Properties

Label 210.3.k.b.167.4
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 167.4
Character \(\chi\) \(=\) 210.167
Dual form 210.3.k.b.83.4

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 - 1.00000i) q^{2} +(-2.09499 + 2.14733i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 + 4.24232i) q^{6} +(2.31291 + 6.60685i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.222012 - 8.99726i) q^{9} +O(q^{10})\) \(q+(1.00000 - 1.00000i) q^{2} +(-2.09499 + 2.14733i) q^{3} -2.00000i q^{4} +(-1.13661 - 4.86910i) q^{5} +(0.0523328 + 4.24232i) q^{6} +(2.31291 + 6.60685i) q^{7} +(-2.00000 - 2.00000i) q^{8} +(-0.222012 - 8.99726i) q^{9} +(-6.00571 - 3.73249i) q^{10} -16.9733i q^{11} +(4.29465 + 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} +(-19.0326 - 8.87473i) q^{21} +(-16.9733 - 16.9733i) q^{22} +(-19.2569 - 19.2569i) q^{23} +(8.48464 - 0.104666i) q^{24} +(-22.4162 + 11.0685i) q^{25} -20.4462 q^{26} +(19.7852 + 18.3725i) q^{27} +(13.2137 - 4.62582i) 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} +(29.5405 - 18.7712i) q^{35} +(-17.9945 + 0.444025i) q^{36} +(40.5381 + 40.5381i) q^{37} +(24.7369 - 24.7369i) q^{38} +(43.3696 - 0.535003i) q^{39} +(-7.46497 + 12.0114i) q^{40} -0.885911 q^{41} +(-27.9073 + 10.1578i) 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} +(58.9301 - 22.2766i) q^{63} +8.00000i q^{64} +(-38.1575 + 61.3969i) q^{65} +(72.0061 - 0.888260i) q^{66} +(-4.46192 - 4.46192i) q^{67} +(-17.5975 + 17.5975i) q^{68} +(81.6941 - 1.00777i) q^{69} +(10.7693 - 48.3117i) q^{70} +137.180i q^{71} +(-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} +(112.140 - 39.2577i) 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} +(-17.7495 + 38.0652i) 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} +(-7.73884 + 68.8630i) q^{98} +(-152.713 + 3.76828i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} + O(q^{10}) \) \( 32q + 32q^{2} - 4q^{7} - 64q^{8} + 16q^{9} - 8q^{14} - 4q^{15} - 128q^{16} - 4q^{18} + 12q^{21} - 40q^{22} - 24q^{23} + 16q^{25} - 8q^{28} + 112q^{29} + 28q^{30} - 128q^{32} + 48q^{35} - 40q^{36} + 32q^{37} - 64q^{39} - 20q^{42} - 32q^{43} - 80q^{44} - 48q^{46} + 8q^{50} + 84q^{51} + 136q^{53} + 340q^{57} + 112q^{58} + 64q^{60} + 168q^{63} + 200q^{65} + 32q^{67} - 72q^{72} + 64q^{74} - 88q^{77} - 4q^{78} + 76q^{81} - 64q^{84} - 40q^{85} - 80q^{88} - 272q^{91} - 48q^{92} - 388q^{93} - 544q^{95} - 128q^{98} - 160q^{99} + O(q^{100}) \)

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
\(7\) 2.31291 + 6.60685i 0.330415 + 0.943836i
\(8\) −2.00000 2.00000i −0.250000 0.250000i
\(9\) −0.222012 8.99726i −0.0246680 0.999696i
\(10\) −6.00571 3.73249i −0.600571 0.373249i
\(11\) 16.9733i 1.54303i −0.636213 0.771513i \(-0.719500\pi\)
0.636213 0.771513i \(-0.280500\pi\)
\(12\) 4.29465 + 4.18999i 0.357888 + 0.349165i
\(13\) −10.2231 10.2231i −0.786392 0.786392i 0.194509 0.980901i \(-0.437689\pi\)
−0.980901 + 0.194509i \(0.937689\pi\)
\(14\) 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 \(-0.369266\pi\)
−0.916837 + 0.399262i \(0.869266\pi\)
\(18\) −9.21927 8.77525i −0.512182 0.487514i
\(19\) 24.7369 1.30194 0.650972 0.759102i \(-0.274361\pi\)
0.650972 + 0.759102i \(0.274361\pi\)
