Properties

Label 405.2.r.a.152.7
Level $405$
Weight $2$
Character 405.152
Analytic conductor $3.234$
Analytic rank $0$
Dimension $192$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.r (of order \(36\), degree \(12\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(192\)
Relative dimension: \(16\) over \(\Q(\zeta_{36})\)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 152.7
Character \(\chi\) \(=\) 405.152
Dual form 405.2.r.a.8.7

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +O(q^{10})\) \(q+(-0.263290 - 0.184358i) q^{2} +(-0.648706 - 1.78231i) q^{4} +(-2.21531 + 0.303968i) q^{5} +(2.07991 + 4.46037i) q^{7} +(-0.324162 + 1.20979i) q^{8} +(0.639309 + 0.328378i) q^{10} +(-0.0393995 - 0.0469545i) q^{11} +(0.0455832 + 0.0650996i) q^{13} +(0.274686 - 1.55782i) q^{14} +(-2.59752 + 2.17957i) q^{16} +(1.04290 + 3.89214i) q^{17} +(1.80193 - 1.04035i) q^{19} +(1.97885 + 3.75118i) q^{20} +(0.00171708 + 0.0196263i) q^{22} +(5.88782 + 2.74553i) q^{23} +(4.81521 - 1.34677i) q^{25} -0.0255437i q^{26} +(6.60050 - 6.60050i) q^{28} +(1.24585 + 7.06559i) q^{29} +(0.209263 - 0.0761654i) q^{31} +(3.58112 - 0.313308i) q^{32} +(0.442962 - 1.21703i) q^{34} +(-5.96345 - 9.24888i) q^{35} +(-6.33380 + 1.69714i) q^{37} +(-0.666227 - 0.0582873i) q^{38} +(0.350383 - 2.77860i) q^{40} +(2.22023 + 0.391486i) q^{41} +(-0.325424 + 3.71962i) q^{43} +(-0.0581286 + 0.100682i) q^{44} +(-1.04404 - 1.80834i) q^{46} +(-1.26917 + 0.591824i) q^{47} +(-11.0694 + 13.1920i) q^{49} +(-1.51608 - 0.533130i) q^{50} +(0.0864573 - 0.123474i) q^{52} +(-8.67464 - 8.67464i) q^{53} +(0.101555 + 0.0920427i) q^{55} +(-6.07034 + 1.07036i) q^{56} +(0.974575 - 2.08998i) q^{58} +(0.888968 + 0.745933i) q^{59} +(-6.77967 - 2.46760i) q^{61} +(-0.0691385 - 0.0185256i) q^{62} +(4.87243 + 2.81310i) q^{64} +(-0.120769 - 0.130360i) q^{65} +(6.22807 - 4.36094i) q^{67} +(6.26045 - 4.38361i) q^{68} +(-0.134987 + 3.53455i) q^{70} +(-6.33059 - 3.65497i) q^{71} +(6.42123 + 1.72056i) q^{73} +(1.98051 + 0.720846i) q^{74} +(-3.02314 - 2.53672i) q^{76} +(0.127487 - 0.273398i) q^{77} +(-6.06016 + 1.06857i) q^{79} +(5.09178 - 5.61800i) q^{80} +(-0.512391 - 0.512391i) q^{82} +(2.31193 - 3.30178i) q^{83} +(-3.49342 - 8.30529i) q^{85} +(0.771422 - 0.919344i) q^{86} +(0.0695770 - 0.0324443i) q^{88} +(5.25350 + 9.09933i) q^{89} +(-0.195560 + 0.338719i) q^{91} +(1.07392 - 12.2749i) q^{92} +(0.443268 + 0.0781601i) q^{94} +(-3.67561 + 2.85242i) q^{95} +(9.77698 + 0.855375i) q^{97} +(5.34651 - 1.43259i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 192 q + 12 q^{2} + 12 q^{5} - 12 q^{7} + 18 q^{8} - 6 q^{10} + 36 q^{11} - 12 q^{13} - 24 q^{16} + 18 q^{17} - 36 q^{20} - 12 q^{22} + 36 q^{23} - 30 q^{25} - 24 q^{28} - 24 q^{31} + 48 q^{32} - 36 q^{35} - 6 q^{37} - 12 q^{38} - 36 q^{40} - 24 q^{41} - 12 q^{43} - 12 q^{46} + 6 q^{47} - 36 q^{50} + 12 q^{52} - 24 q^{55} - 180 q^{56} - 12 q^{58} - 60 q^{61} + 18 q^{62} + 84 q^{65} + 24 q^{67} + 60 q^{68} - 12 q^{70} + 36 q^{71} - 6 q^{73} - 72 q^{76} - 132 q^{77} - 24 q^{82} - 48 q^{83} - 12 q^{85} - 12 q^{86} - 48 q^{88} - 12 q^{91} - 258 q^{92} - 18 q^{95} + 24 q^{97} - 324 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(e\left(\frac{17}{18}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.263290 0.184358i −0.186174 0.130361i 0.476774 0.879026i \(-0.341806\pi\)
−0.662948 + 0.748665i \(0.730695\pi\)
\(3\) 0 0
\(4\) −0.648706 1.78231i −0.324353 0.891153i
\(5\) −2.21531 + 0.303968i −0.990717 + 0.135939i
\(6\) 0 0
\(7\) 2.07991 + 4.46037i 0.786130 + 1.68586i 0.726024 + 0.687670i \(0.241366\pi\)
0.0601067 + 0.998192i \(0.480856\pi\)
\(8\) −0.324162 + 1.20979i −0.114609 + 0.427725i
\(9\) 0 0
\(10\) 0.639309 + 0.328378i 0.202167 + 0.103842i
\(11\) −0.0393995 0.0469545i −0.0118794 0.0141573i 0.760072 0.649839i \(-0.225164\pi\)
−0.771951 + 0.635682i \(0.780719\pi\)
\(12\) 0 0
\(13\) 0.0455832 + 0.0650996i 0.0126425 + 0.0180554i 0.825424 0.564514i \(-0.190936\pi\)
−0.812781 + 0.582569i \(0.802047\pi\)
\(14\) 0.274686 1.55782i 0.0734128 0.416345i
\(15\) 0 0
\(16\) −2.59752 + 2.17957i −0.649379 + 0.544894i
\(17\) 1.04290 + 3.89214i 0.252939 + 0.943982i 0.969225 + 0.246175i \(0.0791739\pi\)
−0.716286 + 0.697807i \(0.754159\pi\)
\(18\) 0 0
\(19\) 1.80193 1.04035i 0.413392 0.238672i −0.278854 0.960333i \(-0.589955\pi\)
0.692246 + 0.721662i \(0.256621\pi\)
\(20\) 1.97885 + 3.75118i 0.442484 + 0.838789i
\(21\) 0 0
\(22\) 0.00171708 + 0.0196263i 0.000366082 + 0.00418434i
\(23\) 5.88782 + 2.74553i 1.22769 + 0.572483i 0.924768 0.380531i \(-0.124259\pi\)
0.302926 + 0.953014i \(0.402036\pi\)
\(24\) 0 0
\(25\) 4.81521 1.34677i 0.963041 0.269354i
\(26\) 0.0255437i 0.00500954i
\(27\) 0 0
\(28\) 6.60050 6.60050i 1.24738 1.24738i
\(29\) 1.24585 + 7.06559i 0.231349 + 1.31205i 0.850167 + 0.526512i \(0.176501\pi\)
−0.618818 + 0.785534i \(0.712388\pi\)
\(30\) 0 0
\(31\) 0.209263 0.0761654i 0.0375847 0.0136797i −0.323159 0.946345i \(-0.604745\pi\)
0.360744 + 0.932665i \(0.382523\pi\)
\(32\) 3.58112 0.313308i 0.633059 0.0553855i
\(33\) 0 0
\(34\) 0.442962 1.21703i 0.0759674 0.208719i
\(35\) −5.96345 9.24888i −1.00801 1.56335i
\(36\) 0 0
\(37\) −6.33380 + 1.69714i −1.04127 + 0.279007i −0.738640 0.674101i \(-0.764531\pi\)
