Properties

Label 546.2.p.c.281.2
Level $546$
Weight $2$
Character 546.281
Analytic conductor $4.360$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 546.p (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(20\)
Relative dimension: \(10\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} - \cdots)\)
Defining polynomial: \(x^{20} - 4 x^{19} + 8 x^{18} - 20 x^{17} + 56 x^{16} - 140 x^{15} + 288 x^{14} - 532 x^{13} + 1065 x^{12} - 2080 x^{11} + 3712 x^{10} - 6240 x^{9} + 9585 x^{8} - 14364 x^{7} + 23328 x^{6} - 34020 x^{5} + 40824 x^{4} - 43740 x^{3} + 52488 x^{2} - 78732 x + 59049\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 281.2
Root \(0.831607 - 1.51935i\) of defining polynomial
Character \(\chi\) \(=\) 546.281
Dual form 546.2.p.c.239.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} -1.00000i q^{4} +(-2.72859 + 2.72859i) q^{5} +(1.51935 + 0.831607i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} +O(q^{10})\) \(q+(-0.707107 + 0.707107i) q^{2} +(-0.486309 - 1.66238i) q^{3} -1.00000i q^{4} +(-2.72859 + 2.72859i) q^{5} +(1.51935 + 0.831607i) q^{6} +(0.707107 - 0.707107i) q^{7} +(0.707107 + 0.707107i) q^{8} +(-2.52701 + 1.61686i) q^{9} -3.85881i q^{10} +(0.0114588 + 0.0114588i) q^{11} +(-1.66238 + 0.486309i) q^{12} +(1.73087 - 3.16292i) q^{13} +1.00000i q^{14} +(5.86288 + 3.20901i) q^{15} -1.00000 q^{16} +5.61037 q^{17} +(0.643571 - 2.93016i) q^{18} +(-0.157765 - 0.157765i) q^{19} +(2.72859 + 2.72859i) q^{20} +(-1.51935 - 0.831607i) q^{21} -0.0162051 q^{22} -2.57099 q^{23} +(0.831607 - 1.51935i) q^{24} -9.89038i q^{25} +(1.01261 + 3.46044i) q^{26} +(3.91674 + 3.41455i) q^{27} +(-0.707107 - 0.707107i) q^{28} -7.70551i q^{29} +(-6.41480 + 1.87657i) q^{30} +(6.66648 + 6.66648i) q^{31} +(0.707107 - 0.707107i) q^{32} +(0.0134763 - 0.0246213i) q^{33} +(-3.96713 + 3.96713i) q^{34} +3.85881i q^{35} +(1.61686 + 2.52701i) q^{36} +(7.86287 - 7.86287i) q^{37} +0.223113 q^{38} +(-6.09972 - 1.33921i) q^{39} -3.85881 q^{40} +(5.18774 - 5.18774i) q^{41} +(1.66238 - 0.486309i) q^{42} -5.09898i q^{43} +(0.0114588 - 0.0114588i) q^{44} +(2.48342 - 11.3069i) q^{45} +(1.81796 - 1.81796i) q^{46} +(-3.31273 - 3.31273i) q^{47} +(0.486309 + 1.66238i) q^{48} -1.00000i q^{49} +(6.99356 + 6.99356i) q^{50} +(-2.72837 - 9.32656i) q^{51} +(-3.16292 - 1.73087i) q^{52} -2.49125i q^{53} +(-5.18400 + 0.355103i) q^{54} -0.0625325 q^{55} +1.00000 q^{56} +(-0.185543 + 0.338988i) q^{57} +(5.44862 + 5.44862i) q^{58} +(2.10029 + 2.10029i) q^{59} +(3.20901 - 5.86288i) q^{60} +1.82875 q^{61} -9.42782 q^{62} +(-0.643571 + 2.93016i) q^{63} +1.00000i q^{64} +(3.90748 + 13.3531i) q^{65} +(0.00788071 + 0.0269391i) q^{66} +(8.61829 + 8.61829i) q^{67} -5.61037i q^{68} +(1.25029 + 4.27396i) q^{69} +(-2.72859 - 2.72859i) q^{70} +(-2.76005 + 2.76005i) q^{71} +(-2.93016 - 0.643571i) q^{72} +(-9.83977 + 9.83977i) q^{73} +11.1198i q^{74} +(-16.4416 + 4.80978i) q^{75} +(-0.157765 + 0.157765i) q^{76} +0.0162051 q^{77} +(5.26011 - 3.36619i) q^{78} -5.90280 q^{79} +(2.72859 - 2.72859i) q^{80} +(3.77153 - 8.17163i) q^{81} +7.33658i q^{82} +(11.9527 - 11.9527i) q^{83} +(-0.831607 + 1.51935i) q^{84} +(-15.3084 + 15.3084i) q^{85} +(3.60552 + 3.60552i) q^{86} +(-12.8095 + 3.74726i) q^{87} +0.0162051i q^{88} +(5.15703 + 5.15703i) q^{89} +(6.23915 + 9.75123i) q^{90} +(-1.01261 - 3.46044i) q^{91} +2.57099i q^{92} +(7.84024 - 14.3242i) q^{93} +4.68491 q^{94} +0.860951 q^{95} +(-1.51935 - 0.831607i) q^{96} +(5.94479 + 5.94479i) q^{97} +(0.707107 + 0.707107i) q^{98} +(-0.0474836 - 0.0104292i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} + O(q^{10}) \) \( 20q - 4q^{5} - 4q^{6} - 8q^{9} - 16q^{11} - 8q^{12} + 4q^{13} - 4q^{15} - 20q^{16} + 12q^{17} - 8q^{18} + 12q^{19} + 4q^{20} + 4q^{21} - 12q^{22} - 4q^{23} + 4q^{24} + 24q^{27} + 12q^{30} - 8q^{31} - 48q^{33} - 4q^{34} + 32q^{37} - 4q^{38} - 16q^{39} - 4q^{40} + 8q^{41} + 8q^{42} - 16q^{44} + 16q^{45} - 8q^{46} + 32q^{50} - 8q^{51} - 8q^{52} + 28q^{54} + 28q^{55} + 20q^{56} + 36q^{57} - 4q^{58} + 20q^{59} - 4q^{60} - 4q^{61} + 48q^{62} + 8q^{63} + 52q^{65} - 36q^{67} + 68q^{69} - 4q^{70} - 28q^{71} - 16q^{72} - 24q^{73} - 76q^{75} + 12q^{76} + 12q^{77} + 40q^{78} - 64q^{79} + 4q^{80} + 32q^{81} - 24q^{83} - 4q^{84} + 24q^{85} + 4q^{86} + 4q^{87} - 4q^{89} - 8q^{90} - 32q^{93} - 40q^{94} - 76q^{95} + 4q^{96} + 32q^{97} - 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).

