Properties

Label 637.2.f.l.295.5
Level $637$
Weight $2$
Character 637.295
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 8 x^{14} + 45 x^{12} + 124 x^{10} + 248 x^{8} + 250 x^{6} + 177 x^{4} + 14 x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.5
Root \(-0.141226 - 0.244611i\) of defining polynomial
Character \(\chi\) \(=\) 637.295
Dual form 637.2.f.l.393.5

$q$-expansion

\(f(q)\) \(=\) \(q+(0.760387 - 1.31703i) q^{2} +(-1.06311 + 1.84135i) q^{3} +(-0.156376 - 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 - 1.31703i) q^{9} +O(q^{10})\) \(q+(0.760387 - 1.31703i) q^{2} +(-1.06311 + 1.84135i) q^{3} +(-0.156376 - 0.270851i) q^{4} -0.589391 q^{5} +(1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 - 1.31703i) q^{9} +(-0.448165 + 0.776245i) q^{10} +(-0.760387 + 1.31703i) q^{11} +0.664976 q^{12} +(-3.32565 + 1.39285i) q^{13} +(0.626585 - 1.08528i) q^{15} +(2.26384 - 3.92109i) q^{16} +(2.39740 + 4.15241i) q^{17} -2.31275 q^{18} +(0.841957 + 1.45831i) q^{19} +(0.0921666 + 0.159637i) q^{20} +(1.15638 + 2.00290i) q^{22} +(-0.886972 + 1.53628i) q^{23} +(-2.72785 + 4.72477i) q^{24} -4.65262 q^{25} +(-0.694354 + 5.43908i) q^{26} -3.14515 q^{27} +(-3.44625 + 5.96909i) q^{29} +(-0.952894 - 1.65046i) q^{30} +6.08640 q^{31} +(-0.876873 - 1.51879i) q^{32} +(-1.61674 - 2.80028i) q^{33} +7.29179 q^{34} +(-0.237812 + 0.411903i) q^{36} +(-0.704563 + 1.22034i) q^{37} +2.56085 q^{38} +(0.970785 - 7.60445i) q^{39} -1.51233 q^{40} +(0.677729 - 1.17386i) q^{41} +(5.77978 + 10.0109i) q^{43} +0.475625 q^{44} +(0.448165 + 0.776245i) q^{45} +(1.34888 + 2.33633i) q^{46} +0.464832 q^{47} +(4.81341 + 8.33707i) q^{48} +(-3.53779 + 6.12763i) q^{50} -10.1947 q^{51} +(0.897307 + 0.682948i) q^{52} +8.24681 q^{53} +(-2.39153 + 4.14225i) q^{54} +(0.448165 - 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 + 9.07763i) q^{58} +(-5.93782 - 10.2846i) q^{59} -0.391931 q^{60} +(1.24009 + 2.14789i) q^{61} +(4.62802 - 8.01596i) q^{62} +6.38833 q^{64} +(1.96011 - 0.820936i) q^{65} -4.91740 q^{66} +(3.78642 - 6.55827i) q^{67} +(0.749790 - 1.29867i) q^{68} +(-1.88589 - 3.26646i) q^{69} +(-3.30235 - 5.71984i) q^{71} +(-1.95109 - 3.37939i) q^{72} +16.3712 q^{73} +(1.07148 + 1.85586i) q^{74} +(4.94622 - 8.56711i) q^{75} +(0.263323 - 0.456090i) q^{76} +(-9.27710 - 7.06087i) q^{78} -14.9623 q^{79} +(-1.33429 + 2.31106i) q^{80} +(5.62478 - 9.74241i) q^{81} +(-1.03067 - 1.78518i) q^{82} -10.1222 q^{83} +(-1.41300 - 2.44740i) q^{85} +17.5795 q^{86} +(-7.32746 - 12.6915i) q^{87} +(-1.95109 + 3.37939i) q^{88} +(8.24250 - 14.2764i) q^{89} +1.36312 q^{90} +0.554804 q^{92} +(-6.47049 + 11.2072i) q^{93} +(0.353452 - 0.612196i) q^{94} +(-0.496242 - 0.859516i) q^{95} +3.72883 q^{96} +(-0.486935 - 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} + O(q^{10}) \) \( 16 q + 4 q^{2} - 12 q^{4} + 24 q^{8} - 4 q^{9} - 4 q^{11} - 8 q^{15} - 4 q^{16} - 56 q^{18} + 28 q^{22} + 12 q^{23} - 24 q^{25} + 8 q^{29} + 28 q^{30} + 4 q^{36} - 8 q^{37} - 4 q^{39} + 32 q^{43} - 8 q^{44} - 4 q^{46} + 36 q^{50} - 88 q^{51} - 8 q^{53} - 96 q^{57} - 48 q^{58} + 128 q^{60} - 64 q^{64} + 16 q^{65} + 20 q^{67} + 8 q^{71} + 28 q^{72} + 76 q^{74} + 28 q^{78} - 8 q^{79} + 56 q^{81} + 36 q^{85} + 8 q^{86} + 28 q^{88} - 160 q^{92} + 8 q^{93} + 52 q^{95} + 56 q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.760387 1.31703i 0.537675 0.931280i −0.461354 0.887216i \(-0.652636\pi\)
0.999029 0.0440636i \(-0.0140304\pi\)
\(3\) −1.06311 + 1.84135i −0.613784 + 1.06311i 0.376812 + 0.926290i \(0.377020\pi\)
−0.990596 + 0.136816i \(0.956313\pi\)
\(4\) −0.156376 0.270851i −0.0781880 0.135426i
\(5\) −0.589391 −0.263584 −0.131792 0.991277i \(-0.542073\pi\)
−0.131792 + 0.991277i \(0.542073\pi\)
\(6\) 1.61674 + 2.80028i 0.660032 + 1.14321i
\(7\) 0 0
\(8\) 2.56592 0.907190
\(9\) −0.760387 1.31703i −0.253462 0.439009i
\(10\) −0.448165 + 0.776245i −0.141722 + 0.245470i
\(11\) −0.760387 + 1.31703i −0.229265 + 0.397099i −0.957591 0.288132i \(-0.906966\pi\)
0.728325 + 0.685232i \(0.240299\pi\)
\(12\) 0.664976 0.191962
\(13\) −3.32565 + 1.39285i −0.922370 + 0.386308i
\(14\) 0 0
\(15\) 0.626585 1.08528i 0.161784 0.280217i
\(16\) 2.26384 3.92109i 0.565961 0.980274i
\(17\) 2.39740 + 4.15241i 0.581454 + 1.00711i 0.995307 + 0.0967643i \(0.0308493\pi\)
−0.413853 + 0.910344i \(0.635817\pi\)
\(18\) −2.31275 −0.545121
\(19\) 0.841957 + 1.45831i 0.193158 + 0.334560i 0.946295 0.323304i \(-0.104794\pi\)
−0.753137 + 0.657864i \(0.771460\pi\)
\(20\) 0.0921666 + 0.159637i 0.0206091 + 0.0356960i
\(21\) 0 0
\(22\) 1.15638 + 2.00290i 0.246540 + 0.427020i
\(23\) −0.886972 + 1.53628i −0.184946 + 0.320337i −0.943558 0.331206i \(-0.892544\pi\)
0.758612 + 0.651543i \(0.225878\pi\)
\(24\) −2.72785 + 4.72477i −0.556819 + 0.964439i
\(25\) −4.65262 −0.930524
\(26\) −0.694354 + 5.43908i −0.136174 + 1.06669i
\(27\) −3.14515 −0.605284
\(28\) 0 0
\(29\) −3.44625 + 5.96909i −0.639953 + 1.10843i 0.345489 + 0.938423i \(0.387713\pi\)
−0.985443 + 0.170009i \(0.945620\pi\)
\(30\) −0.952894 1.65046i −0.173974 0.301332i
\(31\) 6.08640 1.09315 0.546575 0.837410i \(-0.315931\pi\)
0.546575 + 0.837410i \(0.315931\pi\)
\(32\) −0.876873 1.51879i −0.155011 0.268486i
\(33\) −1.61674 2.80028i −0.281439 0.487466i
\(34\) 7.29179 1.25053
\(35\) 0 0
\(36\) −0.237812 + 0.411903i −0.0396354 + 0.0686505i
