Properties

Label 1110.2.bb.d.1009.1
Level $1110$
Weight $2$
Character 1110.1009
Analytic conductor $8.863$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $4$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 1009.1
Character \(\chi\) \(=\) 1110.1009
Dual form 1110.2.bb.d.1099.1

$q$-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 \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 0.500000i −0.612372 0.353553i
\(3\) −0.866025 + 0.500000i −0.500000 + 0.288675i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) −0.00835632 + 2.23605i −0.00373706 + 0.999993i
\(6\) 1.00000 0.408248
\(7\) 3.70065 2.13657i 1.39871 0.807548i 0.404456 0.914557i \(-0.367461\pi\)
0.994258 + 0.107009i \(0.0341275\pi\)
\(8\) 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 −0.642608 0.766195i \(-0.722147\pi\)
0.342241 + 0.939612i \(0.388814\pi\)
\(14\) −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 −0.999459 0.0328820i \(-0.989531\pi\)
−0.528206 0.849116i \(-0.677135\pi\)
\(18\) −0.866025 + 0.500000i −0.204124 + 0.117851i
\(19\) 2.05756 + 3.56380i 0.472037 + 0.817593i 0.999488 0.0319930i \(-0.0101854\pi\)
−0.527451 + 0.849586i \(0.676852\pi\)
\(20\) −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 \(-0.744516\pi\)
0.694820 0.719183i \(-0.255484\pi\)
\(24\) 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 0.742933 0.669366i \(-0.233434\pi\)
−0.951154 + 0.308715i \(0.900101\pi\)
\(42\) 3.70065 2.13657i 0.571023 0.329680i
\(43\) 9.04279i 1.37901i 0.724280 + 0.689506i \(0.242172\pi\)
−0.724280 + 0.689506i \(0.757828\pi\)
\(44\) −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 \(0.109476\pi\)
−0.941437 + 0.337188i \(0.890524\pi\)
\(48\) 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 0.406885 0.913479i \(-0.366615\pi\)
−0.587653 + 0.809113i \(0.699948\pi\)
\(54\) 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 −0.869617 0.493726i \(-0.835634\pi\)
0.862388 + 0.506248i \(0.168968\pi\)
\(60\) 1.12526 1.93230i 0.145271 0.249459i
\(61\) −6.14118 10.6368i −0.786298 1.36191i −0.928221 0.372030i \(-0.878662\pi\)
0.141923 0.989878i \(-0.454671\pi\)
\(62\) 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 −0.746335 0.665571i \(-0.768188\pi\)
0.203234 + 0.979130i \(0.434855\pi\)
\(68\) 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 0.569436 0.822035i \(-0.307161\pi\)
−0.996622 + 0.0821287i \(0.973828\pi\)
\(72\) −0.866025 0.500000i −0.102062 0.0589256i
\(73\) 3.36158i 0.393443i −0.980459 0.196722i \(-0.936970\pi\)
0.980459 0.196722i \(-0.0630295\pi\)
\(74\) 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 0.607088 0.794635i \(-0.292338\pi\)
−0.991718 + 0.128436i \(0.959004\pi\)
\(80\) −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 0.101627 0.994823i \(-0.467595\pi\)
−0.810728 + 0.585423i \(0.800928\pi\)
\(84\) −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 −0.533165 0.846011i \(-0.678998\pi\)
0.999250 + 0.0387290i \(0.0123309\pi\)
\(90\) −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 \(-0.789288\pi\)
0.788782 0.614673i \(-0.210712\pi\)
\(98\) −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 \(0.0503618\pi\)
−0.987510 + 0.157557i \(0.949638\pi\)
\(104\) 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 −0.786915 0.617062i \(-0.788323\pi\)
0.140934 + 0.990019i \(0.454990\pi\)
\(108\) −0.866025 + 0.500000i −0.0833333 + 0.0481125i
\(109\) −3.85417 + 6.67561i −0.369162 + 0.639408i −0.989435 0.144979i \(-0.953689\pi\)
0.620273 + 0.784386i \(0.287022\pi\)
\(110\) −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 0.973489 0.228733i \(-0.0734584\pi\)
0.288656 + 0.957433i \(0.406792\pi\)
\(114\) 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 −0.215167 0.976577i \(-0.569029\pi\)
−0.953324 + 0.301949i \(0.902363\pi\)
\(128\) 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 −0.240106 0.970747i \(-0.577182\pi\)
0.960744 0.277435i \(-0.0894844\pi\)
\(132\) 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 \(0.445194\pi\)
