Properties

Label 570.2.k.a.533.6
Level $570$
Weight $2$
Character 570.533
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 533.6
Character \(\chi\) \(=\) 570.533
Dual form 570.2.k.a.77.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.668751 + 1.59774i) q^{3} +1.00000i q^{4} +(-0.595769 - 2.15524i) q^{5} +(0.656894 - 1.60265i) q^{6} +(-0.0702822 + 0.0702822i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.10554 + 2.13698i) q^{9} +O(q^{10})\) \(q+(-0.707107 - 0.707107i) q^{2} +(0.668751 + 1.59774i) q^{3} +1.00000i q^{4} +(-0.595769 - 2.15524i) q^{5} +(0.656894 - 1.60265i) q^{6} +(-0.0702822 + 0.0702822i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.10554 + 2.13698i) q^{9} +(-1.10271 + 1.94526i) q^{10} +3.25490i q^{11} +(-1.59774 + 0.668751i) q^{12} +(1.84783 + 1.84783i) q^{13} +0.0993940 q^{14} +(3.04509 - 2.39320i) q^{15} -1.00000 q^{16} +(3.76548 + 3.76548i) q^{17} +(2.99992 - 0.0222303i) q^{18} -1.00000i q^{19} +(2.15524 - 0.595769i) q^{20} +(-0.159294 - 0.0652913i) q^{21} +(2.30156 - 2.30156i) q^{22} +(-1.02394 + 1.02394i) q^{23} +(1.60265 + 0.656894i) q^{24} +(-4.29012 + 2.56805i) q^{25} -2.61323i q^{26} +(-4.82242 - 1.93500i) q^{27} +(-0.0702822 - 0.0702822i) q^{28} +6.98010 q^{29} +(-3.84545 - 0.460953i) q^{30} +9.93413 q^{31} +(0.707107 + 0.707107i) q^{32} +(-5.20048 + 2.17672i) q^{33} -5.32519i q^{34} +(0.193347 + 0.109603i) q^{35} +(-2.13698 - 2.10554i) q^{36} +(-3.00157 + 3.00157i) q^{37} +(-0.707107 + 0.707107i) q^{38} +(-1.71661 + 4.18809i) q^{39} +(-1.94526 - 1.10271i) q^{40} +8.72182i q^{41} +(0.0664699 + 0.158806i) q^{42} +(-2.35540 - 2.35540i) q^{43} -3.25490 q^{44} +(5.86012 + 3.26480i) q^{45} +1.44807 q^{46} +(-0.871132 - 0.871132i) q^{47} +(-0.668751 - 1.59774i) q^{48} +6.99012i q^{49} +(4.84946 + 1.21769i) q^{50} +(-3.49808 + 8.53442i) q^{51} +(-1.84783 + 1.84783i) q^{52} +(-8.49654 + 8.49654i) q^{53} +(2.04172 + 4.77822i) q^{54} +(7.01508 - 1.93917i) q^{55} +0.0993940i q^{56} +(1.59774 - 0.668751i) q^{57} +(-4.93568 - 4.93568i) q^{58} -2.24875 q^{59} +(2.39320 + 3.04509i) q^{60} +8.33970 q^{61} +(-7.02449 - 7.02449i) q^{62} +(-0.00220956 - 0.298174i) q^{63} -1.00000i q^{64} +(2.88164 - 5.08340i) q^{65} +(5.21646 + 2.13812i) q^{66} +(2.25310 - 2.25310i) q^{67} +(-3.76548 + 3.76548i) q^{68} +(-2.32074 - 0.951225i) q^{69} +(-0.0592159 - 0.214218i) q^{70} -6.67876i q^{71} +(0.0222303 + 2.99992i) q^{72} +(-4.70997 - 4.70997i) q^{73} +4.24487 q^{74} +(-6.97210 - 5.13710i) q^{75} +1.00000 q^{76} +(-0.228761 - 0.228761i) q^{77} +(4.17525 - 1.74760i) q^{78} -9.81442i q^{79} +(0.595769 + 2.15524i) q^{80} +(-0.133378 - 8.99901i) q^{81} +(6.16725 - 6.16725i) q^{82} +(10.5506 - 10.5506i) q^{83} +(0.0652913 - 0.159294i) q^{84} +(5.87215 - 10.3589i) q^{85} +3.33103i q^{86} +(4.66795 + 11.1524i) q^{87} +(2.30156 + 2.30156i) q^{88} +0.330099 q^{89} +(-1.83517 - 6.45230i) q^{90} -0.259739 q^{91} +(-1.02394 - 1.02394i) q^{92} +(6.64346 + 15.8722i) q^{93} +1.23197i q^{94} +(-2.15524 + 0.595769i) q^{95} +(-0.656894 + 1.60265i) q^{96} +(-3.68496 + 3.68496i) q^{97} +(4.94276 - 4.94276i) q^{98} +(-6.95565 - 6.85333i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} + O(q^{10}) \) \( 36q + 4q^{3} + 4q^{6} - 12q^{7} - 4q^{10} - 4q^{12} + 8q^{13} + 4q^{15} - 36q^{16} - 32q^{21} - 4q^{22} + 32q^{25} + 28q^{27} - 12q^{28} - 8q^{30} + 8q^{31} + 36q^{33} + 4q^{36} - 32q^{37} - 8q^{40} + 12q^{42} - 24q^{43} - 28q^{45} - 16q^{46} - 4q^{48} - 40q^{51} - 8q^{52} - 4q^{55} + 4q^{57} - 4q^{58} - 24q^{60} + 200q^{61} + 28q^{63} + 12q^{70} - 68q^{73} - 36q^{75} + 36q^{76} + 24q^{78} - 92q^{81} + 24q^{82} + 24q^{85} + 28q^{87} - 4q^{88} - 68q^{90} + 64q^{91} + 16q^{93} - 4q^{96} - 148q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(191\) \(211\) \(457\)
\(\chi(n)\) \(-1\) \(1\) \(e\left(\frac{3}{4}\right)\)

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
\(3\) 0.668751 + 1.59774i 0.386104 + 0.922455i
\(4\) 1.00000i 0.500000i
\(5\) −0.595769 2.15524i −0.266436 0.963853i
\(6\) 0.656894 1.60265i 0.268176 0.654280i
\(7\) −0.0702822 + 0.0702822i −0.0265642 + 0.0265642i −0.720264 0.693700i \(-0.755979\pi\)
0.693700 + 0.720264i \(0.255979\pi\)
\(8\) 0.707107 0.707107i 0.250000 0.250000i
\(9\) −2.10554 + 2.13698i −0.701848 + 0.712327i
\(10\) −1.10271 + 1.94526i −0.348708 + 0.615144i
\(11\) 3.25490i 0.981388i 0.871332 + 0.490694i \(0.163257\pi\)
−0.871332 + 0.490694i \(0.836743\pi\)
\(12\) −1.59774 + 0.668751i −0.461228 + 0.193052i
\(13\) 1.84783 + 1.84783i 0.512496 + 0.512496i 0.915290 0.402795i \(-0.131961\pi\)
−0.402795 + 0.915290i \(0.631961\pi\)
\(14\) 0.0993940 0.0265642
\(15\) 3.04509 2.39320i 0.786239 0.617923i
\(16\) −1.00000 −0.250000
\(17\) 3.76548 + 3.76548i 0.913262 + 0.913262i 0.996527 0.0832653i \(-0.0265349\pi\)
−0.0832653 + 0.996527i \(0.526535\pi\)
\(18\) 2.99992 0.0222303i 0.707087 0.00523973i
\(19\) 1.00000i 0.229416i
\(20\) 2.15524 0.595769i 0.481926 0.133218i
\(21\) −0.159294 0.0652913i −0.0347608 0.0142477i
\(22\) 2.30156 2.30156i 0.490694 0.490694i
\(23\) −1.02394 + 1.02394i −0.213506 + 0.213506i −0.805755 0.592249i \(-0.798240\pi\)
0.592249 + 0.805755i \(0.298240\pi\)
\(24\) 1.60265 + 0.656894i 0.327140 + 0.134088i
\(25\) −4.29012 + 2.56805i −0.858024 + 0.513610i
\(26\) 2.61323i 0.512496i
\(27\) −4.82242 1.93500i −0.928076 0.372391i
\(28\) −0.0702822 0.0702822i −0.0132821 0.0132821i
\(29\) 6.98010 1.29617 0.648086 0.761567i \(-0.275570\pi\)
0.648086 + 0.761567i \(0.275570\pi\)
\(30\) −3.84545 0.460953i −0.702081 0.0841582i
\(31\) 9.93413 1.78422 0.892111 0.451816i \(-0.149224\pi\)
0.892111 + 0.451816i \(0.149224\pi\)
\(32\) 0.707107 + 0.707107i 0.125000 + 0.125000i
\(33\) −5.20048 + 2.17672i −0.905287 + 0.378918i
\(34\) 5.32519i 0.913262i
\(35\) 0.193347 + 0.109603i 0.0326816 + 0.0185263i
\(36\) −2.13698 2.10554i −0.356164 0.350924i
