Properties

Label 731.2.e.a.307.15
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.15
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.15

$q$-expansion

\(f(q)\) \(=\) \(q-0.317626 q^{2} +(-0.924775 + 1.60176i) q^{3} -1.89911 q^{4} +(1.30757 - 2.26478i) q^{5} +(0.293732 - 0.508759i) q^{6} +(0.730298 + 1.26491i) q^{7} +1.23846 q^{8} +(-0.210416 - 0.364452i) q^{9} +O(q^{10})\) \(q-0.317626 q^{2} +(-0.924775 + 1.60176i) q^{3} -1.89911 q^{4} +(1.30757 - 2.26478i) q^{5} +(0.293732 - 0.508759i) q^{6} +(0.730298 + 1.26491i) q^{7} +1.23846 q^{8} +(-0.210416 - 0.364452i) q^{9} +(-0.415317 + 0.719351i) q^{10} -3.65173 q^{11} +(1.75625 - 3.04192i) q^{12} +(-1.01343 - 1.75531i) q^{13} +(-0.231961 - 0.401769i) q^{14} +(2.41841 + 4.18881i) q^{15} +3.40486 q^{16} +(0.500000 + 0.866025i) q^{17} +(0.0668336 + 0.115759i) q^{18} +(-2.93240 + 5.07906i) q^{19} +(-2.48322 + 4.30107i) q^{20} -2.70144 q^{21} +1.15988 q^{22} +(-1.46103 + 2.53057i) q^{23} +(-1.14529 + 1.98371i) q^{24} +(-0.919473 - 1.59257i) q^{25} +(0.321890 + 0.557530i) q^{26} -4.77030 q^{27} +(-1.38692 - 2.40221i) q^{28} +(-3.83679 - 6.64551i) q^{29} +(-0.768150 - 1.33047i) q^{30} +(2.86782 - 4.96720i) q^{31} -3.55839 q^{32} +(3.37703 - 5.84918i) q^{33} +(-0.158813 - 0.275072i) q^{34} +3.81966 q^{35} +(0.399605 + 0.692136i) q^{36} +(-0.832940 + 1.44269i) q^{37} +(0.931405 - 1.61324i) q^{38} +3.74876 q^{39} +(1.61937 - 2.80483i) q^{40} -12.0950 q^{41} +0.858048 q^{42} +(-6.55646 + 0.113221i) q^{43} +6.93505 q^{44} -1.10054 q^{45} +(0.464060 - 0.803775i) q^{46} -5.06323 q^{47} +(-3.14873 + 5.45376i) q^{48} +(2.43333 - 4.21465i) q^{49} +(0.292048 + 0.505842i) q^{50} -1.84955 q^{51} +(1.92461 + 3.33353i) q^{52} +(-2.10235 + 3.64138i) q^{53} +1.51517 q^{54} +(-4.77489 + 8.27034i) q^{55} +(0.904444 + 1.56654i) q^{56} +(-5.42361 - 9.39398i) q^{57} +(1.21866 + 2.11078i) q^{58} -3.29302 q^{59} +(-4.59284 - 7.95504i) q^{60} +(-4.13775 - 7.16679i) q^{61} +(-0.910892 + 1.57771i) q^{62} +(0.307333 - 0.532317i) q^{63} -5.67949 q^{64} -5.30050 q^{65} +(-1.07263 + 1.85785i) q^{66} +(3.90956 - 6.77155i) q^{67} +(-0.949557 - 1.64468i) q^{68} +(-2.70224 - 4.68042i) q^{69} -1.21322 q^{70} +(1.20531 + 2.08766i) q^{71} +(-0.260592 - 0.451358i) q^{72} +(1.29291 + 2.23938i) q^{73} +(0.264563 - 0.458237i) q^{74} +3.40122 q^{75} +(5.56896 - 9.64572i) q^{76} +(-2.66685 - 4.61912i) q^{77} -1.19070 q^{78} +(-0.697761 - 1.20856i) q^{79} +(4.45209 - 7.71125i) q^{80} +(5.04270 - 8.73421i) q^{81} +3.84168 q^{82} +(-6.09457 + 10.5561i) q^{83} +5.13035 q^{84} +2.61514 q^{85} +(2.08250 - 0.0359617i) q^{86} +14.1927 q^{87} -4.52251 q^{88} +(-3.42380 + 5.93020i) q^{89} +0.349558 q^{90} +(1.48021 - 2.56379i) q^{91} +(2.77466 - 4.80585i) q^{92} +(5.30417 + 9.18708i) q^{93} +1.60821 q^{94} +(7.66863 + 13.2824i) q^{95} +(3.29071 - 5.69967i) q^{96} +8.27776 q^{97} +(-0.772888 + 1.33868i) q^{98} +(0.768383 + 1.33088i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.317626 −0.224595 −0.112298 0.993675i \(-0.535821\pi\)
−0.112298 + 0.993675i \(0.535821\pi\)
\(3\) −0.924775 + 1.60176i −0.533919 + 0.924775i 0.465296 + 0.885155i \(0.345948\pi\)
−0.999215 + 0.0396195i \(0.987385\pi\)
\(4\) −1.89911 −0.949557
\(5\) 1.30757 2.26478i 0.584763 1.01284i −0.410142 0.912022i \(-0.634521\pi\)
0.994905 0.100817i \(-0.0321457\pi\)
\(6\) 0.293732 0.508759i 0.119916 0.207700i
\(7\) 0.730298 + 1.26491i 0.276027 + 0.478092i 0.970394 0.241529i \(-0.0776489\pi\)
−0.694367 + 0.719621i \(0.744316\pi\)
\(8\) 1.23846 0.437861
\(9\) −0.210416 0.364452i −0.0701388 0.121484i
\(10\) −0.415317 + 0.719351i −0.131335 + 0.227479i
\(11\) −3.65173 −1.10104 −0.550519 0.834823i \(-0.685570\pi\)
−0.550519 + 0.834823i \(0.685570\pi\)
\(12\) 1.75625 3.04192i 0.506986 0.878126i
\(13\) −1.01343 1.75531i −0.281074 0.486834i 0.690576 0.723260i \(-0.257357\pi\)
−0.971650 + 0.236426i \(0.924024\pi\)
\(14\) −0.231961 0.401769i −0.0619943 0.107377i
\(15\) 2.41841 + 4.18881i 0.624432 + 1.08155i
\(16\) 3.40486 0.851215
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) 0.0668336 + 0.115759i 0.0157528 + 0.0272847i
\(19\) −2.93240 + 5.07906i −0.672738 + 1.16522i 0.304386 + 0.952549i \(0.401549\pi\)
−0.977124 + 0.212668i \(0.931785\pi\)
\(20\) −2.48322 + 4.30107i −0.555265 + 0.961748i
\(21\) −2.70144 −0.589503
\(22\) 1.15988 0.247288
\(23\) −1.46103 + 2.53057i −0.304645 + 0.527661i −0.977182 0.212402i \(-0.931871\pi\)
0.672537 + 0.740063i \(0.265205\pi\)
\(24\) −1.14529 + 1.98371i −0.233782 + 0.404923i
\(25\) −0.919473 1.59257i −0.183895 0.318515i
\(26\) 0.321890 + 0.557530i 0.0631279 + 0.109341i
\(27\) −4.77030 −0.918044
\(28\) −1.38692 2.40221i −0.262103 0.453976i
\(29\) −3.83679 6.64551i −0.712474 1.23404i −0.963926 0.266171i \(-0.914241\pi\)
0.251452 0.967870i \(-0.419092\pi\)
\(30\) −0.768150 1.33047i −0.140244 0.242910i
\(31\) 2.86782 4.96720i 0.515075 0.892136i −0.484772 0.874640i \(-0.661097\pi\)
0.999847 0.0174953i \(-0.00556920\pi\)
\(32\) −3.55839 −0.629040
\(33\) 3.37703 5.84918i 0.587865 1.01821i
\(34\) −0.158813 0.275072i −0.0272362 0.0471744i
\(35\) 3.81966 0.645640
\(36\) 0.399605 + 0.692136i 0.0666008 + 0.115356i
\(37\) −0.832940 + 1.44269i −0.136935 + 0.237178i −0.926335 0.376701i \(-0.877058\pi\)
0.789400 + 0.613879i \(0.210392\pi\)
\(38\) 0.931405 1.61324i 0.151094 0.261702i
\(39\) 3.74876 0.600283
\(40\) 1.61937 2.80483i 0.256045 0.443483i
\(41\) −12.0950 −1.88892 −0.944461 0.328624i \(-0.893415\pi\)
−0.944461 + 0.328624i \(0.893415\pi\)
\(42\) 0.858048 0.132400
\(43\) −6.55646 + 0.113221i −0.999851 + 0.0172660i
