Properties

Label 273.2.k.d.211.1
Level $273$
Weight $2$
Character 273.211
Analytic conductor $2.180$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 273 = 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 273.k (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.17991597518\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.771147.1
Defining polynomial: \(x^{6} - x^{5} + 5 x^{4} + 6 x^{3} + 15 x^{2} + 4 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(-0.136945 - 0.237196i\) of defining polynomial
Character \(\chi\) \(=\) 273.211
Dual form 273.2.k.d.22.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.825547 - 1.42989i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.363055 + 0.628829i) q^{4} +2.92498 q^{5} +(0.825547 - 1.42989i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.10331 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.41471 - 4.18240i) q^{10} +(2.18860 + 3.79077i) q^{11} -0.726109 q^{12} +(2.56580 - 2.53311i) q^{13} -1.65109 q^{14} +(1.46249 + 2.53311i) q^{15} +(2.46249 + 4.26516i) q^{16} +(-1.82555 + 3.16194i) q^{17} +1.65109 q^{18} +(2.87720 - 4.98346i) q^{19} +(-1.06193 + 1.83932i) q^{20} +1.00000 q^{21} +(3.61359 - 6.25891i) q^{22} +(-3.51415 - 6.08668i) q^{23} +(-1.05166 - 1.82152i) q^{24} +3.55553 q^{25} +(-5.74026 - 1.57761i) q^{26} -1.00000 q^{27} +(0.363055 + 0.628829i) q^{28} +(-0.599437 - 1.03826i) q^{29} +(2.41471 - 4.18240i) q^{30} -6.47277 q^{31} +(1.96249 - 3.39914i) q^{32} +(-2.18860 + 3.79077i) q^{33} +6.02830 q^{34} +(1.46249 - 2.53311i) q^{35} +(-0.363055 - 0.628829i) q^{36} +(1.46249 + 2.53311i) q^{37} -9.50106 q^{38} +(3.47664 + 0.955496i) q^{39} -6.15215 q^{40} +(4.30219 + 7.45161i) q^{41} +(-0.825547 - 1.42989i) q^{42} +(2.86305 - 4.95896i) q^{43} -3.17833 q^{44} +(-1.46249 + 2.53311i) q^{45} +(-5.80219 + 10.0497i) q^{46} -9.58383 q^{47} +(-2.46249 + 4.26516i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-2.93526 - 5.08401i) q^{50} -3.65109 q^{51} +(0.661367 + 2.53311i) q^{52} -0.302187 q^{53} +(0.825547 + 1.42989i) q^{54} +(6.40162 + 11.0879i) q^{55} +(-1.05166 + 1.82152i) q^{56} +5.75441 q^{57} +(-0.989727 + 1.71426i) q^{58} +(-1.51415 + 2.62258i) q^{59} -2.12386 q^{60} +(0.151093 - 0.261701i) q^{61} +(5.34357 + 9.25533i) q^{62} +(0.500000 + 0.866025i) q^{63} +3.36945 q^{64} +(7.50494 - 7.40931i) q^{65} +7.22717 q^{66} +(4.35384 + 7.54108i) q^{67} +(-1.32555 - 2.29591i) q^{68} +(3.51415 - 6.08668i) q^{69} -4.82942 q^{70} +(-6.76855 + 11.7235i) q^{71} +(1.05166 - 1.82152i) q^{72} +0.932734 q^{73} +(2.41471 - 4.18240i) q^{74} +(1.77777 + 3.07918i) q^{75} +(2.08916 + 3.61854i) q^{76} +4.37720 q^{77} +(-1.50388 - 5.76002i) q^{78} -16.9426 q^{79} +(7.20275 + 12.4755i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(7.10331 - 12.3033i) q^{82} -1.26614 q^{83} +(-0.363055 + 0.628829i) q^{84} +(-5.33969 + 9.24862i) q^{85} -9.45434 q^{86} +(0.599437 - 1.03826i) q^{87} +(-4.60331 - 7.97317i) q^{88} +(6.69887 + 11.6028i) q^{89} +4.82942 q^{90} +(-0.910836 - 3.48861i) q^{91} +5.10331 q^{92} +(-3.23638 - 5.60558i) q^{93} +(7.91190 + 13.7038i) q^{94} +(8.41577 - 14.5765i) q^{95} +3.92498 q^{96} +(-5.96249 + 10.3273i) q^{97} +(-0.825547 + 1.42989i) q^{98} -4.37720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} + O(q^{10}) \) \( 6q + 2q^{2} + 3q^{3} - 4q^{4} - 2q^{6} + 3q^{7} - 6q^{8} - 3q^{9} - 13q^{10} + 8q^{11} - 8q^{12} + 4q^{14} + 6q^{16} - 4q^{17} - 4q^{18} + 7q^{19} + 13q^{20} + 6q^{21} - q^{22} - 9q^{23} - 3q^{24} + 22q^{25} - 26q^{26} - 6q^{27} + 4q^{28} + 7q^{29} + 13q^{30} - 14q^{31} + 3q^{32} - 8q^{33} + 12q^{34} - 4q^{36} - 8q^{38} + 26q^{40} - 2q^{41} + 2q^{42} + 19q^{43} - 30q^{44} - 7q^{46} - 34q^{47} - 6q^{48} - 3q^{49} + 16q^{50} - 8q^{51} - 26q^{52} + 26q^{53} - 2q^{54} - 3q^{56} + 14q^{57} - 22q^{58} + 3q^{59} + 26q^{60} - 13q^{61} + 17q^{62} + 3q^{63} + 2q^{64} - 2q^{66} - 5q^{67} - q^{68} + 9q^{69} - 26q^{70} - 8q^{71} + 3q^{72} - 4q^{73} + 13q^{74} + 11q^{75} + 18q^{76} + 16q^{77} - 13q^{78} - 2q^{79} + 26q^{80} - 3q^{81} + 36q^{82} + 4q^{83} - 4q^{84} - 13q^{85} + 34q^{86} - 7q^{87} - 21q^{88} + 19q^{89} + 26q^{90} + 24q^{92} - 7q^{93} - 7q^{94} + 6q^{96} - 27q^{97} + 2q^{98} - 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/273\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(106\) \(157\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.825547 1.42989i −0.583750 1.01108i −0.995030 0.0995752i \(-0.968252\pi\)
0.411280 0.911509i \(-0.365082\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) −0.363055 + 0.628829i −0.181527 + 0.314415i
\(5\) 2.92498 1.30809 0.654046 0.756455i \(-0.273070\pi\)
0.654046 + 0.756455i \(0.273070\pi\)
\(6\) 0.825547 1.42989i 0.337028 0.583750i
\(7\) 0.500000 0.866025i 0.188982 0.327327i
\(8\) −2.10331 −0.743633
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −2.41471 4.18240i −0.763599 1.32259i
\(11\) 2.18860 + 3.79077i 0.659888 + 1.14296i 0.980644 + 0.195798i \(0.0627297\pi\)
−0.320756 + 0.947162i \(0.603937\pi\)
\(12\) −0.726109 −0.209610
\(13\) 2.56580 2.53311i 0.711626 0.702558i
\(14\) −1.65109 −0.441273
\(15\) 1.46249 + 2.53311i 0.377614 + 0.654046i
\(16\) 2.46249 + 4.26516i 0.615623 + 1.06629i
\(17\) −1.82555 + 3.16194i −0.442760 + 0.766883i −0.997893 0.0648786i \(-0.979334\pi\)
0.555133 + 0.831762i \(0.312667\pi\)
\(18\) 1.65109 0.389166
\(19\) 2.87720 4.98346i 0.660076 1.14328i −0.320520 0.947242i \(-0.603858\pi\)
0.980595 0.196043i \(-0.0628091\pi\)
\(20\) −1.06193 + 1.83932i −0.237455 + 0.411283i
\(21\) 1.00000 0.218218
\(22\) 3.61359 6.25891i 0.770419 1.33440i
\(23\) −3.51415 6.08668i −0.732751 1.26916i −0.955703 0.294332i \(-0.904903\pi\)
0.222953 0.974829i \(-0.428430\pi\)
\(24\) −1.05166 1.82152i −0.214668 0.371817i
\(25\) 3.55553 0.711106
\(26\) −5.74026 1.57761i −1.12576 0.309396i
