773564i \(-0.281528\pi\)
−0.773564 + 0.633718i \(0.781528\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −1.30976 + 0.876246i −0.115318 + 0.0771491i
\(130\) −2.43520 8.28223i −0.213581 0.726400i
\(131\) 19.0035i 1.66034i −0.557509 0.830171i \(-0.688243\pi\)
0.557509 0.830171i \(-0.311757\pi\)
\(132\) 5.36176 + 1.06331i 0.466681 + 0.0925494i
\(133\) 0.804978 0.804978i 0.0698004 0.0698004i
\(134\) −5.47128 −0.472647
\(135\) −11.0953 3.44866i −0.954936 0.296813i
\(136\) 2.88801 0.247645
\(137\) −15.2239 + 15.2239i −1.30066 + 1.30066i −0.372720 + 0.927944i \(0.621575\pi\)
−0.927944 + 0.372720i \(0.878425\pi\)
\(138\) −4.37682 0.867985i −0.372580 0.0738878i
\(139\) 15.0510i 1.27661i 0.769785 + 0.638304i \(0.220364\pi\)
−0.769785 + 0.638304i \(0.779636\pi\)
\(140\) 1.21913 2.23464i 0.103036 0.188861i
\(141\) −6.56724 + 4.39356i −0.553061 + 0.370004i
\(142\) −0.667940 0.667940i −0.0560523 0.0560523i
\(143\) 8.61540 + 8.61540i 0.720456 + 0.720456i
\(144\) −2.77296 1.14486i −0.231080 0.0954050i
\(145\) 11.7852 3.46517i 0.978706 0.287766i
\(146\) 5.11793i 0.423563i
\(147\) −1.92185 + 9.69093i −0.158511 + 0.799294i
\(148\) 7.25575 7.25575i 0.596419 0.596419i
\(149\) 13.7188 1.12389 0.561945 0.827174i \(-0.310053\pi\)
0.561945 + 0.827174i \(0.310053\pi\)
\(150\) 3.44598 7.94514i 0.281363 0.648718i
\(151\) −14.9068 −1.21310 −0.606549 0.795046i \(-0.707447\pi\)
−0.606549 + 0.795046i \(0.707447\pi\)
\(152\) 0.707107 0.707107i 0.0573539 0.0573539i
\(153\) 8.00069 3.32479i 0.646818 0.268793i
\(154\) 3.59271i 0.289509i
\(155\) 10.8853 3.20058i 0.874331 0.257077i
\(156\) −3.71827 5.55786i −0.297700 0.444985i
\(157\) 2.63322 + 2.63322i 0.210153 + 0.210153i 0.804333 0.594179i \(-0.202523\pi\)
−0.594179 + 0.804333i \(0.702523\pi\)
\(158\) 10.6253 + 10.6253i 0.845300 + 0.845300i
\(159\) −4.31626 6.45170i −0.342301 0.511653i
\(160\) 1.07091 1.96295i 0.0846628 0.155184i
\(161\) 2.93274i 0.231132i
\(162\) −8.99998 + 0.0207168i −0.707105 + 0.00162767i
\(163\) −8.49310 + 8.49310i −0.665231 + 0.665231i −0.956608 0.291377i \(-0.905887\pi\)
0.291377 + 0.956608i \(0.405887\pi\)
\(164\) −6.31900 −0.493431
\(165\) 1.10093 + 12.1731i 0.0857071 + 0.947671i
\(166\) 7.84753 0.609086
\(167\) 2.26247 2.26247i 0.175075 0.175075i −0.614130 0.789205i \(-0.710493\pi\)
0.789205 + 0.614130i \(0.210493\pi\)
\(168\) 0.383563 1.93412i 0.0295925 0.149221i
\(169\) 1.90511i 0.146547i
\(170\) 1.82165 + 6.19552i 0.139714 + 0.475175i
\(171\) 1.14486 2.77296i 0.0875496 0.212053i
\(172\) −0.643335 0.643335i −0.0490539 0.0490539i
\(173\) −6.00022 6.00022i −0.456189 0.456189i 0.441214 0.897402i \(-0.354548\pi\)
−0.897402 + 0.441214i \(0.854548\pi\)
\(174\) 7.90854 5.29091i 0.599545 0.401103i
\(175\) 5.56286 + 1.20583i 0.420513 + 0.0911520i
\(176\) 3.15590i 0.237885i
\(177\) −2.15108 0.426591i −0.161685 0.0320645i
\(178\) 2.31464 2.31464i 0.173490 0.173490i
\(179\) 10.5263 0.786776 0.393388 0.919373i \(-0.371303\pi\)
0.393388 + 0.919373i \(0.371303\pi\)
\(180\) 0.706935 6.67085i 0.0526919 0.497216i
\(181\) −20.9226 −1.55516 −0.777582 0.628781i \(-0.783554\pi\)
−0.777582 + 0.628781i \(0.783554\pi\)
\(182\) 3.10779 3.10779i 0.230365 0.230365i
\(183\) −4.59347 0.910950i −0.339559 0.0673394i
\(184\) 2.57617i 0.189918i
\(185\) 20.1421 + 10.9888i 1.48088 + 0.807912i
\(186\) 7.30469 4.88692i 0.535606 0.358326i
\(187\) −6.44475 6.44475i −0.471287 0.471287i
\(188\) −3.22573 3.22573i −0.235260 0.235260i
\(189\) −1.16404 5.79969i −0.0846717 0.421866i
\(190\) 1.96295 + 1.07091i 0.142407 + 0.0776919i
\(191\) 24.7912i 1.79383i 0.442204 + 0.896915i \(0.354197\pi\)
−0.442204 + 0.896915i \(0.645803\pi\)
\(192\) 0.336929 1.69896i 0.0243157 0.122612i
\(193\) 17.4625 17.4625i 1.25698 1.25698i 0.304450 0.952528i \(-0.401527\pi\)
0.952528 0.304450i \(-0.0984726\pi\)
\(194\) −4.09766 −0.294195
\(195\) 9.57769 11.4824i 0.685873 0.822268i
\(196\) −5.70402 −0.407430
\(197\) 1.66630 1.66630i 0.118719 0.118719i −0.645252 0.763970i \(-0.723247\pi\)
0.763970 + 0.645252i \(0.223247\pi\)
\(198\) 3.63319 + 8.74283i 0.258200 + 0.621326i
\(199\) 27.4124i 1.94321i 0.236606 + 0.971606i \(0.423965\pi\)
−0.236606 + 0.971606i \(0.576035\pi\)
\(200\) 4.88652 + 1.05922i 0.345529 + 0.0748982i
\(201\) −5.26942 7.87642i −0.371676 0.555560i
\(202\) −11.9366 11.9366i −0.839853 0.839853i
\(203\) 4.42222 + 4.42222i 0.310379 + 0.310379i
\(204\) 2.78145 + 4.15756i 0.194741 + 0.291087i
\(205\) −3.98580 13.5559i −0.278380 0.946784i