\(n\) \(157\) \(365\) \(379\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707107 + 0.707107i −0.500000 + 0.500000i
\(3\) −0.486309 1.66238i −0.280771 0.959775i
\(4\) 1.00000i 0.500000i
\(5\) −2.72859 + 2.72859i −1.22026 + 1.22026i −0.252723 + 0.967539i \(0.581326\pi\)
−0.967539 + 0.252723i \(0.918674\pi\)
\(6\) 1.51935 + 0.831607i 0.620273 + 0.339502i
\(7\) 0.707107 0.707107i 0.267261 0.267261i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) −2.52701 + 1.61686i −0.842336 + 0.538953i
\(10\) 3.85881i 1.22026i
\(11\) 0.0114588 + 0.0114588i 0.00345495 + 0.00345495i 0.708832 0.705377i \(-0.249222\pi\)
−0.705377 + 0.708832i \(0.749222\pi\)
\(12\) −1.66238 + 0.486309i −0.479887 + 0.140385i
\(13\) 1.73087 3.16292i 0.480058 0.877237i
\(14\) 1.00000i 0.267261i
\(15\) 5.86288 + 3.20901i 1.51379 + 0.828563i
\(16\) −1.00000 −0.250000
\(17\) 5.61037 1.36071 0.680357 0.732881i \(-0.261825\pi\)
0.680357 + 0.732881i \(0.261825\pi\)
\(18\) 0.643571 2.93016i 0.151691 0.690644i
\(19\) −0.157765 0.157765i −0.0361938 0.0361938i 0.688778 0.724972i \(-0.258147\pi\)
−0.724972 + 0.688778i \(0.758147\pi\)
\(20\) 2.72859 + 2.72859i 0.610131 + 0.610131i
\(21\) −1.51935 0.831607i −0.331550 0.181472i
\(22\) −0.0162051 −0.00345495
\(23\) −2.57099 −0.536088 −0.268044 0.963407i \(-0.586377\pi\)
−0.268044 + 0.963407i \(0.586377\pi\)
\(24\) 0.831607 1.51935i 0.169751 0.310136i
\(25\) 9.89038i 1.97808i
\(26\) 1.01261 + 3.46044i 0.198590 + 0.678647i
\(27\) 3.91674 + 3.41455i 0.753777 + 0.657130i
\(28\) −0.707107 0.707107i −0.133631 0.133631i
\(29\) 7.70551i 1.43088i −0.698675 0.715439i \(-0.746227\pi\)
0.698675 0.715439i \(-0.253773\pi\)
\(30\) −6.41480 + 1.87657i −1.17118 + 0.342614i
\(31\) 6.66648 + 6.66648i 1.19733 + 1.19733i 0.974962 + 0.222373i \(0.0713802\pi\)
0.222373 + 0.974962i \(0.428620\pi\)
\(32\) 0.707107 0.707107i 0.125000 0.125000i
\(33\) 0.0134763 0.0246213i 0.00234592 0.00428602i
\(34\) −3.96713 + 3.96713i −0.680357 + 0.680357i
\(35\) 3.85881i 0.652257i
\(36\) 1.61686 + 2.52701i 0.269477 + 0.421168i
\(37\) 7.86287 7.86287i 1.29265 1.29265i 0.359503 0.933144i \(-0.382946\pi\)
0.933144 0.359503i \(-0.117054\pi\)
\(38\) 0.223113 0.0361938
\(39\) −6.09972 1.33921i −0.976736 0.214445i
\(40\) −3.85881 −0.610131
\(41\) 5.18774 5.18774i 0.810189 0.810189i −0.174473 0.984662i \(-0.555822\pi\)
0.984662 + 0.174473i \(0.0558221\pi\)
\(42\) 1.66238 0.486309i 0.256511 0.0750391i
\(43\) 5.09898i 0.777587i −0.921325 0.388793i \(-0.872892\pi\)
0.921325 0.388793i \(-0.127108\pi\)
\(44\) 0.0114588 0.0114588i 0.00172747 0.00172747i
\(45\) 2.48342 11.3069i 0.370206 1.68553i
\(46\) 1.81796 1.81796i 0.268044 0.268044i
\(47\) −3.31273 3.31273i −0.483211 0.483211i 0.422944 0.906156i \(-0.360997\pi\)
−0.906156 + 0.422944i \(0.860997\pi\)
\(48\) 0.486309 + 1.66238i 0.0701927 + 0.239944i
\(49\) 1.00000i 0.142857i
\(50\) 6.99356 + 6.99356i 0.989038 + 0.989038i
\(51\) −2.72837 9.32656i −0.382049 1.30598i
\(52\) −3.16292 1.73087i −0.438618 0.240029i
\(53\) 2.49125i 0.342200i −0.985254 0.171100i \(-0.945268\pi\)
0.985254 0.171100i \(-0.0547321\pi\)
\(54\) −5.18400 + 0.355103i −0.705454 + 0.0483234i
\(55\) −0.0625325 −0.00843188
\(56\) 1.00000 0.133631
\(57\) −0.185543 + 0.338988i −0.0245757 + 0.0449000i
\(58\) 5.44862 + 5.44862i 0.715439 + 0.715439i
\(59\) 2.10029 + 2.10029i 0.273435 + 0.273435i 0.830481 0.557047i \(-0.188066\pi\)
−0.557047 + 0.830481i \(0.688066\pi\)
\(60\) 3.20901 5.86288i 0.414281 0.756895i
\(61\) 1.82875 0.234148 0.117074 0.993123i \(-0.462649\pi\)
0.117074 + 0.993123i \(0.462649\pi\)
\(62\) −9.42782 −1.19733
\(63\) −0.643571 + 2.93016i −0.0810823 + 0.369165i
\(64\) 1.00000i 0.125000i
\(65\) 3.90748 + 13.3531i 0.484663 + 1.65625i
\(66\) 0.00788071 + 0.0269391i 0.000970048 + 0.00331597i
\(67\) 8.61829 + 8.61829i 1.05289 + 1.05289i 0.998521 + 0.0543710i \(0.0173154\pi\)
0.0543710 + 0.998521i \(0.482685\pi\)
\(68\) 5.61037i 0.680357i
\(69\) 1.25029 + 4.27396i 0.150518 + 0.514524i
\(70\) −2.72859 2.72859i −0.326129 0.326129i
\(71\) −2.76005 + 2.76005i −0.327557 + 0.327557i −0.851657 0.524100i \(-0.824402\pi\)
0.524100 + 0.851657i \(0.324402\pi\)
\(72\) −2.93016 0.643571i −0.345322 0.0758456i
\(73\) −9.83977 + 9.83977i −1.15166 + 1.15166i −0.165438 + 0.986220i \(0.552904\pi\)
−0.986220 + 0.165438i \(0.947096\pi\)
\(74\) 11.1198i 1.29265i
\(75\) −16.4416 + 4.80978i −1.89851 + 0.555386i
\(76\) −0.157765 + 0.157765i −0.0180969 + 0.0180969i
\(77\) 0.0162051 0.00184675
\(78\) 5.26011 3.36619i 0.595590 0.381146i
\(79\) −5.90280 −0.664117 −0.332058 0.943259i \(-0.607743\pi\)
−0.332058 + 0.943259i \(0.607743\pi\)
\(80\) 2.72859 2.72859i 0.305065 0.305065i
\(81\) 3.77153 8.17163i 0.419059 0.907959i
\(82\) 7.33658i 0.810189i
\(83\) 11.9527 11.9527i 1.31197 1.31197i 0.392017 0.919958i \(-0.371778\pi\)
0.919958 0.392017i \(-0.128222\pi\)
\(84\) −0.831607 + 1.51935i −0.0907358 + 0.165775i
\(85\) −15.3084 + 15.3084i −1.66043 + 1.66043i
\(86\) 3.60552 + 3.60552i 0.388793 + 0.388793i
\(87\) −12.8095 + 3.74726i −1.37332 + 0.401749i
\(88\) 0.0162051i 0.00172747i
\(89\) 5.15703 + 5.15703i 0.546645 + 0.546645i 0.925469 0.378824i \(-0.123671\pi\)
−0.378824 + 0.925469i \(0.623671\pi\)
\(90\) 6.23915 + 9.75123i 0.657664 + 1.02787i
\(91\) −1.01261 3.46044i −0.106151 0.362752i
\(92\) 2.57099i 0.268044i
\(93\) 7.84024 14.3242i 0.812995 1.48535i
\(94\) 4.68491 0.483211
\(95\) 0.860951 0.0883318
\(96\) −1.51935 0.831607i −0.155068 0.0848755i
\(97\) 5.94479 + 5.94479i 0.603602 + 0.603602i 0.941266 0.337665i \(-0.109637\pi\)
−0.337665 + 0.941266i \(0.609637\pi\)
\(98\) 0.707107 + 0.707107i 0.0714286 + 0.0714286i
\(99\) −0.0474836 0.0104292i −0.00477228 0.00104817i
\(100\) −9.89038 −0.989038
\(101\) −4.06932 −0.404913 −0.202456 0.979291i \(-0.564892\pi\)
−0.202456 + 0.979291i \(0.564892\pi\)
\(102\) 8.52412 + 4.66562i 0.844014 + 0.461965i
\(103\) 17.5417i 1.72843i 0.503118 + 0.864217i \(0.332186\pi\)
−0.503118 + 0.864217i \(0.667814\pi\)
\(104\) 3.46044 1.01261i 0.339324 0.0992948i
\(105\) 6.41480 1.87657i 0.626020 0.183135i
