Properties

Label 507.2.e.g.22.1
Level $507$
Weight $2$
Character 507.22
Analytic conductor $4.048$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{17})\)
Defining polynomial: \(x^{4} - x^{3} + 5 x^{2} + 4 x + 16\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 39)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 22.1
Root \(-0.780776 + 1.35234i\) of defining polynomial
Character \(\chi\) \(=\) 507.22
Dual form 507.2.e.g.484.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.780776 + 1.35234i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +3.56155 q^{5} +(-0.780776 - 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.780776 + 1.35234i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.219224 - 0.379706i) q^{4} +3.56155 q^{5} +(-0.780776 - 1.35234i) q^{6} +(0.280776 + 0.486319i) q^{7} -2.43845 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-2.78078 + 4.81645i) q^{10} +(-1.00000 + 1.73205i) q^{11} +0.438447 q^{12} -0.876894 q^{14} +(-1.78078 + 3.08440i) q^{15} +(2.34233 - 4.05703i) q^{16} +(0.780776 + 1.35234i) q^{17} +1.56155 q^{18} +(3.56155 + 6.16879i) q^{19} +(-0.780776 - 1.35234i) q^{20} -0.561553 q^{21} +(-1.56155 - 2.70469i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(1.21922 - 2.11176i) q^{24} +7.68466 q^{25} +1.00000 q^{27} +(0.123106 - 0.213225i) q^{28} +(-3.34233 + 5.78908i) q^{29} +(-2.78078 - 4.81645i) q^{30} -2.56155 q^{31} +(1.21922 + 2.11176i) q^{32} +(-1.00000 - 1.73205i) q^{33} -2.43845 q^{34} +(1.00000 + 1.73205i) q^{35} +(-0.219224 + 0.379706i) q^{36} +(3.78078 - 6.54850i) q^{37} -11.1231 q^{38} -8.68466 q^{40} +(-0.780776 + 1.35234i) q^{41} +(0.438447 - 0.759413i) q^{42} +(-2.28078 - 3.95042i) q^{43} +0.876894 q^{44} +(-1.78078 - 3.08440i) q^{45} +(-1.56155 - 2.70469i) q^{46} -8.24621 q^{47} +(2.34233 + 4.05703i) q^{48} +(3.34233 - 5.78908i) q^{49} +(-6.00000 + 10.3923i) q^{50} -1.56155 q^{51} -0.684658 q^{53} +(-0.780776 + 1.35234i) q^{54} +(-3.56155 + 6.16879i) q^{55} +(-0.684658 - 1.18586i) q^{56} -7.12311 q^{57} +(-5.21922 - 9.03996i) q^{58} +(-1.43845 - 2.49146i) q^{59} +1.56155 q^{60} +(-1.93845 - 3.35749i) q^{61} +(2.00000 - 3.46410i) q^{62} +(0.280776 - 0.486319i) q^{63} +5.56155 q^{64} +3.12311 q^{66} +(2.28078 - 3.95042i) q^{67} +(0.342329 - 0.592932i) q^{68} +(-1.00000 - 1.73205i) q^{69} -3.12311 q^{70} +(7.00000 + 12.1244i) q^{71} +(1.21922 + 2.11176i) q^{72} +10.1231 q^{73} +(5.90388 + 10.2258i) q^{74} +(-3.84233 + 6.65511i) q^{75} +(1.56155 - 2.70469i) q^{76} -1.12311 q^{77} +5.43845 q^{79} +(8.34233 - 14.4493i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.21922 - 2.11176i) q^{82} +0.876894 q^{83} +(0.123106 + 0.213225i) q^{84} +(2.78078 + 4.81645i) q^{85} +7.12311 q^{86} +(-3.34233 - 5.78908i) q^{87} +(2.43845 - 4.22351i) q^{88} +(2.43845 - 4.22351i) q^{89} +5.56155 q^{90} +0.876894 q^{92} +(1.28078 - 2.21837i) q^{93} +(6.43845 - 11.1517i) q^{94} +(12.6847 + 21.9705i) q^{95} -2.43845 q^{96} +(-4.28078 - 7.41452i) q^{97} +(5.21922 + 9.03996i) q^{98} +2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + q^{2} - 2q^{3} - 5q^{4} + 6q^{5} + q^{6} - 3q^{7} - 18q^{8} - 2q^{9} + O(q^{10}) \) \( 4q + q^{2} - 2q^{3} - 5q^{4} + 6q^{5} + q^{6} - 3q^{7} - 18q^{8} - 2q^{9} - 7q^{10} - 4q^{11} + 10q^{12} - 20q^{14} - 3q^{15} - 3q^{16} - q^{17} - 2q^{18} + 6q^{19} + q^{20} + 6q^{21} + 2q^{22} - 4q^{23} + 9q^{24} + 6q^{25} + 4q^{27} - 16q^{28} - q^{29} - 7q^{30} - 2q^{31} + 9q^{32} - 4q^{33} - 18q^{34} + 4q^{35} - 5q^{36} + 11q^{37} - 28q^{38} - 10q^{40} + q^{41} + 10q^{42} - 5q^{43} + 20q^{44} - 3q^{45} + 2q^{46} - 3q^{48} + q^{49} - 24q^{50} + 2q^{51} + 22q^{53} + q^{54} - 6q^{55} + 22q^{56} - 12q^{57} - 25q^{58} - 14q^{59} - 2q^{60} - 16q^{61} + 8q^{62} - 3q^{63} + 14q^{64} - 4q^{66} + 5q^{67} - 11q^{68} - 4q^{69} + 4q^{70} + 28q^{71} + 9q^{72} + 24q^{73} + 3q^{74} - 3q^{75} - 2q^{76} + 12q^{77} + 30q^{79} + 21q^{80} - 2q^{81} - 9q^{82} + 20q^{83} - 16q^{84} + 7q^{85} + 12q^{86} - q^{87} + 18q^{88} + 18q^{89} + 14q^{90} + 20q^{92} + q^{93} + 34q^{94} + 26q^{95} - 18q^{96} - 13q^{97} + 25q^{98} + 8q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.780776 + 1.35234i −0.552092 + 0.956252i 0.446031 + 0.895017i \(0.352837\pi\)
−0.998123 + 0.0612344i \(0.980496\pi\)
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) −0.219224 0.379706i −0.109612 0.189853i
\(5\) 3.56155 1.59277 0.796387 0.604787i \(-0.206742\pi\)
0.796387 + 0.604787i \(0.206742\pi\)
\(6\) −0.780776 1.35234i −0.318751 0.552092i
\(7\) 0.280776 + 0.486319i 0.106124 + 0.183811i 0.914197 0.405271i \(-0.132823\pi\)
−0.808073 + 0.589082i \(0.799489\pi\)
\(8\) −2.43845 −0.862121
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −2.78078 + 4.81645i −0.879359 + 1.52309i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 0.438447 0.126569
\(13\) 0 0
\(14\) −0.876894 −0.234360
\(15\) −1.78078 + 3.08440i −0.459794 + 0.796387i
\(16\) 2.34233 4.05703i 0.585582 1.01426i
\(17\) 0.780776 + 1.35234i 0.189366 + 0.327992i 0.945039 0.326957i \(-0.106023\pi\)
−0.755673 + 0.654949i \(0.772690\pi\)
\(18\) 1.56155 0.368062
\(19\) 3.56155 + 6.16879i 0.817076 + 1.41522i 0.907827 + 0.419344i \(0.137740\pi\)
−0.0907512 + 0.995874i \(0.528927\pi\)
\(20\) −0.780776 1.35234i −0.174587 0.302393i
\(21\) −0.561553 −0.122541
\(22\) −1.56155 2.70469i −0.332924 0.576642i
\(23\) −1.00000 + 1.73205i −0.208514 + 0.361158i −0.951247 0.308431i \(-0.900196\pi\)
0.742732 + 0.669588i \(0.233529\pi\)
\(24\) 1.21922 2.11176i 0.248873 0.431061i
\(25\) 7.68466 1.53693
