Properties

Label 637.2.h.m.471.4
Level $637$
Weight $2$
Character 637.471
Analytic conductor $5.086$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.h (of order \(3\), degree \(2\), not 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 471.4
Root \(-0.141226 + 0.244611i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.m.165.4

$q$-expansion

\(f(q)\) \(=\) \(q-1.52077 q^{2} +(1.06311 - 1.84135i) q^{3} +0.312752 q^{4} +(-0.294696 + 0.510428i) q^{5} +(-1.61674 + 2.80028i) q^{6} +2.56592 q^{8} +(-0.760387 - 1.31703i) q^{9} +O(q^{10})\) \(q-1.52077 q^{2} +(1.06311 - 1.84135i) q^{3} +0.312752 q^{4} +(-0.294696 + 0.510428i) 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} +(0.332488 - 0.575886i) q^{12} +(3.32565 + 1.39285i) q^{13} +(0.626585 + 1.08528i) q^{15} -4.52769 q^{16} +4.79479 q^{17} +(1.15638 + 2.00290i) q^{18} +(-0.841957 - 1.45831i) q^{19} +(-0.0921666 + 0.159637i) q^{20} +(1.15638 - 2.00290i) q^{22} +1.77394 q^{23} +(2.72785 - 4.72477i) q^{24} +(2.32631 + 4.02929i) q^{25} +(-5.05756 - 2.11821i) q^{26} +3.14515 q^{27} +(-3.44625 - 5.96909i) q^{29} +(-0.952894 - 1.65046i) q^{30} +(3.04320 + 5.27098i) q^{31} +1.75375 q^{32} +(1.61674 + 2.80028i) q^{33} -7.29179 q^{34} +(-0.237812 - 0.411903i) q^{36} +1.40913 q^{37} +(1.28043 + 2.21776i) q^{38} +(6.10025 - 4.64295i) q^{39} +(-0.756166 + 1.30972i) q^{40} +(-0.677729 - 1.17386i) q^{41} +(5.77978 - 10.0109i) q^{43} +(-0.237812 + 0.411903i) q^{44} +0.896331 q^{45} -2.69777 q^{46} +(0.232416 - 0.402556i) q^{47} +(-4.81341 + 8.33707i) q^{48} +(-3.53779 - 6.12763i) q^{50} +(5.09737 - 8.82890i) q^{51} +(1.04010 + 0.435617i) q^{52} +(-4.12340 - 7.14194i) q^{53} -4.78306 q^{54} +(-0.448165 - 0.776245i) q^{55} -3.58035 q^{57} +(5.24097 + 9.07763i) q^{58} -11.8756 q^{59} +(0.195966 + 0.339422i) q^{60} +(-1.24009 - 2.14789i) q^{61} +(-4.62802 - 8.01596i) q^{62} +6.38833 q^{64} +(-1.69101 + 1.28704i) q^{65} +(-2.45870 - 4.25859i) q^{66} +(3.78642 - 6.55827i) q^{67} +1.49958 q^{68} +(1.88589 - 3.26646i) q^{69} +(-3.30235 + 5.71984i) q^{71} +(-1.95109 - 3.37939i) q^{72} +(8.18558 + 14.1778i) q^{73} -2.14296 q^{74} +9.89245 q^{75} +(-0.263323 - 0.456090i) q^{76} +(-9.27710 + 7.06087i) q^{78} +(7.48116 - 12.9577i) 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} +(-8.78973 + 15.2243i) q^{86} -14.6549 q^{87} +(-1.95109 + 3.37939i) q^{88} +16.4850 q^{89} -1.36312 q^{90} +0.554804 q^{92} +12.9410 q^{93} +(-0.353452 + 0.612196i) q^{94} +0.992484 q^{95} +(1.86442 - 3.22927i) q^{96} +(0.486935 - 0.843396i) q^{97} +2.31275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} + O(q^{10}) \) \( 16q - 8q^{2} + 24q^{4} + 24q^{8} - 4q^{9} - 4q^{11} - 8q^{15} + 8q^{16} + 28q^{18} + 28q^{22} - 24q^{23} + 12q^{25} + 8q^{29} + 28q^{30} + 4q^{36} + 16q^{37} + 20q^{39} + 32q^{43} + 4q^{44} + 8q^{46} + 36q^{50} + 44q^{51} + 4q^{53} - 96q^{57} - 48q^{58} - 64q^{60} - 64q^{64} - 68q^{65} + 20q^{67} + 8q^{71} + 28q^{72} - 152q^{74} + 28q^{78} + 4q^{79} + 56q^{81} + 36q^{85} - 4q^{86} + 28q^{88} - 160q^{92} - 16q^{93} - 104q^{95} + 56q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.52077 −1.07535 −0.537675 0.843152i \(-0.680697\pi\)
−0.537675 + 0.843152i \(0.680697\pi\)
\(3\) 1.06311 1.84135i 0.613784 1.06311i −0.376812 0.926290i \(-0.622980\pi\)
0.990596 0.136816i \(-0.0436869\pi\)
\(4\) 0.312752 0.156376
\(5\) −0.294696 + 0.510428i −0.131792 + 0.228270i −0.924367 0.381504i \(-0.875406\pi\)
0.792575 + 0.609774i \(0.208740\pi\)
\(6\) −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 \(0.240299\pi\)
\(12\) 0.332488 0.575886i 0.0959811 0.166244i
\(13\) 3.32565 + 1.39285i 0.922370 + 0.386308i
\(14\) 0 0
\(15\) 0.626585 + 1.08528i 0.161784 + 0.280217i
\(16\) −4.52769 −1.13192
\(17\) 4.79479 1.16291 0.581454 0.813579i \(-0.302484\pi\)
0.581454 + 0.813579i \(0.302484\pi\)
\(18\) 1.15638 + 2.00290i 0.272560 + 0.472088i
\(19\) −0.841957 1.45831i −0.193158 0.334560i 0.753137 0.657864i \(-0.228540\pi\)
−0.946295 + 0.323304i \(0.895206\pi\)
\(20\) −0.0921666 + 0.159637i −0.0206091 + 0.0356960i
\(21\) 0 0
\(22\) 1.15638 2.00290i 0.246540 0.427020i
\(23\) 1.77394 0.369893 0.184946 0.982749i \(-0.440789\pi\)
0.184946 + 0.982749i \(0.440789\pi\)
\(24\) 2.72785 4.72477i 0.556819 0.964439i
\(25\) 2.32631 + 4.02929i 0.465262 + 0.805857i
\(26\) −5.05756 2.11821i −0.991870 0.415416i
\(27\) 3.14515 0.605284
\(28\) 0 0
\(29\) −3.44625 5.96909i −0.639953 1.10843i −0.985443 0.170009i \(-0.945620\pi\)
0.345489 0.938423i \(-0.387713\pi\)
\(30\) −0.952894 1.65046i −0.173974 0.301332i
