Properties

Label 546.2.e.g.545.7
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: \(x^{8} + 5 x^{6} + 16 x^{4} + 45 x^{2} + 81\)
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 545.7
Root \(1.26217 - 1.18614i\) of defining polynomial
Character \(\chi\) \(=\) 546.545
Dual form 546.2.e.g.545.8

$q$-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} +(4.12590 - 1.99422i) 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} +(5.55842 - 2.84674i) q^{39} +3.37228i q^{40} -8.37228i q^{41} +(4.12590 - 1.99422i) 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} +(2.84216 - 7.41095i) 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} +(5.55842 - 2.84674i) q^{78} -3.62772 q^{79} +3.37228i q^{80} +(-8.93070 - 1.11469i) q^{81} -8.37228i q^{82} +6.74456i q^{83} +(4.12590 - 1.99422i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 10q^{9} + O(q^{10}) \) \( 8q + 8q^{2} + 8q^{4} + 8q^{8} - 10q^{9} + 32q^{15} + 8q^{16} - 10q^{18} + 14q^{21} - 28q^{25} + 32q^{30} + 8q^{32} - 10q^{36} + 10q^{39} + 14q^{42} - 44q^{43} - 28q^{50} - 8q^{51} + 24q^{57} + 32q^{60} - 4q^{63} + 8q^{64} - 4q^{65} - 16q^{71} - 10q^{72} + 10q^{78} - 52q^{79} - 14q^{81} + 14q^{84} - 44q^{86} + 24q^{91} - 30q^{93} - 66q^{99} + O(q^{100}) \)

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 \(-0.833333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 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 \(-0.530630\pi\)
−0.0960789 + 0.995374i \(0.530630\pi\)
\(18\) 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
\(21\) 4.12590 1.99422i 0.900346 0.435174i
\(22\) −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 \(-0.758654\pi\)
0.726067 0.687623i \(-0.241346\pi\)
\(38\) 2.37686 0.385578
\(39\) 5.55842 2.84674i 0.890060 0.455844i
\(40\) 3.37228i 0.533204i
\(41\) 8.37228i 1.30753i −0.756697 0.653765i \(-0.773188\pi\)
0.756697 0.653765i \(-0.226812\pi\)
\(42\) 4.12590 1.99422i 0.636641 0.307715i
\(43\) −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 \(-0.834877\pi\)
0.868440 0.495795i \(-0.165123\pi\)
\(62\) −4.10891 −0.521832
\(63\) 2.84216 7.41095i 0.358079 0.933691i
\(64\) 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 \(0.119205\pi\)
−0.930693 + 0.365802i \(0.880795\pi\)
\(68\) −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 \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 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
\(78\) 5.55842 2.84674i 0.629367 0.322330i
\(79\) −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 \(0.879304\pi\)
\(84\) 4.12590 1.99422i 0.450173 0.217587i
\(85\) 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 \(-0.158122\pi\)
0.879133 + 0.476576i \(0.158122\pi\)
\(102\) −1.00000 + 0.939764i −0.0990148 + 0.0930505i
\(103\) 7.37228i 0.726412i 0.931709 + 0.363206i \(0.118318\pi\)
−0.931709 + 0.363206i \(0.881682\pi\)
\(104\) 3.46410 + 1.00000i 0.339683 + 0.0980581i
\(105\) 6.72507 + 13.9137i 0.656300 + 1.35784i
\(106\) 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 \(0.392328\pi\)
−0.331848 + 0.943333i \(0.607672\pi\)
\(110\) 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
\(117\) 3.63903 10.1861i 0.336428 0.941709i
\(118\) 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
\(126\) 2.84216 7.41095i 0.253200 0.660219i
\(127\) −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 \(-0.444636\pi\)
0.173056 + 0.984912i \(0.444636\pi\)
\(132\) −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 \(-0.781703\pi\)
−0.773913 + 0.633292i \(0.781703\pi\)
\(138\) −0.174928 0.186141i −0.0148909 0.0158453i
\(139\) 5.25544i 0.445760i 0.974846 + 0.222880i \(0.0715459\pi\)
−0.974846 + 0.222880i \(0.928454\pi\)
\(140\) −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
\(147\) 11.9952 1.76518i 0.989345 0.145590i