−0.302630 + 0.953108i \(0.597865\pi\)
\(38\) −0.666227 0.0582873i −0.108076 0.00945545i
\(39\) 0 0
\(40\) 0.350383 2.77860i 0.0554004 0.439335i
\(41\) 2.22023 + 0.391486i 0.346742 + 0.0611399i 0.344307 0.938857i \(-0.388114\pi\)
0.00243462 + 0.999997i \(0.499225\pi\)
\(42\) 0 0
\(43\) −0.325424 + 3.71962i −0.0496267 + 0.567236i 0.930155 + 0.367167i \(0.119672\pi\)
−0.979782 + 0.200069i \(0.935883\pi\)
\(44\) −0.0581286 + 0.100682i −0.00876322 + 0.0151783i
\(45\) 0 0
\(46\) −1.04404 1.80834i −0.153936 0.266625i
\(47\) −1.26917 + 0.591824i −0.185128 + 0.0863264i −0.512972 0.858405i \(-0.671456\pi\)
0.327844 + 0.944732i \(0.393678\pi\)
\(48\) 0 0
\(49\) −11.0694 + 13.1920i −1.58134 + 1.88457i
\(50\) −1.51608 0.533130i −0.214407 0.0753960i
\(51\) 0 0
\(52\) 0.0864573 0.123474i 0.0119895 0.0171227i
\(53\) −8.67464 8.67464i −1.19155 1.19155i −0.976631 0.214923i \(-0.931050\pi\)
−0.214923 0.976631i \(-0.568950\pi\)
\(54\) 0 0
\(55\) 0.101555 + 0.0920427i 0.0136937 + 0.0124110i
\(56\) −6.07034 + 1.07036i −0.811183 + 0.143033i
\(57\) 0 0
\(58\) 0.974575 2.08998i 0.127968 0.274428i
\(59\) 0.888968 + 0.745933i 0.115734 + 0.0971121i 0.698818 0.715300i \(-0.253710\pi\)
−0.583084 + 0.812412i \(0.698154\pi\)
\(60\) 0 0
\(61\) −6.77967 2.46760i −0.868048 0.315944i −0.130672 0.991426i \(-0.541713\pi\)
−0.737377 + 0.675482i \(0.763936\pi\)
\(62\) −0.0691385 0.0185256i −0.00878060 0.00235275i
\(63\) 0 0
\(64\) 4.87243 + 2.81310i 0.609054 + 0.351637i
\(65\) −0.120769 0.130360i −0.0149796 0.0161692i
\(66\) 0 0
\(67\) 6.22807 4.36094i 0.760880 0.532774i −0.127524 0.991835i \(-0.540703\pi\)
0.888405 + 0.459061i \(0.151814\pi\)
\(68\) 6.26045 4.38361i 0.759191 0.531591i
\(69\) 0 0
\(70\) −0.134987 + 3.53455i −0.0161340 + 0.422459i
\(71\) −6.33059 3.65497i −0.751303 0.433765i 0.0748614 0.997194i \(-0.476149\pi\)
−0.826165 + 0.563429i \(0.809482\pi\)
\(72\) 0 0
\(73\) 6.42123 + 1.72056i 0.751549 + 0.201377i 0.614205 0.789147i \(-0.289477\pi\)
0.137344 + 0.990523i \(0.456144\pi\)
\(74\) 1.98051 + 0.720846i 0.230229 + 0.0837966i
\(75\) 0 0
\(76\) −3.02314 2.53672i −0.346778 0.290981i
\(77\) 0.127487 0.273398i 0.0145285 0.0311565i
\(78\) 0 0
\(79\) −6.06016 + 1.06857i −0.681821 + 0.120223i −0.503822 0.863807i \(-0.668073\pi\)
−0.177999 + 0.984031i \(0.556962\pi\)
\(80\) 5.09178 5.61800i 0.569279 0.628111i
\(81\) 0 0
\(82\) −0.512391 0.512391i −0.0565841 0.0565841i
\(83\) 2.31193 3.30178i 0.253767 0.362417i −0.671974 0.740575i \(-0.734553\pi\)
0.925741 + 0.378158i \(0.123442\pi\)
\(84\) 0 0
\(85\) −3.49342 8.30529i −0.378915 0.900835i
\(86\) 0.771422 0.919344i 0.0831845 0.0991355i
\(87\) 0 0
\(88\) 0.0695770 0.0324443i 0.00741693 0.00345857i
\(89\) 5.25350 + 9.09933i 0.556870 + 0.964527i 0.997755 + 0.0669633i \(0.0213311\pi\)
−0.440886 + 0.897563i \(0.645336\pi\)
\(90\) 0 0
\(91\) −0.195560 + 0.338719i −0.0205002 + 0.0355074i
\(92\) 1.07392 12.2749i 0.111964 1.27975i
\(93\) 0 0
\(94\) 0.443268 + 0.0781601i 0.0457196 + 0.00806160i
\(95\) −3.67561 + 2.85242i −0.377109 + 0.292652i
\(96\) 0 0
\(97\) 9.77698 + 0.855375i 0.992702 + 0.0868501i 0.571918 0.820311i \(-0.306200\pi\)
0.420784 + 0.907161i \(0.361755\pi\)
\(98\) 5.34651 1.43259i 0.540079 0.144714i
\(99\) 0 0
\(100\) −5.52401 7.70852i −0.552401 0.770852i
\(101\) −1.28534 + 3.53144i −0.127896 + 0.351391i −0.987069 0.160293i \(-0.948756\pi\)
0.859173 + 0.511684i \(0.170978\pi\)
\(102\) 0 0
\(103\) −2.41848 + 0.211590i −0.238300 + 0.0208485i −0.205680 0.978619i \(-0.565941\pi\)
−0.0326198 + 0.999468i \(0.510385\pi\)
\(104\) −0.0935332 + 0.0340433i −0.00917169 + 0.00333822i
\(105\) 0 0
\(106\) 0.684711 + 3.88319i 0.0665050 + 0.377168i
\(107\) −1.54852 + 1.54852i −0.149701 + 0.149701i −0.777984 0.628284i \(-0.783758\pi\)
0.628284 + 0.777984i \(0.283758\pi\)
\(108\) 0 0
\(109\) 0.257274i 0.0246424i 0.999924 + 0.0123212i \(0.00392206\pi\)
−0.999924 + 0.0123212i \(0.996078\pi\)
\(110\) −0.00976963 0.0429564i −0.000931497 0.00409573i
\(111\) 0 0
\(112\) −15.1243 7.05257i −1.42911 0.666406i
\(113\) −0.980488 11.2070i −0.0922366 1.05427i −0.891419 0.453180i \(-0.850289\pi\)
0.799182 0.601089i \(-0.205266\pi\)
\(114\) 0 0
\(115\) −13.8779 4.29250i −1.29412 0.400278i
\(116\) 11.7848 6.80398i 1.09420 0.631734i
\(117\) 0 0
\(118\) −0.0965380 0.360285i −0.00888705 0.0331669i
\(119\) −15.1913 + 12.7470i −1.39258 + 1.16851i
\(120\) 0 0
\(121\) 1.90948 10.8292i 0.173589 0.984471i
\(122\) 1.33010 + 1.89958i 0.120422 + 0.171980i
\(123\) 0 0
\(124\) −0.271500 0.323561i −0.0243814 0.0290567i
\(125\) −10.2578 + 4.44718i −0.917486 + 0.397768i
\(126\) 0 0
\(127\) −2.00243 + 7.47317i −0.177687 + 0.663137i 0.818391 + 0.574661i \(0.194866\pi\)
−0.996078 + 0.0884755i \(0.971801\pi\)
\(128\) −3.80270 8.15493i −0.336115 0.720800i
\(129\) 0 0
\(130\) 0.00776448 + 0.0565873i 0.000680990 + 0.00496303i
\(131\) −3.14700 8.64630i −0.274954 0.755431i −0.997915 0.0645417i \(-0.979441\pi\)
0.722961 0.690889i \(-0.242781\pi\)
\(132\) 0 0
\(133\) 8.38818 + 5.87347i 0.727347 + 0.509294i
\(134\) −2.44376 −0.211109
\(135\) 0 0
\(136\) −5.04674 −0.432754
\(137\) 11.2654 + 7.88810i 0.962466 + 0.673926i 0.945394 0.325928i \(-0.105677\pi\)
0.0170715 + 0.999854i \(0.494566\pi\)
