Properties

Label 1110.2.x.d.751.1
Level $1110$
Weight $2$
Character 1110.751
Analytic conductor $8.863$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 60 x^{14} + 1362 x^{12} + 15028 x^{10} + 86441 x^{8} + 260376 x^{6} + 382684 x^{4} + 224224 x^{2} + 38416\)
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.1
Root \(-4.75759i\) of defining polynomial
Character \(\chi\) \(=\) 1110.751
Dual form 1110.2.x.d.841.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-2.37879 + 4.12019i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{5} -1.00000i q^{6} +(-2.37879 + 4.12019i) q^{7} +1.00000i q^{8} +(-0.500000 - 0.866025i) q^{9} +1.00000 q^{10} -5.36873 q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.67740 - 0.968450i) q^{13} -4.75759i q^{14} +(0.866025 - 0.500000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.25417 - 1.87879i) q^{17} +(0.866025 + 0.500000i) q^{18} +(1.63763 + 0.945484i) q^{19} +(-0.866025 + 0.500000i) q^{20} +(-2.37879 - 4.12019i) q^{21} +(4.64945 - 2.68436i) q^{22} +0.204849i q^{23} +(-0.866025 - 0.500000i) q^{24} +(0.500000 + 0.866025i) q^{25} +1.93690 q^{26} +1.00000 q^{27} +(2.37879 + 4.12019i) q^{28} -2.07147i q^{29} +(-0.500000 + 0.866025i) q^{30} -1.95056i q^{31} +(0.866025 + 0.500000i) q^{32} +(2.68436 - 4.64945i) q^{33} +(-1.87879 + 3.25417i) q^{34} +(4.12019 - 2.37879i) q^{35} -1.00000 q^{36} +(2.60554 + 5.49647i) q^{37} -1.89097 q^{38} +(1.67740 - 0.968450i) q^{39} +(0.500000 - 0.866025i) q^{40} +(3.63525 - 6.29644i) q^{41} +(4.12019 + 2.37879i) q^{42} +1.74571i q^{43} +(-2.68436 + 4.64945i) q^{44} +1.00000i q^{45} +(-0.102424 - 0.177404i) q^{46} +8.35130 q^{47} +1.00000 q^{48} +(-7.81733 - 13.5400i) q^{49} +(-0.866025 - 0.500000i) q^{50} +3.75759i q^{51} +(-1.67740 + 0.968450i) q^{52} +(-6.35084 - 11.0000i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(4.64945 + 2.68436i) q^{55} +(-4.12019 - 2.37879i) q^{56} +(-1.63763 + 0.945484i) q^{57} +(1.03573 + 1.79395i) q^{58} +(-8.23050 + 4.75188i) q^{59} -1.00000i q^{60} +(-3.60010 - 2.07852i) q^{61} +(0.975279 + 1.68923i) q^{62} +4.75759 q^{63} -1.00000 q^{64} +(0.968450 + 1.67740i) q^{65} +5.36873i q^{66} +(-2.26454 + 3.92230i) q^{67} -3.75759i q^{68} +(-0.177404 - 0.102424i) q^{69} +(-2.37879 + 4.12019i) q^{70} +(4.89062 - 8.47081i) q^{71} +(0.866025 - 0.500000i) q^{72} +15.0985 q^{73} +(-5.00470 - 3.45731i) q^{74} -1.00000 q^{75} +(1.63763 - 0.945484i) q^{76} +(12.7711 - 22.1202i) q^{77} +(-0.968450 + 1.67740i) q^{78} +(-10.1927 - 5.88473i) q^{79} +1.00000i q^{80} +(-0.500000 + 0.866025i) q^{81} +7.27050i q^{82} +(-2.10501 - 3.64598i) q^{83} -4.75759 q^{84} -3.75759 q^{85} +(-0.872855 - 1.51183i) q^{86} +(1.79395 + 1.03573i) q^{87} -5.36873i q^{88} +(5.32602 - 3.07498i) q^{89} +(-0.500000 - 0.866025i) q^{90} +(7.98040 - 4.60749i) q^{91} +(0.177404 + 0.102424i) q^{92} +(1.68923 + 0.975279i) q^{93} +(-7.23244 + 4.17565i) q^{94} +(-0.945484 - 1.63763i) q^{95} +(-0.866025 + 0.500000i) q^{96} +2.30537i q^{97} +(13.5400 + 7.81733i) q^{98} +(2.68436 + 4.64945i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + O(q^{10}) \) \( 16q - 8q^{3} + 8q^{4} - 2q^{7} - 8q^{9} + 16q^{10} - 8q^{11} + 8q^{12} - 6q^{13} - 8q^{16} + 6q^{17} - 12q^{19} - 2q^{21} + 8q^{25} + 4q^{26} + 16q^{27} + 2q^{28} - 8q^{30} + 4q^{33} + 6q^{34} + 6q^{35} - 16q^{36} + 12q^{37} - 4q^{38} + 6q^{39} + 8q^{40} + 4q^{41} + 6q^{42} - 4q^{44} - 2q^{46} + 68q^{47} + 16q^{48} - 4q^{49} - 6q^{52} - 12q^{53} - 6q^{56} + 12q^{57} - 6q^{58} + 6q^{59} + 12q^{61} + 4q^{62} + 4q^{63} - 16q^{64} + 2q^{65} - 36q^{67} + 18q^{69} - 2q^{70} + 6q^{71} - 16q^{73} + 14q^{74} - 16q^{75} - 12q^{76} + 26q^{77} - 2q^{78} - 24q^{79} - 8q^{81} + 12q^{83} - 4q^{84} + 12q^{85} - 2q^{86} + 24q^{89} - 8q^{90} + 60q^{91} - 18q^{92} - 30q^{93} + 6q^{94} - 2q^{95} - 12q^{98} + 4q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{5}{6}\right)\) \(1\)

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
\(3\) −0.500000 + 0.866025i −0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.866025 0.500000i −0.387298 0.223607i
\(6\) 1.00000i 0.408248i
\(7\) −2.37879 + 4.12019i −0.899100 + 1.55729i −0.0704527 + 0.997515i \(0.522444\pi\)
−0.828647 + 0.559771i \(0.810889\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) 1.00000 0.316228
\(11\) −5.36873 −1.61873 −0.809366 0.587304i \(-0.800189\pi\)
−0.809366 + 0.587304i \(0.800189\pi\)
\(12\) 0.500000 + 0.866025i 0.144338 + 0.250000i
\(13\) −1.67740 0.968450i −0.465228 0.268600i 0.249012 0.968500i \(-0.419894\pi\)
−0.714240 + 0.699901i \(0.753228\pi\)
\(14\) 4.75759i 1.27152i
\(15\) 0.866025 0.500000i 0.223607 0.129099i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 3.25417 1.87879i 0.789252 0.455675i −0.0504475 0.998727i \(-0.516065\pi\)
0.839699 + 0.543052i \(0.182731\pi\)
\(18\) 0.866025 + 0.500000i 0.204124 + 0.117851i
\(19\) 1.63763 + 0.945484i 0.375697 + 0.216909i 0.675945 0.736952i \(-0.263736\pi\)
−0.300247 + 0.953861i \(0.597069\pi\)
\(20\) −0.866025 + 0.500000i −0.193649 + 0.111803i
\(21\) −2.37879 4.12019i −0.519095 0.899100i
\(22\) 4.64945 2.68436i 0.991267 0.572308i
\(23\) 0.204849i 0.0427139i 0.999772 + 0.0213570i \(0.00679865\pi\)
−0.999772 + 0.0213570i \(0.993201\pi\)
\(24\) −0.866025 0.500000i −0.176777 0.102062i
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 1.93690 0.379857
\(27\) 1.00000 0.192450
\(28\) 2.37879 + 4.12019i 0.449550 + 0.778643i
\(29\) 2.07147i 0.384662i −0.981330 0.192331i \(-0.938395\pi\)
0.981330 0.192331i \(-0.0616048\pi\)
\(30\) −0.500000 + 0.866025i −0.0912871 + 0.158114i
\(31\) 1.95056i 0.350331i −0.984539 0.175165i \(-0.943954\pi\)
0.984539 0.175165i \(-0.0560460\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 2.68436 4.64945i 0.467288 0.809366i
