Properties

Label 325.2.e.e.276.6
Level $325$
Weight $2$
Character 325.276
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 276.6
Root \(1.27287 - 2.20467i\) of defining polynomial
Character \(\chi\) \(=\) 325.276
Dual form 325.2.e.e.126.6

$q$-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 \(\left(\mathbb{Z}/325\mathbb{Z}\right)^\times\).

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

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 0.827421 + 0.561582i \(0.189807\pi\)
0.0726333 + 0.997359i \(0.476860\pi\)
\(3\) 1.07646 + 1.86449i 0.621496 + 1.07646i 0.989207 + 0.146523i \(0.0468082\pi\)
−0.367711 + 0.929940i \(0.619858\pi\)
\(4\) −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 −0.442543 0.896747i \(-0.645924\pi\)
0.997877 0.0651198i \(-0.0207430\pi\)
\(8\) −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 0.909919 0.414787i \(-0.136144\pi\)
−0.814175 + 0.580619i \(0.802811\pi\)
\(12\) −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 \(-0.785912\pi\)
0.930646 + 0.365920i \(0.119246\pi\)
\(18\) −4.16251 −0.981113
\(19\) −0.682456 + 1.18205i −0.156566 + 0.271180i −0.933628 0.358244i \(-0.883376\pi\)
0.777062 + 0.629424i \(0.216709\pi\)
\(20\) 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 \(-0.238728\pi\)
−0.956157 + 0.292856i \(0.905394\pi\)
\(24\) −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 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 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 \(-0.198746\pi\)
−0.911936 + 0.410333i \(0.865412\pi\)
\(38\) −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 0.933168 + 0.359440i \(0.117032\pi\)
−0.155300 + 0.987867i \(0.549634\pi\)
\(42\) 8.05279 + 13.9478i 1.24257 + 2.15220i
\(43\) 0.683650 1.18412i 0.104256 0.180576i −0.809178 0.587563i \(-0.800087\pi\)
0.913434 + 0.406987i \(0.133421\pi\)
\(44\) −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 \(-0.648412\pi\)
−0.449540 + 0.893260i \(0.648412\pi\)
\(48\) 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 \(-0.485954\pi\)
0.0441123 + 0.999027i \(0.485954\pi\)
\(54\) 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 −0.999980 0.00633858i \(-0.997982\pi\)
0.505479 + 0.862839i \(0.331316\pi\)
\(60\) 0 0
\(61\) 1.13509 1.96603i 0.145333 0.251725i −0.784164 0.620554i \(-0.786908\pi\)
0.929497 + 0.368829i \(0.120241\pi\)
\(62\) −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 \(-0.329857\pi\)
−0.999940 + 0.0109212i \(0.996524\pi\)
\(68\) 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 −0.933555 0.358435i \(-0.883311\pi\)
0.777191 + 0.629265i \(0.216644\pi\)
\(72\) 5.16315 8.94284i 0.608483 1.05392i
\(73\) −10.3263 −1.20860 −0.604301 0.796756i \(-0.706547\pi\)
−0.604301 + 0.796756i \(0.706547\pi\)
\(74\) 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 \(-0.274730\pi\)
0.650092 + 0.759855i \(0.274730\pi\)
\(84\) −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 0.979126 + 0.203253i \(0.0651513\pi\)
−0.313541 + 0.949575i \(0.601515\pi\)
\(90\) 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 −0.197031 0.980397i \(-0.563130\pi\)
0.947564 0.319565i \(-0.103537\pi\)
\(98\) 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 −0.981054 0.193732i \(-0.937941\pi\)
0.322750 0.946484i \(-0.395393\pi\)
\(102\) 3.35412 + 5.80951i 0.332108 + 0.575228i
\(103\) 10.9686 1.08077 0.540383 0.841419i \(-0.318279\pi\)
0.540383 + 0.841419i \(0.318279\pi\)
\(104\) −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 0.999829 + 0.0184903i \(0.00588599\pi\)
−0.483901 + 0.875123i \(0.660781\pi\)
\(108\) −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 \(-0.749578\pi\)
0.966268 + 0.257537i \(0.0829110\pi\)
\(114\) −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 0.940493 + 0.339813i \(0.110364\pi\)
−0.175959 + 0.984397i \(0.556303\pi\)
\(128\) −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 \(-0.712532\pi\)
