Properties

Label 804.2.e.b.535.11
Level 804
Weight 2
Character 804.535
Analytic conductor 6.420
Analytic rank 0
Dimension 34
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 804 = 2^{2} \cdot 3 \cdot 67 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 804.e (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.41997232251\)
Analytic rank: \(0\)
Dimension: \(34\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 535.11
Character \(\chi\) = 804.535
Dual form 804.2.e.b.535.12

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.707921 - 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 + 1.73338i) q^{4} -3.14565i q^{5} +(-0.707921 - 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 - 0.00564312i) q^{8} +1.00000 q^{9} +O(q^{10})\) \(q+(-0.707921 - 1.22427i) q^{2} +1.00000 q^{3} +(-0.997695 + 1.73338i) q^{4} -3.14565i q^{5} +(-0.707921 - 1.22427i) q^{6} +1.38193 q^{7} +(2.82842 - 0.00564312i) q^{8} +1.00000 q^{9} +(-3.85114 + 2.22687i) q^{10} +2.19154 q^{11} +(-0.997695 + 1.73338i) q^{12} -1.11168i q^{13} +(-0.978299 - 1.69186i) q^{14} -3.14565i q^{15} +(-2.00921 - 3.45877i) q^{16} +0.639776 q^{17} +(-0.707921 - 1.22427i) q^{18} +2.14755i q^{19} +(5.45260 + 3.13840i) q^{20} +1.38193 q^{21} +(-1.55144 - 2.68304i) q^{22} -5.50995i q^{23} +(2.82842 - 0.00564312i) q^{24} -4.89510 q^{25} +(-1.36100 + 0.786978i) q^{26} +1.00000 q^{27} +(-1.37875 + 2.39541i) q^{28} +6.70206 q^{29} +(-3.85114 + 2.22687i) q^{30} +4.75833 q^{31} +(-2.81212 + 4.90836i) q^{32} +2.19154 q^{33} +(-0.452911 - 0.783262i) q^{34} -4.34707i q^{35} +(-0.997695 + 1.73338i) q^{36} -10.7663 q^{37} +(2.62919 - 1.52030i) q^{38} -1.11168i q^{39} +(-0.0177513 - 8.89722i) q^{40} -2.53783i q^{41} +(-0.978299 - 1.69186i) q^{42} -5.51787 q^{43} +(-2.18649 + 3.79877i) q^{44} -3.14565i q^{45} +(-6.74569 + 3.90061i) q^{46} +2.88421i q^{47} +(-2.00921 - 3.45877i) q^{48} -5.09026 q^{49} +(3.46535 + 5.99295i) q^{50} +0.639776 q^{51} +(1.92696 + 1.10911i) q^{52} -0.00678779i q^{53} +(-0.707921 - 1.22427i) q^{54} -6.89381i q^{55} +(3.90869 - 0.00779841i) q^{56} +2.14755i q^{57} +(-4.74453 - 8.20516i) q^{58} -0.119485i q^{59} +(5.45260 + 3.13840i) q^{60} -10.3863i q^{61} +(-3.36852 - 5.82550i) q^{62} +1.38193 q^{63} +(7.99994 - 0.0319223i) q^{64} -3.49694 q^{65} +(-1.55144 - 2.68304i) q^{66} +(8.18434 - 0.128944i) q^{67} +(-0.638302 + 1.10897i) q^{68} -5.50995i q^{69} +(-5.32201 + 3.07738i) q^{70} -5.27216i q^{71} +(2.82842 - 0.00564312i) q^{72} +2.16400 q^{73} +(7.62168 + 13.1809i) q^{74} -4.89510 q^{75} +(-3.72252 - 2.14260i) q^{76} +3.02855 q^{77} +(-1.36100 + 0.786978i) q^{78} +1.72829 q^{79} +(-10.8801 + 6.32026i) q^{80} +1.00000 q^{81} +(-3.10700 + 1.79658i) q^{82} -6.31463i q^{83} +(-1.37875 + 2.39541i) q^{84} -2.01251i q^{85} +(3.90622 + 6.75539i) q^{86} +6.70206 q^{87} +(6.19859 - 0.0123671i) q^{88} -13.2000 q^{89} +(-3.85114 + 2.22687i) q^{90} -1.53626i q^{91} +(9.55084 + 5.49725i) q^{92} +4.75833 q^{93} +(3.53106 - 2.04179i) q^{94} +6.75544 q^{95} +(-2.81212 + 4.90836i) q^{96} +5.12276i q^{97} +(3.60351 + 6.23188i) q^{98} +2.19154 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 34q + 34q^{3} + 2q^{4} + 4q^{7} - 6q^{8} + 34q^{9} + O(q^{10}) \) \( 34q + 34q^{3} + 2q^{4} + 4q^{7} - 6q^{8} + 34q^{9} - 6q^{10} + 2q^{12} - 4q^{14} + 2q^{16} - 12q^{20} + 4q^{21} - 8q^{22} - 6q^{24} - 34q^{25} + 10q^{26} + 34q^{27} - 8q^{28} - 16q^{29} - 6q^{30} - 4q^{31} + 2q^{36} + 12q^{37} + 26q^{38} - 18q^{40} - 4q^{42} - 4q^{43} + 26q^{44} - 4q^{46} + 2q^{48} + 46q^{49} - 18q^{50} + 32q^{52} + 14q^{56} + 4q^{58} - 12q^{60} - 2q^{62} + 4q^{63} + 26q^{64} - 8q^{66} - 18q^{67} - 34q^{68} + 56q^{70} - 6q^{72} + 12q^{73} + 22q^{74} - 34q^{75} - 32q^{76} - 8q^{77} + 10q^{78} - 12q^{79} - 2q^{80} + 34q^{81} + 26q^{82} - 8q^{84} + 6q^{86} - 16q^{87} - 28q^{88} - 6q^{90} - 46q^{92} - 4q^{93} + 32q^{94} - 40q^{95} - 40q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).

\(n\) \(269\) \(337\) \(403\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.707921 1.22427i −0.500576 0.865693i
\(3\) 1.00000 0.577350
\(4\) −0.997695 + 1.73338i −0.498848 + 0.866690i
\(5\) 3.14565i 1.40678i −0.710806 0.703388i \(-0.751670\pi\)
0.710806 0.703388i \(-0.248330\pi\)
\(6\) −0.707921 1.22427i −0.289008 0.499808i
\(7\) 1.38193 0.522321 0.261161 0.965295i \(-0.415895\pi\)
0.261161 + 0.965295i \(0.415895\pi\)
\(8\) 2.82842 0.00564312i 0.999998 0.00199515i
\(9\) 1.00000 0.333333
\(10\) −3.85114 + 2.22687i −1.21784 + 0.704198i
\(11\) 2.19154 0.660773 0.330387 0.943846i \(-0.392821\pi\)
0.330387 + 0.943846i \(0.392821\pi\)
\(12\) −0.997695 + 1.73338i −0.288010 + 0.500384i
\(13\) 1.11168i 0.308323i −0.988046 0.154162i \(-0.950732\pi\)
0.988046 0.154162i \(-0.0492676\pi\)
\(14\) −0.978299 1.69186i −0.261461 0.452170i
\(15\) 3.14565i 0.812203i
\(16\) −2.00921 3.45877i −0.502302 0.864692i
\(17\) 0.639776 0.155169 0.0775843 0.996986i \(-0.475279\pi\)
0.0775843 + 0.996986i \(0.475279\pi\)
\(18\) −0.707921 1.22427i −0.166859 0.288564i
\(19\) 2.14755i 0.492682i 0.969183 + 0.246341i \(0.0792283\pi\)
−0.969183 + 0.246341i \(0.920772\pi\)
\(20\) 5.45260 + 3.13840i 1.21924 + 0.701767i
\(21\) 1.38193 0.301562
\(22\) −1.55144 2.68304i −0.330767 0.572027i
\(23\) 5.50995i 1.14890i −0.818538 0.574452i \(-0.805215\pi\)
0.818538 0.574452i \(-0.194785\pi\)
\(24\) 2.82842 0.00564312i 0.577349 0.00115190i
\(25\) −4.89510 −0.979020
