Properties

Label 546.2.e.h.545.8
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.10070523904.11
Defining polynomial: \(x^{8} - 10 x^{4} + 81\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.8
Root \(1.68014 + 0.420861i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.h.545.7

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.68014 + 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(1.68014 + 0.420861i) q^{6} +(0.595188 + 2.57794i) q^{7} +1.00000 q^{8} +(2.64575 + 1.41421i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.68014 + 0.420861i) q^{3} +1.00000 q^{4} +0.841723i q^{5} +(1.68014 + 0.420861i) q^{6} +(0.595188 + 2.57794i) q^{7} +1.00000 q^{8} +(2.64575 + 1.41421i) q^{9} +0.841723i q^{10} +(1.68014 + 0.420861i) q^{12} +(-2.27533 - 2.79694i) q^{13} +(0.595188 + 2.57794i) q^{14} +(-0.354249 + 1.41421i) q^{15} +1.00000 q^{16} -4.33981 q^{17} +(2.64575 + 1.41421i) q^{18} -4.55066 q^{19} +0.841723i q^{20} +(-0.0849536 + 4.58179i) q^{21} -7.98430i q^{23} +(1.68014 + 0.420861i) q^{24} +4.29150 q^{25} +(-2.27533 - 2.79694i) q^{26} +(3.85005 + 3.48957i) q^{27} +(0.595188 + 2.57794i) q^{28} +2.32744i q^{29} +(-0.354249 + 1.41421i) q^{30} +5.53019 q^{31} +1.00000 q^{32} -4.33981 q^{34} +(-2.16991 + 0.500983i) q^{35} +(2.64575 + 1.41421i) q^{36} +5.15587i q^{37} -4.55066 q^{38} +(-2.64575 - 5.65685i) q^{39} +0.841723i q^{40} -10.8896i q^{41} +(-0.0849536 + 4.58179i) q^{42} +8.00000 q^{43} +(-1.19038 + 2.22699i) q^{45} -7.98430i q^{46} -7.82087i q^{47} +(1.68014 + 0.420861i) q^{48} +(-6.29150 + 3.06871i) q^{49} +4.29150 q^{50} +(-7.29150 - 1.82646i) q^{51} +(-2.27533 - 2.79694i) q^{52} -7.98430i q^{53} +(3.85005 + 3.48957i) q^{54} +(0.595188 + 2.57794i) q^{56} +(-7.64575 - 1.91520i) q^{57} +2.32744i q^{58} +3.91044i q^{59} +(-0.354249 + 1.41421i) q^{60} +5.59388i q^{61} +5.53019 q^{62} +(-2.07103 + 7.66230i) q^{63} +1.00000 q^{64} +(2.35425 - 1.91520i) q^{65} +1.82646i q^{67} -4.33981 q^{68} +(3.36028 - 13.4148i) q^{69} +(-2.16991 + 0.500983i) q^{70} -14.5830 q^{71} +(2.64575 + 1.41421i) q^{72} -3.14944 q^{73} +5.15587i q^{74} +(7.21033 + 1.80613i) q^{75} -4.55066 q^{76} +(-2.64575 - 5.65685i) q^{78} -11.2915 q^{79} +0.841723i q^{80} +(5.00000 + 7.48331i) q^{81} -10.8896i q^{82} -7.27733i q^{83} +(-0.0849536 + 4.58179i) q^{84} -3.65292i q^{85} +8.00000 q^{86} +(-0.979531 + 3.91044i) q^{87} +12.5730i q^{89} +(-1.19038 + 2.22699i) q^{90} +(5.85608 - 7.53036i) q^{91} -7.98430i q^{92} +(9.29150 + 2.32744i) q^{93} -7.82087i q^{94} -3.83039i q^{95} +(1.68014 + 0.420861i) q^{96} +9.87000 q^{97} +(-6.29150 + 3.06871i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} + O(q^{10}) \) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 24q^{15} + 8q^{16} + 8q^{21} - 8q^{25} - 24q^{30} + 8q^{32} + 8q^{42} + 64q^{43} - 8q^{49} - 8q^{50} - 16q^{51} - 40q^{57} - 24q^{60} - 8q^{63} + 8q^{64} + 40q^{65} - 32q^{71} - 48q^{79} + 40q^{81} + 8q^{84} + 64q^{86} - 32q^{91} + 32q^{93} - 8q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.68014 + 0.420861i 0.970030 + 0.242984i
\(4\) 1.00000 0.500000
\(5\) 0.841723i 0.376430i 0.982128 + 0.188215i \(0.0602702\pi\)
−0.982128 + 0.188215i \(0.939730\pi\)
\(6\) 1.68014 + 0.420861i 0.685915 + 0.171816i
\(7\) 0.595188 + 2.57794i 0.224960 + 0.974368i
\(8\) 1.00000 0.353553
\(9\) 2.64575 + 1.41421i 0.881917 + 0.471405i
\(10\) 0.841723i 0.266176i
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 1.68014 + 0.420861i 0.485015 + 0.121492i
\(13\) −2.27533 2.79694i −0.631063 0.775732i
\(14\) 0.595188 + 2.57794i 0.159071 + 0.688982i
\(15\) −0.354249 + 1.41421i −0.0914666 + 0.365148i
\(16\) 1.00000 0.250000
\(17\) −4.33981 −1.05256 −0.526280 0.850311i \(-0.676414\pi\)
−0.526280 + 0.850311i \(0.676414\pi\)
\(18\) 2.64575 + 1.41421i 0.623610 + 0.333333i
\(19\) −4.55066 −1.04399 −0.521996 0.852948i \(-0.674813\pi\)
−0.521996 + 0.852948i \(0.674813\pi\)
\(20\) 0.841723i 0.188215i
\(21\) −0.0849536 + 4.58179i −0.0185384 + 0.999828i
\(22\) 0 0
\(23\) 7.98430i 1.66484i −0.554144 0.832421i \(-0.686954\pi\)
0.554144 0.832421i \(-0.313046\pi\)
\(24\) 1.68014 + 0.420861i 0.342957 + 0.0859080i
\(25\) 4.29150 0.858301
\(26\) −2.27533 2.79694i −0.446229 0.548525i
\(27\) 3.85005 + 3.48957i 0.740942 + 0.671569i
\(28\) 0.595188 + 2.57794i 0.112480 + 0.487184i
\(29\) 2.32744i 0.432195i 0.976372 + 0.216098i \(0.0693330\pi\)
−0.976372 + 0.216098i \(0.930667\pi\)
\(30\) −0.354249 + 1.41421i −0.0646767 + 0.258199i
\(31\) 5.53019 0.993252 0.496626 0.867965i \(-0.334572\pi\)
0.496626 + 0.867965i \(0.334572\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −4.33981 −0.744272
\(35\) −2.16991 + 0.500983i −0.366781 + 0.0846816i
\(36\) 2.64575 + 1.41421i 0.440959 + 0.235702i
\(37\) 5.15587i 0.847620i 0.905751 + 0.423810i \(0.139308\pi\)
−0.905751 + 0.423810i \(0.860692\pi\)
\(38\) −4.55066 −0.738214
\(39\) −2.64575 5.65685i −0.423659 0.905822i
\(40\) 0.841723i 0.133088i
\(41\) 10.8896i 1.70067i −0.526244 0.850334i \(-0.676400\pi\)
