Properties

Label 690.2.i.e.47.9
Level $690$
Weight $2$
Character 690.47
Analytic conductor $5.510$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 690.i (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.50967773947\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 47.9
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.e.323.9

$q$-expansion

\(f(q)\) \(=\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.67204 - 0.451971i) q^{3} -1.00000i q^{4} +(-0.664484 - 2.13506i) q^{5} +(-1.50190 + 0.862720i) q^{6} +(2.34139 + 2.34139i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59144 + 1.51143i) q^{9} +O(q^{10})\) \(q+(0.707107 - 0.707107i) q^{2} +(-1.67204 - 0.451971i) q^{3} -1.00000i q^{4} +(-0.664484 - 2.13506i) q^{5} +(-1.50190 + 0.862720i) q^{6} +(2.34139 + 2.34139i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.59144 + 1.51143i) q^{9} +(-1.97957 - 1.03985i) q^{10} -4.92608i q^{11} +(-0.451971 + 1.67204i) q^{12} +(2.78495 - 2.78495i) q^{13} +3.31122 q^{14} +(0.146062 + 3.87023i) q^{15} -1.00000 q^{16} +(-2.05101 + 2.05101i) q^{17} +(2.90117 - 0.763687i) q^{18} -3.73962i q^{19} +(-2.13506 + 0.664484i) q^{20} +(-2.85666 - 4.97313i) q^{21} +(-3.48326 - 3.48326i) q^{22} +(-0.707107 - 0.707107i) q^{23} +(0.862720 + 1.50190i) q^{24} +(-4.11692 + 2.83742i) q^{25} -3.93852i q^{26} +(-3.64988 - 3.69843i) q^{27} +(2.34139 - 2.34139i) q^{28} -9.53664 q^{29} +(2.83995 + 2.63338i) q^{30} -2.15514 q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.22644 + 8.23661i) q^{33} +2.90057i q^{34} +(3.44317 - 6.55480i) q^{35} +(1.51143 - 2.59144i) q^{36} +(-1.67965 - 1.67965i) q^{37} +(-2.64431 - 2.64431i) q^{38} +(-5.91528 + 3.39784i) q^{39} +(-1.03985 + 1.97957i) q^{40} +5.18461i q^{41} +(-5.53650 - 1.49657i) q^{42} +(2.73681 - 2.73681i) q^{43} -4.92608 q^{44} +(1.50501 - 6.53720i) q^{45} -1.00000 q^{46} +(8.67231 - 8.67231i) q^{47} +(1.67204 + 0.451971i) q^{48} +3.96417i q^{49} +(-0.904744 + 4.91746i) q^{50} +(4.35637 - 2.50238i) q^{51} +(-2.78495 - 2.78495i) q^{52} +(8.92096 + 8.92096i) q^{53} +(-5.19604 - 0.0343279i) q^{54} +(-10.5174 + 3.27330i) q^{55} -3.31122i q^{56} +(-1.69020 + 6.25279i) q^{57} +(-6.74342 + 6.74342i) q^{58} -4.44157 q^{59} +(3.87023 - 0.146062i) q^{60} -2.83318 q^{61} +(-1.52391 + 1.52391i) q^{62} +(2.52873 + 9.60641i) q^{63} +1.00000i q^{64} +(-7.79659 - 4.09547i) q^{65} +(4.24983 + 7.39849i) q^{66} +(-6.60677 - 6.60677i) q^{67} +(2.05101 + 2.05101i) q^{68} +(0.862720 + 1.50190i) q^{69} +(-2.20025 - 7.06964i) q^{70} -1.39093i q^{71} +(-0.763687 - 2.90117i) q^{72} +(7.65822 - 7.65822i) q^{73} -2.37538 q^{74} +(8.16609 - 2.88356i) q^{75} -3.73962 q^{76} +(11.5338 - 11.5338i) q^{77} +(-1.78010 + 6.58537i) q^{78} -1.62454i q^{79} +(0.664484 + 2.13506i) q^{80} +(4.43117 + 7.83356i) q^{81} +(3.66607 + 3.66607i) q^{82} +(0.357742 + 0.357742i) q^{83} +(-4.97313 + 2.85666i) q^{84} +(5.74189 + 3.01616i) q^{85} -3.87043i q^{86} +(15.9457 + 4.31028i) q^{87} +(-3.48326 + 3.48326i) q^{88} +7.92555 q^{89} +(-3.55829 - 5.68670i) q^{90} +13.0413 q^{91} +(-0.707107 + 0.707107i) q^{92} +(3.60348 + 0.974060i) q^{93} -12.2645i q^{94} +(-7.98429 + 2.48492i) q^{95} +(1.50190 - 0.862720i) q^{96} +(5.52335 + 5.52335i) q^{97} +(2.80309 + 2.80309i) q^{98} +(7.44541 - 12.7657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} + O(q^{10}) \) \( 32q + 4q^{3} - 4q^{6} - 8q^{7} - 8q^{10} - 4q^{12} - 4q^{15} - 32q^{16} + 8q^{18} - 32q^{21} - 8q^{22} + 4q^{27} - 8q^{28} + 20q^{30} - 24q^{31} + 20q^{36} - 32q^{37} - 16q^{40} + 8q^{42} + 144q^{43} + 36q^{45} - 32q^{46} - 4q^{48} + 12q^{51} - 64q^{55} + 52q^{57} + 16q^{58} + 4q^{60} - 24q^{61} - 116q^{63} + 12q^{66} - 16q^{67} - 80q^{70} - 8q^{72} + 40q^{73} + 44q^{75} + 24q^{76} - 36q^{78} - 108q^{81} - 32q^{82} - 80q^{85} + 68q^{87} - 8q^{88} + 16q^{90} + 120q^{91} + 12q^{93} + 4q^{96} - 8q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).

\(n\) \(277\) \(461\) \(511\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.707107 0.707107i 0.500000 0.500000i
\(3\) −1.67204 0.451971i −0.965354 0.260946i
\(4\) 1.00000i 0.500000i
\(5\) −0.664484 2.13506i −0.297166 0.954826i
\(6\) −1.50190 + 0.862720i −0.613150 + 0.352204i
\(7\) 2.34139 + 2.34139i 0.884961 + 0.884961i 0.994034 0.109073i \(-0.0347883\pi\)
−0.109073 + 0.994034i \(0.534788\pi\)
\(8\) −0.707107 0.707107i −0.250000 0.250000i
\(9\) 2.59144 + 1.51143i 0.863815 + 0.503809i
\(10\) −1.97957 1.03985i −0.625996 0.328830i
\(11\) 4.92608i 1.48527i −0.669697 0.742634i \(-0.733576\pi\)
0.669697 0.742634i \(-0.266424\pi\)
\(12\) −0.451971 + 1.67204i −0.130473 + 0.482677i
\(13\) 2.78495 2.78495i 0.772407 0.772407i −0.206120 0.978527i \(-0.566084\pi\)
0.978527 + 0.206120i \(0.0660836\pi\)
\(14\) 3.31122 0.884961
\(15\) 0.146062 + 3.87023i 0.0377131 + 0.999289i
\(16\) −1.00000 −0.250000
\(17\) −2.05101 + 2.05101i −0.497443 + 0.497443i −0.910641 0.413198i \(-0.864412\pi\)
0.413198 + 0.910641i \(0.364412\pi\)
\(18\) 2.90117 0.763687i 0.683812 0.180003i
\(19\) 3.73962i 0.857927i −0.903322 0.428963i \(-0.858879\pi\)
0.903322 0.428963i \(-0.141121\pi\)
\(20\) −2.13506 + 0.664484i −0.477413 + 0.148583i
\(21\) −2.85666 4.97313i −0.623373 1.08523i
\(22\) −3.48326 3.48326i −0.742634 0.742634i
\(23\) −0.707107 0.707107i −0.147442 0.147442i
\(24\) 0.862720 + 1.50190i 0.176102 + 0.306575i
\(25\) −4.11692 + 2.83742i −0.823384 + 0.567484i
\(26\) 3.93852i 0.772407i
\(27\) −3.64988 3.69843i −0.702420 0.711763i
\(28\) 2.34139 2.34139i 0.442480 0.442480i
\(29\) −9.53664 −1.77091 −0.885455 0.464725i \(-0.846153\pi\)
−0.885455 + 0.464725i \(0.846153\pi\)
\(30\) 2.83995 + 2.63338i 0.518501 + 0.480788i
\(31\) −2.15514 −0.387074 −0.193537 0.981093i \(-0.561996\pi\)
−0.193537 + 0.981093i \(0.561996\pi\)
\(32\) −0.707107 + 0.707107i −0.125000 + 0.125000i
\(33\) −2.22644 + 8.23661i −0.387574 + 1.43381i