\(20\) −9.73820 + 2.27322i −0.486910 + 0.113661i
\(21\) −19.0326 8.87473i −0.906313 0.422606i
\(22\) −16.9733 16.9733i −0.771513 0.771513i
\(23\) −19.2569 19.2569i −0.837258 0.837258i 0.151239 0.988497i \(-0.451674\pi\)
−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
\(28\) 13.2137 4.62582i 0.471918 0.165208i
\(29\) −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
\(35\) 29.5405 18.7712i 0.844015 0.536320i
\(36\) −17.9945 + 0.444025i −0.499848 + 0.0123340i
\(37\) 40.5381 + 40.5381i 1.09562 + 1.09562i 0.994916 + 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 \(-0.503439\pi\)
−0.0108038 + 0.999942i \(0.503439\pi\)
\(42\) −27.9073 + 10.1578i −0.664460 + 0.241853i
\(43\) −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 0.968229 0.250064i \(-0.0804517\pi\)
−0.250064 + 0.968229i \(0.580452\pi\)
\(48\) 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 \(0.140810\pi\)
−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
\(63\) 58.9301 22.2766i 0.935398 0.353597i
\(64\) 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
\(70\) 10.7693 48.3117i 0.153847 0.690167i
\(71\) 137.180i 1.93212i 0.258322 + 0.966059i \(0.416831\pi\)
−0.258322 + 0.966059i \(0.583169\pi\)
\(72\) −17.5505 + 18.4385i −0.243757 + 0.256091i
\(73\) 53.3244 + 53.3244i 0.730471 + 0.730471i 0.970713 0.240242i \(-0.0772268\pi\)
−0.240242 + 0.970713i \(0.577227\pi\)
\(74\) 81.0762 1.09562
\(75\) 23.1941 71.3235i 0.309254 0.950979i
\(76\) 49.4739i 0.650972i
\(77\) 112.140 39.2577i 1.45636 0.509840i
\(78\) 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 −0.246227 0.969212i \(-0.579191\pi\)
0.969212 + 0.246227i \(0.0791910\pi\)
\(84\) −17.7495 + 38.0652i −0.211303 + 0.453157i
\(85\) −32.8413 + 52.8429i −0.386368 + 0.621681i
\(86\) 19.7485i 0.229634i
\(87\) 3.51913 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 \(-0.750636\pi\)
0.705693 + 0.708518i \(0.250636\pi\)
\(98\) −7.73884 + 68.8630i −0.0789678 + 0.702683i
\(99\) −152.713 + 3.76828i −1.54256 + 0.0380634i
\(100\) 22.1371 + 44.8325i 0.221371 + 0.448325i
\(101\) 21.6785 0.214638 0.107319 0.994225i \(-0.465773\pi\)
0.107319 + 0.994225i \(0.465773\pi\)
\(102\) 36.8667 37.7877i 0.361438 0.370467i
\(103\) −49.4148 49.4148i −0.479755 0.479755i 0.425298 0.905053i \(-0.360169\pi\)
−0.905053 + 0.425298i \(0.860169\pi\)
\(104\) 40.8924i 0.393196i
\(105\) −21.5793 + 102.759i −0.205517 + 0.978654i
\(106\) 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
\(112\) −9.25163 26.4274i −0.0826039 0.235959i
\(113\) −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
\(126\) 36.6534 81.2067i 0.290900 0.644498i
\(127\) −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 \(-0.480107\pi\)
0.0624544 + 0.998048i \(0.480107\pi\)
\(132\) 71.1179 72.8944i 0.538772 0.552230i
\(133\) 57.2143 + 163.433i 0.430183 + 1.22882i
\(134\) −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 \(-0.406461\pi\)
0.289650 + 0.957133i \(0.406461\pi\)
\(140\) −37.5424 59.0810i −0.268160 0.422007i
\(141\) −143.194 + 1.76643i −1.01556 + 0.0125279i
\(142\) 137.180 + 137.180i 0.966059 + 0.966059i
\(143\) −173.520 + 173.520i −1.21342 + 1.21342i
\(144\) 0.888049 + 35.9890i 0.00616701 + 0.249924i
\(145\) 1.90926 + 8.17902i 0.0131673 + 0.0564071i
\(146\) 106.649 0.730471
