Properties

Label 325.2.e.e.126.1
Level $325$
Weight $2$
Character 325.126
Analytic conductor $2.595$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 325 = 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 325.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.59513806569\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
Defining polynomial: \(x^{12} + 8 x^{10} + 54 x^{8} + 78 x^{6} + 92 x^{4} + 10 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 126.1
Root \(-1.27287 - 2.20467i\) of defining polynomial
Character \(\chi\) \(=\) 325.126
Dual form 325.2.e.e.276.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +O(q^{10})\) \(q+(-1.27287 + 2.20467i) q^{2} +(-1.07646 + 1.86449i) q^{3} +(-2.24039 - 3.88048i) q^{4} +(-2.74039 - 4.74650i) q^{6} +(-1.46928 - 2.54486i) q^{7} +6.31544 q^{8} +(-0.817544 - 1.41603i) q^{9} +(0.317544 - 0.550003i) q^{11} +9.64680 q^{12} +(-0.0716710 - 3.60484i) q^{13} +7.48079 q^{14} +(-3.55794 + 6.16253i) q^{16} +(-0.611979 - 1.05998i) q^{17} +4.16251 q^{18} +(-0.682456 - 1.18205i) q^{19} +6.32648 q^{21} +(0.808385 + 1.40016i) q^{22} +(1.07646 - 1.86449i) q^{23} +(-6.79833 + 11.7751i) q^{24} +(8.03872 + 4.43048i) q^{26} -2.93855 q^{27} +(-6.58351 + 11.4030i) q^{28} +(-1.50000 + 2.59808i) q^{29} -8.96157 q^{31} +(-2.74215 - 4.74954i) q^{32} +(0.683650 + 1.18412i) q^{33} +3.11588 q^{34} +(-3.66324 + 6.34492i) q^{36} +(0.611979 - 1.05998i) q^{37} +3.47471 q^{38} +(6.79833 + 3.74685i) q^{39} +(4.98079 - 8.62698i) q^{41} +(-8.05279 + 13.9478i) q^{42} +(-0.683650 - 1.18412i) q^{43} -2.84570 q^{44} +(2.74039 + 4.74650i) q^{46} +6.16379 q^{47} +(-7.65998 - 13.2675i) q^{48} +(-0.817544 + 1.41603i) q^{49} +2.63509 q^{51} +(-13.8279 + 8.35437i) q^{52} -0.642285 q^{53} +(3.74039 - 6.47855i) q^{54} +(-9.27912 - 16.0719i) q^{56} +2.93855 q^{57} +(-3.81861 - 6.61402i) q^{58} +(-3.79833 - 6.57890i) q^{59} +(1.13509 + 1.96603i) q^{61} +(11.4069 - 19.7574i) q^{62} +(-2.40240 + 4.16107i) q^{63} -0.270178 q^{64} -3.48079 q^{66} +(4.01502 - 6.95421i) q^{67} +(-2.74215 + 4.74954i) q^{68} +(2.31754 + 4.01410i) q^{69} +(-1.31754 - 2.28205i) q^{71} +(-5.16315 - 8.94284i) q^{72} +10.3263 q^{73} +(1.55794 + 2.69843i) q^{74} +(-3.05794 + 5.29650i) q^{76} -1.86624 q^{77} +(-16.9140 + 10.2189i) q^{78} +1.03843 q^{79} +(5.61588 - 9.72698i) q^{81} +(12.6798 + 21.9620i) q^{82} -11.8452 q^{83} +(-14.1738 - 24.5498i) q^{84} +3.48079 q^{86} +(-3.22939 - 5.59346i) q^{87} +(2.00543 - 3.47351i) q^{88} +(6.27912 - 10.8758i) q^{89} +(-9.06851 + 5.47890i) q^{91} -9.64680 q^{92} +(9.64680 - 16.7087i) q^{93} +(-7.84570 + 13.5891i) q^{94} +11.8073 q^{96} +(-7.39190 - 12.8031i) q^{97} +(-2.08125 - 3.60484i) q^{98} -1.03843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + O(q^{10}) \) \( 12 q - 4 q^{4} - 10 q^{6} - 6 q^{9} + 44 q^{14} - 16 q^{16} - 12 q^{19} - 8 q^{21} - 32 q^{24} + 24 q^{26} - 18 q^{29} - 16 q^{31} - 16 q^{34} - 2 q^{36} + 32 q^{39} + 14 q^{41} + 4 q^{44} + 10 q^{46} - 6 q^{49} + 24 q^{51} + 22 q^{54} - 16 q^{56} + 4 q^{59} + 6 q^{61} + 12 q^{64} + 4 q^{66} + 24 q^{69} - 12 q^{71} - 8 q^{74} - 10 q^{76} + 104 q^{79} + 14 q^{81} - 90 q^{84} - 4 q^{86} - 20 q^{89} - 44 q^{91} - 56 q^{94} + 12 q^{96} - 104 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

\(n\) \(27\) \(301\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.27287 + 2.20467i −0.900055 + 1.55894i −0.0726333 + 0.997359i \(0.523140\pi\)
−0.827421 + 0.561582i \(0.810193\pi\)
\(3\) −1.07646 + 1.86449i −0.621496 + 1.07646i 0.367711 + 0.929940i \(0.380142\pi\)
−0.989207 + 0.146523i \(0.953192\pi\)
\(4\) −2.24039 3.88048i −1.12020 1.94024i
\(5\) 0 0
\(6\) −2.74039 4.74650i −1.11876 1.93775i
\(7\) −1.46928 2.54486i −0.555334 0.961867i −0.997877 0.0651198i \(-0.979257\pi\)
0.442543 0.896747i \(-0.354076\pi\)
\(8\) 6.31544 2.23284
\(9\) −0.817544 1.41603i −0.272515 0.472010i
\(10\) 0 0
\(11\) 0.317544 0.550003i 0.0957433 0.165832i −0.814175 0.580619i \(-0.802811\pi\)
0.909919 + 0.414787i \(0.136144\pi\)
\(12\) 9.64680 2.78479
\(13\) −0.0716710 3.60484i −0.0198779 0.999802i
\(14\) 7.48079 1.99932
\(15\) 0 0
\(16\) −3.55794 + 6.16253i −0.889484 + 1.54063i
\(17\) −0.611979 1.05998i −0.148427 0.257082i 0.782220 0.623003i \(-0.214088\pi\)
−0.930646 + 0.365920i \(0.880754\pi\)
\(18\) 4.16251 0.981113
\(19\) −0.682456 1.18205i −0.156566 0.271180i 0.777062 0.629424i \(-0.216709\pi\)
−0.933628 + 0.358244i \(0.883376\pi\)
\(20\) 0 0
\(21\) 6.32648 1.38055
\(22\) 0.808385 + 1.40016i 0.172348 + 0.298516i
\(23\) 1.07646 1.86449i 0.224458 0.388773i −0.731699 0.681628i \(-0.761272\pi\)
0.956157 + 0.292856i \(0.0946055\pi\)
\(24\) −6.79833 + 11.7751i −1.38770 + 2.40357i
\(25\) 0 0
\(26\) 8.03872 + 4.43048i 1.57652 + 0.868888i
\(27\) −2.93855 −0.565525
\(28\) −6.58351 + 11.4030i −1.24417 + 2.15496i
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) 0 0
\(31\) −8.96157 −1.60955 −0.804773 0.593583i \(-0.797713\pi\)
−0.804773 + 0.593583i \(0.797713\pi\)
\(32\) −2.74215 4.74954i −0.484747 0.839607i
\(33\) 0.683650 + 1.18412i 0.119008 + 0.206128i
\(34\) 3.11588 0.534368
\(35\) 0 0
