Properties

Label 441.2.h.f.214.2
Level $441$
Weight $2$
Character 441.214
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 214.2
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.f.373.2

$q$-expansion

\(f(q)\) \(=\) \(q-1.84124 q^{2} +(-1.39291 - 1.02946i) q^{3} +1.39017 q^{4} +(0.667377 - 1.15593i) q^{5} +(2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(0.880416 + 2.86790i) q^{9} +O(q^{10})\) \(q-1.84124 q^{2} +(-1.39291 - 1.02946i) q^{3} +1.39017 q^{4} +(0.667377 - 1.15593i) q^{5} +(2.56469 + 1.89549i) q^{6} +1.12285 q^{8} +(0.880416 + 2.86790i) q^{9} +(-1.22880 + 2.12835i) q^{10} +(-0.756508 - 1.31031i) q^{11} +(-1.93638 - 1.43112i) q^{12} +(2.58800 + 4.48254i) q^{13} +(-2.11958 + 0.923072i) q^{15} -4.84777 q^{16} +(-0.774463 + 1.34141i) q^{17} +(-1.62106 - 5.28050i) q^{18} +(1.25211 + 2.16872i) q^{19} +(0.927765 - 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(3.68039 - 6.37463i) q^{23} +(-1.56403 - 1.15593i) q^{24} +(1.60922 + 2.78725i) q^{25} +(-4.76513 - 8.25344i) q^{26} +(1.72605 - 4.90110i) q^{27} +(-0.0309713 + 0.0536439i) q^{29} +(3.90267 - 1.69960i) q^{30} +3.84777 q^{31} +6.68021 q^{32} +(-0.295165 + 2.60395i) q^{33} +(1.42597 - 2.46986i) q^{34} +(1.22392 + 3.98687i) q^{36} +(-0.281608 - 0.487760i) q^{37} +(-2.30543 - 3.99313i) q^{38} +(1.00975 - 8.90804i) q^{39} +(0.749363 - 1.29794i) q^{40} +(-4.51188 - 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +(-1.05167 - 1.82155i) q^{44} +(3.90267 + 0.896273i) q^{45} +(-6.77649 + 11.7372i) q^{46} +9.51851 q^{47} +(6.75252 + 4.99060i) q^{48} +(-2.96296 - 5.13199i) q^{50} +(2.45969 - 1.07119i) q^{51} +(3.59775 + 6.23148i) q^{52} +(0.755374 - 1.30835i) q^{53} +(-3.17808 + 9.02410i) q^{54} -2.01950 q^{55} +(0.488532 - 4.30983i) q^{57} +(0.0570257 - 0.0987714i) q^{58} +8.44331 q^{59} +(-2.94658 + 1.28322i) q^{60} -3.23917 q^{61} -7.08467 q^{62} -2.60434 q^{64} +6.90868 q^{65} +(0.543469 - 4.79449i) q^{66} +6.93339 q^{67} +(-1.07663 + 1.86478i) q^{68} +(-11.6889 + 5.09048i) q^{69} -12.3304 q^{71} +(0.988574 + 3.22022i) q^{72} +(1.37936 - 2.38912i) q^{73} +(0.518508 + 0.898083i) q^{74} +(0.627864 - 5.53902i) q^{75} +(1.74064 + 3.01488i) q^{76} +(-1.85920 + 16.4018i) q^{78} -5.91938 q^{79} +(-3.23529 + 5.60368i) q^{80} +(-7.44974 + 5.04989i) q^{81} +(8.30746 + 14.3889i) q^{82} +(-2.80111 + 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-9.39010 + 16.2641i) q^{86} +(0.0983648 - 0.0428375i) q^{87} +(-0.849444 - 1.47128i) q^{88} +(-0.703287 - 1.21813i) q^{89} +(-7.18575 - 1.65025i) q^{90} +(5.11636 - 8.86180i) q^{92} +(-5.35961 - 3.96113i) q^{93} -17.5259 q^{94} +3.34251 q^{95} +(-9.30496 - 6.87703i) q^{96} +(6.09713 - 10.5605i) q^{97} +(3.09180 - 3.32321i) 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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.84124 −1.30195 −0.650977 0.759098i \(-0.725641\pi\)
−0.650977 + 0.759098i \(0.725641\pi\)
\(3\) −1.39291 1.02946i −0.804199 0.594360i
\(4\) 1.39017 0.695084
\(5\) 0.667377 1.15593i 0.298460 0.516948i −0.677324 0.735685i \(-0.736860\pi\)
0.975784 + 0.218737i \(0.0701937\pi\)
\(6\) 2.56469 + 1.89549i 1.04703 + 0.773830i
\(7\) 0 0
\(8\) 1.12285 0.396987
\(9\) 0.880416 + 2.86790i 0.293472 + 0.955968i
\(10\) −1.22880 + 2.12835i −0.388581 + 0.673042i
\(11\) −0.756508 1.31031i −0.228096 0.395073i 0.729148 0.684356i \(-0.239917\pi\)
−0.957244 + 0.289283i \(0.906583\pi\)
\(12\) −1.93638 1.43112i −0.558986 0.413130i
\(13\) 2.58800 + 4.48254i 0.717781 + 1.24323i 0.961877 + 0.273482i \(0.0881755\pi\)
−0.244096 + 0.969751i \(0.578491\pi\)
\(14\) 0 0
\(15\) −2.11958 + 0.923072i −0.547274 + 0.238336i
\(16\) −4.84777 −1.21194
\(17\) −0.774463 + 1.34141i −0.187835 + 0.325340i −0.944528 0.328430i \(-0.893480\pi\)
0.756693 + 0.653770i \(0.226814\pi\)
\(18\) −1.62106 5.28050i −0.382087 1.24463i
\(19\) 1.25211 + 2.16872i 0.287254 + 0.497538i 0.973153 0.230158i \(-0.0739244\pi\)
−0.685900 + 0.727696i \(0.740591\pi\)
\(20\) 0.927765 1.60694i 0.207455 0.359322i
\(21\) 0 0
\(22\) 1.39291 + 2.41260i 0.296970 + 0.514367i
\(23\) 3.68039 6.37463i 0.767415 1.32920i −0.171545 0.985176i \(-0.554876\pi\)
0.938960 0.344025i \(-0.111791\pi\)
\(24\) −1.56403 1.15593i −0.319257 0.235953i
\(25\) 1.60922 + 2.78725i 0.321843 + 0.557449i
\(26\) −4.76513 8.25344i −0.934518 1.61863i
\(27\) 1.72605 4.90110i 0.332179 0.943216i
\(28\) 0 0
\(29\) −0.0309713 + 0.0536439i −0.00575123 + 0.00996143i −0.868887 0.495011i \(-0.835164\pi\)
0.863135 + 0.504972i \(0.168497\pi\)
\(30\) 3.90267 1.69960i 0.712526 0.310303i
\(31\) 3.84777 0.691080 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(32\) 6.68021 1.18091
\(33\) −0.295165 + 2.60395i −0.0513816 + 0.453289i
\(34\) 1.42597 2.46986i 0.244552 0.423577i
\(35\) 0 0
\(36\) 1.22392 + 3.98687i 0.203987 + 0.664478i
\(37\) −0.281608 0.487760i −0.0462961 0.0801872i 0.841949 0.539557i \(-0.181408\pi\)
−0.888245 + 0.459370i \(0.848075\pi\)
\(38\) −2.30543 3.99313i −0.373991 0.647771i
\(39\) 1.00975 8.90804i 0.161690 1.42643i
\(40\) 0.749363 1.29794i 0.118485 0.205222i
\(41\) −4.51188 7.81481i −0.704638 1.22047i −0.966822 0.255450i \(-0.917776\pi\)
0.262185 0.965018i \(-0.415557\pi\)
\(42\) 0 0
\(43\) 5.09988 8.83325i 0.777724 1.34706i −0.155526 0.987832i \(-0.549707\pi\)
0.933251 0.359226i \(-0.116959\pi\)
\(44\) −1.05167 1.82155i −0.158546 0.274609i