\(206\) 2.08287i 0.145121i
\(207\) −2.96579 7.13680i −0.206137 0.496042i
\(208\) 2.72994 2.72994i 0.189287 0.189287i
\(209\) −3.15590 −0.218298
\(210\) 4.39112 0.397132i 0.303016 0.0274047i
\(211\) −3.68643 −0.253785 −0.126892 0.991917i \(-0.540500\pi\)
−0.126892 + 0.991917i \(0.540500\pi\)
\(212\) 3.16898 3.16898i 0.217646 0.217646i
\(213\) 0.318266 1.60486i 0.0218073 0.109963i
\(214\) 12.5115i 0.855269i
\(215\) 0.974328 1.78591i 0.0664486 0.121798i
\(216\) −1.02252 5.09455i −0.0695734 0.346640i
\(217\) 4.08457 + 4.08457i 0.277278 + 0.277278i
\(218\) −4.83605 4.83605i −0.327539 0.327539i
\(219\) −7.36773 + 4.92910i −0.497865 + 0.333078i
\(220\) −6.77022 + 1.99063i −0.456448 + 0.134208i
\(221\) 11.1498i 0.750015i
\(222\) 17.4334 + 3.45728i 1.17005 + 0.232038i
\(223\) −18.9631 + 18.9631i −1.26987 + 1.26987i −0.323709 + 0.946157i \(0.604930\pi\)
−0.946157 + 0.323709i \(0.895070\pi\)
\(224\) 1.13841 0.0760633
\(225\) 14.7566 2.69118i 0.983774 0.179412i
\(226\) 20.3025 1.35050
\(227\) −2.05681 + 2.05681i −0.136515 + 0.136515i −0.772062 0.635547i \(-0.780775\pi\)
0.635547 + 0.772062i \(0.280775\pi\)
\(228\) 1.69896 + 0.336929i 0.112517 + 0.0223136i
\(229\) 15.8734i 1.04895i 0.851427 + 0.524473i \(0.175738\pi\)
−0.851427 + 0.524473i \(0.824262\pi\)
\(230\) 5.52655 1.62496i 0.364410 0.107147i
\(231\) −5.17204 + 3.46015i −0.340295 + 0.227661i
\(232\) 3.88456 + 3.88456i 0.255034 + 0.255034i
\(233\) −15.6011 15.6011i −1.02206 1.02206i −0.999751 0.0223132i \(-0.992897\pi\)
−0.0223132 0.999751i \(-0.507103\pi\)
\(234\) 4.41997 10.7056i 0.288943 0.699847i
\(235\) 4.88535 8.95470i 0.318685 0.584140i
\(236\) 1.26612i 0.0824171i
\(237\) −5.06282 + 25.5293i −0.328865 + 1.65830i
\(238\) −2.32478 + 2.32478i −0.150693 + 0.150693i
\(239\) 4.84839 0.313616 0.156808 0.987629i \(-0.449880\pi\)
0.156808 + 0.987629i \(0.449880\pi\)
\(240\) 3.85724 0.348848i 0.248984 0.0225180i
\(241\) −17.0520 −1.09842 −0.549209 0.835685i \(-0.685071\pi\)
−0.549209 + 0.835685i \(0.685071\pi\)
\(242\) −0.735615 + 0.735615i −0.0472871 + 0.0472871i
\(243\) −8.69774 12.9364i −0.557960 0.829868i
\(244\) 2.70369i 0.173086i
\(245\) −3.59790 12.2366i −0.229861 0.781768i
\(246\) −6.08585 9.09679i −0.388020 0.579990i
\(247\) 2.72994 + 2.72994i 0.173702 + 0.173702i
\(248\) 3.58795 + 3.58795i 0.227835 + 0.227835i
\(249\) 7.55799 + 11.2973i 0.478968 + 0.715934i
\(250\) 0.809943 + 11.1510i 0.0512253 + 0.705249i
\(251\) 7.93870i 0.501087i 0.968105 + 0.250543i \(0.0806092\pi\)
−0.968105 + 0.250543i \(0.919391\pi\)
\(252\) 3.15376 1.31058i 0.198668 0.0825590i
\(253\) −5.74887 + 5.74887i −0.361428 + 0.361428i
\(254\) 2.22877 0.139845
\(255\) −7.16459 + 8.58938i −0.448664 + 0.537888i
\(256\) 1.00000 0.0625000
\(257\) 16.9891 16.9891i 1.05975 1.05975i 0.0616541 0.998098i \(-0.480362\pi\)
0.998098 0.0616541i \(-0.0196376\pi\)
\(258\) 0.306542 1.54574i 0.0190845 0.0962336i
\(259\) 11.6814i 0.725849i
\(260\) 7.57837 + 4.13447i 0.469990 + 0.256409i
\(261\) 15.2335 + 6.28939i 0.942930 + 0.389304i
\(262\) 13.4375 + 13.4375i 0.830171 + 0.830171i
\(263\) 2.30249 + 2.30249i 0.141977 + 0.141977i 0.774523 0.632546i \(-0.217990\pi\)
−0.632546 + 0.774523i \(0.717990\pi\)
\(264\) −4.54321 + 3.03946i −0.279615 + 0.187066i
\(265\) 8.79715 + 4.79939i 0.540405 + 0.294824i
\(266\) 1.13841i 0.0698004i
\(267\) 5.56138 + 1.10290i 0.340351 + 0.0674965i
\(268\) 3.86878 3.86878i 0.236323 0.236323i
\(269\) −15.9676 −0.973559 −0.486780 0.873525i \(-0.661829\pi\)
−0.486780 + 0.873525i \(0.661829\pi\)
\(270\) 10.2842 5.40703i 0.625874 0.329061i
\(271\) −5.91297 −0.359188 −0.179594 0.983741i \(-0.557478\pi\)
−0.179594 + 0.983741i \(0.557478\pi\)
\(272\) −2.04213 + 2.04213i −0.123822 + 0.123822i
\(273\) 7.46708 + 1.48083i 0.451928 + 0.0896238i
\(274\) 21.5298i 1.30066i
\(275\) −8.54083 13.2682i −0.515031 0.800105i
\(276\) 3.70864 2.48112i 0.223234 0.149346i
\(277\) 17.6393 + 17.6393i 1.05984 + 1.05984i 0.998092 + 0.0617480i \(0.0196675\pi\)
0.0617480 + 0.998092i \(0.480332\pi\)
\(278\) −10.6426 10.6426i −0.638304 0.638304i
\(279\) 14.0704 + 5.80917i 0.842370 + 0.347786i
\(280\) 0.718070 + 2.44219i 0.0429129 + 0.145949i
\(281\) 11.7923i 0.703472i 0.936099 + 0.351736i \(0.114408\pi\)
−0.936099 + 0.351736i \(0.885592\pi\)
\(282\) 1.53702 7.75045i 0.0915285 0.461533i
\(283\) −4.82604 + 4.82604i −0.286878 + 0.286878i −0.835845 0.548966i \(-0.815022\pi\)
0.548966 + 0.835845i \(0.315022\pi\)
