Properties

Label 225.2.h.b.91.1
Level $225$
Weight $2$
Character 225.91
Analytic conductor $1.797$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 225 = 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 225.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.79663404548\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 25)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 91.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 225.91
Dual form 225.2.h.b.136.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +O(q^{10})\) \(q+(0.500000 + 0.363271i) q^{2} +(-0.500000 - 1.53884i) q^{4} +(1.80902 - 1.31433i) q^{5} -1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +1.38197 q^{10} +(-0.618034 - 0.449028i) q^{11} +(3.92705 - 2.85317i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(0.236068 - 0.726543i) q^{17} +(-1.80902 + 5.56758i) q^{19} +(-2.92705 - 2.12663i) q^{20} +(-0.145898 - 0.449028i) q^{22} +(6.66312 + 4.84104i) q^{23} +(1.54508 - 4.75528i) q^{25} +3.00000 q^{26} +(0.809017 + 2.48990i) q^{28} +(0.427051 + 1.31433i) q^{29} +(-0.927051 + 2.85317i) q^{31} -5.61803 q^{32} +(0.381966 - 0.277515i) q^{34} +(-2.92705 + 2.12663i) q^{35} +(-3.42705 + 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(-1.54508 - 4.75528i) q^{40} +(-4.23607 + 3.07768i) q^{41} +1.85410 q^{43} +(-0.381966 + 1.17557i) q^{44} +(1.57295 + 4.84104i) q^{46} +(0.500000 + 1.53884i) q^{47} -4.38197 q^{49} +(2.50000 - 1.81636i) q^{50} +(-6.35410 - 4.61653i) q^{52} +(-1.69098 - 5.20431i) q^{53} -1.70820 q^{55} +(-1.11803 + 3.44095i) q^{56} +(-0.263932 + 0.812299i) q^{58} +(-3.35410 + 2.43690i) q^{59} +(3.80902 + 2.76741i) q^{61} +(-1.50000 + 1.08981i) q^{62} +(0.190983 + 0.138757i) q^{64} +(3.35410 - 10.3229i) q^{65} +(2.85410 - 8.78402i) q^{67} -1.23607 q^{68} -2.23607 q^{70} +(1.35410 + 4.16750i) q^{71} +(7.28115 + 5.29007i) q^{73} -2.61803 q^{74} +9.47214 q^{76} +(1.00000 + 0.726543i) q^{77} +(0.954915 + 2.93893i) q^{79} +(-1.28115 + 3.94298i) q^{80} -3.23607 q^{82} +(0.545085 - 1.67760i) q^{83} +(-0.527864 - 1.62460i) q^{85} +(0.927051 + 0.673542i) q^{86} +(-1.38197 + 1.00406i) q^{88} +(7.23607 + 5.25731i) q^{89} +(-6.35410 + 4.61653i) q^{91} +(4.11803 - 12.6740i) q^{92} +(-0.309017 + 0.951057i) q^{94} +(4.04508 + 12.4495i) q^{95} +(0.881966 + 2.71441i) q^{97} +(-2.19098 - 1.59184i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} + 5 q^{5} - 2 q^{7} + 5 q^{8} + 10 q^{10} + 2 q^{11} + 9 q^{13} - q^{14} - 6 q^{16} - 8 q^{17} - 5 q^{19} - 5 q^{20} - 14 q^{22} + 11 q^{23} - 5 q^{25} + 12 q^{26} + q^{28} - 5 q^{29} + 3 q^{31} - 18 q^{32} + 6 q^{34} - 5 q^{35} - 7 q^{37} - 5 q^{38} + 5 q^{40} - 8 q^{41} - 6 q^{43} - 6 q^{44} + 13 q^{46} + 2 q^{47} - 22 q^{49} + 10 q^{50} - 12 q^{52} - 9 q^{53} + 20 q^{55} - 10 q^{58} + 13 q^{61} - 6 q^{62} + 3 q^{64} - 2 q^{67} + 4 q^{68} - 8 q^{71} + 9 q^{73} - 6 q^{74} + 20 q^{76} + 4 q^{77} + 15 q^{79} + 15 q^{80} - 4 q^{82} - 9 q^{83} - 20 q^{85} - 3 q^{86} - 10 q^{88} + 20 q^{89} - 12 q^{91} + 12 q^{92} + q^{94} + 5 q^{95} + 8 q^{97} - 11 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.363271i 0.353553 + 0.256872i 0.750358 0.661031i \(-0.229881\pi\)
−0.396805 + 0.917903i \(0.629881\pi\)
\(3\) 0 0
\(4\) −0.500000 1.53884i −0.250000 0.769421i
\(5\) 1.80902 1.31433i 0.809017 0.587785i
\(6\) 0 0
\(7\) −1.61803 −0.611559 −0.305780 0.952102i \(-0.598917\pi\)
−0.305780 + 0.952102i \(0.598917\pi\)
\(8\) 0.690983 2.12663i 0.244299 0.751876i
\(9\) 0 0
\(10\) 1.38197 0.437016
\(11\) −0.618034 0.449028i −0.186344 0.135387i 0.490702 0.871327i \(-0.336740\pi\)
−0.677046 + 0.735940i \(0.736740\pi\)
\(12\) 0 0
\(13\) 3.92705 2.85317i 1.08917 0.791327i 0.109909 0.993942i \(-0.464944\pi\)
0.979259 + 0.202615i \(0.0649439\pi\)
\(14\) −0.809017 0.587785i −0.216219 0.157092i
\(15\) 0 0
\(16\) −1.50000 + 1.08981i −0.375000 + 0.272453i
\(17\) 0.236068 0.726543i 0.0572549 0.176212i −0.918339 0.395794i \(-0.870469\pi\)
0.975594 + 0.219582i \(0.0704693\pi\)
\(18\) 0 0
\(19\) −1.80902 + 5.56758i −0.415017 + 1.27729i 0.497219 + 0.867625i \(0.334355\pi\)
−0.912236 + 0.409666i \(0.865645\pi\)
\(20\) −2.92705 2.12663i −0.654508 0.475528i
\(21\) 0 0
\(22\) −0.145898 0.449028i −0.0311056 0.0957331i
\(23\) 6.66312 + 4.84104i 1.38936 + 1.00943i 0.995936 + 0.0900679i \(0.0287084\pi\)
0.393421 + 0.919359i \(0.371292\pi\)
\(24\) 0 0
\(25\) 1.54508 4.75528i 0.309017 0.951057i
\(26\) 3.00000 0.588348
\(27\) 0 0
\(28\) 0.809017 + 2.48990i 0.152890 + 0.470547i
\(29\) 0.427051 + 1.31433i 0.0793014 + 0.244065i 0.982846 0.184430i \(-0.0590440\pi\)
−0.903544 + 0.428495i \(0.859044\pi\)
\(30\) 0 0
\(31\) −0.927051 + 2.85317i −0.166503 + 0.512444i −0.999144 0.0413693i \(-0.986828\pi\)
0.832641 + 0.553814i \(0.186828\pi\)
\(32\) −5.61803 −0.993137
\(33\) 0 0
\(34\) 0.381966 0.277515i 0.0655066 0.0475934i
\(35\) −2.92705 + 2.12663i −0.494762 + 0.359466i