\(34\) −1.87879 + 3.25417i −0.322211 + 0.558085i
\(35\) 4.12019 2.37879i 0.696440 0.402090i
\(36\) −1.00000 −0.166667
\(37\) 2.60554 + 5.49647i 0.428348 + 0.903614i
\(38\) −1.89097 −0.306756
\(39\) 1.67740 0.968450i 0.268600 0.155076i
\(40\) 0.500000 0.866025i 0.0790569 0.136931i
\(41\) 3.63525 6.29644i 0.567731 0.983338i −0.429059 0.903276i \(-0.641155\pi\)
0.996790 0.0800620i \(-0.0255118\pi\)
\(42\) 4.12019 + 2.37879i 0.635760 + 0.367056i
\(43\) 1.74571i 0.266218i 0.991101 + 0.133109i \(0.0424961\pi\)
−0.991101 + 0.133109i \(0.957504\pi\)
\(44\) −2.68436 + 4.64945i −0.404683 + 0.700932i
\(45\) 1.00000i 0.149071i
\(46\) −0.102424 0.177404i −0.0151017 0.0261568i
\(47\) 8.35130 1.21816 0.609081 0.793108i \(-0.291538\pi\)
0.609081 + 0.793108i \(0.291538\pi\)
\(48\) 1.00000 0.144338
\(49\) −7.81733 13.5400i −1.11676 1.93429i
\(50\) −0.866025 0.500000i −0.122474 0.0707107i
\(51\) 3.75759i 0.526168i
\(52\) −1.67740 + 0.968450i −0.232614 + 0.134300i
\(53\) −6.35084 11.0000i −0.872356 1.51096i −0.859553 0.511046i \(-0.829258\pi\)
−0.0128024 0.999918i \(-0.504075\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 4.64945 + 2.68436i 0.626932 + 0.361960i
\(56\) −4.12019 2.37879i −0.550584 0.317880i
\(57\) −1.63763 + 0.945484i −0.216909 + 0.125232i
\(58\) 1.03573 + 1.79395i 0.135999 + 0.235557i
\(59\) −8.23050 + 4.75188i −1.07152 + 0.618642i −0.928596 0.371092i \(-0.878984\pi\)
−0.142923 + 0.989734i \(0.545650\pi\)
\(60\) 1.00000i 0.129099i
\(61\) −3.60010 2.07852i −0.460945 0.266127i 0.251496 0.967858i \(-0.419077\pi\)
−0.712442 + 0.701731i \(0.752411\pi\)
\(62\) 0.975279 + 1.68923i 0.123861 + 0.214533i
\(63\) 4.75759 0.599400
\(64\) −1.00000 −0.125000
\(65\) 0.968450 + 1.67740i 0.120121 + 0.208056i
\(66\) 5.36873i 0.660845i
\(67\) −2.26454 + 3.92230i −0.276658 + 0.479185i −0.970552 0.240892i \(-0.922560\pi\)
0.693894 + 0.720077i \(0.255894\pi\)
\(68\) 3.75759i 0.455675i
\(69\) −0.177404 0.102424i −0.0213570 0.0123305i
\(70\) −2.37879 + 4.12019i −0.284320 + 0.492457i
\(71\) 4.89062 8.47081i 0.580410 1.00530i −0.415020 0.909812i \(-0.636226\pi\)
0.995431 0.0954878i \(-0.0304411\pi\)
\(72\) 0.866025 0.500000i 0.102062 0.0589256i
\(73\) 15.0985 1.76714 0.883572 0.468295i \(-0.155131\pi\)
0.883572 + 0.468295i \(0.155131\pi\)
\(74\) −5.00470 3.45731i −0.581784 0.401904i
\(75\) −1.00000 −0.115470
\(76\) 1.63763 0.945484i 0.187849 0.108454i
\(77\) 12.7711 22.1202i 1.45540 2.52083i
\(78\) −0.968450 + 1.67740i −0.109655 + 0.189929i
\(79\) −10.1927 5.88473i −1.14676 0.662084i −0.198667 0.980067i \(-0.563661\pi\)
−0.948097 + 0.317983i \(0.896995\pi\)
\(80\) 1.00000i 0.111803i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 7.27050i 0.802892i
\(83\) −2.10501 3.64598i −0.231054 0.400198i 0.727064 0.686569i \(-0.240884\pi\)
−0.958119 + 0.286371i \(0.907551\pi\)
\(84\) −4.75759 −0.519095
\(85\) −3.75759 −0.407568
\(86\) −0.872855 1.51183i −0.0941223 0.163025i
\(87\) 1.79395 + 1.03573i 0.192331 + 0.111042i
\(88\) 5.36873i 0.572308i
\(89\) 5.32602 3.07498i 0.564557 0.325947i −0.190415 0.981704i \(-0.560983\pi\)
0.754973 + 0.655756i \(0.227650\pi\)
\(90\) −0.500000 0.866025i −0.0527046 0.0912871i
\(91\) 7.98040 4.60749i 0.836573 0.482996i
\(92\) 0.177404 + 0.102424i 0.0184957 + 0.0106785i
\(93\) 1.68923 + 0.975279i 0.175165 + 0.101132i
\(94\) −7.23244 + 4.17565i −0.745969 + 0.430685i
\(95\) −0.945484 1.63763i −0.0970046 0.168017i
\(96\) −0.866025 + 0.500000i −0.0883883 + 0.0510310i
\(97\) 2.30537i 0.234075i 0.993128 + 0.117037i \(0.0373397\pi\)
−0.993128 + 0.117037i \(0.962660\pi\)
\(98\) 13.5400 + 7.81733i 1.36775 + 0.789669i
\(99\) 2.68436 + 4.64945i 0.269789 + 0.467288i
\(100\) 1.00000 0.100000
\(101\) 3.28606 0.326975 0.163487 0.986545i \(-0.447726\pi\)
0.163487 + 0.986545i \(0.447726\pi\)
\(102\) −1.87879 3.25417i −0.186028 0.322211i
\(103\) 11.9300i 1.17550i 0.809042 + 0.587751i \(0.199986\pi\)
−0.809042 + 0.587751i \(0.800014\pi\)
\(104\) 0.968450 1.67740i 0.0949643 0.164483i
\(105\) 4.75759i 0.464293i
\(106\) 11.0000 + 6.35084i 1.06841 + 0.616849i
\(107\) 7.21086 12.4896i 0.697100 1.20741i −0.272368 0.962193i \(-0.587807\pi\)
0.969468 0.245219i \(-0.0788600\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) −2.91578 + 1.68342i −0.279281 + 0.161243i −0.633098 0.774072i \(-0.718217\pi\)
0.353817 + 0.935315i \(0.384884\pi\)
\(110\) −5.36873 −0.511888
\(111\) −6.06285 0.491772i −0.575460 0.0466769i
\(112\) 4.75759 0.449550
\(113\) 5.48942 3.16932i 0.516401 0.298144i −0.219060 0.975711i \(-0.570299\pi\)
0.735461 + 0.677567i \(0.236966\pi\)
\(114\) 0.945484 1.63763i 0.0885527 0.153378i
\(115\) 0.102424 0.177404i 0.00955113 0.0165430i
\(116\) −1.79395 1.03573i −0.166564 0.0961656i
\(117\) 1.93690i 0.179066i
\(118\) 4.75188 8.23050i 0.437446 0.757679i
\(119\) 17.8771i 1.63879i
\(120\) 0.500000 + 0.866025i 0.0456435 + 0.0790569i
\(121\) 17.8232 1.62029
\(122\) 4.15704 0.376360
\(123\) 3.63525 + 6.29644i 0.327779 + 0.567731i
\(124\) −1.68923 0.975279i −0.151698 0.0875826i
\(125\) 1.00000i 0.0894427i
\(126\) −4.12019 + 2.37879i −0.367056 + 0.211920i
\(127\) −6.26976 10.8595i −0.556351 0.963629i −0.997797 0.0663409i \(-0.978868\pi\)
0.441446 0.897288i \(-0.354466\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −1.51183 0.872855i −0.133109 0.0768506i
\(130\) −1.67740 0.968450i −0.147118 0.0849387i
\(131\) 3.17214 1.83144i 0.277151 0.160013i −0.354982 0.934873i \(-0.615513\pi\)
0.632133 + 0.774860i \(0.282180\pi\)
\(132\) −2.68436 4.64945i −0.233644 0.404683i
\(133\) −7.79115 + 4.49822i −0.675579 + 0.390045i
\(134\) 4.52908i 0.391253i
\(135\) −0.866025 0.500000i −0.0745356 0.0430331i