\(27\) −1.00000 −0.192450
\(28\) 0.363055 + 0.628829i 0.0686109 + 0.118838i
\(29\) −0.599437 1.03826i −0.111313 0.192799i 0.804987 0.593292i \(-0.202172\pi\)
−0.916300 + 0.400493i \(0.868839\pi\)
\(30\) 2.41471 4.18240i 0.440864 0.763599i
\(31\) −6.47277 −1.16254 −0.581271 0.813710i \(-0.697445\pi\)
−0.581271 + 0.813710i \(0.697445\pi\)
\(32\) 1.96249 3.39914i 0.346923 0.600888i
\(33\) −2.18860 + 3.79077i −0.380987 + 0.659888i
\(34\) 6.02830 1.03384
\(35\) 1.46249 2.53311i 0.247206 0.428174i
\(36\) −0.363055 0.628829i −0.0605091 0.104805i
\(37\) 1.46249 + 2.53311i 0.240432 + 0.416441i 0.960837 0.277113i \(-0.0893775\pi\)
−0.720405 + 0.693553i \(0.756044\pi\)
\(38\) −9.50106 −1.54128
\(39\) 3.47664 + 0.955496i 0.556708 + 0.153002i
\(40\) −6.15215 −0.972741
\(41\) 4.30219 + 7.45161i 0.671889 + 1.16375i 0.977368 + 0.211547i \(0.0678500\pi\)
−0.305479 + 0.952199i \(0.598817\pi\)
\(42\) −0.825547 1.42989i −0.127385 0.220637i
\(43\) 2.86305 4.95896i 0.436612 0.756234i −0.560814 0.827942i \(-0.689512\pi\)
0.997426 + 0.0717081i \(0.0228450\pi\)
\(44\) −3.17833 −0.479151
\(45\) −1.46249 + 2.53311i −0.218015 + 0.377614i
\(46\) −5.80219 + 10.0497i −0.855486 + 1.48174i
\(47\) −9.58383 −1.39794 −0.698972 0.715149i \(-0.746359\pi\)
−0.698972 + 0.715149i \(0.746359\pi\)
\(48\) −2.46249 + 4.26516i −0.355430 + 0.615623i
\(49\) −0.500000 0.866025i −0.0714286 0.123718i
\(50\) −2.93526 5.08401i −0.415108 0.718988i
\(51\) −3.65109 −0.511255
\(52\) 0.661367 + 2.53311i 0.0917150 + 0.351279i
\(53\) −0.302187 −0.0415086 −0.0207543 0.999785i \(-0.506607\pi\)
−0.0207543 + 0.999785i \(0.506607\pi\)
\(54\) 0.825547 + 1.42989i 0.112343 + 0.194583i
\(55\) 6.40162 + 11.0879i 0.863195 + 1.49510i
\(56\) −1.05166 + 1.82152i −0.140533 + 0.243411i
\(57\) 5.75441 0.762190
\(58\) −0.989727 + 1.71426i −0.129958 + 0.225093i
\(59\) −1.51415 + 2.62258i −0.197125 + 0.341431i −0.947595 0.319474i \(-0.896494\pi\)
0.750470 + 0.660905i \(0.229827\pi\)
\(60\) −2.12386 −0.274189
\(61\) 0.151093 0.261701i 0.0193455 0.0335074i −0.856191 0.516660i \(-0.827175\pi\)
0.875536 + 0.483153i \(0.160508\pi\)
\(62\) 5.34357 + 9.25533i 0.678634 + 1.17543i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 3.36945 0.421182
\(65\) 7.50494 7.40931i 0.930873 0.919011i
\(66\) 7.22717 0.889603
\(67\) 4.35384 + 7.54108i 0.531907 + 0.921289i 0.999306 + 0.0372431i \(0.0118576\pi\)
−0.467400 + 0.884046i \(0.654809\pi\)
\(68\) −1.32555 2.29591i −0.160746 0.278420i
\(69\) 3.51415 6.08668i 0.423054 0.732751i
\(70\) −4.82942 −0.577226
\(71\) −6.76855 + 11.7235i −0.803280 + 1.39132i 0.114167 + 0.993462i \(0.463580\pi\)
−0.917446 + 0.397859i \(0.869753\pi\)
\(72\) 1.05166 1.82152i 0.123939 0.214668i
\(73\) 0.932734 0.109168 0.0545841 0.998509i \(-0.482617\pi\)
0.0545841 + 0.998509i \(0.482617\pi\)
\(74\) 2.41471 4.18240i 0.280704 0.486194i
\(75\) 1.77777 + 3.07918i 0.205279 + 0.355553i
\(76\) 2.08916 + 3.61854i 0.239644 + 0.415075i
\(77\) 4.37720 0.498829
\(78\) −1.50388 5.76002i −0.170280 0.652193i
\(79\) −16.9426 −1.90619 −0.953096 0.302668i \(-0.902123\pi\)
−0.953096 + 0.302668i \(0.902123\pi\)
\(80\) 7.20275 + 12.4755i 0.805292 + 1.39481i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 7.10331 12.3033i 0.784430 1.35867i
\(83\) −1.26614 −0.138977 −0.0694885 0.997583i \(-0.522137\pi\)
−0.0694885 + 0.997583i \(0.522137\pi\)
\(84\) −0.363055 + 0.628829i −0.0396125 + 0.0686109i
\(85\) −5.33969 + 9.24862i −0.579171 + 1.00315i
\(86\) −9.45434 −1.01949
\(87\) 0.599437 1.03826i 0.0642664 0.111313i
\(88\) −4.60331 7.97317i −0.490715 0.849943i
\(89\) 6.69887 + 11.6028i 0.710079 + 1.22989i 0.964827 + 0.262886i \(0.0846743\pi\)
−0.254748 + 0.967008i \(0.581992\pi\)
\(90\) 4.82942 0.509066
\(91\) −0.910836 3.48861i −0.0954815 0.365705i
\(92\) 5.10331 0.532057
\(93\) −3.23638 5.60558i −0.335597 0.581271i
\(94\) 7.91190 + 13.7038i 0.816050 + 1.41344i
\(95\) 8.41577 14.5765i 0.863440 1.49552i
\(96\) 3.92498 0.400592
\(97\) −5.96249 + 10.3273i −0.605399 + 1.04858i 0.386589 + 0.922252i \(0.373653\pi\)
−0.991988 + 0.126330i \(0.959680\pi\)
\(98\) −0.825547 + 1.42989i −0.0833928 + 0.144441i
\(99\) −4.37720 −0.439925
\(100\) −1.29085 + 2.23582i −0.129085 + 0.223582i
\(101\) −5.51415 9.55078i −0.548678 0.950339i −0.998365 0.0571525i \(-0.981798\pi\)
0.449687 0.893186i \(-0.351535\pi\)
\(102\) 3.01415 + 5.22066i 0.298445 + 0.516922i
\(103\) −19.4543 −1.91689 −0.958447 0.285272i \(-0.907916\pi\)
−0.958447 + 0.285272i \(0.907916\pi\)
\(104\) −5.39669 + 5.32792i −0.529189 + 0.522446i
\(105\) 2.92498 0.285449
\(106\) 0.249469 + 0.432094i 0.0242306 + 0.0419686i
\(107\) 0.711961 + 1.23315i 0.0688279 + 0.119213i 0.898386 0.439208i \(-0.144741\pi\)
−0.829558 + 0.558421i \(0.811407\pi\)
\(108\) 0.363055 0.628829i 0.0349350 0.0605091i
\(109\) −0.0467198 −0.00447494 −0.00223747 0.999997i \(-0.500712\pi\)
−0.00223747 + 0.999997i \(0.500712\pi\)
\(110\) 10.5697 18.3072i 1.00778 1.74553i
\(111\) −1.46249 + 2.53311i −0.138814 + 0.240432i
\(112\) 4.92498 0.465367
\(113\) 5.16912 8.95317i 0.486270 0.842244i −0.513606 0.858026i \(-0.671691\pi\)
0.999875 + 0.0157826i \(0.00502397\pi\)
\(114\) −4.75053 8.22816i −0.444928 0.770638i
\(115\) −10.2788 17.8035i −0.958506 1.66018i
\(116\) 0.870514 0.0808252
\(117\) 0.910836 + 3.48861i 0.0842068 + 0.322522i
\(118\) 5.00000 0.460287
\(119\) 1.82555 + 3.16194i 0.167348 + 0.289855i
\(120\) −3.07608 5.32792i −0.280806 0.486371i
\(121\) −4.07995 + 7.06668i −0.370905 + 0.642426i
\(122\) −0.498939 −0.0451718
\(123\) −4.30219 + 7.45161i −0.387915 + 0.671889i
\(124\) 2.34997 4.07026i 0.211033 0.365520i
\(125\) −4.22505 −0.377900
\(126\) 0.825547 1.42989i 0.0735455 0.127385i
\(127\) 2.73638 + 4.73955i 0.242815 + 0.420567i 0.961515 0.274753i \(-0.0885960\pi\)
−0.718700 + 0.695320i \(0.755263\pi\)