0.526244 0.850334i \(-0.323600\pi\)
\(42\) −0.0849536 + 4.58179i −0.0131086 + 0.706985i
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) −1.19038 + 2.22699i −0.177451 + 0.331980i
\(46\) 7.98430i 1.17722i
\(47\) 7.82087i 1.14079i −0.821370 0.570396i \(-0.806790\pi\)
0.821370 0.570396i \(-0.193210\pi\)
\(48\) 1.68014 + 0.420861i 0.242508 + 0.0607461i
\(49\) −6.29150 + 3.06871i −0.898786 + 0.438387i
\(50\) 4.29150 0.606910
\(51\) −7.29150 1.82646i −1.02101 0.255756i
\(52\) −2.27533 2.79694i −0.315531 0.387866i
\(53\) 7.98430i 1.09673i −0.836240 0.548364i \(-0.815251\pi\)
0.836240 0.548364i \(-0.184749\pi\)
\(54\) 3.85005 + 3.48957i 0.523925 + 0.474871i
\(55\) 0 0
\(56\) 0.595188 + 2.57794i 0.0795353 + 0.344491i
\(57\) −7.64575 1.91520i −1.01270 0.253674i
\(58\) 2.32744i 0.305608i
\(59\) 3.91044i 0.509095i 0.967060 + 0.254548i \(0.0819266\pi\)
−0.967060 + 0.254548i \(0.918073\pi\)
\(60\) −0.354249 + 1.41421i −0.0457333 + 0.182574i
\(61\) 5.59388i 0.716223i 0.933679 + 0.358112i \(0.116579\pi\)
−0.933679 + 0.358112i \(0.883421\pi\)
\(62\) 5.53019 0.702335
\(63\) −2.07103 + 7.66230i −0.260926 + 0.965359i
\(64\) 1.00000 0.125000
\(65\) 2.35425 1.91520i 0.292009 0.237551i
\(66\) 0 0
\(67\) 1.82646i 0.223138i 0.993757 + 0.111569i \(0.0355876\pi\)
−0.993757 + 0.111569i \(0.964412\pi\)
\(68\) −4.33981 −0.526280
\(69\) 3.36028 13.4148i 0.404531 1.61495i
\(70\) −2.16991 + 0.500983i −0.259354 + 0.0598790i
\(71\) −14.5830 −1.73068 −0.865342 0.501182i \(-0.832899\pi\)
−0.865342 + 0.501182i \(0.832899\pi\)
\(72\) 2.64575 + 1.41421i 0.311805 + 0.166667i
\(73\) −3.14944 −0.368614 −0.184307 0.982869i \(-0.559004\pi\)
−0.184307 + 0.982869i \(0.559004\pi\)
\(74\) 5.15587i 0.599358i
\(75\) 7.21033 + 1.80613i 0.832577 + 0.208554i
\(76\) −4.55066 −0.521996
\(77\) 0 0
\(78\) −2.64575 5.65685i −0.299572 0.640513i
\(79\) −11.2915 −1.27039 −0.635197 0.772350i \(-0.719081\pi\)
−0.635197 + 0.772350i \(0.719081\pi\)
\(80\) 0.841723i 0.0941075i
\(81\) 5.00000 + 7.48331i 0.555556 + 0.831479i
\(82\) 10.8896i 1.20255i
\(83\) 7.27733i 0.798790i −0.916779 0.399395i \(-0.869220\pi\)
0.916779 0.399395i \(-0.130780\pi\)
\(84\) −0.0849536 + 4.58179i −0.00926920 + 0.499914i
\(85\) 3.65292i 0.396215i
\(86\) 8.00000 0.862662
\(87\) −0.979531 + 3.91044i −0.105017 + 0.419243i
\(88\) 0 0
\(89\) 12.5730i 1.33274i 0.745622 + 0.666369i \(0.232152\pi\)
−0.745622 + 0.666369i \(0.767848\pi\)
\(90\) −1.19038 + 2.22699i −0.125477 + 0.234745i
\(91\) 5.85608 7.53036i 0.613884 0.789396i
\(92\) 7.98430i 0.832421i
\(93\) 9.29150 + 2.32744i 0.963484 + 0.241345i
\(94\) 7.82087i 0.806661i
\(95\) 3.83039i 0.392990i
\(96\) 1.68014 + 0.420861i 0.171479 + 0.0429540i
\(97\) 9.87000 1.00215 0.501074 0.865405i \(-0.332939\pi\)
0.501074 + 0.865405i \(0.332939\pi\)
\(98\) −6.29150 + 3.06871i −0.635538 + 0.309987i
\(99\) 0 0
\(100\) 4.29150 0.429150
\(101\) −5.74103 −0.571254 −0.285627 0.958341i \(-0.592202\pi\)
−0.285627 + 0.958341i \(0.592202\pi\)
\(102\) −7.29150 1.82646i −0.721966 0.180847i
\(103\) 9.20614i 0.907108i 0.891229 + 0.453554i \(0.149844\pi\)
−0.891229 + 0.453554i \(0.850156\pi\)
\(104\) −2.27533 2.79694i −0.223114 0.274263i
\(105\) −3.85660 0.0715074i −0.376365 0.00697841i
\(106\) 7.98430i 0.775504i
\(107\) 5.65685i 0.546869i 0.961891 + 0.273434i \(0.0881596\pi\)
−0.961891 + 0.273434i \(0.911840\pi\)
\(108\) 3.85005 + 3.48957i 0.370471 + 0.335784i
\(109\) 15.4676i 1.48153i −0.671765 0.740764i \(-0.734464\pi\)
0.671765 0.740764i \(-0.265536\pi\)
\(110\) 0 0
\(111\) −2.16991 + 8.66259i −0.205958 + 0.822217i
\(112\) 0.595188 + 2.57794i 0.0562400 + 0.243592i
\(113\) 14.1421i 1.33038i 0.746674 + 0.665190i \(0.231650\pi\)
−0.746674 + 0.665190i \(0.768350\pi\)
\(114\) −7.64575 1.91520i −0.716090 0.179375i
\(115\) 6.72057 0.626696
\(116\) 2.32744i 0.216098i
\(117\) −2.06448 10.6178i −0.190862 0.981617i
\(118\) 3.91044i 0.359985i
\(119\) −2.58301 11.1878i −0.236784 1.02558i
\(120\) −0.354249 + 1.41421i −0.0323383 + 0.129099i
\(121\) −11.0000 −1.00000
\(122\) 5.59388i 0.506446i
\(123\) 4.58301 18.2960i 0.413236 1.64970i
\(124\) 5.53019 0.496626
\(125\) 7.82087i 0.699520i
\(126\) −2.07103 + 7.66230i −0.184502 + 0.682612i
\(127\) −6.58301 −0.584147 −0.292074 0.956396i \(-0.594345\pi\)
−0.292074 + 0.956396i \(0.594345\pi\)
\(128\) 1.00000 0.0883883
\(129\) 13.4411 + 3.36689i 1.18343 + 0.296438i
\(130\) 2.35425 1.91520i 0.206481 0.167974i
\(131\) −1.40122 −0.122425 −0.0612126 0.998125i \(-0.519497\pi\)
−0.0612126 + 0.998125i \(0.519497\pi\)
\(132\) 0 0
\(133\) −2.70850 11.7313i −0.234857 1.01723i
\(134\) 1.82646i 0.157782i
\(135\) −2.93725 + 3.24067i −0.252799 + 0.278913i
\(136\) −4.33981 −0.372136
\(137\) 1.29150 0.110341 0.0551703 0.998477i \(-0.482430\pi\)
0.0551703 + 0.998477i \(0.482430\pi\)
\(138\) 3.36028 13.4148i 0.286046 1.14194i
\(139\) 8.66259i 0.734752i 0.930073 + 0.367376i \(0.119744\pi\)
−0.930073 + 0.367376i \(0.880256\pi\)
\(140\) −2.16991 + 0.500983i −0.183391 + 0.0423408i
\(141\) 3.29150 13.1402i 0.277195 1.10660i
