Properties

Label 1110.2.bb.d.1009.9
Level $1110$
Weight $2$
Character 1110.1009
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.bb (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(14\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1009.9
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.d.1099.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-2.13568 + 0.662460i) q^{5} +1.00000 q^{6} +(-1.09384 + 0.631530i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-2.18079 - 0.494135i) q^{10} -4.99195 q^{11} +(0.866025 + 0.500000i) q^{12} +(-4.64326 + 2.68079i) q^{13} -1.26306 q^{14} +(-1.51833 + 1.64155i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(3.69192 + 2.13153i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-3.67492 - 6.36515i) q^{19} +(-1.64155 - 1.51833i) q^{20} +(-0.631530 + 1.09384i) q^{21} +(-4.32315 - 2.49597i) q^{22} -7.94839i q^{23} +(0.500000 + 0.866025i) q^{24} +(4.12229 - 2.82961i) q^{25} -5.36157 q^{26} -1.00000i q^{27} +(-1.09384 - 0.631530i) q^{28} +0.263060 q^{29} +(-2.13568 + 0.662460i) q^{30} -8.35352 q^{31} +(-0.866025 + 0.500000i) q^{32} +(-4.32315 + 2.49597i) q^{33} +(2.13153 + 3.69192i) q^{34} +(1.91774 - 2.07338i) q^{35} +1.00000 q^{36} +(-5.93579 - 1.32904i) q^{37} -7.34984i q^{38} +(-2.68079 + 4.64326i) q^{39} +(-0.662460 - 2.13568i) q^{40} +(3.74009 + 6.47803i) q^{41} +(-1.09384 + 0.631530i) q^{42} +11.0032i q^{43} +(-2.49597 - 4.32315i) q^{44} +(-0.494135 + 2.18079i) q^{45} +(3.97419 - 6.88350i) q^{46} +3.66980i q^{47} +1.00000i q^{48} +(-2.70234 + 4.68059i) q^{49} +(4.98482 - 0.389366i) q^{50} +4.26306 q^{51} +(-4.64326 - 2.68079i) q^{52} +(7.06383 + 4.07831i) q^{53} +(0.500000 - 0.866025i) q^{54} +(10.6612 - 3.30696i) q^{55} +(-0.631530 - 1.09384i) q^{56} +(-6.36515 - 3.67492i) q^{57} +(0.227817 + 0.131530i) q^{58} +(-2.45264 + 4.24810i) q^{59} +(-2.18079 - 0.494135i) q^{60} +(0.390022 + 0.675539i) q^{61} +(-7.23436 - 4.17676i) q^{62} +1.26306i q^{63} -1.00000 q^{64} +(8.14062 - 8.80129i) q^{65} -4.99195 q^{66} +(-3.05829 + 1.76570i) q^{67} +4.26306i q^{68} +(-3.97419 - 6.88350i) q^{69} +(2.69750 - 0.836727i) q^{70} +(-0.141422 - 0.244950i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.54371i q^{73} +(-4.47603 - 4.11888i) q^{74} +(2.15521 - 4.51166i) q^{75} +(3.67492 - 6.36515i) q^{76} +(5.46040 - 3.15256i) q^{77} +(-4.64326 + 2.68079i) q^{78} +(-4.05244 - 7.01903i) q^{79} +(0.494135 - 2.18079i) q^{80} +(-0.500000 - 0.866025i) q^{81} +7.48019i q^{82} +(11.9301 + 6.88783i) q^{83} -1.26306 q^{84} +(-9.29683 - 2.10653i) q^{85} +(-5.50161 + 9.52907i) q^{86} +(0.227817 - 0.131530i) q^{87} -4.99195i q^{88} +(6.52339 - 11.2988i) q^{89} +(-1.51833 + 1.64155i) q^{90} +(3.38600 - 5.86472i) q^{91} +(6.88350 - 3.97419i) q^{92} +(-7.23436 + 4.17676i) q^{93} +(-1.83490 + 3.17814i) q^{94} +(12.0651 + 11.1595i) q^{95} +(-0.500000 + 0.866025i) q^{96} +6.02010i q^{97} +(-4.68059 + 2.70234i) q^{98} +(-2.49597 + 4.32315i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + O(q^{10}) \) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + 4q^{10} - 12q^{11} + 8q^{14} + 2q^{15} - 14q^{16} - 20q^{19} - 2q^{20} + 4q^{21} + 14q^{24} - 8q^{25} - 20q^{26} - 36q^{29} + 2q^{30} + 24q^{31} + 38q^{34} - 2q^{35} + 28q^{36} - 10q^{39} + 2q^{40} - 6q^{44} + 4q^{45} + 8q^{46} + 50q^{49} - 4q^{50} + 76q^{51} + 14q^{54} - 28q^{55} + 4q^{56} - 26q^{59} + 4q^{60} - 28q^{61} - 28q^{64} + 60q^{65} - 12q^{66} - 8q^{69} - 10q^{70} - 64q^{71} + 24q^{74} - 8q^{75} + 20q^{76} + 32q^{79} - 4q^{80} - 14q^{81} + 8q^{84} + 16q^{85} - 8q^{86} + 76q^{89} + 2q^{90} - 8q^{91} - 38q^{94} - 70q^{95} - 14q^{96} - 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.612372 + 0.353553i
\(3\) 0.866025 0.500000i 0.500000 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −2.13568 + 0.662460i −0.955107 + 0.296261i
\(6\) 1.00000 0.408248
\(7\) −1.09384 + 0.631530i −0.413434 + 0.238696i −0.692264 0.721644i \(-0.743387\pi\)
0.278830 + 0.960340i \(0.410053\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 0.866025i 0.166667 0.288675i
\(10\) −2.18079 0.494135i −0.689625 0.156259i
\(11\) −4.99195 −1.50513 −0.752564 0.658519i \(-0.771183\pi\)
−0.752564 + 0.658519i \(0.771183\pi\)
\(12\) 0.866025 + 0.500000i 0.250000 + 0.144338i
\(13\) −4.64326 + 2.68079i −1.28781 + 0.743516i −0.978263 0.207368i \(-0.933510\pi\)
−0.309545 + 0.950885i \(0.600177\pi\)
\(14\) −1.26306 −0.337567
\(15\) −1.51833 + 1.64155i −0.392030 + 0.423846i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 3.69192 + 2.13153i 0.895422 + 0.516972i 0.875712 0.482834i \(-0.160392\pi\)
0.0197097 + 0.999806i \(0.493726\pi\)
\(18\) 0.866025 0.500000i 0.204124 0.117851i
\(19\) −3.67492 6.36515i −0.843085 1.46027i −0.887274 0.461243i \(-0.847404\pi\)
0.0441891 0.999023i \(-0.485930\pi\)
\(20\) −1.64155 1.51833i −0.367062 0.339508i
\(21\) −0.631530 + 1.09384i −0.137811 + 0.238696i
\(22\) −4.32315 2.49597i −0.921699 0.532143i
\(23\) 7.94839i 1.65735i −0.559728 0.828677i \(-0.689094\pi\)
0.559728 0.828677i \(-0.310906\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 4.12229 2.82961i 0.824459 0.565922i
\(26\) −5.36157 −1.05149
\(27\) 1.00000i 0.192450i
\(28\) −1.09384 0.631530i −0.206717 0.119348i
\(29\) 0.263060 0.0488491 0.0244245 0.999702i \(-0.492225\pi\)
0.0244245 + 0.999702i \(0.492225\pi\)
\(30\) −2.13568 + 0.662460i −0.389921 + 0.120948i
\(31\) −8.35352 −1.50034 −0.750168 0.661247i \(-0.770027\pi\)
−0.750168 + 0.661247i \(0.770027\pi\)
\(32\) −0.866025 + 0.500000i −0.153093 + 0.0883883i
\(33\) −4.32315 + 2.49597i −0.752564 + 0.434493i
\(34\) 2.13153 + 3.69192i 0.365554 + 0.633159i
\(35\) 1.91774 2.07338i 0.324157 0.350464i
\(36\) 1.00000 0.166667
\(37\) −5.93579 1.32904i −0.975839 0.218492i
\(38\) 7.34984i 1.19230i
\(39\) −2.68079 + 4.64326i −0.429269 + 0.743516i
