Properties

Label 210.3.k.b.83.13
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 83.13
Character \(\chi\) \(=\) 210.83
Dual form 210.3.k.b.167.13

$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).

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

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
\(3\) 2.09499 + 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 \(0.280500\pi\)
−0.636213 + 0.771513i \(0.719500\pi\)
\(12\) −4.29465 + 4.18999i −0.357888 + 0.349165i
\(13\) 10.2231 10.2231i 0.786392 0.786392i −0.194509 0.980901i \(-0.562311\pi\)
0.980901 + 0.194509i \(0.0623114\pi\)
\(14\) 8.91976 + 4.29394i 0.637126 + 0.306710i
\(15\) 12.8367 7.76005i 0.855782 0.517337i
\(16\) −4.00000 −0.250000
\(17\) 8.79877 8.79877i 0.517575 0.517575i −0.399262 0.916837i \(-0.630734\pi\)
0.916837 + 0.399262i \(0.130734\pi\)
\(18\) −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 −0.988497 0.151239i \(-0.951674\pi\)
0.151239 + 0.988497i \(0.451674\pi\)
\(24\) −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 \(-0.797094\pi\)
0.803616 0.595147i \(-0.202906\pi\)
\(32\) −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 0.100708 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 \(0.496561\pi\)
\(42\) 9.46634 + 28.1494i 0.225389 + 0.670224i
\(43\) −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
\(45\) 43.5562 + 11.3074i 0.967916 + 0.251275i
\(46\) −38.5139 −0.837258
\(47\) −33.7538 + 33.7538i −0.718165 + 0.718165i −0.968229 0.250064i \(-0.919548\pi\)
0.250064 + 0.968229i \(0.419548\pi\)
\(48\) −8.37997 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 −0.585113 0.810952i \(-0.698950\pi\)
0.810952 + 0.585113i \(0.198950\pi\)
\(54\) −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 \(0.140810\pi\)
−0.903740 + 0.428081i \(0.859190\pi\)
\(60\) 15.5201 + 25.6735i 0.258668 + 0.427891i
\(61\) 80.6872i 1.32274i −0.750059 0.661370i \(-0.769975\pi\)
0.750059 0.661370i \(-0.230025\pi\)
\(62\) 36.8991 36.8991i 0.595147 0.595147i
\(63\) 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 −0.739620 0.673024i \(-0.764995\pi\)
0.673024 + 0.739620i \(0.264995\pi\)
\(68\) 17.5975 + 17.5975i 0.258787 + 0.258787i
\(69\) −81.6941 1.00777i −1.18397 0.0146053i
\(70\) 31.0459 38.5506i 0.443513 0.550723i
\(71\) 137.180i 1.93212i −0.258322 0.966059i \(-0.583169\pi\)
0.258322 0.966059i \(-0.416831\pi\)
\(72\) −17.5505 18.4385i −0.243757 0.256091i
\(73\) −53.3244 + 53.3244i −0.730471 + 0.730471i −0.970713 0.240242i \(-0.922773\pi\)
0.240242 + 0.970713i \(0.422773\pi\)
\(74\) 81.0762 1.09562
\(75\) −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 \(0.300381\pi\)
−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
\(87\) −3.51913 3.60704i −0.0404498 0.0414602i
\(88\) −33.9466 33.9466i −0.385757 0.385757i
\(89\) 51.3826i 0.577332i −0.957430 0.288666i \(-0.906788\pi\)
0.957430 0.288666i \(-0.0932117\pi\)
\(90\) 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 0.708518 0.705693i \(-0.249364\pi\)
−0.705693 + 0.708518i \(0.749364\pi\)
\(98\) 68.8630 + 7.73884i 0.702683 + 0.0789678i
\(99\) −152.713 3.76828i −1.54256 0.0380634i
\(100\) 22.1371 44.8325i 0.221371 0.448325i
\(101\) −21.6785 −0.214638 −0.107319 0.994225i \(-0.534227\pi\)
−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 −0.425298 0.905053i \(-0.639831\pi\)
0.905053 + 0.425298i \(0.139831\pi\)
\(104\) 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 0.877932 0.478785i \(-0.158923\pi\)
−0.478785 + 0.877932i \(0.658923\pi\)
\(108\) −36.7449 39.5703i −0.340231 0.366392i
\(109\) 69.1171i 0.634102i 0.948408 + 0.317051i \(0.102693\pi\)
−0.948408 + 0.317051i \(0.897307\pi\)
\(110\) 63.3526 + 101.937i 0.575933 + 0.926697i
\(111\) 171.975 + 2.12147i 1.54933 + 0.0191123i
\(112\) −26.4274 + 9.25163i −0.235959 + 0.0826039i
\(113\) −58.1205 + 58.1205i −0.514341 + 0.514341i −0.915853 0.401513i \(-0.868485\pi\)
