Properties

Label 210.3.k.a.83.5
Level 210
Weight 3
Character 210.83
Analytic conductor 5.722
Analytic rank 0
Dimension 32
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 210.k (of order \(4\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.72208555157\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 83.5
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.5

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(-2.14733 - 2.09499i) q^{3} +2.00000i q^{4} +(-1.13661 + 4.86910i) q^{5} +(0.0523328 + 4.24232i) q^{6} +(6.60685 - 2.31291i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.222012 + 8.99726i) q^{9} +O(q^{10})\) \(q+(-1.00000 - 1.00000i) q^{2} +(-2.14733 - 2.09499i) q^{3} +2.00000i q^{4} +(-1.13661 + 4.86910i) q^{5} +(0.0523328 + 4.24232i) q^{6} +(6.60685 - 2.31291i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.222012 + 8.99726i) q^{9} +(6.00571 - 3.73249i) q^{10} -16.9733i q^{11} +(4.18999 - 4.29465i) q^{12} +(10.2231 - 10.2231i) q^{13} +(-8.91976 - 4.29394i) q^{14} +(12.6414 - 8.07434i) q^{15} -4.00000 q^{16} +(-8.79877 + 8.79877i) q^{17} +(8.77525 - 9.21927i) q^{18} -24.7369 q^{19} +(-9.73820 - 2.27322i) q^{20} +(-19.0326 - 8.87473i) q^{21} +(-16.9733 + 16.9733i) q^{22} +(19.2569 - 19.2569i) q^{23} +(-8.48464 + 0.104666i) q^{24} +(-22.4162 - 11.0685i) q^{25} -20.4462 q^{26} +(18.3725 - 19.7852i) q^{27} +(4.62582 + 13.2137i) q^{28} +1.67978 q^{29} +(-20.7157 - 4.56706i) q^{30} -36.8991i q^{31} +(4.00000 + 4.00000i) q^{32} +(-35.5589 + 36.4472i) q^{33} +17.5975 q^{34} +(3.75235 + 34.7983i) q^{35} +(-17.9945 + 0.444025i) q^{36} +(40.5381 - 40.5381i) q^{37} +(24.7369 + 24.7369i) q^{38} +(-43.3696 + 0.535003i) q^{39} +(7.46497 + 12.0114i) q^{40} -0.885911 q^{41} +(10.1578 + 27.9073i) q^{42} +(-9.87427 - 9.87427i) q^{43} +33.9466 q^{44} +(-44.0609 - 9.14540i) q^{45} -38.5139 q^{46} +(33.7538 - 33.7538i) q^{47} +(8.58930 + 8.37997i) q^{48} +(38.3009 - 30.5621i) q^{49} +(11.3477 + 33.4848i) q^{50} +(37.3272 - 0.460464i) q^{51} +(20.4462 + 20.4462i) q^{52} +(-11.9694 + 11.9694i) q^{53} +(-38.1576 + 1.41270i) q^{54} +(82.6446 + 19.2920i) q^{55} +(8.58788 - 17.8395i) q^{56} +(53.1183 + 51.8237i) q^{57} +(-1.67978 - 1.67978i) q^{58} -50.5136i q^{59} +(16.1487 + 25.2828i) q^{60} -80.6872i q^{61} +(-36.8991 + 36.8991i) q^{62} +(22.2766 + 58.9301i) q^{63} -8.00000i q^{64} +(38.1575 + 61.3969i) q^{65} +(72.0061 - 0.888260i) q^{66} +(-4.46192 + 4.46192i) q^{67} +(-17.5975 - 17.5975i) q^{68} +(-81.6941 + 1.00777i) q^{69} +(31.0459 - 38.5506i) q^{70} +137.180i q^{71} +(18.4385 + 17.5505i) q^{72} +(-53.3244 + 53.3244i) q^{73} -81.0762 q^{74} +(24.9464 + 70.7296i) q^{75} -49.4739i q^{76} +(-39.2577 - 112.140i) q^{77} +(43.9046 + 42.8346i) q^{78} +127.936i q^{79} +(4.54645 - 19.4764i) q^{80} +(-80.9014 + 3.99500i) q^{81} +(0.885911 + 0.885911i) q^{82} +(60.0077 + 60.0077i) q^{83} +(17.7495 - 38.0652i) q^{84} +(-32.8413 - 52.8429i) q^{85} +19.7485i q^{86} +(-3.60704 - 3.51913i) q^{87} +(-33.9466 - 33.9466i) q^{88} +51.3826i q^{89} +(34.9155 + 53.2063i) q^{90} +(43.8974 - 91.1875i) q^{91} +(38.5139 + 38.5139i) q^{92} +(-77.3034 + 79.2345i) q^{93} -67.5075 q^{94} +(28.1163 - 120.447i) q^{95} +(-0.209331 - 16.9693i) q^{96} +(0.274025 + 0.274025i) q^{97} +(-68.8630 - 7.73884i) q^{98} +(152.713 - 3.76828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + O(q^{10}) \) \( 32q - 32q^{2} - 4q^{7} + 64q^{8} - 16q^{9} + 8q^{14} - 20q^{15} - 128q^{16} + 36q^{18} + 12q^{21} - 40q^{22} + 24q^{23} + 16q^{25} - 8q^{28} - 112q^{29} + 68q^{30} + 128q^{32} - 48q^{35} - 40q^{36} + 32q^{37} + 64q^{39} - 44q^{42} - 32q^{43} + 80q^{44} - 48q^{46} - 8q^{50} + 84q^{51} - 136q^{53} + 244q^{57} + 112q^{58} - 96q^{60} + 72q^{63} - 200q^{65} + 32q^{67} + 8q^{72} - 64q^{74} + 88q^{77} - 124q^{78} + 76q^{81} + 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} + 48q^{92} - 452q^{93} + 544q^{95} + 128q^{98} + 160q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

\(n\) \(31\) \(71\) \(127\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{3}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.00000 1.00000i −0.500000 0.500000i
\(3\) −2.14733 2.09499i −0.715775 0.698331i
\(4\) 2.00000i 0.500000i
\(5\) −1.13661 + 4.86910i −0.227322 + 0.973820i
\(6\) 0.0523328 + 4.24232i 0.00872213 + 0.707053i
\(7\) 6.60685 2.31291i 0.943836 0.330415i
\(8\) 2.00000 2.00000i 0.250000 0.250000i
\(9\) 0.222012 + 8.99726i 0.0246680 + 0.999696i
\(10\) 6.00571 3.73249i 0.600571 0.373249i
\(11\) 16.9733i 1.54303i −0.636213 0.771513i \(-0.719500\pi\)
0.636213 0.771513i \(-0.280500\pi\)
\(12\) 4.18999 4.29465i 0.349165 0.357888i
\(13\) 10.2231 10.2231i 0.786392 0.786392i −0.194509 0.980901i \(-0.562311\pi\)
0.980901 + 0.194509i \(0.0623114\pi\)
\(14\) −8.91976 4.29394i −0.637126 0.306710i
\(15\) 12.6414 8.07434i 0.842760 0.538290i
\(16\) −4.00000 −0.250000
\(17\) −8.79877 + 8.79877i −0.517575 + 0.517575i −0.916837 0.399262i \(-0.869266\pi\)
0.399262 + 0.916837i \(0.369266\pi\)
\(18\) 8.77525 9.21927i 0.487514 0.512182i
\(19\) −24.7369 −1.30194 −0.650972 0.759102i \(-0.725639\pi\)
−0.650972 + 0.759102i \(0.725639\pi\)
\(20\) −9.73820 2.27322i −0.486910 0.113661i
\(21\) −19.0326 8.87473i −0.906313 0.422606i
\(22\) −16.9733 + 16.9733i −0.771513 + 0.771513i
\(23\) 19.2569 19.2569i 0.837258 0.837258i −0.151239 0.988497i \(-0.548326\pi\)
0.988497 + 0.151239i \(0.0483263\pi\)
\(24\) −8.48464 + 0.104666i −0.353526 + 0.00436106i
\(25\) −22.4162 11.0685i −0.896649 0.442742i
\(26\) −20.4462 −0.786392
\(27\) 18.3725 19.7852i 0.680462 0.732784i
\(28\) 4.62582 + 13.2137i 0.165208 + 0.471918i
\(29\) 1.67978 0.0579235 0.0289618 0.999581i \(-0.490780\pi\)
0.0289618 + 0.999581i \(0.490780\pi\)
\(30\) −20.7157 4.56706i −0.690525 0.152235i
\(31\) 36.8991i 1.19029i −0.803616 0.595147i \(-0.797094\pi\)