\(37\) −0.704563 + 1.22034i −0.115830 + 0.200623i −0.918111 0.396323i \(-0.870286\pi\)
0.802282 + 0.596946i \(0.203619\pi\)
\(38\) 2.56085 0.415425
\(39\) 0.970785 7.60445i 0.155450 1.21769i
\(40\) −1.51233 −0.239121
\(41\) 0.677729 1.17386i 0.105843 0.183326i −0.808239 0.588855i \(-0.799579\pi\)
0.914082 + 0.405528i \(0.132912\pi\)
\(42\) 0 0
\(43\) 5.77978 + 10.0109i 0.881408 + 1.52664i 0.849776 + 0.527144i \(0.176737\pi\)
0.0316319 + 0.999500i \(0.489930\pi\)
\(44\) 0.475625 0.0717031
\(45\) 0.448165 + 0.776245i 0.0668085 + 0.115716i
\(46\) 1.34888 + 2.33633i 0.198882 + 0.344474i
\(47\) 0.464832 0.0678027 0.0339013 0.999425i \(-0.489207\pi\)
0.0339013 + 0.999425i \(0.489207\pi\)
\(48\) 4.81341 + 8.33707i 0.694756 + 1.20335i
\(49\) 0 0
\(50\) −3.53779 + 6.12763i −0.500319 + 0.866578i
\(51\) −10.1947 −1.42755
\(52\) 0.897307 + 0.682948i 0.124434 + 0.0947078i
\(53\) 8.24681 1.13279 0.566393 0.824135i \(-0.308338\pi\)
0.566393 + 0.824135i \(0.308338\pi\)
\(54\) −2.39153 + 4.14225i −0.325446 + 0.563689i
\(55\) 0.448165 0.776245i 0.0604306 0.104669i
\(56\) 0 0
\(57\) −3.58035 −0.474230
\(58\) 5.24097 + 9.07763i 0.688173 + 1.19195i
\(59\) −5.93782 10.2846i −0.773038 1.33894i −0.935890 0.352291i \(-0.885403\pi\)
0.162852 0.986651i \(-0.447931\pi\)
\(60\) −0.391931 −0.0505981
\(61\) 1.24009 + 2.14789i 0.158777 + 0.275009i 0.934428 0.356153i \(-0.115912\pi\)
−0.775651 + 0.631162i \(0.782578\pi\)
\(62\) 4.62802 8.01596i 0.587759 1.01803i
\(63\) 0 0
\(64\) 6.38833 0.798541
\(65\) 1.96011 0.820936i 0.243122 0.101825i
\(66\) −4.91740 −0.605290
\(67\) 3.78642 6.55827i 0.462585 0.801220i −0.536504 0.843898i \(-0.680255\pi\)
0.999089 + 0.0426774i \(0.0135888\pi\)
\(68\) 0.749790 1.29867i 0.0909254 0.157487i
\(69\) −1.88589 3.26646i −0.227034 0.393235i
\(70\) 0 0
\(71\) −3.30235 5.71984i −0.391917 0.678821i 0.600785 0.799411i \(-0.294855\pi\)
−0.992702 + 0.120590i \(0.961521\pi\)
\(72\) −1.95109 3.37939i −0.229939 0.398265i
\(73\) 16.3712 1.91610 0.958049 0.286604i \(-0.0925263\pi\)
0.958049 + 0.286604i \(0.0925263\pi\)
\(74\) 1.07148 + 1.85586i 0.124557 + 0.215739i
\(75\) 4.94622 8.56711i 0.571141 0.989245i
\(76\) 0.263323 0.456090i 0.0302053 0.0523171i
\(77\) 0 0
\(78\) −9.27710 7.06087i −1.05042 0.799486i
\(79\) −14.9623 −1.68339 −0.841696 0.539951i \(-0.818443\pi\)
−0.841696 + 0.539951i \(0.818443\pi\)
\(80\) −1.33429 + 2.31106i −0.149178 + 0.258384i
\(81\) 5.62478 9.74241i 0.624976 1.08249i
\(82\) −1.03067 1.78518i −0.113819 0.197140i
\(83\) −10.1222 −1.11105 −0.555526 0.831499i \(-0.687483\pi\)
−0.555526 + 0.831499i \(0.687483\pi\)
\(84\) 0 0
\(85\) −1.41300 2.44740i −0.153262 0.265457i
\(86\) 17.5795 1.89564
\(87\) −7.32746 12.6915i −0.785586 1.36068i
\(88\) −1.95109 + 3.37939i −0.207987 + 0.360244i
\(89\) 8.24250 14.2764i 0.873703 1.51330i 0.0155650 0.999879i \(-0.495045\pi\)
0.858138 0.513419i \(-0.171621\pi\)
\(90\) 1.36312 0.143685
\(91\) 0 0
\(92\) 0.554804 0.0578423
\(93\) −6.47049 + 11.2072i −0.670958 + 1.16213i
\(94\) 0.353452 0.612196i 0.0364558 0.0631432i
\(95\) −0.496242 0.859516i −0.0509133 0.0881845i
\(96\) 3.72883 0.380573
\(97\) −0.486935 0.843396i −0.0494407 0.0856338i 0.840246 0.542205i \(-0.182411\pi\)
−0.889687 + 0.456572i \(0.849077\pi\)
\(98\) 0 0
\(99\) 2.31275 0.232440
\(100\) 0.727557 + 1.26017i 0.0727557 + 0.126017i
\(101\) −1.47012 + 2.54632i −0.146282 + 0.253368i −0.929851 0.367937i \(-0.880064\pi\)
0.783568 + 0.621305i \(0.213397\pi\)
\(102\) −7.75195 + 13.4268i −0.767557 + 1.32945i
\(103\) −0.528682 −0.0520926 −0.0260463 0.999661i \(-0.508292\pi\)
−0.0260463 + 0.999661i \(0.508292\pi\)
\(104\) −8.53336 + 3.57395i −0.836765 + 0.350455i
\(105\) 0 0
\(106\) 6.27076 10.8613i 0.609070 1.05494i
\(107\) 9.66119 16.7337i 0.933983 1.61771i 0.157545 0.987512i \(-0.449642\pi\)
0.776438 0.630194i \(-0.217024\pi\)
\(108\) 0.491825 + 0.851866i 0.0473259 + 0.0819709i
\(109\) −5.73240 −0.549064 −0.274532 0.961578i \(-0.588523\pi\)
−0.274532 + 0.961578i \(0.588523\pi\)
\(110\) −0.681558 1.18049i −0.0649840 0.112556i
\(111\) −1.49805 2.59470i −0.142189 0.246278i
\(112\) 0 0
\(113\) −2.57480 4.45968i −0.242216 0.419531i 0.719129 0.694877i \(-0.244541\pi\)
−0.961345 + 0.275346i \(0.911208\pi\)
\(114\) −2.72245 + 4.71543i −0.254981 + 0.441640i
\(115\) 0.522774 0.905470i 0.0487489 0.0844355i
\(116\) 2.15564 0.200147
\(117\) 4.36321 + 3.32087i 0.403379 + 0.307015i
\(118\) −18.0602 −1.66257
\(119\) 0 0
\(120\) 1.60777 2.78474i 0.146769 0.254211i
\(121\) 4.34362 + 7.52338i 0.394875 + 0.683943i
\(122\) 3.77178 0.341481
\(123\) 1.44099 + 2.49588i 0.129930 + 0.225045i
\(124\) −0.951766 1.64851i −0.0854711 0.148040i
\(125\) 5.68917 0.508855
\(126\) 0 0
\(127\) 4.50166 7.79710i 0.399457 0.691881i −0.594202 0.804316i \(-0.702532\pi\)
0.993659 + 0.112436i \(0.0358652\pi\)
\(128\) 6.61135 11.4512i 0.584366 1.01215i
\(129\) −24.5781 −2.16398
\(130\) 0.409246 3.20575i 0.0358933 0.281163i
\(131\) −6.79840 −0.593979 −0.296989 0.954881i \(-0.595983\pi\)
−0.296989 + 0.954881i \(0.595983\pi\)
\(132\) −0.505639 + 0.875793i −0.0440102 + 0.0762280i
\(133\) 0 0
\(134\) −5.75829 9.97364i −0.497440 0.861592i
\(135\) 1.85372 0.159543
\(136\) 6.15153 + 10.6548i 0.527490 + 0.913639i
\(137\) 7.03779 + 12.1898i 0.601279 + 1.04145i 0.992628 + 0.121203i \(0.0386753\pi\)