0.401513 + 0.915853i \(0.368485\pi\)
\(114\) 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 −0.735648 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 \(0.519893\pi\)
\(132\) −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 0.973476 0.228788i \(-0.0734764\pi\)
−0.228788 + 0.973476i \(0.573476\pi\)
\(138\) −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 0.762070 0.647494i \(-0.224183\pi\)
−0.647494 + 0.762070i \(0.724183\pi\)
\(158\) −127.936 + 127.936i −0.809721 + 0.809721i
\(159\) 50.7781 + 0.626394i 0.319359 + 0.00393958i
\(160\) −24.0228 + 14.9299i −0.150143 + 0.0933121i
\(161\) −82.6882 + 171.767i −0.513591 + 1.06688i
\(162\) −76.9064 84.8964i −0.474731 0.524052i
\(163\) 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
\(165\) 131.714 + 217.882i 0.798264 + 1.32049i
\(166\) 120.015i 0.722985i
\(167\) −11.1296 + 11.1296i −0.0666444 + 0.0666444i −0.739643 0.672999i \(-0.765006\pi\)
0.672999 + 0.739643i \(0.265006\pi\)
\(168\) −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 0.987607 0.156946i \(-0.0501648\pi\)
−0.156946 + 0.987607i \(0.550165\pi\)
\(174\) 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 \(0.0885040\pi\)
−0.961594 + 0.274475i \(0.911496\pi\)
\(182\) 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 \(0.0346510\pi\)
−0.994081 + 0.108645i \(0.965349\pi\)
\(192\) 17.1786 16.7599i 0.0894719 0.0872914i
\(193\) 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
\(195\) 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 0.0932539 0.995642i \(-0.470273\pi\)
−0.995642 + 0.0932539i \(0.970273\pi\)
\(198\) −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 −0.970482 0.241174i \(-0.922468\pi\)
0.241174 + 0.970482i \(0.422468\pi\)
\(224\) −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 −0.135179 + 0.990821i \(0.543161\pi\)
−0.990821 + 0.135179i \(0.956839\pi\)
\(228\) 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 −0.742115 0.670272i \(-0.766177\pi\)
0.670272 + 0.742115i \(0.266177\pi\)
\(234\) −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 \(0.372569\pi\)
−0.389729 + 0.920929i \(0.627431\pi\)
\(242\) −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 −0.259560 0.965727i \(-0.583578\pi\)
0.965727 + 0.259560i \(0.0835776\pi\)
\(258\) 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 −0.961841 0.273608i \(-0.911783\pi\)
0.273608 + 0.961841i \(0.411783\pi\)
\(264\) 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 \(-0.880557\pi\)
0.930419 0.366497i \(-0.119443\pi\)
\(270\) −50.2490 + 184.188i −0.186107 + 0.682176i
\(271\) 311.811i 1.15059i −0.817945 0.575296i \(-0.804887\pi\)
0.817945 0.575296i \(-0.195113\pi\)
\(272\) −35.1951 + 35.1951i −0.129394 + 0.129394i
\(273\) 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 −0.352131 0.935951i \(-0.614543\pi\)
0.935951 + 0.352131i \(0.114543\pi\)
\(278\) −80.5228 80.5228i −0.289650 0.289650i
\(279\) 331.991 + 8.19206i 1.18993 + 0.0293622i
\(280\) 77.1013 + 62.0918i 0.275362 + 0.221757i
\(281\) 182.531i 0.649576i −0.945787 0.324788i \(-0.894707\pi\)
0.945787 0.324788i \(-0.105293\pi\)
\(282\) −141.428 144.961i −0.501517 0.514045i
\(283\) −13.2471 + 13.2471i −0.0468095 + 0.0468095i −0.730124 0.683315i \(-0.760538\pi\)
0.683315 + 0.730124i \(0.260538\pi\)
\(284\) 274.361 0.966059
\(285\) −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 0.624559 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
\(297\) −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 0.104396 0.994536i \(-0.466709\pi\)
−0.994536 + 0.104396i \(0.966709\pi\)
\(308\) −224.280 + 78.5153i −0.728182 + 0.254920i
\(309\) 209.633 + 2.58601i 0.678425 + 0.00836898i
\(310\) −137.726 221.606i −0.444276 0.714857i
\(311\) −408.594 −1.31381 −0.656903 0.753975i \(-0.728134\pi\)
−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 −0.129795 0.991541i \(-0.541432\pi\)