\(128\) −6.70662 11.6162i −0.592787 1.02674i
\(129\) 5.72611 0.504156
\(130\) −16.7902 4.61450i −1.47259 0.404718i
\(131\) 16.1706 1.41283 0.706415 0.707798i \(-0.250311\pi\)
0.706415 + 0.707798i \(0.250311\pi\)
\(132\) −1.58916 2.75251i −0.138319 0.239576i
\(133\) −2.87720 4.98346i −0.249485 0.432121i
\(134\) 7.18860 12.4510i 0.621001 1.07560i
\(135\) −2.92498 −0.251743
\(136\) 3.83969 6.65055i 0.329251 0.570280i
\(137\) 6.00881 10.4076i 0.513367 0.889178i −0.486512 0.873674i \(-0.661731\pi\)
0.999880 0.0155048i \(-0.00493551\pi\)
\(138\) −11.6044 −0.987830
\(139\) −0.674453 + 1.16819i −0.0572064 + 0.0990844i −0.893210 0.449639i \(-0.851553\pi\)
0.836004 + 0.548723i \(0.184886\pi\)
\(140\) 1.06193 + 1.83932i 0.0897494 + 0.155451i
\(141\) −4.79191 8.29984i −0.403552 0.698972i
\(142\) 22.3510 1.87566
\(143\) 15.2180 + 4.18240i 1.27259 + 0.349750i
\(144\) −4.92498 −0.410415
\(145\) −1.75334 3.03688i −0.145607 0.252199i
\(146\) −0.770016 1.33371i −0.0637269 0.110378i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) −2.12386 −0.174580
\(149\) 1.53751 2.66304i 0.125958 0.218165i −0.796149 0.605100i \(-0.793133\pi\)
0.922107 + 0.386935i \(0.126466\pi\)
\(150\) 2.93526 5.08401i 0.239663 0.415108i
\(151\) 16.6610 1.35585 0.677925 0.735131i \(-0.262879\pi\)
0.677925 + 0.735131i \(0.262879\pi\)
\(152\) −6.05166 + 10.4818i −0.490854 + 0.850184i
\(153\) −1.82555 3.16194i −0.147587 0.255628i
\(154\) −3.61359 6.25891i −0.291191 0.504358i
\(155\) −18.9327 −1.52071
\(156\) −1.86305 + 1.83932i −0.149164 + 0.147263i
\(157\) 12.8294 1.02390 0.511950 0.859015i \(-0.328923\pi\)
0.511950 + 0.859015i \(0.328923\pi\)
\(158\) 13.9869 + 24.2260i 1.11274 + 1.92732i
\(159\) −0.151093 0.261701i −0.0119825 0.0207543i
\(160\) 5.74026 9.94242i 0.453807 0.786017i
\(161\) −7.02830 −0.553907
\(162\) −0.825547 + 1.42989i −0.0648611 + 0.112343i
\(163\) 10.8022 18.7099i 0.846093 1.46548i −0.0385764 0.999256i \(-0.512282\pi\)
0.884669 0.466220i \(-0.154384\pi\)
\(164\) −6.24772 −0.487865
\(165\) −6.40162 + 11.0879i −0.498366 + 0.863195i
\(166\) 1.04526 + 1.81044i 0.0811278 + 0.140517i
\(167\) −10.6599 18.4635i −0.824888 1.42875i −0.902005 0.431726i \(-0.857905\pi\)
0.0771165 0.997022i \(-0.475429\pi\)
\(168\) −2.10331 −0.162274
\(169\) 0.166703 12.9989i 0.0128233 0.999918i
\(170\) 17.6327 1.35236
\(171\) 2.87720 + 4.98346i 0.220025 + 0.381095i
\(172\) 2.07889 + 3.60074i 0.158514 + 0.274554i
\(173\) −1.56087 + 2.70350i −0.118671 + 0.205543i −0.919241 0.393695i \(-0.871197\pi\)
0.800570 + 0.599239i \(0.204530\pi\)
\(174\) −1.97945 −0.150062
\(175\) 1.77777 3.07918i 0.134386 0.232764i
\(176\) −10.7788 + 18.6695i −0.812485 + 1.40726i
\(177\) −3.02830 −0.227621
\(178\) 11.0605 19.1573i 0.829017 1.43590i
\(179\) −9.48545 16.4293i −0.708976 1.22798i −0.965237 0.261375i \(-0.915824\pi\)
0.256261 0.966608i \(-0.417509\pi\)
\(180\) −1.06193 1.83932i −0.0791515 0.137094i
\(181\) −1.93273 −0.143659 −0.0718295 0.997417i \(-0.522884\pi\)
−0.0718295 + 0.997417i \(0.522884\pi\)
\(182\) −4.23638 + 4.18240i −0.314022 + 0.310020i
\(183\) 0.302187 0.0223383
\(184\) 7.39135 + 12.8022i 0.544898 + 0.943790i
\(185\) 4.27777 + 7.40931i 0.314508 + 0.544743i
\(186\) −5.34357 + 9.25533i −0.391810 + 0.678634i
\(187\) −15.9816 −1.16869
\(188\) 3.47945 6.02659i 0.253765 0.439534i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) −27.7905 −2.01613
\(191\) 1.13695 1.96925i 0.0822665 0.142490i −0.821957 0.569550i \(-0.807117\pi\)
0.904223 + 0.427060i \(0.140451\pi\)
\(192\) 1.68473 + 2.91803i 0.121585 + 0.210591i
\(193\) 2.19354 + 3.79932i 0.157894 + 0.273481i 0.934109 0.356988i \(-0.116196\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(194\) 19.6893 1.41361
\(195\) 10.1691 + 2.79481i 0.728226 + 0.200141i
\(196\) 0.726109 0.0518650
\(197\) 2.62920 + 4.55390i 0.187322 + 0.324452i 0.944357 0.328923i \(-0.106686\pi\)
−0.757034 + 0.653375i \(0.773352\pi\)
\(198\) 3.61359 + 6.25891i 0.256806 + 0.444802i
\(199\) −6.59798 + 11.4280i −0.467718 + 0.810111i −0.999320 0.0368831i \(-0.988257\pi\)
0.531601 + 0.846995i \(0.321590\pi\)
\(200\) −7.47839 −0.528802
\(201\) −4.35384 + 7.54108i −0.307096 + 0.531907i
\(202\) −9.10437 + 15.7692i −0.640581 + 1.10952i
\(203\) −1.19887 −0.0841445
\(204\) 1.32555 2.29591i 0.0928068 0.160746i
\(205\) 12.5838 + 21.7958i 0.878893 + 1.52229i
\(206\) 16.0605 + 27.8175i 1.11899 + 1.93814i
\(207\) 7.02830 0.488500
\(208\) 17.1224 + 4.70580i 1.18722 + 0.326289i
\(209\) 25.1882 1.74230
\(210\) −2.41471 4.18240i −0.166631 0.288613i
\(211\) 8.72077 + 15.1048i 0.600363 + 1.03986i 0.992766 + 0.120065i \(0.0383105\pi\)
−0.392403 + 0.919793i \(0.628356\pi\)
\(212\) 0.109710 0.190024i 0.00753494 0.0130509i
\(213\) −13.5371 −0.927547
\(214\) 1.17551 2.03605i 0.0803565 0.139182i
\(215\) 8.37439 14.5049i 0.571129 0.989224i
\(216\) 2.10331 0.143112
\(217\) −3.23638 + 5.60558i −0.219700 + 0.380531i
\(218\) 0.0385694 + 0.0668041i 0.00261225 + 0.00452454i
\(219\) 0.466367 + 0.807771i 0.0315142 + 0.0545841i
\(220\) −9.29656 −0.626774
\(221\) 3.32555 + 12.7372i 0.223700 + 0.856799i
\(222\) 4.82942 0.324130
\(223\) −4.00106 6.93004i −0.267931 0.464070i 0.700396 0.713754i \(-0.253007\pi\)
−0.968327 + 0.249684i \(0.919673\pi\)
\(224\) −1.96249 3.39914i −0.131125 0.227114i
\(225\) −1.77777 + 3.07918i −0.118518 + 0.205279i
\(226\) −17.0694 −1.13544
\(227\) 4.02976 6.97975i 0.267464 0.463262i −0.700742 0.713415i \(-0.747148\pi\)
0.968206 + 0.250153i \(0.0804809\pi\)
\(228\) −2.08916 + 3.61854i −0.138358 + 0.239644i
\(229\) −8.48052 −0.560408 −0.280204 0.959940i \(-0.590402\pi\)
−0.280204 + 0.959940i \(0.590402\pi\)
\(230\) −16.9713 + 29.3952i −1.11905 + 1.93826i
\(231\) 2.18860 + 3.79077i 0.143999 + 0.249414i
\(232\) 1.26080 + 2.18378i 0.0827758 + 0.143372i
\(233\) −10.2456 −0.671211 −0.335606 0.942003i \(-0.608941\pi\)
