Properties

Label 441.2.h.f.373.4
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.4
Root \(-0.335166 - 0.580525i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.f.214.4

$q$-expansion

\(f(q)\) \(=\) \(q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +O(q^{10})\) \(q+0.670333 q^{2} +(-1.65263 - 0.518475i) q^{3} -1.55065 q^{4} +(0.712469 + 1.23403i) q^{5} +(-1.10781 - 0.347551i) q^{6} -2.38012 q^{8} +(2.46237 + 1.71369i) q^{9} +(0.477591 + 0.827212i) q^{10} +(2.46539 - 4.27018i) q^{11} +(2.56266 + 0.803975i) q^{12} +(1.37730 - 2.38556i) q^{13} +(-0.537632 - 2.40879i) q^{15} +1.50584 q^{16} +(-0.559839 - 0.969670i) q^{17} +(1.65061 + 1.14874i) q^{18} +(2.00752 - 3.47713i) q^{19} +(-1.10479 - 1.91356i) q^{20} +(1.65263 - 2.86244i) q^{22} +(-2.71830 - 4.70824i) q^{23} +(3.93346 + 1.23403i) q^{24} +(1.48478 - 2.57171i) q^{25} +(0.923251 - 1.59912i) q^{26} +(-3.18087 - 4.10878i) q^{27} +(3.40555 + 5.89858i) q^{29} +(-0.360392 - 1.61469i) q^{30} -2.50584 q^{31} +5.76965 q^{32} +(-6.28835 + 5.77878i) q^{33} +(-0.375279 - 0.650002i) q^{34} +(-3.81828 - 2.65735i) q^{36} +(0.709787 - 1.22939i) q^{37} +(1.34571 - 2.33083i) q^{38} +(-3.51302 + 3.22835i) q^{39} +(-1.69576 - 2.93714i) q^{40} +(-0.124384 + 0.215440i) q^{41} +(-0.498313 - 0.863104i) q^{43} +(-3.82296 + 6.62156i) q^{44} +(-0.360392 + 4.25959i) q^{45} +(-1.82217 - 3.15609i) q^{46} +9.47579 q^{47} +(-2.48859 - 0.780738i) q^{48} +(0.995294 - 1.72390i) q^{50} +(0.422457 + 1.89277i) q^{51} +(-2.13572 + 3.69917i) q^{52} +(-0.410229 - 0.710537i) q^{53} +(-2.13224 - 2.75425i) q^{54} +7.02604 q^{55} +(-5.12050 + 4.70556i) q^{57} +(2.28285 + 3.95401i) q^{58} +6.58407 q^{59} +(0.833682 + 3.73521i) q^{60} -0.0752645 q^{61} -1.67974 q^{62} +0.855913 q^{64} +3.92514 q^{65} +(-4.21529 + 3.87370i) q^{66} -12.5877 q^{67} +(0.868117 + 1.50362i) q^{68} +(2.05125 + 9.19035i) q^{69} +0.0804951 q^{71} +(-5.86073 - 4.07880i) q^{72} +(-5.34551 - 9.25869i) q^{73} +(0.475793 - 0.824098i) q^{74} +(-3.78715 + 3.48026i) q^{75} +(-3.11297 + 5.39183i) q^{76} +(-2.35489 + 2.16407i) q^{78} -1.84491 q^{79} +(1.07286 + 1.85825i) q^{80} +(3.12651 + 8.43949i) q^{81} +(-0.0833788 + 0.144416i) q^{82} +(7.23583 + 12.5328i) q^{83} +(0.797736 - 1.38172i) q^{85} +(-0.334036 - 0.578567i) q^{86} +(-2.56984 - 11.5139i) q^{87} +(-5.86792 + 10.1635i) q^{88} +(-6.76292 + 11.7137i) q^{89} +(-0.241583 + 2.85534i) q^{90} +(4.21515 + 7.30085i) q^{92} +(4.14122 + 1.29921i) q^{93} +6.35193 q^{94} +5.72119 q^{95} +(-9.53509 - 2.99142i) q^{96} +(-2.70160 - 4.67930i) q^{97} +(13.3885 - 6.28982i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + O(q^{10}) \) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + 7q^{10} + 4q^{11} + 20q^{12} + 8q^{13} - 19q^{15} - 4q^{16} - 12q^{17} + 4q^{18} - q^{19} - 5q^{20} - q^{22} + 3q^{23} - 6q^{24} - q^{25} - 11q^{26} + 7q^{27} + 7q^{29} + 16q^{30} - 6q^{31} + 4q^{32} - 14q^{33} - 3q^{34} + 34q^{36} - 20q^{38} + 2q^{39} + 3q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + 16q^{45} + 3q^{46} + 54q^{47} + 5q^{48} + 19q^{50} - 9q^{51} + 10q^{52} - 21q^{53} - q^{54} - 4q^{55} - 4q^{57} - 10q^{58} + 60q^{59} + 10q^{60} - 28q^{61} + 12q^{62} - 50q^{64} + 22q^{65} - 19q^{66} + 4q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 36q^{72} - 15q^{73} - 36q^{74} + 14q^{75} - 5q^{76} - 20q^{78} + 8q^{79} - 20q^{80} + 23q^{81} + 5q^{82} - 9q^{83} - 6q^{85} - 8q^{86} - 2q^{87} - 18q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 6q^{93} - 6q^{94} + 28q^{95} - 59q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.670333 0.473997 0.236998 0.971510i \(-0.423836\pi\)
0.236998 + 0.971510i \(0.423836\pi\)
\(3\) −1.65263 0.518475i −0.954146 0.299342i
\(4\) −1.55065 −0.775327
\(5\) 0.712469 + 1.23403i 0.318626 + 0.551876i 0.980202 0.198002i \(-0.0634454\pi\)
−0.661576 + 0.749878i \(0.730112\pi\)
\(6\) −1.10781 0.347551i −0.452262 0.141887i
\(7\) 0 0
\(8\) −2.38012 −0.841499
\(9\) 2.46237 + 1.71369i 0.820789 + 0.571231i
\(10\) 0.477591 + 0.827212i 0.151028 + 0.261587i
\(11\) 2.46539 4.27018i 0.743342 1.28751i −0.207623 0.978209i \(-0.566573\pi\)
0.950965 0.309297i \(-0.100094\pi\)
\(12\) 2.56266 + 0.803975i 0.739775 + 0.232088i
\(13\) 1.37730 2.38556i 0.381995 0.661635i −0.609352 0.792900i \(-0.708571\pi\)
0.991347 + 0.131265i \(0.0419038\pi\)
\(14\) 0 0
\(15\) −0.537632 2.40879i −0.138816 0.621948i
\(16\) 1.50584 0.376459
\(17\) −0.559839 0.969670i −0.135781 0.235180i 0.790115 0.612959i \(-0.210021\pi\)
−0.925896 + 0.377780i \(0.876688\pi\)
\(18\) 1.65061 + 1.14874i 0.389051 + 0.270762i
\(19\) 2.00752 3.47713i 0.460557 0.797709i −0.538431 0.842669i \(-0.680983\pi\)
0.998989 + 0.0449606i \(0.0143162\pi\)
\(20\) −1.10479 1.91356i −0.247039 0.427884i
\(21\) 0 0
\(22\) 1.65263 2.86244i 0.352342 0.610274i
\(23\) −2.71830 4.70824i −0.566806 0.981736i −0.996879 0.0789424i \(-0.974846\pi\)
0.430073 0.902794i \(-0.358488\pi\)
\(24\) 3.93346 + 1.23403i 0.802913 + 0.251896i
\(25\) 1.48478 2.57171i 0.296955 0.514342i
\(26\) 0.923251 1.59912i 0.181064 0.313613i
\(27\) −3.18087 4.10878i −0.612160 0.790734i
\(28\) 0 0
\(29\) 3.40555 + 5.89858i 0.632394 + 1.09534i 0.987061 + 0.160346i \(0.0512611\pi\)
−0.354667 + 0.934993i \(0.615406\pi\)
\(30\) −0.360392 1.61469i −0.0657984 0.294801i
\(31\) −2.50584 −0.450061 −0.225031 0.974352i \(-0.572248\pi\)
−0.225031 + 0.974352i \(0.572248\pi\)
\(32\) 5.76965 1.01994
\(33\) −6.28835 + 5.77878i −1.09466 + 1.00596i
\(34\) −0.375279 0.650002i −0.0643597 0.111474i