\(34\) 2.90057i 0.497443i
\(35\) 3.44317 6.55480i 0.582003 1.10796i
\(36\) 1.51143 2.59144i 0.251905 0.431907i
\(37\) −1.67965 1.67965i −0.276133 0.276133i 0.555430 0.831563i \(-0.312554\pi\)
−0.831563 + 0.555430i \(0.812554\pi\)
\(38\) −2.64431 2.64431i −0.428963 0.428963i
\(39\) −5.91528 + 3.39784i −0.947202 + 0.544090i
\(40\) −1.03985 + 1.97957i −0.164415 + 0.312998i
\(41\) 5.18461i 0.809700i 0.914383 + 0.404850i \(0.132676\pi\)
−0.914383 + 0.404850i \(0.867324\pi\)
\(42\) −5.53650 1.49657i −0.854300 0.230926i
\(43\) 2.73681 2.73681i 0.417359 0.417359i −0.466933 0.884292i \(-0.654641\pi\)
0.884292 + 0.466933i \(0.154641\pi\)
\(44\) −4.92608 −0.742634
\(45\) 1.50501 6.53720i 0.224353 0.974508i
\(46\) −1.00000 −0.147442
\(47\) 8.67231 8.67231i 1.26499 1.26499i 0.316341 0.948645i \(-0.397545\pi\)
0.948645 0.316341i \(-0.102455\pi\)
\(48\) 1.67204 + 0.451971i 0.241338 + 0.0652364i
\(49\) 3.96417i 0.566310i
\(50\) −0.904744 + 4.91746i −0.127950 + 0.695434i
\(51\) 4.35637 2.50238i 0.610014 0.350403i
\(52\) −2.78495 2.78495i −0.386204 0.386204i
\(53\) 8.92096 + 8.92096i 1.22539 + 1.22539i 0.965690 + 0.259697i \(0.0836228\pi\)
0.259697 + 0.965690i \(0.416377\pi\)
\(54\) −5.19604 0.0343279i −0.707091 0.00467144i
\(55\) −10.5174 + 3.27330i −1.41817 + 0.441372i
\(56\) 3.31122i 0.442480i
\(57\) −1.69020 + 6.25279i −0.223872 + 0.828203i
\(58\) −6.74342 + 6.74342i −0.885455 + 0.885455i
\(59\) −4.44157 −0.578243 −0.289122 0.957292i \(-0.593363\pi\)
−0.289122 + 0.957292i \(0.593363\pi\)
\(60\) 3.87023 0.146062i 0.499644 0.0188565i
\(61\) −2.83318 −0.362752 −0.181376 0.983414i \(-0.558055\pi\)
−0.181376 + 0.983414i \(0.558055\pi\)
\(62\) −1.52391 + 1.52391i −0.193537 + 0.193537i
\(63\) 2.52873 + 9.60641i 0.318591 + 1.21029i
\(64\) 1.00000i 0.125000i
\(65\) −7.79659 4.09547i −0.967048 0.507981i
\(66\) 4.24983 + 7.39849i 0.523118 + 0.910692i
\(67\) −6.60677 6.60677i −0.807146 0.807146i 0.177055 0.984201i \(-0.443343\pi\)
−0.984201 + 0.177055i \(0.943343\pi\)
\(68\) 2.05101 + 2.05101i 0.248722 + 0.248722i
\(69\) 0.862720 + 1.50190i 0.103859 + 0.180808i
\(70\) −2.20025 7.06964i −0.262980 0.844983i
\(71\) 1.39093i 0.165073i −0.996588 0.0825365i \(-0.973698\pi\)
0.996588 0.0825365i \(-0.0263021\pi\)
\(72\) −0.763687 2.90117i −0.0900014 0.341906i
\(73\) 7.65822 7.65822i 0.896327 0.896327i −0.0987822 0.995109i \(-0.531495\pi\)
0.995109 + 0.0987822i \(0.0314947\pi\)
\(74\) −2.37538 −0.276133
\(75\) 8.16609 2.88356i 0.942939 0.332964i
\(76\) −3.73962 −0.428963
\(77\) 11.5338 11.5338i 1.31440 1.31440i
\(78\) −1.78010 + 6.58537i −0.201556 + 0.745646i
\(79\) 1.62454i 0.182775i −0.995815 0.0913877i \(-0.970870\pi\)
0.995815 0.0913877i \(-0.0291303\pi\)
\(80\) 0.664484 + 2.13506i 0.0742916 + 0.238706i
\(81\) 4.43117 + 7.83356i 0.492352 + 0.870396i
\(82\) 3.66607 + 3.66607i 0.404850 + 0.404850i
\(83\) 0.357742 + 0.357742i 0.0392673 + 0.0392673i 0.726468 0.687201i \(-0.241161\pi\)
−0.687201 + 0.726468i \(0.741161\pi\)
\(84\) −4.97313 + 2.85666i −0.542613 + 0.311687i
\(85\) 5.74189 + 3.01616i 0.622795 + 0.327148i
\(86\) 3.87043i 0.417359i
\(87\) 15.9457 + 4.31028i 1.70955 + 0.462111i
\(88\) −3.48326 + 3.48326i −0.371317 + 0.371317i
\(89\) 7.92555 0.840106 0.420053 0.907499i \(-0.362011\pi\)
0.420053 + 0.907499i \(0.362011\pi\)
\(90\) −3.55829 5.68670i −0.375077 0.599431i
\(91\) 13.0413 1.36710
\(92\) −0.707107 + 0.707107i −0.0737210 + 0.0737210i
\(93\) 3.60348 + 0.974060i 0.373664 + 0.101005i
\(94\) 12.2645i 1.26499i
\(95\) −7.98429 + 2.48492i −0.819171 + 0.254947i
\(96\) 1.50190 0.862720i 0.153287 0.0880510i
\(97\) 5.52335 + 5.52335i 0.560811 + 0.560811i 0.929538 0.368726i \(-0.120206\pi\)
−0.368726 + 0.929538i \(0.620206\pi\)
\(98\) 2.80309 + 2.80309i 0.283155 + 0.283155i
\(99\) 7.44541 12.7657i 0.748292 1.28300i
\(100\) 2.83742 + 4.11692i 0.283742 + 0.411692i
\(101\) 18.2907i 1.81999i −0.414619 0.909995i \(-0.636085\pi\)
0.414619 0.909995i \(-0.363915\pi\)
\(102\) 1.31097 4.84987i 0.129806 0.480209i
\(103\) 8.14075 8.14075i 0.802132 0.802132i −0.181297 0.983428i \(-0.558029\pi\)
0.983428 + 0.181297i \(0.0580294\pi\)
\(104\) −3.93852 −0.386204
\(105\) −8.71971 + 9.40368i −0.850956 + 0.917706i
\(106\) 12.6161 1.22539
\(107\) −2.27414 + 2.27414i −0.219849 + 0.219849i −0.808435 0.588586i \(-0.799685\pi\)
0.588586 + 0.808435i \(0.299685\pi\)
\(108\) −3.69843 + 3.64988i −0.355881 + 0.351210i
\(109\) 3.20141i 0.306640i 0.988177 + 0.153320i \(0.0489965\pi\)
−0.988177 + 0.153320i \(0.951003\pi\)
\(110\) −5.12239 + 9.75153i −0.488400 + 0.929772i
\(111\) 2.04929 + 3.56760i 0.194510 + 0.338621i
\(112\) −2.34139 2.34139i −0.221240 0.221240i
\(113\) 6.56397 + 6.56397i 0.617486 + 0.617486i 0.944886 0.327400i \(-0.106172\pi\)
−0.327400 + 0.944886i \(0.606172\pi\)
\(114\) 3.22624 + 5.61654i 0.302165 + 0.526037i
\(115\) −1.03985 + 1.97957i −0.0969666 + 0.184596i
\(116\) 9.53664i 0.885455i
\(117\) 11.4263 3.00780i 1.05636 0.278071i
\(118\) −3.14067 + 3.14067i −0.289122 + 0.289122i
\(119\) −9.60441 −0.880435
\(120\) 2.63338 2.83995i 0.240394 0.259250i
\(121\) −13.2663 −1.20602
\(122\) −2.00336 + 2.00336i −0.181376 + 0.181376i
\(123\) 2.34329 8.66888i 0.211288 0.781647i
\(124\) 2.15514i 0.193537i
\(125\) 8.79368 + 6.90443i 0.786531 + 0.617551i
\(126\) 8.58084 + 5.00467i 0.764442 + 0.445851i
\(127\) 8.84885 + 8.84885i 0.785209 + 0.785209i 0.980705 0.195496i \(-0.0626316\pi\)
−0.195496 + 0.980705i \(0.562632\pi\)
\(128\) 0.707107 + 0.707107i 0.0625000 + 0.0625000i
\(129\) −5.81301 + 3.33910i −0.511807 + 0.293991i
\(130\) −8.40896 + 2.61708i −0.737514 + 0.229533i
\(131\) 0.892813i 0.0780054i −0.999239 0.0390027i \(-0.987582\pi\)
0.999239 0.0390027i \(-0.0124181\pi\)
\(132\) 8.23661 + 2.22644i 0.716905 + 0.193787i
\(133\) 8.75588 8.75588i 0.759231 0.759231i
\(134\) −9.34339 −0.807146