0.989637 + 0.143593i \(0.0458657\pi\)
\(138\) 11.7997 1.00446
\(139\) −7.16324 + 12.4071i −0.607578 + 1.05236i 0.384060 + 0.923308i \(0.374526\pi\)
−0.991638 + 0.129048i \(0.958808\pi\)
\(140\) 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 −0.264826 0.964296i \(-0.585315\pi\)
0.967518 0.252802i \(-0.0813521\pi\)
\(150\) 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 \(-0.761800\pi\)
−0.732829 + 0.680413i \(0.761800\pi\)
\(158\) 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 \(-0.783126\pi\)
0.933814 + 0.357760i \(0.116459\pi\)
\(164\) −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 \(-0.202936\pi\)
−0.917258 + 0.398294i \(0.869602\pi\)
\(168\) −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 \(-0.849886\pi\)
0.838866 + 0.544337i \(0.183219\pi\)
\(174\) 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 0.683061 0.730362i \(-0.260648\pi\)
−0.974042 + 0.226367i \(0.927315\pi\)
\(180\) 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 −0.941489 0.337043i \(-0.890573\pi\)
0.762633 + 0.646832i \(0.223906\pi\)
\(192\) −0.290836 0.503743i −0.0209893 0.0363545i
\(193\) −2.47822 4.29240i −0.178386 0.308974i 0.762942 0.646467i \(-0.223754\pi\)
−0.941328 + 0.337493i \(0.890421\pi\)
\(194\) 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 \(-0.243912\pi\)
−0.960799 + 0.277246i \(0.910578\pi\)
\(198\) −1.32178 2.28939i −0.0939349 0.162700i
\(199\) −2.58772 + 4.48207i −0.183439 + 0.317725i −0.943049 0.332653i \(-0.892056\pi\)
0.759611 + 0.650378i \(0.225390\pi\)
\(200\) 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 0.999799 0.0200732i \(-0.00638994\pi\)
−0.517283 + 0.855814i \(0.673057\pi\)
\(212\) −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 \(-0.166578\pi\)
−0.865886 + 0.500241i \(0.833245\pi\)
\(224\) −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 \(-0.955277\pi\)
0.616351 + 0.787471i \(0.288610\pi\)
\(228\) 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 \(-0.426900\pi\)
0.227636 + 0.973746i \(0.426900\pi\)
\(234\) −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 0.349310 + 0.937007i \(0.386416\pi\)
−0.986127 + 0.165992i \(0.946917\pi\)
\(242\) 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 −0.918153 0.396226i \(-0.870320\pi\)
0.802218 + 0.597031i \(0.203653\pi\)
\(252\) −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 \(-0.0308962\pi\)
−0.581574 + 0.813494i \(0.697563\pi\)
\(258\) 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 0.777674 + 0.628667i \(0.216399\pi\)
0.155605 + 0.987819i \(0.450267\pi\)
\(264\) 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 −0.297203 0.954814i \(-0.596054\pi\)
0.975495 0.220022i \(-0.0706129\pi\)
\(270\) 0 0
\(271\) 5.91421 + 10.2437i 0.359262 + 0.622261i 0.987838 0.155488i \(-0.0496950\pi\)
−0.628575 + 0.777749i \(0.716362\pi\)
\(272\) −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 −0.495729 0.868477i \(-0.665099\pi\)
0.999988 0.00492452i \(-0.00156753\pi\)
\(278\) −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 \(-0.251055\pi\)
−0.966778 + 0.255617i \(0.917721\pi\)
\(284\) −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 0.0764476 + 0.997074i \(0.475642\pi\)
−0.901715 + 0.432331i \(0.857691\pi\)
\(294\) 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 \(-0.618261\pi\)
−0.363039 + 0.931774i \(0.618261\pi\)
\(308\) −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 \(-0.744460\pi\)
−0.694692 + 0.719307i \(0.744460\pi\)
\(314\) −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 \(-0.497905\pi\)
0.00658196 + 0.999978i \(0.497905\pi\)
\(318\) −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 −0.496334 0.868132i \(-0.665321\pi\)
0.999991 0.00422829i \(-0.00134591\pi\)
\(332\) −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 \(-0.303051\pi\)
0.580003 + 0.814614i \(0.303051\pi\)
\(338\) −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 \(-0.865987\pi\)
