Properties

Label 210.3.k.b.167.13
Level 210
Weight 3
Character 210.167
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 167.13
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.b.83.13

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(2.09499 - 2.14733i) q^{3} -2.00000i q^{4} +(1.13661 + 4.86910i) q^{5} +(-0.0523328 - 4.24232i) q^{6} +(6.60685 + 2.31291i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.222012 - 8.99726i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(2.09499 - 2.14733i) 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} +(-4.29465 - 4.18999i) q^{12} +(10.2231 + 10.2231i) q^{13} +(8.91976 - 4.29394i) q^{14} +(12.8367 + 7.76005i) q^{15} -4.00000 q^{16} +(8.79877 + 8.79877i) q^{17} +(-9.21927 - 8.77525i) 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} +(-19.7852 - 18.3725i) q^{27} +(4.62582 - 13.2137i) q^{28} -1.67978 q^{29} +(20.5968 - 5.07668i) q^{30} +36.8991i q^{31} +(-4.00000 + 4.00000i) q^{32} +(-36.4472 - 35.5589i) 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} +(9.46634 - 28.1494i) q^{42} +(-9.87427 + 9.87427i) q^{43} -33.9466 q^{44} +(43.5562 - 11.3074i) q^{45} -38.5139 q^{46} +(-33.7538 - 33.7538i) q^{47} +(-8.37997 + 8.58930i) 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} +(-51.8237 + 53.1183i) q^{57} +(-1.67978 + 1.67978i) q^{58} -50.5136i q^{59} +(15.5201 - 25.6735i) q^{60} +80.6872i q^{61} +(36.8991 + 36.8991i) q^{62} +(19.3430 - 59.9570i) 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} +(-17.5505 + 18.4385i) q^{72} +(-53.3244 - 53.3244i) q^{73} +81.0762 q^{74} +(-23.1941 + 71.3235i) q^{75} +49.4739i q^{76} +(39.2577 - 112.140i) q^{77} +(42.8346 - 43.9046i) 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} +(-3.51913 + 3.60704i) q^{87} +(-33.9466 + 33.9466i) q^{88} +51.3826i q^{89} +(32.2488 - 54.8636i) q^{90} +(43.8974 + 91.1875i) q^{91} +(-38.5139 + 38.5139i) q^{92} +(79.2345 + 77.3034i) 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

Character values

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

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

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
\(3\) 2.09499 2.14733i 0.698331 0.715775i
\(4\) 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 \(-0.280500\pi\)
\(12\) −4.29465 4.18999i −0.357888 0.349165i
\(13\) 10.2231 + 10.2231i 0.786392 + 0.786392i 0.980901 0.194509i \(-0.0623114\pi\)
−0.194509 + 0.980901i \(0.562311\pi\)
\(14\) 8.91976 4.29394i 0.637126 0.306710i
\(15\) 12.8367 + 7.76005i 0.855782 + 0.517337i
\(16\) −4.00000 −0.250000
\(17\) 8.79877 + 8.79877i 0.517575 + 0.517575i 0.916837 0.399262i \(-0.130734\pi\)
−0.399262 + 0.916837i \(0.630734\pi\)
\(18\) −9.21927 8.77525i −0.512182 0.487514i
\(19\) −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
\(21\) 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 \(-0.451674\pi\)
−0.988497 + 0.151239i \(0.951674\pi\)
\(24\) −8.48464 + 0.104666i −0.353526 + 0.00436106i
\(25\) −22.4162 + 11.0685i −0.896649 + 0.442742i
\(26\) 20.4462 0.786392
\(27\) −19.7852 18.3725i −0.732784 0.680462i
\(28\) 4.62582 13.2137i 0.165208 0.471918i
\(29\) −1.67978 −0.0579235 −0.0289618 0.999581i \(-0.509220\pi\)
−0.0289618 + 0.999581i \(0.509220\pi\)
\(30\) 20.5968 5.07668i 0.686559 0.169223i
\(31\) 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
\(33\) −36.4472 35.5589i −1.10446 1.07754i
\(34\) 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 0.994916 + 0.100708i \(0.0321107\pi\)
0.100708 + 0.994916i \(0.467889\pi\)
\(38\) −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 \(0.496561\pi\)
\(42\) 9.46634 28.1494i 0.225389 0.670224i
\(43\) −9.87427 + 9.87427i −0.229634 + 0.229634i −0.812540 0.582906i \(-0.801916\pi\)
0.582906 + 0.812540i \(0.301916\pi\)
\(44\) −33.9466 −0.771513
\(45\) 43.5562 11.3074i 0.967916 0.251275i