\(148\) 8.36530i 0.687623i
\(149\) −7.62772 −0.624887 −0.312444 0.949936i \(-0.601148\pi\)
−0.312444 + 0.949936i \(0.601148\pi\)
\(150\) −8.04290 + 7.55842i −0.656700 + 0.617143i
\(151\) 17.8178i 1.45000i −0.688751 0.724998i \(-0.741841\pi\)
0.688751 0.724998i \(-0.258159\pi\)
\(152\) 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
\(156\) 5.55842 2.84674i 0.445030 0.227922i
\(157\) 8.25544i 0.658856i 0.944181 + 0.329428i \(0.106856\pi\)
−0.944181 + 0.329428i \(0.893144\pi\)
\(158\) −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 \(-0.895700\pi\)
0.946796 0.321835i \(-0.104300\pi\)
\(164\) 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 \(0.837515\pi\)
\(168\) 4.12590 1.99422i 0.318320 0.153857i
\(169\) 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 \(-0.366830\pi\)
0.406269 + 0.913754i \(0.366830\pi\)
\(174\) −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 \(0.273399\pi\)
−0.653264 + 0.757130i \(0.726601\pi\)
\(182\) 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
\(189\) −5.20313 12.7251i −0.378472 0.925613i
\(190\) 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 \(-0.730988\pi\)
0.663637 0.748054i \(-0.269012\pi\)
\(194\) −9.15759 −0.657476
\(195\) 9.60002 + 18.7446i 0.687472 + 1.34233i
\(196\) 5.74456 + 4.00000i 0.410326 + 0.285714i
\(197\) 21.1168 1.50451 0.752256 0.658870i \(-0.228965\pi\)
0.752256 + 0.658870i \(0.228965\pi\)
\(198\) −1.06930 + 17.2005i −0.0759916 + 1.22239i
\(199\) 12.1168i 0.858940i −0.903081 0.429470i \(-0.858700\pi\)
0.903081 0.429470i \(-0.141300\pi\)
\(200\) −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
\(210\) 6.72507 + 13.9137i 0.464074 + 0.960137i
\(211\) 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
\(231\) −23.7015 + 11.4559i −1.55945 + 0.753744i
\(232\) 2.37686i 0.156049i
\(233\) 10.7422i 0.703742i 0.936048 + 0.351871i \(0.114454\pi\)
−0.936048 + 0.351871i \(0.885546\pi\)
\(234\) 3.63903 10.1861i 0.237891 0.665889i
\(235\) −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 \(-0.302207\pi\)
0.582162 + 0.813073i \(0.302207\pi\)
\(240\) 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 \(-0.431351\pi\)
0.213998 + 0.976834i \(0.431351\pi\)
\(252\) 2.84216 7.41095i 0.179039 0.466846i
\(253\) 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 \(-0.299272\pi\)
0.589633 + 0.807671i \(0.299272\pi\)
\(258\) −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 \(-0.645758\pi\)
−0.442077 + 0.896977i \(0.645758\pi\)
\(270\) 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
\(273\) 16.2868 2.78228i 0.985720 0.168391i
\(274\) −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 \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 12.3030 + 13.0916i 0.732632 + 0.779592i
\(283\) 0.372281i 0.0221298i 0.999939 + 0.0110649i \(0.00352214\pi\)
−0.999939 + 0.0110649i \(0.996478\pi\)
\(284\) −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 \(-0.108939\pi\)
\(294\) 11.9952 1.76518i 0.699573 0.102948i
\(295\) −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 \(-0.595202\pi\)
−0.294647 + 0.955606i \(0.595202\pi\)
\(312\) 5.55842 2.84674i 0.314684 0.161165i
\(313\) 2.74456i 0.155132i −0.996987 0.0775659i \(-0.975285\pi\)
0.996987 0.0775659i \(-0.0247148\pi\)
\(314\) 8.25544i 0.465881i
\(315\) 24.9918 + 9.58457i 1.40813 + 0.540030i
\(316\) −3.62772 −0.204075
\(317\) −3.86141 −0.216878 −0.108439 0.994103i \(-0.534585\pi\)
−0.108439 + 0.994103i \(0.534585\pi\)
\(318\) −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 \(0.155535\pi\)
−0.882979 + 0.469413i \(0.844465\pi\)
\(332\) 6.74456i 0.370156i
\(333\) −25.0475 1.55712i −1.37260 0.0853298i
\(334\) 12.6277i 0.690958i
\(335\) −20.1947 −1.10335
\(336\) 4.12590 1.99422i 0.225087 0.108794i
\(337\) 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