\(37\) −3.00157 + 3.00157i −0.493456 + 0.493456i −0.909393 0.415938i \(-0.863453\pi\)
0.415938 + 0.909393i \(0.363453\pi\)
\(38\) −0.707107 + 0.707107i −0.114708 + 0.114708i
\(39\) −1.71661 + 4.18809i −0.274878 + 0.670631i
\(40\) −1.94526 1.10271i −0.307572 0.174354i
\(41\) 8.72182i 1.36212i 0.732228 + 0.681059i \(0.238480\pi\)
−0.732228 + 0.681059i \(0.761520\pi\)
\(42\) 0.0664699 + 0.158806i 0.0102565 + 0.0245043i
\(43\) −2.35540 2.35540i −0.359195 0.359195i 0.504321 0.863516i \(-0.331743\pi\)
−0.863516 + 0.504321i \(0.831743\pi\)
\(44\) −3.25490 −0.490694
\(45\) 5.86012 + 3.26480i 0.873576 + 0.486688i
\(46\) 1.44807 0.213506
\(47\) −0.871132 0.871132i −0.127068 0.127068i 0.640713 0.767781i \(-0.278639\pi\)
−0.767781 + 0.640713i \(0.778639\pi\)
\(48\) −0.668751 1.59774i −0.0965260 0.230614i
\(49\) 6.99012i 0.998589i
\(50\) 4.84946 + 1.21769i 0.685817 + 0.172207i
\(51\) −3.49808 + 8.53442i −0.489829 + 1.19506i
\(52\) −1.84783 + 1.84783i −0.256248 + 0.256248i
\(53\) −8.49654 + 8.49654i −1.16709 + 1.16709i −0.184201 + 0.982889i \(0.558970\pi\)
−0.982889 + 0.184201i \(0.941030\pi\)
\(54\) 2.04172 + 4.77822i 0.277843 + 0.650233i
\(55\) 7.01508 1.93917i 0.945914 0.261477i
\(56\) 0.0993940i 0.0132821i
\(57\) 1.59774 0.668751i 0.211626 0.0885783i
\(58\) −4.93568 4.93568i −0.648086 0.648086i
\(59\) −2.24875 −0.292762 −0.146381 0.989228i \(-0.546763\pi\)
−0.146381 + 0.989228i \(0.546763\pi\)
\(60\) 2.39320 + 3.04509i 0.308961 + 0.393119i
\(61\) 8.33970 1.06779 0.533895 0.845551i \(-0.320728\pi\)
0.533895 + 0.845551i \(0.320728\pi\)
\(62\) −7.02449 7.02449i −0.892111 0.892111i
\(63\) −0.00220956 0.298174i −0.000278378 0.0375664i
\(64\) 1.00000i 0.125000i
\(65\) 2.88164 5.08340i 0.357423 0.630518i
\(66\) 5.21646 + 2.13812i 0.642102 + 0.263185i
\(67\) 2.25310 2.25310i 0.275260 0.275260i −0.555954 0.831213i \(-0.687647\pi\)
0.831213 + 0.555954i \(0.187647\pi\)
\(68\) −3.76548 + 3.76548i −0.456631 + 0.456631i
\(69\) −2.32074 0.951225i −0.279385 0.114514i
\(70\) −0.0592159 0.214218i −0.00707765 0.0256039i
\(71\) 6.67876i 0.792623i −0.918116 0.396311i \(-0.870290\pi\)
0.918116 0.396311i \(-0.129710\pi\)
\(72\) 0.0222303 + 2.99992i 0.00261986 + 0.353544i
\(73\) −4.70997 4.70997i −0.551260 0.551260i 0.375544 0.926805i \(-0.377456\pi\)
−0.926805 + 0.375544i \(0.877456\pi\)
\(74\) 4.24487 0.493456
\(75\) −6.97210 5.13710i −0.805069 0.593182i
\(76\) 1.00000 0.114708
\(77\) −0.228761 0.228761i −0.0260698 0.0260698i
\(78\) 4.17525 1.74760i 0.472754 0.197877i
\(79\) 9.81442i 1.10421i −0.833775 0.552104i \(-0.813825\pi\)
0.833775 0.552104i \(-0.186175\pi\)
\(80\) 0.595769 + 2.15524i 0.0666090 + 0.240963i
\(81\) −0.133378 8.99901i −0.0148198 0.999890i
\(82\) 6.16725 6.16725i 0.681059 0.681059i
\(83\) 10.5506 10.5506i 1.15808 1.15808i 0.173188 0.984889i \(-0.444593\pi\)
0.984889 0.173188i \(-0.0554067\pi\)
\(84\) 0.0652913 0.159294i 0.00712387 0.0173804i
\(85\) 5.87215 10.3589i 0.636924 1.12358i
\(86\) 3.33103i 0.359195i
\(87\) 4.66795 + 11.1524i 0.500457 + 1.19566i
\(88\) 2.30156 + 2.30156i 0.245347 + 0.245347i
\(89\) 0.330099 0.0349904 0.0174952 0.999847i \(-0.494431\pi\)
0.0174952 + 0.999847i \(0.494431\pi\)
\(90\) −1.83517 6.45230i −0.193444 0.680132i
\(91\) −0.259739 −0.0272280
\(92\) −1.02394 1.02394i −0.106753 0.106753i
\(93\) 6.64346 + 15.8722i 0.688895 + 1.64587i
\(94\) 1.23197i 0.127068i
\(95\) −2.15524 + 0.595769i −0.221123 + 0.0611246i
\(96\) −0.656894 + 1.60265i −0.0670439 + 0.163570i
\(97\) −3.68496 + 3.68496i −0.374151 + 0.374151i −0.868986 0.494836i \(-0.835228\pi\)
0.494836 + 0.868986i \(0.335228\pi\)
\(98\) 4.94276 4.94276i 0.499294 0.499294i
\(99\) −6.95565 6.85333i −0.699070 0.688785i
\(100\) −2.56805 4.29012i −0.256805 0.429012i
\(101\) 10.2407i 1.01898i 0.860475 + 0.509492i \(0.170167\pi\)
−0.860475 + 0.509492i \(0.829833\pi\)
\(102\) 8.50826 3.56123i 0.842443 0.352614i
\(103\) −6.21848 6.21848i −0.612725 0.612725i 0.330930 0.943655i \(-0.392638\pi\)
−0.943655 + 0.330930i \(0.892638\pi\)
\(104\) 2.61323 0.256248
\(105\) −0.0458160 + 0.382215i −0.00447119 + 0.0373004i
\(106\) 12.0159 1.16709
\(107\) −8.75189 8.75189i −0.846077 0.846077i 0.143564 0.989641i \(-0.454144\pi\)
−0.989641 + 0.143564i \(0.954144\pi\)
\(108\) 1.93500 4.82242i 0.186195 0.464038i
\(109\) 13.5040i 1.29345i −0.762725 0.646723i \(-0.776139\pi\)
0.762725 0.646723i \(-0.223861\pi\)
\(110\) −6.33161 3.58922i −0.603696 0.342218i
\(111\) −6.80304 2.78843i −0.645716 0.264666i
\(112\) 0.0702822 0.0702822i 0.00664104 0.00664104i
\(113\) 1.54982 1.54982i 0.145794 0.145794i −0.630442 0.776236i \(-0.717126\pi\)
0.776236 + 0.630442i \(0.217126\pi\)
\(114\) −1.60265 0.656894i −0.150102 0.0615237i
\(115\) 2.81686 + 1.59680i 0.262674 + 0.148902i
\(116\) 6.98010i 0.648086i
\(117\) −7.83946 + 0.0580928i −0.724758 + 0.00537068i
\(118\) 1.59010 + 1.59010i 0.146381 + 0.146381i
\(119\) −0.529292 −0.0485201
\(120\) 0.460953 3.84545i 0.0420791 0.351040i
\(121\) 0.405644 0.0368767
\(122\) −5.89706 5.89706i −0.533895 0.533895i
\(123\) −13.9352 + 5.83273i −1.25649 + 0.525919i
\(124\) 9.93413i 0.892111i
\(125\) 8.09069 + 7.71627i 0.723653 + 0.690164i
\(126\) −0.209278 + 0.212403i −0.0186440 + 0.0189224i
\(127\) −15.2603 + 15.2603i −1.35413 + 1.35413i −0.473148 + 0.880983i \(0.656882\pi\)
−0.880983 + 0.473148i \(0.843118\pi\)
\(128\) −0.707107 + 0.707107i −0.0625000 + 0.0625000i
\(129\) 2.18814 5.33849i 0.192655 0.470028i
\(130\) −5.63213 + 1.55688i −0.493970 + 0.136547i
\(131\) 3.07551i 0.268709i 0.990933 + 0.134354i \(0.0428960\pi\)
−0.990933 + 0.134354i \(0.957104\pi\)
\(132\) −2.17672 5.20048i −0.189459 0.452643i
\(133\) 0.0702822 + 0.0702822i 0.00609424 + 0.00609424i
\(134\) −3.18636 −0.275260
\(135\) −1.29734 + 11.5463i −0.111657 + 0.993747i
\(136\) 5.32519 0.456631
\(137\) −8.96502 8.96502i −0.765934 0.765934i 0.211454 0.977388i \(-0.432180\pi\)
−0.977388 + 0.211454i \(0.932180\pi\)
