Properties

Label 507.2.e.l.22.1
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 507 = 3 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 507.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.04841538248\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.64827.1
Defining polynomial: \(x^{6} - x^{5} + 3 x^{4} + 5 x^{2} - 2 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(0.900969 - 1.56052i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.l.484.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02446 + 1.77441i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.09903 - 1.90358i) q^{4} -3.35690 q^{5} +(1.02446 + 1.77441i) q^{6} +(1.12349 + 1.94594i) q^{7} +0.405813 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.02446 + 1.77441i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.09903 - 1.90358i) q^{4} -3.35690 q^{5} +(1.02446 + 1.77441i) q^{6} +(1.12349 + 1.94594i) q^{7} +0.405813 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.43900 - 5.95652i) q^{10} +(2.46950 - 4.27730i) q^{11} -2.19806 q^{12} -4.60388 q^{14} +(-1.67845 + 2.90716i) q^{15} +(1.78232 - 3.08707i) q^{16} +(-0.455927 - 0.789689i) q^{17} +2.04892 q^{18} +(-1.90097 - 3.29257i) q^{19} +(3.68933 + 6.39011i) q^{20} +2.24698 q^{21} +(5.05980 + 8.76383i) q^{22} +(-1.01357 + 1.75556i) q^{23} +(0.202907 - 0.351445i) q^{24} +6.26875 q^{25} -1.00000 q^{27} +(2.46950 - 4.27730i) q^{28} +(1.96950 - 3.41127i) q^{29} +(-3.43900 - 5.95652i) q^{30} +8.82908 q^{31} +(4.05765 + 7.02805i) q^{32} +(-2.46950 - 4.27730i) q^{33} +1.86831 q^{34} +(-3.77144 - 6.53232i) q^{35} +(-1.09903 + 1.90358i) q^{36} +(4.40097 - 7.62270i) q^{37} +7.78986 q^{38} -1.36227 q^{40} +(3.46950 - 6.00935i) q^{41} +(-2.30194 + 3.98707i) q^{42} +(1.14310 + 1.97991i) q^{43} -10.8562 q^{44} +(1.67845 + 2.90716i) q^{45} +(-2.07673 - 3.59700i) q^{46} -3.80194 q^{47} +(-1.78232 - 3.08707i) q^{48} +(0.975541 - 1.68969i) q^{49} +(-6.42208 + 11.1234i) q^{50} -0.911854 q^{51} +0.542877 q^{53} +(1.02446 - 1.77441i) q^{54} +(-8.28986 + 14.3585i) q^{55} +(0.455927 + 0.789689i) q^{56} -3.80194 q^{57} +(4.03534 + 6.98942i) q^{58} +(-2.35690 - 4.08226i) q^{59} +7.37867 q^{60} +(-1.83997 - 3.18692i) q^{61} +(-9.04503 + 15.6665i) q^{62} +(1.12349 - 1.94594i) q^{63} -9.49827 q^{64} +10.1196 q^{66} +(-0.760553 + 1.31732i) q^{67} +(-1.00216 + 1.73578i) q^{68} +(1.01357 + 1.75556i) q^{69} +15.4547 q^{70} +(1.18933 + 2.05999i) q^{71} +(-0.202907 - 0.351445i) q^{72} -7.41119 q^{73} +(9.01722 + 15.6183i) q^{74} +(3.13437 - 5.42890i) q^{75} +(-4.17845 + 7.23728i) q^{76} +11.0978 q^{77} -3.74094 q^{79} +(-5.98307 + 10.3630i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(7.10872 + 12.3127i) q^{82} -2.30798 q^{83} +(-2.46950 - 4.27730i) q^{84} +(1.53050 + 2.65090i) q^{85} -4.68425 q^{86} +(-1.96950 - 3.41127i) q^{87} +(1.00216 - 1.73578i) q^{88} +(-5.02930 + 8.71101i) q^{89} -6.87800 q^{90} +4.45580 q^{92} +(4.41454 - 7.64621i) q^{93} +(3.89493 - 6.74621i) q^{94} +(6.38135 + 11.0528i) q^{95} +8.11529 q^{96} +(-8.06465 - 13.9684i) q^{97} +(1.99880 + 3.46203i) q^{98} -4.93900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 3q^{2} + 3q^{3} - 11q^{4} - 12q^{5} - 3q^{6} + 2q^{7} - 24q^{8} - 3q^{9} + O(q^{10}) \) \( 6q + 3q^{2} + 3q^{3} - 11q^{4} - 12q^{5} - 3q^{6} + 2q^{7} - 24q^{8} - 3q^{9} + q^{10} + 5q^{11} - 22q^{12} - 10q^{14} - 6q^{15} - 11q^{16} + q^{17} - 6q^{18} - 7q^{19} + 15q^{20} + 4q^{21} + 9q^{22} - 12q^{24} + 22q^{25} - 6q^{27} + 5q^{28} + 2q^{29} - q^{30} + 32q^{31} + 22q^{32} - 5q^{33} + 16q^{34} - 4q^{35} - 11q^{36} + 22q^{37} + 6q^{40} + 11q^{41} - 5q^{42} + 15q^{43} - 32q^{44} + 6q^{45} - 7q^{46} - 14q^{47} + 11q^{48} + 15q^{49} - 3q^{50} + 2q^{51} - 34q^{53} - 3q^{54} - 3q^{55} - q^{56} - 14q^{57} + 12q^{58} - 6q^{59} + 30q^{60} + 13q^{61} + 2q^{62} + 2q^{63} + 18q^{66} + 11q^{67} + 13q^{68} + 48q^{70} + 12q^{72} - 12q^{73} - 15q^{74} + 11q^{75} - 21q^{76} + 30q^{77} + 6q^{79} - 20q^{80} - 3q^{81} + 3q^{82} - 24q^{83} - 5q^{84} + 19q^{85} + 58q^{86} - 2q^{87} - 13q^{88} + q^{89} - 2q^{90} + 14q^{92} + 16q^{93} + 21q^{95} + 44q^{96} - 5q^{97} - 29q^{98} - 10q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).

\(n\) \(170\) \(340\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02446 + 1.77441i −0.724402 + 1.25470i 0.234818 + 0.972039i \(0.424551\pi\)
−0.959220 + 0.282661i \(0.908783\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.09903 1.90358i −0.549516 0.951789i
\(5\) −3.35690 −1.50125 −0.750625 0.660729i \(-0.770247\pi\)
−0.750625 + 0.660729i \(0.770247\pi\)
\(6\) 1.02446 + 1.77441i 0.418234 + 0.724402i
\(7\) 1.12349 + 1.94594i 0.424639 + 0.735497i 0.996387 0.0849330i \(-0.0270676\pi\)
−0.571747 + 0.820430i \(0.693734\pi\)
\(8\) 0.405813 0.143477
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 3.43900 5.95652i 1.08751 1.88362i
\(11\) 2.46950 4.27730i 0.744582 1.28965i −0.205807 0.978593i \(-0.565982\pi\)
0.950390 0.311062i \(-0.100685\pi\)
\(12\) −2.19806 −0.634526
\(13\) 0 0
\(14\) −4.60388 −1.23044
\(15\) −1.67845 + 2.90716i −0.433373 + 0.750625i
\(16\) 1.78232 3.08707i 0.445581 0.771769i
\(17\) −0.455927 0.789689i −0.110579 0.191528i 0.805425 0.592698i \(-0.201937\pi\)
−0.916004 + 0.401170i \(0.868604\pi\)
\(18\) 2.04892 0.482934
\(19\) −1.90097 3.29257i −0.436112 0.755368i 0.561274 0.827630i \(-0.310312\pi\)
−0.997386 + 0.0722619i \(0.976978\pi\)
\(20\) 3.68933 + 6.39011i 0.824960 + 1.42887i
\(21\) 2.24698 0.490331
\(22\) 5.05980 + 8.76383i 1.07875 + 1.86846i