−0.391349 + 0.920242i \(0.627991\pi\)
\(138\) −5.73602 −0.488283
\(139\) 8.64313 + 14.9703i 0.733101 + 1.26977i 0.955552 + 0.294824i \(0.0952611\pi\)
−0.222451 + 0.974944i \(0.571406\pi\)
\(140\) 0 0
\(141\) −0.494165 + 0.855919i −0.0416162 + 0.0720814i
\(142\) −10.0443 −0.842896
\(143\) 0.694354 5.43908i 0.0580648 0.454839i
\(144\) −6.88559 −0.573799
\(145\) 2.03119 3.51813i 0.168681 0.292165i
\(146\) 12.4484 21.5613i 1.03024 1.78442i
\(147\) 0 0
\(148\) 0.440707 0.0362259
\(149\) 8.56260 + 14.8309i 0.701475 + 1.21499i 0.967949 + 0.251148i \(0.0808082\pi\)
−0.266473 + 0.963842i \(0.585858\pi\)
\(150\) −7.52209 13.0286i −0.614176 1.06378i
\(151\) 15.7975 1.28558 0.642789 0.766043i \(-0.277777\pi\)
0.642789 + 0.766043i \(0.277777\pi\)
\(152\) 2.16040 + 3.74191i 0.175231 + 0.303509i
\(153\) 3.64590 6.31488i 0.294753 0.510528i
\(154\) 0 0
\(155\) −3.58727 −0.288137
\(156\) −2.21148 + 0.926214i −0.177060 + 0.0741565i
\(157\) 3.78351 0.301957 0.150979 0.988537i \(-0.451758\pi\)
0.150979 + 0.988537i \(0.451758\pi\)
\(158\) −11.3771 + 19.7058i −0.905117 + 1.56771i
\(159\) −8.76722 + 15.1853i −0.695286 + 1.20427i
\(160\) 0.516821 + 0.895161i 0.0408583 + 0.0707687i
\(161\) 0 0
\(162\) −8.55402 14.8160i −0.672067 1.16406i
\(163\) −0.857757 1.48568i −0.0671847 0.116367i 0.830476 0.557054i \(-0.188068\pi\)
−0.897661 + 0.440687i \(0.854735\pi\)
\(164\) −0.423922 −0.0331027
\(165\) 0.952894 + 1.65046i 0.0741827 + 0.128488i
\(166\) −7.69677 + 13.3312i −0.597385 + 1.03470i
\(167\) 6.32605 10.9570i 0.489524 0.847881i −0.510403 0.859935i \(-0.670504\pi\)
0.999927 + 0.0120542i \(0.00383706\pi\)
\(168\) 0 0
\(169\) 9.11992 9.26429i 0.701532 0.712638i
\(170\) −4.29772 −0.329620
\(171\) 1.28043 2.21776i 0.0979166 0.169596i
\(172\) 1.80764 3.13092i 0.137831 0.238730i
\(173\) −5.74371 9.94839i −0.436686 0.756362i 0.560746 0.827988i \(-0.310515\pi\)
−0.997432 + 0.0716259i \(0.977181\pi\)
\(174\) −22.2868 −1.68956
\(175\) 0 0
\(176\) 3.44280 + 5.96310i 0.259510 + 0.449485i
\(177\) 25.2501 1.89792
\(178\) −12.5350 21.7112i −0.939536 1.62732i
\(179\) 1.09225 1.89184i 0.0816389 0.141403i −0.822315 0.569032i \(-0.807318\pi\)
0.903954 + 0.427630i \(0.140651\pi\)
\(180\) 0.140165 0.242772i 0.0104472 0.0180952i
\(181\) 11.5981 0.862081 0.431041 0.902333i \(-0.358147\pi\)
0.431041 + 0.902333i \(0.358147\pi\)
\(182\) 0 0
\(183\) −5.27337 −0.389819
\(184\) −2.27590 + 3.94198i −0.167782 + 0.290606i
\(185\) 0.415264 0.719258i 0.0305308 0.0528809i
\(186\) 9.84014 + 17.0436i 0.721514 + 1.24970i
\(187\) −7.29179 −0.533229
\(188\) −0.0726885 0.125900i −0.00530135 0.00918221i
\(189\) 0 0
\(190\) −1.50934 −0.109499
\(191\) −8.87961 15.3799i −0.642506 1.11285i −0.984871 0.173286i \(-0.944561\pi\)
0.342365 0.939567i \(-0.388772\pi\)
\(192\) −6.79147 + 11.7632i −0.490132 + 0.848934i
\(193\) −11.3189 + 19.6050i −0.814756 + 1.41120i 0.0947474 + 0.995501i \(0.469796\pi\)
−0.909503 + 0.415697i \(0.863538\pi\)
\(194\) −1.48103 −0.106332
\(195\) −0.572172 + 4.48200i −0.0409741 + 0.320962i
\(196\) 0 0
\(197\) −10.0032 + 17.3260i −0.712696 + 1.23442i 0.251146 + 0.967949i \(0.419193\pi\)
−0.963842 + 0.266476i \(0.914141\pi\)
\(198\) 1.75859 3.04596i 0.124977 0.216467i
\(199\) −0.924426 1.60115i −0.0655309 0.113503i 0.831398 0.555677i \(-0.187541\pi\)
−0.896929 + 0.442174i \(0.854207\pi\)
\(200\) −11.9383 −0.844162
\(201\) 8.05073 + 13.9443i 0.567854 + 0.983553i
\(202\) 2.23572 + 3.87237i 0.157304 + 0.272459i
\(203\) 0 0
\(204\) 1.59421 + 2.76126i 0.111617 + 0.193327i
\(205\) −0.399447 + 0.691863i −0.0278986 + 0.0483218i
\(206\) −0.402003 + 0.696289i −0.0280088 + 0.0485127i
\(207\) 2.69777 0.187508
\(208\) −2.06725 + 16.1934i −0.143338 + 1.12281i
\(209\) −2.56085 −0.177138
\(210\) 0 0
\(211\) 8.08474 14.0032i 0.556576 0.964019i −0.441203 0.897407i \(-0.645448\pi\)
0.997779 0.0666110i \(-0.0212187\pi\)
\(212\) −1.28960 2.23366i −0.0885702 0.153408i
\(213\) 14.0430 0.962210
\(214\) −14.6925 25.4481i −1.00436 1.73960i
\(215\) −3.40655 5.90032i −0.232325 0.402399i
\(216\) −8.07020 −0.549108
\(217\) 0 0
\(218\) −4.35884 + 7.54973i −0.295218 + 0.511332i
\(219\) −17.4043 + 30.1451i −1.17607 + 2.03701i
\(220\) −0.280329 −0.0188998
\(221\) −13.7566 10.4703i −0.925369 0.704306i
\(222\) −4.55639 −0.305805
\(223\) −6.21589 + 10.7662i −0.416247 + 0.720961i −0.995558 0.0941455i \(-0.969988\pi\)
0.579312 + 0.815106i \(0.303321\pi\)
\(224\) 0 0
\(225\) 3.53779 + 6.12763i 0.235853 + 0.408509i
\(226\) −7.83136 −0.520934
\(227\) 0.617487 + 1.06952i 0.0409841 + 0.0709865i 0.885790 0.464087i \(-0.153617\pi\)
−0.844806 + 0.535073i \(0.820284\pi\)
\(228\) 0.559881 + 0.969743i 0.0370790 + 0.0642228i
\(229\) −6.55514 −0.433176 −0.216588 0.976263i \(-0.569493\pi\)
−0.216588 + 0.976263i \(0.569493\pi\)
\(230\) −0.795020 1.37702i −0.0524221 0.0907977i
\(231\) 0 0
\(232\) −8.84282 + 15.3162i −0.580559 + 1.00556i
\(233\) 6.29887 0.412653 0.206326 0.978483i \(-0.433849\pi\)
0.206326 + 0.978483i \(0.433849\pi\)
\(234\) 7.69141 3.22132i 0.502803 0.210585i
\(235\) −0.273968 −0.0178717
\(236\) −1.85706 + 3.21653i −0.120885 + 0.209378i
\(237\) 15.9065 27.5509i 1.03324 1.78962i
\(238\) 0 0
\(239\) −18.9193 −1.22379 −0.611895 0.790939i \(-0.709592\pi\)
−0.611895 + 0.790939i \(0.709592\pi\)
\(240\) −2.83698 4.91380i −0.183126 0.317184i