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0.123106 0.213225i 0.0232648 0.0402958i
\(29\) −3.34233 + 5.78908i −0.620655 + 1.07501i 0.368709 + 0.929545i \(0.379800\pi\)
−0.989364 + 0.145461i \(0.953533\pi\)
\(30\) −2.78078 4.81645i −0.507698 0.879359i
\(31\) −2.56155 −0.460068 −0.230034 0.973183i \(-0.573884\pi\)
−0.230034 + 0.973183i \(0.573884\pi\)
\(32\) 1.21922 + 2.11176i 0.215530 + 0.373309i
\(33\) −1.00000 1.73205i −0.174078 0.301511i
\(34\) −2.43845 −0.418190
\(35\) 1.00000 + 1.73205i 0.169031 + 0.292770i
\(36\) −0.219224 + 0.379706i −0.0365373 + 0.0632844i
\(37\) 3.78078 6.54850i 0.621556 1.07657i −0.367640 0.929968i \(-0.619834\pi\)
0.989196 0.146598i \(-0.0468324\pi\)
\(38\) −11.1231 −1.80441
\(39\) 0 0
\(40\) −8.68466 −1.37317
\(41\) −0.780776 + 1.35234i −0.121937 + 0.211201i −0.920531 0.390669i \(-0.872244\pi\)
0.798595 + 0.601869i \(0.205577\pi\)
\(42\) 0.438447 0.759413i 0.0676539 0.117180i
\(43\) −2.28078 3.95042i −0.347815 0.602433i 0.638046 0.769998i \(-0.279743\pi\)
−0.985861 + 0.167565i \(0.946410\pi\)
\(44\) 0.876894 0.132197
\(45\) −1.78078 3.08440i −0.265462 0.459794i
\(46\) −1.56155 2.70469i −0.230238 0.398785i
\(47\) −8.24621 −1.20283 −0.601417 0.798935i \(-0.705397\pi\)
−0.601417 + 0.798935i \(0.705397\pi\)
\(48\) 2.34233 + 4.05703i 0.338086 + 0.585582i
\(49\) 3.34233 5.78908i 0.477476 0.827012i
\(50\) −6.00000 + 10.3923i −0.848528 + 1.46969i
\(51\) −1.56155 −0.218661
\(52\) 0 0
\(53\) −0.684658 −0.0940451 −0.0470225 0.998894i \(-0.514973\pi\)
−0.0470225 + 0.998894i \(0.514973\pi\)
\(54\) −0.780776 + 1.35234i −0.106250 + 0.184031i
\(55\) −3.56155 + 6.16879i −0.480240 + 0.831800i
\(56\) −0.684658 1.18586i −0.0914913 0.158468i
\(57\) −7.12311 −0.943478
\(58\) −5.21922 9.03996i −0.685318 1.18700i
\(59\) −1.43845 2.49146i −0.187270 0.324361i 0.757069 0.653335i \(-0.226631\pi\)
−0.944339 + 0.328974i \(0.893297\pi\)
\(60\) 1.56155 0.201596
\(61\) −1.93845 3.35749i −0.248193 0.429882i 0.714832 0.699297i \(-0.246503\pi\)
−0.963024 + 0.269414i \(0.913170\pi\)
\(62\) 2.00000 3.46410i 0.254000 0.439941i
\(63\) 0.280776 0.486319i 0.0353745 0.0612704i
\(64\) 5.56155 0.695194
\(65\) 0 0
\(66\) 3.12311 0.384428
\(67\) 2.28078 3.95042i 0.278641 0.482621i −0.692406 0.721508i \(-0.743449\pi\)
0.971047 + 0.238887i \(0.0767826\pi\)
\(68\) 0.342329 0.592932i 0.0415135 0.0719035i
\(69\) −1.00000 1.73205i −0.120386 0.208514i
\(70\) −3.12311 −0.373283
\(71\) 7.00000 + 12.1244i 0.830747 + 1.43890i 0.897447 + 0.441123i \(0.145420\pi\)
−0.0666994 + 0.997773i \(0.521247\pi\)
\(72\) 1.21922 + 2.11176i 0.143687 + 0.248873i
\(73\) 10.1231 1.18482 0.592410 0.805637i \(-0.298177\pi\)
0.592410 + 0.805637i \(0.298177\pi\)
\(74\) 5.90388 + 10.2258i 0.686312 + 1.18873i
\(75\) −3.84233 + 6.65511i −0.443674 + 0.768466i
\(76\) 1.56155 2.70469i 0.179122 0.310249i
\(77\) −1.12311 −0.127990
\(78\) 0 0
\(79\) 5.43845 0.611873 0.305937 0.952052i \(-0.401030\pi\)
0.305937 + 0.952052i \(0.401030\pi\)
\(80\) 8.34233 14.4493i 0.932701 1.61549i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) −1.21922 2.11176i −0.134641 0.233205i
\(83\) 0.876894 0.0962517 0.0481258 0.998841i \(-0.484675\pi\)
0.0481258 + 0.998841i \(0.484675\pi\)
\(84\) 0.123106 + 0.213225i 0.0134319 + 0.0232648i
\(85\) 2.78078 + 4.81645i 0.301618 + 0.522417i
\(86\) 7.12311 0.768104
\(87\) −3.34233 5.78908i −0.358335 0.620655i
\(88\) 2.43845 4.22351i 0.259939 0.450228i
\(89\) 2.43845 4.22351i 0.258475 0.447692i −0.707359 0.706855i \(-0.750113\pi\)
0.965834 + 0.259163i \(0.0834467\pi\)
\(90\) 5.56155 0.586239
\(91\) 0 0
\(92\) 0.876894 0.0914226
\(93\) 1.28078 2.21837i 0.132810 0.230034i
\(94\) 6.43845 11.1517i 0.664075 1.15021i
\(95\) 12.6847 + 21.9705i 1.30142 + 2.25412i
\(96\) −2.43845 −0.248873
\(97\) −4.28078 7.41452i −0.434647 0.752831i 0.562620 0.826716i \(-0.309794\pi\)
−0.997267 + 0.0738851i \(0.976460\pi\)
\(98\) 5.21922 + 9.03996i 0.527221 + 0.913174i
\(99\) 2.00000 0.201008
\(100\) −1.68466 2.91791i −0.168466 0.291791i
\(101\) 3.78078 6.54850i 0.376201 0.651600i −0.614305 0.789069i \(-0.710563\pi\)
0.990506 + 0.137469i \(0.0438968\pi\)
\(102\) 1.21922 2.11176i 0.120721 0.209095i
\(103\) −3.43845 −0.338800 −0.169400 0.985547i \(-0.554183\pi\)
−0.169400 + 0.985547i \(0.554183\pi\)
\(104\) 0 0
\(105\) −2.00000 −0.195180
\(106\) 0.534565 0.925894i 0.0519216 0.0899308i
\(107\) 4.12311 7.14143i 0.398596 0.690388i −0.594957 0.803757i \(-0.702831\pi\)
0.993553 + 0.113369i \(0.0361644\pi\)
\(108\) −0.219224 0.379706i −0.0210948 0.0365373i
\(109\) 2.80776 0.268935 0.134468 0.990918i \(-0.457068\pi\)
0.134468 + 0.990918i \(0.457068\pi\)
\(110\) −5.56155 9.63289i −0.530273 0.918460i
\(111\) 3.78078 + 6.54850i 0.358855 + 0.621556i
\(112\) 2.63068 0.248576
\(113\) −2.90388 5.02967i −0.273174 0.473152i 0.696499 0.717558i \(-0.254740\pi\)
−0.969673 + 0.244406i \(0.921407\pi\)
\(114\) 5.56155 9.63289i 0.520887 0.902203i
\(115\) −3.56155 + 6.16879i −0.332117 + 0.575243i
\(116\) 2.93087 0.272124
\(117\) 0 0
\(118\) 4.49242 0.413561
\(119\) −0.438447 + 0.759413i −0.0401924 + 0.0696153i
\(120\) 4.34233 7.52113i 0.396399 0.686583i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) 6.05398 0.548101
\(123\) −0.780776 1.35234i −0.0704002 0.121937i
\(124\) 0.561553 + 0.972638i 0.0504289 + 0.0873455i
\(125\) 9.56155 0.855211
\(126\) 0.438447 + 0.759413i 0.0390600 + 0.0676539i
\(127\) −2.71922 + 4.70983i −0.241292 + 0.417930i −0.961083 0.276261i \(-0.910905\pi\)
0.719791 + 0.694191i \(0.244238\pi\)
