Properties

Label 507.2.e.l.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.l.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 \(-0.519789\pi\)
0.895416 0.445230i \(-0.146878\pi\)
\(3\) 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 \(-0.809141\pi\)
−0.825561 + 0.564313i \(0.809141\pi\)
\(6\) −1.17845 2.04113i −0.481099 0.833289i
\(7\) −0.400969 0.694498i −0.151552 0.262496i 0.780246 0.625473i \(-0.215094\pi\)
−0.931798 + 0.362977i \(0.881760\pi\)
\(8\) −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 −0.996854 0.0792636i \(-0.974743\pi\)
0.567071 + 0.823669i \(0.308076\pi\)
\(12\) −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 0.691034 0.722822i \(-0.257156\pi\)
−0.971499 + 0.237042i \(0.923822\pi\)
\(20\) 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 \(-0.567532\pi\)
−0.210571 + 0.977579i \(0.567532\pi\)
\(32\) −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 \(-0.623707\pi\)
0.990907 0.134552i \(-0.0429595\pi\)
\(38\) −5.76271 −0.934835
\(39\) 0 0
\(40\) 13.5308 2.13941
\(41\) −0.425428 + 0.736862i −0.0664406 + 0.115079i −0.897332 0.441356i \(-0.854498\pi\)
0.830892 + 0.556434i \(0.187831\pi\)
\(42\) −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 \(-0.557067\pi\)
−0.178323 + 0.983972i \(0.557067\pi\)
\(48\) 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 0.635861 0.771804i \(-0.280645\pi\)
−0.986332 + 0.164770i \(0.947312\pi\)
\(60\) 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 \(-0.491386\pi\)
0.852180 0.523249i \(-0.175280\pi\)
\(68\) −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 0.999790 0.0205142i \(-0.00653033\pi\)
−0.517661 + 0.855586i \(0.673197\pi\)
\(72\) 1.83244 + 3.17387i 0.215955 + 0.374045i
\(73\) 11.8877 1.39135 0.695674 0.718357i \(-0.255106\pi\)
0.695674 + 0.718357i \(0.255106\pi\)
\(74\) −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 \(-0.626440\pi\)
−0.386860 + 0.922139i \(0.626440\pi\)
\(84\) 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 −0.834477 0.551043i \(-0.814230\pi\)
0.894456 + 0.447156i \(0.147563\pi\)
\(90\) 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 0.674759 0.738038i \(-0.264247\pi\)
−0.976539 + 0.215340i \(0.930914\pi\)
\(98\) −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 \(-0.472764\pi\)
0.0854611 + 0.996342i \(0.472764\pi\)
\(110\) −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 0.994169 0.107829i \(-0.0343900\pi\)
−0.590468 + 0.807061i \(0.701057\pi\)
\(138\) −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 \(0.125806\pi\)
−0.128014 + 0.991772i \(0.540860\pi\)
\(150\) −10.1712 17.6171i −0.830476 1.43843i
\(151\) 12.3623 1.00603 0.503014 0.864278i \(-0.332225\pi\)
0.503014 + 0.864278i \(0.332225\pi\)
\(152\) 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 0.999815 0.0192348i \(-0.00612301\pi\)
−0.516565 + 0.856248i \(0.672790\pi\)
\(164\) 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 −0.553318 0.832970i \(-0.686638\pi\)
0.998032 + 0.0627020i \(0.0199718\pi\)
\(168\) 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 \(-0.456098\pi\)
0.789059 0.614318i \(-0.210569\pi\)
\(194\) −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 \(-0.557016\pi\)
0.941252 0.337705i \(-0.109651\pi\)
\(198\) 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 \(0.364477\pi\)
−0.995218 + 0.0976835i \(0.968857\pi\)
\(224\) −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 \(0.0294819\pi\)
−0.417760 + 0.908557i \(0.637185\pi\)
\(228\) 4.34601 + 7.52751i 0.287822 + 0.498522i
\(229\) −18.7603 −1.23972 −0.619858 0.784714i \(-0.712810\pi\)
−0.619858 + 0.784714i \(0.712810\pi\)
\(230\) 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 \(-0.508426\pi\)
−0.0264667 + 0.999650i \(0.508426\pi\)
\(240\) −2.82036 4.88500i −0.182053 0.315325i
\(241\) 3.01626 + 5.22432i 0.194295 + 0.336528i 0.946669 0.322208i \(-0.104425\pi\)
−0.752375 + 0.658736i \(0.771092\pi\)
\(242\) 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 \(0.392462\pi\)
−0.982796 + 0.184693i \(0.940871\pi\)
\(272\) 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 \(-0.642406\pi\)
−0.432608 + 0.901582i \(0.642406\pi\)
\(282\) 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 \(-0.884544\pi\)
0.160191 0.987086i \(-0.448789\pi\)
\(294\) −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 \(-0.424380\pi\)
0.235340 + 0.971913i \(0.424380\pi\)
\(308\) −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 \(-0.438437\pi\)
0.192203 + 0.981355i \(0.438437\pi\)
\(318\) 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 0.966110 0.258130i \(-0.0831065\pi\)
−0.706603 + 0.707611i \(0.749773\pi\)
\(332\) 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 −0.691827 0.722063i \(-0.743194\pi\)
0.971239 + 0.238109i \(0.0765274\pi\)
\(350\) −16.3134 −0.871986
\(351\) 0 0
\(352\) 10.6304 0.566604