\(106\) 1.76158 + 1.76158i 0.171100 + 0.171100i
\(107\) 0.228357i 0.0220761i 0.999939 + 0.0110381i \(0.00351360\pi\)
−0.999939 + 0.0110381i \(0.996486\pi\)
\(108\) 3.41455 3.91674i 0.328565 0.376889i
\(109\) −8.58774 8.58774i −0.822556 0.822556i 0.163918 0.986474i \(-0.447587\pi\)
−0.986474 + 0.163918i \(0.947587\pi\)
\(110\) 0.0442171 0.0442171i 0.00421594 0.00421594i
\(111\) −16.8948 9.24728i −1.60359 0.877713i
\(112\) −0.707107 + 0.707107i −0.0668153 + 0.0668153i
\(113\) 2.22102i 0.208936i −0.994528 0.104468i \(-0.966686\pi\)
0.994528 0.104468i \(-0.0333140\pi\)
\(114\) −0.108502 0.370899i −0.0101622 0.0347379i
\(115\) 7.01517 7.01517i 0.654168 0.654168i
\(116\) −7.70551 −0.715439
\(117\) 0.740077 + 10.7913i 0.0684202 + 0.997657i
\(118\) −2.97026 −0.273435
\(119\) 3.96713 3.96713i 0.363666 0.363666i
\(120\) 1.87657 + 6.41480i 0.171307 + 0.585588i
\(121\) 10.9997i 0.999976i
\(122\) −1.29312 + 1.29312i −0.117074 + 0.117074i
\(123\) −11.1468 6.10115i −1.00508 0.550122i
\(124\) 6.66648 6.66648i 0.598667 0.598667i
\(125\) 13.3438 + 13.3438i 1.19351 + 1.19351i
\(126\) −1.61686 2.52701i −0.144041 0.225124i
\(127\) 4.31508i 0.382901i 0.981502 + 0.191451i \(0.0613192\pi\)
−0.981502 + 0.191451i \(0.938681\pi\)
\(128\) −0.707107 0.707107i −0.0625000 0.0625000i
\(129\) −8.47643 + 2.47968i −0.746308 + 0.218324i
\(130\) −12.2051 6.67910i −1.07046 0.585796i
\(131\) 0.111141i 0.00971047i 0.999988 + 0.00485524i \(0.00154548\pi\)
−0.999988 + 0.00485524i \(0.998455\pi\)
\(132\) −0.0246213 0.0134763i −0.00214301 0.00117296i
\(133\) −0.223113 −0.0193464
\(134\) −12.1881 −1.05289
\(135\) −20.0041 + 1.37027i −1.72168 + 0.117934i
\(136\) 3.96713 + 3.96713i 0.340178 + 0.340178i
\(137\) 1.03778 + 1.03778i 0.0886637 + 0.0886637i 0.750048 0.661384i \(-0.230031\pi\)
−0.661384 + 0.750048i \(0.730031\pi\)
\(138\) −3.90624 2.13805i −0.332521 0.182003i
\(139\) −13.8241 −1.17254 −0.586271 0.810115i \(-0.699405\pi\)
−0.586271 + 0.810115i \(0.699405\pi\)
\(140\) 3.85881 0.326129
\(141\) −3.89600 + 7.11802i −0.328102 + 0.599446i
\(142\) 3.90330i 0.327557i
\(143\) 0.0560768 0.0164095i 0.00468938 0.00137223i
\(144\) 2.52701 1.61686i 0.210584 0.134738i
\(145\) 21.0252 + 21.0252i 1.74605 + 1.74605i
\(146\) 13.9155i 1.15166i
\(147\) −1.66238 + 0.486309i −0.137111 + 0.0401101i
\(148\) −7.86287 7.86287i −0.646324 0.646324i
\(149\) 9.29931 9.29931i 0.761829 0.761829i −0.214823 0.976653i \(-0.568918\pi\)
0.976653 + 0.214823i \(0.0689176\pi\)
\(150\) 8.22491 15.0270i 0.671561 1.22695i
\(151\) 0.393892 0.393892i 0.0320545 0.0320545i −0.690898 0.722952i \(-0.742785\pi\)
0.722952 + 0.690898i \(0.242785\pi\)
\(152\) 0.223113i 0.0180969i
\(153\) −14.1774 + 9.07118i −1.14618 + 0.733361i
\(154\) −0.0114588 + 0.0114588i −0.000923373 + 0.000923373i
\(155\) −36.3801 −2.92212
\(156\) −1.33921 + 6.09972i −0.107222 + 0.488368i
\(157\) 10.2524 0.818233 0.409117 0.912482i \(-0.365837\pi\)
0.409117 + 0.912482i \(0.365837\pi\)
\(158\) 4.17391 4.17391i 0.332058 0.332058i
\(159\) −4.14140 + 1.21152i −0.328435 + 0.0960797i
\(160\) 3.85881i 0.305065i
\(161\) −1.81796 + 1.81796i −0.143276 + 0.143276i
\(162\) 3.11134 + 8.44509i 0.244450 + 0.663509i
\(163\) 3.68210 3.68210i 0.288404 0.288404i −0.548045 0.836449i \(-0.684628\pi\)
0.836449 + 0.548045i \(0.184628\pi\)
\(164\) −5.18774 5.18774i −0.405095 0.405095i
\(165\) 0.0304101 + 0.103953i 0.00236742 + 0.00809270i
\(166\) 16.9036i 1.31197i
\(167\) 0.964267 + 0.964267i 0.0746173 + 0.0746173i 0.743430 0.668813i \(-0.233197\pi\)
−0.668813 + 0.743430i \(0.733197\pi\)
\(168\) −0.486309 1.66238i −0.0375196 0.128255i
\(169\) −7.00816 10.9492i −0.539089 0.842249i
\(170\) 21.6493i 1.66043i
\(171\) 0.653757 + 0.143589i 0.0499941 + 0.0109806i
\(172\) −5.09898 −0.388793
\(173\) −11.1981 −0.851378 −0.425689 0.904870i \(-0.639968\pi\)
−0.425689 + 0.904870i \(0.639968\pi\)
\(174\) 6.40796 11.7074i 0.485786 0.887535i
\(175\) −6.99356 6.99356i −0.528663 0.528663i
\(176\) −0.0114588 0.0114588i −0.000863737 0.000863737i
\(177\) 2.47009 4.51287i 0.185663 0.339208i
\(178\) −7.29315 −0.546645
\(179\) −4.63389 −0.346354 −0.173177 0.984891i \(-0.555403\pi\)
−0.173177 + 0.984891i \(0.555403\pi\)
\(180\) −11.3069 2.48342i −0.842767 0.185103i
\(181\) 15.3210i 1.13880i −0.822060 0.569401i \(-0.807175\pi\)
0.822060 0.569401i \(-0.192825\pi\)
\(182\) 3.16292 + 1.73087i 0.234451 + 0.128301i
\(183\) −0.889340 3.04008i −0.0657419 0.224729i
\(184\) −1.81796 1.81796i −0.134022 0.134022i
\(185\) 42.9090i 3.15473i
\(186\) 4.58483 + 15.6726i 0.336176 + 1.14917i
\(187\) 0.0642879 + 0.0642879i 0.00470119 + 0.00470119i
\(188\) −3.31273 + 3.31273i −0.241606 + 0.241606i
\(189\) 5.18400 0.355103i 0.377081 0.0258299i
\(190\) −0.608785 + 0.608785i −0.0441659 + 0.0441659i
\(191\) 12.6760i 0.917203i −0.888642 0.458601i \(-0.848351\pi\)
0.888642 0.458601i \(-0.151649\pi\)
\(192\) 1.66238 0.486309i 0.119972 0.0350963i
\(193\) 5.53338 5.53338i 0.398301 0.398301i −0.479332 0.877634i \(-0.659121\pi\)
0.877634 + 0.479332i \(0.159121\pi\)
\(194\) −8.40720 −0.603602
\(195\) 20.2978 12.9895i 1.45355 0.930195i
\(196\) −1.00000 −0.0714286
\(197\) −17.4414 + 17.4414i −1.24265 + 1.24265i −0.283747 + 0.958899i \(0.591578\pi\)
−0.958899 + 0.283747i \(0.908422\pi\)
\(198\) 0.0409505 0.0262014i 0.00291022 0.00186206i
\(199\) 16.2501i 1.15194i −0.817471 0.575970i \(-0.804624\pi\)
0.817471 0.575970i \(-0.195376\pi\)
\(200\) 6.99356 6.99356i 0.494519 0.494519i
\(201\) 10.1357 18.5180i 0.714918 1.30616i
\(202\) 2.87744 2.87744i 0.202456 0.202456i
\(203\) −5.44862 5.44862i −0.382418 0.382418i
\(204\) −9.32656 + 2.72837i −0.652990 + 0.191024i
\(205\) 28.3104i 1.97729i
\(206\) −12.4039 12.4039i −0.864217 0.864217i
\(207\) 6.49690 4.15693i 0.451566 0.288926i
\(208\) −1.73087 + 3.16292i −0.120014 + 0.219309i
\(209\) 0.00361558i 0.000250095i
\(210\) −3.20901 + 5.86288i −0.221443 + 0.404577i
\(211\) 12.6989 0.874230 0.437115 0.899406i \(-0.356000\pi\)
0.437115 + 0.899406i \(0.356000\pi\)
\(212\) −2.49125 −0.171100
\(213\) 5.93048 + 3.24601i 0.406350 + 0.222413i