\(36\) −3.66324 + 6.34492i −0.610540 + 1.05749i
\(37\) 0.611979 1.05998i 0.100609 0.174259i −0.811327 0.584593i \(-0.801254\pi\)
0.911936 + 0.410333i \(0.134588\pi\)
\(38\) 3.47471 0.563672
\(39\) 6.79833 + 3.74685i 1.08860 + 0.599975i
\(40\) 0 0
\(41\) 4.98079 8.62698i 0.777868 1.34731i −0.155300 0.987867i \(-0.549634\pi\)
0.933168 0.359440i \(-0.117032\pi\)
\(42\) −8.05279 + 13.9478i −1.24257 + 2.15220i
\(43\) −0.683650 1.18412i −0.104256 0.180576i 0.809178 0.587563i \(-0.199913\pi\)
−0.913434 + 0.406987i \(0.866579\pi\)
\(44\) −2.84570 −0.429005
\(45\) 0 0
\(46\) 2.74039 + 4.74650i 0.404049 + 0.699833i
\(47\) 6.16379 0.899081 0.449540 0.893260i \(-0.351588\pi\)
0.449540 + 0.893260i \(0.351588\pi\)
\(48\) −7.65998 13.2675i −1.10562 1.91499i
\(49\) −0.817544 + 1.41603i −0.116792 + 0.202290i
\(50\) 0 0
\(51\) 2.63509 0.368986
\(52\) −13.8279 + 8.35437i −1.91759 + 1.15854i
\(53\) −0.642285 −0.0882246 −0.0441123 0.999027i \(-0.514046\pi\)
−0.0441123 + 0.999027i \(0.514046\pi\)
\(54\) 3.74039 6.47855i 0.509003 0.881619i
\(55\) 0 0
\(56\) −9.27912 16.0719i −1.23997 2.14770i
\(57\) 2.93855 0.389221
\(58\) −3.81861 6.61402i −0.501408 0.868464i
\(59\) −3.79833 6.57890i −0.494501 0.856500i 0.505479 0.862839i \(-0.331316\pi\)
−0.999980 + 0.00633858i \(0.997982\pi\)
\(60\) 0 0
\(61\) 1.13509 + 1.96603i 0.145333 + 0.251725i 0.929497 0.368829i \(-0.120241\pi\)
−0.784164 + 0.620554i \(0.786908\pi\)
\(62\) 11.4069 19.7574i 1.44868 2.50919i
\(63\) −2.40240 + 4.16107i −0.302674 + 0.524246i
\(64\) −0.270178 −0.0337722
\(65\) 0 0
\(66\) −3.48079 −0.428455
\(67\) 4.01502 6.95421i 0.490512 0.849592i −0.509428 0.860513i \(-0.670143\pi\)
0.999940 + 0.0109212i \(0.00347639\pi\)
\(68\) −2.74215 + 4.74954i −0.332534 + 0.575966i
\(69\) 2.31754 + 4.01410i 0.279000 + 0.483241i
\(70\) 0 0
\(71\) −1.31754 2.28205i −0.156364 0.270830i 0.777191 0.629265i \(-0.216644\pi\)
−0.933555 + 0.358435i \(0.883311\pi\)
\(72\) −5.16315 8.94284i −0.608483 1.05392i
\(73\) 10.3263 1.20860 0.604301 0.796756i \(-0.293453\pi\)
0.604301 + 0.796756i \(0.293453\pi\)
\(74\) 1.55794 + 2.69843i 0.181107 + 0.313686i
\(75\) 0 0
\(76\) −3.05794 + 5.29650i −0.350770 + 0.607551i
\(77\) −1.86624 −0.212678
\(78\) −16.9140 + 10.2189i −1.91513 + 1.15706i
\(79\) 1.03843 0.116832 0.0584161 0.998292i \(-0.481395\pi\)
0.0584161 + 0.998292i \(0.481395\pi\)
\(80\) 0 0
\(81\) 5.61588 9.72698i 0.623986 1.08078i
\(82\) 12.6798 + 21.9620i 1.40025 + 2.42530i
\(83\) −11.8452 −1.30018 −0.650092 0.759855i \(-0.725270\pi\)
−0.650092 + 0.759855i \(0.725270\pi\)
\(84\) −14.1738 24.5498i −1.54649 2.67860i
\(85\) 0 0
\(86\) 3.48079 0.375343
\(87\) −3.22939 5.59346i −0.346227 0.599682i
\(88\) 2.00543 3.47351i 0.213780 0.370277i
\(89\) 6.27912 10.8758i 0.665585 1.15283i −0.313541 0.949575i \(-0.601515\pi\)
0.979126 0.203253i \(-0.0651513\pi\)
\(90\) 0 0
\(91\) −9.06851 + 5.47890i −0.950638 + 0.574344i
\(92\) −9.64680 −1.00575
\(93\) 9.64680 16.7087i 1.00033 1.73262i
\(94\) −7.84570 + 13.5891i −0.809222 + 1.40161i
\(95\) 0 0
\(96\) 11.8073 1.20507
\(97\) −7.39190 12.8031i −0.750534 1.29996i −0.947564 0.319565i \(-0.896463\pi\)
0.197031 0.980397i \(-0.436870\pi\)
\(98\) −2.08125 3.60484i −0.210238 0.364144i
\(99\) −1.03843 −0.104366
\(100\) 0 0
\(101\) −6.61588 + 11.4590i −0.658304 + 1.14022i 0.322750 + 0.946484i \(0.395393\pi\)
−0.981054 + 0.193732i \(0.937941\pi\)
\(102\) −3.35412 + 5.80951i −0.332108 + 0.575228i
\(103\) −10.9686 −1.08077 −0.540383 0.841419i \(-0.681721\pi\)
−0.540383 + 0.841419i \(0.681721\pi\)
\(104\) −0.452633 22.7661i −0.0443843 2.23240i
\(105\) 0 0
\(106\) 0.817544 1.41603i 0.0794069 0.137537i
\(107\) −5.33680 + 9.24360i −0.515928 + 0.893613i 0.483901 + 0.875123i \(0.339219\pi\)
−0.999829 + 0.0184903i \(0.994114\pi\)
\(108\) 6.58351 + 11.4030i 0.633499 + 1.09725i
\(109\) −3.27018 −0.313226 −0.156613 0.987660i \(-0.550058\pi\)
−0.156613 + 0.987660i \(0.550058\pi\)
\(110\) 0 0
\(111\) 1.31754 + 2.28205i 0.125056 + 0.216603i
\(112\) 20.9104 1.97584
\(113\) −2.76490 4.78895i −0.260100 0.450507i 0.706168 0.708044i \(-0.250422\pi\)
−0.966268 + 0.257537i \(0.917089\pi\)
\(114\) −3.74039 + 6.47855i −0.350320 + 0.606772i
\(115\) 0 0
\(116\) 13.4424 1.24809
\(117\) −5.04596 + 3.04860i −0.466499 + 0.281844i
\(118\) 19.3391 1.78031
\(119\) −1.79833 + 3.11480i −0.164853 + 0.285533i
\(120\) 0 0
\(121\) 5.29833 + 9.17698i 0.481666 + 0.834271i
\(122\) −5.77928 −0.523231
\(123\) 10.7233 + 18.5732i 0.966884 + 1.67469i
\(124\) 20.0774 + 34.7752i 1.80301 + 3.12290i
\(125\) 0 0
\(126\) −6.11588 10.5930i −0.544845 0.943700i
\(127\) −8.61586 + 14.9231i −0.764534 + 1.32421i 0.175959 + 0.984397i \(0.443697\pi\)
−0.940493 + 0.339813i \(0.889636\pi\)
\(128\) 5.82819 10.0947i 0.515144 0.892256i
\(129\) 2.94369 0.259178
\(130\) 0 0
\(131\) 10.0000 0.873704 0.436852 0.899533i \(-0.356093\pi\)
0.436852 + 0.899533i \(0.356093\pi\)
\(132\) 3.06329 5.30577i 0.266625 0.461808i
\(133\) −2.00543 + 3.47351i −0.173893 + 0.301191i
\(134\) 10.2212 + 17.7036i 0.882975 + 1.52936i
\(135\) 0 0
\(136\) −3.86491 6.69422i −0.331413 0.574025i
\(137\) −4.33616 7.51044i −0.370463 0.641661i 0.619174 0.785254i \(-0.287468\pi\)