\(35\) 0 0
\(36\) −3.81828 2.65735i −0.636380 0.442891i
\(37\) 0.709787 1.22939i 0.116688 0.202110i −0.801765 0.597639i \(-0.796106\pi\)
0.918453 + 0.395529i \(0.129439\pi\)
\(38\) 1.34571 2.33083i 0.218303 0.378111i
\(39\) −3.51302 + 3.22835i −0.562534 + 0.516949i
\(40\) −1.69576 2.93714i −0.268123 0.464403i
\(41\) −0.124384 + 0.215440i −0.0194256 + 0.0336460i −0.875575 0.483083i \(-0.839517\pi\)
0.856149 + 0.516729i \(0.172850\pi\)
\(42\) 0 0
\(43\) −0.498313 0.863104i −0.0759921 0.131622i 0.825525 0.564365i \(-0.190879\pi\)
−0.901517 + 0.432743i \(0.857546\pi\)
\(44\) −3.82296 + 6.62156i −0.576333 + 0.998238i
\(45\) −0.360392 + 4.25959i −0.0537241 + 0.634983i
\(46\) −1.82217 3.15609i −0.268664 0.465340i
\(47\) 9.47579 1.38219 0.691093 0.722766i \(-0.257129\pi\)
0.691093 + 0.722766i \(0.257129\pi\)
\(48\) −2.48859 0.780738i −0.359197 0.112690i
\(49\) 0 0
\(50\) 0.995294 1.72390i 0.140756 0.243796i
\(51\) 0.422457 + 1.89277i 0.0591559 + 0.265041i
\(52\) −2.13572 + 3.69917i −0.296171 + 0.512983i
\(53\) −0.410229 0.710537i −0.0563493 0.0975998i 0.836475 0.548005i \(-0.184613\pi\)
−0.892824 + 0.450406i \(0.851279\pi\)
\(54\) −2.13224 2.75425i −0.290162 0.374805i
\(55\) 7.02604 0.947392
\(56\) 0 0
\(57\) −5.12050 + 4.70556i −0.678226 + 0.623267i
\(58\) 2.28285 + 3.95401i 0.299753 + 0.519187i
\(59\) 6.58407 0.857173 0.428586 0.903501i \(-0.359012\pi\)
0.428586 + 0.903501i \(0.359012\pi\)
\(60\) 0.833682 + 3.73521i 0.107628 + 0.482213i
\(61\) −0.0752645 −0.00963663 −0.00481831 0.999988i \(-0.501534\pi\)
−0.00481831 + 0.999988i \(0.501534\pi\)
\(62\) −1.67974 −0.213328
\(63\) 0 0
\(64\) 0.855913 0.106989
\(65\) 3.92514 0.486854
\(66\) −4.21529 + 3.87370i −0.518866 + 0.476820i
\(67\) −12.5877 −1.53783 −0.768916 0.639350i \(-0.779204\pi\)
−0.768916 + 0.639350i \(0.779204\pi\)
\(68\) 0.868117 + 1.50362i 0.105275 + 0.182341i
\(69\) 2.05125 + 9.19035i 0.246941 + 1.10639i
\(70\) 0 0
\(71\) 0.0804951 0.00955301 0.00477651 0.999989i \(-0.498480\pi\)
0.00477651 + 0.999989i \(0.498480\pi\)
\(72\) −5.86073 4.07880i −0.690694 0.480691i
\(73\) −5.34551 9.25869i −0.625644 1.08365i −0.988416 0.151769i \(-0.951503\pi\)
0.362772 0.931878i \(-0.381830\pi\)
\(74\) 0.475793 0.824098i 0.0553098 0.0957995i
\(75\) −3.78715 + 3.48026i −0.437303 + 0.401866i
\(76\) −3.11297 + 5.39183i −0.357083 + 0.618485i
\(77\) 0 0
\(78\) −2.35489 + 2.16407i −0.266639 + 0.245032i
\(79\) −1.84491 −0.207569 −0.103785 0.994600i \(-0.533095\pi\)
−0.103785 + 0.994600i \(0.533095\pi\)
\(80\) 1.07286 + 1.85825i 0.119950 + 0.207759i
\(81\) 3.12651 + 8.43949i 0.347390 + 0.937721i
\(82\) −0.0833788 + 0.144416i −0.00920765 + 0.0159481i
\(83\) 7.23583 + 12.5328i 0.794236 + 1.37566i 0.923323 + 0.384023i \(0.125462\pi\)
−0.129088 + 0.991633i \(0.541205\pi\)
\(84\) 0 0
\(85\) 0.797736 1.38172i 0.0865266 0.149868i
\(86\) −0.334036 0.578567i −0.0360200 0.0623885i
\(87\) −2.56984 11.5139i −0.275516 1.23442i
\(88\) −5.86792 + 10.1635i −0.625522 + 1.08344i
\(89\) −6.76292 + 11.7137i −0.716868 + 1.24165i 0.245366 + 0.969430i \(0.421092\pi\)
−0.962235 + 0.272222i \(0.912242\pi\)
\(90\) −0.241583 + 2.85534i −0.0254651 + 0.300980i
\(91\) 0 0
\(92\) 4.21515 + 7.30085i 0.439460 + 0.761167i
\(93\) 4.14122 + 1.29921i 0.429424 + 0.134722i
\(94\) 6.35193 0.655152
\(95\) 5.72119 0.586982
\(96\) −9.53509 2.99142i −0.973171 0.305310i
\(97\) −2.70160 4.67930i −0.274306 0.475111i 0.695654 0.718377i \(-0.255115\pi\)
−0.969960 + 0.243266i \(0.921781\pi\)
\(98\) 0 0
\(99\) 13.3885 6.28982i 1.34559 0.632151i
\(100\) −2.30238 + 3.98783i −0.230238 + 0.398783i
\(101\) −2.56770 + 4.44739i −0.255496 + 0.442531i −0.965030 0.262139i \(-0.915572\pi\)
0.709534 + 0.704671i \(0.248905\pi\)
\(102\) 0.283187 + 1.26878i 0.0280397 + 0.125628i
\(103\) −7.10561 12.3073i −0.700137 1.21267i −0.968418 0.249332i \(-0.919789\pi\)
0.268282 0.963341i \(-0.413544\pi\)
\(104\) −3.27814 + 5.67791i −0.321448 + 0.556765i
\(105\) 0 0
\(106\) −0.274990 0.476296i −0.0267094 0.0462620i
\(107\) 3.83015 6.63401i 0.370274 0.641334i −0.619333 0.785128i \(-0.712597\pi\)
0.989608 + 0.143794i \(0.0459303\pi\)
\(108\) 4.93244 + 6.37129i 0.474624 + 0.613078i
\(109\) −0.849394 1.47119i −0.0813572 0.140915i 0.822476 0.568800i \(-0.192592\pi\)
−0.903833 + 0.427885i \(0.859259\pi\)
\(110\) 4.70979 0.449061
\(111\) −1.81042 + 1.66371i −0.171838 + 0.157913i
\(112\) 0 0
\(113\) −0.300351 + 0.520224i −0.0282547 + 0.0489385i −0.879807 0.475331i \(-0.842328\pi\)
0.851552 + 0.524270i \(0.175662\pi\)
\(114\) −3.43244 + 3.15429i −0.321477 + 0.295426i
\(115\) 3.87341 6.70895i 0.361198 0.625613i
\(116\) −5.28083 9.14666i −0.490312 0.849246i
\(117\) 7.47954 3.51385i 0.691484 0.324855i
\(118\) 4.41352 0.406297
\(119\) 0 0
\(120\) 1.27963 + 5.73322i 0.116814 + 0.523369i
\(121\) −6.65626 11.5290i −0.605115 1.04809i
\(122\) −0.0504522 −0.00456773
\(123\) 0.317261 0.291552i 0.0286065 0.0262884i
\(124\) 3.88569 0.348945
\(125\) 11.3561 1.01572
\(126\) 0 0
\(127\) 7.25977 0.644200 0.322100 0.946706i \(-0.395611\pi\)
0.322100 + 0.946706i \(0.395611\pi\)
\(128\) −10.9656 −0.969227
\(129\) 0.376030 + 1.68475i 0.0331076 + 0.148334i
\(130\) 2.63115 0.230767
\(131\) −10.2265 17.7128i −0.893492 1.54757i −0.835660 0.549248i \(-0.814914\pi\)
−0.0578326 0.998326i \(-0.518419\pi\)
\(132\) 9.75105 8.96088i 0.848720 0.779945i
\(133\) 0 0
\(134\) −8.43794 −0.728927
\(135\) 2.80409 6.85267i 0.241337 0.589784i
\(136\) 1.33248 + 2.30793i 0.114260 + 0.197903i