\(36\) 0 0
\(37\) −3.42705 + 2.48990i −0.563404 + 0.409337i −0.832703 0.553720i \(-0.813208\pi\)
0.269299 + 0.963057i \(0.413208\pi\)
\(38\) −2.92705 + 2.12663i −0.474830 + 0.344984i
\(39\) 0 0
\(40\) −1.54508 4.75528i −0.244299 0.751876i
\(41\) −4.23607 + 3.07768i −0.661563 + 0.480653i −0.867190 0.497977i \(-0.834076\pi\)
0.205628 + 0.978630i \(0.434076\pi\)
\(42\) 0 0
\(43\) 1.85410 0.282748 0.141374 0.989956i \(-0.454848\pi\)
0.141374 + 0.989956i \(0.454848\pi\)
\(44\) −0.381966 + 1.17557i −0.0575835 + 0.177224i
\(45\) 0 0
\(46\) 1.57295 + 4.84104i 0.231919 + 0.713772i
\(47\) 0.500000 + 1.53884i 0.0729325 + 0.224463i 0.980877 0.194626i \(-0.0623494\pi\)
−0.907945 + 0.419089i \(0.862349\pi\)
\(48\) 0 0
\(49\) −4.38197 −0.625995
\(50\) 2.50000 1.81636i 0.353553 0.256872i
\(51\) 0 0
\(52\) −6.35410 4.61653i −0.881155 0.640197i
\(53\) −1.69098 5.20431i −0.232274 0.714867i −0.997471 0.0710707i \(-0.977358\pi\)
0.765197 0.643796i \(-0.222642\pi\)
\(54\) 0 0
\(55\) −1.70820 −0.230334
\(56\) −1.11803 + 3.44095i −0.149404 + 0.459817i
\(57\) 0 0
\(58\) −0.263932 + 0.812299i −0.0346560 + 0.106660i
\(59\) −3.35410 + 2.43690i −0.436667 + 0.317257i −0.784309 0.620370i \(-0.786982\pi\)
0.347642 + 0.937627i \(0.386982\pi\)
\(60\) 0 0
\(61\) 3.80902 + 2.76741i 0.487695 + 0.354331i 0.804297 0.594227i \(-0.202542\pi\)
−0.316602 + 0.948558i \(0.602542\pi\)
\(62\) −1.50000 + 1.08981i −0.190500 + 0.138406i
\(63\) 0 0
\(64\) 0.190983 + 0.138757i 0.0238729 + 0.0173447i
\(65\) 3.35410 10.3229i 0.416025 1.28039i
\(66\) 0 0
\(67\) 2.85410 8.78402i 0.348684 1.07314i −0.610898 0.791709i \(-0.709191\pi\)
0.959582 0.281430i \(-0.0908086\pi\)
\(68\) −1.23607 −0.149895
\(69\) 0 0
\(70\) −2.23607 −0.267261
\(71\) 1.35410 + 4.16750i 0.160702 + 0.494591i 0.998694 0.0510922i \(-0.0162702\pi\)
−0.837992 + 0.545683i \(0.816270\pi\)
\(72\) 0 0
\(73\) 7.28115 + 5.29007i 0.852194 + 0.619156i 0.925750 0.378136i \(-0.123435\pi\)
−0.0735557 + 0.997291i \(0.523435\pi\)
\(74\) −2.61803 −0.304340
\(75\) 0 0
\(76\) 9.47214 1.08653
\(77\) 1.00000 + 0.726543i 0.113961 + 0.0827972i
\(78\) 0 0
\(79\) 0.954915 + 2.93893i 0.107436 + 0.330655i 0.990295 0.138985i \(-0.0443839\pi\)
−0.882858 + 0.469640i \(0.844384\pi\)
\(80\) −1.28115 + 3.94298i −0.143237 + 0.440839i
\(81\) 0 0
\(82\) −3.23607 −0.357364
\(83\) 0.545085 1.67760i 0.0598308 0.184140i −0.916674 0.399636i \(-0.869137\pi\)
0.976505 + 0.215495i \(0.0691366\pi\)
\(84\) 0 0
\(85\) −0.527864 1.62460i −0.0572549 0.176212i
\(86\) 0.927051 + 0.673542i 0.0999665 + 0.0726299i
\(87\) 0 0
\(88\) −1.38197 + 1.00406i −0.147318 + 0.107033i
\(89\) 7.23607 + 5.25731i 0.767022 + 0.557274i 0.901056 0.433703i \(-0.142793\pi\)
−0.134034 + 0.990977i \(0.542793\pi\)
\(90\) 0 0
\(91\) −6.35410 + 4.61653i −0.666091 + 0.483943i
\(92\) 4.11803 12.6740i 0.429335 1.32136i
\(93\) 0 0
\(94\) −0.309017 + 0.951057i −0.0318727 + 0.0980940i
\(95\) 4.04508 + 12.4495i 0.415017 + 1.27729i
\(96\) 0 0
\(97\) 0.881966 + 2.71441i 0.0895501 + 0.275607i 0.985795 0.167953i \(-0.0537155\pi\)
−0.896245 + 0.443559i \(0.853716\pi\)
\(98\) −2.19098 1.59184i −0.221323 0.160800i
\(99\) 0 0
\(100\) −8.09017 −0.809017
\(101\) 7.47214 0.743505 0.371753 0.928332i \(-0.378757\pi\)
0.371753 + 0.928332i \(0.378757\pi\)
\(102\) 0 0
\(103\) −3.57295 10.9964i −0.352053 1.08351i −0.957699 0.287773i \(-0.907085\pi\)
0.605645 0.795735i \(-0.292915\pi\)
\(104\) −3.35410 10.3229i −0.328897 1.01224i
\(105\) 0 0
\(106\) 1.04508 3.21644i 0.101508 0.312408i
\(107\) −10.4164 −1.00699 −0.503496 0.863998i \(-0.667953\pi\)
−0.503496 + 0.863998i \(0.667953\pi\)
\(108\) 0 0
\(109\) −8.09017 + 5.87785i −0.774898 + 0.562996i −0.903443 0.428707i \(-0.858969\pi\)
0.128546 + 0.991704i \(0.458969\pi\)
\(110\) −0.854102 0.620541i −0.0814354 0.0591663i
\(111\) 0 0
\(112\) 2.42705 1.76336i 0.229335 0.166621i
\(113\) 8.20820 5.96361i 0.772163 0.561009i −0.130454 0.991454i \(-0.541643\pi\)
0.902617 + 0.430445i \(0.141643\pi\)
\(114\) 0 0
\(115\) 18.4164 1.71734
\(116\) 1.80902 1.31433i 0.167963 0.122032i
\(117\) 0 0
\(118\) −2.56231 −0.235879
\(119\) −0.381966 + 1.17557i −0.0350148 + 0.107764i
\(120\) 0 0
\(121\) −3.21885 9.90659i −0.292622 0.900599i
\(122\) 0.899187 + 2.76741i 0.0814086 + 0.250550i
\(123\) 0 0
\(124\) 4.85410 0.435911
\(125\) −3.45492 10.6331i −0.309017 0.951057i
\(126\) 0 0
\(127\) 12.8541 + 9.33905i 1.14062 + 0.828707i 0.987205 0.159455i \(-0.0509738\pi\)
0.153412 + 0.988162i \(0.450974\pi\)
\(128\) 3.51722 + 10.8249i 0.310881 + 0.956794i
\(129\) 0 0
\(130\) 5.42705 3.94298i 0.475984 0.345823i
\(131\) 5.50000 16.9273i 0.480537 1.47894i −0.357805 0.933797i \(-0.616475\pi\)
0.838342 0.545145i \(-0.183525\pi\)
\(132\) 0 0
\(133\) 2.92705 9.00854i 0.253808 0.781139i
\(134\) 4.61803 3.35520i 0.398937 0.289845i
\(135\) 0 0
\(136\) −1.38197 1.00406i −0.118503 0.0860972i
\(137\) 4.80902 3.49396i 0.410862 0.298509i −0.363089 0.931755i \(-0.618278\pi\)