\(136\) 1.87879 + 3.25417i 0.161105 + 0.279043i
\(137\) −10.1933 −0.870871 −0.435436 0.900220i \(-0.643406\pi\)
−0.435436 + 0.900220i \(0.643406\pi\)
\(138\) 0.204849 0.0174379
\(139\) 6.53350 + 11.3164i 0.554164 + 0.959841i 0.997968 + 0.0637169i \(0.0202955\pi\)
−0.443804 + 0.896124i \(0.646371\pi\)
\(140\) 4.75759i 0.402090i
\(141\) −4.17565 + 7.23244i −0.351653 + 0.609081i
\(142\) 9.78125i 0.820824i
\(143\) 9.00553 + 5.19934i 0.753080 + 0.434791i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) −1.03573 + 1.79395i −0.0860131 + 0.148979i
\(146\) −13.0757 + 7.54925i −1.08215 + 0.624780i
\(147\) 15.6347 1.28952
\(148\) 6.06285 + 0.491772i 0.498363 + 0.0404234i
\(149\) −11.9826 −0.981652 −0.490826 0.871258i \(-0.663305\pi\)
−0.490826 + 0.871258i \(0.663305\pi\)
\(150\) 0.866025 0.500000i 0.0707107 0.0408248i
\(151\) 6.34419 10.9885i 0.516283 0.894229i −0.483538 0.875323i \(-0.660649\pi\)
0.999821 0.0189053i \(-0.00601809\pi\)
\(152\) −0.945484 + 1.63763i −0.0766889 + 0.132829i
\(153\) −3.25417 1.87879i −0.263084 0.151892i
\(154\) 25.5422i 2.05825i
\(155\) −0.975279 + 1.68923i −0.0783363 + 0.135682i
\(156\) 1.93690i 0.155076i
\(157\) 3.39699 + 5.88376i 0.271109 + 0.469575i 0.969146 0.246487i \(-0.0792761\pi\)
−0.698037 + 0.716062i \(0.745943\pi\)
\(158\) 11.7695 0.936329
\(159\) 12.7017 1.00731
\(160\) −0.500000 0.866025i −0.0395285 0.0684653i
\(161\) −0.844017 0.487293i −0.0665179 0.0384041i
\(162\) 1.00000i 0.0785674i
\(163\) −0.157804 + 0.0911079i −0.0123601 + 0.00713613i −0.506167 0.862435i \(-0.668938\pi\)
0.493807 + 0.869571i \(0.335605\pi\)
\(164\) −3.63525 6.29644i −0.283865 0.491669i
\(165\) −4.64945 + 2.68436i −0.361960 + 0.208977i
\(166\) 3.64598 + 2.10501i 0.282983 + 0.163380i
\(167\) −22.0553 12.7336i −1.70669 0.985359i −0.938591 0.345031i \(-0.887868\pi\)
−0.768101 0.640329i \(-0.778798\pi\)
\(168\) 4.12019 2.37879i 0.317880 0.183528i
\(169\) −4.62421 8.00937i −0.355708 0.616105i
\(170\) 3.25417 1.87879i 0.249583 0.144097i
\(171\) 1.89097i 0.144606i
\(172\) 1.51183 + 0.872855i 0.115276 + 0.0665545i
\(173\) −2.64127 4.57482i −0.200812 0.347817i 0.747978 0.663723i \(-0.231025\pi\)
−0.948790 + 0.315906i \(0.897691\pi\)
\(174\) −2.07147 −0.157038
\(175\) −4.75759 −0.359640
\(176\) 2.68436 + 4.64945i 0.202342 + 0.350466i
\(177\) 9.50376i 0.714346i
\(178\) −3.07498 + 5.32602i −0.230479 + 0.399202i
\(179\) 14.1350i 1.05650i 0.849090 + 0.528248i \(0.177151\pi\)
−0.849090 + 0.528248i \(0.822849\pi\)
\(180\) 0.866025 + 0.500000i 0.0645497 + 0.0372678i
\(181\) −5.33735 + 9.24456i −0.396722 + 0.687143i −0.993319 0.115398i \(-0.963186\pi\)
0.596597 + 0.802541i \(0.296519\pi\)
\(182\) −4.60749 + 7.98040i −0.341530 + 0.591547i
\(183\) 3.60010 2.07852i 0.266127 0.153648i
\(184\) −0.204849 −0.0151017
\(185\) 0.491772 6.06285i 0.0361558 0.445750i
\(186\) −1.95056 −0.143022
\(187\) −17.4707 + 10.0867i −1.27759 + 0.737615i
\(188\) 4.17565 7.23244i 0.304541 0.527480i
\(189\) −2.37879 + 4.12019i −0.173032 + 0.299700i
\(190\) 1.63763 + 0.945484i 0.118806 + 0.0685926i
\(191\) 16.1575i 1.16912i −0.811352 0.584558i \(-0.801268\pi\)
0.811352 0.584558i \(-0.198732\pi\)
\(192\) 0.500000 0.866025i 0.0360844 0.0625000i
\(193\) 14.4537i 1.04040i −0.854045 0.520199i \(-0.825858\pi\)
0.854045 0.520199i \(-0.174142\pi\)
\(194\) −1.15268 1.99651i −0.0827578 0.143341i
\(195\) −1.93690 −0.138704
\(196\) −15.6347 −1.11676
\(197\) 2.12901 + 3.68755i 0.151685 + 0.262727i 0.931847 0.362851i \(-0.118197\pi\)
−0.780162 + 0.625578i \(0.784863\pi\)
\(198\) −4.64945 2.68436i −0.330422 0.190769i
\(199\) 25.8669i 1.83366i −0.399279 0.916829i \(-0.630740\pi\)
0.399279 0.916829i \(-0.369260\pi\)
\(200\) −0.866025 + 0.500000i −0.0612372 + 0.0353553i
\(201\) −2.26454 3.92230i −0.159728 0.276658i
\(202\) −2.84581 + 1.64303i −0.200230 + 0.115603i
\(203\) 8.53486 + 4.92760i 0.599029 + 0.345850i
\(204\) 3.25417 + 1.87879i 0.227837 + 0.131542i
\(205\) −6.29644 + 3.63525i −0.439762 + 0.253897i
\(206\) −5.96502 10.3317i −0.415603 0.719845i
\(207\) 0.177404 0.102424i 0.0123305 0.00711899i
\(208\) 1.93690i 0.134300i
\(209\) −8.79197 5.07605i −0.608153 0.351117i
\(210\) −2.37879 4.12019i −0.164152 0.284320i
\(211\) 15.0540 1.03636 0.518180 0.855271i \(-0.326610\pi\)
0.518180 + 0.855271i \(0.326610\pi\)
\(212\) −12.7017 −0.872356
\(213\) 4.89062 + 8.47081i 0.335100 + 0.580410i
\(214\) 14.4217i 0.985848i
\(215\) 0.872855 1.51183i 0.0595282 0.103106i
\(216\) 1.00000i 0.0680414i
\(217\) 8.03668 + 4.63998i 0.545565 + 0.314982i
\(218\) 1.68342 2.91578i 0.114016 0.197481i
\(219\) −7.54925 + 13.0757i −0.510131 + 0.883572i
\(220\) 4.64945 2.68436i 0.313466 0.180980i
\(221\) −7.27807 −0.489576
\(222\) 5.49647 2.60554i 0.368899 0.174872i
\(223\) −18.2023 −1.21892 −0.609459 0.792817i \(-0.708613\pi\)
−0.609459 + 0.792817i \(0.708613\pi\)
\(224\) −4.12019 + 2.37879i −0.275292 + 0.158940i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −3.16932 + 5.48942i −0.210820 + 0.365151i
\(227\) −3.03976 1.75501i −0.201756 0.116484i 0.395718 0.918372i \(-0.370496\pi\)
−0.597474 + 0.801888i \(0.703829\pi\)
\(228\) 1.89097i 0.125232i
\(229\) 0.950846 1.64691i 0.0628337 0.108831i −0.832897 0.553428i \(-0.813320\pi\)
0.895731 + 0.444596i \(0.146653\pi\)
\(230\) 0.204849i 0.0135073i
\(231\) 12.7711 + 22.1202i 0.840277 + 1.45540i
\(232\) 2.07147 0.135999
\(233\) −15.8822 −1.04048 −0.520240 0.854020i \(-0.674157\pi\)
−0.520240 + 0.854020i \(0.674157\pi\)
\(234\) −0.968450 1.67740i −0.0633095 0.109655i
\(235\) −7.23244 4.17565i −0.471792 0.272389i
\(236\) 9.50376i 0.618642i
\(237\) 10.1927 5.88473i 0.662084 0.382255i
\(238\) −8.93853 15.4820i −0.579399 1.00355i
\(239\) −21.4695 + 12.3954i −1.38875 + 0.801793i −0.993174 0.116642i \(-0.962787\pi\)