\(137\) −6.10581 + 10.5756i −0.521655 + 0.903532i 0.478028 + 0.878345i \(0.341352\pi\)
−0.999683 + 0.0251879i \(0.991982\pi\)
\(138\) 1.37502 + 6.16059i 0.117049 + 0.524425i
\(139\) 1.24092 2.14933i 0.105253 0.182304i −0.808588 0.588375i \(-0.799768\pi\)
0.913842 + 0.406071i \(0.133101\pi\)
\(140\) 0 0
\(141\) −15.6600 4.91296i −1.31881 0.413746i
\(142\) 0.0539585 0.00452810
\(143\) −6.79117 11.7626i −0.567906 0.983642i
\(144\) 3.70792 + 2.58054i 0.308994 + 0.215045i
\(145\) −4.85269 + 8.40511i −0.402994 + 0.698006i
\(146\) −3.58327 6.20640i −0.296553 0.513645i
\(147\) 0 0
\(148\) −1.10063 + 1.90635i −0.0904715 + 0.156701i
\(149\) 4.27797 + 7.40966i 0.350465 + 0.607023i 0.986331 0.164777i \(-0.0526903\pi\)
−0.635866 + 0.771799i \(0.719357\pi\)
\(150\) −2.53865 + 2.33293i −0.207280 + 0.190483i
\(151\) 8.82962 15.2933i 0.718544 1.24455i −0.243033 0.970018i \(-0.578142\pi\)
0.961577 0.274537i \(-0.0885244\pi\)
\(152\) −4.77814 + 8.27599i −0.387559 + 0.671271i
\(153\) 0.283187 3.34708i 0.0228943 0.270595i
\(154\) 0 0
\(155\) −1.78533 3.09228i −0.143401 0.248378i
\(156\) 5.44748 5.00605i 0.436148 0.400805i
\(157\) −6.32149 −0.504510 −0.252255 0.967661i \(-0.581172\pi\)
−0.252255 + 0.967661i \(0.581172\pi\)
\(158\) −1.23671 −0.0983871
\(159\) 0.309561 + 1.38695i 0.0245498 + 0.109992i
\(160\) 4.11070 + 7.11993i 0.324979 + 0.562880i
\(161\) 0 0
\(162\) 2.09580 + 5.65726i 0.164662 + 0.444477i
\(163\) −4.01134 + 6.94784i −0.314192 + 0.544197i −0.979265 0.202581i \(-0.935067\pi\)
0.665073 + 0.746778i \(0.268400\pi\)
\(164\) 0.192877 0.334073i 0.0150612 0.0260867i
\(165\) −11.6114 3.64283i −0.903950 0.283594i
\(166\) 4.85041 + 8.40116i 0.376465 + 0.652057i
\(167\) −1.06038 + 1.83663i −0.0820545 + 0.142123i −0.904132 0.427253i \(-0.859482\pi\)
0.822078 + 0.569375i \(0.192815\pi\)
\(168\) 0 0
\(169\) 2.70608 + 4.68706i 0.208160 + 0.360543i
\(170\) 0.534749 0.926212i 0.0410133 0.0710372i
\(171\) 10.9020 5.12170i 0.833697 0.391666i
\(172\) 0.772712 + 1.33838i 0.0589187 + 0.102050i
\(173\) 18.2881 1.39042 0.695208 0.718808i \(-0.255312\pi\)
0.695208 + 0.718808i \(0.255312\pi\)
\(174\) −1.72265 7.71812i −0.130594 0.585109i
\(175\) 0 0
\(176\) 3.71247 6.43018i 0.279838 0.484693i
\(177\) −10.8810 3.41367i −0.817868 0.256587i
\(178\) −4.53341 + 7.85209i −0.339793 + 0.588539i
\(179\) 3.81276 + 6.60389i 0.284979 + 0.493598i 0.972604 0.232468i \(-0.0746801\pi\)
−0.687625 + 0.726066i \(0.741347\pi\)
\(180\) 0.558844 6.60516i 0.0416538 0.492319i
\(181\) −15.5305 −1.15438 −0.577188 0.816611i \(-0.695850\pi\)
−0.577188 + 0.816611i \(0.695850\pi\)
\(182\) 0 0
\(183\) 0.124384 + 0.0390227i 0.00919475 + 0.00288464i
\(184\) 6.46989 + 11.2062i 0.476967 + 0.826130i
\(185\) 2.02280 0.148719
\(186\) 2.77599 + 0.870905i 0.203546 + 0.0638578i
\(187\) −5.52088 −0.403727
\(188\) −14.6937 −1.07165
\(189\) 0 0
\(190\) 3.83510 0.278227
\(191\) 14.8325 1.07324 0.536620 0.843824i \(-0.319701\pi\)
0.536620 + 0.843824i \(0.319701\pi\)
\(192\) −1.41451 0.443769i −0.102083 0.0320263i
\(193\) 16.5677 1.19257 0.596286 0.802772i \(-0.296642\pi\)
0.596286 + 0.802772i \(0.296642\pi\)
\(194\) −1.81097 3.13669i −0.130020 0.225201i
\(195\) −6.48680 2.03509i −0.464529 0.145736i
\(196\) 0 0
\(197\) −4.03740 −0.287653 −0.143826 0.989603i \(-0.545941\pi\)
−0.143826 + 0.989603i \(0.545941\pi\)
\(198\) 8.97472 4.21628i 0.637806 0.299638i
\(199\) 12.6407 + 21.8943i 0.896076 + 1.55205i 0.832468 + 0.554074i \(0.186927\pi\)
0.0636081 + 0.997975i \(0.479739\pi\)
\(200\) −3.53395 + 6.12097i −0.249888 + 0.432818i
\(201\) 20.8028 + 6.52640i 1.46732 + 0.460337i
\(202\) −1.72121 + 2.98123i −0.121104 + 0.209758i
\(203\) 0 0
\(204\) −0.655085 2.93503i −0.0458651 0.205493i
\(205\) −0.354480 −0.0247579
\(206\) −4.76312 8.24997i −0.331862 0.574803i
\(207\) 1.37502 16.2518i 0.0955703 1.12958i
\(208\) 2.07399 3.59226i 0.143805 0.249078i
\(209\) −9.89864 17.1449i −0.684703 1.18594i
\(210\) 0 0
\(211\) −3.76246 + 6.51678i −0.259019 + 0.448634i −0.965979 0.258619i \(-0.916732\pi\)
0.706961 + 0.707253i \(0.250066\pi\)
\(212\) 0.636123 + 1.10180i 0.0436891 + 0.0756718i
\(213\) −0.133029 0.0417347i −0.00911497 0.00285961i
\(214\) 2.56747 4.44699i 0.175509 0.303990i
\(215\) 0.710065 1.22987i 0.0484261 0.0838764i
\(216\) 7.57086 + 9.77938i 0.515132 + 0.665402i
\(217\) 0 0
\(218\) −0.569377 0.986190i −0.0385631 0.0667932i
\(219\) 4.03374 + 18.0727i 0.272575 + 1.22124i
\(220\) −10.8950 −0.734538
\(221\) −3.08427 −0.207471
\(222\) −1.21358 + 1.11524i −0.0814504 + 0.0748501i
\(223\) −6.49230 11.2450i −0.434757 0.753020i 0.562519 0.826784i \(-0.309832\pi\)
−0.997276 + 0.0737638i \(0.976499\pi\)
\(224\) 0 0
\(225\) 8.06319 3.78804i 0.537546 0.252536i
\(226\) −0.201335 + 0.348723i −0.0133926 + 0.0231967i
\(227\) −14.4832 + 25.0857i −0.961286 + 1.66500i −0.242009 + 0.970274i \(0.577806\pi\)
−0.719277 + 0.694723i \(0.755527\pi\)
\(228\) 7.94012 7.29670i 0.525847 0.483235i
\(229\) 7.71790 + 13.3678i 0.510013 + 0.883369i 0.999933 + 0.0116012i \(0.00369285\pi\)
−0.489919 + 0.871768i \(0.662974\pi\)
\(230\) 2.59648 4.49723i 0.171207 0.296538i
\(231\) 0 0
\(232\) −8.10561 14.0393i −0.532159 0.921727i
\(233\) −2.47324 + 4.28378i −0.162027 + 0.280640i −0.935596 0.353073i \(-0.885137\pi\)
0.773568 + 0.633713i \(0.218470\pi\)
\(234\) 5.01378 2.35545i 0.327761 0.153980i
\(235\) 6.75121 + 11.6934i 0.440400 + 0.762795i
\(236\) −10.2096 −0.664589
\(237\) 3.04896 + 0.956542i 0.198051 + 0.0621341i
\(238\) 0 0
\(239\) 6.51732 11.2883i 0.421571 0.730182i −0.574523 0.818489i \(-0.694812\pi\)
