Properties

Label 546.2.e.f.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.f.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} +(5.00000 - 3.74166i) 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} +(-5.00000 + 3.74166i) 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} +(-8.56458 - 4.20095i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + O(q^{10}) \) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} + 24 q^{15} + 8 q^{16} - 8 q^{21} - 8 q^{25} - 24 q^{30} - 8 q^{32} + 40 q^{39} + 8 q^{42} + 64 q^{43} - 8 q^{49} + 8 q^{50} - 16 q^{51} + 40 q^{57} + 24 q^{60} + 8 q^{63} + 8 q^{64} - 40 q^{65} + 32 q^{71} - 40 q^{78} - 48 q^{79} + 40 q^{81} - 8 q^{84} - 64 q^{86} - 32 q^{91} - 32 q^{93} + 8 q^{98} + O(q^{100}) \)

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 \(-0.939730\pi\)
0.982128 0.188215i \(-0.0602702\pi\)
\(6\) −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 \(-0.325187\pi\)
0.521996 + 0.852948i \(0.325187\pi\)
\(20\) 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 \(-0.665428\pi\)
−0.496626 + 0.867965i \(0.665428\pi\)
\(32\) −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 \(-0.860692\pi\)
0.905751 0.423810i \(-0.139308\pi\)
\(38\) −4.55066 −0.738214
\(39\) 5.00000 3.74166i 0.800641 0.599145i
\(40\) 0.841723i 0.133088i
\(41\) 10.8896i 1.70067i 0.526244 + 0.850334i \(0.323600\pi\)
−0.526244 + 0.850334i \(0.676400\pi\)
\(42\) −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 \(0.193210\pi\)
−0.821370 + 0.570396i \(0.806790\pi\)
\(48\) 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 \(-0.918073\pi\)
0.967060 0.254548i \(-0.0819266\pi\)
\(60\) 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 \(-0.964412\pi\)
0.993757 0.111569i \(-0.0355876\pi\)
\(68\) −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 \(-0.167101\pi\)
0.865342 + 0.501182i \(0.167101\pi\)
\(72\) −2.64575 1.41421i −0.311805 0.166667i
\(73\) 3.14944 0.368614 0.184307 0.982869i \(-0.440996\pi\)
0.184307 + 0.982869i \(0.440996\pi\)
\(74\) 5.15587i 0.599358i
\(75\) 7.21033 + 1.80613i 0.832577 + 0.208554i
\(76\) 4.55066 0.521996
\(77\) 0 0
\(78\) −5.00000 + 3.74166i −0.566139 + 0.423659i
\(79\) −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 \(0.130780\pi\)
−0.916779 + 0.399395i \(0.869220\pi\)
\(84\) 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 \(-0.767848\pi\)
0.745622 0.666369i \(-0.232152\pi\)
\(90\) −1.19038 + 2.22699i −0.125477 + 0.234745i
\(91\) −8.56458 4.20095i −0.897812 0.440379i
\(92\) 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 \(-0.667061\pi\)
−0.501074 + 0.865405i \(0.667061\pi\)
\(98\) 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 \(0.265536\pi\)
−0.671765 + 0.740764i \(0.734464\pi\)
\(110\) 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
\(117\) 9.97543 4.18221i 0.922229 0.386645i
\(118\) 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 \(-0.517570\pi\)
−0.0551703 + 0.998477i \(0.517570\pi\)
\(138\) −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 \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −7.21033 1.80613i −0.588721 0.147470i
\(151\) 13.6412i 1.11010i 0.831817 + 0.555051i \(0.187301\pi\)
−0.831817 + 0.555051i \(0.812699\pi\)
\(152\) −4.55066 −0.369107
\(153\) −11.4821 6.13742i −0.928270 0.496181i
\(154\) 0 0
\(155\) 4.65489i 0.373890i
\(156\) 5.00000 3.74166i 0.400320 0.299572i
\(157\) 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 \(-0.892172\pi\)
0.943170 0.332309i \(-0.107828\pi\)
\(164\) 10.8896i 0.850334i
\(165\) 0 0
\(166\) 7.27733i 0.564830i
\(167\) 1.68345i 0.130269i 0.997876 + 0.0651345i \(0.0207476\pi\)
−0.997876 + 0.0651345i \(0.979252\pi\)
\(168\) −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 \(0.870540\pi\)
\(182\) 8.56458 + 4.20095i 0.634849 + 0.311395i
\(183\) −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 \(0.0987875\pi\)
−0.952227 + 0.305392i \(0.901213\pi\)
\(194\) 9.87000 0.708625
\(195\) −3.14944 4.20861i −0.225536 0.301385i
\(196\) −6.29150 + 3.06871i −0.449393 + 0.219194i