\(31\) 3.04320 + 5.27098i 0.546575 + 0.946695i 0.998506 + 0.0546426i \(0.0174019\pi\)
−0.451931 + 0.892053i \(0.649265\pi\)
\(32\) 1.75375 0.310021
\(33\) 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
\(37\) 1.40913 0.231659 0.115830 0.993269i \(-0.463047\pi\)
0.115830 + 0.993269i \(0.463047\pi\)
\(38\) 1.28043 + 2.21776i 0.207712 + 0.359768i
\(39\) 6.10025 4.64295i 0.976822 0.743467i
\(40\) −0.756166 + 1.30972i −0.119560 + 0.207085i
\(41\) −0.677729 1.17386i −0.105843 0.183326i 0.808239 0.588855i \(-0.200421\pi\)
−0.914082 + 0.405528i \(0.867088\pi\)
\(42\) 0 0
\(43\) 5.77978 10.0109i 0.881408 1.52664i 0.0316319 0.999500i \(-0.489930\pi\)
0.849776 0.527144i \(-0.176737\pi\)
\(44\) −0.237812 + 0.411903i −0.0358516 + 0.0620967i
\(45\) 0.896331 0.133617
\(46\) −2.69777 −0.397764
\(47\) 0.232416 0.402556i 0.0339013 0.0587188i −0.848577 0.529072i \(-0.822540\pi\)
0.882478 + 0.470353i \(0.155873\pi\)
\(48\) −4.81341 + 8.33707i −0.694756 + 1.20335i
\(49\) 0 0
\(50\) −3.53779 6.12763i −0.500319 0.866578i
\(51\) 5.09737 8.82890i 0.713775 1.23629i
\(52\) 1.04010 + 0.435617i 0.144236 + 0.0604093i
\(53\) −4.12340 7.14194i −0.566393 0.981021i −0.996919 0.0784430i \(-0.975005\pi\)
0.430526 0.902578i \(-0.358328\pi\)
\(54\) −4.78306 −0.650892
\(55\) −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
\(59\) −11.8756 −1.54608 −0.773038 0.634359i \(-0.781264\pi\)
−0.773038 + 0.634359i \(0.781264\pi\)
\(60\) 0.195966 + 0.339422i 0.0252991 + 0.0438193i
\(61\) −1.24009 2.14789i −0.158777 0.275009i 0.775651 0.631162i \(-0.217422\pi\)
−0.934428 + 0.356153i \(0.884088\pi\)
\(62\) −4.62802 8.01596i −0.587759 1.01803i
\(63\) 0 0
\(64\) 6.38833 0.798541
\(65\) −1.69101 + 1.28704i −0.209744 + 0.159637i
\(66\) −2.45870 4.25859i −0.302645 0.524196i
\(67\) 3.78642 6.55827i 0.462585 0.801220i −0.536504 0.843898i \(-0.680255\pi\)
0.999089 + 0.0426774i \(0.0135888\pi\)
\(68\) 1.49958 0.181851
\(69\) 1.88589 3.26646i 0.227034 0.393235i
\(70\) 0 0
\(71\) −3.30235 + 5.71984i −0.391917 + 0.678821i −0.992702 0.120590i \(-0.961521\pi\)
0.600785 + 0.799411i \(0.294855\pi\)
\(72\) −1.95109 3.37939i −0.229939 0.398265i
\(73\) 8.18558 + 14.1778i 0.958049 + 1.65939i 0.727231 + 0.686393i \(0.240807\pi\)
0.230819 + 0.972997i \(0.425860\pi\)
\(74\) −2.14296 −0.249114
\(75\) 9.89245 1.14228
\(76\) −0.263323 0.456090i −0.0302053 0.0523171i
\(77\) 0 0
\(78\) −9.27710 + 7.06087i −1.05042 + 0.799486i
\(79\) 7.48116 12.9577i 0.841696 1.45786i −0.0467635 0.998906i \(-0.514891\pi\)
0.888460 0.458955i \(-0.151776\pi\)
\(80\) 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 \(-0.312517\pi\)
0.555526 + 0.831499i \(0.312517\pi\)
\(84\) 0 0
\(85\) −1.41300 + 2.44740i −0.153262 + 0.265457i
\(86\) −8.78973 + 15.2243i −0.947821 + 1.64167i
\(87\) −14.6549 −1.57117
\(88\) −1.95109 + 3.37939i −0.207987 + 0.360244i
\(89\) 16.4850 1.74741 0.873703 0.486460i \(-0.161712\pi\)
0.873703 + 0.486460i \(0.161712\pi\)
\(90\) −1.36312 −0.143685
\(91\) 0 0
\(92\) 0.554804 0.0578423
\(93\) 12.9410 1.34192
\(94\) −0.353452 + 0.612196i −0.0364558 + 0.0631432i
\(95\) 0.992484 0.101827
\(96\) 1.86442 3.22927i 0.190286 0.329586i
\(97\) 0.486935 0.843396i 0.0494407 0.0856338i −0.840246 0.542205i \(-0.817589\pi\)
0.889687 + 0.456572i \(0.150923\pi\)
\(98\) 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 −0.783568 0.621305i \(-0.786603\pi\)
0.929851 + 0.367937i \(0.119936\pi\)
\(102\) −7.75195 + 13.4268i −0.767557 + 1.32945i
\(103\) −0.264341 + 0.457852i −0.0260463 + 0.0451135i −0.878755 0.477274i \(-0.841625\pi\)
0.852708 + 0.522387i \(0.174958\pi\)
\(104\) 8.53336 + 3.57395i 0.836765 + 0.350455i
\(105\) 0 0
\(106\) 6.27076 + 10.8613i 0.609070 + 1.05494i
\(107\) −19.3224 −1.86797 −0.933983 0.357318i \(-0.883691\pi\)
−0.933983 + 0.357318i \(0.883691\pi\)
\(108\) 0.983651 0.0946518
\(109\) 2.86620 + 4.96440i 0.274532 + 0.475503i 0.970017 0.243037i \(-0.0781437\pi\)
−0.695485 + 0.718541i \(0.744810\pi\)
\(110\) 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 −0.961345 0.275346i \(-0.911208\pi\)
0.719129 + 0.694877i \(0.244541\pi\)
\(114\) 5.44491 0.509962
\(115\) −0.522774 + 0.905470i −0.0487489 + 0.0844355i
\(116\) −1.07782 1.86684i −0.100073 0.173332i
\(117\) −0.694354 5.43908i −0.0641931 0.502844i
\(118\) 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
\(122\) 1.88589 + 3.26646i 0.170740 + 0.295731i
\(123\) −2.88199 −0.259860
\(124\) 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 0.993659 0.112436i \(-0.0358652\pi\)