−0.335606 + 0.942003i \(0.608941\pi\)
\(234\) 4.23638 4.18240i 0.276941 0.273412i
\(235\) −28.0325 −1.82864
\(236\) −1.09944 1.90428i −0.0715673 0.123958i
\(237\) −8.47130 14.6727i −0.550270 0.953096i
\(238\) 3.01415 5.22066i 0.195378 0.338405i
\(239\) −11.3022 −0.731078 −0.365539 0.930796i \(-0.619115\pi\)
−0.365539 + 0.930796i \(0.619115\pi\)
\(240\) −7.20275 + 12.4755i −0.464935 + 0.805292i
\(241\) −0.518023 + 0.897242i −0.0333688 + 0.0577965i −0.882228 0.470823i \(-0.843957\pi\)
0.848859 + 0.528620i \(0.177290\pi\)
\(242\) 13.4728 0.866062
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 0.109710 + 0.190024i 0.00702349 + 0.0121650i
\(245\) −1.46249 2.53311i −0.0934352 0.161834i
\(246\) 14.2066 0.905781
\(247\) −5.24132 20.0749i −0.333497 1.27733i
\(248\) 13.6142 0.864506
\(249\) −0.633070 1.09651i −0.0401192 0.0694885i
\(250\) 3.48797 + 6.04135i 0.220599 + 0.382088i
\(251\) −6.64188 + 11.5041i −0.419232 + 0.726131i −0.995862 0.0908742i \(-0.971034\pi\)
0.576631 + 0.817005i \(0.304367\pi\)
\(252\) −0.726109 −0.0457406
\(253\) 15.3821 26.6426i 0.967067 1.67501i
\(254\) 4.51802 7.82545i 0.283486 0.491012i
\(255\) −10.6794 −0.668769
\(256\) −7.70381 + 13.3434i −0.481488 + 0.833962i
\(257\) −6.22077 10.7747i −0.388041 0.672107i 0.604145 0.796875i \(-0.293515\pi\)
−0.992186 + 0.124768i \(0.960181\pi\)
\(258\) −4.72717 8.18770i −0.294301 0.509744i
\(259\) 2.92498 0.181750
\(260\) 1.93449 + 7.40931i 0.119972 + 0.459506i
\(261\) 1.19887 0.0742085
\(262\) −13.3496 23.1221i −0.824739 1.42849i
\(263\) −3.29579 5.70847i −0.203227 0.352000i 0.746339 0.665566i \(-0.231810\pi\)
−0.949566 + 0.313566i \(0.898476\pi\)
\(264\) 4.60331 7.97317i 0.283314 0.490715i
\(265\) −0.883892 −0.0542970
\(266\) −4.75053 + 8.22816i −0.291274 + 0.504501i
\(267\) −6.69887 + 11.6028i −0.409964 + 0.710079i
\(268\) −6.32273 −0.386222
\(269\) 1.35812 2.35233i 0.0828059 0.143424i −0.821648 0.569995i \(-0.806945\pi\)
0.904454 + 0.426571i \(0.140279\pi\)
\(270\) 2.41471 + 4.18240i 0.146955 + 0.254533i
\(271\) 15.3627 + 26.6089i 0.933215 + 1.61638i 0.777787 + 0.628528i \(0.216342\pi\)
0.155428 + 0.987847i \(0.450324\pi\)
\(272\) −17.9816 −1.09029
\(273\) 2.56580 2.53311i 0.155290 0.153311i
\(274\) −19.8422 −1.19871
\(275\) 7.78164 + 13.4782i 0.469251 + 0.812766i
\(276\) 2.55166 + 4.41960i 0.153592 + 0.266029i
\(277\) 10.7827 18.6762i 0.647870 1.12214i −0.335761 0.941947i \(-0.608993\pi\)
0.983631 0.180196i \(-0.0576732\pi\)
\(278\) 2.22717 0.133577
\(279\) 3.23638 5.60558i 0.193757 0.335597i
\(280\) −3.07608 + 5.32792i −0.183831 + 0.318404i
\(281\) 33.2058 1.98089 0.990447 0.137896i \(-0.0440340\pi\)
0.990447 + 0.137896i \(0.0440340\pi\)
\(282\) −7.91190 + 13.7038i −0.471147 + 0.816050i
\(283\) −0.741719 1.28470i −0.0440906 0.0763672i 0.843138 0.537697i \(-0.180706\pi\)
−0.887229 + 0.461330i \(0.847372\pi\)
\(284\) −4.91471 8.51253i −0.291634 0.505126i
\(285\) 16.8315 0.997015
\(286\) −6.58277 25.2128i −0.389247 1.49086i
\(287\) 8.60437 0.507900
\(288\) 1.96249 + 3.39914i 0.115641 + 0.200296i
\(289\) 1.83476 + 3.17789i 0.107927 + 0.186935i
\(290\) −2.89494 + 5.01418i −0.169996 + 0.294442i
\(291\) −11.9250 −0.699055
\(292\) −0.338633 + 0.586530i −0.0198170 + 0.0343241i
\(293\) −4.41577 + 7.64834i −0.257972 + 0.446821i −0.965699 0.259666i \(-0.916388\pi\)
0.707726 + 0.706487i \(0.249721\pi\)
\(294\) −1.65109 −0.0962937
\(295\) −4.42886 + 7.67101i −0.257858 + 0.446623i
\(296\) −3.07608 5.32792i −0.178793 0.309679i
\(297\) −2.18860 3.79077i −0.126996 0.219963i
\(298\) −5.07714 −0.294111
\(299\) −24.4349 6.71551i −1.41310 0.388368i
\(300\) −2.58170 −0.149055
\(301\) −2.86305 4.95896i −0.165024 0.285829i
\(302\) −13.7544 23.8233i −0.791477 1.37088i
\(303\) 5.51415 9.55078i 0.316780 0.548678i
\(304\) 28.3404 1.62543
\(305\) 0.441946 0.765473i 0.0253057 0.0438308i
\(306\) −3.01415 + 5.22066i −0.172307 + 0.298445i
\(307\) 11.6532 0.665084 0.332542 0.943088i \(-0.392094\pi\)
0.332542 + 0.943088i \(0.392094\pi\)
\(308\) −1.58916 + 2.75251i −0.0905510 + 0.156839i
\(309\) −9.72717 16.8480i −0.553359 0.958447i
\(310\) 15.6299 + 27.0717i 0.887716 + 1.53757i
\(311\) −25.0099 −1.41818 −0.709090 0.705118i \(-0.750894\pi\)
−0.709090 + 0.705118i \(0.750894\pi\)
\(312\) −7.31246 2.00971i −0.413987 0.113777i
\(313\) −0.186078 −0.0105178 −0.00525889 0.999986i \(-0.501674\pi\)
−0.00525889 + 0.999986i \(0.501674\pi\)
\(314\) −10.5913 18.3446i −0.597701 1.03525i
\(315\) 1.46249 + 2.53311i 0.0824021 + 0.142725i
\(316\) 6.15109 10.6540i 0.346026 0.599335i
\(317\) −0.540031 −0.0303312 −0.0151656 0.999885i \(-0.504828\pi\)
−0.0151656 + 0.999885i \(0.504828\pi\)
\(318\) −0.249469 + 0.432094i −0.0139895 + 0.0242306i
\(319\) 2.62386 4.54466i 0.146908 0.254452i
\(320\) 9.85560 0.550945
\(321\) −0.711961 + 1.23315i −0.0397378 + 0.0688279i
\(322\) 5.80219 + 10.0497i 0.323343 + 0.560047i
\(323\) 10.5049 + 18.1951i 0.584510 + 1.01240i
\(324\) 0.726109 0.0403394
\(325\) 9.12280 9.00655i 0.506042 0.499594i
\(326\) −35.6708 −1.97563
\(327\) −0.0233599 0.0404605i −0.00129180 0.00223747i
\(328\) −9.04884 15.6731i −0.499639 0.865400i
\(329\) −4.79191 + 8.29984i −0.264187 + 0.457585i
\(330\) 21.1394 1.16368
\(331\) −0.770016 + 1.33371i −0.0423239 + 0.0733071i −0.886411 0.462898i \(-0.846809\pi\)
0.844087 + 0.536206i \(0.180143\pi\)
\(332\) 0.459678 0.796186i 0.0252281 0.0436964i
\(333\) −2.92498 −0.160288
\(334\) −17.6005 + 30.4850i −0.963056 + 1.66806i
\(335\) 12.7349 + 22.0575i 0.695783 + 1.20513i
\(336\) 2.46249 + 4.26516i 0.134340 + 0.232684i
\(337\) 2.82942 0.154128 0.0770642 0.997026i \(-0.475445\pi\)
0.0770642 + 0.997026i \(0.475445\pi\)
\(338\) −18.7246 + 10.4929i −1.01849 + 0.570736i
\(339\) 10.3382 0.561496
\(340\) −3.87720 6.71551i −0.210271 0.364200i
\(341\) −14.1663 24.5368i −0.767148 1.32874i
