Properties

Label 731.2.e.a.307.6
Level 731
Weight 2
Character 731.307
Analytic conductor 5.837
Analytic rank 0
Dimension 58
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) = \( 731 = 17 \cdot 43 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 731.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.83706438776\)
Analytic rank: \(0\)
Dimension: \(58\)
Relative dimension: \(29\) over \(\Q(\zeta_{3})\)
Coefficient ring index: multiple of None
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 307.6
Character \(\chi\) = 731.307
Dual form 731.2.e.a.681.6

$q$-expansion

\(f(q)\) \(=\) \(q-1.94880 q^{2} +(-0.712581 + 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 - 3.66650i) q^{5} +(1.38867 - 2.40525i) q^{6} +(-0.444390 - 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 + 0.839105i) q^{9} +O(q^{10})\) \(q-1.94880 q^{2} +(-0.712581 + 1.23423i) q^{3} +1.79780 q^{4} +(2.11686 - 3.66650i) q^{5} +(1.38867 - 2.40525i) q^{6} +(-0.444390 - 0.769706i) q^{7} +0.394042 q^{8} +(0.484458 + 0.839105i) q^{9} +(-4.12532 + 7.14527i) q^{10} +0.221862 q^{11} +(-1.28108 + 2.21889i) q^{12} +(2.82311 + 4.88976i) q^{13} +(0.866025 + 1.50000i) q^{14} +(3.01686 + 5.22536i) q^{15} -4.36351 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.944108 - 1.63524i) q^{18} +(-0.611190 + 1.05861i) q^{19} +(3.80569 - 6.59165i) q^{20} +1.26666 q^{21} -0.432365 q^{22} +(3.95772 - 6.85498i) q^{23} +(-0.280786 + 0.486336i) q^{24} +(-6.46217 - 11.1928i) q^{25} +(-5.50166 - 9.52915i) q^{26} -5.65634 q^{27} +(-0.798926 - 1.38378i) q^{28} +(3.73607 + 6.47107i) q^{29} +(-5.87925 - 10.1832i) q^{30} +(3.84897 - 6.66661i) q^{31} +7.71551 q^{32} +(-0.158095 + 0.273828i) q^{33} +(-0.974398 - 1.68771i) q^{34} -3.76284 q^{35} +(0.870959 + 1.50855i) q^{36} +(-4.34553 + 7.52669i) q^{37} +(1.19108 - 2.06302i) q^{38} -8.04676 q^{39} +(0.834130 - 1.44476i) q^{40} +1.62069 q^{41} -2.46845 q^{42} +(5.99219 + 2.66338i) q^{43} +0.398865 q^{44} +4.10211 q^{45} +(-7.71279 + 13.3590i) q^{46} -1.62246 q^{47} +(3.10935 - 5.38556i) q^{48} +(3.10503 - 5.37808i) q^{49} +(12.5934 + 21.8125i) q^{50} -1.42516 q^{51} +(5.07539 + 8.79083i) q^{52} +(-0.771661 + 1.33656i) q^{53} +11.0231 q^{54} +(0.469651 - 0.813460i) q^{55} +(-0.175108 - 0.303296i) q^{56} +(-0.871044 - 1.50869i) q^{57} +(-7.28084 - 12.6108i) q^{58} +8.90841 q^{59} +(5.42372 + 9.39417i) q^{60} +(1.45489 + 2.51993i) q^{61} +(-7.50086 + 12.9919i) q^{62} +(0.430576 - 0.745780i) q^{63} -6.30892 q^{64} +23.9045 q^{65} +(0.308095 - 0.533636i) q^{66} +(1.47997 - 2.56338i) q^{67} +(0.898901 + 1.55694i) q^{68} +(5.64040 + 9.76945i) q^{69} +7.33301 q^{70} +(-1.96779 - 3.40832i) q^{71} +(0.190896 + 0.330642i) q^{72} +(4.30753 + 7.46087i) q^{73} +(8.46856 - 14.6680i) q^{74} +18.4193 q^{75} +(-1.09880 + 1.90318i) q^{76} +(-0.0985935 - 0.170769i) q^{77} +15.6815 q^{78} +(-8.35148 - 14.4652i) q^{79} +(-9.23693 + 15.9988i) q^{80} +(2.57723 - 4.46389i) q^{81} -3.15839 q^{82} +(-8.77140 + 15.1925i) q^{83} +2.27720 q^{84} +4.23371 q^{85} +(-11.6776 - 5.19039i) q^{86} -10.6490 q^{87} +0.0874230 q^{88} +(3.45530 - 5.98475i) q^{89} -7.99417 q^{90} +(2.50912 - 4.34592i) q^{91} +(7.11521 - 12.3239i) q^{92} +(5.48540 + 9.50100i) q^{93} +3.16184 q^{94} +(2.58760 + 4.48186i) q^{95} +(-5.49792 + 9.52268i) q^{96} +15.6672 q^{97} +(-6.05108 + 10.4808i) q^{98} +(0.107483 + 0.186166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + O(q^{10}) \) \( 58q - 6q^{2} + 3q^{3} + 54q^{4} - q^{5} + 12q^{6} + 7q^{7} - 12q^{8} - 22q^{9} + 4q^{10} + 16q^{11} + 12q^{12} + 2q^{13} - 11q^{14} + 7q^{15} + 30q^{16} + 29q^{17} + 8q^{18} + 8q^{19} - 33q^{20} - 26q^{21} - 22q^{22} - 5q^{23} + 12q^{24} - 36q^{25} - 12q^{27} + 15q^{28} + 2q^{29} + 11q^{30} + 3q^{31} - 40q^{32} + 17q^{33} - 3q^{34} + 38q^{35} - 7q^{36} + 2q^{37} + q^{38} - 54q^{39} + 5q^{40} + 14q^{41} - 112q^{42} + 31q^{43} - 24q^{44} - 46q^{45} - 13q^{46} - 28q^{47} - 28q^{49} - 13q^{50} + 6q^{51} + 85q^{52} - 10q^{53} + 34q^{54} + 36q^{55} - 54q^{56} - 23q^{57} + 3q^{58} + 12q^{59} + 2q^{60} - q^{61} - q^{62} - 14q^{63} + 28q^{64} + 80q^{65} - 74q^{66} + 11q^{67} + 27q^{68} - 11q^{69} + 2q^{70} + 16q^{71} + 21q^{72} + 14q^{73} + 21q^{74} - 54q^{75} + 44q^{76} + 25q^{77} + 88q^{78} - 4q^{79} - 112q^{80} + 11q^{81} - 176q^{82} - 3q^{83} + 100q^{84} - 2q^{85} + 44q^{86} + 8q^{87} - 106q^{88} + 82q^{89} + 54q^{90} - 15q^{91} + 42q^{92} + 88q^{94} + 29q^{95} + 20q^{96} + 20q^{97} + 44q^{98} - 54q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.94880 −1.37801 −0.689003 0.724758i \(-0.741951\pi\)
−0.689003 + 0.724758i \(0.741951\pi\)
\(3\) −0.712581 + 1.23423i −0.411409 + 0.712581i −0.995044 0.0994351i \(-0.968296\pi\)
0.583635 + 0.812016i \(0.301630\pi\)
\(4\) 1.79780 0.898901
\(5\) 2.11686 3.66650i 0.946687 1.63971i 0.194350 0.980932i \(-0.437740\pi\)
0.752337 0.658778i \(-0.228927\pi\)
\(6\) 1.38867 2.40525i 0.566924 0.981941i
\(7\) −0.444390 0.769706i −0.167964 0.290922i 0.769740 0.638357i \(-0.220386\pi\)
−0.937704 + 0.347436i \(0.887052\pi\)
\(8\) 0.394042 0.139315
\(9\) 0.484458 + 0.839105i 0.161486 + 0.279702i
\(10\) −4.12532 + 7.14527i −1.30454 + 2.25953i
\(11\) 0.221862 0.0668941 0.0334470 0.999440i \(-0.489351\pi\)
0.0334470 + 0.999440i \(0.489351\pi\)
\(12\) −1.28108 + 2.21889i −0.369816 + 0.640540i
\(13\) 2.82311 + 4.88976i 0.782989 + 1.35618i 0.930193 + 0.367070i \(0.119639\pi\)
−0.147204 + 0.989106i \(0.547028\pi\)
\(14\) 0.866025 + 1.50000i 0.231455 + 0.400892i
\(15\) 3.01686 + 5.22536i 0.778951 + 1.34918i
\(16\) −4.36351 −1.09088
\(17\) 0.500000 + 0.866025i 0.121268 + 0.210042i
\(18\) −0.944108 1.63524i −0.222528 0.385431i
\(19\) −0.611190 + 1.05861i −0.140217 + 0.242862i −0.927578 0.373629i \(-0.878113\pi\)