\(142\) −14.5830 −1.22378
\(143\) 0 0
\(144\) 2.64575 + 1.41421i 0.220479 + 0.117851i
\(145\) −1.95906 −0.162691
\(146\) −3.14944 −0.260649
\(147\) −11.8621 + 2.50802i −0.978371 + 0.206858i
\(148\) 5.15587i 0.423810i
\(149\) 6.00000 0.491539 0.245770 0.969328i \(-0.420959\pi\)
0.245770 + 0.969328i \(0.420959\pi\)
\(150\) 7.21033 + 1.80613i 0.588721 + 0.147470i
\(151\) 13.6412i 1.11010i −0.831817 0.555051i \(-0.812699\pi\)
0.831817 0.555051i \(-0.187301\pi\)
\(152\) −4.55066 −0.369107
\(153\) −11.4821 6.13742i −0.928270 0.496181i
\(154\) 0 0
\(155\) 4.65489i 0.373890i
\(156\) −2.64575 5.65685i −0.211830 0.452911i
\(157\) 17.8687i 1.42608i 0.701123 + 0.713040i \(0.252682\pi\)
−0.701123 + 0.713040i \(0.747318\pi\)
\(158\) −11.2915 −0.898304
\(159\) 3.36028 13.4148i 0.266488 1.06386i
\(160\) 0.841723i 0.0665440i
\(161\) 20.5830 4.75216i 1.62217 0.374523i
\(162\) 5.00000 + 7.48331i 0.392837 + 0.587945i
\(163\) 8.48528i 0.664619i 0.943170 + 0.332309i \(0.107828\pi\)
−0.943170 + 0.332309i \(0.892172\pi\)
\(164\) 10.8896i 0.850334i
\(165\) 0 0
\(166\) 7.27733i 0.564830i
\(167\) 1.68345i 0.130269i −0.997876 0.0651345i \(-0.979252\pi\)
0.997876 0.0651345i \(-0.0207476\pi\)
\(168\) −0.0849536 + 4.58179i −0.00655431 + 0.353493i
\(169\) −2.64575 + 12.7279i −0.203519 + 0.979071i
\(170\) 3.65292i 0.280166i
\(171\) −12.0399 6.43560i −0.920715 0.492143i
\(172\) 8.00000 0.609994
\(173\) −14.4207 −1.09638 −0.548191 0.836353i \(-0.684683\pi\)
−0.548191 + 0.836353i \(0.684683\pi\)
\(174\) −0.979531 + 3.91044i −0.0742581 + 0.296449i
\(175\) 2.55425 + 11.0632i 0.193083 + 0.836301i
\(176\) 0 0
\(177\) −1.64575 + 6.57008i −0.123702 + 0.493838i
\(178\) 12.5730i 0.942388i
\(179\) 11.3137i 0.845626i −0.906217 0.422813i \(-0.861043\pi\)
0.906217 0.422813i \(-0.138957\pi\)
\(180\) −1.19038 + 2.22699i −0.0887254 + 0.165990i
\(181\) 10.6442i 0.791178i 0.918428 + 0.395589i \(0.129460\pi\)
−0.918428 + 0.395589i \(0.870540\pi\)
\(182\) 5.85608 7.53036i 0.434082 0.558187i
\(183\) −2.35425 + 9.39851i −0.174031 + 0.694758i
\(184\) 7.98430i 0.588610i
\(185\) −4.33981 −0.319070
\(186\) 9.29150 + 2.32744i 0.681286 + 0.170656i
\(187\) 0 0
\(188\) 7.82087i 0.570396i
\(189\) −6.70439 + 12.0021i −0.487673 + 0.873026i
\(190\) 3.83039i 0.277886i
\(191\) 0.500983i 0.0362499i 0.999836 + 0.0181249i \(0.00576966\pi\)
−0.999836 + 0.0181249i \(0.994230\pi\)
\(192\) 1.68014 + 0.420861i 0.121254 + 0.0303731i
\(193\) 8.48528i 0.610784i −0.952227 0.305392i \(-0.901213\pi\)
0.952227 0.305392i \(-0.0987875\pi\)
\(194\) 9.87000 0.708625
\(195\) 4.76150 2.22699i 0.340978 0.159478i
\(196\) −6.29150 + 3.06871i −0.449393 + 0.219194i
\(197\) 8.58301 0.611514 0.305757 0.952110i \(-0.401091\pi\)
0.305757 + 0.952110i \(0.401091\pi\)
\(198\) 0 0
\(199\) 25.4442i 1.80369i −0.432056 0.901847i \(-0.642212\pi\)
0.432056 0.901847i \(-0.357788\pi\)
\(200\) 4.29150 0.303455
\(201\) −0.768687 + 3.06871i −0.0542190 + 0.216450i
\(202\) −5.74103 −0.403938
\(203\) −6.00000 + 1.38527i −0.421117 + 0.0972266i
\(204\) −7.29150 1.82646i −0.510507 0.127878i
\(205\) 9.16601 0.640182
\(206\) 9.20614i 0.641422i
\(207\) 11.2915 21.1245i 0.784814 1.46825i
\(208\) −2.27533 2.79694i −0.157766 0.193933i
\(209\) 0 0
\(210\) −3.85660 0.0715074i −0.266130 0.00493448i
\(211\) 10.5830 0.728564 0.364282 0.931289i \(-0.381314\pi\)
0.364282 + 0.931289i \(0.381314\pi\)
\(212\) 7.98430i 0.548364i
\(213\) −24.5015 6.13742i −1.67882 0.420529i
\(214\) 5.65685i 0.386695i
\(215\) 6.73378i 0.459240i
\(216\) 3.85005 + 3.48957i 0.261963 + 0.237435i
\(217\) 3.29150 + 14.2565i 0.223442 + 0.967793i
\(218\) 15.4676i 1.04760i
\(219\) −5.29150 1.32548i −0.357567 0.0895675i
\(220\) 0 0
\(221\) 9.87451 + 12.1382i 0.664231 + 0.816504i
\(222\) −2.16991 + 8.66259i −0.145635 + 0.581395i
\(223\) −14.6315 −0.979798 −0.489899 0.871779i \(-0.662966\pi\)
−0.489899 + 0.871779i \(0.662966\pi\)
\(224\) 0.595188 + 2.57794i 0.0397677 + 0.172246i
\(225\) 11.3542 + 6.06910i 0.756950 + 0.404607i
\(226\) 14.1421i 0.940721i
\(227\) 8.96077i 0.594747i 0.954761 + 0.297374i \(0.0961107\pi\)
−0.954761 + 0.297374i \(0.903889\pi\)
\(228\) −7.64575 1.91520i −0.506352 0.126837i
\(229\) 24.2907 1.60517 0.802586 0.596536i \(-0.203457\pi\)
0.802586 + 0.596536i \(0.203457\pi\)
\(230\) 6.72057 0.443141
\(231\) 0 0
\(232\) 2.32744i 0.152804i
\(233\) 22.6274i 1.48237i 0.671300 + 0.741186i \(0.265736\pi\)
−0.671300 + 0.741186i \(0.734264\pi\)
\(234\) −2.06448 10.6178i −0.134960 0.694108i
\(235\) 6.58301 0.429428
\(236\) 3.91044i 0.254548i
\(237\) −18.9713 4.75216i −1.23232 0.308686i
\(238\) −2.58301 11.1878i −0.167431 0.725195i
\(239\) −21.8745 −1.41494 −0.707472 0.706741i \(-0.750165\pi\)
−0.707472 + 0.706741i \(0.750165\pi\)
\(240\) −0.354249 + 1.41421i −0.0228667 + 0.0912871i
\(241\) 25.6919 1.65496 0.827480 0.561495i \(-0.189774\pi\)
0.827480 + 0.561495i \(0.189774\pi\)
\(242\) −11.0000 −0.707107
\(243\) 5.25127 + 14.6773i 0.336869 + 0.941551i
\(244\) 5.59388i 0.358112i
