Properties

Label 731.2.j.a.135.19
Level 731
Weight 2
Character 731.135
Analytic conductor 5.837
Analytic rank 0
Dimension 128
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.j (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(128\)
Relative dimension: \(64\) over \(\Q(\zeta_{6})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 135.19
Character \(\chi\) = 731.135
Dual form 731.2.j.a.509.19

$q$-expansion

\(f(q)\) \(=\) \(q-1.28732 q^{2} +(-1.78909 - 1.03293i) q^{3} -0.342809 q^{4} +(0.933959 + 0.539221i) q^{5} +(2.30313 + 1.32971i) q^{6} +(3.12985 - 1.80702i) q^{7} +3.01594 q^{8} +(0.633889 + 1.09793i) q^{9} +O(q^{10})\) \(q-1.28732 q^{2} +(-1.78909 - 1.03293i) q^{3} -0.342809 q^{4} +(0.933959 + 0.539221i) q^{5} +(2.30313 + 1.32971i) q^{6} +(3.12985 - 1.80702i) q^{7} +3.01594 q^{8} +(0.633889 + 1.09793i) q^{9} +(-1.20230 - 0.694150i) q^{10} +0.177327i q^{11} +(0.613316 + 0.354098i) q^{12} +(1.54576 + 2.67733i) q^{13} +(-4.02912 + 2.32621i) q^{14} +(-1.11396 - 1.92943i) q^{15} -3.19686 q^{16} +(-3.93247 + 1.23922i) q^{17} +(-0.816018 - 1.41338i) q^{18} +(-3.12605 + 5.41448i) q^{19} +(-0.320170 - 0.184850i) q^{20} -7.46611 q^{21} -0.228276i q^{22} +(2.81165 + 1.62330i) q^{23} +(-5.39579 - 3.11526i) q^{24} +(-1.91848 - 3.32291i) q^{25} +(-1.98988 - 3.44658i) q^{26} +3.57853i q^{27} +(-1.07294 + 0.619463i) q^{28} +(8.29720 - 4.79039i) q^{29} +(1.43402 + 2.48379i) q^{30} +(4.80690 + 2.77526i) q^{31} -1.91650 q^{32} +(0.183166 - 0.317253i) q^{33} +(5.06235 - 1.59527i) q^{34} +3.89754 q^{35} +(-0.217303 - 0.376380i) q^{36} +(8.63973 + 4.98815i) q^{37} +(4.02422 - 6.97016i) q^{38} -6.38664i q^{39} +(2.81677 + 1.62626i) q^{40} -2.79126i q^{41} +9.61126 q^{42} +(-2.00435 + 6.24360i) q^{43} -0.0607892i q^{44} +1.36723i q^{45} +(-3.61949 - 2.08971i) q^{46} -7.36141 q^{47} +(5.71947 + 3.30214i) q^{48} +(3.03065 - 5.24924i) q^{49} +(2.46970 + 4.27764i) q^{50} +(8.31556 + 1.84491i) q^{51} +(-0.529900 - 0.917813i) q^{52} +(2.82653 - 4.89570i) q^{53} -4.60671i q^{54} +(-0.0956184 + 0.165616i) q^{55} +(9.43946 - 5.44987i) q^{56} +(11.1856 - 6.45798i) q^{57} +(-10.6812 + 6.16677i) q^{58} +10.3588 q^{59} +(0.381874 + 0.661426i) q^{60} +(-4.31816 + 2.49309i) q^{61} +(-6.18801 - 3.57265i) q^{62} +(3.96796 + 2.29090i) q^{63} +8.86088 q^{64} +3.33402i q^{65} +(-0.235793 + 0.408406i) q^{66} +(6.45627 - 11.1826i) q^{67} +(1.34809 - 0.424814i) q^{68} +(-3.35352 - 5.80847i) q^{69} -5.01738 q^{70} +(5.19633 - 3.00010i) q^{71} +(1.91177 + 3.31129i) q^{72} +(10.7620 - 6.21343i) q^{73} +(-11.1221 - 6.42134i) q^{74} +7.92663i q^{75} +(1.07164 - 1.85613i) q^{76} +(0.320433 + 0.555007i) q^{77} +8.22164i q^{78} +(-4.09496 + 2.36422i) q^{79} +(-2.98574 - 1.72382i) q^{80} +(5.59804 - 9.69608i) q^{81} +3.59324i q^{82} +(-5.26997 + 9.12786i) q^{83} +2.55945 q^{84} +(-4.34098 - 0.963098i) q^{85} +(2.58024 - 8.03751i) q^{86} -19.7926 q^{87} +0.534808i q^{88} +(-6.29446 + 10.9023i) q^{89} -1.76006i q^{90} +(9.67599 + 5.58643i) q^{91} +(-0.963858 - 0.556484i) q^{92} +(-5.73331 - 9.93038i) q^{93} +9.47648 q^{94} +(-5.83920 + 3.37127i) q^{95} +(3.42879 + 1.97961i) q^{96} -3.39436i q^{97} +(-3.90142 + 6.75745i) q^{98} +(-0.194692 + 0.112406i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + O(q^{10}) \) \( 128q - 4q^{2} + 116q^{4} - 12q^{8} + 70q^{9} + 4q^{13} - 12q^{15} + 76q^{16} + 2q^{17} - 16q^{18} - 2q^{19} - 20q^{21} + 60q^{25} - 2q^{26} - 28q^{30} - 48q^{32} + 22q^{33} - 18q^{34} - 112q^{35} + 36q^{36} - 40q^{38} + 36q^{42} + 10q^{43} + 36q^{47} + 52q^{49} + 16q^{50} + 10q^{51} + 10q^{52} + 24q^{55} - 12q^{59} - 78q^{60} + 36q^{64} + 14q^{66} + 10q^{67} - q^{68} - 64q^{70} - 68q^{72} - 22q^{76} - 28q^{77} - 20q^{81} - 6q^{83} + 32q^{84} + 6q^{85} - 58q^{86} + 32q^{87} + 36q^{89} + 6q^{93} + 132q^{94} - 48q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).

\(n\) \(173\) \(562\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.28732 −0.910272 −0.455136 0.890422i \(-0.650409\pi\)
−0.455136 + 0.890422i \(0.650409\pi\)
\(3\) −1.78909 1.03293i −1.03293 0.596363i −0.115107 0.993353i \(-0.536721\pi\)
−0.917823 + 0.396991i \(0.870055\pi\)
\(4\) −0.342809 −0.171405
\(5\) 0.933959 + 0.539221i 0.417679 + 0.241147i 0.694084 0.719894i \(-0.255810\pi\)
−0.276405 + 0.961041i \(0.589143\pi\)
\(6\) 2.30313 + 1.32971i 0.940248 + 0.542852i
\(7\) 3.12985 1.80702i 1.18297 0.682990i 0.226273 0.974064i \(-0.427346\pi\)
0.956701 + 0.291074i \(0.0940126\pi\)
\(8\) 3.01594 1.06630
\(9\) 0.633889 + 1.09793i 0.211296 + 0.365976i
\(10\) −1.20230 0.694150i −0.380202 0.219510i
\(11\) 0.177327i 0.0534660i 0.999643 + 0.0267330i \(0.00851040\pi\)
−0.999643 + 0.0267330i \(0.991490\pi\)
\(12\) 0.613316 + 0.354098i 0.177049 + 0.102219i
\(13\) 1.54576 + 2.67733i 0.428716 + 0.742558i 0.996759 0.0804407i \(-0.0256327\pi\)
−0.568043 + 0.822999i \(0.692299\pi\)
\(14\) −4.02912 + 2.32621i −1.07683 + 0.621707i
\(15\) −1.11396 1.92943i −0.287622 0.498176i
\(16\) −3.19686 −0.799216
\(17\) −3.93247 + 1.23922i −0.953765 + 0.300554i
\(18\) −0.816018 1.41338i −0.192337 0.333138i
\(19\) −3.12605 + 5.41448i −0.717165 + 1.24217i 0.244954 + 0.969535i \(0.421227\pi\)
−0.962119 + 0.272631i \(0.912106\pi\)
\(20\) −0.320170 0.184850i −0.0715921 0.0413337i
\(21\) −7.46611 −1.62924
\(22\) 0.228276i 0.0486686i
\(23\) 2.81165 + 1.62330i 0.586269 + 0.338482i 0.763621 0.645665i \(-0.223420\pi\)
−0.177352 + 0.984147i \(0.556753\pi\)
\(24\) −5.39579 3.11526i −1.10141 0.635900i
\(25\) −1.91848 3.32291i −0.383696 0.664581i
\(26\) −1.98988 3.44658i −0.390248 0.675930i
\(27\) 3.57853i 0.688688i
\(28\) −1.07294 + 0.619463i −0.202767 + 0.117068i
