Properties

Label 690.2.i.e.47.4
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 47.4
Character \(\chi\) \(=\) 690.47
Dual form 690.2.i.e.323.4

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.451971 + 1.67204i) q^{3} -1.00000i q^{4} +(0.664484 + 2.13506i) q^{5} +(-1.50190 - 0.862720i) q^{6} +(2.34139 + 2.34139i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.59144 + 1.51143i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(0.451971 + 1.67204i) 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} +(1.67204 - 0.451971i) q^{12} +(2.78495 - 2.78495i) q^{13} -3.31122 q^{14} +(-3.26957 + 2.07603i) q^{15} -1.00000 q^{16} +(2.05101 - 2.05101i) q^{17} +(0.763687 - 2.90117i) 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} +(-3.69843 - 3.64988i) q^{27} +(2.34139 - 2.34139i) q^{28} +9.53664 q^{29} +(0.843964 - 3.77991i) q^{30} -2.15514 q^{31} +(0.707107 - 0.707107i) q^{32} +(-8.23661 + 2.22644i) 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} +(-1.49657 - 5.53650i) q^{42} +(2.73681 - 2.73681i) q^{43} +4.92608 q^{44} +(-4.94896 - 4.52856i) q^{45} -1.00000 q^{46} +(-8.67231 + 8.67231i) q^{47} +(-0.451971 - 1.67204i) 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} +(6.25279 - 1.69020i) q^{57} +(-6.74342 + 6.74342i) q^{58} +4.44157 q^{59} +(2.07603 + 3.26957i) q^{60} -2.83318 q^{61} +(1.52391 - 1.52391i) q^{62} +(-9.60641 - 2.52873i) 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} +(-2.90117 - 0.763687i) q^{72} +(7.65822 - 7.65822i) q^{73} +2.37538 q^{74} +(-6.60501 - 5.60123i) q^{75} -3.73962 q^{76} +(-11.5338 + 11.5338i) q^{77} +(-6.58537 + 1.78010i) 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} +(4.31028 + 15.9457i) q^{87} +(-3.48326 + 3.48326i) q^{88} -7.92555 q^{89} +(6.70161 - 0.297267i) q^{90} +13.0413 q^{91} +(0.707107 - 0.707107i) q^{92} +(-0.974060 - 3.60348i) 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
\(3\) 0.451971 + 1.67204i 0.260946 + 0.965354i
\(4\) 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 \(0.266424\pi\)
−0.669697 + 0.742634i \(0.733576\pi\)
\(12\) 1.67204 0.451971i 0.482677 0.130473i
\(13\) 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
\(15\) −3.26957 + 2.07603i −0.844200 + 0.536028i
\(16\) −1.00000 −0.250000
\(17\) 2.05101 2.05101i 0.497443 0.497443i −0.413198 0.910641i \(-0.635588\pi\)
0.910641 + 0.413198i \(0.135588\pi\)
\(18\) 0.763687 2.90117i 0.180003 0.683812i
\(19\) 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
\(27\) −3.69843 3.64988i −0.711763 0.702420i
\(28\) 2.34139 2.34139i 0.442480 0.442480i
\(29\) 9.53664 1.77091 0.885455 0.464725i \(-0.153847\pi\)
0.885455 + 0.464725i \(0.153847\pi\)
\(30\) 0.843964 3.77991i 0.154086 0.690114i
\(31\) −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
\(33\) −8.23661 + 2.22644i −1.43381 + 0.387574i
\(34\) 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 \(-0.867324\pi\)
0.914383 0.404850i \(-0.132676\pi\)
\(42\) −1.49657 5.53650i −0.230926 0.854300i
\(43\) 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
\(45\) −4.94896 4.52856i −0.737747 0.675077i
\(46\) −1.00000 −0.147442
\(47\) −8.67231 + 8.67231i −1.26499 + 1.26499i −0.316341 + 0.948645i \(0.602455\pi\)
−0.948645 + 0.316341i \(0.897545\pi\)
\(48\) −0.451971 1.67204i −0.0652364 0.241338i