0.787362 + 0.616492i \(0.211447\pi\)
\(20\) 3.80569 6.59165i 0.850978 1.47394i
\(21\) 1.26666 0.276407
\(22\) −0.432365 −0.0921804
\(23\) 3.95772 6.85498i 0.825243 1.42936i −0.0764910 0.997070i \(-0.524372\pi\)
0.901734 0.432292i \(-0.142295\pi\)
\(24\) −0.280786 + 0.486336i −0.0573153 + 0.0992730i
\(25\) −6.46217 11.1928i −1.29243 2.23856i
\(26\) −5.50166 9.52915i −1.07896 1.86882i
\(27\) −5.65634 −1.08856
\(28\) −0.798926 1.38378i −0.150983 0.261510i
\(29\) 3.73607 + 6.47107i 0.693771 + 1.20165i 0.970593 + 0.240726i \(0.0773855\pi\)
−0.276822 + 0.960921i \(0.589281\pi\)
\(30\) −5.87925 10.1832i −1.07340 1.85918i
\(31\) 3.84897 6.66661i 0.691296 1.19736i −0.280118 0.959966i \(-0.590374\pi\)
0.971414 0.237393i \(-0.0762931\pi\)
\(32\) 7.71551 1.36392
\(33\) −0.158095 + 0.273828i −0.0275208 + 0.0476674i
\(34\) −0.974398 1.68771i −0.167108 0.289439i
\(35\) −3.76284 −0.636036
\(36\) 0.870959 + 1.50855i 0.145160 + 0.251424i
\(37\) −4.34553 + 7.52669i −0.714401 + 1.23738i 0.248788 + 0.968558i \(0.419968\pi\)
−0.963190 + 0.268822i \(0.913366\pi\)
\(38\) 1.19108 2.06302i 0.193219 0.334666i
\(39\) −8.04676 −1.28851
\(40\) 0.834130 1.44476i 0.131887 0.228436i
\(41\) 1.62069 0.253109 0.126555 0.991960i \(-0.459608\pi\)
0.126555 + 0.991960i \(0.459608\pi\)
\(42\) −2.46845 −0.380890
\(43\) 5.99219 + 2.66338i 0.913801 + 0.406162i
\(44\) 0.398865 0.0601312
\(45\) 4.10211 0.611506
\(46\) −7.71279 + 13.3590i −1.13719 + 1.96967i
\(47\) −1.62246 −0.236660 −0.118330 0.992974i \(-0.537754\pi\)
−0.118330 + 0.992974i \(0.537754\pi\)
\(48\) 3.10935 5.38556i 0.448797 0.777338i
\(49\) 3.10503 5.37808i 0.443576 0.768297i
\(50\) 12.5934 + 21.8125i 1.78098 + 3.08475i
\(51\) −1.42516 −0.199563
\(52\) 5.07539 + 8.79083i 0.703830 + 1.21907i
\(53\) −0.771661 + 1.33656i −0.105996 + 0.183590i −0.914145 0.405388i \(-0.867136\pi\)
0.808149 + 0.588978i \(0.200470\pi\)
\(54\) 11.0231 1.50005
\(55\) 0.469651 0.813460i 0.0633278 0.109687i
\(56\) −0.175108 0.303296i −0.0233998 0.0405297i
\(57\) −0.871044 1.50869i −0.115373 0.199831i
\(58\) −7.28084 12.6108i −0.956021 1.65588i
\(59\) 8.90841 1.15978 0.579888 0.814696i \(-0.303096\pi\)
0.579888 + 0.814696i \(0.303096\pi\)
\(60\) 5.42372 + 9.39417i 0.700200 + 1.21278i
\(61\) 1.45489 + 2.51993i 0.186279 + 0.322645i 0.944007 0.329926i \(-0.107024\pi\)
−0.757728 + 0.652571i \(0.773691\pi\)
\(62\) −7.50086 + 12.9919i −0.952610 + 1.64997i
\(63\) 0.430576 0.745780i 0.0542475 0.0939594i
\(64\) −6.30892 −0.788615
\(65\) 23.9045 2.96498
\(66\) 0.308095 0.533636i 0.0379238 0.0656860i
\(67\) 1.47997 2.56338i 0.180807 0.313166i −0.761349 0.648342i \(-0.775463\pi\)
0.942155 + 0.335176i \(0.108796\pi\)
\(68\) 0.898901 + 1.55694i 0.109008 + 0.188807i
\(69\) 5.64040 + 9.76945i 0.679024 + 1.17610i
\(70\) 7.33301 0.876462
\(71\) −1.96779 3.40832i −0.233534 0.404493i 0.725312 0.688421i \(-0.241696\pi\)
−0.958846 + 0.283928i \(0.908362\pi\)
\(72\) 0.190896 + 0.330642i 0.0224974 + 0.0389666i
\(73\) 4.30753 + 7.46087i 0.504159 + 0.873228i 0.999988 + 0.00480863i \(0.00153064\pi\)
−0.495830 + 0.868420i \(0.665136\pi\)
\(74\) 8.46856 14.6680i 0.984450 1.70512i
\(75\) 18.4193 2.12687
\(76\) −1.09880 + 1.90318i −0.126041 + 0.218309i
\(77\) −0.0985935 0.170769i −0.0112358 0.0194609i
\(78\) 15.6815 1.77558
\(79\) −8.35148 14.4652i −0.939615 1.62746i −0.766190 0.642614i \(-0.777850\pi\)
−0.173426 0.984847i \(-0.555484\pi\)
\(80\) −9.23693 + 15.9988i −1.03272 + 1.78872i
\(81\) 2.57723 4.46389i 0.286359 0.495988i
\(82\) −3.15839 −0.348786
\(83\) −8.77140 + 15.1925i −0.962787 + 1.66760i −0.247339 + 0.968929i \(0.579556\pi\)
−0.715448 + 0.698666i \(0.753777\pi\)
\(84\) 2.27720 0.248462
\(85\) 4.23371 0.459211
\(86\) −11.6776 5.19039i −1.25922 0.559694i
\(87\) −10.6490 −1.14169
\(88\) 0.0874230 0.00931933
\(89\) 3.45530 5.98475i 0.366261 0.634382i −0.622717 0.782447i \(-0.713971\pi\)
0.988978 + 0.148065i \(0.0473045\pi\)
\(90\) −7.99417 −0.842660
\(91\) 2.50912 4.34592i 0.263027 0.455577i
\(92\) 7.11521 12.3239i 0.741812 1.28486i
\(93\) 5.48540 + 9.50100i 0.568810 + 0.985208i
\(94\) 3.16184 0.326119
\(95\) 2.58760 + 4.48186i 0.265483 + 0.459829i
\(96\) −5.49792 + 9.52268i −0.561129 + 0.971904i
\(97\) 15.6672 1.59077 0.795383 0.606107i \(-0.207269\pi\)
0.795383 + 0.606107i \(0.207269\pi\)
\(98\) −6.05108 + 10.4808i −0.611251 + 1.05872i
\(99\) 0.107483 + 0.186166i 0.0108024 + 0.0187104i
\(100\) −11.6177 20.1225i −1.16177 2.01225i
\(101\) −3.62521 6.27905i −0.360722 0.624789i 0.627358 0.778731i \(-0.284136\pi\)
−0.988080 + 0.153942i \(0.950803\pi\)
\(102\) 2.77735 0.274998
\(103\) −5.22444 9.04899i −0.514779 0.891623i −0.999853 0.0171501i \(-0.994541\pi\)
0.485074 0.874473i \(-0.338793\pi\)
\(104\) 1.11242 + 1.92677i 0.109082 + 0.188935i
\(105\) 2.68133 4.64420i 0.261671 0.453227i
\(106\) 1.50381 2.60468i 0.146063 0.252988i
\(107\) 12.5385 1.21214 0.606071 0.795411i \(-0.292745\pi\)
0.606071 + 0.795411i \(0.292745\pi\)
\(108\) −10.1690 −0.978512
\(109\) 7.12181 12.3353i 0.682145 1.18151i −0.292179 0.956364i \(-0.594380\pi\)
0.974325 0.225147i \(-0.0722862\pi\)
\(110\) −0.915254 + 1.58527i −0.0872660 + 0.151149i
\(111\) −6.19309 10.7267i −0.587822 1.01814i
\(112\) 1.93910 + 3.35862i 0.183228 + 0.317360i
\(113\) 17.9491 1.68851 0.844255 0.535941i \(-0.180043\pi\)
0.844255 + 0.535941i \(0.180043\pi\)
\(114\) 1.69749 + 2.94013i 0.158984 + 0.275369i
\(115\) −16.7559 29.0220i −1.56249 2.70632i
\(116\) 6.71672 + 11.6337i 0.623632 + 1.08016i
\(117\) −2.73535 + 4.73777i −0.252883 + 0.438007i
\(118\) −17.3607 −1.59818
\(119\) 0.444390 0.769706i 0.0407372 0.0705588i
\(120\) 1.18877 + 2.05901i 0.108519 + 0.187961i
\(121\) −10.9508 −0.995525
\(122\) −2.83527 4.91084i −0.256694 0.444606i
