Properties

Label 546.2.e.e.545.2
Level $546$
Weight $2$
Character 546.545
Analytic conductor $4.360$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.0.303595776.1
Defining polynomial: \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 545.2
Root \(-1.26217 + 1.18614i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.e.545.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.00000 q^{2} +(-1.26217 + 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(1.26217 - 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} -1.00000 q^{8} +(0.186141 - 2.99422i) q^{9} +O(q^{10})\) \(q-1.00000 q^{2} +(-1.26217 + 1.18614i) q^{3} +1.00000 q^{4} +3.37228i q^{5} +(1.26217 - 1.18614i) q^{6} +(2.52434 - 0.792287i) q^{7} -1.00000 q^{8} +(0.186141 - 2.99422i) q^{9} -3.37228i q^{10} +5.74456 q^{11} +(-1.26217 + 1.18614i) q^{12} +(3.46410 - 1.00000i) q^{13} +(-2.52434 + 0.792287i) q^{14} +(-4.00000 - 4.25639i) q^{15} +1.00000 q^{16} +0.792287 q^{17} +(-0.186141 + 2.99422i) q^{18} +2.37686 q^{19} +3.37228i q^{20} +(-2.24638 + 3.99422i) q^{21} -5.74456 q^{22} -0.147477i q^{23} +(1.26217 - 1.18614i) q^{24} -6.37228 q^{25} +(-3.46410 + 1.00000i) q^{26} +(3.31662 + 4.00000i) q^{27} +(2.52434 - 0.792287i) q^{28} -2.37686i q^{29} +(4.00000 + 4.25639i) q^{30} -4.10891 q^{31} -1.00000 q^{32} +(-7.25061 + 6.81386i) q^{33} -0.792287 q^{34} +(2.67181 + 8.51278i) q^{35} +(0.186141 - 2.99422i) q^{36} +8.36530i q^{37} -2.37686 q^{38} +(-3.18614 + 5.37108i) q^{39} -3.37228i q^{40} -8.37228i q^{41} +(2.24638 - 3.99422i) q^{42} -2.62772 q^{43} +5.74456 q^{44} +(10.0974 + 0.627719i) q^{45} +0.147477i q^{46} +10.3723i q^{47} +(-1.26217 + 1.18614i) q^{48} +(5.74456 - 4.00000i) q^{49} +6.37228 q^{50} +(-1.00000 + 0.939764i) q^{51} +(3.46410 - 1.00000i) q^{52} -10.0974i q^{53} +(-3.31662 - 4.00000i) q^{54} +19.3723i q^{55} +(-2.52434 + 0.792287i) q^{56} +(-3.00000 + 2.81929i) q^{57} +2.37686i q^{58} +2.74456i q^{59} +(-4.00000 - 4.25639i) q^{60} +7.74456i q^{61} +4.10891 q^{62} +(-1.90240 - 7.70590i) q^{63} +1.00000 q^{64} +(3.37228 + 11.6819i) q^{65} +(7.25061 - 6.81386i) q^{66} -5.98844i q^{67} +0.792287 q^{68} +(0.174928 + 0.186141i) q^{69} +(-2.67181 - 8.51278i) q^{70} +2.00000 q^{71} +(-0.186141 + 2.99422i) q^{72} -10.2448 q^{73} -8.36530i q^{74} +(8.04290 - 7.55842i) q^{75} +2.37686 q^{76} +(14.5012 - 4.55134i) q^{77} +(3.18614 - 5.37108i) q^{78} -3.62772 q^{79} +3.37228i q^{80} +(-8.93070 - 1.11469i) q^{81} +8.37228i q^{82} +6.74456i q^{83} +(-2.24638 + 3.99422i) q^{84} +2.67181i q^{85} +2.62772 q^{86} +(2.81929 + 3.00000i) q^{87} -5.74456 q^{88} -10.0000i q^{89} +(-10.0974 - 0.627719i) q^{90} +(7.95228 - 5.26890i) q^{91} -0.147477i q^{92} +(5.18614 - 4.87375i) q^{93} -10.3723i q^{94} +8.01544i q^{95} +(1.26217 - 1.18614i) q^{96} -9.15759 q^{97} +(-5.74456 + 4.00000i) q^{98} +(1.06930 - 17.2005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 8 q^{2} + 8 q^{4} - 8 q^{8} - 10 q^{9} - 32 q^{15} + 8 q^{16} + 10 q^{18} - 14 q^{21} - 28 q^{25} + 32 q^{30} - 8 q^{32} - 10 q^{36} - 14 q^{39} + 14 q^{42} - 44 q^{43} + 28 q^{50} - 8 q^{51} - 24 q^{57} - 32 q^{60} + 4 q^{63} + 8 q^{64} + 4 q^{65} + 16 q^{71} + 10 q^{72} + 14 q^{78} - 52 q^{79} - 14 q^{81} - 14 q^{84} + 44 q^{86} + 24 q^{91} + 30 q^{93} + 66 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(-1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 −0.707107
\(3\) −1.26217 + 1.18614i −0.728714 + 0.684819i
\(4\) 1.00000 0.500000
\(5\) 3.37228i 1.50813i 0.656800 + 0.754065i \(0.271910\pi\)
−0.656800 + 0.754065i \(0.728090\pi\)
\(6\) 1.26217 1.18614i 0.515278 0.484240i
\(7\) 2.52434 0.792287i 0.954110 0.299456i
\(8\) −1.00000 −0.353553
\(9\) 0.186141 2.99422i 0.0620469 0.998073i
\(10\) 3.37228i 1.06641i
\(11\) 5.74456 1.73205 0.866025 0.500000i \(-0.166667\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) −1.26217 + 1.18614i −0.364357 + 0.342409i
\(13\) 3.46410 1.00000i 0.960769 0.277350i
\(14\) −2.52434 + 0.792287i −0.674658 + 0.211748i
\(15\) −4.00000 4.25639i −1.03280 1.09899i
\(16\) 1.00000 0.250000
\(17\) 0.792287 0.192158 0.0960789 0.995374i \(-0.469370\pi\)
0.0960789 + 0.995374i \(0.469370\pi\)
\(18\) −0.186141 + 2.99422i −0.0438738 + 0.705744i
\(19\) 2.37686 0.545289 0.272645 0.962115i \(-0.412102\pi\)
0.272645 + 0.962115i \(0.412102\pi\)
\(20\) 3.37228i 0.754065i
\(21\) −2.24638 + 3.99422i −0.490200 + 0.871610i
\(22\) −5.74456 −1.22474
\(23\) 0.147477i 0.0307510i −0.999882 0.0153755i \(-0.995106\pi\)
0.999882 0.0153755i \(-0.00489437\pi\)
\(24\) 1.26217 1.18614i 0.257639 0.242120i
\(25\) −6.37228 −1.27446
\(26\) −3.46410 + 1.00000i −0.679366 + 0.196116i
\(27\) 3.31662 + 4.00000i 0.638285 + 0.769800i
\(28\) 2.52434 0.792287i 0.477055 0.149728i
\(29\) 2.37686i 0.441372i −0.975345 0.220686i \(-0.929170\pi\)
0.975345 0.220686i \(-0.0708296\pi\)
\(30\) 4.00000 + 4.25639i 0.730297 + 0.777107i
\(31\) −4.10891 −0.737982 −0.368991 0.929433i \(-0.620297\pi\)
−0.368991 + 0.929433i \(0.620297\pi\)
\(32\) −1.00000 −0.176777
\(33\) −7.25061 + 6.81386i −1.26217 + 1.18614i
\(34\) −0.792287 −0.135876
\(35\) 2.67181 + 8.51278i 0.451619 + 1.43892i
\(36\) 0.186141 2.99422i 0.0310234 0.499037i
\(37\) 8.36530i 1.37525i 0.726067 + 0.687623i \(0.241346\pi\)