\(26\) −1.36100 + 0.786978i −0.266913 + 0.154339i
\(27\) 1.00000 0.192450
\(28\) −1.37875 + 2.39541i −0.260559 + 0.452690i
\(29\) 6.70206 1.24454 0.622271 0.782802i \(-0.286210\pi\)
0.622271 + 0.782802i \(0.286210\pi\)
\(30\) −3.85114 + 2.22687i −0.703118 + 0.406569i
\(31\) 4.75833 0.854620 0.427310 0.904105i \(-0.359461\pi\)
0.427310 + 0.904105i \(0.359461\pi\)
\(32\) −2.81212 + 4.90836i −0.497117 + 0.867683i
\(33\) 2.19154 0.381498
\(34\) −0.452911 0.783262i −0.0776736 0.134328i
\(35\) 4.34707i 0.734789i
\(36\) −0.997695 + 1.73338i −0.166283 + 0.288897i
\(37\) −10.7663 −1.76997 −0.884983 0.465624i \(-0.845830\pi\)
−0.884983 + 0.465624i \(0.845830\pi\)
\(38\) 2.62919 1.52030i 0.426511 0.246625i
\(39\) 1.11168i 0.178011i
\(40\) −0.0177513 8.89722i −0.00280672 1.40677i
\(41\) 2.53783i 0.396342i −0.980167 0.198171i \(-0.936500\pi\)
0.980167 0.198171i \(-0.0635002\pi\)
\(42\) −0.978299 1.69186i −0.150955 0.261060i
\(43\) −5.51787 −0.841467 −0.420734 0.907184i \(-0.638227\pi\)
−0.420734 + 0.907184i \(0.638227\pi\)
\(44\) −2.18649 + 3.79877i −0.329625 + 0.572685i
\(45\) 3.14565i 0.468926i
\(46\) −6.74569 + 3.90061i −0.994598 + 0.575114i
\(47\) 2.88421i 0.420705i 0.977626 + 0.210353i \(0.0674612\pi\)
−0.977626 + 0.210353i \(0.932539\pi\)
\(48\) −2.00921 3.45877i −0.290004 0.499230i
\(49\) −5.09026 −0.727181
\(50\) 3.46535 + 5.99295i 0.490074 + 0.847531i
\(51\) 0.639776 0.0895866
\(52\) 1.92696 + 1.10911i 0.267221 + 0.153806i
\(53\) 0.00678779i 0.000932375i −1.00000 0.000466188i \(-0.999852\pi\)
1.00000 0.000466188i \(-0.000148392\pi\)
\(54\) −0.707921 1.22427i −0.0963359 0.166603i
\(55\) 6.89381i 0.929560i
\(56\) 3.90869 0.00779841i 0.522320 0.00104211i
\(57\) 2.14755i 0.284450i
\(58\) −4.74453 8.20516i −0.622987 1.07739i
\(59\) 0.119485i 0.0155556i −0.999970 0.00777779i \(-0.997524\pi\)
0.999970 0.00777779i \(-0.00247577\pi\)
\(60\) 5.45260 + 3.13840i 0.703928 + 0.405165i
\(61\) 10.3863i 1.32983i −0.746917 0.664917i \(-0.768467\pi\)
0.746917 0.664917i \(-0.231533\pi\)
\(62\) −3.36852 5.82550i −0.427802 0.739839i
\(63\) 1.38193 0.174107
\(64\) 7.99994 0.0319223i 0.999992 0.00399028i
\(65\) −3.49694 −0.433742
\(66\) −1.55144 2.68304i −0.190969 0.330260i
\(67\) 8.18434 0.128944i 0.999876 0.0157530i
\(68\) −0.638302 + 1.10897i −0.0774055 + 0.134483i
\(69\) 5.50995i 0.663320i
\(70\) −5.32201 + 3.07738i −0.636102 + 0.367818i
\(71\) 5.27216i 0.625690i −0.949804 0.312845i \(-0.898718\pi\)
0.949804 0.312845i \(-0.101282\pi\)
\(72\) 2.82842 0.00564312i 0.333333 0.000665048i
\(73\) 2.16400 0.253277 0.126639 0.991949i \(-0.459581\pi\)
0.126639 + 0.991949i \(0.459581\pi\)
\(74\) 7.62168 + 13.1809i 0.886002 + 1.53225i
\(75\) −4.89510 −0.565238
\(76\) −3.72252 2.14260i −0.427002 0.245773i
\(77\) 3.02855 0.345136
\(78\) −1.36100 + 0.786978i −0.154102 + 0.0891078i
\(79\) 1.72829 0.194447 0.0972237 0.995263i \(-0.469004\pi\)
0.0972237 + 0.995263i \(0.469004\pi\)
\(80\) −10.8801 + 6.32026i −1.21643 + 0.706627i
\(81\) 1.00000 0.111111
\(82\) −3.10700 + 1.79658i −0.343111 + 0.198399i
\(83\) 6.31463i 0.693121i −0.938028 0.346561i \(-0.887350\pi\)
0.938028 0.346561i \(-0.112650\pi\)
\(84\) −1.37875 + 2.39541i −0.150434 + 0.261361i
\(85\) 2.01251i 0.218287i
\(86\) 3.90622 + 6.75539i 0.421218 + 0.728452i
\(87\) 6.70206 0.718536
\(88\) 6.19859 0.0123671i 0.660772 0.00131834i
\(89\) −13.2000 −1.39919 −0.699597 0.714537i \(-0.746637\pi\)
−0.699597 + 0.714537i \(0.746637\pi\)
\(90\) −3.85114 + 2.22687i −0.405945 + 0.234733i
\(91\) 1.53626i 0.161044i
\(92\) 9.55084 + 5.49725i 0.995744 + 0.573128i
\(93\) 4.75833 0.493415
\(94\) 3.53106 2.04179i 0.364201 0.210595i
\(95\) 6.75544 0.693093
\(96\) −2.81212 + 4.90836i −0.287011 + 0.500957i
\(97\) 5.12276i 0.520138i 0.965590 + 0.260069i \(0.0837453\pi\)
−0.965590 + 0.260069i \(0.916255\pi\)
\(98\) 3.60351 + 6.23188i 0.364009 + 0.629515i
\(99\) 2.19154 0.220258
\(100\) 4.88382 8.48507i 0.488382 0.848507i
\(101\) 6.31707i 0.628572i −0.949328 0.314286i \(-0.898235\pi\)
0.949328 0.314286i \(-0.101765\pi\)
\(102\) −0.452911 0.783262i −0.0448449 0.0775545i
\(103\) 18.2109i 1.79437i 0.441652 + 0.897186i \(0.354393\pi\)
−0.441652 + 0.897186i \(0.645607\pi\)
\(104\) −0.00627332 3.14429i −0.000615150 0.308323i
\(105\) 4.34707i 0.424231i
\(106\) −0.00831012 + 0.00480522i −0.000807150 + 0.000466724i
\(107\) 16.8450i 1.62846i 0.580540 + 0.814232i \(0.302842\pi\)
−0.580540 + 0.814232i \(0.697158\pi\)
\(108\) −0.997695 + 1.73338i −0.0960033 + 0.166795i
\(109\) 12.4899i 1.19632i −0.801378 0.598158i \(-0.795900\pi\)
0.801378 0.598158i \(-0.204100\pi\)
\(110\) −8.43991 + 4.88027i −0.804714 + 0.465316i
\(111\) −10.7663 −1.02189
\(112\) −2.77659 4.77978i −0.262363 0.451647i
\(113\) 6.63902i 0.624547i 0.949992 + 0.312273i \(0.101090\pi\)
−0.949992 + 0.312273i \(0.898910\pi\)
\(114\) 2.62919 1.52030i 0.246246 0.142389i
\(115\) −17.3324 −1.61625
\(116\) −6.68661 + 11.6172i −0.620836 + 1.07863i
\(117\) 1.11168i 0.102774i
\(118\) −0.146282 + 0.0845857i −0.0134664 + 0.00778675i
\(119\) 0.884127 0.0810478
\(120\) −0.0177513 8.89722i −0.00162046 0.812201i
\(121\) −6.19716 −0.563379
\(122\) −12.7157 + 7.35271i −1.15123 + 0.665683i
\(123\) 2.53783i 0.228828i
\(124\) −4.74736 + 8.24798i −0.426325 + 0.740691i
\(125\) 0.329971i 0.0295135i
\(126\) −0.978299 1.69186i −0.0871538 0.150723i
\(127\) 10.8899i 0.966319i 0.875532 + 0.483159i \(0.160511\pi\)