\(23\) −1.01357 + 1.75556i −0.211345 + 0.366060i −0.952136 0.305676i \(-0.901118\pi\)
0.740791 + 0.671736i \(0.234451\pi\)
\(24\) 0.202907 0.351445i 0.0414181 0.0717383i
\(25\) 6.26875 1.25375
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 2.46950 4.27730i 0.466692 0.808334i
\(29\) 1.96950 3.41127i 0.365727 0.633458i −0.623165 0.782090i \(-0.714154\pi\)
0.988893 + 0.148632i \(0.0474870\pi\)
\(30\) −3.43900 5.95652i −0.627873 1.08751i
\(31\) 8.82908 1.58575 0.792875 0.609384i \(-0.208583\pi\)
0.792875 + 0.609384i \(0.208583\pi\)
\(32\) 4.05765 + 7.02805i 0.717297 + 1.24240i
\(33\) −2.46950 4.27730i −0.429885 0.744582i
\(34\) 1.86831 0.320413
\(35\) −3.77144 6.53232i −0.637489 1.10416i
\(36\) −1.09903 + 1.90358i −0.183172 + 0.317263i
\(37\) 4.40097 7.62270i 0.723515 1.25316i −0.236068 0.971737i \(-0.575859\pi\)
0.959582 0.281428i \(-0.0908080\pi\)
\(38\) 7.78986 1.26368
\(39\) 0 0
\(40\) −1.36227 −0.215394
\(41\) 3.46950 6.00935i 0.541845 0.938503i −0.456953 0.889491i \(-0.651059\pi\)
0.998798 0.0490123i \(-0.0156073\pi\)
\(42\) −2.30194 + 3.98707i −0.355197 + 0.615219i
\(43\) 1.14310 + 1.97991i 0.174322 + 0.301934i 0.939926 0.341377i \(-0.110893\pi\)
−0.765605 + 0.643311i \(0.777560\pi\)
\(44\) −10.8562 −1.63664
\(45\) 1.67845 + 2.90716i 0.250208 + 0.433373i
\(46\) −2.07673 3.59700i −0.306197 0.530349i
\(47\) −3.80194 −0.554570 −0.277285 0.960788i \(-0.589435\pi\)
−0.277285 + 0.960788i \(0.589435\pi\)
\(48\) −1.78232 3.08707i −0.257256 0.445581i
\(49\) 0.975541 1.68969i 0.139363 0.241384i
\(50\) −6.42208 + 11.1234i −0.908219 + 1.57308i
\(51\) −0.911854 −0.127685
\(52\) 0 0
\(53\) 0.542877 0.0745698 0.0372849 0.999305i \(-0.488129\pi\)
0.0372849 + 0.999305i \(0.488129\pi\)
\(54\) 1.02446 1.77441i 0.139411 0.241467i
\(55\) −8.28986 + 14.3585i −1.11780 + 1.93609i
\(56\) 0.455927 + 0.789689i 0.0609258 + 0.105527i
\(57\) −3.80194 −0.503579
\(58\) 4.03534 + 6.98942i 0.529867 + 0.917756i
\(59\) −2.35690 4.08226i −0.306842 0.531465i 0.670828 0.741613i \(-0.265939\pi\)
−0.977670 + 0.210148i \(0.932606\pi\)
\(60\) 7.37867 0.952582
\(61\) −1.83997 3.18692i −0.235584 0.408043i 0.723858 0.689949i \(-0.242367\pi\)
−0.959442 + 0.281905i \(0.909034\pi\)
\(62\) −9.04503 + 15.6665i −1.14872 + 1.98964i
\(63\) 1.12349 1.94594i 0.141546 0.245166i
\(64\) −9.49827 −1.18728
\(65\) 0 0
\(66\) 10.1196 1.24564
\(67\) −0.760553 + 1.31732i −0.0929164 + 0.160936i −0.908737 0.417369i \(-0.862952\pi\)
0.815821 + 0.578305i \(0.196286\pi\)
\(68\) −1.00216 + 1.73578i −0.121529 + 0.210495i
\(69\) 1.01357 + 1.75556i 0.122020 + 0.211345i
\(70\) 15.4547 1.84719
\(71\) 1.18933 + 2.05999i 0.141148 + 0.244475i 0.927929 0.372757i \(-0.121587\pi\)
−0.786781 + 0.617232i \(0.788254\pi\)
\(72\) −0.202907 0.351445i −0.0239128 0.0414181i
\(73\) −7.41119 −0.867414 −0.433707 0.901054i \(-0.642795\pi\)
−0.433707 + 0.901054i \(0.642795\pi\)
\(74\) 9.01722 + 15.6183i 1.04823 + 1.81559i
\(75\) 3.13437 5.42890i 0.361926 0.626875i
\(76\) −4.17845 + 7.23728i −0.479301 + 0.830173i
\(77\) 11.0978 1.26472
\(78\) 0 0
\(79\) −3.74094 −0.420888 −0.210444 0.977606i \(-0.567491\pi\)
−0.210444 + 0.977606i \(0.567491\pi\)
\(80\) −5.98307 + 10.3630i −0.668928 + 1.15862i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.10872 + 12.3127i 0.785027 + 1.35971i
\(83\) −2.30798 −0.253334 −0.126667 0.991945i \(-0.540428\pi\)
−0.126667 + 0.991945i \(0.540428\pi\)
\(84\) −2.46950 4.27730i −0.269445 0.466692i
\(85\) 1.53050 + 2.65090i 0.166006 + 0.287531i
\(86\) −4.68425 −0.505116
\(87\) −1.96950 3.41127i −0.211153 0.365727i
\(88\) 1.00216 1.73578i 0.106830 0.185035i
\(89\) −5.02930 + 8.71101i −0.533105 + 0.923365i 0.466147 + 0.884707i \(0.345642\pi\)
−0.999253 + 0.0386580i \(0.987692\pi\)
\(90\) −6.87800 −0.725005
\(91\) 0 0
\(92\) 4.45580 0.464549
\(93\) 4.41454 7.64621i 0.457767 0.792875i
\(94\) 3.89493 6.74621i 0.401731 0.695819i
\(95\) 6.38135 + 11.0528i 0.654713 + 1.13400i
\(96\) 8.11529 0.828264
\(97\) −8.06465 13.9684i −0.818841 1.41827i −0.906537 0.422127i \(-0.861284\pi\)
0.0876961 0.996147i \(-0.472050\pi\)
\(98\) 1.99880 + 3.46203i 0.201910 + 0.349718i
\(99\) −4.93900 −0.496388
\(100\) −6.88955 11.9331i −0.688955 1.19331i
\(101\) 4.97434 8.61582i 0.494966 0.857306i −0.505017 0.863109i \(-0.668514\pi\)
0.999983 + 0.00580325i \(0.00184724\pi\)
\(102\) 0.934157 1.61801i 0.0924953 0.160207i
\(103\) −10.9879 −1.08267 −0.541336 0.840806i \(-0.682081\pi\)
−0.541336 + 0.840806i \(0.682081\pi\)
\(104\) 0 0
\(105\) −7.54288 −0.736109
\(106\) −0.556155 + 0.963288i −0.0540185 + 0.0935628i
\(107\) 4.93631 8.54994i 0.477211 0.826554i −0.522448 0.852671i \(-0.674981\pi\)
0.999659 + 0.0261171i \(0.00831428\pi\)
\(108\) 1.09903 + 1.90358i 0.105754 + 0.183172i
\(109\) −20.2446 −1.93908 −0.969540 0.244934i \(-0.921234\pi\)
−0.969540 + 0.244934i \(0.921234\pi\)
\(110\) −16.9852 29.4193i −1.61948 2.80502i
\(111\) −4.40097 7.62270i −0.417721 0.723515i
\(112\) 8.00969 0.756844
\(113\) −4.84601 8.39354i −0.455874 0.789598i 0.542864 0.839821i \(-0.317340\pi\)
−0.998738 + 0.0502233i \(0.984007\pi\)
\(114\) 3.89493 6.74621i 0.364793 0.631841i
\(115\) 3.40246 5.89324i 0.317281 0.549547i
\(116\) −8.65817 −0.803891
\(117\) 0 0
\(118\) 9.65817 0.889107
\(119\) 1.02446 1.77441i 0.0939120 0.162660i
\(120\) −0.681136 + 1.17976i −0.0621790 + 0.107697i
\(121\) −6.69687 11.5993i −0.608806 1.05448i
\(122\) 7.53989 0.682630
\(123\) −3.46950 6.00935i −0.312834 0.541845i
\(124\) −9.70344 16.8068i −0.871395 1.50930i
\(125\) −4.25906 −0.380942