−0.989637 + 0.143593i \(0.954134\pi\)
\(138\) −11.7997 −1.00446
\(139\) −7.16324 12.4071i −0.607578 1.05236i −0.991638 0.129048i \(-0.958808\pi\)
0.384060 0.923308i \(-0.374526\pi\)
\(140\) 0 0
\(141\) −6.63509 + 11.4923i −0.558775 + 0.967827i
\(142\) 6.70825 0.562944
\(143\) −2.00543 1.10528i −0.167703 0.0924279i
\(144\) 11.6351 0.969591
\(145\) 0 0
\(146\) −13.1440 + 22.7661i −1.08781 + 1.88414i
\(147\) −1.76011 3.04860i −0.145172 0.251445i
\(148\) −5.48429 −0.450806
\(149\) 8.57745 + 14.8566i 0.702692 + 1.21710i 0.967518 + 0.252802i \(0.0813521\pi\)
−0.264826 + 0.964296i \(0.585315\pi\)
\(150\) 0 0
\(151\) −21.3828 −1.74011 −0.870053 0.492957i \(-0.835916\pi\)
−0.870053 + 0.492957i \(0.835916\pi\)
\(152\) −4.31000 7.46515i −0.349587 0.605503i
\(153\) −1.00064 + 1.73316i −0.0808969 + 0.140118i
\(154\) 2.37548 4.11446i 0.191422 0.331552i
\(155\) 0 0
\(156\) −0.691395 34.7752i −0.0553559 2.78424i
\(157\) 18.3646 1.46566 0.732829 0.680413i \(-0.238200\pi\)
0.732829 + 0.680413i \(0.238200\pi\)
\(158\) −1.32178 + 2.28939i −0.105155 + 0.182134i
\(159\) 0.691395 1.19753i 0.0548312 0.0949705i
\(160\) 0 0
\(161\) −6.32648 −0.498597
\(162\) 14.2966 + 24.7624i 1.12324 + 1.94551i
\(163\) −2.00543 3.47351i −0.157078 0.272066i 0.776736 0.629826i \(-0.216874\pi\)
−0.933814 + 0.357760i \(0.883541\pi\)
\(164\) −44.6357 −3.48546
\(165\) 0 0
\(166\) 15.0774 26.1149i 1.17024 2.02691i
\(167\) 1.46928 2.54486i 0.113696 0.196927i −0.803562 0.595221i \(-0.797064\pi\)
0.917258 + 0.398294i \(0.130398\pi\)
\(168\) 39.9545 3.08256
\(169\) −12.9897 + 0.516725i −0.999210 + 0.0397480i
\(170\) 0 0
\(171\) −1.11588 + 1.93275i −0.0853331 + 0.147801i
\(172\) −3.06329 + 5.30577i −0.233574 + 0.404561i
\(173\) 0.683650 + 1.18412i 0.0519769 + 0.0900267i 0.890843 0.454311i \(-0.150114\pi\)
−0.838866 + 0.544337i \(0.816781\pi\)
\(174\) 16.4424 1.24649
\(175\) 0 0
\(176\) 2.25961 + 3.91375i 0.170324 + 0.295010i
\(177\) 16.3550 1.22932
\(178\) 15.9850 + 27.6868i 1.19813 + 2.07522i
\(179\) −3.89306 + 6.74299i −0.290981 + 0.503994i −0.974042 0.226367i \(-0.927315\pi\)
0.683061 + 0.730362i \(0.260648\pi\)
\(180\) 0 0
\(181\) −3.86684 −0.287420 −0.143710 0.989620i \(-0.545903\pi\)
−0.143710 + 0.989620i \(0.545903\pi\)
\(182\) −0.536155 26.9670i −0.0397425 1.99893i
\(183\) −4.88752 −0.361296
\(184\) 6.79833 11.7751i 0.501180 0.868069i
\(185\) 0 0
\(186\) 24.5582 + 42.5361i 1.80070 + 3.11890i
\(187\) −0.777322 −0.0568434
\(188\) −13.8093 23.9184i −1.00715 1.74443i
\(189\) 4.31754 + 7.47821i 0.314055 + 0.543959i
\(190\) 0 0
\(191\) −2.47185 4.28136i −0.178857 0.309789i 0.762633 0.646832i \(-0.223906\pi\)
−0.941489 + 0.337043i \(0.890573\pi\)
\(192\) 0.290836 0.503743i 0.0209893 0.0363545i
\(193\) 2.47822 4.29240i 0.178386 0.308974i −0.762942 0.646467i \(-0.776246\pi\)
0.941328 + 0.337493i \(0.109579\pi\)
\(194\) 37.6357 2.70208
\(195\) 0 0
\(196\) 7.32648 0.523320
\(197\) 3.37273 5.84174i 0.240297 0.416207i −0.720502 0.693453i \(-0.756088\pi\)
0.960799 + 0.277246i \(0.0894218\pi\)
\(198\) 1.32178 2.28939i 0.0939349 0.162700i
\(199\) −2.58772 4.48207i −0.183439 0.317725i 0.759611 0.650378i \(-0.225390\pi\)
−0.943049 + 0.332653i \(0.892056\pi\)
\(200\) 0 0
\(201\) 8.64403 + 14.9719i 0.609703 + 1.05604i
\(202\) −16.8423 29.1717i −1.18502 2.05251i
\(203\) 8.81566 0.618738
\(204\) −5.90364 10.2254i −0.413337 0.715921i
\(205\) 0 0
\(206\) 13.9616 24.1822i 0.972749 1.68485i
\(207\) −3.52022 −0.244673
\(208\) 22.4699 + 12.3841i 1.55801 + 0.858684i
\(209\) −0.866840 −0.0599606
\(210\) 0 0
\(211\) 7.00894 12.1398i 0.482515 0.835741i −0.517283 0.855814i \(-0.673057\pi\)
0.999799 + 0.0200732i \(0.00638994\pi\)
\(212\) 1.43897 + 2.49237i 0.0988289 + 0.171177i
\(213\) 5.67315 0.388718
\(214\) −13.5861 23.5318i −0.928726 1.60860i
\(215\) 0 0
\(216\) −18.5582 −1.26273
\(217\) 13.1670 + 22.8060i 0.893836 + 1.54817i
\(218\) 4.16251 7.20968i 0.281921 0.488301i
\(219\) −11.1159 + 19.2533i −0.751141 + 1.30101i
\(220\) 0 0
\(221\) −3.77719 + 2.28205i −0.254081 + 0.153508i
\(222\) −6.70825 −0.450228
\(223\) −0.00415245 + 0.00719226i −0.000278069 + 0.000481629i −0.866164 0.499759i \(-0.833422\pi\)
0.865886 + 0.500241i \(0.166755\pi\)
\(224\) −8.05794 + 13.9568i −0.538394 + 0.932525i
\(225\) 0 0
\(226\) 14.0774 0.936418
\(227\) 5.63179 + 9.75454i 0.373795 + 0.647431i 0.990146 0.140040i \(-0.0447231\pi\)
−0.616351 + 0.787471i \(0.711390\pi\)
\(228\) −6.58351 11.4030i −0.436004 0.755181i
\(229\) −16.5404 −1.09302 −0.546509 0.837453i \(-0.684043\pi\)
−0.546509 + 0.837453i \(0.684043\pi\)
\(230\) 0 0
\(231\) 2.00894 3.47959i 0.132179 0.228940i
\(232\) −9.47315 + 16.4080i −0.621943 + 1.07724i
\(233\) −6.94941 −0.455271 −0.227636 0.973746i \(-0.573100\pi\)
−0.227636 + 0.973746i \(0.573100\pi\)
\(234\) −0.298331 15.0052i −0.0195025 0.980919i
\(235\) 0 0
\(236\) −17.0195 + 29.4787i −1.10788 + 1.91890i
\(237\) −1.11783 + 1.93613i −0.0726107 + 0.125765i
\(238\) −4.57808 7.92947i −0.296753 0.513991i
\(239\) 4.00000 0.258738 0.129369 0.991596i \(-0.458705\pi\)
0.129369 + 0.991596i \(0.458705\pi\)
\(240\) 0 0