\(214\) −0.161473 0.161473i −0.0110381 0.0110381i
\(215\) 13.9130 + 13.9130i 0.948859 + 0.948859i
\(216\) 0.355103 + 5.18400i 0.0241617 + 0.352727i
\(217\) 9.42782 0.640002
\(218\) 12.1449 0.822556
\(219\) 21.1426 + 11.5723i 1.42868 + 0.781981i
\(220\) 0.0625325i 0.00421594i
\(221\) 9.71083 17.7452i 0.653221 1.19367i
\(222\) 18.4853 5.40765i 1.24065 0.362937i
\(223\) 0.153697 + 0.153697i 0.0102923 + 0.0102923i 0.712234 0.701942i \(-0.247683\pi\)
−0.701942 + 0.712234i \(0.747683\pi\)
\(224\) 1.00000i 0.0668153i
\(225\) 15.9914 + 24.9931i 1.06609 + 1.66620i
\(226\) 1.57050 + 1.57050i 0.104468 + 0.104468i
\(227\) 8.19047 8.19047i 0.543620 0.543620i −0.380968 0.924588i \(-0.624409\pi\)
0.924588 + 0.380968i \(0.124409\pi\)
\(228\) 0.338988 + 0.185543i 0.0224500 + 0.0122879i
\(229\) −5.81934 + 5.81934i −0.384553 + 0.384553i −0.872739 0.488186i \(-0.837659\pi\)
0.488186 + 0.872739i \(0.337659\pi\)
\(230\) 9.92094i 0.654168i
\(231\) −0.00788071 0.0269391i −0.000518512 0.00177246i
\(232\) 5.44862 5.44862i 0.357720 0.357720i
\(233\) 9.95377 0.652093 0.326047 0.945354i \(-0.394283\pi\)
0.326047 + 0.945354i \(0.394283\pi\)
\(234\) −8.15392 7.10729i −0.533038 0.464618i
\(235\) 18.0781 1.17929
\(236\) 2.10029 2.10029i 0.136717 0.136717i
\(237\) 2.87059 + 9.81269i 0.186465 + 0.637403i
\(238\) 5.61037i 0.363666i
\(239\) −12.3472 + 12.3472i −0.798673 + 0.798673i −0.982886 0.184213i \(-0.941026\pi\)
0.184213 + 0.982886i \(0.441026\pi\)
\(240\) −5.86288 3.20901i −0.378447 0.207141i
\(241\) 7.54377 7.54377i 0.485937 0.485937i −0.421084 0.907022i \(-0.638350\pi\)
0.907022 + 0.421084i \(0.138350\pi\)
\(242\) 7.77799 + 7.77799i 0.499988 + 0.499988i
\(243\) −15.4185 2.29577i −0.989096 0.147274i
\(244\) 1.82875i 0.117074i
\(245\) 2.72859 + 2.72859i 0.174323 + 0.174323i
\(246\) 12.1962 3.56784i 0.777599 0.227477i
\(247\) −0.772070 + 0.225928i −0.0491256 + 0.0143754i
\(248\) 9.42782i 0.598667i
\(249\) −25.6825 14.0572i −1.62756 0.890836i
\(250\) −18.8710 −1.19351
\(251\) 26.2173 1.65482 0.827410 0.561599i \(-0.189814\pi\)
0.827410 + 0.561599i \(0.189814\pi\)
\(252\) 2.93016 + 0.643571i 0.184583 + 0.0405412i
\(253\) −0.0294603 0.0294603i −0.00185216 0.00185216i
\(254\) −3.05122 3.05122i −0.191451 0.191451i
\(255\) 32.8929 + 18.0037i 2.05984 + 1.12744i
\(256\) 1.00000 0.0625000
\(257\) 30.7002 1.91503 0.957513 0.288390i \(-0.0931201\pi\)
0.957513 + 0.288390i \(0.0931201\pi\)
\(258\) 4.24035 7.74714i 0.263992 0.482316i
\(259\) 11.1198i 0.690949i
\(260\) 13.3531 3.90748i 0.828127 0.242331i
\(261\) 12.4587 + 19.4719i 0.771176 + 1.20528i
\(262\) −0.0785889 0.0785889i −0.00485524 0.00485524i
\(263\) 14.7267i 0.908089i 0.890979 + 0.454045i \(0.150019\pi\)
−0.890979 + 0.454045i \(0.849981\pi\)
\(264\) 0.0269391 0.00788071i 0.00165799 0.000485024i
\(265\) 6.79760 + 6.79760i 0.417573 + 0.417573i
\(266\) 0.157765 0.157765i 0.00967319 0.00967319i
\(267\) 6.06503 11.0809i 0.371174 0.678138i
\(268\) 8.61829 8.61829i 0.526446 0.526446i
\(269\) 18.3642i 1.11969i −0.828598 0.559843i \(-0.810861\pi\)
0.828598 0.559843i \(-0.189139\pi\)
\(270\) 13.1761 15.1139i 0.801871 0.919805i
\(271\) −8.96232 + 8.96232i −0.544422 + 0.544422i −0.924822 0.380400i \(-0.875786\pi\)
0.380400 + 0.924822i \(0.375786\pi\)
\(272\) −5.61037 −0.340178
\(273\) −5.26011 + 3.36619i −0.318356 + 0.203731i
\(274\) −1.46765 −0.0886637
\(275\) 0.113332 0.113332i 0.00683415 0.00683415i
\(276\) 4.27396 1.25029i 0.257262 0.0752589i
\(277\) 13.4939i 0.810772i 0.914146 + 0.405386i \(0.132863\pi\)
−0.914146 + 0.405386i \(0.867137\pi\)
\(278\) 9.77510 9.77510i 0.586271 0.586271i
\(279\) −27.6250 6.06747i −1.65386 0.363250i
\(280\) −2.72859 + 2.72859i −0.163064 + 0.163064i
\(281\) −18.7437 18.7437i −1.11815 1.11815i −0.992012 0.126142i \(-0.959740\pi\)
−0.126142 0.992012i \(-0.540260\pi\)
\(282\) −2.27831 7.78809i −0.135672 0.463774i
\(283\) 0.555789i 0.0330382i −0.999864 0.0165191i \(-0.994742\pi\)
0.999864 0.0165191i \(-0.00525844\pi\)
\(284\) 2.76005 + 2.76005i 0.163779 + 0.163779i
\(285\) −0.418689 1.43123i −0.0248010 0.0847786i
\(286\) −0.0280490 + 0.0512556i −0.00165857 + 0.00303081i
\(287\) 7.33658i 0.433064i
\(288\) −0.643571 + 2.93016i −0.0379228 + 0.172661i
\(289\) 14.4762 0.851542
\(290\) −29.7341 −1.74605
\(291\) 6.99148 12.7735i 0.409848 0.748795i
\(292\) 9.83977 + 9.83977i 0.575829 + 0.575829i
\(293\) −6.73256 6.73256i −0.393321 0.393321i 0.482549 0.875869i \(-0.339711\pi\)
−0.875869 + 0.482549i \(0.839711\pi\)
\(294\) 0.831607 1.51935i 0.0485003 0.0886104i
\(295\) −11.4617 −0.667323
\(296\) 11.1198 0.646324
\(297\) 0.00575449 + 0.0840075i 0.000333909 + 0.00487461i
\(298\) 13.1512i 0.761829i
\(299\) −4.45005 + 8.13184i −0.257353 + 0.470276i
\(300\) 4.80978 + 16.4416i 0.277693 + 0.949254i
\(301\) −3.60552 3.60552i −0.207819 0.207819i
\(302\) 0.557047i 0.0320545i
\(303\) 1.97895 + 6.76475i 0.113688 + 0.388625i
\(304\) 0.157765 + 0.157765i 0.00904845 + 0.00904845i
\(305\) −4.98992 + 4.98992i −0.285722 + 0.285722i
\(306\) 3.61067 16.4393i 0.206408 0.939770i
\(307\) −13.6798 + 13.6798i −0.780748 + 0.780748i −0.979957 0.199209i \(-0.936163\pi\)
0.199209 + 0.979957i \(0.436163\pi\)
\(308\) 0.0162051i 0.000923373i
\(309\) 29.1609 8.53069i 1.65891 0.485294i
\(310\) 25.7246 25.7246i 1.46106 1.46106i
\(311\) −3.04815 −0.172845 −0.0864225 0.996259i \(-0.527543\pi\)
−0.0864225 + 0.996259i \(0.527543\pi\)
\(312\) −3.36619 5.26011i −0.190573 0.297795i
\(313\) 19.2531 1.08825 0.544124 0.839005i \(-0.316862\pi\)
0.544124 + 0.839005i \(0.316862\pi\)
\(314\) −7.24957 + 7.24957i −0.409117 + 0.409117i
\(315\) −6.23915 9.75123i −0.351536 0.549419i
\(316\) 5.90280i 0.332058i
\(317\) −12.2211 + 12.2211i −0.686403 + 0.686403i −0.961435 0.275032i \(-0.911312\pi\)
0.275032 + 0.961435i \(0.411312\pi\)
\(318\) 2.07174 3.78509i 0.116178 0.212257i
\(319\) 0.0882957 0.0882957i 0.00494361 0.00494361i
\(320\) −2.72859 2.72859i −0.152533 0.152533i
\(321\) 0.379616 0.111052i 0.0211881 0.00619833i
\(322\) 2.57099i 0.143276i
\(323\) −0.885120 0.885120i −0.0492494 0.0492494i
\(324\) −8.17163 3.77153i −0.453980 0.209529i