\(123\) −1.15487 + 2.00030i −0.104131 + 0.180361i
\(124\) 6.91969 11.9853i 0.621406 1.07631i
\(125\) −33.5494 −3.00075
\(126\) −0.839105 + 1.45337i −0.0747534 + 0.129477i
\(127\) 4.55963 0.404602 0.202301 0.979323i \(-0.435158\pi\)
0.202301 + 0.979323i \(0.435158\pi\)
\(128\) −3.13622 −0.277206
\(129\) −7.55714 + 5.49785i −0.665369 + 0.484058i
\(130\) −46.5849 −4.08576
\(131\) 14.2904 1.24856 0.624279 0.781201i \(-0.285393\pi\)
0.624279 + 0.781201i \(0.285393\pi\)
\(132\) −0.284223 + 0.492289i −0.0247385 + 0.0428483i
\(133\) 1.08643 0.0942052
\(134\) −2.88415 + 4.99549i −0.249153 + 0.431545i
\(135\) −11.9737 + 20.7390i −1.03053 + 1.78493i
\(136\) 0.197021 + 0.341250i 0.0168944 + 0.0292619i
\(137\) 5.63189 0.481165 0.240582 0.970629i \(-0.422662\pi\)
0.240582 + 0.970629i \(0.422662\pi\)
\(138\) −10.9920 19.0387i −0.935699 1.62068i
\(139\) 5.23377 9.06515i 0.443922 0.768896i −0.554054 0.832481i \(-0.686920\pi\)
0.997976 + 0.0635846i \(0.0202533\pi\)
\(140\) −6.76485 −0.571734
\(141\) 1.15613 2.00248i 0.0973640 0.168639i
\(142\) 3.83482 + 6.64211i 0.321811 + 0.557393i
\(143\) 0.626341 + 1.08486i 0.0523773 + 0.0907201i
\(144\) −2.11394 3.66144i −0.176161 0.305120i
\(145\) 31.6349 2.62714
\(146\) −8.39450 14.5397i −0.694734 1.20331i
\(147\) 4.42518 + 7.66463i 0.364982 + 0.632168i
\(148\) −7.81241 + 13.5315i −0.642176 + 1.11228i
\(149\) −0.956779 + 1.65719i −0.0783824 + 0.135762i −0.902552 0.430581i \(-0.858309\pi\)
0.824170 + 0.566343i \(0.191642\pi\)
\(150\) −35.8954 −2.93085
\(151\) −11.2328 −0.914109 −0.457055 0.889439i \(-0.651096\pi\)
−0.457055 + 0.889439i \(0.651096\pi\)
\(152\) −0.240834 + 0.417137i −0.0195342 + 0.0338343i
\(153\) −0.484458 + 0.839105i −0.0391661 + 0.0678376i
\(154\) 0.192139 + 0.332794i 0.0154830 + 0.0268173i
\(155\) −16.2954 28.2245i −1.30888 2.26705i
\(156\) −14.4665 −1.15825
\(157\) 1.21447 + 2.10352i 0.0969249 + 0.167879i 0.910410 0.413706i \(-0.135766\pi\)
−0.813485 + 0.581585i \(0.802433\pi\)
\(158\) 16.2753 + 28.1897i 1.29480 + 2.24265i
\(159\) −1.09974 1.90481i −0.0872152 0.151061i
\(160\) 16.3326 28.2889i 1.29121 2.23644i
\(161\) −7.03509 −0.554443
\(162\) −5.02249 + 8.69921i −0.394604 + 0.683475i
\(163\) 6.74265 + 11.6786i 0.528125 + 0.914739i 0.999462 + 0.0327864i \(0.0104381\pi\)
−0.471337 + 0.881953i \(0.656229\pi\)
\(164\) 2.91368 0.227520
\(165\) 0.669329 + 1.15931i 0.0521072 + 0.0902523i
\(166\) 17.0937 29.6071i 1.32673 2.29796i
\(167\) −7.24570 + 12.5499i −0.560689 + 0.971142i 0.436748 + 0.899584i \(0.356130\pi\)
−0.997436 + 0.0715576i \(0.977203\pi\)
\(168\) 0.499115 0.0385075
\(169\) −9.43986 + 16.3503i −0.726143 + 1.25772i
\(170\) −8.25064 −0.632795
\(171\) −1.18438 −0.0905720
\(172\) 10.7728 + 4.78824i 0.821417 + 0.365100i
\(173\) 17.7279 1.34782 0.673912 0.738811i \(-0.264613\pi\)
0.673912 + 0.738811i \(0.264613\pi\)
\(174\) 20.7527 1.57326
\(175\) −5.74345 + 9.94794i −0.434164 + 0.751994i
\(176\) −0.968099 −0.0729732
\(177\) −6.34796 + 10.9950i −0.477142 + 0.826434i
\(178\) −6.73367 + 11.6631i −0.504710 + 0.874183i
\(179\) −1.09798 1.90176i −0.0820670 0.142144i 0.822071 0.569386i \(-0.192819\pi\)
−0.904138 + 0.427241i \(0.859485\pi\)
\(180\) 7.37478 0.549684
\(181\) −0.164604 0.285102i −0.0122349 0.0211914i 0.859843 0.510558i \(-0.170561\pi\)
−0.872078 + 0.489367i \(0.837228\pi\)
\(182\) −4.88976 + 8.46932i −0.362453 + 0.627788i
\(183\) −4.14689 −0.306547
\(184\) 1.55951 2.70115i 0.114968 0.199131i
\(185\) 18.3978 + 31.8658i 1.35263 + 2.34282i
\(186\) −10.6899 18.5155i −0.783824 1.35762i
\(187\) 0.110931 + 0.192139i 0.00811210 + 0.0140506i
\(188\) −2.91686 −0.212734
\(189\) 2.51362 + 4.35372i 0.182839 + 0.316687i
\(190\) −5.04271 8.73423i −0.365837 0.633648i
\(191\) −6.57361 + 11.3858i −0.475649 + 0.823849i −0.999611 0.0278929i \(-0.991120\pi\)
0.523961 + 0.851742i \(0.324454\pi\)
\(192\) 4.49561 7.78663i 0.324443 0.561952i
\(193\) −19.6460 −1.41415 −0.707076 0.707137i \(-0.749986\pi\)
−0.707076 + 0.707137i \(0.749986\pi\)
\(194\) −30.5322 −2.19209
\(195\) −17.0339 + 29.5035i −1.21982 + 2.11279i
\(196\) 5.58224 9.66872i 0.398731 0.690623i
\(197\) −8.64661 14.9764i −0.616046 1.06702i −0.990200 0.139656i \(-0.955400\pi\)
0.374154 0.927366i \(-0.377933\pi\)
\(198\) −0.209462 0.362799i −0.0148858 0.0257830i
\(199\) −24.9613 −1.76946 −0.884730 0.466103i \(-0.845658\pi\)
−0.884730 + 0.466103i \(0.845658\pi\)
\(200\) −2.54636 4.41043i −0.180055 0.311865i
\(201\) 2.10919 + 3.65322i 0.148771 + 0.257679i
\(202\) 7.06480 + 12.2366i 0.497077 + 0.860963i
\(203\) 3.32055 5.75136i 0.233057 0.403666i
\(204\) −2.56216 −0.179387
\(205\) 3.43077 5.94227i 0.239615 0.415026i
\(206\) 10.1814 + 17.6346i 0.709369 + 1.22866i
\(207\) 7.66940 0.533060
\(208\) −12.3187 21.3365i −0.854145 1.47942i
\(209\) −0.135600 + 0.234866i −0.00937966 + 0.0162460i
\(210\) −5.22536 + 9.05059i −0.360584 + 0.624550i
\(211\) −8.64696 −0.595281 −0.297641 0.954678i \(-0.596200\pi\)
−0.297641 + 0.954678i \(0.596200\pi\)
\(212\) −1.38729 + 2.40287i −0.0952798 + 0.165029i
\(213\) 5.60884 0.384312
\(214\) −24.4349 −1.67034
\(215\) 22.4499 16.3324i 1.53107 1.11386i
\(216\) −2.22883 −0.151653
\(217\) −6.84178 −0.464450
\(218\) −13.8789 + 24.0390i −0.940001 + 1.62813i
\(219\) −12.2779 −0.829661
\(220\) 0.844340 1.46244i 0.0569254 0.0985977i
\(221\) −2.82311 + 4.88976i −0.189903 + 0.328921i
\(222\) 12.0691 + 20.9042i 0.810022 + 1.40300i
\(223\) 1.12416 0.0752796 0.0376398 0.999291i \(-0.488016\pi\)
0.0376398 + 0.999291i \(0.488016\pi\)
\(224\) −3.42869 5.93867i −0.229089 0.396794i
\(225\) 6.26129 10.8449i 0.417420 0.722992i
\(226\) −34.9791 −2.32678
\(227\) 5.72577 9.91732i 0.380032 0.658235i −0.611034 0.791604i \(-0.709246\pi\)