\(197\) −8.58301 −0.611514 −0.305757 0.952110i \(-0.598909\pi\)
−0.305757 + 0.952110i \(0.598909\pi\)
\(198\) 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 \(-0.337034\pi\)
0.489899 + 0.871779i \(0.337034\pi\)
\(224\) 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 \(-0.903889\pi\)
0.954761 0.297374i \(-0.0961107\pi\)
\(228\) 7.64575 + 1.91520i 0.506352 + 0.126837i
\(229\) −24.2907 −1.60517 −0.802586 0.596536i \(-0.796543\pi\)
−0.802586 + 0.596536i \(0.796543\pi\)
\(230\) 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 \(0.734264\pi\)
\(234\) −9.97543 + 4.18221i −0.652114 + 0.273399i
\(235\) 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 \(-0.249835\pi\)
0.707472 + 0.706741i \(0.249835\pi\)
\(240\) 0.354249 1.41421i 0.0228667 0.0912871i
\(241\) −25.6919 −1.65496 −0.827480 0.561495i \(-0.810226\pi\)
−0.827480 + 0.561495i \(0.810226\pi\)
\(242\) 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 \(-0.249586\pi\)
0.708025 + 0.706187i \(0.249586\pi\)
\(272\) −4.33981 −0.263140
\(273\) −12.6217 10.6627i −0.763899 0.645335i
\(274\) 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 \(-0.629759\pi\)
−0.396452 + 0.918055i \(0.629759\pi\)
\(282\) 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 \(-0.874843\pi\)
0.923691 0.383139i \(-0.125157\pi\)
\(294\) 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 \(-0.418351\pi\)
0.253703 + 0.967282i \(0.418351\pi\)
\(308\) 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 \(0.564907\pi\)
\(312\) −5.00000 + 3.74166i −0.283069 + 0.211830i
\(313\) 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 \(-0.446109\pi\)
0.168497 + 0.985702i \(0.446109\pi\)
\(318\) −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 \(-0.925081\pi\)
0.972430 0.233197i \(-0.0749186\pi\)
\(332\) 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 \(-0.637206\pi\)
−0.417820 + 0.908530i \(0.637206\pi\)
\(350\) 2.55425 + 11.0632i 0.136530 + 0.591354i
\(351\) 18.5203 2.82843i 0.988538 0.150970i
\(352\) 0 0
\(353\) 5.83925i 0.310792i 0.987852 + 0.155396i \(0.0496653\pi\)
−0.987852 + 0.155396i \(0.950335\pi\)
\(354\) −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 \(-0.354652\pi\)
0.440920 + 0.897546i \(0.354652\pi\)
\(360\) −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
\(364\) −8.56458 4.20095i −0.448906 0.220189i
\(365\) 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 \(0.127162\pi\)
−0.921259 + 0.388950i \(0.872838\pi\)
\(380\) 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 \(-0.513733\pi\)
0.0431294 0.999069i \(-0.486267\pi\)
\(384\) −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 \(0.896177\pi\)
\(390\) 3.14944 + 4.20861i 0.159478 + 0.213111i
\(391\) 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 \(-0.368201\pi\)
0.402330 + 0.915495i \(0.368201\pi\)
\(398\) 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 \(-0.547867\pi\)
−0.149813 + 0.988714i \(0.547867\pi\)
\(402\) −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 \(-0.509369\pi\)
−0.0294301 + 0.999567i \(0.509369\pi\)
\(410\) −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 \(-0.907041\pi\)
0.957659 0.287906i \(-0.0929592\pi\)
\(422\) −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 \(-0.556190\pi\)
−0.175610 + 0.984460i \(0.556190\pi\)
\(432\) 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 \(-0.244742\pi\)
0.718689 + 0.695331i \(0.244742\pi\)
\(450\) −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
\(455\) −3.53603 + 7.20900i −0.165772 + 0.337963i
\(456\) −7.64575 1.91520i −0.358045 0.0896873i
\(457\) 12.1382i 0.567801i −0.958854 0.283901i \(-0.908371\pi\)
0.958854 0.283901i \(-0.0916286\pi\)
\(458\) 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 \(0.116725\pi\)
−0.933514 + 0.358540i \(0.883275\pi\)
\(462\) 0 0
\(463\) 25.7794i 1.19807i 0.800724 + 0.599034i \(0.204449\pi\)
−0.800724 + 0.599034i \(0.795551\pi\)
\(464\) 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 \(0.446139\pi\)
\(468\) 9.97543 4.18221i 0.461114 0.193323i
