Properties

Label 125.2.d.a.76.1
Level $125$
Weight $2$
Character 125.76
Analytic conductor $0.998$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 125 = 5^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 125.d (of order \(5\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.998130025266\)
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 76.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 125.76
Dual form 125.2.d.a.51.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.190983 - 0.587785i) q^{6} +1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.363271i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(0.190983 - 0.587785i) q^{6} +1.61803 q^{7} +(0.690983 - 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +(0.618034 + 0.449028i) q^{11} +(-1.30902 + 0.951057i) q^{12} +(-3.92705 + 2.85317i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-1.50000 + 1.08981i) q^{16} +(0.236068 - 0.726543i) q^{17} +1.23607 q^{18} +(-1.80902 + 5.56758i) q^{19} +(-0.500000 - 1.53884i) q^{21} +(0.145898 + 0.449028i) q^{22} +(6.66312 + 4.84104i) q^{23} -2.23607 q^{24} -3.00000 q^{26} +(-4.04508 - 2.93893i) q^{27} +(-0.809017 - 2.48990i) q^{28} +(-0.427051 - 1.31433i) q^{29} +(-0.927051 + 2.85317i) q^{31} -5.61803 q^{32} +(0.236068 - 0.726543i) q^{33} +(0.381966 - 0.277515i) q^{34} +(-2.61803 - 1.90211i) q^{36} +(3.42705 - 2.48990i) q^{37} +(-2.92705 + 2.12663i) q^{38} +(3.92705 + 2.85317i) q^{39} +(4.23607 - 3.07768i) q^{41} +(0.309017 - 0.951057i) q^{42} -1.85410 q^{43} +(0.381966 - 1.17557i) q^{44} +(1.57295 + 4.84104i) q^{46} +(0.500000 + 1.53884i) q^{47} +(1.50000 + 1.08981i) q^{48} -4.38197 q^{49} -0.763932 q^{51} +(6.35410 + 4.61653i) q^{52} +(-1.69098 - 5.20431i) q^{53} +(-0.954915 - 2.93893i) q^{54} +(1.11803 - 3.44095i) q^{56} +5.85410 q^{57} +(0.263932 - 0.812299i) q^{58} +(3.35410 - 2.43690i) q^{59} +(3.80902 + 2.76741i) q^{61} +(-1.50000 + 1.08981i) q^{62} +(2.61803 - 1.90211i) q^{63} +(0.190983 + 0.138757i) q^{64} +(0.381966 - 0.277515i) q^{66} +(-2.85410 + 8.78402i) q^{67} -1.23607 q^{68} +(2.54508 - 7.83297i) q^{69} +(-1.35410 - 4.16750i) q^{71} +(-1.38197 - 4.25325i) q^{72} +(-7.28115 - 5.29007i) q^{73} +2.61803 q^{74} +9.47214 q^{76} +(1.00000 + 0.726543i) q^{77} +(0.927051 + 2.85317i) q^{78} +(0.954915 + 2.93893i) q^{79} +(0.309017 - 0.951057i) q^{81} +3.23607 q^{82} +(0.545085 - 1.67760i) q^{83} +(-2.11803 + 1.53884i) q^{84} +(-0.927051 - 0.673542i) q^{86} +(-1.11803 + 0.812299i) q^{87} +(1.38197 - 1.00406i) q^{88} +(-7.23607 - 5.25731i) q^{89} +(-6.35410 + 4.61653i) q^{91} +(4.11803 - 12.6740i) q^{92} +3.00000 q^{93} +(-0.309017 + 0.951057i) q^{94} +(1.73607 + 5.34307i) q^{96} +(-0.881966 - 2.71441i) q^{97} +(-2.19098 - 1.59184i) q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{7} + 5 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + q^{3} - 2 q^{4} + 3 q^{6} + 2 q^{7} + 5 q^{8} + 2 q^{9} - 2 q^{11} - 3 q^{12} - 9 q^{13} + q^{14} - 6 q^{16} - 8 q^{17} - 4 q^{18} - 5 q^{19} - 2 q^{21} + 14 q^{22} + 11 q^{23} - 12 q^{26} - 5 q^{27} - q^{28} + 5 q^{29} + 3 q^{31} - 18 q^{32} - 8 q^{33} + 6 q^{34} - 6 q^{36} + 7 q^{37} - 5 q^{38} + 9 q^{39} + 8 q^{41} - q^{42} + 6 q^{43} + 6 q^{44} + 13 q^{46} + 2 q^{47} + 6 q^{48} - 22 q^{49} - 12 q^{51} + 12 q^{52} - 9 q^{53} - 15 q^{54} + 10 q^{57} + 10 q^{58} + 13 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} + 6 q^{66} + 2 q^{67} + 4 q^{68} - q^{69} + 8 q^{71} - 10 q^{72} - 9 q^{73} + 6 q^{74} + 20 q^{76} + 4 q^{77} - 3 q^{78} + 15 q^{79} - q^{81} + 4 q^{82} - 9 q^{83} - 4 q^{84} + 3 q^{86} + 10 q^{88} - 20 q^{89} - 12 q^{91} + 12 q^{92} + 12 q^{93} + q^{94} - 2 q^{96} - 8 q^{97} - 11 q^{98} + 24 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/125\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\)

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 \(0.629881\pi\)
\(3\) −0.309017 0.951057i −0.178411 0.549093i 0.821362 0.570408i \(-0.193215\pi\)
−0.999773 + 0.0213149i \(0.993215\pi\)
\(4\) −0.500000 1.53884i −0.250000 0.769421i
\(5\) 0 0
\(6\) 0.190983 0.587785i 0.0779685 0.239962i
\(7\) 1.61803 0.611559 0.305780 0.952102i \(-0.401083\pi\)
0.305780 + 0.952102i \(0.401083\pi\)
\(8\) 0.690983 2.12663i 0.244299 0.751876i
\(9\) 1.61803 1.17557i 0.539345 0.391857i
\(10\) 0 0
\(11\) 0.618034 + 0.449028i 0.186344 + 0.135387i 0.677046 0.735940i \(-0.263260\pi\)
−0.490702 + 0.871327i \(0.663260\pi\)
\(12\) −1.30902 + 0.951057i −0.377881 + 0.274546i
\(13\) −3.92705 + 2.85317i −1.08917 + 0.791327i −0.979259 0.202615i \(-0.935056\pi\)
