Properties

Label 91.2.e.b.53.2
Level $91$
Weight $2$
Character 91.53
Analytic conductor $0.727$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 91.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.726638658394\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{5})\)
Defining polynomial: \(x^{4} - x^{3} + 2 x^{2} + x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 53.2
Root \(0.809017 + 1.40126i\) of defining polynomial
Character \(\chi\) \(=\) 91.53
Dual form 91.2.e.b.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(1.30902 + 2.26728i) q^{2} +(1.11803 - 1.93649i) q^{3} +(-2.42705 + 4.20378i) q^{4} +(-1.11803 - 1.93649i) q^{5} +5.85410 q^{6} +(-2.00000 + 1.73205i) q^{7} -7.47214 q^{8} +(-1.00000 - 1.73205i) q^{9} +(2.92705 - 5.06980i) q^{10} +(1.50000 - 2.59808i) q^{11} +(5.42705 + 9.39993i) q^{12} -1.00000 q^{13} +(-6.54508 - 2.26728i) q^{14} -5.00000 q^{15} +(-4.92705 - 8.53390i) q^{16} +(-0.736068 + 1.27491i) q^{17} +(2.61803 - 4.53457i) q^{18} +(-1.50000 - 2.59808i) q^{19} +10.8541 q^{20} +(1.11803 + 5.80948i) q^{21} +7.85410 q^{22} +(4.11803 + 7.13264i) q^{23} +(-8.35410 + 14.4697i) q^{24} +(-1.30902 - 2.26728i) q^{26} +2.23607 q^{27} +(-2.42705 - 12.6113i) q^{28} +4.47214 q^{29} +(-6.54508 - 11.3364i) q^{30} +(-2.50000 + 4.33013i) q^{31} +(5.42705 - 9.39993i) q^{32} +(-3.35410 - 5.80948i) q^{33} -3.85410 q^{34} +(5.59017 + 1.93649i) q^{35} +9.70820 q^{36} +(-2.35410 - 4.07742i) q^{37} +(3.92705 - 6.80185i) q^{38} +(-1.11803 + 1.93649i) q^{39} +(8.35410 + 14.4697i) q^{40} -4.47214 q^{41} +(-11.7082 + 10.1396i) q^{42} -8.00000 q^{43} +(7.28115 + 12.6113i) q^{44} +(-2.23607 + 3.87298i) q^{45} +(-10.7812 + 18.6735i) q^{46} +(3.73607 + 6.47106i) q^{47} -22.0344 q^{48} +(1.00000 - 6.92820i) q^{49} +(1.64590 + 2.85078i) q^{51} +(2.42705 - 4.20378i) q^{52} +(3.73607 - 6.47106i) q^{53} +(2.92705 + 5.06980i) q^{54} -6.70820 q^{55} +(14.9443 - 12.9421i) q^{56} -6.70820 q^{57} +(5.85410 + 10.1396i) q^{58} +(0.736068 - 1.27491i) q^{59} +(12.1353 - 21.0189i) q^{60} +(-1.50000 - 2.59808i) q^{61} -13.0902 q^{62} +(5.00000 + 1.73205i) q^{63} +8.70820 q^{64} +(1.11803 + 1.93649i) q^{65} +(8.78115 - 15.2094i) q^{66} +(1.50000 - 2.59808i) q^{67} +(-3.57295 - 6.18853i) q^{68} +18.4164 q^{69} +(2.92705 + 15.2094i) q^{70} -8.94427 q^{71} +(7.47214 + 12.9421i) q^{72} +(1.35410 - 2.34537i) q^{73} +(6.16312 - 10.6748i) q^{74} +14.5623 q^{76} +(1.50000 + 7.79423i) q^{77} -5.85410 q^{78} +(1.35410 + 2.34537i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-5.85410 - 10.1396i) q^{82} +(-27.1353 - 9.39993i) q^{84} +3.29180 q^{85} +(-10.4721 - 18.1383i) q^{86} +(5.00000 - 8.66025i) q^{87} +(-11.2082 + 19.4132i) q^{88} +(-1.11803 - 1.93649i) q^{89} -11.7082 q^{90} +(2.00000 - 1.73205i) q^{91} -39.9787 q^{92} +(5.59017 + 9.68246i) q^{93} +(-9.78115 + 16.9415i) q^{94} +(-3.35410 + 5.80948i) q^{95} +(-12.1353 - 21.0189i) q^{96} +9.41641 q^{97} +(17.0172 - 6.80185i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + O(q^{10}) \) \( 4 q + 3 q^{2} - 3 q^{4} + 10 q^{6} - 8 q^{7} - 12 q^{8} - 4 q^{9} + 5 q^{10} + 6 q^{11} + 15 q^{12} - 4 q^{13} - 15 q^{14} - 20 q^{15} - 13 q^{16} + 6 q^{17} + 6 q^{18} - 6 q^{19} + 30 q^{20} + 18 q^{22} + 12 q^{23} - 20 q^{24} - 3 q^{26} - 3 q^{28} - 15 q^{30} - 10 q^{31} + 15 q^{32} - 2 q^{34} + 12 q^{36} + 4 q^{37} + 9 q^{38} + 20 q^{40} - 20 q^{42} - 32 q^{43} + 9 q^{44} - 23 q^{46} + 6 q^{47} - 30 q^{48} + 4 q^{49} + 20 q^{51} + 3 q^{52} + 6 q^{53} + 5 q^{54} + 24 q^{56} + 10 q^{58} - 6 q^{59} + 15 q^{60} - 6 q^{61} - 30 q^{62} + 20 q^{63} + 8 q^{64} + 15 q^{66} + 6 q^{67} - 21 q^{68} + 20 q^{69} + 5 q^{70} + 12 q^{72} - 8 q^{73} + 9 q^{74} + 18 q^{76} + 6 q^{77} - 10 q^{78} - 8 q^{79} - 15 q^{80} + 22 q^{81} - 10 q^{82} - 75 q^{84} + 40 q^{85} - 24 q^{86} + 20 q^{87} - 18 q^{88} - 20 q^{90} + 8 q^{91} - 66 q^{92} - 19 q^{94} - 15 q^{96} - 16 q^{97} + 39 q^{98} - 24 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30902 + 2.26728i 0.925615 + 1.60321i 0.790569 + 0.612372i \(0.209785\pi\)
0.135045 + 0.990839i \(0.456882\pi\)
\(3\) 1.11803 1.93649i 0.645497 1.11803i −0.338689 0.940898i \(-0.609984\pi\)
0.984186 0.177136i \(-0.0566831\pi\)
\(4\) −2.42705 + 4.20378i −1.21353 + 2.10189i
\(5\) −1.11803 1.93649i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(6\) 5.85410 2.38993
\(7\) −2.00000 + 1.73205i −0.755929 + 0.654654i
\(8\) −7.47214 −2.64180
\(9\) −1.00000 1.73205i −0.333333 0.577350i
\(10\) 2.92705 5.06980i 0.925615 1.60321i
\(11\) 1.50000 2.59808i 0.452267 0.783349i −0.546259 0.837616i \(-0.683949\pi\)
0.998526 + 0.0542666i \(0.0172821\pi\)
\(12\) 5.42705 + 9.39993i 1.56665 + 2.71353i
\(13\) −1.00000 −0.277350
\(14\) −6.54508 2.26728i −1.74925 0.605957i
\(15\) −5.00000 −1.29099
\(16\) −4.92705 8.53390i −1.23176 2.13348i
\(17\) −0.736068 + 1.27491i −0.178523 + 0.309210i −0.941375 0.337363i \(-0.890465\pi\)
0.762852 + 0.646573i \(0.223798\pi\)
\(18\) 2.61803 4.53457i 0.617077 1.06881i
\(19\) −1.50000 2.59808i −0.344124 0.596040i 0.641071 0.767482i \(-0.278491\pi\)
−0.985194 + 0.171442i \(0.945157\pi\)
\(20\) 10.8541 2.42705
\(21\) 1.11803 + 5.80948i 0.243975 + 1.26773i
\(22\) 7.85410 1.67450
\(23\) 4.11803 + 7.13264i 0.858669 + 1.48726i 0.873199 + 0.487365i \(0.162042\pi\)
−0.0145291 + 0.999894i \(0.504625\pi\)
\(24\) −8.35410 + 14.4697i −1.70527 + 2.95362i
\(25\) 0 0
\(26\) −1.30902 2.26728i −0.256719 0.444651i
\(27\) 2.23607 0.430331
\(28\) −2.42705 12.6113i −0.458670 2.38332i
\(29\) 4.47214 0.830455 0.415227 0.909718i \(-0.363702\pi\)
0.415227 + 0.909718i \(0.363702\pi\)
