Properties

Label 1110.2.bb.d.1099.1
Level $1110$
Weight $2$
Character 1110.1099
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1099.1
Character \(\chi\) \(=\) 1110.1099
Dual form 1110.2.bb.d.1009.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.00835632 - 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 + 2.13657i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.00835632 - 2.23605i) q^{5} +1.00000 q^{6} +(3.70065 + 2.13657i) q^{7} +1.00000i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.12526 + 1.93230i) q^{10} -5.93869 q^{11} +(-0.866025 + 0.500000i) q^{12} +(-1.08299 - 0.625263i) q^{13} -4.27314 q^{14} +(-1.11079 + 1.94066i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-6.29873 + 3.63657i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(2.05756 - 3.56380i) q^{19} +(-1.94066 - 1.11079i) q^{20} +(-2.13657 - 3.70065i) q^{21} +(5.14305 - 2.96934i) q^{22} +6.89816i q^{23} +(0.500000 - 0.866025i) q^{24} +(-4.99986 + 0.0373703i) q^{25} +1.25053 q^{26} -1.00000i q^{27} +(3.70065 - 2.13657i) q^{28} +3.27314 q^{29} +(-0.00835632 - 2.23605i) q^{30} -2.68816 q^{31} +(0.866025 + 0.500000i) q^{32} +(5.14305 + 2.96934i) q^{33} +(3.63657 - 6.29873i) q^{34} +(4.74656 - 8.29270i) q^{35} +1.00000 q^{36} +(-3.08237 + 5.24395i) q^{37} +4.11513i q^{38} +(0.625263 + 1.08299i) q^{39} +(2.23605 - 0.00835632i) q^{40} +(-1.33327 + 2.30929i) q^{41} +(3.70065 + 2.13657i) q^{42} -9.04279i q^{43} +(-2.96934 + 5.14305i) q^{44} +(1.93230 - 1.12526i) q^{45} +(-3.44908 - 5.97399i) q^{46} -4.62329i q^{47} +1.00000i q^{48} +(5.62987 + 9.75123i) q^{49} +(4.31132 - 2.53229i) q^{50} +7.27314 q^{51} +(-1.08299 + 0.625263i) q^{52} +(-1.31601 + 0.759799i) q^{53} +(0.500000 + 0.866025i) q^{54} +(0.0496256 + 13.2792i) q^{55} +(-2.13657 + 3.70065i) q^{56} +(-3.56380 + 2.05756i) q^{57} +(-2.83462 + 1.63657i) q^{58} +(-0.0555279 - 0.0961772i) q^{59} +(1.12526 + 1.93230i) q^{60} +(-6.14118 + 10.6368i) q^{61} +(2.32802 - 1.34408i) q^{62} +4.27314i q^{63} -1.00000 q^{64} +(-1.38907 + 2.42684i) q^{65} -5.93869 q^{66} +(-4.44547 - 2.56660i) q^{67} +7.27314i q^{68} +(3.44908 - 5.97399i) q^{69} +(0.0357078 + 9.55497i) q^{70} +(-3.59953 + 6.23456i) q^{71} +(-0.866025 + 0.500000i) q^{72} +3.36158i q^{73} +(0.0474386 - 6.08258i) q^{74} +(4.34869 + 2.46757i) q^{75} +(-2.05756 - 3.56380i) q^{76} +(-21.9770 - 12.6884i) q^{77} +(-1.08299 - 0.625263i) q^{78} +(-3.41867 + 5.92130i) q^{79} +(-1.93230 + 1.12526i) q^{80} +(-0.500000 + 0.866025i) q^{81} -2.66654i q^{82} +(-6.46021 + 3.72981i) q^{83} -4.27314 q^{84} +(8.18420 + 14.0539i) q^{85} +(4.52139 + 7.83128i) q^{86} +(-2.83462 - 1.63657i) q^{87} -5.93869i q^{88} +(4.39703 + 7.61589i) q^{89} +(-1.11079 + 1.94066i) q^{90} +(-2.67184 - 4.62776i) q^{91} +(5.97399 + 3.44908i) q^{92} +(2.32802 + 1.34408i) q^{93} +(2.31165 + 4.00389i) q^{94} +(-7.98605 - 4.57104i) q^{95} +(-0.500000 - 0.866025i) q^{96} +12.1077i q^{97} +(-9.75123 - 5.62987i) q^{98} +(-2.96934 - 5.14305i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + O(q^{10}) \) \( 28q + 14q^{4} + 2q^{5} + 28q^{6} + 14q^{9} + 4q^{10} - 12q^{11} + 8q^{14} + 2q^{15} - 14q^{16} - 20q^{19} - 2q^{20} + 4q^{21} + 14q^{24} - 8q^{25} - 20q^{26} - 36q^{29} + 2q^{30} + 24q^{31} + 38q^{34} - 2q^{35} + 28q^{36} - 10q^{39} + 2q^{40} - 6q^{44} + 4q^{45} + 8q^{46} + 50q^{49} - 4q^{50} + 76q^{51} + 14q^{54} - 28q^{55} + 4q^{56} - 26q^{59} + 4q^{60} - 28q^{61} - 28q^{64} + 60q^{65} - 12q^{66} - 8q^{69} - 10q^{70} - 64q^{71} + 24q^{74} - 8q^{75} + 20q^{76} + 32q^{79} - 4q^{80} - 14q^{81} + 8q^{84} + 16q^{85} - 8q^{86} + 76q^{89} + 2q^{90} - 8q^{91} - 38q^{94} - 70q^{95} - 14q^{96} - 6q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −0.866025 0.500000i −0.500000 0.288675i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −0.00835632 2.23605i −0.00373706 0.999993i
\(6\) 1.00000 0.408248
\(7\) 3.70065 + 2.13657i 1.39871 + 0.807548i 0.994258 0.107009i \(-0.0341275\pi\)
0.404456 + 0.914557i \(0.367461\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 1.12526 + 1.93230i 0.355839 + 0.611047i
\(11\) −5.93869 −1.79058 −0.895291 0.445482i \(-0.853032\pi\)
−0.895291 + 0.445482i \(0.853032\pi\)
\(12\) −0.866025 + 0.500000i −0.250000 + 0.144338i
\(13\) −1.08299 0.625263i −0.300367 0.173417i 0.342241 0.939612i \(-0.388814\pi\)
−0.642608 + 0.766195i \(0.722147\pi\)
\(14\) −4.27314 −1.14205
\(15\) −1.11079 + 1.94066i −0.286805 + 0.501075i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −6.29873 + 3.63657i −1.52767 + 0.881998i −0.528206 + 0.849116i \(0.677135\pi\)
−0.999459 + 0.0328820i \(0.989531\pi\)
\(18\) −0.866025 0.500000i −0.204124 0.117851i
\(19\) 2.05756 3.56380i 0.472037 0.817593i −0.527451 0.849586i \(-0.676852\pi\)
0.999488 + 0.0319930i \(0.0101854\pi\)
\(20\) −1.94066 1.11079i −0.433944 0.248380i
\(21\) −2.13657 3.70065i −0.466238 0.807548i
\(22\) 5.14305 2.96934i 1.09650 0.633066i
\(23\) 6.89816i 1.43837i 0.694820 + 0.719183i \(0.255484\pi\)
−0.694820 + 0.719183i \(0.744516\pi\)
\(24\) 0.500000 0.866025i 0.102062 0.176777i
\(25\) −4.99986 + 0.0373703i −0.999972 + 0.00747407i
\(26\) 1.25053 0.245248
\(27\) 1.00000i 0.192450i
\(28\) 3.70065 2.13657i 0.699357 0.403774i
\(29\) 3.27314 0.607807 0.303904 0.952703i \(-0.401710\pi\)
0.303904 + 0.952703i \(0.401710\pi\)
\(30\) −0.00835632 2.23605i −0.00152565 0.408245i
\(31\) −2.68816 −0.482808 −0.241404 0.970425i \(-0.577608\pi\)
−0.241404 + 0.970425i \(0.577608\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 5.14305 + 2.96934i 0.895291 + 0.516896i
\(34\) 3.63657 6.29873i 0.623667 1.08022i
\(35\) 4.74656 8.29270i 0.802315 1.40172i
\(36\) 1.00000 0.166667
\(37\) −3.08237 + 5.24395i −0.506739 + 0.862100i
\(38\) 4.11513i 0.667562i
\(39\) 0.625263 + 1.08299i 0.100122 + 0.173417i
\(40\) 2.23605 0.00835632i 0.353551 0.00132125i