−0.875532 + 0.483159i \(0.839489\pi\)
\(128\) −5.70241 9.77152i −0.504026 0.863688i
\(129\) −5.51787 −0.485821
\(130\) 2.47556 + 4.28121i 0.217121 + 0.375487i
\(131\) 6.00800i 0.524922i 0.964943 + 0.262461i \(0.0845340\pi\)
−0.964943 + 0.262461i \(0.915466\pi\)
\(132\) −2.18649 + 3.79877i −0.190309 + 0.330640i
\(133\) 2.96777i 0.257338i
\(134\) −5.95173 9.92859i −0.514151 0.857700i
\(135\) 3.14565i 0.270734i
\(136\) 1.80956 0.00361034i 0.155168 0.000309584i
\(137\) 11.6091i 0.991834i 0.868370 + 0.495917i \(0.165168\pi\)
−0.868370 + 0.495917i \(0.834832\pi\)
\(138\) −6.74569 + 3.90061i −0.574232 + 0.332042i
\(139\) 10.4089 0.882871 0.441436 0.897293i \(-0.354469\pi\)
0.441436 + 0.897293i \(0.354469\pi\)
\(140\) 7.53512 + 4.33705i 0.636834 + 0.366548i
\(141\) 2.88421i 0.242894i
\(142\) −6.45457 + 3.73227i −0.541656 + 0.313205i
\(143\) 2.43628i 0.203732i
\(144\) −2.00921 3.45877i −0.167434 0.288231i
\(145\) 21.0823i 1.75079i
\(146\) −1.53194 2.64933i −0.126784 0.219260i
\(147\) −5.09026 −0.419838
\(148\) 10.7415 18.6620i 0.882943 1.53401i
\(149\) 18.0368 1.47763 0.738815 0.673908i \(-0.235386\pi\)
0.738815 + 0.673908i \(0.235386\pi\)
\(150\) 3.46535 + 5.99295i 0.282944 + 0.489322i
\(151\) 22.5460i 1.83476i 0.398008 + 0.917382i \(0.369702\pi\)
−0.398008 + 0.917382i \(0.630298\pi\)
\(152\) 0.0121189 + 6.07418i 0.000982972 + 0.492681i
\(153\) 0.639776 0.0517228
\(154\) −2.14398 3.70778i −0.172767 0.298782i
\(155\) 14.9680i 1.20226i
\(156\) 1.92696 + 1.10911i 0.154280 + 0.0888001i
\(157\) 15.4129 1.23008 0.615040 0.788496i \(-0.289140\pi\)
0.615040 + 0.788496i \(0.289140\pi\)
\(158\) −1.22349 2.11590i −0.0973357 0.168332i
\(159\) 0.00678779i 0.000538307i
\(160\) 15.4400 + 8.84594i 1.22064 + 0.699333i
\(161\) 7.61438i 0.600097i
\(162\) −0.707921 1.22427i −0.0556195 0.0961881i
\(163\) 4.46026i 0.349354i 0.984626 + 0.174677i \(0.0558882\pi\)
−0.984626 + 0.174677i \(0.944112\pi\)
\(164\) 4.39902 + 2.53198i 0.343506 + 0.197714i
\(165\) 6.89381i 0.536682i
\(166\) −7.73084 + 4.47026i −0.600030 + 0.346960i
\(167\) 3.92760i 0.303927i 0.988386 + 0.151964i \(0.0485596\pi\)
−0.988386 + 0.151964i \(0.951440\pi\)
\(168\) 3.90869 0.00779841i 0.301562 0.000601660i
\(169\) 11.7642 0.904937
\(170\) −2.46387 + 1.42470i −0.188970 + 0.109269i
\(171\) 2.14755i 0.164227i
\(172\) 5.50515 9.56456i 0.419764 0.729291i
\(173\) 14.8244 1.12708 0.563540 0.826089i \(-0.309439\pi\)
0.563540 + 0.826089i \(0.309439\pi\)
\(174\) −4.74453 8.20516i −0.359682 0.622032i
\(175\) −6.76470 −0.511363
\(176\) −4.40325 7.58002i −0.331908 0.571366i
\(177\) 0.119485i 0.00898102i
\(178\) 9.34454 + 16.1604i 0.700403 + 1.21127i
\(179\) 7.74057 0.578558 0.289279 0.957245i \(-0.406585\pi\)
0.289279 + 0.957245i \(0.406585\pi\)
\(180\) 5.45260 + 3.13840i 0.406413 + 0.233922i
\(181\) 6.47986 0.481645 0.240822 0.970569i \(-0.422583\pi\)
0.240822 + 0.970569i \(0.422583\pi\)
\(182\) −1.88080 + 1.08755i −0.139414 + 0.0806146i
\(183\) 10.3863i 0.767780i
\(184\) −0.0310933 15.5845i −0.00229223 1.14890i
\(185\) 33.8669i 2.48995i
\(186\) −3.36852 5.82550i −0.246992 0.427146i
\(187\) 1.40209 0.102531
\(188\) −4.99943 2.87756i −0.364621 0.209868i
\(189\) 1.38193 0.100521
\(190\) −4.78232 8.27051i −0.346946 0.600006i
\(191\) 4.35527 0.315136 0.157568 0.987508i \(-0.449635\pi\)
0.157568 + 0.987508i \(0.449635\pi\)
\(192\) 7.99994 0.0319223i 0.577346 0.00230379i
\(193\) −9.69919 −0.698163 −0.349082 0.937092i \(-0.613506\pi\)
−0.349082 + 0.937092i \(0.613506\pi\)
\(194\) 6.27167 3.62651i 0.450279 0.260368i
\(195\) −3.49694 −0.250421
\(196\) 5.07853 8.82336i 0.362752 0.630240i
\(197\) 9.45364i 0.673544i 0.941586 + 0.336772i \(0.109335\pi\)
−0.941586 + 0.336772i \(0.890665\pi\)
\(198\) −1.55144 2.68304i −0.110256 0.190676i
\(199\) 14.4262i 1.02265i 0.859389 + 0.511323i \(0.170844\pi\)
−0.859389 + 0.511323i \(0.829156\pi\)
\(200\) −13.8454 + 0.0276237i −0.979019 + 0.00195329i
\(201\) 8.18434 0.128944i 0.577279 0.00909499i
\(202\) −7.73383 + 4.47199i −0.544150 + 0.314648i
\(203\) 9.26179 0.650050
\(204\) −0.638302 + 1.10897i −0.0446901 + 0.0776438i
\(205\) −7.98312 −0.557565
\(206\) 22.2951 12.8919i 1.55338 0.898220i
\(207\) 5.50995i 0.382968i
\(208\) −3.84503 + 2.23359i −0.266605 + 0.154871i
\(209\) 4.70644i 0.325551i
\(210\) −5.32201 + 3.07738i −0.367253 + 0.212360i
\(211\) 0.971455i 0.0668777i −0.999441 0.0334388i \(-0.989354\pi\)
0.999441 0.0334388i \(-0.0106459\pi\)
\(212\) 0.0117658 + 0.00677215i 0.000808080 + 0.000465113i
\(213\) 5.27216i 0.361243i
\(214\) 20.6229 11.9249i 1.40975 0.815170i
\(215\) 17.3573i 1.18376i
\(216\) 2.82842 0.00564312i 0.192450 0.000383966i
\(217\) 6.57568 0.446386
\(218\) −15.2911 + 8.84187i −1.03564 + 0.598847i
\(219\) 2.16400 0.146230
\(220\) 11.9496 + 6.87792i 0.805640 + 0.463709i
\(221\) 0.711223i 0.0478421i
\(222\) 7.62168 + 13.1809i 0.511533 + 0.884643i
\(223\) 1.40727i 0.0942379i −0.998889 0.0471189i \(-0.984996\pi\)
0.998889 0.0471189i \(-0.0150040\pi\)
\(224\) −3.88616 + 6.78302i −0.259655 + 0.453209i
\(225\) −4.89510 −0.326340
\(226\) 8.12798 4.69990i 0.540665 0.312633i
\(227\) 1.05501i 0.0700238i −0.999387 0.0350119i \(-0.988853\pi\)
0.999387 0.0350119i \(-0.0111469\pi\)
\(228\) −3.72252 2.14260i −0.246530 0.141897i
\(229\) 19.5924i 1.29470i 0.762193 + 0.647350i \(0.224123\pi\)
−0.762193 + 0.647350i \(0.775877\pi\)
\(230\) 12.2700 + 21.2196i 0.809057 + 1.39918i
\(231\) 3.02855 0.199264