\(128\) −6.78078 + 11.7446i −0.599342 + 1.03809i
\(129\) 4.56155 0.401622
\(130\) 0 0
\(131\) 7.36932 0.643860 0.321930 0.946763i \(-0.395668\pi\)
0.321930 + 0.946763i \(0.395668\pi\)
\(132\) −0.438447 + 0.759413i −0.0381619 + 0.0660984i
\(133\) −2.00000 + 3.46410i −0.173422 + 0.300376i
\(134\) 3.56155 + 6.16879i 0.307671 + 0.532902i
\(135\) 3.56155 0.306530
\(136\) −1.90388 3.29762i −0.163257 0.282769i
\(137\) −2.78078 4.81645i −0.237578 0.411497i 0.722441 0.691433i \(-0.243020\pi\)
−0.960019 + 0.279936i \(0.909687\pi\)
\(138\) 3.12311 0.265856
\(139\) 8.96543 + 15.5286i 0.760438 + 1.31712i 0.942625 + 0.333854i \(0.108349\pi\)
−0.182187 + 0.983264i \(0.558318\pi\)
\(140\) 0.438447 0.759413i 0.0370556 0.0641821i
\(141\) 4.12311 7.14143i 0.347228 0.601417i
\(142\) −21.8617 −1.83460
\(143\) 0 0
\(144\) −4.68466 −0.390388
\(145\) −11.9039 + 20.6181i −0.988564 + 1.71224i
\(146\) −7.90388 + 13.6899i −0.654130 + 1.13299i
\(147\) 3.34233 + 5.78908i 0.275671 + 0.477476i
\(148\) −3.31534 −0.272519
\(149\) −1.21922 2.11176i −0.0998827 0.173002i 0.811753 0.584001i \(-0.198513\pi\)
−0.911636 + 0.410999i \(0.865180\pi\)
\(150\) −6.00000 10.3923i −0.489898 0.848528i
\(151\) 9.36932 0.762464 0.381232 0.924479i \(-0.375500\pi\)
0.381232 + 0.924479i \(0.375500\pi\)
\(152\) −8.68466 15.0423i −0.704419 1.22009i
\(153\) 0.780776 1.35234i 0.0631220 0.109331i
\(154\) 0.876894 1.51883i 0.0706622 0.122390i
\(155\) −9.12311 −0.732785
\(156\) 0 0
\(157\) 20.3693 1.62565 0.812824 0.582509i \(-0.197929\pi\)
0.812824 + 0.582509i \(0.197929\pi\)
\(158\) −4.24621 + 7.35465i −0.337810 + 0.585105i
\(159\) 0.342329 0.592932i 0.0271485 0.0470225i
\(160\) 4.34233 + 7.52113i 0.343291 + 0.594598i
\(161\) −1.12311 −0.0885131
\(162\) −0.780776 1.35234i −0.0613436 0.106250i
\(163\) −2.40388 4.16365i −0.188287 0.326122i 0.756393 0.654118i \(-0.226960\pi\)
−0.944679 + 0.327996i \(0.893627\pi\)
\(164\) 0.684658 0.0534628
\(165\) −3.56155 6.16879i −0.277267 0.480240i
\(166\) −0.684658 + 1.18586i −0.0531398 + 0.0920408i
\(167\) 5.12311 8.87348i 0.396438 0.686650i −0.596846 0.802356i \(-0.703580\pi\)
0.993284 + 0.115706i \(0.0369129\pi\)
\(168\) 1.36932 0.105645
\(169\) 0 0
\(170\) −8.68466 −0.666083
\(171\) 3.56155 6.16879i 0.272359 0.471739i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) −10.1231 17.5337i −0.769645 1.33307i −0.937755 0.347297i \(-0.887100\pi\)
0.168110 0.985768i \(-0.446234\pi\)
\(174\) 10.4384 0.791337
\(175\) 2.15767 + 3.73720i 0.163105 + 0.282505i
\(176\) 4.68466 + 8.11407i 0.353119 + 0.611621i
\(177\) 2.87689 0.216241
\(178\) 3.80776 + 6.59524i 0.285404 + 0.494334i
\(179\) 2.43845 4.22351i 0.182258 0.315680i −0.760391 0.649466i \(-0.774993\pi\)
0.942649 + 0.333785i \(0.108326\pi\)
\(180\) −0.780776 + 1.35234i −0.0581956 + 0.100798i
\(181\) −2.68466 −0.199549 −0.0997745 0.995010i \(-0.531812\pi\)
−0.0997745 + 0.995010i \(0.531812\pi\)
\(182\) 0 0
\(183\) 3.87689 0.286588
\(184\) 2.43845 4.22351i 0.179765 0.311362i
\(185\) 13.4654 23.3228i 0.989998 1.71473i
\(186\) 2.00000 + 3.46410i 0.146647 + 0.254000i
\(187\) −3.12311 −0.228384
\(188\) 1.80776 + 3.13114i 0.131845 + 0.228362i
\(189\) 0.280776 + 0.486319i 0.0204235 + 0.0353745i
\(190\) −39.6155 −2.87401
\(191\) 4.56155 + 7.90084i 0.330062 + 0.571685i 0.982524 0.186137i \(-0.0595969\pi\)
−0.652461 + 0.757822i \(0.726264\pi\)
\(192\) −2.78078 + 4.81645i −0.200685 + 0.347597i
\(193\) −6.74621 + 11.6848i −0.485603 + 0.841089i −0.999863 0.0165453i \(-0.994733\pi\)
0.514260 + 0.857634i \(0.328067\pi\)
\(194\) 13.3693 0.959861
\(195\) 0 0
\(196\) −2.93087 −0.209348
\(197\) 6.68466 11.5782i 0.476262 0.824910i −0.523368 0.852107i \(-0.675325\pi\)
0.999630 + 0.0271965i \(0.00865798\pi\)
\(198\) −1.56155 + 2.70469i −0.110975 + 0.192214i
\(199\) −11.0885 19.2059i −0.786046 1.36147i −0.928372 0.371651i \(-0.878792\pi\)
0.142327 0.989820i \(-0.454542\pi\)
\(200\) −18.7386 −1.32502
\(201\) 2.28078 + 3.95042i 0.160874 + 0.278641i
\(202\) 5.90388 + 10.2258i 0.415396 + 0.719486i
\(203\) −3.75379 −0.263464
\(204\) 0.342329 + 0.592932i 0.0239678 + 0.0415135i
\(205\) −2.78078 + 4.81645i −0.194218 + 0.336395i
\(206\) 2.68466 4.64996i 0.187049 0.323978i
\(207\) 2.00000 0.139010
\(208\) 0 0
\(209\) −14.2462 −0.985431
\(210\) 1.56155 2.70469i 0.107757 0.186641i
\(211\) −9.84233 + 17.0474i −0.677574 + 1.17359i 0.298136 + 0.954524i \(0.403635\pi\)
−0.975709 + 0.219069i \(0.929698\pi\)
\(212\) 0.150093 + 0.259969i 0.0103084 + 0.0178548i
\(213\) −14.0000 −0.959264
\(214\) 6.43845 + 11.1517i 0.440123 + 0.762316i
\(215\) −8.12311 14.0696i −0.553991 0.959541i
\(216\) −2.43845 −0.165915
\(217\) −0.719224 1.24573i −0.0488241 0.0845658i
\(218\) −2.19224 + 3.79706i −0.148477 + 0.257170i
\(219\) −5.06155 + 8.76687i −0.342028 + 0.592410i
\(220\) 3.12311 0.210560
\(221\) 0 0
\(222\) −11.8078 −0.792485
\(223\) 4.00000 6.92820i 0.267860 0.463947i −0.700449 0.713702i \(-0.747017\pi\)
0.968309 + 0.249756i \(0.0803503\pi\)
\(224\) −0.684658 + 1.18586i −0.0457457 + 0.0792338i
\(225\) −3.84233 6.65511i −0.256155 0.443674i
\(226\) 9.06913 0.603270
\(227\) 3.56155 + 6.16879i 0.236389 + 0.409437i 0.959675 0.281111i \(-0.0907028\pi\)
−0.723287 + 0.690548i \(0.757370\pi\)
\(228\) 1.56155 + 2.70469i 0.103416 + 0.179122i
\(229\) 16.2462 1.07358 0.536790 0.843716i \(-0.319637\pi\)
0.536790 + 0.843716i \(0.319637\pi\)
\(230\) −5.56155 9.63289i −0.366718 0.635174i
\(231\) 0.561553 0.972638i 0.0369475 0.0639949i
\(232\) 8.15009 14.1164i 0.535080 0.926785i
\(233\) 26.0000 1.70332 0.851658 0.524097i \(-0.175597\pi\)