\(138\) 0.968396 + 2.31363i 0.0824354 + 0.196949i
\(139\) 8.80702i 0.747002i −0.927630 0.373501i \(-0.878157\pi\)
0.927630 0.373501i \(-0.121843\pi\)
\(140\) −0.109603 + 0.193347i −0.00926315 + 0.0163408i
\(141\) 0.809272 1.97441i 0.0681530 0.166276i
\(142\) −4.72260 + 4.72260i −0.396311 + 0.396311i
\(143\) −6.01449 + 6.01449i −0.502957 + 0.502957i
\(144\) 2.10554 2.13698i 0.175462 0.178082i
\(145\) −4.15853 15.0438i −0.345347 1.24932i
\(146\) 6.66091i 0.551260i
\(147\) −11.1684 + 4.67465i −0.921153 + 0.385559i
\(148\) −3.00157 3.00157i −0.246728 0.246728i
\(149\) 19.3731 1.58710 0.793552 0.608503i \(-0.208230\pi\)
0.793552 + 0.608503i \(0.208230\pi\)
\(150\) 1.29754 + 8.56250i 0.105944 + 0.699125i
\(151\) 15.4311 1.25577 0.627883 0.778308i \(-0.283922\pi\)
0.627883 + 0.778308i \(0.283922\pi\)
\(152\) −0.707107 0.707107i −0.0573539 0.0573539i
\(153\) −15.9751 + 0.118380i −1.29151 + 0.00957049i
\(154\) 0.323517i 0.0260698i
\(155\) −5.91845 21.4104i −0.475381 1.71973i
\(156\) −4.18809 1.71661i −0.335315 0.137439i
\(157\) 13.5743 13.5743i 1.08335 1.08335i 0.0871534 0.996195i \(-0.472223\pi\)
0.996195 0.0871534i \(-0.0277770\pi\)
\(158\) −6.93985 + 6.93985i −0.552104 + 0.552104i
\(159\) −19.2573 7.89318i −1.52721 0.625970i
\(160\) 1.10271 1.94526i 0.0871771 0.153786i
\(161\) 0.143929i 0.0113432i
\(162\) −6.26895 + 6.45757i −0.492535 + 0.507355i
\(163\) −1.79928 1.79928i −0.140930 0.140930i 0.633122 0.774052i \(-0.281773\pi\)
−0.774052 + 0.633122i \(0.781773\pi\)
\(164\) −8.72182 −0.681059
\(165\) 7.78963 + 9.91146i 0.606422 + 0.771606i
\(166\) −14.9208 −1.15808
\(167\) −3.31894 3.31894i −0.256827 0.256827i 0.566935 0.823762i \(-0.308129\pi\)
−0.823762 + 0.566935i \(0.808129\pi\)
\(168\) −0.158806 + 0.0664699i −0.0122521 + 0.00512826i
\(169\) 6.17105i 0.474696i
\(170\) −11.4771 + 3.17258i −0.880250 + 0.243326i
\(171\) 2.13698 + 2.10554i 0.163419 + 0.161015i
\(172\) 2.35540 2.35540i 0.179597 0.179597i
\(173\) −2.84866 + 2.84866i −0.216580 + 0.216580i −0.807056 0.590476i \(-0.798940\pi\)
0.590476 + 0.807056i \(0.298940\pi\)
\(174\) 4.58518 11.1867i 0.347602 0.848059i
\(175\) 0.121031 0.482007i 0.00914906 0.0364363i
\(176\) 3.25490i 0.245347i
\(177\) −1.50385 3.59291i −0.113037 0.270060i
\(178\) −0.233415 0.233415i −0.0174952 0.0174952i
\(179\) 7.34939 0.549319 0.274660 0.961541i \(-0.411435\pi\)
0.274660 + 0.961541i \(0.411435\pi\)
\(180\) −3.26480 + 5.86012i −0.243344 + 0.436788i
\(181\) −24.4774 −1.81939 −0.909695 0.415277i \(-0.863685\pi\)
−0.909695 + 0.415277i \(0.863685\pi\)
\(182\) 0.183663 + 0.183663i 0.0136140 + 0.0136140i
\(183\) 5.57719 + 13.3247i 0.412278 + 0.984988i
\(184\) 1.44807i 0.106753i
\(185\) 8.25736 + 4.68087i 0.607093 + 0.344144i
\(186\) 6.52567 15.9209i 0.478485 1.16738i
\(187\) −12.2562 + 12.2562i −0.896265 + 0.896265i
\(188\) 0.871132 0.871132i 0.0635339 0.0635339i
\(189\) 0.474927 0.202935i 0.0345458 0.0147613i
\(190\) 1.94526 + 1.10271i 0.141124 + 0.0799992i
\(191\) 1.13422i 0.0820694i −0.999158 0.0410347i \(-0.986935\pi\)
0.999158 0.0410347i \(-0.0130654\pi\)
\(192\) 1.59774 0.668751i 0.115307 0.0482630i
\(193\) 6.15920 + 6.15920i 0.443349 + 0.443349i 0.893136 0.449787i \(-0.148500\pi\)
−0.449787 + 0.893136i \(0.648500\pi\)
\(194\) 5.21132 0.374151
\(195\) 10.0490 + 1.20458i 0.719627 + 0.0862614i
\(196\) −6.99012 −0.499294
\(197\) −7.62320 7.62320i −0.543130 0.543130i 0.381315 0.924445i \(-0.375471\pi\)
−0.924445 + 0.381315i \(0.875471\pi\)
\(198\) 0.0723573 + 9.76442i 0.00514221 + 0.693927i
\(199\) 1.98374i 0.140624i −0.997525 0.0703119i \(-0.977601\pi\)
0.997525 0.0703119i \(-0.0223994\pi\)
\(200\) −1.21769 + 4.84946i −0.0861034 + 0.342908i
\(201\) 5.10663 + 2.09310i 0.360194 + 0.147636i
\(202\) 7.24125 7.24125i 0.509492 0.509492i
\(203\) −0.490577 + 0.490577i −0.0344317 + 0.0344317i
\(204\) −8.53442 3.49808i −0.597529 0.244915i
\(205\) 18.7976 5.19619i 1.31288 0.362918i
\(206\) 8.79426i 0.612725i
\(207\) −0.0321909 4.34408i −0.00223742 0.301934i
\(208\) −1.84783 1.84783i −0.128124 0.128124i
\(209\) 3.25490 0.225146
\(210\) 0.302664 0.237870i 0.0208858 0.0164146i
\(211\) −9.94617 −0.684723 −0.342361 0.939568i \(-0.611227\pi\)
−0.342361 + 0.939568i \(0.611227\pi\)
\(212\) −8.49654 8.49654i −0.583545 0.583545i
\(213\) 10.6709 4.46643i 0.731159 0.306035i
\(214\) 12.3770i 0.846077i
\(215\) −3.67317 + 6.47972i −0.250508 + 0.441913i
\(216\) −4.77822 + 2.04172i −0.325117 + 0.138921i
\(217\) −0.698192 + 0.698192i −0.0473964 + 0.0473964i
\(218\) −9.54875 + 9.54875i −0.646723 + 0.646723i
\(219\) 4.37551 10.6751i 0.295669 0.721357i
\(220\) 1.93917 + 7.01508i 0.130739 + 0.472957i
\(221\) 13.9159i 0.936086i
\(222\) 2.83876 + 6.78219i 0.190525 + 0.455191i
\(223\) 10.6374 + 10.6374i 0.712332 + 0.712332i 0.967023 0.254691i \(-0.0819736\pi\)
−0.254691 + 0.967023i \(0.581974\pi\)
\(224\) −0.0993940 −0.00664104
\(225\) 3.54515 14.5750i 0.236343 0.971670i
\(226\) −2.19177 −0.145794
\(227\) −0.315490 0.315490i −0.0209398 0.0209398i 0.696559 0.717499i \(-0.254713\pi\)
−0.717499 + 0.696559i \(0.754713\pi\)
\(228\) 0.668751 + 1.59774i 0.0442891 + 0.105813i
\(229\) 2.55362i 0.168748i 0.996434 + 0.0843740i \(0.0268890\pi\)
−0.996434 + 0.0843740i \(0.973111\pi\)
\(230\) −0.862713 3.12093i −0.0568856 0.205788i
\(231\) 0.212517 0.518485i 0.0139826 0.0341138i
\(232\) 4.93568 4.93568i 0.324043 0.324043i
\(233\) 16.5030 16.5030i 1.08115 1.08115i 0.0847454 0.996403i \(-0.472992\pi\)
0.996403 0.0847454i \(-0.0270077\pi\)
\(234\) 5.58441 + 5.50226i 0.365065 + 0.359694i
\(235\) −1.35851 + 2.39649i −0.0886191 + 0.156330i
\(236\) 2.24875i 0.146381i
\(237\) 15.6809 6.56341i 1.01858 0.426339i
\(238\) 0.374266 + 0.374266i 0.0242600 + 0.0242600i
\(239\) 12.9423 0.837167 0.418583 0.908178i \(-0.362527\pi\)
0.418583 + 0.908178i \(0.362527\pi\)
\(240\) −3.04509 + 2.39320i −0.196560 + 0.154481i