−0.395572 + 0.918435i \(0.629454\pi\)
\(240\) −0.866025 0.500000i −0.0559017 0.0322749i
\(241\) −3.96591 2.28972i −0.255467 0.147494i 0.366798 0.930301i \(-0.380454\pi\)
−0.622265 + 0.782807i \(0.713787\pi\)
\(242\) −15.4354 + 8.91162i −0.992224 + 0.572861i
\(243\) −0.500000 0.866025i −0.0320750 0.0555556i
\(244\) −3.60010 + 2.07852i −0.230473 + 0.133063i
\(245\) 15.6347i 0.998861i
\(246\) −6.29644 3.63525i −0.401446 0.231775i
\(247\) −1.83131 3.17192i −0.116523 0.201824i
\(248\) 1.95056 0.123861
\(249\) 4.21001 0.266799
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 2.61798i 0.165246i −0.996581 0.0826228i \(-0.973670\pi\)
0.996581 0.0826228i \(-0.0263297\pi\)
\(252\) 2.37879 4.12019i 0.149850 0.259548i
\(253\) 1.09978i 0.0691424i
\(254\) 10.8595 + 6.26976i 0.681389 + 0.393400i
\(255\) 1.87879 3.25417i 0.117655 0.203784i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −6.30900 + 3.64250i −0.393545 + 0.227213i −0.683695 0.729768i \(-0.739628\pi\)
0.290150 + 0.956981i \(0.406295\pi\)
\(258\) 1.74571 0.108683
\(259\) −28.8446 2.33965i −1.79231 0.145379i
\(260\) 1.93690 0.120121
\(261\) −1.79395 + 1.03573i −0.111042 + 0.0641104i
\(262\) −1.83144 + 3.17214i −0.113146 + 0.195975i
\(263\) −7.84447 + 13.5870i −0.483711 + 0.837812i −0.999825 0.0187079i \(-0.994045\pi\)
0.516114 + 0.856520i \(0.327378\pi\)
\(264\) 4.64945 + 2.68436i 0.286154 + 0.165211i
\(265\) 12.7017i 0.780259i
\(266\) 4.49822 7.79115i 0.275804 0.477706i
\(267\) 6.14996i 0.376371i
\(268\) 2.26454 + 3.92230i 0.138329 + 0.239593i
\(269\) −10.8924 −0.664120 −0.332060 0.943258i \(-0.607744\pi\)
−0.332060 + 0.943258i \(0.607744\pi\)
\(270\) 1.00000 0.0608581
\(271\) 6.68920 + 11.5860i 0.406340 + 0.703801i 0.994476 0.104960i \(-0.0334715\pi\)
−0.588136 + 0.808762i \(0.700138\pi\)
\(272\) −3.25417 1.87879i −0.197313 0.113919i
\(273\) 9.21497i 0.557716i
\(274\) 8.82764 5.09664i 0.533297 0.307899i
\(275\) −2.68436 4.64945i −0.161873 0.280373i
\(276\) −0.177404 + 0.102424i −0.0106785 + 0.00616523i
\(277\) 6.82382 + 3.93974i 0.410004 + 0.236716i 0.690791 0.723054i \(-0.257262\pi\)
−0.280788 + 0.959770i \(0.590596\pi\)
\(278\) −11.3164 6.53350i −0.678710 0.391853i
\(279\) −1.68923 + 0.975279i −0.101132 + 0.0583884i
\(280\) 2.37879 + 4.12019i 0.142160 + 0.246229i
\(281\) −9.54036 + 5.50813i −0.569130 + 0.328588i −0.756802 0.653644i \(-0.773239\pi\)
0.187672 + 0.982232i \(0.439906\pi\)
\(282\) 8.35130i 0.497313i
\(283\) −22.5402 13.0136i −1.33988 0.773579i −0.353090 0.935590i \(-0.614869\pi\)
−0.986789 + 0.162010i \(0.948202\pi\)
\(284\) −4.89062 8.47081i −0.290205 0.502650i
\(285\) 1.89097 0.112011
\(286\) −10.3987 −0.614887
\(287\) 17.2950 + 29.9559i 1.02089 + 1.76824i
\(288\) 1.00000i 0.0589256i
\(289\) −1.44026 + 2.49461i −0.0847214 + 0.146742i
\(290\) 2.07147i 0.121641i
\(291\) −1.99651 1.15268i −0.117037 0.0675715i
\(292\) 7.54925 13.0757i 0.441786 0.765196i
\(293\) −13.3314 + 23.0906i −0.778827 + 1.34897i 0.153791 + 0.988103i \(0.450852\pi\)
−0.932618 + 0.360865i \(0.882482\pi\)
\(294\) −13.5400 + 7.81733i −0.789669 + 0.455916i
\(295\) 9.50376 0.553330
\(296\) −5.49647 + 2.60554i −0.319476 + 0.151444i
\(297\) −5.36873 −0.311525
\(298\) 10.3772 5.99129i 0.601136 0.347066i
\(299\) 0.198386 0.343614i 0.0114730 0.0198717i
\(300\) −0.500000 + 0.866025i −0.0288675 + 0.0500000i
\(301\) −7.19266 4.15268i −0.414578 0.239357i
\(302\) 12.6884i 0.730135i
\(303\) −1.64303 + 2.84581i −0.0943895 + 0.163487i
\(304\) 1.89097i 0.108454i
\(305\) 2.07852 + 3.60010i 0.119016 + 0.206141i
\(306\) 3.75759 0.214807
\(307\) −14.8746 −0.848937 −0.424468 0.905443i \(-0.639539\pi\)
−0.424468 + 0.905443i \(0.639539\pi\)
\(308\) −12.7711 22.1202i −0.727701 1.26042i
\(309\) −10.3317 5.96502i −0.587751 0.339338i
\(310\) 1.95056i 0.110784i
\(311\) 25.1237 14.5052i 1.42464 0.822514i 0.427945 0.903805i \(-0.359238\pi\)
0.996690 + 0.0812907i \(0.0259042\pi\)
\(312\) 0.968450 + 1.67740i 0.0548277 + 0.0949643i
\(313\) 19.3094 11.1483i 1.09143 0.630140i 0.157476 0.987523i \(-0.449664\pi\)
0.933958 + 0.357383i \(0.116331\pi\)
\(314\) −5.88376 3.39699i −0.332040 0.191703i
\(315\) −4.12019 2.37879i −0.232147 0.134030i
\(316\) −10.1927 + 5.88473i −0.573382 + 0.331042i
\(317\) 3.90714 + 6.76736i 0.219447 + 0.380093i 0.954639 0.297766i \(-0.0962415\pi\)
−0.735192 + 0.677859i \(0.762908\pi\)
\(318\) −11.0000 + 6.35084i −0.616849 + 0.356138i
\(319\) 11.1212i 0.622665i
\(320\) 0.866025 + 0.500000i 0.0484123 + 0.0279508i
\(321\) 7.21086 + 12.4896i 0.402471 + 0.697100i
\(322\) 0.974587 0.0543116
\(323\) 7.10548 0.395359
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 1.93690i 0.107440i
\(326\) 0.0911079 0.157804i 0.00504600 0.00873993i
\(327\) 3.36685i 0.186187i
\(328\) 6.29644 + 3.63525i 0.347663 + 0.200723i
\(329\) −19.8660 + 34.4090i −1.09525 + 1.89703i
\(330\) 2.68436 4.64945i 0.147769 0.255944i
\(331\) 21.6889 12.5221i 1.19213 0.688277i 0.233342 0.972395i \(-0.425034\pi\)
0.958790 + 0.284117i \(0.0917005\pi\)
\(332\) −4.21001 −0.231054
\(333\) 3.45731 5.00470i 0.189460 0.274256i
\(334\) 25.4673 1.39351
\(335\) 3.92230 2.26454i 0.214298 0.123725i
\(336\) −2.37879 + 4.12019i −0.129774 + 0.224775i
\(337\) 12.0335 20.8426i 0.655505 1.13537i −0.326262 0.945279i \(-0.605789\pi\)
0.981767 0.190088i \(-0.0608775\pi\)
\(338\) 8.00937 + 4.62421i 0.435652 + 0.251524i
\(339\) 6.33864i 0.344268i
\(340\) −1.87879 + 3.25417i −0.101892 + 0.176482i
\(341\) 10.4720i 0.567091i
\(342\) 0.945484 + 1.63763i 0.0511259 + 0.0885527i
\(343\) 41.0801 2.21812
\(344\) −1.74571 −0.0941223
\(345\) 0.102424 + 0.177404i 0.00551435 + 0.00955113i
\(346\) 4.57482 + 2.64127i 0.245944 + 0.141996i
\(347\) 32.7869i 1.76009i 0.474887 + 0.880047i \(0.342489\pi\)