0.810270 + 0.586057i \(0.199321\pi\)
\(348\) 14.4702 + 25.0631i 0.775684 + 1.34352i
\(349\) −12.1632 21.0674i −0.651083 1.12771i −0.982860 0.184352i \(-0.940981\pi\)
0.331777 0.943358i \(-0.392352\pi\)
\(350\) 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 −0.960958 0.276696i \(-0.910761\pi\)
0.240853 0.970562i \(-0.422573\pi\)
\(354\) −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 \(-0.224652\pi\)
−0.942276 + 0.334836i \(0.891319\pi\)
\(368\) −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 \(-0.814262\pi\)
0.894411 + 0.447247i \(0.147595\pi\)
\(374\) 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 0.791880 0.610677i \(-0.209103\pi\)
−0.924802 + 0.380449i \(0.875769\pi\)
\(380\) 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 0.471611 + 0.881807i \(0.343673\pi\)
−0.999473 + 0.0324760i \(0.989661\pi\)
\(384\) 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 \(-0.909042\pi\)
0.723839 + 0.689969i \(0.242376\pi\)
\(398\) −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 −0.990940 0.134308i \(-0.957119\pi\)
0.379156 0.925333i \(-0.376214\pi\)
\(402\) 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 −0.0565671 + 0.998399i \(0.518015\pi\)
−0.836355 + 0.548188i \(0.815318\pi\)
\(410\) 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 0.937623 0.347655i \(-0.113022\pi\)
−0.769889 + 0.638178i \(0.779689\pi\)
\(420\) 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 0.992629 0.121193i \(-0.0386719\pi\)
−0.601270 + 0.799046i \(0.705339\pi\)
\(432\) −10.4552 18.1089i −0.503025 0.871265i
\(433\) 0.128130 0.221929i 0.00615756 0.0106652i −0.862930 0.505323i \(-0.831373\pi\)
0.869088 + 0.494658i \(0.164707\pi\)
\(434\) −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 0.942318 0.334718i \(-0.108641\pi\)
−0.761034 + 0.648712i \(0.775308\pi\)
\(440\) 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 \(-0.532743\pi\)
−0.102683 + 0.994714i \(0.532743\pi\)
\(444\) 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 −0.902208 0.431301i \(-0.858055\pi\)
0.824622 + 0.565685i \(0.191388\pi\)
\(450\) 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 \(-0.284163\pi\)
−0.988093 + 0.153859i \(0.950830\pi\)
\(458\) −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 0.389611 + 0.920979i \(0.372609\pi\)
−0.992397 + 0.123076i \(0.960724\pi\)
\(462\) −5.11424 + 8.85812i −0.237936 + 0.412117i
\(463\) −7.04045 −0.327197 −0.163599 0.986527i \(-0.552310\pi\)
−0.163599 + 0.986527i \(0.552310\pi\)
\(464\) −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 \(-0.643337\pi\)
−0.435241 + 0.900314i \(0.643337\pi\)
\(468\) −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 0.998051 0.0624114i \(-0.0198791\pi\)
−0.553075 + 0.833131i \(0.686546\pi\)
\(480\) 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 0.223495 + 0.974705i \(0.428253\pi\)
−0.955867 + 0.293800i \(0.905080\pi\)
\(488\) −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 −0.983848 0.179007i \(-0.942711\pi\)
0.336899 0.941541i \(-0.390622\pi\)
\(492\) −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 0.361551 + 0.932352i \(0.382247\pi\)
−0.988216 + 0.153063i \(0.951086\pi\)
\(504\) −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 0.531427 0.847104i \(-0.321656\pi\)
−0.999327 + 0.0366773i \(0.988323\pi\)
\(510\) 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 −0.982416 0.186706i \(-0.940219\pi\)
0.329516 0.944150i \(-0.393114\pi\)
\(524\) −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 \(-0.479313\pi\)
0.0649454 + 0.997889i \(0.479313\pi\)
\(548\) 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 \(-0.0221639\pi\)
−0.559041 + 0.829140i \(0.688831\pi\)
\(558\) 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 \(-0.759147\pi\)
0.958091 + 0.286464i \(0.0924799\pi\)
\(564\) 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 −0.833416 0.552647i \(-0.813618\pi\)