−0.171327 + 0.985214i \(0.554806\pi\)
\(138\) 6.89816i 0.587211i
\(139\) −4.48645 + 7.77075i −0.380535 + 0.659107i −0.991139 0.132830i \(-0.957594\pi\)
0.610603 + 0.791937i \(0.290927\pi\)
\(140\) −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 0.992646 0.121053i \(-0.0386271\pi\)
−0.601158 + 0.799130i \(0.705294\pi\)
\(152\) 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 0.173156 0.984894i \(-0.444604\pi\)
−0.766366 + 0.642405i \(0.777937\pi\)
\(158\) 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 −0.998804 0.0488890i \(-0.984432\pi\)
−0.541741 0.840545i \(-0.682235\pi\)
\(164\) 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 −0.645388 0.763855i \(-0.723304\pi\)
0.338824 + 0.940850i \(0.389971\pi\)
\(168\) 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 0.546518 0.837447i \(-0.315953\pi\)
−0.451991 + 0.892022i \(0.649286\pi\)
\(174\) 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 −0.953692 0.300784i \(-0.902752\pi\)
0.216359 0.976314i \(-0.430582\pi\)
\(182\) 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 \(-0.640212\pi\)
0.426382 0.904543i \(-0.359788\pi\)
\(194\) −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 0.464175 0.885744i \(-0.346351\pi\)
−0.534989 + 0.844859i \(0.679684\pi\)
\(198\) 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 \(-0.775157\pi\)
0.760727 0.649072i \(-0.224843\pi\)
\(224\) 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 −0.661109 0.750289i \(-0.729914\pi\)
0.319215 + 0.947682i \(0.396581\pi\)
\(228\) 4.11513i 0.272531i
\(229\) 4.45902 + 7.72325i 0.294660 + 0.510367i 0.974906 0.222618i \(-0.0714602\pi\)
−0.680246 + 0.732984i \(0.738127\pi\)
\(230\) −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 \(0.0199621\pi\)
−0.998034 + 0.0626718i \(0.980038\pi\)
\(234\) 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 0.497776 + 0.867306i \(0.334150\pi\)
−0.999997 + 0.00256635i \(0.999183\pi\)
\(240\) 2.23605 + 0.00835632i 0.144337 + 0.000539398i
\(241\) −5.55610 9.62345i −0.357900 0.619901i 0.629710 0.776830i \(-0.283174\pi\)
−0.987610 + 0.156929i \(0.949840\pi\)
\(242\) −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 0.985861 0.167563i \(-0.0535898\pi\)
0.347817 + 0.937563i \(0.386923\pi\)
\(258\) 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 −0.988222 0.153029i \(-0.951097\pi\)
−0.361584 + 0.932340i \(0.617764\pi\)
\(264\) −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 −0.994365 0.106006i \(-0.966194\pi\)
0.588987 + 0.808143i \(0.299527\pi\)
\(272\) 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 0.0730329 0.997330i \(-0.476732\pi\)
0.900229 + 0.435416i \(0.143399\pi\)
\(278\) 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 −0.977870 0.209214i \(-0.932909\pi\)
0.670120 + 0.742253i \(0.266243\pi\)
\(282\) 4.62329i 0.275313i
\(283\) −5.24310 + 3.02711i −0.311670 + 0.179943i −0.647674 0.761918i \(-0.724258\pi\)
0.336003 + 0.941861i \(0.390925\pi\)
\(284\) 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 −0.359469 0.933157i \(-0.617042\pi\)
0.628403 + 0.777888i \(0.283709\pi\)
\(294\) 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 \(0.174672\pi\)
−0.853178 + 0.521620i \(0.825328\pi\)
\(308\) −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 −0.0924383 + 0.995718i \(0.529466\pi\)
−0.816098 + 0.577913i \(0.803867\pi\)
\(312\) −1.08299 0.625263i −0.0613121 0.0353985i
\(313\) 7.68688 + 4.43802i 0.434488 + 0.250852i 0.701257 0.712909i \(-0.252623\pi\)
−0.266769 + 0.963761i \(0.585956\pi\)
\(314\) 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 0.603553 0.797323i \(-0.293751\pi\)
−0.388725 + 0.921354i \(0.627085\pi\)
\(318\) −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 0.0597696 + 0.998212i \(0.480963\pi\)
−0.894362 + 0.447344i \(0.852370\pi\)
\(332\) 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 −0.945951 0.324310i \(-0.894868\pi\)
−0.192115 + 0.981372i \(0.561535\pi\)
\(338\) 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 \(0.281766\pi\)