\(245\) −2.58301 5.29570i −0.165022 0.338330i
\(246\) 4.58301 18.2960i 0.292202 1.16651i
\(247\) 10.3542 + 12.7279i 0.658825 + 0.809858i
\(248\) 5.53019 0.351167
\(249\) 3.06275 12.2269i 0.194094 0.774851i
\(250\) 7.82087i 0.494635i
\(251\) 5.74103 0.362371 0.181185 0.983449i \(-0.442007\pi\)
0.181185 + 0.983449i \(0.442007\pi\)
\(252\) −2.07103 + 7.66230i −0.130463 + 0.482679i
\(253\) 0 0
\(254\) −6.58301 −0.413054
\(255\) 1.53737 6.13742i 0.0962741 0.384340i
\(256\) 1.00000 0.0625000
\(257\) 15.8219 0.986942 0.493471 0.869762i \(-0.335728\pi\)
0.493471 + 0.869762i \(0.335728\pi\)
\(258\) 13.4411 + 3.36689i 0.836808 + 0.209614i
\(259\) −13.2915 + 3.06871i −0.825894 + 0.190681i
\(260\) 2.35425 1.91520i 0.146004 0.118775i
\(261\) −3.29150 + 6.15784i −0.203739 + 0.381161i
\(262\) −1.40122 −0.0865677
\(263\) 16.4696i 1.01556i −0.861487 0.507779i \(-0.830467\pi\)
0.861487 0.507779i \(-0.169533\pi\)
\(264\) 0 0
\(265\) 6.72057 0.412841
\(266\) −2.70850 11.7313i −0.166069 0.719292i
\(267\) −5.29150 + 21.1245i −0.323835 + 1.29280i
\(268\) 1.82646i 0.111569i
\(269\) 23.1003 1.40845 0.704225 0.709977i \(-0.251295\pi\)
0.704225 + 0.709977i \(0.251295\pi\)
\(270\) −2.93725 + 3.24067i −0.178756 + 0.197221i
\(271\) −23.3111 −1.41605 −0.708025 0.706187i \(-0.750414\pi\)
−0.708025 + 0.706187i \(0.750414\pi\)
\(272\) −4.33981 −0.263140
\(273\) 13.0083 10.1875i 0.787297 0.616574i
\(274\) 1.29150 0.0780225
\(275\) 0 0
\(276\) 3.36028 13.4148i 0.202265 0.807473i
\(277\) 31.1660 1.87258 0.936292 0.351222i \(-0.114234\pi\)
0.936292 + 0.351222i \(0.114234\pi\)
\(278\) 8.66259i 0.519548i
\(279\) 14.6315 + 7.82087i 0.875965 + 0.468223i
\(280\) −2.16991 + 0.500983i −0.129677 + 0.0299395i
\(281\) 13.2915 0.792905 0.396452 0.918055i \(-0.370241\pi\)
0.396452 + 0.918055i \(0.370241\pi\)
\(282\) 3.29150 13.1402i 0.196006 0.782486i
\(283\) 14.8000i 0.879770i −0.898054 0.439885i \(-0.855019\pi\)
0.898054 0.439885i \(-0.144981\pi\)
\(284\) −14.5830 −0.865342
\(285\) 1.61206 6.43560i 0.0954905 0.381212i
\(286\) 0 0
\(287\) 28.0726 6.48135i 1.65708 0.382582i
\(288\) 2.64575 + 1.41421i 0.155902 + 0.0833333i
\(289\) 1.83399 0.107882
\(290\) −1.95906 −0.115040
\(291\) 16.5830 + 4.15390i 0.972113 + 0.243506i
\(292\) −3.14944 −0.184307
\(293\) 13.1166i 0.766278i 0.923691 + 0.383139i \(0.125157\pi\)
−0.923691 + 0.383139i \(0.874843\pi\)
\(294\) −11.8621 + 2.50802i −0.691813 + 0.146271i
\(295\) −3.29150 −0.191639
\(296\) 5.15587i 0.299679i
\(297\) 0 0
\(298\) 6.00000 0.347571
\(299\) −22.3316 + 18.1669i −1.29147 + 1.05062i
\(300\) 7.21033 + 1.80613i 0.416289 + 0.104277i
\(301\) 4.76150 + 20.6235i 0.274449 + 1.18872i
\(302\) 13.6412i 0.784960i
\(303\) −9.64575 2.41618i −0.554134 0.138806i
\(304\) −4.55066 −0.260998
\(305\) −4.70850 −0.269608
\(306\) −11.4821 6.13742i −0.656386 0.350853i
\(307\) −8.89047 −0.507406 −0.253703 0.967282i \(-0.581649\pi\)
−0.253703 + 0.967282i \(0.581649\pi\)
\(308\) 0 0
\(309\) −3.87451 + 15.4676i −0.220413 + 0.879922i
\(310\) 4.65489i 0.264380i
\(311\) −7.14226 −0.405000 −0.202500 0.979282i \(-0.564907\pi\)
−0.202500 + 0.979282i \(0.564907\pi\)
\(312\) −2.64575 5.65685i −0.149786 0.320256i
\(313\) 33.5633i 1.89711i 0.316614 + 0.948555i \(0.397454\pi\)
−0.316614 + 0.948555i \(0.602546\pi\)
\(314\) 17.8687i 1.00839i
\(315\) −6.44953 1.74324i −0.363390 0.0982202i
\(316\) −11.2915 −0.635197
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 3.36028 13.4148i 0.188435 0.752262i
\(319\) 0 0
\(320\) 0.841723i 0.0470537i
\(321\) −2.38075 + 9.50432i −0.132881 + 0.530479i
\(322\) 20.5830 4.75216i 1.14705 0.264827i
\(323\) 19.7490 1.09886
\(324\) 5.00000 + 7.48331i 0.277778 + 0.415740i
\(325\) −9.76458 12.0031i −0.541642 0.665811i
\(326\) 8.48528i 0.469956i
\(327\) 6.50972 25.9878i 0.359988 1.43713i
\(328\) 10.8896i 0.601277i
\(329\) 20.1617 4.65489i 1.11155 0.256632i
\(330\) 0 0
\(331\) 8.48528i 0.466393i 0.972430 + 0.233197i \(0.0749186\pi\)
−0.972430 + 0.233197i \(0.925081\pi\)
\(332\) 7.27733i 0.399395i
\(333\) −7.29150 + 13.6412i −0.399572 + 0.747531i
\(334\) 1.68345i 0.0921141i
\(335\) −1.53737 −0.0839957
\(336\) −0.0849536 + 4.58179i −0.00463460 + 0.249957i
\(337\) 11.8745 0.646846 0.323423 0.946255i \(-0.395166\pi\)
0.323423 + 0.946255i \(0.395166\pi\)
\(338\) −2.64575 + 12.7279i −0.143910 + 0.692308i
\(339\) −5.95188 + 23.7608i −0.323262 + 1.29051i
\(340\) 3.65292i 0.198107i
\(341\) 0 0
\(342\) −12.0399 6.43560i −0.651044 0.347998i
\(343\) −11.6556 14.3926i −0.629342 0.777129i
\(344\) 8.00000 0.431331
\(345\) 11.2915 + 2.82843i 0.607914 + 0.152277i
\(346\) −14.4207 −0.775260
\(347\) 2.00393i 0.107577i 0.998552 + 0.0537884i \(0.0171296\pi\)
−0.998552 + 0.0537884i \(0.982870\pi\)
\(348\) −0.979531 + 3.91044i −0.0525084 + 0.209621i
\(349\) 15.6110 0.835640 0.417820 0.908530i \(-0.362794\pi\)
0.417820 + 0.908530i \(0.362794\pi\)
\(350\) 2.55425 + 11.0632i 0.136530 + 0.591354i
\(351\) 1.00000 18.7083i 0.0533761 0.998574i
\(352\) 0 0
\(353\) 5.83925i 0.310792i −0.987852 0.155396i \(-0.950335\pi\)