\(138\) 0 0
\(139\) −0.364140 1.00047i −0.0308860 0.0848586i 0.923291 0.384101i \(-0.125488\pi\)
−0.954177 + 0.299242i \(0.903266\pi\)
\(140\) −12.6158 + 16.6285i −1.06623 + 1.40536i
\(141\) 0 0
\(142\) 0.992961 + 2.12941i 0.0833274 + 0.178696i
\(143\) 0.00126076 0.00470524i 0.000105430 0.000393472i
\(144\) 0 0
\(145\) −4.90767 15.2738i −0.407560 1.26842i
\(146\) −1.37345 1.63681i −0.113667 0.135464i
\(147\) 0 0
\(148\) 7.13359 + 10.1878i 0.586378 + 0.837434i
\(149\) 3.12678 17.7328i 0.256156 1.45273i −0.536933 0.843625i \(-0.680417\pi\)
0.793089 0.609106i \(-0.208472\pi\)
\(150\) 0 0
\(151\) 7.30896 6.13294i 0.594795 0.499092i −0.294973 0.955506i \(-0.595311\pi\)
0.889768 + 0.456414i \(0.150866\pi\)
\(152\) 0.674482 + 2.51720i 0.0547077 + 0.204172i
\(153\) 0 0
\(154\) −0.0839692 + 0.0484796i −0.00676643 + 0.00390660i
\(155\) −0.440430 + 0.232339i −0.0353762 + 0.0186619i
\(156\) 0 0
\(157\) 1.41313 + 16.1522i 0.112780 + 1.28908i 0.815975 + 0.578087i \(0.196201\pi\)
−0.703195 + 0.710997i \(0.748244\pi\)
\(158\) 1.79258 + 0.835893i 0.142610 + 0.0665001i
\(159\) 0 0
\(160\) −7.83807 + 1.78262i −0.619654 + 0.140929i
\(161\) 31.9723i 2.51977i
\(162\) 0 0
\(163\) −7.81801 + 7.81801i −0.612354 + 0.612354i −0.943559 0.331205i \(-0.892545\pi\)
0.331205 + 0.943559i \(0.392545\pi\)
\(164\) −0.742528 4.21109i −0.0579817 0.328831i
\(165\) 0 0
\(166\) −1.21742 + 0.443103i −0.0944898 + 0.0343915i
\(167\) 13.0293 1.13992i 1.00824 0.0882093i 0.428946 0.903330i \(-0.358885\pi\)
0.579291 + 0.815121i \(0.303329\pi\)
\(168\) 0 0
\(169\) 4.44410 12.2101i 0.341854 0.939236i
\(170\) −0.611361 + 2.83074i −0.0468892 + 0.217108i
\(171\) 0 0
\(172\) 6.84060 1.83293i 0.521591 0.139760i
\(173\) 22.6663 + 1.98304i 1.72329 + 0.150768i 0.905385 0.424592i \(-0.139582\pi\)
0.817900 + 0.575360i \(0.195138\pi\)
\(174\) 0 0
\(175\) 16.0223 + 18.6765i 1.21117 + 1.41181i
\(176\) 0.204682 + 0.0360909i 0.0154285 + 0.00272046i
\(177\) 0 0
\(178\) 0.294337 3.36429i 0.0220615 0.252164i
\(179\) 9.11136 15.7813i 0.681015 1.17955i −0.293656 0.955911i \(-0.594872\pi\)
0.974671 0.223642i \(-0.0717945\pi\)
\(180\) 0 0
\(181\) 6.18809 + 10.7181i 0.459957 + 0.796669i 0.998958 0.0456358i \(-0.0145314\pi\)
−0.539001 + 0.842305i \(0.681198\pi\)
\(182\) 0.113934 0.0531285i 0.00844539 0.00393815i
\(183\) 0 0
\(184\) −5.23013 + 6.23302i −0.385570 + 0.459504i
\(185\) 13.5155 5.68496i 0.993676 0.417966i
\(186\) 0 0
\(187\) 0.141664 0.202317i 0.0103595 0.0147949i
\(188\) 1.87813 + 1.87813i 0.136977 + 0.136977i
\(189\) 0 0
\(190\) 1.49362 0.0733872i 0.108358 0.00532407i
\(191\) −12.0893 + 2.13167i −0.874752 + 0.154242i −0.592959 0.805233i \(-0.702040\pi\)
−0.281793 + 0.959475i \(0.590929\pi\)
\(192\) 0 0
\(193\) 7.49551 16.0742i 0.539538 1.15704i −0.427874 0.903838i \(-0.640737\pi\)
0.967413 0.253205i \(-0.0814848\pi\)
\(194\) −2.41649 2.02767i −0.173494 0.145579i
\(195\) 0 0
\(196\) 30.6929 + 11.1713i 2.19235 + 0.797951i
\(197\) −8.80113 2.35826i −0.627055 0.168019i −0.0687218 0.997636i \(-0.521892\pi\)
−0.558333 + 0.829617i \(0.688559\pi\)
\(198\) 0 0
\(199\) 9.38387 + 5.41778i 0.665205 + 0.384056i 0.794257 0.607581i \(-0.207860\pi\)
−0.129052 + 0.991638i \(0.541193\pi\)
\(200\) 0.0683980 + 6.26196i 0.00483647 + 0.442787i
\(201\) 0 0
\(202\) 0.989466 0.692831i 0.0696186 0.0487474i
\(203\) −28.9239 + 20.2527i −2.03006 + 1.42146i
\(204\) 0 0
\(205\) −5.03750 0.192385i −0.351834 0.0134368i
\(206\) 0.675770 + 0.390156i 0.0470831 + 0.0271835i
\(207\) 0 0
\(208\) −0.260293 0.0697452i −0.0180480 0.00483596i
\(209\) −0.119844 0.0436198i −0.00828980 0.00301724i
\(210\) 0 0
\(211\) −1.55684 1.30634i −0.107177 0.0899325i 0.587624 0.809134i \(-0.300063\pi\)
−0.694802 + 0.719202i \(0.744508\pi\)
\(212\) −9.83357 + 21.0882i −0.675372 + 1.44834i
\(213\) 0 0
\(214\) 0.693191 0.122228i 0.0473856 0.00835535i
\(215\) −0.409729 8.33903i −0.0279433 0.568717i
\(216\) 0 0
\(217\) 0.774973 + 0.774973i 0.0526086 + 0.0526086i
\(218\) 0.0474305 0.0677378i 0.00321240 0.00458779i
\(219\) 0 0
\(220\) 0.0981690 0.240711i 0.00661855 0.0162287i
\(221\) −0.205838 + 0.245308i −0.0138462 + 0.0165012i
\(222\) 0 0
\(223\) −2.46881 + 1.15123i −0.165324 + 0.0770918i −0.503519 0.863984i \(-0.667961\pi\)
0.338195 + 0.941076i \(0.390184\pi\)
\(224\) 8.84586 + 15.3215i 0.591039 + 1.02371i
\(225\) 0 0
\(226\) −1.80795 + 3.13146i −0.120263 + 0.208302i
\(227\) 1.23497 14.1158i 0.0819680 0.936899i −0.838197 0.545368i \(-0.816390\pi\)
0.920165 0.391531i \(-0.128054\pi\)
\(228\) 0 0
\(229\) 13.0574 + 2.30237i 0.862857 + 0.152145i 0.587527 0.809205i \(-0.300102\pi\)
0.275330 + 0.961350i \(0.411213\pi\)
\(230\) 2.86256 + 3.68867i 0.188752 + 0.243224i
\(231\) 0 0
\(232\) −8.95173 0.783175i −0.587710 0.0514180i
\(233\) 6.55427 1.75621i 0.429384 0.115053i −0.0376527 0.999291i \(-0.511988\pi\)
0.467037 + 0.884238i \(0.345321\pi\)
\(234\) 0 0
\(235\) 2.63171 1.69686i 0.171674 0.110691i
\(236\) 0.752801 2.06830i 0.0490032 0.134635i
\(237\) 0 0
\(238\) 6.34972 0.555528i 0.411591 0.0360095i
\(239\) −17.1554 + 6.24407i −1.10969 + 0.403895i −0.830881 0.556451i \(-0.812163\pi\)
−0.278812 + 0.960346i \(0.589941\pi\)
\(240\) 0 0
\(241\) −2.76886 15.7030i −0.178358 1.01152i −0.934196 0.356759i \(-0.883882\pi\)