0.991541 + 0.129795i \(0.0414320\pi\)
\(314\) 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 0.988493 0.151266i \(-0.0483352\pi\)
−0.151266 + 0.988493i \(0.548335\pi\)
\(318\) 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 −0.944566 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
\(342\) 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 0.764215 0.644961i \(-0.223126\pi\)
−0.644961 + 0.764215i \(0.723126\pi\)
\(348\) 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 0.857923 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
\(357\) 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 0.929041 + 0.369976i \(0.120634\pi\)
0.369976 + 0.929041i \(0.379366\pi\)
\(368\) 77.0278 77.0278i 0.209315 0.209315i
\(369\) −0.196683 + 7.97077i −0.000533016 + 0.0216010i
\(370\) 92.1521 394.768i 0.249060 1.06694i
\(371\) 51.3960 106.764i 0.138534 0.287775i
\(372\) 154.607 + 158.469i 0.415610 + 0.425992i
\(373\) 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
\(375\) −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 \(-0.827574\pi\)
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
\(385\) 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 0.893895 0.448277i \(-0.147962\pi\)
−0.448277 + 0.893895i \(0.647962\pi\)
\(398\) −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 \(0.0192984\pi\)
−0.998163 + 0.0605905i \(0.980702\pi\)
\(402\) −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 \(-0.969225\pi\)
0.995330 0.0965306i \(-0.0307746\pi\)
\(420\) 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 \(-0.766553\pi\)
0.742906 0.669396i \(-0.233447\pi\)
\(432\) 79.1406 73.4899i 0.183196 0.170115i
\(433\) −42.9015 + 42.9015i −0.0990797 + 0.0990797i −0.754909 0.655829i \(-0.772319\pi\)
0.655829 + 0.754909i \(0.272319\pi\)
\(434\) 158.443 329.131i 0.365075 0.758367i
\(435\) −21.5629 + 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 −0.718858 0.695157i \(-0.755335\pi\)
0.695157 + 0.718858i \(0.255335\pi\)
\(444\) −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 −0.823500 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 \(0.577245\pi\)
\(462\) −477.788 + 160.675i −1.03417 + 0.347781i
\(463\) −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
\(465\) −286.339 473.664i −0.615783 1.01863i
\(466\) −33.4788 −0.0718429
\(467\) −229.349 + 229.349i −0.491111 + 0.491111i −0.908656 0.417545i \(-0.862891\pi\)
0.417545 + 0.908656i \(0.362891\pi\)
\(468\) −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 \(0.0554483\pi\)
−0.984866 + 0.173316i \(0.944552\pi\)
\(480\) −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 −0.392521 + 0.919743i \(0.628397\pi\)
−0.919743 + 0.392521i \(0.871603\pi\)
\(488\) 161.374 + 161.374i 0.330685 + 0.330685i
\(489\) −4.72898 + 383.351i −0.00967071 + 0.783949i
\(490\) 115.952 326.505i 0.236636 0.666336i
\(491\) 148.567i 0.302581i −0.988489 0.151291i \(-0.951657\pi\)
0.988489 0.151291i \(-0.0483429\pi\)
\(492\) −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 \(-0.843372\pi\)
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
\(507\) 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 \(-0.693934\pi\)
0.572263 0.820070i \(-0.306066\pi\)
\(510\) 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 0.0749699 0.997186i \(-0.476114\pi\)
0.997186 0.0749699i \(-0.0238861\pi\)
\(524\) 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 −0.436036 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
\(552\) 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 0.147731 0.989028i \(-0.452803\pi\)
−0.989028 + 0.147731i \(0.952803\pi\)
\(558\) 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 0.716796 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
\(567\) −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 0.998766 + 0.0496572i \(0.0158129\pi\)