\(29\) 8.29720 4.79039i 1.54075 0.889554i 0.541961 0.840404i \(-0.317682\pi\)
0.998791 0.0491498i \(-0.0156512\pi\)
\(30\) 1.43402 + 2.48379i 0.261815 + 0.453476i
\(31\) 4.80690 + 2.77526i 0.863344 + 0.498452i 0.865131 0.501546i \(-0.167235\pi\)
−0.00178654 + 0.999998i \(0.500569\pi\)
\(32\) −1.91650 −0.338793
\(33\) 0.183166 0.317253i 0.0318851 0.0552267i
\(34\) 5.06235 1.59527i 0.868186 0.273586i
\(35\) 3.89754 0.658804
\(36\) −0.217303 0.376380i −0.0362172 0.0627300i
\(37\) 8.63973 + 4.98815i 1.42036 + 0.820047i 0.996330 0.0856001i \(-0.0272807\pi\)
0.424033 + 0.905647i \(0.360614\pi\)
\(38\) 4.02422 6.97016i 0.652815 1.13071i
\(39\) 6.38664i 1.02268i
\(40\) 2.81677 + 1.62626i 0.445370 + 0.257135i
\(41\) 2.79126i 0.435921i −0.975958 0.217961i \(-0.930060\pi\)
0.975958 0.217961i \(-0.0699405\pi\)
\(42\) 9.61126 1.48305
\(43\) −2.00435 + 6.24360i −0.305661 + 0.952141i
\(44\) 0.0607892i 0.00916432i
\(45\) 1.36723i 0.203814i
\(46\) −3.61949 2.08971i −0.533664 0.308111i
\(47\) −7.36141 −1.07377 −0.536886 0.843655i \(-0.680399\pi\)
−0.536886 + 0.843655i \(0.680399\pi\)
\(48\) 5.71947 + 3.30214i 0.825534 + 0.476622i
\(49\) 3.03065 5.24924i 0.432950 0.749892i
\(50\) 2.46970 + 4.27764i 0.349268 + 0.604950i
\(51\) 8.31556 + 1.84491i 1.16441 + 0.258338i
\(52\) −0.529900 0.917813i −0.0734839 0.127278i
\(53\) 2.82653 4.89570i 0.388254 0.672476i −0.603961 0.797014i \(-0.706412\pi\)
0.992215 + 0.124538i \(0.0397450\pi\)
\(54\) 4.60671i 0.626893i
\(55\) −0.0956184 + 0.165616i −0.0128932 + 0.0223316i
\(56\) 9.43946 5.44987i 1.26140 0.728270i
\(57\) 11.1856 6.45798i 1.48156 0.855381i
\(58\) −10.6812 + 6.16677i −1.40250 + 0.809736i
\(59\) 10.3588 1.34860 0.674302 0.738456i \(-0.264445\pi\)
0.674302 + 0.738456i \(0.264445\pi\)
\(60\) 0.381874 + 0.661426i 0.0492998 + 0.0853897i
\(61\) −4.31816 + 2.49309i −0.552884 + 0.319208i −0.750284 0.661115i \(-0.770083\pi\)
0.197400 + 0.980323i \(0.436750\pi\)
\(62\) −6.18801 3.57265i −0.785878 0.453727i
\(63\) 3.96796 + 2.29090i 0.499916 + 0.288627i
\(64\) 8.86088 1.10761
\(65\) 3.33402i 0.413535i
\(66\) −0.235793 + 0.408406i −0.0290242 + 0.0502713i
\(67\) 6.45627 11.1826i 0.788758 1.36617i −0.137969 0.990436i \(-0.544058\pi\)
0.926728 0.375733i \(-0.122609\pi\)
\(68\) 1.34809 0.424814i 0.163480 0.0515163i
\(69\) −3.35352 5.80847i −0.403716 0.699257i
\(70\) −5.01738 −0.599691
\(71\) 5.19633 3.00010i 0.616691 0.356047i −0.158888 0.987297i \(-0.550791\pi\)
0.775580 + 0.631250i \(0.217458\pi\)
\(72\) 1.91177 + 3.31129i 0.225305 + 0.390239i
\(73\) 10.7620 6.21343i 1.25959 0.727226i 0.286598 0.958051i \(-0.407476\pi\)
0.972995 + 0.230824i \(0.0741423\pi\)
\(74\) −11.1221 6.42134i −1.29292 0.746466i
\(75\) 7.92663i 0.915288i
\(76\) 1.07164 1.85613i 0.122925 0.212913i
\(77\) 0.320433 + 0.555007i 0.0365168 + 0.0632489i
\(78\) 8.22164i 0.930918i
\(79\) −4.09496 + 2.36422i −0.460719 + 0.265996i −0.712346 0.701828i \(-0.752367\pi\)
0.251628 + 0.967824i \(0.419034\pi\)
\(80\) −2.98574 1.72382i −0.333816 0.192729i
\(81\) 5.59804 9.69608i 0.622004 1.07734i
\(82\) 3.59324i 0.396807i
\(83\) −5.26997 + 9.12786i −0.578455 + 1.00191i 0.417202 + 0.908814i \(0.363011\pi\)
−0.995657 + 0.0930992i \(0.970323\pi\)
\(84\) 2.55945 0.279259
\(85\) −4.34098 0.963098i −0.470845 0.104463i
\(86\) 2.58024 8.03751i 0.278234 0.866707i
\(87\) −19.7926 −2.12199
\(88\) 0.534808i 0.0570107i
\(89\) −6.29446 + 10.9023i −0.667211 + 1.15564i 0.311469 + 0.950256i \(0.399179\pi\)
−0.978681 + 0.205388i \(0.934154\pi\)
\(90\) 1.76006i 0.185526i
\(91\) 9.67599 + 5.58643i 1.01432 + 0.585617i
\(92\) −0.963858 0.556484i −0.100489 0.0580174i
\(93\) −5.73331 9.93038i −0.594516 1.02973i
\(94\) 9.47648 0.977425
\(95\) −5.83920 + 3.37127i −0.599090 + 0.345885i
\(96\) 3.42879 + 1.97961i 0.349949 + 0.202043i
\(97\) 3.39436i 0.344645i −0.985041 0.172322i \(-0.944873\pi\)
0.985041 0.172322i \(-0.0551271\pi\)
\(98\) −3.90142 + 6.75745i −0.394103 + 0.682606i
\(99\) −0.194692 + 0.112406i −0.0195673 + 0.0112972i
\(100\) 0.657673 + 1.13912i 0.0657673 + 0.113912i
\(101\) −3.02047 5.23160i −0.300548 0.520564i 0.675712 0.737165i \(-0.263836\pi\)
−0.976260 + 0.216602i \(0.930503\pi\)
\(102\) −10.7048 2.37498i −1.05993 0.235158i
\(103\) 9.33686 + 16.1719i 0.919988 + 1.59347i 0.799429 + 0.600761i \(0.205135\pi\)
0.120559 + 0.992706i \(0.461531\pi\)
\(104\) 4.66192 + 8.07468i 0.457139 + 0.791787i
\(105\) −6.97304 4.02589i −0.680499 0.392886i
\(106\) −3.63865 + 6.30233i −0.353417 + 0.612136i
\(107\) 13.4825i 1.30341i −0.758474 0.651703i \(-0.774055\pi\)
0.758474 0.651703i \(-0.225945\pi\)
\(108\) 1.22675i 0.118044i
\(109\) 9.40354 + 5.42914i 0.900696 + 0.520017i 0.877426 0.479712i \(-0.159259\pi\)
0.0232698 + 0.999729i \(0.492592\pi\)
\(110\) 0.123091 0.213201i 0.0117363 0.0203279i
\(111\) −10.3048 17.8485i −0.978090 1.69410i
\(112\) −10.0057 + 5.77680i −0.945451 + 0.545856i
\(113\) 1.70186i 0.160097i −0.996791 0.0800487i \(-0.974492\pi\)
0.996791 0.0800487i \(-0.0255076\pi\)
\(114\) −14.3994 + 8.31348i −1.34863 + 0.778629i
\(115\) 1.75064 + 3.03220i 0.163248 + 0.282754i
\(116\) −2.84436 + 1.64219i −0.264092 + 0.152474i
\(117\) −1.95968 + 3.39426i −0.181172 + 0.313800i
\(118\) −13.3351 −1.22760
\(119\) −10.0688 + 10.9846i −0.923003 + 1.00696i
\(120\) −3.35963 5.81905i −0.306691 0.531204i
\(121\) 10.9686 0.997141
\(122\) 5.55885 3.20941i 0.503275 0.290566i
\(123\) −2.88318 + 4.99381i −0.259967 + 0.450276i
\(124\) −1.64785 0.951386i −0.147981 0.0854369i
\(125\) 9.53016i 0.852403i
\(126\) −5.10803 2.94912i −0.455060 0.262729i
\(127\) −8.99424 −0.798110 −0.399055 0.916927i \(-0.630662\pi\)
−0.399055 + 0.916927i \(0.630662\pi\)
\(128\) −7.57377 −0.669433
\(129\) 10.0352 9.10000i 0.883547 0.801210i