0.755839 0.654758i \(-0.227229\pi\)
\(242\) −2.49919 + 2.49919i −0.160654 + 0.160654i
\(243\) 0 0
\(244\) 13.6842i 0.876041i
\(245\) 20.5122 32.5891i 1.31048 2.08204i
\(246\) 0 0
\(247\) 0.149864 + 0.0698828i 0.00953562 + 0.00444653i
\(248\) 0.0243091 + 0.277854i 0.00154363 + 0.0176437i
\(249\) 0 0
\(250\) 3.52065 + 0.720208i 0.222666 + 0.0455499i
\(251\) −14.9016 + 8.60342i −0.940578 + 0.543043i −0.890141 0.455684i \(-0.849395\pi\)
−0.0504364 + 0.998727i \(0.516061\pi\)
\(252\) 0 0
\(253\) −0.103062 0.384632i −0.00647945 0.0241816i
\(254\) 1.90496 1.59845i 0.119528 0.100296i
\(255\) 0 0
\(256\) 1.45175 8.23327i 0.0907343 0.514580i
\(257\) 5.37032 + 7.66961i 0.334991 + 0.478417i 0.950943 0.309367i \(-0.100117\pi\)
−0.615952 + 0.787784i \(0.711228\pi\)
\(258\) 0 0
\(259\) −20.7436 24.7212i −1.28894 1.53610i
\(260\) −0.153998 + 0.299813i −0.00955053 + 0.0185936i
\(261\) 0 0
\(262\) −0.765440 + 2.85666i −0.0472890 + 0.176485i
\(263\) 0.386147 + 0.828096i 0.0238109 + 0.0510626i 0.917854 0.396919i \(-0.129921\pi\)
−0.894043 + 0.447982i \(0.852143\pi\)
\(264\) 0 0
\(265\) 21.8538 + 16.5802i 1.34247 + 1.01851i
\(266\) −1.12571 3.09285i −0.0690215 0.189635i
\(267\) 0 0
\(268\) −11.8127 8.27136i −0.721577 0.505254i
\(269\) 27.6508 1.68590 0.842951 0.537990i \(-0.180816\pi\)
0.842951 + 0.537990i \(0.180816\pi\)
\(270\) 0 0
\(271\) −18.0879 −1.09876 −0.549380 0.835572i \(-0.685136\pi\)
−0.549380 + 0.835572i \(0.685136\pi\)
\(272\) −11.1921 7.83682i −0.678623 0.475177i
\(273\) 0 0
\(274\) −1.51183 4.15372i −0.0913330 0.250935i
\(275\) −0.252954 0.173034i −0.0152537 0.0104343i
\(276\) 0 0
\(277\) 2.18829 + 4.69280i 0.131481 + 0.281963i 0.961016 0.276492i \(-0.0891721\pi\)
−0.829535 + 0.558455i \(0.811394\pi\)
\(278\) −0.0885694 + 0.330545i −0.00531204 + 0.0198248i
\(279\) 0 0
\(280\) 13.1223 4.21638i 0.784209 0.251977i
\(281\) 4.92653 + 5.87122i 0.293892 + 0.350247i 0.892705 0.450642i \(-0.148805\pi\)
−0.598812 + 0.800889i \(0.704360\pi\)
\(282\) 0 0
\(283\) 5.43511 + 7.76215i 0.323084 + 0.461412i 0.947535 0.319652i \(-0.103566\pi\)
−0.624451 + 0.781064i \(0.714677\pi\)
\(284\) −2.40758 + 13.6541i −0.142863 + 0.810219i
\(285\) 0 0
\(286\) −0.00119939 + 0.00100641i −7.09216e−5 + 5.95103e-5i
\(287\) 2.87169 + 10.7173i 0.169511 + 0.632622i
\(288\) 0 0
\(289\) 0.661319 0.381813i 0.0389011 0.0224596i
\(290\) −1.52370 + 4.92620i −0.0894747 + 0.289277i
\(291\) 0 0
\(292\) −1.09892 12.5607i −0.0643096 0.735062i
\(293\) −7.74397 3.61107i −0.452408 0.210961i 0.183039 0.983106i \(-0.441406\pi\)
−0.635447 + 0.772144i \(0.719184\pi\)
\(294\) 0 0
\(295\) −2.19608 1.38225i −0.127861 0.0804780i
\(296\) 8.21271i 0.477354i
\(297\) 0 0
\(298\) −4.09244 + 4.09244i −0.237069 + 0.237069i
\(299\) 0.0896526 + 0.508445i 0.00518474 + 0.0294041i
\(300\) 0 0
\(301\) −17.2677 + 6.28494i −0.995295 + 0.362258i
\(302\) −3.05503 + 0.267281i −0.175797 + 0.0153803i
\(303\) 0 0
\(304\) −2.41304 + 6.62976i −0.138397 + 0.380243i
\(305\) 15.7692 + 3.40570i 0.902939 + 0.195010i
\(306\) 0 0
\(307\) −20.4909 + 5.49053i −1.16948 + 0.313361i −0.790746 0.612145i \(-0.790307\pi\)
−0.378734 + 0.925506i \(0.623640\pi\)
\(308\) −0.569980 0.0498668i −0.0324776 0.00284142i
\(309\) 0 0
\(310\) 0.158795 + 0.0200241i 0.00901892 + 0.00113729i
\(311\) 19.3816 + 3.41750i 1.09903 + 0.193788i 0.693616 0.720345i \(-0.256017\pi\)
0.405413 + 0.914134i \(0.367128\pi\)
\(312\) 0 0
\(313\) 0.366189 4.18556i 0.0206983 0.236582i −0.978798 0.204830i \(-0.934336\pi\)
0.999496 0.0317519i \(-0.0101087\pi\)
\(314\) 2.60572 4.51323i 0.147049 0.254696i
\(315\) 0 0
\(316\) 5.83578 + 10.1079i 0.328288 + 0.568612i
\(317\) −15.1326 + 7.05644i −0.849930 + 0.396329i −0.798244 0.602334i \(-0.794237\pi\)
−0.0516863 + 0.998663i \(0.516460\pi\)
\(318\) 0 0
\(319\) 0.282675 0.336879i 0.0158268 0.0188616i
\(320\) −11.6490 4.75082i −0.651201 0.265579i
\(321\) 0 0
\(322\) 5.89434 8.41799i 0.328479 0.469116i
\(323\) 5.92840 + 5.92840i 0.329865 + 0.329865i
\(324\) 0 0
\(325\) 0.307167 + 0.252078i 0.0170386 + 0.0139828i
\(326\) 3.49972 0.617095i 0.193831 0.0341777i
\(327\) 0 0
\(328\) −1.19333 + 2.55911i −0.0658907 + 0.141303i
\(329\) −5.27951 4.43004i −0.291069 0.244236i
\(330\) 0 0
\(331\) −12.4570 4.53397i −0.684698 0.249210i −0.0238345 0.999716i \(-0.507587\pi\)
−0.660863 + 0.750506i \(0.729810\pi\)
\(332\) −7.38454 1.97868i −0.405279 0.108594i
\(333\) 0 0
\(334\) −3.64064 2.10192i −0.199207 0.115012i
\(335\) −12.4715 + 11.5540i −0.681393 + 0.631261i
\(336\) 0 0
\(337\) 17.4071 12.1886i 0.948223 0.663953i 0.00637058 0.999980i \(-0.497972\pi\)
0.941852 + 0.336027i \(0.109083\pi\)
\(338\) −3.42111 + 2.39549i −0.186084 + 0.130297i
\(339\) 0 0
\(340\) −12.5364 + 11.6140i −0.679880 + 0.629860i
\(341\) −0.0118212 0.00682495i −0.000640152 0.000369592i
\(342\) 0 0
\(343\) −48.5880 13.0191i −2.62350 0.702966i
\(344\) −4.39446 1.59945i −0.236934 0.0862368i
\(345\) 0 0
\(346\) −5.60222 4.70082i −0.301177 0.252718i
\(347\) 13.3295 28.5852i 0.715565 1.53453i −0.124603 0.992207i \(-0.539766\pi\)
0.840168 0.542327i \(-0.182456\pi\)
\(348\) 0 0
\(349\) 16.6978 2.94427i 0.893813 0.157603i 0.292168 0.956367i \(-0.405623\pi\)
