Properties

Label 210.3.k.a.83.12
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 83.12
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.a.167.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 1.00000i) q^{2} +(2.14733 + 2.09499i) q^{3} +2.00000i q^{4} +(1.13661 - 4.86910i) q^{5} +(-0.0523328 - 4.24232i) q^{6} +(2.31291 - 6.60685i) q^{7} +(2.00000 - 2.00000i) q^{8} +(0.222012 + 8.99726i) q^{9} +O(q^{10})\) \(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} +(2.31291 - 6.60685i) 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} +(18.8079 - 9.34153i) 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} +(13.2137 + 4.62582i) 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} +(-29.5405 - 18.7712i) 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} +(-28.1494 - 9.46634i) 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} +(59.9570 + 19.3430i) 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} +(10.7693 + 48.3117i) 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} +(-112.140 - 39.2577i) 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} +(18.6831 + 37.6157i) 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} +(7.73884 + 68.8630i) 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
\(7\) 2.31291 6.60685i 0.330415 0.943836i
\(8\) 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 −0.980901 0.194509i \(-0.937689\pi\)
0.194509 + 0.980901i \(0.437689\pi\)
\(14\) −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 −0.399262 0.916837i \(-0.630734\pi\)
0.916837 + 0.399262i \(0.130734\pi\)
\(18\) 8.77525 9.21927i 0.487514 0.512182i
\(19\) 24.7369 1.30194 0.650972 0.759102i \(-0.274361\pi\)
0.650972 + 0.759102i \(0.274361\pi\)
\(20\) 9.73820 + 2.27322i 0.486910 + 0.113661i
\(21\) 18.8079 9.34153i 0.895613 0.444835i
\(22\) −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
\(28\) 13.2137 + 4.62582i 0.471918 + 0.165208i
\(29\) 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 \(0.202906\pi\)
−0.803616 + 0.595147i \(0.797094\pi\)
\(32\) 4.00000 + 4.00000i 0.125000 + 0.125000i
\(33\) 35.5589 36.4472i 1.07754 1.10446i
\(34\) −17.5975 −0.517575
\(35\) −29.5405 18.7712i −0.844015 0.536320i
\(36\) −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 \(-0.496561\pi\)
0.0108038 + 0.999942i \(0.496561\pi\)
\(42\) −28.1494 9.46634i −0.670224 0.225389i
\(43\) −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 −0.968229 0.250064i \(-0.919548\pi\)
0.250064 + 0.968229i \(0.419548\pi\)
\(48\) −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 \(0.140810\pi\)
−0.903740 + 0.428081i \(0.859190\pi\)
\(60\) 16.1487 + 25.2828i 0.269145 + 0.421380i
\(61\) 80.6872i 1.32274i 0.750059 + 0.661370i \(0.230025\pi\)
−0.750059 + 0.661370i \(0.769975\pi\)
\(62\) 36.8991 36.8991i 0.595147 0.595147i
\(63\) 59.9570 + 19.3430i 0.951699 + 0.307032i
\(64\) 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
\(70\) 10.7693 + 48.3117i 0.153847 + 0.690167i
\(71\) 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 −0.240242 0.970713i \(-0.577227\pi\)
0.970713 + 0.240242i \(0.0772268\pi\)
\(74\) −81.0762 −1.09562
\(75\) −24.9464 70.7296i −0.332619 0.943061i
\(76\) 49.4739i 0.650972i
\(77\) −112.140 39.2577i −1.45636 0.509840i
\(78\) 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 0.246227 0.969212i \(-0.420809\pi\)
−0.969212 + 0.246227i \(0.920809\pi\)
\(84\) 18.6831 + 37.6157i 0.222417 + 0.447806i
\(85\) −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 \(-0.906788\pi\)
0.957430 0.288666i \(-0.0932117\pi\)
