Properties

Label 1110.2.bb.d.1009.6
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 1009.6
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.d.1099.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.64155 - 1.51833i) q^{5} +1.00000 q^{6} +(1.09384 - 0.631530i) q^{7} -1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(-0.866025 + 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.64155 - 1.51833i) 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} +(-0.662460 + 2.13568i) 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} +(2.13568 + 0.662460i) q^{20} +(-0.631530 + 1.09384i) q^{21} +(4.32315 + 2.49597i) q^{22} +7.94839i q^{23} +(0.500000 + 0.866025i) q^{24} +(0.389366 - 4.98482i) q^{25} -5.36157 q^{26} +1.00000i q^{27} +(1.09384 + 0.631530i) q^{28} +0.263060 q^{29} +(1.64155 - 1.51833i) q^{30} -8.35352 q^{31} +(0.866025 - 0.500000i) q^{32} +(4.32315 - 2.49597i) q^{33} +(2.13153 + 3.69192i) q^{34} +(0.836727 - 2.69750i) q^{35} +1.00000 q^{36} +(5.93579 + 1.32904i) q^{37} +7.34984i q^{38} +(-2.68079 + 4.64326i) q^{39} +(-1.51833 - 1.64155i) 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} +(-2.82961 + 4.12229i) q^{50} +4.26306 q^{51} +(4.64326 + 2.68079i) q^{52} +(-7.06383 - 4.07831i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-8.19452 + 7.57941i) 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} +(3.55183 - 11.4506i) q^{65} -4.99195 q^{66} +(3.05829 - 1.76570i) q^{67} -4.26306i q^{68} +(-3.97419 - 6.88350i) q^{69} +(-2.07338 + 1.91774i) 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} +(-0.662460 + 2.13568i) 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} +(-15.6969 - 4.86898i) 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
\(5\) 1.64155 1.51833i 0.734123 0.679016i
\(6\) 1.00000 0.408248
\(7\) 1.09384 0.631530i 0.413434 0.238696i −0.278830 0.960340i \(-0.589947\pi\)
0.692264 + 0.721644i \(0.256613\pi\)
\(8\) 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 0.309545 0.950885i \(-0.399823\pi\)
0.978263 + 0.207368i \(0.0664898\pi\)
\(14\) −1.26306 −0.337567
\(15\) −0.662460 + 2.13568i −0.171046 + 0.551431i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −3.69192 2.13153i −0.895422 0.516972i −0.0197097 0.999806i \(-0.506274\pi\)
−0.875712 + 0.482834i \(0.839608\pi\)
\(18\) −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 \(-0.485930\pi\)
\(20\) 2.13568 + 0.662460i 0.477554 + 0.148130i
\(21\) −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 \(0.310906\pi\)
−0.559728 + 0.828677i \(0.689094\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0.389366 4.98482i 0.0778733 0.996963i
\(26\) −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 \(0.492225\pi\)
\(30\) 1.64155 1.51833i 0.299704 0.277207i
\(31\) −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
\(35\) 0.836727 2.69750i 0.141433 0.455960i
\(36\) 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
\(40\) −1.51833 1.64155i −0.240069 0.259552i
\(41\) 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 \(-0.683148\pi\)
0.544150 0.838988i \(-0.316852\pi\)
\(44\) −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 \(-0.913754\pi\)
0.963517 0.267648i \(-0.0862464\pi\)
\(48\) 1.00000i 0.144338i
\(49\) −2.70234 + 4.68059i −0.386048 + 0.668656i
\(50\) −2.82961 + 4.12229i −0.400167 + 0.582980i
\(51\) 4.26306 0.596948
\(52\) 4.64326 + 2.68079i 0.643904 + 0.371758i
\(53\) −7.06383 4.07831i −0.970292 0.560198i −0.0709668 0.997479i \(-0.522608\pi\)
