Properties

Label 546.2.l.i.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.l (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(1.28078 - 2.21837i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.i.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 + 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.78078 + 3.08440i) q^{10} +(-1.28078 - 2.21837i) q^{11} +1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} -1.00000 q^{14} +(1.78078 + 3.08440i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-3.84233 + 6.65511i) q^{19} +(1.78078 - 3.08440i) q^{20} -1.00000 q^{21} +(-1.28078 + 2.21837i) q^{22} +(4.56155 + 7.90084i) q^{23} +(-0.500000 - 0.866025i) q^{24} +7.68466 q^{25} +(3.34233 - 1.35234i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(0.500000 + 0.866025i) q^{29} +(1.78078 - 3.08440i) q^{30} +5.12311 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.28078 + 2.21837i) q^{33} -5.00000 q^{34} +(-1.78078 + 3.08440i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(4.90388 + 8.49377i) q^{37} +7.68466 q^{38} +(3.34233 - 1.35234i) q^{39} -3.56155 q^{40} +(-2.06155 - 3.57071i) q^{41} +(0.500000 + 0.866025i) q^{42} +(1.43845 - 2.49146i) q^{43} +2.56155 q^{44} +(1.78078 - 3.08440i) q^{45} +(4.56155 - 7.90084i) q^{46} -7.68466 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-3.84233 - 6.65511i) q^{50} -5.00000 q^{51} +(-2.84233 - 2.21837i) q^{52} -3.87689 q^{53} +(-0.500000 - 0.866025i) q^{54} +(4.56155 + 7.90084i) q^{55} +(0.500000 - 0.866025i) q^{56} +7.68466 q^{57} +(0.500000 - 0.866025i) q^{58} +(-6.56155 + 11.3649i) q^{59} -3.56155 q^{60} +(0.500000 - 0.866025i) q^{61} +(-2.56155 - 4.43674i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(1.78078 - 12.7173i) q^{65} +2.56155 q^{66} +(-0.561553 - 0.972638i) q^{67} +(2.50000 + 4.33013i) q^{68} +(4.56155 - 7.90084i) q^{69} +3.56155 q^{70} +(2.00000 - 3.46410i) q^{71} +(-0.500000 + 0.866025i) q^{72} -2.43845 q^{73} +(4.90388 - 8.49377i) q^{74} +(-3.84233 - 6.65511i) q^{75} +(-3.84233 - 6.65511i) q^{76} -2.56155 q^{77} +(-2.84233 - 2.21837i) q^{78} +1.43845 q^{79} +(1.78078 + 3.08440i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.06155 + 3.57071i) q^{82} -10.2462 q^{83} +(0.500000 - 0.866025i) q^{84} +(-8.90388 + 15.4220i) q^{85} -2.87689 q^{86} +(0.500000 - 0.866025i) q^{87} +(-1.28078 - 2.21837i) q^{88} +(4.84233 + 8.38716i) q^{89} -3.56155 q^{90} +(2.84233 + 2.21837i) q^{91} -9.12311 q^{92} +(-2.56155 - 4.43674i) q^{93} +(3.84233 + 6.65511i) q^{94} +(13.6847 - 23.7025i) q^{95} +1.00000 q^{96} +(-6.12311 + 10.6055i) q^{97} +(-0.500000 + 0.866025i) q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} - 2q^{3} - 2q^{4} - 6q^{5} - 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + 3q^{10} - q^{11} + 4q^{12} - 2q^{13} - 4q^{14} + 3q^{15} - 2q^{16} + 10q^{17} + 4q^{18} - 3q^{19} + 3q^{20} - 4q^{21} - q^{22} + 10q^{23} - 2q^{24} + 6q^{25} + q^{26} + 4q^{27} + 2q^{28} + 2q^{29} + 3q^{30} + 4q^{31} - 2q^{32} - q^{33} - 20q^{34} - 3q^{35} - 2q^{36} - q^{37} + 6q^{38} + q^{39} - 6q^{40} + 2q^{42} + 14q^{43} + 2q^{44} + 3q^{45} + 10q^{46} - 6q^{47} - 2q^{48} - 2q^{49} - 3q^{50} - 20q^{51} + q^{52} - 32q^{53} - 2q^{54} + 10q^{55} + 2q^{56} + 6q^{57} + 2q^{58} - 18q^{59} - 6q^{60} + 2q^{61} - 2q^{62} + 2q^{63} + 4q^{64} + 3q^{65} + 2q^{66} + 6q^{67} + 10q^{68} + 10q^{69} + 6q^{70} + 8q^{71} - 2q^{72} - 18q^{73} - q^{74} - 3q^{75} - 3q^{76} - 2q^{77} + q^{78} + 14q^{79} + 3q^{80} - 2q^{81} - 8q^{83} + 2q^{84} - 15q^{85} - 28q^{86} + 2q^{87} - q^{88} + 7q^{89} - 6q^{90} - q^{91} - 20q^{92} - 2q^{93} + 3q^{94} + 30q^{95} + 4q^{96} - 8q^{97} - 2q^{98} + 2q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 0.866025i −0.353553 0.612372i
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −3.56155 −1.59277 −0.796387 0.604787i \(-0.793258\pi\)
−0.796387 + 0.604787i \(0.793258\pi\)
\(6\) −0.500000 + 0.866025i −0.204124 + 0.353553i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) 1.00000 0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 1.78078 + 3.08440i 0.563131 + 0.975371i
\(11\) −1.28078 2.21837i −0.386169 0.668864i 0.605762 0.795646i \(-0.292868\pi\)
−0.991931 + 0.126782i \(0.959535\pi\)
\(12\) 1.00000 0.288675
\(13\) −0.500000 + 3.57071i −0.138675 + 0.990338i
\(14\) −1.00000 −0.267261
\(15\) 1.78078 + 3.08440i 0.459794 + 0.796387i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 2.50000 4.33013i 0.606339 1.05021i −0.385499 0.922708i \(-0.625971\pi\)
0.991838 0.127502i \(-0.0406959\pi\)
\(18\) 1.00000 0.235702
\(19\) −3.84233 + 6.65511i −0.881491 + 1.52679i −0.0318071 + 0.999494i \(0.510126\pi\)
−0.849684 + 0.527293i \(0.823207\pi\)
\(20\) 1.78078 3.08440i 0.398194 0.689692i
\(21\) −1.00000 −0.218218
\(22\) −1.28078 + 2.21837i −0.273062 + 0.472958i
\(23\) 4.56155 + 7.90084i 0.951150 + 1.64744i 0.742943 + 0.669354i \(0.233429\pi\)
0.208206 + 0.978085i \(0.433237\pi\)
\(24\) −0.500000 0.866025i −0.102062 0.176777i
\(25\) 7.68466 1.53693
\(26\) 3.34233 1.35234i 0.655485 0.265217i
\(27\) 1.00000 0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 0.500000 + 0.866025i 0.0928477 + 0.160817i 0.908708 0.417432i \(-0.137070\pi\)
−0.815861 + 0.578249i \(0.803736\pi\)
\(30\) 1.78078 3.08440i 0.325124 0.563131i
\(31\) 5.12311 0.920137 0.460068 0.887883i \(-0.347825\pi\)
0.460068 + 0.887883i \(0.347825\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) −1.28078 + 2.21837i −0.222955 + 0.386169i
\(34\) −5.00000 −0.857493
\(35\) −1.78078 + 3.08440i −0.301006 + 0.521358i
\(36\) −0.500000 0.866025i −0.0833333 0.144338i
\(37\) 4.90388 + 8.49377i 0.806193 + 1.39637i 0.915483 + 0.402358i \(0.131809\pi\)