\(126\) 2.30194 + 3.98707i 0.205073 + 0.355197i
\(127\) −6.90581 + 11.9612i −0.612792 + 1.06139i 0.377976 + 0.925815i \(0.376620\pi\)
−0.990768 + 0.135571i \(0.956713\pi\)
\(128\) 1.61529 2.79777i 0.142773 0.247290i
\(129\) 2.28621 0.201289
\(130\) 0 0
\(131\) 2.99462 0.261641 0.130821 0.991406i \(-0.458239\pi\)
0.130821 + 0.991406i \(0.458239\pi\)
\(132\) −5.42812 + 9.40177i −0.472457 + 0.818319i
\(133\) 4.27144 7.39835i 0.370381 0.641518i
\(134\) −1.55831 2.69907i −0.134618 0.233164i
\(135\) 3.35690 0.288916
\(136\) −0.185021 0.320466i −0.0158654 0.0274797i
\(137\) 11.5097 + 19.9354i 0.983339 + 1.70319i 0.649096 + 0.760706i \(0.275147\pi\)
0.334243 + 0.942487i \(0.391519\pi\)
\(138\) −4.15346 −0.353566
\(139\) −0.491271 0.850906i −0.0416690 0.0721729i 0.844439 0.535652i \(-0.179934\pi\)
−0.886108 + 0.463479i \(0.846601\pi\)
\(140\) −8.28986 + 14.3585i −0.700621 + 1.21351i
\(141\) −1.90097 + 3.29257i −0.160090 + 0.277285i
\(142\) −4.87369 −0.408991
\(143\) 0 0
\(144\) −3.56465 −0.297054
\(145\) −6.61141 + 11.4513i −0.549048 + 0.950978i
\(146\) 7.59246 13.1505i 0.628356 1.08835i
\(147\) −0.975541 1.68969i −0.0804613 0.139363i
\(148\) −19.3472 −1.59033
\(149\) 5.12953 + 8.88461i 0.420228 + 0.727855i 0.995961 0.0897817i \(-0.0286169\pi\)
−0.575734 + 0.817637i \(0.695284\pi\)
\(150\) 6.42208 + 11.1234i 0.524360 + 0.908219i
\(151\) 20.1685 1.64129 0.820646 0.571438i \(-0.193614\pi\)
0.820646 + 0.571438i \(0.193614\pi\)
\(152\) −0.771438 1.33617i −0.0625719 0.108378i
\(153\) −0.455927 + 0.789689i −0.0368595 + 0.0638425i
\(154\) −11.3693 + 19.6922i −0.916162 + 1.58684i
\(155\) −29.6383 −2.38061
\(156\) 0 0
\(157\) 10.4383 0.833070 0.416535 0.909120i \(-0.363244\pi\)
0.416535 + 0.909120i \(0.363244\pi\)
\(158\) 3.83244 6.63798i 0.304892 0.528089i
\(159\) 0.271438 0.470145i 0.0215265 0.0372849i
\(160\) −13.6211 23.5924i −1.07684 1.86515i
\(161\) −4.55496 −0.358981
\(162\) −1.02446 1.77441i −0.0804891 0.139411i
\(163\) −5.52326 9.56657i −0.432615 0.749312i 0.564482 0.825445i \(-0.309076\pi\)
−0.997098 + 0.0761335i \(0.975742\pi\)
\(164\) −15.2524 −1.19101
\(165\) 8.28986 + 14.3585i 0.645364 + 1.11780i
\(166\) 2.36443 4.09531i 0.183515 0.317858i
\(167\) 4.05496 7.02339i 0.313782 0.543487i −0.665396 0.746491i \(-0.731737\pi\)
0.979178 + 0.203004i \(0.0650705\pi\)
\(168\) 0.911854 0.0703511
\(169\) 0 0
\(170\) −6.27173 −0.481020
\(171\) −1.90097 + 3.29257i −0.145371 + 0.251789i
\(172\) 2.51261 4.35198i 0.191585 0.331835i
\(173\) 9.02811 + 15.6371i 0.686394 + 1.18887i 0.972996 + 0.230820i \(0.0741409\pi\)
−0.286602 + 0.958050i \(0.592526\pi\)
\(174\) 8.07069 0.611837
\(175\) 7.04288 + 12.1986i 0.532391 + 0.922129i
\(176\) −8.80290 15.2471i −0.663543 1.14929i
\(177\) −4.71379 −0.354310
\(178\) −10.3046 17.8481i −0.772364 1.33777i
\(179\) 9.93512 17.2081i 0.742585 1.28620i −0.208729 0.977974i \(-0.566933\pi\)
0.951314 0.308222i \(-0.0997340\pi\)
\(180\) 3.68933 6.39011i 0.274987 0.476291i
\(181\) −10.0828 −0.749446 −0.374723 0.927137i \(-0.622262\pi\)
−0.374723 + 0.927137i \(0.622262\pi\)
\(182\) 0 0
\(183\) −3.67994 −0.272029
\(184\) −0.411322 + 0.712430i −0.0303230 + 0.0525210i
\(185\) −14.7736 + 25.5886i −1.08618 + 1.88131i
\(186\) 9.04503 + 15.6665i 0.663214 + 1.14872i
\(187\) −4.50365 −0.329339
\(188\) 4.17845 + 7.23728i 0.304745 + 0.527833i
\(189\) −1.12349 1.94594i −0.0817219 0.141546i
\(190\) −26.1497 −1.89710
\(191\) 3.29374 + 5.70493i 0.238327 + 0.412794i 0.960234 0.279196i \(-0.0900678\pi\)
−0.721908 + 0.691990i \(0.756734\pi\)
\(192\) −4.74914 + 8.22574i −0.342739 + 0.593642i
\(193\) 5.43362 9.41131i 0.391121 0.677441i −0.601477 0.798890i \(-0.705421\pi\)
0.992598 + 0.121449i \(0.0387541\pi\)
\(194\) 33.0476 2.37268
\(195\) 0 0
\(196\) −4.28860 −0.306329
\(197\) 4.62080 8.00346i 0.329218 0.570223i −0.653139 0.757238i \(-0.726548\pi\)
0.982357 + 0.187015i \(0.0598814\pi\)
\(198\) 5.05980 8.76383i 0.359585 0.622819i
\(199\) 0.782323 + 1.35502i 0.0554574 + 0.0960551i 0.892421 0.451203i \(-0.149005\pi\)
−0.836964 + 0.547258i \(0.815672\pi\)
\(200\) 2.54394 0.179884
\(201\) 0.760553 + 1.31732i 0.0536453 + 0.0929164i
\(202\) 10.1920 + 17.6531i 0.717108 + 1.24207i
\(203\) 8.85086 0.621208
\(204\) 1.00216 + 1.73578i 0.0701649 + 0.121529i
\(205\) −11.6468 + 20.1728i −0.813444 + 1.40893i
\(206\) 11.2567 19.4971i 0.784289 1.35843i
\(207\) 2.02715 0.140896
\(208\) 0 0
\(209\) −18.7778 −1.29889
\(210\) 7.72737 13.3842i 0.533239 0.923597i
\(211\) −11.6223 + 20.1304i −0.800112 + 1.38583i 0.119430 + 0.992843i \(0.461893\pi\)
−0.919542 + 0.392991i \(0.871440\pi\)
\(212\) −0.596638 1.03341i −0.0409773 0.0709747i
\(213\) 2.37867 0.162984
\(214\) 10.1141 + 17.5181i 0.691385 + 1.19751i
\(215\) −3.83728 6.64637i −0.261700 0.453278i
\(216\) −0.405813 −0.0276121
\(217\) 9.91939 + 17.1809i 0.673372 + 1.16631i
\(218\) 20.7397 35.9223i 1.40467 2.43296i
\(219\) −3.70560 + 6.41828i −0.250401 + 0.433707i
\(220\) 36.4432 2.45700
\(221\) 0 0
\(222\) 18.0344 1.21039
\(223\) 5.36927 9.29985i 0.359553 0.622764i −0.628333 0.777944i \(-0.716262\pi\)
0.987886 + 0.155180i \(0.0495958\pi\)
\(224\) −9.11745 + 15.7919i −0.609185 + 1.05514i
\(225\) −3.13437 5.42890i −0.208958 0.361926i
\(226\) 19.8582 1.32094
\(227\) −3.48792 6.04125i −0.231501 0.400972i 0.726749 0.686903i \(-0.241030\pi\)
−0.958250 + 0.285931i \(0.907697\pi\)
\(228\) 4.17845 + 7.23728i 0.276724 + 0.479301i
\(229\) 16.8049 1.11050 0.555250 0.831683i \(-0.312622\pi\)
0.555250 + 0.831683i \(0.312622\pi\)
\(230\) 6.97136 + 12.0748i 0.459678 + 0.796186i
