Properties

Label 637.2.g.d.263.1
Level $637$
Weight $2$
Character 637.263
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 263.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 637.263
Dual form 637.2.g.d.373.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 1.50000i) q^{2} -2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} +O(q^{10})\) \(q+(-0.866025 + 1.50000i) q^{2} -2.73205 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.866025 + 1.50000i) q^{5} +(2.36603 - 4.09808i) q^{6} -1.73205 q^{8} +4.46410 q^{9} -3.00000 q^{10} +1.26795 q^{11} +(1.36603 + 2.36603i) q^{12} +(-3.59808 - 0.232051i) q^{13} +(-2.36603 - 4.09808i) q^{15} +(2.50000 - 4.33013i) q^{16} +(-3.86603 - 6.69615i) q^{17} +(-3.86603 + 6.69615i) q^{18} -2.00000 q^{19} +(0.866025 - 1.50000i) q^{20} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 + 4.09808i) q^{23} +4.73205 q^{24} +(1.00000 - 1.73205i) q^{25} +(3.46410 - 5.19615i) q^{26} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +8.19615 q^{30} +(2.09808 - 3.63397i) q^{31} +(2.59808 + 4.50000i) q^{32} -3.46410 q^{33} +13.3923 q^{34} +(-2.23205 - 3.86603i) q^{36} +(3.50000 - 6.06218i) q^{37} +(1.73205 - 3.00000i) q^{38} +(9.83013 + 0.633975i) q^{39} +(-1.50000 - 2.59808i) q^{40} +(-2.59808 - 4.50000i) q^{41} +(0.0980762 - 0.169873i) q^{43} +(-0.633975 - 1.09808i) q^{44} +(3.86603 + 6.69615i) q^{45} +(-4.09808 - 7.09808i) q^{46} +(6.46410 + 11.1962i) q^{47} +(-6.83013 + 11.8301i) q^{48} +(1.73205 + 3.00000i) q^{50} +(10.5622 + 18.2942i) q^{51} +(1.59808 + 3.23205i) q^{52} +(4.96410 - 8.59808i) q^{53} +(3.46410 - 6.00000i) q^{54} +(1.09808 + 1.90192i) q^{55} +5.46410 q^{57} -5.19615 q^{58} +(3.63397 + 6.29423i) q^{59} +(-2.36603 + 4.09808i) q^{60} +4.80385 q^{61} +(3.63397 + 6.29423i) q^{62} +1.00000 q^{64} +(-2.76795 - 5.59808i) q^{65} +(3.00000 - 5.19615i) q^{66} -6.19615 q^{67} +(-3.86603 + 6.69615i) q^{68} +(6.46410 - 11.1962i) q^{69} +(-3.00000 + 5.19615i) q^{71} -7.73205 q^{72} +(-1.59808 + 2.76795i) q^{73} +(6.06218 + 10.5000i) q^{74} +(-2.73205 + 4.73205i) q^{75} +(1.00000 + 1.73205i) q^{76} +(-9.46410 + 14.1962i) q^{78} +(-8.09808 - 14.0263i) q^{79} +8.66025 q^{80} -2.46410 q^{81} +9.00000 q^{82} +2.19615 q^{83} +(6.69615 - 11.5981i) q^{85} +(0.169873 + 0.294229i) q^{86} +(-4.09808 - 7.09808i) q^{87} -2.19615 q^{88} +(6.46410 - 11.1962i) q^{89} -13.3923 q^{90} +4.73205 q^{92} +(-5.73205 + 9.92820i) q^{93} -22.3923 q^{94} +(-1.73205 - 3.00000i) q^{95} +(-7.09808 - 12.2942i) q^{96} +(3.19615 - 5.53590i) q^{97} +5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} - 2 q^{4} + 6 q^{6} + 4 q^{9} - 12 q^{10} + 12 q^{11} + 2 q^{12} - 4 q^{13} - 6 q^{15} + 10 q^{16} - 12 q^{17} - 12 q^{18} - 8 q^{19} + 6 q^{22} - 6 q^{23} + 12 q^{24} + 4 q^{25} - 16 q^{27} + 6 q^{29} + 12 q^{30} - 2 q^{31} + 12 q^{34} - 2 q^{36} + 14 q^{37} + 22 q^{39} - 6 q^{40} - 10 q^{43} - 6 q^{44} + 12 q^{45} - 6 q^{46} + 12 q^{47} - 10 q^{48} + 18 q^{51} - 4 q^{52} + 6 q^{53} - 6 q^{55} + 8 q^{57} + 18 q^{59} - 6 q^{60} + 40 q^{61} + 18 q^{62} + 4 q^{64} - 18 q^{65} + 12 q^{66} - 4 q^{67} - 12 q^{68} + 12 q^{69} - 12 q^{71} - 24 q^{72} + 4 q^{73} - 4 q^{75} + 4 q^{76} - 24 q^{78} - 22 q^{79} + 4 q^{81} + 36 q^{82} - 12 q^{83} + 6 q^{85} + 18 q^{86} - 6 q^{87} + 12 q^{88} + 12 q^{89} - 12 q^{90} + 12 q^{92} - 16 q^{93} - 48 q^{94} - 18 q^{96} - 8 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 1.50000i −0.612372 + 1.06066i 0.378467 + 0.925615i \(0.376451\pi\)
−0.990839 + 0.135045i \(0.956882\pi\)
\(3\) −2.73205 −1.57735 −0.788675 0.614810i \(-0.789233\pi\)
−0.788675 + 0.614810i \(0.789233\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0.866025 + 1.50000i 0.387298 + 0.670820i 0.992085 0.125567i \(-0.0400750\pi\)
−0.604787 + 0.796387i \(0.706742\pi\)
\(6\) 2.36603 4.09808i 0.965926 1.67303i
\(7\) 0 0
\(8\) −1.73205 −0.612372
\(9\) 4.46410 1.48803
\(10\) −3.00000 −0.948683
\(11\) 1.26795 0.382301 0.191151 0.981561i \(-0.438778\pi\)
0.191151 + 0.981561i \(0.438778\pi\)
\(12\) 1.36603 + 2.36603i 0.394338 + 0.683013i
\(13\) −3.59808 0.232051i −0.997927 0.0643593i
\(14\) 0 0
\(15\) −2.36603 4.09808i −0.610905 1.05812i
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −3.86603 6.69615i −0.937649 1.62406i −0.769841 0.638236i \(-0.779664\pi\)
−0.167808 0.985820i \(-0.553669\pi\)
\(18\) −3.86603 + 6.69615i −0.911231 + 1.57830i
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0.866025 1.50000i 0.193649 0.335410i
\(21\) 0 0
\(22\) −1.09808 + 1.90192i −0.234111 + 0.405492i
\(23\) −2.36603 + 4.09808i −0.493350 + 0.854508i −0.999971 0.00766135i \(-0.997561\pi\)
0.506620 + 0.862169i \(0.330895\pi\)
\(24\) 4.73205 0.965926
\(25\) 1.00000 1.73205i 0.200000 0.346410i
\(26\) 3.46410 5.19615i 0.679366 1.01905i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 1.50000 + 2.59808i 0.278543 + 0.482451i 0.971023 0.238987i \(-0.0768152\pi\)
−0.692480 + 0.721437i \(0.743482\pi\)
\(30\) 8.19615 1.49641
\(31\) 2.09808 3.63397i 0.376826 0.652681i −0.613773 0.789483i \(-0.710349\pi\)
0.990598 + 0.136802i \(0.0436823\pi\)
\(32\) 2.59808 + 4.50000i 0.459279 + 0.795495i
\(33\) −3.46410 −0.603023
\(34\) 13.3923 2.29676
\(35\) 0 0
\(36\) −2.23205 3.86603i −0.372008 0.644338i