0.996093 + 0.0883069i \(0.0281456\pi\)
\(240\) −0.809586 3.62725i −0.0522586 0.234138i
\(241\) 7.29123 12.6288i 0.469670 0.813492i −0.529729 0.848167i \(-0.677706\pi\)
0.999399 + 0.0346754i \(0.0110397\pi\)
\(242\) −4.46191 7.72826i −0.286823 0.496791i
\(243\) −0.791301 15.5684i −0.0507620 0.998711i
\(244\) 0.116709 0.00747154
\(245\) 0 0
\(246\) 0.212671 0.195437i 0.0135594 0.0124606i
\(247\) −5.52993 9.57812i −0.351861 0.609441i
\(248\) 5.96419 0.378726
\(249\) −5.46019 24.4637i −0.346026 1.55032i
\(250\) 7.61238 0.481449
\(251\) 14.0715 0.888187 0.444094 0.895980i \(-0.353526\pi\)
0.444094 + 0.895980i \(0.353526\pi\)
\(252\) 0 0
\(253\) −26.8067 −1.68532
\(254\) 4.86646 0.305349
\(255\) −2.03475 + 1.86986i −0.127421 + 0.117095i
\(256\) −9.06240 −0.566400
\(257\) −4.18108 7.24184i −0.260808 0.451733i 0.705649 0.708562i \(-0.250656\pi\)
−0.966457 + 0.256829i \(0.917322\pi\)
\(258\) 0.252065 + 1.12935i 0.0156929 + 0.0703100i
\(259\) 0 0
\(260\) −6.08653 −0.377471
\(261\) −1.72265 + 20.3605i −0.106629 + 1.26029i
\(262\) −6.85515 11.8735i −0.423512 0.733545i
\(263\) −1.63533 + 2.83247i −0.100839 + 0.174658i −0.912030 0.410122i \(-0.865486\pi\)
0.811192 + 0.584780i \(0.198819\pi\)
\(264\) 14.9670 13.7542i 0.921157 0.846511i
\(265\) 0.584551 1.01247i 0.0359087 0.0621956i
\(266\) 0 0
\(267\) 17.2499 15.8520i 1.05568 0.970129i
\(268\) 19.5192 1.19232
\(269\) 7.69349 + 13.3255i 0.469081 + 0.812471i 0.999375 0.0353420i \(-0.0112521\pi\)
−0.530295 + 0.847813i \(0.677919\pi\)
\(270\) 1.87967 4.59357i 0.114393 0.279556i
\(271\) −4.06308 + 7.03747i −0.246815 + 0.427496i −0.962640 0.270783i \(-0.912717\pi\)
0.715825 + 0.698279i \(0.246051\pi\)
\(272\) −0.843026 1.46016i −0.0511160 0.0885355i
\(273\) 0 0
\(274\) −4.09293 + 7.08915i −0.247263 + 0.428271i
\(275\) −7.32110 12.6805i −0.441479 0.764664i
\(276\) −3.18077 14.2511i −0.191460 0.857813i
\(277\) −6.42287 + 11.1247i −0.385913 + 0.668421i −0.991895 0.127057i \(-0.959447\pi\)
0.605982 + 0.795478i \(0.292780\pi\)
\(278\) 0.831826 1.44077i 0.0498896 0.0864114i
\(279\) −6.17029 4.29423i −0.369406 0.257089i
\(280\) 0 0
\(281\) −0.724081 1.25415i −0.0431951 0.0748161i 0.843620 0.536941i \(-0.180420\pi\)
−0.886815 + 0.462125i \(0.847087\pi\)
\(282\) −10.4974 3.29332i −0.625111 0.196114i
\(283\) 17.4385 1.03661 0.518306 0.855195i \(-0.326563\pi\)
0.518306 + 0.855195i \(0.326563\pi\)
\(284\) −0.124820 −0.00740671
\(285\) −9.45500 2.96629i −0.560066 0.175708i
\(286\) −4.55234 7.88489i −0.269186 0.466243i
\(287\) 0 0
\(288\) 14.2070 + 9.88741i 0.837156 + 0.582621i
\(289\) 7.87316 13.6367i 0.463127 0.802160i
\(290\) −3.25292 + 5.63422i −0.191018 + 0.330853i
\(291\) 2.03864 + 9.13386i 0.119507 + 0.535437i
\(292\) 8.28903 + 14.3570i 0.485079 + 0.840181i
\(293\) 0.900048 1.55893i 0.0525814 0.0910736i −0.838537 0.544845i \(-0.816588\pi\)
0.891118 + 0.453772i \(0.149922\pi\)
\(294\) 0 0
\(295\) 4.69094 + 8.12495i 0.273117 + 0.473053i
\(296\) −1.68938 + 2.92609i −0.0981931 + 0.170075i
\(297\) −25.3873 + 3.45317i −1.47312 + 0.200373i
\(298\) 2.86766 + 4.96693i 0.166119 + 0.287727i
\(299\) −14.9757 −0.866068
\(300\) 5.87256 5.39668i 0.339053 0.311578i
\(301\) 0 0
\(302\) 5.91878 10.2516i 0.340588 0.589915i
\(303\) 6.54931 6.01859i 0.376248 0.345759i
\(304\) 3.02300 5.23599i 0.173381 0.300305i
\(305\) −0.0536236 0.0928787i −0.00307048 0.00531822i
\(306\) 0.189830 2.24366i 0.0108518 0.128261i
\(307\) −1.06478 −0.0607699 −0.0303850 0.999538i \(-0.509673\pi\)
−0.0303850 + 0.999538i \(0.509673\pi\)
\(308\) 0 0
\(309\) 5.36193 + 24.0234i 0.305029 + 1.36665i
\(310\) −1.19676 2.07286i −0.0679717 0.117730i
\(311\) 16.9293 0.959970 0.479985 0.877277i \(-0.340642\pi\)
0.479985 + 0.877277i \(0.340642\pi\)
\(312\) 8.36141 7.68385i 0.473372 0.435012i
\(313\) 8.27856 0.467932 0.233966 0.972245i \(-0.424830\pi\)
0.233966 + 0.972245i \(0.424830\pi\)
\(314\) −4.23750 −0.239136
\(315\) 0 0
\(316\) 2.86082 0.160934
\(317\) 6.54741 0.367739 0.183870 0.982951i \(-0.441138\pi\)
0.183870 + 0.982951i \(0.441138\pi\)
\(318\) 0.207509 + 0.929717i 0.0116365 + 0.0521359i
\(319\) 33.5840 1.88034
\(320\) 0.609811 + 1.05622i 0.0340895 + 0.0590447i
\(321\) −9.76938 + 8.97773i −0.545274 + 0.501088i
\(322\) 0 0
\(323\) −4.49556 −0.250140
\(324\) −4.84814 13.0867i −0.269341 0.727040i
\(325\) −4.08997 7.08404i −0.226871 0.392952i
\(326\) −2.68893 + 4.65736i −0.148926 + 0.257947i
\(327\) 0.640957 + 2.87173i 0.0354450 + 0.158807i
\(328\) 0.296049 0.512773i 0.0163466 0.0283131i
\(329\) 0 0
\(330\) −7.78353 2.44191i −0.428469 0.134422i
\(331\) −26.7258 −1.46899 −0.734493 0.678617i \(-0.762580\pi\)
−0.734493 + 0.678617i \(0.762580\pi\)
\(332\) −11.2203 19.4341i −0.615792 1.06658i
\(333\) 3.85455 1.81085i 0.211228 0.0992337i
\(334\) −0.710806 + 1.23115i −0.0388936 + 0.0673657i
\(335\) −8.96834 15.5336i −0.489993 0.848692i
\(336\) 0 0
\(337\) −4.76164 + 8.24740i −0.259383 + 0.449264i −0.966077 0.258255i \(-0.916853\pi\)
0.706694 + 0.707520i \(0.250186\pi\)
\(338\) 1.81397 + 3.14189i 0.0986670 + 0.170896i
\(339\) 0.766092 0.704012i 0.0416084 0.0382367i
\(340\) −1.23701 + 2.14257i −0.0670864 + 0.116197i
\(341\) −6.17786 + 10.7004i −0.334550 + 0.579457i
\(342\) 7.30796 3.43324i 0.395169 0.185648i
\(343\) 0 0
\(344\) 1.18605 + 2.05429i 0.0639473 + 0.110760i
\(345\) −9.87974 + 9.07914i −0.531907 + 0.488805i
\(346\) 12.2591 0.659053
\(347\) −18.7031 −1.00404 −0.502018 0.864857i \(-0.667409\pi\)
−0.502018 + 0.864857i \(0.667409\pi\)