\(45\) 3.90267 + 0.896273i 0.581775 + 0.133608i
\(46\) −6.77649 + 11.7372i −0.999139 + 1.73056i
\(47\) 9.51851 1.38842 0.694209 0.719774i \(-0.255755\pi\)
0.694209 + 0.719774i \(0.255755\pi\)
\(48\) 6.75252 + 4.99060i 0.974643 + 0.720330i
\(49\) 0 0
\(50\) −2.96296 5.13199i −0.419025 0.725773i
\(51\) 2.45969 1.07119i 0.344426 0.149996i
\(52\) 3.59775 + 6.23148i 0.498918 + 0.864151i
\(53\) 0.755374 1.30835i 0.103759 0.179715i −0.809472 0.587159i \(-0.800246\pi\)
0.913230 + 0.407444i \(0.133580\pi\)
\(54\) −3.17808 + 9.02410i −0.432482 + 1.22802i
\(55\) −2.01950 −0.272310
\(56\) 0 0
\(57\) 0.488532 4.30983i 0.0647077 0.570851i
\(58\) 0.0570257 0.0987714i 0.00748784 0.0129693i
\(59\) 8.44331 1.09923 0.549613 0.835419i \(-0.314775\pi\)
0.549613 + 0.835419i \(0.314775\pi\)
\(60\) −2.94658 + 1.28322i −0.380401 + 0.165664i
\(61\) −3.23917 −0.414733 −0.207367 0.978263i \(-0.566489\pi\)
−0.207367 + 0.978263i \(0.566489\pi\)
\(62\) −7.08467 −0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) 6.90868 0.856916
\(66\) 0.543469 4.79449i 0.0668964 0.590161i
\(67\) 6.93339 0.847049 0.423524 0.905885i \(-0.360793\pi\)
0.423524 + 0.905885i \(0.360793\pi\)
\(68\) −1.07663 + 1.86478i −0.130561 + 0.226138i
\(69\) −11.6889 + 5.09048i −1.40718 + 0.612822i
\(70\) 0 0
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) 0.988574 + 3.22022i 0.116505 + 0.379507i
\(73\) 1.37936 2.38912i 0.161442 0.279625i −0.773944 0.633254i \(-0.781719\pi\)
0.935386 + 0.353629i \(0.115052\pi\)
\(74\) 0.518508 + 0.898083i 0.0602754 + 0.104400i
\(75\) 0.627864 5.53902i 0.0724995 0.639591i
\(76\) 1.74064 + 3.01488i 0.199665 + 0.345830i
\(77\) 0 0
\(78\) −1.85920 + 16.4018i −0.210512 + 1.85714i
\(79\) −5.91938 −0.665982 −0.332991 0.942930i \(-0.608058\pi\)
−0.332991 + 0.942930i \(0.608058\pi\)
\(80\) −3.23529 + 5.60368i −0.361716 + 0.626511i
\(81\) −7.44974 + 5.04989i −0.827749 + 0.561099i
\(82\) 8.30746 + 14.3889i 0.917406 + 1.58899i
\(83\) −2.80111 + 4.85167i −0.307462 + 0.532540i −0.977806 0.209510i \(-0.932813\pi\)
0.670344 + 0.742050i \(0.266146\pi\)
\(84\) 0 0
\(85\) 1.03372 + 1.79045i 0.112122 + 0.194202i
\(86\) −9.39010 + 16.2641i −1.01256 + 1.75381i
\(87\) 0.0983648 0.0428375i 0.0105458 0.00459267i
\(88\) −0.849444 1.47128i −0.0905511 0.156839i
\(89\) −0.703287 1.21813i −0.0745483 0.129121i 0.826341 0.563169i \(-0.190418\pi\)
−0.900890 + 0.434048i \(0.857085\pi\)
\(90\) −7.18575 1.65025i −0.757444 0.173952i
\(91\) 0 0
\(92\) 5.11636 8.86180i 0.533418 0.923906i
\(93\) −5.35961 3.96113i −0.555766 0.410750i
\(94\) −17.5259 −1.80765
\(95\) 3.34251 0.342935
\(96\) −9.30496 6.87703i −0.949683 0.701884i
\(97\) 6.09713 10.5605i 0.619070 1.07226i −0.370586 0.928798i \(-0.620843\pi\)
0.989656 0.143462i \(-0.0458236\pi\)
\(98\) 0 0
\(99\) 3.09180 3.32321i 0.310738 0.333995i
\(100\) 2.23708 + 3.87474i 0.223708 + 0.387474i
\(101\) 0.559336 + 0.968798i 0.0556560 + 0.0963990i 0.892511 0.451025i \(-0.148942\pi\)
−0.836855 + 0.547425i \(0.815608\pi\)
\(102\) −4.52888 + 1.97231i −0.448426 + 0.195288i
\(103\) 0.965224 1.67182i 0.0951063 0.164729i −0.814547 0.580098i \(-0.803014\pi\)
0.909653 + 0.415369i \(0.136348\pi\)
\(104\) 2.90593 + 5.03322i 0.284950 + 0.493548i
\(105\) 0 0
\(106\) −1.39082 + 2.40898i −0.135089 + 0.233981i
\(107\) 2.88969 + 5.00509i 0.279357 + 0.483860i 0.971225 0.238163i \(-0.0765454\pi\)
−0.691868 + 0.722024i \(0.743212\pi\)
\(108\) 2.39951 6.81334i 0.230892 0.655614i
\(109\) −4.12106 + 7.13788i −0.394726 + 0.683685i −0.993066 0.117557i \(-0.962494\pi\)
0.598340 + 0.801242i \(0.295827\pi\)
\(110\) 3.71839 0.354535
\(111\) −0.109874 + 0.969312i −0.0104288 + 0.0920030i
\(112\) 0 0
\(113\) 7.25105 + 12.5592i 0.682121 + 1.18147i 0.974332 + 0.225115i \(0.0722758\pi\)
−0.292211 + 0.956354i \(0.594391\pi\)
\(114\) −0.899505 + 7.93544i −0.0842464 + 0.743222i
\(115\) −4.91242 8.50856i −0.458085 0.793427i
\(116\) −0.0430553 + 0.0745740i −0.00399759 + 0.00692403i
\(117\) −10.5770 + 11.3686i −0.977843 + 1.05103i
\(118\) −15.5462 −1.43114
\(119\) 0 0
\(120\) −2.37997 + 1.03647i −0.217261 + 0.0946164i
\(121\) 4.35539 7.54376i 0.395945 0.685796i
\(122\) 5.96409 0.539963
\(123\) −1.76039 + 15.5302i −0.158729 + 1.40031i
\(124\) 5.34904 0.480358
\(125\) 10.9696 0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) −8.56521 −0.757065
\(129\) −16.1972 + 7.05382i −1.42608 + 0.621054i
\(130\) −12.7205 −1.11566
\(131\) −1.00673 + 1.74371i −0.0879585 + 0.152349i −0.906648 0.421888i \(-0.861368\pi\)
0.818690 + 0.574236i \(0.194701\pi\)
\(132\) −0.410328 + 3.61992i −0.0357145 + 0.315074i
\(133\) 0 0
\(134\) −12.7660 −1.10282
\(135\) −4.51340 5.26608i −0.388451 0.453232i
\(136\) −0.869605 + 1.50620i −0.0745680 + 0.129156i
\(137\) −1.10870 1.92032i −0.0947225 0.164064i 0.814770 0.579784i \(-0.196863\pi\)
−0.909493 + 0.415720i \(0.863530\pi\)
\(138\) 21.5221 9.37280i 1.83208 0.797865i
\(139\) −0.377669 0.654143i −0.0320335 0.0554836i 0.849564 0.527485i \(-0.176865\pi\)
−0.881598 + 0.472002i \(0.843532\pi\)
\(140\) 0 0
\(141\) −13.2585 9.79894i −1.11656 0.825220i
\(142\) 22.7032 1.90521
\(143\) 3.91568 6.78216i 0.327446 0.567153i
\(144\) −4.26805 13.9029i −0.355671 1.15858i
\(145\) 0.0413391 + 0.0716014i 0.00343303 + 0.00594618i
\(146\) −2.53973 + 4.39894i −0.210189 + 0.364059i
\(147\) 0 0
\(148\) −0.391482 0.678068i −0.0321797 0.0557368i