\(41\) −1.33327 + 2.30929i −0.208222 + 0.360651i −0.951154 0.308715i \(-0.900101\pi\)
0.742933 + 0.669366i \(0.233434\pi\)
\(42\) 3.70065 + 2.13657i 0.571023 + 0.329680i
\(43\) 9.04279i 1.37901i −0.724280 0.689506i \(-0.757828\pi\)
0.724280 0.689506i \(-0.242172\pi\)
\(44\) −2.96934 + 5.14305i −0.447645 + 0.775345i
\(45\) 1.93230 1.12526i 0.288050 0.167744i
\(46\) −3.44908 5.97399i −0.508539 0.880816i
\(47\) 4.62329i 0.674377i −0.941437 0.337188i \(-0.890524\pi\)
0.941437 0.337188i \(-0.109476\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 5.62987 + 9.75123i 0.804268 + 1.39303i
\(50\) 4.31132 2.53229i 0.609713 0.358120i
\(51\) 7.27314 1.01844
\(52\) −1.08299 + 0.625263i −0.150183 + 0.0867084i
\(53\) −1.31601 + 0.759799i −0.180768 + 0.104366i −0.587653 0.809113i \(-0.699948\pi\)
0.406885 + 0.913479i \(0.366615\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) 0.0496256 + 13.2792i 0.00669151 + 1.79057i
\(56\) −2.13657 + 3.70065i −0.285511 + 0.494520i
\(57\) −3.56380 + 2.05756i −0.472037 + 0.272531i
\(58\) −2.83462 + 1.63657i −0.372204 + 0.214892i
\(59\) −0.0555279 0.0961772i −0.00722912 0.0125212i 0.862388 0.506248i \(-0.168968\pi\)
−0.869617 + 0.493726i \(0.835634\pi\)
\(60\) 1.12526 + 1.93230i 0.145271 + 0.249459i
\(61\) −6.14118 + 10.6368i −0.786298 + 1.36191i 0.141923 + 0.989878i \(0.454671\pi\)
−0.928221 + 0.372030i \(0.878662\pi\)
\(62\) 2.32802 1.34408i 0.295658 0.170698i
\(63\) 4.27314i 0.538365i
\(64\) −1.00000 −0.125000
\(65\) −1.38907 + 2.42684i −0.172293 + 0.301013i
\(66\) −5.93869 −0.731002
\(67\) −4.44547 2.56660i −0.543101 0.313560i 0.203234 0.979130i \(-0.434855\pi\)
−0.746335 + 0.665571i \(0.768188\pi\)
\(68\) 7.27314i 0.881998i
\(69\) 3.44908 5.97399i 0.415221 0.719183i
\(70\) 0.0357078 + 9.55497i 0.00426789 + 1.14204i
\(71\) −3.59953 + 6.23456i −0.427185 + 0.739907i −0.996622 0.0821287i \(-0.973828\pi\)
0.569436 + 0.822035i \(0.307161\pi\)
\(72\) −0.866025 + 0.500000i −0.102062 + 0.0589256i
\(73\) 3.36158i 0.393443i 0.980459 + 0.196722i \(0.0630295\pi\)
−0.980459 + 0.196722i \(0.936970\pi\)
\(74\) 0.0474386 6.08258i 0.00551462 0.707085i
\(75\) 4.34869 + 2.46757i 0.502144 + 0.284930i
\(76\) −2.05756 3.56380i −0.236019 0.408796i
\(77\) −21.9770 12.6884i −2.50451 1.44598i
\(78\) −1.08299 0.625263i −0.122624 0.0707971i
\(79\) −3.41867 + 5.92130i −0.384630 + 0.666199i −0.991718 0.128436i \(-0.959004\pi\)
0.607088 + 0.794635i \(0.292338\pi\)
\(80\) −1.93230 + 1.12526i −0.216038 + 0.125808i
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 2.66654i 0.294470i
\(83\) −6.46021 + 3.72981i −0.709101 + 0.409399i −0.810728 0.585423i \(-0.800928\pi\)
0.101627 + 0.994823i \(0.467595\pi\)
\(84\) −4.27314 −0.466238
\(85\) 8.18420 + 14.0539i 0.887701 + 1.52436i
\(86\) 4.52139 + 7.83128i 0.487554 + 0.844469i
\(87\) −2.83462 1.63657i −0.303904 0.175459i
\(88\) 5.93869i 0.633066i
\(89\) 4.39703 + 7.61589i 0.466085 + 0.807282i 0.999250 0.0387290i \(-0.0123309\pi\)
−0.533165 + 0.846011i \(0.678998\pi\)
\(90\) −1.11079 + 1.94066i −0.117087 + 0.204563i
\(91\) −2.67184 4.62776i −0.280085 0.485121i
\(92\) 5.97399 + 3.44908i 0.622831 + 0.359592i
\(93\) 2.32802 + 1.34408i 0.241404 + 0.139375i
\(94\) 2.31165 + 4.00389i 0.238428 + 0.412970i
\(95\) −7.98605 4.57104i −0.819351 0.468979i
\(96\) −0.500000 0.866025i −0.0510310 0.0883883i
\(97\) 12.1077i 1.22935i 0.788782 + 0.614673i \(0.210712\pi\)
−0.788782 + 0.614673i \(0.789288\pi\)
\(98\) −9.75123 5.62987i −0.985023 0.568703i
\(99\) −2.96934 5.14305i −0.298430 0.516896i
\(100\) −2.46757 + 4.34869i −0.246757 + 0.434869i
\(101\) −7.20776 −0.717199 −0.358599 0.933492i \(-0.616746\pi\)
−0.358599 + 0.933492i \(0.616746\pi\)
\(102\) −6.29873 + 3.63657i −0.623667 + 0.360074i
\(103\) 3.19806i 0.315114i −0.987510 0.157557i \(-0.949638\pi\)
0.987510 0.157557i \(-0.0503618\pi\)
\(104\) 0.625263 1.08299i 0.0613121 0.106196i
\(105\) −8.25699 + 4.80841i −0.805800 + 0.469253i
\(106\) 0.759799 1.31601i 0.0737982 0.127822i
\(107\) −6.68208 3.85790i −0.645981 0.372957i 0.140934 0.990019i \(-0.454990\pi\)
−0.786915 + 0.617062i \(0.788323\pi\)
\(108\) −0.866025 0.500000i −0.0833333 0.0481125i
\(109\) −3.85417 6.67561i −0.369162 0.639408i 0.620273 0.784386i \(-0.287022\pi\)
−0.989435 + 0.144979i \(0.953689\pi\)
\(110\) −6.68259 11.4753i −0.637160 1.09413i
\(111\) 5.29139 3.00021i 0.502236 0.284767i
\(112\) 4.27314i 0.403774i
\(113\) 13.4168 7.74618i 1.26214 0.728700i 0.288656 0.957433i \(-0.406792\pi\)
0.973489 + 0.228733i \(0.0734584\pi\)
\(114\) 2.05756 3.56380i 0.192708 0.333781i
\(115\) 15.4247 0.0576433i 1.43836 0.00537526i
\(116\) 1.63657 2.83462i 0.151952 0.263188i
\(117\) 1.25053i 0.115611i
\(118\) 0.0961772 + 0.0555279i 0.00885383 + 0.00511176i
\(119\) −31.0792 −2.84902
\(120\) −1.94066 1.11079i −0.177157 0.101401i
\(121\) 24.2680 2.20618
\(122\) 12.2824i 1.11199i
\(123\) 2.30929 1.33327i 0.208222 0.120217i
\(124\) −1.34408 + 2.32802i −0.120702 + 0.209062i
\(125\) 0.125342 + 11.1796i 0.0112110 + 0.999937i
\(126\) −2.13657 3.70065i −0.190341 0.329680i
\(127\) −13.1682 + 7.60268i −1.16849 + 0.674628i −0.953324 0.301949i \(-0.902363\pi\)
−0.215167 + 0.976577i \(0.569029\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −4.52139 + 7.83128i −0.398086 + 0.689506i
\(130\) −0.0104498 2.79624i −0.000916508 0.245247i
\(131\) 8.24808 + 14.2861i 0.720638 + 1.24818i 0.960744 + 0.277435i \(0.0894844\pi\)
−0.240106 + 0.970747i \(0.577182\pi\)
\(132\) 5.14305 2.96934i 0.447645 0.258448i
\(133\) 15.2286 8.79226i 1.32049 0.762386i
\(134\) 5.13319 0.443440
\(135\) −2.23605 + 0.00835632i −0.192449 + 0.000719198i
\(136\) −3.63657 6.29873i −0.311833 0.540111i
\(137\) 23.0633i 1.97043i −0.171327 0.985214i \(-0.554806\pi\)
0.171327 0.985214i \(-0.445194\pi\)
\(138\) 6.89816i 0.587211i
\(139\) −4.48645 7.77075i −0.380535 0.659107i 0.610603 0.791937i \(-0.290927\pi\)