\(147\) 14.6134 146.272i 0.0994110 0.995046i
\(148\) 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 \(-0.775817\pi\)
0.647494 + 0.762070i \(0.275817\pi\)
\(158\) −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 0.739643 0.672999i \(-0.234994\pi\)
−0.672999 + 0.739643i \(0.734994\pi\)
\(168\) 20.3157 + 55.8146i 0.120927 + 0.332230i
\(169\) 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 \(-0.949835\pi\)
0.156946 + 0.987607i \(0.449835\pi\)
\(174\) −0.0879077 7.12617i −0.000505216 0.0409550i
\(175\) −124.975 122.500i −0.714142 0.700001i
\(176\) 67.8932i 0.385757i
\(177\) −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 \(0.911496\pi\)
\(182\) −47.2901 135.085i −0.259836 0.742224i
\(183\) 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
\(189\) −75.6228 + 173.211i −0.400121 + 0.916462i
\(190\) −148.563 92.3303i −0.781910 0.485949i
\(191\) 41.5022i 0.217289i −0.994081 0.108645i \(-0.965349\pi\)
0.994081 0.108645i \(-0.0346510\pi\)
\(192\) −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 \(-0.435969\pi\)
0.199805 + 0.979836i \(0.435969\pi\)
\(200\) 66.9696 + 22.6954i 0.334848 + 0.113477i
\(201\) 18.9289 0.233505i 0.0941736 0.00116172i
\(202\) 21.6785 21.6785i 0.107319 0.107319i
\(203\) −3.88518 11.0981i −0.0191388 0.0546703i
\(204\) −0.920928 74.6544i −0.00451435 0.365953i
\(205\) 1.00694 + 4.31359i 0.00491189 + 0.0210419i
\(206\) −98.8296 −0.479755
\(207\) −168.984 + 177.535i −0.816350 + 0.857657i
\(208\) 40.8924 + 40.8924i 0.196598 + 0.196598i
\(209\) 419.867i 2.00894i
\(210\) 81.1793 + 124.338i 0.386568 + 0.592085i
\(211\) 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
\(217\) 243.787 85.3443i 1.12344 0.393292i
\(218\) −69.1171 69.1171i −0.317051 0.317051i
\(219\) −226.219 + 2.79061i −1.03296 + 0.0127425i
\(220\) 38.5841 + 165.289i 0.175382 + 0.751315i
\(221\) 179.901i 0.814033i
\(222\) −169.854 + 174.097i −0.765108 + 0.784220i
\(223\) 162.636 + 162.636i 0.729308 + 0.729308i 0.970482 0.241174i \(-0.0775325\pi\)
−0.241174 + 0.970482i \(0.577532\pi\)
\(224\) −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 \(0.0431610\pi\)
0.135179 + 0.990821i \(0.456839\pi\)
\(228\) 106.237 + 103.647i 0.465950 + 0.454594i
\(229\) 188.516 0.823212 0.411606 0.911362i \(-0.364968\pi\)
0.411606 + 0.911362i \(0.364968\pi\)
\(230\) 43.7753 + 187.528i 0.190328 + 0.815338i
\(231\) −150.633 + 323.046i −0.652093 + 1.39847i
\(232\) 3.35956 + 3.35956i 0.0144809 + 0.0144809i
\(233\) −16.7394 16.7394i −0.0718429 0.0718429i 0.670272 0.742115i \(-0.266177\pi\)
−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
\(238\) −40.7015 116.264i −0.171015 0.488506i
\(239\) 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
\(245\) 192.343 + 151.754i 0.785073 + 0.619403i
\(246\) −0.0463622 3.75831i −0.000188464 0.0152777i
\(247\) −252.888 252.888i −1.02384 1.02384i
\(248\) −73.7983 + 73.7983i −0.297574 + 0.297574i
\(249\) 3.14037 + 254.572i 0.0126119 + 1.02238i
\(250\) 175.939 + 17.1938i 0.703754 + 0.0687750i
\(251\) −387.377 −1.54334 −0.771668 0.636026i \(-0.780577\pi\)
−0.771668 + 0.636026i \(0.780577\pi\)
\(252\) −44.5533 117.860i −0.176799 0.467699i
\(253\) −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 \(-0.416422\pi\)