−0.633139 + 0.774038i \(0.718234\pi\)
\(348\) −2.83462 1.63657i −0.151952 0.0877294i
\(349\) 11.6328 20.1486i 0.622689 1.07853i −0.366294 0.930499i \(-0.619374\pi\)
0.988983 0.148029i \(-0.0472930\pi\)
\(350\) 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 0.495486 0.868616i \(-0.334990\pi\)
−0.504501 + 0.863411i \(0.668323\pi\)
\(354\) −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 −0.454134 0.890933i \(-0.650051\pi\)
0.544504 + 0.838759i \(0.316718\pi\)
\(368\) 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 −0.157419 0.987532i \(-0.550317\pi\)
0.776518 + 0.630095i \(0.216984\pi\)
\(374\) −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 −0.939686 0.342039i \(-0.888882\pi\)
0.766057 + 0.642772i \(0.222216\pi\)
\(380\) −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 −0.778402 0.627766i \(-0.783970\pi\)
0.154460 + 0.987999i \(0.450636\pi\)
\(384\) −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 0.929732 0.368236i \(-0.120038\pi\)
−0.783768 + 0.621054i \(0.786705\pi\)
\(390\) −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 \(-0.904159\pi\)
0.955013 0.296565i \(-0.0958411\pi\)
\(398\) −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 −0.828814 0.559524i \(-0.810984\pi\)
0.898969 + 0.438012i \(0.144317\pi\)
\(410\) −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 −0.799836 0.600219i \(-0.795080\pi\)
0.919723 + 0.392569i \(0.128414\pi\)
\(420\) 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 0.648065 0.761585i \(-0.275578\pi\)
−0.983584 + 0.180449i \(0.942245\pi\)
\(432\) −0.866025 0.500000i −0.0416667 0.0240563i
\(433\) 22.8789i 1.09949i 0.835332 + 0.549746i \(0.185275\pi\)
−0.835332 + 0.549746i \(0.814725\pi\)
\(434\) 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 0.716582 0.697502i \(-0.245705\pi\)
−0.962346 + 0.271827i \(0.912372\pi\)
\(440\) −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 \(0.169927\pi\)
−0.860859 + 0.508844i \(0.830073\pi\)
\(444\) 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 −0.936924 0.349533i \(-0.886340\pi\)
0.165757 0.986167i \(-0.446993\pi\)
\(450\) 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 −0.703738 0.710459i \(-0.748487\pi\)
0.263407 + 0.964685i \(0.415154\pi\)
\(458\) 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 −0.303856 0.952718i \(-0.598274\pi\)
0.977006 0.213212i \(-0.0683925\pi\)
\(462\) −21.9770 + 12.6884i −1.02246 + 0.590319i
\(463\) 32.1719 18.5745i 1.49516 0.863229i 0.495172 0.868795i \(-0.335105\pi\)
0.999985 + 0.00556589i \(0.00177169\pi\)
\(464\) −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 \(0.173054\pi\)
−0.855819 + 0.517276i \(0.826946\pi\)
\(468\) −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 −0.717634 0.696420i \(-0.754775\pi\)
0.961935 + 0.273279i \(0.0881084\pi\)
\(480\) −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 \(0.0943656\pi\)
−0.956377 + 0.292135i \(0.905634\pi\)
\(488\) −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 0.710350 0.703849i \(-0.248537\pi\)
−0.964726 + 0.263256i \(0.915204\pi\)
\(500\) 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 0.622899 0.782302i \(-0.285955\pi\)
−0.366044 + 0.930598i \(0.619288\pi\)
\(504\) −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 −0.765575 0.643347i \(-0.777545\pi\)
0.939942 + 0.341334i \(0.110879\pi\)
\(510\) 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 0.963367 + 0.268188i \(0.0864249\pi\)
−0.249425 + 0.968394i \(0.580242\pi\)
\(522\) −2.83462 + 1.63657i −0.124068 + 0.0716308i
\(523\) 10.8426 6.26000i 0.474116 0.273731i −0.243845 0.969814i \(-0.578409\pi\)
0.717961 + 0.696083i \(0.245076\pi\)
\(524\) 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 \(0.272666\pi\)
−0.655006 + 0.755624i \(0.727334\pi\)
\(548\) −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 0.386299 0.922374i \(-0.373753\pi\)
−0.605650 + 0.795731i \(0.707087\pi\)
\(558\) 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 \(-0.912436\pi\)
0.962401 0.271634i \(-0.0875641\pi\)