0.991066 + 0.133369i \(0.0425795\pi\)
\(228\) −1.56597 2.71233i −0.103709 0.179629i
\(229\) 1.15901 + 2.00746i 0.0765892 + 0.132656i 0.901776 0.432203i \(-0.142264\pi\)
−0.825187 + 0.564860i \(0.808930\pi\)
\(230\) 32.6538 + 56.5580i 2.15313 + 3.72932i
\(231\) 0.281023 0.0184900
\(232\) 1.47217 + 2.54987i 0.0966526 + 0.167407i
\(233\) 7.28549 + 12.6188i 0.477289 + 0.826688i 0.999661 0.0260293i \(-0.00828631\pi\)
−0.522373 + 0.852717i \(0.674953\pi\)
\(234\) 5.33064 9.23293i 0.348475 0.603576i
\(235\) −3.43451 + 5.94875i −0.224043 + 0.388054i
\(236\) 16.0156 1.04252
\(237\) 23.8044 1.54626
\(238\) −0.866025 + 1.50000i −0.0561361 + 0.0972305i
\(239\) 3.58093 6.20235i 0.231631 0.401197i −0.726657 0.687000i \(-0.758927\pi\)
0.958288 + 0.285803i \(0.0922604\pi\)
\(240\) −13.1641 22.8009i −0.849740 1.47179i
\(241\) −1.55519 2.69368i −0.100179 0.173515i 0.811579 0.584242i \(-0.198608\pi\)
−0.911758 + 0.410727i \(0.865275\pi\)
\(242\) 21.3408 1.37184
\(243\) −4.81155 8.33385i −0.308661 0.534617i
\(244\) 2.61560 + 4.53034i 0.167446 + 0.290026i
\(245\) −13.1458 22.7692i −0.839856 1.45467i
\(246\) 2.25061 3.89817i 0.143494 0.248538i
\(247\) −6.90182 −0.439152
\(248\) 1.51665 2.62692i 0.0963077 0.166810i
\(249\) −12.5007 21.6518i −0.792197 1.37213i
\(250\) 65.3809 4.13505
\(251\) −0.133387 0.231033i −0.00841931 0.0145827i 0.861785 0.507274i \(-0.169347\pi\)
−0.870204 + 0.492691i \(0.836013\pi\)
\(252\) 0.774091 1.34076i 0.0487631 0.0844602i
\(253\) 0.878071 1.52086i 0.0552038 0.0956158i
\(254\) −8.88579 −0.557544
\(255\) −3.01686 + 5.22536i −0.188923 + 0.327225i
\(256\) 18.7297 1.17061
\(257\) −7.24510 −0.451937 −0.225968 0.974135i \(-0.572555\pi\)
−0.225968 + 0.974135i \(0.572555\pi\)
\(258\) 14.7273 10.7142i 0.916883 0.667035i
\(259\) 7.72445 0.479974
\(260\) 42.9755 2.66523
\(261\) −3.61994 + 6.26992i −0.224069 + 0.388098i
\(262\) −27.8491 −1.72052
\(263\) 2.30196 3.98711i 0.141945 0.245856i −0.786284 0.617865i \(-0.787998\pi\)
0.928229 + 0.372009i \(0.121331\pi\)
\(264\) −0.0622960 + 0.107900i −0.00383405 + 0.00664077i
\(265\) 3.26699 + 5.65860i 0.200690 + 0.347605i
\(266\) −2.11722 −0.129815
\(267\) 4.92436 + 8.52924i 0.301366 + 0.521981i
\(268\) 2.66069 4.60844i 0.162527 0.281505i
\(269\) 11.7498 0.716399 0.358199 0.933645i \(-0.383391\pi\)
0.358199 + 0.933645i \(0.383391\pi\)
\(270\) 23.3342 40.4161i 1.42008 2.45964i
\(271\) −5.73715 9.93704i −0.348507 0.603632i 0.637477 0.770469i \(-0.279978\pi\)
−0.985984 + 0.166837i \(0.946645\pi\)
\(272\) −2.18176 3.77891i −0.132288 0.229130i
\(273\) 3.57590 + 6.19364i 0.216423 + 0.374856i
\(274\) −10.9754 −0.663048
\(275\) −1.43371 2.48326i −0.0864562 0.149746i
\(276\) 10.1403 + 17.5635i 0.610375 + 1.05720i
\(277\) −7.51319 + 13.0132i −0.451424 + 0.781889i −0.998475 0.0552102i \(-0.982417\pi\)
0.547051 + 0.837099i \(0.315750\pi\)
\(278\) −10.1995 + 17.6661i −0.611728 + 1.05954i
\(279\) 7.45865 0.446538
\(280\) −1.48272 −0.0886092
\(281\) −3.85532 + 6.67761i −0.229989 + 0.398353i −0.957805 0.287420i \(-0.907202\pi\)
0.727815 + 0.685773i \(0.240536\pi\)
\(282\) −2.25307 + 3.90243i −0.134168 + 0.232386i
\(283\) −10.1947 17.6577i −0.606009 1.04964i −0.991891 0.127091i \(-0.959436\pi\)
0.385882 0.922548i \(-0.373897\pi\)
\(284\) −3.53770 6.12748i −0.209924 0.363599i
\(285\) −7.37551 −0.436887
\(286\) −1.22061 2.11416i −0.0721762 0.125013i
\(287\) −0.720219 1.24746i −0.0425132 0.0736349i
\(288\) 3.73783 + 6.47412i 0.220254 + 0.381491i
\(289\) −0.500000 + 0.866025i −0.0294118 + 0.0509427i
\(290\) −61.6500 −3.62021
\(291\) −11.1642 + 19.3369i −0.654455 + 1.13355i
\(292\) 7.74409 + 13.4132i 0.453189 + 0.784946i
\(293\) −11.3504 −0.663095 −0.331547 0.943439i \(-0.607571\pi\)
−0.331547 + 0.943439i \(0.607571\pi\)
\(294\) −8.62376 14.9368i −0.502948 0.871131i
\(295\) 18.8578 32.6627i 1.09795 1.90170i
\(296\) −1.71232 + 2.96583i −0.0995267 + 0.172385i
\(297\) −1.25493 −0.0728185
\(298\) 1.86457 3.22952i 0.108011 0.187081i
\(299\) 44.6923 2.58462
\(300\) 33.1142 1.91185
\(301\) −0.612849 5.79581i −0.0353240 0.334065i
\(302\) 21.8904 1.25965
\(303\) 10.3330 0.593617
\(304\) 2.66693 4.61927i 0.152959 0.264933i
\(305\) 12.3191 0.705392
\(306\) 0.944108 1.63524i 0.0539711 0.0934807i
\(307\) −5.81376 + 10.0697i −0.331809 + 0.574710i −0.982867 0.184318i \(-0.940992\pi\)
0.651058 + 0.759028i \(0.274326\pi\)
\(308\) −0.177252 0.307009i −0.0100998 0.0174934i
\(309\) 14.8913 0.847138
\(310\) 31.7565 + 55.0038i 1.80365 + 3.12401i
\(311\) −1.28734 + 2.22974i −0.0729985 + 0.126437i −0.900214 0.435447i \(-0.856590\pi\)
0.827216 + 0.561885i \(0.189923\pi\)
\(312\) −3.17076 −0.179509
\(313\) −8.40064 + 14.5503i −0.474832 + 0.822434i −0.999585 0.0288214i \(-0.990825\pi\)
0.524752 + 0.851255i \(0.324158\pi\)
\(314\) −2.36674 4.09932i −0.133563 0.231338i
\(315\) −1.82294 3.15742i −0.102711 0.177900i
\(316\) −15.0143 26.0056i −0.844621 1.46293i
\(317\) −24.8706 −1.39687 −0.698437 0.715671i \(-0.746121\pi\)
−0.698437 + 0.715671i \(0.746121\pi\)
\(318\) 2.14317 + 3.71208i 0.120183 + 0.208163i
\(319\) 0.828895 + 1.43569i 0.0464092 + 0.0803831i
\(320\) −13.3551 + 23.1317i −0.746572 + 1.29310i
\(321\) −8.93469 + 15.4753i −0.498685 + 0.863749i
\(322\) 13.7100 0.764026
\(323\) −1.22238 −0.0680150
\(324\) 4.63335 8.02520i 0.257408 0.445844i
\(325\) 36.4868 63.1970i 2.02392 3.50554i
\(326\) −13.1400 22.7592i −0.727760 1.26052i
\(327\) 10.1497 + 17.5798i 0.561281 + 0.972167i
\(328\) 0.638619 0.0352618
\(329\) 0.721005 + 1.24882i 0.0397503 + 0.0688495i
\(330\) −1.30438 2.25926i −0.0718040 0.124368i
\(331\) −4.85266 8.40505i −0.266726 0.461983i 0.701288 0.712878i \(-0.252609\pi\)
−0.968014 + 0.250895i \(0.919275\pi\)
\(332\) −15.7692 + 27.3131i −0.865450 + 1.49900i