0.987852 0.155396i \(-0.0496653\pi\)
\(354\) −1.64575 + 6.57008i −0.0874707 + 0.349196i
\(355\) 12.2748i 0.651481i
\(356\) 12.5730i 0.666369i
\(357\) 0.368683 19.8841i 0.0195128 1.05238i
\(358\) 11.3137i 0.597948i
\(359\) −16.7085 −0.881841 −0.440920 0.897546i \(-0.645348\pi\)
−0.440920 + 0.897546i \(0.645348\pi\)
\(360\) −1.19038 + 2.22699i −0.0627383 + 0.117373i
\(361\) 1.70850 0.0899209
\(362\) 10.6442i 0.559448i
\(363\) −18.4816 4.62948i −0.970030 0.242984i
\(364\) 5.85608 7.53036i 0.306942 0.394698i
\(365\) 2.65095i 0.138757i
\(366\) −2.35425 + 9.39851i −0.123059 + 0.491268i
\(367\) 8.11905i 0.423811i −0.977290 0.211905i \(-0.932033\pi\)
0.977290 0.211905i \(-0.0679669\pi\)
\(368\) 7.98430i 0.416210i
\(369\) 15.4002 28.8111i 0.801702 1.49985i
\(370\) −4.33981 −0.225616
\(371\) 20.5830 4.75216i 1.06862 0.246720i
\(372\) 9.29150 + 2.32744i 0.481742 + 0.120672i
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −3.29150 + 13.1402i −0.169972 + 0.678555i
\(376\) 7.82087i 0.403331i
\(377\) 6.50972 5.29570i 0.335268 0.272743i
\(378\) −6.70439 + 12.0021i −0.344837 + 0.617323i
\(379\) 15.1441i 0.777900i −0.921259 0.388950i \(-0.872838\pi\)
0.921259 0.388950i \(-0.127162\pi\)
\(380\) 3.83039i 0.196495i
\(381\) −11.0604 2.77053i −0.566640 0.141939i
\(382\) 0.500983i 0.0256325i
\(383\) 39.1044i 1.99814i 0.0431294 + 0.999069i \(0.486267\pi\)
−0.0431294 + 0.999069i \(0.513733\pi\)
\(384\) 1.68014 + 0.420861i 0.0857394 + 0.0214770i
\(385\) 0 0
\(386\) 8.48528i 0.431889i
\(387\) 21.1660 + 11.3137i 1.07593 + 0.575108i
\(388\) 9.87000 0.501074
\(389\) 12.6392i 0.640832i 0.947277 + 0.320416i \(0.103823\pi\)
−0.947277 + 0.320416i \(0.896177\pi\)
\(390\) 4.76150 2.22699i 0.241108 0.112768i
\(391\) 34.6504i 1.75234i
\(392\) −6.29150 + 3.06871i −0.317769 + 0.154993i
\(393\) −2.35425 0.589720i −0.118756 0.0297474i
\(394\) 8.58301 0.432406
\(395\) 9.50432i 0.478214i
\(396\) 0 0
\(397\) −16.0327 −0.804660 −0.402330 0.915495i \(-0.631799\pi\)
−0.402330 + 0.915495i \(0.631799\pi\)
\(398\) 25.4442i 1.27540i
\(399\) 0.386595 20.8502i 0.0193540 1.04381i
\(400\) 4.29150 0.214575
\(401\) 6.00000 0.299626 0.149813 0.988714i \(-0.452133\pi\)
0.149813 + 0.988714i \(0.452133\pi\)
\(402\) −0.768687 + 3.06871i −0.0383386 + 0.153053i
\(403\) −12.5830 15.4676i −0.626804 0.770497i
\(404\) −5.74103 −0.285627
\(405\) −6.29888 + 4.20861i −0.312994 + 0.209128i
\(406\) −6.00000 + 1.38527i −0.297775 + 0.0687496i
\(407\) 0 0
\(408\) −7.29150 1.82646i −0.360983 0.0904233i
\(409\) 1.19038 0.0588603 0.0294301 0.999567i \(-0.490631\pi\)
0.0294301 + 0.999567i \(0.490631\pi\)
\(410\) 9.16601 0.452677
\(411\) 2.16991 + 0.543544i 0.107034 + 0.0268110i
\(412\) 9.20614i 0.453554i
\(413\) −10.0808 + 2.32744i −0.496046 + 0.114526i
\(414\) 11.2915 21.1245i 0.554947 1.03821i
\(415\) 6.12549 0.300689
\(416\) −2.27533 2.79694i −0.111557 0.137131i
\(417\) −3.64575 + 14.5544i −0.178533 + 0.712731i
\(418\) 0 0
\(419\) 25.9027 1.26543 0.632716 0.774384i \(-0.281940\pi\)
0.632716 + 0.774384i \(0.281940\pi\)
\(420\) −3.85660 0.0715074i −0.188183 0.00348920i
\(421\) 11.8147i 0.575813i 0.957659 + 0.287906i \(0.0929592\pi\)
−0.957659 + 0.287906i \(0.907041\pi\)
\(422\) 10.5830 0.515173
\(423\) 11.0604 20.6921i 0.537774 1.00608i
\(424\) 7.98430i 0.387752i
\(425\) −18.6243 −0.903412
\(426\) −24.5015 6.13742i −1.18710 0.297359i
\(427\) −14.4207 + 3.32941i −0.697865 + 0.161121i
\(428\) 5.65685i 0.273434i
\(429\) 0 0
\(430\) 6.73378i 0.324732i
\(431\) 7.29150 0.351219 0.175610 0.984460i \(-0.443810\pi\)
0.175610 + 0.984460i \(0.443810\pi\)
\(432\) 3.85005 + 3.48957i 0.185236 + 0.167892i
\(433\) 17.3252i 0.832595i −0.909228 0.416298i \(-0.863327\pi\)
0.909228 0.416298i \(-0.136673\pi\)
\(434\) 3.29150 + 14.2565i 0.157997 + 0.684333i
\(435\) −3.29150 0.824494i −0.157815 0.0395315i
\(436\) 15.4676i 0.740764i
\(437\) 36.3338i 1.73808i
\(438\) −5.29150 1.32548i −0.252838 0.0633338i
\(439\) 8.11905i 0.387501i −0.981051 0.193751i \(-0.937935\pi\)
0.981051 0.193751i \(-0.0620652\pi\)
\(440\) 0 0
\(441\) −20.9856 0.778479i −0.999313 0.0370704i
\(442\) 9.87451 + 12.1382i 0.469682 + 0.577355i
\(443\) 5.65685i 0.268765i 0.990930 + 0.134383i \(0.0429051\pi\)
−0.990930 + 0.134383i \(0.957095\pi\)
\(444\) −2.16991 + 8.66259i −0.102979 + 0.411108i
\(445\) −10.5830 −0.501683
\(446\) −14.6315 −0.692822
\(447\) 10.0808 + 2.52517i 0.476808 + 0.119436i
\(448\) 0.595188 + 2.57794i 0.0281200 + 0.121796i
\(449\) −30.4575 −1.43738 −0.718689 0.695331i \(-0.755258\pi\)
−0.718689 + 0.695331i \(0.755258\pi\)
\(450\) 11.3542 + 6.06910i 0.535244 + 0.286100i
\(451\) 0 0
\(452\) 14.1421i 0.665190i
\(453\) 5.74103 22.9191i 0.269737 1.07683i
\(454\) 8.96077i 0.420550i
\(455\) 6.33847 + 4.92920i 0.297152 + 0.231084i
\(456\) −7.64575 1.91520i −0.358045 0.0896873i
\(457\) 12.1382i 0.567801i 0.958854 + 0.283901i \(0.0916286\pi\)
−0.958854 + 0.283901i \(0.908371\pi\)
\(458\) 24.2907 1.13503
\(459\) −16.7085 15.1441i −0.779886 0.706866i