−0.594202 + 0.804316i \(0.702532\pi\)
\(128\) −13.2227 −1.16873
\(129\) −12.2890 21.2852i −1.08199 1.87406i
\(130\) 2.57164 1.95729i 0.225548 0.171666i
\(131\) −3.39920 + 5.88758i −0.296989 + 0.514401i −0.975446 0.220240i \(-0.929316\pi\)
0.678456 + 0.734641i \(0.262649\pi\)
\(132\) 0.505639 + 0.875793i 0.0440102 + 0.0762280i
\(133\) 0 0
\(134\) −5.75829 + 9.97364i −0.497440 + 0.861592i
\(135\) −0.926861 + 1.60537i −0.0797715 + 0.138168i
\(136\) 12.3031 1.05498
\(137\) −14.0756 −1.20256 −0.601279 0.799039i \(-0.705342\pi\)
−0.601279 + 0.799039i \(0.705342\pi\)
\(138\) −2.86801 + 4.96754i −0.244141 + 0.422865i
\(139\) −8.64313 + 14.9703i −0.733101 + 1.26977i 0.222451 + 0.974944i \(0.428594\pi\)
−0.955552 + 0.294824i \(0.904739\pi\)
\(140\) 0 0
\(141\) −0.494165 0.855919i −0.0416162 0.0720814i
\(142\) 5.02213 8.69859i 0.421448 0.729969i
\(143\) −4.36321 + 3.32087i −0.364870 + 0.277705i
\(144\) 3.44280 + 5.96310i 0.286900 + 0.496925i
\(145\) 4.06238 0.337363
\(146\) −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 \(0.585858\pi\)
\(150\) −15.0442 −1.22835
\(151\) −7.89873 13.6810i −0.642789 1.11334i −0.984807 0.173650i \(-0.944444\pi\)
0.342018 0.939693i \(-0.388890\pi\)
\(152\) −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
\(156\) 1.90787 1.45209i 0.152751 0.116260i
\(157\) 1.89176 + 3.27662i 0.150979 + 0.261503i 0.931587 0.363517i \(-0.118424\pi\)
−0.780609 + 0.625020i \(0.785091\pi\)
\(158\) −11.3771 + 19.7058i −0.905117 + 1.56771i
\(159\) −17.5344 −1.39057
\(160\) −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 \(0.854735\pi\)
\(164\) −0.211961 0.367127i −0.0165514 0.0286678i
\(165\) −1.90579 −0.148365
\(166\) −15.3935 −1.19477
\(167\) −6.32605 10.9570i −0.489524 0.847881i 0.510403 0.859935i \(-0.329496\pi\)
−0.999927 + 0.0120542i \(0.996163\pi\)
\(168\) 0 0
\(169\) 9.11992 + 9.26429i 0.701532 + 0.712638i
\(170\) 2.14886 3.72193i 0.164810 0.285459i
\(171\) −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 0.997432 0.0716259i \(-0.0228188\pi\)
−0.560746 + 0.827988i \(0.689485\pi\)
\(174\) 22.2868 1.68956
\(175\) 0 0
\(176\) 3.44280 5.96310i 0.259510 0.449485i
\(177\) −12.6251 + 21.8672i −0.948958 + 1.64364i
\(178\) −25.0699 −1.87907
\(179\) 1.09225 1.89184i 0.0816389 0.141403i −0.822315 0.569032i \(-0.807318\pi\)
0.903954 + 0.427630i \(0.140651\pi\)
\(180\) 0.280329 0.0208945
\(181\) −11.5981 −0.862081 −0.431041 0.902333i \(-0.641853\pi\)
−0.431041 + 0.902333i \(0.641853\pi\)
\(182\) 0 0
\(183\) −5.27337 −0.389819
\(184\) 4.55180 0.335563
\(185\) −0.415264 + 0.719258i −0.0305308 + 0.0528809i
\(186\) −19.6803 −1.44303
\(187\) −3.64590 + 6.31488i −0.266614 + 0.461790i
\(188\) 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 \(0.863538\pi\)
\(194\) −0.740517 + 1.28261i −0.0531660 + 0.0920863i
\(195\) 0.572172 + 4.48200i 0.0409741 + 0.320962i
\(196\) 0 0
\(197\) −10.0032 17.3260i −0.712696 1.23442i −0.963842 0.266476i \(-0.914141\pi\)
0.251146 0.967949i \(-0.419193\pi\)
\(198\) −3.51717 −0.249954
\(199\) −1.84885 −0.131062 −0.0655309 0.997851i \(-0.520874\pi\)
−0.0655309 + 0.997851i \(0.520874\pi\)
\(200\) 5.96913 + 10.3388i 0.422081 + 0.731066i
\(201\) −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
\(205\) 0.798895 0.0557972
\(206\) 0.402003 0.696289i 0.0280088 0.0485127i
\(207\) −1.34888 2.33633i −0.0937539 0.162386i
\(208\) −15.0575 6.30641i −1.04405 0.437271i
\(209\) 2.56085 0.177138
\(210\) 0 0
\(211\) 8.08474 + 14.0032i 0.556576 + 0.964019i 0.997779 + 0.0666110i \(0.0212187\pi\)
−0.441203 + 0.897407i \(0.645448\pi\)
\(212\) −1.28960 2.23366i −0.0885702 0.153408i
\(213\) 7.02150 + 12.1616i 0.481105 + 0.833299i
\(214\) 29.3850 2.00871
\(215\) 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
\(219\) 34.8085 2.35214
\(220\) −0.140165 0.242772i −0.00944989 0.0163677i
\(221\) 15.9458 + 6.67844i 1.07263 + 0.449241i
\(222\) −2.27820 + 3.94595i −0.152902 + 0.264835i
\(223\) 6.21589 + 10.7662i 0.416247 + 0.720961i 0.995558 0.0941455i \(-0.0300119\pi\)
−0.579312 + 0.815106i \(0.696679\pi\)
\(224\) 0 0
\(225\) 3.53779 6.12763i 0.235853 0.408509i
\(226\) 3.91568 6.78216i 0.260467 0.451142i
\(227\) 1.23497 0.0819681 0.0409841 0.999160i \(-0.486951\pi\)
0.0409841 + 0.999160i \(0.486951\pi\)
\(228\) −1.11976 −0.0741581
\(229\) −3.27757 + 5.67692i −0.216588 + 0.375141i −0.953763 0.300561i \(-0.902826\pi\)
0.737175 + 0.675702i \(0.236159\pi\)
\(230\) 0.795020 1.37702i 0.0524221 0.0907977i
\(231\) 0 0
\(232\) −8.84282 15.3162i −0.580559 1.00556i
