Properties

Label 507.2.e.i.22.2
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 22.2
Root \(0.222521 - 0.385418i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.i.484.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.17845 + 2.04113i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.77748 - 3.07868i) q^{4} +3.69202 q^{5} +(1.17845 + 2.04113i) q^{6} +(0.400969 + 0.694498i) q^{7} +3.66487 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-1.17845 + 2.04113i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-1.77748 - 3.07868i) q^{4} +3.69202 q^{5} +(1.17845 + 2.04113i) q^{6} +(0.400969 + 0.694498i) q^{7} +3.66487 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-4.35086 + 7.53590i) q^{10} +(1.42543 - 2.46891i) q^{11} -3.55496 q^{12} -1.89008 q^{14} +(1.84601 - 3.19738i) q^{15} +(-0.763906 + 1.32312i) q^{16} +(-1.46950 - 2.54525i) q^{17} +2.35690 q^{18} +(1.22252 + 2.11747i) q^{19} +(-6.56249 - 11.3666i) q^{20} +0.801938 q^{21} +(3.35958 + 5.81897i) q^{22} +(3.89493 - 6.74621i) q^{23} +(1.83244 - 3.17387i) q^{24} +8.63102 q^{25} -1.00000 q^{27} +(1.42543 - 2.46891i) q^{28} +(-1.92543 + 3.33494i) q^{29} +(4.35086 + 7.53590i) q^{30} +2.34481 q^{31} +(1.86443 + 3.22929i) q^{32} +(-1.42543 - 2.46891i) q^{33} +6.92692 q^{34} +(1.48039 + 2.56410i) q^{35} +(-1.77748 + 3.07868i) q^{36} +(-3.72252 + 6.44760i) q^{37} -5.76271 q^{38} +13.5308 q^{40} +(0.425428 - 0.736862i) q^{41} +(-0.945042 + 1.63686i) q^{42} +(0.807979 + 1.39946i) q^{43} -10.1347 q^{44} +(-1.84601 - 3.19738i) q^{45} +(9.17994 + 15.9001i) q^{46} +2.44504 q^{47} +(0.763906 + 1.32312i) q^{48} +(3.17845 - 5.50523i) q^{49} +(-10.1712 + 17.6171i) q^{50} -2.93900 q^{51} -9.96077 q^{53} +(1.17845 - 2.04113i) q^{54} +(5.26271 - 9.11528i) q^{55} +(1.46950 + 2.54525i) q^{56} +2.44504 q^{57} +(-4.53803 - 7.86010i) q^{58} +(2.69202 + 4.66272i) q^{59} -13.1250 q^{60} +(6.62833 + 11.4806i) q^{61} +(-2.76324 + 4.78607i) q^{62} +(0.400969 - 0.694498i) q^{63} -11.8442 q^{64} +6.71917 q^{66} +(-7.19687 + 12.4653i) q^{67} +(-5.22401 + 9.04826i) q^{68} +(-3.89493 - 6.74621i) q^{69} -6.97823 q^{70} +(-4.06249 - 7.03644i) q^{71} +(-1.83244 - 3.17387i) q^{72} -11.8877 q^{73} +(-8.77359 - 15.1963i) q^{74} +(4.31551 - 7.47468i) q^{75} +(4.34601 - 7.52751i) q^{76} +2.28621 q^{77} +5.40581 q^{79} +(-2.82036 + 4.88500i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00269 + 1.73671i) q^{82} +7.04892 q^{83} +(-1.42543 - 2.46891i) q^{84} +(-5.42543 - 9.39712i) q^{85} -3.80864 q^{86} +(1.92543 + 3.33494i) q^{87} +(5.22401 - 9.04826i) q^{88} +(-0.565843 + 0.980069i) q^{89} +8.70171 q^{90} -27.6926 q^{92} +(1.17241 - 2.03067i) q^{93} +(-2.88135 + 4.99065i) q^{94} +(4.51357 + 7.81774i) q^{95} +3.72886 q^{96} +(2.97219 + 5.14798i) q^{97} +(7.49127 + 12.9753i) q^{98} -2.85086 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.17845 + 2.04113i −0.833289 + 1.44330i 0.0621278 + 0.998068i \(0.480211\pi\)
−0.895416 + 0.445230i \(0.853122\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) −1.77748 3.07868i −0.888740 1.53934i
\(5\) 3.69202 1.65112 0.825561 0.564313i \(-0.190859\pi\)
0.825561 + 0.564313i \(0.190859\pi\)
\(6\) 1.17845 + 2.04113i 0.481099 + 0.833289i
\(7\) 0.400969 + 0.694498i 0.151552 + 0.262496i 0.931798 0.362977i \(-0.118240\pi\)
−0.780246 + 0.625473i \(0.784906\pi\)
\(8\) 3.66487 1.29573
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −4.35086 + 7.53590i −1.37586 + 2.38306i
\(11\) 1.42543 2.46891i 0.429783 0.744405i −0.567071 0.823669i \(-0.691924\pi\)
0.996854 + 0.0792636i \(0.0252569\pi\)
\(12\) −3.55496 −1.02623
\(13\) 0 0
\(14\) −1.89008 −0.505146
\(15\) 1.84601 3.19738i 0.476638 0.825561i
\(16\) −0.763906 + 1.32312i −0.190976 + 0.330781i
\(17\) −1.46950 2.54525i −0.356406 0.617314i 0.630951 0.775822i \(-0.282665\pi\)
−0.987358 + 0.158509i \(0.949331\pi\)
\(18\) 2.35690 0.555526
\(19\) 1.22252 + 2.11747i 0.280466 + 0.485781i 0.971499 0.237042i \(-0.0761778\pi\)
−0.691034 + 0.722822i \(0.742844\pi\)
\(20\) −6.56249 11.3666i −1.46742 2.54164i
\(21\) 0.801938 0.174997
\(22\) 3.35958 + 5.81897i 0.716266 + 1.24061i
\(23\) 3.89493 6.74621i 0.812149 1.40668i −0.0992087 0.995067i \(-0.531631\pi\)
0.911357 0.411616i \(-0.135036\pi\)
\(24\) 1.83244 3.17387i 0.374045 0.647864i
\(25\) 8.63102 1.72620
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 1.42543 2.46891i 0.269380 0.466581i
\(29\) −1.92543 + 3.33494i −0.357543 + 0.619282i −0.987550 0.157307i \(-0.949719\pi\)
0.630007 + 0.776590i \(0.283052\pi\)
\(30\) 4.35086 + 7.53590i 0.794354 + 1.37586i
\(31\) 2.34481 0.421141 0.210571 0.977579i \(-0.432468\pi\)
0.210571 + 0.977579i \(0.432468\pi\)
\(32\) 1.86443 + 3.22929i 0.329588 + 0.570862i
\(33\) −1.42543 2.46891i −0.248135 0.429783i
\(34\) 6.92692 1.18796
\(35\) 1.48039 + 2.56410i 0.250231 + 0.433413i
\(36\) −1.77748 + 3.07868i −0.296247 + 0.513114i
\(37\) −3.72252 + 6.44760i −0.611979 + 1.05998i 0.378928 + 0.925426i \(0.376293\pi\)
−0.990907 + 0.134552i \(0.957040\pi\)
\(38\) −5.76271 −0.934835
\(39\) 0 0
\(40\) 13.5308 2.13941
\(41\) 0.425428 0.736862i 0.0664406 0.115079i −0.830892 0.556434i \(-0.812169\pi\)
0.897332 + 0.441356i \(0.145502\pi\)
\(42\) −0.945042 + 1.63686i −0.145823 + 0.252573i
\(43\) 0.807979 + 1.39946i 0.123216 + 0.213416i 0.921034 0.389482i \(-0.127346\pi\)
−0.797818 + 0.602898i \(0.794013\pi\)