−0.474887 + 0.880047i \(0.657511\pi\)
\(348\) 1.79395 1.03573i 0.0961656 0.0555212i
\(349\) −14.3818 24.9100i −0.769840 1.33340i −0.937649 0.347583i \(-0.887003\pi\)
0.167809 0.985819i \(-0.446331\pi\)
\(350\) 4.12019 2.37879i 0.220234 0.127152i
\(351\) −1.67740 0.968450i −0.0895332 0.0516920i
\(352\) −4.64945 2.68436i −0.247817 0.143077i
\(353\) 8.80262 5.08220i 0.468516 0.270498i −0.247102 0.968989i \(-0.579478\pi\)
0.715618 + 0.698491i \(0.246145\pi\)
\(354\) 4.75188 + 8.23050i 0.252560 + 0.437446i
\(355\) −8.47081 + 4.89062i −0.449584 + 0.259567i
\(356\) 6.14996i 0.325947i
\(357\) −15.4820 8.93853i −0.819394 0.473077i
\(358\) −7.06748 12.2412i −0.373528 0.646969i
\(359\) 26.4697 1.39702 0.698509 0.715601i \(-0.253847\pi\)
0.698509 + 0.715601i \(0.253847\pi\)
\(360\) −1.00000 −0.0527046
\(361\) −7.71212 13.3578i −0.405901 0.703041i
\(362\) 10.6747i 0.561050i
\(363\) −8.91162 + 15.4354i −0.467739 + 0.810147i
\(364\) 9.21497i 0.482996i
\(365\) −13.0757 7.54925i −0.684412 0.395146i
\(366\) −2.07852 + 3.60010i −0.108646 + 0.188180i
\(367\) −3.31961 + 5.74973i −0.173282 + 0.300134i −0.939565 0.342369i \(-0.888771\pi\)
0.766283 + 0.642503i \(0.222104\pi\)
\(368\) 0.177404 0.102424i 0.00924784 0.00533924i
\(369\) −7.27050 −0.378487
\(370\) 2.60554 + 5.49647i 0.135455 + 0.285748i
\(371\) 60.4294 3.13734
\(372\) 1.68923 0.975279i 0.0875826 0.0505659i
\(373\) −14.8306 + 25.6874i −0.767900 + 1.33004i 0.170799 + 0.985306i \(0.445365\pi\)
−0.938700 + 0.344736i \(0.887968\pi\)
\(374\) 10.0867 17.4707i 0.521573 0.903390i
\(375\) 0.866025 + 0.500000i 0.0447214 + 0.0258199i
\(376\) 8.35130i 0.430685i
\(377\) −2.00611 + 3.47469i −0.103320 + 0.178956i
\(378\) 4.75759i 0.244704i
\(379\) 11.9535 + 20.7040i 0.614009 + 1.06349i 0.990558 + 0.137097i \(0.0437773\pi\)
−0.376549 + 0.926397i \(0.622889\pi\)
\(380\) −1.89097 −0.0970046
\(381\) 12.5395 0.642419
\(382\) 8.07875 + 13.9928i 0.413345 + 0.715935i
\(383\) 31.7499 + 18.3308i 1.62234 + 0.936660i 0.986291 + 0.165014i \(0.0527670\pi\)
0.636052 + 0.771646i \(0.280566\pi\)
\(384\) 1.00000i 0.0510310i
\(385\) −22.1202 + 12.7711i −1.12735 + 0.650876i
\(386\) 7.22683 + 12.5172i 0.367836 + 0.637111i
\(387\) 1.51183 0.872855i 0.0768506 0.0443697i
\(388\) 1.99651 + 1.15268i 0.101357 + 0.0585186i
\(389\) −30.0362 17.3414i −1.52290 0.879244i −0.999633 0.0270719i \(-0.991382\pi\)
−0.523262 0.852172i \(-0.675285\pi\)
\(390\) 1.67740 0.968450i 0.0849387 0.0490394i
\(391\) 0.384869 + 0.666613i 0.0194637 + 0.0337120i
\(392\) 13.5400 7.81733i 0.683874 0.394835i
\(393\) 3.66287i 0.184767i
\(394\) −3.68755 2.12901i −0.185776 0.107258i
\(395\) 5.88473 + 10.1927i 0.296093 + 0.512848i
\(396\) 5.36873 0.269789
\(397\) 25.0721 1.25833 0.629166 0.777271i \(-0.283397\pi\)
0.629166 + 0.777271i \(0.283397\pi\)
\(398\) 12.9335 + 22.4014i 0.648296 + 1.12288i
\(399\) 8.99645i 0.450386i
\(400\) 0.500000 0.866025i 0.0250000 0.0433013i
\(401\) 12.1747i 0.607974i 0.952676 + 0.303987i \(0.0983180\pi\)
−0.952676 + 0.303987i \(0.901682\pi\)
\(402\) 3.92230 + 2.26454i 0.195627 + 0.112945i
\(403\) −1.88902 + 3.27187i −0.0940987 + 0.162984i
\(404\) 1.64303 2.84581i 0.0817437 0.141584i
\(405\) 0.866025 0.500000i 0.0430331 0.0248452i
\(406\) −9.85520 −0.489105
\(407\) −13.9884 29.5090i −0.693381 1.46271i
\(408\) −3.75759 −0.186028
\(409\) 17.4322 10.0645i 0.861965 0.497656i −0.00270462 0.999996i \(-0.500861\pi\)
0.864670 + 0.502340i \(0.167528\pi\)
\(410\) 3.63525 6.29644i 0.179532 0.310959i
\(411\) 5.09664 8.82764i 0.251399 0.435436i
\(412\) 10.3317 + 5.96502i 0.509007 + 0.293875i
\(413\) 45.2150i 2.22488i
\(414\) −0.102424 + 0.177404i −0.00503389 + 0.00871895i
\(415\) 4.21001i 0.206661i
\(416\) −0.968450 1.67740i −0.0474822 0.0822415i
\(417\) −13.0670 −0.639894
\(418\) 10.1521 0.496555
\(419\) −11.8802 20.5772i −0.580388 1.00526i −0.995433 0.0954604i \(-0.969568\pi\)
0.415046 0.909801i \(-0.363766\pi\)
\(420\) 4.12019 + 2.37879i 0.201045 + 0.116073i
\(421\) 2.63292i 0.128321i 0.997940 + 0.0641603i \(0.0204369\pi\)
−0.997940 + 0.0641603i \(0.979563\pi\)
\(422\) −13.0372 + 7.52700i −0.634639 + 0.366409i
\(423\) −4.17565 7.23244i −0.203027 0.351653i
\(424\) 11.0000 6.35084i 0.534207 0.308424i
\(425\) 3.25417 + 1.87879i 0.157850 + 0.0911349i
\(426\) −8.47081 4.89062i −0.410412 0.236951i
\(427\) 17.1278 9.88873i 0.828872 0.478549i
\(428\) −7.21086 12.4896i −0.348550 0.603706i
\(429\) −9.00553 + 5.19934i −0.434791 + 0.251027i
\(430\) 1.74571i 0.0841856i
\(431\) −20.3340 11.7398i −0.979454 0.565488i −0.0773485 0.997004i \(-0.524645\pi\)
−0.902105 + 0.431516i \(0.857979\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −23.3059 −1.12001 −0.560006 0.828489i \(-0.689201\pi\)
−0.560006 + 0.828489i \(0.689201\pi\)
\(434\) −9.27995 −0.445452
\(435\) −1.03573 1.79395i −0.0496597 0.0860131i
\(436\) 3.36685i 0.161243i
\(437\) −0.193681 + 0.335466i −0.00926503 + 0.0160475i
\(438\) 15.0985i 0.721434i
\(439\) −34.7240 20.0479i −1.65729 0.956834i −0.973960 0.226721i \(-0.927200\pi\)
−0.683326 0.730114i \(-0.739467\pi\)
\(440\) −2.68436 + 4.64945i −0.127972 + 0.221654i
\(441\) −7.81733 + 13.5400i −0.372254 + 0.644762i
\(442\) 6.30300 3.63904i 0.299803 0.173091i
\(443\) 8.21144 0.390137 0.195069 0.980790i \(-0.437507\pi\)
0.195069 + 0.980790i \(0.437507\pi\)
\(444\) −3.45731 + 5.00470i −0.164077 + 0.237512i
\(445\) −6.14996 −0.291536
\(446\) 15.7637 9.10117i 0.746432 0.430953i
\(447\) 5.99129 10.3772i 0.283378 0.490826i
\(448\) 2.37879 4.12019i 0.112387 0.194661i
\(449\) −16.5471 9.55346i −0.780905 0.450856i 0.0558459 0.998439i \(-0.482214\pi\)
−0.836751 + 0.547584i \(0.815548\pi\)
\(450\) 1.00000i 0.0471405i
\(451\) −19.5167 + 33.8039i −0.919004 + 1.59176i