\(49\) 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 \(-0.916377\pi\)
−0.259697 0.965690i \(-0.583623\pi\)
\(54\) 5.19604 0.0343279i 0.707091 0.00467144i
\(55\) −10.5174 + 3.27330i −1.41817 + 0.441372i
\(56\) 3.31122i 0.442480i
\(57\) 6.25279 1.69020i 0.828203 0.223872i
\(58\) −6.74342 + 6.74342i −0.885455 + 0.885455i
\(59\) 4.44157 0.578243 0.289122 0.957292i \(-0.406637\pi\)
0.289122 + 0.957292i \(0.406637\pi\)
\(60\) 2.07603 + 3.26957i 0.268014 + 0.422100i
\(61\) −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
\(63\) −9.60641 2.52873i −1.21029 0.318591i
\(64\) 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 \(0.0263021\pi\)
−0.996588 + 0.0825365i \(0.973698\pi\)
\(72\) −2.90117 0.763687i −0.341906 0.0900014i
\(73\) 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
\(75\) −6.60501 5.60123i −0.762681 0.646774i
\(76\) −3.73962 −0.428963
\(77\) −11.5338 + 11.5338i −1.31440 + 1.31440i
\(78\) −6.58537 + 1.78010i −0.745646 + 0.201556i
\(79\) 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 0.687201 0.726468i \(-0.258839\pi\)
−0.726468 + 0.687201i \(0.758839\pi\)
\(84\) 4.97313 + 2.85666i 0.542613 + 0.311687i
\(85\) 5.74189 + 3.01616i 0.622795 + 0.327148i
\(86\) 3.87043i 0.417359i
\(87\) 4.31028 + 15.9457i 0.462111 + 1.70955i
\(88\) −3.48326 + 3.48326i −0.371317 + 0.371317i
\(89\) −7.92555 −0.840106 −0.420053 0.907499i \(-0.637989\pi\)
−0.420053 + 0.907499i \(0.637989\pi\)
\(90\) 6.70161 0.297267i 0.706412 0.0313347i
\(91\) 13.0413 1.36710
\(92\) 0.707107 0.707107i 0.0737210 0.0737210i
\(93\) −0.974060 3.60348i −0.101005 0.373664i
\(94\) 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 \(0.363915\pi\)
−0.414619 + 0.909995i \(0.636085\pi\)
\(102\) −4.84987 + 1.31097i −0.480209 + 0.129806i
\(103\) 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
\(105\) −12.5161 2.79455i −1.22145 0.272720i
\(106\) 12.6161 1.22539
\(107\) 2.27414 2.27414i 0.219849 0.219849i −0.588586 0.808435i \(-0.700315\pi\)
0.808435 + 0.588586i \(0.200315\pi\)
\(108\) −3.64988 + 3.69843i −0.351210 + 0.355881i
\(109\) 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 0.327400 0.944886i \(-0.393828\pi\)
−0.944886 + 0.327400i \(0.893828\pi\)
\(114\) −3.22624 + 5.61654i −0.302165 + 0.526037i
\(115\) −1.03985 + 1.97957i −0.0969666 + 0.184596i
\(116\) 9.53664i 0.885455i
\(117\) −3.00780 + 11.4263i −0.278071 + 1.05636i
\(118\) −3.14067 + 3.14067i −0.289122 + 0.289122i
\(119\) 9.60441 0.880435
\(120\) −3.77991 0.843964i −0.345057 0.0770430i
\(121\) −13.2663 −1.20602
\(122\) 2.00336 2.00336i 0.181376 0.181376i
\(123\) 8.66888 2.34329i 0.781647 0.211288i
\(124\) 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 \(0.0124181\pi\)
−0.999239 + 0.0390027i \(0.987582\pi\)
\(132\) 2.22644 + 8.23661i 0.193787 + 0.716905i
\(133\) 8.75588 8.75588i 0.759231 0.759231i
\(134\) 9.34339 0.807146
\(135\) 5.33515 10.3216i 0.459177 0.888345i
\(136\) 2.90057 0.248722
\(137\) 5.62646 5.62646i 0.480701 0.480701i −0.424655 0.905355i \(-0.639604\pi\)
0.905355 + 0.424655i \(0.139604\pi\)
\(138\) −0.451971 1.67204i −0.0384743 0.142334i
\(139\) 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
\(147\) −6.62826 + 1.79169i −0.546690 + 0.147776i
\(148\) −1.67965 + 1.67965i −0.138066 + 0.138066i