\(40\) −0.662460 2.13568i −0.104744 0.337681i
\(41\) 3.74009 + 6.47803i 0.584104 + 1.01170i 0.994986 + 0.100010i \(0.0318875\pi\)
−0.410882 + 0.911689i \(0.634779\pi\)
\(42\) −1.09384 + 0.631530i −0.168784 + 0.0974472i
\(43\) 11.0032i 1.67798i 0.544150 + 0.838988i \(0.316852\pi\)
−0.544150 + 0.838988i \(0.683148\pi\)
\(44\) −2.49597 4.32315i −0.376282 0.651740i
\(45\) −0.494135 + 2.18079i −0.0736613 + 0.325092i
\(46\) 3.97419 6.88350i 0.585963 1.01492i
\(47\) 3.66980i 0.535296i 0.963517 + 0.267648i \(0.0862464\pi\)
−0.963517 + 0.267648i \(0.913754\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.70234 + 4.68059i −0.386048 + 0.668656i
\(50\) 4.98482 0.389366i 0.704959 0.0550647i
\(51\) 4.26306 0.596948
\(52\) −4.64326 2.68079i −0.643904 0.371758i
\(53\) 7.06383 + 4.07831i 0.970292 + 0.560198i 0.899325 0.437280i \(-0.144058\pi\)
0.0709668 + 0.997479i \(0.477392\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 10.6612 3.30696i 1.43756 0.445911i
\(56\) −0.631530 1.09384i −0.0843918 0.146171i
\(57\) −6.36515 3.67492i −0.843085 0.486755i
\(58\) 0.227817 + 0.131530i 0.0299138 + 0.0172708i
\(59\) −2.45264 + 4.24810i −0.319307 + 0.553055i −0.980344 0.197298i \(-0.936783\pi\)
0.661037 + 0.750353i \(0.270117\pi\)
\(60\) −2.18079 0.494135i −0.281538 0.0637926i
\(61\) 0.390022 + 0.675539i 0.0499373 + 0.0864939i 0.889914 0.456129i \(-0.150765\pi\)
−0.839976 + 0.542623i \(0.817431\pi\)
\(62\) −7.23436 4.17676i −0.918765 0.530449i
\(63\) 1.26306i 0.159131i
\(64\) −1.00000 −0.125000
\(65\) 8.14062 8.80129i 1.00972 1.09167i
\(66\) −4.99195 −0.614466
\(67\) −3.05829 + 1.76570i −0.373629 + 0.215715i −0.675043 0.737779i \(-0.735875\pi\)
0.301414 + 0.953494i \(0.402542\pi\)
\(68\) 4.26306i 0.516972i
\(69\) −3.97419 6.88350i −0.478437 0.828677i
\(70\) 2.69750 0.836727i 0.322413 0.100008i
\(71\) −0.141422 0.244950i −0.0167837 0.0290702i 0.857512 0.514465i \(-0.172009\pi\)
−0.874295 + 0.485394i \(0.838676\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 1.54371i 0.180677i 0.995911 + 0.0903387i \(0.0287950\pi\)
−0.995911 + 0.0903387i \(0.971205\pi\)
\(74\) −4.47603 4.11888i −0.520328 0.478810i
\(75\) 2.15521 4.51166i 0.248862 0.520962i
\(76\) 3.67492 6.36515i 0.421542 0.730133i
\(77\) 5.46040 3.15256i 0.622271 0.359268i
\(78\) −4.64326 + 2.68079i −0.525746 + 0.303539i
\(79\) −4.05244 7.01903i −0.455935 0.789703i 0.542806 0.839858i \(-0.317362\pi\)
−0.998741 + 0.0501551i \(0.984028\pi\)
\(80\) 0.494135 2.18079i 0.0552460 0.243819i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 7.48019i 0.826048i
\(83\) 11.9301 + 6.88783i 1.30950 + 0.756038i 0.982012 0.188819i \(-0.0604659\pi\)
0.327484 + 0.944857i \(0.393799\pi\)
\(84\) −1.26306 −0.137811
\(85\) −9.29683 2.10653i −1.00838 0.228485i
\(86\) −5.50161 + 9.52907i −0.593254 + 1.02755i
\(87\) 0.227817 0.131530i 0.0244245 0.0141015i
\(88\) 4.99195i 0.532143i
\(89\) 6.52339 11.2988i 0.691478 1.19768i −0.279876 0.960036i \(-0.590293\pi\)
0.971354 0.237639i \(-0.0763734\pi\)
\(90\) −1.51833 + 1.64155i −0.160046 + 0.173034i
\(91\) 3.38600 5.86472i 0.354949 0.614789i
\(92\) 6.88350 3.97419i 0.717655 0.414338i
\(93\) −7.23436 + 4.17676i −0.750168 + 0.433110i
\(94\) −1.83490 + 3.17814i −0.189256 + 0.327800i
\(95\) 12.0651 + 11.1595i 1.23786 + 1.14494i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 6.02010i 0.611249i 0.952152 + 0.305624i \(0.0988651\pi\)
−0.952152 + 0.305624i \(0.901135\pi\)
\(98\) −4.68059 + 2.70234i −0.472811 + 0.272977i
\(99\) −2.49597 + 4.32315i −0.250855 + 0.434493i
\(100\) 4.51166 + 2.15521i 0.451166 + 0.215521i
\(101\) −19.5101 −1.94133 −0.970665 0.240435i \(-0.922710\pi\)
−0.970665 + 0.240435i \(0.922710\pi\)
\(102\) 3.69192 + 2.13153i 0.365554 + 0.211053i
\(103\) 8.49192i 0.836733i −0.908278 0.418367i \(-0.862603\pi\)
0.908278 0.418367i \(-0.137397\pi\)
\(104\) −2.68079 4.64326i −0.262873 0.455309i
\(105\) 0.624123 2.75447i 0.0609081 0.268808i
\(106\) 4.07831 + 7.06383i 0.396120 + 0.686100i
\(107\) −13.5483 + 7.82214i −1.30977 + 0.756195i −0.982057 0.188583i \(-0.939610\pi\)
−0.327711 + 0.944778i \(0.606277\pi\)
\(108\) 0.866025 0.500000i 0.0833333 0.0481125i
\(109\) 5.13717 8.89784i 0.492051 0.852258i −0.507907 0.861412i \(-0.669581\pi\)
0.999958 + 0.00915400i \(0.00291385\pi\)
\(110\) 10.8864 + 2.46670i 1.03797 + 0.235190i
\(111\) −5.80507 + 1.81692i −0.550993 + 0.172454i
\(112\) 1.26306i 0.119348i
\(113\) 15.6594 + 9.04098i 1.47312 + 0.850503i 0.999542 0.0302513i \(-0.00963074\pi\)
0.473573 + 0.880755i \(0.342964\pi\)
\(114\) −3.67492 6.36515i −0.344188 0.596151i
\(115\) 5.26549 + 16.9752i 0.491009 + 1.58295i
\(116\) 0.131530 + 0.227817i 0.0122123 + 0.0211523i
\(117\) 5.36157i 0.495678i
\(118\) −4.24810 + 2.45264i −0.391069 + 0.225784i
\(119\) −5.38450 −0.493597
\(120\) −1.64155 1.51833i −0.149852 0.138604i
\(121\) 13.9195 1.26541
\(122\) 0.780045i 0.0706219i
\(123\) 6.47803 + 3.74009i 0.584104 + 0.337233i
\(124\) −4.17676 7.23436i −0.375084 0.649665i
\(125\) −6.92942 + 8.77401i −0.619786 + 0.784771i
\(126\) −0.631530 + 1.09384i −0.0562612 + 0.0974472i
\(127\) 3.82426 + 2.20794i 0.339348 + 0.195923i 0.659984 0.751280i \(-0.270563\pi\)
−0.320635 + 0.947203i \(0.603896\pi\)
\(128\) −0.866025 0.500000i −0.0765466 0.0441942i
\(129\) 5.50161 + 9.52907i 0.484390 + 0.838988i
\(130\) 11.4506 3.55183i 1.00429 0.311516i
\(131\) 4.83306 8.37111i 0.422267 0.731388i −0.573894 0.818930i \(-0.694568\pi\)
0.996161 + 0.0875420i \(0.0279012\pi\)
\(132\) −4.32315 2.49597i −0.376282 0.217247i
\(133\) 8.03957 + 4.64165i 0.697119 + 0.402482i
\(134\) −3.53141 −0.305067
\(135\) 0.662460 + 2.13568i 0.0570155 + 0.183810i
\(136\) −2.13153 + 3.69192i −0.182777 + 0.316579i
\(137\) 14.3318i 1.22445i −0.790684 0.612225i \(-0.790275\pi\)
0.790684 0.612225i \(-0.209725\pi\)
\(138\) 7.94839i 0.676612i