\(241\) −27.2768 −1.75705 −0.878526 0.477694i \(-0.841473\pi\)
−0.878526 + 0.477694i \(0.841473\pi\)
\(242\) −0.286834 0.286834i −0.0184384 0.0184384i
\(243\) 14.2889 6.23121i 0.916632 0.399732i
\(244\) 8.33970i 0.533895i
\(245\) 15.0654 4.16450i 0.962492 0.266060i
\(246\) 13.9780 + 5.72931i 0.891206 + 0.365287i
\(247\) 1.84783 1.84783i 0.117575 0.117575i
\(248\) 7.02449 7.02449i 0.446056 0.446056i
\(249\) 23.9128 + 9.80136i 1.51541 + 0.621136i
\(250\) −0.264753 11.1772i −0.0167444 0.706908i
\(251\) 3.84899i 0.242946i −0.992595 0.121473i \(-0.961238\pi\)
0.992595 0.121473i \(-0.0387618\pi\)
\(252\) 0.298174 0.00220956i 0.0187832 0.000139189i
\(253\) −3.33281 3.33281i −0.209532 0.209532i
\(254\) 21.5813 1.35413
\(255\) 20.4778 + 2.45466i 1.28237 + 0.153717i
\(256\) 1.00000 0.0625000
\(257\) 1.91882 + 1.91882i 0.119693 + 0.119693i 0.764416 0.644723i \(-0.223027\pi\)
−0.644723 + 0.764416i \(0.723027\pi\)
\(258\) −5.32213 + 2.22763i −0.331341 + 0.138686i
\(259\) 0.421914i 0.0262165i
\(260\) 5.08340 + 2.88164i 0.315259 + 0.178711i
\(261\) −14.6969 + 14.9163i −0.909715 + 0.923298i
\(262\) 2.17471 2.17471i 0.134354 0.134354i
\(263\) −1.90216 + 1.90216i −0.117292 + 0.117292i −0.763317 0.646024i \(-0.776430\pi\)
0.646024 + 0.763317i \(0.276430\pi\)
\(264\) −2.13812 + 5.21646i −0.131592 + 0.321051i
\(265\) 23.3741 + 13.2501i 1.43586 + 0.813948i
\(266\) 0.0993940i 0.00609424i
\(267\) 0.220754 + 0.527412i 0.0135099 + 0.0322771i
\(268\) 2.25310 + 2.25310i 0.137630 + 0.137630i
\(269\) 11.5783 0.705939 0.352970 0.935635i \(-0.385172\pi\)
0.352970 + 0.935635i \(0.385172\pi\)
\(270\) 9.08182 7.24711i 0.552702 0.441045i
\(271\) 10.6701 0.648161 0.324081 0.946029i \(-0.394945\pi\)
0.324081 + 0.946029i \(0.394945\pi\)
\(272\) −3.76548 3.76548i −0.228316 0.228316i
\(273\) −0.173701 0.414995i −0.0105129 0.0251167i
\(274\) 12.6785i 0.765934i
\(275\) −8.35874 13.9639i −0.504051 0.842054i
\(276\) 0.951225 2.32074i 0.0572570 0.139692i
\(277\) −14.7968 + 14.7968i −0.889056 + 0.889056i −0.994432 0.105376i \(-0.966395\pi\)
0.105376 + 0.994432i \(0.466395\pi\)
\(278\) −6.22750 + 6.22750i −0.373501 + 0.373501i
\(279\) −20.9167 + 21.2290i −1.25225 + 1.27095i
\(280\) 0.214218 0.0592159i 0.0128020 0.00353883i
\(281\) 3.17823i 0.189597i 0.995496 + 0.0947985i \(0.0302207\pi\)
−0.995496 + 0.0947985i \(0.969779\pi\)
\(282\) −1.96836 + 0.823880i −0.117214 + 0.0490613i
\(283\) 12.7639 + 12.7639i 0.758734 + 0.758734i 0.976092 0.217358i \(-0.0697439\pi\)
−0.217358 + 0.976092i \(0.569744\pi\)
\(284\) 6.67876 0.396311
\(285\) −2.39320 3.04509i −0.141761 0.180376i
\(286\) 8.50578 0.502957
\(287\) −0.612988 0.612988i −0.0361836 0.0361836i
\(288\) −2.99992 + 0.0222303i −0.176772 + 0.00130993i
\(289\) 11.3576i 0.668095i
\(290\) −7.69704 + 13.5781i −0.451986 + 0.797333i
\(291\) −8.35192 3.42328i −0.489598 0.200676i
\(292\) 4.70997 4.70997i 0.275630 0.275630i
\(293\) 19.9916 19.9916i 1.16792 1.16792i 0.185226 0.982696i \(-0.440698\pi\)
0.982696 0.185226i \(-0.0593017\pi\)
\(294\) 11.2027 + 4.59177i 0.653356 + 0.267797i
\(295\) 1.33973 + 4.84659i 0.0780023 + 0.282179i
\(296\) 4.24487i 0.246728i
\(297\) 6.29822 15.6965i 0.365460 0.910803i
\(298\) −13.6988 13.6988i −0.793552 0.793552i
\(299\) −3.78412 −0.218841
\(300\) 5.13710 6.97210i 0.296591 0.402534i
\(301\) 0.331085 0.0190834
\(302\) −10.9114 10.9114i −0.627883 0.627883i
\(303\) −16.3619 + 6.84846i −0.939968 + 0.393434i
\(304\) 1.00000i 0.0573539i
\(305\) −4.96854 17.9741i −0.284498 1.02919i
\(306\) 11.3798 + 11.2124i 0.650541 + 0.640971i
\(307\) −22.8303 + 22.8303i −1.30299 + 1.30299i −0.376629 + 0.926364i \(0.622917\pi\)
−0.926364 + 0.376629i \(0.877083\pi\)
\(308\) 0.228761 0.228761i 0.0130349 0.0130349i
\(309\) 5.77689 14.0941i 0.328636 0.801787i
\(310\) −10.9545 + 19.3244i −0.622173 + 1.09755i
\(311\) 23.6135i 1.33900i −0.742814 0.669498i \(-0.766509\pi\)
0.742814 0.669498i \(-0.233491\pi\)
\(312\) 1.74760 + 4.17525i 0.0989383 + 0.236377i
\(313\) 17.4841 + 17.4841i 0.988260 + 0.988260i 0.999932 0.0116720i \(-0.00371538\pi\)
−0.0116720 + 0.999932i \(0.503715\pi\)
\(314\) −19.1970 −1.08335
\(315\) −0.641320 + 0.182405i −0.0361343 + 0.0102774i
\(316\) 9.81442 0.552104
\(317\) 7.39204 + 7.39204i 0.415178 + 0.415178i 0.883538 0.468360i \(-0.155155\pi\)
−0.468360 + 0.883538i \(0.655155\pi\)
\(318\) 8.03567 + 19.1983i 0.450618 + 1.07659i
\(319\) 22.7195i 1.27205i
\(320\) −2.15524 + 0.595769i −0.120482 + 0.0333045i
\(321\) 8.13040 19.8361i 0.453795 1.10714i
\(322\) −0.101773 + 0.101773i −0.00567160 + 0.00567160i
\(323\) 3.76548 3.76548i 0.209517 0.209517i
\(324\) 8.99901 0.133378i 0.499945 0.00740989i
\(325\) −12.6727 3.18209i −0.702956 0.176510i
\(326\) 2.54457i 0.140930i
\(327\) 21.5758 9.03080i 1.19315 0.499404i
\(328\) 6.16725 + 6.16725i 0.340530 + 0.340530i
\(329\) 0.122450 0.00675090
\(330\) 1.50036 12.5166i 0.0825919 0.689014i
\(331\) 2.95830 0.162603 0.0813014 0.996690i \(-0.474092\pi\)
0.0813014 + 0.996690i \(0.474092\pi\)
\(332\) 10.5506 + 10.5506i 0.579038 + 0.579038i
\(333\) −0.0943646 12.7342i −0.00517115 0.697833i
\(334\) 4.69368i 0.256827i
\(335\) −6.19829 3.51364i −0.338649 0.191971i
\(336\) 0.159294 + 0.0652913i 0.00869020 + 0.00356193i
\(337\) −7.56158 + 7.56158i −0.411905 + 0.411905i −0.882402 0.470497i \(-0.844075\pi\)
0.470497 + 0.882402i \(0.344075\pi\)
\(338\) −4.36359 + 4.36359i −0.237348 + 0.237348i
\(339\) 3.51264 + 1.43976i 0.190781 + 0.0781970i
\(340\) 10.3589 + 5.87215i 0.561788 + 0.318462i
\(341\) 32.3346i 1.75102i
\(342\) −0.0222303 2.99992i −0.00120208 0.162217i
\(343\) −0.983256 0.983256i −0.0530909 0.0530909i
\(344\) −3.33103 −0.179597
\(345\) −0.667491 + 5.56847i −0.0359365 + 0.299796i
\(346\) 4.02862 0.216580
\(347\) −1.03476 1.03476i −0.0555491 0.0555491i 0.678787 0.734336i \(-0.262506\pi\)
−0.734336 + 0.678787i \(0.762506\pi\)
\(348\) −11.1524 + 4.66795i −0.597830 + 0.250228i
