Properties

Label 38.3.d.a.27.1
Level $38$
Weight $3$
Character 38.27
Analytic conductor $1.035$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 38.d (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.03542500457\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 27.1
Root \(-1.22474 - 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 38.27
Dual form 38.3.d.a.31.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +O(q^{10})\) \(q+(-1.22474 - 0.707107i) q^{2} +(2.72474 + 1.57313i) q^{3} +(1.00000 + 1.73205i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-2.22474 - 3.85337i) q^{6} +6.89898 q^{7} -2.82843i q^{8} +(0.449490 + 0.778539i) q^{9} +(-1.22474 + 0.707107i) q^{10} -14.8990 q^{11} +6.29253i q^{12} +(-14.8485 + 8.57277i) q^{13} +(-8.44949 - 4.87832i) q^{14} +(2.72474 - 1.57313i) q^{15} +(-2.00000 + 3.46410i) q^{16} +(1.05051 - 1.81954i) q^{17} -1.27135i q^{18} +(11.3485 - 15.2385i) q^{19} +2.00000 q^{20} +(18.7980 + 10.8530i) q^{21} +(18.2474 + 10.5352i) q^{22} +(-13.5227 - 23.4220i) q^{23} +(4.44949 - 7.70674i) q^{24} +(12.0000 + 20.7846i) q^{25} +24.2474 q^{26} -25.4880i q^{27} +(6.89898 + 11.9494i) q^{28} +(-5.54541 + 3.20164i) q^{29} -4.44949 q^{30} +31.1769i q^{31} +(4.89898 - 2.82843i) q^{32} +(-40.5959 - 23.4381i) q^{33} +(-2.57321 + 1.48565i) q^{34} +(3.44949 - 5.97469i) q^{35} +(-0.898979 + 1.55708i) q^{36} +28.9199i q^{37} +(-24.6742 + 10.6387i) q^{38} -53.9444 q^{39} +(-2.44949 - 1.41421i) q^{40} +(55.9393 + 32.2966i) q^{41} +(-15.3485 - 26.5843i) q^{42} +(37.6691 - 65.2449i) q^{43} +(-14.8990 - 25.8058i) q^{44} +0.898979 q^{45} +38.2480i q^{46} +(5.77015 + 9.99420i) q^{47} +(-10.8990 + 6.29253i) q^{48} -1.40408 q^{49} -33.9411i q^{50} +(5.72474 - 3.30518i) q^{51} +(-29.6969 - 17.1455i) q^{52} +(-69.2878 + 40.0033i) q^{53} +(-18.0227 + 31.2162i) q^{54} +(-7.44949 + 12.9029i) q^{55} -19.5133i q^{56} +(54.8939 - 23.6684i) q^{57} +9.05561 q^{58} +(50.9166 + 29.3967i) q^{59} +(5.44949 + 3.14626i) q^{60} +(-1.09592 - 1.89819i) q^{61} +(22.0454 - 38.1838i) q^{62} +(3.10102 + 5.37113i) q^{63} -8.00000 q^{64} +17.1455i q^{65} +(33.1464 + 57.4113i) q^{66} +(-51.6589 + 29.8253i) q^{67} +4.20204 q^{68} -85.0920i q^{69} +(-8.44949 + 4.87832i) q^{70} +(87.5227 + 50.5313i) q^{71} +(2.20204 - 1.27135i) q^{72} +(63.6918 - 110.317i) q^{73} +(20.4495 - 35.4196i) q^{74} +75.5103i q^{75} +(37.7423 + 4.41761i) q^{76} -102.788 q^{77} +(66.0681 + 38.1444i) q^{78} +(-5.78036 - 3.33729i) q^{79} +(2.00000 + 3.46410i) q^{80} +(44.1413 - 76.4550i) q^{81} +(-45.6742 - 79.1101i) q^{82} -1.30306 q^{83} +43.4120i q^{84} +(-1.05051 - 1.81954i) q^{85} +(-92.2702 + 53.2722i) q^{86} -20.1464 q^{87} +42.1407i q^{88} +(5.84847 - 3.37662i) q^{89} +(-1.10102 - 0.635674i) q^{90} +(-102.439 + 59.1433i) q^{91} +(27.0454 - 46.8440i) q^{92} +(-49.0454 + 84.9491i) q^{93} -16.3205i q^{94} +(-7.52270 - 17.4473i) q^{95} +17.7980 q^{96} +(-114.152 - 65.9054i) q^{97} +(1.71964 + 0.992836i) q^{98} +(-6.69694 - 11.5994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 6q^{3} + 4q^{4} + 2q^{5} - 4q^{6} + 8q^{7} - 8q^{9} + O(q^{10}) \) \( 4q + 6q^{3} + 4q^{4} + 2q^{5} - 4q^{6} + 8q^{7} - 8q^{9} - 40q^{11} - 30q^{13} - 24q^{14} + 6q^{15} - 8q^{16} + 14q^{17} + 16q^{19} + 8q^{20} + 36q^{21} + 24q^{22} - 10q^{23} + 8q^{24} + 48q^{25} + 48q^{26} + 8q^{28} + 66q^{29} - 8q^{30} - 84q^{33} + 24q^{34} + 4q^{35} + 16q^{36} - 84q^{38} - 108q^{39} + 18q^{41} - 32q^{42} + 38q^{43} - 40q^{44} - 16q^{45} - 70q^{47} - 24q^{48} - 84q^{49} + 18q^{51} - 60q^{52} - 42q^{53} - 28q^{54} - 20q^{55} + 102q^{57} + 144q^{58} + 42q^{59} + 12q^{60} + 74q^{61} + 32q^{63} - 32q^{64} + 64q^{66} + 102q^{67} + 56q^{68} - 24q^{70} + 306q^{71} + 48q^{72} + 98q^{73} + 72q^{74} + 4q^{76} - 176q^{77} + 132q^{78} - 126q^{79} + 8q^{80} + 10q^{81} - 168q^{82} - 64q^{83} - 14q^{85} - 276q^{86} - 12q^{87} - 6q^{89} - 24q^{90} - 204q^{91} + 20q^{92} - 108q^{93} + 14q^{95} + 32q^{96} - 486q^{97} - 96q^{98} + 32q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.22474 0.707107i −0.612372 0.353553i
\(3\) 2.72474 + 1.57313i 0.908248 + 0.524377i 0.879867 0.475220i \(-0.157631\pi\)
0.0283812 + 0.999597i \(0.490965\pi\)
\(4\) 1.00000 + 1.73205i 0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.100000 0.173205i −0.811684 0.584096i \(-0.801449\pi\)
0.911684 + 0.410891i \(0.134782\pi\)
\(6\) −2.22474 3.85337i −0.370791 0.642229i
\(7\) 6.89898 0.985568 0.492784 0.870152i \(-0.335979\pi\)
0.492784 + 0.870152i \(0.335979\pi\)
\(8\) 2.82843i 0.353553i
\(9\) 0.449490 + 0.778539i 0.0499433 + 0.0865043i
\(10\) −1.22474 + 0.707107i −0.122474 + 0.0707107i
\(11\) −14.8990 −1.35445 −0.677226 0.735775i \(-0.736818\pi\)
−0.677226 + 0.735775i \(0.736818\pi\)
\(12\) 6.29253i 0.524377i
\(13\) −14.8485 + 8.57277i −1.14219 + 0.659444i −0.946972 0.321316i \(-0.895875\pi\)
−0.195218 + 0.980760i \(0.562541\pi\)
\(14\) −8.44949 4.87832i −0.603535 0.348451i
\(15\) 2.72474 1.57313i 0.181650 0.104875i
\(16\) −2.00000 + 3.46410i −0.125000 + 0.216506i
\(17\) 1.05051 1.81954i 0.0617947 0.107032i −0.833473 0.552560i \(-0.813651\pi\)
0.895268 + 0.445529i \(0.146984\pi\)
\(18\) 1.27135i 0.0706305i
\(19\) 11.3485 15.2385i 0.597288 0.802027i
\(20\) 2.00000 0.100000
\(21\) 18.7980 + 10.8530i 0.895141 + 0.516810i
\(22\) 18.2474 + 10.5352i 0.829429 + 0.478871i
\(23\) −13.5227 23.4220i −0.587944 1.01835i −0.994501 0.104723i \(-0.966604\pi\)
0.406558 0.913625i \(-0.366729\pi\)
\(24\) 4.44949 7.70674i 0.185395 0.321114i
\(25\) 12.0000 + 20.7846i 0.480000 + 0.831384i
\(26\) 24.2474 0.932594
\(27\) 25.4880i 0.943998i
\(28\) 6.89898 + 11.9494i 0.246392 + 0.426764i
\(29\) −5.54541 + 3.20164i −0.191221 + 0.110401i −0.592554 0.805531i \(-0.701880\pi\)
0.401333 + 0.915932i \(0.368547\pi\)