\(149\) −3.29249 + 5.70277i −0.269732 + 0.467189i −0.968792 0.247873i \(-0.920268\pi\)
0.699061 + 0.715062i \(0.253602\pi\)
\(150\) −1.15605 + 10.1987i −0.0943909 + 0.832718i
\(151\) −6.33356 10.9700i −0.515417 0.892729i −0.999840 0.0178950i \(-0.994304\pi\)
0.484422 0.874834i \(-0.339030\pi\)
\(152\) 1.40593 + 2.43514i 0.114036 + 0.197516i
\(153\) −4.52888 1.04009i −0.366138 0.0840861i
\(154\) 0 0
\(155\) 2.56791 4.44775i 0.206260 0.357252i
\(156\) 1.40372 12.3837i 0.112388 0.991487i
\(157\) 17.3074 1.38128 0.690642 0.723197i \(-0.257328\pi\)
0.690642 + 0.723197i \(0.257328\pi\)
\(158\) 10.8990 0.867078
\(159\) −2.39906 + 1.04478i −0.190258 + 0.0828567i
\(160\) 4.45822 7.72186i 0.352453 0.610467i
\(161\) 0 0
\(162\) 13.7168 9.29807i 1.07769 0.730525i
\(163\) 6.10963 + 10.5822i 0.478543 + 0.828861i 0.999697 0.0246014i \(-0.00783167\pi\)
−0.521154 + 0.853463i \(0.674498\pi\)
\(164\) −6.27227 10.8639i −0.489782 0.848327i
\(165\) 2.81299 + 2.07900i 0.218991 + 0.161850i
\(166\) 5.15752 8.93309i 0.400301 0.693342i
\(167\) −1.76248 3.05270i −0.136385 0.236225i 0.789741 0.613440i \(-0.210215\pi\)
−0.926126 + 0.377215i \(0.876882\pi\)
\(168\) 0 0
\(169\) −6.89546 + 11.9433i −0.530420 + 0.918714i
\(170\) −1.90332 3.29665i −0.145978 0.252842i
\(171\) −5.11729 + 5.50030i −0.391329 + 0.420618i
\(172\) 7.08968 12.2797i 0.540583 0.936318i
\(173\) −10.1409 −0.770999 −0.385500 0.922708i \(-0.625971\pi\)
−0.385500 + 0.922708i \(0.625971\pi\)
\(174\) −0.181113 + 0.0788742i −0.0137302 + 0.00597944i
\(175\) 0 0
\(176\) 3.66738 + 6.35208i 0.276439 + 0.478806i
\(177\) −11.7608 8.69207i −0.883996 0.653336i
\(178\) 1.29492 + 2.24287i 0.0970584 + 0.168110i
\(179\) 0.850579 1.47325i 0.0635752 0.110116i −0.832486 0.554046i \(-0.813083\pi\)
0.896061 + 0.443931i \(0.146416\pi\)
\(180\) 5.42536 + 1.24597i 0.404382 + 0.0928690i
\(181\) 16.9941 1.26316 0.631581 0.775310i \(-0.282406\pi\)
0.631581 + 0.775310i \(0.282406\pi\)
\(182\) 0 0
\(183\) 4.51188 + 3.33460i 0.333528 + 0.246501i
\(184\) 4.13252 7.15774i 0.304654 0.527676i
\(185\) −0.751755 −0.0552701
\(186\) 9.86833 + 7.29340i 0.723581 + 0.534778i
\(187\) 2.34355 0.171377
\(188\) 13.2323 0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) 22.6939 1.64208 0.821038 0.570873i \(-0.193395\pi\)
0.821038 + 0.570873i \(0.193395\pi\)
\(192\) 3.62762 + 2.68107i 0.261801 + 0.193490i
\(193\) 6.18698 0.445348 0.222674 0.974893i \(-0.428521\pi\)
0.222674 + 0.974893i \(0.428521\pi\)
\(194\) −11.2263 + 19.4445i −0.806001 + 1.39603i
\(195\) −9.62319 7.11222i −0.689131 0.509317i
\(196\) 0 0
\(197\) 9.77010 0.696091 0.348045 0.937478i \(-0.386846\pi\)
0.348045 + 0.937478i \(0.386846\pi\)
\(198\) −5.69275 + 6.11883i −0.404566 + 0.434846i
\(199\) 4.33973 7.51664i 0.307636 0.532840i −0.670209 0.742172i \(-0.733796\pi\)
0.977845 + 0.209332i \(0.0671289\pi\)
\(200\) 1.80691 + 3.12965i 0.127768 + 0.221300i
\(201\) −9.65762 7.13767i −0.681196 0.503452i
\(202\) −1.02987 1.78379i −0.0724615 0.125507i
\(203\) 0 0
\(204\) 3.41938 1.48913i 0.239405 0.104260i
\(205\) −12.0445 −0.841224
\(206\) −1.77721 + 3.07822i −0.123824 + 0.214470i
\(207\) 21.5221 + 4.94269i 1.49589 + 0.343541i
\(208\) −12.5460 21.7303i −0.869909 1.50673i
\(209\) 1.89446 3.28130i 0.131043 0.226973i
\(210\) 0 0
\(211\) −2.84219 4.92283i −0.195665 0.338901i 0.751453 0.659786i \(-0.229353\pi\)
−0.947118 + 0.320885i \(0.896020\pi\)
\(212\) 1.05010 1.81882i 0.0721209 0.124917i
\(213\) 17.1751 + 12.6936i 1.17682 + 0.869754i
\(214\) −5.32062 9.21558i −0.363710 0.629964i
\(215\) −6.80708 11.7902i −0.464239 0.804086i
\(216\) 1.93810 5.50319i 0.131871 0.374445i
\(217\) 0 0
\(218\) 7.58786 13.1426i 0.513915 0.890126i
\(219\) −4.38083 + 1.90784i −0.296029 + 0.128920i
\(220\) −2.80745 −0.189278
\(221\) −8.01723 −0.539298
\(222\) 0.202305 1.78474i 0.0135778 0.119784i
\(223\) −5.86133 + 10.1521i −0.392503 + 0.679836i −0.992779 0.119957i \(-0.961724\pi\)
0.600276 + 0.799793i \(0.295058\pi\)
\(224\) 0 0
\(225\) −6.57677 + 7.06901i −0.438451 + 0.471267i
\(226\) −13.3509 23.1245i −0.888091 1.53822i
\(227\) 5.59154 + 9.68482i 0.371123 + 0.642804i 0.989739 0.142890i \(-0.0456394\pi\)
−0.618615 + 0.785694i \(0.712306\pi\)
\(228\) 0.679141 5.99139i 0.0449772 0.396790i
\(229\) −4.82824 + 8.36275i −0.319059 + 0.552626i −0.980292 0.197554i \(-0.936700\pi\)
0.661233 + 0.750181i \(0.270033\pi\)
\(230\) 9.04494 + 15.6663i 0.596406 + 1.03301i
\(231\) 0 0
\(232\) −0.0347761 + 0.0602340i −0.00228317 + 0.00395456i
\(233\) −9.64492 16.7055i −0.631860 1.09441i −0.987171 0.159666i \(-0.948958\pi\)
0.355311 0.934748i \(-0.384375\pi\)
\(234\) 19.4748 20.9324i 1.27311 1.36839i
\(235\) 6.35243 11.0027i 0.414387 0.717739i
\(236\) 11.7376 0.764054
\(237\) 8.24519 + 6.09378i 0.535582 + 0.395833i
\(238\) 0 0
\(239\) −0.194641 0.337128i −0.0125903 0.0218070i 0.859662 0.510864i \(-0.170674\pi\)
−0.872252 + 0.489057i \(0.837341\pi\)
\(240\) 10.2753 4.47484i 0.663265 0.288850i
\(241\) 5.31807 + 9.21117i 0.342567 + 0.593344i 0.984909 0.173075i \(-0.0553703\pi\)
−0.642342 + 0.766419i \(0.722037\pi\)
\(242\) −8.01932 + 13.8899i −0.515502 + 0.892875i
\(243\) 15.5755 + 0.635158i 0.999170 + 0.0407454i
\(244\) −4.50299 −0.288274
\(245\) 0 0
\(246\) 3.24130 28.5948i 0.206658 1.82314i
\(247\) −6.48091 + 11.2253i −0.412370 + 0.714247i