−0.726067 + 0.687623i \(0.758654\pi\)
\(38\) −2.37686 −0.385578
\(39\) −3.18614 + 5.37108i −0.510191 + 0.860061i
\(40\) 3.37228i 0.533204i
\(41\) 8.37228i 1.30753i −0.756697 0.653765i \(-0.773188\pi\)
0.756697 0.653765i \(-0.226812\pi\)
\(42\) 2.24638 3.99422i 0.346623 0.616321i
\(43\) −2.62772 −0.400723 −0.200362 0.979722i \(-0.564212\pi\)
−0.200362 + 0.979722i \(0.564212\pi\)
\(44\) 5.74456 0.866025
\(45\) 10.0974 + 0.627719i 1.50522 + 0.0935748i
\(46\) 0.147477i 0.0217443i
\(47\) 10.3723i 1.51295i 0.654021 + 0.756476i \(0.273081\pi\)
−0.654021 + 0.756476i \(0.726919\pi\)
\(48\) −1.26217 + 1.18614i −0.182178 + 0.171205i
\(49\) 5.74456 4.00000i 0.820652 0.571429i
\(50\) 6.37228 0.901177
\(51\) −1.00000 + 0.939764i −0.140028 + 0.131593i
\(52\) 3.46410 1.00000i 0.480384 0.138675i
\(53\) 10.0974i 1.38698i −0.720467 0.693489i \(-0.756073\pi\)
0.720467 0.693489i \(-0.243927\pi\)
\(54\) −3.31662 4.00000i −0.451335 0.544331i
\(55\) 19.3723i 2.61216i
\(56\) −2.52434 + 0.792287i −0.337329 + 0.105874i
\(57\) −3.00000 + 2.81929i −0.397360 + 0.373424i
\(58\) 2.37686i 0.312097i
\(59\) 2.74456i 0.357312i 0.983912 + 0.178656i \(0.0571749\pi\)
−0.983912 + 0.178656i \(0.942825\pi\)
\(60\) −4.00000 4.25639i −0.516398 0.549497i
\(61\) 7.74456i 0.991590i 0.868440 + 0.495795i \(0.165123\pi\)
−0.868440 + 0.495795i \(0.834877\pi\)
\(62\) 4.10891 0.521832
\(63\) −1.90240 7.70590i −0.239680 0.970852i
\(64\) 1.00000 0.125000
\(65\) 3.37228 + 11.6819i 0.418280 + 1.44896i
\(66\) 7.25061 6.81386i 0.892488 0.838728i
\(67\) 5.98844i 0.731604i −0.930693 0.365802i \(-0.880795\pi\)
0.930693 0.365802i \(-0.119205\pi\)
\(68\) 0.792287 0.0960789
\(69\) 0.174928 + 0.186141i 0.0210589 + 0.0224087i
\(70\) −2.67181 8.51278i −0.319343 1.01747i
\(71\) 2.00000 0.237356 0.118678 0.992933i \(-0.462134\pi\)
0.118678 + 0.992933i \(0.462134\pi\)
\(72\) −0.186141 + 2.99422i −0.0219369 + 0.352872i
\(73\) −10.2448 −1.19907 −0.599533 0.800350i \(-0.704647\pi\)
−0.599533 + 0.800350i \(0.704647\pi\)
\(74\) 8.36530i 0.972446i
\(75\) 8.04290 7.55842i 0.928714 0.872771i
\(76\) 2.37686 0.272645
\(77\) 14.5012 4.55134i 1.65257 0.518674i
\(78\) 3.18614 5.37108i 0.360759 0.608155i
\(79\) −3.62772 −0.408150 −0.204075 0.978955i \(-0.565419\pi\)
−0.204075 + 0.978955i \(0.565419\pi\)
\(80\) 3.37228i 0.377033i
\(81\) −8.93070 1.11469i −0.992300 0.123855i
\(82\) 8.37228i 0.924564i
\(83\) 6.74456i 0.740312i 0.928970 + 0.370156i \(0.120696\pi\)
−0.928970 + 0.370156i \(0.879304\pi\)
\(84\) −2.24638 + 3.99422i −0.245100 + 0.435805i
\(85\) 2.67181i 0.289799i
\(86\) 2.62772 0.283354
\(87\) 2.81929 + 3.00000i 0.302260 + 0.321634i
\(88\) −5.74456 −0.612372
\(89\) 10.0000i 1.06000i −0.847998 0.529999i \(-0.822192\pi\)
0.847998 0.529999i \(-0.177808\pi\)
\(90\) −10.0974 0.627719i −1.06435 0.0661674i
\(91\) 7.95228 5.26890i 0.833625 0.552331i
\(92\) 0.147477i 0.0153755i
\(93\) 5.18614 4.87375i 0.537778 0.505384i
\(94\) 10.3723i 1.06982i
\(95\) 8.01544i 0.822367i
\(96\) 1.26217 1.18614i 0.128820 0.121060i
\(97\) −9.15759 −0.929812 −0.464906 0.885360i \(-0.653912\pi\)
−0.464906 + 0.885360i \(0.653912\pi\)
\(98\) −5.74456 + 4.00000i −0.580288 + 0.404061i
\(99\) 1.06930 17.2005i 0.107468 1.72871i
\(100\) −6.37228 −0.637228
\(101\) −17.6704 −1.75827 −0.879133 0.476576i \(-0.841878\pi\)
−0.879133 + 0.476576i \(0.841878\pi\)
\(102\) 1.00000 0.939764i 0.0990148 0.0930505i
\(103\) 7.37228i 0.726412i −0.931709 0.363206i \(-0.881682\pi\)
0.931709 0.363206i \(-0.118318\pi\)
\(104\) −3.46410 + 1.00000i −0.339683 + 0.0980581i
\(105\) −13.4696 7.57541i −1.31450 0.739285i
\(106\) 10.0974i 0.980741i
\(107\) 17.0256i 1.64592i 0.568098 + 0.822961i \(0.307680\pi\)
−0.568098 + 0.822961i \(0.692320\pi\)
\(108\) 3.31662 + 4.00000i 0.319142 + 0.384900i
\(109\) 19.6974i 1.88667i −0.331848 0.943333i \(-0.607672\pi\)
0.331848 0.943333i \(-0.392328\pi\)
\(110\) 19.3723i 1.84707i
\(111\) −9.92242 10.5584i −0.941795 1.00216i
\(112\) 2.52434 0.792287i 0.238528 0.0748641i
\(113\) 5.69349i 0.535598i −0.963475 0.267799i \(-0.913704\pi\)
0.963475 0.267799i \(-0.0862963\pi\)
\(114\) 3.00000 2.81929i 0.280976 0.264051i
\(115\) 0.497333 0.0463766
\(116\) 2.37686i 0.220686i
\(117\) −2.34941 10.5584i −0.217203 0.976126i
\(118\) 2.74456i 0.252657i
\(119\) 2.00000 0.627719i 0.183340 0.0575429i
\(120\) 4.00000 + 4.25639i 0.365148 + 0.388553i
\(121\) 22.0000 2.00000
\(122\) 7.74456i 0.701160i
\(123\) 9.93070 + 10.5672i 0.895421 + 0.952815i
\(124\) −4.10891 −0.368991
\(125\) 4.62772i 0.413916i
\(126\) 1.90240 + 7.70590i 0.169479 + 0.686496i
\(127\) −10.3723 −0.920391 −0.460196 0.887818i \(-0.652221\pi\)
−0.460196 + 0.887818i \(0.652221\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 3.31662 3.11684i 0.292013 0.274423i
\(130\) −3.37228 11.6819i −0.295769 1.02457i
\(131\) −3.96143 −0.346112 −0.173056 0.984912i \(-0.555364\pi\)
−0.173056 + 0.984912i \(0.555364\pi\)
\(132\) −7.25061 + 6.81386i −0.631084 + 0.593070i
\(133\) 6.00000 1.88316i 0.520266 0.163290i
\(134\) 5.98844i 0.517322i
\(135\) −13.4891 + 11.1846i −1.16096 + 0.962616i
\(136\) −0.792287 −0.0679380
\(137\) 18.1168 1.54783 0.773913 0.633292i \(-0.218297\pi\)
0.773913 + 0.633292i \(0.218297\pi\)