\(348\) 3.98494 + 17.8540i 0.213615 + 0.957076i
\(349\) 15.0542 + 26.0747i 0.805834 + 1.39574i 0.915727 + 0.401801i \(0.131616\pi\)
−0.109893 + 0.993943i \(0.535051\pi\)
\(350\) 0 0
\(351\) −14.1827 + 1.92913i −0.757019 + 0.102970i
\(352\) 14.2244 24.6374i 0.758164 1.31318i
\(353\) 3.12966 5.42074i 0.166575 0.288517i −0.770638 0.637273i \(-0.780062\pi\)
0.937214 + 0.348756i \(0.113396\pi\)
\(354\) −7.29391 2.28830i −0.387667 0.121622i
\(355\) 0.0573502 + 0.0993335i 0.00304383 + 0.00527208i
\(356\) 10.4870 18.1639i 0.555807 0.962686i
\(357\) 0 0
\(358\) 2.55582 + 4.42680i 0.135079 + 0.233964i
\(359\) −5.09755 + 8.82921i −0.269038 + 0.465988i −0.968614 0.248571i \(-0.920039\pi\)
0.699575 + 0.714559i \(0.253372\pi\)
\(360\) 0.857777 10.1383i 0.0452088 0.534338i
\(361\) 1.43970 + 2.49364i 0.0757739 + 0.131244i
\(362\) −10.4106 −0.547171
\(363\) 5.02285 + 22.5042i 0.263631 + 1.18117i
\(364\) 0 0
\(365\) 7.61701 13.1931i 0.398693 0.690556i
\(366\) 0.0833788 + 0.0261582i 0.00435828 + 0.00136731i
\(367\) −14.3278 + 24.8165i −0.747906 + 1.29541i 0.200918 + 0.979608i \(0.435608\pi\)
−0.948824 + 0.315804i \(0.897726\pi\)
\(368\) −4.09332 7.08984i −0.213379 0.369584i
\(369\) −0.675478 + 0.317336i −0.0351640 + 0.0165198i
\(370\) 1.35595 0.0704926
\(371\) 0 0
\(372\) −6.42160 2.01463i −0.332944 0.104454i
\(373\) 8.03670 + 13.9200i 0.416124 + 0.720749i 0.995546 0.0942796i \(-0.0300548\pi\)
−0.579421 + 0.815028i \(0.696721\pi\)
\(374\) −3.70083 −0.191365
\(375\) −18.7674 5.88786i −0.969147 0.304048i
\(376\) −22.5535 −1.16311
\(377\) 18.7619 0.966286
\(378\) 0 0
\(379\) −1.01893 −0.0523388 −0.0261694 0.999658i \(-0.508331\pi\)
−0.0261694 + 0.999658i \(0.508331\pi\)
\(380\) −8.87158 −0.455103
\(381\) −11.9977 3.76401i −0.614661 0.192836i
\(382\) 9.94270 0.508713
\(383\) −5.79327 10.0342i −0.296022 0.512725i 0.679200 0.733953i \(-0.262327\pi\)
−0.975222 + 0.221228i \(0.928994\pi\)
\(384\) 18.1220 + 5.68536i 0.924784 + 0.290130i
\(385\) 0 0
\(386\) 11.1059 0.565275
\(387\) 0.252065 2.97924i 0.0128132 0.151443i
\(388\) 4.18924 + 7.25598i 0.212677 + 0.368367i
\(389\) −8.90675 + 15.4270i −0.451590 + 0.782178i −0.998485 0.0550239i \(-0.982476\pi\)
0.546895 + 0.837201i \(0.315810\pi\)
\(390\) −4.34831 1.36418i −0.220185 0.0690782i
\(391\) −3.04363 + 5.27172i −0.153923 + 0.266602i
\(392\) 0 0
\(393\) 7.71695 + 34.5749i 0.389269 + 1.74407i
\(394\) −2.70640 −0.136346
\(395\) −1.31444 2.27668i −0.0661369 0.114552i
\(396\) −20.7609 + 9.75334i −1.04327 + 0.490124i
\(397\) 6.54229 11.3316i 0.328348 0.568715i −0.653836 0.756636i \(-0.726841\pi\)
0.982184 + 0.187921i \(0.0601748\pi\)
\(398\) 8.47348 + 14.6765i 0.424737 + 0.735666i
\(399\) 0 0
\(400\) 2.23583 3.87257i 0.111792 0.193629i
\(401\) −7.05165 12.2138i −0.352143 0.609929i 0.634482 0.772938i \(-0.281213\pi\)
−0.986625 + 0.163009i \(0.947880\pi\)
\(402\) 13.9448 + 4.37486i 0.695503 + 0.218198i
\(403\) −3.45129 + 5.97782i −0.171921 + 0.297776i
\(404\) 3.98161 6.89636i 0.198093 0.343107i
\(405\) −8.18706 + 9.87108i −0.406818 + 0.490498i
\(406\) 0 0
\(407\) −3.49980 6.06183i −0.173479 0.300474i
\(408\) −1.00550 4.50501i −0.0497796 0.223031i
\(409\) 2.64599 0.130836 0.0654179 0.997858i \(-0.479162\pi\)
0.0654179 + 0.997858i \(0.479162\pi\)
\(410\) −0.237619 −0.0117352
\(411\) 15.5738 14.3118i 0.768200 0.705949i
\(412\) 11.0183 + 19.0843i 0.542835 + 0.940217i
\(413\) 0 0
\(414\) 0.921719 10.8941i 0.0453000 0.535415i
\(415\) −10.3106 + 17.8585i −0.506128 + 0.876639i
\(416\) 7.94655 13.7638i 0.389612 0.674827i
\(417\) −3.16515 + 2.90866i −0.154998 + 0.142438i
\(418\) −6.63538 11.4928i −0.324547 0.562132i
\(419\) −16.7567 + 29.0235i −0.818619 + 1.41789i 0.0880816 + 0.996113i \(0.471926\pi\)
−0.906700 + 0.421776i \(0.861407\pi\)
\(420\) 0 0
\(421\) −2.41950 4.19071i −0.117919 0.204242i 0.801024 0.598633i \(-0.204289\pi\)
−0.918943 + 0.394390i \(0.870956\pi\)
\(422\) −2.52210 + 4.36841i −0.122774 + 0.212651i
\(423\) 23.3329 + 16.2386i 1.13448 + 0.789548i
\(424\) 0.976394 + 1.69116i 0.0474179 + 0.0821302i
\(425\) −3.32495 −0.161284
\(426\) −0.0891734 0.0279761i −0.00432047 0.00135545i
\(427\) 0 0
\(428\) −5.93923 + 10.2871i −0.287084 + 0.497244i
\(429\) 5.12465 + 22.9603i 0.247420 + 1.10854i
\(430\) 0.475980 0.824422i 0.0229538 0.0397571i
\(431\) 17.6643 + 30.5954i 0.850858 + 1.47373i 0.880435 + 0.474166i \(0.157251\pi\)
−0.0295774 + 0.999562i \(0.509416\pi\)
\(432\) −4.78988 6.18714i −0.230453 0.297679i
\(433\) −5.47404 −0.263066 −0.131533 0.991312i \(-0.541990\pi\)
−0.131533 + 0.991312i \(0.541990\pi\)
\(434\) 0 0
\(435\) 12.3775 11.3745i 0.593458 0.545367i
\(436\) 1.31712 + 2.28131i 0.0630785 + 0.109255i
\(437\) −21.8282 −1.04419
\(438\) 2.70395 + 12.1147i 0.129200 + 0.578864i
\(439\) −6.39812 −0.305365 −0.152683 0.988275i \(-0.548791\pi\)
−0.152683 + 0.988275i \(0.548791\pi\)
\(440\) −16.7228 −0.797229
\(441\) 0 0
\(442\) −2.06749 −0.0983404
\(443\) −6.38682 −0.303447 −0.151723 0.988423i \(-0.548482\pi\)
−0.151723 + 0.988423i \(0.548482\pi\)
\(444\) 2.80734 2.57985i 0.133230 0.122434i
\(445\) −19.2735 −0.913650
\(446\) −4.35200 7.53789i −0.206073 0.356929i
\(447\) −3.22817 14.4634i −0.152687 0.684097i
\(448\) 0 0
\(449\) −11.7460 −0.554327 −0.277163 0.960823i \(-0.589394\pi\)
−0.277163 + 0.960823i \(0.589394\pi\)
\(450\) 5.40502 2.53925i 0.254795 0.119701i
\(451\) 0.613311 + 1.06229i 0.0288797 + 0.0500210i
\(452\) 0.465741 0.806687i 0.0219066 0.0379434i
\(453\) −22.5213 + 20.6963i −1.05814 + 0.972397i
\(454\) −9.70859 + 16.8158i −0.455647 + 0.789203i