\(342\) 4.75053 8.22816i 0.256879 0.444928i
\(343\) −1.00000 −0.0539949
\(344\) −6.02190 + 10.4302i −0.324679 + 0.562361i
\(345\) 10.2788 17.8035i 0.553393 0.958506i
\(346\) 5.15428 0.277096
\(347\) 12.6950 21.9884i 0.681503 1.18040i −0.293019 0.956107i \(-0.594660\pi\)
0.974522 0.224292i \(-0.0720068\pi\)
\(348\) 0.435257 + 0.753887i 0.0233322 + 0.0404126i
\(349\) 0.542845 + 0.940235i 0.0290578 + 0.0503296i 0.880189 0.474624i \(-0.157416\pi\)
−0.851131 + 0.524954i \(0.824083\pi\)
\(350\) −5.87051 −0.313792
\(351\) −2.56580 + 2.53311i −0.136953 + 0.135207i
\(352\) 17.1805 0.915721
\(353\) −5.26468 9.11869i −0.280211 0.485339i 0.691226 0.722639i \(-0.257071\pi\)
−0.971436 + 0.237300i \(0.923738\pi\)
\(354\) 2.50000 + 4.33013i 0.132874 + 0.230144i
\(355\) −19.7979 + 34.2910i −1.05076 + 1.81998i
\(356\) −9.72823 −0.515595
\(357\) −1.82555 + 3.16194i −0.0966182 + 0.167348i
\(358\) −15.6614 + 27.1263i −0.827729 + 1.43367i
\(359\) 27.2087 1.43602 0.718011 0.696031i \(-0.245053\pi\)
0.718011 + 0.696031i \(0.245053\pi\)
\(360\) 3.07608 5.32792i 0.162124 0.280806i
\(361\) −7.05659 12.2224i −0.371400 0.643283i
\(362\) 1.59556 + 2.76359i 0.0838609 + 0.145251i
\(363\) −8.15990 −0.428284
\(364\) 2.52442 + 0.693795i 0.132316 + 0.0363647i
\(365\) 2.72823 0.142802
\(366\) −0.249469 0.432094i −0.0130400 0.0225859i
\(367\) 3.12920 + 5.41993i 0.163343 + 0.282918i 0.936065 0.351826i \(-0.114439\pi\)
−0.772723 + 0.634744i \(0.781106\pi\)
\(368\) 17.3071 29.9768i 0.902196 1.56265i
\(369\) −8.60437 −0.447926
\(370\) 7.06299 12.2335i 0.367187 0.635987i
\(371\) −0.151093 + 0.261701i −0.00784438 + 0.0135869i
\(372\) 4.69994 0.243680
\(373\) 0.589164 1.02046i 0.0305058 0.0528375i −0.850369 0.526186i \(-0.823622\pi\)
0.880875 + 0.473349i \(0.156955\pi\)
\(374\) 13.1935 + 22.8519i 0.682222 + 1.18164i
\(375\) −2.11252 3.65900i −0.109090 0.188950i
\(376\) 20.1578 1.03956
\(377\) −4.16806 1.14552i −0.214666 0.0589973i
\(378\) 1.65109 0.0849231
\(379\) 12.1033 + 20.9636i 0.621705 + 1.07683i 0.989168 + 0.146787i \(0.0468932\pi\)
−0.367463 + 0.930038i \(0.619773\pi\)
\(380\) 6.11077 + 10.5842i 0.313476 + 0.542956i
\(381\) −2.73638 + 4.73955i −0.140189 + 0.242815i
\(382\) −3.75441 −0.192092
\(383\) 1.24559 2.15743i 0.0636469 0.110240i −0.832446 0.554106i \(-0.813060\pi\)
0.896093 + 0.443866i \(0.146394\pi\)
\(384\) 6.70662 11.6162i 0.342246 0.592787i
\(385\) 12.8032 0.652514
\(386\) 3.62174 6.27303i 0.184341 0.319289i
\(387\) 2.86305 + 4.95896i 0.145537 + 0.252078i
\(388\) −4.32942 7.49878i −0.219793 0.380693i
\(389\) 23.6065 1.19690 0.598448 0.801161i \(-0.295784\pi\)
0.598448 + 0.801161i \(0.295784\pi\)
\(390\) −4.39881 16.8480i −0.222742 0.853129i
\(391\) 25.6610 1.29773
\(392\) 1.05166 + 1.82152i 0.0531167 + 0.0920007i
\(393\) 8.08529 + 14.0041i 0.407849 + 0.706415i
\(394\) 4.34105 7.51891i 0.218699 0.378797i
\(395\) −49.5569 −2.49348
\(396\) 1.58916 2.75251i 0.0798585 0.138319i
\(397\) 4.42352 7.66177i 0.222010 0.384533i −0.733408 0.679789i \(-0.762071\pi\)
0.955418 + 0.295256i \(0.0954048\pi\)
\(398\) 21.7877 1.09212
\(399\) 2.87720 4.98346i 0.144040 0.249485i
\(400\) 8.75547 + 15.1649i 0.437773 + 0.758246i
\(401\) 9.45716 + 16.3803i 0.472268 + 0.817992i 0.999496 0.0317317i \(-0.0101022\pi\)
−0.527229 + 0.849723i \(0.676769\pi\)
\(402\) 14.3772 0.717070
\(403\) −16.6078 + 16.3962i −0.827296 + 0.816754i
\(404\) 8.00775 0.398400
\(405\) −1.46249 2.53311i −0.0726718 0.125871i
\(406\) 0.989727 + 1.71426i 0.0491193 + 0.0850772i
\(407\) −6.40162 + 11.0879i −0.317317 + 0.549609i
\(408\) 7.67939 0.380186
\(409\) −1.74947 + 3.03017i −0.0865057 + 0.149832i −0.906032 0.423210i \(-0.860903\pi\)
0.819526 + 0.573042i \(0.194237\pi\)
\(410\) 20.7771 35.9869i 1.02611 1.77727i
\(411\) 12.0176 0.592786
\(412\) 7.06299 12.2335i 0.347969 0.602699i
\(413\) 1.51415 + 2.62258i 0.0745064 + 0.129049i
\(414\) −5.80219 10.0497i −0.285162 0.493915i
\(415\) −3.70344 −0.181795
\(416\) −3.57502 13.6927i −0.175280 0.671341i
\(417\) −1.34891 −0.0660562
\(418\) −20.7940 36.0163i −1.01707 1.76162i
\(419\) −14.4158 24.9688i −0.704257 1.21981i −0.966959 0.254931i \(-0.917947\pi\)
0.262703 0.964877i \(-0.415386\pi\)
\(420\) −1.06193 + 1.83932i −0.0518168 + 0.0897494i
\(421\) 34.3227 1.67279 0.836394 0.548129i \(-0.184660\pi\)
0.836394 + 0.548129i \(0.184660\pi\)
\(422\) 14.3988 24.9395i 0.700923 1.21403i
\(423\) 4.79191 8.29984i 0.232991 0.403552i
\(424\) 0.635593 0.0308671
\(425\) −6.49079 + 11.2424i −0.314849 + 0.545335i
\(426\) 11.1755 + 19.3566i 0.541455 + 0.937828i
\(427\) −0.151093 0.261701i −0.00731192 0.0126646i
\(428\) −1.03392 −0.0499766
\(429\) 3.98691 + 15.2703i 0.192490 + 0.737259i
\(430\) −27.6538 −1.33358
\(431\) −14.6779 25.4229i −0.707011 1.22458i −0.965961 0.258688i \(-0.916710\pi\)
0.258950 0.965891i \(-0.416624\pi\)
\(432\) −2.46249 4.26516i −0.118477 0.205208i
\(433\) −14.3032 + 24.7740i −0.687370 + 1.19056i 0.285315 + 0.958434i \(0.407902\pi\)
−0.972686 + 0.232126i \(0.925432\pi\)
\(434\) 10.6871 0.512999
\(435\) 1.75334 3.03688i 0.0840664 0.145607i
\(436\) 0.0169618 0.0293788i 0.000812325 0.00140699i
\(437\) −40.4437 −1.93468
\(438\) 0.770016 1.33371i 0.0367928 0.0637269i
\(439\) −17.2399 29.8603i −0.822813 1.42515i −0.903579 0.428422i \(-0.859070\pi\)
0.0807654 0.996733i \(-0.474264\pi\)
\(440\) −13.4646 23.3214i −0.641900 1.11180i
\(441\) 1.00000 0.0476190
\(442\) 15.4674 15.2703i 0.735711 0.726336i
\(443\) −12.9066 −0.613209 −0.306605 0.951837i \(-0.599193\pi\)
−0.306605 + 0.951837i \(0.599193\pi\)
\(444\) −1.06193 1.83932i −0.0503969 0.0872900i
\(445\) 19.5941 + 33.9380i 0.928849 + 1.60881i
\(446\) −6.60613 + 11.4421i −0.312809 + 0.541801i
\(447\) 3.07502 0.145443
\(448\) 1.68473 2.91803i 0.0795958 0.137864i
\(449\) 2.81915 4.88291i 0.133044 0.230439i −0.791805 0.610774i \(-0.790858\pi\)