\(44\) 6.93505 1.04550
\(45\) −1.10054 −0.164058
\(46\) 0.464060 0.803775i 0.0684219 0.118510i
\(47\) −5.06323 −0.738548 −0.369274 0.929321i \(-0.620394\pi\)
−0.369274 + 0.929321i \(0.620394\pi\)
\(48\) −3.14873 + 5.45376i −0.454480 + 0.787182i
\(49\) 2.43333 4.21465i 0.347619 0.602093i
\(50\) 0.292048 + 0.505842i 0.0413019 + 0.0715369i
\(51\) −1.84955 −0.258989
\(52\) 1.92461 + 3.33353i 0.266896 + 0.462277i
\(53\) −2.10235 + 3.64138i −0.288780 + 0.500181i −0.973519 0.228607i \(-0.926583\pi\)
0.684739 + 0.728788i \(0.259916\pi\)
\(54\) 1.51517 0.206188
\(55\) −4.77489 + 8.27034i −0.643845 + 1.11517i
\(56\) 0.904444 + 1.56654i 0.120861 + 0.209338i
\(57\) −5.42361 9.39398i −0.718375 1.24426i
\(58\) 1.21866 + 2.11078i 0.160018 + 0.277160i
\(59\) −3.29302 −0.428714 −0.214357 0.976755i \(-0.568766\pi\)
−0.214357 + 0.976755i \(0.568766\pi\)
\(60\) −4.59284 7.95504i −0.592933 1.02699i
\(61\) −4.13775 7.16679i −0.529784 0.917613i −0.999396 0.0347401i \(-0.988940\pi\)
0.469612 0.882873i \(-0.344394\pi\)
\(62\) −0.910892 + 1.57771i −0.115683 + 0.200369i
\(63\) 0.307333 0.532317i 0.0387204 0.0670656i
\(64\) −5.67949 −0.709936
\(65\) −5.30050 −0.657446
\(66\) −1.07263 + 1.85785i −0.132032 + 0.228685i
\(67\) 3.90956 6.77155i 0.477628 0.827277i −0.522043 0.852919i \(-0.674830\pi\)
0.999671 + 0.0256425i \(0.00816317\pi\)
\(68\) −0.949557 1.64468i −0.115151 0.199447i
\(69\) −2.70224 4.68042i −0.325312 0.563456i
\(70\) −1.21322 −0.145008
\(71\) 1.20531 + 2.08766i 0.143044 + 0.247759i 0.928641 0.370978i \(-0.120978\pi\)
−0.785598 + 0.618738i \(0.787644\pi\)
\(72\) −0.260592 0.451358i −0.0307111 0.0531931i
\(73\) 1.29291 + 2.23938i 0.151323 + 0.262100i 0.931714 0.363192i \(-0.118313\pi\)
−0.780391 + 0.625292i \(0.784980\pi\)
\(74\) 0.264563 0.458237i 0.0307548 0.0532689i
\(75\) 3.40122 0.392739
\(76\) 5.56896 9.64572i 0.638803 1.10644i
\(77\) −2.66685 4.61912i −0.303916 0.526397i
\(78\) −1.19070 −0.134821
\(79\) −0.697761 1.20856i −0.0785042 0.135973i 0.824101 0.566444i \(-0.191681\pi\)
−0.902605 + 0.430470i \(0.858348\pi\)
\(80\) 4.45209 7.71125i 0.497759 0.862144i
\(81\) 5.04270 8.73421i 0.560300 0.970468i
\(82\) 3.84168 0.424243
\(83\) −6.09457 + 10.5561i −0.668966 + 1.15868i 0.309227 + 0.950988i \(0.399930\pi\)
−0.978194 + 0.207696i \(0.933404\pi\)
\(84\) 5.13035 0.559767
\(85\) 2.61514 0.283652
\(86\) 2.08250 0.0359617i 0.224562 0.00387785i
\(87\) 14.1927 1.52161
\(88\) −4.52251 −0.482101
\(89\) −3.42380 + 5.93020i −0.362922 + 0.628600i −0.988440 0.151610i \(-0.951554\pi\)
0.625518 + 0.780210i \(0.284888\pi\)
\(90\) 0.349558 0.0368467
\(91\) 1.48021 2.56379i 0.155168 0.268758i
\(92\) 2.77466 4.80585i 0.289278 0.501044i
\(93\) 5.30417 + 9.18708i 0.550016 + 0.952656i
\(94\) 1.60821 0.165874
\(95\) 7.66863 + 13.2824i 0.786784 + 1.36275i
\(96\) 3.29071 5.69967i 0.335856 0.581720i
\(97\) 8.27776 0.840480 0.420240 0.907413i \(-0.361946\pi\)
0.420240 + 0.907413i \(0.361946\pi\)
\(98\) −0.772888 + 1.33868i −0.0780735 + 0.135227i
\(99\) 0.768383 + 1.33088i 0.0772254 + 0.133758i
\(100\) 1.74618 + 3.02448i 0.174618 + 0.302448i
\(101\) −5.51376 9.55011i −0.548640 0.950272i −0.998368 0.0571063i \(-0.981813\pi\)
0.449729 0.893165i \(-0.351521\pi\)
\(102\) 0.587464 0.0581676
\(103\) 6.01182 + 10.4128i 0.592362 + 1.02600i 0.993913 + 0.110165i \(0.0351378\pi\)
−0.401551 + 0.915837i \(0.631529\pi\)
\(104\) −1.25509 2.17387i −0.123071 0.213166i
\(105\) −3.53232 + 6.11817i −0.344720 + 0.597072i
\(106\) 0.667760 1.15659i 0.0648586 0.112338i
\(107\) −9.73427 −0.941047 −0.470524 0.882387i \(-0.655935\pi\)
−0.470524 + 0.882387i \(0.655935\pi\)
\(108\) 9.05934 0.871735
\(109\) −9.16471 + 15.8737i −0.877820 + 1.52043i −0.0240922 + 0.999710i \(0.507670\pi\)
−0.853728 + 0.520719i \(0.825664\pi\)
\(110\) 1.51663 2.62687i 0.144605 0.250463i
\(111\) −1.54056 2.66833i −0.146224 0.253267i
\(112\) 2.48656 + 4.30685i 0.234958 + 0.406959i
\(113\) 9.75856 0.918008 0.459004 0.888434i \(-0.348206\pi\)
0.459004 + 0.888434i \(0.348206\pi\)
\(114\) 1.72268 + 2.98377i 0.161344 + 0.279455i
\(115\) 3.82079 + 6.61780i 0.356290 + 0.617113i
\(116\) 7.28650 + 12.6206i 0.676534 + 1.17179i
\(117\) −0.426483 + 0.738690i −0.0394284 + 0.0682919i
\(118\) 1.04595 0.0962872
\(119\) −0.730298 + 1.26491i −0.0669463 + 0.115954i
\(120\) 2.99510 + 5.18767i 0.273414 + 0.473568i
\(121\) 2.33511 0.212283
\(122\) 1.31425 + 2.27635i 0.118987 + 0.206091i
\(123\) 11.1851 19.3732i 1.00853 1.74683i
\(124\) −5.44631 + 9.43328i −0.489093 + 0.847134i
\(125\) 8.26659 0.739386
\(126\) −0.0976169 + 0.169077i −0.00869641 + 0.0150626i
\(127\) −1.26987 −0.112683 −0.0563413 0.998412i \(-0.517943\pi\)
−0.0563413 + 0.998412i \(0.517943\pi\)
\(128\) 8.92073 0.788488
\(129\) 5.88190 10.6066i 0.517872 0.933855i
\(130\) 1.68357 0.147659
\(131\) 1.38019 0.120588 0.0602939 0.998181i \(-0.480796\pi\)
0.0602939 + 0.998181i \(0.480796\pi\)
\(132\) −6.41336 + 11.1083i −0.558211 + 0.966850i
\(133\) −8.56610 −0.742775
\(134\) −1.24178 + 2.15082i −0.107273 + 0.185802i
\(135\) −6.23749 + 10.8037i −0.536838 + 0.929830i
\(136\) 0.619229 + 1.07254i 0.0530985 + 0.0919692i
\(137\) −4.30382 −0.367700 −0.183850 0.982954i \(-0.558856\pi\)
−0.183850 + 0.982954i \(0.558856\pi\)
\(138\) 0.858301 + 1.48662i 0.0730634 + 0.126550i
\(139\) −10.7801 + 18.6718i −0.914360 + 1.58372i −0.106524 + 0.994310i \(0.533972\pi\)
−0.807836 + 0.589407i \(0.799361\pi\)
\(140\) −7.25397 −0.613072
\(141\) 4.68235 8.11007i 0.394325 0.682991i
\(142\) −0.382837 0.663094i −0.0321270 0.0556456i