\(130\) 4.29195i 0.376429i
\(131\) 3.82898i 0.334540i 0.985911 + 0.167270i \(0.0534951\pi\)
−0.985911 + 0.167270i \(0.946505\pi\)
\(132\) −0.0627910 + 0.108757i −0.00546526 + 0.00946610i
\(133\) 22.5954i 1.95927i
\(134\) −8.31128 + 14.3956i −0.717985 + 1.24359i
\(135\) −1.92962 + 3.34220i −0.166075 + 0.287651i
\(136\) −11.8601 + 3.73740i −1.01700 + 0.320480i
\(137\) 10.9588 0.936272 0.468136 0.883656i \(-0.344926\pi\)
0.468136 + 0.883656i \(0.344926\pi\)
\(138\) 4.31705 + 7.47735i 0.367492 + 0.636514i
\(139\) 11.5217 + 6.65207i 0.977260 + 0.564221i 0.901442 0.432900i \(-0.142510\pi\)
0.0758182 + 0.997122i \(0.475843\pi\)
\(140\) −1.33611 −0.112922
\(141\) 13.1702 + 7.60382i 1.10913 + 0.640357i
\(142\) −6.68934 + 3.86209i −0.561357 + 0.324100i
\(143\) −0.474762 + 0.274104i −0.0397016 + 0.0229217i
\(144\) −2.02646 3.50993i −0.168872 0.292494i
\(145\) 10.3323 0.858053
\(146\) −13.8541 + 7.99866i −1.14657 + 0.661974i
\(147\) −10.8442 + 6.26091i −0.894415 + 0.516391i
\(148\) −2.96178 1.70998i −0.243457 0.140560i
\(149\) 8.83069 15.2952i 0.723439 1.25303i −0.236175 0.971711i \(-0.575894\pi\)
0.959613 0.281322i \(-0.0907729\pi\)
\(150\) 10.2041i 0.833161i
\(151\) 1.55509 0.126552 0.0632758 0.997996i \(-0.479845\pi\)
0.0632758 + 0.997996i \(0.479845\pi\)
\(152\) −9.42799 + 16.3298i −0.764711 + 1.32452i
\(153\) −3.85332 3.53205i −0.311523 0.285549i
\(154\) −0.412500 0.714471i −0.0332402 0.0575737i
\(155\) 2.99296 + 5.18396i 0.240401 + 0.416386i
\(156\) 2.18940i 0.175292i
\(157\) −4.30846 7.46247i −0.343852 0.595570i 0.641292 0.767297i \(-0.278399\pi\)
−0.985145 + 0.171727i \(0.945065\pi\)
\(158\) 5.27152 3.04351i 0.419379 0.242129i
\(159\) −10.1138 + 5.83922i −0.802079 + 0.463080i
\(160\) −1.78993 1.03342i −0.141507 0.0816990i
\(161\) 11.7334 0.924720
\(162\) −7.20646 + 12.4820i −0.566193 + 0.980675i
\(163\) 6.79190 3.92130i 0.531983 0.307140i −0.209841 0.977736i \(-0.567295\pi\)
0.741823 + 0.670595i \(0.233961\pi\)
\(164\) 0.956869i 0.0747189i
\(165\) 0.342139 0.197534i 0.0266355 0.0153780i
\(166\) 6.78414 11.7505i 0.526551 0.912013i
\(167\) −17.2909 9.98292i −1.33801 0.772502i −0.351500 0.936188i \(-0.614328\pi\)
−0.986512 + 0.163686i \(0.947662\pi\)
\(168\) −22.5174 −1.73725
\(169\) 1.72127 2.98132i 0.132405 0.229332i
\(170\) 5.58823 + 1.23981i 0.428597 + 0.0950894i
\(171\) −7.92628 −0.606138
\(172\) 0.687109 2.14036i 0.0523916 0.163201i
\(173\) 23.0689i 1.75389i −0.480586 0.876947i \(-0.659576\pi\)
0.480586 0.876947i \(-0.340424\pi\)
\(174\) 25.4794 1.93158
\(175\) −12.0091 6.93347i −0.907804 0.524121i
\(176\) 0.566890i 0.0427309i
\(177\) −18.5328 10.6999i −1.39301 0.804257i
\(178\) 8.10298 14.0348i 0.607344 1.05195i
\(179\) 8.01703 + 13.8859i 0.599221 + 1.03788i 0.992936 + 0.118648i \(0.0378561\pi\)
−0.393716 + 0.919232i \(0.628811\pi\)
\(180\) 0.468698i 0.0349347i
\(181\) −5.57176 + 3.21686i −0.414146 + 0.239107i −0.692570 0.721351i \(-0.743521\pi\)
0.278424 + 0.960458i \(0.410188\pi\)
\(182\) −12.4561 7.19152i −0.923307 0.533071i
\(183\) 10.3008 0.761454
\(184\) 8.47976 + 4.89579i 0.625136 + 0.360923i
\(185\) 5.37943 + 9.31745i 0.395504 + 0.685033i
\(186\) 7.38060 + 12.7836i 0.541172 + 0.937337i
\(187\) −0.219746 0.697333i −0.0160694 0.0509940i
\(188\) 2.52356 0.184049
\(189\) 6.46647 + 11.2003i 0.470367 + 0.814699i
\(190\) 7.51692 4.33990i 0.545335 0.314849i
\(191\) −1.56176 + 2.70505i −0.113005 + 0.195730i −0.916980 0.398932i \(-0.869381\pi\)
0.803976 + 0.594662i \(0.202714\pi\)
\(192\) −15.8529 9.15267i −1.14408 0.660537i
\(193\) 22.5076i 1.62013i 0.586340 + 0.810065i \(0.300568\pi\)
−0.586340 + 0.810065i \(0.699432\pi\)
\(194\) 4.36962i 0.313720i
\(195\) 3.44381 5.96486i 0.246617 0.427152i
\(196\) −1.03894 + 1.79949i −0.0742097 + 0.128535i
\(197\) −0.772951 + 0.446264i −0.0550705 + 0.0317950i −0.527282 0.849690i \(-0.676789\pi\)
0.472212 + 0.881485i \(0.343456\pi\)
\(198\) 0.250631 0.144702i 0.0178116 0.0102835i
\(199\) 16.9316i 1.20025i −0.799906 0.600126i \(-0.795117\pi\)
0.799906 0.600126i \(-0.204883\pi\)
\(200\) −5.78603 10.0217i −0.409134 0.708641i
\(201\) −23.1016 + 13.3377i −1.62946 + 0.940772i
\(202\) 3.88830 + 6.73474i 0.273580 + 0.473855i
\(203\) 17.3127 29.9865i 1.21511 2.10464i
\(204\) −2.85065 0.632450i −0.199585 0.0442804i
\(205\) 1.50511 2.60692i 0.105121 0.182075i
\(206\) −12.0195 20.8184i −0.837440 1.45049i
\(207\) 4.11598i 0.286081i
\(208\) −4.94158 8.55906i −0.342637 0.593464i
\(209\) −0.960132 0.554332i −0.0664137 0.0383440i
\(210\) 8.97653 + 5.18260i 0.619439 + 0.357633i
\(211\) 6.06357i 0.417433i 0.977976 + 0.208717i \(0.0669286\pi\)
−0.977976 + 0.208717i \(0.933071\pi\)
\(212\) −0.968961 + 1.67829i −0.0665485 + 0.115265i
\(213\) −12.3956 −0.849332
\(214\) 17.3563i 1.18645i
\(215\) −5.23867 + 4.75048i −0.357274 + 0.323980i
\(216\) 10.7926i 0.734346i
\(217\) 20.0598 1.36175
\(218\) −12.1054 6.98903i −0.819878 0.473357i
\(219\) −25.6721 −1.73476
\(220\) 0.0327789 0.0567747i 0.00220995 0.00382775i
\(221\) −9.39644 8.61300i −0.632073 0.579373i
\(222\) 13.2656 + 22.9767i 0.890328 + 1.54209i
\(223\) −26.0662 −1.74553 −0.872763 0.488145i \(-0.837674\pi\)
−0.872763 + 0.488145i \(0.837674\pi\)
\(224\) −5.99837 + 3.46316i −0.400783 + 0.231392i
\(225\) 2.43221 4.21271i 0.162147 0.280847i
\(226\) 2.19084i 0.145732i
\(227\) −18.6870 10.7889i −1.24030 0.716086i −0.271142 0.962539i \(-0.587401\pi\)
−0.969155 + 0.246454i \(0.920735\pi\)
\(228\) −3.83451 + 2.21386i −0.253947 + 0.146616i
\(229\) 13.4158 + 23.2369i 0.886542 + 1.53554i 0.843936 + 0.536444i \(0.180233\pi\)
0.0426062 + 0.999092i \(0.486434\pi\)
\(230\) −2.25363 3.90341i −0.148600 0.257383i
\(231\) 1.32394i 0.0871089i