0.803616 0.595147i \(-0.202906\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) −35.5589 + 36.4472i −1.07754 + 1.10446i
\(34\) 17.5975 0.517575
\(35\) 3.75235 + 34.7983i 0.107210 + 0.994236i
\(36\) −17.9945 + 0.444025i −0.499848 + 0.0123340i
\(37\) 40.5381 40.5381i 1.09562 1.09562i 0.100708 0.994916i \(-0.467889\pi\)
0.994916 0.100708i \(-0.0321107\pi\)
\(38\) 24.7369 + 24.7369i 0.650972 + 0.650972i
\(39\) −43.3696 + 0.535003i −1.11204 + 0.0137180i
\(40\) 7.46497 + 12.0114i 0.186624 + 0.300285i
\(41\) −0.885911 −0.0216076 −0.0108038 0.999942i \(-0.503439\pi\)
−0.0108038 + 0.999942i \(0.503439\pi\)
\(42\) 10.1578 + 27.9073i 0.241853 + 0.664460i
\(43\) −9.87427 9.87427i −0.229634 0.229634i 0.582906 0.812540i \(-0.301916\pi\)
−0.812540 + 0.582906i \(0.801916\pi\)
\(44\) 33.9466 0.771513
\(45\) −44.0609 9.14540i −0.979131 0.203231i
\(46\) −38.5139 −0.837258
\(47\) 33.7538 33.7538i 0.718165 0.718165i −0.250064 0.968229i \(-0.580452\pi\)
0.968229 + 0.250064i \(0.0804517\pi\)
\(48\) 8.58930 + 8.37997i 0.178944 + 0.174583i
\(49\) 38.3009 30.5621i 0.781651 0.623716i
\(50\) 11.3477 + 33.4848i 0.226954 + 0.669696i
\(51\) 37.3272 0.460464i 0.731906 0.00902871i
\(52\) 20.4462 + 20.4462i 0.393196 + 0.393196i
\(53\) −11.9694 + 11.9694i −0.225838 + 0.225838i −0.810952 0.585113i \(-0.801050\pi\)
0.585113 + 0.810952i \(0.301050\pi\)
\(54\) −38.1576 + 1.41270i −0.706623 + 0.0261611i
\(55\) 82.6446 + 19.2920i 1.50263 + 0.350765i
\(56\) 8.58788 17.8395i 0.153355 0.318563i
\(57\) 53.1183 + 51.8237i 0.931899 + 0.909188i
\(58\) −1.67978 1.67978i −0.0289618 0.0289618i
\(59\) 50.5136i 0.856162i −0.903740 0.428081i \(-0.859190\pi\)
0.903740 0.428081i \(-0.140810\pi\)
\(60\) 16.1487 + 25.2828i 0.269145 + 0.421380i
\(61\) 80.6872i 1.32274i −0.750059 0.661370i \(-0.769975\pi\)
0.750059 0.661370i \(-0.230025\pi\)
\(62\) −36.8991 + 36.8991i −0.595147 + 0.595147i
\(63\) 22.2766 + 58.9301i 0.353597 + 0.935398i
\(64\) 8.00000i 0.125000i
\(65\) 38.1575 + 61.3969i 0.587039 + 0.944568i
\(66\) 72.0061 0.888260i 1.09100 0.0134585i
\(67\) −4.46192 + 4.46192i −0.0665959 + 0.0665959i −0.739620 0.673024i \(-0.764995\pi\)
0.673024 + 0.739620i \(0.264995\pi\)
\(68\) −17.5975 17.5975i −0.258787 0.258787i
\(69\) −81.6941 + 1.00777i −1.18397 + 0.0146053i
\(70\) 31.0459 38.5506i 0.443513 0.550723i
\(71\) 137.180i 1.93212i 0.258322 + 0.966059i \(0.416831\pi\)
−0.258322 + 0.966059i \(0.583169\pi\)
\(72\) 18.4385 + 17.5505i 0.256091 + 0.243757i
\(73\) −53.3244 + 53.3244i −0.730471 + 0.730471i −0.970713 0.240242i \(-0.922773\pi\)
0.240242 + 0.970713i \(0.422773\pi\)
\(74\) −81.0762 −1.09562
\(75\) 24.9464 + 70.7296i 0.332619 + 0.943061i
\(76\) 49.4739i 0.650972i
\(77\) −39.2577 112.140i −0.509840 1.45636i
\(78\) 43.9046 + 42.8346i 0.562880 + 0.549162i
\(79\) 127.936i 1.61944i 0.586816 + 0.809721i \(0.300381\pi\)
−0.586816 + 0.809721i \(0.699619\pi\)
\(80\) 4.54645 19.4764i 0.0568306 0.243455i
\(81\) −80.9014 + 3.99500i −0.998783 + 0.0493210i
\(82\) 0.885911 + 0.885911i 0.0108038 + 0.0108038i
\(83\) 60.0077 + 60.0077i 0.722985 + 0.722985i 0.969212 0.246227i \(-0.0791910\pi\)
−0.246227 + 0.969212i \(0.579191\pi\)
\(84\) 17.7495 38.0652i 0.211303 0.453157i
\(85\) −32.8413 52.8429i −0.386368 0.621681i
\(86\) 19.7485i 0.229634i
\(87\) −3.60704 3.51913i −0.0414602 0.0404498i
\(88\) −33.9466 33.9466i −0.385757 0.385757i
\(89\) 51.3826i 0.577332i 0.957430 + 0.288666i \(0.0932117\pi\)
−0.957430 + 0.288666i \(0.906788\pi\)
\(90\) 34.9155 + 53.2063i 0.387950 + 0.591181i
\(91\) 43.8974 91.1875i 0.482388 1.00206i
\(92\) 38.5139 + 38.5139i 0.418629 + 0.418629i
\(93\) −77.3034 + 79.2345i −0.831220 + 0.851984i
\(94\) −67.5075 −0.718165
\(95\) 28.1163 120.447i 0.295961 1.26786i
\(96\) −0.209331 16.9693i −0.00218053 0.176763i
\(97\) 0.274025 + 0.274025i 0.00282500 + 0.00282500i 0.708518 0.705693i \(-0.249364\pi\)
−0.705693 + 0.708518i \(0.749364\pi\)
\(98\) −68.8630 7.73884i −0.702683 0.0789678i
\(99\) 152.713 3.76828i 1.54256 0.0380634i
\(100\) 22.1371 44.8325i 0.221371 0.448325i
\(101\) 21.6785 0.214638 0.107319 0.994225i \(-0.465773\pi\)
0.107319 + 0.994225i \(0.465773\pi\)
\(102\) −37.7877 36.8667i −0.370467 0.361438i
\(103\) 49.4148 49.4148i 0.479755 0.479755i −0.425298 0.905053i \(-0.639831\pi\)
0.905053 + 0.425298i \(0.139831\pi\)
\(104\) 40.8924i 0.393196i
\(105\) 64.8446 82.5844i 0.617568 0.786518i
\(106\) 23.9389 0.225838
\(107\) −42.7088 42.7088i −0.399147 0.399147i 0.478785 0.877932i \(-0.341077\pi\)
−0.877932 + 0.478785i \(0.841077\pi\)
\(108\) 39.5703 + 36.7449i 0.366392 + 0.340231i
\(109\) 69.1171i 0.634102i 0.948408 + 0.317051i \(0.102693\pi\)
−0.948408 + 0.317051i \(0.897307\pi\)
\(110\) −63.3526 101.937i −0.575933 0.926697i
\(111\) −171.975 + 2.12147i −1.54933 + 0.0191123i
\(112\) −26.4274 + 9.25163i −0.235959 + 0.0826039i
\(113\) 58.1205 58.1205i 0.514341 0.514341i −0.401513 0.915853i \(-0.631515\pi\)
0.915853 + 0.401513i \(0.131515\pi\)
\(114\) −1.29455 104.942i −0.0113557 0.920544i
\(115\) 71.8763 + 115.652i 0.625011 + 1.00567i
\(116\) 3.35956i 0.0289618i
\(117\) 94.2495 + 89.7102i 0.805551 + 0.766754i
\(118\) −50.5136 + 50.5136i −0.428081 + 0.428081i
\(119\) −37.7814 + 78.4829i −0.317491 + 0.659520i
\(120\) 9.13411 41.4315i 0.0761176 0.345262i
\(121\) −167.093 −1.38093
\(122\) −80.6872 + 80.6872i −0.661370 + 0.661370i
\(123\) 1.90234 + 1.85598i 0.0154662 + 0.0150892i
\(124\) 73.7983 0.595147
\(125\) 79.3724 96.5662i 0.634979 0.772529i
\(126\) 36.6534 81.2067i 0.290900 0.644498i
\(127\) −7.40218 + 7.40218i −0.0582849 + 0.0582849i −0.735648 0.677364i \(-0.763122\pi\)
0.677364 + 0.735648i \(0.263122\pi\)
\(128\) −8.00000 + 8.00000i −0.0625000 + 0.0625000i
\(129\) 0.516748 + 41.8898i 0.00400580 + 0.324727i
\(130\) 23.2394 99.5545i 0.178764 0.765804i
\(131\) 16.3631 0.124909 0.0624544 0.998048i \(-0.480107\pi\)
0.0624544 + 0.998048i \(0.480107\pi\)