−0.109909 + 0.993942i \(0.535056\pi\)
\(14\) 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 \(0.0704693\pi\)
\(18\) 1.23607 0.291344
\(19\) −1.80902 + 5.56758i −0.415017 + 1.27729i 0.497219 + 0.867625i \(0.334355\pi\)
−0.912236 + 0.409666i \(0.865645\pi\)
\(20\) 0 0
\(21\) −0.500000 1.53884i −0.109109 0.335803i
\(22\) 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 \(0.371292\pi\)
\(24\) −2.23607 −0.456435
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) −4.04508 2.93893i −0.778477 0.565597i
\(28\) −0.809017 2.48990i −0.152890 0.470547i
\(29\) −0.427051 1.31433i −0.0793014 0.244065i 0.903544 0.428495i \(-0.140956\pi\)
−0.982846 + 0.184430i \(0.940956\pi\)
\(30\) 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
\(33\) 0.236068 0.726543i 0.0410942 0.126475i
\(34\) 0.381966 0.277515i 0.0655066 0.0475934i
\(35\) 0 0
\(36\) −2.61803 1.90211i −0.436339 0.317019i
\(37\) 3.42705 2.48990i 0.563404 0.409337i −0.269299 0.963057i \(-0.586792\pi\)
0.832703 + 0.553720i \(0.186792\pi\)
\(38\) −2.92705 + 2.12663i −0.474830 + 0.344984i
\(39\) 3.92705 + 2.85317i 0.628831 + 0.456873i
\(40\) 0 0
\(41\) 4.23607 3.07768i 0.661563 0.480653i −0.205628 0.978630i \(-0.565924\pi\)
0.867190 + 0.497977i \(0.165924\pi\)
\(42\) 0.309017 0.951057i 0.0476824 0.146751i
\(43\) −1.85410 −0.282748 −0.141374 0.989956i \(-0.545152\pi\)
−0.141374 + 0.989956i \(0.545152\pi\)
\(44\) 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 \(0.862349\pi\)
\(48\) 1.50000 + 1.08981i 0.216506 + 0.157301i
\(49\) −4.38197 −0.625995
\(50\) 0 0
\(51\) −0.763932 −0.106972
\(52\) 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 \(-0.222642\pi\)
\(54\) −0.954915 2.93893i −0.129947 0.399937i
\(55\) 0 0
\(56\) 1.11803 3.44095i 0.149404 0.459817i
\(57\) 5.85410 0.775395
\(58\) 0.263932 0.812299i 0.0346560 0.106660i
\(59\) 3.35410 2.43690i 0.436667 0.317257i −0.347642 0.937627i \(-0.613018\pi\)
0.784309 + 0.620370i \(0.213018\pi\)
\(60\) 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
\(63\) 2.61803 1.90211i 0.329841 0.239644i
\(64\) 0.190983 + 0.138757i 0.0238729 + 0.0173447i
\(65\) 0 0
\(66\) 0.381966 0.277515i 0.0470168 0.0341597i
\(67\) −2.85410 + 8.78402i −0.348684 + 1.07314i 0.610898 + 0.791709i \(0.290809\pi\)
−0.959582 + 0.281430i \(0.909191\pi\)
\(68\) −1.23607 −0.149895
\(69\) 2.54508 7.83297i 0.306392 0.942978i
\(70\) 0 0
\(71\) −1.35410 4.16750i −0.160702 0.494591i 0.837992 0.545683i \(-0.183730\pi\)
−0.998694 + 0.0510922i \(0.983730\pi\)
\(72\) −1.38197 4.25325i −0.162866 0.501251i
\(73\) −7.28115 5.29007i −0.852194 0.619156i 0.0735557 0.997291i \(-0.476565\pi\)
−0.925750 + 0.378136i \(0.876565\pi\)
\(74\) 2.61803 0.304340
\(75\) 0 0
\(76\) 9.47214 1.08653
\(77\) 1.00000 + 0.726543i 0.113961 + 0.0827972i
\(78\) 0.927051 + 2.85317i 0.104968 + 0.323058i
\(79\) 0.954915 + 2.93893i 0.107436 + 0.330655i 0.990295 0.138985i \(-0.0443839\pi\)
−0.882858 + 0.469640i \(0.844384\pi\)
\(80\) 0 0
\(81\) 0.309017 0.951057i 0.0343352 0.105673i
\(82\) 3.23607 0.357364
\(83\) 0.545085 1.67760i 0.0598308 0.184140i −0.916674 0.399636i \(-0.869137\pi\)
0.976505 + 0.215495i \(0.0691366\pi\)
\(84\) −2.11803 + 1.53884i −0.231096 + 0.167901i
\(85\) 0 0
\(86\) −0.927051 0.673542i −0.0999665 0.0726299i
\(87\) −1.11803 + 0.812299i −0.119866 + 0.0870876i
\(88\) 1.38197 1.00406i 0.147318 0.107033i
\(89\) −7.23607 5.25731i −0.767022 0.557274i 0.134034 0.990977i \(-0.457207\pi\)
−0.901056 + 0.433703i \(0.857207\pi\)
\(90\) 0 0
\(91\) −6.35410 + 4.61653i −0.666091 + 0.483943i
\(92\) 4.11803 12.6740i 0.429335 1.32136i
\(93\) 3.00000 0.311086
\(94\) −0.309017 + 0.951057i −0.0318727 + 0.0980940i
\(95\) 0 0
\(96\) 1.73607 + 5.34307i 0.177187 + 0.545325i
\(97\) −0.881966 2.71441i −0.0895501 0.275607i 0.896245 0.443559i \(-0.146284\pi\)
−0.985795 + 0.167953i \(0.946284\pi\)
\(98\) −2.19098 1.59184i −0.221323 0.160800i
\(99\) 1.52786 0.153556
\(100\) 0 0
\(101\) −7.47214 −0.743505 −0.371753 0.928332i \(-0.621243\pi\)
−0.371753 + 0.928332i \(0.621243\pi\)
\(102\) −0.381966 0.277515i −0.0378203 0.0274780i
\(103\) 3.57295 + 10.9964i 0.352053 + 1.08351i 0.957699 + 0.287773i \(0.0929150\pi\)
−0.605645 + 0.795735i \(0.707085\pi\)
\(104\) 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 \(0.667953\pi\)
\(108\) −2.50000 + 7.69421i −0.240563 + 0.740376i
\(109\) −8.09017 + 5.87785i −0.774898 + 0.562996i −0.903443 0.428707i \(-0.858969\pi\)
0.128546 + 0.991704i \(0.458969\pi\)
\(110\) 0 0
\(111\) −3.42705 2.48990i −0.325281 0.236331i