0.851658 + 0.524097i \(0.175597\pi\)
\(234\) 0 0
\(235\) −29.3693 −1.91584
\(236\) −0.630683 + 1.09238i −0.0410540 + 0.0711076i
\(237\) −2.71922 + 4.70983i −0.176633 + 0.305937i
\(238\) −0.684658 1.18586i −0.0443798 0.0768681i
\(239\) 25.3693 1.64100 0.820502 0.571643i \(-0.193694\pi\)
0.820502 + 0.571643i \(0.193694\pi\)
\(240\) 8.34233 + 14.4493i 0.538495 + 0.932701i
\(241\) −8.90388 15.4220i −0.573549 0.993417i −0.996198 0.0871229i \(-0.972233\pi\)
0.422648 0.906294i \(-0.361101\pi\)
\(242\) −10.9309 −0.702663
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −0.849907 + 1.47208i −0.0544097 + 0.0942404i
\(245\) 11.9039 20.6181i 0.760511 1.31724i
\(246\) 2.43845 0.155470
\(247\) 0 0
\(248\) 6.24621 0.396635
\(249\) −0.438447 + 0.759413i −0.0277855 + 0.0481258i
\(250\) −7.46543 + 12.9305i −0.472156 + 0.817797i
\(251\) −9.36932 16.2281i −0.591386 1.02431i −0.994046 0.108961i \(-0.965248\pi\)
0.402660 0.915350i \(-0.368086\pi\)
\(252\) −0.246211 −0.0155099
\(253\) −2.00000 3.46410i −0.125739 0.217786i
\(254\) −4.24621 7.35465i −0.266431 0.461472i
\(255\) −5.56155 −0.348278
\(256\) −5.02699 8.70700i −0.314187 0.544187i
\(257\) −14.5885 + 25.2681i −0.910008 + 1.57618i −0.0959583 + 0.995385i \(0.530592\pi\)
−0.814050 + 0.580795i \(0.802742\pi\)
\(258\) −3.56155 + 6.16879i −0.221733 + 0.384052i
\(259\) 4.24621 0.263847
\(260\) 0 0
\(261\) 6.68466 0.413770
\(262\) −5.75379 + 9.96585i −0.355470 + 0.615693i
\(263\) −4.68466 + 8.11407i −0.288868 + 0.500335i −0.973540 0.228517i \(-0.926612\pi\)
0.684672 + 0.728852i \(0.259946\pi\)
\(264\) 2.43845 + 4.22351i 0.150076 + 0.259939i
\(265\) −2.43845 −0.149793
\(266\) −3.12311 5.40938i −0.191490 0.331670i
\(267\) 2.43845 + 4.22351i 0.149231 + 0.258475i
\(268\) −2.00000 −0.122169
\(269\) 10.6847 + 18.5064i 0.651455 + 1.12835i 0.982770 + 0.184833i \(0.0591745\pi\)
−0.331315 + 0.943520i \(0.607492\pi\)
\(270\) −2.78078 + 4.81645i −0.169233 + 0.293120i
\(271\) −14.9654 + 25.9209i −0.909085 + 1.57458i −0.0937481 + 0.995596i \(0.529885\pi\)
−0.815337 + 0.578986i \(0.803449\pi\)
\(272\) 7.31534 0.443558
\(273\) 0 0
\(274\) 8.68466 0.524659
\(275\) −7.68466 + 13.3102i −0.463402 + 0.802636i
\(276\) −0.438447 + 0.759413i −0.0263914 + 0.0457113i
\(277\) −2.65767 4.60322i −0.159684 0.276581i 0.775071 0.631874i \(-0.217714\pi\)
−0.934755 + 0.355294i \(0.884381\pi\)
\(278\) −28.0000 −1.67933
\(279\) 1.28078 + 2.21837i 0.0766781 + 0.132810i
\(280\) −2.43845 4.22351i −0.145725 0.252403i
\(281\) −17.8078 −1.06232 −0.531161 0.847271i \(-0.678244\pi\)
−0.531161 + 0.847271i \(0.678244\pi\)
\(282\) 6.43845 + 11.1517i 0.383404 + 0.664075i
\(283\) 6.84233 11.8513i 0.406734 0.704484i −0.587787 0.809015i \(-0.700001\pi\)
0.994522 + 0.104531i \(0.0333342\pi\)
\(284\) 3.06913 5.31589i 0.182119 0.315440i
\(285\) −25.3693 −1.50275
\(286\) 0 0
\(287\) −0.876894 −0.0517614
\(288\) 1.21922 2.11176i 0.0718434 0.124436i
\(289\) 7.28078 12.6107i 0.428281 0.741804i
\(290\) −18.5885 32.1963i −1.09156 1.89063i
\(291\) 8.56155 0.501887
\(292\) −2.21922 3.84381i −0.129870 0.224942i
\(293\) 10.2192 + 17.7002i 0.597013 + 1.03406i 0.993259 + 0.115913i \(0.0369794\pi\)
−0.396246 + 0.918144i \(0.629687\pi\)
\(294\) −10.4384 −0.608783
\(295\) −5.12311 8.87348i −0.298279 0.516634i
\(296\) −9.21922 + 15.9682i −0.535856 + 0.928131i
\(297\) −1.00000 + 1.73205i −0.0580259 + 0.100504i
\(298\) 3.80776 0.220578
\(299\) 0 0
\(300\) 3.36932 0.194528
\(301\) 1.28078 2.21837i 0.0738227 0.127865i
\(302\) −7.31534 + 12.6705i −0.420951 + 0.729108i
\(303\) 3.78078 + 6.54850i 0.217200 + 0.376201i
\(304\) 33.3693 1.91386
\(305\) −6.90388 11.9579i −0.395315 0.684706i
\(306\) 1.21922 + 2.11176i 0.0696984 + 0.120721i
\(307\) −30.8078 −1.75829 −0.879146 0.476553i \(-0.841886\pi\)
−0.879146 + 0.476553i \(0.841886\pi\)
\(308\) 0.246211 + 0.426450i 0.0140292 + 0.0242993i
\(309\) 1.71922 2.97778i 0.0978032 0.169400i
\(310\) 7.12311 12.3376i 0.404565 0.700728i
\(311\) −19.1231 −1.08437 −0.542186 0.840259i \(-0.682403\pi\)
−0.542186 + 0.840259i \(0.682403\pi\)
\(312\) 0 0
\(313\) −13.6847 −0.773503 −0.386751 0.922184i \(-0.626403\pi\)
−0.386751 + 0.922184i \(0.626403\pi\)
\(314\) −15.9039 + 27.5463i −0.897508 + 1.55453i
\(315\) 1.00000 1.73205i 0.0563436 0.0975900i
\(316\) −1.19224 2.06501i −0.0670685 0.116166i
\(317\) −14.0540 −0.789350 −0.394675 0.918821i \(-0.629143\pi\)
−0.394675 + 0.918821i \(0.629143\pi\)
\(318\) 0.534565 + 0.925894i 0.0299769 + 0.0519216i
\(319\) −6.68466 11.5782i −0.374269 0.648253i
\(320\) 19.8078 1.10729
\(321\) 4.12311 + 7.14143i 0.230129 + 0.398596i
\(322\) 0.876894 1.51883i 0.0488674 0.0846408i
\(323\) −5.56155 + 9.63289i −0.309453 + 0.535988i
\(324\) 0.438447 0.0243582
\(325\) 0 0
\(326\) 7.50758 0.415806
\(327\) −1.40388 + 2.43160i −0.0776349 + 0.134468i
\(328\) 1.90388 3.29762i 0.105124 0.182081i
\(329\) −2.31534 4.01029i −0.127649 0.221094i
\(330\) 11.1231 0.612307
\(331\) −1.59612 2.76456i −0.0877306 0.151954i 0.818821 0.574049i \(-0.194628\pi\)
−0.906552 + 0.422095i \(0.861295\pi\)
\(332\) −0.192236 0.332962i −0.0105503 0.0182737i
\(333\) −7.56155 −0.414371
\(334\) 8.00000 + 13.8564i 0.437741 + 0.758189i
\(335\) 8.12311 14.0696i 0.443813 0.768706i
\(336\) −1.31534 + 2.27824i −0.0717578 + 0.124288i
\(337\) −6.12311 −0.333547 −0.166773 0.985995i \(-0.553335\pi\)
−0.166773 + 0.985995i \(0.553335\pi\)
\(338\) 0 0
\(339\) 5.80776 0.315434
\(340\) 1.21922 2.11176i 0.0661217 0.114526i
\(341\) 2.56155 4.43674i 0.138716 0.240263i