−0.109289 + 0.994010i \(0.534857\pi\)
\(38\) 7.68466 1.24662
\(39\) 3.34233 1.35234i 0.535201 0.216548i
\(40\) −3.56155 −0.563131
\(41\) −2.06155 3.57071i −0.321960 0.557652i 0.658932 0.752202i \(-0.271008\pi\)
−0.980892 + 0.194551i \(0.937675\pi\)
\(42\) 0.500000 + 0.866025i 0.0771517 + 0.133631i
\(43\) 1.43845 2.49146i 0.219361 0.379945i −0.735252 0.677794i \(-0.762936\pi\)
0.954613 + 0.297850i \(0.0962694\pi\)
\(44\) 2.56155 0.386169
\(45\) 1.78078 3.08440i 0.265462 0.459794i
\(46\) 4.56155 7.90084i 0.672564 1.16492i
\(47\) −7.68466 −1.12092 −0.560461 0.828181i \(-0.689376\pi\)
−0.560461 + 0.828181i \(0.689376\pi\)
\(48\) −0.500000 + 0.866025i −0.0721688 + 0.125000i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −3.84233 6.65511i −0.543387 0.941175i
\(51\) −5.00000 −0.700140
\(52\) −2.84233 2.21837i −0.394160 0.307633i
\(53\) −3.87689 −0.532532 −0.266266 0.963900i \(-0.585790\pi\)
−0.266266 + 0.963900i \(0.585790\pi\)
\(54\) −0.500000 0.866025i −0.0680414 0.117851i
\(55\) 4.56155 + 7.90084i 0.615080 + 1.06535i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 7.68466 1.01786
\(58\) 0.500000 0.866025i 0.0656532 0.113715i
\(59\) −6.56155 + 11.3649i −0.854241 + 1.47959i 0.0231056 + 0.999733i \(0.492645\pi\)
−0.877347 + 0.479857i \(0.840689\pi\)
\(60\) −3.56155 −0.459794
\(61\) 0.500000 0.866025i 0.0640184 0.110883i −0.832240 0.554416i \(-0.812942\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) −2.56155 4.43674i −0.325318 0.563466i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 1.78078 12.7173i 0.220878 1.57739i
\(66\) 2.56155 0.315305
\(67\) −0.561553 0.972638i −0.0686046 0.118827i 0.829683 0.558235i \(-0.188521\pi\)
−0.898287 + 0.439409i \(0.855188\pi\)
\(68\) 2.50000 + 4.33013i 0.303170 + 0.525105i
\(69\) 4.56155 7.90084i 0.549146 0.951150i
\(70\) 3.56155 0.425687
\(71\) 2.00000 3.46410i 0.237356 0.411113i −0.722599 0.691268i \(-0.757052\pi\)
0.959955 + 0.280155i \(0.0903858\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) −2.43845 −0.285399 −0.142699 0.989766i \(-0.545578\pi\)
−0.142699 + 0.989766i \(0.545578\pi\)
\(74\) 4.90388 8.49377i 0.570065 0.987381i
\(75\) −3.84233 6.65511i −0.443674 0.768466i
\(76\) −3.84233 6.65511i −0.440745 0.763393i
\(77\) −2.56155 −0.291916
\(78\) −2.84233 2.21837i −0.321830 0.251181i
\(79\) 1.43845 0.161838 0.0809190 0.996721i \(-0.474214\pi\)
0.0809190 + 0.996721i \(0.474214\pi\)
\(80\) 1.78078 + 3.08440i 0.199097 + 0.344846i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.06155 + 3.57071i −0.227660 + 0.394319i
\(83\) −10.2462 −1.12467 −0.562334 0.826910i \(-0.690096\pi\)
−0.562334 + 0.826910i \(0.690096\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) −8.90388 + 15.4220i −0.965762 + 1.67275i
\(86\) −2.87689 −0.310223
\(87\) 0.500000 0.866025i 0.0536056 0.0928477i
\(88\) −1.28078 2.21837i −0.136531 0.236479i
\(89\) 4.84233 + 8.38716i 0.513286 + 0.889037i 0.999881 + 0.0154098i \(0.00490527\pi\)
−0.486595 + 0.873627i \(0.661761\pi\)
\(90\) −3.56155 −0.375421
\(91\) 2.84233 + 2.21837i 0.297957 + 0.232548i
\(92\) −9.12311 −0.951150
\(93\) −2.56155 4.43674i −0.265621 0.460068i
\(94\) 3.84233 + 6.65511i 0.396306 + 0.686422i
\(95\) 13.6847 23.7025i 1.40402 2.43183i
\(96\) 1.00000 0.102062
\(97\) −6.12311 + 10.6055i −0.621707 + 1.07683i 0.367461 + 0.930039i \(0.380227\pi\)
−0.989168 + 0.146789i \(0.953106\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 2.56155 0.257446
\(100\) −3.84233 + 6.65511i −0.384233 + 0.665511i
\(101\) 9.78078 + 16.9408i 0.973224 + 1.68567i 0.685677 + 0.727906i \(0.259506\pi\)
0.287547 + 0.957767i \(0.407160\pi\)
\(102\) 2.50000 + 4.33013i 0.247537 + 0.428746i
\(103\) −11.3693 −1.12025 −0.560126 0.828407i \(-0.689247\pi\)
−0.560126 + 0.828407i \(0.689247\pi\)
\(104\) −0.500000 + 3.57071i −0.0490290 + 0.350137i
\(105\) 3.56155 0.347572
\(106\) 1.93845 + 3.35749i 0.188279 + 0.326108i
\(107\) 4.71922 + 8.17394i 0.456225 + 0.790204i 0.998758 0.0498303i \(-0.0158680\pi\)
−0.542533 + 0.840034i \(0.682535\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 0.876894 0.0839912 0.0419956 0.999118i \(-0.486628\pi\)
0.0419956 + 0.999118i \(0.486628\pi\)
\(110\) 4.56155 7.90084i 0.434927 0.753316i
\(111\) 4.90388 8.49377i 0.465456 0.806193i
\(112\) −1.00000 −0.0944911
\(113\) −8.46543 + 14.6626i −0.796361 + 1.37934i 0.125610 + 0.992080i \(0.459911\pi\)
−0.921971 + 0.387258i \(0.873422\pi\)
\(114\) −3.84233 6.65511i −0.359867 0.623308i
\(115\) −16.2462 28.1393i −1.51497 2.62400i
\(116\) −1.00000 −0.0928477
\(117\) −2.84233 2.21837i −0.262773 0.205088i
\(118\) 13.1231 1.20808
\(119\) −2.50000 4.33013i −0.229175 0.396942i
\(120\) 1.78078 + 3.08440i 0.162562 + 0.281565i
\(121\) 2.21922 3.84381i 0.201748 0.349437i
\(122\) −1.00000 −0.0905357
\(123\) −2.06155 + 3.57071i −0.185884 + 0.321960i
\(124\) −2.56155 + 4.43674i −0.230034 + 0.398431i
\(125\) −9.56155 −0.855211
\(126\) 0.500000 0.866025i 0.0445435 0.0771517i
\(127\) −1.12311 1.94528i −0.0996595 0.172615i 0.811884 0.583818i \(-0.198442\pi\)
−0.911544 + 0.411203i \(0.865109\pi\)
\(128\) −0.500000 0.866025i −0.0441942 0.0765466i
\(129\) −2.87689 −0.253296
\(130\) −11.9039 + 4.81645i −1.04404 + 0.422430i
\(131\) −16.4924 −1.44095 −0.720475 0.693481i \(-0.756076\pi\)
−0.720475 + 0.693481i \(0.756076\pi\)
\(132\) −1.28078 2.21837i −0.111477 0.193084i
\(133\) 3.84233 + 6.65511i 0.333172 + 0.577071i
\(134\) −0.561553 + 0.972638i −0.0485108 + 0.0840231i
\(135\) −3.56155 −0.306530
\(136\) 2.50000 4.33013i 0.214373 0.371305i
\(137\) 2.90388 5.02967i 0.248095 0.429714i −0.714902 0.699225i \(-0.753529\pi\)
0.962997 + 0.269511i \(0.0868620\pi\)
\(138\) −9.12311 −0.776610