\(30\) −4.44949 −0.148316
\(31\) 31.1769i 1.00571i 0.864372 + 0.502853i \(0.167716\pi\)
−0.864372 + 0.502853i \(0.832284\pi\)
\(32\) 4.89898 2.82843i 0.153093 0.0883883i
\(33\) −40.5959 23.4381i −1.23018 0.710244i
\(34\) −2.57321 + 1.48565i −0.0756828 + 0.0436955i
\(35\) 3.44949 5.97469i 0.0985568 0.170705i
\(36\) −0.898979 + 1.55708i −0.0249717 + 0.0432522i
\(37\) 28.9199i 0.781620i 0.920471 + 0.390810i \(0.127805\pi\)
−0.920471 + 0.390810i \(0.872195\pi\)
\(38\) −24.6742 + 10.6387i −0.649322 + 0.279966i
\(39\) −53.9444 −1.38319
\(40\) −2.44949 1.41421i −0.0612372 0.0353553i
\(41\) 55.9393 + 32.2966i 1.36437 + 0.787721i 0.990202 0.139639i \(-0.0445942\pi\)
0.374170 + 0.927360i \(0.377928\pi\)
\(42\) −15.3485 26.5843i −0.365440 0.632960i
\(43\) 37.6691 65.2449i 0.876026 1.51732i 0.0203609 0.999793i \(-0.493518\pi\)
0.855665 0.517529i \(-0.173148\pi\)
\(44\) −14.8990 25.8058i −0.338613 0.586495i
\(45\) 0.898979 0.0199773
\(46\) 38.2480i 0.831478i
\(47\) 5.77015 + 9.99420i 0.122769 + 0.212642i 0.920859 0.389896i \(-0.127489\pi\)
−0.798090 + 0.602539i \(0.794156\pi\)
\(48\) −10.8990 + 6.29253i −0.227062 + 0.131094i
\(49\) −1.40408 −0.0286547
\(50\) 33.9411i 0.678823i
\(51\) 5.72474 3.30518i 0.112250 0.0648075i
\(52\) −29.6969 17.1455i −0.571095 0.329722i
\(53\) −69.2878 + 40.0033i −1.30732 + 0.754779i −0.981647 0.190705i \(-0.938923\pi\)
−0.325669 + 0.945484i \(0.605589\pi\)
\(54\) −18.0227 + 31.2162i −0.333754 + 0.578078i
\(55\) −7.44949 + 12.9029i −0.135445 + 0.234598i
\(56\) 19.5133i 0.348451i
\(57\) 54.8939 23.6684i 0.963050 0.415235i
\(58\) 9.05561 0.156131
\(59\) 50.9166 + 29.3967i 0.862993 + 0.498249i 0.865013 0.501749i \(-0.167310\pi\)
−0.00202049 + 0.999998i \(0.500643\pi\)
\(60\) 5.44949 + 3.14626i 0.0908248 + 0.0524377i
\(61\) −1.09592 1.89819i −0.0179659 0.0311178i 0.856903 0.515478i \(-0.172386\pi\)
−0.874869 + 0.484360i \(0.839052\pi\)
\(62\) 22.0454 38.1838i 0.355571 0.615867i
\(63\) 3.10102 + 5.37113i 0.0492225 + 0.0852560i
\(64\) −8.00000 −0.125000
\(65\) 17.1455i 0.263777i
\(66\) 33.1464 + 57.4113i 0.502219 + 0.869868i
\(67\) −51.6589 + 29.8253i −0.771029 + 0.445154i −0.833241 0.552909i \(-0.813518\pi\)
0.0622127 + 0.998063i \(0.480184\pi\)
\(68\) 4.20204 0.0617947
\(69\) 85.0920i 1.23322i
\(70\) −8.44949 + 4.87832i −0.120707 + 0.0696902i
\(71\) 87.5227 + 50.5313i 1.23271 + 0.711708i 0.967595 0.252508i \(-0.0812553\pi\)
0.265119 + 0.964216i \(0.414589\pi\)
\(72\) 2.20204 1.27135i 0.0305839 0.0176576i
\(73\) 63.6918 110.317i 0.872491 1.51120i 0.0130791 0.999914i \(-0.495837\pi\)
0.859412 0.511284i \(-0.170830\pi\)
\(74\) 20.4495 35.4196i 0.276344 0.478643i
\(75\) 75.5103i 1.00680i
\(76\) 37.7423 + 4.41761i 0.496610 + 0.0581265i
\(77\) −102.788 −1.33491
\(78\) 66.0681 + 38.1444i 0.847027 + 0.489031i
\(79\) −5.78036 3.33729i −0.0731691 0.0422442i 0.462969 0.886374i \(-0.346784\pi\)
−0.536138 + 0.844130i \(0.680117\pi\)
\(80\) 2.00000 + 3.46410i 0.0250000 + 0.0433013i
\(81\) 44.1413 76.4550i 0.544955 0.943889i
\(82\) −45.6742 79.1101i −0.557003 0.964757i
\(83\) −1.30306 −0.0156995 −0.00784977 0.999969i \(-0.502499\pi\)
−0.00784977 + 0.999969i \(0.502499\pi\)
\(84\) 43.4120i 0.516810i
\(85\) −1.05051 1.81954i −0.0123589 0.0214063i
\(86\) −92.2702 + 53.2722i −1.07291 + 0.619444i
\(87\) −20.1464 −0.231568
\(88\) 42.1407i 0.478871i
\(89\) 5.84847 3.37662i 0.0657131 0.0379395i −0.466783 0.884372i \(-0.654587\pi\)
0.532497 + 0.846432i \(0.321254\pi\)
\(90\) −1.10102 0.635674i −0.0122336 0.00706305i
\(91\) −102.439 + 59.1433i −1.12571 + 0.649927i
\(92\) 27.0454 46.8440i 0.293972 0.509174i
\(93\) −49.0454 + 84.9491i −0.527370 + 0.913432i
\(94\) 16.3205i 0.173622i
\(95\) −7.52270 17.4473i −0.0791864 0.183656i
\(96\) 17.7980 0.185395
\(97\) −114.152 65.9054i −1.17682 0.679437i −0.221543 0.975151i \(-0.571109\pi\)
−0.955277 + 0.295713i \(0.904443\pi\)
\(98\) 1.71964 + 0.992836i 0.0175474 + 0.0101310i
\(99\) −6.69694 11.5994i −0.0676458 0.117166i
\(100\) −24.0000 + 41.5692i −0.240000 + 0.415692i
\(101\) −3.24235 5.61591i −0.0321024 0.0556031i 0.849528 0.527544i \(-0.176887\pi\)
−0.881630 + 0.471941i \(0.843554\pi\)
\(102\) −9.34847 −0.0916517
\(103\) 80.0243i 0.776935i −0.921462 0.388467i \(-0.873005\pi\)
0.921462 0.388467i \(-0.126995\pi\)
\(104\) 24.2474 + 41.9978i 0.233149 + 0.403825i
\(105\) 18.7980 10.8530i 0.179028 0.103362i
\(106\) 113.146 1.06742
\(107\) 80.0243i 0.747890i −0.927451 0.373945i \(-0.878005\pi\)
0.927451 0.373945i \(-0.121995\pi\)
\(108\) 44.1464 25.4880i 0.408763 0.236000i
\(109\) −14.2423 8.22282i −0.130664 0.0754387i 0.433243 0.901277i \(-0.357369\pi\)
−0.563907 + 0.825838i \(0.690702\pi\)
\(110\) 18.2474 10.5352i 0.165886 0.0957743i
\(111\) −45.4949 + 78.7995i −0.409864 + 0.709905i
\(112\) −13.7980 + 23.8988i −0.123196 + 0.213382i
\(113\) 132.843i 1.17560i 0.809006 + 0.587801i \(0.200006\pi\)
−0.809006 + 0.587801i \(0.799994\pi\)
\(114\) −83.9671 9.82806i −0.736553 0.0862111i
\(115\) −27.0454 −0.235177
\(116\) −11.0908 6.40329i −0.0956105 0.0552007i
\(117\) −13.3485 7.70674i −0.114089 0.0658696i
\(118\) −41.5732 72.0069i −0.352315 0.610228i
\(119\) 7.24745 12.5529i 0.0609029 0.105487i
\(120\) −4.44949 7.70674i −0.0370791 0.0642229i
\(121\) 100.980 0.834542
\(122\) 3.09972i 0.0254076i
\(123\) 101.614 + 176.000i 0.826126 + 1.43089i
\(124\) −54.0000 + 31.1769i −0.435484 + 0.251427i
\(125\) 49.0000 0.392000
\(126\) 8.77101i 0.0696112i
\(127\) 108.826 62.8306i 0.856896 0.494729i −0.00607575 0.999982i \(-0.501934\pi\)
0.862972 + 0.505253i \(0.168601\pi\)
\(128\) 9.79796 + 5.65685i 0.0765466 + 0.0441942i
\(129\) 205.278 118.517i 1.59130 0.918737i
\(130\) 12.1237 20.9989i 0.0932594 0.161530i
\(131\) −53.6237 + 92.8790i −0.409341 + 0.709000i −0.994816 0.101691i \(-0.967575\pi\)