\(44\) −10.1347 −1.52786
\(45\) −1.84601 3.19738i −0.275187 0.476638i
\(46\) 9.17994 + 15.9001i 1.35351 + 2.34435i
\(47\) 2.44504 0.356646 0.178323 0.983972i \(-0.442933\pi\)
0.178323 + 0.983972i \(0.442933\pi\)
\(48\) 0.763906 + 1.32312i 0.110260 + 0.190976i
\(49\) 3.17845 5.50523i 0.454064 0.786462i
\(50\) −10.1712 + 17.6171i −1.43843 + 2.49143i
\(51\) −2.93900 −0.411542
\(52\) 0 0
\(53\) −9.96077 −1.36822 −0.684109 0.729380i \(-0.739809\pi\)
−0.684109 + 0.729380i \(0.739809\pi\)
\(54\) 1.17845 2.04113i 0.160366 0.277763i
\(55\) 5.26271 9.11528i 0.709624 1.22910i
\(56\) 1.46950 + 2.54525i 0.196370 + 0.340123i
\(57\) 2.44504 0.323854
\(58\) −4.53803 7.86010i −0.595873 1.03208i
\(59\) 2.69202 + 4.66272i 0.350471 + 0.607034i 0.986332 0.164770i \(-0.0526881\pi\)
−0.635861 + 0.771804i \(0.719355\pi\)
\(60\) −13.1250 −1.69443
\(61\) 6.62833 + 11.4806i 0.848671 + 1.46994i 0.882394 + 0.470510i \(0.155930\pi\)
−0.0337232 + 0.999431i \(0.510736\pi\)
\(62\) −2.76324 + 4.78607i −0.350932 + 0.607832i
\(63\) 0.400969 0.694498i 0.0505173 0.0874986i
\(64\) −11.8442 −1.48052
\(65\) 0 0
\(66\) 6.71917 0.827072
\(67\) −7.19687 + 12.4653i −0.879237 + 1.52288i −0.0270575 + 0.999634i \(0.508614\pi\)
−0.852180 + 0.523249i \(0.824720\pi\)
\(68\) −5.22401 + 9.04826i −0.633505 + 1.09726i
\(69\) −3.89493 6.74621i −0.468894 0.812149i
\(70\) −6.97823 −0.834058
\(71\) −4.06249 7.03644i −0.482129 0.835072i 0.517661 0.855586i \(-0.326803\pi\)
−0.999790 + 0.0205142i \(0.993470\pi\)
\(72\) −1.83244 3.17387i −0.215955 0.374045i
\(73\) −11.8877 −1.39135 −0.695674 0.718357i \(-0.744894\pi\)
−0.695674 + 0.718357i \(0.744894\pi\)
\(74\) −8.77359 15.1963i −1.01991 1.76654i
\(75\) 4.31551 7.47468i 0.498312 0.863102i
\(76\) 4.34601 7.52751i 0.498522 0.863465i
\(77\) 2.28621 0.260538
\(78\) 0 0
\(79\) 5.40581 0.608202 0.304101 0.952640i \(-0.401644\pi\)
0.304101 + 0.952640i \(0.401644\pi\)
\(80\) −2.82036 + 4.88500i −0.315325 + 0.546160i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 1.00269 + 1.73671i 0.110728 + 0.191787i
\(83\) 7.04892 0.773719 0.386860 0.922139i \(-0.373560\pi\)
0.386860 + 0.922139i \(0.373560\pi\)
\(84\) −1.42543 2.46891i −0.155527 0.269380i
\(85\) −5.42543 9.39712i −0.588470 1.01926i
\(86\) −3.80864 −0.410696
\(87\) 1.92543 + 3.33494i 0.206427 + 0.357543i
\(88\) 5.22401 9.04826i 0.556882 0.964547i
\(89\) −0.565843 + 0.980069i −0.0599793 + 0.103887i −0.894456 0.447156i \(-0.852437\pi\)
0.834477 + 0.551043i \(0.185770\pi\)
\(90\) 8.70171 0.917241
\(91\) 0 0
\(92\) −27.6926 −2.88715
\(93\) 1.17241 2.03067i 0.121573 0.210571i
\(94\) −2.88135 + 4.99065i −0.297189 + 0.514746i
\(95\) 4.51357 + 7.81774i 0.463083 + 0.802083i
\(96\) 3.72886 0.380575
\(97\) 2.97219 + 5.14798i 0.301780 + 0.522698i 0.976539 0.215340i \(-0.0690858\pi\)
−0.674759 + 0.738038i \(0.735753\pi\)
\(98\) 7.49127 + 12.9753i 0.756733 + 1.31070i
\(99\) −2.85086 −0.286522
\(100\) −15.3415 26.5722i −1.53415 2.65722i
\(101\) −2.31282 + 4.00593i −0.230134 + 0.398605i −0.957848 0.287277i \(-0.907250\pi\)
0.727713 + 0.685882i \(0.240583\pi\)
\(102\) 3.46346 5.99889i 0.342934 0.593978i
\(103\) 1.20775 0.119003 0.0595016 0.998228i \(-0.481049\pi\)
0.0595016 + 0.998228i \(0.481049\pi\)
\(104\) 0 0
\(105\) 2.96077 0.288942
\(106\) 11.7383 20.3312i 1.14012 1.97475i
\(107\) 4.76055 8.24552i 0.460220 0.797124i −0.538752 0.842465i \(-0.681104\pi\)
0.998972 + 0.0453402i \(0.0144372\pi\)
\(108\) 1.77748 + 3.07868i 0.171038 + 0.296247i
\(109\) −1.78448 −0.170922 −0.0854611 0.996342i \(-0.527236\pi\)
−0.0854611 + 0.996342i \(0.527236\pi\)
\(110\) 12.4037 + 21.4838i 1.18264 + 2.04840i
\(111\) 3.72252 + 6.44760i 0.353326 + 0.611979i
\(112\) −1.22521 −0.115771
\(113\) −2.47554 4.28776i −0.232879 0.403359i 0.725775 0.687932i \(-0.241481\pi\)
−0.958654 + 0.284573i \(0.908148\pi\)
\(114\) −2.88135 + 4.99065i −0.269864 + 0.467417i
\(115\) 14.3802 24.9072i 1.34096 2.32261i
\(116\) 13.6896 1.27105
\(117\) 0 0
\(118\) −12.6896 −1.16817
\(119\) 1.17845 2.04113i 0.108028 0.187110i
\(120\) 6.76540 11.7180i 0.617593 1.06970i
\(121\) 1.43631 + 2.48777i 0.130574 + 0.226161i
\(122\) −31.2446 −2.82875
\(123\) −0.425428 0.736862i −0.0383595 0.0664406i
\(124\) −4.16786 7.21894i −0.374285 0.648280i
\(125\) 13.4058 1.19905
\(126\) 0.945042 + 1.63686i 0.0841910 + 0.145823i
\(127\) −2.83513 + 4.91058i −0.251577 + 0.435744i −0.963960 0.266047i \(-0.914282\pi\)
0.712383 + 0.701791i \(0.247616\pi\)
\(128\) 10.2289 17.7169i 0.904112 1.56597i
\(129\) 1.61596 0.142277
\(130\) 0 0
\(131\) 18.2228 1.59213 0.796067 0.605208i \(-0.206910\pi\)
0.796067 + 0.605208i \(0.206910\pi\)
\(132\) −5.06734 + 8.77688i −0.441055 + 0.763930i
\(133\) −0.980386 + 1.69808i −0.0850102 + 0.147242i
\(134\) −16.9623 29.3795i −1.46532 2.53800i
\(135\) −3.69202 −0.317759
\(136\) −5.38553 9.32802i −0.461806 0.799871i
\(137\) −4.72521 8.18430i −0.403702 0.699232i 0.590468 0.807061i \(-0.298943\pi\)
−0.994169 + 0.107829i \(0.965610\pi\)
\(138\) 18.3599 1.56290
\(139\) −2.00753 3.47715i −0.170277 0.294928i 0.768240 0.640162i \(-0.221133\pi\)
−0.938517 + 0.345234i \(0.887799\pi\)
\(140\) 5.26271 9.11528i 0.444780 0.770382i
\(141\) 1.22252 2.11747i 0.102955 0.178323i
\(142\) 19.1497 1.60701
\(143\) 0 0
\(144\) 1.52781 0.127318
\(145\) −7.10872 + 12.3127i −0.590347 + 1.02251i
\(146\) 14.0090 24.2643i 1.15940 2.00813i