0.924848 + 0.380336i \(0.124192\pi\)
\(450\) 5.87051 0.276739
\(451\) −18.8315 + 32.6172i −0.886743 + 1.53588i
\(452\) 3.75334 + 6.50098i 0.176542 + 0.305781i
\(453\) 8.33048 + 14.4288i 0.391400 + 0.677925i
\(454\) −13.3070 −0.624529
\(455\) −2.66418 10.2041i −0.124899 0.478376i
\(456\) −12.1033 −0.566790
\(457\) −18.9947 32.8997i −0.888533 1.53898i −0.841610 0.540086i \(-0.818392\pi\)
−0.0469228 0.998899i \(-0.514941\pi\)
\(458\) 7.00106 + 12.1262i 0.327138 + 0.566620i
\(459\) 1.82555 3.16194i 0.0852092 0.147587i
\(460\) 14.9271 0.695980
\(461\) 3.30365 5.72209i 0.153866 0.266504i −0.778779 0.627298i \(-0.784161\pi\)
0.932646 + 0.360794i \(0.117494\pi\)
\(462\) 3.61359 6.25891i 0.168119 0.291191i
\(463\) 9.98933 0.464243 0.232122 0.972687i \(-0.425433\pi\)
0.232122 + 0.972687i \(0.425433\pi\)
\(464\) 2.95222 5.11339i 0.137053 0.237383i
\(465\) −9.46637 16.3962i −0.438992 0.760357i
\(466\) 8.45822 + 14.6501i 0.391819 + 0.678651i
\(467\) 3.42100 0.158305 0.0791525 0.996863i \(-0.474779\pi\)
0.0791525 + 0.996863i \(0.474779\pi\)
\(468\) −2.52442 0.693795i −0.116691 0.0320707i
\(469\) 8.70769 0.402084
\(470\) 23.1422 + 40.0834i 1.06747 + 1.84891i
\(471\) 6.41471 + 11.1106i 0.295574 + 0.511950i
\(472\) 3.18473 5.51611i 0.146589 0.253899i
\(473\) 25.0643 1.15246
\(474\) −13.9869 + 24.2260i −0.642440 + 1.11274i
\(475\) 10.2300 17.7189i 0.469384 0.812997i
\(476\) −2.65109 −0.121513
\(477\) 0.151093 0.261701i 0.00691809 0.0119825i
\(478\) 9.33048 + 16.1609i 0.426766 + 0.739181i
\(479\) −9.92071 17.1832i −0.453289 0.785119i 0.545299 0.838241i \(-0.316416\pi\)
−0.998588 + 0.0531223i \(0.983083\pi\)
\(480\) 11.4805 0.524011
\(481\) 10.1691 + 2.79481i 0.463672 + 0.127432i
\(482\) 1.71061 0.0779161
\(483\) −3.51415 6.08668i −0.159899 0.276954i
\(484\) −2.96249 5.13119i −0.134659 0.233236i
\(485\) −17.4402 + 30.2073i −0.791918 + 1.37164i
\(486\) −1.65109 −0.0748951
\(487\) 3.05166 5.28562i 0.138284 0.239514i −0.788563 0.614954i \(-0.789175\pi\)
0.926847 + 0.375439i \(0.122508\pi\)
\(488\) −0.317797 + 0.550440i −0.0143860 + 0.0249172i
\(489\) 21.6044 0.976984
\(490\) −2.41471 + 4.18240i −0.109086 + 0.188942i
\(491\) 1.18326 + 2.04947i 0.0534000 + 0.0924915i 0.891490 0.453041i \(-0.149661\pi\)
−0.838090 + 0.545532i \(0.816328\pi\)
\(492\) −3.12386 5.41068i −0.140834 0.243932i
\(493\) 4.37720 0.197139
\(494\) −24.3779 + 24.0672i −1.09681 + 1.08284i
\(495\) −12.8032 −0.575463
\(496\) −15.9391 27.6074i −0.715688 1.23961i
\(497\) 6.76855 + 11.7235i 0.303611 + 0.525870i
\(498\) −1.04526 + 1.81044i −0.0468391 + 0.0811278i
\(499\) −4.29231 −0.192150 −0.0960752 0.995374i \(-0.530629\pi\)
−0.0960752 + 0.995374i \(0.530629\pi\)
\(500\) 1.53392 2.65683i 0.0685992 0.118817i
\(501\) 10.6599 18.4635i 0.476249 0.824888i
\(502\) 21.9327 0.978906
\(503\) 1.05553 1.82823i 0.0470638 0.0815169i −0.841534 0.540204i \(-0.818347\pi\)
0.888598 + 0.458687i \(0.151680\pi\)
\(504\) −1.05166 1.82152i −0.0468445 0.0811370i
\(505\) −16.1288 27.9359i −0.717722 1.24313i
\(506\) −50.7947 −2.25810
\(507\) 11.3408 6.35510i 0.503661 0.282240i
\(508\) −3.97383 −0.176310
\(509\) 12.1882 + 21.1106i 0.540233 + 0.935710i 0.998890 + 0.0470972i \(0.0149970\pi\)
−0.458658 + 0.888613i \(0.651670\pi\)
\(510\) 8.81633 + 15.2703i 0.390394 + 0.676182i
\(511\) 0.466367 0.807771i 0.0206309 0.0357337i
\(512\) −1.38708 −0.0613007
\(513\) −2.87720 + 4.98346i −0.127032 + 0.220025i
\(514\) −10.2711 + 17.7900i −0.453038 + 0.784684i
\(515\) −56.9036 −2.50747
\(516\) −2.07889 + 3.60074i −0.0915181 + 0.158514i
\(517\) −20.9752 36.3301i −0.922487 1.59779i
\(518\) −2.41471 4.18240i −0.106096 0.183764i
\(519\) −3.12174 −0.137029
\(520\) −15.7852 + 15.5841i −0.692228 + 0.683407i
\(521\) −17.8401 −0.781589 −0.390794 0.920478i \(-0.627800\pi\)
−0.390794 + 0.920478i \(0.627800\pi\)
\(522\) −0.989727 1.71426i −0.0433192 0.0750310i
\(523\) 15.5279 + 26.8951i 0.678987 + 1.17604i 0.975286 + 0.220945i \(0.0709143\pi\)
−0.296299 + 0.955095i \(0.595752\pi\)
\(524\) −5.87080 + 10.1685i −0.256467 + 0.444214i
\(525\) 3.55553 0.155176
\(526\) −5.44166 + 9.42522i −0.237267 + 0.410959i
\(527\) 11.8163 20.4665i 0.514728 0.891534i
\(528\) −21.5577 −0.938176
\(529\) −13.1985 + 22.8604i −0.573847 + 0.993932i
\(530\) 0.729694 + 1.26387i 0.0316959 + 0.0548989i
\(531\) −1.51415 2.62258i −0.0657084 0.113810i
\(532\) 4.17833 0.181154
\(533\) 29.9143 + 8.22145i 1.29573 + 0.356110i
\(534\) 22.1209 0.957266
\(535\) 2.08248 + 3.60695i 0.0900333 + 0.155942i
\(536\) −9.15749 15.8612i −0.395543 0.685101i
\(537\) 9.48545 16.4293i 0.409327 0.708976i
\(538\) −4.48476 −0.193352
\(539\) 2.18860 3.79077i 0.0942697 0.163280i
\(540\) 1.06193 1.83932i 0.0456982 0.0791515i
\(541\) −33.3900 −1.43555 −0.717774 0.696276i \(-0.754839\pi\)
−0.717774 + 0.696276i \(0.754839\pi\)
\(542\) 25.3652 43.9338i 1.08953 1.88712i
\(543\) −0.966367 1.67380i −0.0414708 0.0718295i
\(544\) 7.16524 + 12.4106i 0.307207 + 0.532098i
\(545\) −0.136655 −0.00585364
\(546\) −5.74026 1.57761i −0.245660 0.0675156i
\(547\) 9.12306 0.390074 0.195037 0.980796i \(-0.437517\pi\)
0.195037 + 0.980796i \(0.437517\pi\)
\(548\) 4.36305 + 7.55703i 0.186380 + 0.322820i
\(549\) 0.151093 + 0.261701i 0.00644851 + 0.0111691i
\(550\) 12.8482 22.2538i 0.547850 0.948904i
\(551\) −6.89881 −0.293899
\(552\) −7.39135 + 12.8022i −0.314597 + 0.544898i
\(553\) −8.47130 + 14.6727i −0.360236 + 0.623948i
\(554\) −35.6065 −1.51278
\(555\) −4.27777 + 7.40931i −0.181581 + 0.314508i
\(556\) −0.489727 0.848232i −0.0207690 0.0359730i
\(557\) 19.0148 + 32.9346i 0.805683 + 1.39548i 0.915829 + 0.401569i \(0.131535\pi\)
−0.110145 + 0.993915i \(0.535132\pi\)
\(558\) −10.6871 −0.452423
\(559\) −5.21555 19.9761i −0.220594 0.844901i
\(560\) 14.4055 0.608743
\(561\) −7.99079 13.8405i −0.337371 0.584344i