\(232\) 25.0239 14.4476i 1.64290 0.948528i
\(233\) −3.95948 + 2.28600i −0.259394 + 0.149761i −0.624058 0.781378i \(-0.714517\pi\)
0.364664 + 0.931139i \(0.381184\pi\)
\(234\) 2.52273 4.36950i 0.164916 0.285643i
\(235\) −6.87525 3.96943i −0.448492 0.258937i
\(236\) −3.55110 −0.231157
\(237\) 9.76832 0.634520
\(238\) 12.9617 14.1407i 0.840184 0.916607i
\(239\) −2.19407 + 3.80024i −0.141923 + 0.245817i −0.928221 0.372030i \(-0.878662\pi\)
0.786298 + 0.617848i \(0.211995\pi\)
\(240\) 3.56117 + 6.16812i 0.229872 + 0.398150i
\(241\) 5.78403 3.33941i 0.372582 0.215111i −0.302004 0.953307i \(-0.597655\pi\)
0.674586 + 0.738196i \(0.264322\pi\)
\(242\) −14.1200 −0.907670
\(243\) −10.7335 + 6.19697i −0.688552 + 0.397536i
\(244\) 1.48031 0.854655i 0.0947668 0.0547137i
\(245\) 5.66101 3.26839i 0.361669 0.208810i
\(246\) 3.71157 6.42862i 0.236641 0.409874i
\(247\) −19.3285 −1.22984
\(248\) 14.4973 + 8.37004i 0.920581 + 0.531498i
\(249\) 18.8569 10.8870i 1.19501 0.689937i
\(250\) 12.2684i 0.775919i
\(251\) −9.67163 16.7518i −0.610468 1.05736i −0.991162 0.132660i \(-0.957648\pi\)
0.380694 0.924701i \(-0.375685\pi\)
\(252\) −1.36025 0.785343i −0.0856879 0.0494719i
\(253\) −0.287855 + 0.498580i −0.0180973 + 0.0313455i
\(254\) 11.5785 0.726497
\(255\) 6.77158 + 6.20700i 0.424053 + 0.388697i
\(256\) −7.97189 −0.498243
\(257\) −17.1199 −1.06791 −0.533956 0.845512i \(-0.679295\pi\)
−0.533956 + 0.845512i \(0.679295\pi\)
\(258\) −12.9185 + 11.7146i −0.804268 + 0.729319i
\(259\) 36.0548 2.24033
\(260\) 1.14293i 0.0708817i
\(261\) 10.5190 + 6.07316i 0.651111 + 0.375919i
\(262\) 4.92912i 0.304522i
\(263\) 6.68360 11.5763i 0.412129 0.713828i −0.582994 0.812477i \(-0.698119\pi\)
0.995122 + 0.0986489i \(0.0314521\pi\)
\(264\) 0.552419 0.956817i 0.0339990 0.0588880i
\(265\) 5.27973 3.04825i 0.324331 0.187253i
\(266\) 29.0874i 1.78347i
\(267\) 22.5227 13.0035i 1.37837 0.795800i
\(268\) −2.21327 + 3.83349i −0.135197 + 0.234168i
\(269\) 6.27199i 0.382410i 0.981550 + 0.191205i \(0.0612396\pi\)
−0.981550 + 0.191205i \(0.938760\pi\)
\(270\) 2.48404 4.30248i 0.151174 0.261840i
\(271\) 12.9037 + 22.3499i 0.783845 + 1.35766i 0.929687 + 0.368352i \(0.120078\pi\)
−0.145841 + 0.989308i \(0.546589\pi\)
\(272\) 12.5716 3.96160i 0.762264 0.240207i
\(273\) −11.5408 19.9892i −0.698481 1.20980i
\(274\) −14.1075 −0.852263
\(275\) 0.589240 0.340198i 0.0355325 0.0205147i
\(276\) 1.14962 + 1.99120i 0.0691988 + 0.119856i
\(277\) −0.703887 0.406389i −0.0422925 0.0244176i 0.478705 0.877976i \(-0.341106\pi\)
−0.520997 + 0.853558i \(0.674440\pi\)
\(278\) −14.8321 8.56334i −0.889573 0.513595i
\(279\) 7.03684i 0.421285i
\(280\) 11.7548 0.702481
\(281\) −13.6317 + 23.6108i −0.813201 + 1.40851i 0.0974119 + 0.995244i \(0.468944\pi\)
−0.910613 + 0.413261i \(0.864390\pi\)
\(282\) −16.9543 9.78855i −1.00961 0.582899i
\(283\) 10.1285 5.84768i 0.602076 0.347609i −0.167782 0.985824i \(-0.553660\pi\)
0.769858 + 0.638216i \(0.220327\pi\)
\(284\) −1.78135 + 1.02846i −0.105704 + 0.0610281i
\(285\) 13.9291 0.825090
\(286\) 0.611171 0.352860i 0.0361393 0.0208650i
\(287\) −5.04387 8.73623i −0.297730 0.515683i
\(288\) −1.21485 2.10418i −0.0715858 0.123990i
\(289\) 13.9287 9.74636i 0.819335 0.573315i
\(290\) −13.3010 −0.781062
\(291\) −3.50613 + 6.07280i −0.205533 + 0.355994i
\(292\) −3.68930 + 2.13002i −0.215900 + 0.124650i
\(293\) 14.3523 0.838471 0.419236 0.907877i \(-0.362298\pi\)
0.419236 + 0.907877i \(0.362298\pi\)
\(294\) 13.9600 8.05978i 0.814161 0.470056i
\(295\) 9.67472 + 5.58570i 0.563284 + 0.325212i
\(296\) 26.0569 + 15.0440i 1.51453 + 0.874413i
\(297\) −0.634569 −0.0368214
\(298\) −11.3679 + 19.6898i −0.658526 + 1.14060i
\(299\) 10.0369i 0.580451i
\(300\) 2.71732i 0.156885i
\(301\) 5.00900 + 23.1635i 0.288714 + 1.33512i
\(302\) −2.00190 −0.115196
\(303\) 12.4797i 0.716941i
\(304\) 9.99355 17.3093i 0.573170 0.992759i
\(305\) −5.37732 −0.307904
\(306\) 4.96046 + 4.54688i 0.283570 + 0.259928i
\(307\) −2.09917 + 3.63587i −0.119806 + 0.207510i −0.919691 0.392644i \(-0.871561\pi\)
0.799885 + 0.600154i \(0.204894\pi\)
\(308\) −0.109847 0.190261i −0.00625914 0.0108411i
\(309\) 38.5773i 2.19459i
\(310\) −3.85290 6.67342i −0.218830 0.379025i
\(311\) 17.9145 + 10.3430i 1.01584 + 0.586495i 0.912896 0.408192i \(-0.133841\pi\)
0.102943 + 0.994687i \(0.467174\pi\)
\(312\) 19.2617i 1.09048i
\(313\) 24.2468 + 13.9989i 1.37051 + 0.791263i 0.990992 0.133922i \(-0.0427573\pi\)
0.379516 + 0.925185i \(0.376091\pi\)
\(314\) 5.54636 + 9.60658i 0.312999 + 0.542131i
\(315\) 2.47061 + 4.27922i 0.139203 + 0.241107i
\(316\) 1.40379 0.810478i 0.0789693 0.0455929i
\(317\) 3.69149i 0.207335i 0.994612 + 0.103667i \(0.0330577\pi\)
−0.994612 + 0.103667i \(0.966942\pi\)
\(318\) 13.0197 7.51694i 0.730110 0.421529i
\(319\) 0.849465 + 1.47132i 0.0475609 + 0.0823779i
\(320\) 8.27570 + 4.77798i 0.462625 + 0.267097i
\(321\) −13.9265 + 24.1215i −0.777303 + 1.34633i
\(322\) −15.1046 −0.841747
\(323\) 5.58340 25.1661i 0.310669 1.40028i
\(324\) −1.91906 + 3.32391i −0.106614 + 0.184661i
\(325\) 5.93101 10.2728i 0.328993 0.569833i
\(326\) −8.74334 + 5.04797i −0.484249 + 0.279581i
\(327\) −11.2158 19.4264i −0.620237 1.07428i
\(328\) 8.41828i 0.464822i
\(329\) −23.0401 + 13.3022i −1.27024 + 0.733375i
\(330\) −0.440443 + 0.254290i −0.0242456 + 0.0139982i
\(331\) 5.55108 + 9.61475i 0.305115 + 0.528474i 0.977287 0.211921i \(-0.0679718\pi\)
−0.672172 + 0.740395i \(0.734639\pi\)
\(332\) 1.80659 3.12911i 0.0991498 0.171732i
\(333\) 12.6477i 0.693092i
\(334\) 22.2589 + 12.8512i 1.21796 + 0.703187i
\(335\) 12.0598 6.96271i 0.658896 0.380414i
\(336\) 23.8681 1.30211
\(337\) −19.5264 + 11.2735i −1.06367 + 0.614109i −0.926445 0.376431i \(-0.877151\pi\)