\(37\) 3.50000 6.06218i 0.575396 0.996616i −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 1.73205 3.00000i 0.280976 0.486664i
\(39\) 9.83013 + 0.633975i 1.57408 + 0.101517i
\(40\) −1.50000 2.59808i −0.237171 0.410792i
\(41\) −2.59808 4.50000i −0.405751 0.702782i 0.588657 0.808383i \(-0.299657\pi\)
−0.994409 + 0.105601i \(0.966323\pi\)
\(42\) 0 0
\(43\) 0.0980762 0.169873i 0.0149565 0.0259054i −0.858450 0.512897i \(-0.828572\pi\)
0.873407 + 0.486991i \(0.161906\pi\)
\(44\) −0.633975 1.09808i −0.0955753 0.165541i
\(45\) 3.86603 + 6.69615i 0.576313 + 0.998203i
\(46\) −4.09808 7.09808i −0.604228 1.04655i
\(47\) 6.46410 + 11.1962i 0.942886 + 1.63313i 0.759929 + 0.650006i \(0.225234\pi\)
0.182957 + 0.983121i \(0.441433\pi\)
\(48\) −6.83013 + 11.8301i −0.985844 + 1.70753i
\(49\) 0 0
\(50\) 1.73205 + 3.00000i 0.244949 + 0.424264i
\(51\) 10.5622 + 18.2942i 1.47900 + 2.56170i
\(52\) 1.59808 + 3.23205i 0.221613 + 0.448205i
\(53\) 4.96410 8.59808i 0.681872 1.18104i −0.292537 0.956254i \(-0.594500\pi\)
0.974409 0.224782i \(-0.0721671\pi\)
\(54\) 3.46410 6.00000i 0.471405 0.816497i
\(55\) 1.09808 + 1.90192i 0.148065 + 0.256455i
\(56\) 0 0
\(57\) 5.46410 0.723738
\(58\) −5.19615 −0.682288
\(59\) 3.63397 + 6.29423i 0.473103 + 0.819439i 0.999526 0.0307841i \(-0.00980044\pi\)
−0.526423 + 0.850223i \(0.676467\pi\)
\(60\) −2.36603 + 4.09808i −0.305453 + 0.529059i
\(61\) 4.80385 0.615070 0.307535 0.951537i \(-0.400496\pi\)
0.307535 + 0.951537i \(0.400496\pi\)
\(62\) 3.63397 + 6.29423i 0.461515 + 0.799368i
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −2.76795 5.59808i −0.343322 0.694356i
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) −6.19615 −0.756980 −0.378490 0.925605i \(-0.623557\pi\)
−0.378490 + 0.925605i \(0.623557\pi\)
\(68\) −3.86603 + 6.69615i −0.468824 + 0.812028i
\(69\) 6.46410 11.1962i 0.778186 1.34786i
\(70\) 0 0
\(71\) −3.00000 + 5.19615i −0.356034 + 0.616670i −0.987294 0.158901i \(-0.949205\pi\)
0.631260 + 0.775571i \(0.282538\pi\)
\(72\) −7.73205 −0.911231
\(73\) −1.59808 + 2.76795i −0.187041 + 0.323964i −0.944262 0.329194i \(-0.893223\pi\)
0.757222 + 0.653158i \(0.226556\pi\)
\(74\) 6.06218 + 10.5000i 0.704714 + 1.22060i
\(75\) −2.73205 + 4.73205i −0.315470 + 0.546410i
\(76\) 1.00000 + 1.73205i 0.114708 + 0.198680i
\(77\) 0 0
\(78\) −9.46410 + 14.1962i −1.07160 + 1.60740i
\(79\) −8.09808 14.0263i −0.911105 1.57808i −0.812506 0.582952i \(-0.801897\pi\)
−0.0985985 0.995127i \(-0.531436\pi\)
\(80\) 8.66025 0.968246
\(81\) −2.46410 −0.273789
\(82\) 9.00000 0.993884
\(83\) 2.19615 0.241059 0.120530 0.992710i \(-0.461541\pi\)
0.120530 + 0.992710i \(0.461541\pi\)
\(84\) 0 0
\(85\) 6.69615 11.5981i 0.726300 1.25799i
\(86\) 0.169873 + 0.294229i 0.0183179 + 0.0317275i
\(87\) −4.09808 7.09808i −0.439360 0.760994i
\(88\) −2.19615 −0.234111
\(89\) 6.46410 11.1962i 0.685193 1.18679i −0.288183 0.957575i \(-0.593051\pi\)
0.973376 0.229214i \(-0.0736157\pi\)
\(90\) −13.3923 −1.41167
\(91\) 0 0
\(92\) 4.73205 0.493350
\(93\) −5.73205 + 9.92820i −0.594386 + 1.02951i
\(94\) −22.3923 −2.30959
\(95\) −1.73205 3.00000i −0.177705 0.307794i
\(96\) −7.09808 12.2942i −0.724444 1.25477i
\(97\) 3.19615 5.53590i 0.324520 0.562085i −0.656895 0.753982i \(-0.728131\pi\)
0.981415 + 0.191897i \(0.0614639\pi\)
\(98\) 0 0
\(99\) 5.66025 0.568877
\(100\) −2.00000 −0.200000
\(101\) 7.73205 0.769368 0.384684 0.923048i \(-0.374310\pi\)
0.384684 + 0.923048i \(0.374310\pi\)
\(102\) −36.5885 −3.62280
\(103\) −7.19615 12.4641i −0.709058 1.22812i −0.965207 0.261487i \(-0.915787\pi\)
0.256149 0.966637i \(-0.417546\pi\)
\(104\) 6.23205 + 0.401924i 0.611103 + 0.0394119i
\(105\) 0 0
\(106\) 8.59808 + 14.8923i 0.835119 + 1.44647i
\(107\) 3.92820 6.80385i 0.379754 0.657753i −0.611273 0.791420i \(-0.709342\pi\)
0.991026 + 0.133667i \(0.0426754\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 4.19615 7.26795i 0.401919 0.696143i −0.592039 0.805909i \(-0.701677\pi\)
0.993957 + 0.109766i \(0.0350102\pi\)
\(110\) −3.80385 −0.362683
\(111\) −9.56218 + 16.5622i −0.907602 + 1.57201i
\(112\) 0 0
\(113\) −6.69615 + 11.5981i −0.629921 + 1.09106i 0.357646 + 0.933857i \(0.383579\pi\)
−0.987567 + 0.157198i \(0.949754\pi\)
\(114\) −4.73205 + 8.19615i −0.443197 + 0.767640i
\(115\) −8.19615 −0.764295
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) −16.0622 1.03590i −1.48495 0.0957688i
\(118\) −12.5885 −1.15886
\(119\) 0 0
\(120\) 4.09808 + 7.09808i 0.374101 + 0.647963i
\(121\) −9.39230 −0.853846
\(122\) −4.16025 + 7.20577i −0.376652 + 0.652380i
\(123\) 7.09808 + 12.2942i 0.640012 + 1.10853i
\(124\) −4.19615 −0.376826
\(125\) 12.1244 1.08444
\(126\) 0 0
\(127\) −9.19615 15.9282i −0.816027 1.41340i −0.908588 0.417693i \(-0.862839\pi\)
0.0925619 0.995707i \(-0.470494\pi\)
\(128\) −6.06218 + 10.5000i −0.535826 + 0.928078i
\(129\) −0.267949 + 0.464102i −0.0235916 + 0.0408619i
\(130\) 10.7942 + 0.696152i 0.946716 + 0.0610566i
\(131\) −1.73205 3.00000i −0.151330 0.262111i 0.780387 0.625297i \(-0.215022\pi\)
−0.931717 + 0.363186i \(0.881689\pi\)
\(132\) 1.73205 + 3.00000i 0.150756 + 0.261116i
\(133\) 0 0
\(134\) 5.36603 9.29423i 0.463554 0.802899i
\(135\) −3.46410 6.00000i −0.298142 0.516398i
\(136\) 6.69615 + 11.5981i 0.574190 + 0.994527i