\(138\) −0.174928 0.186141i −0.0148909 0.0158453i
\(139\) 5.25544i 0.445760i −0.974846 0.222880i \(-0.928454\pi\)
0.974846 0.222880i \(-0.0715459\pi\)
\(140\) 2.67181 + 8.51278i 0.225810 + 0.719461i
\(141\) −12.3030 13.0916i −1.03610 1.10251i
\(142\) −2.00000 −0.167836
\(143\) 19.8997 5.74456i 1.66410 0.480384i
\(144\) 0.186141 2.99422i 0.0155117 0.249518i
\(145\) 8.01544 0.665646
\(146\) 10.2448 0.847868
\(147\) −2.50605 + 11.8625i −0.206695 + 0.978405i
\(148\) 8.36530i 0.687623i
\(149\) 7.62772 0.624887 0.312444 0.949936i \(-0.398852\pi\)
0.312444 + 0.949936i \(0.398852\pi\)
\(150\) −8.04290 + 7.55842i −0.656700 + 0.617143i
\(151\) 17.8178i 1.45000i 0.688751 + 0.724998i \(0.258159\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(152\) −2.37686 −0.192789
\(153\) 0.147477 2.37228i 0.0119228 0.191788i
\(154\) −14.5012 + 4.55134i −1.16854 + 0.366758i
\(155\) 13.8564i 1.11297i
\(156\) −3.18614 + 5.37108i −0.255095 + 0.430031i
\(157\) 8.25544i 0.658856i −0.944181 0.329428i \(-0.893144\pi\)
0.944181 0.329428i \(-0.106856\pi\)
\(158\) 3.62772 0.288606
\(159\) 11.9769 + 12.7446i 0.949828 + 1.01071i
\(160\) 3.37228i 0.266602i
\(161\) −0.116844 0.372281i −0.00920859 0.0293399i
\(162\) 8.93070 + 1.11469i 0.701662 + 0.0875785i
\(163\) 8.21782i 0.643670i 0.946796 + 0.321835i \(0.104300\pi\)
−0.946796 + 0.321835i \(0.895700\pi\)
\(164\) 8.37228i 0.653765i
\(165\) −22.9783 24.4511i −1.78885 1.90351i
\(166\) 6.74456i 0.523480i
\(167\) 12.6277i 0.977162i 0.872518 + 0.488581i \(0.162485\pi\)
−0.872518 + 0.488581i \(0.837515\pi\)
\(168\) 2.24638 3.99422i 0.173312 0.308161i
\(169\) 11.0000 6.92820i 0.846154 0.532939i
\(170\) 2.67181i 0.204919i
\(171\) 0.442430 7.11684i 0.0338335 0.544239i
\(172\) −2.62772 −0.200362
\(173\) −10.6873 −0.812537 −0.406269 0.913754i \(-0.633170\pi\)
−0.406269 + 0.913754i \(0.633170\pi\)
\(174\) −2.81929 3.00000i −0.213730 0.227429i
\(175\) −16.0858 + 5.04868i −1.21597 + 0.381644i
\(176\) 5.74456 0.433013
\(177\) −3.25544 3.46410i −0.244694 0.260378i
\(178\) 10.0000i 0.749532i
\(179\) 20.1947i 1.50942i −0.656057 0.754711i \(-0.727777\pi\)
0.656057 0.754711i \(-0.272223\pi\)
\(180\) 10.0974 + 0.627719i 0.752612 + 0.0467874i
\(181\) 20.3723i 1.51426i −0.653264 0.757130i \(-0.726601\pi\)
0.653264 0.757130i \(-0.273399\pi\)
\(182\) −7.95228 + 5.26890i −0.589462 + 0.390557i
\(183\) −9.18614 9.77495i −0.679059 0.722585i
\(184\) 0.147477i 0.0108721i
\(185\) −28.2101 −2.07405
\(186\) −5.18614 + 4.87375i −0.380266 + 0.357360i
\(187\) 4.55134 0.332827
\(188\) 10.3723i 0.756476i
\(189\) 11.5414 + 7.46963i 0.839515 + 0.543336i
\(190\) 8.01544i 0.581501i
\(191\) 2.96677i 0.214668i −0.994223 0.107334i \(-0.965769\pi\)
0.994223 0.107334i \(-0.0342314\pi\)
\(192\) −1.26217 + 1.18614i −0.0910892 + 0.0856023i
\(193\) 20.7846i 1.49611i 0.663637 + 0.748054i \(0.269012\pi\)
−0.663637 + 0.748054i \(0.730988\pi\)
\(194\) 9.15759 0.657476
\(195\) −18.1128 10.7446i −1.29708 0.769434i
\(196\) 5.74456 4.00000i 0.410326 0.285714i
\(197\) −21.1168 −1.50451 −0.752256 0.658870i \(-0.771035\pi\)
−0.752256 + 0.658870i \(0.771035\pi\)
\(198\) −1.06930 + 17.2005i −0.0759916 + 1.22239i
\(199\) 12.1168i 0.858940i 0.903081 + 0.429470i \(0.141300\pi\)
−0.903081 + 0.429470i \(0.858700\pi\)
\(200\) 6.37228 0.450588
\(201\) 7.10313 + 7.55842i 0.501016 + 0.533130i
\(202\) 17.6704 1.24328
\(203\) −1.88316 6.00000i −0.132172 0.421117i
\(204\) −1.00000 + 0.939764i −0.0700140 + 0.0657966i
\(205\) 28.2337 1.97193
\(206\) 7.37228i 0.513651i
\(207\) −0.441578 0.0274514i −0.0306918 0.00190801i
\(208\) 3.46410 1.00000i 0.240192 0.0693375i
\(209\) 13.6540 0.944469
\(210\) 13.4696 + 7.57541i 0.929493 + 0.522753i
\(211\) 17.3723 1.19596 0.597979 0.801512i \(-0.295971\pi\)
0.597979 + 0.801512i \(0.295971\pi\)
\(212\) 10.0974i 0.693489i
\(213\) −2.52434 + 2.37228i −0.172965 + 0.162546i
\(214\) 17.0256i 1.16384i
\(215\) 8.86141i 0.604343i
\(216\) −3.31662 4.00000i −0.225668 0.272166i
\(217\) −10.3723 + 3.25544i −0.704116 + 0.220993i
\(218\) 19.6974i 1.33407i
\(219\) 12.9307 12.1518i 0.873776 0.821143i
\(220\) 19.3723i 1.30608i
\(221\) 2.74456 0.792287i 0.184619 0.0532950i
\(222\) 9.92242 + 10.5584i 0.665949 + 0.708635i
\(223\) −0.644810 −0.0431797 −0.0215898 0.999767i \(-0.506873\pi\)
−0.0215898 + 0.999767i \(0.506873\pi\)
\(224\) −2.52434 + 0.792287i −0.168664 + 0.0529369i
\(225\) −1.18614 + 19.0800i −0.0790760 + 1.27200i
\(226\) 5.69349i 0.378725i
\(227\) 11.4891i 0.762560i 0.924460 + 0.381280i \(0.124517\pi\)
−0.924460 + 0.381280i \(0.875483\pi\)
\(228\) −3.00000 + 2.81929i −0.198680 + 0.186712i
\(229\) 5.04868 0.333626 0.166813 0.985989i \(-0.446652\pi\)
0.166813 + 0.985989i \(0.446652\pi\)
\(230\) −0.497333 −0.0327932
\(231\) −12.9045 + 22.9450i −0.849051 + 1.50967i
\(232\) 2.37686i 0.156049i
\(233\) 10.7422i 0.703742i 0.936048 + 0.351871i \(0.114454\pi\)
−0.936048 + 0.351871i \(0.885546\pi\)
\(234\) 2.34941 + 10.5584i 0.153586 + 0.690226i
\(235\) −34.9783 −2.28173
\(236\) 2.74456i 0.178656i
\(237\) 4.57879 4.30298i 0.297425 0.279509i
\(238\) −2.00000 + 0.627719i −0.129641 + 0.0406890i
\(239\) −18.0000 −1.16432 −0.582162 0.813073i \(-0.697793\pi\)
−0.582162 + 0.813073i \(0.697793\pi\)
\(240\) −4.00000 4.25639i −0.258199 0.274749i