\(325\) −31.2825 17.1190i −1.73524 0.949590i
\(326\) 5.20727i 0.288404i
\(327\) −10.0998 + 18.4524i −0.558519 + 1.02042i
\(328\) 7.33658 0.405095
\(329\) −4.68491 −0.258287
\(330\) −0.0950088 0.0520024i −0.00523006 0.00286264i
\(331\) −9.25094 9.25094i −0.508478 0.508478i 0.405581 0.914059i \(-0.367069\pi\)
−0.914059 + 0.405581i \(0.867069\pi\)
\(332\) −11.9527 11.9527i −0.655987 0.655987i
\(333\) −7.15636 + 32.5827i −0.392166 + 1.78552i
\(334\) −1.36368 −0.0746173
\(335\) −47.0315 −2.56961
\(336\) 1.51935 + 0.831607i 0.0828874 + 0.0453679i
\(337\) 3.92073i 0.213576i 0.994282 + 0.106788i \(0.0340566\pi\)
−0.994282 + 0.106788i \(0.965943\pi\)
\(338\) 12.6978 + 2.78676i 0.690669 + 0.151580i
\(339\) −3.69218 + 1.08010i −0.200532 + 0.0586631i
\(340\) 15.3084 + 15.3084i 0.830213 + 0.830213i
\(341\) 0.152779i 0.00827345i
\(342\) −0.563809 + 0.360743i −0.0304873 + 0.0195068i
\(343\) −0.707107 0.707107i −0.0381802 0.0381802i
\(344\) 3.60552 3.60552i 0.194397 0.194397i
\(345\) −15.0734 8.25032i −0.811525 0.444183i
\(346\) 7.91827 7.91827i 0.425689 0.425689i
\(347\) 11.8159i 0.634311i −0.948374 0.317156i \(-0.897272\pi\)
0.948374 0.317156i \(-0.102728\pi\)
\(348\) 3.74726 + 12.8095i 0.200874 + 0.686660i
\(349\) 8.77505 8.77505i 0.469717 0.469717i −0.432106 0.901823i \(-0.642229\pi\)
0.901823 + 0.432106i \(0.142229\pi\)
\(350\) 9.89038 0.528663
\(351\) 17.5793 6.47820i 0.938315 0.345781i
\(352\) 0.0162051 0.000863737
\(353\) 0.431441 0.431441i 0.0229633 0.0229633i −0.695532 0.718495i \(-0.744831\pi\)
0.718495 + 0.695532i \(0.244831\pi\)
\(354\) 1.44446 + 4.93770i 0.0767724 + 0.262436i
\(355\) 15.0621i 0.799411i
\(356\) 5.15703 5.15703i 0.273322 0.273322i
\(357\) −8.52412 4.66562i −0.451144 0.246931i
\(358\) 3.27666 3.27666i 0.173177 0.173177i
\(359\) 1.98976 + 1.98976i 0.105015 + 0.105015i 0.757662 0.652647i \(-0.226341\pi\)
−0.652647 + 0.757662i \(0.726341\pi\)
\(360\) 9.75123 6.23915i 0.513935 0.328832i
\(361\) 18.9502i 0.997380i
\(362\) 10.8336 + 10.8336i 0.569401 + 0.569401i
\(363\) −18.2857 + 5.34927i −0.959752 + 0.280764i
\(364\) −3.46044 + 1.01261i −0.181376 + 0.0530753i
\(365\) 53.6974i 2.81065i
\(366\) 2.77852 + 1.52080i 0.145236 + 0.0794937i
\(367\) −6.88839 −0.359571 −0.179785 0.983706i \(-0.557540\pi\)
−0.179785 + 0.983706i \(0.557540\pi\)
\(368\) 2.57099 0.134022
\(369\) −4.72161 + 21.4973i −0.245797 + 1.11911i
\(370\) −30.3413 30.3413i −1.57737 1.57737i
\(371\) −1.76158 1.76158i −0.0914567 0.0914567i
\(372\) −14.3242 7.84024i −0.742674 0.406498i
\(373\) −7.13093 −0.369225 −0.184613 0.982811i \(-0.559103\pi\)
−0.184613 + 0.982811i \(0.559103\pi\)
\(374\) −0.0909168 −0.00470119
\(375\) 15.6933 28.6717i 0.810397 1.48060i
\(376\) 4.68491i 0.241606i
\(377\) −24.3719 13.3373i −1.25522 0.686904i
\(378\) −3.41455 + 3.91674i −0.175625 + 0.201455i
\(379\) 26.5110 + 26.5110i 1.36178 + 1.36178i 0.871649 + 0.490131i \(0.163051\pi\)
0.490131 + 0.871649i \(0.336949\pi\)
\(380\) 0.860951i 0.0441659i
\(381\) 7.17330 2.09846i 0.367499 0.107507i
\(382\) 8.96328 + 8.96328i 0.458601 + 0.458601i
\(383\) −20.2050 + 20.2050i −1.03243 + 1.03243i −0.0329712 + 0.999456i \(0.510497\pi\)
−0.999456 + 0.0329712i \(0.989503\pi\)
\(384\) −0.831607 + 1.51935i −0.0424378 + 0.0775341i
\(385\) −0.0442171 + 0.0442171i −0.00225351 + 0.00225351i
\(386\) 7.82538i 0.398301i
\(387\) 8.24433 + 12.8852i 0.419083 + 0.654989i
\(388\) 5.94479 5.94479i 0.301801 0.301801i
\(389\) 3.37710 0.171226 0.0856128 0.996328i \(-0.472715\pi\)
0.0856128 + 0.996328i \(0.472715\pi\)
\(390\) −5.16774 + 23.5376i −0.261679 + 1.19187i
\(391\) −14.4242 −0.729462
\(392\) 0.707107 0.707107i 0.0357143 0.0357143i
\(393\) 0.184759 0.0540491i 0.00931987 0.00272642i
\(394\) 24.6658i 1.24265i
\(395\) 16.1063 16.1063i 0.810396 0.810396i
\(396\) −0.0104292 + 0.0474836i −0.000524085 + 0.00238614i
\(397\) −2.62666 + 2.62666i −0.131828 + 0.131828i −0.769942 0.638114i \(-0.779715\pi\)
0.638114 + 0.769942i \(0.279715\pi\)
\(398\) 11.4906 + 11.4906i 0.575970 + 0.575970i
\(399\) 0.108502 + 0.370899i 0.00543190 + 0.0185682i
\(400\) 9.89038i 0.494519i
\(401\) 17.3405 + 17.3405i 0.865943 + 0.865943i 0.992020 0.126078i \(-0.0402388\pi\)
−0.126078 + 0.992020i \(0.540239\pi\)
\(402\) 5.92719 + 20.2612i 0.295621 + 1.01054i
\(403\) 32.6244 9.54673i 1.62514 0.475557i
\(404\) 4.06932i 0.202456i
\(405\) 12.0061 + 32.5880i 0.596586 + 1.61931i
\(406\) 7.70551 0.382418
\(407\) 0.180197 0.00893205
\(408\) 4.66562 8.52412i 0.230983 0.422007i
\(409\) −12.2005 12.2005i −0.603276 0.603276i 0.337905 0.941180i \(-0.390282\pi\)
−0.941180 + 0.337905i \(0.890282\pi\)
\(410\) −20.0185 20.0185i −0.988643 0.988643i
\(411\) 1.22050 2.22987i 0.0602030 0.109991i
\(412\) 17.5417 0.864217
\(413\) 2.97026 0.146157
\(414\) −1.65461 + 7.53340i −0.0813198 + 0.370246i
\(415\) 65.2278i 3.20190i
\(416\) −1.01261 3.46044i −0.0496474 0.169662i
\(417\) 6.72277 + 22.9808i 0.329216 + 1.12538i
\(418\) 0.00255660 + 0.00255660i 0.000125048 + 0.000125048i
\(419\) 15.1275i 0.739027i 0.929225 + 0.369514i \(0.120476\pi\)
−0.929225 + 0.369514i \(0.879524\pi\)
\(420\) −1.87657 6.41480i −0.0915674 0.313010i
\(421\) −3.41592 3.41592i −0.166482 0.166482i 0.618949 0.785431i \(-0.287559\pi\)
−0.785431 + 0.618949i \(0.787559\pi\)
\(422\) −8.97949 + 8.97949i −0.437115 + 0.437115i
\(423\) 13.7275 + 3.01507i 0.667454 + 0.146598i
\(424\) 1.76158 1.76158i 0.0855499 0.0855499i
\(425\) 55.4887i 2.69160i
\(426\) −6.48876 + 1.89821i −0.314381 + 0.0919685i
\(427\) 1.29312 1.29312i 0.0625787 0.0625787i
\(428\) 0.228357 0.0110381
\(429\) −0.0545495 0.0852408i −0.00263368 0.00411547i
\(430\) −19.6760 −0.948859
\(431\) −3.91881 + 3.91881i −0.188762 + 0.188762i −0.795161 0.606399i \(-0.792614\pi\)
0.606399 + 0.795161i \(0.292614\pi\)
\(432\) −3.91674 3.41455i −0.188444 0.164283i
\(433\) 15.2572i 0.733212i 0.930376 + 0.366606i \(0.119480\pi\)
−0.930376 + 0.366606i \(0.880520\pi\)
\(434\) −6.66648 + 6.66648i −0.320001 + 0.320001i
\(435\) 24.7271 45.1765i 1.18557 2.16605i
\(436\) −8.58774 + 8.58774i −0.411278 + 0.411278i