\(112\) −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 \(0.141643\pi\)
\(114\) 2.92705 + 2.12663i 0.274143 + 0.199177i
\(115\) 0 0
\(116\) −1.80902 + 1.31433i −0.167963 + 0.122032i
\(117\) −3.00000 + 9.23305i −0.277350 + 0.853596i
\(118\) 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
\(123\) −4.23607 3.07768i −0.381953 0.277505i
\(124\) 4.85410 0.435911
\(125\) 0 0
\(126\) 2.00000 0.178174
\(127\) −12.8541 9.33905i −1.14062 0.828707i −0.153412 0.988162i \(-0.549026\pi\)
−0.987205 + 0.159455i \(0.949026\pi\)
\(128\) 3.51722 + 10.8249i 0.310881 + 0.956794i
\(129\) 0.572949 + 1.76336i 0.0504453 + 0.155255i
\(130\) 0 0
\(131\) −5.50000 + 16.9273i −0.480537 + 1.47894i 0.357805 + 0.933797i \(0.383525\pi\)
−0.838342 + 0.545145i \(0.816475\pi\)
\(132\) −1.23607 −0.107586
\(133\) −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 \(0.218278\pi\)
\(138\) 4.11803 2.99193i 0.350550 0.254690i
\(139\) −4.04508 2.93893i −0.343100 0.249276i 0.402869 0.915258i \(-0.368013\pi\)
−0.745968 + 0.665981i \(0.768013\pi\)
\(140\) 0 0
\(141\) 1.30902 0.951057i 0.110239 0.0800934i
\(142\) 0.836881 2.57565i 0.0702295 0.216144i
\(143\) −3.70820 −0.310096
\(144\) −1.14590 + 3.52671i −0.0954915 + 0.293893i
\(145\) 0 0
\(146\) −1.71885 5.29007i −0.142253 0.437809i
\(147\) 1.35410 + 4.16750i 0.111684 + 0.343729i
\(148\) −5.54508 4.02874i −0.455803 0.331160i
\(149\) 13.9443 1.14236 0.571180 0.820825i \(-0.306486\pi\)
0.571180 + 0.820825i \(0.306486\pi\)
\(150\) 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
\(153\) −0.472136 1.45309i −0.0381699 0.117475i
\(154\) 0.236068 + 0.726543i 0.0190229 + 0.0585465i
\(155\) 0 0
\(156\) 2.42705 7.46969i 0.194320 0.598054i
\(157\) 9.18034 0.732671 0.366335 0.930483i \(-0.380612\pi\)
0.366335 + 0.930483i \(0.380612\pi\)
\(158\) −0.590170 + 1.81636i −0.0469514 + 0.144502i
\(159\) −4.42705 + 3.21644i −0.351088 + 0.255080i
\(160\) 0 0
\(161\) 10.7812 + 7.83297i 0.849674 + 0.617324i
\(162\) 0.500000 0.363271i 0.0392837 0.0285413i
\(163\) 8.89919 6.46564i 0.697038 0.506428i −0.181928 0.983312i \(-0.558234\pi\)
0.878966 + 0.476884i \(0.158234\pi\)
\(164\) −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 \(0.0309557\pi\)
\(168\) −3.61803 −0.279137
\(169\) 3.26393 10.0453i 0.251072 0.772719i
\(170\) 0 0
\(171\) 3.61803 + 11.1352i 0.276678 + 0.851527i
\(172\) 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 \(0.921898\pi\)
\(174\) −0.854102 −0.0647493
\(175\) 0 0
\(176\) −1.41641 −0.106766
\(177\) −3.35410 2.43690i −0.252110 0.183168i
\(178\) −1.70820 5.25731i −0.128035 0.394052i
\(179\) −2.92705 9.00854i −0.218778 0.673330i −0.998864 0.0476570i \(-0.984825\pi\)
0.780086 0.625673i \(-0.215175\pi\)
\(180\) 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
\(183\) 1.45492 4.47777i 0.107550 0.331006i
\(184\) 14.8992 10.8249i 1.09838 0.798022i
\(185\) 0 0
\(186\) 1.50000 + 1.08981i 0.109985 + 0.0799090i
\(187\) 0.472136 0.343027i 0.0345260 0.0250846i
\(188\) 2.11803 1.53884i 0.154474 0.112232i
\(189\) −6.54508 4.75528i −0.476085 0.345896i
\(190\) 0 0
\(191\) 19.5623 14.2128i 1.41548 1.02841i 0.422982 0.906138i \(-0.360984\pi\)
0.992497 0.122267i \(-0.0390165\pi\)
\(192\) 0.0729490 0.224514i 0.00526464 0.0162029i
\(193\) 5.70820 0.410886 0.205443 0.978669i \(-0.434137\pi\)
0.205443 + 0.978669i \(0.434137\pi\)
\(194\) 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 \(0.787594\pi\)
\(198\) 0.763932 + 0.555029i 0.0542903 + 0.0394442i
\(199\) 2.56231 0.181637 0.0908185 0.995867i \(-0.471052\pi\)
0.0908185 + 0.995867i \(0.471052\pi\)
\(200\) 0 0
\(201\) 9.23607 0.651462
\(202\) −3.73607 2.71441i −0.262869 0.190985i
\(203\) −0.690983 2.12663i −0.0484975 0.149260i
\(204\) 0.381966 + 1.17557i 0.0267430 + 0.0823064i
\(205\) 0 0
\(206\) −2.20820 + 6.79615i −0.153853 + 0.473510i
\(207\) 16.4721 1.14489
\(208\) 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
\(213\) −3.54508 + 2.57565i −0.242905 + 0.176481i
\(214\) −5.20820 3.78398i −0.356025 0.258668i
\(215\) 0 0
\(216\) −9.04508 + 6.57164i −0.615440 + 0.447143i
\(217\) −1.50000 + 4.61653i −0.101827 + 0.313390i
\(218\) −6.18034 −0.418585
\(219\) −2.78115 + 8.55951i −0.187933 + 0.578398i
\(220\) 0 0
\(221\) 1.14590 + 3.52671i 0.0770814 + 0.237232i
\(222\) −0.809017 2.48990i −0.0542977 0.167111i
\(223\) 17.9443 + 13.0373i 1.20164 + 0.873041i 0.994445 0.105260i \(-0.0335673\pi\)
0.207193 + 0.978300i \(0.433567\pi\)
\(224\) −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 \(0.479608\pi\)
\(228\) −2.92705 9.00854i −0.193849 0.596605i