\(241\) 16.4356 1.05871 0.529357 0.848399i \(-0.322433\pi\)
0.529357 + 0.848399i \(0.322433\pi\)
\(242\) −22.0000 −1.41421
\(243\) 12.5942 9.18614i 0.807921 0.589291i
\(244\) 7.74456i 0.495795i
\(245\) 13.4891 + 19.3723i 0.861789 + 1.23765i
\(246\) −9.93070 10.5672i −0.633159 0.673742i
\(247\) 8.23369 2.37686i 0.523897 0.151236i
\(248\) 4.10891 0.260916
\(249\) −8.00000 8.51278i −0.506979 0.539475i
\(250\) 4.62772i 0.292683i
\(251\) −6.78073 −0.427996 −0.213998 0.976834i \(-0.568649\pi\)
−0.213998 + 0.976834i \(0.568649\pi\)
\(252\) −1.90240 7.70590i −0.119840 0.485426i
\(253\) 0.847190i 0.0532624i
\(254\) 10.3723 0.650815
\(255\) −3.16915 3.37228i −0.198460 0.211180i
\(256\) 1.00000 0.0625000
\(257\) −18.9051 −1.17927 −0.589633 0.807671i \(-0.700728\pi\)
−0.589633 + 0.807671i \(0.700728\pi\)
\(258\) −3.31662 + 3.11684i −0.206484 + 0.194046i
\(259\) 6.62772 + 21.1168i 0.411826 + 1.31214i
\(260\) 3.37228 + 11.6819i 0.209140 + 0.724482i
\(261\) −7.11684 0.442430i −0.440522 0.0273858i
\(262\) 3.96143 0.244738
\(263\) 7.22316i 0.445399i 0.974887 + 0.222699i \(0.0714869\pi\)
−0.974887 + 0.222699i \(0.928513\pi\)
\(264\) 7.25061 6.81386i 0.446244 0.419364i
\(265\) 34.0511 2.09174
\(266\) −6.00000 + 1.88316i −0.367884 + 0.115464i
\(267\) 11.8614 + 12.6217i 0.725906 + 0.772435i
\(268\) 5.98844i 0.365802i
\(269\) 14.5012 0.884155 0.442077 0.896977i \(-0.354242\pi\)
0.442077 + 0.896977i \(0.354242\pi\)
\(270\) 13.4891 11.1846i 0.820922 0.680673i
\(271\) −11.3321 −0.688374 −0.344187 0.938901i \(-0.611845\pi\)
−0.344187 + 0.938901i \(0.611845\pi\)
\(272\) 0.792287 0.0480395
\(273\) −3.78746 + 16.0828i −0.229227 + 0.973373i
\(274\) −18.1168 −1.09448
\(275\) −36.6060 −2.20742
\(276\) 0.174928 + 0.186141i 0.0105294 + 0.0112044i
\(277\) 17.4891 1.05082 0.525410 0.850849i \(-0.323912\pi\)
0.525410 + 0.850849i \(0.323912\pi\)
\(278\) 5.25544i 0.315200i
\(279\) −0.764836 + 12.3030i −0.0457895 + 0.736560i
\(280\) −2.67181 8.51278i −0.159671 0.508736i
\(281\) 14.0000 0.835170 0.417585 0.908638i \(-0.362877\pi\)
0.417585 + 0.908638i \(0.362877\pi\)
\(282\) 12.3030 + 13.0916i 0.732632 + 0.779592i
\(283\) 0.372281i 0.0221298i −0.999939 0.0110649i \(-0.996478\pi\)
0.999939 0.0110649i \(-0.00352214\pi\)
\(284\) 2.00000 0.118678
\(285\) −9.50744 10.1168i −0.563172 0.599270i
\(286\) −19.8997 + 5.74456i −1.17670 + 0.339683i
\(287\) −6.63325 21.1345i −0.391548 1.24753i
\(288\) −0.186141 + 2.99422i −0.0109684 + 0.176436i
\(289\) −16.3723 −0.963075
\(290\) −8.01544 −0.470683
\(291\) 11.5584 10.8622i 0.677567 0.636753i
\(292\) −10.2448 −0.599533
\(293\) 11.4891i 0.671202i −0.942004 0.335601i \(-0.891061\pi\)
0.942004 0.335601i \(-0.108939\pi\)
\(294\) 2.50605 11.8625i 0.146156 0.691837i
\(295\) −9.25544 −0.538872
\(296\) 8.36530i 0.486223i
\(297\) 19.0526 + 22.9783i 1.10554 + 1.33333i
\(298\) −7.62772 −0.441862
\(299\) −0.147477 0.510875i −0.00852880 0.0295446i
\(300\) 8.04290 7.55842i 0.464357 0.436386i
\(301\) −6.63325 + 2.08191i −0.382334 + 0.119999i
\(302\) 17.8178i 1.02530i
\(303\) 22.3030 20.9595i 1.28127 1.20409i
\(304\) 2.37686 0.136322
\(305\) −26.1168 −1.49545
\(306\) −0.147477 + 2.37228i −0.00843069 + 0.135614i
\(307\) 31.8766 1.81930 0.909648 0.415381i \(-0.136352\pi\)
0.909648 + 0.415381i \(0.136352\pi\)
\(308\) 14.5012 4.55134i 0.826284 0.259337i
\(309\) 8.74456 + 9.30506i 0.497461 + 0.529347i
\(310\) 13.8564i 0.786991i
\(311\) 10.3923 0.589294 0.294647 0.955606i \(-0.404798\pi\)
0.294647 + 0.955606i \(0.404798\pi\)
\(312\) 3.18614 5.37108i 0.180380 0.304078i
\(313\) 2.74456i 0.155132i 0.996987 + 0.0775659i \(0.0247148\pi\)
−0.996987 + 0.0775659i \(0.975285\pi\)
\(314\) 8.25544i 0.465881i
\(315\) 25.9865 6.41543i 1.46417 0.361468i
\(316\) −3.62772 −0.204075
\(317\) 3.86141 0.216878 0.108439 0.994103i \(-0.465415\pi\)
0.108439 + 0.994103i \(0.465415\pi\)
\(318\) −11.9769 12.7446i −0.671630 0.714680i
\(319\) 13.6540i 0.764479i
\(320\) 3.37228i 0.188516i
\(321\) −20.1947 21.4891i −1.12716 1.19941i
\(322\) 0.116844 + 0.372281i 0.00651146 + 0.0207464i
\(323\) 1.88316 0.104782
\(324\) −8.93070 1.11469i −0.496150 0.0619273i
\(325\) −22.0742 + 6.37228i −1.22446 + 0.353471i
\(326\) 8.21782i 0.455143i
\(327\) 23.3639 + 24.8614i 1.29202 + 1.37484i
\(328\) 8.37228i 0.462282i
\(329\) 8.21782 + 26.1831i 0.453063 + 1.44352i
\(330\) 22.9783 + 24.4511i 1.26491 + 1.34599i
\(331\) 17.0805i 0.938827i −0.882979 0.469413i \(-0.844465\pi\)
0.882979 0.469413i \(-0.155535\pi\)
\(332\) 6.74456i 0.370156i
\(333\) 25.0475 + 1.55712i 1.37260 + 0.0853298i
\(334\) 12.6277i 0.690958i
\(335\) 20.1947 1.10335
\(336\) −2.24638 + 3.99422i −0.122550 + 0.217903i
\(337\) 5.00000 0.272367 0.136184 0.990684i \(-0.456516\pi\)
0.136184 + 0.990684i \(0.456516\pi\)
\(338\) −11.0000 + 6.92820i −0.598321 + 0.376845i
\(339\) 6.75327 + 7.18614i 0.366788 + 0.390298i
\(340\) 2.67181i 0.144899i
\(341\) −23.6039 −1.27822
\(342\) −0.442430 + 7.11684i −0.0239239 + 0.384835i
\(343\) 11.3321 14.6487i 0.611874 0.790955i
\(344\) 2.62772 0.141677
\(345\) −0.627719 + 0.589907i −0.0337952 + 0.0317595i
\(346\) 10.6873 0.574551
\(347\) 19.2000i 1.03071i −0.856976 0.515356i \(-0.827660\pi\)
0.856976 0.515356i \(-0.172340\pi\)