\(233\) −3.14944 + 5.45498i −0.206326 + 0.357368i −0.950555 0.310558i \(-0.899484\pi\)
0.744228 + 0.667925i \(0.232818\pi\)
\(234\) 1.05596 + 8.27162i 0.0690300 + 0.540732i
\(235\) 0.136984 + 0.237263i 0.00893584 + 0.0154773i
\(236\) −3.71413 −0.241769
\(237\) −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
\(241\) 22.2968 1.43626 0.718131 0.695908i \(-0.244998\pi\)
0.718131 + 0.695908i \(0.244998\pi\)
\(242\) −6.60567 11.4414i −0.424628 0.735478i
\(243\) −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
\(247\) −0.768841 6.02256i −0.0489202 0.383206i
\(248\) 7.80861 + 13.5249i 0.495847 + 0.858833i
\(249\) 10.7609 18.6385i 0.681947 1.18117i
\(250\) 8.65194 0.547197
\(251\) 3.47657 6.02160i 0.219439 0.380080i −0.735197 0.677853i \(-0.762910\pi\)
0.954637 + 0.297773i \(0.0962438\pi\)
\(252\) 0 0
\(253\) −1.34888 + 2.33633i −0.0848036 + 0.146884i
\(254\) −6.84600 11.8576i −0.429556 0.744013i
\(255\) 3.00435 + 5.20368i 0.188139 + 0.325867i
\(256\) 7.33206 0.458254
\(257\) 21.1551 1.31962 0.659811 0.751432i \(-0.270636\pi\)
0.659811 + 0.751432i \(0.270636\pi\)
\(258\) 18.6888 + 32.3700i 1.16352 + 2.01527i
\(259\) 0 0
\(260\) −0.528865 + 0.402523i −0.0327988 + 0.0249634i
\(261\) −5.24097 + 9.07763i −0.324408 + 0.561891i
\(262\) 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
\(268\) 1.18421 2.05111i 0.0723371 0.125292i
\(269\) −5.83039 −0.355485 −0.177743 0.984077i \(-0.556879\pi\)
−0.177743 + 0.984077i \(0.556879\pi\)
\(270\) 1.40955 2.44141i 0.0857823 0.148579i
\(271\) 18.4299 1.11954 0.559769 0.828648i \(-0.310890\pi\)
0.559769 + 0.828648i \(0.310890\pi\)
\(272\) −21.7093 −1.31632
\(273\) 0 0
\(274\) 21.4058 1.29317
\(275\) −7.07558 −0.426673
\(276\) 0.589815 1.02159i 0.0355027 0.0614925i
\(277\) −6.18307 −0.371505 −0.185752 0.982597i \(-0.559472\pi\)
−0.185752 + 0.982597i \(0.559472\pi\)
\(278\) 13.1442 22.7665i 0.788340 1.36544i
\(279\) 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 −0.510835 0.859679i \(-0.670664\pi\)
0.999921 + 0.0125564i \(0.00399694\pi\)
\(284\) −1.03282 + 1.78889i −0.0612864 + 0.106151i
\(285\) 1.05512 1.82751i 0.0624996 0.108253i
\(286\) 6.63545 5.05029i 0.392362 0.298630i
\(287\) 0 0
\(288\) −1.33353 2.30973i −0.0785787 0.136102i
\(289\) 5.99003 0.352355
\(290\) −6.17797 −0.362783
\(291\) −1.03533 1.79324i −0.0606919 0.105121i
\(292\) 2.56005 + 4.43414i 0.149816 + 0.259489i
\(293\) −15.3086 + 26.5152i −0.894335 + 1.54903i −0.0597104 + 0.998216i \(0.519018\pi\)
−0.834625 + 0.550819i \(0.814316\pi\)
\(294\) 0 0
\(295\) 3.49970 6.06166i 0.203760 0.352923i
\(296\) 3.61571 0.210159
\(297\) −2.39153 + 4.14225i −0.138771 + 0.240358i
\(298\) −13.0218 22.5544i −0.754331 1.30654i
\(299\) 5.89952 + 2.47084i 0.341178 + 0.142893i
\(300\) 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
\(304\) 3.81212 + 6.60278i 0.218640 + 0.378696i
\(305\) 1.46179 0.0837019
\(306\) 5.54458 + 9.60350i 0.316963 + 0.548995i
\(307\) −9.96020 −0.568459 −0.284229 0.958756i \(-0.591738\pi\)
−0.284229 + 0.958756i \(0.591738\pi\)
\(308\) 0 0
\(309\) 0.562044 + 0.973489i 0.0319736 + 0.0553799i
\(310\) 5.45543 0.309847
\(311\) −13.8734 24.0294i −0.786687 1.36258i −0.927986 0.372615i \(-0.878461\pi\)
0.141299 0.989967i \(-0.454872\pi\)
\(312\) 15.6528 11.9134i 0.886164 0.674466i
\(313\) 8.26136 14.3091i 0.466960 0.808798i −0.532328 0.846538i \(-0.678683\pi\)
0.999288 + 0.0377401i \(0.0120159\pi\)
\(314\) −2.87693 4.98300i −0.162355 0.281207i
\(315\) 0 0
\(316\) 2.33975 4.05256i 0.131621 0.227974i
\(317\) −11.8396 + 20.5069i −0.664980 + 1.15178i 0.314310 + 0.949320i \(0.398227\pi\)
−0.979291 + 0.202459i \(0.935107\pi\)
\(318\) 26.6659 1.49535
\(319\) 10.4819 0.586876
\(320\) −1.88261 + 3.26078i −0.105241 + 0.182283i
\(321\) −20.5417 + 35.5793i −1.14653 + 1.98584i
\(322\) 0 0
\(323\) −4.03701 6.99230i −0.224625 0.389062i
\(324\) 1.75916 3.04696i 0.0977312 0.169275i
\(325\) 2.12429 + 16.6402i 0.117834 + 0.923033i
\(326\) 1.30445 + 2.25938i 0.0722470 + 0.125136i
\(327\) 12.1883 0.674014
\(328\) −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 \(0.903464\pi\)
\(332\) 3.16573 0.173742
\(333\) −1.07148 1.85586i −0.0587168 0.101700i
\(334\) 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 \(0.569148\pi\)
\(338\) −13.8693 14.0889i −0.754392 0.766334i
\(339\) 5.47456 + 9.48221i 0.297337 + 0.515003i
\(340\) −0.441920 + 0.765427i −0.0239665 + 0.0415111i
\(341\) −9.25603 −0.501242
\(342\) 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
\(346\) −8.73488 15.1292i −0.469590 0.813353i