\(143\) 3.70076 + 6.40990i 0.309473 + 0.536023i
\(144\) −0.716439 1.24091i −0.0597032 0.103409i
\(145\) −20.0675 −1.66651
\(146\) −0.410661 0.711285i −0.0339865 0.0588664i
\(147\) 4.50056 + 7.79521i 0.371200 + 0.642938i
\(148\) 1.58185 2.73984i 0.130027 0.225214i
\(149\) −7.79008 + 13.4928i −0.638189 + 1.10538i 0.347641 + 0.937628i \(0.386983\pi\)
−0.985830 + 0.167747i \(0.946351\pi\)
\(150\) −1.08032 −0.0882074
\(151\) 21.7673 1.77139 0.885697 0.464263i \(-0.153681\pi\)
0.885697 + 0.464263i \(0.153681\pi\)
\(152\) −3.63165 + 6.29021i −0.294566 + 0.510203i
\(153\) 0.210416 0.364452i 0.0170112 0.0294642i
\(154\) 0.847059 + 1.46715i 0.0682580 + 0.118226i
\(155\) −7.49973 12.9899i −0.602393 1.04338i
\(156\) −7.11933 −0.570003
\(157\) 0.727789 + 1.26057i 0.0580839 + 0.100604i 0.893605 0.448854i \(-0.148168\pi\)
−0.835521 + 0.549458i \(0.814834\pi\)
\(158\) 0.221627 + 0.383869i 0.0176317 + 0.0305390i
\(159\) −3.88840 6.73490i −0.308370 0.534113i
\(160\) −4.65284 + 8.05895i −0.367839 + 0.637116i
\(161\) −4.26794 −0.336361
\(162\) −1.60169 + 2.77421i −0.125841 + 0.217962i
\(163\) −0.734253 1.27176i −0.0575111 0.0996122i 0.835836 0.548979i \(-0.184983\pi\)
−0.893348 + 0.449366i \(0.851650\pi\)
\(164\) 22.9698 1.79364
\(165\) −8.83139 15.2964i −0.687522 1.19082i
\(166\) 1.93579 3.35289i 0.150247 0.260235i
\(167\) 6.64196 11.5042i 0.513970 0.890223i −0.485898 0.874015i \(-0.661508\pi\)
0.999869 0.0162073i \(-0.00515916\pi\)
\(168\) −3.34563 −0.258121
\(169\) 4.44593 7.70058i 0.341995 0.592353i
\(170\) −0.830635 −0.0637068
\(171\) 2.46810 0.188740
\(172\) 12.4515 0.215019i 0.949415 0.0163950i
\(173\) 15.1257 1.14999 0.574994 0.818157i \(-0.305004\pi\)
0.574994 + 0.818157i \(0.305004\pi\)
\(174\) −4.50795 −0.341747
\(175\) 1.34298 2.32611i 0.101520 0.175837i
\(176\) −12.4336 −0.937220
\(177\) 3.04530 5.27461i 0.228899 0.396464i
\(178\) 1.08749 1.88358i 0.0815106 0.141181i
\(179\) 3.00072 + 5.19739i 0.224284 + 0.388471i 0.956104 0.293026i \(-0.0946623\pi\)
−0.731820 + 0.681498i \(0.761329\pi\)
\(180\) 2.09004 0.155783
\(181\) 12.7858 + 22.1456i 0.950358 + 1.64607i 0.744650 + 0.667455i \(0.232616\pi\)
0.205708 + 0.978613i \(0.434050\pi\)
\(182\) −0.470151 + 0.814326i −0.0348499 + 0.0603619i
\(183\) 15.3059 1.13145
\(184\) −1.80942 + 3.13401i −0.133392 + 0.231042i
\(185\) 2.17825 + 3.77285i 0.160148 + 0.277385i
\(186\) −1.68474 2.91805i −0.123531 0.213962i
\(187\) −1.82586 3.16249i −0.133520 0.231264i
\(188\) 9.61565 0.701294
\(189\) −3.48374 6.03401i −0.253405 0.438910i
\(190\) −2.43575 4.21885i −0.176708 0.306067i
\(191\) 0.987801 1.71092i 0.0714748 0.123798i −0.828073 0.560620i \(-0.810563\pi\)
0.899548 + 0.436822i \(0.143896\pi\)
\(192\) 5.25225 9.09716i 0.379048 0.656531i
\(193\) 7.24401 0.521435 0.260718 0.965415i \(-0.416041\pi\)
0.260718 + 0.965415i \(0.416041\pi\)
\(194\) −2.62923 −0.188768
\(195\) 4.90177 8.49011i 0.351023 0.607989i
\(196\) −4.62117 + 8.00410i −0.330084 + 0.571722i
\(197\) −12.3717 21.4284i −0.881447 1.52671i −0.849732 0.527214i \(-0.823236\pi\)
−0.0317149 0.999497i \(-0.510097\pi\)
\(198\) −0.244058 0.422721i −0.0173445 0.0300415i
\(199\) 16.8864 1.19705 0.598524 0.801105i \(-0.295754\pi\)
0.598524 + 0.801105i \(0.295754\pi\)
\(200\) −1.13873 1.97234i −0.0805203 0.139465i
\(201\) 7.23092 + 12.5243i 0.510030 + 0.883397i
\(202\) 1.75131 + 3.03336i 0.123222 + 0.213426i
\(203\) 5.60400 9.70641i 0.393323 0.681256i
\(204\) 3.51250 0.245925
\(205\) −15.8150 + 27.3925i −1.10457 + 1.91317i
\(206\) −1.90951 3.30736i −0.133042 0.230435i
\(207\) 1.22970 0.0854698
\(208\) −3.45058 5.97657i −0.239254 0.414401i
\(209\) 10.7083 18.5474i 0.740710 1.28295i
\(210\) 1.12196 1.94329i 0.0774224 0.134099i
\(211\) −20.5746 −1.41642 −0.708208 0.706004i \(-0.750496\pi\)
−0.708208 + 0.706004i \(0.750496\pi\)
\(212\) 3.99260 6.91539i 0.274213 0.474951i
\(213\) −4.45856 −0.305496
\(214\) 3.09185 0.211355
\(215\) −8.31661 + 14.9970i −0.567188 + 1.02278i
\(216\) −5.90781 −0.401976
\(217\) 8.37744 0.568698
\(218\) 2.91095 5.04191i 0.197154 0.341481i
\(219\) −4.78259 −0.323178
\(220\) 9.06805 15.7063i 0.611368 1.05892i
\(221\) 1.01343 1.75531i 0.0681704 0.118075i
\(222\) 0.489323 + 0.847531i 0.0328412 + 0.0568826i
\(223\) −22.6798 −1.51875 −0.759377 0.650651i \(-0.774496\pi\)
−0.759377 + 0.650651i \(0.774496\pi\)
\(224\) −2.59868 4.50105i −0.173632 0.300739i
\(225\) −0.386944 + 0.670207i −0.0257963 + 0.0446805i
\(226\) −3.09957 −0.206180
\(227\) 7.45574 12.9137i 0.494855 0.857114i −0.505127 0.863045i \(-0.668554\pi\)
0.999982 + 0.00593058i \(0.00188777\pi\)
\(228\) 10.3001 + 17.8402i 0.682138 + 1.18150i
\(229\) −5.60596 9.70981i −0.370452 0.641642i 0.619183 0.785247i \(-0.287464\pi\)
−0.989635 + 0.143605i \(0.954131\pi\)
\(230\) −1.21358 2.10198i −0.0800211 0.138601i
\(231\) 9.86494 0.649065
\(232\) −4.75170 8.23019i −0.311965 0.540338i
\(233\) −12.1364 21.0209i −0.795083 1.37713i −0.922786 0.385313i \(-0.874094\pi\)
0.127703 0.991812i \(-0.459240\pi\)
\(234\) 0.135462 0.234627i 0.00885542 0.0153380i
\(235\) −6.62052 + 11.4671i −0.431875 + 0.748030i
\(236\) 6.25382 0.407089
\(237\) 2.58109 0.167660
\(238\) 0.231961 0.401769i 0.0150358 0.0260428i
\(239\) −12.5561 + 21.7478i −0.812187 + 1.40675i 0.0991441 + 0.995073i \(0.468390\pi\)
−0.911331 + 0.411675i \(0.864944\pi\)
\(240\) 8.23436 + 14.2623i 0.531526 + 0.920630i
\(241\) −6.73524 11.6658i −0.433855 0.751459i 0.563346 0.826221i \(-0.309514\pi\)
−0.997201 + 0.0747618i \(0.976180\pi\)
\(242\) −0.741692 −0.0476777
\(243\) 2.17128 + 3.76076i 0.139287 + 0.241253i