\(46\) −38.5139 −0.837258
\(47\) −33.7538 33.7538i −0.718165 0.718165i 0.250064 0.968229i \(-0.419548\pi\)
−0.968229 + 0.250064i \(0.919548\pi\)
\(48\) −8.37997 + 8.58930i −0.174583 + 0.178944i
\(49\) 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 \(-0.198950\pi\)
−0.585113 + 0.810952i \(0.698950\pi\)
\(54\) −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
\(57\) −51.8237 + 53.1183i −0.909188 + 0.931899i
\(58\) −1.67978 + 1.67978i −0.0289618 + 0.0289618i
\(59\) 50.5136i 0.856162i −0.903740 0.428081i \(-0.859190\pi\)
0.903740 0.428081i \(-0.140810\pi\)
\(60\) 15.5201 25.6735i 0.258668 0.427891i
\(61\) 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
\(63\) 19.3430 59.9570i 0.307032 0.951699i
\(64\) 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 0.673024 0.739620i \(-0.264995\pi\)
−0.739620 + 0.673024i \(0.764995\pi\)
\(68\) 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 \(0.583169\pi\)
\(72\) −17.5505 + 18.4385i −0.243757 + 0.256091i
\(73\) −53.3244 53.3244i −0.730471 0.730471i 0.240242 0.970713i \(-0.422773\pi\)
−0.970713 + 0.240242i \(0.922773\pi\)
\(74\) 81.0762 1.09562
\(75\) −23.1941 + 71.3235i −0.309254 + 0.950979i
\(76\) 49.4739i 0.650972i
\(77\) 39.2577 112.140i 0.509840 1.45636i
\(78\) 42.8346 43.9046i 0.549162 0.562880i
\(79\) 127.936i 1.61944i −0.586816 0.809721i \(-0.699619\pi\)
0.586816 0.809721i \(-0.300381\pi\)
\(80\) −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 \(-0.920809\pi\)
0.246227 + 0.969212i \(0.420809\pi\)
\(84\) −18.6831 37.6157i −0.222417 0.447806i
\(85\) −32.8413 + 52.8429i −0.386368 + 0.621681i
\(86\) 19.7485i 0.229634i
\(87\) −3.51913 + 3.60704i −0.0404498 + 0.0414602i
\(88\) −33.9466 + 33.9466i −0.385757 + 0.385757i
\(89\) 51.3826i 0.577332i 0.957430 + 0.288666i \(0.0932117\pi\)
−0.957430 + 0.288666i \(0.906788\pi\)
\(90\) 32.2488 54.8636i 0.358320 0.609596i
\(91\) 43.8974 + 91.1875i 0.482388 + 1.00206i
\(92\) −38.5139 + 38.5139i −0.418629 + 0.418629i
\(93\) 79.2345 + 77.3034i 0.851984 + 0.831220i
\(94\) −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 \(-0.749364\pi\)
0.708518 + 0.705693i \(0.249364\pi\)
\(98\) 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 \(-0.534227\pi\)
−0.107319 + 0.994225i \(0.534227\pi\)
\(102\) 36.8667 37.7877i 0.361438 0.370467i
\(103\) 49.4148 + 49.4148i 0.479755 + 0.479755i 0.905053 0.425298i \(-0.139831\pi\)
−0.425298 + 0.905053i \(0.639831\pi\)
\(104\) 40.8924i 0.393196i
\(105\) 66.8621 + 80.9596i 0.636782 + 0.771044i
\(106\) 23.9389 0.225838
\(107\) 42.7088 42.7088i 0.399147 0.399147i −0.478785 0.877932i \(-0.658923\pi\)
0.877932 + 0.478785i \(0.158923\pi\)
\(108\) −36.7449 + 39.5703i −0.340231 + 0.366392i
\(109\) 69.1171i 0.634102i −0.948408 0.317051i \(-0.897307\pi\)
0.948408 0.317051i \(-0.102693\pi\)
\(110\) 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 \(-0.368485\pi\)
−0.915853 + 0.401513i \(0.868485\pi\)
\(114\) 1.29455 + 104.942i 0.0113557 + 0.920544i
\(115\) 71.8763 115.652i 0.625011 1.00567i
\(116\) 3.35956i 0.0289618i
\(117\) 89.7102 94.2495i 0.766754 0.805551i
\(118\) −50.5136 50.5136i −0.428081 0.428081i
\(119\) 37.7814 + 78.4829i 0.317491 + 0.659520i
\(120\) −10.1534 41.1936i −0.0846114 0.343280i
\(121\) −167.093 −1.38093
\(122\) 80.6872 + 80.6872i 0.661370 + 0.661370i
\(123\) 1.85598 1.90234i 0.0150892 0.0154662i
\(124\) 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 0.677364 0.735648i \(-0.263122\pi\)
−0.735648 + 0.677364i \(0.763122\pi\)
\(128\) 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 \(0.519893\pi\)
\(132\) −71.1179 + 72.8944i −0.538772 + 0.552230i
\(133\) −163.433 57.2143i −1.22882 0.430183i
\(134\) −8.92385 −0.0665959
\(135\) 66.9693 117.218i 0.496069 0.868283i
\(136\) 35.1951i 0.258787i
\(137\) 102.022 102.022i 0.744688 0.744688i −0.228788 0.973476i \(-0.573476\pi\)