\(241\) −9.88605 17.1231i −0.636817 1.10300i −0.986127 0.165992i \(-0.946917\pi\)
0.349310 0.937007i \(-0.386416\pi\)
\(242\) −26.9763 −1.73410
\(243\) 7.68273 + 13.3069i 0.492848 + 0.853637i
\(244\) 5.08609 8.80937i 0.325604 0.563962i
\(245\) 0 0
\(246\) −54.5973 −3.48099
\(247\) −4.21218 + 2.54486i −0.268015 + 0.161926i
\(248\) −56.5962 −3.59386
\(249\) 12.7510 22.0853i 0.808060 1.39960i
\(250\) 0 0
\(251\) −1.83676 3.18136i −0.115935 0.200806i 0.802218 0.597031i \(-0.203653\pi\)
−0.918153 + 0.396226i \(0.870320\pi\)
\(252\) 21.5293 1.35622
\(253\) −0.683650 1.18412i −0.0429807 0.0744447i
\(254\) −21.9337 37.9903i −1.37624 2.38372i
\(255\) 0 0
\(256\) 14.5669 + 25.2306i 0.910430 + 1.57691i
\(257\) −6.63242 + 11.4877i −0.413719 + 0.716583i −0.995293 0.0969108i \(-0.969104\pi\)
0.581574 + 0.813494i \(0.302437\pi\)
\(258\) −3.74694 + 6.48989i −0.233274 + 0.404043i
\(259\) −3.59666 −0.223486
\(260\) 0 0
\(261\) 4.90527 0.303628
\(262\) −12.7287 + 22.0467i −0.786381 + 1.36205i
\(263\) −15.1352 + 26.2150i −0.933279 + 1.61649i −0.155605 + 0.987819i \(0.549733\pi\)
−0.777674 + 0.628667i \(0.783601\pi\)
\(264\) 4.31754 + 7.47821i 0.265726 + 0.460252i
\(265\) 0 0
\(266\) −5.10530 8.84265i −0.313026 0.542177i
\(267\) 13.5185 + 23.4147i 0.827317 + 1.43296i
\(268\) −35.9809 −2.19788
\(269\) 11.1248 + 19.2687i 0.678292 + 1.17484i 0.975495 + 0.220022i \(0.0706129\pi\)
−0.297203 + 0.954814i \(0.596054\pi\)
\(270\) 0 0
\(271\) 5.91421 10.2437i 0.359262 0.622261i −0.628575 0.777749i \(-0.716362\pi\)
0.987838 + 0.155488i \(0.0496950\pi\)
\(272\) 8.70953 0.528093
\(273\) −0.453425 22.8060i −0.0274425 1.38028i
\(274\) 22.0774 1.33375
\(275\) 0 0
\(276\) 10.3844 17.9863i 0.625069 1.08265i
\(277\) −8.39254 14.5363i −0.504259 0.873402i −0.999988 0.00492452i \(-0.998432\pi\)
0.495729 0.868477i \(-0.334901\pi\)
\(278\) 36.4715 2.18741
\(279\) 7.32648 + 12.6898i 0.438625 + 0.759721i
\(280\) 0 0
\(281\) −10.5967 −0.632144 −0.316072 0.948735i \(-0.602364\pi\)
−0.316072 + 0.948735i \(0.602364\pi\)
\(282\) −16.8912 29.2564i −1.00586 1.74219i
\(283\) 4.40783 7.63458i 0.262018 0.453829i −0.704760 0.709446i \(-0.748945\pi\)
0.966778 + 0.255617i \(0.0822786\pi\)
\(284\) −5.90364 + 10.2254i −0.350316 + 0.606766i
\(285\) 0 0
\(286\) 4.98943 3.01445i 0.295031 0.178248i
\(287\) −29.2726 −1.72791
\(288\) −4.48365 + 7.76591i −0.264202 + 0.457611i
\(289\) 7.75096 13.4251i 0.455939 0.789710i
\(290\) 0 0
\(291\) 31.8284 1.86581
\(292\) −23.1350 40.0709i −1.35387 2.34497i
\(293\) 14.1263 + 24.4675i 0.825267 + 1.42940i 0.901715 + 0.432331i \(0.142309\pi\)
−0.0764476 + 0.997074i \(0.524358\pi\)
\(294\) 8.96157 0.522650
\(295\) 0 0
\(296\) 3.86491 6.69422i 0.224643 0.389094i
\(297\) −0.933121 + 1.61621i −0.0541452 + 0.0937822i
\(298\) −43.6719 −2.52984
\(299\) −6.79833 3.74685i −0.393158 0.216686i
\(300\) 0 0
\(301\) −2.00894 + 3.47959i −0.115793 + 0.200560i
\(302\) 27.2175 47.1421i 1.56619 2.71272i
\(303\) −14.2435 24.6704i −0.818267 1.41728i
\(304\) 9.71254 0.557052
\(305\) 0 0
\(306\) −2.54737 4.41217i −0.145623 0.252227i
\(307\) 12.7219 0.726077 0.363039 0.931774i \(-0.381739\pi\)
0.363039 + 0.931774i \(0.381739\pi\)
\(308\) 4.18112 + 7.24190i 0.238241 + 0.412646i
\(309\) 11.8073 20.4508i 0.671692 1.16340i
\(310\) 0 0
\(311\) 27.9231 1.58338 0.791688 0.610925i \(-0.209202\pi\)
0.791688 + 0.610925i \(0.209202\pi\)
\(312\) 42.9344 + 23.6630i 2.43068 + 1.33965i
\(313\) 24.5807 1.38938 0.694692 0.719307i \(-0.255540\pi\)
0.694692 + 0.719307i \(0.255540\pi\)
\(314\) −23.3758 + 40.4880i −1.31917 + 2.28487i
\(315\) 0 0
\(316\) −2.32648 4.02959i −0.130875 0.226682i
\(317\) −0.234377 −0.0131639 −0.00658196 0.999978i \(-0.502095\pi\)
−0.00658196 + 0.999978i \(0.502095\pi\)
\(318\) 1.76011 + 3.04860i 0.0987022 + 0.170957i
\(319\) 0.952633 + 1.65001i 0.0533372 + 0.0923828i
\(320\) 0 0
\(321\) −11.4897 19.9008i −0.641294 1.11075i
\(322\) 8.05279 13.9478i 0.448764 0.777283i
\(323\) −0.835296 + 1.44678i −0.0464771 + 0.0805008i
\(324\) −50.3271 −2.79595
\(325\) 0 0
\(326\) 10.2106 0.565513
\(327\) 3.52022 6.09721i 0.194669 0.337176i
\(328\) 31.4558 54.4831i 1.73686 3.00833i
\(329\) −9.05631 15.6860i −0.499290 0.864796i
\(330\) 0 0
\(331\) 9.16324 + 15.8712i 0.503657 + 0.872360i 0.999991 + 0.00422829i \(0.00134591\pi\)
−0.496334 + 0.868132i \(0.665321\pi\)
\(332\) 26.5380 + 45.9652i 1.45646 + 2.52267i
\(333\) −2.00128 −0.109669
\(334\) 3.74039 + 6.47855i 0.204665 + 0.354491i
\(335\) 0 0
\(336\) −22.5092 + 38.9871i −1.22798 + 2.12692i
\(337\) −21.2949 −1.16001 −0.580003 0.814614i \(-0.696949\pi\)
−0.580003 + 0.814614i \(0.696949\pi\)
\(338\) 15.3950 29.2958i 0.837379 1.59348i
\(339\) 11.9053 0.646605
\(340\) 0 0
\(341\) −2.84570 + 4.92889i −0.154103 + 0.266915i
\(342\) −2.84073 4.92028i −0.153609 0.266059i
\(343\) −15.7651 −0.851234
\(344\) −4.31754 7.47821i −0.232786 0.403198i
\(345\) 0 0
\(346\) −3.48079 −0.187128
\(347\) 1.90761 + 3.30407i 0.102406 + 0.177372i 0.912675 0.408685i \(-0.134013\pi\)
−0.810270 + 0.586057i \(0.800679\pi\)
\(348\) −14.4702 + 25.0631i −0.775684 + 1.34352i
\(349\) −12.1632 + 21.0674i −0.651083 + 1.12771i 0.331777 + 0.943358i \(0.392352\pi\)