\(229\) 2.56231 + 7.88597i 0.169322 + 0.521119i 0.999329 0.0366339i \(-0.0116635\pi\)
−0.830007 + 0.557753i \(0.811664\pi\)
\(230\) 0 0
\(231\) 0.381966 1.17557i 0.0251315 0.0773469i
\(232\) −3.09017 −0.202880
\(233\) −4.61803 + 14.2128i −0.302537 + 0.931115i 0.678047 + 0.735018i \(0.262826\pi\)
−0.980585 + 0.196096i \(0.937174\pi\)
\(234\) −4.85410 + 3.52671i −0.317323 + 0.230548i
\(235\) 0 0
\(236\) −5.42705 3.94298i −0.353271 0.256666i
\(237\) 2.50000 1.81636i 0.162392 0.117985i
\(238\) 0.618034 0.449028i 0.0400612 0.0291062i
\(239\) 23.8435 + 17.3233i 1.54231 + 1.12055i 0.948869 + 0.315669i \(0.102229\pi\)
0.593436 + 0.804881i \(0.297771\pi\)
\(240\) 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
\(243\) −16.0000 −1.02640
\(244\) 2.35410 7.24518i 0.150706 0.463825i
\(245\) 0 0
\(246\) −1.00000 3.07768i −0.0637577 0.196226i
\(247\) −8.78115 27.0256i −0.558731 1.71960i
\(248\) 5.42705 + 3.94298i 0.344618 + 0.250380i
\(249\) −1.76393 −0.111785
\(250\) 0 0
\(251\) −6.81966 −0.430453 −0.215227 0.976564i \(-0.569049\pi\)
−0.215227 + 0.976564i \(0.569049\pi\)
\(252\) −4.23607 3.07768i −0.266847 0.193876i
\(253\) 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 \(0.667983\pi\)
\(258\) −0.354102 + 1.08981i −0.0220454 + 0.0678488i
\(259\) 5.54508 4.02874i 0.344555 0.250334i
\(260\) 0 0
\(261\) −2.23607 1.62460i −0.138409 0.100560i
\(262\) −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 \(0.538485\pi\)
\(264\) −1.38197 1.00406i −0.0850541 0.0617954i
\(265\) 0 0
\(266\) −4.73607 + 3.44095i −0.290387 + 0.210978i
\(267\) −2.76393 + 8.50651i −0.169150 + 0.520590i
\(268\) 14.9443 0.912867
\(269\) −5.32624 + 16.3925i −0.324746 + 0.999467i 0.646808 + 0.762652i \(0.276103\pi\)
−0.971555 + 0.236814i \(0.923897\pi\)
\(270\) 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
\(273\) 6.35410 + 4.61653i 0.384568 + 0.279405i
\(274\) 3.67376 0.221940
\(275\) 0 0
\(276\) −13.3262 −0.802145
\(277\) −9.13525 6.63715i −0.548884 0.398788i 0.278490 0.960439i \(-0.410166\pi\)
−0.827374 + 0.561651i \(0.810166\pi\)
\(278\) −0.954915 2.93893i −0.0572720 0.176265i
\(279\) 1.85410 + 5.70634i 0.111002 + 0.341630i
\(280\) 0 0
\(281\) −0.336881 + 1.03681i −0.0200966 + 0.0618511i −0.960602 0.277928i \(-0.910352\pi\)
0.940505 + 0.339779i \(0.110352\pi\)
\(282\) 1.00000 0.0595491
\(283\) 7.15248 22.0131i 0.425171 1.30854i −0.477660 0.878545i \(-0.658515\pi\)
0.902831 0.429996i \(-0.141485\pi\)
\(284\) −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
\(288\) −9.09017 + 6.60440i −0.535643 + 0.389168i
\(289\) 13.2812 + 9.64932i 0.781244 + 0.567607i
\(290\) 0 0
\(291\) −2.30902 + 1.67760i −0.135357 + 0.0983426i
\(292\) −4.50000 + 13.8496i −0.263343 + 0.810485i
\(293\) 28.4721 1.66336 0.831680 0.555255i \(-0.187379\pi\)
0.831680 + 0.555255i \(0.187379\pi\)
\(294\) −0.836881 + 2.57565i −0.0488079 + 0.150215i
\(295\) 0 0
\(296\) −2.92705 9.00854i −0.170131 0.523611i
\(297\) −1.18034 3.63271i −0.0684903 0.210791i
\(298\) 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
\(303\) 2.30902 + 7.10642i 0.132650 + 0.408253i
\(304\) −3.35410 10.3229i −0.192371 0.592057i
\(305\) 0 0
\(306\) 0.291796 0.898056i 0.0166809 0.0513384i
\(307\) −4.76393 −0.271892 −0.135946 0.990716i \(-0.543407\pi\)
−0.135946 + 0.990716i \(0.543407\pi\)
\(308\) 0.618034 1.90211i 0.0352158 0.108383i
\(309\) 9.35410 6.79615i 0.532136 0.386620i
\(310\) 0 0
\(311\) 23.8713 + 17.3435i 1.35362 + 0.983461i 0.998822 + 0.0485178i \(0.0154498\pi\)
0.354796 + 0.934944i \(0.384550\pi\)
\(312\) 8.78115 6.37988i 0.497135 0.361190i
\(313\) −17.1803 + 12.4822i −0.971090 + 0.705538i −0.955700 0.294343i \(-0.904899\pi\)
−0.0153904 + 0.999882i \(0.504899\pi\)
\(314\) 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 \(-0.131239\pi\)
\(318\) −3.38197 −0.189651
\(319\) 0.326238 1.00406i 0.0182658 0.0562164i
\(320\) 0 0
\(321\) 3.21885 + 9.90659i 0.179659 + 0.552932i
\(322\) 2.54508 + 7.83297i 0.141832 + 0.436514i
\(323\) 3.61803 + 2.62866i 0.201313 + 0.146262i
\(324\) −1.61803 −0.0898908
\(325\) 0 0
\(326\) 6.79837 0.376527
\(327\) 8.09017 + 5.87785i 0.447387 + 0.325046i
\(328\) −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
\(333\) 2.61803 8.05748i 0.143467 0.441547i
\(334\) 2.78115 2.02063i 0.152178 0.110564i
\(335\) 0 0
\(336\) 2.42705 + 1.76336i 0.132406 + 0.0961989i
\(337\) 0.927051 0.673542i 0.0504997 0.0366902i −0.562249 0.826968i \(-0.690064\pi\)
0.612749 + 0.790278i \(0.290064\pi\)
\(338\) 5.28115 3.83698i 0.287257 0.208704i
\(339\) −8.20820 5.96361i −0.445808 0.323899i