\(241\) 11.1484 + 19.3096i 0.718131 + 1.24384i 0.961740 + 0.273965i \(0.0883353\pi\)
−0.243609 + 0.969874i \(0.578331\pi\)
\(242\) 13.2113 0.849257
\(243\) 7.24176 + 12.5431i 0.464559 + 0.804640i
\(244\) 0.387839 0.671757i 0.0248289 0.0430048i
\(245\) 0 0
\(246\) 4.38285 0.279440
\(247\) −4.83127 3.67711i −0.307406 0.233969i
\(248\) 15.6172 0.991695
\(249\) 10.7609 18.6385i 0.681947 1.18117i
\(250\) 4.32597 7.49280i 0.273598 0.473886i
\(251\) −3.47657 6.02160i −0.219439 0.380080i 0.735197 0.677853i \(-0.237090\pi\)
−0.954637 + 0.297773i \(0.903756\pi\)
\(252\) 0 0
\(253\) −1.34888 2.33633i −0.0848036 0.146884i
\(254\) −6.84600 11.8576i −0.429556 0.744013i
\(255\) 6.00869 0.376279
\(256\) −3.66603 6.34975i −0.229127 0.396860i
\(257\) 10.5776 18.3209i 0.659811 1.14283i −0.320853 0.947129i \(-0.603970\pi\)
0.980664 0.195697i \(-0.0626970\pi\)
\(258\) −18.6888 + 32.3700i −1.16352 + 2.01527i
\(259\) 0 0
\(260\) −0.528865 0.402523i −0.0327988 0.0249634i
\(261\) 10.4819 0.648816
\(262\) −5.16941 + 8.95368i −0.319367 + 0.553160i
\(263\) 4.21496 7.30053i 0.259906 0.450170i −0.706311 0.707902i \(-0.749642\pi\)
0.966216 + 0.257732i \(0.0829752\pi\)
\(264\) −4.14844 7.18530i −0.255319 0.442225i
\(265\) −4.86060 −0.298584
\(266\) 0 0
\(267\) 17.5253 + 30.3547i 1.07253 + 1.85768i
\(268\) −2.36842 −0.144674
\(269\) −2.91519 5.04926i −0.177743 0.307859i 0.763364 0.645968i \(-0.223546\pi\)
−0.941107 + 0.338109i \(0.890213\pi\)
\(270\) 1.40955 2.44141i 0.0857823 0.148579i
\(271\) 9.21497 15.9608i 0.559769 0.969549i −0.437746 0.899099i \(-0.644223\pi\)
0.997515 0.0704502i \(-0.0224436\pi\)
\(272\) 21.7093 1.31632
\(273\) 0 0
\(274\) 21.4058 1.29317
\(275\) 3.53779 6.12763i 0.213337 0.369510i
\(276\) −0.589815 + 1.02159i −0.0355027 + 0.0614925i
\(277\) 3.09154 + 5.35470i 0.185752 + 0.321733i 0.943830 0.330432i \(-0.107194\pi\)
−0.758077 + 0.652165i \(0.773861\pi\)
\(278\) 26.2885 1.57668
\(279\) −4.62802 8.01596i −0.277072 0.479903i
\(280\) 0 0
\(281\) −5.64049 −0.336483 −0.168242 0.985746i \(-0.553809\pi\)
−0.168242 + 0.985746i \(0.553809\pi\)
\(282\) 0.751513 + 1.30166i 0.0447520 + 0.0775127i
\(283\) −8.22771 + 14.2508i −0.489086 + 0.847123i −0.999921 0.0125564i \(-0.996003\pi\)
0.510835 + 0.859679i \(0.329336\pi\)
\(284\) −1.03282 + 1.78889i −0.0612864 + 0.106151i
\(285\) 2.11023 0.124999
\(286\) −6.63545 5.05029i −0.392362 0.298630i
\(287\) 0 0
\(288\) −1.33353 + 2.30973i −0.0785787 + 0.136102i
\(289\) −2.99502 + 5.18752i −0.176177 + 0.305148i
\(290\) −3.08898 5.35028i −0.181391 0.314179i
\(291\) 2.07065 0.121384
\(292\) −2.56005 4.43414i −0.149816 0.259489i
\(293\) 15.3086 + 26.5152i 0.894335 + 1.54903i 0.834625 + 0.550819i \(0.185684\pi\)
0.0597104 + 0.998216i \(0.480982\pi\)
\(294\) 0 0
\(295\) 3.49970 + 6.06166i 0.203760 + 0.352923i
\(296\) −1.80785 + 3.13130i −0.105079 + 0.182003i
\(297\) 2.39153 4.14225i 0.138771 0.240358i
\(298\) 26.0435 1.50866
\(299\) 0.809947 6.34456i 0.0468404 0.366915i
\(300\) −3.09388 −0.178625
\(301\) 0 0
\(302\) 12.0122 20.8057i 0.691223 1.19723i
\(303\) −3.12578 5.41401i −0.179571 0.311027i
\(304\) 7.62424 0.437280
\(305\) −0.730896 1.26595i −0.0418510 0.0724880i
\(306\) −5.54458 9.60350i −0.316963 0.548995i
\(307\) 9.96020 0.568459 0.284229 0.958756i \(-0.408262\pi\)
0.284229 + 0.958756i \(0.408262\pi\)
\(308\) 0 0
\(309\) 0.562044 0.973489i 0.0319736 0.0553799i
\(310\) −2.72771 + 4.72454i −0.154924 + 0.268336i
\(311\) −27.7468 −1.57337 −0.786687 0.617352i \(-0.788205\pi\)
−0.786687 + 0.617352i \(0.788205\pi\)
\(312\) 2.49096 19.5124i 0.141023 1.10467i
\(313\) 16.5227 0.933920 0.466960 0.884278i \(-0.345349\pi\)
0.466960 + 0.884278i \(0.345349\pi\)
\(314\) 2.87693 4.98300i 0.162355 0.281207i
\(315\) 0 0
\(316\) 2.33975 + 4.05256i 0.131621 + 0.227974i
\(317\) 23.6793 1.32996 0.664980 0.746861i \(-0.268440\pi\)
0.664980 + 0.746861i \(0.268440\pi\)
\(318\) 13.3330 + 23.0934i 0.747675 + 1.29501i
\(319\) −5.24097 9.07763i −0.293438 0.508250i
\(320\) −3.76523 −0.210483
\(321\) 20.5417 + 35.5793i 1.14653 + 1.98584i
\(322\) 0 0
\(323\) −4.03701 + 6.99230i −0.224625 + 0.389062i
\(324\) −3.51832 −0.195462
\(325\) 15.4730 6.48041i 0.858287 0.359469i
\(326\) −2.60891 −0.144494
\(327\) 6.09414 10.5554i 0.337007 0.583713i
\(328\) 1.73900 3.01203i 0.0960202 0.166312i
\(329\) 0 0
\(330\) 2.89827 0.159545
\(331\) −3.97604 6.88671i −0.218543 0.378528i 0.735820 0.677178i \(-0.236797\pi\)
−0.954363 + 0.298650i \(0.903464\pi\)
\(332\) 1.58286 + 2.74160i 0.0868710 + 0.150465i
\(333\) 2.14296 0.117434
\(334\) −9.62049 16.6632i −0.526410 0.911768i
\(335\) −2.23168 + 3.86539i −0.121930 + 0.211189i
\(336\) 0 0
\(337\) −7.91326 −0.431063 −0.215531 0.976497i \(-0.569148\pi\)
−0.215531 + 0.976497i \(0.569148\pi\)
\(338\) −5.26667 19.0556i −0.286469 1.03649i
\(339\) 10.9491 0.594674
\(340\) −0.441920 + 0.765427i −0.0239665 + 0.0415111i
\(341\) −4.62802 + 8.01596i −0.250621 + 0.434089i
\(342\) −1.94724 3.37271i −0.105294 0.182375i
\(343\) 0 0
\(344\) 14.8305 + 25.6871i 0.799605 + 1.38496i
\(345\) 1.11153 + 1.92522i 0.0598426 + 0.103650i
\(346\) −17.4698 −0.939180
\(347\) −3.56786 6.17971i −0.191533 0.331744i 0.754226 0.656615i \(-0.228012\pi\)
−0.945758 + 0.324871i \(0.894679\pi\)
\(348\) −2.29168 + 3.96930i −0.122847 + 0.212777i