\(452\) 6.33864i 0.298144i
\(453\) 6.34419 + 10.9885i 0.298076 + 0.516283i
\(454\) 3.51002 0.164733
\(455\) −9.21497 −0.432005
\(456\) −0.945484 1.63763i −0.0442763 0.0766889i
\(457\) 23.4540 + 13.5412i 1.09713 + 0.633430i 0.935466 0.353416i \(-0.114980\pi\)
0.161666 + 0.986846i \(0.448313\pi\)
\(458\) 1.90169i 0.0888602i
\(459\) 3.25417 1.87879i 0.151892 0.0876946i
\(460\) −0.102424 0.177404i −0.00477556 0.00827152i
\(461\) 8.89789 5.13720i 0.414416 0.239263i −0.278269 0.960503i \(-0.589761\pi\)
0.692685 + 0.721240i \(0.256427\pi\)
\(462\) −22.1202 12.7711i −1.02912 0.594165i
\(463\) −3.16157 1.82533i −0.146931 0.0848305i 0.424732 0.905319i \(-0.360368\pi\)
−0.571663 + 0.820488i \(0.693702\pi\)
\(464\) −1.79395 + 1.03573i −0.0832818 + 0.0480828i
\(465\) −0.975279 1.68923i −0.0452275 0.0783363i
\(466\) 13.7544 7.94111i 0.637161 0.367865i
\(467\) 41.2635i 1.90945i −0.297496 0.954723i \(-0.596151\pi\)
0.297496 0.954723i \(-0.403849\pi\)
\(468\) 1.67740 + 0.968450i 0.0775380 + 0.0447666i
\(469\) −10.7738 18.6607i −0.497486 0.861671i
\(470\) 8.35130 0.385217
\(471\) −6.79398 −0.313050
\(472\) −4.75188 8.23050i −0.218723 0.378839i
\(473\) 9.37224i 0.430936i
\(474\) −5.88473 + 10.1927i −0.270295 + 0.468164i
\(475\) 1.89097i 0.0867636i
\(476\) 15.4820 + 8.93853i 0.709616 + 0.409697i
\(477\) −6.35084 + 11.0000i −0.290785 + 0.503655i
\(478\) 12.3954 21.4695i 0.566953 0.981992i
\(479\) 0.245953 0.142001i 0.0112379 0.00648818i −0.494371 0.869251i \(-0.664601\pi\)
0.505608 + 0.862763i \(0.331268\pi\)
\(480\) 1.00000 0.0456435
\(481\) 0.952513 11.7431i 0.0434309 0.535441i
\(482\) 4.57944 0.208588
\(483\) 0.844017 0.487293i 0.0384041 0.0221726i
\(484\) 8.91162 15.4354i 0.405074 0.701608i
\(485\) 1.15268 1.99651i 0.0523407 0.0906567i
\(486\) 0.866025 + 0.500000i 0.0392837 + 0.0226805i
\(487\) 31.2302i 1.41518i 0.706626 + 0.707588i \(0.250217\pi\)
−0.706626 + 0.707588i \(0.749783\pi\)
\(488\) 2.07852 3.60010i 0.0940901 0.162969i
\(489\) 0.182216i 0.00824009i
\(490\) −7.81733 13.5400i −0.353151 0.611675i
\(491\) 10.1615 0.458582 0.229291 0.973358i \(-0.426359\pi\)
0.229291 + 0.973358i \(0.426359\pi\)
\(492\) 7.27050 0.327779
\(493\) −3.89187 6.74091i −0.175281 0.303595i
\(494\) 3.17192 + 1.83131i 0.142711 + 0.0823944i
\(495\) 5.36873i 0.241306i
\(496\) −1.68923 + 0.975279i −0.0758488 + 0.0437913i
\(497\) 23.2676 + 40.3006i 1.04369 + 1.80773i
\(498\) −3.64598 + 2.10501i −0.163380 + 0.0943275i
\(499\) 10.6809 + 6.16661i 0.478142 + 0.276055i 0.719642 0.694346i \(-0.244306\pi\)
−0.241500 + 0.970401i \(0.577639\pi\)
\(500\) −0.866025 0.500000i −0.0387298 0.0223607i
\(501\) 22.0553 12.7336i 0.985359 0.568898i
\(502\) 1.30899 + 2.26724i 0.0584231 + 0.101192i
\(503\) 7.02334 4.05493i 0.313155 0.180800i −0.335182 0.942153i \(-0.608798\pi\)
0.648337 + 0.761353i \(0.275465\pi\)
\(504\) 4.75759i 0.211920i
\(505\) −2.84581 1.64303i −0.126637 0.0731138i
\(506\) 0.549889 + 0.952436i 0.0244455 + 0.0423409i
\(507\) 9.24842 0.410737
\(508\) −12.5395 −0.556351
\(509\) −6.20749 10.7517i −0.275142 0.476560i 0.695029 0.718982i \(-0.255392\pi\)
−0.970171 + 0.242422i \(0.922058\pi\)
\(510\) 3.75759i 0.166389i
\(511\) −35.9162 + 62.2087i −1.58884 + 2.75195i
\(512\) 1.00000i 0.0441942i
\(513\) 1.63763 + 0.945484i 0.0723030 + 0.0417441i
\(514\) 3.64250 6.30900i 0.160664 0.278278i
\(515\) 5.96502 10.3317i 0.262850 0.455270i
\(516\) −1.51183 + 0.872855i −0.0665545 + 0.0384253i
\(517\) −44.8359 −1.97188
\(518\) 26.1499 12.3961i 1.14896 0.544652i
\(519\) 5.28255 0.231878
\(520\) −1.67740 + 0.968450i −0.0735590 + 0.0424693i
\(521\) 13.8998 24.0752i 0.608962 1.05475i −0.382450 0.923976i \(-0.624920\pi\)
0.991412 0.130777i \(-0.0417471\pi\)
\(522\) 1.03573 1.79395i 0.0453329 0.0785189i
\(523\) −25.2169 14.5590i −1.10266 0.636619i −0.165740 0.986170i \(-0.553001\pi\)
−0.936918 + 0.349550i \(0.886334\pi\)
\(524\) 3.66287i 0.160013i
\(525\) 2.37879 4.12019i 0.103819 0.179820i
\(526\) 15.6889i 0.684071i
\(527\) −3.66470 6.34744i −0.159637 0.276499i
\(528\) −5.36873 −0.233644
\(529\) 22.9580 0.998176
\(530\) −6.35084 11.0000i −0.275863 0.477809i
\(531\) 8.23050 + 4.75188i 0.357173 + 0.206214i
\(532\) 8.99645i 0.390045i
\(533\) −12.1956 + 7.04111i −0.528249 + 0.304985i
\(534\) −3.07498 5.32602i −0.133067 0.230479i
\(535\) −12.4896 + 7.21086i −0.539971 + 0.311753i
\(536\) −3.92230 2.26454i −0.169418 0.0978133i
\(537\) −12.2412 7.06748i −0.528248 0.304984i
\(538\) 9.43308 5.44619i 0.406689 0.234802i
\(539\) 41.9691 + 72.6926i 1.80774 + 3.13109i
\(540\) −0.866025 + 0.500000i −0.0372678 + 0.0215166i
\(541\) 37.6109i 1.61702i −0.588482 0.808510i \(-0.700274\pi\)
0.588482 0.808510i \(-0.299726\pi\)
\(542\) −11.5860 6.68920i −0.497663 0.287326i
\(543\) −5.33735 9.24456i −0.229048 0.396722i
\(544\) 3.75759 0.161105
\(545\) 3.36685 0.144220
\(546\) −4.60749 7.98040i −0.197182 0.341530i
\(547\) 6.12219i 0.261766i −0.991398 0.130883i \(-0.958219\pi\)
0.991398 0.130883i \(-0.0417812\pi\)
\(548\) −5.09664 + 8.82764i −0.217718 + 0.377098i
\(549\) 4.15704i 0.177418i
\(550\) 4.64945 + 2.68436i 0.198253 + 0.114462i
\(551\) 1.95854 3.39229i 0.0834367 0.144517i
\(552\) 0.102424 0.177404i 0.00435947 0.00755083i
\(553\) 48.4925 27.9971i 2.06211 1.19056i
\(554\) −7.87947 −0.334767
\(555\) 5.00470 + 3.45731i 0.212438 + 0.146755i
\(556\) 13.0670 0.554164
\(557\) 13.0000 7.50554i 0.550826 0.318020i −0.198629 0.980075i \(-0.563649\pi\)
0.749455 + 0.662055i \(0.230315\pi\)
\(558\) 0.975279 1.68923i 0.0412869 0.0715109i
\(559\) 1.69063 2.92826i 0.0715061 0.123852i
\(560\) −4.12019 2.37879i −0.174110 0.100522i
\(561\) 20.1735i 0.851725i
\(562\) 5.50813 9.54036i 0.232346 0.402436i