\(340\) 0 0
\(341\) −1.85410 + 1.34708i −0.100405 + 0.0729487i
\(342\) −2.23607 + 6.88191i −0.120913 + 0.372131i
\(343\) −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 \(0.585754\pi\)
\(348\) 1.80902 + 1.31433i 0.0969735 + 0.0704554i
\(349\) 8.29180 0.443850 0.221925 0.975064i \(-0.428766\pi\)
0.221925 + 0.975064i \(0.428766\pi\)
\(350\) 0 0
\(351\) 24.2705 1.29546
\(352\) −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 \(-0.321520\pi\)
\(354\) −0.791796 2.43690i −0.0420835 0.129520i
\(355\) 0 0
\(356\) −4.47214 + 13.7638i −0.237023 + 0.729481i
\(357\) −1.23607 −0.0654197
\(358\) 1.80902 5.56758i 0.0956095 0.294256i
\(359\) 23.2533 16.8945i 1.22726 0.891658i 0.230580 0.973053i \(-0.425938\pi\)
0.996682 + 0.0813956i \(0.0259377\pi\)
\(360\) 0 0
\(361\) −12.3541 8.97578i −0.650216 0.472409i
\(362\) 6.85410 4.97980i 0.360244 0.261732i
\(363\) −8.42705 + 6.12261i −0.442305 + 0.321354i
\(364\) 10.2812 + 7.46969i 0.538879 + 0.391518i
\(365\) 0 0
\(366\) 2.35410 1.71036i 0.123051 0.0894017i
\(367\) 1.68034 5.17155i 0.0877130 0.269953i −0.897573 0.440866i \(-0.854672\pi\)
0.985286 + 0.170913i \(0.0546716\pi\)
\(368\) −15.2705 −0.796030
\(369\) 3.23607 9.95959i 0.168463 0.518476i
\(370\) 0 0
\(371\) −2.73607 8.42075i −0.142050 0.437184i
\(372\) −1.50000 4.61653i −0.0777714 0.239356i
\(373\) 4.26393 + 3.09793i 0.220778 + 0.160405i 0.692677 0.721248i \(-0.256431\pi\)
−0.471899 + 0.881653i \(0.656431\pi\)
\(374\) 0.360680 0.0186503
\(375\) 0 0
\(376\) 3.61803 0.186586
\(377\) 5.42705 + 3.94298i 0.279507 + 0.203074i
\(378\) −1.54508 4.75528i −0.0794706 0.244585i
\(379\) −10.6910 32.9035i −0.549159 1.69014i −0.710891 0.703303i \(-0.751708\pi\)
0.161732 0.986835i \(-0.448292\pi\)
\(380\) 0 0
\(381\) −4.90983 + 15.1109i −0.251538 + 0.774155i
\(382\) 14.9443 0.764615
\(383\) 3.51064 10.8046i 0.179385 0.552092i −0.820421 0.571760i \(-0.806261\pi\)
0.999807 + 0.0196680i \(0.00626093\pi\)
\(384\) 9.20820 6.69015i 0.469904 0.341405i
\(385\) 0 0
\(386\) 2.85410 + 2.07363i 0.145270 + 0.105545i
\(387\) −3.00000 + 2.17963i −0.152499 + 0.110797i
\(388\) −3.73607 + 2.71441i −0.189670 + 0.137803i
\(389\) −12.1353 8.81678i −0.615282 0.447028i 0.235988 0.971756i \(-0.424167\pi\)
−0.851270 + 0.524727i \(0.824167\pi\)
\(390\) 0 0
\(391\) 5.09017 3.69822i 0.257421 0.187027i
\(392\) −3.02786 + 9.31881i −0.152930 + 0.470671i
\(393\) 17.7984 0.897809
\(394\) −1.85410 + 5.70634i −0.0934083 + 0.287481i
\(395\) 0 0
\(396\) −0.763932 2.35114i −0.0383890 0.118149i
\(397\) 0.0106431 + 0.0327561i 0.000534163 + 0.00164398i 0.951323 0.308195i \(-0.0997249\pi\)
−0.950789 + 0.309839i \(0.899725\pi\)
\(398\) 1.28115 + 0.930812i 0.0642184 + 0.0466574i
\(399\) 9.47214 0.474200
\(400\) 0 0
\(401\) −22.5967 −1.12843 −0.564214 0.825629i \(-0.690821\pi\)
−0.564214 + 0.825629i \(0.690821\pi\)
\(402\) 4.61803 + 3.35520i 0.230327 + 0.167342i
\(403\) −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
\(408\) −0.527864 + 1.62460i −0.0261332 + 0.0804296i
\(409\) −22.9894 + 16.7027i −1.13675 + 0.825898i −0.986663 0.162775i \(-0.947955\pi\)
−0.150087 + 0.988673i \(0.547955\pi\)
\(410\) 0 0
\(411\) −4.80902 3.49396i −0.237211 0.172344i
\(412\) 15.1353 10.9964i 0.745660 0.541754i
\(413\) 5.42705 3.94298i 0.267048 0.194022i
\(414\) 8.23607 + 5.98385i 0.404781 + 0.294090i
\(415\) 0 0
\(416\) 22.0623 16.0292i 1.08169 0.785896i
\(417\) −1.54508 + 4.75528i −0.0756631 + 0.232867i
\(418\) −2.76393 −0.135188
\(419\) −0.163119 + 0.502029i −0.00796888 + 0.0245257i −0.954962 0.296728i \(-0.904104\pi\)
0.946993 + 0.321254i \(0.104104\pi\)
\(420\) 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
\(423\) 2.61803 + 1.90211i 0.127293 + 0.0924839i
\(424\) −12.2361 −0.594236
\(425\) 0 0
\(426\) −2.70820 −0.131213
\(427\) 6.16312 + 4.47777i 0.298254 + 0.216694i
\(428\) 5.20820 + 16.0292i 0.251748 + 0.774801i
\(429\) 1.14590 + 3.52671i 0.0553245 + 0.170271i
\(430\) 0 0
\(431\) 7.36475 22.6664i 0.354747 1.09180i −0.601409 0.798942i \(-0.705394\pi\)
0.956156 0.292858i \(-0.0946064\pi\)
\(432\) 9.27051 0.446028
\(433\) −6.22542 + 19.1599i −0.299175 + 0.920765i 0.682612 + 0.730781i \(0.260844\pi\)
−0.981787 + 0.189985i \(0.939156\pi\)
\(434\) −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
\(438\) −4.50000 + 3.26944i −0.215018 + 0.156220i
\(439\) −4.83688 3.51420i −0.230852 0.167724i 0.466346 0.884602i \(-0.345570\pi\)
−0.697198 + 0.716879i \(0.745570\pi\)
\(440\) 0 0
\(441\) −7.09017 + 5.15131i −0.337627 + 0.245300i
\(442\) −0.708204 + 2.17963i −0.0336858 + 0.103674i