\(349\) −0.688402 + 1.19235i −0.0368493 + 0.0638249i −0.883862 0.467748i \(-0.845065\pi\)
0.847013 + 0.531573i \(0.178399\pi\)
\(350\) 0 0
\(351\) 10.4597 4.38073i 0.558296 0.233826i
\(352\) 2.66705 0.142154
\(353\) −0.346608 + 0.600342i −0.0184481 + 0.0319530i −0.875102 0.483938i \(-0.839206\pi\)
0.856654 + 0.515891i \(0.172539\pi\)
\(354\) 19.1999 33.2551i 1.02046 1.76749i
\(355\) 1.94638 + 3.37123i 0.103303 + 0.178926i
\(356\) −5.15571 −0.273252
\(357\) 0 0
\(358\) −1.66107 2.87706i −0.0877904 0.152057i
\(359\) −5.80365 −0.306305 −0.153152 0.988203i \(-0.548943\pi\)
−0.153152 + 0.988203i \(0.548943\pi\)
\(360\) 1.14996 + 1.99178i 0.0606081 + 0.104976i
\(361\) 8.08222 13.9988i 0.425380 0.736780i
\(362\) 8.81905 15.2750i 0.463519 0.802839i
\(363\) −18.4709 −0.969472
\(364\) 0 0
\(365\) −9.64902 −0.505053
\(366\) −4.00980 + 6.94518i −0.209596 + 0.363030i
\(367\) −3.67578 + 6.36664i −0.191874 + 0.332336i −0.945871 0.324542i \(-0.894790\pi\)
0.753997 + 0.656878i \(0.228123\pi\)
\(368\) 4.01593 + 6.95580i 0.209345 + 0.362596i
\(369\) −2.06134 −0.107309
\(370\) −0.631522 1.09383i −0.0328313 0.0568654i
\(371\) 0 0
\(372\) 4.04731 0.209843
\(373\) −9.19942 15.9339i −0.476328 0.825024i 0.523304 0.852146i \(-0.324699\pi\)
−0.999632 + 0.0271216i \(0.991366\pi\)
\(374\) −5.54458 + 9.60350i −0.286704 + 0.496585i
\(375\) −6.04819 + 10.4758i −0.312327 + 0.540966i
\(376\) 1.19272 0.0615099
\(377\) 3.14698 24.6512i 0.162078 1.26960i
\(378\) 0 0
\(379\) 2.42550 4.20110i 0.124590 0.215796i −0.796983 0.604002i \(-0.793572\pi\)
0.921573 + 0.388206i \(0.126905\pi\)
\(380\) −0.155201 + 0.268815i −0.00796162 + 0.0137899i
\(381\) 9.57147 + 16.5783i 0.490361 + 0.849331i
\(382\) −27.0078 −1.38184
\(383\) 11.4103 + 19.7631i 0.583037 + 1.00985i 0.995117 + 0.0987019i \(0.0314690\pi\)
−0.412080 + 0.911148i \(0.635198\pi\)
\(384\) 14.0571 + 24.3476i 0.717349 + 1.24249i
\(385\) 0 0
\(386\) 17.2136 + 29.8148i 0.876147 + 1.51753i
\(387\) 8.78973 15.2243i 0.446807 0.773893i
\(388\) −0.152290 + 0.263773i −0.00773134 + 0.0133911i
\(389\) −20.3122 −1.02987 −0.514933 0.857230i \(-0.672183\pi\)
−0.514933 + 0.857230i \(0.672183\pi\)
\(390\) 5.46784 + 4.16162i 0.276875 + 0.210732i
\(391\) −8.50569 −0.430151
\(392\) 0 0
\(393\) 7.22741 12.5182i 0.364575 0.631462i
\(394\) 15.2125 + 26.3489i 0.766397 + 1.32744i
\(395\) 8.81866 0.443715
\(396\) −0.361659 0.626411i −0.0181740 0.0314783i
\(397\) 17.0689 + 29.5641i 0.856662 + 1.48378i 0.875095 + 0.483952i \(0.160799\pi\)
−0.0184326 + 0.999830i \(0.505868\pi\)
\(398\) −2.81169 −0.140937
\(399\) 0 0
\(400\) −10.5328 + 18.2434i −0.526640 + 0.912168i
\(401\) 1.51298 2.62056i 0.0755547 0.130865i −0.825773 0.564003i \(-0.809261\pi\)
0.901327 + 0.433139i \(0.142594\pi\)
\(402\) 24.4867 1.22128
\(403\) −20.2412 + 8.47746i −1.00829 + 0.422292i
\(404\) 0.919564 0.0457500
\(405\) −3.31520 + 5.74209i −0.164734 + 0.285327i
\(406\) 0 0
\(407\) −1.07148 1.85586i −0.0531114 0.0919916i
\(408\) −26.1589 −1.29506
\(409\) −2.69162 4.66203i −0.133092 0.230523i 0.791775 0.610813i \(-0.209157\pi\)
−0.924867 + 0.380291i \(0.875824\pi\)
\(410\) 0.607469 + 1.05217i 0.0300008 + 0.0519628i
\(411\) −29.9276 −1.47622
\(412\) 0.0826731 + 0.143194i 0.00407301 + 0.00705466i
\(413\) 0 0
\(414\) 2.05135 3.55304i 0.100818 0.174622i
\(415\) 5.96592 0.292856
\(416\) 5.03162 + 3.82961i 0.246696 + 0.187762i
\(417\) −36.7543 −1.79986
\(418\) −1.94724 + 3.37271i −0.0952425 + 0.164965i
\(419\) −2.94117 + 5.09426i −0.143686 + 0.248871i −0.928882 0.370376i \(-0.879229\pi\)
0.785196 + 0.619247i \(0.212562\pi\)
\(420\) 0 0
\(421\) −28.7614 −1.40174 −0.700872 0.713287i \(-0.747206\pi\)
−0.700872 + 0.713287i \(0.747206\pi\)
\(422\) −12.2951 21.2957i −0.598514 1.03666i
\(423\) −0.353452 0.612196i −0.0171854 0.0297660i
\(424\) 21.1607 1.02765
\(425\) −11.1542 19.3196i −0.541057 0.937138i
\(426\) 10.6781 18.4950i 0.517356 0.896087i
\(427\) 0 0
\(428\) −6.04311 −0.292105
\(429\) 9.27710 + 7.06087i 0.447903 + 0.340902i
\(430\) −10.3612 −0.499661
\(431\) −4.19294 + 7.26238i −0.201967 + 0.349817i −0.949162 0.314788i \(-0.898067\pi\)
0.747195 + 0.664605i \(0.231400\pi\)
\(432\) −7.12013 + 12.3324i −0.342567 + 0.593344i
\(433\) 13.7996 + 23.9017i 0.663168 + 1.14864i 0.979779 + 0.200085i \(0.0641218\pi\)
−0.316611 + 0.948556i \(0.602545\pi\)
\(434\) 0 0
\(435\) 4.31874 + 7.48028i 0.207068 + 0.358652i
\(436\) 0.896409 + 1.55263i 0.0429302 + 0.0743573i
\(437\) −2.98717 −0.142896
\(438\) 26.4679 + 45.8438i 1.26469 + 2.19050i
\(439\) −15.5869 + 26.9973i −0.743921 + 1.28851i 0.206776 + 0.978388i \(0.433703\pi\)
−0.950697 + 0.310121i \(0.899631\pi\)
\(440\) 1.14996 1.99178i 0.0548221 0.0949546i
\(441\) 0 0
\(442\) −24.2500 + 10.1564i −1.15345 + 0.483090i
\(443\) −23.5883 −1.12071 −0.560357 0.828251i \(-0.689336\pi\)
−0.560357 + 0.828251i \(0.689336\pi\)
\(444\) −0.468518 + 0.811497i −0.0222349 + 0.0385119i
\(445\) −4.85806 + 8.41440i −0.230294 + 0.398881i
\(446\) 9.45296 + 16.3730i 0.447611 + 0.775284i
\(447\) −36.4118 −1.72222
\(448\) 0 0
\(449\) −1.41328 2.44787i −0.0666968 0.115522i 0.830749 0.556648i \(-0.187913\pi\)
−0.897445 + 0.441125i \(0.854579\pi\)
\(450\) 10.7604 0.507248
\(451\) 1.03067 + 1.78518i 0.0485324 + 0.0840607i
\(452\) −0.805272 + 1.39477i −0.0378768 + 0.0656046i
\(453\) −16.7944 + 29.0887i −0.789068 + 1.36671i