−0.982860 + 0.184352i \(0.940981\pi\)
\(350\) 0 0
\(351\) 0.210609 + 10.5930i 0.0112415 + 0.565413i
\(352\) −3.48301 −0.185645
\(353\) 13.5295 23.4338i 0.720104 1.24726i −0.240853 0.970562i \(-0.577427\pi\)
0.960958 0.276696i \(-0.0892394\pi\)
\(354\) −20.8178 + 36.0576i −1.10646 + 1.91644i
\(355\) 0 0
\(356\) −56.2708 −2.98235
\(357\) −3.87167 6.70593i −0.204911 0.354916i
\(358\) −9.91073 17.1659i −0.523798 0.907245i
\(359\) 27.0039 1.42521 0.712605 0.701566i \(-0.247515\pi\)
0.712605 + 0.701566i \(0.247515\pi\)
\(360\) 0 0
\(361\) 8.56851 14.8411i 0.450974 0.781110i
\(362\) 4.92198 8.52512i 0.258694 0.448071i
\(363\) −22.8138 −1.19742
\(364\) 41.5777 + 22.9152i 2.17927 + 1.20108i
\(365\) 0 0
\(366\) 6.22118 10.7754i 0.325186 0.563239i
\(367\) 3.47055 6.01118i 0.181161 0.313781i −0.761115 0.648617i \(-0.775348\pi\)
0.942276 + 0.334836i \(0.108681\pi\)
\(368\) 7.65998 + 13.2675i 0.399304 + 0.691615i
\(369\) −16.2881 −0.847922
\(370\) 0 0
\(371\) 0.943693 + 1.63452i 0.0489941 + 0.0848603i
\(372\) −86.4505 −4.48225
\(373\) −1.15644 2.00301i −0.0598781 0.103712i 0.834532 0.550959i \(-0.185738\pi\)
−0.894411 + 0.447247i \(0.852405\pi\)
\(374\) 0.989429 1.71374i 0.0511622 0.0886154i
\(375\) 0 0
\(376\) 38.9270 2.00751
\(377\) 9.47315 + 5.22105i 0.487892 + 0.268898i
\(378\) −21.9827 −1.13067
\(379\) −2.58772 + 4.48207i −0.132922 + 0.230228i −0.924802 0.380449i \(-0.875769\pi\)
0.791880 + 0.610677i \(0.209103\pi\)
\(380\) 0 0
\(381\) −18.5493 32.1283i −0.950309 1.64598i
\(382\) 12.5854 0.643923
\(383\) 10.3305 + 17.8929i 0.527861 + 0.914283i 0.999473 + 0.0324760i \(0.0103393\pi\)
−0.471611 + 0.881807i \(0.656327\pi\)
\(384\) 12.5477 + 21.7332i 0.640320 + 1.10907i
\(385\) 0 0
\(386\) 6.30890 + 10.9273i 0.321115 + 0.556187i
\(387\) −1.11783 + 1.93613i −0.0568224 + 0.0984193i
\(388\) −33.1215 + 57.3682i −1.68149 + 2.91243i
\(389\) 19.7477 1.00125 0.500624 0.865665i \(-0.333104\pi\)
0.500624 + 0.865665i \(0.333104\pi\)
\(390\) 0 0
\(391\) −2.63509 −0.133262
\(392\) −5.16315 + 8.94284i −0.260778 + 0.451681i
\(393\) −10.7646 + 18.6449i −0.543004 + 0.940510i
\(394\) 8.58609 + 14.8715i 0.432561 + 0.749218i
\(395\) 0 0
\(396\) 2.32648 + 4.02959i 0.116910 + 0.202494i
\(397\) 4.69451 + 8.13113i 0.235611 + 0.408090i 0.959450 0.281879i \(-0.0909576\pi\)
−0.723839 + 0.689969i \(0.757624\pi\)
\(398\) 13.1753 0.660420
\(399\) −4.31754 7.47821i −0.216148 0.374379i
\(400\) 0 0
\(401\) −12.2510 + 21.2193i −0.611784 + 1.05964i 0.379156 + 0.925333i \(0.376214\pi\)
−0.990940 + 0.134308i \(0.957119\pi\)
\(402\) −44.0109 −2.19506
\(403\) 0.642285 + 32.3050i 0.0319945 + 1.60923i
\(404\) 59.2887 2.94972
\(405\) 0 0
\(406\) −11.2212 + 19.4357i −0.556898 + 0.964575i
\(407\) −0.388661 0.673180i −0.0192652 0.0333683i
\(408\) 16.6417 0.823889
\(409\) −18.0582 31.2778i −0.892922 1.54659i −0.836355 0.548188i \(-0.815318\pi\)
−0.0565671 0.998399i \(-0.518015\pi\)
\(410\) 0 0
\(411\) 18.6708 0.920965
\(412\) 24.5739 + 42.5633i 1.21067 + 2.09694i
\(413\) −11.1616 + 19.3324i −0.549226 + 0.951288i
\(414\) 4.48079 7.76095i 0.220219 0.381430i
\(415\) 0 0
\(416\) −16.9248 + 10.2254i −0.829805 + 0.501341i
\(417\) 30.8439 1.51043
\(418\) 1.10337 1.91110i 0.0539678 0.0934749i
\(419\) 3.43342 5.94686i 0.167734 0.290523i −0.769889 0.638178i \(-0.779689\pi\)
0.937623 + 0.347655i \(0.113022\pi\)
\(420\) 0 0
\(421\) 33.9795 1.65606 0.828029 0.560686i \(-0.189462\pi\)
0.828029 + 0.560686i \(0.189462\pi\)
\(422\) 17.8429 + 30.9049i 0.868580 + 1.50443i
\(423\) −5.03917 8.72810i −0.245013 0.424375i
\(424\) −4.05631 −0.196992
\(425\) 0 0
\(426\) −7.22118 + 12.5075i −0.349867 + 0.605988i
\(427\) 3.33552 5.77729i 0.161417 0.279582i
\(428\) 47.8261 2.31176
\(429\) 4.21955 2.54931i 0.203722 0.123082i
\(430\) 0 0
\(431\) 8.12482 14.0726i 0.391359 0.677853i −0.601270 0.799046i \(-0.705339\pi\)
0.992629 + 0.121193i \(0.0386719\pi\)
\(432\) 10.4552 18.1089i 0.503025 0.871265i
\(433\) −0.128130 0.221929i −0.00615756 0.0106652i 0.862930 0.505323i \(-0.168627\pi\)
−0.869088 + 0.494658i \(0.835293\pi\)
\(434\) −67.0396 −3.21800
\(435\) 0 0
\(436\) 7.32648 + 12.6898i 0.350875 + 0.607733i
\(437\) −2.93855 −0.140570
\(438\) −28.2981 49.0138i −1.35214 2.34197i
\(439\) 3.79833 6.57890i 0.181284 0.313994i −0.761034 0.648712i \(-0.775308\pi\)
0.942318 + 0.334718i \(0.108641\pi\)
\(440\) 0 0
\(441\) 2.67352 0.127310
\(442\) −0.223318 11.2322i −0.0106221 0.534263i
\(443\) 4.32246 0.205366 0.102683 0.994714i \(-0.467257\pi\)
0.102683 + 0.994714i \(0.467257\pi\)
\(444\) 5.90364 10.2254i 0.280174 0.485276i
\(445\) 0 0
\(446\) −0.0105711 0.0183096i −0.000500554 0.000866986i
\(447\) −36.9332 −1.74688
\(448\) 0.396966 + 0.687565i 0.0187549 + 0.0324844i
\(449\) −1.64403 2.84754i −0.0775865 0.134384i 0.824622 0.565685i \(-0.191388\pi\)
−0.902208 + 0.431301i \(0.858055\pi\)
\(450\) 0 0
\(451\) −3.16324 5.47890i −0.148951 0.257991i
\(452\) −12.3889 + 21.4583i −0.582727 + 1.00931i
\(453\) 23.0178 39.8680i 1.08147 1.87316i
\(454\) −28.6741 −1.34574
\(455\) 0 0
\(456\) 18.5582 0.869069