−0.965727 + 0.259560i \(0.916422\pi\)
\(258\) −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 \(-0.880557\pi\)
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
\(273\) 103.845 + 285.299i 0.380383 + 1.04505i
\(274\) 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
\(280\) −96.6234 21.5386i −0.345084 0.0769237i
\(281\) 182.531i 0.649576i 0.945787 + 0.324788i \(0.105293\pi\)
−0.945787 + 0.324788i \(0.894707\pi\)
\(282\) −141.428 + 144.961i −0.501517 + 0.514045i
\(283\) 13.2471 + 13.2471i 0.0468095 + 0.0468095i 0.730124 0.683315i \(-0.239462\pi\)
−0.683315 + 0.730124i \(0.739462\pi\)
\(284\) 274.361 0.966059
\(285\) 317.541 + 191.960i 1.11418 + 0.673543i
\(286\) 347.039i 1.21342i
\(287\) −2.04903 5.85308i −0.00713948 0.0203940i
\(288\) 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 \(-0.714721\pi\)
0.780978 + 0.624559i \(0.214721\pi\)
\(294\) −131.658 160.885i −0.447818 0.547229i
\(295\) 245.955 57.4143i 0.833747 0.194625i
\(296\) 162.152i 0.547812i
\(297\) 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 \(-0.533291\pi\)
0.994536 + 0.104396i \(0.0332909\pi\)
\(308\) −78.5153 224.280i −0.254920 0.728182i
\(309\) 209.633 2.58601i 0.678425 0.00836898i
\(310\) −137.726 + 221.606i −0.444276 + 0.714857i
\(311\) 408.594 1.31381 0.656903 0.753975i \(-0.271866\pi\)
0.656903 + 0.753975i \(0.271866\pi\)
\(312\) −87.8092 85.6692i −0.281440 0.274581i
\(313\) −269.726 269.726i −0.861746 0.861746i 0.129795 0.991541i \(-0.458568\pi\)
−0.991541 + 0.129795i \(0.958568\pi\)
\(314\) 35.9770i 0.114576i
\(315\) −175.448 261.616i −0.556977 0.830528i
\(316\) −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
\(322\) −89.0791 254.455i −0.276643 0.790234i
\(323\) −217.655 217.655i −0.673854 0.673854i
\(324\) 7.99001 + 161.803i 0.0246605 + 0.499391i
\(325\) 342.318 + 116.008i 1.05329 + 0.356949i
\(326\) 180.727i 0.554378i
\(327\) 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
\(336\) 76.1303 + 35.4989i 0.226578 + 0.105652i
\(337\) −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
\(343\) −290.505 182.361i −0.846955 0.531665i
\(344\) 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 \(-0.800302\pi\)
−0.809573 + 0.587019i \(0.800302\pi\)
\(350\) −247.475 + 2.47482i −0.707071 + 0.00707091i
\(351\) −14.4421 390.089i −0.0411457 1.11136i
\(352\) 67.8932 + 67.8932i 0.192878 + 0.192878i
\(353\) −121.484 + 121.484i −0.344146 + 0.344146i −0.857923 0.513778i \(-0.828246\pi\)
0.513778 + 0.857923i \(0.328246\pi\)
\(354\) −214.295 + 2.64351i −0.605352 + 0.00746756i
\(355\) 667.945 155.921i 1.88153 0.439214i
\(356\) −102.765 −0.288666
\(357\) 89.3766 + 245.550i 0.250355 + 0.687815i
\(358\) 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 \(0.620634\pi\)
−0.929041 + 0.369976i \(0.879366\pi\)
\(368\) 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
\(378\) 97.5886 + 248.834i 0.258171 + 0.658292i
\(379\) 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 −0.620280 0.784381i \(-0.712981\pi\)
0.784381 + 0.620280i \(0.212981\pi\)
\(384\) −33.9385 + 0.418662i −0.0883816 + 0.00109027i
\(385\) −318.609 501.400i −0.827556 1.30234i
\(386\) 224.508i 0.581626i
\(387\) 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