\(135\) −5.47106 + 10.2502i −0.470874 + 0.882201i
\(136\) 2.90057 0.248722
\(137\) −5.62646 + 5.62646i −0.480701 + 0.480701i −0.905355 0.424655i \(-0.860396\pi\)
0.424655 + 0.905355i \(0.360396\pi\)
\(138\) 1.67204 + 0.451971i 0.142334 + 0.0384743i
\(139\) 11.0965i 0.941196i 0.882348 + 0.470598i \(0.155962\pi\)
−0.882348 + 0.470598i \(0.844038\pi\)
\(140\) −6.55480 3.44317i −0.553982 0.291001i
\(141\) −18.4201 + 10.5808i −1.55125 + 0.891067i
\(142\) −0.983536 0.983536i −0.0825365 0.0825365i
\(143\) −13.7189 13.7189i −1.14723 1.14723i
\(144\) −2.59144 1.51143i −0.215954 0.125952i
\(145\) 6.33695 + 20.3613i 0.526255 + 1.69091i
\(146\) 10.8304i 0.896327i
\(147\) 1.79169 6.62826i 0.147776 0.546690i
\(148\) −1.67965 + 1.67965i −0.138066 + 0.138066i
\(149\) −12.7504 −1.04456 −0.522278 0.852775i \(-0.674918\pi\)
−0.522278 + 0.852775i \(0.674918\pi\)
\(150\) 3.73532 7.81328i 0.304988 0.637952i
\(151\) 17.4795 1.42246 0.711230 0.702959i \(-0.248138\pi\)
0.711230 + 0.702959i \(0.248138\pi\)
\(152\) −2.64431 + 2.64431i −0.214482 + 0.214482i
\(153\) −8.41504 + 2.21513i −0.680315 + 0.179082i
\(154\) 16.3113i 1.31440i
\(155\) 1.43206 + 4.60134i 0.115025 + 0.369589i
\(156\) 3.39784 + 5.91528i 0.272045 + 0.473601i
\(157\) 9.49292 + 9.49292i 0.757617 + 0.757617i 0.975888 0.218271i \(-0.0700416\pi\)
−0.218271 + 0.975888i \(0.570042\pi\)
\(158\) −1.14873 1.14873i −0.0913877 0.0913877i
\(159\) −10.8842 18.9482i −0.863173 1.50269i
\(160\) 1.97957 + 1.03985i 0.156499 + 0.0822074i
\(161\) 3.31122i 0.260961i
\(162\) 8.67248 + 2.40586i 0.681374 + 0.189022i
\(163\) −11.6062 + 11.6062i −0.909072 + 0.909072i −0.996197 0.0871258i \(-0.972232\pi\)
0.0871258 + 0.996197i \(0.472232\pi\)
\(164\) 5.18461 0.404850
\(165\) 19.0650 0.719514i 1.48421 0.0560141i
\(166\) 0.505923 0.0392673
\(167\) −2.96090 + 2.96090i −0.229121 + 0.229121i −0.812326 0.583204i \(-0.801799\pi\)
0.583204 + 0.812326i \(0.301799\pi\)
\(168\) −1.49657 + 5.53650i −0.115463 + 0.427150i
\(169\) 2.51194i 0.193226i
\(170\) 6.19287 1.92738i 0.474972 0.147823i
\(171\) 5.65216 9.69101i 0.432232 0.741090i
\(172\) −2.73681 2.73681i −0.208680 0.208680i
\(173\) 16.0409 + 16.0409i 1.21957 + 1.21957i 0.967783 + 0.251786i \(0.0810179\pi\)
0.251786 + 0.967783i \(0.418982\pi\)
\(174\) 14.3231 8.22745i 1.08583 0.623721i
\(175\) −16.2828 2.99580i −1.23086 0.226462i
\(176\) 4.92608i 0.371317i
\(177\) 7.42649 + 2.00746i 0.558209 + 0.150890i
\(178\) 5.60421 5.60421i 0.420053 0.420053i
\(179\) −1.42969 −0.106860 −0.0534301 0.998572i \(-0.517015\pi\)
−0.0534301 + 0.998572i \(0.517015\pi\)
\(180\) −6.53720 1.50501i −0.487254 0.112177i
\(181\) 2.71065 0.201481 0.100740 0.994913i \(-0.467879\pi\)
0.100740 + 0.994913i \(0.467879\pi\)
\(182\) 9.22159 9.22159i 0.683550 0.683550i
\(183\) 4.73720 + 1.28052i 0.350184 + 0.0946585i
\(184\) 1.00000i 0.0737210i
\(185\) −2.47004 + 4.70225i −0.181601 + 0.345716i
\(186\) 3.23681 1.85928i 0.237334 0.136329i
\(187\) 10.1034 + 10.1034i 0.738837 + 0.738837i
\(188\) −8.67231 8.67231i −0.632493 0.632493i
\(189\) 0.113667 17.2052i 0.00826807 1.25150i
\(190\) −3.88864 + 7.40284i −0.282112 + 0.537059i
\(191\) 2.70353i 0.195621i −0.995205 0.0978104i \(-0.968816\pi\)
0.995205 0.0978104i \(-0.0311839\pi\)
\(192\) 0.451971 1.67204i 0.0326182 0.120669i
\(193\) 9.56062 9.56062i 0.688189 0.688189i −0.273643 0.961831i \(-0.588229\pi\)
0.961831 + 0.273643i \(0.0882286\pi\)
\(194\) 7.81120 0.560811
\(195\) 11.1852 + 10.3716i 0.800988 + 0.742728i
\(196\) 3.96417 0.283155
\(197\) −15.6486 + 15.6486i −1.11492 + 1.11492i −0.122441 + 0.992476i \(0.539072\pi\)
−0.992476 + 0.122441i \(0.960928\pi\)
\(198\) −3.76198 14.2914i −0.267352 1.01564i
\(199\) 2.30260i 0.163227i −0.996664 0.0816135i \(-0.973993\pi\)
0.996664 0.0816135i \(-0.0260073\pi\)
\(200\) 4.91746 + 0.904744i 0.347717 + 0.0639750i
\(201\) 8.06073 + 14.0329i 0.568560 + 0.989802i
\(202\) −12.9335 12.9335i −0.909995 0.909995i
\(203\) −22.3290 22.3290i −1.56719 1.56719i
\(204\) −2.50238 4.35637i −0.175201 0.305007i
\(205\) 11.0694 3.44509i 0.773123 0.240616i
\(206\) 11.5128i 0.802132i
\(207\) −0.763687 2.90117i −0.0530799 0.201645i
\(208\) −2.78495 + 2.78495i −0.193102 + 0.193102i
\(209\) −18.4216 −1.27425
\(210\) 0.483644 + 12.8152i 0.0333746 + 0.884331i
\(211\) 24.4727 1.68477 0.842385 0.538875i \(-0.181151\pi\)
0.842385 + 0.538875i \(0.181151\pi\)
\(212\) 8.92096 8.92096i 0.612694 0.612694i
\(213\) −0.628660 + 2.32569i −0.0430751 + 0.159354i
\(214\) 3.21611i 0.219849i
\(215\) −7.66180 4.02467i −0.522530 0.274480i
\(216\) −0.0343279 + 5.19604i −0.00233572 + 0.353546i
\(217\) −5.04601 5.04601i −0.342546 0.342546i
\(218\) 2.26374 + 2.26374i 0.153320 + 0.153320i
\(219\) −16.2662 + 9.34357i −1.09916 + 0.631380i
\(220\) 3.27330 + 10.5174i 0.220686 + 0.709086i
\(221\) 11.4239i 0.768457i
\(222\) 3.97174 + 1.07360i 0.266566 + 0.0720556i
\(223\) 17.0794 17.0794i 1.14372 1.14372i 0.155960 0.987763i \(-0.450153\pi\)
0.987763 0.155960i \(-0.0498472\pi\)
\(224\) −3.31122 −0.221240
\(225\) −14.9573 + 1.13059i −0.997155 + 0.0753725i
\(226\) 9.28286 0.617486
\(227\) 4.15095 4.15095i 0.275508 0.275508i −0.555805 0.831313i \(-0.687590\pi\)
0.831313 + 0.555805i \(0.187590\pi\)
\(228\) 6.25279 + 1.69020i 0.414101 + 0.111936i
\(229\) 4.18617i 0.276630i 0.990388 + 0.138315i \(0.0441686\pi\)
−0.990388 + 0.138315i \(0.955831\pi\)
\(230\) 0.664484 + 2.13506i 0.0438148 + 0.140781i
\(231\) −24.4980 + 14.0721i −1.61185 + 0.925877i
\(232\) 6.74342 + 6.74342i 0.442727 + 0.442727i
\(233\) 17.1678 + 17.1678i 1.12470 + 1.12470i 0.991025 + 0.133674i \(0.0426775\pi\)
0.133674 + 0.991025i \(0.457322\pi\)
\(234\) 5.95279 10.2065i 0.389146 0.667217i
\(235\) −24.2785 12.7533i −1.58375 0.831930i
\(236\) 4.44157i 0.289122i
\(237\) −0.734246 + 2.71630i −0.0476944 + 0.176443i
\(238\) −6.79135 + 6.79135i −0.440218 + 0.440218i