\(460\) 6.72057 0.313348
\(461\) 15.3964i 0.717081i −0.933514 0.358540i \(-0.883275\pi\)
0.933514 0.358540i \(-0.116725\pi\)
\(462\) 0 0
\(463\) 25.7794i 1.19807i −0.800724 0.599034i \(-0.795551\pi\)
0.800724 0.599034i \(-0.204449\pi\)
\(464\) 2.32744i 0.108049i
\(465\) −1.95906 + 7.82087i −0.0908494 + 0.362684i
\(466\) 22.6274i 1.04819i
\(467\) 7.27841 0.336805 0.168402 0.985718i \(-0.446139\pi\)
0.168402 + 0.985718i \(0.446139\pi\)
\(468\) −2.06448 10.6178i −0.0954309 0.490808i
\(469\) −4.70850 + 1.08709i −0.217418 + 0.0501970i
\(470\) 6.58301 0.303651
\(471\) −7.52026 + 30.0220i −0.346515 + 1.38334i
\(472\) 3.91044i 0.179992i
\(473\) 0 0
\(474\) −18.9713 4.75216i −0.871382 0.218274i
\(475\) −19.5292 −0.896060
\(476\) −2.58301 11.1878i −0.118392 0.512790i
\(477\) 11.2915 21.1245i 0.517002 0.967223i
\(478\) −21.8745 −1.00052
\(479\) 17.9215i 0.818856i −0.912342 0.409428i \(-0.865728\pi\)
0.912342 0.409428i \(-0.134272\pi\)
\(480\) −0.354249 + 1.41421i −0.0161692 + 0.0645497i
\(481\) 14.4207 11.7313i 0.657526 0.534901i
\(482\) 25.6919 1.17023
\(483\) 36.5824 + 0.678295i 1.66456 + 0.0308635i
\(484\) −11.0000 −0.500000
\(485\) 8.30781i 0.377238i
\(486\) 5.25127 + 14.6773i 0.238202 + 0.665777i
\(487\) 17.2941i 0.783669i 0.920036 + 0.391835i \(0.128159\pi\)
−0.920036 + 0.391835i \(0.871841\pi\)
\(488\) 5.59388i 0.253223i
\(489\) −3.57113 + 14.2565i −0.161492 + 0.644700i
\(490\) −2.58301 5.29570i −0.116688 0.239235i
\(491\) 26.2803i 1.18602i 0.805197 + 0.593008i \(0.202060\pi\)
−0.805197 + 0.593008i \(0.797940\pi\)
\(492\) 4.58301 18.2960i 0.206618 0.824849i
\(493\) 10.1007i 0.454911i
\(494\) 10.3542 + 12.7279i 0.465860 + 0.572656i
\(495\) 0 0
\(496\) 5.53019 0.248313
\(497\) −8.67963 37.5940i −0.389335 1.68632i
\(498\) 3.06275 12.2269i 0.137245 0.547902i
\(499\) 18.7970i 0.841470i −0.907184 0.420735i \(-0.861772\pi\)
0.907184 0.420735i \(-0.138228\pi\)
\(500\) 7.82087i 0.349760i
\(501\) 0.708497 2.82843i 0.0316533 0.126365i
\(502\) 5.74103 0.256235
\(503\) 8.67963 0.387006 0.193503 0.981100i \(-0.438015\pi\)
0.193503 + 0.981100i \(0.438015\pi\)
\(504\) −2.07103 + 7.66230i −0.0922511 + 0.341306i
\(505\) 4.83236i 0.215037i
\(506\) 0 0
\(507\) −9.80193 + 20.2712i −0.435319 + 0.900276i
\(508\) −6.58301 −0.292074
\(509\) 15.3964i 0.682432i −0.939985 0.341216i \(-0.889161\pi\)
0.939985 0.341216i \(-0.110839\pi\)
\(510\) 1.53737 6.13742i 0.0680760 0.271770i
\(511\) −1.87451 8.11905i −0.0829233 0.359166i
\(512\) 1.00000 0.0441942
\(513\) −17.5203 15.8799i −0.773538 0.701113i
\(514\) 15.8219 0.697873
\(515\) −7.74902 −0.341462
\(516\) 13.4411 + 3.36689i 0.591713 + 0.148219i
\(517\) 0 0
\(518\) −13.2915 + 3.06871i −0.583995 + 0.134831i
\(519\) −24.2288 6.06910i −1.06352 0.266404i
\(520\) 2.35425 1.91520i 0.103241 0.0839869i
\(521\) 2.80244 0.122777 0.0613886 0.998114i \(-0.480447\pi\)
0.0613886 + 0.998114i \(0.480447\pi\)
\(522\) −3.29150 + 6.15784i −0.144065 + 0.269521i
\(523\) 32.1252i 1.40474i −0.711813 0.702369i \(-0.752126\pi\)
0.711813 0.702369i \(-0.247874\pi\)
\(524\) −1.40122 −0.0612126
\(525\) −0.364579 + 19.6628i −0.0159115 + 0.858153i
\(526\) 16.4696i 0.718108i
\(527\) −24.0000 −1.04546
\(528\) 0 0
\(529\) −40.7490 −1.77170
\(530\) 6.72057 0.291923
\(531\) −5.53019 + 10.3460i −0.239990 + 0.448980i
\(532\) −2.70850 11.7313i −0.117428 0.508617i
\(533\) −30.4575 + 24.7774i −1.31926 + 1.07323i
\(534\) −5.29150 + 21.1245i −0.228986 + 0.914145i
\(535\) −4.76150 −0.205858
\(536\) 1.82646i 0.0788911i
\(537\) 4.76150 19.0086i 0.205474 0.820283i
\(538\) 23.1003 0.995924
\(539\) 0 0
\(540\) −2.93725 + 3.24067i −0.126399 + 0.139456i
\(541\) 29.4323i 1.26539i −0.774400 0.632696i \(-0.781948\pi\)
0.774400 0.632696i \(-0.218052\pi\)
\(542\) −23.3111 −1.00130
\(543\) −4.47974 + 17.8838i −0.192244 + 0.767467i
\(544\) −4.33981 −0.186068
\(545\) 13.0194 0.557692
\(546\) 13.0083 10.1875i 0.556703 0.435983i
\(547\) −6.58301 −0.281469 −0.140734 0.990047i \(-0.544946\pi\)
−0.140734 + 0.990047i \(0.544946\pi\)
\(548\) 1.29150 0.0551703
\(549\) −7.91094 + 14.8000i −0.337631 + 0.631649i
\(550\) 0 0
\(551\) 10.5914i 0.451209i
\(552\) 3.36028 13.4148i 0.143023 0.570970i
\(553\) −6.72057 29.1088i −0.285788 1.23783i
\(554\) 31.1660 1.32412
\(555\) −7.29150 1.82646i −0.309507 0.0775289i
\(556\) 8.66259i 0.367376i
\(557\) −23.1660 −0.981575 −0.490788 0.871279i \(-0.663291\pi\)
−0.490788 + 0.871279i \(0.663291\pi\)
\(558\) 14.6315 + 7.82087i 0.619401 + 0.331084i
\(559\) −18.2026 22.3755i −0.769889 0.946384i
\(560\) −2.16991 + 0.500983i −0.0916953 + 0.0211704i
\(561\) 0 0
\(562\) 13.2915 0.560668
\(563\) 7.27841 0.306748 0.153374 0.988168i \(-0.450986\pi\)
0.153374 + 0.988168i \(0.450986\pi\)
\(564\) 3.29150 13.1402i 0.138597 0.553301i
\(565\) −11.9038 −0.500795
\(566\) 14.8000i 0.622091i
\(567\) −16.3156 + 17.3437i −0.685189 + 0.728365i
\(568\) −14.5830 −0.611889
\(569\) 30.1107i 1.26231i −0.775658 0.631154i \(-0.782582\pi\)
0.775658 0.631154i \(-0.217418\pi\)