\(284\) 0.944610 0.0560523
\(285\) 0.348848 + 3.85724i 0.0206640 + 0.228483i
\(286\) −12.1840 −0.720456
\(287\) 5.08665 5.08665i 0.300256 0.300256i
\(288\) 2.77032 1.15124i 0.163242 0.0678374i
\(289\) 8.65941i 0.509377i
\(290\) −5.88314 + 10.7836i −0.345470 + 0.633236i
\(291\) −3.94648 5.89897i −0.231346 0.345804i
\(292\) −3.61892 3.61892i −0.211781 0.211781i
\(293\) −11.3784 11.3784i −0.664732 0.664732i 0.291760 0.956492i \(-0.405759\pi\)
−0.956492 + 0.291760i \(0.905759\pi\)
\(294\) −5.49357 8.21147i −0.320391 0.478903i
\(295\) 2.71614 0.798621i 0.158140 0.0464975i
\(296\) 10.2612i 0.596419i
\(297\) −9.08698 + 13.6506i −0.527280 + 0.792087i
\(298\) −9.70068 + 9.70068i −0.561945 + 0.561945i
\(299\) 9.94585 0.575183
\(300\) 3.18138 + 8.05474i 0.183677 + 0.465041i
\(301\) 1.03574 0.0596992
\(302\) 10.5407 10.5407i 0.606549 0.606549i
\(303\) 5.68764 28.6799i 0.326746 1.64762i
\(304\) 1.00000i 0.0573539i
\(305\) 5.80011 1.70539i 0.332113 0.0976504i
\(306\) −3.30636 + 8.00832i −0.189012 + 0.457805i
\(307\) 3.22856 + 3.22856i 0.184264 + 0.184264i 0.793211 0.608947i \(-0.208408\pi\)
−0.608947 + 0.793211i \(0.708408\pi\)
\(308\) −2.54043 2.54043i −0.144754 0.144754i
\(309\) −2.99849 + 2.00602i −0.170578 + 0.114119i
\(310\) −5.43393 + 9.96024i −0.308627 + 0.565704i
\(311\) 8.13102i 0.461068i −0.973064 0.230534i \(-0.925953\pi\)
0.973064 0.230534i \(-0.0740473\pi\)
\(312\) 6.55921 + 1.30079i 0.371342 + 0.0736425i
\(313\) 19.8596 19.8596i 1.12253 1.12253i 0.131173 0.991359i \(-0.458126\pi\)
0.991359 0.131173i \(-0.0418744\pi\)
\(314\) −3.72393 −0.210153
\(315\) 4.80082 + 5.93895i 0.270496 + 0.334622i
\(316\) −15.0264 −0.845300
\(317\) −7.90002 + 7.90002i −0.443709 + 0.443709i −0.893257 0.449547i \(-0.851585\pi\)
0.449547 + 0.893257i \(0.351585\pi\)
\(318\) 7.61409 + 1.50998i 0.426977 + 0.0846756i
\(319\) 17.3372i 0.970698i
\(320\) 0.630765 + 2.14526i 0.0352608 + 0.119924i
\(321\) 18.0115 12.0499i 1.00530 0.672559i
\(322\) 2.07376 + 2.07376i 0.115566 + 0.115566i
\(323\) −2.04213 2.04213i −0.113627 0.113627i
\(324\) 6.34930 6.37859i 0.352739 0.354366i
\(325\) −4.08934 + 18.8654i −0.226836 + 1.04647i
\(326\) 12.0111i 0.665231i
\(327\) 2.30432 11.6196i 0.127429 0.642563i
\(328\) 4.46821 4.46821i 0.246715 0.246715i
\(329\) 5.19328 0.286315
\(330\) −9.38612 7.82917i −0.516689 0.430982i
\(331\) 29.2265 1.60643 0.803217 0.595687i \(-0.203120\pi\)
0.803217 + 0.595687i \(0.203120\pi\)
\(332\) −5.54904 + 5.54904i −0.304543 + 0.304543i
\(333\) 11.8131 + 28.4267i 0.647352 + 1.55777i
\(334\) 3.19962i 0.175075i
\(335\) 10.7398 + 5.85925i 0.586779 + 0.320125i
\(336\) 1.09641 + 1.63885i 0.0598140 + 0.0894065i
\(337\) −10.9958 10.9958i −0.598982 0.598982i 0.341060 0.940042i \(-0.389214\pi\)
−0.940042 + 0.341060i \(0.889214\pi\)
\(338\) 1.34711 + 1.34711i 0.0732734 + 0.0732734i
\(339\) 19.5534 + 29.2273i 1.06200 + 1.58741i
\(340\) −5.66900 3.09279i −0.307445 0.167730i
\(341\) 16.0134i 0.867176i
\(342\) 1.15124 + 2.77032i 0.0622519 + 0.149802i
\(343\) 10.2265 10.2265i 0.552177 0.552177i
\(344\) 0.909814 0.0490539
\(345\) 7.66192 + 6.39098i 0.412504 + 0.344079i
\(346\) 8.48560 0.456189
\(347\) 19.5400 19.5400i 1.04896 1.04896i 0.0502218 0.998738i \(-0.484007\pi\)
0.998738 0.0502218i \(-0.0159928\pi\)
\(348\) −1.85095 + 9.33342i −0.0992213 + 0.500324i
\(349\) 33.9607i 1.81787i −0.416934 0.908937i \(-0.636895\pi\)
0.416934 0.908937i \(-0.363105\pi\)
\(350\) −4.78619 + 3.08089i −0.255832 + 0.164681i
\(351\) 19.6686 3.94764i 1.04983 0.210709i
\(352\) −2.23156 2.23156i −0.118942 0.118942i
\(353\) −17.4613 17.4613i −0.929372 0.929372i 0.0682931 0.997665i \(-0.478245\pi\)
−0.997665 + 0.0682931i \(0.978245\pi\)
\(354\) 1.82269 1.21940i 0.0968750 0.0648104i
\(355\) 0.595827 + 2.02643i 0.0316232 + 0.107552i
\(356\) 3.27340i 0.173490i
\(357\) −5.58575 1.10773i −0.295629 0.0586275i
\(358\) −7.44325 + 7.44325i −0.393388 + 0.393388i
\(359\) −25.1531 −1.32753 −0.663766 0.747940i \(-0.731043\pi\)
−0.663766 + 0.747940i \(0.731043\pi\)
\(360\) 4.21712 + 5.21688i 0.222262 + 0.274954i
\(361\) −1.00000 −0.0526316
\(362\) 14.7945 14.7945i 0.777582 0.777582i
\(363\) −1.76746 0.350513i −0.0927676 0.0183971i
\(364\) 4.39508i 0.230365i
\(365\) 5.48083 10.0462i 0.286880 0.525843i
\(366\) 3.89221 2.60393i 0.203449 0.136110i
\(367\) −3.86210 3.86210i −0.201600 0.201600i 0.599085 0.800685i \(-0.295531\pi\)
−0.800685 + 0.599085i \(0.795531\pi\)
\(368\) 1.82163 + 1.82163i 0.0949589 + 0.0949589i