\(239\) −3.42360 −0.221454 −0.110727 0.993851i \(-0.535318\pi\)
−0.110727 + 0.993851i \(0.535318\pi\)
\(240\) −0.146062 3.87023i −0.00942827 0.249822i
\(241\) −22.1025 −1.42375 −0.711874 0.702307i \(-0.752153\pi\)
−0.711874 + 0.702307i \(0.752153\pi\)
\(242\) −9.38066 + 9.38066i −0.603011 + 0.603011i
\(243\) −3.86856 15.1008i −0.248168 0.968717i
\(244\) 2.83318i 0.181376i
\(245\) 8.46372 2.63413i 0.540728 0.168288i
\(246\) −4.47287 7.78678i −0.285180 0.496467i
\(247\) −10.4147 10.4147i −0.662669 0.662669i
\(248\) 1.52391 + 1.52391i 0.0967686 + 0.0967686i
\(249\) −0.436470 0.759848i −0.0276602 0.0481534i
\(250\) 11.1002 1.33590i 0.702041 0.0844896i
\(251\) 14.1807i 0.895079i −0.894264 0.447540i \(-0.852300\pi\)
0.894264 0.447540i \(-0.147700\pi\)
\(252\) 9.60641 2.52873i 0.605147 0.159295i
\(253\) −3.48326 + 3.48326i −0.218991 + 0.218991i
\(254\) 12.5142 0.785209
\(255\) −8.23745 7.63830i −0.515849 0.478329i
\(256\) 1.00000 0.0625000
\(257\) 17.2661 17.2661i 1.07703 1.07703i 0.0802573 0.996774i \(-0.474426\pi\)
0.996774 0.0802573i \(-0.0255742\pi\)
\(258\) −1.74932 + 6.47152i −0.108908 + 0.402899i
\(259\) 7.86541i 0.488733i
\(260\) −4.09547 + 7.79659i −0.253990 + 0.483524i
\(261\) −24.7137 14.4139i −1.52974 0.892201i
\(262\) −0.631314 0.631314i −0.0390027 0.0390027i
\(263\) −14.7411 14.7411i −0.908978 0.908978i 0.0872121 0.996190i \(-0.472204\pi\)
−0.996190 + 0.0872121i \(0.972204\pi\)
\(264\) 7.39849 4.24983i 0.455346 0.261559i
\(265\) 13.1189 24.9746i 0.805888 1.53418i
\(266\) 12.3827i 0.759231i
\(267\) −13.2518 3.58212i −0.811000 0.219222i
\(268\) −6.60677 + 6.60677i −0.403573 + 0.403573i
\(269\) 25.7589 1.57054 0.785272 0.619150i \(-0.212523\pi\)
0.785272 + 0.619150i \(0.212523\pi\)
\(270\) 3.37939 + 11.1166i 0.205663 + 0.676537i
\(271\) −0.344837 −0.0209473 −0.0104737 0.999945i \(-0.503334\pi\)
−0.0104737 + 0.999945i \(0.503334\pi\)
\(272\) 2.05101 2.05101i 0.124361 0.124361i
\(273\) −21.8056 5.89429i −1.31973 0.356739i
\(274\) 7.95701i 0.480701i
\(275\) 13.9774 + 20.2803i 0.842866 + 1.22295i
\(276\) 1.50190 0.862720i 0.0904040 0.0519296i
\(277\) −21.8081 21.8081i −1.31032 1.31032i −0.921174 0.389150i \(-0.872769\pi\)
−0.389150 0.921174i \(-0.627231\pi\)
\(278\) 7.84644 + 7.84644i 0.470598 + 0.470598i
\(279\) −5.58492 3.25734i −0.334361 0.195012i
\(280\) −7.06964 + 2.20025i −0.422492 + 0.131490i
\(281\) 7.85543i 0.468616i −0.972162 0.234308i \(-0.924718\pi\)
0.972162 0.234308i \(-0.0752824\pi\)
\(282\) −5.54320 + 20.5068i −0.330093 + 1.22116i
\(283\) −8.05637 + 8.05637i −0.478901 + 0.478901i −0.904780 0.425879i \(-0.859965\pi\)
0.425879 + 0.904780i \(0.359965\pi\)
\(284\) −1.39093 −0.0825365
\(285\) 14.4732 0.546216i 0.857316 0.0323551i
\(286\) −19.4015 −1.14723
\(287\) −12.1392 + 12.1392i −0.716553 + 0.716553i
\(288\) −2.90117 + 0.763687i −0.170953 + 0.0450007i
\(289\) 8.58671i 0.505101i
\(290\) 18.8785 + 9.91668i 1.10858 + 0.582328i
\(291\) −6.73888 11.7317i −0.395040 0.687723i
\(292\) −7.65822 7.65822i −0.448163 0.448163i
\(293\) 21.2971 + 21.2971i 1.24419 + 1.24419i 0.958247 + 0.285941i \(0.0923061\pi\)
0.285941 + 0.958247i \(0.407694\pi\)
\(294\) −3.41997 5.95380i −0.199457 0.347233i
\(295\) 2.95135 + 9.48300i 0.171834 + 0.552122i
\(296\) 2.37538i 0.138066i
\(297\) −18.2187 + 17.9796i −1.05716 + 1.04328i
\(298\) −9.01592 + 9.01592i −0.522278 + 0.522278i
\(299\) −3.93852 −0.227770
\(300\) −2.88356 8.16609i −0.166482 0.471470i
\(301\) 12.8158 0.738693
\(302\) 12.3599 12.3599i 0.711230 0.711230i
\(303\) −8.26686 + 30.5828i −0.474918 + 1.75693i
\(304\) 3.73962i 0.214482i
\(305\) 1.88261 + 6.04900i 0.107798 + 0.346365i
\(306\) −4.38400 + 7.51666i −0.250617 + 0.429699i
\(307\) −7.39676 7.39676i −0.422155 0.422155i 0.463790 0.885945i \(-0.346489\pi\)
−0.885945 + 0.463790i \(0.846489\pi\)
\(308\) −11.5338 11.5338i −0.657202 0.657202i
\(309\) −17.2910 + 9.93229i −0.983653 + 0.565028i
\(310\) 4.26626 + 2.24102i 0.242307 + 0.127282i
\(311\) 23.2216i 1.31678i −0.752679 0.658388i \(-0.771239\pi\)
0.752679 0.658388i \(-0.228761\pi\)
\(312\) 6.58537 + 1.78010i 0.372823 + 0.100778i
\(313\) −5.38747 + 5.38747i −0.304518 + 0.304518i −0.842779 0.538260i \(-0.819082\pi\)
0.538260 + 0.842779i \(0.319082\pi\)
\(314\) 13.4250 0.757617
\(315\) 18.8299 11.7823i 1.06094 0.663857i
\(316\) −1.62454 −0.0913877
\(317\) −4.39344 + 4.39344i −0.246760 + 0.246760i −0.819640 0.572879i \(-0.805826\pi\)
0.572879 + 0.819640i \(0.305826\pi\)
\(318\) −21.0947 5.70213i −1.18293 0.319759i
\(319\) 46.9782i 2.63028i
\(320\) 2.13506 0.664484i 0.119353 0.0371458i
\(321\) 4.83029 2.77461i 0.269601 0.154863i
\(322\) −2.34139 2.34139i −0.130480 0.130480i
\(323\) 7.66999 + 7.66999i 0.426770 + 0.426770i
\(324\) 7.83356 4.43117i 0.435198 0.246176i
\(325\) −3.56335 + 19.3675i −0.197659 + 1.07432i
\(326\) 16.4137i 0.909072i
\(327\) 1.44695 5.35290i 0.0800163 0.296016i
\(328\) 3.66607 3.66607i 0.202425 0.202425i
\(329\) 40.6105 2.23893
\(330\) 12.9723 13.9898i 0.714099 0.770113i
\(331\) 5.50237 0.302437 0.151219 0.988500i \(-0.451680\pi\)
0.151219 + 0.988500i \(0.451680\pi\)
\(332\) 0.357742 0.357742i 0.0196336 0.0196336i
\(333\) −1.81405 6.89139i −0.0994093 0.377646i
\(334\) 4.18734i 0.229121i
\(335\) −9.71573 + 18.4959i −0.530827 + 1.01054i
\(336\) 2.85666 + 4.97313i 0.155843 + 0.271307i
\(337\) 12.2108 + 12.2108i 0.665163 + 0.665163i 0.956592 0.291429i \(-0.0941309\pi\)
−0.291429 + 0.956592i \(0.594131\pi\)
\(338\) −1.77621 1.77621i −0.0966129 0.0966129i
\(339\) −8.00851 13.9420i −0.434962 0.757223i
\(340\) 3.01616 5.74189i 0.163574 0.311397i
\(341\) 10.6164i 0.574909i
\(342\) −2.85590 10.8493i −0.154429 0.586661i
\(343\) 7.10804 7.10804i 0.383798 0.383798i
\(344\) −3.87043 −0.208680
\(345\) 2.63338 2.83995i 0.141777 0.152898i
\(346\) 22.6853 1.21957
\(347\) 20.1140 20.1140i 1.07978 1.07978i 0.0832466 0.996529i \(-0.473471\pi\)