\(333\) −8.42091 −0.461463
\(334\) 14.1204 24.4572i 0.772633 1.33824i
\(335\) −6.26575 10.8526i −0.342335 0.592941i
\(336\) −5.52706 −0.301526
\(337\) 5.67386 + 9.82742i 0.309075 + 0.535334i 0.978160 0.207852i \(-0.0666472\pi\)
−0.669085 + 0.743186i \(0.733314\pi\)
\(338\) 18.3964 31.8634i 1.00063 1.73314i
\(339\) −12.7902 + 22.1533i −0.694668 + 1.20320i
\(340\) 7.61138 0.412785
\(341\) 0.853942 1.47907i 0.0462436 0.0800962i
\(342\) 2.30812 0.124809
\(343\) −11.7408 −0.633946
\(344\) 2.36117 + 1.04948i 0.127306 + 0.0565844i
\(345\) 47.7597 2.57129
\(346\) −34.5480 −1.85731
\(347\) 2.75693 4.77514i 0.148000 0.256343i −0.782488 0.622665i \(-0.786050\pi\)
0.930488 + 0.366322i \(0.119383\pi\)
\(348\) −19.1448 −1.02627
\(349\) −4.87093 + 8.43669i −0.260735 + 0.451606i −0.966437 0.256902i \(-0.917298\pi\)
0.705703 + 0.708508i \(0.250631\pi\)
\(350\) 11.1928 19.3865i 0.598280 1.03625i
\(351\) −15.9685 27.6582i −0.852333 1.47628i
\(352\) 1.71178 0.0912383
\(353\) −0.904159 1.56605i −0.0481235 0.0833524i 0.840960 0.541097i \(-0.181991\pi\)
−0.889084 + 0.457744i \(0.848657\pi\)
\(354\) 12.3709 21.4270i 0.657505 1.13883i
\(355\) −16.6621 −0.884335
\(356\) 6.21194 10.7594i 0.329232 0.570247i
\(357\) 0.633328 + 1.09696i 0.0335192 + 0.0580570i
\(358\) 2.13974 + 3.70614i 0.113089 + 0.195876i
\(359\) 7.56234 + 13.0984i 0.399125 + 0.691305i 0.993618 0.112796i \(-0.0359806\pi\)
−0.594493 + 0.804101i \(0.702647\pi\)
\(360\) 1.61640 0.0851918
\(361\) 8.75289 + 15.1605i 0.460679 + 0.797919i
\(362\) 0.320779 + 0.555605i 0.0168597 + 0.0292019i
\(363\) 7.80331 13.5157i 0.409568 0.709392i
\(364\) 4.51090 7.81311i 0.236436 0.409518i
\(365\) 36.4737 1.90912
\(366\) 8.08144 0.422424
\(367\) −8.34441 + 14.4529i −0.435575 + 0.754437i −0.997342 0.0728577i \(-0.976788\pi\)
0.561768 + 0.827295i \(0.310121\pi\)
\(368\) −17.2696 + 29.9118i −0.900239 + 1.55926i
\(369\) 0.785155 + 1.35993i 0.0408736 + 0.0707951i
\(370\) −35.8535 62.1000i −1.86393 3.22843i
\(371\) 1.37167 0.0712138
\(372\) 9.86167 + 17.0809i 0.511304 + 0.885604i
\(373\) 2.85428 + 4.94376i 0.147789 + 0.255978i 0.930410 0.366520i \(-0.119451\pi\)
−0.782621 + 0.622498i \(0.786118\pi\)
\(374\) −0.216182 0.374439i −0.0111785 0.0193618i
\(375\) 23.9066 41.4075i 1.23453 2.13828i
\(376\) −0.639316 −0.0329702
\(377\) −21.0947 + 36.5370i −1.08643 + 1.88175i
\(378\) −4.89854 8.48451i −0.251954 0.436396i
\(379\) −9.10399 −0.467641 −0.233820 0.972280i \(-0.575123\pi\)
−0.233820 + 0.972280i \(0.575123\pi\)
\(380\) 4.65200 + 8.05750i 0.238643 + 0.413341i
\(381\) −3.24911 + 5.62762i −0.166457 + 0.288312i
\(382\) 12.8106 22.1886i 0.655448 1.13527i
\(383\) −17.3057 −0.884281 −0.442141 0.896946i \(-0.645781\pi\)
−0.442141 + 0.896946i \(0.645781\pi\)
\(384\) 2.23481 3.87081i 0.114045 0.197531i
\(385\) −0.834833 −0.0425470
\(386\) 38.2861 1.94871
\(387\) 0.668105 + 6.31838i 0.0339617 + 0.321181i
\(388\) 28.1666 1.42994
\(389\) −6.72163 −0.340800 −0.170400 0.985375i \(-0.554506\pi\)
−0.170400 + 0.985375i \(0.554506\pi\)
\(390\) 33.1955 57.4963i 1.68092 2.91144i
\(391\) 7.91545 0.400301
\(392\) 1.22351 2.11919i 0.0617967 0.107035i
\(393\) −10.1831 + 17.6376i −0.513668 + 0.889699i
\(394\) 16.8505 + 29.1859i 0.848915 + 1.47036i
\(395\) −70.7156 −3.55809
\(396\) 0.193233 + 0.334690i 0.00971033 + 0.0168188i
\(397\) −5.08295 + 8.80392i −0.255106 + 0.441856i −0.964924 0.262528i \(-0.915444\pi\)
0.709818 + 0.704385i \(0.248777\pi\)
\(398\) 48.6445 2.43833
\(399\) −0.774167 + 1.34090i −0.0387568 + 0.0671288i
\(400\) 28.1977 + 48.8399i 1.40989 + 2.44200i
\(401\) −13.1123 22.7111i −0.654795 1.13414i −0.981945 0.189166i \(-0.939421\pi\)
0.327150 0.944973i \(-0.393912\pi\)
\(402\) −4.11038 7.11938i −0.205007 0.355083i
\(403\) 43.4642 2.16511
\(404\) −6.51742 11.2885i −0.324254 0.561624i
\(405\) −10.9113 18.8988i −0.542185 0.939091i
\(406\) −6.47107 + 11.2082i −0.321154 + 0.556254i
\(407\) −0.964111 + 1.66989i −0.0477892 + 0.0827733i
\(408\) −0.561573 −0.0278020
\(409\) −14.6313 −0.723471 −0.361736 0.932281i \(-0.617816\pi\)
−0.361736 + 0.932281i \(0.617816\pi\)
\(410\) −6.68587 + 11.5803i −0.330191 + 0.571908i
\(411\) −4.01318 + 6.95103i −0.197955 + 0.342869i
\(412\) −9.39250 16.2683i −0.462735 0.801481i
\(413\) −3.95881 6.85686i −0.194800 0.337404i
\(414\) −14.9461 −0.734560
\(415\) 37.1356 + 64.3208i 1.82292 + 3.15738i
\(416\) 21.7817 + 37.7270i 1.06794 + 1.84972i
\(417\) 7.45896 + 12.9193i 0.365267 + 0.632661i
\(418\) 0.264257 0.457706i 0.0129252 0.0223872i
\(419\) −13.5209 −0.660539 −0.330269 0.943887i \(-0.607140\pi\)
−0.330269 + 0.943887i \(0.607140\pi\)
\(420\) 4.82050 8.34935i 0.235216 0.407406i
\(421\) 2.48434 + 4.30301i 0.121079 + 0.209716i 0.920194 0.391464i \(-0.128031\pi\)
−0.799114 + 0.601179i \(0.794698\pi\)
\(422\) 16.8512 0.820301
\(423\) −0.786013 1.36141i −0.0382172 0.0661942i
\(424\) −0.304067 + 0.526659i −0.0147668 + 0.0255768i
\(425\) 6.46217 11.1928i 0.313461 0.542931i
\(426\) −10.9305 −0.529584
\(427\) 1.29307 2.23967i 0.0625762 0.108385i
\(428\) 22.5417 1.08960
\(429\) −1.78528 −0.0861939
\(430\) −43.7503 + 31.8285i −2.10983 + 1.53491i
\(431\) 10.6684 0.513879 0.256939 0.966428i \(-0.417286\pi\)
0.256939 + 0.966428i \(0.417286\pi\)
\(432\) 24.6815 1.18749
\(433\) −10.6850 + 18.5069i −0.513487 + 0.889386i 0.486390 + 0.873742i \(0.338313\pi\)
−0.999878 + 0.0156445i \(0.995020\pi\)
\(434\) 13.3332 0.640015
\(435\) −22.5424 + 39.0447i −1.08083 + 1.87205i
\(436\) 12.8036 22.1765i 0.613181 1.06206i
\(437\) 4.83784 + 8.37939i 0.231425 + 0.400841i
\(438\) 23.9270 1.14328
\(439\) 6.75973 + 11.7082i 0.322624 + 0.558802i 0.981029 0.193863i \(-0.0621016\pi\)
−0.658404 + 0.752665i \(0.728768\pi\)
\(440\) 0.185062 0.320537i 0.00882249 0.0152810i