0.601645 + 0.798764i \(0.294512\pi\)
\(350\) −0.775353 7.87116i −0.0414444 0.420731i
\(351\) 0 0
\(352\) −0.155806 0.155806i −0.00830448 0.00830448i
\(353\) −10.9094 + 15.5802i −0.580648 + 0.829252i −0.996791 0.0800474i \(-0.974493\pi\)
0.416143 + 0.909299i \(0.363382\pi\)
\(354\) 0 0
\(355\) 15.1352 + 6.17260i 0.803294 + 0.327607i
\(356\) 12.8098 15.2661i 0.678918 0.809103i
\(357\) 0 0
\(358\) −5.30835 + 2.47532i −0.280555 + 0.130825i
\(359\) −15.6916 27.1786i −0.828170 1.43443i −0.899473 0.436977i \(-0.856049\pi\)
0.0713028 0.997455i \(-0.477284\pi\)
\(360\) 0 0
\(361\) −7.33536 + 12.7052i −0.386072 + 0.668696i
\(362\) 0.346699 3.96279i 0.0182221 0.208280i
\(363\) 0 0
\(364\) 0.730562 + 0.128818i 0.0382919 + 0.00675189i
\(365\) −14.7480 1.85974i −0.771947 0.0973430i
\(366\) 0 0
\(367\) 17.8579 + 1.56237i 0.932177 + 0.0815549i 0.543117 0.839657i \(-0.317244\pi\)
0.389060 + 0.921212i \(0.372800\pi\)
\(368\) −21.2778 + 5.70137i −1.10918 + 0.297204i
\(369\) 0 0
\(370\) −4.60655 0.994887i −0.239483 0.0517217i
\(371\) 20.6497 56.7346i 1.07208 2.94551i
\(372\) 0 0
\(373\) −5.04230 + 0.441145i −0.261081 + 0.0228416i −0.216945 0.976184i \(-0.569609\pi\)
−0.0441361 + 0.999026i \(0.514054\pi\)
\(374\) −0.0745975 + 0.0271513i −0.00385734 + 0.00140396i
\(375\) 0 0
\(376\) −0.304566 1.72728i −0.0157068 0.0890775i
\(377\) −0.403177 + 0.403177i −0.0207647 + 0.0207647i
\(378\) 0 0
\(379\) 9.89195i 0.508115i −0.967189 0.254058i \(-0.918235\pi\)
0.967189 0.254058i \(-0.0817653\pi\)
\(380\) 7.46828 + 4.70068i 0.383114 + 0.241140i
\(381\) 0 0
\(382\) 3.57599 + 1.66751i 0.182963 + 0.0853173i
\(383\) 1.67206 + 19.1117i 0.0854380 + 0.976561i 0.911043 + 0.412312i \(0.135279\pi\)
−0.825605 + 0.564249i \(0.809166\pi\)
\(384\) 0 0
\(385\) −0.199320 + 0.644413i −0.0101583 + 0.0328423i
\(386\) −4.93689 + 2.85032i −0.251281 + 0.145077i
\(387\) 0 0
\(388\) −4.81785 17.9805i −0.244589 0.912819i
\(389\) −5.65836 + 4.74792i −0.286890 + 0.240729i −0.774863 0.632130i \(-0.782181\pi\)
0.487973 + 0.872859i \(0.337737\pi\)
\(390\) 0 0
\(391\) −4.54562 + 25.7795i −0.229882 + 1.30373i
\(392\) −12.3713 17.6680i −0.624843 0.892368i
\(393\) 0 0
\(394\) 1.88249 + 2.24346i 0.0948384 + 0.113024i
\(395\) 13.1003 4.20931i 0.659149 0.211793i
\(396\) 0 0
\(397\) 3.34227 12.4735i 0.167744 0.626028i −0.829931 0.557866i \(-0.811620\pi\)
0.997674 0.0681611i \(-0.0217132\pi\)
\(398\) −1.47187 3.15644i −0.0737783 0.158218i
\(399\) 0 0
\(400\) −9.57219 + 13.9934i −0.478610 + 0.699668i
\(401\) 2.92360 + 8.03253i 0.145998 + 0.401125i 0.991039 0.133576i \(-0.0426461\pi\)
−0.845041 + 0.534702i \(0.820424\pi\)
\(402\) 0 0
\(403\) 0.0144972 + 0.0101511i 0.000722158 + 0.000505660i
\(404\) 7.12791 0.354627
\(405\) 0 0
\(406\) 11.3491 0.563248
\(407\) 0.329237 + 0.230534i 0.0163197 + 0.0114272i
\(408\) 0 0
\(409\) −4.56883 12.5528i −0.225914 0.620694i 0.774008 0.633176i \(-0.218249\pi\)
−0.999922 + 0.0124819i \(0.996027\pi\)
\(410\) 1.29086 + 0.979355i 0.0637508 + 0.0483669i
\(411\) 0 0
\(412\) 1.94600 + 4.17321i 0.0958725 + 0.205599i
\(413\) −1.47817 + 5.51659i −0.0727359 + 0.271454i
\(414\) 0 0
\(415\) −4.11801 + 8.01721i −0.202145 + 0.393550i
\(416\) 0.183635 + 0.218848i 0.00900347 + 0.0107299i
\(417\) 0 0
\(418\) 0.0235122 + 0.0335789i 0.00115002 + 0.00164240i
\(419\) 4.65475 26.3984i 0.227399 1.28964i −0.630646 0.776071i \(-0.717210\pi\)
0.858045 0.513574i \(-0.171679\pi\)
\(420\) 0 0
\(421\) 19.3371 16.2257i 0.942432 0.790794i −0.0355751 0.999367i \(-0.511326\pi\)
0.978007 + 0.208573i \(0.0668818\pi\)
\(422\) 0.169066 + 0.630963i 0.00823001 + 0.0307148i
\(423\) 0 0
\(424\) 13.3065 7.68250i 0.646220 0.373095i
\(425\) 10.2636 + 17.3369i 0.497856 + 0.840964i
\(426\) 0 0
\(427\) −3.09467 35.3722i −0.149762 1.71178i
\(428\) 3.76447 + 1.75540i 0.181962 + 0.0848504i
\(429\) 0 0
\(430\) −1.42949 + 2.27112i −0.0689360 + 0.109523i
\(431\) 23.0274i 1.10919i −0.832121 0.554595i \(-0.812873\pi\)
0.832121 0.554595i \(-0.187127\pi\)
\(432\) 0 0
\(433\) 12.8672 12.8672i 0.618357 0.618357i −0.326752 0.945110i \(-0.605954\pi\)
0.945110 + 0.326752i \(0.105954\pi\)
\(434\) −0.0611705 0.346915i −0.00293628 0.0166525i
\(435\) 0 0
\(436\) 0.458542 0.166896i 0.0219602 0.00799285i
\(437\) 13.4658 1.17810i 0.644154 0.0563562i
\(438\) 0 0
\(439\) 10.8870 29.9118i 0.519609 1.42761i −0.351343 0.936247i \(-0.614275\pi\)
0.870952 0.491367i \(-0.163503\pi\)
\(440\) −0.144273 + 0.0930233i −0.00687793 + 0.00443471i
\(441\) 0 0
\(442\) 0.0994197 0.0266394i 0.00472891 0.00126711i
\(443\) 8.95244 + 0.783237i 0.425343 + 0.0372127i 0.297818 0.954623i \(-0.403741\pi\)
0.127525 + 0.991835i \(0.459297\pi\)
\(444\) 0 0
\(445\) −14.4040 18.5609i −0.682817 0.879873i
\(446\) 0.862251 + 0.152038i 0.0408288 + 0.00719922i
\(447\) 0 0
\(448\) −2.41327 + 27.5838i −0.114016 + 1.30321i
\(449\) −5.30209 + 9.18349i −0.250221 + 0.433396i −0.963587 0.267396i \(-0.913837\pi\)
0.713365 + 0.700792i \(0.247170\pi\)
\(450\) 0 0
\(451\) −0.0690940 0.119674i −0.00325351 0.00563524i
\(452\) −19.3383 + 9.01760i −0.909598 + 0.424152i
\(453\) 0 0
\(454\) −2.92752 + 3.48888i −0.137395 + 0.163741i
\(455\) 0.330266 0.809812i 0.0154831 0.0379646i
\(456\) 0 0
\(457\) −19.0820 + 27.2519i −0.892617 + 1.27479i 0.0682185 + 0.997670i \(0.478268\pi\)