\(147\) −3.17845 5.50523i −0.262154 0.454064i
\(148\) 26.4668 2.17556
\(149\) −9.70291 16.8059i −0.794893 1.37680i −0.922907 0.385023i \(-0.874194\pi\)
0.128014 0.991772i \(-0.459140\pi\)
\(150\) 10.1712 + 17.6171i 0.830476 + 1.43843i
\(151\) −12.3623 −1.00603 −0.503014 0.864278i \(-0.667775\pi\)
−0.503014 + 0.864278i \(0.667775\pi\)
\(152\) 4.48039 + 7.76026i 0.363407 + 0.629440i
\(153\) −1.46950 + 2.54525i −0.118802 + 0.205771i
\(154\) −2.69418 + 4.66645i −0.217103 + 0.376033i
\(155\) 8.65710 0.695355
\(156\) 0 0
\(157\) −18.6775 −1.49063 −0.745315 0.666712i \(-0.767701\pi\)
−0.745315 + 0.666712i \(0.767701\pi\)
\(158\) −6.37047 + 11.0340i −0.506807 + 0.877816i
\(159\) −4.98039 + 8.62628i −0.394970 + 0.684109i
\(160\) 6.88351 + 11.9226i 0.544189 + 0.942563i
\(161\) 6.24698 0.492331
\(162\) −1.17845 2.04113i −0.0925876 0.160366i
\(163\) −6.16972 10.6863i −0.483250 0.837013i 0.516565 0.856248i \(-0.327210\pi\)
−0.999815 + 0.0192348i \(0.993877\pi\)
\(164\) −3.02475 −0.236194
\(165\) −5.26271 9.11528i −0.409701 0.709624i
\(166\) −8.30678 + 14.3878i −0.644731 + 1.11671i
\(167\) −5.74698 + 9.95406i −0.444715 + 0.770268i −0.998032 0.0627020i \(-0.980028\pi\)
0.553318 + 0.832970i \(0.313362\pi\)
\(168\) 2.93900 0.226749
\(169\) 0 0
\(170\) 25.5743 1.96146
\(171\) 1.22252 2.11747i 0.0934885 0.161927i
\(172\) 2.87233 4.97502i 0.219013 0.379342i
\(173\) −6.05711 10.4912i −0.460514 0.797633i 0.538473 0.842643i \(-0.319002\pi\)
−0.998987 + 0.0450096i \(0.985668\pi\)
\(174\) −9.07606 −0.688055
\(175\) 3.46077 + 5.99423i 0.261610 + 0.453121i
\(176\) 2.17778 + 3.77203i 0.164157 + 0.284328i
\(177\) 5.38404 0.404689
\(178\) −1.33363 2.30992i −0.0999601 0.173136i
\(179\) 0.269282 0.466411i 0.0201271 0.0348612i −0.855786 0.517329i \(-0.826926\pi\)
0.875914 + 0.482468i \(0.160260\pi\)
\(180\) −6.56249 + 11.3666i −0.489139 + 0.847214i
\(181\) −23.2838 −1.73067 −0.865336 0.501192i \(-0.832895\pi\)
−0.865336 + 0.501192i \(0.832895\pi\)
\(182\) 0 0
\(183\) 13.2567 0.979961
\(184\) 14.2744 24.7240i 1.05232 1.82268i
\(185\) −13.7436 + 23.8047i −1.01045 + 1.75015i
\(186\) 2.76324 + 4.78607i 0.202611 + 0.350932i
\(187\) −8.37867 −0.612709
\(188\) −4.34601 7.52751i −0.316965 0.549000i
\(189\) −0.400969 0.694498i −0.0291662 0.0505173i
\(190\) −21.2760 −1.54353
\(191\) −8.38285 14.5195i −0.606561 1.05060i −0.991803 0.127779i \(-0.959215\pi\)
0.385241 0.922816i \(-0.374118\pi\)
\(192\) −5.92208 + 10.2573i −0.427389 + 0.740259i
\(193\) −12.8720 + 22.2949i −0.926544 + 1.60482i −0.137485 + 0.990504i \(0.543902\pi\)
−0.789059 + 0.614318i \(0.789431\pi\)
\(194\) −14.0103 −1.00588
\(195\) 0 0
\(196\) −22.5985 −1.61418
\(197\) −10.7104 + 18.5510i −0.763087 + 1.32171i 0.178165 + 0.984001i \(0.442984\pi\)
−0.941252 + 0.337705i \(0.890349\pi\)
\(198\) 3.35958 5.81897i 0.238755 0.413536i
\(199\) −1.76391 3.05517i −0.125040 0.216576i 0.796709 0.604364i \(-0.206573\pi\)
−0.921749 + 0.387788i \(0.873239\pi\)
\(200\) 31.6316 2.23669
\(201\) 7.19687 + 12.4653i 0.507628 + 0.879237i
\(202\) −5.45108 9.44155i −0.383537 0.664305i
\(203\) −3.08815 −0.216745
\(204\) 5.22401 + 9.04826i 0.365754 + 0.633505i
\(205\) 1.57069 2.72051i 0.109702 0.190009i
\(206\) −1.42327 + 2.46518i −0.0991640 + 0.171757i
\(207\) −7.78986 −0.541432
\(208\) 0 0
\(209\) 6.97046 0.482157
\(210\) −3.48911 + 6.04332i −0.240772 + 0.417029i
\(211\) −0.607760 + 1.05267i −0.0418399 + 0.0724689i −0.886187 0.463328i \(-0.846655\pi\)
0.844347 + 0.535797i \(0.179989\pi\)
\(212\) 17.7051 + 30.6661i 1.21599 + 2.10615i
\(213\) −8.12498 −0.556715
\(214\) 11.2201 + 19.4338i 0.766992 + 1.32847i
\(215\) 2.98307 + 5.16684i 0.203444 + 0.352375i
\(216\) −3.66487 −0.249363
\(217\) 0.940198 + 1.62847i 0.0638248 + 0.110548i
\(218\) 2.10292 3.64236i 0.142427 0.246692i
\(219\) −5.94385 + 10.2950i −0.401648 + 0.695674i
\(220\) −37.4174 −2.52268
\(221\) 0 0
\(222\) −17.5472 −1.17769
\(223\) 8.69418 15.0588i 0.582205 1.00841i −0.413012 0.910725i \(-0.635523\pi\)
0.995218 0.0976835i \(-0.0311433\pi\)
\(224\) −1.49516 + 2.58969i −0.0998993 + 0.173031i
\(225\) −4.31551 7.47468i −0.287701 0.498312i
\(226\) 11.6692 0.776223
\(227\) −8.70775 15.0823i −0.577954 1.00105i −0.995714 0.0924878i \(-0.970518\pi\)
0.417760 0.908557i \(-0.362815\pi\)
\(228\) −4.34601 7.52751i −0.287822 0.498522i
\(229\) 18.7603 1.23972 0.619858 0.784714i \(-0.287190\pi\)
0.619858 + 0.784714i \(0.287190\pi\)
\(230\) 33.8925 + 58.7036i 2.23481 + 3.87080i
\(231\) 1.14310 1.97991i 0.0752107 0.130269i
\(232\) −7.05645 + 12.2221i −0.463279 + 0.802422i
\(233\) 3.95108 0.258844 0.129422 0.991590i \(-0.458688\pi\)
0.129422 + 0.991590i \(0.458688\pi\)
\(234\) 0 0
\(235\) 9.02715 0.588866
\(236\) 9.57002 16.5758i 0.622955 1.07899i
\(237\) 2.70291 4.68157i 0.175573 0.304101i
\(238\) 2.77748 + 4.81073i 0.180037 + 0.311834i
\(239\) 0.818331 0.0529334 0.0264667 0.999650i \(-0.491574\pi\)
0.0264667 + 0.999650i \(0.491574\pi\)
\(240\) 2.82036 + 4.88500i 0.182053 + 0.315325i
\(241\) −3.01626 5.22432i −0.194295 0.336528i 0.752375 0.658736i \(-0.228908\pi\)
−0.946669 + 0.322208i \(0.895575\pi\)
\(242\) −6.77048 −0.435223
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) 23.5635 40.8131i 1.50850 2.61279i
\(245\) 11.7349 20.3254i 0.749715 1.29854i
\(246\) 2.00538 0.127858
\(247\) 0 0
\(248\) 8.59345 0.545685