\(353\) 9.14556 15.8406i 0.486769 0.843108i −0.513115 0.858320i \(-0.671509\pi\)
0.999884 + 0.0152113i \(0.00484208\pi\)
\(354\) −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 \(-0.367953\pi\)
0.403041 + 0.915182i \(0.367953\pi\)
\(360\) −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 −0.970133 0.242572i \(-0.922009\pi\)
0.695140 + 0.718874i \(0.255342\pi\)
\(380\) 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 0.937273 0.348596i \(-0.113341\pi\)
−0.770529 + 0.637405i \(0.780008\pi\)
\(384\) 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 0.664631 0.747172i \(-0.268589\pi\)
−0.979385 + 0.202001i \(0.935256\pi\)
\(398\) −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 −0.551936 0.833886i \(-0.686111\pi\)
0.998135 + 0.0610479i \(0.0194442\pi\)
\(402\) −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 \(-0.924244\pi\)
0.281736 0.959492i \(-0.409090\pi\)
\(410\) −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 \(-0.476423\pi\)
0.0740032 + 0.997258i \(0.476423\pi\)
\(422\) 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 −0.903420 0.428757i \(-0.858952\pi\)
0.823024 + 0.568006i \(0.192285\pi\)
\(432\) 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 0.686727 0.726915i \(-0.259047\pi\)
−0.972891 + 0.231266i \(0.925713\pi\)
\(450\) −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 −0.903528 0.428530i \(-0.859032\pi\)
0.822882 + 0.568213i \(0.192365\pi\)
\(458\) −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 0.776575 0.630024i \(-0.216955\pi\)
−0.933905 + 0.357522i \(0.883622\pi\)
\(462\) −2.69418 4.66645i −0.125344 0.217103i
\(463\) 7.45175 0.346312 0.173156 0.984894i \(-0.444604\pi\)
0.173156 + 0.984894i \(0.444604\pi\)
\(464\) −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 −0.831899 0.554928i \(-0.812746\pi\)
0.896531 + 0.442982i \(0.146079\pi\)
\(480\) 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 \(-0.781532\pi\)
−0.162022 0.986787i \(-0.551801\pi\)
\(488\) −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 \(-0.631536\pi\)
−0.401573 + 0.915827i \(0.631536\pi\)
\(500\) 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 −0.920566 0.390586i \(-0.872272\pi\)
0.798541 + 0.601941i \(0.205606\pi\)
\(510\) 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 \(-0.629930\pi\)
−0.396947 + 0.917842i \(0.629930\pi\)
\(542\) 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 −0.751894 0.659284i \(-0.770860\pi\)
0.946904 + 0.321518i \(0.104193\pi\)
\(558\) 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 \(-0.523656\pi\)
−0.0742489 + 0.997240i \(0.523656\pi\)
\(578\) −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 −0.983024 0.183479i \(-0.941264\pi\)
0.650409 + 0.759584i \(0.274597\pi\)
\(588\) −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 \(-0.157510\pi\)
0.880048 + 0.474885i \(0.157510\pi\)
\(594\) −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 \(0.401978\pi\)
−0.976837 + 0.213985i \(0.931356\pi\)
\(614\) 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 0.958972 0.283501i \(-0.0914958\pi\)
−0.725005 + 0.688744i \(0.758162\pi\)
\(618\) −1.42327 2.46518i −0.0572524 0.0991640i
\(619\) 16.5381 0.664722 0.332361 0.943152i \(-0.392155\pi\)
0.332361 + 0.943152i \(0.392155\pi\)
\(620\) −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 \(-0.908341\pi\)
0.233468 0.972364i \(-0.424993\pi\)
\(632\) −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 0.811706 0.584066i \(-0.198539\pi\)
−0.911669 + 0.410925i \(0.865206\pi\)
\(644\) 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 −0.976334 0.216268i \(-0.930611\pi\)
0.675461 + 0.737396i \(0.263945\pi\)
\(662\) 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 0.992503 0.122223i \(-0.0390022\pi\)
−0.602099 + 0.798421i \(0.705669\pi\)
\(684\) 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 \(-0.655955\pi\)
0.999434 0.0336449i \(-0.0107115\pi\)
\(692\) −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 \(0.0405179\pi\)
−0.386015 + 0.922492i \(0.626149\pi\)
\(710\) −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 \(-0.606565\pi\)
−0.328566 + 0.944481i \(0.606565\pi\)
\(734\) −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 \(0.334533\pi\)
−0.999993 + 0.00376844i \(0.998800\pi\)
\(740\) 97.7160 3.59211
\(741\) 0 0
\(742\) 18.8267 0.691150
\(743\) 4.19298 7.26246i 0.153826 0.266434i −0.778805 0.627266i \(-0.784174\pi\)
0.932631 + 0.360832i \(0.117507\pi\)
\(744\) 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 0.815511 0.578742i \(-0.196456\pi\)
−0.908961 + 0.416882i \(0.863123\pi\)
\(762\) 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 \(0.387775\pi\)
−0.985409 + 0.170202i \(0.945558\pi\)
\(770\) −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 0.805350 0.592800i \(-0.201978\pi\)
−0.916055 + 0.401053i \(0.868644\pi\)
\(774\) −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