\(231\) 5.54892 9.61101i 0.365092 0.632358i
\(232\) 0.799249 1.38434i 0.0524733 0.0908864i
\(233\) 8.69202 0.569433 0.284717 0.958612i \(-0.408100\pi\)
0.284717 + 0.958612i \(0.408100\pi\)
\(234\) 0 0
\(235\) 12.7627 0.832547
\(236\) −5.18060 + 8.97307i −0.337229 + 0.584097i
\(237\) −1.87047 + 3.23975i −0.121500 + 0.210444i
\(238\) 2.09903 + 3.63563i 0.136060 + 0.235663i
\(239\) 22.9191 1.48252 0.741258 0.671220i \(-0.234229\pi\)
0.741258 + 0.671220i \(0.234229\pi\)
\(240\) 5.98307 + 10.3630i 0.386206 + 0.668928i
\(241\) 10.9901 + 19.0354i 0.707933 + 1.22618i 0.965623 + 0.259948i \(0.0837054\pi\)
−0.257690 + 0.966228i \(0.582961\pi\)
\(242\) 27.4426 1.76408
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −4.04437 + 7.00505i −0.258914 + 0.448452i
\(245\) −3.27479 + 5.67210i −0.209219 + 0.362377i
\(246\) 14.2174 0.906471
\(247\) 0 0
\(248\) 3.58296 0.227518
\(249\) −1.15399 + 1.99877i −0.0731311 + 0.126667i
\(250\) 4.36323 7.55734i 0.275955 0.477968i
\(251\) −13.3218 23.0741i −0.840868 1.45643i −0.889162 0.457592i \(-0.848712\pi\)
0.0482946 0.998833i \(-0.484621\pi\)
\(252\) −4.93900 −0.311128
\(253\) 5.00604 + 8.67072i 0.314727 + 0.545123i
\(254\) −14.1494 24.5075i −0.887815 1.53774i
\(255\) 3.06100 0.191687
\(256\) −6.18867 10.7191i −0.386792 0.669943i
\(257\) −11.5722 + 20.0436i −0.721853 + 1.25029i 0.238404 + 0.971166i \(0.423376\pi\)
−0.960256 + 0.279119i \(0.909957\pi\)
\(258\) −2.34213 + 4.05668i −0.145814 + 0.252558i
\(259\) 19.7778 1.22893
\(260\) 0 0
\(261\) −3.93900 −0.243818
\(262\) −3.06787 + 5.31370i −0.189533 + 0.328282i
\(263\) 9.26420 16.0461i 0.571255 0.989443i −0.425182 0.905108i \(-0.639790\pi\)
0.996437 0.0843352i \(-0.0268766\pi\)
\(264\) −1.00216 1.73578i −0.0616784 0.106830i
\(265\) −1.82238 −0.111948
\(266\) 8.75182 + 15.1586i 0.536609 + 0.929434i
\(267\) 5.02930 + 8.71101i 0.307788 + 0.533105i
\(268\) 3.34349 0.204236
\(269\) −4.87920 8.45102i −0.297490 0.515268i 0.678071 0.734996i \(-0.262816\pi\)
−0.975561 + 0.219729i \(0.929483\pi\)
\(270\) −3.43900 + 5.95652i −0.209291 + 0.362503i
\(271\) −11.4010 + 19.7471i −0.692560 + 1.19955i 0.278437 + 0.960455i \(0.410184\pi\)
−0.970996 + 0.239094i \(0.923150\pi\)
\(272\) −3.25044 −0.197087
\(273\) 0 0
\(274\) −47.1648 −2.84933
\(275\) 15.4807 26.8133i 0.933520 1.61690i
\(276\) 2.22790 3.85883i 0.134104 0.232274i
\(277\) 11.9852 + 20.7590i 0.720123 + 1.24729i 0.960950 + 0.276721i \(0.0892478\pi\)
−0.240828 + 0.970568i \(0.577419\pi\)
\(278\) 2.01315 0.120741
\(279\) −4.41454 7.64621i −0.264292 0.457767i
\(280\) −1.53050 2.65090i −0.0914648 0.158422i
\(281\) 4.12498 0.246076 0.123038 0.992402i \(-0.460736\pi\)
0.123038 + 0.992402i \(0.460736\pi\)
\(282\) −3.89493 6.74621i −0.231940 0.401731i
\(283\) 7.82789 13.5583i 0.465320 0.805957i −0.533896 0.845550i \(-0.679273\pi\)
0.999216 + 0.0395927i \(0.0126060\pi\)
\(284\) 2.61423 4.52798i 0.155126 0.268686i
\(285\) 12.7627 0.755998
\(286\) 0 0
\(287\) 15.5918 0.920354
\(288\) 4.05765 7.02805i 0.239099 0.414132i
\(289\) 8.08426 14.0024i 0.475545 0.823668i
\(290\) −13.5462 23.4628i −0.795462 1.37778i
\(291\) −16.1293 −0.945516
\(292\) 8.14513 + 14.1078i 0.476658 + 0.825595i
\(293\) 11.2974 + 19.5677i 0.660001 + 1.14315i 0.980615 + 0.195945i \(0.0627773\pi\)
−0.320614 + 0.947210i \(0.603889\pi\)
\(294\) 3.99761 0.233145
\(295\) 7.91185 + 13.7037i 0.460646 + 0.797862i
\(296\) 1.78597 3.09339i 0.103807 0.179800i
\(297\) −2.46950 + 4.27730i −0.143295 + 0.248194i
\(298\) −21.0200 −1.21765
\(299\) 0 0
\(300\) −13.7791 −0.795537
\(301\) −2.56853 + 4.44883i −0.148048 + 0.256426i
\(302\) −20.6618 + 35.7873i −1.18895 + 2.05933i
\(303\) −4.97434 8.61582i −0.285769 0.494966i
\(304\) −13.5526 −0.777293
\(305\) 6.17659 + 10.6982i 0.353670 + 0.612575i
\(306\) −0.934157 1.61801i −0.0534022 0.0924953i
\(307\) 6.55496 0.374111 0.187056 0.982349i \(-0.440106\pi\)
0.187056 + 0.982349i \(0.440106\pi\)
\(308\) −12.1969 21.1256i −0.694981 1.20374i
\(309\) −5.49396 + 9.51582i −0.312540 + 0.541336i
\(310\) 30.3632 52.5907i 1.72452 2.98695i
\(311\) −12.0392 −0.682682 −0.341341 0.939940i \(-0.610881\pi\)
−0.341341 + 0.939940i \(0.610881\pi\)
\(312\) 0 0
\(313\) −33.8950 −1.91586 −0.957929 0.287005i \(-0.907340\pi\)
−0.957929 + 0.287005i \(0.907340\pi\)
\(314\) −10.6936 + 18.5219i −0.603477 + 1.04525i
\(315\) −3.77144 + 6.53232i −0.212496 + 0.368055i
\(316\) 4.11141 + 7.12117i 0.231285 + 0.400597i
\(317\) 4.49827 0.252648 0.126324 0.991989i \(-0.459682\pi\)
0.126324 + 0.991989i \(0.459682\pi\)
\(318\) 0.556155 + 0.963288i 0.0311876 + 0.0540185i
\(319\) −9.72737 16.8483i −0.544628 0.943323i
\(320\) 31.8847 1.78241
\(321\) −4.93631 8.54994i −0.275518 0.477211i
\(322\) 4.66637 8.08238i 0.260046 0.450414i
\(323\) −1.73341 + 3.00235i −0.0964493 + 0.167055i
\(324\) 2.19806 0.122115
\(325\) 0 0
\(326\) 22.6334 1.25355
\(327\) −10.1223 + 17.5323i −0.559764 + 0.969540i
\(328\) 1.40797 2.43867i 0.0777421 0.134653i
\(329\) −4.27144 7.39835i −0.235492 0.407884i
\(330\) −33.9705 −1.87001
\(331\) −5.60656 9.71085i −0.308165 0.533757i 0.669796 0.742545i \(-0.266381\pi\)
−0.977961 + 0.208788i \(0.933048\pi\)
\(332\) 2.53654 + 4.39342i 0.139211 + 0.241120i
\(333\) −8.80194 −0.482343
\(334\) 8.30827 + 14.3904i 0.454609 + 0.787405i
\(335\) 2.55310 4.42209i 0.139491 0.241605i
\(336\) 4.00484 6.93659i 0.218482 0.378422i
\(337\) 7.04892 0.383979 0.191989 0.981397i \(-0.438506\pi\)
0.191989 + 0.981397i \(0.438506\pi\)
\(338\) 0 0
\(339\) −9.69202 −0.526398
\(340\) 3.36413 5.82685i 0.182446 0.316005i