\(132\) −72.8944 71.1179i −0.552230 0.538772i
\(133\) −163.433 + 57.2143i −1.22882 + 0.430183i
\(134\) 8.92385 0.0665959
\(135\) 75.4535 + 111.945i 0.558915 + 0.829225i
\(136\) 35.1951i 0.258787i
\(137\) −102.022 102.022i −0.744688 0.744688i 0.228788 0.973476i \(-0.426524\pi\)
−0.973476 + 0.228788i \(0.926524\pi\)
\(138\) 82.7018 + 80.6863i 0.599289 + 0.584683i
\(139\) −80.5228 −0.579300 −0.289650 0.957133i \(-0.593539\pi\)
−0.289650 + 0.957133i \(0.593539\pi\)
\(140\) −69.5965 + 7.50470i −0.497118 + 0.0536050i
\(141\) −143.194 + 1.76643i −1.01556 + 0.0125279i
\(142\) 137.180 137.180i 0.966059 0.966059i
\(143\) −173.520 173.520i −1.21342 1.21342i
\(144\) −0.888049 35.9890i −0.00616701 0.249924i
\(145\) −1.90926 + 8.17902i −0.0131673 + 0.0564071i
\(146\) 106.649 0.730471
\(147\) −146.272 14.6134i −0.995046 0.0994110i
\(148\) 81.0762 + 81.0762i 0.547812 + 0.547812i
\(149\) 140.338 0.941864 0.470932 0.882170i \(-0.343918\pi\)
0.470932 + 0.882170i \(0.343918\pi\)
\(150\) 45.7832 95.6760i 0.305221 0.637840i
\(151\) 32.6929 0.216509 0.108255 0.994123i \(-0.465474\pi\)
0.108255 + 0.994123i \(0.465474\pi\)
\(152\) −49.4739 + 49.4739i −0.325486 + 0.325486i
\(153\) −81.1183 77.2114i −0.530185 0.504650i
\(154\) −72.8823 + 151.398i −0.473262 + 0.983102i
\(155\) 179.666 + 41.9400i 1.15913 + 0.270581i
\(156\) −1.07001 86.7392i −0.00685901 0.556021i
\(157\) 17.9885 + 17.9885i 0.114576 + 0.114576i 0.762070 0.647494i \(-0.224183\pi\)
−0.647494 + 0.762070i \(0.724183\pi\)
\(158\) 127.936 127.936i 0.809721 0.809721i
\(159\) 50.7781 0.626394i 0.319359 0.00393958i
\(160\) −24.0228 + 14.9299i −0.150143 + 0.0933121i
\(161\) 82.6882 171.767i 0.513591 1.06688i
\(162\) 84.8964 + 76.9064i 0.524052 + 0.474731i
\(163\) 90.3636 + 90.3636i 0.554378 + 0.554378i 0.927701 0.373324i \(-0.121782\pi\)
−0.373324 + 0.927701i \(0.621782\pi\)
\(164\) 1.77182i 0.0108038i
\(165\) −137.048 214.566i −0.830595 1.30040i
\(166\) 120.015i 0.722985i
\(167\) 11.1296 11.1296i 0.0666444 0.0666444i −0.672999 0.739643i \(-0.734994\pi\)
0.739643 + 0.672999i \(0.234994\pi\)
\(168\) −55.8146 + 20.3157i −0.332230 + 0.120927i
\(169\) 40.0232i 0.236824i
\(170\) −20.0016 + 85.6842i −0.117656 + 0.504024i
\(171\) −5.49190 222.565i −0.0321164 1.30155i
\(172\) 19.7485 19.7485i 0.114817 0.114817i
\(173\) −143.704 143.704i −0.830661 0.830661i 0.156946 0.987607i \(-0.449835\pi\)
−0.987607 + 0.156946i \(0.949835\pi\)
\(174\) 0.0879077 + 7.12617i 0.000505216 + 0.0409550i
\(175\) −173.701 21.2816i −0.992578 0.121609i
\(176\) 67.8932i 0.385757i
\(177\) −105.826 + 108.469i −0.597884 + 0.612819i
\(178\) 51.3826 51.3826i 0.288666 0.288666i
\(179\) −334.691 −1.86978 −0.934891 0.354936i \(-0.884503\pi\)
−0.934891 + 0.354936i \(0.884503\pi\)
\(180\) 18.2908 88.1218i 0.101616 0.489565i
\(181\) 99.3599i 0.548949i 0.961594 + 0.274475i \(0.0885040\pi\)
−0.961594 + 0.274475i \(0.911496\pi\)
\(182\) −135.085 + 47.2901i −0.742224 + 0.259836i
\(183\) −169.039 + 173.262i −0.923711 + 0.946785i
\(184\) 77.0278i 0.418629i
\(185\) 151.308 + 243.460i 0.817880 + 1.31600i
\(186\) 156.538 1.93103i 0.841602 0.0103819i
\(187\) 149.344 + 149.344i 0.798632 + 0.798632i
\(188\) 67.5075 + 67.5075i 0.359083 + 0.359083i
\(189\) 75.6228 173.211i 0.400121 0.916462i
\(190\) −148.563 + 92.3303i −0.781910 + 0.485949i
\(191\) 41.5022i 0.217289i −0.994081 0.108645i \(-0.965349\pi\)
0.994081 0.108645i \(-0.0346510\pi\)
\(192\) −16.7599 + 17.1786i −0.0872914 + 0.0894719i
\(193\) 112.254 + 112.254i 0.581626 + 0.581626i 0.935350 0.353724i \(-0.115085\pi\)
−0.353724 + 0.935350i \(0.615085\pi\)
\(194\) 0.548049i 0.00282500i
\(195\) 46.6894 211.779i 0.239433 1.08605i
\(196\) 61.1241 + 76.6018i 0.311858 + 0.390826i
\(197\) 177.771 + 177.771i 0.902388 + 0.902388i 0.995642 0.0932539i \(-0.0297268\pi\)
−0.0932539 + 0.995642i \(0.529727\pi\)
\(198\) −156.481 148.945i −0.790310 0.752247i
\(199\) −79.5223 −0.399609 −0.199805 0.979836i \(-0.564031\pi\)
−0.199805 + 0.979836i \(0.564031\pi\)
\(200\) −66.9696 + 22.6954i −0.334848 + 0.113477i
\(201\) 18.9289 0.233505i 0.0941736 0.00116172i
\(202\) −21.6785 21.6785i −0.107319 0.107319i
\(203\) 11.0981 3.88518i 0.0546703 0.0191388i
\(204\) 0.920928 + 74.6544i 0.00451435 + 0.365953i
\(205\) 1.00694 4.31359i 0.00491189 0.0210419i
\(206\) −98.8296 −0.479755
\(207\) 177.535 + 168.984i 0.857657 + 0.816350i
\(208\) −40.8924 + 40.8924i −0.196598 + 0.196598i
\(209\) 419.867i 2.00894i
\(210\) −147.429 + 17.7398i −0.702043 + 0.0844750i
\(211\) 398.914 1.89059 0.945294 0.326220i \(-0.105775\pi\)
0.945294 + 0.326220i \(0.105775\pi\)
\(212\) −23.9389 23.9389i −0.112919 0.112919i
\(213\) 287.392 294.571i 1.34926 1.38296i
\(214\) 85.4175i 0.399147i
\(215\) 59.3020 36.8556i 0.275823 0.171421i
\(216\) −2.82540 76.3152i −0.0130805 0.353311i
\(217\) −85.3443 243.787i −0.393292 1.12344i
\(218\) 69.1171 69.1171i 0.317051 0.317051i
\(219\) 226.219 2.79061i 1.03296 0.0127425i
\(220\) −38.5841 + 165.289i −0.175382 + 0.751315i
\(221\) 179.901i 0.814033i
\(222\) 174.097 + 169.854i 0.784220 + 0.765108i
\(223\) −162.636 + 162.636i −0.729308 + 0.729308i −0.970482 0.241174i \(-0.922468\pi\)
0.241174 + 0.970482i \(0.422468\pi\)
\(224\) 35.6790 + 17.1758i 0.159281 + 0.0766775i
\(225\) 94.6100 204.142i 0.420489 0.907298i
\(226\) −116.241 −0.514341
\(227\) 255.602 255.602i 1.12600 1.12600i 0.135179 0.990821i \(-0.456839\pi\)
0.990821 0.135179i \(-0.0431610\pi\)
\(228\) −103.647 + 106.237i −0.454594 + 0.465950i
\(229\) −188.516 −0.823212 −0.411606 0.911362i \(-0.635032\pi\)
−0.411606 + 0.911362i \(0.635032\pi\)
\(230\) 43.7753 187.528i 0.190328 0.815338i
\(231\) −150.633 + 323.046i −0.652093 + 1.39847i
\(232\) 3.35956 3.35956i 0.0144809 0.0144809i
\(233\) 16.7394 16.7394i 0.0718429 0.0718429i −0.670272 0.742115i \(-0.733823\pi\)
0.742115 + 0.670272i \(0.233823\pi\)
\(234\) −4.53930 183.960i −0.0193987 0.786152i