0.585475 + 0.810691i \(0.300908\pi\)
\(132\) 93.7523i 0.710244i
\(133\) 78.2929 105.130i 0.588668 0.790452i
\(134\) 84.3587 0.629542
\(135\) −22.0732 12.7440i −0.163505 0.0943998i
\(136\) −5.14643 2.97129i −0.0378414 0.0218477i
\(137\) 1.05051 + 1.81954i 0.00766796 + 0.0132813i 0.869834 0.493345i \(-0.164226\pi\)
−0.862166 + 0.506626i \(0.830893\pi\)
\(138\) −60.1691 + 104.216i −0.436008 + 0.755188i
\(139\) 15.8712 + 27.4897i 0.114181 + 0.197767i 0.917452 0.397846i \(-0.130242\pi\)
−0.803271 + 0.595614i \(0.796909\pi\)
\(140\) 13.7980 0.0985568
\(141\) 36.3089i 0.257510i
\(142\) −71.4620 123.776i −0.503253 0.871661i
\(143\) 221.227 127.725i 1.54704 0.893185i
\(144\) −3.59592 −0.0249717
\(145\) 6.40329i 0.0441606i
\(146\) −156.012 + 90.0739i −1.06858 + 0.616944i
\(147\) −3.82577 2.20881i −0.0260256 0.0150259i
\(148\) −50.0908 + 28.9199i −0.338451 + 0.195405i
\(149\) −94.8383 + 164.265i −0.636498 + 1.10245i 0.349697 + 0.936863i \(0.386284\pi\)
−0.986196 + 0.165585i \(0.947049\pi\)
\(150\) 53.3939 92.4809i 0.355959 0.616539i
\(151\) 16.2707i 0.107753i −0.998548 0.0538764i \(-0.982842\pi\)
0.998548 0.0538764i \(-0.0171577\pi\)
\(152\) −43.1010 32.0983i −0.283559 0.211173i
\(153\) 1.88877 0.0123449
\(154\) 125.889 + 72.6819i 0.817460 + 0.471961i
\(155\) 27.0000 + 15.5885i 0.174194 + 0.100571i
\(156\) −53.9444 93.4344i −0.345797 0.598939i
\(157\) −135.076 + 233.958i −0.860354 + 1.49018i 0.0112344 + 0.999937i \(0.496424\pi\)
−0.871588 + 0.490239i \(0.836909\pi\)
\(158\) 4.71964 + 8.17466i 0.0298712 + 0.0517384i
\(159\) −251.722 −1.58316
\(160\) 5.65685i 0.0353553i
\(161\) −93.2929 161.588i −0.579459 1.00365i
\(162\) −108.124 + 62.4253i −0.667430 + 0.385341i
\(163\) −156.697 −0.961331 −0.480665 0.876904i \(-0.659605\pi\)
−0.480665 + 0.876904i \(0.659605\pi\)
\(164\) 129.186i 0.787721i
\(165\) −40.5959 + 23.4381i −0.246036 + 0.142049i
\(166\) 1.59592 + 0.921404i 0.00961396 + 0.00555062i
\(167\) −78.0834 + 45.0815i −0.467565 + 0.269949i −0.715220 0.698899i \(-0.753674\pi\)
0.247655 + 0.968848i \(0.420340\pi\)
\(168\) 30.6969 53.1687i 0.182720 0.316480i
\(169\) 62.4847 108.227i 0.369732 0.640394i
\(170\) 2.97129i 0.0174782i
\(171\) 16.9648 + 1.98567i 0.0992093 + 0.0116121i
\(172\) 150.677 0.876026
\(173\) −263.379 152.062i −1.52242 0.878969i −0.999649 0.0264959i \(-0.991565\pi\)
−0.522771 0.852473i \(-0.675102\pi\)
\(174\) 24.6742 + 14.2457i 0.141806 + 0.0818717i
\(175\) 82.7878 + 143.393i 0.473073 + 0.819386i
\(176\) 29.7980 51.6116i 0.169307 0.293248i
\(177\) 92.4898 + 160.197i 0.522541 + 0.905068i
\(178\) −9.55051 −0.0536546
\(179\) 315.198i 1.76088i −0.474156 0.880441i \(-0.657247\pi\)
0.474156 0.880441i \(-0.342753\pi\)
\(180\) 0.898979 + 1.55708i 0.00499433 + 0.00865043i
\(181\) −27.8939 + 16.1045i −0.154110 + 0.0889753i −0.575072 0.818103i \(-0.695026\pi\)
0.420962 + 0.907078i \(0.361693\pi\)
\(182\) 167.283 0.919135
\(183\) 6.89610i 0.0376836i
\(184\) −66.2474 + 38.2480i −0.360040 + 0.207869i
\(185\) 25.0454 + 14.4600i 0.135381 + 0.0781620i
\(186\) 120.136 69.3607i 0.645894 0.372907i
\(187\) −15.6515 + 27.1092i −0.0836980 + 0.144969i
\(188\) −11.5403 + 19.9884i −0.0613846 + 0.106321i
\(189\) 175.841i 0.930375i
\(190\) −3.12372 + 26.6879i −0.0164407 + 0.140462i
\(191\) 280.252 1.46729 0.733644 0.679534i \(-0.237818\pi\)
0.733644 + 0.679534i \(0.237818\pi\)
\(192\) −21.7980 12.5851i −0.113531 0.0655472i
\(193\) 42.0153 + 24.2575i 0.217696 + 0.125687i 0.604883 0.796314i \(-0.293220\pi\)
−0.387187 + 0.922001i \(0.626553\pi\)
\(194\) 93.2043 + 161.435i 0.480435 + 0.832137i
\(195\) −26.9722 + 46.7172i −0.138319 + 0.239575i
\(196\) −1.40408 2.43194i −0.00716368 0.0124079i
\(197\) 251.909 1.27873 0.639363 0.768905i \(-0.279198\pi\)
0.639363 + 0.768905i \(0.279198\pi\)
\(198\) 18.9418i 0.0956657i
\(199\) −129.694 224.637i −0.651729 1.12883i −0.982703 0.185188i \(-0.940710\pi\)
0.330974 0.943640i \(-0.392623\pi\)
\(200\) 58.7878 33.9411i 0.293939 0.169706i
\(201\) −187.677 −0.933714
\(202\) 9.17074i 0.0453997i
\(203\) −38.2577 + 22.0881i −0.188461 + 0.108808i
\(204\) 11.4495 + 6.61037i 0.0561249 + 0.0324038i
\(205\) 55.9393 32.2966i 0.272875 0.157544i
\(206\) −56.5857 + 98.0093i −0.274688 + 0.475773i
\(207\) 12.1566 21.0559i 0.0587277 0.101719i
\(208\) 68.5821i 0.329722i
\(209\) −169.081 + 227.038i −0.808998 + 1.08631i
\(210\) −30.6969 −0.146176
\(211\) 60.2503 + 34.7855i 0.285546 + 0.164860i 0.635932 0.771745i \(-0.280616\pi\)
−0.350385 + 0.936606i \(0.613949\pi\)
\(212\) −138.576 80.0066i −0.653658 0.377390i
\(213\) 158.985 + 275.370i 0.746407 + 1.29281i
\(214\) −56.5857 + 98.0093i −0.264419 + 0.457988i
\(215\) −37.6691 65.2449i −0.175205 0.303464i
\(216\) −72.0908 −0.333754
\(217\) 215.089i 0.991193i
\(218\) 11.6288 + 20.1417i 0.0533432 + 0.0923932i
\(219\) 347.088 200.391i 1.58488 0.915029i
\(220\) −29.7980 −0.135445
\(221\) 36.0231i 0.163001i
\(222\) 111.439 64.3395i 0.501979 0.289818i
\(223\) −5.47730 3.16232i −0.0245619 0.0141808i 0.487669 0.873029i \(-0.337847\pi\)
−0.512231 + 0.858848i \(0.671181\pi\)
\(224\) 33.7980 19.5133i 0.150884 0.0871128i
\(225\) −10.7878 + 18.6849i −0.0479456 + 0.0830442i
\(226\) 93.9342 162.699i 0.415638 0.719906i
\(227\) 55.7402i 0.245552i −0.992434 0.122776i \(-0.960820\pi\)
0.992434 0.122776i \(-0.0391796\pi\)
\(228\) 95.8888 + 71.4106i 0.420565 + 0.313204i
\(229\) −132.313 −0.577787 −0.288894 0.957361i \(-0.593287\pi\)
−0.288894 + 0.957361i \(0.593287\pi\)
\(230\) 33.1237 + 19.1240i 0.144016 + 0.0831478i
\(231\) −280.070 161.699i −1.21243 0.699994i
\(232\) 9.05561 + 15.6848i 0.0390328 + 0.0676068i
\(233\) 111.859 193.745i 0.480080 0.831523i −0.519659 0.854374i \(-0.673941\pi\)
0.999739 + 0.0228507i \(0.00727424\pi\)
\(234\) 10.8990 + 18.8776i 0.0465768 + 0.0806734i