\(137\) −4.03590 6.99038i −0.344810 0.597229i 0.640509 0.767951i \(-0.278723\pi\)
−0.985319 + 0.170722i \(0.945390\pi\)
\(138\) 11.1962 + 19.3923i 0.953080 + 1.65078i
\(139\) −5.29423 + 9.16987i −0.449051 + 0.777778i −0.998324 0.0578639i \(-0.981571\pi\)
0.549274 + 0.835642i \(0.314904\pi\)
\(140\) 0 0
\(141\) −17.6603 30.5885i −1.48726 2.57601i
\(142\) −5.19615 9.00000i −0.436051 0.755263i
\(143\) −4.56218 0.294229i −0.381508 0.0246046i
\(144\) 11.1603 19.3301i 0.930021 1.61084i
\(145\) −2.59808 + 4.50000i −0.215758 + 0.373705i
\(146\) −2.76795 4.79423i −0.229077 0.396773i
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) −6.46410 −0.529560 −0.264780 0.964309i \(-0.585299\pi\)
−0.264780 + 0.964309i \(0.585299\pi\)
\(150\) −4.73205 8.19615i −0.386370 0.669213i
\(151\) −1.00000 + 1.73205i −0.0813788 + 0.140952i −0.903842 0.427865i \(-0.859266\pi\)
0.822464 + 0.568818i \(0.192599\pi\)
\(152\) 3.46410 0.280976
\(153\) −17.2583 29.8923i −1.39525 2.41665i
\(154\) 0 0
\(155\) 7.26795 0.583776
\(156\) −4.36603 8.83013i −0.349562 0.706976i
\(157\) 0.598076 1.03590i 0.0477317 0.0826737i −0.841172 0.540767i \(-0.818134\pi\)
0.888904 + 0.458093i \(0.151467\pi\)
\(158\) 28.0526 2.23174
\(159\) −13.5622 + 23.4904i −1.07555 + 1.86291i
\(160\) −4.50000 + 7.79423i −0.355756 + 0.616188i
\(161\) 0 0
\(162\) 2.13397 3.69615i 0.167661 0.290397i
\(163\) 16.1962 1.26858 0.634290 0.773095i \(-0.281292\pi\)
0.634290 + 0.773095i \(0.281292\pi\)
\(164\) −2.59808 + 4.50000i −0.202876 + 0.351391i
\(165\) −3.00000 5.19615i −0.233550 0.404520i
\(166\) −1.90192 + 3.29423i −0.147618 + 0.255682i
\(167\) −3.29423 5.70577i −0.254915 0.441526i 0.709957 0.704245i \(-0.248714\pi\)
−0.964872 + 0.262719i \(0.915381\pi\)
\(168\) 0 0
\(169\) 12.8923 + 1.66987i 0.991716 + 0.128452i
\(170\) 11.5981 + 20.0885i 0.889532 + 1.54071i
\(171\) −8.92820 −0.682757
\(172\) −0.196152 −0.0149565
\(173\) −8.53590 −0.648972 −0.324486 0.945890i \(-0.605191\pi\)
−0.324486 + 0.945890i \(0.605191\pi\)
\(174\) 14.1962 1.07621
\(175\) 0 0
\(176\) 3.16987 5.49038i 0.238938 0.413853i
\(177\) −9.92820 17.1962i −0.746249 1.29254i
\(178\) 11.1962 + 19.3923i 0.839187 + 1.45351i
\(179\) −6.92820 −0.517838 −0.258919 0.965899i \(-0.583366\pi\)
−0.258919 + 0.965899i \(0.583366\pi\)
\(180\) 3.86603 6.69615i 0.288157 0.499102i
\(181\) −5.58846 −0.415387 −0.207693 0.978194i \(-0.566596\pi\)
−0.207693 + 0.978194i \(0.566596\pi\)
\(182\) 0 0
\(183\) −13.1244 −0.970180
\(184\) 4.09808 7.09808i 0.302114 0.523277i
\(185\) 12.1244 0.891400
\(186\) −9.92820 17.1962i −0.727971 1.26088i
\(187\) −4.90192 8.49038i −0.358464 0.620878i
\(188\) 6.46410 11.1962i 0.471443 0.816563i
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 4.73205 0.342399 0.171200 0.985236i \(-0.445236\pi\)
0.171200 + 0.985236i \(0.445236\pi\)
\(192\) −2.73205 −0.197169
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 5.53590 + 9.58846i 0.397454 + 0.688411i
\(195\) 7.56218 + 15.2942i 0.541539 + 1.09524i
\(196\) 0 0
\(197\) −6.00000 10.3923i −0.427482 0.740421i 0.569166 0.822222i \(-0.307266\pi\)
−0.996649 + 0.0818013i \(0.973933\pi\)
\(198\) −4.90192 + 8.49038i −0.348365 + 0.603385i
\(199\) 1.00000 + 1.73205i 0.0708881 + 0.122782i 0.899291 0.437351i \(-0.144083\pi\)
−0.828403 + 0.560133i \(0.810750\pi\)
\(200\) −1.73205 + 3.00000i −0.122474 + 0.212132i
\(201\) 16.9282 1.19402
\(202\) −6.69615 + 11.5981i −0.471140 + 0.816038i
\(203\) 0 0
\(204\) 10.5622 18.2942i 0.739500 1.28085i
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 24.9282 1.73683
\(207\) −10.5622 + 18.2942i −0.734122 + 1.27154i
\(208\) −10.0000 + 15.0000i −0.693375 + 1.04006i
\(209\) −2.53590 −0.175412
\(210\) 0 0
\(211\) 0.901924 + 1.56218i 0.0620910 + 0.107545i 0.895400 0.445263i \(-0.146890\pi\)
−0.833309 + 0.552808i \(0.813556\pi\)
\(212\) −9.92820 −0.681872
\(213\) 8.19615 14.1962i 0.561591 0.972704i
\(214\) 6.80385 + 11.7846i 0.465101 + 0.805579i
\(215\) 0.339746 0.0231705
\(216\) 6.92820 0.471405
\(217\) 0 0
\(218\) 7.26795 + 12.5885i 0.492248 + 0.852598i
\(219\) 4.36603 7.56218i 0.295029 0.511005i
\(220\) 1.09808 1.90192i 0.0740323 0.128228i
\(221\) 12.3564 + 24.9904i 0.831182 + 1.68103i
\(222\) −16.5622 28.6865i −1.11158 1.92531i
\(223\) −5.00000 8.66025i −0.334825 0.579934i 0.648626 0.761107i \(-0.275344\pi\)
−0.983451 + 0.181173i \(0.942010\pi\)
\(224\) 0 0
\(225\) 4.46410 7.73205i 0.297607 0.515470i
\(226\) −11.5981 20.0885i −0.771493 1.33626i
\(227\) 2.83013 + 4.90192i 0.187842 + 0.325352i 0.944531 0.328424i \(-0.106517\pi\)
−0.756688 + 0.653776i \(0.773184\pi\)
\(228\) −2.73205 4.73205i −0.180934 0.313388i
\(229\) −7.19615 12.4641i −0.475535 0.823651i 0.524072 0.851674i \(-0.324412\pi\)
−0.999607 + 0.0280229i \(0.991079\pi\)
\(230\) 7.09808 12.2942i 0.468033 0.810657i
\(231\) 0 0
\(232\) −2.59808 4.50000i −0.170572 0.295439i
\(233\) 0.928203 + 1.60770i 0.0608086 + 0.105324i 0.894827 0.446413i \(-0.147299\pi\)
−0.834018 + 0.551737i \(0.813965\pi\)
\(234\) 15.4641 23.1962i 1.01092 1.51638i
\(235\) −11.1962 + 19.3923i −0.730356 + 1.26501i
\(236\) 3.63397 6.29423i 0.236552 0.409719i
\(237\) 22.1244 + 38.3205i 1.43713 + 2.48918i
\(238\) 0 0
\(239\) −15.8038 −1.02227 −0.511133 0.859502i \(-0.670774\pi\)
−0.511133 + 0.859502i \(0.670774\pi\)