\(341\) 21.8034 37.7646i 1.18072 2.04507i
\(342\) −3.89493 6.74621i −0.210614 0.364793i
\(343\) 20.1129 1.08599
\(344\) 0.463887 + 0.803475i 0.0250111 + 0.0433205i
\(345\) −3.40246 5.89324i −0.183182 0.317281i
\(346\) −36.9957 −1.98890
\(347\) 1.35205 + 2.34182i 0.0725819 + 0.125716i 0.900032 0.435823i \(-0.143543\pi\)
−0.827450 + 0.561539i \(0.810209\pi\)
\(348\) −4.32908 + 7.49819i −0.232063 + 0.401945i
\(349\) −0.207751 + 0.359835i −0.0111207 + 0.0192615i −0.871532 0.490338i \(-0.836873\pi\)
0.860412 + 0.509600i \(0.170207\pi\)
\(350\) −28.8605 −1.54266
\(351\) 0 0
\(352\) 40.0814 2.13635
\(353\) −16.0836 + 27.8576i −0.856044 + 1.48271i 0.0196301 + 0.999807i \(0.493751\pi\)
−0.875674 + 0.482904i \(0.839582\pi\)
\(354\) 4.82908 8.36422i 0.256663 0.444553i
\(355\) −3.99247 6.91516i −0.211898 0.367018i
\(356\) 22.1094 1.17180
\(357\) −1.02446 1.77441i −0.0542201 0.0939120i
\(358\) 20.3562 + 35.2580i 1.07586 + 1.86344i
\(359\) −22.3521 −1.17970 −0.589850 0.807513i \(-0.700813\pi\)
−0.589850 + 0.807513i \(0.700813\pi\)
\(360\) 0.681136 + 1.17976i 0.0358990 + 0.0621790i
\(361\) 2.27263 3.93632i 0.119612 0.207175i
\(362\) 10.3294 17.8910i 0.542900 0.940331i
\(363\) −13.3937 −0.702989
\(364\) 0 0
\(365\) 24.8786 1.30221
\(366\) 3.76995 6.52974i 0.197058 0.341315i
\(367\) 1.15130 1.99411i 0.0600974 0.104092i −0.834411 0.551142i \(-0.814192\pi\)
0.894509 + 0.447050i \(0.147526\pi\)
\(368\) 3.61303 + 6.25795i 0.188342 + 0.326218i
\(369\) −6.93900 −0.361230
\(370\) −30.2699 52.4290i −1.57366 2.72565i
\(371\) 0.609916 + 1.05641i 0.0316653 + 0.0548459i
\(372\) −19.4069 −1.00620
\(373\) 9.63802 + 16.6935i 0.499038 + 0.864359i 0.999999 0.00111058i \(-0.000353507\pi\)
−0.500961 + 0.865470i \(0.667020\pi\)
\(374\) 4.61380 7.99134i 0.238574 0.413222i
\(375\) −2.12953 + 3.68846i −0.109968 + 0.190471i
\(376\) −1.54288 −0.0795678
\(377\) 0 0
\(378\) 4.60388 0.236798
\(379\) −3.66972 + 6.35614i −0.188501 + 0.326493i −0.944751 0.327790i \(-0.893696\pi\)
0.756250 + 0.654283i \(0.227029\pi\)
\(380\) 14.0266 24.2948i 0.719550 1.24630i
\(381\) 6.90581 + 11.9612i 0.353796 + 0.612792i
\(382\) −13.4972 −0.690577
\(383\) 9.54503 + 16.5325i 0.487728 + 0.844770i 0.999900 0.0141126i \(-0.00449231\pi\)
−0.512172 + 0.858883i \(0.671159\pi\)
\(384\) −1.61529 2.79777i −0.0824301 0.142773i
\(385\) −37.2543 −1.89865
\(386\) 11.1330 + 19.2830i 0.566657 + 0.981479i
\(387\) 1.14310 1.97991i 0.0581072 0.100645i
\(388\) −17.7266 + 30.7034i −0.899932 + 1.55873i
\(389\) −23.9879 −1.21624 −0.608118 0.793847i \(-0.708075\pi\)
−0.608118 + 0.793847i \(0.708075\pi\)
\(390\) 0 0
\(391\) 1.84846 0.0934807
\(392\) 0.395888 0.685697i 0.0199953 0.0346329i
\(393\) 1.49731 2.59342i 0.0755294 0.130821i
\(394\) 9.46764 + 16.3984i 0.476973 + 0.826141i
\(395\) 12.5579 0.631859
\(396\) 5.42812 + 9.40177i 0.272773 + 0.472457i
\(397\) −2.20895 3.82601i −0.110864 0.192022i 0.805255 0.592929i \(-0.202028\pi\)
−0.916119 + 0.400907i \(0.868695\pi\)
\(398\) −3.20583 −0.160694
\(399\) −4.27144 7.39835i −0.213839 0.370381i
\(400\) 11.1729 19.3521i 0.558647 0.967605i
\(401\) −10.2044 + 17.6745i −0.509583 + 0.882624i 0.490355 + 0.871523i \(0.336867\pi\)
−0.999938 + 0.0111015i \(0.996466\pi\)
\(402\) −3.11662 −0.155443
\(403\) 0 0
\(404\) −21.8678 −1.08797
\(405\) 1.67845 2.90716i 0.0834027 0.144458i
\(406\) −9.06734 + 15.7051i −0.450004 + 0.779430i
\(407\) −21.7364 37.6485i −1.07743 1.86617i
\(408\) −0.370042 −0.0183198
\(409\) −11.0746 19.1817i −0.547602 0.948475i −0.998438 0.0558682i \(-0.982207\pi\)
0.450836 0.892607i \(-0.351126\pi\)
\(410\) −23.8632 41.3323i −1.17852 2.04126i
\(411\) 23.0194 1.13546
\(412\) 12.0761 + 20.9164i 0.594945 + 1.03047i
\(413\) 5.29590 9.17276i 0.260594 0.451362i
\(414\) −2.07673 + 3.59700i −0.102066 + 0.176783i
\(415\) 7.74764 0.380317
\(416\) 0 0
\(417\) −0.982542 −0.0481153
\(418\) 19.2371 33.3196i 0.940915 1.62971i
\(419\) −7.37800 + 12.7791i −0.360439 + 0.624299i −0.988033 0.154242i \(-0.950706\pi\)
0.627594 + 0.778541i \(0.284040\pi\)
\(420\) 8.28986 + 14.3585i 0.404504 + 0.700621i
\(421\) −8.47219 −0.412909 −0.206455 0.978456i \(-0.566193\pi\)
−0.206455 + 0.978456i \(0.566193\pi\)
\(422\) −23.8131 41.2455i −1.15920 2.00780i
\(423\) 1.90097 + 3.29257i 0.0924283 + 0.160090i
\(424\) 0.220306 0.0106990
\(425\) −2.85809 4.95036i −0.138638 0.240128i
\(426\) −2.43685 + 4.22074i −0.118066 + 0.204496i
\(427\) 4.13437 7.16095i 0.200076 0.346543i
\(428\) −21.7006 −1.04894
\(429\) 0 0
\(430\) 15.7245 0.758305
\(431\) 1.19591 2.07137i 0.0576048 0.0997744i −0.835785 0.549057i \(-0.814987\pi\)
0.893390 + 0.449283i \(0.148320\pi\)
\(432\) −1.78232 + 3.08707i −0.0857521 + 0.148527i
\(433\) 5.21432 + 9.03147i 0.250584 + 0.434025i 0.963687 0.267035i \(-0.0860439\pi\)
−0.713102 + 0.701060i \(0.752711\pi\)
\(434\) −40.6480 −1.95117
\(435\) 6.61141 + 11.4513i 0.316993 + 0.549048i
\(436\) 22.2494 + 38.5371i 1.06555 + 1.84559i
\(437\) 7.70709 0.368680
\(438\) −7.59246 13.1505i −0.362782 0.628356i
\(439\) 16.2751 28.1893i 0.776767 1.34540i −0.157028 0.987594i \(-0.550191\pi\)
0.933796 0.357807i \(-0.116475\pi\)
\(440\) −3.36413 + 5.82685i −0.160379 + 0.277784i
\(441\) −1.95108 −0.0929087
\(442\) 0 0
\(443\) 9.58211 0.455260 0.227630 0.973748i \(-0.426902\pi\)
0.227630 + 0.973748i \(0.426902\pi\)
\(444\) −9.67360 + 16.7552i −0.459089 + 0.795165i
\(445\) 16.8828 29.2419i 0.800324 1.38620i
\(446\) 11.0012 + 19.0546i 0.520922 + 0.902263i
\(447\) 10.2591 0.485237
\(448\) −10.6712 18.4831i −0.504167 0.873243i