\(347\) 7.13571 0.383065 0.191533 0.981486i \(-0.438654\pi\)
0.191533 + 0.981486i \(0.438654\pi\)
\(348\) −4.58335 −0.245694
\(349\) 0.688402 + 1.19235i 0.0368493 + 0.0638249i 0.883862 0.467748i \(-0.154935\pi\)
−0.847013 + 0.531573i \(0.821601\pi\)
\(350\) 0 0
\(351\) 10.4597 + 4.38073i 0.558296 + 0.233826i
\(352\) −1.33353 + 2.30973i −0.0710771 + 0.123109i
\(353\) 0.346608 0.600342i 0.0184481 0.0319530i −0.856654 0.515891i \(-0.827461\pi\)
0.875102 + 0.483938i \(0.160794\pi\)
\(354\) 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
\(359\) 2.90182 5.02611i 0.153152 0.265268i −0.779232 0.626735i \(-0.784391\pi\)
0.932385 + 0.361467i \(0.117724\pi\)
\(360\) 2.29991 0.121216
\(361\) 8.08222 13.9988i 0.425380 0.736780i
\(362\) 17.6381 0.927038
\(363\) 18.4709 0.969472
\(364\) 0 0
\(365\) −9.64902 −0.505053
\(366\) 8.01960 0.419191
\(367\) 3.67578 6.36664i 0.191874 0.332336i −0.753997 0.656878i \(-0.771877\pi\)
0.945871 + 0.324542i \(0.105210\pi\)
\(368\) −8.03187 −0.418690
\(369\) −1.03067 + 1.78518i −0.0536546 + 0.0929325i
\(370\) 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
\(376\) 0.596361 1.03293i 0.0307550 0.0532692i
\(377\) −3.14698 24.6512i −0.162078 1.26960i
\(378\) 0 0
\(379\) 2.42550 + 4.20110i 0.124590 + 0.215796i 0.921573 0.388206i \(-0.126905\pi\)
−0.796983 + 0.604002i \(0.793572\pi\)
\(380\) 0.310401 0.0159232
\(381\) 19.1429 0.980723
\(382\) 13.5039 + 23.3894i 0.690918 + 1.19671i
\(383\) −11.4103 19.7631i −0.583037 1.00985i −0.995117 0.0987019i \(-0.968531\pi\)
0.412080 0.911148i \(-0.364802\pi\)
\(384\) −14.0571 + 24.3476i −0.717349 + 1.24249i
\(385\) 0 0
\(386\) 17.2136 29.8148i 0.876147 1.51753i
\(387\) −17.5795 −0.893615
\(388\) 0.152290 0.263773i 0.00773134 0.0133911i
\(389\) 10.1561 + 17.5908i 0.514933 + 0.891891i 0.999850 + 0.0173304i \(0.00551672\pi\)
−0.484916 + 0.874561i \(0.661150\pi\)
\(390\) −0.870144 6.81610i −0.0440615 0.345147i
\(391\) 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
\(395\) 4.40933 + 7.63719i 0.221858 + 0.384268i
\(396\) 0.723317 0.0363481
\(397\) −17.0689 29.5641i −0.856662 1.48378i −0.875095 0.483952i \(-0.839201\pi\)
0.0184326 0.999830i \(-0.494132\pi\)
\(398\) 2.81169 0.140937
\(399\) 0 0
\(400\) −10.5328 18.2434i −0.526640 0.912168i
\(401\) −3.02596 −0.151109 −0.0755547 0.997142i \(-0.524073\pi\)
−0.0755547 + 0.997142i \(0.524073\pi\)
\(402\) 12.2433 + 21.2061i 0.610642 + 1.05766i
\(403\) 2.77893 + 21.7682i 0.138428 + 1.08435i
\(404\) 0.459782 0.796365i 0.0228750 0.0396207i
\(405\) 3.31520 + 5.74209i 0.164734 + 0.285327i
\(406\) 0 0
\(407\) −1.07148 + 1.85586i −0.0531114 + 0.0919916i
\(408\) 13.0795 22.6543i 0.647530 1.12155i
\(409\) −5.38325 −0.266184 −0.133092 0.991104i \(-0.542491\pi\)
−0.133092 + 0.991104i \(0.542491\pi\)
\(410\) −1.21494 −0.0600015
\(411\) −14.9638 + 25.9181i −0.738111 + 1.27845i
\(412\) −0.0826731 + 0.143194i −0.00407301 + 0.00705466i
\(413\) 0 0
\(414\) 2.05135 + 3.55304i 0.100818 + 0.174622i
\(415\) −2.98296 + 5.16664i −0.146428 + 0.253620i
\(416\) 5.83235 + 2.44271i 0.285954 + 0.119764i
\(417\) 18.3771 + 31.8301i 0.899932 + 1.55873i
\(418\) −3.89447 −0.190485
\(419\) 2.94117 + 5.09426i 0.143686 + 0.248871i 0.928882 0.370376i \(-0.120771\pi\)
−0.785196 + 0.619247i \(0.787438\pi\)
\(420\) 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
\(423\) −0.706904 −0.0343708
\(424\) −10.5803 18.3257i −0.513826 0.889973i
\(425\) 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
\(429\) 1.47634 + 11.5646i 0.0712786 + 0.558346i
\(430\) −5.18059 8.97305i −0.249830 0.432719i
\(431\) −4.19294 + 7.26238i −0.201967 + 0.349817i −0.949162 0.314788i \(-0.898067\pi\)
0.747195 + 0.664605i \(0.231400\pi\)
\(432\) −14.2403 −0.685135
\(433\) −13.7996 + 23.9017i −0.663168 + 1.14864i 0.316611 + 0.948556i \(0.397455\pi\)
−0.979779 + 0.200085i \(0.935878\pi\)
\(434\) 0 0
\(435\) 4.31874 7.48028i 0.207068 0.358652i
\(436\) 0.896409 + 1.55263i 0.0429302 + 0.0743573i
\(437\) −1.49358 2.58696i −0.0714478 0.123751i
\(438\) −52.9359 −2.52937
\(439\) −31.1737 −1.48784 −0.743921 0.668268i \(-0.767036\pi\)
−0.743921 + 0.668268i \(0.767036\pi\)
\(440\) −1.14996 1.99178i −0.0548221 0.0949546i
\(441\) 0 0
\(442\) −24.2500 10.1564i −1.15345 0.483090i
\(443\) 11.7941 20.4281i 0.560357 0.970566i −0.437109 0.899409i \(-0.643997\pi\)
0.997465 0.0711573i \(-0.0226692\pi\)
\(444\) 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 −0.897445 0.441125i \(-0.854579\pi\)
0.830749 + 0.556648i \(0.187913\pi\)
\(450\) −5.38018 + 9.31874i −0.253624 + 0.439289i