\(240\) −23.6603 −1.52726
\(241\) −10.5981 18.3564i −0.682682 1.18244i −0.974159 0.225862i \(-0.927480\pi\)
0.291477 0.956578i \(-0.405853\pi\)
\(242\) 8.13397 14.0885i 0.522872 0.905640i
\(243\) 18.7321 1.20166
\(244\) −2.40192 4.16025i −0.153767 0.266333i
\(245\) 0 0
\(246\) −24.5885 −1.56770
\(247\) 7.19615 + 0.464102i 0.457880 + 0.0295301i
\(248\) −3.63397 + 6.29423i −0.230758 + 0.399684i
\(249\) −6.00000 −0.380235
\(250\) −10.5000 + 18.1865i −0.664078 + 1.15022i
\(251\) −0.803848 + 1.39230i −0.0507384 + 0.0878815i −0.890279 0.455415i \(-0.849491\pi\)
0.839541 + 0.543297i \(0.182824\pi\)
\(252\) 0 0
\(253\) −3.00000 + 5.19615i −0.188608 + 0.326679i
\(254\) 31.8564 1.99885
\(255\) −18.2942 + 31.6865i −1.14563 + 1.98429i
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) 3.06218 5.30385i 0.191013 0.330845i −0.754573 0.656216i \(-0.772156\pi\)
0.945586 + 0.325371i \(0.105489\pi\)
\(258\) −0.464102 0.803848i −0.0288937 0.0500454i
\(259\) 0 0
\(260\) −3.46410 + 5.19615i −0.214834 + 0.322252i
\(261\) 6.69615 + 11.5981i 0.414481 + 0.717903i
\(262\) 6.00000 0.370681
\(263\) 1.26795 0.0781851 0.0390925 0.999236i \(-0.487553\pi\)
0.0390925 + 0.999236i \(0.487553\pi\)
\(264\) 6.00000 0.369274
\(265\) 17.1962 1.05635
\(266\) 0 0
\(267\) −17.6603 + 30.5885i −1.08079 + 1.87198i
\(268\) 3.09808 + 5.36603i 0.189245 + 0.327782i
\(269\) 2.53590 + 4.39230i 0.154616 + 0.267804i 0.932919 0.360086i \(-0.117252\pi\)
−0.778303 + 0.627889i \(0.783919\pi\)
\(270\) 12.0000 0.730297
\(271\) 2.90192 5.02628i 0.176279 0.305325i −0.764324 0.644832i \(-0.776927\pi\)
0.940603 + 0.339508i \(0.110260\pi\)
\(272\) −38.6603 −2.34412
\(273\) 0 0
\(274\) 13.9808 0.844609
\(275\) 1.26795 2.19615i 0.0764602 0.132433i
\(276\) −12.9282 −0.778186
\(277\) −8.50000 14.7224i −0.510716 0.884585i −0.999923 0.0124177i \(-0.996047\pi\)
0.489207 0.872167i \(-0.337286\pi\)
\(278\) −9.16987 15.8827i −0.549972 0.952580i
\(279\) 9.36603 16.2224i 0.560729 0.971212i
\(280\) 0 0
\(281\) 13.3923 0.798918 0.399459 0.916751i \(-0.369198\pi\)
0.399459 + 0.916751i \(0.369198\pi\)
\(282\) 61.1769 3.64303
\(283\) −10.1962 −0.606098 −0.303049 0.952975i \(-0.598005\pi\)
−0.303049 + 0.952975i \(0.598005\pi\)
\(284\) 6.00000 0.356034
\(285\) 4.73205 + 8.19615i 0.280302 + 0.485498i
\(286\) 4.39230 6.58846i 0.259722 0.389584i
\(287\) 0 0
\(288\) 11.5981 + 20.0885i 0.683423 + 1.18372i
\(289\) −21.3923 + 37.0526i −1.25837 + 2.17956i
\(290\) −4.50000 7.79423i −0.264249 0.457693i
\(291\) −8.73205 + 15.1244i −0.511882 + 0.886605i
\(292\) 3.19615 0.187041
\(293\) −0.401924 + 0.696152i −0.0234806 + 0.0406697i −0.877527 0.479527i \(-0.840808\pi\)
0.854046 + 0.520197i \(0.174141\pi\)
\(294\) 0 0
\(295\) −6.29423 + 10.9019i −0.366464 + 0.634735i
\(296\) −6.06218 + 10.5000i −0.352357 + 0.610300i
\(297\) −5.07180 −0.294295
\(298\) 5.59808 9.69615i 0.324288 0.561683i
\(299\) 9.46410 14.1962i 0.547323 0.820985i
\(300\) 5.46410 0.315470
\(301\) 0 0
\(302\) −1.73205 3.00000i −0.0996683 0.172631i
\(303\) −21.1244 −1.21356
\(304\) −5.00000 + 8.66025i −0.286770 + 0.496700i
\(305\) 4.16025 + 7.20577i 0.238215 + 0.412601i
\(306\) 59.7846 3.41766
\(307\) 4.58846 0.261877 0.130939 0.991390i \(-0.458201\pi\)
0.130939 + 0.991390i \(0.458201\pi\)
\(308\) 0 0
\(309\) 19.6603 + 34.0526i 1.11843 + 1.93718i
\(310\) −6.29423 + 10.9019i −0.357488 + 0.619188i
\(311\) 0.633975 1.09808i 0.0359494 0.0622662i −0.847491 0.530810i \(-0.821888\pi\)
0.883440 + 0.468544i \(0.155221\pi\)
\(312\) −17.0263 1.09808i −0.963923 0.0621663i
\(313\) 14.3923 + 24.9282i 0.813501 + 1.40903i 0.910399 + 0.413731i \(0.135775\pi\)
−0.0968980 + 0.995294i \(0.530892\pi\)
\(314\) 1.03590 + 1.79423i 0.0584591 + 0.101254i
\(315\) 0 0
\(316\) −8.09808 + 14.0263i −0.455552 + 0.789040i
\(317\) 3.23205 + 5.59808i 0.181530 + 0.314419i 0.942402 0.334483i \(-0.108562\pi\)
−0.760872 + 0.648902i \(0.775228\pi\)
\(318\) −23.4904 40.6865i −1.31728 2.28159i
\(319\) 1.90192 + 3.29423i 0.106487 + 0.184441i
\(320\) 0.866025 + 1.50000i 0.0484123 + 0.0838525i
\(321\) −10.7321 + 18.5885i −0.599005 + 1.03751i
\(322\) 0 0
\(323\) 7.73205 + 13.3923i 0.430223 + 0.745168i
\(324\) 1.23205 + 2.13397i 0.0684473 + 0.118554i
\(325\) −4.00000 + 6.00000i −0.221880 + 0.332820i
\(326\) −14.0263 + 24.2942i −0.776844 + 1.34553i
\(327\) −11.4641 + 19.8564i −0.633966 + 1.09806i
\(328\) 4.50000 + 7.79423i 0.248471 + 0.430364i
\(329\) 0 0
\(330\) 10.3923 0.572078
\(331\) 24.9808 1.37307 0.686533 0.727098i \(-0.259132\pi\)
0.686533 + 0.727098i \(0.259132\pi\)
\(332\) −1.09808 1.90192i −0.0602648 0.104382i
\(333\) 15.6244 27.0622i 0.856209 1.48300i
\(334\) 11.4115 0.624412
\(335\) −5.36603 9.29423i −0.293177 0.507798i
\(336\) 0 0
\(337\) 11.0000 0.599208 0.299604 0.954064i \(-0.403145\pi\)
0.299604 + 0.954064i \(0.403145\pi\)
\(338\) −13.6699 + 17.8923i −0.743543 + 0.973213i
\(339\) 18.2942 31.6865i 0.993606 1.72098i
\(340\) −13.3923 −0.726300
\(341\) 2.66025 4.60770i 0.144061 0.249521i
\(342\) 7.73205 13.3923i 0.418101 0.724173i
\(343\) 0 0
\(344\) −0.169873 + 0.294229i −0.00915894 + 0.0158637i
\(345\) 22.3923 1.20556
\(346\) 7.39230 12.8038i 0.397413 0.688339i
\(347\) −3.63397 6.29423i −0.195082 0.337892i 0.751845 0.659339i \(-0.229164\pi\)
−0.946927 + 0.321448i \(0.895831\pi\)