\(139\) 3.84233 6.65511i 0.325902 0.564479i −0.655792 0.754941i \(-0.727665\pi\)
0.981695 + 0.190462i \(0.0609987\pi\)
\(140\) −1.78078 3.08440i −0.150503 0.260679i
\(141\) 3.84233 + 6.65511i 0.323582 + 0.560461i
\(142\) −4.00000 −0.335673
\(143\) 8.56155 3.46410i 0.715953 0.289683i
\(144\) 1.00000 0.0833333
\(145\) −1.78078 3.08440i −0.147885 0.256145i
\(146\) 1.21922 + 2.11176i 0.100904 + 0.174770i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −9.80776 −0.806193
\(149\) 8.90388 15.4220i 0.729434 1.26342i −0.227688 0.973734i \(-0.573117\pi\)
0.957123 0.289683i \(-0.0935500\pi\)
\(150\) −3.84233 + 6.65511i −0.313725 + 0.543387i
\(151\) −17.4384 −1.41912 −0.709560 0.704645i \(-0.751106\pi\)
−0.709560 + 0.704645i \(0.751106\pi\)
\(152\) −3.84233 + 6.65511i −0.311654 + 0.539801i
\(153\) 2.50000 + 4.33013i 0.202113 + 0.350070i
\(154\) 1.28078 + 2.21837i 0.103208 + 0.178761i
\(155\) −18.2462 −1.46557
\(156\) −0.500000 + 3.57071i −0.0400320 + 0.285886i
\(157\) −5.80776 −0.463510 −0.231755 0.972774i \(-0.574447\pi\)
−0.231755 + 0.972774i \(0.574447\pi\)
\(158\) −0.719224 1.24573i −0.0572184 0.0991051i
\(159\) 1.93845 + 3.35749i 0.153729 + 0.266266i
\(160\) 1.78078 3.08440i 0.140783 0.243843i
\(161\) 9.12311 0.719001
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 0.561553 0.972638i 0.0439842 0.0761829i −0.843195 0.537608i \(-0.819328\pi\)
0.887179 + 0.461425i \(0.152662\pi\)
\(164\) 4.12311 0.321960
\(165\) 4.56155 7.90084i 0.355116 0.615080i
\(166\) 5.12311 + 8.87348i 0.397630 + 0.688716i
\(167\) −10.2462 17.7470i −0.792876 1.37330i −0.924179 0.381959i \(-0.875250\pi\)
0.131304 0.991342i \(-0.458084\pi\)
\(168\) −1.00000 −0.0771517
\(169\) −12.5000 3.57071i −0.961538 0.274670i
\(170\) 17.8078 1.36579
\(171\) −3.84233 6.65511i −0.293830 0.508929i
\(172\) 1.43845 + 2.49146i 0.109681 + 0.189972i
\(173\) 2.43845 4.22351i 0.185392 0.321108i −0.758317 0.651886i \(-0.773978\pi\)
0.943708 + 0.330778i \(0.107311\pi\)
\(174\) −1.00000 −0.0758098
\(175\) 3.84233 6.65511i 0.290453 0.503079i
\(176\) −1.28078 + 2.21837i −0.0965422 + 0.167216i
\(177\) 13.1231 0.986393
\(178\) 4.84233 8.38716i 0.362948 0.628644i
\(179\) 8.24621 + 14.2829i 0.616351 + 1.06755i 0.990146 + 0.140040i \(0.0447230\pi\)
−0.373795 + 0.927511i \(0.621944\pi\)
\(180\) 1.78078 + 3.08440i 0.132731 + 0.229897i
\(181\) 13.2462 0.984583 0.492292 0.870430i \(-0.336159\pi\)
0.492292 + 0.870430i \(0.336159\pi\)
\(182\) 0.500000 3.57071i 0.0370625 0.264679i
\(183\) −1.00000 −0.0739221
\(184\) 4.56155 + 7.90084i 0.336282 + 0.582458i
\(185\) −17.4654 30.2510i −1.28408 2.22410i
\(186\) −2.56155 + 4.43674i −0.187822 + 0.325318i
\(187\) −12.8078 −0.936596
\(188\) 3.84233 6.65511i 0.280231 0.485374i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) −27.3693 −1.98558
\(191\) −2.87689 + 4.98293i −0.208165 + 0.360552i −0.951136 0.308771i \(-0.900082\pi\)
0.742972 + 0.669323i \(0.233416\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 10.1847 + 17.6403i 0.733108 + 1.26978i 0.955549 + 0.294834i \(0.0952642\pi\)
−0.222441 + 0.974946i \(0.571402\pi\)
\(194\) 12.2462 0.879227
\(195\) −11.9039 + 4.81645i −0.852455 + 0.344913i
\(196\) 1.00000 0.0714286
\(197\) 0.280776 + 0.486319i 0.0200045 + 0.0346488i 0.875854 0.482576i \(-0.160299\pi\)
−0.855850 + 0.517224i \(0.826965\pi\)
\(198\) −1.28078 2.21837i −0.0910208 0.157653i
\(199\) 8.80776 15.2555i 0.624366 1.08143i −0.364297 0.931283i \(-0.618691\pi\)
0.988663 0.150151i \(-0.0479759\pi\)
\(200\) 7.68466 0.543387
\(201\) −0.561553 + 0.972638i −0.0396089 + 0.0686046i
\(202\) 9.78078 16.9408i 0.688173 1.19195i
\(203\) 1.00000 0.0701862
\(204\) 2.50000 4.33013i 0.175035 0.303170i
\(205\) 7.34233 + 12.7173i 0.512811 + 0.888214i
\(206\) 5.68466 + 9.84612i 0.396069 + 0.686011i
\(207\) −9.12311 −0.634100
\(208\) 3.34233 1.35234i 0.231749 0.0937682i
\(209\) 19.6847 1.36162
\(210\) −1.78078 3.08440i −0.122885 0.212843i
\(211\) 1.43845 + 2.49146i 0.0990268 + 0.171519i 0.911282 0.411783i \(-0.135094\pi\)
−0.812255 + 0.583302i \(0.801760\pi\)
\(212\) 1.93845 3.35749i 0.133133 0.230593i
\(213\) −4.00000 −0.274075
\(214\) 4.71922 8.17394i 0.322599 0.558759i
\(215\) −5.12311 + 8.87348i −0.349393 + 0.605166i
\(216\) 1.00000 0.0680414
\(217\) 2.56155 4.43674i 0.173890 0.301186i
\(218\) −0.438447 0.759413i −0.0296954 0.0514339i
\(219\) 1.21922 + 2.11176i 0.0823875 + 0.142699i
\(220\) −9.12311 −0.615080
\(221\) 14.2116 + 11.0918i 0.955979 + 0.746119i
\(222\) −9.80776 −0.658254
\(223\) 8.24621 + 14.2829i 0.552207 + 0.956451i 0.998115 + 0.0613719i \(0.0195476\pi\)
−0.445908 + 0.895079i \(0.647119\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) −3.84233 + 6.65511i −0.256155 + 0.443674i
\(226\) 16.9309 1.12622
\(227\) −6.56155 + 11.3649i −0.435506 + 0.754318i −0.997337 0.0729341i \(-0.976764\pi\)
0.561831 + 0.827252i \(0.310097\pi\)
\(228\) −3.84233 + 6.65511i −0.254464 + 0.440745i
\(229\) 22.8078 1.50718 0.753590 0.657345i \(-0.228321\pi\)
0.753590 + 0.657345i \(0.228321\pi\)
\(230\) −16.2462 + 28.1393i −1.07124 + 1.85545i
\(231\) 1.28078 + 2.21837i 0.0842689 + 0.145958i
\(232\) 0.500000 + 0.866025i 0.0328266 + 0.0568574i
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) −0.500000 + 3.57071i −0.0326860 + 0.233425i
\(235\) 27.3693 1.78538
\(236\) −6.56155 11.3649i −0.427121 0.739795i
\(237\) −0.719224 1.24573i −0.0467186 0.0809190i
\(238\) −2.50000 + 4.33013i −0.162051 + 0.280680i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 1.78078 3.08440i 0.114949 0.199097i
\(241\) −5.65767 + 9.79937i −0.364443 + 0.631233i −0.988687 0.149996i \(-0.952074\pi\)
0.624244 + 0.781229i \(0.285407\pi\)