\(392\) 137.726 + 15.4777i 0.351342 + 0.0394839i
\(393\) −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 \(-0.852038\pi\)
0.448277 + 0.893895i \(0.352038\pi\)
\(398\) 79.5223 79.5223i 0.199805 0.199805i
\(399\) −470.808 219.534i −1.17997 0.550210i
\(400\) 89.6649 44.2742i 0.224162 0.110685i
\(401\) 48.5936i 0.121181i −0.998163 0.0605905i \(-0.980702\pi\)
0.998163 0.0605905i \(-0.0192984\pi\)
\(402\) 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 \(-0.556268\pi\)
−0.175853 + 0.984416i \(0.556268\pi\)
\(410\) 5.32052 + 3.30665i 0.0129769 + 0.00806500i
\(411\) 5.33910 + 432.811i 0.0129905 + 1.05307i
\(412\) −98.8296 + 98.8296i −0.239878 + 0.239878i
\(413\) −333.735 + 116.833i −0.808076 + 0.282889i
\(414\) 8.55055 + 346.519i 0.0206535 + 0.837003i
\(415\) −360.389 223.978i −0.868407 0.539706i
\(416\) 81.7847 0.196598
\(417\) −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 \(-0.0307746\pi\)
\(420\) 205.517 + 43.1586i 0.489327 + 0.102759i
\(421\) −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
\(427\) 533.088 186.622i 1.24845 0.437054i
\(428\) −85.4175 85.4175i −0.199574 0.199574i
\(429\) −9.08076 736.125i −0.0211673 1.71591i
\(430\) 96.1576 22.4464i 0.223622 0.0522010i
\(431\) 577.019i 1.33879i 0.742906 + 0.669396i \(0.233447\pi\)
−0.742906 + 0.669396i \(0.766553\pi\)
\(432\) −79.1406 73.4899i −0.183196 0.170115i
\(433\) 42.9015 + 42.9015i 0.0990797 + 0.0990797i 0.754909 0.655829i \(-0.227681\pi\)
−0.655829 + 0.754909i \(0.727681\pi\)
\(434\) 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 \(-0.473234\pi\)
0.0839886 + 0.996467i \(0.473234\pi\)
\(440\) 203.873 + 126.705i 0.463349 + 0.287966i
\(441\) 283.478 + 337.818i 0.642808 + 0.766028i
\(442\) 179.901 + 179.901i 0.407017 + 0.407017i
\(443\) −10.4996 10.4996i −0.0237011 0.0237011i 0.695157 0.718858i \(-0.255335\pi\)
−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
\(448\) −52.8548 + 18.5033i −0.117979 + 0.0413019i
\(449\) 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
\(455\) −493.895 110.096i −1.08548 0.241969i
\(456\) 209.884 2.58911i 0.460272 0.00567786i
\(457\) −117.076 117.076i −0.256184 0.256184i 0.567316 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 \(-0.422755\pi\)
0.240297 + 0.970699i \(0.422755\pi\)
\(462\) 172.412 + 473.679i 0.373186 + 1.02528i
\(463\) −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 0.908656 0.417545i \(-0.137109\pi\)
−0.417545 + 0.908656i \(0.637109\pi\)
\(468\) 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
\(483\) 195.609 + 537.409i 0.404988 + 1.11265i
\(484\) 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
\(490\) 344.097 40.5893i 0.702238 0.0828353i
\(491\) 148.567i 0.302581i 0.988489 + 0.151291i \(0.0483429\pi\)
−0.988489 + 0.151291i \(0.951657\pi\)
\(492\) −3.80468 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
\(497\) −906.330 + 317.286i −1.82360 + 0.638402i
\(498\) 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 −0.746437 0.665456i \(-0.768237\pi\)
0.665456 + 0.746437i \(0.268237\pi\)
\(504\) −162.413 73.3068i −0.322249 0.145450i
\(505\) −24.6400 105.555i −0.0487921 0.209019i
\(506\) 653.707i 1.29191i
\(507\) −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
\(518\) 187.522 + 535.658i 0.362011 + 1.03409i