\(449\) −14.1969 24.5897i −0.669992 1.16046i −0.977906 0.209045i \(-0.932964\pi\)
0.307914 0.951414i \(-0.400369\pi\)
\(450\) 12.8442 0.605479
\(451\) −17.1359 29.6802i −0.806896 1.39759i
\(452\) −10.6518 + 18.4495i −0.501020 + 0.867792i
\(453\) 10.0843 17.4665i 0.473800 0.820646i
\(454\) 14.2929 0.670800
\(455\) 0 0
\(456\) −1.54288 −0.0722518
\(457\) 2.49784 4.32639i 0.116844 0.202380i −0.801671 0.597765i \(-0.796056\pi\)
0.918515 + 0.395385i \(0.129389\pi\)
\(458\) −17.2159 + 29.8189i −0.804448 + 1.39335i
\(459\) 0.455927 + 0.789689i 0.0212808 + 0.0368595i
\(460\) −14.9576 −0.697404
\(461\) 0.676292 + 1.17137i 0.0314981 + 0.0545562i 0.881345 0.472474i \(-0.156639\pi\)
−0.849847 + 0.527030i \(0.823306\pi\)
\(462\) 11.3693 + 19.6922i 0.528946 + 0.916162i
\(463\) 3.36467 0.156369 0.0781846 0.996939i \(-0.475088\pi\)
0.0781846 + 0.996939i \(0.475088\pi\)
\(464\) −7.02057 12.1600i −0.325922 0.564513i
\(465\) −14.8192 + 25.6675i −0.687222 + 1.19030i
\(466\) −8.90462 + 15.4232i −0.412498 + 0.714468i
\(467\) 6.91079 0.319793 0.159897 0.987134i \(-0.448884\pi\)
0.159897 + 0.987134i \(0.448884\pi\)
\(468\) 0 0
\(469\) −3.41789 −0.157824
\(470\) −13.0749 + 22.6463i −0.603099 + 1.04460i
\(471\) 5.21917 9.03987i 0.240487 0.416535i
\(472\) −0.956459 1.65664i −0.0440246 0.0762529i
\(473\) 11.2916 0.519188
\(474\) −3.83244 6.63798i −0.176030 0.304892i
\(475\) −11.9167 20.6403i −0.546776 0.947043i
\(476\) −4.50365 −0.206424
\(477\) −0.271438 0.470145i −0.0124283 0.0215265i
\(478\) −23.4797 + 40.6681i −1.07394 + 1.86011i
\(479\) 1.75786 3.04471i 0.0803189 0.139116i −0.823068 0.567943i \(-0.807739\pi\)
0.903387 + 0.428826i \(0.141073\pi\)
\(480\) −27.2422 −1.24343
\(481\) 0 0
\(482\) −45.0355 −2.05131
\(483\) −2.27748 + 3.94471i −0.103629 + 0.179490i
\(484\) −14.7201 + 25.4960i −0.669097 + 1.15891i
\(485\) 27.0722 + 46.8904i 1.22928 + 2.12918i
\(486\) −2.04892 −0.0929408
\(487\) −6.42394 11.1266i −0.291096 0.504194i 0.682973 0.730444i \(-0.260687\pi\)
−0.974069 + 0.226250i \(0.927353\pi\)
\(488\) −0.746684 1.29329i −0.0338008 0.0585447i
\(489\) −11.0465 −0.499541
\(490\) −6.70978 11.6217i −0.303117 0.525014i
\(491\) −14.3354 + 24.8297i −0.646948 + 1.12055i 0.336899 + 0.941541i \(0.390622\pi\)
−0.983848 + 0.179007i \(0.942712\pi\)
\(492\) −7.62618 + 13.2089i −0.343815 + 0.595504i
\(493\) −3.59179 −0.161766
\(494\) 0 0
\(495\) 16.5797 0.745203
\(496\) 15.7363 27.2560i 0.706580 1.22383i
\(497\) −2.67241 + 4.62874i −0.119874 + 0.207628i
\(498\) −2.36443 4.09531i −0.105953 0.183515i
\(499\) 33.5555 1.50215 0.751076 0.660215i \(-0.229535\pi\)
0.751076 + 0.660215i \(0.229535\pi\)
\(500\) 4.68084 + 8.10745i 0.209334 + 0.362576i
\(501\) −4.05496 7.02339i −0.181162 0.313782i
\(502\) 54.5907 2.43650
\(503\) −10.7817 18.6744i −0.480730 0.832650i 0.519025 0.854759i \(-0.326295\pi\)
−0.999756 + 0.0221094i \(0.992962\pi\)
\(504\) 0.455927 0.789689i 0.0203086 0.0351755i
\(505\) −16.6984 + 28.9224i −0.743067 + 1.28703i
\(506\) −20.5139 −0.911955
\(507\) 0 0
\(508\) 30.3588 1.34695
\(509\) −4.44504 + 7.69904i −0.197023 + 0.341254i −0.947562 0.319572i \(-0.896461\pi\)
0.750539 + 0.660826i \(0.229794\pi\)
\(510\) −3.13587 + 5.43148i −0.138859 + 0.240510i
\(511\) −8.32640 14.4217i −0.368338 0.637980i
\(512\) 31.8213 1.40632
\(513\) 1.90097 + 3.29257i 0.0839298 + 0.145371i
\(514\) −23.7104 41.0677i −1.04582 1.81142i
\(515\) 36.8853 1.62536
\(516\) −2.51261 4.35198i −0.110612 0.191585i
\(517\) −9.38889 + 16.2620i −0.412923 + 0.715203i
\(518\) −20.2615 + 35.0940i −0.890240 + 1.54194i
\(519\) 18.0562 0.792580
\(520\) 0 0
\(521\) 19.3478 0.847642 0.423821 0.905746i \(-0.360688\pi\)
0.423821 + 0.905746i \(0.360688\pi\)
\(522\) 4.03534 6.98942i 0.176622 0.305919i
\(523\) 6.29739 10.9074i 0.275366 0.476947i −0.694862 0.719143i \(-0.744534\pi\)
0.970227 + 0.242196i \(0.0778678\pi\)
\(524\) −3.29118 5.70050i −0.143776 0.249027i
\(525\) 14.0858 0.614753
\(526\) 18.9816 + 32.8771i 0.827636 + 1.43351i
\(527\) −4.02542 6.97223i −0.175350 0.303715i
\(528\) −17.6058 −0.766194
\(529\) 9.44534 + 16.3598i 0.410667 + 0.711296i
\(530\) 1.86695 3.23366i 0.0810953 0.140461i
\(531\) −2.35690 + 4.08226i −0.102281 + 0.177155i
\(532\) −18.7778 −0.814120
\(533\) 0 0
\(534\) −20.6093 −0.891850
\(535\) −16.5707 + 28.7013i −0.716413 + 1.24086i
\(536\) −0.308643 + 0.534585i −0.0133313 + 0.0230905i
\(537\) −9.93512 17.2081i −0.428732 0.742585i
\(538\) 19.9941 0.862009
\(539\) −4.81820 8.34537i −0.207535 0.359460i
\(540\) −3.68933 6.39011i −0.158764 0.274987i
\(541\) −29.0019 −1.24689 −0.623445 0.781867i \(-0.714267\pi\)
−0.623445 + 0.781867i \(0.714267\pi\)
\(542\) −23.3596 40.4601i −1.00338 1.73791i
\(543\) −5.04138 + 8.73193i −0.216347 + 0.374723i
\(544\) 3.69998 6.40856i 0.158635 0.274765i
\(545\) 67.9590 2.91104
\(546\) 0 0
\(547\) 27.7006 1.18439 0.592197 0.805793i \(-0.298261\pi\)
0.592197 + 0.805793i \(0.298261\pi\)
\(548\) 25.2990 43.8192i 1.08072 1.87186i
\(549\) −1.83997 + 3.18692i −0.0785280 + 0.136014i
\(550\) 31.7186 + 54.9383i 1.35249 + 2.34258i
\(551\) −14.9758 −0.637992
\(552\) 0.411322 + 0.712430i 0.0175070 + 0.0303230i
\(553\) −4.20291 7.27965i −0.178726 0.309562i
\(554\) −49.1135 −2.08663
\(555\) 14.7736 + 25.5886i 0.627104 + 1.08618i
\(556\) −1.07984 + 1.87034i −0.0457956 + 0.0793203i
\(557\) 3.40485 5.89738i 0.144268 0.249880i −0.784831 0.619709i \(-0.787251\pi\)
0.929100 + 0.369829i \(0.120584\pi\)
\(558\) 18.0901 0.765814
\(559\) 0 0
\(560\) −26.8877 −1.13621
\(561\) −2.25182 + 3.90027i −0.0950721 + 0.164670i