\(249\) 3.52446 6.10454i 0.223353 0.386860i
\(250\) −15.7981 + 27.3630i −0.999157 + 1.73059i
\(251\) 13.4400 + 23.2787i 0.848323 + 1.46934i 0.882704 + 0.469929i \(0.155721\pi\)
−0.0343812 + 0.999409i \(0.510946\pi\)
\(252\) −2.85086 −0.179587
\(253\) −11.1039 19.2325i −0.698095 1.20914i
\(254\) −6.68210 11.5737i −0.419272 0.726200i
\(255\) −10.8509 −0.679507
\(256\) 12.2642 + 21.2422i 0.766513 + 1.32764i
\(257\) 4.52661 7.84033i 0.282362 0.489066i −0.689604 0.724187i \(-0.742215\pi\)
0.971966 + 0.235121i \(0.0755486\pi\)
\(258\) −1.90432 + 3.29838i −0.118558 + 0.205348i
\(259\) −5.97046 −0.370986
\(260\) 0 0
\(261\) 3.85086 0.238362
\(262\) −21.4746 + 37.1952i −1.32671 + 2.29793i
\(263\) −11.5755 + 20.0494i −0.713778 + 1.23630i 0.249651 + 0.968336i \(0.419684\pi\)
−0.963429 + 0.267964i \(0.913649\pi\)
\(264\) −5.22401 9.04826i −0.321516 0.556882i
\(265\) −36.7754 −2.25909
\(266\) −2.31067 4.00219i −0.141676 0.245390i
\(267\) 0.565843 + 0.980069i 0.0346290 + 0.0599793i
\(268\) 51.1691 3.12565
\(269\) 1.21044 + 2.09654i 0.0738018 + 0.127828i 0.900565 0.434722i \(-0.143153\pi\)
−0.826763 + 0.562551i \(0.809820\pi\)
\(270\) 4.35086 7.53590i 0.264785 0.458620i
\(271\) 10.7225 18.5720i 0.651347 1.12817i −0.331450 0.943473i \(-0.607538\pi\)
0.982796 0.184693i \(-0.0591290\pi\)
\(272\) 4.49024 0.272261
\(273\) 0 0
\(274\) 22.2737 1.34560
\(275\) 12.3029 21.3092i 0.741893 1.28500i
\(276\) −13.8463 + 23.9825i −0.833450 + 1.44358i
\(277\) 7.40366 + 12.8235i 0.444843 + 0.770490i 0.998041 0.0625593i \(-0.0199263\pi\)
−0.553199 + 0.833049i \(0.686593\pi\)
\(278\) 9.46309 0.567558
\(279\) −1.17241 2.03067i −0.0701902 0.121573i
\(280\) 5.42543 + 9.39712i 0.324231 + 0.561585i
\(281\) 14.5036 0.865215 0.432608 0.901582i \(-0.357594\pi\)
0.432608 + 0.901582i \(0.357594\pi\)
\(282\) 2.88135 + 4.99065i 0.171582 + 0.297189i
\(283\) −12.8361 + 22.2328i −0.763026 + 1.32160i 0.178258 + 0.983984i \(0.442954\pi\)
−0.941284 + 0.337616i \(0.890379\pi\)
\(284\) −14.4420 + 25.0143i −0.856974 + 1.48432i
\(285\) 9.02715 0.534722
\(286\) 0 0
\(287\) 0.682333 0.0402768
\(288\) 1.86443 3.22929i 0.109863 0.190287i
\(289\) 4.18114 7.24194i 0.245949 0.425997i
\(290\) −16.7545 29.0197i −0.983859 1.70409i
\(291\) 5.94438 0.348466
\(292\) 21.1301 + 36.5984i 1.23655 + 2.14176i
\(293\) 13.2615 + 22.9696i 0.774746 + 1.34190i 0.934937 + 0.354813i \(0.115456\pi\)
−0.160191 + 0.987086i \(0.551211\pi\)
\(294\) 14.9825 0.873800
\(295\) 9.93900 + 17.2149i 0.578671 + 1.00229i
\(296\) −13.6426 + 23.6296i −0.792958 + 1.37344i
\(297\) −1.42543 + 2.46891i −0.0827117 + 0.143261i
\(298\) 45.7375 2.64950
\(299\) 0 0
\(300\) −30.6829 −1.77148
\(301\) −0.647948 + 1.12228i −0.0373471 + 0.0646871i
\(302\) 14.5683 25.2330i 0.838311 1.45200i
\(303\) 2.31282 + 4.00593i 0.132868 + 0.230134i
\(304\) −3.73556 −0.214249
\(305\) 24.4720 + 42.3867i 1.40126 + 2.42705i
\(306\) −3.46346 5.99889i −0.197993 0.342934i
\(307\) −8.24698 −0.470680 −0.235340 0.971913i \(-0.575620\pi\)
−0.235340 + 0.971913i \(0.575620\pi\)
\(308\) −4.06369 7.03851i −0.231550 0.401056i
\(309\) 0.603875 1.04594i 0.0343533 0.0595016i
\(310\) −10.2019 + 17.6703i −0.579432 + 1.00361i
\(311\) −14.4179 −0.817564 −0.408782 0.912632i \(-0.634046\pi\)
−0.408782 + 0.912632i \(0.634046\pi\)
\(312\) 0 0
\(313\) 14.2338 0.804544 0.402272 0.915520i \(-0.368221\pi\)
0.402272 + 0.915520i \(0.368221\pi\)
\(314\) 22.0105 38.1233i 1.24213 2.15142i
\(315\) 1.48039 2.56410i 0.0834103 0.144471i
\(316\) −9.60872 16.6428i −0.540533 0.936230i
\(317\) −6.84415 −0.384406 −0.192203 0.981355i \(-0.561563\pi\)
−0.192203 + 0.981355i \(0.561563\pi\)
\(318\) −11.7383 20.3312i −0.658248 1.14012i
\(319\) 5.48911 + 9.50743i 0.307331 + 0.532314i
\(320\) −43.7289 −2.44452
\(321\) −4.76055 8.24552i −0.265708 0.460220i
\(322\) −7.36174 + 12.7509i −0.410254 + 0.710580i
\(323\) 3.59299 6.22324i 0.199919 0.346270i
\(324\) 3.55496 0.197498
\(325\) 0 0
\(326\) 29.0828 1.61075
\(327\) −0.892240 + 1.54540i −0.0493410 + 0.0854611i
\(328\) 1.55914 2.70051i 0.0860890 0.149111i
\(329\) 0.980386 + 1.69808i 0.0540504 + 0.0936181i
\(330\) 24.8073 1.36560
\(331\) −4.72132 8.17757i −0.259507 0.449480i 0.706603 0.707611i \(-0.250227\pi\)
−0.966110 + 0.258130i \(0.916894\pi\)
\(332\) −12.5293 21.7014i −0.687635 1.19102i
\(333\) 7.44504 0.407986
\(334\) −13.5450 23.4607i −0.741151 1.28371i
\(335\) −26.5710 + 46.0223i −1.45173 + 2.51447i
\(336\) −0.612605 + 1.06106i −0.0334203 + 0.0578857i
\(337\) 2.64310 0.143979 0.0719895 0.997405i \(-0.477065\pi\)
0.0719895 + 0.997405i \(0.477065\pi\)
\(338\) 0 0
\(339\) −4.95108 −0.268906
\(340\) −19.2872 + 33.4064i −1.04599 + 1.81171i
\(341\) 3.34236 5.78914i 0.180999 0.313500i
\(342\) 2.88135 + 4.99065i 0.155806 + 0.269864i
\(343\) 10.7114 0.578361
\(344\) 2.96114 + 5.12884i 0.159654 + 0.276529i
\(345\) −14.3802 24.9072i −0.774202 1.34096i
\(346\) 28.5520 1.53496
\(347\) 5.07942 + 8.79781i 0.272677 + 0.472291i 0.969547 0.244907i \(-0.0787575\pi\)
−0.696869 + 0.717198i \(0.745424\pi\)
\(348\) 6.84481 11.8556i 0.366921 0.635525i
\(349\) −5.21983 + 9.04102i −0.279411 + 0.483954i −0.971239 0.238109i \(-0.923473\pi\)
0.691827 + 0.722063i \(0.256806\pi\)
\(350\) −16.3134 −0.871986
\(351\) 0 0
\(352\) 10.6304 0.566604
\(353\) −9.14556 + 15.8406i −0.486769 + 0.843108i −0.999884 0.0152113i \(-0.995158\pi\)