\(248\) 4.32046 0.274350
\(249\) 8.89631 3.87431i 0.563781 0.245525i
\(250\) −20.1976 −1.27741
\(251\) 3.26628 0.206166 0.103083 0.994673i \(-0.467129\pi\)
0.103083 + 0.994673i \(0.467129\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) −15.6506 −0.982007
\(255\) 0.403323 3.55812i 0.0252570 0.222818i
\(256\) 20.9793 1.31121
\(257\) −2.34787 + 4.06663i −0.146456 + 0.253669i −0.929915 0.367774i \(-0.880120\pi\)
0.783459 + 0.621443i \(0.213453\pi\)
\(258\) 29.8229 12.9878i 1.85669 0.808584i
\(259\) 0 0
\(260\) 9.60421 0.595628
\(261\) −0.181113 0.0415939i −0.0112106 0.00257459i
\(262\) 1.85363 3.21059i 0.114518 0.198351i
\(263\) −9.77491 16.9306i −0.602747 1.04399i −0.992403 0.123028i \(-0.960740\pi\)
0.389656 0.920960i \(-0.372594\pi\)
\(264\) −0.331425 + 2.92384i −0.0203978 + 0.179950i
\(265\) −1.00824 1.74632i −0.0619355 0.107276i
\(266\) 0 0
\(267\) −0.274400 + 2.42076i −0.0167930 + 0.148148i
\(268\) 9.63858 0.588770
\(269\) −7.88365 + 13.6549i −0.480675 + 0.832553i −0.999754 0.0221730i \(-0.992942\pi\)
0.519079 + 0.854726i \(0.326275\pi\)
\(270\) 8.31025 + 9.69611i 0.505746 + 0.590087i
\(271\) −7.39882 12.8151i −0.449446 0.778464i 0.548904 0.835886i \(-0.315045\pi\)
−0.998350 + 0.0574218i \(0.981712\pi\)
\(272\) 3.75442 6.50285i 0.227645 0.394293i
\(273\) 0 0
\(274\) 2.04138 + 3.53578i 0.123324 + 0.213604i
\(275\) 2.43477 4.21715i 0.146822 0.254304i
\(276\) −16.2495 + 7.07662i −0.978107 + 0.425962i
\(277\) 3.72561 + 6.45295i 0.223850 + 0.387720i 0.955974 0.293452i \(-0.0948040\pi\)
−0.732124 + 0.681172i \(0.761471\pi\)
\(278\) 0.695380 + 1.20443i 0.0417061 + 0.0722371i
\(279\) 3.38764 + 11.0350i 0.202812 + 0.660650i
\(280\) 0 0
\(281\) −12.9938 + 22.5060i −0.775146 + 1.34259i 0.159566 + 0.987187i \(0.448991\pi\)
−0.934712 + 0.355406i \(0.884343\pi\)
\(282\) 24.4120 + 18.0422i 1.45371 + 1.07440i
\(283\) −18.7554 −1.11489 −0.557445 0.830214i \(-0.688218\pi\)
−0.557445 + 0.830214i \(0.688218\pi\)
\(284\) −17.1413 −1.01715
\(285\) −4.65583 3.44099i −0.275788 0.203827i
\(286\) −7.20971 + 12.4876i −0.426319 + 0.738406i
\(287\) 0 0
\(288\) 5.88136 + 19.1582i 0.346563 + 1.12891i
\(289\) 7.30041 + 12.6447i 0.429436 + 0.743805i
\(290\) −0.0761152 0.131835i −0.00446964 0.00774165i
\(291\) −19.3645 + 8.43316i −1.13516 + 0.494360i
\(292\) 1.91754 3.32127i 0.112215 0.194363i
\(293\) 1.23089 + 2.13196i 0.0719093 + 0.124551i 0.899738 0.436430i \(-0.143757\pi\)
−0.827829 + 0.560981i \(0.810424\pi\)
\(294\) 0 0
\(295\) 5.63487 9.75988i 0.328075 0.568242i
\(296\) −0.316203 0.547680i −0.0183790 0.0318333i
\(297\) −7.72773 + 1.44605i −0.448408 + 0.0839083i
\(298\) 6.06227 10.5002i 0.351178 0.608258i
\(299\) 38.0994 2.20334
\(300\) 0.872835 7.70016i 0.0503932 0.444569i
\(301\) 0 0
\(302\) 11.6616 + 20.1985i 0.671050 + 1.16229i
\(303\) 0.218235 1.92527i 0.0125372 0.110604i
\(304\) −6.06994 10.5134i −0.348135 0.602987i
\(305\) −2.16175 + 3.74425i −0.123781 + 0.214395i
\(306\) 8.33876 + 1.91505i 0.476695 + 0.109476i
\(307\) 4.66277 0.266118 0.133059 0.991108i \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 0 0
\(309\) −3.06555 + 1.33503i −0.174393 + 0.0759475i
\(310\) −4.72814 + 8.18938i −0.268541 + 0.465126i
\(311\) −27.4821 −1.55837 −0.779183 0.626797i \(-0.784366\pi\)
−0.779183 + 0.626797i \(0.784366\pi\)
\(312\) 1.13380 10.0024i 0.0641887 0.566273i
\(313\) −5.49332 −0.310501 −0.155250 0.987875i \(-0.549618\pi\)
−0.155250 + 0.987875i \(0.549618\pi\)
\(314\) −31.8671 −1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) 9.87758 0.554780 0.277390 0.960757i \(-0.410531\pi\)
0.277390 + 0.960757i \(0.410531\pi\)
\(318\) 4.41725 1.92370i 0.247707 0.107876i
\(319\) 0.0937203 0.00524733
\(320\) −1.73808 + 3.01044i −0.0971614 + 0.168288i
\(321\) 1.12746 9.94649i 0.0629288 0.555159i
\(322\) 0 0
\(323\) −3.87885 −0.215825
\(324\) −10.3564 + 7.02020i −0.575354 + 0.390011i
\(325\) −8.32930 + 14.4268i −0.462026 + 0.800253i
\(326\) −11.2493 19.4844i −0.623041 1.07914i
\(327\) 13.0885 5.69998i 0.723793 0.315209i
\(328\) −5.06616 8.77485i −0.279732 0.484510i
\(329\) 0 0
\(330\) −5.17940 3.82794i −0.285116 0.210721i
\(331\) −20.6942 −1.13746 −0.568729 0.822525i \(-0.692565\pi\)
−0.568729 + 0.822525i \(0.692565\pi\)
\(332\) −3.89401 + 6.74463i −0.213712 + 0.370160i
\(333\) 1.15092 1.23706i 0.0630698 0.0677903i
\(334\) 3.24514 + 5.62076i 0.177566 + 0.307554i
\(335\) 4.62718 8.01452i 0.252810 0.437880i
\(336\) 0 0
\(337\) 0.748747 + 1.29687i 0.0407869 + 0.0706449i 0.885698 0.464261i \(-0.153680\pi\)
−0.844911 + 0.534906i \(0.820347\pi\)
\(338\) 12.6962 21.9905i 0.690582 1.19612i
\(339\) 2.82912 24.9585i 0.153657 1.35556i
\(340\) 1.43704 + 2.48903i 0.0779344 + 0.134986i
\(341\) −2.91087 5.04177i −0.157632 0.273027i
\(342\) 9.42217 10.1274i 0.509493 0.547626i
\(343\) 0 0
\(344\) 5.72639 9.91840i 0.308746 0.534764i
\(345\) −1.91666 + 16.9088i −0.103190 + 0.910341i
\(346\) 18.6719 1.00381
\(347\) −29.5388 −1.58572 −0.792862 0.609401i \(-0.791410\pi\)
−0.792862 + 0.609401i \(0.791410\pi\)
\(348\) 0.136744 0.0595513i 0.00733022 0.00319229i
\(349\) −18.0006 + 31.1780i −0.963551 + 1.66892i −0.250094 + 0.968222i \(0.580461\pi\)
−0.713458 + 0.700698i \(0.752872\pi\)
\(350\) 0 0
\(351\) 26.4364 4.94691i 1.41107 0.264046i
\(352\) −5.05363 8.75315i −0.269360 0.466545i
\(353\) −14.7465 25.5417i −0.784877 1.35945i −0.929073 0.369897i \(-0.879393\pi\)