\(562\) −4.22587 + 7.31943i −0.178258 + 0.308751i
\(563\) 9.62618 + 16.6730i 0.405695 + 0.702684i 0.994402 0.105662i \(-0.0336962\pi\)
−0.588707 + 0.808346i \(0.700363\pi\)
\(564\) 8.35690 0.351889
\(565\) 16.2676 + 28.1762i 0.684381 + 1.18538i
\(566\) 16.0387 + 27.7798i 0.674157 + 1.16767i
\(567\) −2.24698 −0.0943643
\(568\) 0.482647 + 0.835969i 0.0202514 + 0.0350765i
\(569\) −3.92423 + 6.79697i −0.164512 + 0.284944i −0.936482 0.350716i \(-0.885938\pi\)
0.771970 + 0.635659i \(0.219272\pi\)
\(570\) −13.0749 + 22.6463i −0.547646 + 0.948551i
\(571\) 29.8568 1.24947 0.624735 0.780837i \(-0.285207\pi\)
0.624735 + 0.780837i \(0.285207\pi\)
\(572\) 0 0
\(573\) 6.58748 0.275196
\(574\) −15.9731 + 27.6663i −0.666706 + 1.15477i
\(575\) −6.35384 + 11.0052i −0.264973 + 0.458947i
\(576\) 4.74914 + 8.22574i 0.197881 + 0.342739i
\(577\) −8.97823 −0.373769 −0.186884 0.982382i \(-0.559839\pi\)
−0.186884 + 0.982382i \(0.559839\pi\)
\(578\) 16.5640 + 28.6897i 0.688971 + 1.19333i
\(579\) −5.43362 9.41131i −0.225814 0.391121i
\(580\) 29.0646 1.20684
\(581\) −2.59299 4.49119i −0.107575 0.186326i
\(582\) 16.5238 28.6201i 0.684933 1.18634i
\(583\) 1.34063 2.32205i 0.0555234 0.0961693i
\(584\) −3.00756 −0.124454
\(585\) 0 0
\(586\) −46.2948 −1.91242
\(587\) 11.9269 20.6580i 0.492277 0.852648i −0.507684 0.861543i \(-0.669498\pi\)
0.999960 + 0.00889531i \(0.00283150\pi\)
\(588\) −2.14430 + 3.71404i −0.0884295 + 0.153164i
\(589\) −16.7838 29.0704i −0.691565 1.19783i
\(590\) −32.4215 −1.33477
\(591\) −4.62080 8.00346i −0.190074 0.329218i
\(592\) −15.6879 27.1722i −0.644769 1.11677i
\(593\) −11.9866 −0.492230 −0.246115 0.969241i \(-0.579154\pi\)
−0.246115 + 0.969241i \(0.579154\pi\)
\(594\) −5.05980 8.76383i −0.207606 0.359585i
\(595\) −3.43900 + 5.95652i −0.140985 + 0.244194i
\(596\) 11.2750 19.5289i 0.461843 0.799936i
\(597\) 1.56465 0.0640367
\(598\) 0 0
\(599\) 29.1142 1.18958 0.594788 0.803883i \(-0.297236\pi\)
0.594788 + 0.803883i \(0.297236\pi\)
\(600\) 1.27197 2.20312i 0.0519280 0.0899419i
\(601\) −18.5683 + 32.1612i −0.757417 + 1.31188i 0.186747 + 0.982408i \(0.440205\pi\)
−0.944164 + 0.329476i \(0.893128\pi\)
\(602\) −5.26271 9.11528i −0.214492 0.371511i
\(603\) 1.52111 0.0619442
\(604\) −22.1658 38.3924i −0.901915 1.56216i
\(605\) 22.4807 + 38.9377i 0.913970 + 1.58304i
\(606\) 20.3840 0.828045
\(607\) 7.11625 + 12.3257i 0.288840 + 0.500285i 0.973533 0.228546i \(-0.0733972\pi\)
−0.684693 + 0.728831i \(0.740064\pi\)
\(608\) 15.4269 26.7202i 0.625644 1.08365i
\(609\) 4.42543 7.66507i 0.179327 0.310604i
\(610\) −25.3106 −1.02480
\(611\) 0 0
\(612\) 2.00431 0.0810195
\(613\) 15.1570 26.2526i 0.612184 1.06033i −0.378687 0.925525i \(-0.623624\pi\)
0.990872 0.134810i \(-0.0430423\pi\)
\(614\) −6.71528 + 11.6312i −0.271007 + 0.469398i
\(615\) 11.6468 + 20.1728i 0.469642 + 0.813444i
\(616\) 4.50365 0.181457
\(617\) −12.4819 21.6192i −0.502501 0.870358i −0.999996 0.00289086i \(-0.999080\pi\)
0.497494 0.867467i \(-0.334254\pi\)
\(618\) −11.2567 19.4971i −0.452810 0.784289i
\(619\) −35.6122 −1.43138 −0.715688 0.698420i \(-0.753887\pi\)
−0.715688 + 0.698420i \(0.753887\pi\)
\(620\) 32.5734 + 56.4188i 1.30818 + 2.26584i
\(621\) 1.01357 1.75556i 0.0406733 0.0704482i
\(622\) 12.3337 21.3626i 0.494536 0.856561i
\(623\) −22.6015 −0.905509
\(624\) 0 0
\(625\) −17.0465 −0.681861
\(626\) 34.7240 60.1438i 1.38785 2.40383i
\(627\) −9.38889 + 16.2620i −0.374956 + 0.649443i
\(628\) −11.4721 19.8702i −0.457785 0.792907i
\(629\) −8.02608 −0.320021
\(630\) −7.72737 13.3842i −0.307866 0.533239i
\(631\) 11.9415 + 20.6832i 0.475382 + 0.823385i 0.999602 0.0281972i \(-0.00897663\pi\)
−0.524221 + 0.851582i \(0.675643\pi\)
\(632\) −1.51812 −0.0603877
\(633\) 11.6223 + 20.1304i 0.461945 + 0.800112i
\(634\) −4.60829 + 7.98180i −0.183019 + 0.316998i
\(635\) 23.1821 40.1526i 0.919953 1.59341i
\(636\) −1.19328 −0.0473165
\(637\) 0 0
\(638\) 39.8611 1.57812
\(639\) 1.18933 2.05999i 0.0470493 0.0814918i
\(640\) −5.42237 + 9.39182i −0.214338 + 0.371244i
\(641\) 12.3288 + 21.3542i 0.486960 + 0.843440i 0.999888 0.0149922i \(-0.00477233\pi\)
−0.512927 + 0.858432i \(0.671439\pi\)
\(642\) 20.2282 0.798343
\(643\) 23.9083 + 41.4103i 0.942850 + 1.63306i 0.760000 + 0.649923i \(0.225199\pi\)
0.182850 + 0.983141i \(0.441468\pi\)
\(644\) 5.00604 + 8.67072i 0.197266 + 0.341674i
\(645\) −7.67456 −0.302186
\(646\) −3.55161 6.15156i −0.139736 0.242030i
\(647\) 2.69471 4.66737i 0.105940 0.183493i −0.808182 0.588933i \(-0.799548\pi\)
0.914122 + 0.405440i \(0.132882\pi\)
\(648\) −0.202907 + 0.351445i −0.00797092 + 0.0138060i
\(649\) −23.2814 −0.913876
\(650\) 0 0
\(651\) 19.8388 0.777543
\(652\) −12.1405 + 21.0279i −0.475458 + 0.823517i
\(653\) 2.51895 4.36295i 0.0985741 0.170735i −0.812521 0.582933i \(-0.801905\pi\)
0.911095 + 0.412197i \(0.135239\pi\)
\(654\) −20.7397 35.9223i −0.810988 1.40467i
\(655\) −10.0526 −0.392789
\(656\) −12.3675 21.4212i −0.482871 0.836358i
\(657\) 3.70560 + 6.41828i 0.144569 + 0.250401i
\(658\) 17.5036 0.682363
\(659\) 21.9906 + 38.0888i 0.856632 + 1.48373i 0.875122 + 0.483902i \(0.160781\pi\)
−0.0184899 + 0.999829i \(0.505886\pi\)
\(660\) 18.2216 31.5608i 0.709276 1.22850i
\(661\) −19.1097 + 33.0989i −0.743280 + 1.28740i 0.207714 + 0.978190i \(0.433398\pi\)
−0.950994 + 0.309210i \(0.899936\pi\)
\(662\) 22.9748 0.892940
\(663\) 0 0
\(664\) −0.936608 −0.0363474
\(665\) −14.3388 + 24.8355i −0.556034 + 0.963079i
\(666\) 9.01722 15.6183i 0.349410 0.605196i