\(351\) −7.48913 17.1730i −0.399740 0.916629i
\(352\) −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
\(357\) −3.26890 + 1.57999i −0.173009 + 0.0836222i
\(358\) 20.1947i 1.06732i
\(359\) 6.23369 0.329001 0.164501 0.986377i \(-0.447399\pi\)
0.164501 + 0.986377i \(0.447399\pi\)
\(360\) 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 \(0.0395184\pi\)
−0.992303 + 0.123832i \(0.960482\pi\)
\(368\) 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
\(378\) −5.20313 12.7251i −0.267620 0.654507i
\(379\) 18.3152i 0.940787i 0.882457 + 0.470394i \(0.155888\pi\)
−0.882457 + 0.470394i \(0.844112\pi\)
\(380\) 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 \(0.778957\pi\)
\(390\) 9.60002 + 18.7446i 0.486116 + 0.949168i
\(391\) 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
\(399\) 9.80670 4.73998i 0.490949 0.237296i
\(400\) −6.37228 −0.318614
\(401\) 28.9783 1.44710 0.723552 0.690269i \(-0.242508\pi\)
0.723552 + 0.690269i \(0.242508\pi\)
\(402\) 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 \(-0.538200\pi\)
−0.119720 + 0.992808i \(0.538200\pi\)
\(420\) 6.72507 + 13.9137i 0.328150 + 0.678920i
\(421\) 23.0140i 1.12163i −0.827940 0.560817i \(-0.810487\pi\)
0.827940 0.560817i \(-0.189513\pi\)
\(422\) 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
\(429\) −31.9307 + 16.3533i −1.54163 + 0.789544i
\(430\) 8.86141i 0.427335i
\(431\) −28.2337 −1.35997 −0.679984 0.733227i \(-0.738013\pi\)
−0.679984 + 0.733227i \(0.738013\pi\)
\(432\) −3.31662 4.00000i −0.159571 0.192450i
\(433\) 30.4674i 1.46417i 0.681214 + 0.732084i \(0.261452\pi\)
−0.681214 + 0.732084i \(0.738548\pi\)
\(434\) −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 \(0.0427113\pi\)
−0.991011 + 0.133779i \(0.957289\pi\)
\(440\) 19.3723i 0.923537i
\(441\) 13.0462 16.4559i 0.621246 0.783615i
\(442\) −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 \(-0.391903\pi\)
0.333108 + 0.942889i \(0.391903\pi\)
\(450\) −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 \(0.186653\pi\)
−0.832945 + 0.553356i \(0.813347\pi\)
\(458\) 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 \(0.832176\pi\)
\(462\) −23.7015 + 11.4559i −1.10269 + 0.532978i
\(463\) 31.6742i 1.47203i 0.676967 + 0.736014i \(0.263294\pi\)
−0.676967 + 0.736014i \(0.736706\pi\)
\(464\) 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 \(-0.333616\pi\)
0.499230 + 0.866470i \(0.333616\pi\)
\(468\) 3.63903 10.1861i 0.168214 0.470855i
\(469\) −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
\(483\) −0.294101 0.608475i −0.0133821 0.0276866i
\(484\) 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 \(-0.676609\pi\)
0.526802 0.849988i \(-0.323391\pi\)
\(488\) 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 \(0.0751294\pi\)
−0.972275 + 0.233841i \(0.924871\pi\)
\(500\) 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 \(-0.709333\pi\)
−0.611251 + 0.791437i \(0.709333\pi\)
\(504\) 2.84216 7.41095i 0.126600 0.330110i
\(505\) 59.5894i 2.65170i
\(506\) 0.847190i 0.0376622i
\(507\) 22.1017 4.30298i 0.981570 0.191102i
\(508\) −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 \(-0.352561\pi\)
0.446806 + 0.894631i \(0.352561\pi\)
\(522\) −7.11684 0.442430i −0.311496 0.0193647i
\(523\) 37.3505i 1.63322i 0.577186 + 0.816612i \(0.304151\pi\)
−0.577186 + 0.816612i \(0.695849\pi\)
\(524\) 3.96143 0.173056
\(525\) −26.2914 + 12.7077i −1.14745 + 0.554611i
\(526\) 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 \(-0.823834\pi\)
0.850721 0.525617i \(-0.176166\pi\)
\(542\) −11.3321 −0.486754
\(543\) 24.1644 + 25.7133i 1.03699 + 1.10346i
\(544\) −0.792287 −0.0339690
\(545\) −66.4251 −2.84534
\(546\) 16.2868 2.78228i 0.697009 0.119070i
\(547\) −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 \(-0.277499\pi\)