\(90\) −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 0.705693 0.708518i \(-0.250636\pi\)
−0.708518 + 0.705693i \(0.750636\pi\)
\(98\) 7.73884 + 68.8630i 0.0789678 + 0.702683i
\(99\) 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 \(-0.534227\pi\)
−0.107319 + 0.994225i \(0.534227\pi\)
\(102\) −37.7877 36.8667i −0.370467 0.361438i
\(103\) −49.4148 + 49.4148i −0.479755 + 0.479755i −0.905053 0.425298i \(-0.860169\pi\)
0.425298 + 0.905053i \(0.360169\pi\)
\(104\) 40.8924i 0.393196i
\(105\) −24.1076 102.195i −0.229596 0.973286i
\(106\) 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
\(112\) −9.25163 + 26.4274i −0.0826039 + 0.235959i
\(113\) 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
\(126\) −40.6140 79.3001i −0.322333 0.629366i
\(127\) −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 \(-0.519893\pi\)
−0.0624544 + 0.998048i \(0.519893\pi\)
\(132\) 72.8944 + 71.1179i 0.552230 + 0.538772i
\(133\) 57.2143 163.433i 0.430183 1.22882i
\(134\) 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 \(-0.406461\pi\)
0.289650 + 0.957133i \(0.406461\pi\)
\(140\) 37.5424 59.0810i 0.268160 0.422007i
\(141\) −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
\(147\) −18.2172 145.867i −0.123927 0.992291i
\(148\) 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 0.647494 0.762070i \(-0.275817\pi\)
−0.762070 + 0.647494i \(0.775817\pi\)
\(158\) 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 −0.739643 0.672999i \(-0.765006\pi\)
0.672999 + 0.739643i \(0.265006\pi\)
\(168\) 18.9327 56.2988i 0.112694 0.335112i
\(169\) 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 0.987607 0.156946i \(-0.0501648\pi\)
−0.156946 + 0.987607i \(0.550165\pi\)
\(174\) −0.0879077 7.12617i −0.000505216 0.0409550i
\(175\) −124.975 + 122.500i −0.714142 + 0.700001i
\(176\) 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 \(-0.911496\pi\)
0.961594 0.274475i \(-0.0885040\pi\)
\(182\) 47.2901 135.085i 0.259836 0.742224i
\(183\) −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
\(189\) 88.2238 + 167.145i 0.466792 + 0.884367i
\(190\) −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 \(-0.435969\pi\)
0.199805 + 0.979836i \(0.435969\pi\)
\(200\) −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
\(203\) 3.88518 11.0981i 0.0191388 0.0546703i
\(204\) 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
\(210\) −78.0875 + 126.303i −0.371845 + 0.601441i
\(211\) 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
\(217\) 243.787 + 85.3443i 1.12344 + 0.393292i
\(218\) 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 −0.241174 0.970482i \(-0.577532\pi\)
0.970482 + 0.241174i \(0.0775325\pi\)
\(224\) 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 \(0.543161\pi\)
−0.990821 + 0.135179i \(0.956839\pi\)
\(228\) −103.647 + 106.237i −0.454594 + 0.465950i
\(229\) 188.516 0.823212 0.411606 0.911362i \(-0.364968\pi\)
0.411606 + 0.911362i \(0.364968\pi\)
\(230\) −43.7753 + 187.528i −0.190328 + 0.815338i
\(231\) −158.557 319.231i −0.686392 1.38195i
\(232\) 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
\(238\) −40.7015 + 116.264i −0.171015 + 0.488506i
\(239\) −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 \(-0.627431\pi\)
0.389729 0.920929i \(-0.372569\pi\)
\(242\) 167.093 + 167.093i 0.690466 + 0.690466i
\(243\) −182.091 160.909i −0.749346 0.662178i
\(244\) −161.374 −0.661370
\(245\) −192.343 + 151.754i −0.785073 + 0.619403i
\(246\) −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 \(-0.219423\pi\)
0.771668 + 0.636026i \(0.219423\pi\)
\(252\) −38.6861 + 119.914i −0.153516 + 0.475850i