−0.137224 + 0.990540i \(0.543818\pi\)
\(338\) −2.21582 + 3.83791i −0.120525 + 0.208755i
\(339\) −1.75790 + 3.04477i −0.0954761 + 0.165369i
\(340\) 1.48813 + 0.330159i 0.0807050 + 0.0179054i
\(341\) −0.492129 + 0.852392i −0.0266503 + 0.0461596i
\(342\) 10.2037 0.551750
\(343\) 3.39248i 0.183177i
\(344\) −6.04501 + 18.8304i −0.325925 + 1.01526i
\(345\) 7.23316i 0.389420i
\(346\) 29.6970i 1.59652i
\(347\) −8.66893 5.00501i −0.465372 0.268683i 0.248928 0.968522i \(-0.419922\pi\)
−0.714301 + 0.699839i \(0.753255\pi\)
\(348\) 6.78507 0.363718
\(349\) 8.64409 14.9720i 0.462707 0.801433i −0.536387 0.843972i \(-0.680211\pi\)
0.999095 + 0.0425392i \(0.0135447\pi\)
\(350\) 15.4596 + 8.92559i 0.826349 + 0.477093i
\(351\) −9.58090 + 5.53154i −0.511391 + 0.295252i
\(352\) 0.339847i 0.0181139i
\(353\) 6.02356 + 10.4331i 0.320602 + 0.555298i 0.980612 0.195958i \(-0.0627816\pi\)
−0.660011 + 0.751256i \(0.729448\pi\)
\(354\) 23.8577 + 13.7742i 1.26802 + 0.732093i
\(355\) 6.47088 0.343439
\(356\) 2.15780 3.73742i 0.114363 0.198083i
\(357\) 29.3603 9.25212i 1.55391 0.489674i
\(358\) −10.3205 17.8756i −0.545454 0.944754i
\(359\) 7.77667 + 13.4696i 0.410437 + 0.710897i 0.994937 0.100496i \(-0.0320429\pi\)
−0.584501 + 0.811393i \(0.698710\pi\)
\(360\) 4.12348i 0.217326i
\(361\) −10.0444 17.3974i −0.528651 0.915651i
\(362\) 7.17264 4.14112i 0.376986 0.217653i
\(363\) −19.6237 11.3298i −1.02998 0.594658i
\(364\) −3.31702 1.91508i −0.173859 0.100378i
\(365\) 13.4017 0.701474
\(366\) −13.2604 −0.693130
\(367\) −26.9045 15.5333i −1.40440 0.810833i −0.409563 0.912282i \(-0.634319\pi\)
−0.994841 + 0.101449i \(0.967652\pi\)
\(368\) −8.98845 5.18948i −0.468555 0.270520i
\(369\) 3.06460 1.76935i 0.159537 0.0921087i
\(370\) −6.92505 11.9945i −0.360016 0.623566i
\(371\) 20.4304i 1.06069i
\(372\) 1.96543 + 3.40422i 0.101903 + 0.176501i
\(373\) −1.85279 3.20912i −0.0959337 0.166162i 0.814064 0.580775i \(-0.197250\pi\)
−0.909998 + 0.414613i \(0.863917\pi\)
\(374\) 0.282883 + 0.897690i 0.0146276 + 0.0464184i
\(375\) −9.84399 + 17.0503i −0.508341 + 0.880473i
\(376\) −22.2016 −1.14496
\(377\) 25.6509 + 14.8096i 1.32109 + 0.762732i
\(378\) −8.32442 14.4183i −0.428162 0.741598i
\(379\) 13.4112i 0.688888i 0.938807 + 0.344444i \(0.111933\pi\)
−0.938807 + 0.344444i \(0.888067\pi\)
\(380\) 2.00173 1.15570i 0.102687 0.0592862i
\(381\) 16.0915 + 9.29042i 0.824391 + 0.475963i
\(382\) 2.01048 3.48226i 0.102865 0.178168i
\(383\) −29.0493 −1.48435 −0.742174 0.670207i \(-0.766205\pi\)
−0.742174 + 0.670207i \(0.766205\pi\)
\(384\) 13.5501 + 7.82318i 0.691478 + 0.399225i
\(385\) 0.691138i 0.0352237i
\(386\) 28.9744i 1.47476i
\(387\) −8.12557 + 1.75712i −0.413046 + 0.0893195i
\(388\) 1.16362i 0.0590737i
\(389\) −29.9970 −1.52091 −0.760454 0.649392i \(-0.775023\pi\)
−0.760454 + 0.649392i \(0.775023\pi\)
\(390\) −4.43329 + 7.67868i −0.224488 + 0.388825i
\(391\) −13.0683 2.89937i −0.660895 0.146627i
\(392\) 9.14028 15.8314i 0.461654 0.799608i
\(393\) 3.95507 6.85038i 0.199507 0.345556i
\(394\) 0.995035 0.574484i 0.0501292 0.0289421i
\(395\) −5.09936 −0.256577
\(396\) 0.0667422 0.0385337i 0.00335392 0.00193639i
\(397\) 4.93945 + 2.85179i 0.247904 + 0.143127i 0.618804 0.785545i \(-0.287617\pi\)
−0.370900 + 0.928673i \(0.620951\pi\)
\(398\) 21.7964i 1.09256i
\(399\) 23.3394 40.4251i 1.16843 2.02378i
\(400\) 6.13312 + 10.6229i 0.306656 + 0.531144i
\(401\) 20.6280 11.9096i 1.03011 0.594737i 0.113097 0.993584i \(-0.463923\pi\)
0.917017 + 0.398847i \(0.130590\pi\)
\(402\) 29.7392 17.1699i 1.48326 0.856358i
\(403\) 17.1595i 0.854778i
\(404\) 1.03544 + 1.79344i 0.0515152 + 0.0892270i
\(405\) 10.4567 6.03716i 0.519596 0.299989i
\(406\) −22.2870 + 38.6021i −1.10608 + 1.91579i
\(407\) −0.884532 + 1.53206i −0.0438446 + 0.0759412i
\(408\) 25.0793 + 5.56413i 1.24161 + 0.275465i
\(409\) −10.7198 −0.530060 −0.265030 0.964240i \(-0.585382\pi\)
−0.265030 + 0.964240i \(0.585382\pi\)
\(410\) −1.93755 + 3.35594i −0.0956889 + 0.165738i
\(411\) −19.6062 11.3197i −0.967104 0.558358i
\(412\) −3.20076 5.54388i −0.157690 0.273127i
\(413\) 32.4216 18.7186i 1.59536 0.921083i
\(414\) 5.29858i 0.260411i
\(415\) −9.84388 + 5.68337i −0.483217 + 0.278985i
\(416\) −2.96245 5.13111i −0.145246 0.251573i
\(417\) −13.7422 23.8023i −0.672961 1.16560i
\(418\) 1.23600 + 0.713603i 0.0604545 + 0.0349034i
\(419\) 24.6126i 1.20241i 0.799096 + 0.601203i \(0.205312\pi\)
−0.799096 + 0.601203i \(0.794688\pi\)
\(420\) 2.39042 + 1.38011i 0.116641 + 0.0673425i
\(421\) −4.87472 8.44327i −0.237579 0.411500i 0.722440 0.691434i \(-0.243021\pi\)
−0.960019 + 0.279934i \(0.909687\pi\)
\(422\) 7.80575i 0.379978i
\(423\) −4.66632 8.08230i −0.226884 0.392975i
\(424\) 8.52466 14.7651i 0.413994 0.717059i
\(425\) 11.6622 + 10.6898i 0.565698 + 0.518533i
\(426\) 15.9571 0.773123
\(427\) −9.01014 + 15.6060i −0.436031 + 0.755228i
\(428\) 4.62194i 0.223410i
\(429\) 1.13252 0.0546787
\(430\) 6.74384 6.11539i 0.325217 0.294910i
\(431\) 5.03671i 0.242610i 0.992615 + 0.121305i \(0.0387078\pi\)
−0.992615 + 0.121305i \(0.961292\pi\)
\(432\) 11.4401i 0.550410i
\(433\) 7.62040 13.1989i 0.366213 0.634300i −0.622757 0.782415i \(-0.713987\pi\)
0.988970 + 0.148116i \(0.0473208\pi\)
\(434\) −25.8234 −1.23956
\(435\) −18.4854 10.6726i −0.886309 0.511711i
\(436\) −3.22362 1.86116i −0.154383 0.0891333i
\(437\) −17.5787 + 10.1491i −0.840903 + 0.485495i
\(438\) 33.0482 1.57911
\(439\) 27.7183 16.0032i 1.32292 0.763789i 0.338727 0.940885i \(-0.390004\pi\)
0.984194 + 0.177096i \(0.0566702\pi\)
\(440\) −0.288380 + 0.499488i −0.0137480 + 0.0238122i
\(441\) 7.68440 0.365924
\(442\) 12.0962 + 11.0877i 0.575358 + 0.527387i