\(139\) −3.79794 + 6.57823i −0.322137 + 0.557958i −0.980929 0.194367i \(-0.937735\pi\)
0.658791 + 0.752326i \(0.271068\pi\)
\(140\) 2.75447 + 0.624123i 0.232795 + 0.0527480i
\(141\) 1.83490 + 3.17814i 0.154527 + 0.267648i
\(142\) 0.282844i 0.0237357i
\(143\) 23.1789 13.3823i 1.93832 1.11909i
\(144\) 0.500000 + 0.866025i 0.0416667 + 0.0721688i
\(145\) −0.561814 + 0.174267i −0.0466561 + 0.0144721i
\(146\) −0.771854 + 1.33689i −0.0638791 + 0.110642i
\(147\) 5.40468i 0.445770i
\(148\) −1.81692 5.80507i −0.149350 0.477174i
\(149\) −2.64733 −0.216877 −0.108439 0.994103i \(-0.534585\pi\)
−0.108439 + 0.994103i \(0.534585\pi\)
\(150\) 4.12229 2.82961i 0.336584 0.231037i
\(151\) −2.35137 4.07269i −0.191352 0.331431i 0.754347 0.656476i \(-0.227954\pi\)
−0.945698 + 0.325045i \(0.894620\pi\)
\(152\) 6.36515 3.67492i 0.516282 0.298076i
\(153\) 3.69192 2.13153i 0.298474 0.172324i
\(154\) 6.30513 0.508082
\(155\) 17.8405 5.53387i 1.43298 0.444491i
\(156\) −5.36157 −0.429269
\(157\) −11.7867 6.80507i −0.940683 0.543104i −0.0505086 0.998724i \(-0.516084\pi\)
−0.890174 + 0.455620i \(0.849418\pi\)
\(158\) 8.10488i 0.644790i
\(159\) 8.15661 0.646861
\(160\) 1.51833 1.64155i 0.120034 0.129776i
\(161\) 5.01965 + 8.69428i 0.395604 + 0.685205i
\(162\) 1.00000i 0.0785674i
\(163\) −10.5279 6.07828i −0.824609 0.476088i 0.0273945 0.999625i \(-0.491279\pi\)
−0.852003 + 0.523537i \(0.824612\pi\)
\(164\) −3.74009 + 6.47803i −0.292052 + 0.505849i
\(165\) 7.57941 8.19452i 0.590056 0.637943i
\(166\) 6.88783 + 11.9301i 0.534600 + 0.925954i
\(167\) −17.1266 + 9.88805i −1.32530 + 0.765160i −0.984568 0.175001i \(-0.944007\pi\)
−0.340728 + 0.940162i \(0.610674\pi\)
\(168\) −1.09384 0.631530i −0.0843918 0.0487236i
\(169\) 7.87323 13.6368i 0.605633 1.04899i
\(170\) −6.99802 6.47272i −0.536724 0.496435i
\(171\) −7.34984 −0.562057
\(172\) −9.52907 + 5.50161i −0.726585 + 0.419494i
\(173\) −4.03173 2.32772i −0.306527 0.176973i 0.338844 0.940842i \(-0.389964\pi\)
−0.645371 + 0.763869i \(0.723297\pi\)
\(174\) 0.263060 0.0199426
\(175\) −2.72216 + 5.69850i −0.205776 + 0.430766i
\(176\) 2.49597 4.32315i 0.188141 0.325870i
\(177\) 4.90528i 0.368704i
\(178\) 11.2988 6.52339i 0.846884 0.488949i
\(179\) 18.0339 1.34792 0.673958 0.738770i \(-0.264593\pi\)
0.673958 + 0.738770i \(0.264593\pi\)
\(180\) −2.13568 + 0.662460i −0.159185 + 0.0493768i
\(181\) 6.41934 + 11.1186i 0.477146 + 0.826440i 0.999657 0.0261920i \(-0.00833811\pi\)
−0.522511 + 0.852632i \(0.675005\pi\)
\(182\) 5.86472 3.38600i 0.434722 0.250987i
\(183\) 0.675539 + 0.390022i 0.0499373 + 0.0288313i
\(184\) 7.94839 0.585963
\(185\) 13.5574 1.09382i 0.996761 0.0804194i
\(186\) −8.35352 −0.612510
\(187\) −18.4299 10.6405i −1.34772 0.778109i
\(188\) −3.17814 + 1.83490i −0.231790 + 0.133824i
\(189\) 0.631530 + 1.09384i 0.0459371 + 0.0795653i
\(190\) 4.86898 + 15.6969i 0.353233 + 1.13878i
\(191\) −4.45352 −0.322246 −0.161123 0.986934i \(-0.551512\pi\)
−0.161123 + 0.986934i \(0.551512\pi\)
\(192\) −0.866025 + 0.500000i −0.0625000 + 0.0360844i
\(193\) 8.79974i 0.633419i 0.948523 + 0.316709i \(0.102578\pi\)
−0.948523 + 0.316709i \(0.897422\pi\)
\(194\) −3.01005 + 5.21356i −0.216109 + 0.374312i
\(195\) 2.64934 11.6924i 0.189723 0.837314i
\(196\) −5.40468 −0.386048
\(197\) −7.01557 4.05044i −0.499839 0.288582i 0.228808 0.973472i \(-0.426517\pi\)
−0.728647 + 0.684889i \(0.759851\pi\)
\(198\) −4.32315 + 2.49597i −0.307233 + 0.177381i
\(199\) 0.881703 0.0625023 0.0312511 0.999512i \(-0.490051\pi\)
0.0312511 + 0.999512i \(0.490051\pi\)
\(200\) 2.82961 + 4.12229i 0.200084 + 0.291490i
\(201\) −1.76570 + 3.05829i −0.124543 + 0.215715i
\(202\) −16.8963 9.75507i −1.18882 0.686364i
\(203\) −0.287747 + 0.166131i −0.0201959 + 0.0116601i
\(204\) 2.13153 + 3.69192i 0.149237 + 0.258486i
\(205\) −12.2791 11.3574i −0.857609 0.793233i
\(206\) 4.24596 7.35421i 0.295830 0.512392i
\(207\) −6.88350 3.97419i −0.478437 0.276226i
\(208\) 5.36157i 0.371758i
\(209\) 18.3450 + 31.7745i 1.26895 + 2.19789i
\(210\) 1.91774 2.07338i 0.132337 0.143077i
\(211\) −20.2451 −1.39373 −0.696866 0.717201i \(-0.745423\pi\)
−0.696866 + 0.717201i \(0.745423\pi\)
\(212\) 8.15661i 0.560198i
\(213\) −0.244950 0.141422i −0.0167837 0.00969008i
\(214\) −15.6443 −1.06942
\(215\) −7.28919 23.4994i −0.497119 1.60265i
\(216\) 1.00000 0.0680414
\(217\) 9.13743 5.27550i 0.620289 0.358124i
\(218\) 8.89784 5.13717i 0.602637 0.347933i
\(219\) 0.771854 + 1.33689i 0.0521571 + 0.0903387i
\(220\) 8.19452 + 7.57941i 0.552475 + 0.511003i
\(221\) −22.8567 −1.53751
\(222\) −5.93579 1.32904i −0.398384 0.0891991i
\(223\) 18.1705i 1.21679i −0.793635 0.608394i \(-0.791814\pi\)
0.793635 0.608394i \(-0.208186\pi\)
\(224\) 0.631530 1.09384i 0.0421959 0.0730854i
\(225\) −0.389366 4.98482i −0.0259578 0.332321i
\(226\) 9.04098 + 15.6594i 0.601397 + 1.04165i
\(227\) −9.88733 + 5.70845i −0.656245 + 0.378883i −0.790845 0.612017i \(-0.790358\pi\)
0.134600 + 0.990900i \(0.457025\pi\)
\(228\) 7.34984i 0.486755i
\(229\) 7.27924 + 12.6080i 0.481026 + 0.833161i 0.999763 0.0217727i \(-0.00693103\pi\)
−0.518737 + 0.854934i \(0.673598\pi\)
\(230\) −3.92758 + 17.3337i −0.258977 + 1.14295i
\(231\) 3.15256 5.46040i 0.207424 0.359268i
\(232\) 0.263060i 0.0172708i
\(233\) 2.82229i 0.184895i 0.995718 + 0.0924473i \(0.0294690\pi\)
−0.995718 + 0.0924473i \(0.970531\pi\)
\(234\) −2.68079 + 4.64326i −0.175249 + 0.303539i
\(235\) −2.43110 7.83754i −0.158587 0.511265i
\(236\) −4.90528 −0.319307
\(237\) −7.01903 4.05244i −0.455935 0.263234i
\(238\) −4.66312 2.69225i −0.302265 0.174513i
\(239\) 11.2761 19.5308i 0.729390 1.26334i −0.227751 0.973719i \(-0.573137\pi\)
0.957141 0.289621i \(-0.0935294\pi\)
\(240\) −0.662460 2.13568i −0.0427616 0.137858i
\(241\) −2.91315 5.04572i −0.187652 0.325023i 0.756815 0.653629i \(-0.226754\pi\)
−0.944467 + 0.328606i \(0.893421\pi\)