0.996529 0.0832466i \(-0.0265289\pi\)
\(348\) 4.31028 15.9457i 0.231055 0.854777i
\(349\) 4.04914i 0.216746i −0.994110 0.108373i \(-0.965436\pi\)
0.994110 0.108373i \(-0.0345640\pi\)
\(350\) −13.6320 + 9.39532i −0.728663 + 0.502201i
\(351\) −20.4647 0.135201i −1.09232 0.00721650i
\(352\) 3.48326 + 3.48326i 0.185659 + 0.185659i
\(353\) −26.1786 26.1786i −1.39335 1.39335i −0.817692 0.575656i \(-0.804747\pi\)
−0.575656 0.817692i \(-0.695253\pi\)
\(354\) 6.67081 3.83183i 0.354550 0.203660i
\(355\) −2.96971 + 0.924251i −0.157616 + 0.0490541i
\(356\) 7.92555i 0.420053i
\(357\) 16.0590 + 4.34092i 0.849931 + 0.229746i
\(358\) −1.01094 + 1.01094i −0.0534301 + 0.0534301i
\(359\) −18.0793 −0.954191 −0.477096 0.878851i \(-0.658310\pi\)
−0.477096 + 0.878851i \(0.658310\pi\)
\(360\) −5.68670 + 3.55829i −0.299715 + 0.187539i
\(361\) 5.01527 0.263962
\(362\) 1.91672 1.91672i 0.100740 0.100740i
\(363\) 22.1817 + 5.99596i 1.16424 + 0.314706i
\(364\) 13.0413i 0.683550i
\(365\) −21.4395 11.2620i −1.12219 0.589478i
\(366\) 4.25517 2.44424i 0.222421 0.127763i
\(367\) −8.45693 8.45693i −0.441448 0.441448i 0.451050 0.892498i \(-0.351049\pi\)
−0.892498 + 0.451050i \(0.851049\pi\)
\(368\) 0.707107 + 0.707107i 0.0368605 + 0.0368605i
\(369\) −7.83617 + 13.4356i −0.407935 + 0.699431i
\(370\) 1.57840 + 5.07157i 0.0820573 + 0.263659i
\(371\) 41.7748i 2.16884i
\(372\) 0.974060 3.60348i 0.0505027 0.186832i
\(373\) −25.2100 + 25.2100i −1.30532 + 1.30532i −0.380571 + 0.924752i \(0.624272\pi\)
−0.924752 + 0.380571i \(0.875728\pi\)
\(374\) 14.2884 0.738837
\(375\) −11.5828 15.5190i −0.598133 0.801397i
\(376\) −12.2645 −0.632493
\(377\) −26.5591 + 26.5591i −1.36786 + 1.36786i
\(378\) −12.0856 12.2463i −0.621614 0.629882i
\(379\) 12.7386i 0.654337i 0.944966 + 0.327168i \(0.106094\pi\)
−0.944966 + 0.327168i \(0.893906\pi\)
\(380\) 2.48492 + 7.98429i 0.127473 + 0.409585i
\(381\) −10.7962 18.7951i −0.553107 0.962901i
\(382\) −1.91169 1.91169i −0.0978104 0.0978104i
\(383\) 18.8838 + 18.8838i 0.964917 + 0.964917i 0.999405 0.0344882i \(-0.0109801\pi\)
−0.0344882 + 0.999405i \(0.510980\pi\)
\(384\) −0.862720 1.50190i −0.0440255 0.0766437i
\(385\) −32.2895 16.9613i −1.64562 0.864430i
\(386\) 13.5208i 0.688189i
\(387\) 11.2288 2.95580i 0.570790 0.150252i
\(388\) 5.52335 5.52335i 0.280406 0.280406i
\(389\) 33.0424 1.67532 0.837659 0.546193i \(-0.183924\pi\)
0.837659 + 0.546193i \(0.183924\pi\)
\(390\) 15.2430 0.575269i 0.771858 0.0291299i
\(391\) 2.90057 0.146688
\(392\) 2.80309 2.80309i 0.141578 0.141578i
\(393\) −0.403525 + 1.49282i −0.0203552 + 0.0753028i
\(394\) 22.1305i 1.11492i
\(395\) −3.46849 + 1.07948i −0.174519 + 0.0543147i
\(396\) −12.7657 7.44541i −0.641499 0.374146i
\(397\) 9.82206 + 9.82206i 0.492955 + 0.492955i 0.909236 0.416281i \(-0.136667\pi\)
−0.416281 + 0.909236i \(0.636667\pi\)
\(398\) −1.62818 1.62818i −0.0816135 0.0816135i
\(399\) −18.5976 + 10.6828i −0.931045 + 0.534809i
\(400\) 4.11692 2.83742i 0.205846 0.141871i
\(401\) 15.7059i 0.784314i −0.919898 0.392157i \(-0.871729\pi\)
0.919898 0.392157i \(-0.128271\pi\)
\(402\) 15.6225 + 4.22294i 0.779181 + 0.210621i
\(403\) −6.00196 + 6.00196i −0.298979 + 0.298979i
\(404\) −18.2907 −0.909995
\(405\) 13.7807 14.6661i 0.684766 0.728763i
\(406\) −31.5779 −1.56719
\(407\) −8.27409 + 8.27409i −0.410131 + 0.410131i
\(408\) −4.84987 1.31097i −0.240104 0.0649028i
\(409\) 34.5321i 1.70750i −0.520683 0.853750i \(-0.674323\pi\)
0.520683 0.853750i \(-0.325677\pi\)
\(410\) 5.39122 10.2633i 0.266253 0.506869i
\(411\) 11.9507 6.86468i 0.589483 0.338609i
\(412\) −8.14075 8.14075i −0.401066 0.401066i
\(413\) −10.3994 10.3994i −0.511723 0.511723i
\(414\) −2.59144 1.51143i −0.127363 0.0742826i
\(415\) 0.526085 1.00151i 0.0258245 0.0491623i
\(416\) 3.93852i 0.193102i
\(417\) 5.01531 18.5539i 0.245601 0.908587i
\(418\) −13.0261 + 13.0261i −0.637126 + 0.637126i
\(419\) 27.4239 1.33974 0.669872 0.742477i \(-0.266349\pi\)
0.669872 + 0.742477i \(0.266349\pi\)
\(420\) 9.40368 + 8.71971i 0.458853 + 0.425478i
\(421\) −31.6293 −1.54152 −0.770758 0.637128i \(-0.780122\pi\)
−0.770758 + 0.637128i \(0.780122\pi\)
\(422\) 17.3048 17.3048i 0.842385 0.842385i
\(423\) 35.5814 9.36624i 1.73003 0.455402i
\(424\) 12.6161i 0.612694i
\(425\) 2.62427 14.2634i 0.127296 0.691878i
\(426\) 1.19998 + 2.08904i 0.0581394 + 0.101214i
\(427\) −6.63357 6.63357i −0.321021 0.321021i
\(428\) 2.27414 + 2.27414i 0.109924 + 0.109924i
\(429\) 16.7380 + 29.1391i 0.808120 + 1.40685i
\(430\) −8.26358 + 2.57184i −0.398505 + 0.124025i
\(431\) 14.2142i 0.684674i 0.939577 + 0.342337i \(0.111218\pi\)
−0.939577 + 0.342337i \(0.888782\pi\)
\(432\) 3.64988 + 3.69843i 0.175605 + 0.177941i
\(433\) 2.02138 2.02138i 0.0971415 0.0971415i −0.656866 0.754007i \(-0.728118\pi\)
0.754007 + 0.656866i \(0.228118\pi\)
\(434\) −7.13614 −0.342546
\(435\) −1.39294 36.9090i −0.0667865 1.76965i
\(436\) 3.20141 0.153320
\(437\) −2.64431 + 2.64431i −0.126494 + 0.126494i
\(438\) −4.89501 + 18.1088i −0.233892 + 0.865272i
\(439\) 30.8475i 1.47227i −0.676833 0.736137i \(-0.736648\pi\)
0.676833 0.736137i \(-0.263352\pi\)
\(440\) 9.75153 + 5.12239i 0.464886 + 0.244200i
\(441\) −5.99156 + 10.2729i −0.285312 + 0.489187i
\(442\) 8.07795 + 8.07795i 0.384229 + 0.384229i
\(443\) 7.69538 + 7.69538i 0.365618 + 0.365618i 0.865876 0.500258i \(-0.166761\pi\)
−0.500258 + 0.865876i \(0.666761\pi\)
\(444\) 3.56760 2.04929i 0.169311 0.0972550i
\(445\) −5.26640 16.9215i −0.249651 0.802155i
\(446\) 24.1540i 1.14372i
\(447\) 21.3193 + 5.76283i 1.00837 + 0.272572i
\(448\) −2.34139 + 2.34139i −0.110620 + 0.110620i
\(449\) −32.2872 −1.52373 −0.761863 0.647738i \(-0.775715\pi\)
−0.761863 + 0.647738i \(0.775715\pi\)
\(450\) −9.77698 + 11.3759i −0.460891 + 0.536264i
\(451\) 25.5398 1.20262
\(452\) 6.56397 6.56397i 0.308743 0.308743i