\(342\) 5.56155 + 9.63289i 0.300734 + 0.520887i
\(343\) 7.68466 0.414933
\(344\) 5.56155 + 9.63289i 0.299859 + 0.519371i
\(345\) −3.56155 6.16879i −0.191748 0.332117i
\(346\) 31.6155 1.69966
\(347\) −13.8078 23.9157i −0.741240 1.28386i −0.951931 0.306312i \(-0.900905\pi\)
0.210692 0.977553i \(-0.432428\pi\)
\(348\) −1.46543 + 2.53821i −0.0785556 + 0.136062i
\(349\) 3.40388 5.89570i 0.182206 0.315589i −0.760426 0.649425i \(-0.775010\pi\)
0.942631 + 0.333836i \(0.108343\pi\)
\(350\) −6.73863 −0.360195
\(351\) 0 0
\(352\) −4.87689 −0.259939
\(353\) 2.65767 4.60322i 0.141454 0.245005i −0.786591 0.617475i \(-0.788156\pi\)
0.928044 + 0.372470i \(0.121489\pi\)
\(354\) −2.24621 + 3.89055i −0.119385 + 0.206781i
\(355\) 24.9309 + 43.1815i 1.32319 + 2.29184i
\(356\) −2.13826 −0.113328
\(357\) −0.438447 0.759413i −0.0232051 0.0401924i
\(358\) 3.80776 + 6.59524i 0.201247 + 0.348569i
\(359\) 9.36932 0.494494 0.247247 0.968953i \(-0.420474\pi\)
0.247247 + 0.968953i \(0.420474\pi\)
\(360\) 4.34233 + 7.52113i 0.228861 + 0.396399i
\(361\) −15.8693 + 27.4865i −0.835227 + 1.44666i
\(362\) 2.09612 3.63058i 0.110170 0.190819i
\(363\) −7.00000 −0.367405
\(364\) 0 0
\(365\) 36.0540 1.88715
\(366\) −3.02699 + 5.24290i −0.158223 + 0.274051i
\(367\) 8.52699 14.7692i 0.445105 0.770945i −0.552954 0.833212i \(-0.686500\pi\)
0.998060 + 0.0622668i \(0.0198330\pi\)
\(368\) 4.68466 + 8.11407i 0.244205 + 0.422975i
\(369\) 1.56155 0.0812912
\(370\) 21.0270 + 36.4198i 1.09314 + 1.89338i
\(371\) −0.192236 0.332962i −0.00998039 0.0172865i
\(372\) −1.12311 −0.0582303
\(373\) −14.1847 24.5685i −0.734454 1.27211i −0.954963 0.296726i \(-0.904105\pi\)
0.220509 0.975385i \(-0.429228\pi\)
\(374\) 2.43845 4.22351i 0.126089 0.218393i
\(375\) −4.78078 + 8.28055i −0.246878 + 0.427606i
\(376\) 20.1080 1.03699
\(377\) 0 0
\(378\) −0.876894 −0.0451026
\(379\) 11.8423 20.5115i 0.608300 1.05361i −0.383221 0.923657i \(-0.625185\pi\)
0.991521 0.129949i \(-0.0414814\pi\)
\(380\) 5.56155 9.63289i 0.285302 0.494157i
\(381\) −2.71922 4.70983i −0.139310 0.241292i
\(382\) −14.2462 −0.728900
\(383\) −11.3693 19.6922i −0.580945 1.00623i −0.995368 0.0961417i \(-0.969350\pi\)
0.414423 0.910085i \(-0.363984\pi\)
\(384\) −6.78078 11.7446i −0.346030 0.599342i
\(385\) −4.00000 −0.203859
\(386\) −10.5346 18.2464i −0.536195 0.928717i
\(387\) −2.28078 + 3.95042i −0.115938 + 0.200811i
\(388\) −1.87689 + 3.25088i −0.0952849 + 0.165038i
\(389\) 34.0540 1.72661 0.863303 0.504687i \(-0.168392\pi\)
0.863303 + 0.504687i \(0.168392\pi\)
\(390\) 0 0
\(391\) −3.12311 −0.157942
\(392\) −8.15009 + 14.1164i −0.411642 + 0.712985i
\(393\) −3.68466 + 6.38202i −0.185866 + 0.321930i
\(394\) 10.4384 + 18.0799i 0.525881 + 0.910853i
\(395\) 19.3693 0.974576
\(396\) −0.438447 0.759413i −0.0220328 0.0381619i
\(397\) 12.5270 + 21.6974i 0.628711 + 1.08896i 0.987811 + 0.155661i \(0.0497507\pi\)
−0.359099 + 0.933299i \(0.616916\pi\)
\(398\) 34.6307 1.73588
\(399\) −2.00000 3.46410i −0.100125 0.173422i
\(400\) 18.0000 31.1769i 0.900000 1.55885i
\(401\) 7.21922 12.5041i 0.360511 0.624423i −0.627534 0.778589i \(-0.715936\pi\)
0.988045 + 0.154166i \(0.0492691\pi\)
\(402\) −7.12311 −0.355268
\(403\) 0 0
\(404\) −3.31534 −0.164944
\(405\) −1.78078 + 3.08440i −0.0884875 + 0.153265i
\(406\) 2.93087 5.07642i 0.145457 0.251938i
\(407\) 7.56155 + 13.0970i 0.374812 + 0.649194i
\(408\) 3.80776 0.188512
\(409\) 3.18466 + 5.51599i 0.157471 + 0.272748i 0.933956 0.357388i \(-0.116333\pi\)
−0.776485 + 0.630136i \(0.782999\pi\)
\(410\) −4.34233 7.52113i −0.214452 0.371442i
\(411\) 5.56155 0.274331
\(412\) 0.753789 + 1.30560i 0.0371365 + 0.0643223i
\(413\) 0.807764 1.39909i 0.0397475 0.0688446i
\(414\) −1.56155 + 2.70469i −0.0767461 + 0.132928i
\(415\) 3.12311 0.153307
\(416\) 0 0
\(417\) −17.9309 −0.878078
\(418\) 11.1231 19.2658i 0.544049 0.942320i
\(419\) 17.1231 29.6581i 0.836518 1.44889i −0.0562697 0.998416i \(-0.517921\pi\)
0.892788 0.450477i \(-0.148746\pi\)
\(420\) 0.438447 + 0.759413i 0.0213940 + 0.0370556i
\(421\) −31.2462 −1.52285 −0.761424 0.648255i \(-0.775499\pi\)
−0.761424 + 0.648255i \(0.775499\pi\)
\(422\) −15.3693 26.6204i −0.748167 1.29586i
\(423\) 4.12311 + 7.14143i 0.200472 + 0.347228i
\(424\) 1.66950 0.0810783
\(425\) 6.00000 + 10.3923i 0.291043 + 0.504101i
\(426\) 10.9309 18.9328i 0.529602 0.917298i
\(427\) 1.08854 1.88541i 0.0526782 0.0912413i
\(428\) −3.61553 −0.174763
\(429\) 0 0
\(430\) 25.3693 1.22342
\(431\) −5.56155 + 9.63289i −0.267891 + 0.464000i −0.968317 0.249725i \(-0.919660\pi\)
0.700426 + 0.713725i \(0.252993\pi\)
\(432\) 2.34233 4.05703i 0.112695 0.195194i
\(433\) −4.37689 7.58100i −0.210340 0.364320i 0.741481 0.670974i \(-0.234124\pi\)
−0.951821 + 0.306654i \(0.900790\pi\)
\(434\) 2.24621 0.107822
\(435\) −11.9039 20.6181i −0.570747 0.988564i
\(436\) −0.615528 1.06613i −0.0294785 0.0510582i
\(437\) −14.2462 −0.681489
\(438\) −7.90388 13.6899i −0.377662 0.654130i
\(439\) 6.84233 11.8513i 0.326567 0.565630i −0.655262 0.755402i \(-0.727442\pi\)
0.981828 + 0.189772i \(0.0607749\pi\)
\(440\) 8.68466 15.0423i 0.414025 0.717112i
\(441\) −6.68466 −0.318317
\(442\) 0 0
\(443\) −34.7386 −1.65048 −0.825241 0.564781i \(-0.808961\pi\)
−0.825241 + 0.564781i \(0.808961\pi\)
\(444\) 1.65767 2.87117i 0.0786696 0.136260i
\(445\) 8.68466 15.0423i 0.411692 0.713072i
\(446\) 6.24621 + 10.8188i 0.295767 + 0.512283i
\(447\) 2.43845 0.115335
\(448\) 1.56155 + 2.70469i 0.0737764 + 0.127785i
\(449\) −4.12311 7.14143i −0.194581 0.337025i 0.752182 0.658956i \(-0.229002\pi\)