0.773951 + 0.633246i \(0.218278\pi\)
\(138\) 0 0
\(139\) −4.04508 2.93893i −0.343100 0.249276i 0.402869 0.915258i \(-0.368013\pi\)
−0.745968 + 0.665981i \(0.768013\pi\)
\(140\) 4.73607 + 3.44095i 0.400271 + 0.290814i
\(141\) 0 0
\(142\) −0.836881 + 2.57565i −0.0702295 + 0.216144i
\(143\) −3.70820 −0.310096
\(144\) 0 0
\(145\) 2.50000 + 1.81636i 0.207614 + 0.150840i
\(146\) 1.71885 + 5.29007i 0.142253 + 0.437809i
\(147\) 0 0
\(148\) 5.54508 + 4.02874i 0.455803 + 0.331160i
\(149\) −13.9443 −1.14236 −0.571180 0.820825i \(-0.693514\pi\)
−0.571180 + 0.820825i \(0.693514\pi\)
\(150\) 0 0
\(151\) −5.56231 −0.452654 −0.226327 0.974051i \(-0.572672\pi\)
−0.226327 + 0.974051i \(0.572672\pi\)
\(152\) 10.5902 + 7.69421i 0.858976 + 0.624083i
\(153\) 0 0
\(154\) 0.236068 + 0.726543i 0.0190229 + 0.0585465i
\(155\) 2.07295 + 6.37988i 0.166503 + 0.512444i
\(156\) 0 0
\(157\) −9.18034 −0.732671 −0.366335 0.930483i \(-0.619388\pi\)
−0.366335 + 0.930483i \(0.619388\pi\)
\(158\) −0.590170 + 1.81636i −0.0469514 + 0.144502i
\(159\) 0 0
\(160\) −10.1631 + 7.38394i −0.803465 + 0.583752i
\(161\) −10.7812 7.83297i −0.849674 0.617324i
\(162\) 0 0
\(163\) −8.89919 + 6.46564i −0.697038 + 0.506428i −0.878966 0.476884i \(-0.841766\pi\)
0.181928 + 0.983312i \(0.441766\pi\)
\(164\) 6.85410 + 4.97980i 0.535215 + 0.388857i
\(165\) 0 0
\(166\) 0.881966 0.640786i 0.0684538 0.0497346i
\(167\) 1.71885 5.29007i 0.133008 0.409358i −0.862267 0.506455i \(-0.830956\pi\)
0.995275 + 0.0970971i \(0.0309557\pi\)
\(168\) 0 0
\(169\) 3.26393 10.0453i 0.251072 0.772719i
\(170\) 0.326238 1.00406i 0.0250213 0.0770077i
\(171\) 0 0
\(172\) −0.927051 2.85317i −0.0706870 0.217552i
\(173\) −13.6631 9.92684i −1.03879 0.754723i −0.0687392 0.997635i \(-0.521898\pi\)
−0.970049 + 0.242911i \(0.921898\pi\)
\(174\) 0 0
\(175\) −2.50000 + 7.69421i −0.188982 + 0.581628i
\(176\) 1.41641 0.106766
\(177\) 0 0
\(178\) 1.70820 + 5.25731i 0.128035 + 0.394052i
\(179\) 2.92705 + 9.00854i 0.218778 + 0.673330i 0.998864 + 0.0476570i \(0.0151754\pi\)
−0.780086 + 0.625673i \(0.784825\pi\)
\(180\) 0 0
\(181\) 4.23607 13.0373i 0.314864 0.969053i −0.660946 0.750434i \(-0.729845\pi\)
0.975810 0.218619i \(-0.0701553\pi\)
\(182\) −4.85410 −0.359810
\(183\) 0 0
\(184\) 14.8992 10.8249i 1.09838 0.798022i
\(185\) −2.92705 + 9.00854i −0.215201 + 0.662321i
\(186\) 0 0
\(187\) −0.472136 + 0.343027i −0.0345260 + 0.0250846i
\(188\) 2.11803 1.53884i 0.154474 0.112232i
\(189\) 0 0
\(190\) −2.50000 + 7.69421i −0.181369 + 0.558197i
\(191\) −19.5623 + 14.2128i −1.41548 + 1.02841i −0.422982 + 0.906138i \(0.639016\pi\)
−0.992497 + 0.122267i \(0.960984\pi\)
\(192\) 0 0
\(193\) −5.70820 −0.410886 −0.205443 0.978669i \(-0.565863\pi\)
−0.205443 + 0.978669i \(0.565863\pi\)
\(194\) −0.545085 + 1.67760i −0.0391348 + 0.120445i
\(195\) 0 0
\(196\) 2.19098 + 6.74315i 0.156499 + 0.481654i
\(197\) 3.00000 + 9.23305i 0.213741 + 0.657828i 0.999241 + 0.0389652i \(0.0124062\pi\)
−0.785499 + 0.618862i \(0.787594\pi\)
\(198\) 0 0
\(199\) 2.56231 0.181637 0.0908185 0.995867i \(-0.471052\pi\)
0.0908185 + 0.995867i \(0.471052\pi\)
\(200\) −9.04508 6.57164i −0.639584 0.464685i
\(201\) 0 0
\(202\) 3.73607 + 2.71441i 0.262869 + 0.190985i
\(203\) −0.690983 2.12663i −0.0484975 0.149260i
\(204\) 0 0
\(205\) −3.61803 + 11.1352i −0.252694 + 0.777714i
\(206\) 2.20820 6.79615i 0.153853 0.473510i
\(207\) 0 0
\(208\) −2.78115 + 8.55951i −0.192838 + 0.593495i
\(209\) 3.61803 2.62866i 0.250265 0.181828i
\(210\) 0 0
\(211\) −10.6631 7.74721i −0.734079 0.533340i 0.156772 0.987635i \(-0.449891\pi\)
−0.890851 + 0.454295i \(0.849891\pi\)
\(212\) −7.16312 + 5.20431i −0.491965 + 0.357434i
\(213\) 0 0
\(214\) −5.20820 3.78398i −0.356025 0.258668i
\(215\) 3.35410 2.43690i 0.228748 0.166195i
\(216\) 0 0
\(217\) 1.50000 4.61653i 0.101827 0.313390i
\(218\) −6.18034 −0.418585
\(219\) 0 0
\(220\) 0.854102 + 2.62866i 0.0575835 + 0.177224i
\(221\) −1.14590 3.52671i −0.0770814 0.237232i
\(222\) 0 0
\(223\) −17.9443 13.0373i −1.20164 0.873041i −0.207193 0.978300i \(-0.566433\pi\)
−0.994445 + 0.105260i \(0.966433\pi\)
\(224\) 9.09017 0.607363
\(225\) 0 0
\(226\) 6.27051 0.417108
\(227\) 15.5623 + 11.3067i 1.03291 + 0.750451i 0.968888 0.247498i \(-0.0796084\pi\)
0.0640182 + 0.997949i \(0.479608\pi\)
\(228\) 0 0
\(229\) 2.56231 + 7.88597i 0.169322 + 0.521119i 0.999329 0.0366339i \(-0.0116635\pi\)
−0.830007 + 0.557753i \(0.811664\pi\)
\(230\) 9.20820 + 6.69015i 0.607171 + 0.441136i
\(231\) 0 0
\(232\) 3.09017 0.202880
\(233\) −4.61803 + 14.2128i −0.302537 + 0.931115i 0.678047 + 0.735018i \(0.262826\pi\)
−0.980585 + 0.196096i \(0.937174\pi\)
\(234\) 0 0
\(235\) 2.92705 + 2.12663i 0.190940 + 0.138726i
\(236\) 5.42705 + 3.94298i 0.353271 + 0.256666i
\(237\) 0 0
\(238\) −0.618034 + 0.449028i −0.0400612 + 0.0291062i
\(239\) −23.8435 17.3233i −1.54231 1.12055i −0.948869 0.315669i \(-0.897771\pi\)