\(235\) 125.985 + 202.715i 0.536108 + 0.862618i
\(236\) 101.027 0.428081
\(237\) 268.025 274.720i 1.13091 1.15916i
\(238\) 116.264 40.7015i 0.488506 0.171015i
\(239\) −93.1494 −0.389746 −0.194873 0.980828i \(-0.562430\pi\)
−0.194873 + 0.980828i \(0.562430\pi\)
\(240\) −50.5656 + 32.2974i −0.210690 + 0.134572i
\(241\) 443.888i 1.84186i 0.389729 + 0.920929i \(0.372569\pi\)
−0.389729 + 0.920929i \(0.627431\pi\)
\(242\) 167.093 + 167.093i 0.690466 + 0.690466i
\(243\) 182.091 + 160.909i 0.749346 + 0.662178i
\(244\) 161.374 0.661370
\(245\) 105.276 + 221.228i 0.429700 + 0.902972i
\(246\) −0.0463622 3.75831i −0.000188464 0.0152777i
\(247\) −252.888 + 252.888i −1.02384 + 1.02384i
\(248\) −73.7983 73.7983i −0.297574 0.297574i
\(249\) −3.14037 254.572i −0.0126119 1.02238i
\(250\) −175.939 + 17.1938i −0.703754 + 0.0687750i
\(251\) −387.377 −1.54334 −0.771668 0.636026i \(-0.780577\pi\)
−0.771668 + 0.636026i \(0.780577\pi\)
\(252\) −117.860 + 44.5533i −0.467699 + 0.176799i
\(253\) −326.854 326.854i −1.29191 1.29191i
\(254\) 14.8044 0.0582849
\(255\) −40.1845 + 182.273i −0.157586 + 0.714796i
\(256\) 16.0000 0.0625000
\(257\) −181.485 + 181.485i −0.706167 + 0.706167i −0.965727 0.259560i \(-0.916422\pi\)
0.259560 + 0.965727i \(0.416422\pi\)
\(258\) 41.3730 42.4065i 0.160361 0.164366i
\(259\) 174.068 361.590i 0.672078 1.39610i
\(260\) −122.794 + 76.3151i −0.472284 + 0.293520i
\(261\) 0.372932 + 15.1134i 0.00142886 + 0.0579059i
\(262\) −16.3631 16.3631i −0.0624544 0.0624544i
\(263\) 181.005 181.005i 0.688233 0.688233i −0.273608 0.961841i \(-0.588217\pi\)
0.961841 + 0.273608i \(0.0882171\pi\)
\(264\) 1.77652 + 144.012i 0.00672924 + 0.545501i
\(265\) −44.6757 71.8849i −0.168588 0.271264i
\(266\) 220.648 + 106.219i 0.829502 + 0.399319i
\(267\) 107.646 110.335i 0.403169 0.413240i
\(268\) −8.92385 8.92385i −0.0332979 0.0332979i
\(269\) 197.175i 0.732994i 0.930419 + 0.366497i \(0.119443\pi\)
−0.930419 + 0.366497i \(0.880557\pi\)
\(270\) 36.4918 187.399i 0.135155 0.694070i
\(271\) 311.811i 1.15059i −0.817945 0.575296i \(-0.804887\pi\)
0.817945 0.575296i \(-0.195113\pi\)
\(272\) 35.1951 35.1951i 0.129394 0.129394i
\(273\) −285.299 + 103.845i −1.04505 + 0.380383i
\(274\) 204.044i 0.744688i
\(275\) −187.870 + 380.477i −0.683163 + 1.38355i
\(276\) −2.01554 163.388i −0.00730267 0.591986i
\(277\) 161.718 161.718i 0.583820 0.583820i −0.352131 0.935951i \(-0.614543\pi\)
0.935951 + 0.352131i \(0.114543\pi\)
\(278\) 80.5228 + 80.5228i 0.289650 + 0.289650i
\(279\) 331.991 8.19206i 1.18993 0.0293622i
\(280\) 77.1013 + 62.0918i 0.275362 + 0.221757i
\(281\) 182.531i 0.649576i 0.945787 + 0.324788i \(0.105293\pi\)
−0.945787 + 0.324788i \(0.894707\pi\)
\(282\) 144.961 + 141.428i 0.514045 + 0.501517i
\(283\) −13.2471 + 13.2471i −0.0468095 + 0.0468095i −0.730124 0.683315i \(-0.760538\pi\)
0.683315 + 0.730124i \(0.260538\pi\)
\(284\) −274.361 −0.966059
\(285\) −312.710 + 199.735i −1.09723 + 0.700823i
\(286\) 347.039i 1.21342i
\(287\) −5.85308 + 2.04903i −0.0203940 + 0.00713948i
\(288\) −35.1010 + 36.8771i −0.121878 + 0.128045i
\(289\) 134.163i 0.464233i
\(290\) 10.0883 6.26976i 0.0347872 0.0216199i
\(291\) −0.0143405 1.16250i −4.92800e−5 0.00399485i
\(292\) −106.649 106.649i −0.365236 0.365236i
\(293\) 45.8307 + 45.8307i 0.156419 + 0.156419i 0.780978 0.624559i \(-0.214721\pi\)
−0.624559 + 0.780978i \(0.714721\pi\)
\(294\) 131.658 + 160.885i 0.447818 + 0.547229i
\(295\) 245.955 + 57.4143i 0.833747 + 0.194625i
\(296\) 162.152i 0.547812i
\(297\) −335.819 311.841i −1.13070 1.04997i
\(298\) −140.338 140.338i −0.470932 0.470932i
\(299\) 393.731i 1.31683i
\(300\) −141.459 + 49.8928i −0.471531 + 0.166309i
\(301\) −88.0761 42.3995i −0.292612 0.140862i
\(302\) −32.6929 32.6929i −0.108255 0.108255i
\(303\) −46.5508 45.4163i −0.153633 0.149889i
\(304\) 98.9478 0.325486
\(305\) 392.874 + 91.7100i 1.28811 + 0.300689i
\(306\) 3.90687 + 158.330i 0.0127675 + 0.517417i
\(307\) −273.273 273.273i −0.890140 0.890140i 0.104396 0.994536i \(-0.466709\pi\)
−0.994536 + 0.104396i \(0.966709\pi\)
\(308\) 224.280 78.5153i 0.728182 0.254920i
\(309\) −209.633 + 2.58601i −0.678425 + 0.00836898i
\(310\) −137.726 221.606i −0.444276 0.714857i
\(311\) 408.594 1.31381 0.656903 0.753975i \(-0.271866\pi\)
0.656903 + 0.753975i \(0.271866\pi\)
\(312\) −85.6692 + 87.8092i −0.274581 + 0.281440i
\(313\) 269.726 269.726i 0.861746 0.861746i −0.129795 0.991541i \(-0.541432\pi\)
0.991541 + 0.129795i \(0.0414320\pi\)
\(314\) 35.9770i 0.114576i
\(315\) −312.256 + 41.4865i −0.991289 + 0.131703i
\(316\) −255.872 −0.809721
\(317\) −265.401 265.401i −0.837227 0.837227i 0.151266 0.988493i \(-0.451665\pi\)
−0.988493 + 0.151266i \(0.951665\pi\)
\(318\) −51.4045 50.1517i −0.161649 0.157710i
\(319\) 28.5114i 0.0893776i
\(320\) 38.9528 + 9.09290i 0.121727 + 0.0284153i
\(321\) 2.23507 + 181.184i 0.00696283 + 0.564437i
\(322\) −254.455 + 89.0791i −0.790234 + 0.276643i
\(323\) 217.655 217.655i 0.673854 0.673854i
\(324\) −7.99001 161.803i −0.0246605 0.499391i
\(325\) −342.318 + 116.008i −1.05329 + 0.356949i
\(326\) 180.727i 0.554378i
\(327\) 144.800 148.417i 0.442813 0.453875i
\(328\) −1.77182 + 1.77182i −0.00540189 + 0.00540189i
\(329\) 144.937 301.075i 0.440537 0.915123i
\(330\) −77.5180 + 351.614i −0.234903 + 1.06550i
\(331\) 383.355 1.15817 0.579086 0.815266i \(-0.303409\pi\)
0.579086 + 0.815266i \(0.303409\pi\)
\(332\) −120.015 + 120.015i −0.361492 + 0.361492i
\(333\) 373.732 + 355.732i 1.12232 + 1.06826i
\(334\) −22.2592 −0.0666444
\(335\) −16.6541 26.7970i −0.0497136 0.0799911i
\(336\) 76.1303 + 35.4989i 0.226578 + 0.105652i
\(337\) −207.675 + 207.675i −0.616246 + 0.616246i −0.944566 0.328321i \(-0.893517\pi\)
0.328321 + 0.944566i \(0.393517\pi\)
\(338\) −40.0232 + 40.0232i −0.118412 + 0.118412i
\(339\) −246.566 + 3.04161i −0.727333 + 0.00897229i