\(149\) 12.7504 1.04456 0.522278 0.852775i \(-0.325082\pi\)
0.522278 + 0.852775i \(0.325082\pi\)
\(150\) 8.63112 0.709781i 0.704728 0.0579534i
\(151\) 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
\(153\) −2.21513 + 8.41504i −0.179082 + 0.680315i
\(154\) 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
\(162\) 2.40586 + 8.67248i 0.189022 + 0.681374i
\(163\) −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
\(165\) −10.2267 16.1062i −0.796146 1.25386i
\(166\) 0.505923 0.0392673
\(167\) 2.96090 2.96090i 0.229121 0.229121i −0.583204 0.812326i \(-0.698201\pi\)
0.812326 + 0.583204i \(0.198201\pi\)
\(168\) −5.53650 + 1.49657i −0.427150 + 0.115463i
\(169\) 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 \(-0.918982\pi\)
−0.251786 0.967783i \(-0.581018\pi\)
\(174\) −14.3231 8.22745i −1.08583 0.623721i
\(175\) −16.2828 2.99580i −1.23086 0.226462i
\(176\) 4.92608i 0.371317i
\(177\) 2.00746 + 7.42649i 0.150890 + 0.558209i
\(178\) 5.60421 5.60421i 0.420053 0.420053i
\(179\) 1.42969 0.106860 0.0534301 0.998572i \(-0.482985\pi\)
0.0534301 + 0.998572i \(0.482985\pi\)
\(180\) −4.52856 + 4.94896i −0.337539 + 0.368873i
\(181\) 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
\(183\) −1.28052 4.73720i −0.0946585 0.350184i
\(184\) 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 \(0.0311839\pi\)
−0.995205 + 0.0978104i \(0.968816\pi\)
\(192\) −1.67204 + 0.451971i −0.120669 + 0.0326182i
\(193\) 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
\(195\) −3.32397 + 14.8873i −0.238034 + 1.06610i
\(196\) 3.96417 0.283155
\(197\) 15.6486 15.6486i 1.11492 1.11492i 0.122441 0.992476i \(-0.460928\pi\)
0.992476 0.122441i \(-0.0390723\pi\)
\(198\) 14.2914 + 3.76198i 1.01564 + 0.267352i
\(199\) 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
\(207\) −2.90117 0.763687i −0.201645 0.0530799i
\(208\) −2.78495 + 2.78495i −0.193102 + 0.193102i
\(209\) 18.4216 1.27425
\(210\) 10.8263 6.87418i 0.747084 0.474364i
\(211\) 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
\(213\) −2.32569 + 0.628660i −0.159354 + 0.0430751i
\(214\) 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
\(222\) 1.07360 + 3.97174i 0.0720556 + 0.266566i
\(223\) 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
\(225\) 6.38022 13.5754i 0.425348 0.905030i
\(226\) 9.28286 0.617486
\(227\) −4.15095 + 4.15095i −0.275508 + 0.275508i −0.831313 0.555805i \(-0.812410\pi\)
0.555805 + 0.831313i \(0.312410\pi\)
\(228\) −1.69020 6.25279i −0.111936 0.414101i
\(229\) 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 \(-0.957322\pi\)
−0.133674 0.991025i \(-0.542678\pi\)
\(234\) −5.95279 10.2065i −0.389146 0.667217i
\(235\) −24.2785 12.7533i −1.58375 0.831930i
\(236\) 4.44157i 0.289122i
\(237\) 2.71630 0.734246i 0.176443 0.0476944i
\(238\) −6.79135 + 6.79135i −0.440218 + 0.440218i
\(239\) 3.42360 0.221454 0.110727 0.993851i \(-0.464682\pi\)
0.110727 + 0.993851i \(0.464682\pi\)
\(240\) 3.26957 2.07603i 0.211050 0.134007i
\(241\) −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
\(243\) 15.1008 + 3.86856i 0.968717 + 0.248168i
\(244\) 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 \(0.147700\pi\)
−0.894264 + 0.447540i \(0.852300\pi\)
\(252\) −2.52873 + 9.60641i −0.159295 + 0.605147i
\(253\) −3.48326 + 3.48326i −0.218991 + 0.218991i
\(254\) −12.5142 −0.785209