\(454\) 1.87812 0.0881444
\(455\) 0 0
\(456\) −9.18691 −0.430217
\(457\) 18.8716 32.6866i 0.882776 1.52901i 0.0345338 0.999404i \(-0.489005\pi\)
0.848242 0.529609i \(-0.177661\pi\)
\(458\) −4.98444 + 8.63330i −0.232908 + 0.403408i
\(459\) −7.54017 13.0599i −0.351945 0.609586i
\(460\) −0.326997 −0.0152463
\(461\) −17.3293 30.0152i −0.807106 1.39795i −0.914860 0.403771i \(-0.867699\pi\)
0.107754 0.994178i \(-0.465634\pi\)
\(462\) 0 0
\(463\) 18.5114 0.860296 0.430148 0.902758i \(-0.358461\pi\)
0.430148 + 0.902758i \(0.358461\pi\)
\(464\) 15.6036 + 27.0262i 0.724377 + 1.25466i
\(465\) 3.81365 6.60543i 0.176854 0.306320i
\(466\) 4.78958 8.29579i 0.221873 0.384295i
\(467\) 6.62783 0.306700 0.153350 0.988172i \(-0.450994\pi\)
0.153350 + 0.988172i \(0.450994\pi\)
\(468\) 0.217161 1.70108i 0.0100383 0.0786326i
\(469\) 0 0
\(470\) −0.208321 + 0.360823i −0.00960915 + 0.0166435i
\(471\) −4.02227 + 6.96678i −0.185337 + 0.321012i
\(472\) −15.2360 26.3895i −0.701293 1.21468i
\(473\) −17.5795 −0.808305
\(474\) −24.1902 41.8987i −1.11109 1.92447i
\(475\) −3.91730 6.78497i −0.179738 0.311316i
\(476\) 0 0
\(477\) −6.27076 10.8613i −0.287118 0.497304i
\(478\) −14.3860 + 24.9173i −0.658001 + 1.13969i
\(479\) 8.72630 15.1144i 0.398715 0.690594i −0.594853 0.803835i \(-0.702790\pi\)
0.993568 + 0.113240i \(0.0361230\pi\)
\(480\) −2.19774 −0.100313
\(481\) 0.643379 5.03978i 0.0293355 0.229794i
\(482\) 33.9083 1.54448
\(483\) 0 0
\(484\) 1.35848 2.35295i 0.0617489 0.106952i
\(485\) 0.286995 + 0.497090i 0.0130318 + 0.0225717i
\(486\) 22.0261 0.999126
\(487\) 17.7569 + 30.7558i 0.804641 + 1.39368i 0.916533 + 0.399959i \(0.130976\pi\)
−0.111892 + 0.993720i \(0.535691\pi\)
\(488\) 3.18196 + 5.51132i 0.144041 + 0.249486i
\(489\) 3.64754 0.164948
\(490\) 0 0
\(491\) 14.9059 25.8178i 0.672695 1.16514i −0.304442 0.952531i \(-0.598470\pi\)
0.977137 0.212611i \(-0.0681966\pi\)
\(492\) 0.450674 0.780590i 0.0203179 0.0351917i
\(493\) −33.0481 −1.48841
\(494\) −8.51650 + 3.56689i −0.383175 + 0.160482i
\(495\) −1.36312 −0.0612675
\(496\) 13.7787 23.8653i 0.618680 1.07159i
\(497\) 0 0
\(498\) −16.3649 28.3449i −0.733331 1.27017i
\(499\) −7.50966 −0.336178 −0.168089 0.985772i \(-0.553760\pi\)
−0.168089 + 0.985772i \(0.553760\pi\)
\(500\) −0.889649 1.54092i −0.0397863 0.0689119i
\(501\) 13.4505 + 23.2970i 0.600925 + 1.04083i
\(502\) −10.5742 −0.471948
\(503\) −0.492171 0.852466i −0.0219448 0.0380096i 0.854844 0.518884i \(-0.173652\pi\)
−0.876789 + 0.480875i \(0.840319\pi\)
\(504\) 0 0
\(505\) 0.866474 1.50078i 0.0385576 0.0667837i
\(506\) −4.10269 −0.182387
\(507\) 7.36339 + 26.6419i 0.327019 + 1.18321i
\(508\) −2.81580 −0.124931
\(509\) −6.48958 + 11.2403i −0.287646 + 0.498217i −0.973247 0.229760i \(-0.926206\pi\)
0.685602 + 0.727977i \(0.259539\pi\)
\(510\) 4.56893 7.91362i 0.202316 0.350421i
\(511\) 0 0
\(512\) 15.2950 0.675949
\(513\) −2.64808 4.58661i −0.116916 0.202504i
\(514\) −16.0861 27.8619i −0.709527 1.22894i
\(515\) 0.311600 0.0137308
\(516\) 3.84342 + 6.65699i 0.169197 + 0.293058i
\(517\) −0.353452 + 0.612196i −0.0155448 + 0.0269244i
\(518\) 0 0
\(519\) 24.4247 1.07212
\(520\) 5.02949 2.10646i 0.220558 0.0923742i
\(521\) −19.4146 −0.850569 −0.425285 0.905060i \(-0.639826\pi\)
−0.425285 + 0.905060i \(0.639826\pi\)
\(522\) 7.97033 13.8050i 0.348852 0.604229i
\(523\) −13.6360 + 23.6182i −0.596259 + 1.03275i 0.397109 + 0.917771i \(0.370013\pi\)
−0.993368 + 0.114979i \(0.963320\pi\)
\(524\) 1.06311 + 1.84135i 0.0464420 + 0.0804399i
\(525\) 0 0
\(526\) −6.41000 11.1024i −0.279489 0.484090i
\(527\) 14.5915 + 25.2732i 0.635616 + 1.10092i
\(528\) −14.6402 −0.637134
\(529\) 9.92656 + 17.1933i 0.431590 + 0.747535i
\(530\) −3.69593 + 6.40154i −0.160541 + 0.278065i
\(531\) −9.03008 + 15.6406i −0.391872 + 0.678742i
\(532\) 0 0
\(533\) −0.618874 + 4.84783i −0.0268064 + 0.209983i
\(534\) 53.3040 2.30669
\(535\) −5.69422 + 9.86268i −0.246183 + 0.426401i
\(536\) 9.71566 16.8280i 0.419652 0.726859i
\(537\) 2.32236 + 4.02245i 0.100217 + 0.173582i
\(538\) −8.86670 −0.382271
\(539\) 0 0
\(540\) −0.289878 0.502083i −0.0124743 0.0216062i
\(541\) −30.0990 −1.29406 −0.647029 0.762465i \(-0.723989\pi\)
−0.647029 + 0.762465i \(0.723989\pi\)
\(542\) −14.0139 24.2727i −0.601947 1.04260i
\(543\) −12.3300 + 21.3562i −0.529132 + 0.916483i
\(544\) 4.20442 7.28228i 0.180263 0.312225i
\(545\) 3.37863 0.144724
\(546\) 0 0
\(547\) −26.1451 −1.11788 −0.558942 0.829207i \(-0.688793\pi\)
−0.558942 + 0.829207i \(0.688793\pi\)
\(548\) 2.20108 3.81238i 0.0940255 0.162857i
\(549\) 1.88589 3.26646i 0.0804878 0.139409i
\(550\) −5.38018 9.31874i −0.229411 0.397352i
\(551\) −11.6064 −0.494449
\(552\) −4.83905 8.38147i −0.205963 0.356739i
\(553\) 0 0
\(554\) 9.40305 0.399497
\(555\) 0.882938 + 1.52929i 0.0374786 + 0.0649149i
\(556\) 2.70316 4.68200i 0.114639 0.198561i
\(557\) −8.95317 + 15.5073i −0.379358 + 0.657067i −0.990969 0.134091i \(-0.957188\pi\)
0.611611 + 0.791159i \(0.290522\pi\)
\(558\) −14.0763 −0.595899
\(559\) −33.1652 25.2423i −1.40274 1.06764i
\(560\) 0 0
\(561\) 7.75195 13.4268i 0.327287 0.566878i
\(562\) −4.28895 + 7.42868i −0.180919 + 0.313360i
\(563\) 15.8275 + 27.4140i 0.667048 + 1.15536i 0.978726 + 0.205173i \(0.0657756\pi\)
−0.311678 + 0.950188i \(0.600891\pi\)
\(564\) 0.309102 0.0130155