\(30\) −6.54508 11.3364i −1.19496 2.06974i
\(31\) −2.50000 + 4.33013i −0.449013 + 0.777714i −0.998322 0.0579057i \(-0.981558\pi\)
0.549309 + 0.835619i \(0.314891\pi\)
\(32\) 5.42705 9.39993i 0.959376 1.66169i
\(33\) −3.35410 5.80948i −0.583874 1.01130i
\(34\) −3.85410 −0.660973
\(35\) 5.59017 + 1.93649i 0.944911 + 0.327327i
\(36\) 9.70820 1.61803
\(37\) −2.35410 4.07742i −0.387012 0.670324i 0.605034 0.796200i \(-0.293159\pi\)
−0.992046 + 0.125875i \(0.959826\pi\)
\(38\) 3.92705 6.80185i 0.637052 1.10341i
\(39\) −1.11803 + 1.93649i −0.179029 + 0.310087i
\(40\) 8.35410 + 14.4697i 1.32090 + 2.28787i
\(41\) −4.47214 −0.698430 −0.349215 0.937043i \(-0.613552\pi\)
−0.349215 + 0.937043i \(0.613552\pi\)
\(42\) −11.7082 + 10.1396i −1.80662 + 1.56457i
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) 7.28115 + 12.6113i 1.09768 + 1.90123i
\(45\) −2.23607 + 3.87298i −0.333333 + 0.577350i
\(46\) −10.7812 + 18.6735i −1.58959 + 2.75326i
\(47\) 3.73607 + 6.47106i 0.544962 + 0.943901i 0.998609 + 0.0527200i \(0.0167891\pi\)
−0.453648 + 0.891181i \(0.649878\pi\)
\(48\) −22.0344 −3.18040
\(49\) 1.00000 6.92820i 0.142857 0.989743i
\(50\) 0 0
\(51\) 1.64590 + 2.85078i 0.230472 + 0.399189i
\(52\) 2.42705 4.20378i 0.336571 0.582959i
\(53\) 3.73607 6.47106i 0.513188 0.888868i −0.486695 0.873572i \(-0.661798\pi\)
0.999883 0.0152962i \(-0.00486912\pi\)
\(54\) 2.92705 + 5.06980i 0.398321 + 0.689913i
\(55\) −6.70820 −0.904534
\(56\) 14.9443 12.9421i 1.99701 1.72946i
\(57\) −6.70820 −0.888523
\(58\) 5.85410 + 10.1396i 0.768681 + 1.33139i
\(59\) 0.736068 1.27491i 0.0958279 0.165979i −0.814126 0.580688i \(-0.802783\pi\)
0.909954 + 0.414710i \(0.136117\pi\)
\(60\) 12.1353 21.0189i 1.56665 2.71353i
\(61\) −1.50000 2.59808i −0.192055 0.332650i 0.753876 0.657017i \(-0.228182\pi\)
−0.945931 + 0.324367i \(0.894849\pi\)
\(62\) −13.0902 −1.66245
\(63\) 5.00000 + 1.73205i 0.629941 + 0.218218i
\(64\) 8.70820 1.08853
\(65\) 1.11803 + 1.93649i 0.138675 + 0.240192i
\(66\) 8.78115 15.2094i 1.08089 1.87215i
\(67\) 1.50000 2.59808i 0.183254 0.317406i −0.759733 0.650236i \(-0.774670\pi\)
0.942987 + 0.332830i \(0.108004\pi\)
\(68\) −3.57295 6.18853i −0.433284 0.750469i
\(69\) 18.4164 2.21707
\(70\) 2.92705 + 15.2094i 0.349850 + 1.81787i
\(71\) −8.94427 −1.06149 −0.530745 0.847532i \(-0.678088\pi\)
−0.530745 + 0.847532i \(0.678088\pi\)
\(72\) 7.47214 + 12.9421i 0.880600 + 1.52524i
\(73\) 1.35410 2.34537i 0.158486 0.274505i −0.775837 0.630933i \(-0.782672\pi\)
0.934323 + 0.356428i \(0.116006\pi\)
\(74\) 6.16312 10.6748i 0.716448 1.24092i
\(75\) 0 0
\(76\) 14.5623 1.67041
\(77\) 1.50000 + 7.79423i 0.170941 + 0.888235i
\(78\) −5.85410 −0.662847
\(79\) 1.35410 + 2.34537i 0.152348 + 0.263875i 0.932090 0.362226i \(-0.117983\pi\)
−0.779742 + 0.626101i \(0.784650\pi\)
\(80\) −11.0172 + 19.0824i −1.23176 + 2.13348i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) −5.85410 10.1396i −0.646477 1.11973i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) −27.1353 9.39993i −2.96070 1.02562i
\(85\) 3.29180 0.357045
\(86\) −10.4721 18.1383i −1.12924 1.95590i
\(87\) 5.00000 8.66025i 0.536056 0.928477i
\(88\) −11.2082 + 19.4132i −1.19480 + 2.06945i
\(89\) −1.11803 1.93649i −0.118511 0.205268i 0.800667 0.599110i \(-0.204479\pi\)
−0.919178 + 0.393842i \(0.871146\pi\)
\(90\) −11.7082 −1.23415
\(91\) 2.00000 1.73205i 0.209657 0.181568i
\(92\) −39.9787 −4.16807
\(93\) 5.59017 + 9.68246i 0.579674 + 1.00402i
\(94\) −9.78115 + 16.9415i −1.00885 + 1.74738i
\(95\) −3.35410 + 5.80948i −0.344124 + 0.596040i
\(96\) −12.1353 21.0189i −1.23855 2.14523i
\(97\) 9.41641 0.956091 0.478046 0.878335i \(-0.341345\pi\)
0.478046 + 0.878335i \(0.341345\pi\)
\(98\) 17.0172 6.80185i 1.71900 0.687091i
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) 4.50000 7.79423i 0.447767 0.775555i −0.550474 0.834853i \(-0.685553\pi\)
0.998240 + 0.0592978i \(0.0188862\pi\)
\(102\) −4.30902 + 7.46344i −0.426656 + 0.738990i
\(103\) 1.35410 + 2.34537i 0.133424 + 0.231097i 0.924994 0.379981i \(-0.124070\pi\)
−0.791571 + 0.611078i \(0.790736\pi\)
\(104\) 7.47214 0.732703
\(105\) 10.0000 8.66025i 0.975900 0.845154i
\(106\) 19.5623 1.90006
\(107\) 4.88197 + 8.45581i 0.471957 + 0.817454i 0.999485 0.0320835i \(-0.0102142\pi\)
−0.527528 + 0.849538i \(0.676881\pi\)
\(108\) −5.42705 + 9.39993i −0.522218 + 0.904508i
\(109\) 1.35410 2.34537i 0.129699 0.224646i −0.793861 0.608100i \(-0.791932\pi\)
0.923560 + 0.383454i \(0.125265\pi\)
\(110\) −8.78115 15.2094i −0.837250 1.45016i
\(111\) −10.5279 −0.999261
\(112\) 24.6353 + 8.53390i 2.32781 + 0.806378i
\(113\) 2.94427 0.276974 0.138487 0.990364i \(-0.455776\pi\)
0.138487 + 0.990364i \(0.455776\pi\)
\(114\) −8.78115 15.2094i −0.822430 1.42449i
\(115\) 9.20820 15.9491i 0.858669 1.48726i
\(116\) −10.8541 + 18.7999i −1.00778 + 1.74552i
\(117\) 1.00000 + 1.73205i 0.0924500 + 0.160128i
\(118\) 3.85410 0.354799
\(119\) −0.736068 3.82472i −0.0674752 0.350612i
\(120\) 37.3607 3.41055
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 3.92705 6.80185i 0.355538 0.615811i
\(123\) −5.00000 + 8.66025i −0.450835 + 0.780869i
\(124\) −12.1353 21.0189i −1.08978 1.88755i
\(125\) −11.1803 −1.00000
\(126\) 2.61803 + 13.6037i 0.233233 + 1.21191i
\(127\) −11.4164 −1.01304 −0.506521 0.862228i \(-0.669069\pi\)
−0.506521 + 0.862228i \(0.669069\pi\)
\(128\) 0.545085 + 0.944115i 0.0481792 + 0.0834488i
\(129\) −8.94427 + 15.4919i −0.787499 + 1.36399i
\(130\) −2.92705 + 5.06980i −0.256719 + 0.444651i
\(131\) 4.11803 + 7.13264i 0.359794 + 0.623182i 0.987926 0.154925i \(-0.0495135\pi\)