\(244\) 7.85805 + 13.6105i 0.503060 + 0.871326i
\(245\) −6.36349 11.0219i −0.406549 0.704163i
\(246\) −3.55269 + 6.15344i −0.226511 + 0.392329i
\(247\) 11.8871 0.756357
\(248\) 3.55167 6.15167i 0.225531 0.390632i
\(249\) −11.2722 19.5240i −0.714348 1.23729i
\(250\) −2.62568 −0.166063
\(251\) −3.85335 6.67419i −0.243221 0.421271i 0.718409 0.695621i \(-0.244871\pi\)
−0.961630 + 0.274350i \(0.911537\pi\)
\(252\) −0.583661 + 1.01093i −0.0367672 + 0.0636826i
\(253\) 5.33527 9.24096i 0.335426 0.580974i
\(254\) 0.403342 0.0253080
\(255\) −2.41841 + 4.18881i −0.151447 + 0.262314i
\(256\) 8.52553 0.532845
\(257\) −9.25376 −0.577233 −0.288617 0.957445i \(-0.593195\pi\)
−0.288617 + 0.957445i \(0.593195\pi\)
\(258\) −1.86824 + 3.36891i −0.116312 + 0.209739i
\(259\) −2.43318 −0.151190
\(260\) 10.0663 0.624283
\(261\) −1.61465 + 2.79665i −0.0999441 + 0.173108i
\(262\) −0.438384 −0.0270835
\(263\) 11.5966 20.0859i 0.715077 1.23855i −0.247853 0.968798i \(-0.579725\pi\)
0.962930 0.269752i \(-0.0869416\pi\)
\(264\) 4.18231 7.24396i 0.257403 0.445835i
\(265\) 5.49793 + 9.52270i 0.337735 + 0.584975i
\(266\) 2.72081 0.166824
\(267\) −6.33249 10.9682i −0.387542 0.671243i
\(268\) −7.42470 + 12.8600i −0.453535 + 0.785546i
\(269\) 13.0447 0.795349 0.397675 0.917527i \(-0.369817\pi\)
0.397675 + 0.917527i \(0.369817\pi\)
\(270\) 1.98119 3.43152i 0.120571 0.208835i
\(271\) −0.238759 0.413543i −0.0145036 0.0251209i 0.858683 0.512508i \(-0.171283\pi\)
−0.873186 + 0.487387i \(0.837950\pi\)
\(272\) 1.70243 + 2.94870i 0.103225 + 0.178791i
\(273\) 2.73771 + 4.74186i 0.165694 + 0.286990i
\(274\) 1.36700 0.0825837
\(275\) 3.35767 + 5.81565i 0.202475 + 0.350697i
\(276\) 5.13186 + 8.88865i 0.308902 + 0.535034i
\(277\) −5.61884 + 9.73211i −0.337603 + 0.584746i −0.983981 0.178271i \(-0.942950\pi\)
0.646378 + 0.763017i \(0.276283\pi\)
\(278\) 3.42405 5.93063i 0.205361 0.355695i
\(279\) −2.41374 −0.144507
\(280\) 4.73049 0.282701
\(281\) −0.240122 + 0.415904i −0.0143245 + 0.0248107i −0.873099 0.487543i \(-0.837893\pi\)
0.858774 + 0.512354i \(0.171226\pi\)
\(282\) −1.48723 + 2.57596i −0.0885635 + 0.153396i
\(283\) 12.5863 + 21.8002i 0.748181 + 1.29589i 0.948694 + 0.316196i \(0.102406\pi\)
−0.200513 + 0.979691i \(0.564261\pi\)
\(284\) −2.28902 3.96470i −0.135828 0.235262i
\(285\) −28.3670 −1.68032
\(286\) −1.17546 2.03595i −0.0695061 0.120388i
\(287\) −8.83295 15.2991i −0.521393 0.903079i
\(288\) 0.748743 + 1.29686i 0.0441201 + 0.0764183i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) 6.37394 0.374291
\(291\) −7.65507 + 13.2590i −0.448748 + 0.777254i
\(292\) −2.45538 4.25284i −0.143690 0.248879i
\(293\) −4.42180 −0.258325 −0.129162 0.991623i \(-0.541229\pi\)
−0.129162 + 0.991623i \(0.541229\pi\)
\(294\) −1.42949 2.47596i −0.0833698 0.144401i
\(295\) −4.30585 + 7.45795i −0.250696 + 0.434219i
\(296\) −1.03156 + 1.78672i −0.0599583 + 0.103851i
\(297\) 17.4198 1.01080
\(298\) 2.47433 4.28567i 0.143334 0.248262i
\(299\) 5.92257 0.342511
\(300\) −6.45931 −0.372928
\(301\) −4.93138 8.21067i −0.284240 0.473255i
\(302\) −6.91384 −0.397847
\(303\) 20.3959 1.17172
\(304\) −9.98441 + 17.2935i −0.572645 + 0.991851i
\(305\) −21.6416 −1.23919
\(306\) −0.0668336 + 0.115759i −0.00382062 + 0.00661752i
\(307\) 2.60469 4.51145i 0.148657 0.257482i −0.782074 0.623185i \(-0.785838\pi\)
0.930731 + 0.365703i \(0.119172\pi\)
\(308\) 5.06465 + 8.77223i 0.288585 + 0.499844i
\(309\) −22.2383 −1.26509
\(310\) 2.38211 + 4.12593i 0.135295 + 0.234337i
\(311\) 6.75367 11.6977i 0.382966 0.663316i −0.608519 0.793539i \(-0.708236\pi\)
0.991485 + 0.130223i \(0.0415694\pi\)
\(312\) 4.64269 0.262840
\(313\) 1.57374 2.72579i 0.0889528 0.154071i −0.818116 0.575053i \(-0.804981\pi\)
0.907069 + 0.420983i \(0.138315\pi\)
\(314\) −0.231164 0.400388i −0.0130454 0.0225952i
\(315\) −0.803719 1.39208i −0.0452844 0.0784349i
\(316\) 1.32513 + 2.29519i 0.0745442 + 0.129114i
\(317\) 8.05649 0.452498 0.226249 0.974070i \(-0.427354\pi\)
0.226249 + 0.974070i \(0.427354\pi\)
\(318\) 1.23506 + 2.13918i 0.0692584 + 0.119959i
\(319\) 14.0109 + 24.2676i 0.784460 + 1.35872i
\(320\) −7.42632 + 12.8628i −0.415144 + 0.719051i
\(321\) 9.00201 15.5919i 0.502443 0.870257i
\(322\) 1.35561 0.0755450
\(323\) −5.86480 −0.326326
\(324\) −9.57666 + 16.5873i −0.532037 + 0.921515i
\(325\) −1.86364 + 3.22791i −0.103376 + 0.179052i
\(326\) 0.233217 + 0.403945i 0.0129167 + 0.0223724i
\(327\) −16.9506 29.3593i −0.937370 1.62357i
\(328\) −14.9792 −0.827085
\(329\) −3.69767 6.40455i −0.203859 0.353094i
\(330\) 2.80507 + 4.85853i 0.154414 + 0.267453i
\(331\) 7.64356 + 13.2390i 0.420128 + 0.727683i 0.995952 0.0898911i \(-0.0286519\pi\)
−0.575824 + 0.817574i \(0.695319\pi\)
\(332\) 11.5743 20.0473i 0.635222 1.10024i
\(333\) 0.701057 0.0384177
\(334\) −2.10966 + 3.65403i −0.115435 + 0.199940i
\(335\) −10.2240 17.7085i −0.558599 0.967521i
\(336\) −9.19804 −0.501794
\(337\) −1.80742 3.13054i −0.0984565 0.170532i 0.812589 0.582836i \(-0.198057\pi\)
−0.911046 + 0.412305i \(0.864724\pi\)
\(338\) −1.41214 + 2.44590i −0.0768104 + 0.133040i
\(339\) −9.02447 + 15.6308i −0.490142 + 0.848951i
\(340\) −4.96644 −0.269343
\(341\) −10.4725 + 18.1389i −0.567117 + 0.982275i
\(342\) −0.783931 −0.0423901
\(343\) 17.3324 0.935861
\(344\) −8.11990 + 0.140219i −0.437796 + 0.00756010i
\(345\) −14.1335 −0.760920
\(346\) −4.80432 −0.258282
\(347\) 9.34291 16.1824i 0.501554 0.868716i −0.498445 0.866921i \(-0.666095\pi\)
0.999998 0.00179489i \(-0.000571332\pi\)
\(348\) −26.9535 −1.44486
\(349\) −6.09040 + 10.5489i −0.326012 + 0.564669i −0.981717 0.190348i \(-0.939038\pi\)