−0.899325 + 0.437280i \(0.855942\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) −8.19452 + 7.57941i −1.10495 + 1.02201i
\(56\) −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
\(65\) 3.55183 11.4506i 0.440550 1.42028i
\(66\) −4.99195 −0.614466
\(67\) 3.05829 1.76570i 0.373629 0.215715i −0.301414 0.953494i \(-0.597458\pi\)
0.675043 + 0.737779i \(0.264125\pi\)
\(68\) 4.26306i 0.516972i
\(69\) −3.97419 6.88350i −0.478437 0.828677i
\(70\) −2.07338 + 1.91774i −0.247816 + 0.229214i
\(71\) −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 \(-0.971205\pi\)
0.995911 0.0903387i \(-0.0287950\pi\)
\(74\) −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 −0.327484 0.944857i \(-0.606201\pi\)
−0.982012 + 0.188819i \(0.939534\pi\)
\(84\) −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 \(-0.0763734\pi\)
\(90\) −0.662460 + 2.13568i −0.0698294 + 0.225121i
\(91\) 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
\(95\) −15.6969 4.86898i −1.61047 0.499546i
\(96\) −0.500000 + 0.866025i −0.0510310 + 0.0883883i
\(97\) 6.02010i 0.611249i −0.952152 0.305624i \(-0.901135\pi\)
0.952152 0.305624i \(-0.0988651\pi\)
\(98\) 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 \(0.137397\pi\)
−0.908278 + 0.418367i \(0.862603\pi\)
\(104\) −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 0.327711 0.944778i \(-0.393723\pi\)
0.982057 + 0.188583i \(0.0603896\pi\)
\(108\) −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 −0.473573 0.880755i \(-0.657036\pi\)
−0.999542 + 0.0302513i \(0.990369\pi\)
\(114\) −3.67492 6.36515i −0.344188 0.596151i
\(115\) 12.0682 + 13.0477i 1.12537 + 1.21670i
\(116\) 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
\(120\) 2.13568 + 0.662460i 0.194960 + 0.0604740i
\(121\) 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 0.320635 0.947203i \(-0.396104\pi\)
−0.659984 + 0.751280i \(0.729437\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) 5.50161 + 9.52907i 0.484390 + 0.838988i
\(130\) −8.80129 + 8.14062i −0.771924 + 0.713980i
\(131\) 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
\(135\) 1.51833 + 1.64155i 0.130677 + 0.141282i
\(136\) −2.13153 + 3.69192i −0.182777 + 0.316579i
\(137\) 14.3318i 1.22445i 0.790684 + 0.612225i \(0.209725\pi\)
−0.790684 + 0.612225i \(0.790275\pi\)
\(138\) 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
\(145\) 0.431826 0.399412i 0.0358612 0.0331693i
\(146\) −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 \(0.534585\pi\)
\(150\) 0.389366 4.98482i 0.0317916 0.407009i
\(151\) −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
\(155\) −13.7127 + 12.6834i −1.10143 + 1.01875i
\(156\) −5.36157 −0.429269
\(157\) 11.7867 + 6.80507i 0.940683 + 0.543104i 0.890174 0.455620i \(-0.150582\pi\)
0.0505086 + 0.998724i \(0.483916\pi\)
\(158\) 8.10488i 0.644790i
\(159\) 8.15661 0.646861
\(160\) 0.662460 2.13568i 0.0523720 0.168841i
\(161\) 5.01965 + 8.69428i 0.395604 + 0.685205i
\(162\) 1.00000i 0.0785674i
\(163\) 10.5279 + 6.07828i 0.824609 + 0.476088i 0.852003 0.523537i \(-0.175388\pi\)
−0.0273945 + 0.999625i \(0.508721\pi\)
\(164\) −3.74009 + 6.47803i −0.292052 + 0.505849i
\(165\) 3.30696 10.6612i 0.257447 0.829975i
\(166\) 6.88783 + 11.9301i 0.534600 + 0.925954i
\(167\) 17.1266 9.88805i 1.32530 0.765160i 0.340728 0.940162i \(-0.389326\pi\)
0.984568 + 0.175001i \(0.0559930\pi\)
\(168\) 1.09384 + 0.631530i 0.0843918 + 0.0487236i