−0.593436 0.804881i \(-0.702229\pi\)
\(240\) 0 0
\(241\) −9.28115 + 6.74315i −0.597852 + 0.434365i −0.845116 0.534584i \(-0.820468\pi\)
0.247264 + 0.968948i \(0.420468\pi\)
\(242\) 1.98936 6.12261i 0.127881 0.393576i
\(243\) 0 0
\(244\) 2.35410 7.24518i 0.150706 0.463825i
\(245\) −7.92705 + 5.75934i −0.506441 + 0.367951i
\(246\) 0 0
\(247\) 8.78115 + 27.0256i 0.558731 + 1.71960i
\(248\) 5.42705 + 3.94298i 0.344618 + 0.250380i
\(249\) 0 0
\(250\) 2.13525 6.57164i 0.135045 0.415627i
\(251\) 6.81966 0.430453 0.215227 0.976564i \(-0.430951\pi\)
0.215227 + 0.976564i \(0.430951\pi\)
\(252\) 0 0
\(253\) −1.94427 5.98385i −0.122235 0.376202i
\(254\) 3.03444 + 9.33905i 0.190398 + 0.585984i
\(255\) 0 0
\(256\) −2.02786 + 6.24112i −0.126742 + 0.390070i
\(257\) −16.1459 −1.00715 −0.503577 0.863951i \(-0.667983\pi\)
−0.503577 + 0.863951i \(0.667983\pi\)
\(258\) 0 0
\(259\) 5.54508 4.02874i 0.344555 0.250334i
\(260\) −17.5623 −1.08917
\(261\) 0 0
\(262\) 8.89919 6.46564i 0.549794 0.399448i
\(263\) −17.8713 + 12.9843i −1.10199 + 0.800645i −0.981384 0.192055i \(-0.938485\pi\)
−0.120609 + 0.992700i \(0.538485\pi\)
\(264\) 0 0
\(265\) −9.89919 7.19218i −0.608102 0.441812i
\(266\) 4.73607 3.44095i 0.290387 0.210978i
\(267\) 0 0
\(268\) −14.9443 −0.912867
\(269\) 5.32624 16.3925i 0.324746 0.999467i −0.646808 0.762652i \(-0.723897\pi\)
0.971555 0.236814i \(-0.0761033\pi\)
\(270\) 0 0
\(271\) −2.47214 7.60845i −0.150172 0.462181i 0.847468 0.530846i \(-0.178126\pi\)
−0.997640 + 0.0686657i \(0.978126\pi\)
\(272\) 0.437694 + 1.34708i 0.0265391 + 0.0816790i
\(273\) 0 0
\(274\) 3.67376 0.221940
\(275\) −3.09017 + 2.24514i −0.186344 + 0.135387i
\(276\) 0 0
\(277\) 9.13525 + 6.63715i 0.548884 + 0.398788i 0.827374 0.561651i \(-0.189834\pi\)
−0.278490 + 0.960439i \(0.589834\pi\)
\(278\) −0.954915 2.93893i −0.0572720 0.176265i
\(279\) 0 0
\(280\) 2.50000 + 7.69421i 0.149404 + 0.459817i
\(281\) 0.336881 1.03681i 0.0200966 0.0618511i −0.940505 0.339779i \(-0.889648\pi\)
0.960602 + 0.277928i \(0.0896477\pi\)
\(282\) 0 0
\(283\) −7.15248 + 22.0131i −0.425171 + 1.30854i 0.477660 + 0.878545i \(0.341485\pi\)
−0.902831 + 0.429996i \(0.858515\pi\)
\(284\) 5.73607 4.16750i 0.340373 0.247295i
\(285\) 0 0
\(286\) −1.85410 1.34708i −0.109635 0.0796547i
\(287\) 6.85410 4.97980i 0.404585 0.293948i
\(288\) 0 0
\(289\) 13.2812 + 9.64932i 0.781244 + 0.567607i
\(290\) 0.590170 + 1.81636i 0.0346560 + 0.106660i
\(291\) 0 0
\(292\) 4.50000 13.8496i 0.263343 0.810485i
\(293\) 28.4721 1.66336 0.831680 0.555255i \(-0.187379\pi\)
0.831680 + 0.555255i \(0.187379\pi\)
\(294\) 0 0
\(295\) −2.86475 + 8.81678i −0.166792 + 0.513333i
\(296\) 2.92705 + 9.00854i 0.170131 + 0.523611i
\(297\) 0 0
\(298\) −6.97214 5.06555i −0.403885 0.293440i
\(299\) 39.9787 2.31203
\(300\) 0 0
\(301\) −3.00000 −0.172917
\(302\) −2.78115 2.02063i −0.160037 0.116274i
\(303\) 0 0
\(304\) −3.35410 10.3229i −0.192371 0.592057i
\(305\) 10.5279 0.602824
\(306\) 0 0
\(307\) 4.76393 0.271892 0.135946 0.990716i \(-0.456593\pi\)
0.135946 + 0.990716i \(0.456593\pi\)
\(308\) 0.618034 1.90211i 0.0352158 0.108383i
\(309\) 0 0
\(310\) −1.28115 + 3.94298i −0.0727646 + 0.223946i
\(311\) −23.8713 17.3435i −1.35362 0.983461i −0.998822 0.0485178i \(-0.984550\pi\)
−0.354796 0.934944i \(-0.615450\pi\)
\(312\) 0 0
\(313\) 17.1803 12.4822i 0.971090 0.705538i 0.0153904 0.999882i \(-0.495101\pi\)
0.955700 + 0.294343i \(0.0951009\pi\)
\(314\) −4.59017 3.33495i −0.259038 0.188202i
\(315\) 0 0
\(316\) 4.04508 2.93893i 0.227554 0.165328i
\(317\) 7.30902 22.4948i 0.410515 1.26344i −0.505686 0.862718i \(-0.668761\pi\)
0.916201 0.400719i \(-0.131239\pi\)
\(318\) 0 0
\(319\) 0.326238 1.00406i 0.0182658 0.0562164i
\(320\) 0.527864 0.0295085
\(321\) 0 0
\(322\) −2.54508 7.83297i −0.141832 0.436514i
\(323\) 3.61803 + 2.62866i 0.201313 + 0.146262i
\(324\) 0 0
\(325\) −7.50000 23.0826i −0.416025 1.28039i
\(326\) −6.79837 −0.376527
\(327\) 0 0
\(328\) 3.61803 + 11.1352i 0.199773 + 0.614837i
\(329\) −0.809017 2.48990i −0.0446026 0.137273i
\(330\) 0 0
\(331\) 5.29180 16.2865i 0.290863 0.895186i −0.693716 0.720248i \(-0.744028\pi\)
0.984580 0.174937i \(-0.0559722\pi\)
\(332\) −2.85410 −0.156639
\(333\) 0 0
\(334\) 2.78115 2.02063i 0.152178 0.110564i
\(335\) −6.38197 19.6417i −0.348684 1.07314i
\(336\) 0 0
\(337\) −0.927051 + 0.673542i −0.0504997 + 0.0366902i −0.612749 0.790278i \(-0.709936\pi\)
0.562249 + 0.826968i \(0.309936\pi\)
\(338\) 5.28115 3.83698i 0.287257 0.208704i
\(339\) 0 0
\(340\) −2.23607 + 1.62460i −0.121268 + 0.0881062i
\(341\) 1.85410 1.34708i 0.100405 0.0729487i
\(342\) 0 0
\(343\) 18.4164 0.994393
\(344\) 1.28115 3.94298i 0.0690751 0.212591i
\(345\) 0 0
\(346\) −3.22542 9.92684i −0.173400 0.533670i
\(347\) 9.60739 + 29.5685i 0.515752 + 1.58732i 0.781910 + 0.623391i \(0.214246\pi\)
−0.266158 + 0.963929i \(0.585754\pi\)
\(348\) 0 0