0.655705 + 0.755017i \(0.272372\pi\)
\(350\) −0.426564 + 0.738831i −0.0228008 + 0.0394922i
\(351\) 4.83435 + 8.37333i 0.258038 + 0.446935i
\(352\) 12.9943 0.692597
\(353\) 7.82006 + 13.5447i 0.416220 + 0.720914i 0.995556 0.0941752i \(-0.0300214\pi\)
−0.579336 + 0.815089i \(0.696688\pi\)
\(354\) −0.967265 + 1.67535i −0.0514096 + 0.0890440i
\(355\) 6.30410 0.334587
\(356\) 6.50219 11.2621i 0.344616 0.596892i
\(357\) −1.35072 2.33952i −0.0714878 0.123820i
\(358\) −0.953104 1.65083i −0.0503731 0.0872488i
\(359\) 7.93663 + 13.7466i 0.418879 + 0.725520i 0.995827 0.0912608i \(-0.0290897\pi\)
−0.576948 + 0.816781i \(0.695756\pi\)
\(360\) −1.36297 −0.0718347
\(361\) −7.69792 13.3332i −0.405153 0.701746i
\(362\) −4.06108 7.03400i −0.213446 0.369699i
\(363\) −2.15945 + 3.74028i −0.113342 + 0.196314i
\(364\) −2.81108 + 4.86893i −0.147341 + 0.255201i
\(365\) 6.76226 0.353953
\(366\) −4.86155 −0.254118
\(367\) −11.7633 + 20.3746i −0.614037 + 1.06354i 0.376515 + 0.926410i \(0.377122\pi\)
−0.990553 + 0.137134i \(0.956211\pi\)
\(368\) −4.97460 + 8.61625i −0.259319 + 0.449153i
\(369\) 2.54499 + 4.40804i 0.132487 + 0.229474i
\(370\) −0.691869 1.19835i −0.0359686 0.0622994i
\(371\) −6.14137 −0.318844
\(372\) −10.0732 17.4473i −0.522272 0.904601i
\(373\) 15.2399 + 26.3962i 0.789090 + 1.36674i 0.926525 + 0.376233i \(0.122781\pi\)
−0.137435 + 0.990511i \(0.543886\pi\)
\(374\) 0.579941 + 1.00449i 0.0299880 + 0.0519408i
\(375\) −7.64473 + 13.2411i −0.394772 + 0.683766i
\(376\) −6.27060 −0.323382
\(377\) −7.77661 + 13.4695i −0.400516 + 0.693713i
\(378\) 1.10652 + 1.91656i 0.0569135 + 0.0985770i
\(379\) −2.05678 −0.105650 −0.0528248 0.998604i \(-0.516822\pi\)
−0.0528248 + 0.998604i \(0.516822\pi\)
\(380\) −14.5636 25.2249i −0.747097 1.29401i
\(381\) 1.17434 2.03402i 0.0601633 0.104206i
\(382\) −0.313751 + 0.543432i −0.0160529 + 0.0278044i
\(383\) 11.9440 0.610311 0.305155 0.952303i \(-0.401292\pi\)
0.305155 + 0.952303i \(0.401292\pi\)
\(384\) −8.24966 + 14.2888i −0.420989 + 0.729174i
\(385\) −13.9484 −0.710874
\(386\) −2.30088 −0.117112
\(387\) 1.42085 + 2.36569i 0.0722259 + 0.120255i
\(388\) −15.7204 −0.798083
\(389\) 22.5074 1.14117 0.570586 0.821238i \(-0.306716\pi\)
0.570586 + 0.821238i \(0.306716\pi\)
\(390\) −1.55693 + 2.69668i −0.0788381 + 0.136552i
\(391\) −2.92205 −0.147775
\(392\) 3.01358 5.21967i 0.152209 0.263633i
\(393\) −1.27637 + 2.21073i −0.0643842 + 0.111517i
\(394\) 3.92957 + 6.80621i 0.197969 + 0.342892i
\(395\) −3.64948 −0.183625
\(396\) −1.45925 2.52749i −0.0733299 0.127011i
\(397\) 13.6066 23.5673i 0.682896 1.18281i −0.291197 0.956663i \(-0.594054\pi\)
0.974093 0.226147i \(-0.0726130\pi\)
\(398\) −5.36356 −0.268851
\(399\) 7.92171 13.7208i 0.396581 0.686899i
\(400\) −3.13068 5.42250i −0.156534 0.271125i
\(401\) −1.28070 2.21824i −0.0639551 0.110774i 0.832275 0.554363i \(-0.187038\pi\)
−0.896230 + 0.443590i \(0.853705\pi\)
\(402\) −2.29673 3.97804i −0.114550 0.198407i
\(403\) −11.6253 −0.579096
\(404\) 10.4713 + 18.1368i 0.520965 + 0.902337i
\(405\) −13.1874 22.8412i −0.655285 1.13499i
\(406\) −1.77997 + 3.08300i −0.0883386 + 0.153007i
\(407\) 3.04167 5.26833i 0.150770 0.261141i
\(408\) −2.29059 −0.113401
\(409\) 7.31159 0.361535 0.180767 0.983526i \(-0.442142\pi\)
0.180767 + 0.983526i \(0.442142\pi\)
\(410\) 5.02326 8.70055i 0.248081 0.429689i
\(411\) 3.98006 6.89367i 0.196322 0.340040i
\(412\) −11.4171 19.7750i −0.562482 0.974247i
\(413\) −2.40488 4.16538i −0.118337 0.204965i
\(414\) −0.390583 −0.0191961
\(415\) 15.9382 + 27.6057i 0.782373 + 1.35511i
\(416\) 3.60616 + 6.24606i 0.176807 + 0.306238i
\(417\) −19.9384 34.5343i −0.976388 1.69115i
\(418\) −3.40124 + 5.89111i −0.166360 + 0.288144i
\(419\) −21.7351 −1.06183 −0.530915 0.847425i \(-0.678152\pi\)
−0.530915 + 0.847425i \(0.678152\pi\)
\(420\) 6.70829 11.6191i 0.327331 0.566954i
\(421\) −2.23340 3.86836i −0.108849 0.188533i 0.806455 0.591295i \(-0.201383\pi\)
−0.915304 + 0.402763i \(0.868050\pi\)
\(422\) 6.53503 0.318120
\(423\) 1.06539 + 1.84530i 0.0518009 + 0.0897218i
\(424\) −2.60367 + 4.50969i −0.126446 + 0.219010i
\(425\) 0.919473 1.59257i 0.0446010 0.0772512i
\(426\) 1.41615 0.0686128
\(427\) 6.04357 10.4678i 0.292469 0.506571i
\(428\) 18.4865 0.893578
\(429\) −13.6895 −0.660934
\(430\) 2.64157 4.76342i 0.127388 0.229712i
\(431\) −24.6567 −1.18767 −0.593836 0.804586i \(-0.702387\pi\)
−0.593836 + 0.804586i \(0.702387\pi\)
\(432\) −16.2422 −0.781453
\(433\) −11.9372 + 20.6759i −0.573666 + 0.993619i 0.422519 + 0.906354i \(0.361146\pi\)
−0.996185 + 0.0872652i \(0.972187\pi\)
\(434\) −2.66089 −0.127727
\(435\) 18.5579 32.1432i 0.889782 1.54115i
\(436\) 17.4048 30.1461i 0.833540 1.44373i
\(437\) −8.56863 14.8413i −0.409893 0.709955i
\(438\) 1.51907 0.0725842
\(439\) −10.5862 18.3358i −0.505250 0.875119i −0.999982 0.00607292i \(-0.998067\pi\)
0.494731 0.869046i \(-0.335266\pi\)
\(440\) −5.91350 + 10.2425i −0.281915 + 0.488291i
\(441\) −2.04805 −0.0975262
\(442\) −0.321890 + 0.557530i −0.0153108 + 0.0265190i
\(443\) −15.5750 26.9766i −0.739989 1.28170i −0.952499 0.304540i \(-0.901497\pi\)
0.212510 0.977159i \(-0.431836\pi\)
\(444\) 2.92571 + 5.06747i 0.138848 + 0.240492i
\(445\) 8.95372 + 15.5083i 0.424447 + 0.735164i
\(446\) 7.20369 0.341105
\(447\) −14.4081 24.9556i −0.681482 1.18036i
\(448\) −4.14772 7.18406i −0.195961 0.339415i
\(449\) −7.48204 + 12.9593i −0.353099 + 0.611586i −0.986791 0.162000i \(-0.948206\pi\)
0.633691 + 0.773586i \(0.281539\pi\)
\(450\) 0.122903 0.212875i 0.00579372 0.0100350i