−0.628132 + 0.778107i \(0.716180\pi\)
\(132\) 32.5623 2.83418
\(133\) 7.50000 + 2.59808i 0.650332 + 0.225282i
\(134\) 7.85410 0.678491
\(135\) −2.50000 4.33013i −0.215166 0.372678i
\(136\) 5.50000 9.52628i 0.471621 0.816872i
\(137\) 4.11803 7.13264i 0.351827 0.609383i −0.634742 0.772724i \(-0.718894\pi\)
0.986570 + 0.163341i \(0.0522271\pi\)
\(138\) 24.1074 + 41.7552i 2.05216 + 3.55444i
\(139\) −23.4164 −1.98615 −0.993077 0.117466i \(-0.962523\pi\)
−0.993077 + 0.117466i \(0.962523\pi\)
\(140\) −21.7082 + 18.7999i −1.83468 + 1.58888i
\(141\) 16.7082 1.40708
\(142\) −11.7082 20.2792i −0.982531 1.70179i
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) −9.85410 + 17.0678i −0.821175 + 1.42232i
\(145\) −5.00000 8.66025i −0.415227 0.719195i
\(146\) 7.09017 0.586787
\(147\) −12.2984 9.68246i −1.01435 0.798596i
\(148\) 22.8541 1.87860
\(149\) −0.354102 0.613323i −0.0290092 0.0502453i 0.851156 0.524912i \(-0.175902\pi\)
−0.880166 + 0.474667i \(0.842569\pi\)
\(150\) 0 0
\(151\) −10.2082 + 17.6811i −0.830732 + 1.43887i 0.0667268 + 0.997771i \(0.478744\pi\)
−0.897459 + 0.441098i \(0.854589\pi\)
\(152\) 11.2082 + 19.4132i 0.909105 + 1.57462i
\(153\) 2.94427 0.238030
\(154\) −15.7082 + 13.6037i −1.26580 + 1.09622i
\(155\) 11.1803 0.898027
\(156\) −5.42705 9.39993i −0.434512 0.752597i
\(157\) −3.50000 + 6.06218i −0.279330 + 0.483814i −0.971219 0.238190i \(-0.923446\pi\)
0.691888 + 0.722005i \(0.256779\pi\)
\(158\) −3.54508 + 6.14027i −0.282032 + 0.488493i
\(159\) −8.35410 14.4697i −0.662523 1.14752i
\(160\) −24.2705 −1.91875
\(161\) −20.5902 7.13264i −1.62273 0.562131i
\(162\) 28.7984 2.26261
\(163\) 8.20820 + 14.2170i 0.642916 + 1.11356i 0.984779 + 0.173813i \(0.0556090\pi\)
−0.341862 + 0.939750i \(0.611058\pi\)
\(164\) 10.8541 18.7999i 0.847563 1.46802i
\(165\) −7.50000 + 12.9904i −0.583874 + 1.01130i
\(166\) 0 0
\(167\) 22.4721 1.73895 0.869473 0.493980i \(-0.164459\pi\)
0.869473 + 0.493980i \(0.164459\pi\)
\(168\) −8.35410 43.4092i −0.644533 3.34909i
\(169\) 1.00000 0.0769231
\(170\) 4.30902 + 7.46344i 0.330487 + 0.572419i
\(171\) −3.00000 + 5.19615i −0.229416 + 0.397360i
\(172\) 19.4164 33.6302i 1.48049 2.56428i
\(173\) 8.20820 + 14.2170i 0.624058 + 1.08090i 0.988722 + 0.149761i \(0.0478505\pi\)
−0.364664 + 0.931139i \(0.618816\pi\)
\(174\) 26.1803 1.98473
\(175\) 0 0
\(176\) −29.5623 −2.22834
\(177\) −1.64590 2.85078i −0.123713 0.214278i
\(178\) 2.92705 5.06980i 0.219392 0.379998i
\(179\) 10.0623 17.4284i 0.752092 1.30266i −0.194715 0.980860i \(-0.562378\pi\)
0.946807 0.321802i \(-0.104288\pi\)
\(180\) −10.8541 18.7999i −0.809017 1.40126i
\(181\) −25.4164 −1.88919 −0.944593 0.328243i \(-0.893544\pi\)
−0.944593 + 0.328243i \(0.893544\pi\)
\(182\) 6.54508 + 2.26728i 0.485154 + 0.168062i
\(183\) −6.70820 −0.495885
\(184\) −30.7705 53.2961i −2.26843 3.92904i
\(185\) −5.26393 + 9.11740i −0.387012 + 0.670324i
\(186\) −14.6353 + 25.3490i −1.07311 + 1.85868i
\(187\) 2.20820 + 3.82472i 0.161480 + 0.279691i
\(188\) −36.2705 −2.64530
\(189\) −4.47214 + 3.87298i −0.325300 + 0.281718i
\(190\) −17.5623 −1.27410
\(191\) −5.59017 9.68246i −0.404491 0.700598i 0.589772 0.807570i \(-0.299218\pi\)
−0.994262 + 0.106972i \(0.965884\pi\)
\(192\) 9.73607 16.8634i 0.702640 1.21701i
\(193\) −0.354102 + 0.613323i −0.0254888 + 0.0441479i −0.878488 0.477764i \(-0.841448\pi\)
0.853000 + 0.521912i \(0.174781\pi\)
\(194\) 12.3262 + 21.3497i 0.884972 + 1.53282i
\(195\) 5.00000 0.358057
\(196\) 26.6976 + 21.0189i 1.90697 + 1.50135i
\(197\) −9.05573 −0.645194 −0.322597 0.946536i \(-0.604556\pi\)
−0.322597 + 0.946536i \(0.604556\pi\)
\(198\) −7.85410 13.6037i −0.558167 0.966773i
\(199\) 10.3541 17.9338i 0.733983 1.27130i −0.221185 0.975232i \(-0.570993\pi\)
0.955168 0.296064i \(-0.0956741\pi\)
\(200\) 0 0
\(201\) −3.35410 5.80948i −0.236580 0.409769i
\(202\) 23.5623 1.65784
\(203\) −8.94427 + 7.74597i −0.627765 + 0.543660i
\(204\) −15.9787 −1.11873
\(205\) 5.00000 + 8.66025i 0.349215 + 0.604858i
\(206\) −3.54508 + 6.14027i −0.246998 + 0.427813i
\(207\) 8.23607 14.2653i 0.572446 0.991506i
\(208\) 4.92705 + 8.53390i 0.341630 + 0.591720i
\(209\) −9.00000 −0.622543
\(210\) 32.7254 + 11.3364i 2.25827 + 0.782287i
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 18.1353 + 31.4112i 1.24553 + 2.15733i
\(213\) −10.0000 + 17.3205i −0.685189 + 1.18678i
\(214\) −12.7812 + 22.1376i −0.873702 + 1.51330i
\(215\) 8.94427 + 15.4919i 0.609994 + 1.05654i
\(216\) −16.7082 −1.13685
\(217\) −2.50000 12.9904i −0.169711 0.881845i
\(218\) 7.09017 0.480207
\(219\) −3.02786 5.24441i −0.204604 0.354385i
\(220\) 16.2812 28.1998i 1.09768 1.90123i
\(221\) 0.736068 1.27491i 0.0495133 0.0857595i
\(222\) −13.7812 23.8697i −0.924930 1.60203i
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 5.42705 + 28.1998i 0.362610 + 1.88418i
\(225\) 0 0
\(226\) 3.85410 + 6.67550i 0.256371 + 0.444048i
\(227\) −2.97214 + 5.14789i −0.197268 + 0.341677i −0.947642 0.319336i \(-0.896540\pi\)
0.750374 + 0.661014i \(0.229873\pi\)
\(228\) 16.2812 28.1998i 1.07825 1.86758i
\(229\) −12.0623 20.8925i −0.797100 1.38062i −0.921497 0.388385i \(-0.873033\pi\)
0.124398 0.992232i \(-0.460300\pi\)
\(230\) 48.2148 3.17919
\(231\) 16.7705 + 5.80948i 1.10342 + 0.382235i
\(232\) −33.4164 −2.19389
\(233\) −5.97214 10.3440i −0.391248 0.677661i 0.601367 0.798973i \(-0.294623\pi\)
−0.992614 + 0.121312i \(0.961290\pi\)
\(234\) −2.61803 + 4.53457i −0.171146 + 0.296434i
\(235\) 8.35410 14.4697i 0.544962 0.943901i
\(236\) 3.57295 + 6.18853i 0.232579 + 0.402839i
\(237\) 6.05573 0.393362
\(238\) 7.70820 6.67550i 0.499649 0.432708i