\(457\) 7.71304 13.3594i 0.360801 0.624925i −0.627292 0.778784i \(-0.715837\pi\)
0.988093 + 0.153859i \(0.0491701\pi\)
\(458\) 21.0537 36.4661i 0.983775 1.70395i
\(459\) 1.79833 + 3.11480i 0.0839389 + 0.145386i
\(460\) 0 0
\(461\) −12.9424 22.4168i −0.602786 1.04406i −0.992397 0.123076i \(-0.960724\pi\)
0.389611 0.920979i \(-0.372609\pi\)
\(462\) 5.11424 + 8.85812i 0.237936 + 0.412117i
\(463\) 7.04045 0.327197 0.163599 0.986527i \(-0.447690\pi\)
0.163599 + 0.986527i \(0.447690\pi\)
\(464\) −10.6738 18.4876i −0.495519 0.858265i
\(465\) 0 0
\(466\) 8.84570 15.3212i 0.409769 0.709741i
\(467\) 18.8113 0.870482 0.435241 0.900314i \(-0.356663\pi\)
0.435241 + 0.900314i \(0.356663\pi\)
\(468\) 23.1350 + 12.7507i 1.06941 + 0.589399i
\(469\) −23.5967 −1.08959
\(470\) 0 0
\(471\) −19.7688 + 34.2406i −0.910900 + 1.57773i
\(472\) −23.9881 41.5486i −1.10414 1.91243i
\(473\) −0.868356 −0.0399271
\(474\) −2.84570 4.92889i −0.130707 0.226392i
\(475\) 0 0
\(476\) 16.1159 0.738670
\(477\) 0.525096 + 0.909493i 0.0240425 + 0.0416428i
\(478\) −5.09148 + 8.81870i −0.232879 + 0.403358i
\(479\) 9.73876 16.8680i 0.444975 0.770720i −0.553075 0.833131i \(-0.686546\pi\)
0.998051 + 0.0624114i \(0.0198791\pi\)
\(480\) 0 0
\(481\) −3.86491 2.13011i −0.176225 0.0971249i
\(482\) 50.3346 2.29268
\(483\) 6.81023 11.7957i 0.309876 0.536721i
\(484\) 23.7407 41.1201i 1.07912 1.86909i
\(485\) 0 0
\(486\) −39.1165 −1.77436
\(487\) 16.1620 + 27.9935i 0.732372 + 1.26851i 0.955867 + 0.293800i \(0.0949200\pi\)
−0.223495 + 0.974705i \(0.571747\pi\)
\(488\) 7.16858 + 12.4163i 0.324506 + 0.562062i
\(489\) 8.63509 0.390492
\(490\) 0 0
\(491\) −14.3354 + 24.8297i −0.646949 + 1.12055i 0.336899 + 0.941541i \(0.390622\pi\)
−0.983848 + 0.179007i \(0.942711\pi\)
\(492\) 48.0487 83.2227i 2.16620 3.75197i
\(493\) 3.67187 0.165373
\(494\) −0.249036 12.5258i −0.0112046 0.563561i
\(495\) 0 0
\(496\) 31.8847 55.2260i 1.43167 2.47972i
\(497\) −3.87167 + 6.70593i −0.173668 + 0.300802i
\(498\) 32.4606 + 56.2235i 1.45460 + 2.51943i
\(499\) 28.9616 1.29650 0.648249 0.761428i \(-0.275502\pi\)
0.648249 + 0.761428i \(0.275502\pi\)
\(500\) 0 0
\(501\) 3.16324 + 5.47890i 0.141323 + 0.244779i
\(502\) 9.35181 0.417392
\(503\) 14.0546 + 24.3433i 0.626665 + 1.08542i 0.988216 + 0.153063i \(0.0489138\pi\)
−0.361551 + 0.932352i \(0.617753\pi\)
\(504\) −15.1722 + 26.2790i −0.675823 + 1.17056i
\(505\) 0 0
\(506\) 3.48079 0.154740
\(507\) 13.0195 24.7754i 0.578218 1.10032i
\(508\) 77.2116 3.42571
\(509\) −10.5563 + 18.2841i −0.467900 + 0.810427i −0.999327 0.0366773i \(-0.988323\pi\)
0.531427 + 0.847104i \(0.321656\pi\)
\(510\) 0 0
\(511\) −15.1722 26.2790i −0.671178 1.16251i
\(512\) −50.8542 −2.24746
\(513\) 2.00543 + 3.47351i 0.0885420 + 0.153359i
\(514\) −16.8844 29.2447i −0.744740 1.28993i
\(515\) 0 0
\(516\) −6.59503 11.4229i −0.290330 0.502866i
\(517\) 1.95728 3.39010i 0.0860809 0.149097i
\(518\) 4.57808 7.92947i 0.201149 0.348401i
\(519\) −2.94369 −0.129214
\(520\) 0 0
\(521\) 0.673516 0.0295073 0.0147536 0.999891i \(-0.495304\pi\)
0.0147536 + 0.999891i \(0.495304\pi\)
\(522\) −6.24376 + 10.8145i −0.273282 + 0.473339i
\(523\) 14.9313 25.8618i 0.652900 1.13086i −0.329516 0.944150i \(-0.606886\pi\)
0.982416 0.186706i \(-0.0597810\pi\)
\(524\) −22.4039 38.8048i −0.978720 1.69519i
\(525\) 0 0
\(526\) −38.5304 66.7366i −1.68000 2.90985i
\(527\) 5.48429 + 9.49907i 0.238899 + 0.413786i
\(528\) −9.72953 −0.423423
\(529\) 9.18246 + 15.9045i 0.399237 + 0.691499i
\(530\) 0 0
\(531\) −6.21061 + 10.7571i −0.269517 + 0.466818i
\(532\) 17.9718 0.779177
\(533\) −31.4558 17.3366i −1.36250 0.750933i
\(534\) −68.8290 −2.97852
\(535\) 0 0
\(536\) 25.3566 43.9189i 1.09524 1.89701i
\(537\) −8.38148 14.5171i −0.361687 0.626461i
\(538\) −56.6418 −2.44200
\(539\) 0.519213 + 0.899304i 0.0223641 + 0.0387358i
\(540\) 0 0
\(541\) 6.28806 0.270345 0.135172 0.990822i \(-0.456841\pi\)
0.135172 + 0.990822i \(0.456841\pi\)
\(542\) 15.0560 + 26.0778i 0.646712 + 1.12014i
\(543\) 4.16251 7.20968i 0.178630 0.309397i
\(544\) −3.35627 + 5.81323i −0.143899 + 0.249240i
\(545\) 0 0
\(546\) 50.8569 + 28.0294i 2.17647 + 1.19955i
\(547\) −3.03789 −0.129891 −0.0649454 0.997889i \(-0.520687\pi\)
−0.0649454 + 0.997889i \(0.520687\pi\)
\(548\) −19.4294 + 33.6527i −0.829983 + 1.43757i
\(549\) 1.85597 3.21464i 0.0792109 0.137197i
\(550\) 0 0
\(551\) 4.09473 0.174442
\(552\) 14.6363 + 25.3508i 0.622962 + 1.07900i
\(553\) −1.52574 2.64265i −0.0648809 0.112377i
\(554\) 42.7304 1.81544
\(555\) 0 0
\(556\) −32.0970 + 55.5936i −1.36121 + 2.35769i
\(557\) −10.3498 + 17.9264i −0.438536 + 0.759566i −0.997577 0.0695738i \(-0.977836\pi\)
0.559041 + 0.829140i \(0.311169\pi\)
\(558\) −37.3026 −1.57915
\(559\) −4.21955 + 2.54931i −0.178468 + 0.107824i
\(560\) 0 0
\(561\) 0.836758 1.44931i 0.0353279 0.0611898i
\(562\) 13.4882 23.3622i 0.568964 0.985475i
\(563\) −5.48014 9.49188i −0.230960 0.400035i 0.727131 0.686499i \(-0.240853\pi\)
−0.958091 + 0.286464i \(0.907520\pi\)
\(564\) 59.4608 2.50375
\(565\) 0 0
\(566\) 11.2212 + 19.4357i 0.471661 + 0.816941i
\(567\) −33.0051 −1.38608
\(568\) −8.32087 14.4122i −0.349136 0.604721i