\(242\) 12.0547 + 6.95976i 0.774903 + 0.447390i
\(243\) −0.866025 0.500000i −0.0555556 0.0320750i
\(244\) −0.390022 + 0.675539i −0.0249686 + 0.0432469i
\(245\) 2.67064 11.7865i 0.170621 0.753009i
\(246\) 3.74009 + 6.47803i 0.238460 + 0.413024i
\(247\) 34.1272 + 19.7034i 2.17146 + 1.25369i
\(248\) 8.35352i 0.530449i
\(249\) 13.7757 0.872997
\(250\) −10.3881 + 4.13380i −0.656998 + 0.261445i
\(251\) 20.3308 1.28327 0.641633 0.767012i \(-0.278257\pi\)
0.641633 + 0.767012i \(0.278257\pi\)
\(252\) −1.09384 + 0.631530i −0.0689056 + 0.0397827i
\(253\) 39.6779i 2.49453i
\(254\) 2.20794 + 3.82426i 0.138538 + 0.239956i
\(255\) −9.10455 + 2.82411i −0.570149 + 0.176852i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 8.32463 + 4.80623i 0.519276 + 0.299804i 0.736638 0.676287i \(-0.236412\pi\)
−0.217362 + 0.976091i \(0.569745\pi\)
\(258\) 11.0032i 0.685031i
\(259\) 7.33215 2.29488i 0.455598 0.142597i
\(260\) 11.6924 + 2.64934i 0.725135 + 0.164305i
\(261\) 0.131530 0.227817i 0.00814151 0.0141015i
\(262\) 8.37111 4.83306i 0.517169 0.298588i
\(263\) −4.05962 + 2.34382i −0.250327 + 0.144526i −0.619914 0.784670i \(-0.712832\pi\)
0.369587 + 0.929196i \(0.379499\pi\)
\(264\) −2.49597 4.32315i −0.153617 0.266072i
\(265\) −17.7878 4.03047i −1.09270 0.247590i
\(266\) 4.64165 + 8.03957i 0.284598 + 0.492938i
\(267\) 13.0468i 0.798450i
\(268\) −3.05829 1.76570i −0.186815 0.107857i
\(269\) 18.0324 1.09945 0.549727 0.835344i \(-0.314732\pi\)
0.549727 + 0.835344i \(0.314732\pi\)
\(270\) −0.494135 + 2.18079i −0.0300721 + 0.132718i
\(271\) 1.40902 2.44050i 0.0855920 0.148250i −0.820051 0.572290i \(-0.806055\pi\)
0.905643 + 0.424040i \(0.139389\pi\)
\(272\) −3.69192 + 2.13153i −0.223855 + 0.129243i
\(273\) 6.77199i 0.409860i
\(274\) 7.16590 12.4117i 0.432908 0.749819i
\(275\) −20.5783 + 14.1253i −1.24092 + 0.851785i
\(276\) 3.97419 6.88350i 0.239218 0.414338i
\(277\) 16.3046 9.41347i 0.979649 0.565601i 0.0774850 0.996994i \(-0.475311\pi\)
0.902164 + 0.431393i \(0.141978\pi\)
\(278\) −6.57823 + 3.79794i −0.394536 + 0.227786i
\(279\) −4.17676 + 7.23436i −0.250056 + 0.433110i
\(280\) 2.07338 + 1.91774i 0.123908 + 0.114607i
\(281\) 8.14090 14.1005i 0.485646 0.841163i −0.514218 0.857659i \(-0.671918\pi\)
0.999864 + 0.0164965i \(0.00525125\pi\)
\(282\) 3.66980i 0.218534i
\(283\) −9.11635 + 5.26333i −0.541911 + 0.312872i −0.745853 0.666111i \(-0.767958\pi\)
0.203942 + 0.978983i \(0.434624\pi\)
\(284\) 0.141422 0.244950i 0.00839185 0.0145351i
\(285\) 16.0284 + 3.63182i 0.949443 + 0.215130i
\(286\) 26.7647 1.58263
\(287\) −8.18214 4.72396i −0.482977 0.278847i
\(288\) 1.00000i 0.0589256i
\(289\) 0.586842 + 1.01644i 0.0345201 + 0.0597906i
\(290\) −0.573679 0.129987i −0.0336876 0.00763312i
\(291\) 3.01005 + 5.21356i 0.176452 + 0.305624i
\(292\) −1.33689 + 0.771854i −0.0782356 + 0.0451693i
\(293\) −4.47258 + 2.58224i −0.261291 + 0.150856i −0.624923 0.780686i \(-0.714870\pi\)
0.363632 + 0.931542i \(0.381536\pi\)
\(294\) −2.70234 + 4.68059i −0.157604 + 0.272977i
\(295\) 2.42387 10.6974i 0.141123 0.622825i
\(296\) 1.32904 5.93579i 0.0772487 0.345011i
\(297\) 4.99195i 0.289662i
\(298\) −2.29265 1.32366i −0.132810 0.0766778i
\(299\) 21.3079 + 36.9064i 1.23227 + 2.13435i
\(300\) 4.98482 0.389366i 0.287799 0.0224801i
\(301\) −6.94887 12.0358i −0.400526 0.693731i
\(302\) 4.70273i 0.270612i
\(303\) −16.8963 + 9.75507i −0.970665 + 0.560414i
\(304\) 7.34984 0.421542
\(305\) −1.28048 1.18436i −0.0733202 0.0678164i
\(306\) 4.26306 0.243703
\(307\) 15.5648i 0.888333i −0.895944 0.444166i \(-0.853500\pi\)
0.895944 0.444166i \(-0.146500\pi\)
\(308\) 5.46040 + 3.15256i 0.311135 + 0.179634i
\(309\) −4.24596 7.35421i −0.241544 0.418367i
\(310\) 18.2172 + 4.12777i 1.03467 + 0.234441i
\(311\) −8.92380 + 15.4565i −0.506022 + 0.876456i 0.493954 + 0.869488i \(0.335551\pi\)
−0.999976 + 0.00696784i \(0.997782\pi\)
\(312\) −4.64326 2.68079i −0.262873 0.151770i
\(313\) −5.50514 3.17839i −0.311169 0.179653i 0.336281 0.941762i \(-0.390831\pi\)
−0.647449 + 0.762108i \(0.724164\pi\)
\(314\) −6.80507 11.7867i −0.384032 0.665163i
\(315\) −0.836727 2.69750i −0.0471442 0.151987i
\(316\) 4.05244 7.01903i 0.227968 0.394851i
\(317\) −13.7824 7.95728i −0.774097 0.446925i 0.0602370 0.998184i \(-0.480814\pi\)
−0.834334 + 0.551259i \(0.814148\pi\)
\(318\) 7.06383 + 4.07831i 0.396120 + 0.228700i
\(319\) −1.31318 −0.0735241
\(320\) 2.13568 0.662460i 0.119388 0.0370326i
\(321\) −7.82214 + 13.5483i −0.436589 + 0.756195i
\(322\) 10.0393i 0.559468i
\(323\) 31.3328i 1.74341i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −11.5553 + 24.1896i −0.640973 + 1.34180i
\(326\) −6.07828 10.5279i −0.336645 0.583086i
\(327\) 10.2743i 0.568172i
\(328\) −6.47803 + 3.74009i −0.357689 + 0.206512i
\(329\) −2.31759 4.01419i −0.127773 0.221309i
\(330\) 10.6612 3.30696i 0.586881 0.182042i
\(331\) 3.96108 6.86079i 0.217721 0.377103i −0.736390 0.676557i \(-0.763471\pi\)
0.954111 + 0.299454i \(0.0968045\pi\)
\(332\) 13.7757i 0.756038i
\(333\) −4.11888 + 4.47603i −0.225713 + 0.245285i
\(334\) −19.7761 −1.08210
\(335\) 5.36183 5.79698i 0.292948 0.316723i
\(336\) −0.631530 1.09384i −0.0344528 0.0596740i
\(337\) −30.5973 + 17.6654i −1.66674 + 0.962295i −0.697367 + 0.716714i \(0.745645\pi\)
−0.969376 + 0.245581i \(0.921021\pi\)
\(338\) 13.6368 7.87323i 0.741746 0.428247i
\(339\) 18.0820 0.982077
\(340\) −2.82411 9.10455i −0.153159 0.493764i
\(341\) 41.7003 2.25820
\(342\) −6.36515 3.67492i −0.344188 0.198717i
\(343\) 15.6679i 0.845985i
\(344\) −11.0032 −0.593254
\(345\) 13.0477 + 12.0682i 0.702463 + 0.649733i
\(346\) −2.32772 4.03173i −0.125139 0.216747i
\(347\) 3.87172i 0.207845i −0.994585 0.103923i \(-0.966861\pi\)
0.994585 0.103923i \(-0.0331394\pi\)
\(348\) 0.227817 + 0.131530i 0.0122123 + 0.00705076i
\(349\) −7.16648 + 12.4127i −0.383613 + 0.664437i −0.991576 0.129528i \(-0.958654\pi\)