\(169\) 7.87323 13.6368i 0.605633 1.04899i
\(170\) 9.10455 + 2.82411i 0.698287 + 0.216599i
\(171\) −7.34984 −0.562057
\(172\) 9.52907 5.50161i 0.726585 0.419494i
\(173\) 4.03173 + 2.32772i 0.306527 + 0.176973i 0.645371 0.763869i \(-0.276703\pi\)
−0.338844 + 0.940842i \(0.610036\pi\)
\(174\) 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 \(0.264593\pi\)
\(180\) 1.64155 1.51833i 0.122354 0.113169i
\(181\) 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
\(185\) 11.7618 6.83080i 0.864745 0.502210i
\(186\) −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
\(190\) 11.1595 + 12.0651i 0.809593 + 0.875296i
\(191\) −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 \(-0.897422\pi\)
0.948523 0.316709i \(-0.102578\pi\)
\(194\) −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 0.728647 0.684889i \(-0.240149\pi\)
−0.228808 + 0.973472i \(0.573483\pi\)
\(198\) 4.32315 2.49597i 0.307233 0.177381i
\(199\) 0.881703 0.0625023 0.0312511 0.999512i \(-0.490051\pi\)
0.0312511 + 0.999512i \(0.490051\pi\)
\(200\) −4.98482 0.389366i −0.352480 0.0275324i
\(201\) −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
\(205\) 15.9753 + 4.95532i 1.11576 + 0.346095i
\(206\) 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
\(210\) 0.836727 2.69750i 0.0577396 0.186145i
\(211\) −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
\(215\) −16.7065 18.0623i −1.13937 1.23184i
\(216\) 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
\(220\) −10.6612 3.30696i −0.718779 0.222955i
\(221\) −22.8567 −1.53751
\(222\) 5.93579 + 1.32904i 0.398384 + 0.0891991i
\(223\) 18.1705i 1.21679i 0.793635 + 0.608394i \(0.208186\pi\)
−0.793635 + 0.608394i \(0.791814\pi\)
\(224\) 0.631530 1.09384i 0.0421959 0.0730854i
\(225\) −4.12229 2.82961i −0.274820 0.188641i
\(226\) 9.04098 + 15.6594i 0.601397 + 1.04165i
\(227\) 9.88733 5.70845i 0.656245 0.378883i −0.134600 0.990900i \(-0.542975\pi\)
0.790845 + 0.612017i \(0.209642\pi\)
\(228\) 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 \(-0.970531\pi\)
0.995718 0.0924473i \(-0.0294690\pi\)
\(234\) −2.68079 + 4.64326i −0.175249 + 0.303539i
\(235\) −5.57196 6.02416i −0.363475 0.392973i
\(236\) −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 \(-0.0935294\pi\)
\(240\) −1.51833 1.64155i −0.0980076 0.105962i
\(241\) −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
\(250\) 1.61405 + 11.0632i 0.102081 + 0.699700i
\(251\) 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
\(255\) 6.99802 6.47272i 0.438233 0.405337i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.32463 4.80623i −0.519276 0.299804i 0.217362 0.976091i \(-0.430255\pi\)
−0.736638 + 0.676287i \(0.763588\pi\)
\(258\) 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 −0.369587 0.929196i \(-0.620501\pi\)
0.619914 + 0.784670i \(0.287168\pi\)
\(264\) −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
\(275\) −1.94370 + 24.8839i −0.117209 + 1.50056i
\(276\) 3.97419 6.88350i 0.239218 0.414338i
\(277\) −16.3046 + 9.41347i −0.979649 + 0.565601i −0.902164 0.431393i \(-0.858022\pi\)
−0.0774850 + 0.996994i \(0.524689\pi\)
\(278\) 6.57823 3.79794i 0.394536 0.227786i
\(279\) −4.17676 + 7.23436i −0.250056 + 0.433110i
\(280\) −2.69750 0.836727i −0.161206 0.0500040i
\(281\) 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 −0.203942 0.978983i \(-0.565376\pi\)
0.745853 + 0.666111i \(0.232042\pi\)
\(284\) 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 −0.363632 0.931542i \(-0.618464\pi\)