\(348\) −4.09808 + 7.09808i −0.219680 + 0.380497i
\(349\) −12.3923 21.4641i −0.663345 1.14895i −0.979731 0.200317i \(-0.935803\pi\)
0.316386 0.948630i \(-0.397530\pi\)
\(350\) 0 0
\(351\) 14.3923 + 0.928203i 0.768204 + 0.0495438i
\(352\) 3.29423 + 5.70577i 0.175583 + 0.304119i
\(353\) −20.6603 −1.09963 −0.549817 0.835285i \(-0.685303\pi\)
−0.549817 + 0.835285i \(0.685303\pi\)
\(354\) 34.3923 1.82793
\(355\) −10.3923 −0.551566
\(356\) −12.9282 −0.685193
\(357\) 0 0
\(358\) 6.00000 10.3923i 0.317110 0.549250i
\(359\) −9.46410 16.3923i −0.499496 0.865153i 0.500504 0.865734i \(-0.333148\pi\)
−1.00000 0.000581665i \(0.999815\pi\)
\(360\) −6.69615 11.5981i −0.352918 0.611272i
\(361\) −15.0000 −0.789474
\(362\) 4.83975 8.38269i 0.254371 0.440584i
\(363\) 25.6603 1.34681
\(364\) 0 0
\(365\) −5.53590 −0.289762
\(366\) 11.3660 19.6865i 0.594112 1.02903i
\(367\) −4.19615 −0.219037 −0.109519 0.993985i \(-0.534931\pi\)
−0.109519 + 0.993985i \(0.534931\pi\)
\(368\) 11.8301 + 20.4904i 0.616688 + 1.06813i
\(369\) −11.5981 20.0885i −0.603772 1.04576i
\(370\) −10.5000 + 18.1865i −0.545869 + 0.945473i
\(371\) 0 0
\(372\) 11.4641 0.594386
\(373\) −11.3923 −0.589871 −0.294936 0.955517i \(-0.595298\pi\)
−0.294936 + 0.955517i \(0.595298\pi\)
\(374\) 16.9808 0.878054
\(375\) −33.1244 −1.71053
\(376\) −11.1962 19.3923i −0.577397 1.00008i
\(377\) −4.79423 9.69615i −0.246915 0.499377i
\(378\) 0 0
\(379\) −13.2942 23.0263i −0.682879 1.18278i −0.974098 0.226124i \(-0.927394\pi\)
0.291220 0.956656i \(-0.405939\pi\)
\(380\) −1.73205 + 3.00000i −0.0888523 + 0.153897i
\(381\) 25.1244 + 43.5167i 1.28716 + 2.22943i
\(382\) −4.09808 + 7.09808i −0.209676 + 0.363169i
\(383\) 11.6603 0.595811 0.297906 0.954595i \(-0.403712\pi\)
0.297906 + 0.954595i \(0.403712\pi\)
\(384\) 16.5622 28.6865i 0.845185 1.46390i
\(385\) 0 0
\(386\) −4.33013 + 7.50000i −0.220398 + 0.381740i
\(387\) 0.437822 0.758330i 0.0222558 0.0385481i
\(388\) −6.39230 −0.324520
\(389\) 11.7679 20.3827i 0.596659 1.03344i −0.396652 0.917969i \(-0.629828\pi\)
0.993310 0.115474i \(-0.0368387\pi\)
\(390\) −29.4904 1.90192i −1.49330 0.0963077i
\(391\) 36.5885 1.85036
\(392\) 0 0
\(393\) 4.73205 + 8.19615i 0.238700 + 0.413441i
\(394\) 20.7846 1.04711
\(395\) 14.0263 24.2942i 0.705739 1.22238i
\(396\) −2.83013 4.90192i −0.142219 0.246331i
\(397\) 18.7846 0.942773 0.471386 0.881927i \(-0.343754\pi\)
0.471386 + 0.881927i \(0.343754\pi\)
\(398\) −3.46410 −0.173640
\(399\) 0 0
\(400\) −5.00000 8.66025i −0.250000 0.433013i
\(401\) 5.42820 9.40192i 0.271072 0.469510i −0.698065 0.716034i \(-0.745955\pi\)
0.969136 + 0.246525i \(0.0792887\pi\)
\(402\) −14.6603 + 25.3923i −0.731187 + 1.26645i
\(403\) −8.39230 + 12.5885i −0.418050 + 0.627076i
\(404\) −3.86603 6.69615i −0.192342 0.333146i
\(405\) −2.13397 3.69615i −0.106038 0.183663i
\(406\) 0 0
\(407\) 4.43782 7.68653i 0.219975 0.381007i
\(408\) −18.2942 31.6865i −0.905699 1.56872i
\(409\) −8.40192 14.5526i −0.415448 0.719578i 0.580027 0.814597i \(-0.303042\pi\)
−0.995475 + 0.0950195i \(0.969709\pi\)
\(410\) 7.79423 + 13.5000i 0.384930 + 0.666717i
\(411\) 11.0263 + 19.0981i 0.543886 + 0.942039i
\(412\) −7.19615 + 12.4641i −0.354529 + 0.614062i
\(413\) 0 0
\(414\) −18.2942 31.6865i −0.899112 1.55731i
\(415\) 1.90192 + 3.29423i 0.0933618 + 0.161707i
\(416\) −8.30385 16.7942i −0.407130 0.823405i
\(417\) 14.4641 25.0526i 0.708310 1.22683i
\(418\) 2.19615 3.80385i 0.107417 0.186052i
\(419\) −16.0981 27.8827i −0.786442 1.36216i −0.928134 0.372247i \(-0.878587\pi\)
0.141691 0.989911i \(-0.454746\pi\)
\(420\) 0 0
\(421\) −32.1769 −1.56821 −0.784103 0.620630i \(-0.786877\pi\)
−0.784103 + 0.620630i \(0.786877\pi\)
\(422\) −3.12436 −0.152091
\(423\) 28.8564 + 49.9808i 1.40305 + 2.43015i
\(424\) −8.59808 + 14.8923i −0.417559 + 0.723234i
\(425\) −15.4641 −0.750119
\(426\) 14.1962 + 24.5885i 0.687806 + 1.19131i
\(427\) 0 0
\(428\) −7.85641 −0.379754
\(429\) 12.4641 + 0.803848i 0.601772 + 0.0388101i
\(430\) −0.294229 + 0.509619i −0.0141890 + 0.0245760i
\(431\) 0.679492 0.0327300 0.0163650 0.999866i \(-0.494791\pi\)
0.0163650 + 0.999866i \(0.494791\pi\)
\(432\) −10.0000 + 17.3205i −0.481125 + 0.833333i
\(433\) −6.79423 + 11.7679i −0.326510 + 0.565532i −0.981817 0.189831i \(-0.939206\pi\)
0.655307 + 0.755363i \(0.272539\pi\)
\(434\) 0 0
\(435\) 7.09808 12.2942i 0.340327 0.589463i
\(436\) −8.39230 −0.401919
\(437\) 4.73205 8.19615i 0.226365 0.392075i
\(438\) 7.56218 + 13.0981i 0.361335 + 0.625850i
\(439\) 7.29423 12.6340i 0.348135 0.602987i −0.637784 0.770216i \(-0.720149\pi\)
0.985918 + 0.167229i \(0.0534819\pi\)
\(440\) −1.90192 3.29423i −0.0906707 0.157046i
\(441\) 0 0
\(442\) −48.1865 3.10770i −2.29200 0.147818i
\(443\) −11.6603 20.1962i −0.553995 0.959548i −0.997981 0.0635142i \(-0.979769\pi\)
0.443986 0.896034i \(-0.353564\pi\)
\(444\) 19.1244 0.907602
\(445\) 22.3923 1.06150
\(446\) 17.3205 0.820150
\(447\) 17.6603 0.835301
\(448\) 0 0
\(449\) 6.00000 10.3923i 0.283158 0.490443i −0.689003 0.724758i \(-0.741951\pi\)
0.972161 + 0.234315i \(0.0752847\pi\)
\(450\) 7.73205 + 13.3923i 0.364492 + 0.631319i
\(451\) −3.29423 5.70577i −0.155119 0.268674i
\(452\) 13.3923 0.629921
\(453\) 2.73205 4.73205i 0.128363 0.222331i
\(454\) −9.80385 −0.460117
\(455\) 0 0