\(437\) 0.405612 + 0.405612i 0.0194031 + 0.0194031i
\(438\) −23.1329 + 6.76725i −1.10533 + 0.323352i
\(439\) 13.4437i 0.641632i −0.947141 0.320816i \(-0.896043\pi\)
0.947141 0.320816i \(-0.103957\pi\)
\(440\) −0.0442171 0.0442171i −0.00210797 0.00210797i
\(441\) 1.61686 + 2.52701i 0.0769933 + 0.120334i
\(442\) 5.68113 + 19.4143i 0.270224 + 0.923445i
\(443\) 38.0441i 1.80753i −0.428032 0.903764i \(-0.640793\pi\)
0.428032 0.903764i \(-0.359207\pi\)
\(444\) −9.24728 + 16.8948i −0.438856 + 0.801794i
\(445\) −28.1428 −1.33410
\(446\) −0.217361 −0.0102923
\(447\) −19.9813 10.9366i −0.945084 0.517285i
\(448\) 0.707107 + 0.707107i 0.0334077 + 0.0334077i
\(449\) 5.40078 + 5.40078i 0.254879 + 0.254879i 0.822967 0.568089i \(-0.192317\pi\)
−0.568089 + 0.822967i \(0.692317\pi\)
\(450\) −28.9804 6.36516i −1.36615 0.300057i
\(451\) 0.118890 0.00559832
\(452\) −2.22102 −0.104468
\(453\) −0.846351 0.463244i −0.0397650 0.0217651i
\(454\) 11.5831i 0.543620i
\(455\) 12.2051 + 6.67910i 0.572184 + 0.313121i
\(456\) −0.370899 + 0.108502i −0.0173689 + 0.00508108i
\(457\) −23.4514 23.4514i −1.09701 1.09701i −0.994759 0.102249i \(-0.967396\pi\)
−0.102249 0.994759i \(-0.532604\pi\)
\(458\) 8.22979i 0.384553i
\(459\) 21.9744 + 19.1569i 1.02567 + 0.894166i
\(460\) −7.01517 7.01517i −0.327084 0.327084i
\(461\) −21.2145 + 21.2145i −0.988057 + 0.988057i −0.999930 0.0118730i \(-0.996221\pi\)
0.0118730 + 0.999930i \(0.496221\pi\)
\(462\) 0.0246213 + 0.0134763i 0.00114549 + 0.000626974i
\(463\) 23.6011 23.6011i 1.09684 1.09684i 0.102059 0.994778i \(-0.467457\pi\)
0.994778 0.102059i \(-0.0325429\pi\)
\(464\) 7.70551i 0.357720i
\(465\) 17.6920 + 60.4776i 0.820446 + 2.80458i
\(466\) −7.03838 + 7.03838i −0.326047 + 0.326047i
\(467\) 1.29336 0.0598496 0.0299248 0.999552i \(-0.490473\pi\)
0.0299248 + 0.999552i \(0.490473\pi\)
\(468\) 10.7913 0.740077i 0.498828 0.0342101i
\(469\) 12.1881 0.562794
\(470\) −12.7832 + 12.7832i −0.589644 + 0.589644i
\(471\) −4.98585 17.0434i −0.229736 0.785320i
\(472\) 2.97026i 0.136717i
\(473\) 0.0584280 0.0584280i 0.00268652 0.00268652i
\(474\) −8.96843 4.90881i −0.411934 0.225469i
\(475\) −1.56036 + 1.56036i −0.0715941 + 0.0715941i
\(476\) −3.96713 3.96713i −0.181833 0.181833i
\(477\) 4.02800 + 6.29541i 0.184430 + 0.288247i
\(478\) 17.4616i 0.798673i
\(479\) −14.5097 14.5097i −0.662966 0.662966i 0.293112 0.956078i \(-0.405309\pi\)
−0.956078 + 0.293112i \(0.905309\pi\)
\(480\) 6.41480 1.87657i 0.292794 0.0856534i
\(481\) −11.2600 38.4793i −0.513413 1.75450i
\(482\) 10.6685i 0.485937i
\(483\) 3.90624 + 2.13805i 0.177740 + 0.0972847i
\(484\) −10.9997 −0.499988
\(485\) −32.4417 −1.47310
\(486\) 12.5259 9.27916i 0.568185 0.420911i
\(487\) 16.4423 + 16.4423i 0.745074 + 0.745074i 0.973550 0.228476i \(-0.0733742\pi\)
−0.228476 + 0.973550i \(0.573374\pi\)
\(488\) 1.29312 + 1.29312i 0.0585370 + 0.0585370i
\(489\) −7.91168 4.33040i −0.357778 0.195828i
\(490\) −3.85881 −0.174323
\(491\) 5.23186 0.236111 0.118055 0.993007i \(-0.462334\pi\)
0.118055 + 0.993007i \(0.462334\pi\)
\(492\) −6.10115 + 11.1468i −0.275061 + 0.502538i
\(493\) 43.2308i 1.94702i
\(494\) 0.386181 0.705691i 0.0173751 0.0317505i
\(495\) 0.158020 0.101106i 0.00710247 0.00454439i
\(496\) −6.66648 6.66648i −0.299334 0.299334i
\(497\) 3.90330i 0.175087i
\(498\) 28.1002 8.22038i 1.25920 0.368364i
\(499\) −21.9429 21.9429i −0.982297 0.982297i 0.0175490 0.999846i \(-0.494414\pi\)
−0.999846 + 0.0175490i \(0.994414\pi\)
\(500\) 13.3438 13.3438i 0.596754 0.596754i
\(501\) 1.13405 2.07191i 0.0506654 0.0925661i
\(502\) −18.5384 + 18.5384i −0.827410 + 0.827410i
\(503\) 14.1370i 0.630336i 0.949036 + 0.315168i \(0.102061\pi\)
−0.949036 + 0.315168i \(0.897939\pi\)
\(504\) −2.52701 + 1.61686i −0.112562 + 0.0720207i
\(505\) 11.1035 11.1035i 0.494099 0.494099i
\(506\) 0.0416632 0.00185216
\(507\) −14.7936 + 16.9749i −0.657008 + 0.753883i
\(508\) 4.31508 0.191451
\(509\) 24.6460 24.6460i 1.09241 1.09241i 0.0971423 0.995271i \(-0.469030\pi\)
0.995271 0.0971423i \(-0.0309702\pi\)
\(510\) −35.9894 + 10.5283i −1.59364 + 0.466199i
\(511\) 13.9155i 0.615587i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −0.0792282 1.15662i −0.00349801 0.0510661i
\(514\) −21.7083 + 21.7083i −0.957513 + 0.957513i
\(515\) −47.8641 47.8641i −2.10914 2.10914i
\(516\) 2.47968 + 8.47643i 0.109162 + 0.373154i
\(517\) 0.0759196i 0.00333894i
\(518\) 7.86287 + 7.86287i 0.345474 + 0.345474i
\(519\) 5.44575 + 18.6155i 0.239042 + 0.817131i
\(520\) −6.67910 + 12.2051i −0.292898 + 0.535229i
\(521\) 42.9249i 1.88057i 0.340383 + 0.940287i \(0.389443\pi\)
−0.340383 + 0.940287i \(0.610557\pi\)
\(522\) −22.5784 4.95905i −0.988228 0.217052i
\(523\) −9.09629 −0.397753 −0.198877 0.980025i \(-0.563729\pi\)
−0.198877 + 0.980025i \(0.563729\pi\)
\(524\) 0.111141 0.00485524
\(525\) −8.22491 + 15.0270i −0.358964 + 0.655831i
\(526\) −10.4134 10.4134i −0.454045 0.454045i
\(527\) 37.4014 + 37.4014i 1.62923 + 1.62923i
\(528\) −0.0134763 + 0.0246213i −0.000586481 + 0.00107150i
\(529\) −16.3900 −0.712610
\(530\) −9.61326 −0.417573
\(531\) −8.70332 1.91157i −0.377692 0.0829552i
\(532\) 0.223113i 0.00967319i
\(533\) −7.42911 25.3877i −0.321790 1.09967i
\(534\) 3.54672 + 12.1240i 0.153482 + 0.524656i
\(535\) −0.623093 0.623093i −0.0269386 0.0269386i
\(536\) 12.1881i 0.526446i
\(537\) 2.25350 + 7.70329i 0.0972459 + 0.332421i
\(538\) 12.9855 + 12.9855i 0.559843 + 0.559843i
\(539\) 0.0114588 0.0114588i 0.000493564 0.000493564i
\(540\) 1.37027 + 20.0041i 0.0589671 + 0.860838i
\(541\) −25.9593 + 25.9593i −1.11608 + 1.11608i −0.123765 + 0.992312i \(0.539497\pi\)
−0.992312 + 0.123765i \(0.960503\pi\)
\(542\) 12.6746i 0.544422i
\(543\) −25.4693 + 7.45074i −1.09299 + 0.319742i
\(544\) 3.96713 3.96713i 0.170089 0.170089i
\(545\) 46.8648 2.00747
\(546\) 1.33921 6.09972i 0.0573128 0.261044i
\(547\) 5.50448 0.235355 0.117677 0.993052i \(-0.462455\pi\)
0.117677 + 0.993052i \(0.462455\pi\)
\(548\) 1.03778 1.03778i 0.0443319 0.0443319i
\(549\) −4.62127 + 2.95684i −0.197231 + 0.126195i
\(550\) 0.160275i 0.00683415i