\(443\) −12.0557 −0.572785 −0.286392 0.958112i \(-0.592456\pi\)
−0.286392 + 0.958112i \(0.592456\pi\)
\(444\) −2.11803 + 6.51864i −0.100517 + 0.309361i
\(445\) 0 0
\(446\) 4.23607 + 13.0373i 0.200584 + 0.617333i
\(447\) −4.30902 13.2618i −0.203810 0.627261i
\(448\) 0.309017 + 0.224514i 0.0145997 + 0.0106073i
\(449\) 20.3262 0.959254 0.479627 0.877472i \(-0.340772\pi\)
0.479627 + 0.877472i \(0.340772\pi\)
\(450\) 0 0
\(451\) 4.00000 0.188353
\(452\) −13.2812 9.64932i −0.624693 0.453866i
\(453\) 1.71885 + 5.29007i 0.0807585 + 0.248549i
\(454\) 3.67376 + 11.3067i 0.172418 + 0.530649i
\(455\) 0 0
\(456\) 4.04508 12.4495i 0.189428 0.583001i
\(457\) −5.41641 −0.253369 −0.126684 0.991943i \(-0.540434\pi\)
−0.126684 + 0.991943i \(0.540434\pi\)
\(458\) −1.58359 + 4.87380i −0.0739964 + 0.227738i
\(459\) −3.09017 + 2.24514i −0.144237 + 0.104794i
\(460\) 0 0
\(461\) −18.7533 13.6251i −0.873428 0.634582i 0.0580768 0.998312i \(-0.481503\pi\)
−0.931505 + 0.363730i \(0.881503\pi\)
\(462\) 0.618034 0.449028i 0.0287535 0.0208907i
\(463\) 13.0451 9.47781i 0.606257 0.440471i −0.241838 0.970317i \(-0.577750\pi\)
0.848094 + 0.529846i \(0.177750\pi\)
\(464\) 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 \(-0.128713\pi\)
\(468\) 15.7082 0.726112
\(469\) −4.61803 + 14.2128i −0.213241 + 0.656288i
\(470\) 0 0
\(471\) −2.83688 8.73102i −0.130717 0.402304i
\(472\) −2.86475 8.81678i −0.131861 0.405825i
\(473\) −1.14590 0.832544i −0.0526884 0.0382804i
\(474\) 1.90983 0.0877214
\(475\) 0 0
\(476\) −2.00000 −0.0916698
\(477\) −8.85410 6.43288i −0.405401 0.294541i
\(478\) 5.62868 + 17.3233i 0.257450 + 0.792349i
\(479\) −1.28115 3.94298i −0.0585374 0.180160i 0.917512 0.397708i \(-0.130194\pi\)
−0.976050 + 0.217548i \(0.930194\pi\)
\(480\) 0 0
\(481\) −6.35410 + 19.5559i −0.289722 + 0.891673i
\(482\) −7.09017 −0.322948
\(483\) 4.11803 12.6740i 0.187377 0.576687i
\(484\) −13.6353 + 9.90659i −0.619784 + 0.450300i
\(485\) 0 0
\(486\) −8.00000 5.81234i −0.362887 0.263653i
\(487\) −7.75329 + 5.63309i −0.351335 + 0.255260i −0.749429 0.662085i \(-0.769672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(488\) 8.51722 6.18812i 0.385556 0.280123i
\(489\) −8.89919 6.46564i −0.402435 0.292386i
\(490\) 0 0
\(491\) −30.1353 + 21.8945i −1.35999 + 0.988087i −0.361539 + 0.932357i \(0.617749\pi\)
−0.998446 + 0.0557300i \(0.982251\pi\)
\(492\) −2.61803 + 8.05748i −0.118030 + 0.363259i
\(493\) −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
\(498\) −0.881966 0.640786i −0.0395218 0.0287143i
\(499\) −12.5623 −0.562366 −0.281183 0.959654i \(-0.590727\pi\)
−0.281183 + 0.959654i \(0.590727\pi\)
\(500\) 0 0
\(501\) −5.56231 −0.248506
\(502\) −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 \(0.824180\pi\)
\(504\) −2.23607 6.88191i −0.0996024 0.306545i
\(505\) 0 0
\(506\) −1.20163 + 3.69822i −0.0534188 + 0.164406i
\(507\) −10.5623 −0.469088
\(508\) −7.94427 + 24.4500i −0.352470 + 1.08479i
\(509\) 3.78115 2.74717i 0.167597 0.121766i −0.500825 0.865548i \(-0.666970\pi\)
0.668422 + 0.743782i \(0.266970\pi\)
\(510\) 0 0
\(511\) −11.7812 8.55951i −0.521168 0.378650i
\(512\) 15.1353 10.9964i 0.668890 0.485977i
\(513\) 23.6803 17.2048i 1.04551 0.759609i
\(514\) −8.07295 5.86534i −0.356083 0.258709i
\(515\) 0 0
\(516\) 2.42705 1.76336i 0.106845 0.0776274i
\(517\) −0.381966 + 1.17557i −0.0167988 + 0.0517015i
\(518\) 4.23607 0.186122
\(519\) −5.21885 + 16.0620i −0.229082 + 0.705042i
\(520\) 0 0
\(521\) −4.74671 14.6089i −0.207957 0.640026i −0.999579 0.0290150i \(-0.990763\pi\)
0.791622 0.611011i \(-0.209237\pi\)
\(522\) −0.527864 1.62460i −0.0231040 0.0711067i
\(523\) −16.0623 11.6699i −0.702356 0.510291i 0.178343 0.983968i \(-0.442926\pi\)
−0.880699 + 0.473677i \(0.842926\pi\)
\(524\) 28.7984 1.25806
\(525\) 0 0
\(526\) −13.6525 −0.595276
\(527\) 1.85410 + 1.34708i 0.0807660 + 0.0586799i
\(528\) 0.437694 + 1.34708i 0.0190482 + 0.0586243i
\(529\) 13.8541 + 42.6385i 0.602352 + 1.85385i
\(530\) 0 0
\(531\) 2.56231 7.88597i 0.111195 0.342222i
\(532\) 15.3262 0.664477
\(533\) −7.85410 + 24.1724i −0.340199 + 1.04702i
\(534\) −4.47214 + 3.24920i −0.193528 + 0.140607i
\(535\) 0 0
\(536\) 16.7082 + 12.1392i 0.721684 + 0.524334i
\(537\) −7.66312 + 5.56758i −0.330688 + 0.240259i
\(538\) −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
\(543\) −13.7082 −0.588275
\(544\) −1.32624 + 4.08174i −0.0568620 + 0.175003i
\(545\) 0 0
\(546\) 1.50000 + 4.61653i 0.0641941 + 0.197569i
\(547\) 10.7254 + 33.0095i 0.458586 + 1.41138i 0.866873 + 0.498529i \(0.166126\pi\)