\(255\) −2.44797 + 10.9639i −0.153298 + 0.686585i
\(256\) 1.00000 0.0625000
\(257\) −17.2661 + 17.2661i −1.07703 + 1.07703i −0.0802573 + 0.996774i \(0.525574\pi\)
−0.996774 + 0.0802573i \(0.974426\pi\)
\(258\) −6.47152 + 1.74932i −0.402899 + 0.108908i
\(259\) 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 0.996190 0.0872121i \(-0.0277958\pi\)
−0.0872121 + 0.996190i \(0.527796\pi\)
\(264\) −7.39849 4.24983i −0.455346 0.261559i
\(265\) 13.1189 24.9746i 0.805888 1.53418i
\(266\) 12.3827i 0.759231i
\(267\) −3.58212 13.2518i −0.219222 0.811000i
\(268\) −6.60677 + 6.60677i −0.403573 + 0.403573i
\(269\) −25.7589 −1.57054 −0.785272 0.619150i \(-0.787477\pi\)
−0.785272 + 0.619150i \(0.787477\pi\)
\(270\) 3.52598 + 11.0710i 0.214584 + 0.673761i
\(271\) −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
\(273\) 5.89429 + 21.8056i 0.356739 + 1.31973i
\(274\) 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 \(0.0752824\pi\)
−0.972162 + 0.234308i \(0.924718\pi\)
\(282\) 20.5068 5.54320i 1.22116 0.330093i
\(283\) −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
\(285\) 7.76355 + 12.2269i 0.459873 + 0.724262i
\(286\) −19.4015 −1.14723
\(287\) 12.1392 12.1392i 0.716553 0.716553i
\(288\) −0.763687 + 2.90117i −0.0450007 + 0.170953i
\(289\) 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 \(-0.907694\pi\)
−0.285941 0.958247i \(-0.592306\pi\)
\(294\) 3.41997 5.95380i 0.199457 0.347233i
\(295\) 2.95135 + 9.48300i 0.171834 + 0.552122i
\(296\) 2.37538i 0.138066i
\(297\) 17.9796 18.2187i 1.04328 1.05716i
\(298\) −9.01592 + 9.01592i −0.522278 + 0.522278i
\(299\) 3.93852 0.227770
\(300\) −5.60123 + 6.60501i −0.323387 + 0.381341i
\(301\) 12.8158 0.738693
\(302\) −12.3599 + 12.3599i −0.711230 + 0.711230i
\(303\) −30.5828 + 8.26686i −1.75693 + 0.474918i
\(304\) 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 \(0.228761\pi\)
−0.752679 + 0.658388i \(0.771239\pi\)
\(312\) 1.78010 + 6.58537i 0.100778 + 0.372823i
\(313\) −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
\(315\) −0.984317 22.1905i −0.0554600 1.25029i
\(316\) −1.62454 −0.0913877
\(317\) 4.39344 4.39344i 0.246760 0.246760i −0.572879 0.819640i \(-0.694174\pi\)
0.819640 + 0.572879i \(0.194174\pi\)
\(318\) 5.70213 + 21.0947i 0.319759 + 1.18293i
\(319\) 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
\(327\) −5.35290 + 1.44695i −0.296016 + 0.0800163i
\(328\) 3.66607 3.66607i 0.202425 0.202425i
\(329\) −40.6105 −2.23893
\(330\) 18.6201 + 4.15743i 1.02500 + 0.228859i
\(331\) 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
\(333\) 6.89139 + 1.81405i 0.377646 + 0.0994093i
\(334\) 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
\(342\) −10.8493 2.85590i −0.586661 0.154429i
\(343\) 7.10804 7.10804i 0.383798 0.383798i
\(344\) 3.87043 0.208680
\(345\) −3.77991 0.843964i −0.203504 0.0454375i
\(346\) 22.6853 1.21957
\(347\) −20.1140 + 20.1140i −1.07978 + 1.07978i −0.0832466 + 0.996529i \(0.526529\pi\)
−0.996529 + 0.0832466i \(0.973471\pi\)
\(348\) 15.9457 4.31028i 0.854777 0.231055i
\(349\) 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 \(0.195253\pi\)
0.575656 + 0.817692i \(0.304747\pi\)
\(354\) −6.67081 3.83183i −0.354550 0.203660i
\(355\) −2.96971 + 0.924251i −0.157616 + 0.0490541i
\(356\) 7.92555i 0.420053i