\(242\) −4.43845 −0.285314
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0.500000 + 0.866025i 0.0320092 + 0.0554416i
\(245\) 1.78078 + 3.08440i 0.113770 + 0.197055i
\(246\) 4.12311 0.262880
\(247\) −21.8423 17.0474i −1.38979 1.08470i
\(248\) 5.12311 0.325318
\(249\) 5.12311 + 8.87348i 0.324664 + 0.562334i
\(250\) 4.78078 + 8.28055i 0.302363 + 0.523708i
\(251\) −4.24621 + 7.35465i −0.268018 + 0.464222i −0.968350 0.249596i \(-0.919702\pi\)
0.700332 + 0.713818i \(0.253035\pi\)
\(252\) −1.00000 −0.0629941
\(253\) 11.6847 20.2384i 0.734608 1.27238i
\(254\) −1.12311 + 1.94528i −0.0704699 + 0.122057i
\(255\) 17.8078 1.11517
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 7.37689 + 12.7772i 0.460158 + 0.797017i 0.998968 0.0454100i \(-0.0144594\pi\)
−0.538810 + 0.842427i \(0.681126\pi\)
\(258\) 1.43845 + 2.49146i 0.0895538 + 0.155112i
\(259\) 9.80776 0.609425
\(260\) 10.1231 + 7.90084i 0.627808 + 0.489989i
\(261\) −1.00000 −0.0618984
\(262\) 8.24621 + 14.2829i 0.509453 + 0.882398i
\(263\) 10.2462 + 17.7470i 0.631808 + 1.09432i 0.987182 + 0.159600i \(0.0510204\pi\)
−0.355373 + 0.934724i \(0.615646\pi\)
\(264\) −1.28078 + 2.21837i −0.0788263 + 0.136531i
\(265\) 13.8078 0.848204
\(266\) 3.84233 6.65511i 0.235588 0.408051i
\(267\) 4.84233 8.38716i 0.296346 0.513286i
\(268\) 1.12311 0.0686046
\(269\) 2.43845 4.22351i 0.148675 0.257512i −0.782063 0.623199i \(-0.785833\pi\)
0.930738 + 0.365687i \(0.119166\pi\)
\(270\) 1.78078 + 3.08440i 0.108375 + 0.187710i
\(271\) −6.56155 11.3649i −0.398586 0.690371i 0.594966 0.803751i \(-0.297166\pi\)
−0.993552 + 0.113380i \(0.963832\pi\)
\(272\) −5.00000 −0.303170
\(273\) 0.500000 3.57071i 0.0302614 0.216109i
\(274\) −5.80776 −0.350860
\(275\) −9.84233 17.0474i −0.593515 1.02800i
\(276\) 4.56155 + 7.90084i 0.274573 + 0.475575i
\(277\) 1.78078 3.08440i 0.106996 0.185323i −0.807556 0.589791i \(-0.799210\pi\)
0.914552 + 0.404468i \(0.132543\pi\)
\(278\) −7.68466 −0.460895
\(279\) −2.56155 + 4.43674i −0.153356 + 0.265621i
\(280\) −1.78078 + 3.08440i −0.106422 + 0.184328i
\(281\) 7.80776 0.465772 0.232886 0.972504i \(-0.425183\pi\)
0.232886 + 0.972504i \(0.425183\pi\)
\(282\) 3.84233 6.65511i 0.228807 0.396306i
\(283\) −4.24621 7.35465i −0.252411 0.437189i 0.711778 0.702404i \(-0.247890\pi\)
−0.964189 + 0.265216i \(0.914557\pi\)
\(284\) 2.00000 + 3.46410i 0.118678 + 0.205557i
\(285\) −27.3693 −1.62122
\(286\) −7.28078 5.68247i −0.430521 0.336012i
\(287\) −4.12311 −0.243379
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) −1.78078 + 3.08440i −0.104571 + 0.181122i
\(291\) 12.2462 0.717886
\(292\) 1.21922 2.11176i 0.0713497 0.123581i
\(293\) 2.34233 4.05703i 0.136840 0.237014i −0.789459 0.613804i \(-0.789639\pi\)
0.926299 + 0.376789i \(0.122972\pi\)
\(294\) 1.00000 0.0583212
\(295\) 23.3693 40.4768i 1.36061 2.35665i
\(296\) 4.90388 + 8.49377i 0.285032 + 0.493691i
\(297\) −1.28078 2.21837i −0.0743182 0.128723i
\(298\) −17.8078 −1.03158
\(299\) −30.4924 + 12.3376i −1.76342 + 0.713501i
\(300\) 7.68466 0.443674
\(301\) −1.43845 2.49146i −0.0829107 0.143606i
\(302\) 8.71922 + 15.1021i 0.501735 + 0.869030i
\(303\) 9.78078 16.9408i 0.561891 0.973224i
\(304\) 7.68466 0.440745
\(305\) −1.78078 + 3.08440i −0.101967 + 0.176612i
\(306\) 2.50000 4.33013i 0.142915 0.247537i
\(307\) −33.9309 −1.93654 −0.968269 0.249912i \(-0.919598\pi\)
−0.968269 + 0.249912i \(0.919598\pi\)
\(308\) 1.28078 2.21837i 0.0729790 0.126403i
\(309\) 5.68466 + 9.84612i 0.323389 + 0.560126i
\(310\) 9.12311 + 15.8017i 0.518158 + 0.897475i
\(311\) 22.5616 1.27935 0.639674 0.768646i \(-0.279069\pi\)
0.639674 + 0.768646i \(0.279069\pi\)
\(312\) 3.34233 1.35234i 0.189222 0.0765614i
\(313\) 27.6155 1.56092 0.780461 0.625205i \(-0.214984\pi\)
0.780461 + 0.625205i \(0.214984\pi\)
\(314\) 2.90388 + 5.02967i 0.163876 + 0.283841i
\(315\) −1.78078 3.08440i −0.100335 0.173786i
\(316\) −0.719224 + 1.24573i −0.0404595 + 0.0700779i
\(317\) −11.5616 −0.649362 −0.324681 0.945824i \(-0.605257\pi\)
−0.324681 + 0.945824i \(0.605257\pi\)
\(318\) 1.93845 3.35749i 0.108703 0.188279i
\(319\) 1.28078 2.21837i 0.0717097 0.124205i
\(320\) −3.56155 −0.199097
\(321\) 4.71922 8.17394i 0.263401 0.456225i
\(322\) −4.56155 7.90084i −0.254205 0.440297i
\(323\) 19.2116 + 33.2755i 1.06896 + 1.85150i
\(324\) 1.00000 0.0555556
\(325\) −3.84233 + 27.4397i −0.213134 + 1.52208i
\(326\) −1.12311 −0.0622031
\(327\) −0.438447 0.759413i −0.0242462 0.0419956i
\(328\) −2.06155 3.57071i −0.113830 0.197160i
\(329\) −3.84233 + 6.65511i −0.211834 + 0.366908i
\(330\) −9.12311 −0.502210
\(331\) 17.6847 30.6307i 0.972037 1.68362i 0.282651 0.959223i \(-0.408786\pi\)
0.689386 0.724394i \(-0.257880\pi\)
\(332\) 5.12311 8.87348i 0.281167 0.486995i
\(333\) −9.80776 −0.537462
\(334\) −10.2462 + 17.7470i −0.560648 + 0.971070i
\(335\) 2.00000 + 3.46410i 0.109272 + 0.189264i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) −29.4924 −1.60655 −0.803277 0.595605i \(-0.796912\pi\)
−0.803277 + 0.595605i \(0.796912\pi\)
\(338\) 3.15767 + 12.6107i 0.171755 + 0.685930i
\(339\) 16.9309 0.919559
\(340\) −8.90388 15.4220i −0.482881 0.836374i
\(341\) −6.56155 11.3649i −0.355328 0.615446i
\(342\) −3.84233 + 6.65511i −0.207769 + 0.359867i
\(343\) −1.00000 −0.0539949
\(344\) 1.43845 2.49146i 0.0775559 0.134331i
\(345\) −16.2462 + 28.1393i −0.874667 + 1.51497i
\(346\) −4.87689 −0.262183
\(347\) 0.157671 0.273094i 0.00846421 0.0146604i −0.861762 0.507312i \(-0.830639\pi\)
0.870226 + 0.492652i \(0.163972\pi\)
\(348\) 0.500000 + 0.866025i 0.0268028 + 0.0464238i
\(349\) 3.24621 + 5.62260i 0.173766 + 0.300971i 0.939733 0.341908i \(-0.111073\pi\)
−0.765968 + 0.642879i \(0.777740\pi\)