\(235\) 11.5403 0.0491077
\(236\) 117.587i 0.498249i
\(237\) −10.5000 18.1865i −0.0443038 0.0767364i
\(238\) −17.7526 + 10.2494i −0.0745906 + 0.0430649i
\(239\) −71.3235 −0.298425 −0.149212 0.988805i \(-0.547674\pi\)
−0.149212 + 0.988805i \(0.547674\pi\)
\(240\) 12.5851i 0.0524377i
\(241\) 120.727 69.7018i 0.500942 0.289219i −0.228160 0.973624i \(-0.573271\pi\)
0.729103 + 0.684405i \(0.239938\pi\)
\(242\) −123.674 71.4034i −0.511051 0.295055i
\(243\) 41.8888 24.1845i 0.172382 0.0995247i
\(244\) 2.19184 3.79637i 0.00898293 0.0155589i
\(245\) −0.702041 + 1.21597i −0.00286547 + 0.00496315i
\(246\) 287.406i 1.16832i
\(247\) −37.8712 + 323.556i −0.153325 + 1.30994i
\(248\) 88.1816 0.355571
\(249\) −3.55051 2.04989i −0.0142591 0.00823248i
\(250\) −60.0125 34.6482i −0.240050 0.138593i
\(251\) −120.038 207.912i −0.478239 0.828334i 0.521450 0.853282i \(-0.325391\pi\)
−0.999689 + 0.0249476i \(0.992058\pi\)
\(252\) −6.20204 + 10.7423i −0.0246113 + 0.0426280i
\(253\) 201.474 + 348.964i 0.796342 + 1.37930i
\(254\) −177.712 −0.699652
\(255\) 6.61037i 0.0259230i
\(256\) −8.00000 13.8564i −0.0312500 0.0541266i
\(257\) 8.37857 4.83737i 0.0326014 0.0188224i −0.483611 0.875283i \(-0.660675\pi\)
0.516212 + 0.856461i \(0.327342\pi\)
\(258\) −335.217 −1.29929
\(259\) 199.518i 0.770340i
\(260\) −29.6969 + 17.1455i −0.114219 + 0.0659444i
\(261\) −4.98521 2.87821i −0.0191004 0.0110276i
\(262\) 131.351 75.8354i 0.501339 0.289448i
\(263\) 56.9620 98.6611i 0.216586 0.375137i −0.737176 0.675700i \(-0.763841\pi\)
0.953762 + 0.300563i \(0.0971747\pi\)
\(264\) −66.2929 + 114.823i −0.251109 + 0.434934i
\(265\) 80.0066i 0.301912i
\(266\) −170.227 + 73.3962i −0.639951 + 0.275926i
\(267\) 21.2474 0.0795785
\(268\) −103.318 59.6506i −0.385514 0.222577i
\(269\) −348.090 200.970i −1.29402 0.747100i −0.314652 0.949207i \(-0.601888\pi\)
−0.979364 + 0.202106i \(0.935221\pi\)
\(270\) 18.0227 + 31.2162i 0.0667508 + 0.115616i
\(271\) −199.492 + 345.530i −0.736133 + 1.27502i 0.218091 + 0.975928i \(0.430017\pi\)
−0.954224 + 0.299092i \(0.903316\pi\)
\(272\) 4.20204 + 7.27815i 0.0154487 + 0.0267579i
\(273\) −372.161 −1.36323
\(274\) 2.97129i 0.0108441i
\(275\) −178.788 309.669i −0.650137 1.12607i
\(276\) 147.384 85.0920i 0.533999 0.308304i
\(277\) 529.444 1.91135 0.955675 0.294424i \(-0.0951278\pi\)
0.955675 + 0.294424i \(0.0951278\pi\)
\(278\) 44.8905i 0.161476i
\(279\) −24.2724 + 14.0137i −0.0869980 + 0.0502283i
\(280\) −16.8990 9.75663i −0.0603535 0.0348451i
\(281\) 47.4092 27.3717i 0.168716 0.0974082i −0.413264 0.910611i \(-0.635611\pi\)
0.581980 + 0.813203i \(0.302278\pi\)
\(282\) 25.6742 44.4691i 0.0910434 0.157692i
\(283\) 74.4671 128.981i 0.263135 0.455762i −0.703939 0.710261i \(-0.748577\pi\)
0.967073 + 0.254498i \(0.0819103\pi\)
\(284\) 202.125i 0.711708i
\(285\) 6.94949 59.3737i 0.0243842 0.208329i
\(286\) −361.262 −1.26315
\(287\) 385.924 + 222.813i 1.34468 + 0.776353i
\(288\) 4.40408 + 2.54270i 0.0152920 + 0.00882881i
\(289\) 142.293 + 246.458i 0.492363 + 0.852797i
\(290\) 4.52781 7.84239i 0.0156131 0.0270427i
\(291\) −207.356 359.151i −0.712563 1.23420i
\(292\) 254.767 0.872491
\(293\) 145.685i 0.497218i 0.968604 + 0.248609i \(0.0799734\pi\)
−0.968604 + 0.248609i \(0.920027\pi\)
\(294\) 3.12372 + 5.41045i 0.0106249 + 0.0184029i
\(295\) 50.9166 29.3967i 0.172599 0.0996498i
\(296\) 81.7980 0.276344
\(297\) 379.744i 1.27860i
\(298\) 232.305 134.122i 0.779548 0.450072i
\(299\) 401.583 + 231.854i 1.34309 + 0.775431i
\(300\) −130.788 + 75.5103i −0.435959 + 0.251701i
\(301\) 259.879 450.123i 0.863384 1.49542i
\(302\) −11.5051 + 19.9274i −0.0380964 + 0.0659848i
\(303\) 20.4026i 0.0673352i
\(304\) 30.0908 + 69.7893i 0.0989829 + 0.229570i
\(305\) −2.19184 −0.00718635
\(306\) −2.31327 1.33557i −0.00755970 0.00436459i
\(307\) 98.0380 + 56.6023i 0.319342 + 0.184372i 0.651099 0.758993i \(-0.274308\pi\)
−0.331757 + 0.943365i \(0.607641\pi\)
\(308\) −102.788 178.034i −0.333726 0.578031i
\(309\) 125.889 218.046i 0.407407 0.705650i
\(310\) −22.0454 38.1838i −0.0711142 0.123173i
\(311\) −105.666 −0.339763 −0.169882 0.985464i \(-0.554339\pi\)
−0.169882 + 0.985464i \(0.554339\pi\)
\(312\) 152.578i 0.489031i
\(313\) −124.121 214.984i −0.396552 0.686849i 0.596746 0.802431i \(-0.296460\pi\)
−0.993298 + 0.115582i \(0.963127\pi\)
\(314\) 330.866 191.026i 1.05371 0.608362i
\(315\) 6.20204 0.0196890
\(316\) 13.3492i 0.0422442i
\(317\) −196.061 + 113.196i −0.618488 + 0.357084i −0.776280 0.630388i \(-0.782896\pi\)
0.157792 + 0.987472i \(0.449562\pi\)
\(318\) 308.295 + 177.994i 0.969482 + 0.559730i
\(319\) 82.6209 47.7012i 0.259000 0.149534i
\(320\) −4.00000 + 6.92820i −0.0125000 + 0.0216506i
\(321\) 125.889 218.046i 0.392177 0.679270i
\(322\) 263.872i 0.819478i
\(323\) −15.8054 36.6572i −0.0489330 0.113490i
\(324\) 176.565 0.544955
\(325\) −356.363 205.746i −1.09650 0.633066i
\(326\) 191.914 + 110.801i 0.588693 + 0.339882i
\(327\) −25.8712 44.8102i −0.0791167 0.137034i
\(328\) 91.3485 158.220i 0.278501 0.482379i
\(329\) 39.8082 + 68.9498i 0.120997 + 0.209574i
\(330\) 66.2929 0.200887
\(331\) 293.328i 0.886188i 0.896475 + 0.443094i \(0.146119\pi\)
−0.896475 + 0.443094i \(0.853881\pi\)
\(332\) −1.30306 2.25697i −0.00392488 0.00679810i
\(333\) −22.5153 + 12.9992i −0.0676135 + 0.0390367i
\(334\) 127.510 0.381766
\(335\) 59.6506i 0.178061i
\(336\) −75.1918 + 43.4120i −0.223785 + 0.129202i
\(337\) −399.393 230.590i −1.18514 0.684243i −0.227945 0.973674i \(-0.573201\pi\)
−0.957199 + 0.289431i \(0.906534\pi\)
\(338\) −153.056 + 88.3667i −0.452827 + 0.261440i
\(339\) −208.980 + 361.963i −0.616459 + 1.06774i
\(340\) 2.10102 3.63907i 0.00617947 0.0107032i
\(341\) 464.504i 1.36218i
\(342\) −19.3735 14.4279i −0.0566476 0.0421867i
\(343\) −347.737 −1.01381