\(357\) 4.34092 + 16.0590i 0.229746 + 0.849931i
\(358\) −1.01094 + 1.01094i −0.0534301 + 0.0534301i
\(359\) 18.0793 0.954191 0.477096 0.878851i \(-0.341690\pi\)
0.477096 + 0.878851i \(0.341690\pi\)
\(360\) −0.297267 6.70161i −0.0156674 0.353206i
\(361\) 5.01527 0.263962
\(362\) −1.91672 + 1.91672i −0.100740 + 0.100740i
\(363\) −5.99596 22.1817i −0.314706 1.16424i
\(364\) 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
\(372\) −3.60348 + 0.974060i −0.186832 + 0.0505027i
\(373\) −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
\(375\) 7.57001 17.8240i 0.390914 0.920427i
\(376\) −12.2645 −0.632493
\(377\) 26.5591 26.5591i 1.36786 1.36786i
\(378\) 12.2463 + 12.0856i 0.629882 + 0.621614i
\(379\) 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 0.0344882 0.999405i \(-0.489020\pi\)
−0.999405 + 0.0344882i \(0.989020\pi\)
\(384\) 0.862720 1.50190i 0.0440255 0.0766437i
\(385\) −32.2895 16.9613i −1.64562 0.864430i
\(386\) 13.5208i 0.688189i
\(387\) −2.95580 + 11.2288i −0.150252 + 0.570790i
\(388\) 5.52335 5.52335i 0.280406 0.280406i
\(389\) −33.0424 −1.67532 −0.837659 0.546193i \(-0.816076\pi\)
−0.837659 + 0.546193i \(0.816076\pi\)
\(390\) −8.17648 12.8773i −0.414032 0.652066i
\(391\) 2.90057 0.146688
\(392\) −2.80309 + 2.80309i −0.141578 + 0.141578i
\(393\) −1.49282 + 0.403525i −0.0753028 + 0.0203552i
\(394\) 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 \(0.128271\pi\)
−0.919898 + 0.392157i \(0.871729\pi\)
\(402\) 4.22294 + 15.6225i 0.210621 + 0.779181i
\(403\) −6.00196 + 6.00196i −0.298979 + 0.298979i
\(404\) 18.2907 0.909995
\(405\) 19.6695 + 4.25551i 0.977387 + 0.211458i
\(406\) −31.5779 −1.56719
\(407\) 8.27409 8.27409i 0.410131 0.410131i
\(408\) 1.31097 + 4.84987i 0.0649028 + 0.240104i
\(409\) 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
\(417\) −18.5539 + 5.01531i −0.908587 + 0.245601i
\(418\) −13.0261 + 13.0261i −0.637126 + 0.637126i
\(419\) −27.4239 −1.33974 −0.669872 0.742477i \(-0.733651\pi\)
−0.669872 + 0.742477i \(0.733651\pi\)
\(420\) −2.79455 + 12.5161i −0.136360 + 0.610724i
\(421\) −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
\(423\) 9.36624 35.5814i 0.455402 1.73003i
\(424\) 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 \(-0.888782\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(432\) 3.69843 + 3.64988i 0.177941 + 0.175605i
\(433\) 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
\(435\) −31.1807 + 19.7983i −1.49500 + 0.949257i
\(436\) 3.20141 0.153320
\(437\) 2.64431 2.64431i 0.126494 0.126494i
\(438\) −18.1088 + 4.89501i −0.865272 + 0.233892i
\(439\) 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 0.500258 0.865876i \(-0.333239\pi\)
−0.865876 + 0.500258i \(0.833239\pi\)
\(444\) −3.56760 2.04929i −0.169311 0.0972550i
\(445\) −5.26640 16.9215i −0.249651 0.802155i
\(446\) 24.1540i 1.14372i
\(447\) 5.76283 + 21.3193i 0.272572 + 1.00837i
\(448\) −2.34139 + 2.34139i −0.110620 + 0.110620i
\(449\) 32.2872 1.52373 0.761863 0.647738i \(-0.224285\pi\)
0.761863 + 0.647738i \(0.224285\pi\)
\(450\) 5.08780 + 14.1108i 0.239841 + 0.665189i
\(451\) 25.5398 1.20262
\(452\) −6.56397 + 6.56397i −0.308743 + 0.308743i
\(453\) 7.90022 + 29.2264i 0.371185 + 1.37318i
\(454\) 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 \(-0.927705\pi\)