\(340\) 105.686 65.6826i 0.310840 0.193184i
\(341\) −626.300 −1.83666
\(342\) −217.073 + 228.057i −0.634716 + 0.666832i
\(343\) 182.361 290.505i 0.531665 0.846955i
\(344\) −39.4971 −0.114817
\(345\) 87.9475 398.922i 0.254920 1.15630i
\(346\) 287.409i 0.830661i
\(347\) −41.3813 41.3813i −0.119254 0.119254i 0.644961 0.764215i \(-0.276874\pi\)
−0.764215 + 0.644961i \(0.776874\pi\)
\(348\) 7.03826 7.21408i 0.0202249 0.0207301i
\(349\) 565.082 1.61915 0.809573 0.587019i \(-0.199698\pi\)
0.809573 + 0.587019i \(0.199698\pi\)
\(350\) 152.420 + 194.983i 0.435485 + 0.557094i
\(351\) −14.4421 390.089i −0.0411457 1.11136i
\(352\) 67.8932 67.8932i 0.192878 0.192878i
\(353\) −121.484 121.484i −0.344146 0.344146i 0.513778 0.857923i \(-0.328246\pi\)
−0.857923 + 0.513778i \(0.828246\pi\)
\(354\) 214.295 2.64351i 0.605352 0.00746756i
\(355\) −667.945 155.921i −1.88153 0.439214i
\(356\) −102.765 −0.288666
\(357\) 245.550 89.3766i 0.687815 0.250355i
\(358\) 334.691 + 334.691i 0.934891 + 0.934891i
\(359\) −129.751 −0.361424 −0.180712 0.983536i \(-0.557840\pi\)
−0.180712 + 0.983536i \(0.557840\pi\)
\(360\) −106.413 + 69.8310i −0.295590 + 0.193975i
\(361\) 250.916 0.695059
\(362\) 99.3599 99.3599i 0.274475 0.274475i
\(363\) 358.802 + 350.058i 0.988437 + 0.964347i
\(364\) 182.375 + 87.7947i 0.501030 + 0.241194i
\(365\) −199.033 320.251i −0.545295 0.877399i
\(366\) 342.301 4.22258i 0.935248 0.0115371i
\(367\) 476.739 + 476.739i 1.29902 + 1.29902i 0.929041 + 0.369976i \(0.120634\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(368\) −77.0278 + 77.0278i −0.209315 + 0.209315i
\(369\) −0.196683 7.97077i −0.000533016 0.0216010i
\(370\) 92.1521 394.768i 0.249060 1.06694i
\(371\) −51.3960 + 106.764i −0.138534 + 0.287775i
\(372\) −158.469 154.607i −0.425992 0.415610i
\(373\) 76.1479 + 76.1479i 0.204150 + 0.204150i 0.801775 0.597626i \(-0.203889\pi\)
−0.597626 + 0.801775i \(0.703889\pi\)
\(374\) 298.688i 0.798632i
\(375\) −372.744 + 41.0744i −0.993983 + 0.109532i
\(376\) 135.015i 0.359083i
\(377\) 17.1726 17.1726i 0.0455506 0.0455506i
\(378\) −248.834 + 97.5886i −0.658292 + 0.258171i
\(379\) 390.814i 1.03117i −0.856838 0.515585i \(-0.827574\pi\)
0.856838 0.515585i \(-0.172426\pi\)
\(380\) 240.893 + 56.2326i 0.633929 + 0.147981i
\(381\) 31.4024 0.387377i 0.0824210 0.00101674i
\(382\) −41.5022 + 41.5022i −0.108645 + 0.108645i
\(383\) 62.8508 + 62.8508i 0.164101 + 0.164101i 0.784381 0.620280i \(-0.212981\pi\)
−0.620280 + 0.784381i \(0.712981\pi\)
\(384\) 33.9385 0.418662i 0.0883816 0.00109027i
\(385\) 590.641 63.6898i 1.53413 0.165428i
\(386\) 224.508i 0.581626i
\(387\) 86.6492 91.0336i 0.223900 0.235229i
\(388\) −0.548049 + 0.548049i −0.00141250 + 0.00141250i
\(389\) 24.2532 0.0623476 0.0311738 0.999514i \(-0.490075\pi\)
0.0311738 + 0.999514i \(0.490075\pi\)
\(390\) −258.468 + 165.090i −0.662739 + 0.423306i
\(391\) 338.875i 0.866688i
\(392\) 15.4777 137.726i 0.0394839 0.351342i
\(393\) −35.1368 34.2805i −0.0894066 0.0872277i
\(394\) 355.541i 0.902388i
\(395\) −622.932 145.413i −1.57704 0.368135i
\(396\) 7.53656 + 305.426i 0.0190317 + 0.771279i
\(397\) 176.911 + 176.911i 0.445618 + 0.445618i 0.893895 0.448277i \(-0.147962\pi\)
−0.448277 + 0.893895i \(0.647962\pi\)
\(398\) 79.5223 + 79.5223i 0.199805 + 0.199805i
\(399\) 470.808 + 219.534i 1.17997 + 0.550210i
\(400\) 89.6649 + 44.2742i 0.224162 + 0.110685i
\(401\) 48.5936i 0.121181i −0.998163 0.0605905i \(-0.980702\pi\)
0.998163 0.0605905i \(-0.0192984\pi\)
\(402\) −19.1624 18.6954i −0.0476677 0.0465060i
\(403\) −377.223 377.223i −0.936038 0.936038i
\(404\) 43.3570i 0.107319i
\(405\) 72.5015 398.458i 0.179016 0.983846i
\(406\) −14.9833 7.21289i −0.0369046 0.0177657i
\(407\) −688.065 688.065i −1.69058 1.69058i
\(408\) 73.7334 75.5753i 0.180719 0.185234i
\(409\) 143.848 0.351706 0.175853 0.984416i \(-0.443732\pi\)
0.175853 + 0.984416i \(0.443732\pi\)
\(410\) −5.32052 + 3.30665i −0.0129769 + 0.00806500i
\(411\) 5.33910 + 432.811i 0.0129905 + 1.05307i
\(412\) 98.8296 + 98.8296i 0.239878 + 0.239878i
\(413\) −116.833 333.735i −0.282889 0.808076i
\(414\) −8.55055 346.519i −0.0206535 0.837003i
\(415\) −360.389 + 223.978i −0.868407 + 0.539706i
\(416\) 81.7847 0.196598
\(417\) 172.909 + 168.695i 0.414649 + 0.404543i
\(418\) 419.867 419.867i 1.00447 1.00447i
\(419\) 80.8927i 0.193061i 0.995330 + 0.0965306i \(0.0307746\pi\)
−0.995330 + 0.0965306i \(0.969225\pi\)
\(420\) 165.169 + 129.689i 0.393259 + 0.308784i
\(421\) −194.231 −0.461355 −0.230678 0.973030i \(-0.574094\pi\)
−0.230678 + 0.973030i \(0.574094\pi\)
\(422\) −398.914 398.914i −0.945294 0.945294i
\(423\) 311.185 + 296.198i 0.735662 + 0.700231i
\(424\) 47.8777i 0.112919i
\(425\) 294.625 99.8456i 0.693235 0.234931i
\(426\) −581.963 + 7.17903i −1.36611 + 0.0168522i
\(427\) −186.622 533.088i −0.437054 1.24845i
\(428\) 85.4175 85.4175i 0.199574 0.199574i
\(429\) 9.08076 + 736.125i 0.0211673 + 1.71591i
\(430\) −96.1576 22.4464i −0.223622 0.0522010i
\(431\) 577.019i 1.33879i 0.742906 + 0.669396i \(0.233447\pi\)
−0.742906 + 0.669396i \(0.766553\pi\)
\(432\) −73.4899 + 79.1406i −0.170115 + 0.183196i
\(433\) −42.9015 + 42.9015i −0.0990797 + 0.0990797i −0.754909 0.655829i \(-0.772319\pi\)
0.655829 + 0.754909i \(0.272319\pi\)
\(434\) −158.443 + 329.131i −0.365075 + 0.758367i
\(435\) 21.2348 13.5631i 0.0488156 0.0311796i
\(436\) −138.234 −0.317051
\(437\) −476.358 + 476.358i −1.09006 + 1.09006i
\(438\) −229.010 223.428i −0.522853 0.510110i
\(439\) −73.7420 −0.167977 −0.0839886 0.996467i \(-0.526766\pi\)
−0.0839886 + 0.996467i \(0.526766\pi\)
\(440\) 203.873 126.705i 0.463349 0.287966i
\(441\) 283.478 + 337.818i 0.642808 + 0.766028i
\(442\) 179.901 179.901i 0.407017 0.407017i
\(443\) 10.4996 10.4996i 0.0237011 0.0237011i −0.695157 0.718858i \(-0.744665\pi\)
0.718858 + 0.695157i \(0.244665\pi\)
\(444\) −4.24294 343.951i −0.00955617 0.774664i