\(349\) 8.29180 0.443850 0.221925 0.975064i \(-0.428766\pi\)
0.221925 + 0.975064i \(0.428766\pi\)
\(350\) −4.04508 + 2.93893i −0.216219 + 0.157092i
\(351\) 0 0
\(352\) 3.47214 + 2.52265i 0.185065 + 0.134458i
\(353\) −7.44427 22.9111i −0.396219 1.21944i −0.928008 0.372559i \(-0.878480\pi\)
0.531790 0.846876i \(-0.321520\pi\)
\(354\) 0 0
\(355\) 7.92705 + 5.75934i 0.420724 + 0.305674i
\(356\) 4.47214 13.7638i 0.237023 0.729481i
\(357\) 0 0
\(358\) −1.80902 + 5.56758i −0.0956095 + 0.294256i
\(359\) −23.2533 + 16.8945i −1.22726 + 0.891658i −0.996682 0.0813956i \(-0.974062\pi\)
−0.230580 + 0.973053i \(0.574062\pi\)
\(360\) 0 0
\(361\) −12.3541 8.97578i −0.650216 0.472409i
\(362\) 6.85410 4.97980i 0.360244 0.261732i
\(363\) 0 0
\(364\) 10.2812 + 7.46969i 0.538879 + 0.391518i
\(365\) 20.1246 1.05337
\(366\) 0 0
\(367\) −1.68034 + 5.17155i −0.0877130 + 0.269953i −0.985286 0.170913i \(-0.945328\pi\)
0.897573 + 0.440866i \(0.145328\pi\)
\(368\) −15.2705 −0.796030
\(369\) 0 0
\(370\) −4.73607 + 3.44095i −0.246216 + 0.178887i
\(371\) 2.73607 + 8.42075i 0.142050 + 0.437184i
\(372\) 0 0
\(373\) −4.26393 3.09793i −0.220778 0.160405i 0.471899 0.881653i \(-0.343569\pi\)
−0.692677 + 0.721248i \(0.743569\pi\)
\(374\) −0.360680 −0.0186503
\(375\) 0 0
\(376\) 3.61803 0.186586
\(377\) 5.42705 + 3.94298i 0.279507 + 0.203074i
\(378\) 0 0
\(379\) −10.6910 32.9035i −0.549159 1.69014i −0.710891 0.703303i \(-0.751708\pi\)
0.161732 0.986835i \(-0.448292\pi\)
\(380\) 17.1353 12.4495i 0.879020 0.638645i
\(381\) 0 0
\(382\) −14.9443 −0.764615
\(383\) 3.51064 10.8046i 0.179385 0.552092i −0.820421 0.571760i \(-0.806261\pi\)
0.999807 + 0.0196680i \(0.00626093\pi\)
\(384\) 0 0
\(385\) 2.76393 0.140863
\(386\) −2.85410 2.07363i −0.145270 0.105545i
\(387\) 0 0
\(388\) 3.73607 2.71441i 0.189670 0.137803i
\(389\) 12.1353 + 8.81678i 0.615282 + 0.447028i 0.851270 0.524727i \(-0.175833\pi\)
−0.235988 + 0.971756i \(0.575833\pi\)
\(390\) 0 0
\(391\) 5.09017 3.69822i 0.257421 0.187027i
\(392\) −3.02786 + 9.31881i −0.152930 + 0.470671i
\(393\) 0 0
\(394\) −1.85410 + 5.70634i −0.0934083 + 0.287481i
\(395\) 5.59017 + 4.06150i 0.281272 + 0.204356i
\(396\) 0 0
\(397\) −0.0106431 0.0327561i −0.000534163 0.00164398i 0.950789 0.309839i \(-0.100275\pi\)
−0.951323 + 0.308195i \(0.900275\pi\)
\(398\) 1.28115 + 0.930812i 0.0642184 + 0.0466574i
\(399\) 0 0
\(400\) 2.86475 + 8.81678i 0.143237 + 0.440839i
\(401\) 22.5967 1.12843 0.564214 0.825629i \(-0.309179\pi\)
0.564214 + 0.825629i \(0.309179\pi\)
\(402\) 0 0
\(403\) 4.50000 + 13.8496i 0.224161 + 0.689897i
\(404\) −3.73607 11.4984i −0.185876 0.572069i
\(405\) 0 0
\(406\) 0.427051 1.31433i 0.0211942 0.0652290i
\(407\) 3.23607 0.160406
\(408\) 0 0
\(409\) −22.9894 + 16.7027i −1.13675 + 0.825898i −0.986663 0.162775i \(-0.947955\pi\)
−0.150087 + 0.988673i \(0.547955\pi\)
\(410\) −5.85410 + 4.25325i −0.289113 + 0.210053i
\(411\) 0 0
\(412\) −15.1353 + 10.9964i −0.745660 + 0.541754i
\(413\) 5.42705 3.94298i 0.267048 0.194022i
\(414\) 0 0
\(415\) −1.21885 3.75123i −0.0598308 0.184140i
\(416\) −22.0623 + 16.0292i −1.08169 + 0.785896i
\(417\) 0 0
\(418\) 2.76393 0.135188
\(419\) 0.163119 0.502029i 0.00796888 0.0245257i −0.946993 0.321254i \(-0.895896\pi\)
0.954962 + 0.296728i \(0.0958956\pi\)
\(420\) 0 0
\(421\) 9.88854 + 30.4338i 0.481938 + 1.48325i 0.836367 + 0.548170i \(0.184675\pi\)
−0.354429 + 0.935083i \(0.615325\pi\)
\(422\) −2.51722 7.74721i −0.122536 0.377128i
\(423\) 0 0
\(424\) −12.2361 −0.594236
\(425\) −3.09017 2.24514i −0.149895 0.108905i
\(426\) 0 0
\(427\) −6.16312 4.47777i −0.298254 0.216694i
\(428\) 5.20820 + 16.0292i 0.251748 + 0.774801i
\(429\) 0 0
\(430\) 2.56231 0.123565
\(431\) −7.36475 + 22.6664i −0.354747 + 1.09180i 0.601409 + 0.798942i \(0.294606\pi\)
−0.956156 + 0.292858i \(0.905394\pi\)
\(432\) 0 0
\(433\) 6.22542 19.1599i 0.299175 0.920765i −0.682612 0.730781i \(-0.739156\pi\)
0.981787 0.189985i \(-0.0608438\pi\)
\(434\) 2.42705 1.76336i 0.116502 0.0846438i
\(435\) 0 0
\(436\) 13.0902 + 9.51057i 0.626905 + 0.455473i
\(437\) −39.0066 + 28.3399i −1.86594 + 1.35568i
\(438\) 0 0
\(439\) −4.83688 3.51420i −0.230852 0.167724i 0.466346 0.884602i \(-0.345570\pi\)
−0.697198 + 0.716879i \(0.745570\pi\)
\(440\) −1.18034 + 3.63271i −0.0562705 + 0.173183i
\(441\) 0 0
\(442\) 0.708204 2.17963i 0.0336858 0.103674i
\(443\) −12.0557 −0.572785 −0.286392 0.958112i \(-0.592456\pi\)
−0.286392 + 0.958112i \(0.592456\pi\)
\(444\) 0 0
\(445\) 20.0000 0.948091
\(446\) −4.23607 13.0373i −0.200584 0.617333i
\(447\) 0 0
\(448\) −0.309017 0.224514i −0.0145997 0.0106073i
\(449\) −20.3262 −0.959254 −0.479627 0.877472i \(-0.659228\pi\)
−0.479627 + 0.877472i \(0.659228\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −13.2812 9.64932i −0.624693 0.453866i
\(453\) 0 0
\(454\) 3.67376 + 11.3067i 0.172418 + 0.530649i
\(455\) −5.42705 + 16.7027i −0.254424 + 0.783037i