\(453\) −29.2264 7.90022i −1.37318 0.371185i
\(454\) 5.87033i 0.275508i
\(455\) −8.66574 27.8439i −0.406256 1.30534i
\(456\) 5.61654 3.22624i 0.263019 0.151083i
\(457\) 12.4523 + 12.4523i 0.582494 + 0.582494i 0.935588 0.353094i \(-0.114870\pi\)
−0.353094 + 0.935588i \(0.614870\pi\)
\(458\) 2.96007 + 2.96007i 0.138315 + 0.138315i
\(459\) 15.0715 + 0.0995704i 0.703476 + 0.00464755i
\(460\) 1.97957 + 1.03985i 0.0922981 + 0.0484833i
\(461\) 9.66933i 0.450345i 0.974319 + 0.225173i \(0.0722946\pi\)
−0.974319 + 0.225173i \(0.927705\pi\)
\(462\) −7.37224 + 27.2732i −0.342988 + 1.26886i
\(463\) −9.39853 + 9.39853i −0.436787 + 0.436787i −0.890929 0.454142i \(-0.849946\pi\)
0.454142 + 0.890929i \(0.349946\pi\)
\(464\) 9.53664 0.442727
\(465\) −0.314784 8.34088i −0.0145978 0.386799i
\(466\) 24.2789 1.12470
\(467\) −9.89416 + 9.89416i −0.457847 + 0.457847i −0.897948 0.440101i \(-0.854943\pi\)
0.440101 + 0.897948i \(0.354943\pi\)
\(468\) −3.00780 11.4263i −0.139035 0.528181i
\(469\) 30.9380i 1.42858i
\(470\) −26.1854 + 8.14957i −1.20784 + 0.375912i
\(471\) −11.5820 20.1631i −0.533672 0.929065i
\(472\) 3.14067 + 3.14067i 0.144561 + 0.144561i
\(473\) −13.4817 13.4817i −0.619890 0.619890i
\(474\) 1.40153 + 2.43991i 0.0643742 + 0.112069i
\(475\) 10.6109 + 15.3957i 0.486860 + 0.706403i
\(476\) 9.60441i 0.440218i
\(477\) 9.63478 + 36.6015i 0.441146 + 1.67587i
\(478\) −2.42085 + 2.42085i −0.110727 + 0.110727i
\(479\) −18.0640 −0.825365 −0.412683 0.910875i \(-0.635408\pi\)
−0.412683 + 0.910875i \(0.635408\pi\)
\(480\) −2.83995 2.63338i −0.129625 0.120197i
\(481\) −9.35549 −0.426574
\(482\) −15.6288 + 15.6288i −0.711874 + 0.711874i
\(483\) −1.49657 + 5.53650i −0.0680965 + 0.251919i
\(484\) 13.2663i 0.603011i
\(485\) 8.12248 15.4628i 0.368823 0.702132i
\(486\) −13.4134 7.94240i −0.608443 0.360275i
\(487\) 2.25954 + 2.25954i 0.102389 + 0.102389i 0.756446 0.654056i \(-0.226934\pi\)
−0.654056 + 0.756446i \(0.726934\pi\)
\(488\) 2.00336 + 2.00336i 0.0906880 + 0.0906880i
\(489\) 24.6518 14.1604i 1.11479 0.640357i
\(490\) 4.12215 7.84737i 0.186220 0.354508i
\(491\) 4.50123i 0.203138i −0.994829 0.101569i \(-0.967614\pi\)
0.994829 0.101569i \(-0.0323862\pi\)
\(492\) −8.66888 2.34329i −0.390823 0.105644i
\(493\) 19.5598 19.5598i 0.880927 0.880927i
\(494\) −14.7286 −0.662669
\(495\) −32.2027 7.41379i −1.44741 0.333225i
\(496\) 2.15514 0.0967686
\(497\) 3.25670 3.25670i 0.146083 0.146083i
\(498\) −0.845925 0.228663i −0.0379068 0.0102466i
\(499\) 7.38579i 0.330634i 0.986241 + 0.165317i \(0.0528647\pi\)
−0.986241 + 0.165317i \(0.947135\pi\)
\(500\) 6.90443 8.79368i 0.308776 0.393265i
\(501\) 6.28899 3.61250i 0.280971 0.161395i
\(502\) −10.0273 10.0273i −0.447540 0.447540i
\(503\) 27.9883 + 27.9883i 1.24793 + 1.24793i 0.956630 + 0.291304i \(0.0940892\pi\)
0.291304 + 0.956630i \(0.405911\pi\)
\(504\) 5.00467 8.58084i 0.222926 0.382221i
\(505\) −39.0516 + 12.1539i −1.73777 + 0.540840i
\(506\) 4.92608i 0.218991i
\(507\) −1.13532 + 4.20006i −0.0504214 + 0.186531i
\(508\) 8.84885 8.84885i 0.392604 0.392604i
\(509\) 2.48509 0.110150 0.0550749 0.998482i \(-0.482460\pi\)
0.0550749 + 0.998482i \(0.482460\pi\)
\(510\) −11.2259 + 0.423663i −0.497089 + 0.0187601i
\(511\) 35.8617 1.58643
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) −13.8307 + 13.6492i −0.610640 + 0.602625i
\(514\) 24.4180i 1.07703i
\(515\) −22.7903 11.9715i −1.00426 0.527529i
\(516\) 3.33910 + 5.81301i 0.146996 + 0.255904i
\(517\) −42.7205 42.7205i −1.87885 1.87885i
\(518\) −5.56169 5.56169i −0.244367 0.244367i
\(519\) −19.5711 34.0711i −0.859074 1.49556i
\(520\) 2.61708 + 8.40896i 0.114767 + 0.368757i
\(521\) 23.6509i 1.03617i 0.855331 + 0.518083i \(0.173354\pi\)
−0.855331 + 0.518083i \(0.826646\pi\)
\(522\) −27.6674 + 7.28301i −1.21097 + 0.318769i
\(523\) −7.85518 + 7.85518i −0.343483 + 0.343483i −0.857675 0.514192i \(-0.828092\pi\)
0.514192 + 0.857675i \(0.328092\pi\)
\(524\) −0.892813 −0.0390027
\(525\) 25.8715 + 12.3685i 1.12912 + 0.539804i
\(526\) −20.8471 −0.908978
\(527\) 4.42021 4.42021i 0.192548 0.192548i
\(528\) 2.22644 8.23661i 0.0968936 0.358452i
\(529\) 1.00000i 0.0434783i
\(530\) −8.38322 26.9361i −0.364144 1.17003i
\(531\) −11.5101 6.71312i −0.499495 0.291324i
\(532\) −8.75588 8.75588i −0.379616 0.379616i
\(533\) 14.4389 + 14.4389i 0.625418 + 0.625418i
\(534\) −11.9034 + 6.83753i −0.515111 + 0.295889i
\(535\) 6.36653 + 3.34428i 0.275249 + 0.144586i
\(536\) 9.34339i 0.403573i
\(537\) 2.39050 + 0.646179i 0.103158 + 0.0278847i
\(538\) 18.2143 18.2143i 0.785272 0.785272i
\(539\) 19.5278 0.841123
\(540\) 10.2502 + 5.47106i 0.441100 + 0.235437i
\(541\) −11.8517 −0.509544 −0.254772 0.967001i \(-0.582000\pi\)
−0.254772 + 0.967001i \(0.582000\pi\)
\(542\) −0.243836 + 0.243836i −0.0104737 + 0.0104737i
\(543\) −4.53231 1.22513i −0.194500 0.0525755i
\(544\) 2.90057i 0.124361i
\(545\) 6.83520 2.12729i 0.292788 0.0911231i
\(546\) −19.5868 + 11.2510i −0.838237 + 0.481498i
\(547\) 16.4980 + 16.4980i 0.705404 + 0.705404i 0.965565 0.260161i \(-0.0837756\pi\)
−0.260161 + 0.965565i \(0.583776\pi\)
\(548\) 5.62646 + 5.62646i 0.240350 + 0.240350i
\(549\) −7.34204 4.28215i −0.313351 0.182758i
\(550\) 24.2238 + 4.45684i 1.03291 + 0.190040i
\(551\) 35.6634i 1.51931i
\(552\) 0.451971 1.67204i 0.0192372 0.0711668i
\(553\) 3.80368 3.80368i 0.161749 0.161749i
\(554\) −30.8414 −1.31032
\(555\) 6.25529 6.74596i 0.265522 0.286350i
\(556\) 11.0965 0.470598
\(557\) −10.6327 + 10.6327i −0.450523 + 0.450523i −0.895528 0.445005i \(-0.853202\pi\)
0.445005 + 0.895528i \(0.353202\pi\)
\(558\) −6.25242 + 1.64585i −0.264686 + 0.0696744i
\(559\) 15.2438i 0.644742i
\(560\) −3.44317 + 6.55480i −0.145501 + 0.276991i
\(561\) −12.3269 21.4598i −0.520442 0.906035i
\(562\) −5.55463 5.55463i −0.234308 0.234308i
\(563\) 25.0671 + 25.0671i 1.05645 + 1.05645i 0.998308 + 0.0581420i \(0.0185176\pi\)