\(232\) 18.9562 0.0378205i 1.24454 0.00248304i
\(233\) 7.76027i 0.508392i −0.967153 0.254196i \(-0.918189\pi\)
0.967153 0.254196i \(-0.0818109\pi\)
\(234\) −1.36100 + 0.786978i −0.0889711 + 0.0514464i
\(235\) 9.07271 0.591838
\(236\) 0.207112 + 0.119209i 0.0134819 + 0.00775986i
\(237\) 1.72829 0.112264
\(238\) −0.625892 1.08241i −0.0405706 0.0701625i
\(239\) 12.9701 0.838968 0.419484 0.907763i \(-0.362211\pi\)
0.419484 + 0.907763i \(0.362211\pi\)
\(240\) −10.8801 + 6.32026i −0.702306 + 0.407971i
\(241\) −11.1159 −0.716040 −0.358020 0.933714i \(-0.616548\pi\)
−0.358020 + 0.933714i \(0.616548\pi\)
\(242\) 4.38710 + 7.58703i 0.282014 + 0.487713i
\(243\) 1.00000 0.0641500
\(244\) 18.0035 + 10.3624i 1.15255 + 0.663385i
\(245\) 16.0122i 1.02298i
\(246\) −3.10700 + 1.79658i −0.198095 + 0.114546i
\(247\) 2.38738 0.151905
\(248\) 13.4585 0.0268518i 0.854619 0.00170509i
\(249\) 6.31463i 0.400174i
\(250\) −0.403975 + 0.233593i −0.0255496 + 0.0147737i
\(251\) 16.3410 1.03143 0.515716 0.856760i \(-0.327526\pi\)
0.515716 + 0.856760i \(0.327526\pi\)
\(252\) −1.37875 + 2.39541i −0.0868529 + 0.150897i
\(253\) 12.0753i 0.759166i
\(254\) 13.3322 7.70916i 0.836535 0.483716i
\(255\) 2.01251i 0.126028i
\(256\) −7.92617 + 13.8988i −0.495385 + 0.868673i
\(257\) 20.2146 1.26095 0.630476 0.776209i \(-0.282860\pi\)
0.630476 + 0.776209i \(0.282860\pi\)
\(258\) 3.90622 + 6.75539i 0.243190 + 0.420572i
\(259\) −14.8783 −0.924490
\(260\) 3.48888 6.06152i 0.216371 0.375920i
\(261\) 6.70206 0.414847
\(262\) 7.35544 4.25319i 0.454421 0.262763i
\(263\) 27.8557i 1.71765i −0.512266 0.858827i \(-0.671194\pi\)
0.512266 0.858827i \(-0.328806\pi\)
\(264\) 6.19859 0.0123671i 0.381497 0.000761143i
\(265\) −0.0213520 −0.00131164
\(266\) 3.63336 2.10095i 0.222776 0.128817i
\(267\) −13.2000 −0.807825
\(268\) −7.94197 + 14.3152i −0.485133 + 0.874440i
\(269\) −10.6172 −0.647340 −0.323670 0.946170i \(-0.604917\pi\)
−0.323670 + 0.946170i \(0.604917\pi\)
\(270\) −3.85114 + 2.22687i −0.234373 + 0.135523i
\(271\) −5.63033 −0.342018 −0.171009 0.985269i \(-0.554703\pi\)
−0.171009 + 0.985269i \(0.554703\pi\)
\(272\) −1.28544 2.21284i −0.0779415 0.134173i
\(273\) 1.53626i 0.0929786i
\(274\) 14.2127 8.21834i 0.858623 0.496488i
\(275\) −10.7278 −0.646911
\(276\) 9.55084 + 5.49725i 0.574893 + 0.330896i
\(277\) −14.7953 −0.888962 −0.444481 0.895788i \(-0.646612\pi\)
−0.444481 + 0.895788i \(0.646612\pi\)
\(278\) −7.36868 12.7433i −0.441944 0.764295i
\(279\) 4.75833 0.284873
\(280\) −0.0245311 12.2953i −0.00146601 0.734788i
\(281\) 12.3188i 0.734881i −0.930047 0.367440i \(-0.880234\pi\)
0.930047 0.367440i \(-0.119766\pi\)
\(282\) 3.53106 2.04179i 0.210272 0.121587i
\(283\) 7.50228i 0.445964i −0.974823 0.222982i \(-0.928421\pi\)
0.974823 0.222982i \(-0.0715792\pi\)
\(284\) 9.13866 + 5.26001i 0.542279 + 0.312124i
\(285\) 6.75544 0.400158
\(286\) −2.98267 + 1.72469i −0.176369 + 0.101983i
\(287\) 3.50711i 0.207018i
\(288\) −2.81212 + 4.90836i −0.165706 + 0.289228i
\(289\) −16.5907 −0.975923
\(290\) −25.8105 + 14.9246i −1.51565 + 0.876404i
\(291\) 5.12276i 0.300302i
\(292\) −2.15901 + 3.75104i −0.126347 + 0.219513i
\(293\) −6.01579 −0.351446 −0.175723 0.984440i \(-0.556226\pi\)
−0.175723 + 0.984440i \(0.556226\pi\)
\(294\) 3.60351 + 6.23188i 0.210161 + 0.363451i
\(295\) −0.375857 −0.0218832
\(296\) −30.4516 + 0.0607554i −1.76996 + 0.00353134i
\(297\) 2.19154 0.127166
\(298\) −12.7686 22.0820i −0.739666 1.27917i
\(299\) −6.12528 −0.354234
\(300\) 4.88382 8.48507i 0.281968 0.489886i
\(301\) −7.62532 −0.439516
\(302\) 27.6024 15.9608i 1.58834 0.918438i
\(303\) 6.31707i 0.362906i
\(304\) 7.42788 4.31487i 0.426018 0.247475i
\(305\) −32.6718 −1.87078
\(306\) −0.452911 0.783262i −0.0258912 0.0447761i
\(307\) 12.3473i 0.704698i 0.935869 + 0.352349i \(0.114617\pi\)
−0.935869 + 0.352349i \(0.885383\pi\)
\(308\) −3.02158 + 5.24963i −0.172170 + 0.299126i
\(309\) 18.2109i 1.03598i
\(310\) −18.3250 + 10.5962i −1.04079 + 0.601822i
\(311\) −18.7816 −1.06501 −0.532503 0.846428i \(-0.678748\pi\)
−0.532503 + 0.846428i \(0.678748\pi\)
\(312\) −0.00627332 3.14429i −0.000355157 0.178010i
\(313\) 34.2048i 1.93337i 0.255965 + 0.966686i \(0.417607\pi\)
−0.255965 + 0.966686i \(0.582393\pi\)
\(314\) −10.9111 18.8696i −0.615749 1.06487i
\(315\) 4.34707i 0.244930i
\(316\) −1.72430 + 2.99578i −0.0969997 + 0.168526i
\(317\) −17.1962 −0.965837 −0.482919 0.875665i \(-0.660423\pi\)
−0.482919 + 0.875665i \(0.660423\pi\)
\(318\) −0.00831012 + 0.00480522i −0.000466008 + 0.000269463i
\(319\) 14.6878 0.822360
\(320\) −0.100416 25.1650i −0.00561344 1.40677i
\(321\) 16.8450i 0.940194i
\(322\) −9.32209 + 5.39038i −0.519500 + 0.300394i
\(323\) 1.37395i 0.0764487i
\(324\) −0.997695 + 1.73338i −0.0554275 + 0.0962989i
\(325\) 5.44176i 0.301855i
\(326\) 5.46058 3.15751i 0.302434 0.174878i
\(327\) 12.4899i 0.690693i
\(328\) −0.0143213 7.17805i −0.000790761 0.396342i
\(329\) 3.98578i 0.219743i
\(330\) −8.43991 + 4.88027i −0.464602 + 0.268650i
\(331\) −30.2833 −1.66452 −0.832260 0.554385i \(-0.812953\pi\)
−0.832260 + 0.554385i \(0.812953\pi\)
\(332\) 10.9457 + 6.30008i 0.600721 + 0.345762i
\(333\) −10.7663 −0.589988
\(334\) 4.80846 2.78043i 0.263107 0.152139i
\(335\) −0.405612 25.7450i −0.0221609 1.40660i
\(336\) −2.77659 4.77978i −0.151475 0.260759i
\(337\) 27.7390i 1.51104i 0.655127 + 0.755519i \(0.272615\pi\)
−0.655127 + 0.755519i \(0.727385\pi\)