0.643457 + 0.765482i \(0.277499\pi\)
\(558\) −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 \(-0.437554\pi\)
0.194924 + 0.980818i \(0.437554\pi\)
\(564\) 12.3030 + 13.0916i 0.518049 + 0.551255i
\(565\) 19.2000 0.807752
\(566\) 0.372281i 0.0156482i
\(567\) −21.6610 9.88954i −0.909675 0.415322i
\(568\) −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
\(585\) 34.3505 + 12.2718i 1.42022 + 0.507378i
\(586\) 11.4891i 0.474611i
\(587\) 16.7446i 0.691122i 0.938396 + 0.345561i \(0.112311\pi\)
−0.938396 + 0.345561i \(0.887689\pi\)
\(588\) 11.9952 1.76518i 0.494673 0.0727950i
\(589\) −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 \(0.177914\pi\)
−0.847822 + 0.530281i \(0.822086\pi\)
\(602\) −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 \(-0.880156\pi\)
0.929956 0.367670i \(-0.119844\pi\)
\(608\) 2.37686 0.0963944
\(609\) −4.73998 9.80670i −0.192074 0.397388i
\(610\) 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 \(-0.889285\pi\)
0.940118 0.340850i \(-0.110715\pi\)
\(614\) 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 \(-0.615313\pi\)
−0.354395 + 0.935096i \(0.615313\pi\)
\(618\) 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
\(624\) 5.55842 2.84674i 0.222515 0.113961i
\(625\) −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
\(630\) 24.9918 + 9.58457i 0.995697 + 0.381859i
\(631\) 12.1793i 0.484849i 0.970170 + 0.242424i \(0.0779426\pi\)
−0.970170 + 0.242424i \(0.922057\pi\)
\(632\) −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 \(-0.671690\pi\)
−0.513604 + 0.858028i \(0.671690\pi\)
\(648\) −8.93070 1.11469i −0.350831 0.0437892i
\(649\) 15.7663i 0.618882i
\(650\) −22.0742 6.37228i −0.865823 0.249941i
\(651\) −16.9530 + 8.19407i −0.664440 + 0.321151i
\(652\) 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
\(663\) −4.40387 + 2.25544i −0.171032 + 0.0875939i
\(664\) 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
\(672\) 4.12590 1.99422i 0.159160 0.0769287i
\(673\) −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 \(-0.629185\pi\)
−0.394796 + 0.918769i \(0.629185\pi\)
\(678\) −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 \(-0.618421\pi\)
−0.363507 + 0.931591i \(0.618421\pi\)
\(684\) 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
\(693\) −16.3270 + 42.5726i −0.620211 + 1.61720i
\(694\) 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 \(0.919394\pi\)
\(702\) −7.48913 17.1730i −0.282659 0.648154i
\(703\) 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 \(-0.781890\pi\)
0.774284 0.632839i \(-0.218110\pi\)
\(710\) 6.74456i 0.253119i
\(711\) −0.675266 + 10.8622i −0.0253245 + 0.407364i
\(712\) 10.0000i 0.374766i
\(713\) 0.605969i 0.0226937i
\(714\) −3.26890 + 1.57999i −0.122336 + 0.0591298i
\(715\) 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 \(-0.599149\pi\)
−0.306473 + 0.951879i \(0.599149\pi\)
\(720\) 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 \(-0.993279\pi\)
0.999777 0.0211140i \(-0.00672131\pi\)
\(728\) 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
\(735\) 5.95270 + 40.4511i 0.219569 + 1.49206i
\(736\) 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 \(-0.691241\pi\)
0.565303 0.824883i \(-0.308759\pi\)
\(740\) 28.2101 1.03703
\(741\) 13.2116 6.76631i 0.485340 0.248567i
\(742\) 8.00000 25.4891i 0.293689 0.935735i
\(743\) 0.978251 0.0358885 0.0179443 0.999839i \(-0.494288\pi\)
0.0179443 + 0.999839i \(0.494288\pi\)
\(744\) −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
\(756\) −5.20313 12.7251i −0.189236 0.462806i
\(757\) 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
\(777\) −16.6822 34.5144i −0.598472 1.23820i
\(778\) 25.2434i 0.905019i
\(779\) 19.8997i 0.712982i
\(780\) 9.60002 + 18.7446i 0.343736 + 0.671163i
\(781\) 11.4891 0.411113