\(563\) 12.6975i 0.535135i 0.963539 + 0.267567i \(0.0862198\pi\)
−0.963539 + 0.267567i \(0.913780\pi\)
\(564\) 4.17565 + 7.23244i 0.175827 + 0.304541i
\(565\) −6.33864 −0.266668
\(566\) 26.0272 1.09401
\(567\) −2.37879 4.12019i −0.0999000 0.173032i
\(568\) 8.47081 + 4.89062i 0.355427 + 0.205206i
\(569\) 37.5046i 1.57227i 0.618053 + 0.786137i \(0.287922\pi\)
−0.618053 + 0.786137i \(0.712078\pi\)
\(570\) −1.63763 + 0.945484i −0.0685926 + 0.0396020i
\(571\) −19.6205 33.9837i −0.821091 1.42217i −0.904870 0.425688i \(-0.860032\pi\)
0.0837786 0.996484i \(-0.473301\pi\)
\(572\) 9.00553 5.19934i 0.376540 0.217395i
\(573\) 13.9928 + 8.07875i 0.584558 + 0.337495i
\(574\) −29.9559 17.2950i −1.25033 0.721880i
\(575\) −0.177404 + 0.102424i −0.00739827 + 0.00427139i
\(576\) 0.500000 + 0.866025i 0.0208333 + 0.0360844i
\(577\) −4.09848 + 2.36626i −0.170622 + 0.0985085i −0.582879 0.812559i \(-0.698074\pi\)
0.412257 + 0.911067i \(0.364741\pi\)
\(578\) 2.88053i 0.119814i
\(579\) 12.5172 + 7.22683i 0.520199 + 0.300337i
\(580\) 1.03573 + 1.79395i 0.0430066 + 0.0744895i
\(581\) 20.0295 0.830964
\(582\) 2.30537 0.0955605
\(583\) 34.0960 + 59.0559i 1.41211 + 2.44585i
\(584\) 15.0985i 0.624780i
\(585\) 0.968450 1.67740i 0.0400405 0.0693521i
\(586\) 26.6627i 1.10143i
\(587\) 14.5676 + 8.41058i 0.601267 + 0.347142i 0.769540 0.638599i \(-0.220486\pi\)
−0.168273 + 0.985740i \(0.553819\pi\)
\(588\) 7.81733 13.5400i 0.322381 0.558380i
\(589\) 1.84422 3.19429i 0.0759898 0.131618i
\(590\) −8.23050 + 4.75188i −0.338844 + 0.195632i
\(591\) −4.25801 −0.175151
\(592\) 3.45731 5.00470i 0.142095 0.205692i
\(593\) −29.3265 −1.20429 −0.602147 0.798385i \(-0.705688\pi\)
−0.602147 + 0.798385i \(0.705688\pi\)
\(594\) 4.64945 2.68436i 0.190769 0.110141i
\(595\) 8.93853 15.4820i 0.366444 0.634700i
\(596\) −5.99129 + 10.3772i −0.245413 + 0.425068i
\(597\) 22.4014 + 12.9335i 0.916829 + 0.529332i
\(598\) 0.396772i 0.0162252i
\(599\) 7.12556 12.3418i 0.291143 0.504274i −0.682938 0.730477i \(-0.739298\pi\)
0.974080 + 0.226203i \(0.0726313\pi\)
\(600\) 1.00000i 0.0408248i
\(601\) −0.461616 0.799543i −0.0188297 0.0326140i 0.856457 0.516218i \(-0.172661\pi\)
−0.875287 + 0.483604i \(0.839327\pi\)
\(602\) 8.30537 0.338501
\(603\) 4.52908 0.184439
\(604\) −6.34419 10.9885i −0.258142 0.447114i
\(605\) −15.4354 8.91162i −0.627537 0.362309i
\(606\) 3.28606i 0.133487i
\(607\) 21.3290 12.3143i 0.865718 0.499823i −0.000204616 1.00000i \(-0.500065\pi\)
0.865923 + 0.500177i \(0.166732\pi\)
\(608\) 0.945484 + 1.63763i 0.0383444 + 0.0664145i
\(609\) −8.53486 + 4.92760i −0.345850 + 0.199676i
\(610\) −3.60010 2.07852i −0.145764 0.0841567i
\(611\) −14.0085 8.08781i −0.566723 0.327198i
\(612\) −3.25417 + 1.87879i −0.131542 + 0.0759458i
\(613\) −9.14393 15.8378i −0.369320 0.639681i 0.620139 0.784492i \(-0.287076\pi\)
−0.989459 + 0.144811i \(0.953743\pi\)
\(614\) 12.8818 7.43729i 0.519866 0.300145i
\(615\) 7.27050i 0.293175i
\(616\) 22.1202 + 12.7711i 0.891248 + 0.514562i
\(617\) −2.88264 4.99288i −0.116051 0.201006i 0.802149 0.597125i \(-0.203690\pi\)
−0.918199 + 0.396119i \(0.870357\pi\)
\(618\) 11.9300 0.479896
\(619\) 22.5666 0.907030 0.453515 0.891249i \(-0.350170\pi\)
0.453515 + 0.891249i \(0.350170\pi\)
\(620\) 0.975279 + 1.68923i 0.0391681 + 0.0678412i
\(621\) 0.204849i 0.00822030i
\(622\) −14.5052 + 25.1237i −0.581605 + 1.00737i
\(623\) 29.2590i 1.17224i
\(624\) −1.67740 0.968450i −0.0671499 0.0387690i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −11.1483 + 19.3094i −0.445576 + 0.771761i
\(627\) 8.79197 5.07605i 0.351117 0.202718i
\(628\) 6.79398 0.271109
\(629\) 18.8056 + 12.9912i 0.749828 + 0.517991i
\(630\) 4.75759 0.189547
\(631\) 8.15056 4.70573i 0.324469 0.187332i −0.328914 0.944360i \(-0.606683\pi\)
0.653383 + 0.757028i \(0.273349\pi\)
\(632\) 5.88473 10.1927i 0.234082 0.405442i
\(633\) −7.52700 + 13.0372i −0.299172 + 0.518180i
\(634\) −6.76736 3.90714i −0.268766 0.155172i
\(635\) 12.5395i 0.497616i
\(636\) 6.35084 11.0000i 0.251827 0.436178i
\(637\) 30.2828i 1.19985i
\(638\) −5.56058 9.63121i −0.220145 0.381303i
\(639\) −9.78125 −0.386940
\(640\) −1.00000 −0.0395285
\(641\) −5.14868 8.91778i −0.203361 0.352231i 0.746248 0.665667i \(-0.231853\pi\)
−0.949609 + 0.313436i \(0.898520\pi\)
\(642\) −12.4896 7.21086i −0.492924 0.284590i
\(643\) 22.3349i 0.880802i −0.897801 0.440401i \(-0.854836\pi\)
0.897801 0.440401i \(-0.145164\pi\)
\(644\) −0.844017 + 0.487293i −0.0332589 + 0.0192020i
\(645\) 0.872855 + 1.51183i 0.0343686 + 0.0595282i
\(646\) −6.15353 + 3.55274i −0.242107 + 0.139781i
\(647\) −22.5961 13.0459i −0.888344 0.512886i −0.0149437 0.999888i \(-0.504757\pi\)
−0.873401 + 0.487003i \(0.838090\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 44.1873 25.5115i 1.73450 1.00142i
\(650\) 0.968450 + 1.67740i 0.0379857 + 0.0657932i
\(651\) −8.03668 + 4.63998i −0.314982 + 0.181855i
\(652\) 0.182216i 0.00713613i
\(653\) 31.7581 + 18.3355i 1.24279 + 0.717525i 0.969661 0.244453i \(-0.0786084\pi\)
0.273128 + 0.961978i \(0.411942\pi\)
\(654\) 1.68342 + 2.91578i 0.0658271 + 0.114016i
\(655\) −3.66287 −0.143120
\(656\) −7.27050 −0.283865
\(657\) −7.54925 13.0757i −0.294524 0.510131i
\(658\) 39.7320i 1.54892i
\(659\) 24.9009 43.1297i 0.970003 1.68009i 0.274475 0.961594i \(-0.411496\pi\)
0.695527 0.718500i \(-0.255171\pi\)
\(660\) 5.36873i 0.208977i
\(661\) 10.7505 + 6.20682i 0.418147 + 0.241417i 0.694284 0.719701i \(-0.255721\pi\)
−0.276137 + 0.961118i \(0.589054\pi\)
\(662\) −12.5221 + 21.6889i −0.486686 + 0.842964i
\(663\) 3.63904 6.30300i 0.141328 0.244788i
\(664\) 3.64598 2.10501i 0.141491 0.0816900i
\(665\) 8.99645 0.348867
\(666\) −0.491772 + 6.06285i −0.0190558 + 0.234931i
\(667\) 0.424338 0.0164304