\(667\) 3.99247 + 6.91516i 0.154589 + 0.267756i
\(668\) −17.8261 −0.689713
\(669\) −5.36927 9.29985i −0.207588 0.359553i
\(670\) 5.23109 + 9.06051i 0.202094 + 0.350038i
\(671\) −18.1752 −0.701647
\(672\) 9.11745 + 15.7919i 0.351713 + 0.609185i
\(673\) 3.33244 5.77195i 0.128456 0.222492i −0.794623 0.607104i \(-0.792331\pi\)
0.923079 + 0.384611i \(0.125665\pi\)
\(674\) −7.22132 + 12.5077i −0.278155 + 0.481779i
\(675\) −6.26875 −0.241284
\(676\) 0 0
\(677\) 4.80194 0.184553 0.0922767 0.995733i \(-0.470586\pi\)
0.0922767 + 0.995733i \(0.470586\pi\)
\(678\) 9.92908 17.1977i 0.381324 0.660472i
\(679\) 18.1211 31.3867i 0.695424 1.20451i
\(680\) 0.621097 + 1.07577i 0.0238180 + 0.0412539i
\(681\) −6.97584 −0.267315
\(682\) 44.6734 + 77.3766i 1.71063 + 2.96290i
\(683\) 5.62953 + 9.75063i 0.215408 + 0.373098i 0.953399 0.301713i \(-0.0975585\pi\)
−0.737991 + 0.674811i \(0.764225\pi\)
\(684\) 8.35690 0.319534
\(685\) −38.6368 66.9209i −1.47624 2.55692i
\(686\) −20.6048 + 35.6886i −0.786696 + 1.36260i
\(687\) 8.40246 14.5535i 0.320574 0.555250i
\(688\) 8.14952 0.310698
\(689\) 0 0
\(690\) 13.9427 0.530790
\(691\) −12.3572 + 21.4033i −0.470090 + 0.814219i −0.999415 0.0341997i \(-0.989112\pi\)
0.529325 + 0.848419i \(0.322445\pi\)
\(692\) 19.8443 34.3714i 0.754369 1.30660i
\(693\) −5.54892 9.61101i −0.210786 0.365092i
\(694\) −5.54048 −0.210314
\(695\) 1.64914 + 2.85640i 0.0625556 + 0.108350i
\(696\) −0.799249 1.38434i −0.0302955 0.0524733i
\(697\) −6.32736 −0.239666
\(698\) −0.425665 0.737273i −0.0161116 0.0279062i
\(699\) 4.34601 7.52751i 0.164381 0.284717i
\(700\) 15.4807 26.8133i 0.585115 1.01345i
\(701\) 25.8920 0.977927 0.488964 0.872304i \(-0.337375\pi\)
0.488964 + 0.872304i \(0.337375\pi\)
\(702\) 0 0
\(703\) −33.4644 −1.26213
\(704\) −23.4560 + 40.6270i −0.884031 + 1.53119i
\(705\) 6.38135 11.0528i 0.240336 0.416274i
\(706\) −32.9540 57.0779i −1.24024 2.14816i
\(707\) 22.3545 0.840728
\(708\) 5.18060 + 8.97307i 0.194699 + 0.337229i
\(709\) 0.0425810 + 0.0737525i 0.00159916 + 0.00276983i 0.866824 0.498614i \(-0.166158\pi\)
−0.865225 + 0.501384i \(0.832824\pi\)
\(710\) 16.3605 0.613998
\(711\) 1.87047 + 3.23975i 0.0701481 + 0.121500i
\(712\) −2.04096 + 3.53504i −0.0764881 + 0.132481i
\(713\) −8.94893 + 15.5000i −0.335140 + 0.580479i
\(714\) 4.19806 0.157109
\(715\) 0 0
\(716\) −43.6760 −1.63225
\(717\) 11.4596 19.8486i 0.427966 0.741258i
\(718\) 22.8988 39.6619i 0.854576 1.48017i
\(719\) −13.5254 23.4267i −0.504413 0.873669i −0.999987 0.00510319i \(-0.998376\pi\)
0.495574 0.868566i \(-0.334958\pi\)
\(720\) 11.9661 0.445952
\(721\) −12.3448 21.3818i −0.459745 0.796302i
\(722\) 4.65644 + 8.06519i 0.173295 + 0.300155i
\(723\) 21.9801 0.817451
\(724\) 11.0813 + 19.1933i 0.411832 + 0.713315i
\(725\) 12.3463 21.3844i 0.458530 0.794198i
\(726\) 13.7213 23.7660i 0.509246 0.882040i
\(727\) −47.1584 −1.74901 −0.874503 0.485019i \(-0.838813\pi\)
−0.874503 + 0.485019i \(0.838813\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −25.4871 + 44.1449i −0.943320 + 1.63388i
\(731\) 1.04234 1.80539i 0.0385525 0.0667749i
\(732\) 4.04437 + 7.00505i 0.149484 + 0.258914i
\(733\) 9.68186 0.357608 0.178804 0.983885i \(-0.442777\pi\)
0.178804 + 0.983885i \(0.442777\pi\)
\(734\) 2.35892 + 4.08577i 0.0870693 + 0.150809i
\(735\) 3.27479 + 5.67210i 0.120792 + 0.209219i
\(736\) −16.4509 −0.606388
\(737\) 3.75637 + 6.50623i 0.138368 + 0.239660i
\(738\) 7.10872 12.3127i 0.261676 0.453235i
\(739\) 18.1570 31.4488i 0.667915 1.15686i −0.310571 0.950550i \(-0.600520\pi\)
0.978486 0.206313i \(-0.0661464\pi\)
\(740\) 64.9466 2.38748
\(741\) 0 0
\(742\) −2.49934 −0.0917535
\(743\) −20.8768 + 36.1597i −0.765896 + 1.32657i 0.173876 + 0.984768i \(0.444371\pi\)
−0.939772 + 0.341803i \(0.888963\pi\)
\(744\) 1.79148 3.10293i 0.0656788 0.113759i
\(745\) −17.2193 29.8247i −0.630866 1.09269i
\(746\) −39.4950 −1.44602
\(747\) 1.15399 + 1.99877i 0.0422223 + 0.0731311i
\(748\) 4.94965 + 8.57304i 0.180977 + 0.313462i
\(749\) 22.1836 0.810571
\(750\) −4.36323 7.55734i −0.159323 0.275955i
\(751\) 11.0963 19.2194i 0.404911 0.701327i −0.589400 0.807841i \(-0.700636\pi\)
0.994311 + 0.106515i \(0.0339691\pi\)
\(752\) −6.77628 + 11.7369i −0.247106 + 0.427999i
\(753\) −26.6437 −0.970950
\(754\) 0 0
\(755\) −67.7036 −2.46399
\(756\) −2.46950 + 4.27730i −0.0898149 + 0.155564i
\(757\) −4.61865 + 7.99973i −0.167868 + 0.290755i −0.937670 0.347527i \(-0.887021\pi\)
0.769802 + 0.638282i \(0.220355\pi\)
\(758\) −7.51895 13.0232i −0.273101 0.473024i
\(759\) 10.0121 0.363416
\(760\) 2.58964 + 4.48538i 0.0939360 + 0.162702i
\(761\) −3.75086 6.49669i −0.135969 0.235505i 0.789998 0.613109i \(-0.210081\pi\)
−0.925967 + 0.377604i \(0.876748\pi\)
\(762\) −28.2989 −1.02516
\(763\) −22.7446 39.3948i −0.823409 1.42619i
\(764\) 7.23985 12.5398i 0.261929 0.453673i
\(765\) 1.53050 2.65090i 0.0553353 0.0958436i
\(766\) −39.1140 −1.41325
\(767\) 0 0
\(768\) −12.3773 −0.446629
\(769\) 2.57002 4.45141i 0.0926774 0.160522i −0.815959 0.578109i \(-0.803791\pi\)
0.908637 + 0.417587i \(0.137124\pi\)
\(770\) 38.1655 66.1045i 1.37539 2.38224i
\(771\) 11.5722 + 20.0436i 0.416762 + 0.721853i
\(772\) −23.8869 −0.859708
\(773\) −4.25086 7.36271i −0.152893 0.264818i 0.779397 0.626531i \(-0.215526\pi\)
−0.932290 + 0.361712i \(0.882192\pi\)
\(774\) 2.34213 + 4.05668i 0.0841860 + 0.145814i
\(775\) 55.3473 1.98813
\(776\) −3.27274 5.66855i −0.117485 0.203489i
\(777\) 9.88889 17.1281i 0.354762 0.614466i
\(778\) 24.5746 42.5645i 0.881043 1.52601i
\(779\) −26.3817 −0.945221
\(780\) 0 0