\(455\) 0 0
\(456\) 12.1874 11.1998i 0.570727 0.524478i
\(457\) 10.5224 0.492217 0.246108 0.969242i \(-0.420848\pi\)
0.246108 + 0.969242i \(0.420848\pi\)
\(458\) 5.17356 + 8.96087i 0.241745 + 0.418714i
\(459\) −2.20338 + 5.38465i −0.102845 + 0.251334i
\(460\) −6.00633 + 10.4033i −0.280046 + 0.485055i
\(461\) 3.54278 + 6.13627i 0.165004 + 0.285794i 0.936657 0.350249i \(-0.113903\pi\)
−0.771653 + 0.636044i \(0.780570\pi\)
\(462\) 0 0
\(463\) 16.3760 28.3641i 0.761059 1.31819i −0.181246 0.983438i \(-0.558013\pi\)
0.942305 0.334755i \(-0.108654\pi\)
\(464\) 5.12820 + 8.88230i 0.238071 + 0.412350i
\(465\) 1.34722 + 6.03604i 0.0624758 + 0.279915i
\(466\) −1.65789 + 2.87156i −0.0768004 + 0.133022i
\(467\) −1.96216 + 3.39856i −0.0907978 + 0.157266i −0.907847 0.419301i \(-0.862275\pi\)
0.817049 + 0.576568i \(0.195608\pi\)
\(468\) −11.5982 + 5.44876i −0.536126 + 0.251869i
\(469\) 0 0
\(470\) 4.52555 + 7.83849i 0.208748 + 0.361563i
\(471\) 10.4471 + 3.27753i 0.481376 + 0.151021i
\(472\) −15.6709 −0.721310
\(473\) −4.91414 −0.225952
\(474\) 2.04382 + 0.641201i 0.0938757 + 0.0294513i
\(475\) −5.96145 10.3255i −0.273530 0.473768i
\(476\) 0 0
\(477\) 0.207509 2.45261i 0.00950117 0.112297i
\(478\) 4.36878 7.56694i 0.199823 0.346104i
\(479\) 8.04324 13.9313i 0.367505 0.636537i −0.621670 0.783279i \(-0.713545\pi\)
0.989175 + 0.146742i \(0.0468787\pi\)
\(480\) −3.10195 13.8979i −0.141584 0.634350i
\(481\) −1.95518 3.38647i −0.0891486 0.154410i
\(482\) 4.88755 8.46549i 0.222622 0.385592i
\(483\) 0 0
\(484\) 10.3216 + 17.8775i 0.469162 + 0.812612i
\(485\) 3.84961 6.66771i 0.174802 0.302765i
\(486\) −0.530435 10.4360i −0.0240610 0.473386i
\(487\) −1.75172 3.03407i −0.0793781 0.137487i 0.823604 0.567166i \(-0.191960\pi\)
−0.902982 + 0.429679i \(0.858627\pi\)
\(488\) 0.179138 0.00810921
\(489\) 10.2315 9.40242i 0.462686 0.425192i
\(490\) 0 0
\(491\) −20.5546 + 35.6017i −0.927618 + 1.60668i −0.140321 + 0.990106i \(0.544814\pi\)
−0.787296 + 0.616575i \(0.788520\pi\)
\(492\) −0.491962 + 0.452096i −0.0221794 + 0.0203821i
\(493\) 3.81312 6.60452i 0.171734 0.297452i
\(494\) −3.70689 6.42053i −0.166781 0.288873i
\(495\) 17.3007 + 12.0405i 0.777609 + 0.541180i
\(496\) −3.77338 −0.169430
\(497\) 0 0
\(498\) −3.66015 16.3988i −0.164015 0.734849i
\(499\) −5.91486 10.2448i −0.264785 0.458622i 0.702722 0.711465i \(-0.251968\pi\)
−0.967507 + 0.252843i \(0.918634\pi\)
\(500\) −17.6094 −0.787517
\(501\) 2.70466 2.48549i 0.120835 0.111043i
\(502\) 9.43261 0.420998
\(503\) −21.8595 −0.974665 −0.487332 0.873217i \(-0.662030\pi\)
−0.487332 + 0.873217i \(0.662030\pi\)
\(504\) 0 0
\(505\) −7.31762 −0.325630
\(506\) −17.9694 −0.798837
\(507\) −2.04202 9.14901i −0.0906892 0.406322i
\(508\) −11.2574 −0.499466
\(509\) 8.44831 + 14.6329i 0.374465 + 0.648592i 0.990247 0.139324i \(-0.0444931\pi\)
−0.615782 + 0.787917i \(0.711160\pi\)
\(510\) −1.36396 + 1.25343i −0.0603971 + 0.0555029i
\(511\) 0 0
\(512\) 15.8563 0.700756
\(513\) −20.6724 + 2.81186i −0.912710 + 0.124147i
\(514\) −2.80271 4.85444i −0.123622 0.214120i
\(515\) 10.1250 17.5371i 0.446163 0.772777i
\(516\) −0.583092 2.61247i −0.0256692 0.115008i
\(517\) 23.3615 40.4633i 1.02744 1.77957i
\(518\) 0 0
\(519\) −30.2234 9.48190i −1.32666 0.416209i
\(520\) −9.34230 −0.409687
\(521\) 17.2466 + 29.8720i 0.755587 + 1.30872i 0.945082 + 0.326834i \(0.105982\pi\)
−0.189495 + 0.981882i \(0.560685\pi\)
\(522\) −1.15475 + 13.6483i −0.0505420 + 0.597371i
\(523\) −0.995615 + 1.72445i −0.0435352 + 0.0754051i −0.886972 0.461823i \(-0.847195\pi\)
0.843437 + 0.537229i \(0.180529\pi\)
\(524\) 15.8577 + 27.4664i 0.692749 + 1.19988i
\(525\) 0 0
\(526\) −1.09622 + 1.89870i −0.0477972 + 0.0827873i
\(527\) 1.40287 + 2.42983i 0.0611098 + 0.105845i
\(528\) −9.46922 + 8.70189i −0.412095 + 0.378701i
\(529\) −3.27836 + 5.67829i −0.142538 + 0.246882i
\(530\) 0.391843 0.678693i 0.0170206 0.0294805i
\(531\) 16.2124 + 11.2831i 0.703558 + 0.489644i
\(532\) 0 0
\(533\) 0.342629 + 0.593452i 0.0148409 + 0.0257052i
\(534\) 11.5632 10.6261i 0.500387 0.459838i
\(535\) 10.9154 0.471916
\(536\) 29.9602 1.29408
\(537\) −2.87712 12.8906i −0.124157 0.556270i
\(538\) 5.15720 + 8.93253i 0.222343 + 0.385109i
\(539\) 0 0
\(540\) −4.34817 + 10.6261i −0.187115 + 0.457276i
\(541\) −15.0681 + 26.0988i −0.647830 + 1.12207i 0.335810 + 0.941930i \(0.390990\pi\)
−0.983640 + 0.180145i \(0.942343\pi\)
\(542\) −2.72362 + 4.71745i −0.116989 + 0.202632i
\(543\) 25.6662 + 8.05220i 1.10144 + 0.345553i
\(544\) −3.23008 5.59466i −0.138488 0.239869i
\(545\) 1.21033 2.09636i 0.0518450 0.0897982i
\(546\) 0 0
\(547\) 7.68070 + 13.3034i 0.328403 + 0.568810i 0.982195 0.187864i \(-0.0601563\pi\)
−0.653792 + 0.756674i \(0.726823\pi\)
\(548\) 9.46800 16.3991i 0.404453 0.700533i
\(549\) −0.185329 0.128980i −0.00790964 0.00550474i
\(550\) −4.90757 8.50016i −0.209260 0.362448i
\(551\) 27.3469 1.16502
\(552\) −4.88221 21.8741i −0.207801 0.931025i
\(553\) 0 0
\(554\) −4.30546 + 7.45728i −0.182921 + 0.316829i
\(555\) −3.34294 1.04877i −0.141900 0.0445179i
\(556\) −1.92423 + 3.33287i −0.0816056 + 0.141345i
\(557\) −11.6412 20.1631i −0.493252 0.854338i 0.506718 0.862112i \(-0.330859\pi\)
−0.999970 + 0.00777438i \(0.997525\pi\)
\(558\) −4.13615 2.87857i −0.175097 0.121859i
\(559\) −2.74531 −0.116114
\(560\) 0 0
\(561\) 9.12397 + 2.86244i 0.385214 + 0.120852i
\(562\) −0.485375 0.840695i −0.0204743 0.0354626i
\(563\) −4.55885 −0.192133 −0.0960663 0.995375i \(-0.530626\pi\)