\(456\) 0 0
\(457\) 5.41641 0.253369 0.126684 0.991943i \(-0.459566\pi\)
0.126684 + 0.991943i \(0.459566\pi\)
\(458\) −1.58359 + 4.87380i −0.0739964 + 0.227738i
\(459\) 0 0
\(460\) −9.20820 28.3399i −0.429335 1.32136i
\(461\) 18.7533 + 13.6251i 0.873428 + 0.634582i 0.931505 0.363730i \(-0.118497\pi\)
−0.0580768 + 0.998312i \(0.518497\pi\)
\(462\) 0 0
\(463\) −13.0451 + 9.47781i −0.606257 + 0.440471i −0.848094 0.529846i \(-0.822250\pi\)
0.241838 + 0.970317i \(0.422250\pi\)
\(464\) −2.07295 1.50609i −0.0962342 0.0699183i
\(465\) 0 0
\(466\) −7.47214 + 5.42882i −0.346140 + 0.251485i
\(467\) 8.79180 27.0584i 0.406836 1.25211i −0.512517 0.858677i \(-0.671287\pi\)
0.919353 0.393435i \(-0.128713\pi\)
\(468\) 0 0
\(469\) −4.61803 + 14.2128i −0.213241 + 0.656288i
\(470\) 0.690983 + 2.12663i 0.0318727 + 0.0980940i
\(471\) 0 0
\(472\) 2.86475 + 8.81678i 0.131861 + 0.405825i
\(473\) −1.14590 0.832544i −0.0526884 0.0382804i
\(474\) 0 0
\(475\) 23.6803 + 17.2048i 1.08653 + 0.789409i
\(476\) 2.00000 0.0916698
\(477\) 0 0
\(478\) −5.62868 17.3233i −0.257450 0.792349i
\(479\) 1.28115 + 3.94298i 0.0585374 + 0.180160i 0.976050 0.217548i \(-0.0698059\pi\)
−0.917512 + 0.397708i \(0.869806\pi\)
\(480\) 0 0
\(481\) −6.35410 + 19.5559i −0.289722 + 0.891673i
\(482\) −7.09017 −0.322948
\(483\) 0 0
\(484\) −13.6353 + 9.90659i −0.619784 + 0.450300i
\(485\) 5.16312 + 3.75123i 0.234445 + 0.170334i
\(486\) 0 0
\(487\) 7.75329 5.63309i 0.351335 0.255260i −0.398094 0.917345i \(-0.630328\pi\)
0.749429 + 0.662085i \(0.230328\pi\)
\(488\) 8.51722 6.18812i 0.385556 0.280123i
\(489\) 0 0
\(490\) −6.05573 −0.273570
\(491\) 30.1353 21.8945i 1.35999 0.988087i 0.361539 0.932357i \(-0.382251\pi\)
0.998446 0.0557300i \(-0.0177486\pi\)
\(492\) 0 0
\(493\) 1.05573 0.0475476
\(494\) −5.42705 + 16.7027i −0.244175 + 0.751492i
\(495\) 0 0
\(496\) −1.71885 5.29007i −0.0771785 0.237531i
\(497\) −2.19098 6.74315i −0.0982790 0.302472i
\(498\) 0 0
\(499\) −12.5623 −0.562366 −0.281183 0.959654i \(-0.590727\pi\)
−0.281183 + 0.959654i \(0.590727\pi\)
\(500\) −14.6353 + 10.6331i −0.654508 + 0.475528i
\(501\) 0 0
\(502\) 3.40983 + 2.47739i 0.152188 + 0.110571i
\(503\) 3.27051 + 10.0656i 0.145825 + 0.448803i 0.997116 0.0758907i \(-0.0241800\pi\)
−0.851291 + 0.524693i \(0.824180\pi\)
\(504\) 0 0
\(505\) 13.5172 9.82084i 0.601508 0.437021i
\(506\) 1.20163 3.69822i 0.0534188 0.164406i
\(507\) 0 0
\(508\) 7.94427 24.4500i 0.352470 1.08479i
\(509\) −3.78115 + 2.74717i −0.167597 + 0.121766i −0.668422 0.743782i \(-0.733030\pi\)
0.500825 + 0.865548i \(0.333030\pi\)
\(510\) 0 0
\(511\) −11.7812 8.55951i −0.521168 0.378650i
\(512\) 15.1353 10.9964i 0.668890 0.485977i
\(513\) 0 0
\(514\) −8.07295 5.86534i −0.356083 0.258709i
\(515\) −20.9164 15.1967i −0.921687 0.669645i
\(516\) 0 0
\(517\) 0.381966 1.17557i 0.0167988 0.0517015i
\(518\) 4.23607 0.186122
\(519\) 0 0
\(520\) −19.6353 14.2658i −0.861063 0.625599i
\(521\) 4.74671 + 14.6089i 0.207957 + 0.640026i 0.999579 + 0.0290150i \(0.00923706\pi\)
−0.791622 + 0.611011i \(0.790763\pi\)
\(522\) 0 0
\(523\) 16.0623 + 11.6699i 0.702356 + 0.510291i 0.880699 0.473677i \(-0.157074\pi\)
−0.178343 + 0.983968i \(0.557074\pi\)
\(524\) −28.7984 −1.25806
\(525\) 0 0
\(526\) −13.6525 −0.595276
\(527\) 1.85410 + 1.34708i 0.0807660 + 0.0586799i
\(528\) 0 0
\(529\) 13.8541 + 42.6385i 0.602352 + 1.85385i
\(530\) −2.33688 7.19218i −0.101508 0.312408i
\(531\) 0 0
\(532\) −15.3262 −0.664477
\(533\) −7.85410 + 24.1724i −0.340199 + 1.04702i
\(534\) 0 0
\(535\) −18.8435 + 13.6906i −0.814674 + 0.591895i
\(536\) −16.7082 12.1392i −0.721684 0.524334i
\(537\) 0 0
\(538\) 8.61803 6.26137i 0.371550 0.269947i
\(539\) 2.70820 + 1.96763i 0.116651 + 0.0847516i
\(540\) 0 0
\(541\) 10.6180 7.71445i 0.456505 0.331670i −0.335654 0.941985i \(-0.608957\pi\)
0.792159 + 0.610315i \(0.208957\pi\)
\(542\) 1.52786 4.70228i 0.0656274 0.201980i
\(543\) 0 0
\(544\) −1.32624 + 4.08174i −0.0568620 + 0.175003i
\(545\) −6.90983 + 21.2663i −0.295985 + 0.910947i
\(546\) 0 0
\(547\) −10.7254 33.0095i −0.458586 1.41138i −0.866873 0.498529i \(-0.833874\pi\)
0.408287 0.912854i \(-0.366126\pi\)
\(548\) −7.78115 5.65334i −0.332394 0.241499i
\(549\) 0 0
\(550\) −2.36068 −0.100660
\(551\) −8.09017 −0.344653
\(552\) 0 0
\(553\) −1.54508 4.75528i −0.0657037 0.202215i
\(554\) 2.15654 + 6.63715i 0.0916227 + 0.281986i
\(555\) 0 0
\(556\) −2.50000 + 7.69421i −0.106024 + 0.326307i
\(557\) −9.23607 −0.391345 −0.195672 0.980669i \(-0.562689\pi\)
−0.195672 + 0.980669i \(0.562689\pi\)
\(558\) 0 0
\(559\) 7.28115 5.29007i 0.307960 0.223746i
\(560\) 2.07295 6.37988i 0.0875981 0.269599i
\(561\) 0 0
\(562\) 0.545085 0.396027i 0.0229930 0.0167054i
\(563\) 7.78115 5.65334i 0.327936 0.238260i −0.411618 0.911356i \(-0.635036\pi\)
0.739555 + 0.673097i \(0.235036\pi\)
\(564\) 0 0
\(565\) 7.01064 21.5765i 0.294940 0.907732i
\(566\) −11.5729 + 8.40824i −0.486447 + 0.353425i