\(349\) 3.40331i 0.182175i −0.995843 0.0910876i \(-0.970966\pi\)
0.995843 0.0910876i \(-0.0290343\pi\)
\(350\) −0.426412 + 0.255249i −0.0227927 + 0.0136436i
\(351\) −5.33547 12.4866i −0.284786 0.666484i
\(352\) −2.30156 + 2.30156i −0.122674 + 0.122674i
\(353\) 11.6964 11.6964i 0.622536 0.622536i −0.323643 0.946179i \(-0.604908\pi\)
0.946179 + 0.323643i \(0.104908\pi\)
\(354\) −1.47719 + 3.60396i −0.0785117 + 0.191548i
\(355\) −14.3943 + 3.97900i −0.763972 + 0.211183i
\(356\) 0.330099i 0.0174952i
\(357\) −0.353965 0.845670i −0.0187338 0.0447576i
\(358\) −5.19681 5.19681i −0.274660 0.274660i
\(359\) −17.2125 −0.908438 −0.454219 0.890890i \(-0.650082\pi\)
−0.454219 + 0.890890i \(0.650082\pi\)
\(360\) 6.45230 1.83517i 0.340066 0.0967219i
\(361\) −1.00000 −0.0526316
\(362\) 17.3081 + 17.3081i 0.909695 + 0.909695i
\(363\) 0.271275 + 0.648114i 0.0142383 + 0.0340171i
\(364\) 0.259739i 0.0136140i
\(365\) −7.34506 + 12.9572i −0.384458 + 0.678210i
\(366\) 5.47830 13.3656i 0.286355 0.698633i
\(367\) −9.63368 + 9.63368i −0.502874 + 0.502874i −0.912330 0.409456i \(-0.865719\pi\)
0.409456 + 0.912330i \(0.365719\pi\)
\(368\) 1.02394 1.02394i 0.0533764 0.0533764i
\(369\) −18.6384 18.3642i −0.970274 0.956000i
\(370\) −2.52896 9.14871i −0.131474 0.475619i
\(371\) 1.19431i 0.0620055i
\(372\) −15.8722 + 6.64346i −0.822933 + 0.344448i
\(373\) −9.07273 9.07273i −0.469768 0.469768i 0.432071 0.901839i \(-0.357783\pi\)
−0.901839 + 0.432071i \(0.857783\pi\)
\(374\) 17.3329 0.896265
\(375\) −6.91793 + 18.0871i −0.357240 + 0.934012i
\(376\) −1.23197 −0.0635339
\(377\) 12.8980 + 12.8980i 0.664282 + 0.664282i
\(378\) −0.479320 0.192327i −0.0246536 0.00989225i
\(379\) 9.80779i 0.503792i −0.967754 0.251896i \(-0.918946\pi\)
0.967754 0.251896i \(-0.0810542\pi\)
\(380\) −0.595769 2.15524i −0.0305623 0.110561i
\(381\) −34.5873 14.1766i −1.77196 0.726290i
\(382\) −0.802016 + 0.802016i −0.0410347 + 0.0410347i
\(383\) 4.82382 4.82382i 0.246486 0.246486i −0.573041 0.819527i \(-0.694236\pi\)
0.819527 + 0.573041i \(0.194236\pi\)
\(384\) −1.60265 0.656894i −0.0817849 0.0335220i
\(385\) −0.356747 + 0.629324i −0.0181815 + 0.0320733i
\(386\) 8.71042i 0.443349i
\(387\) 9.99283 0.0740499i 0.507964 0.00376417i
\(388\) −3.68496 3.68496i −0.187075 0.187075i
\(389\) −12.4320 −0.630330 −0.315165 0.949037i \(-0.602060\pi\)
−0.315165 + 0.949037i \(0.602060\pi\)
\(390\) −6.25398 7.95751i −0.316683 0.402944i
\(391\) −7.71122 −0.389973
\(392\) 4.94276 + 4.94276i 0.249647 + 0.249647i
\(393\) −4.91386 + 2.05675i −0.247872 + 0.103749i
\(394\) 10.7808i 0.543130i
\(395\) −21.1524 + 5.84713i −1.06429 + 0.294201i
\(396\) 6.85333 6.95565i 0.344393 0.349535i
\(397\) 24.5965 24.5965i 1.23446 1.23446i 0.272234 0.962231i \(-0.412238\pi\)
0.962231 0.272234i \(-0.0877623\pi\)
\(398\) −1.40272 + 1.40272i −0.0703119 + 0.0703119i
\(399\) −0.0652913 + 0.159294i −0.00326865 + 0.00797467i
\(400\) 4.29012 2.56805i 0.214506 0.128403i
\(401\) 31.8360i 1.58981i 0.606731 + 0.794907i \(0.292480\pi\)
−0.606731 + 0.794907i \(0.707520\pi\)
\(402\) −2.13088 5.09098i −0.106279 0.253915i
\(403\) 18.3566 + 18.3566i 0.914406 + 0.914406i
\(404\) −10.2407 −0.509492
\(405\) −19.3156 + 5.64880i −0.959798 + 0.280691i
\(406\) 0.693780 0.0344317
\(407\) −9.76981 9.76981i −0.484272 0.484272i
\(408\) 3.56123 + 8.50826i 0.176307 + 0.421222i
\(409\) 18.0144i 0.890754i 0.895343 + 0.445377i \(0.146930\pi\)
−0.895343 + 0.445377i \(0.853070\pi\)
\(410\) −16.9662 9.61765i −0.837900 0.474982i
\(411\) 8.32840 20.3191i 0.410810 1.00227i
\(412\) 6.21848 6.21848i 0.306363 0.306363i
\(413\) 0.158047 0.158047i 0.00777698 0.00777698i
\(414\) −3.04897 + 3.09449i −0.149848 + 0.152086i
\(415\) −29.0247 16.4533i −1.42477 0.807662i
\(416\) 2.61323i 0.128124i
\(417\) 14.0713 5.88971i 0.689076 0.288420i
\(418\) −2.30156 2.30156i −0.112573 0.112573i
\(419\) 18.0752 0.883032 0.441516 0.897253i \(-0.354441\pi\)
0.441516 + 0.897253i \(0.354441\pi\)
\(420\) −0.382215 0.0458160i −0.0186502 0.00223559i
\(421\) 34.7735 1.69475 0.847377 0.530991i \(-0.178180\pi\)
0.847377 + 0.530991i \(0.178180\pi\)
\(422\) 7.03301 + 7.03301i 0.342361 + 0.342361i
\(423\) 3.69580 0.0273870i 0.179696 0.00133160i
\(424\) 12.0159i 0.583545i
\(425\) −25.8243 6.48440i −1.25266 0.314540i
\(426\) −10.7037 4.38724i −0.518597 0.212562i
\(427\) −0.586133 + 0.586133i −0.0283649 + 0.0283649i
\(428\) 8.75189 8.75189i 0.423038 0.423038i
\(429\) −13.6318 5.58739i −0.658149 0.269762i
\(430\) 7.17918 1.98453i 0.346211 0.0957024i
\(431\) 23.0890i 1.11216i 0.831130 + 0.556079i \(0.187695\pi\)
−0.831130 + 0.556079i \(0.812305\pi\)
\(432\) 4.82242 + 1.93500i 0.232019 + 0.0930977i
\(433\) −27.1524 27.1524i −1.30486 1.30486i −0.925073 0.379790i \(-0.875996\pi\)
−0.379790 0.925073i \(-0.624004\pi\)
\(434\) 0.987393 0.0473964
\(435\) 21.2550 16.7048i 1.01910 0.800934i
\(436\) 13.5040 0.646723
\(437\) 1.02394 + 1.02394i 0.0489816 + 0.0489816i
\(438\) −10.6424 + 4.45449i −0.508513 + 0.212844i
\(439\) 4.16128i 0.198607i −0.995057 0.0993035i \(-0.968339\pi\)
0.995057 0.0993035i \(-0.0316615\pi\)
\(440\) 3.58922 6.33161i 0.171109 0.301848i
\(441\) −14.9378 14.7180i −0.711322 0.700857i
\(442\) 9.84004 9.84004i 0.468043 0.468043i
\(443\) 7.44535 7.44535i 0.353739 0.353739i −0.507760 0.861499i \(-0.669526\pi\)
0.861499 + 0.507760i \(0.169526\pi\)
\(444\) 2.78843 6.80304i 0.132333 0.322858i
\(445\) −0.196663 0.711442i −0.00932270 0.0337256i
\(446\) 15.0435i 0.712332i
\(447\) 12.9558 + 30.9531i 0.612787 + 1.46403i
\(448\) 0.0702822 + 0.0702822i 0.00332052 + 0.00332052i
\(449\) −11.6674 −0.550618 −0.275309 0.961356i \(-0.588780\pi\)
−0.275309 + 0.961356i \(0.588780\pi\)
\(450\) −12.8129 + 7.79931i −0.604007 + 0.367663i
\(451\) −28.3886 −1.33677
\(452\) 1.54982 + 1.54982i 0.0728972 + 0.0728972i
\(453\) 10.3196 + 24.6549i 0.484856 + 1.15839i
\(454\) 0.446170i 0.0209398i