\(451\) 44.1676 2.07977
\(452\) −18.5326 −0.871701
\(453\) −20.1298 + 34.8659i −0.945781 + 1.63814i
\(454\) −2.36814 + 4.10173i −0.111142 + 0.192504i
\(455\) −3.87094 6.70467i −0.181473 0.314320i
\(456\) −6.71692 11.6340i −0.314549 0.544814i
\(457\) −20.9126 −0.978248 −0.489124 0.872214i \(-0.662683\pi\)
−0.489124 + 0.872214i \(0.662683\pi\)
\(458\) 1.78060 + 3.08408i 0.0832018 + 0.144110i
\(459\) −2.38515 4.13120i −0.111329 0.192828i
\(460\) −7.25611 12.5680i −0.338318 0.585984i
\(461\) −10.2344 + 17.7265i −0.476663 + 0.825604i −0.999642 0.0267413i \(-0.991487\pi\)
0.522980 + 0.852345i \(0.324820\pi\)
\(462\) −3.13336 −0.145777
\(463\) −10.0030 + 17.3257i −0.464880 + 0.805195i −0.999196 0.0400892i \(-0.987236\pi\)
0.534316 + 0.845285i \(0.320569\pi\)
\(464\) −13.0637 22.6271i −0.606469 1.05043i
\(465\) 27.7423 1.28652
\(466\) 3.85484 + 6.67678i 0.178572 + 0.309296i
\(467\) −0.516312 + 0.894279i −0.0238921 + 0.0413823i −0.877724 0.479166i \(-0.840939\pi\)
0.853832 + 0.520548i \(0.174272\pi\)
\(468\) 0.809940 1.40286i 0.0374395 0.0648471i
\(469\) 11.4206 0.527353
\(470\) 2.10285 3.64224i 0.0969971 0.168004i
\(471\) −2.69216 −0.124048
\(472\) −4.07827 −0.187717
\(473\) 23.9424 0.413451i 1.10087 0.0190105i
\(474\) −0.819819 −0.0376555
\(475\) 10.7850 0.494852
\(476\) 1.38692 2.40221i 0.0635693 0.110105i
\(477\) 1.76947 0.0810187
\(478\) 3.98814 6.90766i 0.182413 0.315949i
\(479\) 17.8406 30.9009i 0.815159 1.41190i −0.0940545 0.995567i \(-0.529983\pi\)
0.909214 0.416330i \(-0.136684\pi\)
\(480\) −8.60565 14.9054i −0.392793 0.680337i
\(481\) 3.37649 0.153955
\(482\) 2.13929 + 3.70535i 0.0974418 + 0.168774i
\(483\) 3.94688 6.83620i 0.179589 0.311058i
\(484\) −4.43465 −0.201575
\(485\) 10.8237 18.7473i 0.491481 0.851270i
\(486\) −0.689653 1.19451i −0.0312833 0.0541842i
\(487\) 8.13868 + 14.0966i 0.368799 + 0.638779i 0.989378 0.145365i \(-0.0464357\pi\)
−0.620579 + 0.784144i \(0.713102\pi\)
\(488\) −5.12443 8.87577i −0.231972 0.401787i
\(489\) 2.71607 0.122825
\(490\) 2.02121 + 3.50084i 0.0913089 + 0.158152i
\(491\) 12.0142 + 20.8092i 0.542192 + 0.939104i 0.998778 + 0.0494246i \(0.0157388\pi\)
−0.456586 + 0.889679i \(0.650928\pi\)
\(492\) −21.2419 + 36.7920i −0.957658 + 1.65871i
\(493\) 3.83679 6.64551i 0.172800 0.299299i
\(494\) −3.77564 −0.169874
\(495\) 4.01886 0.180634
\(496\) 9.76451 16.9126i 0.438440 0.759400i
\(497\) −1.76047 + 3.04922i −0.0789679 + 0.136776i
\(498\) 3.58034 + 6.20134i 0.160439 + 0.277889i
\(499\) −8.46047 14.6540i −0.378743 0.656002i 0.612137 0.790752i \(-0.290310\pi\)
−0.990880 + 0.134750i \(0.956977\pi\)
\(500\) −15.6992 −0.702090
\(501\) 12.2846 + 21.2776i 0.548837 + 0.950613i
\(502\) 1.22392 + 2.11989i 0.0546263 + 0.0946155i
\(503\) −1.61884 2.80392i −0.0721806 0.125020i 0.827676 0.561206i \(-0.189662\pi\)
−0.899857 + 0.436186i \(0.856329\pi\)
\(504\) 0.380619 0.659252i 0.0169541 0.0293654i
\(505\) −28.8385 −1.28330
\(506\) −1.69462 + 2.93517i −0.0753350 + 0.130484i
\(507\) 8.22297 + 14.2426i 0.365195 + 0.632536i
\(508\) 2.41162 0.106998
\(509\) 13.9957 + 24.2412i 0.620347 + 1.07447i 0.989421 + 0.145073i \(0.0463417\pi\)
−0.369073 + 0.929400i \(0.620325\pi\)
\(510\) 0.768150 1.33047i 0.0340143 0.0589144i
\(511\) −1.88842 + 3.27083i −0.0835386 + 0.144693i
\(512\) −20.5494 −0.908163
\(513\) 13.9884 24.2286i 0.617603 1.06972i
\(514\) 2.93923 0.129644
\(515\) 31.4435 1.38556
\(516\) −11.1704 + 20.1431i −0.491749 + 0.886749i
\(517\) 18.4895 0.813169
\(518\) 0.772840 0.0339566
\(519\) −13.9879 + 24.2278i −0.614001 + 1.06348i
\(520\) −6.56445 −0.287870
\(521\) −21.8205 + 37.7943i −0.955975 + 1.65580i −0.223854 + 0.974623i \(0.571864\pi\)
−0.732121 + 0.681174i \(0.761470\pi\)
\(522\) 0.512853 0.888287i 0.0224470 0.0388793i
\(523\) 17.1244 + 29.6604i 0.748798 + 1.29696i 0.948399 + 0.317080i \(0.102702\pi\)
−0.199601 + 0.979877i \(0.563964\pi\)
\(524\) −2.62114 −0.114505
\(525\) 2.48391 + 4.30225i 0.108407 + 0.187766i
\(526\) −3.68338 + 6.37979i −0.160603 + 0.278172i
\(527\) 5.73563 0.249848
\(528\) 11.4983 19.9156i 0.500399 0.866717i
\(529\) 7.23080 + 12.5241i 0.314383 + 0.544527i
\(530\) −1.74628 3.02465i −0.0758537 0.131383i
\(531\) 0.692905 + 1.20015i 0.0300695 + 0.0520819i
\(532\) 16.2680 0.705307
\(533\) 12.2574 + 21.2304i 0.530927 + 0.919592i
\(534\) 2.01136 + 3.48378i 0.0870402 + 0.150758i
\(535\) −12.7282 + 22.0459i −0.550289 + 0.953129i
\(536\) 4.84182 8.38629i 0.209135 0.362232i
\(537\) −11.0999 −0.478998
\(538\) −4.14333 −0.178632
\(539\) −8.88586 + 15.3908i −0.382741 + 0.662927i
\(540\) 11.8457 20.5174i 0.509758 0.882927i
\(541\) −13.8111 23.9215i −0.593785 1.02847i −0.993717 0.111921i \(-0.964299\pi\)
0.399932 0.916545i \(-0.369034\pi\)
\(542\) 0.0758360 + 0.131352i 0.00325743 + 0.00564204i
\(543\) −47.2958 −2.02966
\(544\) −1.77919 3.08165i −0.0762823 0.132125i
\(545\) 23.9670 + 41.5120i 1.02663 + 1.77818i
\(546\) −0.869568 1.50614i −0.0372141 0.0644567i
\(547\) 20.9855 36.3479i 0.897273 1.55412i 0.0663072 0.997799i \(-0.478878\pi\)
0.830966 0.556323i \(-0.187788\pi\)
\(548\) 8.17344 0.349152
\(549\) −1.74130 + 3.01602i −0.0743168 + 0.128721i
\(550\) −1.06648 1.84720i −0.0454749 0.0787648i
\(551\) 45.0040 1.91723
\(552\) −3.34661 5.79651i −0.142441 0.246716i
\(553\) 1.01915 1.76521i 0.0433385 0.0750645i
\(554\) 1.78469 3.09117i 0.0758241 0.131331i
\(555\) −8.05757 −0.342025
\(556\) 20.4727 35.4598i 0.868237 1.50383i
\(557\) 11.9376 0.505811 0.252906 0.967491i \(-0.418614\pi\)
0.252906 + 0.967491i \(0.418614\pi\)
\(558\) 0.766666 0.0324556