0.513115 + 0.858320i \(0.328491\pi\)
\(354\) −6.34481 + 10.9895i −0.337223 + 0.584087i
\(355\) −14.9988 25.9787i −0.796054 1.37881i
\(356\) 4.02310 0.213224
\(357\) −1.17845 2.04113i −0.0623701 0.108028i
\(358\) 0.634670 + 1.09928i 0.0335434 + 0.0580988i
\(359\) −15.2731 −0.806081 −0.403041 0.915182i \(-0.632047\pi\)
−0.403041 + 0.915182i \(0.632047\pi\)
\(360\) −6.76540 11.7180i −0.356568 0.617593i
\(361\) 6.51089 11.2772i 0.342678 0.593536i
\(362\) 27.4388 47.5253i 1.44215 2.49788i
\(363\) 2.87263 0.150774
\(364\) 0 0
\(365\) −43.8896 −2.29729
\(366\) −15.6223 + 27.0586i −0.816590 + 1.41438i
\(367\) 11.1359 19.2879i 0.581288 1.00682i −0.414040 0.910259i \(-0.635882\pi\)
0.995327 0.0965606i \(-0.0307842\pi\)
\(368\) 5.95071 + 10.3069i 0.310202 + 0.537286i
\(369\) −0.850855 −0.0442937
\(370\) −32.3923 56.1051i −1.68400 2.91677i
\(371\) −3.99396 6.91774i −0.207356 0.359151i
\(372\) −8.33572 −0.432187
\(373\) −2.06315 3.57349i −0.106826 0.185028i 0.807657 0.589653i \(-0.200735\pi\)
−0.914483 + 0.404625i \(0.867402\pi\)
\(374\) 9.87382 17.1020i 0.510563 0.884321i
\(375\) 6.70291 11.6098i 0.346137 0.599526i
\(376\) 8.96077 0.462116
\(377\) 0 0
\(378\) 1.89008 0.0972154
\(379\) 5.35354 9.27261i 0.274993 0.476302i −0.695140 0.718874i \(-0.744658\pi\)
0.970133 + 0.242572i \(0.0779911\pi\)
\(380\) 16.0456 27.7917i 0.823120 1.42569i
\(381\) 2.83513 + 4.91058i 0.145248 + 0.251577i
\(382\) 39.5150 2.02176
\(383\) −3.26324 5.65210i −0.166744 0.288809i 0.770529 0.637405i \(-0.219992\pi\)
−0.937273 + 0.348596i \(0.886659\pi\)
\(384\) −10.2289 17.7169i −0.521989 0.904112i
\(385\) 8.44073 0.430179
\(386\) −30.3379 52.5467i −1.54416 2.67456i
\(387\) 0.807979 1.39946i 0.0410719 0.0711385i
\(388\) 10.5660 18.3009i 0.536408 0.929085i
\(389\) −11.7922 −0.597891 −0.298945 0.954270i \(-0.596635\pi\)
−0.298945 + 0.954270i \(0.596635\pi\)
\(390\) 0 0
\(391\) −22.8944 −1.15782
\(392\) 11.6486 20.1760i 0.588344 1.01904i
\(393\) 9.11141 15.7814i 0.459610 0.796067i
\(394\) −25.2434 43.7228i −1.27174 2.20272i
\(395\) 19.9584 1.00422
\(396\) 5.06734 + 8.77688i 0.254643 + 0.441055i
\(397\) 6.27144 + 10.8624i 0.314754 + 0.545171i 0.979385 0.202001i \(-0.0647445\pi\)
−0.664631 + 0.747172i \(0.731411\pi\)
\(398\) 8.31468 0.416777
\(399\) 0.980386 + 1.69808i 0.0490807 + 0.0850102i
\(400\) −6.59329 + 11.4199i −0.329664 + 0.570995i
\(401\) −8.93512 + 15.4761i −0.446198 + 0.772838i −0.998135 0.0610479i \(-0.980556\pi\)
0.551936 + 0.833886i \(0.313889\pi\)
\(402\) −33.9245 −1.69200
\(403\) 0 0
\(404\) 16.4440 0.818118
\(405\) −1.84601 + 3.19738i −0.0917290 + 0.158879i
\(406\) 3.63922 6.30331i 0.180611 0.312828i
\(407\) 10.6124 + 18.3812i 0.526036 + 0.911120i
\(408\) −10.7711 −0.533247
\(409\) 13.9559 + 24.1724i 0.690076 + 1.19525i 0.971812 + 0.235755i \(0.0757563\pi\)
−0.281736 + 0.959492i \(0.590910\pi\)
\(410\) 3.70195 + 6.41196i 0.182826 + 0.316664i
\(411\) −9.45042 −0.466155
\(412\) −2.14675 3.71828i −0.105763 0.183187i
\(413\) −2.15883 + 3.73921i −0.106229 + 0.183994i
\(414\) 9.17994 15.9001i 0.451169 0.781448i
\(415\) 26.0248 1.27750
\(416\) 0 0
\(417\) −4.01507 −0.196619
\(418\) −8.21432 + 14.2276i −0.401776 + 0.695896i
\(419\) 8.20171 14.2058i 0.400680 0.693998i −0.593128 0.805108i \(-0.702107\pi\)
0.993808 + 0.111110i \(0.0354407\pi\)
\(420\) −5.26271 9.11528i −0.256794 0.444780i
\(421\) −3.03684 −0.148006 −0.0740032 0.997258i \(-0.523577\pi\)
−0.0740032 + 0.997258i \(0.523577\pi\)
\(422\) −1.43243 2.48104i −0.0697295 0.120775i
\(423\) −1.22252 2.11747i −0.0594410 0.102955i
\(424\) −36.5050 −1.77284
\(425\) −12.6833 21.9681i −0.615230 1.06561i
\(426\) 9.57487 16.5842i 0.463904 0.803505i
\(427\) −5.31551 + 9.20674i −0.257236 + 0.445545i
\(428\) −33.8471 −1.63606
\(429\) 0 0
\(430\) −14.0616 −0.678110
\(431\) 1.66905 2.89089i 0.0803955 0.139249i −0.823024 0.568006i \(-0.807715\pi\)
0.903420 + 0.428757i \(0.141048\pi\)
\(432\) 0.763906 1.32312i 0.0367534 0.0636588i
\(433\) −5.95138 10.3081i −0.286005 0.495375i 0.686847 0.726802i \(-0.258994\pi\)
−0.972852 + 0.231426i \(0.925661\pi\)
\(434\) −4.43190 −0.212738
\(435\) 7.10872 + 12.3127i 0.340837 + 0.590347i
\(436\) 3.17187 + 5.49385i 0.151905 + 0.263108i
\(437\) 19.0465 0.911119
\(438\) −14.0090 24.2643i −0.669377 1.15940i
\(439\) −1.85905 + 3.21997i −0.0887277 + 0.153681i −0.906974 0.421188i \(-0.861613\pi\)
0.818246 + 0.574868i \(0.194947\pi\)
\(440\) 19.2872 33.4064i 0.919480 1.59259i
\(441\) −6.35690 −0.302709
\(442\) 0 0
\(443\) 1.45712 0.0692300 0.0346150 0.999401i \(-0.488979\pi\)
0.0346150 + 0.999401i \(0.488979\pi\)
\(444\) 13.2334 22.9209i 0.628030 1.08778i
\(445\) −2.08911 + 3.61844i −0.0990331 + 0.171530i
\(446\) 20.4913 + 35.4919i 0.970290 + 1.68059i
\(447\) −19.4058 −0.917863
\(448\) −4.74914 8.22574i −0.224376 0.388630i
\(449\) 6.06369 + 10.5026i 0.286163 + 0.495649i 0.972891 0.231266i \(-0.0742867\pi\)
−0.686727 + 0.726915i \(0.740953\pi\)
\(450\) 20.3424 0.958951
\(451\) −1.21283 2.10069i −0.0571100 0.0989175i
\(452\) −8.80045 + 15.2428i −0.413938 + 0.716962i
\(453\) −6.18114 + 10.7060i −0.290415 + 0.503014i
\(454\) 41.0465 1.92641
\(455\) 0 0
\(456\) 8.96077 0.419627
\(457\) 1.72401 2.98608i 0.0806459 0.139683i −0.822882 0.568213i \(-0.807635\pi\)
0.903528 + 0.428530i \(0.140968\pi\)
\(458\) −22.1081 + 38.2923i −1.03304 + 1.78928i