0.144196 0.989549i \(-0.453940\pi\)
\(354\) 21.6545 + 16.0042i 1.15092 + 0.850613i
\(355\) −8.22900 + 14.2530i −0.436750 + 0.756473i
\(356\) −0.977687 1.69340i −0.0518173 0.0897502i
\(357\) 0 0
\(358\) −1.56612 + 2.71260i −0.0827720 + 0.143365i
\(359\) 2.70535 + 4.68580i 0.142783 + 0.247307i 0.928544 0.371224i \(-0.121062\pi\)
−0.785761 + 0.618531i \(0.787728\pi\)
\(360\) 4.38210 + 1.00638i 0.230957 + 0.0530408i
\(361\) 6.36444 11.0235i 0.334971 0.580186i
\(362\) −31.2902 −1.64458
\(363\) −13.8327 + 6.02409i −0.726028 + 0.316183i
\(364\) 0 0
\(365\) −1.84110 3.18888i −0.0963676 0.166914i
\(366\) −8.30746 6.13980i −0.434238 0.320933i
\(367\) −11.5422 19.9916i −0.602496 1.04355i −0.992442 0.122715i \(-0.960840\pi\)
0.389946 0.920838i \(-0.372494\pi\)
\(368\) −17.8417 + 30.9027i −0.930063 + 1.61092i
\(369\) 18.4398 19.8199i 0.959937 1.03178i
\(370\) 1.38416 0.0719591
\(371\) 0 0
\(372\) −7.45075 5.50664i −0.386304 0.285506i
\(373\) −10.7515 + 18.6222i −0.556692 + 0.964219i 0.441078 + 0.897469i \(0.354596\pi\)
−0.997770 + 0.0667498i \(0.978737\pi\)
\(374\) −4.31504 −0.223125
\(375\) −15.2797 11.2928i −0.789039 0.583156i
\(376\) 10.6878 0.551184
\(377\) −0.320615 −0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) 4.64665 0.238368
\(381\) −11.8398 8.75047i −0.606572 0.448300i
\(382\) −41.7850 −2.13791
\(383\) −17.4604 + 30.2424i −0.892187 + 1.54531i −0.0549390 + 0.998490i \(0.517496\pi\)
−0.837248 + 0.546823i \(0.815837\pi\)
\(384\) 11.9306 + 8.81756i 0.608831 + 0.449969i
\(385\) 0 0
\(386\) −11.3917 −0.579823
\(387\) 29.8229 + 6.84903i 1.51598 + 0.348156i
\(388\) 8.47603 14.6809i 0.430305 0.745311i
\(389\) 14.4411 + 25.0127i 0.732192 + 1.26819i 0.955944 + 0.293548i \(0.0948361\pi\)
−0.223752 + 0.974646i \(0.571831\pi\)
\(390\) 17.7186 + 13.0953i 0.897216 + 0.663107i
\(391\) 5.70066 + 9.87383i 0.288295 + 0.499341i
\(392\) 0 0
\(393\) 3.19737 1.39244i 0.161286 0.0702395i
\(394\) −17.9891 −0.906278
\(395\) −3.95046 + 6.84239i −0.198769 + 0.344278i
\(396\) 4.29812 4.61982i 0.215989 0.232155i
\(397\) −5.59226 9.68607i −0.280667 0.486130i 0.690882 0.722968i \(-0.257222\pi\)
−0.971549 + 0.236838i \(0.923889\pi\)
\(398\) −7.99049 + 13.8399i −0.400527 + 0.693734i
\(399\) 0 0
\(400\) −7.80111 13.5119i −0.390056 0.675596i
\(401\) 0.541061 0.937146i 0.0270193 0.0467988i −0.852200 0.523217i \(-0.824732\pi\)
0.879219 + 0.476418i \(0.158065\pi\)
\(402\) 17.7820 + 13.1422i 0.886885 + 0.655471i
\(403\) 9.95802 + 17.2478i 0.496044 + 0.859174i
\(404\) 0.777570 + 1.34679i 0.0386856 + 0.0670054i
\(405\) 0.865544 + 11.9816i 0.0430092 + 0.595368i
\(406\) 0 0
\(407\) −0.426078 + 0.737988i −0.0211199 + 0.0365807i
\(408\) 2.76186 1.20278i 0.136732 0.0595465i
\(409\) 21.7349 1.07472 0.537360 0.843353i \(-0.319422\pi\)
0.537360 + 0.843353i \(0.319422\pi\)
\(410\) 22.1768 1.09524
\(411\) −0.432578 + 3.81621i −0.0213375 + 0.188240i
\(412\) 1.34182 2.32410i 0.0661069 0.114500i
\(413\) 0 0
\(414\) −39.6273 9.10068i −1.94758 0.447274i
\(415\) 3.73879 + 6.47578i 0.183530 + 0.317884i
\(416\) 17.2884 + 29.9443i 0.847632 + 1.46814i
\(417\) −0.147354 + 1.29996i −0.00721597 + 0.0636593i
\(418\) −3.48816 + 6.04167i −0.170611 + 0.295508i
\(419\) −12.5906 21.8075i −0.615090 1.06537i −0.990369 0.138455i \(-0.955787\pi\)
0.375279 0.926912i \(-0.377547\pi\)
\(420\) 0 0
\(421\) −14.8304 + 25.6869i −0.722788 + 1.25191i 0.237090 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280418i \(0.909527\pi\)
\(422\) 5.23316 + 9.06411i 0.254746 + 0.441234i
\(423\) 8.38024 + 27.2982i 0.407461 + 1.32728i
\(424\) 0.848171 1.46907i 0.0411908 0.0713446i
\(425\) −4.98512 −0.241814
\(426\) −31.6236 23.3721i −1.53217 1.13238i
\(427\) 0 0
\(428\) 4.01715 + 6.95791i 0.194176 + 0.336323i
\(429\) −12.4362 + 5.41591i −0.600424 + 0.261483i
\(430\) 12.5335 + 21.7086i 0.604418 + 1.04688i
\(431\) 2.44517 4.23516i 0.117780 0.204000i −0.801108 0.598520i \(-0.795756\pi\)
0.918887 + 0.394520i \(0.129089\pi\)
\(432\) −8.36752 + 23.7594i −0.402582 + 1.14312i
\(433\) −9.71430 −0.466839 −0.233420 0.972376i \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(434\) 0 0
\(435\) 0.0161292 0.142292i 0.000773334 0.00682236i
\(436\) −5.72896 + 9.92285i −0.274367 + 0.475218i
\(437\) 18.4330 0.881771
\(438\) 8.06616 3.51279i 0.385416 0.167847i
\(439\) 14.8235 0.707488 0.353744 0.935342i \(-0.384908\pi\)
0.353744 + 0.935342i \(0.384908\pi\)
\(440\) −2.26760 −0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) −21.9020 −1.04059 −0.520297 0.853986i \(-0.674179\pi\)
−0.520297 + 0.853986i \(0.674179\pi\)
\(444\) −0.152744 + 1.34751i −0.00724889 + 0.0639498i
\(445\) −1.87743 −0.0889987
\(446\) 10.7921 18.6925i 0.511021 0.885115i
\(447\) 10.4569 4.55396i 0.494596 0.215395i
\(448\) 0 0
\(449\) 21.4952 1.01442 0.507212 0.861822i \(-0.330676\pi\)
0.507212 + 0.861822i \(0.330676\pi\)
\(450\) 12.1094 13.0158i 0.570843 0.613568i
\(451\) −6.82655 + 11.8239i −0.321450 + 0.556767i
\(452\) 10.0802 + 17.4594i 0.474131 + 0.821220i
\(453\) −2.47115 + 21.8005i −0.116105 + 1.02428i
\(454\) −10.2954 17.8321i −0.483185 0.836902i
\(455\) 0 0
\(456\) 0.548548 4.83929i 0.0256881 0.226621i
\(457\) 40.6255 1.90038 0.950190 0.311670i \(-0.100888\pi\)
0.950190 + 0.311670i \(0.100888\pi\)
\(458\) 8.88995 15.3978i 0.415400 0.719494i
\(459\) 5.23761 + 6.11107i 0.244471 + 0.285240i