−0.408287 + 0.912854i \(0.633874\pi\)
\(548\) −7.78115 5.65334i −0.332394 0.241499i
\(549\) 9.41641 0.401882
\(550\) 0 0
\(551\) 8.09017 0.344653
\(552\) −14.8992 10.8249i −0.634152 0.460738i
\(553\) 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 \(0.562689\pi\)
\(558\) −1.14590 + 3.52671i −0.0485097 + 0.149298i
\(559\) 7.28115 5.29007i 0.307960 0.223746i
\(560\) 0 0
\(561\) −0.472136 0.343027i −0.0199336 0.0144826i
\(562\) −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 \(0.235036\pi\)
\(564\) −2.11803 1.53884i −0.0891853 0.0647969i
\(565\) 0 0
\(566\) 11.5729 8.40824i 0.486447 0.353425i
\(567\) 0.500000 1.53884i 0.0209980 0.0646253i
\(568\) −9.79837 −0.411131
\(569\) 9.10739 28.0297i 0.381802 1.17506i −0.556972 0.830531i \(-0.688037\pi\)
0.938774 0.344534i \(-0.111963\pi\)
\(570\) 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
\(573\) −19.5623 14.2128i −0.817227 0.593750i
\(574\) 5.23607 0.218549
\(575\) 0 0
\(576\) 0.472136 0.0196723
\(577\) 30.5623 + 22.2048i 1.27233 + 0.924399i 0.999293 0.0376062i \(-0.0119732\pi\)
0.273033 + 0.962005i \(0.411973\pi\)
\(578\) 3.13525 + 9.64932i 0.130409 + 0.401359i
\(579\) −1.76393 5.42882i −0.0733065 0.225614i
\(580\) 0 0
\(581\) 0.881966 2.71441i 0.0365901 0.112613i
\(582\) −1.76393 −0.0731173
\(583\) 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 \(0.173827\pi\)
\(588\) 5.73607 4.16750i 0.236551 0.171865i
\(589\) −14.2082 10.3229i −0.585439 0.425346i
\(590\) 0 0
\(591\) 7.85410 5.70634i 0.323075 0.234727i
\(592\) −2.42705 + 7.46969i −0.0997512 + 0.307003i
\(593\) 22.0902 0.907135 0.453567 0.891222i \(-0.350151\pi\)
0.453567 + 0.891222i \(0.350151\pi\)
\(594\) 0.729490 2.24514i 0.0299313 0.0921192i
\(595\) 0 0
\(596\) −6.97214 21.4580i −0.285590 0.878955i
\(597\) −0.791796 2.43690i −0.0324061 0.0997356i
\(598\) −19.9894 14.5231i −0.817426 0.593894i
\(599\) −0.527864 −0.0215679 −0.0107840 0.999942i \(-0.503433\pi\)
−0.0107840 + 0.999942i \(0.503433\pi\)
\(600\) 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
\(603\) 5.70820 + 17.5680i 0.232456 + 0.715426i
\(604\) 2.78115 + 8.55951i 0.113164 + 0.348281i
\(605\) 0 0
\(606\) −1.42705 + 4.39201i −0.0579700 + 0.178413i
\(607\) 15.4377 0.626597 0.313298 0.949655i \(-0.398566\pi\)
0.313298 + 0.949655i \(0.398566\pi\)
\(608\) 10.1631 31.2789i 0.412169 1.26853i
\(609\) −1.80902 + 1.31433i −0.0733051 + 0.0532592i
\(610\) 0 0
\(611\) −6.35410 4.61653i −0.257059 0.186765i
\(612\) −2.00000 + 1.45309i −0.0808452 + 0.0587375i
\(613\) 25.8713 18.7966i 1.04493 0.759188i 0.0736905 0.997281i \(-0.476522\pi\)
0.971242 + 0.238093i \(0.0765223\pi\)
\(614\) −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 \(0.162971\pi\)
\(618\) 7.14590 0.287450
\(619\) 12.1976 37.5402i 0.490261 1.50887i −0.333952 0.942590i \(-0.608382\pi\)
0.824213 0.566279i \(-0.191618\pi\)
\(620\) 0 0
\(621\) −12.7254 39.1648i −0.510654 1.57163i
\(622\) 5.63525 + 17.3435i 0.225953 + 0.695412i
\(623\) −11.7082 8.50651i −0.469079 0.340806i
\(624\) −9.00000 −0.360288
\(625\) 0 0
\(626\) −13.1246 −0.524565
\(627\) 3.61803 + 2.62866i 0.144490 + 0.104978i
\(628\) −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
\(633\) −4.07295 + 12.5352i −0.161885 + 0.498231i
\(634\) 11.8262 8.59226i 0.469680 0.341242i
\(635\) 0 0
\(636\) 7.16312 + 5.20431i 0.284036 + 0.206364i
\(637\) 17.2082 12.5025i 0.681814 0.495367i
\(638\) 0.527864 0.383516i 0.0208983 0.0151835i
\(639\) −7.09017 5.15131i −0.280483 0.203783i
\(640\) 0 0
\(641\) −8.16312 + 5.93085i −0.322424 + 0.234255i −0.737209 0.675665i \(-0.763857\pi\)
0.414785 + 0.909919i \(0.363857\pi\)
\(642\) −1.98936 + 6.12261i −0.0785137 + 0.241640i
\(643\) −22.8328 −0.900438 −0.450219 0.892918i \(-0.648654\pi\)
−0.450219 + 0.892918i \(0.648654\pi\)
\(644\) 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 \(-0.304970\pi\)
\(648\) −1.80902 1.31433i −0.0710649 0.0516317i
\(649\) 3.16718 0.124323
\(650\) 0 0
\(651\) 4.85410 0.190247
\(652\) −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 \(0.949463\pi\)
\(654\) 1.90983 + 5.87785i 0.0746803 + 0.229842i
\(655\) 0 0
\(656\) −3.00000 + 9.23305i −0.117130 + 0.360490i
\(657\) −18.0000 −0.702247
\(658\) −0.500000 + 1.53884i −0.0194920 + 0.0599903i
\(659\) −19.7984 + 14.3844i −0.771235 + 0.560335i −0.902336 0.431034i \(-0.858149\pi\)
0.131101 + 0.991369i \(0.458149\pi\)
\(660\) 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
\(663\) 3.00000 2.17963i 0.116510 0.0846497i
\(664\) −3.19098 2.31838i −0.123834 0.0899708i
\(665\) 0 0