0.624923 + 0.780686i \(0.285130\pi\)
\(294\) −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
\(300\) −2.82961 + 4.12229i −0.163368 + 0.238001i
\(301\) −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
\(305\) 1.66593 + 0.516748i 0.0953908 + 0.0295889i
\(306\) 4.26306 0.243703
\(307\) 15.5648i 0.888333i 0.895944 + 0.444166i \(0.146500\pi\)
−0.895944 + 0.444166i \(0.853500\pi\)
\(308\) −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 0.647449 0.762108i \(-0.275836\pi\)
−0.336281 + 0.941762i \(0.609169\pi\)
\(314\) −6.80507 11.7867i −0.384032 0.665163i
\(315\) −1.91774 2.07338i −0.108052 0.116821i
\(316\) 4.05244 7.01903i 0.227968 0.394851i
\(317\) 13.7824 + 7.95728i 0.774097 + 0.446925i 0.834334 0.551259i \(-0.185852\pi\)
−0.0602370 + 0.998184i \(0.519186\pi\)
\(318\) −7.06383 4.07831i −0.396120 0.228700i
\(319\) −1.31318 −0.0735241
\(320\) −1.64155 + 1.51833i −0.0917654 + 0.0848771i
\(321\) −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
\(330\) −8.19452 + 7.57941i −0.451094 + 0.417233i
\(331\) 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
\(335\) 2.33941 7.54197i 0.127816 0.412062i
\(336\) −0.631530 1.09384i −0.0344528 0.0596740i
\(337\) 30.5973 17.6654i 1.66674 0.962295i 0.697367 0.716714i \(-0.254355\pi\)
0.969376 0.245581i \(-0.0789787\pi\)
\(338\) −13.6368 + 7.87323i −0.741746 + 0.428247i
\(339\) 18.0820 0.982077
\(340\) −6.47272 6.99802i −0.351033 0.379521i
\(341\) 41.7003 2.25820
\(342\) 6.36515 + 3.67492i 0.344188 + 0.198717i
\(343\) 15.6679i 0.845985i
\(344\) −11.0032 −0.593254
\(345\) −16.9752 5.26549i −0.913916 0.283484i
\(346\) −2.32772 4.03173i −0.125139 0.216747i
\(347\) 3.87172i 0.207845i 0.994585 + 0.103923i \(0.0331394\pi\)
−0.994585 + 0.103923i \(0.966861\pi\)
\(348\) −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 \(0.291987\pi\)
\(350\) −0.491793 + 6.29612i −0.0262875 + 0.336542i
\(351\) 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 0.465086 0.885265i \(-0.346023\pi\)
−0.534119 + 0.845409i \(0.679357\pi\)
\(354\) −2.45264 + 4.24810i −0.130356 + 0.225784i
\(355\) −0.604066 0.187373i −0.0320605 0.00994471i
\(356\) 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
\(365\) −2.34385 2.53407i −0.122683 0.132639i
\(366\) 0.390022 + 0.675539i 0.0203868 + 0.0353110i
\(367\) 15.9066 9.18365i 0.830315 0.479383i −0.0236452 0.999720i \(-0.507527\pi\)
0.853961 + 0.520338i \(0.174194\pi\)
\(368\) −6.88350 3.97419i −0.358827 0.207169i
\(369\) 7.48019 0.389403
\(370\) −13.6014 + 0.0347405i −0.707104 + 0.00180607i
\(371\) −10.3023 −0.534868
\(372\) 7.23436 + 4.17676i 0.375084 + 0.216555i
\(373\) 7.08648 4.09138i 0.366924 0.211844i −0.305190 0.952292i \(-0.598720\pi\)
0.672114 + 0.740448i \(0.265387\pi\)
\(374\) −10.6405 18.4299i −0.550206 0.952985i
\(375\) 10.3881 + 4.13380i 0.536437 + 0.213469i
\(376\) −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 \(0.679019\pi\)
−0.999247 + 0.0387959i \(0.987648\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −4.17689 + 13.4658i −0.212874 + 0.686279i
\(386\) −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 \(-0.336686\pi\)
\(390\) 3.55183 11.4506i 0.179854 0.579825i
\(391\) 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
\(395\) −17.3095 5.36916i −0.870934 0.270152i
\(396\) −4.99195 −0.250855
\(397\) 19.1670i 0.961964i −0.876730 0.480982i \(-0.840280\pi\)
0.876730 0.480982i \(-0.159720\pi\)
\(398\) −0.763578 0.440852i −0.0382747 0.0220979i