\(455\) 0.154744 + 0.559800i 0.00725453 + 0.0262438i
\(456\) 0.656894 1.60265i 0.0307619 0.0750510i
\(457\) −13.3405 + 13.3405i −0.624041 + 0.624041i −0.946562 0.322521i \(-0.895470\pi\)
0.322521 + 0.946562i \(0.395470\pi\)
\(458\) 1.80568 1.80568i 0.0843740 0.0843740i
\(459\) −10.8725 25.4449i −0.507486 1.18767i
\(460\) −1.59680 + 2.81686i −0.0744512 + 0.131337i
\(461\) 11.7687i 0.548122i 0.961712 + 0.274061i \(0.0883670\pi\)
−0.961712 + 0.274061i \(0.911633\pi\)
\(462\) −0.516896 + 0.216353i −0.0240482 + 0.0100656i
\(463\) 17.0577 + 17.0577i 0.792739 + 0.792739i 0.981939 0.189200i \(-0.0605894\pi\)
−0.189200 + 0.981939i \(0.560589\pi\)
\(464\) −6.98010 −0.324043
\(465\) 30.2503 23.7744i 1.40283 1.10251i
\(466\) −23.3388 −1.08115
\(467\) −20.8943 20.8943i −0.966874 0.966874i 0.0325947 0.999469i \(-0.489623\pi\)
−0.999469 + 0.0325947i \(0.989623\pi\)
\(468\) −0.0580928 7.83946i −0.00268534 0.362379i
\(469\) 0.316705i 0.0146241i
\(470\) 2.65519 0.733968i 0.122475 0.0338554i
\(471\) 30.7661 + 12.6104i 1.41763 + 0.581055i
\(472\) −1.59010 + 1.59010i −0.0731905 + 0.0731905i
\(473\) 7.66658 7.66658i 0.352510 0.352510i
\(474\) −15.7291 6.44703i −0.722461 0.296122i
\(475\) 2.56805 + 4.29012i 0.117830 + 0.196844i
\(476\) 0.529292i 0.0242600i
\(477\) −0.267117 36.0468i −0.0122305 1.65047i
\(478\) −9.15158 9.15158i −0.418583 0.418583i
\(479\) −27.6237 −1.26216 −0.631079 0.775718i \(-0.717388\pi\)
−0.631079 + 0.775718i \(0.717388\pi\)
\(480\) 3.84545 + 0.460953i 0.175520 + 0.0210396i
\(481\) −11.0928 −0.505788
\(482\) 19.2876 + 19.2876i 0.878526 + 0.878526i
\(483\) 0.229961 0.0962528i 0.0104636 0.00437965i
\(484\) 0.405644i 0.0184384i
\(485\) 10.1373 + 5.74658i 0.460313 + 0.260939i
\(486\) −14.5099 5.69764i −0.658182 0.258450i
\(487\) −15.5968 + 15.5968i −0.706757 + 0.706757i −0.965852 0.259095i \(-0.916576\pi\)
0.259095 + 0.965852i \(0.416576\pi\)
\(488\) 5.89706 5.89706i 0.266947 0.266947i
\(489\) 1.67151 4.07805i 0.0755883 0.184416i
\(490\) −13.5976 7.70809i −0.614276 0.348216i
\(491\) 36.7768i 1.65971i −0.557978 0.829856i \(-0.688422\pi\)
0.557978 0.829856i \(-0.311578\pi\)
\(492\) −5.83273 13.9352i −0.262960 0.628247i
\(493\) 26.2834 + 26.2834i 1.18374 + 1.18374i
\(494\) −2.61323 −0.117575
\(495\) −10.6266 + 19.0741i −0.477630 + 0.857317i
\(496\) −9.93413 −0.446056
\(497\) 0.469398 + 0.469398i 0.0210554 + 0.0210554i
\(498\) −9.97829 23.8395i −0.447138 1.06827i
\(499\) 27.0776i 1.21216i −0.795404 0.606080i \(-0.792741\pi\)
0.795404 0.606080i \(-0.207259\pi\)
\(500\) −7.71627 + 8.09069i −0.345082 + 0.361826i
\(501\) 3.08325 7.52234i 0.137749 0.336073i
\(502\) −2.72165 + 2.72165i −0.121473 + 0.121473i
\(503\) −22.6492 + 22.6492i −1.00988 + 1.00988i −0.00992738 + 0.999951i \(0.503160\pi\)
−0.999951 + 0.00992738i \(0.996840\pi\)
\(504\) −0.212403 0.209278i −0.00946119 0.00932200i
\(505\) 22.0711 6.10108i 0.982151 0.271494i
\(506\) 4.71331i 0.209532i
\(507\) 9.85973 4.12690i 0.437886 0.183282i
\(508\) −15.2603 15.2603i −0.677065 0.677065i
\(509\) 24.2312 1.07403 0.537015 0.843572i \(-0.319552\pi\)
0.537015 + 0.843572i \(0.319552\pi\)
\(510\) −12.7443 16.2157i −0.564325 0.718042i
\(511\) 0.662054 0.0292876
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) −1.93500 + 4.82242i −0.0854323 + 0.212915i
\(514\) 2.71362i 0.119693i
\(515\) −9.69754 + 17.1071i −0.427325 + 0.753829i
\(516\) 5.33849 + 2.18814i 0.235014 + 0.0963273i
\(517\) 2.83545 2.83545i 0.124703 0.124703i
\(518\) −0.298338 + 0.298338i −0.0131082 + 0.0131082i
\(519\) −6.45647 2.64637i −0.283408 0.116163i
\(520\) −1.55688 5.63213i −0.0682737 0.246985i
\(521\) 36.4402i 1.59647i 0.602343 + 0.798237i \(0.294234\pi\)
−0.602343 + 0.798237i \(0.705766\pi\)
\(522\) 20.9397 0.155170i 0.916507 0.00679159i
\(523\) −7.87242 7.87242i −0.344237 0.344237i 0.513721 0.857957i \(-0.328267\pi\)
−0.857957 + 0.513721i \(0.828267\pi\)
\(524\) −3.07551 −0.134354
\(525\) 0.851061 0.128968i 0.0371434 0.00562860i
\(526\) 2.69006 0.117292
\(527\) 37.4067 + 37.4067i 1.62946 + 1.62946i
\(528\) 5.20048 2.17672i 0.226322 0.0947295i
\(529\) 20.9031i 0.908831i
\(530\) −7.15872 25.8972i −0.310955 1.12490i
\(531\) 4.73483 4.80553i 0.205474 0.208542i
\(532\) −0.0702822 + 0.0702822i −0.00304712 + 0.00304712i
\(533\) −16.1164 + 16.1164i −0.698080 + 0.698080i
\(534\) 0.216840 0.529033i 0.00938358 0.0228935i
\(535\) −13.6483 + 24.0765i −0.590068 + 1.04092i
\(536\) 3.18636i 0.137630i
\(537\) 4.91492 + 11.7424i 0.212094 + 0.506723i
\(538\) −8.18707 8.18707i −0.352970 0.352970i
\(539\) −22.7521 −0.980003
\(540\) −11.5463 1.29734i −0.496873 0.0558285i
\(541\) −22.5624 −0.970033 −0.485017 0.874505i \(-0.661186\pi\)
−0.485017 + 0.874505i \(0.661186\pi\)
\(542\) −7.54489 7.54489i −0.324081 0.324081i
\(543\) −16.3693 39.1085i −0.702474 1.67831i
\(544\) 5.32519i 0.228316i
\(545\) −29.1043 + 8.04525i −1.24669 + 0.344620i
\(546\) −0.170621 + 0.416271i −0.00730190 + 0.0178148i
\(547\) 30.2103 30.2103i 1.29170 1.29170i 0.357966 0.933735i \(-0.383470\pi\)
0.933735 0.357966i \(-0.116530\pi\)
\(548\) 8.96502 8.96502i 0.382967 0.382967i
\(549\) −17.5596 + 17.8218i −0.749426 + 0.760615i
\(550\) −3.96344 + 15.7845i −0.169002 + 0.673053i
\(551\) 6.98010i 0.297362i
\(552\) −2.31363 + 0.968396i −0.0984747 + 0.0412177i
\(553\) 0.689779 + 0.689779i 0.0293324 + 0.0293324i
\(554\) 20.9259 0.889056
\(555\) −1.95669 + 16.3234i −0.0830567 + 0.692891i
\(556\) 8.80702 0.373501
\(557\) 26.8130 + 26.8130i 1.13610 + 1.13610i 0.989142 + 0.146962i \(0.0469495\pi\)
0.146962 + 0.989142i \(0.453050\pi\)
\(558\) 29.8016 0.220839i 1.26160 0.00934884i
\(559\) 8.70474i 0.368171i
\(560\) −0.193347 0.109603i −0.00817040 0.00463157i
\(561\) −27.7787 11.3859i −1.17282 0.480713i
\(562\) 2.24735 2.24735i 0.0947985 0.0947985i
\(563\) 20.9853 20.9853i 0.884426 0.884426i −0.109555 0.993981i \(-0.534942\pi\)