\(253\) −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 −0.259560 0.965727i \(-0.583578\pi\)
0.965727 + 0.259560i \(0.0835776\pi\)
\(258\) −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 \(-0.880557\pi\)
0.930419 0.366497i \(-0.119443\pi\)
\(270\) 36.4918 187.399i 0.135155 0.694070i
\(271\) 311.811i 1.15059i 0.817945 + 0.575296i \(0.195113\pi\)
−0.817945 + 0.575296i \(0.804887\pi\)
\(272\) −35.1951 + 35.1951i −0.129394 + 0.129394i
\(273\) −96.7752 + 287.774i −0.354488 + 1.05412i
\(274\) 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
\(280\) −96.6234 + 21.5386i −0.345084 + 0.0769237i
\(281\) 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 −0.683315 0.730124i \(-0.739462\pi\)
0.730124 + 0.683315i \(0.239462\pi\)
\(284\) −274.361 −0.966059
\(285\) 312.710 199.735i 1.09723 0.700823i
\(286\) 347.039i 1.21342i
\(287\) 2.04903 5.85308i 0.00713948 0.0203940i
\(288\) −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 0.624559 0.780978i \(-0.285279\pi\)
−0.780978 + 0.624559i \(0.785279\pi\)
\(294\) −127.650 + 164.084i −0.434182 + 0.558109i
\(295\) 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 0.994536 0.104396i \(-0.0332909\pi\)
−0.104396 + 0.994536i \(0.533291\pi\)
\(308\) 78.5153 224.280i 0.254920 0.728182i
\(309\) −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 \(-0.728134\pi\)
−0.656903 + 0.753975i \(0.728134\pi\)
\(312\) −85.6692 + 87.8092i −0.274581 + 0.281440i
\(313\) −269.726 + 269.726i −0.861746 + 0.861746i −0.991541 0.129795i \(-0.958568\pi\)
0.129795 + 0.991541i \(0.458568\pi\)
\(314\) 35.9770i 0.114576i
\(315\) 162.331 269.951i 0.515337 0.856988i
\(316\) −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
\(322\) −89.0791 + 254.455i −0.276643 + 0.790234i
\(323\) 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
\(336\) −75.2315 + 37.3661i −0.223903 + 0.111209i
\(337\) −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
\(343\) −290.505 + 182.361i −0.846955 + 0.531665i
\(344\) −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 \(-0.800302\pi\)
−0.809573 + 0.587019i \(0.800302\pi\)
\(350\) 247.475 + 2.47482i 0.707071 + 0.00707091i
\(351\) −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 0.857923 0.513778i \(-0.171754\pi\)
−0.513778 + 0.857923i \(0.671754\pi\)
\(354\) 214.295 2.64351i 0.605352 0.00746756i
\(355\) 667.945 + 155.921i 1.88153 + 0.439214i
\(356\) 102.765 0.288666
\(357\) 83.2921 247.680i 0.233311 0.693782i
\(358\) 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 \(-0.879366\pi\)
−0.369976 0.929041i \(-0.620634\pi\)
\(368\) −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
\(378\) 78.9216 255.369i 0.208787 0.675580i
\(379\) 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 0.620280 0.784381i \(-0.287019\pi\)
−0.784381 + 0.620280i \(0.787019\pi\)
\(384\) −33.9385 + 0.418662i −0.0883816 + 0.00109027i
\(385\) −318.609 + 501.400i −0.827556 + 1.30234i
\(386\) 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
\(392\) −137.726 + 15.4777i −0.351342 + 0.0394839i
\(393\) −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 0.448277 0.893895i \(-0.352038\pi\)
−0.893895 + 0.448277i \(0.852038\pi\)
\(398\) −79.5223 79.5223i −0.199805 0.199805i
\(399\) 465.249 231.081i 1.16604 0.579150i
\(400\) 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 \(-0.556268\pi\)
−0.175853 + 0.984416i \(0.556268\pi\)
\(410\) −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
\(413\) 333.735 + 116.833i 0.808076 + 0.282889i
\(414\) −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 \(-0.969225\pi\)