\(399\) 9.28330 0.464746
\(400\) 4.12229 + 2.82961i 0.206115 + 0.141480i
\(401\) −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
\(405\) −2.13568 0.662460i −0.106123 0.0329179i
\(406\) −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 \(0.783206\pi\)
\(410\) −11.3574 12.2791i −0.560900 0.606421i
\(411\) −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 \(0.0269047\pi\)
\(420\) −2.07338 + 1.91774i −0.101170 + 0.0935761i
\(421\) 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
\(425\) −12.0628 + 17.5736i −0.585132 + 0.852444i
\(426\) −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 \(-0.965089\pi\)
0.993992 0.109456i \(-0.0349108\pi\)
\(434\) 10.5510 0.506464
\(435\) −0.174267 + 0.561814i −0.00835546 + 0.0269369i
\(436\) 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 \(0.738026\pi\)
\(440\) 7.57941 + 8.19452i 0.361334 + 0.390659i
\(441\) 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 \(-0.898170\pi\)
0.949264 0.314480i \(-0.101830\pi\)
\(444\) −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 \(-0.328967\pi\)
0.999906 0.0137183i \(-0.00436681\pi\)
\(458\) 14.5585i 0.680273i
\(459\) 2.13153 3.69192i 0.0994913 0.172324i
\(460\) −5.26549 + 16.9752i −0.245505 + 0.791475i
\(461\) −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 0.192561 0.981285i \(-0.438321\pi\)
0.946098 + 0.323880i \(0.104987\pi\)
\(464\) −0.131530 + 0.227817i −0.00610614 + 0.0105761i
\(465\) 5.53387 17.8405i 0.256627 0.827332i
\(466\) −1.41115 + 2.44418i −0.0653701 + 0.113224i
\(467\) 19.4357i 0.899378i 0.893185 + 0.449689i \(0.148465\pi\)
−0.893185 + 0.449689i \(0.851535\pi\)
\(468\) 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
\(485\) −9.14048 9.88229i −0.415048 0.448732i
\(486\) −0.500000 0.866025i −0.0226805 0.0392837i
\(487\) 17.3440i 0.785931i 0.919553 + 0.392965i \(0.128551\pi\)
−0.919553 + 0.392965i \(0.871449\pi\)
\(488\) 0.675539 0.390022i 0.0305802 0.0176555i
\(489\) −12.1566 −0.549739
\(490\) 3.58038 11.5427i 0.161745 0.521445i
\(491\) −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 \(0.864491\pi\)
\(500\) 4.13380 10.3881i 0.184869 0.464568i
\(501\) −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 0.847167 0.531327i \(-0.178306\pi\)
−0.0365587 + 0.999332i \(0.511640\pi\)
\(504\) −1.26306 −0.0562612
\(505\) −32.0268 + 29.6228i −1.42518 + 1.31820i
\(506\) −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
\(515\) 12.8935 + 13.9399i 0.568156 + 0.614265i
\(516\) −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
\(520\) −11.4506 3.55183i −0.502143 0.155758i
\(521\) −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 \(0.678786\pi\)
−0.999275 + 0.0380645i \(0.987881\pi\)
\(524\) 9.66613 0.422267
\(525\) 5.20671 + 3.57397i 0.227239 + 0.155981i
\(526\) −4.68764 −0.204391
\(527\) 30.8405 + 17.8058i 1.34343 + 0.775632i
\(528\) 4.99195i 0.217247i
\(529\) −40.1769 −1.74682
\(530\) 17.4199 + 5.40343i 0.756674 + 0.234710i
\(531\) 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
\(535\) 10.3637 33.4112i 0.448062 1.44449i
\(536\) −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
\(540\) −0.662460 + 2.13568i −0.0285077 + 0.0919052i
\(541\) 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 \(0.176426\pi\)
−0.850292 + 0.526312i \(0.823574\pi\)
\(548\) −12.4117 + 7.16590i −0.530202 + 0.306112i
\(549\) 0.780045 0.0332915
\(550\) 14.1253 20.5783i 0.602303 0.877460i