\(369\) 7.23436 17.5223i 0.376606 0.912175i
\(370\) −22.0129 + 6.47239i −1.14440 + 0.336484i
\(371\) 5.10191i 0.264878i
\(372\) −1.70962 + 8.62077i −0.0886397 + 0.446966i
\(373\) −6.37524 + 6.37524i −0.330098 + 0.330098i −0.852623 0.522526i \(-0.824990\pi\)
0.522526 + 0.852623i \(0.324990\pi\)
\(374\) 9.11425 0.471287
\(375\) −15.2728 + 11.9055i −0.788684 + 0.614799i
\(376\) 4.56187 0.235260
\(377\) −14.9972 + 14.9972i −0.772393 + 0.772393i
\(378\) 4.92411 + 3.27790i 0.253269 + 0.168597i
\(379\) 14.0745i 0.722958i 0.932380 + 0.361479i \(0.117728\pi\)
−0.932380 + 0.361479i \(0.882272\pi\)
\(380\) −2.14526 + 0.630765i −0.110049 + 0.0323576i
\(381\) 2.14654 + 3.20852i 0.109970 + 0.164378i
\(382\) −17.5300 17.5300i −0.896915 0.896915i
\(383\) 5.66358 + 5.66358i 0.289396 + 0.289396i 0.836841 0.547446i \(-0.184400\pi\)
−0.547446 + 0.836841i \(0.684400\pi\)
\(384\) 0.963104 + 1.43959i 0.0491482 + 0.0734640i
\(385\) 3.84746 7.05229i 0.196085 0.359418i
\(386\) 24.6957i 1.25698i
\(387\) 2.52047 1.04741i 0.128123 0.0532430i
\(388\) 2.89748 2.89748i 0.147097 0.147097i
\(389\) 1.77092 0.0897890 0.0448945 0.998992i \(-0.485705\pi\)
0.0448945 + 0.998992i \(0.485705\pi\)
\(390\) 1.34680 + 14.8917i 0.0681979 + 0.754071i
\(391\) −7.44000 −0.376257
\(392\) 4.03335 4.03335i 0.203715 0.203715i
\(393\) −6.40282 + 32.2862i −0.322980 + 1.62863i
\(394\) 2.35650i 0.118719i
\(395\) −9.47811 32.2355i −0.476896 1.62194i
\(396\) −8.75117 3.61306i −0.439763 0.181563i
\(397\) −13.5159 13.5159i −0.678345 0.678345i 0.281281 0.959626i \(-0.409241\pi\)
−0.959626 + 0.281281i \(0.909241\pi\)
\(398\) −19.3835 19.3835i −0.971606 0.971606i
\(399\) −1.63885 + 1.09641i −0.0820451 + 0.0548891i
\(400\) −4.20427 + 2.70631i −0.210214 + 0.135315i
\(401\) 33.0944i 1.65266i 0.563188 + 0.826329i \(0.309575\pi\)
−0.563188 + 0.826329i \(0.690425\pi\)
\(402\) 9.29551 + 1.84343i 0.463618 + 0.0919420i
\(403\) −13.8521 + 13.8521i −0.690020 + 0.690020i
\(404\) 16.8808 0.839853
\(405\) 17.6886 + 9.59749i 0.878956 + 0.476903i
\(406\) −6.25397 −0.310379
\(407\) 22.8984 22.8984i 1.13503 1.13503i
\(408\) −4.90662 0.973053i −0.242914 0.0481733i
\(409\) 12.5812i 0.622098i 0.950394 + 0.311049i \(0.100680\pi\)
−0.950394 + 0.311049i \(0.899320\pi\)
\(410\) 12.4038 + 6.76707i 0.612582 + 0.334202i
\(411\) 30.9942 20.7355i 1.52883 1.02280i
\(412\) −1.47281 1.47281i −0.0725603 0.0725603i
\(413\) 1.01919 + 1.01919i 0.0501513 + 0.0501513i
\(414\) 7.14361 + 2.94935i 0.351089 + 0.144953i
\(415\) −15.4043 8.40399i −0.756166 0.412536i
\(416\) 3.86071i 0.189287i
\(417\) 5.07111 25.5711i 0.248333 1.25222i
\(418\) 2.23156 2.23156i 0.109149 0.109149i
\(419\) −33.5096 −1.63705 −0.818525 0.574471i \(-0.805208\pi\)
−0.818525 + 0.574471i \(0.805208\pi\)
\(420\) −2.82418 + 3.38581i −0.137806 + 0.165211i
\(421\) −29.7747 −1.45113 −0.725564 0.688154i \(-0.758421\pi\)
−0.725564 + 0.688154i \(0.758421\pi\)
\(422\) 2.60670 2.60670i 0.126892 0.126892i
\(423\) 12.6378 5.25180i 0.614472 0.255351i
\(424\) 4.48161i 0.217646i
\(425\) 3.05903 14.1123i 0.148385 0.684547i
\(426\) 0.909759 + 1.35986i 0.0440779 + 0.0658852i
\(427\) 2.17641 + 2.17641i 0.105324 + 0.105324i
\(428\) 8.84697 + 8.84697i 0.427634 + 0.427634i
\(429\) −11.7345 17.5400i −0.566546 0.846840i
\(430\) 0.573879 + 1.95179i 0.0276749 + 0.0941235i
\(431\) 16.7696i 0.807763i 0.914811 + 0.403882i \(0.132339\pi\)
−0.914811 + 0.403882i \(0.867661\pi\)
\(432\) 4.32542 + 2.87936i 0.208107 + 0.138533i
\(433\) −0.841474 + 0.841474i −0.0404387 + 0.0404387i −0.727037 0.686598i \(-0.759103\pi\)
0.686598 + 0.727037i \(0.259103\pi\)
\(434\) −5.77645 −0.277278
\(435\) −21.1901 + 1.91643i −1.01599 + 0.0918857i
\(436\) 6.83921 0.327539
\(437\) −1.82163 + 1.82163i −0.0871402 + 0.0871402i
\(438\) 1.72438 8.69517i 0.0823939 0.415471i
\(439\) 32.4072i 1.54671i −0.633973 0.773355i \(-0.718577\pi\)
0.633973 0.773355i \(-0.281423\pi\)
\(440\) 3.37968 6.19485i 0.161120 0.295328i
\(441\) 6.53030 15.8170i 0.310967 0.753191i
\(442\) −7.88408 7.88408i −0.375007 0.375007i
\(443\) 15.3966 + 15.3966i 0.731515 + 0.731515i 0.970920 0.239405i \(-0.0769523\pi\)
−0.239405 + 0.970920i \(0.576952\pi\)
\(444\) −14.7719 + 9.88258i −0.701044 + 0.469007i
\(445\) −7.02228 + 2.06474i −0.332888 + 0.0978782i
\(446\) 26.8179i 1.26987i
\(447\) −23.3078 4.62227i −1.10242 0.218626i
\(448\) −0.804978 + 0.804978i −0.0380316 + 0.0380316i
\(449\) −3.69496 −0.174376 −0.0871879 0.996192i \(-0.527788\pi\)