\(348\) 2.81929 + 3.00000i 0.151130 + 0.160817i
\(349\) −16.4356 −0.879780 −0.439890 0.898052i \(-0.644983\pi\)
−0.439890 + 0.898052i \(0.644983\pi\)
\(350\) 16.0858 5.04868i 0.859822 0.269863i
\(351\) 15.4891 + 10.5398i 0.826748 + 0.562572i
\(352\) −5.74456 −0.306186
\(353\) 11.1168i 0.591690i −0.955236 0.295845i \(-0.904399\pi\)
0.955236 0.295845i \(-0.0956012\pi\)
\(354\) 3.25544 + 3.46410i 0.173025 + 0.184115i
\(355\) 6.74456i 0.357964i
\(356\) 10.0000i 0.529999i
\(357\) −1.77978 + 3.16457i −0.0941957 + 0.167487i
\(358\) 20.1947i 1.06732i
\(359\) −6.23369 −0.329001 −0.164501 0.986377i \(-0.552601\pi\)
−0.164501 + 0.986377i \(0.552601\pi\)
\(360\) −10.0974 0.627719i −0.532177 0.0330837i
\(361\) −13.3505 −0.702660
\(362\) 20.3723i 1.07074i
\(363\) −27.7677 + 26.0951i −1.45743 + 1.36964i
\(364\) 7.95228 5.26890i 0.416812 0.276165i
\(365\) 34.5484i 1.80835i
\(366\) 9.18614 + 9.77495i 0.480167 + 0.510945i
\(367\) 4.74456i 0.247664i −0.992303 0.123832i \(-0.960482\pi\)
0.992303 0.123832i \(-0.0395184\pi\)
\(368\) 0.147477i 0.00768776i
\(369\) −25.0684 1.55842i −1.30501 0.0811282i
\(370\) 28.2101 1.46658
\(371\) −8.00000 25.4891i −0.415339 1.32333i
\(372\) 5.18614 4.87375i 0.268889 0.252692i
\(373\) −12.2337 −0.633436 −0.316718 0.948520i \(-0.602581\pi\)
−0.316718 + 0.948520i \(0.602581\pi\)
\(374\) −4.55134 −0.235344
\(375\) 5.48913 + 5.84096i 0.283457 + 0.301626i
\(376\) 10.3723i 0.534910i
\(377\) −2.37686 8.23369i −0.122415 0.424057i
\(378\) −11.5414 7.46963i −0.593627 0.384196i
\(379\) 18.3152i 0.940787i −0.882457 0.470394i \(-0.844112\pi\)
0.882457 0.470394i \(-0.155888\pi\)
\(380\) 8.01544i 0.411184i
\(381\) 13.0916 12.3030i 0.670701 0.630301i
\(382\) 2.96677i 0.151793i
\(383\) 3.51087i 0.179397i 0.995969 + 0.0896987i \(0.0285904\pi\)
−0.995969 + 0.0896987i \(0.971410\pi\)
\(384\) 1.26217 1.18614i 0.0644098 0.0605300i
\(385\) 15.3484 + 48.9022i 0.782227 + 2.49229i
\(386\) 20.7846i 1.05791i
\(387\) −0.489125 + 7.86797i −0.0248636 + 0.399951i
\(388\) −9.15759 −0.464906
\(389\) 25.2434i 1.27989i 0.768421 + 0.639945i \(0.221043\pi\)
−0.768421 + 0.639945i \(0.778957\pi\)
\(390\) 18.1128 + 10.7446i 0.917177 + 0.544072i
\(391\) 0.116844i 0.00590905i
\(392\) −5.74456 + 4.00000i −0.290144 + 0.202031i
\(393\) 5.00000 4.69882i 0.252217 0.237024i
\(394\) 21.1168 1.06385
\(395\) 12.2337i 0.615544i
\(396\) 1.06930 17.2005i 0.0537342 0.864357i
\(397\) −6.63325 −0.332913 −0.166457 0.986049i \(-0.553233\pi\)
−0.166457 + 0.986049i \(0.553233\pi\)
\(398\) 12.1168i 0.607363i
\(399\) −5.33933 + 9.49370i −0.267301 + 0.475280i
\(400\) −6.37228 −0.318614
\(401\) −28.9783 −1.44710 −0.723552 0.690269i \(-0.757492\pi\)
−0.723552 + 0.690269i \(0.757492\pi\)
\(402\) −7.10313 7.55842i −0.354272 0.376980i
\(403\) −14.2337 + 4.10891i −0.709030 + 0.204679i
\(404\) −17.6704 −0.879133
\(405\) 3.75906 30.1168i 0.186789 1.49652i
\(406\) 1.88316 + 6.00000i 0.0934595 + 0.297775i
\(407\) 48.0550i 2.38200i
\(408\) 1.00000 0.939764i 0.0495074 0.0465252i
\(409\) −29.7947 −1.47325 −0.736627 0.676299i \(-0.763583\pi\)
−0.736627 + 0.676299i \(0.763583\pi\)
\(410\) −28.2337 −1.39436
\(411\) −22.8665 + 21.4891i −1.12792 + 1.05998i
\(412\) 7.37228i 0.363206i
\(413\) 2.17448 + 6.92820i 0.106999 + 0.340915i
\(414\) 0.441578 + 0.0274514i 0.0217024 + 0.00134916i
\(415\) −22.7446 −1.11649
\(416\) −3.46410 + 1.00000i −0.169842 + 0.0490290i
\(417\) 6.23369 + 6.63325i 0.305265 + 0.324832i
\(418\) −13.6540 −0.667840
\(419\) 4.90120 0.239439 0.119720 0.992808i \(-0.461800\pi\)
0.119720 + 0.992808i \(0.461800\pi\)
\(420\) −13.4696 7.57541i −0.657251 0.369642i
\(421\) 23.0140i 1.12163i 0.827940 + 0.560817i \(0.189513\pi\)
−0.827940 + 0.560817i \(0.810487\pi\)
\(422\) −17.3723 −0.845669
\(423\) 31.0569 + 1.93070i 1.51004 + 0.0938740i
\(424\) 10.0974i 0.490371i
\(425\) −5.04868 −0.244897
\(426\) 2.52434 2.37228i 0.122305 0.114937i
\(427\) 6.13592 + 19.5499i 0.296938 + 0.946086i
\(428\) 17.0256i 0.822961i
\(429\) −18.3030 + 30.8545i −0.883676 + 1.48967i
\(430\) 8.86141i 0.427335i
\(431\) 28.2337 1.35997 0.679984 0.733227i \(-0.261987\pi\)
0.679984 + 0.733227i \(0.261987\pi\)
\(432\) 3.31662 + 4.00000i 0.159571 + 0.192450i
\(433\) 30.4674i 1.46417i −0.681214 0.732084i \(-0.738548\pi\)
0.681214 0.732084i \(-0.261452\pi\)
\(434\) 10.3723 3.25544i 0.497885 0.156266i
\(435\) −10.1168 + 9.50744i −0.485066 + 0.455847i
\(436\) 19.6974i 0.943333i
\(437\) 0.350532i 0.0167682i
\(438\) −12.9307 + 12.1518i −0.617853 + 0.580636i
\(439\) 5.60597i 0.267558i −0.991011 0.133779i \(-0.957289\pi\)
0.991011 0.133779i \(-0.0427113\pi\)
\(440\) 19.3723i 0.923537i
\(441\) −10.9076 17.9450i −0.519409 0.854526i
\(442\) −2.74456 + 0.792287i −0.130546 + 0.0376852i
\(443\) 16.7306i 0.794895i −0.917625 0.397447i \(-0.869896\pi\)
0.917625 0.397447i \(-0.130104\pi\)
\(444\) −9.92242 10.5584i −0.470897 0.501081i
\(445\) 33.7228 1.59861
\(446\) 0.644810 0.0305326
\(447\) −9.62747 + 9.04755i −0.455364 + 0.427934i
\(448\) 2.52434 0.792287i 0.119264 0.0374320i
\(449\) −14.1168 −0.666215 −0.333108 0.942889i \(-0.608097\pi\)
−0.333108 + 0.942889i \(0.608097\pi\)
\(450\) 1.18614 19.0800i 0.0559152 0.899440i
\(451\) 48.0951i 2.26471i
\(452\) 5.69349i 0.267799i
\(453\) −21.1345 22.4891i −0.992984 1.05663i