\(562\) −27.4130 47.4806i −1.15635 2.00285i
\(563\) 1.68326 2.91550i 0.0709411 0.122874i −0.828373 0.560177i \(-0.810733\pi\)
0.899314 + 0.437303i \(0.144066\pi\)
\(564\) 6.95891 0.293023
\(565\) 15.1196 26.1879i 0.636086 1.10173i
\(566\) −1.22465 + 2.12115i −0.0514758 + 0.0891587i
\(567\) −1.00000 −0.0419961
\(568\) 14.2364 24.6581i 0.597345 1.03463i
\(569\) 8.96637 + 15.5302i 0.375890 + 0.651060i 0.990460 0.137802i \(-0.0440038\pi\)
−0.614570 + 0.788862i \(0.710671\pi\)
\(570\) −13.8952 24.0672i −0.582007 1.00807i
\(571\) 39.4274 1.64998 0.824992 0.565144i \(-0.191180\pi\)
0.824992 + 0.565144i \(0.191180\pi\)
\(572\) −8.15497 + 8.05106i −0.340976 + 0.336632i
\(573\) 2.27389 0.0949931
\(574\) −7.10331 12.3033i −0.296487 0.513530i
\(575\) −12.4947 21.6414i −0.521063 0.902508i
\(576\) −1.68473 + 2.91803i −0.0701969 + 0.121585i
\(577\) 16.4239 0.683737 0.341868 0.939748i \(-0.388940\pi\)
0.341868 + 0.939748i \(0.388940\pi\)
\(578\) 3.02936 5.24700i 0.126005 0.218246i
\(579\) −2.19354 + 3.79932i −0.0911603 + 0.157894i
\(580\) 2.54624 0.105727
\(581\) −0.633070 + 1.09651i −0.0262642 + 0.0454909i
\(582\) 9.84463 + 17.0514i 0.408073 + 0.706803i
\(583\) −0.661367 1.14552i −0.0273910 0.0474426i
\(584\) −1.96183 −0.0811811
\(585\) 2.66418 + 10.2041i 0.110150 + 0.421888i
\(586\) 14.5817 0.602365
\(587\) 7.46355 + 12.9273i 0.308054 + 0.533565i 0.977937 0.208902i \(-0.0669890\pi\)
−0.669883 + 0.742467i \(0.733656\pi\)
\(588\) 0.363055 + 0.628829i 0.0149721 + 0.0259325i
\(589\) −18.6235 + 32.2568i −0.767366 + 1.32912i
\(590\) 14.6249 0.602098
\(591\) −2.62920 + 4.55390i −0.108151 + 0.187322i
\(592\) −7.20275 + 12.4755i −0.296031 + 0.512741i
\(593\) 29.9164 1.22852 0.614260 0.789103i \(-0.289454\pi\)
0.614260 + 0.789103i \(0.289454\pi\)
\(594\) −3.61359 + 6.25891i −0.148267 + 0.256806i
\(595\) 5.33969 + 9.24862i 0.218906 + 0.379157i
\(596\) 1.11640 + 1.93366i 0.0457295 + 0.0792058i
\(597\) −13.1960 −0.540074
\(598\) 10.5697 + 40.4831i 0.432226 + 1.65548i
\(599\) 35.1911 1.43787 0.718935 0.695077i \(-0.244630\pi\)
0.718935 + 0.695077i \(0.244630\pi\)
\(600\) −3.73920 6.47648i −0.152652 0.264401i
\(601\) −8.56580 14.8364i −0.349406 0.605190i 0.636738 0.771080i \(-0.280283\pi\)
−0.986144 + 0.165891i \(0.946950\pi\)
\(602\) −4.72717 + 8.18770i −0.192665 + 0.333706i
\(603\) −8.70769 −0.354604
\(604\) −6.04884 + 10.4769i −0.246124 + 0.426299i
\(605\) −11.9338 + 20.6699i −0.485178 + 0.840353i
\(606\) −18.2087 −0.739680
\(607\) −11.2233 + 19.4393i −0.455540 + 0.789018i −0.998719 0.0505990i \(-0.983887\pi\)
0.543180 + 0.839617i \(0.317220\pi\)
\(608\) −11.2930 19.5600i −0.457991 0.793263i
\(609\) −0.599437 1.03826i −0.0242904 0.0420722i
\(610\) −1.45939 −0.0590889
\(611\) −24.5902 + 24.2769i −0.994814 + 0.982138i
\(612\) 2.65109 0.107164
\(613\) 10.1029 + 17.4988i 0.408053 + 0.706768i 0.994672 0.103095i \(-0.0328746\pi\)
−0.586619 + 0.809863i \(0.699541\pi\)
\(614\) −9.62027 16.6628i −0.388243 0.672456i
\(615\) −12.5838 + 21.7958i −0.507429 + 0.878893i
\(616\) −9.20662 −0.370945
\(617\) −19.3408 + 33.4992i −0.778630 + 1.34863i 0.154102 + 0.988055i \(0.450751\pi\)
−0.932732 + 0.360571i \(0.882582\pi\)
\(618\) −16.0605 + 27.8175i −0.646047 + 1.11899i
\(619\) 32.5109 1.30672 0.653362 0.757045i \(-0.273358\pi\)
0.653362 + 0.757045i \(0.273358\pi\)
\(620\) 6.87362 11.9055i 0.276051 0.478135i
\(621\) 3.51415 + 6.08668i 0.141018 + 0.244250i
\(622\) 20.6468 + 35.7613i 0.827862 + 1.43390i
\(623\) 13.3977 0.536769
\(624\) 4.48585 + 17.1813i 0.179578 + 0.687804i
\(625\) −30.1359 −1.20543
\(626\) 0.153616 + 0.266071i 0.00613975 + 0.0106344i
\(627\) 12.5941 + 21.8136i 0.502960 + 0.871152i
\(628\) −4.65778 + 8.06752i −0.185866 + 0.321929i
\(629\) −10.6794 −0.425815
\(630\) 2.41471 4.18240i 0.0962044 0.166631i
\(631\) 18.9310 32.7894i 0.753630 1.30533i −0.192422 0.981312i \(-0.561634\pi\)
0.946052 0.324014i \(-0.105032\pi\)
\(632\) 35.6356 1.41751
\(633\) −8.72077 + 15.1048i −0.346620 + 0.600363i
\(634\) 0.445821 + 0.772184i 0.0177058 + 0.0306674i
\(635\) 8.00388 + 13.8631i 0.317624 + 0.550141i
\(636\) 0.219421 0.00870060
\(637\) −3.47664 0.955496i −0.137749 0.0378581i
\(638\) −8.66447 −0.343030
\(639\) −6.76855 11.7235i −0.267760 0.463774i
\(640\) −19.6168 33.9772i −0.775421 1.34307i
\(641\) −11.4314 + 19.7997i −0.451512 + 0.782042i −0.998480 0.0551112i \(-0.982449\pi\)
0.546968 + 0.837154i \(0.315782\pi\)
\(642\) 2.35103 0.0927877
\(643\) −21.7915 + 37.7440i −0.859373 + 1.48848i 0.0131542 + 0.999913i \(0.495813\pi\)
−0.872528 + 0.488565i \(0.837521\pi\)
\(644\) 2.55166 4.41960i 0.100549 0.174157i
\(645\) 16.7488 0.659483
\(646\) 17.3446 30.0418i 0.682415 1.18198i
\(647\) 1.50388 + 2.60479i 0.0591234 + 0.102405i 0.894072 0.447923i \(-0.147836\pi\)
−0.834949 + 0.550328i \(0.814503\pi\)
\(648\) 1.05166 + 1.82152i 0.0413130 + 0.0715561i
\(649\) −13.2555 −0.520323
\(650\) −20.4097 5.60926i −0.800533 0.220013i
\(651\) −6.47277 −0.253688
\(652\) 7.84357 + 13.5855i 0.307178 + 0.532048i
\(653\) 16.9621 + 29.3792i 0.663778 + 1.14970i 0.979615 + 0.200884i \(0.0643813\pi\)
−0.315837 + 0.948813i \(0.602285\pi\)
\(654\) −0.0385694 + 0.0668041i −0.00150818 + 0.00261225i
\(655\) 47.2987 1.84811
\(656\) −21.1882 + 36.6990i −0.827260 + 1.43286i
\(657\) −0.466367 + 0.807771i −0.0181947 + 0.0315142i
\(658\) 15.8238 0.616876
\(659\) 21.7297 37.6369i 0.846469 1.46613i −0.0378709 0.999283i \(-0.512058\pi\)
0.884340 0.466844i \(-0.154609\pi\)
\(660\) −4.64828 8.05106i −0.180934 0.313387i
\(661\) −19.1429 33.1565i −0.744574 1.28964i −0.950393 0.311050i \(-0.899319\pi\)
0.205819 0.978590i \(-0.434014\pi\)
\(662\) 2.54274 0.0988262
\(663\) −9.36799 + 9.24862i −0.363823 + 0.359187i
\(664\) 2.66309 0.103348
\(665\) −8.41577 14.5765i −0.326350 0.565254i
\(666\) 2.41471 + 4.18240i 0.0935681 + 0.162065i