0.993981 + 0.109555i \(0.0349425\pi\)
\(564\) 1.97441 + 0.809272i 0.0831378 + 0.0340765i
\(565\) −4.26356 2.41689i −0.179369 0.101679i
\(566\) 18.0509i 0.758734i
\(567\) 0.641844 + 0.623096i 0.0269549 + 0.0261676i
\(568\) −4.72260 4.72260i −0.198156 0.198156i
\(569\) 10.5079 0.440513 0.220257 0.975442i \(-0.429311\pi\)
0.220257 + 0.975442i \(0.429311\pi\)
\(570\) −0.460953 + 3.84545i −0.0193072 + 0.161068i
\(571\) 43.4684 1.81910 0.909548 0.415598i \(-0.136428\pi\)
0.909548 + 0.415598i \(0.136428\pi\)
\(572\) −6.01449 6.01449i −0.251479 0.251479i
\(573\) 1.81219 0.758513i 0.0757054 0.0316873i
\(574\) 0.866896i 0.0361836i
\(575\) 1.76329 7.02234i 0.0735342 0.292852i
\(576\) 2.13698 + 2.10554i 0.0890409 + 0.0877310i
\(577\) 17.9007 17.9007i 0.745215 0.745215i −0.228362 0.973576i \(-0.573337\pi\)
0.973576 + 0.228362i \(0.0733369\pi\)
\(578\) 8.03105 8.03105i 0.334048 0.334048i
\(579\) −5.72182 + 13.9598i −0.237791 + 0.580148i
\(580\) 15.0438 4.15853i 0.624659 0.172673i
\(581\) 1.48304i 0.0615267i
\(582\) 3.48507 + 8.32632i 0.144461 + 0.345137i
\(583\) −27.6554 27.6554i −1.14537 1.14537i
\(584\) −6.66091 −0.275630
\(585\) 4.79571 + 16.8613i 0.198278 + 0.697129i
\(586\) −28.2724 −1.16792
\(587\) 13.5624 + 13.5624i 0.559781 + 0.559781i 0.929245 0.369464i \(-0.120459\pi\)
−0.369464 + 0.929245i \(0.620459\pi\)
\(588\) −4.67465 11.1684i −0.192779 0.460577i
\(589\) 9.93413i 0.409329i
\(590\) 2.47972 4.37439i 0.102089 0.180091i
\(591\) 7.08186 17.2779i 0.291309 0.710718i
\(592\) 3.00157 3.00157i 0.123364 0.123364i
\(593\) −7.39960 + 7.39960i −0.303865 + 0.303865i −0.842524 0.538659i \(-0.818931\pi\)
0.538659 + 0.842524i \(0.318931\pi\)
\(594\) −15.5526 + 6.64558i −0.638132 + 0.272671i
\(595\) 0.315336 + 1.14075i 0.0129275 + 0.0467662i
\(596\) 19.3731i 0.793552i
\(597\) 3.16950 1.32663i 0.129719 0.0542954i
\(598\) 2.67578 + 2.67578i 0.109421 + 0.109421i
\(599\) −20.8602 −0.852326 −0.426163 0.904646i \(-0.640135\pi\)
−0.426163 + 0.904646i \(0.640135\pi\)
\(600\) −8.56250 + 1.29754i −0.349563 + 0.0529718i
\(601\) −15.2975 −0.624000 −0.312000 0.950082i \(-0.600999\pi\)
−0.312000 + 0.950082i \(0.600999\pi\)
\(602\) −0.234112 0.234112i −0.00954171 0.00954171i
\(603\) 0.0708337 + 9.55882i 0.00288457 + 0.389265i
\(604\) 15.4311i 0.627883i
\(605\) −0.241670 0.874261i −0.00982529 0.0355437i
\(606\) 16.4122 + 6.72703i 0.666701 + 0.273267i
\(607\) 33.6117 33.6117i 1.36426 1.36426i 0.495849 0.868409i \(-0.334857\pi\)
0.868409 0.495849i \(-0.165143\pi\)
\(608\) 0.707107 0.707107i 0.0286770 0.0286770i
\(609\) −1.11189 0.455740i −0.0450560 0.0184675i
\(610\) −9.19629 + 16.2229i −0.372347 + 0.656845i
\(611\) 3.21941i 0.130243i
\(612\) −0.118380 15.9751i −0.00478525 0.645756i
\(613\) −7.47342 7.47342i −0.301849 0.301849i 0.539888 0.841737i \(-0.318467\pi\)
−0.841737 + 0.539888i \(0.818467\pi\)
\(614\) 32.2869 1.30299
\(615\) 20.8731 + 26.5587i 0.841684 + 1.07095i
\(616\) −0.323517 −0.0130349
\(617\) −5.02881 5.02881i −0.202452 0.202452i 0.598598 0.801050i \(-0.295725\pi\)
−0.801050 + 0.598598i \(0.795725\pi\)
\(618\) −14.0509 + 5.88117i −0.565211 + 0.236575i
\(619\) 40.6819i 1.63514i −0.575826 0.817572i \(-0.695319\pi\)
0.575826 0.817572i \(-0.304681\pi\)
\(620\) 21.4104 5.91845i 0.859864 0.237691i
\(621\) 6.91918 2.95654i 0.277657 0.118642i
\(622\) −16.6972 + 16.6972i −0.669498 + 0.669498i
\(623\) −0.0232001 + 0.0232001i −0.000929491 + 0.000929491i
\(624\) 1.71661 4.18809i 0.0687195 0.167658i
\(625\) 11.8102 22.0345i 0.472409 0.881379i
\(626\) 24.7263i 0.988260i
\(627\) 2.17672 + 5.20048i 0.0869297 + 0.207687i
\(628\) 13.5743 + 13.5743i 0.541674 + 0.541674i
\(629\) −22.6047 −0.901309
\(630\) 0.582461 + 0.324502i 0.0232058 + 0.0129285i
\(631\) 37.2313 1.48215 0.741077 0.671420i \(-0.234315\pi\)
0.741077 + 0.671420i \(0.234315\pi\)
\(632\) −6.93985 6.93985i −0.276052 0.276052i
\(633\) −6.65152 15.8914i −0.264374 0.631626i
\(634\) 10.4539i 0.415178i
\(635\) 41.9812 + 23.7980i 1.66597 + 0.944393i
\(636\) 7.89318 19.2573i 0.312985 0.763603i
\(637\) −12.9166 + 12.9166i −0.511772 + 0.511772i
\(638\) 16.0651 16.0651i 0.636024 0.636024i
\(639\) 14.2724 + 14.0624i 0.564607 + 0.556301i
\(640\) 1.94526 + 1.10271i 0.0768930 + 0.0435885i
\(641\) 19.9142i 0.786564i 0.919418 + 0.393282i \(0.128660\pi\)
−0.919418 + 0.393282i \(0.871340\pi\)
\(642\) −19.7753 + 8.27716i −0.780468 + 0.326674i
\(643\) −30.9151 30.9151i −1.21917 1.21917i −0.967922 0.251251i \(-0.919158\pi\)
−0.251251 0.967922i \(-0.580842\pi\)
\(644\) 0.143929 0.00567160
\(645\) −12.8093 1.53545i −0.504367 0.0604584i
\(646\) −5.32519 −0.209517
\(647\) −2.55700 2.55700i −0.100526 0.100526i 0.655055 0.755581i \(-0.272645\pi\)
−0.755581 + 0.655055i \(0.772645\pi\)
\(648\) −6.45757 6.26895i −0.253677 0.246268i
\(649\) 7.31944i 0.287313i
\(650\) 6.71090 + 11.2110i 0.263223 + 0.439733i
\(651\) −1.58245 0.648612i −0.0620210 0.0254211i
\(652\) 1.79928 1.79928i 0.0704652 0.0704652i
\(653\) 2.83582 2.83582i 0.110974 0.110974i −0.649439 0.760413i \(-0.724996\pi\)
0.760413 + 0.649439i \(0.224996\pi\)
\(654\) −21.6421 8.87067i −0.846275 0.346871i
\(655\) 6.62846 1.83229i 0.258995 0.0715936i
\(656\) 8.72182i 0.340530i
\(657\) 19.9822 0.148074i 0.779579 0.00577691i
\(658\) −0.0865854 0.0865854i −0.00337545 0.00337545i
\(659\) −19.5551 −0.761760 −0.380880 0.924624i \(-0.624379\pi\)
−0.380880 + 0.924624i \(0.624379\pi\)
\(660\) −9.91146 + 7.78963i −0.385803 + 0.303211i
\(661\) 4.07898 0.158654 0.0793269 0.996849i \(-0.474723\pi\)
0.0793269 + 0.996849i \(0.474723\pi\)
\(662\) −2.09183 2.09183i −0.0813014 0.0813014i
\(663\) −22.2340 + 9.30629i −0.863497 + 0.361426i
\(664\) 14.9208i 0.579038i
\(665\) 0.109603 0.193347i 0.00425022 0.00749767i
\(666\) −8.93775 + 9.07120i −0.346331 + 0.351502i
\(667\) −7.14718 + 7.14718i −0.276740 + 0.276740i
\(668\) 3.31894 3.31894i 0.128413 0.128413i
\(669\) −9.88200 + 24.1095i −0.382060 + 0.932129i