−0.0618981 0.998082i \(-0.519715\pi\)
\(570\) 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 \(-0.375144\pi\)
0.382265 + 0.924053i \(0.375144\pi\)
\(578\) −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 \(-0.171284\pi\)
−0.873187 + 0.487385i \(0.837951\pi\)
\(588\) 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 \(-0.223738\pi\)
0.762975 + 0.646428i \(0.223738\pi\)
\(594\) −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 0.717258 0.696807i \(-0.245397\pi\)
−0.962082 + 0.272760i \(0.912063\pi\)
\(602\) 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 −0.143809 0.989606i \(-0.545935\pi\)
0.928928 0.370261i \(-0.120732\pi\)
\(608\) 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 \(-0.280161\pi\)
−0.986081 + 0.166269i \(0.946828\pi\)
\(614\) −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 −0.466464 0.884540i \(-0.654472\pi\)
0.999266 0.0383009i \(-0.0121945\pi\)
\(618\) −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 −0.582851 0.812579i \(-0.698063\pi\)
0.995140 + 0.0984745i \(0.0313963\pi\)
\(632\) −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 −0.995785 0.0917132i \(-0.970766\pi\)
0.577319 + 0.816519i \(0.304099\pi\)
\(642\) −58.4997 −2.30880
\(643\) −5.76682 + 9.98843i −0.227421 + 0.393905i −0.957043 0.289946i \(-0.906363\pi\)
0.729622 + 0.683851i \(0.239696\pi\)
\(644\) 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 −0.973444 0.228925i \(-0.926479\pi\)
0.288467 0.957490i \(-0.406854\pi\)
\(648\) −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 \(-0.0227830\pi\)
−0.560653 + 0.828051i \(0.689450\pi\)
\(654\) 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 −0.857460 0.514550i \(-0.827959\pi\)
0.874344 + 0.485307i \(0.161292\pi\)
\(660\) 0 0
\(661\) −6.65430 11.5256i −0.258822 0.448293i 0.707104 0.707109i \(-0.250001\pi\)
−0.965927 + 0.258816i \(0.916668\pi\)
\(662\) 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 \(-0.200554\pi\)
−0.914252 + 0.405146i \(0.867221\pi\)
\(674\) 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 \(-0.470568\pi\)
0.0923316 + 0.995728i \(0.470568\pi\)
\(678\) 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 \(-0.761082\pi\)
0.956331 + 0.292284i \(0.0944154\pi\)
\(684\) 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 0.816021 0.578022i \(-0.196175\pi\)
−0.908593 + 0.417684i \(0.862842\pi\)
\(692\) −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 −0.509527 0.860455i \(-0.670180\pi\)
0.999939 + 0.0110357i \(0.00351286\pi\)
\(710\) 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 0.289858 + 0.957070i \(0.406392\pi\)
−0.973776 + 0.227510i \(0.926941\pi\)
\(720\) 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 \(-0.338107\pi\)
0.486958 + 0.873425i \(0.338107\pi\)
\(728\) 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 \(-0.699664\pi\)
−0.586931 + 0.809637i \(0.699664\pi\)
\(734\) 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 0.987977 + 0.154599i \(0.0494085\pi\)
−0.360102 + 0.932913i \(0.617258\pi\)
\(740\) 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 \(-0.148436\pi\)
−0.835984 + 0.548753i \(0.815103\pi\)
\(744\) 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 0.852169 0.523266i \(-0.175287\pi\)
−0.879246 + 0.476367i \(0.841953\pi\)
\(752\) 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 \(-0.137124\pi\)
−0.815960 + 0.578109i \(0.803791\pi\)
\(758\) 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 −0.459037 0.888417i \(-0.651806\pi\)
0.998910 0.0466707i \(-0.0148611\pi\)
\(762\) −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 0.640880 0.767641i \(-0.278570\pi\)
−0.985237 + 0.171198i \(0.945236\pi\)
\(770\) 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 0.0400400 0.999198i \(-0.487251\pi\)
0.845311 0.534275i \(-0.179415\pi\)
\(774\) −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
\(786\) −27.4039 +