Properties

Label 637.2.h.m.471.3
Level $637$
Weight $2$
Character 637.471
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.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 471.3
Root \(0.141226 - 0.244611i\) of defining polynomial
Character \(\chi\) \(=\) 637.471
Dual form 637.2.h.m.165.3

$q$-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 \(0.377020\pi\)
−0.990596 + 0.136816i \(0.956313\pi\)
\(4\) 0.312752 0.156376
\(5\) 0.294696 0.510428i 0.131792 0.228270i −0.792575 0.609774i \(-0.791260\pi\)
0.924367 + 0.381504i \(0.124594\pi\)
\(6\) 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 \(-0.697516\pi\)
−0.581454 + 0.813579i \(0.697516\pi\)
\(18\) 1.15638 + 2.00290i 0.272560 + 0.472088i
\(19\) 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
\(23\) 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 \(-0.982598\pi\)
0.451931 0.892053i \(-0.350735\pi\)
\(32\) 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 0.914082 0.405528i \(-0.132912\pi\)
−0.808239 + 0.588855i \(0.799579\pi\)
\(42\) 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 −0.882478 0.470353i \(-0.844127\pi\)
0.848577 + 0.529072i \(0.177460\pi\)
\(48\) 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 \(-0.218736\pi\)
0.773038 + 0.634359i \(0.218736\pi\)
\(60\) 0.195966 + 0.339422i 0.0252991 + 0.0438193i
\(61\) 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
\(65\) −1.69101 + 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 \(-0.759193\pi\)
−0.230819 0.972997i \(-0.574140\pi\)
\(74\) −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 \(-0.687483\pi\)
−0.555526 + 0.831499i \(0.687483\pi\)
\(84\) 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 \(-0.838288\pi\)
−0.873703 + 0.486460i \(0.838288\pi\)
\(90\) 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 −0.889687 0.456572i \(-0.849077\pi\)
0.840246 + 0.542205i \(0.182411\pi\)
\(98\) 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
\(103\) 0.264341 0.457852i 0.0260463 0.0451135i −0.852708 0.522387i \(-0.825042\pi\)
0.878755 + 0.477274i \(0.158375\pi\)
\(104\) −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 −0.678456 0.734641i \(-0.737351\pi\)
0.975446 + 0.220240i \(0.0706841\pi\)
\(132\) −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 \(-0.571406\pi\)
0.955552 0.294824i \(-0.0952611\pi\)
\(140\) 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 0.780609 0.625020i \(-0.214909\pi\)
−0.931587 + 0.363517i \(0.881576\pi\)
\(158\) −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 0.999927 0.0120542i \(-0.00383706\pi\)
−0.510403 + 0.859935i \(0.670504\pi\)
\(168\) 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 0.560746 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
\(177\) −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 \(-0.358147\pi\)
0.431041 + 0.902333i \(0.358147\pi\)
\(182\) 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 \(-0.479126\pi\)
0.0655309 + 0.997851i \(0.479126\pi\)
\(200\) 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 0.579312 0.815106i \(-0.303321\pi\)
−0.995558 + 0.0941455i \(0.969988\pi\)
\(224\) 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 \(-0.513049\pi\)
−0.0409841 + 0.999160i \(0.513049\pi\)
\(228\) −1.11976 −0.0741581
\(229\) 3.27757 5.67692i 0.216588 0.375141i −0.737175 0.675702i \(-0.763841\pi\)
0.953763 + 0.300561i \(0.0971739\pi\)
\(230\) −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 \(-0.755002\pi\)
−0.718131 + 0.695908i \(0.755002\pi\)
\(242\) −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 −0.954637 0.297773i \(-0.903756\pi\)
0.735197 + 0.677853i \(0.237090\pi\)
\(252\) 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 \(-0.729364\pi\)
−0.659811 + 0.751432i \(0.729364\pi\)
\(258\) −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 \(-0.443121\pi\)
0.177743 + 0.984077i \(0.443121\pi\)
\(270\) 1.40955 2.44141i 0.0857823 0.148579i
\(271\) −18.4299 −1.11954 −0.559769 0.828648i \(-0.689110\pi\)
−0.559769 + 0.828648i \(0.689110\pi\)
\(272\) 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 −0.999921 0.0125564i \(-0.996003\pi\)
0.510835 + 0.859679i \(0.329336\pi\)
\(284\) −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 \(-0.480982\pi\)
0.834625 0.550819i \(-0.185684\pi\)
\(294\) 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 \(-0.408262\pi\)
0.284229 + 0.958756i \(0.408262\pi\)
\(308\) 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 \(0.121539\pi\)
−0.141299 + 0.989967i \(0.545128\pi\)
\(312\) 15.6528 11.9134i 0.886164 0.674466i
\(313\) −8.26136 + 14.3091i −0.466960 + 0.808798i −0.999288 0.0377401i \(-0.987984\pi\)