\(451\) 2.06134 0.0970649
\(452\) −0.805272 + 1.39477i −0.0378768 + 0.0656046i
\(453\) −33.5887 −1.57814
\(454\) −1.87812 −0.0881444
\(455\) 0 0
\(456\) −9.18691 −0.430217
\(457\) −37.7432 −1.76555 −0.882776 0.469795i \(-0.844328\pi\)
−0.882776 + 0.469795i \(0.844328\pi\)
\(458\) 4.98444 8.63330i 0.232908 0.403408i
\(459\) 15.0803 0.703890
\(460\) −0.163498 + 0.283188i −0.00762315 + 0.0132037i
\(461\) 17.3293 30.0152i 0.807106 1.39795i −0.107754 0.994178i \(-0.534366\pi\)
0.914860 0.403771i \(-0.132301\pi\)
\(462\) 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
\(467\) 3.31392 5.73987i 0.153350 0.265610i −0.779107 0.626891i \(-0.784327\pi\)
0.932457 + 0.361281i \(0.117661\pi\)
\(468\) −0.217161 1.70108i −0.0100383 0.0786326i
\(469\) 0 0
\(470\) −0.208321 0.360823i −0.00960915 0.0166435i
\(471\) 8.04455 0.370673
\(472\) −30.4720 −1.40259
\(473\) 8.78973 + 15.2243i 0.404152 + 0.700012i
\(474\) 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
\(478\) 28.7720 1.31600
\(479\) −8.72630 + 15.1144i −0.398715 + 0.690594i −0.993568 0.113240i \(-0.963877\pi\)
0.594853 + 0.803835i \(0.297210\pi\)
\(480\) 1.09887 + 1.90330i 0.0501564 + 0.0868734i
\(481\) 4.68626 + 1.96271i 0.213675 + 0.0894917i
\(482\) −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
\(486\) 11.0131 + 19.0752i 0.499563 + 0.865269i
\(487\) −35.5138 −1.60928 −0.804641 0.593762i \(-0.797642\pi\)
−0.804641 + 0.593762i \(0.797642\pi\)
\(488\) −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 0.977137 + 0.212611i \(0.0681966\pi\)
−0.304442 + 0.952531i \(0.598470\pi\)
\(492\) −0.901347 −0.0406359
\(493\) −16.5241 28.6205i −0.744207 1.28900i
\(494\) 1.16923 + 9.15895i 0.0526063 + 0.412081i
\(495\) −0.681558 + 1.18049i −0.0306338 + 0.0530592i
\(496\) −13.7787 23.8653i −0.618680 1.07159i
\(497\) 0 0
\(498\) −16.3649 + 28.3449i −0.733331 + 1.27017i
\(499\) 3.75483 6.50355i 0.168089 0.291139i −0.769659 0.638455i \(-0.779574\pi\)
0.937748 + 0.347316i \(0.112907\pi\)
\(500\) −1.77930 −0.0795726
\(501\) −26.9010 −1.20185
\(502\) −5.28708 + 9.15750i −0.235974 + 0.408719i
\(503\) 0.492171 0.852466i 0.0219448 0.0380096i −0.854844 0.518884i \(-0.826348\pi\)
0.876789 + 0.480875i \(0.159681\pi\)
\(504\) 0 0
\(505\) 0.866474 + 1.50078i 0.0385576 + 0.0667837i
\(506\) 2.05135 3.55304i 0.0911934 0.157952i
\(507\) 26.7543 6.94407i 1.18820 0.308397i
\(508\) 1.40790 + 2.43856i 0.0624655 + 0.108193i
\(509\) −12.9792 −0.575291 −0.287646 0.957737i \(-0.592873\pi\)
−0.287646 + 0.957737i \(0.592873\pi\)
\(510\) −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
\(514\) −32.1722 −1.41905
\(515\) −0.155800 0.269854i −0.00686538 0.0118912i
\(516\) −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
\(520\) −4.33899 + 3.30244i −0.190277 + 0.144822i
\(521\) −9.70730 16.8135i −0.425285 0.736614i 0.571162 0.820837i \(-0.306493\pi\)
−0.996447 + 0.0842226i \(0.973159\pi\)
\(522\) 7.97033 13.8050i 0.348852 0.604229i
\(523\) −27.2719 −1.19252 −0.596259 0.802792i \(-0.703347\pi\)
−0.596259 + 0.802792i \(0.703347\pi\)
\(524\) −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
\(528\) −7.32011 12.6788i −0.318567 0.551774i
\(529\) −19.8531 −0.863179
\(530\) −7.39187 −0.321082
\(531\) 9.03008 + 15.6406i 0.391872 + 0.678742i
\(532\) 0 0
\(533\) −0.618874 4.84783i −0.0268064 0.209983i
\(534\) −26.6520 + 46.1626i −1.15334 + 1.99765i
\(535\) 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
\(541\) 15.0495 26.0665i 0.647029 1.12069i −0.336799 0.941576i \(-0.609344\pi\)
0.983829 0.179111i \(-0.0573223\pi\)
\(542\) −28.0278 −1.20389
\(543\) −12.3300 + 21.3562i −0.529132 + 0.916483i
\(544\) 8.40885 0.360526
\(545\) −3.37863 −0.144724
\(546\) 0 0
\(547\) −26.1451 −1.11788 −0.558942 0.829207i \(-0.688793\pi\)
−0.558942 + 0.829207i \(0.688793\pi\)
\(548\) −4.40216 −0.188051
\(549\) −1.88589 + 3.26646i −0.0804878 + 0.139409i
\(550\) 10.7604 0.458823
\(551\) −5.80319 + 10.0514i −0.247224 + 0.428205i
\(552\) 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 \(0.290522\pi\)
\(558\) −7.03817 + 12.1905i −0.297949 + 0.516063i
\(559\) 33.1652 25.2423i 1.40274 1.06764i
\(560\) 0 0
\(561\) 7.75195 + 13.4268i 0.327287 + 0.566878i
\(562\) 8.57790 0.361837
\(563\) 31.6549 1.33410 0.667048 0.745015i \(-0.267558\pi\)
0.667048 + 0.745015i \(0.267558\pi\)
\(564\) −0.154551 0.267690i −0.00650777 0.0112718i
\(565\) −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
\(569\) −26.1111 −1.09463 −0.547317 0.836925i \(-0.684351\pi\)