\(565\) 1.51756 + 2.62850i 0.0638443 + 0.110582i
\(566\) 12.5125 + 21.6722i 0.525939 + 0.910953i
\(567\) 0 0
\(568\) −8.47358 14.6767i −0.355544 0.615820i
\(569\) 13.0555 22.6129i 0.547317 0.947981i −0.451140 0.892453i \(-0.648983\pi\)
0.998457 0.0555278i \(-0.0176841\pi\)
\(570\) 1.60459 2.77923i 0.0672089 0.116409i
\(571\) 13.3041 0.556760 0.278380 0.960471i \(-0.410203\pi\)
0.278380 + 0.960471i \(0.410203\pi\)
\(572\) −1.58176 + 0.662475i −0.0661368 + 0.0276995i
\(573\) 37.7599 1.57744
\(574\) 0 0
\(575\) 4.12674 7.14773i 0.172097 0.298081i
\(576\) −4.85760 8.41361i −0.202400 0.350567i
\(577\) −16.7713 −0.698198 −0.349099 0.937086i \(-0.613512\pi\)
−0.349099 + 0.937086i \(0.613512\pi\)
\(578\) 4.55474 + 7.88904i 0.189452 + 0.328141i
\(579\) −24.0665 41.6844i −1.00017 1.73234i
\(580\) −1.27052 −0.0527554
\(581\) 0 0
\(582\) 1.57450 2.72711i 0.0652650 0.113042i
\(583\) −6.27076 + 10.8613i −0.259708 + 0.449828i
\(584\) 42.0071 1.73827
\(585\) −2.57164 1.95729i −0.106324 0.0809241i
\(586\) 46.5617 1.92345
\(587\) 5.03261 8.71673i 0.207718 0.359778i −0.743277 0.668983i \(-0.766730\pi\)
0.950995 + 0.309205i \(0.100063\pi\)
\(588\) 0 0
\(589\) 5.12448 + 8.87587i 0.211151 + 0.365724i
\(590\) 10.6445 0.438227
\(591\) −21.2688 36.8387i −0.874883 1.51534i
\(592\) 3.19004 + 5.52532i 0.131110 + 0.227089i
\(593\) 39.4322 1.61929 0.809643 0.586923i \(-0.199661\pi\)
0.809643 + 0.586923i \(0.199661\pi\)
\(594\) −3.63697 6.29942i −0.149227 0.258468i
\(595\) 0 0
\(596\) 2.67797 4.63838i 0.109694 0.189995i
\(597\) 3.93105 0.160887
\(598\) −7.74009 5.89104i −0.316516 0.240902i
\(599\) 13.7720 0.562709 0.281355 0.959604i \(-0.409216\pi\)
0.281355 + 0.959604i \(0.409216\pi\)
\(600\) 12.6916 21.9825i 0.518133 0.897433i
\(601\) −16.6312 + 28.8060i −0.678399 + 1.17502i 0.297064 + 0.954858i \(0.403993\pi\)
−0.975463 + 0.220164i \(0.929341\pi\)
\(602\) 0 0
\(603\) −11.5166 −0.468991
\(604\) −2.47034 4.27876i −0.100517 0.174100i
\(605\) −2.56009 4.43421i −0.104083 0.180276i
\(606\) −9.50720 −0.386204
\(607\) −21.9824 38.0747i −0.892240 1.54540i −0.837184 0.546921i \(-0.815800\pi\)
−0.0550554 0.998483i \(-0.517534\pi\)
\(608\) 1.47658 2.55751i 0.0598831 0.103721i
\(609\) 0 0
\(610\) −2.22305 −0.0900088
\(611\) −1.54587 + 0.647442i −0.0625391 + 0.0261927i
\(612\) −2.28052 −0.0921846
\(613\) −1.35045 + 2.33906i −0.0545443 + 0.0944736i −0.892008 0.452019i \(-0.850704\pi\)
0.837464 + 0.546492i \(0.184037\pi\)
\(614\) 7.57361 13.1179i 0.305646 0.529394i
\(615\) −0.849310 1.47105i −0.0342475 0.0593184i
\(616\) 0 0
\(617\) −3.00208 5.19975i −0.120859 0.209334i 0.799248 0.601002i \(-0.205232\pi\)
−0.920107 + 0.391668i \(0.871898\pi\)
\(618\) −0.854742 1.48046i −0.0343828 0.0595527i
\(619\) −13.3641 −0.537148 −0.268574 0.963259i \(-0.586552\pi\)
−0.268574 + 0.963259i \(0.586552\pi\)
\(620\) 0.560963 + 0.971616i 0.0225288 + 0.0390210i
\(621\) 2.78966 4.83183i 0.111945 0.193895i
\(622\) −21.0983 + 36.5433i −0.845963 + 1.46525i
\(623\) 0 0
\(624\) −27.6201 21.0218i −1.10569 0.841547i
\(625\) 19.9099 0.796398
\(626\) 12.5637 21.7609i 0.502145 0.869741i
\(627\) 2.72245 4.71543i 0.108724 0.188316i
\(628\) −0.591650 1.02477i −0.0236094 0.0408927i
\(629\) −6.75647 −0.269398
\(630\) 0 0
\(631\) −20.2228 35.0270i −0.805059 1.39440i −0.916251 0.400604i \(-0.868800\pi\)
0.111192 0.993799i \(-0.464533\pi\)
\(632\) −38.3921 −1.52716
\(633\) 17.1899 + 29.7737i 0.683236 + 1.18340i
\(634\) 18.0054 31.1863i 0.715086 1.23857i
\(635\) −2.65324 + 4.59554i −0.105291 + 0.182369i
\(636\) 5.48393 0.217452
\(637\) 0 0
\(638\) −15.9407 −0.631097
\(639\) −5.02213 + 8.69859i −0.198672 + 0.344111i
\(640\) −3.89667 + 6.74923i −0.154029 + 0.266787i
\(641\) −5.10991 8.85062i −0.201829 0.349578i 0.747289 0.664500i \(-0.231355\pi\)
−0.949118 + 0.314921i \(0.898022\pi\)
\(642\) 62.4786 2.46584
\(643\) −15.9014 27.5420i −0.627088 1.08615i −0.988133 0.153600i \(-0.950913\pi\)
0.361045 0.932548i \(-0.382420\pi\)
\(644\) 0 0
\(645\) 14.4861 0.570389
\(646\) 6.13937 + 10.6337i 0.241550 + 0.418378i
\(647\) 17.2617 29.8981i 0.678626 1.17541i −0.296769 0.954949i \(-0.595909\pi\)
0.975395 0.220465i \(-0.0707575\pi\)
\(648\) 14.4328 24.9983i 0.566972 0.982025i
\(649\) 18.0602 0.708923
\(650\) 3.23057 25.3060i 0.126713 0.992582i
\(651\) 0 0
\(652\) −0.268265 + 0.464649i −0.0105061 + 0.0181970i
\(653\) −5.05899 + 8.76244i −0.197974 + 0.342901i −0.947871 0.318653i \(-0.896769\pi\)
0.749898 + 0.661554i \(0.230103\pi\)
\(654\) −9.26781 16.0523i −0.362400 0.627695i
\(655\) 4.00692 0.156563
\(656\) −3.06855 5.31488i −0.119807 0.207511i
\(657\) −12.4484 21.5613i −0.485659 0.841185i
\(658\) 0 0
\(659\) 17.3841 + 30.1101i 0.677187 + 1.17292i 0.975824 + 0.218556i \(0.0701345\pi\)
−0.298637 + 0.954367i \(0.596532\pi\)
\(660\) 0.298019 0.516185i 0.0116004 0.0200925i
\(661\) 8.28076 14.3427i 0.322084 0.557866i −0.658834 0.752289i \(-0.728950\pi\)
0.980918 + 0.194422i \(0.0622833\pi\)
\(662\) −12.0933 −0.470020
\(663\) 33.9042 14.1998i 1.31673 0.551474i
\(664\) −25.9727 −1.00794
\(665\) 0 0
\(666\) 1.62948 2.82234i 0.0631411 0.109364i
\(667\) −6.11346 10.5888i −0.236714 0.410001i
\(668\) −3.95697 −0.153100
\(669\) −13.2163 22.8913i −0.510972 0.885029i
\(670\) 3.39388 + 5.87838i 0.131117 + 0.227102i
\(671\) −3.77178 −0.145608
\(672\) 0 0