\(567\) 0 0
\(568\) 9.79837 0.411131
\(569\) −9.10739 + 28.0297i −0.381802 + 1.17506i 0.556972 + 0.830531i \(0.311963\pi\)
−0.938774 + 0.344534i \(0.888037\pi\)
\(570\) 0 0
\(571\) 9.92705 + 30.5523i 0.415434 + 1.27857i 0.911862 + 0.410497i \(0.134645\pi\)
−0.496428 + 0.868078i \(0.665355\pi\)
\(572\) 1.85410 + 5.70634i 0.0775239 + 0.238594i
\(573\) 0 0
\(574\) 5.23607 0.218549
\(575\) 33.3156 24.2052i 1.38936 1.00943i
\(576\) 0 0
\(577\) −30.5623 22.2048i −1.27233 0.924399i −0.273033 0.962005i \(-0.588027\pi\)
−0.999293 + 0.0376062i \(0.988027\pi\)
\(578\) 3.13525 + 9.64932i 0.130409 + 0.401359i
\(579\) 0 0
\(580\) 1.54508 4.75528i 0.0641562 0.197452i
\(581\) −0.881966 + 2.71441i −0.0365901 + 0.112613i
\(582\) 0 0
\(583\) −1.29180 + 3.97574i −0.0535007 + 0.164658i
\(584\) 16.2812 11.8290i 0.673719 0.489485i
\(585\) 0 0
\(586\) 14.2361 + 10.3431i 0.588087 + 0.427270i
\(587\) 15.1353 10.9964i 0.624699 0.453870i −0.229861 0.973224i \(-0.573827\pi\)
0.854560 + 0.519353i \(0.173827\pi\)
\(588\) 0 0
\(589\) −14.2082 10.3229i −0.585439 0.425346i
\(590\) −4.63525 + 3.36771i −0.190830 + 0.138646i
\(591\) 0 0
\(592\) 2.42705 7.46969i 0.0997512 0.307003i
\(593\) 22.0902 0.907135 0.453567 0.891222i \(-0.350151\pi\)
0.453567 + 0.891222i \(0.350151\pi\)
\(594\) 0 0
\(595\) 0.854102 + 2.62866i 0.0350148 + 0.107764i
\(596\) 6.97214 + 21.4580i 0.285590 + 0.878955i
\(597\) 0 0
\(598\) 19.9894 + 14.5231i 0.817426 + 0.593894i
\(599\) 0.527864 0.0215679 0.0107840 0.999942i \(-0.496567\pi\)
0.0107840 + 0.999942i \(0.496567\pi\)
\(600\) 0 0
\(601\) 36.2705 1.47950 0.739752 0.672879i \(-0.234943\pi\)
0.739752 + 0.672879i \(0.234943\pi\)
\(602\) −1.50000 1.08981i −0.0611354 0.0444175i
\(603\) 0 0
\(604\) 2.78115 + 8.55951i 0.113164 + 0.348281i
\(605\) −18.8435 13.6906i −0.766096 0.556601i
\(606\) 0 0
\(607\) −15.4377 −0.626597 −0.313298 0.949655i \(-0.601434\pi\)
−0.313298 + 0.949655i \(0.601434\pi\)
\(608\) 10.1631 31.2789i 0.412169 1.26853i
\(609\) 0 0
\(610\) 5.26393 + 3.82447i 0.213130 + 0.154848i
\(611\) 6.35410 + 4.61653i 0.257059 + 0.186765i
\(612\) 0 0
\(613\) −25.8713 + 18.7966i −1.04493 + 0.759188i −0.971242 0.238093i \(-0.923478\pi\)
−0.0736905 + 0.997281i \(0.523478\pi\)
\(614\) 2.38197 + 1.73060i 0.0961283 + 0.0698413i
\(615\) 0 0
\(616\) 2.23607 1.62460i 0.0900937 0.0654569i
\(617\) −3.01722 + 9.28605i −0.121469 + 0.373842i −0.993241 0.116069i \(-0.962971\pi\)
0.871772 + 0.489911i \(0.162971\pi\)
\(618\) 0 0
\(619\) 12.1976 37.5402i 0.490261 1.50887i −0.333952 0.942590i \(-0.608382\pi\)
0.824213 0.566279i \(-0.191618\pi\)
\(620\) 8.78115 6.37988i 0.352660 0.256222i
\(621\) 0 0
\(622\) −5.63525 17.3435i −0.225953 0.695412i
\(623\) −11.7082 8.50651i −0.469079 0.340806i
\(624\) 0 0
\(625\) −20.2254 14.6946i −0.809017 0.587785i
\(626\) 13.1246 0.524565
\(627\) 0 0
\(628\) 4.59017 + 14.1271i 0.183168 + 0.563732i
\(629\) 1.00000 + 3.07768i 0.0398726 + 0.122715i
\(630\) 0 0
\(631\) −1.78115 + 5.48183i −0.0709066 + 0.218228i −0.980230 0.197862i \(-0.936600\pi\)
0.909323 + 0.416090i \(0.136600\pi\)
\(632\) 6.90983 0.274858
\(633\) 0 0
\(634\) 11.8262 8.59226i 0.469680 0.341242i
\(635\) 35.5279 1.40988
\(636\) 0 0
\(637\) −17.2082 + 12.5025i −0.681814 + 0.495367i
\(638\) 0.527864 0.383516i 0.0208983 0.0151835i
\(639\) 0 0
\(640\) 20.5902 + 14.9596i 0.813898 + 0.591331i
\(641\) 8.16312 5.93085i 0.322424 0.234255i −0.414785 0.909919i \(-0.636143\pi\)
0.737209 + 0.675665i \(0.236143\pi\)
\(642\) 0 0
\(643\) 22.8328 0.900438 0.450219 0.892918i \(-0.351346\pi\)
0.450219 + 0.892918i \(0.351346\pi\)
\(644\) −6.66312 + 20.5070i −0.262564 + 0.808088i
\(645\) 0 0
\(646\) 0.854102 + 2.62866i 0.0336042 + 0.103423i
\(647\) −9.43769 29.0462i −0.371034 1.14193i −0.946116 0.323829i \(-0.895030\pi\)
0.575082 0.818096i \(-0.304970\pi\)
\(648\) 0 0
\(649\) 3.16718 0.124323
\(650\) 4.63525 14.2658i 0.181810 0.559553i
\(651\) 0 0
\(652\) 14.3992 + 10.4616i 0.563916 + 0.409709i
\(653\) −2.44427 7.52270i −0.0956518 0.294386i 0.891771 0.452487i \(-0.149463\pi\)
−0.987423 + 0.158101i \(0.949463\pi\)
\(654\) 0 0
\(655\) −12.2984 37.8505i −0.480537 1.47894i
\(656\) 3.00000 9.23305i 0.117130 0.360490i
\(657\) 0 0
\(658\) 0.500000 1.53884i 0.0194920 0.0599903i
\(659\) 19.7984 14.3844i 0.771235 0.560335i −0.131101 0.991369i \(-0.541851\pi\)
0.902336 + 0.431034i \(0.141851\pi\)
\(660\) 0 0
\(661\) 32.9164 + 23.9152i 1.28030 + 0.930192i 0.999562 0.0295922i \(-0.00942086\pi\)
0.280738 + 0.959784i \(0.409421\pi\)
\(662\) 8.56231 6.22088i 0.332783 0.241781i
\(663\) 0 0
\(664\) −3.19098 2.31838i −0.123834 0.0899708i
\(665\) −6.54508 20.1437i −0.253808 0.781139i
\(666\) 0 0
\(667\) −3.51722 + 10.8249i −0.136187 + 0.419142i
\(668\) −9.00000 −0.348220
\(669\) 0 0
\(670\) 3.94427 12.1392i 0.152381 0.468979i
\(671\) −1.11146 3.42071i −0.0429073 0.132055i
\(672\) 0 0