−0.991139 + 0.132830i \(0.957594\pi\)
\(140\) −4.80841 8.25699i −0.406385 0.697843i
\(141\) −2.31165 + 4.00389i −0.194676 + 0.337188i
\(142\) 7.19905i 0.604131i
\(143\) 6.43152 + 3.71324i 0.537831 + 0.310517i
\(144\) 0.500000 0.866025i 0.0416667 0.0721688i
\(145\) −0.0273514 7.31892i −0.00227141 0.607803i
\(146\) −1.68079 2.91122i −0.139103 0.240934i
\(147\) 11.2597i 0.928688i
\(148\) 3.00021 + 5.29139i 0.246615 + 0.434949i
\(149\) 12.1069 0.991838 0.495919 0.868369i \(-0.334831\pi\)
0.495919 + 0.868369i \(0.334831\pi\)
\(150\) −4.99986 + 0.0373703i −0.408237 + 0.00305128i
\(151\) 4.81068 8.33235i 0.391488 0.678077i −0.601158 0.799130i \(-0.705294\pi\)
0.992646 + 0.121053i \(0.0386271\pi\)
\(152\) 3.56380 + 2.05756i 0.289063 + 0.166890i
\(153\) −6.29873 3.63657i −0.509222 0.293999i
\(154\) 25.3769 2.04493
\(155\) 0.0224631 + 6.01087i 0.00180428 + 0.482805i
\(156\) 1.25053 0.100122
\(157\) −7.43290 + 4.29139i −0.593210 + 0.342490i −0.766366 0.642405i \(-0.777937\pi\)
0.173156 + 0.984894i \(0.444604\pi\)
\(158\) 6.83733i 0.543949i
\(159\) 1.51960 0.120512
\(160\) 1.11079 1.94066i 0.0878156 0.153422i
\(161\) −14.7384 + 25.5277i −1.16155 + 2.01186i
\(162\) 1.00000i 0.0785674i
\(163\) −19.6684 + 11.3555i −1.54055 + 0.889434i −0.541741 + 0.840545i \(0.682235\pi\)
−0.998804 + 0.0488890i \(0.984432\pi\)
\(164\) 1.33327 + 2.30929i 0.104111 + 0.180325i
\(165\) 6.59663 11.5250i 0.513547 0.897216i
\(166\) 3.72981 6.46021i 0.289489 0.501410i
\(167\) −3.96167 2.28727i −0.306564 0.176995i 0.338824 0.940850i \(-0.389971\pi\)
−0.645388 + 0.763855i \(0.723304\pi\)
\(168\) 3.70065 2.13657i 0.285511 0.164840i
\(169\) −5.71809 9.90403i −0.439853 0.761848i
\(170\) −14.1147 8.07893i −1.08255 0.619626i
\(171\) 4.11513 0.314692
\(172\) −7.83128 4.52139i −0.597130 0.344753i
\(173\) 1.24331 0.717825i 0.0945270 0.0545752i −0.451991 0.892022i \(-0.649286\pi\)
0.546518 + 0.837447i \(0.315953\pi\)
\(174\) 3.27314 0.248136
\(175\) −18.5826 10.5443i −1.40471 0.797071i
\(176\) 2.96934 + 5.14305i 0.223823 + 0.387672i
\(177\) 0.111056i 0.00834747i
\(178\) −7.61589 4.39703i −0.570835 0.329572i
\(179\) 11.3781 0.850437 0.425218 0.905091i \(-0.360197\pi\)
0.425218 + 0.905091i \(0.360197\pi\)
\(180\) −0.00835632 2.23605i −0.000622843 0.166666i
\(181\) −9.91980 + 17.1816i −0.737333 + 1.27710i 0.216359 + 0.976314i \(0.430582\pi\)
−0.953692 + 0.300784i \(0.902752\pi\)
\(182\) 4.62776 + 2.67184i 0.343032 + 0.198050i
\(183\) 10.6368 6.14118i 0.786298 0.453969i
\(184\) −6.89816 −0.508539
\(185\) 11.7515 + 6.84852i 0.863987 + 0.503514i
\(186\) −2.68816 −0.197106
\(187\) 37.4062 21.5965i 2.73541 1.57929i
\(188\) −4.00389 2.31165i −0.292014 0.168594i
\(189\) 2.13657 3.70065i 0.155413 0.269183i
\(190\) 9.20164 0.0343873i 0.667557 0.00249472i
\(191\) 11.1024 0.803339 0.401670 0.915785i \(-0.368430\pi\)
0.401670 + 0.915785i \(0.368430\pi\)
\(192\) 0.866025 + 0.500000i 0.0625000 + 0.0360844i
\(193\) 25.1326i 1.80909i 0.426382 + 0.904543i \(0.359788\pi\)
−0.426382 + 0.904543i \(0.640212\pi\)
\(194\) −6.05383 10.4855i −0.434639 0.752818i
\(195\) 2.41639 1.40717i 0.173041 0.100770i
\(196\) 11.2597 0.804268
\(197\) −0.993932 + 0.573847i −0.0708148 + 0.0408849i −0.534989 0.844859i \(-0.679684\pi\)
0.464175 + 0.885744i \(0.346351\pi\)
\(198\) 5.14305 + 2.96934i 0.365501 + 0.211022i
\(199\) 6.59776 0.467703 0.233851 0.972272i \(-0.424867\pi\)
0.233851 + 0.972272i \(0.424867\pi\)
\(200\) −0.0373703 4.99986i −0.00264248 0.353544i
\(201\) 2.56660 + 4.44547i 0.181034 + 0.313560i
\(202\) 6.24210 3.60388i 0.439193 0.253568i
\(203\) 12.1128 + 6.99330i 0.850149 + 0.490834i
\(204\) 3.63657 6.29873i 0.254611 0.440999i
\(205\) 5.17484 + 2.96197i 0.361427 + 0.206873i
\(206\) 1.59903 + 2.76960i 0.111410 + 0.192967i
\(207\) −5.97399 + 3.44908i −0.415221 + 0.239728i
\(208\) 1.25053i 0.0867084i
\(209\) −12.2192 + 21.1643i −0.845221 + 1.46397i
\(210\) 4.74656 8.29270i 0.327544 0.572251i
\(211\) 18.6041 1.28076 0.640380 0.768058i \(-0.278777\pi\)
0.640380 + 0.768058i \(0.278777\pi\)
\(212\) 1.51960i 0.104366i
\(213\) 6.23456 3.59953i 0.427185 0.246636i
\(214\) 7.71580 0.527442
\(215\) −20.2201 + 0.0755644i −1.37900 + 0.00515345i
\(216\) 1.00000 0.0680414
\(217\) −9.94795 5.74345i −0.675311 0.389891i
\(218\) 6.67561 + 3.85417i 0.452129 + 0.261037i
\(219\) 1.68079 2.91122i 0.113577 0.196722i
\(220\) 11.5250 + 6.59663i 0.777012 + 0.444745i
\(221\) 9.09525 0.611813
\(222\) −3.08237 + 5.24395i −0.206875 + 0.351951i
\(223\) 19.3854i 1.29814i 0.760727 + 0.649072i \(0.224843\pi\)
−0.760727 + 0.649072i \(0.775157\pi\)
\(224\) 2.13657 + 3.70065i 0.142756 + 0.247260i
\(225\) −2.53229 4.31132i −0.168820 0.287421i
\(226\) −7.74618 + 13.4168i −0.515268 + 0.892471i
\(227\) −5.15116 2.97402i −0.341895 0.197393i 0.319215 0.947682i \(-0.396581\pi\)
−0.661109 + 0.750289i \(0.729914\pi\)
\(228\) 4.11513i 0.272531i
\(229\) 4.45902 7.72325i 0.294660 0.510367i −0.680246 0.732984i \(-0.738127\pi\)
0.974906 + 0.222618i \(0.0714602\pi\)
\(230\) −13.3293 + 7.76225i −0.878910 + 0.511828i
\(231\) 12.6884 + 21.9770i 0.834837 + 1.44598i
\(232\) 3.27314i 0.214892i
\(233\) 1.91329i 0.125344i −0.998034 0.0626718i \(-0.980038\pi\)
0.998034 0.0626718i \(-0.0199621\pi\)
\(234\) 0.625263 + 1.08299i 0.0408747 + 0.0707971i
\(235\) −10.3379 + 0.0386337i −0.674372 + 0.00252019i
\(236\) −0.111056 −0.00722912
\(237\) 5.92130 3.41867i 0.384630 0.222066i
\(238\) 26.9154 15.5396i 1.74466 1.00728i
\(239\) −7.76415 13.4479i −0.502221 0.869872i −0.999997 0.00256635i \(-0.999183\pi\)
0.497776 0.867306i \(-0.334150\pi\)
\(240\) 2.23605 0.00835632i 0.144337 0.000539398i
\(241\) −5.55610 + 9.62345i −0.357900 + 0.619901i −0.987610 0.156929i \(-0.949840\pi\)
0.629710 + 0.776830i \(0.283174\pi\)
\(242\) −21.0167 + 12.1340i −1.35101 + 0.780003i