\(344\) −184.540 106.544i −0.536454 0.309722i
\(345\) −73.6918 42.5460i −0.213600 0.123322i
\(346\) 215.048 + 372.474i 0.621525 + 1.07651i
\(347\) −152.129 + 263.495i −0.438412 + 0.759351i −0.997567 0.0697116i \(-0.977792\pi\)
0.559156 + 0.829063i \(0.311125\pi\)
\(348\) −20.1464 34.8946i −0.0578920 0.100272i
\(349\) 50.4337 0.144509 0.0722545 0.997386i \(-0.476981\pi\)
0.0722545 + 0.997386i \(0.476981\pi\)
\(350\) 234.159i 0.669026i
\(351\) 218.502 + 378.457i 0.622514 + 1.07823i
\(352\) −72.9898 + 42.1407i −0.207357 + 0.119718i
\(353\) −316.817 −0.897500 −0.448750 0.893657i \(-0.648131\pi\)
−0.448750 + 0.893657i \(0.648131\pi\)
\(354\) 261.601i 0.738985i
\(355\) 87.5227 50.5313i 0.246543 0.142342i
\(356\) 11.6969 + 6.75323i 0.0328566 + 0.0189697i
\(357\) 39.4949 22.8024i 0.110630 0.0638722i
\(358\) −222.879 + 386.037i −0.622566 + 1.07832i
\(359\) −74.7043 + 129.392i −0.208090 + 0.360423i −0.951113 0.308844i \(-0.900058\pi\)
0.743023 + 0.669266i \(0.233391\pi\)
\(360\) 2.54270i 0.00706305i
\(361\) −103.424 345.868i −0.286494 0.958082i
\(362\) 45.5505 0.125830
\(363\) 275.144 + 158.854i 0.757971 + 0.437615i
\(364\) −204.879 118.287i −0.562853 0.324963i
\(365\) −63.6918 110.317i −0.174498 0.302240i
\(366\) −4.87628 + 8.44596i −0.0133232 + 0.0230764i
\(367\) −117.038 202.716i −0.318905 0.552359i 0.661355 0.750073i \(-0.269982\pi\)
−0.980260 + 0.197714i \(0.936648\pi\)
\(368\) 108.182 0.293972
\(369\) 58.0679i 0.157366i
\(370\) −20.4495 35.4196i −0.0552689 0.0957285i
\(371\) −478.015 + 275.982i −1.28845 + 0.743887i
\(372\) −196.182 −0.527370
\(373\) 639.738i 1.71512i −0.514387 0.857558i \(-0.671981\pi\)
0.514387 0.857558i \(-0.328019\pi\)
\(374\) 38.3383 22.1346i 0.102509 0.0591834i
\(375\) 133.512 + 77.0835i 0.356033 + 0.205556i
\(376\) 28.2679 16.3205i 0.0751805 0.0434055i
\(377\) 54.8939 95.0790i 0.145607 0.252199i
\(378\) −124.338 + 215.360i −0.328937 + 0.569736i
\(379\) 108.366i 0.285927i 0.989728 + 0.142963i \(0.0456631\pi\)
−0.989728 + 0.142963i \(0.954337\pi\)
\(380\) 22.6969 30.4770i 0.0597288 0.0802027i
\(381\) 395.363 1.03770
\(382\) −343.237 198.168i −0.898527 0.518765i
\(383\) 215.552 + 124.449i 0.562800 + 0.324933i 0.754268 0.656566i \(-0.227992\pi\)
−0.191469 + 0.981499i \(0.561325\pi\)
\(384\) 17.7980 + 30.8270i 0.0463489 + 0.0802786i
\(385\) −51.3939 + 89.0168i −0.133491 + 0.231212i
\(386\) −34.3054 59.4186i −0.0888740 0.153934i
\(387\) 67.7276 0.175007
\(388\) 263.622i 0.679437i
\(389\) 335.560 + 581.207i 0.862623 + 1.49411i 0.869389 + 0.494129i \(0.164513\pi\)
−0.00676592 + 0.999977i \(0.502154\pi\)
\(390\) 66.0681 38.1444i 0.169405 0.0978063i
\(391\) −56.8230 −0.145327
\(392\) 3.97134i 0.0101310i
\(393\) −292.222 + 168.714i −0.743567 + 0.429299i
\(394\) −308.524 178.127i −0.783057 0.452098i
\(395\) −5.78036 + 3.33729i −0.0146338 + 0.00844884i
\(396\) 13.3939 23.1989i 0.0338229 0.0585830i
\(397\) 46.6816 80.8550i 0.117586 0.203665i −0.801225 0.598364i \(-0.795818\pi\)
0.918811 + 0.394699i \(0.129151\pi\)
\(398\) 366.830i 0.921684i
\(399\) 378.712 163.288i 0.949152 0.409243i
\(400\) −96.0000 −0.240000
\(401\) 242.484 + 139.998i 0.604699 + 0.349123i 0.770888 0.636971i \(-0.219813\pi\)
−0.166189 + 0.986094i \(0.553146\pi\)
\(402\) 229.856 + 132.707i 0.571781 + 0.330118i
\(403\) −267.272 462.929i −0.663207 1.14871i
\(404\) 6.48469 11.2318i 0.0160512 0.0278015i
\(405\) −44.1413 76.4550i −0.108991 0.188778i
\(406\) 62.4745 0.153878
\(407\) 430.878i 1.05867i
\(408\) −9.34847 16.1920i −0.0229129 0.0396863i
\(409\) −555.833 + 320.910i −1.35900 + 0.784621i −0.989490 0.144604i \(-0.953809\pi\)
−0.369514 + 0.929225i \(0.620476\pi\)
\(410\) −91.3485 −0.222801
\(411\) 6.61037i 0.0160836i
\(412\) 138.606 80.0243i 0.336423 0.194234i
\(413\) 351.272 + 202.807i 0.850539 + 0.491059i
\(414\) −29.7775 + 17.1921i −0.0719264 + 0.0415268i
\(415\) −0.651531 + 1.12848i −0.00156995 + 0.00271924i
\(416\) −48.4949 + 83.9956i −0.116574 + 0.201913i
\(417\) 99.8698i 0.239496i
\(418\) 367.621 158.506i 0.879476 0.379201i
\(419\) 668.879 1.59637 0.798184 0.602413i \(-0.205794\pi\)
0.798184 + 0.602413i \(0.205794\pi\)
\(420\) 37.5959 + 21.7060i 0.0895141 + 0.0516810i
\(421\) 433.711 + 250.403i 1.03019 + 0.594782i 0.917040 0.398795i \(-0.130572\pi\)
0.113153 + 0.993578i \(0.463905\pi\)
\(422\) −49.1941 85.2067i −0.116574 0.201912i
\(423\) −5.18725 + 8.98458i −0.0122630 + 0.0212401i
\(424\) 113.146 + 195.975i 0.266855 + 0.462206i
\(425\) 50.4245 0.118646
\(426\) 449.677i 1.05558i
\(427\) −7.56072 13.0955i −0.0177066 0.0306687i
\(428\) 138.606 80.0243i 0.323846 0.186973i
\(429\) 803.716 1.87346
\(430\) 106.544i 0.247778i
\(431\) 120.553 69.6015i 0.279706 0.161488i −0.353584 0.935403i \(-0.615037\pi\)
0.633290 + 0.773914i \(0.281704\pi\)
\(432\) 88.2929 + 50.9759i 0.204382 + 0.118000i
\(433\) 180.349 104.125i 0.416510 0.240472i −0.277073 0.960849i \(-0.589364\pi\)
0.693583 + 0.720377i \(0.256031\pi\)
\(434\) 152.091 263.429i 0.350440 0.606979i
\(435\) −10.0732 + 17.4473i −0.0231568 + 0.0401088i
\(436\) 32.8913i 0.0754387i
\(437\) −510.379 59.7381i −1.16791 0.136700i
\(438\) −566.792 −1.29405
\(439\) 65.6748 + 37.9173i 0.149601 + 0.0863721i 0.572932 0.819603i \(-0.305806\pi\)
−0.423331 + 0.905975i \(0.639139\pi\)
\(440\) 36.4949 + 21.0703i 0.0829429 + 0.0478871i
\(441\) −0.631120 1.09313i −0.00143111 0.00247876i
\(442\) 25.4722 44.1191i 0.0576294 0.0998170i
\(443\) 227.628 + 394.264i 0.513834 + 0.889986i 0.999871 + 0.0160481i \(0.00510848\pi\)
−0.486038 + 0.873938i \(0.661558\pi\)
\(444\) −181.980 −0.409864
\(445\) 6.75323i 0.0151758i
\(446\) 4.47219 + 7.74607i 0.0100273 + 0.0173679i
\(447\) −516.820 + 298.386i −1.15620 + 0.667531i
\(448\) −55.1918 −0.123196
\(449\) 8.44993i 0.0188194i 0.999956 + 0.00940972i \(0.00299525\pi\)