\(460\) −6.82908 11.8283i −0.318408 0.551498i
\(461\) −1.41541 + 2.45155i −0.0659220 + 0.114180i −0.897103 0.441822i \(-0.854332\pi\)
0.831181 + 0.556003i \(0.187666\pi\)
\(462\) 0 0
\(463\) −13.9324 24.1317i −0.647494 1.12149i −0.983719 0.179711i \(-0.942484\pi\)
0.336225 0.941782i \(-0.390850\pi\)
\(464\) 0.150142 0.260053i 0.00697016 0.0120727i
\(465\) −8.15567 + 3.55177i −0.378210 + 0.164709i
\(466\) 17.7586 + 30.7588i 0.822653 + 1.42488i
\(467\) 13.3219 + 23.0742i 0.616464 + 1.06775i 0.990126 + 0.140182i \(0.0447689\pi\)
−0.373661 + 0.927565i \(0.621898\pi\)
\(468\) −14.7038 + 15.8043i −0.679682 + 0.730554i
\(469\) 0 0
\(470\) −11.6964 + 20.2587i −0.539513 + 0.934463i
\(471\) −24.1078 17.8173i −1.11083 0.820980i
\(472\) 9.48056 0.436378
\(473\) −15.4324 −0.709582
\(474\) −15.1814 11.2201i −0.697304 0.515357i
\(475\) −4.02983 + 6.97987i −0.184901 + 0.320258i
\(476\) 0 0
\(477\) 4.41725 + 1.01445i 0.202252 + 0.0464485i
\(478\) 0.358381 + 0.620734i 0.0163920 + 0.0283917i
\(479\) −15.7895 27.3483i −0.721443 1.24958i −0.960422 0.278551i \(-0.910146\pi\)
0.238979 0.971025i \(-0.423187\pi\)
\(480\) −14.1593 + 6.16632i −0.646280 + 0.281453i
\(481\) 1.45760 2.52464i 0.0664609 0.115114i
\(482\) −9.79185 16.9600i −0.446007 0.772506i
\(483\) 0 0
\(484\) 6.05472 10.4871i 0.275215 0.476686i
\(485\) −8.13817 14.0957i −0.369535 0.640054i
\(486\) −28.6783 1.16948i −1.30087 0.0530486i
\(487\) −0.153087 + 0.265154i −0.00693703 + 0.0120153i −0.869473 0.493980i \(-0.835541\pi\)
0.862536 + 0.505996i \(0.168875\pi\)
\(488\) −3.63710 −0.164644
\(489\) 2.38378 21.0297i 0.107798 0.950996i
\(490\) 0 0
\(491\) −9.06981 15.7094i −0.409315 0.708954i 0.585498 0.810674i \(-0.300899\pi\)
−0.994813 + 0.101720i \(0.967566\pi\)
\(492\) −2.44723 + 21.5895i −0.110330 + 0.973331i
\(493\) −0.0479723 0.0830905i −0.00216057 0.00374221i
\(494\) 11.9329 20.6684i 0.536887 0.929916i
\(495\) −1.77800 5.79174i −0.0799153 0.260319i
\(496\) −18.6531 −0.837549
\(497\) 0 0
\(498\) −16.3803 + 7.13355i −0.734017 + 0.319662i
\(499\) 10.6546 18.4543i 0.476964 0.826126i −0.522687 0.852524i \(-0.675070\pi\)
0.999652 + 0.0263983i \(0.00840381\pi\)
\(500\) 15.2496 0.681981
\(501\) −0.687661 + 6.06655i −0.0307224 + 0.271033i
\(502\) −6.01401 −0.268418
\(503\) 17.0738 0.761285 0.380642 0.924722i \(-0.375703\pi\)
0.380642 + 0.924722i \(0.375703\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) 20.5059 0.911597
\(507\) 21.8999 9.53735i 0.972610 0.423568i
\(508\) 11.8165 0.524271
\(509\) 18.3868 31.8468i 0.814979 1.41159i −0.0943635 0.995538i \(-0.530082\pi\)
0.909343 0.416048i \(-0.136585\pi\)
\(510\) −0.742614 + 6.55135i −0.0328835 + 0.290099i
\(511\) 0 0
\(512\) −21.4975 −0.950065
\(513\) 12.7903 2.39338i 0.564705 0.105670i
\(514\) 4.32299 7.48764i 0.190679 0.330265i
\(515\) −1.28834 2.23146i −0.0567709 0.0983300i
\(516\) −22.5168 + 9.80599i −0.991247 + 0.431685i
\(517\) −7.20083 12.4722i −0.316692 0.548527i
\(518\) 0 0
\(519\) 14.1254 + 10.4397i 0.620037 + 0.458251i
\(520\) 7.75740 0.340184
\(521\) 9.57535 16.5850i 0.419504 0.726602i −0.576386 0.817178i \(-0.695537\pi\)
0.995890 + 0.0905758i \(0.0288707\pi\)
\(522\) 0.333473 + 0.0765843i 0.0145957 + 0.00335200i
\(523\) 20.9715 + 36.3236i 0.917018 + 1.58832i 0.803920 + 0.594737i \(0.202744\pi\)
0.113097 + 0.993584i \(0.463923\pi\)
\(524\) −1.39952 + 2.42405i −0.0611385 + 0.105895i
\(525\) 0 0
\(526\) 17.9980 + 31.1734i 0.784749 + 1.35922i
\(527\) −2.97996 + 5.16144i −0.129809 + 0.224836i
\(528\) 1.43089 12.6233i 0.0622715 0.549360i
\(529\) −15.5906 27.0037i −0.677851 1.17407i
\(530\) 1.85641 + 3.21539i 0.0806372 + 0.139668i
\(531\) 7.43362 + 24.2146i 0.322592 + 1.05082i
\(532\) 0 0
\(533\) 23.3535 40.4494i 1.01155 1.75206i
\(534\) 0.505236 4.45719i 0.0218637 0.192882i
\(535\) 7.71405 0.333507
\(536\) 7.78515 0.336267
\(537\) −2.70143 + 1.17646i −0.116575 + 0.0507682i
\(538\) 14.5157 25.1419i 0.625816 1.08395i
\(539\) 0 0
\(540\) −6.27438 7.32073i −0.270006 0.315034i
\(541\) −1.44272 2.49886i −0.0620273 0.107434i 0.833344 0.552754i \(-0.186423\pi\)
−0.895371 + 0.445320i \(0.853090\pi\)
\(542\) 13.6230 + 23.5957i 0.585158 + 1.01352i
\(543\) −23.6713 17.4948i −1.01583 0.750773i
\(544\) −5.17358 + 8.96090i −0.221815 + 0.384196i
\(545\) 5.50059 + 9.52731i 0.235620 + 0.408105i
\(546\) 0 0
\(547\) 1.38738 2.40301i 0.0593201 0.102745i −0.834840 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147773\pi\)
\(548\) −1.54128 2.66957i −0.0658401 0.114038i
\(549\) −2.85181 9.28962i −0.121712 0.396471i
\(550\) −4.48300 + 7.76478i −0.191156 + 0.331091i
\(551\) −0.155118 −0.00660825
\(552\) −13.1249 + 5.71584i −0.558632 + 0.243282i
\(553\) 0 0
\(554\) −6.85975 11.8814i −0.291443 0.504794i
\(555\) 1.04713 + 0.773903i 0.0444482 + 0.0328504i
\(556\) −0.525024 0.909368i −0.0222660 0.0385658i
\(557\) 15.5344 26.9064i 0.658214 1.14006i −0.322864 0.946445i \(-0.604646\pi\)
0.981078 0.193614i \(-0.0620211\pi\)
\(558\) −6.23745 20.3181i −0.264052 0.860136i
\(559\) 52.7939 2.23294
\(560\) 0 0
\(561\) −3.26436 2.41260i −0.137822 0.101860i
\(562\) 23.9248 41.4389i 1.00920 1.74799i
\(563\) −0.288041 −0.0121395 −0.00606973 0.999982i \(-0.501932\pi\)
−0.00606973 + 0.999982i \(0.501932\pi\)
\(564\) −18.4315 13.6222i −0.776105 0.573597i
\(565\) 19.3567 0.814344