0.974319 0.225173i \(-0.0722946\pi\)
\(462\) 27.2732 7.37224i 1.26886 0.342988i
\(463\) −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
\(465\) 7.04638 4.47413i 0.326768 0.207483i
\(466\) 24.2789 1.12470
\(467\) 9.89416 9.89416i 0.457847 0.457847i −0.440101 0.897948i \(-0.645057\pi\)
0.897948 + 0.440101i \(0.145057\pi\)
\(468\) 11.4263 + 3.00780i 0.528181 + 0.139035i
\(469\) 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
\(477\) 36.6015 + 9.63478i 1.67587 + 0.441146i
\(478\) −2.42085 + 2.42085i −0.110727 + 0.110727i
\(479\) 18.0640 0.825365 0.412683 0.910875i \(-0.364592\pi\)
0.412683 + 0.910875i \(0.364592\pi\)
\(480\) −0.843964 + 3.77991i −0.0385215 + 0.172529i
\(481\) −9.35549 −0.426574
\(482\) 15.6288 15.6288i 0.711874 0.711874i
\(483\) −5.53650 + 1.49657i −0.251919 + 0.0680965i
\(484\) 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 \(0.0323862\pi\)
−0.994829 + 0.101569i \(0.967614\pi\)
\(492\) −2.34329 8.66888i −0.105644 0.390823i
\(493\) 19.5598 19.5598i 0.880927 0.880927i
\(494\) 14.7286 0.662669
\(495\) 22.3080 24.3789i 1.00267 1.09575i
\(496\) 2.15514 0.0967686
\(497\) −3.25670 + 3.25670i −0.146083 + 0.146083i
\(498\) 0.228663 + 0.845925i 0.0102466 + 0.0379068i
\(499\) 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 \(-0.905911\pi\)
−0.291304 0.956630i \(-0.594089\pi\)
\(504\) −5.00467 8.58084i −0.222926 0.382221i
\(505\) −39.0516 + 12.1539i −1.73777 + 0.540840i
\(506\) 4.92608i 0.218991i
\(507\) 4.20006 1.13532i 0.186531 0.0504214i
\(508\) 8.84885 8.84885i 0.392604 0.392604i
\(509\) −2.48509 −0.110150 −0.0550749 0.998482i \(-0.517540\pi\)
−0.0550749 + 0.998482i \(0.517540\pi\)
\(510\) −6.02166 9.48362i −0.266644 0.419942i
\(511\) 35.8617 1.58643
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −13.6492 + 13.8307i −0.602625 + 0.610640i
\(514\) 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 \(-0.826646\pi\)
0.855331 0.518083i \(-0.173354\pi\)
\(522\) 7.28301 27.6674i 0.318769 1.21097i
\(523\) −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
\(525\) −2.35024 28.5795i −0.102573 1.24731i
\(526\) −20.8471 −0.908978
\(527\) −4.42021 + 4.42021i −0.192548 + 0.192548i
\(528\) 8.23661 2.22644i 0.358452 0.0968936i
\(529\) 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
\(537\) 0.646179 + 2.39050i 0.0278847 + 0.103158i
\(538\) 18.2143 18.2143i 0.785272 0.785272i
\(539\) −19.5278 −0.841123
\(540\) −10.3216 5.33515i −0.444172 0.229588i
\(541\) −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
\(543\) 1.22513 + 4.53231i 0.0525755 + 0.194500i
\(544\) 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
\(552\) −1.67204 + 0.451971i −0.0711668 + 0.0192372i
\(553\) 3.80368 3.80368i 0.161749 0.161749i
\(554\) 30.8414 1.31032
\(555\) 8.97874 + 2.00474i 0.381126 + 0.0850964i
\(556\) 11.0965 0.470598
\(557\) 10.6327 10.6327i 0.450523 0.450523i −0.445005 0.895528i \(-0.646798\pi\)
0.895528 + 0.445005i \(0.146798\pi\)
\(558\) −1.64585 + 6.25242i −0.0696744 + 0.264686i
\(559\) 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 \(-0.981482\pi\)
−0.0581420 0.998308i \(-0.518518\pi\)
\(564\) −10.5808 + 18.4201i −0.445533 + 0.775626i
\(565\) 9.65279 18.3761i 0.406096 0.773088i
\(566\) 11.3934i 0.478901i
\(567\) 28.7165 7.96632i 1.20598 0.334554i