\(441\) 6.01703 0.286525
\(442\) 5.50166 9.52915i 0.261687 0.453255i
\(443\) −7.01635 12.1527i −0.333357 0.577391i 0.649811 0.760096i \(-0.274848\pi\)
−0.983168 + 0.182705i \(0.941515\pi\)
\(444\) −11.1339 19.2846i −0.528394 0.915205i
\(445\) −14.6287 25.3377i −0.693469 1.20112i
\(446\) −2.19077 −0.103736
\(447\) −1.36357 2.36176i −0.0644944 0.111708i
\(448\) 2.80362 + 4.85601i 0.132459 + 0.229425i
\(449\) −10.7643 + 18.6444i −0.508000 + 0.879883i 0.491957 + 0.870620i \(0.336282\pi\)
−0.999957 + 0.00926289i \(0.997051\pi\)
\(450\) −12.2020 + 21.1344i −0.575207 + 0.996287i
\(451\) 0.359570 0.0169315
\(452\) 32.2690 1.51780
\(453\) 8.00425 13.8638i 0.376072 0.651377i
\(454\) −11.1583 + 19.3268i −0.523687 + 0.907052i
\(455\) −10.6229 18.3994i −0.498009 0.862577i
\(456\) −0.343228 0.594488i −0.0160731 0.0278394i
\(457\) 16.2500 0.760141 0.380070 0.924958i \(-0.375900\pi\)
0.380070 + 0.924958i \(0.375900\pi\)
\(458\) −2.25866 3.91212i −0.105540 0.182801i
\(459\) −2.82817 4.89854i −0.132008 0.228644i
\(460\) −30.1238 52.1759i −1.40453 2.43271i
\(461\) 19.4012 33.6038i 0.903602 1.56508i 0.0808186 0.996729i \(-0.474247\pi\)
0.822783 0.568355i \(-0.192420\pi\)
\(462\) −0.547657 −0.0254793
\(463\) 0.00203399 0.00352297i 9.45273e−5 0.000163726i −0.865978 0.500082i \(-0.833303\pi\)
0.866073 + 0.499918i \(0.166637\pi\)
\(464\) −16.3024 28.2366i −0.756820 1.31085i
\(465\) 46.4473 2.15394
\(466\) −14.1979 24.5915i −0.657707 1.13918i
\(467\) −3.00474 + 5.20436i −0.139043 + 0.240829i −0.927135 0.374729i \(-0.877736\pi\)
0.788092 + 0.615558i \(0.211069\pi\)
\(468\) −4.91762 + 8.51757i −0.227317 + 0.393725i
\(469\) −2.63073 −0.121476
\(470\) 6.69317 11.5929i 0.308733 0.534741i
\(471\) −3.46162 −0.159503
\(472\) 3.51028 0.161574
\(473\) 1.32944 + 0.590905i 0.0611279 + 0.0271698i
\(474\) −46.3899 −2.13076
\(475\) 15.7985 0.724883
\(476\) 0.798926 1.38378i 0.0366187 0.0634254i
\(477\) −1.49535 −0.0684673
\(478\) −6.97850 + 12.0871i −0.319189 + 0.552852i
\(479\) −17.6591 + 30.5865i −0.806865 + 1.39753i 0.108159 + 0.994134i \(0.465504\pi\)
−0.915024 + 0.403398i \(0.867829\pi\)
\(480\) 23.2766 + 40.3163i 1.06243 + 1.84018i
\(481\) −49.0716 −2.23747
\(482\) 3.03076 + 5.24942i 0.138047 + 0.239105i
\(483\) 5.01307 8.68290i 0.228103 0.395085i
\(484\) −19.6873 −0.894879
\(485\) 33.1653 57.4440i 1.50596 2.60840i
\(486\) 9.37672 + 16.2410i 0.425337 + 0.736705i
\(487\) 18.0870 + 31.3275i 0.819598 + 1.41959i 0.905979 + 0.423323i \(0.139137\pi\)
−0.0863807 + 0.996262i \(0.527530\pi\)
\(488\) 0.573285 + 0.992959i 0.0259514 + 0.0449491i
\(489\) −19.2187 −0.869101
\(490\) 25.6185 + 44.3726i 1.15733 + 2.00455i
\(491\) 6.16598 + 10.6798i 0.278267 + 0.481972i 0.970954 0.239266i \(-0.0769068\pi\)
−0.692687 + 0.721238i \(0.743573\pi\)
\(492\) −2.07623 + 3.59614i −0.0936038 + 0.162127i
\(493\) −3.73607 + 6.47107i −0.168264 + 0.291442i
\(494\) 13.4502 0.605154
\(495\) 0.910104 0.0409061
\(496\) −16.7950 + 29.0898i −0.754119 + 1.30617i
\(497\) −1.74893 + 3.02924i −0.0784504 + 0.135880i
\(498\) 24.3612 + 42.1949i 1.09165 + 1.89080i
\(499\) 18.7265 + 32.4352i 0.838312 + 1.45200i 0.891305 + 0.453404i \(0.149790\pi\)
−0.0529937 + 0.998595i \(0.516876\pi\)
\(500\) −60.3152 −2.69738
\(501\) −10.3263 17.8857i −0.461345 0.799072i
\(502\) 0.259944 + 0.450236i 0.0116019 + 0.0200950i
\(503\) −4.61599 7.99512i −0.205817 0.356485i 0.744576 0.667538i \(-0.232652\pi\)
−0.950393 + 0.311053i \(0.899318\pi\)
\(504\) 0.169665 0.293868i 0.00755748 0.0130899i
\(505\) −30.6962 −1.36596
\(506\) −1.71118 + 2.96385i −0.0760712 + 0.131759i
\(507\) −13.4533 23.3018i −0.597483 1.03487i
\(508\) 8.19732 0.363697
\(509\) 15.8510 + 27.4547i 0.702582 + 1.21691i 0.967557 + 0.252653i \(0.0813031\pi\)
−0.264974 + 0.964255i \(0.585364\pi\)
\(510\) 5.87925 10.1832i 0.260337 0.450918i
\(511\) 3.82845 6.63107i 0.169361 0.293341i
\(512\) −30.2279 −1.33590
\(513\) 3.45710 5.98788i 0.152635 0.264371i
\(514\) 14.1192 0.622772
\(515\) −44.2375 −1.94934
\(516\) −13.5862 + 9.88404i −0.598101 + 0.435121i
\(517\) −0.359963 −0.0158311
\(518\) −15.0534 −0.661407
\(519\) −12.6325 + 21.8802i −0.554507 + 0.960434i
\(520\) 9.41935 0.413066
\(521\) 21.4765 37.1984i 0.940902 1.62969i 0.177147 0.984184i \(-0.443313\pi\)
0.763755 0.645506i \(-0.223353\pi\)
\(522\) 7.05452 12.2188i 0.308768 0.534802i
\(523\) 8.11627 + 14.0578i 0.354900 + 0.614704i 0.987101 0.160100i \(-0.0511817\pi\)
−0.632201 + 0.774804i \(0.717848\pi\)
\(524\) 25.6913 1.12233
\(525\) −8.18534 14.1774i −0.357238 0.618754i
\(526\) −4.48605 + 7.77006i −0.195601 + 0.338791i
\(527\) 7.69794 0.335328
\(528\) 0.689849 1.19485i 0.0300218 0.0519993i
\(529\) −19.8272 34.3417i −0.862051 1.49312i
\(530\) −6.36670 11.0275i −0.276552 0.479002i
\(531\) 4.31575 + 7.47509i 0.187287 + 0.324391i
\(532\) 1.95318 0.0846812
\(533\) 4.57538 + 7.92479i 0.198182 + 0.343261i
\(534\) −9.59656 16.6217i −0.415284 0.719293i
\(535\) 26.5422 45.9724i 1.14752 1.98756i
\(536\) 0.583168 1.01008i 0.0251890 0.0436287i
\(537\) 3.12960 0.135052
\(538\) −22.8980 −0.987202
\(539\) 0.688891 1.19319i 0.0296726 0.0513945i
\(540\) −21.5263 + 37.2846i −0.926344 + 1.60448i
\(541\) −8.72975 15.1204i −0.375321 0.650075i 0.615054 0.788485i \(-0.289134\pi\)
−0.990375 + 0.138410i \(0.955801\pi\)
\(542\) 11.1805 + 19.3652i 0.480245 + 0.831809i
\(543\) 0.469173 0.0201342
\(544\) 3.85775 + 6.68182i 0.165400 + 0.286481i
\(545\) −30.1517 52.2243i −1.29156 2.23704i
\(546\) −6.96870 12.0701i −0.298233 0.516554i
\(547\) −7.34043 + 12.7140i −0.313854 + 0.543611i −0.979193 0.202930i \(-0.934954\pi\)
0.665339 + 0.746541i \(0.268287\pi\)
\(548\) 10.1250 0.432520
\(549\) −1.40966 + 2.44160i −0.0601628 + 0.104205i