−0.999956 + 0.00940972i \(0.997005\pi\)
\(450\) 26.4245 15.2562i 0.0587211 0.0339026i
\(451\) −833.438 481.186i −1.84798 1.06693i
\(452\) −230.091 + 132.843i −0.509050 + 0.293900i
\(453\) 25.5959 44.3334i 0.0565031 0.0978663i
\(454\) −39.4143 + 68.2675i −0.0868156 + 0.150369i
\(455\) 118.287i 0.259971i
\(456\) −66.9444 155.263i −0.146808 0.340490i
\(457\) 208.424 0.456071 0.228036 0.973653i \(-0.426770\pi\)
0.228036 + 0.973653i \(0.426770\pi\)
\(458\) 162.050 + 93.5596i 0.353821 + 0.204279i
\(459\) −46.3763 26.7754i −0.101038 0.0583341i
\(460\) −27.0454 46.8440i −0.0587944 0.101835i
\(461\) 308.808 534.871i 0.669865 1.16024i −0.308077 0.951361i \(-0.599685\pi\)
0.977942 0.208878i \(-0.0669813\pi\)
\(462\) 228.677 + 396.079i 0.494971 + 0.857315i
\(463\) 640.958 1.38436 0.692179 0.721725i \(-0.256651\pi\)
0.692179 + 0.721725i \(0.256651\pi\)
\(464\) 25.6131i 0.0552007i
\(465\) 49.0454 + 84.9491i 0.105474 + 0.182686i
\(466\) −273.997 + 158.192i −0.587976 + 0.339468i
\(467\) 164.111 0.351416 0.175708 0.984442i \(-0.443779\pi\)
0.175708 + 0.984442i \(0.443779\pi\)
\(468\) 30.8270i 0.0658696i
\(469\) −356.394 + 205.764i −0.759902 + 0.438729i
\(470\) −14.1339 8.16023i −0.0300722 0.0173622i
\(471\) −736.093 + 424.983i −1.56283 + 0.902300i
\(472\) 83.1464 144.014i 0.176158 0.305114i
\(473\) −561.232 + 972.082i −1.18654 + 2.05514i
\(474\) 29.6985i 0.0626550i
\(475\) 452.908 + 53.0114i 0.953491 + 0.111603i
\(476\) 28.9898 0.0609029
\(477\) −62.2883 35.9621i −0.130583 0.0753923i
\(478\) 87.3531 + 50.4333i 0.182747 + 0.105509i
\(479\) −401.401 695.247i −0.837998 1.45146i −0.891566 0.452892i \(-0.850392\pi\)
0.0535671 0.998564i \(-0.482941\pi\)
\(480\) 8.89898 15.4135i 0.0185395 0.0321114i
\(481\) −247.924 429.417i −0.515434 0.892759i
\(482\) −197.146 −0.409017
\(483\) 587.048i 1.21542i
\(484\) 100.980 + 174.902i 0.208636 + 0.361367i
\(485\) −114.152 + 65.9054i −0.235364 + 0.135887i
\(486\) −68.4041 −0.140749
\(487\) 454.391i 0.933041i −0.884510 0.466521i \(-0.845507\pi\)
0.884510 0.466521i \(-0.154493\pi\)
\(488\) −5.36888 + 3.09972i −0.0110018 + 0.00635189i
\(489\) −426.959 246.505i −0.873127 0.504100i
\(490\) 1.71964 0.992836i 0.00350947 0.00202620i
\(491\) −259.826 + 450.031i −0.529177 + 0.916561i 0.470244 + 0.882536i \(0.344166\pi\)
−0.999421 + 0.0340247i \(0.989168\pi\)
\(492\) −203.227 + 352.000i −0.413063 + 0.715446i
\(493\) 13.4534i 0.0272889i
\(494\) 275.171 369.495i 0.557027 0.747966i
\(495\) −13.3939 −0.0270583
\(496\) −108.000 62.3538i −0.217742 0.125713i
\(497\) 603.817 + 348.614i 1.21492 + 0.701437i
\(498\) 2.89898 + 5.02118i 0.00582124 + 0.0100827i
\(499\) −221.543 + 383.724i −0.443974 + 0.768986i −0.997980 0.0635269i \(-0.979765\pi\)
0.554006 + 0.832513i \(0.313098\pi\)
\(500\) 49.0000 + 84.8705i 0.0980000 + 0.169741i
\(501\) −283.677 −0.566221
\(502\) 339.519i 0.676332i
\(503\) 120.841 + 209.302i 0.240240 + 0.416107i 0.960782 0.277303i \(-0.0894406\pi\)
−0.720543 + 0.693410i \(0.756107\pi\)
\(504\) 15.1918 8.77101i 0.0301425 0.0174028i
\(505\) −6.48469 −0.0128410
\(506\) 569.856i 1.12620i
\(507\) 340.510 196.593i 0.671617 0.387758i
\(508\) 217.652 + 125.661i 0.428448 + 0.247365i
\(509\) 357.485 206.394i 0.702329 0.405490i −0.105886 0.994378i \(-0.533768\pi\)
0.808214 + 0.588889i \(0.200434\pi\)
\(510\) −4.67423 + 8.09601i −0.00916517 + 0.0158745i
\(511\) 439.409 761.078i 0.859900 1.48939i
\(512\) 22.6274i 0.0441942i
\(513\) −388.398 289.249i −0.757112 0.563839i
\(514\) −13.6821 −0.0266190
\(515\) −69.3031 40.0121i −0.134569 0.0776935i
\(516\) 410.555 + 237.034i 0.795649 + 0.459368i
\(517\) −85.9694 148.903i −0.166285 0.288014i
\(518\) 141.081 244.359i 0.272356 0.471735i
\(519\) −478.426 828.659i −0.921823 1.59664i
\(520\) 48.4949 0.0932594
\(521\) 888.839i 1.70602i 0.521891 + 0.853012i \(0.325227\pi\)
−0.521891 + 0.853012i \(0.674773\pi\)
\(522\) 4.07041 + 7.05015i 0.00779771 + 0.0135060i
\(523\) 132.856 76.7047i 0.254027 0.146663i −0.367580 0.929992i \(-0.619813\pi\)
0.621607 + 0.783329i \(0.286480\pi\)
\(524\) −214.495 −0.409341
\(525\) 520.944i 0.992275i
\(526\) −139.528 + 80.5564i −0.265262 + 0.153149i
\(527\) 56.7276 + 32.7517i 0.107642 + 0.0621474i
\(528\) 162.384 93.7523i 0.307545 0.177561i
\(529\) −101.227 + 175.330i −0.191355 + 0.331437i
\(530\) 56.5732 97.9877i 0.106742 0.184882i
\(531\) 52.8541i 0.0995368i
\(532\) 260.384 + 30.4770i 0.489443 + 0.0572876i
\(533\) −1107.48 −2.07783
\(534\) −26.0227 15.0242i −0.0487317 0.0281352i
\(535\) −69.3031 40.0121i −0.129538 0.0747890i
\(536\) 84.3587 + 146.114i 0.157386 + 0.272600i
\(537\) 495.848 858.834i 0.923367 1.59932i
\(538\) 284.215 + 492.274i 0.528280 + 0.915007i
\(539\) 20.9194 0.0388115
\(540\) 50.9759i 0.0943998i
\(541\) 446.424 + 773.229i 0.825183 + 1.42926i 0.901779 + 0.432197i \(0.142261\pi\)
−0.0765964 + 0.997062i \(0.524405\pi\)
\(542\) 488.654 282.124i 0.901575 0.520525i
\(543\) −101.338 −0.186627
\(544\) 11.8852i 0.0218477i
\(545\) −14.2423 + 8.22282i −0.0261327 + 0.0150877i
\(546\) 455.803 + 263.158i 0.834803 + 0.481974i
\(547\) −748.841 + 432.343i −1.36900 + 0.790390i −0.990800 0.135336i \(-0.956789\pi\)
−0.378196 + 0.925726i \(0.623455\pi\)
\(548\) −2.10102 + 3.63907i −0.00383398 + 0.00664065i
\(549\) 0.985208 1.70643i 0.00179455 0.00310825i
\(550\) 505.688i 0.919433i
\(551\) −14.1436 + 120.838i −0.0256690 + 0.219306i
\(552\) −240.677 −0.436008
\(553\) −39.8786 23.0239i −0.0721131 0.0416345i
\(554\) −648.434 374.373i −1.17046 0.675764i
\(555\) 45.4949 + 78.7995i 0.0819728 + 0.141981i
\(556\) −31.7423 + 54.9794i −0.0570906 + 0.0988837i
\(557\) −374.853 649.265i −0.672986 1.16565i −0.977053 0.212995i \(-0.931678\pi\)
0.304068 0.952650i \(-0.401655\pi\)
\(558\) 39.6367 0.0710336