\(239\) 19.4164 1.25594 0.627972 0.778236i \(-0.283885\pi\)
0.627972 + 0.778236i \(0.283885\pi\)
\(240\) 24.6353 + 42.6695i 1.59020 + 2.75431i
\(241\) −2.35410 + 4.07742i −0.151641 + 0.262650i −0.931831 0.362893i \(-0.881789\pi\)
0.780190 + 0.625543i \(0.215122\pi\)
\(242\) −2.61803 + 4.53457i −0.168294 + 0.291493i
\(243\) −8.94427 15.4919i −0.573775 0.993808i
\(244\) 14.5623 0.932256
\(245\) −14.5344 + 5.80948i −0.928571 + 0.371154i
\(246\) −26.1803 −1.66920
\(247\) 1.50000 + 2.59808i 0.0954427 + 0.165312i
\(248\) 18.6803 32.3553i 1.18620 2.05456i
\(249\) 0 0
\(250\) −14.6353 25.3490i −0.925615 1.60321i
\(251\) 1.52786 0.0964379 0.0482190 0.998837i \(-0.484645\pi\)
0.0482190 + 0.998837i \(0.484645\pi\)
\(252\) −19.4164 + 16.8151i −1.22312 + 1.05925i
\(253\) 24.7082 1.55339
\(254\) −14.9443 25.8842i −0.937687 1.62412i
\(255\) 3.68034 6.37454i 0.230472 0.399189i
\(256\) 7.28115 12.6113i 0.455072 0.788208i
\(257\) 0.0278640 + 0.0482619i 0.00173811 + 0.00301050i 0.866893 0.498494i \(-0.166113\pi\)
−0.865155 + 0.501504i \(0.832780\pi\)
\(258\) −46.8328 −2.91568
\(259\) 11.7705 + 4.07742i 0.731384 + 0.253359i
\(260\) −10.8541 −0.673143
\(261\) −4.47214 7.74597i −0.276818 0.479463i
\(262\) −10.7812 + 18.6735i −0.666062 + 1.15365i
\(263\) −13.0623 + 22.6246i −0.805456 + 1.39509i 0.110526 + 0.993873i \(0.464746\pi\)
−0.915983 + 0.401218i \(0.868587\pi\)
\(264\) 25.0623 + 43.4092i 1.54248 + 2.67165i
\(265\) −16.7082 −1.02638
\(266\) 3.92705 + 20.4056i 0.240783 + 1.25114i
\(267\) −5.00000 −0.305995
\(268\) 7.28115 + 12.6113i 0.444767 + 0.770359i
\(269\) −6.73607 + 11.6672i −0.410705 + 0.711362i −0.994967 0.100203i \(-0.968051\pi\)
0.584262 + 0.811565i \(0.301384\pi\)
\(270\) 6.54508 11.3364i 0.398321 0.689913i
\(271\) 10.2082 + 17.6811i 0.620104 + 1.07405i 0.989466 + 0.144766i \(0.0462430\pi\)
−0.369362 + 0.929286i \(0.620424\pi\)
\(272\) 14.5066 0.879590
\(273\) −1.11803 5.80948i −0.0676665 0.351605i
\(274\) 21.5623 1.30263
\(275\) 0 0
\(276\) −44.6976 + 77.4184i −2.69048 + 4.66004i
\(277\) 0.208204 0.360620i 0.0125098 0.0216675i −0.859703 0.510795i \(-0.829351\pi\)
0.872213 + 0.489127i \(0.162685\pi\)
\(278\) −30.6525 53.0916i −1.83841 3.18423i
\(279\) 10.0000 0.598684
\(280\) −41.7705 14.4697i −2.49627 0.864732i
\(281\) 26.9443 1.60736 0.803680 0.595061i \(-0.202872\pi\)
0.803680 + 0.595061i \(0.202872\pi\)
\(282\) 21.8713 + 37.8822i 1.30242 + 2.25585i
\(283\) −13.0623 + 22.6246i −0.776473 + 1.34489i 0.157489 + 0.987521i \(0.449660\pi\)
−0.933963 + 0.357371i \(0.883673\pi\)
\(284\) 21.7082 37.5997i 1.28814 2.23113i
\(285\) 7.50000 + 12.9904i 0.444262 + 0.769484i
\(286\) −7.85410 −0.464423
\(287\) 8.94427 7.74597i 0.527964 0.457230i
\(288\) −21.7082 −1.27917
\(289\) 7.41641 + 12.8456i 0.436259 + 0.755623i
\(290\) 13.0902 22.6728i 0.768681 1.33139i
\(291\) 10.5279 18.2348i 0.617154 1.06894i
\(292\) 6.57295 + 11.3847i 0.384653 + 0.666238i
\(293\) −14.9443 −0.873054 −0.436527 0.899691i \(-0.643792\pi\)
−0.436527 + 0.899691i \(0.643792\pi\)
\(294\) 5.85410 40.5584i 0.341418 2.36541i
\(295\) −3.29180 −0.191656
\(296\) 17.5902 + 30.4671i 1.02241 + 1.77086i
\(297\) 3.35410 5.80948i 0.194625 0.337100i
\(298\) 0.927051 1.60570i 0.0537026 0.0930157i
\(299\) −4.11803 7.13264i −0.238152 0.412491i
\(300\) 0 0
\(301\) 16.0000 13.8564i 0.922225 0.798670i
\(302\) −53.4508 −3.07575
\(303\) −10.0623 17.4284i −0.578064 1.00124i
\(304\) −14.7812 + 25.6017i −0.847757 + 1.46836i
\(305\) −3.35410 + 5.80948i −0.192055 + 0.332650i
\(306\) 3.85410 + 6.67550i 0.220324 + 0.381613i
\(307\) 19.4164 1.10815 0.554076 0.832466i \(-0.313072\pi\)
0.554076 + 0.832466i \(0.313072\pi\)
\(308\) −36.4058 12.6113i −2.07441 0.718597i
\(309\) 6.05573 0.344498
\(310\) 14.6353 + 25.3490i 0.831227 + 1.43973i
\(311\) 13.8820 24.0443i 0.787174 1.36343i −0.140518 0.990078i \(-0.544877\pi\)
0.927692 0.373347i \(-0.121790\pi\)
\(312\) 8.35410 14.4697i 0.472958 0.819187i
\(313\) 2.79180 + 4.83553i 0.157802 + 0.273320i 0.934076 0.357075i \(-0.116226\pi\)
−0.776274 + 0.630396i \(0.782893\pi\)
\(314\) −18.3262 −1.03421
\(315\) −2.23607 11.6190i −0.125988 0.654654i
\(316\) −13.1459 −0.739515
\(317\) 4.11803 + 7.13264i 0.231292 + 0.400609i 0.958189 0.286138i \(-0.0923714\pi\)
−0.726897 + 0.686747i \(0.759038\pi\)
\(318\) 21.8713 37.8822i 1.22648 2.12433i
\(319\) 6.70820 11.6190i 0.375587 0.650536i
\(320\) −9.73607 16.8634i −0.544263 0.942691i
\(321\) 21.8328 1.21859
\(322\) −10.7812 56.0205i −0.600810 3.12190i
\(323\) 4.41641 0.245736
\(324\) 26.6976 + 46.2415i 1.48320 + 2.56897i
\(325\) 0 0
\(326\) −21.4894 + 37.2207i −1.19019 + 2.06146i
\(327\) −3.02786 5.24441i −0.167441 0.290017i
\(328\) 33.4164 1.84511
\(329\) −18.6803 6.47106i −1.02988 0.356761i
\(330\) −39.2705 −2.16177
\(331\) 0.791796 + 1.37143i 0.0435210 + 0.0753807i 0.886965 0.461836i \(-0.152809\pi\)
−0.843444 + 0.537217i \(0.819476\pi\)
\(332\) 0 0
\(333\) −4.70820 + 8.15485i −0.258008 + 0.446883i
\(334\) 29.4164 + 50.9507i 1.60959 + 2.78790i
\(335\) −6.70820 −0.366508
\(336\) 44.0689 38.1648i 2.40415 2.08206i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 1.30902 + 2.26728i 0.0712011 + 0.123324i
\(339\) 3.29180 5.70156i 0.178786 0.309666i
\(340\) −7.98936 + 13.8380i −0.433284 + 0.750469i
\(341\) 7.50000 + 12.9904i 0.406148 + 0.703469i
\(342\) −15.7082 −0.849402
\(343\) 10.0000 + 15.5885i 0.539949 + 0.841698i
\(344\) 59.7771 3.22296
\(345\) −20.5902 35.6632i −1.10854 1.92004i
\(346\) −21.4894 + 37.2207i −1.15527 + 2.00099i
\(347\) −11.5344 + 19.9782i −0.619201 + 1.07249i 0.370430 + 0.928860i \(0.379210\pi\)