−0.0871879 + 0.996192i \(0.527788\pi\)
\(450\) −8.53155 + 12.3375i −0.402181 + 0.581593i
\(451\) −19.9421 −0.939037
\(452\) −14.3560 + 14.3560i −0.675250 + 0.675250i
\(453\) 25.3261 + 5.02253i 1.18992 + 0.235979i
\(454\) 2.90877i 0.136515i
\(455\) −9.42858 + 2.77226i −0.442019 + 0.129966i
\(456\) −1.43959 + 0.963104i −0.0674151 + 0.0451015i
\(457\) 6.23351 + 6.23351i 0.291591 + 0.291591i 0.837709 0.546117i \(-0.183895\pi\)
−0.546117 + 0.837709i \(0.683895\pi\)
\(458\) −11.2242 11.2242i −0.524473 0.524473i
\(459\) −14.7131 + 2.95303i −0.686749 + 0.137836i
\(460\) −2.75884 + 5.05688i −0.128632 + 0.235778i
\(461\) 3.01803i 0.140563i −0.997527 0.0702817i \(-0.977610\pi\)
0.997527 0.0702817i \(-0.0223898\pi\)
\(462\) 1.21049 6.10388i 0.0563169 0.283978i
\(463\) 17.1200 17.1200i 0.795634 0.795634i −0.186770 0.982404i \(-0.559802\pi\)
0.982404 + 0.186770i \(0.0598018\pi\)
\(464\) −5.49359 −0.255034
\(465\) −19.5722 + 1.77010i −0.907637 + 0.0820864i
\(466\) 22.0633 1.02206
\(467\) −3.42627 + 3.42627i −0.158549 + 0.158549i −0.781923 0.623375i \(-0.785761\pi\)
0.623375 + 0.781923i \(0.285761\pi\)
\(468\) 4.44461 + 10.6954i 0.205452 + 0.494395i
\(469\) 6.22857i 0.287608i
\(470\) 2.87747 + 9.78639i 0.132728 + 0.451413i
\(471\) −3.58653 5.36094i −0.165259 0.247019i
\(472\) 0.895279 + 0.895279i 0.0412085 + 0.0412085i
\(473\) −2.03030 2.03030i −0.0933533 0.0933533i
\(474\) −14.4720 21.6319i −0.664720 0.993585i
\(475\) −2.70631 4.20427i −0.124174 0.192905i
\(476\) 3.28774i 0.150693i
\(477\) 5.15941 + 12.4155i 0.236233 + 0.568465i
\(478\) −3.42833 + 3.42833i −0.156808 + 0.156808i
\(479\) 18.0199 0.823349 0.411674 0.911331i \(-0.364944\pi\)
0.411674 + 0.911331i \(0.364944\pi\)
\(480\) −2.48081 + 2.97415i −0.113233 + 0.135751i
\(481\) −39.6155 −1.80631
\(482\) 12.0576 12.0576i 0.549209 0.549209i
\(483\) −0.988124 + 4.98262i −0.0449612 + 0.226717i
\(484\) 1.04032i 0.0472871i
\(485\) 8.04348 + 4.38822i 0.365236 + 0.199259i
\(486\) 15.2976 + 2.99715i 0.693914 + 0.135954i
\(487\) −3.32991 3.32991i −0.150893 0.150893i 0.627624 0.778517i \(-0.284028\pi\)
−0.778517 + 0.627624i \(0.784028\pi\)
\(488\) 1.91180 + 1.91180i 0.0865429 + 0.0865429i
\(489\) 17.2910 11.5679i 0.781928 0.523119i
\(490\) 11.1967 + 6.10849i 0.505814 + 0.275953i
\(491\) 40.7725i 1.84004i 0.391873 + 0.920020i \(0.371827\pi\)
−0.391873 + 0.920020i \(0.628173\pi\)
\(492\) 10.7357 + 2.12905i 0.484005 + 0.0959851i
\(493\) 11.2186 11.2186i 0.505262 0.505262i
\(494\) −3.86071 −0.173702
\(495\) 2.23102 21.0525i 0.100277 0.946240i
\(496\) −5.07413 −0.227835
\(497\) −0.760391 + 0.760391i −0.0341082 + 0.0341082i
\(498\) −13.3327 2.64406i −0.597451 0.118483i
\(499\) 28.4698i 1.27449i −0.770663 0.637243i \(-0.780075\pi\)
0.770663 0.637243i \(-0.219925\pi\)
\(500\) −8.45764 7.31221i −0.378237 0.327012i
\(501\) −4.60615 + 3.08157i −0.205788 + 0.137674i
\(502\) −5.61351 5.61351i −0.250543 0.250543i
\(503\) 19.2777 + 19.2777i 0.859549 + 0.859549i 0.991285 0.131736i \(-0.0420551\pi\)
−0.131736 + 0.991285i \(0.542055\pi\)
\(504\) −1.30332 + 3.15677i −0.0580545 + 0.140614i
\(505\) 10.6478 + 36.2138i 0.473823 + 1.61149i
\(506\) 8.13012i 0.361428i
\(507\) −0.641885 + 3.23671i −0.0285071 + 0.143747i
\(508\) −1.57598 + 1.57598i −0.0699227 + 0.0699227i
\(509\) −30.9140 −1.37024 −0.685120 0.728431i \(-0.740250\pi\)
−0.685120 + 0.728431i \(0.740250\pi\)
\(510\) −1.00747 11.1397i −0.0446117 0.493276i
\(511\) 5.82630 0.257740
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −2.87936 + 4.32542i −0.127127 + 0.190972i
\(514\) 24.0262i 1.05975i
\(515\) 2.23057 4.08856i 0.0982905 0.180164i
\(516\) 0.876246 + 1.30976i 0.0385746 + 0.0576591i
\(517\) −10.1801 10.1801i −0.447719 0.447719i
\(518\) −8.26002 8.26002i −0.362924 0.362924i
\(519\) 8.17252 + 12.2158i 0.358734 + 0.536215i
\(520\) −8.28223 + 2.43520i −0.363200 + 0.106791i
\(521\) 24.0255i 1.05258i 0.850306 + 0.526289i \(0.176417\pi\)
−0.850306 + 0.526289i \(0.823583\pi\)
\(522\) −15.2190 + 6.32444i −0.666117 + 0.276813i
\(523\) −28.0008 + 28.0008i −1.22439 + 1.22439i −0.258331 + 0.966056i \(0.583172\pi\)
−0.966056 + 0.258331i \(0.916828\pi\)
\(524\) −19.0035 −0.830171
\(525\) −9.04483 3.92295i −0.394749 0.171211i
\(526\) −3.25621 −0.141977
\(527\) 10.3620 10.3620i 0.451377 0.451377i
\(528\) 1.06331 5.36176i 0.0462747 0.233340i
\(529\) 16.3634i 0.711450i
\(530\) −9.61421 + 2.82684i −0.417615 + 0.122790i
\(531\) 3.51088 + 1.44952i 0.152359 + 0.0629040i