\(459\) 1.46950 + 2.54525i 0.0685904 + 0.118802i
\(460\) −102.242 −4.76704
\(461\) 3.37800 + 5.85087i 0.157329 + 0.272502i 0.933905 0.357522i \(-0.116378\pi\)
−0.776575 + 0.630024i \(0.783045\pi\)
\(462\) 2.69418 + 4.66645i 0.125344 + 0.217103i
\(463\) −7.45175 −0.346312 −0.173156 0.984894i \(-0.555396\pi\)
−0.173156 + 0.984894i \(0.555396\pi\)
\(464\) −2.94169 5.09516i −0.136565 0.236537i
\(465\) 4.32855 7.49727i 0.200732 0.347678i
\(466\) −4.65615 + 8.06468i −0.215692 + 0.373589i
\(467\) 32.6098 1.50900 0.754502 0.656298i \(-0.227879\pi\)
0.754502 + 0.656298i \(0.227879\pi\)
\(468\) 0 0
\(469\) −11.5429 −0.533001
\(470\) −10.6380 + 18.4256i −0.490695 + 0.849909i
\(471\) −9.33877 + 16.1752i −0.430308 + 0.745315i
\(472\) 9.86592 + 17.0883i 0.454116 + 0.786552i
\(473\) 4.60686 0.211824
\(474\) 6.37047 + 11.0340i 0.292605 + 0.506807i
\(475\) 10.5516 + 18.2759i 0.484141 + 0.838557i
\(476\) −8.37867 −0.384036
\(477\) 4.98039 + 8.62628i 0.228036 + 0.394970i
\(478\) −0.964361 + 1.67032i −0.0441088 + 0.0763987i
\(479\) −1.41454 + 2.45006i −0.0646321 + 0.111946i −0.896531 0.442982i \(-0.853921\pi\)
0.831899 + 0.554928i \(0.187254\pi\)
\(480\) 13.7670 0.628376
\(481\) 0 0
\(482\) 14.2180 0.647614
\(483\) 3.12349 5.41004i 0.142124 0.246165i
\(484\) 5.10603 8.84391i 0.232092 0.401996i
\(485\) 10.9734 + 19.0065i 0.498276 + 0.863039i
\(486\) −2.35690 −0.106911
\(487\) 20.6468 + 35.7612i 0.935594 + 1.62050i 0.773572 + 0.633709i \(0.218468\pi\)
0.162022 + 0.986787i \(0.448199\pi\)
\(488\) 24.2920 + 42.0750i 1.09965 + 1.90465i
\(489\) −12.3394 −0.558009
\(490\) 27.6579 + 47.9049i 1.24946 + 2.16412i
\(491\) 17.3349 30.0249i 0.782313 1.35501i −0.148279 0.988946i \(-0.547373\pi\)
0.930591 0.366060i \(-0.119293\pi\)
\(492\) −1.51238 + 2.61951i −0.0681832 + 0.118097i
\(493\) 11.3177 0.509722
\(494\) 0 0
\(495\) −10.5254 −0.473082
\(496\) −1.79122 + 3.10248i −0.0804280 + 0.139305i
\(497\) 3.25786 5.64279i 0.146135 0.253114i
\(498\) 8.30678 + 14.3878i 0.372236 + 0.644731i
\(499\) 17.9409 0.803146 0.401573 0.915827i \(-0.368464\pi\)
0.401573 + 0.915827i \(0.368464\pi\)
\(500\) −23.8286 41.2723i −1.06565 1.84575i
\(501\) 5.74698 + 9.95406i 0.256756 + 0.444715i
\(502\) −63.3532 −2.82759
\(503\) 13.0906 + 22.6736i 0.583681 + 1.01096i 0.995038 + 0.0994909i \(0.0317214\pi\)
−0.411358 + 0.911474i \(0.634945\pi\)
\(504\) 1.46950 2.54525i 0.0654568 0.113374i
\(505\) −8.53899 + 14.7900i −0.379980 + 0.658145i
\(506\) 52.3414 2.32686
\(507\) 0 0
\(508\) 20.1575 0.894345
\(509\) 2.75302 4.76837i 0.122025 0.211354i −0.798541 0.601941i \(-0.794394\pi\)
0.920566 + 0.390586i \(0.127728\pi\)
\(510\) 12.7872 22.1480i 0.566225 0.980731i
\(511\) −4.76659 8.25598i −0.210862 0.365223i
\(512\) −16.8955 −0.746681
\(513\) −1.22252 2.11747i −0.0539756 0.0934885i
\(514\) 10.6688 + 18.4788i 0.470579 + 0.815066i
\(515\) 4.45904 0.196489
\(516\) −2.87233 4.97502i −0.126447 0.219013i
\(517\) 3.48523 6.03660i 0.153280 0.265489i
\(518\) 7.03588 12.1865i 0.309139 0.535444i
\(519\) −12.1142 −0.531756
\(520\) 0 0
\(521\) −26.7211 −1.17067 −0.585336 0.810791i \(-0.699037\pi\)
−0.585336 + 0.810791i \(0.699037\pi\)
\(522\) −4.53803 + 7.86010i −0.198624 + 0.344027i
\(523\) −18.2615 + 31.6299i −0.798520 + 1.38308i 0.122060 + 0.992523i \(0.461050\pi\)
−0.920580 + 0.390555i \(0.872283\pi\)
\(524\) −32.3907 56.1023i −1.41499 2.45084i
\(525\) 6.92154 0.302081
\(526\) −27.2823 47.2544i −1.18957 2.06039i
\(527\) −3.44571 5.96814i −0.150097 0.259976i
\(528\) 4.35557 0.189552
\(529\) −18.8409 32.6334i −0.819171 1.41885i
\(530\) 43.3379 75.0634i 1.88248 3.26055i
\(531\) 2.69202 4.66272i 0.116824 0.202345i
\(532\) 6.97046 0.302208
\(533\) 0 0
\(534\) −2.66727 −0.115424
\(535\) 17.5761 30.4426i 0.759880 1.31615i
\(536\) −26.3756 + 45.6839i −1.13925 + 1.97324i
\(537\) −0.269282 0.466411i −0.0116204 0.0201271i
\(538\) −5.70576 −0.245993
\(539\) −9.06129 15.6946i −0.390298 0.676015i
\(540\) 6.56249 + 11.3666i 0.282405 + 0.489139i
\(541\) 18.4655 0.793893 0.396947 0.917842i \(-0.370070\pi\)
0.396947 + 0.917842i \(0.370070\pi\)
\(542\) 25.2719 + 43.7722i 1.08552 + 1.88018i
\(543\) −11.6419 + 20.1644i −0.499602 + 0.865336i
\(544\) 5.47956 9.49087i 0.234934 0.406918i
\(545\) −6.58834 −0.282213
\(546\) 0 0
\(547\) 39.8471 1.70374 0.851870 0.523753i \(-0.175468\pi\)
0.851870 + 0.523753i \(0.175468\pi\)
\(548\) −16.7979 + 29.0949i −0.717572 + 1.24287i
\(549\) 6.62833 11.4806i 0.282890 0.489981i
\(550\) 28.9966 + 50.2237i 1.23642 + 2.14154i
\(551\) −9.41550 −0.401114
\(552\) −14.2744 24.7240i −0.607560 1.05232i
\(553\) 2.16756 + 3.75433i 0.0921741 + 0.159650i
\(554\) −34.8993 −1.48273
\(555\) 13.7436 + 23.8047i 0.583384 + 1.01045i
\(556\) −7.13669 + 12.3611i −0.302663 + 0.524228i
\(557\) −4.60238 + 7.97156i −0.195009 + 0.337766i −0.946904 0.321518i \(-0.895807\pi\)
0.751894 + 0.659284i \(0.229140\pi\)
\(558\) 5.52648 0.233955
\(559\) 0 0
\(560\) −4.52350 −0.191153
\(561\) −4.18933 + 7.25614i −0.176874 + 0.306354i
\(562\) −17.0918 + 29.6039i −0.720974 + 1.24876i
\(563\) 0.487623 + 0.844588i 0.0205509 + 0.0355951i 0.876118 0.482097i \(-0.160125\pi\)
−0.855567 + 0.517692i \(0.826791\pi\)
\(564\) −8.69202 −0.366000
\(565\) −9.13975 15.8305i −0.384512 0.665995i
\(566\) −30.2533 52.4003i −1.27164 2.20255i
\(567\) −0.801938 −0.0336782
\(568\) −14.8885 25.7877i −0.624708 1.08203i