−0.989632 + 0.143628i \(0.954123\pi\)
\(348\) 24.2705 + 42.0378i 1.30104 + 2.25346i
\(349\) −29.4164 −1.57462 −0.787312 0.616555i \(-0.788528\pi\)
−0.787312 + 0.616555i \(0.788528\pi\)
\(350\) 0 0
\(351\) −2.23607 −0.119352
\(352\) −16.2812 28.1998i −0.867788 1.50305i
\(353\) −8.64590 + 14.9751i −0.460175 + 0.797046i −0.998969 0.0453912i \(-0.985547\pi\)
0.538795 + 0.842437i \(0.318880\pi\)
\(354\) 4.30902 7.46344i 0.229022 0.396677i
\(355\) 10.0000 + 17.3205i 0.530745 + 0.919277i
\(356\) 10.8541 0.575266
\(357\) −8.22949 2.85078i −0.435551 0.150879i
\(358\) 52.6869 2.78459
\(359\) −5.97214 10.3440i −0.315197 0.545938i 0.664282 0.747482i \(-0.268737\pi\)
−0.979479 + 0.201544i \(0.935404\pi\)
\(360\) 16.7082 28.9395i 0.880600 1.52524i
\(361\) 5.00000 8.66025i 0.263158 0.455803i
\(362\) −33.2705 57.6262i −1.74866 3.02877i
\(363\) 4.47214 0.234726
\(364\) 2.42705 + 12.6113i 0.127212 + 0.661013i
\(365\) −6.05573 −0.316971
\(366\) −8.78115 15.2094i −0.458998 0.795008i
\(367\) 6.35410 11.0056i 0.331681 0.574489i −0.651160 0.758940i \(-0.725717\pi\)
0.982842 + 0.184451i \(0.0590508\pi\)
\(368\) 40.5795 70.2858i 2.11535 3.66390i
\(369\) 4.47214 + 7.74597i 0.232810 + 0.403239i
\(370\) −27.5623 −1.43290
\(371\) 3.73607 + 19.4132i 0.193967 + 1.00788i
\(372\) −54.2705 −2.81379
\(373\) 0.791796 + 1.37143i 0.0409976 + 0.0710100i 0.885796 0.464075i \(-0.153613\pi\)
−0.844798 + 0.535085i \(0.820280\pi\)
\(374\) −5.78115 + 10.0133i −0.298936 + 0.517773i
\(375\) −12.5000 + 21.6506i −0.645497 + 1.11803i
\(376\) −27.9164 48.3526i −1.43968 2.49360i
\(377\) −4.47214 −0.230327
\(378\) −14.6353 5.06980i −0.752756 0.260762i
\(379\) −15.4164 −0.791888 −0.395944 0.918275i \(-0.629583\pi\)
−0.395944 + 0.918275i \(0.629583\pi\)
\(380\) −16.2812 28.1998i −0.835206 1.44662i
\(381\) −12.7639 + 22.1078i −0.653916 + 1.13262i
\(382\) 14.6353 25.3490i 0.748805 1.29697i
\(383\) −7.50000 12.9904i −0.383232 0.663777i 0.608290 0.793715i \(-0.291856\pi\)
−0.991522 + 0.129937i \(0.958522\pi\)
\(384\) 2.43769 0.124398
\(385\) 13.4164 11.6190i 0.683763 0.592157i
\(386\) −1.85410 −0.0943713
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) −22.8541 + 39.5845i −1.16024 + 2.00960i
\(389\) −0.736068 + 1.27491i −0.0373201 + 0.0646404i −0.884082 0.467332i \(-0.845215\pi\)
0.846762 + 0.531972i \(0.178549\pi\)
\(390\) 6.54508 + 11.3364i 0.331423 + 0.574042i
\(391\) −12.1246 −0.613168
\(392\) −7.47214 + 51.7685i −0.377400 + 2.61470i
\(393\) 18.4164 0.928985
\(394\) −11.8541 20.5319i −0.597201 1.03438i
\(395\) 3.02786 5.24441i 0.152348 0.263875i
\(396\) 14.5623 25.2227i 0.731783 1.26749i
\(397\) 13.0623 + 22.6246i 0.655578 + 1.13549i 0.981748 + 0.190184i \(0.0609084\pi\)
−0.326170 + 0.945311i \(0.605758\pi\)
\(398\) 54.2148 2.71754
\(399\) 13.4164 11.6190i 0.671660 0.581675i
\(400\) 0 0
\(401\) −7.11803 12.3288i −0.355458 0.615671i 0.631739 0.775182i \(-0.282342\pi\)
−0.987196 + 0.159511i \(0.949008\pi\)
\(402\) 8.78115 15.2094i 0.437964 0.758576i
\(403\) 2.50000 4.33013i 0.124534 0.215699i
\(404\) 21.8435 + 37.8340i 1.08675 + 1.88231i
\(405\) −24.5967 −1.22222
\(406\) −29.2705 10.1396i −1.45267 0.503220i
\(407\) −14.1246 −0.700131
\(408\) −12.2984 21.3014i −0.608860 1.05458i
\(409\) −4.35410 + 7.54153i −0.215296 + 0.372904i −0.953364 0.301822i \(-0.902405\pi\)
0.738068 + 0.674727i \(0.235738\pi\)
\(410\) −13.0902 + 22.6728i −0.646477 + 1.11973i
\(411\) −9.20820 15.9491i −0.454207 0.786710i
\(412\) −13.1459 −0.647652
\(413\) 0.736068 + 3.82472i 0.0362195 + 0.188202i
\(414\) 43.1246 2.11946
\(415\) 0 0
\(416\) −5.42705 + 9.39993i −0.266083 + 0.460869i
\(417\) −26.1803 + 45.3457i −1.28206 + 2.22059i
\(418\) −11.7812 20.4056i −0.576235 0.998068i
\(419\) 32.9443 1.60943 0.804717 0.593659i \(-0.202317\pi\)
0.804717 + 0.593659i \(0.202317\pi\)
\(420\) 12.1353 + 63.0566i 0.592140 + 3.07685i
\(421\) 13.4164 0.653876 0.326938 0.945046i \(-0.393983\pi\)
0.326938 + 0.945046i \(0.393983\pi\)
\(422\) 5.23607 + 9.06914i 0.254888 + 0.441479i
\(423\) 7.47214 12.9421i 0.363308 0.629267i
\(424\) −27.9164 + 48.3526i −1.35574 + 2.34821i
\(425\) 0 0
\(426\) −52.3607 −2.53688
\(427\) 7.50000 + 2.59808i 0.362950 + 0.125730i
\(428\) −47.3951 −2.29093
\(429\) 3.35410 + 5.80948i 0.161938 + 0.280484i
\(430\) −23.4164 + 40.5584i −1.12924 + 1.95590i
\(431\) 15.6803 27.1591i 0.755295 1.30821i −0.189932 0.981797i \(-0.560827\pi\)
0.945227 0.326413i \(-0.105840\pi\)
\(432\) −11.0172 19.0824i −0.530066 0.918102i
\(433\) 29.4164 1.41366 0.706831 0.707382i \(-0.250124\pi\)
0.706831 + 0.707382i \(0.250124\pi\)
\(434\) 26.1803 22.6728i 1.25670 1.08833i
\(435\) −22.3607 −1.07211
\(436\) 6.57295 + 11.3847i 0.314787 + 0.545227i
\(437\) 12.3541 21.3979i 0.590977 1.02360i
\(438\) 7.92705 13.7301i 0.378769 0.656047i
\(439\) −12.0623 20.8925i −0.575702 0.997146i −0.995965 0.0897433i \(-0.971395\pi\)
0.420262 0.907403i \(-0.361938\pi\)
\(440\) 50.1246 2.38960
\(441\) −13.0000 + 5.19615i −0.619048 + 0.247436i
\(442\) 3.85410 0.183321
\(443\) −1.11803 1.93649i −0.0531194 0.0920055i 0.838243 0.545297i \(-0.183583\pi\)
−0.891362 + 0.453291i \(0.850250\pi\)
\(444\) 25.5517 44.2568i 1.21263 2.10033i
\(445\) −2.50000 + 4.33013i −0.118511 + 0.205268i
\(446\) −5.23607 9.06914i −0.247935 0.429436i
\(447\) −1.58359 −0.0749013
\(448\) −17.4164 + 15.0831i −0.822848 + 0.712607i
\(449\) −34.3607 −1.62158 −0.810790 0.585337i \(-0.800962\pi\)
−0.810790 + 0.585337i \(0.800962\pi\)
\(450\) 0 0
\(451\) −6.70820 + 11.6190i −0.315877 + 0.547115i
\(452\) −7.14590 + 12.3771i −0.336115 + 0.582168i