\(532\) −0.804978 0.804978i −0.0349002 0.0349002i
\(533\) 17.2505 + 17.2505i 0.747200 + 0.747200i
\(534\) −4.71236 + 3.15262i −0.203924 + 0.136427i
\(535\) −13.3987 + 24.5594i −0.579276 + 1.06180i
\(536\) 5.47128i 0.236323i
\(537\) −17.8839 3.54663i −0.771746 0.153048i
\(538\) 11.2908 11.2908i 0.486780 0.486780i
\(539\) −18.0013 −0.775371
\(540\) −3.44866 + 11.0953i −0.148407 + 0.477468i
\(541\) 30.2843 1.30202 0.651012 0.759067i \(-0.274345\pi\)
0.651012 + 0.759067i \(0.274345\pi\)
\(542\) 4.18110 4.18110i 0.179594 0.179594i
\(543\) 35.5467 + 7.04942i 1.52546 + 0.302520i
\(544\) 2.88801i 0.123822i
\(545\) 4.31393 + 14.6719i 0.184788 + 0.628474i
\(546\) −6.32713 + 4.23292i −0.270776 + 0.181152i
\(547\) −20.9852 20.9852i −0.897263 0.897263i 0.0979302 0.995193i \(-0.468778\pi\)
−0.995193 + 0.0979302i \(0.968778\pi\)
\(548\) 15.2239 + 15.2239i 0.650332 + 0.650332i
\(549\) 7.49721 + 3.09534i 0.319973 + 0.132106i
\(550\) 15.4213 + 3.34279i 0.657568 + 0.142537i
\(551\) 5.49359i 0.234035i
\(552\) −0.867985 + 4.37682i −0.0369439 + 0.186290i
\(553\) 12.0959 12.0959i 0.514370 0.514370i
\(554\) −24.9457 −1.05984
\(555\) −30.5183 25.4560i −1.29543 1.08055i
\(556\) 15.0510 0.638304
\(557\) −19.6777 + 19.6777i −0.833770 + 0.833770i −0.988030 0.154260i \(-0.950701\pi\)
0.154260 + 0.988030i \(0.450701\pi\)
\(558\) −14.0569 + 5.84154i −0.595078 + 0.247292i
\(559\) 3.51253i 0.148564i
\(560\) −2.23464 1.21913i −0.0944307 0.0515178i
\(561\) 8.77798 + 13.1208i 0.370606 + 0.553961i
\(562\) −8.33844 8.33844i −0.351736 0.351736i
\(563\) −11.9658 11.9658i −0.504296 0.504296i 0.408474 0.912770i \(-0.366061\pi\)
−0.912770 + 0.408474i \(0.866061\pi\)
\(564\) 4.39356 + 6.56724i 0.185002 + 0.276531i
\(565\) −39.8526 21.7421i −1.67661 0.914697i
\(566\) 6.82505i 0.286878i
\(567\) 0.0235843 + 10.2457i 0.000990446 + 0.430278i
\(568\) −0.667940 + 0.667940i −0.0280262 + 0.0280262i
\(569\) −27.2399 −1.14195 −0.570977 0.820966i \(-0.693436\pi\)
−0.570977 + 0.820966i \(0.693436\pi\)
\(570\) −2.97415 2.48081i −0.124574 0.103910i
\(571\) 6.63803 0.277793 0.138896 0.990307i \(-0.455644\pi\)
0.138896 + 0.990307i \(0.455644\pi\)
\(572\) 8.61540 8.61540i 0.360228 0.360228i
\(573\) 8.35287 42.1194i 0.348946 1.75956i
\(574\) 7.19361i 0.300256i
\(575\) −12.5885 2.72873i −0.524977 0.113796i
\(576\) −1.14486 + 2.77296i −0.0477025 + 0.115540i
\(577\) 24.2437 + 24.2437i 1.00928 + 1.00928i 0.999957 + 0.00932364i \(0.00296785\pi\)
0.00932364 + 0.999957i \(0.497032\pi\)
\(578\) −6.12313 6.12313i −0.254689 0.254689i
\(579\) −35.5518 + 23.7845i −1.47748 + 0.988452i
\(580\) −3.46517 11.7852i −0.143883 0.489353i
\(581\) 8.93371i 0.370633i
\(582\) 6.96178 + 1.38062i 0.288575 + 0.0572285i
\(583\) 10.0010 10.0010i 0.414197 0.414197i
\(584\) 5.11793 0.211781
\(585\) −20.1409 + 16.2811i −0.832723 + 0.673141i
\(586\) 16.0915 0.664732
\(587\) −30.9059 + 30.9059i −1.27562 + 1.27562i −0.332528 + 0.943093i \(0.607902\pi\)
−0.943093 + 0.332528i \(0.892098\pi\)
\(588\) 9.69093 + 1.92185i 0.399647 + 0.0792557i
\(589\) 5.07413i 0.209076i
\(590\) −1.35589 + 2.48531i −0.0558213 + 0.102319i
\(591\) −3.39240 + 2.26955i −0.139545 + 0.0933570i
\(592\) −7.25575 7.25575i −0.298209 0.298209i
\(593\) −25.3962 25.3962i −1.04290 1.04290i −0.999038 0.0438587i \(-0.986035\pi\)
−0.0438587 0.999038i \(-0.513965\pi\)
\(594\) −3.22695 16.0779i −0.132404 0.659683i
\(595\) 7.05305 2.07379i 0.289147 0.0850171i
\(596\) 13.7188i 0.561945i
\(597\) 9.23601 46.5726i 0.378005 1.90609i
\(598\) −7.03278 + 7.03278i −0.287592 + 0.287592i
\(599\) 24.9746 1.02043 0.510217 0.860046i \(-0.329565\pi\)
0.510217 + 0.860046i \(0.329565\pi\)
\(600\) −7.94514 3.44598i −0.324359 0.140682i
\(601\) 32.6339 1.33116 0.665582 0.746325i \(-0.268183\pi\)
0.665582 + 0.746325i \(0.268183\pi\)
\(602\) −0.732380 + 0.732380i −0.0298496 + 0.0298496i
\(603\) 6.29876 + 15.1572i 0.256505 + 0.617248i
\(604\) 14.9068i 0.606549i
\(605\) 2.23175 0.656195i 0.0907335 0.0266781i
\(606\) 16.2580 + 24.3016i 0.660437 + 0.987183i
\(607\) −8.92349 8.92349i −0.362193 0.362193i 0.502427 0.864620i \(-0.332441\pi\)
−0.864620 + 0.502427i \(0.832441\pi\)
\(608\) −0.707107 0.707107i −0.0286770 0.0286770i
\(609\) −6.02322 9.00317i −0.244073 0.364827i
\(610\) −2.89540 + 5.30719i −0.117231 + 0.214882i
\(611\) 17.6121i 0.712508i
\(612\) −3.32479 8.00069i −0.134397 0.323409i
\(613\) −3.94769 + 3.94769i −0.159446 + 0.159446i −0.782321 0.622875i \(-0.785964\pi\)