0.995330 0.0965306i \(-0.0307746\pi\)
\(420\) 204.390 48.2152i 0.486643 0.114798i
\(421\) −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
\(427\) 533.088 + 186.622i 1.24845 + 0.437054i
\(428\) 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 −0.655829 0.754909i \(-0.727681\pi\)
0.754909 + 0.655829i \(0.227681\pi\)
\(434\) −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 \(-0.473234\pi\)
0.0839886 + 0.996467i \(0.473234\pi\)
\(440\) −203.873 + 126.705i −0.463349 + 0.287966i
\(441\) 266.472 351.388i 0.604244 0.796799i
\(442\) 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
\(448\) −52.8548 18.5033i −0.117979 0.0413019i
\(449\) −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
\(455\) 493.895 110.096i 1.08548 0.241969i
\(456\) 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 \(-0.577245\pi\)
−0.240297 + 0.970699i \(0.577245\pi\)
\(462\) −160.675 + 477.788i −0.347781 + 1.03417i
\(463\) −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 −0.908656 0.417545i \(-0.862891\pi\)
0.417545 + 0.908656i \(0.362891\pi\)
\(468\) 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 \(0.0554483\pi\)
−0.984866 + 0.173316i \(0.944552\pi\)
\(480\) 82.8630 + 18.2682i 0.172631 + 0.0380588i
\(481\) 828.849i 1.72318i
\(482\) −443.888 + 443.888i −0.920929 + 0.920929i
\(483\) 182.293 542.071i 0.377418 1.12230i
\(484\) 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
\(490\) 344.097 + 40.5893i 0.702238 + 0.0828353i
\(491\) 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
\(497\) 906.330 + 317.286i 1.82360 + 0.638402i
\(498\) −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 0.746437 0.665456i \(-0.231763\pi\)
−0.665456 + 0.746437i \(0.731763\pi\)
\(504\) 158.600 81.2280i 0.314683 0.161167i
\(505\) −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 \(-0.693934\pi\)
0.572263 0.820070i \(-0.306066\pi\)
\(510\) −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
\(518\) −187.522 + 535.658i −0.362011 + 1.03409i
\(519\) 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 \(-0.730709\pi\)
−0.662980 + 0.748637i \(0.730709\pi\)
\(522\) 14.7405 15.4864i 0.0282385 0.0296674i
\(523\) −560.737 + 560.737i −1.07216 + 1.07216i −0.0749699 + 0.997186i \(0.523886\pi\)
−0.997186 + 0.0749699i \(0.976114\pi\)
\(524\) 32.7261i 0.0624544i
\(525\) −524.999 + 1.22605i −0.999997 + 0.00233532i
\(526\) −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
\(532\) 326.866 + 114.429i 0.614411 + 0.215091i
\(533\) −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
\(546\) 384.549 190.999i 0.704302 0.349814i
\(547\) 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
\(553\) 845.253 + 295.904i 1.52849 + 0.535088i
\(554\) −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
\(560\) 118.162 + 75.0848i 0.211004 + 0.134080i
\(561\) −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 0.716796 0.697283i \(-0.245608\pi\)
−0.697283 + 0.716796i \(0.745608\pi\)
\(564\) −3.53286 286.388i −0.00626393 0.507781i
\(565\) −216.934 349.055i −0.383954 0.617796i
\(566\) −26.4942 −0.0468095
\(567\) −160.723 + 543.744i −0.283462 + 0.958983i
\(568\) 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 \(-0.984187\pi\)
−0.0496572 0.998766i \(-0.515813\pi\)
\(578\) 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 −0.336990 0.941508i \(-0.609409\pi\)
0.941508 + 0.336990i \(0.109409\pi\)
\(588\) 291.734 36.4344i 0.496146 0.0619633i
\(589\) 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 0.256715 0.966487i \(-0.417360\pi\)
−0.966487 + 0.256715i \(0.917360\pi\)
\(594\) −23.9781 647.661i −0.0403672 1.09034i