0.973476 + 0.228788i \(0.0734764\pi\)
\(138\) −80.6863 + 82.7018i −0.584683 + 0.599289i
\(139\) −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
\(147\) 145.867 18.2172i 0.992291 0.123927i
\(148\) 81.0762 81.0762i 0.547812 0.547812i
\(149\) −140.338 −0.941864 −0.470932 0.882170i \(-0.656082\pi\)
−0.470932 + 0.882170i \(0.656082\pi\)
\(150\) 48.1294 + 94.5175i 0.320863 + 0.630117i
\(151\) 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
\(153\) 77.2114 81.1183i 0.504650 0.530185i
\(154\) −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 \(-0.724183\pi\)
0.762070 + 0.647494i \(0.224183\pi\)
\(158\) −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
\(162\) −76.9064 + 84.8964i −0.474731 + 0.524052i
\(163\) 90.3636 90.3636i 0.554378 0.554378i −0.373324 0.927701i \(-0.621782\pi\)
0.927701 + 0.373324i \(0.121782\pi\)
\(164\) 1.77182i 0.0108038i
\(165\) 131.714 217.882i 0.798264 1.32049i
\(166\) 120.015i 0.722985i
\(167\) −11.1296 11.1296i −0.0666444 0.0666444i 0.672999 0.739643i \(-0.265006\pi\)
−0.739643 + 0.672999i \(0.765006\pi\)
\(168\) −56.2988 18.9327i −0.335112 0.112694i
\(169\) 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 \(-0.550165\pi\)
0.987607 + 0.156946i \(0.0501648\pi\)
\(174\) 0.0879077 + 7.12617i 0.000505216 + 0.0409550i
\(175\) −173.701 + 21.2816i −0.992578 + 0.121609i
\(176\) 67.8932i 0.385757i
\(177\) −108.469 105.826i −0.612819 0.597884i
\(178\) 51.3826 + 51.3826i 0.288666 + 0.288666i
\(179\) 334.691 1.86978 0.934891 0.354936i \(-0.115497\pi\)
0.934891 + 0.354936i \(0.115497\pi\)
\(180\) −22.6148 87.1124i −0.125638 0.483958i
\(181\) 99.3599i 0.548949i −0.961594 0.274475i \(-0.911496\pi\)
0.961594 0.274475i \(-0.0885040\pi\)
\(182\) 135.085 + 47.2901i 0.742224 + 0.259836i
\(183\) 173.262 + 169.039i 0.946785 + 0.923711i
\(184\) 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 \(-0.0346510\pi\)
\(192\) 17.1786 + 16.7599i 0.0894719 + 0.0872914i
\(193\) 112.254 112.254i 0.581626 0.581626i −0.353724 0.935350i \(-0.615085\pi\)
0.935350 + 0.353724i \(0.115085\pi\)
\(194\) 0.548049i 0.00282500i
\(195\) 51.8994 + 210.563i 0.266151 + 1.07981i
\(196\) 61.1241 76.6018i 0.311858 0.390826i
\(197\) −177.771 + 177.771i −0.902388 + 0.902388i −0.995642 0.0932539i \(-0.970273\pi\)
0.0932539 + 0.995642i \(0.470273\pi\)
\(198\) −148.945 + 156.481i −0.752247 + 0.790310i
\(199\) −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
\(207\) −168.984 + 177.535i −0.816350 + 0.857657i
\(208\) −40.8924 40.8924i −0.196598 0.196598i
\(209\) 419.867i 2.00894i
\(210\) 147.822 + 14.0976i 0.703913 + 0.0671313i
\(211\) 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
\(213\) 294.571 + 287.392i 1.38296 + 1.34926i
\(214\) 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
\(222\) 169.854 174.097i 0.765108 0.784220i
\(223\) −162.636 162.636i −0.729308 0.729308i 0.241174 0.970482i \(-0.422468\pi\)
−0.970482 + 0.241174i \(0.922468\pi\)
\(224\) −35.6790 + 17.1758i −0.159281 + 0.0766775i
\(225\) 104.563 + 199.227i 0.464726 + 0.885455i
\(226\) −116.241 −0.514341
\(227\) −255.602 255.602i −1.12600 1.12600i −0.990821 0.135179i \(-0.956839\pi\)
−0.135179 0.990821i \(-0.543161\pi\)
\(228\) 106.237 + 103.647i 0.465950 + 0.454594i
\(229\) −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
\(231\) −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 \(-0.266177\pi\)
−0.742115 + 0.670272i \(0.766177\pi\)
\(234\) −4.53930 183.960i −0.0193987 0.786152i
\(235\) 125.985 202.715i 0.536108 0.862618i
\(236\) −101.027 −0.428081
\(237\) −274.720 268.025i −1.15916 1.13091i
\(238\) 116.264 + 40.7015i 0.488506 + 0.171015i
\(239\) 93.1494 0.389746 0.194873 0.980828i \(-0.437570\pi\)
0.194873 + 0.980828i \(0.437570\pi\)
\(240\) −51.3469 31.0402i −0.213946 0.129334i
\(241\) 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