\(668\) −22.0553 + 12.7336i −0.853346 + 0.492680i
\(669\) 9.10117 15.7637i 0.351871 0.609459i
\(670\) −2.26454 + 3.92230i −0.0874869 + 0.151532i
\(671\) 19.3280 + 11.1590i 0.746147 + 0.430788i
\(672\) 4.75759i 0.183528i
\(673\) 24.9387 43.1950i 0.961315 1.66505i 0.242110 0.970249i \(-0.422161\pi\)
0.719205 0.694798i \(-0.244506\pi\)
\(674\) 24.0669i 0.927024i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) −9.24842 −0.355708
\(677\) −39.4514 −1.51624 −0.758120 0.652115i \(-0.773882\pi\)
−0.758120 + 0.652115i \(0.773882\pi\)
\(678\) −3.16932 5.48942i −0.121717 0.210820i
\(679\) −9.49856 5.48399i −0.364521 0.210456i
\(680\) 3.75759i 0.144097i
\(681\) 3.03976 1.75501i 0.116484 0.0672521i
\(682\) −5.23601 9.06903i −0.200497 0.347271i
\(683\) −16.1531 + 9.32598i −0.618080 + 0.356849i −0.776121 0.630584i \(-0.782815\pi\)
0.158041 + 0.987433i \(0.449482\pi\)
\(684\) −1.63763 0.945484i −0.0626162 0.0361515i
\(685\) 8.82764 + 5.09664i 0.337287 + 0.194733i
\(686\) −35.5764 + 20.5401i −1.35831 + 0.784223i
\(687\) 0.950846 + 1.64691i 0.0362770 + 0.0628337i
\(688\) 1.51183 0.872855i 0.0576379 0.0332773i
\(689\) 24.6019i 0.937258i
\(690\) −0.177404 0.102424i −0.00675367 0.00389923i
\(691\) −10.9603 18.9839i −0.416951 0.722181i 0.578680 0.815555i \(-0.303568\pi\)
−0.995631 + 0.0933739i \(0.970235\pi\)
\(692\) −5.28255 −0.200812
\(693\) −25.5422 −0.970268
\(694\) −16.3935 28.3943i −0.622287 1.07783i
\(695\) 13.0670i 0.495660i
\(696\) −1.03573 + 1.79395i −0.0392594 + 0.0679993i
\(697\) 27.3195i 1.03480i
\(698\) 24.9100 + 14.3818i 0.942858 + 0.544359i
\(699\) 7.94111 13.7544i 0.300360 0.520240i
\(700\) −2.37879 + 4.12019i −0.0899100 + 0.155729i
\(701\) −24.8824 + 14.3659i −0.939797 + 0.542592i −0.889897 0.456162i \(-0.849224\pi\)
−0.0499001 + 0.998754i \(0.515890\pi\)
\(702\) 1.93690 0.0731036
\(703\) −0.929925 + 11.4647i −0.0350728 + 0.432398i
\(704\) 5.36873 0.202342
\(705\) 7.23244 4.17565i 0.272389 0.157264i
\(706\) −5.08220 + 8.80262i −0.191271 + 0.331291i
\(707\) −7.81685 + 13.5392i −0.293983 + 0.509194i
\(708\) −8.23050 4.75188i −0.309321 0.178587i
\(709\) 4.43747i 0.166653i 0.996522 + 0.0833263i \(0.0265544\pi\)
−0.996522 + 0.0833263i \(0.973446\pi\)
\(710\) 4.89062 8.47081i 0.183542 0.317904i
\(711\) 11.7695i 0.441390i
\(712\) 3.07498 + 5.32602i 0.115240 + 0.199601i
\(713\) 0.399570 0.0149640
\(714\) 17.8771 0.669032
\(715\) −5.19934 9.00553i −0.194444 0.336788i
\(716\) 12.2412 + 7.06748i 0.457476 + 0.264124i
\(717\) 24.7908i 0.925831i
\(718\) −22.9235 + 13.2349i −0.855496 + 0.493921i
\(719\) 22.3711 + 38.7479i 0.834302 + 1.44505i 0.894598 + 0.446873i \(0.147462\pi\)
−0.0602957 + 0.998181i \(0.519204\pi\)
\(720\) 0.866025 0.500000i 0.0322749 0.0186339i
\(721\) −49.1541 28.3791i −1.83059 1.05689i
\(722\) 13.3578 + 7.71212i 0.497125 + 0.287015i
\(723\) 3.96591 2.28972i 0.147494 0.0851556i
\(724\) 5.33735 + 9.24456i 0.198361 + 0.343571i
\(725\) 1.79395 1.03573i 0.0666255 0.0384662i
\(726\) 17.8232i 0.661482i
\(727\) −37.3973 21.5914i −1.38699 0.800779i −0.394015 0.919104i \(-0.628914\pi\)
−0.992975 + 0.118325i \(0.962248\pi\)
\(728\) 4.60749 + 7.98040i 0.170765 + 0.295773i
\(729\) 1.00000 0.0370370
\(730\) 15.0985 0.558820
\(731\) 3.27983 + 5.68083i 0.121309 + 0.210113i
\(732\) 4.15704i 0.153648i
\(733\) −14.5314 + 25.1691i −0.536729 + 0.929641i 0.462349 + 0.886698i \(0.347007\pi\)
−0.999078 + 0.0429432i \(0.986327\pi\)
\(734\) 6.63922i 0.245058i
\(735\) −13.5400 7.81733i −0.499431 0.288346i
\(736\) −0.102424 + 0.177404i −0.00377542 + 0.00653921i
\(737\) 12.1577 21.0578i 0.447835 0.775673i
\(738\) 6.29644 3.63525i 0.231775 0.133815i
\(739\) 44.2733 1.62862 0.814309 0.580431i \(-0.197116\pi\)
0.814309 + 0.580431i \(0.197116\pi\)
\(740\) −5.00470 3.45731i −0.183976 0.127093i
\(741\) 3.66262 0.134550
\(742\) −52.3334 + 30.2147i −1.92122 + 1.10922i
\(743\) −20.8251 + 36.0701i −0.763997 + 1.32328i 0.176778 + 0.984251i \(0.443433\pi\)
−0.940775 + 0.339031i \(0.889901\pi\)
\(744\) −0.975279 + 1.68923i −0.0357555 + 0.0619303i
\(745\) 10.3772 + 5.99129i 0.380192 + 0.219504i
\(746\) 29.6612i 1.08597i
\(747\) −2.10501 + 3.64598i −0.0770181 + 0.133399i
\(748\) 20.1735i 0.737615i
\(749\) 34.3063 + 59.4203i 1.25352 + 2.17117i
\(750\) −1.00000 −0.0365148
\(751\) 15.8097 0.576905 0.288452 0.957494i \(-0.406859\pi\)
0.288452 + 0.957494i \(0.406859\pi\)
\(752\) −4.17565 7.23244i −0.152270 0.263740i
\(753\) 2.26724 + 1.30899i 0.0826228 + 0.0477023i
\(754\) 4.01223i 0.146117i
\(755\) −10.9885 + 6.34419i −0.399911 + 0.230889i
\(756\) 2.37879 + 4.12019i 0.0865159 + 0.149850i
\(757\) −17.1132 + 9.88032i −0.621991 + 0.359107i −0.777644 0.628705i \(-0.783585\pi\)
0.155653 + 0.987812i \(0.450252\pi\)
\(758\) −20.7040 11.9535i −0.752004 0.434170i
\(759\) 0.952436 + 0.549889i 0.0345712 + 0.0199597i
\(760\) 1.63763 0.945484i 0.0594029 0.0342963i
\(761\) 15.1511 + 26.2424i 0.549225 + 0.951286i 0.998328 + 0.0578061i \(0.0184105\pi\)
−0.449102 + 0.893480i \(0.648256\pi\)
\(762\) −10.8595 + 6.26976i −0.393400 + 0.227130i
\(763\) 16.0181i 0.579893i
\(764\) −13.9928 8.07875i −0.506242 0.292279i
\(765\) 1.87879 + 3.25417i 0.0679280 + 0.117655i
\(766\) −36.6616 −1.32464
\(767\) 18.4078 0.664668
\(768\) −0.500000 0.866025i −0.0180422 0.0312500i
\(769\) 10.9287i 0.394097i −0.980394 0.197049i \(-0.936864\pi\)
0.980394 0.197049i \(-0.0631357\pi\)
\(770\) 12.7711 22.1202i 0.460239 0.797156i
\(771\) 7.28500i 0.262363i
\(772\) −12.5172 7.22683i −0.450505 0.260099i
\(773\) 13.6280 23.6044i 0.490165 0.848991i −0.509771 0.860310i \(-0.670270\pi\)
0.999936 + 0.0113194i \(0.00360314\pi\)
\(774\) −0.872855 + 1.51183i −0.0313741 + 0.0543416i
\(775\) 1.68923 0.975279i 0.0606790 0.0350331i
\(776\) −2.30537 −0.0827578