0.607963 + 0.793966i \(0.291987\pi\)
\(350\) −5.20671 + 3.57397i −0.278310 + 0.191037i
\(351\) 2.68079 + 4.64326i 0.143090 + 0.247839i
\(352\) 4.32315 2.49597i 0.230425 0.133036i
\(353\) 1.29700 + 0.748825i 0.0690325 + 0.0398559i 0.534119 0.845409i \(-0.320643\pi\)
−0.465086 + 0.885265i \(0.653977\pi\)
\(354\) −2.45264 + 4.24810i −0.130356 + 0.225784i
\(355\) 0.464302 + 0.429450i 0.0246426 + 0.0227928i
\(356\) 13.0468 0.691478
\(357\) −4.66312 + 2.69225i −0.246798 + 0.142489i
\(358\) 15.6178 + 9.01694i 0.825426 + 0.476560i
\(359\) −8.83396 −0.466239 −0.233119 0.972448i \(-0.574893\pi\)
−0.233119 + 0.972448i \(0.574893\pi\)
\(360\) −2.18079 0.494135i −0.114938 0.0260432i
\(361\) −17.5101 + 30.3284i −0.921584 + 1.59623i
\(362\) 12.8387i 0.674786i
\(363\) 12.0547 6.95976i 0.632706 0.365293i
\(364\) 6.77199 0.354949
\(365\) −1.02264 3.29687i −0.0535277 0.172566i
\(366\) 0.390022 + 0.675539i 0.0203868 + 0.0353110i
\(367\) −15.9066 + 9.18365i −0.830315 + 0.479383i −0.853961 0.520338i \(-0.825806\pi\)
0.0236452 + 0.999720i \(0.492473\pi\)
\(368\) 6.88350 + 3.97419i 0.358827 + 0.207169i
\(369\) 7.48019 0.389403
\(370\) 12.2880 + 5.83143i 0.638822 + 0.303162i
\(371\) −10.3023 −0.534868
\(372\) −7.23436 4.17676i −0.375084 0.216555i
\(373\) −7.08648 + 4.09138i −0.366924 + 0.211844i −0.672114 0.740448i \(-0.734613\pi\)
0.305190 + 0.952292i \(0.401280\pi\)
\(374\) −10.6405 18.4299i −0.550206 0.952985i
\(375\) −1.61405 + 11.0632i −0.0833491 + 0.571302i
\(376\) −3.66980 −0.189256
\(377\) −1.22146 + 0.705209i −0.0629083 + 0.0363201i
\(378\) 1.26306i 0.0649648i
\(379\) −13.6863 + 23.7054i −0.703019 + 1.21766i 0.264383 + 0.964418i \(0.414832\pi\)
−0.967402 + 0.253247i \(0.918502\pi\)
\(380\) −3.63182 + 16.0284i −0.186308 + 0.822242i
\(381\) 4.41588 0.226232
\(382\) −3.85686 2.22676i −0.197334 0.113931i
\(383\) 29.9910 17.3153i 1.53247 0.884771i 0.533222 0.845975i \(-0.320981\pi\)
0.999247 0.0387959i \(-0.0123522\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −9.57325 + 10.3502i −0.487898 + 0.527494i
\(386\) −4.39987 + 7.62080i −0.223947 + 0.387888i
\(387\) 9.52907 + 5.50161i 0.484390 + 0.279663i
\(388\) −5.21356 + 3.01005i −0.264678 + 0.152812i
\(389\) −10.0409 17.3913i −0.509093 0.881775i −0.999945 0.0105319i \(-0.996648\pi\)
0.490851 0.871243i \(-0.336686\pi\)
\(390\) 8.14062 8.80129i 0.412216 0.445670i
\(391\) 16.9422 29.3448i 0.856805 1.48403i
\(392\) −4.68059 2.70234i −0.236405 0.136489i
\(393\) 9.66613i 0.487592i
\(394\) −4.05044 7.01557i −0.204058 0.353440i
\(395\) 13.3046 + 12.3059i 0.669425 + 0.619175i
\(396\) −4.99195 −0.250855
\(397\) 19.1670i 0.961964i 0.876730 + 0.480982i \(0.159720\pi\)
−0.876730 + 0.480982i \(0.840280\pi\)
\(398\) 0.763578 + 0.440852i 0.0382747 + 0.0220979i
\(399\) 9.28330 0.464746
\(400\) 0.389366 + 4.98482i 0.0194683 + 0.249241i
\(401\) −2.28974 −0.114344 −0.0571721 0.998364i \(-0.518208\pi\)
−0.0571721 + 0.998364i \(0.518208\pi\)
\(402\) −3.05829 + 1.76570i −0.152533 + 0.0880653i
\(403\) 38.7876 22.3940i 1.93215 1.11552i
\(404\) −9.75507 16.8963i −0.485333 0.840621i
\(405\) 1.64155 + 1.51833i 0.0815692 + 0.0754463i
\(406\) −0.332261 −0.0164898
\(407\) 29.6312 + 6.63448i 1.46876 + 0.328859i
\(408\) 4.26306i 0.211053i
\(409\) −18.8834 + 32.7070i −0.933724 + 1.61726i −0.156831 + 0.987625i \(0.550128\pi\)
−0.776893 + 0.629632i \(0.783206\pi\)
\(410\) −4.95532 15.9753i −0.244726 0.788965i
\(411\) −7.16590 12.4117i −0.353468 0.612225i
\(412\) 7.35421 4.24596i 0.362316 0.209183i
\(413\) 6.19567i 0.304869i
\(414\) −3.97419 6.88350i −0.195321 0.338306i
\(415\) −30.0418 6.80704i −1.47469 0.334145i
\(416\) 2.68079 4.64326i 0.131436 0.227654i
\(417\) 7.59589i 0.371972i
\(418\) 36.6900i 1.79457i
\(419\) 8.70163 15.0717i 0.425103 0.736299i −0.571327 0.820722i \(-0.693571\pi\)
0.996430 + 0.0844228i \(0.0269047\pi\)
\(420\) 2.69750 0.836727i 0.131624 0.0408281i
\(421\) 6.81109 0.331952 0.165976 0.986130i \(-0.446923\pi\)
0.165976 + 0.986130i \(0.446923\pi\)
\(422\) −17.5328 10.1226i −0.853484 0.492759i
\(423\) 3.17814 + 1.83490i 0.154527 + 0.0892159i
\(424\) −4.07831 + 7.06383i −0.198060 + 0.343050i
\(425\) 21.2506 1.65989i 1.03080 0.0805166i
\(426\) −0.141422 0.244950i −0.00685192 0.0118679i
\(427\) −0.853246 0.492622i −0.0412915 0.0238396i
\(428\) −13.5483 7.82214i −0.654884 0.378097i
\(429\) 13.3823 23.1789i 0.646106 1.11909i
\(430\) 5.43708 23.9957i 0.262199 1.15717i
\(431\) 10.8020 + 18.7097i 0.520316 + 0.901214i 0.999721 + 0.0236199i \(0.00751915\pi\)
−0.479405 + 0.877594i \(0.659148\pi\)
\(432\) 0.866025 + 0.500000i 0.0416667 + 0.0240563i
\(433\) 4.55525i 0.218911i 0.993992 + 0.109456i \(0.0349108\pi\)
−0.993992 + 0.109456i \(0.965089\pi\)
\(434\) 10.5510 0.506464
\(435\) −0.399412 + 0.431826i −0.0191503 + 0.0207045i
\(436\) 10.2743 0.492051
\(437\) −50.5927 + 29.2097i −2.42018 + 1.39729i
\(438\) 1.54371i 0.0737612i
\(439\) 6.18014 + 10.7043i 0.294962 + 0.510889i 0.974976 0.222310i \(-0.0713597\pi\)
−0.680014 + 0.733199i \(0.738026\pi\)
\(440\) 3.30696 + 10.6612i 0.157653 + 0.508254i
\(441\) 2.70234 + 4.68059i 0.128683 + 0.222885i
\(442\) −19.7945 11.4284i −0.941528 0.543591i
\(443\) 13.2381i 0.628960i 0.949264 + 0.314480i \(0.101830\pi\)
−0.949264 + 0.314480i \(0.898170\pi\)
\(444\) −4.47603 4.11888i −0.212423 0.195473i
\(445\) −6.44687 + 28.4522i −0.305611 + 1.34877i
\(446\) 9.08526 15.7361i 0.430200 0.745127i
\(447\) −2.29265 + 1.32366i −0.108439 + 0.0626071i
\(448\) 1.09384 0.631530i 0.0516792 0.0298370i
\(449\) −18.3409 31.7673i −0.865559 1.49919i −0.866492 0.499192i \(-0.833630\pi\)
0.000932977 1.00000i \(-0.499703\pi\)
\(450\) 2.15521 4.51166i 0.101597 0.212682i
\(451\) −18.6703 32.3380i −0.879152 1.52274i
\(452\) 18.0820i 0.850503i
\(453\) −4.07269 2.35137i −0.191352 0.110477i