−0.946763 + 0.321931i \(0.895668\pi\)
\(450\) 12.0000 0.565685
\(451\) −1.56155 2.70469i −0.0735307 0.127359i
\(452\) −1.27320 + 2.20525i −0.0598862 + 0.103726i
\(453\) −4.68466 + 8.11407i −0.220104 + 0.381232i
\(454\) −11.1231 −0.522033
\(455\) 0 0
\(456\) 17.3693 0.813393
\(457\) 6.30776 10.9254i 0.295065 0.511067i −0.679935 0.733272i \(-0.737992\pi\)
0.975000 + 0.222205i \(0.0713254\pi\)
\(458\) −12.6847 + 21.9705i −0.592715 + 1.02661i
\(459\) 0.780776 + 1.35234i 0.0364435 + 0.0631220i
\(460\) 3.12311 0.145616
\(461\) −8.09612 14.0229i −0.377074 0.653111i 0.613561 0.789647i \(-0.289736\pi\)
−0.990635 + 0.136536i \(0.956403\pi\)
\(462\) 0.876894 + 1.51883i 0.0407968 + 0.0706622i
\(463\) 14.3153 0.665290 0.332645 0.943052i \(-0.392059\pi\)
0.332645 + 0.943052i \(0.392059\pi\)
\(464\) 15.6577 + 27.1199i 0.726889 + 1.25901i
\(465\) 4.56155 7.90084i 0.211537 0.366393i
\(466\) −20.3002 + 35.1610i −0.940388 + 1.62880i
\(467\) −26.0000 −1.20314 −0.601568 0.798821i \(-0.705457\pi\)
−0.601568 + 0.798821i \(0.705457\pi\)
\(468\) 0 0
\(469\) 2.56155 0.118282
\(470\) 22.9309 39.7174i 1.05772 1.83203i
\(471\) −10.1847 + 17.6403i −0.469284 + 0.812824i
\(472\) 3.50758 + 6.07530i 0.161449 + 0.279638i
\(473\) 9.12311 0.419481
\(474\) −4.24621 7.35465i −0.195035 0.337810i
\(475\) 27.3693 + 47.4050i 1.25579 + 2.17509i
\(476\) 0.384472 0.0176222
\(477\) 0.342329 + 0.592932i 0.0156742 + 0.0271485i
\(478\) −19.8078 + 34.3081i −0.905986 + 1.56921i
\(479\) 5.12311 8.87348i 0.234081 0.405440i −0.724924 0.688828i \(-0.758125\pi\)
0.959005 + 0.283389i \(0.0914587\pi\)
\(480\) −8.68466 −0.396399
\(481\) 0 0
\(482\) 27.8078 1.26661
\(483\) 0.561553 0.972638i 0.0255515 0.0442566i
\(484\) 1.53457 2.65794i 0.0697530 0.120816i
\(485\) −15.2462 26.4072i −0.692295 1.19909i
\(486\) 1.56155 0.0708335
\(487\) 3.56155 + 6.16879i 0.161389 + 0.279535i 0.935367 0.353678i \(-0.115069\pi\)
−0.773978 + 0.633213i \(0.781736\pi\)
\(488\) 4.72680 + 8.18706i 0.213972 + 0.370611i
\(489\) 4.80776 0.217415
\(490\) 18.5885 + 32.1963i 0.839745 + 1.45448i
\(491\) 18.1231 31.3901i 0.817884 1.41662i −0.0893539 0.996000i \(-0.528480\pi\)
0.907238 0.420617i \(-0.138186\pi\)
\(492\) −0.342329 + 0.592932i −0.0154334 + 0.0267314i
\(493\) −10.4384 −0.470124
\(494\) 0 0
\(495\) 7.12311 0.320160
\(496\) −6.00000 + 10.3923i −0.269408 + 0.466628i
\(497\) −3.93087 + 6.80847i −0.176324 + 0.305401i
\(498\) −0.684658 1.18586i −0.0306803 0.0531398i
\(499\) −4.49242 −0.201108 −0.100554 0.994932i \(-0.532062\pi\)
−0.100554 + 0.994932i \(0.532062\pi\)
\(500\) −2.09612 3.63058i −0.0937412 0.162365i
\(501\) 5.12311 + 8.87348i 0.228883 + 0.396438i
\(502\) 29.2614 1.30600
\(503\) 14.1231 + 24.4619i 0.629718 + 1.09070i 0.987608 + 0.156940i \(0.0501630\pi\)
−0.357890 + 0.933764i \(0.616504\pi\)
\(504\) −0.684658 + 1.18586i −0.0304971 + 0.0528225i
\(505\) 13.4654 23.3228i 0.599204 1.03785i
\(506\) 6.24621 0.277678
\(507\) 0 0
\(508\) 2.38447 0.105794
\(509\) −6.90388 + 11.9579i −0.306009 + 0.530023i −0.977486 0.211003i \(-0.932327\pi\)
0.671476 + 0.741026i \(0.265660\pi\)
\(510\) 4.34233 7.52113i 0.192282 0.333041i
\(511\) 2.84233 + 4.92306i 0.125737 + 0.217783i
\(512\) −11.4233 −0.504843
\(513\) 3.56155 + 6.16879i 0.157246 + 0.272359i
\(514\) −22.7808 39.4575i −1.00482 1.74039i
\(515\) −12.2462 −0.539633
\(516\) −1.00000 1.73205i −0.0440225 0.0762493i
\(517\) 8.24621 14.2829i 0.362668 0.628159i
\(518\) −3.31534 + 5.74234i −0.145668 + 0.252304i
\(519\) 20.2462 0.888710
\(520\) 0 0
\(521\) −9.06913 −0.397326 −0.198663 0.980068i \(-0.563660\pi\)
−0.198663 + 0.980068i \(0.563660\pi\)
\(522\) −5.21922 + 9.03996i −0.228439 + 0.395668i
\(523\) −16.9309 + 29.3251i −0.740335 + 1.28230i 0.212007 + 0.977268i \(0.432000\pi\)
−0.952343 + 0.305030i \(0.901333\pi\)
\(524\) −1.61553 2.79818i −0.0705747 0.122239i
\(525\) −4.31534 −0.188337
\(526\) −7.31534 12.6705i −0.318964 0.552462i
\(527\) −2.00000 3.46410i −0.0871214 0.150899i
\(528\) −9.36932 −0.407747
\(529\) 9.50000 + 16.4545i 0.413043 + 0.715412i
\(530\) 1.90388 3.29762i 0.0826994 0.143239i
\(531\) −1.43845 + 2.49146i −0.0624233 + 0.108120i
\(532\) 1.75379 0.0760364
\(533\) 0 0
\(534\) −7.61553 −0.329556
\(535\) 14.6847 25.4346i 0.634873 1.09963i
\(536\) −5.56155 + 9.63289i −0.240222 + 0.416078i
\(537\) 2.43845 + 4.22351i 0.105227 + 0.182258i
\(538\) −33.3693 −1.43865
\(539\) 6.68466 + 11.5782i 0.287929 + 0.498707i
\(540\) −0.780776 1.35234i −0.0335993 0.0581956i
\(541\) −19.7386 −0.848630 −0.424315 0.905515i \(-0.639485\pi\)
−0.424315 + 0.905515i \(0.639485\pi\)
\(542\) −23.3693 40.4768i −1.00380 1.73863i
\(543\) 1.34233 2.32498i 0.0576049 0.0997745i
\(544\) −1.90388 + 3.29762i −0.0816283 + 0.141384i
\(545\) 10.0000 0.428353
\(546\) 0 0
\(547\) 3.93087 0.168072 0.0840359 0.996463i \(-0.473219\pi\)
0.0840359 + 0.996463i \(0.473219\pi\)
\(548\) −1.21922 + 2.11176i −0.0520827 + 0.0902098i
\(549\) −1.93845 + 3.35749i −0.0827309 + 0.143294i
\(550\) −12.0000 20.7846i −0.511682 0.886259i
\(551\) −47.6155 −2.02849
\(552\) 2.43845 + 4.22351i 0.103787 + 0.179765i
\(553\) 1.52699 + 2.64482i 0.0649341 + 0.112469i
\(554\) 8.30019 0.352641
\(555\) 13.4654 + 23.3228i 0.571576 + 0.989998i
\(556\) 3.93087 6.80847i 0.166706 0.288743i
\(557\) −21.4654 + 37.1792i −0.909520 + 1.57533i −0.0947869 + 0.995498i \(0.530217\pi\)
−0.814733 + 0.579837i \(0.803116\pi\)
\(558\) −4.00000 −0.169334
\(559\) 0 0
\(560\) 9.36932 0.395926
\(561\) 1.56155 2.70469i 0.0659288 0.114192i
\(562\) 13.9039 24.0822i 0.586500 1.01585i