\(243\) 0.866025 0.500000i 0.0555556 0.0320750i
\(244\) 6.14118 + 10.6368i 0.393149 + 0.680954i
\(245\) 21.7572 12.6702i 1.39002 0.809468i
\(246\) −1.33327 + 2.30929i −0.0850062 + 0.147235i
\(247\) −4.45663 + 2.57304i −0.283569 + 0.163718i
\(248\) 2.68816i 0.170698i
\(249\) 7.45961 0.472734
\(250\) −5.69837 9.61918i −0.360396 0.608370i
\(251\) 13.3364 0.841789 0.420894 0.907110i \(-0.361716\pi\)
0.420894 + 0.907110i \(0.361716\pi\)
\(252\) 3.70065 + 2.13657i 0.233119 + 0.134591i
\(253\) 40.9660i 2.57551i
\(254\) 7.60268 13.1682i 0.477034 0.826248i
\(255\) −0.0607767 16.2631i −0.00380599 1.01844i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 21.3805 12.3440i 1.33368 0.769999i 0.347817 0.937563i \(-0.386923\pi\)
0.985861 + 0.167563i \(0.0535898\pi\)
\(258\) 9.04279i 0.562979i
\(259\) −22.6108 + 12.8203i −1.40497 + 0.796615i
\(260\) 1.40717 + 2.41639i 0.0872690 + 0.149858i
\(261\) 1.63657 + 2.83462i 0.101301 + 0.175459i
\(262\) −14.2861 8.24808i −0.882598 0.509568i
\(263\) −21.8902 12.6383i −1.34981 0.779311i −0.361584 0.932340i \(-0.617764\pi\)
−0.988222 + 0.153029i \(0.951097\pi\)
\(264\) −2.96934 + 5.14305i −0.182750 + 0.316533i
\(265\) 1.70995 + 2.93632i 0.105041 + 0.180377i
\(266\) −8.79226 + 15.2286i −0.539088 + 0.933728i
\(267\) 8.79407i 0.538188i
\(268\) −4.44547 + 2.56660i −0.271551 + 0.156780i
\(269\) −25.0272 −1.52594 −0.762968 0.646436i \(-0.776259\pi\)
−0.762968 + 0.646436i \(0.776259\pi\)
\(270\) 1.93230 1.12526i 0.117596 0.0684813i
\(271\) −6.67337 11.5586i −0.405379 0.702136i 0.588987 0.808143i \(-0.299527\pi\)
−0.994365 + 0.106006i \(0.966194\pi\)
\(272\) 6.29873 + 3.63657i 0.381916 + 0.220500i
\(273\) 5.34368i 0.323414i
\(274\) 11.5316 + 19.9734i 0.696652 + 1.20664i
\(275\) 29.6926 0.221931i 1.79053 0.0133829i
\(276\) −3.44908 5.97399i −0.207610 0.359592i
\(277\) 16.1983 + 9.35210i 0.973262 + 0.561913i 0.900229 0.435416i \(-0.143399\pi\)
0.0730329 + 0.997330i \(0.476732\pi\)
\(278\) 7.77075 + 4.48645i 0.466059 + 0.269079i
\(279\) −1.34408 2.32802i −0.0804680 0.139375i
\(280\) 8.29270 + 4.74656i 0.495584 + 0.283661i
\(281\) −5.15883 8.93535i −0.307750 0.533038i 0.670120 0.742253i \(-0.266243\pi\)
−0.977870 + 0.209214i \(0.932909\pi\)
\(282\) 4.62329i 0.275313i
\(283\) −5.24310 3.02711i −0.311670 0.179943i 0.336003 0.941861i \(-0.390925\pi\)
−0.647674 + 0.761918i \(0.724258\pi\)
\(284\) 3.59953 + 6.23456i 0.213593 + 0.369953i
\(285\) 4.63060 + 7.95166i 0.274293 + 0.471016i
\(286\) −7.42648 −0.439137
\(287\) −9.86794 + 5.69726i −0.582486 + 0.336298i
\(288\) 1.00000i 0.0589256i
\(289\) 17.9493 31.0891i 1.05584 1.82877i
\(290\) 3.68315 + 6.32469i 0.216282 + 0.371399i
\(291\) 6.05383 10.4855i 0.354882 0.614673i
\(292\) 2.91122 + 1.68079i 0.170366 + 0.0983608i
\(293\) 4.60340 + 2.65778i 0.268934 + 0.155269i 0.628403 0.777888i \(-0.283709\pi\)
−0.359469 + 0.933157i \(0.617042\pi\)
\(294\) 5.62987 + 9.75123i 0.328341 + 0.568703i
\(295\) −0.214593 + 0.124967i −0.0124941 + 0.00727586i
\(296\) −5.24395 3.08237i −0.304798 0.179159i
\(297\) 5.93869i 0.344598i
\(298\) −10.4849 + 6.05346i −0.607374 + 0.350668i
\(299\) 4.31317 7.47062i 0.249437 0.432037i
\(300\) 4.31132 2.53229i 0.248914 0.146202i
\(301\) 19.3206 33.4642i 1.11362 1.92884i
\(302\) 9.62137i 0.553648i
\(303\) 6.24210 + 3.60388i 0.358599 + 0.207037i
\(304\) −4.11513 −0.236019
\(305\) 23.8358 + 13.6431i 1.36484 + 0.781203i
\(306\) 7.27314 0.415778
\(307\) 18.2790i 1.04324i −0.853178 0.521620i \(-0.825328\pi\)
0.853178 0.521620i \(-0.174672\pi\)
\(308\) −21.9770 + 12.6884i −1.25226 + 0.722990i
\(309\) −1.59903 + 2.76960i −0.0909656 + 0.157557i
\(310\) −3.02489 5.19433i −0.171802 0.295018i
\(311\) −16.0222 27.7513i −0.908537 1.57363i −0.816098 0.577913i \(-0.803867\pi\)
−0.0924383 0.995718i \(-0.529466\pi\)
\(312\) −1.08299 + 0.625263i −0.0613121 + 0.0353985i
\(313\) 7.68688 4.43802i 0.434488 0.250852i −0.266769 0.963761i \(-0.585956\pi\)
0.701257 + 0.712909i \(0.252623\pi\)
\(314\) 4.29139 7.43290i 0.242177 0.419463i
\(315\) 9.55497 0.0357078i 0.538362 0.00201190i
\(316\) 3.41867 + 5.92130i 0.192315 + 0.333099i
\(317\) 3.82489 2.20830i 0.214827 0.124031i −0.388725 0.921354i \(-0.627085\pi\)
0.603553 + 0.797323i \(0.293751\pi\)
\(318\) −1.31601 + 0.759799i −0.0737982 + 0.0426074i
\(319\) −19.4382 −1.08833
\(320\) 0.00835632 + 2.23605i 0.000467133 + 0.124999i
\(321\) 3.85790 + 6.68208i 0.215327 + 0.372957i
\(322\) 29.4768i 1.64268i
\(323\) 29.9299i 1.66534i
\(324\) 0.500000 + 0.866025i 0.0277778 + 0.0481125i
\(325\) 5.43815 + 3.08576i 0.301654 + 0.171167i
\(326\) 11.3555 19.6684i 0.628925 1.08933i
\(327\) 7.70833i 0.426272i
\(328\) −2.30929 1.33327i −0.127509 0.0736176i
\(329\) 9.87800 17.1092i 0.544592 0.943260i
\(330\) 0.0496256 + 13.2792i 0.00273180 + 0.730997i
\(331\) −15.1841 26.2996i −0.834592 1.44556i −0.894362 0.447344i \(-0.852370\pi\)
0.0597696 0.998212i \(-0.480963\pi\)
\(332\) 7.45961i 0.409399i
\(333\) −6.08258 0.0474386i −0.333323 0.00259962i
\(334\) 4.57455 0.250308
\(335\) −5.70189 + 9.96176i −0.311528 + 0.544269i
\(336\) −2.13657 + 3.70065i −0.116560 + 0.201887i
\(337\) −20.8921 12.0621i −1.13807 0.657063i −0.192115 0.981372i \(-0.561535\pi\)
−0.945951 + 0.324310i \(0.894868\pi\)
\(338\) 9.90403 + 5.71809i 0.538708 + 0.311023i
\(339\) −15.4924 −0.841430
\(340\) 16.2631 0.0607767i 0.881992 0.00329608i
\(341\) 15.9642 0.864507
\(342\) −3.56380 + 2.05756i −0.192708 + 0.111260i
\(343\) 18.2025i 0.982843i
\(344\) 9.04279 0.487554
\(345\) −13.3870 7.66241i −0.720730 0.412530i
\(346\) −0.717825 + 1.24331i −0.0385905 + 0.0668407i
\(347\) 28.8375i 1.54808i −0.633139 0.774038i \(-0.718234\pi\)
0.633139 0.774038i \(-0.281766\pi\)
\(348\) −2.83462 + 1.63657i −0.151952 + 0.0877294i
\(349\) 11.6328 + 20.1486i 0.622689 + 1.07853i 0.988983 + 0.148029i \(0.0472930\pi\)