\(559\) 6.84323 + 11.3939i 0.289438 + 0.481909i
\(560\) 13.0054 0.549579
\(561\) 6.75405 0.285156
\(562\) 0.0762689 0.132102i 0.00321721 0.00557237i
\(563\) −9.99689 −0.421319 −0.210659 0.977560i \(-0.567561\pi\)
−0.210659 + 0.977560i \(0.567561\pi\)
\(564\) −8.89231 + 15.4019i −0.374434 + 0.648539i
\(565\) 12.7600 22.1010i 0.536817 0.929794i
\(566\) −3.99775 6.92430i −0.168038 0.291050i
\(567\) 14.7307 0.618631
\(568\) 1.49273 + 2.58548i 0.0626334 + 0.108484i
\(569\) −11.0982 + 19.2226i −0.465261 + 0.805855i −0.999213 0.0396592i \(-0.987373\pi\)
0.533952 + 0.845514i \(0.320706\pi\)
\(570\) 9.01009 0.377391
\(571\) 8.41851 14.5813i 0.352303 0.610208i −0.634349 0.773047i \(-0.718732\pi\)
0.986653 + 0.162839i \(0.0520652\pi\)
\(572\) −7.02816 12.1731i −0.293862 0.508984i
\(573\) 1.82699 + 3.16443i 0.0763234 + 0.132196i
\(574\) 2.80557 + 4.85939i 0.117102 + 0.202827i
\(575\) 5.37350 0.224090
\(576\) 1.19506 + 2.06990i 0.0497941 + 0.0862458i
\(577\) 14.8732 + 25.7611i 0.619178 + 1.07245i 0.989636 + 0.143599i \(0.0458675\pi\)
−0.370458 + 0.928849i \(0.620799\pi\)
\(578\) 0.158813 0.275072i 0.00660574 0.0114415i
\(579\) −6.69908 + 11.6031i −0.278404 + 0.482210i
\(580\) 38.1104 1.58245
\(581\) −17.8034 −0.738610
\(582\) 2.43144 4.21139i 0.100787 0.174568i
\(583\) 7.67721 13.2973i 0.317957 0.550718i
\(584\) 1.60121 + 2.77338i 0.0662586 + 0.114763i
\(585\) 1.11531 + 1.93178i 0.0461125 + 0.0798691i
\(586\) 1.40448 0.0580185
\(587\) −7.61534 13.1901i −0.314319 0.544416i 0.664974 0.746867i \(-0.268443\pi\)
−0.979292 + 0.202451i \(0.935109\pi\)
\(588\) −8.54708 14.8040i −0.352476 0.610506i
\(589\) 16.8192 + 29.1316i 0.693021 + 1.20035i
\(590\) 1.36765 2.36884i 0.0563052 0.0975234i
\(591\) 45.7641 1.88249
\(592\) −2.83605 + 4.91218i −0.116561 + 0.201889i
\(593\) −21.1992 36.7180i −0.870546 1.50783i −0.861433 0.507871i \(-0.830433\pi\)
−0.00911212 0.999958i \(-0.502901\pi\)
\(594\) −5.53298 −0.227021
\(595\) 1.90983 + 3.30792i 0.0782954 + 0.135612i
\(596\) 14.7943 25.6244i 0.605996 1.04962i
\(597\) −15.6161 + 27.0480i −0.639126 + 1.10700i
\(598\) −1.88116 −0.0769264
\(599\) −9.39898 + 16.2795i −0.384032 + 0.665163i −0.991634 0.129078i \(-0.958798\pi\)
0.607602 + 0.794241i \(0.292131\pi\)
\(600\) 4.21227 0.171965
\(601\) 1.24268 0.0506901 0.0253451 0.999679i \(-0.491932\pi\)
0.0253451 + 0.999679i \(0.491932\pi\)
\(602\) 1.56633 + 2.60792i 0.0638390 + 0.106291i
\(603\) −3.29054 −0.134001
\(604\) −41.3385 −1.68204
\(605\) 3.05332 5.28851i 0.124135 0.215008i
\(606\) −6.47827 −0.263162
\(607\) 7.87106 13.6331i 0.319477 0.553350i −0.660902 0.750472i \(-0.729826\pi\)
0.980379 + 0.197122i \(0.0631596\pi\)
\(608\) 10.4346 18.0733i 0.423179 0.732968i
\(609\) 10.3649 + 17.9525i 0.420006 + 0.727471i
\(610\) 6.87391 0.278317
\(611\) 5.13121 + 8.88752i 0.207587 + 0.359551i
\(612\) −0.399605 + 0.692136i −0.0161531 + 0.0279779i
\(613\) −3.06992 −0.123993 −0.0619964 0.998076i \(-0.519747\pi\)
−0.0619964 + 0.998076i \(0.519747\pi\)
\(614\) −0.827315 + 1.43295i −0.0333877 + 0.0578292i
\(615\) −29.2507 50.6637i −1.17950 2.04296i
\(616\) −3.30278 5.72059i −0.133073 0.230489i
\(617\) 0.620254 + 1.07431i 0.0249705 + 0.0432501i 0.878241 0.478219i \(-0.158717\pi\)
−0.853270 + 0.521469i \(0.825384\pi\)
\(618\) 7.06346 0.284134
\(619\) 3.85096 + 6.67006i 0.154783 + 0.268092i 0.932980 0.359928i \(-0.117199\pi\)
−0.778197 + 0.628020i \(0.783865\pi\)
\(620\) 14.2428 + 24.6693i 0.572006 + 0.990744i
\(621\) 6.96953 12.0716i 0.279678 0.484416i
\(622\) −2.14514 + 3.71549i −0.0860123 + 0.148978i
\(623\) −10.0016 −0.400705
\(624\) 12.7640 0.510970
\(625\) 15.4065 26.6848i 0.616260 1.06739i
\(626\) −0.499859 + 0.865780i −0.0199784 + 0.0346035i
\(627\) 19.8056 + 34.3042i 0.790958 + 1.36998i
\(628\) −1.38215 2.39396i −0.0551539 0.0955294i
\(629\) −1.66588 −0.0664230
\(630\) 0.255282 + 0.442161i 0.0101707 + 0.0176161i
\(631\) 4.97235 + 8.61237i 0.197946 + 0.342853i 0.947862 0.318680i \(-0.103240\pi\)
−0.749916 + 0.661533i \(0.769906\pi\)
\(632\) −0.864148 1.49675i −0.0343740 0.0595374i
\(633\) 19.0269 32.9556i 0.756251 1.30987i
\(634\) −2.55895 −0.101629
\(635\) −1.66044 + 2.87597i −0.0658925 + 0.114129i
\(636\) 7.38451 + 12.7904i 0.292815 + 0.507170i
\(637\) −9.86400 −0.390826
\(638\) −4.45022 7.70801i −0.176186 0.305163i
\(639\) 0.507234 0.878555i 0.0200659 0.0347551i
\(640\) 11.6645 20.2034i 0.461079 0.798611i
\(641\) −38.3708 −1.51556 −0.757778 0.652513i \(-0.773715\pi\)
−0.757778 + 0.652513i \(0.773715\pi\)
\(642\) −2.85927 + 4.95240i −0.112846 + 0.195456i
\(643\) −25.7147 −1.01409 −0.507045 0.861920i \(-0.669262\pi\)
−0.507045 + 0.861920i \(0.669262\pi\)
\(644\) 8.10530 0.319394
\(645\) −16.3305 27.1900i −0.643013 1.07060i
\(646\) 1.86281 0.0732913
\(647\) −2.40913 −0.0947128 −0.0473564 0.998878i \(-0.515080\pi\)
−0.0473564 + 0.998878i \(0.515080\pi\)
\(648\) 6.24517 10.8170i 0.245334 0.424930i
\(649\) 12.0252 0.472031
\(650\) 0.591939 1.02527i 0.0232177 0.0402143i
\(651\) −7.74724 + 13.4186i −0.303638 + 0.525917i
\(652\) 1.39443 + 2.41522i 0.0546101 + 0.0945874i
\(653\) 5.17845 0.202648 0.101324 0.994853i \(-0.467692\pi\)
0.101324 + 0.994853i \(0.467692\pi\)
\(654\) 5.38394 + 9.32526i 0.210529 + 0.364646i
\(655\) 1.80470 3.12582i 0.0705153 0.122136i
\(656\) −41.1818 −1.60788
\(657\) 0.544098 0.942405i 0.0212273 0.0367667i
\(658\) 1.17447 + 2.03425i 0.0457858 + 0.0793033i
\(659\) 0.229184 + 0.396958i 0.00892773 + 0.0154633i 0.870455 0.492248i \(-0.163825\pi\)
−0.861527 + 0.507712i \(0.830492\pi\)
\(660\) 16.7718 + 29.0496i 0.652842 + 1.13076i