\(563\) 11.6847 + 20.2384i 0.492450 + 0.852948i 0.999962 0.00869657i \(-0.00276824\pi\)
−0.507513 + 0.861644i \(0.669435\pi\)
\(564\) −3.61553 −0.152241
\(565\) −10.3423 17.9134i −0.435105 0.753624i
\(566\) 10.6847 + 18.5064i 0.449110 + 0.777881i
\(567\) −0.561553 −0.0235830
\(568\) −17.0691 29.5646i −0.716205 1.24050i
\(569\) 4.36932 7.56788i 0.183171 0.317262i −0.759787 0.650171i \(-0.774697\pi\)
0.942959 + 0.332910i \(0.108030\pi\)
\(570\) 19.8078 34.3081i 0.829656 1.43701i
\(571\) −5.36932 −0.224699 −0.112349 0.993669i \(-0.535838\pi\)
−0.112349 + 0.993669i \(0.535838\pi\)
\(572\) 0 0
\(573\) −9.12311 −0.381123
\(574\) 0.684658 1.18586i 0.0285771 0.0494970i
\(575\) −7.68466 + 13.3102i −0.320472 + 0.555074i
\(576\) −2.78078 4.81645i −0.115866 0.200685i
\(577\) 17.3153 0.720847 0.360424 0.932789i \(-0.382632\pi\)
0.360424 + 0.932789i \(0.382632\pi\)
\(578\) 11.3693 + 19.6922i 0.472901 + 0.819089i
\(579\) −6.74621 11.6848i −0.280363 0.485603i
\(580\) 10.4384 0.433433
\(581\) 0.246211 + 0.426450i 0.0102146 + 0.0176921i
\(582\) −6.68466 + 11.5782i −0.277088 + 0.479931i
\(583\) 0.684658 1.18586i 0.0283557 0.0491134i
\(584\) −24.6847 −1.02146
\(585\) 0 0
\(586\) −31.9157 −1.31843
\(587\) 19.6847 34.0948i 0.812473 1.40724i −0.0986556 0.995122i \(-0.531454\pi\)
0.911128 0.412123i \(-0.135212\pi\)
\(588\) 1.46543 2.53821i 0.0604335 0.104674i
\(589\) −9.12311 15.8017i −0.375911 0.651097i
\(590\) 16.0000 0.658710
\(591\) 6.68466 + 11.5782i 0.274970 + 0.476262i
\(592\) −17.7116 30.6775i −0.727944 1.26084i
\(593\) 17.4233 0.715489 0.357744 0.933820i \(-0.383546\pi\)
0.357744 + 0.933820i \(0.383546\pi\)
\(594\) −1.56155 2.70469i −0.0640713 0.110975i
\(595\) −1.56155 + 2.70469i −0.0640174 + 0.110881i
\(596\) −0.534565 + 0.925894i −0.0218966 + 0.0379261i
\(597\) 22.1771 0.907648
\(598\) 0 0
\(599\) −41.6155 −1.70036 −0.850182 0.526489i \(-0.823508\pi\)
−0.850182 + 0.526489i \(0.823508\pi\)
\(600\) 9.36932 16.2281i 0.382501 0.662511i
\(601\) 3.53457 6.12205i 0.144178 0.249723i −0.784888 0.619638i \(-0.787280\pi\)
0.929066 + 0.369914i \(0.120613\pi\)
\(602\) 2.00000 + 3.46410i 0.0815139 + 0.141186i
\(603\) −4.56155 −0.185761
\(604\) −2.05398 3.55759i −0.0835751 0.144756i
\(605\) 12.4654 + 21.5908i 0.506792 + 0.877789i
\(606\) −11.8078 −0.479658
\(607\) 8.00000 + 13.8564i 0.324710 + 0.562414i 0.981454 0.191700i \(-0.0614000\pi\)
−0.656744 + 0.754114i \(0.728067\pi\)
\(608\) −8.68466 + 15.0423i −0.352209 + 0.610045i
\(609\) 1.87689 3.25088i 0.0760556 0.131732i
\(610\) 21.5616 0.873002
\(611\) 0 0
\(612\) −0.684658 −0.0276757
\(613\) −17.4309 + 30.1912i −0.704026 + 1.21941i 0.263016 + 0.964792i \(0.415283\pi\)
−0.967042 + 0.254618i \(0.918050\pi\)
\(614\) 24.0540 41.6627i 0.970739 1.68137i
\(615\) −2.78078 4.81645i −0.112132 0.194218i
\(616\) 2.73863 0.110343
\(617\) 4.90388 + 8.49377i 0.197423 + 0.341946i 0.947692 0.319186i \(-0.103409\pi\)
−0.750269 + 0.661132i \(0.770076\pi\)
\(618\) 2.68466 + 4.64996i 0.107993 + 0.187049i
\(619\) −29.3002 −1.17767 −0.588837 0.808252i \(-0.700414\pi\)
−0.588837 + 0.808252i \(0.700414\pi\)
\(620\) 2.00000 + 3.46410i 0.0803219 + 0.139122i
\(621\) −1.00000 + 1.73205i −0.0401286 + 0.0695048i
\(622\) 14.9309 25.8610i 0.598673 1.03693i
\(623\) 2.73863 0.109721
\(624\) 0 0
\(625\) −4.36932 −0.174773
\(626\) 10.6847 18.5064i 0.427045 0.739663i
\(627\) 7.12311 12.3376i 0.284469 0.492716i
\(628\) −4.46543 7.73436i −0.178190 0.308635i
\(629\) 11.8078 0.470806
\(630\) 1.56155 + 2.70469i 0.0622138 + 0.107757i
\(631\) −9.28078 16.0748i −0.369462 0.639927i 0.620020 0.784586i \(-0.287125\pi\)
−0.989481 + 0.144660i \(0.953791\pi\)
\(632\) −13.2614 −0.527509
\(633\) −9.84233 17.0474i −0.391197 0.677574i
\(634\) 10.9730 19.0058i 0.435794 0.754817i
\(635\) −9.68466 + 16.7743i −0.384324 + 0.665669i
\(636\) −0.300187 −0.0119032
\(637\) 0 0
\(638\) 20.8769 0.826524
\(639\) 7.00000 12.1244i 0.276916 0.479632i
\(640\) −24.1501 + 41.8292i −0.954616 + 1.65344i
\(641\) 9.58854 + 16.6078i 0.378725 + 0.655970i 0.990877 0.134770i \(-0.0430294\pi\)
−0.612152 + 0.790740i \(0.709696\pi\)
\(642\) −12.8769 −0.508210
\(643\) −15.7732 27.3200i −0.622034 1.07739i −0.989106 0.147202i \(-0.952973\pi\)
0.367072 0.930192i \(-0.380360\pi\)
\(644\) 0.246211 + 0.426450i 0.00970208 + 0.0168045i
\(645\) 16.2462 0.639694
\(646\) −8.68466 15.0423i −0.341693 0.591830i
\(647\) 3.19224 5.52911i 0.125500 0.217372i −0.796428 0.604733i \(-0.793280\pi\)
0.921928 + 0.387361i \(0.126613\pi\)
\(648\) 1.21922 2.11176i 0.0478956 0.0829577i
\(649\) 5.75379 0.225856
\(650\) 0 0
\(651\) 1.43845 0.0563772
\(652\) −1.05398 + 1.82554i −0.0412769 + 0.0714936i
\(653\) −11.5616 + 20.0252i −0.452439 + 0.783647i −0.998537 0.0540745i \(-0.982779\pi\)
0.546098 + 0.837721i \(0.316112\pi\)
\(654\) −2.19224 3.79706i −0.0857232 0.148477i
\(655\) 26.2462 1.02552
\(656\) 3.65767 + 6.33527i 0.142808 + 0.247351i
\(657\) −5.06155 8.76687i −0.197470 0.342028i
\(658\) 7.23106 0.281896
\(659\) 1.12311 + 1.94528i 0.0437500 + 0.0757772i 0.887071 0.461633i \(-0.152736\pi\)
−0.843321 + 0.537410i \(0.819403\pi\)
\(660\) −1.56155 + 2.70469i −0.0607834 + 0.105280i
\(661\) 2.81534 4.87631i 0.109504 0.189667i −0.806065 0.591827i \(-0.798407\pi\)
0.915569 + 0.402160i \(0.131740\pi\)
\(662\) 4.98485 0.193742
\(663\) 0 0
\(664\) −2.13826 −0.0829806
\(665\) −7.12311 + 12.3376i −0.276222 + 0.478431i
\(666\) 5.90388 10.2258i 0.228771 0.396243i
\(667\) −6.68466 11.5782i −0.258831 0.448308i
\(668\) −4.49242 −0.173817