−0.366294 + 0.930499i \(0.619374\pi\)
\(350\) 21.3651 0.159689i 1.14201 0.00853573i
\(351\) −0.625263 + 1.08299i −0.0333741 + 0.0578056i
\(352\) −5.14305 2.96934i −0.274126 0.158267i
\(353\) −0.169377 + 0.0977899i −0.00901503 + 0.00520483i −0.504501 0.863411i \(-0.668323\pi\)
0.495486 + 0.868616i \(0.334990\pi\)
\(354\) −0.0555279 0.0961772i −0.00295128 0.00511176i
\(355\) 13.9709 + 7.99663i 0.741498 + 0.424417i
\(356\) 8.79407 0.466085
\(357\) 26.9154 + 15.5396i 1.42451 + 0.822442i
\(358\) −9.85370 + 5.68904i −0.520784 + 0.300675i
\(359\) 3.52995 0.186303 0.0931517 0.995652i \(-0.470306\pi\)
0.0931517 + 0.995652i \(0.470306\pi\)
\(360\) 1.12526 + 1.93230i 0.0593066 + 0.101841i
\(361\) 1.03287 + 1.78898i 0.0543615 + 0.0941570i
\(362\) 19.8396i 1.04275i
\(363\) −21.0167 12.1340i −1.10309 0.636870i
\(364\) −5.34368 −0.280085
\(365\) 7.51667 0.0280905i 0.393441 0.00147032i
\(366\) −6.14118 + 10.6368i −0.321005 + 0.555996i
\(367\) 1.73122 + 0.999522i 0.0903691 + 0.0521746i 0.544504 0.838759i \(-0.316718\pi\)
−0.454134 + 0.890933i \(0.650051\pi\)
\(368\) 5.97399 3.44908i 0.311416 0.179796i
\(369\) −2.66654 −0.138815
\(370\) −13.6014 0.0552472i −0.707101 0.00287217i
\(371\) −6.49346 −0.337124
\(372\) 2.32802 1.34408i 0.120702 0.0696873i
\(373\) 11.9568 + 6.90326i 0.619099 + 0.357437i 0.776518 0.630095i \(-0.216984\pi\)
−0.157419 + 0.987532i \(0.550317\pi\)
\(374\) −21.5965 + 37.4062i −1.11673 + 1.93423i
\(375\) 5.48127 9.74452i 0.283052 0.503205i
\(376\) 4.62329 0.238428
\(377\) −3.54477 2.04657i −0.182565 0.105404i
\(378\) 4.27314i 0.219787i
\(379\) −3.38018 5.85465i −0.173628 0.300733i 0.766057 0.642772i \(-0.222216\pi\)
−0.939686 + 0.342039i \(0.888882\pi\)
\(380\) −7.95166 + 4.63060i −0.407911 + 0.237545i
\(381\) 15.2054 0.778994
\(382\) −9.61493 + 5.55119i −0.491943 + 0.284023i
\(383\) −12.2108 7.04991i −0.623943 0.360233i 0.154460 0.987999i \(-0.450636\pi\)
−0.778402 + 0.627766i \(0.783970\pi\)
\(384\) −1.00000 −0.0510310
\(385\) −28.1883 + 49.2478i −1.43661 + 2.50990i
\(386\) −12.5663 21.7655i −0.639609 1.10783i
\(387\) 7.83128 4.52139i 0.398086 0.229835i
\(388\) 10.4855 + 6.05383i 0.532322 + 0.307336i
\(389\) 2.87886 4.98634i 0.145964 0.252817i −0.783768 0.621054i \(-0.786705\pi\)
0.929732 + 0.368236i \(0.120038\pi\)
\(390\) −1.38907 + 2.42684i −0.0703383 + 0.122888i
\(391\) −25.0857 43.4497i −1.26864 2.19734i
\(392\) −9.75123 + 5.62987i −0.492511 + 0.284352i
\(393\) 16.4962i 0.832121i
\(394\) 0.573847 0.993932i 0.0289100 0.0500736i
\(395\) 13.2689 + 7.59484i 0.667632 + 0.382138i
\(396\) −5.93869 −0.298430
\(397\) 11.8180i 0.593130i 0.955013 + 0.296565i \(0.0958411\pi\)
−0.955013 + 0.296565i \(0.904159\pi\)
\(398\) −5.71382 + 3.29888i −0.286408 + 0.165358i
\(399\) −17.5845 −0.880327
\(400\) 2.53229 + 4.31132i 0.126615 + 0.215566i
\(401\) 5.04044 0.251708 0.125854 0.992049i \(-0.459833\pi\)
0.125854 + 0.992049i \(0.459833\pi\)
\(402\) −4.44547 2.56660i −0.221720 0.128010i
\(403\) 2.91124 + 1.68081i 0.145019 + 0.0837270i
\(404\) −3.60388 + 6.24210i −0.179300 + 0.310556i
\(405\) 1.94066 + 1.11079i 0.0964320 + 0.0551956i
\(406\) −13.9866 −0.694144
\(407\) 18.3052 31.1422i 0.907357 1.54366i
\(408\) 7.27314i 0.360074i
\(409\) 1.41880 + 2.45743i 0.0701549 + 0.121512i 0.898969 0.438012i \(-0.144317\pi\)
−0.828814 + 0.559524i \(0.810984\pi\)
\(410\) −5.96253 + 0.0222825i −0.294468 + 0.00110045i
\(411\) −11.5316 + 19.9734i −0.568814 + 0.985214i
\(412\) −2.76960 1.59903i −0.136448 0.0787785i
\(413\) 0.474557i 0.0233514i
\(414\) 3.44908 5.97399i 0.169513 0.293605i
\(415\) 8.39403 + 14.4142i 0.412046 + 0.707566i
\(416\) −0.625263 1.08299i −0.0306560 0.0530978i
\(417\) 8.97289i 0.439404i
\(418\) 24.4384i 1.19532i
\(419\) 2.45402 + 4.25048i 0.119887 + 0.207650i 0.919723 0.392569i \(-0.128414\pi\)
−0.799836 + 0.600219i \(0.795080\pi\)
\(420\) 0.0357078 + 9.55497i 0.00174236 + 0.466235i
\(421\) −25.3784 −1.23687 −0.618433 0.785837i \(-0.712232\pi\)
−0.618433 + 0.785837i \(0.712232\pi\)
\(422\) −16.1116 + 9.30206i −0.784303 + 0.452817i
\(423\) 4.00389 2.31165i 0.194676 0.112396i
\(424\) −0.759799 1.31601i −0.0368991 0.0639111i
\(425\) 31.3569 18.4177i 1.52103 0.893391i
\(426\) −3.59953 + 6.23456i −0.174398 + 0.302066i
\(427\) −45.4527 + 26.2421i −2.19961 + 1.26995i
\(428\) −6.68208 + 3.85790i −0.322991 + 0.186479i
\(429\) −3.71324 6.43152i −0.179277 0.310517i
\(430\) 17.4734 10.1755i 0.842641 0.490707i
\(431\) −6.96555 + 12.0647i −0.335519 + 0.581136i −0.983584 0.180449i \(-0.942245\pi\)
0.648065 + 0.761585i \(0.275578\pi\)
\(432\) −0.866025 + 0.500000i −0.0416667 + 0.0240563i
\(433\) 22.8789i 1.09949i −0.835332 0.549746i \(-0.814725\pi\)
0.835332 0.549746i \(-0.185275\pi\)
\(434\) 11.4869 0.551389
\(435\) −3.63577 + 6.35204i −0.174322 + 0.304557i
\(436\) −7.70833 −0.369162
\(437\) 24.5837 + 14.1934i 1.17600 + 0.678963i
\(438\) 3.36158i 0.160623i
\(439\) −5.14932 + 8.91889i −0.245764 + 0.425675i −0.962346 0.271827i \(-0.912372\pi\)
0.716582 + 0.697502i \(0.245705\pi\)
\(440\) −13.2792 + 0.0496256i −0.633062 + 0.00236581i
\(441\) −5.62987 + 9.75123i −0.268089 + 0.464344i
\(442\) −7.87672 + 4.54763i −0.374657 + 0.216309i
\(443\) 21.4199i 1.01769i −0.860859 0.508844i \(-0.830073\pi\)
0.860859 0.508844i \(-0.169927\pi\)
\(444\) 0.0474386 6.08258i 0.00225134 0.288666i
\(445\) 16.9928 9.89564i 0.805535 0.469098i
\(446\) −9.69271 16.7883i −0.458963 0.794947i
\(447\) −10.4849 6.05346i −0.495919 0.286319i
\(448\) −3.70065 2.13657i −0.174839 0.100944i
\(449\) −16.3407 + 28.3030i −0.771167 + 1.33570i 0.165757 + 0.986167i \(0.446993\pi\)
−0.936924 + 0.349533i \(0.886340\pi\)
\(450\) 4.34869 + 2.46757i 0.204999 + 0.116322i
\(451\) 7.91788 13.7142i 0.372838 0.645775i
\(452\) 15.4924i 0.728700i
\(453\) −8.33235 + 4.81068i −0.391488 + 0.226026i
\(454\) 5.94805 0.279156
\(455\) −10.3256 + 6.01304i −0.484071 + 0.281896i