\(551\) −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
\(555\) −6.77063 + 11.7966i −0.287397 + 0.500736i
\(556\) −7.59589 −0.322137
\(557\) −12.1937 7.04001i −0.516662 0.298295i 0.218906 0.975746i \(-0.429751\pi\)
−0.735568 + 0.677451i \(0.763085\pi\)
\(558\) 7.23436 4.17676i 0.306255 0.176816i
\(559\) −29.4973 51.0908i −1.24760 2.16091i
\(560\) 1.91774 + 2.07338i 0.0810392 + 0.0876161i
\(561\) −21.2810 −0.898483
\(562\) −14.1005 + 8.14090i −0.594792 + 0.343403i
\(563\) 18.2964i 0.771101i −0.922687 0.385551i \(-0.874011\pi\)
0.922687 0.385551i \(-0.125989\pi\)
\(564\) −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 \(0.321581\pi\)
\(570\) −15.6969 4.86898i −0.657473 0.203939i
\(571\) 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
\(575\) 39.6212 + 3.09483i 1.65232 + 0.129064i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 0.213185 + 0.123082i 0.00887501 + 0.00512399i 0.504431 0.863452i \(-0.331702\pi\)
−0.495556 + 0.868576i \(0.665036\pi\)
\(578\) 1.17368i 0.0488188i
\(579\) 4.39987 + 7.62080i 0.182852 + 0.316709i
\(580\) 0.561814 + 0.174267i 0.0233281 + 0.00723604i
\(581\) −17.3995 −0.721853
\(582\) 6.02010i 0.249541i
\(583\) 35.2623 + 20.3587i 1.46041 + 0.843171i
\(584\) −1.54371 −0.0638791
\(585\) −8.14062 8.80129i −0.336573 0.363888i
\(586\) −5.16449 −0.213343
\(587\) 24.5330 14.1641i 1.01258 0.584616i 0.100637 0.994923i \(-0.467912\pi\)
0.911947 + 0.410307i \(0.134579\pi\)
\(588\) 4.68059 2.70234i 0.193024 0.111443i
\(589\) 30.6985 + 53.1714i 1.26491 + 2.19089i
\(590\) 3.24955 10.4761i 0.133782 0.431296i
\(591\) −8.10089 −0.333226
\(592\) −4.11888 + 4.47603i −0.169285 + 0.183964i
\(593\) 32.0201i 1.31491i −0.753494 0.657455i \(-0.771633\pi\)
0.753494 0.657455i \(-0.228367\pi\)
\(594\) −2.49597 + 4.32315i −0.102411 + 0.177381i
\(595\) −8.83892 + 8.17544i −0.362361 + 0.335160i
\(596\) −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
\(605\) 22.8496 21.1344i 0.928968 0.859235i
\(606\) −19.5101 −0.792545
\(607\) 9.55271 + 5.51526i 0.387733 + 0.223858i 0.681177 0.732118i \(-0.261468\pi\)
−0.293445 + 0.955976i \(0.594802\pi\)
\(608\) −6.36515 3.67492i −0.258141 0.149038i
\(609\) −0.166131 + 0.287747i −0.00673195 + 0.0116601i
\(610\) −1.18436 1.28048i −0.0479535 0.0518452i
\(611\) −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 0.0771512 0.997019i \(-0.475418\pi\)
−0.824869 + 0.565325i \(0.808751\pi\)
\(614\) 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 0.456827 0.889555i \(-0.348986\pi\)
−0.541964 + 0.840402i \(0.682319\pi\)
\(618\) 8.49192i 0.341595i
\(619\) 41.1110 1.65239 0.826196 0.563382i \(-0.190500\pi\)
0.826196 + 0.563382i \(0.190500\pi\)
\(620\) −17.8405 5.53387i −0.716491 0.222246i
\(621\) −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
\(625\) −24.6968 3.88184i −0.987872 0.155274i
\(626\) −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 \(-0.976727\pi\)
0.997328 0.0730502i \(-0.0232733\pi\)
\(644\) −5.01965 + 8.69428i −0.197802 + 0.342603i
\(645\) 23.4994 + 7.28919i 0.925288 + 0.287012i
\(646\) 15.6664 27.1350i 0.616387 1.06761i
\(647\) 3.89440 2.24843i 0.153105 0.0883950i −0.421490 0.906833i \(-0.638493\pi\)
0.574595 + 0.818438i \(0.305160\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) 12.2434 21.2063i 0.480597 0.832419i
\(650\) −2.08762 + 26.7265i −0.0818831 + 1.04830i
\(651\) 5.27550 9.13743i 0.206763 0.358124i
\(652\) 12.1566i 0.476088i
\(653\) −19.3934 + 11.1968i −0.758921 + 0.438163i −0.828908 0.559385i \(-0.811037\pi\)