\(454\) 11.4891i 0.539211i
\(455\) 17.7682 + 26.8173i 0.832987 + 1.25721i
\(456\) 3.00000 2.81929i 0.140488 0.132025i
\(457\) 23.6588i 1.10671i −0.832945 0.553356i \(-0.813347\pi\)
0.832945 0.553356i \(-0.186653\pi\)
\(458\) −5.04868 −0.235909
\(459\) 2.62772 + 3.16915i 0.122651 + 0.147923i
\(460\) 0.497333 0.0231883
\(461\) 21.6060i 1.00629i 0.864202 + 0.503145i \(0.167824\pi\)
−0.864202 + 0.503145i \(0.832176\pi\)
\(462\) 12.9045 22.9450i 0.600369 1.06750i
\(463\) 31.6742i 1.47203i −0.676967 0.736014i \(-0.736706\pi\)
0.676967 0.736014i \(-0.263294\pi\)
\(464\) 2.37686i 0.110343i
\(465\) 16.4356 + 17.4891i 0.762185 + 0.811039i
\(466\) 10.7422i 0.497621i
\(467\) −21.5769 −0.998460 −0.499230 0.866470i \(-0.666384\pi\)
−0.499230 + 0.866470i \(0.666384\pi\)
\(468\) −2.34941 10.5584i −0.108601 0.488063i
\(469\) −4.74456 15.1168i −0.219084 0.698031i
\(470\) 34.9783 1.61343
\(471\) 9.79211 + 10.4198i 0.451197 + 0.480117i
\(472\) 2.74456i 0.126329i
\(473\) −15.0951 −0.694073
\(474\) −4.57879 + 4.30298i −0.210311 + 0.197643i
\(475\) −15.1460 −0.694947
\(476\) 2.00000 0.627719i 0.0916698 0.0287714i
\(477\) −30.2337 1.87953i −1.38431 0.0860577i
\(478\) 18.0000 0.823301
\(479\) 28.6277i 1.30803i −0.756480 0.654017i \(-0.773082\pi\)
0.756480 0.654017i \(-0.226918\pi\)
\(480\) 4.00000 + 4.25639i 0.182574 + 0.194277i
\(481\) 8.36530 + 28.9783i 0.381425 + 1.32129i
\(482\) −16.4356 −0.748623
\(483\) 0.589055 + 0.331289i 0.0268029 + 0.0150741i
\(484\) 22.0000 1.00000
\(485\) 30.8820i 1.40228i
\(486\) −12.5942 + 9.18614i −0.571286 + 0.416692i
\(487\) 37.5152i 1.69998i 0.526802 + 0.849988i \(0.323391\pi\)
−0.526802 + 0.849988i \(0.676609\pi\)
\(488\) 7.74456i 0.350580i
\(489\) −9.74749 10.3723i −0.440797 0.469051i
\(490\) −13.4891 19.3723i −0.609377 0.875150i
\(491\) 11.6819i 0.527198i −0.964632 0.263599i \(-0.915090\pi\)
0.964632 0.263599i \(-0.0849095\pi\)
\(492\) 9.93070 + 10.5672i 0.447711 + 0.476408i
\(493\) 1.88316i 0.0848131i
\(494\) −8.23369 + 2.37686i −0.370451 + 0.106940i
\(495\) 58.0049 + 3.60597i 2.60712 + 0.162076i
\(496\) −4.10891 −0.184496
\(497\) 5.04868 1.58457i 0.226464 0.0710779i
\(498\) 8.00000 + 8.51278i 0.358489 + 0.381467i
\(499\) 10.4472i 0.467681i −0.972275 0.233841i \(-0.924871\pi\)
0.972275 0.233841i \(-0.0751294\pi\)
\(500\) 4.62772i 0.206958i
\(501\) −14.9783 15.9383i −0.669179 0.712071i
\(502\) 6.78073 0.302639
\(503\) 27.4179 1.22250 0.611251 0.791437i \(-0.290667\pi\)
0.611251 + 0.791437i \(0.290667\pi\)
\(504\) 1.90240 + 7.70590i 0.0847396 + 0.343248i
\(505\) 59.5894i 2.65170i
\(506\) 0.847190i 0.0376622i
\(507\) −5.66603 + 21.7921i −0.251637 + 0.967822i
\(508\) −10.3723 −0.460196
\(509\) 22.1168i 0.980312i −0.871635 0.490156i \(-0.836940\pi\)
0.871635 0.490156i \(-0.163060\pi\)
\(510\) 3.16915 + 3.37228i 0.140332 + 0.149327i
\(511\) −25.8614 + 8.11684i −1.14404 + 0.359068i
\(512\) −1.00000 −0.0441942
\(513\) 7.88316 + 9.50744i 0.348050 + 0.419764i
\(514\) 18.9051 0.833867
\(515\) 24.8614 1.09552
\(516\) 3.31662 3.11684i 0.146006 0.137211i
\(517\) 59.5842i 2.62051i
\(518\) −6.62772 21.1168i −0.291205 0.927821i
\(519\) 13.4891 12.6766i 0.592107 0.556441i
\(520\) −3.37228 11.6819i −0.147884 0.512286i
\(521\) −20.3971 −0.893612 −0.446806 0.894631i \(-0.647439\pi\)
−0.446806 + 0.894631i \(0.647439\pi\)
\(522\) 7.11684 + 0.442430i 0.311496 + 0.0193647i
\(523\) 37.3505i 1.63322i −0.577186 0.816612i \(-0.695849\pi\)
0.577186 0.816612i \(-0.304151\pi\)
\(524\) −3.96143 −0.173056
\(525\) 14.3145 25.4523i 0.624738 1.11083i
\(526\) 7.22316i 0.314945i
\(527\) −3.25544 −0.141809
\(528\) −7.25061 + 6.81386i −0.315542 + 0.296535i
\(529\) 22.9783 0.999054
\(530\) −34.0511 −1.47909
\(531\) 8.21782 + 0.510875i 0.356623 + 0.0221701i
\(532\) 6.00000 1.88316i 0.260133 0.0816452i
\(533\) −8.37228 29.0024i −0.362644 1.25623i
\(534\) −11.8614 12.6217i −0.513293 0.546194i
\(535\) −57.4150 −2.48227
\(536\) 5.98844i 0.258661i
\(537\) 23.9538 + 25.4891i 1.03368 + 1.09994i
\(538\) −14.5012 −0.625192
\(539\) 33.0000 22.9783i 1.42141 0.989743i
\(540\) −13.4891 + 11.1846i −0.580480 + 0.481308i
\(541\) 24.4511i 1.05123i 0.850721 + 0.525617i \(0.176166\pi\)
−0.850721 + 0.525617i \(0.823834\pi\)
\(542\) 11.3321 0.486754
\(543\) 24.1644 + 25.7133i 1.03699 + 1.10346i
\(544\) −0.792287 −0.0339690
\(545\) 66.4251 2.84534
\(546\) 3.78746 16.0828i 0.162088 0.688279i
\(547\) −5.48913 −0.234698 −0.117349 0.993091i \(-0.537440\pi\)
−0.117349 + 0.993091i \(0.537440\pi\)
\(548\) 18.1168 0.773913
\(549\) 23.1889 + 1.44158i 0.989679 + 0.0615251i
\(550\) 36.6060 1.56088
\(551\) 5.64947i 0.240675i
\(552\) −0.174928 0.186141i −0.00744544 0.00792267i
\(553\) −9.15759 + 2.87419i −0.389420 + 0.122223i
\(554\) −17.4891 −0.743042
\(555\) 35.6060 33.4612i 1.51139 1.42035i
\(556\) 5.25544i 0.222880i
\(557\) −30.3723 −1.28691 −0.643457 0.765482i \(-0.722501\pi\)
−0.643457 + 0.765482i \(0.722501\pi\)
\(558\) 0.764836 12.3030i 0.0323781 0.520827i
\(559\) −9.10268 + 2.62772i −0.385003 + 0.111141i
\(560\) 2.67181 + 8.51278i 0.112905 + 0.359730i
\(561\) −5.74456 + 5.39853i −0.242536 + 0.227926i
\(562\) −14.0000 −0.590554
\(563\) −9.25016 −0.389848 −0.194924 0.980818i \(-0.562446\pi\)