\(453\) 22.8262 + 39.5362i 1.07247 + 1.85757i
\(454\) −15.5623 −0.730375
\(455\) −5.59017 1.93649i −0.262071 0.0907841i
\(456\) 50.1246 2.34730
\(457\) 3.06231 + 5.30407i 0.143249 + 0.248114i 0.928718 0.370786i \(-0.120912\pi\)
−0.785470 + 0.618900i \(0.787578\pi\)
\(458\) 31.5795 54.6973i 1.47561 2.55584i
\(459\) −1.64590 + 2.85078i −0.0768239 + 0.133063i
\(460\) 44.6976 + 77.4184i 2.08403 + 3.60965i
\(461\) 34.3607 1.60034 0.800168 0.599776i \(-0.204744\pi\)
0.800168 + 0.599776i \(0.204744\pi\)
\(462\) 8.78115 + 45.6282i 0.408536 + 2.12282i
\(463\) −24.0000 −1.11537 −0.557687 0.830051i \(-0.688311\pi\)
−0.557687 + 0.830051i \(0.688311\pi\)
\(464\) −22.0344 38.1648i −1.02292 1.77176i
\(465\) 12.5000 21.6506i 0.579674 1.00402i
\(466\) 15.6353 27.0811i 0.724289 1.25451i
\(467\) −4.82624 8.35929i −0.223332 0.386822i 0.732486 0.680782i \(-0.238360\pi\)
−0.955818 + 0.293960i \(0.905027\pi\)
\(468\) −9.70820 −0.448762
\(469\) 1.50000 + 7.79423i 0.0692636 + 0.359904i
\(470\) 43.7426 2.01770
\(471\) 7.82624 + 13.5554i 0.360614 + 0.624602i
\(472\) −5.50000 + 9.52628i −0.253158 + 0.438483i
\(473\) −12.0000 + 20.7846i −0.551761 + 0.955677i
\(474\) 7.92705 + 13.7301i 0.364102 + 0.630642i
\(475\) 0 0
\(476\) 17.8647 + 6.18853i 0.818829 + 0.283651i
\(477\) −14.9443 −0.684251
\(478\) 25.4164 + 44.0225i 1.16252 + 2.01354i
\(479\) −11.9164 + 20.6398i −0.544475 + 0.943058i 0.454165 + 0.890917i \(0.349938\pi\)
−0.998640 + 0.0521401i \(0.983396\pi\)
\(480\) −27.1353 + 46.9996i −1.23855 + 2.14523i
\(481\) 2.35410 + 4.07742i 0.107338 + 0.185915i
\(482\) −12.3262 −0.561445
\(483\) −36.8328 + 31.8982i −1.67595 + 1.45142i
\(484\) −9.70820 −0.441282
\(485\) −10.5279 18.2348i −0.478046 0.827999i
\(486\) 23.4164 40.5584i 1.06219 1.83977i
\(487\) 10.9164 18.9078i 0.494670 0.856793i −0.505311 0.862937i \(-0.668622\pi\)
0.999981 + 0.00614405i \(0.00195572\pi\)
\(488\) 11.2082 + 19.4132i 0.507372 + 0.878793i
\(489\) 36.7082 1.66000
\(490\) −32.1976 25.3490i −1.45454 1.14515i
\(491\) −25.5279 −1.15206 −0.576028 0.817430i \(-0.695398\pi\)
−0.576028 + 0.817430i \(0.695398\pi\)
\(492\) −24.2705 42.0378i −1.09420 1.89521i
\(493\) −3.29180 + 5.70156i −0.148255 + 0.256785i
\(494\) −3.92705 + 6.80185i −0.176686 + 0.306030i
\(495\) 6.70820 + 11.6190i 0.301511 + 0.522233i
\(496\) 49.2705 2.21231
\(497\) 17.8885 15.4919i 0.802411 0.694908i
\(498\) 0 0
\(499\) −13.2082 22.8773i −0.591280 1.02413i −0.994060 0.108831i \(-0.965289\pi\)
0.402780 0.915297i \(-0.368044\pi\)
\(500\) 27.1353 46.9996i 1.21353 2.10189i
\(501\) 25.1246 43.5171i 1.12248 1.94420i
\(502\) 2.00000 + 3.46410i 0.0892644 + 0.154610i
\(503\) 20.9443 0.933859 0.466929 0.884295i \(-0.345360\pi\)
0.466929 + 0.884295i \(0.345360\pi\)
\(504\) −37.3607 12.9421i −1.66418 0.576488i
\(505\) −20.1246 −0.895533
\(506\) 32.3435 + 56.0205i 1.43784 + 2.49042i
\(507\) 1.11803 1.93649i 0.0496536 0.0860026i
\(508\) 27.7082 47.9920i 1.22935 2.12930i
\(509\) 10.1180 + 17.5249i 0.448474 + 0.776780i 0.998287 0.0585081i \(-0.0186343\pi\)
−0.549813 + 0.835288i \(0.685301\pi\)
\(510\) 19.2705 0.853313
\(511\) 1.35410 + 7.03612i 0.0599019 + 0.311260i
\(512\) 40.3050 1.78124
\(513\) −3.35410 5.80948i −0.148087 0.256495i
\(514\) −0.0729490 + 0.126351i −0.00321764 + 0.00557312i
\(515\) 3.02786 5.24441i 0.133424 0.231097i
\(516\) −43.4164 75.1994i −1.91130 3.31047i
\(517\) 22.4164 0.985872
\(518\) 6.16312 + 32.0245i 0.270792 + 1.40708i
\(519\) 36.7082 1.61131
\(520\) −8.35410 14.4697i −0.366352 0.634540i
\(521\) 8.97214 15.5402i 0.393076 0.680828i −0.599777 0.800167i \(-0.704744\pi\)
0.992854 + 0.119339i \(0.0380775\pi\)
\(522\) 11.7082 20.2792i 0.512454 0.887597i
\(523\) −16.3541 28.3261i −0.715115 1.23862i −0.962915 0.269804i \(-0.913041\pi\)
0.247800 0.968811i \(-0.420292\pi\)
\(524\) −39.9787 −1.74648
\(525\) 0 0
\(526\) −68.3951 −2.98217
\(527\) −3.68034 6.37454i −0.160318 0.277679i
\(528\) −33.0517 + 57.2472i −1.43839 + 2.49136i
\(529\) −22.4164 + 38.8264i −0.974626 + 1.68810i
\(530\) −21.8713 37.8822i −0.950030 1.64550i
\(531\) −2.94427 −0.127771
\(532\) −29.1246 + 25.2227i −1.26271 + 1.09354i
\(533\) 4.47214 0.193710
\(534\) −6.54508 11.3364i −0.283234 0.490575i
\(535\) 10.9164 18.9078i 0.471957 0.817454i
\(536\) −11.2082 + 19.4132i −0.484121 + 0.838522i
\(537\) −22.5000 38.9711i −0.970947 1.68173i
\(538\) −35.2705 −1.52062
\(539\) −16.5000 12.9904i −0.710705 0.559535i
\(540\) 24.2705 1.04444
\(541\) −0.645898 1.11873i −0.0277693 0.0480979i 0.851807 0.523856i \(-0.175507\pi\)
−0.879576 + 0.475758i \(0.842174\pi\)
\(542\) −26.7254 + 46.2898i −1.14796 + 1.98832i
\(543\) −28.4164 + 49.2187i −1.21946 + 2.11217i
\(544\) 7.98936 + 13.8380i 0.342541 + 0.593298i
\(545\) −6.05573 −0.259399
\(546\) 11.7082 10.1396i 0.501065 0.433935i
\(547\) −4.58359 −0.195980 −0.0979901 0.995187i \(-0.531241\pi\)
−0.0979901 + 0.995187i \(0.531241\pi\)
\(548\) 19.9894 + 34.6226i 0.853903 + 1.47900i
\(549\) −3.00000 + 5.19615i −0.128037 + 0.221766i
\(550\) 0 0
\(551\) −6.70820 11.6190i −0.285779 0.494984i
\(552\) −137.610 −5.85707
\(553\) −6.77051 2.34537i −0.287911 0.0997354i
\(554\) 1.09017 0.0463169
\(555\) 11.7705 + 20.3871i 0.499630 + 0.865385i
\(556\) 56.8328 98.4373i 2.41025 4.17467i
\(557\) 9.35410 16.2018i 0.396346 0.686491i −0.596926 0.802296i \(-0.703611\pi\)
0.993272 + 0.115805i \(0.0369447\pi\)
\(558\) 13.0902 + 22.6728i 0.554151 + 0.959818i
\(559\) 8.00000 0.338364
\(560\) −11.0172 57.2472i −0.465563 2.41913i
\(561\) 9.87539 0.416939
\(562\) 35.2705 + 61.0903i 1.48780 + 2.57694i