\(569\) −21.3566 + 36.9907i −0.895314 + 1.55073i −0.0618981 + 0.998082i \(0.519715\pi\)
−0.833416 + 0.552647i \(0.813618\pi\)
\(570\) 0 0
\(571\) −23.6145 −0.988238 −0.494119 0.869394i \(-0.664509\pi\)
−0.494119 + 0.869394i \(0.664509\pi\)
\(572\) 0.203954 + 10.2583i 0.00852774 + 0.428920i
\(573\) 10.6434 0.444635
\(574\) 37.2602 64.5366i 1.55521 2.69370i
\(575\) 0 0
\(576\) 0.220882 + 0.382579i 0.00920343 + 0.0159408i
\(577\) −18.3646 −0.764530 −0.382265 0.924053i \(-0.624856\pi\)
−0.382265 + 0.924053i \(0.624856\pi\)
\(578\) 19.7319 + 34.1767i 0.820740 + 1.42156i
\(579\) 5.33542 + 9.24123i 0.221733 + 0.384052i
\(580\) 0 0
\(581\) 17.4039 + 30.1445i 0.722037 + 1.25060i
\(582\) −40.5134 + 70.1713i −1.67934 + 2.90869i
\(583\) −0.203954 + 0.353259i −0.00844691 + 0.0146305i
\(584\) 65.2151 2.69862
\(585\) 0 0
\(586\) −71.9237 −2.97114
\(587\) 0.351448 0.608726i 0.0145058 0.0251248i −0.858681 0.512510i \(-0.828716\pi\)
0.873187 + 0.487385i \(0.162049\pi\)
\(588\) −7.88669 + 13.6601i −0.325242 + 0.563335i
\(589\) 6.11588 + 10.5930i 0.252000 + 0.436477i
\(590\) 0 0
\(591\) 7.26124 + 12.5768i 0.298687 + 0.517342i
\(592\) 4.35476 + 7.54267i 0.178980 + 0.310002i
\(593\) −37.1593 −1.52595 −0.762975 0.646428i \(-0.776262\pi\)
−0.762975 + 0.646428i \(0.776262\pi\)
\(594\) −2.37548 4.11446i −0.0974672 0.168818i
\(595\) 0 0
\(596\) 38.4337 66.5692i 1.57431 2.72678i
\(597\) 11.1423 0.456026
\(598\) 16.9140 10.2189i 0.691663 0.417880i
\(599\) −15.6914 −0.641133 −0.320567 0.947226i \(-0.603873\pi\)
−0.320567 + 0.947226i \(0.603873\pi\)
\(600\) 0 0
\(601\) −6.00193 + 10.3956i −0.244824 + 0.424047i −0.962082 0.272760i \(-0.912063\pi\)
0.717258 + 0.696807i \(0.245397\pi\)
\(602\) −5.11424 8.85812i −0.208441 0.361030i
\(603\) −13.1298 −0.534687
\(604\) 47.9059 + 82.9754i 1.94926 + 3.37622i
\(605\) 0 0
\(606\) 72.5204 2.94594
\(607\) −19.3433 33.5035i −0.785119 1.35987i −0.928928 0.370261i \(-0.879268\pi\)
0.143809 0.989606i \(-0.454065\pi\)
\(608\) −3.74278 + 6.48269i −0.151790 + 0.262908i
\(609\) −9.48973 + 16.4367i −0.384543 + 0.666048i
\(610\) 0 0
\(611\) −0.441765 22.2195i −0.0178719 0.898903i
\(612\) 8.96730 0.362482
\(613\) 8.64201 14.9684i 0.349047 0.604568i −0.637033 0.770836i \(-0.719839\pi\)
0.986081 + 0.166269i \(0.0531719\pi\)
\(614\) −16.1933 + 28.0477i −0.653509 + 1.13191i
\(615\) 0 0
\(616\) −11.7861 −0.474877
\(617\) −13.2345 22.9229i −0.532803 0.922841i −0.999266 0.0383009i \(-0.987805\pi\)
0.466464 0.884540i \(-0.345528\pi\)
\(618\) 30.0582 + 52.0624i 1.20912 + 2.09426i
\(619\) −31.0039 −1.24615 −0.623075 0.782162i \(-0.714117\pi\)
−0.623075 + 0.782162i \(0.714117\pi\)
\(620\) 0 0
\(621\) −3.16324 + 5.47890i −0.126937 + 0.219861i
\(622\) −35.5425 + 61.5615i −1.42513 + 2.46839i
\(623\) −36.9030 −1.47849
\(624\) −47.2781 + 28.5639i −1.89264 + 1.14347i
\(625\) 0 0
\(626\) −31.2881 + 54.1925i −1.25052 + 2.16597i
\(627\) 0.933121 1.61621i 0.0372653 0.0645453i
\(628\) −41.1440 71.2635i −1.64182 2.84372i
\(629\) −1.49807 −0.0597320
\(630\) 0 0
\(631\) 10.3566 + 17.9381i 0.412288 + 0.714104i 0.995140 0.0984745i \(-0.0313963\pi\)
−0.582851 + 0.812579i \(0.698063\pi\)
\(632\) 6.55812 0.260868
\(633\) 15.0897 + 26.1362i 0.599763 + 1.03882i
\(634\) 0.298331 0.516725i 0.0118482 0.0205218i
\(635\) 0 0
\(636\) −6.19599 −0.245687
\(637\) 5.16315 + 2.84563i 0.204571 + 0.112748i
\(638\) −4.85031 −0.192026
\(639\) −2.15430 + 3.73136i −0.0852229 + 0.147610i
\(640\) 0 0
\(641\) −10.5947 18.3506i −0.418467 0.724806i 0.577319 0.816519i \(-0.304099\pi\)
−0.995785 + 0.0917132i \(0.970766\pi\)
\(642\) 58.4997 2.30880
\(643\) 5.76682 + 9.98843i 0.227421 + 0.393905i 0.957043 0.289946i \(-0.0936372\pi\)
−0.729622 + 0.683851i \(0.760304\pi\)
\(644\) 14.1738 + 24.5498i 0.558526 + 0.967396i
\(645\) 0 0
\(646\) −2.12645 3.68311i −0.0836639 0.144910i
\(647\) 17.4232 30.1779i 0.684977 1.18641i −0.288467 0.957490i \(-0.593146\pi\)
0.973444 0.228925i \(-0.0735211\pi\)
\(648\) 35.4667 61.4301i 1.39326 2.41320i
\(649\) −4.82456 −0.189380
\(650\) 0 0
\(651\) −56.6953 −2.22206
\(652\) −8.98591 + 15.5641i −0.351915 + 0.609535i
\(653\) −11.1616 + 19.3324i −0.436787 + 0.756537i −0.997440 0.0715139i \(-0.977217\pi\)
0.560653 + 0.828051i \(0.310550\pi\)
\(654\) 8.96157 + 15.5219i 0.350425 + 0.606954i
\(655\) 0 0
\(656\) 35.4427 + 61.3885i 1.38380 + 2.39682i
\(657\) −8.44221 14.6223i −0.329362 0.570471i
\(658\) 46.1100 1.79755
\(659\) 0.433420 + 0.750705i 0.0168836 + 0.0292433i 0.874344 0.485307i \(-0.161292\pi\)
−0.857460 + 0.514550i \(0.827959\pi\)
\(660\) 0 0
\(661\) −6.65430 + 11.5256i −0.258822 + 0.448293i −0.965927 0.258816i \(-0.916668\pi\)
0.707104 + 0.707109i \(0.250001\pi\)
\(662\) −46.6544 −1.81328
\(663\) −0.188859 9.49907i −0.00733469 0.368913i
\(664\) −74.8079 −2.90311
\(665\) 0 0
\(666\) 2.54737 4.41217i 0.0987085 0.170968i
\(667\) 3.22939 + 5.59346i 0.125042 + 0.216580i
\(668\) −13.1670 −0.509448
\(669\) −0.00893993 0.0154844i −0.000345637 0.000598662i
\(670\) 0 0
\(671\) 1.44176 0.0556587
\(672\) −17.3481 30.0479i −0.669219 1.15912i
\(673\) 2.75660 4.77457i 0.106259 0.184046i −0.807993 0.589192i \(-0.799446\pi\)