\(338\) −8.32811 14.4026i −0.452989 0.783397i
\(339\) 6.63902i 0.360582i
\(340\) 3.48844 + 2.00787i 0.189187 + 0.108892i
\(341\) 10.4280 0.564710
\(342\) 2.62919 1.52030i 0.142170 0.0822082i
\(343\) −16.7079 −0.902143
\(344\) −15.6069 + 0.0311380i −0.841466 + 0.00167885i
\(345\) −17.3324 −0.933144
\(346\) −10.4945 18.1492i −0.564189 0.975705i
\(347\) −13.7586 −0.738598 −0.369299 0.929311i \(-0.620402\pi\)
−0.369299 + 0.929311i \(0.620402\pi\)
\(348\) −6.68661 + 11.6172i −0.358440 + 0.622748i
\(349\) 27.9839 1.49795 0.748973 0.662600i \(-0.230547\pi\)
0.748973 + 0.662600i \(0.230547\pi\)
\(350\) 4.78887 + 8.28185i 0.255976 + 0.442683i
\(351\) 1.11168i 0.0593368i
\(352\) −6.16287 + 10.7568i −0.328482 + 0.573342i
\(353\) 12.7760i 0.680000i −0.940425 0.340000i \(-0.889573\pi\)
0.940425 0.340000i \(-0.110427\pi\)
\(354\) −0.146282 + 0.0845857i −0.00777480 + 0.00449568i
\(355\) −16.5844 −0.880207
\(356\) 13.1696 22.8806i 0.697985 1.21267i
\(357\) 0.884127 0.0467930
\(358\) −5.47972 9.47659i −0.289612 0.500853i
\(359\) 15.8329i 0.835626i −0.908533 0.417813i \(-0.862797\pi\)
0.908533 0.417813i \(-0.137203\pi\)
\(360\) −0.0177513 8.89722i −0.000935575 0.468925i
\(361\) 14.3880 0.757265
\(362\) −4.58723 7.93313i −0.241100 0.416956i
\(363\) −6.19716 −0.325267
\(364\) 2.66292 + 1.53272i 0.139575 + 0.0803363i
\(365\) 6.80719i 0.356305i
\(366\) −12.7157 + 7.35271i −0.664662 + 0.384332i
\(367\) 10.9260 0.570331 0.285166 0.958478i \(-0.407951\pi\)
0.285166 + 0.958478i \(0.407951\pi\)
\(368\) −19.0577 + 11.0706i −0.993449 + 0.577097i
\(369\) 2.53783i 0.132114i
\(370\) 41.4624 23.9751i 2.15553 1.24641i
\(371\) 0.00938027i 0.000486999i
\(372\) −4.74736 + 8.24798i −0.246139 + 0.427638i
\(373\) 14.1215i 0.731184i 0.930775 + 0.365592i \(0.119133\pi\)
−0.930775 + 0.365592i \(0.880867\pi\)
\(374\) −0.992572 1.71655i −0.0513247 0.0887605i
\(375\) 0.329971i 0.0170396i
\(376\) 0.0162760 + 8.15776i 0.000839368 + 0.420704i
\(377\) 7.45051i 0.383721i
\(378\) −0.978299 1.69186i −0.0503183 0.0870201i
\(379\) 14.1951 0.729152 0.364576 0.931174i \(-0.381214\pi\)
0.364576 + 0.931174i \(0.381214\pi\)
\(380\) −6.73987 + 11.7097i −0.345748 + 0.600697i
\(381\) 10.8899i 0.557904i
\(382\) −3.08319 5.33205i −0.157750 0.272811i
\(383\) −13.5159 −0.690628 −0.345314 0.938487i \(-0.612228\pi\)
−0.345314 + 0.938487i \(0.612228\pi\)
\(384\) −5.70241 9.77152i −0.291000 0.498651i
\(385\) 9.52677i 0.485529i
\(386\) 6.86626 + 11.8745i 0.349484 + 0.604395i
\(387\) −5.51787 −0.280489
\(388\) −8.87969 5.11096i −0.450798 0.259469i
\(389\) 13.3769 0.678235 0.339118 0.940744i \(-0.389872\pi\)
0.339118 + 0.940744i \(0.389872\pi\)
\(390\) 2.47556 + 4.28121i 0.125355 + 0.216788i
\(391\) 3.52514i 0.178274i
\(392\) −14.3974 + 0.0287250i −0.727179 + 0.00145083i
\(393\) 6.00800i 0.303064i
\(394\) 11.5739 6.69243i 0.583082 0.337160i
\(395\) 5.43658i 0.273544i
\(396\) −2.18649 + 3.79877i −0.109875 + 0.190895i
\(397\) −12.0757 −0.606064 −0.303032 0.952980i \(-0.597999\pi\)
−0.303032 + 0.952980i \(0.597999\pi\)
\(398\) 17.6616 10.2126i 0.885297 0.511912i
\(399\) 2.96777i 0.148574i
\(400\) 9.83528 + 16.9310i 0.491764 + 0.846551i
\(401\) 28.7633i 1.43637i −0.695853 0.718184i \(-0.744973\pi\)
0.695853 0.718184i \(-0.255027\pi\)
\(402\) −5.95173 9.92859i −0.296845 0.495193i
\(403\) 5.28971i 0.263499i
\(404\) 10.9499 + 6.30251i 0.544777 + 0.313562i
\(405\) 3.14565i 0.156309i
\(406\) −6.55662 11.3390i −0.325399 0.562744i
\(407\) −23.5947 −1.16955
\(408\) 1.80956 0.00361034i 0.0895864 0.000178738i
\(409\) 17.2602i 0.853460i 0.904379 + 0.426730i \(0.140335\pi\)
−0.904379 + 0.426730i \(0.859665\pi\)
\(410\) 5.65142 + 9.77353i 0.279104 + 0.482680i
\(411\) 11.6091i 0.572636i
\(412\) −31.5664 18.1689i −1.55516 0.895119i
\(413\) 0.165120i 0.00812501i
\(414\) −6.74569 + 3.90061i −0.331533 + 0.191705i
\(415\) −19.8636 −0.975067
\(416\) 5.45650 + 3.12617i 0.267527 + 0.153273i
\(417\) 10.4089 0.509726
\(418\) 5.76197 3.33179i 0.281827 0.162963i
\(419\) 7.97231i 0.389473i −0.980856 0.194737i \(-0.937615\pi\)
0.980856 0.194737i \(-0.0623852\pi\)
\(420\) 7.53512 + 4.33705i 0.367676 + 0.211626i
\(421\) 21.6191 1.05365 0.526825 0.849974i \(-0.323382\pi\)
0.526825 + 0.849974i \(0.323382\pi\)
\(422\) −1.18933 + 0.687713i −0.0578955 + 0.0334774i
\(423\) 2.88421i 0.140235i
\(424\) −3.83043e−5 0.0191987i −1.86022e−6 0.000932373i
\(425\) −3.13177 −0.151913
\(426\) −6.45457 + 3.73227i −0.312725 + 0.180829i
\(427\) 14.3532i 0.694600i
\(428\) −29.1987 16.8061i −1.41137 0.812355i
\(429\) 2.43628i 0.117625i
\(430\) 21.2501 12.2876i 1.02477 0.592560i
\(431\) 0.433829i 0.0208968i 0.999945 + 0.0104484i \(0.00332589\pi\)
−0.999945 + 0.0104484i \(0.996674\pi\)
\(432\) −2.00921 3.45877i −0.0966681 0.166410i
\(433\) 28.9747i 1.39244i −0.717831 0.696218i \(-0.754865\pi\)
0.717831 0.696218i \(-0.245135\pi\)
\(434\) −4.65506 8.05044i −0.223450 0.386433i
\(435\) 21.0823i 1.01082i
\(436\) 21.6497 + 12.4611i 1.03683 + 0.596779i
\(437\) 11.8329 0.566044
\(438\) −1.53194 2.64933i −0.0731991 0.126590i
\(439\) 14.7047i 0.701817i 0.936410 + 0.350909i \(0.114127\pi\)
−0.936410 + 0.350909i \(0.885873\pi\)
\(440\) −0.0389026 19.4986i −0.00185461 0.929559i
\(441\) −5.09026 −0.242394
\(442\) −0.870733 + 0.503490i −0.0414165 + 0.0239486i
\(443\) −31.2739 −1.48587 −0.742935 0.669364i \(-0.766567\pi\)
−0.742935 + 0.669364i \(0.766567\pi\)
\(444\) 10.7415 18.6620i 0.509767 0.885661i