\(563\) −6.29837 + 10.9091i −0.265445 + 0.459764i −0.967680 0.252181i \(-0.918852\pi\)
0.702235 + 0.711945i \(0.252185\pi\)
\(564\) −40.5517 + 70.2375i −1.70753 + 2.95753i
\(565\) −3.29180 5.70156i −0.138487 0.239866i
\(566\) −68.3951 −2.87486
\(567\) 5.50000 + 28.5788i 0.230978 + 1.20020i
\(568\) 66.8328 2.80424
\(569\) −12.7361 22.0595i −0.533924 0.924783i −0.999215 0.0396252i \(-0.987384\pi\)
0.465291 0.885158i \(-0.345950\pi\)
\(570\) −19.6353 + 34.0093i −0.822430 + 1.42449i
\(571\) 18.0623 31.2848i 0.755884 1.30923i −0.189050 0.981968i \(-0.560541\pi\)
0.944934 0.327262i \(-0.106126\pi\)
\(572\) −7.28115 12.6113i −0.304440 0.527306i
\(573\) −25.0000 −1.04439
\(574\) 29.2705 + 10.1396i 1.22173 + 0.423219i
\(575\) 0 0
\(576\) −8.70820 15.0831i −0.362842 0.628460i
\(577\) 9.64590 16.7072i 0.401564 0.695529i −0.592351 0.805680i \(-0.701800\pi\)
0.993915 + 0.110151i \(0.0351334\pi\)
\(578\) −19.4164 + 33.6302i −0.807616 + 1.39883i
\(579\) 0.791796 + 1.37143i 0.0329059 + 0.0569947i
\(580\) 48.5410 2.01556
\(581\) 0 0
\(582\) 55.1246 2.28499
\(583\) −11.2082 19.4132i −0.464196 0.804012i
\(584\) −10.1180 + 17.5249i −0.418687 + 0.725188i
\(585\) 2.23607 3.87298i 0.0924500 0.160128i
\(586\) −19.5623 33.8829i −0.808111 1.39969i
\(587\) −6.11146 −0.252247 −0.126123 0.992015i \(-0.540254\pi\)
−0.126123 + 0.992015i \(0.540254\pi\)
\(588\) 70.5517 28.1998i 2.90950 1.16294i
\(589\) 15.0000 0.618064
\(590\) −4.30902 7.46344i −0.177399 0.307265i
\(591\) −10.1246 + 17.5363i −0.416471 + 0.721349i
\(592\) −23.1976 + 40.1794i −0.953414 + 1.65136i
\(593\) −13.8820 24.0443i −0.570064 0.987380i −0.996559 0.0828898i \(-0.973585\pi\)
0.426495 0.904490i \(-0.359748\pi\)
\(594\) 17.5623 0.720590
\(595\) −6.58359 + 5.70156i −0.269901 + 0.233741i
\(596\) 3.43769 0.140813
\(597\) −23.1525 40.1013i −0.947568 1.64124i
\(598\) 10.7812 18.6735i 0.440874 0.763616i
\(599\) 8.53444 14.7821i 0.348708 0.603980i −0.637312 0.770606i \(-0.719954\pi\)
0.986020 + 0.166626i \(0.0532872\pi\)
\(600\) 0 0
\(601\) −22.0000 −0.897399 −0.448699 0.893683i \(-0.648113\pi\)
−0.448699 + 0.893683i \(0.648113\pi\)
\(602\) 52.3607 + 18.1383i 2.13406 + 0.739261i
\(603\) −6.00000 −0.244339
\(604\) −49.5517 85.8260i −2.01623 3.49221i
\(605\) 2.23607 3.87298i 0.0909091 0.157459i
\(606\) 26.3435 45.6282i 1.07013 1.85352i
\(607\) −12.0623 20.8925i −0.489594 0.848001i 0.510334 0.859976i \(-0.329522\pi\)
−0.999928 + 0.0119745i \(0.996188\pi\)
\(608\) −32.5623 −1.32058
\(609\) 5.00000 + 25.9808i 0.202610 + 1.05279i
\(610\) −17.5623 −0.711077
\(611\) −3.73607 6.47106i −0.151145 0.261791i
\(612\) −7.14590 + 12.3771i −0.288856 + 0.500313i
\(613\) 9.06231 15.6964i 0.366023 0.633971i −0.622917 0.782288i \(-0.714052\pi\)
0.988940 + 0.148318i \(0.0473858\pi\)
\(614\) 25.4164 + 44.0225i 1.02572 + 1.77660i
\(615\) 22.3607 0.901670
\(616\) −11.2082 58.2395i −0.451591 2.34654i
\(617\) −4.47214 −0.180041 −0.0900207 0.995940i \(-0.528693\pi\)
−0.0900207 + 0.995940i \(0.528693\pi\)
\(618\) 7.92705 + 13.7301i 0.318873 + 0.552304i
\(619\) −8.50000 + 14.7224i −0.341644 + 0.591744i −0.984738 0.174042i \(-0.944317\pi\)
0.643094 + 0.765787i \(0.277650\pi\)
\(620\) −27.1353 + 46.9996i −1.08978 + 1.88755i
\(621\) 9.20820 + 15.9491i 0.369512 + 0.640014i
\(622\) 72.6869 2.91448
\(623\) 5.59017 + 1.93649i 0.223965 + 0.0775839i
\(624\) 22.0344 0.882084
\(625\) 12.5000 + 21.6506i 0.500000 + 0.866025i
\(626\) −7.30902 + 12.6596i −0.292127 + 0.505979i
\(627\) −10.0623 + 17.4284i −0.401850 + 0.696024i
\(628\) −16.9894 29.4264i −0.677949 1.17424i
\(629\) 6.93112 0.276362
\(630\) 23.4164 20.2792i 0.932932 0.807943i
\(631\) 22.8328 0.908960 0.454480 0.890757i \(-0.349825\pi\)
0.454480 + 0.890757i \(0.349825\pi\)
\(632\) −10.1180 17.5249i −0.402474 0.697105i
\(633\) 4.47214 7.74597i 0.177751 0.307875i
\(634\) −10.7812 + 18.6735i −0.428174 + 0.741620i
\(635\) 12.7639 + 22.1078i 0.506521 + 0.877320i
\(636\) 81.1033 3.21596
\(637\) −1.00000 + 6.92820i −0.0396214 + 0.274505i
\(638\) 35.1246 1.39060
\(639\) 8.94427 + 15.4919i 0.353830 + 0.612851i
\(640\) 1.21885 2.11111i 0.0481792 0.0834488i
\(641\) −5.97214 + 10.3440i −0.235885 + 0.408565i −0.959530 0.281608i \(-0.909132\pi\)
0.723644 + 0.690173i \(0.242466\pi\)
\(642\) 28.5795 + 49.5012i 1.12794 + 1.95366i
\(643\) 34.8328 1.37367 0.686836 0.726812i \(-0.258999\pi\)
0.686836 + 0.726812i \(0.258999\pi\)
\(644\) 79.9574 69.2452i 3.15076 2.72864i
\(645\) 40.0000 1.57500
\(646\) 5.78115 + 10.0133i 0.227456 + 0.393966i
\(647\) −10.1180 + 17.5249i −0.397781 + 0.688977i −0.993452 0.114252i \(-0.963553\pi\)
0.595671 + 0.803229i \(0.296886\pi\)
\(648\) −41.0967 + 71.1817i −1.61443 + 2.79628i
\(649\) −2.20820 3.82472i −0.0866796 0.150133i
\(650\) 0 0
\(651\) −27.9508 9.68246i −1.09548 0.379485i
\(652\) −79.6869 −3.12078
\(653\) −2.26393 3.92125i −0.0885945 0.153450i 0.818323 0.574759i \(-0.194904\pi\)
−0.906917 + 0.421309i \(0.861571\pi\)
\(654\) 7.92705 13.7301i 0.309972 0.536888i
\(655\) 9.20820 15.9491i 0.359794 0.623182i
\(656\) 22.0344 + 38.1648i 0.860300 + 1.49008i
\(657\) −5.41641 −0.211314
\(658\) −9.78115 50.8244i −0.381309 1.98134i
\(659\) −8.94427 −0.348419 −0.174210 0.984709i \(-0.555737\pi\)
−0.174210 + 0.984709i \(0.555737\pi\)
\(660\) −36.4058 63.0566i −1.41709 2.45448i
\(661\) 3.35410 5.80948i 0.130459 0.225962i −0.793394 0.608708i \(-0.791688\pi\)
0.923854 + 0.382746i \(0.125021\pi\)
\(662\) −2.07295 + 3.59045i −0.0805675 + 0.139547i
\(663\) −1.64590 2.85078i −0.0639214 0.110715i
\(664\) 0 0
\(665\) −3.35410 17.4284i −0.130066 0.675845i
\(666\) −24.6525 −0.955264
\(667\) 18.4164 + 31.8982i 0.713086 + 1.23510i