\(454\) −11.4169 −0.535822
\(455\) −3.34628 + 14.7683i −0.156876 + 0.692347i
\(456\) 3.67492 6.36515i 0.172094 0.298076i
\(457\) −32.3173 + 18.6584i −1.51174 + 0.872803i −0.511833 + 0.859085i \(0.671033\pi\)
−0.999906 + 0.0137183i \(0.995633\pi\)
\(458\) 14.5585i 0.680273i
\(459\) 2.13153 3.69192i 0.0994913 0.172324i
\(460\) −12.0682 + 13.0477i −0.562685 + 0.608351i
\(461\) −11.8742 + 20.5667i −0.553036 + 0.957887i 0.445017 + 0.895522i \(0.353198\pi\)
−0.998053 + 0.0623650i \(0.980136\pi\)
\(462\) 5.46040 3.15256i 0.254041 0.146671i
\(463\) −24.5010 + 14.1457i −1.13866 + 0.657405i −0.946098 0.323880i \(-0.895013\pi\)
−0.192561 + 0.981285i \(0.561679\pi\)
\(464\) −0.131530 + 0.227817i −0.00610614 + 0.0105761i
\(465\) 12.6834 13.7127i 0.588177 0.635912i
\(466\) −1.41115 + 2.44418i −0.0653701 + 0.113224i
\(467\) 19.4357i 0.899378i −0.893185 0.449689i \(-0.851535\pi\)
0.893185 0.449689i \(-0.148465\pi\)
\(468\) −4.64326 + 2.68079i −0.214635 + 0.123919i
\(469\) 2.23019 3.86280i 0.102981 0.178368i
\(470\) 1.81338 8.00306i 0.0836449 0.369153i
\(471\) −13.6101 −0.627122
\(472\) −4.24810 2.45264i −0.195535 0.112892i
\(473\) 54.9275i 2.52557i
\(474\) −4.05244 7.01903i −0.186135 0.322395i
\(475\) −33.1600 15.8404i −1.52149 0.726809i
\(476\) −2.69225 4.66312i −0.123399 0.213734i
\(477\) 7.06383 4.07831i 0.323431 0.186733i
\(478\) 19.5308 11.2761i 0.893317 0.515757i
\(479\) −18.7548 + 32.4842i −0.856926 + 1.48424i 0.0179197 + 0.999839i \(0.494296\pi\)
−0.874846 + 0.484401i \(0.839038\pi\)
\(480\) 0.494135 2.18079i 0.0225541 0.0995388i
\(481\) 31.1243 9.74154i 1.41915 0.444176i
\(482\) 5.82630i 0.265380i
\(483\) 8.69428 + 5.01965i 0.395604 + 0.228402i
\(484\) 6.95976 + 12.0547i 0.316353 + 0.547939i
\(485\) −3.98807 12.8570i −0.181089 0.583808i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 17.3440i 0.785931i −0.919553 0.392965i \(-0.871449\pi\)
0.919553 0.392965i \(-0.128551\pi\)
\(488\) −0.675539 + 0.390022i −0.0305802 + 0.0176555i
\(489\) −12.1566 −0.549739
\(490\) 8.20607 8.87204i 0.370712 0.400798i
\(491\) −2.30071 −0.103829 −0.0519147 0.998652i \(-0.516532\pi\)
−0.0519147 + 0.998652i \(0.516532\pi\)
\(492\) 7.48019i 0.337233i
\(493\) 0.971197 + 0.560721i 0.0437405 + 0.0252536i
\(494\) 19.7034 + 34.1272i 0.886496 + 1.53546i
\(495\) 2.46670 10.8864i 0.110870 0.489306i
\(496\) 4.17676 7.23436i 0.187542 0.324832i
\(497\) 0.309387 + 0.178625i 0.0138779 + 0.00801241i
\(498\) 11.9301 + 6.88783i 0.534600 + 0.308651i
\(499\) −2.18307 3.78119i −0.0977276 0.169269i 0.813016 0.582241i \(-0.197824\pi\)
−0.910744 + 0.412972i \(0.864491\pi\)
\(500\) −11.0632 1.61405i −0.494762 0.0721824i
\(501\) −9.88805 + 17.1266i −0.441766 + 0.765160i
\(502\) 17.6070 + 10.1654i 0.785837 + 0.453703i
\(503\) −18.1801 10.4963i −0.810608 0.468005i 0.0365587 0.999332i \(-0.488360\pi\)
−0.847167 + 0.531327i \(0.821694\pi\)
\(504\) −1.26306 −0.0562612
\(505\) 41.6675 12.9247i 1.85418 0.575140i
\(506\) −19.8390 + 34.3621i −0.881949 + 1.52758i
\(507\) 15.7465i 0.699325i
\(508\) 4.41588i 0.195923i
\(509\) −18.8359 + 32.6247i −0.834886 + 1.44607i 0.0592368 + 0.998244i \(0.481133\pi\)
−0.894123 + 0.447821i \(0.852200\pi\)
\(510\) −9.29683 2.10653i −0.411670 0.0932786i
\(511\) −0.974898 1.68857i −0.0431270 0.0746981i
\(512\) 1.00000i 0.0441942i
\(513\) −6.36515 + 3.67492i −0.281028 + 0.162252i
\(514\) 4.80623 + 8.32463i 0.211993 + 0.367184i
\(515\) 5.62555 + 18.1361i 0.247891 + 0.799170i
\(516\) −5.50161 + 9.52907i −0.242195 + 0.419494i
\(517\) 18.3195i 0.805689i
\(518\) 7.49727 + 1.67865i 0.329411 + 0.0737558i
\(519\) −4.65544 −0.204351
\(520\) 8.80129 + 8.14062i 0.385962 + 0.356990i
\(521\) −18.1788 31.4866i −0.796428 1.37945i −0.921929 0.387360i \(-0.873387\pi\)
0.125501 0.992094i \(-0.459946\pi\)
\(522\) 0.227817 0.131530i 0.00997128 0.00575692i
\(523\) 35.0328 20.2262i 1.53188 0.884430i 0.532602 0.846366i \(-0.321214\pi\)
0.999275 0.0380645i \(-0.0121192\pi\)
\(524\) 9.66613 0.422267
\(525\) 0.491793 + 6.29612i 0.0214636 + 0.274785i
\(526\) −4.68764 −0.204391
\(527\) −30.8405 17.8058i −1.34343 0.775632i
\(528\) 4.99195i 0.217247i
\(529\) −40.1769 −1.74682
\(530\) −13.3895 12.3844i −0.581602 0.537944i
\(531\) 2.45264 + 4.24810i 0.106436 + 0.184352i
\(532\) 9.28330i 0.402482i
\(533\) −34.7324 20.0528i −1.50443 0.868582i
\(534\) 6.52339 11.2988i 0.282295 0.488949i
\(535\) 23.7531 25.6809i 1.02694 1.11028i
\(536\) −1.76570 3.05829i −0.0762667 0.132098i
\(537\) 15.6178 9.01694i 0.673958 0.389110i
\(538\) 15.6165 + 9.01620i 0.673276 + 0.388716i
\(539\) 13.4899 23.3652i 0.581052 1.00641i
\(540\) −1.51833 + 1.64155i −0.0653384 + 0.0706410i
\(541\) 13.0090 0.559299 0.279649 0.960102i \(-0.409782\pi\)
0.279649 + 0.960102i \(0.409782\pi\)
\(542\) 2.44050 1.40902i 0.104828 0.0605227i
\(543\) 11.1186 + 6.41934i 0.477146 + 0.275480i
\(544\) −4.26306 −0.182777
\(545\) −5.07691 + 22.4061i −0.217471 + 0.959773i
\(546\) 3.38600 5.86472i 0.144907 0.250987i
\(547\) 24.6188i 1.05262i −0.850292 0.526312i \(-0.823574\pi\)
0.850292 0.526312i \(-0.176426\pi\)
\(548\) 12.4117 7.16590i 0.530202 0.306112i
\(549\) 0.780045 0.0332915
\(550\) −24.8839 + 1.94370i −1.06105 + 0.0828795i
\(551\) −0.966726 1.67442i −0.0411839 0.0713327i
\(552\) 6.88350 3.97419i 0.292981 0.169153i
\(553\) 8.86546 + 5.11848i 0.376998 + 0.217660i
\(554\) 18.8269 0.799880
\(555\) 11.1942 7.72599i 0.475165 0.327950i
\(556\) −7.59589 −0.322137
\(557\) 12.1937 + 7.04001i 0.516662 + 0.298295i 0.735568 0.677451i \(-0.236915\pi\)
−0.218906 + 0.975746i \(0.570249\pi\)
\(558\) −7.23436 + 4.17676i −0.306255 + 0.176816i
\(559\) −29.4973 51.0908i −1.24760 2.16091i
\(560\) 0.836727 + 2.69750i 0.0353582 + 0.113990i
\(561\) −21.2810 −0.898483
\(562\) 14.1005 8.14090i 0.594792 0.343403i
\(563\) 18.2964i 0.771101i 0.922687 + 0.385551i \(0.125989\pi\)