\(443\) 11.4737 + 19.8729i 0.545130 + 0.944192i 0.998599 + 0.0529202i \(0.0168529\pi\)
−0.453469 + 0.891272i \(0.649814\pi\)
\(444\) 3.53259 + 6.11862i 0.167649 + 0.290377i
\(445\) −11.7575 + 6.78821i −0.557360 + 0.321792i
\(446\) 33.5556 1.58890
\(447\) −31.5978 + 18.2430i −1.49452 + 0.862863i
\(448\) 27.7332 16.0118i 1.31027 0.756486i
\(449\) −5.74998 3.31975i −0.271358 0.156669i 0.358146 0.933665i \(-0.383409\pi\)
−0.629505 + 0.776997i \(0.716742\pi\)
\(450\) −3.13103 + 5.42310i −0.147598 + 0.255647i
\(451\) 0.494965 0.0233070
\(452\) 0.583413i 0.0274414i
\(453\) −2.78220 1.60630i −0.130719 0.0754706i
\(454\) 24.0561 + 13.8888i 1.12901 + 0.651833i
\(455\) 6.02465 + 10.4350i 0.282440 + 0.489200i
\(456\) 33.7350 19.4769i 1.57979 0.912090i
\(457\) −19.6258 −0.918055 −0.459027 0.888422i \(-0.651802\pi\)
−0.459027 + 0.888422i \(0.651802\pi\)
\(458\) −17.2704 29.9133i −0.806995 1.39776i
\(459\) −4.43457 14.0725i −0.206988 0.656846i
\(460\) −0.600136 1.03947i −0.0279815 0.0484653i
\(461\) 8.46295 14.6583i 0.394159 0.682703i −0.598835 0.800873i \(-0.704369\pi\)
0.992993 + 0.118169i \(0.0377026\pi\)
\(462\) 1.70433i 0.0792928i
\(463\) −19.7322 + 34.1772i −0.917033 + 1.58835i −0.113136 + 0.993580i \(0.536090\pi\)
−0.803897 + 0.594768i \(0.797244\pi\)
\(464\) −26.5250 + 15.3142i −1.23139 + 0.710945i
\(465\) 12.3661i 0.573464i
\(466\) 5.09711 2.94282i 0.236119 0.136323i
\(467\) 4.70008 8.14079i 0.217494 0.376711i −0.736547 0.676386i \(-0.763545\pi\)
0.954041 + 0.299676i \(0.0968784\pi\)
\(468\) 0.671796 1.16358i 0.0310538 0.0537867i
\(469\) 46.6664i 2.15486i
\(470\) 8.85065 + 5.10992i 0.408250 + 0.235703i
\(471\) 17.8013i 0.820243i
\(472\) 31.2416 1.43801
\(473\) −1.10716 0.355425i −0.0509072 0.0163425i
\(474\) −12.5749 −0.577586
\(475\) 23.9891 1.10069
\(476\) 3.45167 3.76563i 0.158207 0.172597i
\(477\) 7.16684 0.328147
\(478\) 2.82447 4.89213i 0.129188 0.223761i
\(479\) 12.1107 + 6.99214i 0.553354 + 0.319479i 0.750474 0.660900i \(-0.229825\pi\)
−0.197120 + 0.980379i \(0.563159\pi\)
\(480\) 2.13490 + 3.69775i 0.0974444 + 0.168779i
\(481\) 30.8419i 1.40627i
\(482\) −7.44590 + 4.29889i −0.339151 + 0.195809i
\(483\) −20.9920 12.1198i −0.955171 0.551468i
\(484\) −3.76012 −0.170915
\(485\) 1.83031 3.17019i 0.0831101 0.143951i
\(486\) 13.8174 7.97748i 0.626770 0.361866i
\(487\) −17.6080 + 10.1660i −0.797896 + 0.460665i −0.842735 0.538329i \(-0.819056\pi\)
0.0448390 + 0.998994i \(0.485723\pi\)
\(488\) −13.0233 + 7.51902i −0.589539 + 0.340370i
\(489\) −16.2017 −0.732668
\(490\) −7.28753 + 4.20746i −0.329217 + 0.190074i
\(491\) −6.39319 11.0733i −0.288521 0.499732i 0.684936 0.728603i \(-0.259830\pi\)
−0.973457 + 0.228871i \(0.926497\pi\)
\(492\) 0.988379 1.71192i 0.0445596 0.0771794i
\(493\) −26.6922 + 29.1201i −1.20216 + 1.31150i
\(494\) 24.8819 1.11949
\(495\) −0.242446 −0.0108971
\(496\) −15.3670 8.87214i −0.689998 0.398371i
\(497\) 10.8425 18.7798i 0.486353 0.842388i
\(498\) −24.2748 + 14.0151i −1.08778 + 0.628031i
\(499\) −29.4962 + 17.0296i −1.32043 + 0.762351i −0.983797 0.179284i \(-0.942622\pi\)
−0.336634 + 0.941636i \(0.609289\pi\)
\(500\) 3.26703i 0.146106i
\(501\) 20.6233 + 35.7206i 0.921382 + 1.59588i
\(502\) 12.4505 + 21.5649i 0.555692 + 0.962487i
\(503\) −8.79449 + 5.07750i −0.392127 + 0.226395i −0.683081 0.730342i \(-0.739361\pi\)
0.290954 + 0.956737i \(0.406027\pi\)
\(504\) 11.9671 + 6.90924i 0.533059 + 0.307762i
\(505\) 6.51480i 0.289905i
\(506\) 0.370562 0.641832i 0.0164735 0.0285329i
\(507\) −6.15899 + 3.55590i −0.273530 + 0.157923i
\(508\) 3.08331 0.136800
\(509\) 3.22587 + 5.58737i 0.142984 + 0.247656i 0.928619 0.371035i \(-0.120997\pi\)
−0.785635 + 0.618690i \(0.787664\pi\)
\(510\) −8.71719 7.99038i −0.386004 0.353820i
\(511\) 22.4556 38.8942i 0.993377 1.72058i
\(512\) 25.4099 1.12297
\(513\) −19.3759 11.1867i −0.855465 0.493903i
\(514\) 22.0388 0.972090
\(515\) 20.1385i 0.887410i
\(516\) −3.44015 + 3.11956i −0.151444 + 0.137331i
\(517\) 1.30537i 0.0574103i
\(518\) −46.4140 −2.03931
\(519\) −23.8285 + 41.2723i −1.04596 + 1.81165i
\(520\) 10.0552i 0.440951i
\(521\) −6.83694 3.94731i −0.299532 0.172935i 0.342701 0.939445i \(-0.388658\pi\)
−0.642233 + 0.766510i \(0.721992\pi\)
\(522\) −13.5413 7.81809i −0.592688 0.342189i
\(523\) 3.34452 + 5.79288i 0.146246 + 0.253305i 0.929837 0.367972i \(-0.119948\pi\)
−0.783591 + 0.621277i \(0.786614\pi\)
\(524\) 1.31261i 0.0573416i
\(525\) 14.3236 + 24.8092i 0.625132 + 1.08276i
\(526\) −8.60393 + 14.9024i −0.375149 + 0.649778i
\(527\) −22.3421 4.95687i −0.973239 0.215925i
\(528\) −0.585557 + 1.01422i −0.0254831 + 0.0441380i
\(529\) −6.22977 10.7903i −0.270859 0.469142i
\(530\) −6.79670 + 3.92408i −0.295230 + 0.170451i
\(531\) 6.56635 + 11.3732i 0.284955 + 0.493557i
\(532\) 7.74589i 0.335827i
\(533\) 7.47313 4.31461i 0.323697 0.186887i
\(534\) −28.9939 + 16.7396i −1.25469 + 0.724394i
\(535\) 7.27008 12.5921i 0.314313 0.544406i
\(536\) 19.4717 33.7260i 0.841051 1.45674i
\(537\) 33.1241i 1.42941i
\(538\) 8.07406i 0.348097i
\(539\) 0.930832 + 0.537416i 0.0400938 + 0.0231481i
\(540\) 0.661491 1.14574i 0.0284660 0.0493046i
\(541\) 24.1942 13.9685i 1.04019 0.600554i 0.120302 0.992737i \(-0.461614\pi\)
0.919887 + 0.392184i \(0.128280\pi\)
\(542\) −16.6112 28.7715i −0.713512 1.23584i
\(543\) 13.2912 0.570378
\(544\) 7.53659 2.37496i 0.323129 0.101826i
\(545\) 5.85501 + 10.1412i 0.250801 + 0.434400i
\(546\) 14.8567 + 25.7325i 0.635807 + 1.10125i
\(547\) −17.9746 10.3777i −0.768540 0.443717i 0.0638136 0.997962i \(-0.479674\pi\)
−0.832354 + 0.554245i \(0.813007\pi\)
\(548\) −3.75677 −0.160481
\(549\) −5.47447 3.16069i −0.233645 0.134895i
\(550\) −0.758540 + 0.437943i −0.0323443 + 0.0186740i