\(666\) 4.23607 3.07768i 0.164144 0.119258i
\(667\) 3.51722 10.8249i 0.136187 0.419142i
\(668\) −9.00000 −0.348220
\(669\) 6.85410 21.0948i 0.264995 0.815570i
\(670\) 0 0
\(671\) 1.11146 + 3.42071i 0.0429073 + 0.132055i
\(672\) 2.80902 + 8.64527i 0.108360 + 0.333498i
\(673\) −8.23607 5.98385i −0.317477 0.230661i 0.417621 0.908621i \(-0.362864\pi\)
−0.735098 + 0.677961i \(0.762864\pi\)
\(674\) 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 \(0.648505\pi\)
\(678\) −1.93769 5.96361i −0.0744167 0.229031i
\(679\) −1.42705 4.39201i −0.0547652 0.168550i
\(680\) 0 0
\(681\) 5.94427 18.2946i 0.227785 0.701050i
\(682\) −1.41641 −0.0542371
\(683\) 1.39919 4.30625i 0.0535384 0.164774i −0.920712 0.390242i \(-0.872391\pi\)
0.974251 + 0.225468i \(0.0723912\pi\)
\(684\) 15.3262 11.1352i 0.586013 0.425764i
\(685\) 0 0
\(686\) −9.20820 6.69015i −0.351571 0.255431i
\(687\) 6.70820 4.87380i 0.255934 0.185947i
\(688\) 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
\(693\) 2.47214 0.0939087
\(694\) −5.93769 + 18.2743i −0.225392 + 0.693685i
\(695\) 0 0
\(696\) 0.954915 + 2.93893i 0.0361960 + 0.111400i
\(697\) −1.23607 3.80423i −0.0468194 0.144095i
\(698\) 4.14590 + 3.01217i 0.156925 + 0.114012i
\(699\) 14.9443 0.565244
\(700\) 0 0
\(701\) 35.0132 1.32243 0.661214 0.750197i \(-0.270041\pi\)
0.661214 + 0.750197i \(0.270041\pi\)
\(702\) 12.1353 + 8.81678i 0.458016 + 0.332768i
\(703\) 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
\(708\) −2.07295 + 6.37988i −0.0779062 + 0.239771i
\(709\) −27.1353 + 19.7149i −1.01909 + 0.740409i −0.966095 0.258186i \(-0.916875\pi\)
−0.0529906 + 0.998595i \(0.516875\pi\)
\(710\) 0 0
\(711\) 5.00000 + 3.63271i 0.187515 + 0.136237i
\(712\) −16.1803 + 11.7557i −0.606384 + 0.440564i
\(713\) −19.9894 + 14.5231i −0.748607 + 0.543895i
\(714\) −0.618034 0.449028i −0.0231293 0.0168044i
\(715\) 0 0
\(716\) −12.3992 + 9.00854i −0.463379 + 0.336665i
\(717\) 9.10739 28.0297i 0.340122 1.04679i
\(718\) 17.7639 0.662944
\(719\) −11.3435 + 34.9116i −0.423040 + 1.30198i 0.481819 + 0.876271i \(0.339976\pi\)
−0.904859 + 0.425712i \(0.860024\pi\)
\(720\) 0 0
\(721\) 5.78115 + 17.7926i 0.215301 + 0.662630i
\(722\) −2.91641 8.97578i −0.108537 0.334044i
\(723\) 9.28115 + 6.74315i 0.345170 + 0.250781i
\(724\) −22.1803 −0.824326
\(725\) 0 0
\(726\) −6.43769 −0.238925
\(727\) 3.59017 + 2.60841i 0.133152 + 0.0967406i 0.652368 0.757903i \(-0.273776\pi\)
−0.519216 + 0.854643i \(0.673776\pi\)
\(728\) 5.42705 + 16.7027i 0.201140 + 0.619045i
\(729\) 4.01722 + 12.3637i 0.148786 + 0.457916i
\(730\) 0 0
\(731\) −0.437694 + 1.34708i −0.0161887 + 0.0498237i
\(732\) −7.61803 −0.281571
\(733\) −8.33688 + 25.6583i −0.307930 + 0.947710i 0.670638 + 0.741785i \(0.266020\pi\)
−0.978568 + 0.205925i \(0.933980\pi\)
\(734\) 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
\(738\) 5.23607 3.80423i 0.192742 0.140035i
\(739\) 25.0623 + 18.2088i 0.921932 + 0.669823i 0.944004 0.329934i \(-0.107026\pi\)
−0.0220723 + 0.999756i \(0.507026\pi\)
\(740\) 0 0
\(741\) −22.9894 + 16.7027i −0.844535 + 0.613591i
\(742\) 1.69098 5.20431i 0.0620779 0.191056i
\(743\) 16.3607 0.600215 0.300108 0.953905i \(-0.402977\pi\)
0.300108 + 0.953905i \(0.402977\pi\)
\(744\) 2.07295 6.37988i 0.0759980 0.233898i
\(745\) 0 0
\(746\) 1.00658 + 3.09793i 0.0368534 + 0.113423i
\(747\) −1.09017 3.35520i −0.0398872 0.122760i
\(748\) −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
\(753\) 2.10739 + 6.48588i 0.0767976 + 0.236359i
\(754\) 1.28115 + 3.94298i 0.0466568 + 0.143595i
\(755\) 0 0
\(756\) −4.04508 + 12.4495i −0.147118 + 0.452784i
\(757\) −3.58359 −0.130248 −0.0651239 0.997877i \(-0.520744\pi\)
−0.0651239 + 0.997877i \(0.520744\pi\)
\(758\) 6.60739 20.3355i 0.239991 0.738617i
\(759\) 5.09017 3.69822i 0.184761 0.134237i
\(760\) 0 0
\(761\) −30.2984 22.0131i −1.09832 0.797973i −0.117531 0.993069i \(-0.537498\pi\)
−0.980784 + 0.195096i \(0.937498\pi\)
\(762\) −7.94427 + 5.77185i −0.287791 + 0.209092i
\(763\) −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
\(768\) 6.56231 0.236797
\(769\) −4.14590 + 12.7598i −0.149505 + 0.460129i −0.997563 0.0697749i \(-0.977772\pi\)
0.848058 + 0.529904i \(0.177772\pi\)
\(770\) 0 0
\(771\) 4.98936 + 15.3557i 0.179687 + 0.553021i
\(772\) −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 \(0.496627\pi\)
\(774\) −2.29180 −0.0823769
\(775\) 0 0
\(776\) −6.38197 −0.229099
\(777\) −5.54508 4.02874i −0.198929 0.144530i
\(778\) −2.86475 8.81678i −0.102706 0.316097i
\(779\) 9.47214 + 29.1522i 0.339374 + 1.04449i
\(780\) 0 0