\(668\) −54.5410 + 94.4678i −2.11026 + 3.65507i
\(669\) −4.47214 + 7.74597i −0.172903 + 0.299476i
\(670\) −8.78115 15.2094i −0.339246 0.587591i
\(671\) −9.00000 −0.347441
\(672\) 60.6763 + 21.0189i 2.34064 + 0.810821i
\(673\) −9.41641 −0.362976 −0.181488 0.983393i \(-0.558091\pi\)
−0.181488 + 0.983393i \(0.558091\pi\)
\(674\) 23.5623 + 40.8111i 0.907586 + 1.57199i
\(675\) 0 0
\(676\) −2.42705 + 4.20378i −0.0933481 + 0.161684i
\(677\) 1.44427 + 2.50155i 0.0555079 + 0.0961425i 0.892444 0.451158i \(-0.148989\pi\)
−0.836936 + 0.547300i \(0.815656\pi\)
\(678\) 17.2361 0.661947
\(679\) −18.8328 + 16.3097i −0.722737 + 0.625909i
\(680\) −24.5967 −0.943242
\(681\) 6.64590 + 11.5110i 0.254671 + 0.441104i
\(682\) −19.6353 + 34.0093i −0.751873 + 1.30228i
\(683\) 6.73607 11.6672i 0.257748 0.446433i −0.707890 0.706323i \(-0.750353\pi\)
0.965638 + 0.259889i \(0.0836861\pi\)
\(684\) −14.5623 25.2227i −0.556804 0.964412i
\(685\) −18.4164 −0.703655
\(686\) −22.2533 + 43.0784i −0.849635 + 1.64474i
\(687\) −53.9443 −2.05810
\(688\) 39.4164 + 68.2712i 1.50274 + 2.60282i
\(689\) −3.73607 + 6.47106i −0.142333 + 0.246528i
\(690\) 53.9058 93.3675i 2.05216 3.55444i
\(691\) 25.9164 + 44.8885i 0.985907 + 1.70764i 0.637836 + 0.770172i \(0.279830\pi\)
0.348070 + 0.937468i \(0.386837\pi\)
\(692\) −79.6869 −3.02924
\(693\) 12.0000 10.3923i 0.455842 0.394771i
\(694\) −60.3951 −2.29257
\(695\) 26.1803 + 45.3457i 0.993077 + 1.72006i
\(696\) −37.3607 + 64.7106i −1.41615 + 2.45285i
\(697\) 3.29180 5.70156i 0.124686 0.215962i
\(698\) −38.5066 66.6953i −1.45750 2.52446i
\(699\) −26.7082 −1.01020
\(700\) 0 0
\(701\) −22.3607 −0.844551 −0.422276 0.906467i \(-0.638769\pi\)
−0.422276 + 0.906467i \(0.638769\pi\)
\(702\) −2.92705 5.06980i −0.110474 0.191347i
\(703\) −7.06231 + 12.2323i −0.266360 + 0.461349i
\(704\) 13.0623 22.6246i 0.492304 0.852696i
\(705\) −18.6803 32.3553i −0.703542 1.21857i
\(706\) −45.2705 −1.70378
\(707\) 4.50000 + 23.3827i 0.169240 + 0.879396i
\(708\) 15.9787 0.600517
\(709\) 25.0623 + 43.4092i 0.941235 + 1.63027i 0.763120 + 0.646256i \(0.223666\pi\)
0.178114 + 0.984010i \(0.443000\pi\)
\(710\) −26.1803 + 45.3457i −0.982531 + 1.70179i
\(711\) 2.70820 4.69075i 0.101566 0.175917i
\(712\) 8.35410 + 14.4697i 0.313083 + 0.542276i
\(713\) −41.1803 −1.54222
\(714\) −4.30902 22.3903i −0.161261 0.837936i
\(715\) 6.70820 0.250873
\(716\) 48.8435 + 84.5994i 1.82537 + 3.16163i
\(717\) 21.7082 37.5997i 0.810708 1.40419i
\(718\) 15.6353 27.0811i 0.583503 1.01066i
\(719\) −12.3541 21.3979i −0.460730 0.798008i 0.538267 0.842774i \(-0.319079\pi\)
−0.998998 + 0.0447660i \(0.985746\pi\)
\(720\) 44.0689 1.64235
\(721\) −6.77051 2.34537i −0.252147 0.0873463i
\(722\) 26.1803 0.974331
\(723\) 5.26393 + 9.11740i 0.195768 + 0.339080i
\(724\) 61.6869 106.845i 2.29258 3.97086i
\(725\) 0 0
\(726\) 5.85410 + 10.1396i 0.217266 + 0.376316i
\(727\) −38.8328 −1.44023 −0.720115 0.693855i \(-0.755911\pi\)
−0.720115 + 0.693855i \(0.755911\pi\)
\(728\) −14.9443 + 12.9421i −0.553872 + 0.479667i
\(729\) −7.00000 −0.259259
\(730\) −7.92705 13.7301i −0.293393 0.508172i
\(731\) 5.88854 10.1993i 0.217796 0.377233i
\(732\) 16.2812 28.1998i 0.601769 1.04229i
\(733\) −14.3541 24.8620i −0.530181 0.918300i −0.999380 0.0352078i \(-0.988791\pi\)
0.469199 0.883092i \(-0.344543\pi\)
\(734\) 33.2705 1.22804
\(735\) −5.00000 + 34.6410i −0.184428 + 1.27775i
\(736\) 89.3951 3.29515
\(737\) −4.50000 7.79423i −0.165760 0.287104i
\(738\) −11.7082 + 20.2792i −0.430985 + 0.746488i
\(739\) 8.91641 15.4437i 0.327995 0.568105i −0.654119 0.756392i \(-0.726960\pi\)
0.982114 + 0.188287i \(0.0602936\pi\)
\(740\) −25.5517 44.2568i −0.939298 1.62691i
\(741\) 6.70820 0.246432
\(742\) −39.1246 + 33.8829i −1.43631 + 1.24388i
\(743\) 32.9443 1.20861 0.604304 0.796754i \(-0.293451\pi\)
0.604304 + 0.796754i \(0.293451\pi\)
\(744\) −41.7705 72.3486i −1.53138 2.65243i
\(745\) −0.791796 + 1.37143i −0.0290092 + 0.0502453i
\(746\) −2.07295 + 3.59045i −0.0758961 + 0.131456i
\(747\) 0 0
\(748\) −21.4377 −0.783840
\(749\) −24.4098 8.45581i −0.891916 0.308969i
\(750\) −65.4508 −2.38993
\(751\) 5.06231 + 8.76817i 0.184726 + 0.319955i 0.943484 0.331417i \(-0.107527\pi\)
−0.758758 + 0.651373i \(0.774194\pi\)
\(752\) 36.8156 63.7665i 1.34253 2.32532i
\(753\) 1.70820 2.95870i 0.0622504 0.107821i
\(754\) −5.85410 10.1396i −0.213194 0.369263i
\(755\) 45.6525 1.66146
\(756\) −5.42705 28.1998i −0.197380 1.02562i
\(757\) −52.8328 −1.92024 −0.960121 0.279586i \(-0.909803\pi\)
−0.960121 + 0.279586i \(0.909803\pi\)
\(758\) −20.1803 34.9534i −0.732983 1.26956i
\(759\) 27.6246 47.8472i 1.00271 1.73674i
\(760\) 25.0623 43.4092i 0.909105 1.57462i
\(761\) 16.7705 + 29.0474i 0.607931 + 1.05297i 0.991581 + 0.129488i \(0.0413334\pi\)
−0.383650 + 0.923478i \(0.625333\pi\)
\(762\) −66.8328 −2.42110
\(763\) 1.35410 + 7.03612i 0.0490218 + 0.254725i
\(764\) 54.2705 1.96344
\(765\) −3.29180 5.70156i −0.119015 0.206140i
\(766\) 19.6353 34.0093i 0.709451 1.22880i
\(767\) −0.736068 + 1.27491i −0.0265779 + 0.0460342i
\(768\) −16.2812 28.1998i −0.587496 1.01757i
\(769\) 46.0000 1.65880 0.829401 0.558653i \(-0.188682\pi\)
0.829401 + 0.558653i \(0.188682\pi\)
\(770\) 43.9058 + 15.2094i 1.58225 + 0.548109i
\(771\) 0.124612 0.00448778
\(772\) −1.71885 2.97713i −0.0618627 0.107149i
\(773\) 23.5344 40.7628i 0.846475 1.46614i −0.0378590 0.999283i \(-0.512054\pi\)
0.884334 0.466855i \(-0.154613\pi\)
\(774\) −20.9443 + 36.2765i −0.752826 + 1.30393i
\(775\) 0 0
\(776\) −70.3607 −2.52580
\(777\) 21.0557 18.2348i 0.755370 0.654170i