\(519\) −7.52045 609.640i −0.0144903 1.17464i
\(520\) 199.109 46.4788i 0.382902 0.0893822i
\(521\) 690.826 1.32596 0.662980 0.748637i \(-0.269291\pi\)
0.662980 + 0.748637i \(0.269291\pi\)
\(522\) 15.4864 + 14.7405i 0.0296674 + 0.0282385i
\(523\) −560.737 560.737i −1.07216 1.07216i −0.997186 0.0749699i \(-0.976114\pi\)
−0.0749699 0.997186i \(-0.523886\pi\)
\(524\) 32.7261i 0.0624544i
\(525\) 524.869 11.7250i 0.999751 0.0223333i
\(526\) −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
\(532\) 326.866 114.429i 0.614411 0.215091i
\(533\) 9.05675 + 9.05675i 0.0169920 + 0.0169920i
\(534\) 217.981 2.68899i 0.408204 0.00503557i
\(535\) −256.496 159.410i −0.479433 0.297962i
\(536\) 17.8477i 0.0332979i
\(537\) −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
\(546\) 389.144 + 181.454i 0.712717 + 0.332334i
\(547\) 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
\(553\) 845.253 295.904i 1.52849 0.535088i
\(554\) 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
\(560\) −118.162 + 75.0848i −0.211004 + 0.134080i
\(561\) −7.81559 633.565i −0.0139315 1.12935i
\(562\) 182.531 + 182.531i 0.324788 + 0.324788i
\(563\) −10.9862 + 10.9862i −0.0195137 + 0.0195137i −0.716796 0.697283i \(-0.754392\pi\)
0.697283 + 0.716796i \(0.254392\pi\)
\(564\) 3.53286 + 286.388i 0.00626393 + 0.507781i
\(565\) −216.934 + 349.055i −0.383954 + 0.617796i
\(566\) 26.4942 0.0468095
\(567\) −213.512 525.263i −0.376564 0.926390i
\(568\) 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 \(0.515813\pi\)
−0.998766 + 0.0496572i \(0.984187\pi\)
\(578\) −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 \(-0.390591\pi\)
−0.941508 + 0.336990i \(0.890591\pi\)
\(588\) −292.544 29.2268i −0.497523 0.0497055i
\(589\) 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 \(-0.582640\pi\)
0.966487 + 0.256715i \(0.0826403\pi\)
\(594\) −23.9781 647.661i −0.0403672 1.09034i
\(595\) −425.084 94.7568i −0.714426 0.159255i
\(596\) 280.675i 0.470932i
\(597\) −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 \(0.906327\pi\)
\(602\) −130.476 + 45.6766i −0.216737 + 0.0758747i
\(603\) −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 \(-0.957349\pi\)
0.133592 + 0.991036i \(0.457349\pi\)
\(608\) −98.9478 + 98.9478i −0.162743 + 0.162743i
\(609\) 31.9706 + 14.9076i 0.0524969 + 0.0244789i
\(610\) −301.164 + 484.584i −0.493711 + 0.794400i
\(611\) 690.136i 1.12952i
\(612\) 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 \(-0.336512\pi\)
0.491326 + 0.870976i \(0.336512\pi\)
\(620\) 83.8800 + 359.331i 0.135290 + 0.579566i
\(621\) −27.2042 734.799i −0.0438072 1.18325i
\(622\) 408.594 408.594i 0.656903 0.656903i
\(623\) 339.477 118.843i 0.544907 0.190759i
\(624\) −173.478 + 2.14001i −0.278010 + 0.00342950i
\(625\) 379.974 496.230i 0.607959 0.793968i
\(626\) −539.453 −0.861746
\(627\) 901.592 + 879.619i 1.43795 + 1.40290i
\(628\) 35.9770 + 35.9770i 0.0572882 + 0.0572882i
\(629\) 713.371i 1.13413i
\(630\) −437.064 86.1686i −0.693752 0.136775i
\(631\) 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
\(637\) 703.993 + 79.1149i 1.10517 + 0.124199i
\(638\) 28.5114 + 28.5114i 0.0446888 + 0.0446888i
\(639\) 1234.25 30.4557i 1.93153 0.0476615i
\(640\) 29.8599 48.0457i 0.0466561 0.0750714i