\(570\) 1.61206 6.43560i 0.0675220 0.269558i
\(571\) −1.41699 −0.0592994 −0.0296497 0.999560i \(-0.509439\pi\)
−0.0296497 + 0.999560i \(0.509439\pi\)
\(572\) 0 0
\(573\) −0.210845 + 0.841723i −0.00880816 + 0.0351635i
\(574\) 28.0726 6.48135i 1.17173 0.270526i
\(575\) 34.2646i 1.42893i
\(576\) 2.64575 + 1.41421i 0.110240 + 0.0589256i
\(577\) 5.53019 0.230225 0.115112 0.993352i \(-0.463277\pi\)
0.115112 + 0.993352i \(0.463277\pi\)
\(578\) 1.83399 0.0762839
\(579\) 3.57113 14.2565i 0.148411 0.592479i
\(580\) −1.95906 −0.0813457
\(581\) 18.7605 4.33138i 0.778316 0.179696i
\(582\) 16.5830 + 4.15390i 0.687388 + 0.172185i
\(583\) 0 0
\(584\) −3.14944 −0.130325
\(585\) 8.93725 1.73772i 0.369510 0.0718461i
\(586\) 13.1166i 0.541841i
\(587\) 8.36441i 0.345236i −0.984989 0.172618i \(-0.944777\pi\)
0.984989 0.172618i \(-0.0552227\pi\)
\(588\) −11.8621 + 2.50802i −0.489185 + 0.103429i
\(589\) −25.1660 −1.03695
\(590\) −3.29150 −0.135509
\(591\) 14.4207 + 3.61226i 0.593187 + 0.148588i
\(592\) 5.15587i 0.211905i
\(593\) 41.0860i 1.68720i 0.536973 + 0.843599i \(0.319568\pi\)
−0.536973 + 0.843599i \(0.680432\pi\)
\(594\) 0 0
\(595\) 9.41699 2.17417i 0.386059 0.0891325i
\(596\) 6.00000 0.245770
\(597\) 10.7085 42.7499i 0.438270 1.74964i
\(598\) −22.3316 + 18.1669i −0.913207 + 0.742900i
\(599\) 23.7754i 0.971437i −0.874115 0.485719i \(-0.838558\pi\)
0.874115 0.485719i \(-0.161442\pi\)
\(600\) 7.21033 + 1.80613i 0.294361 + 0.0737349i
\(601\) 22.3755i 0.912717i −0.889796 0.456358i \(-0.849154\pi\)
0.889796 0.456358i \(-0.150846\pi\)
\(602\) 4.76150 + 20.6235i 0.194064 + 0.840550i
\(603\) −2.58301 + 4.83236i −0.105188 + 0.196789i
\(604\) 13.6412i 0.555051i
\(605\) 9.25895i 0.376430i
\(606\) −9.64575 2.41618i −0.391832 0.0981506i
\(607\) 26.5313i 1.07687i 0.842666 + 0.538437i \(0.180985\pi\)
−0.842666 + 0.538437i \(0.819015\pi\)
\(608\) −4.55066 −0.184554
\(609\) −10.6639 0.197725i −0.432121 0.00801221i
\(610\) −4.70850 −0.190641
\(611\) −21.8745 + 17.7951i −0.884948 + 0.719911i
\(612\) −11.4821 6.13742i −0.464135 0.248091i
\(613\) 32.4382i 1.31017i 0.755557 + 0.655083i \(0.227366\pi\)
−0.755557 + 0.655083i \(0.772634\pi\)
\(614\) −8.89047 −0.358790
\(615\) 15.4002 + 3.85762i 0.620996 + 0.155554i
\(616\) 0 0
\(617\) 11.1660 0.449527 0.224763 0.974413i \(-0.427839\pi\)
0.224763 + 0.974413i \(0.427839\pi\)
\(618\) −3.87451 + 15.4676i −0.155856 + 0.622199i
\(619\) −26.2497 −1.05507 −0.527533 0.849535i \(-0.676883\pi\)
−0.527533 + 0.849535i \(0.676883\pi\)
\(620\) 4.65489i 0.186945i
\(621\) 27.8618 30.7399i 1.11806 1.23355i
\(622\) −7.14226 −0.286378
\(623\) −32.4125 + 7.48331i −1.29858 + 0.299813i
\(624\) −2.64575 5.65685i −0.105915 0.226455i
\(625\) 14.8745 0.594980
\(626\) 33.5633i 1.34146i
\(627\) 0 0
\(628\) 17.8687i 0.713040i
\(629\) 22.3755i 0.892171i
\(630\) −6.44953 1.74324i −0.256956 0.0694521i
\(631\) 19.1205i 0.761176i 0.924745 + 0.380588i \(0.124278\pi\)
−0.924745 + 0.380588i \(0.875722\pi\)
\(632\) −11.2915 −0.449152
\(633\) 17.7809 + 4.45398i 0.706729 + 0.177030i
\(634\) −6.00000 −0.238290
\(635\) 5.54107i 0.219890i
\(636\) 3.36028 13.4148i 0.133244 0.531929i
\(637\) 22.8982 + 10.6146i 0.907262 + 0.420567i
\(638\) 0 0
\(639\) −38.5830 20.6235i −1.52632 0.815852i
\(640\) 0.841723i 0.0332720i
\(641\) 13.1402i 0.519005i −0.965742 0.259503i \(-0.916441\pi\)
0.965742 0.259503i \(-0.0835587\pi\)
\(642\) −2.38075 + 9.50432i −0.0939608 + 0.375105i
\(643\) −4.55066 −0.179460 −0.0897302 0.995966i \(-0.528600\pi\)
−0.0897302 + 0.995966i \(0.528600\pi\)
\(644\) 20.5830 4.75216i 0.811084 0.187261i
\(645\) −2.83399 + 11.3137i −0.111588 + 0.445477i
\(646\) 19.7490 0.777015
\(647\) 2.80244 0.110175 0.0550877 0.998482i \(-0.482456\pi\)
0.0550877 + 0.998482i \(0.482456\pi\)
\(648\) 5.00000 + 7.48331i 0.196419 + 0.293972i
\(649\) 0 0
\(650\) −9.76458 12.0031i −0.382998 0.470799i
\(651\) −0.469810 + 25.3382i −0.0184133 + 0.993081i
\(652\) 8.48528i 0.332309i
\(653\) 32.2607i 1.26246i −0.775596 0.631229i \(-0.782551\pi\)
0.775596 0.631229i \(-0.217449\pi\)
\(654\) 6.50972 25.9878i 0.254550 1.01620i
\(655\) 1.17944i 0.0460845i
\(656\) 10.8896i 0.425167i
\(657\) −8.33263 4.45398i −0.325087 0.173766i
\(658\) 20.1617 4.65489i 0.785985 0.181466i
\(659\) 1.00197i 0.0390311i −0.999810 0.0195155i \(-0.993788\pi\)
0.999810 0.0195155i \(-0.00621238\pi\)
\(660\) 0 0
\(661\) 31.4329 1.22260 0.611300 0.791399i \(-0.290647\pi\)
0.611300 + 0.791399i \(0.290647\pi\)
\(662\) 8.48528i 0.329790i
\(663\) 11.4821 + 24.5497i 0.445927 + 0.953431i
\(664\) 7.27733i 0.282415i
\(665\) 9.87451 2.27980i 0.382917 0.0884070i
\(666\) −7.29150 + 13.6412i −0.282540 + 0.528584i
\(667\) 18.5830 0.719537
\(668\) 1.68345i 0.0651345i
\(669\) −24.5830 6.15784i −0.950434 0.238076i
\(670\) −1.53737 −0.0593939
\(671\) 0 0
\(672\) −0.0849536 + 4.58179i −0.00327716 + 0.176746i
\(673\) 2.00000 0.0770943 0.0385472 0.999257i \(-0.487727\pi\)
0.0385472 + 0.999257i \(0.487727\pi\)
\(674\) 11.8745 0.457389
\(675\) 16.5225 + 14.9755i 0.635951 + 0.576408i