−0.194924 + 0.980818i \(0.562446\pi\)
\(564\) −12.3030 13.0916i −0.518049 0.551255i
\(565\) 19.2000 0.807752
\(566\) 0.372281i 0.0156482i
\(567\) −23.4273 + 4.26182i −0.983853 + 0.178980i
\(568\) −2.00000 −0.0839181
\(569\) 10.1523i 0.425605i −0.977095 0.212802i \(-0.931741\pi\)
0.977095 0.212802i \(-0.0682590\pi\)
\(570\) 9.50744 + 10.1168i 0.398223 + 0.423748i
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 19.8997 5.74456i 0.832050 0.240192i
\(573\) 3.51900 + 3.74456i 0.147009 + 0.156431i
\(574\) 6.63325 + 21.1345i 0.276866 + 0.882136i
\(575\) 0.939764i 0.0391909i
\(576\) 0.186141 2.99422i 0.00775586 0.124759i
\(577\) −6.92820 −0.288425 −0.144212 0.989547i \(-0.546065\pi\)
−0.144212 + 0.989547i \(0.546065\pi\)
\(578\) 16.3723 0.680997
\(579\) −24.6535 26.2337i −1.02456 1.09023i
\(580\) 8.01544 0.332823
\(581\) 5.34363 + 17.0256i 0.221691 + 0.706339i
\(582\) −11.5584 + 10.8622i −0.479112 + 0.450252i
\(583\) 58.0049i 2.40232i
\(584\) 10.2448 0.423934
\(585\) 35.6060 7.92287i 1.47213 0.327570i
\(586\) 11.4891i 0.474611i
\(587\) 16.7446i 0.691122i 0.938396 + 0.345561i \(0.112311\pi\)
−0.938396 + 0.345561i \(0.887689\pi\)
\(588\) −2.50605 + 11.8625i −0.103348 + 0.489203i
\(589\) −9.76631 −0.402414
\(590\) 9.25544 0.381040
\(591\) 26.6530 25.0475i 1.09636 1.03032i
\(592\) 8.36530i 0.343812i
\(593\) 19.2554i 0.790726i −0.918525 0.395363i \(-0.870619\pi\)
0.918525 0.395363i \(-0.129381\pi\)
\(594\) −19.0526 22.9783i −0.781736 0.942809i
\(595\) 2.11684 + 6.74456i 0.0867821 + 0.276500i
\(596\) 7.62772 0.312444
\(597\) −14.3723 15.2935i −0.588218 0.625921i
\(598\) 0.147477 + 0.510875i 0.00603078 + 0.0208912i
\(599\) 11.8294i 0.483336i 0.970359 + 0.241668i \(0.0776945\pi\)
−0.970359 + 0.241668i \(0.922305\pi\)
\(600\) −8.04290 + 7.55842i −0.328350 + 0.308571i
\(601\) 26.0000i 1.06056i −0.847822 0.530281i \(-0.822086\pi\)
0.847822 0.530281i \(-0.177914\pi\)
\(602\) 6.63325 2.08191i 0.270351 0.0848522i
\(603\) −17.9307 1.11469i −0.730195 0.0453938i
\(604\) 17.8178i 0.724998i
\(605\) 74.1902i 3.01626i
\(606\) −22.3030 + 20.9595i −0.905997 + 0.851423i
\(607\) 18.1168i 0.735340i 0.929956 + 0.367670i \(0.119844\pi\)
−0.929956 + 0.367670i \(0.880156\pi\)
\(608\) −2.37686 −0.0963944
\(609\) 9.49370 + 5.33933i 0.384704 + 0.216360i
\(610\) 26.1168 1.05744
\(611\) 10.3723 + 35.9306i 0.419618 + 1.45360i
\(612\) 0.147477 2.37228i 0.00596140 0.0958938i
\(613\) 16.8781i 0.681699i 0.940118 + 0.340850i \(0.110715\pi\)
−0.940118 + 0.340850i \(0.889285\pi\)
\(614\) −31.8766 −1.28644
\(615\) −35.6357 + 33.4891i −1.43697 + 1.35041i
\(616\) −14.5012 + 4.55134i −0.584271 + 0.183379i
\(617\) 17.6060 0.708790 0.354395 0.935096i \(-0.384687\pi\)
0.354395 + 0.935096i \(0.384687\pi\)
\(618\) −8.74456 9.30506i −0.351758 0.374305i
\(619\) −13.0641 −0.525091 −0.262546 0.964920i \(-0.584562\pi\)
−0.262546 + 0.964920i \(0.584562\pi\)
\(620\) 13.8564i 0.556487i
\(621\) 0.589907 0.489125i 0.0236722 0.0196279i
\(622\) −10.3923 −0.416693
\(623\) −7.92287 25.2434i −0.317423 1.01135i
\(624\) −3.18614 + 5.37108i −0.127548 + 0.215015i
\(625\) −16.2554 −0.650217
\(626\) 2.74456i 0.109695i
\(627\) −17.2337 + 16.1956i −0.688247 + 0.646790i
\(628\) 8.25544i 0.329428i
\(629\) 6.62772i 0.264264i
\(630\) −25.9865 + 6.41543i −1.03533 + 0.255597i
\(631\) 12.1793i 0.484849i −0.970170 0.242424i \(-0.922057\pi\)
0.970170 0.242424i \(-0.0779426\pi\)
\(632\) 3.62772 0.144303
\(633\) −21.9268 + 20.6060i −0.871510 + 0.819014i
\(634\) −3.86141 −0.153356
\(635\) 34.9783i 1.38807i
\(636\) 11.9769 + 12.7446i 0.474914 + 0.505355i
\(637\) 15.8997 19.6010i 0.629971 0.776619i
\(638\) 13.6540i 0.540568i
\(639\) 0.372281 5.98844i 0.0147272 0.236899i
\(640\) 3.37228i 0.133301i
\(641\) 8.86263i 0.350053i 0.984564 + 0.175026i \(0.0560011\pi\)
−0.984564 + 0.175026i \(0.943999\pi\)
\(642\) 20.1947 + 21.4891i 0.797021 + 0.848108i
\(643\) −18.4077 −0.725931 −0.362965 0.931803i \(-0.618236\pi\)
−0.362965 + 0.931803i \(0.618236\pi\)
\(644\) −0.116844 0.372281i −0.00460430 0.0146699i
\(645\) 10.5109 + 11.1846i 0.413865 + 0.440393i
\(646\) −1.88316 −0.0740918
\(647\) 26.1282 1.02721 0.513604 0.858028i \(-0.328310\pi\)
0.513604 + 0.858028i \(0.328310\pi\)
\(648\) 8.93070 + 1.11469i 0.350831 + 0.0437892i
\(649\) 15.7663i 0.618882i
\(650\) 22.0742 6.37228i 0.865823 0.249941i
\(651\) 9.23016 16.4119i 0.361759 0.643233i
\(652\) 8.21782i 0.321835i
\(653\) 14.6487i 0.573248i 0.958043 + 0.286624i \(0.0925330\pi\)
−0.958043 + 0.286624i \(0.907467\pi\)
\(654\) −23.3639 24.8614i −0.913599 0.972158i
\(655\) 13.3591i 0.521982i
\(656\) 8.37228i 0.326883i
\(657\) −1.90698 + 30.6753i −0.0743983 + 1.19676i
\(658\) −8.21782 26.1831i −0.320364 1.02073i
\(659\) 37.9200i 1.47715i 0.674170 + 0.738576i \(0.264501\pi\)
−0.674170 + 0.738576i \(0.735499\pi\)
\(660\) −22.9783 24.4511i −0.894427 0.951757i
\(661\) 42.2689 1.64407 0.822035 0.569436i \(-0.192838\pi\)
0.822035 + 0.569436i \(0.192838\pi\)
\(662\) 17.0805i 0.663851i
\(663\) −2.52434 + 4.25544i −0.0980372 + 0.165267i
\(664\) 6.74456i 0.261740i
\(665\) 6.35053 + 20.2337i 0.246263 + 0.784629i
\(666\) −25.0475 1.55712i −0.970573 0.0603373i
\(667\) −0.350532 −0.0135726
\(668\) 12.6277i 0.488581i
\(669\) 0.813859 0.764836i 0.0314656 0.0295703i