\(551\) 59.9000i 2.55183i
\(552\) −10.1140 17.5180i −0.430482 0.745616i
\(553\) −8.54441 + 14.7994i −0.363345 + 0.629332i
\(554\) 0.906127 + 0.523153i 0.0384977 + 0.0222266i
\(555\) 22.2263i 0.943455i
\(556\) −3.94975 2.28039i −0.167507 0.0967101i
\(557\) −12.8405 −0.544071 −0.272036 0.962287i \(-0.587697\pi\)
−0.272036 + 0.962287i \(0.587697\pi\)
\(558\) 9.05866i 0.383484i
\(559\) −19.8144 + 4.28479i −0.838061 + 0.181227i
\(560\) −12.4599 −0.526527
\(561\) −0.327151 + 1.47457i −0.0138123 + 0.0622565i
\(562\) 17.5484 30.3947i 0.740234 1.28212i
\(563\) 10.6454 0.448648 0.224324 0.974515i \(-0.427983\pi\)
0.224324 + 0.974515i \(0.427983\pi\)
\(564\) −4.51487 2.60666i −0.190110 0.109760i
\(565\) 0.917679 1.58947i 0.0386070 0.0668694i
\(566\) −13.0386 + 7.52783i −0.548053 + 0.316418i
\(567\) 40.4631i 1.69929i
\(568\) 15.6718 9.04814i 0.657576 0.379652i
\(569\) 20.0755 34.7717i 0.841607 1.45771i −0.0469285 0.998898i \(-0.514943\pi\)
0.888536 0.458808i \(-0.151723\pi\)
\(570\) −17.9312 −0.751057
\(571\) 4.52246 + 2.61105i 0.189259 + 0.109269i 0.591636 0.806205i \(-0.298482\pi\)
−0.402377 + 0.915474i \(0.631816\pi\)
\(572\) 0.162753 0.0939654i 0.00680504 0.00392889i
\(573\) 5.58825 3.22638i 0.233452 0.134784i
\(574\) 6.49307 + 11.2463i 0.271015 + 0.469412i
\(575\) 12.4571i 0.519497i
\(576\) 5.61682 + 9.72861i 0.234034 + 0.405359i
\(577\) 2.58907 + 4.48441i 0.107785 + 0.186688i 0.914872 0.403743i \(-0.132291\pi\)
−0.807088 + 0.590431i \(0.798958\pi\)
\(578\) −17.9307 + 12.5467i −0.745818 + 0.521873i
\(579\) 23.2487 40.2680i 0.966185 1.67348i
\(580\) −3.54202 −0.147074
\(581\) 38.0918i 1.58031i
\(582\) 4.51351 7.81763i 0.187091 0.324051i
\(583\) 0.868138 + 0.501220i 0.0359546 + 0.0207584i
\(584\) 32.4575 18.7393i 1.34310 0.775439i
\(585\) −3.66052 + 2.11340i −0.151344 + 0.0873784i
\(586\) −18.4760 −0.763237
\(587\) 23.5407 + 40.7737i 0.971628 + 1.68291i 0.690641 + 0.723197i \(0.257328\pi\)
0.280987 + 0.959712i \(0.409338\pi\)
\(588\) 3.71749 2.14630i 0.153307 0.0885117i
\(589\) −30.0532 + 17.3512i −1.23832 + 0.714945i
\(590\) −12.4544 7.19058i −0.512742 0.296031i
\(591\) 1.84384 0.0758453
\(592\) −27.6200 15.9464i −1.13518 0.655394i
\(593\) 10.4485 + 18.0973i 0.429067 + 0.743166i 0.996791 0.0800530i \(-0.0255090\pi\)
−0.567723 + 0.823219i \(0.692176\pi\)
\(594\) 0.816892 0.0335175
\(595\) −15.3270 + 4.82989i −0.628344 + 0.198006i
\(596\) −3.02724 + 5.24334i −0.124001 + 0.214775i
\(597\) −17.4892 + 30.2922i −0.715785 + 1.23978i
\(598\) 12.9207i 0.528369i
\(599\) 14.1716 24.5460i 0.579037 1.00292i −0.416553 0.909112i \(-0.636762\pi\)
0.995590 0.0938104i \(-0.0299048\pi\)
\(600\) 23.9063i 0.975969i
\(601\) 37.9169i 1.54666i −0.634002 0.773332i \(-0.718589\pi\)
0.634002 0.773332i \(-0.281411\pi\)
\(602\) −6.44819 29.8188i −0.262808 1.21532i
\(603\) 16.3702 0.666648
\(604\) −0.533100 −0.0216915
\(605\) 10.2442 + 5.91448i 0.416485 + 0.240458i
\(606\) 16.0654i 0.652612i
\(607\) 1.73804 + 1.00346i 0.0705449 + 0.0407291i 0.534858 0.844942i \(-0.320365\pi\)
−0.464313 + 0.885671i \(0.653699\pi\)
\(608\) 5.99108 10.3769i 0.242970 0.420837i
\(609\) −61.9478 + 35.7656i −2.51025 + 1.44929i
\(610\) 6.92232 0.280277
\(611\) −11.3790 19.7089i −0.460343 0.797338i
\(612\) 1.32095 + 1.21082i 0.0533964 + 0.0489444i
\(613\) −29.0994 −1.17532 −0.587658 0.809110i \(-0.699950\pi\)
−0.587658 + 0.809110i \(0.699950\pi\)
\(614\) 2.70230 4.68053i 0.109056 0.188891i
\(615\) −5.38554 + 3.10934i −0.217166 + 0.125381i
\(616\) 0.966409 + 1.67387i 0.0389377 + 0.0674421i
\(617\) −10.1037 + 5.83339i −0.406761 + 0.234843i −0.689397 0.724384i \(-0.742124\pi\)
0.282636 + 0.959227i \(0.408791\pi\)
\(618\) 49.6613i 1.99767i
\(619\) 7.02992 4.05872i 0.282556 0.163134i −0.352024 0.935991i \(-0.614506\pi\)
0.634580 + 0.772857i \(0.281173\pi\)
\(620\) −1.02602 1.77711i −0.0412058 0.0713705i
\(621\) −5.80904 + 10.0615i −0.233109 + 0.403756i
\(622\) −23.0617 13.3147i −0.924691 0.533870i
\(623\) 45.4969i 1.82279i
\(624\) 20.4172i 0.817343i
\(625\) −4.45354 + 7.71375i −0.178141 + 0.308550i
\(626\) −31.2133 18.0210i −1.24753 0.720265i
\(627\) 1.14517 + 1.98350i 0.0457338 + 0.0792133i
\(628\) 1.47698 + 2.55820i 0.0589379 + 0.102083i
\(629\) −40.1569 8.90928i −1.60116 0.355236i
\(630\) −3.18046 5.50872i −0.126713 0.219473i
\(631\) −2.29373 3.97286i −0.0913120 0.158157i 0.816751 0.576990i \(-0.195773\pi\)
−0.908063 + 0.418833i \(0.862439\pi\)
\(632\) −12.3502 + 7.13037i −0.491263 + 0.283631i
\(633\) 6.26324 10.8483i 0.248942 0.431179i
\(634\) 4.75212i 0.188731i
\(635\) −8.40025 4.84989i −0.333354 0.192462i
\(636\) 3.46711 2.00174i 0.137480 0.0793741i
\(637\) 18.7386 0.742451
\(638\) −1.09353 1.89405i −0.0432934 0.0749863i
\(639\) 6.58780 + 3.80347i 0.260609 + 0.150463i
\(640\) −7.07359 4.08394i −0.279608 0.161432i
\(641\) 5.36225i 0.211796i −0.994377 0.105898i \(-0.966228\pi\)
0.994377 0.105898i \(-0.0337717\pi\)
\(642\) 17.9279 31.0520i 0.707557 1.22553i
\(643\) 18.0418i 0.711499i 0.934581 + 0.355750i \(0.115774\pi\)
−0.934581 + 0.355750i \(0.884226\pi\)
\(644\) −4.02231 −0.158501
\(645\) 14.2793 3.08785i 0.562249 0.121584i
\(646\) −7.18762 + 32.3968i −0.282793 + 1.27464i
\(647\) −14.8038 −0.581997 −0.290998 0.956724i \(-0.593987\pi\)
−0.290998 + 0.956724i \(0.593987\pi\)
\(648\) 16.8834 29.2428i 0.663241 1.14877i
\(649\) 1.83690i 0.0721045i
\(650\) −7.63511 + 13.2244i −0.299473 + 0.518703i
\(651\) −35.8888 20.7204i −1.40659 0.812097i
\(652\) −2.32832 + 1.34426i −0.0911842 + 0.0526452i
\(653\) 41.4657i 1.62268i −0.584577 0.811338i \(-0.698739\pi\)
0.584577 0.811338i \(-0.301261\pi\)
\(654\) 14.4384 + 25.0080i 0.564585 + 0.977889i
\(655\) −2.06467 + 3.57611i −0.0806733 + 0.139730i