0.532328 + 0.846538i \(0.321317\pi\)
\(314\) 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 0.847013 0.531573i \(-0.178399\pi\)
−0.883862 + 0.467748i \(0.845065\pi\)
\(350\) 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 −0.875102 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
\(359\) 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 −0.945871 0.324542i \(-0.894790\pi\)
0.753997 + 0.656878i \(0.228123\pi\)
\(368\) −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 \(0.0314690\pi\)
−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
\(387\) −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 \(0.160799\pi\)
−0.0184326 + 0.999830i \(0.505868\pi\)
\(398\) −2.81169 −0.140937
\(399\) 0 0
\(400\) −10.5328 18.2434i −0.526640 0.912168i
\(401\) −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 \(-0.457509\pi\)
0.133092 + 0.991104i \(0.457509\pi\)
\(410\) −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 0.785196 0.619247i \(-0.212562\pi\)
−0.928882 + 0.370376i \(0.879229\pi\)
\(420\) 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 \(-0.602545\pi\)
0.979779 0.200085i \(-0.0641218\pi\)
\(434\) 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 \(-0.232964\pi\)
0.743921 + 0.668268i \(0.232964\pi\)
\(440\) 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 \(0.465634\pi\)
−0.914860 + 0.403771i \(0.867699\pi\)
\(462\) 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 −0.932457 0.361281i \(-0.882339\pi\)
0.779107 + 0.626891i \(0.215673\pi\)
\(468\) 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 −0.594853 0.803835i \(-0.702790\pi\)
0.993568 + 0.113240i \(0.0361230\pi\)
\(480\) 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 −0.876789 0.480875i \(-0.840319\pi\)
0.854844 + 0.518884i \(0.173652\pi\)
\(504\) 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 \(-0.407127\pi\)
0.287646 + 0.957737i \(0.407127\pi\)
\(510\) 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 0.996447 0.0842226i \(-0.0268407\pi\)
−0.571162 + 0.820837i \(0.693507\pi\)
\(522\) 7.97033 13.8050i 0.348852 0.604229i
\(523\) 27.2719 1.19252 0.596259 0.802792i \(-0.296653\pi\)
0.596259 + 0.802792i \(0.296653\pi\)
\(524\) 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 \(-0.732442\pi\)
−0.667048 + 0.745015i \(0.732442\pi\)
\(564\) −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 0.986090 0.166214i \(-0.0531544\pi\)
−0.636991 + 0.770871i \(0.719821\pi\)
\(578\) −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 0.950995 0.309205i \(-0.100063\pi\)
−0.743277 + 0.668983i \(0.766730\pi\)
\(588\) 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 \(0.467006\pi\)
−0.913111 + 0.407710i \(0.866327\pi\)
\(594\) −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 \(-0.929341\pi\)
0.297064 0.954858i \(-0.403993\pi\)
\(602\) 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 \(-0.815800\pi\)
−0.0550554 0.998483i \(-0.517534\pi\)
\(608\) 1.47658 + 2.55751i 0.0598831 + 0.103721i
\(609\) 0 0
\(610\) −2.22305 −0.0900088
\(611\) 1.33364 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 0.968494 0.249038i \(-0.0801143\pi\)
−0.699920 + 0.714221i \(0.746781\pi\)
\(620\) −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 \(0.382420\pi\)
−0.988133 + 0.153600i \(0.950913\pi\)
\(644\) 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
\(649\) −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 −0.658834 0.752289i \(-0.728950\pi\)
0.980918 + 0.194422i \(0.0622833\pi\)
\(662\) 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 \(-0.625828\pi\)
0.991781 0.127947i \(-0.0408387\pi\)
\(678\) 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 \(-0.462978\pi\)
0.116046 + 0.993244i \(0.462978\pi\)
\(692\) −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 \(-0.990358\pi\)
0.473542 0.880771i \(-0.342975\pi\)
\(720\) 4.05831 0.151244
\(721\) 0 0
\(722\) −12.2912 + 21.2890i −0.457432 + 0.792295i
\(723\) 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 \(-0.382155\pi\)
0.361823 + 0.932247i \(0.382155\pi\)
\(728\) 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 −0.614366 0.789021i \(-0.710588\pi\)
0.990495 + 0.137546i \(0.0439215\pi\)
\(734\) 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 0.897460 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
\(765\) 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 0.909376 0.415976i \(-0.136560\pi\)
−0.814933 + 0.579555i \(0.803227\pi\)
\(770\) 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 \(-0.239339\pi\)
0.730388 + 0.683032i \(0.239339\pi\)
\(774\) 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 + 18.7737i