\(456\) −2.05756 3.56380i −0.0963542 0.166890i
\(457\) −9.41322 5.43472i −0.440332 0.254226i 0.263407 0.964685i \(-0.415154\pi\)
−0.703738 + 0.710459i \(0.748487\pi\)
\(458\) 8.91804i 0.416713i
\(459\) 3.63657 + 6.29873i 0.169741 + 0.293999i
\(460\) 7.66241 13.3870i 0.357262 0.624171i
\(461\) 14.4531 + 25.0336i 0.673150 + 1.16593i 0.977006 + 0.213212i \(0.0683925\pi\)
−0.303856 + 0.952718i \(0.598274\pi\)
\(462\) −21.9770 12.6884i −1.02246 0.590319i
\(463\) 32.1719 + 18.5745i 1.49516 + 0.863229i 0.999985 0.00556589i \(-0.00177169\pi\)
0.495172 + 0.868795i \(0.335105\pi\)
\(464\) −1.63657 2.83462i −0.0759759 0.131594i
\(465\) 2.98598 5.21680i 0.138472 0.241923i
\(466\) 0.956644 + 1.65696i 0.0443157 + 0.0767570i
\(467\) 22.3568i 1.03455i −0.855819 0.517276i \(-0.826946\pi\)
0.855819 0.517276i \(-0.173054\pi\)
\(468\) −1.08299 0.625263i −0.0500611 0.0289028i
\(469\) −10.9674 18.9961i −0.506429 0.877160i
\(470\) 8.93359 5.20242i 0.412076 0.239970i
\(471\) 8.58277 0.395473
\(472\) 0.0961772 0.0555279i 0.00442691 0.00255588i
\(473\) 53.7023i 2.46923i
\(474\) −3.41867 + 5.92130i −0.157025 + 0.271975i
\(475\) −10.1543 + 17.8954i −0.465913 + 0.821098i
\(476\) −15.5396 + 26.9154i −0.712256 + 1.23366i
\(477\) −1.31601 0.759799i −0.0602560 0.0347888i
\(478\) 13.4479 + 7.76415i 0.615092 + 0.355124i
\(479\) 5.34678 + 9.26089i 0.244300 + 0.423141i 0.961935 0.273279i \(-0.0881084\pi\)
−0.717634 + 0.696420i \(0.754775\pi\)
\(480\) −1.93230 + 1.12526i −0.0881970 + 0.0513610i
\(481\) 6.61702 3.75184i 0.301710 0.171069i
\(482\) 11.1122i 0.506147i
\(483\) 25.5277 14.7384i 1.16155 0.670621i
\(484\) 12.1340 21.0167i 0.551546 0.955305i
\(485\) 27.0733 0.101175i 1.22934 0.00459414i
\(486\) −0.500000 + 0.866025i −0.0226805 + 0.0392837i
\(487\) 12.8937i 0.584270i −0.956377 0.292135i \(-0.905634\pi\)
0.956377 0.292135i \(-0.0943656\pi\)
\(488\) −10.6368 6.14118i −0.481507 0.277998i
\(489\) 22.7111 1.02703
\(490\) −12.5072 + 21.8513i −0.565018 + 0.987141i
\(491\) −38.5951 −1.74177 −0.870885 0.491486i \(-0.836454\pi\)
−0.870885 + 0.491486i \(0.836454\pi\)
\(492\) 2.66654i 0.120217i
\(493\) −20.6166 + 11.9030i −0.928526 + 0.536085i
\(494\) 2.57304 4.45663i 0.115766 0.200513i
\(495\) −11.4753 + 6.68259i −0.515778 + 0.300360i
\(496\) 1.34408 + 2.32802i 0.0603510 + 0.104531i
\(497\) −26.6412 + 15.3813i −1.19502 + 0.689945i
\(498\) −6.46021 + 3.72981i −0.289489 + 0.167137i
\(499\) −5.68234 + 9.84210i −0.254376 + 0.440593i −0.964726 0.263256i \(-0.915204\pi\)
0.710350 + 0.703849i \(0.248537\pi\)
\(500\) 9.74452 + 5.48127i 0.435788 + 0.245130i
\(501\) 2.28727 + 3.96167i 0.102188 + 0.176995i
\(502\) −11.5497 + 6.66822i −0.515488 + 0.297617i
\(503\) 5.76066 3.32592i 0.256855 0.148295i −0.366044 0.930598i \(-0.619288\pi\)
0.622899 + 0.782302i \(0.285955\pi\)
\(504\) −4.27314 −0.190341
\(505\) 0.0602304 + 16.1169i 0.00268022 + 0.717194i
\(506\) 20.4830 + 35.4776i 0.910581 + 1.57717i
\(507\) 11.4362i 0.507899i
\(508\) 15.2054i 0.674628i
\(509\) 3.93391 + 6.81372i 0.174367 + 0.302013i 0.939942 0.341334i \(-0.110879\pi\)
−0.765575 + 0.643347i \(0.777545\pi\)
\(510\) 8.18420 + 14.0539i 0.362402 + 0.622317i
\(511\) −7.18226 + 12.4400i −0.317724 + 0.550315i
\(512\) 1.00000i 0.0441942i
\(513\) −3.56380 2.05756i −0.157346 0.0908436i
\(514\) −12.3440 + 21.3805i −0.544472 + 0.943053i
\(515\) −7.15103 + 0.0267240i −0.315112 + 0.00117760i
\(516\) 4.52139 + 7.83128i 0.199043 + 0.344753i
\(517\) 27.4563i 1.20753i
\(518\) 13.1714 22.4081i 0.578719 0.984557i
\(519\) −1.43565 −0.0630180
\(520\) −2.42684 1.38907i −0.106424 0.0609148i
\(521\) 16.2960 28.2255i 0.713941 1.23658i −0.249425 0.968394i \(-0.580242\pi\)
0.963367 0.268188i \(-0.0864249\pi\)
\(522\) −2.83462 1.63657i −0.124068 0.0716308i
\(523\) 10.8426 + 6.26000i 0.474116 + 0.273731i 0.717961 0.696083i \(-0.245076\pi\)
−0.243845 + 0.969814i \(0.578409\pi\)
\(524\) 16.4962 0.720638
\(525\) 10.8209 + 18.4229i 0.472261 + 0.804041i
\(526\) 25.2766 1.10211
\(527\) 16.9320 9.77569i 0.737569 0.425836i
\(528\) 5.93869i 0.258448i
\(529\) −24.5847 −1.06890
\(530\) −2.94902 1.68795i −0.128097 0.0733200i
\(531\) 0.0555279 0.0961772i 0.00240971 0.00417373i
\(532\) 17.5845i 0.762386i
\(533\) 2.88783 1.66729i 0.125086 0.0722183i
\(534\) 4.39703 + 7.61589i 0.190278 + 0.329572i
\(535\) −8.57063 + 14.9737i −0.370541 + 0.647371i
\(536\) 2.56660 4.44547i 0.110860 0.192015i
\(537\) −9.85370 5.68904i −0.425218 0.245500i
\(538\) 21.6742 12.5136i 0.934442 0.539500i
\(539\) −33.4341 57.9095i −1.44011 2.49434i
\(540\) −1.11079 + 1.94066i −0.0478008 + 0.0835126i
\(541\) 4.12381 0.177297 0.0886483 0.996063i \(-0.471745\pi\)
0.0886483 + 0.996063i \(0.471745\pi\)
\(542\) 11.5586 + 6.67337i 0.496485 + 0.286646i
\(543\) 17.1816 9.91980i 0.737333 0.425699i
\(544\) −7.27314 −0.311833
\(545\) −14.8948 + 8.67390i −0.638023 + 0.371549i
\(546\) −2.67184 4.62776i −0.114344 0.198050i
\(547\) 35.3451i 1.51125i −0.655006 0.755624i \(-0.727334\pi\)
0.655006 0.755624i \(-0.272666\pi\)
\(548\) −19.9734 11.5316i −0.853221 0.492607i
\(549\) −12.2824 −0.524198
\(550\) −25.6036 + 15.0385i −1.09174 + 0.641244i
\(551\) 6.73470 11.6648i 0.286908 0.496939i
\(552\) 5.97399 + 3.44908i 0.254270 + 0.146803i
\(553\) −25.3026 + 14.6085i −1.07598 + 0.621215i
\(554\) −18.7042 −0.794665
\(555\) −6.75283 11.8067i −0.286642 0.501168i
\(556\) −8.97289 −0.380535
\(557\) −5.17687 + 2.98887i −0.219351 + 0.126642i −0.605650 0.795731i \(-0.707087\pi\)
0.386299 + 0.922374i \(0.373753\pi\)
\(558\) 2.32802 + 1.34408i 0.0985528 + 0.0568995i
\(559\) −5.65412 + 9.79322i −0.239144 + 0.414209i
\(560\) −9.55497 + 0.0357078i −0.403771 + 0.00150893i
\(561\) −43.1929 −1.82361
\(562\) 8.93535 + 5.15883i 0.376915 + 0.217612i
\(563\) 12.8905i 0.543268i 0.962401 + 0.271634i \(0.0875641\pi\)