−0.922687 + 0.385551i \(0.874011\pi\)
\(564\) −1.83490 + 3.17814i −0.0772633 + 0.133824i
\(565\) −39.4329 8.93493i −1.65895 0.375895i
\(566\) −10.5267 −0.442468
\(567\) 1.09384 + 0.631530i 0.0459371 + 0.0265218i
\(568\) 0.244950 0.141422i 0.0102779 0.00593394i
\(569\) 25.3625 1.06325 0.531625 0.846980i \(-0.321581\pi\)
0.531625 + 0.846980i \(0.321581\pi\)
\(570\) 12.0651 + 11.1595i 0.505353 + 0.467419i
\(571\) 21.1056 36.5560i 0.883241 1.52982i 0.0355254 0.999369i \(-0.488690\pi\)
0.847716 0.530450i \(-0.177977\pi\)
\(572\) 23.1789 + 13.3823i 0.969158 + 0.559544i
\(573\) −3.85686 + 2.22676i −0.161123 + 0.0930243i
\(574\) −4.72396 8.18214i −0.197174 0.341516i
\(575\) −22.4908 32.7656i −0.937932 1.36642i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −0.213185 0.123082i −0.00887501 0.00512399i 0.495556 0.868576i \(-0.334964\pi\)
−0.504431 + 0.863452i \(0.668298\pi\)
\(578\) 1.17368i 0.0488188i
\(579\) 4.39987 + 7.62080i 0.182852 + 0.316709i
\(580\) −0.431826 0.399412i −0.0179306 0.0165847i
\(581\) −17.3995 −0.721853
\(582\) 6.02010i 0.249541i
\(583\) −35.2623 20.3587i −1.46041 0.843171i
\(584\) −1.54371 −0.0638791
\(585\) −3.55183 11.4506i −0.146850 0.473425i
\(586\) −5.16449 −0.213343
\(587\) −24.5330 + 14.1641i −1.01258 + 0.584616i −0.911947 0.410307i \(-0.865421\pi\)
−0.100637 + 0.994923i \(0.532088\pi\)
\(588\) −4.68059 + 2.70234i −0.193024 + 0.111443i
\(589\) 30.6985 + 53.1714i 1.26491 + 2.19089i
\(590\) 7.44782 8.05226i 0.306622 0.331506i
\(591\) −8.10089 −0.333226
\(592\) 4.11888 4.47603i 0.169285 0.183964i
\(593\) 32.0201i 1.31491i 0.753494 + 0.657455i \(0.228367\pi\)
−0.753494 + 0.657455i \(0.771633\pi\)
\(594\) −2.49597 + 4.32315i −0.102411 + 0.177381i
\(595\) 11.4996 3.56702i 0.471438 0.146233i
\(596\) −1.32366 2.29265i −0.0542194 0.0939107i
\(597\) 0.763578 0.440852i 0.0312511 0.0180429i
\(598\) 42.6159i 1.74269i
\(599\) 8.52695 + 14.7691i 0.348402 + 0.603449i 0.985966 0.166948i \(-0.0533912\pi\)
−0.637564 + 0.770397i \(0.720058\pi\)
\(600\) 4.51166 + 2.15521i 0.184188 + 0.0879860i
\(601\) −5.27568 + 9.13774i −0.215199 + 0.372736i −0.953334 0.301917i \(-0.902373\pi\)
0.738135 + 0.674653i \(0.235707\pi\)
\(602\) 13.8977i 0.566429i
\(603\) 3.53141i 0.143810i
\(604\) 2.35137 4.07269i 0.0956758 0.165715i
\(605\) −29.7277 + 9.22112i −1.20860 + 0.374892i
\(606\) −19.5101 −0.792545
\(607\) −9.55271 5.51526i −0.387733 0.223858i 0.293445 0.955976i \(-0.405198\pi\)
−0.681177 + 0.732118i \(0.738532\pi\)
\(608\) 6.36515 + 3.67492i 0.258141 + 0.149038i
\(609\) −0.166131 + 0.287747i −0.00673195 + 0.0116601i
\(610\) −0.516748 1.66593i −0.0209225 0.0674515i
\(611\) −9.83796 17.0398i −0.398001 0.689358i
\(612\) 3.69192 + 2.13153i 0.149237 + 0.0861620i
\(613\) 18.5126 + 10.6883i 0.747717 + 0.431695i 0.824869 0.565325i \(-0.191249\pi\)
−0.0771512 + 0.997019i \(0.524582\pi\)
\(614\) 7.78242 13.4796i 0.314073 0.543990i
\(615\) −16.3127 3.69622i −0.657791 0.149046i
\(616\) 3.15256 + 5.46040i 0.127020 + 0.220006i
\(617\) 2.11476 + 1.22095i 0.0851368 + 0.0491538i 0.541964 0.840402i \(-0.317681\pi\)
−0.456827 + 0.889555i \(0.651014\pi\)
\(618\) 8.49192i 0.341595i
\(619\) 41.1110 1.65239 0.826196 0.563382i \(-0.190500\pi\)
0.826196 + 0.563382i \(0.190500\pi\)
\(620\) 13.7127 + 12.6834i 0.550716 + 0.509377i
\(621\) −7.94839 −0.318958
\(622\) −15.4565 + 8.92380i −0.619748 + 0.357812i
\(623\) 16.4789i 0.660212i
\(624\) −2.68079 4.64326i −0.107317 0.185879i
\(625\) 8.98662 23.3290i 0.359465 0.933159i
\(626\) −3.17839 5.50514i −0.127034 0.220029i
\(627\) 31.7745 + 18.3450i 1.26895 + 0.732629i
\(628\) 13.6101i 0.543104i
\(629\) −19.0816 17.5590i −0.760833 0.700124i
\(630\) 0.624123 2.75447i 0.0248656 0.109741i
\(631\) 8.88206 15.3842i 0.353589 0.612434i −0.633286 0.773918i \(-0.718294\pi\)
0.986875 + 0.161483i \(0.0516278\pi\)
\(632\) 7.01903 4.05244i 0.279202 0.161197i
\(633\) −17.5328 + 10.1226i −0.696866 + 0.402336i
\(634\) −7.95728 13.7824i −0.316024 0.547369i
\(635\) −9.63009 2.18204i −0.382158 0.0865917i
\(636\) 4.07831 + 7.06383i 0.161715 + 0.280099i
\(637\) 28.9776i 1.14813i
\(638\) −1.13725 0.656592i −0.0450242 0.0259947i
\(639\) −0.282844 −0.0111891
\(640\) 2.18079 + 0.494135i 0.0862032 + 0.0195324i
\(641\) 10.1835 17.6384i 0.402225 0.696674i −0.591769 0.806108i \(-0.701570\pi\)
0.993994 + 0.109433i \(0.0349036\pi\)
\(642\) −13.5483 + 7.82214i −0.534710 + 0.308715i
\(643\) 3.70473i 0.146100i 0.997328 + 0.0730502i \(0.0232733\pi\)
−0.997328 + 0.0730502i \(0.976727\pi\)
\(644\) −5.01965 + 8.69428i −0.197802 + 0.342603i
\(645\) −18.0623 16.7065i −0.711203 0.657817i
\(646\) 15.6664 27.1350i 0.616387 1.06761i
\(647\) −3.89440 + 2.24843i −0.153105 + 0.0883950i −0.574595 0.818438i \(-0.694840\pi\)
0.421490 + 0.906833i \(0.361507\pi\)
\(648\) 0.866025 0.500000i 0.0340207 0.0196419i
\(649\) 12.2434 21.2063i 0.480597 0.832419i
\(650\) −22.1020 + 15.1712i −0.866911 + 0.595062i
\(651\) 5.27550 9.13743i 0.206763 0.358124i
\(652\) 12.1566i 0.476088i
\(653\) 19.3934 11.1968i 0.758921 0.438163i −0.0699875 0.997548i \(-0.522296\pi\)
0.828908 + 0.559385i \(0.188963\pi\)
\(654\) 5.13717 8.89784i 0.200879 0.347933i
\(655\) −4.77637 + 21.0798i −0.186628 + 0.823655i
\(656\) −7.48019 −0.292052
\(657\) 1.33689 + 0.771854i 0.0521571 + 0.0301129i
\(658\) 4.63518i 0.180698i
\(659\) 1.35816 + 2.35241i 0.0529065 + 0.0916368i 0.891266 0.453481i \(-0.149818\pi\)
−0.838359 + 0.545118i \(0.816485\pi\)
\(660\) 10.8864 + 2.46670i 0.423751 + 0.0960160i
\(661\) 3.15588 + 5.46614i 0.122749 + 0.212608i 0.920851 0.389915i \(-0.127495\pi\)
−0.798102 + 0.602523i \(0.794162\pi\)
\(662\) 6.86079 3.96108i 0.266652 0.153952i
\(663\) −19.7945 + 11.4284i −0.768754 + 0.443841i
\(664\) −6.88783 + 11.9301i −0.267300 + 0.462977i
\(665\) −20.2449 4.58720i −0.785063 0.177884i
\(666\) −5.80507 + 1.81692i −0.224942 + 0.0704042i