\(661\) −19.8284 −0.771234 −0.385617 0.922659i \(-0.626011\pi\)
−0.385617 + 0.922659i \(0.626011\pi\)
\(662\) −2.42779 4.20505i −0.0943587 0.163434i
\(663\) 1.87438 + 3.24653i 0.0727950 + 0.126085i
\(664\) −7.54788 + 13.0733i −0.292914 + 0.507343i
\(665\) −11.2008 + 19.4003i −0.434347 + 0.752311i
\(666\) −0.222674 −0.00862843
\(667\) 22.4226 0.868207
\(668\) −12.6138 + 21.8478i −0.488044 + 0.845317i
\(669\) 20.9737 36.3276i 0.810891 1.40450i
\(670\) 3.24741 + 5.62469i 0.125459 + 0.217301i
\(671\) 15.1099 + 26.1711i 0.583312 + 1.01033i
\(672\) 9.61279 0.370821
\(673\) 9.25416 + 16.0287i 0.356721 + 0.617860i 0.987411 0.158176i \(-0.0505612\pi\)
−0.630690 + 0.776035i \(0.717228\pi\)
\(674\) 0.574083 + 0.994341i 0.0221129 + 0.0383006i
\(675\) 4.38616 + 7.59705i 0.168823 + 0.292411i
\(676\) −8.44334 + 14.6243i −0.324744 + 0.562473i
\(677\) −26.4589 −1.01690 −0.508449 0.861092i \(-0.669781\pi\)
−0.508449 + 0.861092i \(0.669781\pi\)
\(678\) 2.86640 4.96476i 0.110084 0.190670i
\(679\) 6.04523 + 10.4707i 0.231995 + 0.401827i
\(680\) 3.23874 0.124200
\(681\) 13.7898 + 23.8846i 0.528425 + 0.915259i
\(682\) 3.32633 5.76137i 0.127372 0.220614i
\(683\) 15.5446 26.9241i 0.594799 1.03022i −0.398776 0.917048i \(-0.630565\pi\)
0.993575 0.113174i \(-0.0361019\pi\)
\(684\) −4.68720 −0.179220
\(685\) −5.62754 + 9.74718i −0.215017 + 0.372421i
\(686\) −5.50521 −0.210190
\(687\) 20.7370 0.791166
\(688\) −22.3238 + 0.385500i −0.851089 + 0.0146971i
\(689\) 8.52231 0.324674
\(690\) 4.48915 0.170899
\(691\) −0.809090 + 1.40138i −0.0307792 + 0.0533112i −0.881005 0.473108i \(-0.843132\pi\)
0.850225 + 0.526419i \(0.176466\pi\)
\(692\) −28.7255 −1.09198
\(693\) −1.12230 + 1.94388i −0.0426325 + 0.0738417i
\(694\) −2.96755 + 5.13994i −0.112647 + 0.195110i
\(695\) 28.1916 + 48.8292i 1.06937 + 1.85220i
\(696\) 17.5770 0.666255
\(697\) −6.04750 10.4746i −0.229065 0.396753i
\(698\) 1.93447 3.35060i 0.0732207 0.126822i
\(699\) 44.8938 1.69804
\(700\) −2.55047 + 4.41754i −0.0963987 + 0.166967i
\(701\) 18.5157 + 32.0701i 0.699327 + 1.21127i 0.968700 + 0.248234i \(0.0798501\pi\)
−0.269373 + 0.963036i \(0.586817\pi\)
\(702\) −1.53551 2.65958i −0.0579542 0.100380i
\(703\) −4.88502 8.46111i −0.184242 0.319117i
\(704\) 20.7399 0.781666
\(705\) −12.2450 21.2089i −0.461173 0.798775i
\(706\) −2.48385 4.30216i −0.0934809 0.161914i
\(707\) 8.05337 13.9489i 0.302878 0.524601i
\(708\) −5.78337 + 10.0171i −0.217352 + 0.376465i
\(709\) 12.8209 0.481500 0.240750 0.970587i \(-0.422607\pi\)
0.240750 + 0.970587i \(0.422607\pi\)
\(710\) −2.00234 −0.0751467
\(711\) −0.293641 + 0.508601i −0.0110124 + 0.0190740i
\(712\) −4.24024 + 7.34431i −0.158910 + 0.275240i
\(713\) 8.37991 + 14.5144i 0.313830 + 0.543570i
\(714\) 0.429024 + 0.743091i 0.0160558 + 0.0278095i
\(715\) 19.3560 0.723873
\(716\) −5.69870 9.87044i −0.212971 0.368876i
\(717\) −23.2231 40.2236i −0.867283 1.50218i
\(718\) −2.52088 4.36629i −0.0940783 0.162948i
\(719\) −15.3601 + 26.6045i −0.572837 + 0.992182i 0.423436 + 0.905926i \(0.360824\pi\)
−0.996273 + 0.0862564i \(0.972510\pi\)
\(720\) −3.74717 −0.139649
\(721\) −8.78084 + 15.2089i −0.327015 + 0.566407i
\(722\) 2.44506 + 4.23496i 0.0909955 + 0.157609i
\(723\) 24.9143 0.926574
\(724\) −24.2816 42.0570i −0.902419 1.56304i
\(725\) −7.05565 + 12.2207i −0.262040 + 0.453867i
\(726\) 0.685898 1.18801i 0.0254561 0.0440912i
\(727\) −7.39849 −0.274395 −0.137197 0.990544i \(-0.543809\pi\)
−0.137197 + 0.990544i \(0.543809\pi\)
\(728\) 1.83317 3.17515i 0.0679419 0.117679i
\(729\) 22.2244 0.823127
\(730\) −2.14787 −0.0794962
\(731\) −3.37628 5.62145i −0.124876 0.207917i
\(732\) −29.0677 −1.07437
\(733\) −36.3881 −1.34403 −0.672013 0.740539i \(-0.734570\pi\)
−0.672013 + 0.740539i \(0.734570\pi\)
\(734\) 3.73631 6.47149i 0.137910 0.238867i
\(735\) 23.5392 0.868256
\(736\) 5.19890 9.00476i 0.191634 0.331920i
\(737\) −14.2766 + 24.7279i −0.525887 + 0.910863i
\(738\) −0.808353 1.40011i −0.0297559 0.0515387i
\(739\) −33.3948 −1.22845 −0.614225 0.789131i \(-0.710531\pi\)
−0.614225 + 0.789131i \(0.710531\pi\)
\(740\) −4.13675 7.16506i −0.152070 0.263393i
\(741\) −10.9929 + 19.0402i −0.403833 + 0.699460i
\(742\) 1.95065 0.0716108
\(743\) 2.05251 3.55506i 0.0752994 0.130422i −0.825917 0.563792i \(-0.809342\pi\)
0.901216 + 0.433369i \(0.142675\pi\)
\(744\) 6.56899 + 11.3778i 0.240831 + 0.417131i
\(745\) 20.3721 + 35.2856i 0.746378 + 1.29276i
\(746\) −4.84057 8.38411i −0.177226 0.306964i
\(747\) 5.12959 0.187682
\(748\) 3.46752 + 6.00593i 0.126785 + 0.219598i
\(749\) −7.10892 12.3130i −0.259754 0.449907i
\(750\) 2.42816 4.20570i 0.0886640 0.153571i
\(751\) 19.1879 33.2345i 0.700177 1.21274i −0.268227 0.963356i \(-0.586438\pi\)
0.968404 0.249387i \(-0.0802291\pi\)
\(752\) −17.2396 −0.628664
\(753\) 14.2539 0.519441
\(754\) 2.47005 4.27825i 0.0899539 0.155805i
\(755\) 28.4622 49.2980i 1.03585 1.79414i
\(756\) 6.61602 + 11.4593i 0.240622 + 0.416770i
\(757\) 1.04356 + 1.80750i 0.0379288 + 0.0656946i 0.884367 0.466793i \(-0.154591\pi\)
−0.846438 + 0.532488i \(0.821257\pi\)
\(758\) 0.653286 0.0237284
\(759\) 9.86785 + 17.0916i 0.358180 + 0.620386i
\(760\) 9.49727 + 16.4498i 0.344502 + 0.596696i
\(761\) 7.78649 + 13.4866i 0.282260 + 0.488889i 0.971941 0.235225i \(-0.0755826\pi\)
−0.689681 + 0.724113i \(0.742249\pi\)
\(762\) −0.373001 + 0.646056i −0.0135124 + 0.0234042i
\(763\) −26.7719 −0.969207
\(764\) −1.87595 + 3.24923i −0.0678694 + 0.117553i
\(765\) −0.550268 0.953092i −0.0198950 0.0344591i
\(766\) −3.79372 −0.137073
\(767\) 3.33723 + 5.78025i 0.120500 + 0.208713i