\(350\) −7.68466 −0.410762
\(351\) −0.500000 + 3.57071i −0.0266880 + 0.190591i
\(352\) 2.56155 0.136531
\(353\) 4.90388 + 8.49377i 0.261007 + 0.452078i 0.966510 0.256629i \(-0.0826120\pi\)
−0.705503 + 0.708707i \(0.749279\pi\)
\(354\) −6.56155 11.3649i −0.348743 0.604040i
\(355\) −7.12311 + 12.3376i −0.378055 + 0.654811i
\(356\) −9.68466 −0.513286
\(357\) −2.50000 + 4.33013i −0.132314 + 0.229175i
\(358\) 8.24621 14.2829i 0.435826 0.754872i
\(359\) −4.63068 −0.244398 −0.122199 0.992506i \(-0.538995\pi\)
−0.122199 + 0.992506i \(0.538995\pi\)
\(360\) 1.78078 3.08440i 0.0938552 0.162562i
\(361\) −20.0270 34.6878i −1.05405 1.82567i
\(362\) −6.62311 11.4716i −0.348103 0.602932i
\(363\) −4.43845 −0.232958
\(364\) −3.34233 + 1.35234i −0.175186 + 0.0708821i
\(365\) 8.68466 0.454576
\(366\) 0.500000 + 0.866025i 0.0261354 + 0.0452679i
\(367\) −5.68466 9.84612i −0.296737 0.513963i 0.678651 0.734461i \(-0.262565\pi\)
−0.975387 + 0.220498i \(0.929232\pi\)
\(368\) 4.56155 7.90084i 0.237787 0.411860i
\(369\) 4.12311 0.214640
\(370\) −17.4654 + 30.2510i −0.907985 + 1.57268i
\(371\) −1.93845 + 3.35749i −0.100639 + 0.174312i
\(372\) 5.12311 0.265621
\(373\) −10.7808 + 18.6729i −0.558207 + 0.966844i 0.439439 + 0.898273i \(0.355177\pi\)
−0.997646 + 0.0685711i \(0.978156\pi\)
\(374\) 6.40388 + 11.0918i 0.331137 + 0.573546i
\(375\) 4.78078 + 8.28055i 0.246878 + 0.427606i
\(376\) −7.68466 −0.396306
\(377\) −3.34233 + 1.35234i −0.172139 + 0.0696493i
\(378\) −1.00000 −0.0514344
\(379\) −0.246211 0.426450i −0.0126470 0.0219053i 0.859633 0.510913i \(-0.170692\pi\)
−0.872280 + 0.489007i \(0.837359\pi\)
\(380\) 13.6847 + 23.7025i 0.702008 + 1.21591i
\(381\) −1.12311 + 1.94528i −0.0575384 + 0.0996595i
\(382\) 5.75379 0.294389
\(383\) −4.15767 + 7.20130i −0.212447 + 0.367969i −0.952480 0.304602i \(-0.901477\pi\)
0.740033 + 0.672571i \(0.234810\pi\)
\(384\) −0.500000 + 0.866025i −0.0255155 + 0.0441942i
\(385\) 9.12311 0.464957
\(386\) 10.1847 17.6403i 0.518385 0.897870i
\(387\) 1.43845 + 2.49146i 0.0731204 + 0.126648i
\(388\) −6.12311 10.6055i −0.310854 0.538414i
\(389\) 18.6847 0.947350 0.473675 0.880700i \(-0.342927\pi\)
0.473675 + 0.880700i \(0.342927\pi\)
\(390\) 10.1231 + 7.90084i 0.512603 + 0.400075i
\(391\) 45.6155 2.30688
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 8.24621 + 14.2829i 0.415966 + 0.720475i
\(394\) 0.280776 0.486319i 0.0141453 0.0245004i
\(395\) −5.12311 −0.257771
\(396\) −1.28078 + 2.21837i −0.0643614 + 0.111477i
\(397\) −0.842329 + 1.45896i −0.0422753 + 0.0732230i −0.886389 0.462942i \(-0.846794\pi\)
0.844114 + 0.536164i \(0.180127\pi\)
\(398\) −17.6155 −0.882987
\(399\) 3.84233 6.65511i 0.192357 0.333172i
\(400\) −3.84233 6.65511i −0.192116 0.332755i
\(401\) −7.58854 13.1437i −0.378954 0.656367i 0.611957 0.790891i \(-0.290383\pi\)
−0.990910 + 0.134524i \(0.957049\pi\)
\(402\) 1.12311 0.0560154
\(403\) −2.56155 + 18.2931i −0.127600 + 0.911247i
\(404\) −19.5616 −0.973224
\(405\) 1.78078 + 3.08440i 0.0884875 + 0.153265i
\(406\) −0.500000 0.866025i −0.0248146 0.0429801i
\(407\) 12.5616 21.7572i 0.622653 1.07847i
\(408\) −5.00000 −0.247537
\(409\) 15.2192 26.3605i 0.752542 1.30344i −0.194045 0.980993i \(-0.562161\pi\)
0.946587 0.322449i \(-0.104506\pi\)
\(410\) 7.34233 12.7173i 0.362612 0.628062i
\(411\) −5.80776 −0.286476
\(412\) 5.68466 9.84612i 0.280063 0.485083i
\(413\) 6.56155 + 11.3649i 0.322873 + 0.559232i
\(414\) 4.56155 + 7.90084i 0.224188 + 0.388305i
\(415\) 36.4924 1.79134
\(416\) −2.84233 2.21837i −0.139357 0.108765i
\(417\) −7.68466 −0.376319
\(418\) −9.84233 17.0474i −0.481404 0.833816i
\(419\) −11.3693 19.6922i −0.555427 0.962029i −0.997870 0.0652318i \(-0.979221\pi\)
0.442443 0.896797i \(-0.354112\pi\)
\(420\) −1.78078 + 3.08440i −0.0868930 + 0.150503i
\(421\) 8.43845 0.411265 0.205632 0.978629i \(-0.434075\pi\)
0.205632 + 0.978629i \(0.434075\pi\)
\(422\) 1.43845 2.49146i 0.0700225 0.121283i
\(423\) 3.84233 6.65511i 0.186820 0.323582i
\(424\) −3.87689 −0.188279
\(425\) 19.2116 33.2755i 0.931902 1.61410i
\(426\) 2.00000 + 3.46410i 0.0969003 + 0.167836i
\(427\) −0.500000 0.866025i −0.0241967 0.0419099i
\(428\) −9.43845 −0.456225
\(429\) −7.28078 5.68247i −0.351519 0.274352i
\(430\) 10.2462 0.494116
\(431\) 9.36932 + 16.2281i 0.451304 + 0.781682i 0.998467 0.0553443i \(-0.0176256\pi\)
−0.547163 + 0.837026i \(0.684292\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) 2.65767 4.60322i 0.127720 0.221217i −0.795073 0.606514i \(-0.792568\pi\)
0.922793 + 0.385297i \(0.125901\pi\)
\(434\) −5.12311 −0.245917
\(435\) −1.78078 + 3.08440i −0.0853817 + 0.147885i
\(436\) −0.438447 + 0.759413i −0.0209978 + 0.0363693i
\(437\) −70.1080 −3.35372
\(438\) 1.21922 2.11176i 0.0582568 0.100904i
\(439\) 14.2462 + 24.6752i 0.679935 + 1.17768i 0.975000 + 0.222204i \(0.0713252\pi\)
−0.295066 + 0.955477i \(0.595342\pi\)
\(440\) 4.56155 + 7.90084i 0.217463 + 0.376658i
\(441\) 1.00000 0.0476190
\(442\) 2.50000 17.8536i 0.118913 0.849208i
\(443\) −34.4233 −1.63550 −0.817750 0.575574i \(-0.804779\pi\)
−0.817750 + 0.575574i \(0.804779\pi\)
\(444\) 4.90388 + 8.49377i 0.232728 + 0.403097i
\(445\) −17.2462 29.8713i −0.817549 1.41604i
\(446\) 8.24621 14.2829i 0.390469 0.676313i
\(447\) −17.8078 −0.842278
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −9.00000 + 15.5885i −0.424736 + 0.735665i −0.996396 0.0848262i \(-0.972967\pi\)
0.571660 + 0.820491i \(0.306300\pi\)
\(450\) 7.68466 0.362258
\(451\) −5.28078 + 9.14657i −0.248662 + 0.430695i
\(452\) −8.46543 14.6626i −0.398181 0.689669i
\(453\) 8.71922 + 15.1021i 0.409665 + 0.709560i
\(454\) 13.1231 0.615898
\(455\) −10.1231 7.90084i −0.474579 0.370397i