\(445\) 41.5225i 1.96835i
\(446\) −1.72289 + 0.996237i −0.0815810 + 0.0471732i
\(447\) 18.0368 0.853110
\(448\) 11.0554 0.0441144i 0.522317 0.00208421i
\(449\) −19.0234 −0.897770 −0.448885 0.893590i \(-0.648179\pi\)
−0.448885 + 0.893590i \(0.648179\pi\)
\(450\) 3.46535 + 5.99295i 0.163358 + 0.282510i
\(451\) 5.56175i 0.261893i
\(452\) −11.5079 6.62372i −0.541288 0.311554i
\(453\) 22.5460i 1.05930i
\(454\) −1.29163 + 0.746867i −0.0606191 + 0.0350522i
\(455\) −4.83253 −0.226553
\(456\) 0.0121189 + 6.07418i 0.000567519 + 0.284449i
\(457\) −33.5199 −1.56800 −0.783998 0.620764i \(-0.786823\pi\)
−0.783998 + 0.620764i \(0.786823\pi\)
\(458\) 23.9864 13.8698i 1.12081 0.648096i
\(459\) 0.639776 0.0298622
\(460\) 17.2924 30.0436i 0.806264 1.40079i
\(461\) 11.4031 0.531093 0.265547 0.964098i \(-0.414448\pi\)
0.265547 + 0.964098i \(0.414448\pi\)
\(462\) −2.14398 3.70778i −0.0997469 0.172502i
\(463\) 38.3973 1.78447 0.892236 0.451569i \(-0.149135\pi\)
0.892236 + 0.451569i \(0.149135\pi\)
\(464\) −13.4658 23.1809i −0.625136 1.07615i
\(465\) 14.9680i 0.694125i
\(466\) −9.50071 + 5.49366i −0.440112 + 0.254489i
\(467\) 12.4776i 0.577394i 0.957420 + 0.288697i \(0.0932220\pi\)
−0.957420 + 0.288697i \(0.906778\pi\)
\(468\) 1.92696 + 1.10911i 0.0890735 + 0.0512688i
\(469\) 11.3102 0.178192i 0.522256 0.00822812i
\(470\) −6.42276 11.1075i −0.296260 0.512350i
\(471\) 15.4129 0.710187
\(472\) −0.000674267 0.337953i −3.10356e−5 0.0155555i
\(473\) −12.0926 −0.556019
\(474\) −1.22349 2.11590i −0.0561968 0.0971864i
\(475\) 10.5125i 0.482346i
\(476\) −0.882089 + 1.53253i −0.0404305 + 0.0702433i
\(477\) 0.00678779i 0.000310792i
\(478\) −9.18183 15.8790i −0.419967 0.726288i
\(479\) 5.48777i 0.250743i 0.992110 + 0.125371i \(0.0400122\pi\)
−0.992110 + 0.125371i \(0.959988\pi\)
\(480\) 15.4400 + 8.84594i 0.704735 + 0.403760i
\(481\) 11.9686i 0.545721i
\(482\) 7.86920 + 13.6089i 0.358432 + 0.619871i
\(483\) 7.61438i 0.346466i
\(484\) 6.18288 10.7420i 0.281040 0.488274i
\(485\) 16.1144 0.731718
\(486\) −0.707921 1.22427i −0.0321120 0.0555342i
\(487\) −30.2314 −1.36992 −0.684958 0.728583i \(-0.740179\pi\)
−0.684958 + 0.728583i \(0.740179\pi\)
\(488\) −0.0586114 29.3769i −0.00265321 1.32983i
\(489\) 4.46026i 0.201700i
\(490\) 19.6033 11.3354i 0.885587 0.512079i
\(491\) 26.7584i 1.20759i 0.797140 + 0.603795i \(0.206345\pi\)
−0.797140 + 0.603795i \(0.793655\pi\)
\(492\) 4.39902 + 2.53198i 0.198323 + 0.114151i
\(493\) 4.28782 0.193114
\(494\) −1.69008 2.92281i −0.0760401 0.131503i
\(495\) 6.89381i 0.309853i
\(496\) −9.56047 16.4579i −0.429278 0.738984i
\(497\) 7.28577i 0.326811i
\(498\) −7.73084 + 4.47026i −0.346427 + 0.200317i
\(499\) 28.4951 1.27561 0.637807 0.770196i \(-0.279842\pi\)
0.637807 + 0.770196i \(0.279842\pi\)
\(500\) 0.571964 + 0.329210i 0.0255790 + 0.0147227i
\(501\) 3.92760i 0.175472i
\(502\) −11.5681 20.0058i −0.516310 0.892903i
\(503\) −38.6829 −1.72478 −0.862392 0.506241i \(-0.831035\pi\)
−0.862392 + 0.506241i \(0.831035\pi\)
\(504\) 3.90869 0.00779841i 0.174107 0.000347369i
\(505\) −19.8713 −0.884261
\(506\) −14.7834 + 8.54834i −0.657204 + 0.380020i
\(507\) 11.7642 0.522465
\(508\) −18.8763 10.8648i −0.837499 0.482046i
\(509\) 26.3881 1.16963 0.584816 0.811166i \(-0.301167\pi\)
0.584816 + 0.811166i \(0.301167\pi\)
\(510\) −2.46387 + 1.42470i −0.109102 + 0.0630867i
\(511\) 2.99050 0.132292
\(512\) 22.6270 0.135434i 0.999982 0.00598540i
\(513\) 2.14755i 0.0948166i
\(514\) −14.3103 24.7482i −0.631202 1.09160i
\(515\) 57.2851 2.52428
\(516\) 5.50515 9.56456i 0.242351 0.421056i
\(517\) 6.32085i 0.277991i
\(518\) 10.5326 + 18.2151i 0.462777 + 0.800324i
\(519\) 14.8244 0.650720
\(520\) −9.89082 + 0.0197337i −0.433741 + 0.000865378i
\(521\) 8.86494i 0.388380i −0.980964 0.194190i \(-0.937792\pi\)
0.980964 0.194190i \(-0.0622078\pi\)
\(522\) −4.74453 8.20516i −0.207662 0.359130i
\(523\) 3.50424i 0.153230i −0.997061 0.0766148i \(-0.975589\pi\)
0.997061 0.0766148i \(-0.0244112\pi\)
\(524\) −10.4141 5.99416i −0.454944 0.261856i
\(525\) −6.76470 −0.295236
\(526\) −34.1030 + 19.7196i −1.48696 + 0.859816i
\(527\) 3.04426 0.132610
\(528\) −4.40325 7.58002i −0.191627 0.329878i
\(529\) −7.35958 −0.319982
\(530\) 0.0151155 + 0.0261407i 0.000656577 + 0.00113548i
\(531\) 0.119485i 0.00518519i
\(532\) −5.14427 2.96093i −0.223032 0.128372i
\(533\) −2.82124 −0.122202
\(534\) 9.34454 + 16.1604i 0.404378 + 0.699329i
\(535\) 52.9883 2.29089
\(536\) 23.1480 0.410893i 0.999842 0.0177479i
\(537\) 7.74057 0.334030
\(538\) 7.51612 + 12.9983i 0.324043 + 0.560398i
\(539\) −11.1555 −0.480502
\(540\) 5.45260 + 3.13840i 0.234643 + 0.135055i
\(541\) 30.5009i 1.31134i −0.755049 0.655669i \(-0.772387\pi\)
0.755049 0.655669i \(-0.227613\pi\)
\(542\) 3.98583 + 6.89307i 0.171206 + 0.296083i
\(543\) 6.47986 0.278078
\(544\) −1.79913 + 3.14025i −0.0771370 + 0.134637i
\(545\) −39.2889 −1.68295
\(546\) −1.88080 + 1.08755i −0.0804909 + 0.0465429i
\(547\) −24.1720 −1.03352 −0.516760 0.856130i \(-0.672862\pi\)
−0.516760 + 0.856130i \(0.672862\pi\)
\(548\) −20.1230 11.5824i −0.859612 0.494774i
\(549\) 10.3863i 0.443278i
\(550\) 7.59444 + 13.1338i 0.323828 + 0.560026i
\(551\) 14.3930i 0.613163i
\(552\) −0.0310933 15.5845i −0.00132342 0.663319i
\(553\) 2.38837 0.101564
\(554\) 10.4739 + 18.1135i 0.444993 + 0.769568i
\(555\) 33.8669i 1.43757i
\(556\) −10.3849 + 18.0426i −0.440418 + 0.765175i