\(564\) 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 −0.478985 0.877823i \(-0.658995\pi\)
0.999710 0.0240989i \(-0.00767165\pi\)
\(572\) 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 0.365975 0.930625i \(-0.380736\pi\)
−0.622957 + 0.782256i \(0.714069\pi\)
\(578\) 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 −0.665964 0.745984i \(-0.731980\pi\)
0.313059 + 0.949734i \(0.398646\pi\)
\(588\) −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 \(-0.807971\pi\)
0.823481 0.567343i \(-0.192029\pi\)
\(594\) −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 0.992341 0.123527i \(-0.0394205\pi\)
−0.603148 + 0.797629i \(0.706087\pi\)
\(600\) −2.46757 4.34869i −0.100738 0.177535i
\(601\) −17.3651 + 30.0773i −0.708338 + 1.22688i 0.257135 + 0.966375i \(0.417221\pi\)
−0.965473 + 0.260502i \(0.916112\pi\)
\(602\) 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 0.421187 0.906974i \(-0.361614\pi\)
−0.574869 + 0.818245i \(0.694947\pi\)
\(608\) 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 0.507479 0.861664i \(-0.330577\pi\)
−0.492483 + 0.870322i \(0.663911\pi\)
\(614\) 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 0.230010 0.973188i \(-0.426124\pi\)
−0.727801 + 0.685789i \(0.759457\pi\)
\(618\) 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 −0.975294 0.220911i \(-0.929097\pi\)
0.678961 + 0.734174i \(0.262430\pi\)
\(632\) −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 0.381426 + 0.924399i \(0.375433\pi\)
−0.991266 + 0.131875i \(0.957900\pi\)
\(642\) −6.68208 + 3.85790i −0.263721 + 0.152259i
\(643\) 6.52207i 0.257205i −0.991696 0.128603i \(-0.958951\pi\)
0.991696 0.128603i \(-0.0410492\pi\)
\(644\) 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 −0.0687382 0.997635i \(-0.521897\pi\)
0.829608 + 0.558346i \(0.188564\pi\)
\(648\) −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 0.237483 0.971392i \(-0.423678\pi\)
0.959991 + 0.280030i \(0.0903443\pi\)
\(654\) −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 0.870569 0.492046i \(-0.163751\pi\)
−0.861409 + 0.507912i \(0.830418\pi\)
\(660\) −6.68259 + 11.4753i −0.260119 + 0.446676i
\(661\) 9.15487 + 15.8567i 0.356083 + 0.616754i 0.987303 0.158850i \(-0.0507787\pi\)
−0.631220 + 0.775604i \(0.717445\pi\)
\(662\) 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 −0.446882 0.894593i \(-0.647466\pi\)
0.551299 + 0.834308i \(0.314132\pi\)
\(674\) 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 \(-0.831202\pi\)
0.862658 0.505787i \(-0.168798\pi\)
\(678\) 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 0.494306 0.869288i \(-0.335422\pi\)
−0.505672 + 0.862726i \(0.668756\pi\)
\(684\) 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 −0.997961 0.0638196i \(-0.979672\pi\)
0.554250 + 0.832350i \(0.313005\pi\)
\(692\) 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 0.195091 0.980785i \(-0.437500\pi\)
0.751839 0.659347i \(-0.229167\pi\)
\(702\) 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 −0.614826 0.788663i \(-0.710774\pi\)
0.990415 + 0.138123i \(0.0441070\pi\)
\(720\) −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 0.180903 0.983501i \(-0.442098\pi\)
0.942188 + 0.335084i \(0.108765\pi\)
\(728\) 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 −0.573158 0.819445i \(-0.694282\pi\)
0.423081 + 0.906092i \(0.360949\pi\)
\(734\) −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 −0.975535 0.219843i \(-0.929445\pi\)
−0.297378 + 0.954760i \(0.596112\pi\)
\(744\) −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 −0.118799 0.992918i \(-0.537904\pi\)
−0.919292 + 0.393576i \(0.871238\pi\)
\(758\) 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 0.0289860 0.999580i \(-0.490772\pi\)
0.851169 0.524893i \(-0.175894\pi\)
\(762\) −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 −0.763160 0.646210i \(-0.776353\pi\)
0.178054 + 0.984021i \(0.443020\pi\)
\(774\) −4.52139 7.83128i −0.162518 0.281490i
\(775\) 13.4404 + 0.100458i 0.482795 + 0.00360854i
\(776\) −12.1077 −0.434639