\(550\) 2.79401 + 4.83937i 0.119137 + 0.206352i
\(551\) −9.13380 −0.389113
\(552\) 2.22255 + 3.84957i 0.0945980 + 0.163849i
\(553\) −7.42263 + 12.8564i −0.315642 + 0.546709i
\(554\) 14.6417 25.3601i 0.622065 1.07745i
\(555\) −52.4395 −2.22593
\(556\) 9.40928 16.2974i 0.399042 0.691162i
\(557\) −29.5345 −1.25142 −0.625708 0.780058i \(-0.715190\pi\)
−0.625708 + 0.780058i \(0.715190\pi\)
\(558\) −14.5354 −0.615332
\(559\) 3.89329 + 36.8194i 0.164668 + 1.55730i
\(560\) 16.4192 0.693838
\(561\) −0.316190 −0.0133495
\(562\) 7.51323 13.0133i 0.316927 0.548933i
\(563\) 5.74524 0.242133 0.121066 0.992644i \(-0.461369\pi\)
0.121066 + 0.992644i \(0.461369\pi\)
\(564\) 2.07850 3.60007i 0.0875206 0.151590i
\(565\) 37.9957 65.8105i 1.59849 2.76867i
\(566\) 19.8673 + 34.4112i 0.835085 + 1.44641i
\(567\) −4.58118 −0.192391
\(568\) −0.775392 1.34302i −0.0325347 0.0563518i
\(569\) 4.69661 8.13476i 0.196892 0.341027i −0.750627 0.660726i \(-0.770249\pi\)
0.947519 + 0.319699i \(0.103582\pi\)
\(570\) 14.3734 0.602034
\(571\) −5.17269 + 8.95936i −0.216470 + 0.374938i −0.953726 0.300676i \(-0.902788\pi\)
0.737256 + 0.675613i \(0.236121\pi\)
\(572\) 1.12604 + 1.95036i 0.0470820 + 0.0815484i
\(573\) −9.36845 16.2266i −0.391373 0.677877i
\(574\) 1.40356 + 2.43103i 0.0585834 + 0.101469i
\(575\) −102.302 −4.26629
\(576\) −3.05640 5.29385i −0.127350 0.220577i
\(577\) −11.4201 19.7802i −0.475426 0.823462i 0.524178 0.851609i \(-0.324373\pi\)
−0.999604 + 0.0281467i \(0.991039\pi\)
\(578\) 0.974398 1.68771i 0.0405296 0.0701993i
\(579\) 13.9994 24.2477i 0.581795 1.00770i
\(580\) 56.8734 2.36154
\(581\) 15.5917 0.646853
\(582\) 21.7567 37.6837i 0.901843 1.56204i
\(583\) −0.171203 + 0.296532i −0.00709049 + 0.0122811i
\(584\) 1.69735 + 2.93989i 0.0702367 + 0.121654i
\(585\) 11.5807 + 20.0583i 0.478803 + 0.829311i
\(586\) 22.1195 0.913749
\(587\) −7.67742 13.2977i −0.316881 0.548854i 0.662955 0.748660i \(-0.269302\pi\)
−0.979836 + 0.199806i \(0.935969\pi\)
\(588\) 7.95559 + 13.7795i 0.328083 + 0.568257i
\(589\) 4.70491 + 8.14913i 0.193862 + 0.335779i
\(590\) −36.7501 + 63.6530i −1.51298 + 2.62055i
\(591\) 24.6456 1.01379
\(592\) 18.9618 32.8428i 0.779325 1.34983i
\(593\) −9.19090 15.9191i −0.377425 0.653719i 0.613262 0.789880i \(-0.289857\pi\)
−0.990687 + 0.136160i \(0.956524\pi\)
\(594\) 2.44560 0.100344
\(595\) −1.88142 3.25872i −0.0771307 0.133594i
\(596\) −1.72010 + 2.97930i −0.0704581 + 0.122037i
\(597\) 17.7870 30.8079i 0.727971 1.26088i
\(598\) −87.0962 −3.56163
\(599\) −16.0198 + 27.7472i −0.654553 + 1.13372i 0.327453 + 0.944868i \(0.393810\pi\)
−0.982006 + 0.188852i \(0.939523\pi\)
\(600\) 7.25796 0.296305
\(601\) −19.8551 −0.809906 −0.404953 0.914337i \(-0.632712\pi\)
−0.404953 + 0.914337i \(0.632712\pi\)
\(602\) 1.19432 + 11.2948i 0.0486767 + 0.460344i
\(603\) 2.86792 0.116791
\(604\) −20.1943 −0.821694
\(605\) −23.1812 + 40.1511i −0.942451 + 1.63237i
\(606\) −20.1369 −0.818008
\(607\) −9.64815 + 16.7111i −0.391606 + 0.678282i −0.992662 0.120925i \(-0.961414\pi\)
0.601055 + 0.799208i \(0.294747\pi\)
\(608\) −4.71564 + 8.16773i −0.191244 + 0.331245i
\(609\) 4.73232 + 8.19661i 0.191763 + 0.332144i
\(610\) −24.0075 −0.972034
\(611\) −4.58038 7.93344i −0.185302 0.320953i
\(612\) −0.870959 + 1.50855i −0.0352064 + 0.0609793i
\(613\) 4.18296 0.168948 0.0844741 0.996426i \(-0.473079\pi\)
0.0844741 + 0.996426i \(0.473079\pi\)
\(614\) 11.3298 19.6239i 0.457235 0.791954i
\(615\) 4.88940 + 8.46869i 0.197160 + 0.341491i
\(616\) −0.0388499 0.0672901i −0.00156531 0.00271119i
\(617\) 1.09940 + 1.90422i 0.0442603 + 0.0766610i 0.887307 0.461180i \(-0.152574\pi\)
−0.843047 + 0.537841i \(0.819240\pi\)
\(618\) −29.0201 −1.16736
\(619\) 10.7808 + 18.6729i 0.433317 + 0.750527i 0.997157 0.0753571i \(-0.0240097\pi\)
−0.563839 + 0.825884i \(0.690676\pi\)
\(620\) −29.2960 50.7421i −1.17656 2.03785i
\(621\) −22.3863 + 38.7741i −0.898329 + 1.55595i
\(622\) 2.50877 4.34531i 0.100592 0.174231i
\(623\) −6.14200 −0.246074
\(624\) 35.1121 1.40561
\(625\) −38.7084 + 67.0450i −1.54834 + 2.68180i
\(626\) 16.3711 28.3556i 0.654322 1.13332i
\(627\) −0.193252 0.334722i −0.00771775 0.0133675i
\(628\) 2.18337 + 3.78171i 0.0871259 + 0.150906i
\(629\) −8.69107 −0.346536
\(630\) 3.55253 + 6.15316i 0.141536 + 0.245148i
\(631\) −15.3758 26.6317i −0.612101 1.06019i −0.990886 0.134705i \(-0.956991\pi\)
0.378785 0.925485i \(-0.376342\pi\)
\(632\) −3.29083 5.69989i −0.130902 0.226729i
\(633\) 6.16166 10.6723i 0.244904 0.424186i
\(634\) 48.4678 1.92490
\(635\) 9.65210 16.7179i 0.383032 0.663430i
\(636\) −1.97712 3.42447i −0.0783979 0.135789i
\(637\) 35.0634 1.38926
\(638\) −1.61535 2.79786i −0.0639522 0.110768i
\(639\) 1.90662 3.30237i 0.0754249 0.130640i
\(640\) −6.63894 + 11.4990i −0.262427 + 0.454537i
\(641\) 49.2992 1.94720 0.973601 0.228258i \(-0.0733029\pi\)
0.973601 + 0.228258i \(0.0733029\pi\)
\(642\) 17.4119 30.1582i 0.687192 1.19025i
\(643\) −19.2722 −0.760023 −0.380011 0.924982i \(-0.624080\pi\)
−0.380011 + 0.924982i \(0.624080\pi\)
\(644\) −12.6477 −0.498390
\(645\) 4.16049 + 39.3464i 0.163819 + 1.54926i
\(646\) 2.38217 0.0937252
\(647\) −12.7590 −0.501609 −0.250805 0.968038i \(-0.580695\pi\)
−0.250805 + 0.968038i \(0.580695\pi\)
\(648\) 1.01554 1.75896i 0.0398940 0.0690984i
\(649\) 1.97644 0.0775821
\(650\) −71.1053 + 123.158i −2.78898 + 4.83065i
\(651\) 4.87532 8.44430i 0.191079 0.330958i
\(652\) 12.1220 + 20.9958i 0.474732 + 0.822260i
\(653\) −38.8026 −1.51846 −0.759232 0.650820i \(-0.774425\pi\)
−0.759232 + 0.650820i \(0.774425\pi\)
\(654\) −19.7797 34.2595i −0.773449 1.33965i
\(655\) 30.2508 52.3958i 1.18199 2.04727i
\(656\) −7.07190 −0.276111
\(657\) −4.17363 + 7.22895i −0.162829 + 0.282028i
\(658\) −1.40509 2.43369i −0.0547761 0.0948751i