\(557\) 25.5094 1.08087 0.540435 0.841386i \(-0.318260\pi\)
0.540435 + 0.841386i \(0.318260\pi\)
\(558\) −3.36852 5.82550i −0.142601 0.246613i
\(559\) 6.13408i 0.259444i
\(560\) −15.0355 + 8.73417i −0.635366 + 0.369086i
\(561\) 1.40209 0.0591964
\(562\) −15.0816 + 8.72077i −0.636181 + 0.367864i
\(563\) −27.1023 −1.14222 −0.571112 0.820872i \(-0.693488\pi\)
−0.571112 + 0.820872i \(0.693488\pi\)
\(564\) −4.99943 2.87756i −0.210514 0.121167i
\(565\) 20.8840 0.878597
\(566\) −9.18485 + 5.31103i −0.386068 + 0.223239i
\(567\) 1.38193 0.0580357
\(568\) −0.0297515 14.9119i −0.00124834 0.625689i
\(569\) −26.4581 −1.10918 −0.554590 0.832123i \(-0.687125\pi\)
−0.554590 + 0.832123i \(0.687125\pi\)
\(570\) −4.78232 8.27051i −0.200309 0.346413i
\(571\) 11.9001i 0.498002i 0.968503 + 0.249001i \(0.0801022\pi\)
−0.968503 + 0.249001i \(0.919898\pi\)
\(572\) 4.22299 + 2.43066i 0.176572 + 0.101631i
\(573\) 4.35527 0.181944
\(574\) −4.29366 + 2.48276i −0.179214 + 0.103628i
\(575\) 26.9718i 1.12480i
\(576\) 7.99994 0.0319223i 0.333331 0.00133009i
\(577\) 41.8269i 1.74128i −0.491924 0.870638i \(-0.663706\pi\)
0.491924 0.870638i \(-0.336294\pi\)
\(578\) 11.7449 + 20.3116i 0.488523 + 0.844849i
\(579\) −9.69919 −0.403085
\(580\) 36.5437 + 21.0337i 1.51739 + 0.873378i
\(581\) 8.72639i 0.362032i
\(582\) 6.27167 3.62651i 0.259969 0.150324i
\(583\) 0.0148757i 0.000616089i
\(584\) 6.12071 0.0122117i 0.253277 0.000505325i
\(585\) −3.49694 −0.144581
\(586\) 4.25870 + 7.36498i 0.175925 + 0.304244i
\(587\) 5.82667 0.240492 0.120246 0.992744i \(-0.461632\pi\)
0.120246 + 0.992744i \(0.461632\pi\)
\(588\) 5.07853 8.82336i 0.209435 0.363869i
\(589\) 10.2187i 0.421056i
\(590\) 0.266077 + 0.460152i 0.0109542 + 0.0189441i
\(591\) 9.45364i 0.388871i
\(592\) 21.6317 + 37.2381i 0.889057 + 1.53048i
\(593\) 36.1548i 1.48470i 0.670013 + 0.742349i \(0.266289\pi\)
−0.670013 + 0.742349i \(0.733711\pi\)
\(594\) −1.55144 2.68304i −0.0636562 0.110087i
\(595\) 2.78115i 0.114016i
\(596\) −17.9952 + 31.2646i −0.737112 + 1.28065i
\(597\) 14.4262i 0.590425i
\(598\) 4.33621 + 7.49902i 0.177321 + 0.306658i
\(599\) 7.36156 0.300785 0.150393 0.988626i \(-0.451946\pi\)
0.150393 + 0.988626i \(0.451946\pi\)
\(600\) −13.8454 + 0.0276237i −0.565237 + 0.00112773i
\(601\) −7.88351 −0.321575 −0.160788 0.986989i \(-0.551403\pi\)
−0.160788 + 0.986989i \(0.551403\pi\)
\(602\) 5.39813 + 9.33548i 0.220011 + 0.380486i
\(603\) 8.18434 0.128944i 0.333292 0.00525100i
\(604\) −39.0807 22.4940i −1.59017 0.915268i
\(605\) 19.4941i 0.792548i
\(606\) −7.73383 + 4.47199i −0.314165 + 0.181662i
\(607\) 31.0113i 1.25871i 0.777118 + 0.629355i \(0.216681\pi\)
−0.777118 + 0.629355i \(0.783319\pi\)
\(608\) −10.5409 6.03917i −0.427492 0.244921i
\(609\) 9.26179 0.375307
\(610\) 23.1290 + 39.9992i 0.936467 + 1.61952i
\(611\) 3.20630 0.129713
\(612\) −0.638302 + 1.10897i −0.0258018 + 0.0448277i
\(613\) −26.0434 −1.05188 −0.525941 0.850521i \(-0.676287\pi\)
−0.525941 + 0.850521i \(0.676287\pi\)
\(614\) 15.1165 8.74092i 0.610052 0.352755i
\(615\) −7.98312 −0.321910
\(616\) 8.56603 0.0170905i 0.345135 0.000688596i
\(617\) 24.7270 0.995472 0.497736 0.867329i \(-0.334165\pi\)
0.497736 + 0.867329i \(0.334165\pi\)
\(618\) 22.2951 12.8919i 0.896842 0.518587i
\(619\) 21.3340i 0.857487i −0.903426 0.428743i \(-0.858956\pi\)
0.903426 0.428743i \(-0.141044\pi\)
\(620\) 25.9453 + 14.9335i 1.04199 + 0.599745i
\(621\) 5.50995i 0.221107i
\(622\) 13.2959 + 22.9938i 0.533116 + 0.921968i
\(623\) −18.2415 −0.730829
\(624\) −3.84503 + 2.23359i −0.153924 + 0.0894150i
\(625\) −25.5135 −1.02054
\(626\) 41.8761 24.2143i 1.67371 0.967799i
\(627\) 4.70644i 0.187957i
\(628\) −15.3773 + 26.7163i −0.613623 + 1.06610i
\(629\) −6.88801 −0.274643
\(630\) −5.32201 + 3.07738i −0.212034 + 0.122606i
\(631\) 34.0951 1.35731 0.678653 0.734459i \(-0.262564\pi\)
0.678653 + 0.734459i \(0.262564\pi\)
\(632\) 4.88832 0.00975293i 0.194447 0.000387951i
\(633\) 0.971455i 0.0386119i
\(634\) 12.1736 + 21.0529i 0.483475 + 0.836118i
\(635\) 34.2557 1.35939
\(636\) 0.0117658 + 0.00677215i 0.000466545 + 0.000268533i
\(637\) 5.65872i 0.224207i
\(638\) −10.3978 17.9819i −0.411653 0.711911i
\(639\) 5.27216i 0.208563i
\(640\) −30.7378 + 17.9378i −1.21502 + 0.709052i
\(641\) 27.8415i 1.09967i −0.835273 0.549836i \(-0.814690\pi\)
0.835273 0.549836i \(-0.185310\pi\)
\(642\) 20.6229 11.9249i 0.813919 0.470638i
\(643\) 4.70790i 0.185662i −0.995682 0.0928308i \(-0.970408\pi\)
0.995682 0.0928308i \(-0.0295916\pi\)
\(644\) 13.1986 + 7.59683i 0.520098 + 0.299357i
\(645\) 17.3573i 0.683442i
\(646\) 1.68209 0.972649i 0.0661811 0.0382684i
\(647\) −40.9256 −1.60895 −0.804475 0.593986i \(-0.797553\pi\)
−0.804475 + 0.593986i \(0.797553\pi\)
\(648\) 2.82842 0.00564312i 0.111111 0.000221683i
\(649\) 0.261855i 0.0102787i
\(650\) 6.66221 3.85234i 0.261313 0.151101i
\(651\) 6.57568 0.257721
\(652\) −7.73132 4.44998i −0.302782 0.174275i
\(653\) 1.64074i 0.0642071i 0.999485 + 0.0321036i \(0.0102206\pi\)
−0.999485 + 0.0321036i \(0.989779\pi\)
\(654\) −15.2911 + 8.84187i −0.597928 + 0.345744i
\(655\) 18.8991 0.738448
\(656\) −8.77777 + 5.09903i −0.342714 + 0.199084i
\(657\) 2.16400 0.0844258
\(658\) 4.87969 2.82162i 0.190230 0.109998i
\(659\) 1.17743i 0.0458661i −0.999737 0.0229331i \(-0.992700\pi\)
0.999737 0.0229331i \(-0.00730046\pi\)
\(660\) 11.9496 + 6.87792i 0.465137 + 0.267723i
\(661\) 6.28049i 0.244283i 0.992513 + 0.122141i \(0.0389762\pi\)