\(595\) −425.084 + 94.7568i −0.714426 + 0.159255i
\(596\) 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 \(-0.906327\pi\)
0.957010 0.290054i \(-0.0936734\pi\)
\(602\) 130.476 + 45.6766i 0.216737 + 0.0758747i
\(603\) −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 0.133592 0.991036i \(-0.457349\pi\)
−0.991036 + 0.133592i \(0.957349\pi\)
\(608\) 98.9478 + 98.9478i 0.162743 + 0.162743i
\(609\) 31.5931 15.6917i 0.0518770 0.0257664i
\(610\) −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 \(-0.336512\pi\)
0.491326 + 0.870976i \(0.336512\pi\)
\(620\) −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
\(623\) −339.477 118.843i −0.544907 0.190759i
\(624\) 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
\(630\) −432.282 + 107.620i −0.686162 + 0.170826i
\(631\) 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
\(637\) 703.993 79.1149i 1.10517 0.124199i
\(638\) −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 −0.00540613 0.999985i \(-0.501721\pi\)
0.999985 + 0.00540613i \(0.00172083\pi\)
\(644\) 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 \(0.506179\pi\)
−0.999812 + 0.0194122i \(0.993821\pi\)
\(648\) −153.813 + 169.793i −0.237365 + 0.262026i
\(649\) 857.382 1.32108
\(650\) −458.326 226.310i −0.705117 0.348169i
\(651\) 344.694 + 693.994i 0.529485 + 1.06604i
\(652\) −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
\(658\) 156.139 446.012i 0.237293 0.677830i
\(659\) −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 \(0.126908\pi\)
−0.921569 + 0.388215i \(0.873092\pi\)
\(662\) −383.355 383.355i −0.579086 0.579086i
\(663\) −376.892 + 386.307i −0.568464 + 0.582665i
\(664\) −240.031 −0.361492
\(665\) −730.742 464.342i −1.09886 0.698259i
\(666\) −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
\(672\) 112.598 + 37.8653i 0.167556 + 0.0563472i
\(673\) −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 \(-0.397471\pi\)
0.948571 0.316565i \(-0.102529\pi\)
\(678\) −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 \(0.192561\pi\)
−0.822532 + 0.568718i \(0.807439\pi\)
\(692\) −287.409 + 287.409i −0.415331 + 0.415331i
\(693\) 328.315 1017.67i 0.473759 1.46850i
\(694\) 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
\(700\) −245.000 249.950i −0.350000 0.357071i
\(701\) 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
\(707\) −50.1403 + 143.226i −0.0709199 + 0.202583i
\(708\) −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
\(714\) −330.972 + 164.388i −0.463547 + 0.230235i
\(715\) 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 \(0.165243\pi\)
−0.868254 + 0.496121i \(0.834757\pi\)
\(720\) −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 0.250425 0.968136i \(-0.419430\pi\)
−0.968136 + 0.250425i \(0.919430\pi\)
\(728\) 270.170 + 94.5803i 0.371112 + 0.129918i
\(729\) −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 −0.785355 0.619046i \(-0.787519\pi\)
0.619046 + 0.785355i \(0.287519\pi\)
\(734\) 953.479i 1.29902i
\(735\) −730.946 77.0926i −0.994484 0.104888i
\(736\) 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
\(742\) 55.3684 158.160i 0.0746205 0.213154i
\(743\) 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
\(756\) −334.291 + 176.448i −0.442183 + 0.233396i
\(757\) −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 \(-0.744056\pi\)
−0.693780 + 0.720187i \(0.744056\pi\)
\(762\) 31.7898 + 31.0150i 0.0417189 + 0.0407021i
\(763\) 456.647 + 159.862i 0.598488 + 0.209517i
\(764\) 83.0045 0.108645
\(765\) 468.150 307.213i 0.611961 0.401586i
\(766\) 125.702i 0.164101i