\(469\) −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 \(0.134272\pi\)
−0.912342 + 0.409428i \(0.865728\pi\)
\(480\) −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 \(-0.871841\pi\)
0.920036 0.391835i \(-0.128159\pi\)
\(488\) 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 \(0.138228\pi\)
−0.907184 + 0.420735i \(0.861772\pi\)
\(500\) 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
\(507\) 0.911455 22.4982i 0.0404791 0.999180i
\(508\) −6.58301 −0.292074
\(509\) 15.3964i 0.682432i 0.939985 + 0.341216i \(0.110839\pi\)
−0.939985 + 0.341216i \(0.889161\pi\)
\(510\) 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 \(0.218052\pi\)
−0.774400 + 0.632696i \(0.781948\pi\)
\(542\) −23.3111 −1.00130
\(543\) −4.47974 + 17.8838i −0.192244 + 0.767467i
\(544\) 4.33981 0.186068
\(545\) 13.0194 0.557692
\(546\) 12.6217 + 10.6627i 0.540159 + 0.456321i
\(547\) −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 \(-0.336709\pi\)
0.490788 + 0.871279i \(0.336709\pi\)
\(558\) 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 \(-0.536723\pi\)
−0.115112 + 0.993352i \(0.536723\pi\)
\(578\) −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
\(585\) −3.52026 8.39655i −0.145545 0.347154i
\(586\) 13.1166i 0.541841i
\(587\) 8.36441i 0.345236i 0.984989 + 0.172618i \(0.0552227\pi\)
−0.984989 + 0.172618i \(0.944777\pi\)
\(588\) −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 \(-0.680432\pi\)
0.536973 0.843599i \(-0.319568\pi\)
\(594\) 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 \(-0.772634\pi\)
0.755557 0.655083i \(-0.227366\pi\)
\(614\) −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 \(-0.572161\pi\)
−0.224763 + 0.974413i \(0.572161\pi\)
\(618\) 3.87451 15.4676i 0.155856 0.622199i
\(619\) 26.2497 1.05507 0.527533 0.849535i \(-0.323117\pi\)
0.527533 + 0.849535i \(0.323117\pi\)
\(620\) 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
\(624\) 5.00000 3.74166i 0.200160 0.149786i
\(625\) 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 \(-0.875722\pi\)
0.924745 0.380588i \(-0.124278\pi\)
\(632\) 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
\(637\) −5.73224 + 24.5793i −0.227119 + 0.973867i
\(638\) 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 \(-0.471400\pi\)
0.0897302 + 0.995966i \(0.471400\pi\)
\(644\) −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 \(-0.709353\pi\)
−0.611300 + 0.791399i \(0.709353\pi\)
\(662\) 8.48528i 0.329790i
\(663\) −21.6991 + 16.2381i −0.842722 + 0.630636i
\(664\) 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 \(-0.918944\pi\)
−0.967752 + 0.251903i \(0.918944\pi\)
\(684\) 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 \(-0.595965\pi\)
−0.296936 + 0.954897i \(0.595965\pi\)
\(692\) −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 \(0.945719\pi\)
\(702\) −18.5203 + 2.82843i −0.699002 + 0.106752i
\(703\) 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 \(0.181775\pi\)
−0.841327 + 0.540526i \(0.818225\pi\)
\(710\) 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 \(0.921470\pi\)
\(728\) 8.56458 + 4.20095i 0.317424 + 0.155697i
\(729\) 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 \(-0.438314\pi\)
0.192581 + 0.981281i \(0.438314\pi\)
\(734\) 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 \(-0.887631\pi\)
0.938334 0.345730i \(-0.112369\pi\)
\(740\) −4.33981 −0.159535
\(741\) 22.7533 17.0270i 0.835863 0.625503i
\(742\) 20.5830 4.75216i 0.755626 0.174457i
\(743\) 7.29150 0.267499 0.133750 0.991015i \(-0.457298\pi\)
0.133750 + 0.991015i \(0.457298\pi\)
\(744\) 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 \(-0.933245\pi\)
0.978090 0.208183i \(-0.0667548\pi\)
\(762\) 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 \(-0.371579\pi\)
0.392591 + 0.919713i \(0.371579\pi\)
\(770\) 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 \(0.0595721\pi\)
−0.982538 + 0.186061i \(0.940428\pi\)
\(774\) −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
\(780\) −3.14944 4.20861i −0.112768 0.150693i
\(781\) 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
\(785\)