−0.960836 + 0.277119i \(0.910620\pi\)
\(458\) −3.01343 3.01343i −0.140808 0.140808i
\(459\) 0 0
\(460\) 1.35213 + 27.5192i 0.0630432 + 1.28309i
\(461\) −7.72166 + 1.36154i −0.359634 + 0.0634131i −0.350546 0.936546i \(-0.614004\pi\)
−0.00908790 + 0.999959i \(0.502893\pi\)
\(462\) 0 0
\(463\) −7.47769 + 16.0360i −0.347518 + 0.745254i −0.999920 0.0126183i \(-0.995983\pi\)
0.652403 + 0.757873i \(0.273761\pi\)
\(464\) −18.6361 15.6375i −0.865159 0.725955i
\(465\) 0 0
\(466\) −2.04945 0.745938i −0.0949388 0.0345549i
\(467\) 15.2854 + 4.09572i 0.707325 + 0.189527i 0.594509 0.804089i \(-0.297346\pi\)
0.112816 + 0.993616i \(0.464013\pi\)
\(468\) 0 0
\(469\) 32.4052 + 18.7092i 1.49633 + 0.863909i
\(470\) −1.00573 0.0384096i −0.0463911 0.00177170i
\(471\) 0 0
\(472\) −1.19059 + 0.833661i −0.0548014 + 0.0383724i
\(473\) 0.187475 0.131271i 0.00862009 0.00603585i
\(474\) 0 0
\(475\) 7.27557 7.43627i 0.333826 0.341199i
\(476\) 32.5737 + 18.8064i 1.49301 + 0.861991i
\(477\) 0 0
\(478\) 5.66800 + 1.51874i 0.259248 + 0.0694654i
\(479\) 25.2585 + 9.19333i 1.15409 + 0.420054i 0.846982 0.531621i \(-0.178417\pi\)
0.307106 + 0.951675i \(0.400639\pi\)
\(480\) 0 0
\(481\) −0.399198 0.334967i −0.0182019 0.0152732i
\(482\) −2.16595 + 4.64490i −0.0986564 + 0.211569i
\(483\) 0 0
\(484\) −20.5396 + 3.62169i −0.933619 + 0.164622i
\(485\) −21.9191 + 1.07697i −0.995293 + 0.0489026i
\(486\) 0 0
\(487\) −12.2573 12.2573i −0.555433 0.555433i 0.372571 0.928004i \(-0.378476\pi\)
−0.928004 + 0.372571i \(0.878476\pi\)
\(488\) 5.18299 7.40208i 0.234623 0.335076i
\(489\) 0 0
\(490\) −11.4087 + 4.79881i −0.515393 + 0.216788i
\(491\) −8.64628 + 10.3042i −0.390201 + 0.465024i −0.925006 0.379952i \(-0.875941\pi\)
0.534805 + 0.844976i \(0.320385\pi\)
\(492\) 0 0
\(493\) −26.2010 + 12.2177i −1.18003 + 0.550258i
\(494\) −0.0265743 0.0460281i −0.00119563 0.00207090i
\(495\) 0 0
\(496\) −0.377555 + 0.653944i −0.0169527 + 0.0293630i
\(497\) 3.13549 35.8388i 0.140646 1.60759i
\(498\) 0 0
\(499\) −37.5256 6.61678i −1.67988 0.296208i −0.749281 0.662252i \(-0.769601\pi\)
−0.930597 + 0.366044i \(0.880712\pi\)
\(500\) 14.5805 + 15.3976i 0.652061 + 0.688603i
\(501\) 0 0
\(502\) 5.50954 + 0.482022i 0.245903 + 0.0215137i
\(503\) −18.4828 + 4.95246i −0.824109 + 0.220819i −0.646142 0.763217i \(-0.723619\pi\)
−0.177967 + 0.984036i \(0.556952\pi\)
\(504\) 0 0
\(505\) 1.77398 8.21394i 0.0789411 0.365515i
\(506\) −0.0437748 + 0.120270i −0.00194603 + 0.00534666i
\(507\) 0 0
\(508\) 14.6185 1.27895i 0.648590 0.0567442i
\(509\) −22.8762 + 8.32625i −1.01397 + 0.369054i −0.794956 0.606667i \(-0.792506\pi\)
−0.219013 + 0.975722i \(0.570284\pi\)
\(510\) 0 0
\(511\) 5.68120 + 32.2197i 0.251322 + 1.42532i
\(512\) −14.6251 + 14.6251i −0.646346 + 0.646346i
\(513\) 0 0
\(514\) 3.00939i 0.132739i
\(515\) 5.29337 1.20388i 0.233254 0.0530492i
\(516\) 0 0
\(517\) 0.0777936 + 0.0362758i 0.00342136 + 0.00159541i
\(518\) 0.904028 + 10.3331i 0.0397207 + 0.454010i
\(519\) 0 0
\(520\) 0.196857 0.103848i 0.00863276 0.00455402i
\(521\) −23.8927 + 13.7944i −1.04676 + 0.604345i −0.921739 0.387810i \(-0.873232\pi\)
−0.125017 + 0.992155i \(0.539898\pi\)
\(522\) 0 0
\(523\) 3.35607 + 12.5250i 0.146751 + 0.547681i 0.999671 + 0.0256401i \(0.00816240\pi\)
−0.852921 + 0.522041i \(0.825171\pi\)
\(524\) −13.3689 + 11.2178i −0.584022 + 0.490053i
\(525\) 0 0
\(526\) 0.0509971 0.289219i 0.00222358 0.0126105i
\(527\) 0.514685 + 0.735047i 0.0224200 + 0.0320191i
\(528\) 0 0
\(529\) 12.3443 + 14.7114i 0.536709 + 0.639625i
\(530\) −2.69721 8.39434i −0.117159 0.364627i
\(531\) 0 0
\(532\) 5.02685 18.7605i 0.217942 0.813369i
\(533\) 0.0757196 + 0.162381i 0.00327978 + 0.00703351i
\(534\) 0 0
\(535\) 2.95975 3.90115i 0.127961 0.168661i
\(536\) 3.25692 + 8.94831i 0.140677 + 0.386508i
\(537\) 0 0
\(538\) −7.28020 5.09765i −0.313872 0.219775i
\(539\) 1.05555 0.0454659
\(540\) 0 0
\(541\) 37.8477 1.62720 0.813600 0.581425i \(-0.197505\pi\)
0.813600 + 0.581425i \(0.197505\pi\)
\(542\) 4.76236 + 3.33464i 0.204561 + 0.143235i
\(543\) 0 0
\(544\) 4.95417 + 13.6115i 0.212408 + 0.583587i
\(545\) −0.0782032 0.569943i −0.00334986 0.0244137i
\(546\) 0 0
\(547\) −6.27224 13.4509i −0.268182 0.575117i 0.725388 0.688340i \(-0.241660\pi\)
−0.993570 + 0.113223i \(0.963883\pi\)
\(548\) 6.75109 25.1954i 0.288392 1.07629i
\(549\) 0 0
\(550\) 0.0347001 + 0.0921921i 0.00147962 + 0.00393109i
\(551\) 9.59560 + 11.4356i 0.408786 + 0.487173i
\(552\) 0 0
\(553\) −17.3708 24.8080i −0.738680 1.05494i
\(554\) 0.288999 1.63900i 0.0122784 0.0696342i
\(555\) 0 0
\(556\) −1.54692 + 1.29802i −0.0656040 + 0.0550483i
\(557\) −3.75036 13.9965i −0.158908 0.593052i −0.998739 0.0502041i \(-0.984013\pi\)
0.839831 0.542847i \(-0.182654\pi\)
\(558\) 0 0
\(559\) −0.256980 + 0.148367i −0.0108691 + 0.00627527i
\(560\) 35.6488 + 11.0263i 1.50644 + 0.465948i
\(561\) 0 0
\(562\) −0.214704 2.45408i −0.00905674 0.103519i
\(563\) 31.0550 + 14.4812i 1.30881 + 0.610309i 0.946787 0.321859i \(-0.104308\pi\)
0.362025 + 0.932169i \(0.382086\pi\)
\(564\) 0 0
\(565\) 5.57867 + 24.5290i 0.234696 + 1.03194i
\(566\) 3.04570i 0.128020i
\(567\) 0 0
\(568\) 6.47388 6.47388i 0.271638 0.271638i