\(569\) 8.44720 14.6310i 0.354125 0.613362i −0.632843 0.774280i \(-0.718112\pi\)
0.986968 + 0.160918i \(0.0514454\pi\)
\(570\) −10.6380 + 18.4256i −0.445578 + 0.771763i
\(571\) −44.3226 −1.85484 −0.927421 0.374019i \(-0.877979\pi\)
−0.927421 + 0.374019i \(0.877979\pi\)
\(572\) 0 0
\(573\) −16.7657 −0.700397
\(574\) −0.804094 + 1.39273i −0.0335622 + 0.0581315i
\(575\) 33.6172 58.2267i 1.40193 2.42822i
\(576\) 5.92208 + 10.2573i 0.246753 + 0.427389i
\(577\) 3.56704 0.148498 0.0742489 0.997240i \(-0.476344\pi\)
0.0742489 + 0.997240i \(0.476344\pi\)
\(578\) 9.85450 + 17.0685i 0.409893 + 0.709956i
\(579\) 12.8720 + 22.2949i 0.534940 + 0.926544i
\(580\) 50.5424 2.09866
\(581\) 2.82640 + 4.89546i 0.117259 + 0.203098i
\(582\) −7.00514 + 12.1333i −0.290372 + 0.502940i
\(583\) −14.1984 + 24.5923i −0.588036 + 1.01851i
\(584\) −43.5669 −1.80281
\(585\) 0 0
\(586\) −62.5120 −2.58235
\(587\) 8.05861 13.9579i 0.332614 0.576105i −0.650409 0.759584i \(-0.725403\pi\)
0.983024 + 0.183479i \(0.0587360\pi\)
\(588\) −11.2992 + 19.5709i −0.465973 + 0.807089i
\(589\) 2.86658 + 4.96507i 0.118116 + 0.204582i
\(590\) −46.8504 −1.92880
\(591\) 10.7104 + 18.5510i 0.440569 + 0.763087i
\(592\) −5.68731 9.85071i −0.233747 0.404862i
\(593\) −42.8611 −1.76010 −0.880048 0.474885i \(-0.842490\pi\)
−0.880048 + 0.474885i \(0.842490\pi\)
\(594\) −3.35958 5.81897i −0.137845 0.238755i
\(595\) 4.35086 7.53590i 0.178368 0.308942i
\(596\) −34.4934 + 59.7444i −1.41291 + 2.44722i
\(597\) −3.52781 −0.144384
\(598\) 0 0
\(599\) 40.9420 1.67284 0.836422 0.548086i \(-0.184643\pi\)
0.836422 + 0.548086i \(0.184643\pi\)
\(600\) 15.8158 27.3938i 0.645678 1.11835i
\(601\) −0.593523 + 1.02801i −0.0242103 + 0.0419335i −0.877877 0.478887i \(-0.841040\pi\)
0.853666 + 0.520820i \(0.174374\pi\)
\(602\) −1.52715 2.64510i −0.0622419 0.107806i
\(603\) 14.3937 0.586158
\(604\) 21.9737 + 38.0595i 0.894096 + 1.54862i
\(605\) 5.30290 + 9.18489i 0.215593 + 0.373419i
\(606\) −10.9022 −0.442870
\(607\) −9.99612 17.3138i −0.405730 0.702745i 0.588676 0.808369i \(-0.299649\pi\)
−0.994406 + 0.105624i \(0.966316\pi\)
\(608\) −4.55861 + 7.89574i −0.184876 + 0.320214i
\(609\) −1.54407 + 2.67441i −0.0625690 + 0.108373i
\(610\) −115.356 −4.67062
\(611\) 0 0
\(612\) 10.4480 0.422336
\(613\) 16.6809 28.8922i 0.673735 1.16694i −0.303102 0.952958i \(-0.598022\pi\)
0.976837 0.213985i \(-0.0686445\pi\)
\(614\) 9.71864 16.8332i 0.392212 0.679332i
\(615\) −1.57069 2.72051i −0.0633362 0.109702i
\(616\) 8.37867 0.337586
\(617\) −5.81163 10.0660i −0.233967 0.405243i 0.725005 0.688744i \(-0.241838\pi\)
−0.958972 + 0.283501i \(0.908504\pi\)
\(618\) 1.42327 + 2.46518i 0.0572524 + 0.0991640i
\(619\) −16.5381 −0.664722 −0.332361 0.943152i \(-0.607845\pi\)
−0.332361 + 0.943152i \(0.607845\pi\)
\(620\) −15.3878 26.6525i −0.617990 1.07039i
\(621\) −3.89493 + 6.74621i −0.156298 + 0.270716i
\(622\) 16.9907 29.4288i 0.681267 1.17999i
\(623\) −0.907542 −0.0363599
\(624\) 0 0
\(625\) 6.33944 0.253577
\(626\) −16.7738 + 29.0531i −0.670417 + 1.16120i
\(627\) 3.48523 6.03660i 0.139187 0.241078i
\(628\) 33.1989 + 57.5023i 1.32478 + 2.29459i
\(629\) 21.8810 0.872452
\(630\) 3.48911 + 6.04332i 0.139010 + 0.240772i
\(631\) 18.2208 + 31.5593i 0.725358 + 1.25636i 0.958826 + 0.283993i \(0.0916592\pi\)
−0.233468 + 0.972364i \(0.575007\pi\)
\(632\) 19.8116 0.788064
\(633\) 0.607760 + 1.05267i 0.0241563 + 0.0418399i
\(634\) 8.06547 13.9698i 0.320321 0.554812i
\(635\) −10.4673 + 18.1300i −0.415384 + 0.719466i
\(636\) 35.4101 1.40410
\(637\) 0 0
\(638\) −25.8745 −1.02438
\(639\) −4.06249 + 7.03644i −0.160710 + 0.278357i
\(640\) 37.7652 65.4112i 1.49280 2.58560i
\(641\) −13.6033 23.5617i −0.537300 0.930630i −0.999048 0.0436195i \(-0.986111\pi\)
0.461748 0.887011i \(-0.347222\pi\)
\(642\) 22.4403 0.885646
\(643\) 2.53481 + 4.39042i 0.0999632 + 0.173141i 0.911669 0.410925i \(-0.134794\pi\)
−0.811706 + 0.584066i \(0.801461\pi\)
\(644\) −11.1039 19.2325i −0.437554 0.757866i
\(645\) 5.96615 0.234917
\(646\) 8.46830 + 14.6675i 0.333181 + 0.577086i
\(647\) −9.66033 + 16.7322i −0.379787 + 0.657810i −0.991031 0.133632i \(-0.957336\pi\)
0.611244 + 0.791442i \(0.290669\pi\)
\(648\) −1.83244 + 3.17387i −0.0719849 + 0.124682i
\(649\) 15.3491 0.602506
\(650\) 0 0
\(651\) 1.88040 0.0736985
\(652\) −21.9331 + 37.9892i −0.858966 + 1.48777i
\(653\) −17.6177 + 30.5148i −0.689436 + 1.19414i 0.282585 + 0.959242i \(0.408808\pi\)
−0.972021 + 0.234895i \(0.924525\pi\)
\(654\) −2.10292 3.64236i −0.0822305 0.142427i
\(655\) 67.2790 2.62881
\(656\) 0.649973 + 1.12579i 0.0253772 + 0.0439546i
\(657\) 5.94385 + 10.2950i 0.231891 + 0.401648i
\(658\) −4.62133 −0.180158
\(659\) 2.18084 + 3.77733i 0.0849535 + 0.147144i 0.905371 0.424621i \(-0.139592\pi\)
−0.820418 + 0.571764i \(0.806259\pi\)
\(660\) −18.7087 + 32.4044i −0.728236 + 1.26134i
\(661\) 7.73543 13.3982i 0.300873 0.521128i −0.675461 0.737396i \(-0.736055\pi\)
0.976334 + 0.216268i \(0.0693885\pi\)
\(662\) 22.2553 0.864978
\(663\) 0 0
\(664\) 25.8334 1.00253
\(665\) −3.61960 + 6.26934i −0.140362 + 0.243115i
\(666\) −8.77359 + 15.1963i −0.339970 + 0.588845i
\(667\) 14.9988 + 25.9787i 0.580756 + 1.00590i
\(668\) 40.8605 1.58094
\(669\) −8.69418 15.0588i −0.336136 0.582205i
\(670\) −62.6250 108.470i −2.41942 4.19055i
\(671\) 37.7928 1.45898
\(672\) 1.49516 + 2.58969i 0.0576769 + 0.0998993i