\(456\) −9.46410 −0.443197
\(457\) −5.50000 + 9.52628i −0.257279 + 0.445621i −0.965512 0.260358i \(-0.916159\pi\)
0.708233 + 0.705979i \(0.249493\pi\)
\(458\) 24.9282 1.16482
\(459\) 15.4641 + 26.7846i 0.721802 + 1.25020i
\(460\) 4.09808 + 7.09808i 0.191074 + 0.330950i
\(461\) −7.79423 + 13.5000i −0.363013 + 0.628758i −0.988455 0.151513i \(-0.951585\pi\)
0.625442 + 0.780271i \(0.284919\pi\)
\(462\) 0 0
\(463\) −4.58846 −0.213244 −0.106622 0.994300i \(-0.534003\pi\)
−0.106622 + 0.994300i \(0.534003\pi\)
\(464\) 15.0000 0.696358
\(465\) −19.8564 −0.920819
\(466\) −3.21539 −0.148950
\(467\) 12.7583 + 22.0981i 0.590385 + 1.02258i 0.994180 + 0.107728i \(0.0343575\pi\)
−0.403795 + 0.914849i \(0.632309\pi\)
\(468\) 7.13397 + 14.4282i 0.329768 + 0.666944i
\(469\) 0 0
\(470\) −19.3923 33.5885i −0.894500 1.54932i
\(471\) −1.63397 + 2.83013i −0.0752896 + 0.130405i
\(472\) −6.29423 10.9019i −0.289715 0.501802i
\(473\) 0.124356 0.215390i 0.00571788 0.00990366i
\(474\) −76.6410 −3.52024
\(475\) −2.00000 + 3.46410i −0.0917663 + 0.158944i
\(476\) 0 0
\(477\) 22.1603 38.3827i 1.01465 1.75742i
\(478\) 13.6865 23.7058i 0.626007 1.08428i
\(479\) −1.26795 −0.0579341 −0.0289670 0.999580i \(-0.509222\pi\)
−0.0289670 + 0.999580i \(0.509222\pi\)
\(480\) 12.2942 21.2942i 0.561152 0.971944i
\(481\) −14.0000 + 21.0000i −0.638345 + 0.957518i
\(482\) 36.7128 1.67222
\(483\) 0 0
\(484\) 4.69615 + 8.13397i 0.213461 + 0.369726i
\(485\) 11.0718 0.502744
\(486\) −16.2224 + 28.0981i −0.735864 + 1.27455i
\(487\) −20.3923 35.3205i −0.924064 1.60052i −0.793060 0.609143i \(-0.791514\pi\)
−0.131003 0.991382i \(-0.541820\pi\)
\(488\) −8.32051 −0.376652
\(489\) −44.2487 −2.00100
\(490\) 0 0
\(491\) −3.80385 6.58846i −0.171665 0.297333i 0.767337 0.641244i \(-0.221581\pi\)
−0.939002 + 0.343911i \(0.888248\pi\)
\(492\) 7.09808 12.2942i 0.320006 0.554267i
\(493\) 11.5981 20.0885i 0.522351 0.904739i
\(494\) −6.92820 + 10.3923i −0.311715 + 0.467572i
\(495\) 4.90192 + 8.49038i 0.220325 + 0.381614i
\(496\) −10.4904 18.1699i −0.471032 0.815851i
\(497\) 0 0
\(498\) 5.19615 9.00000i 0.232845 0.403300i
\(499\) 19.4904 + 33.7583i 0.872509 + 1.51123i 0.859393 + 0.511316i \(0.170842\pi\)
0.0131168 + 0.999914i \(0.495825\pi\)
\(500\) −6.06218 10.5000i −0.271109 0.469574i
\(501\) 9.00000 + 15.5885i 0.402090 + 0.696441i
\(502\) −1.39230 2.41154i −0.0621416 0.107632i
\(503\) −9.29423 + 16.0981i −0.414409 + 0.717778i −0.995366 0.0961565i \(-0.969345\pi\)
0.580957 + 0.813934i \(0.302678\pi\)
\(504\) 0 0
\(505\) 6.69615 + 11.5981i 0.297975 + 0.516108i
\(506\) −5.19615 9.00000i −0.230997 0.400099i
\(507\) −35.2224 4.56218i −1.56428 0.202613i
\(508\) −9.19615 + 15.9282i −0.408013 + 0.706700i
\(509\) 6.86603 11.8923i 0.304331 0.527117i −0.672781 0.739842i \(-0.734900\pi\)
0.977112 + 0.212725i \(0.0682337\pi\)
\(510\) −31.6865 54.8827i −1.40310 2.43025i
\(511\) 0 0
\(512\) 8.66025 0.382733
\(513\) 8.00000 0.353209
\(514\) 5.30385 + 9.18653i 0.233943 + 0.405201i
\(515\) 12.4641 21.5885i 0.549234 0.951301i
\(516\) 0.535898 0.0235916
\(517\) 8.19615 + 14.1962i 0.360466 + 0.624346i
\(518\) 0 0
\(519\) 23.3205 1.02366
\(520\) 4.79423 + 9.69615i 0.210241 + 0.425204i
\(521\) −12.0622 + 20.8923i −0.528454 + 0.915308i 0.470996 + 0.882135i \(0.343895\pi\)
−0.999450 + 0.0331732i \(0.989439\pi\)
\(522\) −23.1962 −1.01527
\(523\) −14.5885 + 25.2679i −0.637909 + 1.10489i 0.347982 + 0.937501i \(0.386867\pi\)
−0.985891 + 0.167389i \(0.946466\pi\)
\(524\) −1.73205 + 3.00000i −0.0756650 + 0.131056i
\(525\) 0 0
\(526\) −1.09808 + 1.90192i −0.0478784 + 0.0829278i
\(527\) −32.4449 −1.41332
\(528\) −8.66025 + 15.0000i −0.376889 + 0.652791i
\(529\) 0.303848 + 0.526279i 0.0132108 + 0.0228817i
\(530\) −14.8923 + 25.7942i −0.646880 + 1.12043i
\(531\) 16.2224 + 28.0981i 0.703994 + 1.21935i
\(532\) 0 0
\(533\) 8.30385 + 16.7942i 0.359680 + 0.727439i
\(534\) −30.5885 52.9808i −1.32369 2.29270i
\(535\) 13.6077 0.588312
\(536\) 10.7321 0.463554
\(537\) 18.9282 0.816812
\(538\) −8.78461 −0.378731
\(539\) 0 0
\(540\) −3.46410 + 6.00000i −0.149071 + 0.258199i
\(541\) 7.30385 + 12.6506i 0.314017 + 0.543893i 0.979228 0.202762i \(-0.0649918\pi\)
−0.665211 + 0.746655i \(0.731658\pi\)
\(542\) 5.02628 + 8.70577i 0.215897 + 0.373945i
\(543\) 15.2679 0.655210
\(544\) 20.0885 34.7942i 0.861285 1.49179i
\(545\) 14.5359 0.622649
\(546\) 0 0
\(547\) 17.8038 0.761238 0.380619 0.924732i \(-0.375711\pi\)
0.380619 + 0.924732i \(0.375711\pi\)
\(548\) −4.03590 + 6.99038i −0.172405 + 0.298614i
\(549\) 21.4449 0.915244
\(550\) 2.19615 + 3.80385i 0.0936443 + 0.162197i
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) −11.1962 + 19.3923i −0.476540 + 0.825391i
\(553\) 0 0
\(554\) 29.4449 1.25099
\(555\) −33.1244 −1.40605
\(556\) 10.5885 0.449051
\(557\) 43.6410 1.84913 0.924565 0.381025i \(-0.124429\pi\)
0.924565 + 0.381025i \(0.124429\pi\)
\(558\) 16.2224 + 28.0981i 0.686750 + 1.18949i
\(559\) −0.392305 + 0.588457i −0.0165927 + 0.0248891i
\(560\) 0 0
\(561\) 13.3923 + 23.1962i 0.565424 + 0.979342i
\(562\) −11.5981 + 20.0885i −0.489235 + 0.847380i
\(563\) 14.0263 + 24.2942i 0.591137 + 1.02388i 0.994080 + 0.108654i \(0.0346542\pi\)
−0.402942 + 0.915225i \(0.632013\pi\)
\(564\) −17.6603 + 30.5885i −0.743631 + 1.28801i