0.622875 + 0.782321i \(0.285964\pi\)
\(614\) −4.56587 −0.184264
\(615\) 2.20437 + 24.3739i 0.0888887 + 0.982850i
\(616\) 3.59271 0.144754
\(617\) 4.00994 4.00994i 0.161434 0.161434i −0.621768 0.783202i \(-0.713585\pi\)
0.783202 + 0.621768i \(0.213585\pi\)
\(618\) 0.701779 3.53873i 0.0282297 0.142348i
\(619\) 13.4636i 0.541147i 0.962699 + 0.270573i \(0.0872133\pi\)
−0.962699 + 0.270573i \(0.912787\pi\)
\(620\) −3.20058 10.8853i −0.128539 0.437165i
\(621\) 2.63417 + 13.1244i 0.105706 + 0.526665i
\(622\) 5.74950 + 5.74950i 0.230534 + 0.230534i
\(623\) −2.63501 2.63501i −0.105570 0.105570i
\(624\) −5.55786 + 3.71827i −0.222492 + 0.148850i
\(625\) 10.3518 22.7561i 0.414072 0.910244i
\(626\) 28.0858i 1.12253i
\(627\) 5.36176 + 1.06331i 0.214128 + 0.0424646i
\(628\) 2.63322 2.63322i 0.105077 0.105077i
\(629\) 29.6344 1.18160
\(630\) −7.59417 0.804783i −0.302559 0.0320633i
\(631\) 24.4689 0.974092 0.487046 0.873376i \(-0.338074\pi\)
0.487046 + 0.873376i \(0.338074\pi\)
\(632\) 10.6253 10.6253i 0.422650 0.422650i
\(633\) 6.26312 + 1.24207i 0.248937 + 0.0493677i
\(634\) 11.1723i 0.443709i
\(635\) −4.37495 2.38681i −0.173615 0.0947177i
\(636\) −6.45170 + 4.31626i −0.255826 + 0.171151i
\(637\) 15.5716 + 15.5716i 0.616970 + 0.616970i
\(638\) 12.2593 + 12.2593i 0.485349 + 0.485349i
\(639\) −1.08145 + 2.61937i −0.0427814 + 0.103620i
\(640\) −1.96295 1.07091i −0.0775922 0.0423314i
\(641\) 14.3767i 0.567845i −0.958847 0.283922i \(-0.908364\pi\)
0.958847 0.283922i \(-0.0916358\pi\)
\(642\) −4.21549 + 21.2566i −0.166372 + 0.838931i
\(643\) 2.63234 2.63234i 0.103809 0.103809i −0.653294 0.757104i \(-0.726614\pi\)
0.757104 + 0.653294i \(0.226614\pi\)
\(644\) −2.93274 −0.115566
\(645\) −2.25707 + 2.70593i −0.0888722 + 0.106546i
\(646\) 2.88801 0.113627
\(647\) −7.51216 + 7.51216i −0.295333 + 0.295333i −0.839183 0.543849i \(-0.816966\pi\)
0.543849 + 0.839183i \(0.316966\pi\)
\(648\) 0.0207168 + 8.99998i 0.000813834 + 0.353552i
\(649\) 3.99573i 0.156846i
\(650\) −10.4483 16.2315i −0.409815 0.636651i
\(651\) −5.56332 8.31574i −0.218044 0.325919i
\(652\) 8.49310 + 8.49310i 0.332616 + 0.332616i
\(653\) −7.41773 7.41773i −0.290278 0.290278i 0.546912 0.837190i \(-0.315803\pi\)
−0.837190 + 0.546912i \(0.815803\pi\)
\(654\) 6.58687 + 9.84568i 0.257567 + 0.384996i
\(655\) −11.9867 40.7674i −0.468360 1.59291i
\(656\) 6.31900i 0.246715i
\(657\) 14.1783 5.89196i 0.553147 0.229867i
\(658\) −3.67220 + 3.67220i −0.143157 + 0.143157i
\(659\) 31.2034 1.21551 0.607755 0.794124i \(-0.292070\pi\)
0.607755 + 0.794124i \(0.292070\pi\)
\(660\) 12.1731 1.10093i 0.473835 0.0428535i
\(661\) −27.3601 −1.06418 −0.532092 0.846687i \(-0.678594\pi\)
−0.532092 + 0.846687i \(0.678594\pi\)
\(662\) −20.6663 + 20.6663i −0.803217 + 0.803217i
\(663\) 3.75668 18.9431i 0.145897 0.735687i
\(664\) 7.84753i 0.304543i
\(665\) 1.21913 2.23464i 0.0472760 0.0866555i
\(666\) −28.4538 11.7476i −1.10256 0.455210i
\(667\) −10.0073 10.0073i −0.387483 0.387483i
\(668\) −2.26247 2.26247i −0.0875377 0.0875377i
\(669\) 38.6069 25.8285i 1.49263 0.998586i
\(670\) −11.7373 + 3.45109i −0.453452 + 0.133327i
\(671\) 8.53256i 0.329396i
\(672\) −1.93412 0.383563i −0.0746103 0.0147963i
\(673\) −20.4515 + 20.4515i −0.788346 + 0.788346i −0.981223 0.192877i \(-0.938218\pi\)
0.192877 + 0.981223i \(0.438218\pi\)
\(674\) 15.5505 0.598982
\(675\) −25.9777 0.399710i −0.999882 0.0153848i
\(676\) −1.90511 −0.0732734
\(677\) 26.1264 26.1264i 1.00412 1.00412i 0.00412796 0.999991i \(-0.498686\pi\)
0.999991 0.00412796i \(-0.00131397\pi\)
\(678\) −34.4932 6.84049i −1.32470 0.262707i
\(679\) 4.66482i 0.179019i
\(680\) 6.19552 1.82165i 0.237587 0.0698572i
\(681\) 4.18744 2.80144i 0.160463 0.107352i
\(682\) 11.3232 + 11.3232i 0.433588 + 0.433588i
\(683\) 17.6171 + 17.6171i 0.674101 + 0.674101i 0.958659 0.284558i \(-0.0918468\pi\)
−0.284558 + 0.958659i \(0.591847\pi\)
\(684\) −2.77296 1.14486i −0.106027 0.0437748i
\(685\) −23.0565 + 42.2619i −0.880943 + 1.61474i
\(686\) 14.4624i 0.552177i
\(687\) 5.34821 26.9684i 0.204047 1.02891i
\(688\) −0.643335 + 0.643335i −0.0245269 + 0.0245269i
\(689\) −17.3022 −0.659162
\(690\) −9.93691 + 0.898691i −0.378292 + 0.0342126i
\(691\) 31.9422 1.21514 0.607569 0.794267i \(-0.292145\pi\)
0.607569 + 0.794267i \(0.292145\pi\)
\(692\) −6.00022 + 6.00022i −0.228094 + 0.228094i
\(693\) 9.95293 4.13607i 0.378081 0.157116i
\(694\) 27.6337i 1.04896i
\(695\) 9.49363 + 32.2882i 0.360114 + 1.22476i