\(641\) 1036.40i 1.61685i −0.588597 0.808427i \(-0.700319\pi\)
0.588597 0.808427i \(-0.299681\pi\)
\(642\) 183.419 + 178.949i 0.285700 + 0.278737i
\(643\) 639.514 + 639.514i 0.994579 + 0.994579i 0.999985 0.00540613i \(-0.00172083\pi\)
−0.00540613 + 0.999985i \(0.501721\pi\)
\(644\) −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 \(0.00617949\pi\)
0.0194122 + 0.999812i \(0.493821\pi\)
\(648\) 169.793 + 153.813i 0.262026 + 0.237365i
\(649\) 857.382 1.32108
\(650\) 458.326 226.310i 0.705117 0.348169i
\(651\) −327.470 + 702.286i −0.503026 + 1.07878i
\(652\) −180.727 180.727i −0.277189 0.277189i
\(653\) −334.285 334.285i −0.511921 0.511921i 0.403194 0.915115i \(-0.367900\pi\)
−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
\(658\) 156.139 + 446.012i 0.237293 + 0.677830i
\(659\) 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
\(665\) 730.742 464.342i 1.09886 0.698259i
\(666\) −17.9999 729.463i −0.0270269 1.09529i
\(667\) 32.3475 + 32.3475i 0.0484970 + 0.0484970i
\(668\) 22.2592 22.2592i 0.0333222 0.0333222i
\(669\) −689.952 + 8.51117i −1.03132 + 0.0127222i
\(670\) 10.1430 + 43.4511i 0.0151387 + 0.0648524i
\(671\) −1369.53 −2.04102
\(672\) 111.629 40.6314i 0.166115 0.0604634i
\(673\) −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 \(-0.897471\pi\)
−0.316565 0.948571i \(-0.602529\pi\)
\(678\) 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 \(-0.807439\pi\)
0.822532 0.568718i \(-0.192561\pi\)
\(692\) 287.409 + 287.409i 0.415331 + 0.415331i
\(693\) −378.108 1000.24i −0.545610 1.44334i
\(694\) 82.7625i 0.119254i
\(695\) −91.5231 392.073i −0.131688 0.564134i
\(696\) −14.2523 + 0.175815i −0.0204775 + 0.000252608i
\(697\) 7.79493 + 7.79493i 0.0111835 + 0.0111835i
\(698\) −565.082 + 565.082i −0.809573 + 0.809573i
\(699\) 71.0138 0.876019i 0.101593 0.00125325i
\(700\) −245.000 + 249.950i −0.350000 + 0.357071i
\(701\) 462.898i 0.660340i −0.943922 0.330170i \(-0.892894\pi\)
0.943922 0.330170i \(-0.107106\pi\)
\(702\) −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
\(707\) 50.1403 + 143.226i 0.0709199 + 0.202583i
\(708\) −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
\(714\) 334.927 + 156.174i 0.469085 + 0.218730i
\(715\) 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 \(-0.919430\pi\)
0.250425 + 0.968136i \(0.419430\pi\)
\(728\) −270.170 + 94.5803i −0.371112 + 0.129918i
\(729\) 53.9052 + 727.004i 0.0739440 + 0.997262i
\(730\) −121.218 519.283i −0.166052 0.711347i
\(731\) 173.763 0.237706
\(732\) 338.078 346.523i 0.461855 0.473393i
\(733\) −121.904 121.904i −0.166309 0.166309i 0.619046 0.785355i \(-0.287519\pi\)
−0.785355 + 0.619046i \(0.787519\pi\)
\(734\) 953.479i 1.29902i
\(735\) −728.822 + 95.1001i −0.991594 + 0.129388i
\(736\) 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
\(742\) 55.3684 + 158.160i 0.0746205 + 0.213154i
\(743\) −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
\(756\) 346.423 + 151.246i 0.458231 + 0.200060i
\(757\) −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 \(-0.255944\pi\)
0.693780 + 0.720187i \(0.255944\pi\)
\(762\) 31.0150 31.7898i 0.0407021 0.0417189i
\(763\) 456.647 159.862i 0.598488 0.209517i
\(764\) −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