\(667\) 2.09091i 0.0809602i
\(668\) −17.1266 9.88805i −0.662648 0.382580i
\(669\) −9.08526 15.7361i −0.351256 0.608394i
\(670\) 7.54197 2.33941i 0.291372 0.0903794i
\(671\) −1.94697 3.37225i −0.0751620 0.130184i
\(672\) 1.26306i 0.0487236i
\(673\) 3.67729 2.12308i 0.141749 0.0818388i −0.427448 0.904040i \(-0.640587\pi\)
0.569197 + 0.822201i \(0.307254\pi\)
\(674\) −35.3308 −1.36089
\(675\) −2.82961 4.12229i −0.108912 0.158667i
\(676\) 15.7465 0.605633
\(677\) 38.4405i 1.47739i 0.674041 + 0.738693i \(0.264557\pi\)
−0.674041 + 0.738693i \(0.735443\pi\)
\(678\) 15.6594 + 9.04098i 0.601397 + 0.347217i
\(679\) −3.80187 6.58504i −0.145903 0.252711i
\(680\) 2.10653 9.29683i 0.0807817 0.356517i
\(681\) −5.70845 + 9.88733i −0.218748 + 0.378883i
\(682\) 36.1135 + 20.8502i 1.38286 + 0.798394i
\(683\) −41.5997 24.0176i −1.59177 0.919009i −0.993004 0.118085i \(-0.962325\pi\)
−0.598766 0.800924i \(-0.704342\pi\)
\(684\) −3.67492 6.36515i −0.140514 0.243378i
\(685\) 9.49425 + 30.6082i 0.362756 + 1.16948i
\(686\) 7.83393 13.5688i 0.299101 0.518058i
\(687\) 12.6080 + 7.27924i 0.481026 + 0.277720i
\(688\) −9.52907 5.50161i −0.363292 0.209747i
\(689\) −43.7323 −1.66607
\(690\) 5.26549 + 16.9752i 0.200454 + 0.646237i
\(691\) 15.9446 27.6169i 0.606561 1.05060i −0.385241 0.922816i \(-0.625882\pi\)
0.991803 0.127779i \(-0.0407849\pi\)
\(692\) 4.65544i 0.176973i
\(693\) 6.30513i 0.239512i
\(694\) 1.93586 3.35301i 0.0734843 0.127279i
\(695\) 3.75340 16.5650i 0.142374 0.628347i
\(696\) 0.131530 + 0.227817i 0.00498564 + 0.00863538i
\(697\) 31.8885i 1.20786i
\(698\) −12.4127 + 7.16648i −0.469828 + 0.271255i
\(699\) 1.41115 + 2.44418i 0.0533745 + 0.0924473i
\(700\) −6.29612 + 0.491793i −0.237971 + 0.0185880i
\(701\) −1.65838 + 2.87241i −0.0626363 + 0.108489i −0.895643 0.444774i \(-0.853284\pi\)
0.833007 + 0.553263i \(0.186617\pi\)
\(702\) 5.36157i 0.202360i
\(703\) 13.3541 + 42.6663i 0.503658 + 1.60919i
\(704\) 4.99195 0.188141
\(705\) −6.02416 5.57196i −0.226883 0.209852i
\(706\) 0.748825 + 1.29700i 0.0281824 + 0.0488134i
\(707\) 21.3410 12.3212i 0.802611 0.463388i
\(708\) −4.24810 + 2.45264i −0.159653 + 0.0921759i
\(709\) −17.1332 −0.643449 −0.321724 0.946833i \(-0.604262\pi\)
−0.321724 + 0.946833i \(0.604262\pi\)
\(710\) 0.187373 + 0.604066i 0.00703197 + 0.0226702i
\(711\) −8.10488 −0.303957
\(712\) 11.2988 + 6.52339i 0.423442 + 0.244474i
\(713\) 66.3970i 2.48659i
\(714\) −5.38450 −0.201510
\(715\) −40.6375 + 43.9355i −1.51976 + 1.64310i
\(716\) 9.01694 + 15.6178i 0.336979 + 0.583664i
\(717\) 22.5522i 0.842227i
\(718\) −7.65044 4.41698i −0.285512 0.164840i
\(719\) −4.90657 + 8.49843i −0.182984 + 0.316938i −0.942895 0.333089i \(-0.891909\pi\)
0.759911 + 0.650027i \(0.225242\pi\)
\(720\) −1.64155 1.51833i −0.0611769 0.0565847i
\(721\) 5.36290 + 9.28882i 0.199725 + 0.345934i
\(722\) −30.3284 + 17.5101i −1.12871 + 0.651658i
\(723\) −5.04572 2.91315i −0.187652 0.108341i
\(724\) −6.41934 + 11.1186i −0.238573 + 0.413220i
\(725\) 1.08441 0.744358i 0.0402741 0.0276448i
\(726\) 13.9195 0.516602
\(727\) 17.4136 10.0537i 0.645835 0.372873i −0.141024 0.990006i \(-0.545039\pi\)
0.786859 + 0.617133i \(0.211706\pi\)
\(728\) 5.86472 + 3.38600i 0.217361 + 0.125493i
\(729\) −1.00000 −0.0370370
\(730\) 0.762801 3.36650i 0.0282325 0.124600i
\(731\) −23.4537 + 40.6230i −0.867466 + 1.50250i
\(732\) 0.780045i 0.0288313i
\(733\) 15.5016 8.94984i 0.572564 0.330570i −0.185609 0.982624i \(-0.559426\pi\)
0.758173 + 0.652054i \(0.226092\pi\)
\(734\) −18.3673 −0.677950
\(735\) −3.58038 11.5427i −0.132064 0.425758i
\(736\) 3.97419 + 6.88350i 0.146491 + 0.253729i
\(737\) 15.2668 8.81429i 0.562360 0.324679i
\(738\) 6.47803 + 3.74009i 0.238460 + 0.137675i
\(739\) 20.5194 0.754818 0.377409 0.926047i \(-0.376815\pi\)
0.377409 + 0.926047i \(0.376815\pi\)
\(740\) 7.72599 + 11.1942i 0.284013 + 0.411505i
\(741\) 39.4067 1.44764
\(742\) −8.92205 5.15115i −0.327539 0.189105i
\(743\) −5.03166 + 2.90503i −0.184594 + 0.106575i −0.589449 0.807805i \(-0.700655\pi\)
0.404855 + 0.914381i \(0.367322\pi\)
\(744\) −4.17676 7.23436i −0.153127 0.265224i
\(745\) 5.65385 1.75375i 0.207141 0.0642523i
\(746\) −8.18276 −0.299592
\(747\) 11.9301 6.88783i 0.436499 0.252013i
\(748\) 21.2810i 0.778109i
\(749\) 9.87983 17.1124i 0.361001 0.625273i
\(750\) −6.92942 + 8.77401i −0.253027 + 0.320381i
\(751\) 21.8875 0.798687 0.399343 0.916801i \(-0.369238\pi\)
0.399343 + 0.916801i \(0.369238\pi\)
\(752\) −3.17814 1.83490i −0.115895 0.0669120i
\(753\) 17.6070 10.1654i 0.641633 0.370447i
\(754\) −1.41042 −0.0513644
\(755\) 7.71977 + 7.14029i 0.280951 + 0.259862i
\(756\) −0.631530 + 1.09384i −0.0229685 + 0.0397827i
\(757\) −2.78518 1.60802i −0.101229 0.0584445i 0.448531 0.893767i \(-0.351947\pi\)
−0.549760 + 0.835323i \(0.685281\pi\)
\(758\) −23.7054 + 13.6863i −0.861019 + 0.497110i
\(759\) 19.8390 + 34.3621i 0.720109 + 1.24726i
\(760\) −11.1595 + 12.0651i −0.404796 + 0.437648i
\(761\) 3.34598 5.79541i 0.121292 0.210083i −0.798986 0.601350i \(-0.794630\pi\)
0.920277 + 0.391267i \(0.127963\pi\)
\(762\) 3.82426 + 2.20794i 0.138538 + 0.0799852i
\(763\) 12.9771i 0.469803i
\(764\) −2.22676 3.85686i −0.0805614 0.139536i
\(765\) −6.47272 + 6.99802i −0.234022 + 0.253014i
\(766\) 34.6306 1.25126
\(767\) 26.3000i 0.949639i
\(768\) −0.866025 0.500000i −0.0312500 0.0180422i
\(769\) 26.6101 0.959585 0.479793 0.877382i \(-0.340712\pi\)
0.479793 + 0.877382i \(0.340712\pi\)
\(770\) −13.4658 + 4.17689i −0.485272 + 0.150525i
\(771\) 9.61245 0.346184
\(772\) −7.62080 + 4.39987i −0.274278 + 0.158355i
\(773\) −24.3315 + 14.0478i −0.875145 + 0.505265i −0.869054 0.494716i \(-0.835272\pi\)
−0.00609016 + 0.999981i \(0.501939\pi\)
\(774\) 5.50161 + 9.52907i 0.197751 + 0.342515i
\(775\) −34.4357 + 23.6372i −1.23697 + 0.849073i
\(776\) −6.02010 −0.216109