\(243\) −160.909 + 182.091i −0.662178 + 0.749346i
\(244\) 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 \(-0.219423\pi\)
0.771668 + 0.636026i \(0.219423\pi\)
\(252\) −119.914 38.6861i −0.475850 0.153516i
\(253\) −326.854 + 326.854i −1.29191 + 1.29191i
\(254\) −14.8044 −0.0582849
\(255\) 44.6686 + 181.226i 0.175171 + 0.710692i
\(256\) 16.0000 0.0625000
\(257\) 181.485 + 181.485i 0.706167 + 0.706167i 0.965727 0.259560i \(-0.0835776\pi\)
−0.259560 + 0.965727i \(0.583578\pi\)
\(258\) 42.4065 + 41.3730i 0.164366 + 0.160361i
\(259\) 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 \(-0.411783\pi\)
−0.961841 + 0.273608i \(0.911783\pi\)
\(264\) 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
\(267\) 110.335 + 107.646i 0.413240 + 0.403169i
\(268\) −8.92385 + 8.92385i −0.0332979 + 0.0332979i
\(269\) 197.175i 0.732994i 0.930419 + 0.366497i \(0.119443\pi\)
−0.930419 + 0.366497i \(0.880557\pi\)
\(270\) −50.2490 184.188i −0.186107 0.682176i
\(271\) 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
\(273\) 287.774 + 96.7752i 1.05412 + 0.354488i
\(274\) 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 0.935951 0.352131i \(-0.114543\pi\)
−0.352131 + 0.935951i \(0.614543\pi\)
\(278\) −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 \(0.894707\pi\)
\(282\) −141.428 + 144.961i −0.501517 + 0.514045i
\(283\) −13.2471 13.2471i −0.0468095 0.0468095i 0.683315 0.730124i \(-0.260538\pi\)
−0.730124 + 0.683315i \(0.760538\pi\)
\(284\) 274.361 0.966059
\(285\) −317.541 191.960i −1.11418 0.673543i
\(286\) 347.039i 1.21342i
\(287\) 5.85308 + 2.04903i 0.0203940 + 0.00713948i
\(288\) 36.8771 + 35.1010i 0.128045 + 0.121878i
\(289\) 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 \(-0.785279\pi\)
0.624559 + 0.780978i \(0.285279\pi\)
\(294\) 127.650 164.084i 0.434182 0.558109i
\(295\) 245.955 57.4143i 0.833747 0.194625i
\(296\) 162.152i 0.547812i
\(297\) −311.841 + 335.819i −1.04997 + 1.13070i
\(298\) −140.338 + 140.338i −0.470932 + 0.470932i
\(299\) 393.731i 1.31683i
\(300\) 142.647 + 46.3881i 0.475490 + 0.154627i
\(301\) −88.0761 + 42.3995i −0.292612 + 0.140862i
\(302\) 32.6929 32.6929i 0.108255 0.108255i
\(303\) −45.4163 + 46.5508i −0.149889 + 0.153633i
\(304\) 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 \(-0.966709\pi\)
0.104396 + 0.994536i \(0.466709\pi\)
\(308\) −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 \(-0.728134\pi\)
−0.656903 + 0.753975i \(0.728134\pi\)
\(312\) −87.8092 85.6692i −0.281440 0.274581i
\(313\) 269.726 + 269.726i 0.861746 + 0.861746i 0.991541 0.129795i \(-0.0414320\pi\)
−0.129795 + 0.991541i \(0.541432\pi\)
\(314\) 35.9770i 0.114576i
\(315\) 313.922 + 26.0352i 0.996579 + 0.0826516i
\(316\) −255.872 −0.809721
\(317\) 265.401 265.401i 0.837227 0.837227i −0.151266 0.988493i \(-0.548335\pi\)
0.988493 + 0.151266i \(0.0483352\pi\)
\(318\) 50.1517 51.4045i 0.157710 0.161649i
\(319\) 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
\(327\) −148.417 144.800i −0.453875 0.442813i
\(328\) −1.77182 1.77182i −0.00540189 0.00540189i
\(329\) −144.937 301.075i −0.440537 0.915123i
\(330\) −86.1680 349.595i −0.261115 1.05938i
\(331\) 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
\(333\) 355.732 373.732i 1.06826 1.12232i
\(334\) −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 0.328321 0.944566i \(-0.393517\pi\)
−0.944566 + 0.328321i \(0.893517\pi\)
\(338\) 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
\(342\) 228.057 + 217.073i 0.666832 + 0.634716i
\(343\) 182.361 + 290.505i 0.531665 + 0.846955i
\(344\) 39.4971 0.114817
\(345\) −97.7614 396.631i −0.283366 1.14965i
\(346\) 287.409i 0.830661i
\(347\) 41.3813 41.3813i 0.119254 0.119254i −0.644961 0.764215i \(-0.723126\pi\)
0.764215 + 0.644961i \(0.223126\pi\)
\(348\) 7.21408 + 7.03826i 0.0207301 + 0.0202249i