\(445\) −250.187 58.4020i −0.562217 0.131241i
\(446\) 325.271 0.729308
\(447\) −301.351 294.006i −0.674163 0.657732i
\(448\) −18.5033 52.8548i −0.0413019 0.117979i
\(449\) −284.237 −0.633044 −0.316522 0.948585i \(-0.602515\pi\)
−0.316522 + 0.948585i \(0.602515\pi\)
\(450\) −298.752 + 109.532i −0.663893 + 0.243405i
\(451\) 15.0368i 0.0333411i
\(452\) 116.241 + 116.241i 0.257170 + 0.257170i
\(453\) −70.2023 68.4914i −0.154972 0.151195i
\(454\) −511.204 −1.12600
\(455\) 394.107 + 317.385i 0.866168 + 0.697550i
\(456\) 209.884 2.58911i 0.460272 0.00567786i
\(457\) −117.076 + 117.076i −0.256184 + 0.256184i −0.823500 0.567316i \(-0.807982\pi\)
0.567316 + 0.823500i \(0.307982\pi\)
\(458\) 188.516 + 188.516i 0.411606 + 0.411606i
\(459\) 12.4300 + 335.740i 0.0270806 + 0.731460i
\(460\) −231.303 + 143.753i −0.502833 + 0.312505i
\(461\) 221.554 0.480594 0.240297 0.970699i \(-0.422755\pi\)
0.240297 + 0.970699i \(0.422755\pi\)
\(462\) 473.679 172.412i 1.02528 0.373186i
\(463\) −315.054 315.054i −0.680462 0.680462i 0.279642 0.960104i \(-0.409784\pi\)
−0.960104 + 0.279642i \(0.909784\pi\)
\(464\) −6.71913 −0.0144809
\(465\) −297.936 466.457i −0.640723 1.00313i
\(466\) −33.4788 −0.0718429
\(467\) 229.349 229.349i 0.491111 0.491111i −0.417545 0.908656i \(-0.637109\pi\)
0.908656 + 0.417545i \(0.137109\pi\)
\(468\) −179.420 + 188.499i −0.383377 + 0.402776i
\(469\) −19.1592 + 39.7993i −0.0408513 + 0.0848599i
\(470\) 76.7299 328.701i 0.163255 0.699363i
\(471\) −0.941388 76.3129i −0.00199870 0.162023i
\(472\) −101.027 101.027i −0.214041 0.214041i
\(473\) −167.599 + 167.599i −0.354332 + 0.354332i
\(474\) −542.745 + 6.69524i −1.14503 + 0.0141250i
\(475\) 554.509 + 273.802i 1.16739 + 0.576425i
\(476\) −156.966 75.5628i −0.329760 0.158745i
\(477\) −110.349 105.035i −0.231341 0.220199i
\(478\) 93.1494 + 93.1494i 0.194873 + 0.194873i
\(479\) 166.037i 0.346633i −0.984866 0.173316i \(-0.944552\pi\)
0.984866 0.173316i \(-0.0554483\pi\)
\(480\) 82.8630 + 18.2682i 0.172631 + 0.0380588i
\(481\) 828.849i 1.72318i
\(482\) 443.888 443.888i 0.920929 0.920929i
\(483\) −537.409 + 195.609i −1.11265 + 0.404988i
\(484\) 334.185i 0.690466i
\(485\) −1.64571 + 1.02279i −0.00339322 + 0.00210885i
\(486\) −21.1819 343.000i −0.0435841 0.705762i
\(487\) −639.073 + 639.073i −1.31226 + 1.31226i −0.392521 + 0.919743i \(0.628397\pi\)
−0.919743 + 0.392521i \(0.871603\pi\)
\(488\) −161.374 161.374i −0.330685 0.330685i
\(489\) −4.72898 383.351i −0.00967071 0.783949i
\(490\) 115.952 326.505i 0.236636 0.666336i
\(491\) 148.567i 0.302581i 0.988489 + 0.151291i \(0.0483429\pi\)
−0.988489 + 0.151291i \(0.951657\pi\)
\(492\) −3.71195 + 3.80468i −0.00754462 + 0.00773308i
\(493\) −14.7800 + 14.7800i −0.0299798 + 0.0299798i
\(494\) 505.776 1.02384
\(495\) −155.227 + 747.858i −0.313591 + 1.51083i
\(496\) 147.597i 0.297574i
\(497\) 317.286 + 906.330i 0.638402 + 1.82360i
\(498\) −251.431 + 257.712i −0.504882 + 0.517494i
\(499\) 471.498i 0.944885i −0.881361 0.472443i \(-0.843372\pi\)
0.881361 0.472443i \(-0.156628\pi\)
\(500\) 193.132 + 158.745i 0.386265 + 0.317490i
\(501\) −47.2153 + 0.582443i −0.0942422 + 0.00116256i
\(502\) 387.377 + 387.377i 0.771668 + 0.771668i
\(503\) −40.7334 40.7334i −0.0809810 0.0809810i 0.665456 0.746437i \(-0.268237\pi\)
−0.746437 + 0.665456i \(0.768237\pi\)
\(504\) 162.413 + 73.3068i 0.322249 + 0.145450i
\(505\) −24.6400 + 105.555i −0.0487921 + 0.209019i
\(506\) 653.707i 1.29191i
\(507\) −83.8483 + 85.9428i −0.165381 + 0.169512i
\(508\) −14.8044 14.8044i −0.0291424 0.0291424i
\(509\) 834.832i 1.64014i 0.572263 + 0.820070i \(0.306066\pi\)
−0.572263 + 0.820070i \(0.693934\pi\)
\(510\) 222.458 142.089i 0.436191 0.278605i
\(511\) −228.972 + 475.641i −0.448086 + 0.930803i
\(512\) −16.0000 16.0000i −0.0312500 0.0312500i
\(513\) −454.479 + 489.424i −0.885923 + 0.954044i
\(514\) 362.970 0.706167
\(515\) 184.440 + 296.771i 0.358136 + 0.576254i
\(516\) −83.7796 + 1.03350i −0.162364 + 0.00200290i
\(517\) −572.913 572.913i −1.10815 1.10815i
\(518\) −535.658 + 187.522i −1.03409 + 0.362011i
\(519\) 7.52045 + 609.640i 0.0144903 + 1.17464i
\(520\) 199.109 + 46.4788i 0.382902 + 0.0893822i
\(521\) 690.826 1.32596 0.662980 0.748637i \(-0.269291\pi\)
0.662980 + 0.748637i \(0.269291\pi\)
\(522\) 14.7405 15.4864i 0.0282385 0.0296674i
\(523\) 560.737 560.737i 1.07216 1.07216i 0.0749699 0.997186i \(-0.476114\pi\)
0.997186 0.0749699i \(-0.0238861\pi\)
\(524\) 32.7261i 0.0624544i
\(525\) 328.408 + 409.601i 0.625539 + 0.780193i
\(526\) −362.011 −0.688233
\(527\) 324.667 + 324.667i 0.616067 + 0.616067i
\(528\) 142.236 145.789i 0.269386 0.276115i
\(529\) 212.659i 0.402003i
\(530\) −27.2092 + 116.561i −0.0513381 + 0.219926i
\(531\) 454.484 11.2146i 0.855902 0.0211198i
\(532\) −114.429 326.866i −0.215091 0.614411i
\(533\) −9.05675 + 9.05675i −0.0169920 + 0.0169920i
\(534\) −217.981 + 2.68899i −0.408204 + 0.00503557i
\(535\) 256.496 159.410i 0.479433 0.297962i
\(536\) 17.8477i 0.0332979i
\(537\) 718.690 + 701.175i 1.33834 + 1.30573i
\(538\) 197.175 197.175i 0.366497 0.366497i
\(539\) −518.739 650.093i −0.962410 1.20611i
\(540\) −223.891 + 150.907i −0.414612 + 0.279457i
\(541\) 655.178 1.21105 0.605525 0.795827i \(-0.292963\pi\)
0.605525 + 0.795827i \(0.292963\pi\)
\(542\) −311.811 + 311.811i −0.575296 + 0.575296i
\(543\) 208.158 213.358i 0.383348 0.392924i
\(544\) −70.3902 −0.129394
\(545\) −336.538 78.5594i −0.617501 0.144146i
\(546\) 389.144 + 181.454i 0.712717 + 0.332334i
\(547\) 253.750 253.750i 0.463894 0.463894i −0.436036 0.899929i \(-0.643618\pi\)
0.899929 + 0.436036i \(0.143618\pi\)
\(548\) 204.044 204.044i 0.372344 0.372344i
\(549\) 725.964 17.9135i 1.32234 0.0326294i
\(550\) 568.347 192.607i 1.03336 0.350195i
\(551\) −41.5527 −0.0754132
\(552\) −161.373 + 165.404i −0.292342 + 0.299644i
\(553\) 295.904 + 845.253i 0.535088 + 1.52849i
\(554\) −323.436 −0.583820