−0.0960663 + 0.995375i \(0.530626\pi\)
\(564\) 24.2832 + 7.61830i 1.02251 + 0.320788i
\(565\) −0.855964 −0.0360107
\(566\) 11.6896 0.491351
\(567\) 0 0
\(568\) −0.191588 −0.00803885
\(569\) 18.1995 0.762963 0.381482 0.924376i \(-0.375414\pi\)
0.381482 + 0.924376i \(0.375414\pi\)
\(570\) −6.33800 1.98840i −0.265470 0.0832850i
\(571\) −17.0455 −0.713332 −0.356666 0.934232i \(-0.616087\pi\)
−0.356666 + 0.934232i \(0.616087\pi\)
\(572\) 10.5307 + 18.2398i 0.440313 + 0.762644i
\(573\) −24.5126 7.69027i −1.02403 0.321266i
\(574\) 0 0
\(575\) −16.1443 −0.673264
\(576\) 2.10757 + 1.46677i 0.0878155 + 0.0611155i
\(577\) 5.70473 + 9.88088i 0.237491 + 0.411346i 0.959994 0.280022i \(-0.0903417\pi\)
−0.722503 + 0.691368i \(0.757008\pi\)
\(578\) 5.27764 9.14113i 0.219521 0.380221i
\(579\) −27.3803 8.58995i −1.13789 0.356986i
\(580\) 7.52485 13.0334i 0.312452 0.541183i
\(581\) 0 0
\(582\) 1.36657 + 6.12273i 0.0566460 + 0.253795i
\(583\) −4.04549 −0.167547
\(584\) 12.7229 + 22.0368i 0.526479 + 0.911889i
\(585\) 9.66514 + 6.72649i 0.399604 + 0.278106i
\(586\) 0.603332 1.04500i 0.0249234 0.0431686i
\(587\) −2.52544 4.37420i −0.104236 0.180543i 0.809190 0.587548i \(-0.199906\pi\)
−0.913426 + 0.407005i \(0.866573\pi\)
\(588\) 0 0
\(589\) −5.03052 + 8.71312i −0.207279 + 0.359018i
\(590\) 3.14449 + 5.44642i 0.129457 + 0.224226i
\(591\) 6.67232 + 2.09329i 0.274463 + 0.0861064i
\(592\) 1.06882 1.85126i 0.0439283 0.0760861i
\(593\) 9.98892 17.3013i 0.410196 0.710480i −0.584715 0.811239i \(-0.698794\pi\)
0.994911 + 0.100759i \(0.0321271\pi\)
\(594\) −17.0179 + 2.31477i −0.698254 + 0.0949763i
\(595\) 0 0
\(596\) −6.63365 11.4898i −0.271725 0.470641i
\(597\) −9.53873 42.7371i −0.390394 1.74911i
\(598\) −10.0387 −0.410513
\(599\) 4.39321 0.179502 0.0897508 0.995964i \(-0.471393\pi\)
0.0897508 + 0.995964i \(0.471393\pi\)
\(600\) 9.01387 8.28344i 0.367990 0.338170i
\(601\) −12.1778 21.0926i −0.496743 0.860385i 0.503250 0.864141i \(-0.332138\pi\)
−0.999993 + 0.00375637i \(0.998804\pi\)
\(602\) 0 0
\(603\) −30.9955 21.5715i −1.26224 0.878457i
\(604\) −13.6917 + 23.7147i −0.557107 + 0.964937i
\(605\) 9.48476 16.4281i 0.385610 0.667897i
\(606\) 4.39022 4.03446i 0.178340 0.163889i
\(607\) 6.56281 + 11.3671i 0.266376 + 0.461377i 0.967923 0.251246i \(-0.0808403\pi\)
−0.701547 + 0.712623i \(0.747507\pi\)
\(608\) 11.5827 20.0618i 0.469741 0.813615i
\(609\) 0 0
\(610\) −0.0359456 0.0622597i −0.00145540 0.00252082i
\(611\) 13.0510 22.6051i 0.527988 0.914502i
\(612\) −0.439125 + 5.19016i −0.0177506 + 0.209800i
\(613\) −23.2403 40.2534i −0.938667 1.62582i −0.767960 0.640497i \(-0.778728\pi\)
−0.170707 0.985322i \(-0.554605\pi\)
\(614\) −0.713754 −0.0288048
\(615\) 0.585823 + 0.183789i 0.0236227 + 0.00741108i
\(616\) 0 0
\(617\) 14.1948 24.5862i 0.571463 0.989803i −0.424953 0.905215i \(-0.639709\pi\)
0.996416 0.0845873i \(-0.0269572\pi\)
\(618\) 3.59427 + 16.1037i 0.144583 + 0.647786i
\(619\) 15.9606 27.6446i 0.641511 1.11113i −0.343585 0.939122i \(-0.611641\pi\)
0.985096 0.172008i \(-0.0550254\pi\)
\(620\) 2.76843 + 4.79506i 0.111183 + 0.192574i
\(621\) −10.6985 + 26.1452i −0.429317 + 1.04917i
\(622\) 11.3482 0.455023
\(623\) 0 0
\(624\) −5.29004 + 4.86136i −0.211771 + 0.194610i
\(625\) 0.666993 + 1.15527i 0.0266797 + 0.0462106i
\(626\) 5.54939 0.221798
\(627\) 7.46956 + 33.4664i 0.298306 + 1.33652i
\(628\) 9.80244 0.391160
\(629\) −1.58947 −0.0633762
\(630\) 0 0
\(631\) 38.7184 1.54135 0.770677 0.637226i \(-0.219918\pi\)
0.770677 + 0.637226i \(0.219918\pi\)
\(632\) 4.39112 0.174669
\(633\) 9.59675 8.81908i 0.381436 0.350527i
\(634\) 4.38895 0.174307
\(635\) 5.17236 + 8.95878i 0.205259 + 0.355519i
\(636\) −0.480022 2.15068i −0.0190341 0.0852799i
\(637\) 0 0
\(638\) 22.5124 0.891276
\(639\) 0.198209 + 0.137944i 0.00784101 + 0.00545698i
\(640\) −7.81261 13.5318i −0.308821 0.534893i
\(641\) 20.2001 34.9875i 0.797854 1.38192i −0.123157 0.992387i \(-0.539302\pi\)
0.921011 0.389537i \(-0.127365\pi\)
\(642\) −6.54874 + 6.01806i −0.258458 + 0.237514i
\(643\) −6.27355 + 10.8661i −0.247405 + 0.428517i −0.962805 0.270198i \(-0.912911\pi\)
0.715400 + 0.698715i \(0.246244\pi\)
\(644\) 0 0
\(645\) −1.81113 + 1.66437i −0.0713132 + 0.0655344i
\(646\) −3.01352 −0.118565
\(647\) −17.2774 29.9253i −0.679245 1.17649i −0.975209 0.221287i \(-0.928974\pi\)
0.295964 0.955199i \(-0.404359\pi\)
\(648\) −7.44147 20.0870i −0.292328 0.789091i
\(649\) 16.2323 28.1151i 0.637173 1.10362i
\(650\) −2.74164 4.74866i −0.107536 0.186258i
\(651\) 0 0
\(652\) 6.22019 10.7737i 0.243602 0.421930i
\(653\) 11.1472 + 19.3075i 0.436223 + 0.755560i 0.997395 0.0721392i \(-0.0229826\pi\)
−0.561172 + 0.827699i \(0.689649\pi\)
\(654\) 0.429654 + 1.92501i 0.0168008 + 0.0752740i
\(655\) 14.5721 25.2396i 0.569379 0.986194i
\(656\) −0.187302 + 0.324417i −0.00731293 + 0.0126664i
\(657\) 2.70395 31.9589i 0.105491 1.24683i
\(658\) 0 0
\(659\) 3.57493 + 6.19196i 0.139259 + 0.241204i 0.927217 0.374526i \(-0.122194\pi\)
−0.787957 + 0.615730i \(0.788861\pi\)
\(660\) 18.0053 + 5.64876i 0.700857 + 0.219878i
\(661\) −42.9060 −1.66885 −0.834425 0.551122i \(-0.814200\pi\)
−0.834425 + 0.551122i \(0.814200\pi\)
\(662\) −17.9152 −0.696294
\(663\) 5.09716 + 1.59912i 0.197957 + 0.0621046i
\(664\) −17.2221 29.8296i −0.668349 1.15761i
\(665\) 0 0
\(666\) 2.58383 1.21387i 0.100121 0.0470365i
\(667\) 18.5146 32.0683i 0.716889 1.24169i
\(668\) 1.64428 2.84798i 0.0636191 0.110192i
\(669\) 4.89912 + 21.9499i 0.189411 + 0.848632i
\(670\) −6.01177 10.4127i −0.232255 0.402277i