\(659\) 16.7907 + 29.0824i 0.654073 + 1.13289i 0.982125 + 0.188229i \(0.0602746\pi\)
−0.328052 + 0.944660i \(0.606392\pi\)
\(660\) 1.20332 + 2.08421i 0.0468392 + 0.0811279i
\(661\) −33.7051 −1.31098 −0.655488 0.755205i \(-0.727537\pi\)
−0.655488 + 0.755205i \(0.727537\pi\)
\(662\) 9.45684 + 16.3797i 0.367550 + 0.636616i
\(663\) −4.02338 6.96870i −0.156255 0.270642i
\(664\) −3.45630 + 5.98648i −0.134130 + 0.232321i
\(665\) 2.29981 3.98339i 0.0891829 0.154469i
\(666\) 16.4106 0.635899
\(667\) 59.1454 2.29012
\(668\) −13.0263 + 22.5623i −0.504004 + 0.872960i
\(669\) −0.801057 + 1.38747i −0.0309707 + 0.0536428i
\(670\) 12.2107 + 21.1495i 0.471739 + 0.817076i
\(671\) 0.322784 + 0.559079i 0.0124610 + 0.0215830i
\(672\) 9.77289 0.376997
\(673\) 3.67455 + 6.36450i 0.141643 + 0.245334i 0.928116 0.372292i \(-0.121428\pi\)
−0.786472 + 0.617626i \(0.788095\pi\)
\(674\) −11.0572 19.1516i −0.425907 0.737693i
\(675\) 36.5523 + 63.3104i 1.40690 + 2.43682i
\(676\) −16.9710 + 29.3946i −0.652731 + 1.13056i
\(677\) 26.4021 1.01471 0.507357 0.861736i \(-0.330623\pi\)
0.507357 + 0.861736i \(0.330623\pi\)
\(678\) 24.9255 43.1722i 0.957257 1.65802i
\(679\) −6.96236 12.0592i −0.267191 0.462788i
\(680\) 1.66826 0.0639748
\(681\) 8.16014 + 14.1338i 0.312697 + 0.541607i
\(682\) −1.66416 + 2.88241i −0.0637239 + 0.110373i
\(683\) −7.84981 + 13.5963i −0.300365 + 0.520247i −0.976219 0.216789i \(-0.930442\pi\)
0.675854 + 0.737036i \(0.263775\pi\)
\(684\) −2.12929 −0.0814153
\(685\) 11.9219 20.6494i 0.455513 0.788971i
\(686\) 22.8805 0.873582
\(687\) −3.30354 −0.126038
\(688\) −26.1470 11.6217i −0.996845 0.443073i
\(689\) −8.71393 −0.331974
\(690\) −93.0738 −3.54326
\(691\) −0.598797 + 1.03715i −0.0227793 + 0.0394549i −0.877190 0.480143i \(-0.840585\pi\)
0.854411 + 0.519598i \(0.173918\pi\)
\(692\) 31.8712 1.21156
\(693\) 0.0955287 0.165461i 0.00362884 0.00628533i
\(694\) −5.37269 + 9.30578i −0.203945 + 0.353242i
\(695\) −22.1583 38.3793i −0.840511 1.45581i
\(696\) −4.19615 −0.159055
\(697\) 0.810345 + 1.40356i 0.0306940 + 0.0531636i
\(698\) 9.49244 16.4414i 0.359294 0.622315i
\(699\) −20.7660 −0.785443
\(700\) −10.3256 + 17.8844i −0.390270 + 0.675968i
\(701\) −18.8268 32.6089i −0.711078 1.23162i −0.964453 0.264255i \(-0.914874\pi\)
0.253375 0.967368i \(-0.418459\pi\)
\(702\) 31.1193 + 53.9001i 1.17452 + 2.03433i
\(703\) −5.31190 9.20047i −0.200342 0.347002i
\(704\) −1.39971 −0.0527536
\(705\) −4.89474 8.47794i −0.184347 0.319298i
\(706\) 1.76202 + 3.05191i 0.0663145 + 0.114860i
\(707\) −3.22202 + 5.58070i −0.121176 + 0.209884i
\(708\) −11.4124 + 19.7668i −0.428903 + 0.742883i
\(709\) −46.6831 −1.75322 −0.876610 0.481201i \(-0.840201\pi\)
−0.876610 + 0.481201i \(0.840201\pi\)
\(710\) 32.4711 1.21862
\(711\) 8.09188 14.0155i 0.303469 0.525624i
\(712\) 1.36153 2.35824i 0.0510255 0.0883788i
\(713\) −30.4663 52.7692i −1.14097 1.97622i
\(714\) −1.23423 2.13774i −0.0461897 0.0800030i
\(715\) 5.30350 0.198340
\(716\) −1.97395 3.41899i −0.0737701 0.127774i
\(717\) 5.10340 + 8.83936i 0.190590 + 0.330112i
\(718\) −14.7374 25.5260i −0.549997 0.952622i
\(719\) 3.38775 5.86776i 0.126342 0.218831i −0.795915 0.605409i \(-0.793010\pi\)
0.922257 + 0.386578i \(0.126343\pi\)
\(720\) −17.8996 −0.667079
\(721\) −4.64337 + 8.04256i −0.172928 + 0.299521i
\(722\) −17.0576 29.5446i −0.634818 1.09954i
\(723\) 4.43281 0.164858
\(724\) −0.295925 0.512557i −0.0109980 0.0190490i
\(725\) 48.2863 83.6343i 1.79331 3.10610i
\(726\) −15.2071 + 26.3394i −0.564387 + 0.977547i
\(727\) 17.3106 0.642015 0.321008 0.947077i \(-0.395978\pi\)
0.321008 + 0.947077i \(0.395978\pi\)
\(728\) 0.988698 1.71247i 0.0366436 0.0634685i
\(729\) 29.1778 1.08066
\(730\) −71.0798 −2.63078
\(731\) 0.689540 + 6.52108i 0.0255035 + 0.241191i
\(732\) −7.45529 −0.275556
\(733\) −15.2017 −0.561487 −0.280743 0.959783i \(-0.590581\pi\)
−0.280743 + 0.959783i \(0.590581\pi\)
\(734\) 16.2615 28.1658i 0.600224 1.03962i
\(735\) 37.4699 1.38210
\(736\) 30.5359 52.8896i 1.12557 1.94954i
\(737\) 0.328349 0.568717i 0.0120949 0.0209490i
\(738\) −1.53011 2.65022i −0.0563240 0.0975561i
\(739\) 24.3880 0.897128 0.448564 0.893751i \(-0.351936\pi\)
0.448564 + 0.893751i \(0.351936\pi\)
\(740\) 33.0755 + 57.2885i 1.21588 + 2.10597i
\(741\) 4.91810 8.51840i 0.180671 0.312931i
\(742\) −2.67311 −0.0981331
\(743\) 13.7332 23.7866i 0.503823 0.872647i −0.496167 0.868227i \(-0.665260\pi\)
0.999990 0.00442035i \(-0.00140705\pi\)
\(744\) 2.16148 + 3.74379i 0.0792436 + 0.137254i
\(745\) 4.05073 + 7.01607i 0.148407 + 0.257049i
\(746\) −5.56241 9.63437i −0.203654 0.352739i
\(747\) −16.9975 −0.621906
\(748\) 0.199432 + 0.345427i 0.00729197 + 0.0126301i
\(749\) −5.57198 9.65095i −0.203596 0.352638i
\(750\) −46.5892 + 80.6948i −1.70120 + 2.94656i
\(751\) 5.44792 9.43607i 0.198797 0.344327i −0.749341 0.662184i \(-0.769630\pi\)
0.948139 + 0.317857i \(0.102963\pi\)
\(752\) 7.07962 0.258167
\(753\) 0.380196 0.0138551
\(754\) 41.1092 71.2032i 1.49711 2.59307i
\(755\) −23.7782 + 41.1850i −0.865376 + 1.49887i
\(756\) 4.51900 + 7.82713i 0.164354 + 0.284670i
\(757\) −2.92627 5.06844i −0.106357 0.184216i 0.807935 0.589272i \(-0.200585\pi\)
−0.914292 + 0.405056i \(0.867252\pi\)
\(758\) 17.7418 0.644412
\(759\) 1.25139 + 2.16748i 0.0454227 + 0.0786744i
\(760\) 1.01962 + 1.76604i 0.0369856 + 0.0640610i
\(761\) −11.7394 20.3332i −0.425553 0.737079i 0.570919 0.821006i \(-0.306587\pi\)
−0.996472 + 0.0839270i \(0.973254\pi\)
\(762\) 6.33185 10.9671i 0.229379 0.397295i
\(763\) −12.6594 −0.458303
\(764\) −11.8180 + 20.4695i −0.427562 + 0.740559i
\(765\) 2.05105 + 3.55253i 0.0741560 + 0.128442i
\(766\) 33.7253 1.21855
\(767\) 25.1494 + 43.5600i 0.908092 + 1.57286i
\(768\) −13.3464 +