\(565\) −23.1962 −0.975869
\(566\) 8.83013 15.2942i 0.371158 0.642864i
\(567\) 0 0
\(568\) 5.19615 9.00000i 0.218026 0.377632i
\(569\) −21.4641 + 37.1769i −0.899822 + 1.55854i −0.0721010 + 0.997397i \(0.522970\pi\)
−0.827721 + 0.561140i \(0.810363\pi\)
\(570\) −16.3923 −0.686598
\(571\) −8.39230 + 14.5359i −0.351207 + 0.608308i −0.986461 0.163995i \(-0.947562\pi\)
0.635254 + 0.772303i \(0.280895\pi\)
\(572\) 2.02628 + 4.09808i 0.0847230 + 0.171349i
\(573\) −12.9282 −0.540083
\(574\) 0 0
\(575\) 4.73205 + 8.19615i 0.197340 + 0.341803i
\(576\) 4.46410 0.186004
\(577\) 21.5981 37.4090i 0.899140 1.55736i 0.0705436 0.997509i \(-0.477527\pi\)
0.828596 0.559847i \(-0.189140\pi\)
\(578\) −37.0526 64.1769i −1.54118 2.66941i
\(579\) −13.6603 −0.567701
\(580\) 5.19615 0.215758
\(581\) 0 0
\(582\) −15.1244 26.1962i −0.626925 1.08587i
\(583\) 6.29423 10.9019i 0.260680 0.451512i
\(584\) 2.76795 4.79423i 0.114539 0.198387i
\(585\) −12.3564 24.9904i −0.510875 1.03323i
\(586\) −0.696152 1.20577i −0.0287578 0.0498100i
\(587\) 8.19615 + 14.1962i 0.338291 + 0.585938i 0.984111 0.177552i \(-0.0568177\pi\)
−0.645820 + 0.763490i \(0.723484\pi\)
\(588\) 0 0
\(589\) −4.19615 + 7.26795i −0.172899 + 0.299471i
\(590\) −10.9019 18.8827i −0.448825 0.777388i
\(591\) 16.3923 + 28.3923i 0.674289 + 1.16790i
\(592\) −17.5000 30.3109i −0.719246 1.24577i
\(593\) −8.72243 15.1077i −0.358187 0.620399i 0.629471 0.777024i \(-0.283272\pi\)
−0.987658 + 0.156626i \(0.949938\pi\)
\(594\) 4.39230 7.60770i 0.180218 0.312148i
\(595\) 0 0
\(596\) 3.23205 + 5.59808i 0.132390 + 0.229306i
\(597\) −2.73205 4.73205i −0.111815 0.193670i
\(598\) 13.0981 + 26.4904i 0.535620 + 1.08327i
\(599\) −21.9282 + 37.9808i −0.895962 + 1.55185i −0.0633527 + 0.997991i \(0.520179\pi\)
−0.832609 + 0.553861i \(0.813154\pi\)
\(600\) 4.73205 8.19615i 0.193185 0.334607i
\(601\) −14.9904 25.9641i −0.611470 1.05910i −0.990993 0.133915i \(-0.957245\pi\)
0.379522 0.925183i \(-0.376088\pi\)
\(602\) 0 0
\(603\) −27.6603 −1.12641
\(604\) 2.00000 0.0813788
\(605\) −8.13397 14.0885i −0.330693 0.572777i
\(606\) 18.2942 31.6865i 0.743152 1.28718i
\(607\) 14.3923 0.584166 0.292083 0.956393i \(-0.405652\pi\)
0.292083 + 0.956393i \(0.405652\pi\)
\(608\) −5.19615 9.00000i −0.210732 0.364998i
\(609\) 0 0
\(610\) −14.4115 −0.583506
\(611\) −20.6603 41.7846i −0.835824 1.69042i
\(612\) −17.2583 + 29.8923i −0.697627 + 1.20832i
\(613\) 3.39230 0.137014 0.0685070 0.997651i \(-0.478176\pi\)
0.0685070 + 0.997651i \(0.478176\pi\)
\(614\) −3.97372 + 6.88269i −0.160366 + 0.277763i
\(615\) −12.2942 + 21.2942i −0.495751 + 0.858666i
\(616\) 0 0
\(617\) −24.6962 + 42.7750i −0.994230 + 1.72206i −0.404214 + 0.914664i \(0.632455\pi\)
−0.590016 + 0.807392i \(0.700878\pi\)
\(618\) −68.1051 −2.73959
\(619\) 17.6865 30.6340i 0.710882 1.23128i −0.253645 0.967297i \(-0.581629\pi\)
0.964527 0.263986i \(-0.0850373\pi\)
\(620\) −3.63397 6.29423i −0.145944 0.252782i
\(621\) 9.46410 16.3923i 0.379781 0.657801i
\(622\) 1.09808 + 1.90192i 0.0440288 + 0.0762602i
\(623\) 0 0
\(624\) 27.3205 40.9808i 1.09370 1.64054i
\(625\) 5.50000 + 9.52628i 0.220000 + 0.381051i
\(626\) −49.8564 −1.99266
\(627\) 6.92820 0.276686
\(628\) −1.19615 −0.0477317
\(629\) −54.1244 −2.15808
\(630\) 0 0
\(631\) 6.39230 11.0718i 0.254474 0.440761i −0.710279 0.703920i \(-0.751431\pi\)
0.964752 + 0.263159i \(0.0847645\pi\)
\(632\) 14.0263 + 24.2942i 0.557935 + 0.966373i
\(633\) −2.46410 4.26795i −0.0979392 0.169636i
\(634\) −11.1962 −0.444656
\(635\) 15.9282 27.5885i 0.632091 1.09481i
\(636\) 27.1244 1.07555
\(637\) 0 0
\(638\) −6.58846 −0.260840
\(639\) −13.3923 + 23.1962i −0.529791 + 0.917626i
\(640\) −21.0000 −0.830098
\(641\) −14.4282 24.9904i −0.569880 0.987061i −0.996577 0.0826663i \(-0.973656\pi\)
0.426698 0.904394i \(-0.359677\pi\)
\(642\) −18.5885 32.1962i −0.733628 1.27068i
\(643\) −0.392305 + 0.679492i −0.0154710 + 0.0267965i −0.873657 0.486542i \(-0.838258\pi\)
0.858186 + 0.513338i \(0.171591\pi\)
\(644\) 0 0
\(645\) −0.928203 −0.0365480
\(646\) −26.7846 −1.05383
\(647\) −45.0333 −1.77044 −0.885221 0.465170i \(-0.845993\pi\)
−0.885221 + 0.465170i \(0.845993\pi\)
\(648\) 4.26795 0.167661
\(649\) 4.60770 + 7.98076i 0.180868 + 0.313272i
\(650\) −5.53590 11.1962i −0.217136 0.439149i
\(651\) 0 0
\(652\) −8.09808 14.0263i −0.317145 0.549311i
\(653\) 18.9282 32.7846i 0.740718 1.28296i −0.211451 0.977389i \(-0.567819\pi\)
0.952169 0.305572i \(-0.0988478\pi\)
\(654\) −19.8564 34.3923i −0.776447 1.34485i
\(655\) 3.00000 5.19615i 0.117220 0.203030i
\(656\) −25.9808 −1.01438
\(657\) −7.13397 + 12.3564i −0.278323 + 0.482069i
\(658\) 0 0
\(659\) −14.1962 + 24.5885i −0.553004 + 0.957830i 0.445052 + 0.895505i \(0.353185\pi\)
−0.998056 + 0.0623257i \(0.980148\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) 33.1962 1.29118 0.645590 0.763684i \(-0.276611\pi\)
0.645590 + 0.763684i \(0.276611\pi\)
\(662\) −21.6340 + 37.4711i −0.840828 + 1.45636i
\(663\) −33.7583 68.2750i −1.31106 2.65158i
\(664\) −3.80385 −0.147618
\(665\) 0 0
\(666\) 27.0622 + 46.8731i 1.04864 + 1.81629i
\(667\) −14.1962 −0.549677
\(668\) −3.29423 + 5.70577i −0.127458 + 0.220763i
\(669\) 13.6603 + 23.6603i 0.528136 + 0.914758i
\(670\) 18.5885 0.718135
\(671\) 6.09103 0.235142
\(672\) 0 0