−0.547317 + 0.836925i \(0.684351\pi\)
\(570\) −1.60459 + 2.77923i −0.0672089 + 0.116409i
\(571\) −6.65205 11.5217i −0.278380 0.482168i 0.692602 0.721320i \(-0.256464\pi\)
−0.970982 + 0.239152i \(0.923131\pi\)
\(572\) −1.36460 + 1.03861i −0.0570569 + 0.0434264i
\(573\) −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
\(577\) −8.38564 14.5244i −0.349099 0.604657i 0.636991 0.770871i \(-0.280179\pi\)
−0.986090 + 0.166214i \(0.946846\pi\)
\(578\) −9.10948 −0.378905
\(579\) 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
\(583\) 12.5415 0.519417
\(584\) 21.0036 + 36.3792i 0.869133 + 1.50538i
\(585\) 2.98088 + 1.24846i 0.123244 + 0.0516173i
\(586\) 23.2808 40.3236i 0.961723 1.66575i
\(587\) −5.03261 8.71673i −0.207718 0.359778i 0.743277 0.668983i \(-0.233270\pi\)
−0.950995 + 0.309205i \(0.899937\pi\)
\(588\) 0 0
\(589\) 5.12448 8.87587i 0.211151 0.365724i
\(590\) −5.32225 + 9.21841i −0.219114 + 0.379516i
\(591\) −42.5377 −1.74977
\(592\) −6.38009 −0.262220
\(593\) 19.7161 34.1493i 0.809643 1.40234i −0.103468 0.994633i \(-0.532994\pi\)
0.913111 0.407710i \(-0.133673\pi\)
\(594\) 3.63697 6.29942i 0.149227 0.258468i
\(595\) 0 0
\(596\) 2.67797 + 4.63838i 0.109694 + 0.189995i
\(597\) −1.96553 + 3.40439i −0.0804436 + 0.139332i
\(598\) −8.97183 3.75759i −0.366886 0.153659i
\(599\) −6.88601 11.9269i −0.281355 0.487321i 0.690364 0.723462i \(-0.257450\pi\)
−0.971719 + 0.236142i \(0.924117\pi\)
\(600\) 25.3833 1.03627
\(601\) 16.6312 + 28.8060i 0.678399 + 1.17502i 0.975463 + 0.220164i \(0.0706592\pi\)
−0.297064 + 0.954858i \(0.596007\pi\)
\(602\) 0 0
\(603\) −11.5166 −0.468991
\(604\) −2.47034 4.27876i −0.100517 0.174100i
\(605\) −5.12019 −0.208165
\(606\) 4.75360 + 8.23348i 0.193102 + 0.334462i
\(607\) 21.9824 + 38.0747i 0.892240 + 1.54540i 0.837184 + 0.546921i \(0.184200\pi\)
0.0550554 + 0.998483i \(0.482466\pi\)
\(608\) −1.47658 2.55751i −0.0598831 0.103721i
\(609\) 0 0
\(610\) −2.22305 −0.0900088
\(611\) 1.33364 1.01504i 0.0539531 0.0410641i
\(612\) −1.14026 1.97499i −0.0460923 0.0798342i
\(613\) −1.35045 + 2.33906i −0.0545443 + 0.0944736i −0.892008 0.452019i \(-0.850704\pi\)
0.837464 + 0.546492i \(0.184037\pi\)
\(614\) 15.1472 0.611292
\(615\) 0.849310 1.47105i 0.0342475 0.0593184i
\(616\) 0 0
\(617\) −3.00208 + 5.19975i −0.120859 + 0.209334i −0.920107 0.391668i \(-0.871898\pi\)
0.799248 + 0.601002i \(0.205232\pi\)
\(618\) −0.854742 1.48046i −0.0343828 0.0595527i
\(619\) −6.68204 11.5736i −0.268574 0.465184i 0.699920 0.714221i \(-0.253219\pi\)
−0.968494 + 0.249038i \(0.919886\pi\)
\(620\) −1.12193 −0.0450576
\(621\) 5.57932 0.223890
\(622\) 21.0983 + 36.5433i 0.845963 + 1.46525i
\(623\) 0 0
\(624\) −27.6201 + 21.0218i −1.10569 + 0.841547i
\(625\) −9.95497 + 17.2425i −0.398199 + 0.689701i
\(626\) −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 0.111192 + 0.993799i \(0.464533\pi\)
−0.916251 + 0.400604i \(0.868800\pi\)
\(632\) 19.1961 33.2486i 0.763579 1.32256i
\(633\) 34.3797 1.36647
\(634\) 18.0054 31.1863i 0.715086 1.23857i
\(635\) −5.30648 −0.210581
\(636\) −5.48393 −0.217452
\(637\) 0 0
\(638\) −15.9407 −0.631097
\(639\) 10.0443 0.397345
\(640\) 3.89667 6.74923i 0.154029 0.266787i
\(641\) 10.2198 0.403658 0.201829 0.979421i \(-0.435311\pi\)
0.201829 + 0.979421i \(0.435311\pi\)
\(642\) 31.2393 54.1081i 1.23292 2.13548i
\(643\) 15.9014 27.5420i 0.627088 1.08615i −0.361045 0.932548i \(-0.617580\pi\)
0.988133 0.153600i \(-0.0490868\pi\)
\(644\) 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 \(0.404091\pi\)
−0.975395 + 0.220465i \(0.929243\pi\)
\(648\) 14.4328 24.9983i 0.566972 0.982025i
\(649\) 9.03008 15.6406i 0.354462 0.613946i
\(650\) −3.23057 25.3060i −0.126713 0.992582i
\(651\) 0 0
\(652\) −0.268265 0.464649i −0.0105061 0.0181970i
\(653\) 10.1180 0.395947 0.197974 0.980207i \(-0.436564\pi\)
0.197974 + 0.980207i \(0.436564\pi\)
\(654\) −18.5356 −0.724800
\(655\) −2.00346 3.47009i −0.0782816 0.135588i
\(656\) 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 −0.298637 0.954367i \(-0.596532\pi\)
0.975824 0.218556i \(-0.0701345\pi\)
\(660\) −0.596039 −0.0232008
\(661\) −8.28076 + 14.3427i −0.322084 + 0.557866i −0.980918 0.194422i \(-0.937717\pi\)
0.658834 + 0.752289i \(0.271050\pi\)
\(662\) 6.04666 + 10.4731i 0.235010 + 0.407050i
\(663\) 29.2494 22.2620i 1.13595 0.864583i
\(664\) 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
\(668\) −1.97848 3.42683i −0.0765498 0.132588i
\(669\) 26.4326 1.02194
\(670\) −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 0.914713 + 0.404104i \(0.132417\pi\)