\(555\) 185.140 839.776i 0.333585 1.51311i
\(556\) 161.046i 0.289650i
\(557\) 468.602 + 468.602i 0.841296 + 0.841296i 0.989028 0.147731i \(-0.0471971\pi\)
−0.147731 + 0.989028i \(0.547197\pi\)
\(558\) −340.183 323.799i −0.609647 0.580285i
\(559\) −201.891 −0.361165
\(560\) −15.0094 139.193i −0.0268025 0.248559i
\(561\) −7.81559 633.565i −0.0139315 1.12935i
\(562\) 182.531 182.531i 0.324788 0.324788i
\(563\) −10.9862 10.9862i −0.0195137 0.0195137i 0.697283 0.716796i \(-0.254392\pi\)
−0.716796 + 0.697283i \(0.754392\pi\)
\(564\) −3.53286 286.388i −0.00626393 0.507781i
\(565\) 216.934 + 349.055i 0.383954 + 0.617796i
\(566\) 26.4942 0.0468095
\(567\) −525.263 + 213.512i −0.926390 + 0.376564i
\(568\) 274.361 + 274.361i 0.483029 + 0.483029i
\(569\) 122.993 0.216157 0.108079 0.994142i \(-0.465530\pi\)
0.108079 + 0.994142i \(0.465530\pi\)
\(570\) 512.444 + 112.975i 0.899025 + 0.198202i
\(571\) −863.540 −1.51233 −0.756164 0.654382i \(-0.772929\pi\)
−0.756164 + 0.654382i \(0.772929\pi\)
\(572\) 347.039 347.039i 0.606712 0.606712i
\(573\) −86.9469 + 89.1188i −0.151740 + 0.155530i
\(574\) 7.90211 + 3.80405i 0.0137667 + 0.00662726i
\(575\) −644.814 + 218.522i −1.12142 + 0.380037i
\(576\) 71.9781 1.77610i 0.124962 0.00308350i
\(577\) 604.940 + 604.940i 1.04842 + 1.04842i 0.998766 + 0.0496572i \(0.0158129\pi\)
0.0496572 + 0.998766i \(0.484187\pi\)
\(578\) 134.163 134.163i 0.232116 0.232116i
\(579\) −5.87455 476.216i −0.0101460 0.822481i
\(580\) −16.3580 3.81852i −0.0282035 0.00658366i
\(581\) 535.254 + 257.670i 0.921264 + 0.443493i
\(582\) −1.14816 + 1.17684i −0.00197278 + 0.00202206i
\(583\) 203.161 + 203.161i 0.348475 + 0.348475i
\(584\) 213.298i 0.365236i
\(585\) −543.933 + 356.944i −0.929799 + 0.610161i
\(586\) 91.6614i 0.156419i
\(587\) −354.852 + 354.852i −0.604518 + 0.604518i −0.941508 0.336990i \(-0.890591\pi\)
0.336990 + 0.941508i \(0.390591\pi\)
\(588\) 29.2268 292.544i 0.0497055 0.497523i
\(589\) 912.772i 1.54970i
\(590\) −188.541 303.370i −0.319561 0.514186i
\(591\) −9.30322 754.159i −0.0157415 1.27607i
\(592\) −162.152 + 162.152i −0.273906 + 0.273906i
\(593\) 420.895 + 420.895i 0.709772 + 0.709772i 0.966487 0.256715i \(-0.0826403\pi\)
−0.256715 + 0.966487i \(0.582640\pi\)
\(594\) 23.9781 + 647.661i 0.0403672 + 1.09034i
\(595\) −339.198 273.166i −0.570081 0.459102i
\(596\) 280.675i 0.470932i
\(597\) 170.760 + 166.599i 0.286030 + 0.279060i
\(598\) −393.731 + 393.731i −0.658413 + 0.658413i
\(599\) 761.718 1.27165 0.635824 0.771834i \(-0.280660\pi\)
0.635824 + 0.771834i \(0.280660\pi\)
\(600\) 191.352 + 91.5664i 0.318920 + 0.152611i
\(601\) 348.645i 0.580109i 0.957010 + 0.290054i \(0.0936734\pi\)
−0.957010 + 0.290054i \(0.906327\pi\)
\(602\) 45.6766 + 130.476i 0.0758747 + 0.216737i
\(603\) −41.1357 39.1545i −0.0682184 0.0649328i
\(604\) 65.3858i 0.108255i
\(605\) 189.920 813.591i 0.313917 1.34478i
\(606\) 1.13449 + 91.9670i 0.00187210 + 0.151761i
\(607\) 520.469 + 520.469i 0.857444 + 0.857444i 0.991036 0.133592i \(-0.0426512\pi\)
−0.133592 + 0.991036i \(0.542651\pi\)
\(608\) −98.9478 98.9478i −0.162743 0.162743i
\(609\) −31.9706 14.9076i −0.0524969 0.0244789i
\(610\) −301.164 484.584i −0.493711 0.794400i
\(611\) 690.136i 1.12952i
\(612\) 154.423 162.237i 0.252325 0.265092i
\(613\) 82.1048 + 82.1048i 0.133939 + 0.133939i 0.770898 0.636959i \(-0.219808\pi\)
−0.636959 + 0.770898i \(0.719808\pi\)
\(614\) 546.546i 0.890140i
\(615\) −11.1992 + 7.15315i −0.0182100 + 0.0116311i
\(616\) −302.795 145.765i −0.491551 0.236631i
\(617\) −186.511 186.511i −0.302286 0.302286i 0.539621 0.841908i \(-0.318567\pi\)
−0.841908 + 0.539621i \(0.818567\pi\)
\(618\) 212.219 + 207.047i 0.343397 + 0.335028i
\(619\) −608.262 −0.982652 −0.491326 0.870976i \(-0.663488\pi\)
−0.491326 + 0.870976i \(0.663488\pi\)
\(620\) −83.8800 + 359.331i −0.135290 + 0.579566i
\(621\) −27.2042 734.799i −0.0438072 1.18325i
\(622\) −408.594 408.594i −0.656903 0.656903i
\(623\) 118.843 + 339.477i 0.190759 + 0.544907i
\(624\) 173.478 2.14001i 0.278010 0.00342950i
\(625\) 379.974 + 496.230i 0.607959 + 0.793968i
\(626\) −539.453 −0.861746
\(627\) 879.619 901.592i 1.40290 1.43795i
\(628\) −35.9770 + 35.9770i −0.0572882 + 0.0572882i
\(629\) 713.371i 1.13413i
\(630\) 353.743 + 270.770i 0.561496 + 0.429793i
\(631\) 180.633 0.286265 0.143132 0.989704i \(-0.454283\pi\)
0.143132 + 0.989704i \(0.454283\pi\)
\(632\) 255.872 + 255.872i 0.404860 + 0.404860i
\(633\) −856.598 835.722i −1.35324 1.32026i
\(634\) 530.802i 0.837227i
\(635\) −27.6285 44.4553i −0.0435095 0.0700084i
\(636\) 1.25279 + 101.556i 0.00196979 + 0.159680i
\(637\) 79.1149 703.993i 0.124199 1.10517i
\(638\) −28.5114 + 28.5114i −0.0446888 + 0.0446888i
\(639\) −1234.25 + 30.4557i −1.93153 + 0.0476615i
\(640\) −29.8599 48.0457i −0.0466561 0.0750714i
\(641\) 1036.40i 1.61685i −0.588597 0.808427i \(-0.700319\pi\)
0.588597 0.808427i \(-0.299681\pi\)
\(642\) 178.949 183.419i 0.278737 0.285700i
\(643\) −639.514 + 639.514i −0.994579 + 0.994579i −0.999985 0.00540613i \(-0.998279\pi\)
0.00540613 + 0.999985i \(0.498279\pi\)
\(644\) 343.534 + 165.376i 0.533439 + 0.256796i
\(645\) −204.553 45.0963i −0.317136 0.0699168i
\(646\) −435.309 −0.673854
\(647\) 659.438 659.438i 1.01922 1.01922i 0.0194122 0.999812i \(-0.493821\pi\)
0.999812 0.0194122i \(-0.00617949\pi\)
\(648\) −153.813 + 169.793i −0.237365 + 0.262026i
\(649\) −857.382 −1.32108
\(650\) 458.326 + 226.310i 0.705117 + 0.348169i
\(651\) −327.470 + 702.286i −0.503026 + 1.07878i
\(652\) −180.727 + 180.727i −0.277189 + 0.277189i
\(653\) 334.285 334.285i 0.511921 0.511921i −0.403194 0.915115i \(-0.632100\pi\)
0.915115 + 0.403194i \(0.132100\pi\)
\(654\) −293.217 + 3.61709i −0.448344 + 0.00553072i
\(655\) −18.5984 + 79.6733i −0.0283946 + 0.121639i
\(656\) 3.54364 0.00540189
\(657\) −491.612 467.935i −0.748268 0.712229i