\(568\) −0.983536 + 0.983536i −0.0412682 + 0.0412682i
\(569\) −10.7487 −0.450610 −0.225305 0.974288i \(-0.572338\pi\)
−0.225305 + 0.974288i \(0.572338\pi\)
\(570\) −14.1354 3.15610i −0.592067 0.132195i
\(571\) 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
\(573\) −4.52042 + 1.22192i −0.188843 + 0.0510464i
\(574\) 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
\(582\) −3.53044 13.0606i −0.146341 0.541381i
\(583\) 43.9453 43.9453i 1.82003 1.82003i
\(584\) 10.8304 0.448163
\(585\) −26.3944 + 1.17079i −1.09128 + 0.0484063i
\(586\) 30.1186 1.24419
\(587\) 14.5522 14.5522i 0.600635 0.600635i −0.339846 0.940481i \(-0.610375\pi\)
0.940481 + 0.339846i \(0.110375\pi\)
\(588\) 1.79169 + 6.62826i 0.0738881 + 0.273345i
\(589\) 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 0.873489 0.486844i \(-0.161852\pi\)
−0.486844 + 0.873489i \(0.661852\pi\)
\(594\) 0.169102 + 25.5961i 0.00693834 + 1.05022i
\(595\) 6.38198 + 20.5060i 0.261636 + 0.840662i
\(596\) 12.7504i 0.522278i
\(597\) 3.85004 1.04071i 0.157572 0.0425934i
\(598\) −2.78495 + 2.78495i −0.113885 + 0.113885i
\(599\) −25.4679 −1.04059 −0.520294 0.853987i \(-0.674178\pi\)
−0.520294 + 0.853987i \(0.674178\pi\)
\(600\) −0.709781 8.63112i −0.0289767 0.352364i
\(601\) 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
\(603\) 27.1068 + 7.13543i 1.10387 + 0.290577i
\(604\) 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
\(612\) 8.41504 + 2.21513i 0.340158 + 0.0895411i
\(613\) 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
\(615\) 10.7634 + 16.9515i 0.434022 + 0.683549i
\(616\) −16.3113 −0.657202
\(617\) 1.76987 1.76987i 0.0712523 0.0712523i −0.670583 0.741835i \(-0.733956\pi\)
0.741835 + 0.670583i \(0.233956\pi\)
\(618\) −19.2498 + 5.20343i −0.774341 + 0.209313i
\(619\) 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
\(627\) 8.32605 + 30.8017i 0.332510 + 1.23010i
\(628\) 9.49292 9.49292i 0.378809 0.378809i
\(629\) −6.88996 −0.274721
\(630\) 16.3871 + 14.9950i 0.652877 + 0.597417i
\(631\) −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
\(633\) 11.0610 + 40.9194i 0.439633 + 1.62640i
\(634\) 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 \(0.110179\pi\)
−0.940691 + 0.339266i \(0.889821\pi\)
\(642\) −5.37747 + 1.45359i −0.212232 + 0.0573686i
\(643\) −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
\(645\) −3.26650 + 14.6299i −0.128618 + 0.576051i
\(646\) 10.8470 0.426770
\(647\) 11.5427 11.5427i 0.453790 0.453790i −0.442820 0.896610i \(-0.646022\pi\)
0.896610 + 0.442820i \(0.146022\pi\)
\(648\) 8.67248 2.40586i 0.340687 0.0945110i
\(649\) 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 0.943992 0.329967i \(-0.107038\pi\)
−0.329967 + 0.943992i \(0.607038\pi\)
\(654\) 2.76192 4.80822i 0.108000 0.188016i
\(655\) −1.90620 + 0.593260i −0.0744816 + 0.0231806i
\(656\) 5.18461i 0.202425i
\(657\) −8.27100 + 31.4207i −0.322683 + 1.22584i
\(658\) 28.7159 28.7159i 1.11946 1.11946i
\(659\) −3.17418 −0.123649 −0.0618243 0.998087i \(-0.519692\pi\)
−0.0618243 + 0.998087i \(0.519692\pi\)
\(660\) −16.1062 + 10.2267i −0.626932 + 0.398073i
\(661\) −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
\(663\) 19.1013 5.16329i 0.741833 0.200526i
\(664\) 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
\(672\) 1.49657 + 5.53650i 0.0577316 + 0.213575i