\(566\) 34.5331 1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) −16.0801 −0.674112 −0.337056 0.941485i \(-0.609431\pi\)
−0.337056 + 0.941485i \(0.609431\pi\)
\(570\) 8.57251 + 6.33569i 0.359063 + 0.265373i
\(571\) −15.2858 −0.639690 −0.319845 0.947470i \(-0.603631\pi\)
−0.319845 + 0.947470i \(0.603631\pi\)
\(572\) 5.44345 9.42834i 0.227602 0.394218i
\(573\) −31.6107 23.3626i −1.32056 0.975985i
\(574\) 0 0
\(575\) 23.6902 0.987950
\(576\) −2.29290 7.46900i −0.0955376 0.311208i
\(577\) −12.0812 + 20.9253i −0.502949 + 0.871133i 0.497045 + 0.867725i \(0.334418\pi\)
−0.999994 + 0.00340833i \(0.998915\pi\)
\(578\) −13.4418 23.2819i −0.559106 0.968400i
\(579\) −8.61793 6.36926i −0.358149 0.264697i
\(580\) 0.0574683 + 0.0995380i 0.00238624 + 0.00413309i
\(581\) 0 0
\(582\) 35.6546 15.5275i 1.47793 0.643634i
\(583\) −2.28579 −0.0946676
\(584\) 1.54881 2.68262i 0.0640902 0.111007i
\(585\) 6.08251 + 19.8134i 0.251481 + 0.819184i
\(586\) −2.26636 3.92546i −0.0936226 0.162159i
\(587\) −18.0145 + 31.2020i −0.743537 + 1.28784i 0.207339 + 0.978269i \(0.433520\pi\)
−0.950875 + 0.309574i \(0.899814\pi\)
\(588\) 0 0
\(589\) 4.81783 + 8.34472i 0.198515 + 0.343838i
\(590\) −10.3752 + 17.9703i −0.427138 + 0.739825i
\(591\) −13.6089 10.0579i −0.559795 0.413729i
\(592\) 1.36517 + 2.36455i 0.0561082 + 0.0971823i
\(593\) −12.4668 21.5932i −0.511951 0.886726i −0.999904 0.0138558i \(-0.995589\pi\)
0.487953 0.872870i \(-0.337744\pi\)
\(594\) 14.2286 2.66253i 0.583807 0.109245i
\(595\) 0 0
\(596\) −4.57712 + 7.92780i −0.187486 + 0.324735i
\(597\) −13.7830 + 6.00244i −0.564099 + 0.245663i
\(598\) −70.1501 −2.86865
\(599\) 39.5283 1.61508 0.807542 0.589810i \(-0.200797\pi\)
0.807542 + 0.589810i \(0.200797\pi\)
\(600\) 0.704996 6.21948i 0.0287813 0.253909i
\(601\) −1.86447 + 3.22936i −0.0760534 + 0.131728i −0.901544 0.432688i \(-0.857565\pi\)
0.825490 + 0.564416i \(0.190899\pi\)
\(602\) 0 0
\(603\) 6.10427 + 19.8843i 0.248585 + 0.809751i
\(604\) −8.80470 15.2502i −0.358258 0.620521i
\(605\) −5.81337 10.0691i −0.236347 0.409365i
\(606\) −0.401822 + 3.54488i −0.0163229 + 0.144001i
\(607\) 11.8264 20.4839i 0.480018 0.831415i −0.519719 0.854337i \(-0.673964\pi\)
0.999737 + 0.0229218i \(0.00729686\pi\)
\(608\) 8.36436 + 14.4875i 0.339219 + 0.587545i
\(609\) 0 0
\(610\) 3.98029 6.89407i 0.161157 0.279133i
\(611\) 24.6339 + 42.6671i 0.996580 + 1.72613i
\(612\) −6.29590 1.44590i −0.254497 0.0584469i
\(613\) 1.89952 3.29006i 0.0767208 0.132884i −0.825113 0.564968i \(-0.808888\pi\)
0.901833 + 0.432084i \(0.142222\pi\)
\(614\) −8.58528 −0.346474
\(615\) 16.7769 + 12.3994i 0.676512 + 0.499990i
\(616\) 0 0
\(617\) −17.5615 30.4174i −0.706999 1.22456i −0.965965 0.258672i \(-0.916715\pi\)
0.258966 0.965886i \(-0.416618\pi\)
\(618\) 5.64441 2.45812i 0.227051 0.0988801i
\(619\) −10.5816 18.3279i −0.425311 0.736660i 0.571138 0.820854i \(-0.306502\pi\)
−0.996449 + 0.0841934i \(0.973169\pi\)
\(620\) 3.56983 6.18312i 0.143368 0.248320i
\(621\) −24.8901 29.0409i −0.998805 1.16537i
\(622\) 50.6011 2.02892
\(623\) 0 0
\(624\) −4.89504 + 43.1841i −0.195959 + 1.72875i
\(625\) −0.725240 + 1.25615i −0.0290096 + 0.0502461i
\(626\) 10.1145 0.404257
\(627\) −6.01680 + 2.62030i −0.240288 + 0.104645i
\(628\) 24.0602 0.960107
\(629\) 0.872381 0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) −6.64657 −0.264386
\(633\) −1.10893 + 9.78300i −0.0440761 + 0.388839i
\(634\) −18.1870 −0.722298
\(635\) 5.67273 9.82546i 0.225115 0.389911i
\(636\) −3.33510 + 1.45242i −0.132245 + 0.0575924i
\(637\) 0 0
\(638\) −0.172562 −0.00683178
\(639\) −10.8558 35.3623i −0.429451 1.39891i
\(640\) −5.71622 + 9.90078i −0.225953 + 0.391363i
\(641\) 4.93735 + 8.55174i 0.195013 + 0.337773i 0.946905 0.321514i \(-0.104192\pi\)
−0.751891 + 0.659287i \(0.770858\pi\)
\(642\) −2.07593 + 18.3139i −0.0819304 + 0.722791i
\(643\) −21.9748 38.0615i −0.866602 1.50100i −0.865448 0.501000i \(-0.832966\pi\)
−0.00115462 0.999999i \(-0.500368\pi\)
\(644\) 0 0
\(645\) −2.65590 + 23.4304i −0.104576 + 0.922570i
\(646\) 7.14190 0.280994
\(647\) −22.1936 + 38.4404i −0.872521 + 1.51125i −0.0131398 + 0.999914i \(0.504183\pi\)
−0.859381 + 0.511336i \(0.829151\pi\)
\(648\) −8.36493 + 5.67027i −0.328605 + 0.222749i
\(649\) −6.38743 11.0634i −0.250729 0.434275i
\(650\) 15.3362 26.5631i 0.601537 1.04189i
\(651\) 0 0
\(652\) 8.49341 + 14.7110i 0.332628 + 0.576128i
\(653\) −20.9956 + 36.3655i −0.821622 + 1.42309i 0.0828523 + 0.996562i \(0.473597\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(654\) −24.0990 + 10.4950i −0.942345 + 0.410388i
\(655\) 1.34374 + 2.32742i 0.0525042 + 0.0909399i
\(656\) 21.8726 + 37.8844i 0.853980 + 1.47914i
\(657\) 8.06616 + 1.85245i 0.314691 + 0.0722708i
\(658\) 0 0
\(659\) −19.6365 + 34.0114i −0.764928 + 1.32489i 0.175356 + 0.984505i \(0.443892\pi\)
−0.940284 + 0.340390i \(0.889441\pi\)
\(660\) 3.91053 + 2.89016i 0.152217 + 0.112499i
\(661\) 0.186739 0.00726330 0.00363165 0.999993i \(-0.498844\pi\)
0.00363165 + 0.999993i \(0.498844\pi\)
\(662\) 38.1030 1.48092
\(663\) 11.1673 + 8.25344i 0.433703 + 0.320537i
\(664\) −3.14522 + 5.44769i −0.122058 + 0.211411i
\(665\) 0 0
\(666\) −2.11911 + 2.27772i −0.0821139 + 0.0882598i
\(667\) 0.227973 + 0.394862i 0.00882717 + 0.0152891i
\(668\) −2.45014 4.24376i −0.0947987 0.164196i
\(669\) 18.6155 8.10700i 0.719718 0.313435i