\(349\) 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 \(-0.671754\pi\)
0.857923 + 0.513778i \(0.171754\pi\)
\(354\) −214.295 + 2.64351i −0.605352 + 0.00746756i
\(355\) −667.945 + 155.921i −1.88153 + 0.439214i
\(356\) 102.765 0.288666
\(357\) 247.680 + 83.2921i 0.693782 + 0.233311i
\(358\) 334.691 334.691i 0.934891 0.934891i
\(359\) 129.751 0.361424 0.180712 0.983536i \(-0.442160\pi\)
0.180712 + 0.983536i \(0.442160\pi\)
\(360\) −109.727 64.4976i −0.304798 0.179160i
\(361\) 250.916 0.695059
\(362\) −99.3599 99.3599i −0.274475 0.274475i
\(363\) −350.058 + 358.802i −0.964347 + 0.988437i
\(364\) 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 0.369976 0.929041i \(-0.379366\pi\)
0.929041 0.369976i \(-0.120634\pi\)
\(368\) 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
\(372\) 154.607 158.469i 0.415610 0.425992i
\(373\) 76.1479 76.1479i 0.204150 0.204150i −0.597626 0.801775i \(-0.703889\pi\)
0.801775 + 0.597626i \(0.203889\pi\)
\(374\) 298.688i 0.798632i
\(375\) −373.644 31.8670i −0.996383 0.0849787i
\(376\) 135.015i 0.359083i
\(377\) −17.1726 17.1726i −0.0455506 0.0455506i
\(378\) −255.369 78.9216i −0.675580 0.208787i
\(379\) 390.814i 1.03117i 0.856838 + 0.515585i \(0.172426\pi\)
−0.856838 + 0.515585i \(0.827574\pi\)
\(380\) −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 \(-0.787019\pi\)
0.620280 + 0.784381i \(0.287019\pi\)
\(384\) 33.9385 0.418662i 0.0883816 0.00109027i
\(385\) 590.641 + 63.6898i 1.53413 + 0.165428i
\(386\) 224.508i 0.581626i
\(387\) 91.0336 + 86.6492i 0.235229 + 0.223900i
\(388\) −0.548049 0.548049i −0.00141250 0.00141250i
\(389\) −24.2532 −0.0623476 −0.0311738 0.999514i \(-0.509925\pi\)
−0.0311738 + 0.999514i \(0.509925\pi\)
\(390\) 262.462 + 158.663i 0.672980 + 0.406829i
\(391\) 338.875i 0.866688i
\(392\) −15.4777 137.726i −0.0394839 0.351342i
\(393\) −34.2805 + 35.1368i −0.0872277 + 0.0894066i
\(394\) 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 \(-0.647962\pi\)
0.893895 + 0.448277i \(0.147962\pi\)
\(398\) −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 \(-0.0192984\pi\)
\(402\) −18.6954 + 19.1624i −0.0465060 + 0.0476677i
\(403\) −377.223 + 377.223i −0.936038 + 0.936038i
\(404\) 43.3570i 0.107319i
\(405\) −111.406 389.376i −0.275076 0.961423i
\(406\) −14.9833 + 7.21289i −0.0369046 + 0.0177657i
\(407\) 688.065 688.065i 1.69058 1.69058i
\(408\) −75.5753 73.7334i −0.185234 0.180719i
\(409\) 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
\(417\) −168.695 + 172.909i −0.404543 + 0.414649i
\(418\) 419.867 + 419.867i 1.00447 + 1.00447i
\(419\) 80.8927i 0.193061i 0.995330 + 0.0965306i \(0.0307746\pi\)
−0.995330 + 0.0965306i \(0.969225\pi\)
\(420\) 161.919 133.724i 0.385522 0.318391i
\(421\) −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
\(423\) −296.198 + 311.185i −0.700231 + 0.735662i
\(424\) 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 \(0.766553\pi\)
\(432\) 79.1406 + 73.4899i 0.183196 + 0.170115i
\(433\) −42.9015 42.9015i −0.0990797 0.0990797i 0.655829 0.754909i \(-0.272319\pi\)
−0.754909 + 0.655829i \(0.772319\pi\)
\(434\) 158.443 + 329.131i 0.365075 + 0.758367i
\(435\) −21.5629 13.0352i −0.0495699 0.0299660i
\(436\) −138.234 −0.317051
\(437\) 476.358 + 476.358i 1.09006 + 1.09006i
\(438\) −223.428 + 229.010i −0.510110 + 0.522853i
\(439\) −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
\(441\) 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 \(-0.255335\pi\)
−0.718858 + 0.695157i \(0.755335\pi\)
\(444\) −4.24294 343.951i −0.00955617 0.774664i
\(445\) −250.187 + 58.4020i −0.562217 + 0.131241i
\(446\) −325.271 −0.729308
\(447\) −294.006 + 301.351i −0.657732 + 0.674163i
\(448\) −18.5033 + 52.8548i −0.0413019 + 0.117979i
\(449\) 284.237 0.633044 0.316522 0.948585i \(-0.397485\pi\)
0.316522 + 0.948585i \(0.397485\pi\)