\(670\) 1.89834 + 6.86737i 0.0733391 + 0.265310i
\(671\) 27.1449i 1.04792i
\(672\) −0.0664699 0.158806i −0.00256413 0.00612607i
\(673\) 3.90944 + 3.90944i 0.150698 + 0.150698i 0.778430 0.627732i \(-0.216017\pi\)
−0.627732 + 0.778430i \(0.716017\pi\)
\(674\) 10.6937 0.411905
\(675\) 25.6579 4.08285i 0.987575 0.157149i
\(676\) 6.17105 0.237348
\(677\) −12.6939 12.6939i −0.487866 0.487866i 0.419766 0.907632i \(-0.362112\pi\)
−0.907632 + 0.419766i \(0.862112\pi\)
\(678\) −1.46575 3.50188i −0.0562918 0.134489i
\(679\) 0.517974i 0.0198780i
\(680\) −3.17258 11.4771i −0.121663 0.440125i
\(681\) 0.293086 0.715054i 0.0112311 0.0274009i
\(682\) 22.8640 22.8640i 0.875508 0.875508i
\(683\) 21.0801 21.0801i 0.806609 0.806609i −0.177510 0.984119i \(-0.556804\pi\)
0.984119 + 0.177510i \(0.0568041\pi\)
\(684\) −2.10554 + 2.13698i −0.0805074 + 0.0817095i
\(685\) −13.9807 + 24.6629i −0.534175 + 0.942320i
\(686\) 1.39053i 0.0530909i
\(687\) −4.08002 + 1.70774i −0.155662 + 0.0651542i
\(688\) 2.35540 + 2.35540i 0.0897987 + 0.0897987i
\(689\) −31.4003 −1.19626
\(690\) 4.40949 3.46552i 0.167866 0.131930i
\(691\) 13.9849 0.532010 0.266005 0.963972i \(-0.414296\pi\)
0.266005 + 0.963972i \(0.414296\pi\)
\(692\) −2.84866 2.84866i −0.108290 0.108290i
\(693\) 0.970525 0.00719188i 0.0368672 0.000273197i
\(694\) 1.46338i 0.0555491i
\(695\) −18.9812 + 5.24695i −0.719999 + 0.199028i
\(696\) 11.1867 + 4.58518i 0.424029 + 0.173801i
\(697\) −32.8418 + 32.8418i −1.24397 + 1.24397i
\(698\) −2.40651 + 2.40651i −0.0910876 + 0.0910876i
\(699\) 37.4039 + 15.3311i 1.41475 + 0.579875i
\(700\) 0.482007 + 0.121031i 0.0182182 + 0.00457453i
\(701\) 45.3072i 1.71123i −0.517614 0.855614i \(-0.673180\pi\)
0.517614 0.855614i \(-0.326820\pi\)
\(702\) −5.05659 + 12.6021i −0.190849 + 0.475635i
\(703\) 3.00157 + 3.00157i 0.113206 + 0.113206i
\(704\) 3.25490 0.122674
\(705\) −4.73747 0.567880i −0.178424 0.0213876i
\(706\) −16.5412 −0.622536
\(707\) −0.719737 0.719737i −0.0270685 0.0270685i
\(708\) 3.59291 1.50385i 0.135030 0.0565183i
\(709\) 34.5259i 1.29665i 0.761365 + 0.648323i \(0.224530\pi\)
−0.761365 + 0.648323i \(0.775470\pi\)
\(710\) 12.9919 + 7.36475i 0.487577 + 0.276394i
\(711\) 20.9732 + 20.6647i 0.786558 + 0.774986i
\(712\) 0.233415 0.233415i 0.00874760 0.00874760i
\(713\) −10.1719 + 10.1719i −0.380942 + 0.380942i
\(714\) −0.347688 + 0.848270i −0.0130119 + 0.0317457i
\(715\) 16.5459 + 9.37943i 0.618783 + 0.350771i
\(716\) 7.34939i 0.274660i
\(717\) 8.65517 + 20.6784i 0.323233 + 0.772249i
\(718\) 12.1710 + 12.1710i 0.454219 + 0.454219i
\(719\) −2.64921 −0.0987990 −0.0493995 0.998779i \(-0.515731\pi\)
−0.0493995 + 0.998779i \(0.515731\pi\)
\(720\) −5.86012 3.26480i −0.218394 0.121672i
\(721\) 0.874097 0.0325531
\(722\) 0.707107 + 0.707107i 0.0263158 + 0.0263158i
\(723\) −18.2414 43.5812i −0.678405 1.62080i
\(724\) 24.4774i 0.909695i
\(725\) −29.9455 + 17.9252i −1.11215 + 0.665727i
\(726\) 0.266465 0.650106i 0.00988945 0.0241277i
\(727\) 2.05295 2.05295i 0.0761398 0.0761398i −0.668011 0.744151i \(-0.732854\pi\)
0.744151 + 0.668011i \(0.232854\pi\)
\(728\) −0.183663 + 0.183663i −0.00680701 + 0.00680701i
\(729\) 19.5116 + 18.6628i 0.722650 + 0.691214i
\(730\) 14.3559 3.96836i 0.531334 0.146876i
\(731\) 17.7384i 0.656078i
\(732\) −13.3247 + 5.57719i −0.492494 + 0.206139i
\(733\) −1.89006 1.89006i −0.0698111 0.0698111i 0.671339 0.741150i \(-0.265719\pi\)
−0.741150 + 0.671339i \(0.765719\pi\)
\(734\) 13.6241 0.502874
\(735\) 16.7288 + 21.2856i 0.617050 + 0.785129i
\(736\) −1.44807 −0.0533764
\(737\) 7.33360 + 7.33360i 0.270137 + 0.270137i
\(738\) 0.193888 + 26.1647i 0.00713713 + 0.963137i
\(739\) 16.9189i 0.622373i −0.950349 0.311187i \(-0.899274\pi\)
0.950349 0.311187i \(-0.100726\pi\)
\(740\) −4.68087 + 8.25736i −0.172072 + 0.303546i
\(741\) 4.18809 + 1.71661i 0.153853 + 0.0630613i
\(742\) −0.844505 + 0.844505i −0.0310028 + 0.0310028i
\(743\) −13.2213 + 13.2213i −0.485044 + 0.485044i −0.906738 0.421694i \(-0.861436\pi\)
0.421694 + 0.906738i \(0.361436\pi\)
\(744\) 15.9209 + 6.52567i 0.583690 + 0.239243i
\(745\) −11.5419 41.7536i −0.422862 1.52973i
\(746\) 12.8308i 0.469768i
\(747\) 0.331693 + 44.7611i 0.0121360 + 1.63772i
\(748\) −12.2562 12.2562i −0.448132 0.448132i
\(749\) 1.23020 0.0449507
\(750\) 17.6812 7.89778i 0.645626 0.288386i
\(751\) 9.73721 0.355316 0.177658 0.984092i \(-0.443148\pi\)
0.177658 + 0.984092i \(0.443148\pi\)
\(752\) 0.871132 + 0.871132i 0.0317669 + 0.0317669i
\(753\) 6.14968 2.57402i 0.224107 0.0938024i
\(754\) 18.2406i 0.664282i
\(755\) −9.19338 33.2577i −0.334581 1.21037i
\(756\) 0.202935 + 0.474927i 0.00738066 + 0.0172729i
\(757\) 23.5741 23.5741i 0.856814 0.856814i −0.134148 0.990961i \(-0.542830\pi\)
0.990961 + 0.134148i \(0.0428296\pi\)
\(758\) −6.93516 + 6.93516i −0.251896 + 0.251896i
\(759\) 3.09614 7.55379i 0.112383 0.274185i
\(760\) −1.10271 + 1.94526i −0.0399996 + 0.0705619i
\(761\) 6.55642i 0.237670i 0.992914 + 0.118835i \(0.0379160\pi\)
−0.992914 + 0.118835i \(0.962084\pi\)
\(762\) 14.4325 + 34.4813i 0.522835 + 1.24913i
\(763\) 0.949088 + 0.949088i 0.0343593 + 0.0343593i
\(764\) 1.13422 0.0410347
\(765\) 9.77262 + 34.3597i 0.353330 + 1.24228i
\(766\) −6.82192 −0.246486
\(767\) −4.15530 4.15530i −0.150039 0.150039i
\(768\) 0.668751 + 1.59774i 0.0241315 + 0.0576535i
\(769\) 3.44513i 0.124235i 0.998069 + 0.0621173i \(0.0197853\pi\)
−0.998069 + 0.0621173i \(0.980215\pi\)
\(770\) 0.697257 0.192742i 0.0251274 0.00694593i
\(771\) −1.78256 + 4.34899i −0.0641974 + 0.156625i
\(772\) −6.15920 + 6.15920i −0.221674 + 0.221674i
\(773\) 28.7349 28.7349i 1.03352 1.03352i 0.0341034 0.999418i \(-0.489142\pi\)
0.999418 0.0341034i \(-0.0108576\pi\)
\(774\) −7.11836 7.01364i −0.255864 0.252100i
\(775\) −42.6186 + 25.5113i −1.53090 + 0.916395i
\(776\) 5.21132i 0.187075i
\(777\) 0.674109 0.282156i 0.0241835 − <