0.0581420 + 0.998308i \(0.481482\pi\)
\(564\) 10.5808 + 18.4201i 0.445533 + 0.775626i
\(565\) 9.65279 18.3761i 0.406096 0.773088i
\(566\) 11.3934i 0.478901i
\(567\) −7.96632 + 28.7165i −0.334554 + 1.20598i
\(568\) −0.983536 + 0.983536i −0.0412682 + 0.0412682i
\(569\) 10.7487 0.450610 0.225305 0.974288i \(-0.427662\pi\)
0.225305 + 0.974288i \(0.427662\pi\)
\(570\) 9.84784 10.6203i 0.412481 0.444836i
\(571\) 0.866963 0.0362813 0.0181406 0.999835i \(-0.494225\pi\)
0.0181406 + 0.999835i \(0.494225\pi\)
\(572\) −13.7189 + 13.7189i −0.573616 + 0.573616i
\(573\) −1.22192 + 4.52042i −0.0510464 + 0.188843i
\(574\) 17.1674i 0.716553i
\(575\) 4.91746 + 0.904744i 0.205072 + 0.0377304i
\(576\) −1.51143 + 2.59144i −0.0629762 + 0.107977i
\(577\) 0.374062 + 0.374062i 0.0155724 + 0.0155724i 0.714850 0.699278i \(-0.246495\pi\)
−0.699278 + 0.714850i \(0.746495\pi\)
\(578\) 6.07172 + 6.07172i 0.252550 + 0.252550i
\(579\) −20.3069 + 11.6646i −0.843925 + 0.484766i
\(580\) 20.3613 6.33695i 0.845455 0.263127i
\(581\) 1.67522i 0.0695000i
\(582\) −13.0606 3.53044i −0.541381 0.146341i
\(583\) 43.9453 43.9453i 1.82003 1.82003i
\(584\) −10.8304 −0.448163
\(585\) −14.0144 22.3972i −0.579425 0.926009i
\(586\) 30.1186 1.24419
\(587\) −14.5522 + 14.5522i −0.600635 + 0.600635i −0.940481 0.339846i \(-0.889625\pi\)
0.339846 + 0.940481i \(0.389625\pi\)
\(588\) −6.62826 1.79169i −0.273345 0.0738881i
\(589\) 8.05939i 0.332081i
\(590\) 8.79242 + 4.61857i 0.361978 + 0.190144i
\(591\) 33.2378 19.0924i 1.36722 0.785356i
\(592\) 1.67965 + 1.67965i 0.0690332 + 0.0690332i
\(593\) −9.41542 9.41542i −0.386645 0.386645i 0.486844 0.873489i \(-0.338148\pi\)
−0.873489 + 0.486844i \(0.838148\pi\)
\(594\) −0.169102 + 25.5961i −0.00693834 + 1.05022i
\(595\) 6.38198 + 20.5060i 0.261636 + 0.840662i
\(596\) 12.7504i 0.522278i
\(597\) −1.04071 + 3.85004i −0.0425934 + 0.157572i
\(598\) −2.78495 + 2.78495i −0.113885 + 0.113885i
\(599\) 25.4679 1.04059 0.520294 0.853987i \(-0.325822\pi\)
0.520294 + 0.853987i \(0.325822\pi\)
\(600\) −7.81328 3.73532i −0.318976 0.152494i
\(601\) 33.4525 1.36456 0.682278 0.731093i \(-0.260989\pi\)
0.682278 + 0.731093i \(0.260989\pi\)
\(602\) 9.06217 9.06217i 0.369346 0.369346i
\(603\) −7.13543 27.1068i −0.290577 1.10387i
\(604\) 17.4795i 0.711230i
\(605\) 8.81521 + 28.3242i 0.358389 + 1.15154i
\(606\) 15.7797 + 27.4708i 0.641008 + 1.11593i
\(607\) 15.2508 + 15.2508i 0.619012 + 0.619012i 0.945278 0.326266i \(-0.105791\pi\)
−0.326266 + 0.945278i \(0.605791\pi\)
\(608\) 2.64431 + 2.64431i 0.107241 + 0.107241i
\(609\) 27.2429 + 47.4270i 1.10394 + 1.92184i
\(610\) 5.60849 + 2.94609i 0.227081 + 0.119284i
\(611\) 48.3040i 1.95417i
\(612\) 2.21513 + 8.41504i 0.0895411 + 0.340158i
\(613\) 7.09175 7.09175i 0.286433 0.286433i −0.549235 0.835668i \(-0.685081\pi\)
0.835668 + 0.549235i \(0.185081\pi\)
\(614\) −10.4606 −0.422155
\(615\) −20.0656 + 0.757275i −0.809124 + 0.0305363i
\(616\) −16.3113 −0.657202
\(617\) −1.76987 + 1.76987i −0.0712523 + 0.0712523i −0.741835 0.670583i \(-0.766044\pi\)
0.670583 + 0.741835i \(0.266044\pi\)
\(618\) −5.20343 + 19.2498i −0.209313 + 0.774341i
\(619\) 49.0210i 1.97032i 0.171638 + 0.985160i \(0.445094\pi\)
−0.171638 + 0.985160i \(0.554906\pi\)
\(620\) 4.60134 1.43206i 0.184794 0.0575127i
\(621\) −0.0343279 + 5.19604i −0.00137753 + 0.208510i
\(622\) −16.4202 16.4202i −0.658388 0.658388i
\(623\) 18.5568 + 18.5568i 0.743461 + 0.743461i
\(624\) 5.91528 3.39784i 0.236801 0.136022i
\(625\) 8.89809 23.3629i 0.355923 0.934515i
\(626\) 7.61904i 0.304518i
\(627\) 30.8017 + 8.32605i 1.23010 + 0.332510i
\(628\) 9.49292 9.49292i 0.378809 0.378809i
\(629\) 6.88996 0.274721
\(630\) 4.98341 21.6461i 0.198544 0.862401i
\(631\) −3.87479 −0.154253 −0.0771264 0.997021i \(-0.524575\pi\)
−0.0771264 + 0.997021i \(0.524575\pi\)
\(632\) −1.14873 + 1.14873i −0.0456938 + 0.0456938i
\(633\) −40.9194 11.0610i −1.62640 0.439633i
\(634\) 6.21327i 0.246760i
\(635\) 13.0129 24.7727i 0.516400 0.983075i
\(636\) −18.9482 + 10.8842i −0.751346 + 0.431586i
\(637\) 11.0400 + 11.0400i 0.437422 + 0.437422i
\(638\) 33.2186 + 33.2186i 1.31514 + 1.31514i
\(639\) 2.10229 3.60452i 0.0831653 0.142592i
\(640\) 1.03985 1.97957i 0.0411037 0.0782495i
\(641\) 17.1790i 0.678532i −0.940691 0.339266i \(-0.889821\pi\)
0.940691 0.339266i \(-0.110179\pi\)
\(642\) 1.45359 5.37747i 0.0573686 0.212232i
\(643\) −3.69628 + 3.69628i −0.145767 + 0.145767i −0.776224 0.630457i \(-0.782867\pi\)
0.630457 + 0.776224i \(0.282867\pi\)
\(644\) −3.31122 −0.130480
\(645\) 10.9918 + 10.1923i 0.432802 + 0.401322i
\(646\) 10.8470 0.426770
\(647\) −11.5427 + 11.5427i −0.453790 + 0.453790i −0.896610 0.442820i \(-0.853978\pi\)
0.442820 + 0.896610i \(0.353978\pi\)
\(648\) 2.40586 8.67248i 0.0945110 0.340687i
\(649\) 21.8795i 0.858847i
\(650\) 11.1752 + 16.2146i 0.438329 + 0.635988i
\(651\) 6.15649 + 10.7178i 0.241292 + 0.420063i
\(652\) 11.6062 + 11.6062i 0.454536 + 0.454536i
\(653\) −15.6907 15.6907i −0.614025 0.614025i 0.329967 0.943992i \(-0.392962\pi\)
−0.943992 + 0.329967i \(0.892962\pi\)
\(654\) −2.76192 4.80822i −0.108000 0.188016i
\(655\) −1.90620 + 0.593260i −0.0744816 + 0.0231806i
\(656\) 5.18461i 0.202425i
\(657\) 31.4207 8.27100i 1.22584 0.322683i
\(658\) 28.7159 28.7159i 1.11946 1.11946i
\(659\) 3.17418 0.123649 0.0618243 0.998087i \(-0.480308\pi\)
0.0618243 + 0.998087i \(0.480308\pi\)
\(660\) −0.719514 19.0650i −0.0280070 0.742106i
\(661\) −12.5898 −0.489687 −0.244843 0.969563i \(-0.578737\pi\)
−0.244843 + 0.969563i \(0.578737\pi\)
\(662\) 3.89076 3.89076i 0.151219 0.151219i
\(663\) 5.16329 19.1013i 0.200526 0.741833i
\(664\) 0.505923i 0.0196336i
\(665\) −24.5124 12.8761i −0.950552 0.499316i
\(666\) −6.15567 3.59022i −0.238528 0.139118i
\(667\) 6.74342 + 6.74342i 0.261106 + 0.261106i
\(668\) 2.96090 + 2.96090i 0.114561 + 0.114561i