\(450\) 303.791 + 94.6640i 0.675090 + 0.210364i
\(451\) 15.0368i 0.0333411i
\(452\) −116.241 + 116.241i −0.257170 + 0.257170i
\(453\) 68.4914 70.2023i 0.151195 0.154972i
\(454\) −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 0.567316 0.823500i \(-0.307982\pi\)
−0.823500 + 0.567316i \(0.807982\pi\)
\(458\) −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 \(0.577245\pi\)
\(462\) −477.788 160.675i −1.03417 0.347781i
\(463\) −315.054 + 315.054i −0.680462 + 0.680462i −0.960104 0.279642i \(-0.909784\pi\)
0.279642 + 0.960104i \(0.409784\pi\)
\(464\) 6.71913 0.0144809
\(465\) −286.339 + 473.664i −0.615783 + 1.01863i
\(466\) −33.4788 −0.0718429
\(467\) −229.349 229.349i −0.491111 0.491111i 0.417545 0.908656i \(-0.362891\pi\)
−0.908656 + 0.417545i \(0.862891\pi\)
\(468\) −188.499 179.420i −0.402776 0.383377i
\(469\) −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
\(477\) 105.035 110.349i 0.220199 0.231341i
\(478\) 93.1494 93.1494i 0.194873 0.194873i
\(479\) 166.037i 0.346633i −0.984866 0.173316i \(-0.944552\pi\)
0.984866 0.173316i \(-0.0554483\pi\)
\(480\) −82.3871 + 20.3067i −0.171640 + 0.0423057i
\(481\) 828.849i 1.72318i
\(482\) −443.888 443.888i −0.920929 0.920929i
\(483\) −542.071 182.293i −1.12230 0.377418i
\(484\) 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 −0.919743 0.392521i \(-0.871603\pi\)
−0.392521 0.919743i \(-0.628397\pi\)
\(488\) 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 \(0.951657\pi\)
\(492\) −3.80468 3.71195i −0.00773308 0.00754462i
\(493\) −14.7800 14.7800i −0.0299798 0.0299798i
\(494\) −505.776 −1.02384
\(495\) −191.924 739.292i −0.387725 1.49352i
\(496\) 147.597i 0.297574i
\(497\) −317.286 + 906.330i −0.638402 + 1.82360i
\(498\) 257.712 + 251.431i 0.517494 + 0.504882i
\(499\) 471.498i 0.944885i 0.881361 + 0.472443i \(0.156628\pi\)
−0.881361 + 0.472443i \(0.843372\pi\)
\(500\) −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 \(-0.731763\pi\)
0.746437 + 0.665456i \(0.231763\pi\)
\(504\) −158.600 + 81.2280i −0.314683 + 0.161167i
\(505\) −24.6400 105.555i −0.0487921 0.209019i
\(506\) 653.707i 1.29191i
\(507\) 85.9428 + 83.8483i 0.169512 + 0.165381i
\(508\) −14.8044 + 14.8044i −0.0291424 + 0.0291424i
\(509\) 834.832i 1.64014i 0.572263 + 0.820070i \(0.306066\pi\)
−0.572263 + 0.820070i \(0.693934\pi\)
\(510\) 225.895 + 136.558i 0.442931 + 0.267760i
\(511\) −228.972 475.641i −0.448086 0.930803i
\(512\) 16.0000 16.0000i 0.0312500 0.0312500i
\(513\) 489.424 + 454.479i 0.954044 + 0.885923i
\(514\) 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 \(-0.730709\pi\)
−0.662980 + 0.748637i \(0.730709\pi\)
\(522\) 15.4864 + 14.7405i 0.0296674 + 0.0282385i
\(523\) 560.737 + 560.737i 1.07216 + 1.07216i 0.997186 + 0.0749699i \(0.0238861\pi\)
0.0749699 + 0.997186i \(0.476114\pi\)
\(524\) 32.7261i 0.0624544i
\(525\) −318.204 + 417.578i −0.606103 + 0.795386i
\(526\) −362.011 −0.688233
\(527\) −324.667 + 324.667i −0.616067 + 0.616067i
\(528\) 145.789 + 142.236i 0.276115 + 0.269386i
\(529\) 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
\(537\) 701.175 718.690i 1.30573 1.33834i
\(538\) 197.175 + 197.175i 0.366497 + 0.366497i
\(539\) 518.739 650.093i 0.962410 1.20611i
\(540\) −234.436 133.939i −0.434142 0.248034i
\(541\) 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
\(543\) −213.358 208.158i −0.392924 0.383348i
\(544\) −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 0.899929 0.436036i \(-0.143618\pi\)
−0.436036 + 0.899929i \(0.643618\pi\)
\(548\) −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
\(552\) 165.404 + 161.373i 0.299644 + 0.292342i
\(553\) 295.904 845.253i 0.535088 1.52849i
\(554\) 323.436 0.583820
\(555\) 205.799 + 834.954i 0.370809 + 1.50442i
\(556\) 161.046i 0.289650i
\(557\) −468.602 + 468.602i −0.841296 + 0.841296i −0.989028 0.147731i \(-0.952803\pi\)