\(673\) 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
\(675\) 25.5824 + 4.53228i 0.984666 + 0.174447i
\(676\) −2.51194 −0.0966129
\(677\) 30.0984 30.0984i 1.15678 1.15678i 0.171610 0.985165i \(-0.445103\pi\)
0.985165 0.171610i \(-0.0548970\pi\)
\(678\) 4.19558 + 15.5213i 0.161130 + 0.596093i
\(679\) 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 0.689587 0.724202i \(-0.257792\pi\)
−0.724202 + 0.689587i \(0.757792\pi\)
\(684\) 9.69101 5.65216i 0.370545 0.216116i
\(685\) 15.7515 + 8.27411i 0.601834 + 0.316137i
\(686\) 10.0523i 0.383798i
\(687\) −6.99945 + 1.89203i −0.267046 + 0.0721854i
\(688\) −2.73681 + 2.73681i −0.104340 + 0.104340i
\(689\) −49.6889 −1.89300
\(690\) 3.26957 2.07603i 0.124471 0.0790330i
\(691\) −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
\(693\) 12.4567 47.3219i 0.473193 1.79761i
\(694\) 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 \(0.0130595\pi\)
−0.999158 + 0.0410162i \(0.986940\pi\)
\(702\) 14.3751 14.5663i 0.542554 0.549771i
\(703\) −6.28124 + 6.28124i −0.236902 + 0.236902i
\(704\) −4.92608 −0.185659
\(705\) 10.3508 46.3587i 0.389834 1.74597i
\(706\) −37.0222 −1.39335
\(707\) −42.8255 + 42.8255i −1.61062 + 1.61062i
\(708\) 7.42649 2.00746i 0.279105 0.0754450i
\(709\) 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
\(717\) 1.54737 + 5.72440i 0.0577874 + 0.213781i
\(718\) −12.7840 + 12.7840i −0.477096 + 0.477096i
\(719\) −7.85539 −0.292957 −0.146478 0.989214i \(-0.546794\pi\)
−0.146478 + 0.989214i \(0.546794\pi\)
\(720\) 4.94896 + 4.52856i 0.184437 + 0.168769i
\(721\) 38.1213 1.41971
\(722\) −3.54633 + 3.54633i −0.131981 + 0.131981i
\(723\) −9.98969 36.9563i −0.371521 1.37442i
\(724\) 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
\(732\) −4.73720 + 1.28052i −0.175092 + 0.0473292i
\(733\) 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
\(735\) −8.22973 12.9611i −0.303558 0.478079i
\(736\) 1.00000 0.0368605
\(737\) 32.5455 32.5455i 1.19883 1.19883i
\(738\) −15.0414 3.95942i −0.553683 0.145748i
\(739\) 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 \(0.00946946\pi\)
0.0297448 + 0.999558i \(0.490531\pi\)
\(744\) 1.85928 3.23681i 0.0681646 0.118667i
\(745\) 8.47246 + 27.2229i 0.310407 + 0.997369i
\(746\) 35.6523i 1.30532i
\(747\) 1.46777 + 0.386367i 0.0537029 + 0.0141364i
\(748\) 10.1034 10.1034i 0.369418 0.369418i
\(749\) 10.6493 0.389115
\(750\) 7.25066 + 17.9563i 0.264757 + 0.655671i
\(751\) −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
\(753\) −23.7108 + 6.40927i −0.864068 + 0.233567i
\(754\) 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 \(0.161773\pi\)
−0.873609 + 0.486628i \(0.838227\pi\)
\(762\) −5.65604 20.9242i −0.204897 0.758004i
\(763\) −7.49575 + 7.49575i −0.271364 + 0.271364i
\(764\) 2.70353 0.0978104
\(765\) −19.4385 + 0.862243i −0.702800 + 0.0311745i
\(766\) 26.7057 0.964917
\(767\) 12.3696 12.3696i 0.446639 0.446639i
\(768\) 0.451971 + 1.67204i 0.0163091 + 0.0603346i
\(769\) 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 0.925068 0.379801i \(-0.124008\pi\)
−0.379801 + 0.925068i \(0.624008\pi\)
\(774\) −5.84988 10.0300i −0.210269 0.360521i
\(775\) 8.87254 6.11504i 0.318711 0.219659i
\(776\) 7.81120i 0.280406i
\(777\) 13.1513 3.55494i 0.471800 0.127533i
\(778\) 23.3645 23.3645i