0.914252 + 0.405146i \(0.132779\pi\)
\(674\) 27.1056 46.9483i 1.04407 1.80838i
\(675\) 0 0
\(676\) 31.1072 + 49.2486i 1.19643 + 1.89418i
\(677\) −4.80479 −0.184663 −0.0923316 0.995728i \(-0.529432\pi\)
−0.0923316 + 0.995728i \(0.529432\pi\)
\(678\) −15.1539 + 26.2472i −0.581980 + 1.00802i
\(679\) −21.7215 + 37.6227i −0.833594 + 1.44383i
\(680\) 0 0
\(681\) −24.2496 −0.929248
\(682\) −7.24440 12.5477i −0.277403 0.480475i
\(683\) −5.88126 10.1866i −0.225040 0.389781i 0.731291 0.682065i \(-0.238918\pi\)
−0.956331 + 0.292284i \(0.905585\pi\)
\(684\) 10.0000 0.382360
\(685\) 0 0
\(686\) 20.0669 34.7569i 0.766157 1.32702i
\(687\) 17.8051 30.8393i 0.679306 1.17659i
\(688\) 9.72953 0.370935
\(689\) 0.0460332 + 2.31533i 0.00175372 + 0.0882071i
\(690\) 0 0
\(691\) −2.43342 + 4.21481i −0.0925717 + 0.160339i −0.908593 0.417684i \(-0.862842\pi\)
0.816021 + 0.578022i \(0.196175\pi\)
\(692\) 3.06329 5.30577i 0.116449 0.201695i
\(693\) 1.52574 + 2.64265i 0.0579579 + 0.100386i
\(694\) −9.71254 −0.368683
\(695\) 0 0
\(696\) −20.3950 35.3252i −0.773070 1.33900i
\(697\) −12.1925 −0.461825
\(698\) −30.9644 53.6320i −1.17202 2.03000i
\(699\) 7.48079 12.9571i 0.282949 0.490083i
\(700\) 0 0
\(701\) 21.3828 0.807617 0.403808 0.914844i \(-0.367686\pi\)
0.403808 + 0.914844i \(0.367686\pi\)
\(702\) −23.6222 13.0192i −0.891563 0.491378i
\(703\) −1.67059 −0.0630076
\(704\) −0.0857934 + 0.148599i −0.00323346 + 0.00560052i
\(705\) 0 0
\(706\) 34.4427 + 59.6564i 1.29627 + 2.24520i
\(707\) 38.8822 1.46232
\(708\) −36.6417 63.4654i −1.37708 2.38517i
\(709\) 13.0582 + 22.6175i 0.490412 + 0.849419i 0.999939 0.0110357i \(-0.00351286\pi\)
−0.509527 + 0.860455i \(0.670180\pi\)
\(710\) 0 0
\(711\) −0.848960 1.47044i −0.0318385 0.0551459i
\(712\) 39.6554 68.6851i 1.48615 2.57408i
\(713\) −9.64680 + 16.7087i −0.361276 + 0.625748i
\(714\) 19.7125 0.737723
\(715\) 0 0
\(716\) 34.8880 1.30383
\(717\) −4.30585 + 7.45795i −0.160805 + 0.278522i
\(718\) −34.3724 + 59.5347i −1.28277 + 2.22182i
\(719\) −18.3387 31.7635i −0.683918 1.18458i −0.973776 0.227510i \(-0.926941\pi\)
0.289858 0.957070i \(-0.406392\pi\)
\(720\) 0 0
\(721\) 16.1159 + 27.9135i 0.600187 + 1.03955i
\(722\) 21.8132 + 37.7815i 0.811803 + 1.40608i
\(723\) 42.5679 1.58312
\(724\) 8.66324 + 15.0052i 0.321967 + 0.557663i
\(725\) 0 0
\(726\) 29.0390 50.2971i 1.07774 1.86670i
\(727\) −26.2596 −0.973916 −0.486958 0.873425i \(-0.661893\pi\)
−0.486958 + 0.873425i \(0.661893\pi\)
\(728\) −57.2716 + 34.6016i −2.12263 + 1.28242i
\(729\) 0.614542 0.0227608
\(730\) 0 0
\(731\) −0.836758 + 1.44931i −0.0309486 + 0.0536046i
\(732\) 10.9500 + 18.9659i 0.404723 + 0.701000i
\(733\) 31.7811 1.17386 0.586931 0.809637i \(-0.300336\pi\)
0.586931 + 0.809637i \(0.300336\pi\)
\(734\) 8.83513 + 15.3029i 0.326110 + 0.564840i
\(735\) 0 0
\(736\) −11.8073 −0.435222
\(737\) −2.54989 4.41654i −0.0939265 0.162685i
\(738\) 20.7326 35.9099i 0.763176 1.32186i
\(739\) 17.0685 29.5635i 0.627875 1.08751i −0.360102 0.932913i \(-0.617258\pi\)
0.987977 0.154599i \(-0.0494085\pi\)
\(740\) 0 0
\(741\) −0.210609 10.5930i −0.00773691 0.389144i
\(742\) −4.80479 −0.176390
\(743\) −1.56031 + 2.70254i −0.0572423 + 0.0991465i −0.893227 0.449607i \(-0.851564\pi\)
0.835984 + 0.548753i \(0.184897\pi\)
\(744\) 60.9237 105.523i 2.23357 3.86866i
\(745\) 0 0
\(746\) 5.88798 0.215574
\(747\) 9.68401 + 16.7732i 0.354320 + 0.613699i
\(748\) 1.74151 + 3.01638i 0.0636758 + 0.110290i
\(749\) 31.3649 1.14605
\(750\) 0 0
\(751\) −0.742024 + 1.28522i −0.0270769 + 0.0468985i −0.879246 0.476367i \(-0.841953\pi\)
0.852169 + 0.523266i \(0.175287\pi\)
\(752\) −21.9304 + 37.9845i −0.799718 + 1.38515i
\(753\) 7.90881 0.288213
\(754\) −23.5688 + 14.2395i −0.858325 + 0.518572i
\(755\) 0 0
\(756\) 19.3460 33.5082i 0.703607 1.21868i
\(757\) −2.54989 + 4.41654i −0.0926774 + 0.160522i −0.908637 0.417587i \(-0.862876\pi\)
0.815960 + 0.578109i \(0.196209\pi\)
\(758\) −6.58767 11.4102i −0.239275 0.414436i
\(759\) 2.94369 0.106849
\(760\) 0 0
\(761\) 14.8931 + 25.7955i 0.539873 + 0.935088i 0.998910 + 0.0466707i \(0.0148611\pi\)
−0.459037 + 0.888417i \(0.651806\pi\)
\(762\) 94.4433 3.42132
\(763\) 4.80479 + 8.32215i 0.173945 + 0.301282i
\(764\) −11.0758 + 19.1839i −0.400709 + 0.694048i
\(765\) 0 0
\(766\) −52.5973 −1.90042
\(767\) −23.4437 + 14.1639i −0.846501 + 0.511428i
\(768\) −62.7228 −2.26331
\(769\) −9.54930 + 16.5399i −0.344356 + 0.596443i −0.985237 0.171198i \(-0.945236\pi\)
0.640880 + 0.767641i \(0.278570\pi\)
\(770\) 0 0
\(771\) −14.2791 24.7322i −0.514250 0.890707i
\(772\) −22.2088 −0.799311
\(773\) −24.6153 42.6350i −0.885351 1.53347i −0.845311 0.534275i \(-0.820585\pi\)
−0.0400400 0.999198i \(-0.512749\pi\)
\(774\) −2.84570 4.92889i −0.102286 0.177165i
\(775\) 0 0
\(776\) −46.6831 80.8574i −1.67582 2.90261i
\(777\) 3.87167 6.70593i 0.138895 0.240574i
\(778\) −25.1362 + 43.5373i −0.901178 + 1.56089i
\(779\) −13.5967 −0.487151
\(780\) 0 0
\(781\) −1.67352 −0.0598831
\(782\) 3.35412 5.80951i 0.119943 0.207748i
\(783\) 4.40783 7.63458i 0.157523 0.272838i
\(784\) −5.81754 10.0763i −0.207769 0.359867i
\(785\) 0 0
\(786\)