\(671\) −0.185556 + 0.321392i −0.00716331 + 0.0124072i
\(672\) 0 0
\(673\) −18.8270 32.6094i −0.725729 1.25700i −0.958673 0.284510i \(-0.908169\pi\)
0.232944 0.972490i \(-0.425164\pi\)
\(674\) −3.19188 + 5.52850i −0.122947 + 0.212950i
\(675\) −15.2895 + 2.07967i −0.588492 + 0.0800465i
\(676\) −4.19619 7.26801i −0.161392 0.279539i
\(677\) 26.3616 1.01316 0.506580 0.862193i \(-0.330910\pi\)
0.506580 + 0.862193i \(0.330910\pi\)
\(678\) 0.513537 0.471923i 0.0197223 0.0181241i
\(679\) 0 0
\(680\) −1.89871 + 3.28866i −0.0728121 + 0.126114i
\(681\) 36.9417 33.9482i 1.41561 1.30090i
\(682\) −4.14122 + 7.17280i −0.158575 + 0.274661i
\(683\) 1.96588 + 3.40500i 0.0752222 + 0.130289i 0.901183 0.433439i \(-0.142700\pi\)
−0.825961 + 0.563728i \(0.809367\pi\)
\(684\) −16.9052 + 7.94198i −0.646387 + 0.303669i
\(685\) −17.4008 −0.664850
\(686\) 0 0
\(687\) −5.82396 26.0936i −0.222198 0.995531i
\(688\) −0.750378 1.29969i −0.0286079 0.0495503i
\(689\) −2.26004 −0.0861006
\(690\) −6.62271 + 6.08604i −0.252122 + 0.231692i
\(691\) −19.9010 −0.757072 −0.378536 0.925587i \(-0.623572\pi\)
−0.378536 + 0.925587i \(0.623572\pi\)
\(692\) −28.3585 −1.07803
\(693\) 0 0
\(694\) −12.5373 −0.475910
\(695\) 3.53645 0.134145
\(696\) 6.11653 + 27.4044i 0.231847 + 1.03876i
\(697\) 0.278541 0.0105505
\(698\) 10.0913 + 17.4787i 0.381963 + 0.661579i
\(699\) 6.30838 5.79718i 0.238605 0.219270i
\(700\) 0 0
\(701\) 43.7908 1.65396 0.826979 0.562234i \(-0.190058\pi\)
0.826979 + 0.562234i \(0.190058\pi\)
\(702\) −9.50716 + 1.29316i −0.358825 + 0.0488072i
\(703\) −2.84983 4.93604i −0.107483 0.186166i
\(704\) 2.11016 3.65490i 0.0795295 0.137749i
\(705\) −5.09449 22.8252i −0.191870 0.859648i
\(706\) 2.09792 3.63370i 0.0789561 0.136756i
\(707\) 0 0
\(708\) 16.8727 + 5.29343i 0.634115 + 0.198939i
\(709\) 44.6344 1.67628 0.838139 0.545457i \(-0.183644\pi\)
0.838139 + 0.545457i \(0.183644\pi\)
\(710\) 0.0384437 + 0.0665865i 0.00144277 + 0.00249895i
\(711\) −4.54286 3.16162i −0.170371 0.118570i
\(712\) 16.0966 27.8801i 0.603244 1.04485i
\(713\) 6.81163 + 11.7981i 0.255097 + 0.441842i
\(714\) 0 0
\(715\) 9.67699 16.7610i 0.361899 0.626827i
\(716\) −5.91227 10.2403i −0.220952 0.382700i
\(717\) −16.6234 + 15.2764i −0.620814 + 0.570506i
\(718\) −3.41705 + 5.91851i −0.127523 + 0.220877i
\(719\) 19.5096 33.7917i 0.727586 1.26022i −0.230315 0.973116i \(-0.573976\pi\)
0.957901 0.287100i \(-0.0926912\pi\)
\(720\) −0.542692 + 6.41425i −0.0202249 + 0.239045i
\(721\) 0 0
\(722\) 0.965081 + 1.67157i 0.0359166 + 0.0622094i
\(723\) −18.5974 + 17.0904i −0.691645 + 0.635598i
\(724\) 24.0825 0.895019
\(725\) 20.2259 0.751171
\(726\) 3.36698 + 15.0853i 0.124960 + 0.559869i
\(727\) 11.2554 + 19.4949i 0.417439 + 0.723025i 0.995681 0.0928402i \(-0.0295946\pi\)
−0.578242 + 0.815865i \(0.696261\pi\)
\(728\) 0 0
\(729\) −6.76407 + 26.1390i −0.250521 + 0.968111i
\(730\) 5.10593 8.84373i 0.188979 0.327321i
\(731\) −0.557951 + 0.966399i −0.0206366 + 0.0357436i
\(732\) −0.192877 0.0605107i −0.00712894 0.00223654i
\(733\) −0.448519 0.776858i −0.0165664 0.0286939i 0.857623 0.514278i \(-0.171940\pi\)
−0.874190 + 0.485584i \(0.838607\pi\)
\(734\) −9.60441 + 16.6353i −0.354505 + 0.614021i
\(735\) 0 0
\(736\) −15.6837 27.1649i −0.578108 1.00131i
\(737\) −31.0335 + 53.7517i −1.14314 + 1.97997i
\(738\) −0.452795 + 0.212720i −0.0166676 + 0.00783035i
\(739\) 1.79032 + 3.10092i 0.0658578 + 0.114069i 0.897074 0.441880i \(-0.145688\pi\)
−0.831216 + 0.555949i \(0.812355\pi\)
\(740\) −3.13667 −0.115306
\(741\) 4.17291 + 18.6962i 0.153296 + 0.686823i
\(742\) 0 0
\(743\) −24.7964 + 42.9486i −0.909691 + 1.57563i −0.0951977 + 0.995458i \(0.530348\pi\)
−0.814493 + 0.580173i \(0.802985\pi\)
\(744\) −9.85660 3.09228i −0.361360 0.113369i
\(745\) −6.09583 + 10.5583i −0.223334 + 0.386826i
\(746\) 5.38726 + 9.33101i 0.197242 + 0.341633i
\(747\) −3.66015 + 43.2604i −0.133918 + 1.58282i
\(748\) 8.56098 0.313020
\(749\) 0 0
\(750\) −12.5804 3.94682i −0.459373 0.144118i
\(751\) 21.4515 + 37.1551i 0.782776 + 1.35581i 0.930319 + 0.366752i \(0.119530\pi\)
−0.147543 + 0.989056i \(0.547136\pi\)
\(752\) 14.2690 0.520337
\(753\) −23.2550 7.29574i −0.847461 0.265871i
\(754\) 12.5767 0.458016
\(755\) 25.1633 0.915786
\(756\) 0 0
\(757\) 13.8029 0.501677 0.250838 0.968029i \(-0.419294\pi\)
0.250838 + 0.968029i \(0.419294\pi\)
\(758\) −0.683021 −0.0248084
\(759\) 44.3015 + 13.8986i 1.60804 + 0.504487i
\(760\) −13.6171 −0.493945
\(761\) 20.3599 + 35.2643i 0.738044 + 1.27833i 0.953375 + 0.301789i \(0.0975839\pi\)
−0.215330 + 0.976541i \(0.569083\pi\)
\(762\) −8.04245 2.52314i −0.291347 0.0914036i
\(763\) 0 0
\(764\) −23.0001 −0.832113
\(765\) 4.33216 2.03523i 0.156630 0.0735838i
\(766\) −3.88342 6.72627i −0.140313 0.243030i
\(767\) 9.06826 15.7067i 0.327436 0.567135i
\(768\) 14.9768 + 4.69862i 0.540428 + 0.169547i
\(769\) −5.57381 + 9.65413i −0.200997 + 0.348137i −0.948850 0.315728i \(-0.897751\pi\)
0.747853 + 0.663864i \(0.231085\pi\)
\(770\) 0 0
\(771\) 3.15506 + 14.1359i 0.113627 + 0.509090i
\(772\) −25.6908 −0.924633
\(773\) 0.462831 + 0.801647i 0.0166469 + 0.0288332i 0.874229 0.485514i \(-0.161368\pi\)
−0.857582 + 0.514347i \(0.828034\pi\)
\(774\) 0.168967 1.99708i 0.00607341 0.0717835i
\(775\) −3.72061 + 6.44428i −0.133648 + 0.231485i
\(776\) 6.43012 + 11.1373i 0.230828 + 0.399806i
\(777\) 0 0
\(778\) −5.97049 + 10.3412i −0.214052 + 0.370750i
\(779\) 0.499408 + 0.865001i 0.0178932 + 0.0309919i
\(780\) 10.0588 + 3.15571i 0.360162 + 0.112993i