0.0496572 + 0.998766i \(0.484187\pi\)
\(578\) −134.163 + 134.163i −0.232116 + 0.232116i
\(579\) −5.87455 + 476.216i −0.0101460 + 0.822481i
\(580\) −16.3580 3.81852i −0.0282035 0.00658366i
\(581\) −535.254 257.670i −0.921264 0.443493i
\(582\) −1.17684 + 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 −0.336990 0.941508i \(-0.609409\pi\)
0.941508 + 0.336990i \(0.109409\pi\)
\(588\) −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 0.256715 0.966487i \(-0.417360\pi\)
−0.966487 + 0.256715i \(0.917360\pi\)
\(594\) 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 \(0.0936734\pi\)
−0.957010 + 0.290054i \(0.906327\pi\)
\(602\) −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 0.991036 0.133592i \(-0.0426512\pi\)
−0.133592 + 0.991036i \(0.542651\pi\)
\(608\) 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 0.770898 0.636959i \(-0.219808\pi\)
−0.636959 + 0.770898i \(0.719808\pi\)
\(614\) 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 0.841908 0.539621i \(-0.181433\pi\)
−0.539621 + 0.841908i \(0.681433\pi\)
\(618\) 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 \(0.299681\pi\)
−0.588597 + 0.808427i \(0.700319\pi\)
\(642\) −183.419 + 178.949i −0.285700 + 0.278737i
\(643\) −639.514 + 639.514i −0.994579 + 0.994579i −0.999985 0.00540613i \(-0.998279\pi\)
0.00540613 + 0.999985i \(0.498279\pi\)
\(644\) −343.534 165.376i −0.533439 0.256796i
\(645\) −203.378 50.1285i −0.315315 0.0777187i
\(646\) −435.309 −0.673854
\(647\) −659.438 + 659.438i −1.01922 + 1.01922i −0.0194122 + 0.999812i \(0.506179\pi\)
−0.999812 + 0.0194122i \(0.993821\pi\)
\(648\) 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 −0.915115 0.403194i \(-0.867900\pi\)
0.403194 + 0.915115i \(0.367900\pi\)
\(654\) −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 \(-0.873092\pi\)
0.921569 0.388215i \(-0.126908\pi\)
\(662\) 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 0.630092 0.776521i \(-0.283017\pi\)
−0.776521 + 0.630092i \(0.783017\pi\)
\(674\) −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 0.316565 0.948571i \(-0.397471\pi\)
0.948571 0.316565i \(-0.102529\pi\)
\(678\) −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 −0.325575 0.945516i \(-0.605558\pi\)
0.945516 + 0.325575i \(0.105558\pi\)
\(684\) 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 \(-0.807439\pi\)
0.822532 0.568718i \(-0.192561\pi\)
\(692\) −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 \(0.107106\pi\)
−0.943922 + 0.330170i \(0.892894\pi\)
\(702\) −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 \(-0.767241\pi\)
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
\(717\) 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 \(0.165243\pi\)
−0.868254 + 0.496121i \(0.834757\pi\)
\(720\) −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 0.968136 0.250425i \(-0.0805702\pi\)
−0.250425 + 0.968136i \(0.580570\pi\)
\(728\) 94.5803 + 270.170i 0.129918 + 0.371112i
\(729\) 53.9052 727.004i 0.0739440 0.997262i
\(730\) −121.218 + 519.283i −0.166052 + 0.711347i
\(731\) −173.763 −0.237706
\(732\) 338.078 + 346.523i 0.461855 + 0.473393i
\(733\) 121.904 121.904i 0.166309 0.166309i −0.619046 0.785355i \(-0.712481\pi\)
0.785355 + 0.619046i \(0.212481\pi\)
\(734\) 953.479i 1.29902i
\(735\) 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 \(-0.840948\pi\)
0.877737 0.479142i \(-0.159052\pi\)
\(740\) 486.920 302.616i 0.658000 0.408940i
\(741\) −1072.83 13.2343i −1.44782 0.0178601i
\(742\) 158.160 55.3684i 0.213154 0.0746205i
\(743\) −212.648 + 212.648i −0.286202 + 0.286202i −0.835576 0.549374i \(-0.814866\pi\)
0.549374 + 0.835576i \(0.314866\pi\)
\(744\) −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 −0.987278 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 \(0.744056\pi\)
\(762\) −31.0150 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