\(456\) 7.68466 0.359867
\(457\) 6.65767 + 11.5314i 0.311433 + 0.539417i 0.978673 0.205425i \(-0.0658578\pi\)
−0.667240 + 0.744843i \(0.732524\pi\)
\(458\) −11.4039 19.7521i −0.532868 0.922955i
\(459\) 2.50000 4.33013i 0.116690 0.202113i
\(460\) 32.4924 1.51497
\(461\) −15.0270 + 26.0275i −0.699877 + 1.21222i 0.268632 + 0.963243i \(0.413428\pi\)
−0.968509 + 0.248979i \(0.919905\pi\)
\(462\) 1.28078 2.21837i 0.0595871 0.103208i
\(463\) −11.6847 −0.543032 −0.271516 0.962434i \(-0.587525\pi\)
−0.271516 + 0.962434i \(0.587525\pi\)
\(464\) 0.500000 0.866025i 0.0232119 0.0402042i
\(465\) 9.12311 + 15.8017i 0.423074 + 0.732785i
\(466\) 3.00000 + 5.19615i 0.138972 + 0.240707i
\(467\) 28.0000 1.29569 0.647843 0.761774i \(-0.275671\pi\)
0.647843 + 0.761774i \(0.275671\pi\)
\(468\) 3.34233 1.35234i 0.154499 0.0625121i
\(469\) −1.12311 −0.0518602
\(470\) −13.6847 23.7025i −0.631226 1.09332i
\(471\) 2.90388 + 5.02967i 0.133804 + 0.231755i
\(472\) −6.56155 + 11.3649i −0.302020 + 0.523114i
\(473\) −7.36932 −0.338842
\(474\) −0.719224 + 1.24573i −0.0330350 + 0.0572184i
\(475\) −29.5270 + 51.1422i −1.35479 + 2.34657i
\(476\) 5.00000 0.229175
\(477\) 1.93845 3.35749i 0.0887554 0.153729i
\(478\) −2.00000 3.46410i −0.0914779 0.158444i
\(479\) 1.28078 + 2.21837i 0.0585202 + 0.101360i 0.893801 0.448463i \(-0.148028\pi\)
−0.835281 + 0.549823i \(0.814695\pi\)
\(480\) −3.56155 −0.162562
\(481\) −32.7808 + 13.2635i −1.49467 + 0.604762i
\(482\) 11.3153 0.515400
\(483\) −4.56155 7.90084i −0.207558 0.359501i
\(484\) 2.21922 + 3.84381i 0.100874 + 0.174719i
\(485\) 21.8078 37.7722i 0.990240 1.71515i
\(486\) 1.00000 0.0453609
\(487\) −11.8423 + 20.5115i −0.536627 + 0.929466i 0.462456 + 0.886642i \(0.346968\pi\)
−0.999083 + 0.0428230i \(0.986365\pi\)
\(488\) 0.500000 0.866025i 0.0226339 0.0392031i
\(489\) −1.12311 −0.0507886
\(490\) 1.78078 3.08440i 0.0804473 0.139339i
\(491\) 0.876894 + 1.51883i 0.0395737 + 0.0685436i 0.885134 0.465337i \(-0.154067\pi\)
−0.845560 + 0.533880i \(0.820733\pi\)
\(492\) −2.06155 3.57071i −0.0929420 0.160980i
\(493\) 5.00000 0.225189
\(494\) −3.84233 + 27.4397i −0.172875 + 1.23457i
\(495\) −9.12311 −0.410053
\(496\) −2.56155 4.43674i −0.115017 0.199215i
\(497\) −2.00000 3.46410i −0.0897123 0.155386i
\(498\) 5.12311 8.87348i 0.229572 0.397630i
\(499\) −27.3693 −1.22522 −0.612609 0.790386i \(-0.709880\pi\)
−0.612609 + 0.790386i \(0.709880\pi\)
\(500\) 4.78078 8.28055i 0.213803 0.370317i
\(501\) −10.2462 + 17.7470i −0.457767 + 0.792876i
\(502\) 8.49242 0.379035
\(503\) −10.2462 + 17.7470i −0.456856 + 0.791298i −0.998793 0.0491215i \(-0.984358\pi\)
0.541937 + 0.840419i \(0.317691\pi\)
\(504\) 0.500000 + 0.866025i 0.0222718 + 0.0385758i
\(505\) −34.8348 60.3356i −1.55013 2.68490i
\(506\) −23.3693 −1.03889
\(507\) 3.15767 + 12.6107i 0.140237 + 0.560060i
\(508\) 2.24621 0.0996595
\(509\) −13.6577 23.6558i −0.605366 1.04852i −0.991994 0.126288i \(-0.959694\pi\)
0.386628 0.922236i \(-0.373640\pi\)
\(510\) −8.90388 15.4220i −0.394271 0.682897i
\(511\) −1.21922 + 2.11176i −0.0539353 + 0.0934186i
\(512\) 1.00000 0.0441942
\(513\) −3.84233 + 6.65511i −0.169643 + 0.293830i
\(514\) 7.37689 12.7772i 0.325381 0.563576i
\(515\) 40.4924 1.78431
\(516\) 1.43845 2.49146i 0.0633241 0.109681i
\(517\) 9.84233 + 17.0474i 0.432865 + 0.749744i
\(518\) −4.90388 8.49377i −0.215464 0.373195i
\(519\) −4.87689 −0.214072
\(520\) 1.78078 12.7173i 0.0780922 0.557690i
\(521\) −17.0000 −0.744784 −0.372392 0.928076i \(-0.621462\pi\)
−0.372392 + 0.928076i \(0.621462\pi\)
\(522\) 0.500000 + 0.866025i 0.0218844 + 0.0379049i
\(523\) −7.59612 13.1569i −0.332155 0.575309i 0.650779 0.759267i \(-0.274442\pi\)
−0.982934 + 0.183958i \(0.941109\pi\)
\(524\) 8.24621 14.2829i 0.360237 0.623949i
\(525\) −7.68466 −0.335386
\(526\) 10.2462 17.7470i 0.446756 0.773804i
\(527\) 12.8078 22.1837i 0.557915 0.966337i
\(528\) 2.56155 0.111477
\(529\) −30.1155 + 52.1616i −1.30937 + 2.26790i
\(530\) −6.90388 11.9579i −0.299885 0.519417i
\(531\) −6.56155 11.3649i −0.284747 0.493197i
\(532\) −7.68466 −0.333172
\(533\) 13.7808 5.57586i 0.596912 0.241517i
\(534\) −9.68466 −0.419096
\(535\) −16.8078 29.1119i −0.726663 1.25862i
\(536\) −0.561553 0.972638i −0.0242554 0.0420116i
\(537\) 8.24621 14.2829i 0.355850 0.616351i
\(538\) −4.87689 −0.210258
\(539\) −1.28078 + 2.21837i −0.0551669 + 0.0955520i
\(540\) 1.78078 3.08440i 0.0766324 0.132731i
\(541\) 1.56155 0.0671364 0.0335682 0.999436i \(-0.489313\pi\)
0.0335682 + 0.999436i \(0.489313\pi\)
\(542\) −6.56155 + 11.3649i −0.281843 + 0.488166i
\(543\) −6.62311 11.4716i −0.284225 0.492292i
\(544\) 2.50000 + 4.33013i 0.107187 + 0.185653i
\(545\) −3.12311 −0.133779
\(546\) −3.34233 + 1.35234i −0.143038 + 0.0578750i
\(547\) −22.7386 −0.972234 −0.486117 0.873894i \(-0.661587\pi\)
−0.486117 + 0.873894i \(0.661587\pi\)
\(548\) 2.90388 + 5.02967i 0.124048 + 0.214857i
\(549\) 0.500000 + 0.866025i 0.0213395 + 0.0369611i
\(550\) −9.84233 + 17.0474i −0.419678 + 0.726904i
\(551\) −7.68466 −0.327377
\(552\) 4.56155 7.90084i 0.194153 0.336282i
\(553\) 0.719224 1.24573i 0.0305845 0.0529739i
\(554\) −3.56155 −0.151316
\(555\) −17.4654 + 30.2510i −0.741366 + 1.28408i
\(556\) 3.84233 + 6.65511i 0.162951 + 0.282240i
\(557\) −10.8693 18.8262i −0.460548 0.797692i 0.538441 0.842664i \(-0.319014\pi\)
−0.998988 + 0.0449714i \(0.985680\pi\)
\(558\) 5.12311 0.216878
\(559\) 8.17708 + 6.38202i 0.345854 + 0.269930i
\(560\) 3.56155 0.150503
\(561\) 6.40388 + 11.0918i 0.270372 + 0.468298i
\(562\) −3.90388 6.76172i −0.164675 0.285226i
\(563\) 0.315342 0.546188i 0.0132901 0.0230191i −0.859304 0.511465i \(-0.829103\pi\)
0.872594 + 0.488446i \(0.162436\pi\)