\(559\) 1291.71i 2.31076i
\(560\) 13.7980 + 23.8988i 0.0246392 + 0.0426764i
\(561\) −85.2929 + 49.2439i −0.152037 + 0.0877787i
\(562\) −77.4189 −0.137756
\(563\) 162.777i 0.289125i −0.989496 0.144563i \(-0.953823\pi\)
0.989496 0.144563i \(-0.0461775\pi\)
\(564\) −62.8888 + 36.3089i −0.111505 + 0.0643774i
\(565\) 115.045 + 66.4215i 0.203620 + 0.117560i
\(566\) −182.406 + 105.312i −0.322273 + 0.186064i
\(567\) 304.530 527.462i 0.537090 0.930267i
\(568\) 142.924 247.552i 0.251627 0.435830i
\(569\) 296.076i 0.520345i −0.965562 0.260173i \(-0.916221\pi\)
0.965562 0.260173i \(-0.0837795\pi\)
\(570\) −50.4949 + 67.8036i −0.0885875 + 0.118954i
\(571\) 274.758 0.481188 0.240594 0.970626i \(-0.422658\pi\)
0.240594 + 0.970626i \(0.422658\pi\)
\(572\) 442.454 + 255.451i 0.773521 + 0.446593i
\(573\) 763.615 + 440.873i 1.33266 + 0.769413i
\(574\) −315.106 545.779i −0.548964 0.950834i
\(575\) 324.545 562.128i 0.564426 0.977614i
\(576\) −3.59592 6.22831i −0.00624291 0.0108130i
\(577\) 524.595 0.909177 0.454588 0.890702i \(-0.349786\pi\)
0.454588 + 0.890702i \(0.349786\pi\)
\(578\) 402.465i 0.696306i
\(579\) 76.3207 + 132.191i 0.131815 + 0.228310i
\(580\) −11.0908 + 6.40329i −0.0191221 + 0.0110401i
\(581\) −8.98979 −0.0154730
\(582\) 586.491i 1.00772i
\(583\) 1032.32 596.008i 1.77070 1.02231i
\(584\) −312.025 180.148i −0.534289 0.308472i
\(585\) −13.3485 + 7.70674i −0.0228179 + 0.0131739i
\(586\) 103.015 178.427i 0.175793 0.304483i
\(587\) 375.568 650.503i 0.639809 1.10818i −0.345665 0.938358i \(-0.612347\pi\)
0.985474 0.169824i \(-0.0543200\pi\)
\(588\) 8.83523i 0.0150259i
\(589\) 475.090 + 353.810i 0.806604 + 0.600697i
\(590\) −83.1464 −0.140926
\(591\) 686.388 + 396.286i 1.16140 + 0.670535i
\(592\) −100.182 57.8399i −0.169226 0.0977025i
\(593\) 285.030 + 493.687i 0.480658 + 0.832524i 0.999754 0.0221922i \(-0.00706458\pi\)
−0.519096 + 0.854716i \(0.673731\pi\)
\(594\) 268.520 465.090i 0.452054 0.782980i
\(595\) −7.24745 12.5529i −0.0121806 0.0210974i
\(596\) −379.353 −0.636498
\(597\) 816.104i 1.36701i
\(598\) −327.891 567.924i −0.548313 0.949706i
\(599\) −341.447 + 197.134i −0.570028 + 0.329106i −0.757160 0.653229i \(-0.773414\pi\)
0.187133 + 0.982335i \(0.440081\pi\)
\(600\) 213.576 0.355959
\(601\) 241.665i 0.402105i 0.979580 + 0.201053i \(0.0644362\pi\)
−0.979580 + 0.201053i \(0.935564\pi\)
\(602\) −636.570 + 367.524i −1.05743 + 0.610505i
\(603\) −46.4403 26.8123i −0.0770154 0.0444649i
\(604\) 28.1816 16.2707i 0.0466583 0.0269382i
\(605\) 50.4898 87.4509i 0.0834542 0.144547i
\(606\) −14.4268 + 24.9879i −0.0238066 + 0.0412342i
\(607\) 369.224i 0.608276i 0.952628 + 0.304138i \(0.0983685\pi\)
−0.952628 + 0.304138i \(0.901632\pi\)
\(608\) 12.4949 106.751i 0.0205508 0.175578i
\(609\) −138.990 −0.228226
\(610\) 2.68444 + 1.54986i 0.00440072 + 0.00254076i
\(611\) −171.356 98.9324i −0.280451 0.161919i
\(612\) 1.88877 + 3.27145i 0.00308623 + 0.00534551i
\(613\) −190.171 + 329.386i −0.310230 + 0.537334i −0.978412 0.206664i \(-0.933739\pi\)
0.668182 + 0.743998i \(0.267073\pi\)
\(614\) −80.0477 138.647i −0.130371 0.225809i
\(615\) 203.227 0.330450
\(616\) 290.728i 0.471961i
\(617\) −277.869 481.283i −0.450355 0.780037i 0.548053 0.836444i \(-0.315369\pi\)
−0.998408 + 0.0564062i \(0.982036\pi\)
\(618\) −308.363 + 178.034i −0.498970 + 0.288080i
\(619\) −624.152 −1.00832 −0.504162 0.863609i \(-0.668198\pi\)
−0.504162 + 0.863609i \(0.668198\pi\)
\(620\) 62.3538i 0.100571i
\(621\) −596.979 + 344.666i −0.961319 + 0.555018i
\(622\) 129.414 + 74.7174i 0.208062 + 0.120124i
\(623\) 40.3485 23.2952i 0.0647648 0.0373920i
\(624\) 107.889 186.869i 0.172899 0.299469i
\(625\) −275.500 + 477.180i −0.440800 + 0.763488i
\(626\) 351.067i 0.560810i
\(627\) −817.863 + 352.635i −1.30441 + 0.562417i
\(628\) −540.302 −0.860354
\(629\) 52.6209 + 30.3807i 0.0836581 + 0.0483000i
\(630\) −7.59592 4.38551i −0.0120570 0.00696112i
\(631\) −42.7247 74.0014i −0.0677096 0.117276i 0.830183 0.557491i \(-0.188236\pi\)
−0.897893 + 0.440214i \(0.854902\pi\)
\(632\) −9.43928 + 16.3493i −0.0149356 + 0.0258692i
\(633\) 109.444 + 189.563i 0.172898 + 0.299468i
\(634\) 320.166 0.504993
\(635\) 125.661i 0.197892i
\(636\) −251.722 435.995i −0.395789 0.685527i
\(637\) 20.8485 12.0369i 0.0327292 0.0188962i
\(638\) −134.919 −0.211472
\(639\) 90.8531i 0.142180i
\(640\) 9.79796 5.65685i 0.0153093 0.00883883i
\(641\) 599.893 + 346.348i 0.935870 + 0.540325i 0.888663 0.458560i \(-0.151635\pi\)
0.0472069 + 0.998885i \(0.484968\pi\)
\(642\) −308.363 + 178.034i −0.480317 + 0.277311i
\(643\) 252.123 436.690i 0.392105 0.679145i −0.600622 0.799533i \(-0.705080\pi\)
0.992727 + 0.120388i \(0.0384138\pi\)
\(644\) 186.586 323.176i 0.289729 0.501826i
\(645\) 237.034i 0.367495i
\(646\) −6.56301 + 56.0718i −0.0101595 + 0.0867984i
\(647\) −797.868 −1.23318 −0.616591 0.787284i \(-0.711487\pi\)
−0.616591 + 0.787284i \(0.711487\pi\)
\(648\) −216.247 124.851i −0.333715 0.192671i
\(649\) −758.605 437.981i −1.16888 0.674855i
\(650\) 290.969 + 503.974i 0.447645 + 0.775344i
\(651\) −338.363 + 586.062i −0.519759 + 0.900249i
\(652\) −156.697 271.407i −0.240333 0.416268i
\(653\) −651.383 −0.997523 −0.498762 0.866739i \(-0.666212\pi\)
−0.498762 + 0.866739i \(0.666212\pi\)
\(654\) 73.1747i 0.111888i
\(655\) 53.6237 + 92.8790i 0.0818683 + 0.141800i
\(656\) −223.757 + 129.186i −0.341093 + 0.196930i
\(657\) 114.515 0.174300
\(658\) 112.594i 0.171116i
\(659\) −395.082 + 228.101i −0.599518 + 0.346132i −0.768852 0.639427i \(-0.779172\pi\)
0.169334 + 0.985559i \(0.445838\pi\)
\(660\) −81.1918 46.8761i −0.123018 0.0710244i
\(661\) 495.696 286.190i 0.749919 0.432966i −0.0757457 0.997127i \(-0.524134\pi\)
0.825665 + 0.564161i \(0.190800\pi\)
\(662\) 207.414 359.252i 0.313315 0.542677i