−0.992513 + 0.122141i \(0.961024\pi\)
\(662\) 21.4382 + 37.0751i 0.833219 + 1.44096i
\(663\) 0.711223i 0.0276216i
\(664\) −0.0356343 17.8604i −0.00138288 0.693120i
\(665\) 9.33555 0.362017
\(666\) 7.62168 + 13.1809i 0.295334 + 0.510749i
\(667\) 36.9280i 1.42986i
\(668\) −6.80803 3.91855i −0.263410 0.151613i
\(669\) 1.40727i 0.0544083i
\(670\) −31.2319 + 18.7220i −1.20659 + 0.723296i
\(671\) 22.7620i 0.878719i
\(672\) −3.88616 + 6.78302i −0.149912 + 0.261660i
\(673\) 15.5875i 0.600853i 0.953805 + 0.300426i \(0.0971289\pi\)
−0.953805 + 0.300426i \(0.902871\pi\)
\(674\) 33.9601 19.6370i 1.30809 0.756389i
\(675\) −4.89510 −0.188413
\(676\) −11.7371 + 20.3918i −0.451426 + 0.784299i
\(677\) 4.46472i 0.171593i 0.996313 + 0.0857967i \(0.0273435\pi\)
−0.996313 + 0.0857967i \(0.972656\pi\)
\(678\) 8.12798 4.69990i 0.312153 0.180499i
\(679\) 7.07931i 0.271679i
\(680\) −0.0113568 5.69223i −0.000435515 0.218287i
\(681\) 1.05501i 0.0404282i
\(682\) −7.38223 12.7668i −0.282680 0.488866i
\(683\) −10.6789 −0.408616 −0.204308 0.978907i \(-0.565494\pi\)
−0.204308 + 0.978907i \(0.565494\pi\)
\(684\) −3.72252 2.14260i −0.142334 0.0819244i
\(685\) 36.5182 1.39529
\(686\) 11.8279 + 20.4551i 0.451591 + 0.780979i
\(687\) 19.5924i 0.747495i
\(688\) 11.0865 + 19.0850i 0.422671 + 0.727610i
\(689\) −0.00754582 −0.000287473
\(690\) 12.2700 + 21.2196i 0.467109 + 0.807816i
\(691\) 36.5726i 1.39129i 0.718387 + 0.695643i \(0.244881\pi\)
−0.718387 + 0.695643i \(0.755119\pi\)
\(692\) −14.7903 + 25.6963i −0.562241 + 0.976829i
\(693\) 3.02855 0.115045
\(694\) 9.73997 + 16.8442i 0.369724 + 0.639399i
\(695\) 32.7427i 1.24200i
\(696\) 18.9562 0.0378205i 0.718535 0.00143358i
\(697\) 1.62364i 0.0614999i
\(698\) −19.8104 34.2600i −0.749836 1.29676i
\(699\) 7.76027i 0.293521i
\(700\) 6.74911 11.7258i 0.255092 0.443193i
\(701\) 52.7118i 1.99090i −0.0952943 0.995449i \(-0.530379\pi\)
0.0952943 0.995449i \(-0.469621\pi\)
\(702\) −1.36100 + 0.786978i −0.0513675 + 0.0297026i
\(703\) 23.1211i 0.872029i
\(704\) 17.5322 0.0699588i 0.660768 0.00263667i
\(705\) 9.07271 0.341698
\(706\) −15.6414 + 9.04443i −0.588671 + 0.340392i
\(707\) 8.72976i 0.328317i
\(708\) 0.207112 + 0.119209i 0.00778376 + 0.00448016i
\(709\) −30.2718 −1.13688 −0.568441 0.822724i \(-0.692453\pi\)
−0.568441 + 0.822724i \(0.692453\pi\)
\(710\) 11.7404 + 20.3038i 0.440610 + 0.761988i
\(711\) 1.72829 0.0648158
\(712\) −37.3351 + 0.0744891i −1.39919 + 0.00279160i
\(713\) 26.2181i 0.981877i
\(714\) −0.625892 1.08241i −0.0234234 0.0405083i
\(715\) −7.66367 −0.286605
\(716\) −7.72273 + 13.4174i −0.288612 + 0.501430i
\(717\) 12.9701 0.484378
\(718\) −19.3838 + 11.2084i −0.723395 + 0.418294i
\(719\) 31.4605i 1.17328i 0.809849 + 0.586639i \(0.199549\pi\)
−0.809849 + 0.586639i \(0.800451\pi\)
\(720\) −10.8801 + 6.32026i −0.405476 + 0.235542i
\(721\) 25.1662i 0.937239i
\(722\) −10.1856 17.6149i −0.379068 0.655559i
\(723\) −11.1159 −0.413406
\(724\) −6.46493 + 11.2321i −0.240267 + 0.417436i
\(725\) −32.8073 −1.21843
\(726\) 4.38710 + 7.58703i 0.162821 + 0.281581i
\(727\) 12.3523 0.458120 0.229060 0.973412i \(-0.426435\pi\)
0.229060 + 0.973412i \(0.426435\pi\)
\(728\) −0.00866930 4.34519i −0.000321306 0.161043i
\(729\) 1.00000 0.0370370
\(730\) −8.33387 + 4.81895i −0.308450 + 0.178357i
\(731\) −3.53020 −0.130569
\(732\) 18.0035 + 10.3624i 0.665427 + 0.383005i
\(733\) 34.5045i 1.27445i −0.770677 0.637226i \(-0.780082\pi\)
0.770677 0.637226i \(-0.219918\pi\)
\(734\) −7.73473 13.3764i −0.285494 0.493732i
\(735\) 16.0122i 0.590618i
\(736\) 27.0448 + 15.4947i 0.996885 + 0.571141i
\(737\) 17.9363 0.282585i 0.660691 0.0104092i
\(738\) −3.10700 + 1.79658i −0.114370 + 0.0661331i
\(739\) −10.6844 −0.393032 −0.196516 0.980501i \(-0.562963\pi\)
−0.196516 + 0.980501i \(0.562963\pi\)
\(740\) −58.7042 33.7889i −2.15801 1.24210i
\(741\) 2.38738 0.0877025
\(742\) −0.0114840 + 0.00664049i −0.000421592 + 0.000243780i
\(743\) 34.7212i 1.27380i −0.770947 0.636899i \(-0.780217\pi\)
0.770947 0.636899i \(-0.219783\pi\)
\(744\) 13.4585 0.0268518i 0.493414 0.000984435i
\(745\) 56.7374i 2.07870i
\(746\) 17.2886 9.99691i 0.632981 0.366013i
\(747\) 6.31463i 0.231040i
\(748\) −1.39886 + 2.43036i −0.0511475 + 0.0888628i
\(749\) 23.2786i 0.850581i
\(750\) −0.403975 + 0.233593i −0.0147511 + 0.00852962i
\(751\) 42.8498i 1.56361i −0.623522 0.781806i \(-0.714299\pi\)
0.623522 0.781806i \(-0.285701\pi\)
\(752\) 9.97582 5.79498i 0.363781 0.211321i
\(753\) 16.3410 0.595497
\(754\) −9.12147 + 5.27438i −0.332184 + 0.192081i
\(755\) 70.9216 2.58110
\(756\) −1.37875 + 2.39541i −0.0501445 + 0.0871203i
\(757\) 28.2434i 1.02652i 0.858232 + 0.513262i \(0.171563\pi\)
−0.858232 + 0.513262i \(0.828437\pi\)
\(758\) −10.0490 17.3787i −0.364996 0.631222i
\(759\) 12.0753i 0.438304i
\(760\) 19.1072 0.0381218i 0.693092 0.00138282i
\(761\) 49.9893 1.81211 0.906056 0.423158i \(-0.139079\pi\)
0.906056 + 0.423158i \(0.139079\pi\)
\(762\) 13.3322 7.70916i 0.482974 0.279273i
\(763\) 17.2602i 0.624861i
\(764\) −4.34523 + 7.54934i −0.157205 + 0.273125i
\(765\) 2.01251i 0.0727625i
\(766\) 9.56816 + 16.5471i 0.345712 + 0.597872i
\(767\) −0.132828 −0.00479615
\(768\) −7.92617 + 13.8988i −0.286011 + 0.501529i
\(769\) 14.2597i 0.514219i −0.966382 0.257110i \(-0.917230\pi\)
0.966382 0.257110i \(-0.0827702\pi\)
\(770\) −11.6634 + 6.74420i −0.420319 + 0.243044i
\(771\) 20.2146 0.728011
\(772\) 9.67684