\(673\) 22.0885 + 38.2583i 0.851447 + 1.47475i 0.879902 + 0.475155i \(0.157608\pi\)
−0.0284546 + 0.999595i \(0.509059\pi\)
\(674\) −9.52628 + 16.5000i −0.366939 + 0.635556i
\(675\) −4.00000 + 6.92820i −0.153960 + 0.266667i
\(676\) −5.00000 12.0000i −0.192308 0.461538i
\(677\) −11.5359 19.9808i −0.443361 0.767923i 0.554576 0.832133i \(-0.312881\pi\)
−0.997936 + 0.0642101i \(0.979547\pi\)
\(678\) 31.6865 + 54.8827i 1.21691 + 2.10776i
\(679\) 0 0
\(680\) −11.5981 + 20.0885i −0.444766 + 0.770357i
\(681\) −7.73205 13.3923i −0.296293 0.513194i
\(682\) 4.60770 + 7.98076i 0.176438 + 0.305599i
\(683\) −7.73205 13.3923i −0.295859 0.512442i 0.679326 0.733837i \(-0.262272\pi\)
−0.975184 + 0.221395i \(0.928939\pi\)
\(684\) 4.46410 + 7.73205i 0.170689 + 0.295642i
\(685\) 6.99038 12.1077i 0.267089 0.462611i
\(686\) 0 0
\(687\) 19.6603 + 34.0526i 0.750085 + 1.29919i
\(688\) −0.490381 0.849365i −0.0186956 0.0323817i
\(689\) −19.8564 + 29.7846i −0.756469 + 1.13470i
\(690\) −19.3923 + 33.5885i −0.738252 + 1.27869i
\(691\) 0.196152 0.339746i 0.00746199 0.0129245i −0.862270 0.506448i \(-0.830958\pi\)
0.869732 + 0.493524i \(0.164291\pi\)
\(692\) 4.26795 + 7.39230i 0.162243 + 0.281013i
\(693\) 0 0
\(694\) 12.5885 0.477851
\(695\) −18.3397 −0.695666
\(696\) 7.09808 + 12.2942i 0.269052 + 0.466012i
\(697\) −20.0885 + 34.7942i −0.760905 + 1.31793i
\(698\) 42.9282 1.62486
\(699\) −2.53590 4.39230i −0.0959165 0.166132i
\(700\) 0 0
\(701\) 20.7846 0.785024 0.392512 0.919747i \(-0.371606\pi\)
0.392512 + 0.919747i \(0.371606\pi\)
\(702\) −13.8564 + 20.7846i −0.522976 + 0.784465i
\(703\) −7.00000 + 12.1244i −0.264010 + 0.457279i
\(704\) 1.26795 0.0477876
\(705\) 30.5885 52.9808i 1.15203 1.99537i
\(706\) 17.8923 30.9904i 0.673386 1.16634i
\(707\) 0 0
\(708\) −9.92820 + 17.1962i −0.373125 + 0.646271i
\(709\) 30.1769 1.13332 0.566659 0.823952i \(-0.308236\pi\)
0.566659 + 0.823952i \(0.308236\pi\)
\(710\) 9.00000 15.5885i 0.337764 0.585024i
\(711\) −36.1506 62.6147i −1.35575 2.34824i
\(712\) −11.1962 + 19.3923i −0.419594 + 0.726757i
\(713\) 9.92820 + 17.1962i 0.371814 + 0.644001i
\(714\) 0 0
\(715\) −3.50962 7.09808i −0.131252 0.265453i
\(716\) 3.46410 + 6.00000i 0.129460 + 0.224231i
\(717\) 43.1769 1.61247
\(718\) 32.7846 1.22351
\(719\) 7.26795 0.271049 0.135524 0.990774i \(-0.456728\pi\)
0.135524 + 0.990774i \(0.456728\pi\)
\(720\) 38.6603 1.44078
\(721\) 0 0
\(722\) 12.9904 22.5000i 0.483452 0.837363i
\(723\) 28.9545 + 50.1506i 1.07683 + 1.86512i
\(724\) 2.79423 + 4.83975i 0.103847 + 0.179868i
\(725\) 6.00000 0.222834
\(726\) −22.2224 + 38.4904i −0.824752 + 1.42851i
\(727\) 41.1769 1.52717 0.763584 0.645709i \(-0.223438\pi\)
0.763584 + 0.645709i \(0.223438\pi\)
\(728\) 0 0
\(729\) −43.7846 −1.62165
\(730\) 4.79423 8.30385i 0.177442 0.307339i
\(731\) −1.51666 −0.0560957
\(732\) 6.56218 + 11.3660i 0.242545 + 0.420100i
\(733\) 11.7942 + 20.4282i 0.435630 + 0.754533i 0.997347 0.0727965i \(-0.0231924\pi\)
−0.561717 + 0.827329i \(0.689859\pi\)
\(734\) 3.63397 6.29423i 0.134132 0.232324i
\(735\) 0 0
\(736\) −24.5885 −0.906343
\(737\) −7.85641 −0.289394
\(738\) 40.1769 1.47893
\(739\) 40.7846 1.50029 0.750143 0.661276i \(-0.229985\pi\)
0.750143 + 0.661276i \(0.229985\pi\)
\(740\) −6.06218 10.5000i −0.222850 0.385988i
\(741\) −19.6603 1.26795i −0.722237 0.0465793i
\(742\) 0 0
\(743\) 3.80385 + 6.58846i 0.139550 + 0.241707i 0.927326 0.374254i \(-0.122101\pi\)
−0.787777 + 0.615961i \(0.788768\pi\)
\(744\) 9.92820 17.1962i 0.363986 0.630442i
\(745\) −5.59808 9.69615i −0.205098 0.355240i
\(746\) 9.86603 17.0885i 0.361221 0.625653i
\(747\) 9.80385 0.358704
\(748\) −4.90192 + 8.49038i −0.179232 + 0.310439i
\(749\) 0 0
\(750\) 28.6865 49.6865i 1.04748 1.81430i
\(751\) −17.9019 + 31.0070i −0.653250 + 1.13146i 0.329079 + 0.944302i \(0.393262\pi\)
−0.982329 + 0.187161i \(0.940072\pi\)
\(752\) 64.6410 2.35722
\(753\) 2.19615 3.80385i 0.0800322 0.138620i
\(754\) 18.6962 + 1.20577i 0.680874 + 0.0439116i
\(755\) −3.46410 −0.126072
\(756\) 0 0
\(757\) 8.00000 + 13.8564i 0.290765 + 0.503620i 0.973991 0.226587i \(-0.0727569\pi\)
−0.683226 + 0.730207i \(0.739424\pi\)
\(758\) 46.0526 1.67270
\(759\) 8.19615 14.1962i 0.297501 0.515288i
\(760\) 3.00000 + 5.19615i 0.108821 + 0.188484i
\(761\) −41.3205 −1.49787 −0.748934 0.662645i \(-0.769434\pi\)
−0.748934 + 0.662645i \(0.769434\pi\)
\(762\) −87.0333 −3.15288
\(763\) 0 0
\(764\) −2.36603 4.09808i −0.0855998 0.148263i
\(765\) 29.8923 51.7750i 1.08076 1.87193i
\(766\) −10.0981 + 17.4904i −0.364858 + 0.631953i
\(767\) −11.6147 23.4904i −0.419384 0.848189i
\(768\) 25.9545 + 44.9545i 0.936552 + 1.62216i
\(769\) 7.58846 + 13.1436i 0.273647 + 0.473970i 0.969793 0.243930i \(-0.0784367\pi\)
−0.696146 + 0.717900i \(0.745103\pi\)
\(770\) 0 0
\(771\) −8.36603 + 14.4904i −0.301295 + 0.521858i
\(772\) −2.50000 4.33013i −0.0899770 0.155845i
\(773\) −6.46410 11.1962i −0.232498 0.402698i 0.726045 0.687647i \(-0.241356\pi\)
−0.958542 + 0.284950i \(0.908023\pi\)
\(774\) 0.758330 + 1.31347i 0.0272576 + 0.0472116i
\(775\) −4.19615 7.26795i −0.150730 0.261072i
\(776\) −5.53590 + 9.58846i −0.198727 + 0.344206i
\(777\) 0 0
\(778\) 20.3827 + 35.3038i 0.730755 + 1.26570i
\(779\) 5.19615 + 9.00000i 0.186171 + 0.322458i
\(780\) 9.46410 14.1962i