\(696\) −5.29091 7.90854i −0.200551 0.299773i
\(697\) −12.9042 12.9042i −0.488782 0.488782i
\(698\) 24.0138 + 24.0138i 0.908937 + 0.908937i
\(699\) 21.2493 + 31.7622i 0.803722 + 1.20136i
\(700\) 1.20583 5.56286i 0.0455760 0.210257i
\(701\) 25.7033i 0.970801i −0.874292 0.485401i \(-0.838674\pi\)
0.874292 0.485401i \(-0.161326\pi\)
\(702\) −11.1164 + 16.6992i −0.419562 + 0.630271i
\(703\) 7.25575 7.25575i 0.273656 0.273656i
\(704\) 3.15590 0.118942
\(705\) −11.3171 + 13.5677i −0.426228 + 0.510989i
\(706\) 24.6940 0.929372
\(707\) −13.5887 + 13.5887i −0.511056 + 0.511056i
\(708\) −0.426591 + 2.15108i −0.0160323 + 0.0808427i
\(709\) 33.4122i 1.25482i 0.778689 + 0.627410i \(0.215885\pi\)
−0.778689 + 0.627410i \(0.784115\pi\)
\(710\) −1.85422 1.01159i −0.0695876 0.0379644i
\(711\) 17.2031 41.6675i 0.645166 1.56265i
\(712\) −2.31464 2.31464i −0.0867448 0.0867448i
\(713\) −9.24318 9.24318i −0.346160 0.346160i
\(714\) 4.73301 3.16644i 0.177128 0.118501i
\(715\) 23.9165 + 13.0480i 0.894428 + 0.487966i
\(716\) 10.5263i 0.393388i
\(717\) −8.23724 1.63356i −0.307625 0.0610065i
\(718\) 17.7860 17.7860i 0.663766 0.663766i
\(719\) 0.187398 0.00698877 0.00349439 0.999994i \(-0.498888\pi\)
0.00349439 + 0.999994i \(0.498888\pi\)
\(720\) −6.67085 0.706935i −0.248608 0.0263459i
\(721\) 2.37116 0.0883068
\(722\) 0.707107 0.707107i 0.0263158 0.0263158i
\(723\) 28.9708 + 5.74532i 1.07744 + 0.213671i
\(724\) 20.9226i 0.777582i
\(725\) 23.0966 14.8674i 0.857785 0.552160i
\(726\) 1.49763 1.00193i 0.0555824 0.0371852i
\(727\) 0.711792 + 0.711792i 0.0263989 + 0.0263989i 0.720183 0.693784i \(-0.244058\pi\)
−0.693784 + 0.720183i \(0.744058\pi\)
\(728\) −3.10779 3.10779i −0.115182 0.115182i
\(729\) 10.4185 + 24.9089i 0.385871 + 0.922553i
\(730\) 3.22821 + 10.9793i 0.119481 + 0.406361i
\(731\) 2.62755i 0.0971834i
\(732\) −0.910950 + 4.59347i −0.0336697 + 0.169779i
\(733\) −12.3766 + 12.3766i −0.457142 + 0.457142i −0.897716 0.440574i \(-0.854775\pi\)
0.440574 + 0.897716i \(0.354775\pi\)
\(734\) 5.46183 0.201600
\(735\) 1.98983 + 22.0018i 0.0733961 + 0.811548i
\(736\) −2.57617 −0.0949589
\(737\) 12.2095 12.2095i 0.449742 0.449742i
\(738\) 7.27468 + 17.5056i 0.267785 + 0.644391i
\(739\) 0.0763442i 0.00280837i −0.999999 0.00140418i \(-0.999553\pi\)
0.999999 0.00140418i \(-0.000446966\pi\)
\(740\) 10.9888 20.1421i 0.403956 0.740439i
\(741\) −3.71827 5.55786i −0.136594 0.204173i
\(742\) −3.60760 3.60760i −0.132439 0.132439i
\(743\) 33.1046 + 33.1046i 1.21449 + 1.21449i 0.969534 + 0.244956i \(0.0787734\pi\)
0.244956 + 0.969534i \(0.421227\pi\)
\(744\) −4.88692 7.30469i −0.179163 0.267803i
\(745\) 29.4304 8.65336i 1.07825 0.317034i
\(746\) 9.01595i 0.330098i
\(747\) −9.03439 21.7401i −0.330551 0.795430i
\(748\) −6.44475 + 6.44475i −0.235643 + 0.235643i
\(749\) −14.2432 −0.520436
\(750\) 2.38102 19.2180i 0.0869424 0.701741i
\(751\) 33.2419 1.21301 0.606506 0.795079i \(-0.292570\pi\)
0.606506 + 0.795079i \(0.292570\pi\)
\(752\) −3.22573 + 3.22573i −0.117630 + 0.117630i
\(753\) 2.67478 13.4876i 0.0974743 0.491515i
\(754\) 21.2092i 0.772393i
\(755\) −31.9789 + 9.40269i −1.16383 + 0.342199i
\(756\) −5.79969 + 1.16404i −0.210933 + 0.0423358i
\(757\) 18.1270 + 18.1270i 0.658838 + 0.658838i 0.955105 0.296267i \(-0.0957420\pi\)
−0.296267 + 0.955105i \(0.595742\pi\)
\(758\) −9.95217 9.95217i −0.361479 0.361479i
\(759\) 11.7041 7.83016i 0.424831 0.284217i
\(760\) 1.07091 1.96295i 0.0388460 0.0712035i
\(761\) 16.7931i 0.608751i 0.952552 + 0.304375i \(0.0984477\pi\)
−0.952552 + 0.304375i \(0.901552\pi\)
\(762\) −3.78660 0.750937i −0.137174 0.0272036i
\(763\) −5.50541 + 5.50541i −0.199309 + 0.199309i
\(764\) 24.7912 0.896915
\(765\) 15.0664 12.1791i 0.544727 0.440336i
\(766\) −8.00952 −0.289396
\(767\) −3.45641 + 3.45641i −0.124804 + 0.124804i
\(768\) −1.69896 0.336929i −0.0613061 0.0121579i
\(769\) 0.877088i 0.0316286i 0.999875 + 0.0158143i \(0.00503406\pi\)
−0.999875 + 0.0158143i \(0.994966\pi\)
\(770\) 2.26615 + 7.70729i 0.0816665 + 0.277751i
\(771\) −34.5880 + 23.1398i −1.24566 + 0.833359i
\(772\) −17.4625 17.4625i −0.628489 0.628489i
\(773\) 19.6669 + 19.6669i 0.707370 + 0.707370i 0.965981 0.258611i \(-0.0832649\pi\)
−0.258611 + 0.965981i \(0.583265\pi\)
\(774\) −1.04161 + 2.52288i −0.0374399 + 0.0906829i
\(775\) 21.3330 13.7322i 0.766305 0.493274i
\(776\) 4.09766i 0.147097i
\(777\) 3.93581 19.8463i 0.141196 0.711983i
\(778\) −1.25223 + 1.25223i