0.147731 + 0.989028i \(0.452803\pi\)
\(558\) 323.799 340.183i 0.580285 0.609647i
\(559\) −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 \(-0.745608\pi\)
0.716796 + 0.697283i \(0.245608\pi\)
\(564\) 3.53286 + 286.388i 0.00626393 + 0.507781i
\(565\) 216.934 349.055i 0.383954 0.617796i
\(566\) −26.4942 −0.0468095
\(567\) −543.744 160.723i −0.958983 0.283462i
\(568\) 274.361 274.361i 0.483029 0.483029i
\(569\) −122.993 −0.216157 −0.108079 0.994142i \(-0.534470\pi\)
−0.108079 + 0.994142i \(0.534470\pi\)
\(570\) −509.501 + 125.582i −0.893862 + 0.220319i
\(571\) −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
\(573\) −89.1188 86.9469i −0.155530 0.151740i
\(574\) 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 0.0496572 0.998766i \(-0.484187\pi\)
0.998766 0.0496572i \(-0.0158129\pi\)
\(578\) −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
\(582\) −1.17684 1.14816i −0.00202206 0.00197278i
\(583\) 203.161 203.161i 0.348475 0.348475i
\(584\) 213.298i 0.365236i
\(585\) 560.876 + 329.683i 0.958762 + 0.563560i
\(586\) 91.6614i 0.156419i
\(587\) 354.852 + 354.852i 0.604518 + 0.604518i 0.941508 0.336990i \(-0.109409\pi\)
−0.336990 + 0.941508i \(0.609409\pi\)
\(588\) −36.4344 291.734i −0.0619633 0.496146i
\(589\) 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 \(-0.917360\pi\)
0.256715 + 0.966487i \(0.417360\pi\)
\(594\) 23.9781 + 647.661i 0.0403672 + 1.09034i
\(595\) −339.198 + 273.166i −0.570081 + 0.459102i
\(596\) 280.675i 0.470932i
\(597\) −166.599 + 170.760i −0.279060 + 0.286030i
\(598\) −393.731 393.731i −0.658413 0.658413i
\(599\) −761.718 −1.27165 −0.635824 0.771834i \(-0.719340\pi\)
−0.635824 + 0.771834i \(0.719340\pi\)
\(600\) 189.035 96.2588i 0.315058 0.160431i
\(601\) 348.645i 0.580109i −0.957010 0.290054i \(-0.906327\pi\)
0.957010 0.290054i \(-0.0936734\pi\)
\(602\) −45.6766 + 130.476i −0.0758747 + 0.216737i
\(603\) −39.1545 + 41.1357i −0.0649328 + 0.0682184i
\(604\) 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 \(-0.542651\pi\)
0.991036 + 0.133592i \(0.0426512\pi\)
\(608\) 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
\(612\) −162.237 154.423i −0.265092 0.252325i
\(613\) 82.1048 82.1048i 0.133939 0.133939i −0.636959 0.770898i \(-0.719808\pi\)
0.770898 + 0.636959i \(0.219808\pi\)
\(614\) 546.546i 0.890140i
\(615\) 11.3722 + 6.87471i 0.0184914 + 0.0111784i
\(616\) −302.795 + 145.765i −0.491551 + 0.236631i
\(617\) 186.511 186.511i 0.302286 0.302286i −0.539621 0.841908i \(-0.681433\pi\)
0.841908 + 0.539621i \(0.181433\pi\)
\(618\) 207.047 212.219i 0.335028 0.343397i
\(619\) −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
\(627\) 901.592 + 879.619i 1.43795 + 1.40290i
\(628\) −35.9770 35.9770i −0.0572882 0.0572882i
\(629\) 713.371i 1.13413i
\(630\) 339.957 287.887i 0.539615 0.456963i
\(631\) 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
\(633\) 835.722 856.598i 1.32026 1.35324i
\(634\) 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 \(-0.299681\pi\)
\(642\) −183.419 178.949i −0.285700 0.278737i
\(643\) −639.514 639.514i −0.994579 0.994579i 0.00540613 0.999985i \(-0.498279\pi\)
−0.999985 + 0.00540613i \(0.998279\pi\)
\(644\) −343.534 + 165.376i −0.533439 + 0.256796i
\(645\) −203.378 + 50.1285i −0.315315 + 0.0777187i
\(646\) −435.309 −0.673854
\(647\) −659.438 659.438i −1.01922 1.01922i −0.999812 0.0194122i \(-0.993821\pi\)
−0.0194122 0.999812i \(-0.506179\pi\)
\(648\) 169.793 + 153.813i 0.262026 + 0.237365i
\(649\) −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 \(-0.367900\pi\)
−0.915115 + 0.403194i \(0.867900\pi\)
\(654\) −293.217 + 3.61709i −0.448344 + 0.00553072i
\(655\) −18.5984 79.6733i −0.0283946 0.121639i
\(656\) −3.54364 −0.00540189
\(657\) −467.935 + 491.612i −0.712229 + 0.748268i
\(658\) −446.012 156.139i −0.677830 0.237293i