\(676\) −2.64575 + 12.7279i −0.101760 + 0.489535i
\(677\) −43.2620 −1.66269 −0.831347 0.555754i \(-0.812430\pi\)
−0.831347 + 0.555754i \(0.812430\pi\)
\(678\) −5.95188 + 23.7608i −0.228581 + 0.912528i
\(679\) 5.87451 + 25.4442i 0.225443 + 0.976460i
\(680\) 3.65292i 0.140083i
\(681\) −3.77124 + 15.0554i −0.144514 + 0.576923i
\(682\) 0 0
\(683\) 50.5830 1.93550 0.967752 0.251903i \(-0.0810564\pi\)
0.967752 + 0.251903i \(0.0810564\pi\)
\(684\) −12.0399 6.43560i −0.460358 0.246071i
\(685\) 1.08709i 0.0415355i
\(686\) −11.6556 14.3926i −0.445012 0.549513i
\(687\) 40.8118 + 10.2230i 1.55707 + 0.390032i
\(688\) 8.00000 0.304997
\(689\) −22.3316 + 18.1669i −0.850766 + 0.692104i
\(690\) 11.2915 + 2.82843i 0.429860 + 0.107676i
\(691\) 15.6110 0.593872 0.296936 0.954897i \(-0.404035\pi\)
0.296936 + 0.954897i \(0.404035\pi\)
\(692\) −14.4207 −0.548191
\(693\) 0 0
\(694\) 2.00393i 0.0760683i
\(695\) −7.29150 −0.276582
\(696\) −0.979531 + 3.91044i −0.0371290 + 0.148225i
\(697\) 47.2588i 1.79005i
\(698\) 15.6110 0.590887
\(699\) −9.52301 + 38.0173i −0.360193 + 1.43794i
\(700\) 2.55425 + 11.0632i 0.0965416 + 0.418150i
\(701\) 8.98626i 0.339407i 0.985495 + 0.169703i \(0.0542809\pi\)
−0.985495 + 0.169703i \(0.945719\pi\)
\(702\) 1.00000 18.7083i 0.0377426 0.706099i
\(703\) 23.4626i 0.884909i
\(704\) 0 0
\(705\) 11.0604 + 2.77053i 0.416558 + 0.104344i
\(706\) 5.83925i 0.219763i
\(707\) −3.41699 14.8000i −0.128509 0.556612i
\(708\) −1.64575 + 6.57008i −0.0618511 + 0.246919i
\(709\) 28.7853i 1.08105i −0.841327 0.540526i \(-0.818225\pi\)
0.841327 0.540526i \(-0.181775\pi\)
\(710\) 12.2748i 0.460667i
\(711\) −29.8745 15.9686i −1.12038 0.598869i
\(712\) 12.5730i 0.471194i
\(713\) 44.1547i 1.65361i
\(714\) 0.368683 19.8841i 0.0137976 0.744144i
\(715\) 0 0
\(716\) 11.3137i 0.422813i
\(717\) −36.7523 9.20614i −1.37254 0.343809i
\(718\) −16.7085 −0.623556
\(719\) −27.3040 −1.01827 −0.509133 0.860688i \(-0.670034\pi\)
−0.509133 + 0.860688i \(0.670034\pi\)
\(720\) −1.19038 + 2.22699i −0.0443627 + 0.0829950i
\(721\) −23.7328 + 5.47938i −0.883857 + 0.204063i
\(722\) 1.70850 0.0635837
\(723\) 43.1660 + 10.8127i 1.60536 + 0.402130i
\(724\) 10.6442i 0.395589i
\(725\) 9.98823i 0.370954i
\(726\) −18.4816 4.62948i −0.685915 0.171816i
\(727\) 13.1694i 0.488426i 0.969722 + 0.244213i \(0.0785295\pi\)
−0.969722 + 0.244213i \(0.921470\pi\)
\(728\) 5.85608 7.53036i 0.217041 0.279094i
\(729\) 2.64575 + 26.8701i 0.0979908 + 0.995187i
\(730\) 2.65095i 0.0981162i
\(731\) −34.7185 −1.28411
\(732\) −2.35425 + 9.39851i −0.0870155 + 0.347379i
\(733\) −10.4278 −0.385161 −0.192581 0.981281i \(-0.561686\pi\)
−0.192581 + 0.981281i \(0.561686\pi\)
\(734\) 8.11905i 0.299680i
\(735\) −2.11106 9.98462i −0.0778675 0.368288i
\(736\) 7.98430i 0.294305i
\(737\) 0 0
\(738\) 15.4002 28.8111i 0.566889 1.06055i
\(739\) 18.7970i 0.691460i 0.938334 + 0.345730i \(0.112369\pi\)
−0.938334 + 0.345730i \(0.887631\pi\)
\(740\) −4.33981 −0.159535
\(741\) 12.0399 + 25.7424i 0.442297 + 0.945671i
\(742\) 20.5830 4.75216i 0.755626 0.174457i
\(743\) −7.29150 −0.267499 −0.133750 0.991015i \(-0.542702\pi\)
−0.133750 + 0.991015i \(0.542702\pi\)
\(744\) 9.29150 + 2.32744i 0.340643 + 0.0853282i
\(745\) 5.05034i 0.185030i
\(746\) −22.0000 −0.805477
\(747\) 10.2917 19.2540i 0.376553 0.704467i
\(748\) 0 0
\(749\) −14.5830 + 3.36689i −0.532851 + 0.123024i
\(750\) −3.29150 + 13.1402i −0.120189 + 0.479811i
\(751\) 13.1660 0.480435 0.240217 0.970719i \(-0.422781\pi\)
0.240217 + 0.970719i \(0.422781\pi\)
\(752\) 7.82087i 0.285198i
\(753\) 9.64575 + 2.41618i 0.351511 + 0.0880505i
\(754\) 6.50972 5.29570i 0.237070 0.192858i
\(755\) 11.4821 0.417875
\(756\) −6.70439 + 12.0021i −0.243836 + 0.436513i
\(757\) 4.58301 0.166572 0.0832861 0.996526i \(-0.473458\pi\)
0.0832861 + 0.996526i \(0.473458\pi\)
\(758\) 15.1441i 0.550059i
\(759\) 0 0
\(760\) 3.83039i 0.138943i
\(761\) 11.4859i 0.416365i 0.978090 + 0.208183i \(0.0667548\pi\)
−0.978090 + 0.208183i \(0.933245\pi\)
\(762\) −11.0604 2.77053i −0.400675 0.100366i
\(763\) 39.8745 9.20614i 1.44355 0.333285i
\(764\) 0.500983i 0.0181249i
\(765\) 5.16601 9.66472i 0.186778 0.349429i
\(766\) 39.1044i 1.41290i
\(767\) 10.9373 8.89753i 0.394921 0.321271i
\(768\) 1.68014 + 0.420861i 0.0606269 + 0.0151865i
\(769\) −21.7738 −0.785182 −0.392591 0.919713i \(-0.628421\pi\)
−0.392591 + 0.919713i \(0.628421\pi\)
\(770\) 0 0
\(771\) 26.5830 + 6.65882i 0.957364 + 0.239812i
\(772\) 8.48528i 0.305392i
\(773\) 10.3460i 0.372121i −0.982538 0.186061i \(-0.940428\pi\)
0.982538 0.186061i \(-0.0595721\pi\)
\(774\) 21.1660 + 11.3137i 0.760797 + 0.406663i
\(775\) 23.7328 0.852508
\(776\) 9.87000 0.354313
\(777\) −23.6231 0.438010i −0.847474 0.0157135i
\(778\) 12.6392i 0.453137i
\(779\) 49.5548i 1.77548i
\(780\) 4.76150 2.22699i 0.170489 0.0797390i
\(781\) 0 0
\(782\) 34.6504i 1.23909i
\(783\) −8.12179 + 8.96077i −0.290249 + 0.320232i
\(784\) −6.29150 + 3.06871i −0.224697 + 0.109597i
\(785\) −15.0405 −0.536819