\(670\) −8.51976 + 14.7567i −0.329147 + 0.570099i
\(671\) 2.45046 + 4.24432i 0.0945989 + 0.163850i
\(672\) 0 0
\(673\) −5.43382 + 9.41166i −0.209458 + 0.362793i −0.951544 0.307512i \(-0.900503\pi\)
0.742086 + 0.670305i \(0.233837\pi\)
\(674\) −1.37862 2.38785i −0.0531026 0.0919764i
\(675\) 16.4381 3.07599i 0.632705 0.118395i
\(676\) −9.58584 + 16.6032i −0.368686 + 0.638583i
\(677\) −28.3901 −1.09112 −0.545560 0.838072i \(-0.683683\pi\)
−0.545560 + 0.838072i \(0.683683\pi\)
\(678\) −5.20910 + 45.9547i −0.200054 + 1.76488i
\(679\) 0 0
\(680\) 1.16071 + 2.01041i 0.0445111 + 0.0770956i
\(681\) 2.18163 19.2464i 0.0836004 0.737524i
\(682\) 5.35961 + 9.28312i 0.205230 + 0.355469i
\(683\) 5.92034 10.2543i 0.226536 0.392371i −0.730243 0.683187i \(-0.760593\pi\)
0.956779 + 0.290816i \(0.0939267\pi\)
\(684\) −7.11389 + 7.64634i −0.272007 + 0.292365i
\(685\) −2.95968 −0.113083
\(686\) 0 0
\(687\) 15.3345 6.67810i 0.585046 0.254786i
\(688\) −24.7230 + 42.8216i −0.942557 + 1.63256i
\(689\) 7.81962 0.297904
\(690\) 3.52904 31.1332i 0.134348 1.18522i
\(691\) −11.9083 −0.453014 −0.226507 0.974010i \(-0.572731\pi\)
−0.226507 + 0.974010i \(0.572731\pi\)
\(692\) −14.0976 −0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) −1.00819 −0.0382429
\(696\) 0.110449 0.0481001i 0.00418655 0.00182323i
\(697\) 13.9771 0.529422
\(698\) 33.1435 57.4062i 1.25450 2.17286i
\(699\) −3.76313 + 33.1984i −0.142335 + 1.25568i
\(700\) 0 0
\(701\) −31.3902 −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(702\) −48.6758 + 9.10844i −1.83715 + 0.343776i
\(703\) 0.705208 1.22146i 0.0265974 0.0460681i
\(704\) 1.97020 + 3.41249i 0.0742549 + 0.128613i
\(705\) −20.1753 + 8.78627i −0.759845 + 0.330910i
\(706\) 27.1518 + 47.0284i 1.02187 + 1.76994i
\(707\) 0 0
\(708\) −16.3495 12.0834i −0.614451 0.454123i
\(709\) 0.625218 0.0234806 0.0117403 0.999931i \(-0.496263\pi\)
0.0117403 + 0.999931i \(0.496263\pi\)
\(710\) 15.1516 26.2433i 0.568628 0.984893i
\(711\) −5.21152 16.9762i −0.195447 0.636658i
\(712\) −0.789685 1.36777i −0.0295947 0.0512595i
\(713\) 14.1613 24.5281i 0.530345 0.918584i
\(714\) 0 0
\(715\) −5.22647 9.05251i −0.195459 0.338545i
\(716\) 1.18245 2.04806i 0.0441901 0.0765395i
\(717\) −0.0759426 + 0.669966i −0.00283613 + 0.0250203i
\(718\) −4.98119 8.62768i −0.185897 0.321982i
\(719\) −12.1969 21.1257i −0.454869 0.787857i 0.543811 0.839208i \(-0.316981\pi\)
−0.998681 + 0.0513506i \(0.983647\pi\)
\(720\) −18.9192 4.34492i −0.705078 0.161926i
\(721\) 0 0
\(722\) −11.7185 + 20.2970i −0.436116 + 0.755376i
\(723\) 2.07494 18.3051i 0.0771678 0.680775i
\(724\) 23.6246 0.878003
\(725\) −0.199358 −0.00740399
\(726\) 25.4693 11.0918i 0.945255 0.411655i
\(727\) 18.9253 32.7796i 0.701900 1.21573i −0.265899 0.964001i \(-0.585669\pi\)
0.967799 0.251726i \(-0.0809980\pi\)
\(728\) 0 0
\(729\) −21.0415 16.9191i −0.779314 0.626634i
\(730\) 3.38991 + 5.87150i 0.125466 + 0.217314i
\(731\) 7.89934 + 13.6821i 0.292168 + 0.506049i
\(732\) 6.27227 + 4.63565i 0.231830 + 0.171339i
\(733\) 1.20077 2.07980i 0.0443516 0.0768193i −0.842997 0.537918i \(-0.819211\pi\)
0.887349 + 0.461098i \(0.152544\pi\)
\(734\) 21.2519 + 36.8093i 0.784421 + 1.35866i
\(735\) 0 0
\(736\) 24.5858 42.5839i 0.906245 1.56966i
\(737\) −5.24517 9.08490i −0.193208 0.334646i
\(738\) −33.9521 + 36.4932i −1.24979 + 1.34333i
\(739\) −15.1940 + 26.3167i −0.558920 + 0.968077i 0.438667 + 0.898650i \(0.355451\pi\)
−0.997587 + 0.0694277i \(0.977883\pi\)
\(740\) −1.04507 −0.0384174
\(741\) 20.5833 8.96397i 0.756148 0.329300i
\(742\) 0 0
\(743\) −2.54785 4.41300i −0.0934715 0.161897i 0.815498 0.578760i \(-0.196463\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(744\) −6.01803 4.44775i −0.220632 0.163063i
\(745\) 4.39467 + 7.61179i 0.161008 + 0.278874i
\(746\) 19.7961 34.2879i 0.724787 1.25537i
\(747\) −16.3803 3.76183i −0.599322 0.137638i
\(748\) 3.25793 0.119122
\(749\) 0 0
\(750\) 28.1336 + 20.7927i 1.02729 + 0.759242i
\(751\) 0.487506 0.844384i 0.0177893 0.0308120i −0.856994 0.515327i \(-0.827671\pi\)
0.874783 + 0.484515i \(0.161004\pi\)
\(752\) −46.1435 −1.68268
\(753\) −4.54965 3.36251i −0.165798 0.122537i
\(754\) 0.590329 0.0214985
\(755\) −16.9075 −0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) −10.5350 −0.382648
\(759\) 15.5129 + 11.4651i 0.563081 + 0.416157i
\(760\) 3.75314 0.136141
\(761\) −27.0875 + 46.9169i −0.981920 + 1.70073i −0.327023 + 0.945016i \(0.606045\pi\)
−0.654897 + 0.755718i \(0.727288\pi\)
\(762\) 21.8000 + 16.1117i 0.789729 + 0.583666i
\(763\) 0 0
\(764\) 31.5484 1.14138
\(765\) −4.22474 + 4.54094i −0.152746 + 0.164178i
\(766\) 32.1489 55.6835i 1.16159 2.01193i
\(767\) 21.8513 + 37.8475i 0.789004 + 1.36659i
\(768\) −29.2223 21.5974i −1.05447 0.779328i
\(769\) 10.4326 + 18.0698i 0.376208 + 0.651612i 0.990507 0.137462i \(-0.0438943\pi\)
−0.614299 + 0.789074i \(0.710561\pi\)
\(770\) 0 0
\(771\) 7.45681 3.24742i 0.268551 0.116953i
\(772\) 8.60094 0.309554
\(773\) 27.4972 47.6266i 0.989007 1.71301i 0.366447 0.930439i \(-0.380574\pi\)
0.622561 0.782572i \(-0.286092\pi\)
\(774\) −54.9112 12.6107i −1.97374 0.453283i
\(775\) 6.19189 + 10.7247i 0.222419 + 0.385242i
\(776\) 6.84616 11.8579i 0.245763 0.425674i
\(777\) 0 0
\(778\) −26.5895 46.0544i −0.953281 1.65113i
\(779\) 11.2987 19.5700i 0.404819 0.701168i
\(780\) −13.3778 9.88718i −0.479003 0.354018i