\(667\) −4.21302 + 7.29717i −0.163129 + 0.282548i
\(668\) 15.4805 0.598959
\(669\) 4.00106 6.93004i 0.154690 0.267931i
\(670\) 21.0265 36.4190i 0.812326 1.40699i
\(671\) 1.32273 0.0510635
\(672\) 1.96249 3.39914i 0.0757048 0.131125i
\(673\) −14.0902 24.4050i −0.543138 0.940743i −0.998722 0.0505499i \(-0.983903\pi\)
0.455583 0.890193i \(-0.349431\pi\)
\(674\) −2.33582 4.04576i −0.0899724 0.155837i
\(675\) −3.55553 −0.136852
\(676\) 8.11359 + 4.82415i 0.312061 + 0.185544i
\(677\) −31.7253 −1.21930 −0.609651 0.792670i \(-0.708691\pi\)
−0.609651 + 0.792670i \(0.708691\pi\)
\(678\) −8.53469 14.7825i −0.327773 0.567719i
\(679\) 5.96249 + 10.3273i 0.228819 + 0.396327i
\(680\) 11.2310 19.4527i 0.430691 0.745979i
\(681\) 8.05952 0.308841
\(682\) −23.3899 + 40.5125i −0.895645 + 1.55130i
\(683\) −4.28698 + 7.42526i −0.164037 + 0.284120i −0.936313 0.351167i \(-0.885785\pi\)
0.772276 + 0.635287i \(0.219118\pi\)
\(684\) −4.17833 −0.159762
\(685\) 17.5757 30.4420i 0.671532 1.16313i
\(686\) 0.825547 + 1.42989i 0.0315195 + 0.0545934i
\(687\) −4.24026 7.34434i −0.161776 0.280204i
\(688\) 28.2010 1.07515
\(689\) −0.775352 + 0.765473i −0.0295386 + 0.0291622i
\(690\) −33.9426 −1.29217
\(691\) 3.47518 + 6.01919i 0.132202 + 0.228981i 0.924525 0.381121i \(-0.124462\pi\)
−0.792323 + 0.610102i \(0.791129\pi\)
\(692\) −1.13336 1.96304i −0.0430839 0.0746235i
\(693\) −2.18860 + 3.79077i −0.0831381 + 0.143999i
\(694\) −41.9213 −1.59131
\(695\) −1.97277 + 3.41693i −0.0748312 + 0.129612i
\(696\) −1.26080 + 2.18378i −0.0477906 + 0.0827758i
\(697\) −31.4154 −1.18994
\(698\) 0.896287 1.55242i 0.0339250 0.0587598i
\(699\) −5.12280 8.87294i −0.193762 0.335606i
\(700\) 1.29085 + 2.23582i 0.0487896 + 0.0845061i
\(701\) −21.8443 −0.825049 −0.412525 0.910946i \(-0.635353\pi\)
−0.412525 + 0.910946i \(0.635353\pi\)
\(702\) 5.74026 + 1.57761i 0.216652 + 0.0595432i
\(703\) 16.8315 0.634814
\(704\) 7.37439 + 12.7728i 0.277933 + 0.481394i
\(705\) −14.0163 24.2769i −0.527883 0.914321i
\(706\) −8.69248 + 15.0558i −0.327146 + 0.566633i
\(707\) −11.0283 −0.414762
\(708\) 1.09944 1.90428i 0.0413194 0.0715673i
\(709\) −4.87187 + 8.43832i −0.182967 + 0.316908i −0.942890 0.333106i \(-0.891903\pi\)
0.759923 + 0.650013i \(0.225237\pi\)
\(710\) 65.3764 2.45353
\(711\) 8.47130 14.6727i 0.317699 0.550270i
\(712\) −14.0898 24.4043i −0.528039 0.914590i
\(713\) 22.7463 + 39.3977i 0.851854 + 1.47545i
\(714\) 6.02830 0.225603
\(715\) 44.5123 + 12.2335i 1.66467 + 0.457505i
\(716\) 13.7750 0.514794
\(717\) −5.65109 9.78798i −0.211044 0.365539i
\(718\) −22.4621 38.9055i −0.838278 1.45194i
\(719\) 2.52296 4.36989i 0.0940905 0.162970i −0.815138 0.579267i \(-0.803339\pi\)
0.909229 + 0.416297i \(0.136672\pi\)
\(720\) −14.4055 −0.536861
\(721\) −9.72717 + 16.8480i −0.362259 + 0.627451i
\(722\) −11.6511 + 20.1803i −0.433609 + 0.751032i
\(723\) −1.03605 −0.0385310
\(724\) 0.701688 1.21536i 0.0260780 0.0451685i
\(725\) −2.13132 3.69155i −0.0791552 0.137101i
\(726\) 6.73638 + 11.6678i 0.250011 + 0.433031i
\(727\) 6.66659 0.247250 0.123625 0.992329i \(-0.460548\pi\)
0.123625 + 0.992329i \(0.460548\pi\)
\(728\) 1.91577 + 7.33763i 0.0710032 + 0.271951i
\(729\) 1.00000 0.0370370
\(730\) −2.25228 3.90107i −0.0833607 0.144385i
\(731\) 10.4533 + 18.1056i 0.386629 + 0.669660i
\(732\) −0.109710 + 0.190024i −0.00405501 + 0.00702349i
\(733\) 47.4076 1.75104 0.875520 0.483181i \(-0.160519\pi\)
0.875520 + 0.483181i \(0.160519\pi\)
\(734\) 5.16659 8.94880i 0.190702 0.330306i
\(735\) 1.46249 2.53311i 0.0539448 0.0934352i
\(736\) −27.5860 −1.01683
\(737\) −19.0577 + 33.0088i −0.701998 + 1.21590i
\(738\) 7.10331 + 12.3033i 0.261477 + 0.452891i
\(739\) −3.09023 5.35243i −0.113676 0.196892i 0.803574 0.595205i \(-0.202929\pi\)
−0.917250 + 0.398313i \(0.869596\pi\)
\(740\) −6.21225 −0.228367
\(741\) 14.7647 14.5765i 0.542394 0.535483i
\(742\) 0.498939 0.0183166
\(743\) 11.6667 + 20.2073i 0.428010 + 0.741335i 0.996696 0.0812197i \(-0.0258815\pi\)
−0.568686 + 0.822554i \(0.692548\pi\)
\(744\) 6.80712 + 11.7903i 0.249561 + 0.432253i
\(745\) 4.49719 7.78936i 0.164764 0.285380i
\(746\) −1.94553 −0.0712309
\(747\) 0.633070 1.09651i 0.0231628 0.0401192i
\(748\) 5.80219 10.0497i 0.212149 0.367453i
\(749\) 1.42392 0.0520290
\(750\) −3.48797 + 6.04135i −0.127363 + 0.220599i
\(751\) 0.488375 + 0.845890i 0.0178211 + 0.0308670i 0.874798 0.484487i \(-0.160994\pi\)
−0.856977 + 0.515354i \(0.827660\pi\)
\(752\) −23.6001 40.8766i −0.860607 1.49062i
\(753\) −13.2838 −0.484087
\(754\) 1.80296 + 6.90554i 0.0656598 + 0.251485i
\(755\) 48.7331 1.77358
\(756\) −0.363055 0.628829i −0.0132042 0.0228703i
\(757\) 4.38254 + 7.59078i 0.159286 + 0.275892i 0.934611 0.355670i \(-0.115747\pi\)
−0.775325 + 0.631562i \(0.782414\pi\)
\(758\) 19.9837 34.6128i 0.725841 1.25719i
\(759\) 30.7643 1.11667
\(760\) −17.7010 + 30.6590i −0.642083 + 1.11212i
\(761\) 10.7276 18.5807i 0.388874 0.673550i −0.603424 0.797420i \(-0.706197\pi\)
0.992298 + 0.123871i \(0.0395308\pi\)
\(762\) 9.03605 0.327341
\(763\) −0.0233599 + 0.0404605i −0.000845685 + 0.00146477i
\(764\) 0.825547 + 1.42989i 0.0298672 + 0.0517316i
\(765\) −5.33969 9.24862i −0.193057 0.334385i
\(766\) −4.11319 −0.148615
\(767\) 2.75828 + 10.5645i 0.0995957 + 0.381463i
\(768\) −15.4076 −0.555975
\(769\) −11.0750 19.1825i −0.399375 0.691738i 0.594274 0.804263i \(-0.297440\pi\)
−0.993649 + 0.112525i \(0.964106\pi\)
\(770\) −10.5697 18.3072i −0.380905 0.659746i
\(771\) 6.22077 10.7747i 0.224036 0.388041i
\(772\) −3.18550 −0.114649
\(773\) 9.57995 16.5930i 0.344567 0.596807i −0.640708 0.767785i \(-0.721359\pi\)
0.985275 + 0.170977i \(0.0546924\pi\)
\(774\) 4.72717 8.18770i 0.169915 0.294301i
\(775\) −23.0141 −0.826692
\(776\) 12.5410 21.7216i 0.450195 0.779761i
\(777\) 1.46249 + 2.53311i 0.0524666 + 0.0908748i
\(778\) −19.4883