\(669\) −36.2769 + 20.8381i −1.40255 + 0.805648i
\(670\) 6.20853 + 19.9487i 0.239857 + 0.770684i
\(671\) 13.9565i 0.538784i
\(672\) 5.53650 + 1.49657i 0.213575 + 0.0577316i
\(673\) 20.3975 20.3975i 0.786267 0.786267i −0.194613 0.980880i \(-0.562345\pi\)
0.980880 + 0.194613i \(0.0623451\pi\)
\(674\) 17.2686 0.665163
\(675\) 25.5203 + 4.86989i 0.982276 + 0.187442i
\(676\) −2.51194 −0.0966129
\(677\) −30.0984 + 30.0984i −1.15678 + 1.15678i −0.171610 + 0.985165i \(0.554897\pi\)
−0.985165 + 0.171610i \(0.945103\pi\)
\(678\) −15.5213 4.19558i −0.596093 0.161130i
\(679\) 25.8646i 0.992592i
\(680\) −1.92738 6.19287i −0.0739117 0.237486i
\(681\) −8.81667 + 5.06445i −0.337855 + 0.194070i
\(682\) 7.50692 + 7.50692i 0.287455 + 0.287455i
\(683\) 0.904638 + 0.904638i 0.0346150 + 0.0346150i 0.724202 0.689587i \(-0.242208\pi\)
−0.689587 + 0.724202i \(0.742208\pi\)
\(684\) −9.69101 5.65216i −0.370545 0.216116i
\(685\) 15.7515 + 8.27411i 0.601834 + 0.316137i
\(686\) 10.0523i 0.383798i
\(687\) 1.89203 6.99945i 0.0721854 0.267046i
\(688\) −2.73681 + 2.73681i −0.104340 + 0.104340i
\(689\) 49.6889 1.89300
\(690\) −0.146062 3.87023i −0.00556049 0.147337i
\(691\) −8.98103 −0.341654 −0.170827 0.985301i \(-0.554644\pi\)
−0.170827 + 0.985301i \(0.554644\pi\)
\(692\) 16.0409 16.0409i 0.609784 0.609784i
\(693\) 47.3219 12.4567i 1.79761 0.473193i
\(694\) 28.4455i 1.07978i
\(695\) 23.6917 7.37347i 0.898678 0.279692i
\(696\) −8.22745 14.3231i −0.311861 0.542916i
\(697\) −10.6337 10.6337i −0.402780 0.402780i
\(698\) −2.86317 2.86317i −0.108373 0.108373i
\(699\) −20.9459 36.4646i −0.792247 1.37922i
\(700\) −2.99580 + 16.2828i −0.113231 + 0.615432i
\(701\) 2.17193i 0.0820325i −0.999158 0.0410162i \(-0.986940\pi\)
0.999158 0.0410162i \(-0.0130595\pi\)
\(702\) −14.5663 + 14.3751i −0.549771 + 0.542554i
\(703\) −6.28124 + 6.28124i −0.236902 + 0.236902i
\(704\) 4.92608 0.185659
\(705\) 34.8305 + 32.2971i 1.31179 + 1.21638i
\(706\) −37.0222 −1.39335
\(707\) 42.8255 42.8255i 1.61062 1.61062i
\(708\) 2.00746 7.42649i 0.0754450 0.279105i
\(709\) 40.6428i 1.52637i 0.646179 + 0.763185i \(0.276366\pi\)
−0.646179 + 0.763185i \(0.723634\pi\)
\(710\) −1.44636 + 2.75345i −0.0542809 + 0.103335i
\(711\) 2.45538 4.20991i 0.0920840 0.157884i
\(712\) −5.60421 5.60421i −0.210027 0.210027i
\(713\) 1.52391 + 1.52391i 0.0570710 + 0.0570710i
\(714\) 14.4249 8.28592i 0.539838 0.310093i
\(715\) −20.1746 + 38.4066i −0.754488 + 1.43633i
\(716\) 1.42969i 0.0534301i
\(717\) 5.72440 + 1.54737i 0.213781 + 0.0577874i
\(718\) −12.7840 + 12.7840i −0.477096 + 0.477096i
\(719\) 7.85539 0.292957 0.146478 0.989214i \(-0.453206\pi\)
0.146478 + 0.989214i \(0.453206\pi\)
\(720\) −1.50501 + 6.53720i −0.0560884 + 0.243627i
\(721\) 38.1213 1.41971
\(722\) 3.54633 3.54633i 0.131981 0.131981i
\(723\) 36.9563 + 9.98969i 1.37442 + 0.371521i
\(724\) 2.71065i 0.100740i
\(725\) 39.2616 27.0595i 1.45814 1.00496i
\(726\) 19.9246 11.4451i 0.739472 0.424766i
\(727\) −29.7420 29.7420i −1.10307 1.10307i −0.994039 0.109029i \(-0.965226\pi\)
−0.109029 0.994039i \(-0.534774\pi\)
\(728\) −9.22159 9.22159i −0.341775 0.341775i
\(729\) −0.356738 + 26.9976i −0.0132125 + 0.999913i
\(730\) −23.1234 + 7.19660i −0.855836 + 0.266358i
\(731\) 11.2264i 0.415225i
\(732\) 1.28052 4.73720i 0.0473292 0.175092i
\(733\) 18.7628 18.7628i 0.693019 0.693019i −0.269876 0.962895i \(-0.586983\pi\)
0.962895 + 0.269876i \(0.0869828\pi\)
\(734\) −11.9599 −0.441448
\(735\) −15.3422 + 0.579015i −0.565907 + 0.0213573i
\(736\) 1.00000 0.0368605
\(737\) −32.5455 + 32.5455i −1.19883 + 1.19883i
\(738\) 3.95942 + 15.0414i 0.145748 + 0.553683i
\(739\) 4.14954i 0.152643i −0.997083 0.0763217i \(-0.975682\pi\)
0.997083 0.0763217i \(-0.0243176\pi\)
\(740\) 4.70225 + 2.47004i 0.172858 + 0.0908006i
\(741\) 12.7066 + 22.1209i 0.466789 + 0.812630i
\(742\) 29.5392 + 29.5392i 1.08442 + 1.08442i
\(743\) −28.0568 28.0568i −1.02930 1.02930i −0.999558 0.0297448i \(-0.990531\pi\)
−0.0297448 0.999558i \(-0.509469\pi\)
\(744\) −1.85928 3.23681i −0.0681646 0.118667i
\(745\) 8.47246 + 27.2229i 0.310407 + 0.997369i
\(746\) 35.6523i 1.30532i
\(747\) 0.386367 + 1.46777i 0.0141364 + 0.0537029i
\(748\) 10.1034 10.1034i 0.369418 0.369418i
\(749\) −10.6493 −0.389115
\(750\) −19.1639 2.78331i −0.699765 0.101632i
\(751\) −26.4718 −0.965969 −0.482984 0.875629i \(-0.660447\pi\)
−0.482984 + 0.875629i \(0.660447\pi\)
\(752\) −8.67231 + 8.67231i −0.316247 + 0.316247i
\(753\) −6.40927 + 23.7108i −0.233567 + 0.864068i
\(754\) 37.5602i 1.36786i
\(755\) −11.6148 37.3197i −0.422708 1.35820i
\(756\) −17.2052 0.113667i −0.625748 0.00413404i
\(757\) −20.0922 20.0922i −0.730265 0.730265i 0.240407 0.970672i \(-0.422719\pi\)
−0.970672 + 0.240407i \(0.922719\pi\)
\(758\) 9.00754 + 9.00754i 0.327168 + 0.327168i
\(759\) 7.39849 4.24983i 0.268548 0.154259i
\(760\) 7.40284 + 3.88864i 0.268529 + 0.141056i
\(761\) 26.8485i 0.973256i −0.873609 0.486628i \(-0.838227\pi\)
0.873609 0.486628i \(-0.161773\pi\)
\(762\) −20.9242 5.65604i −0.758004 0.204897i
\(763\) −7.49575 + 7.49575i −0.271364 + 0.271364i
\(764\) −2.70353 −0.0978104
\(765\) 10.3211 + 16.4947i 0.373159 + 0.596365i
\(766\) 26.7057 0.964917
\(767\) −12.3696 + 12.3696i −0.446639 + 0.446639i
\(768\) −1.67204 0.451971i −0.0603346 0.0163091i
\(769\) 7.25381i 0.261579i 0.991410 + 0.130790i \(0.0417512\pi\)
−0.991410 + 0.130790i \(0.958249\pi\)
\(770\) −34.8256 + 10.8386i −1.25503 + 0.390597i
\(771\) −36.6735 + 21.0659i −1.32076 + 0.758670i
\(772\) −9.56062 9.56062i −0.344094 0.344094i
\(773\) −15.1600 15.1600i −0.545267 0.545267i 0.379801 0.925068i \(-0.375992\pi\)
−0.925068 + 0.379801i \(0.875992\pi\)
\(774\) 5.84988 10.0300i 0.210269 0.360521i
\(775\) 8.87254 6.11504i 0.318711 0.219659i
\(776\) 7.81120i 0.280406i
\(777\) −3.55494 + 13.1513i −0.127533 + 0.471800i
\(778\) 23.3645