\(659\) 231.047 0.350602 0.175301 0.984515i \(-0.443910\pi\)
0.175301 + 0.984515i \(0.443910\pi\)
\(660\) −435.763 263.427i −0.660247 0.399132i
\(661\) 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
\(663\) 386.307 + 376.892i 0.582665 + 0.568464i
\(664\) 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
\(672\) −37.8653 + 112.598i −0.0563472 + 0.167556i
\(673\) −98.5465 + 98.5465i −0.146429 + 0.146429i −0.776521 0.630092i \(-0.783017\pi\)
0.630092 + 0.776521i \(0.283017\pi\)
\(674\) −415.350 −0.616246
\(675\) 646.865 + 192.848i 0.958319 + 0.285701i
\(676\) 80.0464 0.118412
\(677\) 856.497 + 856.497i 1.26514 + 1.26514i 0.948571 + 0.316565i \(0.102529\pi\)
0.316565 + 0.948571i \(0.397471\pi\)
\(678\) −243.524 + 249.607i −0.359180 + 0.368152i
\(679\) 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 \(-0.105558\pi\)
−0.325575 + 0.945516i \(0.605558\pi\)
\(684\) 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
\(687\) −394.939 + 404.804i −0.574874 + 0.589235i
\(688\) 39.4971 39.4971i 0.0574085 0.0574085i
\(689\) 244.729i 0.355195i
\(690\) −494.392 298.870i −0.716511 0.433144i
\(691\) 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
\(693\) −1017.67 328.315i −1.46850 0.473759i
\(694\) 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 \(-0.107106\pi\)
\(702\) −404.531 375.647i −0.576255 0.535109i
\(703\) −1002.79 1002.79i −1.42644 1.42644i
\(704\) 135.786 0.192878
\(705\) −171.357 695.219i −0.243060 0.986126i
\(706\) 242.967i 0.344146i
\(707\) −143.226 50.1403i −0.202583 0.0709199i
\(708\) −211.651 + 216.938i −0.298942 + 0.306410i
\(709\) 946.923i 1.33558i 0.744352 + 0.667788i \(0.232759\pi\)
−0.744352 + 0.667788i \(0.767241\pi\)
\(710\) −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
\(717\) 195.147 200.022i 0.272172 0.278971i
\(718\) 129.751 129.751i 0.180712 0.180712i
\(719\) 713.422i 0.992242i −0.868254 0.496121i \(-0.834757\pi\)
0.868254 0.496121i \(-0.165243\pi\)
\(720\) −174.225 + 45.2296i −0.241979 + 0.0628189i
\(721\) 212.184 + 440.768i 0.294292 + 0.611329i
\(722\) 250.916 250.916i 0.347530 0.347530i
\(723\) −953.172 929.942i −1.31836 1.28623i
\(724\) −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 \(-0.580570\pi\)
0.968136 + 0.250425i \(0.0805702\pi\)
\(728\) 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
\(732\) 338.078 346.523i 0.461855 0.473393i
\(733\) 121.904 + 121.904i 0.166309 + 0.166309i 0.785355 0.619046i \(-0.212481\pi\)
−0.619046 + 0.785355i \(0.712481\pi\)
\(734\) 953.479i 1.29902i
\(735\) 254.495 + 689.534i 0.346252 + 0.938141i
\(736\) 154.056 0.209315
\(737\) −75.7335 + 75.7335i −0.102759 + 0.102759i
\(738\) −8.16745 7.77409i −0.0110670 0.0105340i
\(739\) 708.172i 0.958284i 0.877737 + 0.479142i \(0.159052\pi\)
−0.877737 + 0.479142i \(0.840948\pi\)
\(740\) 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 \(-0.314866\pi\)
−0.835576 + 0.549374i \(0.814866\pi\)
\(744\) −3.86207 313.076i −0.00519095 0.420801i
\(745\) −159.509 683.318i −0.214107 0.917205i
\(746\) 152.296i 0.204150i
\(747\) 553.228 + 526.583i 0.740599 + 0.704930i
\(748\) −298.688 298.688i −0.399316 0.399316i
\(749\) 380.952 183.389i 0.508614 0.244845i
\(750\) −405.511 + 341.777i −0.540681 + 0.455702i
\(751\) −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
\(753\) 811.552 831.825i 1.07776 1.10468i
\(754\) −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 0.159003 0.987278i \(-0.449172\pi\)
−0.987278 + 0.159003i \(0.949172\pi\)
\(758\) 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 \(0.744056\pi\)
\(762\) −31.0150 + 31.7898i −0.0407021 + 0.0417189i
\(763\) 159.862 456.647i 0.209517 0.598488i
\(764\) −83.0045 −0.108645
\(765\) 482.732 + 283.750i 0.631023 + 0.370915i
\(766\) 125.702i 0.164101i
\(767\) 516.405 516.405i 0.673279 0.673279i
\(768\) 33.5199 34.3572i 0.0436457 0.0447359i
\(76