\(673\) 5.87047 10.1680i 0.226290 0.391946i −0.730416 0.683003i \(-0.760674\pi\)
0.956706 + 0.291057i \(0.0940070\pi\)
\(674\) −3.11476 + 5.39492i −0.119976 + 0.207805i
\(675\) −8.63102 −0.332208
\(676\) 0 0
\(677\) 3.44504 0.132404 0.0662019 0.997806i \(-0.478912\pi\)
0.0662019 + 0.997806i \(0.478912\pi\)
\(678\) 5.83459 10.1058i 0.224076 0.388111i
\(679\) −2.38351 + 4.12836i −0.0914707 + 0.158432i
\(680\) −19.8835 34.4393i −0.762498 1.32068i
\(681\) −17.4155 −0.667363
\(682\) 7.87760 + 13.6444i 0.301649 + 0.522471i
\(683\) −10.2029 17.6720i −0.390403 0.676198i 0.602099 0.798421i \(-0.294331\pi\)
−0.992503 + 0.122223i \(0.960998\pi\)
\(684\) −8.69202 −0.332348
\(685\) −17.4456 30.2166i −0.666561 1.15452i
\(686\) −12.6228 + 21.8634i −0.481942 + 0.834748i
\(687\) 9.38016 16.2469i 0.357875 0.619858i
\(688\) −2.46888 −0.0941251
\(689\) 0 0
\(690\) 67.7851 2.58053
\(691\) −13.9019 + 24.0788i −0.528854 + 0.916002i 0.470580 + 0.882358i \(0.344045\pi\)
−0.999434 + 0.0336449i \(0.989288\pi\)
\(692\) −21.5328 + 37.2959i −0.818554 + 1.41778i
\(693\) −1.14310 1.97991i −0.0434229 0.0752107i
\(694\) −23.9433 −0.908876
\(695\) −7.41185 12.8377i −0.281148 0.486962i
\(696\) 7.05645 + 12.2221i 0.267474 + 0.463279i
\(697\) −2.50066 −0.0947194
\(698\) −12.3026 21.3087i −0.465660 0.806547i
\(699\) 1.97554 3.42174i 0.0747218 0.129422i
\(700\) 12.3029 21.3092i 0.465006 0.805414i
\(701\) 11.9715 0.452158 0.226079 0.974109i \(-0.427409\pi\)
0.226079 + 0.974109i \(0.427409\pi\)
\(702\) 0 0
\(703\) −18.2034 −0.686556
\(704\) −16.8830 + 29.2422i −0.636301 + 1.10211i
\(705\) 4.51357 7.81774i 0.169991 0.294433i
\(706\) −21.5551 37.3346i −0.811238 1.40510i
\(707\) −3.70948 −0.139509
\(708\) −9.57002 16.5758i −0.359664 0.622955i
\(709\) −16.1332 27.9435i −0.605894 1.04944i −0.991909 0.126947i \(-0.959482\pi\)
0.386015 0.922492i \(-0.373851\pi\)
\(710\) 70.7012 2.65337
\(711\) −2.70291 4.68157i −0.101367 0.175573i
\(712\) −2.07374 + 3.59183i −0.0777169 + 0.134610i
\(713\) 9.13288 15.8186i 0.342029 0.592412i
\(714\) 5.55496 0.207889
\(715\) 0 0
\(716\) −1.91457 −0.0715510
\(717\) 0.409166 0.708696i 0.0152806 0.0264667i
\(718\) 17.9985 31.1743i 0.671698 1.16342i
\(719\) −6.05429 10.4863i −0.225787 0.391075i 0.730768 0.682626i \(-0.239162\pi\)
−0.956555 + 0.291551i \(0.905829\pi\)
\(720\) 5.64071 0.210217
\(721\) 0.484271 + 0.838781i 0.0180352 + 0.0312378i
\(722\) 15.3455 + 26.5791i 0.571100 + 0.989173i
\(723\) −6.03252 −0.224352
\(724\) 41.3865 + 71.6835i 1.53812 + 2.66410i
\(725\) −16.6184 + 28.7839i −0.617192 + 1.06901i
\(726\) −3.38524 + 5.86341i −0.125638 + 0.217611i
\(727\) −16.6200 −0.616402 −0.308201 0.951321i \(-0.599727\pi\)
−0.308201 + 0.951321i \(0.599727\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 51.7216 89.5845i 1.91430 3.31567i
\(731\) 2.37465 4.11301i 0.0878296 0.152125i
\(732\) −23.5635 40.8131i −0.870930 1.50850i
\(733\) 17.7912 0.657132 0.328566 0.944481i \(-0.393435\pi\)
0.328566 + 0.944481i \(0.393435\pi\)
\(734\) 26.2461 + 45.4595i 0.968760 + 1.67794i
\(735\) −11.7349 20.3254i −0.432848 0.749715i
\(736\) 29.0473 1.07070
\(737\) 20.5172 + 35.5369i 0.755762 + 1.30902i
\(738\) 1.00269 1.73671i 0.0369095 0.0639291i
\(739\) 13.6809 23.6960i 0.503260 0.871672i −0.496733 0.867903i \(-0.665467\pi\)
0.999993 0.00376844i \(-0.00119954\pi\)
\(740\) 97.7160 3.59211
\(741\) 0 0
\(742\) 18.8267 0.691150
\(743\) −4.19298 + 7.26246i −0.153826 + 0.266434i −0.932631 0.360832i \(-0.882493\pi\)
0.778805 + 0.627266i \(0.215826\pi\)
\(744\) 4.29672 7.44215i 0.157526 0.272842i
\(745\) −35.8233 62.0478i −1.31247 2.27326i
\(746\) 9.72528 0.356068
\(747\) −3.52446 6.10454i −0.128953 0.223353i
\(748\) 14.8929 + 25.7953i 0.544538 + 0.943168i
\(749\) 7.63533 0.278989
\(750\) 15.7981 + 27.3630i 0.576863 + 0.999157i
\(751\) 19.3889 33.5825i 0.707511 1.22544i −0.258267 0.966073i \(-0.583152\pi\)
0.965778 0.259371i \(-0.0835151\pi\)
\(752\) −1.86778 + 3.23509i −0.0681110 + 0.117972i
\(753\) 26.8799 0.979559
\(754\) 0 0
\(755\) −45.6418 −1.66107
\(756\) −1.42543 + 2.46891i −0.0518423 + 0.0897935i
\(757\) −6.48643 + 11.2348i −0.235753 + 0.408336i −0.959491 0.281738i \(-0.909089\pi\)
0.723738 + 0.690075i \(0.242422\pi\)
\(758\) 12.6177 + 21.8546i 0.458297 + 0.793794i
\(759\) −22.2078 −0.806090
\(760\) 16.5417 + 28.6510i 0.600030 + 1.03928i
\(761\) 2.57792 + 4.46510i 0.0934497 + 0.161860i 0.908961 0.416882i \(-0.136877\pi\)
−0.815511 + 0.578742i \(0.803544\pi\)
\(762\) −13.3642 −0.484134
\(763\) −0.715521 1.23932i −0.0259036 0.0448663i
\(764\) −29.8007 + 51.6163i −1.07815 + 1.86741i
\(765\) −5.42543 + 9.39712i −0.196157 + 0.339753i
\(766\) 15.3822 0.555783
\(767\) 0 0
\(768\) 24.5284 0.885092
\(769\) 17.7506 30.7450i 0.640104 1.10869i −0.345305 0.938490i \(-0.612225\pi\)
0.985409 0.170202i \(-0.0544421\pi\)
\(770\) −9.94696 + 17.2286i −0.358464 + 0.620877i
\(771\) −4.52661 7.84033i −0.163022 0.282362i
\(772\) 91.5186 3.29383
\(773\) 3.07792 + 5.33112i 0.110705 + 0.191747i 0.916055 0.401053i \(-0.131356\pi\)
−0.805350 + 0.592800i \(0.798022\pi\)
\(774\) 1.90432 + 3.29838i 0.0684494 + 0.118558i
\(775\) 20.2381 0.726976
\(776\) 10.8927 + 18.8667i 0.391025 + 0.677275i
\(777\) −2.98523 + 5.17057i −0.107095 + 0.185493i
\(778\) 13.8966 24.0695i 0.498216 0.862935i
\(779\) 2.08038 0.0745372
\(780\) 0 0
\(781\) −23.1631