\(569\) −1.25548 7.12016i −0.0526323 0.298493i 0.947117 0.320889i \(-0.103982\pi\)
−0.999749 + 0.0223961i \(0.992870\pi\)
\(570\) 0 0
\(571\) 25.3539 9.22807i 1.06103 0.386183i 0.248214 0.968705i \(-0.420156\pi\)
0.812815 + 0.582522i \(0.197934\pi\)
\(572\) −0.00920404 0.000805249i −0.000384840 3.36691e-5i
\(573\) 0 0
\(574\) 1.21973 3.35118i 0.0509105 0.139876i
\(575\) 32.0486 + 5.29079i 1.33652 + 0.220641i
\(576\) 0 0
\(577\) −6.14870 + 1.64754i −0.255974 + 0.0685880i −0.384524 0.923115i \(-0.625634\pi\)
0.128550 + 0.991703i \(0.458968\pi\)
\(578\) −0.244509 0.0213918i −0.0101702 0.000889781i
\(579\) 0 0
\(580\) −24.0389 + 18.6552i −0.998161 + 0.774613i
\(581\) 19.5357 + 3.44468i 0.810479 + 0.142909i
\(582\) 0 0
\(583\) −0.0655370 + 0.749091i −0.00271426 + 0.0310242i
\(584\) −4.16304 + 7.21060i −0.172268 + 0.298377i
\(585\) 0 0
\(586\) 1.37318 + 2.37842i 0.0567256 + 0.0982517i
\(587\) −34.3204 + 16.0039i −1.41656 + 0.660550i −0.971952 0.235177i \(-0.924433\pi\)
−0.444603 + 0.895728i \(0.646655\pi\)
\(588\) 0 0
\(589\) 0.297839 0.354951i 0.0122722 0.0146255i
\(590\) 0.323377 + 0.768799i 0.0133132 + 0.0316509i
\(591\) 0 0
\(592\) 12.7531 18.2133i 0.524149 0.748563i
\(593\) 3.48236 + 3.48236i 0.143004 + 0.143004i 0.774984 0.631981i \(-0.217758\pi\)
−0.631981 + 0.774984i \(0.717758\pi\)
\(594\) 0 0
\(595\) 29.7787 32.8562i 1.22081 1.34697i
\(596\) −33.6337 + 5.93053i −1.37769 + 0.242924i
\(597\) 0 0
\(598\) 0.0701311 0.150397i 0.00286788 0.00615018i
\(599\) 7.62357 + 6.39694i 0.311491 + 0.261372i 0.785108 0.619359i \(-0.212608\pi\)
−0.473617 + 0.880731i \(0.657052\pi\)
\(600\) 0 0
\(601\) −16.6225 6.05010i −0.678046 0.246789i −0.0200379 0.999799i \(-0.506379\pi\)
−0.658008 + 0.753011i \(0.728601\pi\)
\(602\) 5.70510 + 1.52868i 0.232523 + 0.0623042i
\(603\) 0 0
\(604\) −15.6721 9.04832i −0.637691 0.368171i
\(605\) −0.938360 + 24.5704i −0.0381498 + 0.998930i
\(606\) 0 0
\(607\) −11.9526 + 8.36932i −0.485142 + 0.339700i −0.790422 0.612563i \(-0.790139\pi\)
0.305280 + 0.952263i \(0.401250\pi\)
\(608\) 6.12699 4.29017i 0.248482 0.173989i
\(609\) 0 0
\(610\) −3.52400 3.80385i −0.142683 0.154014i
\(611\) −0.0963805 0.0556453i −0.00389914 0.00225117i
\(612\) 0 0
\(613\) 36.6597 + 9.82295i 1.48067 + 0.396745i 0.906576 0.422042i \(-0.138687\pi\)
0.574097 + 0.818787i \(0.305353\pi\)
\(614\) 6.40729 + 2.33206i 0.258577 + 0.0941143i
\(615\) 0 0
\(616\) 0.289427 + 0.242858i 0.0116613 + 0.00978503i
\(617\) 2.31069 4.95529i 0.0930249 0.199493i −0.854290 0.519797i \(-0.826007\pi\)
0.947315 + 0.320305i \(0.103785\pi\)
\(618\) 0 0
\(619\) 35.6556 6.28705i 1.43312 0.252698i 0.597440 0.801913i \(-0.296184\pi\)
0.835681 + 0.549215i \(0.185073\pi\)
\(620\) 0.699809 + 0.634261i 0.0281050 + 0.0254726i
\(621\) 0 0
\(622\) −4.47294 4.47294i −0.179349 0.179349i
\(623\) −29.6596 + 42.3583i −1.18829 + 1.69705i
\(624\) 0 0
\(625\) 21.3724 12.9699i 0.854897 0.518797i
\(626\) −0.868056 + 1.03451i −0.0346945 + 0.0413473i
\(627\) 0 0
\(628\) 27.8714 12.9967i 1.11219 0.518623i
\(629\) −13.2110 22.8821i −0.526756 0.912368i
\(630\) 0 0
\(631\) 8.04151 13.9283i 0.320128 0.554477i −0.660387 0.750926i \(-0.729608\pi\)
0.980514 + 0.196449i \(0.0629409\pi\)
\(632\) 0.671730 7.67791i 0.0267200 0.305411i
\(633\) 0 0
\(634\) 5.28517 + 0.931918i 0.209901 + 0.0370112i
\(635\) 2.16440 17.1641i 0.0858916 0.681135i
\(636\) 0 0
\(637\) −1.36337 0.119280i −0.0540188 0.00472603i
\(638\) −0.136532 + 0.0365836i −0.00540535 + 0.00144836i
\(639\) 0 0
\(640\) 10.9030 + 16.9098i 0.430979 + 0.668418i
\(641\) −12.7590 + 35.0551i −0.503951 + 1.38459i 0.383436 + 0.923567i \(0.374741\pi\)
−0.887387 + 0.461026i \(0.847482\pi\)
\(642\) 0 0
\(643\) −14.3985 + 1.25970i −0.567821 + 0.0496779i −0.367452 0.930043i \(-0.619770\pi\)
−0.200369 + 0.979720i \(0.564214\pi\)
\(644\) 56.9844 20.7406i 2.24550 0.817295i
\(645\) 0 0
\(646\) −0.467943 2.65384i −0.0184110 0.104414i
\(647\) −18.6385 + 18.6385i −0.732757 + 0.732757i −0.971165 0.238408i \(-0.923374\pi\)
0.238408 + 0.971165i \(0.423374\pi\)
\(648\) 0 0
\(649\) 0.0711305i 0.00279212i
\(650\) −0.0344015 0.122998i −0.00134934 0.00482439i
\(651\) 0 0
\(652\) 19.0057 + 8.86250i 0.744320 + 0.347082i
\(653\) −1.32123 15.1018i −0.0517038 0.590977i −0.977214 0.212255i \(-0.931919\pi\)
0.925510 0.378722i \(-0.123636\pi\)
\(654\) 0 0
\(655\) 9.59978 + 18.1977i 0.375094 + 0.711042i
\(656\) −6.62035 + 3.82226i −0.258481 + 0.149234i
\(657\) 0 0
\(658\) 0.573332 + 2.13970i 0.0223508 + 0.0834144i
\(659\) −14.6857 + 12.3228i −0.572075 + 0.480028i −0.882334 0.470624i \(-0.844029\pi\)
0.310258 + 0.950652i \(0.399584\pi\)
\(660\) 0 0
\(661\) 3.24511 18.4039i 0.126220 0.715829i −0.854356 0.519689i \(-0.826048\pi\)
0.980576 0.196141i \(-0.0628409\pi\)
\(662\) 2.44393 + 3.49029i 0.0949860 + 0.135654i
\(663\) 0 0
\(664\) 3.24502 + 3.86726i 0.125931 + 0.150079i
\(665\) −20.3678 10.4618i −0.789828 0.405692i
\(666\) 0 0
\(667\) −12.0634 + 45.0214i −0.467099 + 1.74324i
\(668\) −10.4839 22.4827i −0.405633 0.869883i
\(669\) 0 0
\(670\) 5.41370 0.742827i 0.209149 0.0286979i
\(671\) 0.151251 + 0.415559i 0.00583898 + 0.0160425i
\(672\) 0 0
\(673\) 6.71034 + 4.69863i 0.258665 + 0.181119i 0.695715 0.718318i \(-0.255088\pi\)