\(551\) −1.21566 + 1.21566i −0.0517889 + 0.0517889i
\(552\) −2.13805 + 3.90624i −0.0910015 + 0.166260i
\(553\) −4.17391 + 4.17391i −0.177493 + 0.177493i
\(554\) −9.54165 9.54165i −0.405386 0.405386i
\(555\) 71.3311 20.8671i 3.02784 0.885757i
\(556\) 13.8241i 0.586271i
\(557\) −1.35829 1.35829i −0.0575525 0.0575525i 0.677745 0.735297i \(-0.262957\pi\)
−0.735297 + 0.677745i \(0.762957\pi\)
\(558\) 23.8242 15.2435i 1.00856 0.645307i
\(559\) −16.1277 8.82568i −0.682128 0.373287i
\(560\) 3.85881i 0.163064i
\(561\) 0.0756070 0.138135i 0.00319213 0.00583205i
\(562\) 26.5076 1.11815
\(563\) −37.6045 −1.58484 −0.792420 0.609976i \(-0.791179\pi\)
−0.792420 + 0.609976i \(0.791179\pi\)
\(564\) 7.11802 + 3.89600i 0.299723 + 0.164051i
\(565\) 6.06025 + 6.06025i 0.254957 + 0.254957i
\(566\) 0.393002 + 0.393002i 0.0165191 + 0.0165191i
\(567\) −3.11134 8.44509i −0.130664 0.354660i
\(568\) −3.90330 −0.163779
\(569\) 12.8584 0.539053 0.269527 0.962993i \(-0.413133\pi\)
0.269527 + 0.962993i \(0.413133\pi\)
\(570\) 1.30809 + 0.715973i 0.0547898 + 0.0299888i
\(571\) 30.6551i 1.28288i 0.767174 + 0.641439i \(0.221662\pi\)
−0.767174 + 0.641439i \(0.778338\pi\)
\(572\) −0.0164095 0.0560768i −0.000686117 0.00234469i
\(573\) −21.0723 + 6.16445i −0.880308 + 0.257524i
\(574\) 5.18774 + 5.18774i 0.216532 + 0.216532i
\(575\) 25.4280i 1.06042i
\(576\) −1.61686 2.52701i −0.0673692 0.105292i
\(577\) 21.0219 + 21.0219i 0.875155 + 0.875155i 0.993029 0.117874i \(-0.0376079\pi\)
−0.117874 + 0.993029i \(0.537608\pi\)
\(578\) −10.2362 + 10.2362i −0.425771 + 0.425771i
\(579\) −11.8895 6.50764i −0.494111 0.270448i
\(580\) 21.0252 21.0252i 0.873023 0.873023i
\(581\) 16.9036i 0.701280i
\(582\) 4.08850 + 13.9759i 0.169474 + 0.579322i
\(583\) 0.0285467 0.0285467i 0.00118228 0.00118228i
\(584\) −13.9155 −0.575829
\(585\) −31.4644 27.4257i −1.30089 1.13391i
\(586\) 9.52128 0.393321
\(587\) 19.4406 19.4406i 0.802398 0.802398i −0.181072 0.983470i \(-0.557957\pi\)
0.983470 + 0.181072i \(0.0579566\pi\)
\(588\) 0.486309 + 1.66238i 0.0200550 + 0.0685553i
\(589\) 2.10347i 0.0866721i
\(590\) 8.10461 8.10461i 0.333662 0.333662i
\(591\) 37.4761 + 20.5123i 1.54156 + 0.843762i
\(592\) −7.86287 + 7.86287i −0.323162 + 0.323162i
\(593\) 23.9101 + 23.9101i 0.981871 + 0.981871i 0.999839 0.0179672i \(-0.00571946\pi\)
−0.0179672 + 0.999839i \(0.505719\pi\)
\(594\) −0.0634713 0.0553332i −0.00260426 0.00227035i
\(595\) 21.6493i 0.887535i
\(596\) −9.29931 9.29931i −0.380915 0.380915i
\(597\) −27.0139 + 7.90258i −1.10560 + 0.323431i
\(598\) −2.60342 8.89674i −0.106462 0.363815i
\(599\) 30.5039i 1.24636i 0.782080 + 0.623178i \(0.214159\pi\)
−0.782080 + 0.623178i \(0.785841\pi\)
\(600\) −15.0270 8.22491i −0.613473 0.335780i
\(601\) 32.8095 1.33833 0.669165 0.743114i \(-0.266652\pi\)
0.669165 + 0.743114i \(0.266652\pi\)
\(602\) 5.09898 0.207819
\(603\) −35.7130 7.84391i −1.45435 0.319429i
\(604\) −0.393892 0.393892i −0.0160272 0.0160272i
\(605\) 30.0137 + 30.0137i 1.22023 + 1.22023i
\(606\) −6.18273 3.38408i −0.251156 0.137469i
\(607\) −23.8071 −0.966299 −0.483149 0.875538i \(-0.660507\pi\)
−0.483149 + 0.875538i \(0.660507\pi\)
\(608\) −0.223113 −0.00904845
\(609\) −6.40796 + 11.7074i −0.259664 + 0.474407i
\(610\) 7.05681i 0.285722i
\(611\) −16.2118 + 4.74400i −0.655860 + 0.191922i
\(612\) 9.07118 + 14.1774i 0.366681 + 0.573089i
\(613\) 2.22797 + 2.22797i 0.0899870 + 0.0899870i 0.750667 0.660680i \(-0.229732\pi\)
−0.660680 + 0.750667i \(0.729732\pi\)
\(614\) 19.3462i 0.780748i
\(615\) 47.0626 13.7676i 1.89775 0.555164i
\(616\) 0.0114588 + 0.0114588i 0.000461687 + 0.000461687i
\(617\) −9.41224 + 9.41224i −0.378922 + 0.378922i −0.870713 0.491791i \(-0.836342\pi\)
0.491791 + 0.870713i \(0.336342\pi\)
\(618\) −14.5878 + 26.6520i −0.586807 + 1.07210i
\(619\) −30.1524 + 30.1524i −1.21193 + 1.21193i −0.241535 + 0.970392i \(0.577651\pi\)
−0.970392 + 0.241535i \(0.922349\pi\)
\(620\) 36.3801i 1.46106i
\(621\) −10.0699 8.77876i −0.404091 0.352280i
\(622\) 2.15537 2.15537i 0.0864225 0.0864225i
\(623\) 7.29315 0.292194
\(624\) 6.09972 + 1.33921i 0.244184 + 0.0536112i
\(625\) −23.3677 −0.934709
\(626\) −13.6140 + 13.6140i −0.544124 + 0.544124i
\(627\) −0.00601047 + 0.00175829i −0.000240035 + 7.02194e-5i
\(628\) 10.2524i 0.409117i
\(629\) 44.1136 44.1136i 1.75892 1.75892i
\(630\) 11.3069 + 2.48342i 0.450478 + 0.0989416i
\(631\) −17.9690 + 17.9690i −0.715334 + 0.715334i −0.967646 0.252312i \(-0.918809\pi\)
0.252312 + 0.967646i \(0.418809\pi\)
\(632\) −4.17391 4.17391i −0.166029 0.166029i
\(633\) −6.17560 21.1104i −0.245458 0.839064i
\(634\) 17.2832i 0.686403i
\(635\) −11.7741 11.7741i −0.467240 0.467240i
\(636\) 1.21152 + 4.14140i 0.0480398 + 0.164217i
\(637\) −3.16292 1.73087i −0.125320 0.0685797i
\(638\) 0.124869i 0.00494361i
\(639\) 2.51205 11.4373i 0.0993751 0.452451i
\(640\) 3.85881 0.152533
\(641\) −6.22306 −0.245796 −0.122898 0.992419i \(-0.539219\pi\)
−0.122898 + 0.992419i \(0.539219\pi\)
\(642\) −0.189903 + 0.346955i −0.00749489 + 0.0136932i
\(643\) 2.90196 + 2.90196i 0.114442 + 0.114442i 0.762009 0.647567i \(-0.224213\pi\)
−0.647567 + 0.762009i \(0.724213\pi\)
\(644\) 1.81796 + 1.81796i 0.0716378 + 0.0716378i
\(645\) 16.3627 29.8947i 0.644279 1.17710i
\(646\) 1.25175 0.0492494
\(647\) 14.3535 0.564293 0.282147 0.959371i \(-0.408954\pi\)
0.282147 + 0.959371i \(0.408954\pi\)
\(648\) 8.44509 3.11134i 0.331754 0.122225i
\(649\) 0.0481335i 0.00188940i
\(650\) 34.2250 10.0151i 1.34242 0.392826i
\(651\) −4.58483 15.6726i −0.179694 0.614258i
\(652\) −3.68210 3.68210i −0.144202 0.144202i
\(653\) 4.91046i 0.192161i 0.995374 + 0.0960805i \(0.0306306\pi\)
−0.995374 + 0.0960805i \(0.969369\pi\)
\(654\) −5.90617 20.1894i −0.230950 0.789469i
\(655\) −0.303259 0.303259i −0.0118493 0.0118493i
\(656\) −5.18774 + 5.18774i −0.202547 + 0.202547i
\(657\) 8.95564 40.7747i 0.349393 1.59077i
\(658\) 3.31273 3.31273i 0.129144 0.129144i
\(659\) 29.9426i 1.16640i 0.812329 + 0.583199i \(0.198199\pi\)
−0.812329 + 0.583199i \(0.801801\pi\)
\(660\) 0.103953 0.0304101i 0.00404635 0.00118371i