\(669\) 4.00000 + 6.92820i 0.154649 + 0.267860i
\(670\) 12.6847 + 21.9705i 0.490051 + 0.848793i
\(671\) 7.75379 0.299332
\(672\) −0.684658 1.18586i −0.0264113 0.0457457i
\(673\) 11.6231 20.1318i 0.448038 0.776024i −0.550220 0.835019i \(-0.685456\pi\)
0.998258 + 0.0589952i \(0.0187897\pi\)
\(674\) 4.78078 8.28055i 0.184149 0.318955i
\(675\) 7.68466 0.295783
\(676\) 0 0
\(677\) −15.6155 −0.600153 −0.300077 0.953915i \(-0.597012\pi\)
−0.300077 + 0.953915i \(0.597012\pi\)
\(678\) −4.53457 + 7.85410i −0.174149 + 0.301635i
\(679\) 2.40388 4.16365i 0.0922525 0.159786i
\(680\) −6.78078 11.7446i −0.260031 0.450387i
\(681\) −7.12311 −0.272958
\(682\) 4.00000 + 6.92820i 0.153168 + 0.265295i
\(683\) −19.0540 33.0025i −0.729080 1.26280i −0.957272 0.289188i \(-0.906615\pi\)
0.228192 0.973616i \(-0.426719\pi\)
\(684\) −3.12311 −0.119415
\(685\) −9.90388 17.1540i −0.378408 0.655422i
\(686\) −6.00000 + 10.3923i −0.229081 + 0.396780i
\(687\) −8.12311 + 14.0696i −0.309916 + 0.536790i
\(688\) −21.3693 −0.814698
\(689\) 0 0
\(690\) 11.1231 0.423449
\(691\) −25.6501 + 44.4273i −0.975776 + 1.69009i −0.298424 + 0.954433i \(0.596461\pi\)
−0.677352 + 0.735659i \(0.736872\pi\)
\(692\) −4.43845 + 7.68762i −0.168724 + 0.292239i
\(693\) 0.561553 + 0.972638i 0.0213316 + 0.0369475i
\(694\) 43.1231 1.63693
\(695\) 31.9309 + 55.3059i 1.21121 + 2.09787i
\(696\) 8.15009 + 14.1164i 0.308928 + 0.535080i
\(697\) −2.43845 −0.0923628
\(698\) 5.31534 + 9.20644i 0.201189 + 0.348469i
\(699\) −13.0000 + 22.5167i −0.491705 + 0.851658i
\(700\) 0.946025 1.63856i 0.0357564 0.0619319i
\(701\) −5.36932 −0.202796 −0.101398 0.994846i \(-0.532332\pi\)
−0.101398 + 0.994846i \(0.532332\pi\)
\(702\) 0 0
\(703\) 53.8617 2.03143
\(704\) −5.56155 + 9.63289i −0.209609 + 0.363053i
\(705\) 14.6847 25.4346i 0.553056 0.957921i
\(706\) 4.15009 + 7.18817i 0.156191 + 0.270530i
\(707\) 4.24621 0.159695
\(708\) −0.630683 1.09238i −0.0237025 0.0410540i
\(709\) −3.74621 6.48863i −0.140692 0.243686i 0.787065 0.616869i \(-0.211599\pi\)
−0.927757 + 0.373184i \(0.878266\pi\)
\(710\) −77.8617 −2.92210
\(711\) −2.71922 4.70983i −0.101979 0.176633i
\(712\) −5.94602 + 10.2988i −0.222837 + 0.385964i
\(713\) 2.56155 4.43674i 0.0959309 0.166157i
\(714\) 1.36932 0.0512454
\(715\) 0 0
\(716\) −2.13826 −0.0799106
\(717\) −12.6847 + 21.9705i −0.473717 + 0.820502i
\(718\) −7.31534 + 12.6705i −0.273006 + 0.472860i
\(719\) 11.6847 + 20.2384i 0.435764 + 0.754766i 0.997358 0.0726475i \(-0.0231448\pi\)
−0.561593 + 0.827413i \(0.689811\pi\)
\(720\) −16.6847 −0.621801
\(721\) −0.965435 1.67218i −0.0359547 0.0622753i
\(722\) −24.7808 42.9216i −0.922245 1.59738i
\(723\) 17.8078 0.662278
\(724\) 0.588540 + 1.01938i 0.0218729 + 0.0378850i
\(725\) −25.6847 + 44.4871i −0.953904 + 1.65221i
\(726\) 5.46543 9.46641i 0.202841 0.351331i
\(727\) −38.6695 −1.43417 −0.717086 0.696984i \(-0.754525\pi\)
−0.717086 + 0.696984i \(0.754525\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) −28.1501 + 48.7574i −1.04188 + 1.80459i
\(731\) 3.56155 6.16879i 0.131729 0.228161i
\(732\) −0.849907 1.47208i −0.0314135 0.0544097i
\(733\) −20.5076 −0.757465 −0.378732 0.925506i \(-0.623640\pi\)
−0.378732 + 0.925506i \(0.623640\pi\)
\(734\) 13.3153 + 23.0628i 0.491478 + 0.851265i
\(735\) 11.9039 + 20.6181i 0.439081 + 0.760511i
\(736\) −4.87689 −0.179765
\(737\) 4.56155 + 7.90084i 0.168027 + 0.291031i
\(738\) −1.21922 + 2.11176i −0.0448802 + 0.0777349i
\(739\) 5.12311 8.87348i 0.188456 0.326416i −0.756279 0.654249i \(-0.772985\pi\)
0.944736 + 0.327833i \(0.106318\pi\)
\(740\) −11.8078 −0.434062
\(741\) 0 0
\(742\) 0.600373 0.0220404
\(743\) −6.31534 + 10.9385i −0.231687 + 0.401294i −0.958305 0.285748i \(-0.907758\pi\)
0.726617 + 0.687042i \(0.241091\pi\)
\(744\) −3.12311 + 5.40938i −0.114499 + 0.198317i
\(745\) −4.34233 7.52113i −0.159091 0.275553i
\(746\) 44.3002 1.62195
\(747\) −0.438447 0.759413i −0.0160419 0.0277855i
\(748\) 0.684658 + 1.18586i 0.0250336 + 0.0433595i
\(749\) 4.63068 0.169201
\(750\) −7.46543 12.9305i −0.272599 0.472156i
\(751\) −22.0540 + 38.1986i −0.804761 + 1.39389i 0.111691 + 0.993743i \(0.464373\pi\)
−0.916452 + 0.400144i \(0.868960\pi\)
\(752\) −19.3153 + 33.4552i −0.704358 + 1.21998i
\(753\) 18.7386 0.682874
\(754\) 0 0
\(755\) 33.3693 1.21443
\(756\) 0.123106 0.213225i 0.00447731 0.00775493i
\(757\) −15.0000 + 25.9808i −0.545184 + 0.944287i 0.453411 + 0.891302i \(0.350207\pi\)
−0.998595 + 0.0529853i \(0.983126\pi\)
\(758\) 18.4924 + 32.0298i 0.671675 + 1.16338i
\(759\) 4.00000 0.145191
\(760\) −30.9309 53.5738i −1.12198 1.94333i
\(761\) 4.68466 + 8.11407i 0.169819 + 0.294135i 0.938356 0.345670i \(-0.112348\pi\)
−0.768537 + 0.639805i \(0.779015\pi\)
\(762\) 8.49242 0.307648
\(763\) 0.788354 + 1.36547i 0.0285403 + 0.0494333i
\(764\) 2.00000 3.46410i 0.0723575 0.125327i
\(765\) 2.78078 4.81645i 0.100539 0.174139i
\(766\) 35.5076 1.28294
\(767\) 0 0
\(768\) 10.0540 0.362792
\(769\) −9.00000 + 15.5885i −0.324548 + 0.562134i −0.981421 0.191867i \(-0.938546\pi\)
0.656873 + 0.754002i \(0.271879\pi\)
\(770\) 3.12311 5.40938i 0.112549 0.194940i
\(771\) −14.5885 25.2681i −0.525393 0.910008i
\(772\) 5.91571 0.212911
\(773\) −12.1231 20.9978i −0.436038 0.755240i 0.561342 0.827584i \(-0.310285\pi\)
−0.997380 + 0.0723444i \(0.976952\pi\)
\(774\) −3.56155 6.16879i −0.128017 0.221733i
\(775\) −19.6847 −0.707094
\(776\) 10.4384 + 18.0799i 0.374718 + 0.649031i
\(777\) −2.12311 + 3.67733i −0.0761660 + 0.131923i
\(778\) −26.5885 + 46.0527i −0.953245 + 1.65107i
\(779\) −11.1231 −0.398527