\(658\) −446.012 + 156.139i −0.677830 + 0.237293i
\(659\) −231.047 −0.350602 −0.175301 0.984515i \(-0.556090\pi\)
−0.175301 + 0.984515i \(0.556090\pi\)
\(660\) 429.132 274.096i 0.650201 0.415298i
\(661\) 513.220i 0.776429i −0.921569 0.388215i \(-0.873092\pi\)
0.921569 0.388215i \(-0.126908\pi\)
\(662\) −383.355 383.355i −0.579086 0.579086i
\(663\) 376.892 386.307i 0.568464 0.582665i
\(664\) 240.031 0.361492
\(665\) −92.8217 860.803i −0.139582 1.29444i
\(666\) −17.9999 729.463i −0.0270269 1.09529i
\(667\) 32.3475 32.3475i 0.0484970 0.0484970i
\(668\) 22.2592 + 22.2592i 0.0333222 + 0.0333222i
\(669\) 689.952 8.51117i 1.03132 0.0127222i
\(670\) −10.1430 + 43.4511i −0.0151387 + 0.0648524i
\(671\) −1369.53 −2.04102
\(672\) −40.6314 111.629i −0.0604634 0.166115i
\(673\) −98.5465 98.5465i −0.146429 0.146429i 0.630092 0.776521i \(-0.283017\pi\)
−0.776521 + 0.630092i \(0.783017\pi\)
\(674\) 415.350 0.616246
\(675\) −630.834 + 240.152i −0.934569 + 0.355781i
\(676\) 80.0464 0.118412
\(677\) −856.497 + 856.497i −1.26514 + 1.26514i −0.316565 + 0.948571i \(0.602529\pi\)
−0.948571 + 0.316565i \(0.897471\pi\)
\(678\) 249.607 + 243.524i 0.368152 + 0.359180i
\(679\) 2.44423 + 1.17665i 0.00359976 + 0.00173291i
\(680\) −171.368 40.0032i −0.252012 0.0588282i
\(681\) −1084.35 + 13.3764i −1.59228 + 0.0196422i
\(682\) 626.300 + 626.300i 0.918329 + 0.918329i
\(683\) −423.420 + 423.420i −0.619941 + 0.619941i −0.945516 0.325575i \(-0.894442\pi\)
0.325575 + 0.945516i \(0.394442\pi\)
\(684\) 445.129 10.9838i 0.650774 0.0160582i
\(685\) 612.716 380.796i 0.894476 0.555907i
\(686\) −472.867 + 108.144i −0.689310 + 0.157645i
\(687\) 404.804 + 394.939i 0.589235 + 0.574874i
\(688\) 39.4971 + 39.4971i 0.0574085 + 0.0574085i
\(689\) 244.729i 0.355195i
\(690\) −486.869 + 310.974i −0.705608 + 0.450687i
\(691\) 785.969i 1.13744i −0.822532 0.568718i \(-0.807439\pi\)
0.822532 0.568718i \(-0.192561\pi\)
\(692\) 287.409 287.409i 0.415331 0.415331i
\(693\) 1000.24 378.108i 1.44334 0.545610i
\(694\) 82.7625i 0.119254i
\(695\) 91.5231 392.073i 0.131688 0.564134i
\(696\) −14.2523 + 0.175815i −0.0204775 + 0.000252608i
\(697\) 7.79493 7.79493i 0.0111835 0.0111835i
\(698\) −565.082 565.082i −0.809573 0.809573i
\(699\) −71.0138 + 0.876019i −0.101593 + 0.00125325i
\(700\) 42.5631 347.402i 0.0608045 0.496289i
\(701\) 462.898i 0.660340i −0.943922 0.330170i \(-0.892894\pi\)
0.943922 0.330170i \(-0.107106\pi\)
\(702\) −375.647 + 404.531i −0.535109 + 0.576255i
\(703\) −1002.79 + 1002.79i −1.42644 + 1.42644i
\(704\) −135.786 −0.192878
\(705\) 154.155 699.234i 0.218660 0.991822i
\(706\) 242.967i 0.344146i
\(707\) 143.226 50.1403i 0.202583 0.0709199i
\(708\) −216.938 211.651i −0.306410 0.298942i
\(709\) 946.923i 1.33558i −0.744352 0.667788i \(-0.767241\pi\)
0.744352 0.667788i \(-0.232759\pi\)
\(710\) 512.024 + 823.865i 0.721160 + 1.16037i
\(711\) −1151.07 + 28.4033i −1.61895 + 0.0399484i
\(712\) 102.765 + 102.765i 0.144333 + 0.144333i
\(713\) −710.565 710.565i −0.996584 0.996584i
\(714\) −334.927 156.174i −0.469085 0.218730i
\(715\) 1042.11 647.659i 1.45749 0.905817i
\(716\) 669.382i 0.934891i
\(717\) 200.022 + 195.147i 0.278971 + 0.272172i
\(718\) 129.751 + 129.751i 0.180712 + 0.180712i
\(719\) 713.422i 0.992242i −0.868254 0.496121i \(-0.834757\pi\)
0.868254 0.496121i \(-0.165243\pi\)
\(720\) 176.244 + 36.5816i 0.244783 + 0.0508078i
\(721\) 212.184 440.768i 0.294292 0.611329i
\(722\) −250.916 250.916i −0.347530 0.347530i
\(723\) 929.942 953.172i 1.28623 1.31836i
\(724\) −198.720 −0.274475
\(725\) −37.6544 18.5928i −0.0519371 0.0256452i
\(726\) −8.74443 708.861i −0.0120447 0.976392i
\(727\) 521.776 + 521.776i 0.717711 + 0.717711i 0.968136 0.250425i \(-0.0805702\pi\)
−0.250425 + 0.968136i \(0.580570\pi\)
\(728\) −94.5803 270.170i −0.129918 0.371112i
\(729\) −53.9052 727.004i −0.0739440 0.997262i
\(730\) −121.218 + 519.283i −0.166052 + 0.711347i
\(731\) 173.763 0.237706
\(732\) −346.523 338.078i −0.473393 0.461855i
\(733\) 121.904 121.904i 0.166309 0.166309i −0.619046 0.785355i \(-0.712481\pi\)
0.785355 + 0.619046i \(0.212481\pi\)
\(734\) 953.479i 1.29902i
\(735\) 237.408 695.602i 0.323005 0.946397i
\(736\) 154.056 0.209315
\(737\) 75.7335 + 75.7335i 0.102759 + 0.102759i
\(738\) −7.77409 + 8.16745i −0.0105340 + 0.0110670i
\(739\) 708.172i 0.958284i −0.877737 0.479142i \(-0.840948\pi\)
0.877737 0.479142i \(-0.159052\pi\)
\(740\) −486.920 + 302.616i −0.658000 + 0.408940i
\(741\) 1072.83 13.2343i 1.44782 0.0178601i
\(742\) 158.160 55.3684i 0.213154 0.0746205i
\(743\) 212.648 212.648i 0.286202 0.286202i −0.549374 0.835576i \(-0.685134\pi\)
0.835576 + 0.549374i \(0.185134\pi\)
\(744\) 3.86207 + 313.076i 0.00519095 + 0.420801i
\(745\) −159.509 + 683.318i −0.214107 + 0.917205i
\(746\) 152.296i 0.204150i
\(747\) −526.583 + 553.228i −0.704930 + 0.740599i
\(748\) −298.688 + 298.688i −0.399316 + 0.399316i
\(749\) −380.952 183.389i −0.508614 0.244845i
\(750\) 413.818 + 331.669i 0.551757 + 0.442226i
\(751\) −588.834 −0.784067 −0.392034 0.919951i \(-0.628228\pi\)
−0.392034 + 0.919951i \(0.628228\pi\)
\(752\) −135.015 + 135.015i −0.179541 + 0.179541i
\(753\) 831.825 + 811.552i 1.10468 + 1.07776i
\(754\) −34.3451 −0.0455506
\(755\) −37.1591 + 159.185i −0.0492174 + 0.210841i
\(756\) 346.423 + 151.246i 0.458231 + 0.200060i
\(757\) −627.004 + 627.004i −0.828275 + 0.828275i −0.987278 0.159003i \(-0.949172\pi\)
0.159003 + 0.987278i \(0.449172\pi\)
\(758\) −390.814 + 390.814i −0.515585 + 0.515585i
\(759\) 17.1052 + 1386.62i 0.0225364 + 1.82690i
\(760\) −184.661 297.126i −0.242974 0.390955i
\(761\) 1055.93 1.38756 0.693780 0.720187i \(-0.255944\pi\)
0.693780 + 0.720187i \(0.255944\pi\)
\(762\) −31.7898 31.0150i −0.0417189 0.0407021i
\(763\) 159.862 + 456.647i 0.209517 + 0.598488i
\(764\) 83.0045 0.108645
\(765\) 468.150 307.213i 0.611961 0.401586i
\(766\) 125.702i 0.164101i
\(767\)