\(661\) 5.12233 5.12233i 0.199236 0.199236i −0.600437 0.799672i \(-0.705007\pi\)
0.799672 + 0.600437i \(0.205007\pi\)
\(662\) 13.0828 0.508478
\(663\) −34.2216 7.51344i −1.32906 0.291798i
\(664\) 16.9036 0.655987
\(665\) 0.608785 0.608785i 0.0236077 0.0236077i
\(666\) −17.9791 28.0997i −0.696676 1.08884i
\(667\) 19.8108i 0.767077i
\(668\) 0.964267 0.964267i 0.0373086 0.0373086i
\(669\) 0.180759 0.330248i 0.00698854 0.0127681i
\(670\) 33.2563 33.2563i 1.28480 1.28480i
\(671\) 0.0209553 + 0.0209553i 0.000808969 + 0.000808969i
\(672\) −1.66238 + 0.486309i −0.0641277 + 0.0187598i
\(673\) 0.955996i 0.0368509i 0.999830 + 0.0184255i \(0.00586534\pi\)
−0.999830 + 0.0184255i \(0.994135\pi\)
\(674\) −2.77238 2.77238i −0.106788 0.106788i
\(675\) 33.7712 38.7381i 1.29985 1.49103i
\(676\) −10.9492 + 7.00816i −0.421124 + 0.269545i
\(677\) 22.6377i 0.870037i −0.900421 0.435019i \(-0.856742\pi\)
0.900421 0.435019i \(-0.143258\pi\)
\(678\) 1.84702 3.37451i 0.0709342 0.129597i
\(679\) 8.40720 0.322639
\(680\) −21.6493 −0.830213
\(681\) −17.5988 9.63256i −0.674386 0.369121i
\(682\) −0.108031 0.108031i −0.00413673 0.00413673i
\(683\) 28.9868 + 28.9868i 1.10915 + 1.10915i 0.993263 + 0.115885i \(0.0369705\pi\)
0.115885 + 0.993263i \(0.463029\pi\)
\(684\) 0.143589 0.653757i 0.00549028 0.0249970i
\(685\) −5.66336 −0.216386
\(686\) 1.00000 0.0381802
\(687\) 12.5040 + 6.84395i 0.477056 + 0.261113i
\(688\) 5.09898i 0.194397i
\(689\) −7.87964 4.31204i −0.300190 0.164276i
\(690\) 16.4924 4.82464i 0.627854 0.183671i
\(691\) 14.1906 + 14.1906i 0.539837 + 0.539837i 0.923481 0.383644i \(-0.125331\pi\)
−0.383644 + 0.923481i \(0.625331\pi\)
\(692\) 11.1981i 0.425689i
\(693\) −0.0409505 + 0.0262014i −0.00155558 + 0.000995310i
\(694\) 8.35511 + 8.35511i 0.317156 + 0.317156i
\(695\) 37.7202 37.7202i 1.43081 1.43081i
\(696\) −11.7074 6.40796i −0.443767 0.242893i
\(697\) 29.1051 29.1051i 1.10244 1.10244i
\(698\) 12.4098i 0.469717i
\(699\) −4.84061 16.5469i −0.183089 0.625863i
\(700\) −6.99356 + 6.99356i −0.264332 + 0.264332i
\(701\) 1.82380 0.0688840 0.0344420 0.999407i \(-0.489035\pi\)
0.0344420 + 0.999407i \(0.489035\pi\)
\(702\) −7.84969 + 17.0112i −0.296267 + 0.642048i
\(703\) −2.48097 −0.0935716
\(704\) −0.0114588 + 0.0114588i −0.000431868 + 0.000431868i
\(705\) −8.79157 30.0527i −0.331110 1.13185i
\(706\) 0.610149i 0.0229633i
\(707\) −2.87744 + 2.87744i −0.108217 + 0.108217i
\(708\) −4.51287 2.47009i −0.169604 0.0928316i
\(709\) 13.5253 13.5253i 0.507953 0.507953i −0.405945 0.913898i \(-0.633057\pi\)
0.913898 + 0.405945i \(0.133057\pi\)
\(710\) 10.6505 + 10.6505i 0.399706 + 0.399706i
\(711\) 14.9164 9.54400i 0.559409 0.357928i
\(712\) 7.29315i 0.273322i
\(713\) −17.1394 17.1394i −0.641877 0.641877i
\(714\) 9.32656 2.72837i 0.349038 0.102107i
\(715\) −0.108236 + 0.197785i −0.00404779 + 0.00739675i
\(716\) 4.63389i 0.173177i
\(717\) 26.5302 + 14.5212i 0.990790 + 0.542302i
\(718\) −2.81394 −0.105015
\(719\) 10.2208 0.381172 0.190586 0.981670i \(-0.438961\pi\)
0.190586 + 0.981670i \(0.438961\pi\)
\(720\) −2.48342 + 11.3069i −0.0925514 + 0.421383i
\(721\) 12.4039 + 12.4039i 0.461944 + 0.461944i
\(722\) 13.3998 + 13.3998i 0.498690 + 0.498690i
\(723\) −16.2092 8.87200i −0.602827 0.329953i
\(724\) −15.3210 −0.569401
\(725\) −76.2105 −2.83039
\(726\) 9.14746 16.7125i 0.339494 0.620258i
\(727\) 43.8339i 1.62571i 0.582466 + 0.812855i \(0.302088\pi\)
−0.582466 + 0.812855i \(0.697912\pi\)
\(728\) 1.73087 3.16292i 0.0641504 0.117226i
\(729\) 3.68171 + 26.7478i 0.136360 + 0.990659i
\(730\) 37.9698 + 37.9698i 1.40532 + 1.40532i
\(731\) 28.6071i 1.05807i
\(732\) −3.04008 + 0.889340i −0.112365 + 0.0328709i
\(733\) −8.47954 8.47954i −0.313199 0.313199i 0.532949 0.846148i \(-0.321084\pi\)
−0.846148 + 0.532949i \(0.821084\pi\)
\(734\) 4.87082 4.87082i 0.179785 0.179785i
\(735\) 3.20901 5.86288i 0.118366 0.216256i
\(736\) −1.81796 + 1.81796i −0.0670110 + 0.0670110i
\(737\) 0.197510i 0.00727537i
\(738\) −11.8622 18.5396i −0.436654 0.682451i
\(739\) −23.8959 + 23.8959i −0.879025 + 0.879025i −0.993434 0.114409i \(-0.963503\pi\)
0.114409 + 0.993434i \(0.463503\pi\)
\(740\) 42.9090 1.57737
\(741\) 0.751042 + 1.17360i 0.0275902 + 0.0431133i
\(742\) 2.49125 0.0914567
\(743\) 3.43994 3.43994i 0.126199 0.126199i −0.641186 0.767385i \(-0.721557\pi\)
0.767385 + 0.641186i \(0.221557\pi\)
\(744\) 15.6726 4.58483i 0.574586 0.168088i
\(745\) 50.7480i 1.85926i
\(746\) 5.04233 5.04233i 0.184613 0.184613i
\(747\) −10.8787 + 49.5302i −0.398030 + 1.81222i
\(748\) 0.0642879 0.0642879i 0.00235060 0.00235060i
\(749\) 0.161473 + 0.161473i 0.00590009 + 0.00590009i
\(750\) 9.17715 + 31.3708i 0.335102 + 1.14550i
\(751\) 9.39451i 0.342810i −0.985201 0.171405i \(-0.945169\pi\)
0.985201 0.171405i \(-0.0548307\pi\)
\(752\) 3.31273 + 3.31273i 0.120803 + 0.120803i
\(753\) −12.7497 43.5830i −0.464625 1.58825i
\(754\) 26.6644 7.80270i 0.971062 0.284158i
\(755\) 2.14954i 0.0782297i
\(756\) −0.355103 5.18400i −0.0129150 0.188540i
\(757\) 35.0626 1.27437 0.637187 0.770709i \(-0.280098\pi\)
0.637187 + 0.770709i \(0.280098\pi\)
\(758\) −37.4923 −1.36178
\(759\) −0.0346474 + 0.0633011i −0.00125762 + 0.00229768i
\(760\) 0.608785 + 0.608785i 0.0220829 + 0.0220829i
\(761\) 21.2949 + 21.2949i 0.771940 + 0.771940i 0.978445 0.206506i \(-0.0662092\pi\)
−0.206506 + 0.978445i \(0.566209\pi\)
\(762\) −3.58845 + 6.55612i −0.129996 + 0.237503i
\(763\) −12.1449 −0.439675
\(764\) −12.6760 −0.458601
\(765\) 13.9329 63.4359i 0.503744 2.29353i
\(766\) 28.5742i 1.03243i
\(767\) 10.2784 3.00772i 0.371131 0.108603i
\(768\) −0.486309 1.66238i −0.0175482 0.0599859i
\(769\) −10.2910 10.2910i −0.371104 0.371104i 0.496775 0.867879i \(-0.334517\pi\)
−0.867879 + 0.496775i \(0.834517\pi\)
\(770\) 0.0625325i 0.00225351i
\(771\) −14.9298 51.0354i −0.537683 1.83799i
\(772\) −5.53338 5.53338i −0.199151 0.199151i
\(773\) −34.9528 + 34.9528i −1.25717 + 1.25717i −0.304727 + 0.952440i \(0.598565\pi\)
−0.952440 + 0.304727i \(0.901435\pi\)
\(774\) −14.9408 3.28156i −0.537036 0.117953i
\(775\) 65.9340 65.9340i 2.36842 2.36842i
\(776\) 8.40720i