\(564\) −7.68466 −0.323582
\(565\) 30.1501 52.2215i 1.26842 2.19697i
\(566\) −4.24621 + 7.35465i −0.178482 + 0.309139i
\(567\) −1.00000 −0.0419961
\(568\) 2.00000 3.46410i 0.0839181 0.145350i
\(569\) −5.80776 10.0593i −0.243474 0.421710i 0.718227 0.695808i \(-0.244954\pi\)
−0.961702 + 0.274099i \(0.911620\pi\)
\(570\) 13.6847 + 23.7025i 0.573187 + 0.992789i
\(571\) 13.7538 0.575578 0.287789 0.957694i \(-0.407080\pi\)
0.287789 + 0.957694i \(0.407080\pi\)
\(572\) −1.28078 + 9.14657i −0.0535520 + 0.382437i
\(573\) 5.75379 0.240368
\(574\) 2.06155 + 3.57071i 0.0860476 + 0.149039i
\(575\) 35.0540 + 60.7153i 1.46185 + 2.53200i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 31.3153 1.30367 0.651837 0.758359i \(-0.273998\pi\)
0.651837 + 0.758359i \(0.273998\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 10.1847 17.6403i 0.423260 0.733108i
\(580\) 3.56155 0.147885
\(581\) −5.12311 + 8.87348i −0.212542 + 0.368134i
\(582\) −6.12311 10.6055i −0.253811 0.439613i
\(583\) 4.96543 + 8.60039i 0.205647 + 0.356192i
\(584\) −2.43845 −0.100904
\(585\) 10.1231 + 7.90084i 0.418539 + 0.326660i
\(586\) −4.68466 −0.193521
\(587\) −15.6847 27.1666i −0.647375 1.12129i −0.983747 0.179558i \(-0.942533\pi\)
0.336372 0.941729i \(-0.390800\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) −19.6847 + 34.0948i −0.811092 + 1.40485i
\(590\) −46.7386 −1.92420
\(591\) 0.280776 0.486319i 0.0115496 0.0200045i
\(592\) 4.90388 8.49377i 0.201548 0.349092i
\(593\) 32.6155 1.33936 0.669680 0.742650i \(-0.266431\pi\)
0.669680 + 0.742650i \(0.266431\pi\)
\(594\) −1.28078 + 2.21837i −0.0525509 + 0.0910208i
\(595\) 8.90388 + 15.4220i 0.365024 + 0.632239i
\(596\) 8.90388 + 15.4220i 0.364717 + 0.631709i
\(597\) −17.6155 −0.720956
\(598\) 25.9309 + 20.2384i 1.06039 + 0.827611i
\(599\) −22.8769 −0.934725 −0.467362 0.884066i \(-0.654796\pi\)
−0.467362 + 0.884066i \(0.654796\pi\)
\(600\) −3.84233 6.65511i −0.156862 0.271694i
\(601\) −18.4654 31.9831i −0.753221 1.30462i −0.946254 0.323424i \(-0.895166\pi\)
0.193033 0.981192i \(-0.438167\pi\)
\(602\) −1.43845 + 2.49146i −0.0586267 + 0.101544i
\(603\) 1.12311 0.0457364
\(604\) 8.71922 15.1021i 0.354780 0.614497i
\(605\) −7.90388 + 13.6899i −0.321339 + 0.556575i
\(606\) −19.5616 −0.794634
\(607\) −10.5616 + 18.2931i −0.428680 + 0.742496i −0.996756 0.0804802i \(-0.974355\pi\)
0.568076 + 0.822976i \(0.307688\pi\)
\(608\) −3.84233 6.65511i −0.155827 0.269900i
\(609\) −0.500000 0.866025i −0.0202610 0.0350931i
\(610\) 3.56155 0.144203
\(611\) 3.84233 27.4397i 0.155444 1.11009i
\(612\) −5.00000 −0.202113
\(613\) −18.1501 31.4369i −0.733075 1.26972i −0.955563 0.294788i \(-0.904751\pi\)
0.222487 0.974936i \(-0.428582\pi\)
\(614\) 16.9654 + 29.3850i 0.684669 + 1.18588i
\(615\) 7.34233 12.7173i 0.296071 0.512811i
\(616\) −2.56155 −0.103208
\(617\) 13.7116 23.7493i 0.552010 0.956110i −0.446119 0.894973i \(-0.647194\pi\)
0.998129 0.0611360i \(-0.0194723\pi\)
\(618\) 5.68466 9.84612i 0.228670 0.396069i
\(619\) 4.31534 0.173448 0.0867241 0.996232i \(-0.472360\pi\)
0.0867241 + 0.996232i \(0.472360\pi\)
\(620\) 9.12311 15.8017i 0.366393 0.634611i
\(621\) 4.56155 + 7.90084i 0.183049 + 0.317050i
\(622\) −11.2808 19.5389i −0.452318 0.783438i
\(623\) 9.68466 0.388008
\(624\) −2.84233 2.21837i −0.113784 0.0888059i
\(625\) −4.36932 −0.174773
\(626\) −13.8078 23.9157i −0.551869 0.955866i
\(627\) −9.84233 17.0474i −0.393065 0.680808i
\(628\) 2.90388 5.02967i 0.115878 0.200706i
\(629\) 49.0388 1.95531
\(630\) −1.78078 + 3.08440i −0.0709478 + 0.122885i
\(631\) −11.5961 + 20.0851i −0.461634 + 0.799574i −0.999043 0.0437483i \(-0.986070\pi\)
0.537408 + 0.843322i \(0.319403\pi\)
\(632\) 1.43845 0.0572184
\(633\) 1.43845 2.49146i 0.0571731 0.0990268i
\(634\) 5.78078 + 10.0126i 0.229584 + 0.397651i
\(635\) 4.00000 + 6.92820i 0.158735 + 0.274937i
\(636\) −3.87689 −0.153729
\(637\) 3.34233 1.35234i 0.132428 0.0535818i
\(638\) −2.56155 −0.101413
\(639\) 2.00000 + 3.46410i 0.0791188 + 0.137038i
\(640\) 1.78078 + 3.08440i 0.0703914 + 0.121921i
\(641\) −18.4654 + 31.9831i −0.729341 + 1.26326i 0.227821 + 0.973703i \(0.426840\pi\)
−0.957162 + 0.289552i \(0.906494\pi\)
\(642\) −9.43845 −0.372506
\(643\) 13.2808 23.0030i 0.523743 0.907149i −0.475875 0.879513i \(-0.657869\pi\)
0.999618 0.0276362i \(-0.00879800\pi\)
\(644\) −4.56155 + 7.90084i −0.179750 + 0.311337i
\(645\) 10.2462 0.403444
\(646\) 19.2116 33.2755i 0.755872 1.30921i
\(647\) 10.4039 + 18.0201i 0.409019 + 0.708441i 0.994780 0.102042i \(-0.0325377\pi\)
−0.585761 + 0.810484i \(0.699204\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) 33.6155 1.31952
\(650\) 25.6847 10.3923i 1.00744 0.407620i
\(651\) −5.12311 −0.200790
\(652\) 0.561553 + 0.972638i 0.0219921 + 0.0380914i
\(653\) 9.40388 + 16.2880i 0.368002 + 0.637399i 0.989253 0.146213i \(-0.0467085\pi\)
−0.621251 + 0.783612i \(0.713375\pi\)
\(654\) −0.438447 + 0.759413i −0.0171446 + 0.0296954i
\(655\) 58.7386 2.29511
\(656\) −2.06155 + 3.57071i −0.0804901 + 0.139413i
\(657\) 1.21922 2.11176i 0.0475664 0.0823875i
\(658\) 7.68466 0.299579
\(659\) 14.1577 24.5218i 0.551505 0.955234i −0.446662 0.894703i \(-0.647387\pi\)
0.998166 0.0605310i \(-0.0192794\pi\)
\(660\) 4.56155 + 7.90084i 0.177558 + 0.307540i
\(661\) 4.90388 + 8.49377i 0.190739 + 0.330369i 0.945495 0.325636i \(-0.105578\pi\)
−0.754756 + 0.656005i \(0.772245\pi\)
\(662\) −35.3693 −1.37467
\(663\) 2.50000 17.8536i 0.0970920 0.693375i
\(664\) −10.2462 −0.397630
\(665\) −13.6847 23.7025i −0.530668 0.919144i
\(666\) 4.90388 + 8.49377i 0.190022 + 0.329127i
\(667\) −4.56155 + 7.90084i −0.176624 + 0.305922i
\(668\) 20.4924 0.792876