−0.962401 + 0.271634i \(0.912436\pi\)
\(564\) 2.31165 + 4.00389i 0.0973379 + 0.168594i
\(565\) −17.4330 29.9359i −0.733411 1.25941i
\(566\) 6.05422 0.254478
\(567\) −3.70065 + 2.13657i −0.155413 + 0.0897276i
\(568\) −6.23456 3.59953i −0.261597 0.151033i
\(569\) 10.8120 0.453261 0.226631 0.973981i \(-0.427229\pi\)
0.226631 + 0.973981i \(0.427229\pi\)
\(570\) −7.98605 4.57104i −0.334499 0.191460i
\(571\) 12.4430 + 21.5520i 0.520725 + 0.901922i 0.999710 + 0.0240989i \(0.00767165\pi\)
−0.478985 + 0.877823i \(0.658995\pi\)
\(572\) 6.43152 3.71324i 0.268915 0.155258i
\(573\) −9.61493 5.55119i −0.401670 0.231904i
\(574\) 5.69726 9.86794i 0.237799 0.411880i
\(575\) −0.257787 34.4899i −0.0107505 1.43833i
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) −6.17293 + 3.56394i −0.256982 + 0.148369i −0.622957 0.782256i \(-0.714069\pi\)
0.365975 + 0.930625i \(0.380736\pi\)
\(578\) 35.8986i 1.49318i
\(579\) 12.5663 21.7655i 0.522238 0.904543i
\(580\) −6.35204 3.63577i −0.263754 0.150967i
\(581\) −31.8760 −1.32244
\(582\) 12.1077i 0.501878i
\(583\) 7.81538 4.51221i 0.323680 0.186877i
\(584\) −3.36158 −0.139103
\(585\) −2.79624 + 0.0104498i −0.115610 + 0.000432046i
\(586\) −5.31555 −0.219583
\(587\) −8.55022 4.93647i −0.352905 0.203750i 0.313059 0.949734i \(-0.398646\pi\)
−0.665964 + 0.745984i \(0.731980\pi\)
\(588\) −9.75123 5.62987i −0.402134 0.232172i
\(589\) −5.53106 + 9.58008i −0.227903 + 0.394740i
\(590\) 0.123360 0.215521i 0.00507864 0.00887287i
\(591\) 1.14769 0.0472098
\(592\) 6.08258 + 0.0474386i 0.249992 + 0.00194971i
\(593\) 27.6314i 1.13469i 0.823481 + 0.567343i \(0.192029\pi\)
−0.823481 + 0.567343i \(0.807971\pi\)
\(594\) −2.96934 5.14305i −0.121834 0.211022i
\(595\) 0.259708 + 69.4947i 0.0106470 + 2.84900i
\(596\) 6.05346 10.4849i 0.247959 0.429478i
\(597\) −5.71382 3.29888i −0.233851 0.135014i
\(598\) 8.62633i 0.352757i
\(599\) 9.52530 16.4983i 0.389193 0.674102i −0.603148 0.797629i \(-0.706087\pi\)
0.992341 + 0.123527i \(0.0394205\pi\)
\(600\) −2.46757 + 4.34869i −0.100738 + 0.177535i
\(601\) −17.3651 30.0773i −0.708338 1.22688i −0.965473 0.260502i \(-0.916112\pi\)
0.257135 0.966375i \(-0.417221\pi\)
\(602\) 38.6411i 1.57489i
\(603\) 5.13319i 0.209040i
\(604\) −4.81068 8.33235i −0.195744 0.339039i
\(605\) −0.202791 54.2645i −0.00824464 2.20617i
\(606\) −7.20776 −0.292795
\(607\) −3.78634 + 2.18604i −0.153683 + 0.0887288i −0.574869 0.818245i \(-0.694947\pi\)
0.421187 + 0.906974i \(0.361614\pi\)
\(608\) 3.56380 2.05756i 0.144531 0.0834452i
\(609\) −6.99330 12.1128i −0.283383 0.490834i
\(610\) −27.4640 + 0.102635i −1.11199 + 0.00415559i
\(611\) −2.89078 + 5.00697i −0.116948 + 0.202560i
\(612\) −6.29873 + 3.63657i −0.254611 + 0.147000i
\(613\) 0.371275 0.214356i 0.0149957 0.00865775i −0.492483 0.870322i \(-0.663911\pi\)
0.507479 + 0.861664i \(0.330577\pi\)
\(614\) 9.13952 + 15.8301i 0.368841 + 0.638851i
\(615\) −3.00056 5.15256i −0.120994 0.207771i
\(616\) 12.6884 21.9770i 0.511231 0.885479i
\(617\) −12.3649 + 7.13885i −0.497790 + 0.287399i −0.727801 0.685789i \(-0.759457\pi\)
0.230010 + 0.973188i \(0.426124\pi\)
\(618\) 3.19806i 0.128645i
\(619\) 12.0527 0.484441 0.242220 0.970221i \(-0.422124\pi\)
0.242220 + 0.970221i \(0.422124\pi\)
\(620\) 5.21680 + 2.98598i 0.209512 + 0.119920i
\(621\) 6.89816 0.276814
\(622\) 27.7513 + 16.0222i 1.11273 + 0.642432i
\(623\) 37.5783i 1.50554i
\(624\) 0.625263 1.08299i 0.0250306 0.0433542i
\(625\) 24.9972 0.373693i 0.999888 0.0149477i
\(626\) −4.43802 + 7.68688i −0.177379 + 0.307230i
\(627\) 21.1643 12.2192i 0.845221 0.487989i
\(628\) 8.58277i 0.342490i
\(629\) 0.345028 44.2395i 0.0137572 1.76394i
\(630\) −8.25699 + 4.80841i −0.328966 + 0.191572i
\(631\) −7.44379 12.8930i −0.296333 0.513263i 0.678961 0.734174i \(-0.262430\pi\)
−0.975294 + 0.220911i \(0.929097\pi\)
\(632\) −5.92130 3.41867i −0.235537 0.135987i
\(633\) −16.1116 9.30206i −0.640380 0.369724i
\(634\) −2.20830 + 3.82489i −0.0877029 + 0.151906i
\(635\) 17.1100 + 29.3813i 0.678990 + 1.16596i
\(636\) 0.759799 1.31601i 0.0301280 0.0521832i
\(637\) 14.0806i 0.557894i
\(638\) 16.8339 9.71909i 0.666462 0.384782i
\(639\) −7.19905 −0.284790
\(640\) −1.12526 1.93230i −0.0444799 0.0763809i
\(641\) −15.4399 26.7427i −0.609840 1.05627i −0.991266 0.131875i \(-0.957900\pi\)
0.381426 0.924399i \(-0.375433\pi\)
\(642\) −6.68208 3.85790i −0.263721 0.152259i
\(643\) 6.52207i 0.257205i 0.991696 + 0.128603i \(0.0410492\pi\)
−0.991696 + 0.128603i \(0.958951\pi\)
\(644\) 14.7384 + 25.5277i 0.580775 + 1.00593i
\(645\) 17.5489 + 10.0446i 0.690989 + 0.395507i
\(646\) −14.9649 25.9201i −0.588788 1.01981i
\(647\) 19.3536 + 11.1738i 0.760870 + 0.439288i 0.829608 0.558346i \(-0.188564\pi\)
−0.0687382 + 0.997635i \(0.521897\pi\)
\(648\) −0.866025 0.500000i −0.0340207 0.0196419i
\(649\) 0.329763 + 0.571166i 0.0129443 + 0.0224202i
\(650\) −6.25246 + 0.0467326i −0.245241 + 0.00183300i
\(651\) 5.74345 + 9.94795i 0.225104 + 0.389891i
\(652\) 22.7111i 0.889434i
\(653\) 30.6001 + 17.6670i 1.19747 + 0.691362i 0.959991 0.280030i \(-0.0903443\pi\)
0.237483 + 0.971392i \(0.423678\pi\)
\(654\) −3.85417 6.67561i −0.150710 0.261037i
\(655\) 31.8755 18.5625i 1.24548 0.725298i
\(656\) 2.66654 0.104111
\(657\) −2.91122 + 1.68079i −0.113577 + 0.0655739i
\(658\) 19.7560i 0.770169i
\(659\) 0.235145 0.407284i 0.00915996 0.0158655i −0.861409 0.507912i \(-0.830418\pi\)
0.870569 + 0.492046i \(0.163751\pi\)
\(660\) −6.68259 11.4753i −0.260119 0.446676i
\(661\) 9.15487 15.8567i 0.356083 0.616754i −0.631220 0.775604i \(-0.717445\pi\)
0.987303 + 0.158850i \(0.0507787\pi\)
\(662\) 26.2996 + 15.1841i 1.02216 + 0.590146i
\(663\) −7.87672 4.54763i −0.305906 0.176615i
\(664\) −3.72981 6.46021i −0.144745 0.250705i
\(665\) −19.7872 33.9786i −0.767315 1.31763i
\(666\) 5.29139 3.00021i 0.205037 0.116256i
\(667\) 22.5787i 0.874250i