−0.437050 + 0.899437i \(0.643977\pi\)
\(674\) −6.83016 −0.263088
\(675\) 0 0
\(676\) −24.6450 −0.947884
\(677\) 32.8363 + 22.9922i 1.26200 + 0.883663i 0.996753 0.0805166i \(-0.0256570\pi\)
0.265249 + 0.964180i \(0.414546\pi\)
\(678\) 0 0
\(679\) 16.5199 + 45.3880i 0.633976 + 1.74183i
\(680\) 11.1801 1.53405i 0.428737 0.0588280i
\(681\) 0 0
\(682\) 0.00185416 + 0.00397627i 7.09996e−5 + 0.000152259i
\(683\) 0.244432 0.912231i 0.00935292 0.0349056i −0.961092 0.276230i \(-0.910915\pi\)
0.970445 + 0.241324i \(0.0775817\pi\)
\(684\) 0 0
\(685\) −27.3540 14.0503i −1.04514 0.536834i
\(686\) 10.3926 + 12.3854i 0.396790 + 0.472876i
\(687\) 0 0
\(688\) −7.26189 10.3710i −0.276857 0.395393i
\(689\) 0.169298 0.960134i 0.00644972 0.0365782i
\(690\) 0 0
\(691\) −19.0181 + 15.9581i −0.723481 + 0.607073i −0.928346 0.371717i \(-0.878769\pi\)
0.204865 + 0.978790i \(0.434325\pi\)
\(692\) −11.1694 41.6847i −0.424596 1.58461i
\(693\) 0 0
\(694\) −8.77943 + 5.06881i −0.333263 + 0.192409i
\(695\) 1.11079 + 2.10566i 0.0421348 + 0.0798722i
\(696\) 0 0
\(697\) 0.791748 + 9.04972i 0.0299896 + 0.342783i
\(698\) −4.93917 2.30317i −0.186950 0.0871763i
\(699\) 0 0
\(700\) 22.8934 40.6721i 0.865290 1.53726i
\(701\) 30.1877i 1.14018i −0.821584 0.570088i \(-0.806909\pi\)
0.821584 0.570088i \(-0.193091\pi\)
\(702\) 0 0
\(703\) −9.64747 + 9.64747i −0.363861 + 0.363861i
\(704\) −0.0598837 0.339617i −0.00225695 0.0127998i
\(705\) 0 0
\(706\) 5.74467 2.09089i 0.216204 0.0786917i
\(707\) −18.4249 + 1.61197i −0.692940 + 0.0606244i
\(708\) 0 0
\(709\) −17.1846 + 47.2142i −0.645379 + 1.77317i −0.0112523 + 0.999937i \(0.503582\pi\)
−0.634127 + 0.773229i \(0.718640\pi\)
\(710\) −2.84699 4.41548i −0.106846 0.165710i
\(711\) 0 0
\(712\) −12.7113 + 3.40597i −0.476374 + 0.127644i
\(713\) 1.44121 + 0.126090i 0.0539739 + 0.00472211i
\(714\) 0 0
\(715\) −0.00136274 + 0.0108068i −5.09637e−5 + 0.000404151i
\(716\) −34.0378 6.00178i −1.27205 0.224297i
\(717\) 0 0
\(718\) −0.879150 + 10.0487i −0.0328096 + 0.375015i
\(719\) −6.68387 + 11.5768i −0.249266 + 0.431742i −0.963322 0.268346i \(-0.913523\pi\)
0.714056 + 0.700089i \(0.246856\pi\)
\(720\) 0 0
\(721\) −5.97397 10.3472i −0.222482 0.385351i
\(722\) 4.27363 1.99283i 0.159048 0.0741654i
\(723\) 0 0
\(724\) 15.0887 17.9820i 0.560766 0.668295i
\(725\) 15.5147 + 32.3444i 0.576203 + 1.20124i
\(726\) 0 0
\(727\) 13.6862 19.5460i 0.507595 0.724920i −0.480800 0.876830i \(-0.659654\pi\)
0.988394 + 0.151910i \(0.0485425\pi\)
\(728\) −0.346386 0.346386i −0.0128379 0.0128379i
\(729\) 0 0
\(730\) 3.54015 + 3.20856i 0.131027 + 0.118754i
\(731\) −14.8167 + 2.61258i −0.548014 + 0.0966296i
\(732\) 0 0
\(733\) −9.86921 + 21.1646i −0.364527 + 0.781732i 0.635427 + 0.772161i \(0.280824\pi\)
−0.999954 + 0.00957046i \(0.996954\pi\)
\(734\) −4.41379 3.70361i −0.162916 0.136703i
\(735\) 0 0
\(736\) 21.9452 + 7.98740i 0.808910 + 0.294419i
\(737\) −0.450149 0.120617i −0.0165815 0.00444299i
\(738\) 0 0
\(739\) −3.52276 2.03387i −0.129587 0.0748169i 0.433805 0.901007i \(-0.357171\pi\)
−0.563392 + 0.826190i \(0.690504\pi\)
\(740\) −18.8999 20.4008i −0.694774 0.749949i
\(741\) 0 0
\(742\) −15.8963 + 11.1307i −0.583572 + 0.408622i
\(743\) 41.2248 28.8659i 1.51239 1.05899i 0.535683 0.844419i \(-0.320054\pi\)
0.976709 0.214569i \(-0.0688345\pi\)
\(744\) 0 0
\(745\) −1.53657 + 40.2342i −0.0562955 + 1.47407i
\(746\) 1.40892 + 0.813439i 0.0515842 + 0.0297821i
\(747\) 0 0
\(748\) −0.452489 0.121244i −0.0165447 0.00443313i
\(749\) −10.1277 3.68619i −0.370059 0.134691i
\(750\) 0 0
\(751\) 2.00167 + 1.67960i 0.0730419 + 0.0612895i 0.678578 0.734529i \(-0.262597\pi\)
−0.605536 + 0.795818i \(0.707041\pi\)
\(752\) 2.00677 4.30353i 0.0731793 0.156933i
\(753\) 0 0
\(754\) 0.180481 0.0318237i 0.00657274 0.00115895i
\(755\) −14.3274 + 15.8081i −0.521427 + 0.575315i
\(756\) 0 0
\(757\) 28.7222 + 28.7222i 1.04393 + 1.04393i 0.998990 + 0.0449357i \(0.0143083\pi\)
0.0449357 + 0.998990i \(0.485692\pi\)
\(758\) −1.82366 + 2.60445i −0.0662383 + 0.0945980i
\(759\) 0 0
\(760\) −2.25934 5.37136i −0.0819547 0.194840i
\(761\) −3.22815 + 3.84716i −0.117020 + 0.139459i −0.821374 0.570389i \(-0.806792\pi\)
0.704354 + 0.709849i \(0.251237\pi\)
\(762\) 0 0
\(763\) −1.14754 + 0.535106i −0.0415437 + 0.0193722i
\(764\) 11.6417 + 20.1640i 0.421182 + 0.729509i
\(765\) 0 0
\(766\) 3.08315 5.34017i 0.111399 0.192948i
\(767\) −0.00803789 + 0.0918735i −0.000290231 + 0.00331736i
\(768\) 0 0
\(769\) −41.2856 7.27976i −1.48880 0.262515i −0.630709 0.776019i \(-0.717236\pi\)
−0.858087 + 0.513504i \(0.828347\pi\)
\(770\) 0.171282 0.132921i 0.00617256 0.00479015i
\(771\) 0 0
\(772\) −33.5115 2.93187i −1.20610 0.105520i
\(773\) 5.88204 1.57609i 0.211562 0.0566879i −0.151481 0.988460i \(-0.548404\pi\)
0.363043 + 0.931772i \(0.381738\pi\)
\(774\) 0 0
\(775\) 0.905066 0.648580i 0.0325109 0.0232977i
\(776\) −4.20415 + 11.5508i −0.150920 + 0.414650i
\(777\) 0 0
\(778\) 2.36511 0.206920i 0.0847932 0.00741844i
\(779\) 4.40798 1.60437i 0.157932 0.0574827i
\(780\) 0 0
\(781\) 0.0778050 + 0.441254i 0.00278408 + 0.0157893i
\(782\) 5.94947 5.94947i 0.212753 0.212753i
\(783\) 0 0
\(784\) 58.3929i 2.08546i
\(785\) −8.04028 35.3526i −0.286970 1.26179i
\(786\) 0 0