\(669\) 8.24621 14.2829i 0.318817 0.552207i
\(670\) 2.00000 3.46410i 0.0772667 0.133830i
\(671\) −2.56155 −0.0988876
\(672\) 0.500000 0.866025i 0.0192879 0.0334077i
\(673\) −4.37689 7.58100i −0.168717 0.292226i 0.769252 0.638945i \(-0.220629\pi\)
−0.937969 + 0.346719i \(0.887296\pi\)
\(674\) 14.7462 + 25.5412i 0.568003 + 0.983810i
\(675\) 7.68466 0.295783
\(676\) 9.34233 9.03996i 0.359320 0.347691i
\(677\) −8.38447 −0.322241 −0.161121 0.986935i \(-0.551511\pi\)
−0.161121 + 0.986935i \(0.551511\pi\)
\(678\) −8.46543 14.6626i −0.325113 0.563112i
\(679\) 6.12311 + 10.6055i 0.234983 + 0.407003i
\(680\) −8.90388 + 15.4220i −0.341448 + 0.591406i
\(681\) 13.1231 0.502879
\(682\) −6.56155 + 11.3649i −0.251255 + 0.435186i
\(683\) −2.00000 + 3.46410i −0.0765279 + 0.132550i −0.901750 0.432259i \(-0.857717\pi\)
0.825222 + 0.564809i \(0.191050\pi\)
\(684\) 7.68466 0.293830
\(685\) −10.3423 + 17.9134i −0.395160 + 0.684437i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) −11.4039 19.7521i −0.435085 0.753590i
\(688\) −2.87689 −0.109681
\(689\) 1.93845 13.8433i 0.0738490 0.527387i
\(690\) 32.4924 1.23697
\(691\) 14.2462 + 24.6752i 0.541951 + 0.938687i 0.998792 + 0.0491388i \(0.0156477\pi\)
−0.456841 + 0.889549i \(0.651019\pi\)
\(692\) 2.43845 + 4.22351i 0.0926959 + 0.160554i
\(693\) 1.28078 2.21837i 0.0486527 0.0842689i
\(694\) −0.315342 −0.0119702
\(695\) −13.6847 + 23.7025i −0.519089 + 0.899088i
\(696\) 0.500000 0.866025i 0.0189525 0.0328266i
\(697\) −20.6155 −0.780869
\(698\) 3.24621 5.62260i 0.122871 0.212819i
\(699\) 3.00000 + 5.19615i 0.113470 + 0.196537i
\(700\) 3.84233 + 6.65511i 0.145226 + 0.251539i
\(701\) 9.05398 0.341964 0.170982 0.985274i \(-0.445306\pi\)
0.170982 + 0.985274i \(0.445306\pi\)
\(702\) 3.34233 1.35234i 0.126148 0.0510410i
\(703\) −75.3693 −2.84261
\(704\) −1.28078 2.21837i −0.0482711 0.0836080i
\(705\) −13.6847 23.7025i −0.515394 0.892689i
\(706\) 4.90388 8.49377i 0.184560 0.319667i
\(707\) 19.5616 0.735688
\(708\) −6.56155 + 11.3649i −0.246598 + 0.427121i
\(709\) −10.1501 + 17.5805i −0.381195 + 0.660249i −0.991233 0.132123i \(-0.957821\pi\)
0.610039 + 0.792372i \(0.291154\pi\)
\(710\) 14.2462 0.534651
\(711\) −0.719224 + 1.24573i −0.0269730 + 0.0467186i
\(712\) 4.84233 + 8.38716i 0.181474 + 0.314322i
\(713\) 23.3693 + 40.4768i 0.875188 + 1.51587i
\(714\) 5.00000 0.187120
\(715\) −30.4924 + 12.3376i −1.14035 + 0.461399i
\(716\) −16.4924 −0.616351
\(717\) −2.00000 3.46410i −0.0746914 0.129369i
\(718\) 2.31534 + 4.01029i 0.0864078 + 0.149663i
\(719\) −10.9654 + 18.9927i −0.408942 + 0.708308i −0.994771 0.102126i \(-0.967435\pi\)
0.585830 + 0.810434i \(0.300769\pi\)
\(720\) −3.56155 −0.132731
\(721\) −5.68466 + 9.84612i −0.211708 + 0.366689i
\(722\) −20.0270 + 34.6878i −0.745327 + 1.29094i
\(723\) 11.3153 0.420822
\(724\) −6.62311 + 11.4716i −0.246146 + 0.426337i
\(725\) 3.84233 + 6.65511i 0.142701 + 0.247165i
\(726\) 2.21922 + 3.84381i 0.0823631 + 0.142657i
\(727\) 50.2462 1.86353 0.931764 0.363063i \(-0.118269\pi\)
0.931764 + 0.363063i \(0.118269\pi\)
\(728\) 2.84233 + 2.21837i 0.105344 + 0.0822183i
\(729\) 1.00000 0.0370370
\(730\) −4.34233 7.52113i −0.160717 0.278370i
\(731\) −7.19224 12.4573i −0.266014 0.460751i
\(732\) 0.500000 0.866025i 0.0184805 0.0320092i
\(733\) 32.6155 1.20468 0.602341 0.798239i \(-0.294235\pi\)
0.602341 + 0.798239i \(0.294235\pi\)
\(734\) −5.68466 + 9.84612i −0.209825 + 0.363427i
\(735\) 1.78078 3.08440i 0.0656849 0.113770i
\(736\) −9.12311 −0.336282
\(737\) −1.43845 + 2.49146i −0.0529859 + 0.0917742i
\(738\) −2.06155 3.57071i −0.0758868 0.131440i
\(739\) −23.6847 41.0230i −0.871254 1.50906i −0.860700 0.509112i \(-0.829974\pi\)
−0.0105542 0.999944i \(-0.503360\pi\)
\(740\) 34.9309 1.28408
\(741\) −3.84233 + 27.4397i −0.141151 + 1.00802i
\(742\) 3.87689 0.142325
\(743\) −4.31534 7.47439i −0.158315 0.274209i 0.775946 0.630799i \(-0.217273\pi\)
−0.934261 + 0.356590i \(0.883939\pi\)
\(744\) −2.56155 4.43674i −0.0939111 0.162659i
\(745\) −31.7116 + 54.9262i −1.16182 + 2.01234i
\(746\) 21.5616 0.789425
\(747\) 5.12311 8.87348i 0.187445 0.324664i
\(748\) 6.40388 11.0918i 0.234149 0.405558i
\(749\) 9.43845 0.344873
\(750\) 4.78078 8.28055i 0.174569 0.302363i
\(751\) 0.403882 + 0.699544i 0.0147379 + 0.0255267i 0.873300 0.487182i \(-0.161975\pi\)
−0.858562 + 0.512709i \(0.828642\pi\)
\(752\) 3.84233 + 6.65511i 0.140115 + 0.242687i
\(753\) 8.49242 0.309481
\(754\) 2.84233 + 2.21837i 0.103512 + 0.0807883i
\(755\) 62.1080 2.26034
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) 3.56155 + 6.16879i 0.129447 + 0.224209i 0.923462 0.383689i \(-0.125347\pi\)
−0.794016 + 0.607897i \(0.792013\pi\)
\(758\) −0.246211 + 0.426450i −0.00894280 + 0.0154894i
\(759\) −23.3693 −0.848252
\(760\) 13.6847 23.7025i 0.496395 0.859781i
\(761\) 21.2462 36.7995i 0.770175 1.33398i −0.167292 0.985907i \(-0.553502\pi\)
0.937467 0.348074i \(-0.113164\pi\)
\(762\) 2.24621 0.0813716
\(763\) 0.438447 0.759413i 0.0158729 0.0274926i
\(764\) −2.87689 4.98293i −0.104082 0.180276i
\(765\) −8.90388 15.4220i −0.321921 0.557583i
\(766\) 8.31534 0.300446
\(767\) −37.3002 29.1119i −1.34683 1.05117i
\(768\) 1.00000 0.0360844
\(769\) 11.4924 + 19.9055i 0.414427 + 0.717809i 0.995368 0.0961366i \(-0.0306486\pi\)
−0.580941 + 0.813946i \(0.697315\pi\)
\(770\) −4.56155 7.90084i −0.164387 0.284727i
\(771\) 7.37689 12.7772i 0.265672 0.460158i
\(772\) −20.3693 −0.733108
\(773\) −13.2462 + 22.9431i −0.476433 + 0.825206i −0.999635 0.0270022i \(-0.991404\pi\)
0.523202 + 0.852209i \(0.324737\pi\)
\(774\) 1.43845 2.49146i 0.0517039 0.0895538i
\(775\) 39.3693 1.41419
\(776\) −6.12311 + 10.6055i −0.219807 + 0.380716i
\(777\) −4.90388