\(663\) −56.6691 + 98.1538i −0.0854738 + 0.148045i
\(664\) 3.68561i 0.00555062i
\(665\) −51.8990 120.369i −0.0780436 0.181006i
\(666\) 36.7673 0.0552062
\(667\) 149.978 + 86.5897i 0.224854 + 0.129820i
\(668\) −156.167 90.1630i −0.233783 0.134975i
\(669\) −9.94949 17.2330i −0.0148722 0.0257594i
\(670\) 42.1793 73.0568i 0.0629542 0.109040i
\(671\) 16.3281 + 28.2810i 0.0243339 + 0.0421476i
\(672\) 122.788 0.182720
\(673\) 914.574i 1.35895i 0.733698 + 0.679476i \(0.237793\pi\)
−0.733698 + 0.679476i \(0.762207\pi\)
\(674\) 326.103 + 564.828i 0.483833 + 0.838023i
\(675\) 529.757 305.855i 0.784825 0.453119i
\(676\) 249.939 0.369732
\(677\) 272.492i 0.402500i 0.979540 + 0.201250i \(0.0645003\pi\)
−0.979540 + 0.201250i \(0.935500\pi\)
\(678\) 511.893 295.542i 0.755005 0.435902i
\(679\) −787.529 454.680i −1.15984 0.669632i
\(680\) −5.14643 + 2.97129i −0.00756828 + 0.00436955i
\(681\) 87.6867 151.878i 0.128762 0.223022i
\(682\) −328.454 + 568.899i −0.481604 + 0.834163i
\(683\) 164.842i 0.241350i −0.992692 0.120675i \(-0.961494\pi\)
0.992692 0.120675i \(-0.0385058\pi\)
\(684\) 13.5255 + 31.3696i 0.0197741 + 0.0458619i
\(685\) 2.10102 0.00306718
\(686\) 425.889 + 245.887i 0.620829 + 0.358436i
\(687\) −360.520 208.146i −0.524774 0.302979i
\(688\) 150.677 + 260.979i 0.219007 + 0.379331i
\(689\) 685.878 1187.98i 0.995469 1.72420i
\(690\) 60.1691 + 104.216i 0.0872016 + 0.151038i
\(691\) 1040.21 1.50537 0.752685 0.658380i \(-0.228758\pi\)
0.752685 + 0.658380i \(0.228758\pi\)
\(692\) 608.247i 0.878969i
\(693\) −46.2020 80.0243i −0.0666696 0.115475i
\(694\) 372.638 215.143i 0.536942 0.310004i
\(695\) 31.7423 0.0456724
\(696\) 56.9827i 0.0818717i
\(697\) 117.530 67.8557i 0.168622 0.0973540i
\(698\) −61.7684 35.6620i −0.0884934 0.0510917i
\(699\) 609.573 351.937i 0.872064 0.503486i
\(700\) −165.576 + 286.785i −0.236536 + 0.409693i
\(701\) 37.8179 65.5024i 0.0539484 0.0934414i −0.837790 0.545993i \(-0.816153\pi\)
0.891738 + 0.452551i \(0.149486\pi\)
\(702\) 618.018i 0.880367i
\(703\) 440.697 + 328.197i 0.626880 + 0.466852i
\(704\) 119.192 0.169307
\(705\) 31.4444 + 18.1544i 0.0446020 + 0.0257510i
\(706\) 388.020 + 224.024i 0.549604 + 0.317314i
\(707\) −22.3689 38.7440i −0.0316392 0.0548006i
\(708\) −184.980 + 320.394i −0.261271 + 0.452534i
\(709\) 451.379 + 781.811i 0.636641 + 1.10269i 0.986165 + 0.165767i \(0.0530101\pi\)
−0.349524 + 0.936928i \(0.613657\pi\)
\(710\) −142.924 −0.201301
\(711\) 6.00031i 0.00843926i
\(712\) −9.55051 16.5420i −0.0134136 0.0232331i
\(713\) 730.226 421.596i 1.02416 0.591299i
\(714\) −64.4949 −0.0903290
\(715\) 255.451i 0.357274i
\(716\) 545.939 315.198i 0.762484 0.440221i
\(717\) −194.338 112.201i −0.271044 0.156487i
\(718\) 182.988 105.648i 0.254857 0.147142i
\(719\) −586.734 + 1016.25i −0.816042 + 1.41343i 0.0925359 + 0.995709i \(0.470503\pi\)
−0.908578 + 0.417716i \(0.862831\pi\)
\(720\) −1.79796 + 3.11416i −0.00249717 + 0.00432522i
\(721\) 552.086i 0.765722i
\(722\) −117.897 + 496.732i −0.163292 + 0.687994i
\(723\) 438.601 0.606640
\(724\) −55.7878 32.2091i −0.0770549 0.0444877i
\(725\) −133.090 76.8394i −0.183572 0.105985i
\(726\) −224.654 389.112i −0.309441 0.535967i
\(727\) −288.552 + 499.787i −0.396908 + 0.687465i −0.993343 0.115197i \(-0.963250\pi\)
0.596434 + 0.802662i \(0.296584\pi\)
\(728\) 167.283 + 289.742i 0.229784 + 0.397997i
\(729\) −642.362 −0.881155
\(730\) 180.148i 0.246778i
\(731\) −79.1436 137.081i −0.108268 0.187525i
\(732\) 11.9444 6.89610i 0.0163175 0.00942090i
\(733\) −812.332 −1.10823 −0.554114 0.832441i \(-0.686943\pi\)
−0.554114 + 0.832441i \(0.686943\pi\)
\(734\) 331.033i 0.450999i
\(735\) −3.82577 + 2.20881i −0.00520512 + 0.00300518i
\(736\) −132.495 76.4960i −0.180020 0.103935i
\(737\) 769.665 444.366i 1.04432 0.602940i
\(738\) 41.0602 71.1184i 0.0556371 0.0963663i
\(739\) 380.931 659.792i 0.515469 0.892818i −0.484370 0.874863i \(-0.660951\pi\)
0.999839 0.0179548i \(-0.00571549\pi\)
\(740\) 57.8399i 0.0781620i
\(741\) −612.186 + 822.032i −0.826162 + 1.10936i
\(742\) 780.595 1.05201
\(743\) −118.810 68.5950i −0.159906 0.0923216i 0.417912 0.908488i \(-0.362762\pi\)
−0.577817 + 0.816166i \(0.696095\pi\)
\(744\) 240.272 + 138.721i 0.322947 + 0.186453i
\(745\) 94.8383 + 164.265i 0.127300 + 0.220490i
\(746\) −452.363 + 783.516i −0.606385 + 1.05029i
\(747\) −0.585713 1.01448i −0.000784087 0.00135808i
\(748\) −62.6061 −0.0836980
\(749\) 552.086i 0.737097i
\(750\) −109.012 188.815i −0.145350 0.251754i
\(751\) 95.0686 54.8879i 0.126589 0.0730864i −0.435368 0.900253i \(-0.643382\pi\)
0.561957 + 0.827166i \(0.310048\pi\)
\(752\) −46.1612 −0.0613846
\(753\) 755.343i 1.00311i
\(754\) −134.462 + 77.6317i −0.178332 + 0.102960i
\(755\) −14.0908 8.13534i −0.0186633 0.0107753i
\(756\) 304.565 175.841i 0.402864 0.232594i
\(757\) −133.257 + 230.808i −0.176033 + 0.304898i −0.940518 0.339743i \(-0.889660\pi\)
0.764485 + 0.644641i \(0.222993\pi\)
\(758\) 76.6265 132.721i 0.101090 0.175094i
\(759\) 1267.78i 1.67033i
\(760\) −49.3485 + 21.2774i −0.0649322 + 0.0279966i
\(761\) 1227.85 1.61346 0.806732 0.590918i \(-0.201234\pi\)
0.806732 + 0.590918i \(0.201234\pi\)
\(762\) −484.219 279.564i −0.635458 0.366882i
\(763\) −98.2577 56.7291i −0.128778 0.0743500i
\(764\) 280.252 + 485.411i 0.366822 + 0.635354i
\(765\) 0.944387 1.63573i 0.00123449 0.00213820i
\(766\) −175.998 304.837i −0.229762 0.397959i
\(767\) −1008.04 −1.31427
\(768\) 50.3402i 0.0655472i
\(769\) −334.115 578.705i −0.434480 0.752542i 0.562773 0.826612i \(-0.309735\pi\)
−0.997253 + 0.0740698i \(0.976401\pi\)
\(770\) 125.889 72.6819i 0.163492 0.0943921i
\(771\) 30.4393 0.0394803
\(772\) 97.0302i 0.125687i
\(773\) −492.591 + 284.397i −0.637246 + 0.367914i −0.783553 0.621325i \(-0.786595\pi\)
0.146307 + 0.989239i \(0.453261\pi\)
\(774\) −82