\(670\) −20.1947 −0.780189
\(671\) 44.4891i 1.71748i
\(672\) 2.24638 3.99422i 0.0866559 0.154080i
\(673\) −45.2337 −1.74363 −0.871815 0.489835i \(-0.837057\pi\)
−0.871815 + 0.489835i \(0.837057\pi\)
\(674\) −5.00000 −0.192593
\(675\) −21.1345 25.4891i −0.813466 0.981077i
\(676\) 11.0000 6.92820i 0.423077 0.266469i
\(677\) 20.5446 0.789592 0.394796 0.918769i \(-0.370815\pi\)
0.394796 + 0.918769i \(0.370815\pi\)
\(678\) −6.75327 7.18614i −0.259358 0.275982i
\(679\) −23.1168 + 7.25544i −0.887143 + 0.278438i
\(680\) 2.67181i 0.102459i
\(681\) −13.6277 14.5012i −0.522215 0.555688i
\(682\) 23.6039 0.903840
\(683\) 19.0000 0.727015 0.363507 0.931591i \(-0.381579\pi\)
0.363507 + 0.931591i \(0.381579\pi\)
\(684\) 0.442430 7.11684i 0.0169168 0.272119i
\(685\) 61.0951i 2.33432i
\(686\) −11.3321 + 14.6487i −0.432660 + 0.559290i
\(687\) −6.37228 + 5.98844i −0.243118 + 0.228473i
\(688\) −2.62772 −0.100181
\(689\) −10.0974 34.9783i −0.384678 1.33257i
\(690\) 0.627719 0.589907i 0.0238968 0.0224574i
\(691\) 31.1769 1.18603 0.593013 0.805193i \(-0.297938\pi\)
0.593013 + 0.805193i \(0.297938\pi\)
\(692\) −10.6873 −0.406269
\(693\) −10.9285 44.2670i −0.415138 1.68156i
\(694\) 19.2000i 0.728823i
\(695\) 17.7228 0.672265
\(696\) −2.81929 3.00000i −0.106865 0.113715i
\(697\) 6.63325i 0.251252i
\(698\) 16.4356 0.622098
\(699\) −12.7417 13.5584i −0.481936 0.512827i
\(700\) −16.0858 + 5.04868i −0.607986 + 0.190822i
\(701\) 13.2665i 0.501069i 0.968108 + 0.250534i \(0.0806063\pi\)
−0.968108 + 0.250534i \(0.919394\pi\)
\(702\) −15.4891 10.5398i −0.584599 0.397798i
\(703\) 19.8832i 0.749907i
\(704\) 5.74456 0.216506
\(705\) 44.1485 41.4891i 1.66273 1.56257i
\(706\) 11.1168i 0.418388i
\(707\) −44.6060 + 14.0000i −1.67758 + 0.526524i
\(708\) −3.25544 3.46410i −0.122347 0.130189i
\(709\) 33.7013i 1.26568i 0.774284 + 0.632839i \(0.218110\pi\)
−0.774284 + 0.632839i \(0.781890\pi\)
\(710\) 6.74456i 0.253119i
\(711\) −0.675266 + 10.8622i −0.0253245 + 0.407364i
\(712\) 10.0000i 0.374766i
\(713\) 0.605969i 0.0226937i
\(714\) 1.77978 3.16457i 0.0666064 0.118431i
\(715\) 19.3723 + 67.1076i 0.724482 + 2.50968i
\(716\) 20.1947i 0.754711i
\(717\) 22.7190 21.3505i 0.848458 0.797350i
\(718\) 6.23369 0.232639
\(719\) 16.4356 0.612946 0.306473 0.951879i \(-0.400851\pi\)
0.306473 + 0.951879i \(0.400851\pi\)
\(720\) 10.0974 + 0.627719i 0.376306 + 0.0233937i
\(721\) −5.84096 18.6101i −0.217529 0.693077i
\(722\) 13.3505 0.496855
\(723\) −20.7446 + 19.4950i −0.771499 + 0.725026i
\(724\) 20.3723i 0.757130i
\(725\) 15.1460i 0.562509i
\(726\) 27.7677 26.0951i 1.03056 0.968480i
\(727\) 1.13859i 0.0422281i 0.999777 + 0.0211140i \(0.00672131\pi\)
−0.999777 + 0.0211140i \(0.993279\pi\)
\(728\) −7.95228 + 5.26890i −0.294731 + 0.195278i
\(729\) −5.00000 + 26.5330i −0.185185 + 0.982704i
\(730\) 34.5484i 1.27870i
\(731\) −2.08191 −0.0770021
\(732\) −9.18614 9.77495i −0.339530 0.361292i
\(733\) 18.6101 0.687381 0.343690 0.939083i \(-0.388323\pi\)
0.343690 + 0.939083i \(0.388323\pi\)
\(734\) 4.74456i 0.175125i
\(735\) −40.0038 8.45109i −1.47556 0.311723i
\(736\) 0.147477i 0.00543607i
\(737\) 34.4010i 1.26718i
\(738\) 25.0684 + 1.55842i 0.922782 + 0.0573663i
\(739\) 44.8482i 1.64977i 0.565303 + 0.824883i \(0.308759\pi\)
−0.565303 + 0.824883i \(0.691241\pi\)
\(740\) −28.2101 −1.03703
\(741\) −7.57301 + 12.7663i −0.278202 + 0.468982i
\(742\) 8.00000 + 25.4891i 0.293689 + 0.935735i
\(743\) −0.978251 −0.0358885 −0.0179443 0.999839i \(-0.505712\pi\)
−0.0179443 + 0.999839i \(0.505712\pi\)
\(744\) −5.18614 + 4.87375i −0.190133 + 0.178680i
\(745\) 25.7228i 0.942411i
\(746\) 12.2337 0.447907
\(747\) 20.1947 + 1.25544i 0.738886 + 0.0459341i
\(748\) 4.55134 0.166414
\(749\) 13.4891 + 42.9783i 0.492882 + 1.57039i
\(750\) −5.48913 5.84096i −0.200435 0.213282i
\(751\) 18.6060 0.678941 0.339471 0.940617i \(-0.389752\pi\)
0.339471 + 0.940617i \(0.389752\pi\)
\(752\) 10.3723i 0.378238i
\(753\) 8.55842 8.04290i 0.311886 0.293099i
\(754\) 2.37686 + 8.23369i 0.0865602 + 0.299853i
\(755\) −60.0868 −2.18678
\(756\) 11.5414 + 7.46963i 0.419758 + 0.271668i
\(757\) 50.4674 1.83427 0.917134 0.398579i \(-0.130497\pi\)
0.917134 + 0.398579i \(0.130497\pi\)
\(758\) 18.3152i 0.665237i
\(759\) 1.00489 + 1.06930i 0.0364751 + 0.0388130i
\(760\) 8.01544i 0.290751i
\(761\) 2.13859i 0.0775239i 0.999248 + 0.0387620i \(0.0123414\pi\)
−0.999248 + 0.0387620i \(0.987659\pi\)
\(762\) −13.0916 + 12.3030i −0.474258 + 0.445690i
\(763\) −15.6060 49.7228i −0.564974 1.80009i
\(764\) 2.96677i 0.107334i
\(765\) 8.00000 + 0.497333i 0.289241 + 0.0179811i
\(766\) 3.51087i 0.126853i
\(767\) 2.74456 + 9.50744i 0.0991004 + 0.343294i
\(768\) −1.26217 + 1.18614i −0.0455446 + 0.0428012i
\(769\) −34.1986 −1.23323 −0.616616 0.787264i \(-0.711497\pi\)
−0.616616 + 0.787264i \(0.711497\pi\)
\(770\) −15.3484 48.9022i −0.553118 1.76231i
\(771\) 23.8614 22.4241i 0.859348 0.807584i
\(772\) 20.7846i 0.748054i
\(773\) 18.8614i 0.678398i 0.940715 + 0.339199i \(0.110156\pi\)
−0.940715 + 0.339199i \(0.889844\pi\)
\(774\) 0.489125 7.86797i 0.0175812 0.282808i
\(775\) 26.1831 0.940526
\(776\) 9.15759 0.328738
\(777\) −33.4128 18.7916i −1.19868 0.674146i
\(778\) 25.2434i 0.905019i
\(779\) 19.8997i 0.712982i