\(673\) 20.9437 36.2756i 0.807321 1.39832i −0.107393 0.994217i \(-0.534250\pi\)
0.914713 0.404104i \(-0.132417\pi\)
\(674\) −6.01714 + 10.4220i −0.231771 + 0.401440i
\(675\) 14.6332 0.563231
\(676\) −3.93538 1.02143i −0.151361 0.0392857i
\(677\) −31.5715 −1.21339 −0.606696 0.794934i \(-0.707505\pi\)
−0.606696 + 0.794934i \(0.707505\pi\)
\(678\) 8.32556 14.4203i 0.319741 0.553808i
\(679\) 0 0
\(680\) −3.62566 6.27983i −0.139038 0.240820i
\(681\) −2.62582 −0.100621
\(682\) 7.03817 + 12.1905i 0.269505 + 0.466797i
\(683\) 13.1338 + 22.7484i 0.502551 + 0.870444i 0.999996 + 0.00294809i \(0.000938408\pi\)
−0.497445 + 0.867496i \(0.665728\pi\)
\(684\) −0.800911 −0.0306236
\(685\) −4.14801 7.18457i −0.158487 0.274508i
\(686\) 0 0
\(687\) 6.96880 12.0703i 0.265876 0.460512i
\(688\) 52.3381 1.99537
\(689\) −27.4260 + 11.4866i −1.04485 + 0.437604i
\(690\) 3.38076 0.128703
\(691\) −3.05047 + 5.28358i −0.116046 + 0.200997i −0.918197 0.396124i \(-0.870355\pi\)
0.802152 + 0.597120i \(0.203689\pi\)
\(692\) −1.79635 + 3.11138i −0.0682872 + 0.118277i
\(693\) 0 0
\(694\) −10.8518 −0.411929
\(695\) −5.09419 8.82339i −0.193234 0.334690i
\(696\) −18.8017 32.5655i −0.712677 1.23439i
\(697\) 6.49914 0.246172
\(698\) 1.04690 + 1.81329i 0.0396259 + 0.0686341i
\(699\) −6.69636 + 11.5984i −0.253280 + 0.438693i
\(700\) 0 0
\(701\) −20.5701 −0.776921 −0.388461 0.921465i \(-0.626993\pi\)
−0.388461 + 0.921465i \(0.626993\pi\)
\(702\) 2.18385 17.1067i 0.0824240 0.645652i
\(703\) −2.37285 −0.0894936
\(704\) −4.85760 + 8.41361i −0.183078 + 0.317100i
\(705\) 0.291257 0.504471i 0.0109694 0.0189995i
\(706\) 0.527111 + 0.912984i 0.0198381 + 0.0343606i
\(707\) 0 0
\(708\) −3.94851 6.83902i −0.148394 0.257026i
\(709\) 21.5764 + 37.3715i 0.810320 + 1.40352i 0.912640 + 0.408764i \(0.134040\pi\)
−0.102320 + 0.994751i \(0.532627\pi\)
\(710\) 5.92000 0.222174
\(711\) 11.3771 + 19.7058i 0.426676 + 0.739025i
\(712\) 21.1496 36.6322i 0.792615 1.37285i
\(713\) −5.39847 + 9.35042i −0.202174 + 0.350176i
\(714\) 0 0
\(715\) −0.409246 + 3.20575i −0.0153050 + 0.119888i
\(716\) −0.683209 −0.0255327
\(717\) 20.1132 34.8372i 0.751143 1.30102i
\(718\) −4.41302 + 7.64357i −0.164692 + 0.285255i
\(719\) −14.1042 24.4292i −0.525999 0.911057i −0.999541 0.0302857i \(-0.990358\pi\)
0.473542 0.880771i \(-0.342975\pi\)
\(720\) 4.05831 0.151244
\(721\) 0 0
\(722\) −12.2912 21.2890i −0.457432 0.792295i
\(723\) −47.4076 −1.76311
\(724\) −1.81367 3.14136i −0.0674044 0.116748i
\(725\) 16.0341 27.7719i 0.595492 1.03142i
\(726\) −14.0450 + 24.3267i −0.521260 + 0.902850i
\(727\) 19.5116 0.723646 0.361823 0.932247i \(-0.382155\pi\)
0.361823 + 0.932247i \(0.382155\pi\)
\(728\) 0 0
\(729\) 2.95370 0.109396
\(730\) −7.33698 + 12.7080i −0.271554 + 0.470345i
\(731\) −27.7128 + 48.0000i −1.02500 + 1.77535i
\(732\) 0.824628 + 1.42830i 0.0304791 + 0.0527914i
\(733\) −20.3666 −0.752259 −0.376129 0.926567i \(-0.622745\pi\)
−0.376129 + 0.926567i \(0.622745\pi\)
\(734\) 5.59003 + 9.68222i 0.206332 + 0.357377i
\(735\) 0 0
\(736\) 3.11105 0.114675
\(737\) 5.75829 + 9.97364i 0.212109 + 0.367384i
\(738\) −1.56742 + 2.71485i −0.0576975 + 0.0999349i
\(739\) 5.20995 9.02391i 0.191651 0.331950i −0.754146 0.656706i \(-0.771949\pi\)
0.945798 + 0.324757i \(0.105282\pi\)
\(740\) −0.259749 −0.00954856
\(741\) 11.9070 4.98691i 0.437415 0.183199i
\(742\) 0 0
\(743\) 8.70470 15.0770i 0.319344 0.553121i −0.661007 0.750380i \(-0.729871\pi\)
0.980351 + 0.197259i \(0.0632040\pi\)
\(744\) −16.6028 + 28.7568i −0.608687 + 1.05428i
\(745\) −5.04672 8.74118i −0.184898 0.320252i
\(746\) −27.9805 −1.02444
\(747\) 7.69677 + 13.3312i 0.281610 + 0.487763i
\(748\) 1.14026 + 1.97499i 0.0416921 + 0.0722128i
\(749\) 0 0
\(750\) 9.19792 + 15.9313i 0.335861 + 0.581728i
\(751\) 0.907626 1.57205i 0.0331197 0.0573651i −0.848990 0.528408i \(-0.822789\pi\)
0.882110 + 0.471043i \(0.156122\pi\)
\(752\) 1.05231 1.82265i 0.0383737 0.0664652i
\(753\) 14.7839 0.538754
\(754\) −30.0734 22.8891i −1.09521 0.833573i
\(755\) −9.31088 −0.338858
\(756\) 0 0
\(757\) −26.7814 + 46.3867i −0.973385 + 1.68595i −0.288220 + 0.957564i \(0.593063\pi\)
−0.685165 + 0.728388i \(0.740270\pi\)
\(758\) −3.68864 6.38892i −0.133978 0.232056i
\(759\) 5.73602 0.208204
\(760\) −1.27332 2.20545i −0.0461881 0.0800001i
\(761\) 1.84083 + 3.18841i 0.0667300 + 0.115580i 0.897460 0.441096i \(-0.145410\pi\)
−0.830730 + 0.556675i \(0.812077\pi\)
\(762\) 29.1121 1.05462
\(763\) 0 0
\(764\) −2.77711 + 4.81010i −0.100472 + 0.174023i
\(765\) −2.14886 + 3.72193i −0.0776922 + 0.134567i
\(766\) 34.7048 1.25394
\(767\) 34.0721 + 25.9325i 1.23027 + 0.936369i
\(768\) 15.5895 0.562538
\(769\) 2.61897 4.53619i 0.0944424 0.163579i −0.814933 0.579555i \(-0.803227\pi\)
0.909376 + 0.415976i \(0.136560\pi\)
\(770\) 0 0
\(771\) 22.4902 + 38.9541i 0.809963 + 1.40290i
\(772\) 7.08004 0.254816
\(773\) −20.3069 35.1726i −0.730388 1.26507i −0.956717 0.291019i \(-0.906006\pi\)
0.226329 0.974051i \(-0.427328\pi\)
\(774\) −13.3672 23.1527i −0.480474 0.832205i
\(775\) −28.3177 −1.01720
\(776\) −1.24944 2.16409i −0.0448522 0.0776862i
\(777\) 0 0
\(778\) −15.4451 + 26.7517i −0.553733 + 0.959094i
\(779\) 2.28247 0.0817781
\(780\) 1.30343 0.545903i 0.0466702 0.0195465i
\(781\) 10.0443 0.359412
\(782\) −6.46762 + 11.2022i −0.231281 + 0.400591i
\(783\) 10.8390 18.7737i 0.387353