\(668\) −3.96167 + 2.28727i −0.153282 + 0.0884973i
\(669\) 9.69271 16.7883i 0.374742 0.649072i
\(670\) −0.0428946 11.4781i −0.00165716 0.443437i
\(671\) 36.4706 63.1689i 1.40793 2.43861i
\(672\) 4.27314i 0.164840i
\(673\) 2.70882 + 1.56394i 0.104418 + 0.0602855i 0.551299 0.834308i \(-0.314132\pi\)
−0.446882 + 0.894593i \(0.647466\pi\)
\(674\) 24.1241 0.929227
\(675\) 0.0373703 + 4.99986i 0.00143839 + 0.192445i
\(676\) −11.4362 −0.439853
\(677\) 26.3204i 1.01157i 0.862658 + 0.505787i \(0.168798\pi\)
−0.862658 + 0.505787i \(0.831202\pi\)
\(678\) 13.4168 7.74618i 0.515268 0.297490i
\(679\) −25.8689 + 44.8062i −0.992756 + 1.71950i
\(680\) −14.0539 + 8.18420i −0.538942 + 0.313850i
\(681\) 2.97402 + 5.15116i 0.113965 + 0.197393i
\(682\) −13.8254 + 7.98208i −0.529400 + 0.305650i
\(683\) −0.297050 + 0.171502i −0.0113663 + 0.00656234i −0.505672 0.862726i \(-0.668756\pi\)
0.494306 + 0.869288i \(0.335422\pi\)
\(684\) 2.05756 3.56380i 0.0786729 0.136265i
\(685\) −51.5707 + 0.192724i −1.97041 + 0.00736361i
\(686\) −9.10125 15.7638i −0.347487 0.601866i
\(687\) −7.72325 + 4.45902i −0.294660 + 0.170122i
\(688\) −7.83128 + 4.52139i −0.298565 + 0.172376i
\(689\) 1.90030 0.0723956
\(690\) 15.4247 0.0576433i 0.587207 0.00219444i
\(691\) −11.6638 20.2023i −0.443711 0.768531i 0.554250 0.832350i \(-0.313005\pi\)
−0.997961 + 0.0638196i \(0.979672\pi\)
\(692\) 1.43565i 0.0545752i
\(693\) 25.3769i 0.963987i
\(694\) 14.4187 + 24.9740i 0.547328 + 0.947999i
\(695\) −17.3383 + 10.0969i −0.657680 + 0.382996i
\(696\) 1.63657 2.83462i 0.0620341 0.107446i
\(697\) 19.3941i 0.734605i
\(698\) −20.1486 11.6328i −0.762635 0.440307i
\(699\) −0.956644 + 1.65696i −0.0361836 + 0.0626718i
\(700\) −18.4229 + 10.8209i −0.696320 + 0.408990i
\(701\) 25.0713 + 43.4248i 0.946930 + 1.64013i 0.751839 + 0.659347i \(0.229167\pi\)
0.195091 + 0.980785i \(0.437500\pi\)
\(702\) 1.25053i 0.0471981i
\(703\) 12.3462 + 21.7747i 0.465647 + 0.821249i
\(704\) 5.93869 0.223823
\(705\) 8.97223 + 5.13551i 0.337914 + 0.193414i
\(706\) 0.0977899 0.169377i 0.00368037 0.00637459i
\(707\) −26.6734 15.3999i −1.00316 0.579173i
\(708\) 0.0961772 + 0.0555279i 0.00361456 + 0.00208687i
\(709\) −39.5030 −1.48357 −0.741784 0.670639i \(-0.766020\pi\)
−0.741784 + 0.670639i \(0.766020\pi\)
\(710\) −16.0975 + 0.0601576i −0.604127 + 0.00225768i
\(711\) −6.83733 −0.256420
\(712\) −7.61589 + 4.39703i −0.285417 + 0.164786i
\(713\) 18.5434i 0.694455i
\(714\) −31.0792 −1.16311
\(715\) 8.24926 14.4123i 0.308505 0.538988i
\(716\) 5.68904 9.85370i 0.212609 0.368250i
\(717\) 15.5283i 0.579915i
\(718\) −3.05702 + 1.76497i −0.114087 + 0.0658682i
\(719\) 10.0711 + 17.4437i 0.375589 + 0.650540i 0.990415 0.138123i \(-0.0441070\pi\)
−0.614826 + 0.788663i \(0.710774\pi\)
\(720\) −1.94066 1.11079i −0.0723240 0.0413967i
\(721\) 6.83288 11.8349i 0.254470 0.440754i
\(722\) −1.78898 1.03287i −0.0665790 0.0384394i
\(723\) 9.62345 5.55610i 0.357900 0.206634i
\(724\) 9.91980 + 17.1816i 0.368666 + 0.638549i
\(725\) −16.3653 + 0.122318i −0.607790 + 0.00454279i
\(726\) 24.2680 0.900670
\(727\) 30.2818 + 17.4832i 1.12309 + 0.648417i 0.942188 0.335084i \(-0.108765\pi\)
0.180903 + 0.983501i \(0.442098\pi\)
\(728\) 4.62776 2.67184i 0.171516 0.0990249i
\(729\) −1.00000 −0.0370370
\(730\) −6.49558 + 3.78266i −0.240412 + 0.140003i
\(731\) 32.8847 + 56.9580i 1.21629 + 2.10667i
\(732\) 12.2824i 0.453969i
\(733\) −4.06319 2.34588i −0.150077 0.0866471i 0.423081 0.906092i \(-0.360949\pi\)
−0.573158 + 0.819445i \(0.694282\pi\)
\(734\) −1.99904 −0.0737861
\(735\) −25.1774 + 0.0940901i −0.928682 + 0.00347056i
\(736\) −3.44908 + 5.97399i −0.127135 + 0.220204i
\(737\) 26.4003 + 15.2422i 0.972467 + 0.561454i
\(738\) 2.30929 1.33327i 0.0850062 0.0490784i
\(739\) 19.3032 0.710079 0.355040 0.934851i \(-0.384467\pi\)
0.355040 + 0.934851i \(0.384467\pi\)
\(740\) 11.8067 6.75283i 0.434025 0.248239i
\(741\) 5.14607 0.189046
\(742\) 5.62350 3.24673i 0.206445 0.119191i
\(743\) −34.6971 20.0324i −1.27291 0.734917i −0.297378 0.954760i \(-0.596112\pi\)
−0.975535 + 0.219843i \(0.929445\pi\)
\(744\) −1.34408 + 2.32802i −0.0492764 + 0.0853492i
\(745\) −0.101169 27.0717i −0.00370656 0.991831i
\(746\) −13.8065 −0.505492
\(747\) −6.46021 3.72981i −0.236367 0.136466i
\(748\) 43.1929i 1.57929i
\(749\) −16.4854 28.5535i −0.602362 1.04332i
\(750\) 0.125342 + 11.1796i 0.00457686 + 0.408223i
\(751\) −9.68222 −0.353309 −0.176655 0.984273i \(-0.556528\pi\)
−0.176655 + 0.984273i \(0.556528\pi\)
\(752\) −4.00389 + 2.31165i −0.146007 + 0.0842971i
\(753\) −11.5497 6.66822i −0.420894 0.243003i
\(754\) 4.09315 0.149064
\(755\) −18.6718 10.6873i −0.679535 0.388951i
\(756\) −2.13657 3.70065i −0.0777063 0.134591i
\(757\) −28.5617 + 16.4901i −1.03809 + 0.599342i −0.919292 0.393576i \(-0.871238\pi\)
−0.118799 + 0.992918i \(0.537904\pi\)
\(758\) 5.85465 + 3.38018i 0.212650 + 0.122774i
\(759\) −20.4830 + 35.4776i −0.743487 + 1.28776i
\(760\) 4.57104 7.98605i 0.165809 0.289684i
\(761\) 24.2801 + 42.0544i 0.880155 + 1.52447i 0.851169 + 0.524893i \(0.175894\pi\)
0.0289860 + 0.999580i \(0.490772\pi\)
\(762\) −13.1682 + 7.60268i −0.477034 + 0.275416i
\(763\) 32.9388i 1.19246i
\(764\) 5.55119 9.61493i 0.200835 0.347856i
\(765\) −8.07893 + 14.1147i −0.292094 + 0.510317i
\(766\) 14.0998 0.509447
\(767\) 0.138878i 0.00501460i
\(768\) 0.866025 0.500000i 0.0312500 0.0180422i
\(769\) 41.0894 1.48172 0.740861 0.671659i \(-0.234418\pi\)
0.740861 + 0.671659i \(0.234418\pi\)
\(770\) −0.212057 56.7440i −0.00764201 2.04491i
\(771\) −24.6881 −0.889119
\(772\) 21.7655 + 12.5663i 0.783357 + 0.452272i
\(773\) −16.2676 9.39211i −0.585105 0.337811i 0.178054 0.984021i \(-0.443020\pi\)
−0.763160 + 0.646210i \(0.776353\pi\)
\(774\) −4.52139 + 7.83128i −0.162518 + 0.281490i
\(775\) 13.4404 0.100458i 0.482795 0.00360854i
\(776\) −12.1077 −0.434639