−0.107393 + 0.994217i \(0.534250\pi\)
\(674\) 12.0343 0.463543
\(675\) 7.31659 + 12.6727i 0.281616 + 0.487772i
\(676\) 2.85227 + 2.89742i 0.109703 + 0.111439i
\(677\) −15.7858 + 27.3417i −0.606696 + 1.05083i 0.385085 + 0.922881i \(0.374172\pi\)
−0.991781 + 0.127947i \(0.959161\pi\)
\(678\) −8.32556 14.4203i −0.319741 0.553808i
\(679\) 0 0
\(680\) −3.62566 + 6.27983i −0.139038 + 0.240820i
\(681\) 1.31291 2.27402i 0.0503107 0.0871408i
\(682\) 14.0763 0.539011
\(683\) −26.2676 −1.00510 −0.502551 0.864548i \(-0.667605\pi\)
−0.502551 + 0.864548i \(0.667605\pi\)
\(684\) −0.400455 + 0.693609i −0.0153118 + 0.0265208i
\(685\) 4.14801 7.18457i 0.158487 0.274508i
\(686\) 0 0
\(687\) 6.96880 + 12.0703i 0.265876 + 0.460512i
\(688\) −26.1690 + 45.3261i −0.997686 + 1.72804i
\(689\) −3.76532 29.4949i −0.143447 1.12367i
\(690\) −1.69038 2.92783i −0.0643517 0.111460i
\(691\) −6.10095 −0.232091 −0.116046 0.993244i \(-0.537022\pi\)
−0.116046 + 0.993244i \(0.537022\pi\)
\(692\) 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
\(696\) −37.6034 −1.42535
\(697\) −3.24957 5.62842i −0.123086 0.213192i
\(698\) −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 \(0.626993\pi\)
\(702\) −15.9068 6.66210i −0.600363 0.251445i
\(703\) −1.18642 2.05495i −0.0447468 0.0775038i
\(704\) −4.85760 + 8.41361i −0.183078 + 0.317100i
\(705\) 0.582513 0.0219387
\(706\) −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 \(0.532627\pi\)
\(710\) 2.96000 + 5.12687i 0.111087 + 0.192408i
\(711\) −22.7543 −0.853353
\(712\) 42.2992 1.58523
\(713\) 5.39847 + 9.35042i 0.202174 + 0.350176i
\(714\) 0 0
\(715\) −0.409246 3.20575i −0.0153050 0.119888i
\(716\) 0.341605 0.591677i 0.0127664 0.0221120i
\(717\) −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 \(0.00964171\pi\)
−0.473542 + 0.880771i \(0.657025\pi\)
\(720\) −4.05831 −0.151244
\(721\) 0 0
\(722\) −12.2912 + 21.2890i −0.457432 + 0.792295i
\(723\) 23.7038 41.0562i 0.881555 1.52690i
\(724\) −3.62733 −0.134809
\(725\) 16.0341 27.7719i 0.595492 1.03142i
\(726\) −28.0901 −1.04252
\(727\) −19.5116 −0.723646 −0.361823 0.932247i \(-0.617845\pi\)
−0.361823 + 0.932247i \(0.617845\pi\)
\(728\) 0 0
\(729\) 2.95370 0.109396
\(730\) 14.6740 0.543108
\(731\) 27.7128 48.0000i 1.02500 1.77535i
\(732\) −1.64926 −0.0609582
\(733\) −10.1833 + 17.6380i −0.376129 + 0.651475i −0.990495 0.137546i \(-0.956078\pi\)
0.614366 + 0.789021i \(0.289412\pi\)
\(734\) −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 \(0.105282\pi\)
\(740\) −0.129874 + 0.224949i −0.00477428 + 0.00826929i
\(741\) −11.9070 4.98691i −0.437415 0.183199i
\(742\) 0 0
\(743\) 8.70470 + 15.0770i 0.319344 + 0.553121i 0.980351 0.197259i \(-0.0632040\pi\)
−0.661007 + 0.750380i \(0.729871\pi\)
\(744\) 33.2055 1.21737
\(745\) −10.0934 −0.369795
\(746\) 13.9902 + 24.2318i 0.512219 + 0.887189i
\(747\) −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
\(751\) −1.81525 −0.0662395 −0.0331197 0.999451i \(-0.510544\pi\)
−0.0331197 + 0.999451i \(0.510544\pi\)
\(752\) −1.05231 + 1.82265i −0.0383737 + 0.0664652i
\(753\) −7.39193 12.8032i −0.269377 0.466575i
\(754\) 4.78584 + 37.4889i 0.174290 + 1.36527i
\(755\) 9.31088 0.338858
\(756\) 0 0
\(757\) −26.7814 46.3867i −0.973385 1.68595i −0.685165 0.728388i \(-0.740270\pi\)
−0.288220 0.957564i \(-0.593063\pi\)
\(758\) −3.68864 6.38892i −0.133978 0.232056i
\(759\) 2.86801 + 4.96754i 0.104102 + 0.180310i
\(760\) 2.54664 0.0923762
\(761\) −1.84083 3.18841i −0.0667300 0.115580i 0.830730 0.556675i \(-0.187923\pi\)
−0.897460 + 0.441096i \(0.854590\pi\)
\(762\) −29.1121 −1.05462
\(763\) 0 0
\(764\) −2.77711 4.81010i −0.100472 0.174023i
\(765\) 4.29772 0.155384
\(766\) 17.3524 + 30.0553i 0.626968 + 1.08594i
\(767\) −39.4942 16.5410i −1.42605 0.597262i
\(768\) 7.79476 13.5009i 0.281269 0.487172i
\(769\) −2.61897 4.53619i −0.0944424 0.163579i 0.814933 0.579555i \(-0.196773\pi\)
−0.909376 + 0.415976i \(0.863440\pi\)
\(770\) 0 0
\(771\) 22.4902 38.9541i 0.809963 1.40290i
\(772\) −3.54002 + 6.13150i −0.127408 + 0.220677i
\(773\) −40.6138 −1.46078 −0.730388 0.683032i \(-0.760661\pi\)
−0.730388 + 0.683032i \(0.760661\pi\)
\(774\) 26.7344 0.960948
\(775\) −14.1588 + 24.5238i −0.508601 + 0.880922i
\(776\) 1.24944 2.16409i 0.0448522 0.0776862i
\(777\) 0 0
\(778\) −15.4451 26.7517i −0.553733 0.959094i
\(779\) −1.14124 + 1.97668i −0.0408890 + 0.0708219i
\(780\) 0.178948 + 1.40175i 0.00640736 + 0.0501908i
\(781\) −5.02213 8.69859i −0.179706 0.311260i
\(782\) −12.9352 −0.462563
\(783\) −10.8390