\(673\) 8.23607 + 5.98385i 0.317477 + 0.230661i 0.735098 0.677961i \(-0.237136\pi\)
−0.417621 + 0.908621i \(0.637136\pi\)
\(674\) −0.708204 −0.0272790
\(675\) 0 0
\(676\) −17.0902 −0.657314
\(677\) 6.78115 + 4.92680i 0.260621 + 0.189352i 0.710421 0.703777i \(-0.248505\pi\)
−0.449800 + 0.893129i \(0.648505\pi\)
\(678\) 0 0
\(679\) −1.42705 4.39201i −0.0547652 0.168550i
\(680\) −3.81966 −0.146477
\(681\) 0 0
\(682\) 1.41641 0.0542371
\(683\) 1.39919 4.30625i 0.0535384 0.164774i −0.920712 0.390242i \(-0.872391\pi\)
0.974251 + 0.225468i \(0.0723912\pi\)
\(684\) 0 0
\(685\) 4.10739 12.6412i 0.156935 0.482997i
\(686\) 9.20820 + 6.69015i 0.351571 + 0.255431i
\(687\) 0 0
\(688\) −2.78115 + 2.02063i −0.106030 + 0.0770356i
\(689\) −21.4894 15.6129i −0.818679 0.594805i
\(690\) 0 0
\(691\) −2.20820 + 1.60435i −0.0840040 + 0.0610325i −0.628995 0.777410i \(-0.716533\pi\)
0.544991 + 0.838442i \(0.316533\pi\)
\(692\) −8.44427 + 25.9888i −0.321003 + 0.987946i
\(693\) 0 0
\(694\) −5.93769 + 18.2743i −0.225392 + 0.693685i
\(695\) −11.1803 −0.424094
\(696\) 0 0
\(697\) 1.23607 + 3.80423i 0.0468194 + 0.144095i
\(698\) 4.14590 + 3.01217i 0.156925 + 0.114012i
\(699\) 0 0
\(700\) 13.0902 0.494762
\(701\) −35.0132 −1.32243 −0.661214 0.750197i \(-0.729959\pi\)
−0.661214 + 0.750197i \(0.729959\pi\)
\(702\) 0 0
\(703\) −7.66312 23.5847i −0.289020 0.889512i
\(704\) −0.0557281 0.171513i −0.00210033 0.00646416i
\(705\) 0 0
\(706\) 4.60081 14.1598i 0.173154 0.532913i
\(707\) −12.0902 −0.454698
\(708\) 0 0
\(709\) −27.1353 + 19.7149i −1.01909 + 0.740409i −0.966095 0.258186i \(-0.916875\pi\)
−0.0529906 + 0.998595i \(0.516875\pi\)
\(710\) 1.87132 + 5.75934i 0.0702295 + 0.216144i
\(711\) 0 0
\(712\) 16.1803 11.7557i 0.606384 0.440564i
\(713\) −19.9894 + 14.5231i −0.748607 + 0.543895i
\(714\) 0 0
\(715\) −6.70820 + 4.87380i −0.250873 + 0.182270i
\(716\) 12.3992 9.00854i 0.463379 0.336665i
\(717\) 0 0
\(718\) −17.7639 −0.662944
\(719\) 11.3435 34.9116i 0.423040 1.30198i −0.481819 0.876271i \(-0.660024\pi\)
0.904859 0.425712i \(-0.139976\pi\)
\(720\) 0 0
\(721\) 5.78115 + 17.7926i 0.215301 + 0.662630i
\(722\) −2.91641 8.97578i −0.108537 0.334044i
\(723\) 0 0
\(724\) −22.1803 −0.824326
\(725\) 6.90983 0.256625
\(726\) 0 0
\(727\) −3.59017 2.60841i −0.133152 0.0967406i 0.519216 0.854643i \(-0.326224\pi\)
−0.652368 + 0.757903i \(0.726224\pi\)
\(728\) 5.42705 + 16.7027i 0.201140 + 0.619045i
\(729\) 0 0
\(730\) 10.0623 + 7.31069i 0.372423 + 0.270581i
\(731\) 0.437694 1.34708i 0.0161887 0.0498237i
\(732\) 0 0
\(733\) 8.33688 25.6583i 0.307930 0.947710i −0.670638 0.741785i \(-0.733980\pi\)
0.978568 0.205925i \(-0.0660204\pi\)
\(734\) −2.71885 + 1.97536i −0.100354 + 0.0729118i
\(735\) 0 0
\(736\) −37.4336 27.1971i −1.37982 1.00250i
\(737\) −5.70820 + 4.14725i −0.210264 + 0.152766i
\(738\) 0 0
\(739\) 25.0623 + 18.2088i 0.921932 + 0.669823i 0.944004 0.329934i \(-0.107026\pi\)
−0.0220723 + 0.999756i \(0.507026\pi\)
\(740\) 15.3262 0.563404
\(741\) 0 0
\(742\) −1.69098 + 5.20431i −0.0620779 + 0.191056i
\(743\) 16.3607 0.600215 0.300108 0.953905i \(-0.402977\pi\)
0.300108 + 0.953905i \(0.402977\pi\)
\(744\) 0 0
\(745\) −25.2254 + 18.3273i −0.924188 + 0.671462i
\(746\) −1.00658 3.09793i −0.0368534 0.113423i
\(747\) 0 0
\(748\) 0.763932 + 0.555029i 0.0279321 + 0.0202939i
\(749\) 16.8541 0.615835
\(750\) 0 0
\(751\) −40.8885 −1.49204 −0.746022 0.665921i \(-0.768039\pi\)
−0.746022 + 0.665921i \(0.768039\pi\)
\(752\) −2.42705 1.76336i −0.0885054 0.0643030i
\(753\) 0 0
\(754\) 1.28115 + 3.94298i 0.0466568 + 0.143595i
\(755\) −10.0623 + 7.31069i −0.366205 + 0.266063i
\(756\) 0 0
\(757\) 3.58359 0.130248 0.0651239 0.997877i \(-0.479256\pi\)
0.0651239 + 0.997877i \(0.479256\pi\)
\(758\) 6.60739 20.3355i 0.239991 0.738617i
\(759\) 0 0
\(760\) 29.2705 1.06175
\(761\) 30.2984 + 22.0131i 1.09832 + 0.797973i 0.980784 0.195096i \(-0.0625020\pi\)
0.117531 + 0.993069i \(0.462502\pi\)
\(762\) 0 0
\(763\) 13.0902 9.51057i 0.473896 0.344306i
\(764\) 31.6525 + 22.9969i 1.14515 + 0.831998i
\(765\) 0 0
\(766\) 5.68034 4.12701i 0.205239 0.149115i
\(767\) −6.21885 + 19.1396i −0.224550 + 0.691092i
\(768\) 0 0
\(769\) −4.14590 + 12.7598i −0.149505 + 0.460129i −0.997563 0.0697749i \(-0.977772\pi\)
0.848058 + 0.529904i \(0.177772\pi\)
\(770\) 1.38197 + 1.00406i 0.0498026 + 0.0361837i
\(771\) 0 0
\(772\) 2.85410 + 8.78402i 0.102721 + 0.316144i
\(773\) 26.8262 + 19.4904i 0.964873 + 0.701021i 0.954277 0.298923i \(-0.0966273\pi\)
0.0105954 + 0.999944i \(0.496627\pi\)
\(774\) 0 0
\(775\) 12.1353 + 8.81678i 0.435911 + 0.316708i
\(776\) 6.38197 0.229099
\(777\) 0 0
\(778\) 2.86475 + 8.81678i 0.102706 + 0.316097i
\(779\) −9.47214 29.1522i −0.339374 1.04449i
\(780\) 0 0
\(781\) 1.03444 3.18368i 0.0370152 0.113921i
\(782\) 3.88854 0.139054
\(783\) 0 0
\(784\) 6.57295 4.77553i 0.234748 0.170555i
\(785\) −16.6074 + 12.0660i −0.592743 + 0.430653i
\(786\) 0 0