0.0699875 + 0.997548i \(0.477704\pi\)
\(654\) 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
\(670\) −5.79698 + 5.36183i −0.223957 + 0.207146i
\(671\) −1.94697 3.37225i −0.0751620 0.130184i
\(672\) 1.26306i 0.0487236i
\(673\) −3.67729 + 2.12308i −0.141749 + 0.0818388i −0.569197 0.822201i \(-0.692746\pi\)
0.427448 + 0.904040i \(0.359413\pi\)
\(674\) −35.3308 −1.36089
\(675\) 4.98482 + 0.389366i 0.191866 + 0.0149867i
\(676\) 15.7465 0.605633
\(677\) 38.4405i 1.47739i −0.674041 0.738693i \(-0.735443\pi\)
0.674041 0.738693i \(-0.264557\pi\)
\(678\) −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 \(0.0376754\pi\)
0.598766 + 0.800924i \(0.295658\pi\)
\(684\) −3.67492 6.36515i −0.140514 0.243378i
\(685\) 21.7604 + 23.5264i 0.831421 + 0.898896i
\(686\) 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
\(690\) 12.0682 + 13.0477i 0.459430 + 0.496716i
\(691\) 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
\(700\) 3.57397 5.20671i 0.135083 0.196795i
\(701\) −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
\(705\) 7.83754 + 2.43110i 0.295179 + 0.0915604i
\(706\) 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 \(0.604262\pi\)
\(710\) 0.429450 + 0.464302i 0.0161170 + 0.0174250i
\(711\) −8.10488 −0.303957
\(712\) −11.2988 6.52339i −0.423442 0.244474i
\(713\) 66.3970i 2.48659i
\(714\) −5.38450 −0.201510
\(715\) −17.7305 + 57.1609i −0.663084 + 2.13770i
\(716\) 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 \(0.225242\pi\)
\(720\) 2.13568 + 0.662460i 0.0795923 + 0.0246884i
\(721\) 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
\(725\) 0.102427 1.31131i 0.00380404 0.0487007i
\(726\) 13.9195 0.516602
\(727\) −17.4136 + 10.0537i −0.645835 + 0.372873i −0.786859 0.617133i \(-0.788294\pi\)
0.141024 + 0.990006i \(0.454961\pi\)
\(728\) −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 −0.758173 0.652054i \(-0.773908\pi\)
0.185609 + 0.982624i \(0.440574\pi\)
\(734\) −18.3673 −0.677950
\(735\) −8.20607 8.87204i −0.302685 0.327250i
\(736\) 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 \(0.376815\pi\)
\(740\) 11.7966 + 6.77063i 0.433650 + 0.248893i
\(741\) 39.4067 1.44764
\(742\) 8.92205 + 5.15115i 0.327539 + 0.189105i
\(743\) 5.03166 2.90503i 0.184594 0.106575i −0.404855 0.914381i \(-0.632678\pi\)
0.589449 + 0.807805i \(0.299345\pi\)
\(744\) −4.17676 7.23436i −0.153127 0.265224i
\(745\) −4.34572 + 4.01951i −0.159215 + 0.147263i
\(746\) −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
\(755\) −10.0436 3.11537i −0.365522 0.113380i
\(756\) −0.631530 + 1.09384i −0.0229685 + 0.0397827i
\(757\) 2.78518 + 1.60802i 0.101229 + 0.0584445i 0.549760 0.835323i \(-0.314719\pi\)
−0.448531 + 0.893767i \(0.648053\pi\)
\(758\) 23.7054 13.6863i 0.861019 0.497110i
\(759\) 19.8390 + 34.3621i 0.720109 + 1.24726i
\(760\) −4.86898 + 15.6969i −0.176616 + 0.569388i
\(761\) 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
\(765\) −2.82411 + 9.10455i −0.102106 + 0.329176i
\(766\) 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 \(0.340712\pi\)
\(770\) 10.3502 9.57325i 0.372995 0.344996i
\(771\) 9.61245 0.346184
\(772\) 7.62080 4.39987i 0.274278 0.158355i
\(773\) 24.3315 14.0478i 0.875145 0.505265i 0.00609016 0.999981i \(-0.498061\pi\)
0.869054 + 0.494716i \(0.164728\pi\)
\(774\) 5.50161 + 9.52907i 0.197751 + 0.342515i
\(775\) −3.25258 + 41.6408i −0.116836 + 1.49578i
\(776\) −6.02010 −0.216109
\(777\)