\(656\) 8.92328i 0.348395i
\(657\) 13.6438 + 7.87725i 0.532295 + 0.307321i
\(658\) 29.6600 17.1242i 1.15627 0.667571i
\(659\) −18.3615 31.8031i −0.715264 1.23887i −0.962858 0.270010i \(-0.912973\pi\)
0.247593 0.968864i \(-0.420360\pi\)
\(660\) −0.117289 + 0.0677166i −0.00456545 + 0.00263586i
\(661\) −37.0942 −1.44280 −0.721399 0.692519i \(-0.756501\pi\)
−0.721399 + 0.692519i \(0.756501\pi\)
\(662\) −7.14601 12.3772i −0.277737 0.481055i
\(663\) 7.91442 + 25.1153i 0.307371 + 0.975397i
\(664\) −15.8939 + 27.5291i −0.616804 + 1.06834i
\(665\) −12.1839 + 21.1031i −0.472471 + 0.818344i
\(666\) 16.2817i 0.630902i
\(667\) 31.1051 1.20439
\(668\) 5.92749 + 3.42224i 0.229341 + 0.132410i
\(669\) 46.6348 + 26.9246i 1.80301 + 1.04097i
\(670\) −15.5248 + 8.96324i −0.599775 + 0.346280i
\(671\) −0.442092 0.765726i −0.0170668 0.0295605i
\(672\) 14.3088 0.551974
\(673\) 15.4475 8.91859i 0.595456 0.343787i −0.171796 0.985133i \(-0.554957\pi\)
0.767252 + 0.641346i \(0.221624\pi\)
\(674\) 25.1367 14.5127i 0.968228 0.559006i
\(675\) 11.8911 6.86533i 0.457689 0.264247i
\(676\) −0.590066 + 1.02202i −0.0226948 + 0.0393086i
\(677\) 10.2405i 0.393573i 0.980446 + 0.196786i \(0.0630505\pi\)
−0.980446 + 0.196786i \(0.936949\pi\)
\(678\) 2.26298 3.91960i 0.0869092 0.150531i
\(679\) −6.13368 10.6238i −0.235389 0.407705i
\(680\) −13.0922 2.90465i −0.502061 0.111388i
\(681\) 22.2884 + 38.6046i 0.854093 + 1.47933i
\(682\) 0.633527 1.09730i 0.0242590 0.0420178i
\(683\) 12.6424 + 7.29911i 0.483749 + 0.279293i 0.721978 0.691916i \(-0.243233\pi\)
−0.238228 + 0.971209i \(0.576567\pi\)
\(684\) 2.71720 0.103895
\(685\) 10.2351 + 5.90921i 0.391061 + 0.225779i
\(686\) 4.36721i 0.166741i
\(687\) 55.4304i 2.11480i
\(688\) 6.40763 19.9599i 0.244289 0.760966i
\(689\) 17.4765 0.665803
\(690\) 9.31139i 0.354478i
\(691\) −33.0352 19.0729i −1.25672 0.725566i −0.284283 0.958741i \(-0.591755\pi\)
−0.972435 + 0.233174i \(0.925089\pi\)
\(692\) 7.90822i 0.300626i
\(693\) −0.406239 + 0.703626i −0.0154317 + 0.0267285i
\(694\) 11.1597 + 6.44304i 0.423616 + 0.244575i
\(695\) 7.17388 + 12.4255i 0.272121 + 0.471327i
\(696\) −59.6933 −2.26267
\(697\) 3.45897 + 10.9766i 0.131018 + 0.415767i
\(698\) −11.1277 + 19.2737i −0.421190 + 0.729522i
\(699\) 9.44513 0.357248
\(700\) 4.11684 + 2.37686i 0.155602 + 0.0898367i
\(701\) 6.54669 + 11.3392i 0.247265 + 0.428275i 0.962766 0.270336i \(-0.0871349\pi\)
−0.715501 + 0.698612i \(0.753802\pi\)
\(702\) 12.3337 7.12085i 0.465505 0.268759i
\(703\) −54.0164 + 31.1864i −2.03727 + 1.17622i
\(704\) 1.57127i 0.0592195i
\(705\) 8.20029 + 14.2033i 0.308841 + 0.534928i
\(706\) −7.75424 13.4307i −0.291835 0.505473i
\(707\) −18.9072 10.9161i −0.711080 0.410542i
\(708\) 6.35323 + 3.66804i 0.238769 + 0.137853i
\(709\) 20.9313i 0.786092i 0.919519 + 0.393046i \(0.128579\pi\)
−0.919519 + 0.393046i \(0.871421\pi\)
\(710\) −8.33009 −0.312623
\(711\) −5.19150 2.99731i −0.194696 0.112408i
\(712\) −18.9837 + 32.8808i −0.711445 + 1.23226i
\(713\) 9.01019 + 15.6061i 0.337434 + 0.584454i
\(714\) −37.7960 + 11.9104i −1.41448 + 0.445737i
\(715\) −0.591212 −0.0221101
\(716\) −2.74831 4.76021i −0.102709 0.177897i
\(717\) 7.85077 4.53265i 0.293192 0.169275i
\(718\) −10.0111 17.3397i −0.373609 0.647110i
\(719\) −28.6970 16.5682i −1.07022 0.617890i −0.141976 0.989870i \(-0.545345\pi\)
−0.928241 + 0.371981i \(0.878679\pi\)
\(720\) 4.37084i 0.162892i
\(721\) 58.4460 + 33.7438i 2.17664 + 1.25669i
\(722\) 12.9303 + 22.3960i 0.481217 + 0.833491i
\(723\) −13.7975 −0.513135
\(724\) 1.91005 1.10277i 0.0709865 0.0409841i
\(725\) −31.8360 18.3805i −1.18236 0.682636i
\(726\) 25.2620 + 14.5850i 0.937560 + 0.541300i
\(727\) −12.0813 −0.448070 −0.224035 0.974581i \(-0.571923\pi\)
−0.224035 + 0.974581i \(0.571923\pi\)
\(728\) 29.1822 + 16.8484i 1.08157 + 0.624442i
\(729\) −7.98407 −0.295706
\(730\) −17.2522 −0.638533
\(731\) 0.144883 27.0366i 0.00535869 0.999986i
\(732\) −3.53119 −0.130517
\(733\) −46.5739 −1.72025 −0.860124 0.510085i \(-0.829614\pi\)
−0.860124 + 0.510085i \(0.829614\pi\)
\(734\) 34.6347 + 19.9963i 1.27839 + 0.738079i
\(735\) −13.5041 −0.498105
\(736\) −5.38853 3.11107i −0.198624 0.114675i
\(737\) 1.98297 + 1.14487i 0.0730437 + 0.0421718i
\(738\) −3.94512 + 2.27772i −0.145222 + 0.0838440i
\(739\) −12.1173 −0.445742 −0.222871 0.974848i \(-0.571543\pi\)
−0.222871 + 0.974848i \(0.571543\pi\)
\(740\) −1.84412 3.19411i −0.0677912 0.117418i
\(741\) 34.5803 + 19.9650i 1.27034 + 0.733431i
\(742\) 26.3005i 0.965521i
\(743\) −8.69183 5.01823i −0.318872 0.184101i 0.332018 0.943273i \(-0.392271\pi\)
−0.650890 + 0.759172i \(0.725604\pi\)
\(744\) −17.2913 29.9495i −0.633931 1.09800i
\(745\) 16.4950 9.52340i 0.604331 0.348910i
\(746\) 2.38513 + 4.13117i 0.0873258 + 0.151253i
\(747\) −13.3623 −0.488902
\(748\) 0.0753310 + 0.239052i 0.00275437 + 0.00874061i
\(749\) −24.3632 42.1984i −0.890214 1.54190i
\(750\) 12.6724 21.9492i 0.462729 0.801470i
\(751\) 4.42726 + 2.55608i 0.161553 + 0.0932728i 0.578597 0.815614i \(-0.303600\pi\)
−0.417044 + 0.908886i \(0.636934\pi\)
\(752\) 23.5334 0.858176
\(753\) 39.9605i 1.45624i
\(754\) −33.0209 19.0646i −1.20255 0.694294i
\(755\) 1.45239 + 0.838539i 0.0528580 + 0.0305176i
\(756\) −2.21677 3.83955i −0.0806230 0.139643i
\(757\) −13.3679 23.1538i −0.485863 0.841540i 0.514005 0.857787i \(-0.328161\pi\)
−0.999868 + 0.0162476i \(0.994828\pi\)
\(758\) 17.2645i 0.627075i
\(759\) 1.03000 0.594669i 0.0373865 0.0215851i
\(760\) −17.6107 + 10.1675i −0.638808 + 0.368816i
\(761\) 14.1890 + 24.5760i 0.514349 + 0.890879i 0.999861 + 0.0166489i \(0.00529976\pi\)
−0.485512 + 0.874230i \(0.661367\pi\)
\(762\) −20.7149 11.9597i −0.750421